LMFDB - Embedded newform 425.2.r.a.69.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(69,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.69"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([9, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.r (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			69.19
Character	$\chi$	$=$	425.69
Dual form			425.2.r.a.154.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.256860 + 0.0834589i) q^{2} +(-1.58231 - 2.17787i) q^{3} +(-1.55902 + 1.13270i) q^{4} +(-2.05873 + 0.872706i) q^{5} +(0.588195 + 0.427349i) q^{6} +2.44071i q^{7} +(0.623414 - 0.858055i) q^{8} +(-1.31234 + 4.03896i) q^{9} +(0.455972 - 0.395983i) q^{10} +(-1.38823 - 4.27252i) q^{11} +(4.93372 + 1.60306i) q^{12} +(5.44714 + 1.76988i) q^{13} +(-0.203699 - 0.626921i) q^{14} +(5.15820 + 3.10275i) q^{15} +(1.10247 - 3.39305i) q^{16} +(0.587785 - 0.809017i) q^{17} -1.14697i q^{18} +(0.0243842 + 0.0177162i) q^{19} +(2.22110 - 3.69249i) q^{20} +(5.31554 - 3.86196i) q^{21} +(0.713160 + 0.981580i) q^{22} +(-4.77014 + 1.54991i) q^{23} -2.85516 q^{24} +(3.47677 - 3.59334i) q^{25} -1.54686 q^{26} +(3.19212 - 1.03718i) q^{27} +(-2.76458 - 3.80512i) q^{28} +(5.83966 - 4.24276i) q^{29} +(-1.58389 - 0.366476i) q^{30} +(4.19708 + 3.04936i) q^{31} +3.08478i q^{32} +(-7.10837 + 9.78383i) q^{33} +(-0.0834589 + 0.256860i) q^{34} +(-2.13002 - 5.02477i) q^{35} +(-2.52895 - 7.78330i) q^{36} +(7.37583 + 2.39655i) q^{37} +(-0.00774190 - 0.00251550i) q^{38} +(-4.76450 - 14.6636i) q^{39} +(-0.534613 + 2.31056i) q^{40} +(0.945346 - 2.90948i) q^{41} +(-1.04303 + 1.43561i) q^{42} -4.13209i q^{43} +(7.00374 + 5.08852i) q^{44} +(-0.823070 - 9.46042i) q^{45} +(1.09591 - 0.796222i) q^{46} +(6.38308 + 8.78555i) q^{47} +(-9.13406 + 2.96784i) q^{48} +1.04294 q^{49} +(-0.593147 + 1.21315i) q^{50} -2.69199 q^{51} +(-10.4969 + 3.41066i) q^{52} +(4.56516 + 6.28341i) q^{53} +(-0.733367 + 0.532822i) q^{54} +(6.58664 + 7.58447i) q^{55} +(2.09426 + 1.52157i) q^{56} -0.0811380i q^{57} +(-1.14588 + 1.57717i) q^{58} +(1.13914 - 3.50590i) q^{59} +(-11.5562 + 1.00541i) q^{60} +(-0.443301 - 1.36434i) q^{61} +(-1.33256 - 0.432974i) q^{62} +(-9.85791 - 3.20303i) q^{63} +(1.94749 + 5.99375i) q^{64} +(-12.7588 + 1.11003i) q^{65} +(1.00931 - 3.10633i) q^{66} +(-4.13845 + 5.69609i) q^{67} +1.92706i q^{68} +(10.9234 + 7.93628i) q^{69} +(0.966479 + 1.11289i) q^{70} +(-8.22650 + 5.97690i) q^{71} +(2.64752 + 3.64400i) q^{72} +(3.95117 - 1.28381i) q^{73} -2.09457 q^{74} +(-13.3271 - 1.88615i) q^{75} -0.0580825 q^{76} +(10.4280 - 3.38826i) q^{77} +(2.44762 + 3.36886i) q^{78} +(-1.01656 + 0.738571i) q^{79} +(0.691446 + 7.94752i) q^{80} +(2.99744 + 2.17777i) q^{81} +0.826226i q^{82} +(7.90657 - 10.8825i) q^{83} +(-3.91261 + 12.0418i) q^{84} +(-0.504059 + 2.17851i) q^{85} +(0.344860 + 1.06137i) q^{86} +(-18.4803 - 6.00462i) q^{87} +(-4.53150 - 1.47237i) q^{88} +(-3.20166 - 9.85370i) q^{89} +(1.00097 + 2.36131i) q^{90} +(-4.31977 + 13.2949i) q^{91} +(5.68118 - 7.81947i) q^{92} -13.9657i q^{93} +(-2.37279 - 1.72393i) q^{94} +(-0.0656616 - 0.0151926i) q^{95} +(6.71824 - 4.88108i) q^{96} +(-5.67294 - 7.80814i) q^{97} +(-0.267889 + 0.0870426i) q^{98} +19.0783 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) $ 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.256860	+	0.0834589i	−0.181628	+	0.0590144i	−0.398419	−	0.917204i	$-0.630441\pi$
$2$	−0.256860	+	0.0834589i	−0.181628	+	0.0590144i	0.216791	+	0.976218i	$0.430441\pi$
$3$	−1.58231	−	2.17787i	−0.913548	−	1.25739i	−0.965940	−	0.258765i	$-0.916685\pi$
$3$	−1.58231	−	2.17787i	−0.913548	−	1.25739i	0.0523922	−	0.998627i	$-0.483315\pi$
$4$	−1.55902	+	1.13270i	−0.779511	+	0.566348i
$5$	−2.05873	+	0.872706i	−0.920694	+	0.390286i
$5$	−2.05873	+	0.872706i	−0.920694	+	0.390286i
$6$	0.588195	+	0.427349i	0.240130	+	0.174464i
$7$			2.44071i			0.922501i	0.887270	+	0.461251i	$0.152599\pi$
$7$			2.44071i			0.922501i	−0.887270	+	0.461251i	$0.847401\pi$
$8$	0.623414	−	0.858055i	0.220410	−	0.303368i
$9$	−1.31234	+	4.03896i	−0.437445	+	1.34632i
$10$	0.455972	−	0.395983i	0.144191	−	0.125221i
$11$	−1.38823	−	4.27252i	−0.418566	−	1.28821i	−0.909022	−	0.416747i	$-0.863170\pi$
$11$	−1.38823	−	4.27252i	−0.418566	−	1.28821i	0.490457	−	0.871466i	$-0.336830\pi$
$12$	4.93372	+	1.60306i	1.42424	+	0.462764i
$13$	5.44714	+	1.76988i	1.51076	+	0.490877i	0.943136	−	0.332408i	$-0.107861\pi$
$13$	5.44714	+	1.76988i	1.51076	+	0.490877i	0.567628	+	0.823285i	$0.307861\pi$
$14$	−0.203699	−	0.626921i	−0.0544408	−	0.167552i
$15$	5.15820	+	3.10275i	1.33184	+	0.801127i
$16$	1.10247	−	3.39305i	0.275617	−	0.848263i
$17$	0.587785	−	0.809017i	0.142559	−	0.196215i
$17$	0.587785	−	0.809017i	0.142559	−	0.196215i
$18$		−	1.14697i		−	0.270344i
$19$	0.0243842	+	0.0177162i	0.00559412	+	0.00406437i	0.590579	−	0.806980i	$-0.298899\pi$
$19$	0.0243842	+	0.0177162i	0.00559412	+	0.00406437i	−0.584985	+	0.811044i	$0.698899\pi$
$20$	2.22110	−	3.69249i	0.496653	−	0.825665i
$21$	5.31554	−	3.86196i	1.15995	−	0.842749i
$22$	0.713160	+	0.981580i	0.152046	+	0.209274i
$23$	−4.77014	+	1.54991i	−0.994643	+	0.323179i	−0.760723	−	0.649077i	$-0.775155\pi$
$23$	−4.77014	+	1.54991i	−0.994643	+	0.323179i	−0.233920	+	0.972256i	$0.575155\pi$
$24$	−2.85516			−0.582808
$25$	3.47677	−	3.59334i	0.695354	−	0.718668i
$26$	−1.54686			−0.303365
$27$	3.19212	−	1.03718i	0.614324	−	0.199606i
$28$	−2.76458	−	3.80512i	−0.522457	−	0.719100i
$29$	5.83966	−	4.24276i	1.08440	−	0.787861i	0.105953	−	0.994371i	$-0.466211\pi$
$29$	5.83966	−	4.24276i	1.08440	−	0.787861i	0.978444	+	0.206511i	$0.0662108\pi$
$30$	−1.58389	−	0.366476i	−0.289177	−	0.0669090i
$31$	4.19708	+	3.04936i	0.753817	+	0.547680i	0.897008	−	0.442015i	$-0.145736\pi$
$31$	4.19708	+	3.04936i	0.753817	+	0.547680i	−0.143190	+	0.989695i	$0.545736\pi$
$32$			3.08478i			0.545317i
$33$	−7.10837	+	9.78383i	−1.23741	+	1.70315i
$34$	−0.0834589	+	0.256860i	−0.0143131	+	0.0440512i
$35$	−2.13002	−	5.02477i	−0.360039	−	0.849341i
$36$	−2.52895	−	7.78330i	−0.421491	−	1.29722i
$37$	7.37583	+	2.39655i	1.21258	+	0.393991i	0.844374	−	0.535754i	$-0.179972\pi$
$37$	7.37583	+	2.39655i	1.21258	+	0.393991i	0.368205	+	0.929745i	$0.379972\pi$
$38$	−0.00774190	−	0.00251550i	−0.00125590	−	0.000408067i
$39$	−4.76450	−	14.6636i	−0.762931	−	2.34806i
$40$	−0.534613	+	2.31056i	−0.0845297	+	0.365332i
$41$	0.945346	−	2.90948i	0.147638	−	0.454384i	−0.849703	−	0.527262i	$-0.823219\pi$
$41$	0.945346	−	2.90948i	0.147638	−	0.454384i	0.997341	+	0.0728784i	$0.0232185\pi$
$42$	−1.04303	+	1.43561i	−0.160944	+	0.221520i
$43$		−	4.13209i		−	0.630138i	−0.949069	−	0.315069i	$-0.897972\pi$
$43$		−	4.13209i		−	0.630138i	0.949069	−	0.315069i	$-0.102028\pi$
$44$	7.00374	+	5.08852i	1.05585	+	0.767123i
$45$	−0.823070	−	9.46042i	−0.122696	−	1.41028i
$46$	1.09591	−	0.796222i	0.161582	−	0.117397i
$47$	6.38308	+	8.78555i	0.931067	+	1.28150i	0.959442	+	0.281907i	$0.0909669\pi$
$47$	6.38308	+	8.78555i	0.931067	+	1.28150i	−0.0283744	+	0.999597i	$0.509033\pi$
$48$	−9.13406	+	2.96784i	−1.31839	+	0.428370i
$49$	1.04294			0.148991
$50$	−0.593147	+	1.21315i	−0.0838837	+	0.171566i
$51$	−2.69199			−0.376954
$52$	−10.4969	+	3.41066i	−1.45566	+	0.472974i
$53$	4.56516	+	6.28341i	0.627073	+	0.863092i	0.997844	−	0.0656322i	$-0.0209064\pi$
$53$	4.56516	+	6.28341i	0.627073	+	0.863092i	−0.370771	+	0.928724i	$0.620906\pi$
$54$	−0.733367	+	0.532822i	−0.0997986	+	0.0725079i
$55$	6.58664	+	7.58447i	0.888142	+	1.02269i
$56$	2.09426	+	1.52157i	0.279858	+	0.203329i
$57$		−	0.0811380i		−	0.0107470i
$58$	−1.14588	+	1.57717i	−0.150461	+	0.207092i
$59$	1.13914	−	3.50590i	0.148303	−	0.456429i	−0.849118	−	0.528203i	$-0.822866\pi$
$59$	1.13914	−	3.50590i	0.148303	−	0.456429i	0.997421	+	0.0717738i	$0.0228660\pi$
$60$	−11.5562	+	1.00541i	−1.49190	+	0.129798i
$61$	−0.443301	−	1.36434i	−0.0567589	−	0.174686i	0.918658	−	0.395054i	$-0.129274\pi$
$61$	−0.443301	−	1.36434i	−0.0567589	−	0.174686i	−0.975417	+	0.220368i	$0.929274\pi$
$62$	−1.33256	−	0.432974i	−0.169235	−	0.0549878i
$63$	−9.85791	−	3.20303i	−1.24198	−	0.403544i
$64$	1.94749	+	5.99375i	0.243436	+	0.749218i
$65$	−12.7588	+	1.11003i	−1.58253	+	0.137683i
$66$	1.00931	−	3.10633i	0.124237	−	0.382363i
$67$	−4.13845	+	5.69609i	−0.505593	+	0.695889i	−0.983168	−	0.182702i	$-0.941516\pi$
$67$	−4.13845	+	5.69609i	−0.505593	+	0.695889i	0.477576	+	0.878591i	$0.341516\pi$
$68$			1.92706i			0.233690i
$69$	10.9234	+	7.93628i	1.31502	+	0.955416i
$70$	0.966479	+	1.11289i	0.115516	+	0.133016i
$71$	−8.22650	+	5.97690i	−0.976306	+	0.709328i	−0.956880	−	0.290483i	$-0.906184\pi$
$71$	−8.22650	+	5.97690i	−0.976306	+	0.709328i	−0.0194260	+	0.999811i	$0.506184\pi$
$72$	2.64752	+	3.64400i	0.312013	+	0.429449i
$73$	3.95117	−	1.28381i	0.462450	−	0.150259i	−0.0685201	−	0.997650i	$-0.521828\pi$
$73$	3.95117	−	1.28381i	0.462450	−	0.150259i	0.530970	+	0.847391i	$0.321828\pi$
$74$	−2.09457			−0.243489
