LMFDB - Embedded newform 690.2.j.b.643.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(367,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("690.367");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			643.5
Character	$\chi$	$=$	690.643
Dual form			690.2.j.b.367.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(1.07661 + 1.95982i) q^{5} +1.00000 q^{6} +(-3.43458 - 3.43458i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(1.07661 + 1.95982i) q^{5} +1.00000 q^{6} +(-3.43458 - 3.43458i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(-2.14708 - 0.624526i) q^{10} +1.77870i q^{11} +(-0.707107 + 0.707107i) q^{12} +(1.21834 + 1.21834i) q^{13} +4.85722 q^{14} +(0.624526 - 2.14708i) q^{15} -1.00000 q^{16} +(1.12442 + 1.12442i) q^{17} +(-0.707107 - 0.707107i) q^{18} +2.57499 q^{19} +(1.95982 - 1.07661i) q^{20} +4.85722i q^{21} +(-1.25773 - 1.25773i) q^{22} +(-0.510395 + 4.76859i) q^{23} -1.00000i q^{24} +(-2.68182 + 4.21993i) q^{25} -1.72299 q^{26} +(0.707107 - 0.707107i) q^{27} +(-3.43458 + 3.43458i) q^{28} +3.23574i q^{29} +(1.07661 + 1.95982i) q^{30} +6.41786 q^{31} +(0.707107 - 0.707107i) q^{32} +(1.25773 - 1.25773i) q^{33} -1.59016 q^{34} +(3.03346 - 10.4289i) q^{35} +1.00000 q^{36} +(-0.321856 - 0.321856i) q^{37} +(-1.82079 + 1.82079i) q^{38} -1.72299i q^{39} +(-0.624526 + 2.14708i) q^{40} +10.2290 q^{41} +(-3.43458 - 3.43458i) q^{42} +(-6.47101 + 6.47101i) q^{43} +1.77870 q^{44} +(-1.95982 + 1.07661i) q^{45} +(-3.01100 - 3.73281i) q^{46} +(9.10509 - 9.10509i) q^{47} +(0.707107 + 0.707107i) q^{48} +16.5926i q^{49} +(-1.08761 - 4.88028i) q^{50} -1.59016i q^{51} +(1.21834 - 1.21834i) q^{52} +(-6.42643 + 6.42643i) q^{53} +1.00000i q^{54} +(-3.48594 + 1.91497i) q^{55} -4.85722i q^{56} +(-1.82079 - 1.82079i) q^{57} +(-2.28801 - 2.28801i) q^{58} +10.4081i q^{59} +(-2.14708 - 0.624526i) q^{60} +14.4727i q^{61} +(-4.53812 + 4.53812i) q^{62} +(3.43458 - 3.43458i) q^{63} +1.00000i q^{64} +(-1.07605 + 3.69940i) q^{65} +1.77870i q^{66} +(-0.586681 - 0.586681i) q^{67} +(1.12442 - 1.12442i) q^{68} +(3.73281 - 3.01100i) q^{69} +(5.22934 + 9.51930i) q^{70} -13.3156 q^{71} +(-0.707107 + 0.707107i) q^{72} +(3.84689 + 3.84689i) q^{73} +0.455173 q^{74} +(4.88028 - 1.08761i) q^{75} -2.57499i q^{76} +(6.10909 - 6.10909i) q^{77} +(1.21834 + 1.21834i) q^{78} +6.55768 q^{79} +(-1.07661 - 1.95982i) q^{80} -1.00000 q^{81} +(-7.23299 + 7.23299i) q^{82} +(2.56461 - 2.56461i) q^{83} +4.85722 q^{84} +(-0.993099 + 3.41421i) q^{85} -9.15139i q^{86} +(2.28801 - 2.28801i) q^{87} +(-1.25773 + 1.25773i) q^{88} +3.44952 q^{89} +(0.624526 - 2.14708i) q^{90} -8.36895i q^{91} +(4.76859 + 0.510395i) q^{92} +(-4.53812 - 4.53812i) q^{93} +12.8765i q^{94} +(2.77226 + 5.04652i) q^{95} -1.00000 q^{96} +(-7.79375 - 7.79375i) q^{97} +(-11.7328 - 11.7328i) q^{98} -1.77870 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{6}+O(q^{10}) $ 24 * q + 24 * q^6	$ 24 q + 24 q^{6} + 16 q^{13} - 24 q^{16} + 16 q^{23} - 16 q^{25} + 16 q^{31} + 24 q^{36} + 8 q^{46} + 40 q^{47} - 8 q^{50} + 16 q^{52} - 56 q^{55} - 16 q^{58} - 8 q^{62} + 32 q^{70} + 64 q^{71} - 16 q^{73} + 32 q^{75} + 16 q^{77} + 16 q^{78} - 24 q^{81} + 24 q^{82} - 48 q^{85} + 16 q^{87} + 16 q^{92} - 8 q^{93} + 24 q^{95} - 24 q^{96}+O(q^{100}) $ 24 * q + 24 * q^6 + 16 * q^13 - 24 * q^16 + 16 * q^23 - 16 * q^25 + 16 * q^31 + 24 * q^36 + 8 * q^46 + 40 * q^47 - 8 * q^50 + 16 * q^52 - 56 * q^55 - 16 * q^58 - 8 * q^62 + 32 * q^70 + 64 * q^71 - 16 * q^73 + 32 * q^75 + 16 * q^77 + 16 * q^78 - 24 * q^81 + 24 * q^82 - 48 * q^85 + 16 * q^87 + 16 * q^92 - 8 * q^93 + 24 * q^95 - 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$	1.07661	+	1.95982i	0.481475	+	0.876460i
$5$	1.07661	+	1.95982i	0.481475	+	0.876460i
$6$	1.00000			0.408248
$7$	−3.43458	−	3.43458i	−1.29815	−	1.29815i	−0.929615	−	0.368533i	$-0.879860\pi$
$7$	−3.43458	−	3.43458i	−1.29815	−	1.29815i	−0.368533	−	0.929615i	$-0.620140\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$			1.00000i			0.333333i
