LMFDB - Embedded newform 845.2.o.i.587.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(258,845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("845.258"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.o (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [144,0,4,-80,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			587.17
Character	$\chi$	$=$	845.587
Dual form			845.2.o.i.488.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.344846 - 0.597291i) q^{2} +(0.0849492 + 0.0227621i) q^{3} +(0.762163 - 1.32010i) q^{4} +(2.18944 - 0.454257i) q^{5} +(-0.0156988 - 0.0585888i) q^{6} +(-0.698835 - 0.403473i) q^{7} -2.43070 q^{8} +(-2.59138 - 1.49613i) q^{9} +(-1.02634 - 1.15108i) q^{10} +(-0.115096 + 0.429543i) q^{11} +(0.0947934 - 0.0947934i) q^{12} +0.556544i q^{14} +(0.196331 + 0.0112474i) q^{15} +(-0.686109 - 1.18838i) q^{16} +(-1.35987 - 5.07510i) q^{17} +2.06374i q^{18} +(-6.54191 + 1.75290i) q^{19} +(1.06904 - 3.23651i) q^{20} +(-0.0501816 - 0.0501816i) q^{21} +(0.296253 - 0.0793806i) q^{22} +(1.39222 - 5.19583i) q^{23} +(-0.206486 - 0.0553277i) q^{24} +(4.58730 - 1.98914i) q^{25} +(-0.372642 - 0.372642i) q^{27} +(-1.06525 + 0.615023i) q^{28} +(-4.14945 + 2.39569i) q^{29} +(-0.0609860 - 0.121145i) q^{30} +(0.106205 - 0.106205i) q^{31} +(-2.90390 + 5.02971i) q^{32} +(-0.0195546 + 0.0338695i) q^{33} +(-2.56236 + 2.56236i) q^{34} +(-1.71334 - 0.565929i) q^{35} +(-3.95010 + 2.28059i) q^{36} +(5.17187 - 2.98598i) q^{37} +(3.30294 + 3.30294i) q^{38} +(-5.32187 + 1.10416i) q^{40} +(8.38192 + 2.24593i) q^{41} +(-0.0126681 + 0.0472779i) q^{42} +(9.32785 - 2.49939i) q^{43} +(0.479320 + 0.479320i) q^{44} +(-6.35330 - 2.09854i) q^{45} +(-3.58352 + 0.960201i) q^{46} +9.32662i q^{47} +(-0.0312345 - 0.116569i) q^{48} +(-3.17442 - 5.49826i) q^{49} +(-2.77001 - 2.05401i) q^{50} -0.462079i q^{51} +(5.61903 - 5.61903i) q^{53} +(-0.0940715 + 0.351079i) q^{54} +(-0.0568723 + 0.992743i) q^{55} +(1.69866 + 0.980720i) q^{56} -0.595630 q^{57} +(2.86184 + 1.65229i) q^{58} +(-0.569671 - 2.12604i) q^{59} +(0.164484 - 0.250605i) q^{60} +(-1.51542 + 2.62478i) q^{61} +(-0.100059 - 0.0268108i) q^{62} +(1.20730 + 2.09110i) q^{63} +1.26116 q^{64} +0.0269733 q^{66} +(-5.80593 - 10.0562i) q^{67} +(-7.73610 - 2.07288i) q^{68} +(0.236536 - 0.409692i) q^{69} +(0.252814 + 1.21852i) q^{70} +(-0.369434 - 1.37875i) q^{71} +(6.29886 + 3.63665i) q^{72} -0.265877 q^{73} +(-3.56700 - 2.05941i) q^{74} +(0.434964 - 0.0645592i) q^{75} +(-2.67199 + 9.97200i) q^{76} +(0.253742 - 0.253742i) q^{77} +8.98397i q^{79} +(-2.04202 - 2.29021i) q^{80} +(4.46522 + 7.73400i) q^{81} +(-1.54900 - 5.78094i) q^{82} +2.59025i q^{83} +(-0.104491 + 0.0279984i) q^{84} +(-5.28275 - 10.4939i) q^{85} +(-4.70953 - 4.70953i) q^{86} +(-0.407024 + 0.109062i) q^{87} +(0.279763 - 1.04409i) q^{88} +(-8.33554 - 2.23350i) q^{89} +(0.937469 + 4.51844i) q^{90} +(-5.79794 - 5.79794i) q^{92} +(0.0114394 - 0.00660456i) q^{93} +(5.57070 - 3.21625i) q^{94} +(-13.5269 + 6.80958i) q^{95} +(-0.361171 + 0.361171i) q^{96} +(7.24668 - 12.5516i) q^{97} +(-2.18937 + 3.79210i) q^{98} +(0.940911 - 0.940911i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 4 q^{3} - 80 q^{4} - 12 q^{10} - 128 q^{12} - 80 q^{16} + 8 q^{17} - 24 q^{22} + 36 q^{23} + 96 q^{25} - 128 q^{27} - 4 q^{30} - 80 q^{35} - 56 q^{38} - 48 q^{40} + 56 q^{42} + 76 q^{43} + 76 q^{48}+ \cdots - 92 q^{95}+O(q^{100}) $ 144 * q + 4 * q^3 - 80 * q^4 - 12 * q^10 - 128 * q^12 - 80 * q^16 + 8 * q^17 - 24 * q^22 + 36 * q^23 + 96 * q^25 - 128 * q^27 - 4 * q^30 - 80 * q^35 - 56 * q^38 - 48 * q^40 + 56 * q^42 + 76 * q^43 + 76 * q^48 + 8 * q^49 - 32 * q^53 - 12 * q^55 - 8 * q^61 + 148 * q^62 + 240 * q^64 + 80 * q^66 + 48 * q^68 - 40 * q^69 - 164 * q^75 - 344 * q^77 - 16 * q^81 + 44 * q^82 - 20 * q^87 + 124 * q^88 + 600 * q^90 - 8 * q^92 - 92 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.344846	−	0.597291i	−0.243843	−	0.422348i	0.717963	−	0.696082i	$-0.245075\pi$
$2$	−0.344846	−	0.597291i	−0.243843	−	0.422348i	−0.961806	+	0.273733i	$0.911741\pi$
$3$	0.0849492	+	0.0227621i	0.0490454	+	0.0131417i	0.283258	−	0.959044i	$-0.408585\pi$
$3$	0.0849492	+	0.0227621i	0.0490454	+	0.0131417i	−0.234213	+	0.972185i	$0.575251\pi$
$4$	0.762163	−	1.32010i	0.381081	−	0.660052i
$5$	2.18944	−	0.454257i	0.979148	−	0.203150i
$5$	2.18944	−	0.454257i	0.979148	−	0.203150i
$6$	−0.0156988	−	0.0585888i	−0.00640901	−	0.0239188i
$7$	−0.698835	−	0.403473i	−0.264135	−	0.152498i	0.362084	−	0.932145i	$-0.382065\pi$
$7$	−0.698835	−	0.403473i	−0.264135	−	0.152498i	−0.626219	+	0.779647i	$0.715399\pi$
$8$	−2.43070			−0.859382
$9$	−2.59138	−	1.49613i	−0.863793	−	0.498711i
$10$	−1.02634	−	1.15108i	−0.324558	−	0.364005i
$11$	−0.115096	+	0.429543i	−0.0347027	+	0.129512i	−0.981104	−	0.193481i	$-0.938022\pi$
$11$	−0.115096	+	0.429543i	−0.0347027	+	0.129512i	0.946401	+	0.322993i	$0.104689\pi$
$12$	0.0947934	−	0.0947934i	0.0273645	−	0.0273645i
$13$		0			0
$13$		0			0
$14$			0.556544i			0.148743i
$15$	0.196331	+	0.0112474i	0.0506925	+	0.00290407i
$16$	−0.686109	−	1.18838i	−0.171527	−	0.297094i
$17$	−1.35987	−	5.07510i	−0.329816	−	1.23089i	−0.909381	−	0.415965i	$-0.863444\pi$
$17$	−1.35987	−	5.07510i	−0.329816	−	1.23089i	0.579564	−	0.814927i	$-0.303223\pi$
$18$			2.06374i			0.486428i
$19$	−6.54191	+	1.75290i	−1.50082	+	0.402143i	−0.913374	−	0.407122i	$-0.866532\pi$
$19$	−6.54191	+	1.75290i	−1.50082	+	0.402143i	−0.587444	+	0.809265i	$0.699866\pi$
$20$	1.06904	−	3.23651i	0.239045	−	0.723705i
$21$	−0.0501816	−	0.0501816i	−0.0109505	−	0.0109505i
$22$	0.296253	−	0.0793806i	0.0631613	−	0.0169240i
$23$	1.39222	−	5.19583i	0.290298	−	1.08341i	−0.654583	−	0.755990i	$-0.727156\pi$
$23$	1.39222	−	5.19583i	0.290298	−	1.08341i	0.944881	−	0.327415i	$-0.106178\pi$
$24$	−0.206486	−	0.0553277i	−0.0421488	−	0.0112937i
$25$	4.58730	−	1.98914i	0.917460	−	0.397828i
$26$		0			0
$27$	−0.372642	−	0.372642i	−0.0717149	−	0.0717149i
$28$	−1.06525	+	0.615023i	−0.201314	+	0.116229i
$29$	−4.14945	+	2.39569i	−0.770534	+	0.444868i	−0.833065	−	0.553175i	$-0.813416\pi$
$29$	−4.14945	+	2.39569i	−0.770534	+	0.444868i	0.0625310	+	0.998043i	$0.480083\pi$
$30$	−0.0609860	−	0.121145i	−0.0111345	−	0.0221180i
$31$	0.106205	−	0.106205i	0.0190749	−	0.0190749i	−0.697505	−	0.716580i	$-0.745707\pi$
$31$	0.106205	−	0.106205i	0.0190749	−	0.0190749i	0.716580	+	0.697505i	$0.245707\pi$
$32$	−2.90390	+	5.02971i	−0.513342	+	0.889135i
$33$	−0.0195546	+	0.0338695i	−0.00340402	+	0.00589593i
$34$	−2.56236	+	2.56236i	−0.439442	+	0.439442i
$35$	−1.71334	−	0.565929i	−0.289607	−	0.0956594i
$36$	−3.95010	+	2.28059i	−0.658350	+	0.380099i
$37$	5.17187	−	2.98598i	0.850250	−	0.490892i	−0.0104851	−	0.999945i	$-0.503338\pi$
$37$	5.17187	−	2.98598i	0.850250	−	0.490892i	0.860735	+	0.509053i	$0.170004\pi$
$38$	3.30294	+	3.30294i	0.535808	+	0.535808i
$39$		0			0
$40$	−5.32187	+	1.10416i	−0.841461	+	0.174583i
$41$	8.38192	+	2.24593i	1.30904	+	0.350755i	0.844860	−	0.534988i	$-0.179684\pi$
$41$	8.38192	+	2.24593i	1.30904	+	0.350755i	0.464176	+	0.885743i	$0.346351\pi$
$42$	−0.0126681	+	0.0472779i	−0.00195473	+	0.00729514i
$43$	9.32785	−	2.49939i	1.42248	−	0.381153i	0.536119	−	0.844142i	$-0.319890\pi$
$43$	9.32785	−	2.49939i	1.42248	−	0.381153i	0.886364	+	0.462989i	$0.153223\pi$
$44$	0.479320	+	0.479320i	0.0722603	+	0.0722603i
$45$	−6.35330	−	2.09854i	−0.947094	−	0.312832i
$46$	−3.58352	+	0.960201i	−0.528361	+	0.141574i
$47$			9.32662i			1.36043i	0.733014	+	0.680214i	$0.238113\pi$
$47$			9.32662i			1.36043i	−0.733014	+	0.680214i	$0.761887\pi$
$48$	−0.0312345	−	0.116569i	−0.00450831	−	0.0168253i
$49$	−3.17442	−	5.49826i	−0.453489	−	0.785465i
$50$	−2.77001	−	2.05401i	−0.391738	−	0.290480i
$51$		−	0.462079i		−	0.0647040i
$52$		0			0
$53$	5.61903	−	5.61903i	0.771833	−	0.771833i	−0.206594	−	0.978427i	$-0.566238\pi$
$53$	5.61903	−	5.61903i	0.771833	−	0.771833i	0.978427	+	0.206594i	$0.0662378\pi$
$54$	−0.0940715	+	0.351079i	−0.0128015	+	0.0477759i
$55$	−0.0568723	+	0.992743i	−0.00766866	+	0.133861i
$56$	1.69866	+	0.980720i	0.226993	+	0.131054i
$57$	−0.595630			−0.0788931
$58$	2.86184	+	1.65229i	0.375779	+	0.216956i
$59$	−0.569671	−	2.12604i	−0.0741648	−	0.276787i	0.918878	−	0.394542i	$-0.129097\pi$
$59$	−0.569671	−	2.12604i	−0.0741648	−	0.276787i	−0.993043	+	0.117755i	$0.962430\pi$
$60$	0.164484	−	0.250605i	0.0212348	−	0.0323530i
$61$	−1.51542	+	2.62478i	−0.194029	+	0.336069i	−0.946582	−	0.322463i	$-0.895489\pi$
$61$	−1.51542	+	2.62478i	−0.194029	+	0.336069i	0.752553	+	0.658532i	$0.228822\pi$
$62$	−0.100059	−	0.0268108i	−0.0127075	−	0.00340497i
$63$	1.20730	+	2.09110i	0.152105	+	0.263454i
$64$	1.26116			0.157645
$65$		0			0
$66$	0.0269733			0.00332018
$67$	−5.80593	−	10.0562i	−0.709308	−	1.22856i	−0.965114	−	0.261829i	$-0.915674\pi$
$67$	−5.80593	−	10.0562i	−0.709308	−	1.22856i	0.255807	−	0.966728i	$-0.417659\pi$
$68$	−7.73610	−	2.07288i	−0.938140	−	0.251374i
$69$	0.236536	−	0.409692i	0.0284755	−	0.0493211i
$70$	0.252814	+	1.21852i	0.0302170	+	0.145641i
$71$	−0.369434	−	1.37875i	−0.0438437	−	0.163627i	0.940533	−	0.339703i	$-0.110326\pi$
