LMFDB - Embedded newform 625.2.h.a.174.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(24,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([11]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("625.24");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.h (of order $50$, degree $20$, not 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:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{50})$
Twist minimal:	no (minimal twist has level 125)
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			174.4
Character	$\chi$	$=$	625.174
Dual form			625.2.h.a.449.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.164819 + 1.30468i) q^{2} +(-0.834940 + 0.690722i) q^{3} +(0.262149 + 0.0673084i) q^{4} +(-0.763556 - 1.20317i) q^{6} +(1.21231 - 0.393902i) q^{7} +(-1.09922 + 2.77633i) q^{8} +(-0.342117 + 1.79344i) q^{9} +O(q^{10})$	\(q+(-0.164819 + 1.30468i) q^{2} +(-0.834940 + 0.690722i) q^{3} +(0.262149 + 0.0673084i) q^{4} +(-0.763556 - 1.20317i) q^{6} +(1.21231 - 0.393902i) q^{7} +(-1.09922 + 2.77633i) q^{8} +(-0.342117 + 1.79344i) q^{9} +(-3.74238 - 0.472772i) q^{11} +(-0.265370 + 0.124874i) q^{12} +(5.95805 + 1.13656i) q^{13} +(0.314104 + 1.64659i) q^{14} +(-2.96669 - 1.63095i) q^{16} +(0.00423762 + 0.0165044i) q^{17} +(-2.28347 - 0.741945i) q^{18} +(0.137279 - 0.165942i) q^{19} +(-0.740126 + 1.16625i) q^{21} +(1.23363 - 4.80467i) q^{22} +(-6.31419 + 6.72393i) q^{23} +(-0.999883 - 3.07732i) q^{24} +(-2.46484 + 7.58601i) q^{26} +(-2.51923 - 4.58246i) q^{27} +(0.344318 - 0.0216626i) q^{28} +(0.437061 + 6.94688i) q^{29} +(-0.602769 + 0.154765i) q^{31} +(-0.893439 + 1.22971i) q^{32} +(3.45121 - 2.19021i) q^{33} +(-0.0222314 + 0.00280848i) q^{34} +(-0.210399 + 0.447121i) q^{36} +(-0.851322 + 1.54855i) q^{37} +(0.193875 + 0.206456i) q^{38} +(-5.75966 + 3.16640i) q^{39} +(7.92308 - 7.44027i) q^{41} +(-1.39960 - 1.15785i) q^{42} +(1.68397 + 2.31778i) q^{43} +(-0.949239 - 0.375830i) q^{44} +(-7.73186 - 9.34622i) q^{46} +(-2.05868 - 5.19962i) q^{47} +(3.60354 - 0.687412i) q^{48} +(-4.34859 + 3.15944i) q^{49} +(-0.0149382 - 0.0108532i) q^{51} +(1.48540 + 0.698974i) q^{52} +(-5.79344 - 3.67663i) q^{53} +(6.39385 - 2.53150i) q^{54} +(-0.238997 + 3.79875i) q^{56} +0.233374i q^{57} +(-9.13547 - 0.574755i) q^{58} +(-2.05519 - 4.36749i) q^{59} +(-2.18307 - 2.05004i) q^{61} +(-0.102570 - 0.811927i) q^{62} +(0.291689 + 2.30896i) q^{63} +(-6.39289 - 6.00332i) q^{64} +(2.28869 + 4.86371i) q^{66} +(-4.60439 - 0.289684i) q^{67} +0.00461185i q^{68} +(0.627601 - 9.97543i) q^{69} +(9.58206 - 3.79380i) q^{71} +(-4.60311 - 2.92122i) q^{72} +(7.84339 + 3.69082i) q^{73} +(-1.88004 - 1.36593i) q^{74} +(0.0471569 - 0.0342615i) q^{76} +(-4.72314 + 0.900987i) q^{77} +(-3.18183 - 8.03638i) q^{78} +(5.56012 + 6.72103i) q^{79} +(0.175913 + 0.0696488i) q^{81} +(8.40127 + 11.5634i) q^{82} +(3.38646 + 2.80153i) q^{83} +(-0.272522 + 0.255915i) q^{84} +(-3.30151 + 1.81502i) q^{86} +(-5.16329 - 5.49834i) q^{87} +(5.42628 - 9.87038i) q^{88} +(-1.31589 + 2.79641i) q^{89} +(7.67068 - 0.969032i) q^{91} +(-2.10784 + 1.33767i) q^{92} +(0.396376 - 0.545565i) q^{93} +(7.12313 - 1.82891i) q^{94} +(-0.103423 - 1.64386i) q^{96} +(9.71591 - 0.611273i) q^{97} +(-3.40531 - 6.19424i) q^{98} +(2.12822 - 6.54998i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 20 q^{2} + 20 q^{3} - 20 q^{4} - 20 q^{6} + 25 q^{7} + 35 q^{8} - 20 q^{9}+O(q^{10}) $ 240 * q + 20 * q^2 + 20 * q^3 - 20 * q^4 - 20 * q^6 + 25 * q^7 + 35 * q^8 - 20 * q^9	$ 240 q + 20 q^{2} + 20 q^{3} - 20 q^{4} - 20 q^{6} + 25 q^{7} + 35 q^{8} - 20 q^{9} - 25 q^{11} - 60 q^{12} + 20 q^{13} - 30 q^{14} - 40 q^{16} + 15 q^{17} + 25 q^{18} - 10 q^{19} - 35 q^{21} + 25 q^{22} - 70 q^{23} + 15 q^{24} - 45 q^{26} + 20 q^{27} + 10 q^{28} - 10 q^{29} - 30 q^{31} + 25 q^{32} + 35 q^{33} - 20 q^{34} + 170 q^{36} + 55 q^{37} + 40 q^{38} - 35 q^{41} + 10 q^{42} + 25 q^{43} + 15 q^{44} - 40 q^{46} - 100 q^{47} - 5 q^{48} + 35 q^{49} - 55 q^{51} + 15 q^{52} + 15 q^{53} + 30 q^{54} + 65 q^{56} - 255 q^{58} + 5 q^{59} - 40 q^{61} - 5 q^{62} + 35 q^{63} + 25 q^{64} - 95 q^{66} - 105 q^{67} - 10 q^{69} + 45 q^{71} + 30 q^{72} + 40 q^{73} + 35 q^{74} - 65 q^{76} + 35 q^{77} - 100 q^{78} - 95 q^{81} - 175 q^{82} - 20 q^{83} + 45 q^{84} - 80 q^{86} + 5 q^{87} + 5 q^{88} + 30 q^{89} + 65 q^{91} + 55 q^{92} - 275 q^{93} + 60 q^{94} - 135 q^{96} - 35 q^{97} + 15 q^{98} + 45 q^{99}+O(q^{100}) $ 240 * q + 20 * q^2 + 20 * q^3 - 20 * q^4 - 20 * q^6 + 25 * q^7 + 35 * q^8 - 20 * q^9 - 25 * q^11 - 60 * q^12 + 20 * q^13 - 30 * q^14 - 40 * q^16 + 15 * q^17 + 25 * q^18 - 10 * q^19 - 35 * q^21 + 25 * q^22 - 70 * q^23 + 15 * q^24 - 45 * q^26 + 20 * q^27 + 10 * q^28 - 10 * q^29 - 30 * q^31 + 25 * q^32 + 35 * q^33 - 20 * q^34 + 170 * q^36 + 55 * q^37 + 40 * q^38 - 35 * q^41 + 10 * q^42 + 25 * q^43 + 15 * q^44 - 40 * q^46 - 100 * q^47 - 5 * q^48 + 35 * q^49 - 55 * q^51 + 15 * q^52 + 15 * q^53 + 30 * q^54 + 65 * q^56 - 255 * q^58 + 5 * q^59 - 40 * q^61 - 5 * q^62 + 35 * q^63 + 25 * q^64 - 95 * q^66 - 105 * q^67 - 10 * q^69 + 45 * q^71 + 30 * q^72 + 40 * q^73 + 35 * q^74 - 65 * q^76 + 35 * q^77 - 100 * q^78 - 95 * q^81 - 175 * q^82 - 20 * q^83 + 45 * q^84 - 80 * q^86 + 5 * q^87 + 5 * q^88 + 30 * q^89 + 65 * q^91 + 55 * q^92 - 275 * q^93 + 60 * q^94 - 135 * q^96 - 35 * q^97 + 15 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{27}{50}\right)$

Coefficient data

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

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

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

$2$	−0.164819	+	1.30468i	−0.116545	+	0.922546i	0.820089	+	0.572236i	$0.193924\pi$
$2$	−0.164819	+	1.30468i	−0.116545	+	0.922546i	−0.936634	+	0.350310i	$0.886076\pi$
$3$	−0.834940	+	0.690722i	−0.482053	+	0.398789i	−0.846461	−	0.532451i	$-0.821271\pi$
$3$	−0.834940	+	0.690722i	−0.482053	+	0.398789i	0.364408	+	0.931239i	$0.381271\pi$
$4$	0.262149	+	0.0673084i	0.131074	+	0.0336542i
$5$		0			0
$5$		0			0
$6$	−0.763556	−	1.20317i	−0.311720	−	0.491193i
$7$	1.21231	−	0.393902i	0.458209	−	0.148881i	−0.0708124	−	0.997490i	$-0.522559\pi$
$7$	1.21231	−	0.393902i	0.458209	−	0.148881i	0.529021	+	0.848609i	$0.322559\pi$
$8$	−1.09922	+	2.77633i	−0.388635	+	0.981579i
$9$	−0.342117	+	1.79344i	−0.114039	+	0.597813i
$10$		0			0
$11$	−3.74238	−	0.472772i	−1.12837	−	0.142546i	−0.461090	−	0.887353i	$-0.652541\pi$
$11$	−3.74238	−	0.472772i	−1.12837	−	0.142546i	−0.667280	+	0.744807i	$0.732541\pi$
$12$	−0.265370	+	0.124874i	−0.0766057	+	0.0360479i
$13$	5.95805	+	1.13656i	1.65247	+	0.315225i	0.927574	−	0.373639i	$-0.121890\pi$
$13$	5.95805	+	1.13656i	1.65247	+	0.315225i	0.724891	+	0.688863i	$0.241890\pi$
$14$	0.314104	+	1.64659i	0.0839479	+	0.440070i
$15$		0			0
$16$	−2.96669	−	1.63095i	−0.741672	−	0.407737i
$17$	0.00423762	+	0.0165044i	0.00102777	+	0.00400292i	0.969095	−	0.246688i	$-0.0793423\pi$
$17$	0.00423762	+	0.0165044i	0.00102777	+	0.00400292i	−0.968067	+	0.250691i	$0.919342\pi$
$18$	−2.28347	−	0.741945i	−0.538219	−	0.174878i
$19$	0.137279	−	0.165942i	0.0314940	−	0.0380698i	−0.754531	−	0.656264i	$-0.772136\pi$
$19$	0.137279	−	0.165942i	0.0314940	−	0.0380698i	0.786025	+	0.618195i	$0.212136\pi$
$20$		0			0
$21$	−0.740126	+	1.16625i	−0.161509	+	0.254497i
$22$	1.23363	−	4.80467i	0.263011	−	1.02436i
$23$	−6.31419	+	6.72393i	−1.31660	+	1.40204i	−0.458380	+	0.888756i	$0.651570\pi$
$23$	−6.31419	+	6.72393i	−1.31660	+	1.40204i	−0.858221	+	0.513281i	$0.828430\pi$
$24$	−0.999883	−	3.07732i	−0.204100	−	0.628156i
$25$		0			0
$26$	−2.46484	+	7.58601i	−0.483395	+	1.48774i
$27$	−2.51923	−	4.58246i	−0.484826	−	0.881895i
$28$	0.344318	−	0.0216626i	0.0650700	−	0.00409385i
$29$	0.437061	+	6.94688i	0.0811601	+	1.29000i	0.802177	+	0.597086i	$0.203675\pi$
$29$	0.437061	+	6.94688i	0.0811601	+	1.29000i	−0.721017	+	0.692917i	$0.756325\pi$
$30$		0			0
$31$	−0.602769	+	0.154765i	−0.108260	+	0.0277966i	−0.302431	−	0.953171i	$-0.597798\pi$
$31$	−0.602769	+	0.154765i	−0.108260	+	0.0277966i	0.194171	+	0.980968i	$0.437798\pi$
$32$	−0.893439	+	1.22971i	−0.157939	+	0.217385i
$33$	3.45121	−	2.19021i	0.600779	−	0.381266i
$34$	−0.0222314	+	0.00280848i	−0.00381266	+	0.000481651i
$35$		0			0
$36$	−0.210399	+	0.447121i	−0.0350665	+	0.0745201i
$37$	−0.851322	+	1.54855i	−0.139956	+	0.254580i	−0.936991	−	0.349354i	$-0.886401\pi$
$37$	−0.851322	+	1.54855i	−0.139956	+	0.254580i	0.797034	+	0.603934i	$0.206401\pi$
$38$	0.193875	+	0.206456i	0.0314506	+	0.0334915i
$39$	−5.75966	+	3.16640i	−0.922284	+	0.507030i
$40$		0			0
$41$	7.92308	−	7.44027i	1.23738	−	1.16197i	0.256669	−	0.966499i	$-0.417375\pi$
$41$	7.92308	−	7.44027i	1.23738	−	1.16197i	0.980709	−	0.195475i	$-0.0626250\pi$
$42$	−1.39960	−	1.15785i	−0.215962	−	0.178660i
$43$	1.68397	+	2.31778i	0.256803	+	0.353459i	0.917879	−	0.396860i	$-0.129900\pi$
$43$	1.68397	+	2.31778i	0.256803	+	0.353459i	−0.661076	+	0.750319i	$0.729900\pi$
$44$	−0.949239	−	0.375830i	−0.143103	−	0.0566585i
$45$		0			0
$46$	−7.73186	−	9.34622i	−1.14000	−	1.37802i
