LMFDB - Embedded newform 25.9.f.a.2.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,9,Mod(2,25)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("25.2");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	25.f (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.1844652515$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$19$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			2.10
Character	$\chi$	$=$	25.2
Dual form			25.9.f.a.13.10

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.758404 - 0.120119i) q^{2} +(-20.5624 - 40.3560i) q^{3} +(-242.910 - 78.9262i) q^{4} +(-609.477 - 138.431i) q^{5} +(10.7471 + 33.0761i) q^{6} +(3191.92 + 3191.92i) q^{7} +(349.890 + 178.278i) q^{8} +(2650.67 - 3648.33i) q^{9} +O(q^{10})$	\(q+(-0.758404 - 0.120119i) q^{2} +(-20.5624 - 40.3560i) q^{3} +(-242.910 - 78.9262i) q^{4} +(-609.477 - 138.431i) q^{5} +(10.7471 + 33.0761i) q^{6} +(3191.92 + 3191.92i) q^{7} +(349.890 + 178.278i) q^{8} +(2650.67 - 3648.33i) q^{9} +(445.602 + 178.197i) q^{10} +(-13389.0 + 9727.70i) q^{11} +(1809.66 + 11425.8i) q^{12} +(45351.3 - 7182.93i) q^{13} +(-2037.35 - 2804.18i) q^{14} +(6945.78 + 27442.5i) q^{15} +(52653.7 + 38255.1i) q^{16} +(-45324.7 + 88954.6i) q^{17} +(-2448.51 + 2448.51i) q^{18} +(-59144.2 + 19217.1i) q^{19} +(137122. + 81729.9i) q^{20} +(63179.5 - 194446. i) q^{21} +(11322.8 - 5769.25i) q^{22} +(-28228.6 + 178228. i) q^{23} -17786.0i q^{24} +(352299. + 168741. i) q^{25} -35257.4 q^{26} +(-495242. - 78438.6i) q^{27} +(-523422. - 1.02727e6i) q^{28} +(-13581.0 - 4412.75i) q^{29} +(-1971.33 - 21646.8i) q^{30} +(102649. + 315921. i) q^{31} +(-106422. - 106422. i) q^{32} +(667881. + 340303. i) q^{33} +(45059.6 - 62019.2i) q^{34} +(-1.50354e6 - 2.38726e6i) q^{35} +(-931822. + 677008. i) q^{36} +(25399.2 + 160364. i) q^{37} +(47163.6 - 7469.98i) q^{38} +(-1.22240e6 - 1.68249e6i) q^{39} +(-188571. - 157092. i) q^{40} +(2.08174e6 + 1.51248e6i) q^{41} +(-71272.4 + 139880. i) q^{42} +(-462623. + 462623. i) q^{43} +(4.02010e6 - 1.30621e6i) q^{44} +(-2.12056e6 + 1.85664e6i) q^{45} +(42817.3 - 131778. i) q^{46} +(3.80085e6 - 1.93663e6i) q^{47} +(461137. - 2.91151e6i) q^{48} +1.46119e7i q^{49} +(-246916. - 170292. i) q^{50} +4.52183e6 q^{51} +(-1.15832e7 - 1.83460e6i) q^{52} +(2.26551e6 + 4.44632e6i) q^{53} +(366172. + 118976. i) q^{54} +(9.50692e6 - 4.07535e6i) q^{55} +(547772. + 1.68587e6i) q^{56} +(1.99167e6 + 1.99167e6i) q^{57} +(9769.86 + 4977.99i) q^{58} +(-1.21021e7 + 1.66572e7i) q^{59} +(478733. - 7.21425e6i) q^{60} +(1.14573e7 - 8.32419e6i) q^{61} +(-39901.2 - 251926. i) q^{62} +(2.01059e7 - 3.18446e6i) q^{63} +(-9.72539e6 - 1.33858e7i) q^{64} +(-2.86349e7 - 1.90019e6i) q^{65} +(-465647. - 338313. i) q^{66} +(-1.03762e7 + 2.03645e7i) q^{67} +(1.80306e7 - 1.80306e7i) q^{68} +(7.77302e6 - 2.52561e6i) q^{69} +(853535. + 1.99111e6i) q^{70} +(-7.08274e6 + 2.17984e7i) q^{71} +(1.57786e6 - 803959. i) q^{72} +(4.60331e6 - 2.90642e7i) q^{73} -124672. i q^{74} +(-434398. - 1.76871e7i) q^{75} +1.58834e7 q^{76} +(-7.37868e7 - 1.16867e7i) q^{77} +(724976. + 1.42285e6i) q^{78} +(-3.40860e6 - 1.10752e6i) q^{79} +(-2.67955e7 - 3.06045e7i) q^{80} +(-2.12512e6 - 6.54044e6i) q^{81} +(-1.39713e6 - 1.39713e6i) q^{82} +(-1.55857e7 - 7.94132e6i) q^{83} +(-3.06938e7 + 4.22464e7i) q^{84} +(3.99384e7 - 4.79414e7i) q^{85} +(406425. - 295285. i) q^{86} +(101178. + 638812. i) q^{87} +(-6.41892e6 + 1.01666e6i) q^{88} +(5.59375e7 + 7.69914e7i) q^{89} +(1.83126e6 - 1.15336e6i) q^{90} +(1.67685e8 + 1.21830e8i) q^{91} +(2.09239e7 - 4.10654e7i) q^{92} +(1.06386e7 - 1.06386e7i) q^{93} +(-3.11521e6 + 1.01219e6i) q^{94} +(3.87073e7 - 3.52499e6i) q^{95} +(-2.10647e6 + 6.48306e6i) q^{96} +(-7.87576e7 + 4.01290e7i) q^{97} +(1.75517e6 - 1.10817e7i) q^{98} +7.46325e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q - 8 q^{2} + 62 q^{3} - 10 q^{4} - 230 q^{5} - 6 q^{6} + 2342 q^{7} + 8210 q^{8} - 10 q^{9}+O(q^{10}) $ 152 * q - 8 * q^2 + 62 * q^3 - 10 * q^4 - 230 * q^5 - 6 * q^6 + 2342 * q^7 + 8210 * q^8 - 10 * q^9	\( 152 q - 8 q^{2} + 62 q^{3} - 10 q^{4} - 230 q^{5} - 6 q^{6} + 2342 q^{7} + 8210 q^{8} - 10 q^{9} - 30880 q^{10} - 6 q^{11} + 45902 q^{12} + 119132 q^{13} - 10 q^{14} - 241450 q^{15} + 524282 q^{16} - 105158 q^{17} + 454052 q^{18} + 718890 q^{19} + 340370 q^{20} - 6 q^{21} - 1986746 q^{22} - 899198 q^{23} + 2032310 q^{25} - 913936 q^{26} + 1904300 q^{27} - 998002 q^{28} - 1956910 q^{29} - 4500490 q^{30} - 6 q^{31} - 3033938 q^{32} + 1003994 q^{33} + 10303990 q^{34} + 4124560 q^{35} - 8100358 q^{36} + 9534392 q^{37} - 14259280 q^{38} - 22510410 q^{39} - 4123060 q^{40} - 4374726 q^{41} + 52199634 q^{42} + 13583342 q^{43} - 2138860 q^{44} - 33978380 q^{45} - 6 q^{46} - 11197058 q^{47} - 32869688 q^{48} + 13239250 q^{50} - 16 q^{51} + 93509212 q^{52} + 53717512 q^{53} + 57025140 q^{54} - 14642290 q^{55} - 262150 q^{56} - 93310490 q^{57} - 97437640 q^{58} + 24222740 q^{59} - 66375070 q^{60} - 18369126 q^{61} + 6782124 q^{62} + 96012652 q^{63} + 112817140 q^{64} + 89469970 q^{65} + 6718458 q^{66} + 74549142 q^{67} - 62262702 q^{68} - 128418860 q^{69} - 177099410 q^{70} + 60703854 q^{71} - 444425220 q^{72} - 171988248 q^{73} + 257329110 q^{75} - 262160 q^{76} + 292751454 q^{77} + 385000804 q^{78} + 138506190 q^{79} + 245270230 q^{80} + 110809772 q^{81} - 73650066 q^{82} - 663197528 q^{83} - 1517250010 q^{84} - 616093620 q^{85} - 6 q^{86} + 494144820 q^{87} + 1287340030 q^{88} + 1051406240 q^{89} + 1480613390 q^{90} - 6 q^{91} - 461835158 q^{92} - 908140736 q^{93} - 1160168810 q^{94} - 920404690 q^{95} + 172437534 q^{96} - 732746208 q^{97} - 167741852 q^{98}+O(q^{100}) \) 152 * q - 8 * q^2 + 62 * q^3 - 10 * q^4 - 230 * q^5 - 6 * q^6 + 2342 * q^7 + 8210 * q^8 - 10 * q^9 - 30880 * q^10 - 6 * q^11 + 45902 * q^12 + 119132 * q^13 - 10 * q^14 - 241450 * q^15 + 524282 * q^16 - 105158 * q^17 + 454052 * q^18 + 718890 * q^19 + 340370 * q^20 - 6 * q^21 - 1986746 * q^22 - 899198 * q^23 + 2032310 * q^25 - 913936 * q^26 + 1904300 * q^27 - 998002 * q^28 - 1956910 * q^29 - 4500490 * q^30 - 6 * q^31 - 3033938 * q^32 + 1003994 * q^33 + 10303990 * q^34 + 4124560 * q^35 - 8100358 * q^36 + 9534392 * q^37 - 14259280 * q^38 - 22510410 * q^39 - 4123060 * q^40 - 4374726 * q^41 + 52199634 * q^42 + 13583342 * q^43 - 2138860 * q^44 - 33978380 * q^45 - 6 * q^46 - 11197058 * q^47 - 32869688 * q^48 + 13239250 * q^50 - 16 * q^51 + 93509212 * q^52 + 53717512 * q^53 + 57025140 * q^54 - 14642290 * q^55 - 262150 * q^56 - 93310490 * q^57 - 97437640 * q^58 + 24222740 * q^59 - 66375070 * q^60 - 18369126 * q^61 + 6782124 * q^62 + 96012652 * q^63 + 112817140 * q^64 + 89469970 * q^65 + 6718458 * q^66 + 74549142 * q^67 - 62262702 * q^68 - 128418860 * q^69 - 177099410 * q^70 + 60703854 * q^71 - 444425220 * q^72 - 171988248 * q^73 + 257329110 * q^75 - 262160 * q^76 + 292751454 * q^77 + 385000804 * q^78 + 138506190 * q^79 + 245270230 * q^80 + 110809772 * q^81 - 73650066 * q^82 - 663197528 * q^83 - 1517250010 * q^84 - 616093620 * q^85 - 6 * q^86 + 494144820 * q^87 + 1287340030 * q^88 + 1051406240 * q^89 + 1480613390 * q^90 - 6 * q^91 - 461835158 * q^92 - 908140736 * q^93 - 1160168810 * q^94 - 920404690 * q^95 + 172437534 * q^96 - 732746208 * q^97 - 167741852 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{20}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.758404	−	0.120119i	−0.0474003	−	0.00750747i	0.132689	−	0.991158i	$-0.457639\pi$
$2$	−0.758404	−	0.120119i	−0.0474003	−	0.00750747i	−0.180090	+	0.983650i	$0.557639\pi$
$3$	−20.5624	−	40.3560i	−0.253857	−	0.498222i	0.728546	−	0.684997i	$-0.240196\pi$
$3$	−20.5624	−	40.3560i	−0.253857	−	0.498222i	−0.982403	+	0.186775i	$0.940196\pi$
$4$	−242.910	−	78.9262i	−0.948866	−	0.308305i
$5$	−609.477	−	138.431i	−0.975163	−	0.221490i
$5$	−609.477	−	138.431i	−0.975163	−	0.221490i
$6$	10.7471	+	33.0761i	0.00829249	+	0.0255217i
$7$	3191.92	+	3191.92i	1.32941	+	1.32941i	0.905882	+	0.423531i	$0.139209\pi$
$7$	3191.92	+	3191.92i	1.32941	+	1.32941i	0.423531	+	0.905882i	$0.360791\pi$
$8$	349.890	+	178.278i	0.0854223	+	0.0435248i
$9$	2650.67	−	3648.33i	0.404004	−	0.556063i
$10$	445.602	+	178.197i	0.0445602	+	0.0178197i
$11$	−13389.0	+	9727.70i	−0.914489	+	0.664415i	−0.942146	−	0.335202i	$-0.891195\pi$
$11$	−13389.0	+	9727.70i	−0.914489	+	0.664415i	0.0276570	+	0.999617i	$0.491195\pi$
$12$	1809.66	+	11425.8i	0.0872716	+	0.551011i
$13$	45351.3	−	7182.93i	1.58787	−	0.251494i	0.700881	−	0.713278i	$-0.252790\pi$
$13$	45351.3	−	7182.93i	1.58787	−	0.251494i	0.886992	+	0.461784i	$0.152790\pi$
$14$	−2037.35	−	2804.18i	−0.0530340	−	0.0729950i
$15$	6945.78	+	27442.5i	0.137201	+	0.542074i
$16$	52653.7	+	38255.1i	0.803431	+	0.583727i
$17$	−45324.7	+	88954.6i	−0.542674	+	1.06506i	0.443020	+	0.896512i	$0.353907\pi$
$17$	−45324.7	+	88954.6i	−0.542674	+	1.06506i	−0.985694	+	0.168546i	$0.946093\pi$
$18$	−2448.51	+	2448.51i	−0.0233245	+	0.0233245i
$19$	−59144.2	+	19217.1i	−0.453835	+	0.147460i	−0.527010	−	0.849859i	$-0.676687\pi$
$19$	−59144.2	+	19217.1i	−0.453835	+	0.147460i	0.0731748	+	0.997319i	$0.476687\pi$
$20$	137122.	+	81729.9i	0.857012	+	0.510812i
$21$	63179.5	−	194446.i	0.324862	−	0.999822i
$22$	11322.8	−	5769.25i	0.0483351	−	0.0246280i
$23$	−28228.6	+	178228.i	−0.100874	+	0.636891i	0.884507	+	0.466526i	$0.154495\pi$
$23$	−28228.6	+	178228.i	−0.100874	+	0.636891i	−0.985381	+	0.170365i	$0.945505\pi$
$24$		−	17786.0i		−	0.0536083i
$25$	352299.	+	168741.i	0.901885	+	0.431977i
$26$	−35257.4			−0.0771537
$27$	−495242.	−	78438.6i	−0.931885	−	0.147596i
$28$	−523422.	−	1.02727e6i	−0.851569	−	1.67130i
$29$	−13581.0	−	4412.75i	−0.0192018	−	0.00623903i	0.299400	−	0.954128i	$-0.403213\pi$
$29$	−13581.0	−	4412.75i	−0.0192018	−	0.00623903i	−0.318602	+	0.947889i	$0.603213\pi$
$30$	−1971.33	−	21646.8i	−0.00243374	−	0.0267245i
$31$	102649.	+	315921.i	0.111150	+	0.342084i	0.991125	−	0.132937i	$-0.0424407\pi$
$31$	102649.	+	315921.i	0.111150	+	0.342084i	−0.879975	+	0.475020i	$0.842441\pi$
$32$	−106422.	−	106422.i	−0.101492	−	0.101492i
$33$	667881.	+	340303.i	0.563175	+	0.286952i
$34$	45059.6	−	62019.2i	0.0337188	−	0.0464099i
$35$	−1.50354e6	−	2.38726e6i	−1.00194	−	1.59084i
$36$	−931822.	+	677008.i	−0.554783	+	0.403073i
$37$	25399.2	+	160364.i	0.0135523	+	0.0855659i	0.993537	−	0.113505i	$-0.0362077\pi$
$37$	25399.2	+	160364.i	0.0135523	+	0.0855659i	−0.979985	+	0.199071i	$0.936208\pi$
$38$	47163.6	−	7469.98i	0.0226190	−	0.00358249i
$39$	−1.22240e6	−	1.68249e6i	−0.528392	−	0.727269i
$40$	−188571.	−	157092.i	−0.0736604	−	0.0613640i
$41$	2.08174e6	+	1.51248e6i	0.736702	+	0.535245i	0.891676	−	0.452673i	$-0.149530\pi$
$41$	2.08174e6	+	1.51248e6i	0.736702	+	0.535245i	−0.154975	+	0.987918i	$0.549530\pi$
$42$	−71272.4	+	139880.i	−0.0229047	+	0.0449530i
$43$	−462623.	+	462623.i	−0.135317	+	0.135317i	−0.771521	−	0.636204i	$-0.780504\pi$