$71$	−0.369434	−	1.37875i	−0.0438437	−	0.163627i	−0.984377	+	0.176075i	$0.943660\pi$
$72$	6.29886	+	3.63665i	0.742328	+	0.428583i
$73$	−0.265877			−0.0311186			−0.0155593	−	0.999879i	$-0.504953\pi$
$73$	−0.265877			−0.0311186			−0.0155593	+	0.999879i	$0.504953\pi$
$74$	−3.56700	−	2.05941i	−0.414655	−	0.239401i
$75$	0.434964	−	0.0645592i	0.0502254	−	0.00745466i
$76$	−2.67199	+	9.97200i	−0.306498	+	1.14387i
$77$	0.253742	−	0.253742i	0.0289166	−	0.0289166i
$78$		0			0
$79$			8.98397i			1.01078i	0.862892	+	0.505388i	$0.168650\pi$
$79$			8.98397i			1.01078i	−0.862892	+	0.505388i	$0.831350\pi$
$80$	−2.04202	−	2.29021i	−0.228305	−	0.256053i
$81$	4.46522	+	7.73400i	0.496136	+	0.859333i
$82$	−1.54900	−	5.78094i	−0.171058	−	0.638398i
$83$			2.59025i			0.284317i	0.989844	+	0.142159i	$0.0454043\pi$
$83$			2.59025i			0.284317i	−0.989844	+	0.142159i	$0.954596\pi$
$84$	−0.104491	+	0.0279984i	−0.0114010	+	0.00305488i
$85$	−5.28275	−	10.4939i	−0.572995	−	1.13822i
$86$	−4.70953	−	4.70953i	−0.507842	−	0.507842i
$87$	−0.407024	+	0.109062i	−0.0436375	+	0.0116926i
$88$	0.279763	−	1.04409i	0.0298229	−	0.111300i
$89$	−8.33554	−	2.23350i	−0.883566	−	0.236751i	−0.211621	−	0.977352i	$-0.567874\pi$
$89$	−8.33554	−	2.23350i	−0.883566	−	0.236751i	−0.671945	+	0.740601i	$0.734541\pi$
$90$	0.937469	+	4.51844i	0.0988179	+	0.476285i
$91$		0			0
$92$	−5.79794	−	5.79794i	−0.604477	−	0.604477i
$93$	0.0114394	−	0.00660456i	0.00118621	−	0.000684860i
$94$	5.57070	−	3.21625i	0.574574	−	0.331731i
$95$	−13.5269	+	6.80958i	−1.38783	+	0.698648i
$96$	−0.361171	+	0.361171i	−0.0368618	+	0.0368618i
$97$	7.24668	−	12.5516i	0.735789	−	1.27442i	−0.218587	−	0.975818i	$-0.570145\pi$
$97$	7.24668	−	12.5516i	0.735789	−	1.27442i	0.954376	−	0.298607i	$-0.0965220\pi$
$98$	−2.18937	+	3.79210i	−0.221160	+	0.383060i
$99$	0.940911	−	0.940911i	0.0945651	−	0.0945651i
$100$	0.870400	−	7.57176i	0.0870400	−	0.757176i
$101$	−3.40597	+	1.96644i	−0.338907	+	0.195668i	−0.659789	−	0.751451i	$-0.729354\pi$
$101$	−3.40597	+	1.96644i	−0.338907	+	0.195668i	0.320882	+	0.947119i	$0.396021\pi$
$102$	−0.275995	+	0.159346i	−0.0273276	+	0.0157776i
$103$	−12.2725	−	12.2725i	−1.20924	−	1.20924i	−0.971272	−	0.237970i	$-0.923518\pi$
$103$	−12.2725	−	12.2725i	−1.20924	−	1.20924i	−0.237970	−	0.971272i	$-0.576482\pi$
$104$		0			0
$105$	−0.132665	−	0.0870743i	−0.0129468	−	0.00849758i
$106$	−5.29389	−	1.41849i	−0.514188	−	0.137776i
$107$	−1.27280	+	4.75017i	−0.123047	+	0.459216i	−0.999763	−	0.0217924i	$-0.993063\pi$
$107$	−1.27280	+	4.75017i	−0.123047	+	0.459216i	0.876716	+	0.481009i	$0.159729\pi$
$108$	−0.775940	+	0.207912i	−0.0746648	+	0.0200064i
$109$	−5.74206	−	5.74206i	−0.549990	−	0.549990i	0.376448	−	0.926438i	$-0.377145\pi$
$109$	−5.74206	−	5.74206i	−0.549990	−	0.549990i	−0.926438	+	0.376448i	$0.877145\pi$
$110$	0.612568	−	0.308374i	0.0584061	−	0.0294023i
$111$	0.507313	−	0.135934i	0.0481521	−	0.0129023i
$112$			1.10730i			0.104630i
$113$	1.23285	+	4.60104i	0.115976	+	0.432830i	0.999358	−	0.0358244i	$-0.0114057\pi$
$113$	1.23285	+	4.60104i	0.115976	+	0.432830i	−0.883382	+	0.468654i	$0.844739\pi$
$114$	0.205401	+	0.355764i	0.0192375	+	0.0333204i
$115$	0.687937	−	12.0084i	0.0641504	−	1.11979i
$116$			7.30362i			0.678124i
$117$		0			0
$118$	−1.07342	+	1.07342i	−0.0988159	+	0.0988159i
$119$	−1.09734	+	4.09533i	−0.100593	+	0.375418i
$120$	−0.477222	−	0.0273391i	−0.0435642	−	0.00249571i
$121$	9.35502	+	5.40112i	0.850456	+	0.491011i
$122$	2.09034			0.189251
$123$	0.660915	+	0.381580i	0.0595927	+	0.0344059i
$124$	−0.0592559	−	0.221146i	−0.00532134	−	0.0198595i
$125$	9.14004	−	6.43891i	0.817510	−	0.575914i
$126$	0.832663	−	1.44221i	0.0741795	−	0.128483i
$127$	14.1542	+	3.79262i	1.25599	+	0.336540i	0.824646	−	0.565650i	$-0.191374\pi$
$127$	14.1542	+	3.79262i	1.25599	+	0.336540i	0.431339	+	0.902190i	$0.358041\pi$
$128$	5.37290	+	9.30613i	0.474902	+	0.822554i
$129$	0.849284			0.0747753
$130$		0			0
$131$	21.1674			1.84941			0.924704	−	0.380686i	$-0.124312\pi$
$131$	21.1674			1.84941			0.924704	+	0.380686i	$0.124312\pi$
$132$	0.0298076	+	0.0516282i	0.00259441	+	0.00449366i
$133$	5.27897	+	1.41449i	0.457744	+	0.122652i
$134$	−4.00430	+	6.93566i	−0.345919	+	0.599150i
$135$	−0.985152	−	0.646602i	−0.0847884	−	0.0556506i
$136$	3.30543	+	12.3360i	0.283438	+	1.05781i
$137$	13.1951	+	7.61820i	1.12733	+	0.650867i	0.943263	−	0.332046i	$-0.107739\pi$
$137$	13.1951	+	7.61820i	1.12733	+	0.650867i	0.184071	+	0.982913i	$0.441072\pi$
$138$	−0.326273			−0.0277742
$139$	10.2809	+	5.93569i	0.872016	+	0.503459i	0.868018	−	0.496533i	$-0.165394\pi$
$139$	10.2809	+	5.93569i	0.872016	+	0.503459i	0.00399825	+	0.999992i	$0.498727\pi$
$140$	−2.05293	+	1.83046i	−0.173504	+	0.154702i
$141$	−0.212293	+	0.792289i	−0.0178783	+	0.0667228i
$142$	−0.696114	+	0.696114i	−0.0584166	+	0.0584166i
$143$		0			0
$144$			4.10604i			0.342170i
$145$	−7.99672	+	7.13014i	−0.664092	+	0.592126i
$146$	0.0916867	+	0.158806i	0.00758805	+	0.0131429i
$147$	−0.144513	−	0.539329i	−0.0119192	−	0.0444831i
$148$		−	9.10321i		−	0.748279i
$149$	13.0327	−	3.49210i	1.06768	−	0.286084i	0.318141	−	0.948043i	$-0.396941\pi$
$149$	13.0327	−	3.49210i	1.06768	−	0.286084i	0.749540	+	0.661959i	$0.230275\pi$
$150$	−0.188556	−	0.237537i	−0.0153956	−	0.0193948i
$151$	−3.86706	−	3.86706i	−0.314697	−	0.314697i	0.532029	−	0.846726i	$-0.321430\pi$
$151$	−3.86706	−	3.86706i	−0.314697	−	0.314697i	−0.846726	+	0.532029i	$0.821430\pi$
$152$	15.9014	−	4.26077i	1.28978	−	0.345594i
$153$	−4.06909	+	15.1860i	−0.328966	+	1.22772i
$154$	−0.239060	−	0.0640558i	−0.0192640	−	0.00516176i
$155$	0.184284	−	0.280773i	0.0148021	−	0.0225522i
$156$		0			0
$157$	−12.0199	−	12.0199i	−0.959293	−	0.959293i	0.0399100	−	0.999203i	$-0.487293\pi$
$157$	−12.0199	−	12.0199i	−0.959293	−	0.959293i	−0.999203	+	0.0399100i	$0.987293\pi$
$158$	5.36604	−	3.09808i	0.426899	−	0.246470i
$159$	0.605233	−	0.349431i	0.0479981	−	0.0277117i
$160$	−4.07314	+	12.3314i	−0.322010	+	0.974880i
$161$	−3.06931	+	3.06931i	−0.241895	+	0.241895i
$162$	3.07963	−	5.33407i	0.241959	−	0.419084i
$163$	−10.4786	+	18.1495i	−0.820750	+	1.42158i	0.0843745	+	0.996434i	$0.473111\pi$
$163$	−10.4786	+	18.1495i	−0.820750	+	1.42158i	−0.905125	+	0.425147i	$0.860223\pi$
$164$	9.35324	−	9.35324i	0.730366	−	0.730366i
$165$	−0.0274281	+	0.0830382i	−0.00213528	+	0.00646451i
$166$	1.54713	−	0.893238i	0.120081	−	0.0693287i
$167$	15.4392	−	8.91383i	1.19472	−	0.689773i	0.235347	−	0.971911i	$-0.424377\pi$
$167$	15.4392	−	8.91383i	1.19472	−	0.689773i	0.959374	+	0.282139i	$0.0910439\pi$
$168$	0.121976	+	0.121976i	0.00941068	+	0.00941068i
$169$		0			0
$170$	−4.44617	+	6.77411i	−0.341006	+	0.519551i
$171$	19.5751	+	5.24514i	1.49695	+	0.401106i
$172$	3.80988	−	14.2187i	0.290501	−	1.08416i
$173$	6.18092	−	1.65617i	0.469927	−	0.125917i	−0.0160815	−	0.999871i	$-0.505119\pi$
$173$	6.18092	−	1.65617i	0.469927	−	0.125917i	0.486008	+	0.873954i	$0.338452\pi$
$174$	0.205502	+	0.205502i	0.0155791	+	0.0155791i
$175$	−4.00833	−	0.460771i	−0.303001	−	0.0348310i
$176$	0.589427	−	0.157936i	0.0444297	−	0.0119049i
$177$		−	0.193572i		−	0.0145498i
$178$	1.54043	+	5.74896i	0.115460	+	0.430902i
$179$	2.60211	+	4.50699i	0.194491	+	0.336868i	0.946733	−	0.322018i	$-0.104361\pi$
$179$	2.60211	+	4.50699i	0.194491	+	0.336868i	−0.752243	+	0.658886i	$0.771028\pi$
$180$	−7.61254	+	6.78758i	−0.567405	+	0.505917i
$181$		−	10.7283i		−	0.797430i	−0.917075	−	0.398715i	$-0.869456\pi$
$181$		−	10.7283i		−	0.797430i	0.917075	−	0.398715i	$-0.130544\pi$
$182$		0			0
$183$	−0.188479	+	0.188479i	−0.0139328	+	0.0139328i
$184$	−3.38406	+	12.6295i	−0.249476	+	0.931058i
$185$	9.96710	−	8.88699i	0.732796	−	0.653384i
$186$	−0.00788968	−	0.00455511i	−0.000578499	−	0.000333997i
$187$	2.33649			0.170861
$188$	12.3121	+	7.10840i	0.897953	+	0.518434i
$189$	0.110064	+	0.410766i	0.00800601	+	0.0298788i
$190$	8.73198	+	5.73121i	0.633485	+	0.415786i
$191$	−8.06763	+	13.9735i	−0.583753	+	1.01109i	0.411277	+	0.911511i	$0.365083\pi$
$191$	−8.06763	+	13.9735i	−0.583753	+	1.01109i	−0.995030	+	0.0995792i	$0.968250\pi$
$192$	0.107135	+	0.0287066i	0.00773177	+	0.00207172i
$193$	−3.80270	−	6.58646i	−0.273724	−	0.474104i	0.696088	−	0.717956i	$-0.254922\pi$
$193$	−3.80270	−	6.58646i	−0.273724	−	0.474104i	−0.969812	+	0.243852i	$0.921589\pi$
$194$	−9.99596			−0.717668
$195$		0			0
$196$	−9.67770			−0.691264
$197$	2.45051	+	4.24441i	0.174592	+	0.302402i	0.940020	−	0.341120i	$-0.110806\pi$
$197$	2.45051	+	4.24441i	0.174592	+	0.302402i	−0.765428	+	0.643521i	$0.777473\pi$
$198$	−0.886466	−	0.237528i	−0.0629984	−	0.0168804i
$199$	−9.98794	+	17.2996i	−0.708027	+	1.22634i	0.257561	+	0.966262i	$0.417081\pi$
$199$	−9.98794	+	17.2996i	−0.708027	+	1.22634i	−0.965588	+	0.260076i	$0.916252\pi$
$200$	−11.1503	+	4.83499i	−0.788448	+	0.341886i
$201$	−0.264310	−	0.986419i	−0.0186430	−	0.0695766i
$202$	2.34907	+	1.35624i	0.165280	+	0.0954246i
$203$	3.86638			0.271367
$204$	−0.609992	−	0.352179i	−0.0427080	−	0.0246575i
$205$	19.3719	+	1.10978i	1.35299	+	0.0775104i
$206$	−3.09812	+	11.5623i	−0.215856	+	0.805587i
$207$	−11.3814	+	11.3814i	−0.791063	+	0.791063i
$208$		0			0
$209$		−	3.01179i		−	0.208330i