$47$	−2.05868	−	5.19962i	−0.300289	−	0.758442i	−0.999070	−	0.0431076i	$-0.986274\pi$
$47$	−2.05868	−	5.19962i	−0.300289	−	0.758442i	0.698782	−	0.715335i	$-0.253726\pi$
$48$	3.60354	−	0.687412i	0.520126	−	0.0992193i
$49$	−4.34859	+	3.15944i	−0.621227	+	0.451348i
$50$		0			0
$51$	−0.0149382	−	0.0108532i	−0.00209176	−	0.00151975i
$52$	1.48540	+	0.698974i	0.205987	+	0.0969303i
$53$	−5.79344	−	3.67663i	−0.795790	−	0.505023i	0.0747025	−	0.997206i	$-0.476199\pi$
$53$	−5.79344	−	3.67663i	−0.795790	−	0.505023i	−0.870492	+	0.492182i	$0.836199\pi$
$54$	6.39385	−	2.53150i	0.870092	−	0.344494i
$55$		0			0
$56$	−0.238997	+	3.79875i	−0.0319373	+	0.507629i
$57$			0.233374i			0.0309111i
$58$	−9.13547	−	0.574755i	−1.19955	−	0.0754691i
$59$	−2.05519	−	4.36749i	−0.267562	−	0.568599i	0.725222	−	0.688515i	$-0.241737\pi$
$59$	−2.05519	−	4.36749i	−0.267562	−	0.568599i	−0.992784	+	0.119917i	$0.961737\pi$
$60$		0			0
$61$	−2.18307	−	2.05004i	−0.279513	−	0.262481i	0.532092	−	0.846687i	$-0.321406\pi$
$61$	−2.18307	−	2.05004i	−0.279513	−	0.262481i	−0.811605	+	0.584206i	$0.801406\pi$
$62$	−0.102570	−	0.811927i	−0.0130264	−	0.103115i
$63$	0.291689	+	2.30896i	0.0367494	+	0.290901i
$64$	−6.39289	−	6.00332i	−0.799111	−	0.750415i
$65$		0			0
$66$	2.28869	+	4.86371i	0.281718	+	0.598681i
$67$	−4.60439	−	0.289684i	−0.562516	−	0.0353905i	−0.221012	−	0.975271i	$-0.570936\pi$
$67$	−4.60439	−	0.289684i	−0.562516	−	0.0353905i	−0.341504	+	0.939880i	$0.610936\pi$
$68$			0.00461185i			0.000559269i
$69$	0.627601	−	9.97543i	0.0755543	−	1.20090i
$70$		0			0
$71$	9.58206	−	3.79380i	1.13718	−	0.450242i	0.277324	−	0.960777i	$-0.410553\pi$
$71$	9.58206	−	3.79380i	1.13718	−	0.450242i	0.859857	+	0.510535i	$0.170553\pi$
$72$	−4.60311	−	2.92122i	−0.542481	−	0.344269i
$73$	7.84339	+	3.69082i	0.918000	+	0.431978i	0.825929	−	0.563775i	$-0.190651\pi$
$73$	7.84339	+	3.69082i	0.918000	+	0.431978i	0.0920710	+	0.995752i	$0.470651\pi$
$74$	−1.88004	−	1.36593i	−0.218550	−	0.158786i
$75$		0			0
$76$	0.0471569	−	0.0342615i	0.00540927	−	0.00393006i
$77$	−4.72314	+	0.900987i	−0.538251	+	0.102677i
$78$	−3.18183	−	8.03638i	−0.360271	−	0.909941i
$79$	5.56012	+	6.72103i	0.625562	+	0.756175i	0.984153	−	0.177320i	$-0.0567427\pi$
$79$	5.56012	+	6.72103i	0.625562	+	0.756175i	−0.358591	+	0.933495i	$0.616743\pi$
$80$		0			0
$81$	0.175913	+	0.0696488i	0.0195459	+	0.00773876i
$82$	8.40127	+	11.5634i	0.927766	+	1.27696i
$83$	3.38646	+	2.80153i	0.371713	+	0.307507i	0.804459	−	0.594008i	$-0.202455\pi$
$83$	3.38646	+	2.80153i	0.371713	+	0.307507i	−0.432746	+	0.901516i	$0.642455\pi$
$84$	−0.272522	+	0.255915i	−0.0297346	+	0.0279226i
$85$		0			0
$86$	−3.30151	+	1.81502i	−0.356011	+	0.195719i
$87$	−5.16329	−	5.49834i	−0.553562	−	0.589484i
$88$	5.42628	−	9.87038i	0.578444	−	1.05219i
$89$	−1.31589	+	2.79641i	−0.139484	+	0.296419i	−0.962348	−	0.271819i	$-0.912375\pi$
$89$	−1.31589	+	2.79641i	−0.139484	+	0.296419i	0.822864	+	0.568238i	$0.192375\pi$
$90$		0			0
$91$	7.67068	−	0.969032i	0.804106	−	0.101582i
$92$	−2.10784	+	1.33767i	−0.219757	+	0.139462i
$93$	0.396376	−	0.545565i	0.0411023	−	0.0565725i
$94$	7.12313	−	1.82891i	0.734695	−	0.188638i
$95$		0			0
$96$	−0.103423	−	1.64386i	−0.0105555	−	0.167775i
$97$	9.71591	−	0.611273i	0.986501	−	0.0620654i	0.438665	−	0.898651i	$-0.355452\pi$
$97$	9.71591	−	0.611273i	0.986501	−	0.0620654i	0.547837	+	0.836585i	$0.315452\pi$
$98$	−3.40531	−	6.19424i	−0.343989	−	0.625713i
$99$	2.12822	−	6.54998i	0.213894	−	0.658298i
$100$		0			0
$101$	4.83870	+	14.8920i	0.481469	+	1.48181i	0.837030	+	0.547156i	$0.184290\pi$
$101$	4.83870	+	14.8920i	0.481469	+	1.48181i	−0.355561	+	0.934653i	$0.615710\pi$
$102$	0.0166220	−	0.0177007i	0.00164583	−	0.00175263i
$103$	0.810687	−	3.15742i	0.0798794	−	0.311110i	−0.916071	−	0.401017i	$-0.868657\pi$
$103$	0.810687	−	3.15742i	0.0798794	−	0.311110i	0.995950	+	0.0899069i	$0.0286569\pi$
$104$	−9.70469	+	15.2921i	−0.951623	+	1.49952i
$105$		0			0
$106$	5.75168	−	6.95259i	0.558652	−	0.675295i
$107$	17.7313	+	5.76123i	1.71415	+	0.556960i	0.991015	−	0.133752i	$-0.0427025\pi$
$107$	17.7313	+	5.76123i	1.71415	+	0.556960i	0.723130	+	0.690711i	$0.242703\pi$
$108$	−0.351975	−	1.37085i	−0.0338688	−	0.131910i
$109$	12.0791	+	6.64056i	1.15697	+	0.636050i	0.940351	−	0.340206i	$-0.110497\pi$
$109$	12.0791	+	6.64056i	1.15697	+	0.636050i	0.216620	+	0.976256i	$0.430497\pi$
$110$		0			0
$111$	−0.358815	−	1.88097i	−0.0340572	−	0.178534i
$112$	−4.23897	−	0.808627i	−0.400545	−	0.0764081i
$113$	5.52931	−	2.60189i	0.520153	−	0.244766i	−0.147735	−	0.989027i	$-0.547198\pi$
$113$	5.52931	−	2.60189i	0.520153	−	0.244766i	0.667888	+	0.744261i	$0.267198\pi$
$114$	−0.304477	−	0.0384644i	−0.0285169	−	0.00360252i
$115$		0			0
$116$	−0.353008	+	1.85053i	−0.0327760	+	0.171818i
$117$	−4.07670	+	10.2966i	−0.376891	+	0.951917i
$118$	6.03690	−	1.96151i	0.555742	−	0.180571i
$119$	0.0116384	+	0.0183392i	0.00106689	+	0.00168116i
$120$		0			0
$121$	3.12747	+	0.802997i	0.284315	+	0.0729997i
$122$	3.03445	−	2.51032i	0.274726	−	0.227273i
$123$	−1.47614	+	11.6848i	−0.133099	+	1.05359i
$124$	−0.168432			−0.0151257
$125$		0			0
$126$	−3.06052			−0.272653
$127$	−1.28839	+	10.1987i	−0.114326	+	0.904985i	0.825754	+	0.564031i	$0.190750\pi$
$127$	−1.28839	+	10.1987i	−0.114326	+	0.904985i	−0.940080	+	0.340954i	$0.889250\pi$
$128$	6.54369	−	5.41341i	0.578386	−	0.478483i
$129$	−3.00696	−	0.772056i	−0.264748	−	0.0679757i
$130$		0			0
$131$	0.231359	+	0.364564i	0.0202139	+	0.0318521i	0.854285	−	0.519805i	$-0.173996\pi$
$131$	0.231359	+	0.364564i	0.0202139	+	0.0318521i	−0.834071	+	0.551658i	$0.813996\pi$
$132$	1.05215	−	0.341865i	0.0915780	−	0.0297555i
$133$	0.101060	−	0.255248i	0.00876298	−	0.0221328i
$134$	1.13684	−	5.95950i	0.0982076	−	0.514822i
$135$		0			0
$136$	−0.0504798	−	0.00637708i	−0.00432861	−	0.000546830i
$137$	0.554025	−	0.260705i	0.0473336	−	0.0222735i	−0.401967	−	0.915654i	$-0.631673\pi$
$137$	0.554025	−	0.260705i	0.0473336	−	0.0222735i	0.449300	+	0.893381i	$0.351673\pi$
$138$	12.9113	+	2.46296i	1.09908	+	0.209661i
$139$	0.536062	+	2.81013i	0.0454681	+	0.238352i	0.997765	−	0.0668209i	$-0.0212856\pi$
$139$	0.536062	+	2.81013i	0.0454681	+	0.238352i	−0.952297	+	0.305173i	$0.901286\pi$
$140$		0			0
$141$	5.31036	+	2.91940i	0.447213	+	0.245858i
$142$	3.37038	+	13.1268i	0.282836	+	1.10158i
$143$	−21.7599	−	7.07023i	−1.81966	−	0.591243i
$144$	3.93996	−	4.76260i	0.328330	−	0.396883i
$145$		0			0
$146$	−6.10807	+	9.62478i	−0.505507	+	0.796552i
$147$	1.44852	−	5.64161i	0.119472	−	0.465312i
$148$	−0.327403	+	0.348649i	−0.0269124	+	0.0286588i
$149$	−4.39110	−	13.5144i	−0.359733	−	1.10715i	−0.953214	−	0.302297i	$-0.902247\pi$
$149$	−4.39110	−	13.5144i	−0.359733	−	1.10715i	0.593481	−	0.804848i	$-0.297753\pi$
$150$		0			0
$151$	2.45647	−	7.56023i	0.199905	−	0.615243i	−0.799980	−	0.600027i	$-0.795156\pi$
$151$	2.45647	−	7.56023i	0.199905	−	0.615243i	0.999884	−	0.0152158i	$-0.00484354\pi$
$152$	0.309809	+	0.563540i	0.0251288	+	0.0457091i
$153$	−0.0310495	+	0.00195347i	−0.00251020	+	0.000157929i
$154$	−0.397034	−	6.31067i	−0.0319939	−	0.508528i
$155$		0			0
$156$	−1.72301	+	0.442395i	−0.137951	+	0.0354199i
$157$	5.53365	−	7.61641i	0.441633	−	0.607856i	−0.528941	−	0.848659i	$-0.677411\pi$
$157$	5.53365	−	7.61641i	0.441633	−	0.607856i	0.970574	+	0.240803i	$0.0774107\pi$
$158$	−9.68519	+	6.14641i	−0.770512	+	0.488982i
$159$	7.37670	−	0.931894i	0.585010	−	0.0739040i
$160$		0			0
$161$	−5.00617	+	10.6386i	−0.394541	+	0.838443i
$162$	−0.119863	+	0.218030i	−0.00941733	+	0.0171301i
$163$	−3.98511	−	4.24371i	−0.312138	−	0.332393i	0.553702	−	0.832715i	$-0.313215\pi$
$163$	−3.98511	−	4.24371i	−0.312138	−	0.332393i	−0.865839	+	0.500322i	$0.833215\pi$
$164$	2.57782	−	1.41717i	0.201294	−	0.110662i
$165$		0			0
$166$	−4.21324	+	3.95650i	−0.327011	+	0.307084i
$167$	3.77349	+	3.12170i	0.292001	+	0.241565i	0.771877	−	0.635772i	$-0.219318\pi$
$167$	3.77349	+	3.12170i	0.292001	+	0.241565i	−0.479876	+	0.877337i	$0.659318\pi$
$168$	−2.42433	−	3.33680i	−0.187041	−	0.257440i
$169$	22.1195	+	8.75773i	1.70150	+	0.673671i
$170$		0			0
$171$	0.250642	+	0.302974i	0.0191670	+	0.0231690i
$172$	0.285444	+	0.720950i	0.0217649	+	0.0549719i
$173$	0.980208	−	0.186985i	0.0745238	−	0.0142162i	−0.149985	−	0.988688i	$-0.547922\pi$
$173$	0.980208	−	0.186985i	0.0745238	−	0.0142162i	0.224508	+	0.974472i	$0.427922\pi$
$174$	8.02457	−	5.83019i	0.608341	−	0.441986i
$175$		0			0
$176$	10.3314	+	7.50620i	0.778758	+	0.565801i
$177$	4.73268	+	2.22703i	0.355730	+	0.167394i
$178$	−3.43153	−	2.17772i	−0.257204	−	0.163227i
$179$	24.5872	−	9.73475i	1.83773	−	0.727609i	0.862636	−	0.505825i	$-0.168812\pi$
$179$	24.5872	−	9.73475i	1.83773	−	0.727609i	0.975096	−	0.221784i	$-0.0711881\pi$
$180$		0			0
$181$	0.746809	−	11.8702i	0.0555099	−	0.882304i	−0.867478	−	0.497476i	$-0.834260\pi$
$181$	0.746809	−	11.8702i	0.0555099	−	0.882304i	0.922988	−	0.384829i	$-0.125740\pi$
$182$			10.1675i			0.753663i
$183$	3.23874	+	0.203764i	0.239415	+	0.0150627i
$184$	−11.7271	−	24.9214i	−0.864534	−	1.83723i
$185$		0			0
$186$	0.646456	+	0.607063i	0.0474005	+	0.0445120i
