LMFDB - Embedded newform 875.2.q.a.401.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [875,2,Mod(51,875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(875, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([24, 10]))

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

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

chi := DirichletCharacter("875.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.q (of order $15$, degree $8$, 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:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			401.7
Character	$\chi$	$=$	875.401
Dual form			875.2.q.a.851.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.868806 - 0.184670i) q^{2} +(1.20920 + 0.538368i) q^{3} +(-1.10637 - 0.492588i) q^{4} +(-0.951135 - 0.691040i) q^{6} +(-1.95148 + 1.78654i) q^{7} +(2.30742 + 1.67644i) q^{8} +(-0.835080 - 0.927450i) q^{9} +O(q^{10})$	\(q+(-0.868806 - 0.184670i) q^{2} +(1.20920 + 0.538368i) q^{3} +(-1.10637 - 0.492588i) q^{4} +(-0.951135 - 0.691040i) q^{6} +(-1.95148 + 1.78654i) q^{7} +(2.30742 + 1.67644i) q^{8} +(-0.835080 - 0.927450i) q^{9} +(2.34038 - 2.59925i) q^{11} +(-1.07262 - 1.19127i) q^{12} +(1.01791 - 3.13281i) q^{13} +(2.02538 - 1.19177i) q^{14} +(-0.0743764 - 0.0826034i) q^{16} +(-0.157801 + 1.50138i) q^{17} +(0.554249 + 0.959988i) q^{18} +(-4.59560 + 2.04609i) q^{19} +(-3.32154 + 1.10966i) q^{21} +(-2.51334 + 1.82605i) q^{22} +(-2.18442 - 0.464312i) q^{23} +(1.88758 + 3.26938i) q^{24} +(-1.46290 + 2.53382i) q^{26} +(-1.73754 - 5.34759i) q^{27} +(3.03909 - 1.01530i) q^{28} +(7.71611 - 5.60608i) q^{29} +(0.622401 - 5.92175i) q^{31} +(-2.80276 - 4.85452i) q^{32} +(4.22933 - 1.88302i) q^{33} +(0.414359 - 1.27526i) q^{34} +(0.467057 + 1.43745i) q^{36} +(2.74991 + 3.05409i) q^{37} +(4.37054 - 0.928986i) q^{38} +(2.91746 - 3.24016i) q^{39} +(3.20915 - 9.87674i) q^{41} +(3.09069 - 0.350685i) q^{42} +0.679370 q^{43} +(-3.86968 + 1.72289i) q^{44} +(1.81209 + 0.806794i) q^{46} +(-0.321738 - 3.06114i) q^{47} +(-0.0454646 - 0.139926i) q^{48} +(0.616571 - 6.97279i) q^{49} +(-0.999107 + 1.73050i) q^{51} +(-2.66937 + 2.96463i) q^{52} +(0.128670 + 0.0572874i) q^{53} +(0.522041 + 4.96688i) q^{54} +(-7.49790 + 0.850749i) q^{56} -6.65853 q^{57} +(-7.73908 + 3.44566i) q^{58} +(0.992644 - 0.210993i) q^{59} +(-2.13396 - 0.453587i) q^{61} +(-1.63432 + 5.02991i) q^{62} +(3.28657 + 0.318002i) q^{63} +(1.60726 + 4.94665i) q^{64} +(-4.02220 + 0.854945i) q^{66} +(1.28814 - 12.2559i) q^{67} +(0.914148 - 1.58335i) q^{68} +(-2.39141 - 1.73746i) q^{69} +(-6.09102 + 4.42539i) q^{71} +(-0.372066 - 3.53997i) q^{72} +(-6.92117 + 7.68673i) q^{73} +(-1.82514 - 3.16123i) q^{74} +6.09232 q^{76} +(0.0764540 + 9.25356i) q^{77} +(-3.13306 + 2.27630i) q^{78} +(-0.998425 - 9.49938i) q^{79} +(0.386594 - 3.67820i) q^{81} +(-4.61207 + 7.98834i) q^{82} +(-4.18519 - 3.04072i) q^{83} +(4.22146 + 0.408460i) q^{84} +(-0.590240 - 0.125459i) q^{86} +(12.3484 - 2.62474i) q^{87} +(9.75770 - 2.07406i) q^{88} +(10.8714 + 2.31079i) q^{89} +(3.61044 + 7.93215i) q^{91} +(2.18806 + 1.58972i) q^{92} +(3.94069 - 6.82547i) q^{93} +(-0.285773 + 2.71895i) q^{94} +(-0.775562 - 7.37898i) q^{96} +(13.0272 - 9.46481i) q^{97} +(-1.82335 + 5.94414i) q^{98} -4.36507 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 3 q^{2} + 3 q^{3} + 13 q^{4} - 12 q^{6} + 22 q^{7} + 2 q^{8} + 11 q^{9}+O(q^{10}) $ 144 * q + 3 * q^2 + 3 * q^3 + 13 * q^4 - 12 * q^6 + 22 * q^7 + 2 * q^8 + 11 * q^9	$ 144 q + 3 q^{2} + 3 q^{3} + 13 q^{4} - 12 q^{6} + 22 q^{7} + 2 q^{8} + 11 q^{9} - 6 q^{11} + 11 q^{12} + 12 q^{13} - 6 q^{14} + 13 q^{16} - 9 q^{17} + 18 q^{18} - 11 q^{19} - 3 q^{21} + 52 q^{22} + 17 q^{23} + 46 q^{24} + 44 q^{26} + 84 q^{27} - 62 q^{28} - 24 q^{29} - 21 q^{31} + 16 q^{32} + 18 q^{33} - 36 q^{34} - 104 q^{36} + 5 q^{37} + 12 q^{38} + 25 q^{39} + 38 q^{41} + 58 q^{42} - 20 q^{43} - 7 q^{44} + 21 q^{46} + q^{47} + 12 q^{48} - 38 q^{49} - 8 q^{51} - 50 q^{52} - 37 q^{53} + 15 q^{54} - 60 q^{56} - 136 q^{57} - 53 q^{58} - 39 q^{59} - 13 q^{61} - 124 q^{62} - 75 q^{63} + 42 q^{64} + 7 q^{66} + 13 q^{67} + 110 q^{68} + 50 q^{69} + 22 q^{71} + 18 q^{72} + 41 q^{73} - 10 q^{74} - 276 q^{76} - 37 q^{77} - 2 q^{78} + 9 q^{79} + 57 q^{81} + 108 q^{82} - 86 q^{83} - 29 q^{84} - 17 q^{86} + 7 q^{87} + 26 q^{88} - 42 q^{89} - 34 q^{91} + 62 q^{92} - 98 q^{93} - 11 q^{94} + 13 q^{96} - 96 q^{97} + 86 q^{98} - 68 q^{99}+O(q^{100}) $ 144 * q + 3 * q^2 + 3 * q^3 + 13 * q^4 - 12 * q^6 + 22 * q^7 + 2 * q^8 + 11 * q^9 - 6 * q^11 + 11 * q^12 + 12 * q^13 - 6 * q^14 + 13 * q^16 - 9 * q^17 + 18 * q^18 - 11 * q^19 - 3 * q^21 + 52 * q^22 + 17 * q^23 + 46 * q^24 + 44 * q^26 + 84 * q^27 - 62 * q^28 - 24 * q^29 - 21 * q^31 + 16 * q^32 + 18 * q^33 - 36 * q^34 - 104 * q^36 + 5 * q^37 + 12 * q^38 + 25 * q^39 + 38 * q^41 + 58 * q^42 - 20 * q^43 - 7 * q^44 + 21 * q^46 + q^47 + 12 * q^48 - 38 * q^49 - 8 * q^51 - 50 * q^52 - 37 * q^53 + 15 * q^54 - 60 * q^56 - 136 * q^57 - 53 * q^58 - 39 * q^59 - 13 * q^61 - 124 * q^62 - 75 * q^63 + 42 * q^64 + 7 * q^66 + 13 * q^67 + 110 * q^68 + 50 * q^69 + 22 * q^71 + 18 * q^72 + 41 * q^73 - 10 * q^74 - 276 * q^76 - 37 * q^77 - 2 * q^78 + 9 * q^79 + 57 * q^81 + 108 * q^82 - 86 * q^83 - 29 * q^84 - 17 * q^86 + 7 * q^87 + 26 * q^88 - 42 * q^89 - 34 * q^91 + 62 * q^92 - 98 * q^93 - 11 * q^94 + 13 * q^96 - 96 * q^97 + 86 * q^98 - 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.868806	−	0.184670i	−0.614338	−	0.130582i	−0.109775	−	0.993956i	$-0.535013\pi$
$2$	−0.868806	−	0.184670i	−0.614338	−	0.130582i	−0.504563	+	0.863375i	$0.668346\pi$
$3$	1.20920	+	0.538368i	0.698129	+	0.310827i	0.724939	−	0.688813i	$-0.241868\pi$
$3$	1.20920	+	0.538368i	0.698129	+	0.310827i	−0.0268095	+	0.999641i	$0.508535\pi$
$4$	−1.10637	−	0.492588i	−0.553185	−	0.246294i
$5$		0			0
$5$		0			0
$6$	−0.951135	−	0.691040i	−0.388299	−	0.282116i
$7$	−1.95148	+	1.78654i	−0.737591	+	0.675248i
$7$	−1.95148	+	1.78654i	−0.737591	+	0.675248i
$8$	2.30742	+	1.67644i	0.815795	+	0.592710i
$9$	−0.835080	−	0.927450i	−0.278360	−	0.309150i
$10$		0			0
$11$	2.34038	−	2.59925i	0.705650	−	0.783704i	−0.278615	−	0.960403i	$-0.589875\pi$
$11$	2.34038	−	2.59925i	0.705650	−	0.783704i	0.984265	+	0.176699i	$0.0565420\pi$
$12$	−1.07262	−	1.19127i	−0.309640	−	0.343890i
$13$	1.01791	−	3.13281i	0.282318	−	0.868884i	−0.704872	−	0.709334i	$-0.748996\pi$
$13$	1.01791	−	3.13281i	0.282318	−	0.868884i	0.987190	−	0.159550i	$-0.0510043\pi$
$14$	2.02538	−	1.19177i	0.541306	−	0.318515i
$15$		0			0
$16$	−0.0743764	−	0.0826034i	−0.0185941	−	0.0206508i
$17$	−0.157801	+	1.50138i	−0.0382724	+	0.364138i	0.958578	+	0.284831i	$0.0919374\pi$
$17$	−0.157801	+	1.50138i	−0.0382724	+	0.364138i	−0.996850	+	0.0793070i	$0.974729\pi$
$18$	0.554249	+	0.959988i	0.130638	+	0.226271i
$19$	−4.59560	+	2.04609i	−1.05430	+	0.469406i	−0.859340	−	0.511405i	$-0.829125\pi$
$19$	−4.59560	+	2.04609i	−1.05430	+	0.469406i	−0.194963	+	0.980811i	$0.562459\pi$
$20$		0			0
$21$	−3.32154	+	1.10966i	−0.724819	+	0.242147i
$22$	−2.51334	+	1.82605i	−0.535845	+	0.389314i
$23$	−2.18442	−	0.464312i	−0.455482	−	0.0968157i	−0.0255433	−	0.999674i	$-0.508132\pi$
$23$	−2.18442	−	0.464312i	−0.455482	−	0.0968157i	−0.429939	+	0.902858i	$0.641465\pi$
$24$	1.88758	+	3.26938i	0.385300	+	0.667359i
$25$		0			0
$26$	−1.46290	+	2.53382i	−0.286899	+	0.496923i
$27$	−1.73754	−	5.34759i	−0.334389	−	1.02914i
$28$	3.03909	−	1.01530i	0.574334	−	0.191873i
$29$	7.71611	−	5.60608i	1.43285	−	1.04102i	0.443367	−	0.896340i	$-0.353784\pi$
$29$	7.71611	−	5.60608i	1.43285	−	1.04102i	0.989478	−	0.144683i	$-0.0462163\pi$
$30$		0			0
$31$	0.622401	−	5.92175i	0.111786	−	1.06358i	−0.784508	−	0.620118i	$-0.787085\pi$
$31$	0.622401	−	5.92175i	0.111786	−	1.06358i	0.896295	−	0.443459i	$-0.146249\pi$
$32$	−2.80276	−	4.85452i	−0.495463	−	0.858167i
$33$	4.22933	−	1.88302i	0.736231	−	0.327791i
$34$	0.414359	−	1.27526i	0.0710619	−	0.218706i
$35$		0			0
$36$	0.467057	+	1.43745i	0.0778428	+	0.239576i
$37$	2.74991	+	3.05409i	0.452083	+	0.502089i	0.925499	−	0.378750i	$-0.123646\pi$
$37$	2.74991	+	3.05409i	0.452083	+	0.502089i	−0.473416	+	0.880839i	$0.656979\pi$
$38$	4.37054	−	0.928986i	0.708994	−	0.150701i
$39$	2.91746	−	3.24016i	0.467167	−	0.518841i
$40$		0			0
$41$	3.20915	−	9.87674i	0.501185	−	1.54249i	−0.305906	−	0.952062i	$-0.598959\pi$
$41$	3.20915	−	9.87674i	0.501185	−	1.54249i	0.807091	−	0.590427i	$-0.201041\pi$
$42$	3.09069	−	0.350685i	0.476904	−	0.0541119i
$43$	0.679370			0.103603			0.0518015	−	0.998657i	$-0.483504\pi$
$43$	0.679370			0.103603			0.0518015	+	0.998657i	$0.483504\pi$
$44$	−3.86968	+	1.72289i	−0.583377	+	0.259736i
$45$		0			0
$46$	1.81209	+	0.806794i	0.267178	+	0.118955i
$47$	−0.321738	−	3.06114i	−0.0469304	−	0.446513i	−0.992604	−	0.121396i	$-0.961263\pi$
$47$	−0.321738	−	3.06114i	−0.0469304	−	0.446513i	0.945674	−	0.325117i	$-0.105404\pi$
$48$	−0.0454646	−	0.139926i	−0.00656224	−	0.0201965i
$49$	0.616571	−	6.97279i	0.0880816	−	0.996113i
$50$		0			0
