LMFDB - Embedded newform 25.9.f.a.2.18

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			2.18
Character	$\chi$	$=$	25.2
Dual form			25.9.f.a.13.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(26.2450 + 4.15680i) q^{2} +(39.3019 + 77.1344i) q^{3} +(428.052 + 139.082i) q^{4} +(614.814 + 112.380i) q^{5} +(710.848 + 2187.76i) q^{6} +(-2106.70 - 2106.70i) q^{7} +(4595.04 + 2341.29i) q^{8} +(-548.613 + 755.101i) q^{9} +O(q^{10})$	\(q+(26.2450 + 4.15680i) q^{2} +(39.3019 + 77.1344i) q^{3} +(428.052 + 139.082i) q^{4} +(614.814 + 112.380i) q^{5} +(710.848 + 2187.76i) q^{6} +(-2106.70 - 2106.70i) q^{7} +(4595.04 + 2341.29i) q^{8} +(-548.613 + 755.101i) q^{9} +(15668.7 + 5505.08i) q^{10} +(-18936.2 + 13757.9i) q^{11} +(6095.22 + 38483.7i) q^{12} +(29486.0 - 4670.12i) q^{13} +(-46533.3 - 64047.6i) q^{14} +(15495.0 + 51840.0i) q^{15} +(17649.2 + 12822.9i) q^{16} +(43555.6 - 85482.7i) q^{17} +(-17537.2 + 17537.2i) q^{18} +(-76800.7 + 24954.0i) q^{19} +(247542. + 133614. i) q^{20} +(79701.7 - 245297. i) q^{21} +(-554169. + 282363. i) q^{22} +(-2133.80 + 13472.3i) q^{23} +446452. i q^{24} +(365366. + 138186. i) q^{25} +793273. q^{26} +(481187. + 76212.5i) q^{27} +(-608772. - 1.19478e6i) q^{28} +(-774551. - 251667. i) q^{29} +(191177. + 1.42495e6i) q^{30} +(74455.5 + 229151. i) q^{31} +(-523639. - 523639. i) q^{32} +(-1.80544e6 - 919916. i) q^{33} +(1.49845e6 - 2.06244e6i) q^{34} +(-1.05848e6 - 1.53198e6i) q^{35} +(-339856. + 246920. i) q^{36} +(-425205. - 2.68464e6i) q^{37} +(-2.11936e6 + 335674. i) q^{38} +(1.51908e6 + 2.09084e6i) q^{39} +(2.56198e6 + 1.95585e6i) q^{40} +(1.39526e6 + 1.01372e6i) q^{41} +(3.11142e6 - 6.10651e6i) q^{42} +(-3.27807e6 + 3.27807e6i) q^{43} +(-1.00191e7 + 3.25542e6i) q^{44} +(-422153. + 402593. i) q^{45} +(-112003. + 344711. i) q^{46} +(3.34505e6 - 1.70439e6i) q^{47} +(-295439. + 1.86533e6i) q^{48} +3.11159e6i q^{49} +(9.01463e6 + 5.14545e6i) q^{50} +8.30547e6 q^{51} +(1.32711e7 + 2.10193e6i) q^{52} +(4.92733e6 + 9.67042e6i) q^{53} +(1.23120e7 + 4.00040e6i) q^{54} +(-1.31883e7 + 6.33051e6i) q^{55} +(-4.74798e6 - 1.46128e7i) q^{56} +(-4.94323e6 - 4.94323e6i) q^{57} +(-1.92820e7 - 9.82466e6i) q^{58} +(397892. - 547652. i) q^{59} +(-577390. + 2.43453e7i) q^{60} +(4.68786e6 - 3.40593e6i) q^{61} +(1.00155e6 + 6.32356e6i) q^{62} +(2.74654e6 - 435009. i) q^{63} +(-1.48489e7 - 2.04378e7i) q^{64} +(1.86532e7 + 442393. i) q^{65} +(-4.35598e7 - 3.16481e7i) q^{66} +(-1.38267e7 + 2.71363e7i) q^{67} +(3.05332e7 - 3.05332e7i) q^{68} +(-1.12304e6 + 364898. i) q^{69} +(-2.14116e7 - 4.46068e7i) q^{70} +(-270632. + 832919. i) q^{71} +(-4.28881e6 + 2.18526e6i) q^{72} +(-7.08753e6 + 4.47489e7i) q^{73} -7.22258e7i q^{74} +(3.70071e6 + 3.36133e7i) q^{75} -3.63453e7 q^{76} +(6.88767e7 + 1.09090e7i) q^{77} +(3.11772e7 + 6.11886e7i) q^{78} +(1.37950e7 + 4.48227e6i) q^{79} +(9.40993e6 + 9.86711e6i) q^{80} +(1.49253e7 + 4.59354e7i) q^{81} +(3.24049e7 + 3.24049e7i) q^{82} +(-1.59790e7 - 8.14168e6i) q^{83} +(6.82329e7 - 9.39145e7i) q^{84} +(3.63852e7 - 4.76611e7i) q^{85} +(-9.96593e7 + 7.24067e7i) q^{86} +(-1.10292e7 - 6.96355e7i) q^{87} +(-1.19224e8 + 1.88832e7i) q^{88} +(338181. + 465466. i) q^{89} +(-1.27529e7 + 8.81125e6i) q^{90} +(-7.19568e7 - 5.22796e7i) q^{91} +(-2.78714e6 + 5.47007e6i) q^{92} +(-1.47491e7 + 1.47491e7i) q^{93} +(9.48756e7 - 3.08269e7i) q^{94} +(-5.00224e7 + 6.71120e6i) q^{95} +(1.98105e7 - 6.09706e7i) q^{96} +(-1.33987e8 + 6.82696e7i) q^{97} +(-1.29343e7 + 8.16637e7i) q^{98} -2.18465e7i 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 $

$2$	26.2450	+	4.15680i	1.64031	+	0.259800i	0.907322	−	0.420437i	$-0.138123\pi$
$2$	26.2450	+	4.15680i	1.64031	+	0.259800i	0.732992	+	0.680237i	$0.238123\pi$
$3$	39.3019	+	77.1344i	0.485209	+	0.952276i	0.995721	+	0.0924060i	$0.0294558\pi$
$3$	39.3019	+	77.1344i	0.485209	+	0.952276i	−0.510512	+	0.859870i	$0.670544\pi$
$4$	428.052	+	139.082i	1.67208	+	0.543291i
$5$	614.814	+	112.380i	0.983702	+	0.179809i
$5$	614.814	+	112.380i	0.983702	+	0.179809i
$6$	710.848	+	2187.76i	0.548494	+	1.68809i
$7$	−2106.70	−	2106.70i	−0.877427	−	0.877427i	0.115841	−	0.993268i	$-0.463044\pi$
$7$	−2106.70	−	2106.70i	−0.877427	−	0.877427i	−0.993268	+	0.115841i	$0.963044\pi$
$8$	4595.04	+	2341.29i	1.12184	+	0.571604i
$9$	−548.613	+	755.101i	−0.0836173	+	0.115089i
$10$	15668.7	+	5505.08i	1.56687	+	0.550508i
$11$	−18936.2	+	13757.9i	−1.29337	+	0.939685i	−0.999868	−	0.0162746i	$-0.994819\pi$
$11$	−18936.2	+	13757.9i	−1.29337	+	0.939685i	−0.293498	+	0.955960i	$0.594819\pi$
$12$	6095.22	+	38483.7i	0.293944	+	1.85589i
$13$	29486.0	−	4670.12i	1.03239	−	0.163514i	0.382823	−	0.923822i	$-0.374952\pi$
$13$	29486.0	−	4670.12i	1.03239	−	0.163514i	0.649563	+	0.760308i	$0.274952\pi$
$14$	−46533.3	−	64047.6i	−1.21130	−	1.66721i
$15$	15495.0	+	51840.0i	0.306073	+	1.02400i
$16$	17649.2	+	12822.9i	0.269305	+	0.195662i
$17$	43555.6	−	85482.7i	0.521493	−	1.02349i	−0.468644	−	0.883387i	$-0.655257\pi$
$17$	43555.6	−	85482.7i	0.521493	−	1.02349i	0.990137	−	0.140100i	$-0.0447426\pi$
$18$	−17537.2	+	17537.2i	−0.167059	+	0.167059i
$19$	−76800.7	+	24954.0i	−0.589319	+	0.191481i	−0.588471	−	0.808518i	$-0.700270\pi$
$19$	−76800.7	+	24954.0i	−0.589319	+	0.191481i	−0.000848001		1.00000i	$0.500270\pi$
$20$	247542.	+	133614.i	1.54714	+	0.835090i
$21$	79701.7	−	245297.i	0.409817	−	1.26129i
$22$	−554169.	+	282363.i	−2.36566	+	1.20536i
$23$	−2133.80	+	13472.3i	−0.00762506	+	0.0481427i	−0.991208	−	0.132317i	$-0.957758\pi$
$23$	−2133.80	+	13472.3i	−0.00762506	+	0.0481427i	0.983582	+	0.180459i	$0.0577584\pi$
$24$			446452.i			1.34564i
$25$	365366.	+	138186.i	0.935338	+	0.353756i
$26$	793273.			1.73592
$27$	481187.	+	76212.5i	0.905438	+	0.143407i
$28$	−608772.	−	1.19478e6i	−0.990427	−	1.94382i
$29$	−774551.	−	251667.i	−1.09511	−	0.355823i	−0.294892	−	0.955531i	$-0.595284\pi$
$29$	−774551.	−	251667.i	−1.09511	−	0.355823i	−0.800219	+	0.599707i	$0.795284\pi$
$30$	191177.	+	1.42495e6i	0.236021	+	1.75920i
$31$	74455.5	+	229151.i	0.0806214	+	0.248127i	0.983241	−	0.182313i	$-0.0583584\pi$
$31$	74455.5	+	229151.i	0.0806214	+	0.248127i	−0.902619	+	0.430440i	$0.858358\pi$
$32$	−523639.	−	523639.i	−0.499381	−	0.499381i
$33$	−1.80544e6	−	919916.i	−1.52239	−	0.775698i
$34$	1.49845e6	−	2.06244e6i	1.12131	−	1.54336i
$35$	−1.05848e6	−	1.53198e6i	−0.705357	−	1.02090i
$36$	−339856.	+	246920.i	−0.202341	+	0.147010i
$37$	−425205.	−	2.68464e6i	−0.226877	−	1.43245i	−0.793551	−	0.608504i	$-0.791770\pi$
$37$	−425205.	−	2.68464e6i	−0.226877	−	1.43245i	0.566673	−	0.823943i	$-0.308230\pi$
$38$	−2.11936e6	+	335674.i	−1.01642	+	0.160984i
$39$	1.51908e6	+	2.09084e6i	0.656634	+	0.903779i
$40$	2.56198e6	+	1.95585e6i	1.00077	+	0.764003i
$41$	1.39526e6	+	1.01372e6i	0.493766	+	0.358742i	0.806631	−	0.591056i	$-0.201289\pi$
$41$	1.39526e6	+	1.01372e6i	0.493766	+	0.358742i	−0.312865	+	0.949798i	$0.601289\pi$
$42$	3.11142e6	−	6.10651e6i	0.999912	−	1.96244i
$43$	−3.27807e6	+	3.27807e6i	−0.958836	+	0.958836i	−0.999186	−	0.0403499i	$-0.987153\pi$
$43$	−3.27807e6	+	3.27807e6i	−0.958836	+	0.958836i	0.0403499	+	0.999186i	$0.487153\pi$
$44$	−1.00191e7	+	3.25542e6i	−2.67313	+	0.868552i
$45$	−422153.	+	402593.i	−0.102949	+	0.0981784i
$46$	−112003.	+	344711.i	−0.0250150	+	0.0769882i
$47$	3.34505e6	−	1.70439e6i	0.685505	−	0.349282i	−0.0763034	−	0.997085i	$-0.524312\pi$
$47$	3.34505e6	−	1.70439e6i	0.685505	−	0.349282i	0.761808	+	0.647802i	$0.224312\pi$
$48$	−295439.	+	1.86533e6i	−0.0556547	+	0.351390i
$49$			3.11159e6i			0.539756i
$50$	9.01463e6	+	5.14545e6i	1.44234	+	0.823272i
$51$	8.30547e6			1.22768
$52$	1.32711e7	+	2.10193e6i	1.81507	+	0.287478i
$53$	4.92733e6	+	9.67042e6i	0.624465	+	1.22558i	0.959056	+	0.283218i	$0.0914019\pi$
$53$	4.92733e6	+	9.67042e6i	0.624465	+	1.22558i	−0.334591	+	0.942363i	$0.608598\pi$
$54$	1.23120e7	+	4.00040e6i	1.44794	+	0.470466i
$55$	−1.31883e7	+	6.33051e6i	−1.44125	+	0.691811i
$56$	−4.74798e6	−	1.46128e7i	−0.482788	−	1.48587i
$57$	−4.94323e6	−	4.94323e6i	−0.468286	−	0.468286i
$58$	−1.92820e7	−	9.82466e6i	−1.70388	−	0.868172i
$59$	397892.	−	547652.i	0.0328365	−	0.0451956i	−0.792283	−	0.610154i	$-0.791108\pi$
$59$	397892.	−	547652.i	0.0328365	−	0.0451956i	0.825120	+	0.564958i	$0.191108\pi$
$60$	−577390.	+	2.43453e7i	−0.0445517	+	1.87849i
$61$	4.68786e6	−	3.40593e6i	0.338575	−	0.245989i	−0.405485	−	0.914102i	$-0.632897\pi$
$61$	4.68786e6	−	3.40593e6i	0.338575	−	0.245989i	0.744061	+	0.668112i	$0.232897\pi$
$62$	1.00155e6	+	6.32356e6i	0.0677809	+	0.427952i
$63$	2.74654e6	−	435009.i	0.174351	−	0.0276144i
$64$	−1.48489e7	−	2.04378e7i	−0.885064	−	1.21819i
$65$	1.86532e7	+	442393.i	1.04496	+	0.0247830i
$66$	−4.35598e7	−	3.16481e7i	−2.29568	−	1.66791i
$67$	−1.38267e7	+	2.71363e7i	−0.686148	+	1.34664i	0.240477	+	0.970655i	$0.422696\pi$
$67$	−1.38267e7	+	2.71363e7i	−0.686148	+	1.34664i	−0.926625	+	0.375987i	$0.877304\pi$
$68$	3.05332e7	−	3.05332e7i	1.42803	−	1.42803i
$69$	−1.12304e6	+	364898.i	−0.0495449	+	0.0160981i
$70$	−2.14116e7	−	4.46068e7i	−0.891779	−	1.85784i
$71$	−270632.	+	832919.i	−0.0106499	+	0.0327770i	−0.956240	−	0.292583i	$-0.905485\pi$
$71$	−270632.	+	832919.i	−0.0106499	+	0.0327770i	0.945590	+	0.325360i	$0.105485\pi$
$72$	−4.28881e6	+	2.18526e6i	−0.159590	+	0.0813153i
$73$	−7.08753e6	+	4.47489e7i	−0.249577	+	1.57576i	0.470838	+	0.882220i	$0.343952\pi$
$73$	−7.08753e6	+	4.47489e7i	−0.249577	+	1.57576i	−0.720414	+	0.693544i	$0.756048\pi$
$74$		−	7.22258e7i		−	2.40861i
$75$	3.70071e6	+	3.36133e7i	0.116961	+	1.06235i
$76$	−3.63453e7			−1.08942
$77$	6.88767e7	+	1.09090e7i	1.95934	+	0.310329i
$78$	3.11772e7	+	6.11886e7i	0.842284	+	1.65307i
$79$	1.37950e7	+	4.48227e6i	0.354172	+	0.115077i	0.480699	−	0.876886i	$-0.340383\pi$
$79$	1.37950e7	+	4.48227e6i	0.354172	+	0.115077i	−0.126527	+	0.991963i	$0.540383\pi$
$80$	9.40993e6	+	9.86711e6i	0.229735	+	0.240896i