$210$	−0.00625968	+	0.109267i	−0.000431959	+	0.00754012i
$211$	−5.84838	−	10.1297i	−0.402619	−	0.697357i	0.591422	−	0.806362i	$-0.298567\pi$
$211$	−5.84838	−	10.1297i	−0.402619	−	0.697357i	−0.994041	+	0.109005i	$0.965233\pi$
$212$	−3.13509	−	11.7003i	−0.215319	−	0.803581i
$213$		−	0.125532i		−	0.00860134i
$214$	3.27615	−	0.877842i	0.223953	−	0.0600081i
$215$	19.2874	−	9.70950i	1.31539	−	0.662183i
$216$	0.905780	+	0.905780i	0.0616305	+	0.0616305i
$217$	−0.117070	+	0.0313688i	−0.00794723	+	0.00212945i
$218$	−1.44955	+	5.40981i	−0.0981761	+	0.366398i
$219$	−0.0225861	−	0.00605192i	−0.00152623	−	0.000408951i
$220$	1.26718	+	0.831709i	0.0854331	+	0.0560738i
$221$		0			0
$222$	−0.256137	−	0.256137i	−0.0171908	−	0.0171908i
$223$	−2.45165	+	1.41546i	−0.164175	+	0.0947864i	−0.579836	−	0.814733i	$-0.696883\pi$
$223$	−2.45165	+	1.41546i	−0.164175	+	0.0947864i	0.415661	+	0.909519i	$0.363550\pi$
$224$	4.05870	−	2.34329i	0.271183	−	0.156568i
$225$	−14.8634	−	1.70860i	−0.990896	−	0.113907i
$226$	2.32302	−	2.32302i	0.154525	−	0.154525i
$227$	7.74649	−	13.4173i	0.514152	−	0.890538i	−0.485713	−	0.874118i	$-0.661440\pi$
$227$	7.74649	−	13.4173i	0.514152	−	0.890538i	0.999865	−	0.0164196i	$-0.00522674\pi$
$228$	−0.453967	+	0.786294i	−0.0300647	+	0.0520736i
$229$	14.5346	−	14.5346i	0.960475	−	0.960475i	−0.0387727	−	0.999248i	$-0.512345\pi$
$229$	14.5346	−	14.5346i	0.960475	−	0.960475i	0.999248	+	0.0387727i	$0.0123448\pi$
$230$	−7.40973	+	3.73014i	−0.488583	+	0.245958i
$231$	0.0273309	−	0.0157795i	0.00179824	−	0.00103821i
$232$	10.0861	−	5.82319i	0.662183	−	0.382311i
$233$	4.84530	+	4.84530i	0.317426	+	0.317426i	0.847778	−	0.530352i	$-0.177940\pi$
$233$	4.84530	+	4.84530i	0.317426	+	0.317426i	−0.530352	+	0.847778i	$0.677940\pi$
$234$		0			0
$235$	4.23668	+	20.4201i	0.276371	+	1.33206i
$236$	−3.24078	−	0.868363i	−0.210957	−	0.0565256i
$237$	−0.204494	+	0.763181i	−0.0132833	+	0.0495739i
$238$	2.82451	−	0.756826i	0.183086	−	0.0490577i
$239$	10.0017	+	10.0017i	0.646957	+	0.646957i	0.952257	−	0.305299i	$-0.0987564\pi$
$239$	10.0017	+	10.0017i	0.646957	+	0.646957i	−0.305299	+	0.952257i	$0.598756\pi$
$240$	−0.121338	−	0.241032i	−0.00783235	−	0.0155585i
$241$	−23.5672	+	6.31480i	−1.51809	+	0.406772i	−0.919114	−	0.393992i	$-0.871094\pi$
$241$	−23.5672	+	6.31480i	−1.51809	+	0.406772i	−0.598980	+	0.800764i	$0.704427\pi$
$242$		−	7.45022i		−	0.478918i
$243$	0.612465	+	2.28575i	0.0392896	+	0.146631i
$244$	2.30999	+	4.00102i	0.147882	+	0.256139i
$245$	−9.44783	−	10.5961i	−0.603599	−	0.676960i
$246$		−	0.526345i		−	0.0335585i
$247$		0			0
$248$	−0.258151	+	0.258151i	−0.0163926	+	0.0163926i
$249$	−0.0589595	+	0.220040i	−0.00373641	+	0.0139445i
$250$	−6.99781	−	3.23883i	−0.442580	−	0.204842i
$251$	4.67210	+	2.69744i	0.294901	+	0.170261i	0.640150	−	0.768250i	$-0.278872\pi$
$251$	4.67210	+	2.69744i	0.294901	+	0.170261i	−0.345249	+	0.938511i	$0.612206\pi$
$252$	3.68063			0.231858
$253$	2.07160	+	1.19604i	0.130240	+	0.0751941i
$254$	−2.61574	−	9.76206i	−0.164126	−	0.612526i
$255$	−0.209903	−	1.01169i	−0.0131446	−	0.0633548i
$256$	4.96680	−	8.60276i	0.310425	−	0.537672i
$257$	−0.383651	−	0.102799i	−0.0239315	−	0.00641242i	0.246833	−	0.969058i	$-0.420610\pi$
$257$	−0.383651	−	0.102799i	−0.0239315	−	0.00641242i	−0.270765	+	0.962645i	$0.587277\pi$
$258$	−0.292872	−	0.507270i	−0.0182334	−	0.0315812i
$259$	−4.81905			−0.299441
$260$		0			0
$261$	14.3371			0.887442
$262$	−7.29951	−	12.6431i	−0.450965	−	0.781094i
$263$	26.1244	+	7.00001i	1.61090	+	0.431639i	0.948310	−	0.317344i	$-0.102791\pi$
$263$	26.1244	+	7.00001i	1.61090	+	0.431639i	0.662589	+	0.748983i	$0.269458\pi$
$264$	0.0475313	−	0.0823267i	0.00292535	−	0.00506686i
$265$	9.75005	−	14.8550i	0.598941	−	0.912536i
$266$	−0.975565	−	3.64086i	−0.0598157	−	0.223235i
$267$	−0.657259	−	0.379468i	−0.0402236	−	0.0232231i
$268$	−17.7003			−1.08122
$269$	−5.89140	−	3.40140i	−0.359205	−	0.207387i	0.309527	−	0.950891i	$-0.399829\pi$
$269$	−5.89140	−	3.40140i	−0.359205	−	0.207387i	−0.668732	+	0.743504i	$0.733163\pi$
$270$	−0.0464835	+	0.811400i	−0.00282890	+	0.0493803i
$271$	0.436921	−	1.63061i	0.0265410	−	0.0990525i	−0.951385	−	0.308005i	$-0.900339\pi$
$271$	0.436921	−	1.63061i	0.0265410	−	0.0990525i	0.977926	+	0.208952i	$0.0670054\pi$
$272$	−5.09810	+	5.09810i	−0.309118	+	0.309118i
$273$		0			0
$274$		−	10.5084i		−	0.634837i
$275$	0.326442	+	2.19939i	0.0196852	+	0.132628i
$276$	−0.360557	−	0.624503i	−0.0217030	−	0.0375907i
$277$	−2.73813	−	10.2188i	−0.164518	−	0.613990i	−0.998101	−	0.0615960i	$-0.980381\pi$
$277$	−2.73813	−	10.2188i	−0.164518	−	0.613990i	0.833583	−	0.552394i	$-0.186286\pi$
$278$		−	8.18759i		−	0.491059i
$279$	−0.434112	+	0.116320i	−0.0259896	+	0.00696390i
$280$	4.16461	+	1.37560i	0.248883	+	0.0822079i
$281$	0.943634	+	0.943634i	0.0562925	+	0.0562925i	0.734693	−	0.678400i	$-0.237326\pi$
$281$	0.943634	+	0.943634i	0.0562925	+	0.0562925i	−0.678400	+	0.734693i	$0.737326\pi$
$282$	0.546435	−	0.146417i	0.0325398	−	0.00871900i
$283$	1.10083	−	4.10837i	0.0654378	−	0.244217i	−0.925458	−	0.378851i	$-0.876319\pi$
$283$	1.10083	−	4.10837i	0.0654378	−	0.244217i	0.990895	+	0.134634i	$0.0429859\pi$
$284$	−2.10166	−	0.563137i	−0.124710	−	0.0334161i
$285$	−1.30410	+	0.270569i	−0.0772480	+	0.0160271i
$286$		0			0
$287$	−4.95141	−	4.95141i	−0.292272	−	0.292272i
$288$	15.0502	−	8.68925i	0.886842	−	0.512019i
$289$	−9.18494	+	5.30293i	−0.540291	+	0.311937i
$290$	7.01640	+	2.31757i	0.412017	+	0.136092i
$291$	0.901301	−	0.901301i	0.0528352	−	0.0528352i
$292$	−0.202642	+	0.350986i	−0.0118587	+	0.0205399i
$293$	−3.37148	+	5.83957i	−0.196964	+	0.341151i	−0.947543	−	0.319630i	$-0.896441\pi$
$293$	−3.37148	+	5.83957i	−0.196964	+	0.341151i	0.750579	+	0.660781i	$0.229775\pi$
$294$	−0.272301	+	0.272301i	−0.0158809	+	0.0158809i
$295$	−2.21303	−	4.39606i	−0.128848	−	0.255949i
$296$	−12.5713	+	7.25802i	−0.730689	+	0.421864i
$297$	0.202955	−	0.117176i	0.0117767	−	0.00679926i
$298$	−6.58008	−	6.58008i	−0.381174	−	0.381174i
$299$		0			0
$300$	0.246289	−	0.623403i	0.0142195	−	0.0359922i
$301$	−7.52706	−	2.01687i	−0.433853	−	0.116250i
$302$	−0.976219	+	3.64330i	−0.0561751	+	0.209648i
$303$	−0.334095	+	0.0895205i	−0.0191933	+	0.00514282i
$304$	6.57157	+	6.57157i	0.376905	+	0.376905i
$305$	−2.12559	+	6.43519i	−0.121711	+	0.368478i
$306$	10.4737	−	2.80642i	0.598741	−	0.160432i
$307$			9.60697i			0.548298i	0.961687	+	0.274149i	$0.0883962\pi$
$307$			9.60697i			0.548298i	−0.961687	+	0.274149i	$0.911604\pi$
$308$	−0.141573	−	0.528358i	−0.00806688	−	0.0301060i
$309$	−0.763190	−	1.32188i	−0.0434164	−	0.0751993i
$310$	−0.231253	−	0.0132480i	−0.0131343	−	0.000752436i
$311$			5.22449i			0.296254i	0.988968	+	0.148127i	$0.0473244\pi$
$311$			5.22449i			0.296254i	−0.988968	+	0.148127i	$0.952676\pi$
$312$		0			0
$313$	2.37979	−	2.37979i	0.134514	−	0.134514i	−0.636644	−	0.771158i	$-0.719678\pi$
$313$	2.37979	−	2.37979i	0.134514	−	0.134514i	0.771158	+	0.636644i	$0.219678\pi$
$314$	−3.03436	+	11.3244i	−0.171239	+	0.639073i
$315$	3.59320	+	4.02992i	0.202454	+	0.227060i
$316$	11.8598	+	6.84724i	0.667164	+	0.385188i
$317$	−14.8061			−0.831593			−0.415796	−	0.909458i	$-0.636497\pi$
$317$	−14.8061			−0.831593			−0.415796	+	0.909458i	$0.636497\pi$
$318$	−0.417424	−	0.241000i	−0.0234080	−	0.0135146i
$319$	−0.551467	−	2.05810i	−0.0308762	−	0.115232i
$320$	2.76123	−	0.572891i	0.154358	−	0.0320256i
$321$	−0.216247	+	0.374551i	−0.0120698	+	0.0209054i
$322$	2.89170	+	0.774830i	0.161148	+	0.0431796i
$323$	17.7923	+	30.8171i	0.989989	+	1.71471i
$324$	13.6129			0.756273
$325$		0			0
$326$	14.4541			0.800536
$327$	−0.357082	−	0.618485i	−0.0197467	−	0.0342023i
$328$	−20.3739	−	5.45917i	−1.12496	−	0.301432i
$329$	3.76304	−	6.51777i	0.207463	−	0.359336i
$330$	0.0590564	−	0.0122528i	0.00325095	−	0.000674495i
$331$	4.03465	+	15.0575i	0.221764	+	0.827636i	0.983675	+	0.179954i	$0.0575948\pi$
$331$	4.03465	+	15.0575i	0.221764	+	0.827636i	−0.761911	+	0.647682i	$0.775739\pi$
$332$	3.41940	+	1.97419i	0.187664	+	0.108348i
$333$	−17.8697			−0.979253
$334$	−10.6483	−	6.14779i	−0.582648	−	0.336392i
$335$	−17.2798	−	19.3800i	−0.944098	−	1.05884i
$336$	−0.0252045	+	0.0940646i	−0.00137502	+	0.00513165i
$337$	18.1944	−	18.1944i	0.991112	−	0.991112i	−0.00884867	−	0.999961i	$-0.502817\pi$
$337$	18.1944	−	18.1944i	0.991112	−	0.991112i	0.999961	+	0.00884867i	$0.00281665\pi$
$338$		0			0
$339$			0.418917i			0.0227525i
$340$	−17.8794	−	1.02427i	−0.969644	−	0.0555490i
$341$	0.0333958	+	0.0578431i	0.00180848	+	0.00313238i
$342$	−3.61753	−	13.5008i	−0.195614	−	0.730041i
$343$			10.7718i			0.581622i
$344$	−22.6732	+	6.07526i	−1.22246	+	0.327556i
$345$	0.331775	−	1.00444i	0.0178622	−	0.0540774i
$346$	−3.12068	−	3.12068i	−0.167769	−	0.167769i
$347$	23.0983	−	6.18918i	1.23998	−	0.332252i	0.421524	−	0.906817i	$-0.361495\pi$
$347$	23.0983	−	6.18918i	1.23998	−	0.332252i	0.818459	+	0.574565i	$0.194829\pi$
$348$	−0.166245	+	0.620436i	−0.00891169	+	0.0332589i
$349$	−10.5636	−	2.83050i	−0.565455	−	0.151513i	−0.0352438	−	0.999379i	$-0.511221\pi$
$349$	−10.5636	−	2.83050i	−0.565455	−	0.151513i	−0.530211	+	0.847865i	$0.677887\pi$