$43$	−462623.	+	462623.i	−0.135317	+	0.135317i	0.636204	+	0.771521i	$0.280504\pi$
$44$	4.02010e6	−	1.30621e6i	1.07257	−	0.348499i
$45$	−2.12056e6	+	1.85664e6i	−0.517132	+	0.452770i
$46$	42817.3	−	131778.i	0.00956287	−	0.0294315i
$47$	3.80085e6	−	1.93663e6i	0.778914	−	0.396876i	−0.0188685	−	0.999822i	$-0.506006\pi$
$47$	3.80085e6	−	1.93663e6i	0.778914	−	0.396876i	0.797782	+	0.602946i	$0.206006\pi$
$48$	461137.	−	2.91151e6i	0.0868691	−	0.548470i
$49$			1.46119e7i			2.53467i
$50$	−246916.	−	170292.i	−0.0395065	−	0.0272467i
$51$	4.52183e6			0.668396
$52$	−1.15832e7	−	1.83460e6i	−1.58422	−	0.250915i
$53$	2.26551e6	+	4.44632e6i	0.287120	+	0.563505i	0.988846	−	0.148942i	$-0.0475869\pi$
$53$	2.26551e6	+	4.44632e6i	0.287120	+	0.563505i	−0.701726	+	0.712447i	$0.747587\pi$
$54$	366172.	+	118976.i	0.0430635	+	0.0139922i
$55$	9.50692e6	−	4.07535e6i	1.03894	−	0.445363i
$56$	547772.	+	1.68587e6i	0.0556990	+	0.171424i
$57$	1.99167e6	+	1.99167e6i	0.188677	+	0.188677i
$58$	9769.86	+	4977.99i	0.000863329	+	0.000439888i
$59$	−1.21021e7	+	1.66572e7i	−0.998743	+	1.37465i	−0.0726500	+	0.997357i	$0.523146\pi$
$59$	−1.21021e7	+	1.66572e7i	−0.998743	+	1.37465i	−0.926093	+	0.377295i	$0.876854\pi$
$60$	478733.	−	7.21425e6i	0.0369393	−	0.556655i
$61$	1.14573e7	−	8.32419e6i	0.827488	−	0.601205i	−0.0913597	−	0.995818i	$-0.529121\pi$
$61$	1.14573e7	−	8.32419e6i	0.827488	−	0.601205i	0.918847	+	0.394613i	$0.129121\pi$
$62$	−39901.2	−	251926.i	−0.00270034	−	0.0170493i
$63$	2.01059e7	−	3.18446e6i	1.27632	−	0.202150i
$64$	−9.72539e6	−	1.33858e7i	−0.579678	−	0.797859i
$65$	−2.86349e7	−	1.90019e6i	−1.60414	−	0.106450i
$66$	−465647.	−	338313.i	−0.0245404	−	0.0178296i
$67$	−1.03762e7	+	2.03645e7i	−0.514921	+	1.01059i	0.476412	+	0.879222i	$0.341937\pi$
$67$	−1.03762e7	+	2.03645e7i	−0.514921	+	1.01059i	−0.991334	+	0.131368i	$0.958063\pi$
$68$	1.80306e7	−	1.80306e7i	0.843287	−	0.843287i
$69$	7.77302e6	−	2.52561e6i	0.342920	−	0.111422i
$70$	853535.	+	1.99111e6i	0.0355491	+	0.0829285i
$71$	−7.08274e6	+	2.17984e7i	−0.278720	+	0.857811i	0.709491	+	0.704714i	$0.248925\pi$
$71$	−7.08274e6	+	2.17984e7i	−0.278720	+	0.857811i	−0.988211	+	0.153097i	$0.951075\pi$
$72$	1.57786e6	−	803959.i	0.0587135	−	0.0299160i
$73$	4.60331e6	−	2.90642e7i	0.162099	−	1.02345i	−0.763738	−	0.645526i	$-0.776638\pi$
$73$	4.60331e6	−	2.90642e7i	0.162099	−	1.02345i	0.925837	−	0.377924i	$-0.123362\pi$
$74$		−	124672.i		−	0.00415759i
$75$	−434398.	−	1.76871e7i	−0.0137291	−	0.558999i
$76$	1.58834e7			0.476091
$77$	−7.37868e7	−	1.16867e7i	−2.09902	−	0.332451i
$78$	724976.	+	1.42285e6i	0.0195860	+	0.0384397i
$79$	−3.40860e6	−	1.10752e6i	−0.0875121	−	0.0284344i	0.264934	−	0.964267i	$-0.414650\pi$
$79$	−3.40860e6	−	1.10752e6i	−0.0875121	−	0.0284344i	−0.352446	+	0.935832i	$0.614650\pi$
$80$	−2.67955e7	−	3.06045e7i	−0.654187	−	0.747181i
$81$	−2.12512e6	−	6.54044e6i	−0.0493677	−	0.151938i
$82$	−1.39713e6	−	1.39713e6i	−0.0309015	−	0.0309015i
$83$	−1.55857e7	−	7.94132e6i	−0.328408	−	0.167332i	0.282010	−	0.959411i	$-0.408999\pi$
$83$	−1.55857e7	−	7.94132e6i	−0.328408	−	0.167332i	−0.610419	+	0.792079i	$0.708999\pi$
$84$	−3.06938e7	+	4.22464e7i	−0.616501	+	0.848541i
$85$	3.99384e7	−	4.79414e7i	0.765094	−	0.918407i
$86$	406425.	−	295285.i	0.00742997	−	0.00539819i
$87$	101178.	+	638812.i	0.00176607	+	0.0111505i
$88$	−6.41892e6	+	1.01666e6i	−0.107036	+	0.0169529i
$89$	5.59375e7	+	7.69914e7i	0.891545	+	1.22711i	0.973087	+	0.230437i	$0.0740154\pi$
$89$	5.59375e7	+	7.69914e7i	0.891545	+	1.22711i	−0.0815423	+	0.996670i	$0.525985\pi$
$90$	1.83126e6	−	1.15336e6i	0.0279113	−	0.0175791i
$91$	1.67685e8	+	1.21830e8i	2.44528	+	1.77660i
$92$	2.09239e7	−	4.10654e7i	0.292072	−	0.573224i
$93$	1.06386e7	−	1.06386e7i	0.142217	−	0.142217i
$94$	−3.11521e6	+	1.01219e6i	−0.0399003	+	0.0129644i
$95$	3.87073e7	−	3.52499e6i	0.475224	−	0.0432777i
$96$	−2.10647e6	+	6.48306e6i	−0.0248011	+	0.0763300i
$97$	−7.87576e7	+	4.01290e7i	−0.889622	+	0.453285i	−0.838182	−	0.545391i	$-0.816381\pi$
$97$	−7.87576e7	+	4.01290e7i	−0.889622	+	0.453285i	−0.0514401	+	0.998676i	$0.516381\pi$
$98$	1.75517e6	−	1.10817e7i	0.0190290	−	0.120144i
$99$			7.46325e7i			0.776940i
$100$	−7.22587e7	−	6.87944e7i	−0.722587	−	0.687944i
$101$	−6.55943e7			−0.630348			−0.315174	−	0.949034i	$-0.602063\pi$
$101$	−6.55943e7			−0.630348			−0.315174	+	0.949034i	$0.602063\pi$
$102$	−3.42938e6	−	543160.i	−0.0316821	−	0.00501796i
$103$	−1.60051e7	−	3.14117e7i	−0.142203	−	0.279089i	0.808910	−	0.587933i	$-0.200058\pi$
$103$	−1.60051e7	−	3.14117e7i	−0.142203	−	0.279089i	−0.951113	+	0.308844i	$0.900058\pi$
$104$	1.71485e7	+	5.57189e6i	0.146586	+	0.0476287i
$105$	−6.54238e7	+	1.09765e8i	−0.538244	+	0.903036i
$106$	−1.18409e6	−	3.64424e6i	−0.00937907	−	0.0288658i
$107$	−5.61237e7	−	5.61237e7i	−0.428165	−	0.428165i	0.459838	−	0.888003i	$-0.347908\pi$
$107$	−5.61237e7	−	5.61237e7i	−0.428165	−	0.428165i	−0.888003	+	0.459838i	$0.847908\pi$
$108$	1.14108e8	+	5.81410e7i	0.838729	+	0.427354i
$109$	1.04410e8	−	1.43708e8i	0.739664	−	1.01806i	−0.258974	−	0.965884i	$-0.583384\pi$
$109$	1.04410e8	−	1.43708e8i	0.739664	−	1.01806i	0.998638	−	0.0521760i	$-0.0166157\pi$
$110$	−7.69962e6	+	1.94880e6i	−0.0525894	+	0.0133106i
$111$	5.94939e6	−	4.32248e6i	0.0391905	−	0.0284735i
$112$	4.59590e7	+	2.90174e8i	0.292078	+	1.84411i
$113$	1.36193e8	−	2.15709e7i	0.835297	−	0.132298i	0.275888	−	0.961190i	$-0.411028\pi$
$113$	1.36193e8	−	2.15709e7i	0.835297	−	0.132298i	0.559409	+	0.828892i	$0.311028\pi$
$114$	−1.27125e6	−	1.74973e6i	−0.00752685	−	0.0103598i
$115$	4.18770e7	−	1.04718e8i	0.239433	−	0.598730i
$116$	2.95068e6	+	2.14380e6i	0.0162964	+	0.0118400i
$117$	9.40054e7	−	1.84496e8i	0.501660	−	0.984563i
$118$	1.11792e7	−	1.11792e7i	0.0576609	−	0.0576609i
$119$	−4.28609e8	+	1.39263e8i	−2.13734	+	0.694463i
$120$	−2.46213e6	+	1.08401e7i	−0.0118737	+	0.0522768i
$121$	1.83975e7	−	5.66218e7i	0.0858259	−	0.264145i
$122$	−9.68914e6	+	4.93686e6i	−0.0437367	+	0.0222849i
$123$	1.82318e7	−	1.15111e8i	0.0796541	−	0.502916i
$124$		−	8.48421e7i		−	0.358860i
$125$	−1.91359e8	−	1.51613e8i	−0.783806	−	0.621006i
$126$	−1.56309e7			−0.0620158
$127$	−2.72036e7	−	4.30863e6i	−0.104571	−	0.0165624i	0.103930	−	0.994585i	$-0.466858\pi$
$127$	−2.72036e7	−	4.30863e6i	−0.104571	−	0.0165624i	−0.208501	+	0.978022i	$0.566858\pi$
$128$	2.32597e7	+	4.56496e7i	0.0866490	+	0.170058i
$129$	2.81822e7	+	9.15696e6i	0.101769	+	0.0330668i
$130$	2.14886e7	+	4.88072e6i	0.0752374	+	0.0170888i
$131$	−1.47658e8	−	4.54446e8i	−0.501387	−	1.54311i	−0.806761	−	0.590878i	$-0.798781\pi$
$131$	−1.47658e8	−	4.54446e8i	−0.501387	−	1.54311i	0.305374	−	0.952233i	$-0.401219\pi$
$132$	−1.35376e8	−	1.35376e8i	−0.445909	−	0.445909i
$133$	−2.50123e8	−	1.27444e8i	−0.799369	−	0.407299i
$134$	1.03156e7	−	1.41982e7i	0.0319944	−	0.0440365i
$135$	2.90980e8	+	1.16363e8i	0.876048	+	0.350333i
$136$	−3.17173e7	+	2.30439e7i	−0.0927129	+	0.0673599i
$137$	−4.10549e6	−	2.59211e7i	−0.0116542	−	0.0735818i	0.981176	−	0.193117i	$-0.0618596\pi$
$137$	−4.10549e6	−	2.59211e7i	−0.0116542	−	0.0735818i	−0.992830	+	0.119535i	$0.961860\pi$
$138$	−6.19846e6	+	981740.i	−0.0170910	+	0.00270695i
$139$	1.22873e8	+	1.69121e8i	0.329153	+	0.453041i	0.941234	−	0.337754i	$-0.109667\pi$
$139$	1.22873e8	+	1.69121e8i	0.329153	+	0.453041i	−0.612081	+	0.790795i	$0.709667\pi$
$140$	1.76807e8	+	6.98558e8i	0.460243	+	1.81840i
$141$	−1.56309e8	−	1.13565e8i	−0.395465	−	0.287322i
$142$	7.98999e6	−	1.56812e7i	0.0196514	−	0.0385680i
$143$	−5.37336e8	+	5.37336e8i	−1.28500	+	1.28500i
$144$	2.79135e8	−	9.06964e7i	0.649178	−	0.210931i
$145$	7.66646e6	+	4.56950e6i	0.0173430	+	0.0103371i
$146$	−6.98234e6	+	2.14894e7i	−0.0153670	+	0.0472948i
$147$	5.89677e8	−	3.00455e8i	1.26283	−	0.643444i
$148$	6.48722e6	−	4.09587e7i	0.0135211	−	0.0853689i
$149$		−	5.17297e8i		−	1.04953i	−0.851247	−	0.524765i	$-0.824153\pi$
$149$		−	5.17297e8i		−	1.04953i	0.851247	−	0.524765i	$-0.175847\pi$
$150$	−1.79511e6	+	1.34661e7i	−0.00354590	+	0.0265998i
$151$	1.81744e8			0.349584			0.174792	−	0.984605i	$-0.444075\pi$
$151$	1.81744e8			0.349584			0.174792	+	0.984605i	$0.444075\pi$
$152$	−2.41200e7	−	3.82023e6i	−0.0451858	−	0.00715673i
$153$	2.04395e8	+	4.01149e8i	0.372997	+	0.732048i
$154$	5.45564e7	+	1.77265e7i	0.0969980	+	0.0315166i
$155$	−1.88289e7	−	2.06757e8i	−0.0326211	−	0.358206i
$156$	1.64141e8	+	5.05174e8i	0.277152	+	0.852987i
$157$	6.35759e8	+	6.35759e8i	1.04639	+	1.04639i	0.998870	+	0.0475197i	$0.0151317\pi$
$157$	6.35759e8	+	6.35759e8i	1.04639	+	1.04639i	0.0475197	+	0.998870i	$0.484868\pi$
$158$	2.45207e6	+	1.24939e6i	0.00393463	+	0.00200479i
$159$	1.32851e8	−	1.82854e8i	0.207863	−	0.286099i
$160$	5.01297e7	+	7.95940e7i	0.0764919	+	0.121451i
$161$	−6.58993e8	+	4.78787e8i	−0.980793	+	0.712588i
$162$	826064.	+	5.21556e6i	0.00119937	+	0.00757253i
$163$	−4.86141e8	+	7.69972e7i	−0.688671	+	0.109075i	−0.490956	−	0.871185i	$-0.663352\pi$
$163$	−4.86141e8	+	7.69972e7i	−0.688671	+	0.109075i	−0.197716	+	0.980259i	$0.563352\pi$
$164$	−3.86302e8	−	5.31699e8i	−0.534012	−	0.735005i
$165$	−3.59950e8	−	2.99862e8i	−0.485631	−	0.404563i
$166$	1.08664e7	+	7.89488e6i	0.0143104	+	0.0103971i
$167$	−6.79382e7	+	1.33336e8i	−0.0873470	+	0.171428i	−0.930548	−	0.366171i	$-0.880669\pi$
$167$	−6.79382e7	+	1.33336e8i	−0.0873470	+	0.171428i	0.843201	+	0.537599i	$0.180669\pi$
$168$	5.67713e7	−	5.67713e7i	0.0712676	−	0.0712676i
$169$	1.22934e9	−	3.99435e8i	1.50704	−	0.489666i
$170$	−3.60482e7	+	3.15616e7i	−0.0431606	+	0.0377888i
$171$	−8.66613e7	+	2.66716e8i	−0.101354	+	0.311935i
$172$	1.48889e8	−	7.58626e7i	0.170117	−	0.0866790i
$173$	−3.62988e7	+	2.29181e8i	−0.0405236	+	0.255856i	−0.999630	−	0.0271889i	$-0.991344\pi$
$173$	−3.62988e7	+	2.29181e8i	−0.0405236	+	0.255856i	0.959107	+	0.283045i	$0.0913444\pi$
$174$		−	496631.i		−	0.000541798i
$175$	5.85901e8	+	1.66312e9i	0.624701	+	1.77325i
$176$	−1.07712e9			−1.12257
$177$	9.21064e8	+	1.45882e8i	0.938419	+	0.148631i
$178$	−3.31751e7	−	6.51098e7i	−0.0330470	−	0.0648584i
$179$	−8.44321e7	−	2.74336e7i	−0.0822423	−	0.0267221i	0.267607	−	0.963528i	$-0.413767\pi$
$179$	−8.44321e7	−	2.74336e7i	−0.0822423	−	0.0267221i	−0.349849	+	0.936806i	$0.613767\pi$
$180$	6.61643e8	−	2.83628e8i	0.630280	−	0.270183i
$181$	−3.64250e8	−	1.12105e9i	−0.339379	−	1.04450i	−0.964525	−	0.263993i	$-0.914960\pi$
$181$	−3.64250e8	−	1.12105e9i	−0.339379	−	1.04450i	0.625146	−	0.780508i	$-0.285040\pi$
$182$	−1.12539e8	−	1.12539e8i	−0.102569	−	0.102569i
$183$	−5.71519e8	−	2.91204e8i	−0.509597	−	0.259652i
$184$	−4.16510e7	+	5.73277e7i	−0.0363374	+	0.0500142i
$185$	6.71917e6	−	1.01254e8i	0.00573626	−	0.0864424i
$186$	−9.34626e6	+	6.79046e6i	−0.00780883	+	0.00567345i
$187$	−2.58471e8	−	1.63192e9i	−0.211371	−	1.33454i
$188$	−1.07611e9	+	1.70440e8i	−0.861444	+	0.136439i
