LMFDB - Embedded newform 784.2.w.f.411.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [784,2,Mod(19,784)] 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("784.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(784, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.w (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [56,-2,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			411.14
Character	$\chi$	$=$	784.411
Dual form			784.2.w.f.227.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41041 - 0.103712i) q^{2} +(0.885661 + 0.237312i) q^{3} +(1.97849 - 0.292553i) q^{4} +(-0.818796 - 3.05579i) q^{5} +(1.27375 + 0.242853i) q^{6} +(2.76013 - 0.617811i) q^{8} +(-1.87000 - 1.07964i) q^{9} +(-1.47176 - 4.22498i) q^{10} +(-1.19363 - 0.319833i) q^{11} +(1.82170 + 0.210417i) q^{12} +(0.430348 + 0.430348i) q^{13} -2.90070i q^{15} +(3.82883 - 1.15762i) q^{16} +(5.14136 - 2.96837i) q^{17} +(-2.74943 - 1.32879i) q^{18} +(0.0537031 + 0.200423i) q^{19} +(-2.51396 - 5.80630i) q^{20} +(-1.71668 - 0.327300i) q^{22} +(-1.77104 + 3.06753i) q^{23} +(2.59115 + 0.107841i) q^{24} +(-4.33729 + 2.50414i) q^{25} +(0.651598 + 0.562333i) q^{26} +(-3.34502 - 3.34502i) q^{27} +(1.84275 - 1.84275i) q^{29} +(-0.300839 - 4.09117i) q^{30} +(3.60177 + 6.23845i) q^{31} +(5.28014 - 2.02981i) q^{32} +(-0.981256 - 0.566528i) q^{33} +(6.94355 - 4.71982i) q^{34} +(-4.01562 - 1.58899i) q^{36} +(11.1964 - 3.00006i) q^{37} +(0.0965294 + 0.277107i) q^{38} +(0.279016 + 0.483270i) q^{39} +(-4.14788 - 7.92851i) q^{40} -9.61218 q^{41} +(-7.30761 + 7.30761i) q^{43} +(-2.45516 - 0.283586i) q^{44} +(-1.76802 + 6.59833i) q^{45} +(-2.17974 + 4.51014i) q^{46} +(-2.87631 + 4.98192i) q^{47} +(3.66576 - 0.116635i) q^{48} +(-5.85763 + 3.98168i) q^{50} +(5.25793 - 1.40886i) q^{51} +(0.977338 + 0.725539i) q^{52} +(-1.33537 + 4.98367i) q^{53} +(-5.06475 - 4.37091i) q^{54} +3.90937i q^{55} +0.190251i q^{57} +(2.40791 - 2.79014i) q^{58} +(0.369264 - 1.37811i) q^{59} +(-0.848609 - 5.73901i) q^{60} +(1.28402 - 0.344053i) q^{61} +(5.72696 + 8.42519i) q^{62} +(7.23662 - 3.41048i) q^{64} +(0.962686 - 1.66742i) q^{65} +(-1.44272 - 0.697266i) q^{66} +(-2.11725 + 7.90167i) q^{67} +(9.30372 - 7.37699i) q^{68} +(-2.29651 + 2.29651i) q^{69} +13.7963 q^{71} +(-5.82845 - 1.82465i) q^{72} +(1.12655 + 1.95123i) q^{73} +(15.4803 - 5.39250i) q^{74} +(-4.43564 + 1.18853i) q^{75} +(0.164885 + 0.380823i) q^{76} +(0.443647 + 0.652669i) q^{78} +(1.47554 + 0.851902i) q^{79} +(-6.67248 - 10.7522i) q^{80} +(1.07019 + 1.85362i) q^{81} +(-13.5571 + 0.996900i) q^{82} +(7.78261 - 7.78261i) q^{83} +(-13.2804 - 13.2804i) q^{85} +(-9.54881 + 11.0646i) q^{86} +(2.06936 - 1.19474i) q^{87} +(-3.49218 - 0.145341i) q^{88} +(-3.05474 + 5.29096i) q^{89} +(-1.80929 + 9.48968i) q^{90} +(-2.60657 + 6.58720i) q^{92} +(1.70949 + 6.37989i) q^{93} +(-3.54008 + 7.32484i) q^{94} +(0.568477 - 0.328210i) q^{95} +(5.15811 - 0.544686i) q^{96} +10.6315i q^{97} +(1.88679 + 1.88679i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} + 6 q^{3} - 4 q^{4} + 6 q^{5} + 4 q^{8} + 24 q^{10} + 2 q^{11} + 6 q^{12} + 8 q^{16} + 12 q^{17} - 30 q^{18} + 6 q^{19} - 28 q^{22} - 12 q^{23} + 6 q^{24} + 6 q^{26} - 24 q^{29} - 18 q^{30}+ \cdots - 16 q^{99}+O(q^{100}) $ 56 * q - 2 * q^2 + 6 * q^3 - 4 * q^4 + 6 * q^5 + 4 * q^8 + 24 * q^10 + 2 * q^11 + 6 * q^12 + 8 * q^16 + 12 * q^17 - 30 * q^18 + 6 * q^19 - 28 * q^22 - 12 * q^23 + 6 * q^24 + 6 * q^26 - 24 * q^29 - 18 * q^30 - 12 * q^32 + 12 * q^33 + 16 * q^36 + 6 * q^37 + 6 * q^38 - 4 * q^39 + 66 * q^40 + 26 * q^44 - 12 * q^45 + 16 * q^46 - 34 * q^51 - 84 * q^52 + 6 * q^53 - 42 * q^54 + 18 * q^58 - 42 * q^59 + 78 * q^60 + 6 * q^61 - 16 * q^64 - 4 * q^65 - 126 * q^66 + 6 * q^67 - 24 * q^68 - 80 * q^71 - 4 * q^72 + 62 * q^74 - 24 * q^75 + 4 * q^78 - 12 * q^80 - 8 * q^81 - 42 * q^82 - 28 * q^85 + 12 * q^87 + 30 * q^88 - 20 * q^92 + 10 * q^93 + 42 * q^94 - 36 * q^96 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.41041	−	0.103712i	0.997307	−	0.0733356i
$2$	1.41041	−	0.103712i	0.997307	−	0.0733356i
$3$	0.885661	+	0.237312i	0.511337	+	0.137012i	0.505256	−	0.862969i	$-0.331398\pi$
$3$	0.885661	+	0.237312i	0.511337	+	0.137012i	0.00608034	+	0.999982i	$0.498065\pi$
$4$	1.97849	−	0.292553i	0.989244	−	0.146276i
$5$	−0.818796	−	3.05579i	−0.366177	−	1.36659i	−0.865818	−	0.500358i	$-0.833202\pi$
$5$	−0.818796	−	3.05579i	−0.366177	−	1.36659i	0.499642	−	0.866232i	$-0.333465\pi$
$6$	1.27375	+	0.242853i	0.520008	+	0.0991442i
$7$		0			0
$7$		0			0
$8$	2.76013	−	0.617811i	0.975853	−	0.218429i
$9$	−1.87000	−	1.07964i	−0.623332	−	0.359881i
$10$	−1.47176	−	4.22498i	−0.465411	−	1.33606i
$11$	−1.19363	−	0.319833i	−0.359894	−	0.0964334i	0.0743409	−	0.997233i	$-0.476315\pi$
$11$	−1.19363	−	0.319833i	−0.359894	−	0.0964334i	−0.434235	+	0.900799i	$0.642981\pi$
$12$	1.82170	+	0.210417i	0.525878	+	0.0607421i
$13$	0.430348	+	0.430348i	0.119357	+	0.119357i	0.764262	−	0.644905i	$-0.223103\pi$
$13$	0.430348	+	0.430348i	0.119357	+	0.119357i	−0.644905	+	0.764262i	$0.723103\pi$
$14$		0			0
$15$		−	2.90070i		−	0.748959i
$16$	3.82883	−	1.15762i	0.957207	−	0.289406i
$17$	5.14136	−	2.96837i	1.24696	−	0.719934i	0.276461	−	0.961025i	$-0.410838\pi$
$17$	5.14136	−	2.96837i	1.24696	−	0.719934i	0.970503	+	0.241091i	$0.0775052\pi$
$18$	−2.74943	−	1.32879i	−0.648046	−	0.313200i
$19$	0.0537031	+	0.200423i	0.0123203	+	0.0459801i	0.971812	−	0.235756i	$-0.0757565\pi$
$19$	0.0537031	+	0.200423i	0.0123203	+	0.0459801i	−0.959492	+	0.281736i	$0.909090\pi$
$20$	−2.51396	−	5.80630i	−0.562138	−	1.29833i
$21$		0			0
$22$	−1.71668	−	0.327300i	−0.365997	−	0.0697807i
$23$	−1.77104	+	3.06753i	−0.369287	+	0.639625i	−0.989454	−	0.144845i	$-0.953732\pi$
$23$	−1.77104	+	3.06753i	−0.369287	+	0.639625i	0.620167	+	0.784470i	$0.287065\pi$
$24$	2.59115	+	0.107841i	0.528917	+	0.0220129i
$25$	−4.33729	+	2.50414i	−0.867459	+	0.500828i
$26$	0.651598	+	0.562333i	0.127789	+	0.110283i
$27$	−3.34502	−	3.34502i	−0.643749	−	0.643749i
$28$		0			0
$29$	1.84275	−	1.84275i	0.342190	−	0.342190i	−0.515000	−	0.857190i	$-0.672208\pi$
$29$	1.84275	−	1.84275i	0.342190	−	0.342190i	0.857190	+	0.515000i	$0.172208\pi$
$30$	−0.300839	−	4.09117i	−0.0549253	−	0.746942i
$31$	3.60177	+	6.23845i	0.646897	+	1.12046i	0.983860	+	0.178940i	$0.0572668\pi$
$31$	3.60177	+	6.23845i	0.646897	+	1.12046i	−0.336963	+	0.941518i	$0.609400\pi$
$32$	5.28014	−	2.02981i	0.933405	−	0.358824i
$33$	−0.981256	−	0.566528i	−0.170815	−	0.0986199i
$34$	6.94355	−	4.71982i	1.19081	−	0.809443i
$35$		0			0
$36$	−4.01562	−	1.58899i	−0.669270	−	0.264831i
$37$	11.1964	−	3.00006i	1.84067	−	0.493207i	0.841761	−	0.539851i	$-0.181519\pi$
$37$	11.1964	−	3.00006i	1.84067	−	0.493207i	0.998912	+	0.0466438i	$0.0148526\pi$
$38$	0.0965294	+	0.277107i	0.0156591	+	0.0449528i
$39$	0.279016	+	0.483270i	0.0446783	+	0.0773851i
$40$	−4.14788	−	7.92851i	−0.655838	−	1.25361i
$41$	−9.61218			−1.50117			−0.750585	−	0.660774i	$-0.770228\pi$
$41$	−9.61218			−1.50117			−0.750585	+	0.660774i	$0.770228\pi$
$42$		0			0
$43$	−7.30761	+	7.30761i	−1.11440	+	1.11440i	−0.121852	+	0.992548i	$0.538883\pi$
$43$	−7.30761	+	7.30761i	−1.11440	+	1.11440i	−0.992548	+	0.121852i	$0.961117\pi$
$44$	−2.45516	−	0.283586i	−0.370129	−	0.0427521i
$45$	−1.76802	+	6.59833i	−0.263560	+	0.983620i
$46$	−2.17974	+	4.51014i	−0.321386	+	0.664984i
$47$	−2.87631	+	4.98192i	−0.419553	+	0.726688i	−0.995895	−	0.0905214i	$-0.971147\pi$
$47$	−2.87631	+	4.98192i	−0.419553	+	0.726688i	0.576341	+	0.817209i	$0.304480\pi$
$48$	3.66576	−	0.116635i	0.529107	−	0.0168348i
$49$		0			0
$50$	−5.85763	+	3.98168i	−0.828395	+	0.563095i
$51$	5.25793	−	1.40886i	0.736258	−	0.197280i
$52$	0.977338	+	0.725539i	0.135532	+	0.100614i
$53$	−1.33537	+	4.98367i	−0.183427	+	0.684560i	0.811534	+	0.584305i	$0.198633\pi$
$53$	−1.33537	+	4.98367i	−0.183427	+	0.684560i	−0.994962	+	0.100256i	$0.968034\pi$
$54$	−5.06475	−	4.37091i	−0.689226	−	0.594806i
$55$			3.90937i			0.527140i
$56$		0			0
$57$			0.190251i			0.0251993i
$58$	2.40791	−	2.79014i	0.316173	−	0.366363i
$59$	0.369264	−	1.37811i	0.0480740	−	0.179415i	−0.937714	−	0.347408i	$-0.887062\pi$
$59$	0.369264	−	1.37811i	0.0480740	−	0.179415i	0.985788	+	0.167993i	$0.0537286\pi$
$60$	−0.848609	−	5.73901i	−0.109555	−	0.740903i
$61$	1.28402	−	0.344053i	0.164403	−	0.0440515i	−0.175679	−	0.984448i	$-0.556212\pi$
$61$	1.28402	−	0.344053i	0.164403	−	0.0440515i	0.340081	+	0.940396i	$0.389545\pi$
$62$	5.72696	+	8.42519i	0.727324	+	1.07000i
$63$		0			0
$64$	7.23662	−	3.41048i	0.904577	−	0.426309i
$65$	0.962686	−	1.66742i	0.119407	−	0.206818i
$66$	−1.44272	−	0.697266i	−0.177587	−	0.0858276i
$67$	−2.11725	+	7.90167i	−0.258663	+	0.965343i	0.707353	+	0.706860i	$0.249889\pi$
$67$	−2.11725	+	7.90167i	−0.258663	+	0.965343i	−0.966016	+	0.258482i	$0.916778\pi$
$68$	9.30372	−	7.37699i	1.12824	−	0.894592i