$187$	−0.00805594	−	0.0637693i	−0.000589109	−	0.00466327i
$188$	−0.189701	−	1.50164i	−0.0138354	−	0.109518i
$189$	−4.85912	−	4.56302i	−0.353449	−	0.331911i
$190$		0			0
$191$	−4.08619	−	8.68359i	−0.295666	−	0.628322i	0.700704	−	0.713452i	$-0.252869\pi$
$191$	−4.08619	−	8.68359i	−0.295666	−	0.628322i	−0.996370	+	0.0851300i	$0.972869\pi$
$192$	9.48431	+	0.596702i	0.684471	+	0.0430633i
$193$			2.12588i			0.153024i	0.997069	+	0.0765120i	$0.0243783\pi$
$193$			2.12588i			0.153024i	−0.997069	+	0.0765120i	$0.975622\pi$
$194$	−0.803853	+	12.7769i	−0.0577133	+	0.917326i
$195$		0			0
$196$	−1.35263	+	0.535546i	−0.0966167	+	0.0382533i
$197$	11.0390	+	7.00559i	0.786499	+	0.499128i	0.867410	−	0.497594i	$-0.165783\pi$
$197$	11.0390	+	7.00559i	0.786499	+	0.499128i	−0.0809110	+	0.996721i	$0.525783\pi$
$198$	8.19484	+	3.85620i	0.582382	+	0.274048i
$199$	6.35509	+	4.61724i	0.450500	+	0.327307i	0.789793	−	0.613373i	$-0.210188\pi$
$199$	6.35509	+	4.61724i	0.450500	+	0.327307i	−0.339293	+	0.940681i	$0.610188\pi$
$200$		0			0
$201$	4.04448	−	2.93849i	0.285276	−	0.207265i
$202$	−20.2268	+	3.85846i	−1.42315	+	0.271480i
$203$	3.26625	+	8.24959i	0.229245	+	0.579008i
$204$	−0.00318551	−	0.00385062i	−0.000223030	−	0.000269597i
$205$		0			0
$206$	3.98580	+	1.57809i	0.277704	+	0.109951i
$207$	−9.89877	−	13.6245i	−0.688012	−	0.946968i
$208$	−15.8220	−	13.0891i	−1.09706	−	0.907565i
$209$	−0.592204	+	0.556117i	−0.0409636	+	0.0384674i
$210$		0			0
$211$	−17.9497	+	9.86793i	−1.23571	+	0.679336i	−0.959486	−	0.281757i	$-0.909083\pi$
$211$	−17.9497	+	9.86793i	−1.23571	+	0.679336i	−0.276222	+	0.961094i	$0.589083\pi$
$212$	−1.27127	−	1.35377i	−0.0873115	−	0.0929773i
$213$	−5.37997	+	9.78614i	−0.368630	+	0.670535i
$214$	−10.4390	+	22.1840i	−0.713595	+	1.51647i
$215$		0			0
$216$	15.4916	−	1.95704i	1.05407	−	0.133160i
$217$	−0.669779	+	0.425055i	−0.0454675	+	0.0288546i
$218$	−10.6547	+	14.6649i	−0.721624	+	0.993231i
$219$	−9.09809	+	2.33599i	−0.614792	+	0.157852i
$220$		0			0
$221$	0.00648969	+	0.103151i	0.000436544	+	0.00693866i
$222$	2.51320	−	0.158117i	0.168675	−	0.0106121i
$223$	1.33474	+	2.42789i	0.0893810	+	0.162584i	0.917218	−	0.398385i	$-0.130429\pi$
$223$	1.33474	+	2.42789i	0.0893810	+	0.162584i	−0.827837	+	0.560968i	$0.810429\pi$
$224$	−0.598736	+	1.84272i	−0.0400047	+	0.123122i
$225$		0			0
$226$	2.48330	+	7.64280i	0.165186	+	0.508392i
$227$	10.4918	−	11.1726i	0.696366	−	0.741555i	−0.279447	−	0.960161i	$-0.590151\pi$
$227$	10.4918	−	11.1726i	0.696366	−	0.741555i	0.975813	+	0.218606i	$0.0701511\pi$
$228$	−0.0157080	+	0.0611786i	−0.00104029	+	0.00405165i
$229$	−3.04205	+	4.79350i	−0.201024	+	0.316763i	−0.929852	−	0.367933i	$-0.880065\pi$
$229$	−3.04205	+	4.79350i	−0.201024	+	0.316763i	0.728828	+	0.684697i	$0.240065\pi$
$230$		0			0
$231$	3.32120	−	4.01465i	0.218519	−	0.264144i
$232$	−19.7672	−	6.42276i	−1.29778	−	0.421675i
$233$	5.25512	+	20.4673i	0.344274	+	1.34086i	0.871191	+	0.490943i	$0.163348\pi$
$233$	5.25512	+	20.4673i	0.344274	+	1.34086i	−0.526917	+	0.849917i	$0.676652\pi$
$234$	−12.7618	−	7.01584i	−0.834263	−	0.458640i
$235$		0			0
$236$	−0.244796	−	1.28326i	−0.0159348	−	0.0835334i
$237$	−9.28473	−	1.77116i	−0.603108	−	0.115049i
$238$	−0.0258450	+	0.0121618i	−0.00167529	+	0.000788329i
$239$	−6.77972	−	0.856478i	−0.438544	−	0.0554010i	−0.0970381	−	0.995281i	$-0.530937\pi$
$239$	−6.77972	−	0.856478i	−0.438544	−	0.0554010i	−0.341506	+	0.939880i	$0.610937\pi$
$240$		0			0
$241$	−3.26884	+	17.1359i	−0.210565	+	1.10382i	0.707296	+	0.706917i	$0.249915\pi$
$241$	−3.26884	+	17.1359i	−0.210565	+	1.10382i	−0.917861	+	0.396902i	$0.870085\pi$
$242$	−1.56312	+	3.94798i	−0.100481	+	0.253786i
$243$	14.7251	−	4.78446i	0.944613	−	0.306923i
$244$	−0.434304	−	0.684354i	−0.0278035	−	0.0438113i
$245$		0			0
$246$	−15.0016	−	3.85176i	−0.956469	−	0.245580i
$247$	1.00652	−	0.832666i	0.0640433	−	0.0529813i
$248$	0.232901	−	1.84360i	0.0147892	−	0.117069i
$249$	−4.76257			−0.301816
$250$		0			0
$251$	−24.7630			−1.56303			−0.781515	−	0.623887i	$-0.785553\pi$
$251$	−24.7630			−1.56303			−0.781515	+	0.623887i	$0.785553\pi$
$252$	−0.0789463	+	0.624924i	−0.00497315	+	0.0393665i
$253$	26.8090	−	22.1783i	1.68547	−	1.39434i
$254$	−13.0936	−	3.36187i	−0.821567	−	0.210942i
$255$		0			0
$256$	−3.41393	−	5.37949i	−0.213370	−	0.336218i
$257$	3.95628	−	1.28547i	0.246786	−	0.0801856i	−0.183012	−	0.983111i	$-0.558585\pi$
$257$	3.95628	−	1.28547i	0.246786	−	0.0801856i	0.429798	+	0.902925i	$0.358585\pi$
$258$	1.50289	−	3.79586i	0.0935657	−	0.236320i
$259$	−0.422086	+	2.21265i	−0.0262272	+	0.137488i
$260$		0			0
$261$	−12.6083	−	1.59280i	−0.780436	−	0.0985920i
$262$	−0.513770	+	0.241762i	−0.0317408	+	0.0149361i
$263$	−2.41082	−	0.459889i	−0.148658	−	0.0283580i	0.112515	−	0.993650i	$-0.464109\pi$
$263$	−2.41082	−	0.459889i	−0.148658	−	0.0283580i	−0.261173	+	0.965292i	$0.584109\pi$
$264$	2.28707	+	11.9892i	0.140759	+	0.737886i
$265$		0			0
$266$	0.316359	+	0.173920i	0.0193972	+	0.0106637i
$267$	−0.832855	−	3.24375i	−0.0509699	−	0.198515i
$268$	−1.18754	−	0.385854i	−0.0725404	−	0.0235698i
$269$	−7.23651	+	8.74743i	−0.441218	+	0.533340i	−0.943504	−	0.331361i	$-0.892492\pi$
$269$	−7.23651	+	8.74743i	−0.441218	+	0.533340i	0.502287	+	0.864701i	$0.332492\pi$
$270$		0			0
$271$	12.6075	−	19.8663i	0.765852	−	1.20679i	−0.207671	−	0.978199i	$-0.566588\pi$
$271$	12.6075	−	19.8663i	0.765852	−	1.20679i	0.973523	−	0.228591i	$-0.0734118\pi$
$272$	0.0143462	−	0.0558749i	0.000869868	−	0.00338791i
$273$	−5.73522	+	6.10739i	−0.347111	+	0.369636i
$274$	0.248821	+	0.765793i	0.0150318	+	0.0462633i
$275$		0			0
$276$	0.835955	−	2.57281i	0.0503186	−	0.154865i
$277$	−12.3816	−	22.5221i	−0.743940	−	1.35322i	−0.928846	−	0.370465i	$-0.879198\pi$
$277$	−12.3816	−	22.5221i	−0.743940	−	1.35322i	0.184906	−	0.982756i	$-0.440802\pi$
$278$	−3.75467	+	0.236224i	−0.225190	+	0.0141678i
$279$	−0.0713438	−	1.13398i	−0.00427124	−	0.0678894i
$280$		0			0
$281$	27.9124	−	7.16670i	1.66512	−	0.427529i	0.705470	−	0.708740i	$-0.250736\pi$
$281$	27.9124	−	7.16670i	1.66512	−	0.427529i	0.959646	+	0.281210i	$0.0907359\pi$
$282$	−4.68412	+	6.44714i	−0.278935	+	0.383921i
$283$	8.02786	−	5.09464i	0.477207	−	0.302845i	−0.275383	−	0.961335i	$-0.588805\pi$
$283$	8.02786	−	5.09464i	0.477207	−	0.302845i	0.752589	+	0.658490i	$0.228805\pi$
$284$	2.76728	−	0.349589i	0.164208	−	0.0207443i
$285$		0			0
$286$	12.8108	−	27.2244i	0.757520	−	1.60981i
$287$	6.67447	−	12.1408i	0.393981	−	0.716649i
$288$	−1.89976	−	2.02303i	−0.111944	−	0.119208i
$289$	14.8970	−	8.18967i	0.876292	−	0.481745i
$290$		0			0
$291$	−7.68998	+	7.22137i	−0.450795	+	0.423324i
$292$	1.80771	+	1.49547i	0.105788	+	0.0875158i
$293$	−16.9423	−	23.3191i	−0.989781	−	1.36232i	−0.931390	−	0.364023i	$-0.881403\pi$
$293$	−16.9423	−	23.3191i	−0.989781	−	1.36232i	−0.0583912	−	0.998294i	$-0.518597\pi$
$294$	7.12173	+	2.81969i	0.415348	+	0.164448i
$295$		0			0
$296$	−3.36348	−	4.06575i	−0.195498	−	0.236317i
$297$	7.26144	+	18.3403i	0.421352	+	1.06421i
$298$	18.3557	−	3.50154i	1.06332	−	0.202839i
$299$	−45.2624	+	32.8851i	−2.61759	+	1.90179i
$300$		0			0
$301$	2.95447	+	2.14655i	0.170293	+	0.123725i
$302$	9.45879	+	4.45097i	0.544292	+	0.256124i
$303$	−14.3263	−	9.09172i	−0.823022	−	0.522306i
$304$	−0.677908	+	0.268403i	−0.0388807	+	0.0153940i
$305$		0			0
$306$	0.00256890	−	0.0408315i	0.000146854	−	0.00233418i
$307$		−	22.6868i		−	1.29480i	−0.762150	−	0.647401i	$-0.775856\pi$
$307$		−	22.6868i		−	1.29480i	0.762150	−	0.647401i	$-0.224144\pi$
$308$	−1.29881	−	0.0817141i	−0.0740065	−	0.00465609i
$309$	1.50402	+	3.19621i	0.0855610	+	0.181826i
$310$		0			0
$311$	13.3524	+	12.5388i	0.757147	+	0.711009i	0.963571	−	0.267454i	$-0.0861824\pi$
$311$	13.3524	+	12.5388i	0.757147	+	0.711009i	−0.206423	+	0.978463i	$0.566182\pi$
$312$	−2.45979	−	19.4713i	−0.139258	−	1.10234i
$313$	−1.47591	−	11.6830i	−0.0834235	−	0.660365i	−0.977271	−	0.211994i	$-0.932004\pi$
$313$	−1.47591	−	11.6830i	−0.0834235	−	0.660365i	0.893848	−	0.448371i	$-0.147996\pi$
$314$	9.02491	+	8.47495i	0.509305	+	0.478269i
$315$		0			0
$316$	1.00520	+	2.13615i	0.0565468	+	0.120168i
$317$	−2.87575	−	0.180927i	−0.161518	−	0.0101619i	−0.0181744	−	0.999835i	$-0.505785\pi$
$317$	−2.87575	−	0.180927i	−0.161518	−	0.0101619i	−0.143344	+	0.989673i	$0.545785\pi$
$318$			9.77780i			0.548312i
$319$	1.64865	−	26.2045i	0.0923065	−	1.46717i
$320$		0			0
$321$	−18.7839	+	7.43709i	−1.04842	+	0.415098i
$322$	−13.0549	−	8.28489i	−0.727521	−	0.461699i
$323$	0.00332052	+	0.00156252i	0.000184759	+	8.69409e-5i
$324$	0.0414274	+	0.0300988i	0.00230152	+	0.00167215i
$325$		0			0
$326$	6.19349	−	4.49983i	0.343026	−	0.249223i
$327$	−14.6721	+	2.79886i	−0.811371	+	0.154777i
$328$	11.9474	+	30.1756i	0.659682	+	1.66617i
$329$	−4.54389	−	5.49262i	−0.250513	−	0.302818i
$330$		0			0
$331$	−23.8599	−	9.44678i	−1.31146	−	0.519242i	−0.394744	−	0.918791i	$-0.629167\pi$
$331$	−23.8599	−	9.44678i	−1.31146	−	0.519242i	−0.916712	+	0.399549i	$0.869167\pi$
$332$	0.699191	+	0.962354i	0.0383731	+	0.0528160i