$189$	−1.33040e9	−	1.83114e9i	−1.04264	−	1.43508i
$190$	−2.97792e7	−	1.97613e6i	−0.0228506	−	0.00151635i
$191$	−3.16370e8	−	2.29856e8i	−0.237718	−	0.172712i	0.462548	−	0.886594i	$-0.346935\pi$
$191$	−3.16370e8	−	2.29856e8i	−0.237718	−	0.172712i	−0.700266	+	0.713882i	$0.746935\pi$
$192$	−3.40222e8	+	6.67722e8i	−0.250355	+	0.491350i
$193$	−2.31836e8	+	2.31836e8i	−0.167091	+	0.167091i	−0.785699	−	0.618609i	$-0.787697\pi$
$193$	−2.31836e8	+	2.31836e8i	−0.167091	+	0.167091i	0.618609	+	0.785699i	$0.287697\pi$
$194$	6.45504e7	−	2.09737e7i	0.0455713	−	0.0148070i
$195$	5.12117e8	+	1.19466e9i	0.354186	+	0.826239i
$196$	1.15326e9	−	3.54937e9i	0.781454	−	2.40507i
$197$	−5.45883e8	+	2.78141e8i	−0.362438	+	0.184672i	−0.625721	−	0.780047i	$-0.715195\pi$
$197$	−5.45883e8	+	2.78141e8i	−0.362438	+	0.184672i	0.263282	+	0.964719i	$0.415195\pi$
$198$	8.96482e6	−	5.66017e7i	0.00583285	−	0.0368272i
$199$			2.70407e9i			1.72427i	0.506679	+	0.862135i	$0.330873\pi$
$199$			2.70407e9i			1.72427i	−0.506679	+	0.862135i	$0.669127\pi$
$200$	9.31830e7	+	1.21848e8i	0.0582394	+	0.0761549i
$201$	1.03519e9			0.634214
$202$	4.97470e7	+	7.87915e6i	0.0298787	+	0.00473232i
$203$	−2.92644e7	−	5.74347e7i	−0.0172328	−	0.0338213i
$204$	−1.09840e9	−	3.56891e8i	−0.634218	−	0.206070i
$205$	−1.05940e9	−	1.21000e9i	−0.599853	−	0.685123i
$206$	8.36515e6	+	2.57453e7i	0.00464520	+	0.0142965i
$207$	5.75411e8	+	5.75411e8i	0.313398	+	0.313398i
$208$	2.66269e9	+	1.35671e9i	1.42255	+	0.724826i
$209$	6.04946e8	−	8.32636e8i	0.317053	−	0.436385i
$210$	6.28026e7	−	7.53873e7i	0.0322924	−	0.0387633i
$211$	−1.55205e9	+	1.12763e9i	−0.783026	+	0.568902i	−0.905886	−	0.423522i	$-0.860794\pi$
$211$	−1.55205e9	+	1.12763e9i	−0.783026	+	0.568902i	0.122859	+	0.992424i	$0.460794\pi$
$212$	−1.99384e8	−	1.25886e9i	−0.0987069	−	0.623211i
$213$	1.02533e9	−	1.62397e8i	0.498135	−	0.0788968i
$214$	3.58229e7	+	4.93060e7i	0.0170807	+	0.0235096i
$215$	3.45999e8	−	2.17917e8i	0.161928	−	0.101985i
$216$	−1.59296e8	−	1.15735e8i	−0.0731797	−	0.0531681i
$217$	−6.80748e8	+	1.33604e9i	−0.307006	+	0.602534i
$218$	−9.64468e7	+	9.64468e7i	−0.0427033	+	0.0427033i
$219$	−1.26757e9	+	4.11858e8i	−0.551055	+	0.179048i
$220$	−2.63098e9	+	2.39598e8i	−1.12312	+	0.102280i
$221$	−1.41657e9	+	4.35977e9i	−0.593841	+	1.82766i
$222$	−5.03126e6	+	2.56355e6i	−0.00207140	+	0.00105543i
$223$	4.06393e8	−	2.56587e9i	0.164334	−	1.03756i	−0.758305	−	0.651899i	$-0.773972\pi$
$223$	4.06393e8	−	2.56587e9i	0.164334	−	1.03756i	0.922639	−	0.385664i	$-0.126028\pi$
$224$		−	6.79382e8i		−	0.269850i
$225$	1.54945e9	−	8.38026e8i	0.604571	−	0.326985i
$226$	−1.05880e8			−0.0405865
$227$	3.09330e9	+	4.89930e8i	1.16498	+	0.184515i	0.708824	−	0.705385i	$-0.249226\pi$
$227$	3.09330e9	+	4.89930e8i	1.16498	+	0.184515i	0.456156	+	0.889900i	$0.349226\pi$
$228$	−3.26602e8	−	6.40992e8i	−0.120859	−	0.237199i
$229$	3.98144e9	+	1.29365e9i	1.44777	+	0.470407i	0.924309	−	0.381645i	$-0.124642\pi$
$229$	3.98144e9	+	1.29365e9i	1.44777	+	0.470407i	0.523456	+	0.852053i	$0.324642\pi$
$230$	−4.43384e7	+	7.43885e7i	−0.0158441	+	0.0265824i
$231$	1.04561e9	+	3.21804e9i	0.367214	+	1.13017i
$232$	−3.96517e6	−	3.96517e6i	−0.00136871	−	0.00136871i
$233$	1.49880e9	+	7.63675e8i	0.508533	+	0.259111i	0.689379	−	0.724401i	$-0.257884\pi$
$233$	1.49880e9	+	7.63675e8i	0.508533	+	0.259111i	−0.180846	+	0.983511i	$0.557884\pi$
$234$	−9.34556e7	+	1.28631e8i	−0.0311704	+	0.0429023i
$235$	−2.58462e9	+	6.54175e8i	−0.847472	+	0.214498i
$236$	4.25441e9	−	3.09101e9i	1.37149	−	0.996443i
$237$	2.53939e7	+	1.60331e8i	0.00804889	+	0.0508187i
$238$	3.41787e8	−	5.41337e7i	0.106524	−	0.0168717i
$239$	2.56076e9	+	3.52458e9i	0.784832	+	1.08023i	0.994732	+	0.102506i	$0.0326862\pi$
$239$	2.56076e9	+	3.52458e9i	0.784832	+	1.08023i	−0.209900	+	0.977723i	$0.567314\pi$
$240$	−6.84095e8	+	1.71066e9i	−0.206192	+	0.515607i
$241$	−9.48446e8	−	6.89086e8i	−0.281154	−	0.204270i	0.438267	−	0.898845i	$-0.355593\pi$
$241$	−9.48446e8	−	6.89086e8i	−0.281154	−	0.204270i	−0.719421	+	0.694575i	$0.755593\pi$
$242$	−2.07542e7	+	4.07323e7i	−0.00605123	+	0.0118762i
$243$	−2.54648e9	+	2.54648e9i	−0.730322	+	0.730322i
$244$	−3.44008e9	+	1.11775e9i	−0.970530	+	0.315344i
$245$	2.02274e9	−	8.90561e9i	0.561404	−	2.47172i
$246$	−2.76541e7	+	8.51106e7i	−0.00755126	+	0.0232404i
$247$	−2.54423e9	+	1.29635e9i	−0.683547	+	0.348285i
$248$	−2.04059e7	+	1.28838e8i	−0.00539447	+	0.0340593i
$249$			7.92269e8i			0.206099i
$250$	1.26916e8	+	1.37970e8i	0.0324904	+	0.0353202i
$251$	5.45502e9			1.37436			0.687181	−	0.726486i	$-0.258848\pi$
$251$	5.45502e9			1.37436			0.687181	+	0.726486i	$0.258848\pi$
$252$	−5.13525e9	−	8.13344e8i	−1.27339	−	0.201684i
$253$	−1.35580e9	−	2.66090e9i	−0.330912	−	0.649452i
$254$	2.01138e7	+	6.53537e6i	0.00483236	+	0.00157013i
$255$	−2.75595e9	−	6.25962e8i	−0.651795	−	0.148043i
$256$	1.29676e9	+	3.99100e9i	0.301924	+	0.929228i
$257$	−4.93050e9	−	4.93050e9i	−1.13021	−	1.13021i	−0.990142	−	0.140065i	$-0.955269\pi$
$257$	−4.93050e9	−	4.93050e9i	−1.13021	−	1.13021i	−0.140065	−	0.990142i	$-0.544731\pi$
$258$	−2.02736e7	−	1.03299e7i	−0.00457564	−	0.00233141i
$259$	−4.30798e8	+	5.92942e8i	−0.0957358	+	0.131769i
$260$	6.80571e9	+	2.72162e9i	1.48929	+	0.595571i
$261$	−5.20980e7	+	3.78514e7i	−0.0112269	+	0.00815680i
$262$	5.73970e7	+	3.62391e8i	0.0121810	+	0.0769080i
$263$	−1.10279e9	+	1.74665e8i	−0.230500	+	0.0365076i	−0.270616	−	0.962687i	$-0.587227\pi$
$263$	−1.10279e9	+	1.74665e8i	−0.230500	+	0.0365076i	0.0401159	+	0.999195i	$0.487227\pi$
$264$	1.73017e8	+	2.38137e8i	0.0356182	+	0.0490242i
$265$	−7.65269e8	−	3.02355e9i	−0.155178	−	0.613103i
$266$	1.74386e8	+	1.26699e8i	0.0348325	+	0.0253073i
$267$	1.95685e9	−	3.84054e9i	0.385046	−	0.755696i
$268$	4.12778e9	−	4.12778e9i	0.800162	−	0.800162i
$269$	−6.36184e9	+	2.06709e9i	−1.21499	+	0.394775i	−0.845256	−	0.534361i	$-0.820552\pi$
$269$	−6.36184e9	+	2.06709e9i	−1.21499	+	0.394775i	−0.369737	+	0.929137i	$0.620552\pi$
$270$	−2.06703e8	−	1.23203e8i	−0.0388948	−	0.0231828i
$271$	1.22480e8	−	3.76953e8i	0.0227084	−	0.0698893i	−0.939060	−	0.343753i	$-0.888302\pi$
$271$	1.22480e8	−	3.76953e8i	0.0227084	−	0.0698893i	0.961769	+	0.273864i	$0.0883017\pi$
$272$	−5.78948e9	+	2.94989e9i	−1.05770	+	0.538927i
$273$	1.46857e9	−	9.27220e9i	0.264390	−	1.66929i
$274$			2.01518e7i			0.00357529i
$275$	−6.35840e9	+	1.16778e9i	−1.11178	+	0.204188i
$276$	−2.08748e9			−0.359737
$277$	−1.52846e9	−	2.42085e8i	−0.259619	−	0.0411195i	0.0252682	−	0.999681i	$-0.491956\pi$
$277$	−1.52846e9	−	2.42085e8i	−0.259619	−	0.0411195i	−0.284887	+	0.958561i	$0.591956\pi$
$278$	−7.28730e7	−	1.43021e8i	−0.0122008	−	0.0239454i
$279$	1.42467e9	+	4.62905e8i	0.235125	+	0.0763967i
$280$	−1.00478e8	−	1.10333e9i	−0.0163470	−	0.179503i
$281$	−8.15789e8	−	2.51074e9i	−0.130844	−	0.402695i	0.864077	−	0.503360i	$-0.167903\pi$
$281$	−8.15789e8	−	2.51074e9i	−0.130844	−	0.402695i	−0.994920	+	0.100665i	$0.967903\pi$
$282$	1.04904e8	+	1.04904e8i	0.0165881	+	0.0165881i
$283$	4.92410e9	+	2.50895e9i	0.767681	+	0.391153i	0.793544	−	0.608512i	$-0.208233\pi$
$283$	4.92410e9	+	2.50895e9i	0.767681	+	0.391153i	−0.0258633	+	0.999665i	$0.508233\pi$
$284$	3.44093e9	−	4.73604e9i	0.528935	−	0.728017i
$285$	−9.38169e8	−	1.48959e9i	−0.142201	−	0.225781i
$286$	4.72063e8	−	3.42974e8i	0.0705562	−	0.0512621i
$287$	1.81706e9	+	1.14725e10i	0.267819	+	1.69094i
$288$	−6.70353e8	+	1.06174e8i	−0.0974392	+	0.0154329i
$289$	−1.75836e9	−	2.42017e9i	−0.252067	−	0.346940i
$290$	−5.26539e6	−	4.38642e6i	−0.000744456	−	0.000620181i
$291$	3.23889e9	+	2.35319e9i	0.451673	+	0.328159i
$292$	−3.41211e9	+	6.69665e9i	−0.469345	+	0.921141i
$293$	1.78885e9	−	1.78885e9i	0.242719	−	0.242719i	−0.575255	−	0.817974i	$-0.695097\pi$
$293$	1.78885e9	−	1.78885e9i	0.242719	−	0.242719i	0.817974	+	0.575255i	$0.195097\pi$
$294$	−4.83304e8	+	1.57035e8i	−0.0646891	+	0.0210188i
$295$	9.68184e9	−	8.47684e9i	1.27841	−	1.11930i
$296$	−1.97025e7	+	6.06380e7i	−0.00256657	+	0.00789910i
$297$	7.39384e9	−	3.76735e9i	0.950264	−	0.484184i
$298$	−6.21374e7	+	3.92320e8i	−0.00787931	+	0.0497480i
$299$			8.28564e9i			1.03667i
$300$	−1.29045e9	+	4.33065e9i	−0.159315	+	0.534648i
$301$	−2.95331e9			−0.359785
$302$	−1.37835e8	−	2.18310e7i	−0.0165704	−	0.00262449i
$303$	1.34877e9	+	2.64712e9i	0.160018	+	0.314053i
$304$	−3.84932e9	−	1.25072e9i	−0.450702	−	0.146442i
$305$	−8.13526e9	+	3.48736e9i	−0.940096	+	0.402993i
$306$	−1.06829e8	−	3.28785e8i	−0.0121843	−	0.0374995i
$307$	1.08793e9	+	1.08793e9i	0.122475	+	0.122475i	0.765688	−	0.643213i	$-0.222399\pi$
$307$	1.08793e9	+	1.08793e9i	0.122475	+	0.122475i	−0.643213	+	0.765688i	$0.722399\pi$
$308$	1.70011e10	+	8.66251e9i	1.88919	+	0.962589i
$309$	−9.38547e8	+	1.29180e9i	−0.102949	+	0.141697i
$310$	−1.05556e7	+	1.59067e8i	−0.00114297	+	0.0172239i
$311$	8.99984e8	−	6.53877e8i	0.0962040	−	0.0698963i	−0.538643	−	0.842534i	$-0.681063\pi$
$311$	8.99984e8	−	6.53877e8i	0.0962040	−	0.0698963i	0.634847	+	0.772638i	$0.281063\pi$
$312$	−1.27755e8	−	8.06615e8i	−0.0134822	−	0.0851232i
$313$	−1.71908e10	+	2.72276e9i	−1.79110	+	0.283682i	−0.961525	−	0.274718i	$-0.911416\pi$
$313$	−1.71908e10	+	2.72276e9i	−1.79110	+	0.283682i	−0.829572	+	0.558400i	$0.811416\pi$
$314$	−4.05795e8	−	5.58529e8i	−0.0417434	−	0.0574549i
$315$	−1.26949e10	−	8.42425e8i	−1.28940	−	0.0855636i
$316$	7.40571e8	+	5.38056e8i	0.0742708	+	0.0539609i
$317$	6.28604e9	−	1.23371e10i	0.622502	−	1.22173i	−0.337392	−	0.941364i	$-0.609545\pi$
$317$	6.28604e9	−	1.23371e10i	0.622502	−	1.22173i	0.959894	−	0.280364i	$-0.0904551\pi$
$318$	−1.22719e8	+	1.22719e8i	−0.0120006	+	0.0120006i
$319$	2.24763e8	−	7.30299e7i	0.0217051	−	0.00705241i
$320$	4.07438e9	+	9.50466e9i	0.388563	+	0.906435i
$321$	−1.11089e9	+	3.41896e9i	−0.104629	+	0.322014i
$322$	5.57295e8	−	2.83956e8i	0.0518396	−	0.0264136i
$323$	9.71239e8	−	6.13216e9i	0.0892311	−	0.563383i
$324$			1.75646e9i			0.159389i
$325$	1.71892e10	+	5.12208e9i	1.54072	+	0.459106i
$326$	3.77940e8			0.0334621
$327$	−7.94637e9	−	1.25858e9i	−0.694988	−	0.110075i
$328$	4.58740e8	+	9.00328e8i	0.0396343	+	0.0777867i
$329$	1.83136e10	+	5.95044e9i	1.56311	+	0.507885i
$330$	2.36968e8	+	2.70654e8i	0.0199818	+	0.0228222i
$331$	3.96975e8	+	1.22176e9i	0.0330713	+	0.101783i	0.966230	−	0.257683i	$-0.0829590\pi$
$331$	3.96975e8	+	1.22176e9i	0.0330713	+	0.101783i	−0.933158	+	0.359466i	$0.882959\pi$
$332$	3.15914e9	+	3.15914e9i	0.260026	+	0.260026i
$333$	6.52387e8	+	3.32408e8i	0.0530552	+	0.0270330i
$334$	6.75409e7	−	9.29621e7i	0.00542726	−	0.00746999i
$335$	9.14316e9	−	1.09753e10i	0.725967	−	0.871440i
$336$	1.07652e10	−	7.82138e9i	0.844628	−	0.613658i
$337$	−1.62260e9	−	1.02447e10i	−0.125804	−	0.794292i	−0.967226	−	0.253915i	$-0.918282\pi$
$337$	−1.62260e9	−	1.02447e10i	−0.125804	−	0.794292i	0.841423	−	0.540377i	$-0.181718\pi$
$338$	−9.80313e8	+	1.55266e8i	−0.0751101	+	0.0118963i