$75$	−13.3271	−	1.88615i	−1.53889	−	0.217794i
$76$	−0.0580825			−0.00666252
$77$	10.4280	−	3.38826i	1.18838	−	0.386128i
$78$	2.44762	+	3.36886i	0.277139	+	0.381449i
$79$	−1.01656	+	0.738571i	−0.114372	+	0.0830958i	−0.643501	−	0.765445i	$-0.722519\pi$
$79$	−1.01656	+	0.738571i	−0.114372	+	0.0830958i	0.529129	+	0.848541i	$0.322519\pi$
$80$	0.691446	+	7.94752i	0.0773060	+	0.888560i
$81$	2.99744	+	2.17777i	0.333049	+	0.241974i
$82$			0.826226i			0.0912414i
$83$	7.90657	−	10.8825i	0.867858	−	1.19450i	−0.111780	−	0.993733i	$-0.535655\pi$
$83$	7.90657	−	10.8825i	0.867858	−	1.19450i	0.979638	−	0.200772i	$-0.0643449\pi$
$84$	−3.91261	+	12.0418i	−0.426901	+	1.31387i
$85$	−0.504059	+	2.17851i	−0.0546729	+	0.236293i
$86$	0.344860	+	1.06137i	0.0371872	+	0.114450i
$87$	−18.4803	−	6.00462i	−1.98130	−	0.643763i
$88$	−4.53150	−	1.47237i	−0.483059	−	0.156955i
$89$	−3.20166	−	9.85370i	−0.339375	−	1.04449i	−0.964526	−	0.263986i	$-0.914963\pi$
$89$	−3.20166	−	9.85370i	−0.339375	−	1.04449i	0.625151	−	0.780504i	$-0.285037\pi$
$90$	1.00097	+	2.36131i	0.105512	+	0.248904i
$91$	−4.31977	+	13.2949i	−0.452835	+	1.39368i
$92$	5.68118	−	7.81947i	0.592304	−	0.815236i
$93$		−	13.9657i		−	1.44818i
$94$	−2.37279	−	1.72393i	−0.244735	−	0.177810i
$95$	−0.0656616	−	0.0151926i	−0.00673674	−	0.00155873i
$96$	6.71824	−	4.88108i	0.685677	−	0.498174i
$97$	−5.67294	−	7.80814i	−0.576000	−	0.792796i	0.417250	−	0.908792i	$-0.362994\pi$
$97$	−5.67294	−	7.80814i	−0.576000	−	0.792796i	−0.993250	+	0.115996i	$0.962994\pi$
$98$	−0.267889	+	0.0870426i	−0.0270609	+	0.00879263i
$99$	19.0783			1.91744
$100$	−1.35020	+	9.54022i	−0.135020	+	0.954022i
$101$	10.5248			1.04725			0.523627	−	0.851948i	$-0.324579\pi$
$101$	10.5248			1.04725			0.523627	+	0.851948i	$0.324579\pi$
$102$	0.691465	−	0.224671i	0.0684652	−	0.0222457i
$103$	1.83075	+	2.51981i	0.180389	+	0.248284i	0.889630	−	0.456682i	$-0.150962\pi$
$103$	1.83075	+	2.51981i	0.180389	+	0.248284i	−0.709241	+	0.704966i	$0.750962\pi$
$104$	4.91448	−	3.57058i	0.481904	−	0.350124i
$105$	−7.57291	+	12.5897i	−0.739041	+	1.22862i
$106$	−1.69701	−	1.23295i	−0.164829	−	0.119755i
$107$			4.64817i			0.449355i	0.974433	+	0.224678i	$0.0721329\pi$
$107$			4.64817i			0.449355i	−0.974433	+	0.224678i	$0.927867\pi$
$108$	−3.80178	+	5.23270i	−0.365826	+	0.503517i
$109$	1.53226	−	4.71581i	0.146764	−	0.451693i	−0.850470	−	0.526024i	$-0.823682\pi$
$109$	1.53226	−	4.71581i	0.146764	−	0.451693i	0.997234	+	0.0743314i	$0.0236822\pi$
$110$	−2.32484	−	1.39843i	−0.221664	−	0.133335i
$111$	−6.45150	−	19.8557i	−0.612349	−	1.88462i
$112$	8.28145	+	2.69081i	0.782524	+	0.254257i
$113$	6.51500	+	2.11685i	0.612880	+	0.199137i	0.598976	−	0.800767i	$-0.295574\pi$
$113$	6.51500	+	2.11685i	0.612880	+	0.199137i	0.0139032	+	0.999903i	$0.495574\pi$
$114$	0.00677169	+	0.0208411i	0.000634227	+	0.00195195i
$115$	8.46783	−	7.35379i	0.789630	−	0.685744i
$116$	−4.29840	+	13.2291i	−0.399096	+	1.22829i
$117$	−14.2969	+	19.6781i	−1.32175	+	1.81924i
$118$			0.995597i			0.0916521i
$119$	1.97458	+	1.43461i	0.181009	+	0.131511i
$120$	5.87802	−	2.49172i	0.536588	−	0.227462i
$121$	−7.42806	+	5.39681i	−0.675279	+	0.490619i
$122$	0.227733	+	0.313447i	0.0206179	+	0.0283782i
$123$	−7.83228	+	2.54486i	−0.706213	+	0.229463i
$124$	−9.99733			−0.897787
$125$	−4.02181	+	10.4319i	−0.359722	+	0.933060i
$126$	2.79943			0.249393
$127$	1.12745	−	0.366330i	0.100045	−	0.0325065i	−0.258567	−	0.965993i	$-0.583250\pi$
$127$	1.12745	−	0.366330i	0.100045	−	0.0325065i	0.358612	+	0.933487i	$0.383250\pi$
$128$	−4.62684	−	6.36830i	−0.408959	−	0.562883i
$129$	−8.99914	+	6.53826i	−0.792330	+	0.575661i
$130$	3.18458	−	1.34996i	0.279306	−	0.118399i
$131$	−16.1448	−	11.7299i	−1.41057	−	1.02484i	−0.993239	−	0.116089i	$-0.962964\pi$
$131$	−16.1448	−	11.7299i	−1.41057	−	1.02484i	−0.417335	−	0.908753i	$-0.637036\pi$
$132$		−	23.3048i		−	2.02842i
$133$	−0.0432400	+	0.0595148i	−0.00374938	+	0.00516058i
$134$	0.587614	−	1.80849i	0.0507621	−	0.156230i
$135$	−5.66657	+	4.92107i	−0.487701	+	0.423538i
$136$	−0.327748	−	1.00870i	−0.0281042	−	0.0864957i
$137$	−7.92522	−	2.57506i	−0.677097	−	0.220002i	−0.0497733	−	0.998761i	$-0.515850\pi$
$137$	−7.92522	−	2.57506i	−0.677097	−	0.220002i	−0.627324	+	0.778758i	$0.715850\pi$
$138$	−3.46813	−	1.12686i	−0.295227	−	0.0959250i
$139$	−4.44030	−	13.6659i	−0.376622	−	1.15912i	−0.942378	−	0.334550i	$-0.891416\pi$
$139$	−4.44030	−	13.6659i	−0.376622	−	1.15912i	0.565756	−	0.824573i	$-0.308584\pi$
$140$	9.01229	+	5.42106i	0.761677	+	0.458163i
$141$	9.03373	−	27.8030i	0.760777	−	2.34143i
$142$	1.61423	−	2.22180i	0.135464	−	0.186450i
$143$		−	25.7300i		−	2.15165i
$144$	12.2576	+	8.90565i	1.02146	+	0.742137i
$145$	−8.31962	+	13.8310i	−0.690907	+	1.14860i
$146$	−0.907753	+	0.659521i	−0.0751262	+	0.0545824i
$147$	−1.65025	−	2.27138i	−0.136111	−	0.187340i
$148$	−14.2137	+	4.61830i	−1.16836	+	0.379622i
$149$	4.96998			0.407157			0.203578	−	0.979059i	$-0.434743\pi$
$149$	4.96998			0.407157			0.203578	+	0.979059i	$0.434743\pi$
$150$	3.58063	−	0.627792i	0.292357	−	0.0512590i
$151$	3.58491			0.291736			0.145868	−	0.989304i	$-0.453403\pi$
$151$	3.58491			0.291736			0.145868	+	0.989304i	$0.453403\pi$
$152$	0.0304029	−	0.00987850i	0.00246600	−	0.000801252i
$153$	2.49621	+	3.43574i	0.201807	+	0.277763i
$154$	−2.39575	+	1.74062i	−0.193055	+	0.140263i
$155$	−11.3019	−	2.61500i	−0.907787	−	0.210041i
$156$	24.0374	+	17.4642i	1.92453	+	1.39825i
$157$			24.7290i			1.97359i	0.161975	+	0.986795i	$0.448213\pi$
$157$			24.7290i			1.97359i	−0.161975	+	0.986795i	$0.551787\pi$
$158$	0.199472	−	0.274550i	0.0158692	−	0.0218420i
$159$	6.46090	−	19.8846i	0.512383	−	1.57695i
$160$	−2.69211	−	6.35074i	−0.212830	−	0.502070i
$161$	−3.78289	−	11.6425i	−0.298133	−	0.917560i
$162$	−0.951677	−	0.309219i	−0.0747708	−	0.0242945i
$163$	14.3748	+	4.67067i	1.12592	+	0.365835i	0.812026	−	0.583622i	$-0.198365\pi$
$163$	14.3748	+	4.67067i	1.12592	+	0.365835i	0.313898	+	0.949457i	$0.398365\pi$
$164$	1.82174	+	5.60673i	0.142254	+	0.437812i
$165$	6.09583	−	26.3458i	0.474560	−	2.05102i
$166$	−1.12264	+	3.45514i	−0.0871341	+	0.268171i
$167$	10.9915	−	15.1286i	0.850551	−	1.17068i	−0.133190	−	0.991091i	$-0.542522\pi$
$167$	10.9915	−	15.1286i	0.850551	−	1.17068i	0.983741	−	0.179593i	$-0.0574780\pi$
$168$		−	6.96862i		−	0.537641i
$169$	16.0216	+	11.6404i	1.23243	+	0.895412i
$170$	−0.0523437	−	0.601642i	−0.00401458	−	0.0461438i
$171$	−0.103555	+	0.0752372i	−0.00791905	+	0.00575353i
$172$	4.68040	+	6.44202i	0.356877	+	0.491200i
$173$	−7.05046	+	2.29083i	−0.536037	+	0.174169i	−0.564511	−	0.825426i	$-0.690935\pi$
$173$	−7.05046	+	2.29083i	−0.536037	+	0.174169i	0.0284741	+	0.999595i	$0.490935\pi$
$174$	5.24800			0.397850
$175$	8.77029	+	8.48578i	0.662972	+	0.641465i
$176$	−16.0274			−1.20811
$177$	−9.43785	+	3.06654i	−0.709392	+	0.230495i
$178$	1.64476	+	2.26381i	0.123280	+	0.169680i
$179$	13.1659	−	9.56556i	0.984063	−	0.714963i	0.0254498	−	0.999676i	$-0.491898\pi$
$179$	13.1659	−	9.56556i	0.984063	−	0.714963i	0.958613	+	0.284713i	$0.0918982\pi$
$180$	11.9990	+	13.8167i	0.894350	+	1.02984i
$181$	−18.7680	−	13.6357i	−1.39501	−	1.01354i	−0.995294	−	0.0968964i	$-0.969108\pi$
$181$	−18.7680	−	13.6357i	−1.39501	−	1.01354i	−0.399717	−	0.916639i	$-0.630892\pi$
$182$		−	3.77545i		−	0.279855i
$183$	−2.26991	+	3.12426i	−0.167796	+	0.230952i
$184$	−1.64386	+	5.05928i	−0.121187	+	0.372975i
$185$	−17.2764	+	1.50307i	−1.27018	+	0.110508i
$186$	1.16556	+	3.58723i	0.0854632	+	0.263029i
$187$	−4.27252	−	1.38823i	−0.312438	−	0.101517i
$188$	−19.9027	−	6.46678i	−1.45155	−	0.471639i
$189$	2.53146	+	7.79104i	0.184137	+	0.566715i
$190$	0.0181338	−	0.00157767i	0.00131556	−	0.000114456i
$191$	−4.15983	+	12.8027i	−0.300995	+	0.926367i	0.680146	+	0.733076i	$0.261916\pi$
$191$	−4.15983	+	12.8027i	−0.300995	+	0.926367i	−0.981141	+	0.193291i	$0.938084\pi$
$192$	9.97204	−	13.7253i	0.719670	−	0.990541i
$193$		−	2.82017i		−	0.203000i	−0.994836	−	0.101500i	$-0.967636\pi$
$193$		−	2.82017i		−	0.203000i	0.994836	−	0.101500i	$-0.0323642\pi$
$194$	2.10881	+	1.53214i	0.151404	+	0.110001i
$195$	22.6059	+	26.0305i	1.61884	+	1.86408i
$196$	−1.62597	+	1.18133i	−0.116140	+	0.0843809i
$197$	12.0456	+	16.5794i	0.858214	+	1.18123i	0.981992	+	0.188920i	$0.0604988\pi$
$197$	12.0456	+	16.5794i	0.858214	+	1.18123i	−0.123778	+	0.992310i	$0.539501\pi$
$198$	−4.90046	+	1.59226i	−0.348261	+	0.113157i
$199$	18.7356			1.32813			0.664066	−	0.747674i	$-0.268829\pi$
$199$	18.7356			1.32813			0.664066	+	0.747674i	$0.268829\pi$
$200$	−0.915818	−	5.22340i	−0.0647581	−	0.369350i
$201$	18.9537			1.33689
$202$	−2.70339	+	0.878386i	−0.190210	+	0.0618030i
$203$	10.3553	+	14.2529i	0.726802	+	1.00036i
$204$	4.19687	−	3.04921i	0.293840	−	0.213487i
$205$	0.592902	+	6.81485i	0.0414100	+	0.475970i
$206$	−0.680546	−	0.494446i	−0.0474159	−	0.0344497i
$207$		−	21.3004i		−	1.48048i