$350$	1.10704	+	2.55303i	0.0591739	+	0.136465i
$351$		0			0
$352$	−1.82625	−	1.82625i	−0.0973394	−	0.0973394i
$353$	0.751066	−	0.433628i	0.0399752	−	0.0230797i	−0.479879	−	0.877335i	$-0.659320\pi$
$353$	0.751066	−	0.433628i	0.0399752	−	0.0230797i	0.519854	+	0.854255i	$0.325986\pi$
$354$	−0.115619	+	0.0667526i	−0.00614508	+	0.00354786i
$355$	−1.43516	−	2.85087i	−0.0761703	−	0.151308i
$356$	−9.30149	+	9.30149i	−0.492978	+	0.492978i
$357$	−0.186436	+	0.322917i	−0.00986725	+	0.0170906i
$358$	1.79465	−	3.10843i	0.0948504	−	0.164286i
$359$	−19.2831	+	19.2831i	−1.01773	+	1.01773i	−0.0178852	+	0.999840i	$0.505693\pi$
$359$	−19.2831	+	19.2831i	−1.01773	+	1.01773i	−0.999840	+	0.0178852i	$0.994307\pi$
$360$	15.4429	+	5.10092i	0.813915	+	0.268842i
$361$	23.2695	−	13.4346i	1.22471	−	0.707087i
$362$	−6.40793	+	3.69962i	−0.336793	+	0.194448i
$363$	0.671761	+	0.671761i	0.0352583	+	0.0352583i
$364$		0			0
$365$	−0.582123	+	0.120777i	−0.0304697	+	0.00632174i
$366$	0.177573	+	0.0475805i	0.00928189	+	0.00248707i
$367$	−4.29139	+	16.0157i	−0.224009	+	0.836011i	0.758791	+	0.651334i	$0.225791\pi$
$367$	−4.29139	+	16.0157i	−0.224009	+	0.836011i	−0.982799	+	0.184677i	$0.940876\pi$
$368$	−7.12981	+	1.91043i	−0.371667	+	0.0995878i
$369$	−18.3605	−	18.3605i	−0.955810	−	0.955810i
$370$	−8.74523	−	2.88861i	−0.454643	−	0.150172i
$371$	−6.19390	+	1.65965i	−0.321571	+	0.0861648i
$372$		−	0.0201350i		−	0.00104395i
$373$	−1.89919	−	7.08788i	−0.0983364	−	0.366996i	0.899168	−	0.437604i	$-0.144173\pi$
$373$	−1.89919	−	7.08788i	−0.0983364	−	0.366996i	−0.997504	+	0.0706076i	$0.977506\pi$
$374$	−0.805729	−	1.39556i	−0.0416632	−	0.0721629i
$375$	0.923002	−	0.338934i	0.0476636	−	0.0175025i
$376$		−	22.6702i		−	1.16913i
$377$		0			0
$378$	0.207391	−	0.207391i	0.0106671	−	0.0106671i
$379$	8.68622	−	32.4174i	0.446181	−	1.66517i	−0.266617	−	0.963803i	$-0.585906\pi$
$379$	8.68622	−	32.4174i	0.446181	−	1.66517i	0.712798	−	0.701369i	$-0.247427\pi$
$380$	−1.32031	+	23.0469i	−0.0677305	+	1.18228i
$381$	1.11606	+	0.644359i	0.0571776	+	0.0330115i
$382$	11.1284			0.569376
$383$	−25.4395	−	14.6875i	−1.29990	−	0.750497i	−0.319512	−	0.947582i	$-0.603519\pi$
$383$	−25.4395	−	14.6875i	−1.29990	−	0.750497i	−0.980386	+	0.197085i	$0.936852\pi$
$384$	0.244597	+	0.912847i	0.0124820	+	0.0465835i
$385$	0.440289	−	0.670817i	0.0224392	−	0.0341880i
$386$	−2.62269	+	4.54263i	−0.133491	+	0.231214i
$387$	−27.9114	−	7.47883i	−1.41882	−	0.380171i
$388$	−11.0463	−	19.1328i	−0.560791	−	0.971319i
$389$	28.8837			1.46446			0.732231	−	0.681056i	$-0.238479\pi$
$389$	28.8837			1.46446			0.732231	+	0.681056i	$0.238479\pi$
$390$		0			0
$391$	−28.2626			−1.42930
$392$	7.71606	+	13.3646i	0.389720	+	0.675014i
$393$	1.79816	+	0.481815i	0.0907051	+	0.0243043i
$394$	1.69010	−	2.92734i	0.0851459	−	0.147477i
$395$	4.08103	+	19.6699i	0.205339	+	0.989698i
$396$	−0.524973	−	1.95923i	−0.0263809	−	0.0984549i
$397$	5.10166	+	2.94544i	0.256045	+	0.147828i	0.622529	−	0.782597i	$-0.286105\pi$
$397$	5.10166	+	2.94544i	0.256045	+	0.147828i	−0.366484	+	0.930424i	$0.619439\pi$
$398$	13.7772			0.690589
$399$	0.416247	+	0.240320i	0.0208384	+	0.0120311i
$400$	−5.51123	−	4.08667i	−0.275561	−	0.204333i
$401$	0.937514	−	3.49885i	0.0468172	−	0.174724i	−0.938558	−	0.345120i	$-0.887838\pi$
$401$	0.937514	−	3.49885i	0.0468172	−	0.174724i	0.985376	+	0.170396i	$0.0545047\pi$
$402$	−0.498032	+	0.498032i	−0.0248396	+	0.0248396i
$403$		0			0
$404$			5.99499i			0.298262i
$405$	13.2896	+	14.9048i	0.660364	+	0.740624i
$406$	−1.33330	−	2.30935i	−0.0661708	−	0.114611i
$407$	0.687348	+	2.56522i	0.0340706	+	0.127153i
$408$			1.12317i			0.0556054i
$409$	−11.5973	+	3.10749i	−0.573450	+	0.153656i	−0.533879	−	0.845561i	$-0.679266\pi$
$409$	−11.5973	+	3.10749i	−0.573450	+	0.153656i	−0.0395719	+	0.999217i	$0.512599\pi$
$410$	−6.01747	−	11.9534i	−0.297182	−	0.590335i
$411$	0.947508	+	0.947508i	0.0467371	+	0.0467371i
$412$	−25.5546	+	6.84732i	−1.25898	+	0.337343i
$413$	−0.459693	+	1.71560i	−0.0226200	+	0.0844190i
$414$	10.7228	+	2.87318i	0.526999	+	0.141209i
$415$	1.17664	+	5.67120i	0.0577590	+	0.278388i
$416$		0			0
$417$	0.738247	+	0.738247i	0.0361521	+	0.0361521i
$418$	−1.79891	+	1.03860i	−0.0879877	+	0.0507997i
$419$	−10.9269	+	6.30863i	−0.533812	+	0.308197i	−0.742567	−	0.669771i	$-0.766392\pi$
$419$	−10.9269	+	6.30863i	−0.533812	+	0.308197i	0.208755	+	0.977968i	$0.433059\pi$
$420$	−0.216059	+	0.108767i	−0.0105426	+	0.00530728i
$421$	2.72216	−	2.72216i	0.132670	−	0.132670i	−0.637653	−	0.770323i	$-0.720095\pi$
$421$	2.72216	−	2.72216i	0.132670	−	0.132670i	0.770323	+	0.637653i	$0.220095\pi$
$422$	−4.03358	+	6.98637i	−0.196352	+	0.340091i
$423$	13.9539	−	24.1688i	0.678460	−	1.17513i
$424$	−13.6582	+	13.6582i	−0.663299	+	0.663299i
$425$	−16.3332	−	20.5760i	−0.792276	−	0.998084i
$426$	−0.0749794	+	0.0432894i	−0.00363276	+	0.00209738i
$427$	2.11805	−	1.22286i	0.102500	−	0.0591783i
$428$	5.30063	+	5.30063i	0.256216	+	0.256216i
$429$		0			0
$430$	−12.4506	−	8.17190i	−0.600420	−	0.394084i
$431$	−13.4852	−	3.61336i	−0.649561	−	0.174049i	−0.0810308	−	0.996712i	$-0.525821\pi$
$431$	−13.4852	−	3.61336i	−0.649561	−	0.174049i	−0.568531	+	0.822662i	$0.692488\pi$
$432$	−0.187165	+	0.698511i	−0.00900500	+	0.0336071i
$433$	32.9387	−	8.82589i	1.58293	−	0.424145i	0.643100	−	0.765782i	$-0.277648\pi$
$433$	32.9387	−	8.82589i	1.58293	−	0.424145i	0.939832	+	0.341637i	$0.110981\pi$
$434$	0.0591074	+	0.0591074i	0.00283725	+	0.00283725i
$435$	−0.841612	+	0.423677i	−0.0403522	+	0.0203138i
$436$	−11.9565	+	3.20374i	−0.572613	+	0.153431i
$437$			36.4311i			1.74273i
$438$	0.00417396	+	0.0155774i	0.000199440	+	0.000744318i
$439$	−14.5420	−	25.1874i	−0.694049	−	1.20213i	−0.970500	−	0.241101i	$-0.922492\pi$
$439$	−14.5420	−	25.1874i	−0.694049	−	1.20213i	0.276451	−	0.961028i	$-0.410842\pi$
$440$	0.138239	−	2.41306i	0.00659030	−	0.115038i
$441$			18.9974i			0.904639i
$442$		0			0
$443$	7.18973	−	7.18973i	0.341594	−	0.341594i	−0.515372	−	0.856966i	$-0.672346\pi$
$443$	7.18973	−	7.18973i	0.341594	−	0.341594i	0.856966	+	0.515372i	$0.172346\pi$
$444$	0.207208	−	0.773310i	0.00983365	−	0.0366997i
$445$	−19.2648	−	1.10364i	−0.913237	−	0.0523176i
$446$	1.69089	+	0.976233i	0.0800658	+	0.0462260i
$447$	1.18661			0.0561245
$448$	−0.881343	−	0.508843i	−0.0416395	−	0.0240406i
$449$	−4.12927	−	15.4106i	−0.194872	−	0.727273i	−0.992300	−	0.123859i	$-0.960473\pi$
$449$	−4.12927	−	15.4106i	−0.194872	−	0.727273i	0.797428	−	0.603415i	$-0.206194\pi$
$450$	4.10507	+	9.46700i	0.193515	+	0.446279i
$451$	−1.92945	+	3.34190i	−0.0908541	+	0.157364i
$452$	7.01349	+	1.87926i	0.329887	+	0.0883929i
$453$	−0.240481	−	0.416526i	−0.0112988	−	0.0195701i
$454$	−10.6854			−0.501490
$455$		0			0
$456$	1.44780			0.0677993
$457$	−9.61451	−	16.6528i	−0.449748	−	0.778986i	0.548622	−	0.836071i	$-0.315153\pi$
$457$	−9.61451	−	16.6528i	−0.449748	−	0.778986i	−0.998369	+	0.0570848i	$0.981819\pi$
$458$	−13.6936	−	3.66919i	−0.639860	−	0.171450i
$459$	−1.38445	+	2.39794i	−0.0646206	+	0.111926i
$460$	−15.3280	−	10.0605i	−0.714672	−	0.469073i
$461$	1.14709	+	4.28099i	0.0534252	+	0.199386i	0.987480	−	0.157744i	$-0.0504221\pi$
$461$	1.14709	+	4.28099i	0.0534252	+	0.199386i	−0.934055	+	0.357130i	$0.883755\pi$
$462$	−0.0188499	−	0.0108830i	−0.000876976	−	0.000506322i
$463$	12.2584			0.569696			0.284848	−	0.958573i	$-0.408057\pi$
$463$	12.2584			0.569696			0.284848	+	0.958573i	$0.408057\pi$
$464$	5.69395	+	3.28741i	0.264335	+	0.152614i
$465$	0.0220458	−	0.0196567i	0.00102235	−	0.000911559i
$466$	1.22317	−	4.56494i	0.0566623	−	0.211467i
$467$	−10.5138	+	10.5138i	−0.486522	+	0.486522i	−0.907207	−	0.420685i	$-0.861790\pi$
$467$	−10.5138	+	10.5138i	−0.486522	+	0.486522i	0.420685	+	0.907207i	$0.361790\pi$
$468$		0			0
$469$			9.37014i			0.432673i
$470$	10.7357	−	9.57232i	0.495202	−	0.441538i
$471$	−0.747484	−	1.29468i	−0.0344422	−	0.0596557i
$472$	1.38470	+	5.16776i	0.0637359	+	0.237866i
$473$			4.29438i			0.197456i
$474$	0.526360	−	0.141038i	0.0241765	−	0.00647807i
$475$	−26.5230	+	21.0539i	−1.21696	+	0.966017i
$476$	4.56991	+	4.56991i	0.209461	+	0.209461i
$477$	−22.9678	+	6.15422i	−1.05163	+	0.281782i
$478$	2.52488	−	9.42299i	0.115485	−	0.430997i
$479$	−11.3671	−	3.04580i	−0.519375	−	0.139166i	−0.0103976	−	0.999946i	$-0.503310\pi$
$479$	−11.3671	−	3.04580i	−0.519375	−	0.139166i	−0.508978	+	0.860780i	$0.669976\pi$
$480$	−0.626697	+	0.954826i	−0.0286047	+	0.0435816i
$481$		0			0
$482$	11.8988	+	11.8988i	0.541976	+	0.541976i
$483$	−0.330599	+	0.190871i	−0.0150428	+	0.00868494i
$484$	14.2601	−	8.23307i	0.648186	−	0.374230i
$485$	10.1645	−	30.7729i	0.461547	−	1.39733i
$486$	1.15405	−	1.15405i	0.0523488	−	0.0523488i
$487$	−13.2499	+	22.9494i	−0.600408	+	1.03994i	0.392351	+	0.919816i	$0.371662\pi$
$487$	−13.2499	+	22.9494i	−0.600408	+	1.03994i	−0.992759	+	0.120122i	$0.961671\pi$
$488$	3.68352	−	6.38005i	0.166745	−	0.288811i
$489$	−1.30327	+	1.30327i	−0.0589360	+	0.0589360i
$490$	−3.07091	+	9.29712i	−0.138730	+	0.420001i
$491$	−12.3414	+	7.12533i	−0.556961	+	0.321562i	−0.751925	−	0.659249i	$-0.770874\pi$
$491$	−12.3414	+	7.12533i	−0.556961	+	0.321562i	0.194964	+	0.980810i	$0.437541\pi$