$339$	−3.67097e9	−	5.05265e9i	−0.277960	−	0.382579i
$340$	−1.34853e10	+	8.49326e9i	−1.00912	+	0.635563i
$341$	−4.44756e9	−	3.23134e9i	−0.328931	−	0.238982i
$342$	9.77621e7	−	1.91869e8i	0.00714605	−	0.0140249i
$343$	−2.82392e10	+	2.82392e10i	−2.04022	+	2.04022i
$344$	−2.44342e8	+	7.93917e7i	−0.0174488	+	0.00566945i
$345$	−5.08709e9	+	4.63271e8i	−0.359082	+	0.0327008i
$346$	5.50583e7	−	1.69452e8i	0.00384165	−	0.0118234i
$347$	1.96750e10	−	1.00249e10i	1.35705	−	0.691453i	0.384281	−	0.923216i	$-0.374449\pi$
$347$	1.96750e10	−	1.00249e10i	1.35705	−	0.691453i	0.972772	+	0.231763i	$0.0744493\pi$
$348$	2.58419e7	−	1.63159e8i	0.00176201	−	0.0111249i
$349$			7.85821e9i			0.529690i	0.964291	+	0.264845i	$0.0853209\pi$
$349$			7.85821e9i			0.529690i	−0.964291	+	0.264845i	$0.914679\pi$
$350$	−2.44577e8	−	1.33169e9i	−0.0162984	−	0.0887426i
$351$	−2.30233e10			−1.51683
$352$	2.46013e9	+	3.89647e8i	0.160246	+	0.0253805i
$353$	−7.03215e9	−	1.38014e10i	−0.452887	−	0.888840i	−0.998702	−	0.0509344i	$-0.983780\pi$
$353$	−7.03215e9	−	1.38014e10i	−0.452887	−	0.888840i	0.545815	−	0.837905i	$-0.316220\pi$
$354$	−6.81016e8	−	2.21275e8i	−0.0433655	−	0.0140903i
$355$	7.33434e9	−	1.23052e10i	0.461793	−	0.774772i
$356$	−7.51113e9	−	2.31169e10i	−0.467633	−	1.43923i
$357$	1.44333e10	+	1.44333e10i	0.888574	+	0.888574i
$358$	6.07383e7	+	3.09477e7i	0.00369769	+	0.00188407i
$359$	1.66042e10	−	2.28537e10i	0.999631	−	1.37587i	0.0740802	−	0.997252i	$-0.476398\pi$
$359$	1.66042e10	−	2.28537e10i	0.999631	−	1.37587i	0.925551	−	0.378622i	$-0.123602\pi$
$360$	−1.07296e9	+	2.71570e8i	−0.0638813	+	0.0161686i
$361$	−1.06112e10	+	7.70952e9i	−0.624795	+	0.453940i
$362$	1.41589e8	+	8.93959e8i	0.00824510	+	0.0520575i
$363$	−2.66332e9	+	4.21829e8i	−0.153390	+	0.0242946i
$364$	−3.11167e10	−	4.28285e10i	−1.77251	−	2.43965i
$365$	−6.82899e9	+	1.70767e10i	−0.384756	+	0.962127i
$366$	3.98464e8	+	2.89501e8i	0.0222057	+	0.0161334i
$367$	−2.12311e9	+	4.16684e9i	−0.117033	+	0.229690i	−0.942091	−	0.335358i	$-0.891143\pi$
$367$	−2.12311e9	+	4.16684e9i	−0.117033	+	0.229690i	0.825058	+	0.565049i	$0.191143\pi$
$368$	−8.30448e9	+	8.30448e9i	−0.452816	+	0.452816i
$369$	1.10360e10	−	3.58582e9i	0.595260	−	0.193412i
$370$	−1.72585e7	+	7.59846e7i	−0.000920864	+	0.00405433i
$371$	−6.96096e9	+	2.14236e10i	−0.367429	+	1.13083i
$372$	−3.42388e9	+	1.74456e9i	−0.178792	+	0.0910989i
$373$	4.62611e9	−	2.92081e10i	0.238990	−	1.50893i	−0.517932	−	0.855422i	$-0.673298\pi$
$373$	4.62611e9	−	2.92081e10i	0.238990	−	1.50893i	0.756923	−	0.653504i	$-0.226702\pi$
$374$			1.26870e9i			0.0648446i
$375$	−2.18368e9	+	1.08400e10i	−0.110424	+	0.548156i
$376$	1.67514e9			0.0838106
$377$	−6.47613e8	−	1.02572e8i	−0.0320590	−	0.00507765i
$378$	7.89027e8	+	1.54855e9i	0.0386478	+	0.0758506i
$379$	−1.75524e9	−	5.70312e8i	−0.0850706	−	0.0276411i	0.266172	−	0.963925i	$-0.414241\pi$
$379$	−1.75524e9	−	5.70312e8i	−0.0850706	−	0.0276411i	−0.351243	+	0.936284i	$0.614241\pi$
$380$	−9.68059e9	−	2.19876e9i	−0.464267	−	0.105449i
$381$	3.85492e8	+	1.18642e9i	0.0182943	+	0.0563041i
$382$	2.12326e8	+	2.12326e8i	0.00997126	+	0.00997126i
$383$	2.05815e10	+	1.04868e10i	0.956492	+	0.487357i	0.861297	−	0.508101i	$-0.169653\pi$
$383$	2.05815e10	+	1.04868e10i	0.956492	+	0.487357i	0.0951951	+	0.995459i	$0.469653\pi$
$384$	1.36396e9	−	1.87733e9i	0.0627302	−	0.0863408i
$385$	4.33535e10	+	1.73371e10i	1.97325	+	0.789104i
$386$	2.03674e8	−	1.47978e8i	0.00917458	−	0.00666572i
$387$	4.61542e8	+	2.91406e9i	0.0205763	+	0.129914i
$388$	2.22982e10	−	3.53169e9i	0.983882	−	0.155832i
$389$	−3.02330e9	−	4.16122e9i	−0.132033	−	0.181728i	0.737882	−	0.674930i	$-0.235826\pi$
$389$	−3.02330e9	−	4.16122e9i	−0.132033	−	0.181728i	−0.869915	+	0.493202i	$0.835826\pi$
$390$	−2.44890e8	−	9.67551e8i	−0.0105855	−	0.0418230i
$391$	−1.45748e10	−	1.05892e10i	−0.623584	−	0.453060i
$392$	−2.60498e9	+	5.11255e9i	−0.110321	+	0.216518i
$393$	−1.53034e10	+	1.53034e10i	−0.641531	+	0.641531i
$394$	4.47410e8	−	1.45372e8i	0.0185661	−	0.00603249i
$395$	1.92415e9	+	1.14687e9i	0.0790406	+	0.0471112i
$396$	5.89046e9	−	1.81290e10i	0.239535	−	0.737212i
$397$	−2.54338e9	+	1.29592e9i	−0.102388	+	0.0521694i	−0.504435	−	0.863450i	$-0.668299\pi$
$397$	−2.54338e9	+	1.29592e9i	−0.102388	+	0.0521694i	0.402046	+	0.915619i	$0.368299\pi$
$398$	3.24811e8	−	2.05078e9i	0.0129449	−	0.0817309i
$399$			1.27145e10i			0.501658i
$400$	1.20946e10	+	2.23621e10i	0.472446	+	0.873518i
$401$	2.17758e10			0.842164			0.421082	−	0.907023i	$-0.361650\pi$
$401$	2.17758e10			0.842164			0.421082	+	0.907023i	$0.361650\pi$
$402$	−7.85093e8	−	1.24346e8i	−0.0300619	−	0.00476134i
$403$	6.92451e9	+	1.35901e10i	0.262524	+	0.515232i
$404$	1.59335e10	+	5.17710e9i	0.598116	+	0.194340i
$405$	3.89810e8	+	4.28043e9i	0.0144888	+	0.159099i
$406$	1.52953e7	+	4.70739e7i	0.000562928	+	0.00173251i
$407$	−1.90005e9	−	1.90005e9i	−0.0692448	−	0.0692448i
$408$	1.58214e9	+	8.06142e8i	0.0570959	+	0.0290918i
$409$	5.66910e9	−	7.80285e9i	0.202591	−	0.278843i	−0.695617	−	0.718413i	$-0.744869\pi$
$409$	5.66910e9	−	7.80285e9i	0.202591	−	0.278843i	0.898209	+	0.439570i	$0.144869\pi$
$410$	6.58110e8	+	1.04492e9i	0.0232897	+	0.0369784i
$411$	−9.61651e8	+	6.98680e8i	−0.0337016	+	0.0244856i
$412$	1.40858e9	+	8.89342e9i	0.0488869	+	0.308660i
$413$	−9.17973e10	+	1.45393e10i	−3.15522	+	0.499738i
$414$	−3.67276e8	−	5.05512e8i	−0.0125023	−	0.0172080i
$415$	8.39980e9	+	6.99759e9i	0.283189	+	0.235915i
$416$	−5.59080e9	−	4.06196e9i	−0.186681	−	0.135632i
$417$	4.29845e9	−	8.43619e9i	0.142157	−	0.278999i
$418$	−5.58809e8	+	5.58809e8i	−0.0183045	+	0.0183045i
$419$	−5.06841e10	+	1.64683e10i	−1.64443	+	0.534308i	−0.977522	−	0.210833i	$-0.932382\pi$
$419$	−5.06841e10	+	1.64683e10i	−1.64443	+	0.534308i	−0.666908	+	0.745140i	$0.732382\pi$
$420$	2.45554e10	−	2.14992e10i	0.789132	−	0.690917i
$421$	1.23853e10	−	3.81180e10i	0.394256	−	1.21339i	−0.535284	−	0.844672i	$-0.679795\pi$
$421$	1.23853e10	−	3.81180e10i	0.394256	−	1.21339i	0.929540	−	0.368722i	$-0.120205\pi$
$422$	1.31253e9	−	6.68769e8i	0.0413867	−	0.0210876i
$423$	3.00932e9	−	1.90001e10i	0.0939956	−	0.593465i
$424$			1.95961e9i			0.0606327i
$425$	−3.09781e10	+	2.36905e10i	−0.949509	+	0.726136i
$426$	−7.97125e8			−0.0242040
$427$	6.31408e10	+	1.00005e10i	1.89932	+	0.300823i
$428$	9.20337e9	+	1.80626e10i	0.274266	+	0.538277i
$429$	3.27336e10	+	1.06358e10i	0.966418	+	0.314008i
$430$	−2.88583e8	+	1.23708e8i	−0.00844107	+	0.00361845i
$431$	5.28712e9	+	1.62721e10i	0.153218	+	0.471557i	0.997976	−	0.0635916i	$-0.0202555\pi$
$431$	5.28712e9	+	1.62721e10i	0.153218	+	0.471557i	−0.844758	+	0.535149i	$0.820256\pi$
$432$	−2.30756e10	−	2.30756e10i	−0.662550	−	0.662550i
$433$	5.20102e10	+	2.65005e10i	1.47958	+	0.753882i	0.992816	−	0.119654i	$-0.0381785\pi$
$433$	5.20102e10	+	2.65005e10i	1.47958	+	0.753882i	0.486760	+	0.873535i	$0.338178\pi$
$434$	6.76767e8	−	9.31490e8i	0.0190757	−	0.0262554i
$435$	2.67659e7	−	4.03347e8i	0.000747522	−	0.0112648i
$436$	−3.67044e10	+	2.66673e10i	−1.01572	+	0.737961i
$437$	−1.75548e9	−	1.10836e10i	−0.0481359	−	0.303918i
$438$	1.01080e9	−	1.60095e8i	0.0274643	−	0.00434992i
$439$	2.83185e10	+	3.89771e10i	0.762452	+	1.04943i	0.997006	+	0.0773226i	$0.0246371\pi$
$439$	2.83185e10	+	3.89771e10i	0.762452	+	1.04943i	−0.234554	+	0.972103i	$0.575363\pi$
$440$	4.05292e9	+	2.68949e8i	0.108133	+	0.00717562i
$441$	5.33090e10	+	3.87313e10i	1.40944	+	1.02402i
$442$	1.59803e9	−	3.13631e9i	0.0418693	−	0.0821731i
$443$	1.30872e10	−	1.30872e10i	0.339806	−	0.339806i	−0.516488	−	0.856294i	$-0.672761\pi$
$443$	1.30872e10	−	1.30872e10i	0.339806	−	0.339806i	0.856294	+	0.516488i	$0.172761\pi$
$444$	−1.78632e9	+	5.80411e8i	−0.0459650	+	0.0149349i
$445$	−2.34346e10	−	5.46680e10i	−0.597610	−	1.39410i
$446$	−6.16421e8	+	1.89715e9i	−0.0155789	+	0.0479471i
$447$	−2.08760e10	+	1.06369e10i	−0.522899	+	0.266430i
$448$	1.16839e10	−	7.37692e10i	0.290052	−	1.83131i
$449$		−	1.81641e10i		−	0.446918i	−0.974713	−	0.223459i	$-0.928265\pi$
$449$		−	1.81641e10i		−	0.446918i	0.974713	−	0.223459i	$-0.0717349\pi$
$450$	−1.27577e9	+	4.49443e8i	−0.0311117	+	0.0109604i
$451$	−4.25855e10			−1.02933
$452$	−3.47851e10	−	5.50942e9i	−0.833374	−	0.131993i
$453$	−3.73708e9	−	7.33444e9i	−0.0887442	−	0.174170i
$454$	−2.28712e9	−	7.43131e8i	−0.0538351	−	0.0174921i
$455$	−8.53349e10	−	9.74655e10i	−1.99105	−	2.27408i
$456$	3.41795e8	+	1.05194e9i	0.00790508	+	0.0243293i
$457$	−1.20935e10	−	1.20935e10i	−0.277261	−	0.277261i	0.554754	−	0.832015i	$-0.312812\pi$
$457$	−1.20935e10	−	1.20935e10i	−0.277261	−	0.277261i	−0.832015	+	0.554754i	$0.812812\pi$
$458$	−2.86415e9	−	1.45936e9i	−0.0650929	−	0.0331665i
$459$	2.94241e10	−	4.04989e10i	0.662908	−	0.912414i
$460$	−1.84373e10	+	2.21319e10i	−0.411781	+	0.494296i
$461$	−3.37163e10	+	2.44963e10i	−0.746511	+	0.542372i	−0.894743	−	0.446580i	$-0.852642\pi$
$461$	−3.37163e10	+	2.44963e10i	−0.746511	+	0.542372i	0.148232	+	0.988953i	$0.452642\pi$
$462$	−4.06442e8	−	2.56617e9i	−0.00892135	−	0.0563272i
$463$	5.07677e10	−	8.04081e9i	1.10475	−	0.174975i	0.422691	−	0.906274i	$-0.361085\pi$
$463$	5.07677e10	−	8.04081e9i	1.10475	−	0.174975i	0.682057	+	0.731299i	$0.261085\pi$
$464$	−5.46281e8	−	7.51892e8i	−0.0117854	−	0.0162212i
$465$	−7.95669e9	+	5.01127e9i	−0.170185	+	0.107185i
$466$	−1.04496e9	−	7.59209e8i	−0.0221593	−	0.0160997i
$467$	1.57174e9	−	3.08471e9i	0.0330456	−	0.0648556i	−0.873893	−	0.486118i	$-0.838413\pi$
$467$	1.57174e9	−	3.08471e9i	0.0330456	−	0.0648556i	0.906939	+	0.421262i	$0.138413\pi$
$468$	−3.73964e10	+	3.73964e10i	−0.779554	+	0.779554i
$469$	−9.81220e10	+	3.18818e10i	−2.02803	+	0.658948i
$470$	2.03877e9	−	1.85666e8i	0.0417807	−	0.00380489i
$471$	1.25839e10	−	3.87294e10i	0.255701	−	0.786967i
$472$	−7.20401e9	+	3.67063e9i	−0.145146	+	0.0739558i
$473$	1.69382e9	−	1.06943e10i	0.0338393	−	0.213653i
$474$		−	1.24646e8i		−	0.00246925i
$475$	−2.40792e10	−	3.20989e9i	−0.473006	−	0.0630544i
$476$	1.15105e11			2.24215
$477$	2.22268e10	+	3.52038e9i	0.429342	+	0.0680010i
$478$	−1.51872e9	−	2.98065e9i	−0.0290915	−	0.0570953i
$479$	9.33534e9	+	3.03324e9i	0.177332	+	0.0576188i	0.396337	−	0.918105i	$-0.370281\pi$
$479$	9.33534e9	+	3.03324e9i	0.177332	+	0.0576188i	−0.219005	+	0.975724i	$0.570281\pi$
$480$	2.18130e9	−	3.65967e9i	0.0410914	−	0.0689410i
$481$	2.30377e9	+	7.09028e9i	0.0430387	+	0.132460i
$482$	6.36533e8	+	6.36533e8i	0.0117932	+	0.0117932i
$483$	3.28724e10	+	1.67493e10i	0.604008	+	0.307757i
$484$	−8.93788e9	+	1.23019e10i	−0.162875	+	0.224178i
$485$	5.35560e10	−	1.35552e10i	0.967924	−	0.244985i
$486$	2.23714e9	−	1.62538e9i	0.0401004	−	0.0291346i
$487$	−2.46614e9	−	1.55706e10i	−0.0438431	−	0.276815i	0.956021	−	0.293298i	$-0.0947529\pi$
$487$	−2.46614e9	−	1.55706e10i	−0.0438431	−	0.276815i	−0.999864	+	0.0164836i	$0.994753\pi$
$488$	5.49280e9	−	8.69974e8i	0.0968533	−	0.0153401i
