LMFDB - Embedded newform 25.9.f.a.2.19

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			2.19
Character	$\chi$	$=$	25.2
Dual form			25.9.f.a.13.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(30.6740 + 4.85828i) q^{2} +(-51.4523 - 100.981i) q^{3} +(673.820 + 218.937i) q^{4} +(-200.608 - 591.930i) q^{5} +(-1087.65 - 3347.46i) q^{6} +(-1139.13 - 1139.13i) q^{7} +(12521.2 + 6379.87i) q^{8} +(-3693.34 + 5083.44i) q^{9} +O(q^{10})$	\(q+(30.6740 + 4.85828i) q^{2} +(-51.4523 - 100.981i) q^{3} +(673.820 + 218.937i) q^{4} +(-200.608 - 591.930i) q^{5} +(-1087.65 - 3347.46i) q^{6} +(-1139.13 - 1139.13i) q^{7} +(12521.2 + 6379.87i) q^{8} +(-3693.34 + 5083.44i) q^{9} +(-3277.69 - 19131.5i) q^{10} +(-266.361 + 193.523i) q^{11} +(-12561.1 - 79307.7i) q^{12} +(31738.7 - 5026.91i) q^{13} +(-29407.4 - 40475.7i) q^{14} +(-49451.9 + 50713.8i) q^{15} +(206344. + 149918. i) q^{16} +(-48707.2 + 95593.2i) q^{17} +(-137986. + 137986. i) q^{18} +(163311. - 53062.9i) q^{19} +(-5578.26 - 442775. i) q^{20} +(-56419.3 + 173641. i) q^{21} +(-9110.55 + 4642.06i) q^{22} +(-50196.5 + 316928. i) q^{23} -1.59266e6i q^{24} +(-310138. + 237492. i) q^{25} +997974. q^{26} +(-31065.3 - 4920.27i) q^{27} +(-518169. - 1.01696e6i) q^{28} +(268214. + 87148.0i) q^{29} +(-1.76327e6 + 1.31534e6i) q^{30} +(-75597.9 - 232666. i) q^{31} +(3.05722e6 + 3.05722e6i) q^{32} +(33247.0 + 16940.2i) q^{33} +(-1.95846e6 + 2.69559e6i) q^{34} +(-445765. + 902802. i) q^{35} +(-3.60160e6 + 2.61671e6i) q^{36} +(-40969.1 - 258668. i) q^{37} +(5.26718e6 - 834240. i) q^{38} +(-2.14065e6 - 2.94635e6i) q^{39} +(1.26458e6 - 8.69153e6i) q^{40} +(-368370. - 267637. i) q^{41} +(-2.57420e6 + 5.05215e6i) q^{42} +(-1.28386e6 + 1.28386e6i) q^{43} +(-221849. + 72083.1i) q^{44} +(3.74996e6 + 1.16642e6i) q^{45} +(-3.07946e6 + 9.47759e6i) q^{46} +(-1.62257e6 + 826740. i) q^{47} +(4.52195e6 - 2.85504e7i) q^{48} -3.16958e6i q^{49} +(-1.06670e7 + 5.77810e6i) q^{50} +1.21592e7 q^{51} +(2.24867e7 + 3.56155e6i) q^{52} +(3.82634e6 + 7.50961e6i) q^{53} +(-928993. - 301848. i) q^{54} +(167986. + 118845. i) q^{55} +(-6.99575e6 - 2.15307e7i) q^{56} +(-1.37611e7 - 1.37611e7i) q^{57} +(7.80380e6 + 3.97624e6i) q^{58} +(9.74856e6 - 1.34177e7i) q^{59} +(-4.44248e7 + 2.33451e7i) q^{60} +(-2.54005e6 + 1.84546e6i) q^{61} +(-1.18853e6 - 7.50408e6i) q^{62} +(9.99786e6 - 1.58351e6i) q^{63} +(4.05452e7 + 5.58057e7i) q^{64} +(-9.34263e6 - 1.77786e7i) q^{65} +(937518. + 681147. i) q^{66} +(1.29265e6 - 2.53698e6i) q^{67} +(-5.37488e7 + 5.37488e7i) q^{68} +(3.45864e7 - 1.12378e7i) q^{69} +(-1.80595e7 + 2.55269e7i) q^{70} +(1.10654e7 - 3.40559e7i) q^{71} +(-7.86766e7 + 4.00878e7i) q^{72} +(-1.11424e6 + 7.03502e6i) q^{73} -8.13343e6i q^{74} +(3.99395e7 + 1.90984e7i) q^{75} +1.21659e8 q^{76} +(523867. + 82972.3i) q^{77} +(-5.13481e7 - 1.00776e8i) q^{78} +(-5.06741e7 - 1.64650e7i) q^{79} +(4.73465e7 - 1.52216e8i) q^{80} +(1.38410e7 + 4.25983e7i) q^{81} +(-9.99913e6 - 9.99913e6i) q^{82} +(1.86230e6 + 948890. i) q^{83} +(-7.60329e7 + 1.04650e8i) q^{84} +(6.63556e7 + 9.65445e6i) q^{85} +(-4.56186e7 + 3.31438e7i) q^{86} +(-4.99995e6 - 3.15685e7i) q^{87} +(-4.56981e6 + 723787. i) q^{88} +(6.14591e7 + 8.45912e7i) q^{89} +(1.09359e8 + 5.39970e7i) q^{90} +(-4.18807e7 - 3.04281e7i) q^{91} +(-1.03211e8 + 2.02563e8i) q^{92} +(-1.96052e7 + 1.96052e7i) q^{93} +(-5.37871e7 + 1.74765e7i) q^{94} +(-6.41710e7 - 8.60237e7i) q^{95} +(1.51419e8 - 4.66021e8i) q^{96} +(-6.77279e7 + 3.45091e7i) q^{97} +(1.53987e7 - 9.72237e7i) q^{98} -2.06878e6i 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 $

$2$	30.6740	+	4.85828i	1.91712	+	0.303643i	0.996272	−	0.0862699i	$-0.0274947\pi$
$2$	30.6740	+	4.85828i	1.91712	+	0.303643i	0.920852	+	0.389912i	$0.127495\pi$
$3$	−51.4523	−	100.981i	−0.635214	−	1.24668i	−0.954271	−	0.298942i	$-0.903366\pi$
$3$	−51.4523	−	100.981i	−0.635214	−	1.24668i	0.319057	−	0.947735i	$-0.396634\pi$
$4$	673.820	+	218.937i	2.63211	+	0.855224i
$5$	−200.608	−	591.930i	−0.320973	−	0.947088i
$5$	−200.608	−	591.930i	−0.320973	−	0.947088i
$6$	−1087.65	−	3347.46i	−0.839239	−	2.58291i
$7$	−1139.13	−	1139.13i	−0.474438	−	0.474438i	0.428909	−	0.903348i	$-0.358898\pi$
$7$	−1139.13	−	1139.13i	−0.474438	−	0.474438i	−0.903348	+	0.428909i	$0.858898\pi$
$8$	12521.2	+	6379.87i	3.05693	+	1.55758i
$9$	−3693.34	+	5083.44i	−0.562923	+	0.774797i
$10$	−3277.69	−	19131.5i	−0.327769	−	1.91315i
$11$	−266.361	+	193.523i	−0.0181928	+	0.0132179i	−0.596845	−	0.802357i	$-0.703579\pi$
$11$	−266.361	+	193.523i	−0.0181928	+	0.0132179i	0.578652	+	0.815575i	$0.303579\pi$
$12$	−12561.1	−	79307.7i	−0.605763	−	3.82464i
$13$	31738.7	−	5026.91i	1.11126	−	0.176006i	0.426296	−	0.904584i	$-0.359818\pi$
$13$	31738.7	−	5026.91i	1.11126	−	0.176006i	0.684963	+	0.728577i	$0.259818\pi$
$14$	−29407.4	−	40475.7i	−0.765497	−	1.05362i
$15$	−49451.9	+	50713.8i	−0.976827	+	1.00175i
$16$	206344.	+	149918.i	3.14856	+	2.28757i
$17$	−48707.2	+	95593.2i	−0.583173	+	1.14454i	0.391347	+	0.920243i	$0.372009\pi$
$17$	−48707.2	+	95593.2i	−0.583173	+	1.14454i	−0.974520	+	0.224298i	$0.927991\pi$
$18$	−137986.	+	137986.i	−1.31445	+	1.31445i
$19$	163311.	−	53062.9i	1.25314	−	0.407171i	0.394096	−	0.919069i	$-0.371058\pi$
$19$	163311.	−	53062.9i	1.25314	−	0.407171i	0.859046	+	0.511899i	$0.171058\pi$
$20$	−5578.26	−	442775.i	−0.0348642	−	2.76734i
$21$	−56419.3	+	173641.i	−0.290102	+	0.892842i
$22$	−9110.55	+	4642.06i	−0.0388914	+	0.0198162i
$23$	−50196.5	+	316928.i	−0.179375	+	1.13253i	0.719554	+	0.694437i	$0.244346\pi$
$23$	−50196.5	+	316928.i	−0.179375	+	1.13253i	−0.898929	+	0.438094i	$0.855654\pi$
$24$		−	1.59266e6i		−	4.80041i
$25$	−310138.	+	237492.i	−0.793952	+	0.607980i
$26$	997974.			2.18387
$27$	−31065.3	−	4920.27i	−0.0584549	−	0.00925835i
$28$	−518169.	−	1.01696e6i	−0.843022	−	1.65452i
$29$	268214.	+	87148.0i	0.379219	+	0.123216i	0.492423	−	0.870356i	$-0.336111\pi$
$29$	268214.	+	87148.0i	0.379219	+	0.123216i	−0.113204	+	0.993572i	$0.536111\pi$
$30$	−1.76327e6	+	1.31534e6i	−2.17687	+	1.62388i
$31$	−75597.9	−	232666.i	−0.0818584	−	0.251934i	0.901748	−	0.432262i	$-0.142284\pi$
$31$	−75597.9	−	232666.i	−0.0818584	−	0.251934i	−0.983607	+	0.180327i	$0.942284\pi$
$32$	3.05722e6	+	3.05722e6i	2.91559	+	2.91559i
$33$	33247.0	+	16940.2i	0.0280348	+	0.0142844i
$34$	−1.95846e6	+	2.69559e6i	−1.46555	+	2.01715i
$35$	−445765.	+	902802.i	−0.297053	+	0.601617i
$36$	−3.60160e6	+	2.61671e6i	−2.14430	+	1.55792i
$37$	−40969.1	−	258668.i	−0.0218599	−	0.138018i	0.974345	−	0.225061i	$-0.0722582\pi$
$37$	−40969.1	−	258668.i	−0.0218599	−	0.138018i	−0.996205	+	0.0870430i	$0.972258\pi$
$38$	5.26718e6	−	834240.i	2.52606	−	0.400089i
$39$	−2.14065e6	−	2.94635e6i	−0.925310	−	1.27358i
$40$	1.26458e6	−	8.69153e6i	0.493976	−	3.39513i
$41$	−368370.	−	267637.i	−0.130361	−	0.0947132i	0.520694	−	0.853744i	$-0.325673\pi$
$41$	−368370.	−	267637.i	−0.130361	−	0.0947132i	−0.651055	+	0.759030i	$0.725673\pi$
$42$	−2.57420e6	+	5.05215e6i	−0.827266	+	1.62360i
$43$	−1.28386e6	+	1.28386e6i	−0.375530	+	0.375530i	−0.869487	−	0.493956i	$-0.835550\pi$
$43$	−1.28386e6	+	1.28386e6i	−0.375530	+	0.375530i	0.493956	+	0.869487i	$0.335550\pi$
$44$	−221849.	+	72083.1i	−0.0591898	+	0.0192319i
$45$	3.74996e6	+	1.16642e6i	0.914484	+	0.284448i
$46$	−3.07946e6	+	9.47759e6i	−0.687769	+	2.11674i
$47$	−1.62257e6	+	826740.i	−0.332515	+	0.169425i	−0.612275	−	0.790645i	$-0.709745\pi$
$47$	−1.62257e6	+	826740.i	−0.332515	+	0.169425i	0.279759	+	0.960070i	$0.409745\pi$
$48$	4.52195e6	−	2.85504e7i	0.851845	−	5.37834i
$49$		−	3.16958e6i		−	0.549816i
$50$	−1.06670e7	+	5.77810e6i	−1.70671	+	0.924495i
$51$	1.21592e7			1.79731
$52$	2.24867e7	+	3.56155e6i	3.07548	+	0.487108i
$53$	3.82634e6	+	7.50961e6i	0.484931	+	0.951731i	0.995755	+	0.0920452i	$0.0293404\pi$
$53$	3.82634e6	+	7.50961e6i	0.484931	+	0.951731i	−0.510824	+	0.859685i	$0.670660\pi$
$54$	−928993.	−	301848.i	−0.109254	−	0.0354988i
$55$	167986.	+	118845.i	0.0183579	+	0.0129876i
$56$	−6.99575e6	−	2.15307e7i	−0.711348	−	2.18930i
$57$	−1.37611e7	−	1.37611e7i	−1.30362	−	1.30362i
$58$	7.80380e6	+	3.97624e6i	0.689595	+	0.351366i
$59$	9.74856e6	−	1.34177e7i	0.804512	−	1.10732i	−0.187635	−	0.982239i	$-0.560082\pi$
$59$	9.74856e6	−	1.34177e7i	0.804512	−	1.10732i	0.992147	−	0.125077i	$-0.0399178\pi$
$60$	−4.44248e7	+	2.33451e7i	−3.42784	+	1.80132i
$61$	−2.54005e6	+	1.84546e6i	−0.183452	+	0.133286i	−0.675721	−	0.737157i	$-0.736168\pi$
$61$	−2.54005e6	+	1.84546e6i	−0.183452	+	0.133286i	0.492269	+	0.870443i	$0.336168\pi$
$62$	−1.18853e6	−	7.50408e6i	−0.0804347	−	0.507845i
$63$	9.99786e6	−	1.58351e6i	0.634665	−	0.100521i
$64$	4.05452e7	+	5.58057e7i	2.41668	+	3.32628i
$65$	−9.34263e6	−	1.77786e7i	−0.523378	−	0.995968i
$66$	937518.	+	681147.i	0.0494088	+	0.0358976i
$67$	1.29265e6	−	2.53698e6i	0.0641480	−	0.125898i	−0.856706	−	0.515805i	$-0.827493\pi$
$67$	1.29265e6	−	2.53698e6i	0.0641480	−	0.125898i	0.920854	+	0.389907i	$0.127493\pi$
$68$	−5.37488e7	+	5.37488e7i	−2.51381	+	2.51381i
$69$	3.45864e7	−	1.12378e7i	1.52584	−	0.495776i
$70$	−1.80595e7	+	2.55269e7i	−0.752164	+	1.06318i
$71$	1.10654e7	−	3.40559e7i	0.435446	−	1.34017i	−0.457182	−	0.889373i	$-0.651141\pi$
$71$	1.10654e7	−	3.40559e7i	0.435446	−	1.34017i	0.892628	−	0.450793i	$-0.148859\pi$
$72$	−7.86766e7	+	4.00878e7i	−2.92763	+	1.49170i
$73$	−1.11424e6	+	7.03502e6i	−0.0392361	+	0.247727i	−0.999509	−	0.0313358i	$-0.990024\pi$
$73$	−1.11424e6	+	7.03502e6i	−0.0392361	+	0.247727i	0.960273	+	0.279063i	$0.0900239\pi$
$74$		−	8.13343e6i		−	0.271236i
$75$	3.99395e7	+	1.90984e7i	1.26228	+	0.603605i
$76$	1.21659e8			3.64663
$77$	523867.	+	82972.3i	0.0149025	+	0.00236032i
$78$	−5.13481e7	−	1.00776e8i	−1.38722	−	2.72258i
$79$	−5.06741e7	−	1.64650e7i	−1.30100	−	0.422721i	−0.425071	−	0.905160i	$-0.639751\pi$
$79$	−5.06741e7	−	1.64650e7i	−1.30100	−	0.422721i	−0.875929	+	0.482439i	$0.839751\pi$