$81$	1.49253e7	+	4.59354e7i	0.346724	+	1.06711i
$82$	3.24049e7	+	3.24049e7i	0.716730	+	0.716730i
$83$	−1.59790e7	−	8.14168e6i	−0.336694	−	0.171554i	0.277466	−	0.960735i	$-0.410505\pi$
$83$	−1.59790e7	−	8.14168e6i	−0.336694	−	0.171554i	−0.614161	+	0.789181i	$0.710505\pi$
$84$	6.82329e7	−	9.39145e7i	1.37049	−	1.88632i
$85$	3.63852e7	−	4.76611e7i	0.697025	−	0.913037i
$86$	−9.96593e7	+	7.24067e7i	−1.82190	+	1.32369i
$87$	−1.10292e7	−	6.96355e7i	−0.192516	−	1.21550i
$88$	−1.19224e8	+	1.88832e7i	−1.98807	+	0.314879i
$89$	338181.	+	465466.i	0.00539000	+	0.00741870i	0.811703	−	0.584070i	$-0.198541\pi$
$89$	338181.	+	465466.i	0.00539000	+	0.00741870i	−0.806313	+	0.591488i	$0.798541\pi$
$90$	−1.27529e7	+	8.81125e6i	−0.194375	+	0.134297i
$91$	−7.19568e7	−	5.22796e7i	−1.04932	−	0.762372i
$92$	−2.78714e6	+	5.47007e6i	−0.0389052	+	0.0763557i
$93$	−1.47491e7	+	1.47491e7i	−0.197167	+	0.197167i
$94$	9.48756e7	−	3.08269e7i	1.21519	−	0.394838i
$95$	−5.00224e7	+	6.71120e6i	−0.614144	+	0.0823959i
$96$	1.98105e7	−	6.09706e7i	0.233245	−	0.717853i
$97$	−1.33987e8	+	6.82696e7i	−1.51347	+	0.771153i	−0.996399	−	0.0847878i	$-0.972979\pi$
$97$	−1.33987e8	+	6.82696e7i	−1.51347	+	0.771153i	−0.517074	+	0.855941i	$0.672979\pi$
$98$	−1.29343e7	+	8.16637e7i	−0.140229	+	0.885369i
$99$		−	2.18465e7i		−	0.227426i
$100$	1.37176e8	+	1.09967e8i	1.37176	+	1.09967i
$101$	−5.58730e6			−0.0536929			−0.0268464	−	0.999640i	$-0.508547\pi$
$101$	−5.58730e6			−0.0536929			−0.0268464	+	0.999640i	$0.508547\pi$
$102$	2.17977e8	+	3.45242e7i	2.01377	+	0.318950i
$103$	−8.55829e7	−	1.67966e8i	−0.760393	−	1.49236i	−0.867137	−	0.498070i	$-0.834042\pi$
$103$	−8.55829e7	−	1.67966e8i	−0.760393	−	1.49236i	0.106744	−	0.994287i	$-0.465958\pi$
$104$	1.46423e8	+	4.75758e7i	1.25163	+	0.406680i
$105$	7.65682e7	−	1.41855e8i	0.629929	−	1.16704i
$106$	8.91198e7	+	2.74282e8i	0.705912	+	2.17257i
$107$	4.25309e7	+	4.25309e7i	0.324466	+	0.324466i	0.850478	−	0.526011i	$-0.176313\pi$
$107$	4.25309e7	+	4.25309e7i	0.324466	+	0.324466i	−0.526011	+	0.850478i	$0.676313\pi$
$108$	1.95373e8	+	9.95475e7i	1.43605	+	0.731704i
$109$	−6.54843e7	+	9.01314e7i	−0.463907	+	0.638513i	−0.975313	−	0.220826i	$-0.929125\pi$
$109$	−6.54843e7	+	9.01314e7i	−0.463907	+	0.638513i	0.511406	+	0.859339i	$0.329125\pi$
$110$	−3.72443e8	+	1.11323e8i	−2.54383	+	0.760351i
$111$	1.90366e8	−	1.38309e8i	1.25400	−	0.911086i
$112$	−1.01676e7	−	6.41956e7i	−0.0646169	−	0.407975i
$113$	−453216.	+	71782.4i	−0.00277966	+	0.000440255i	−0.157824	−	0.987467i	$-0.550448\pi$
$113$	−453216.	+	71782.4i	−0.00277966	+	0.000440255i	0.155044	+	0.987907i	$0.450448\pi$
$114$	−1.09187e8	−	1.50283e8i	−0.646475	−	0.889797i
$115$	−2.82592e6	+	8.04316e6i	−0.0161573	+	0.0459870i
$116$	−2.96546e8	−	2.15453e8i	−1.63779	−	1.18993i
$117$	−1.26500e7	+	2.48270e7i	−0.0675066	+	0.132489i
$118$	1.27192e7	−	1.27192e7i	0.0656041	−	0.0656041i
$119$	−2.71845e8	+	8.83279e7i	−1.35561	+	0.440464i
$120$	−5.01725e7	+	2.74485e8i	−0.241958	+	1.32371i
$121$	1.03057e8	−	3.17177e8i	0.480769	−	1.47966i
$122$	1.37191e8	−	6.99022e7i	0.619278	−	0.315538i
$123$	−2.33560e7	+	1.47464e8i	−0.102042	+	0.644267i
$124$			1.08444e8i			0.458688i
$125$	2.09103e8	+	1.26019e8i	0.856485	+	0.516172i
$126$	7.38912e7			0.293164
$127$	2.76097e8	+	4.37295e7i	1.06132	+	0.168097i	0.662598	−	0.748975i	$-0.269454\pi$
$127$	2.76097e8	+	4.37295e7i	1.06132	+	0.168097i	0.398723	+	0.917072i	$0.369454\pi$
$128$	−2.18688e8	−	4.29199e8i	−0.814675	−	1.59889i
$129$	−3.81686e8	−	1.24017e8i	−1.37831	−	0.447841i
$130$	4.87715e8	+	8.91484e7i	1.70763	+	0.312133i
$131$	−8.47156e7	−	2.60728e8i	−0.287659	−	0.885324i	−0.985589	−	0.169158i	$-0.945895\pi$
$131$	−8.47156e7	−	2.60728e8i	−0.287659	−	0.885324i	0.697930	−	0.716166i	$-0.254105\pi$
$132$	−6.44876e8	−	6.44876e8i	−2.12413	−	2.12413i
$133$	2.14367e8	+	1.09225e8i	0.685095	+	0.349074i
$134$	−4.75681e8	+	6.54719e8i	−1.47536	+	2.03065i
$135$	2.87275e8	+	1.00932e8i	0.864895	+	0.303875i
$136$	4.00279e8	−	2.90820e8i	1.17006	−	0.850097i
$137$	−7.39310e7	−	4.66782e8i	−0.209867	−	1.32505i	−0.837456	−	0.546504i	$-0.815958\pi$
$137$	−7.39310e7	−	4.66782e8i	−0.209867	−	1.32505i	0.627589	−	0.778545i	$-0.284042\pi$
$138$	−3.09911e7	+	4.90850e6i	−0.0854516	+	0.0135342i
$139$	1.32201e8	+	1.81959e8i	0.354140	+	0.487431i	0.948504	−	0.316764i	$-0.102596\pi$
$139$	1.32201e8	+	1.81959e8i	0.354140	+	0.487431i	−0.594365	+	0.804196i	$0.702596\pi$
$140$	−2.40011e8	−	8.02982e8i	−0.624769	−	2.09023i
$141$	2.62934e8	+	1.91032e8i	0.665226	+	0.483315i
$142$	−1.05650e7	+	2.07350e7i	−0.0259846	+	0.0509977i
$143$	−4.94100e8	+	4.94100e8i	−1.18160	+	1.18160i
$144$	−1.93652e7	+	6.29212e6i	−0.0450372	+	0.0146335i
$145$	−4.47922e8	−	2.41773e8i	−1.01328	−	0.546934i
$146$	−3.72025e8	+	1.14498e9i	−0.818768	+	2.51991i
$147$	−2.40010e8	+	1.22291e8i	−0.513997	+	0.261895i
$148$	1.91376e8	−	1.20830e9i	0.398879	−	2.51842i
$149$		−	7.08556e8i		−	1.43757i	−0.695232	−	0.718785i	$-0.744698\pi$
$149$		−	7.08556e8i		−	1.43757i	0.695232	−	0.718785i	$-0.255302\pi$
$150$	−4.25985e7	+	8.97564e8i	−0.0841452	+	1.77297i
$151$	9.47041e8			1.82163			0.910817	−	0.412811i	$-0.135453\pi$
$151$	9.47041e8			1.82163			0.910817	+	0.412811i	$0.135453\pi$
$152$	−4.11326e8	−	6.51477e7i	−0.770570	−	0.122046i
$153$	4.06529e7	+	7.97858e7i	0.0741866	+	0.145599i
$154$	1.76232e9	+	5.72614e8i	3.13331	+	1.01807i
$155$	2.00242e7	+	1.49252e8i	0.0346920	+	0.258579i
$156$	3.59447e8	+	1.10626e9i	0.606927	+	1.86793i
$157$	6.63283e8	+	6.63283e8i	1.09169	+	1.09169i	0.995348	+	0.0963438i	$0.0307148\pi$
$157$	6.63283e8	+	6.63283e8i	1.09169	+	1.09169i	0.0963438	+	0.995348i	$0.469285\pi$
$158$	3.43419e8	+	1.74981e8i	0.551056	+	0.280777i
$159$	−5.52269e8	+	7.60133e8i	−0.864096	+	1.18933i
$160$	−2.63093e8	−	3.80787e8i	−0.401449	−	0.581035i
$161$	3.28774e7	−	2.38869e7i	0.0489322	−	0.0355513i
$162$	2.00771e8	+	1.26762e9i	0.291501	+	1.84047i
$163$	−4.76321e8	+	7.54419e7i	−0.674761	+	0.106872i	−0.484405	−	0.874844i	$-0.660964\pi$
$163$	−4.76321e8	+	7.54419e7i	−0.674761	+	0.106872i	−0.190355	+	0.981715i	$0.560964\pi$
$164$	4.56255e8	+	6.27981e8i	0.630713	+	0.868103i
$165$	−1.00663e9	−	7.68473e8i	−1.35810	−	1.03679i
$166$	−3.85525e8	−	2.80100e8i	−0.507715	−	0.368876i
$167$	2.78724e8	−	5.47026e8i	0.358351	−	0.703303i	−0.639503	−	0.768789i	$-0.720860\pi$
$167$	2.78724e8	−	5.47026e8i	0.358351	−	0.703303i	0.997853	+	0.0654861i	$0.0208598\pi$
$168$	9.40542e8	−	9.40542e8i	1.18070	−	1.18070i
$169$	7.18076e7	−	2.33317e7i	0.0880286	−	0.0286022i
$170$	1.15305e9	−	1.09962e9i	1.38055	−	1.31658i
$171$	2.32910e7	−	7.16824e7i	0.0272398	−	0.0838355i
$172$	−1.85910e9	+	9.47261e8i	−2.12417	+	1.08232i
$173$	−1.55583e8	+	9.82313e8i	−0.173691	+	1.09664i	0.734660	+	0.678435i	$0.237342\pi$
$173$	−1.55583e8	+	9.82313e8i	−0.173691	+	1.09664i	−0.908351	+	0.418208i	$0.862658\pi$
$174$		−	1.87343e9i		−	2.04381i
$175$	−4.78601e8	−	1.06083e9i	−0.510295	−	1.13109i
$176$	−5.10625e8			−0.532171
$177$	5.78807e7	+	9.16740e6i	0.0589713	+	0.00934014i
$178$	6.94071e6	+	1.36219e7i	0.00691391	+	0.0135693i
$179$	4.11575e8	+	1.33729e8i	0.400901	+	0.130260i	0.502526	−	0.864562i	$-0.332404\pi$
$179$	4.11575e8	+	1.33729e8i	0.400901	+	0.130260i	−0.101625	+	0.994823i	$0.532404\pi$
$180$	−2.36697e8	+	1.13616e8i	−0.225477	+	0.108231i
$181$	2.96481e7	+	9.12474e7i	0.0276237	+	0.0850171i	0.963918	−	0.266200i	$-0.0857680\pi$
$181$	2.96481e7	+	9.12474e7i	0.0276237	+	0.0850171i	−0.936294	+	0.351217i	$0.885768\pi$
$182$	−1.67119e9	−	1.67119e9i	−1.52314	−	1.52314i
$183$	4.46957e8	+	2.27736e8i	0.398530	+	0.203061i
$184$	−4.13475e7	+	5.69099e7i	−0.0360726	+	0.0496497i
$185$	4.02789e7	−	1.69834e9i	0.0343867	−	1.44989i
$186$	−4.48401e8	+	3.25782e8i	−0.374640	+	0.272192i
$187$	3.51289e8	+	2.21795e9i	0.287275	+	1.81378i
$188$	1.66890e9	−	2.64328e8i	1.33598	−	0.211598i
$189$	−8.53160e8	−	1.17427e9i	−0.668626	−	0.920285i
$190$	−1.34074e9	−	3.17979e7i	−1.02880	−	0.0243996i
$191$	3.76840e8	+	2.73790e8i	0.283155	+	0.205724i	0.720292	−	0.693671i	$-0.244008\pi$
$191$	3.76840e8	+	2.73790e8i	0.283155	+	0.205724i	−0.437138	+	0.899395i	$0.644008\pi$
$192$	9.92864e8	−	1.94861e9i	0.730609	−	1.43390i
$193$	1.52796e9	−	1.52796e9i	1.10124	−	1.10124i	0.106982	−	0.994261i	$-0.465881\pi$
$193$	1.52796e9	−	1.52796e9i	1.10124	−	1.10124i	0.994261	−	0.106982i	$-0.0341188\pi$
$194$	−3.80027e9	+	1.23478e9i	−2.68292	+	0.871732i
$195$	6.98984e8	+	1.45619e9i	0.483424	+	1.00712i
$196$	−4.32767e8	+	1.33192e9i	−0.293244	+	0.902514i
$197$	−1.73072e9	+	8.81847e8i	−1.14911	+	0.585502i	−0.921549	−	0.388262i	$-0.873076\pi$
$197$	−1.73072e9	+	8.81847e8i	−1.14911	+	0.585502i	−0.227563	+	0.973763i	$0.573076\pi$
$198$	9.08116e7	−	5.73362e8i	0.0590854	−	0.373051i
$199$		−	1.10128e9i		−	0.702242i	−0.936330	−	0.351121i	$-0.885801\pi$
$199$		−	1.10128e9i		−	0.702242i	0.936330	−	0.351121i	$-0.114199\pi$
$200$	1.35534e9	+	1.49040e9i	0.847086	+	0.931498i
$201$	−2.63656e9			−1.61530
$202$	−1.46639e8	−	2.32253e7i	−0.0880731	−	0.0139494i
$203$	1.10156e9	+	2.16194e9i	0.648671	+	1.27309i
$204$	3.55517e9	+	1.15515e9i	2.05277	+	0.666985i
$205$	7.43905e8	+	7.80049e8i	0.421214	+	0.441678i
$206$	−1.54792e9	−	4.76402e9i	−0.859569	−	2.64548i
$207$	−9.00232e6	−	9.00232e6i	−0.00490313	−	0.00490313i
$208$	5.80289e8	+	2.95672e8i	0.310021	+	0.157963i
$209$	1.11099e9	−	1.52915e9i	0.582273	−	0.801430i
$210$	2.59920e9	−	3.40470e9i	1.33648	−	1.75066i
$211$	2.11963e9	−	1.54000e9i	1.06937	−	0.776946i	0.0935745	−	0.995612i	$-0.470171\pi$
$211$	2.11963e9	−	1.54000e9i	1.06937	−	0.776946i	0.975800	+	0.218666i	$0.0701707\pi$
$212$	7.64165e8	+	4.82475e9i	0.378306	+	2.38853i
$213$	−7.48831e7	+	1.18603e7i	−0.0363802	+	0.00576206i
$214$	9.39432e8	+	1.29302e9i	0.447930	+	0.616523i
$215$	−2.38379e9	+	1.64701e9i	−1.11562	+	0.770801i
$216$	2.03264e9	+	1.47680e9i	0.933780	+	0.678431i