$69$	−2.29651	+	2.29651i	−0.276467	+	0.276467i
$70$		0			0
$71$	13.7963			1.63732			0.818661	−	0.574277i	$-0.194717\pi$
$71$	13.7963			1.63732			0.818661	+	0.574277i	$0.194717\pi$
$72$	−5.82845	−	1.82465i	−0.686889	−	0.215037i
$73$	1.12655	+	1.95123i	0.131852	+	0.228375i	0.924391	−	0.381447i	$-0.124574\pi$
$73$	1.12655	+	1.95123i	0.131852	+	0.228375i	−0.792538	+	0.609822i	$0.791241\pi$
$74$	15.4803	−	5.39250i	1.79955	−	0.626865i
$75$	−4.43564	+	1.18853i	−0.512183	+	0.137239i
$76$	0.164885	+	0.380823i	0.0189136	+	0.0436833i
$77$		0			0
$78$	0.443647	+	0.652669i	0.0502331	+	0.0739002i
$79$	1.47554	+	0.851902i	0.166011	+	0.0958465i	0.580704	−	0.814115i	$-0.302778\pi$
$79$	1.47554	+	0.851902i	0.166011	+	0.0958465i	−0.414693	+	0.909962i	$0.636111\pi$
$80$	−6.67248	−	10.7522i	−0.746006	−	1.20214i
$81$	1.07019	+	1.85362i	0.118910	+	0.205958i
$82$	−13.5571	+	0.996900i	−1.49713	+	0.110089i
$83$	7.78261	−	7.78261i	0.854253	−	0.854253i	−0.136401	−	0.990654i	$-0.543554\pi$
$83$	7.78261	−	7.78261i	0.854253	−	0.854253i	0.990654	+	0.136401i	$0.0435536\pi$
$84$		0			0
$85$	−13.2804	−	13.2804i	−1.44046	−	1.44046i
$86$	−9.54881	+	11.0646i	−1.02967	+	1.19313i
$87$	2.06936	−	1.19474i	0.221858	−	0.128090i
$88$	−3.49218	−	0.145341i	−0.372268	−	0.0154934i
$89$	−3.05474	+	5.29096i	−0.323801	+	0.560840i	−0.981269	−	0.192642i	$-0.938294\pi$
$89$	−3.05474	+	5.29096i	−0.323801	+	0.560840i	0.657468	+	0.753483i	$0.271628\pi$
$90$	−1.80929	+	9.48968i	−0.190716	+	1.00030i
$91$		0			0
$92$	−2.60657	+	6.58720i	−0.271753	+	0.686763i
$93$	1.70949	+	6.37989i	0.177266	+	0.661564i
$94$	−3.54008	+	7.32484i	−0.365132	+	0.755499i
$95$	0.568477	−	0.328210i	0.0583245	−	0.0336737i
$96$	5.15811	−	0.544686i	0.526448	−	0.0555918i
$97$			10.6315i			1.07946i	0.841837	+	0.539732i	$0.181474\pi$
$97$			10.6315i			1.07946i	−0.841837	+	0.539732i	$0.818526\pi$
$98$		0			0
$99$	1.88679	+	1.88679i	0.189629	+	0.189629i
$100$	−7.84869	+	6.22329i	−0.784869	+	0.622329i
$101$	−1.23182	−	0.330064i	−0.122570	−	0.0328426i	0.197012	−	0.980401i	$-0.436876\pi$
$101$	−1.23182	−	0.330064i	−0.122570	−	0.0328426i	−0.319583	+	0.947558i	$0.603543\pi$
$102$	7.26970	−	2.53237i	0.719808	−	0.250742i
$103$	8.50599	+	4.91094i	0.838120	+	0.483889i	0.856625	−	0.515940i	$-0.172557\pi$
$103$	8.50599	+	4.91094i	0.838120	+	0.483889i	−0.0185046	+	0.999829i	$0.505891\pi$
$104$	1.45369	+	0.921943i	0.142546	+	0.0904039i
$105$		0			0
$106$	−1.36655	+	7.16750i	−0.132731	+	0.696169i
$107$	−2.68932	−	10.0367i	−0.259986	−	0.970282i	−0.965248	−	0.261335i	$-0.915837\pi$
$107$	−2.68932	−	10.0367i	−0.259986	−	0.970282i	0.705262	−	0.708947i	$-0.250829\pi$
$108$	−7.59667	−	5.63948i	−0.730990	−	0.542660i
$109$	−0.0392146	−	0.0105075i	−0.00375608	−	0.00100644i	0.256941	−	0.966427i	$-0.417286\pi$
$109$	−0.0392146	−	0.0105075i	−0.00375608	−	0.00100644i	−0.260697	+	0.965421i	$0.583952\pi$
$110$	0.405450	+	5.51380i	0.0386581	+	0.525721i
$111$	10.6281			1.00878
$112$		0			0
$113$	−11.0778			−1.04211			−0.521055	−	0.853523i	$-0.674461\pi$
$113$	−11.0778			−1.04211			−0.521055	+	0.853523i	$0.674461\pi$
$114$	0.0197313	+	0.268331i	0.00184801	+	0.0251315i
$115$	10.8239	+	2.90024i	1.00933	+	0.270449i
$116$	3.10675	−	4.18495i	0.288455	−	0.388563i
$117$	−0.340127	−	1.26937i	−0.0314448	−	0.117354i
$118$	0.377885	−	1.98199i	0.0347871	−	0.182457i
$119$		0			0
$120$	−1.79209	−	8.00632i	−0.163594	−	0.730874i
$121$	−8.20381	−	4.73647i	−0.745801	−	0.430588i
$122$	1.77531	−	0.618424i	0.160729	−	0.0559895i
$123$	−8.51314	−	2.28109i	−0.767604	−	0.205679i
$124$	8.95113	+	11.2890i	0.803835	+	1.01378i
$125$	0.0185146	+	0.0185146i	0.00165600	+	0.00165600i
$126$		0			0
$127$			18.0882i			1.60506i	0.596609	+	0.802532i	$0.296514\pi$
$127$			18.0882i			1.60506i	−0.596609	+	0.802532i	$0.703486\pi$
$128$	9.85286	−	5.56068i	0.870878	−	0.491499i
$129$	−8.20626	+	4.73788i	−0.722521	+	0.417147i
$130$	1.18485	−	2.45158i	0.103918	−	0.215018i
$131$	−0.712687	−	2.65978i	−0.0622678	−	0.232386i	0.927778	−	0.373133i	$-0.121716\pi$
$131$	−0.712687	−	2.65978i	−0.0622678	−	0.232386i	−0.990046	+	0.140746i	$0.955050\pi$
$132$	−2.10714	−	0.833800i	−0.183403	−	0.0725730i
$133$		0			0
$134$	−2.16668	+	11.3641i	−0.187172	+	0.981713i
$135$	−7.48278	+	12.9606i	−0.644016	+	1.11547i
$136$	12.3569	−	11.3695i	1.05960	−	0.974923i
$137$	−1.69173	+	0.976720i	−0.144534	+	0.0834468i	−0.570523	−	0.821281i	$-0.693260\pi$
$137$	−1.69173	+	0.976720i	−0.144534	+	0.0834468i	0.425989	+	0.904728i	$0.359926\pi$
$138$	−3.00083	+	3.47718i	−0.255447	+	0.295997i
$139$	−5.22260	−	5.22260i	−0.442975	−	0.442975i	0.450035	−	0.893011i	$-0.351411\pi$
$139$	−5.22260	−	5.22260i	−0.442975	−	0.442975i	−0.893011	+	0.450035i	$0.851411\pi$
$140$		0			0
$141$	−3.72971	+	3.72971i	−0.314098	+	0.314098i
$142$	19.4584	−	1.43085i	1.63291	−	0.120074i
$143$	−0.376039	−	0.651318i	−0.0314460	−	0.0544660i
$144$	−8.40971	−	1.96901i	−0.700810	−	0.164085i
$145$	−7.13988	−	4.12221i	−0.592935	−	0.342331i
$146$	1.79125	+	2.63520i	0.148245	+	0.218090i
$147$		0			0
$148$	21.2742	−	9.21111i	1.74873	−	0.757148i
$149$	−7.37254	+	1.97547i	−0.603982	+	0.161836i	−0.547835	−	0.836586i	$-0.684548\pi$
$149$	−7.37254	+	1.97547i	−0.603982	+	0.161836i	−0.0561464	+	0.998423i	$0.517881\pi$
$150$	−6.13278	+	2.13633i	−0.500740	+	0.174431i
$151$	−7.05310	−	12.2163i	−0.573973	−	0.994151i	−0.996152	−	0.0876383i	$-0.972068\pi$
$151$	−7.05310	−	12.2163i	−0.573973	−	0.994151i	0.422179	−	0.906512i	$-0.361265\pi$
$152$	0.272051	+	0.520014i	0.0220662	+	0.0421787i
$153$	−12.8191			−1.03636
$154$		0			0
$155$	16.1143	−	16.1143i	1.29433	−	1.29433i
$156$	0.693411	+	0.874516i	0.0555173	+	0.0700173i
$157$	−3.78295	+	14.1182i	−0.301912	+	1.12675i	0.633658	+	0.773613i	$0.281552\pi$
$157$	−3.78295	+	14.1182i	−0.301912	+	1.12675i	−0.935571	+	0.353139i	$0.885114\pi$
$158$	2.16946	+	1.04850i	0.172593	+	0.0834139i
$159$	−2.36537	+	4.09695i	−0.187586	+	0.324909i
$160$	−10.5260	−	14.4730i	−0.832157	−	1.14419i
$161$		0			0
$162$	1.70165	+	2.50337i	0.133694	+	0.196683i
$163$	0.403234	−	0.108046i	0.0315837	−	0.00846284i	−0.242993	−	0.970028i	$-0.578129\pi$
$163$	0.403234	−	0.108046i	0.0315837	−	0.00846284i	0.274576	+	0.961565i	$0.411462\pi$
$164$	−19.0176	+	2.81207i	−1.48502	+	0.219586i
$165$	−0.927743	+	3.46238i	−0.0722247	+	0.269546i
$166$	10.1695	−	11.7838i	0.789305	−	0.914599i
$167$		−	3.16944i		−	0.245259i	−0.992453	−	0.122629i	$-0.960867\pi$
$167$		−	3.16944i		−	0.245259i	0.992453	−	0.122629i	$-0.0391326\pi$
$168$		0			0
$169$		−	12.6296i		−	0.971508i
$170$	−20.1081	−	17.3534i	−1.54222	−	1.33095i
$171$	0.115960	−	0.432770i	0.00886771	−	0.0330947i
$172$	−12.3202	+	16.5959i	−0.939404	+	1.26542i
$173$	22.0884	−	5.91858i	1.67935	−	0.449981i	0.711744	−	0.702438i	$-0.247905\pi$
$173$	22.0884	−	5.91858i	1.67935	−	0.449981i	0.967608	+	0.252457i	$0.0812387\pi$
$174$	2.79472	−	1.89969i	0.211867	−	0.144015i
$175$		0			0
$176$	−4.94047	+	0.157192i	−0.372402	+	0.0118488i
$177$	0.654085	−	1.13291i	0.0491640	−	0.0851546i
$178$	−3.75968	+	7.77921i	−0.281800	+	0.583076i
$179$	3.56007	−	13.2864i	0.266092	−	0.993069i	−0.695486	−	0.718539i	$-0.744811\pi$
$179$	3.56007	−	13.2864i	0.266092	−	0.993069i	0.961579	−	0.274530i	$-0.0885223\pi$
$180$	−1.56764	+	13.5719i	−0.116845	+	1.01159i
$181$	−5.01349	+	5.01349i	−0.372650	+	0.372650i	−0.868441	−	0.495792i	$-0.834878\pi$
$181$	−5.01349	+	5.01349i	−0.372650	+	0.372650i	0.495792	+	0.868441i	$0.334878\pi$
$182$		0			0
$183$	1.21886			0.0901007
$184$	−2.99314	+	9.56095i	−0.220658	+	0.704843i
$185$	−18.3351	−	31.7573i	−1.34802	−	2.33484i
$186$	3.07274	+	8.82094i	0.225304	+	0.646783i
$187$	−7.08629	+	1.89877i	−0.518201	+	0.138851i
$188$	−4.23328	+	10.6981i	−0.308743	+	0.780242i
$189$		0			0
$190$	0.767744	−	0.521868i	0.0556980	−	0.0378603i
$191$	−4.65280	−	2.68629i	−0.336665	−	0.194373i	0.322132	−	0.946695i	$-0.395601\pi$
$191$	−4.65280	−	2.68629i	−0.336665	−	0.194373i	−0.658796	+	0.752322i	$0.728934\pi$
$192$	7.21854	−	1.30319i	0.520953	−	0.0940495i
$193$	0.0359286	+	0.0622302i	0.00258620	+	0.00447943i	0.867316	−	0.497759i	$-0.165843\pi$
$193$	0.0359286	+	0.0622302i	0.00258620	+	0.00447943i	−0.864729	+	0.502238i	$0.832510\pi$
$194$	1.10261	+	14.9947i	0.0791631	+	1.07656i
$195$	1.24831	−	1.24831i	0.0893936	−	0.0893936i
$196$		0			0
$197$	2.60367	+	2.60367i	0.185504	+	0.185504i	0.793749	−	0.608245i	$-0.208126\pi$
$197$	2.60367	+	2.60367i	0.185504	+	0.185504i	−0.608245	+	0.793749i	$0.708126\pi$
$198$	2.85682	+	2.46545i	0.203025	+	0.175212i
$199$	−9.01857	+	5.20687i	−0.639310	+	0.369106i	−0.784349	−	0.620320i	$-0.787003\pi$
$199$	−9.01857	+	5.20687i	−0.639310	+	0.369106i	0.145039	+	0.989426i	$0.453669\pi$
$200$	−10.4244	+	9.59137i	−0.737117	+	0.678212i
$201$	−3.75033	+	6.49576i	−0.264528	+	0.458175i
$202$	−1.77159	−	0.337770i	−0.124649	−	0.0237654i
$203$		0			0
$204$	9.99059	−	4.32563i	0.699481	−	0.302855i