$80$	4.73465e7	−	1.52216e8i	1.15592	−	3.71622i
$81$	1.38410e7	+	4.25983e7i	0.321535	+	0.989583i
$82$	−9.99913e6	−	9.99913e6i	−0.221160	−	0.221160i
$83$	1.86230e6	+	948890.i	0.0392408	+	0.0199942i	0.473501	−	0.880793i	$-0.342990\pi$
$83$	1.86230e6	+	948890.i	0.0392408	+	0.0199942i	−0.434260	+	0.900788i	$0.642990\pi$
$84$	−7.60329e7	+	1.04650e8i	−1.52716	+	2.10195i
$85$	6.63556e7	+	9.65445e6i	1.27116	+	0.184949i
$86$	−4.56186e7	+	3.31438e7i	−0.833965	+	0.605911i
$87$	−4.99995e6	−	3.15685e7i	−0.0872748	−	0.551031i
$88$	−4.56981e6	+	723787.i	−0.0762023	+	0.0120693i
$89$	6.14591e7	+	8.45912e7i	0.979549	+	1.34823i	0.937072	+	0.349136i	$0.113525\pi$
$89$	6.14591e7	+	8.45912e7i	0.979549	+	1.34823i	0.0424768	+	0.999097i	$0.486475\pi$
$90$	1.09359e8	+	5.39970e7i	1.66681	+	0.822999i
$91$	−4.18807e7	−	3.04281e7i	−0.610728	−	0.443720i
$92$	−1.03211e8	+	2.02563e8i	−1.44070	+	2.82754i
$93$	−1.96052e7	+	1.96052e7i	−0.262083	+	0.262083i
$94$	−5.37871e7	+	1.74765e7i	−0.688917	+	0.223843i
$95$	−6.41710e7	−	8.60237e7i	−0.787852	−	1.05615i
$96$	1.51419e8	−	4.66021e8i	1.78278	−	5.48682i
$97$	−6.77279e7	+	3.45091e7i	−0.765034	+	0.389804i	−0.792542	−	0.609817i	$-0.791243\pi$
$97$	−6.77279e7	+	3.45091e7i	−0.765034	+	0.389804i	0.0275081	+	0.999622i	$0.491243\pi$
$98$	1.53987e7	−	9.72237e7i	0.166948	−	1.05407i
$99$		−	2.06878e6i		−	0.0215364i
$100$	−2.60973e8	+	9.21263e7i	−2.60973	+	0.921263i
$101$	−1.93977e8			−1.86408			−0.932042	−	0.362349i	$-0.881975\pi$
$101$	−1.93977e8			−1.86408			−0.932042	+	0.362349i	$0.881975\pi$
$102$	3.72971e8	+	5.90728e7i	3.44567	+	0.545741i
$103$	−2.41811e7	−	4.74580e7i	−0.214846	−	0.421658i	0.758281	−	0.651928i	$-0.226039\pi$
$103$	−2.41811e7	−	4.74580e7i	−0.214846	−	0.421658i	−0.973127	+	0.230269i	$0.926039\pi$
$104$	4.29477e8	+	1.39546e8i	3.67119	+	1.19284i
$105$	1.14101e8	−	1.43750e6i	0.938715	−	0.0118263i
$106$	8.08852e7	+	2.48939e8i	0.640687	+	1.97183i
$107$	−1.15145e7	−	1.15145e7i	−0.0878432	−	0.0878432i	0.661820	−	0.749663i	$-0.269784\pi$
$107$	−1.15145e7	−	1.15145e7i	−0.0878432	−	0.0878432i	−0.749663	+	0.661820i	$0.769784\pi$
$108$	−1.98552e7	−	1.01167e7i	−0.145942	−	0.0743610i
$109$	−3.41423e7	+	4.69929e7i	−0.241873	+	0.332910i	−0.912644	−	0.408755i	$-0.865963\pi$
$109$	−3.41423e7	+	4.69929e7i	−0.241873	+	0.332910i	0.670771	+	0.741664i	$0.265963\pi$
$110$	4.57543e6	+	4.46158e6i	0.0312508	+	0.0304732i
$111$	−2.40126e7	+	1.74462e7i	−0.158179	+	0.114923i
$112$	−6.42768e7	−	4.05828e8i	−0.408491	−	2.57911i
$113$	−2.49338e8	+	3.94913e7i	−1.52924	+	0.242208i	−0.863643	−	0.504104i	$-0.831823\pi$
$113$	−2.49338e8	+	3.94913e7i	−1.52924	+	0.242208i	−0.665596	+	0.746312i	$0.731823\pi$
$114$	−3.55251e8	−	4.88961e8i	−2.10337	−	2.89504i
$115$	1.97669e8	−	3.38657e7i	1.13018	−	0.193628i
$116$	1.61648e8	+	1.17444e8i	0.892767	+	0.648633i
$117$	−9.16676e7	+	1.79908e8i	−0.489184	+	0.960078i
$118$	3.64214e8	−	3.64214e8i	1.87858	−	1.87858i
$119$	1.64376e8	−	5.34092e7i	0.819694	−	0.266335i
$120$	−9.42744e8	+	3.19501e8i	−4.54641	+	1.54080i
$121$	−6.62070e7	+	2.03764e8i	−0.308861	+	0.950576i
$122$	−8.68793e7	+	4.42672e7i	−0.392172	+	0.199822i
$123$	−8.07268e6	+	5.09689e7i	−0.0352693	+	0.222682i
$124$		−	1.73326e8i		−	0.733125i
$125$	2.02795e8	+	1.35937e8i	0.830648	+	0.556797i
$126$	3.14367e8			1.24725
$127$	−1.26559e8	−	2.00450e7i	−0.486496	−	0.0770534i	−0.0916319	−	0.995793i	$-0.529208\pi$
$127$	−1.26559e8	−	2.00450e7i	−0.486496	−	0.0770534i	−0.394864	+	0.918740i	$0.629208\pi$
$128$	4.70072e8	+	9.22569e8i	1.75116	+	3.43684i
$129$	1.95703e8	+	6.35879e7i	0.706707	+	0.229623i
$130$	−2.00202e8	−	5.90731e8i	−0.700962	−	2.06831i
$131$	4.55020e7	+	1.40041e8i	0.154506	+	0.475520i	0.998110	−	0.0614447i	$-0.0195708\pi$
$131$	4.55020e7	+	1.40041e8i	0.154506	+	0.475520i	−0.843605	+	0.536965i	$0.819571\pi$
$132$	1.86937e7	+	1.86937e7i	0.0615742	+	0.0615742i
$133$	−2.46477e8	−	1.25586e8i	−0.787716	−	0.401361i
$134$	5.19762e7	−	7.15391e7i	0.161207	−	0.221883i
$135$	3.31951e6	+	1.93756e7i	0.00999399	+	0.0583336i
$136$	−1.21974e9	+	8.86196e8i	−3.56544	+	2.59044i
$137$	2.70954e7	+	1.71073e8i	0.0769153	+	0.485624i	0.995835	+	0.0911785i	$0.0290634\pi$
$137$	2.70954e7	+	1.71073e8i	0.0769153	+	0.485624i	−0.918919	+	0.394446i	$0.870937\pi$
$138$	1.11550e9	−	1.76678e8i	3.07577	−	0.487154i
$139$	4.83642e7	+	6.65676e7i	0.129558	+	0.178321i	0.868868	−	0.495044i	$-0.164848\pi$
$139$	4.83642e7	+	6.65676e7i	0.129558	+	0.178321i	−0.739310	+	0.673365i	$0.764848\pi$
$140$	−4.98022e8	+	5.10731e8i	−1.29639	+	1.32947i
$141$	1.66970e8	+	1.21311e8i	0.422436	+	0.306918i
$142$	5.04874e8	−	9.90870e8i	1.24174	−	2.43704i
$143$	−7.48114e6	+	7.48114e6i	−0.0178905	+	0.0178905i
$144$	−1.52420e9	+	4.95242e8i	−3.54480	+	1.15177i
$145$	−2.22043e6	−	1.76247e8i	−0.00502302	−	0.398702i
$146$	−6.83562e7	+	2.10379e8i	−0.150441	+	0.463010i
$147$	−3.20067e8	+	1.63082e8i	−0.685444	+	0.349251i
$148$	2.90264e7	−	1.83266e8i	0.0604988	−	0.381974i
$149$		−	5.94237e8i		−	1.20563i	−0.797880	−	0.602816i	$-0.794045\pi$
$149$		−	5.94237e8i		−	1.20563i	0.797880	−	0.602816i	$-0.205955\pi$
$150$	1.13232e9	+	7.79862e8i	2.23668	+	1.54047i
$151$	2.34260e8			0.450598			0.225299	−	0.974290i	$-0.427664\pi$
$151$	2.34260e8			0.450598			0.225299	+	0.974290i	$0.427664\pi$
$152$	2.38338e9	+	3.77490e8i	4.46497	+	0.707182i
$153$	−3.06051e8	−	6.00658e8i	−0.558506	−	1.09613i
$154$	1.56660e7	+	5.09018e6i	0.0278532	+	0.00905004i
$155$	−1.22557e8	+	9.14235e7i	−0.212330	+	0.158391i
$156$	−7.97346e8	−	2.45398e9i	−1.34632	−	4.14355i
$157$	−5.77636e8	−	5.77636e8i	−0.950727	−	0.950727i	0.0481150	−	0.998842i	$-0.484679\pi$
$157$	−5.77636e8	−	5.77636e8i	−0.950727	−	0.950727i	−0.998842	+	0.0481150i	$0.984679\pi$
$158$	−1.47438e9	−	7.51236e8i	−2.36582	−	1.20545i
$159$	5.61453e8	−	7.72774e8i	0.878466	−	1.20910i
$160$	1.19636e9	−	2.42296e9i	1.82549	−	3.69715i
$161$	4.18202e8	−	3.03841e8i	0.622419	−	0.452214i
$162$	2.17605e8	+	1.37390e9i	0.315943	+	1.99479i
$163$	2.31471e8	−	3.66614e7i	0.327904	−	0.0519349i	0.00968773	−	0.999953i	$-0.496916\pi$
$163$	2.31471e8	−	3.66614e7i	0.327904	−	0.0519349i	0.318216	+	0.948018i	$0.396916\pi$
$164$	−1.89620e8	−	2.60989e8i	−0.262125	−	0.360784i
$165$	3.35779e6	−	2.30783e7i	0.00453020	−	0.0311363i
$166$	5.25142e7	+	3.81538e7i	0.0691583	+	0.0502465i
$167$	−3.74878e8	+	7.35739e8i	−0.481974	+	0.945928i	0.514127	+	0.857714i	$0.328116\pi$
$167$	−3.74878e8	+	7.35739e8i	−0.481974	+	0.945928i	−0.996102	+	0.0882138i	$0.971884\pi$
$168$	−1.81424e9	+	1.81424e9i	−2.27750	+	2.27750i
$169$	2.06268e8	−	6.70206e7i	0.252863	−	0.0821602i
$170$	1.98849e9	+	6.18515e8i	2.38082	+	0.740550i
$171$	−3.33419e8	+	1.02616e9i	−0.389948	+	1.20014i
$172$	−1.14618e9	+	5.84007e8i	−1.30960	+	0.667274i
$173$	2.74470e7	−	1.73294e8i	0.0306415	−	0.193463i	−0.967619	−	0.252414i	$-0.918776\pi$
$173$	2.74470e7	−	1.73294e8i	0.0306415	−	0.193463i	0.998261	+	0.0589509i	$0.0187755\pi$
$174$		−	9.92622e8i		−	1.08290i
$175$	6.23820e8	+	8.27523e7i	0.665131	+	0.0882323i
$176$	−8.39747e7			−0.0875181
$177$	−1.85652e9	−	2.94044e8i	−1.89150	−	0.299585i
$178$	1.47423e9	+	2.89333e9i	1.46854	+	2.88216i
$179$	6.30424e8	+	2.04837e8i	0.614073	+	0.199525i	0.599507	−	0.800369i	$-0.295363\pi$
$179$	6.30424e8	+	2.04837e8i	0.614073	+	0.199525i	0.0145662	+	0.999894i	$0.495363\pi$
$180$	2.27142e9	+	1.60696e9i	2.16375	+	1.53079i
$181$	2.55828e8	+	7.87359e8i	0.238361	+	0.733598i	0.996658	+	0.0816895i	$0.0260316\pi$
$181$	2.55828e8	+	7.87359e8i	0.238361	+	0.733598i	−0.758297	+	0.651909i	$0.773968\pi$
$182$	−1.13682e9	−	1.13682e9i	−1.03611	−	1.03611i
$183$	3.17047e8	+	1.61544e8i	0.282696	+	0.144041i
$184$	−2.65048e9	+	3.64808e9i	−2.31235	+	3.18268i
$185$	−1.44895e8	+	7.61419e7i	−0.123699	+	0.0650035i
$186$	−6.96616e8	+	5.06121e8i	−0.582025	+	0.422866i
$187$	−5.52577e6	−	3.48883e7i	−0.00451883	−	0.0285308i
$188$	−1.27432e9	+	2.01833e8i	−1.02011	+	0.161570i
$189$	2.97825e7	+	4.09922e7i	0.0233407	+	0.0321258i
$190$	−1.55045e9	−	2.95045e9i	−1.18972	−	2.26399i
$191$	1.61857e9	+	1.17596e9i	1.21618	+	0.883605i	0.995777	−	0.0918040i	$-0.0292633\pi$
$191$	1.61857e9	+	1.17596e9i	1.21618	+	0.883605i	0.220401	+	0.975409i	$0.429263\pi$
$192$	3.54916e9	−	6.96562e9i	2.61168	−	5.12572i
$193$	−2.11445e8	+	2.11445e8i	−0.152394	+	0.152394i	−0.779186	−	0.626792i	$-0.784367\pi$
$193$	−2.11445e8	+	2.11445e8i	−0.152394	+	0.152394i	0.626792	+	0.779186i	$0.284367\pi$
$194$	−2.24514e9	+	7.29490e8i	−1.58503	+	0.515006i
$195$	−1.31460e9	+	1.85818e9i	−0.909193	+	1.28514i
$196$	6.93940e8	−	2.13573e9i	0.470216	−	1.44718i
$197$	2.23809e9	−	1.14037e9i	1.48598	−	0.757145i	0.492411	−	0.870363i	$-0.336116\pi$
$197$	2.23809e9	−	1.14037e9i	1.48598	−	0.757145i	0.993570	+	0.113218i	$0.0361158\pi$
$198$	1.00507e7	−	6.34576e7i	0.00653937	−	0.0412879i
$199$		−	2.38239e9i		−	1.51915i	−0.650421	−	0.759574i	$-0.725407\pi$
$199$		−	2.38239e9i		−	1.51915i	0.650421	−	0.759574i	$-0.274593\pi$
$200$	−5.39846e9	+	9.95050e8i	−3.37404	+	0.621906i
$201$	−3.22696e8			−0.197701
$202$	−5.95006e9	−	9.42397e8i	−3.57368	−	0.566016i
$203$	−2.06257e8	−	4.04803e8i	−0.121458	−	0.238374i
$204$	8.19310e9	+	2.66210e9i	4.73072	+	1.53711i
$205$	−8.45241e7	+	2.71740e8i	−0.0478592	+	0.153864i
$206$	−5.11165e8	−	1.57321e9i	−0.283852	−	0.873608i
$207$	−1.42569e9	−	1.42569e9i	−0.776506	−	0.776506i
$208$	7.30272e9	+	3.72092e9i	3.90150	+	1.98791i
$209$	−3.32308e7	+	4.57383e7i	−0.0174163	+	0.0239715i
$210$	3.50693e9	+	5.10243e8i	1.80322	+	0.262361i
$211$	1.10713e9	−	8.04378e8i	0.558559	−	0.405817i	−0.272372	−	0.962192i	$-0.587808\pi$
$211$	1.10713e9	−	8.04378e8i	0.558559	−	0.405817i	0.830931	+	0.556375i	$0.187808\pi$
$212$	9.34128e8	+	5.89785e9i	0.462448	+	2.91978i
$213$	−4.00833e9	+	6.34858e8i	−1.94736	+	0.308431i
$214$	−2.97254e8	−	4.09135e8i	−0.141733	−	0.195079i
$215$	1.01751e9	+	5.02404e8i	0.476196	+	0.235125i