$333$	−2.48598	−	2.05658i	−0.136231	−	0.112700i
$334$	−4.69476	+	4.40867i	−0.256886	+	0.241232i
$335$		0			0
$336$	4.09782	−	2.25280i	0.223555	−	0.122900i
$337$	−3.51254	−	3.74047i	−0.191340	−	0.203757i	0.626144	−	0.779707i	$-0.284632\pi$
$337$	−3.51254	−	3.74047i	−0.191340	−	0.203757i	−0.817485	+	0.575951i	$0.804632\pi$
$338$	−15.0717	+	27.4154i	−0.819794	+	1.49120i
$339$	−2.81945	+	5.99164i	−0.153132	+	0.325421i
$340$		0			0
$341$	2.32896	−	0.294216i	0.126120	−	0.0159327i
$342$	−0.436593	+	0.277071i	−0.0236083	+	0.0149823i
$343$	−9.27204	+	12.7619i	−0.500643	+	0.689076i
$344$	−8.28598	+	2.12748i	−0.446750	+	0.114706i
$345$		0			0
$346$	0.0823977	+	1.30967i	0.00442973	+	0.0704085i
$347$	−21.1426	+	1.33018i	−1.13499	+	0.0714078i	−0.619148	−	0.785274i	$-0.712522\pi$
$347$	−21.1426	+	1.33018i	−1.13499	+	0.0714078i	−0.515845	+	0.856682i	$0.672522\pi$
$348$	−0.983465	−	1.78892i	−0.0527193	−	0.0958960i
$349$	1.29748	−	3.99324i	0.0694527	−	0.213753i	−0.910306	−	0.413936i	$-0.864154\pi$
$349$	1.29748	−	3.99324i	0.0694527	−	0.213753i	0.979759	+	0.200183i	$0.0641536\pi$
$350$		0			0
$351$	−9.80145	−	30.1658i	−0.523163	−	1.61013i
$352$	3.92496	−	4.17966i	0.209201	−	0.222777i
$353$	−3.00670	+	11.7103i	−0.160031	+	0.623278i	0.837064	+	0.547105i	$0.184270\pi$
$353$	−3.00670	+	11.7103i	−0.160031	+	0.623278i	−0.997095	+	0.0761733i	$0.975730\pi$
$354$	−3.68559	+	5.80756i	−0.195887	+	0.308668i
$355$		0			0
$356$	−0.533182	+	0.644506i	−0.0282586	+	0.0341588i
$357$	−0.0223847	−	0.00727324i	−0.00118473	−	0.000384941i
$358$	8.64827	+	33.6828i	0.457075	+	1.78019i
$359$	2.06317	+	1.13424i	0.108890	+	0.0598628i	0.535268	−	0.844682i	$-0.320211\pi$
$359$	2.06317	+	1.13424i	0.108890	+	0.0598628i	−0.426378	+	0.904545i	$0.640211\pi$
$360$		0			0
$361$	3.55155	+	18.6179i	0.186924	+	0.979889i
$362$	15.3637	+	2.93078i	0.807497	+	0.154038i
$363$	−3.16589	+	1.48976i	−0.166166	+	0.0781919i
$364$	2.07608	+	0.262270i	0.108816	+	0.0137467i
$365$		0			0
$366$	−0.799653	+	4.19193i	−0.0417985	+	0.219115i
$367$	8.48109	−	21.4208i	0.442709	−	1.11816i	−0.521556	−	0.853217i	$-0.674648\pi$
$367$	8.48109	−	21.4208i	0.442709	−	1.11816i	0.964265	−	0.264939i	$-0.0853517\pi$
$368$	29.6986	−	9.64967i	1.54815	−	0.503024i
$369$	10.6330	+	16.7550i	0.553534	+	0.872231i
$370$		0			0
$371$	−8.47165	−	2.17515i	−0.439826	−	0.112928i
$372$	0.140631	−	0.116340i	0.00729136	−	0.00603194i
$373$	1.57768	−	12.4887i	0.0816894	−	0.646638i	−0.897109	−	0.441810i	$-0.854337\pi$
$373$	1.57768	−	12.4887i	0.0816894	−	0.646638i	0.978798	−	0.204828i	$-0.0656635\pi$
$374$	0.0845262			0.00437074
$375$		0			0
$376$	16.6988			0.861174
$377$	−5.29151	+	41.8866i	−0.272527	+	2.15727i
$378$	6.75414	−	5.58751i	0.347395	−	0.287391i
$379$	−33.9763	−	8.72364i	−1.74525	−	0.448103i	−0.764699	−	0.644387i	$-0.777113\pi$
$379$	−33.9763	−	8.72364i	−1.74525	−	0.448103i	−0.980547	+	0.196284i	$0.937113\pi$
$380$		0			0
$381$	−5.96872	−	9.40519i	−0.305787	−	0.481843i
$382$	12.0028	−	3.89993i	0.614115	−	0.199538i
$383$	−3.36007	+	8.48656i	−0.171691	+	0.433643i	−0.989988	−	0.141154i	$-0.954919\pi$
$383$	−3.36007	+	8.48656i	−0.171691	+	0.433643i	0.818296	+	0.574797i	$0.194919\pi$
$384$	−1.72442	+	9.03975i	−0.0879991	+	0.461308i
$385$		0			0
$386$	−2.77358	−	0.350385i	−0.141172	−	0.0178341i
$387$	−4.73292	+	2.22714i	−0.240588	+	0.113212i
$388$	2.58816	+	0.493718i	0.131394	+	0.0250647i
$389$	−3.17698	−	16.6543i	−0.161079	−	0.844408i	−0.967463	−	0.253014i	$-0.918578\pi$
$389$	−3.17698	−	16.6543i	−0.161079	−	0.844408i	0.806383	−	0.591393i	$-0.201422\pi$
$390$		0			0
$391$	−0.137732	−	0.0757188i	−0.00696541	−	0.00382926i
$392$	−3.99154	−	15.5460i	−0.201603	−	0.785193i
$393$	−0.444983	−	0.144584i	−0.0224464	−	0.00729329i
$394$	−10.9595	+	13.2477i	−0.552131	+	0.667411i
$395$		0			0
$396$	0.998779	−	1.57382i	0.0501905	−	0.0790876i
$397$	−7.56209	+	29.4524i	−0.379530	+	1.47817i	0.436258	+	0.899822i	$0.356304\pi$
$397$	−7.56209	+	29.4524i	−0.379530	+	1.47817i	−0.815788	+	0.578351i	$0.803696\pi$
$398$	−7.07145	+	7.53033i	−0.354460	+	0.377461i
$399$	0.0919264	+	0.282920i	0.00460208	+	0.0141637i
$400$		0			0
$401$	5.03124	−	15.4846i	0.251248	−	0.773262i	−0.743298	−	0.668961i	$-0.766739\pi$
$401$	5.03124	−	15.4846i	0.251248	−	0.773262i	0.994546	−	0.104301i	$-0.0332606\pi$
$402$	3.16717	+	5.76106i	0.157964	+	0.287336i
$403$	−3.76723	+	0.237014i	−0.187659	+	0.0118065i
$404$	0.266104	+	4.22961i	0.0132392	+	0.210431i
$405$		0			0
$406$	−11.3014	+	2.90171i	−0.560879	+	0.144009i
$407$	3.91808	−	5.39277i	0.194212	−	0.267310i
$408$	0.0465524	−	0.0295431i	0.00230469	−	0.00146260i
$409$	23.1477	−	2.92424i	1.14458	−	0.144594i	0.469911	−	0.882714i	$-0.344286\pi$
$409$	23.1477	−	2.92424i	1.14458	−	0.144594i	0.674670	+	0.738120i	$0.264286\pi$
$410$		0			0
$411$	−0.282503	+	0.600350i	−0.0139349	+	0.0296131i
$412$	0.425042	−	0.773148i	0.0209403	−	0.0380903i
$413$	−4.21188	−	4.48520i	−0.207253	−	0.220702i
$414$	19.4071	−	10.6691i	0.953805	−	0.524359i
$415$		0			0
$416$	−6.72080	+	6.31125i	−0.329514	+	0.309435i
$417$	−2.38860	−	1.97602i	−0.116970	−	0.0967662i
$418$	−0.627946	−	0.864294i	−0.0307138	−	0.0422740i
$419$	−1.30232	−	0.515623i	−0.0636223	−	0.0251899i	0.336098	−	0.941827i	$-0.390893\pi$
$419$	−1.30232	−	0.515623i	−0.0636223	−	0.0251899i	−0.399720	+	0.916637i	$0.630893\pi$
$420$		0			0
$421$	12.3514	+	14.9303i	0.601972	+	0.727660i	0.980191	−	0.198057i	$-0.0634631\pi$
$421$	12.3514	+	14.9303i	0.601972	+	0.727660i	−0.378218	+	0.925717i	$0.623463\pi$
$422$	−9.91601	−	25.0450i	−0.482704	−	1.21917i
$423$	10.0295	−	1.91323i	0.487651	−	0.0930245i
$424$	16.5758	−	12.0430i	0.804992	−	0.584861i
$425$		0			0
$426$	−11.8810	−	8.63207i	−0.575638	−	0.418225i
$427$	−3.45407	−	1.62536i	−0.167154	−	0.0786567i
$428$	4.26045	+	2.70376i	0.205937	+	0.130691i
$429$	23.0518	−	9.12686i	1.11295	−	0.440649i
$430$		0			0
$431$	−1.24983	+	19.8655i	−0.0602021	+	0.956886i	0.845770	+	0.533548i	$0.179142\pi$
$431$	−1.24983	+	19.8655i	−0.0602021	+	0.956886i	−0.905972	+	0.423338i	$0.860858\pi$
$432$			17.7035i			0.851758i
$433$	−18.4558	−	1.16114i	−0.886927	−	0.0558007i	−0.387212	−	0.921991i	$-0.626562\pi$
$433$	−18.4558	−	1.16114i	−0.886927	−	0.0558007i	−0.499715	+	0.866190i	$0.666562\pi$
$434$	−0.444167	−	0.943902i	−0.0213207	−	0.0453088i
$435$		0			0
$436$	2.71957	+	2.55384i	0.130244	+	0.122307i
$437$	0.248976	+	1.97085i	0.0119101	+	0.0942785i
$438$	−1.54818	−	12.2551i	−0.0739748	−	0.585571i
$439$	−13.8151	−	12.9733i	−0.659361	−	0.619181i	0.280859	−	0.959749i	$-0.409381\pi$
$439$	−13.8151	−	12.9733i	−0.659361	−	0.619181i	−0.940220	+	0.340568i	$0.889381\pi$
$440$		0			0
$441$	−4.17853	−	8.87983i	−0.198978	−	0.422849i
$442$	−0.135648	−	0.00853424i	−0.00645211	−	0.000405933i
$443$		−	15.3167i		−	0.727719i	−0.931454	−	0.363859i	$-0.881459\pi$
$443$		−	15.3167i		−	0.727719i	0.931454	−	0.363859i	$-0.118541\pi$
$444$	0.0325423	−	0.517246i	0.00154439	−	0.0245474i
$445$		0			0
$446$	−3.38760	+	1.34125i	−0.160408	+	0.0635099i
$447$	13.0010	+	8.25070i	0.614927	+	0.390245i
$448$	−10.1149	−	4.75969i	−0.477883	−	0.224874i
$449$	20.9219	+	15.2006i	0.987363	+	0.717361i	0.959342	−	0.282246i	$-0.0910794\pi$
$449$	20.9219	+	15.2006i	0.987363	+	0.717361i	0.0280212	+	0.999607i	$0.491079\pi$
$450$		0			0
$451$	−33.1687	+	24.0985i	−1.56185	+	1.13475i
$452$	1.62463	−	0.309915i	0.0764162	−	0.0145772i
$453$	3.17102	+	8.00908i	0.148987	+	0.376299i
$454$	12.8474	+	15.5299i	0.602961	+	0.728854i
$455$		0			0
$456$	−0.647921	−	0.256530i	−0.0303417	−	0.0120131i
$457$	3.61058	+	4.96953i	0.168896	+	0.232465i	0.885072	−	0.465455i	$-0.154109\pi$
$457$	3.61058	+	4.96953i	0.168896	+	0.232465i	−0.716176	+	0.697920i	$0.754109\pi$
$458$	−5.75258	−	4.75895i	−0.268801	−	0.222371i
$459$	0.0649554	−	0.0609972i	0.00303186	−	0.00284711i
$460$		0			0
$461$	24.8583	−	13.6660i	1.15777	−	0.636487i	0.217210	−	0.976125i	$-0.430305\pi$
$461$	24.8583	−	13.6660i	1.15777	−	0.636487i	0.940556	+	0.339638i	$0.110305\pi$
$462$	4.69042	+	4.99479i	0.218218	+	0.232379i
$463$	−19.4660	+	35.4086i	−0.904664	+	1.64558i	−0.150783	+	0.988567i	$0.548179\pi$
$463$	−19.4660	+	35.4086i	−0.904664	+	1.64558i	−0.753881	+	0.657011i	$0.771821\pi$
$464$	10.0334	−	21.3220i	0.465789	−	0.989851i
$465$		0			0
$466$	−27.5694	+	3.48283i	−1.27713	+	0.161339i
$467$	5.25398	−	3.33428i	0.243125	−	0.154292i	−0.408681	−	0.912677i	$-0.634011\pi$
$467$	5.25398	−	3.33428i	0.243125	−	0.154292i	0.651807	+	0.758385i	$0.274011\pi$
$468$	−1.76175	+	2.42484i	−0.0814368	+	0.112088i
$469$	−5.69604	+	1.46250i	−0.263019	+	0.0675318i
$470$		0			0
$471$	0.640563	+	10.1815i	0.0295156	+	0.469137i
$472$	14.3847	−	0.905008i	0.662109	−	0.0416564i
$473$	−5.20626	−	9.47016i	−0.239384	−	0.435438i
$474$	3.84109	−	11.8217i	0.176427	−	0.542987i
$475$		0			0
$476$	0.00181662	+	0.00559098i	8.32646e−5	+	0.000256262i
$477$	8.57583	−	9.13234i	0.392660	−	0.418141i
$478$	2.23485	−	8.70418i	0.102220	−	0.398120i
$479$	−22.4239	+	35.3344i	−1.02457	+	1.61447i	−0.264780	+	0.964309i	$0.585299\pi$
$479$	−22.4239	+	35.3344i	−1.02457	+	1.61447i	−0.759795	+	0.650162i	$0.774701\pi$