$208$	12.0106	−	16.5312i	0.832785	−	1.14623i
$209$	0.0418419	−	0.128776i	0.00289426	−	0.00890762i
$210$	0.894461	−	3.86581i	0.0617237	−	0.266766i
$211$	8.74058	+	26.9007i	0.601726	+	1.85192i	0.517896	+	0.855444i	$0.326715\pi$
$211$	8.74058	+	26.9007i	0.601726	+	1.85192i	0.0838305	+	0.996480i	$0.473285\pi$
$212$	−14.2344	−	4.62503i	−0.977621	−	0.317648i
$213$	26.0338	+	8.45889i	1.78381	+	0.579593i
$214$	−0.387931	−	1.19393i	−0.0265184	−	0.0816153i
$215$	3.60610	+	8.50688i	0.245934	+	0.580164i
$216$	1.10005	−	3.38561i	0.0748491	−	0.230362i
$217$	−7.44259	+	10.2438i	−0.505236	+	0.695398i
$218$			1.33918i			0.0907010i
$219$	−9.04796	−	6.57373i	−0.611404	−	0.444211i
$220$	−18.8596	−	4.36369i	−1.27151	−	0.294200i
$221$	4.63361	−	3.36651i	0.311690	−	0.226456i
$222$	3.31426	+	4.56169i	0.222439	+	0.306161i
$223$	−1.05165	+	0.341702i	−0.0704238	+	0.0228821i	−0.344017	−	0.938963i	$-0.611788\pi$
$223$	−1.05165	+	0.341702i	−0.0704238	+	0.0228821i	0.273593	+	0.961845i	$0.411788\pi$
$224$	−7.52905			−0.503056
$225$	9.95064	+	18.7582i	0.663376	+	1.25055i
$226$	−1.85011			−0.123068
$227$	22.6964	−	7.37451i	1.50641	−	0.489463i	0.564533	−	0.825411i	$-0.309056\pi$
$227$	22.6964	−	7.37451i	1.50641	−	0.489463i	0.941881	+	0.335947i	$0.109056\pi$
$228$	0.0919047	+	0.126496i	0.00608654	+	0.00837740i
$229$	5.87367	−	4.26747i	0.388143	−	0.282002i	−0.376551	−	0.926396i	$-0.622890\pi$
$229$	5.87367	−	4.26747i	0.388143	−	0.282002i	0.764694	+	0.644394i	$0.222890\pi$
$230$	−1.56131	+	2.59561i	−0.102950	+	0.171150i
$231$	−23.8795	−	17.3495i	−1.57115	−	1.14151i
$232$		−	7.65574i		−	0.502624i
$233$	−10.8139	+	14.8840i	−0.708440	+	0.975084i	0.291389	+	0.956605i	$0.405883\pi$
$233$	−10.8139	+	14.8840i	−0.708440	+	0.975084i	−0.999829	+	0.0184796i	$0.994117\pi$
$234$	2.03001	−	6.24772i	0.132706	−	0.408426i
$235$	−20.8083	−	12.5166i	−1.35738	−	0.816490i
$236$	2.19518	+	6.75607i	0.142894	+	0.439783i
$237$	3.21702	+	1.04527i	0.208968	+	0.0678978i
$238$	−0.626921	−	0.203699i	−0.0406372	−	0.0132038i
$239$	−2.40728	−	7.40884i	−0.155714	−	0.479238i	0.842519	−	0.538667i	$-0.181072\pi$
$239$	−2.40728	−	7.40884i	−0.155714	−	0.479238i	−0.998233	+	0.0594291i	$0.981072\pi$
$240$	16.2145	−	14.0813i	1.04664	−	0.908946i
$241$	−1.73045	+	5.32579i	−0.111468	+	0.343064i	−0.991194	−	0.132417i	$-0.957726\pi$
$241$	−1.73045	+	5.32579i	−0.111468	+	0.343064i	0.879726	+	0.475481i	$0.157726\pi$
$242$	1.45756	−	2.00616i	0.0936957	−	0.128961i
$243$		−	20.0431i		−	1.28577i
$244$	2.23650	+	1.62491i	0.143177	+	0.104024i
$245$	−2.14713	+	0.910179i	−0.137175	+	0.0581492i
$246$	1.79941	−	1.30735i	0.114726	−	0.0833534i
$247$	0.101469	+	0.139659i	0.00645629	+	0.00888632i
$248$	5.23303	−	1.70031i	0.332298	−	0.107970i
$249$	−36.2112			−2.29479
$250$	0.162406	−	3.01520i	0.0102715	−	0.190698i
$251$	20.2219			1.27640			0.638198	−	0.769872i	$-0.279680\pi$
$251$	20.2219			1.27640			0.638198	+	0.769872i	$0.279680\pi$
$252$	18.9968	−	6.17242i	1.19668	−	0.388826i
$253$	13.2441	+	18.2289i	0.832647	+	1.14604i
$254$	−0.259023	+	0.188191i	−0.0162525	+	0.0118082i
$255$	5.54209	−	2.34932i	0.347059	−	0.147120i
$256$	−8.47723	−	6.15907i	−0.529827	−	0.384942i
$257$		−	4.72899i		−	0.294986i	−0.989063	−	0.147493i	$-0.952880\pi$
$257$		−	4.72899i		−	0.294986i	0.989063	−	0.147493i	$-0.0471205\pi$
$258$	1.76584	−	2.43048i	0.109937	−	0.151315i
$259$	−5.84929	+	18.0023i	−0.363457	+	1.11861i
$260$	18.6339	−	16.1824i	1.15563	−	1.00359i
$261$	9.47272	+	29.1540i	0.586347	+	1.80459i
$262$	5.12590	+	1.66551i	0.316679	+	0.102895i
$263$	−21.2415	−	6.90177i	−1.30981	−	0.425582i	−0.430823	−	0.902436i	$-0.641777\pi$
$263$	−21.2415	−	6.90177i	−1.30981	−	0.425582i	−0.878982	+	0.476855i	$0.841777\pi$
$264$	3.96361	+	12.1987i	0.243943	+	0.750781i
$265$	−14.8820	−	8.95182i	−0.914195	−	0.549906i
$266$	0.00613960	−	0.0188957i	0.000376443	−	0.00115857i
$267$	−16.3940	+	22.5644i	−1.00330	+	1.38092i
$268$		−	13.5679i		−	0.828794i
$269$	23.0190	+	16.7243i	1.40350	+	1.01970i	0.994228	+	0.107285i	$0.0342157\pi$
$269$	23.0190	+	16.7243i	1.40350	+	1.01970i	0.409268	+	0.912414i	$0.365784\pi$
$270$	1.04481	−	1.73695i	0.0635851	−	0.105708i
$271$	0.554175	−	0.402632i	0.0336637	−	0.0244581i	−0.570826	−	0.821071i	$-0.693377\pi$
$271$	0.554175	−	0.402632i	0.0336637	−	0.0244581i	0.604490	+	0.796613i	$0.293377\pi$
$272$	−2.09702	−	2.88630i	−0.127151	−	0.175008i
$273$	35.7897	−	11.6288i	2.16609	−	0.703805i
$274$	2.25059			0.135963
$275$	−20.1791	−	9.86620i	−1.21685	−	0.594954i
$276$	−26.0191			−1.56617
$277$	18.3285	−	5.95528i	1.10125	−	0.357818i	0.298667	−	0.954357i	$-0.403458\pi$
$277$	18.3285	−	5.95528i	1.10125	−	0.357818i	0.802584	+	0.596539i	$0.203458\pi$
$278$	2.28107	+	3.13963i	0.136810	+	0.188302i
$279$	−17.8242	+	12.9500i	−1.06711	+	0.775298i
$280$	−5.63942	−	1.30483i	−0.337020	−	0.0779787i
$281$	5.77852	+	4.19834i	0.344718	+	0.250452i	0.746650	−	0.665217i	$-0.231661\pi$
$281$	5.77852	+	4.19834i	0.344718	+	0.250452i	−0.401932	+	0.915670i	$0.631661\pi$
$282$			7.89542i			0.470165i
$283$	16.9944	−	23.3908i	1.01021	−	1.39044i	0.0913691	−	0.995817i	$-0.470876\pi$
$283$	16.9944	−	23.3908i	1.01021	−	1.39044i	0.918844	−	0.394622i	$-0.129124\pi$
$284$	6.05528	−	18.6362i	0.359315	−	1.10586i
$285$	0.0708096	+	0.167042i	0.00419440	+	0.00989469i
$286$	2.14740	+	6.60901i	0.126978	+	0.390799i
$287$	7.10119	+	2.30732i	0.419170	+	0.136197i
$288$	−12.4593	−	4.04827i	−0.734171	−	0.238546i
$289$	−0.309017	−	0.951057i	−0.0181775	−	0.0559445i
$290$	0.982656	−	4.24698i	0.0577036	−	0.249391i
$291$	−8.02871	+	24.7098i	−0.470651	+	1.44852i
$292$	−4.70579	+	6.47697i	−0.275386	+	0.379036i
$293$		−	9.18776i		−	0.536755i	−0.963314	−	0.268377i	$-0.913513\pi$
$293$		−	9.18776i		−	0.536755i	0.963314	−	0.268377i	$-0.0864874\pi$
$294$	0.613452	+	0.445699i	0.0357772	+	0.0259937i
$295$	0.714442	+	8.21184i	0.0415964	+	0.478112i
$296$	6.65457	−	4.83483i	0.386789	−	0.281019i
$297$	−8.86277	−	12.1986i	−0.514270	−	0.707832i
$298$	−1.27659	+	0.414789i	−0.0739509	+	0.0240281i
$299$	−28.7268			−1.66131
$300$	22.9137	−	12.1550i	1.32293	−	0.701772i
$301$	10.0852			0.581303
$302$	−0.920821	+	0.299193i	−0.0529873	+	0.0172166i
$303$	−16.6535	−	22.9215i	−0.956717	−	1.31681i
$304$	0.0869947	−	0.0632053i	0.00498949	−	0.00362507i
$305$	2.10331	+	2.42194i	0.120435	+	0.138680i
$306$	−0.927920	−	0.674174i	−0.0530457	−	0.0385399i
$307$			13.9015i			0.793400i	0.917948	+	0.396700i	$0.129845\pi$
$307$			13.9015i			0.793400i	−0.917948	+	0.396700i	$0.870155\pi$
$308$	−12.4196	+	17.0941i	−0.707672	+	0.974026i
$309$	2.59099	−	7.97424i	0.147396	−	0.453638i
$310$	3.12124	−	0.271553i	0.177275	−	0.0154231i
$311$	−7.66733	−	23.5976i	−0.434774	−	1.33810i	−0.893318	−	0.449426i	$-0.851629\pi$
$311$	−7.66733	−	23.5976i	−0.434774	−	1.33810i	0.458544	−	0.888672i	$-0.348371\pi$
$312$	−15.5525	−	5.05330i	−0.880485	−	0.286087i
$313$	19.6144	+	6.37312i	1.10867	+	0.360230i	0.805435	−	0.592685i	$-0.201932\pi$
$313$	19.6144	+	6.37312i	1.10867	+	0.360230i	0.303239	+	0.952915i	$0.401932\pi$
$314$	−2.06386	−	6.35190i	−0.116470	−	0.358458i
$315$	23.0901	−	2.00887i	1.30098	−	0.113187i
$316$	0.748257	−	2.30290i	0.0420928	−	0.129548i
$317$	−2.53811	+	3.49340i	−0.142554	+	0.196209i	−0.874324	−	0.485343i	$-0.838695\pi$
$317$	−2.53811	+	3.49340i	−0.142554	+	0.196209i	0.731770	+	0.681552i	$0.238695\pi$
$318$			5.64679i			0.316656i
$319$	−26.2340	−	19.0601i	−1.46882	−	1.06716i
$320$	−9.24013	−	10.6399i	−0.516539	−	0.594791i
$321$	10.1231	−	7.35485i	0.565015	−	0.410508i
$322$	1.94335	+	2.67479i	0.108298	+	0.149060i
$323$	0.0286654	−	0.00931394i	0.00159498	−	0.000518241i
$324$	−7.13983			−0.396657
$325$	25.2982	−	13.4199i	1.40329	−	0.744404i
$326$	−4.08213			−0.226088
$327$	−12.6949	+	4.12483i	−0.702030	+	0.228103i
$328$	−1.90715	−	2.62497i	−0.105305	−	0.144940i
$329$	−21.4430	+	15.5792i	−1.18219	+	0.858911i
$330$	0.633017	+	7.27594i	0.0348465	+	0.400527i
$331$	4.76152	+	3.45944i	0.261717	+	0.190148i	0.710903	−	0.703290i	$-0.248286\pi$
$331$	4.76152	+	3.45944i	0.261717	+	0.190148i	−0.449187	+	0.893438i	$0.648286\pi$
$332$			25.9217i			1.42264i
$333$	−19.3591	+	26.6456i	−1.06087	+	1.46017i
$334$	−1.56068	+	4.80327i	−0.0853964	+	0.262823i
$335$	3.54896	−	15.3384i	0.193900	−	0.838026i
$336$	−7.24362	−	22.2936i	−0.395172	−	1.21621i
$337$	−24.0567	−	7.81651i	−1.31045	−	0.425792i	−0.431247	−	0.902234i	$-0.641926\pi$
$337$	−24.0567	−	7.81651i	−1.31045	−	0.425792i	−0.879206	+	0.476441i	$0.841926\pi$
$338$	−5.08680	−	1.65280i	−0.276685	−	0.0899005i
$339$	−5.69854	−	17.5383i	−0.309502	−	0.952550i
$340$	−1.68175	−	3.96730i	−0.0912060	−	0.215157i
$341$	7.20194	−	22.1653i	0.390007	−	1.20032i
$342$	0.0203200	−	0.0279680i	0.00109878	−	0.00151234i
$343$			19.6305i			1.05995i
$344$	−3.54556	−	2.57600i	−0.191164	−	0.138889i
$345$	−29.4143	−	6.80581i	−1.58361	−	0.366413i
$346$	1.61979	−	1.17685i	0.0870806	−	0.0632677i