$216$	−3.57584e8	−	2.59800e8i	−0.164272	−	0.119351i
$217$	−1.78921e8	+	3.51152e8i	−0.0806905	+	0.158364i
$218$	−1.27559e9	+	1.27559e9i	−0.564786	+	0.564786i
$219$	7.67732e8	−	2.49451e8i	0.333759	−	0.108445i
$220$	8.71729e7	+	1.16859e8i	0.0372127	+	0.0498850i
$221$	−1.06536e9	+	3.27885e9i	−0.446610	+	1.37452i
$222$	−8.21321e8	+	4.18484e8i	−0.338143	+	0.172293i
$223$	4.17618e8	−	2.63674e9i	0.168873	−	1.06622i	−0.747021	−	0.664801i	$-0.768516\pi$
$223$	4.17618e8	−	2.63674e9i	0.168873	−	1.06622i	0.915894	−	0.401421i	$-0.131484\pi$
$224$		−	6.96511e9i		−	2.76653i
$225$	−6.18354e7	−	2.45370e9i	−0.0241272	−	0.957397i
$226$	−7.84006e9			−3.00528
$227$	4.33058e9	+	6.85896e8i	1.63096	+	0.258318i	0.903737	−	0.428088i	$-0.140813\pi$
$227$	4.33058e9	+	6.85896e8i	1.63096	+	0.258318i	0.727219	+	0.686406i	$0.240813\pi$
$228$	−6.25966e9	−	1.22853e10i	−2.31639	−	4.54617i
$229$	−5.16111e8	−	1.67695e8i	−0.187673	−	0.0609785i	0.213673	−	0.976905i	$-0.431457\pi$
$229$	−5.16111e8	−	1.67695e8i	−0.187673	−	0.0609785i	−0.401345	+	0.915927i	$0.631457\pi$
$230$	6.22784e9	−	7.84609e7i	2.22549	−	0.0280377i
$231$	−1.85755e7	−	5.71696e7i	−0.00652369	−	0.0200779i
$232$	2.80237e9	+	2.80237e9i	0.967327	+	0.967327i
$233$	1.74618e8	+	8.89724e7i	0.0592469	+	0.0301878i	0.483363	−	0.875420i	$-0.339415\pi$
$233$	1.74618e8	+	8.89724e7i	0.0592469	+	0.0301878i	−0.424116	+	0.905608i	$0.639415\pi$
$234$	−3.68585e9	+	5.07314e9i	−1.22935	+	1.69205i
$235$	8.14873e8	+	7.94596e8i	0.267189	+	0.260540i
$236$	9.50642e9	−	6.90682e9i	3.06457	−	2.22654i
$237$	9.44648e8	+	5.96427e9i	0.299417	+	1.89045i
$238$	5.30156e9	−	8.39684e8i	1.65233	−	0.261703i
$239$	6.75694e8	+	9.30013e8i	0.207090	+	0.285035i	0.899910	−	0.436076i	$-0.143632\pi$
$239$	6.75694e8	+	9.30013e8i	0.207090	+	0.285035i	−0.692820	+	0.721110i	$0.743632\pi$
$240$	−1.78070e10	+	3.05078e9i	−5.36718	+	0.919530i
$241$	1.40524e9	+	1.02097e9i	0.416565	+	0.302652i	0.776254	−	0.630420i	$-0.217117\pi$
$241$	1.40524e9	+	1.02097e9i	0.416565	+	0.302652i	−0.359690	+	0.933072i	$0.617117\pi$
$242$	−3.02078e9	+	5.92861e9i	−0.880759	+	1.72859i
$243$	3.44354e9	−	3.44354e9i	0.987599	−	0.987599i
$244$	−2.11558e9	+	6.87393e8i	−0.596856	+	0.193930i
$245$	−1.87617e9	+	6.35845e8i	−0.520725	+	0.176476i
$246$	−4.95243e8	+	1.52420e9i	−0.135231	+	0.416199i
$247$	4.91653e9	−	2.50509e9i	1.32090	−	0.673033i
$248$	5.37805e8	−	3.39557e9i	0.142173	−	0.897647i
$249$		−	2.36879e8i		−	0.0616211i
$250$	5.56011e9	+	5.15496e9i	1.42339	+	1.31967i
$251$	−6.33332e9			−1.59564			−0.797822	−	0.602893i	$-0.794015\pi$
$251$	−6.33332e9			−1.59564			−0.797822	+	0.602893i	$0.794015\pi$
$252$	7.08344e9	+	1.12191e9i	1.75648	+	0.278198i
$253$	−4.79625e7	−	9.41317e7i	−0.0117063	−	0.0229749i
$254$	−3.78469e9	−	1.22972e9i	−0.909276	−	0.295442i
$255$	−2.43923e9	−	7.19739e9i	−0.576890	−	1.70221i
$256$	4.48003e9	+	1.37881e10i	1.04309	+	3.21029i
$257$	−4.10573e9	−	4.10573e9i	−0.941147	−	0.941147i	0.0572148	−	0.998362i	$-0.481778\pi$
$257$	−4.10573e9	−	4.10573e9i	−0.941147	−	0.941147i	−0.998362	+	0.0572148i	$0.981778\pi$
$258$	5.69408e9	+	2.90128e9i	1.28512	+	0.654803i
$259$	−2.47987e8	+	3.41325e8i	−0.0551100	+	0.0758524i
$260$	−2.40284e9	−	1.40250e10i	−0.525813	−	3.06910i
$261$	−1.43362e9	+	1.04158e9i	−0.308938	+	0.224456i
$262$	7.15370e8	+	4.51667e9i	0.151819	+	0.958546i
$263$	2.07633e9	−	3.28859e8i	0.433984	−	0.0687364i	0.0643797	−	0.997925i	$-0.479493\pi$
$263$	2.07633e9	−	3.28859e8i	0.433984	−	0.0687364i	0.369605	+	0.929189i	$0.379493\pi$
$264$	3.08216e8	+	4.24223e8i	0.0634512	+	0.0873331i
$265$	3.67757e9	−	3.77142e9i	0.745723	−	0.764753i
$266$	−6.95030e9	−	5.04969e9i	−1.38828	−	1.00864i
$267$	5.37988e9	−	1.05586e10i	1.05859	−	2.07760i
$268$	1.42645e9	−	1.42645e9i	0.276515	−	0.276515i
$269$	7.31454e8	−	2.37664e8i	0.139694	−	0.0453894i	−0.238335	−	0.971183i	$-0.576602\pi$
$269$	7.31454e8	−	2.37664e8i	0.139694	−	0.0453894i	0.378030	+	0.925794i	$0.376602\pi$
$270$	7.69074e6	+	6.10452e8i	0.00144715	+	0.114867i
$271$	5.38599e6	−	1.65764e7i	0.000998593	−	0.00307335i	−0.950556	−	0.310553i	$-0.899486\pi$
$271$	5.38599e6	−	1.65764e7i	0.000998593	−	0.00307335i	0.951555	+	0.307480i	$0.0994857\pi$
$272$	−2.43816e10	+	1.24230e10i	−4.45437	+	2.26962i
$273$	−9.17797e8	+	5.79474e9i	−0.165233	+	1.04324i
$274$			5.37914e9i			0.954357i
$275$	3.66485e7	−	1.23278e8i	0.00640804	−	0.0215552i
$276$	2.57654e10			4.44018
$277$	−1.56846e9	−	2.48420e8i	−0.266413	−	0.0421957i	0.0217988	−	0.999762i	$-0.493061\pi$
$277$	−1.56846e9	−	2.48420e8i	−0.266413	−	0.0421957i	−0.288212	+	0.957567i	$0.593061\pi$
$278$	1.16012e9	+	2.27686e9i	0.194233	+	0.381204i
$279$	1.46195e9	+	4.75018e8i	0.241278	+	0.0783959i
$280$	−1.13413e10	+	8.46023e9i	−1.84514	+	1.37642i
$281$	5.45346e8	+	1.67840e9i	0.0874675	+	0.269197i	0.985218	−	0.171308i	$-0.0547993\pi$
$281$	5.45346e8	+	1.67840e9i	0.0874675	+	0.269197i	−0.897750	+	0.440505i	$0.854799\pi$
$282$	4.53227e9	+	4.53227e9i	0.716670	+	0.716670i
$283$	−7.18500e9	−	3.66094e9i	−1.12016	−	0.570751i	−0.206998	−	0.978341i	$-0.566369\pi$
$283$	−7.18500e9	−	3.66094e9i	−1.12016	−	0.570751i	−0.913165	+	0.407590i	$0.866369\pi$
$284$	1.49122e10	−	2.05249e10i	2.29228	−	3.15506i
$285$	−5.38500e9	+	1.09062e10i	−0.816218	+	1.65308i
$286$	−2.65822e8	+	1.93131e8i	−0.0397307	+	0.0288661i
$287$	1.14748e8	+	7.24493e8i	0.0169129	+	0.106784i
$288$	−2.68325e10	+	4.24985e9i	−3.90024	+	0.617737i
$289$	−2.66543e9	−	3.66865e9i	−0.382099	−	0.525914i
$290$	7.88146e8	−	5.41697e9i	0.111433	−	0.765887i
$291$	6.96951e9	+	5.06365e9i	0.971920	+	0.706141i
$292$	−2.29102e9	+	4.49639e9i	−0.315136	+	0.618489i
$293$	−8.37831e9	+	8.37831e9i	−1.13681	+	1.13681i	−0.147786	+	0.989019i	$0.547215\pi$
$293$	−8.37831e9	+	8.37831e9i	−1.13681	+	1.13681i	−0.989019	+	0.147786i	$0.952785\pi$
$294$	−1.06100e10	+	3.44741e9i	−1.42013	+	0.461427i
$295$	−9.89801e9	−	3.07876e9i	−1.30695	−	0.406525i
$296$	1.13729e9	−	3.50022e9i	0.148151	−	0.455961i
$297$	9.22679e6	−	4.70128e6i	0.00118584	−	0.000604214i
$298$	2.88697e9	−	1.82276e10i	0.366081	−	2.31135i
$299$			1.03112e10i			1.29011i
$300$	2.27306e10	+	2.16131e10i	2.80625	+	2.66829i
$301$	2.92497e9			0.356332
$302$	7.18567e9	+	1.13810e9i	0.863853	+	0.136821i
$303$	9.98059e9	+	1.95880e10i	1.18409	+	2.32391i
$304$	4.16533e10	+	1.35340e10i	4.87703	+	1.58464i
$305$	1.60194e9	+	1.13332e9i	0.185117	+	0.130964i
$306$	−6.46962e9	−	1.99115e10i	−0.737893	−	2.27100i
$307$	−6.24264e9	−	6.24264e9i	−0.702773	−	0.702773i	0.262232	−	0.965005i	$-0.415541\pi$
$307$	−6.24264e9	−	6.24264e9i	−0.702773	−	0.702773i	−0.965005	+	0.262232i	$0.915541\pi$
$308$	3.34826e8	+	1.70602e8i	0.0372063	+	0.0189575i
$309$	−3.54818e9	+	4.88365e9i	−0.389199	+	0.535687i
$310$	−4.20346e9	+	2.20891e9i	−0.455156	+	0.239183i
$311$	8.26059e9	−	6.00167e9i	0.883018	−	0.641550i	−0.0510304	−	0.998697i	$-0.516251\pi$
$311$	8.26059e9	−	6.00167e9i	0.883018	−	0.641550i	0.934048	+	0.357147i	$0.116251\pi$
$312$	−8.00617e9	−	5.05489e10i	−0.844902	−	5.33450i
$313$	1.92024e9	−	3.04136e8i	0.200068	−	0.0316877i	−0.0555959	−	0.998453i	$-0.517706\pi$
$313$	1.92024e9	−	3.04136e8i	0.200068	−	0.0316877i	0.255664	+	0.966766i	$0.417706\pi$
$314$	−1.49121e10	−	2.05247e10i	−1.53398	−	2.11134i
$315$	−2.94298e9	−	5.60037e9i	−0.298913	−	0.568820i
$316$	−3.05404e10	−	2.21889e10i	−3.06285	−	2.22529i
$317$	−7.64523e9	+	1.50046e10i	−0.757101	+	1.48589i	0.113306	+	0.993560i	$0.463856\pi$
$317$	−7.64523e9	+	1.50046e10i	−0.757101	+	1.48589i	−0.870407	+	0.492334i	$0.836144\pi$
$318$	2.09764e10	−	2.09764e10i	2.05126	−	2.05126i
$319$	−8.83070e7	+	2.86927e7i	−0.00852771	+	0.00277082i
$320$	2.48994e10	−	3.51950e10i	2.37459	−	3.35646i
$321$	−5.70294e8	+	1.75519e9i	−0.0537129	+	0.165311i
$322$	1.43041e10	−	7.28829e9i	1.33056	−	0.677957i
$323$	−2.88196e9	+	1.81959e10i	−0.264775	+	1.67172i
$324$			3.17339e10i			2.87968i
$325$	−8.64951e9	+	9.09673e9i	−0.775279	+	0.815364i
$326$	7.27825e9			0.644402
$327$	6.50209e9	+	1.02983e9i	0.568672	+	0.0900688i
$328$	−2.90495e9	−	5.70129e9i	−0.250982	−	0.492581i
$329$	2.79007e9	+	9.06549e8i	0.238140	+	0.0773763i
$330$	2.15117e8	−	6.91589e8i	0.0181393	−	0.0583166i
$331$	−6.61388e9	−	2.03554e10i	−0.550991	−	1.69577i	−0.706303	−	0.707910i	$-0.749638\pi$
$331$	−6.61388e9	−	2.03554e10i	−0.550991	−	1.69577i	0.155312	−	0.987865i	$-0.450362\pi$
$332$	1.04711e9	+	1.04711e9i	0.0861864	+	0.0861864i
$333$	1.46624e9	+	7.47086e8i	0.119242	+	0.0607566i
$334$	−1.50734e10	+	2.07468e10i	−1.21123	+	1.66711i
$335$	−1.76103e9	−	2.56222e8i	−0.139826	−	0.0203441i
$336$	−3.76736e10	+	2.73715e10i	−2.95584	+	2.14754i
$337$	−1.60051e9	−	1.01052e10i	−0.124090	−	0.783476i	−0.968726	−	0.248134i	$-0.920183\pi$
$337$	−1.60051e9	−	1.01052e10i	−0.124090	−	0.783476i	0.844635	−	0.535342i	$-0.179817\pi$
$338$	6.65267e9	−	1.05368e9i	0.509717	−	0.0807313i
$339$	1.68169e10	+	2.31465e10i	1.27335	+	1.75261i
$340$	4.25980e10	+	2.10331e10i	3.18767	+	1.57394i
$341$	6.51627e7	+	4.73434e7i	0.00481927	+	0.00350141i
$342$	−1.52127e10	+	2.98565e10i	−1.11199	+	2.18240i
$343$	−1.01774e10	+	1.01774e10i	−0.735292	+	0.735292i
$344$	−2.42664e10	+	7.88463e9i	−1.73289	+	0.563051i
$345$	−1.35903e10	−	1.82184e10i	−0.959298	−	1.28598i
$346$	1.68382e9	−	5.18226e9i	0.117487	−	0.361588i
$347$	1.46821e10	−	7.48092e9i	1.01268	−	0.515985i	0.132779	−	0.991146i	$-0.457610\pi$
$347$	1.46821e10	−	7.48092e9i	1.01268	−	0.515985i	0.879899	+	0.475160i	$0.157610\pi$
$348$	3.54245e9	−	2.23661e10i	0.241538	−	1.52501i
$349$		−	2.51806e10i		−	1.69732i	−0.528939	−	0.848660i	$-0.677410\pi$
$349$		−	2.51806e10i		−	1.69732i	0.528939	−	0.848660i	$-0.322590\pi$
$350$	1.87330e10	+	5.56903e9i	1.24835	+	0.371114i
$351$	−1.01071e9			−0.0665881
$352$	−1.40597e9	−	2.22683e8i	−0.0915807	−	0.0145050i
$353$	−4.62768e9	−	9.08234e9i	−0.298033	−	0.584923i	0.692624	−	0.721299i	$-0.256455\pi$