$480$		0			0
$481$	−6.83223	+	8.25875i	−0.311523	+	0.376567i
$482$	−21.8180	−	7.08911i	−0.993784	−	0.322900i
$483$	−3.16850	−	12.3405i	−0.144172	−	0.561512i
$484$	0.765813	+	0.421009i	0.0348097	+	0.0191368i
$485$		0			0
$486$	3.81521	+	20.0000i	0.173061	+	0.907219i
$487$	7.12658	+	1.35947i	0.322936	+	0.0616034i	0.346301	−	0.938124i	$-0.387438\pi$
$487$	7.12658	+	1.35947i	0.322936	+	0.0616034i	−0.0233643	+	0.999727i	$0.507438\pi$
$488$	8.09126	−	3.80746i	0.366274	−	0.172356i
$489$	6.25855	+	0.790638i	0.283021	+	0.0357539i
$490$		0			0
$491$	3.83747	−	20.1167i	0.173183	−	0.907855i	−0.784522	−	0.620101i	$-0.787091\pi$
$491$	3.83747	−	20.1167i	0.173183	−	0.907855i	0.957704	−	0.287754i	$-0.0929085\pi$
$492$	−1.17345	+	2.96381i	−0.0529034	+	0.133619i
$493$	−0.112802	+	0.0366517i	−0.00508036	+	0.00165071i
$494$	0.920466	+	1.45042i	0.0414137	+	0.0652576i
$495$		0			0
$496$	2.04064	+	0.523947i	0.0916275	+	0.0235259i
$497$	10.1220	−	8.37365i	0.454034	−	0.375610i
$498$	0.784962	−	6.21362i	0.0351750	−	0.278439i
$499$	−14.2353			−0.637260			−0.318630	−	0.947879i	$-0.603223\pi$
$499$	−14.2353			−0.637260			−0.318630	+	0.947879i	$0.603223\pi$
$500$		0			0
$501$	−5.30686			−0.237093
$502$	4.08142	−	32.3078i	0.182163	−	1.44197i
$503$	−23.3767	+	19.3389i	−1.04232	+	0.862280i	−0.990656	−	0.136384i	$-0.956452\pi$
$503$	−23.3767	+	19.3389i	−1.04232	+	0.862280i	−0.0516617	+	0.998665i	$0.516452\pi$
$504$	−6.73105	−	1.72824i	−0.299825	−	0.0769820i
$505$		0			0
$506$	24.5169	+	38.6325i	1.08991	+	1.71742i
$507$	−24.5176	+	7.96625i	−1.08887	+	0.353794i
$508$	−1.02421	+	2.58685i	−0.0454418	+	0.114773i
$509$	0.888182	−	4.65601i	0.0393680	−	0.206374i	−0.957168	−	0.289532i	$-0.906500\pi$
$509$	0.888182	−	4.65601i	0.0393680	−	0.206374i	0.996536	+	0.0831575i	$0.0265005\pi$
$510$		0			0
$511$	10.9624	+	1.38488i	0.484949	+	0.0612633i
$512$	22.9499	−	10.7994i	1.01425	−	0.477271i
$513$	−1.10626	−	0.211031i	−0.0488426	−	0.00931723i
$514$	1.02506	+	5.37354i	0.0452134	+	0.237017i
$515$		0			0
$516$	−0.736305	−	0.404787i	−0.0324140	−	0.0178198i
$517$	5.24610	+	20.4322i	0.230723	+	0.898608i
$518$	−2.81723	−	0.915374i	−0.123782	−	0.0402192i
$519$	−0.689260	+	0.833172i	−0.0302552	+	0.0365722i
$520$		0			0
$521$	−17.3097	+	27.2758i	−0.758353	+	1.19497i	0.217397	+	0.976083i	$0.430243\pi$
$521$	−17.3097	+	27.2758i	−0.758353	+	1.19497i	−0.975750	+	0.218889i	$0.929757\pi$
$522$	4.15619	−	16.1873i	0.181911	−	0.708498i
$523$	2.73779	−	2.91546i	0.119715	−	0.127484i	−0.666319	−	0.745667i	$-0.732131\pi$
$523$	2.73779	−	2.91546i	0.119715	−	0.127484i	0.786034	+	0.618183i	$0.212131\pi$
$524$	0.0361124	+	0.111142i	0.00157758	+	0.00485528i
$525$		0			0
$526$	0.997356	−	3.06955i	0.0434868	−	0.133839i
$527$	−0.00510861	−	0.00929254i	−0.000222535	−	0.000404789i
$528$	−13.8108	+	0.868901i	−0.601038	+	0.0378141i
$529$	−3.89806	−	61.9578i	−0.169481	−	2.69382i
$530$		0			0
$531$	8.53594	−	2.19166i	0.370428	−	0.0951098i
$532$	0.0436730	−	0.0601107i	0.00189346	−	0.00260613i
$533$	55.6624	−	35.3244i	2.41101	−	1.53007i
$534$	4.36932	−	0.551974i	0.189079	−	0.0238862i
$535$		0			0
$536$	5.86552	−	12.4649i	0.253352	−	0.538400i
$537$	−13.8048	+	25.1108i	−0.595721	+	1.08361i
$538$	−10.2199	−	10.8830i	−0.440610	−	0.469202i
$539$	17.7678	−	9.76791i	0.765312	−	0.420734i
$540$		0			0
$541$	4.31234	−	4.04955i	0.185402	−	0.174104i	−0.586289	−	0.810102i	$-0.699412\pi$
$541$	4.31234	−	4.04955i	0.185402	−	0.174104i	0.771690	+	0.635998i	$0.219412\pi$
$542$	23.8411	+	19.7231i	1.02406	+	0.847179i
$543$	7.57547	+	10.4267i	0.325094	+	0.447454i
$544$	−0.0240818	−	0.00953466i	−0.00103250	−	0.000408795i
$545$		0			0
$546$	−7.02290	−	8.48923i	−0.300552	−	0.363305i
$547$	7.36339	+	18.5978i	0.314836	+	0.795185i	0.997897	+	0.0648234i	$0.0206484\pi$
$547$	7.36339	+	18.5978i	0.314836	+	0.795185i	−0.683061	+	0.730362i	$0.739352\pi$
$548$	0.162785	−	0.0310528i	0.00695382	−	0.00132651i
$549$	4.42348	−	3.21385i	0.188790	−	0.137164i
$550$		0			0
$551$	1.21278	+	0.881136i	0.0516662	+	0.0375377i
$552$	27.0052	+	12.7077i	1.14942	+	0.540874i
$553$	9.38800	+	5.95781i	0.399218	+	0.253352i
$554$	31.4248	−	12.4420i	1.33511	−	0.528608i
$555$		0			0
$556$	−0.0486176	+	0.772755i	−0.00206185	+	0.0327721i
$557$		−	3.13554i		−	0.132857i	−0.997791	−	0.0664285i	$-0.978840\pi$
$557$		−	3.13554i		−	0.132857i	0.997791	−	0.0664285i	$-0.0211604\pi$
$558$	1.49123	+	0.0938204i	0.0631289	+	0.00397173i
$559$	7.39887	+	15.7234i	0.312939	+	0.665029i
$560$		0			0
$561$	0.0507731	+	0.0476791i	0.00214364	+	0.00201301i
$562$	4.74972	+	37.5979i	0.200355	+	1.58597i
$563$	−4.61067	−	36.4972i	−0.194317	−	1.53817i	−0.723894	−	0.689912i	$-0.757649\pi$
$563$	−4.61067	−	36.4972i	−0.194317	−	1.53817i	0.529577	−	0.848262i	$-0.322351\pi$
$564$	1.19561	+	1.12275i	0.0503441	+	0.0472762i
$565$		0			0
$566$	5.32371	+	11.3135i	0.223772	+	0.475540i
$567$	0.240695	+	0.0151433i	0.0101082	+	0.000635957i
$568$			30.7731i			1.29121i
$569$	0.570486	−	9.06761i	0.0239160	−	0.380134i	−0.967803	−	0.251708i	$-0.919008\pi$
$569$	0.570486	−	9.06761i	0.0239160	−	0.380134i	0.991719	−	0.128426i	$-0.0409924\pi$
$570$		0			0
$571$	28.1239	−	11.1350i	1.17695	−	0.465987i	0.303465	−	0.952842i	$-0.401856\pi$
$571$	28.1239	−	11.1350i	1.17695	−	0.465987i	0.873482	+	0.486856i	$0.161856\pi$
$572$	−5.22846	−	3.31808i	−0.218613	−	0.138736i
$573$	9.40967	+	4.42785i	0.393094	+	0.184976i
$574$	14.7398	+	10.7091i	0.615226	+	0.446988i
$575$		0			0
$576$	12.9537	−	9.41142i	0.539738	−	0.392142i
$577$	−19.1170	+	3.64676i	−0.795851	+	0.151817i	−0.569243	−	0.822169i	$-0.692764\pi$
$577$	−19.1170	+	3.64676i	−0.795851	+	0.151817i	−0.226608	+	0.973986i	$0.572764\pi$
$578$	8.22958	+	20.7855i	0.342305	+	0.864564i
$579$	−1.46839	−	1.77498i	−0.0610242	−	0.0737656i
$580$		0			0
$581$	5.20896	+	2.06237i	0.216104	+	0.0855617i
$582$	−8.15411	−	11.2232i	−0.337999	−	0.465215i
$583$	19.9430	+	16.4983i	0.825955	+	0.683290i
$584$	−18.8686	+	17.7188i	−0.780787	+	0.733208i
$585$		0			0
$586$	33.2163	−	18.2608i	1.37215	−	0.754348i
$587$	28.4883	+	30.3370i	1.17584	+	1.25214i	0.961324	+	0.275419i	$0.0888165\pi$
$587$	28.4883	+	30.3370i	1.17584	+	1.25214i	0.214513	+	0.976721i	$0.431183\pi$
$588$	0.759455	−	1.38144i	0.0313194	−	0.0569698i
$589$	−0.0570657	+	0.121271i	−0.00235135	+	0.00499688i
$590$		0			0
$591$	−14.0559	+	1.77567i	−0.578181	+	0.0730412i
$592$	5.05121	−	3.20560i	0.207603	−	0.131749i
$593$	19.1735	−	26.3901i	0.787363	−	1.08371i	−0.207068	−	0.978326i	$-0.566392\pi$
$593$	19.1735	−	26.3901i	0.787363	−	1.08371i	0.994431	−	0.105386i	$-0.0336077\pi$
$594$	−25.1250	+	6.45101i	−1.03089	+	0.264688i
$595$		0			0
$596$	−0.241489	−	3.83835i	−0.00989175	−	0.157225i
$597$	−8.49535	+	0.534482i	−0.347691	+	0.0218749i
$598$	−35.4443	−	64.4730i	−1.44943	−	2.63650i
$599$	−1.29644	+	3.99003i	−0.0529711	+	0.163028i	−0.974042	−	0.226366i	$-0.927316\pi$
$599$	−1.29644	+	3.99003i	−0.0529711	+	0.163028i	0.921071	+	0.389394i	$0.127316\pi$
$600$		0			0
$601$	0.589765	+	1.81511i	0.0240570	+	0.0740398i	0.962364	−	0.271763i	$-0.0876066\pi$
$601$	0.589765	+	1.81511i	0.0240570	+	0.0740398i	−0.938307	+	0.345803i	$0.887607\pi$
$602$	−3.28750	+	3.50084i	−0.133989	+	0.142683i
$603$	2.09477	−	8.15859i	0.0853056	−	0.332243i
$604$	1.15283	−	1.81657i	0.0469079	−	0.0739150i
$605$		0			0
$606$	14.2230	−	17.1927i	0.577770	−	0.698404i
$607$	21.4931	+	6.98352i	0.872377	+	0.283452i	0.710788	−	0.703406i	$-0.248338\pi$
$607$	21.4931	+	6.98352i	0.872377	+	0.283452i	0.161588	+	0.986858i	$0.448338\pi$
$608$	0.0814107	+	0.317074i	0.00330164	+	0.0128590i
$609$	−8.42530	−	4.63185i	−0.341410	−	0.187692i
$610$		0			0
$611$	−6.35602	−	33.3194i	−0.257137	−	1.34796i
$612$	−0.00827107	−	0.00157779i	−0.000334338	−	6.37784e-5i
$613$	−0.563300	+	0.265069i	−0.0227515	+	0.0107060i	−0.437121	−	0.899403i	$-0.644002\pi$
$613$	−0.563300	+	0.265069i	−0.0227515	+	0.0107060i	0.414370	+	0.910109i	$0.364002\pi$
$614$	29.5989	+	3.73921i	1.19451	+	0.150902i
$615$		0			0
$616$	2.69036	−	14.1034i	0.108398	−	0.568240i
$617$	3.99597	−	10.0927i	0.160872	−	0.406315i	−0.826874	−	0.562387i	$-0.809883\pi$
$617$	3.99597	−	10.0927i	0.160872	−	0.406315i	0.987746	+	0.156072i	$0.0498831\pi$
$618$	−4.41792	+	1.43547i	−0.177715	+	0.0577430i
$619$	−16.7573	−	26.4053i	−0.673533	−	1.06132i	−0.993494	−	0.113888i	$-0.963670\pi$
$619$	−16.7573	−	26.4053i	−0.673533	−	1.06132i	0.319960	−	0.947431i	$-0.396330\pi$
$620$		0			0
$621$	46.7190	+	11.9954i	1.87477	+	0.481359i
$622$	−18.5598	+	15.3540i	−0.744180	+	0.615639i
$623$	−0.493752	+	3.90845i	−0.0197817	+	0.156589i
$624$	22.2513			0.890767
$625$		0			0
$626$	15.4859			0.618940
$627$	0.110333	−	0.873372i	0.00440626	−	0.0348791i
$628$	1.96329	−	1.62417i	0.0783437	−	0.0648115i
$629$	−0.0291655	−	0.00748843i	−0.00116291	−	0.000298583i
$630$		0			0
$631$	11.4093	+	17.9781i	0.454195	+	0.715697i	0.991842	−	0.127473i	$-0.0406865\pi$
$631$	11.4093	+	17.9781i	0.454195	+	0.715697i	−0.537647	+	0.843170i	$0.680687\pi$
$632$	−24.7716	+	8.04877i	−0.985361	+	0.320163i
$633$	8.17092	−	20.6374i	0.324765	−	0.820262i