$205$	7.87042	+	29.3728i	0.549694	+	2.05148i
$206$	12.5062	+	6.04424i	0.871350	+	0.421122i
$207$	6.62368	−	3.82418i	0.460378	−	0.265799i
$208$	2.14591	+	1.14955i	0.148792	+	0.0797068i
$209$		−	0.256407i		−	0.0177361i
$210$		0			0
$211$	2.30105	+	2.30105i	0.158411	+	0.158411i	0.781862	−	0.623451i	$-0.214270\pi$
$211$	2.30105	+	2.30105i	0.158411	+	0.158411i	−0.623451	+	0.781862i	$0.714270\pi$
$212$	−1.18403	+	10.2508i	−0.0813195	+	0.704028i
$213$	12.2189	+	3.27404i	0.837223	+	0.224333i
$214$	−4.83396	−	13.8769i	−0.330443	−	0.948603i
$215$	28.3140	+	16.3471i	1.93100	+	1.11486i
$216$	−11.2993	−	7.16609i	−0.768818	−	0.487591i
$217$		0			0
$218$	−0.0563983	−	0.0107528i	−0.00381977	−	0.000728274i
$219$	0.534686	+	1.99548i	0.0361308	+	0.134842i
$220$	1.14370	+	7.73465i	0.0771081	+	0.521470i
$221$	3.49001	+	0.935145i	0.234763	+	0.0629046i
$222$	14.9900	−	1.10227i	1.00606	−	0.0739794i
$223$	−21.9153			−1.46756			−0.733778	−	0.679390i	$-0.762245\pi$
$223$	−21.9153			−1.46756			−0.733778	+	0.679390i	$0.762245\pi$
$224$		0			0
$225$	10.8143			0.720954
$226$	−15.6242	+	1.14890i	−1.03930	+	0.0764238i
$227$	11.1925	+	2.99903i	0.742874	+	0.199053i	0.610355	−	0.792128i	$-0.291027\pi$
$227$	11.1925	+	2.99903i	0.742874	+	0.199053i	0.132519	+	0.991180i	$0.457693\pi$
$228$	0.0556584	+	0.376409i	0.00368607	+	0.0249283i
$229$	−5.62429	−	20.9901i	−0.371663	−	1.38707i	−0.858159	−	0.513383i	$-0.828392\pi$
$229$	−5.62429	−	20.9901i	−0.371663	−	1.38707i	0.486496	−	0.873683i	$-0.338275\pi$
$230$	15.5668	+	2.96795i	1.02645	+	0.195701i
$231$		0			0
$232$	3.94775	−	6.22469i	0.259182	−	0.408671i
$233$	−10.8223	−	6.24823i	−0.708989	−	0.409335i	0.101697	−	0.994815i	$-0.467573\pi$
$233$	−10.8223	−	6.24823i	−0.708989	−	0.409335i	−0.810687	+	0.585480i	$0.800906\pi$
$234$	−0.611367	−	1.75506i	−0.0399663	−	0.114732i
$235$	17.5788	+	4.71023i	1.14672	+	0.307262i
$236$	0.327414	−	2.83460i	0.0213128	−	0.184517i
$237$	1.10466	+	1.10466i	0.0717554	+	0.0717554i
$238$		0			0
$239$			7.70978i			0.498704i	0.968413	+	0.249352i	$0.0802176\pi$
$239$			7.70978i			0.498704i	−0.968413	+	0.249352i	$0.919782\pi$
$240$	−3.35792	−	11.1063i	−0.216753	−	0.716908i
$241$	−9.50533	+	5.48790i	−0.612292	+	0.353507i	−0.773862	−	0.633354i	$-0.781678\pi$
$241$	−9.50533	+	5.48790i	−0.612292	+	0.353507i	0.161570	+	0.986861i	$0.448344\pi$
$242$	−12.0619	−	5.82951i	−0.775370	−	0.374735i
$243$	4.18102	+	15.6038i	0.268213	+	1.00098i
$244$	2.43977	−	1.05635i	0.156191	−	0.0676259i
$245$		0			0
$246$	−12.2435	−	2.33434i	−0.780620	−	0.148832i
$247$	−0.0631405	+	0.109363i	−0.00401753	+	0.00695857i
$248$	13.7955	+	14.9937i	0.876017	+	0.952101i
$249$	8.73967	−	5.04585i	0.553854	−	0.319768i
$250$	0.0280334	+	0.0241930i	0.00177299	+	0.00153010i
$251$	18.8899	+	18.8899i	1.19232	+	1.19232i	0.976415	+	0.215903i	$0.0692694\pi$
$251$	18.8899	+	18.8899i	1.19232	+	1.19232i	0.215903	+	0.976415i	$0.430731\pi$
$252$		0			0
$253$	3.09507	−	3.09507i	0.194586	−	0.194586i
$254$	1.87596	+	25.5116i	0.117708	+	1.60074i
$255$	−8.61035	−	14.9136i	−0.539201	−	0.933924i
$256$	13.3198	−	8.86467i	0.832489	−	0.554042i
$257$	−15.2767	−	8.82001i	−0.952935	−	0.550177i	−0.0589435	−	0.998261i	$-0.518773\pi$
$257$	−15.2767	−	8.82001i	−0.952935	−	0.550177i	−0.893991	+	0.448084i	$0.852107\pi$
$258$	−11.0828	+	7.53343i	−0.689983	+	0.469011i
$259$		0			0
$260$	1.41685	−	3.58061i	0.0878696	−	0.222060i
$261$	−5.43544	+	1.45642i	−0.336445	+	0.0901503i
$262$	−1.28103	−	3.67746i	−0.0791423	−	0.227194i
$263$	3.59074	+	6.21934i	0.221414	+	0.383501i	0.955238	−	0.295840i	$-0.0955994\pi$
$263$	3.59074	+	6.21934i	0.221414	+	0.383501i	−0.733823	+	0.679340i	$0.762266\pi$
$264$	−3.05840	−	0.957460i	−0.188231	−	0.0589276i
$265$	16.3225			1.00268
$266$		0			0
$267$	−3.96107	+	3.96107i	−0.242414	+	0.242414i
$268$	−1.87729	+	16.2528i	−0.114674	+	0.992796i
$269$	4.78181	−	17.8459i	0.291552	−	1.08809i	−0.652366	−	0.757904i	$-0.726223\pi$
$269$	4.78181	−	17.8459i	0.291552	−	1.08809i	0.943917	−	0.330182i	$-0.107110\pi$
$270$	−9.20959	+	19.0557i	−0.560478	+	1.15969i
$271$	0.492830	−	0.853607i	0.0299373	−	0.0518529i	−0.850669	−	0.525702i	$-0.823803\pi$
$271$	0.492830	−	0.853607i	0.0299373	−	0.0518529i	0.880606	+	0.473849i	$0.157136\pi$
$272$	16.2491	−	17.3171i	0.985248	−	1.05000i
$273$		0			0
$274$	−2.28473	+	1.55302i	−0.138025	+	0.0938216i
$275$	5.97805	−	1.60181i	0.360490	−	0.0965930i
$276$	−3.87176	+	5.21546i	−0.233052	+	0.313934i
$277$	−0.0226152	+	0.0844010i	−0.00135881	+	0.00507116i	−0.966602	−	0.256283i	$-0.917502\pi$
$277$	−0.0226152	+	0.0844010i	−0.00135881	+	0.00507116i	0.965243	+	0.261354i	$0.0841689\pi$
$278$	−7.90763	−	6.82434i	−0.474268	−	0.409297i
$279$		−	15.5545i		−	0.931224i
$280$		0			0
$281$			13.9541i			0.832431i	0.909266	+	0.416215i	$0.136644\pi$
$281$			13.9541i			0.832431i	−0.909266	+	0.416215i	$0.863356\pi$
$282$	−4.87359	+	5.64722i	−0.290218	+	0.336287i
$283$	3.42009	−	12.7640i	0.203303	−	0.758738i	−0.786657	−	0.617391i	$-0.788190\pi$
$283$	3.42009	−	12.7640i	0.203303	−	0.758738i	0.989960	−	0.141348i	$-0.0451436\pi$
$284$	27.2959	−	4.03615i	1.61971	−	0.239501i
$285$	0.581367	−	0.155777i	0.0344372	−	0.00922742i
$286$	−0.597917	−	0.879623i	−0.0353556	−	0.0520132i
$287$		0			0
$288$	−12.0653	−	1.90492i	−0.710956	−	0.112248i
$289$	9.12239	−	15.8004i	0.536611	−	0.929438i
$290$	−10.4977	−	5.07350i	−0.616443	−	0.297926i
$291$	−2.52298	+	9.41589i	−0.147900	+	0.551969i
$292$	2.79970	+	3.53092i	0.163840	+	0.206631i
$293$	−1.11946	+	1.11946i	−0.0653995	+	0.0653995i	−0.739050	−	0.673651i	$-0.764725\pi$
$293$	−1.11946	+	1.11946i	−0.0653995	+	0.0653995i	0.673651	+	0.739050i	$0.264725\pi$
$294$		0			0
$295$	−4.51357			−0.262790
$296$	29.0500	−	15.1978i	1.68849	−	0.883354i
$297$	2.92288	+	5.06258i	0.169603	+	0.293761i
$298$	−10.1934	+	3.55083i	−0.590487	+	0.205694i
$299$	−2.08227	+	0.557943i	−0.120421	+	0.0322667i
$300$	−8.42815	+	3.64914i	−0.486599	+	0.210683i
$301$		0			0
$302$	−11.2147	−	16.4985i	−0.645334	−	0.949381i
$303$	−1.01264	−	0.584650i	−0.0581748	−	0.0335873i
$304$	0.437633	+	0.705215i	0.0251000	+	0.0404469i
$305$	−2.10271	−	3.64200i	−0.120401	−	0.208540i
$306$	−18.0801	+	1.32950i	−1.03357	+	0.0760023i
$307$	15.8597	−	15.8597i	0.905158	−	0.905158i	−0.0907183	−	0.995877i	$-0.528916\pi$
$307$	15.8597	−	15.8597i	0.905158	−	0.905158i	0.995877	+	0.0907183i	$0.0289163\pi$
$308$		0			0
$309$	6.36800	+	6.36800i	0.362263	+	0.362263i
$310$	21.0564	−	24.3989i	1.19592	−	1.38576i
$311$	−24.7191	+	14.2716i	−1.40169	+	0.809267i	−0.994566	−	0.104106i	$-0.966802\pi$
$311$	−24.7191	+	14.2716i	−1.40169	+	0.809267i	−0.407125	+	0.913373i	$0.633469\pi$
$312$	1.06869	+	1.16151i	0.0605026	+	0.0657574i
$313$	0.0311630	−	0.0539759i	0.00176144	−	0.00305090i	−0.865143	−	0.501525i	$-0.832773\pi$
$313$	0.0311630	−	0.0539759i	0.00176144	−	0.00305090i	0.866905	+	0.498474i	$0.166106\pi$
$314$	−3.87127	+	20.3047i	−0.218468	+	1.14586i
$315$		0			0
$316$	3.16856	+	1.25381i	0.178245	+	0.0705321i
$317$	−5.87456	−	21.9241i	−0.329948	−	1.23138i	−0.909243	−	0.416265i	$-0.863339\pi$
$317$	−5.87456	−	21.9241i	−0.329948	−	1.23138i	0.579295	−	0.815118i	$-0.303328\pi$
$318$	−2.91123	+	6.02368i	−0.163254	+	0.337791i
$319$	−2.78894	+	1.61019i	−0.156151	+	0.0901536i
$320$	−16.3470	−	19.3211i	−0.913826	−	1.08008i
$321$		−	9.52731i		−	0.531762i
$322$		0			0
$323$	0.871034	+	0.871034i	0.0484656	+	0.0484656i
$324$	2.65964	+	3.35428i	0.147758	+	0.186349i
$325$	−2.94420	−	0.788896i	−0.163315	−	0.0437601i
$326$	0.557518	−	0.194209i	0.0308781	−	0.0107563i
$327$	−0.0322373	−	0.0186122i	−0.00178273	−	0.00102926i
$328$	−26.5308	+	5.93851i	−1.46492	+	0.327899i
$329$		0			0
$330$	−0.949402	+	4.97958i	−0.0522629	+	0.274117i
$331$	−4.15970	−	15.5242i	−0.228638	−	0.853289i	−0.980914	−	0.194441i	$-0.937711\pi$
$331$	−4.15970	−	15.5242i	−0.228638	−	0.853289i	0.752276	−	0.658848i	$-0.228956\pi$
$332$	13.1210	−	17.6746i	0.720107	−	0.970021i
$333$	−24.1762	−	6.47799i	−1.32485	−	0.354992i
$334$	−0.328710	−	4.47020i	−0.0179862	−	0.244598i
$335$	25.8794			1.41394
$336$		0			0
$337$	−15.2905			−0.832928			−0.416464	−	0.909152i	$-0.636731\pi$
$337$	−15.2905			−0.832928			−0.416464	+	0.909152i	$0.636731\pi$
$338$	−1.30984	−	17.8129i	−0.0712461	−	0.968892i
$339$	−9.81116	−	2.62889i	−0.532869	−	0.142782i
$340$	−30.1604	−	22.3899i	−1.63568	−	1.21426i
$341$	−2.30393	−	8.59839i	−0.124765	−	0.465629i
$342$	0.118668	−	0.622407i	0.00641681	−	0.0336559i
$343$		0			0
$344$	−15.6552	+	24.6847i	−0.844073	+	1.33091i
$345$	8.89801	+	5.13727i	0.479053	+	0.276581i
$346$	30.5398	−	10.6384i	1.64183	−	0.571926i
$347$	26.6227	+	7.13352i	1.42918	+	0.382948i	0.888731	−	0.458429i	$-0.151588\pi$
$347$	26.6227	+	7.13352i	1.42918	+	0.382948i	0.540449	+	0.841377i	$0.318254\pi$
$348$	3.74467	−	2.96918i	0.200735	−	0.159165i
$349$	17.0806	+	17.0806i	0.914304	+	0.914304i	0.996607	−	0.0823032i	$-0.0262276\pi$