$10$	−2.14708	−	0.624526i	−0.678967	−	0.197492i
$11$			1.77870i			0.536299i	0.963377	+	0.268149i	$0.0864121\pi$
$11$			1.77870i			0.536299i	−0.963377	+	0.268149i	$0.913588\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	1.21834	+	1.21834i	0.337906	+	0.337906i	0.855579	−	0.517673i	$-0.173202\pi$
$13$	1.21834	+	1.21834i	0.337906	+	0.337906i	−0.517673	+	0.855579i	$0.673202\pi$
$14$	4.85722			1.29815
$15$	0.624526	−	2.14708i	0.161252	−	0.554375i
$16$	−1.00000			−0.250000
$17$	1.12442	+	1.12442i	0.272711	+	0.272711i	0.830191	−	0.557480i	$-0.188232\pi$
$17$	1.12442	+	1.12442i	0.272711	+	0.272711i	−0.557480	+	0.830191i	$0.688232\pi$
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	2.57499			0.590742			0.295371	−	0.955383i	$-0.404557\pi$
$19$	2.57499			0.590742			0.295371	+	0.955383i	$0.404557\pi$
$20$	1.95982	−	1.07661i	0.438230	−	0.240737i
$21$			4.85722i			1.05993i
$22$	−1.25773	−	1.25773i	−0.268149	−	0.268149i
$23$	−0.510395	+	4.76859i	−0.106425	+	0.994321i
$23$	−0.510395	+	4.76859i	−0.106425	+	0.994321i
$24$		−	1.00000i		−	0.204124i
$25$	−2.68182	+	4.21993i	−0.536364	+	0.843987i
$26$	−1.72299			−0.337906
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−3.43458	+	3.43458i	−0.649074	+	0.649074i
$29$			3.23574i			0.600862i	0.953804	+	0.300431i	$0.0971305\pi$
$29$			3.23574i			0.600862i	−0.953804	+	0.300431i	$0.902870\pi$
$30$	1.07661	+	1.95982i	0.196561	+	0.357813i
$31$	6.41786			1.15268			0.576341	−	0.817209i	$-0.304480\pi$
$31$	6.41786			1.15268			0.576341	+	0.817209i	$0.304480\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	1.25773	−	1.25773i	0.218943	−	0.218943i
$34$	−1.59016			−0.272711
$35$	3.03346	−	10.4289i	0.512749	−	1.76280i
$36$	1.00000			0.166667
$37$	−0.321856	−	0.321856i	−0.0529127	−	0.0529127i	0.680155	−	0.733068i	$-0.261912\pi$
$37$	−0.321856	−	0.321856i	−0.0529127	−	0.0529127i	−0.733068	+	0.680155i	$0.761912\pi$
$38$	−1.82079	+	1.82079i	−0.295371	+	0.295371i
$39$		−	1.72299i		−	0.275899i
$40$	−0.624526	+	2.14708i	−0.0987462	+	0.339484i
$41$	10.2290			1.59750			0.798750	−	0.601663i	$-0.205495\pi$
$41$	10.2290			1.59750			0.798750	+	0.601663i	$0.205495\pi$
$42$	−3.43458	−	3.43458i	−0.529967	−	0.529967i
$43$	−6.47101	+	6.47101i	−0.986820	+	0.986820i	−0.999914	−	0.0130943i	$-0.995832\pi$
$43$	−6.47101	+	6.47101i	−0.986820	+	0.986820i	0.0130943	+	0.999914i	$0.495832\pi$
$44$	1.77870			0.268149
$45$	−1.95982	+	1.07661i	−0.292153	+	0.160492i
$46$	−3.01100	−	3.73281i	−0.443948	−	0.550373i
$47$	9.10509	−	9.10509i	1.32811	−	1.32811i	0.421100	−	0.907014i	$-0.361644\pi$
$47$	9.10509	−	9.10509i	1.32811	−	1.32811i	0.907014	−	0.421100i	$-0.138356\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$			16.5926i			2.37038i
$50$	−1.08761	−	4.88028i	−0.153812	−	0.690175i
$51$		−	1.59016i		−	0.222667i
$52$	1.21834	−	1.21834i	0.168953	−	0.168953i
$53$	−6.42643	+	6.42643i	−0.882738	+	0.882738i	−0.993812	−	0.111074i	$-0.964571\pi$
$53$	−6.42643	+	6.42643i	−0.882738	+	0.882738i	0.111074	+	0.993812i	$0.464571\pi$
$54$			1.00000i			0.136083i
$55$	−3.48594	+	1.91497i	−0.470044	+	0.258214i
$56$		−	4.85722i		−	0.649074i
$57$	−1.82079	−	1.82079i	−0.241170	−	0.241170i
$58$	−2.28801	−	2.28801i	−0.300431	−	0.300431i
$59$			10.4081i			1.35502i	0.735514	+	0.677510i	$0.236941\pi$
$59$			10.4081i			1.35502i	−0.735514	+	0.677510i	$0.763059\pi$
$60$	−2.14708	−	0.624526i	−0.277187	−	0.0806260i
$61$			14.4727i			1.85303i	0.376252	+	0.926517i	$0.377213\pi$
$61$			14.4727i			1.85303i	−0.376252	+	0.926517i	$0.622787\pi$
$62$	−4.53812	+	4.53812i	−0.576341	+	0.576341i
$63$	3.43458	−	3.43458i	0.432716	−	0.432716i
$64$			1.00000i			0.125000i
$65$	−1.07605	+	3.69940i	−0.133468	+	0.458854i
$66$			1.77870i			0.218943i
$67$	−0.586681	−	0.586681i	−0.0716745	−	0.0716745i	0.670361	−	0.742035i	$-0.266139\pi$
$67$	−0.586681	−	0.586681i	−0.0716745	−	0.0716745i	−0.742035	+	0.670361i	$0.766139\pi$