$217$	3.25896e8	−	6.39608e8i	0.146974	−	0.288453i
$218$	−2.09329e9	+	2.09329e9i	−0.926839	+	0.926839i
$219$	−3.73024e9	+	1.21203e9i	−1.62166	+	0.526909i
$220$	−6.52575e9	+	8.75519e8i	−2.78573	+	0.373745i
$221$	8.85066e8	−	2.72395e9i	0.371028	−	1.14191i
$222$	5.57109e9	−	2.83861e9i	2.29366	−	1.16868i
$223$	1.57497e7	−	9.94399e7i	0.00636875	−	0.0402107i	−0.984299	−	0.176507i	$-0.943520\pi$
$223$	1.57497e7	−	9.94399e7i	0.00636875	−	0.0402107i	0.990668	+	0.136297i	$0.0435201\pi$
$224$			2.20630e9i			0.876340i
$225$	−3.04789e8	+	2.00078e8i	−0.118924	+	0.0780673i
$226$	−1.21931e7			−0.00467389
$227$	1.22836e9	+	1.94553e8i	0.462618	+	0.0732715i	0.383393	−	0.923585i	$-0.374756\pi$
$227$	1.22836e9	+	1.94553e8i	0.462618	+	0.0732715i	0.0792248	+	0.996857i	$0.474756\pi$
$228$	−1.42844e9	−	2.80347e9i	−0.528595	−	1.03743i
$229$	2.83476e9	+	9.21068e8i	1.03080	+	0.334927i	0.775106	−	0.631831i	$-0.217696\pi$
$229$	2.83476e9	+	9.21068e8i	1.03080	+	0.334927i	0.255693	+	0.966758i	$0.417696\pi$
$230$	−1.07600e8	+	1.99346e8i	−0.0384504	+	0.0712355i
$231$	1.86553e9	+	5.74151e9i	0.655170	+	2.01641i
$232$	−2.96987e9	−	2.96987e9i	−1.02514	−	1.02514i
$233$	5.00360e8	+	2.54946e8i	0.169769	+	0.0865017i	0.536810	−	0.843703i	$-0.319629\pi$
$233$	5.00360e8	+	2.54946e8i	0.169769	+	0.0865017i	−0.367041	+	0.930205i	$0.619629\pi$
$234$	−4.35200e8	+	5.99001e8i	−0.145153	+	0.199786i
$235$	2.24812e9	−	6.71962e8i	0.737136	−	0.220330i
$236$	2.46487e8	−	1.79083e8i	0.0794596	−	0.0577308i
$237$	1.96434e8	+	1.24023e9i	0.0622619	+	0.393106i
$238$	−7.50175e9	+	1.18816e9i	−2.33805	+	0.370311i
$239$	−2.98886e9	−	4.11381e9i	−0.916039	−	1.26082i	−0.965062	−	0.262022i	$-0.915611\pi$
$239$	−2.98886e9	−	4.11381e9i	−0.916039	−	1.26082i	0.0490229	−	0.998798i	$-0.484389\pi$
$240$	−3.91266e8	+	1.11363e9i	−0.117931	+	0.335656i
$241$	−4.24562e8	−	3.08462e8i	−0.125856	−	0.0914396i	0.523077	−	0.852286i	$-0.324784\pi$
$241$	−4.24562e8	−	3.08462e8i	−0.125856	−	0.0914396i	−0.648932	+	0.760846i	$0.724784\pi$
$242$	4.02318e9	−	7.89594e9i	1.17303	−	2.30220i
$243$	−6.96394e8	+	6.96394e8i	−0.199724	+	0.199724i
$244$	2.48035e9	−	8.05915e8i	0.699768	−	0.227368i
$245$	−3.49681e8	+	1.91305e9i	−0.0970528	+	0.530959i
$246$	−1.22596e9	+	3.77311e9i	−0.334761	+	1.03029i
$247$	−2.14800e9	+	1.09446e9i	−0.577095	+	0.294045i
$248$	−1.94382e8	+	1.22728e9i	−0.0513864	+	0.324441i
$249$		−	1.55251e9i		−	0.403866i
$250$	4.96407e9	+	4.17656e9i	1.27080	+	1.06920i
$251$	−1.26137e9			−0.317796			−0.158898	−	0.987295i	$-0.550794\pi$
$251$	−1.26137e9			−0.317796			−0.158898	+	0.987295i	$0.550794\pi$
$252$	1.23616e9	+	1.95789e8i	0.306530	+	0.0485496i
$253$	−1.44945e8	−	2.84471e8i	−0.0353770	−	0.0694313i
$254$	7.06440e9	+	2.29536e9i	1.69723	+	0.551463i
$255$	5.10632e9	+	9.33372e8i	1.20767	+	0.220747i
$256$	−1.95690e9	−	6.02271e9i	−0.455626	−	1.40227i
$257$	1.48586e9	+	1.48586e9i	0.340601	+	0.340601i	0.856593	−	0.515992i	$-0.172577\pi$
$257$	1.48586e9	+	1.48586e9i	0.340601	+	0.340601i	−0.515992	+	0.856593i	$0.672577\pi$
$258$	−9.50185e9	−	4.84143e9i	−2.14452	−	1.09269i
$259$	−4.75995e9	+	6.55151e9i	−1.05780	+	1.45594i
$260$	7.92301e9	+	2.78370e9i	1.73379	+	0.609157i
$261$	6.14963e8	−	4.46797e8i	0.132522	−	0.0962826i
$262$	−1.13957e9	−	7.19495e9i	−0.241844	−	1.52694i
$263$	2.03291e9	−	3.21982e8i	0.424909	−	0.0672989i	0.0596817	−	0.998217i	$-0.480991\pi$
$263$	2.03291e9	−	3.21982e8i	0.424909	−	0.0672989i	0.365227	+	0.930919i	$0.380991\pi$
$264$	−6.14226e9	−	8.45410e9i	−1.26448	−	1.74041i
$265$	1.94262e9	+	6.49924e9i	0.393917	+	1.31789i
$266$	5.17203e9	+	3.75770e9i	1.03308	+	0.750578i
$267$	−2.26123e7	+	4.43791e7i	−0.00444937	+	0.00873239i
$268$	−9.69271e9	+	9.69271e9i	−1.87891	+	1.87891i
$269$	1.18590e9	−	3.85323e8i	0.226485	−	0.0735895i	−0.193576	−	0.981085i	$-0.562009\pi$
$269$	1.18590e9	−	3.85323e8i	0.226485	−	0.0735895i	0.420061	+	0.907496i	$0.362009\pi$
$270$	7.11999e9	+	3.84312e9i	1.33975	+	0.723151i
$271$	1.65828e9	−	5.10365e9i	0.307453	−	0.946245i	−0.671297	−	0.741189i	$-0.734262\pi$
$271$	1.65828e9	−	5.10365e9i	0.307453	−	0.946245i	0.978750	−	0.205056i	$-0.0657376\pi$
$272$	1.86486e9	−	9.50192e8i	0.340698	−	0.173594i
$273$	1.20452e9	−	7.60503e9i	0.216852	−	1.36915i
$274$		−	1.25580e10i		−	2.22802i
$275$	−8.81979e9	+	2.40997e9i	−1.54215	+	0.421387i
$276$	−5.31471e8			−0.0915889
$277$	−3.78903e9	−	6.00124e8i	−0.643590	−	0.101935i	−0.173896	−	0.984764i	$-0.555636\pi$
$277$	−3.78903e9	−	6.00124e8i	−0.643590	−	0.101935i	−0.469694	+	0.882829i	$0.655636\pi$
$278$	2.71324e9	+	5.32504e9i	0.454265	+	0.891546i
$279$	−2.13879e8	−	6.94935e7i	−0.0352981	−	0.0114691i
$280$	−1.27693e9	−	9.51771e9i	−0.207747	−	1.54846i
$281$	−2.04535e9	−	6.29493e9i	−0.328051	−	1.00964i	−0.970044	−	0.242928i	$-0.921892\pi$
$281$	−2.04535e9	−	6.29493e9i	−0.328051	−	1.00964i	0.641993	−	0.766710i	$-0.278108\pi$
$282$	6.10661e9	+	6.10661e9i	0.965615	+	0.965615i
$283$	7.23465e9	+	3.68624e9i	1.12790	+	0.574695i	0.915432	−	0.402472i	$-0.131849\pi$
$283$	7.23465e9	+	3.68624e9i	1.12790	+	0.574695i	0.212471	+	0.977167i	$0.431849\pi$
$284$	−2.31689e8	+	3.18892e8i	−0.0356149	+	0.0490197i
$285$	−2.48364e9	−	3.59469e9i	−0.376452	−	0.544856i
$286$	−1.50216e10	+	1.09138e10i	−2.24518	+	1.63122i
$287$	−8.03803e8	−	5.07501e9i	−0.118474	−	0.748014i
$288$	6.82675e8	−	1.08125e8i	0.0992303	−	0.0157165i
$289$	−1.30995e9	−	1.80299e9i	−0.187786	−	0.258466i
$290$	−1.07507e10	−	8.20725e9i	−1.52001	−	1.16039i
$291$	−1.05319e10	−	7.65185e9i	−1.46870	−	1.06707i
$292$	−9.25762e9	+	1.81691e10i	−1.27341	+	2.49921i
$293$	4.87893e9	−	4.87893e9i	0.661994	−	0.661994i	−0.293856	−	0.955850i	$-0.594939\pi$
$293$	4.87893e9	−	4.87893e9i	0.661994	−	0.661994i	0.955850	+	0.293856i	$0.0949385\pi$
$294$	−6.80742e9	+	2.21186e9i	−0.911157	+	0.296053i
$295$	3.06175e8	−	2.91988e8i	0.0404279	−	0.0385547i
$296$	4.33168e9	−	1.33315e10i	0.564273	−	1.73665i
$297$	−1.01604e10	+	5.17696e9i	−1.30582	+	0.665348i
$298$	2.94533e9	−	1.85961e10i	0.373481	−	2.35807i
$299$			4.07210e8i			0.0509487i
$300$	−3.09092e9	+	1.49029e10i	−0.381595	+	1.83987i
$301$	1.38118e10			1.68262
$302$	2.48551e10	+	3.93666e9i	2.98805	+	0.473261i
$303$	−2.19592e8	−	4.30973e8i	−0.0260523	−	0.0511304i
$304$	−1.67545e9	−	5.44388e8i	−0.196172	−	0.0637403i
$305$	3.26492e9	−	1.56719e9i	0.377288	−	0.181101i
$306$	7.35282e8	+	2.26297e9i	0.0838626	+	0.258103i
$307$	−2.19497e8	−	2.19497e8i	−0.0247101	−	0.0247101i	0.694644	−	0.719354i	$-0.255562\pi$
$307$	−2.19497e8	−	2.19497e8i	−0.0247101	−	0.0247101i	−0.719354	+	0.694644i	$0.755562\pi$
$308$	2.79655e10	+	1.42492e10i	3.10757	+	1.58338i
$309$	9.59238e9	−	1.32028e10i	1.05219	−	1.44821i
$310$	−9.48755e7	+	4.00036e9i	−0.0102732	+	0.433164i
$311$	−9.08381e9	+	6.59978e9i	−0.971016	+	0.705485i	−0.955683	−	0.294398i	$-0.904881\pi$
$311$	−9.08381e9	+	6.59978e9i	−0.971016	+	0.705485i	−0.0153334	+	0.999882i	$0.504881\pi$
$312$	2.08499e9	+	1.31641e10i	0.220032	+	1.38923i
$313$	−2.69705e9	+	4.27170e8i	−0.281003	+	0.0445065i	−0.295345	−	0.955391i	$-0.595435\pi$
$313$	−2.69705e9	+	4.27170e8i	−0.281003	+	0.0445065i	0.0143420	+	0.999897i	$0.495435\pi$
$314$	1.46507e10	+	2.01650e10i	1.50710	+	2.07434i
$315$	1.73749e9	+	4.12076e7i	0.176474	+	0.00418539i
$316$	5.28158e9	+	3.83729e9i	0.529682	+	0.384836i
$317$	2.77418e9	−	5.44464e9i	0.274725	−	0.539178i	−0.711881	−	0.702300i	$-0.752156\pi$
$317$	2.77418e9	−	5.44464e9i	0.274725	−	0.539178i	0.986606	+	0.163122i	$0.0521565\pi$
$318$	−1.76540e10	+	1.76540e10i	−1.72638	+	1.72638i
$319$	1.81294e10	−	5.89061e9i	1.75074	−	0.568850i
$320$	−6.83251e9	−	1.42341e10i	−0.651599	−	1.35747i
$321$	−1.60905e9	+	4.95214e9i	−0.151548	+	0.466416i
$322$	9.62162e8	−	4.90246e8i	0.0895004	−	0.0456027i
$323$	−1.21196e9	+	7.65201e9i	−0.111347	+	0.703017i
$324$			2.17386e10i			1.97265i
$325$	1.14185e10	+	2.36824e9i	1.02347	+	0.212272i
$326$	−1.28147e10			−1.13458
$327$	−9.52589e9	−	1.50875e9i	−0.833133	−	0.131955i
$328$	4.03788e9	+	7.92479e9i	0.348866	+	0.684688i
$329$	−1.06376e10	−	3.45638e9i	−0.907950	−	0.295011i
$330$	−2.32246e10	−	2.43529e10i	−1.95836	−	2.05350i
$331$	1.55853e9	+	4.79665e9i	0.129838	+	0.399601i	0.994751	−	0.102321i	$-0.0326268\pi$
$331$	1.55853e9	+	4.79665e9i	0.129838	+	0.399601i	−0.864913	+	0.501921i	$0.832627\pi$
$332$	−5.70745e9	−	5.70745e9i	−0.469775	−	0.469775i
$333$	2.26044e9	+	1.15175e9i	0.183830	+	0.0936662i
$334$	9.58899e9	−	1.31981e10i	0.770526	−	1.06054i
$335$	−1.15504e10	+	1.51299e10i	−0.917103	+	1.20132i
$336$	4.55209e9	−	3.30728e9i	0.357152	−	0.259486i
$337$	−3.65602e9	−	2.30832e10i	−0.283458	−	1.78968i	−0.559803	−	0.828626i	$-0.689123\pi$
$337$	−3.65602e9	−	2.30832e10i	−0.283458	−	1.78968i	0.276345	−	0.961059i	$-0.410877\pi$
$338$	1.98158e9	−	3.13851e8i	0.151825	−	0.0240468i
$339$	−2.33492e7	−	3.21374e7i	−0.00176796	−	0.00243339i
$340$	2.22035e10	−	1.53409e10i	1.66152	−	1.14798i
$341$	−4.56254e9	−	3.31488e9i	−0.337434	−	0.245160i
$342$	9.09243e8	−	1.78449e9i	0.0664623	−	0.130440i
$343$	−5.58953e9	+	5.58953e9i	−0.403830	+	0.403830i
$344$	−2.27377e10	+	7.38794e9i	−1.62373	+	0.527582i
$345$	−7.31468e8	+	9.81365e7i	−0.0516320	+	0.00692715i
$346$	−8.16656e9	+	2.51341e10i	−0.569816	+	1.75371i
$347$	−9.25470e8	+	4.71551e8i	−0.0638329	+	0.0325245i	−0.485616	−	0.874172i	$-0.661405\pi$
$347$	−9.25470e8	+	4.71551e8i	−0.0638329	+	0.0325245i	0.421783	+	0.906697i	$0.361405\pi$
$348$	4.96402e9	−	3.13416e10i	0.338467	−	2.13700i
$349$			5.33455e8i			0.0359581i	0.999838	+	0.0179790i	$0.00572321\pi$
$349$			5.33455e8i			0.0359581i	−0.999838	+	0.0179790i	$0.994277\pi$
$350$	−8.15122e9	−	2.98311e10i	−0.543188	−	1.98791i
$351$	1.45442e10			0.958211
$352$	1.71199e10	+	2.71153e9i	1.11514	+	0.176621i
$353$	−6.95932e9	−	1.36584e10i	−0.448196	−	0.879634i	−0.998987	−	0.0449910i	$-0.985674\pi$
$353$	−6.95932e9	−	1.36584e10i	−0.448196	−	0.879634i	0.550792	−	0.834643i	$-0.314326\pi$