$349$	17.0806	+	17.0806i	0.914304	+	0.914304i	−0.0823032	+	0.996607i	$0.526228\pi$
$350$		0			0
$351$		−	2.87905i		−	0.153672i
$352$	−6.95176	+	0.734092i	−0.370530	+	0.0391272i
$353$	20.2940	−	11.7168i	1.08014	−	0.623621i	0.149208	−	0.988806i	$-0.452328\pi$
$353$	20.2940	−	11.7168i	1.08014	−	0.623621i	0.930935	+	0.365185i	$0.118994\pi$
$354$	0.805029	−	1.66570i	0.0427868	−	0.0885308i
$355$	−11.2964	−	42.1587i	−0.599550	−	2.23755i
$356$	−4.49587	+	11.3618i	−0.238281	+	0.602172i
$357$		0			0
$358$	3.64318	−	19.1084i	0.192548	−	1.00991i
$359$	−4.35778	+	7.54790i	−0.229995	+	0.398363i	−0.957806	−	0.287414i	$-0.907204\pi$
$359$	−4.35778	+	7.54790i	−0.229995	+	0.398363i	0.727811	+	0.685777i	$0.240538\pi$
$360$	−0.803433	+	19.3045i	−0.0423446	+	1.01744i
$361$	16.4172	−	9.47847i	0.864063	−	0.498867i
$362$	−6.55109	+	7.59101i	−0.344318	+	0.398975i
$363$	−6.14177	−	6.14177i	−0.322360	−	0.322360i
$364$		0			0
$365$	5.04015	−	5.04015i	0.263814	−	0.263814i
$366$	1.71909	−	0.126411i	0.0898581	−	0.00660759i
$367$	1.41408	+	2.44926i	0.0738143	+	0.127850i	0.900570	−	0.434711i	$-0.143149\pi$
$367$	1.41408	+	2.44926i	0.0738143	+	0.127850i	−0.826756	+	0.562561i	$0.809816\pi$
$368$	−3.22996	+	13.7952i	−0.168373	+	0.719127i
$369$	17.9747	+	10.3777i	0.935728	+	0.540243i
$370$	−29.1535	−	42.8891i	−1.51562	−	2.22970i
$371$		0			0
$372$	5.24865	+	12.1224i	0.272130	+	0.628519i
$373$	13.6755	−	3.66434i	0.708091	−	0.189733i	0.113239	−	0.993568i	$-0.463877\pi$
$373$	13.6755	−	3.66434i	0.708091	−	0.189733i	0.594852	+	0.803835i	$0.297211\pi$
$374$	−9.79762	+	3.41296i	−0.506623	+	0.176480i
$375$	0.0120040	+	0.0207915i	0.000619882	+	0.00107367i
$376$	−4.86111	+	15.5278i	−0.250693	+	0.800783i
$377$	1.58605			0.0816855
$378$		0			0
$379$	−10.2443	+	10.2443i	−0.526215	+	0.526215i	−0.919442	−	0.393227i	$-0.871359\pi$
$379$	−10.2443	+	10.2443i	−0.526215	+	0.526215i	0.393227	+	0.919442i	$0.371359\pi$
$380$	1.02871	−	0.815670i	0.0527715	−	0.0418430i
$381$	−4.29254	+	16.0200i	−0.219913	+	0.820728i
$382$	−6.84093	−	3.30621i	−0.350012	−	0.169160i
$383$	3.20722	−	5.55507i	0.163881	−	0.283851i	−0.772376	−	0.635165i	$-0.780932\pi$
$383$	3.20722	−	5.55507i	0.163881	−	0.283851i	0.936257	+	0.351315i	$0.114265\pi$
$384$	10.0459	−	2.58667i	0.512653	−	0.132001i
$385$		0			0
$386$	0.0571280	+	0.0840436i	0.00290774	+	0.00427771i
$387$	21.5548	−	5.77560i	1.09569	−	0.293590i
$388$	3.11027	+	21.0343i	0.157900	+	1.06785i
$389$	4.40182	−	16.4278i	0.223181	−	0.832924i	−0.759944	−	0.649989i	$-0.774774\pi$
$389$	4.40182	−	16.4278i	0.223181	−	0.832924i	0.983125	−	0.182935i	$-0.0585598\pi$
$390$	1.63116	−	1.89009i	0.0825971	−	0.0957086i
$391$			21.0284i			1.06345i
$392$		0			0
$393$		−	2.52480i		−	0.127359i
$394$	3.94226	+	3.40220i	0.198608	+	0.171400i
$395$	1.39507	−	5.20647i	0.0701935	−	0.261966i
$396$	4.28497	+	3.18100i	0.215328	+	0.159851i
$397$	−10.6885	+	2.86398i	−0.536441	+	0.143739i	−0.516861	−	0.856069i	$-0.672900\pi$
$397$	−10.6885	+	2.86398i	−0.536441	+	0.143739i	−0.0195801	+	0.999808i	$0.506233\pi$
$398$	−12.1798	+	8.27914i	−0.610519	+	0.414996i
$399$		0			0
$400$	−13.7079	+	14.6089i	−0.685395	+	0.730443i
$401$	−7.59299	+	13.1514i	−0.379176	+	0.656752i	−0.990943	−	0.134286i	$-0.957126\pi$
$401$	−7.59299	+	13.1514i	−0.379176	+	0.656752i	0.611767	+	0.791038i	$0.290459\pi$
$402$	−4.61579	+	9.55061i	−0.230215	+	0.476341i
$403$	−1.13469	+	4.23472i	−0.0565229	+	0.210946i
$404$	−2.53369	−	0.292657i	−0.126056	−	0.0145602i
$405$	4.78802	−	4.78802i	0.237918	−	0.237918i
$406$		0			0
$407$	−14.3239			−0.710009
$408$	13.6422	−	7.13704i	0.675388	−	0.353336i
$409$	−2.65534	−	4.59919i	−0.131298	−	0.227415i	0.792879	−	0.609379i	$-0.208581\pi$
$409$	−2.65534	−	4.59919i	−0.131298	−	0.227415i	−0.924177	+	0.381964i	$0.875248\pi$
$410$	14.1468	+	40.6113i	0.698660	+	2.00565i
$411$	−1.73009	+	0.463575i	−0.0853389	+	0.0228665i
$412$	18.2657	+	7.22778i	0.899887	+	0.356087i
$413$		0			0
$414$	8.94546	−	6.08061i	0.439646	−	0.298846i
$415$	−30.1544	−	17.4096i	−1.48022	−	0.854606i
$416$	3.14583	+	1.39877i	0.154237	+	0.0685804i
$417$	−3.38607	−	5.86484i	−0.165817	−	0.287203i
$418$	−0.0265926	−	0.361638i	−0.00130069	−	0.0176883i
$419$	−7.73525	+	7.73525i	−0.377891	+	0.377891i	−0.870341	−	0.492450i	$-0.836102\pi$
$419$	−7.73525	+	7.73525i	−0.377891	+	0.377891i	0.492450	+	0.870341i	$0.336102\pi$
$420$		0			0
$421$	4.79155	+	4.79155i	0.233526	+	0.233526i	0.814163	−	0.580637i	$-0.197196\pi$
$421$	4.79155	+	4.79155i	0.233526	+	0.233526i	−0.580637	+	0.814163i	$0.697196\pi$
$422$	3.48406	+	3.00677i	0.169602	+	0.146367i
$423$	10.7574	−	6.21079i	0.523043	−	0.301979i
$424$	−0.606828	+	14.5806i	−0.0294702	+	0.708096i
$425$	−14.8664	+	25.7494i	−0.721126	+	1.24903i
$426$	17.5731	+	3.35047i	0.851421	+	0.162331i
$427$		0			0
$428$	−8.25704	−	19.0707i	−0.399119	−	0.921816i
$429$	−0.178477	−	0.666086i	−0.00861696	−	0.0321589i
$430$	41.6296	+	20.1195i	2.00756	+	0.970249i
$431$	2.20553	−	1.27336i	0.106236	−	0.0613356i	−0.445940	−	0.895063i	$-0.647131\pi$
$431$	2.20553	−	1.27336i	0.106236	−	0.0613356i	0.552177	+	0.833727i	$0.313797\pi$
$432$	−16.6798	−	8.93522i	−0.802506	−	0.429896i
$433$		−	19.0390i		−	0.914954i	−0.889221	−	0.457477i	$-0.848753\pi$
$433$		−	19.0390i		−	0.914954i	0.889221	−	0.457477i	$-0.151247\pi$
$434$		0			0
$435$	−5.34527	−	5.34527i	−0.256286	−	0.256286i
$436$	−0.0806596	−	0.00931667i	−0.00386290	−	0.000446188i
$437$	−0.709913	−	0.190221i	−0.0339597	−	0.00909948i
$438$	0.961080	+	2.75898i	0.0459222	+	0.131829i
$439$	−15.2321	−	8.79426i	−0.726988	−	0.419727i	0.0903310	−	0.995912i	$-0.471208\pi$
$439$	−15.2321	−	8.79426i	−0.726988	−	0.419727i	−0.817319	+	0.576185i	$0.804541\pi$
$440$	2.41525	+	10.7904i	0.115143	+	0.514411i
$441$		0			0
$442$	5.01931	+	0.956977i	0.238744	+	0.0455187i
$443$	6.99648	+	26.1112i	0.332413	+	1.24058i	0.906647	+	0.421890i	$0.138633\pi$
$443$	6.99648	+	26.1112i	0.332413	+	1.24058i	−0.574234	+	0.818691i	$0.694700\pi$
$444$	21.0277	−	3.10929i	0.997928	−	0.147560i
$445$	18.6693	+	5.00241i	0.885008	+	0.237137i
$446$	−30.9094	+	2.27288i	−1.46360	+	0.107624i
$447$	−6.99837			−0.331012
$448$		0			0
$449$	−4.60299			−0.217228			−0.108614	−	0.994084i	$-0.534641\pi$
$449$	−4.60299			−0.217228			−0.108614	+	0.994084i	$0.534641\pi$
$450$	15.2526	−	1.12158i	0.719012	−	0.0528716i
$451$	11.4734	+	3.07430i	0.540263	+	0.144763i
$452$	−21.9173	+	3.24083i	−1.03090	+	0.152436i
$453$	−3.34757	−	12.4933i	−0.157283	−	0.586987i
$454$	16.0970	+	3.06905i	0.755472	+	0.144037i
$455$		0			0
$456$	0.117539	+	0.525117i	0.00550427	+	0.0245909i
$457$	−22.3267	−	12.8903i	−1.04440	−	0.602985i	−0.123324	−	0.992367i	$-0.539355\pi$
$457$	−22.3267	−	12.8903i	−1.04440	−	0.602985i	−0.921076	+	0.389382i	$0.872689\pi$
$458$	−10.1095	−	29.0213i	−0.472384	−	1.35608i
$459$	−27.1272	−	7.26871i	−1.26619	−	0.339274i
$460$	22.2633	+	2.57155i	1.03803	+	0.119899i
$461$	−4.40686	−	4.40686i	−0.205248	−	0.205248i	0.596996	−	0.802244i	$-0.296361\pi$
$461$	−4.40686	−	4.40686i	−0.205248	−	0.205248i	−0.802244	+	0.596996i	$0.796361\pi$
$462$		0			0
$463$		−	31.0375i		−	1.44244i	−0.692708	−	0.721218i	$-0.743583\pi$
$463$		−	31.0375i		−	1.44244i	0.692708	−	0.721218i	$-0.256417\pi$
$464$	4.92235	−	9.18877i	0.228514	−	0.426578i
$465$	18.0959	−	10.4477i	0.839177	−	0.484499i
$466$	−15.9118	−	7.69014i	−0.737099	−	0.356239i
$467$	−9.43026	−	35.1942i	−0.436380	−	1.62859i	−0.737741	−	0.675084i	$-0.764107\pi$
$467$	−9.43026	−	35.1942i	−0.436380	−	1.62859i	0.301361	−	0.953510i	$-0.402559\pi$
$468$	−1.04430	−	2.41193i	−0.0482726	−	0.111492i
$469$		0			0
$470$	25.2818	+	4.82020i	1.16616	+	0.222339i
$471$	−6.70083	+	11.6062i	−0.308758	+	0.534784i
$472$	0.167803	−	4.03190i	0.00772377	−	0.185583i
$473$	11.0598	−	6.38540i	0.508532	−	0.293601i
$474$	1.67259	+	1.44345i	0.0768244	+	0.0662999i
$475$	−0.734812	−	0.734812i	−0.0337155	−	0.0337155i
$476$		0			0
$477$	7.87773	−	7.87773i	0.360697	−	0.360697i
$478$	0.799598	+	10.8739i	0.0365728	+	0.497361i
$479$	−4.76900	−	8.26015i	−0.217901	−	0.377416i	0.736265	−	0.676693i	$-0.236588\pi$
$479$	−4.76900	−	8.26015i	−0.217901	−	0.377416i	−0.954166	+	0.299278i	$0.903254\pi$
$480$	−5.88789	−	15.3161i	−0.268744	−	0.699082i
$481$	6.10941	+	3.52727i	0.278565	+	0.160830i
$482$	−12.8372	+	8.72599i	−0.584719	+	0.397458i
$483$		0			0
$484$	−17.6168	−	6.97100i	−0.800764	−	0.316864i
$485$	32.4876	−	8.70502i	1.47518	−	0.395275i
$486$	7.51524	+	21.5741i	0.340898	+	0.978619i
$487$	−1.39542	−	2.41695i	−0.0632327	−	0.109522i	0.832676	−	0.553761i	$-0.186808\pi$
$487$	−1.39542	−	2.41695i	−0.0632327	−	0.109522i	−0.895909	+	0.444238i	$0.853474\pi$
$488$	3.33151	−	1.74292i	0.150811	−	0.0788981i
$489$	0.382770			0.0173094
$490$		0			0
$491$	−14.9085	+	14.9085i	−0.672809	+	0.672809i	−0.958363	−	0.285554i	$-0.907823\pi$
$491$	−14.9085	+	14.9085i	−0.672809	+	0.672809i	0.285554	+	0.958363i	$0.407823\pi$