$68$	1.12442	−	1.12442i	0.136355	−	0.136355i
$69$	3.73281	−	3.01100i	0.449377	−	0.362482i
$70$	5.22934	+	9.51930i	0.625026	+	1.13777i
$71$	−13.3156			−1.58027			−0.790137	−	0.612931i	$-0.789990\pi$
$71$	−13.3156			−1.58027			−0.790137	+	0.612931i	$0.789990\pi$
$72$	−0.707107	+	0.707107i	−0.0833333	+	0.0833333i
$73$	3.84689	+	3.84689i	0.450245	+	0.450245i	0.895436	−	0.445191i	$-0.146864\pi$
$73$	3.84689	+	3.84689i	0.450245	+	0.450245i	−0.445191	+	0.895436i	$0.646864\pi$
$74$	0.455173			0.0529127
$75$	4.88028	−	1.08761i	0.563526	−	0.125587i
$76$		−	2.57499i		−	0.295371i
$77$	6.10909	−	6.10909i	0.696195	−	0.696195i
$78$	1.21834	+	1.21834i	0.137950	+	0.137950i
$79$	6.55768			0.737796			0.368898	−	0.929470i	$-0.379735\pi$
$79$	6.55768			0.737796			0.368898	+	0.929470i	$0.379735\pi$
$80$	−1.07661	−	1.95982i	−0.120369	−	0.219115i
$81$	−1.00000			−0.111111
$82$	−7.23299	+	7.23299i	−0.798750	+	0.798750i
$83$	2.56461	−	2.56461i	0.281502	−	0.281502i	−0.552206	−	0.833708i	$-0.686214\pi$
$83$	2.56461	−	2.56461i	0.281502	−	0.281502i	0.833708	+	0.552206i	$0.186214\pi$
$84$	4.85722			0.529967
$85$	−0.993099	+	3.41421i	−0.107717	+	0.370323i
$86$		−	9.15139i		−	0.986820i
$87$	2.28801	−	2.28801i	0.245301	−	0.245301i
$88$	−1.25773	+	1.25773i	−0.134075	+	0.134075i
$89$	3.44952			0.365648			0.182824	−	0.983146i	$-0.441476\pi$
$89$	3.44952			0.365648			0.182824	+	0.983146i	$0.441476\pi$
$90$	0.624526	−	2.14708i	0.0658308	−	0.226322i
$91$		−	8.36895i		−	0.877304i
$92$	4.76859	+	0.510395i	0.497160	+	0.0532123i
$93$	−4.53812	−	4.53812i	−0.470581	−	0.470581i
$94$			12.8765i			1.32811i
$95$	2.77226	+	5.04652i	0.284428	+	0.517762i
$96$	−1.00000			−0.102062
$97$	−7.79375	−	7.79375i	−0.791335	−	0.791335i	0.190376	−	0.981711i	$-0.439029\pi$
$97$	−7.79375	−	7.79375i	−0.791335	−	0.791335i	−0.981711	+	0.190376i	$0.939029\pi$
$98$	−11.7328	−	11.7328i	−1.18519	−	1.18519i
$99$	−1.77870			−0.178766
$100$	4.21993	+	2.68182i	0.421993	+	0.268182i
$101$	0.109089			0.0108547			0.00542736	−	0.999985i	$-0.498272\pi$
$101$	0.109089			0.0108547			0.00542736	+	0.999985i	$0.498272\pi$
$102$	1.12442	+	1.12442i	0.111334	+	0.111334i
$103$	0.451663	−	0.451663i	0.0445037	−	0.0445037i	−0.684505	−	0.729008i	$-0.739981\pi$
$103$	0.451663	−	0.451663i	0.0445037	−	0.0445037i	0.729008	+	0.684505i	$0.239981\pi$
$104$			1.72299i			0.168953i
$105$	−9.51930	+	5.22934i	−0.928989	+	0.510331i
$106$		−	9.08835i		−	0.882738i
$107$	5.06879	+	5.06879i	0.490018	+	0.490018i	0.908312	−	0.418293i	$-0.137372\pi$
$107$	5.06879	+	5.06879i	0.490018	+	0.490018i	−0.418293	+	0.908312i	$0.637372\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$	−7.67531			−0.735161			−0.367581	−	0.929992i	$-0.619814\pi$
$109$	−7.67531			−0.735161			−0.367581	+	0.929992i	$0.619814\pi$
$110$	1.11085	−	3.81902i	0.105915	−	0.364129i
$111$			0.455173i			0.0432031i
$112$	3.43458	+	3.43458i	0.324537	+	0.324537i
$113$	10.3565	−	10.3565i	0.974254	−	0.974254i	−0.0254229	−	0.999677i	$-0.508093\pi$
$113$	10.3565	−	10.3565i	0.974254	−	0.974254i	0.999677	+	0.0254229i	$0.00809325\pi$
$114$	2.57499			0.241170
$115$	−9.89510	+	4.13364i	−0.922723	+	0.385464i
$116$	3.23574			0.300431
$117$	−1.21834	+	1.21834i	−0.112635	+	0.112635i
$118$	−7.35964	−	7.35964i	−0.677510	−	0.677510i
$119$		−	7.72378i		−	0.708038i
$120$	1.95982	−	1.07661i	0.178907	−	0.0982807i
$121$	7.83622			0.712384
$122$	−10.2337	−	10.2337i	−0.926517	−	0.926517i
$123$	−7.23299	−	7.23299i	−0.652177	−	0.652177i
$124$		−	6.41786i		−	0.576341i
$125$	−11.1576	−	0.712667i	−0.997966	−	0.0637429i
$126$			4.85722i			0.432716i
$127$	8.30451	−	8.30451i	0.736906	−	0.736906i	−0.235072	−	0.971978i	$-0.575533\pi$
$127$	8.30451	−	8.30451i	0.736906	−	0.736906i	0.971978	+	0.235072i	$0.0755326\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	9.15139			0.805735
$130$	−1.85499	−	3.37676i	−0.162693	−	0.296161i
$131$	−12.6605			−1.10615			−0.553077	−	0.833130i	$-0.686546\pi$
$131$	−12.6605			−1.10615			−0.553077	+	0.833130i	$0.686546\pi$