$354$	1.48097e9	+	4.81197e8i	0.0943049	+	0.0306415i
$355$	−2.59992e8	+	4.81676e8i	−0.0163699	+	0.0303279i
$356$	8.00207e7	+	2.46278e8i	0.00498198	+	0.0153330i
$357$	−1.74972e10	−	1.74972e10i	−1.07720	−	1.07720i
$358$	1.02459e10	+	5.22055e9i	0.623761	+	0.317822i
$359$	−5.76495e9	+	7.93478e9i	−0.347071	+	0.477702i	−0.946490	−	0.322733i	$-0.895398\pi$
$359$	−5.76495e9	+	7.93478e9i	−0.347071	+	0.477702i	0.599419	+	0.800435i	$0.295398\pi$
$360$	−2.88240e9	+	8.61547e8i	−0.171610	+	0.0512943i
$361$	−8.46436e9	+	6.14971e9i	−0.498385	+	0.362098i
$362$	3.98817e8	+	2.51803e9i	0.0232241	+	0.146631i
$363$	2.85156e10	−	4.51643e9i	1.64232	−	0.260117i
$364$	−2.35300e10	−	3.23863e10i	−1.34035	−	1.84483i
$365$	−9.38641e9	+	2.67157e10i	−0.528845	+	1.50521i
$366$	1.07837e10	+	7.83484e9i	0.600959	+	0.436622i
$367$	−1.23290e10	+	2.41969e10i	−0.679614	+	1.33382i	0.251062	+	0.967971i	$0.419220\pi$
$367$	−1.23290e10	+	2.41969e10i	−0.679614	+	1.33382i	−0.930675	+	0.365846i	$0.880780\pi$
$368$	−2.10414e8	+	2.10414e8i	−0.0114732	+	0.0114732i
$369$	−1.53092e9	+	4.97426e8i	−0.0825747	+	0.0268302i
$370$	8.11677e9	−	4.44054e10i	0.433088	−	2.36935i
$371$	9.99229e9	−	3.07531e10i	0.527436	−	1.62328i
$372$	−8.36474e9	+	4.26205e9i	−0.436798	+	0.222560i
$373$	1.38868e8	−	8.76779e8i	0.00717410	−	0.0452955i	−0.983842	−	0.179041i	$-0.942701\pi$
$373$	1.38868e8	−	8.76779e8i	0.00717410	−	0.0452955i	0.991016	+	0.133746i	$0.0427005\pi$
$374$			5.96704e10i			3.04981i
$375$	−1.50223e9	+	2.10818e10i	−0.0759644	+	1.06606i
$376$	1.93611e10			0.968675
$377$	−2.40137e10	−	3.80340e9i	−1.18876	−	0.188281i
$378$	−1.75100e10	−	3.43653e10i	−0.857667	−	1.68327i
$379$	1.31531e10	+	4.27371e9i	0.637488	+	0.207132i	0.609889	−	0.792487i	$-0.291214\pi$
$379$	1.31531e10	+	4.27371e9i	0.637488	+	0.207132i	0.0275985	+	0.999619i	$0.491214\pi$
$380$	−2.23456e10	−	4.08450e9i	−1.07166	−	0.195887i
$381$	7.47810e9	+	2.30152e10i	0.354888	+	1.09223i
$382$	8.75208e9	+	8.75208e9i	0.411015	+	0.411015i
$383$	−4.68251e9	−	2.38586e9i	−0.217612	−	0.110879i	0.341787	−	0.939778i	$-0.388968\pi$
$383$	−4.68251e9	−	2.38586e9i	−0.217612	−	0.110879i	−0.559399	+	0.828899i	$0.688968\pi$
$384$	2.45111e10	−	3.37367e10i	1.12730	−	1.55159i
$385$	4.11204e10	+	1.44474e10i	1.87160	+	0.657577i
$386$	4.64528e10	−	3.37500e10i	2.09249	−	1.52028i
$387$	−6.76882e8	−	4.27366e9i	−0.0301765	−	0.190527i
$388$	−6.68483e10	+	1.05877e10i	−2.94960	+	0.467171i
$389$	1.00921e10	+	1.38906e10i	0.440742	+	0.606630i	0.970377	−	0.241596i	$-0.0776709\pi$
$389$	1.00921e10	+	1.38906e10i	0.440742	+	0.606630i	−0.529634	+	0.848226i	$0.677671\pi$
$390$	1.22917e10	+	4.11233e10i	0.531319	+	1.77758i
$391$	1.05871e9	+	7.69198e8i	0.0452971	+	0.0329102i
$392$	−7.28512e9	+	1.42979e10i	−0.308526	+	0.605517i
$393$	1.67816e10	−	1.67816e10i	0.703498	−	0.703498i
$394$	−4.90885e10	+	1.59498e10i	−2.03702	+	0.661867i
$395$	7.97764e9	+	4.30605e9i	0.327707	+	0.176885i
$396$	3.03846e9	−	9.35143e9i	0.123559	−	0.380275i
$397$	−4.78626e9	+	2.43872e9i	−0.192679	+	0.0981748i	−0.547668	−	0.836696i	$-0.684484\pi$
$397$	−4.78626e9	+	2.43872e9i	−0.192679	+	0.0981748i	0.354989	+	0.934870i	$0.384484\pi$
$398$	4.57782e9	−	2.89032e10i	0.182442	−	1.15190i
$399$			2.08278e10i			0.821774i
$400$	4.67648e9	+	7.12393e9i	0.182675	+	0.278278i
$401$	−8.18011e9			−0.316360			−0.158180	−	0.987410i	$-0.550563\pi$
$401$	−8.18011e9			−0.316360			−0.158180	+	0.987410i	$0.550563\pi$
$402$	−6.91965e10	−	1.09597e10i	−2.64960	−	0.419655i
$403$	3.26556e9	+	6.40901e9i	0.123805	+	0.242980i
$404$	−2.39165e9	−	7.77095e8i	−0.0897786	−	0.0291708i
$405$	4.01405e9	+	2.99190e10i	0.149198	+	1.11206i
$406$	1.99238e10	+	6.13190e10i	0.733276	+	2.25679i
$407$	4.49868e10	+	4.49868e10i	1.63948	+	1.63948i
$408$	3.81640e10	+	1.94455e10i	1.37725	+	0.701744i
$409$	−2.45910e9	+	3.38466e9i	−0.0878785	+	0.120954i	−0.850693	−	0.525663i	$-0.823817\pi$
$409$	−2.45910e9	+	3.38466e9i	−0.0878785	+	0.120954i	0.762814	+	0.646618i	$0.223817\pi$
$410$	1.62813e10	+	2.35647e10i	0.576174	+	0.833923i
$411$	3.30993e10	−	2.40481e10i	1.15998	−	0.842777i
$412$	−1.32728e10	−	8.38012e10i	−0.460653	−	2.90845i
$413$	−1.99198e9	+	3.15498e8i	−0.0684675	+	0.0108442i
$414$	−1.98845e8	−	2.73687e8i	−0.00676884	−	0.00931650i
$415$	−8.90911e9	−	6.80134e9i	−0.300360	−	0.229299i
$416$	−1.78855e10	−	1.29946e10i	−0.597210	−	0.433898i
$417$	−8.83953e9	+	1.73485e10i	−0.292338	+	0.573745i
$418$	3.55144e10	−	3.55144e10i	1.16332	−	1.16332i
$419$	−1.54477e10	+	5.01926e9i	−0.501196	+	0.162848i	−0.548695	−	0.836023i	$-0.684875\pi$
$419$	−1.54477e10	+	5.01926e9i	−0.501196	+	0.162848i	0.0474987	+	0.998871i	$0.484875\pi$
$420$	5.25047e10	−	5.00719e10i	1.68733	−	1.60915i
$421$	−1.04406e10	+	3.21329e10i	−0.332352	+	1.02287i	0.635660	+	0.771969i	$0.280728\pi$
$421$	−1.04406e10	+	3.21329e10i	−0.332352	+	1.02287i	−0.968012	+	0.250904i	$0.919272\pi$
$422$	6.20311e10	−	3.16064e10i	1.95596	−	0.996611i
$423$	−5.48152e8	+	3.46090e9i	−0.0171214	+	0.108100i
$424$			5.59722e10i			1.73185i
$425$	2.77263e10	−	2.52137e10i	0.849837	−	0.772825i
$426$	−2.01461e9			−0.0611719
$427$	−1.70512e10	−	2.70065e9i	−0.512913	−	0.0812375i
$428$	1.22901e10	+	2.41207e10i	0.366253	+	0.718812i
$429$	−5.75312e10	−	1.86930e10i	−1.69854	−	0.551887i
$430$	−6.94090e10	+	3.33169e10i	−2.03021	+	0.974519i
$431$	−1.56919e10	−	4.82948e10i	−0.454744	−	1.39956i	−0.871436	−	0.490510i	$-0.836810\pi$
$431$	−1.56919e10	−	4.82948e10i	−0.454744	−	1.39956i	0.416692	−	0.909048i	$-0.363190\pi$
$432$	7.51530e9	+	7.51530e9i	0.215780	+	0.215780i
$433$	−1.69011e10	−	8.61155e9i	−0.480799	−	0.244979i	0.196754	−	0.980453i	$-0.436960\pi$
$433$	−1.69011e10	−	8.61155e9i	−0.480799	−	0.244979i	−0.677554	+	0.735473i	$0.736960\pi$
$434$	1.12119e10	−	1.54318e10i	0.316024	−	0.434969i
$435$	1.04478e9	−	4.40523e10i	0.0291787	−	1.23030i
$436$	−4.05663e10	+	2.94732e10i	−1.12259	+	0.815607i
$437$	−1.72311e8	−	1.08793e9i	−0.00472484	−	0.0298315i
$438$	−1.02938e11	+	1.63038e10i	−2.79692	+	0.442989i
$439$	−3.60589e10	−	4.96308e10i	−0.970855	−	1.33627i	−0.941614	−	0.336695i	$-0.890691\pi$
$439$	−3.60589e10	−	4.96308e10i	−0.970855	−	1.33627i	−0.0292415	−	0.999572i	$-0.509309\pi$
$440$	−7.54224e10	−	1.78877e9i	−2.01229	−	0.0477248i
$441$	−2.34956e9	−	1.70706e9i	−0.0621202	−	0.0451329i
$442$	3.45515e10	−	6.78111e10i	0.905269	−	1.77669i
$443$	−2.84942e10	+	2.84942e10i	−0.739847	+	0.739847i	−0.972548	−	0.232701i	$-0.925244\pi$
$443$	−2.84942e10	+	2.84942e10i	−0.739847	+	0.739847i	0.232701	+	0.972548i	$0.425244\pi$
$444$	1.00723e11	−	3.27269e10i	2.59177	−	0.842118i
$445$	1.55609e8	+	3.24180e8i	0.00396821	+	0.00826695i
$446$	8.26704e8	−	2.54433e9i	0.0208935	−	0.0643035i
$447$	5.46541e10	−	2.78476e10i	1.36896	−	0.697522i
$448$	−1.17741e10	+	7.43385e10i	−0.292290	+	1.84545i
$449$			4.98302e10i			1.22605i	0.790065	+	0.613024i	$0.210047\pi$
$449$			4.98302e10i			1.22605i	−0.790065	+	0.613024i	$0.789953\pi$
$450$	−8.83088e9	+	3.98410e9i	−0.215354	+	0.0971583i
$451$	−4.03676e10			−0.975724
$452$	−2.03984e8	−	3.23078e7i	−0.00488699	−	0.000774023i
$453$	3.72205e10	+	7.30494e10i	0.883873	+	1.73470i
$454$	3.14296e10	+	1.02121e10i	0.739802	+	0.240376i
$455$	−3.83648e10	−	4.02288e10i	−0.895132	−	0.938623i
$456$	−1.11408e10	−	3.42878e10i	−0.257666	−	0.793014i
$457$	9.89937e9	+	9.89937e9i	0.226957	+	0.226957i	0.811420	−	0.584463i	$-0.198695\pi$
$457$	9.89937e9	+	9.89937e9i	0.226957	+	0.226957i	−0.584463	+	0.811420i	$0.698695\pi$
$458$	7.05696e10	+	3.59570e10i	1.60382	+	0.817187i
$459$	2.74732e10	−	3.78137e10i	0.618955	−	0.851918i
$460$	−2.32830e9	+	3.04985e9i	−0.0520005	+	0.0681158i
$461$	3.61637e10	−	2.62744e10i	0.800698	−	0.581741i	−0.110421	−	0.993885i	$-0.535220\pi$
$461$	3.61637e10	−	2.62744e10i	0.800698	−	0.581741i	0.911119	+	0.412144i	$0.135220\pi$
$462$	2.50945e10	+	1.58441e11i	0.550822	+	3.47775i
$463$	5.08283e10	−	8.05041e9i	1.10607	−	0.175184i	0.423421	−	0.905933i	$-0.360829\pi$
$463$	5.08283e10	−	8.05041e9i	1.10607	−	0.175184i	0.682646	+	0.730749i	$0.260829\pi$
$464$	−1.04431e10	−	1.43737e10i	−0.225298	−	0.310097i
$465$	−1.07255e10	+	7.41046e9i	−0.229406	+	0.158501i
$466$	1.20722e10	+	8.77096e9i	0.256001	+	0.185996i
$467$	3.05892e9	−	6.00347e9i	0.0643133	−	0.126222i	−0.856612	−	0.515961i	$-0.827435\pi$
$467$	3.05892e9	−	6.00347e9i	0.0643133	−	0.126222i	0.920925	+	0.389739i	$0.127435\pi$
$468$	−8.86784e9	+	8.86784e9i	−0.184856	+	0.184856i
$469$	8.62968e10	−	2.80395e10i	1.78362	−	0.579535i
$470$	6.17951e10	−	8.29067e9i	1.26638	−	0.169902i
$471$	−2.50936e10	+	7.72302e10i	−0.509894	+	1.56929i
$472$	3.11054e9	−	1.58490e9i	0.0626712	−	0.0319325i
$473$	1.69746e10	−	1.07173e11i	0.339121	−	2.14113i
$474$			3.33665e10i			0.660993i
$475$	−3.15087e10	−	1.49540e9i	−0.618950	−	0.0293754i
$476$	−1.28649e11			−2.50598
$477$	−1.00053e10	−	1.58469e9i	−0.193267	−	0.0306105i
$478$	−6.13424e10	−	1.20391e11i	−1.17503	−	2.30613i
$479$	−5.78780e10	−	1.88057e10i	−1.09944	−	0.357230i	−0.297553	−	0.954705i	$-0.596170\pi$
$479$	−5.78780e10	−	1.88057e10i	−1.09944	−	0.357230i	−0.801887	+	0.597476i	$0.796170\pi$
$480$	1.90317e10	−	3.52592e10i	0.358519	−	0.664214i
$481$	−2.50752e10	−	7.71734e10i	−0.468450	−	1.44174i
$482$	−9.86042e9	−	9.86042e9i	−0.182687	−	0.182687i
$483$	3.13465e9	+	1.59718e9i	0.0575970	+	0.0293471i
$484$	8.82276e10	−	1.21435e11i	1.60777	−	2.21290i
$485$	−9.00490e10	+	2.69156e10i	−1.62747	+	0.486449i
$486$	−2.11716e10	+	1.53821e10i	−0.379498	+	0.275721i
$487$	4.66579e9	+	2.94586e10i	0.0829486	+	0.523717i	0.993818	+	0.111022i	$0.0354124\pi$
$487$	4.66579e9	+	2.94586e10i	0.0829486	+	0.523717i	−0.910869	+	0.412695i	$0.864588\pi$
$488$	2.95152e10	−	4.67474e9i	0.520434	−	0.0824287i
$489$	−2.45395e10	−	3.37758e10i	−0.429171	−	0.590704i
$490$	−1.71295e10	+	4.87544e10i	−0.297140	+	0.845725i
$491$	−9.50030e9	−	6.90237e9i	−0.163460	−	0.118761i	0.503048	−	0.864258i	$-0.332212\pi$