$51$	−0.999107	+	1.73050i	−0.139903	+	0.242319i
$52$	−2.66937	+	2.96463i	−0.370175	+	0.411121i
$53$	0.128670	+	0.0572874i	0.0176741	+	0.00786902i	0.415555	−	0.909568i	$-0.363587\pi$
$53$	0.128670	+	0.0572874i	0.0176741	+	0.00786902i	−0.397881	+	0.917437i	$0.630254\pi$
$54$	0.522041	+	4.96688i	0.0710407	+	0.675907i
$55$		0			0
$56$	−7.49790	+	0.850749i	−1.00195	+	0.113686i
$57$	−6.65853			−0.881944
$58$	−7.73908	+	3.44566i	−1.01619	+	0.452437i
$59$	0.992644	−	0.210993i	0.129231	−	0.0274689i	−0.142842	−	0.989746i	$-0.545624\pi$
$59$	0.992644	−	0.210993i	0.129231	−	0.0274689i	0.272073	+	0.962277i	$0.412291\pi$
$60$		0			0
$61$	−2.13396	−	0.453587i	−0.273226	−	0.0580759i	0.0692611	−	0.997599i	$-0.477936\pi$
$61$	−2.13396	−	0.453587i	−0.273226	−	0.0580759i	−0.342487	+	0.939523i	$0.611269\pi$
$62$	−1.63432	+	5.02991i	−0.207558	+	0.638799i
$63$	3.28657	+	0.318002i	0.414068	+	0.0400645i
$64$	1.60726	+	4.94665i	0.200908	+	0.618331i
$65$		0			0
$66$	−4.02220	+	0.854945i	−0.495099	+	0.105236i
$67$	1.28814	−	12.2559i	0.157372	−	1.49729i	−0.575991	−	0.817456i	$-0.695384\pi$
$67$	1.28814	−	12.2559i	0.157372	−	1.49729i	0.733363	−	0.679838i	$-0.237950\pi$
$68$	0.914148	−	1.58335i	0.110857	−	0.192009i
$69$	−2.39141	−	1.73746i	−0.287892	−	0.209166i
$70$		0			0
$71$	−6.09102	+	4.42539i	−0.722871	+	0.525197i	−0.887300	−	0.461192i	$-0.847422\pi$
$71$	−6.09102	+	4.42539i	−0.722871	+	0.525197i	0.164429	+	0.986389i	$0.447422\pi$
$72$	−0.372066	−	3.53997i	−0.0438484	−	0.417190i
$73$	−6.92117	+	7.68673i	−0.810061	+	0.899664i	−0.996567	−	0.0827898i	$-0.973617\pi$
$73$	−6.92117	+	7.68673i	−0.810061	+	0.899664i	0.186506	+	0.982454i	$0.440284\pi$
$74$	−1.82514	−	3.16123i	−0.212168	−	0.367486i
$75$		0			0
$76$	6.09232			0.698837
$77$	0.0764540	+	9.25356i	0.00871274	+	1.05454i
$78$	−3.13306	+	2.27630i	−0.354750	+	0.257741i
$79$	−0.998425	−	9.49938i	−0.112332	−	1.06876i	−0.894921	−	0.446225i	$-0.852768\pi$
$79$	−0.998425	−	9.49938i	−0.112332	−	1.06876i	0.782589	−	0.622538i	$-0.213899\pi$
$80$		0			0
$81$	0.386594	−	3.67820i	0.0429549	−	0.408689i
$82$	−4.61207	+	7.98834i	−0.509318	+	0.882164i
$83$	−4.18519	−	3.04072i	−0.459384	−	0.333762i	0.333906	−	0.942607i	$-0.391633\pi$
$83$	−4.18519	−	3.04072i	−0.459384	−	0.333762i	−0.793290	+	0.608844i	$0.791633\pi$
$84$	4.22146	+	0.408460i	0.460599	+	0.0445666i
$85$		0			0
$86$	−0.590240	−	0.125459i	−0.0636473	−	0.0135286i
$87$	12.3484	−	2.62474i	1.32389	−	0.281401i
$88$	9.75770	−	2.07406i	1.04017	−	0.221096i
$89$	10.8714	+	2.31079i	1.15237	+	0.244943i	0.744196	−	0.667961i	$-0.232833\pi$
$89$	10.8714	+	2.31079i	1.15237	+	0.244943i	0.408172	+	0.912905i	$0.366166\pi$
$90$		0			0
$91$	3.61044	+	7.93215i	0.378477	+	0.831516i
$92$	2.18806	+	1.58972i	0.228121	+	0.165740i
$93$	3.94069	−	6.82547i	0.408630	−	0.707768i
$94$	−0.285773	+	2.71895i	−0.0294752	+	0.280438i
$95$		0			0
$96$	−0.775562	−	7.37898i	−0.0791555	−	0.753114i
$97$	13.0272	−	9.46481i	1.32271	−	0.961006i	0.322817	−	0.946461i	$-0.395370\pi$
$97$	13.0272	−	9.46481i	1.32271	−	0.961006i	0.999894	−	0.0145450i	$-0.00462999\pi$
$98$	−1.82335	+	5.94414i	−0.184186	+	0.600449i
$99$	−4.36507			−0.438707
$100$		0			0
$101$	−2.95138	−	5.11194i	−0.293673	−	0.508657i	0.681002	−	0.732281i	$-0.261544\pi$
$101$	−2.95138	−	5.11194i	−0.293673	−	0.508657i	−0.974675	+	0.223625i	$0.928211\pi$
$102$	1.18760	−	1.31897i	0.117590	−	0.130597i
$103$	−1.40250	−	13.3439i	−0.138193	−	1.31482i	−0.815346	−	0.578974i	$-0.803453\pi$
$103$	−1.40250	−	13.3439i	−0.138193	−	1.31482i	0.677154	−	0.735842i	$-0.263213\pi$
$104$	7.60070	−	5.52223i	0.745310	−	0.541499i
$105$		0			0
$106$	−0.101210	−	0.0735330i	−0.00983034	−	0.00714216i
$107$	−1.72733	+	2.99182i	−0.166987	+	0.289230i	−0.937359	−	0.348364i	$-0.886737\pi$
$107$	−1.72733	+	2.99182i	−0.166987	+	0.289230i	0.770372	+	0.637595i	$0.220071\pi$
$108$	−0.711798	+	6.77230i	−0.0684928	+	0.651665i
$109$	−1.85729	+	0.394780i	−0.177896	+	0.0378130i	−0.295998	−	0.955188i	$-0.595652\pi$
$109$	−1.85729	+	0.394780i	−0.177896	+	0.0378130i	0.118102	+	0.993001i	$0.462319\pi$
$110$		0			0
$111$	1.68096	+	5.17345i	0.159549	+	0.491042i
$112$	0.292718	+	0.0283229i	0.0276593	+	0.00267626i
$113$	−5.92435	+	18.2333i	−0.557316	+	1.71524i	0.132431	+	0.991192i	$0.457722\pi$
$113$	−5.92435	+	18.2333i	−0.557316	+	1.71524i	−0.689747	+	0.724050i	$0.742278\pi$
$114$	5.78497	+	1.22963i	0.541812	+	0.115166i
$115$		0			0
$116$	−11.2984	+	2.40154i	−1.04903	+	0.222978i
$117$	−3.75556	+	1.67208i	−0.347201	+	0.154584i
$118$	−0.901379			−0.0829786
$119$	−2.37432	−	3.21183i	−0.217654	−	0.294428i
$120$		0			0
$121$	−0.128932	−	1.22671i	−0.0117211	−	0.111519i
$122$	1.77023	+	0.788159i	0.160269	+	0.0713565i
$123$	9.19781	−	10.2152i	0.829339	−	0.921074i
$124$	−3.60559	+	6.24506i	−0.323791	+	0.560823i
$125$		0			0
$126$	−2.79666	−	0.883213i	−0.249146	−	0.0786829i
$127$	1.97625	+	6.08228i	0.175364	+	0.539715i	0.999650	−	0.0264588i	$-0.00842307\pi$
$127$	1.97625	+	6.08228i	0.175364	+	0.539715i	−0.824286	+	0.566174i	$0.808423\pi$
$128$	0.688972	+	6.55513i	0.0608971	+	0.579397i
$129$	0.821491	+	0.365751i	0.0723282	+	0.0322026i
$130$		0			0
$131$	5.90681	−	2.62988i	0.516081	−	0.229774i	−0.132133	−	0.991232i	$-0.542183\pi$
$131$	5.90681	−	2.62988i	0.516081	−	0.229774i	0.648214	+	0.761458i	$0.275516\pi$
$132$	−5.60675			−0.488005
$133$	5.31281	−	12.2031i	0.460679	−	1.05814i
$134$	−3.38245	+	10.4101i	−0.292199	+	0.899295i
$135$		0			0
$136$	−2.88108	+	3.19976i	−0.247051	+	0.274377i
$137$	−6.91290	+	1.46938i	−0.590609	+	0.125538i	−0.493515	−	0.869737i	$-0.664288\pi$
$137$	−6.91290	+	1.46938i	−0.590609	+	0.125538i	−0.0970941	+	0.995275i	$0.530955\pi$
$138$	1.75682	+	1.95114i	0.149550	+	0.166092i
$139$	−0.276312	−	0.850401i	−0.0234365	−	0.0721301i	0.938654	−	0.344860i	$-0.112074\pi$
$139$	−0.276312	−	0.850401i	−0.0234365	−	0.0721301i	−0.962091	+	0.272730i	$0.912074\pi$
$140$		0			0
$141$	1.25897	−	3.87472i	0.106025	−	0.326311i
$142$	6.10915	−	2.71997i	0.512669	−	0.228255i
$143$	−5.76066	−	9.97775i	−0.481730	−	0.834381i
$144$	−0.0145003	+	0.137961i	−0.00120836	+	0.0114967i
$145$		0			0
$146$	7.43266	−	5.40014i	0.615131	−	0.446919i
$147$	4.49949	−	8.09952i	0.371111	−	0.668038i
$148$	−1.53802	−	4.73353i	−0.126424	−	0.389093i
$149$	−10.1562	+	17.5910i	−0.832025	+	1.44111i	0.0644051	+	0.997924i	$0.479485\pi$
$149$	−10.1562	+	17.5910i	−0.832025	+	1.44111i	−0.896430	+	0.443185i	$0.853848\pi$
$150$		0			0
$151$	9.63923	+	16.6956i	0.784429	+	1.35867i	0.929340	+	0.369226i	$0.120377\pi$
$151$	9.63923	+	16.6956i	0.784429	+	1.35867i	−0.144911	+	0.989445i	$0.546289\pi$
$152$	−14.0341	−	2.98304i	−1.13832	−	0.241957i
$153$	1.52423	−	1.10742i	0.123227	−	0.0895294i
$154$	1.64243	−	8.05367i	0.132351	−	0.648983i
$155$		0			0
$156$	−4.82385	+	2.14772i	−0.386217	+	0.171955i
$157$	0.217263	+	0.376310i	0.0173395	+	0.0300328i	0.874565	−	0.484908i	$-0.161147\pi$
$157$	0.217263	+	0.376310i	0.0173395	+	0.0300328i	−0.857225	+	0.514941i	$0.827814\pi$
$158$	−0.886816	+	8.43749i	−0.0705513	+	0.671251i
$159$	0.124745	+	0.138543i	0.00989291	+	0.0109872i
$160$		0			0
$161$	5.09236	−	2.99644i	0.401334	−	0.236153i
$162$	−1.01513	+	3.12425i	−0.0797561	+	0.245464i
$163$	−15.2062	−	16.8882i	−1.19105	−	1.32279i	−0.934375	−	0.356290i	$-0.884041\pi$
$163$	−15.2062	−	16.8882i	−1.19105	−	1.32279i	−0.256670	−	0.966499i	$-0.582625\pi$
$164$	−8.41567	+	9.34655i	−0.657154	+	0.729843i
$165$		0			0
$166$	3.07459	+	3.41467i	0.238634	+	0.265030i
$167$	2.91579	+	2.11844i	0.225630	+	0.163930i	0.694857	−	0.719148i	$-0.255467\pi$
$167$	2.91579	+	2.11844i	0.225630	+	0.163930i	−0.469227	+	0.883077i	$0.655467\pi$
$168$	−9.52444	−	3.00791i	−0.734827	−	0.232065i
$169$	1.73889	+	1.26338i	0.133761	+	0.0971828i
$170$		0			0
$171$	5.73534	+	2.55354i	0.438592	+	0.195274i
$172$	−0.751635	−	0.334649i	−0.0573116	−	0.0255168i
$173$	−7.42767	−	1.57880i	−0.564715	−	0.120034i	−0.0832968	−	0.996525i	$-0.526545\pi$
$173$	−7.42767	−	1.57880i	−0.564715	−	0.120034i	−0.481419	+	0.876491i	$0.659878\pi$
$174$	−11.2131			−0.850062
$175$		0			0
$176$	−0.388776			−0.0293051
$177$	1.31389	+	0.279276i	0.0987581	+	0.0209917i
$178$	−9.01842	−	4.01526i	−0.675959	−	0.300956i
$179$	−22.7815	−	10.1430i	−1.70277	−	0.758122i	−0.998855	−	0.0478378i	$-0.984767\pi$
$179$	−22.7815	−	10.1430i	−1.70277	−	0.758122i	−0.703915	−	0.710284i	$-0.748566\pi$
$180$		0			0
$181$	19.6899	+	14.3055i	1.46354	+	1.06332i	0.982424	+	0.186663i	$0.0597672\pi$
$181$	19.6899	+	14.3055i	1.46354	+	1.06332i	0.481113	+	0.876659i	$0.340233\pi$
$182$	−1.67194	−	7.55824i	−0.123932	−	0.560254i
$183$	−2.33618	−	1.69733i	−0.172695	−	0.125470i
$184$	−4.26197	−	4.73340i	−0.314197	−	0.348951i
$185$		0			0
$186$	−4.68415	+	5.20228i	−0.343459	+	0.381449i
$187$	3.53315	+	3.92396i	0.258369	+	0.286948i
$188$	−1.15192	+	3.54524i	−0.0840122	+	0.258563i
$189$	12.9444	+	7.33155i	0.941569	+	0.533292i
$190$		0			0
$191$	7.32965	+	8.14041i	0.530355	+	0.589019i	0.947474	−	0.319833i	$-0.103627\pi$