$492$	−17.5105	−	2.02256i	−0.789433	−	0.0911842i
$493$	4.00428	−	14.9442i	0.180344	−	0.673052i
$494$	−0.0777115	+	0.160794i	−0.00349640	+	0.00723446i
$495$	4.22073	−	7.31052i	0.189708	−	0.328583i
$496$	21.0123	+	19.7164i	0.943481	+	0.885294i
$497$		0			0
$498$	11.8032	−	8.02310i	0.528912	−	0.359524i
$499$	13.6645	−	3.66140i	0.611708	−	0.163907i	0.0603527	−	0.998177i	$-0.480777\pi$
$499$	13.6645	−	3.66140i	0.611708	−	0.163907i	0.551356	+	0.834270i	$0.314111\pi$
$500$	0.0420475	+	0.0312145i	0.00188042	+	0.00139595i
$501$	0.752147	−	2.80705i	0.0336035	−	0.125410i
$502$	28.6015	+	24.6833i	1.27655	+	1.10167i
$503$		−	0.855211i		−	0.0381320i	−0.999818	−	0.0190660i	$-0.993931\pi$
$503$		−	0.855211i		−	0.0381320i	0.999818	−	0.0190660i	$-0.00606926\pi$
$504$		0			0
$505$			4.03443i			0.179530i
$506$	4.04431	−	4.68631i	0.179792	−	0.208332i
$507$	2.99716	−	11.1855i	0.133108	−	0.496768i
$508$	5.29174	+	35.7872i	0.234783	+	1.58780i
$509$	17.5670	−	4.70706i	0.778642	−	0.208637i	0.152456	−	0.988310i	$-0.451282\pi$
$509$	17.5670	−	4.70706i	0.778642	−	0.208637i	0.626186	+	0.779674i	$0.284615\pi$
$510$	−13.6908	−	20.1412i	−0.606239	−	0.891867i
$511$		0			0
$512$	17.8670	−	13.8842i	0.789616	−	0.613601i
$513$	0.490779	−	0.850055i	0.0216684	−	0.0375308i
$514$	−22.4611	−	10.8554i	−0.990717	−	0.478812i
$515$	8.04211	−	30.0136i	0.354378	−	1.32256i
$516$	−14.8499	+	11.7746i	−0.653730	+	0.518348i
$517$	5.02665	−	5.02665i	0.221072	−	0.221072i
$518$		0			0
$519$	20.9674			0.920368
$520$	1.62699	−	5.19706i	0.0713481	−	0.227906i
$521$	0.473813	+	0.820669i	0.0207581	+	0.0359541i	0.876218	−	0.481915i	$-0.160059\pi$
$521$	0.473813	+	0.820669i	0.0207581	+	0.0359541i	−0.855460	+	0.517869i	$0.826725\pi$
$522$	−7.51513	+	2.61787i	−0.328928	+	0.114581i
$523$	−25.8487	+	6.92613i	−1.13028	+	0.302859i	−0.775038	−	0.631915i	$-0.782269\pi$
$523$	−25.8487	+	6.92613i	−1.13028	+	0.302859i	−0.355245	+	0.934773i	$0.615603\pi$
$524$	−2.18817	−	5.05385i	−0.0955906	−	0.220779i
$525$		0			0
$526$	5.70942	+	8.39939i	0.248942	+	0.366231i
$527$	37.0360	+	21.3827i	1.61331	+	0.931446i
$528$	−4.41288	−	1.03321i	−0.192046	−	0.0449649i
$529$	5.22683	+	9.05314i	0.227254	+	0.393615i
$530$	23.0213	−	1.69284i	0.999981	−	0.0735322i
$531$	−2.17839	+	2.17839i	−0.0945341	+	0.0945341i
$532$		0			0
$533$	−4.13658	−	4.13658i	−0.179175	−	0.179175i
$534$	−5.17590	+	5.99753i	−0.223983	+	0.259538i
$535$	−28.4680	+	16.4360i	−1.23078	+	0.710590i
$536$	−0.962133	+	23.1177i	−0.0415578	+	0.998532i
$537$	6.30603	−	10.9224i	0.272125	−	0.471335i
$538$	4.89344	−	25.6659i	0.210971	−	1.10654i
$539$		0			0
$540$	−11.0130	+	27.8314i	−0.473922	+	1.19767i
$541$	5.34896	+	19.9626i	0.229970	+	0.858259i	0.980352	+	0.197255i	$0.0632027\pi$
$541$	5.34896	+	19.9626i	0.229970	+	0.858259i	−0.750382	+	0.661004i	$0.770131\pi$
$542$	0.606561	−	1.25504i	0.0260540	−	0.0539088i
$543$	−5.63002	+	3.25049i	−0.241607	+	0.139492i
$544$	21.1219	−	26.1094i	0.905592	−	1.11943i
$545$			0.128435i			0.00550156i
$546$		0			0
$547$	3.84440	+	3.84440i	0.164375	+	0.164375i	0.784502	−	0.620127i	$-0.212919\pi$
$547$	3.84440	+	3.84440i	0.164375	+	0.164375i	−0.620127	+	0.784502i	$0.712919\pi$
$548$	−3.06132	+	2.42735i	−0.130773	+	0.103691i
$549$	−2.77258	−	0.742910i	−0.118331	−	0.0317066i
$550$	8.26535	−	2.87920i	0.352436	−	0.122770i
$551$	0.468289	+	0.270367i	0.0199498	+	0.0115180i
$552$	−4.91984	+	7.75746i	−0.209402	+	0.330179i
$553$		0			0
$554$	−0.0231432	+	0.121385i	−0.000983259	+	0.00515716i
$555$	−8.70229	−	32.4774i	−0.369392	−	1.37859i
$556$	−11.8607	−	8.80497i	−0.503007	−	0.373414i
$557$	12.0167	+	3.21987i	0.509165	+	0.136430i	0.504250	−	0.863558i	$-0.331769\pi$
$557$	12.0167	+	3.21987i	0.509165	+	0.136430i	0.00491478	+	0.999988i	$0.498436\pi$
$558$	−1.61319	−	21.9382i	−0.0682919	−	0.928716i
$559$	−6.28964			−0.266023
$560$		0			0
$561$	−6.72665			−0.284000
$562$	1.44721	+	19.6809i	0.0610468	+	0.830189i
$563$	−3.51233	−	0.941127i	−0.148027	−	0.0396638i	0.184044	−	0.982918i	$-0.441081\pi$
$563$	−3.51233	−	0.941127i	−0.148027	−	0.0396638i	−0.332072	+	0.943254i	$0.607748\pi$
$564$	−6.28805	+	8.47032i	−0.264775	+	0.356665i
$565$	9.07045	+	33.8514i	0.381597	+	1.42414i
$566$	3.49994	−	18.3571i	0.147113	−	0.771605i
$567$		0			0
$568$	38.0796	−	8.52352i	1.59779	−	0.357639i
$569$	−14.1011	−	8.14128i	−0.591149	−	0.341300i	0.174402	−	0.984674i	$-0.444201\pi$
$569$	−14.1011	−	8.14128i	−0.591149	−	0.341300i	−0.765552	+	0.643374i	$0.777534\pi$
$570$	0.803807	−	0.280003i	0.0336678	−	0.0117280i
$571$	−7.53618	−	2.01931i	−0.315379	−	0.0845056i	0.0976573	−	0.995220i	$-0.468865\pi$
$571$	−7.53618	−	2.01931i	−0.315379	−	0.0845056i	−0.413036	+	0.910715i	$0.635532\pi$
$572$	−0.934533	−	1.17861i	−0.0390748	−	0.0492803i
$573$	−3.48331	−	3.48331i	−0.145517	−	0.145517i
$574$		0			0
$575$		−	17.7397i		−	0.739798i
$576$	−17.2146	−	1.43539i	−0.717273	−	0.0598078i
$577$	−31.7171	+	18.3119i	−1.32040	+	0.762333i	−0.983792	−	0.179312i	$-0.942613\pi$
$577$	−31.7171	+	18.3119i	−1.32040	+	0.762333i	−0.336607	+	0.941645i	$0.609279\pi$
$578$	11.2276	−	23.2311i	0.467006	−	0.966288i
$579$	0.0170526	+	0.0636412i	0.000708682	+	0.00264484i
$580$	−15.3321	−	6.06696i	−0.636632	−	0.251917i
$581$		0			0
$582$	−2.58188	+	13.5419i	−0.107023	+	0.561329i
$583$	3.18789	−	5.52159i	0.132029	−	0.228681i
$584$	4.31491	+	4.68967i	0.178552	+	0.194060i
$585$	−3.60044	+	2.07872i	−0.148860	+	0.0859443i
$586$	−1.46279	+	1.69499i	−0.0604273	+	0.0700195i
$587$	−26.7399	−	26.7399i	−1.10367	−	1.10367i	−0.993964	−	0.109709i	$-0.965008\pi$
$587$	−26.7399	−	26.7399i	−1.10367	−	1.10367i	−0.109709	−	0.993964i	$-0.534992\pi$
$588$		0			0
$589$	−1.05690	+	1.05690i	−0.0435488	+	0.0435488i
$590$	−6.36596	+	0.468112i	−0.262082	+	0.0192719i
$591$	1.68809	+	2.92385i	0.0694386	+	0.120271i
$592$	39.3960	−	24.4479i	1.61917	−	1.00480i
$593$	4.90827	+	2.83379i	0.201559	+	0.116370i	0.597382	−	0.801957i	$-0.296208\pi$
$593$	4.90827	+	2.83379i	0.201559	+	0.116370i	−0.395824	+	0.918327i	$0.629541\pi$
$594$	4.64750	+	6.83715i	0.190689	+	0.280532i
$595$		0			0
$596$	−14.0085	+	6.06529i	−0.573812	+	0.248444i
$597$	−9.22305	+	2.47131i	−0.377474	+	0.101144i
$598$	−2.87898	+	1.00288i	−0.117730	+	0.0410109i
$599$	5.10517	+	8.84241i	0.208591	+	0.361291i	0.951271	−	0.308356i	$-0.0997788\pi$
$599$	5.10517	+	8.84241i	0.208591	+	0.361291i	−0.742680	+	0.669647i	$0.766445\pi$
$600$	−11.5086	+	6.02087i	−0.469838	+	0.245801i
$601$	2.00211			0.0816677			0.0408339	−	0.999166i	$-0.486999\pi$
$601$	2.00211			0.0816677			0.0408339	+	0.999166i	$0.486999\pi$
$602$		0			0
$603$	12.4902	−	12.4902i	0.508642	−	0.508642i
$604$	−17.5284	−	22.1064i	−0.713220	−	0.899499i
$605$	−7.75641	+	28.9473i	−0.315343	+	1.17688i
$606$	−1.48887	−	0.719570i	−0.0604813	−	0.0292305i
$607$	−14.2213	+	24.6319i	−0.577223	+	0.999779i	0.418573	+	0.908183i	$0.362530\pi$
$607$	−14.2213	+	24.6319i	−0.577223	+	0.999779i	−0.995796	+	0.0915962i	$0.970803\pi$
$608$	0.690380	+	0.949251i	0.0279986	+	0.0384972i
$609$		0			0
$610$	−3.34339	−	4.91862i	−0.135370	−	0.199149i
$611$	−3.38178	+	0.906145i	−0.136812	+	0.0366587i
$612$	−25.3624	+	3.75026i	−1.02522	+	0.151595i
$613$	−4.14311	+	15.4623i	−0.167339	+	0.624517i	0.830392	+	0.557180i	$0.188117\pi$
$613$	−4.14311	+	15.4623i	−0.167339	+	0.624517i	−0.997730	+	0.0673365i	$0.978550\pi$
$614$	20.7237	−	24.0134i	0.836341	−	0.969101i
$615$			27.8821i			1.12431i
$616$		0			0
$617$			41.5070i			1.67101i	0.549485	+	0.835504i	$0.314824\pi$
$617$			41.5070i			1.67101i	−0.549485	+	0.835504i	$0.685176\pi$
$618$	9.64191	+	8.32103i	0.387854	+	0.334721i
$619$	4.63988	−	17.3163i	0.186492	−	0.695999i	−0.807814	−	0.589438i	$-0.799349\pi$
$619$	4.63988	−	17.3163i	0.186492	−	0.695999i	0.994306	−	0.106561i	$-0.0339840\pi$
$620$	27.1676	−	36.5961i	1.09108	−	1.46974i
$621$	16.1851	−	4.33679i	0.649486	−	0.174029i
$622$	−33.3838	+	22.6924i	−1.33857	+	0.909881i
$623$		0			0
$624$	1.62775	+	1.52736i	0.0651621	+	0.0611434i
$625$	−12.4793	+	21.6147i	−0.499171	+	0.864589i
$626$	0.0383545	−	0.0793599i	0.00153296	−	0.00317186i
$627$	0.0608486	−	0.227090i	0.00243006	−	0.00906910i
$628$	−3.35422	+	29.0393i	−0.133848	+	1.15880i
$629$	48.6593	−	48.6593i	1.94017	−	1.94017i
$630$		0			0
$631$	−21.0724			−0.838880			−0.419440	−	0.907783i	$-0.637774\pi$
$631$	−21.0724			−0.838880			−0.419440	+	0.907783i	$0.637774\pi$
$632$	4.59899	+	1.43976i	0.182938	+	0.0572704i
$633$	1.49188	+	2.58402i	0.0592971	+	0.102706i
$634$	−10.5593	−	30.3127i	−0.419364	−	1.20387i
$635$	55.2736	−	14.8105i	2.19347	−	0.587737i
$636$	−3.48129	+	8.79776i	−0.138042	+	0.348854i
$637$		0			0
$638$	−3.76654	+	2.56027i	−0.149119	+	0.101362i
$639$	−25.7991	−	14.8951i	−1.02060	−	0.589242i
$640$	−25.0598	−	25.5552i	−0.990574	−	1.01016i
$641$	13.5748	+	23.5122i	0.536171	+	0.928675i	0.999106	+	0.0422829i	$0.0134631\pi$