$347$	2.94212	+	4.04948i	0.157941	+	0.217387i	0.880653	−	0.473762i	$-0.157104\pi$
$347$	2.94212	+	4.04948i	0.157941	+	0.217387i	−0.722712	+	0.691150i	$0.757104\pi$
$348$	35.6126	−	11.5712i	1.90904	−	0.620284i
$349$	−30.7765			−1.64743			−0.823714	−	0.567005i	$-0.808102\pi$
$349$	−30.7765			−1.64743			−0.823714	+	0.567005i	$0.808102\pi$
$350$	−2.96095	−	1.44770i	−0.158270	−	0.0773828i
$351$	19.2236			1.02608
$352$	13.1798	−	4.28237i	0.702485	−	0.228251i
$353$	0.624079	+	0.858971i	0.0332164	+	0.0457184i	0.825302	−	0.564691i	$-0.191005\pi$
$353$	0.624079	+	0.858971i	0.0332164	+	0.0457184i	−0.792086	+	0.610410i	$0.791005\pi$
$354$	2.16828	−	1.57534i	0.115243	−	0.0837286i
$355$	11.7201	−	19.4842i	0.622038	−	1.03411i
$356$	16.1527	+	11.7356i	0.856092	+	0.621987i
$357$		−	6.57036i		−	0.347741i
$358$	−2.58345	+	3.55582i	−0.136540	+	0.187931i
$359$	0.593873	−	1.82775i	0.0313434	−	0.0964652i	−0.934161	−	0.356852i	$-0.883850\pi$
$359$	0.593873	−	1.82775i	0.0313434	−	0.0964652i	0.965504	+	0.260387i	$0.0838501\pi$
$360$	−8.63067	−	5.19151i	−0.454876	−	0.273617i
$361$	−5.87104	−	18.0692i	−0.309002	−	0.951011i
$362$	5.95876	+	1.93612i	0.313186	+	0.101760i
$363$	23.5070	+	7.63790i	1.23380	+	0.400886i
$364$	−8.32444	−	25.6200i	−0.436319	−	1.34285i
$365$	−7.01402	+	6.09124i	−0.367131	+	0.318830i
$366$	0.322302	−	0.991942i	0.0168470	−	0.0518497i
$367$	−20.0527	+	27.6001i	−1.04674	+	1.44072i	−0.155141	+	0.987892i	$0.549583\pi$
$367$	−20.0527	+	27.6001i	−1.04674	+	1.44072i	−0.891600	+	0.452824i	$0.850417\pi$
$368$			17.8941i			0.932793i
$369$	10.5106	+	7.63642i	0.547162	+	0.397536i
$370$	4.31216	−	1.82794i	0.224179	−	0.0950303i
$371$	−15.3360	+	11.1422i	−0.796204	+	0.578476i
$372$	15.8189	+	21.7728i	0.820171	+	1.12887i
$373$	−27.4200	+	8.90930i	−1.41975	+	0.461306i	−0.915524	−	0.402263i	$-0.868224\pi$
$373$	−27.4200	+	8.90930i	−1.41975	+	0.461306i	−0.504230	+	0.863569i	$0.668224\pi$
$374$	1.21330			0.0627382
$375$	29.0831	−	7.74759i	1.50184	−	0.400084i
$376$	11.5178			0.593984
$377$	39.3186	−	12.7754i	2.02501	−	0.657966i
$378$	−1.30046	−	1.78994i	−0.0668887	−	0.0920643i
$379$	−11.3152	+	8.22096i	−0.581222	+	0.422282i	−0.839164	−	0.543878i	$-0.816956\pi$
$379$	−11.3152	+	8.22096i	−0.581222	+	0.422282i	0.257942	+	0.966160i	$0.416956\pi$
$380$	0.119576	−	0.0506890i	0.00613414	−	0.00260029i
$381$	−2.58179	−	1.87578i	−0.132269	−	0.0960992i
$382$		−	3.63567i		−	0.186017i
$383$	−6.86460	+	9.44831i	−0.350765	+	0.482786i	−0.947547	−	0.319617i	$-0.896446\pi$
$383$	−6.86460	+	9.44831i	−0.350765	+	0.482786i	0.596782	+	0.802403i	$0.296446\pi$
$384$	−6.54819	+	20.1533i	−0.334161	+	1.02844i
$385$	−18.5115	+	16.0761i	−0.943432	+	0.819313i
$386$	0.235368	+	0.724389i	0.0119799	+	0.0368704i
$387$	16.6893	+	5.42269i	0.848366	+	0.275651i
$388$	17.6885	+	5.74734i	0.897997	+	0.291777i
$389$	4.19304	+	12.9049i	0.212596	+	0.654302i	0.999316	+	0.0369921i	$0.0117777\pi$
$389$	4.19304	+	12.9049i	0.212596	+	0.654302i	−0.786720	+	0.617310i	$0.788222\pi$
$390$	−7.97903	−	4.79954i	−0.404034	−	0.243034i
$391$	−1.54991	+	4.77014i	−0.0783825	+	0.241236i
$392$	0.650182	−	0.894899i	0.0328392	−	0.0451992i
$393$			53.7214i			2.70989i
$394$	−4.47773	−	3.25326i	−0.225585	−	0.163897i
$395$	1.44826	−	2.40768i	0.0728700	−	0.121143i
$396$	−29.7435	+	21.6100i	−1.49467	+	1.08594i
$397$	−14.2578	−	19.6241i	−0.715577	−	0.984908i	−0.999659	−	0.0261076i	$-0.991689\pi$
$397$	−14.2578	−	19.6241i	−0.715577	−	0.984908i	0.284082	−	0.958800i	$-0.408311\pi$
$398$	−4.81243	+	1.56365i	−0.241225	+	0.0783789i
$399$	0.198034			0.00991411
$400$	−8.35935	−	15.7584i	−0.417968	−	0.787920i
$401$	−0.832458			−0.0415710			−0.0207855	−	0.999784i	$-0.506617\pi$
$401$	−0.832458			−0.0415710			−0.0207855	+	0.999784i	$0.506617\pi$
$402$	−4.86844	+	1.58185i	−0.242816	+	0.0788956i
$403$	17.4651	+	24.0386i	0.869996	+	1.19745i
$404$	−16.4083	+	11.9214i	−0.816346	+	0.593110i
$405$	−8.07148	−	1.86756i	−0.401075	−	0.0927998i
$406$	−3.84941	−	2.79676i	−0.191043	−	0.138801i
$407$		−	34.8403i		−	1.72697i
$408$	−1.67822	+	2.30988i	−0.0830844	+	0.114356i
$409$	−3.99499	+	12.2953i	−0.197540	+	0.607965i	0.802398	+	0.596790i	$0.203557\pi$
$409$	−3.99499	+	12.2953i	−0.197540	+	0.607965i	−0.999938	+	0.0111753i	$0.996443\pi$
$410$	−0.721053	−	1.70098i	−0.0356102	−	0.0840054i
$411$	6.93204	+	21.3346i	0.341932	+	1.05236i
$412$	−5.70835	−	1.85475i	−0.281230	−	0.0913772i
$413$	8.55688	+	2.78030i	0.421057	+	0.136810i
$414$	1.77771	+	5.47122i	0.0873696	+	0.268896i
$415$	−6.78033	+	29.3042i	−0.332833	+	1.43849i
$416$	−5.45970	+	16.8032i	−0.267684	+	0.823845i
$417$	−22.7364	+	31.2940i	−1.11341	+	1.53248i
$418$			0.0365695i			0.00178867i
$419$	−3.25422	−	2.36433i	−0.158979	−	0.115505i	0.505452	−	0.862855i	$-0.331326\pi$
$419$	−3.25422	−	2.36433i	−0.158979	−	0.115505i	−0.664431	+	0.747350i	$0.731326\pi$
$420$	−2.45391	−	28.2054i	−0.119738	−	1.37628i
$421$	−6.76349	+	4.91397i	−0.329632	+	0.239492i	−0.740275	−	0.672305i	$-0.765305\pi$
$421$	−6.76349	+	4.91397i	−0.329632	+	0.239492i	0.410642	+	0.911797i	$0.365305\pi$
$422$	−4.49021	−	6.18025i	−0.218580	−	0.300850i
$423$	−43.8612	+	14.2514i	−2.13260	+	0.692925i
$424$	8.23750			0.400048
$425$	−0.863479	−	4.92488i	−0.0418849	−	0.238892i
$426$	−7.39301			−0.358192
$427$	3.32996	−	1.08197i	0.161148	−	0.0523601i
$428$	−5.26496	−	7.24659i	−0.254491	−	0.350277i
$429$	−56.0364	+	40.7129i	−2.70547	+	1.96564i
$430$	−1.63624	−	1.88412i	−0.0789064	−	0.0908601i
$431$	8.24675	+	5.99162i	0.397232	+	0.288606i	0.768413	−	0.639955i	$-0.221047\pi$
$431$	8.24675	+	5.99162i	0.397232	+	0.288606i	−0.371180	+	0.928561i	$0.621047\pi$
$432$		−	11.9745i		−	0.576123i
$433$	11.9414	−	16.4359i	0.573867	−	0.789861i	−0.419139	−	0.907922i	$-0.637668\pi$
$433$	11.9414	−	16.4359i	0.573867	−	0.789861i	0.993006	+	0.118061i	$0.0376679\pi$
$434$	1.05676	−	3.25239i	0.0507263	−	0.156120i
$435$	43.2863	−	3.76597i	2.07542	−	0.180565i
$436$	2.95275	+	9.08763i	0.141411	+	0.435219i
$437$	−0.143775	−	0.0467152i	−0.00687767	−	0.00223469i
$438$	2.87270	+	0.933396i	0.137263	+	0.0445994i
$439$	−8.20367	−	25.2483i	−0.391540	−	1.20504i	−0.931624	−	0.363424i	$-0.881607\pi$
$439$	−8.20367	−	25.2483i	−0.391540	−	1.20504i	0.540084	−	0.841611i	$-0.318393\pi$
$440$	10.6141	−	0.923442i	0.506007	−	0.0440234i
$441$	−1.36869	+	4.21238i	−0.0651756	+	0.200590i
$442$	−0.909224	+	1.25144i	−0.0432474	+	0.0595249i
$443$			2.25321i			0.107053i	0.998566	+	0.0535266i	$0.0170462\pi$
$443$			2.25321i			0.107053i	−0.998566	+	0.0535266i	$0.982954\pi$
$444$	32.5485	+	23.6478i	1.54468	+	1.12228i
$445$	15.1907	+	17.4920i	0.720110	+	0.829202i
$446$	0.241609	−	0.175539i	0.0114405	−	0.00831203i
$447$	−7.86406	−	10.8240i	−0.371957	−	0.511956i
$448$	−14.6290	+	4.75325i	−0.691155	+	0.224570i
$449$	36.6350			1.72891			0.864456	−	0.502709i	$-0.167663\pi$
$449$	36.6350			1.72891			0.864456	+	0.502709i	$0.167663\pi$
$450$	−4.12146	−	3.98776i	−0.194288	−	0.187985i
$451$	−13.7431			−0.647140
$452$	−12.5548	+	4.07930i	−0.590527	+	0.191874i
$453$	−5.67245	−	7.80746i	−0.266515	−	0.366826i
$454$	−5.21433	+	3.78843i	−0.244721	+	0.177800i
$455$	−2.70927	−	31.1405i	−0.127012	−	1.45989i
$456$	−0.0696209	−	0.0505825i	−0.00326030	−	0.00236874i
$457$		−	32.6129i		−	1.52557i	−0.646653	−	0.762785i	$-0.723832\pi$
$457$		−	32.6129i		−	1.52557i	0.646653	−	0.762785i	$-0.276168\pi$
$458$	−1.15255	+	1.58635i	−0.0538553	+	0.0741254i
$459$	1.03718	−	3.19212i	0.0484116	−	0.148996i
$460$	−4.87193	+	21.0562i	−0.227155	+	0.981751i
$461$	1.72925	+	5.32207i	0.0805390	+	0.247874i	0.983216	−	0.182445i	$-0.0584012\pi$
$461$	1.72925	+	5.32207i	0.0805390	+	0.247874i	−0.902677	+	0.430319i	$0.858401\pi$
$462$	7.58165	+	2.46343i	0.352730	+	0.114609i
$463$	23.0269	+	7.48190i	1.07015	+	0.347713i	0.790547	−	0.612402i	$-0.209797\pi$
$463$	23.0269	+	7.48190i	1.07015	+	0.347713i	0.279605	+	0.960115i	$0.409797\pi$
$464$	−7.95786	−	24.4918i	−0.369434	−	1.13700i
$465$	12.1880	+	28.7517i	0.565203	+	1.33333i
$466$	1.53545	−	4.72562i	0.0711283	−	0.218910i
$467$	−5.27212	+	7.25645i	−0.243965	+	0.335789i	−0.913386	−	0.407094i	$-0.866542\pi$
$467$	−5.27212	+	7.25645i	−0.243965	+	0.335789i	0.669421	+	0.742883i	$0.266542\pi$
$468$		−	46.8726i		−	2.16669i
$469$	−13.9025	−	10.1008i	−0.641958	−	0.466410i
$470$	6.38943	+	1.47837i	0.294722	+	0.0681922i
$471$	53.8564	−	39.1290i	2.48157	−	1.80297i
$472$	−2.29810	−	3.16307i	−0.105779	−	0.145592i
$473$	−17.6544	+	5.73628i	−0.811752	+	0.263754i
$474$	−0.913561			−0.0419613
$475$	0.148438	−	0.0260257i	0.00681082	−	0.00119414i
$476$	−4.70339			−0.215579
$477$	−31.3694	+	10.1925i	−1.43631	+	0.466685i
$478$	1.23667	+	1.70213i	0.0565639	+	0.0778535i
$479$	−6.83153	+	4.96339i	−0.312140	+	0.226783i	−0.732814	−	0.680429i	$-0.761794\pi$
$479$	−6.83153	+	4.96339i	−0.312140	+	0.226783i	0.420674	+	0.907212i	$0.361794\pi$
$480$	−9.57131	+	15.9119i	−0.436868	+	0.726275i
$481$	35.9355	+	26.1087i	1.63852	+	1.19045i