$634$	0.710029	−	3.72210i	0.0281988	−	0.147824i
$635$		0			0
$636$	1.99652	+	0.252219i	0.0791671	+	0.0100011i
$637$	−29.5000	+	13.8816i	−1.16883	+	0.550011i
$638$	33.9167	+	6.46995i	1.34277	+	0.256148i
$639$	3.52577	+	18.4828i	0.139477	+	0.731166i
$640$		0			0
$641$	−7.17378	−	3.94382i	−0.283347	−	0.155771i	0.333742	−	0.942664i	$-0.391688\pi$
$641$	−7.17378	−	3.94382i	−0.283347	−	0.155771i	−0.617090	+	0.786893i	$0.711688\pi$
$642$	−6.60705	−	25.7328i	−0.260759	−	1.01559i
$643$	30.7257	+	9.98337i	1.21170	+	0.393706i	0.844053	−	0.536259i	$-0.180163\pi$
$643$	30.7257	+	9.98337i	1.21170	+	0.393706i	0.367648	+	0.929965i	$0.380163\pi$
$644$	−2.02843	+	2.45195i	−0.0799314	+	0.0966205i
$645$		0			0
$646$	−0.00258587	+	0.00407468i	−0.000101740	+	0.000160316i
$647$	−8.04195	+	31.3213i	−0.316162	+	1.23137i	0.589640	+	0.807666i	$0.299270\pi$
$647$	−8.04195	+	31.3213i	−0.316162	+	1.23137i	−0.905802	+	0.423702i	$0.860730\pi$
$648$	−0.386735	+	0.411831i	−0.0151924	+	0.0161783i
$649$	5.62645	+	17.3164i	0.220858	+	0.679730i
$650$		0			0
$651$	0.265630	−	0.817526i	0.0104109	−	0.0320414i
$652$	−0.759054	−	1.38071i	−0.0297268	−	0.0540729i
$653$	−38.7945	+	2.44074i	−1.51814	+	0.0955136i	−0.799839	−	0.600214i	$-0.795082\pi$
$653$	−38.7945	+	2.44074i	−1.51814	+	0.0955136i	−0.718306	+	0.695728i	$0.755082\pi$
$654$	−1.23336	−	19.6037i	−0.0482282	−	0.766565i
$655$		0			0
$656$	−35.6400	+	9.15080i	−1.39151	+	0.357279i
$657$	−9.30262	+	12.8040i	−0.362930	+	0.499530i
$658$	7.91501	−	5.02302i	0.308559	−	0.195818i
$659$	−12.1308	+	1.53248i	−0.472550	+	0.0596969i	−0.358002	−	0.933721i	$-0.616542\pi$
$659$	−12.1308	+	1.53248i	−0.472550	+	0.0596969i	−0.114548	+	0.993418i	$0.536542\pi$
$660$		0			0
$661$	−12.3365	+	26.2163i	−0.479833	+	1.01970i	0.507591	+	0.861598i	$0.330536\pi$
$661$	−12.3365	+	26.2163i	−0.479833	+	1.01970i	−0.987423	+	0.158098i	$0.949464\pi$
$662$	16.2576	−	29.5724i	0.631868	−	1.14936i
$663$	−0.0766669	−	0.0816420i	−0.00297750	−	0.00317071i
$664$	−11.5004	+	6.32242i	−0.446303	+	0.245357i
$665$		0			0
$666$	3.09291	−	2.90443i	0.119848	−	0.112544i
$667$	−49.4701	−	40.9252i	−1.91549	−	1.58463i
$668$	0.779099	+	1.07234i	0.0301443	+	0.0414900i
$669$	−2.79143	−	1.10520i	−0.107923	−	0.0427297i
$670$		0			0
$671$	7.20067	+	8.70412i	0.277979	+	0.336019i
$672$	−0.772899	−	1.95212i	−0.0298152	−	0.0753046i
$673$	−24.4074	+	4.65595i	−0.940835	+	0.179474i	−0.634914	−	0.772583i	$-0.718964\pi$
$673$	−24.4074	+	4.65595i	−0.940835	+	0.179474i	−0.305921	+	0.952057i	$0.598964\pi$
$674$	5.45904	−	3.96623i	0.210275	−	0.152773i
$675$		0			0
$676$	5.20913	+	3.78466i	0.200351	+	0.145564i
$677$	−2.15944	−	1.01616i	−0.0829942	−	0.0390541i	0.383834	−	0.923402i	$-0.374603\pi$
$677$	−2.15944	−	1.01616i	−0.0829942	−	0.0390541i	−0.466828	+	0.884348i	$0.654603\pi$
$678$	−7.35246	−	4.66601i	−0.282369	−	0.179197i
$679$	11.5379	−	4.56817i	0.442783	−	0.175310i
$680$		0			0
$681$	−1.04284	+	16.5754i	−0.0399616	+	0.635171i
$682$			3.08703i			0.118209i
$683$	−28.4641	−	1.79081i	−1.08915	−	0.0685234i	−0.491955	−	0.870621i	$-0.663717\pi$
$683$	−28.4641	−	1.79081i	−1.08915	−	0.0685234i	−0.597193	+	0.802098i	$0.703717\pi$
$684$	0.0453127	+	0.0962945i	0.00173258	+	0.00368191i
$685$		0			0
$686$	−15.1219	−	14.2004i	−0.577358	−	0.542175i
$687$	−0.771051	−	6.10350i	−0.0294174	−	0.232863i
$688$	−1.21562	−	9.62261i	−0.0463450	−	0.366859i
$689$	−30.3389	−	28.4901i	−1.15582	−	1.08539i
$690$		0			0
$691$	−3.38597	−	7.19556i	−0.128808	−	0.273732i	0.830012	−	0.557746i	$-0.188334\pi$
$691$	−3.38597	−	7.19556i	−0.128808	−	0.273732i	−0.958820	+	0.284014i	$0.908334\pi$
$692$	0.269546	+	0.0169584i	0.0102466	+	0.000644661i
$693$		−	8.77890i		−	0.333483i
$694$	1.74925	−	27.8035i	0.0664005	−	1.05541i
$695$		0			0
$696$	20.9408	−	8.29105i	0.793759	−	0.314271i
$697$	0.156373	+	0.0992371i	0.00592303	+	0.00375887i
$698$	4.99605	+	2.35096i	0.189103	+	0.0889852i
$699$	−18.5250	−	13.4592i	−0.700678	−	0.509073i
$700$		0			0
$701$	15.7396	−	11.4355i	0.594475	−	0.431912i	−0.249438	−	0.968391i	$-0.580246\pi$
$701$	15.7396	−	11.4355i	0.594475	−	0.431912i	0.843914	+	0.536479i	$0.180246\pi$
$702$	40.9721	−	7.81584i	1.54639	−	0.294990i
$703$	0.140101	+	0.353854i	0.00528400	+	0.0133459i
$704$	21.0864	+	25.4891i	0.794724	+	0.960656i
$705$		0			0
$706$	−14.7827	−	5.85287i	−0.556352	−	0.220275i
$707$	11.7320	+	16.1477i	0.441227	+	0.607297i
$708$	1.09077	+	0.902362i	0.0409936	+	0.0339129i
$709$	−20.4123	+	19.1685i	−0.766602	+	0.719887i	−0.965577	−	0.260118i	$-0.916239\pi$
$709$	−20.4123	+	19.1685i	−0.766602	+	0.719887i	0.198975	+	0.980005i	$0.436239\pi$
$710$		0			0
$711$	−13.9560	+	7.67236i	−0.523389	+	0.287736i
$712$	−6.31729	−	6.72724i	−0.236751	−	0.252114i
$713$	2.76537	−	5.03019i	0.103564	−	0.188382i
$714$	0.0131787	−	0.0280061i	0.000493199	−	0.00104810i
$715$		0			0
$716$	7.10073	−	0.897031i	0.265367	−	0.0335236i
$717$	6.25225	−	3.96780i	0.233494	−	0.148180i
$718$	−1.81987	+	2.50483i	−0.0679168	+	0.0934794i
$719$	9.37729	−	2.40768i	0.349714	−	0.0897912i	−0.0697469	−	0.997565i	$-0.522219\pi$
$719$	9.37729	−	2.40768i	0.349714	−	0.0897912i	0.419461	+	0.907773i	$0.362219\pi$
$720$		0			0
$721$	−0.260913	−	4.14709i	−0.00971691	−	0.154446i
$722$	−24.8757	+	1.56505i	−0.925778	+	0.0582450i
$723$	−9.10685	−	16.5653i	−0.338687	−	0.616070i
$724$	0.994739	−	3.06149i	0.0369692	−	0.113779i
$725$		0			0
$726$	−1.42185	−	4.37601i	−0.0527699	−	0.162409i
$727$	22.9396	−	24.4282i	0.850782	−	0.905991i	−0.145740	−	0.989323i	$-0.546556\pi$
$727$	22.9396	−	24.4282i	0.850782	−	0.905991i	0.996522	+	0.0833319i	$0.0265562\pi$
$728$	−5.74145	+	22.3615i	−0.212792	+	0.828772i
$729$	−9.29394	+	14.6449i	−0.344220	+	0.542404i
$730$		0			0
$731$	−0.0311177	+	0.0376149i	−0.00115093	+	0.00139124i
$732$	0.835317	+	0.271411i	0.0308742	+	0.0100316i
$733$	−0.243524	−	0.948462i	−0.00899475	−	0.0350322i	0.963927	−	0.266165i	$-0.0857567\pi$
$733$	−0.243524	−	0.948462i	−0.00899475	−	0.0350322i	−0.972922	+	0.231133i	$0.925757\pi$
$734$	26.5494	+	14.5956i	0.979955	+	0.538735i
$735$		0			0
$736$	−2.62716	−	13.7721i	−0.0968386	−	0.507646i
$737$	17.0944	+	3.26093i	0.629681	+	0.120118i
$738$	−23.6124	+	11.1112i	−0.869184	+	0.409007i
$739$	−13.0596	−	1.64981i	−0.480403	−	0.0606891i	−0.118597	−	0.992942i	$-0.537840\pi$
$739$	−13.0596	−	1.64981i	−0.480403	−	0.0606891i	−0.361806	+	0.932253i	$0.617840\pi$
$740$		0			0
$741$	−0.265243	+	1.39045i	−0.00974394	+	0.0510795i
$742$	4.23416	−	10.6943i	0.155441	−	0.392599i
$743$	36.2360	−	11.7738i	1.32937	−	0.431938i	0.443667	−	0.896192i	$-0.353677\pi$
$743$	36.2360	−	11.7738i	1.32937	−	0.431938i	0.885703	+	0.464253i	$0.153677\pi$
$744$	1.07896	+	1.70017i	0.0395566	+	0.0623312i
$745$		0			0
$746$	16.0336	+	4.11674i	0.587033	+	0.150724i
$747$	−6.18293	+	5.11496i	−0.226222	+	0.187147i
$748$	0.00218036	−	0.0172593i	7.97217e−5	−	0.000631062i
$749$	23.7651			0.868357
$750$		0			0
$751$	16.8293			0.614109			0.307055	−	0.951692i	$-0.400657\pi$
$751$	16.8293			0.614109			0.307055	+	0.951692i	$0.400657\pi$
$752$	−2.37287	+	18.7832i	−0.0865298	+	0.684954i
$753$	20.6756	−	17.1044i	0.753462	−	0.623318i
$754$	−53.7764	−	13.8074i	−1.95842	−	0.502837i
$755$		0			0
$756$	−0.966683	−	1.52325i	−0.0351579	−	0.0554000i
$757$	14.4407	−	4.69206i	0.524855	−	0.170536i	−0.0345923	−	0.999402i	$-0.511013\pi$
$757$	14.4407	−	4.69206i	0.524855	−	0.170536i	0.559448	+	0.828866i	$0.311013\pi$
$758$	16.9815	−	42.8903i	0.616795	−	1.55785i
$759$	−7.06483	+	37.0351i	−0.256437	+	1.34429i
$760$		0			0
$761$	10.7599	+	1.35930i	0.390047	+	0.0492744i	0.317911	−	0.948120i	$-0.397019\pi$
$761$	10.7599	+	1.35930i	0.390047	+	0.0492744i	0.0721358	+	0.997395i	$0.477019\pi$
$762$	13.2545	−	6.23710i	0.480160	−	0.225946i
$763$	17.2593	+	3.29240i	0.624830	+	0.119193i
$764$	−0.486711	−	2.55143i	−0.0176086	−	0.0923074i
$765$		0			0
$766$	−10.5184	−	5.78255i	−0.380046	−	0.208932i
$767$	−7.28099	−	28.3576i	−0.262901	−	1.02393i
$768$	6.56615	+	2.13347i	0.236936	+	0.0769851i
$769$	2.42566	−	2.93212i	0.0874717	−	0.105735i	−0.724962	−	0.688789i	$-0.758142\pi$
$769$	2.42566	−	2.93212i	0.0874717	−	0.105735i	0.812433	+	0.583054i	$0.198142\pi$
$770$		0			0
$771$	−2.41535	+	3.80598i	−0.0869867	+	0.137069i
$772$	−0.143089	+	0.557296i	−0.00514990	+	0.0200575i
$773$	−29.5184	+	31.4339i	−1.06170	+	1.13060i	−0.0706013	+	0.997505i	$0.522492\pi$
$773$	−29.5184	+	31.4339i	−1.06170	+	1.13060i	−0.991103	+	0.133096i	$0.957508\pi$
$774$	−2.12563	−	6.54201i	−0.0764041	−	0.235148i
$775$		0			0
$776$	−8.98288	+	27.6465i	−0.322467	+	0.992450i
$777$	−1.17591	−	2.13898i	−0.0421856	−	0.0767354i
$778$	22.2521	−	1.39999i	0.797778	−	0.0501919i
$779$	−0.146979	−	2.33617i	−0.00526608	−	0.0837019i
$780$		0			0
$781$	−37.6533	+	9.66772i	−1.34734	+	0.345938i
$782$	0.121489	−	0.167216i	0.00434445	−	0.00597963i
$783$	30.7327	−	19.5036i	1.09830	−	0.697001i
$784$	18.0538	−	2.28072i	0.644778	−	0.0814544i
$785$		0			0
$786$	0.261977	−	0.556729i	0.00934441	−	0.0198579i
$787$	−19.9769	+	36.3378i	−0.712099	+	1.29530i	0.234256	+	0.972175i	$0.424734\pi$