$492$	1.00745	−	0.581651i	0.0454193	−	0.0262229i
$493$	17.8011	+	17.8011i	0.801719	+	0.801719i
$494$		0			0
$495$	1.63265	−	2.48748i	0.0733823	−	0.111804i
$496$	−0.199079	−	0.0533430i	−0.00893890	−	0.00239517i
$497$	−0.298113	+	1.11257i	−0.0133722	+	0.0499057i
$498$	0.151760	−	0.0406639i	0.00680051	−	0.00182219i
$499$	20.1666	+	20.1666i	0.902783	+	0.902783i	0.995676	−	0.0928929i	$-0.0296114\pi$
$499$	20.1666	+	20.1666i	0.902783	+	0.902783i	−0.0928929	+	0.995676i	$0.529611\pi$
$500$	−1.53384	−	16.9733i	−0.0685953	−	0.759069i
$501$	1.51444	−	0.405794i	0.0676604	−	0.0181295i
$502$		−	3.72081i		−	0.166068i
$503$	−2.34893	−	8.76631i	−0.104733	−	0.390870i	0.893581	−	0.448901i	$-0.148184\pi$
$503$	−2.34893	−	8.76631i	−0.104733	−	0.390870i	−0.998315	+	0.0580309i	$0.981518\pi$
$504$	−2.93458	−	5.08283i	−0.130716	−	0.226407i
$505$	−6.56391	+	5.85259i	−0.292090	+	0.260437i
$506$		−	1.64979i		−	0.0733422i
$507$		0			0
$508$	15.7945	−	15.7945i	0.700767	−	0.700767i
$509$	3.54020	−	13.2122i	0.156917	−	0.585621i	−0.842017	−	0.539451i	$-0.818632\pi$
$509$	3.54020	−	13.2122i	0.156917	−	0.585621i	0.998934	−	0.0461698i	$-0.0147015\pi$
$510$	−0.531891	+	0.474252i	−0.0235526	+	0.0210002i
$511$	0.185804	+	0.107274i	0.00821950	+	0.00474553i
$512$	14.6405			0.647023
$513$	3.09099	+	1.78459i	0.136471	+	0.0787914i
$514$	0.0708996	+	0.264601i	0.00312725	+	0.0116710i
$515$	−32.4447	−	21.2950i	−1.42968	−	0.938369i
$516$	0.647293	−	1.12114i	0.0284955	−	0.0493556i
$517$	−4.00619	−	1.07346i	−0.176192	−	0.0472105i
$518$	1.66183	+	2.87837i	0.0730165	+	0.126468i
$519$	0.562762			0.0247025
$520$		0			0
$521$	−29.1893			−1.27881			−0.639403	−	0.768872i	$-0.720819\pi$
$521$	−29.1893			−1.27881			−0.639403	+	0.768872i	$0.720819\pi$
$522$	−4.94408	−	8.56340i	−0.216397	−	0.374810i
$523$	−13.6997	−	3.67083i	−0.599048	−	0.160514i	−0.0534627	−	0.998570i	$-0.517026\pi$
$523$	−13.6997	−	3.67083i	−0.599048	−	0.160514i	−0.545585	+	0.838056i	$0.683692\pi$
$524$	16.1330	−	27.9432i	0.704775	−	1.22071i
$525$	−0.330016	−	0.130380i	−0.0144031	−	0.00569025i
$526$	−4.82785	−	18.0178i	−0.210504	−	0.785613i
$527$	−0.683423	−	0.394574i	−0.0297704	−	0.0171879i
$528$	0.0536663			0.00233553
$529$	−5.13978	−	2.96745i	−0.223469	−	0.129020i
$530$	−12.2350	−	0.700921i	−0.531456	−	0.0304461i
$531$	−1.70461	+	6.36168i	−0.0739736	+	0.276073i
$532$	5.89071	−	5.89071i	0.255395	−	0.255395i
$533$		0			0
$534$			0.523432i			0.0226511i
$535$	−0.628931	+	10.9784i	−0.0271910	+	0.474637i
$536$	14.1125	+	24.4435i	0.609566	+	1.05580i
$537$	0.118459	+	0.442094i	0.00511187	+	0.0190778i
$538$			4.69184i			0.202279i
$539$	2.72710	−	0.730725i	0.117465	−	0.0314745i
$540$	−1.60443	+	0.807688i	−0.0690436	+	0.0347574i
$541$	−10.8210	−	10.8210i	−0.465233	−	0.465233i	0.435133	−	0.900366i	$-0.356701\pi$
$541$	−10.8210	−	10.8210i	−0.465233	−	0.465233i	−0.900366	+	0.435133i	$0.856701\pi$
$542$	−1.12462	+	0.301341i	−0.0483065	+	0.0129437i
$543$	0.244199	−	0.911363i	0.0104796	−	0.0391103i
$544$	29.4752	+	7.89785i	1.26374	+	0.338617i
$545$	−15.1803	−	9.96353i	−0.650251	−	0.426791i
$546$		0			0
$547$	0.334432	+	0.334432i	0.0142993	+	0.0142993i	0.714220	−	0.699921i	$-0.246781\pi$
$547$	0.334432	+	0.334432i	0.0142993	+	0.0142993i	−0.699921	+	0.714220i	$0.746781\pi$
$548$	20.1136	−	11.6126i	0.859212	−	0.496066i
$549$	7.85404	−	4.53453i	0.335202	−	0.193529i
$550$	1.20110	−	0.953430i	0.0512151	−	0.0406544i
$551$	22.9460	−	22.9460i	0.977531	−	0.977531i
$552$	−0.574947	+	0.995837i	−0.0244714	+	0.0423856i
$553$	3.62478	−	6.27831i	0.154142	−	0.266981i
$554$	−5.15938	+	5.15938i	−0.219201	+	0.219201i
$555$	1.04898	−	0.528071i	0.0445269	−	0.0224153i
$556$	15.6715	−	9.04792i	0.664618	−	0.383717i
$557$	−29.7552	+	17.1792i	−1.26077	+	0.727906i	−0.973223	−	0.229861i	$-0.926173\pi$
$557$	−29.7552	+	17.1792i	−1.26077	+	0.727906i	−0.287546	+	0.957767i	$0.592839\pi$
$558$	0.219179	+	0.219179i	0.00927857	+	0.00927857i
$559$		0			0
$560$	0.503001	+	2.42438i	0.0212557	+	0.102449i
$561$	0.198483	+	0.0531833i	0.00837996	+	0.00224540i
$562$	0.238215	−	0.889032i	0.0100485	−	0.0375015i
$563$	−26.0490	+	6.97981i	−1.09783	+	0.294164i	−0.761883	−	0.647715i	$-0.775725\pi$
$563$	−26.0490	+	6.97981i	−1.09783	+	0.294164i	−0.335952	+	0.941879i	$0.609058\pi$
$564$	0.884102	+	0.884102i	0.0372274	+	0.0372274i
$565$	4.78930	+	9.51368i	0.201487	+	0.400244i
$566$	−2.83351	+	0.759237i	−0.119101	+	0.0319131i
$567$		−	7.20638i		−	0.302640i
$568$	0.897982	+	3.35132i	0.0376785	+	0.140618i
$569$	18.2534	+	31.6159i	0.765224	+	1.32541i	0.940128	+	0.340821i	$0.110705\pi$
$569$	18.2534	+	31.6159i	0.765224	+	1.32541i	−0.174905	+	0.984585i	$0.555962\pi$
$570$	0.611321	+	0.685620i	0.0256054	+	0.0287175i
$571$		−	31.2687i		−	1.30855i	−0.756255	−	0.654277i	$-0.772973\pi$
$571$		−	31.2687i		−	1.30855i	0.756255	−	0.654277i	$-0.227027\pi$
$572$		0			0
$573$	−1.00341	+	1.00341i	−0.0419178	+	0.0419178i
$574$	−1.24996	+	4.66490i	−0.0521722	+	0.194709i
$575$	−3.94870	−	26.6041i	−0.164672	−	1.10947i
$576$	−3.26814	−	1.88686i	−0.136173	−	0.0786193i
$577$	−28.3409			−1.17985			−0.589923	−	0.807460i	$-0.700842\pi$
$577$	−28.3409			−1.17985			−0.589923	+	0.807460i	$0.700842\pi$
$578$	6.33478	+	3.65739i	0.263492	+	0.152127i
$579$	−0.173114	−	0.646072i	−0.00719439	−	0.0268498i
$580$	3.31772	+	15.9908i	0.137761	+	0.663983i
$581$	1.04510	−	1.81016i	0.0433579	−	0.0750981i
$582$	−0.849149	−	0.227529i	−0.0351983	−	0.00943137i
$583$	1.76689	+	3.06034i	0.0731771	+	0.126746i
$584$	0.646268			0.0267427
$585$		0			0
$586$	4.65056			0.192113
$587$	10.5591	+	18.2889i	0.435822	+	0.754865i	0.997362	−	0.0725840i	$-0.0231245\pi$
$587$	10.5591	+	18.2889i	0.435822	+	0.754865i	−0.561541	+	0.827449i	$0.689791\pi$
$588$	−0.822113	−	0.220284i	−0.0339033	−	0.00908438i
$589$	−0.508615	+	0.880947i	−0.0209571	+	0.0362988i
$590$	−1.86257	+	2.83779i	−0.0766809	+	0.116830i
$591$	0.111557	+	0.416338i	0.00458886	+	0.0171259i
$592$	−7.09693	−	4.09741i	−0.291682	−	0.168403i
$593$	12.8500			0.527685			0.263843	−	0.964566i	$-0.415010\pi$
$593$	12.8500			0.527685			0.263843	+	0.964566i	$0.415010\pi$
$594$	−0.139977	−	0.0808155i	−0.00574331	−	0.00331590i
$595$	−0.542228	+	9.46495i	−0.0222292	+	0.388025i
$596$	5.32310	−	19.8661i	0.218043	−	0.813746i
$597$	−1.24224	+	1.24224i	−0.0508416	+	0.0508416i
$598$		0			0
$599$			3.15330i			0.128840i	0.997923	+	0.0644201i	$0.0205198\pi$
$599$			3.15330i			0.128840i	−0.997923	+	0.0644201i	$0.979480\pi$
$600$	−1.05727	+	0.156924i	−0.0431628	+	0.00640639i
$601$	−11.8712	−	20.5615i	−0.484236	−	0.838721i	0.515600	−	0.856829i	$-0.327569\pi$
$601$	−11.8712	−	20.5615i	−0.484236	−	0.838721i	−0.999836	+	0.0181082i	$0.994236\pi$
$602$	1.39102	+	5.19135i	0.0566937	+	0.211584i
$603$			34.7458i			1.41496i
$604$	−8.05225	+	2.15759i	−0.327641	+	0.0877912i
$605$	22.9358	+	7.57585i	0.932471	+	0.308002i
$606$	0.168681	+	0.168681i	0.00685220	+	0.00685220i
$607$	4.10062	−	1.09876i	0.166439	−	0.0445972i	−0.174637	−	0.984633i	$-0.555875\pi$
$607$	4.10062	−	1.09876i	0.166439	−	0.0445972i	0.341076	+	0.940036i	$0.389209\pi$
$608$	10.1805	−	37.9942i	0.412874	−	1.54087i
$609$	0.328446	+	0.0880068i	0.0133093	+	0.00356621i
$610$	4.57668	−	0.949553i	0.185304	−	0.0384463i
$611$		0			0
$612$	16.9458	+	16.9458i	0.684995	+	0.684995i
$613$	−37.8364	+	21.8449i	−1.52820	+	0.882306i	−0.528762	+	0.848770i	$0.677343\pi$
$613$	−37.8364	+	21.8449i	−1.52820	+	0.882306i	−0.999438	+	0.0335359i	$0.989323\pi$
$614$	5.73815	−	3.31292i	0.231573	−	0.133699i
$615$	1.62037	+	0.535220i	0.0653396	+	0.0215822i
$616$	−0.616770	+	0.616770i	−0.0248504	+	0.0248504i
$617$	−7.22043	+	12.5062i	−0.290684	+	0.503479i	−0.973972	−	0.226670i	$-0.927216\pi$
$617$	−7.22043	+	12.5062i	−0.290684	+	0.503479i	0.683288	+	0.730149i	$0.260549\pi$
$618$	−0.526366	+	0.911692i	−0.0211735	+	0.0366736i
$619$	3.86804	−	3.86804i	0.155470	−	0.155470i	−0.625086	−	0.780556i	$-0.714936\pi$
$619$	3.86804	−	3.86804i	0.155470	−	0.155470i	0.780556	+	0.625086i	$0.214936\pi$
$620$	−0.230195	−	0.457269i	−0.00924484	−	0.0183644i
$621$	−2.45498	+	1.41738i	−0.0985150	+	0.0568777i
$622$	3.12054	−	1.80164i	0.125122	−	0.0722394i
$623$	4.92401	+	4.92401i	0.197276	+	0.197276i
$624$		0			0
$625$	17.0867	−	18.2495i	0.683466	−	0.729982i
$626$	−2.24209	−	0.600766i	−0.0896118	−	0.0240114i
$627$	0.0685545	−	0.255849i	0.00273780	−	0.0102176i
$628$	−25.0287	+	6.70641i	−0.998752	+	0.267615i
$629$	−22.1872	−	22.1872i	−0.884662	−	0.884662i
$630$	1.16793	−	3.53589i	0.0465314	−	0.140873i
$631$	26.4291	−	7.08167i	1.05213	−	0.281917i	0.308997	−	0.951063i	$-0.400007\pi$
$631$	26.4291	−	7.08167i	1.05213	−	0.281917i	0.743131	+	0.669146i	$0.233340\pi$
$632$		−	21.8373i		−	0.868642i
$633$	−0.266243	−	0.993631i	−0.0105822	−	0.0394933i
$634$	5.10582	+	8.84354i	0.202778	+	0.351222i
$635$	32.7127	+	1.87405i	1.29816	+	0.0743692i
$636$		−	1.06529i		−	0.0422417i
$637$		0			0
$638$	−1.03911	+	1.03911i	−0.0411390	+	0.0411390i
$639$	−1.10544	+	4.12557i	−0.0437307	+	0.163205i
$640$	15.9910	+	17.9345i	0.632100	+	0.708925i
$641$	−31.0306	−	17.9155i	−1.22563	−	0.707620i	−0.259521	−	0.965738i	$-0.583565\pi$