$353$	−4.62768e9	−	9.08234e9i	−0.298033	−	0.584923i	−0.990657	+	0.136376i	$0.956455\pi$
$354$	−5.55184e10	−	1.80390e10i	−3.53528	−	1.14868i
$355$	−2.23785e10	+	2.81934e8i	−1.40902	+	0.0177515i
$356$	2.28922e10	+	7.04549e10i	1.42524	+	4.38643i
$357$	−1.38509e10	−	1.38509e10i	−0.852715	−	0.852715i
$358$	1.83424e10	+	9.34594e9i	1.11667	+	0.568972i
$359$	8.02580e9	−	1.10466e10i	0.483182	−	0.665042i	−0.495931	−	0.868362i	$-0.665173\pi$
$359$	8.02580e9	−	1.10466e10i	0.483182	−	0.665042i	0.979112	+	0.203320i	$0.0651731\pi$
$360$	3.95123e10	+	3.85291e10i	2.35246	+	2.29393i
$361$	1.01147e10	−	7.34879e9i	0.595560	−	0.432700i
$362$	4.02206e9	+	2.53943e10i	0.234215	+	1.47878i
$363$	2.39828e10	−	3.79850e9i	1.38125	−	0.218769i
$364$	−2.15582e10	−	2.96723e10i	−1.22802	−	1.69023i
$365$	4.38777e9	−	7.51733e8i	0.247213	−	0.0423538i
$366$	8.94028e9	+	6.49549e9i	0.498226	+	0.361983i
$367$	5.31449e9	−	1.04303e10i	0.292953	−	0.574952i	−0.696880	−	0.717188i	$-0.745429\pi$
$367$	5.31449e9	−	1.04303e10i	0.292953	−	0.574952i	0.989833	+	0.142235i	$0.0454290\pi$
$368$	−5.78710e10	+	5.78710e10i	−3.15551	+	3.15551i
$369$	2.72103e9	−	8.84117e8i	0.146767	−	0.0476875i
$370$	−4.81442e9	+	1.63163e9i	−0.256884	+	0.0870594i
$371$	4.19572e9	−	1.29131e10i	0.221468	−	0.681607i
$372$	−1.75027e10	+	8.91805e9i	−0.913971	+	0.465691i
$373$	−3.12447e9	+	1.97271e10i	−0.161414	+	1.01913i	0.765386	+	0.643572i	$0.222548\pi$
$373$	−3.12447e9	+	1.97271e10i	−0.161414	+	1.01913i	−0.926800	+	0.375556i	$0.877452\pi$
$374$		−	1.09701e9i		−	0.0560691i
$375$	3.29275e9	−	2.74727e10i	0.166507	−	1.38924i
$376$	−2.55910e10			−1.28037
$377$	8.95085e9	+	1.41768e9i	0.443097	+	0.0701797i
$378$	7.14398e8	+	1.40208e9i	0.0349923	+	0.0686763i
$379$	8.49145e9	+	2.75904e9i	0.411552	+	0.133721i	0.507473	−	0.861667i	$-0.330580\pi$
$379$	8.49145e9	+	2.75904e9i	0.411552	+	0.133721i	−0.0959209	+	0.995389i	$0.530580\pi$
$380$	−2.44059e10	−	7.20139e10i	−1.17047	−	3.45368i
$381$	4.48761e9	+	1.38114e10i	0.212968	+	0.655449i
$382$	4.39348e10	+	4.39348e10i	2.06326	+	2.06326i
$383$	1.03695e10	+	5.28354e9i	0.481908	+	0.245544i	0.678029	−	0.735035i	$-0.262834\pi$
$383$	1.03695e10	+	5.28354e9i	0.481908	+	0.245544i	−0.196121	+	0.980580i	$0.562834\pi$
$384$	6.89755e10	−	9.49366e10i	3.17227	−	4.36625i
$385$	−5.59782e7	−	3.26737e8i	−0.00254786	−	0.0148715i
$386$	−7.51311e9	+	5.45859e9i	−0.338431	+	0.245885i
$387$	−1.78471e9	−	1.12682e10i	−0.0795651	−	0.502354i
$388$	−5.31917e10	+	8.42474e9i	−2.34702	+	0.371732i
$389$	1.19940e10	+	1.65083e10i	0.523800	+	0.720949i	0.986170	−	0.165738i	$-0.0530006\pi$
$389$	1.19940e10	+	1.65083e10i	0.523800	+	0.720949i	−0.462369	+	0.886687i	$0.653001\pi$
$390$	−4.93517e10	+	5.06110e10i	−2.13326	+	2.18770i
$391$	−2.78513e10	−	2.02351e10i	−1.19162	−	0.865764i
$392$	2.02215e10	−	3.96870e10i	0.856386	−	1.68075i
$393$	1.18002e10	−	1.18002e10i	0.494676	−	0.494676i
$394$	7.41914e10	−	2.41063e10i	3.07871	−	1.00033i
$395$	4.19509e8	+	3.32985e10i	0.0172327	+	1.36784i
$396$	4.52933e8	−	1.39398e9i	0.0184184	−	0.0566861i
$397$	2.64185e10	−	1.34609e10i	1.06352	−	0.541891i	0.167487	−	0.985874i	$-0.446435\pi$
$397$	2.64185e10	−	1.34609e10i	1.06352	−	0.541891i	0.896035	+	0.443983i	$0.146435\pi$
$398$	1.15743e10	−	7.30773e10i	0.461278	−	2.91240i
$399$			3.13512e10i			1.23698i
$400$	−9.95994e10	+	2.50999e9i	−3.89060	+	0.0980465i
$401$	1.84736e10			0.714454			0.357227	−	0.934018i	$-0.383722\pi$
$401$	1.84736e10			0.714454			0.357227	+	0.934018i	$0.383722\pi$
$402$	−9.89837e9	−	1.56775e9i	−0.379018	−	0.0600305i
$403$	−3.56897e9	−	7.00450e9i	−0.135308	−	0.265557i
$404$	−1.30706e11	−	4.24689e10i	−4.90647	−	1.59421i
$405$	2.24386e10	−	1.67385e10i	0.834019	−	0.622152i
$406$	−4.36008e9	−	1.34190e10i	−0.160469	−	0.493872i
$407$	6.09709e7	+	6.09709e7i	0.00222200	+	0.00222200i
$408$	1.52248e11	+	7.75740e10i	5.49427	+	2.79947i
$409$	7.67476e9	−	1.05634e10i	0.274266	−	0.377495i	−0.649558	−	0.760312i	$-0.725046\pi$
$409$	7.67476e9	−	1.05634e10i	0.274266	−	0.377495i	0.923824	+	0.382817i	$0.125046\pi$
$410$	−3.91288e9	+	7.92470e9i	−0.138472	+	0.280445i
$411$	1.58810e10	−	1.15382e10i	0.556559	−	0.404364i
$412$	−5.90335e9	−	3.72723e10i	−0.204885	−	1.29359i
$413$	−2.63894e10	+	4.17966e9i	−0.907045	+	0.143662i
$414$	−3.68053e10	−	5.06581e10i	−1.25288	−	1.72444i
$415$	1.88083e8	−	1.29271e9i	0.00634100	−	0.0435821i
$416$	1.12400e11	+	8.16637e10i	3.75314	+	2.72681i
$417$	4.23360e9	−	8.30891e9i	0.140012	−	0.274789i
$418$	−1.24153e9	+	1.24153e9i	−0.0406679	+	0.0406679i
$419$	−3.46732e10	+	1.12660e10i	−1.12496	+	0.365522i	−0.811659	−	0.584131i	$-0.801435\pi$
$419$	−3.46732e10	+	1.12660e10i	−1.12496	+	0.365522i	−0.313303	+	0.949653i	$0.601435\pi$
$420$	7.71985e10	+	2.40124e10i	2.48091	+	0.771683i
$421$	−1.33229e10	+	4.10037e10i	−0.424102	+	1.30525i	0.479749	+	0.877406i	$0.340728\pi$
$421$	−1.33229e10	+	4.10037e10i	−0.424102	+	1.30525i	−0.903851	+	0.427847i	$0.859272\pi$
$422$	3.78680e10	−	1.92947e10i	1.19405	−	0.608399i
$423$	1.79001e9	−	1.13017e10i	0.0559105	−	0.353005i
$424$			1.18441e11i			3.66470i
$425$	−7.59672e9	−	4.12146e10i	−0.232847	−	1.26327i
$426$	−1.26036e11			−3.82698
$427$	4.99565e9	+	7.91233e8i	0.150273	+	0.0238009i
$428$	−5.23772e9	−	1.02796e10i	−0.156087	−	0.306339i
$429$	1.14037e9	+	3.70530e8i	0.0336681	+	0.0109394i
$430$	2.87703e10	+	2.03541e10i	0.841532	+	0.595357i
$431$	7.34000e9	+	2.25902e10i	0.212710	+	0.654653i	0.999308	+	0.0371883i	$0.0118401\pi$
$431$	7.34000e9	+	2.25902e10i	0.212710	+	0.654653i	−0.786599	+	0.617465i	$0.788160\pi$
$432$	−5.67252e9	−	5.67252e9i	−0.162870	−	0.162870i
$433$	−5.04964e10	−	2.57292e10i	−1.43651	−	0.731938i	−0.449603	−	0.893229i	$-0.648434\pi$
$433$	−5.04964e10	−	2.57292e10i	−1.43651	−	0.731938i	−0.986907	+	0.161290i	$0.948434\pi$
$434$	−7.19422e9	+	9.90199e9i	−0.202780	+	0.279102i
$435$	−1.76833e10	+	9.29252e9i	−0.493863	+	0.259523i
$436$	−3.32943e10	+	2.41897e10i	−0.921348	+	0.669399i
$437$	8.61950e9	+	5.44214e10i	0.236350	+	1.49226i
$438$	2.47613e10	−	3.92181e9i	0.672786	−	0.106559i
$439$	2.34780e10	+	3.23147e10i	0.632125	+	0.870045i	0.998165	−	0.0605540i	$-0.0192867\pi$
$439$	2.34780e10	+	3.23147e10i	0.632125	+	0.870045i	−0.366040	+	0.930599i	$0.619287\pi$
$440$	1.34517e9	+	2.55981e9i	0.0358895	+	0.0682964i
$441$	1.61124e10	+	1.17063e10i	0.425996	+	0.309504i
$442$	−4.86085e10	+	9.53996e10i	−1.27357	+	2.49952i
$443$	−5.60105e9	+	5.60105e9i	−0.145430	+	0.145430i	−0.776073	−	0.630643i	$-0.782791\pi$
$443$	−5.60105e9	+	5.60105e9i	−0.145430	+	0.145430i	0.630643	+	0.776073i	$0.282791\pi$
$444$	−1.99998e10	+	6.49833e9i	−0.514628	+	0.167213i
$445$	3.77429e10	−	5.33492e10i	0.962487	−	1.36047i
$446$	2.56200e10	−	7.88504e10i	0.647501	−	1.99280i
$447$	−6.00066e10	+	3.05749e10i	−1.50303	+	0.765834i
$448$	1.73836e10	−	1.09756e11i	0.431547	−	2.72468i
$449$		−	5.94134e10i		−	1.46184i	−0.682465	−	0.730918i	$-0.739092\pi$
$449$		−	5.94134e10i		−	1.46184i	0.682465	−	0.730918i	$-0.260908\pi$
$450$	1.00240e10	−	7.55653e10i	0.244452	−	1.84278i
$451$	1.49914e8			0.00362355
$452$	−1.76655e11	−	2.79794e10i	−4.23226	−	0.670325i
$453$	−1.20532e10	−	2.36557e10i	−0.286226	−	0.561751i
$454$	1.29504e11	+	4.20783e10i	3.04831	+	0.990455i
$455$	−9.60969e9	+	3.08946e10i	−0.224215	+	0.720836i
$456$	−8.45111e10	−	2.60099e11i	−1.95458	−	6.01559i
$457$	4.58749e10	+	4.58749e10i	1.05174	+	1.05174i	0.998586	+	0.0531575i	$0.0169285\pi$
$457$	4.58749e10	+	4.58749e10i	1.05174	+	1.05174i	0.0531575	+	0.998586i	$0.483071\pi$
$458$	−1.50165e10	−	7.65127e9i	−0.341276	−	0.173889i
$459$	1.98345e9	−	2.72998e9i	0.0446859	−	0.0615048i
$460$	1.40608e11	+	2.04579e10i	3.14035	+	0.456908i
$461$	−3.77234e10	+	2.74076e10i	−0.835231	+	0.606831i	−0.921034	−	0.389481i	$-0.872654\pi$
$461$	−3.77234e10	+	2.74076e10i	−0.835231	+	0.606831i	0.0858034	+	0.996312i	$0.472654\pi$
$462$	−2.92039e8	−	1.84386e9i	−0.00641023	−	0.0404726i
$463$	5.15084e10	−	8.15813e9i	1.12087	−	0.177528i	0.431621	−	0.902055i	$-0.357942\pi$
$463$	5.15084e10	−	8.15813e9i	1.12087	−	0.177528i	0.689246	+	0.724527i	$0.257942\pi$
$464$	4.22794e10	+	5.81926e10i	0.912130	+	1.25544i
$465$	1.55379e10	+	7.67193e9i	0.332337	+	0.164094i
$466$	4.92398e9	+	3.57748e9i	0.104417	+	0.0758636i
$467$	3.23782e10	−	6.35457e10i	0.680745	−	1.33604i	−0.249240	−	0.968442i	$-0.580181\pi$
$467$	3.23782e10	−	6.35457e10i	0.680745	−	1.33604i	0.929986	−	0.367596i	$-0.119819\pi$
$468$	−1.01156e11	+	1.01156e11i	−2.10867	+	2.10867i
$469$	−4.36243e9	+	1.41744e9i	−0.0901649	+	0.0292964i
$470$	2.11350e10	+	2.83323e10i	0.433123	+	0.580618i
$471$	−2.86095e10	+	8.80509e10i	−0.581335	+	1.78916i
$472$	2.07667e11	−	1.05812e11i	4.18408	−	2.13189i
$473$	9.35147e7	−	5.90429e8i	0.00186825	−	0.0117957i
$474$			1.87537e11i			3.71513i
$475$	−3.80468e10	+	5.52418e10i	−0.747383	+	1.08516i
$476$	1.22453e11			2.38530
$477$	−5.23066e10	−	8.28455e9i	−1.01038	−	0.160028i
$478$	1.62080e10	+	3.18099e10i	0.310468	+	0.609328i
$479$	−3.75859e10	−	1.22124e10i	−0.713975	−	0.231985i	−0.0705662	−	0.997507i	$-0.522481\pi$
$479$	−3.75859e10	−	1.22124e10i	−0.713975	−	0.231985i	−0.643409	+	0.765522i	$0.722481\pi$
$480$	−3.06228e11	+	3.85799e9i	−5.76873	+	0.0726769i
$481$	−2.60061e9	−	8.00385e9i	−0.0485842	−	0.149527i
$482$	3.81442e10	+	3.81442e10i	0.706708	+	0.706708i
$483$	−5.21996e10	−	2.65970e10i	−0.959133	−	0.488703i
$484$	−8.92232e10	+	1.22805e11i	−1.62591	+	2.23787i
$485$	3.40137e10	+	3.31674e10i	0.614734	+	0.599438i
$486$	1.22357e11	−	8.88975e10i	2.19323	−	1.59347i
$487$	−5.76481e9	−	3.63976e10i	−0.102487	−	0.647078i	−0.984437	−	0.175736i	$-0.943770\pi$
$487$	−5.76481e9	−	3.63976e10i	−0.102487	−	0.647078i	0.881950	−	0.471342i	$-0.156230\pi$
$488$	−4.35783e10	+	6.90212e9i	−0.768406	+	0.121704i
$489$	−1.56118e10	−	2.14878e10i	−0.273035	−	0.375801i
$490$	−6.06387e10	+	1.03889e10i	−1.05188	+	0.180213i
$491$	−5.65233e10	−	4.10665e10i	−0.972526	−	0.706581i	−0.0165001	−	0.999864i	$-0.505252\pi$