$132$	−1.25773	−	1.25773i	−0.109472	−	0.109472i
$133$	−8.84399	−	8.84399i	−0.766871	−	0.766871i
$134$	0.829692			0.0716745
$135$	2.14708	+	0.624526i	0.184792	+	0.0537506i
$136$			1.59016i			0.136355i
$137$	1.04108	+	1.04108i	0.0889456	+	0.0889456i	0.750180	−	0.661234i	$-0.229967\pi$
$137$	1.04108	+	1.04108i	0.0889456	+	0.0889456i	−0.661234	+	0.750180i	$0.729967\pi$
$138$	−0.510395	+	4.76859i	−0.0434477	+	0.405930i
$139$		−	8.89535i		−	0.754494i	−0.926113	−	0.377247i	$-0.876871\pi$
$139$		−	8.89535i		−	0.754494i	0.926113	−	0.377247i	$-0.123129\pi$
$140$	−10.4289	−	3.03346i	−0.881400	−	0.256374i
$141$	−12.8765			−1.08440
$142$	9.41557	−	9.41557i	0.790137	−	0.790137i
$143$	−2.16706	+	2.16706i	−0.181219	+	0.181219i
$144$		−	1.00000i		−	0.0833333i
$145$	−6.34148	+	3.48363i	−0.526631	+	0.289300i
$146$	−5.44033			−0.450245
$147$	11.7328	−	11.7328i	0.967702	−	0.967702i
$148$	−0.321856	+	0.321856i	−0.0264564	+	0.0264564i
$149$	11.3358			0.928666			0.464333	−	0.885661i	$-0.346294\pi$
$149$	11.3358			0.928666			0.464333	+	0.885661i	$0.346294\pi$
$150$	−2.68182	+	4.21993i	−0.218970	+	0.344556i
$151$	−8.75190			−0.712219			−0.356110	−	0.934444i	$-0.615897\pi$
$151$	−8.75190			−0.712219			−0.356110	+	0.934444i	$0.615897\pi$
$152$	1.82079	+	1.82079i	0.147686	+	0.147686i
$153$	−1.12442	+	1.12442i	−0.0909036	+	0.0909036i
$154$			8.63956i			0.696195i
$155$	6.90954	+	12.5779i	0.554988	+	1.01028i
$156$	−1.72299			−0.137950
$157$	−14.2015	−	14.2015i	−1.13340	−	1.13340i	−0.989608	−	0.143791i	$-0.954071\pi$
$157$	−14.2015	−	14.2015i	−1.13340	−	1.13340i	−0.143791	−	0.989608i	$-0.545929\pi$
$158$	−4.63698	+	4.63698i	−0.368898	+	0.368898i
$159$	9.08835			0.720753
$160$	2.14708	+	0.624526i	0.169742	+	0.0493731i
$161$	18.1311	−	14.6251i	1.42893	−	1.15262i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	−3.88265	−	3.88265i	−0.304113	−	0.304113i	0.538508	−	0.842621i	$-0.318988\pi$
$163$	−3.88265	−	3.88265i	−0.304113	−	0.304113i	−0.842621	+	0.538508i	$0.818988\pi$
$164$		−	10.2290i		−	0.798750i
$165$	3.81902	+	1.11085i	0.297310	+	0.0864792i
$166$			3.62690i			0.281502i
$167$	−6.37019	+	6.37019i	−0.492940	+	0.492940i	−0.909231	−	0.416291i	$-0.863330\pi$
$167$	−6.37019	+	6.37019i	−0.492940	+	0.492940i	0.416291	+	0.909231i	$0.363330\pi$
$168$	−3.43458	+	3.43458i	−0.264983	+	0.264983i
$169$		−	10.0313i		−	0.771639i
$170$	−1.71199	−	3.11644i	−0.131303	−	0.239020i
$171$			2.57499i			0.196914i
$172$	6.47101	+	6.47101i	0.493410	+	0.493410i
$173$	6.60779	+	6.60779i	0.502381	+	0.502381i	0.912177	−	0.409796i	$-0.134400\pi$
$173$	6.60779	+	6.60779i	0.502381	+	0.502381i	−0.409796	+	0.912177i	$0.634400\pi$
$174$			3.23574i			0.245301i
$175$	23.7046	−	5.28277i	1.79190	−	0.399340i
$176$		−	1.77870i		−	0.134075i
$177$	7.35964	−	7.35964i	0.553184	−	0.553184i
$178$	−2.43918	+	2.43918i	−0.182824	+	0.182824i
$179$			0.676121i			0.0505357i	0.999681	+	0.0252678i	$0.00804386\pi$
$179$			0.676121i			0.0505357i	−0.999681	+	0.0252678i	$0.991956\pi$
$180$	1.07661	+	1.95982i	0.0802458	+	0.146077i
$181$		−	17.9595i		−	1.33492i	−0.744647	−	0.667458i	$-0.767382\pi$
$181$		−	17.9595i		−	1.33492i	0.744647	−	0.667458i	$-0.232618\pi$
$182$	5.91774	+	5.91774i	0.438652	+	0.438652i
$183$	10.2337	−	10.2337i	0.756498	−	0.756498i
$184$	−3.73281	+	3.01100i	−0.275186	+	0.221974i
$185$	0.284267	−	0.977294i	0.0208997	−	0.0718521i
$186$	6.41786			0.470581
$187$	−2.00000	+	2.00000i	−0.146254	+	0.146254i
$188$	−9.10509	−	9.10509i	−0.664057	−	0.664057i
$189$	−4.85722			−0.353311
$190$	−5.52871	−	1.60815i	−0.401095	−	0.116667i
$191$		−	12.7383i		−	0.921709i	−0.887476	−	0.460855i	$-0.847543\pi$
$191$		−	12.7383i		−	0.921709i	0.887476	−	0.460855i	$-0.152457\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	−1.84399	−	1.84399i	−0.132733	−	0.132733i	0.637619	−	0.770352i	$-0.279919\pi$
$193$	−1.84399	−	1.84399i	−0.132733	−	0.132733i	−0.770352	+	0.637619i	$0.779919\pi$
$194$	11.0220			0.791335