$641$	13.5748	+	23.5122i	0.536171	+	0.928675i	−0.462935	+	0.886392i	$0.653204\pi$
$642$	−0.988098	−	13.4374i	−0.0389971	−	0.530330i
$643$	−21.2081	+	21.2081i	−0.836367	+	0.836367i	−0.988379	−	0.152012i	$-0.951425\pi$
$643$	−21.2081	+	21.2081i	−0.836367	+	0.836367i	0.152012	+	0.988379i	$0.451425\pi$
$644$		0			0
$645$	21.1972	+	21.1972i	0.834640	+	0.834640i
$646$	1.31885	+	1.13817i	0.0518894	+	0.0447809i
$647$	34.8692	−	20.1317i	1.37085	−	0.791460i	0.379814	−	0.925063i	$-0.375988\pi$
$647$	34.8692	−	20.1317i	1.37085	−	0.791460i	0.991035	+	0.133603i	$0.0426546\pi$
$648$	4.09905	+	4.45506i	0.161026	+	0.175011i
$649$	−0.881532	+	1.52686i	−0.0346032	+	0.0599344i
$650$	−4.23433	−	0.807314i	−0.166084	−	0.0316654i
$651$		0			0
$652$	0.766185	−	0.331735i	0.0300061	−	0.0129918i
$653$	−6.02549	−	22.4874i	−0.235796	−	0.880001i	−0.977789	−	0.209594i	$-0.932786\pi$
$653$	−6.02549	−	22.4874i	−0.235796	−	0.880001i	0.741993	−	0.670408i	$-0.233881\pi$
$654$	−0.0473980	−	0.0229074i	−0.00185341	−	0.000895749i
$655$	−7.54420	+	4.35564i	−0.294776	+	0.170189i
$656$	−36.8034	+	11.1273i	−1.43693	+	0.434447i
$657$		−	4.86507i		−	0.189805i
$658$		0			0
$659$	−21.3113	−	21.3113i	−0.830171	−	0.830171i	0.157369	−	0.987540i	$-0.449699\pi$
$659$	−21.3113	−	21.3113i	−0.830171	−	0.830171i	−0.987540	+	0.157369i	$0.949699\pi$
$660$	−0.822598	+	7.12169i	−0.0320196	+	0.277212i
$661$	10.5663	+	2.83124i	0.410983	+	0.110122i	0.458386	−	0.888753i	$-0.348428\pi$
$661$	10.5663	+	2.83124i	0.410983	+	0.110122i	−0.0474031	+	0.998876i	$0.515095\pi$
$662$	−7.47692	−	21.4640i	−0.290599	−	0.834224i
$663$	2.86904	+	1.65644i	0.111424	+	0.0643309i
$664$	16.6728	−	26.2892i	0.647031	−	1.02022i
$665$		0			0
$666$	−34.7701	−	6.62923i	−1.34731	−	0.256877i
$667$	2.38911	+	8.91627i	0.0925066	+	0.345239i
$668$	−0.927228	−	6.27070i	−0.0358755	−	0.242621i
$669$	−19.4095	−	5.20076i	−0.750415	−	0.201073i
$670$	36.5005	−	2.68401i	1.41014	−	0.103692i
$671$	−1.64270			−0.0634156
$672$		0			0
$673$	35.4992			1.36839			0.684197	−	0.729297i	$-0.260153\pi$
$673$	35.4992			1.36839			0.684197	+	0.729297i	$0.260153\pi$
$674$	−21.5659	+	1.58581i	−0.830686	+	0.0610833i
$675$	22.8847	+	6.13194i	0.880833	+	0.236019i
$676$	−3.69482	−	24.9875i	−0.142109	−	0.961058i
$677$	7.81038	+	29.1487i	0.300177	+	1.12028i	0.937018	+	0.349282i	$0.113574\pi$
$677$	7.81038	+	29.1487i	0.300177	+	1.12028i	−0.636840	+	0.770996i	$0.719759\pi$
$678$	−14.1104	−	2.69027i	−0.541905	−	0.103319i
$679$		0			0
$680$	−44.8605	−	28.4509i	−1.72032	−	1.09104i
$681$	9.20109	+	5.31225i	0.352586	+	0.203566i
$682$	−4.14124	−	11.8883i	−0.158576	−	0.455226i
$683$	−32.3188	−	8.65981i	−1.23665	−	0.331358i	−0.419482	−	0.907764i	$-0.637788\pi$
$683$	−32.3188	−	8.65981i	−1.23665	−	0.331358i	−0.817164	+	0.576405i	$0.804455\pi$
$684$	0.102818	−	0.890154i	0.00393135	−	0.0340359i
$685$	4.36983	+	4.36983i	0.166963	+	0.166963i
$686$		0			0
$687$		−	19.9249i		−	0.760180i
$688$	−19.5201	+	36.4390i	−0.744198	+	1.38923i
$689$	−2.71939	+	1.57004i	−0.103601	+	0.0598138i
$690$	13.0826	+	6.32280i	0.498046	+	0.240705i
$691$	11.6842	+	43.6058i	0.444486	+	1.65884i	0.717290	+	0.696775i	$0.245382\pi$
$691$	11.6842	+	43.6058i	0.444486	+	1.65884i	−0.272804	+	0.962070i	$0.587951\pi$
$692$	41.9702	−	18.1719i	1.59547	−	0.690790i
$693$		0			0
$694$	38.2886	+	7.30006i	1.45341	+	0.277107i
$695$	−11.6829	+	20.2354i	−0.443159	+	0.767573i
$696$	4.97356	−	4.57612i	0.188522	−	0.173457i
$697$	−49.4197	+	28.5325i	−1.87190	+	1.08074i
$698$	25.8621	+	22.3191i	0.978893	+	0.844791i
$699$	−8.10207	−	8.10207i	−0.306448	−	0.306448i
$700$		0			0
$701$	7.35956	−	7.35956i	0.277967	−	0.277967i	−0.554330	−	0.832297i	$-0.687026\pi$
$701$	7.35956	−	7.35956i	0.277967	−	0.277967i	0.832297	+	0.554330i	$0.187026\pi$
$702$	−0.298592	−	4.06062i	−0.0112696	−	0.153258i
$703$	1.20256	+	2.08289i	0.0453554	+	0.0785578i
$704$	−9.72866	+	1.75635i	−0.366663	+	0.0661949i
$705$	14.4511	+	8.34334i	0.544259	+	0.314228i
$706$	27.4077	−	18.6301i	1.03150	−	0.701154i
$707$		0			0
$708$	0.962664	−	2.43280i	0.0361791	−	0.0914302i
$709$	−5.98162	+	1.60277i	−0.224644	+	0.0601933i	−0.369385	−	0.929276i	$-0.620432\pi$
$709$	−5.98162	+	1.60277i	−0.224644	+	0.0601933i	0.144741	+	0.989470i	$0.453765\pi$
$710$	−20.3048	−	58.2892i	−0.762027	−	2.18756i
$711$	−1.83950	−	3.18611i	−0.0689867	−	0.119488i
$712$	−5.16265	+	16.4910i	−0.193479	+	0.618025i
$713$	−25.5155			−0.955563
$714$		0			0
$715$	−1.68239	+	1.68239i	−0.0629179	+	0.0629179i
$716$	3.15659	−	27.3284i	0.117967	−	1.02131i
$717$	−1.82962	+	6.82825i	−0.0683286	+	0.255006i
$718$	−5.36343	+	11.0976i	−0.200162	+	0.414157i
$719$	9.05536	−	15.6843i	0.337708	−	0.584927i	−0.646293	−	0.763089i	$-0.723682\pi$
$719$	9.05536	−	15.6843i	0.337708	−	0.584927i	0.984001	+	0.178162i	$0.0570150\pi$
$720$	0.868948	+	27.3105i	0.0323838	+	1.01780i
$721$		0			0
$722$	22.1719	−	15.0712i	0.825152	−	0.560890i
$723$	−9.72085	+	2.60469i	−0.361522	+	0.0968696i
$724$	−8.45242	+	11.3858i	−0.314132	+	0.423151i
$725$	−3.37804	+	12.6070i	−0.125457	+	0.468213i
$726$	−9.29937	−	8.02542i	−0.345132	−	0.297851i
$727$			39.2154i			1.45442i	0.686415	+	0.727210i	$0.259183\pi$
$727$			39.2154i			1.45442i	−0.686415	+	0.727210i	$0.740817\pi$
$728$		0			0
$729$			8.39075i			0.310768i
$730$	6.58593	−	7.63138i	0.243756	−	0.282450i
$731$	−15.8794	+	59.2627i	−0.587321	+	2.19191i
$732$	2.41150	−	0.356580i	0.0891315	−	0.0131796i
$733$	−11.8473	+	3.17448i	−0.437591	+	0.117252i	−0.470887	−	0.882193i	$-0.656066\pi$
$733$	−11.8473	+	3.17448i	−0.437591	+	0.117252i	0.0332965	+	0.999446i	$0.489399\pi$
$734$	2.24844	+	3.30779i	0.0829915	+	0.122093i
$735$		0			0
$736$	−3.12482	+	19.7919i	−0.115182	+	0.729538i
$737$	5.05444	−	8.75454i	0.186183	−	0.322478i
$738$	26.4280	+	12.7726i	0.972827	+	0.470166i
$739$	−6.44036	+	24.0358i	−0.236913	+	0.884170i	0.740365	+	0.672205i	$0.234653\pi$
$739$	−6.44036	+	24.0358i	−0.236913	+	0.884170i	−0.977277	+	0.211964i	$0.932014\pi$
$740$	−45.5665	−	57.4675i	−1.67506	−	2.11255i
$741$	−0.0818741	+	0.0818741i	−0.00300772	+	0.00300772i
$742$		0			0
$743$	18.0234			0.661215			0.330608	−	0.943768i	$-0.392746\pi$
$743$	18.0234			0.661215			0.330608	+	0.943768i	$0.392746\pi$
$744$	8.65997	+	16.5532i	0.317490	+	0.606869i
$745$	12.0732	+	20.9114i	0.442328	+	0.766135i
$746$	18.9080	−	6.58653i	0.692271	−	0.241150i
$747$	−22.9559	+	6.15102i	−0.839913	+	0.225054i
$748$	−13.4646	+	5.82980i	−0.492316	+	0.213158i
$749$		0			0
$750$	0.0190868	+	0.0280794i	0.000696950	+	0.00102532i
$751$	25.9408	+	14.9769i	0.946594	+	0.546516i	0.892021	−	0.451994i	$-0.149287\pi$
$751$	25.9408	+	14.9769i	0.946594	+	0.546516i	0.0545727	+	0.998510i	$0.482620\pi$
$752$	−5.24572	+	22.4046i	−0.191292	+	0.817012i
$753$	12.2472	+	21.2128i	0.446314	+	0.773038i
$754$	2.23697	−	0.164492i	0.0814656	−	0.00599046i
$755$	−31.5555	+	31.5555i	−1.14842	+	1.14842i
$756$		0			0
$757$	−11.9616	−	11.9616i	−0.434752	−	0.434752i	0.455489	−	0.890241i	$-0.349464\pi$
$757$	−11.9616	−	11.9616i	−0.434752	−	0.434752i	−0.890241	+	0.455489i	$0.849464\pi$
$758$	−13.3862	+	15.5111i	−0.486208	+	0.563388i
$759$	3.47569	−	2.00669i	0.126159	−	0.0728382i
$760$	1.36630	−	1.25711i	0.0495608	−	0.0456003i
$761$	−14.7438	+	25.5370i	−0.534462	+	0.925715i	0.464728	+	0.885454i	$0.346152\pi$
$761$	−14.7438	+	25.5370i	−0.534462	+	0.925715i	−0.999189	+	0.0402609i	$0.987181\pi$
$762$	−4.39276	+	23.0399i	−0.159133	+	0.834646i
$763$		0			0
$764$	−9.99138	−	3.95361i	−0.361475	−	0.143037i
$765$	10.4962	+	39.1725i	0.379492	+	1.41628i
$766$	3.94735	−	8.16753i	0.142624	−	0.295105i
$767$	0.751980	−	0.434156i	0.0271524	−	0.0156765i
$768$	13.9005	−	4.69014i	0.501593	−	0.169241i
$769$			19.9592i			0.719746i	0.933001	+	0.359873i	$0.117180\pi$
$769$			19.9592i			0.719746i	−0.933001	+	0.359873i	$0.882820\pi$
$770$		0			0
$771$	−11.4369	−	11.4369i	−0.411890	−	0.411890i
$772$	0.0892900	+	0.112611i	0.00321362	+	0.00405295i
$773$	9.15439	+	2.45291i	0.329261	+	0.0882251i	0.419662	−	0.907680i	$-0.362148\pi$
$773$	9.15439	+	2.45291i	0.329261	+	0.0882251i	−0.0904018	+	0.995905i	$0.528815\pi$
$774$	29.8021	−	10.3814i	1.07121	−	0.373153i
$775$	−31.2439	−	18.0387i	−1.12231	−	0.647968i
$776$	6.56825	+	29.3443i	0.235786	+	1.05340i
$777$		0			0
$778$	4.50459	−	23.6264i	0.161497	−	0.847048i
$779$	−0.516203	−	1.92650i	−0.0184949	−	0.0690239i
$780$	2.10458	−	2.83497i	0.0753559	−	0.101508i
$781$	−16.4678	−	4.41253i	−0.589263	−	0.157893i
$782$	2.18090	+	29.6586i	0.0779888	+	1.06059i
$783$	−12.3280			−0.440569
$784$		0			0
$785$	46.2396			1.65036
$786$	−0.261852	−	3.56099i	−0.00933996	−	0.127016i
$787$	−50.0852	−	13.4203i	−1.78535	−	0.478382i	−0.793804	−	0.608174i	$-0.791902\pi$
$787$	−50.0852	−	13.4203i	−1.78535	−	0.478382i	−0.991541	+	0.129792i	$0.958569\pi$
$788$	5.91304	+	4.38962i	0.210643	+	0.156374i
$789$	1.70425	+	6.36035i	0.0606730	+	0.226435i