$491$	−5.65233e10	−	4.10665e10i	−0.972526	−	0.706581i	−0.956026	+	0.293282i	$0.905252\pi$
$492$	−1.65985e10	+	3.25764e10i	−0.283276	+	0.555960i
$493$	−2.13947e10	+	2.13947e10i	−0.362175	+	0.362175i
$494$	1.62980e11	−	5.29554e10i	2.73669	−	0.889206i
$495$	−1.22457e9	+	4.15014e8i	−0.0203969	+	0.00691261i
$496$	1.92817e10	−	5.93429e10i	0.318580	−	0.980487i
$497$	−5.13989e10	+	2.61890e10i	−0.842419	+	0.429234i
$498$	1.15083e9	−	7.26603e9i	0.0187108	−	0.118135i
$499$		−	8.64975e10i		−	1.39509i	−0.716542	−	0.697544i	$-0.754276\pi$
$499$		−	8.64975e10i		−	1.39509i	0.716542	−	0.697544i	$-0.245724\pi$
$500$	1.06886e11	+	1.35996e11i	1.71017	+	2.17594i
$501$	9.35839e10			1.48542
$502$	−1.94268e11	−	3.07690e10i	−3.05905	−	0.484506i
$503$	3.20902e10	+	6.29806e10i	0.501303	+	0.983863i	0.993549	+	0.113407i	$0.0361763\pi$
$503$	3.20902e10	+	6.29806e10i	0.501303	+	0.983863i	−0.492245	+	0.870457i	$0.663824\pi$
$504$	1.35288e11	+	4.39576e10i	2.09670	+	0.681259i
$505$	3.89135e10	+	1.14821e11i	0.598322	+	1.76545i
$506$	−1.01388e9	−	3.12041e9i	−0.0154663	−	0.0476003i
$507$	−1.73808e10	−	1.73808e10i	−0.263049	−	0.263049i
$508$	−8.08895e10	−	4.12153e10i	−1.21461	−	0.618876i
$509$	6.18549e10	−	8.51359e10i	0.921516	−	1.26836i	−0.0415627	−	0.999136i	$-0.513234\pi$
$509$	6.18549e10	−	8.51359e10i	0.921516	−	1.26836i	0.963078	−	0.269222i	$-0.0867664\pi$
$510$	−3.98541e10	−	2.32623e11i	−0.589104	−	3.43852i
$511$	9.28304e9	−	6.74452e9i	0.136146	−	0.0989162i
$512$	2.89679e10	+	1.82896e11i	0.421539	+	2.66149i
$513$	−5.33439e9	+	8.44884e8i	−0.0770220	+	0.0121991i
$514$	−1.05992e11	−	1.45886e11i	−1.51852	−	2.09007i
$515$	−2.32409e10	+	2.38340e10i	−0.330388	+	0.338819i
$516$	1.17947e11	+	8.56936e10i	1.66375	+	1.20879i
$517$	2.72196e8	−	5.34216e8i	0.00380996	−	0.00747746i
$518$	−9.26501e9	+	9.26501e9i	−0.128685	+	0.128685i
$519$	−1.89115e10	+	6.14473e9i	−0.260650	+	0.0846903i
$520$	−3.55546e9	−	2.82215e11i	−0.0486275	−	3.85981i
$521$	−1.76019e10	+	5.41732e10i	−0.238896	+	0.735247i	0.757684	+	0.652621i	$0.226331\pi$
$521$	−1.76019e10	+	5.41732e10i	−0.238896	+	0.735247i	−0.996581	+	0.0826260i	$0.973669\pi$
$522$	−4.90350e10	+	2.49846e10i	−0.660426	+	0.336504i
$523$	8.00812e9	−	5.05613e10i	0.107035	−	0.675790i	−0.874575	−	0.484890i	$-0.838860\pi$
$523$	8.00812e9	−	5.05613e10i	0.107035	−	0.675790i	0.981610	−	0.190899i	$-0.0611404\pi$
$524$			1.04324e11i			1.38376i
$525$	−2.37406e10	−	6.72517e10i	−0.312503	−	0.885250i
$526$	6.52871e10			0.852873
$527$	2.59235e10	+	4.10588e9i	0.336087	+	0.0532309i
$528$	4.32069e9	+	8.47984e9i	0.0555927	+	0.109107i
$529$	−2.34458e10	−	7.61800e9i	−0.299394	−	0.0972789i
$530$	1.31128e11	−	9.78177e10i	1.66185	−	1.23969i
$531$	3.22036e10	+	9.91125e10i	0.405066	+	1.24667i
$532$	−1.38586e11	−	1.38586e11i	−1.73010	−	1.73010i
$533$	−1.30370e10	−	6.64267e9i	−0.161536	−	0.0823065i
$534$	2.16319e11	−	2.97737e11i	2.66029	−	3.66158i
$535$	−4.50586e9	+	9.12565e9i	−0.0550000	+	0.111391i
$536$	3.23711e10	−	2.35190e10i	0.392192	−	0.284944i
$537$	−1.17521e10	−	7.42001e10i	−0.141325	−	0.892292i
$538$	2.35913e10	−	3.73649e9i	0.281593	−	0.0446000i
$539$	6.13387e8	+	8.44254e8i	0.00726740	+	0.0100027i
$540$	−2.00528e9	+	1.37824e10i	−0.0235830	+	0.162088i
$541$	3.97770e10	+	2.88997e10i	0.464348	+	0.337368i	0.795234	−	0.606302i	$-0.207348\pi$
$541$	3.97770e10	+	2.88997e10i	0.464348	+	0.337368i	−0.330887	+	0.943670i	$0.607348\pi$
$542$	2.45743e8	−	4.82297e8i	0.00284763	−	0.00558878i
$543$	6.63452e10	−	6.63452e10i	0.763151	−	0.763151i
$544$	−4.41158e11	+	1.43341e11i	−5.03730	+	1.63672i
$545$	3.46658e10	+	1.07827e10i	0.392930	+	0.122220i
$546$	−5.63050e10	+	1.73289e11i	−0.633543	+	1.94985i
$547$	−1.39626e11	+	7.11429e10i	−1.55961	+	0.794662i	−0.999432	−	0.0337095i	$-0.989268\pi$
$547$	−1.39626e11	+	7.11429e10i	−1.55961	+	0.794662i	−0.560180	+	0.828371i	$0.689268\pi$
$548$	−1.91970e10	+	1.21205e11i	−0.212868	+	1.34400i
$549$		−	1.97281e10i		−	0.217168i
$550$	1.72307e9	−	3.60336e9i	0.0188301	−	0.0393783i
$551$	4.84266e10			0.525385
$552$	5.04759e11	+	7.99460e10i	5.43661	+	0.861074i
$553$	3.89685e10	+	7.64799e10i	0.416690	+	0.817800i
$554$	−4.69041e10	−	1.52401e10i	−0.497934	−	0.161789i
$555$	1.51441e10	+	1.07139e10i	0.159614	+	0.112922i
$556$	1.80146e10	+	5.54433e10i	0.188506	+	0.580162i
$557$	2.61931e9	+	2.61931e9i	0.0272124	+	0.0272124i	0.720582	−	0.693370i	$-0.243875\pi$
$557$	2.61931e9	+	2.61931e9i	0.0272124	+	0.0272124i	−0.693370	+	0.720582i	$0.743875\pi$
$558$	4.25362e10	+	2.16733e10i	0.438755	+	0.223557i
$559$	−3.42943e10	+	4.72020e10i	−0.351216	+	0.483408i
$560$	−2.27327e11	+	1.19460e11i	−2.31153	+	1.21470i
$561$	−3.23874e9	+	2.35308e9i	−0.0326982	+	0.0237567i
$562$	8.57378e9	+	5.41327e10i	0.0859463	+	0.542643i
$563$	−8.33142e10	+	1.31957e10i	−0.829250	+	0.131340i	−0.556608	−	0.830775i	$-0.687897\pi$
$563$	−8.33142e10	+	1.31957e10i	−0.829250	+	0.131340i	−0.272642	+	0.962116i	$0.587897\pi$
$564$	8.59481e10	+	1.18297e11i	0.849415	+	1.16912i
$565$	7.33955e10	+	1.39669e11i	0.720237	+	1.37058i
$566$	−2.02607e11	−	1.47202e11i	−1.97419	−	1.43433i
$567$	3.27582e10	−	6.42916e10i	0.316948	−	0.622045i
$568$	3.55824e11	−	3.55824e11i	3.41855	−	3.41855i
$569$	5.94283e10	−	1.93094e10i	0.566949	−	0.184213i	−0.0114965	−	0.999934i	$-0.503660\pi$
$569$	5.94283e10	−	1.93094e10i	0.566949	−	0.184213i	0.578446	+	0.815721i	$0.303660\pi$
$570$	−2.18165e11	+	3.08374e11i	−2.06674	+	2.92131i
$571$	3.84533e10	−	1.18347e11i	0.361734	−	1.11330i	−0.590267	−	0.807208i	$-0.700978\pi$
$571$	3.84533e10	−	1.18347e11i	0.361734	−	1.11330i	0.952001	−	0.306095i	$-0.0990224\pi$
$572$	−6.67884e9	+	3.40304e9i	−0.0623903	+	0.0317894i
$573$	3.54702e10	−	2.23950e11i	0.329037	−	2.07746i
$574$			2.27806e10i			0.209854i
$575$	−5.97002e10	−	1.10213e11i	−0.546141	−	1.00823i
$576$	−4.33432e11			−3.93759
$577$	1.29771e11	+	2.05537e10i	1.17078	+	0.185433i	0.711386	−	0.702801i	$-0.248068\pi$
$577$	1.29771e11	+	2.05537e10i	1.17078	+	0.185433i	0.459391	+	0.888234i	$0.348068\pi$
$578$	−6.39360e10	−	1.25482e11i	−0.572841	−	1.12426i
$579$	3.22312e10	+	1.04725e10i	0.286789	+	0.0931833i
$580$	3.70908e10	−	1.19245e11i	0.327759	−	1.05372i
$581$	−1.04049e9	−	3.20230e9i	−0.00913132	−	0.0281033i
$582$	1.89182e11	+	1.89182e11i	1.64888	+	1.64888i
$583$	−2.47247e9	−	1.25979e9i	−0.0214021	−	0.0109049i
$584$	−5.88341e10	+	8.09782e10i	−0.505798	+	0.696172i
$585$	1.24882e11	+	1.81698e10i	1.06629	+	0.155141i
$586$	−2.97700e11	+	2.16292e11i	−2.52458	+	1.83421i
$587$	3.17886e10	+	2.00705e11i	0.267744	+	1.69047i	0.644860	+	0.764301i	$0.276916\pi$
$587$	3.17886e10	+	2.00705e11i	0.267744	+	1.69047i	−0.377117	+	0.926166i	$0.623084\pi$
$588$	−2.51372e11	+	3.98135e10i	−2.10285	+	0.333059i
$589$	−2.46919e10	−	3.39855e10i	−0.205160	−	0.282379i
$590$	−2.88654e11	−	1.42525e11i	−2.38215	−	1.17621i
$591$	−2.30310e11	−	1.67330e11i	−1.88783	−	1.37159i
$592$	3.03253e10	−	5.95168e10i	0.246898	−	0.484565i
$593$	−1.45101e10	+	1.45101e10i	−0.117341	+	0.117341i	−0.763339	−	0.645998i	$-0.776441\pi$
$593$	−1.45101e10	+	1.45101e10i	−0.117341	+	0.117341i	0.645998	+	0.763339i	$0.276441\pi$
$594$	3.05863e8	−	9.93808e7i	0.00245686	−	0.000798282i
$595$	−6.45898e10	−	8.65851e10i	−0.515343	−	0.690836i
$596$	1.30101e11	−	4.00409e11i	1.03109	−	3.17335i
$597$	−2.40576e11	+	1.22579e11i	−1.89389	+	0.964984i
$598$	−5.00948e10	+	3.16286e11i	−0.391731	+	2.47329i
$599$		−	6.37690e9i		−	0.0495339i	−0.999693	−	0.0247669i	$-0.992116\pi$
$599$		−	6.37690e9i		−	0.0495339i	0.999693	−	0.0247669i	$-0.00788437\pi$
$600$	3.78244e11	+	4.93944e11i	2.91855	+	3.81129i
$601$	−2.80720e9			−0.0215167			−0.0107584	−	0.999942i	$-0.503425\pi$
$601$	−2.80720e9			−0.0215167			−0.0107584	+	0.999942i	$0.503425\pi$
$602$	8.97204e10	+	1.42103e10i	0.683133	+	0.108198i
$603$	8.12236e9	+	1.59410e10i	0.0614346	+	0.120572i
$604$	1.57849e11	+	5.12882e10i	1.18602	+	0.385362i
$605$	1.33896e11	−	1.68688e9i	0.999415	−	0.0125911i
$606$	2.10980e11	+	6.49331e11i	1.56441	+	4.81477i
$607$	3.42615e10	+	3.42615e10i	0.252378	+	0.252378i	0.821945	−	0.569567i	$-0.192889\pi$
$607$	3.42615e10	+	3.42615e10i	0.252378	+	0.252378i	−0.569567	+	0.821945i	$0.692889\pi$
$608$	6.61501e11	+	3.37052e11i	4.84079	+	2.46651i
$609$	−3.02649e10	+	4.16561e10i	−0.220024	+	0.302837i
$610$	4.36318e10	+	4.25461e10i	0.315126	+	0.307284i
$611$	−4.73422e10	+	3.43961e10i	−0.339691	+	0.246800i
$612$	−7.47164e10	−	4.71741e11i	−0.532611	−	3.36278i
$613$	1.06126e11	−	1.68087e10i	0.751587	−	0.119040i	0.231125	−	0.972924i	$-0.425760\pi$
$613$	1.06126e11	−	1.68087e10i	0.751587	−	0.119040i	0.520463	+	0.853884i	$0.325760\pi$
$614$	−1.61158e11	−	2.21815e11i	−1.13391	−	1.56069i
$615$	3.17895e10	−	5.44632e9i	0.222220	−	0.0380718i
$616$	6.03008e9	+	4.38111e9i	0.0418794	+	0.0304272i
$617$	−2.55982e10	+	5.02394e10i	−0.176632	+	0.346660i	−0.962301	−	0.271987i	$-0.912319\pi$
$617$	−2.55982e10	+	5.02394e10i	−0.176632	+	0.346660i	0.785669	+	0.618647i	$0.212319\pi$
$618$	−1.32563e11	+	1.32563e11i	−0.908800	+	0.908800i
$619$	−8.46828e10	+	2.75151e10i	−0.576810	+	0.187417i	−0.582871	−	0.812565i	$-0.698071\pi$
$619$	−8.46828e10	+	2.75151e10i	−0.576810	+	0.187417i	0.00606109	+	0.999982i	$0.498071\pi$
$620$	−1.02597e11	+	3.47707e10i	−0.694334	+	0.235314i
$621$	3.11874e9	−	9.59851e9i	0.0209707	−	0.0645412i
$622$	2.82543e11	−	1.43963e11i	1.88766	−	0.961809i
$623$	2.63504e10	−	1.66370e11i	0.174918	−	1.10439i
$624$		−	9.28885e11i		−	6.12666i
$625$	3.97828e10	−	1.47311e11i	0.260720	−	0.965414i
$626$	6.03790e10			0.393178
$627$	6.32849e9	+	1.00233e9i	0.0409478	+	0.00648549i
$628$	−2.62757e11	−	5.15689e11i	−1.68933	−	3.31550i
$629$	2.67224e10	+	8.68265e9i	0.170716	+	0.0554689i
$630$	−6.30647e10	−	1.86083e11i	−0.400335	−	1.18126i
$631$	3.95827e10	+	1.21823e11i	0.249682	+	0.768443i	0.994831	+	0.101545i	$0.0323785\pi$