$641$	−31.0306	−	17.9155i	−1.22563	−	0.707620i	−0.966114	+	0.258117i	$0.916898\pi$
$642$	0.298288			0.0117725
$643$	5.13909	+	2.96706i	0.202666	+	0.117009i	0.597898	−	0.801572i	$-0.296003\pi$
$643$	5.13909	+	2.96706i	0.202666	+	0.117009i	−0.395232	+	0.918581i	$0.629336\pi$
$644$	1.71249	+	6.39111i	0.0674817	+	0.251845i
$645$	1.85946	−	0.385793i	0.0732161	−	0.0151906i
$646$	12.2712	−	21.2543i	0.482804	−	0.836240i
$647$	6.00826	+	1.60991i	0.236209	+	0.0632920i	0.374982	−	0.927032i	$-0.377649\pi$
$647$	6.00826	+	1.60991i	0.236209	+	0.0632920i	−0.138773	+	0.990324i	$0.544316\pi$
$648$	−10.8536	−	18.7990i	−0.426370	−	0.738495i
$649$	0.978793			0.0384210
$650$		0			0
$651$	−0.0106590			−0.000417760
$652$	15.9728	+	27.6658i	0.625545	+	1.08348i
$653$	29.7959	+	7.98379i	1.16600	+	0.312430i	0.789362	−	0.613929i	$-0.210412\pi$
$653$	29.7959	+	7.98379i	1.16600	+	0.312430i	0.376643	+	0.926359i	$0.377078\pi$
$654$	−0.246277	+	0.426564i	−0.00963018	+	0.0166800i
$655$	46.3449	−	9.61546i	1.81084	−	0.375707i
$656$	−3.08190	−	11.5018i	−0.120328	−	0.449070i
$657$	0.688989	+	0.397788i	0.0268800	+	0.0155192i
$658$	−5.19067			−0.202353
$659$	23.2002	+	13.3947i	0.903753	+	0.521782i	0.878416	−	0.477897i	$-0.158601\pi$
$659$	23.2002	+	13.3947i	0.903753	+	0.521782i	0.0253370	+	0.999679i	$0.491934\pi$
$660$	0.0887144	+	0.0994966i	0.00345320	+	0.00387290i
$661$	3.37954	−	12.6126i	0.131449	−	0.490574i	−0.868538	−	0.495622i	$-0.834940\pi$
$661$	3.37954	−	12.6126i	0.131449	−	0.490574i	0.999987	+	0.00504819i	$0.00160689\pi$
$662$	7.60238	−	7.60238i	0.295475	−	0.295475i
$663$		0			0
$664$		−	6.29612i		−	0.244337i
$665$	12.2005	+	0.698944i	0.473116	+	0.0271039i
$666$	6.16229	+	10.6734i	0.238784	+	0.413586i
$667$	6.67064	+	24.8952i	0.258288	+	0.963945i
$668$		−	27.1751i		−	1.05144i
$669$	−0.240485	+	0.0644377i	−0.00929768	+	0.00249131i
$670$	−5.61661	+	17.0042i	−0.216989	+	0.656929i
$671$	−0.953039	−	0.953039i	−0.0367917	−	0.0367917i
$672$	0.398121	−	0.106676i	0.0153579	−	0.00411513i
$673$	−8.43181	+	31.4679i	−0.325022	+	1.21300i	0.589267	+	0.807938i	$0.299417\pi$
$673$	−8.43181	+	31.4679i	−0.325022	+	1.21300i	−0.914289	+	0.405061i	$0.867250\pi$
$674$	−17.1416	−	4.59308i	−0.660270	−	0.176919i
$675$	−2.45066	−	0.968184i	−0.0943258	−	0.0372654i
$676$		0			0
$677$	7.47403	+	7.47403i	0.287250	+	0.287250i	0.835992	−	0.548742i	$-0.184893\pi$
$677$	7.47403	+	7.47403i	0.287250	+	0.287250i	−0.548742	+	0.835992i	$0.684893\pi$
$678$	0.250215	−	0.144462i	0.00960946	−	0.00554802i
$679$	−10.1285	+	5.84768i	−0.388695	+	0.224413i
$680$	12.8408	+	25.5075i	0.492421	+	0.978168i
$681$	0.963464	−	0.963464i	0.0369200	−	0.0369200i
$682$	0.0230328	−	0.0398939i	0.000881971	−	0.00152762i
$683$	−0.644898	+	1.11700i	−0.0246763	+	0.0427406i	−0.878100	−	0.478477i	$-0.841189\pi$
$683$	−0.644898	+	1.11700i	−0.0246763	+	0.0427406i	0.853424	+	0.521218i	$0.174522\pi$
$684$	21.8436	−	21.8436i	0.835210	−	0.835210i
$685$	32.3505	+	10.6856i	1.23605	+	0.408277i
$686$	6.43388	−	3.71460i	0.245647	−	0.141824i
$687$	1.56554	−	0.903867i	0.0597292	−	0.0344847i
$688$	−9.37013	−	9.37013i	−0.357233	−	0.357233i
$689$		0			0
$690$	−0.714356	+	0.148212i	−0.0271951	+	0.00564233i
$691$	−18.1665	−	4.86770i	−0.691087	−	0.185176i	−0.103852	−	0.994593i	$-0.533117\pi$
$691$	−18.1665	−	4.86770i	−0.691087	−	0.185176i	−0.587235	+	0.809417i	$0.699784\pi$
$692$	2.52455	−	9.42174i	0.0959689	−	0.358161i
$693$	−1.03717	+	0.277910i	−0.0393989	+	0.0105569i
$694$	−11.6621	−	11.6621i	−0.442687	−	0.442687i
$695$	25.2058	+	8.32566i	0.956110	+	0.315810i
$696$	0.989352	−	0.265096i	0.0375013	−	0.0100484i
$697$		−	45.5932i		−	1.72697i
$698$	1.95217	+	7.28561i	0.0738909	+	0.275764i
$699$	0.301315	+	0.521894i	0.0113968	+	0.0197398i
$700$	−3.66326	+	4.94023i	−0.138458	+	0.186723i
$701$			21.8278i			0.824425i	0.911088	+	0.412212i	$0.135244\pi$
$701$			21.8278i			0.824425i	−0.911088	+	0.412212i	$0.864756\pi$
$702$		0			0
$703$	−28.5998	+	28.5998i	−1.07866	+	1.07866i
$704$	−0.145154	+	0.541723i	−0.00547070	+	0.0204169i
$705$	−0.104900	+	1.83111i	−0.00395078	+	0.0689634i
$706$	−0.518004	−	0.299070i	−0.0194953	−	0.0112556i
$707$	3.17362			0.119356
$708$	−0.255536	−	0.147534i	−0.00960362	−	0.00554465i
$709$	6.69366	+	24.9811i	0.251386	+	0.938184i	0.970066	+	0.242843i	$0.0780799\pi$
$709$	6.69366	+	24.9811i	0.251386	+	0.938184i	−0.718680	+	0.695341i	$0.755253\pi$
$710$	−1.20789	+	1.84032i	−0.0453312	+	0.0690658i
$711$	13.4412	−	23.2809i	0.504085	−	0.873100i
$712$	20.2612	+	5.42897i	0.759320	+	0.203459i
$713$	−0.403961	−	0.699680i	−0.0151284	−	0.0262032i
$714$	0.257167			0.00962423
$715$		0			0
$716$	7.93292			0.296467
$717$	0.621978	+	1.07730i	0.0232282	+	0.0402324i
$718$	18.1674	+	4.86793i	0.678000	+	0.181669i
$719$	−8.88583	+	15.3907i	−0.331385	+	0.573976i	−0.982784	−	0.184760i	$-0.940849\pi$
$719$	−8.88583	+	15.3907i	−0.331385	+	0.573976i	0.651398	+	0.758736i	$0.274183\pi$
$720$	1.86520	+	8.98993i	0.0695118	+	0.335035i
$721$	3.62483	+	13.5280i	0.134996	+	0.503810i
$722$	−16.0488	−	9.26577i	−0.597274	−	0.344836i
$723$	−2.14575			−0.0798013
$724$	−14.1625	−	8.17673i	−0.526346	−	0.303886i
$725$	−14.2694	+	19.2436i	−0.529954	+	0.714689i
$726$	0.169582	−	0.632890i	0.00629379	−	0.0234888i
$727$	−14.6033	+	14.6033i	−0.541607	+	0.541607i	−0.924000	−	0.382393i	$-0.875100\pi$
$727$	−14.6033	+	14.6033i	−0.541607	+	0.541607i	0.382393	+	0.924000i	$0.375100\pi$
$728$		0			0
$729$		−	26.5832i		−	0.984564i
$730$	0.272881	+	0.306047i	0.0100998	+	0.0113273i
$731$	−25.3693	−	43.9409i	−0.938317	−	1.62521i
$732$	0.105160	+	0.392464i	0.00388684	+	0.0145059i
$733$			5.44505i			0.201118i	0.994931	+	0.100559i	$0.0320630\pi$
$733$			5.44505i			0.201118i	−0.994931	+	0.100559i	$0.967937\pi$
$734$	11.0459	−	2.95973i	0.407711	−	0.109246i
$735$	−0.561396	−	1.11518i	−0.0207074	−	0.0411341i
$736$	22.0906	+	22.0906i	0.814271	+	0.814271i
$737$	4.98780	−	1.33648i	0.183728	−	0.0492298i
$738$	−4.63501	+	17.2981i	−0.170617	+	0.636752i
$739$	29.6278	+	7.93876i	1.08988	+	0.292032i	0.758636	−	0.651514i	$-0.225866\pi$
$739$	29.6278	+	7.93876i	1.08988	+	0.292032i	0.331241	+	0.943546i	$0.392533\pi$
$740$	−4.13520	−	19.9309i	−0.152013	−	0.732676i
$741$		0			0
$742$	3.12723	+	3.12723i	0.114804	+	0.114804i
$743$	0.585066	−	0.337788i	0.0214640	−	0.0123922i	−0.489230	−	0.872155i	$-0.662722\pi$
$743$	0.585066	−	0.337788i	0.0214640	−	0.0123922i	0.510694	+	0.859763i	$0.329389\pi$
$744$	−0.0278058	+	0.0160537i	−0.00101941	+	0.000588557i
$745$	26.9480	−	13.5660i	0.987299	−	0.497018i
$746$	−3.57860	+	3.57860i	−0.131022	+	0.131022i
$747$	3.87536	−	6.71232i	0.141792	−	0.245591i
$748$	1.78078	−	3.08441i	0.0651119	−	0.112777i
$749$	2.80604	−	2.80604i	0.102531	−	0.102531i
$750$	−0.520736	−	0.434421i	−0.0190146	−	0.0158628i
$751$	4.88768	−	2.82190i	0.178354	−	0.102973i	−0.408165	−	0.912908i	$-0.633831\pi$
$751$	4.88768	−	2.82190i	0.178354	−	0.102973i	0.586519	+	0.809935i	$0.300498\pi$
$752$	11.0835	−	6.39908i	0.404175	−	0.233350i
$753$	0.335492	+	0.335492i	0.0122260	+	0.0122260i
$754$		0			0
$755$	−10.2233	−	6.71006i	−0.372065	−	0.244204i
$756$	0.626141	+	0.167774i	0.0227725	+	0.00610188i
$757$	7.82109	−	29.1887i	0.284262	−	1.06088i	−0.665114	−	0.746741i	$-0.731617\pi$
$757$	7.82109	−	29.1887i	0.284262	−	1.06088i	0.949377	−	0.314140i	$-0.101716\pi$
$758$	−22.3580	+	5.99082i	−0.812080	+	0.217596i
$759$	0.148756	+	0.148756i	0.00539950	+	0.00539950i
$760$	32.8797	−	16.5520i	1.19267	−	0.600406i
$761$	18.2206	−	4.88219i	0.660495	−	0.176979i	0.0870258	−	0.996206i	$-0.472264\pi$
$761$	18.2206	−	4.88219i	0.660495	−	0.176979i	0.573470	+	0.819227i	$0.305597\pi$
$762$		−	0.888819i		−	0.0321985i
$763$	1.69599	+	6.32952i	0.0613989	+	0.229144i
$764$	12.2977	+	21.3002i	0.444915	+	0.770615i
$765$	−2.01066	+	35.0973i	−0.0726955	+	1.26895i
$766$			20.2597i			0.732013i
$767$		0			0
$768$	0.617743	−	0.617743i	0.0222909	−	0.0222909i
$769$	3.00782	−	11.2253i	0.108465	−	0.404796i	−0.890250	−	0.455471i	$-0.849471\pi$
$769$	3.00782	−	11.2253i	0.108465	−	0.404796i	0.998715	+	0.0506755i	$0.0161374\pi$
$770$	−0.552505	−	0.0316519i	−0.0199109	−	0.00114066i
$771$	−0.0302509	−	0.0174654i	−0.00108946	−	0.000629000i
$772$	−11.5931			−0.417244
$773$	7.18212	+	4.14660i	0.258323	+	0.149143i	0.623569	−	0.781768i	$-0.285682\pi$
$773$	7.18212	+	4.14660i	0.258323	+	0.149143i	−0.365246	+	0.930911i	$0.619015\pi$
$774$	5.15809	+	19.2503i	0.185404	+	0.691936i
$775$	0.275937	−	0.698448i	0.00991194	−	0.0250890i
$776$	−17.6145	+	30.5092i	−0.632324	+	1.09522i
$777$	−0.409374	−	0.109691i	−0.0146862	−	0.00393516i
$778$	−9.96043	−	17.2520i	−0.357099	−	0.618513i
$779$	−58.7707			−2.10568
$780$		0			0
$781$	0.634752			0.0227132
$782$	9.74623	+	16.8810i	0.348525	+	0.603662i
$783$	2.43899	+	0.653526i	0.0871625	+	0.0233551i
$784$	−4.35599	+	7.54480i	−0.155571	+	0.269457i
$785$	−31.7770	−	20.8568i	−1.13417	−	0.744409i
$786$	−0.332304	−	1.24017i	−0.0118529	−	0.0442356i
$787$	−42.1413	−	24.3303i	−1.50218	−	0.867282i	−0.999997	−	0.00251849i	$-0.999198\pi$
$787$	−42.1413	−	24.3303i	−1.50218	−	0.867282i	−0.502179	−	0.864763i	$-0.667468\pi$
$788$	7.47076			0.266135