$790$	1.42764	−	7.48792i	0.0507931	−	0.266408i
$791$		0			0
$792$	6.37345	+	4.04210i	0.226471	+	0.143630i
$793$	0.700641	+	0.404515i	0.0248805	+	0.0143648i
$794$	−14.7781	+	5.14790i	−0.524455	+	0.182692i
$795$	14.4562	+	3.87352i	0.512708	+	0.137380i
$796$	−16.3198	+	12.9401i	−0.578442	+	0.458651i
$797$	−17.7503	−	17.7503i	−0.628747	−	0.628747i	0.319006	−	0.947753i	$-0.396651\pi$
$797$	−17.7503	−	17.7503i	−0.628747	−	0.628747i	−0.947753	+	0.319006i	$0.896651\pi$
$798$		0			0
$799$			34.1518i			1.20820i
$800$	−17.8186	+	22.0261i	−0.629982	+	0.778740i
$801$	11.4247	−	6.59605i	0.403672	−	0.233060i
$802$	−9.34523	+	19.3364i	−0.329991	+	0.682790i
$803$	−0.720614	−	2.68937i	−0.0254299	−	0.0949058i
$804$	−5.51962	+	13.9489i	−0.194662	+	0.491941i
$805$		0			0
$806$	−1.16118	+	6.09035i	−0.0409008	+	0.214524i
$807$	8.47012	−	14.6707i	0.298162	−	0.516432i
$808$	−3.60389	−	0.149990i	−0.126784	−	0.00527662i
$809$	10.0608	−	5.80862i	0.353720	−	0.204220i	−0.312603	−	0.949884i	$-0.601201\pi$
$809$	10.0608	−	5.80862i	0.353720	−	0.204220i	0.666322	+	0.745664i	$0.267867\pi$
$810$	6.25647	−	7.24962i	0.219830	−	0.254726i
$811$	21.2042	+	21.2042i	0.744579	+	0.744579i	0.973455	−	0.228877i	$-0.0735053\pi$
$811$	21.2042	+	21.2042i	0.744579	+	0.744579i	−0.228877	+	0.973455i	$0.573505\pi$
$812$		0			0
$813$	0.639052	−	0.639052i	0.0224125	−	0.0224125i
$814$	−20.2025	+	1.48556i	−0.708098	+	0.0520690i
$815$	−0.660334	−	1.14373i	−0.0231305	−	0.0400632i
$816$	18.5008	−	11.4810i	0.647657	−	0.401915i
$817$	−1.85705	−	1.07217i	−0.0649700	−	0.0375105i
$818$	−4.22210	−	6.21133i	−0.147622	−	0.217174i
$819$		0			0
$820$	24.1646	+	55.8112i	0.843865	+	1.94901i
$821$	−26.2764	+	7.04075i	−0.917054	+	0.245724i	−0.686326	−	0.727294i	$-0.740778\pi$
$821$	−26.2764	+	7.04075i	−0.917054	+	0.245724i	−0.230728	+	0.973018i	$0.574111\pi$
$822$	−2.39205	+	0.833260i	−0.0834322	+	0.0290633i
$823$	−0.476705	−	0.825677i	−0.0166169	−	0.0287813i	0.857597	−	0.514322i	$-0.171956\pi$
$823$	−0.476705	−	0.825677i	−0.0166169	−	0.0287813i	−0.874214	+	0.485540i	$0.838623\pi$
$824$	26.5117	+	8.29972i	0.923577	+	0.289134i
$825$	5.67466			0.197566
$826$		0			0
$827$	0.699424	−	0.699424i	0.0243213	−	0.0243213i	−0.694842	−	0.719163i	$-0.744526\pi$
$827$	0.699424	−	0.699424i	0.0243213	−	0.0243213i	0.719163	+	0.694842i	$0.244526\pi$
$828$	11.9861	−	9.50388i	0.416546	−	0.330283i
$829$	10.6173	−	39.6244i	0.368755	−	1.37621i	−0.493504	−	0.869743i	$-0.664284\pi$
$829$	10.6173	−	39.6244i	0.368755	−	1.37621i	0.862259	−	0.506468i	$-0.169049\pi$
$830$	−44.3355	−	21.4273i	−1.53891	−	0.743752i
$831$	−0.0400588	+	0.0693838i	−0.00138962	+	0.00240690i
$832$	4.58196	+	1.64657i	0.158851	+	0.0570847i
$833$		0			0
$834$	−5.38399	−	7.92063i	−0.186432	−	0.274269i
$835$	−9.68515	+	2.59513i	−0.335168	+	0.0898081i
$836$	−0.0750126	−	0.507299i	−0.00259437	−	0.0175453i
$837$	8.81974	−	32.9157i	0.304855	−	1.13773i
$838$	−10.1076	+	11.7121i	−0.349161	+	0.404587i
$839$		−	5.46062i		−	0.188522i	−0.995548	−	0.0942608i	$-0.969951\pi$
$839$		−	5.46062i		−	0.188522i	0.995548	−	0.0942608i	$-0.0300488\pi$
$840$		0			0
$841$			22.2086i			0.765813i
$842$	7.25497	+	6.26108i	0.250023	+	0.215771i
$843$	−3.31147	+	12.3586i	−0.114053	+	0.425653i
$844$	5.22578	+	3.87942i	0.179879	+	0.133535i
$845$	−38.5934	+	10.3411i	−1.32765	+	0.355744i
$846$	14.5282	−	9.87540i	0.499488	−	0.339523i
$847$		0			0
$848$	0.656311	+	20.6275i	0.0225378	+	0.708351i
$849$	6.05809	−	10.4929i	0.207913	−	0.360116i
$850$	−18.2971	+	37.8589i	−0.627586	+	1.29855i
$851$	−10.6265	+	39.6585i	−0.364270	+	1.35947i
$852$	25.1327	+	2.90298i	0.861033	+	0.0994544i
$853$	−35.1393	+	35.1393i	−1.20315	+	1.20315i	−0.229943	+	0.973204i	$0.573854\pi$
$853$	−35.1393	+	35.1393i	−1.20315	+	1.20315i	−0.973204	+	0.229943i	$0.926146\pi$
$854$		0			0
$855$	−1.41740			−0.0484741
$856$	−13.6236	−	26.0410i	−0.465646	−	0.890064i
$857$	22.4781	+	38.9331i	0.767836	+	1.32993i	0.938734	+	0.344642i	$0.112000\pi$
$857$	22.4781	+	38.9331i	0.767836	+	1.32993i	−0.170899	+	0.985289i	$0.554667\pi$
$858$	−0.320807	−	0.920941i	−0.0109522	−	0.0314404i
$859$	−22.2036	+	5.94943i	−0.757577	+	0.202992i	−0.616876	−	0.787060i	$-0.711602\pi$
$859$	−22.2036	+	5.94943i	−0.757577	+	0.202992i	−0.140700	+	0.990052i	$0.544935\pi$
$860$	60.8012	+	24.0592i	2.07330	+	0.820411i
$861$		0			0
$862$	2.97862	−	2.02469i	0.101452	−	0.0689614i
$863$	28.2948	+	16.3360i	0.963168	+	0.556085i	0.897147	−	0.441733i	$-0.145636\pi$
$863$	28.2948	+	16.3360i	0.963168	+	0.556085i	0.0660212	+	0.997818i	$0.478969\pi$
$864$	−24.4519	−	10.8724i	−0.831871	−	0.369886i
$865$	−36.1719	−	62.6515i	−1.22988	−	2.13021i
$866$	−1.97457	−	26.8527i	−0.0670987	−	0.912490i
$867$	11.8290	−	11.8290i	0.401734	−	0.401734i
$868$		0			0
$869$	−1.48879	−	1.48879i	−0.0505036	−	0.0505036i
$870$	−8.09336	−	6.98462i	−0.274391	−	0.236801i
$871$	−4.31162	+	2.48932i	−0.146094	+	0.0843473i
$872$	−0.114729	−	0.00477490i	−0.00388522	−	0.000161698i
$873$	11.4782	−	19.8808i	0.388479	−	0.672865i
$874$	−1.02099	−	0.194662i	−0.0345356	−	0.00658452i
$875$		0			0
$876$	1.64165	+	3.79160i	0.0554663	+	0.128106i
$877$	−4.66251	−	17.4007i	−0.157442	−	0.587580i	−0.998884	−	0.0472331i	$-0.984960\pi$
$877$	−4.66251	−	17.4007i	−0.157442	−	0.587580i	0.841442	−	0.540347i	$-0.181707\pi$
$878$	−22.3955	−	10.8237i	−0.755812	−	0.365283i
$879$	−1.25712	+	0.725800i	−0.0424017	+	0.0244806i
$880$	4.52558	+	14.9683i	0.152557	+	0.504582i
$881$			21.0017i			0.707564i	0.935328	+	0.353782i	$0.115105\pi$
$881$			21.0017i			0.707564i	−0.935328	+	0.353782i	$0.884895\pi$
$882$		0			0
$883$	−29.0326	−	29.0326i	−0.977024	−	0.977024i	0.0227184	−	0.999742i	$-0.492768\pi$
$883$	−29.0326	−	29.0326i	−0.977024	−	0.977024i	−0.999742	+	0.0227184i	$0.992768\pi$
$884$	7.17851	+	0.829161i	0.241440	+	0.0278877i
$885$	−3.99749	−	1.07112i	−0.134374	−	0.0360055i
$886$	12.5759	+	36.1018i	0.422496	+	1.21286i
$887$	33.1149	+	19.1189i	1.11189	+	0.641949i	0.939318	−	0.343048i	$-0.111459\pi$
$887$	33.1149	+	19.1189i	1.11189	+	0.641949i	0.172571	+	0.984997i	$0.444793\pi$
$888$	29.3350	−	6.56619i	0.984420	−	0.220347i
$889$		0			0
$890$	26.8500	+	5.11920i	0.900015	+	0.171596i
$891$	−0.684565	−	2.55483i	−0.0229338	−	0.0855901i
$892$	−43.3591	+	6.41137i	−1.45177	+	0.214669i
$893$	−1.15296	−	0.308934i	−0.0385822	−	0.0103381i
$894$	−9.87055	+	0.725817i	−0.330120	+	0.0242749i
$895$	−43.5153			−1.45456
$896$		0			0
$897$	−1.97659			−0.0659966
$898$	−6.49208	+	0.477386i	−0.216643	+	0.0159306i
$899$	18.1330	+	4.85873i	0.604770	+	0.162048i
$900$	21.3960	−	3.16375i	0.713199	−	0.105458i
$901$	7.92774	+	29.5867i	0.264111	+	0.985677i
$902$	16.5010	+	3.14607i	0.549424	+	0.104753i
$903$		0			0
$904$	−30.5761	+	6.84398i	−1.01695	+	0.227627i
$905$	19.4252	+	11.2151i	0.645715	+	0.372804i
$906$	−6.01715	−	17.2735i	−0.199906	−	0.573872i
$907$	51.5149	+	13.8034i	1.71052	+	0.458334i	0.975553	−	0.219764i	$-0.0705288\pi$
$907$	51.5149	+	13.8034i	1.71052	+	0.458334i	0.734972	+	0.678098i	$0.237195\pi$
$908$	23.0217	+	2.65914i	0.764000	+	0.0882466i
$909$	1.94714	+	1.94714i	0.0645826	+	0.0645826i
$910$		0			0
$911$			20.1673i			0.668171i	0.942543	+	0.334086i	$0.108427\pi$
$911$			20.1673i			0.668171i	−0.942543	+	0.334086i	$0.891573\pi$
$912$	0.220239	+	0.728438i	0.00729284	+	0.0241210i
$913$	−11.7787	+	6.80046i	−0.389819	+	0.225062i
$914$	−32.8266	−	15.8651i	−1.08581	−	0.524769i
$915$	−0.997998	−	3.72458i	−0.0329928	−	0.123131i
$916$	−17.2683	−	39.8833i	−0.570560	−	1.31778i
$917$		0			0
$918$	−39.0142	−	7.43841i	−1.28766	−	0.245504i
$919$	6.69691	−	11.5994i	0.220911	−	0.382628i	−0.734174	−	0.678961i	$-0.762430\pi$
$919$	6.69691	−	11.5994i	0.220911	−	0.382628i	0.955085	+	0.296333i	$0.0957638\pi$
$920$	31.6670	+	1.31795i	1.04403	+	0.0434514i
$921$	17.8100	−	10.2826i	0.586859	−	0.338823i
$922$	−6.67250	−	5.75841i	−0.219747	−	0.189643i
$923$	5.93723	+	5.93723i	0.195426	+	0.195426i
$924$		0			0
$925$	−41.0494	+	41.0494i	−1.34970	+	1.34970i
$926$	−3.21897	−	43.7755i	−0.105782	−	1.43855i
$927$	−10.6041	−	18.3669i	−0.348285	−	0.603247i
$928$	5.98953	−	13.4704i	0.196616	−	0.442187i
$929$	−34.7602	−	20.0688i	−1.14044	−	0.658436i	−0.193904	−	0.981020i	$-0.562115\pi$
$929$	−34.7602	−	20.0688i	−1.14044	−	0.658436i	−0.946541	+	0.322584i	$0.895448\pi$
$930$	24.4390	−	16.6122i	0.801386	−	0.544736i
$931$		0			0
$932$	−23.2396	−	9.19597i	−0.761239	−	0.301224i
$933$	−25.2796	+	6.77364i	−0.827616	+	0.221759i
$934$	−16.9506	−	48.6601i	−0.554639	−	1.59221i
$935$	11.6045	+	20.0995i	0.379506	+	0.657324i
$936$	−1.72303	−	3.29350i	−0.0563189	−	0.107651i
$937$	3.61135			0.117978			0.0589888	−	0.998259i	$-0.481212\pi$
$937$	3.61135			0.117978			0.0589888	+	0.998259i	$0.481212\pi$
$938$		0			0
$939$	0.0404090	−	0.0404090i	0.00131870	−	0.00131870i
$940$	36.1575	+	4.17640i	1.17933	+	0.136219i
$941$	3.66828	−	13.6902i	0.119583	−	0.446288i	−0.880006	−	0.474962i	$-0.842462\pi$