$631$	3.95827e10	+	1.21823e11i	0.249682	+	0.768443i	−0.745149	+	0.666898i	$0.767621\pi$
$632$	−5.29455e11	−	5.29455e11i	−3.31865	−	3.31865i
$633$	−1.38191e11	−	7.04119e10i	−0.860727	−	0.438562i
$634$	−3.07406e11	+	4.23109e11i	−1.90264	+	2.61875i
$635$	1.35236e10	+	7.89355e10i	0.0831759	+	0.485487i
$636$	5.47507e11	−	3.97787e11i	3.34627	−	2.43121i
$637$	−1.59332e10	−	1.00598e11i	−0.0967711	−	0.610989i
$638$	−2.84813e9	+	4.51099e8i	−0.0171900	+	0.00272263i
$639$	1.32253e11	+	1.82030e11i	0.793234	+	1.09179i
$640$	4.51796e11	−	4.63325e11i	2.69291	−	2.76163i
$641$	−8.85012e10	−	6.42999e10i	−0.524224	−	0.380871i	0.293969	−	0.955815i	$-0.405024\pi$
$641$	−8.85012e10	−	6.42999e10i	−0.524224	−	0.380871i	−0.818193	+	0.574944i	$0.805024\pi$
$642$	−2.60204e10	+	5.10679e10i	−0.153170	+	0.300613i
$643$	−1.93473e11	+	1.93473e11i	−1.13182	+	1.13182i	−0.141941	+	0.989875i	$0.545334\pi$
$643$	−1.93473e11	+	1.93473e11i	−1.13182	+	1.13182i	−0.989875	+	0.141941i	$0.954666\pi$
$644$	3.48315e11	−	1.13174e11i	2.02502	−	0.657968i
$645$	−1.62015e9	−	1.28599e11i	−0.00936085	−	0.743017i
$646$	−1.76802e11	+	5.44141e11i	−1.01521	+	3.12450i
$647$	3.72292e10	−	1.89692e10i	0.212455	−	0.108251i	−0.344525	−	0.938777i	$-0.611960\pi$
$647$	3.72292e10	−	1.89692e10i	0.212455	−	0.108251i	0.556980	+	0.830526i	$0.311960\pi$
$648$	−9.84654e10	+	6.21686e11i	−0.558449	+	3.52591i
$649$			5.46054e9i			0.0307792i
$650$	−3.09509e11	+	2.37011e11i	−1.73388	+	1.32775i
$651$	4.46656e10			0.248685
$652$	1.63996e11	+	2.59745e10i	0.907494	+	0.143733i
$653$	−4.55400e10	−	8.93773e10i	−0.250461	−	0.491557i	0.731207	−	0.682156i	$-0.238957\pi$
$653$	−4.55400e10	−	8.93773e10i	−0.250461	−	0.491557i	−0.981668	+	0.190598i	$0.938957\pi$
$654$	1.94442e11	+	6.31779e10i	1.06287	+	0.345346i
$655$	7.37662e10	−	5.50273e10i	0.400767	−	0.298960i
$656$	−3.58876e10	−	1.10451e11i	−0.193789	−	0.596421i
$657$	−3.16468e10	−	3.16468e10i	−0.169851	−	0.169851i
$658$	8.11783e10	+	4.13624e10i	0.433048	+	0.220649i
$659$	−1.30859e11	+	1.80111e11i	−0.693842	+	0.954992i	0.306153	+	0.951982i	$0.400958\pi$
$659$	−1.30859e11	+	1.80111e11i	−0.693842	+	0.954992i	−0.999995	+	0.00300965i	$0.999042\pi$
$660$	7.31524e9	−	1.48154e10i	0.0385525	−	0.0780798i
$661$	1.15505e11	−	8.39196e10i	0.605058	−	0.439600i	−0.242613	−	0.970123i	$-0.578004\pi$
$661$	1.15505e11	−	8.39196e10i	0.605058	−	0.439600i	0.847670	+	0.530523i	$0.178004\pi$
$662$	−1.03982e11	−	6.56514e11i	−0.541408	−	3.41831i
$663$	3.85917e11	−	6.11232e10i	1.99728	−	0.316338i
$664$	1.72644e10	+	2.37625e10i	0.0888137	+	0.122242i
$665$	−2.48930e10	+	1.71091e11i	−0.127289	+	0.874863i
$666$	4.13458e10	+	3.00395e10i	0.210153	+	0.152685i
$667$	−4.10831e10	+	8.06302e10i	−0.207568	+	0.407375i
$668$	−4.13681e11	+	4.13681e11i	−2.07759	+	2.07759i
$669$	−2.87748e11	+	9.34949e10i	−1.43651	+	0.466749i
$670$	−5.27730e10	−	1.64149e10i	−0.261886	−	0.0814592i
$671$	3.19434e8	−	9.83117e8i	0.00157576	−	0.00484970i
$672$	−7.03343e11	+	3.58371e11i	−3.44898	+	1.75734i
$673$	−4.47332e10	+	2.82434e11i	−0.218057	+	1.37676i	0.599254	+	0.800559i	$0.295464\pi$
$673$	−4.47332e10	+	2.82434e11i	−0.218057	+	1.37676i	−0.817311	+	0.576197i	$0.804536\pi$
$674$		−	3.17743e11i		−	1.53970i
$675$	1.08031e10	−	5.85182e9i	0.0520393	−	0.0281887i
$676$	1.53661e11			0.735828
$677$	2.91549e11	+	4.61768e10i	1.38790	+	0.219821i	0.805265	−	0.592915i	$-0.202023\pi$
$677$	2.91549e11	+	4.61768e10i	1.38790	+	0.219821i	0.582631	+	0.812737i	$0.302023\pi$
$678$	4.03389e11	+	7.91696e11i	1.90900	+	3.74662i
$679$	1.16461e11	+	3.78404e10i	0.547900	+	0.178023i
$680$	7.69257e11	+	5.44225e11i	3.59779	+	2.54532i
$681$	−1.53556e11	−	4.72596e11i	−0.713967	−	2.19736i
$682$	1.76879e9	+	1.76879e9i	0.00817596	+	0.00817596i
$683$	5.44269e10	+	2.77319e10i	0.250110	+	0.127437i	0.574552	−	0.818468i	$-0.305176\pi$
$683$	5.44269e10	+	2.77319e10i	0.250110	+	0.127437i	−0.324442	+	0.945906i	$0.605176\pi$
$684$	−4.49329e11	+	6.18448e11i	−2.05277	+	2.82539i
$685$	9.58280e10	−	5.03573e10i	0.435241	−	0.228718i
$686$	−3.61626e11	+	2.62737e11i	−1.63291	+	1.18638i
$687$	9.62115e9	+	6.07456e10i	0.0431917	+	0.272702i
$688$	−4.57392e11	+	7.24438e10i	−2.04143	+	0.323331i
$689$	1.59193e11	+	2.19111e11i	0.706395	+	0.972269i
$690$	−3.28360e11	−	6.24855e11i	−1.44862	−	2.75666i
$691$	−2.15623e11	−	1.56660e11i	−0.945766	−	0.687139i	0.00403540	−	0.999992i	$-0.498715\pi$
$691$	−2.15623e11	−	1.56660e11i	−0.945766	−	0.687139i	−0.949802	+	0.312852i	$0.898715\pi$
$692$	5.64347e10	−	1.10759e11i	0.246106	−	0.483010i
$693$	−2.35660e9	+	2.35660e9i	−0.0102177	+	0.0102177i
$694$	4.86704e11	−	1.58140e11i	2.09810	−	0.681716i
$695$	2.97011e10	−	4.19822e10i	0.127301	−	0.179939i
$696$	1.38797e11	−	4.27174e11i	0.591485	−	1.82040i
$697$	4.35266e10	−	2.21779e10i	0.184426	−	0.0939700i
$698$	1.22334e11	−	7.72388e11i	0.515379	−	3.25397i
$699$		−	2.22109e10i		−	0.0930375i
$700$	4.02224e11	+	1.92338e11i	1.67524	+	0.801073i
$701$	−5.57403e10			−0.230833			−0.115416	−	0.993317i	$-0.536820\pi$
$701$	−5.57403e10			−0.230833			−0.115416	+	0.993317i	$0.536820\pi$
$702$	−3.10024e10	−	4.91030e9i	−0.127658	−	0.0202190i
$703$	−2.04164e10	−	4.00694e10i	−0.0835906	−	0.164056i
$704$	−2.15994e10	−	7.01806e9i	−0.0879326	−	0.0285710i
$705$	3.83119e10	−	1.23170e11i	0.155088	−	0.498597i
$706$	−9.78249e10	−	3.01074e11i	−0.393759	−	1.21187i
$707$	2.20965e11	+	2.20965e11i	0.884394	+	0.884394i
$708$	−1.18658e12	−	6.04595e11i	−4.72243	−	2.40620i
$709$	2.42760e11	−	3.34130e11i	0.960709	−	1.32230i	0.0141056	−	0.999901i	$-0.495510\pi$
$709$	2.42760e11	−	3.34130e11i	0.960709	−	1.32230i	0.946603	−	0.322401i	$-0.104490\pi$
$710$	−6.87808e11	−	1.00073e11i	−2.70666	−	0.393807i
$711$	2.70855e11	−	1.96788e11i	1.05989	−	0.770052i
$712$	2.29861e11	+	1.45128e12i	0.894427	+	5.64719i
$713$	7.75334e10	−	1.22801e10i	0.300007	−	0.0475164i
$714$	−3.57570e11	−	4.92152e11i	−1.37584	−	1.89368i
$715$	5.92909e9	+	2.92753e9i	0.0226863	+	0.0112015i
$716$	3.79945e11	+	2.76046e11i	1.44567	+	1.05034i
$717$	5.91475e10	−	1.16084e11i	0.223800	−	0.439232i
$718$	2.99850e11	−	2.99850e11i	1.12825	−	1.12825i
$719$	−3.44871e11	+	1.12055e11i	−1.29045	+	0.419293i	−0.872249	−	0.489062i	$-0.837339\pi$
$719$	−3.44871e11	+	1.12055e11i	−1.29045	+	0.419293i	−0.418201	+	0.908354i	$0.637339\pi$
$720$	5.98915e11	+	8.02869e11i	2.22862	+	2.98755i
$721$	−2.65154e10	+	8.16060e10i	−0.0981199	+	0.301982i
$722$	3.45962e11	−	1.76276e11i	1.27315	−	0.648702i
$723$	3.07952e10	−	1.94433e11i	0.112702	−	0.711570i
$724$			5.86548e11i			2.13476i
$725$	−1.03880e11	+	3.66709e10i	−0.375994	+	0.132730i
$726$	7.54102e11			2.71446
$727$	−4.64392e11	−	7.35525e10i	−1.66244	−	0.263305i	−0.746728	−	0.665130i	$-0.768376\pi$
$727$	−4.64392e11	−	7.35525e10i	−1.66244	−	0.263305i	−0.915717	+	0.401824i	$0.868376\pi$
$728$	−3.30269e11	−	6.48189e11i	−1.17582	−	2.30768i
$729$	−2.45423e11	−	7.97427e10i	−0.868970	−	0.282345i
$730$	1.38242e11	−	1.74164e9i	0.486799	−	0.00613290i
$731$	−6.01953e10	−	1.85262e11i	−0.210811	−	0.648809i
$732$	1.78265e11	+	1.78265e11i	0.620900	+	0.620900i
$733$	2.46195e11	+	1.25442e11i	0.852831	+	0.434539i	0.825040	−	0.565075i	$-0.191153\pi$
$733$	2.46195e11	+	1.25442e11i	0.852831	+	0.434539i	0.0277910	+	0.999614i	$0.491153\pi$
$734$	2.13690e11	−	2.94119e11i	0.736207	−	1.01330i
$735$	1.60741e11	+	1.56742e11i	0.550781	+	0.537075i
$736$	−1.12238e12	+	8.15457e11i	−3.82498	+	2.77901i
$737$	1.46650e8	+	9.25911e8i	0.000497063	+	0.00313833i
$738$	8.77601e10	−	1.38998e10i	0.295850	−	0.0468581i
$739$	1.58319e10	+	2.17908e10i	0.0530830	+	0.0730625i	0.834733	−	0.550654i	$-0.185622\pi$
$739$	1.58319e10	+	2.17908e10i	0.0530830	+	0.0730625i	−0.781650	+	0.623717i	$0.785622\pi$
$740$	−1.14303e11	+	1.95830e10i	−0.381182	+	0.0653059i
$741$	−5.05933e11	−	3.67582e11i	−1.67811	−	1.21922i
$742$	1.91435e11	−	3.75712e11i	0.631546	−	1.23948i
$743$	−6.98063e10	+	6.98063e10i	−0.229055	+	0.229055i	−0.812298	−	0.583243i	$-0.801784\pi$
$743$	−6.98063e10	+	6.98063e10i	−0.229055	+	0.229055i	0.583243	+	0.812298i	$0.301784\pi$
$744$	−3.70559e11	+	1.20402e11i	−1.20939	+	0.392954i
$745$	−3.51747e11	+	1.19209e11i	−1.14184	+	0.386976i
$746$	−1.91680e11	+	5.89930e11i	−0.618901	+	1.90478i
$747$	−1.17017e10	+	5.96233e9i	−0.0375809	+	0.0191484i
$748$	3.91498e9	−	2.47182e10i	0.0125061	−	0.0789607i
$749$			2.62329e10i			0.0833524i
$750$	2.34472e11	−	8.26699e11i	0.741046	−	2.61278i
$751$	4.80941e11			1.51193			0.755966	−	0.654611i	$-0.227168\pi$
$751$	4.80941e11			1.51193			0.755966	+	0.654611i	$0.227168\pi$
$752$	−4.58751e11	−	7.26590e10i	−1.43452	−	0.227205i
$753$	3.25864e11	+	6.39544e11i	1.01358	+	1.98925i
$754$	2.67671e11	+	8.69715e10i	0.828162	+	0.269086i
$755$	−4.69944e10	−	1.38665e11i	−0.144630	−	0.426756i
$756$	1.10934e10	+	3.41418e10i	0.0339606	+	0.104520i
$757$	−6.47503e10	−	6.47503e10i	−0.197178	−	0.197178i	0.601611	−	0.798789i	$-0.294526\pi$
$757$	−6.47503e10	−	6.47503e10i	−0.197178	−	0.197178i	−0.798789	+	0.601611i	$0.794526\pi$
$758$	2.47062e11	+	1.25885e11i	0.748393	+	0.381325i
$759$	−7.03772e9	+	9.68659e9i	−0.0212063	+	0.0291880i
$760$	−2.54678e11	−	1.48652e12i	−0.763373	−	4.45571i
$761$	4.45675e11	−	3.23802e11i	1.32886	−	0.965475i	0.329086	−	0.944300i	$-0.393259\pi$
$761$	4.45675e11	−	3.23802e11i	1.32886	−	0.965475i	0.999776	−	0.0211750i	$-0.00674071\pi$
$762$	7.05529e10	+	4.45454e11i	0.209264	+	1.32124i
$763$	9.24233e10	−	1.46384e10i	0.272699	−	0.0431913i
$764$	8.33161e11	+	1.14675e12i	2.44543	+	3.36585i
$765$	−2.94151e11	+	3.01658e11i	−0.858865	+	0.880782i
$766$	2.92406e11	+	2.12445e11i	0.849320	+	0.617067i
$767$	2.41957e11	−	4.74867e11i	0.699127	−	1.37211i
$768$	1.16183e12	−	1.16183e12i	3.33962	−	3.33962i
$769$	−2.97853e11	+	9.67783e10i	−0.851720	+	0.276741i	−0.702166	−	0.712013i	$-0.747784\pi$
$769$	−2.97853e11	+	9.67783e10i	−0.851720	+	0.276741i	−0.149554	+	0.988754i	$0.547784\pi$