$789$	2.05991	+	1.18929i	0.0733348	+	0.0423399i
$790$	10.3413	−	9.22063i	0.367927	−	0.328055i
$791$	0.994839	−	3.71279i	0.0353724	−	0.132012i
$792$	−2.28707	+	2.28707i	−0.0812675	+	0.0812675i
$793$		0			0
$794$		−	4.06290i		−	0.144187i
$795$	1.16639	−	1.03999i	0.0413676	−	0.0368847i
$796$	15.2249	+	26.3703i	0.539631	+	0.934669i
$797$	13.4213	+	50.0891i	0.475408	+	1.77425i	0.619836	+	0.784731i	$0.287199\pi$
$797$	13.4213	+	50.0891i	0.475408	+	1.77425i	−0.144428	+	0.989515i	$0.546134\pi$
$798$		−	0.331494i		−	0.0117348i
$799$	47.3335	−	12.6830i	1.67454	−	0.448692i
$800$	−3.31629	+	28.8490i	−0.117249	+	1.01997i
$801$	18.2589	+	18.2589i	0.645147	+	0.645147i
$802$	−2.41313	+	0.646596i	−0.0852106	+	0.0228321i
$803$	0.0306014	−	0.114206i	0.00107990	−	0.00403024i
$804$	−1.50362	−	0.402895i	−0.0530287	−	0.0142090i
$805$	−5.32581	+	8.11432i	−0.187710	+	0.285992i
$806$		0			0
$807$	−0.423047	−	0.423047i	−0.0148920	−	0.0148920i
$808$	8.27890	−	4.77982i	0.291251	−	0.168154i
$809$	−9.86309	+	5.69446i	−0.346768	+	0.200206i	−0.663261	−	0.748388i	$-0.730828\pi$
$809$	−9.86309	+	5.69446i	−0.346768	+	0.200206i	0.316493	+	0.948595i	$0.397495\pi$
$810$	4.31962	−	13.0776i	0.151776	−	0.459499i
$811$	−23.0388	+	23.0388i	−0.809003	+	0.809003i	−0.984483	−	0.175480i	$-0.943852\pi$
$811$	−23.0388	+	23.0388i	−0.809003	+	0.809003i	0.175480	+	0.984483i	$0.443852\pi$
$812$	2.94681	−	5.10402i	0.103413	−	0.179116i
$813$	0.0742321	−	0.128574i	0.00260343	−	0.00450928i
$814$	1.29515	−	1.29515i	0.0453950	−	0.0453950i
$815$	−14.6978	+	44.4973i	−0.514841	+	1.55867i
$816$	−0.549123	+	0.317036i	−0.0192232	+	0.0110985i
$817$	−56.6408	+	32.7016i	−1.98161	+	1.14408i
$818$	5.85536	+	5.85536i	0.204728	+	0.204728i
$819$		0			0
$820$	16.2296	−	24.7271i	0.566762	−	0.863509i
$821$	9.99590	+	2.67839i	0.348859	+	0.0934765i	0.428994	−	0.903308i	$-0.358868\pi$
$821$	9.99590	+	2.67839i	0.348859	+	0.0934765i	−0.0801344	+	0.996784i	$0.525535\pi$
$822$	0.239193	−	0.892682i	0.00834283	−	0.0311359i
$823$	−9.74887	+	2.61220i	−0.339824	+	0.0910556i	−0.424695	−	0.905336i	$-0.639619\pi$
$823$	−9.74887	+	2.61220i	−0.339824	+	0.0910556i	0.0848712	+	0.996392i	$0.472952\pi$
$824$	29.8307	+	29.8307i	1.03920	+	1.03920i
$825$	−0.0223316	+	0.194267i	−0.000777486	+	0.00676349i
$826$	1.18323	−	0.317047i	0.0411700	−	0.0110315i
$827$		−	8.88196i		−	0.308856i	−0.988004	−	0.154428i	$-0.950647\pi$
$827$		−	8.88196i		−	0.308856i	0.988004	−	0.154428i	$-0.0493535\pi$
$828$	6.35016	+	23.6991i	0.220683	+	0.823602i
$829$	5.22310	+	9.04668i	0.181406	+	0.314204i	0.942359	−	0.334602i	$-0.108602\pi$
$829$	5.22310	+	9.04668i	0.181406	+	0.314204i	−0.760954	+	0.648806i	$0.775269\pi$
$830$	2.98160	−	2.65849i	0.103493	−	0.0922775i
$831$		−	0.930407i		−	0.0322755i
$832$		0			0
$833$	−23.5874	+	23.5874i	−0.817255	+	0.817255i
$834$	0.186367	−	0.695529i	0.00645335	−	0.0240842i
$835$	29.7540	−	26.5297i	1.02968	−	0.918097i
$836$	−3.97587	−	2.29547i	−0.137508	−	0.0793905i
$837$	−0.0791525			−0.00273591
$838$	7.53617	+	4.35101i	0.260333	+	0.150303i
$839$	6.78279	+	25.3137i	0.234168	+	0.873927i	0.978522	+	0.206142i	$0.0660908\pi$
$839$	6.78279	+	25.3137i	0.234168	+	0.873927i	−0.744354	+	0.667785i	$0.767243\pi$
$840$	0.322469	+	0.211651i	0.0111262	+	0.00730267i
$841$	−3.02136	+	5.23314i	−0.104185	+	0.180453i
$842$	−2.56464	−	0.687194i	−0.0883835	−	0.0236823i
$843$	0.0586819	+	0.101640i	0.00202111	+	0.00350067i
$844$	−17.8297			−0.613723
$845$		0			0
$846$	−19.2477			−0.661751
$847$	−4.35841	−	7.54899i	−0.149757	−	0.259386i
$848$	−10.5328	−	2.82225i	−0.361697	−	0.0969165i
$849$	0.187030	−	0.323945i	0.00641885	−	0.0111178i
$850$	−6.65744	+	16.8512i	−0.228348	+	0.577992i
$851$	−8.31427	−	31.0293i	−0.285010	−	1.06367i
$852$	−0.165716	−	0.0956762i	−0.00567734	−	0.00327781i
$853$	30.8130			1.05502			0.527509	−	0.849550i	$-0.323126\pi$
$853$	30.8130			1.05502			0.527509	+	0.849550i	$0.323126\pi$
$854$	−1.46080	−	0.843396i	−0.0499877	−	0.0288604i
$855$	45.2413	+	2.59178i	1.54722	+	0.0886371i
$856$	3.09380	−	11.5462i	0.105744	−	0.394642i
$857$	7.54399	−	7.54399i	0.257698	−	0.257698i	−0.566419	−	0.824117i	$-0.691672\pi$
$857$	7.54399	−	7.54399i	0.257698	−	0.257698i	0.824117	+	0.566419i	$0.191672\pi$
$858$		0			0
$859$			9.75562i			0.332857i	0.986053	+	0.166429i	$0.0532235\pi$
$859$			9.75562i			0.332857i	−0.986053	+	0.166429i	$0.946776\pi$
$860$	1.88258	−	32.8616i	0.0641953	−	1.12057i
$861$	−0.307914	−	0.533322i	−0.0104937	−	0.0181756i
$862$	2.49211	+	9.30066i	0.0848814	+	0.316782i
$863$		−	35.0410i		−	1.19281i	−0.802683	−	0.596405i	$-0.796595\pi$
$863$		−	35.0410i		−	1.19281i	0.802683	−	0.596405i	$-0.203405\pi$
$864$	2.95639	−	0.792163i	0.100579	−	0.0269499i
$865$	12.7804	−	6.43382i	0.434548	−	0.218756i
$866$	−16.6304	−	16.6304i	−0.565124	−	0.565124i
$867$	−0.900959	+	0.241411i	−0.0305982	+	0.00819875i
$868$	−0.0478163	+	0.178453i	−0.00162299	+	0.00605708i
$869$	−3.85900	−	1.03402i	−0.130908	−	0.0350766i
$870$	0.543285	+	0.356584i	0.0184191	+	0.0120893i
$871$		0			0
$872$	13.9572	+	13.9572i	0.472651	+	0.472651i
$873$	−37.5578	+	21.6840i	−1.27114	+	0.733892i
$874$	21.7599	−	12.5631i	0.736041	−	0.424954i
$875$	−8.98531	+	0.811981i	−0.303759	+	0.0274500i
$876$	−0.0252034	+	0.0252034i	−0.000851545	+	0.000851545i
$877$	18.9576	−	32.8355i	0.640152	−	1.10878i	−0.345246	−	0.938512i	$-0.612204\pi$
$877$	18.9576	−	32.8355i	0.640152	−	1.10878i	0.985398	−	0.170264i	$-0.0544622\pi$
$878$	−10.0295	+	17.3715i	−0.338478	+	0.586261i
$879$	−0.419325	+	0.419325i	−0.0141435	+	0.0141435i
$880$	1.21877	−	0.613544i	0.0410848	−	0.0206826i
$881$	−16.1266	+	9.31069i	−0.543319	+	0.313685i	−0.746423	−	0.665472i	$-0.768230\pi$
$881$	−16.1266	+	9.31069i	−0.543319	+	0.313685i	0.203104	+	0.979157i	$0.434897\pi$
$882$	11.3470	−	6.55118i	0.382073	−	0.220590i
$883$	−13.2901	−	13.2901i	−0.447248	−	0.447248i	0.447191	−	0.894439i	$-0.352425\pi$
$883$	−13.2901	−	13.2901i	−0.447248	−	0.447248i	−0.894439	+	0.447191i	$0.852425\pi$
$884$		0			0
$885$	−0.0879316	−	0.423815i	−0.00295579	−	0.0142464i
$886$	−6.77371	−	1.81501i	−0.227567	−	0.0609764i
$887$	−10.1381	+	37.8360i	−0.340405	+	1.27041i	0.557484	+	0.830188i	$0.311767\pi$
$887$	−10.1381	+	37.8360i	−0.340405	+	1.27041i	−0.897889	+	0.440221i	$0.854900\pi$
$888$	−1.23313	+	0.330415i	−0.0413810	+	0.0110880i
$889$	−8.36126	−	8.36126i	−0.280428	−	0.280428i
$890$	5.98418	+	11.8872i	0.200590	+	0.398461i
$891$	−3.83602	+	1.02786i	−0.128511	+	0.0344345i
$892$			4.31525i			0.144485i
$893$	−16.3486	−	61.0140i	−0.547086	−	2.04175i
$894$	−0.409196	−	0.708748i	−0.0136856	−	0.0237041i
$895$	7.74450	+	8.68575i	0.258870	+	0.290333i
$896$		−	8.67127i		−	0.289687i
$897$		0			0
$898$	−7.78067	+	7.78067i	−0.259644	+	0.259644i
$899$	−0.186258	+	0.695124i	−0.00621205	+	0.0231837i
$900$	−13.5839	+	18.3191i	−0.452797	+	0.610635i
$901$	−36.1583	−	20.8760i	−1.20461	−	0.695480i
$902$	2.66145			0.0886165
$903$	−0.593510	−	0.342663i	−0.0197508	−	0.0114031i
$904$	−2.99668	−	11.1838i	−0.0996680	−	0.371966i
$905$	−4.87342	−	23.4890i	−0.161998	−	0.780802i
$906$	−0.165858	+	0.287274i	−0.00551026	+	0.00954406i
$907$	−36.7338	−	9.84278i	−1.21972	−	0.326824i	−0.409154	−	0.912465i	$-0.634176\pi$
$907$	−36.7338	−	9.84278i	−1.21972	−	0.326824i	−0.810571	+	0.585641i	$0.800843\pi$
$908$	−11.8082	−	20.4523i	−0.391868	−	0.678735i
$909$	11.7682			0.390327
$910$		0			0
$911$	−30.2074			−1.00081			−0.500407	−	0.865790i	$-0.666816\pi$
$911$	−30.2074			−1.00081			−0.500407	+	0.865790i	$0.666816\pi$
$912$	0.408667	+	0.707832i	0.0135323	+	0.0234387i
$913$	−1.11263	−	0.298127i	−0.0368225	−	0.00986657i
$914$	−6.63105	+	11.4853i	−0.219336	+	0.379900i
$915$	−0.327046	+	0.498281i	−0.0108118	+	0.0164727i
$916$	−8.10948	−	30.2650i	−0.267945	−	0.999983i
$917$	−14.7926	−	8.54049i	−0.488493	−	0.282032i
$918$	1.90969			0.0630291
$919$	33.9263	+	19.5873i	1.11912	+	0.646127i	0.941177	−	0.337914i	$-0.109721\pi$
$919$	33.9263	+	19.5873i	1.11912	+	0.646127i	0.177947	+	0.984040i	$0.443054\pi$
$920$	−1.67217	+	29.1888i	−0.0551297	+	0.962325i
$921$	−0.218674	+	0.816104i	−0.00720557	+	0.0268915i
$922$	2.16143	−	2.16143i	0.0711828	−	0.0711828i
$923$		0			0
$924$		−	0.0481061i		−	0.00158258i
$925$	17.7854	−	23.9852i	0.584780	−	0.788627i
$926$	−4.22726	−	7.32182i	−0.138916	−	0.240610i
$927$	13.4414	+	50.1639i	0.441472	+	1.64760i
$928$		−	27.8274i		−	0.913478i
$929$	33.1851	−	8.89192i	1.08877	−	0.291735i	0.330585	−	0.943776i	$-0.392754\pi$
$929$	33.1851	−	8.89192i	1.08877	−	0.291735i	0.758183	+	0.652042i	$0.226087\pi$
$930$	−0.0193432	−	0.00638920i	−0.000634288	−	0.000209510i
$931$	30.4047	+	30.4047i	0.996473	+	0.996473i
$932$	10.0892	−	2.70340i	0.330483	−	0.0885527i
$933$	−0.118920	+	0.443816i	−0.00389327	+	0.0145299i
$934$	9.90546	+	2.65416i	0.324116	+	0.0868467i
$935$	5.11561	−	1.06137i	0.167298	−	0.0347104i
$936$		0			0
$937$	12.4007	+	12.4007i	0.405113	+	0.405113i	0.880030	−	0.474917i	$-0.157522\pi$
$937$	12.4007	+	12.4007i	0.405113	+	0.405113i	−0.474917	+	0.880030i	$0.657522\pi$
$938$	5.59670	−	3.23125i	0.182739	−	0.105504i
$939$	0.256330	−	0.147992i	0.00836502	−	0.00482955i
$940$	30.1857	+	9.97056i	0.984549	+	0.325204i