$195$	3.37676	−	1.85499i	0.241814	−	0.132838i
$196$	16.5926			1.18519
$197$	−12.1629	+	12.1629i	−0.866568	+	0.866568i	−0.992091	−	0.125523i	$-0.959939\pi$
$197$	−12.1629	+	12.1629i	−0.866568	+	0.866568i	0.125523	+	0.992091i	$0.459939\pi$
$198$	1.25773	−	1.25773i	0.0893831	−	0.0893831i
$199$	5.37229			0.380832			0.190416	−	0.981704i	$-0.439016\pi$
$199$	5.37229			0.380832			0.190416	+	0.981704i	$0.439016\pi$
$200$	−4.88028	+	1.08761i	−0.345088	+	0.0769058i
$201$			0.829692i			0.0585219i
$202$	−0.0771372	+	0.0771372i	−0.00542736	+	0.00542736i
$203$	11.1134	−	11.1134i	0.780007	−	0.780007i
$204$	−1.59016			−0.111334
$205$	11.0126	+	20.0470i	0.769156	+	1.40014i
$206$			0.638749i			0.0445037i
$207$	−4.76859	−	0.510395i	−0.331440	−	0.0354749i
$208$	−1.21834	−	1.21834i	−0.0844765	−	0.0844765i
$209$			4.58013i			0.316814i
$210$	3.03346	−	10.4289i	0.209329	−	0.719660i
$211$	8.05312			0.554400			0.277200	−	0.960812i	$-0.410594\pi$
$211$	8.05312			0.554400			0.277200	+	0.960812i	$0.410594\pi$
$212$	6.42643	+	6.42643i	0.441369	+	0.441369i
$213$	9.41557	+	9.41557i	0.645144	+	0.645144i
$214$	−7.16835			−0.490018
$215$	−19.6488	−	5.71528i	−1.34004	−	0.389779i
$216$	1.00000			0.0680414
$217$	−22.0426	−	22.0426i	−1.49635	−	1.49635i
$218$	5.42726	−	5.42726i	0.367581	−	0.367581i
$219$		−	5.44033i		−	0.367623i
$220$	1.91497	+	3.48594i	0.129107	+	0.235022i
$221$			2.73983i			0.184301i
$222$	−0.321856	−	0.321856i	−0.0216015	−	0.0216015i
$223$	7.99544	+	7.99544i	0.535414	+	0.535414i	0.922179	−	0.386764i	$-0.126407\pi$
$223$	7.99544	+	7.99544i	0.535414	+	0.535414i	−0.386764	+	0.922179i	$0.626407\pi$
$224$	−4.85722			−0.324537
$225$	−4.21993	−	2.68182i	−0.281329	−	0.178788i
$226$			14.6462i			0.974254i
$227$	13.1571	+	13.1571i	0.873268	+	0.873268i	0.992827	−	0.119559i	$-0.0381481\pi$
$227$	13.1571	+	13.1571i	0.873268	+	0.873268i	−0.119559	+	0.992827i	$0.538148\pi$
$228$	−1.82079	+	1.82079i	−0.120585	+	0.120585i
$229$	6.27877			0.414913			0.207456	−	0.978244i	$-0.433482\pi$
$229$	6.27877			0.414913			0.207456	+	0.978244i	$0.433482\pi$
$230$	4.07397	−	9.91982i	0.268630	−	0.654093i
$231$	−8.63956			−0.568441
$232$	−2.28801	+	2.28801i	−0.150215	+	0.150215i
$233$	11.9743	+	11.9743i	0.784465	+	0.784465i	0.980581	−	0.196116i	$-0.0628329\pi$
$233$	11.9743	+	11.9743i	0.784465	+	0.784465i	−0.196116	+	0.980581i	$0.562833\pi$
$234$		−	1.72299i		−	0.112635i
$235$	27.6470	+	8.04174i	1.80349	+	0.524585i
$236$	10.4081			0.677510
$237$	−4.63698	−	4.63698i	−0.301204	−	0.301204i
$238$	5.46154	+	5.46154i	0.354019	+	0.354019i
$239$			4.39325i			0.284176i	0.989854	+	0.142088i	$0.0453816\pi$
$239$			4.39325i			0.284176i	−0.989854	+	0.142088i	$0.954618\pi$
$240$	−0.624526	+	2.14708i	−0.0403130	+	0.138594i
$241$		−	7.44107i		−	0.479321i	−0.970857	−	0.239661i	$-0.922964\pi$
$241$		−	7.44107i		−	0.479321i	0.970857	−	0.239661i	$-0.0770362\pi$
$242$	−5.54104	+	5.54104i	−0.356192	+	0.356192i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	14.4727			0.926517
$245$	−32.5186	+	17.8638i	−2.07754	+	1.14128i
$246$	10.2290			0.652177
$247$	3.13720	+	3.13720i	0.199615	+	0.199615i
$248$	4.53812	+	4.53812i	0.288171	+	0.288171i
$249$	−3.62690			−0.229845
$250$	8.39355	−	7.38569i	0.530855	−	0.467112i
$251$			12.7768i			0.806466i	0.915097	+	0.403233i	$0.132114\pi$
$251$			12.7768i			0.806466i	−0.915097	+	0.403233i	$0.867886\pi$
$252$	−3.43458	−	3.43458i	−0.216358	−	0.216358i
$253$	−8.48191	−	0.907840i	−0.533253	−	0.0570754i
$254$			11.7443i			0.736906i
$255$	3.11644	−	1.71199i	0.195159	−	0.107209i
$256$	1.00000			0.0625000
$257$	−12.2990	+	12.2990i	−0.767192	+	0.767192i	−0.977611	−	0.210420i	$-0.932517\pi$
$257$	−12.2990	+	12.2990i	−0.767192	+	0.767192i	0.210420	+	0.977611i	$0.432517\pi$
$258$	−6.47101	+	6.47101i	−0.402868	+	0.402868i
$259$			2.21088i			0.137377i
$260$	3.69940	+	1.07605i	0.229427	+	0.0667339i
$261$	−3.23574			−0.200287
$262$	8.95233	−	8.95233i	0.553077	−	0.553077i