$482$		−	1.51240i		−	0.0688882i
$483$	−19.3702	+	26.6607i	−0.881373	+	1.21311i
$484$	5.46758	−	16.8275i	0.248526	−	0.764885i
$485$	18.4933	+	11.1241i	0.839737	+	0.505118i
$486$	1.67278	+	5.14828i	0.0758787	+	0.233531i
$487$	14.9035	+	4.84246i	0.675344	+	0.219433i	0.626556	−	0.779377i	$-0.284464\pi$
$487$	14.9035	+	4.84246i	0.675344	+	0.219433i	0.0487883	+	0.998809i	$0.484464\pi$
$488$	−1.44704	−	0.470172i	−0.0655044	−	0.0212837i
$489$	−12.5734	−	38.6969i	−0.568588	−	1.74993i
$490$	0.475551	−	0.412986i	0.0214832	−	0.0186568i
$491$	−3.57074	+	10.9896i	−0.161145	+	0.495955i	−0.998732	−	0.0503506i	$-0.983966\pi$
$491$	−3.57074	+	10.9896i	−0.161145	+	0.495955i	0.837586	+	0.546305i	$0.183966\pi$
$492$	9.32815	−	12.8391i	0.420545	−	0.578831i
$493$		−	7.21821i		−	0.325092i
$494$	−0.0377191	−	0.0274045i	−0.00169706	−	0.00123299i
$495$	−39.2772	+	16.6498i	−1.76538	+	0.748352i
$496$	14.9738	−	10.8791i	0.672342	−	0.488485i
$497$	−14.5879	−	20.0785i	−0.654356	−	0.900644i
$498$	9.30121	−	3.02215i	0.416797	−	0.135426i
$499$	26.6675			1.19380			0.596900	−	0.802316i	$-0.296399\pi$
$499$	26.6675			1.19380			0.596900	+	0.802316i	$0.296399\pi$
$500$	−5.54610	−	20.8191i	−0.248029	−	0.931058i
$501$	−50.3400			−2.24903
$502$	−5.19421	+	1.68770i	−0.231829	+	0.0753257i
$503$	−16.9430	−	23.3200i	−0.755449	−	1.03979i	−0.997579	−	0.0695424i	$-0.977846\pi$
$503$	−16.9430	−	23.3200i	−0.755449	−	1.03979i	0.242130	−	0.970244i	$-0.422154\pi$
$504$	−8.89394	+	6.46182i	−0.396167	+	0.287832i
$505$	−21.6677	+	9.18503i	−0.964200	+	0.408728i
$506$	−4.92324	−	3.57694i	−0.218865	−	0.159014i
$507$		−	53.3115i		−	2.36765i
$508$	−1.34278	+	1.84817i	−0.0595760	+	0.0819994i
$509$	−2.37565	+	7.31149i	−0.105299	+	0.324076i	−0.989800	−	0.142461i	$-0.954499\pi$
$509$	−2.37565	+	7.31149i	−0.105299	+	0.324076i	0.884502	+	0.466537i	$0.154499\pi$
$510$	−1.22747	+	1.06598i	−0.0543533	+	0.0472025i
$511$	3.13342	+	9.64366i	0.138614	+	0.426610i
$512$	17.6643	+	5.73947i	0.780657	+	0.253651i
$513$	0.0962123	+	0.0312613i	0.00424788	+	0.00138022i
$514$	0.394677	+	1.21469i	0.0174084	+	0.0535777i
$515$	−5.96807	−	3.58991i	−0.262984	−	0.158190i
$516$	6.62400	−	20.3866i	0.291605	−	0.897469i
$517$	28.6753	−	39.4681i	1.26114	−	1.73581i
$518$		−	5.11224i		−	0.224619i
$519$	16.1452	+	11.7301i	0.708694	+	0.514896i
$520$	−7.00153	+	11.6398i	−0.307038	+	0.510437i
$521$	−23.4288	+	17.0220i	−1.02644	+	0.745749i	−0.967592	−	0.252518i	$-0.918741\pi$
$521$	−23.4288	+	17.0220i	−1.02644	+	0.745749i	−0.0588435	+	0.998267i	$0.518741\pi$
$522$	−4.86633	−	6.69793i	−0.212993	−	0.293160i
$523$	9.53386	−	3.09774i	0.416887	−	0.135455i	−0.0930604	−	0.995660i	$-0.529665\pi$
$523$	9.53386	−	3.09774i	0.416887	−	0.135455i	0.509947	+	0.860206i	$0.329665\pi$
$524$	38.4564			1.67998
$525$	4.60355	−	32.5277i	0.200915	−	1.41962i
$526$	6.03210			0.263012
$527$	4.93396	−	1.60314i	0.214927	−	0.0698339i
$528$	25.3603	+	34.9054i	1.10366	+	1.51906i
$529$	1.74464	−	1.26755i	0.0758538	−	0.0551110i
$530$	4.56971	+	1.05733i	0.198495	+	0.0459274i
$531$	12.6652	+	9.20184i	0.549625	+	0.399326i
$532$		−	0.141763i		−	0.00614619i
$533$	10.2989	−	14.1752i	0.446093	−	0.613994i
$534$	2.32776	−	7.16412i	0.100732	−	0.310022i
$535$	−4.05648	−	9.56933i	−0.175377	−	0.413718i
$536$	2.30759	+	7.10205i	0.0996729	+	0.306762i
$537$	−41.6650	−	13.5378i	−1.79798	−	0.584198i
$538$	−7.30847	−	2.37467i	−0.315090	−	0.102379i
$539$	−1.44783	−	4.45598i	−0.0623627	−	0.191933i
$540$	3.26024	−	14.0906i	0.140298	−	0.606361i
$541$	0.0518510	−	0.159581i	0.00222925	−	0.00686092i	−0.949936	−	0.312445i	$-0.898852\pi$
$541$	0.0518510	−	0.159581i	0.00222925	−	0.00686092i	0.952165	+	0.305585i	$0.0988519\pi$
$542$	−0.108742	+	0.149671i	−0.00467088	+	0.00642892i
$543$			62.4500i			2.67999i
$544$	2.49564	+	1.81319i	0.107000	+	0.0777398i
$545$	0.961001	+	11.0458i	0.0411648	+	0.473150i
$546$	−8.22241	+	5.97393i	−0.351887	+	0.255661i
$547$	−12.8370	−	17.6686i	−0.548871	−	0.755456i	0.440988	−	0.897513i	$-0.354628\pi$
$547$	−12.8370	−	17.6686i	−0.548871	−	0.755456i	−0.989858	+	0.142057i	$0.954628\pi$
$548$	15.2724	−	4.96229i	0.652403	−	0.211979i
$549$	6.09227			0.260012
$550$	6.00664	+	0.850103i	0.256124	+	0.0362485i
$551$	0.217561			0.00926840
$552$	13.6195	−	4.42526i	0.579686	−	0.188351i
$553$	−1.80264	−	2.48112i	−0.0766560	−	0.105508i
$554$	−4.21083	+	3.05935i	−0.178901	+	0.129979i
$555$	30.6101	+	35.2473i	1.29933	+	1.49616i
$556$	22.4018	+	16.2759i	0.950048	+	0.690250i
$557$		−	0.798266i		−	0.0338236i	−0.999857	−	0.0169118i	$-0.994617\pi$
$557$		−	0.798266i		−	0.0338236i	0.999857	−	0.0169118i	$-0.00538346\pi$
$558$	3.49753	−	4.81393i	0.148062	−	0.203790i
$559$	7.31331	−	22.5081i	0.309320	−	0.951990i
$560$	−19.3976	+	1.68762i	−0.819698	+	0.0713149i
$561$	3.73709	+	11.5016i	0.157780	+	0.485597i
$562$	−1.83466	−	0.596117i	−0.0773905	−	0.0251457i
$563$	1.24455	+	0.404380i	0.0524517	+	0.0170426i	0.335125	−	0.942174i	$-0.391221\pi$
$563$	1.24455	+	0.404380i	0.0524517	+	0.0170426i	−0.282674	+	0.959216i	$0.591221\pi$
$564$	17.4085	+	53.5779i	0.733031	+	2.25604i
$565$	−15.2600	+	1.32765i	−0.641995	+	0.0558545i
$566$	−2.41302	+	7.42650i	−0.101427	+	0.312159i
$567$	−5.31530	+	7.31588i	−0.223222	+	0.307238i
$568$			10.7849i			0.452523i
$569$	−3.40675	−	2.47515i	−0.142818	−	0.103764i	0.514082	−	0.857741i	$-0.328133\pi$
$569$	−3.40675	−	2.47515i	−0.142818	−	0.103764i	−0.656900	+	0.753977i	$0.728133\pi$
$570$	−0.0321293	−	0.0369966i	−0.00134575	−	0.00154962i
$571$	15.9802	−	11.6103i	0.668750	−	0.485875i	−0.200857	−	0.979621i	$-0.564373\pi$
$571$	15.9802	−	11.6103i	0.668750	−	0.485875i	0.869606	+	0.493746i	$0.164373\pi$
$572$	29.1443	+	40.1136i	1.21858	+	1.67723i
$573$	34.4646	−	11.1982i	1.43978	−	0.467813i
$574$	−2.01658			−0.0841703
$575$	−11.0153	+	22.5294i	−0.459370	+	0.939542i
$576$	−26.7642			−1.11518
$577$	23.5029	−	7.63657i	0.978441	−	0.317915i	0.224222	−	0.974538i	$-0.428016\pi$
$577$	23.5029	−	7.63657i	0.978441	−	0.317915i	0.754219	+	0.656623i	$0.228016\pi$
$578$	0.158748	+	0.218498i	0.00660306	+	0.00908833i
$579$	−6.14195	+	4.46239i	−0.255251	+	0.185450i
$580$	−2.69587	−	30.9865i	−0.111940	−	1.28664i
$581$	26.5609	+	19.2976i	1.10193	+	0.800601i
$582$		−	7.01703i		−	0.290865i
$583$	20.5085	−	28.2275i	0.849375	−	1.16906i
$584$	1.36163	−	4.19067i	0.0563447	−	0.173411i
$585$	12.2604	−	52.9889i	0.506907	−	2.19082i
$586$	0.766800	+	2.35997i	0.0316762	+	0.0974894i
$587$	−38.9668	−	12.6611i	−1.60833	−	0.522579i	−0.639183	−	0.769054i	$-0.720728\pi$
$587$	−38.9668	−	12.6611i	−1.60833	−	0.522579i	−0.969149	+	0.246475i	$0.920728\pi$
$588$	5.14557	+	1.67190i	0.212200	+	0.0689478i
$589$	0.0483195	+	0.148712i	0.00199097	+	0.00612758i
$590$	−0.868863	−	2.04967i	−0.0357705	−	0.0843835i
$591$	17.0477	−	52.4674i	0.701249	−	2.15822i
$592$	16.2633	−	22.3845i	0.668416	−	0.919995i
$593$			5.88619i			0.241717i	0.992670	+	0.120858i	$0.0385647\pi$
$593$			5.88619i			0.241717i	−0.992670	+	0.120858i	$0.961435\pi$
$594$	3.29457	+	2.39365i	0.135178	+	0.0982125i
$595$	−5.31712	−	1.23026i	−0.217981	−	0.0504358i
$596$	−7.74831	+	5.62948i	−0.317383	+	0.230592i
$597$	−29.6456	−	40.8036i	−1.21331	−	1.66998i
$598$	7.37876	−	2.39751i	0.301740	−	0.0980413i
$599$	−12.2699			−0.501336			−0.250668	−	0.968073i	$-0.580650\pi$
$599$	−12.2699			−0.501336			−0.250668	+	0.968073i	$0.580650\pi$
$600$	−9.92674	+	10.2596i	−0.405258	+	0.418845i
$601$	−28.5572			−1.16487			−0.582436	−	0.812877i	$-0.697900\pi$
$601$	−28.5572			−1.16487			−0.582436	+	0.812877i	$0.697900\pi$
$602$	−2.59049	+	0.841703i	−0.105581	+	0.0343052i
$603$	−17.5752	−	24.1902i	−0.715719	−	0.985102i
$604$	−5.58896	+	4.06062i	−0.227412	+	0.165224i
$605$	10.5826	−	17.5931i	0.430243	−	0.715261i
$606$	6.19062	+	4.49775i	0.251477	+	0.182708i
$607$			39.2099i			1.59148i	0.605637	+	0.795741i	$0.292918\pi$
$607$			39.2099i			1.59148i	−0.605637	+	0.795741i	$0.707082\pi$
$608$	−0.0546505	+	0.0752199i	−0.00221637	+	0.00305057i
$609$	14.6555	−	45.1051i	0.593872	−	1.82775i
$610$	−0.742388	−	0.446561i	−0.0300584	−	0.0180807i
$611$	19.2201	+	59.1534i	0.777562	+	2.39309i
$612$	−7.78330	−	2.52895i	−0.314621	−	0.102227i
$613$	−4.59316	−	1.49241i	−0.185516	−	0.0602778i	0.214786	−	0.976661i	$-0.431095\pi$
$613$	−4.59316	−	1.49241i	−0.185516	−	0.0602778i	−0.400302	+	0.916383i	$0.631095\pi$
$614$	−1.16020	−	3.57074i	−0.0468220	−	0.144103i
$615$	13.9037	−	12.0745i	0.560650	−	0.486890i
$616$	3.59363	−	11.0601i	0.144792	−	0.445623i
$617$	2.82664	−	3.89053i	0.113796	−	0.156627i	−0.748320	−	0.663338i	$-0.769139\pi$
$617$	2.82664	−	3.89053i	0.113796	−	0.156627i	0.862116	+	0.506711i	$0.169139\pi$
$618$			2.26450i			0.0910917i
$619$	15.0731	+	10.9512i	0.605837	+	0.440166i	0.847946	−	0.530083i	$-0.177839\pi$
$619$	15.0731	+	10.9512i	0.605837	+	0.440166i	−0.242109	+	0.970249i	$0.577839\pi$
$620$	20.5818	−	8.72473i	0.826587	−	0.350394i
$621$	−13.6193	+	9.89503i	−0.546525	+	0.397074i