$787$	−19.9769	+	36.3378i	−0.712099	+	1.29530i	−0.946355	+	0.323128i	$0.895266\pi$
$788$	2.42234	+	2.57953i	0.0862922	+	0.0918919i
$789$	2.33055	−	1.28123i	0.0829696	−	0.0456129i
$790$		0			0
$791$	5.67832	−	5.33230i	0.201898	−	0.189595i
$792$	15.8455	+	13.1085i	0.563045	+	0.465791i
$793$	−10.6768	−	14.6954i	−0.379146	−	0.521850i
$794$	−37.1795	−	14.7204i	−1.31945	−	0.522407i
$795$		0			0
$796$	1.35520	+	1.63815i	0.0480338	+	0.0580629i
$797$	−12.9545	−	32.7192i	−0.458871	−	1.15898i	−0.956538	−	0.291607i	$-0.905810\pi$
$797$	−12.9545	−	32.7192i	−0.458871	−	1.15898i	0.497667	−	0.867368i	$-0.334190\pi$
$798$	−0.384271	+	0.0733036i	−0.0136031	+	0.00259492i
$799$	0.0770930	−	0.0560113i	0.00272735	−	0.00198154i
$800$		0			0
$801$	−4.56501	−	3.31667i	−0.161297	−	0.117189i
$802$	19.3731	+	9.11629i	0.684088	+	0.321907i
$803$	−27.6080	−	17.5206i	−0.974266	−	0.618288i
$804$	1.25804	−	0.498094i	0.0443677	−	0.0175664i
$805$		0			0
$806$	0.311684	−	4.95408i	0.0109786	−	0.174500i
$807$		−	12.3020i		−	0.433051i
$808$	−46.6639	−	2.93584i	−1.64163	−	0.103283i
$809$	7.04446	+	14.9702i	0.247670	+	0.526326i	0.989547	−	0.144210i	$-0.0460642\pi$
$809$	7.04446	+	14.9702i	0.247670	+	0.526326i	−0.741877	+	0.670536i	$0.766064\pi$
$810$		0			0
$811$	−1.55279	−	1.45817i	−0.0545258	−	0.0512032i	0.656805	−	0.754060i	$-0.271907\pi$
$811$	−1.55279	−	1.45817i	−0.0545258	−	0.0512032i	−0.711331	+	0.702857i	$0.751907\pi$
$812$	0.300976	+	2.38247i	0.0105622	+	0.0836082i
$813$	3.19556	+	25.2954i	0.112073	+	0.887149i
$814$	6.39005	+	6.00066i	0.223971	+	0.210323i
$815$		0			0
$816$	0.0266158	+	0.0565614i	0.000931739	+	0.00198005i
$817$	0.615792	+	0.0387424i	0.0215438	+	0.00135542i
$818$			30.6823i			1.07278i
$819$	−0.886368	+	14.0884i	−0.0309722	+	0.492289i
$820$		0			0
$821$	−34.0182	+	13.4688i	−1.18724	+	0.470063i	−0.876952	−	0.480578i	$-0.840427\pi$
$821$	−34.0182	+	13.4688i	−1.18724	+	0.470063i	−0.310292	+	0.950641i	$0.600427\pi$
$822$	−0.736701	−	0.467525i	−0.0256954	−	0.0163068i
$823$	12.8589	+	6.05094i	0.448233	+	0.210922i	0.636628	−	0.771171i	$-0.280329\pi$
$823$	12.8589	+	6.05094i	0.448233	+	0.210922i	−0.188395	+	0.982093i	$0.560329\pi$
$824$	7.87489	+	5.72145i	0.274335	+	0.199316i
$825$		0			0
$826$	6.54593	−	4.75590i	0.227762	−	0.165479i
$827$	38.8769	−	7.41617i	1.35188	−	0.257886i	0.539980	−	0.841678i	$-0.318432\pi$
$827$	38.8769	−	7.41617i	1.35188	−	0.257886i	0.811903	+	0.583792i	$0.198432\pi$
$828$	−1.67791	−	4.23792i	−0.0583114	−	0.147278i
$829$	−7.62450	−	9.21644i	−0.264810	−	0.320100i	0.621302	−	0.783571i	$-0.286604\pi$
$829$	−7.62450	−	9.21644i	−0.264810	−	0.320100i	−0.886112	+	0.463471i	$0.846604\pi$
$830$		0			0
$831$	25.8944	+	10.2523i	0.898268	+	0.355649i
$832$	−31.2660	−	43.0340i	−1.08395	−	1.49193i
$833$	−0.0705724	−	0.0583826i	−0.00244519	−	0.00202284i
$834$	2.97176	−	2.79067i	0.102904	−	0.0966329i
$835$		0			0
$836$	−0.192677	+	0.105925i	−0.00666387	+	0.00366349i
$837$	2.22772	+	2.37228i	0.0770011	+	0.0819979i
$838$	0.887369	−	1.61412i	0.0306536	−	0.0557588i
$839$	11.8724	−	25.2302i	0.409881	−	0.871043i	−0.588175	−	0.808733i	$-0.700154\pi$
$839$	11.8724	−	25.2302i	0.409881	−	0.871043i	0.998057	−	0.0623091i	$-0.0198465\pi$
$840$		0			0
$841$	−19.2968	+	2.43775i	−0.665407	+	0.0840605i
$842$	−21.5150	+	13.6538i	−0.741456	+	0.470542i
$843$	−18.3550	+	25.2635i	−0.632180	+	0.870121i
$844$	−5.36969	+	1.37870i	−0.184832	+	0.0474569i
$845$		0			0
$846$	0.843095	+	13.4006i	0.0289862	+	0.460722i
$847$	4.10775	−	0.258438i	0.141144	−	0.00888003i
$848$	11.1909	+	20.3562i	0.384298	+	0.699035i
$849$	−3.18380	+	9.79874i	−0.109268	+	0.336292i
$850$		0			0
$851$	−5.03693	−	15.5021i	−0.172664	−	0.531404i
$852$	−2.06904	+	2.20331i	−0.0708843	+	0.0754841i
$853$	−8.43096	+	32.8364i	−0.288671	+	1.12430i	0.644424	+	0.764668i	$0.277097\pi$
$853$	−8.43096	+	32.8364i	−0.288671	+	1.12430i	−0.933095	+	0.359630i	$0.882903\pi$
$854$	2.68987	−	4.23855i	0.0920453	−	0.145040i
$855$		0			0
$856$	−35.4857	+	42.8948i	−1.21288	+	1.46612i
$857$	−7.22375	−	2.34714i	−0.246759	−	0.0801767i	0.183026	−	0.983108i	$-0.441411\pi$
$857$	−7.22375	−	2.34714i	−0.246759	−	0.0801767i	−0.429785	+	0.902931i	$0.641411\pi$
$858$	8.10823	+	31.5795i	0.276810	+	1.07810i
$859$	−9.70682	−	5.33637i	−0.331193	−	0.182075i	0.307478	−	0.951555i	$-0.400515\pi$
$859$	−9.70682	−	5.33637i	−0.331193	−	0.182075i	−0.638670	+	0.769481i	$0.720515\pi$
$860$		0			0
$861$	2.81315	+	14.7470i	0.0958719	+	0.502578i
$862$	−25.7120	−	4.90483i	−0.875755	−	0.167059i
$863$	−45.1626	+	21.2519i	−1.53735	+	0.723423i	−0.993293	−	0.115624i	$-0.963113\pi$
$863$	−45.1626	+	21.2519i	−1.53735	+	0.723423i	−0.544059	+	0.839047i	$0.683113\pi$
$864$	7.88589	+	0.996220i	0.268283	+	0.0338921i
$865$		0			0
$866$	4.55677	−	23.8874i	0.154845	−	0.811728i
$867$	−6.78127	+	17.1275i	−0.230304	+	0.581682i
$868$	−0.204191	+	0.0663458i	−0.00693071	+	0.00225192i
$869$	−17.6305	−	27.7813i	−0.598075	−	0.942416i
$870$		0			0
$871$	−27.1040	−	6.95911i	−0.918382	−	0.235801i
$872$	−31.7140	+	26.2361i	−1.07397	+	0.888467i
$873$	−2.22769	+	17.6340i	−0.0753960	+	0.596821i
$874$	−2.61236			−0.0883643
$875$		0			0
$876$	−2.54229			−0.0858959
$877$	0.876205	−	6.93588i	0.0295873	−	0.234208i	−0.970386	−	0.241561i	$-0.922341\pi$
$877$	0.876205	−	6.93588i	0.0295873	−	0.234208i	0.999973	+	0.00735316i	$0.00234060\pi$
$878$	19.2029	−	15.8861i	0.648068	−	0.536128i
$879$	30.2528	+	7.76761i	1.02040	+	0.261995i
$880$		0			0
$881$	−21.7097	−	34.2090i	−0.731419	−	1.15253i	−0.982805	−	0.184645i	$-0.940886\pi$
$881$	−21.7097	−	34.2090i	−0.731419	−	1.15253i	0.251386	−	0.967887i	$-0.419114\pi$
$882$	12.2740	−	3.98807i	0.413287	−	0.134285i
$883$	0.321501	−	0.812018i	0.0108194	−	0.0273266i	−0.924266	−	0.381748i	$-0.875322\pi$
$883$	0.321501	−	0.812018i	0.0108194	−	0.0273266i	0.935086	+	0.354422i	$0.115322\pi$
$884$	−0.00524164	+	0.0274776i	−0.000176295	+	0.000924173i
$885$		0			0
$886$	19.9834	+	2.52449i	0.671354	+	0.0848118i
$887$	−17.0651	+	8.03024i	−0.572991	+	0.269629i	−0.690368	−	0.723458i	$-0.742551\pi$
$887$	−17.0651	+	8.03024i	−0.572991	+	0.269629i	0.117377	+	0.993087i	$0.462551\pi$
$888$	5.61661	+	1.07142i	0.188481	+	0.0359547i
$889$	2.45535	+	12.8714i	0.0823499	+	0.431693i
$890$		0			0
$891$	−0.625404	−	0.343819i	−0.0209518	−	0.0115184i
$892$	0.186484	+	0.726308i	0.00624395	+	0.0243186i
$893$	−1.14545	−	0.372179i	−0.0383310	−	0.0124545i
$894$	−12.9073	+	15.6023i	−0.431685	+	0.521818i
$895$		0			0
$896$	5.80061	−	9.14029i	0.193785	−	0.305356i
$897$	15.0769	−	58.7208i	0.503405	−	1.96063i
$898$	−23.2802	+	24.7909i	−0.776871	+	0.827284i
$899$	−1.33858	−	4.11972i	−0.0446441	−	0.137400i
$900$		0			0
$901$	0.0361303	−	0.111198i	0.00120367	−	0.00370453i
$902$	−25.9739	−	47.2464i	−0.864837	−	1.57313i
$903$	−3.94947	+	0.248480i	−0.131430	+	0.00826889i
$904$	1.14575	+	18.2112i	0.0381072	+	0.605696i
$905$		0			0
$906$	−10.9719	+	2.81711i	−0.364517	+	0.0935921i
$907$	−3.14888	+	4.33406i	−0.104557	+	0.143910i	−0.858089	−	0.513501i	$-0.828348\pi$
$907$	−3.14888	+	4.33406i	−0.104557	+	0.143910i	0.753532	+	0.657411i	$0.228348\pi$
$908$	3.50243	−	2.22271i	0.116232	−	0.0737632i
$909$	−28.3633	+	3.58312i	−0.940751	+	0.118844i
$910$		0			0
$911$	−0.0341816	+	0.0726395i	−0.00113249	+	0.00240665i	−0.905392	−	0.424576i	$-0.860423\pi$
$911$	−0.0341816	+	0.0726395i	−0.00113249	+	0.00240665i	0.904260	+	0.426982i	$0.140423\pi$
$912$	0.380621	−	0.692347i	0.0126036	−	0.0229259i
$913$	−11.3489	−	12.0854i	−0.375595	−	0.399968i
$914$	−7.07872	+	3.89156i	−0.234143	+	0.128721i
$915$		0			0
$916$	−1.12011	+	1.05186i	−0.0370096	+	0.0347543i
$917$	0.424081	+	0.350830i	0.0140044	+	0.0115854i
$918$	0.0688758	+	0.0947994i	0.00227324	+	0.00312885i
$919$	22.3730	+	8.85811i	0.738018	+	0.292202i	0.706900	−	0.707314i	$-0.250093\pi$
$919$	22.3730	+	8.85811i	0.738018	+	0.292202i	0.0311181	+	0.999516i	$0.490093\pi$
$920$		0			0
$921$	15.6703	+	18.9421i	0.516352	+	0.624163i
$922$	13.7325	+	34.6845i	0.452257	+	1.14227i
$923$	61.4022	−	11.7131i	2.02108	−	0.385542i
$924$	1.14087	−	0.828890i	0.0375318	−	0.0272685i
$925$		0			0
$926$	−42.9884	−	31.2329i	−1.41269	−	1.02638i
$927$	5.38529	+	2.53412i	0.176876	+	0.0832316i
$928$	−8.93316	−	5.66916i	−0.293245	−	0.186099i
$929$	21.2556	−	8.41569i	0.697374	−	0.276110i	0.00742959	−	0.999972i	$-0.497635\pi$
$929$	21.2556	−	8.41569i	0.697374	−	0.276110i	0.689944	+	0.723863i	$0.257635\pi$
$930$		0			0
$931$	−0.0726878	+	1.15534i	−0.00238225	+	0.0378647i
$932$			5.71920i			0.187339i
$933$	−19.8093	−	1.24630i	−0.648527	−	0.0408019i
$934$	3.48420	+	7.40431i	0.114007	+	0.242276i
$935$		0			0
$936$	−24.1054	−	22.6365i	−0.787910	−	0.739896i
$937$	1.89946	+	15.0358i	0.0620527	+	0.491198i	0.992261	+	0.124167i	$0.0396258\pi$
$937$	1.89946	+	15.0358i	0.0620527	+	0.491198i	−0.930209	+	0.367031i	$0.880374\pi$
$938$	−0.969268	−	7.67254i	−0.0316477	−	0.250517i
$939$	9.30204	+	8.73519i	0.303561	+	0.285062i
$940$		0			0
$941$	−19.9554	−	42.4075i	−0.650529	−	1.38244i	−0.909151	−	0.416466i	$-0.863269\pi$