$191$	7.32965	+	8.14041i	0.530355	+	0.589019i	−0.417119	+	0.908852i	$0.636960\pi$
$192$	−0.719624	+	6.84677i	−0.0519344	+	0.494123i
$193$	5.68325	+	9.84368i	0.409089	+	0.708563i	0.994788	−	0.101966i	$-0.0325132\pi$
$193$	5.68325	+	9.84368i	0.409089	+	0.708563i	−0.585699	+	0.810529i	$0.699180\pi$
$194$	−13.0660	+	5.81735i	−0.938082	+	0.417661i
$195$		0			0
$196$	−4.11687	+	7.41078i	−0.294062	+	0.529341i
$197$	14.0244	−	10.1893i	0.999195	−	0.725957i	0.0372792	−	0.999305i	$-0.488131\pi$
$197$	14.0244	−	10.1893i	0.999195	−	0.725957i	0.961915	+	0.273348i	$0.0881309\pi$
$198$	3.79240	+	0.806100i	0.269514	+	0.0572870i
$199$	−0.258580	−	0.447874i	−0.0183303	−	0.0317489i	0.856715	−	0.515790i	$-0.172502\pi$
$199$	−0.258580	−	0.447874i	−0.0183303	−	0.0317489i	−0.875045	+	0.484042i	$0.839168\pi$
$200$		0			0
$201$	8.15580	−	14.1263i	0.575265	−	0.996389i
$202$	1.62015	+	4.98631i	0.113993	+	0.350836i
$203$	−5.04238	+	24.7253i	−0.353906	+	1.73537i
$204$	1.95781	−	1.42243i	0.137074	−	0.0995901i
$205$		0			0
$206$	−1.24572	+	11.8523i	−0.0867937	+	0.825787i
$207$	1.39353	+	2.41367i	0.0968574	+	0.167762i
$208$	−0.334489	+	0.148924i	−0.0231926	+	0.0103260i
$209$	−5.43712	+	16.7337i	−0.376094	+	1.15750i
$210$		0			0
$211$	2.30280	+	7.08728i	0.158531	+	0.487909i	0.998502	−	0.0547235i	$-0.0174277\pi$
$211$	2.30280	+	7.08728i	0.158531	+	0.487909i	−0.839970	+	0.542632i	$0.817428\pi$
$212$	−0.114137	−	0.126762i	−0.00783897	−	0.00870606i
$213$	−9.74772	+	2.07194i	−0.667903	+	0.141967i
$214$	2.05321	−	2.28033i	0.140355	−	0.155880i
$215$		0			0
$216$	4.95567	−	15.2520i	0.337191	−	1.03777i
$217$	9.36482	+	12.6681i	0.635725	+	0.859969i
$218$	1.68653			0.114226
$219$	−12.5073	+	5.56862i	−0.845167	+	0.376293i
$220$		0			0
$221$	4.54290	+	2.02263i	0.305589	+	0.136057i
$222$	−0.505041	−	4.80515i	−0.0338962	−	0.322500i
$223$	4.03572	+	12.4207i	0.270252	+	0.831750i	0.990437	+	0.137968i	$0.0440570\pi$
$223$	4.03572	+	12.4207i	0.270252	+	0.831750i	−0.720185	+	0.693782i	$0.755943\pi$
$224$	14.1423	+	4.46628i	0.944924	+	0.298416i
$225$		0			0
$226$	8.51426	−	14.7471i	0.566360	−	0.980964i
$227$	−5.97349	+	6.63423i	−0.396474	+	0.440329i	−0.908020	−	0.418927i	$-0.862406\pi$
$227$	−5.97349	+	6.63423i	−0.396474	+	0.440329i	0.511546	+	0.859256i	$0.329073\pi$
$228$	7.36680	+	3.27991i	0.487878	+	0.217217i
$229$	−1.80253	−	17.1499i	−0.119115	−	1.13330i	−0.876859	−	0.480748i	$-0.840365\pi$
$229$	−1.80253	−	17.1499i	−0.119115	−	1.13330i	0.757745	−	0.652551i	$-0.226301\pi$
$230$		0			0
$231$	−4.88938	+	11.2305i	−0.321697	+	0.738914i
$232$	27.2025			1.78593
$233$	−0.285084	+	0.126928i	−0.0186765	+	0.00831531i	−0.416054	−	0.909340i	$-0.636587\pi$
$233$	−0.285084	+	0.126928i	−0.0186765	+	0.00831531i	0.397377	+	0.917655i	$0.369920\pi$
$234$	3.57163	−	0.759174i	0.233485	−	0.0496288i
$235$		0			0
$236$	−1.20216	−	0.255528i	−0.0782542	−	0.0166335i
$237$	3.90687	−	12.0241i	0.253779	−	0.781050i
$238$	1.46969	+	3.22892i	0.0952661	+	0.209300i
$239$	4.24656	+	13.0696i	0.274687	+	0.845401i	0.989302	+	0.145882i	$0.0466021\pi$
$239$	4.24656	+	13.0696i	0.274687	+	0.845401i	−0.714615	+	0.699518i	$0.753398\pi$
$240$		0			0
$241$	6.04280	−	1.28444i	0.389251	−	0.0827378i	−0.00912913	−	0.999958i	$-0.502906\pi$
$241$	6.04280	−	1.28444i	0.389251	−	0.0827378i	0.398380	+	0.917221i	$0.369573\pi$
$242$	−0.114520	+	1.08958i	−0.00736161	+	0.0700410i
$243$	−5.98648	+	10.3689i	−0.384033	+	0.665165i
$244$	2.13752	+	1.55300i	0.136841	+	0.0994206i
$245$		0			0
$246$	−9.87756	+	7.17647i	−0.629770	+	0.457555i
$247$	1.73210	+	16.4799i	0.110211	+	1.04859i
$248$	11.3636	−	12.6205i	0.721588	−	0.801404i
$249$	−3.42368	−	5.92999i	−0.216967	−	0.375798i
$250$		0			0
$251$	−22.8510			−1.44234			−0.721171	−	0.692757i	$-0.756396\pi$
$251$	−22.8510			−1.44234			−0.721171	+	0.692757i	$0.756396\pi$
$252$	−3.47952	−	1.97075i	−0.219189	−	0.124146i
$253$	−6.31922	+	4.59118i	−0.397286	+	0.288645i
$254$	−0.593763	−	5.64928i	−0.0372560	−	0.354467i
$255$		0			0
$256$	1.69931	−	16.1678i	0.106207	−	1.01049i
$257$	−13.3636	+	23.1465i	−0.833599	+	1.44384i	0.0615664	+	0.998103i	$0.480390\pi$
$257$	−13.3636	+	23.1465i	−0.833599	+	1.44384i	−0.895166	+	0.445733i	$0.852943\pi$
$258$	−0.646172	−	0.469472i	−0.0402289	−	0.0292280i
$259$	−10.8226	−	1.04718i	−0.672486	−	0.0650685i
$260$		0			0
$261$	−11.6429	−	2.47478i	−0.720679	−	0.153185i
$262$	−5.61754	+	1.19404i	−0.347053	+	0.0737683i
$263$	4.58502	−	0.974576i	0.282725	−	0.0600950i	−0.0643667	−	0.997926i	$-0.520503\pi$
$263$	4.58502	−	0.974576i	0.282725	−	0.0600950i	0.347091	+	0.937831i	$0.387169\pi$
$264$	12.9156	+	2.74529i	0.794899	+	0.168961i
$265$		0			0
$266$	−6.86936	+	9.62102i	−0.421187	+	0.589903i
$267$	11.9016	+	8.64703i	0.728367	+	0.529190i
$268$	−7.46226	+	12.9250i	−0.455830	+	0.789521i
$269$	0.368325	−	3.50438i	0.0224572	−	0.213666i	−0.977539	−	0.210757i	$-0.932407\pi$
$269$	0.368325	−	3.50438i	0.0224572	−	0.213666i	0.999996	−	0.00290928i	$-0.000926053\pi$
$270$		0			0
$271$	−1.80909	−	17.2123i	−0.109894	−	1.04558i	−0.900977	−	0.433866i	$-0.857149\pi$
$271$	−1.80909	−	17.2123i	−0.109894	−	1.04558i	0.791083	−	0.611709i	$-0.209518\pi$
$272$	0.135756	−	0.0986322i	0.00823139	−	0.00598046i
$273$	0.0953057	+	11.5353i	0.00576816	+	0.698146i
$274$	6.27732			0.379227
$275$		0			0
$276$	1.78994	+	3.10026i	0.107742	+	0.186614i
$277$	11.5900	−	12.8719i	0.696373	−	0.773400i	−0.286421	−	0.958104i	$-0.592466\pi$
$277$	11.5900	−	12.8719i	0.696373	−	0.773400i	0.982794	+	0.184703i	$0.0591324\pi$
$278$	0.0830176	+	0.789860i	0.00497907	+	0.0473727i
$279$	−6.01188	+	4.36788i	−0.359922	+	0.261498i
$280$		0			0
$281$	−7.84201	−	5.69756i	−0.467815	−	0.339888i	0.328774	−	0.944409i	$-0.393365\pi$
$281$	−7.84201	−	5.69756i	−0.467815	−	0.339888i	−0.796589	+	0.604521i	$0.793365\pi$
$282$	−1.80935	+	3.13389i	−0.107745	+	0.186620i
$283$	0.00709367	−	0.0674918i	0.000421675	−	0.00401197i	−0.994309	−	0.106534i	$-0.966025\pi$
$283$	0.00709367	−	0.0674918i	0.000421675	−	0.00401197i	0.994731	+	0.102522i	$0.0326913\pi$
$284$	8.91882	−	1.89575i	0.529234	−	0.112492i
$285$		0			0
$286$	3.16230	+	9.73255i	0.186991	+	0.575498i
$287$	11.3826	+	25.0076i	0.671892	+	1.47615i
$288$	−2.16180	+	6.65333i	−0.127385	+	0.392051i
$289$	14.3993	+	3.06066i	0.847016	+	0.180039i
$290$		0			0
$291$	20.8480	−	4.43138i	1.22213	−	0.259772i
$292$	11.4438	−	5.09509i	0.669696	−	0.298168i
$293$	−4.92985			−0.288005			−0.144003	−	0.989577i	$-0.545997\pi$
$293$	−4.92985			−0.288005			−0.144003	+	0.989577i	$0.545997\pi$
$294$	−5.40492	+	6.20599i	−0.315221	+	0.361941i
$295$		0			0
$296$	1.22521	+	11.6571i	0.0712139	+	0.677555i
$297$	−17.9662	−	7.99907i	−1.04250	−	0.464153i
$298$	12.0723	−	13.4076i	0.699327	−	0.776682i
$299$	−3.67814	+	6.37072i	−0.212712	+	0.368428i
$300$		0			0
$301$	−1.32578	+	1.21372i	−0.0764166	+	0.0699576i
$302$	−5.29143	−	16.2853i	−0.304487	−	0.937116i
$303$	−0.816687	−	7.77026i	−0.0469175	−	0.446390i
$304$	0.510818	+	0.227431i	0.0292974	+	0.0130441i
$305$		0			0
$306$	−1.52877	+	0.680651i	−0.0873938	+	0.0389102i
$307$	−11.3117			−0.645591			−0.322796	−	0.946469i	$-0.604623\pi$
$307$	−11.3117			−0.645591			−0.322796	+	0.946469i	$0.604623\pi$
$308$	4.47361	−	10.2755i	0.254907	−	0.585503i
$309$	5.48804	−	16.8905i	0.312204	−	0.960865i
$310$		0			0
$311$	3.49852	−	3.88550i	0.198383	−	0.220327i	−0.635743	−	0.771901i	$-0.719306\pi$
$311$	3.49852	−	3.88550i	0.198383	−	0.220327i	0.834126	+	0.551574i	$0.185973\pi$
$312$	12.1637	−	2.58548i	0.688635	−	0.146374i
$313$	−11.8223	−	13.1300i	−0.668239	−	0.742154i	0.309749	−	0.950818i	$-0.399755\pi$
$313$	−11.8223	−	13.1300i	−0.668239	−	0.742154i	−0.977987	+	0.208664i	$0.933088\pi$
$314$	−0.119266	−	0.367063i	−0.00673056	−	0.0207145i
$315$		0			0
$316$	−3.57465	+	11.0016i	−0.201090	+	0.618891i
$317$	−3.07403	+	1.36864i	−0.172655	+	0.0768707i	−0.491244	−	0.871022i	$-0.663458\pi$
$317$	−3.07403	+	1.36864i	−0.172655	+	0.0768707i	0.318589	+	0.947893i	$0.396791\pi$
$318$	−0.0827942	−	0.143404i	−0.00464287	−	0.00804168i
$319$	3.48698	−	33.1764i	0.195234	−	1.85752i
$320$		0			0
$321$	−3.69938	+	2.68776i	−0.206479	+	0.150016i
$322$	−4.97763	+	1.66292i	−0.277392	+	0.0926708i
$323$	−2.34677	−	7.22261i	−0.130578	−	0.401877i
$324$	−2.23955	+	3.87902i	−0.124420	+	0.215501i
$325$		0			0
$326$	10.0925	+	17.4807i	0.558973	+	0.968169i
$327$	−2.45837	−	0.522542i	−0.135948	−	0.0288966i
$328$	23.9626	−	17.4098i	1.32311	−	0.961297i
$329$	6.09670	+	5.39896i	0.336122	+	0.297654i
$330$		0			0
$331$	−0.496941	+	0.221253i	−0.0273144	+	0.0121611i	−0.420348	−	0.907363i	$-0.638092\pi$
$331$	−0.496941	+	0.221253i	−0.0273144	+	0.0121611i	0.393034	+	0.919524i	$0.371425\pi$
$332$	3.13255	+	5.42573i	0.171921	+	0.297776i
$333$	0.536117	−	5.10081i	0.0293790	−	0.279523i
$334$	−2.14204	−	2.37897i	−0.117207	−	0.130172i
$335$		0			0
$336$	0.338705	+	0.191838i	0.0184779	+	0.0104656i
$337$	−7.22905	+	22.2487i	−0.393791	+	1.21196i	0.536108	+	0.844150i	$0.319894\pi$
$337$	−7.22905	+	22.2487i	−0.393791	+	1.21196i	−0.929899	+	0.367815i	$0.880106\pi$