$263$	−0.838721	+	0.838721i	−0.0517177	+	0.0517177i	−0.732493	−	0.680775i	$-0.761643\pi$
$263$	−0.838721	+	0.838721i	−0.0517177	+	0.0517177i	0.680775	+	0.732493i	$0.261643\pi$
$264$	1.77870			0.109472
$265$	−19.5134	−	5.67591i	−1.19870	−	0.348668i
$266$	12.5073			0.766871
$267$	−2.43918	−	2.43918i	−0.149275	−	0.149275i
$268$	−0.586681	+	0.586681i	−0.0358372	+	0.0358372i
$269$		−	25.8476i		−	1.57595i	−0.615704	−	0.787977i	$-0.711128\pi$
$269$		−	25.8476i		−	1.57595i	0.615704	−	0.787977i	$-0.288872\pi$
$270$	−1.95982	+	1.07661i	−0.119271	+	0.0655204i
$271$	−32.0433			−1.94649			−0.973246	−	0.229764i	$-0.926205\pi$
$271$	−32.0433			−1.94649			−0.973246	+	0.229764i	$0.926205\pi$
$272$	−1.12442	−	1.12442i	−0.0681777	−	0.0681777i
$273$	−5.91774	+	5.91774i	−0.358158	+	0.358158i
$274$	−1.47231			−0.0889456
$275$	−7.50601	−	4.77016i	−0.452629	−	0.287651i
$276$	−3.01100	−	3.73281i	−0.181241	−	0.224689i
$277$	−18.2414	+	18.2414i	−1.09602	+	1.09602i	−0.101147	+	0.994871i	$0.532251\pi$
$277$	−18.2414	+	18.2414i	−1.09602	+	1.09602i	−0.994871	+	0.101147i	$0.967749\pi$
$278$	6.28997	+	6.28997i	0.377247	+	0.377247i
$279$			6.41786i			0.384227i
$280$	9.51930	−	5.22934i	0.568887	−	0.312513i
$281$		−	3.19489i		−	0.190591i	−0.995449	−	0.0952954i	$-0.969620\pi$
$281$		−	3.19489i		−	0.190591i	0.995449	−	0.0952954i	$-0.0303796\pi$
$282$	9.10509	−	9.10509i	0.542200	−	0.542200i
$283$	−22.6171	+	22.6171i	−1.34444	+	1.34444i	−0.452865	+	0.891579i	$0.649598\pi$
$283$	−22.6171	+	22.6171i	−1.34444	+	1.34444i	−0.891579	+	0.452865i	$0.850402\pi$
$284$			13.3156i			0.790137i
$285$	1.60815	−	5.52871i	0.0952583	−	0.327493i
$286$		−	3.06468i		−	0.181219i
$287$	−35.1323	−	35.1323i	−2.07379	−	2.07379i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$		−	14.4714i		−	0.851258i
$290$	2.02080	−	6.94740i	0.118666	−	0.407965i
$291$			11.0220i			0.646123i
$292$	3.84689	−	3.84689i	0.225122	−	0.225122i
$293$	2.26468	−	2.26468i	0.132304	−	0.132304i	−0.637854	−	0.770158i	$-0.720177\pi$
$293$	2.26468	−	2.26468i	0.132304	−	0.132304i	0.770158	+	0.637854i	$0.220177\pi$
$294$			16.5926i			0.967702i
$295$	−20.3981	+	11.2055i	−1.18762	+	0.652408i
$296$		−	0.455173i		−	0.0264564i
$297$	1.25773	+	1.25773i	0.0729810	+	0.0729810i
$298$	−8.01563	+	8.01563i	−0.464333	+	0.464333i
$299$	−6.43159	+	5.18792i	−0.371948	+	0.300025i
$300$	−1.08761	−	4.88028i	−0.0627933	−	0.281763i
$301$	44.4504			2.56208
$302$	6.18852	−	6.18852i	0.356110	−	0.356110i
$303$	−0.0771372	−	0.0771372i	−0.00443142	−	0.00443142i
$304$	−2.57499			−0.147686
$305$	−28.3639	+	15.5814i	−1.62411	+	0.892190i
$306$		−	1.59016i		−	0.0909036i
$307$	6.36515	−	6.36515i	0.363278	−	0.363278i	−0.501740	−	0.865018i	$-0.667307\pi$
$307$	6.36515	−	6.36515i	0.363278	−	0.363278i	0.865018	+	0.501740i	$0.167307\pi$
$308$	−6.10909	−	6.10909i	−0.348098	−	0.348098i
$309$	−0.638749			−0.0363371
$310$	−13.7797	−	4.00812i	−0.782634	−	0.227646i
$311$	11.5795			0.656615			0.328307	−	0.944571i	$-0.393522\pi$
$311$	11.5795			0.656615			0.328307	+	0.944571i	$0.393522\pi$
$312$	1.21834	−	1.21834i	0.0689748	−	0.0689748i
$313$	−0.636677	+	0.636677i	−0.0359871	+	0.0359871i	−0.724871	−	0.688884i	$-0.758101\pi$
$313$	−0.636677	+	0.636677i	−0.0359871	+	0.0359871i	0.688884	+	0.724871i	$0.258101\pi$
$314$	20.0839			1.13340
$315$	10.4289	+	3.03346i	0.587600	+	0.170916i
$316$		−	6.55768i		−	0.368898i
$317$	16.8675	−	16.8675i	0.947373	−	0.947373i	−0.0513100	−	0.998683i	$-0.516340\pi$
$317$	16.8675	−	16.8675i	0.947373	−	0.947373i	0.998683	+	0.0513100i	$0.0163396\pi$
$318$	−6.42643	+	6.42643i	−0.360376	+	0.360376i
$319$	−5.75542			−0.322241
$320$	−1.95982	+	1.07661i	−0.109557	+	0.0601844i
$321$		−	7.16835i		−	0.400098i
$322$	−2.47910	+	23.1621i	−0.138155	+	1.29078i
$323$	2.89535	+	2.89535i	0.161102	+	0.161102i
$324$			1.00000i			0.0555556i
$325$	−8.40866	+	1.87394i	−0.466429	+	0.103948i
$326$	5.49090			0.304113
$327$	5.42726	+	5.42726i	0.300128	+	0.300128i
$328$	7.23299	+	7.23299i	0.399375	+	0.399375i