$491$	−9.50030e9	−	6.90237e9i	−0.163460	−	0.118761i	−0.666508	+	0.745498i	$0.732212\pi$
$492$	−3.05072e10	+	5.98738e10i	−0.520646	+	1.02182i
$493$	−5.52492e10	+	5.52492e10i	−0.935273	+	0.935273i
$494$	−6.09239e10	+	1.97954e10i	−1.02301	+	0.332396i
$495$	2.45512e9	−	1.34315e10i	0.0408932	−	0.223720i
$496$	−1.62429e9	+	4.99906e9i	−0.0268372	+	0.0825965i
$497$	2.32485e9	−	1.18457e9i	0.0381039	−	0.0194149i
$498$	6.45348e9	−	4.07457e10i	0.104924	−	0.662467i
$499$		−	3.34831e10i		−	0.540037i	−0.962855	−	0.270019i	$-0.912970\pi$
$499$		−	3.34831e10i		−	0.540037i	0.962855	−	0.270019i	$-0.0870299\pi$
$500$	7.19798e10	+	8.30250e10i	1.15168	+	1.32840i
$501$	5.31489e10			0.843613
$502$	−3.31047e10	−	5.24327e9i	−0.521284	−	0.0825633i
$503$	2.03526e10	+	3.99443e10i	0.317942	+	0.623997i	0.993567	−	0.113249i	$-0.0361258\pi$
$503$	2.03526e10	+	3.99443e10i	0.317942	+	0.623997i	−0.675624	+	0.737246i	$0.736126\pi$
$504$	1.36389e10	+	4.43155e9i	0.211377	+	0.0686806i
$505$	−3.43515e9	−	6.27903e8i	−0.0528177	−	0.00965444i
$506$	−2.62160e9	−	8.06845e9i	−0.0399911	−	0.123080i
$507$	4.62186e9	+	4.62186e9i	0.0699495	+	0.0699495i
$508$	1.12102e11	+	5.71187e10i	1.68328	+	0.857677i
$509$	7.33636e9	−	1.00976e10i	0.109297	−	0.150435i	−0.750864	−	0.660457i	$-0.770363\pi$
$509$	7.33636e9	−	1.00976e10i	0.109297	−	0.150435i	0.860161	+	0.510022i	$0.170363\pi$
$510$	1.30136e11	+	4.57223e10i	1.92360	+	0.675846i
$511$	1.09204e11	−	7.93413e10i	1.60160	−	1.16363i
$512$	−7.03279e9	−	4.44033e10i	−0.102341	−	0.646153i
$513$	−3.88573e10	+	6.15439e9i	−0.561052	+	0.0888618i
$514$	3.28200e10	+	4.51729e10i	0.470204	+	0.647181i
$515$	−3.37415e10	−	1.12886e11i	−0.479662	−	1.60476i
$516$	−1.46133e11	−	1.06172e11i	−2.06134	−	1.49765i
$517$	−3.98935e10	+	7.82954e10i	−0.558393	+	1.09591i
$518$	−1.52158e11	+	1.52158e11i	−2.11338	+	2.11338i
$519$	−8.18848e10	+	2.66060e10i	−1.12858	+	0.366699i
$520$	8.46764e10	+	4.57054e10i	1.15811	+	0.625106i
$521$	−3.71230e10	+	1.14253e11i	−0.503839	+	1.55066i	0.298874	+	0.954293i	$0.403389\pi$
$521$	−3.71230e10	+	1.14253e11i	−0.503839	+	1.55066i	−0.802713	+	0.596365i	$0.796611\pi$
$522$	1.79970e10	−	9.16991e9i	0.242391	−	0.123505i
$523$	−7.31725e9	+	4.61993e10i	−0.0978005	+	0.617488i	0.889292	+	0.457339i	$0.151197\pi$
$523$	−7.31725e9	+	4.61993e10i	−0.0978005	+	0.617488i	−0.987093	+	0.160149i	$0.948803\pi$
$524$		−	1.23387e11i		−	1.63661i
$525$	6.30169e10	−	7.86095e10i	0.829506	−	1.03476i
$526$	5.46922e10			0.714468
$527$	2.28314e10	+	3.61613e9i	0.295998	+	0.0468815i
$528$	−2.00685e10	−	3.93867e10i	−0.258214	−	0.506774i
$529$	7.43012e10	+	2.41419e10i	0.948797	+	0.308283i
$530$	2.39681e10	+	1.78648e11i	0.303759	+	2.26409i
$531$	1.95243e8	+	6.00898e8i	0.00245583	+	0.00755827i
$532$	7.65688e10	+	7.65688e10i	0.955884	+	0.955884i
$533$	4.58750e10	+	2.33745e10i	0.568417	+	0.289623i
$534$	−7.77934e8	+	1.07073e9i	−0.00956705	+	0.0131679i
$535$	2.13689e10	+	3.09282e10i	0.260836	+	0.377520i
$536$	−1.27068e11	+	9.23203e10i	−1.53949	+	1.11851i
$537$	5.86060e9	+	3.70024e10i	0.0704766	+	0.444972i
$538$	3.27257e10	−	5.18325e9i	0.390625	−	0.0618689i
$539$	−4.28090e10	−	5.89215e10i	−0.507201	−	0.698102i
$540$	1.08931e11	+	8.31592e10i	1.28108	+	0.977992i
$541$	7.65674e10	+	5.56295e10i	0.893830	+	0.649405i	0.936874	−	0.349668i	$-0.113706\pi$
$541$	7.65674e10	+	5.56295e10i	0.893830	+	0.649405i	−0.0430441	+	0.999073i	$0.513706\pi$
$542$	6.47363e10	−	1.27052e11i	0.750155	−	1.47226i
$543$	−5.87309e9	+	5.87309e9i	−0.0675565	+	0.0675565i
$544$	−6.75695e10	+	2.19546e10i	−0.771534	+	0.250686i
$545$	−5.03896e10	+	4.80548e10i	−0.571156	+	0.544692i
$546$	6.32252e10	−	1.94587e11i	0.711410	−	2.18949i
$547$	6.66424e10	−	3.39560e10i	0.744392	−	0.379287i	−0.0402878	−	0.999188i	$-0.512827\pi$
$547$	6.66424e10	−	3.39560e10i	0.744392	−	0.379287i	0.784680	+	0.619902i	$0.212827\pi$
$548$	3.32749e10	−	2.10089e11i	0.368973	−	2.32960i
$549$			5.40835e9i			0.0595354i
$550$	−2.41493e11	+	2.65876e10i	−2.63909	+	0.290555i
$551$	6.57662e10			0.713503
$552$	−6.01475e9	−	9.52642e8i	−0.0647830	−	0.0102606i
$553$	−1.96192e10	−	3.85048e10i	−0.209788	−	0.411732i
$554$	−9.69487e10	−	3.15005e10i	−1.02921	−	0.334410i
$555$	1.32583e11	−	6.36410e10i	1.39739	−	0.670756i
$556$	3.12815e10	+	9.62745e10i	0.327332	+	1.00742i
$557$	1.89348e10	+	1.89348e10i	0.196716	+	0.196716i	0.798590	−	0.601875i	$-0.205579\pi$
$557$	1.89348e10	+	1.89348e10i	0.196716	+	0.196716i	−0.601875	+	0.798590i	$0.705579\pi$
$558$	−5.32439e9	−	2.71291e9i	−0.0549203	−	0.0279833i
$559$	−8.13481e10	+	1.11966e11i	−0.833106	+	1.14667i
$560$	9.63159e8	−	4.06110e10i	0.00979368	−	0.412944i
$561$	−1.57274e11	+	1.14266e11i	−1.58783	+	1.15363i
$562$	−2.75134e10	−	1.73713e11i	−0.275803	−	1.74135i
$563$	−6.24634e10	+	9.89322e9i	−0.621716	+	0.0984701i	−0.459342	−	0.888259i	$-0.651915\pi$
$563$	−6.24634e10	+	9.89322e9i	−0.621716	+	0.0984701i	−0.162373	+	0.986729i	$0.551915\pi$
$564$	8.59799e10	+	1.18341e11i	0.849729	+	1.16955i
$565$	−2.86710e8	−	6.79983e6i	−0.00281352	−	6.67274e-5i
$566$	1.74551e11	+	1.26818e11i	1.70081	+	1.23571i
$567$	6.53290e10	−	1.28215e11i	0.632082	−	1.24053i
$568$	−3.19367e9	+	3.19367e9i	−0.0306829	+	0.0306829i
$569$	1.37018e11	−	4.45200e10i	1.30716	−	0.424723i	0.429095	−	0.903259i	$-0.358832\pi$
$569$	1.37018e11	−	4.45200e10i	1.30716	−	0.424723i	0.878068	+	0.478536i	$0.158832\pi$
$570$	−5.02408e10	−	1.04667e11i	−0.475946	−	0.991537i
$571$	8.51617e9	−	2.62101e10i	0.0801125	−	0.246561i	−0.902976	−	0.429690i	$-0.858623\pi$
$571$	8.51617e9	−	2.62101e10i	0.0801125	−	0.246561i	0.983089	+	0.183129i	$0.0586227\pi$
$572$	−2.80221e11	+	1.42780e11i	−2.61768	+	1.33378i
$573$	−6.30811e9	+	3.98278e10i	−0.0585168	+	0.369461i
$574$		−	1.36535e11i		−	1.25776i
$575$	−2.64130e9	+	4.62747e9i	−0.0241628	+	0.0423323i
$576$	2.35789e10			0.214207
$577$	8.26031e10	+	1.30830e10i	0.745235	+	0.118034i	0.517492	−	0.855688i	$-0.326866\pi$
$577$	8.26031e10	+	1.30830e10i	0.745235	+	0.118034i	0.227742	+	0.973721i	$0.426866\pi$
$578$	−2.68850e10	−	5.27648e10i	−0.240879	−	0.472752i
$579$	1.77910e11	+	5.78065e10i	1.58302	+	0.514355i
$580$	−1.58108e11	−	1.65789e11i	−1.39714	−	1.46502i
$581$	1.65108e10	+	5.08150e10i	0.144898	+	0.445951i
$582$	−2.44602e11	−	2.44602e11i	−2.13191	−	2.13191i
$583$	−2.26350e11	−	1.15331e11i	−1.95932	−	0.998324i
$584$	−1.37338e11	+	1.89029e11i	−1.18070	+	1.62509i
$585$	−1.05674e10	+	1.38424e10i	−0.0902291	+	0.118192i
$586$	1.48328e11	−	1.07767e11i	1.25786	−	0.913892i
$587$	−1.24934e10	−	7.88805e10i	−0.105228	−	0.664381i	−0.982763	−	0.184870i	$-0.940814\pi$
$587$	−1.24934e10	−	7.88805e10i	−0.105228	−	0.664381i	0.877535	−	0.479512i	$-0.159186\pi$
$588$	−1.19745e11	+	1.89658e10i	−1.00173	+	0.158658i
$589$	−1.14365e10	−	1.57409e10i	−0.0950234	−	0.130789i
$590$	9.24930e9	−	6.39053e9i	0.0763310	−	0.0527386i
$591$	−1.36041e11	−	9.88399e10i	−1.11512	−	0.810182i
$592$	2.69203e10	−	5.28340e10i	0.219176	−	0.430157i
$593$	−2.40610e10	+	2.40610e10i	−0.194578	+	0.194578i	−0.797671	−	0.603093i	$-0.793935\pi$
$593$	−2.40610e10	+	2.40610e10i	−0.194578	+	0.194578i	0.603093	+	0.797671i	$0.293935\pi$
$594$	−2.88178e11	+	9.36348e10i	−2.31481	+	0.752128i
$595$	−1.77060e11	+	2.37551e10i	−1.41271	+	0.189535i
$596$	9.85477e10	−	3.03299e11i	0.781019	−	2.40373i
$597$	8.49468e10	−	4.32825e10i	0.668728	−	0.340734i
$598$	−1.69269e9	+	1.06872e10i	−0.0132365	+	0.0835719i
$599$			1.04240e11i			0.809707i	0.914382	+	0.404853i	$0.132677\pi$
$599$			1.04240e11i			0.809707i	−0.914382	+	0.404853i	$0.867323\pi$
$600$	−6.16935e10	+	1.63119e11i	−0.476030	+	1.25863i
$601$	7.03676e10			0.539355			0.269677	−	0.962951i	$-0.413083\pi$
$601$	7.03676e10			0.539355			0.269677	+	0.962951i	$0.413083\pi$
$602$	3.62492e11	+	5.74130e10i	2.76002	+	0.437144i
$603$	−1.29052e10	−	2.53279e10i	−0.0976102	−	0.191571i
$604$	4.05382e11	+	1.31717e11i	3.04591	+	0.989676i
$605$	9.90055e10	−	1.83423e11i	0.738989	−	1.36909i
$606$	−3.97172e9	−	1.22237e10i	−0.0294502	−	0.0906383i
$607$	−1.01829e11	−	1.01829e11i	−0.750098	−	0.750098i	0.224399	−	0.974497i	$-0.427958\pi$
$607$	−1.01829e11	−	1.01829e11i	−0.750098	−	0.750098i	−0.974497	+	0.224399i	$0.927958\pi$
$608$	5.32827e10	+	2.71489e10i	0.389917	+	0.198673i
$609$	−1.23466e11	+	1.69937e11i	−0.897591	+	1.23543i
$610$	9.22024e10	−	2.75593e10i	0.665921	−	0.199044i
$611$	9.06723e10	−	6.58773e10i	0.650594	−	0.472684i
$612$	6.30474e9	+	3.98065e10i	0.0449429	+	0.283758i
$613$	−8.93208e10	+	1.41470e10i	−0.632573	+	0.100190i	−0.464483	−	0.885582i	$-0.653760\pi$
$613$	−8.93208e10	+	1.41470e10i	−0.632573	+	0.100190i	−0.168090	+	0.985772i	$0.553760\pi$
$614$	−4.84829e9	−	6.67310e9i	−0.0341126	−	0.0469520i
$615$	−3.09317e10	+	8.80381e10i	−0.216223	+	0.615418i
$616$	2.90950e11	+	2.11387e11i	2.02067	+	1.46810i
$617$	−8.20735e10	+	1.61078e11i	−0.566321	+	1.11147i	0.413297	+	0.910596i	$0.364377\pi$
$617$	−8.20735e10	+	1.61078e11i	−0.566321	+	1.11147i	−0.979618	+	0.200871i	$0.935623\pi$
$618$	3.06634e11	−	3.06634e11i	2.10216	−	2.10216i
$619$	−1.10201e11	+	3.58065e10i	−0.750625	+	0.243893i	−0.659250	−	0.751924i	$-0.729126\pi$
$619$	−1.10201e11	+	3.58065e10i	−0.750625	+	0.243893i	−0.0913751	+	0.995817i	$0.529126\pi$
$620$	−1.21869e10	+	6.66727e10i	−0.0824761	+	0.451212i
$621$	−2.05352e9	+	6.32008e9i	−0.0138080	+	0.0424968i
$622$	−2.65839e11	+	1.35452e11i	−1.77606	+	0.904946i
$623$	2.68152e8	−	1.69304e9i	0.00178003	−	0.0112387i
$624$			5.63807e10i			0.371871i
$625$	1.14397e11	+	1.00977e11i	0.749713	+	0.661763i
$626$	−7.25597e10			−0.472496
$627$	1.61614e11	+	2.55972e10i	1.04571	+	0.165624i
$628$	1.91668e11	+	3.76170e11i	1.23229	+	2.41850i
$629$	−2.48010e11	−	8.05833e10i	−1.58441	−	0.514805i
$630$	4.54293e10	+	8.30392e9i	0.288386	+	0.0527134i
$631$	1.56413e9	+	4.81390e9i	0.00986632	+	0.0303654i	0.955868	−	0.293795i	$-0.0949183\pi$