$622$	3.93886	+	5.42138i	0.157934	+	0.217377i
$623$	24.0500	−	7.81432i	0.963543	−	0.313074i
$624$	−55.0072			−2.20205
$625$	−0.824163	−	24.9864i	−0.0329665	−	0.999456i
$626$	−5.57006			−0.222624
$627$	−0.346664	+	0.112638i	−0.0138444	+	0.00449832i
$628$	−28.0104	−	38.5531i	−1.11774	−	1.53844i
$629$	6.27426	−	4.55852i	0.250171	−	0.181760i
$630$	−5.76327	+	2.44308i	−0.229614	+	0.0973345i
$631$	−25.4898	−	18.5195i	−1.01473	−	0.737248i	−0.0495378	−	0.998772i	$-0.515775\pi$
$631$	−25.4898	−	18.5195i	−1.01473	−	0.737248i	−0.965197	+	0.261524i	$0.915775\pi$
$632$			1.33270i			0.0530118i
$633$	44.7559	−	61.6012i	1.77889	−	2.44843i
$634$	0.360383	−	1.10914i	0.0143126	−	0.0440497i
$635$	−2.00142	+	1.73811i	−0.0794238	+	0.0689746i
$636$	12.4505	+	38.3188i	0.493696	+	1.51944i
$637$	5.68103	+	1.84588i	0.225091	+	0.0731364i
$638$	8.32922	+	2.70633i	0.329757	+	0.107144i
$639$	−13.3445	−	41.0702i	−0.527901	−	1.62471i
$640$	15.0831	+	9.07276i	0.596211	+	0.358632i
$641$	−14.0200	+	43.1491i	−0.553757	+	1.70429i	0.145446	+	0.989366i	$0.453538\pi$
$641$	−14.0200	+	43.1491i	−0.553757	+	1.70429i	−0.699203	+	0.714923i	$0.746462\pi$
$642$	−1.98639	+	2.73403i	−0.0783965	+	0.107903i
$643$			11.9257i			0.470302i	0.971959	+	0.235151i	$0.0755585\pi$
$643$			11.9257i			0.470302i	−0.971959	+	0.235151i	$0.924442\pi$
$644$	19.0851	+	13.8661i	0.752056	+	0.546401i
$645$	12.8209	−	21.3141i	0.504821	−	0.839243i
$646$	−0.00658566	+	0.00478476i	−0.000259109	+	0.000188254i
$647$	12.2184	+	16.8171i	0.480353	+	0.661149i	0.978573	−	0.205902i	$-0.0660127\pi$
$647$	12.2184	+	16.8171i	0.480353	+	0.661149i	−0.498220	+	0.867051i	$0.666013\pi$
$648$	3.73729	−	1.21432i	0.146815	−	0.0477030i
$649$	−16.5604			−0.650053
$650$	−5.37809	+	5.55841i	−0.210946	+	0.218019i
$651$	34.0862			1.33594
$652$	−27.7011	+	9.00064i	−1.08486	+	0.352492i
$653$	1.15398	+	1.58831i	0.0451586	+	0.0621555i	0.830999	−	0.556274i	$-0.187769\pi$
$653$	1.15398	+	1.58831i	0.0451586	+	0.0621555i	−0.785841	+	0.618429i	$0.787769\pi$
$654$	2.91656	−	2.11901i	0.114047	−	0.0828597i
$655$	43.4745	+	10.0590i	1.69869	+	0.393038i
$656$	−8.82979	−	6.41522i	−0.344745	−	0.250472i
$657$			17.6434i			0.688335i
$658$	4.20762	−	5.79129i	0.164030	−	0.225768i
$659$	−6.07573	+	18.6992i	−0.236677	+	0.728416i	0.760218	+	0.649668i	$0.225092\pi$
$659$	−6.07573	+	18.6992i	−0.236677	+	0.728416i	−0.996895	+	0.0787478i	$0.974908\pi$
$660$	20.3383	+	47.9784i	0.791666	+	1.86756i
$661$	−14.7084	−	45.2679i	−0.572092	−	1.76072i	−0.645874	−	0.763444i	$-0.723507\pi$
$661$	−14.7084	−	45.2679i	−0.572092	−	1.76072i	0.0737822	−	0.997274i	$-0.476493\pi$
$662$	−1.51176	−	0.491202i	−0.0587564	−	0.0190911i
$663$	−14.6636	−	4.76450i	−0.569488	−	0.185038i
$664$	−4.40869	−	13.5685i	−0.171090	−	0.526562i
$665$	0.0370808	−	0.160261i	0.00143793	−	0.00621465i
$666$	2.74878	−	8.45988i	0.106513	−	0.327814i
$667$	−21.2801	+	29.2895i	−0.823968	+	1.13409i
$668$			36.0358i			1.39427i
$669$	2.40822	+	1.74968i	0.0931072	+	0.0676464i
$670$	0.368539	+	4.23601i	0.0142379	+	0.163652i
$671$	−5.21377	+	3.78802i	−0.201275	+	0.146235i
$672$	11.9133	+	16.3973i	0.459566	+	0.632538i
$673$	26.1365	−	8.49225i	1.00749	−	0.327352i	0.241633	−	0.970368i	$-0.422317\pi$
$673$	26.1365	−	8.49225i	1.00749	−	0.327352i	0.765853	+	0.643016i	$0.222317\pi$
$674$	6.83157			0.263142
$675$	7.37132	−	15.0764i	0.283722	−	0.580292i
$676$	−38.1630			−1.46781
$677$	−47.6084	+	15.4689i	−1.82974	+	0.594519i	−0.830440	+	0.557108i	$0.811911\pi$
$677$	−47.6084	+	15.4689i	−1.82974	+	0.594519i	−0.999300	+	0.0374105i	$0.988089\pi$
$678$	2.92746	+	4.02930i	0.112428	+	0.154744i
$679$	19.0574	−	13.8460i	0.731356	−	0.531361i
$680$	1.55505	+	1.79063i	0.0596334	+	0.0686674i
$681$	−51.9735	−	37.7609i	−1.99163	−	1.44700i
$682$			6.29445i			0.241027i
$683$	−8.47733	+	11.6680i	−0.324376	+	0.446465i	−0.939797	−	0.341733i	$-0.888986\pi$
$683$	−8.47733	+	11.6680i	−0.324376	+	0.446465i	0.615421	+	0.788199i	$0.288986\pi$
$684$	0.0762238	−	0.234593i	0.00291449	−	0.00896988i
$685$	18.5632	−	1.61502i	0.709263	−	0.0617069i
$686$	−1.63834	−	5.04229i	−0.0625520	−	0.192515i
$687$	−18.5879	−	6.03959i	−0.709174	−	0.230425i
$688$	−14.0204	−	4.55550i	−0.534523	−	0.173677i
$689$	13.7462	+	42.3064i	0.523687	+	1.61174i
$690$	8.12337	−	0.706745i	0.309251	−	0.0269053i
$691$	14.1396	−	43.5173i	0.537897	−	1.65548i	−0.199408	−	0.979917i	$-0.563902\pi$
$691$	14.1396	−	43.5173i	0.537897	−	1.65548i	0.737305	−	0.675560i	$-0.236098\pi$
$692$	8.39701	−	11.5575i	0.319206	−	0.439350i
$693$			46.5647i			1.76885i
$694$	−1.09368	−	0.794604i	−0.0415154	−	0.0301627i
$695$	21.0677	+	24.2593i	0.799143	+	0.920207i
$696$	−16.6732	+	12.1138i	−0.631995	+	0.459171i
$697$	−1.79816	−	2.47495i	−0.0681100	−	0.0937454i
$698$	7.90526	−	2.56857i	0.299218	−	0.0972220i
$699$	49.5263			1.87326
$700$	−23.2849	−	3.29544i	−0.880086	−	0.124556i
$701$	7.59802			0.286973			0.143487	−	0.989652i	$-0.454169\pi$
$701$	7.59802			0.286973			0.143487	+	0.989652i	$0.454169\pi$
$702$	−4.93778	+	1.60438i	−0.186365	+	0.0605535i
$703$	0.137396	+	0.189109i	0.00518199	+	0.00713240i
$704$	22.9048	−	16.6413i	0.863259	−	0.627194i
$705$	5.66577	+	65.1227i	0.213385	+	2.45266i
$706$	−0.231990	−	0.168551i	−0.00873106	−	0.00634348i
$707$			25.6879i			0.966093i
$708$	11.2404	−	15.4710i	0.422438	−	0.581436i
$709$	−8.61599	+	26.5173i	−0.323580	+	0.995877i	0.648497	+	0.761217i	$0.275398\pi$
$709$	−8.61599	+	26.5173i	−0.323580	+	0.995877i	−0.972077	+	0.234660i	$0.924602\pi$
$710$	−1.38430	+	5.98285i	−0.0519518	+	0.224532i
$711$	−1.64899	−	5.07508i	−0.0618421	−	0.190330i
$712$	−10.4510	−	3.39573i	−0.391667	−	0.127260i
$713$	−24.7469	−	8.04075i	−0.926778	−	0.301129i
$714$	0.548355	+	1.68766i	0.0205217	+	0.0631593i
$715$	22.4547	+	52.9712i	0.839759	+	1.98101i
$716$	−9.69100	+	29.8258i	−0.362170	+	1.11464i
$717$	−12.3264	+	16.9658i	−0.460338	+	0.633600i
$718$			0.519041i			0.0193704i
$719$	28.0301	+	20.3651i	1.04535	+	0.759489i	0.971322	−	0.237768i	$-0.0764157\pi$
$719$	28.0301	+	20.3651i	1.04535	+	0.759489i	0.0740244	+	0.997256i	$0.476416\pi$
$720$	−33.0071	−	7.63710i	−1.23010	−	0.284618i
$721$	−6.15011	+	4.46832i	−0.229042	+	0.166409i
$722$	3.01607	+	4.15127i	0.112247	+	0.154494i
$723$	14.3370	−	4.65836i	0.533198	−	0.173246i
$724$	44.7048			1.66144
$725$	5.05746	−	35.7350i	0.187830	−	1.32716i
$726$	−6.67547			−0.247750
$727$	−4.29826	+	1.39659i	−0.159414	+	0.0517967i	−0.387637	−	0.921812i	$-0.626708\pi$
$727$	−4.29826	+	1.39659i	−0.159414	+	0.0517967i	0.228223	+	0.973609i	$0.426708\pi$
$728$	8.71474	+	11.9948i	0.322990	+	0.444557i
$729$	−34.6589	+	25.1812i	−1.28366	+	0.932636i
$730$	1.29325	−	2.14998i	0.0478655	−	0.0795743i
$731$	−3.34293	−	2.42878i	−0.123643	−	0.0898318i
$732$		−	7.44191i		−	0.275061i
$733$	8.24429	−	11.3473i	0.304510	−	0.419122i	−0.629149	−	0.777284i	$-0.716597\pi$
$733$	8.24429	−	11.3473i	0.304510	−	0.419122i	0.933659	+	0.358163i	$0.116597\pi$
$734$	2.84726	−	8.76295i	0.105094	−	0.323446i
$735$	5.37968	+	3.23598i	0.198433	+	0.119361i
$736$	−4.78114	−	14.7148i	−0.176235	−	0.542396i
$737$	30.0818	+	9.77416i	1.10808	+	0.360036i
$738$	−3.33709	−	1.08429i	−0.122840	−	0.0399131i
$739$	10.8250	+	33.3159i	0.398204	+	1.22554i	0.926438	+	0.376446i	$0.122854\pi$
$739$	10.8250	+	33.3159i	0.398204	+	1.22554i	−0.528235	+	0.849098i	$0.677146\pi$
$740$	25.2317	−	21.9122i	0.927536	−	0.805508i
$741$	0.143605	−	0.441970i	0.00527545	−	0.0162362i
$742$	3.00928	−	4.14192i	0.110474	−	0.152055i
$743$			14.3412i			0.526126i	0.964779	+	0.263063i	$0.0847328\pi$
$743$			14.3412i			0.526126i	−0.964779	+	0.263063i	$0.915267\pi$
$744$	−11.9833	−	8.70641i	−0.439331	−	0.319192i
$745$	−10.2319	+	4.33733i	−0.374867	+	0.158908i
$746$	6.29955	−	4.57689i	0.230643	−	0.167572i
$747$	33.5777	+	46.2157i	1.22854	+	1.69094i
$748$	8.23339	−	2.67519i	0.301043	−	0.0978147i
$749$	−11.3448			−0.414531
$750$	−6.82368	+	4.41729i	−0.249166	+	0.161297i
$751$	−1.29225			−0.0471549			−0.0235774	−	0.999722i	$-0.507506\pi$
$751$	−1.29225			−0.0471549			−0.0235774	+	0.999722i	$0.507506\pi$
$752$	36.8470	−	11.9723i	1.34367	−	0.436585i
$753$	−31.9974	−	44.0406i	−1.16605	−	1.60493i
$754$	−9.03316	+	6.56297i	−0.328968	+	0.239009i
$755$	−7.38038	+	3.12858i	−0.268600	+	0.113861i
$756$	−12.7715	−	9.27903i	−0.464495	−	0.337475i
$757$		−	31.9511i		−	1.16128i	−0.814159	−	0.580642i	$-0.802802\pi$
$757$		−	31.9511i		−	1.16128i	0.814159	−	0.580642i	$-0.197198\pi$
$758$	2.22031	−	3.05599i	0.0806452	−	0.110999i
$759$	18.7438	−	57.6876i	0.680358	−	2.09393i
$760$	−0.0539704	+	0.0468700i	−0.00195771	+	0.00170015i
$761$	−0.978614	−	3.01186i	−0.0354747	−	0.109180i	0.931751	−	0.363097i	$-0.118281\pi$
$761$	−0.978614	−	3.01186i	−0.0354747	−	0.109180i	−0.967226	+	0.253918i	$0.918281\pi$
$762$	0.819710	+	0.266340i	0.0296950	+	0.00964847i
$763$	11.5099	+	3.73980i	0.416687	+	0.135390i
$764$	−8.01624	−	24.6714i	−0.290017	−	0.892582i