$338$	−1.27745	−	1.41875i	−0.0694840	−	0.0771698i
$339$	−16.9799	+	18.8581i	−0.922223	+	1.02423i
$340$		0			0
$341$	−13.9355	−	15.4769i	−0.754647	−	0.838121i
$342$	−4.51133	−	3.27767i	−0.243945	−	0.177236i
$343$	11.2539	+	14.7088i	0.607655	+	0.794201i
$344$	1.56759	+	1.13892i	0.0845188	+	0.0614065i
$345$		0			0
$346$	6.16165	+	2.74334i	0.331252	+	0.147483i
$347$	−11.3316	−	5.04517i	−0.608315	−	0.270839i	0.0793740	−	0.996845i	$-0.474708\pi$
$347$	−11.3316	−	5.04517i	−0.608315	−	0.270839i	−0.687689	+	0.726006i	$0.741375\pi$
$348$	−14.9548	−	3.17875i	−0.801664	−	0.170399i
$349$	2.23368			0.119566			0.0597832	−	0.998211i	$-0.480959\pi$
$349$	2.23368			0.119566			0.0597832	+	0.998211i	$0.480959\pi$
$350$		0			0
$351$	−18.5216			−0.988610
$352$	−19.1776	−	4.07633i	−1.02217	−	0.217269i
$353$	3.59700	+	1.60149i	0.191449	+	0.0852385i	0.500222	−	0.865897i	$-0.333252\pi$
$353$	3.59700	+	1.60149i	0.191449	+	0.0852385i	−0.308773	+	0.951136i	$0.599918\pi$
$354$	−1.08994	−	0.485274i	−0.0579298	−	0.0257920i
$355$		0			0
$356$	−10.8896	−	7.91172i	−0.577145	−	0.419321i
$357$	−1.14187	−	5.16199i	−0.0604341	−	0.273202i
$358$	17.9196	+	13.0193i	0.947080	+	0.688094i
$359$	17.5167	+	19.4543i	0.924496	+	1.02676i	0.999562	+	0.0295787i	$0.00941657\pi$
$359$	17.5167	+	19.4543i	0.924496	+	1.02676i	−0.0750661	+	0.997179i	$0.523917\pi$
$360$		0			0
$361$	4.21956	−	4.68629i	0.222082	−	0.246647i
$362$	−14.4649	−	16.0649i	−0.760256	−	0.844350i
$363$	0.504517	−	1.55274i	0.0264803	−	0.0814979i
$364$	−0.0872013	−	10.5544i	−0.00457059	−	0.553199i
$365$		0			0
$366$	1.71624	+	1.90608i	0.0897092	+	0.0996321i
$367$	2.59118	−	24.6535i	0.135259	−	1.28690i	−0.690688	−	0.723153i	$-0.742692\pi$
$367$	2.59118	−	24.6535i	0.135259	−	1.28690i	0.825947	−	0.563748i	$-0.190641\pi$
$368$	0.124115	+	0.214974i	0.00646996	+	0.0112063i
$369$	−11.8401	+	5.27154i	−0.616370	+	0.274426i
$370$		0			0
$371$	−0.353442	+	0.118078i	−0.0183498	+	0.00613028i
$372$	−7.72200	+	5.61036i	−0.400367	+	0.290884i
$373$	26.2883	+	5.58775i	1.36116	+	0.289323i	0.829911	−	0.557896i	$-0.188391\pi$
$373$	26.2883	+	5.58775i	1.36116	+	0.289323i	0.531245	+	0.847218i	$0.321724\pi$
$374$	−2.34498	−	4.06162i	−0.121256	−	0.210021i
$375$		0			0
$376$	4.38942	−	7.60269i	0.226367	−	0.392079i
$377$	−9.70846	−	29.8796i	−0.500011	−	1.53888i
$378$	−9.89228	−	8.76014i	−0.508804	−	0.450573i
$379$	23.8531	−	17.3303i	1.22525	−	0.890196i	0.228724	−	0.973491i	$-0.426545\pi$
$379$	23.8531	−	17.3303i	1.22525	−	0.890196i	0.996525	+	0.0832957i	$0.0265446\pi$
$380$		0			0
$381$	−0.884832	+	8.41862i	−0.0453313	+	0.431299i
$382$	−4.86475	−	8.42600i	−0.248902	−	0.431112i
$383$	2.02368	−	0.901001i	0.103405	−	0.0460390i	−0.354382	−	0.935101i	$-0.615309\pi$
$383$	2.02368	−	0.901001i	0.103405	−	0.0460390i	0.457787	+	0.889062i	$0.348642\pi$
$384$	−2.69597	+	8.29736i	−0.137578	+	0.423423i
$385$		0			0
$386$	−3.11980	−	9.60177i	−0.158794	−	0.488717i
$387$	−0.567328	−	0.630082i	−0.0288389	−	0.0320288i
$388$	−19.0752	+	4.05455i	−0.968395	+	0.205839i
$389$	4.09541	−	4.54841i	0.207645	−	0.230614i	−0.630322	−	0.776334i	$-0.717077\pi$
$389$	4.09541	−	4.54841i	0.207645	−	0.230614i	0.837968	+	0.545720i	$0.183744\pi$
$390$		0			0
$391$	1.04181	−	3.20637i	0.0526867	−	0.162153i
$392$	13.1121	−	15.0555i	0.662263	−	0.760418i
$393$	8.55834			0.431711
$394$	−14.0661	+	6.26263i	−0.708640	+	0.315507i
$395$		0			0
$396$	4.82939	+	2.15018i	0.242686	+	0.108051i
$397$	−0.100308	−	0.954368i	−0.00503432	−	0.0478983i	0.991716	−	0.128447i	$-0.0409993\pi$
$397$	−0.100308	−	0.954368i	−0.00503432	−	0.0478983i	−0.996751	+	0.0805490i	$0.974333\pi$
$398$	0.141947	+	0.436867i	0.00711515	+	0.0218982i
$399$	12.9940	−	11.8957i	0.650514	−	0.595530i
$400$		0			0
$401$	3.10446	−	5.37707i	0.155029	−	0.268518i	−0.778041	−	0.628214i	$-0.783786\pi$
$401$	3.10446	−	5.37707i	0.155029	−	0.268518i	0.933070	+	0.359696i	$0.117120\pi$
$402$	−9.69450	+	10.7668i	−0.483518	+	0.537001i
$403$	−17.9181	−	7.97767i	−0.892566	−	0.397396i
$404$	0.747240	+	7.10951i	0.0371766	+	0.353711i
$405$		0			0
$406$	8.94688	−	20.5503i	0.444026	−	1.01989i
$407$	14.3742			0.712501
$408$	−5.20644	+	2.31806i	−0.257757	+	0.114761i
$409$	36.7614	−	7.81387i	1.81773	−	0.386371i	0.832012	−	0.554758i	$-0.187189\pi$
$409$	36.7614	−	7.81387i	1.81773	−	0.386371i	0.985721	+	0.168387i	$0.0538557\pi$
$410$		0			0
$411$	−9.15011	−	1.94492i	−0.451342	−	0.0959356i
$412$	−5.02137	+	15.4542i	−0.247385	+	0.761373i
$413$	−1.56018	+	2.18514i	−0.0767715	+	0.107524i
$414$	−0.764977	−	2.35436i	−0.0375966	−	0.115710i
$415$		0			0
$416$	−18.0612	+	3.83904i	−0.885525	+	0.188224i
$417$	0.123714	−	1.17706i	0.00605829	−	0.0576408i
$418$	7.81403	−	13.5343i	0.382197	−	0.661984i
$419$	−6.33236	−	4.60073i	−0.309356	−	0.224760i	0.422264	−	0.906473i	$-0.361235\pi$
$419$	−6.33236	−	4.60073i	−0.309356	−	0.224760i	−0.731620	+	0.681713i	$0.761235\pi$
$420$		0			0
$421$	10.2646	−	7.45765i	0.500265	−	0.363464i	−0.308853	−	0.951110i	$-0.599945\pi$
$421$	10.2646	−	7.45765i	0.500265	−	0.363464i	0.809118	+	0.587646i	$0.199945\pi$
$422$	−0.691873	−	6.58273i	−0.0336798	−	0.320442i
$423$	−2.57037	+	2.85469i	−0.124976	+	0.138800i
$424$	0.200856	+	0.347892i	0.00975441	+	0.0168951i
$425$		0			0
$426$	8.85150			0.428857
$427$	4.97474	−	2.92723i	0.240745	−	0.141659i
$428$	3.38480	−	2.45920i	0.163611	−	0.118870i
$429$	−1.59405	−	15.1664i	−0.0769616	−	0.732241i
$430$		0			0
$431$	−2.06446	+	19.6421i	−0.0994417	+	0.946125i	0.825085	+	0.565008i	$0.191127\pi$
$431$	−2.06446	+	19.6421i	−0.0994417	+	0.946125i	−0.924527	+	0.381117i	$0.875540\pi$
$432$	−0.312497	+	0.541261i	−0.0150350	+	0.0260414i
$433$	−10.7560	−	7.81470i	−0.516901	−	0.375551i	0.298534	−	0.954399i	$-0.403502\pi$
$433$	−10.7560	−	7.81470i	−0.516901	−	0.375551i	−0.815435	+	0.578848i	$0.803502\pi$
$434$	−5.79678	−	12.7355i	−0.278254	−	0.611326i
$435$		0			0
$436$	2.24932	+	0.478107i	0.107723	+	0.0228972i
$437$	10.9887	−	2.33573i	0.525662	−	0.111733i
$438$	11.8948	−	2.52832i	0.568356	−	0.120808i
$439$	−24.2332	−	5.15092i	−1.15659	−	0.245840i	−0.410609	−	0.911812i	$-0.634684\pi$
$439$	−24.2332	−	5.15092i	−1.15659	−	0.245840i	−0.745977	+	0.665972i	$0.768017\pi$
$440$		0			0
$441$	−6.98180	+	5.25100i	−0.332467	+	0.250048i
$442$	−3.57338	−	2.59621i	−0.169968	−	0.123489i
$443$	11.5941	−	20.0816i	0.550852	−	0.954104i	−0.447361	−	0.894354i	$-0.647636\pi$
$443$	11.5941	−	20.0816i	0.550852	−	0.954104i	0.998213	−	0.0597508i	$-0.0190306\pi$
$444$	0.688619	−	6.55177i	0.0326804	−	0.310933i
$445$		0			0
$446$	−1.21253	−	11.5364i	−0.0574149	−	0.546266i
$447$	−21.7512	+	15.8032i	−1.02880	+	0.747464i
$448$	−11.9739	−	6.78187i	−0.565715	−	0.320413i
$449$	4.86545			0.229615			0.114807	−	0.993388i	$-0.463375\pi$
$449$	4.86545			0.229615			0.114807	+	0.993388i	$0.463375\pi$
$450$		0			0
$451$	−18.1615	−	31.4567i	−0.855193	−	1.48124i
$452$	15.5360	−	17.2545i	0.730753	−	0.811584i
$453$	2.66731	+	25.3777i	0.125321	+	1.19235i
$454$	6.41495	−	4.66073i	0.301068	−	0.218739i
$455$		0			0
$456$	−15.3640	−	11.1626i	−0.719485	−	0.522737i
$457$	3.24470	−	5.61998i	0.151781	−	0.262892i	−0.780102	−	0.625653i	$-0.784833\pi$
$457$	3.24470	−	5.61998i	0.151781	−	0.262892i	0.931882	+	0.362761i	$0.118166\pi$
$458$	−1.60103	+	15.2328i	−0.0748114	+	0.711783i
$459$	8.30294	−	1.76484i	0.387548	−	0.0823758i
$460$		0			0
$461$	−1.33141	−	4.09765i	−0.0620099	−	0.190847i	0.915252	−	0.402881i	$-0.131991\pi$
$461$	−1.33141	−	4.09765i	−0.0620099	−	0.190847i	−0.977262	+	0.212034i	$0.931991\pi$
$462$	6.32186	−	8.85422i	0.294120	−	0.411936i
$463$	10.1876	−	31.3543i	0.473459	−	1.45716i	−0.374565	−	0.927201i	$-0.622208\pi$
$463$	10.1876	−	31.3543i	0.473459	−	1.45716i	0.848024	−	0.529957i	$-0.177792\pi$
$464$	−1.03698	−	0.220416i	−0.0481405	−	0.0102326i
$465$		0			0
$466$	0.271123	−	0.0576289i	0.0125595	−	0.00266961i
$467$	−14.2056	+	6.32475i	−0.657358	+	0.292675i	−0.708179	−	0.706033i	$-0.750483\pi$
$467$	−14.2056	+	6.32475i	−0.657358	+	0.292675i	0.0508207	+	0.998708i	$0.483816\pi$
$468$	4.97868			0.230140
$469$	19.3818	+	26.2185i	0.894968	+	1.21066i
$470$		0			0
$471$	0.0601196	+	0.572000i	0.00277017	+	0.0263564i
$472$	2.64416	+	1.17726i	0.121707	+	0.0541876i
$473$	1.58998	−	1.76585i	0.0731074	−	0.0811940i
$474$	−5.61481	+	9.72514i	−0.257897	+	0.446690i
$475$		0			0
$476$	1.04477	+	4.72304i	0.0478870	+	0.216480i
$477$	−0.0543181	−	0.167174i	−0.00248706	−	0.00765437i
$478$	−1.27587	−	12.1391i	−0.0583571	−	0.555231i
$479$	13.1578	+	5.85821i	0.601193	+	0.267669i	0.684684	−	0.728840i	$-0.259940\pi$
$479$	13.1578	+	5.85821i	0.601193	+	0.267669i	−0.0834906	+	0.996509i	$0.526607\pi$
$480$		0			0
$481$	12.3670	−	5.50615i	0.563888	−	0.251059i
$482$	−5.48721			−0.249936
$483$	7.77085	−	0.881718i	0.353586	−	0.0401196i
$484$	−0.461615	+	1.42071i	−0.0209825	+	0.0645775i
$485$		0			0
$486$	7.11592	−	7.90303i	0.322785	−	0.358489i
$487$	3.73200	−	0.793262i	0.169113	−	0.0359461i	−0.122577	−	0.992459i	$-0.539116\pi$