$631$	1.56413e9	+	4.81390e9i	0.00986632	+	0.0303654i	−0.946002	+	0.324160i	$0.894918\pi$
$632$	5.28943e10	+	5.28943e10i	0.331544	+	0.331544i
$633$	2.02092e11	+	1.02971e11i	1.25874	+	0.641359i
$634$	9.54408e10	−	1.31363e11i	0.590714	−	0.813048i
$635$	1.64834e11	+	5.79134e10i	1.01380	+	0.356192i
$636$	−3.42121e11	+	2.48565e11i	−2.09098	+	1.51919i
$637$	1.45315e10	+	9.17482e10i	0.0882577	+	0.557237i
$638$	5.00294e11	−	7.92388e10i	3.01955	−	0.478250i
$639$	−4.80466e8	−	6.61305e8i	−0.00288177	−	0.00396641i
$640$	−8.62187e10	−	2.88454e11i	−0.513903	−	1.71932i
$641$	−1.27918e11	−	9.29378e10i	−0.757703	−	0.550504i	0.140502	−	0.990080i	$-0.455128\pi$
$641$	−1.27918e11	−	9.29378e10i	−0.757703	−	0.550504i	−0.898205	+	0.439577i	$0.855128\pi$
$642$	−6.28146e10	+	1.23281e11i	−0.369760	+	0.725696i
$643$	2.23406e10	−	2.23406e10i	0.130693	−	0.130693i	−0.638735	−	0.769427i	$-0.720542\pi$
$643$	2.23406e10	−	2.23406e10i	0.130693	−	0.130693i	0.769427	+	0.638735i	$0.220542\pi$
$644$	1.73955e10	−	5.65214e9i	0.101133	−	0.0328601i
$645$	−2.20729e11	−	1.19142e11i	−1.27532	−	0.688374i
$646$	−6.36158e10	+	1.95789e11i	−0.365288	+	1.12424i
$647$	−7.30501e10	+	3.72209e10i	−0.416873	+	0.212407i	−0.649830	−	0.760080i	$-0.725160\pi$
$647$	−7.30501e10	+	3.72209e10i	−0.416873	+	0.212407i	0.232957	+	0.972487i	$0.425160\pi$
$648$	−3.89656e10	+	2.46019e11i	−0.220995	+	1.39530i
$649$			1.58446e10i			0.0893105i
$650$	2.89835e11	+	1.09619e11i	1.62367	+	0.614092i
$651$	6.21441e10			0.346000
$652$	−2.14383e11	−	3.39549e10i	−1.18631	−	0.187894i
$653$	1.40159e10	+	2.75077e10i	0.0770845	+	0.151287i	0.926332	−	0.376708i	$-0.122944\pi$
$653$	1.40159e10	+	2.75077e10i	0.0770845	+	0.151287i	−0.849248	+	0.527995i	$0.822944\pi$
$654$	−2.43736e11	−	7.91945e10i	−1.33232	−	0.432896i
$655$	−2.27836e10	−	1.69819e11i	−0.123782	−	0.922618i
$656$	1.16265e10	+	3.57827e10i	0.0627818	+	0.193222i
$657$	−2.99016e10	−	2.99016e10i	−0.160485	−	0.160485i
$658$	−2.64818e11	−	1.34931e11i	−1.41268	−	0.719796i
$659$	7.06349e10	−	9.72206e10i	0.374522	−	0.515486i	−0.579601	−	0.814901i	$-0.696791\pi$
$659$	7.06349e10	−	9.72206e10i	0.374522	−	0.515486i	0.954123	+	0.299415i	$0.0967914\pi$
$660$	−3.24007e11	−	4.68950e11i	−1.70757	−	2.47144i
$661$	4.25542e10	−	3.09174e10i	0.222913	−	0.161956i	−0.470724	−	0.882281i	$-0.656007\pi$
$661$	4.25542e10	−	3.09174e10i	0.222913	−	0.161956i	0.693637	+	0.720325i	$0.256007\pi$
$662$	2.09648e10	+	1.32367e11i	0.109159	+	0.689202i
$663$	2.44895e11	−	3.87876e10i	1.26744	−	0.200742i
$664$	−5.43619e10	−	7.48227e10i	−0.279655	−	0.384912i
$665$	1.19521e11	+	9.12439e10i	0.611163	+	0.466570i
$666$	5.45378e10	+	3.96240e10i	0.277205	+	0.201401i
$667$	5.04328e9	−	9.89799e9i	0.0254806	−	0.0500085i
$668$	1.95390e11	−	1.95390e11i	0.981287	−	0.981287i
$669$	8.28923e9	−	2.69334e9i	0.0413819	−	0.0134458i
$670$	−3.66033e11	+	3.49073e11i	−1.81644	+	1.73228i
$671$	−4.19116e10	+	1.28991e11i	−0.206749	+	0.636309i
$672$	−1.70182e11	+	8.67119e10i	−0.834518	+	0.425208i
$673$	3.81679e10	−	2.40983e11i	0.186054	−	1.17470i	−0.701045	−	0.713117i	$-0.747283\pi$
$673$	3.81679e10	−	2.40983e11i	0.186054	−	1.17470i	0.887099	−	0.461580i	$-0.152717\pi$
$674$		−	6.21016e11i		−	3.00929i
$675$	1.65278e11	+	9.43387e10i	0.796159	+	0.454438i
$676$	3.39824e10			0.162730
$677$	−3.12905e11	−	4.95592e10i	−1.48956	−	0.235923i	−0.642032	−	0.766678i	$-0.721908\pi$
$677$	−3.12905e11	−	4.95592e10i	−1.48956	−	0.235923i	−0.847525	+	0.530755i	$0.821908\pi$
$678$	−4.79211e8	−	9.40504e8i	−0.00226782	−	0.00445084i
$679$	4.26094e11	+	1.38446e11i	2.00459	+	0.651332i
$680$	2.78780e11	−	1.33816e11i	1.30384	−	0.625855i
$681$	3.32702e10	+	1.02395e11i	0.154692	+	0.476092i
$682$	−1.05965e11	−	1.05965e11i	−0.489805	−	0.489805i
$683$	−3.76953e11	−	1.92067e11i	−1.73223	−	0.882614i	−0.972676	−	0.232166i	$-0.925419\pi$
$683$	−3.76953e11	−	1.92067e11i	−1.73223	−	0.882614i	−0.759551	−	0.650448i	$-0.774581\pi$
$684$	1.99395e10	−	2.74444e10i	0.0910941	−	0.125380i
$685$	7.00336e9	−	2.95292e11i	0.0318086	−	1.34119i
$686$	−1.69932e11	+	1.23463e11i	−0.767324	+	0.557493i
$687$	4.03654e10	+	2.54857e11i	0.181210	+	1.14411i
$688$	−9.98896e10	+	1.58210e10i	−0.445827	+	0.0706121i
$689$	1.90449e11	+	2.62131e11i	0.845089	+	1.16316i
$690$	−1.96053e10	−	4.64974e8i	−0.0864924	−	0.00205131i
$691$	−1.76930e11	−	1.28547e11i	−0.776049	−	0.563833i	0.127741	−	0.991807i	$-0.459227\pi$
$691$	−1.76930e11	−	1.28547e11i	−0.776049	−	0.563833i	−0.903791	+	0.427975i	$0.859227\pi$
$692$	−2.03220e11	+	3.98842e11i	−0.886221	+	1.73931i
$693$	−4.60241e10	+	4.60241e10i	−0.199550	+	0.199550i
$694$	−2.62491e10	+	8.52886e9i	−0.113156	+	0.0367666i
$695$	6.08302e10	+	1.26727e11i	0.260723	+	0.543164i
$696$	1.12357e11	−	3.45800e11i	0.478811	−	1.47363i
$697$	1.47427e11	−	7.51178e10i	0.624663	−	0.318282i
$698$	−2.21747e9	+	1.40005e10i	−0.00934191	+	0.0589825i
$699$			4.86148e10i			0.203638i
$700$	−5.73226e10	−	5.20657e11i	−0.238745	−	2.16850i
$701$	−1.73621e11			−0.719000			−0.359500	−	0.933145i	$-0.617053\pi$
$701$	−1.73621e11			−0.719000			−0.359500	+	0.933145i	$0.617053\pi$
$702$	3.81713e11	+	6.04573e10i	1.57177	+	0.248943i
$703$	9.96485e10	+	1.95571e11i	0.407990	+	0.800726i
$704$	5.62363e11	+	1.82723e11i	2.28942	+	0.743878i
$705$	1.40187e11	+	1.46998e11i	0.567480	+	0.595052i
$706$	−1.25872e11	−	3.87394e11i	−0.506653	−	1.55932i
$707$	1.17708e10	+	1.17708e10i	0.0471116	+	0.0471116i
$708$	2.35009e10	+	1.19743e10i	0.0935301	+	0.0476560i
$709$	−1.20726e11	+	1.66165e11i	−0.477767	+	0.657590i	−0.978074	−	0.208258i	$-0.933220\pi$
$709$	−1.20726e11	+	1.66165e11i	−0.477767	+	0.657590i	0.500307	+	0.865848i	$0.333220\pi$
$710$	−8.82572e9	+	1.15609e10i	−0.0347310	+	0.0454943i
$711$	−1.09527e10	+	7.95760e9i	−0.0428591	+	0.0311389i
$712$	4.64163e8	+	2.93061e9i	0.00180614	+	0.0114035i
$713$	−3.24606e9	+	5.14126e8i	−0.0125603	+	0.00198935i
$714$	−3.86481e11	−	5.31946e11i	−1.48708	−	2.04680i
$715$	−3.59307e11	+	2.48252e11i	−1.37481	+	0.949881i
$716$	1.57576e11	+	1.14486e11i	0.599567	+	0.435611i
$717$	1.99848e11	−	3.92225e11i	0.756178	−	1.48408i
$718$	−1.84285e11	+	1.84285e11i	−0.693412	+	0.693412i
$719$	4.12659e11	−	1.34081e11i	1.54410	−	0.501709i	0.591596	−	0.806234i	$-0.298498\pi$
$719$	4.12659e11	−	1.34081e11i	1.54410	−	0.501709i	0.952504	+	0.304526i	$0.0984979\pi$
$720$	−1.26131e10	+	1.69222e9i	−0.0469344	+	0.00629689i
$721$	−1.73557e11	+	5.34152e11i	−0.642244	+	1.97662i
$722$	−2.47710e11	+	1.26215e11i	−0.911581	+	0.464474i
$723$	7.10695e9	−	4.48715e10i	0.0260094	−	0.164217i
$724$			4.31821e10i			0.157163i
$725$	−2.48218e11	−	1.98983e11i	−0.898424	−	0.720217i
$726$	7.67167e11			2.76149
$727$	1.66936e11	+	2.64401e10i	0.597604	+	0.0946511i	0.447906	−	0.894081i	$-0.352170\pi$
$727$	1.66936e11	+	2.64401e10i	0.597604	+	0.0946511i	0.149698	+	0.988732i	$0.452170\pi$
$728$	−2.08242e11	−	4.08698e11i	−0.741384	−	1.45505i
$729$	2.20296e11	+	7.15787e10i	0.780005	+	0.253439i
$730$	−3.57399e11	+	6.62138e11i	−1.25852	+	2.33162i
$731$	1.37440e11	+	4.22996e11i	0.481330	+	1.48138i
$732$	1.59646e11	+	1.59646e11i	0.556051	+	0.556051i
$733$	−1.92533e11	−	9.81004e10i	−0.666943	−	0.339825i	0.0875239	−	0.996162i	$-0.472105\pi$
$733$	−1.92533e11	−	9.81004e10i	−0.666943	−	0.339825i	−0.754467	+	0.656338i	$0.772105\pi$
$734$	−4.24156e11	+	5.83800e11i	−1.46131	+	2.01131i
$735$	−1.61305e11	+	4.82139e10i	−0.552711	+	0.165205i
$736$	8.17197e9	−	5.93728e9i	0.0278494	−	0.0202338i
$737$	−1.11516e11	−	7.04084e11i	−0.377979	−	2.38646i
$738$	−4.22468e10	+	6.69123e9i	−0.142419	+	0.0225570i
$739$	−2.83315e10	−	3.89950e10i	−0.0949932	−	0.130747i	0.758875	−	0.651237i	$-0.225749\pi$
$739$	−2.83315e10	−	3.89950e10i	−0.0949932	−	0.130747i	−0.853868	+	0.520490i	$0.825749\pi$
$740$	2.53450e11	−	7.21373e11i	0.845212	−	2.40565i
$741$	−1.68842e11	−	1.22671e11i	−0.560024	−	0.406881i
$742$	3.90083e11	−	7.65580e11i	1.28689	−	2.52566i
$743$	−3.58046e11	+	3.58046e11i	−1.17485	+	1.17485i	−0.193817	+	0.981038i	$0.562087\pi$
$743$	−3.58046e11	+	3.58046e11i	−1.17485	+	1.17485i	−0.981038	+	0.193817i	$0.937913\pi$
$744$	−1.02305e11	+	3.32409e10i	−0.333891	+	0.108488i
$745$	7.96278e10	−	4.35630e11i	0.258488	−	1.41414i
$746$	7.28919e9	−	2.24338e10i	0.0235355	−	0.0724350i
$747$	1.49141e10	−	7.59909e9i	0.0478976	−	0.0244050i
$748$	−1.58108e11	+	9.98255e11i	−0.505065	+	3.18886i
$749$		−	1.79200e11i		−	0.569391i
$750$	−1.27059e11	+	5.47047e11i	−0.401568	+	1.72894i
$751$	−4.00758e11			−1.25986			−0.629931	−	0.776651i	$-0.716917\pi$
$751$	−4.00758e11			−1.25986			−0.629931	+	0.776651i	$0.716917\pi$
$752$	8.08926e10	+	1.28121e10i	0.252951	+	0.0400636i
$753$	−4.95743e10	−	9.72950e10i	−0.154197	−	0.302629i
$754$	−6.14431e11	−	1.99641e11i	−1.90102	−	0.617680i
$755$	5.82253e11	+	1.06429e11i	1.79194	+	0.327545i
$756$	−2.01876e11	−	6.21310e11i	−0.618012	−	1.90205i
$757$	1.00930e11	+	1.00930e11i	0.307353	+	0.307353i	0.843882	−	0.536529i	$-0.180265\pi$
$757$	1.00930e11	+	1.00930e11i	0.307353	+	0.307353i	−0.536529	+	0.843882i	$0.680265\pi$
$758$	3.27439e11	+	1.66838e11i	0.991867	+	0.505381i
$759$	1.62459e10	−	2.23605e10i	0.0489526	−	0.0673774i
$760$	−2.45568e11	−	8.62787e10i	−0.736066	−	0.258612i
$761$	3.55548e11	−	2.58321e11i	1.06013	−	0.770231i	0.0860196	−	0.996293i	$-0.472585\pi$
$761$	3.55548e11	−	2.58321e11i	1.06013	−	0.770231i	0.974113	+	0.226062i	$0.0725852\pi$
$762$	1.00593e11	+	6.35120e11i	0.298365	+	1.88381i
$763$	3.27836e11	−	5.19241e10i	0.967293	−	0.153204i
$764$	1.23228e11	+	1.69608e11i	0.361688	+	0.497821i
$765$	1.60276e10	+	5.36220e10i	0.0467975	+	0.156566i
$766$	−1.12975e11	−	8.20811e10i	−0.328146	−	0.238412i
$767$	9.17465e9	−	1.80063e10i	0.0265099	−	0.0520286i
$768$	3.87648e11	−	3.87648e11i	1.11428	−	1.11428i
$769$	5.35224e10	−	1.73905e10i	0.153049	−	0.0497286i	−0.231491	−	0.972837i	$-0.574360\pi$
$769$	5.35224e10	−	1.73905e10i	0.153049	−	0.0497286i	0.384539	+	0.923109i	$0.374360\pi$