$765$	−8.13743	−	4.89482i	−0.294209	−	0.176972i
$766$	0.974696	−	2.99981i	0.0352172	−	0.108387i
$767$	12.4101	−	17.0810i	0.448101	−	0.616758i
$768$			28.2078i			1.01786i
$769$	5.29612	+	3.84785i	0.190983	+	0.138757i	0.679168	−	0.733983i	$-0.262341\pi$
$769$	5.29612	+	3.84785i	0.190983	+	0.138757i	−0.488185	+	0.872740i	$0.662341\pi$
$770$	3.41317	−	5.67425i	0.123002	−	0.204486i
$771$	−10.2991	+	7.48274i	−0.370913	+	0.269484i
$772$	3.19439	+	4.39671i	0.114969	+	0.158241i
$773$	17.7411	−	5.76444i	0.638104	−	0.207332i	0.0279423	−	0.999610i	$-0.491105\pi$
$773$	17.7411	−	5.76444i	0.638104	−	0.207332i	0.610162	+	0.792277i	$0.291105\pi$
$774$	−4.73940			−0.170354
$775$	25.5496	−	4.47962i	0.917770	−	0.160913i
$776$	−10.2364			−0.367465
$777$	48.4619	−	15.7462i	1.73856	−	0.564893i
$778$	−2.15405	−	2.96480i	−0.0772265	−	0.106293i
$779$	0.0745963	−	0.0541974i	0.00267269	−	0.00194182i
$780$	−64.7277	−	14.9765i	−2.31762	−	0.536246i
$781$	36.9567	+	26.8506i	1.32241	+	0.960790i
$782$		−	1.35461i		−	0.0484409i
$783$	14.2404	−	19.6002i	0.508910	−	0.700454i
$784$	1.14981	−	3.53875i	0.0410646	−	0.126384i
$785$	−21.5812	−	50.9104i	−0.770264	−	1.81707i
$786$	−4.48353	−	13.7989i	−0.159922	−	0.492190i
$787$	−20.8036	−	6.75949i	−0.741568	−	0.240950i	−0.0862187	−	0.996276i	$-0.527478\pi$
$787$	−20.8036	−	6.75949i	−0.741568	−	0.240950i	−0.655349	+	0.755326i	$0.727478\pi$
$788$	−37.5587	−	12.2036i	−1.33797	−	0.434734i
$789$	18.5795	+	57.1818i	0.661448	+	2.03573i
$790$	−0.171059	+	0.739307i	−0.00608600	+	0.0263034i
$791$	−5.16662	+	15.9012i	−0.183704	+	0.565382i
$792$	11.8937	−	16.3703i	0.422624	−	0.581692i
$793$		−	8.21634i		−	0.291771i
$794$	5.30006	+	3.85072i	0.188092	+	0.136657i
$795$	4.05215	+	46.5756i	0.143715	+	1.65187i
$796$	−29.2092	+	21.2218i	−1.03529	+	0.752185i
$797$	6.84000	+	9.41445i	0.242285	+	0.333477i	0.912791	−	0.408428i	$-0.133923\pi$
$797$	6.84000	+	9.41445i	0.242285	+	0.333477i	−0.670506	+	0.741904i	$0.733923\pi$
$798$	−0.0508671	+	0.0165277i	−0.00180068	+	0.000585075i
$799$	10.8595			0.384183
$800$	11.0847	+	10.7251i	0.391902	+	0.379188i
$801$	44.0003			1.55467
$802$	0.213825	−	0.0694761i	0.00755044	−	0.00245329i
$803$	−10.9702	−	15.0992i	−0.387131	−	0.532840i
$804$	−29.5492	+	21.4687i	−1.04212	+	0.757144i
$805$	17.9485	+	20.6675i	0.632600	+	0.728434i
$806$	−6.49231	−	4.71694i	−0.228682	−	0.166147i
$807$		−	76.5955i		−	2.69629i
$808$	6.56128	−	9.03083i	0.230825	−	0.317704i
$809$	3.60811	−	11.1046i	0.126854	−	0.390417i	−0.867380	−	0.497646i	$-0.834198\pi$
$809$	3.60811	−	11.1046i	0.126854	−	0.390417i	0.994234	+	0.107229i	$0.0341978\pi$
$810$	2.22911	−	0.193936i	0.0783228	−	0.00681420i
$811$	−14.0961	−	43.3833i	−0.494981	−	1.52339i	−0.816986	−	0.576657i	$-0.804357\pi$
$811$	−14.0961	−	43.3833i	−0.494981	−	1.52339i	0.322006	−	0.946738i	$-0.395643\pi$
$812$	−32.2884	−	10.4911i	−1.13310	−	0.368167i
$813$	−1.75376	−	0.569830i	−0.0615069	−	0.0199848i
$814$	2.90774	+	8.94910i	0.101916	+	0.313666i
$815$	−33.6701	+	2.92934i	−1.17941	+	0.102610i
$816$	−2.96784	+	9.13406i	−0.103895	+	0.319756i
$817$	0.0732048	−	0.100758i	0.00256111	−	0.00352507i
$818$		−	3.49160i		−	0.122081i
$819$	−48.0284	−	34.8947i	−1.67825	−	1.21932i
$820$	−8.64350	−	9.95292i	−0.301844	−	0.347571i
$821$	17.1490	−	12.4595i	0.598505	−	0.434839i	−0.246843	−	0.969055i	$-0.579393\pi$
$821$	17.1490	−	12.4595i	0.598505	−	0.434839i	0.845348	+	0.534216i	$0.179393\pi$
$822$	−3.56113	−	4.90147i	−0.124209	−	0.170958i
$823$	−47.6498	+	15.4824i	−1.66097	+	0.539681i	−0.981075	−	0.193630i	$-0.937974\pi$
$823$	−47.6498	+	15.4824i	−1.66097	+	0.539681i	−0.679893	+	0.733311i	$0.737974\pi$
$824$	3.30344			0.115081
$825$	10.4425	+	59.5589i	0.363560	+	2.07357i
$826$	−2.42996			−0.0845492
$827$	5.34750	−	1.73751i	0.185951	−	0.0604191i	−0.214561	−	0.976711i	$-0.568832\pi$
$827$	5.34750	−	1.73751i	0.185951	−	0.0604191i	0.400512	+	0.916291i	$0.368832\pi$
$828$	24.1269	+	33.2078i	0.838467	+	1.15405i
$829$	−16.0754	+	11.6795i	−0.558322	+	0.405645i	−0.830844	−	0.556505i	$-0.812142\pi$
$829$	−16.0754	+	11.6795i	−0.558322	+	0.405645i	0.272522	+	0.962149i	$0.412142\pi$
$830$	−0.704099	−	8.09296i	−0.0244396	−	0.280911i
$831$	−41.9711	−	30.4938i	−1.45596	−	1.05782i
$832$			36.0956i			1.25139i
$833$	0.613024	−	0.843755i	0.0212400	−	0.0292344i
$834$	3.22832	−	9.93575i	0.111788	−	0.344047i
$835$	−9.42587	+	40.7381i	−0.326196	+	1.40980i
$836$	0.0806317	+	0.248159i	0.00278870	+	0.00858275i
$837$	16.5603	+	5.38078i	0.572409	+	0.185987i
$838$	1.03321	+	0.335709i	0.0356915	+	0.0115969i
$839$	10.0525	+	30.9384i	0.347051	+	1.06811i	0.960477	+	0.278360i	$0.0897908\pi$
$839$	10.0525	+	30.9384i	0.347051	+	1.06811i	−0.613426	+	0.789752i	$0.710209\pi$
$840$	6.08156	+	14.3465i	0.209834	+	0.495003i
$841$	7.13909	−	21.9719i	0.246176	−	0.757651i
$842$	1.32716	−	1.82668i	0.0457369	−	0.0629514i
$843$		−	19.2279i		−	0.662245i
$844$	−44.0971	−	32.0384i	−1.51789	−	1.10281i
$845$	−43.1428	−	9.98227i	−1.48416	−	0.343401i
$846$	10.0768	−	7.32121i	0.346447	−	0.251709i
$847$	−13.1720	−	18.1297i	−0.452596	−	0.622945i
$848$	26.3529	−	8.56257i	0.904961	−	0.294040i
$849$	−77.8325			−2.67120
$850$	0.632818	+	1.19294i	0.0217055	+	0.0409175i
$851$	−38.8982			−1.33341
$852$	−50.1686	+	16.3008i	−1.71875	+	0.558455i
$853$	−4.57169	−	6.29240i	−0.156532	−	0.215448i	0.723547	−	0.690275i	$-0.242510\pi$
$853$	−4.57169	−	6.29240i	−0.156532	−	0.215448i	−0.880079	+	0.474827i	$0.842510\pi$
$854$	−0.765033	+	0.555829i	−0.0261789	+	0.0190201i
$855$	0.147532	−	0.245266i	0.00504550	−	0.00838793i
$856$	3.98838	+	2.89773i	0.136320	+	0.0990424i
$857$			13.0143i			0.444559i	0.974983	+	0.222279i	$0.0713497\pi$
$857$			13.0143i			0.444559i	−0.974983	+	0.222279i	$0.928650\pi$
$858$	10.9957	−	15.1343i	0.375386	−	0.516675i
$859$	12.1841	−	37.4987i	0.415715	−	1.27944i	−0.495895	−	0.868383i	$-0.665160\pi$
$859$	12.1841	−	37.4987i	0.415715	−	1.27944i	0.911610	−	0.411057i	$-0.134840\pi$
$860$	−15.2577	−	9.17779i	−0.520283	−	0.312960i
$861$	−6.21127	−	19.1163i	−0.211679	−	0.651482i
$862$	−2.61832	−	0.850743i	−0.0891802	−	0.0289764i
$863$	−16.6040	−	5.39498i	−0.565208	−	0.183647i	0.0124550	−	0.999922i	$-0.496035\pi$
$863$	−16.6040	−	5.39498i	−0.565208	−	0.183647i	−0.577663	+	0.816275i	$0.696035\pi$
$864$	3.19948	+	9.84700i	0.108849	+	0.335002i
$865$	12.5158	−	10.8692i	0.425550	−	0.369564i
$866$	−1.69555	+	5.21835i	−0.0576170	+	0.177327i
$867$	−1.58231	+	2.17787i	−0.0537381	+	0.0739642i
$868$		−	24.4006i		−	0.828209i
$869$	4.56677	+	3.31795i	0.154917	+	0.112554i
$870$	−10.8042	+	4.57996i	−0.366298	+	0.155275i
$871$	−32.6241	+	23.7028i	−1.10543	+	0.803139i
$872$	−3.09119	−	4.25466i	−0.104681	−	0.144081i
$873$	38.9815	−	12.6659i	1.31932	−	0.428675i
$874$	0.0408288			0.00138105
$875$	−25.4613	−	9.81607i	−0.860749	−	0.331844i
$876$	21.5520			0.728175
$877$	16.7931	−	5.45642i	0.567063	−	0.184250i	−0.0114335	−	0.999935i	$-0.503639\pi$
$877$	16.7931	−	5.45642i	0.567063	−	0.184250i	0.578497	+	0.815685i	$0.303639\pi$
$878$	4.21439	+	5.80061i	0.142229	+	0.195761i
$879$	−20.0097	+	14.5379i	−0.674911	+	0.490351i
$880$	32.9961	−	13.9872i	1.11230	−	0.471507i
$881$	35.2902	+	25.6399i	1.18896	+	0.863829i	0.993154	−	0.116814i	$-0.0372681\pi$
$881$	35.2902	+	25.6399i	1.18896	+	0.863829i	0.195805	+	0.980643i	$0.437268\pi$
$882$		−	1.19622i		−	0.0402789i
$883$	15.2410	−	20.9775i	0.512901	−	0.705947i	−0.471504	−	0.881864i	$-0.656289\pi$
$883$	15.2410	−	20.9775i	0.512901	−	0.705947i	0.984405	+	0.175916i	$0.0562888\pi$
$884$	−3.41066	+	10.4969i	−0.114713	+	0.353050i
$885$	16.7538	−	14.5497i	0.563174	−	0.489081i
$886$	−0.188050	−	0.578760i	−0.00631768	−	0.0194438i
$887$	−16.3423	−	5.30994i	−0.548721	−	0.178290i	0.0215191	−	0.999768i	$-0.493150\pi$
$887$	−16.3423	−	5.30994i	−0.548721	−	0.178290i	−0.570240	+	0.821478i	$0.693150\pi$
$888$	−21.0592	−	6.84255i	−0.706701	−	0.229621i
$889$	0.894105	+	2.75177i	0.0299873	+	0.0922914i
$890$	−5.36176	−	3.22520i	−0.179727	−	0.108109i
$891$	5.14343	−	15.8299i	0.172311	−	0.530320i
$892$	1.25250	−	1.72392i	0.0419369	−	0.0577212i
$893$			0.327312i			0.0109531i
$894$	2.92332	+	2.12392i	0.0977704	+	0.0710344i
$895$	−18.7571	+	31.1829i	−0.626980	+	1.04233i
$896$	15.5432	−	11.2928i	0.519261	−	0.377265i
$897$	45.4547	+	62.5630i	1.51769	+	2.08892i
$898$	−9.41007	+	3.05752i	−0.314018	+	0.102031i
$899$	37.4472			1.24893
$900$	−36.7606	−	17.9734i	−1.22535	−	0.599112i
$901$	7.76672			0.258747
$902$	3.53007	−	1.14699i	0.117538	−	0.0381905i
$903$	−15.9580	−	21.9643i	−0.531048	−	0.730925i
$904$	5.87792	−	4.27056i	0.195497	−	0.142037i
$905$	50.5382	+	11.6934i	1.67995	+	0.388702i
$906$	2.10863	+	1.53201i	0.0700545	+	0.0508976i
$907$			13.9148i			0.462035i	0.972950	+	0.231017i	$0.0742054\pi$
$907$			13.9148i			0.462035i	−0.972950	+	0.231017i	$0.925795\pi$
$908$	−27.0311	+	37.2051i	−0.897059	+	1.23470i
$909$	−13.8120	+	42.5091i	−0.458116	+	1.40994i