$941$	3.66828	−	13.6902i	0.119583	−	0.446288i	0.999589	+	0.0286739i	$0.00912842\pi$
$942$	−8.24718	+	17.0644i	−0.268708	+	0.555987i
$943$	17.0236	−	29.4857i	0.554363	−	0.960185i
$944$	−0.181487	−	5.70401i	−0.00590688	−	0.185650i
$945$		0			0
$946$	14.9366	−	10.1530i	0.485631	−	0.330104i
$947$	−42.8152	+	11.4723i	−1.39131	+	0.372799i	−0.875215	−	0.483734i	$-0.839280\pi$
$947$	−42.8152	+	11.4723i	−1.39131	+	0.372799i	−0.516091	+	0.856534i	$0.672613\pi$
$948$	2.50873	+	1.86239i	0.0814797	+	0.0604875i
$949$	−0.354903	+	1.32452i	−0.0115207	+	0.0429957i
$950$	−1.11259	−	0.960174i	−0.0360972	−	0.0311521i
$951$		−	20.8115i		−	0.674858i
$952$		0			0
$953$		−	54.7099i		−	1.77223i	−0.463467	−	0.886114i	$-0.653395\pi$
$953$		−	54.7099i		−	1.77223i	0.463467	−	0.886114i	$-0.346605\pi$
$954$	10.2938	−	11.9278i	0.333273	−	0.386177i
$955$	−4.39905	+	16.4175i	−0.142350	+	0.531258i
$956$	2.25551	+	15.2537i	0.0729485	+	0.493340i
$957$	−2.85217	+	0.764238i	−0.0921977	+	0.0247043i
$958$	−7.58290	−	11.1556i	−0.244992	−	0.360420i
$959$		0			0
$960$	−9.89278	−	20.9913i	−0.319288	−	0.677491i
$961$	−10.4455	+	18.0921i	−0.336951	+	0.583616i
$962$	8.98257	+	4.34126i	0.289610	+	0.139968i
$963$	−5.80701	+	21.6721i	−0.187128	+	0.698373i
$964$	−17.2007	+	13.6386i	−0.553996	+	0.439268i
$965$	0.160744	−	0.160744i	0.00517454	−	0.00517454i
$966$		0			0
$967$	−57.5321			−1.85011			−0.925054	−	0.379836i	$-0.875980\pi$
$967$	−57.5321			−1.85011			−0.925054	+	0.379836i	$0.875980\pi$
$968$	−25.5698	−	8.00487i	−0.821845	−	0.257286i
$969$	0.564734	+	0.978148i	0.0181419	+	0.0314227i
$970$	44.9178	−	15.6470i	1.44222	−	0.502394i
$971$	15.8100	−	4.23628i	0.507367	−	0.135949i	0.00395008	−	0.999992i	$-0.498743\pi$
$971$	15.8100	−	4.23628i	0.507367	−	0.135949i	0.503417	+	0.864044i	$0.332076\pi$
$972$	12.8370	+	29.6487i	0.411748	+	0.950984i
$973$		0			0
$974$	−2.21878	−	3.26415i	−0.0710944	−	0.104590i
$975$	−2.42035	−	1.39739i	−0.0775132	−	0.0447523i
$976$	4.51802	−	2.80374i	0.144618	−	0.0897455i
$977$	−17.3630	−	30.0736i	−0.555491	−	0.962139i	−0.997865	−	0.0653083i	$-0.979197\pi$
$977$	−17.3630	−	30.0736i	−0.555491	−	0.962139i	0.442374	−	0.896831i	$-0.354136\pi$
$978$	0.539861	−	0.0396979i	0.0172628	−	0.00126940i
$979$	5.33846	−	5.33846i	0.170618	−	0.170618i
$980$		0			0
$981$	0.0619868	+	0.0619868i	0.00197909	+	0.00197909i
$982$	−19.4808	+	22.5732i	−0.621656	+	0.720338i
$983$	−18.2841	+	10.5563i	−0.583173	+	0.336695i	−0.762393	−	0.647114i	$-0.775976\pi$
$983$	−18.2841	+	10.5563i	−0.583173	+	0.336695i	0.179220	+	0.983809i	$0.442642\pi$
$984$	−24.9066	−	1.03659i	−0.793994	−	0.0330452i
$985$	5.82439	−	10.0881i	0.185581	−	0.321435i
$986$	4.09777	−	21.4926i	0.130499	−	0.684465i
$987$		0			0
$988$	−0.0929284	+	0.234844i	−0.00295645	+	0.00747139i
$989$	−9.47426	−	35.3584i	−0.301264	−	1.12433i
$990$	5.19475	−	10.7485i	0.165100	−	0.341611i
$991$	−31.5056	+	18.1898i	−1.00081	+	0.577817i	−0.908488	−	0.417912i	$-0.862762\pi$
$991$	−31.5056	+	18.1898i	−1.00081	+	0.577817i	−0.0923215	+	0.995729i	$0.529429\pi$
$992$	31.6807	+	25.6289i	1.00586	+	0.813719i
$993$		−	14.7364i		−	0.467644i
$994$		0			0
$995$	23.2955	+	23.2955i	0.738516	+	0.738516i
$996$	15.8151	−	12.5400i	0.501122	−	0.397344i
$997$	48.0643	+	12.8788i	1.52221	+	0.407875i	0.920469	−	0.390816i	$-0.127807\pi$
$997$	48.0643	+	12.8788i	1.52221	+	0.407875i	0.601742	+	0.798691i	$0.294474\pi$
$998$	18.8928	−	6.58124i	0.598041	−	0.208325i
$999$	−47.4873	−	27.4168i	−1.50243	−	0.867430i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.w.f.411.14		56
7.2	even	3		784.2.j.a.587.9		56
7.3	odd	6	inner	784.2.w.f.619.4		56
7.4	even	3		112.2.v.a.59.4	yes	56
7.5	odd	6		784.2.j.a.587.10		56
7.6	odd	2		112.2.v.a.75.14	yes	56
16.3	odd	4	inner	784.2.w.f.19.4		56
28.11	odd	6		448.2.z.a.143.9		56
28.27	even	2		448.2.z.a.271.9		56
56.11	odd	6		896.2.z.a.31.6		56
56.13	odd	2		896.2.z.b.159.9		56
56.27	even	2		896.2.z.a.159.6		56
56.53	even	6		896.2.z.b.31.9		56
112.3	even	12	inner	784.2.w.f.227.14		56
112.11	odd	12		896.2.z.b.479.9		56
112.13	odd	4		448.2.z.a.47.9		56
112.19	even	12		784.2.j.a.195.9		56
112.27	even	4		896.2.z.b.607.9		56
112.51	odd	12		784.2.j.a.195.10		56
112.53	even	12		896.2.z.a.479.6		56
112.67	odd	12		112.2.v.a.3.14	✓	56
112.69	odd	4		896.2.z.a.607.6		56
112.83	even	4		112.2.v.a.19.4	yes	56
112.109	even	12		448.2.z.a.367.9		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.14	✓	56	112.67	odd	12
112.2.v.a.19.4	yes	56	112.83	even	4
112.2.v.a.59.4	yes	56	7.4	even	3
112.2.v.a.75.14	yes	56	7.6	odd	2
448.2.z.a.47.9		56	112.13	odd	4
448.2.z.a.143.9		56	28.11	odd	6
448.2.z.a.271.9		56	28.27	even	2
448.2.z.a.367.9		56	112.109	even	12
784.2.j.a.195.9		56	112.19	even	12
784.2.j.a.195.10		56	112.51	odd	12
784.2.j.a.587.9		56	7.2	even	3
784.2.j.a.587.10		56	7.5	odd	6
784.2.w.f.19.4		56	16.3	odd	4	inner
784.2.w.f.227.14		56	112.3	even	12	inner
784.2.w.f.411.14		56	1.1	even	1	trivial
784.2.w.f.619.4		56	7.3	odd	6	inner
896.2.z.a.31.6		56	56.11	odd	6
896.2.z.a.159.6		56	56.27	even	2
896.2.z.a.479.6		56	112.53	even	12
896.2.z.a.607.6		56	112.69	odd	4
896.2.z.b.31.9		56	56.53	even	6
896.2.z.b.159.9		56	56.13	odd	2
896.2.z.b.479.9		56	112.11	odd	12
896.2.z.b.607.9		56	112.27	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.w (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.41041 - 0.103712i) q^{2} +(0.885661 + 0.237312i) q^{3} +(1.97849 - 0.292553i) q^{4} +(-0.818796 - 3.05579i) q^{5} +(1.27375 + 0.242853i) q^{6} +(2.76013 - 0.617811i) q^{8} +(-1.87000 - 1.07964i) q^{9} +(-1.47176 - 4.22498i) q^{10} +(-1.19363 - 0.319833i) q^{11} +(1.82170 + 0.210417i) q^{12} +(0.430348 + 0.430348i) q^{13} -2.90070i q^{15} +(3.82883 - 1.15762i) q^{16} +(5.14136 - 2.96837i) q^{17} +(-2.74943 - 1.32879i) q^{18} +(0.0537031 + 0.200423i) q^{19} +(-2.51396 - 5.80630i) q^{20} +(-1.71668 - 0.327300i) q^{22} +(-1.77104 + 3.06753i) q^{23} +(2.59115 + 0.107841i) q^{24} +(-4.33729 + 2.50414i) q^{25} +(0.651598 + 0.562333i) q^{26} +(-3.34502 - 3.34502i) q^{27} +(1.84275 - 1.84275i) q^{29} +(-0.300839 - 4.09117i) q^{30} +(3.60177 + 6.23845i) q^{31} +(5.28014 - 2.02981i) q^{32} +(-0.981256 - 0.566528i) q^{33} +(6.94355 - 4.71982i) q^{34} +(-4.01562 - 1.58899i) q^{36} +(11.1964 - 3.00006i) q^{37} +(0.0965294 + 0.277107i) q^{38} +(0.279016 + 0.483270i) q^{39} +(-4.14788 - 7.92851i) q^{40} -9.61218 q^{41} +(-7.30761 + 7.30761i) q^{43} +(-2.45516 - 0.283586i) q^{44} +(-1.76802 + 6.59833i) q^{45} +(-2.17974 + 4.51014i) q^{46} +(-2.87631 + 4.98192i) q^{47} +(3.66576 - 0.116635i) q^{48} +(-5.85763 + 3.98168i) q^{50} +(5.25793 - 1.40886i) q^{51} +(0.977338 + 0.725539i) q^{52} +(-1.33537 + 4.98367i) q^{53} +(-5.06475 - 4.37091i) q^{54} +3.90937i q^{55} +0.190251i q^{57} +(2.40791 - 2.79014i) q^{58} +(0.369264 - 1.37811i) q^{59} +(-0.848609 - 5.73901i) q^{60} +(1.28402 - 0.344053i) q^{61} +(5.72696 + 8.42519i) q^{62} +(7.23662 - 3.41048i) q^{64} +(0.962686 - 1.66742i) q^{65} +(-1.44272 - 0.697266i) q^{66} +(-2.11725 + 7.90167i) q^{67} +(9.30372 - 7.37699i) q^{68} +(-2.29651 + 2.29651i) q^{69} +13.7963 q^{71} +(-5.82845 - 1.82465i) q^{72} +(1.12655 + 1.95123i) q^{73} +(15.4803 - 5.39250i) q^{74} +(-4.43564 + 1.18853i) q^{75} +(0.164885 + 0.380823i) q^{76} +(0.443647 + 0.652669i) q^{78} +(1.47554 + 0.851902i) q^{79} +(-6.67248 - 10.7522i) q^{80} +(1.07019 + 1.85362i) q^{81} +(-13.5571 + 0.996900i) q^{82} +(7.78261 - 7.78261i) q^{83} +(-13.2804 - 13.2804i) q^{85} +(-9.54881 + 11.0646i) q^{86} +(2.06936 - 1.19474i) q^{87} +(-3.49218 - 0.145341i) q^{88} +(-3.05474 + 5.29096i) q^{89} +(-1.80929 + 9.48968i) q^{90} +(-2.60657 + 6.58720i) q^{92} +(1.70949 + 6.37989i) q^{93} +(-3.54008 + 7.32484i) q^{94} +(0.568477 - 0.328210i) q^{95} +(5.15811 - 0.544686i) q^{96} +10.6315i q^{97} +(1.88679 + 1.88679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} + 6 q^{3} - 4 q^{4} + 6 q^{5} + 4 q^{8} + 24 q^{10} + 2 q^{11} + 6 q^{12} + 8 q^{16} + 12 q^{17} - 30 q^{18} + 6 q^{19} - 28 q^{22} - 12 q^{23} + 6 q^{24} + 6 q^{26} - 24 q^{29} - 18 q^{30}+ \cdots - 16 q^{99}+O(q^{100}) \) 56 * q - 2 * q^2 + 6 * q^3 - 4 * q^4 + 6 * q^5 + 4 * q^8 + 24 * q^10 + 2 * q^11 + 6 * q^12 + 8 * q^16 + 12 * q^17 - 30 * q^18 + 6 * q^19 - 28 * q^22 - 12 * q^23 + 6 * q^24 + 6 * q^26 - 24 * q^29 - 18 * q^30 - 12 * q^32 + 12 * q^33 + 16 * q^36 + 6 * q^37 + 6 * q^38 - 4 * q^39 + 66 * q^40 + 26 * q^44 - 12 * q^45 + 16 * q^46 - 34 * q^51 - 84 * q^52 + 6 * q^53 - 42 * q^54 + 18 * q^58 - 42 * q^59 + 78 * q^60 + 6 * q^61 - 16 * q^64 - 4 * q^65 - 126 * q^66 + 6 * q^67 - 24 * q^68 - 80 * q^71 - 4 * q^72 + 62 * q^74 - 24 * q^75 + 4 * q^78 - 12 * q^80 - 8 * q^81 - 42 * q^82 - 28 * q^85 + 12 * q^87 + 30 * q^88 - 20 * q^92 + 10 * q^93 + 42 * q^94 - 36 * q^96 - 16 * q^99

Introduction

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