$329$	−62.5443			−3.44818
$330$	−3.48594	+	1.91497i	−0.191895	+	0.105416i
$331$	−9.50258			−0.522309			−0.261155	−	0.965297i	$-0.584103\pi$
$331$	−9.50258			−0.522309			−0.261155	+	0.965297i	$0.584103\pi$
$332$	−2.56461	−	2.56461i	−0.140751	−	0.140751i
$333$	0.321856	−	0.321856i	0.0176376	−	0.0176376i
$334$		−	9.00881i		−	0.492940i
$335$	0.518164	−	1.78142i	0.0283103	−	0.0973292i
$336$		−	4.85722i		−	0.264983i
$337$	12.5879	+	12.5879i	0.685708	+	0.685708i	0.961280	−	0.275572i	$-0.0888673\pi$
$337$	12.5879	+	12.5879i	0.685708	+	0.685708i	−0.275572	+	0.961280i	$0.588867\pi$
$338$	7.09321	+	7.09321i	0.385820	+	0.385820i
$339$	−14.6462			−0.795475
$340$	3.41421	+	0.993099i	0.185162	+	0.0538583i
$341$			11.4155i			0.618182i
$342$	−1.82079	−	1.82079i	−0.0984571	−	0.0984571i
$343$	32.9466	−	32.9466i	1.77895	−	1.77895i
$344$	−9.15139			−0.493410
$345$	9.91982	+	4.07397i	0.534065	+	0.219335i
$346$	−9.34483			−0.502381
$347$	−17.5983	+	17.5983i	−0.944725	+	0.944725i	−0.998550	−	0.0538250i	$-0.982859\pi$
$347$	−17.5983	+	17.5983i	−0.944725	+	0.944725i	0.0538250	+	0.998550i	$0.482859\pi$
$348$	−2.28801	−	2.28801i	−0.122650	−	0.122650i
$349$			21.7045i			1.16181i	0.813970	+	0.580907i	$0.197302\pi$
$349$			21.7045i			1.16181i	−0.813970	+	0.580907i	$0.802698\pi$
$350$	−13.0262	+	20.4972i	−0.696280	+	1.09562i
$351$	1.72299			0.0919664
$352$	1.25773	+	1.25773i	0.0670374	+	0.0670374i
$353$	13.2550	+	13.2550i	0.705492	+	0.705492i	0.965584	−	0.260092i	$-0.0837528\pi$
$353$	13.2550	+	13.2550i	0.705492	+	0.705492i	−0.260092	+	0.965584i	$0.583753\pi$
$354$			10.4081i			0.553184i
$355$	−14.3357	−	26.0963i	−0.760862	−	1.38505i
$356$		−	3.44952i		−	0.182824i
$357$	−5.46154	+	5.46154i	−0.289055	+	0.289055i
$358$	−0.478090	−	0.478090i	−0.0252678	−	0.0252678i
$359$	9.12191			0.481436			0.240718	−	0.970595i	$-0.422617\pi$
$359$	9.12191			0.481436			0.240718	+	0.970595i	$0.422617\pi$
$360$	−2.14708	−	0.624526i	−0.113161	−	0.0329154i
$361$	−12.3694			−0.651023
$362$	12.6993	+	12.6993i	0.667458	+	0.667458i
$363$	−5.54104	−	5.54104i	−0.290829	−	0.290829i
$364$	−8.36895			−0.438652
$365$	−3.39762	+	11.6808i	−0.177840	+	0.611403i
$366$			14.4727i			0.756498i
$367$	14.3884	+	14.3884i	0.751067	+	0.751067i	0.974678	−	0.223611i	$-0.0717846\pi$
$367$	14.3884	+	14.3884i	0.751067	+	0.751067i	−0.223611	+	0.974678i	$0.571785\pi$
$368$	0.510395	−	4.76859i	0.0266062	−	0.248580i
$369$			10.2290i			0.532500i
$370$	0.490044	+	0.892058i	0.0254762	+	0.0463759i
$371$	44.1441			2.29185
$372$	−4.53812	+	4.53812i	−0.235290	+	0.235290i
$373$	2.31754	−	2.31754i	0.119998	−	0.119998i	−0.644558	−	0.764556i	$-0.722959\pi$
$373$	2.31754	−	2.31754i	0.119998	−	0.119998i	0.764556	+	0.644558i	$0.222959\pi$
$374$		−	2.82843i		−	0.146254i
$375$	7.38569	+	8.39355i	0.381395	+	0.433441i
$376$	12.8765			0.664057
$377$	−3.94222	+	3.94222i	−0.203035	+	0.203035i
$378$	3.43458	−	3.43458i	0.176656	−	0.176656i
$379$	29.3993			1.51014			0.755070	−	0.655644i	$-0.227603\pi$
$379$	29.3993			1.51014			0.755070	+	0.655644i	$0.227603\pi$
$380$	5.04652	−	2.77226i	0.258881	−	0.142214i
$381$	−11.7443			−0.601681
$382$	9.00732	+	9.00732i	0.460855	+	0.460855i
$383$	−8.99894	+	8.99894i	−0.459824	+	0.459824i	−0.898598	−	0.438773i	$-0.855413\pi$
$383$	−8.99894	+	8.99894i	−0.459824	+	0.459824i	0.438773	+	0.898598i	$0.355413\pi$
$384$			1.00000i			0.0510310i
$385$	18.5498	+	5.39563i	0.945388	+	0.274987i
$386$	2.60779			0.132733
$387$	−6.47101	−	6.47101i	−0.328940	−	0.328940i
$388$	−7.79375	+	7.79375i	−0.395668	+	0.395668i
$389$	28.2251			1.43107			0.715534	−	0.698578i	$-0.246183\pi$
$389$	28.2251			1.43107			0.715534	+	0.698578i	$0.246183\pi$
$390$	−1.07605	+	3.69940i	−0.0544880	+	0.187326i
$391$	−5.93578	+	4.78799i	−0.300185	+	0.242139i
$392$	−11.7328	+	11.7328i	−0.592594	+	0.592594i
$393$	8.95233	+	8.95233i	0.451585	+	0.451585i
$394$		−	17.2009i		−	0.866568i
$395$	7.06007	+	12.8519i	0.355230	+	0.646649i