$770$	1.01915e12	+	5.50101e11i	2.89918	+	1.56488i
$771$	−5.62138e10	+	1.73008e11i	−0.159084	+	0.489609i
$772$	8.66559e11	−	4.41534e11i	2.43966	−	1.24307i
$773$	4.03489e10	−	2.54753e11i	0.113009	−	0.713512i	−0.864502	−	0.502629i	$-0.832366\pi$
$773$	4.03489e10	−	2.54753e11i	0.113009	−	0.713512i	0.977511	−	0.210883i	$-0.0676338\pi$
$774$		−	1.14976e11i		−	0.320364i
$775$	−4.46185e9	+	9.40126e10i	−0.0123682	+	0.260603i
$776$	−7.75513e11			−2.13866
$777$	−6.92422e11	−	1.09669e11i	−1.89971	−	0.300884i
$778$	2.07128e11	+	4.06511e11i	0.565353	+	1.10957i
$779$	−1.32454e11	−	4.30368e10i	−0.359678	−	0.116867i
$780$	9.66706e10	+	7.20541e11i	0.261165	+	1.94662i
$781$	−6.33451e9	−	1.94956e10i	−0.0170259	−	0.0524002i
$782$	2.45885e10	+	2.45885e10i	0.0657513	+	0.0657513i
$783$	−3.53524e11	−	1.80129e11i	−0.940527	−	0.479223i
$784$	−3.98996e10	+	5.49170e10i	−0.105610	+	0.145359i
$785$	3.33255e11	+	4.82335e11i	0.877603	+	1.27019i
$786$	5.10191e11	−	3.70675e11i	1.33673	−	0.971189i
$787$	−8.67928e9	−	5.47988e10i	−0.0226248	−	0.142847i	0.973790	−	0.227449i	$-0.0730384\pi$
$787$	−8.67928e9	−	5.47988e10i	−0.0226248	−	0.142847i	−0.996415	+	0.0846012i	$0.973038\pi$
$788$	−8.63488e11	+	1.36763e11i	−2.23950	+	0.354702i
$789$	1.04733e11	+	1.44153e11i	0.270257	+	0.371976i
$790$	1.91474e11	+	1.46174e11i	0.491588	+	0.375285i
$791$	1.10602e9	+	8.03568e8i	0.00282524	+	0.00205266i
$792$	5.11489e10	−	1.00385e11i	0.129998	−	0.255135i
$793$	1.22320e11	−	1.22320e11i	0.309318	−	0.309318i
$794$	−1.35753e11	+	4.41087e10i	−0.341560	+	0.110979i
$795$	−4.24966e11	+	4.05276e11i	−1.06386	+	1.01457i
$796$	1.53169e11	−	4.71406e11i	0.381521	−	1.17420i
$797$	1.29543e11	−	6.60053e10i	0.321055	−	0.163586i	−0.286034	−	0.958219i	$-0.592337\pi$
$797$	1.29543e11	−	6.60053e10i	0.321055	−	0.163586i	0.607089	+	0.794634i	$0.292337\pi$
$798$	−8.65772e10	+	5.46627e11i	−0.213497	+	1.34797i
$799$		−	3.60179e11i		−	0.883754i
$800$	−1.18960e11	−	2.63679e11i	−0.290431	−	0.643749i
$801$	−5.37004e8			−0.00130451
$802$	−2.14687e11	−	3.40031e10i	−0.518930	−	0.0821904i
$803$	−4.81442e11	−	9.44883e11i	−1.15793	−	2.27256i
$804$	−1.12858e12	−	3.66699e11i	−2.70091	−	0.877578i
$805$	2.28979e10	−	1.09912e10i	0.0545271	−	0.0261734i
$806$	5.90636e10	+	1.81779e11i	0.139952	+	0.430728i
$807$	7.63299e10	+	7.63299e10i	0.179970	+	0.179970i
$808$	−2.56738e10	−	1.30815e10i	−0.0602345	−	0.0306910i
$809$	8.90631e10	−	1.22585e11i	0.207924	−	0.286182i	−0.692300	−	0.721609i	$-0.743403\pi$
$809$	8.90631e10	−	1.22585e11i	0.207924	−	0.286182i	0.900224	+	0.435427i	$0.143403\pi$
$810$	−1.90187e10	+	8.01910e11i	−0.0441815	+	1.86288i
$811$	−6.51769e10	+	4.73538e10i	−0.150664	+	0.109464i	−0.660564	−	0.750770i	$-0.729683\pi$
$811$	−6.51769e10	+	4.73538e10i	−0.150664	+	0.109464i	0.509899	+	0.860234i	$0.329683\pi$
$812$	1.70838e11	+	1.07863e12i	0.392971	+	2.48112i
$813$	4.58840e11	−	7.26731e10i	1.05027	−	0.166346i
$814$	9.93678e11	+	1.36768e12i	2.26333	+	3.11521i
$815$	−3.01327e11	−	7.14648e9i	−0.682979	−	0.0161980i
$816$	1.46585e11	+	1.06500e11i	0.330620	+	0.240209i
$817$	1.69957e11	−	3.33559e11i	0.381461	−	0.748659i
$818$	−7.86084e10	+	7.86084e10i	−0.175572	+	0.175572i
$819$	7.89528e10	−	2.56533e10i	0.175482	−	0.0570175i
$820$	2.09939e11	+	4.37365e11i	0.464342	+	0.967362i
$821$	3.84600e10	−	1.18368e11i	0.0846519	−	0.260532i	−0.899767	−	0.436370i	$-0.856264\pi$
$821$	3.84600e10	−	1.18368e11i	0.0846519	−	0.260532i	0.984419	+	0.175839i	$0.0562637\pi$
$822$	9.68656e11	−	4.93555e11i	2.12169	−	1.08106i
$823$	−2.63048e10	+	1.66082e11i	−0.0573371	+	0.362012i	0.942292	+	0.334791i	$0.108666\pi$
$823$	−2.63048e10	+	1.66082e11i	−0.0573371	+	0.362012i	−0.999629	+	0.0272210i	$0.991334\pi$
$824$		−	9.72184e11i		−	2.10882i
$825$	−5.32526e11	−	5.85593e11i	−1.14954	−	1.26409i
$826$	−5.35910e10			−0.115126
$827$	−1.11271e11	−	1.76237e10i	−0.237882	−	0.0376768i	0.0363550	−	0.999339i	$-0.488425\pi$
$827$	−1.11271e11	−	1.76237e10i	−0.237882	−	0.0376768i	−0.274237	+	0.961662i	$0.588425\pi$
$828$	−2.60139e9	−	5.10552e9i	−0.00553458	−	0.0108622i
$829$	−6.23016e11	−	2.02430e11i	−1.31911	−	0.428605i	−0.436921	−	0.899500i	$-0.643931\pi$
$829$	−6.23016e11	−	2.02430e11i	−1.31911	−	0.428605i	−0.882189	+	0.470895i	$0.843931\pi$
$830$	−2.05548e11	−	2.15535e11i	−0.433113	−	0.454156i
$831$	−1.02626e11	−	3.15851e11i	−0.215206	−	0.662336i
$832$	−5.33282e11	−	5.33282e11i	−1.11292	−	1.11292i
$833$	2.65987e11	+	1.35527e11i	0.552434	+	0.281479i
$834$	−3.04108e11	+	4.18569e11i	−0.628585	+	0.865173i
$835$	2.32838e11	−	3.04996e11i	0.478970	−	0.627405i
$836$	6.88241e11	−	5.00036e11i	1.40901	−	1.02371i
$837$	1.83629e10	+	1.15939e11i	0.0374144	+	0.236225i
$838$	−4.26289e11	+	6.75175e10i	−0.864426	+	0.136912i
$839$	1.45405e11	+	2.00133e11i	0.293448	+	0.403897i	0.930130	−	0.367230i	$-0.119694\pi$
$839$	1.45405e11	+	2.00133e11i	0.293448	+	0.403897i	−0.636682	+	0.771126i	$0.719694\pi$
$840$	6.83957e11	−	4.72560e11i	1.37376	−	0.949160i
$841$	1.31886e11	+	9.58205e10i	0.263641	+	0.191547i
$842$	−4.07585e11	+	7.99930e11i	−0.810904	+	1.59149i
$843$	4.05170e11	−	4.05170e11i	0.802281	−	0.802281i
$844$	1.12150e12	−	3.64396e11i	2.21018	−	0.718132i
$845$	4.67703e10	−	6.27488e9i	0.0917368	−	0.0123078i
$846$	−2.87725e10	+	8.85527e10i	−0.0561690	+	0.172870i
$847$	−8.85309e11	+	4.51088e11i	−1.72013	+	0.876450i
$848$	−3.70395e10	+	2.33858e11i	−0.0716277	+	0.452240i
$849$			7.02917e11i			1.35292i
$850$	8.32485e11	−	5.46482e11i	1.59478	−	1.04689i
$851$	3.70756e10			0.0706919
$852$	−3.37034e10	−	5.33809e9i	−0.0639610	−	0.0101304i
$853$	4.31344e11	+	8.46559e11i	0.814755	+	1.59905i	0.800639	+	0.599147i	$0.204494\pi$
$853$	4.31344e11	+	8.46559e11i	0.814755	+	1.59905i	0.0141164	+	0.999900i	$0.495506\pi$
$854$	−4.36283e11	−	1.41757e11i	−0.820233	−	0.266510i
$855$	2.23753e10	−	4.14538e10i	0.0418702	−	0.0775712i
$856$	9.58540e10	+	2.95008e11i	0.178532	+	0.549464i
$857$	2.69604e11	+	2.69604e11i	0.499808	+	0.499808i	0.911378	−	0.411570i	$-0.135019\pi$
$857$	2.69604e11	+	2.69604e11i	0.499808	+	0.499808i	−0.411570	+	0.911378i	$0.635019\pi$
$858$	−1.43221e12	−	7.29745e11i	−2.64275	−	1.34655i
$859$	5.52927e11	−	7.61039e11i	1.01554	−	1.39777i	0.100249	−	0.994962i	$-0.468036\pi$
$859$	5.52927e11	−	7.61039e11i	1.01554	−	1.39777i	0.915287	−	0.402803i	$-0.131964\pi$
$860$	−1.24946e12	+	3.73462e11i	−2.28416	+	0.682736i
$861$	3.59867e11	−	2.61459e11i	0.654831	−	0.475763i
$862$	−2.11083e11	−	1.33273e12i	−0.382317	−	2.41386i
$863$	−8.35354e11	+	1.32307e11i	−1.50601	+	0.238528i	−0.854236	−	0.519886i	$-0.825974\pi$
$863$	−8.35354e11	+	1.32307e11i	−1.50601	+	0.238528i	−0.651773	+	0.758414i	$0.725974\pi$
$864$	−2.12060e11	−	2.91876e11i	−0.380543	−	0.523773i
$865$	−2.06047e11	+	5.86455e11i	−0.368046	+	1.04754i
$866$	−4.07774e11	−	2.96265e11i	−0.725016	−	0.526755i
$867$	8.75892e10	−	1.71903e11i	0.155015	−	0.304234i
$868$	2.28459e11	−	2.28459e11i	0.402465	−	0.402465i
$869$	−3.22892e11	+	1.04914e11i	−0.566210	+	0.183973i
$870$	2.10537e11	−	1.15181e12i	0.367495	−	2.01050i
$871$	−2.80963e11	+	8.64714e11i	−0.488175	+	1.50245i
$872$	−5.11926e11	+	2.60839e11i	−0.885404	+	0.451136i
$873$	2.19564e10	−	1.38627e11i	0.0378010	−	0.238666i
$874$		−	2.92690e10i		−	0.0501605i
$875$	−1.75034e11	−	7.06001e11i	−0.298599	−	1.20441i
$876$	−1.76530e12			−2.99780
$877$	8.46587e11	+	1.34086e11i	1.43111	+	0.226666i	0.823386	−	0.567482i	$-0.192082\pi$
$877$	8.46587e11	+	1.34086e11i	1.43111	+	0.226666i	0.607725	+	0.794148i	$0.292082\pi$
$878$	−7.40061e11	−	1.45245e12i	−1.24534	−	2.44413i
$879$	5.68085e11	+	1.84582e11i	0.951607	+	0.309196i
$880$	−3.13939e11	−	5.73842e10i	−0.523497	−	0.0956889i
$881$	4.80388e10	+	1.47848e11i	0.0797423	+	0.245422i	0.982978	−	0.183723i	$-0.0588150\pi$
$881$	4.80388e10	+	1.47848e11i	0.0797423	+	0.245422i	−0.903236	+	0.429145i	$0.858815\pi$
$882$	−5.45684e10	−	5.45684e10i	−0.0901710	−	0.0901710i
$883$	1.04012e12	+	5.29967e11i	1.71096	+	0.871778i	0.982399	+	0.186797i	$0.0598106\pi$
$883$	1.04012e12	+	5.29967e11i	1.71096	+	0.871778i	0.728561	+	0.684981i	$0.240189\pi$
$884$	7.57708e11	−	1.04290e12i	1.24077	−	1.70778i
$885$	3.45556e10	+	1.21409e10i	0.0563307	+	0.0197915i
$886$	−8.66276e11	+	6.29387e11i	−1.40579	+	1.02137i
$887$	1.13803e11	+	7.18524e11i	0.183848	+	1.16077i	0.891099	+	0.453809i	$0.149935\pi$
$887$	1.13803e11	+	7.18524e11i	0.183848	+	1.16077i	−0.707251	+	0.706963i	$0.750065\pi$
$888$	1.19856e12	−	1.89834e11i	1.92756	−	0.305296i
$889$	−4.89529e11	−	6.73779e11i	−0.783739	−	1.07872i
$890$	2.73641e9	+	9.15493e9i	0.00436135	+	0.0145913i
$891$	−9.14604e11	−	6.64499e11i	−1.45118	−	1.05435i
$892$	2.05720e10	−	4.03749e10i	0.0324951	−	0.0637753i
$893$	−2.14370e11	+	2.14370e11i	−0.337100	+	0.337100i
$894$	1.55015e12	−	5.03676e11i	2.42675	−	0.788498i
$895$	2.38013e11	+	1.28471e11i	0.370945	+	0.200223i
$896$	−4.43484e11	+	1.36490e12i	−0.688092	+	2.11773i
$897$	−3.14099e10	+	1.60041e10i	−0.0485173	+	0.0247208i
$898$	−2.07134e11	+	1.30779e12i	−0.318527	+	2.01110i
$899$		−	1.96227e11i		−	0.300414i
$900$	−1.58293e11	+	4.32529e10i	−0.241263	+	0.0659242i
$901$	1.04127e12			1.58002
$902$	−1.05945e12	−	1.67800e11i	−1.60049	−	0.253493i
$903$	5.42832e11	+	1.06537e12i	0.816421	+	1.60232i
$904$	−2.25061e9	−	7.31267e8i	−0.00336997	−	0.00109497i
$905$	7.97362e9	+	5.94320e10i	0.0118867	+	0.0885985i
$906$	6.73202e11	+	2.07190e12i	0.999154	+	3.07508i
$907$	8.46701e11	+	8.46701e11i	1.25113	+	1.25113i	0.955216	+	0.295910i	$0.0956228\pi$
$907$	8.46701e11	+	8.46701e11i	1.25113	+	1.25113i	0.295910	+	0.955216i	$0.404377\pi$
$908$	4.98743e11	+	2.54122e11i	0.733725	+	0.373851i
$909$	3.06527e9	−	4.21898e9i	0.00448965	−	0.00617947i
$910$	−8.39661e11	−	1.21528e12i	−1.22444	−	1.77219i
$911$	−5.54699e11	+	4.03012e11i	−0.805348	+	0.585120i	−0.912478	−	0.409125i	$-0.865834\pi$
$911$	−5.54699e11	+	4.03012e11i	−0.805348	+	0.585120i	0.107130	+	0.994245i	$0.465834\pi$