$770$	−1.29692e8	−	1.02943e10i	−0.000368935	−	0.0292842i
$771$	−2.03351e11	+	6.25849e11i	−0.575477	+	1.77114i
$772$	−1.88769e11	+	9.61825e10i	−0.531448	+	0.270786i
$773$	−1.22770e10	+	7.75137e10i	−0.0343853	+	0.217100i	−0.998898	−	0.0469367i	$-0.985054\pi$
$773$	−1.22770e10	+	7.75137e10i	−0.0343853	+	0.217100i	0.964513	+	0.264037i	$0.0850541\pi$
$774$		−	3.54311e11i		−	0.987235i
$775$	7.87022e10	+	5.42047e10i	0.218163	+	0.150255i
$776$	−1.06820e12			−2.94581
$777$	4.72268e10	+	7.48000e9i	0.129570	+	0.0205219i
$778$	2.87702e11	+	5.64647e11i	0.785279	+	1.54120i
$779$	−7.43604e10	−	2.41612e10i	−0.201926	−	0.0656097i
$780$	−1.29263e12	+	9.64262e11i	−3.49217	+	2.60505i
$781$	3.64319e9	+	1.12126e10i	0.00979214	+	0.0301371i
$782$	−7.56002e11	−	7.56002e11i	−2.02160	−	2.02160i
$783$	−7.90337e9	−	4.02697e9i	−0.0210264	−	0.0107135i
$784$	4.75177e11	−	6.54025e11i	1.25774	−	1.73113i
$785$	−2.26042e11	+	4.57799e11i	−0.595264	+	1.20558i
$786$	4.19289e11	−	3.04632e11i	1.09856	−	0.798150i
$787$	6.68668e10	+	4.22181e11i	0.174306	+	1.10052i	0.907360	+	0.420354i	$0.138094\pi$
$787$	6.68668e10	+	4.22181e11i	0.174306	+	1.10052i	−0.733054	+	0.680170i	$0.761906\pi$
$788$	1.75774e12	−	2.78399e11i	4.55879	−	0.722041i
$789$	−1.40041e11	−	1.92749e11i	−0.361365	−	0.497376i
$790$	−1.48906e11	+	1.02344e12i	−0.382299	+	2.62756i
$791$	3.29014e11	+	2.39042e11i	0.840442	+	0.610617i
$792$	1.31985e10	−	2.59036e10i	0.0335448	−	0.0658353i
$793$	−7.13410e10	+	7.13410e10i	−0.180404	+	0.180404i
$794$	8.75758e11	−	2.84551e11i	2.20344	−	0.715942i
$795$	−5.70060e11	−	1.77316e11i	−1.42709	−	0.443895i
$796$	5.21594e11	−	1.60530e12i	1.29921	−	3.99856i
$797$	4.77140e11	−	2.43115e11i	1.18253	−	0.602529i	0.251638	−	0.967822i	$-0.419031\pi$
$797$	4.77140e11	−	2.43115e11i	1.18253	−	0.602529i	0.930893	+	0.365292i	$0.119031\pi$
$798$	−1.52313e11	+	9.61665e11i	−0.375599	+	2.37144i
$799$		−	1.95375e11i		−	0.479381i
$800$	−1.67422e12	−	2.22093e11i	−4.08746	−	0.542218i
$801$	−6.57003e11			−1.59602
$802$	5.66659e11	+	8.97500e10i	1.36970	+	0.216939i
$803$	−1.06465e9	−	2.08949e9i	−0.00256061	−	0.00502548i
$804$	−2.17439e11	−	7.06502e10i	−0.520371	−	0.169079i
$805$	−2.63748e11	−	1.86593e11i	−0.628066	−	0.444337i
$806$	−7.54448e10	−	2.32195e11i	−0.178768	−	0.550190i
$807$	−6.16345e10	−	6.16345e10i	−0.145322	−	0.145322i
$808$	−2.42883e12	−	1.23755e12i	−5.69838	−	2.90347i
$809$	−4.24030e11	+	5.83628e11i	−0.989926	+	1.36252i	−0.0586194	+	0.998280i	$0.518670\pi$
$809$	−4.24030e11	+	5.83628e11i	−0.989926	+	1.36252i	−0.931307	+	0.364236i	$0.881330\pi$
$810$	7.69602e11	−	4.04423e11i	1.78783	−	0.939499i
$811$	4.42906e11	−	3.21790e11i	1.02383	−	0.743856i	0.0567654	−	0.998388i	$-0.481921\pi$
$811$	4.42906e11	−	3.21790e11i	1.02383	−	0.743856i	0.967064	+	0.254532i	$0.0819213\pi$
$812$	−5.03538e10	−	3.17921e11i	−0.115827	−	0.731300i
$813$	−1.95102e9	+	3.09011e8i	−0.00446580	+	0.000707313i
$814$	1.57401e9	+	2.16643e9i	0.00358516	+	0.00493455i
$815$	−6.81360e10	−	1.29660e11i	−0.154435	−	0.293884i
$816$	2.50898e12	+	1.82288e12i	5.65896	+	4.11147i
$817$	−1.41543e11	+	2.77794e11i	−0.317688	+	0.623498i
$818$	2.86736e11	−	2.86736e11i	0.640425	−	0.640425i
$819$	3.09359e11	−	1.00517e11i	0.687586	−	0.223410i
$820$	−1.16448e11	+	1.64598e11i	−0.257559	+	0.364057i
$821$	−2.55715e11	+	7.87010e11i	−0.562839	+	1.73224i	0.111449	+	0.993770i	$0.464451\pi$
$821$	−2.55715e11	+	7.87010e11i	−0.562839	+	1.73224i	−0.674288	+	0.738469i	$0.735549\pi$
$822$	5.43190e11	−	2.76769e11i	1.18977	−	0.606220i
$823$	2.92711e10	−	1.84810e11i	0.0638028	−	0.402835i	−0.935032	−	0.354565i	$-0.884629\pi$
$823$	2.92711e10	−	1.84810e11i	0.0638028	−	0.402835i	0.998834	−	0.0482704i	$-0.0153709\pi$
$824$		−	7.48503e11i		−	1.62362i
$825$	−1.43343e10	+	2.64212e9i	−0.0309429	+	0.00570343i
$826$	−8.29773e11			−1.78254
$827$	−4.63745e11	−	7.34499e10i	−0.991418	−	0.157025i	−0.360404	−	0.932796i	$-0.617361\pi$
$827$	−4.63745e11	−	7.34499e10i	−0.991418	−	0.157025i	−0.631014	+	0.775771i	$0.717361\pi$
$828$	−6.48523e11	−	1.27280e12i	−1.37976	−	2.70794i
$829$	−4.80242e11	−	1.56040e11i	−1.01682	−	0.330383i	−0.247250	−	0.968952i	$-0.579527\pi$
$829$	−4.80242e11	−	1.56040e11i	−1.01682	−	0.330383i	−0.769565	+	0.638568i	$0.779527\pi$
$830$	1.20496e10	−	3.87387e10i	0.0253899	−	0.0816268i
$831$	5.56154e10	+	1.71167e11i	0.116625	+	0.358934i
$832$	1.56738e12	+	1.56738e12i	3.27101	+	3.27101i
$833$	3.02991e11	+	1.54381e11i	0.629288	+	0.320638i
$834$	1.70228e11	−	2.34299e11i	0.351858	−	0.484292i
$835$	5.10710e11	+	7.43061e10i	1.05058	+	0.152855i
$836$	−3.24054e10	+	2.35439e10i	−0.0663425	+	0.0482007i
$837$	1.20369e9	+	7.59982e9i	0.00245253	+	0.0154847i
$838$	−1.11830e12	+	1.77121e11i	−2.26768	+	0.359165i
$839$	−4.97953e11	−	6.85373e11i	−1.00494	−	1.38318i	−0.922245	−	0.386607i	$-0.873647\pi$
$839$	−4.97953e11	−	6.85373e11i	−1.00494	−	1.38318i	−0.0826954	−	0.996575i	$-0.526353\pi$
$840$	1.43786e12	+	7.09952e11i	2.88801	+	1.42598i
$841$	−3.40364e11	−	2.47289e11i	−0.680392	−	0.494334i
$842$	−6.07874e11	+	1.19302e12i	−1.20939	+	2.37356i
$843$	1.41427e11	−	1.41427e11i	0.280042	−	0.280042i
$844$	9.22115e11	−	2.99613e11i	1.81725	−	0.590461i
$845$	−8.10506e10	−	1.08651e11i	−0.158975	−	0.213112i
$846$	1.09813e11	−	3.37970e11i	0.214375	−	0.659777i
$847$	3.07532e11	−	1.56695e11i	0.597525	−	0.304454i
$848$	−3.36282e11	+	2.12320e12i	−0.650310	+	4.10590i
$849$			9.13912e11i			1.75903i
$850$	−3.27894e10	−	1.30112e12i	−0.0628142	−	2.49254i
$851$	8.40359e10			0.160231
$852$	−2.83989e12	−	4.49794e11i	−5.38943	−	0.853602i
$853$	5.44648e10	+	1.06893e11i	0.102877	+	0.201908i	0.936707	−	0.350113i	$-0.113857\pi$
$853$	5.44648e10	+	1.06893e11i	0.102877	+	0.201908i	−0.833830	+	0.552021i	$0.813857\pi$
$854$	1.49392e11	+	4.85405e10i	0.280865	+	0.0912585i
$855$	6.74301e11	−	8.49513e9i	1.26180	−	0.0158967i
$856$	−7.07141e10	−	2.17635e11i	−0.131708	−	0.405354i
$857$	3.90239e10	+	3.90239e10i	0.0723449	+	0.0723449i	0.742353	−	0.670009i	$-0.233710\pi$
$857$	3.90239e10	+	3.90239e10i	0.0723449	+	0.0723449i	−0.670009	+	0.742353i	$0.733710\pi$
$858$	3.31797e10	+	1.69059e10i	0.0612242	+	0.0311953i
$859$	8.80062e10	−	1.21130e11i	0.161637	−	0.222474i	−0.720515	−	0.693440i	$-0.756094\pi$
$859$	8.80062e10	−	1.21130e11i	0.161637	−	0.222474i	0.882152	+	0.470965i	$0.156094\pi$
$860$	5.75624e11	+	5.61301e11i	1.05231	+	1.02613i
$861$	6.72558e10	−	4.88642e10i	0.122382	−	0.0889157i
$862$	1.15398e11	+	7.28591e11i	0.209010	+	1.31964i
$863$	7.28107e10	−	1.15321e10i	0.131266	−	0.0207905i	−0.0904557	−	0.995900i	$-0.528832\pi$
$863$	7.28107e10	−	1.15321e10i	0.131266	−	0.0207905i	0.221722	+	0.975110i	$0.428832\pi$
$864$	−7.99311e10	−	1.10016e11i	−0.143437	−	0.197424i
$865$	−1.08084e11	+	1.85174e10i	−0.193062	+	0.0330762i
$866$	−1.42393e12	−	1.03454e12i	−2.53172	−	1.83940i
$867$	−2.33321e11	+	4.57918e11i	−0.412931	+	0.810423i
$868$	−1.97441e11	+	1.97441e11i	−0.347823	+	0.347823i
$869$	1.66840e10	−	5.42095e9i	0.0292564	−	0.00950597i
$870$	−5.87563e11	+	1.99128e11i	−1.02560	+	0.347581i
$871$	2.82740e10	−	8.70183e10i	0.0491263	−	0.151195i
$872$	−7.27312e11	+	3.70584e11i	−1.25792	+	0.640944i
$873$	7.47170e10	−	4.71744e11i	0.128636	−	0.812175i
$874$			1.71120e12i			2.93261i
$875$	−7.61599e10	−	3.85859e11i	−0.129925	−	0.658258i
$876$	5.71927e11			0.971235
$877$	9.76747e11	+	1.54702e11i	1.65114	+	0.261515i	0.911443	−	0.411426i	$-0.134969\pi$
$877$	9.76747e11	+	1.54702e11i	1.65114	+	0.261515i	0.739696	+	0.672941i	$0.234969\pi$
$878$	5.63170e11	+	1.10528e12i	0.947679	+	1.85992i
$879$	1.27713e12	+	4.14966e11i	2.13934	+	0.695115i
$880$	1.68460e10	+	4.97072e10i	0.0280910	+	0.0828873i
$881$	1.60497e11	+	4.93959e11i	0.266418	+	0.819950i	0.991363	+	0.131144i	$0.0418649\pi$
$881$	1.60497e11	+	4.93959e11i	0.266418	+	0.819950i	−0.724945	+	0.688806i	$0.758135\pi$
$882$	4.37358e11	+	4.37358e11i	0.722708	+	0.722708i
$883$	−9.94970e11	−	5.06963e11i	−1.63669	−	0.833937i	−0.997915	−	0.0645454i	$-0.979440\pi$
$883$	−9.94970e11	−	5.06963e11i	−1.63669	−	0.833937i	−0.638778	−	0.769391i	$-0.720560\pi$
$884$	−1.43573e12	+	1.97611e12i	−2.35105	+	3.23595i
$885$	1.98380e11	+	1.15792e12i	0.323389	+	1.88758i
$886$	−1.99018e11	+	1.44595e11i	−0.322966	+	0.234649i
$887$	9.99778e10	+	6.31235e11i	0.161514	+	1.01976i	0.926660	+	0.375900i	$0.122667\pi$
$887$	9.99778e10	+	6.31235e11i	0.161514	+	1.01976i	−0.765147	+	0.643856i	$0.777333\pi$
$888$	−4.11971e11	+	6.52498e10i	−0.662544	+	0.104937i
$889$	1.21333e11	+	1.67001e11i	0.194255	+	0.267369i
$890$	1.41691e12	−	1.45307e12i	2.25830	−	2.31593i
$891$	−1.19305e10	−	8.66799e9i	−0.0189298	−	0.0137533i
$892$	8.58680e11	−	1.68525e12i	1.35635	−	2.66199i
$893$	−2.21114e11	+	2.21114e11i	−0.347704	+	0.347704i
$894$	−1.98918e12	+	6.46325e11i	−3.11404	+	1.01181i
$895$	−5.21901e9	−	4.14259e11i	−0.00813384	−	0.645624i
$896$	5.15451e11	−	1.58639e12i	0.799752	−	2.46138i
$897$	1.04124e12	−	5.30537e11i	1.60835	−	0.819494i
$898$	2.88647e11	−	1.82244e12i	0.443876	−	2.80252i
$899$		−	6.89926e10i		−	0.105624i
$900$	4.95541e11	−	1.66689e12i	0.755283	−	2.54061i
$901$	−9.04238e11			−1.37209
$902$	4.59844e9	+	7.28322e8i	0.00694680	+	0.00110027i
$903$	−1.50496e11	−	2.95366e11i	−0.226347	−	0.444231i
$904$	−3.37396e12	−	1.09627e12i	−5.05204	−	1.64151i
$905$	4.14740e11	−	3.09383e11i	0.618275	−	0.461214i
$906$	−2.54793e11	−	7.84173e11i	−0.378160	−	1.16386i
$907$	−8.24270e11	−	8.24270e11i	−1.21798	−	1.21798i	−0.968338	−	0.249642i	$-0.919687\pi$
$907$	−8.24270e11	−	8.24270e11i	−1.21798	−	1.21798i	−0.249642	−	0.968338i	$-0.580313\pi$
$908$	2.76786e12	+	1.41029e12i	4.07193	+	2.07475i
$909$	7.16424e11	−	9.86073e11i	1.04934	−	1.44429i
$910$	−4.44862e11	+	9.00973e11i	−0.648724	+	1.31385i
$911$	4.21973e11	−	3.06581e11i	0.612648	−	0.445115i	−0.237698	−	0.971339i	$-0.576393\pi$
$911$	4.21973e11	−	3.06581e11i	0.612648	−	0.445115i	0.850346	+	0.526224i	$0.176393\pi$