$489$	1.31035e10	+	1.80354e10i	0.229167	+	0.315422i
$490$	−2.60379e9	+	6.51108e9i	−0.0451671	+	0.112945i
$491$	−1.53184e10	−	1.11295e10i	−0.263565	−	0.191491i	0.448152	−	0.893957i	$-0.352082\pi$
$491$	−1.53184e10	−	1.11295e10i	−0.263565	−	0.191491i	−0.711717	+	0.702466i	$0.752082\pi$
$492$	−1.35139e10	+	2.65226e10i	−0.230633	+	0.452643i
$493$	1.00809e9	−	1.00809e9i	0.0170652	−	0.0170652i
$494$	2.08527e9	−	6.77546e8i	0.0350151	−	0.0113771i
$495$	1.03315e10	−	4.54868e10i	0.172084	−	0.757643i
$496$	−6.68076e9	+	2.05613e10i	−0.110382	+	0.339722i
$497$	−9.21863e10	+	4.69713e10i	−1.51092	+	0.769851i
$498$	9.51669e7	−	6.00860e8i	0.00154728	−	0.00976913i
$499$			9.07907e10i			1.46433i	0.681127	+	0.732165i	$0.261490\pi$
$499$			9.07907e10i			1.46433i	−0.681127	+	0.732165i	$0.738510\pi$
$500$	3.45167e10	+	5.19314e10i	0.552267	+	0.830903i
$501$	6.77788e9			0.107583
$502$	−4.13711e9	−	6.55253e8i	−0.0651451	−	0.0103180i
$503$	−3.70599e10	−	7.27341e10i	−0.578938	−	1.13623i	−0.975864	−	0.218379i	$-0.929923\pi$
$503$	−3.70599e10	−	7.27341e10i	−0.578938	−	1.13623i	0.396926	−	0.917851i	$-0.370077\pi$
$504$	7.60257e9	+	2.47022e9i	0.117825	+	0.0382837i
$505$	3.99782e10	+	9.08028e9i	0.614692	+	0.139616i
$506$	7.08617e8	+	2.18090e9i	0.0108096	+	0.0332685i
$507$	−4.13977e10	−	4.13977e10i	−0.626533	−	0.626533i
$508$	6.26796e9	+	3.19368e9i	0.0941177	+	0.0479554i
$509$	−4.62289e9	+	6.36286e9i	−0.0688719	+	0.0947940i	−0.842063	−	0.539379i	$-0.818659\pi$
$509$	−4.62289e9	+	6.36286e9i	−0.0688719	+	0.0947940i	0.773191	+	0.634173i	$0.218659\pi$
$510$	2.01494e9	+	8.05776e8i	0.0297838	+	0.0119106i
$511$	1.07464e11	−	7.80771e10i	1.57608	−	1.14509i
$512$	−2.55584e9	−	1.61369e10i	−0.0371923	−	0.234823i
$513$	3.07981e10	−	4.87793e9i	0.444686	−	0.0704314i
$514$	3.14706e9	+	4.33156e9i	0.0450872	+	0.0620571i
$515$	5.40636e9	+	2.13603e10i	0.0768556	+	0.303653i
$516$	−6.12301e9	−	4.44863e9i	−0.0863707	−	0.0627520i
$517$	−3.20508e10	+	6.29032e10i	−0.448618	+	0.880461i
$518$	3.97943e8	−	3.97943e8i	0.00552715	−	0.00552715i
$519$	9.99522e9	−	3.24765e9i	0.137760	−	0.0447609i
$520$	−9.68029e9	−	5.76982e9i	−0.132396	−	0.0789131i
$521$	−3.49755e10	+	1.07643e11i	−0.474693	+	1.46095i	0.371679	+	0.928361i	$0.378782\pi$
$521$	−3.49755e10	+	1.07643e11i	−0.474693	+	1.46095i	−0.846372	+	0.532593i	$0.821218\pi$
$522$	4.40580e7	−	2.24487e7i	0.000593394	−	0.000302349i
$523$	2.13725e10	−	1.34941e11i	0.285659	−	1.80358i	−0.260036	−	0.965599i	$-0.583735\pi$
$523$	2.13725e10	−	1.34941e11i	0.285659	−	1.80358i	0.545696	−	0.837983i	$-0.316265\pi$
$524$			1.22043e11i			1.61879i
$525$	5.50691e10	−	5.78423e10i	0.724888	−	0.761391i
$526$	8.57343e8			0.0111998
$527$	−3.27552e10	−	5.18791e9i	−0.424657	−	0.0672590i
$528$	2.21481e10	+	4.34681e10i	0.284971	+	0.559287i
$529$	4.35097e10	+	1.41372e10i	0.555602	+	0.180526i
$530$	2.17197e8	+	2.38500e9i	0.00275264	+	0.0302262i
$531$	2.86921e10	+	8.83052e10i	0.360898	+	1.11073i
$532$	5.06987e10	+	5.06987e10i	0.632922	+	0.632922i
$533$	1.05274e11	+	5.36396e10i	1.30440	+	0.664625i
$534$	−1.94541e9	+	2.67763e9i	−0.0239247	+	0.0329295i
$535$	2.64368e10	+	4.19754e10i	0.322697	+	0.512365i
$536$	−7.26108e9	+	5.27549e9i	−0.0879716	+	0.0639151i
$537$	6.29014e8	+	3.97144e9i	0.00756420	+	0.0477585i
$538$	5.07315e9	−	8.03507e8i	0.0605548	−	0.00959093i
$539$	−1.42140e11	−	1.95639e11i	−1.68408	−	2.31793i
$540$	−6.14978e10	−	5.12317e10i	−0.723243	−	0.602509i
$541$	1.88845e10	+	1.37204e10i	0.220453	+	0.160168i	0.692530	−	0.721389i	$-0.256496\pi$
$541$	1.88845e10	+	1.37204e10i	0.220453	+	0.160168i	−0.472078	+	0.881557i	$0.656496\pi$
$542$	−1.38168e8	+	2.71171e8i	−0.00160108	+	0.00314229i
$543$	−3.77510e10	+	3.77510e10i	−0.434240	+	0.434240i
$544$	1.42903e10	−	4.64320e9i	0.163172	−	0.0530178i
$545$	−8.35288e10	+	7.31329e10i	−0.946783	+	0.828947i
$546$	−2.22754e9	+	6.85568e9i	−0.0250643	+	0.0771400i
$547$	−1.03139e10	+	5.25520e9i	−0.115206	+	0.0587002i	−0.510644	−	0.859792i	$-0.670593\pi$
$547$	−1.03139e10	+	5.25520e9i	−0.115206	+	0.0587002i	0.395438	+	0.918493i	$0.370593\pi$
$548$	−1.04859e9	+	6.62051e9i	−0.0116274	+	0.0734124i
$549$		−	6.38646e10i		−	0.703025i
$550$	4.96251e9	−	1.21880e8i	0.0542314	−	0.00133193i
$551$	8.88040e8			0.00963443
$552$	3.16996e9	+	5.02072e8i	0.0341427	+	0.00540767i
$553$	−7.34487e9	−	1.44151e10i	−0.0785387	−	0.154141i
$554$	1.13011e9	+	3.67196e8i	0.0119973	+	0.00389815i
$555$	−4.22438e9	+	1.81087e9i	−0.0445237	+	0.0190860i
$556$	−1.64991e10	−	5.07789e10i	−0.172648	−	0.531355i
$557$	2.99509e10	+	2.99509e10i	0.311164	+	0.311164i	0.845360	−	0.534197i	$-0.179386\pi$
$557$	2.99509e10	+	2.99509e10i	0.311164	+	0.311164i	−0.534197	+	0.845360i	$0.679386\pi$
$558$	−1.02488e9	−	5.22200e8i	−0.0105714	−	0.00538642i
$559$	−1.76575e10	+	2.43035e10i	−0.180835	+	0.248898i
$560$	1.21581e10	−	1.83216e11i	0.123627	−	1.86300i
$561$	−6.05430e10	+	4.39871e10i	−0.611241	+	0.444092i
$562$	3.17109e8	+	2.00215e9i	0.00317880	+	0.0200702i
$563$	−7.32739e10	+	1.16054e10i	−0.729316	+	0.115512i	−0.510040	−	0.860151i	$-0.670369\pi$
$563$	−7.32739e10	+	1.16054e10i	−0.729316	+	0.115512i	−0.219276	+	0.975663i	$0.570369\pi$
$564$	2.90057e10	+	3.99230e10i	0.286660	+	0.394554i
$565$	−8.59926e10	−	5.70641e9i	−0.843853	−	0.0559976i
$566$	−3.43308e9	−	2.49428e9i	−0.0334517	−	0.0243041i
$567$	1.40933e10	−	2.76597e10i	0.136358	−	0.267618i
$568$	−6.36435e9	+	6.36435e9i	−0.0611450	+	0.0611450i
$569$	1.50731e11	−	4.89753e10i	1.43798	−	0.467227i	0.516711	−	0.856160i	$-0.327156\pi$
$569$	1.50731e11	−	4.89753e10i	1.43798	−	0.467227i	0.921266	+	0.388932i	$0.127156\pi$
$570$	5.32583e8	+	1.24240e9i	0.00504531	+	0.0117696i
$571$	4.26094e10	−	1.31138e11i	0.400831	−	1.23363i	−0.523496	−	0.852028i	$-0.675372\pi$
$571$	4.26094e10	−	1.31138e11i	0.400831	−	1.23363i	0.924327	−	0.381602i	$-0.124628\pi$
$572$	1.72934e11	−	8.81143e10i	1.61546	−	0.823118i
$573$	−2.77075e9	+	1.74938e10i	−0.0257027	+	0.162280i
$574$		−	8.91902e9i		−	0.0821618i
$575$	−4.00193e10	+	5.80262e10i	−0.366099	+	0.530827i
$576$	−7.46148e10			−0.677852
$577$	−1.23870e11	−	1.96191e10i	−1.11754	−	0.177001i	−0.429776	−	0.902935i	$-0.641408\pi$
$577$	−1.23870e11	−	1.96191e10i	−1.11754	−	0.177001i	−0.687764	+	0.725934i	$0.741408\pi$
$578$	1.04284e9	+	2.04668e9i	0.00934339	+	0.0183374i
$579$	1.41231e10	+	4.58887e9i	0.125665	+	0.0408311i
$580$	−1.50161e9	−	1.71506e9i	−0.0132692	−	0.0151554i
$581$	−2.44003e10	−	7.50964e10i	−0.214136	−	0.659044i
$582$	−2.17372e9	−	2.17372e9i	−0.0189458	−	0.0189458i
$583$	−7.35856e10	−	3.74937e10i	−0.636969	−	0.324552i
$584$	6.79215e9	−	9.34859e9i	0.0583923	−	0.0803701i
$585$	−8.28341e10	+	9.94327e10i	−0.707270	+	0.848996i
$586$	−1.57155e9	+	1.14180e9i	−0.0133272	+	0.00968275i
$587$	−1.63856e10	−	1.03455e11i	−0.138010	−	0.871362i	−0.955408	−	0.295288i	$-0.904584\pi$
$587$	−1.63856e10	−	1.03455e11i	−0.138010	−	0.871362i	0.817398	−	0.576073i	$-0.195416\pi$
$588$	−1.66952e11	+	2.64426e10i	−1.39663	+	0.221205i
$589$	−1.21422e10	−	1.67123e10i	−0.100887	−	0.138859i
$590$	−8.36098e9	+	5.26589e9i	−0.0690000	+	0.0434574i
$591$	2.24493e10	+	1.63104e10i	0.184015	+	0.133695i
$592$	−4.79740e9	+	9.41542e9i	−0.0390588	+	0.0766572i
$593$	4.32067e10	−	4.32067e10i	0.349408	−	0.349408i	−0.510481	−	0.859889i	$-0.670533\pi$
$593$	4.32067e10	−	4.32067e10i	0.349408	−	0.349408i	0.859889	+	0.510481i	$0.170533\pi$
$594$	−6.06005e9	+	1.96903e9i	−0.0486777	+	0.0158164i
$595$	2.80505e11	−	2.55450e10i	2.23807	−	0.203816i
$596$	−4.08283e10	+	1.25656e11i	−0.323576	+	0.995863i
$597$	1.09125e11	−	5.56021e10i	0.859069	−	0.437717i
$598$	9.95266e8	−	6.28386e9i	0.00778277	−	0.0491385i
$599$			1.04431e11i			0.811188i	0.914053	+	0.405594i	$0.132935\pi$
$599$			1.04431e11i			0.811188i	−0.914053	+	0.405594i	$0.867065\pi$
$600$	3.00122e9	−	6.26597e9i	0.0231576	−	0.0483485i
$601$	−1.66514e11			−1.27630			−0.638152	−	0.769910i	$-0.720301\pi$
$601$	−1.66514e11			−1.27630			−0.638152	+	0.769910i	$0.720301\pi$
$602$	2.23980e9	+	3.54750e8i	0.0170539	+	0.00270107i
$603$	4.67926e10	+	9.18356e10i	0.353922	+	0.694611i
$604$	−4.41473e10	−	1.43443e10i	−0.331708	−	0.107779i
$605$	−1.90511e10	+	3.19629e10i	−0.142200	+	0.238575i
$606$	−7.04946e8	−	2.16960e9i	−0.00522715	−	0.0160875i
$607$	9.19143e10	+	9.19143e10i	0.677062	+	0.677062i	0.959334	−	0.282273i	$-0.0910883\pi$
$607$	9.19143e10	+	9.19143e10i	0.677062	+	0.677062i	−0.282273	+	0.959334i	$0.591088\pi$
$608$	8.33939e9	+	4.24913e9i	0.0610267	+	0.0310947i
$609$	−1.71609e9	+	2.36199e9i	−0.0124758	+	0.0171715i
$610$	6.58872e9	−	1.66762e9i	0.0475863	−	0.0120442i
$611$	1.58463e11	−	1.15130e11i	1.13700	−	0.826082i
$612$	−1.79885e10	−	1.13575e11i	−0.128230	−	0.809612i
$613$	−3.24131e10	+	5.13373e9i	−0.229551	+	0.0363573i	−0.270150	−	0.962818i	$-0.587073\pi$
$613$	−3.24131e10	+	5.13373e9i	−0.229551	+	0.0363573i	0.0405993	+	0.999176i	$0.487073\pi$
$614$	−6.94409e8	−	9.55772e8i	−0.00488587	−	0.00672482i
$615$	−2.70468e10	+	6.76335e10i	−0.189067	+	0.472783i
$616$	−2.37338e10	−	1.72436e10i	−0.164833	−	0.119758i
$617$	9.29509e10	−	1.82426e11i	0.641376	−	1.25877i	−0.309999	−	0.950737i	$-0.600329\pi$
$617$	9.29509e10	−	1.82426e11i	0.641376	−	1.25877i	0.951375	−	0.308035i	$-0.0996713\pi$
$618$	8.66968e8	−	8.66968e8i	0.00594360	−	0.00594360i
$619$	−1.37225e11	+	4.45871e10i	−0.934696	+	0.303701i	−0.736482	−	0.676457i	$-0.763514\pi$
$619$	−1.37225e11	+	4.45871e10i	−0.934696	+	0.303701i	−0.198215	+	0.980159i	$0.563514\pi$
$620$	−1.17448e10	+	5.17093e10i	−0.0794837	+	0.349946i
$621$	2.79599e10	−	8.60518e10i	0.188005	−	0.578620i
$622$	−7.61095e8	+	3.87797e8i	−0.00508484	+	0.00259086i
$623$	−6.72023e10	+	4.24298e11i	−0.446100	+	2.81656i
$624$		−	1.35353e11i		−	0.892748i
$625$	9.56408e10	+	1.18894e11i	0.626792	+	0.779187i
$626$	1.33646e10			0.0870282
$627$	−4.60410e10	−	7.29217e9i	−0.297903	−	0.0471831i
$628$	−1.04254e11	−	2.04610e11i	−0.670276	−	1.31549i
$629$	−1.54164e10	−	5.00908e9i	−0.0984871	−	0.0320004i
$630$	9.52668e9	+	2.16380e9i	0.0604755	+	0.0137359i
$631$	−3.00662e10	−	9.25344e10i	−0.189654	−	0.583695i	0.810344	−	0.585955i	$-0.199280\pi$
$631$	−3.00662e10	−	9.25344e10i	−0.189654	−	0.583695i	−0.999997	+	0.00226040i	$0.999280\pi$
$632$	−9.95190e8	−	9.95190e8i	−0.00623789	−	0.00623789i
$633$	7.74206e10	+	3.94477e10i	0.482216	+	0.245701i
$634$	−6.24928e9	+	8.60140e9i	−0.0386788	+	0.0532368i
$635$	1.59835e10	+	6.39183e9i	0.0983054	+	0.0393125i
$636$	−4.67028e10	+	3.39316e10i	−0.285440	+	0.207384i
$637$	1.04956e11	+	6.62668e11i	0.637457	+	4.02474i
$638$	−1.79233e8	+	2.83878e7i	−0.00108177	+	0.000171336i
$639$	6.07539e10	+	8.36205e10i	0.364393	+	0.501545i
$640$	−7.85689e9	−	3.10422e10i	−0.0468307	−	0.185026i
$641$	−2.03157e11	−	1.47602e11i	−1.20337	−	0.874300i	−0.208758	−	0.977967i	$-0.566942\pi$
$641$	−2.03157e11	−	1.47602e11i	−1.20337	−	0.874300i	−0.994612	+	0.103668i	$0.966942\pi$