$941$	−19.9554	−	42.4075i	−0.650529	−	1.38244i	0.258622	−	0.965978i	$-0.416731\pi$
$942$	−13.3891	−	0.842370i	−0.436240	−	0.0274459i
$943$			100.254i			3.26471i
$944$	−1.02607	+	16.3089i	−0.0333957	+	0.530809i
$945$		0			0
$946$	13.2136	−	5.23163i	0.429611	−	0.170095i
$947$	−6.31667	−	4.00868i	−0.205264	−	0.130265i	0.429221	−	0.903199i	$-0.358788\pi$
$947$	−6.31667	−	4.00868i	−0.205264	−	0.130265i	−0.634486	+	0.772935i	$0.718788\pi$
$948$	−2.31477	−	1.08925i	−0.0751801	−	0.0353771i
$949$	42.5365	+	30.9046i	1.38079	+	1.00320i
$950$		0			0
$951$	2.52605	−	1.83528i	0.0819126	−	0.0595130i
$952$	−0.0637090	+	0.0121531i	−0.00206482	+	0.000393885i
$953$	4.74863	+	11.9937i	0.153823	+	0.388513i	0.986169	−	0.165744i	$-0.0530025\pi$
$953$	4.74863	+	11.9937i	0.153823	+	0.388513i	−0.832346	+	0.554257i	$0.813002\pi$
$954$	10.5013	+	12.6939i	0.339992	+	0.410980i
$955$		0			0
$956$	−1.71965	−	0.680857i	−0.0556174	−	0.0220205i
$957$	16.7235	+	23.0179i	0.540594	+	0.744064i
$958$	−42.4041	−	35.0798i	−1.37002	−	1.13338i
$959$	0.568957	−	0.534286i	0.0183726	−	0.0172530i
$960$		0			0
$961$	−26.8261	+	14.7478i	−0.865359	+	0.475735i
$962$	−9.64892	−	10.2751i	−0.311094	−	0.331281i
$963$	−16.3986	+	29.8289i	−0.528437	+	0.961223i
$964$	−2.01031	+	4.27213i	−0.0647478	+	0.137596i
$965$		0			0
$966$	16.6226	−	2.09992i	0.534823	−	0.0675639i
$967$	13.0656	−	8.29170i	0.420162	−	0.266643i	−0.308895	−	0.951096i	$-0.599959\pi$
$967$	13.0656	−	8.29170i	0.420162	−	0.266643i	0.729057	+	0.684453i	$0.239959\pi$
$968$	−5.66717	+	7.80019i	−0.182150	+	0.250708i
$969$	−0.00385170		0.000988949i	−0.000123735		3.17696e-5i
$970$		0			0
$971$	0.389787	+	6.19549i	0.0125089	+	0.198823i	0.999318	+	0.0369331i	$0.0117589\pi$
$971$	0.389787	+	6.19549i	0.0125089	+	0.198823i	−0.986809	+	0.161890i	$0.948241\pi$
$972$	4.18219	−	0.263121i	0.134144	−	0.00843961i
$973$	1.75679	+	3.19559i	0.0563201	+	0.102446i
$974$	−2.94826	+	9.07382i	−0.0944685	+	0.290744i
$975$		0			0
$976$	3.13297	+	9.64230i	0.100284	+	0.308643i
$977$	−6.31426	+	6.72400i	−0.202011	+	0.215120i	−0.821995	−	0.569494i	$-0.807139\pi$
$977$	−6.31426	+	6.72400i	−0.202011	+	0.215120i	0.619984	+	0.784614i	$0.287139\pi$
$978$	−2.06306	+	8.03507i	−0.0659692	+	0.256933i
$979$	6.24664	−	9.84312i	0.199643	−	0.314588i
$980$		0			0
$981$	−16.0419	+	19.3913i	−0.512179	+	0.619118i
$982$	25.6134	+	8.32228i	0.817355	+	0.265575i
$983$	6.22467	+	24.2435i	0.198536	+	0.773247i	0.987342	+	0.158605i	$0.0506997\pi$
$983$	6.22467	+	24.2435i	0.198536	+	0.773247i	−0.788806	+	0.614642i	$0.789300\pi$
$984$	−30.8183	−	16.9425i	−0.982451	−	0.540107i
$985$		0			0
$986$	−0.0292267	−	0.153212i	−0.000930767	−	0.00487925i
$987$	7.58775	+	1.44744i	0.241521	+	0.0460725i
$988$	0.319903	−	0.150535i	0.0101775	−	0.00478916i
$989$	−26.2175	−	3.31205i	−0.833669	−	0.105317i
$990$		0			0
$991$	−8.79859	+	46.1238i	−0.279496	+	1.46517i	0.514627	+	0.857414i	$0.327931\pi$
$991$	−8.79859	+	46.1238i	−0.279496	+	1.46517i	−0.794123	+	0.607757i	$0.792069\pi$
$992$	0.348221	−	0.879506i	0.0110560	−	0.0279244i
$993$	26.4466	−	8.59304i	0.839259	−	0.272692i
$994$	9.25661	+	14.5861i	0.293602	+	0.462643i
$995$		0			0
$996$	−1.24850	−	0.320561i	−0.0395603	−	0.0101574i
$997$	41.1892	−	34.0746i	1.30447	−	1.07915i	0.312876	−	0.949794i	$-0.398708\pi$
$997$	41.1892	−	34.0746i	1.30447	−	1.07915i	0.991598	−	0.129361i	$-0.0412925\pi$
$998$	2.34625	−	18.5725i	0.0742693	−	0.587902i
$999$	9.24083			0.292367

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.h.a.174.4		240
5.2	odd	4		625.2.g.b.451.7		480
5.3	odd	4		625.2.g.b.451.18		480
5.4	even	2		125.2.h.a.109.9	yes	240
125.27	odd	100		625.2.g.b.176.7		480
125.39	even	50	inner	625.2.h.a.449.4		240
125.86	even	25		125.2.h.a.39.9	✓	240
125.98	odd	100		625.2.g.b.176.18		480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.h.a.39.9	✓	240	125.86	even	25
125.2.h.a.109.9	yes	240	5.4	even	2
625.2.g.b.176.7		480	125.27	odd	100
625.2.g.b.176.18		480	125.98	odd	100
625.2.g.b.451.7		480	5.2	odd	4
625.2.g.b.451.18		480	5.3	odd	4
625.2.h.a.174.4		240	1.1	even	1	trivial
625.2.h.a.449.4		240	125.39	even	50	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:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.h (of order \(50\), degree \(20\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.164819 + 1.30468i) q^{2} +(-0.834940 + 0.690722i) q^{3} +(0.262149 + 0.0673084i) q^{4} +(-0.763556 - 1.20317i) q^{6} +(1.21231 - 0.393902i) q^{7} +(-1.09922 + 2.77633i) q^{8} +(-0.342117 + 1.79344i) q^{9} +O(q^{10})\)	\(q+(-0.164819 + 1.30468i) q^{2} +(-0.834940 + 0.690722i) q^{3} +(0.262149 + 0.0673084i) q^{4} +(-0.763556 - 1.20317i) q^{6} +(1.21231 - 0.393902i) q^{7} +(-1.09922 + 2.77633i) q^{8} +(-0.342117 + 1.79344i) q^{9} +(-3.74238 - 0.472772i) q^{11} +(-0.265370 + 0.124874i) q^{12} +(5.95805 + 1.13656i) q^{13} +(0.314104 + 1.64659i) q^{14} +(-2.96669 - 1.63095i) q^{16} +(0.00423762 + 0.0165044i) q^{17} +(-2.28347 - 0.741945i) q^{18} +(0.137279 - 0.165942i) q^{19} +(-0.740126 + 1.16625i) q^{21} +(1.23363 - 4.80467i) q^{22} +(-6.31419 + 6.72393i) q^{23} +(-0.999883 - 3.07732i) q^{24} +(-2.46484 + 7.58601i) q^{26} +(-2.51923 - 4.58246i) q^{27} +(0.344318 - 0.0216626i) q^{28} +(0.437061 + 6.94688i) q^{29} +(-0.602769 + 0.154765i) q^{31} +(-0.893439 + 1.22971i) q^{32} +(3.45121 - 2.19021i) q^{33} +(-0.0222314 + 0.00280848i) q^{34} +(-0.210399 + 0.447121i) q^{36} +(-0.851322 + 1.54855i) q^{37} +(0.193875 + 0.206456i) q^{38} +(-5.75966 + 3.16640i) q^{39} +(7.92308 - 7.44027i) q^{41} +(-1.39960 - 1.15785i) q^{42} +(1.68397 + 2.31778i) q^{43} +(-0.949239 - 0.375830i) q^{44} +(-7.73186 - 9.34622i) q^{46} +(-2.05868 - 5.19962i) q^{47} +(3.60354 - 0.687412i) q^{48} +(-4.34859 + 3.15944i) q^{49} +(-0.0149382 - 0.0108532i) q^{51} +(1.48540 + 0.698974i) q^{52} +(-5.79344 - 3.67663i) q^{53} +(6.39385 - 2.53150i) q^{54} +(-0.238997 + 3.79875i) q^{56} +0.233374i q^{57} +(-9.13547 - 0.574755i) q^{58} +(-2.05519 - 4.36749i) q^{59} +(-2.18307 - 2.05004i) q^{61} +(-0.102570 - 0.811927i) q^{62} +(0.291689 + 2.30896i) q^{63} +(-6.39289 - 6.00332i) q^{64} +(2.28869 + 4.86371i) q^{66} +(-4.60439 - 0.289684i) q^{67} +0.00461185i q^{68} +(0.627601 - 9.97543i) q^{69} +(9.58206 - 3.79380i) q^{71} +(-4.60311 - 2.92122i) q^{72} +(7.84339 + 3.69082i) q^{73} +(-1.88004 - 1.36593i) q^{74} +(0.0471569 - 0.0342615i) q^{76} +(-4.72314 + 0.900987i) q^{77} +(-3.18183 - 8.03638i) q^{78} +(5.56012 + 6.72103i) q^{79} +(0.175913 + 0.0696488i) q^{81} +(8.40127 + 11.5634i) q^{82} +(3.38646 + 2.80153i) q^{83} +(-0.272522 + 0.255915i) q^{84} +(-3.30151 + 1.81502i) q^{86} +(-5.16329 - 5.49834i) q^{87} +(5.42628 - 9.87038i) q^{88} +(-1.31589 + 2.79641i) q^{89} +(7.67068 - 0.969032i) q^{91} +(-2.10784 + 1.33767i) q^{92} +(0.396376 - 0.545565i) q^{93} +(7.12313 - 1.82891i) q^{94} +(-0.103423 - 1.64386i) q^{96} +(9.71591 - 0.611273i) q^{97} +(-3.40531 - 6.19424i) q^{98} +(2.12822 - 6.54998i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 20 q^{2} + 20 q^{3} - 20 q^{4} - 20 q^{6} + 25 q^{7} + 35 q^{8} - 20 q^{9}+O(q^{10}) \) 240 * q + 20 * q^2 + 20 * q^3 - 20 * q^4 - 20 * q^6 + 25 * q^7 + 35 * q^8 - 20 * q^9	\( 240 q + 20 q^{2} + 20 q^{3} - 20 q^{4} - 20 q^{6} + 25 q^{7} + 35 q^{8} - 20 q^{9} - 25 q^{11} - 60 q^{12} + 20 q^{13} - 30 q^{14} - 40 q^{16} + 15 q^{17} + 25 q^{18} - 10 q^{19} - 35 q^{21} + 25 q^{22} - 70 q^{23} + 15 q^{24} - 45 q^{26} + 20 q^{27} + 10 q^{28} - 10 q^{29} - 30 q^{31} + 25 q^{32} + 35 q^{33} - 20 q^{34} + 170 q^{36} + 55 q^{37} + 40 q^{38} - 35 q^{41} + 10 q^{42} + 25 q^{43} + 15 q^{44} - 40 q^{46} - 100 q^{47} - 5 q^{48} + 35 q^{49} - 55 q^{51} + 15 q^{52} + 15 q^{53} + 30 q^{54} + 65 q^{56} - 255 q^{58} + 5 q^{59} - 40 q^{61} - 5 q^{62} + 35 q^{63} + 25 q^{64} - 95 q^{66} - 105 q^{67} - 10 q^{69} + 45 q^{71} + 30 q^{72} + 40 q^{73} + 35 q^{74} - 65 q^{76} + 35 q^{77} - 100 q^{78} - 95 q^{81} - 175 q^{82} - 20 q^{83} + 45 q^{84} - 80 q^{86} + 5 q^{87} + 5 q^{88} + 30 q^{89} + 65 q^{91} + 55 q^{92} - 275 q^{93} + 60 q^{94} - 135 q^{96} - 35 q^{97} + 15 q^{98} + 45 q^{99}+O(q^{100}) \) 240 * q + 20 * q^2 + 20 * q^3 - 20 * q^4 - 20 * q^6 + 25 * q^7 + 35 * q^8 - 20 * q^9 - 25 * q^11 - 60 * q^12 + 20 * q^13 - 30 * q^14 - 40 * q^16 + 15 * q^17 + 25 * q^18 - 10 * q^19 - 35 * q^21 + 25 * q^22 - 70 * q^23 + 15 * q^24 - 45 * q^26 + 20 * q^27 + 10 * q^28 - 10 * q^29 - 30 * q^31 + 25 * q^32 + 35 * q^33 - 20 * q^34 + 170 * q^36 + 55 * q^37 + 40 * q^38 - 35 * q^41 + 10 * q^42 + 25 * q^43 + 15 * q^44 - 40 * q^46 - 100 * q^47 - 5 * q^48 + 35 * q^49 - 55 * q^51 + 15 * q^52 + 15 * q^53 + 30 * q^54 + 65 * q^56 - 255 * q^58 + 5 * q^59 - 40 * q^61 - 5 * q^62 + 35 * q^63 + 25 * q^64 - 95 * q^66 - 105 * q^67 - 10 * q^69 + 45 * q^71 + 30 * q^72 + 40 * q^73 + 35 * q^74 - 65 * q^76 + 35 * q^77 - 100 * q^78 - 95 * q^81 - 175 * q^82 - 20 * q^83 + 45 * q^84 - 80 * q^86 + 5 * q^87 + 5 * q^88 + 30 * q^89 + 65 * q^91 + 55 * q^92 - 275 * q^93 + 60 * q^94 - 135 * q^96 - 35 * q^97 + 15 * q^98 + 45 * q^99

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