$912$	−7.76486e11	−	4.90254e12i	−1.12242	−	7.08667i
$913$	−6.79677e8	+	1.07650e8i	−0.000978181	+	0.000154929i
$914$	1.18429e12	+	1.63004e12i	1.69697	+	2.33568i
$915$	3.20202e10	−	2.20077e11i	0.0456815	−	0.313971i
$916$	−3.11051e11	−	2.25992e11i	−0.441824	−	0.321004i
$917$	1.07692e11	−	2.11357e11i	0.152302	−	0.298909i
$918$	7.41033e10	−	7.41033e10i	0.104344	−	0.104344i
$919$	1.14460e11	−	3.71902e10i	0.160469	−	0.0521395i	−0.227681	−	0.973736i	$-0.573114\pi$
$919$	1.14460e11	−	3.71902e10i	0.160469	−	0.0521395i	0.388150	+	0.921596i	$0.373114\pi$
$920$	2.69112e12	+	8.37066e11i	3.75648	+	1.16845i
$921$	−3.09189e11	+	9.51586e11i	−0.429720	+	1.32254i
$922$	−1.29028e12	+	6.57430e11i	−1.78550	+	0.909758i
$923$	1.80006e11	−	1.13651e12i	0.248016	−	1.56591i
$924$		−	4.25889e10i		−	0.0584263i
$925$	7.41378e10	+	7.04930e10i	0.101268	+	0.0962895i
$926$	1.61960e12			2.20275
$927$	3.30559e11	+	5.23554e10i	0.447641	+	0.0708994i
$928$	5.53558e11	+	1.08642e12i	0.746399	+	1.46489i
$929$	−5.98095e11	−	1.94333e11i	−0.802985	−	0.260906i	−0.121361	−	0.992608i	$-0.538726\pi$
$929$	−5.98095e11	−	1.94333e11i	−0.802985	−	0.260906i	−0.681624	+	0.731703i	$0.738726\pi$
$930$	4.39335e11	+	3.10816e11i	0.587306	+	0.415501i
$931$	−1.68187e11	−	5.17627e11i	−0.223869	−	0.688998i
$932$	9.81818e10	+	9.81818e10i	0.130127	+	0.130127i
$933$	−1.03108e12	−	5.25362e11i	−1.36071	−	0.693317i
$934$	1.30189e12	−	1.79190e12i	1.71075	−	2.35465i
$935$	−1.95429e10	+	1.02698e10i	−0.0255707	+	0.0134373i
$936$	−2.29558e12	+	1.66783e12i	−2.99081	+	2.17295i
$937$	−1.16031e11	−	7.32593e11i	−0.150528	−	0.950395i	−0.941125	−	0.338059i	$-0.890230\pi$
$937$	−1.16031e11	−	7.32593e11i	−0.150528	−	0.950395i	0.790597	−	0.612337i	$-0.209770\pi$
$938$	−1.40700e11	+	2.22846e10i	−0.181753	+	0.0287868i
$939$	−1.29513e11	−	1.78259e11i	−0.166591	−	0.229292i
$940$	3.75111e11	+	7.13820e11i	0.480450	+	0.914276i
$941$	4.52435e10	+	3.28713e10i	0.0577029	+	0.0419236i	0.616263	−	0.787541i	$-0.288646\pi$
$941$	4.52435e10	+	3.28713e10i	0.0577029	+	0.0419236i	−0.558560	+	0.829464i	$0.688646\pi$
$942$	−1.30534e12	+	2.56188e12i	−1.65776	+	3.25353i
$943$	1.03313e11	−	1.03313e11i	0.130649	−	0.130649i
$944$	4.02312e12	−	1.30719e12i	5.06611	−	1.64608i
$945$	1.82899e10	−	2.58526e10i	0.0229342	−	0.0324173i
$946$	5.73694e9	−	1.76565e10i	0.00716334	−	0.0220465i
$947$	−6.94591e11	+	3.53912e11i	−0.863633	+	0.440043i	−0.828928	−	0.559355i	$-0.811049\pi$
$947$	−6.94591e11	+	3.53912e11i	−0.863633	+	0.440043i	−0.0347044	+	0.999398i	$0.511049\pi$
$948$	−6.69279e11	+	4.22566e12i	−0.828656	+	5.23193i
$949$			2.28883e11i			0.282195i
$950$	−1.43543e12	+	1.50964e12i	−1.76233	+	1.85345i
$951$	1.90854e12			2.33335
$952$	2.39893e12	+	3.79954e11i	2.92059	+	0.462576i
$953$	−3.32213e11	−	6.52006e11i	−0.402759	−	0.790460i	0.597173	−	0.802113i	$-0.296291\pi$
$953$	−3.32213e11	−	6.52006e11i	−0.402759	−	0.790460i	−0.999932	+	0.0116530i	$0.996291\pi$
$954$	−1.56420e12	−	5.08240e11i	−1.88842	−	0.613586i
$955$	3.71387e11	−	1.19399e12i	0.446491	−	1.43544i
$956$	2.51681e11	+	7.74596e11i	0.301314	+	0.927350i
$957$	7.44102e9	+	7.44102e9i	0.00887124	+	0.00887124i
$958$	−1.09358e12	−	5.57206e11i	−1.29834	−	0.661537i
$959$	1.64009e11	−	2.25739e11i	0.193907	−	0.266890i
$960$	−4.83515e12	−	7.03494e11i	−5.69279	−	0.828277i
$961$	6.41585e11	−	4.66139e11i	0.752247	−	0.546539i
$962$	−4.08861e10	−	2.58144e11i	−0.0477392	−	0.301413i
$963$	1.01060e11	−	1.60063e10i	0.117510	−	0.0186117i
$964$	7.23351e11	+	9.95607e11i	0.837608	+	1.15287i
$965$	1.67578e11	+	8.27429e10i	0.193245	+	0.0954161i
$966$	−1.47195e12	−	1.06944e12i	−1.69039	−	1.22814i
$967$	−5.35501e11	+	1.05098e12i	−0.612427	+	1.20196i	0.351600	+	0.936150i	$0.385638\pi$
$967$	−5.35501e11	+	1.05098e12i	−0.612427	+	1.20196i	−0.964027	+	0.265805i	$0.914362\pi$
$968$	−2.12898e12	+	2.12898e12i	−2.42477	+	2.42477i
$969$	1.98573e12	−	6.45201e11i	2.25229	−	0.731813i
$970$	8.82201e11	+	1.18262e12i	0.996507	+	1.33586i
$971$	−4.04075e11	+	1.24361e12i	−0.454554	+	1.39897i	0.417105	+	0.908858i	$0.363045\pi$
$971$	−4.04075e11	+	1.24361e12i	−0.454554	+	1.39897i	−0.871659	+	0.490114i	$0.836955\pi$
$972$	3.07425e12	−	1.56641e12i	3.44408	−	1.75485i
$973$	2.07360e10	−	1.30922e11i	0.0231352	−	0.146070i
$974$		−	1.14447e12i		−	1.27165i
$975$	1.36363e12	+	4.05387e11i	1.50896	+	0.448592i
$976$	−8.00792e11			−0.882512
$977$	−1.50488e12	−	2.38349e11i	−1.65167	−	0.261599i	−0.740025	−	0.672579i	$-0.765186\pi$
$977$	−1.50488e12	−	2.38349e11i	−1.65167	−	0.261599i	−0.911644	+	0.410981i	$0.865186\pi$
$978$	−3.74483e11	−	7.34964e11i	−0.409333	−	0.803361i
$979$	−3.27407e10	−	1.06381e10i	−0.0356416	−	0.0115806i
$980$	−1.40341e12	+	1.76808e10i	−1.52153	+	0.0191689i
$981$	−1.12787e11	−	3.47121e11i	−0.121781	−	0.374805i
$982$	−1.53428e12	−	1.53428e12i	−1.64990	−	1.64990i
$983$	2.49282e10	+	1.27015e10i	0.0266978	+	0.0136032i	0.467288	−	0.884105i	$-0.345231\pi$
$983$	2.49282e10	+	1.27015e10i	0.0266978	+	0.0136032i	−0.440591	+	0.897708i	$0.645231\pi$
$984$	−4.26254e11	+	5.86689e11i	−0.454662	+	0.625788i
$985$	−1.12400e12	−	1.09603e12i	−1.19404	−	1.16433i
$986$	−7.60203e11	+	5.52320e11i	−0.804307	+	0.584363i
$987$	−5.20115e10	−	3.28388e11i	−0.0548064	−	0.346034i
$988$	3.86131e12	−	6.11571e11i	4.05235	−	0.641829i
$989$	−3.42448e11	−	4.71339e11i	−0.357939	−	0.492661i
$990$	−3.95787e10	+	6.78082e9i	−0.0412023	+	0.00705897i
$991$	8.87688e11	+	6.44943e11i	0.920377	+	0.668693i	0.943618	−	0.331037i	$-0.107398\pi$
$991$	8.87688e11	+	6.44943e11i	0.920377	+	0.668693i	−0.0232406	+	0.999730i	$0.507398\pi$
$992$	4.80193e11	−	9.42431e11i	0.495871	−	0.973202i
$993$	−1.71521e12	+	1.71521e12i	−1.76409	+	1.76409i
$994$	−1.70384e12	+	5.53612e11i	−1.74535	+	0.567100i
$995$	−1.41021e12	+	4.77927e11i	−1.43877	+	0.487606i
$996$	5.18617e10	−	1.59614e11i	0.0526999	−	0.162194i
$997$	−5.27447e11	+	2.68747e11i	−0.533824	+	0.271997i	−0.700054	−	0.714090i	$-0.746841\pi$
$997$	−5.27447e11	+	2.68747e11i	−0.533824	+	0.271997i	0.166230	+	0.986087i	$0.446841\pi$
$998$	4.20229e11	−	2.65322e12i	0.423608	−	2.67455i
$999$			8.23720e9i			0.00827023i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.9.f.a.2.19	✓	152
25.13	odd	20	inner	25.9.f.a.13.19	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.9.f.a.2.19	✓	152	1.1	even	1	trivial
25.9.f.a.13.19	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)

\(f(q)\)	\(=\)	\(q+(30.6740 + 4.85828i) q^{2} +(-51.4523 - 100.981i) q^{3} +(673.820 + 218.937i) q^{4} +(-200.608 - 591.930i) q^{5} +(-1087.65 - 3347.46i) q^{6} +(-1139.13 - 1139.13i) q^{7} +(12521.2 + 6379.87i) q^{8} +(-3693.34 + 5083.44i) q^{9} +O(q^{10})\)	\(q+(30.6740 + 4.85828i) q^{2} +(-51.4523 - 100.981i) q^{3} +(673.820 + 218.937i) q^{4} +(-200.608 - 591.930i) q^{5} +(-1087.65 - 3347.46i) q^{6} +(-1139.13 - 1139.13i) q^{7} +(12521.2 + 6379.87i) q^{8} +(-3693.34 + 5083.44i) q^{9} +(-3277.69 - 19131.5i) q^{10} +(-266.361 + 193.523i) q^{11} +(-12561.1 - 79307.7i) q^{12} +(31738.7 - 5026.91i) q^{13} +(-29407.4 - 40475.7i) q^{14} +(-49451.9 + 50713.8i) q^{15} +(206344. + 149918. i) q^{16} +(-48707.2 + 95593.2i) q^{17} +(-137986. + 137986. i) q^{18} +(163311. - 53062.9i) q^{19} +(-5578.26 - 442775. i) q^{20} +(-56419.3 + 173641. i) q^{21} +(-9110.55 + 4642.06i) q^{22} +(-50196.5 + 316928. i) q^{23} -1.59266e6i q^{24} +(-310138. + 237492. i) q^{25} +997974. q^{26} +(-31065.3 - 4920.27i) q^{27} +(-518169. - 1.01696e6i) q^{28} +(268214. + 87148.0i) q^{29} +(-1.76327e6 + 1.31534e6i) q^{30} +(-75597.9 - 232666. i) q^{31} +(3.05722e6 + 3.05722e6i) q^{32} +(33247.0 + 16940.2i) q^{33} +(-1.95846e6 + 2.69559e6i) q^{34} +(-445765. + 902802. i) q^{35} +(-3.60160e6 + 2.61671e6i) q^{36} +(-40969.1 - 258668. i) q^{37} +(5.26718e6 - 834240. i) q^{38} +(-2.14065e6 - 2.94635e6i) q^{39} +(1.26458e6 - 8.69153e6i) q^{40} +(-368370. - 267637. i) q^{41} +(-2.57420e6 + 5.05215e6i) q^{42} +(-1.28386e6 + 1.28386e6i) q^{43} +(-221849. + 72083.1i) q^{44} +(3.74996e6 + 1.16642e6i) q^{45} +(-3.07946e6 + 9.47759e6i) q^{46} +(-1.62257e6 + 826740. i) q^{47} +(4.52195e6 - 2.85504e7i) q^{48} -3.16958e6i q^{49} +(-1.06670e7 + 5.77810e6i) q^{50} +1.21592e7 q^{51} +(2.24867e7 + 3.56155e6i) q^{52} +(3.82634e6 + 7.50961e6i) q^{53} +(-928993. - 301848. i) q^{54} +(167986. + 118845. i) q^{55} +(-6.99575e6 - 2.15307e7i) q^{56} +(-1.37611e7 - 1.37611e7i) q^{57} +(7.80380e6 + 3.97624e6i) q^{58} +(9.74856e6 - 1.34177e7i) q^{59} +(-4.44248e7 + 2.33451e7i) q^{60} +(-2.54005e6 + 1.84546e6i) q^{61} +(-1.18853e6 - 7.50408e6i) q^{62} +(9.99786e6 - 1.58351e6i) q^{63} +(4.05452e7 + 5.58057e7i) q^{64} +(-9.34263e6 - 1.77786e7i) q^{65} +(937518. + 681147. i) q^{66} +(1.29265e6 - 2.53698e6i) q^{67} +(-5.37488e7 + 5.37488e7i) q^{68} +(3.45864e7 - 1.12378e7i) q^{69} +(-1.80595e7 + 2.55269e7i) q^{70} +(1.10654e7 - 3.40559e7i) q^{71} +(-7.86766e7 + 4.00878e7i) q^{72} +(-1.11424e6 + 7.03502e6i) q^{73} -8.13343e6i q^{74} +(3.99395e7 + 1.90984e7i) q^{75} +1.21659e8 q^{76} +(523867. + 82972.3i) q^{77} +(-5.13481e7 - 1.00776e8i) q^{78} +(-5.06741e7 - 1.64650e7i) q^{79} +(4.73465e7 - 1.52216e8i) q^{80} +(1.38410e7 + 4.25983e7i) q^{81} +(-9.99913e6 - 9.99913e6i) q^{82} +(1.86230e6 + 948890. i) q^{83} +(-7.60329e7 + 1.04650e8i) q^{84} +(6.63556e7 + 9.65445e6i) q^{85} +(-4.56186e7 + 3.31438e7i) q^{86} +(-4.99995e6 - 3.15685e7i) q^{87} +(-4.56981e6 + 723787. i) q^{88} +(6.14591e7 + 8.45912e7i) q^{89} +(1.09359e8 + 5.39970e7i) q^{90} +(-4.18807e7 - 3.04281e7i) q^{91} +(-1.03211e8 + 2.02563e8i) q^{92} +(-1.96052e7 + 1.96052e7i) q^{93} +(-5.37871e7 + 1.74765e7i) q^{94} +(-6.41710e7 - 8.60237e7i) q^{95} +(1.51419e8 - 4.66021e8i) q^{96} +(-6.77279e7 + 3.45091e7i) q^{97} +(1.53987e7 - 9.72237e7i) q^{98} -2.06878e6i 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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