$642$	1.25319e9	−	2.45952e9i	0.00737693	−	0.0144780i
$643$	5.30187e10	−	5.30187e10i	0.310159	−	0.310159i	−0.534812	−	0.844971i	$-0.679618\pi$
$643$	5.30187e10	−	5.30187e10i	0.310159	−	0.310159i	0.844971	+	0.534812i	$0.179618\pi$
$644$	1.97865e11	−	6.42901e10i	1.15034	−	0.373767i
$645$	−1.59088e10	−	9.48225e9i	−0.0919176	−	0.0547864i
$646$	−1.47318e9	+	4.53400e9i	−0.00845916	+	0.0260346i
$647$	4.84943e10	−	2.47091e10i	0.276741	−	0.141007i	−0.310112	−	0.950700i	$-0.600367\pi$
$647$	4.84943e10	−	2.47091e10i	0.276741	−	0.141007i	0.586853	+	0.809693i	$0.300367\pi$
$648$	4.22458e8	−	2.66729e9i	0.00239598	−	0.0151276i
$649$		−	3.40749e11i		−	1.92068i
$650$	−1.24211e10	−	5.94937e9i	−0.0695838	−	0.0333286i
$651$	6.79151e10			0.378131
$652$	1.24165e11	+	1.96659e10i	0.687085	+	0.108824i
$653$	7.24440e10	+	1.42179e11i	0.398428	+	0.781958i	0.999856	−	0.0169684i	$-0.00540147\pi$
$653$	7.24440e10	+	1.42179e11i	0.398428	+	0.781958i	−0.601428	+	0.798927i	$0.705401\pi$
$654$	5.87538e9	+	1.90903e9i	0.0321163	+	0.0104352i
$655$	2.70850e10	+	2.97415e11i	0.147151	+	1.61584i
$656$	5.17515e10	+	1.59275e11i	0.279452	+	0.860066i
$657$	−9.38339e10	−	9.38339e10i	−0.503614	−	0.503614i
$658$	−1.31743e10	−	6.71266e9i	−0.0702789	−	0.0358089i
$659$	1.42534e11	−	1.96182e11i	0.755749	−	1.04020i	−0.241807	−	0.970324i	$-0.577740\pi$
$659$	1.42534e11	−	1.96182e11i	0.755749	−	1.04020i	0.997556	−	0.0698749i	$-0.0222600\pi$
$660$	6.37683e10	+	1.01249e11i	0.336070	+	0.533598i
$661$	−4.54468e9	+	3.30190e9i	−0.0238066	+	0.0172965i	−0.599625	−	0.800281i	$-0.704684\pi$
$661$	−4.54468e9	+	3.30190e9i	−0.0238066	+	0.0172965i	0.575818	+	0.817578i	$0.304684\pi$
$662$	−1.54310e8	−	9.74274e8i	−0.000803456	−	0.00507282i
$663$	2.05071e11	−	3.24800e10i	1.06133	−	0.168098i
$664$	−4.03752e9	−	5.55717e9i	−0.0207703	−	0.0285879i
$665$	1.34802e11	+	1.12299e11i	0.689302	+	0.574235i
$666$	−4.54845e8	−	3.30464e8i	−0.00231188	−	0.00167968i
$667$	1.16985e9	−	2.29596e9i	0.00591053	−	0.0116001i
$668$	2.70266e10	−	2.70266e10i	0.135733	−	0.135733i
$669$	−1.11904e11	+	3.63599e10i	−0.558654	+	0.181518i
$670$	−8.25256e9	+	7.22545e9i	−0.0409534	+	0.0358563i
$671$	−7.24265e10	+	2.22906e11i	−0.357279	+	1.09959i
$672$	−2.74171e10	+	1.39697e10i	−0.134445	+	0.0685031i
$673$	2.81262e10	−	1.77582e11i	0.137104	−	0.865642i	−0.819251	−	0.573435i	$-0.805611\pi$
$673$	2.81262e10	−	1.77582e11i	0.137104	−	0.865642i	0.956355	−	0.292207i	$-0.0943895\pi$
$674$			7.96455e9i			0.0385941i
$675$	−1.61237e11	−	1.11201e11i	−0.776694	−	0.535667i
$676$	−3.30143e11			−1.58094
$677$	1.81143e11	+	2.86902e10i	0.862316	+	0.136577i	0.571900	−	0.820323i	$-0.306206\pi$
$677$	1.81143e11	+	2.86902e10i	0.862316	+	0.136577i	0.290416	+	0.956901i	$0.406206\pi$
$678$	2.17716e9	+	4.27291e9i	0.0103032	+	0.0202211i
$679$	−3.79476e11	−	1.23299e11i	−1.78528	−	0.580072i
$680$	2.25209e10	−	9.65409e9i	0.105330	−	0.0451519i
$681$	−4.38340e10	−	1.34907e11i	−0.203809	−	0.627259i
$682$	2.98490e9	+	2.98490e9i	0.0137973	+	0.0137973i
$683$	−2.73082e11	−	1.39142e11i	−1.25490	−	0.639405i	−0.305119	−	0.952314i	$-0.598696\pi$
$683$	−2.73082e11	−	1.39142e11i	−1.25490	−	0.639405i	−0.949783	+	0.312909i	$0.898696\pi$
$684$	4.21017e10	−	5.79481e10i	0.192343	−	0.264737i
$685$	−1.08608e9	+	1.63666e10i	−0.00493286	+	0.0743355i
$686$	2.48088e10	−	1.80247e10i	0.112024	−	0.0813899i
$687$	−2.96615e10	−	1.87275e11i	−0.133158	−	0.840724i
$688$	−4.20565e10	+	6.66110e9i	−0.187707	+	0.0297298i
$689$	1.34682e11	+	1.85373e11i	0.597628	+	0.822565i
$690$	3.91372e9	+	2.59712e8i	0.0172661	+	0.00114577i
$691$	−1.02032e10	−	7.41309e9i	−0.0447534	−	0.0325152i	0.565184	−	0.824965i	$-0.308805\pi$
$691$	−1.02032e10	−	7.41309e9i	−0.0447534	−	0.0325152i	−0.609937	+	0.792450i	$0.708805\pi$
$692$	2.69057e10	−	5.28055e10i	0.117333	−	0.230279i
$693$	−2.38221e11	+	2.38221e11i	−1.03287	+	1.03287i
$694$	−1.61258e10	+	5.23959e9i	−0.0695158	+	0.0225870i
$695$	−5.14769e10	−	1.20085e11i	−0.220634	−	0.514692i
$696$	−7.84849e7	+	2.41552e8i	−0.000334464	+	0.00102937i
$697$	−2.28896e11	+	1.16628e11i	−0.969856	+	0.494166i
$698$	9.43924e8	−	5.95970e9i	0.00397663	−	0.0251075i
$699$		−	7.61884e10i		−	0.319139i
$700$	−1.10577e10	−	4.50230e11i	−0.0460547	−	1.87518i
$701$	4.31403e11			1.78653			0.893266	−	0.449528i	$-0.148408\pi$
$701$	4.31403e11			1.78653			0.893266	+	0.449528i	$0.148408\pi$
$702$	1.74609e10	+	2.76554e9i	0.0718984	+	0.0113876i
$703$	−4.58396e9	−	8.99653e9i	−0.0187681	−	0.0368344i
$704$	2.60427e11	+	8.46179e10i	1.06022	+	0.344486i
$705$	7.95458e10	+	9.08534e10i	0.322004	+	0.367777i
$706$	3.67540e9	+	1.13117e10i	0.0147940	+	0.0455313i
$707$	−2.09372e11	−	2.09372e11i	−0.837992	−	0.837992i
$708$	−2.12222e11	−	1.08132e11i	−0.844610	−	0.430350i
$709$	−7.43393e10	+	1.02319e11i	−0.294194	+	0.404923i	−0.930371	−	0.366620i	$-0.880515\pi$
$709$	−7.43393e10	+	1.02319e11i	−0.294194	+	0.404923i	0.636177	+	0.771543i	$0.280515\pi$
$710$	−7.04049e9	+	8.45129e9i	−0.0277057	+	0.0332575i
$711$	−1.30757e10	+	9.50004e9i	−0.0511666	+	0.0371747i
$712$	5.84612e9	+	3.69109e10i	0.0227482	+	0.143627i
$713$	−5.92037e10	+	9.37695e9i	−0.229082	+	0.0362830i
$714$	−9.21257e9	−	1.26800e10i	−0.0354477	−	0.0487896i
$715$	4.01878e11	−	2.53110e11i	1.53769	−	0.968467i
$716$	1.83441e10	+	1.33278e10i	0.0697983	+	0.0507115i
$717$	8.95825e10	−	1.75816e11i	0.338959	−	0.665244i
$718$	−1.53379e10	+	1.53379e10i	−0.0577121	+	0.0577121i
$719$	−1.11534e11	+	3.62397e10i	−0.417343	+	0.135603i	−0.510159	−	0.860080i	$-0.670413\pi$
$719$	−1.11534e11	+	3.62397e10i	−0.417343	+	0.135603i	0.0928155	+	0.995683i	$0.470413\pi$
$720$	−1.82681e11	+	1.66364e10i	−0.679774	+	0.0619056i
$721$	4.91767e10	−	1.51350e11i	0.181978	−	0.560070i
$722$	8.97368e9	−	4.57232e9i	0.0330234	−	0.0168263i
$723$	−8.30642e9	+	5.24447e10i	−0.0303991	+	0.191932i
$724$			3.01062e11i			1.09572i
$725$	−4.03997e9	−	3.84628e9i	−0.0146226	−	0.0139216i
$726$	2.07055e9			0.00745313
$727$	−2.68261e11	−	4.24883e10i	−0.960328	−	0.152101i	−0.343460	−	0.939167i	$-0.611599\pi$
$727$	−2.68261e11	−	4.24883e10i	−0.960328	−	0.152101i	−0.616868	+	0.787066i	$0.711599\pi$
$728$	3.69516e10	+	7.25216e10i	0.131555	+	0.258192i
$729$	1.12215e11	+	3.64610e10i	0.397322	+	0.129098i
$730$	7.23038e9	−	1.21307e10i	0.0254607	−	0.0427165i
$731$	−2.01842e10	−	6.21207e10i	−0.0706875	−	0.217554i
$732$	1.15844e11	+	1.15844e11i	0.403487	+	0.403487i
$733$	−7.08611e9	−	3.61055e9i	−0.0245466	−	0.0125071i	0.441674	−	0.897176i	$-0.354385\pi$
$733$	−7.08611e9	−	3.61055e9i	−0.0245466	−	0.0125071i	−0.466221	+	0.884668i	$0.654385\pi$
$734$	2.11070e9	−	2.90512e9i	0.00727179	−	0.0100088i
$735$	−4.00987e11	+	1.01491e11i	−1.37398	+	0.347759i
$736$	2.19716e10	−	1.59633e10i	0.0748773	−	0.0544015i
$737$	−5.91722e10	−	3.73598e11i	−0.200562	−	1.26630i
$738$	−8.80049e9	+	1.39386e9i	−0.0296675	+	0.00469888i
$739$	1.09724e11	+	1.51022e11i	0.367894	+	0.506363i	0.952327	−	0.305079i	$-0.0986829\pi$
$739$	1.09724e11	+	1.51022e11i	0.367894	+	0.506363i	−0.584433	+	0.811442i	$0.698683\pi$
$740$	−9.62377e9	+	2.40653e10i	−0.0320936	+	0.0802537i
$741$	1.04631e11	+	7.60188e10i	0.347046	+	0.252144i
$742$	7.85262e9	−	1.54116e10i	0.0259059	−	0.0508432i
$743$	4.17140e11	−	4.17140e11i	1.36876	−	1.36876i	0.506543	−	0.862215i	$-0.330923\pi$
$743$	4.17140e11	−	4.17140e11i	1.36876	−	1.36876i	0.862215	−	0.506543i	$-0.169077\pi$
$744$	5.61896e9	−	1.82571e9i	0.0183385	−	0.00595855i
$745$	−7.16100e10	+	3.15280e11i	−0.232460	+	1.02346i
$746$	−7.01692e9	+	2.15959e10i	−0.0226564	+	0.0697293i
$747$	−7.02851e10	+	3.58120e10i	−0.225726	+	0.115013i
$748$	−6.60162e10	+	4.16810e11i	−0.210884	+	1.33147i
$749$		−	3.58285e11i		−	1.13842i
$750$	2.95821e9	−	7.95879e9i	0.00934940	−	0.0251537i
$751$	−1.57729e10			−0.0495852			−0.0247926	−	0.999693i	$-0.507893\pi$
$751$	−1.57729e10			−0.0495852			−0.0247926	+	0.999693i	$0.507893\pi$
$752$	2.74215e11	+	4.34314e10i	0.857471	+	0.135810i
$753$	−1.12168e11	−	2.20142e11i	−0.348891	−	0.684737i
$754$	4.78832e8	+	1.55582e8i	0.00148149	+	0.000481364i
$755$	−1.10769e11	−	2.51590e10i	−0.340901	−	0.0774293i
$756$	1.78643e11	+	5.49806e11i	0.546887	+	1.68315i
$757$	1.39141e11	+	1.39141e11i	0.423714	+	0.423714i	0.886480	−	0.462766i	$-0.153143\pi$
$757$	1.39141e11	+	1.39141e11i	0.423714	+	0.423714i	−0.462766	+	0.886480i	$0.653143\pi$
$758$	1.26268e9	+	6.43365e8i	0.00382485	+	0.00194886i
$759$	−7.95048e10	+	1.09429e11i	−0.239567	+	0.329735i
$760$	1.41717e10	+	5.66729e9i	0.0424784	+	0.0169872i
$761$	−4.35342e10	+	3.16295e10i	−0.129805	+	0.0943090i	−0.650793	−	0.759255i	$-0.725564\pi$
$761$	−4.35342e10	+	3.16295e10i	−0.129805	+	0.0943090i	0.520988	+	0.853564i	$0.325564\pi$
$762$	−1.49847e8	−	9.46094e8i	−0.000444454	−	0.00280617i
$763$	7.91970e11	−	1.25436e11i	2.33674	−	0.370103i
$764$	5.87077e10	+	8.08042e10i	0.172314	+	0.237170i
$765$	−6.90428e10	−	2.72785e11i	−0.201592	−	0.796481i
$766$	−1.43494e10	−	1.04255e10i	−0.0416792	−	0.0302817i
$767$	−4.29200e11	+	8.42352e11i	−1.24016	+	2.43395i
$768$	1.34396e11	−	1.34396e11i	0.386316	−	0.386316i
$769$	1.39762e11	−	4.54114e10i	0.399653	−	0.129855i	−0.102292	−	0.994754i	$-0.532618\pi$
$769$	1.39762e11	−	4.54114e10i	0.399653	−	0.129855i	0.501946	+	0.864899i	$0.332618\pi$
$770$	−3.07970e10	−	1.83562e10i	−0.0876083	−	0.0522178i
$771$	−9.75921e10	+	3.00358e11i	−0.276183	+	0.850005i
$772$	7.46133e10	−	3.80174e10i	0.210062	−	0.107032i
$773$	−4.03193e10	+	2.54566e11i	−0.112926	+	0.712988i	0.864645	+	0.502383i	$0.167543\pi$
$773$	−4.03193e10	+	2.54566e11i	−0.112926	+	0.712988i	−0.977571	+	0.210605i	$0.932457\pi$
$774$		−	2.26548e9i		−	0.00631242i
$775$	−1.71457e10	+	1.28620e11i	−0.0475280	+	0.356534i
$776$	−3.47106e10			−0.0957227
$777$	3.27870e10	+	5.19295e9i	0.0899533	+	0.0142472i
$778$	1.79304e9	+	3.51904e9i	0.00489409	+	0.00960520i
$779$	−1.52189e11	−	4.94491e10i	−0.413268	−	0.134279i
$780$	−3.01083e10	−	3.30614e11i	−0.0813408	−	0.893188i
$781$	−1.17218e11	−	3.60759e11i	−0.315057	−	0.969645i
$782$	9.78160e9	+	9.78160e9i	0.0261567	+	0.0261567i
$783$	6.37977e9	+	3.25065e9i	0.0169730	+	0.00864816i
$784$	−5.58980e11	+	7.69370e11i	−1.47956	+	2.03644i
$785$	−2.99471e11	−	4.75489e11i	−0.788636	−	1.25217i
$786$	1.34444e10	−	9.76793e9i	0.0352250	−	0.0255925i
$787$	−6.33391e10	−	3.99907e11i	−0.165110	−	1.04246i	−0.921510	−	0.388354i	$-0.873044\pi$
$787$	−6.33391e10	−	3.99907e11i	−0.165110	−	1.04246i	0.756401	−	0.654109i	$-0.226956\pi$
$788$	1.54553e11	−	2.44788e10i	0.400841	−	0.0634869i
$789$	2.97248e10	+	4.09127e10i	0.0767028	+	0.105572i
$790$	−1.32152e9	−	1.10092e9i	−0.00339286	−	0.00282648i
$791$	5.03570e11	+	3.65865e11i	1.28633	+	0.934576i
$792$	−1.33053e10	+	2.61132e10i	−0.0338162	+	0.0663680i
$793$	4.59809e11	−	4.59809e11i	1.16275	−	1.16275i
$794$	2.08458e9	−	6.77320e8i	0.00524488	−	0.00170417i
$795$	−1.06282e11	+	9.30545e10i	−0.266068	+	0.232953i