$487$	3.73200	−	0.793262i	0.169113	−	0.0359461i	0.291690	+	0.956513i	$0.405782\pi$
$488$	−4.16353	−	4.62407i	−0.188474	−	0.209322i
$489$	−9.29522	−	28.6077i	−0.420344	−	1.29369i
$490$		0			0
$491$	−1.99140	+	6.12889i	−0.0898705	+	0.276593i	−0.985883	−	0.167436i	$-0.946451\pi$
$491$	−1.99140	+	6.12889i	−0.0898705	+	0.276593i	0.896012	+	0.444029i	$0.146451\pi$
$492$	−15.2081	+	6.77107i	−0.685633	+	0.305264i
$493$	7.19924	+	12.4694i	0.324237	+	0.561596i
$494$	1.53848	−	14.6377i	0.0692195	−	0.658580i
$495$		0			0
$496$	−0.535448	+	0.389026i	−0.0240423	+	0.0174678i
$497$	3.98041	−	19.5179i	0.178546	−	0.875497i
$498$	1.87942	+	5.78427i	0.0842189	+	0.259199i
$499$	−5.82680	+	10.0923i	−0.260844	+	0.451794i	−0.966466	−	0.256793i	$-0.917334\pi$
$499$	−5.82680	+	10.0923i	−0.260844	+	0.451794i	0.705623	+	0.708588i	$0.250667\pi$
$500$		0			0
$501$	2.38525	+	4.13138i	0.106565	+	0.184576i
$502$	19.8531	+	4.21990i	0.886086	+	0.188343i
$503$	23.4336	−	17.0255i	1.04485	−	0.759130i	0.0736253	−	0.997286i	$-0.476543\pi$
$503$	23.4336	−	17.0255i	1.04485	−	0.759130i	0.971227	+	0.238156i	$0.0765431\pi$
$504$	7.05037	+	6.24348i	0.314048	+	0.278107i
$505$		0			0
$506$	6.33803	−	2.82187i	0.281760	−	0.125447i
$507$	1.42249	+	2.46383i	0.0631751	+	0.109423i
$508$	0.809590	−	7.70274i	0.0359198	−	0.341754i
$509$	−2.23725	−	2.48472i	−0.0991643	−	0.110133i	0.691520	−	0.722358i	$-0.256942\pi$
$509$	−2.23725	−	2.48472i	−0.0991643	−	0.110133i	−0.790684	+	0.612225i	$0.790275\pi$
$510$		0			0
$511$	−0.226096	−	27.3654i	−0.0100019	−	1.21058i
$512$	−0.388473	+	1.19560i	−0.0171682	+	0.0528384i
$513$	18.9267	+	21.0202i	0.835633	+	0.928065i
$514$	15.8848	−	17.6419i	0.700651	−	0.778151i
$515$		0			0
$516$	−0.728709	−	0.809313i	−0.0320796	−	0.0356280i
$517$	−8.70965	−	6.32793i	−0.383050	−	0.278302i
$518$	9.20939	+	2.90842i	0.404637	+	0.127788i
$519$	−8.13153	−	5.90790i	−0.356934	−	0.259328i
$520$		0			0
$521$	−35.3388	−	15.7338i	−1.54822	−	0.689312i	−0.558131	−	0.829753i	$-0.688481\pi$
$521$	−35.3388	−	15.7338i	−1.54822	−	0.689312i	−0.990089	+	0.140441i	$0.955148\pi$
$522$	9.65842	+	4.30021i	0.422738	+	0.188215i
$523$	−37.0825	−	7.88213i	−1.62150	−	0.344661i	−0.694436	−	0.719554i	$-0.744346\pi$
$523$	−37.0825	−	7.88213i	−1.62150	−	0.344661i	−0.927068	+	0.374893i	$0.877679\pi$
$524$	−7.83058			−0.342080
$525$		0			0
$526$	−4.16347			−0.181536
$527$	8.79257	+	1.86892i	0.383010	+	0.0814114i
$528$	−0.470106	−	0.209305i	−0.0204587	−	0.00910881i
$529$	−16.4555	−	7.32644i	−0.715455	−	0.318541i
$530$		0			0
$531$	−1.02462	−	0.744431i	−0.0444648	−	0.0323056i
$532$	−11.8891	+	10.8841i	−0.515456	+	0.471888i
$533$	−27.6753	−	20.1073i	−1.19875	−	0.870943i
$534$	−8.74334	−	9.71046i	−0.378361	−	0.420213i
$535$		0			0
$536$	23.5185	−	26.1199i	1.01584	−	1.12821i
$537$	−22.0866	−	24.5297i	−0.953108	−	1.05853i
$538$	−0.967158	+	2.97661i	−0.0416971	+	0.128331i
$539$	−16.6810	−	17.9216i	−0.718503	−	0.771937i
$540$		0			0
$541$	−9.83065	−	10.9180i	−0.422653	−	0.469404i	0.493783	−	0.869585i	$-0.335614\pi$
$541$	−9.83065	−	10.9180i	−0.422653	−	0.469404i	−0.916436	+	0.400182i	$0.868947\pi$
$542$	−1.60686	+	15.2883i	−0.0690206	+	0.656687i
$543$	16.1073	+	27.8986i	0.691228	+	1.19724i
$544$	7.73076	−	3.44195i	0.331453	−	0.147573i
$545$		0			0
$546$	2.04742	−	10.0395i	0.0876215	−	0.429651i
$547$	−14.1586	+	10.2869i	−0.605380	+	0.439834i	−0.847784	−	0.530341i	$-0.822064\pi$
$547$	−14.1586	+	10.2869i	−0.605380	+	0.439834i	0.242405	+	0.970175i	$0.422064\pi$
$548$	8.37203	+	1.77953i	0.357635	+	0.0760177i
$549$	1.36135	+	2.35792i	0.0581009	+	0.100634i
$550$		0			0
$551$	−23.9896	+	41.5512i	−1.02199	+	1.77014i
$552$	−2.60524	−	8.01811i	−0.110886	−	0.341273i
$553$	18.9194	+	16.7541i	0.804534	+	0.712459i
$554$	−12.4465	+	9.04290i	−0.528800	+	0.384196i
$555$		0			0
$556$	−0.113194	+	1.07697i	−0.00480049	+	0.0456736i
$557$	1.28318	+	2.22253i	0.0543700	+	0.0941717i	0.891929	−	0.452175i	$-0.149352\pi$
$557$	1.28318	+	2.22253i	0.0543700	+	0.0941717i	−0.837559	+	0.546346i	$0.816018\pi$
$558$	6.02977	−	2.68463i	0.255261	−	0.113649i
$559$	0.691538	−	2.12833i	0.0292489	−	0.0900190i
$560$		0			0
$561$	2.15973	+	6.64696i	0.0911838	+	0.280635i
$562$	5.76102	+	6.39826i	0.243014	+	0.269894i
$563$	23.3465	−	4.96245i	0.983938	−	0.209142i	0.312269	−	0.949994i	$-0.398911\pi$
$563$	23.3465	−	4.96245i	0.983938	−	0.209142i	0.671669	+	0.740851i	$0.265578\pi$
$564$	−3.30153	+	3.66673i	−0.139020	+	0.154397i
$565$		0			0
$566$	−0.0186267	+	0.0573272i	−0.000782941	+	0.00240964i
$567$	5.81681	+	7.86861i	0.244283	+	0.330450i
$568$	−21.4734			−0.901004
$569$	39.6844	−	17.6686i	1.66366	−	0.740708i	0.663684	−	0.748013i	$-0.268992\pi$
$569$	39.6844	−	17.6686i	1.66366	−	0.740708i	0.999973	+	0.00730530i	$0.00232537\pi$
$570$		0			0
$571$	23.5613	+	10.4901i	0.986008	+	0.438999i	0.835429	−	0.549599i	$-0.185219\pi$
$571$	23.5613	+	10.4901i	0.986008	+	0.438999i	0.150579	+	0.988598i	$0.451886\pi$
$572$	1.45850	+	13.8767i	0.0609830	+	0.580215i
$573$	4.48045	+	13.7894i	0.187173	+	0.576060i
$574$	−5.27109	−	23.8287i	−0.220011	−	0.994592i
$575$		0			0
$576$	3.24558	−	5.62150i	0.135232	−	0.234229i
$577$	1.48028	−	1.64402i	0.0616250	−	0.0684415i	−0.711544	−	0.702642i	$-0.752004\pi$
$577$	1.48028	−	1.64402i	0.0616250	−	0.0684415i	0.773169	+	0.634200i	$0.218670\pi$
$578$	−11.9450	−	5.31824i	−0.496845	−	0.221210i
$579$	1.57263	+	14.9626i	0.0653564	+	0.621825i
$580$		0			0
$581$	13.5997	−	1.54309i	0.564210	−	0.0640180i
$582$	−18.9312			−0.784723
$583$	0.450039	−	0.200370i	0.0186387	−	0.00829849i
$584$	−28.8563	+	6.13360i	−1.19408	+	0.253810i
$585$		0			0
$586$	4.28309	+	0.910398i	0.176933	+	0.0376082i
$587$	−9.69149	+	29.8273i	−0.400010	+	1.23111i	0.524980	+	0.851115i	$0.324073\pi$
$587$	−9.69149	+	29.8273i	−0.400010	+	1.23111i	−0.924990	+	0.379991i	$0.875927\pi$
$588$	−8.96783	+	6.74468i	−0.369827	+	0.278146i
$589$	9.25614	+	28.4875i	0.381393	+	1.17381i
$590$		0			0
$591$	22.4438	−	4.77057i	0.923214	−	0.196235i
$592$	0.0477493	−	0.454304i	0.00196248	−	0.0186718i
$593$	15.5893	−	27.0014i	0.640175	−	1.10881i	−0.345219	−	0.938522i	$-0.612195\pi$
$593$	15.5893	−	27.0014i	0.640175	−	1.10881i	0.985394	−	0.170293i	$-0.0544713\pi$
$594$	14.1319	+	10.2675i	0.579841	+	0.421279i
$595$		0			0
$596$	19.9016	−	14.4593i	0.815201	−	0.592278i
$597$	−0.0715527	−	0.680778i	−0.00292846	−	0.0278624i
$598$	4.37207	−	4.85568i	0.178787	−	0.198563i
$599$	21.6143	+	37.4371i	0.883137	+	1.52964i	0.847834	+	0.530261i	$0.177906\pi$
$599$	21.6143	+	37.4371i	0.883137	+	1.52964i	0.0353023	+	0.999377i	$0.488761\pi$
$600$		0			0
$601$	−40.2989			−1.64383			−0.821913	−	0.569613i	$-0.807093\pi$
$601$	−40.2989			−1.64383			−0.821913	+	0.569613i	$0.807093\pi$
$602$	1.37598	−	0.809654i	0.0560808	−	0.0329991i
$603$	−12.4424	+	9.03994i	−0.506694	+	0.368135i
$604$	−2.44049	−	23.2197i	−0.0993022	−	0.944797i
$605$		0			0
$606$	−0.725394	+	6.90166i	−0.0294671	+	0.280361i
$607$	13.4384	−	23.2760i	0.545448	−	0.944743i	−0.453131	−	0.891444i	$-0.649693\pi$
$607$	13.4384	−	23.2760i	0.545448	−	0.944743i	0.998579	−	0.0532991i	$-0.0169737\pi$
$608$	22.8132	+	16.5747i	0.925196	+	0.672194i
$609$	−19.4085	+	27.1830i	−0.786474	+	1.10151i
$610$		0			0
$611$	−9.91745	−	2.10802i	−0.401217	−	0.0852813i
$612$	−2.23186	+	0.474397i	−0.0902177	+	0.0191764i
$613$	29.6863	−	6.31002i	1.19902	−	0.254859i	0.435226	−	0.900321i	$-0.356668\pi$
$613$	29.6863	−	6.31002i	1.19902	−	0.254859i	0.763792	+	0.645462i	$0.223335\pi$
$614$	9.82764	+	2.08893i	0.396611	+	0.0843024i
$615$		0			0
$616$	−15.3366	+	21.4800i	−0.617929	+	0.865454i
$617$	−16.9090	−	12.2851i	−0.680732	−	0.494581i	0.192868	−	0.981225i	$-0.438221\pi$
$617$	−16.9090	−	12.2851i	−0.680732	−	0.494581i	−0.873601	+	0.486644i	$0.838221\pi$
$618$	−7.88721	+	13.6611i	−0.317270	+	0.549528i
$619$	−0.726428	+	6.91151i	−0.0291976	+	0.277797i	0.970176	+	0.242402i	$0.0779354\pi$
$619$	−0.726428	+	6.91151i	−0.0291976	+	0.277797i	−0.999373	+	0.0353944i	$0.988731\pi$
$620$		0			0
$621$	1.31255	+	12.4881i	0.0526709	+	0.501131i
$622$	−3.75707	+	2.72967i	−0.150645	+	0.109450i
$623$	−25.3437	+	14.9127i	−1.01537	+	0.597466i
$624$	−0.484638			−0.0194011
$625$		0			0
$626$	7.84659	+	13.5907i	0.313613	+	0.543193i
$627$	−15.5835	+	17.3072i	−0.622343	+	0.691182i
$628$	−0.0550074	−	0.523360i	−0.00219503	−	0.0208843i
$629$	−5.01928	+	3.64672i	−0.200132	+	0.145404i
$630$		0			0
$631$	15.6955	+	11.4035i	0.624829	+	0.453965i	0.854605	−	0.519279i	$-0.173799\pi$
$631$	15.6955	+	11.4035i	0.624829	+	0.453965i	−0.229776	+	0.973244i	$0.573799\pi$
$632$	13.6213	−	23.5928i	0.541827	−	0.938472i
$633$	−1.03104	+	9.80966i	−0.0409800	+	0.389899i
$634$	2.92348	−	0.621405i	0.116106	−	0.0246791i
$635$		0			0
$636$	−0.0697693	−	0.214728i	−0.00276653	−	0.00851452i
$637$	−21.2168	−	9.02928i	−0.840640	−	0.357753i
$638$	−9.15622	+	28.1799i	−0.362498	+	1.11565i
$639$	9.19081	+	1.95357i	0.363583	+	0.0772819i
$640$		0			0
$641$	−11.8189	+	2.51219i	−0.466820	+	0.0992256i	−0.435315	−	0.900278i	$-0.643363\pi$