$941$	−0.542863	+	0.542863i	−0.0176968	+	0.0176968i	−0.715900	−	0.698203i	$-0.753983\pi$
$941$	−0.542863	+	0.542863i	−0.0176968	+	0.0176968i	0.698203	+	0.715900i	$0.253983\pi$
$942$	−0.515533	+	0.892930i	−0.0167970	+	0.0290932i
$943$	23.3389	−	40.4242i	0.760020	−	1.31639i
$944$	−2.13568	+	2.13568i	−0.0695104	+	0.0695104i
$945$	0.427573	+	0.849350i	0.0139089	+	0.0276294i
$946$	2.56500	−	1.48090i	0.0833952	−	0.0481482i
$947$	−24.0447	+	13.8822i	−0.781347	+	0.451111i	−0.836908	−	0.547344i	$-0.815639\pi$
$947$	−24.0447	+	13.8822i	−0.781347	+	0.451111i	0.0555602	+	0.998455i	$0.482306\pi$
$948$	0.851621	+	0.851621i	0.0276594	+	0.0276594i
$949$		0			0
$950$	21.7216	+	8.58158i	0.704742	+	0.278423i
$951$	−1.25777	−	0.337017i	−0.0407858	−	0.0109285i
$952$	2.66730	−	9.95450i	0.0864477	−	0.322627i
$953$	−8.40939	+	2.25329i	−0.272407	+	0.0729912i	−0.392437	−	0.919779i	$-0.628368\pi$
$953$	−8.40939	+	2.25329i	−0.272407	+	0.0729912i	0.120030	+	0.992770i	$0.461701\pi$
$954$	11.5962	+	11.5962i	0.375442	+	0.375442i
$955$	−11.3160	+	34.2590i	−0.366177	+	1.10860i
$956$	20.8263	−	5.58038i	0.673569	−	0.180482i
$957$		−	0.187387i		−	0.00605736i
$958$	2.10066	+	7.83978i	0.0678693	+	0.253292i
$959$	−6.14747	−	10.6477i	−0.198512	−	0.343833i
$960$	0.247605	+	0.0141848i	0.00799141	+	0.000457812i
$961$			30.9774i			0.999272i
$962$		0			0
$963$	10.4052	−	10.4052i	0.335303	−	0.335303i
$964$	−9.62581	+	35.9240i	−0.310026	+	1.15703i
$965$	−11.3177	−	12.6933i	−0.364330	−	0.408611i
$966$	0.228011	+	0.131642i	0.00733614	+	0.00423552i
$967$	0.785304			0.0252537			0.0126268	−	0.999920i	$-0.495981\pi$
$967$	0.785304			0.0252537			0.0126268	+	0.999920i	$0.495981\pi$
$968$	−22.7392	−	13.1285i	−0.730866	−	0.421966i
$969$	0.809978	+	3.02288i	0.0260203	+	0.0971089i
$970$	−21.8856	+	4.54074i	−0.702703	+	0.145794i
$971$	23.6294	−	40.9274i	0.758305	−	1.31342i	−0.185409	−	0.982661i	$-0.559361\pi$
$971$	23.6294	−	40.9274i	0.758305	−	1.31342i	0.943714	−	0.330761i	$-0.107306\pi$
$972$	3.48422	+	0.933595i	0.111757	+	0.0299451i
$973$	−4.78978	−	8.29614i	−0.153553	−	0.265962i
$974$	18.2766			0.585621
$975$		0			0
$976$	4.15897			0.133125
$977$	−2.20168	−	3.81342i	−0.0704380	−	0.122002i	0.828655	−	0.559759i	$-0.189106\pi$
$977$	−2.20168	−	3.81342i	−0.0704380	−	0.122002i	−0.899093	+	0.437757i	$0.855773\pi$
$978$	1.22786	+	0.329004i	0.0392627	+	0.0105204i
$979$	1.91877	−	3.32341i	0.0613242	−	0.106217i
$980$	−21.1887	+	4.39616i	−0.676849	+	0.140430i
$981$	6.28896	+	23.4707i	0.200791	+	0.749363i
$982$	8.51178	+	4.91428i	0.271622	+	0.156821i
$983$	33.3973			1.06521			0.532604	−	0.846364i	$-0.321213\pi$
$983$	33.3973			1.06521			0.532604	+	0.846364i	$0.321213\pi$
$984$	−1.60649	−	0.927505i	−0.0512129	−	0.0295678i
$985$	7.29331	+	8.17973i	0.232384	+	0.260628i
$986$	4.49378	−	16.7710i	0.143111	−	0.534098i
$987$	0.468025	−	0.468025i	0.0148974	−	0.0148974i
$988$		0			0
$989$		−	51.9456i		−	1.65177i
$990$	−2.04876	−	0.117370i	−0.0651140	−	0.00373025i
$991$	23.0270	+	39.8839i	0.731475	+	1.26695i	0.956253	+	0.292542i	$0.0945013\pi$
$991$	23.0270	+	39.8839i	0.731475	+	1.26695i	−0.224777	+	0.974410i	$0.572165\pi$
$992$	0.225770	+	0.842585i	0.00716820	+	0.0267521i
$993$			1.37096i			0.0435061i
$994$	0.767332	−	0.205606i	0.0243383	−	0.00652143i
$995$	−14.0095	+	42.4136i	−0.444132	+	1.34460i
$996$	0.245539	+	0.245539i	0.00778020	+	0.00778020i
$997$	−12.6101	+	3.37888i	−0.399367	+	0.107010i	−0.452912	−	0.891555i	$-0.649615\pi$
$997$	−12.6101	+	3.37888i	−0.399367	+	0.107010i	0.0535447	+	0.998565i	$0.482948\pi$
$998$	5.09096	−	18.9997i	0.161152	−	0.601426i
$999$	−3.03996	−	0.814554i	−0.0961800	−	0.0257713i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.o.i.587.17		144
5.3	odd	4		845.2.t.i.418.17		144
13.2	odd	12		845.2.f.f.437.17	yes	72
13.3	even	3		845.2.k.f.577.20	yes	72
13.4	even	6	inner	845.2.o.i.357.20		144
13.5	odd	4		845.2.t.i.427.17		144
13.6	odd	12		845.2.t.i.657.20		144
13.7	odd	12		845.2.t.i.657.17		144
13.8	odd	4		845.2.t.i.427.20		144
13.9	even	3	inner	845.2.o.i.357.17		144
13.10	even	6		845.2.k.f.577.17	yes	72
13.11	odd	12		845.2.f.f.437.20	yes	72
13.12	even	2	inner	845.2.o.i.587.20		144
65.3	odd	12		845.2.f.f.408.17	✓	72
65.8	even	4	inner	845.2.o.i.258.17		144
65.18	even	4	inner	845.2.o.i.258.20		144
65.23	odd	12		845.2.f.f.408.20	yes	72
65.28	even	12		845.2.k.f.268.17	yes	72
65.33	even	12	inner	845.2.o.i.488.17		144
65.38	odd	4		845.2.t.i.418.20		144
65.43	odd	12		845.2.t.i.188.17		144
65.48	odd	12		845.2.t.i.188.20		144
65.58	even	12	inner	845.2.o.i.488.20		144
65.63	even	12		845.2.k.f.268.20	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.f.f.408.17	✓	72	65.3	odd	12
845.2.f.f.408.20	yes	72	65.23	odd	12
845.2.f.f.437.17	yes	72	13.2	odd	12
845.2.f.f.437.20	yes	72	13.11	odd	12
845.2.k.f.268.17	yes	72	65.28	even	12
845.2.k.f.268.20	yes	72	65.63	even	12
845.2.k.f.577.17	yes	72	13.10	even	6
845.2.k.f.577.20	yes	72	13.3	even	3
845.2.o.i.258.17		144	65.8	even	4	inner
845.2.o.i.258.20		144	65.18	even	4	inner
845.2.o.i.357.17		144	13.9	even	3	inner
845.2.o.i.357.20		144	13.4	even	6	inner
845.2.o.i.488.17		144	65.33	even	12	inner
845.2.o.i.488.20		144	65.58	even	12	inner
845.2.o.i.587.17		144	1.1	even	1	trivial
845.2.o.i.587.20		144	13.12	even	2	inner
845.2.t.i.188.17		144	65.43	odd	12
845.2.t.i.188.20		144	65.48	odd	12
845.2.t.i.418.17		144	5.3	odd	4
845.2.t.i.418.20		144	65.38	odd	4
845.2.t.i.427.17		144	13.5	odd	4
845.2.t.i.427.20		144	13.8	odd	4
845.2.t.i.657.17		144	13.7	odd	12
845.2.t.i.657.20		144	13.6	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.o (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.344846 - 0.597291i) q^{2} +(0.0849492 + 0.0227621i) q^{3} +(0.762163 - 1.32010i) q^{4} +(2.18944 - 0.454257i) q^{5} +(-0.0156988 - 0.0585888i) q^{6} +(-0.698835 - 0.403473i) q^{7} -2.43070 q^{8} +(-2.59138 - 1.49613i) q^{9} +(-1.02634 - 1.15108i) q^{10} +(-0.115096 + 0.429543i) q^{11} +(0.0947934 - 0.0947934i) q^{12} +0.556544i q^{14} +(0.196331 + 0.0112474i) q^{15} +(-0.686109 - 1.18838i) q^{16} +(-1.35987 - 5.07510i) q^{17} +2.06374i q^{18} +(-6.54191 + 1.75290i) q^{19} +(1.06904 - 3.23651i) q^{20} +(-0.0501816 - 0.0501816i) q^{21} +(0.296253 - 0.0793806i) q^{22} +(1.39222 - 5.19583i) q^{23} +(-0.206486 - 0.0553277i) q^{24} +(4.58730 - 1.98914i) q^{25} +(-0.372642 - 0.372642i) q^{27} +(-1.06525 + 0.615023i) q^{28} +(-4.14945 + 2.39569i) q^{29} +(-0.0609860 - 0.121145i) q^{30} +(0.106205 - 0.106205i) q^{31} +(-2.90390 + 5.02971i) q^{32} +(-0.0195546 + 0.0338695i) q^{33} +(-2.56236 + 2.56236i) q^{34} +(-1.71334 - 0.565929i) q^{35} +(-3.95010 + 2.28059i) q^{36} +(5.17187 - 2.98598i) q^{37} +(3.30294 + 3.30294i) q^{38} +(-5.32187 + 1.10416i) q^{40} +(8.38192 + 2.24593i) q^{41} +(-0.0126681 + 0.0472779i) q^{42} +(9.32785 - 2.49939i) q^{43} +(0.479320 + 0.479320i) q^{44} +(-6.35330 - 2.09854i) q^{45} +(-3.58352 + 0.960201i) q^{46} +9.32662i q^{47} +(-0.0312345 - 0.116569i) q^{48} +(-3.17442 - 5.49826i) q^{49} +(-2.77001 - 2.05401i) q^{50} -0.462079i q^{51} +(5.61903 - 5.61903i) q^{53} +(-0.0940715 + 0.351079i) q^{54} +(-0.0568723 + 0.992743i) q^{55} +(1.69866 + 0.980720i) q^{56} -0.595630 q^{57} +(2.86184 + 1.65229i) q^{58} +(-0.569671 - 2.12604i) q^{59} +(0.164484 - 0.250605i) q^{60} +(-1.51542 + 2.62478i) q^{61} +(-0.100059 - 0.0268108i) q^{62} +(1.20730 + 2.09110i) q^{63} +1.26116 q^{64} +0.0269733 q^{66} +(-5.80593 - 10.0562i) q^{67} +(-7.73610 - 2.07288i) q^{68} +(0.236536 - 0.409692i) q^{69} +(0.252814 + 1.21852i) q^{70} +(-0.369434 - 1.37875i) q^{71} +(6.29886 + 3.63665i) q^{72} -0.265877 q^{73} +(-3.56700 - 2.05941i) q^{74} +(0.434964 - 0.0645592i) q^{75} +(-2.67199 + 9.97200i) q^{76} +(0.253742 - 0.253742i) q^{77} +8.98397i q^{79} +(-2.04202 - 2.29021i) q^{80} +(4.46522 + 7.73400i) q^{81} +(-1.54900 - 5.78094i) q^{82} +2.59025i q^{83} +(-0.104491 + 0.0279984i) q^{84} +(-5.28275 - 10.4939i) q^{85} +(-4.70953 - 4.70953i) q^{86} +(-0.407024 + 0.109062i) q^{87} +(0.279763 - 1.04409i) q^{88} +(-8.33554 - 2.23350i) q^{89} +(0.937469 + 4.51844i) q^{90} +(-5.79794 - 5.79794i) q^{92} +(0.0114394 - 0.00660456i) q^{93} +(5.57070 - 3.21625i) q^{94} +(-13.5269 + 6.80958i) q^{95} +(-0.361171 + 0.361171i) q^{96} +(7.24668 - 12.5516i) q^{97} +(-2.18937 + 3.79210i) q^{98} +(0.940911 - 0.940911i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 4 q^{3} - 80 q^{4} - 12 q^{10} - 128 q^{12} - 80 q^{16} + 8 q^{17} - 24 q^{22} + 36 q^{23} + 96 q^{25} - 128 q^{27} - 4 q^{30} - 80 q^{35} - 56 q^{38} - 48 q^{40} + 56 q^{42} + 76 q^{43} + 76 q^{48}+ \cdots - 92 q^{95}+O(q^{100}) \) 144 * q + 4 * q^3 - 80 * q^4 - 12 * q^10 - 128 * q^12 - 80 * q^16 + 8 * q^17 - 24 * q^22 + 36 * q^23 + 96 * q^25 - 128 * q^27 - 4 * q^30 - 80 * q^35 - 56 * q^38 - 48 * q^40 + 56 * q^42 + 76 * q^43 + 76 * q^48 + 8 * q^49 - 32 * q^53 - 12 * q^55 - 8 * q^61 + 148 * q^62 + 240 * q^64 + 80 * q^66 + 48 * q^68 - 40 * q^69 - 164 * q^75 - 344 * q^77 - 16 * q^81 + 44 * q^82 - 20 * q^87 + 124 * q^88 + 600 * q^90 - 8 * q^92 - 92 * q^95

Introduction

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