$796$	2.13422e11	−	6.56844e11i	0.531602	−	1.63610i
$797$	−4.38133e11	+	2.23240e11i	−1.08586	+	0.553272i	−0.902901	−	0.429848i	$-0.858567\pi$
$797$	−4.38133e11	+	2.23240e11i	−1.08586	+	0.553272i	−0.182957	+	0.983121i	$0.558567\pi$
$798$	1.52726e9	−	9.64274e9i	0.00376618	−	0.0237787i
$799$			4.25880e11i			1.04496i
$800$	−1.95346e10	−	5.54502e10i	−0.0476919	−	0.135376i
$801$	4.29162e11			1.04254
$802$	−1.65149e10	−	2.61570e9i	−0.0399188	−	0.00632252i
$803$	2.21094e11	+	4.33921e11i	0.531758	+	1.04363i
$804$	−2.51458e11	−	8.17036e10i	−0.601784	−	0.195532i
$805$	4.67920e11	−	2.00584e11i	1.11426	−	0.477654i
$806$	−3.61914e9	−	1.11386e10i	−0.00857561	−	0.0263930i
$807$	2.14234e11	+	2.14234e11i	0.505120	+	0.505120i
$808$	−2.29508e10	−	1.16940e10i	−0.0538458	−	0.0274358i
$809$	−2.62954e11	+	3.61925e11i	−0.613883	+	0.844938i	−0.996890	−	0.0788078i	$-0.974889\pi$
$809$	−2.62954e11	+	3.61925e11i	−0.613883	+	0.844938i	0.383007	+	0.923746i	$0.374889\pi$
$810$	2.18529e8	−	3.29312e9i	0.000507656	−	0.00765010i
$811$	−4.87771e11	+	3.54387e11i	−1.12754	+	0.819207i	−0.985335	−	0.170630i	$-0.945420\pi$
$811$	−4.87771e11	+	3.54387e11i	−1.12754	+	0.819207i	−0.142207	+	0.989837i	$0.545420\pi$
$812$	2.57552e9	+	1.62612e10i	0.00592434	+	0.0374048i
$813$	−1.77308e10	+	2.80828e9i	−0.0405850	+	0.00642804i
$814$	1.21277e9	+	1.66924e9i	0.00276237	+	0.00380207i
$815$	3.06950e11	+	2.03690e10i	0.695725	+	0.0461679i
$816$	2.38091e11	+	1.72983e11i	0.537010	+	0.390161i
$817$	1.84712e10	−	3.62518e10i	0.0414578	−	0.0813656i
$818$	−5.23674e9	+	5.23674e9i	−0.0116963	+	0.0116963i
$819$	8.88954e11	−	2.88839e11i	1.97580	−	0.641977i
$820$	1.61838e11	+	3.77534e11i	0.357953	+	0.835028i
$821$	2.02705e11	−	6.23861e11i	0.446160	−	1.37314i	−0.435046	−	0.900408i	$-0.643268\pi$
$821$	2.02705e11	−	6.23861e11i	0.446160	−	1.37314i	0.881206	−	0.472732i	$-0.156732\pi$
$822$	8.13245e8	−	4.14369e8i	0.00178129	−	0.000907612i
$823$	5.75207e10	−	3.63172e11i	0.125379	−	0.791612i	−0.842222	−	0.539130i	$-0.818753\pi$
$823$	5.75207e10	−	3.63172e11i	0.125379	−	0.791612i	0.967602	−	0.252482i	$-0.0812469\pi$
$824$		−	1.38440e10i		−	0.0300298i
$825$	1.77871e11	+	2.32587e11i	0.383962	+	0.502076i
$826$	7.13659e10			0.153310
$827$	−5.60073e11	−	8.87068e10i	−1.19735	−	0.189642i	−0.474255	−	0.880387i	$-0.657283\pi$
$827$	−5.60073e11	−	8.87068e10i	−1.19735	−	0.189642i	−0.723098	+	0.690745i	$0.757283\pi$
$828$	−9.43579e10	−	1.85188e11i	−0.200751	−	0.393995i
$829$	−7.10273e11	−	2.30782e11i	−1.50386	−	0.488634i	−0.562719	−	0.826648i	$-0.690245\pi$
$829$	−7.10273e11	−	2.30782e11i	−1.50386	−	0.488634i	−0.941141	+	0.338015i	$0.890245\pi$
$830$	−5.52990e9	−	6.31599e9i	−0.0116521	−	0.0133085i
$831$	2.16593e10	+	6.66604e10i	0.0454192	+	0.139786i
$832$	−5.37208e11	−	5.37208e11i	−1.12111	−	1.12111i
$833$	−1.29980e12	−	6.62279e11i	−2.69957	−	1.37550i
$834$	−4.27332e9	+	5.88172e9i	−0.00883285	+	0.0121574i
$835$	5.98646e10	−	7.18605e10i	0.123147	−	0.147824i
$836$	−2.12664e11	+	1.54509e11i	−0.435380	+	0.316322i
$837$	−2.60557e10	−	1.64509e11i	−0.0530885	−	0.335188i
$838$	4.04172e10	−	6.40145e9i	0.0819577	−	0.0129808i
$839$	6.23194e10	+	8.57754e10i	0.125770	+	0.173107i	0.867258	−	0.497858i	$-0.165880\pi$
$839$	6.23194e10	+	8.57754e10i	0.125770	+	0.173107i	−0.741489	+	0.670965i	$0.765880\pi$
$840$	−4.24597e10	+	2.67419e10i	−0.0852825	+	0.0537124i
$841$	−4.04543e11	−	2.93918e11i	−0.808687	−	0.587546i
$842$	−1.39718e10	+	2.74212e10i	−0.0277974	+	0.0545554i
$843$	−8.45488e10	+	8.45488e10i	−0.167416	+	0.167416i
$844$	4.66008e11	−	1.51415e11i	0.918383	−	0.298401i
$845$	−8.04546e11	+	7.32683e10i	−1.57806	+	0.143711i
$846$	−4.56457e9	+	1.40483e10i	−0.00891083	+	0.0274247i
$847$	2.39456e11	−	1.22009e11i	0.465255	−	0.237059i
$848$	−5.08070e10	+	3.20783e11i	−0.0982517	+	0.620337i
$849$		−	2.50307e11i		−	0.481772i
$850$	2.63396e10	−	1.42459e10i	0.0504584	−	0.0272906i
$851$	−2.92984e10			−0.0558632
$852$	−2.61881e11	−	4.14779e10i	−0.496988	−	0.0787151i
$853$	1.00769e11	+	1.97771e11i	0.190341	+	0.373565i	0.966379	−	0.257121i	$-0.0827738\pi$
$853$	1.00769e11	+	1.97771e11i	0.190341	+	0.373565i	−0.776038	+	0.630686i	$0.782774\pi$
$854$	−4.66850e10	−	1.51689e10i	−0.0877700	−	0.0285182i
$855$	8.97398e10	−	1.50561e11i	0.167927	−	0.281739i
$856$	−9.63151e9	−	2.96427e10i	−0.0179390	−	0.0552107i
$857$	−1.19064e11	−	1.19064e11i	−0.220728	−	0.220728i	0.588077	−	0.808805i	$-0.299885\pi$
$857$	−1.19064e11	−	1.19064e11i	−0.220728	−	0.220728i	−0.808805	+	0.588077i	$0.799885\pi$
$858$	−2.35478e10	−	1.19982e10i	−0.0434511	−	0.0221394i
$859$	−1.86315e11	+	2.56441e11i	−0.342196	+	0.470993i	−0.945081	−	0.326835i	$-0.894018\pi$
$859$	−1.86315e11	+	2.56441e11i	−0.342196	+	0.470993i	0.602885	+	0.797828i	$0.294018\pi$
$860$	−1.01246e11	+	2.56256e10i	−0.185090	+	0.0468469i
$861$	4.25619e11	−	3.09230e11i	0.774476	−	0.562690i
$862$	−2.05518e9	−	1.29759e10i	−0.00372239	−	0.0235022i
$863$	2.20629e11	−	3.49442e10i	0.397758	−	0.0629987i	0.0456487	−	0.998958i	$-0.485465\pi$
$863$	2.20629e11	−	3.49442e10i	0.397758	−	0.0629987i	0.352109	+	0.935959i	$0.385465\pi$
$864$	4.43571e10	+	6.10523e10i	0.0795991	+	0.109559i
$865$	5.38491e10	−	1.34656e11i	0.0961864	−	0.240525i
$866$	−3.62616e10	−	2.63456e10i	−0.0644726	−	0.0468421i
$867$	−6.15123e10	+	1.20725e11i	−0.108864	+	0.213658i
$868$	2.70809e11	−	2.70809e11i	0.477072	−	0.477072i
$869$	5.64116e10	−	1.83292e10i	0.0989212	−	0.0321414i
$870$	−6.87492e7	+	3.02685e8i	−0.000120003	+	0.000528341i
$871$	−3.24299e11	+	9.98089e11i	−0.563472	+	1.73419i
$872$	6.21517e10	−	3.16679e10i	0.107495	−	0.0547713i
$873$	−6.23563e10	+	3.93702e11i	−0.107355	+	0.677815i
$874$			8.61675e9i			0.0147672i
$875$	−1.26866e11	−	1.09474e12i	−0.216428	−	1.86757i
$876$	3.40411e11			0.578079
$877$	8.70703e11	+	1.37906e11i	1.47188	+	0.233123i	0.840271	−	0.542166i	$-0.182396\pi$
$877$	8.70703e11	+	1.37906e11i	1.47188	+	0.233123i	0.631607	+	0.775289i	$0.282396\pi$
$878$	−1.67950e10	−	3.29620e10i	−0.0282619	−	0.0554672i
$879$	−1.08974e11	−	3.54078e10i	−0.182544	−	0.0593121i
$880$	6.56478e11	+	1.49106e11i	1.09469	+	0.248637i
$881$	2.22072e11	+	6.83467e11i	0.368630	+	1.13453i	0.947677	+	0.319231i	$0.103425\pi$
$881$	2.22072e11	+	6.83467e11i	0.368630	+	1.13453i	−0.579047	+	0.815294i	$0.696575\pi$
$882$	−3.57774e10	−	3.57774e10i	−0.0591200	−	0.0591200i
$883$	1.96932e11	+	1.00342e11i	0.323947	+	0.165059i	0.608400	−	0.793631i	$-0.291812\pi$
$883$	1.96932e11	+	1.00342e11i	0.323947	+	0.165059i	−0.284453	+	0.958690i	$0.591812\pi$
$884$	6.88199e11	−	9.47225e11i	1.12695	−	1.55112i
$885$	−5.41173e11	−	2.16416e11i	−0.882191	−	0.352790i
$886$	−1.14974e10	+	8.35336e9i	−0.0186580	+	0.0135558i
$887$	6.30412e10	+	3.98026e11i	0.101843	+	0.643010i	0.984818	+	0.173590i	$0.0555368\pi$
$887$	6.30412e10	+	3.98026e11i	0.101843	+	0.643010i	−0.882975	+	0.469420i	$0.844463\pi$
$888$	2.85223e9	−	4.51749e8i	0.00458705	−	0.000726517i
$889$	−7.30789e10	−	1.00585e11i	−0.117000	−	0.161036i
$890$	1.12062e10	+	4.42754e10i	0.0178607	+	0.0705671i
$891$	9.20767e10	+	6.68977e10i	0.146096	+	0.106145i
$892$	−3.01231e11	+	5.91199e11i	−0.475817	+	0.933844i
$893$	−1.87582e11	+	1.87582e11i	−0.294975	+	0.294975i
$894$	1.71102e10	−	5.55943e9i	0.0267858	−	0.00870322i
$895$	4.76617e10	+	2.84082e10i	0.0742809	+	0.0442743i
$896$	−7.14670e10	+	2.19953e11i	−0.110885	+	0.341270i
$897$	3.34375e11	−	1.70372e11i	0.516492	−	0.263166i
$898$	−2.18186e9	+	1.37757e10i	−0.00335522	+	0.0211841i
$899$		−	4.74350e9i		−	0.00726207i
$900$	−4.42519e11	+	8.12725e10i	−0.674468	+	0.123872i
$901$	−4.98205e11			−0.755977
$902$	3.22970e10	+	5.11534e9i	0.0487906	+	0.00772767i
$903$	6.07271e10	+	1.19184e11i	0.0913338	+	0.179253i
$904$	5.14982e10	+	1.67328e10i	0.0771113	+	0.0250550i
$905$	6.68142e10	+	7.33675e11i	0.0996035	+	1.09373i
$906$	1.95321e9	+	6.01137e9i	0.00289892	+	0.00892197i
$907$	8.38530e11	+	8.38530e11i	1.23905	+	1.23905i	0.960389	+	0.278664i	$0.0898915\pi$
$907$	8.38530e11	+	8.38530e11i	1.23905	+	1.23905i	0.278664	+	0.960389i	$0.410109\pi$
$908$	−7.12724e11	−	3.63151e11i	−1.04852	−	0.534249i
$909$	−1.73869e11	+	2.39310e11i	−0.254663	+	0.350513i
$910$	5.30109e10	+	8.41686e10i	0.0773036	+	0.122740i
$911$	−2.95830e11	+	2.14933e11i	−0.429506	+	0.312054i	−0.781451	−	0.623966i	$-0.785520\pi$
$911$	−2.95830e11	+	2.14933e11i	−0.429506	+	0.312054i	0.351945	+	0.936021i	$0.385520\pi$
$912$	2.86772e10	+	1.81061e11i	0.0414531	+	0.261725i
$913$	2.85928e11	−	4.52866e10i	0.411504	−	0.0651759i
$914$	7.71912e9	+	1.06245e10i	0.0110607	+	0.0152238i
$915$	3.08016e11	+	2.56598e11i	0.439429	+	0.366074i
$916$	−8.65028e11	−	6.28479e11i	−1.22871	−	0.892707i
$917$	9.79241e11	−	1.92187e12i	1.38488	−	2.71798i
$918$	−2.71801e10	+	2.71801e10i	−0.0382719	+	0.0382719i
$919$	−1.79676e11	+	5.83802e10i	−0.251900	+	0.0818472i	−0.432245	−	0.901756i	$-0.642278\pi$
$919$	−1.79676e11	+	5.83802e10i	−0.251900	+	0.0818472i	0.180345	+	0.983603i	$0.442278\pi$
$920$	3.33213e10	−	2.91741e10i	0.0465125	−	0.0407236i
$921$	2.15340e10	−	6.62748e10i	0.0299286	−	0.0921107i
$922$	2.85131e10	−	1.45281e10i	0.0394567	−	0.0201042i
$923$	−1.64634e11	+	1.03946e12i	−0.226837	+	1.43219i
$924$		−	8.64219e11i		−	1.18559i
$925$	−1.81119e10	+	6.07820e10i	−0.0247399	+	0.0830249i
$926$	−3.94683e10			−0.0536790
$927$	−1.57024e11	−	2.48702e10i	−0.212641	−	0.0336791i
$928$	9.75709e8	+	1.91494e9i	0.00131561	+	0.00258204i
$929$	1.34780e12	+	4.37926e11i	1.80951	+	0.587946i	1.00000		0.000843939i	$0.000268634\pi$
$929$	1.34780e12	+	4.37926e11i	1.80951	+	0.587946i	0.809513	+	0.587102i	$0.199731\pi$
$930$	6.63634e9	−	2.84481e9i	0.00887149	−	0.00380296i
$931$	−2.80799e11	−	8.64209e11i	−0.373763	−	1.15032i
$932$	−3.03798e11	−	3.03798e11i	−0.402645	−	0.402645i
$933$	−4.48936e10	−	2.28745e10i	−0.0592459	−	0.0301873i
$934$	−1.56255e9	+	2.15066e9i	−0.00205327	+	0.00282608i
$935$	−6.83766e10	+	1.03040e12i	−0.0894666	+	1.34821i
$936$	6.57831e10	−	4.77942e10i	0.0857059	−	0.0622690i
$937$	1.46435e11	+	9.24552e11i	0.189970	+	1.19942i	0.879761	+	0.475416i	$0.157702\pi$
$937$	1.46435e11	+	9.24552e11i	0.189970	+	1.19942i	−0.689791	+	0.724008i	$0.742298\pi$
$938$	7.82458e10	−	1.23929e10i	0.101076	−	0.0160089i
$939$	4.63364e11	+	6.37765e11i	0.596018	+	0.820349i
$940$	6.79461e11	+	4.50886e10i	0.870268	+	0.0577504i
$941$	3.95247e11	+	2.87164e11i	0.504093	+	0.366245i	0.810578	−	0.585630i	$-0.199153\pi$
$941$	3.95247e11	+	2.87164e11i	0.504093	+	0.366245i	−0.306485	+	0.951875i	$0.599153\pi$
$942$	−1.41959e10	+	2.78609e10i	−0.0180284	+	0.0353828i
$943$	−3.28330e11	+	3.28330e11i	−0.415207	+	0.415207i
$944$	−1.27444e12	+	4.14092e11i	−1.60484	+	0.521445i
$945$	5.57362e11	+	1.30021e12i	0.698892	+	1.63037i
$946$	−2.56920e9	+	7.90717e9i	−0.00320799	+	0.00987317i
$947$	−3.58589e11	+	1.82710e11i	−0.445859	+	0.227176i	−0.662480	−	0.749079i	$-0.730496\pi$