$641$	−11.8189	+	2.51219i	−0.466820	+	0.0992256i	−0.0315044	+	0.999504i	$0.510030\pi$
$642$	3.71039	−	1.65197i	0.146437	−	0.0651982i
$643$	−45.2261			−1.78354			−0.891771	−	0.452487i	$-0.850537\pi$
$643$	−45.2261			−1.78354			−0.891771	+	0.452487i	$0.850537\pi$
$644$	−7.11005	+	0.806741i	−0.280175	+	0.0317900i
$645$		0			0
$646$	0.705084	+	6.70842i	0.0277411	+	0.263939i
$647$	6.75892	+	3.00927i	0.265721	+	0.118306i	0.535273	−	0.844679i	$-0.320209\pi$
$647$	6.75892	+	3.00927i	0.265721	+	0.118306i	−0.269552	+	0.962986i	$0.586876\pi$
$648$	7.05830	−	7.83904i	0.277276	−	0.307946i
$649$	1.77474	−	3.07393i	0.0696645	−	0.120662i
$650$		0			0
$651$	4.50377	+	20.3600i	0.176517	+	0.797970i
$652$	8.50480	+	26.1751i	0.333074	+	1.02510i
$653$	−0.00114984	−	0.0109400i	−4.49967e−5	−	0.000428115i	0.994499	−	0.104743i	$-0.0334018\pi$
$653$	−0.00114984	−	0.0109400i	−4.49967e−5	−	0.000428115i	−0.994544	+	0.104314i	$0.966735\pi$
$654$	2.03934	+	0.907975i	0.0797447	+	0.0355046i
$655$		0			0
$656$	−1.05454	+	0.469510i	−0.0411728	+	0.0183313i
$657$	12.9088			0.503620
$658$	−4.29982	−	5.81652i	−0.167624	−	0.226752i
$659$	13.2465	−	40.7685i	0.516009	−	1.58811i	−0.265428	−	0.964131i	$-0.585513\pi$
$659$	13.2465	−	40.7685i	0.516009	−	1.58811i	0.781438	−	0.623983i	$-0.214487\pi$
$660$		0			0
$661$	−18.3267	+	20.3538i	−0.712825	+	0.791672i	−0.985362	−	0.170473i	$-0.945470\pi$
$661$	−18.3267	+	20.3538i	−0.712825	+	0.791672i	0.272537	+	0.962145i	$0.412137\pi$
$662$	0.472604	−	0.100455i	0.0183683	−	0.00390430i
$663$	4.40433	+	4.89151i	0.171050	+	0.189970i
$664$	−4.55941	−	14.0324i	−0.176939	−	0.544563i
$665$		0			0
$666$	−1.40775	+	4.33261i	−0.0545492	+	0.167885i
$667$	−19.4582	+	8.66333i	−0.753423	+	0.335445i
$668$	−2.18242	−	3.78006i	−0.0844404	−	0.146255i
$669$	−1.80692	+	17.1917i	−0.0698597	+	0.664671i
$670$		0			0
$671$	−6.17326	+	4.48514i	−0.238316	+	0.173147i
$672$	14.6963	+	13.0144i	0.566923	+	0.502041i
$673$	5.91243	+	18.1966i	0.227907	+	0.701427i	0.997983	+	0.0634746i	$0.0202182\pi$
$673$	5.91243	+	18.1966i	0.227907	+	0.701427i	−0.770076	+	0.637952i	$0.779782\pi$
$674$	10.3893	−	17.9948i	0.400181	−	0.693135i
$675$		0			0
$676$	−1.30153	−	2.25432i	−0.0500589	−	0.0867045i
$677$	18.1093	+	3.84926i	0.695998	+	0.147939i	0.542307	−	0.840180i	$-0.317551\pi$
$677$	18.1093	+	3.84926i	0.695998	+	0.147939i	0.153690	+	0.988119i	$0.450884\pi$
$678$	18.2348	−	13.2483i	0.700303	−	0.508800i
$679$	−8.51312	+	41.7440i	−0.326703	+	1.60199i
$680$		0			0
$681$	−10.7948	+	4.80614i	−0.413657	+	0.184172i
$682$	9.24908	+	16.0199i	0.354166	+	0.613433i
$683$	−3.04319	+	28.9540i	−0.116445	+	1.10790i	0.767741	+	0.640760i	$0.221381\pi$
$683$	−3.04319	+	28.9540i	−0.116445	+	1.10790i	−0.884186	+	0.467136i	$0.845286\pi$
$684$	−5.08757	−	5.65032i	−0.194528	−	0.216045i
$685$		0			0
$686$	−7.06119	−	14.8574i	−0.269598	−	0.567257i
$687$	7.05337	−	21.7080i	0.269103	−	0.828213i
$688$	−0.0505291	−	0.0561183i	−0.00192640	−	0.00213949i
$689$	0.310444	−	0.344783i	0.0118270	−	0.0131352i
$690$		0			0
$691$	8.25989	+	9.17353i	0.314221	+	0.348978i	0.879480	−	0.475936i	$-0.157891\pi$
$691$	8.25989	+	9.17353i	0.314221	+	0.348978i	−0.565259	+	0.824913i	$0.691224\pi$
$692$	7.44006	+	5.40552i	0.282829	+	0.205487i
$693$	8.51837	−	7.79837i	0.323586	−	0.296235i
$694$	8.91330	+	6.47589i	0.338344	+	0.245822i
$695$		0			0
$696$	32.8932	+	14.6450i	1.24681	+	0.555116i
$697$	14.3223	+	6.37671i	0.542497	+	0.241535i
$698$	−1.94064	−	0.412495i	−0.0734542	−	0.0156132i
$699$	−0.413056			−0.0156232
$700$		0			0
$701$	21.5378			0.813471			0.406735	−	0.913546i	$-0.366667\pi$
$701$	21.5378			0.813471			0.406735	+	0.913546i	$0.366667\pi$
$702$	16.0917	+	3.42039i	0.607341	+	0.129094i
$703$	−18.8864	−	8.40878i	−0.712315	−	0.317143i
$704$	16.6192	+	7.39934i	0.626359	+	0.278873i
$705$		0			0
$706$	−2.82934	−	2.05564i	−0.106484	−	0.0773650i
$707$	14.8922	+	4.70311i	0.560080	+	0.176879i
$708$	−1.31608	−	0.956190i	−0.0494614	−	0.0359358i
$709$	−6.78935	−	7.54034i	−0.254980	−	0.283183i	0.602042	−	0.798465i	$-0.294354\pi$
$709$	−6.78935	−	7.54034i	−0.254980	−	0.283183i	−0.857021	+	0.515281i	$0.827687\pi$
$710$		0			0
$711$	−7.97643	+	8.85872i	−0.299139	+	0.332228i
$712$	21.2110	+	23.5572i	0.794916	+	0.882844i
$713$	−4.10912	+	12.6466i	−0.153888	+	0.473618i
$714$	0.0387959	+	4.69564i	0.00145190	+	0.175730i
$715$		0			0
$716$	20.2085	+	22.4438i	0.755227	+	0.838764i
$717$	−1.90132	+	18.0899i	−0.0710062	+	0.675579i
$718$	−11.6260	−	20.1368i	−0.433878	−	0.751499i
$719$	−31.3164	+	13.9430i	−1.16791	+	0.519985i	−0.896745	−	0.442549i	$-0.854074\pi$
$719$	−31.3164	+	13.9430i	−1.16791	+	0.519985i	−0.271161	+	0.962534i	$0.587408\pi$
$720$		0			0
$721$	26.5764	+	23.5348i	0.989756	+	0.876482i
$722$	−4.53139	+	3.29225i	−0.168641	+	0.122525i
$723$	7.99842	+	1.70012i	0.297464	+	0.0632280i
$724$	−14.7376	−	25.5262i	−0.547717	−	0.948674i
$725$		0			0
$726$	−0.725073	+	1.25586i	−0.0269100	+	0.0466095i
$727$	1.93172	+	5.94521i	0.0716434	+	0.220496i	0.980467	−	0.196686i	$-0.0630179\pi$
$727$	1.93172	+	5.94521i	0.0716434	+	0.220496i	−0.908823	+	0.417182i	$0.863018\pi$
$728$	−4.96696	+	24.3555i	−0.184088	+	0.902673i
$729$	−21.7975	+	15.8368i	−0.807313	+	0.586547i
$730$		0			0
$731$	−0.107205	+	1.01999i	−0.00396514	+	0.0377257i
$732$	1.74859	+	3.02865i	0.0646299	+	0.111942i
$733$	22.9905	−	10.2360i	0.849174	−	0.378077i	0.0644494	−	0.997921i	$-0.479471\pi$
$733$	22.9905	−	10.2360i	0.849174	−	0.378077i	0.784725	+	0.619844i	$0.212804\pi$
$734$	−6.80400	+	20.9406i	−0.251140	+	0.772930i
$735$		0			0
$736$	3.86838	+	11.9057i	0.142590	+	0.438848i
$737$	−28.8414	−	32.0316i	−1.06239	−	1.17990i
$738$	11.2602	−	2.39343i	0.414495	−	0.0881036i
$739$	−26.2405	+	29.1430i	−0.965271	+	1.07204i	0.0320930	+	0.999485i	$0.489783\pi$
$739$	−26.2405	+	29.1430i	−0.965271	+	1.07204i	−0.997364	+	0.0725574i	$0.976884\pi$
$740$		0			0
$741$	−6.77778	+	20.8599i	−0.248988	+	0.766307i
$742$	0.328878	−	0.0373161i	0.0120735	−	0.00136992i
$743$	1.82616			0.0669953			0.0334976	−	0.999439i	$-0.489335\pi$
$743$	1.82616			0.0669953			0.0334976	+	0.999439i	$0.489335\pi$
$744$	20.5353	−	9.14289i	0.752860	−	0.335195i
$745$		0			0
$746$	−21.8075	−	9.70933i	−0.798430	−	0.355484i
$747$	0.674853	+	6.42079i	0.0246916	+	0.234925i
$748$	−1.97608	−	6.08173i	−0.0722525	−	0.222370i
$749$	−1.97415	−	8.92443i	−0.0721338	−	0.326092i
$750$		0			0
$751$	20.3973	−	35.3292i	0.744310	−	1.28918i	−0.206207	−	0.978508i	$-0.566112\pi$
$751$	20.3973	−	35.3292i	0.744310	−	1.28918i	0.950517	−	0.310674i	$-0.100555\pi$
$752$	−0.228930	+	0.254253i	−0.00834823	+	0.00927165i
$753$	−27.6313	−	12.3023i	−1.00694	−	0.448319i
$754$	2.91689	+	27.7524i	0.106227	+	1.01068i
$755$		0			0
$756$	−10.7099	−	14.4877i	−0.389516	−	0.526912i
$757$	26.3319			0.957050			0.478525	−	0.878074i	$-0.341172\pi$
$757$	26.3319			0.957050			0.478525	+	0.878074i	$0.341172\pi$
$758$	−23.9241	+	10.6517i	−0.868961	+	0.386886i
$759$	−10.1129	+	2.14957i	−0.367075	+	0.0780243i
$760$		0			0
$761$	28.8793	+	6.13848i	1.04687	+	0.222520i	0.699074	−	0.715050i	$-0.253596\pi$
$761$	28.8793	+	6.13848i	1.04687	+	0.222520i	0.347799	+	0.937569i	$0.386929\pi$
$762$	2.32342	−	7.15074i	0.0841685	−	0.259044i
$763$	2.91919	−	4.08853i	0.105682	−	0.148015i
$764$	−4.09945	−	12.6168i	−0.148313	−	0.456460i
$765$		0			0
$766$	−1.92457	+	0.409081i	−0.0695377	+	0.0147807i
$767$	0.349422	−	3.32453i	0.0126169	−	0.120042i
$768$	10.7590	−	18.6352i	0.388233	−	0.672440i
$769$	33.9181	+	24.6430i	1.22312	+	0.888648i	0.996355	−	0.0853012i	$-0.0271853\pi$
$769$	33.9181	+	24.6430i	1.22312	+	0.888648i	0.226764	+	0.973950i	$0.427185\pi$
$770$		0			0
$771$	−28.6205	+	20.7940i	−1.03074	+	0.748879i
$772$	−1.43890	−	13.6903i	−0.0517873	−	0.492723i
$773$	26.7783	−	29.7403i	0.963148	−	1.06968i	−0.0343792	−	0.999409i	$-0.510945\pi$
$773$	26.7783	−	29.7403i	0.963148	−	1.06968i	0.997528	−	0.0702758i	$-0.0223879\pi$
$774$	0.376540	+	0.652187i	0.0135345	+	0.0234424i
$775$		0			0
$776$	45.9263			1.64866
$777$	−12.5229	−	7.09281i	−0.449257	−	0.254453i
$778$	−4.39807	+	3.19539i	−0.157678	+	0.114560i
$779$	5.46077	+	51.9558i	0.195652	+	1.86151i
$780$		0			0
$781$	−2.75259	+	26.1892i	−0.0984955	+	0.937122i
$782$	−1.49725	+	2.59332i	−0.0535416	+	0.0927368i
$783$	−43.3860	−	31.5218i	−1.55049	−	1.12650i
$784$	−0.621835	+	0.467680i	−0.0222084	+	0.0167029i
$785$		0			0
$786$	−7.43553	−	1.58047i	−0.265217	−	0.0563735i
$787$	5.50806	−	1.17078i	0.196341	−	0.0417336i	−0.108691	−	0.994076i	$-0.534666\pi$
$787$	5.50806	−	1.17078i	0.196341	−	0.0417336i	0.305033	+	0.952342i	$0.401333\pi$
$788$	−20.5353	+	4.36491i	−0.731539	+	0.155493i
$789$	6.06887	+	1.28998i	0.216057	+	0.0459244i
$790$		0			0
$791$	−21.0132	−	46.1660i	−0.747142	−	1.64147i
$792$	−10.0720	−	7.31777i	−0.357895	−	0.260026i
$793$	−3.59318	+	6.22357i	−0.127598	+	0.221006i
$794$	−0.0890952	+	0.847684i	−0.00316187	+	0.0300832i
$795$		0			0
$796$	0.0654682	+	0.622888i	0.00232046	+	0.0220777i
$797$	2.82844	−	2.05498i	0.100189	−	0.0727912i	−0.536563	−	0.843860i	$-0.680278\pi$