$910$	3.29485	+	7.77264i	0.109223	+	0.257660i
$911$	2.34129	+	7.20575i	0.0775704	+	0.238737i	0.982321	−	0.187205i	$-0.0599428\pi$
$911$	2.34129	+	7.20575i	0.0775704	+	0.238737i	−0.904751	+	0.425942i	$0.859943\pi$
$912$	−0.275305	−	0.0894522i	−0.00911627	−	0.00296206i
$913$	−57.4716	−	18.6737i	−1.90203	−	0.618008i
$914$	2.72184	+	8.37697i	0.0900305	+	0.277085i
$915$	1.94658	−	8.41299i	0.0643518	−	0.278125i
$916$	−4.32343	+	13.3062i	−0.142850	+	0.439648i
$917$	28.6292	−	39.4047i	0.945418	−	1.30126i
$918$			0.906491i			0.0299187i
$919$	10.6432	+	7.73272i	0.351086	+	0.255079i	0.749324	−	0.662203i	$-0.230378\pi$
$919$	10.6432	+	7.73272i	0.351086	+	0.255079i	−0.398238	+	0.917282i	$0.630378\pi$
$920$	−1.03100	−	11.8503i	−0.0339909	−	0.390694i
$921$	30.2756	−	21.9965i	0.997615	−	0.724810i
$922$	−0.888349	−	1.22271i	−0.0292562	−	0.0402677i
$923$	−55.3893	+	17.9971i	−1.82316	+	0.592381i
$924$	56.8803			1.87122
$925$	34.2557	−	18.1716i	1.12632	−	0.597479i
$926$	−6.53913			−0.214889
$927$	−12.5799	+	4.08747i	−0.413179	+	0.134250i
$928$	13.0880	+	18.0141i	0.429634	+	0.591340i
$929$	12.3728	−	8.98934i	0.405937	−	0.294931i	−0.366018	−	0.930608i	$-0.619279\pi$
$929$	12.3728	−	8.98934i	0.405937	−	0.294931i	0.771955	+	0.635677i	$0.219279\pi$
$930$	−5.53018	−	6.36796i	−0.181342	−	0.208814i
$931$	0.0254312	+	0.0184769i	0.000833475	+	0.000605555i
$932$		−	35.4533i		−	1.16131i
$933$	−39.2603	+	54.0372i	−1.28532	+	1.76910i
$934$	0.748582	−	2.30390i	0.0244944	−	0.0753859i
$935$	10.0075	−	0.870666i	0.327280	−	0.0284738i
$936$	7.97195	+	24.5351i	0.260571	+	0.801956i
$937$	20.2415	+	6.57685i	0.661260	+	0.214856i	0.620372	−	0.784307i	$-0.286982\pi$
$937$	20.2415	+	6.57685i	0.661260	+	0.214856i	0.0408873	+	0.999164i	$0.486982\pi$
$938$	4.41400	+	1.43420i	0.144122	+	0.0468281i
$939$	−17.1564	−	52.8019i	−0.559877	−	1.72312i
$940$	46.6180	−	4.05583i	1.52051	−	0.132287i
$941$	−3.21873	+	9.90622i	−0.104927	+	0.322933i	−0.989713	−	0.143064i	$-0.954304\pi$
$941$	−3.21873	+	9.90622i	−0.104927	+	0.322933i	0.884786	+	0.465998i	$0.154304\pi$
$942$	−10.5679	+	14.5455i	−0.344321	+	0.473917i
$943$			15.3438i			0.499664i
$944$	−10.6398	−	7.73029i	−0.346297	−	0.251600i
$945$	−12.0109	−	13.8305i	−0.390715	−	0.449905i
$946$	4.05598	−	2.94684i	0.131871	−	0.0958101i
$947$	−11.4756	−	15.7948i	−0.372906	−	0.513261i	0.580782	−	0.814059i	$-0.302747\pi$
$947$	−11.4756	−	15.7948i	−0.372906	−	0.513261i	−0.953688	+	0.300798i	$0.902747\pi$
$948$	−6.19938	+	2.01430i	−0.201346	+	0.0654214i
$949$	23.7948			0.772411
$950$	−0.0359558	+	0.0190735i	−0.00116656	+	0.000618825i
$951$	11.6242			0.376942
$952$	2.46195	−	0.799937i	0.0797924	−	0.0259261i
$953$	−22.2804	−	30.6663i	−0.721732	−	0.993378i	−0.999465	−	0.0327200i	$-0.989583\pi$
$953$	−22.2804	−	30.6663i	−0.721732	−	0.993378i	0.277733	−	0.960658i	$-0.410417\pi$
$954$	7.20690	−	5.23612i	0.233332	−	0.169526i
$955$	−2.60896	−	29.9876i	−0.0844240	−	0.970375i
$956$	12.1450	+	8.82383i	0.392796	+	0.285383i
$957$			87.2933i			2.82179i
$958$	1.34051	−	1.84505i	0.0433098	−	0.0596109i
$959$	6.28497	−	19.3432i	0.202952	−	0.624623i
$960$	−8.55159	+	36.9595i	−0.276001	+	1.19286i
$961$	−1.26264	−	3.88599i	−0.0407302	−	0.125355i
$962$	−11.4094	−	3.70714i	−0.367854	−	0.119523i
$963$	−18.7737	−	6.09995i	−0.604975	−	0.196568i
$964$	−3.33468	−	10.2631i	−0.107403	−	0.330552i
$965$	2.46118	+	5.80598i	0.0792281	+	0.186901i
$966$	2.75035	−	8.46469i	0.0884909	−	0.272347i
$967$	10.4464	−	14.3783i	0.335934	−	0.462374i	−0.607314	−	0.794462i	$-0.707753\pi$
$967$	10.4464	−	14.3783i	0.335934	−	0.462374i	0.943248	+	0.332088i	$0.107753\pi$
$968$			9.73813i			0.312995i
$969$	−0.0656420	−	0.0476917i	−0.00210873	−	0.00153208i
$970$	−5.67859	−	1.31390i	−0.182329	−	0.0421867i
$971$	6.95491	−	5.05304i	0.223194	−	0.162160i	−0.470569	−	0.882363i	$-0.655951\pi$
$971$	6.95491	−	5.05304i	0.223194	−	0.162160i	0.693763	+	0.720203i	$0.255951\pi$
$972$	22.7028	+	31.2477i	0.728191	+	1.00227i
$973$	33.3544	−	10.8375i	1.06929	−	0.347434i
$974$	−4.23227			−0.135611
$975$	−69.2565	−	33.8616i	−2.21798	−	1.08444i
$976$	−5.11800			−0.163823
$977$	−25.5156	+	8.29052i	−0.816316	+	0.265237i	−0.687270	−	0.726402i	$-0.741191\pi$
$977$	−25.5156	+	8.29052i	−0.816316	+	0.265237i	−0.129045	+	0.991639i	$0.541191\pi$
$978$	6.45920	+	8.89033i	0.206543	+	0.284281i
$979$	−37.6555	+	27.3583i	−1.20347	+	0.874375i
$980$	2.31647	−	3.85104i	0.0739970	−	0.123017i
$981$	17.0361	+	12.3775i	0.543921	+	0.395182i
$982$		−	3.12081i		−	0.0995889i
$983$	−12.7341	+	17.5269i	−0.406153	+	0.559022i	−0.962275	−	0.272079i	$-0.912289\pi$
$983$	−12.7341	+	17.5269i	−0.406153	+	0.559022i	0.556122	+	0.831101i	$0.312289\pi$
$984$	−2.69912	+	8.30703i	−0.0860448	+	0.264819i
$985$	−39.2676	−	23.6202i	−1.25117	−	0.752602i
$986$	0.602424	+	1.85407i	0.0191851	+	0.0590457i
$987$	67.8589	+	22.0487i	2.15997	+	0.701818i
$988$	−0.316383	−	0.102799i	−0.0100655	−	0.00327048i
$989$	6.40438	+	19.7107i	0.203648	+	0.626763i
$990$	8.69918	−	7.55470i	0.276478	−	0.240104i
$991$	1.24385	−	3.82819i	0.0395123	−	0.121606i	−0.929355	−	0.369188i	$-0.879636\pi$
$991$	1.24385	−	3.82819i	0.0395123	−	0.121606i	0.968867	+	0.247582i	$0.0796358\pi$
$992$	−9.40659	+	12.9471i	−0.298660	+	0.411070i
$993$		−	15.8439i		−	0.502790i
$994$	5.42277	+	3.93988i	0.172000	+	0.124965i
$995$	−38.5716	+	16.3507i	−1.22280	+	0.518351i
$996$	56.4540	−	41.0163i	1.78881	−	1.29965i
$997$	10.5692	+	14.5473i	0.334730	+	0.460716i	0.942893	−	0.333096i	$-0.108093\pi$
$997$	10.5692	+	14.5473i	0.334730	+	0.460716i	−0.608163	+	0.793812i	$0.708093\pi$
$998$	−6.84981	+	2.22564i	−0.216827	+	0.0704514i
$999$	26.0302			0.823560

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.r.a.69.19	✓	160
25.4	even	10	inner	425.2.r.a.154.19	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.r.a.69.19	✓	160	1.1	even	1	trivial
425.2.r.a.154.19	yes	160	25.4	even	10	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.256860 + 0.0834589i) q^{2} +(-1.58231 - 2.17787i) q^{3} +(-1.55902 + 1.13270i) q^{4} +(-2.05873 + 0.872706i) q^{5} +(0.588195 + 0.427349i) q^{6} +2.44071i q^{7} +(0.623414 - 0.858055i) q^{8} +(-1.31234 + 4.03896i) q^{9} +(0.455972 - 0.395983i) q^{10} +(-1.38823 - 4.27252i) q^{11} +(4.93372 + 1.60306i) q^{12} +(5.44714 + 1.76988i) q^{13} +(-0.203699 - 0.626921i) q^{14} +(5.15820 + 3.10275i) q^{15} +(1.10247 - 3.39305i) q^{16} +(0.587785 - 0.809017i) q^{17} -1.14697i q^{18} +(0.0243842 + 0.0177162i) q^{19} +(2.22110 - 3.69249i) q^{20} +(5.31554 - 3.86196i) q^{21} +(0.713160 + 0.981580i) q^{22} +(-4.77014 + 1.54991i) q^{23} -2.85516 q^{24} +(3.47677 - 3.59334i) q^{25} -1.54686 q^{26} +(3.19212 - 1.03718i) q^{27} +(-2.76458 - 3.80512i) q^{28} +(5.83966 - 4.24276i) q^{29} +(-1.58389 - 0.366476i) q^{30} +(4.19708 + 3.04936i) q^{31} +3.08478i q^{32} +(-7.10837 + 9.78383i) q^{33} +(-0.0834589 + 0.256860i) q^{34} +(-2.13002 - 5.02477i) q^{35} +(-2.52895 - 7.78330i) q^{36} +(7.37583 + 2.39655i) q^{37} +(-0.00774190 - 0.00251550i) q^{38} +(-4.76450 - 14.6636i) q^{39} +(-0.534613 + 2.31056i) q^{40} +(0.945346 - 2.90948i) q^{41} +(-1.04303 + 1.43561i) q^{42} -4.13209i q^{43} +(7.00374 + 5.08852i) q^{44} +(-0.823070 - 9.46042i) q^{45} +(1.09591 - 0.796222i) q^{46} +(6.38308 + 8.78555i) q^{47} +(-9.13406 + 2.96784i) q^{48} +1.04294 q^{49} +(-0.593147 + 1.21315i) q^{50} -2.69199 q^{51} +(-10.4969 + 3.41066i) q^{52} +(4.56516 + 6.28341i) q^{53} +(-0.733367 + 0.532822i) q^{54} +(6.58664 + 7.58447i) q^{55} +(2.09426 + 1.52157i) q^{56} -0.0811380i q^{57} +(-1.14588 + 1.57717i) q^{58} +(1.13914 - 3.50590i) q^{59} +(-11.5562 + 1.00541i) q^{60} +(-0.443301 - 1.36434i) q^{61} +(-1.33256 - 0.432974i) q^{62} +(-9.85791 - 3.20303i) q^{63} +(1.94749 + 5.99375i) q^{64} +(-12.7588 + 1.11003i) q^{65} +(1.00931 - 3.10633i) q^{66} +(-4.13845 + 5.69609i) q^{67} +1.92706i q^{68} +(10.9234 + 7.93628i) q^{69} +(0.966479 + 1.11289i) q^{70} +(-8.22650 + 5.97690i) q^{71} +(2.64752 + 3.64400i) q^{72} +(3.95117 - 1.28381i) q^{73} -2.09457 q^{74} +(-13.3271 - 1.88615i) q^{75} -0.0580825 q^{76} +(10.4280 - 3.38826i) q^{77} +(2.44762 + 3.36886i) q^{78} +(-1.01656 + 0.738571i) q^{79} +(0.691446 + 7.94752i) q^{80} +(2.99744 + 2.17777i) q^{81} +0.826226i q^{82} +(7.90657 - 10.8825i) q^{83} +(-3.91261 + 12.0418i) q^{84} +(-0.504059 + 2.17851i) q^{85} +(0.344860 + 1.06137i) q^{86} +(-18.4803 - 6.00462i) q^{87} +(-4.53150 - 1.47237i) q^{88} +(-3.20166 - 9.85370i) q^{89} +(1.00097 + 2.36131i) q^{90} +(-4.31977 + 13.2949i) q^{91} +(5.68118 - 7.81947i) q^{92} -13.9657i q^{93} +(-2.37279 - 1.72393i) q^{94} +(-0.0656616 - 0.0151926i) q^{95} +(6.71824 - 4.88108i) q^{96} +(-5.67294 - 7.80814i) q^{97} +(-0.267889 + 0.0870426i) q^{98} +19.0783 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) \) 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Introduction

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