$947$	−3.58589e11	+	1.82710e11i	−0.445859	+	0.227176i	0.216622	+	0.976256i	$0.430496\pi$
$948$	6.48587e9	−	4.09502e10i	0.00803036	−	0.0507017i
$949$		−	1.35116e12i		−	1.66588i
$950$	1.78762e10	+	5.32677e9i	0.0219472	+	0.00653987i
$951$	−6.27130e11			−0.766718
$952$	−1.74793e11	−	2.76846e10i	−0.212803	−	0.0337046i
$953$	1.29447e11	+	2.54053e11i	0.156935	+	0.308002i	0.956064	−	0.293157i	$-0.0947059\pi$
$953$	1.29447e11	+	2.54053e11i	0.156935	+	0.308002i	−0.799129	+	0.601159i	$0.794706\pi$
$954$	−1.64340e10	−	5.33974e9i	−0.0198404	−	0.00644654i
$955$	1.61001e11	+	1.83887e11i	0.193560	+	0.221074i
$956$	−3.43851e11	−	1.05827e12i	−0.411661	−	1.26696i
$957$	−7.56885e9	−	7.56885e9i	−0.00902365	−	0.00902365i
$958$	−6.71562e9	−	3.42178e9i	−0.00797304	−	0.00406247i
$959$	6.96335e10	−	9.58423e10i	0.0823273	−	0.113314i
$960$	2.99791e11	−	3.59864e11i	0.352966	−	0.423695i
$961$	6.00734e11	−	4.36459e11i	0.704350	−	0.511740i
$962$	−8.95510e8	−	5.65403e9i	−0.00104561	−	0.00660173i
$963$	−3.53523e11	+	5.59926e10i	−0.411067	+	0.0651067i
$964$	1.76000e11	+	2.42243e11i	0.203800	+	0.280506i
$965$	1.73392e11	−	1.09206e11i	0.199950	−	0.125932i
$966$	−2.29186e10	−	1.66514e10i	−0.0263197	−	0.0191223i
$967$	−1.79896e10	+	3.53065e10i	−0.0205738	+	0.0403784i	−0.901065	−	0.433685i	$-0.857213\pi$
$967$	−1.79896e10	+	3.53065e10i	−0.0205738	+	0.0403784i	0.880491	+	0.474063i	$0.157213\pi$
$968$	1.65315e10	−	1.65315e10i	0.0188283	−	0.0188283i
$969$	−2.67440e11	+	8.68966e10i	−0.303341	+	0.0985616i
$970$	−4.22454e10	+	3.84720e9i	−0.0477191	+	0.00434568i
$971$	3.15715e11	−	9.71671e11i	0.355155	−	1.09306i	−0.600764	−	0.799426i	$-0.705137\pi$
$971$	3.15715e11	−	9.71671e11i	0.355155	−	1.09306i	0.955919	−	0.293629i	$-0.0948631\pi$
$972$	8.19548e11	−	4.17580e11i	0.918140	−	0.467816i
$973$	−1.47618e11	+	9.32021e11i	−0.164697	+	1.03986i
$974$			1.21050e10i			0.0134502i
$975$	−1.46746e11	−	7.99010e11i	−0.162385	−	0.884166i
$976$	9.21710e11			1.01577
$977$	7.13782e11	+	1.13052e11i	0.783407	+	0.124080i	0.535310	−	0.844656i	$-0.320195\pi$
$977$	7.13782e11	+	1.13052e11i	0.783407	+	0.124080i	0.248097	+	0.968735i	$0.420195\pi$
$978$	−7.77136e9	−	1.52521e10i	−0.00849457	−	0.0166715i
$979$	−1.49790e12	−	4.86697e11i	−1.63062	−	0.529819i
$980$	−1.19423e12	+	2.00361e12i	−1.29474	+	2.17225i
$981$	−2.47537e11	−	7.61842e11i	−0.267279	−	0.822600i
$982$	1.02807e10	+	1.02807e10i	0.0110554	+	0.0110554i
$983$	−3.25350e11	−	1.65774e11i	−0.348447	−	0.177543i	0.271004	−	0.962578i	$-0.412644\pi$
$983$	−3.25350e11	−	1.65774e11i	−0.348447	−	0.177543i	−0.619450	+	0.785036i	$0.712644\pi$
$984$	2.69008e10	−	3.70258e10i	0.0286936	−	0.0394934i
$985$	3.71206e11	−	9.39534e10i	0.394339	−	0.0998085i
$986$	−8.85631e8	+	6.43449e8i	−0.000937012	+	0.000680779i
$987$	−1.36435e11	−	8.61417e11i	−0.143766	−	0.907705i
$988$	7.20334e11	−	1.14090e11i	0.755973	−	0.119734i
$989$	−6.93933e10	−	9.55116e10i	−0.0725324	−	0.0998323i
$990$	−1.32993e10	+	3.32564e10i	−0.0138448	+	0.0346206i
$991$	4.31464e11	+	3.13477e11i	0.447353	+	0.325021i	0.788550	−	0.614971i	$-0.210832\pi$
$991$	4.31464e11	+	3.13477e11i	0.447353	+	0.325021i	−0.341197	+	0.939992i	$0.610832\pi$
$992$	2.26969e10	−	4.45452e10i	0.0234380	−	0.0459996i
$993$	4.11426e10	−	4.11426e10i	0.0423151	−	0.0423151i
$994$	7.55567e10	−	2.45499e10i	0.0773976	−	0.0251480i
$995$	3.74327e11	−	1.64807e12i	0.381908	−	1.68144i
$996$	6.25307e10	−	1.92450e11i	0.0635413	−	0.195560i
$997$	−1.17364e11	+	5.98000e10i	−0.118783	+	0.0605230i	−0.512372	−	0.858763i	$-0.671233\pi$
$997$	−1.17364e11	+	5.98000e10i	−0.118783	+	0.0605230i	0.393589	+	0.919286i	$0.371233\pi$
$998$	1.09057e10	−	6.88561e10i	0.0109934	−	0.0694097i
$999$		−	8.14114e10i		−	0.0817378i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.9.f.a.2.10	✓	152
25.13	odd	20	inner	25.9.f.a.13.10	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.9.f.a.2.10	✓	152	1.1	even	1	trivial
25.9.f.a.13.10	yes	152	25.13	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	25.f (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.758404 - 0.120119i) q^{2} +(-20.5624 - 40.3560i) q^{3} +(-242.910 - 78.9262i) q^{4} +(-609.477 - 138.431i) q^{5} +(10.7471 + 33.0761i) q^{6} +(3191.92 + 3191.92i) q^{7} +(349.890 + 178.278i) q^{8} +(2650.67 - 3648.33i) q^{9} +O(q^{10})\)	\(q+(-0.758404 - 0.120119i) q^{2} +(-20.5624 - 40.3560i) q^{3} +(-242.910 - 78.9262i) q^{4} +(-609.477 - 138.431i) q^{5} +(10.7471 + 33.0761i) q^{6} +(3191.92 + 3191.92i) q^{7} +(349.890 + 178.278i) q^{8} +(2650.67 - 3648.33i) q^{9} +(445.602 + 178.197i) q^{10} +(-13389.0 + 9727.70i) q^{11} +(1809.66 + 11425.8i) q^{12} +(45351.3 - 7182.93i) q^{13} +(-2037.35 - 2804.18i) q^{14} +(6945.78 + 27442.5i) q^{15} +(52653.7 + 38255.1i) q^{16} +(-45324.7 + 88954.6i) q^{17} +(-2448.51 + 2448.51i) q^{18} +(-59144.2 + 19217.1i) q^{19} +(137122. + 81729.9i) q^{20} +(63179.5 - 194446. i) q^{21} +(11322.8 - 5769.25i) q^{22} +(-28228.6 + 178228. i) q^{23} -17786.0i q^{24} +(352299. + 168741. i) q^{25} -35257.4 q^{26} +(-495242. - 78438.6i) q^{27} +(-523422. - 1.02727e6i) q^{28} +(-13581.0 - 4412.75i) q^{29} +(-1971.33 - 21646.8i) q^{30} +(102649. + 315921. i) q^{31} +(-106422. - 106422. i) q^{32} +(667881. + 340303. i) q^{33} +(45059.6 - 62019.2i) q^{34} +(-1.50354e6 - 2.38726e6i) q^{35} +(-931822. + 677008. i) q^{36} +(25399.2 + 160364. i) q^{37} +(47163.6 - 7469.98i) q^{38} +(-1.22240e6 - 1.68249e6i) q^{39} +(-188571. - 157092. i) q^{40} +(2.08174e6 + 1.51248e6i) q^{41} +(-71272.4 + 139880. i) q^{42} +(-462623. + 462623. i) q^{43} +(4.02010e6 - 1.30621e6i) q^{44} +(-2.12056e6 + 1.85664e6i) q^{45} +(42817.3 - 131778. i) q^{46} +(3.80085e6 - 1.93663e6i) q^{47} +(461137. - 2.91151e6i) q^{48} +1.46119e7i q^{49} +(-246916. - 170292. i) q^{50} +4.52183e6 q^{51} +(-1.15832e7 - 1.83460e6i) q^{52} +(2.26551e6 + 4.44632e6i) q^{53} +(366172. + 118976. i) q^{54} +(9.50692e6 - 4.07535e6i) q^{55} +(547772. + 1.68587e6i) q^{56} +(1.99167e6 + 1.99167e6i) q^{57} +(9769.86 + 4977.99i) q^{58} +(-1.21021e7 + 1.66572e7i) q^{59} +(478733. - 7.21425e6i) q^{60} +(1.14573e7 - 8.32419e6i) q^{61} +(-39901.2 - 251926. i) q^{62} +(2.01059e7 - 3.18446e6i) q^{63} +(-9.72539e6 - 1.33858e7i) q^{64} +(-2.86349e7 - 1.90019e6i) q^{65} +(-465647. - 338313. i) q^{66} +(-1.03762e7 + 2.03645e7i) q^{67} +(1.80306e7 - 1.80306e7i) q^{68} +(7.77302e6 - 2.52561e6i) q^{69} +(853535. + 1.99111e6i) q^{70} +(-7.08274e6 + 2.17984e7i) q^{71} +(1.57786e6 - 803959. i) q^{72} +(4.60331e6 - 2.90642e7i) q^{73} -124672. i q^{74} +(-434398. - 1.76871e7i) q^{75} +1.58834e7 q^{76} +(-7.37868e7 - 1.16867e7i) q^{77} +(724976. + 1.42285e6i) q^{78} +(-3.40860e6 - 1.10752e6i) q^{79} +(-2.67955e7 - 3.06045e7i) q^{80} +(-2.12512e6 - 6.54044e6i) q^{81} +(-1.39713e6 - 1.39713e6i) q^{82} +(-1.55857e7 - 7.94132e6i) q^{83} +(-3.06938e7 + 4.22464e7i) q^{84} +(3.99384e7 - 4.79414e7i) q^{85} +(406425. - 295285. i) q^{86} +(101178. + 638812. i) q^{87} +(-6.41892e6 + 1.01666e6i) q^{88} +(5.59375e7 + 7.69914e7i) q^{89} +(1.83126e6 - 1.15336e6i) q^{90} +(1.67685e8 + 1.21830e8i) q^{91} +(2.09239e7 - 4.10654e7i) q^{92} +(1.06386e7 - 1.06386e7i) q^{93} +(-3.11521e6 + 1.01219e6i) q^{94} +(3.87073e7 - 3.52499e6i) q^{95} +(-2.10647e6 + 6.48306e6i) q^{96} +(-7.87576e7 + 4.01290e7i) q^{97} +(1.75517e6 - 1.10817e7i) q^{98} +7.46325e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q - 8 q^{2} + 62 q^{3} - 10 q^{4} - 230 q^{5} - 6 q^{6} + 2342 q^{7} + 8210 q^{8} - 10 q^{9}+O(q^{10}) \) 152 * q - 8 * q^2 + 62 * q^3 - 10 * q^4 - 230 * q^5 - 6 * q^6 + 2342 * q^7 + 8210 * q^8 - 10 * q^9	\( 152 q - 8 q^{2} + 62 q^{3} - 10 q^{4} - 230 q^{5} - 6 q^{6} + 2342 q^{7} + 8210 q^{8} - 10 q^{9} - 30880 q^{10} - 6 q^{11} + 45902 q^{12} + 119132 q^{13} - 10 q^{14} - 241450 q^{15} + 524282 q^{16} - 105158 q^{17} + 454052 q^{18} + 718890 q^{19} + 340370 q^{20} - 6 q^{21} - 1986746 q^{22} - 899198 q^{23} + 2032310 q^{25} - 913936 q^{26} + 1904300 q^{27} - 998002 q^{28} - 1956910 q^{29} - 4500490 q^{30} - 6 q^{31} - 3033938 q^{32} + 1003994 q^{33} + 10303990 q^{34} + 4124560 q^{35} - 8100358 q^{36} + 9534392 q^{37} - 14259280 q^{38} - 22510410 q^{39} - 4123060 q^{40} - 4374726 q^{41} + 52199634 q^{42} + 13583342 q^{43} - 2138860 q^{44} - 33978380 q^{45} - 6 q^{46} - 11197058 q^{47} - 32869688 q^{48} + 13239250 q^{50} - 16 q^{51} + 93509212 q^{52} + 53717512 q^{53} + 57025140 q^{54} - 14642290 q^{55} - 262150 q^{56} - 93310490 q^{57} - 97437640 q^{58} + 24222740 q^{59} - 66375070 q^{60} - 18369126 q^{61} + 6782124 q^{62} + 96012652 q^{63} + 112817140 q^{64} + 89469970 q^{65} + 6718458 q^{66} + 74549142 q^{67} - 62262702 q^{68} - 128418860 q^{69} - 177099410 q^{70} + 60703854 q^{71} - 444425220 q^{72} - 171988248 q^{73} + 257329110 q^{75} - 262160 q^{76} + 292751454 q^{77} + 385000804 q^{78} + 138506190 q^{79} + 245270230 q^{80} + 110809772 q^{81} - 73650066 q^{82} - 663197528 q^{83} - 1517250010 q^{84} - 616093620 q^{85} - 6 q^{86} + 494144820 q^{87} + 1287340030 q^{88} + 1051406240 q^{89} + 1480613390 q^{90} - 6 q^{91} - 461835158 q^{92} - 908140736 q^{93} - 1160168810 q^{94} - 920404690 q^{95} + 172437534 q^{96} - 732746208 q^{97} - 167741852 q^{98}+O(q^{100}) \) 152 * q - 8 * q^2 + 62 * q^3 - 10 * q^4 - 230 * q^5 - 6 * q^6 + 2342 * q^7 + 8210 * q^8 - 10 * q^9 - 30880 * q^10 - 6 * q^11 + 45902 * q^12 + 119132 * q^13 - 10 * q^14 - 241450 * q^15 + 524282 * q^16 - 105158 * q^17 + 454052 * q^18 + 718890 * q^19 + 340370 * q^20 - 6 * q^21 - 1986746 * q^22 - 899198 * q^23 + 2032310 * q^25 - 913936 * q^26 + 1904300 * q^27 - 998002 * q^28 - 1956910 * q^29 - 4500490 * q^30 - 6 * q^31 - 3033938 * q^32 + 1003994 * q^33 + 10303990 * q^34 + 4124560 * q^35 - 8100358 * q^36 + 9534392 * q^37 - 14259280 * q^38 - 22510410 * q^39 - 4123060 * q^40 - 4374726 * q^41 + 52199634 * q^42 + 13583342 * q^43 - 2138860 * q^44 - 33978380 * q^45 - 6 * q^46 - 11197058 * q^47 - 32869688 * q^48 + 13239250 * q^50 - 16 * q^51 + 93509212 * q^52 + 53717512 * q^53 + 57025140 * q^54 - 14642290 * q^55 - 262150 * q^56 - 93310490 * q^57 - 97437640 * q^58 + 24222740 * q^59 - 66375070 * q^60 - 18369126 * q^61 + 6782124 * q^62 + 96012652 * q^63 + 112817140 * q^64 + 89469970 * q^65 + 6718458 * q^66 + 74549142 * q^67 - 62262702 * q^68 - 128418860 * q^69 - 177099410 * q^70 + 60703854 * q^71 - 444425220 * q^72 - 171988248 * q^73 + 257329110 * q^75 - 262160 * q^76 + 292751454 * q^77 + 385000804 * q^78 + 138506190 * q^79 + 245270230 * q^80 + 110809772 * q^81 - 73650066 * q^82 - 663197528 * q^83 - 1517250010 * q^84 - 616093620 * q^85 - 6 * q^86 + 494144820 * q^87 + 1287340030 * q^88 + 1051406240 * q^89 + 1480613390 * q^90 - 6 * q^91 - 461835158 * q^92 - 908140736 * q^93 - 1160168810 * q^94 - 920404690 * q^95 + 172437534 * q^96 - 732746208 * q^97 - 167741852 * q^98

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