$797$	2.82844	−	2.05498i	0.100189	−	0.0727912i	0.636752	+	0.771069i	$0.280278\pi$
$798$	−13.4860	+	7.93545i	−0.477401	+	0.280912i
$799$	4.64669			0.164388
$800$		0			0
$801$	−6.93536	−	12.0124i	−0.245049	−	0.424437i
$802$	−3.69015	+	4.09833i	−0.130304	+	0.144717i
$803$	3.78162	+	35.9797i	0.133450	+	1.26970i
$804$	−15.9818	+	11.6114i	−0.563633	+	0.409503i
$805$		0			0
$806$	14.0941	+	10.2400i	0.496445	+	0.360688i
$807$	2.33202	−	4.03918i	0.0820911	−	0.142186i
$808$	1.75978	−	16.7432i	0.0619088	−	0.589023i
$809$	−29.7280	+	6.31889i	−1.04518	+	0.222160i	−0.698342	−	0.715764i	$-0.746079\pi$
$809$	−29.7280	+	6.31889i	−1.04518	+	0.222160i	−0.346840	+	0.937924i	$0.612745\pi$
$810$		0			0
$811$	3.79643	+	11.6842i	0.133311	+	0.410288i	0.995323	−	0.0965986i	$-0.0307963\pi$
$811$	3.79643	+	11.6842i	0.133311	+	0.410288i	−0.862013	+	0.506886i	$0.830796\pi$
$812$	17.7581	−	24.8715i	0.623188	−	0.872819i
$813$	7.07904	−	21.7870i	0.248273	−	0.764105i
$814$	−12.4884	−	2.65448i	−0.437717	−	0.0930395i
$815$		0			0
$816$	0.217256	−	0.0461791i	0.00760546	−	0.00161659i
$817$	−3.12211	+	1.39005i	−0.109229	+	0.0486318i
$818$	−33.3815			−1.16716
$819$	4.34167	−	9.97248i	0.151710	−	0.348467i
$820$		0			0
$821$	−4.99538	−	47.5278i	−0.174340	−	1.65873i	−0.636010	−	0.771681i	$-0.719416\pi$
$821$	−4.99538	−	47.5278i	−0.174340	−	1.65873i	0.461670	−	0.887052i	$-0.347251\pi$
$822$	7.59050	+	3.37951i	0.264749	+	0.117874i
$823$	−21.0852	+	23.4175i	−0.734985	+	0.816284i	−0.988528	−	0.151041i	$-0.951738\pi$
$823$	−21.0852	+	23.4175i	−0.734985	+	0.816284i	0.253542	+	0.967324i	$0.418404\pi$
$824$	19.1341	−	33.1412i	0.666567	−	1.15453i
$825$		0			0
$826$	1.75902	−	1.61035i	0.0612043	−	0.0560311i
$827$	−0.406798	−	1.25200i	−0.0141458	−	0.0435362i	0.943734	−	0.330704i	$-0.107286\pi$
$827$	−0.406798	−	1.25200i	−0.0141458	−	0.0435362i	−0.957880	+	0.287168i	$0.907286\pi$
$828$	−0.352820	−	3.35686i	−0.0122613	−	0.116659i
$829$	10.8850	+	4.84630i	0.378051	+	0.168319i	0.586960	−	0.809616i	$-0.300325\pi$
$829$	10.8850	+	4.84630i	0.378051	+	0.168319i	−0.208909	+	0.977935i	$0.566991\pi$
$830$		0			0
$831$	20.9444	−	9.32503i	0.726552	−	0.323482i
$832$	17.1330			0.593978
$833$	10.3715	+	2.02602i	0.359351	+	0.0701975i
$834$	−0.324851	+	0.999789i	−0.0112487	+	0.0346199i
$835$		0			0
$836$	14.2583	−	15.8355i	0.493134	−	0.547681i
$837$	−32.7485	+	6.96091i	−1.13195	+	0.240604i
$838$	4.65197	+	5.16654i	0.160700	+	0.178475i
$839$	−11.8043	−	36.3299i	−0.407529	−	1.25425i	−0.918765	−	0.394805i	$-0.870812\pi$
$839$	−11.8043	−	36.3299i	−0.407529	−	1.25425i	0.511236	−	0.859441i	$-0.329188\pi$
$840$		0			0
$841$	19.1487	−	58.9336i	0.660300	−	2.03219i
$842$	−10.2951	+	4.58369i	−0.354793	+	0.157964i
$843$	−6.41514	−	11.1113i	−0.220949	−	0.382695i
$844$	0.943363	−	8.97549i	0.0324719	−	0.308949i
$845$		0			0
$846$	2.76033	−	2.00550i	0.0949021	−	0.0689504i
$847$	2.44317	+	2.16356i	0.0839484	+	0.0743408i
$848$	−0.00483785	−	0.0148894i	−0.000166132	−	0.000511303i
$849$	0.0449131	−	0.0777917i	0.00154141	−	0.00266980i
$850$		0			0
$851$	−4.58890	−	7.94821i	−0.157306	−	0.272461i
$852$	11.8052	+	2.50927i	0.404440	+	0.0859663i
$853$	22.7770	−	16.5484i	0.779868	−	0.566607i	−0.125071	−	0.992148i	$-0.539916\pi$
$853$	22.7770	−	16.5484i	0.779868	−	0.566607i	0.904939	+	0.425540i	$0.139916\pi$
$854$	−4.86265	+	1.62451i	−0.166397	+	0.0555896i
$855$		0			0
$856$	−9.00127	+	4.00762i	−0.307657	+	0.136978i
$857$	−9.05790	−	15.6887i	−0.309412	−	0.535917i	0.668822	−	0.743423i	$-0.266799\pi$
$857$	−9.05790	−	15.6887i	−0.309412	−	0.535917i	−0.978234	+	0.207506i	$0.933466\pi$
$858$	−1.41586	+	13.4710i	−0.0483367	+	0.459893i
$859$	−12.0774	−	13.4133i	−0.412077	−	0.457657i	0.500999	−	0.865448i	$-0.332966\pi$
$859$	−12.0774	−	13.4133i	−0.412077	−	0.457657i	−0.913076	+	0.407791i	$0.866299\pi$
$860$		0			0
$861$	0.300469	+	36.3670i	0.0102399	+	1.23939i
$862$	5.42093	−	16.6839i	0.184637	−	0.568256i
$863$	−13.9546	−	15.4982i	−0.475022	−	0.527565i	0.457243	−	0.889342i	$-0.348837\pi$
$863$	−13.9546	−	15.4982i	−0.475022	−	0.527565i	−0.932265	+	0.361777i	$0.882170\pi$
$864$	−21.0901	+	23.4229i	−0.717499	+	0.796864i
$865$		0			0
$866$	7.90174	+	8.77577i	0.268512	+	0.298213i
$867$	15.7638	+	11.4530i	0.535366	+	0.388966i
$868$	−4.12079	−	18.6286i	−0.139869	−	0.632297i
$869$	−27.0280	−	19.6370i	−0.916860	−	0.666138i
$870$		0			0
$871$	−37.0841	−	16.5109i	−1.25655	−	0.559450i
$872$	−4.94737	−	2.20271i	−0.167539	−	0.0745933i
$873$	−19.6569	−	4.17820i	−0.665285	−	0.141411i
$874$	−9.97841			−0.337525
$875$		0			0
$876$	16.5808			0.560213
$877$	22.2420	+	4.72769i	0.751060	+	0.159643i	0.567509	−	0.823367i	$-0.307907\pi$
$877$	22.2420	+	4.72769i	0.751060	+	0.159643i	0.183552	+	0.983010i	$0.441241\pi$
$878$	20.1027	+	8.95029i	0.678433	+	0.302058i
$879$	−5.96116	−	2.65408i	−0.201065	−	0.0895198i
$880$		0			0
$881$	11.9712	+	8.69756i	0.403319	+	0.293028i	0.770891	−	0.636967i	$-0.219811\pi$
$881$	11.9712	+	8.69756i	0.403319	+	0.293028i	−0.367573	+	0.929995i	$0.619811\pi$
$882$	7.03553	−	3.27276i	0.236899	−	0.110200i
$883$	37.9652	+	27.5833i	1.27763	+	0.928253i	0.999479	−	0.0322836i	$-0.0102780\pi$
$883$	37.9652	+	27.5833i	1.27763	+	0.928253i	0.278152	+	0.960537i	$0.410278\pi$
$884$	−4.02981	−	4.47556i	−0.135537	−	0.150529i
$885$		0			0
$886$	−13.7815	+	15.3059i	−0.462998	+	0.514212i
$887$	8.97897	+	9.97216i	0.301484	+	0.334832i	0.874784	−	0.484514i	$-0.161003\pi$
$887$	8.97897	+	9.97216i	0.301484	+	0.334832i	−0.573299	+	0.819346i	$0.694337\pi$
$888$	−4.79430	+	14.7553i	−0.160886	+	0.495156i
$889$	−14.7228	−	8.33882i	−0.493788	−	0.279675i
$890$		0			0
$891$	−8.65579	−	9.61322i	−0.289980	−	0.322055i
$892$	1.65327	−	15.7298i	0.0553556	−	0.526673i
$893$	7.74195	+	13.4094i	0.259074	+	0.448730i
$894$	21.8159	−	9.71309i	0.729634	−	0.324854i
$895$		0			0
$896$	−13.0555	−	11.5614i	−0.436154	−	0.386238i
$897$	−7.87738	+	5.72325i	−0.263018	+	0.191094i
$898$	−4.22713	−	0.898505i	−0.141061	−	0.0299835i
$899$	−28.3953	−	49.1821i	−0.947036	−	1.64031i
$900$		0			0
$901$	−0.106314	+	0.184142i	−0.00354184	+	0.00613465i
$902$	9.96972	+	30.6836i	0.331955	+	1.02165i
$903$	−2.25655	+	0.753866i	−0.0750934	+	0.0250871i
$904$	−44.2369	+	32.1400i	−1.47130	+	1.06896i
$905$		0			0
$906$	2.36914	−	22.5409i	0.0787095	−	0.748871i
$907$	10.6957	+	18.5255i	0.355145	+	0.615128i	0.987143	−	0.159841i	$-0.0510983\pi$
$907$	10.6957	+	18.5255i	0.355145	+	0.615128i	−0.631998	+	0.774970i	$0.717765\pi$
$908$	9.87683	−	4.39745i	0.327774	−	0.145934i
$909$	−2.27643	+	7.00613i	−0.0755044	+	0.232379i
$910$		0			0
$911$	12.2568	+	37.7225i	0.406085	+	1.24980i	0.919986	+	0.391952i	$0.128200\pi$
$911$	12.2568	+	37.7225i	0.406085	+	1.24980i	−0.513901	+	0.857850i	$0.671800\pi$
$912$	0.495237	+	0.550017i	0.0163989	+	0.0182129i
$913$	−17.6985	+	3.76193i	−0.585735	+	0.124502i
$914$	−3.85686	+	4.28347i	−0.127573	+	0.141685i
$915$		0			0
$916$	−6.45358	+	19.8621i	−0.213232	+	0.656261i
$917$	−6.82866	+	15.6849i	−0.225502	+	0.517962i
$918$	−7.53955			−0.248842
$919$	11.0167	−	4.90497i	0.363409	−	0.161800i	−0.216906	−	0.976193i	$-0.569596\pi$
$919$	11.0167	−	4.90497i	0.363409	−	0.161800i	0.580314	+	0.814393i	$0.302930\pi$
$920$		0			0
$921$	−13.6780	−	6.08985i	−0.450706	−	0.200667i
$922$	0.400020	+	3.80594i	0.0131740	+	0.125342i
$923$	7.66376	+	23.5866i	0.252256	+	0.776363i
$924$	10.9415	−	10.0167i	0.359948	−	0.329524i
$925$		0			0
$926$	−14.6413	+	25.3594i	−0.481142	+	0.833363i
$927$	−11.2046	+	12.4440i	−0.368008	+	0.408714i
$928$	−48.8413	−	21.7455i	−1.60329	−	0.713832i
$929$	0.754839	+	7.18181i	0.0247655	+	0.235628i	0.999902	+	0.0140214i	$0.00446330\pi$
$929$	0.754839	+	7.18181i	0.0247655	+	0.235628i	−0.975136	+	0.221606i	$0.928870\pi$
$930$		0			0
$931$	11.4335	+	33.3057i	0.374717	+	1.09155i
$932$	0.377932			0.0123796
$933$	6.32223	−	2.81484i	0.206980	−	0.0921536i
$934$	13.5099	−	2.87162i	0.442058	−	0.0939624i
$935$		0			0
$936$	−11.4688	−	2.43776i	−0.374869	−	0.0796808i
$937$	14.3885	−	44.2832i	0.470051	−	1.44667i	−0.382466	−	0.923969i	$-0.624925\pi$
$937$	14.3885	−	44.2832i	0.470051	−	1.44667i	0.852517	−	0.522699i	$-0.175075\pi$
$938$	−11.9972	−	26.3580i	−0.391724	−	0.860619i
$939$	−7.22672	−	22.2416i	−0.235835	−	0.725826i
$940$		0			0
$941$	26.5182	−	5.63662i	0.864470	−	0.183749i	0.245724	−	0.969340i	$-0.420974\pi$
$941$	26.5182	−	5.63662i	0.864470	−	0.183749i	0.618746	+	0.785591i	$0.287641\pi$
$942$	0.0533992	−	0.508059i	0.00173984	−	0.0165535i
$943$	−11.5960	+	20.0849i	−0.377618	+	0.654053i
$944$	−0.0912580	−	0.0663028i	−0.00297019	−	0.00215797i
$945$		0			0
$946$	−1.70749	+	1.24056i	−0.0555151	+	0.0403341i
$947$	3.30214	+	31.4178i	0.107305	+	1.02094i	0.907171	+	0.420761i	$0.138237\pi$
$947$	3.30214	+	31.4178i	0.107305	+	1.02094i	−0.799866	+	0.600178i	$0.795096\pi$
$948$	−10.2454	+	11.3787i	−0.332755	+	0.369561i
$949$	17.0359	+	29.5071i	0.553009	+	0.957840i
$950$		0			0
$951$	−4.45393			−0.144429
$952$	−0.0941174	−	11.3914i	−0.00305036	−	0.369199i