$912$	−2.38575e10	−	1.50631e11i	−0.0344863	−	0.217738i
$913$	4.14593e11	−	6.56651e10i	0.596676	−	0.0945042i
$914$	2.18659e11	+	3.00959e11i	0.313317	+	0.431243i
$915$	2.49202e11	+	1.90244e11i	0.355522	+	0.271411i
$916$	1.08532e12	+	7.88530e11i	1.54161	+	1.12005i
$917$	−3.70805e11	+	7.27746e11i	−0.524407	+	1.02921i
$918$	8.78219e11	−	8.78219e11i	1.23661	−	1.23661i
$919$	−2.57576e11	+	8.36915e10i	−0.361113	+	0.117333i	−0.483954	−	0.875094i	$-0.660800\pi$
$919$	−2.57576e11	+	8.36915e10i	−0.361113	+	0.117333i	0.122841	+	0.992426i	$0.460800\pi$
$920$	−3.18165e10	+	3.03423e10i	−0.0444121	+	0.0423543i
$921$	8.30410e9	−	2.55574e10i	0.0115413	−	0.0355204i
$922$	1.05833e12	−	5.39248e11i	1.46453	−	0.746216i
$923$	−4.09001e9	+	2.58233e10i	−0.00563531	+	0.0355800i
$924$			2.71712e12i			3.72753i
$925$	2.15624e11	−	1.03963e12i	0.294530	−	1.42008i
$926$	1.36745e12			1.85981
$927$	1.73783e11	+	2.75246e10i	0.235336	+	0.0372736i
$928$	2.73803e11	+	5.37368e11i	0.369186	+	0.724569i
$929$	−1.15241e12	−	3.74442e11i	−1.54720	−	0.502715i	−0.593846	−	0.804579i	$-0.702391\pi$
$929$	−1.15241e12	−	3.74442e11i	−1.54720	−	0.502715i	−0.953351	+	0.301864i	$0.902391\pi$
$930$	−3.12294e11	+	1.49904e11i	−0.417477	+	0.200392i
$931$	−7.76467e10	−	2.38972e11i	−0.103353	−	0.318089i
$932$	1.78721e11	+	1.78721e11i	0.236871	+	0.236871i
$933$	−8.66081e11	−	4.41290e11i	−1.14296	−	0.582368i
$934$	1.05237e11	−	1.44846e11i	0.138286	−	0.190335i
$935$	−3.32770e10	+	1.40310e12i	−0.0435409	+	1.83588i
$936$	−1.16254e11	+	8.44637e10i	−0.151463	+	0.110044i
$937$	−1.73129e11	−	1.09309e12i	−0.224601	−	1.41807i	−0.799901	−	0.600131i	$-0.795115\pi$
$937$	−1.73129e11	−	1.09309e12i	−0.224601	−	1.41807i	0.575301	−	0.817942i	$-0.304885\pi$
$938$	2.38142e12	−	3.77179e11i	3.07627	−	0.487233i
$939$	−1.38949e11	−	1.91246e11i	−0.178728	−	0.245998i
$940$	1.05577e12	+	2.50394e10i	1.35225	+	0.0320710i
$941$	−9.81264e11	−	7.12930e11i	−1.25149	−	0.909260i	−0.253182	−	0.967419i	$-0.581477\pi$
$941$	−9.81264e11	−	7.12930e11i	−1.25149	−	0.909260i	−0.998307	+	0.0581582i	$0.981477\pi$
$942$	−9.79613e11	+	1.92260e12i	−1.24409	+	2.44166i
$943$	−1.66344e10	+	1.66344e10i	−0.0210358	+	0.0210358i
$944$	1.40450e10	−	4.56348e9i	0.0176861	−	0.00574657i
$945$	−3.92569e11	−	8.17838e11i	−0.492253	−	1.02551i
$946$	8.90998e11	−	2.74221e12i	1.11253	−	3.42402i
$947$	−7.35870e11	+	3.74945e11i	−0.914958	+	0.466195i	−0.847060	−	0.531498i	$-0.821629\pi$
$947$	−7.35870e11	+	3.74945e11i	−0.914958	+	0.466195i	−0.0678985	+	0.997692i	$0.521629\pi$
$948$	−8.84108e10	+	5.58204e11i	−0.109464	+	0.691130i
$949$			1.35257e12i			1.66761i
$950$	−8.20730e11	−	1.70222e11i	−1.00764	−	0.208988i
$951$	5.29000e11			0.646746
$952$	−1.45594e12	−	2.30598e11i	−1.77254	−	0.280742i
$953$	3.96639e11	+	7.78447e11i	0.480865	+	0.943751i	0.996228	+	0.0867787i	$0.0276573\pi$
$953$	3.96639e11	+	7.78447e11i	0.480865	+	0.943751i	−0.515362	+	0.856972i	$0.672343\pi$
$954$	−2.56003e11	−	8.31805e10i	−0.309066	−	0.100422i
$955$	2.00918e11	+	2.10679e11i	0.241549	+	0.253285i
$956$	−7.07227e11	−	2.17662e12i	−0.846696	−	2.60586i
$957$	1.16689e12	+	1.16689e12i	1.39118	+	1.39118i
$958$	−1.44084e12	−	7.34143e11i	−1.71062	−	0.871603i
$959$	−8.27620e11	+	1.13912e12i	−0.978491	+	1.34678i
$960$	8.29411e11	−	1.08645e12i	0.976529	−	1.27916i
$961$	6.43037e11	−	4.67194e11i	0.753950	−	0.547777i
$962$	−3.37303e11	−	2.12965e12i	−0.393841	−	2.48661i
$963$	−5.54481e10	+	8.78212e9i	−0.0644736	+	0.0102116i
$964$	−1.38833e11	−	1.91087e11i	−0.160762	−	0.221270i
$965$	1.11112e12	−	7.67699e11i	1.28131	−	0.885282i
$966$	7.56297e10	+	5.49482e10i	0.0868528	+	0.0631022i
$967$	−1.35049e11	+	2.65049e11i	−0.154449	+	0.303124i	−0.955246	−	0.295812i	$-0.904410\pi$
$967$	−1.35049e11	+	2.65049e11i	−0.154449	+	0.303124i	0.800797	+	0.598936i	$0.204410\pi$
$968$	1.21616e12	−	1.21616e12i	1.38512	−	1.38512i
$969$	−6.37866e11	+	2.07255e11i	−0.723493	+	0.235077i
$970$	−2.47522e12	+	3.32085e11i	−2.79593	+	0.375113i
$971$	1.78647e11	−	5.49819e11i	0.200964	−	0.618504i	−0.798891	−	0.601476i	$-0.794580\pi$
$971$	1.78647e11	−	5.49819e11i	0.200964	−	0.618504i	0.999855	−	0.0170282i	$-0.00542049\pi$
$972$	−3.94949e11	+	2.01236e11i	−0.442462	+	0.225445i
$973$	1.04825e11	−	6.61840e11i	0.116954	−	0.738417i
$974$			7.92537e11i			0.880610i
$975$	2.66097e11	+	9.73838e11i	0.294457	+	1.07763i
$976$	1.26411e11			0.139311
$977$	−3.73706e11	−	5.91892e10i	−0.410159	−	0.0649628i	−0.0520542	−	0.998644i	$-0.516577\pi$
$977$	−3.73706e11	−	5.91892e10i	−0.410159	−	0.0649628i	−0.358105	+	0.933681i	$0.616577\pi$
$978$	−5.03641e11	−	9.88451e11i	−0.550511	−	1.08044i
$979$	−1.28077e10	−	4.16147e9i	−0.0139425	−	0.00453019i
$980$	−4.15753e11	+	7.70248e11i	−0.450745	+	0.835076i
$981$	−3.21328e10	−	9.88945e10i	−0.0346954	−	0.106782i
$982$	−2.20644e11	−	2.20644e11i	−0.237272	−	0.237272i
$983$	−3.18757e11	−	1.62415e11i	−0.341386	−	0.173945i	0.274889	−	0.961476i	$-0.411359\pi$
$983$	−3.18757e11	−	1.62415e11i	−0.341386	−	0.173945i	−0.616275	+	0.787531i	$0.711359\pi$
$984$	−4.52577e11	+	6.22919e11i	−0.482739	+	0.664433i
$985$	−1.16317e12	+	3.47672e11i	−1.23566	+	0.369339i
$986$	−1.67968e12	+	1.22036e12i	−1.77713	+	1.29116i
$987$	−1.51474e11	−	9.56371e11i	−0.159614	−	1.00776i
$988$	−1.07168e12	+	1.69737e11i	−1.12470	+	0.178135i
$989$	−3.71684e10	−	5.11579e10i	−0.0388498	−	0.0534722i
$990$	1.20267e11	−	3.42305e11i	0.125200	−	0.356347i
$991$	8.71859e11	+	6.33442e11i	0.903965	+	0.656769i	0.939481	−	0.342600i	$-0.111308\pi$
$991$	8.71859e11	+	6.33442e11i	0.903965	+	0.656769i	−0.0355166	+	0.999369i	$0.511308\pi$
$992$	8.10043e10	−	1.58980e11i	0.0836491	−	0.164171i
$993$	−3.08734e11	+	3.08734e11i	−0.317532	+	0.317532i
$994$	6.59398e10	−	2.14252e10i	0.0675464	−	0.0219472i
$995$	1.23763e11	−	6.77084e11i	0.126269	−	0.690796i
$996$	2.15927e11	−	6.64555e11i	0.219417	−	0.675295i
$997$	−9.20200e11	+	4.68865e11i	−0.931326	+	0.474534i	−0.852718	−	0.522371i	$-0.825048\pi$
$997$	−9.20200e11	+	4.68865e11i	−0.931326	+	0.474534i	−0.0786079	+	0.996906i	$0.525048\pi$
$998$	1.39183e11	−	8.78765e11i	0.140302	−	0.885831i
$999$		−	1.32422e12i		−	1.32953i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.9.f.a.2.18	✓	152
25.13	odd	20	inner	25.9.f.a.13.18	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.9.f.a.2.18	✓	152	1.1	even	1	trivial
25.9.f.a.13.18	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)

\(f(q)\)	\(=\)	\(q+(26.2450 + 4.15680i) q^{2} +(39.3019 + 77.1344i) q^{3} +(428.052 + 139.082i) q^{4} +(614.814 + 112.380i) q^{5} +(710.848 + 2187.76i) q^{6} +(-2106.70 - 2106.70i) q^{7} +(4595.04 + 2341.29i) q^{8} +(-548.613 + 755.101i) q^{9} +O(q^{10})\)	\(q+(26.2450 + 4.15680i) q^{2} +(39.3019 + 77.1344i) q^{3} +(428.052 + 139.082i) q^{4} +(614.814 + 112.380i) q^{5} +(710.848 + 2187.76i) q^{6} +(-2106.70 - 2106.70i) q^{7} +(4595.04 + 2341.29i) q^{8} +(-548.613 + 755.101i) q^{9} +(15668.7 + 5505.08i) q^{10} +(-18936.2 + 13757.9i) q^{11} +(6095.22 + 38483.7i) q^{12} +(29486.0 - 4670.12i) q^{13} +(-46533.3 - 64047.6i) q^{14} +(15495.0 + 51840.0i) q^{15} +(17649.2 + 12822.9i) q^{16} +(43555.6 - 85482.7i) q^{17} +(-17537.2 + 17537.2i) q^{18} +(-76800.7 + 24954.0i) q^{19} +(247542. + 133614. i) q^{20} +(79701.7 - 245297. i) q^{21} +(-554169. + 282363. i) q^{22} +(-2133.80 + 13472.3i) q^{23} +446452. i q^{24} +(365366. + 138186. i) q^{25} +793273. q^{26} +(481187. + 76212.5i) q^{27} +(-608772. - 1.19478e6i) q^{28} +(-774551. - 251667. i) q^{29} +(191177. + 1.42495e6i) q^{30} +(74455.5 + 229151. i) q^{31} +(-523639. - 523639. i) q^{32} +(-1.80544e6 - 919916. i) q^{33} +(1.49845e6 - 2.06244e6i) q^{34} +(-1.05848e6 - 1.53198e6i) q^{35} +(-339856. + 246920. i) q^{36} +(-425205. - 2.68464e6i) q^{37} +(-2.11936e6 + 335674. i) q^{38} +(1.51908e6 + 2.09084e6i) q^{39} +(2.56198e6 + 1.95585e6i) q^{40} +(1.39526e6 + 1.01372e6i) q^{41} +(3.11142e6 - 6.10651e6i) q^{42} +(-3.27807e6 + 3.27807e6i) q^{43} +(-1.00191e7 + 3.25542e6i) q^{44} +(-422153. + 402593. i) q^{45} +(-112003. + 344711. i) q^{46} +(3.34505e6 - 1.70439e6i) q^{47} +(-295439. + 1.86533e6i) q^{48} +3.11159e6i q^{49} +(9.01463e6 + 5.14545e6i) q^{50} +8.30547e6 q^{51} +(1.32711e7 + 2.10193e6i) q^{52} +(4.92733e6 + 9.67042e6i) q^{53} +(1.23120e7 + 4.00040e6i) q^{54} +(-1.31883e7 + 6.33051e6i) q^{55} +(-4.74798e6 - 1.46128e7i) q^{56} +(-4.94323e6 - 4.94323e6i) q^{57} +(-1.92820e7 - 9.82466e6i) q^{58} +(397892. - 547652. i) q^{59} +(-577390. + 2.43453e7i) q^{60} +(4.68786e6 - 3.40593e6i) q^{61} +(1.00155e6 + 6.32356e6i) q^{62} +(2.74654e6 - 435009. i) q^{63} +(-1.48489e7 - 2.04378e7i) q^{64} +(1.86532e7 + 442393. i) q^{65} +(-4.35598e7 - 3.16481e7i) q^{66} +(-1.38267e7 + 2.71363e7i) q^{67} +(3.05332e7 - 3.05332e7i) q^{68} +(-1.12304e6 + 364898. i) q^{69} +(-2.14116e7 - 4.46068e7i) q^{70} +(-270632. + 832919. i) q^{71} +(-4.28881e6 + 2.18526e6i) q^{72} +(-7.08753e6 + 4.47489e7i) q^{73} -7.22258e7i q^{74} +(3.70071e6 + 3.36133e7i) q^{75} -3.63453e7 q^{76} +(6.88767e7 + 1.09090e7i) q^{77} +(3.11772e7 + 6.11886e7i) q^{78} +(1.37950e7 + 4.48227e6i) q^{79} +(9.40993e6 + 9.86711e6i) q^{80} +(1.49253e7 + 4.59354e7i) q^{81} +(3.24049e7 + 3.24049e7i) q^{82} +(-1.59790e7 - 8.14168e6i) q^{83} +(6.82329e7 - 9.39145e7i) q^{84} +(3.63852e7 - 4.76611e7i) q^{85} +(-9.96593e7 + 7.24067e7i) q^{86} +(-1.10292e7 - 6.96355e7i) q^{87} +(-1.19224e8 + 1.88832e7i) q^{88} +(338181. + 465466. i) q^{89} +(-1.27529e7 + 8.81125e6i) q^{90} +(-7.19568e7 - 5.22796e7i) q^{91} +(-2.78714e6 + 5.47007e6i) q^{92} +(-1.47491e7 + 1.47491e7i) q^{93} +(9.48756e7 - 3.08269e7i) q^{94} +(-5.00224e7 + 6.71120e6i) q^{95} +(1.98105e7 - 6.09706e7i) q^{96} +(-1.33987e8 + 6.82696e7i) q^{97} +(-1.29343e7 + 8.16637e7i) q^{98} -2.18465e7i 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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