$953$	−18.0966	+	13.1480i	−0.586207	+	0.425904i	−0.840956	−	0.541103i	$-0.818007\pi$
$953$	−18.0966	+	13.1480i	−0.586207	+	0.425904i	0.254750	+	0.967007i	$0.418007\pi$
$954$	0.0163198	+	0.155273i	0.000528374	+	0.00502714i
$955$		0			0
$956$	1.73964	−	16.5516i	0.0562641	−	0.535317i
$957$	22.0776	−	38.2395i	0.713667	−	1.23611i
$958$	−10.3497	−	7.51950i	−0.334384	−	0.242944i
$959$	10.8653	−	15.2176i	0.350859	−	0.491403i
$960$		0			0
$961$	−4.35714	−	0.926139i	−0.140553	−	0.0298754i
$962$	−11.7614	+	2.49996i	−0.379202	+	0.0806018i
$963$	4.21722	−	0.896398i	0.135898	−	0.0288860i
$964$	−7.31827	−	1.55555i	−0.235706	−	0.0501008i
$965$		0			0
$966$	−6.91418	−	0.669003i	−0.222460	−	0.0215248i
$967$	8.87751	+	6.44989i	0.285482	+	0.207414i	0.721305	−	0.692618i	$-0.243543\pi$
$967$	8.87751	+	6.44989i	0.285482	+	0.207414i	−0.435823	+	0.900032i	$0.643543\pi$
$968$	1.75900	−	3.04668i	0.0565364	−	0.0979239i
$969$	1.05072	−	9.99697i	0.0337541	−	0.321149i
$970$		0			0
$971$	4.19698	+	39.9316i	0.134687	+	1.28147i	0.827959	+	0.560789i	$0.189502\pi$
$971$	4.19698	+	39.9316i	0.134687	+	1.28147i	−0.693271	+	0.720677i	$0.743831\pi$
$972$	11.7309	−	8.52297i	0.376268	−	0.273374i
$973$	2.05849	+	1.16590i	0.0659922	+	0.0373771i
$974$	−3.38888			−0.108587
$975$		0			0
$976$	0.121249	+	0.210009i	0.00388107	+	0.00672221i
$977$	5.81964	−	6.46336i	0.186187	−	0.206781i	−0.642824	−	0.766014i	$-0.722237\pi$
$977$	5.81964	−	6.46336i	0.186187	−	0.206781i	0.829011	+	0.559232i	$0.188904\pi$
$978$	2.79274	+	26.5711i	0.0893019	+	0.849651i
$979$	31.4495	−	22.8494i	1.00513	−	0.730271i
$980$		0			0
$981$	1.91713	+	1.39287i	0.0612091	+	0.0444710i
$982$	2.86196	−	4.95706i	0.0913289	−	0.158186i
$983$	0.736130	−	7.00381i	0.0234789	−	0.223387i	−0.976490	−	0.215561i	$-0.930842\pi$
$983$	0.736130	−	7.00381i	0.0234789	−	0.223387i	0.999969	−	0.00782623i	$-0.00249119\pi$
$984$	38.3483	−	8.15119i	1.22250	−	0.259851i
$985$		0			0
$986$	−3.95200	−	12.1630i	−0.125857	−	0.387349i
$987$	4.46547	+	9.81066i	0.142138	+	0.312277i
$988$	6.20143	−	19.0860i	0.197294	−	0.607208i
$989$	−1.48403	−	0.315440i	−0.0471893	−	0.0100304i
$990$		0			0
$991$	−8.52557	+	1.81216i	−0.270824	+	0.0575653i	−0.341322	−	0.939947i	$-0.610874\pi$
$991$	−8.52557	+	1.81216i	−0.270824	+	0.0575653i	0.0704980	+	0.997512i	$0.477541\pi$
$992$	−30.4917	+	13.5758i	−0.968113	+	0.431031i
$993$	−0.720015			−0.0228490
$994$	−7.06258	+	16.2222i	−0.224011	+	0.514537i
$995$		0			0
$996$	0.866820	+	8.24724i	0.0274662	+	0.261324i
$997$	−24.6456	−	10.9729i	−0.780533	−	0.347516i	−0.0225124	−	0.999747i	$-0.507167\pi$
$997$	−24.6456	−	10.9729i	−0.780533	−	0.347516i	−0.758020	+	0.652231i	$0.773833\pi$
$998$	6.92611	−	7.69223i	0.219242	−	0.243493i
$999$	11.5539	−	20.0120i	0.365550	−	0.633151i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.q.a.401.7		144
5.2	odd	4		875.2.u.b.849.23		288
5.3	odd	4		875.2.u.b.849.14		288
5.4	even	2		175.2.q.a.156.12	yes	144
7.4	even	3	inner	875.2.q.a.151.12		144
25.3	odd	20		875.2.u.b.149.23		288
25.4	even	10		175.2.q.a.121.7	yes	144
25.21	even	5	inner	875.2.q.a.226.12		144
25.22	odd	20		875.2.u.b.149.14		288
35.4	even	6		175.2.q.a.81.7	yes	144
35.18	odd	12		875.2.u.b.599.14		288
35.32	odd	12		875.2.u.b.599.23		288
175.4	even	30		175.2.q.a.46.12	✓	144
175.46	even	15	inner	875.2.q.a.851.7		144
175.53	odd	60		875.2.u.b.774.23		288
175.172	odd	60		875.2.u.b.774.14		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.q.a.46.12	✓	144	175.4	even	30
175.2.q.a.81.7	yes	144	35.4	even	6
175.2.q.a.121.7	yes	144	25.4	even	10
175.2.q.a.156.12	yes	144	5.4	even	2
875.2.q.a.151.12		144	7.4	even	3	inner
875.2.q.a.226.12		144	25.21	even	5	inner
875.2.q.a.401.7		144	1.1	even	1	trivial
875.2.q.a.851.7		144	175.46	even	15	inner
875.2.u.b.149.14		288	25.22	odd	20
875.2.u.b.149.23		288	25.3	odd	20
875.2.u.b.599.14		288	35.18	odd	12
875.2.u.b.599.23		288	35.32	odd	12
875.2.u.b.774.14		288	175.172	odd	60
875.2.u.b.774.23		288	175.53	odd	60
875.2.u.b.849.14		288	5.3	odd	4
875.2.u.b.849.23		288	5.2	odd	4

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:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.q (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.868806 - 0.184670i) q^{2} +(1.20920 + 0.538368i) q^{3} +(-1.10637 - 0.492588i) q^{4} +(-0.951135 - 0.691040i) q^{6} +(-1.95148 + 1.78654i) q^{7} +(2.30742 + 1.67644i) q^{8} +(-0.835080 - 0.927450i) q^{9} +O(q^{10})\)	\(q+(-0.868806 - 0.184670i) q^{2} +(1.20920 + 0.538368i) q^{3} +(-1.10637 - 0.492588i) q^{4} +(-0.951135 - 0.691040i) q^{6} +(-1.95148 + 1.78654i) q^{7} +(2.30742 + 1.67644i) q^{8} +(-0.835080 - 0.927450i) q^{9} +(2.34038 - 2.59925i) q^{11} +(-1.07262 - 1.19127i) q^{12} +(1.01791 - 3.13281i) q^{13} +(2.02538 - 1.19177i) q^{14} +(-0.0743764 - 0.0826034i) q^{16} +(-0.157801 + 1.50138i) q^{17} +(0.554249 + 0.959988i) q^{18} +(-4.59560 + 2.04609i) q^{19} +(-3.32154 + 1.10966i) q^{21} +(-2.51334 + 1.82605i) q^{22} +(-2.18442 - 0.464312i) q^{23} +(1.88758 + 3.26938i) q^{24} +(-1.46290 + 2.53382i) q^{26} +(-1.73754 - 5.34759i) q^{27} +(3.03909 - 1.01530i) q^{28} +(7.71611 - 5.60608i) q^{29} +(0.622401 - 5.92175i) q^{31} +(-2.80276 - 4.85452i) q^{32} +(4.22933 - 1.88302i) q^{33} +(0.414359 - 1.27526i) q^{34} +(0.467057 + 1.43745i) q^{36} +(2.74991 + 3.05409i) q^{37} +(4.37054 - 0.928986i) q^{38} +(2.91746 - 3.24016i) q^{39} +(3.20915 - 9.87674i) q^{41} +(3.09069 - 0.350685i) q^{42} +0.679370 q^{43} +(-3.86968 + 1.72289i) q^{44} +(1.81209 + 0.806794i) q^{46} +(-0.321738 - 3.06114i) q^{47} +(-0.0454646 - 0.139926i) q^{48} +(0.616571 - 6.97279i) q^{49} +(-0.999107 + 1.73050i) q^{51} +(-2.66937 + 2.96463i) q^{52} +(0.128670 + 0.0572874i) q^{53} +(0.522041 + 4.96688i) q^{54} +(-7.49790 + 0.850749i) q^{56} -6.65853 q^{57} +(-7.73908 + 3.44566i) q^{58} +(0.992644 - 0.210993i) q^{59} +(-2.13396 - 0.453587i) q^{61} +(-1.63432 + 5.02991i) q^{62} +(3.28657 + 0.318002i) q^{63} +(1.60726 + 4.94665i) q^{64} +(-4.02220 + 0.854945i) q^{66} +(1.28814 - 12.2559i) q^{67} +(0.914148 - 1.58335i) q^{68} +(-2.39141 - 1.73746i) q^{69} +(-6.09102 + 4.42539i) q^{71} +(-0.372066 - 3.53997i) q^{72} +(-6.92117 + 7.68673i) q^{73} +(-1.82514 - 3.16123i) q^{74} +6.09232 q^{76} +(0.0764540 + 9.25356i) q^{77} +(-3.13306 + 2.27630i) q^{78} +(-0.998425 - 9.49938i) q^{79} +(0.386594 - 3.67820i) q^{81} +(-4.61207 + 7.98834i) q^{82} +(-4.18519 - 3.04072i) q^{83} +(4.22146 + 0.408460i) q^{84} +(-0.590240 - 0.125459i) q^{86} +(12.3484 - 2.62474i) q^{87} +(9.75770 - 2.07406i) q^{88} +(10.8714 + 2.31079i) q^{89} +(3.61044 + 7.93215i) q^{91} +(2.18806 + 1.58972i) q^{92} +(3.94069 - 6.82547i) q^{93} +(-0.285773 + 2.71895i) q^{94} +(-0.775562 - 7.37898i) q^{96} +(13.0272 - 9.46481i) q^{97} +(-1.82335 + 5.94414i) q^{98} -4.36507 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 3 q^{2} + 3 q^{3} + 13 q^{4} - 12 q^{6} + 22 q^{7} + 2 q^{8} + 11 q^{9}+O(q^{10}) \) 144 * q + 3 * q^2 + 3 * q^3 + 13 * q^4 - 12 * q^6 + 22 * q^7 + 2 * q^8 + 11 * q^9	\( 144 q + 3 q^{2} + 3 q^{3} + 13 q^{4} - 12 q^{6} + 22 q^{7} + 2 q^{8} + 11 q^{9} - 6 q^{11} + 11 q^{12} + 12 q^{13} - 6 q^{14} + 13 q^{16} - 9 q^{17} + 18 q^{18} - 11 q^{19} - 3 q^{21} + 52 q^{22} + 17 q^{23} + 46 q^{24} + 44 q^{26} + 84 q^{27} - 62 q^{28} - 24 q^{29} - 21 q^{31} + 16 q^{32} + 18 q^{33} - 36 q^{34} - 104 q^{36} + 5 q^{37} + 12 q^{38} + 25 q^{39} + 38 q^{41} + 58 q^{42} - 20 q^{43} - 7 q^{44} + 21 q^{46} + q^{47} + 12 q^{48} - 38 q^{49} - 8 q^{51} - 50 q^{52} - 37 q^{53} + 15 q^{54} - 60 q^{56} - 136 q^{57} - 53 q^{58} - 39 q^{59} - 13 q^{61} - 124 q^{62} - 75 q^{63} + 42 q^{64} + 7 q^{66} + 13 q^{67} + 110 q^{68} + 50 q^{69} + 22 q^{71} + 18 q^{72} + 41 q^{73} - 10 q^{74} - 276 q^{76} - 37 q^{77} - 2 q^{78} + 9 q^{79} + 57 q^{81} + 108 q^{82} - 86 q^{83} - 29 q^{84} - 17 q^{86} + 7 q^{87} + 26 q^{88} - 42 q^{89} - 34 q^{91} + 62 q^{92} - 98 q^{93} - 11 q^{94} + 13 q^{96} - 96 q^{97} + 86 q^{98} - 68 q^{99}+O(q^{100}) \) 144 * q + 3 * q^2 + 3 * q^3 + 13 * q^4 - 12 * q^6 + 22 * q^7 + 2 * q^8 + 11 * q^9 - 6 * q^11 + 11 * q^12 + 12 * q^13 - 6 * q^14 + 13 * q^16 - 9 * q^17 + 18 * q^18 - 11 * q^19 - 3 * q^21 + 52 * q^22 + 17 * q^23 + 46 * q^24 + 44 * q^26 + 84 * q^27 - 62 * q^28 - 24 * q^29 - 21 * q^31 + 16 * q^32 + 18 * q^33 - 36 * q^34 - 104 * q^36 + 5 * q^37 + 12 * q^38 + 25 * q^39 + 38 * q^41 + 58 * q^42 - 20 * q^43 - 7 * q^44 + 21 * q^46 + q^47 + 12 * q^48 - 38 * q^49 - 8 * q^51 - 50 * q^52 - 37 * q^53 + 15 * q^54 - 60 * q^56 - 136 * q^57 - 53 * q^58 - 39 * q^59 - 13 * q^61 - 124 * q^62 - 75 * q^63 + 42 * q^64 + 7 * q^66 + 13 * q^67 + 110 * q^68 + 50 * q^69 + 22 * q^71 + 18 * q^72 + 41 * q^73 - 10 * q^74 - 276 * q^76 - 37 * q^77 - 2 * q^78 + 9 * q^79 + 57 * q^81 + 108 * q^82 - 86 * q^83 - 29 * q^84 - 17 * q^86 + 7 * q^87 + 26 * q^88 - 42 * q^89 - 34 * q^91 + 62 * q^92 - 98 * q^93 - 11 * q^94 + 13 * q^96 - 96 * q^97 + 86 * q^98 - 68 * q^99

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