$396$			1.77870i			0.0893831i
$397$	8.54761	−	8.54761i	0.428992	−	0.428992i	−0.459293	−	0.888285i	$-0.651897\pi$
$397$	8.54761	−	8.54761i	0.428992	−	0.428992i	0.888285	+	0.459293i	$0.151897\pi$
$398$	−3.79878	+	3.79878i	−0.190416	+	0.190416i
$399$			12.5073i			0.626147i
$400$	2.68182	−	4.21993i	0.134091	−	0.210997i
$401$			38.2744i			1.91133i	0.294451	+	0.955667i	$0.404863\pi$
$401$			38.2744i			1.91133i	−0.294451	+	0.955667i	$0.595137\pi$
$402$	−0.586681	−	0.586681i	−0.0292610	−	0.0292610i
$403$	7.81912	+	7.81912i	0.389498	+	0.389498i
$404$		−	0.109089i		−	0.00542736i
$405$	−1.07661	−	1.95982i	−0.0534972	−	0.0973844i
$406$			15.7167i			0.780007i
$407$	0.572485	−	0.572485i	0.0283770	−	0.0283770i
$408$	1.12442	−	1.12442i	0.0556669	−	0.0556669i
$409$			32.8990i			1.62675i	0.581738	+	0.813376i	$0.302373\pi$
$409$			32.8990i			1.62675i	−0.581738	+	0.813376i	$0.697627\pi$
$410$	−21.9625	−	6.38827i	−1.08465	−	0.315494i
$411$		−	1.47231i		−	0.0726238i
$412$	−0.451663	−	0.451663i	−0.0222519	−	0.0222519i
$413$	35.7474	−	35.7474i	1.75902	−	1.75902i
$414$	3.73281	−	3.01100i	0.183458	−	0.147983i
$415$	7.78726	+	2.26509i	0.382261	+	0.111189i
$416$	1.72299			0.0844765
$417$	−6.28997	+	6.28997i	−0.308021	+	0.308021i
$418$	−3.23864	−	3.23864i	−0.158407	−	0.158407i
$419$	−22.0511			−1.07727			−0.538634	−	0.842540i	$-0.681059\pi$
$419$	−22.0511			−1.07727			−0.538634	+	0.842540i	$0.681059\pi$
$420$	5.22934	+	9.51930i	0.255166	+	0.464495i
$421$		−	36.8446i		−	1.79570i	−0.440305	−	0.897848i	$-0.645130\pi$
$421$		−	36.8446i		−	1.79570i	0.440305	−	0.897848i	$-0.354870\pi$
$422$	−5.69442	+	5.69442i	−0.277200	+	0.277200i
$423$	9.10509	+	9.10509i	0.442705	+	0.442705i
$424$	−9.08835			−0.441369
$425$	−7.76044	+	1.72948i	−0.376437	+	0.0838921i
$426$	−13.3156			−0.645144
$427$	49.7075	−	49.7075i	2.40551	−	2.40551i
$428$	5.06879	−	5.06879i	0.245009	−	0.245009i
$429$	3.06468			0.147964
$430$	17.9351	−	9.85249i	0.864908	−	0.475129i
$431$		−	32.4060i		−	1.56094i	−0.625192	−	0.780471i	$-0.714979\pi$
$431$		−	32.4060i		−	1.56094i	0.625192	−	0.780471i	$-0.285021\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	1.69960	−	1.69960i	0.0816773	−	0.0816773i	−0.665088	−	0.746765i	$-0.731606\pi$
$433$	1.69960	−	1.69960i	0.0816773	−	0.0816773i	0.746765	+	0.665088i	$0.231606\pi$
$434$	31.1730			1.49635
$435$	6.94740	+	2.02080i	0.333102	+	0.0968901i
$436$			7.67531i			0.367581i
$437$	−1.31426	+	12.2791i	−0.0628695	+	0.587387i
$438$	3.84689	+	3.84689i	0.183812	+	0.183812i
$439$		−	33.8924i		−	1.61760i	−0.588085	−	0.808799i	$-0.700118\pi$
$439$		−	33.8924i		−	1.61760i	0.588085	−	0.808799i	$-0.299882\pi$
$440$	−3.81902	−	1.11085i	−0.182065	−	0.0529575i
$441$	−16.5926			−0.790125
$442$	−1.93736	−	1.93736i	−0.0921506	−	0.0921506i
$443$	2.44684	+	2.44684i	0.116253	+	0.116253i	0.762840	−	0.646587i	$-0.223804\pi$
$443$	2.44684	+	2.44684i	0.116253	+	0.116253i	−0.646587	+	0.762840i	$0.723804\pi$
$444$	0.455173			0.0216015
$445$	3.71379	+	6.76045i	0.176050	+	0.320476i
$446$	−11.3073			−0.535414
$447$	−8.01563	−	8.01563i	−0.379126	−	0.379126i
$448$	3.43458	−	3.43458i	0.162268	−	0.162268i
$449$			4.49307i			0.212041i	0.994364	+	0.106021i	$0.0338110\pi$
$449$			4.49307i			0.212041i	−0.994364	+	0.106021i	$0.966189\pi$
$450$	4.88028	−	1.08761i	0.230058	−	0.0512705i
$451$			18.1943i			0.856738i
$452$	−10.3565	−	10.3565i	−0.487127	−	0.487127i
$453$	6.18852	+	6.18852i	0.290762	+	0.290762i
$454$	−18.6070			−0.873268
$455$	16.4017	−	9.01010i	0.768922	−	0.422400i
$456$		−	2.57499i		−	0.120585i
$457$	1.48242	+	1.48242i	0.0693445	+	0.0693445i	0.740928	−	0.671584i	$-0.234386\pi$
$457$	1.48242	+	1.48242i	0.0693445	+	0.0693445i	−0.671584	+	0.740928i	$0.734386\pi$
$458$	−4.43976	+	4.43976i	−0.207456	+	0.207456i
$459$	1.59016			0.0742225
$460$	4.13364	+	9.89510i	0.192732	+	0.461362i
$461$	−0.0650793			−0.00303104			−0.00151552	−	0.999999i	$-0.500482\pi$
$461$	−0.0650793			−0.00303104			−0.00151552	+	0.999999i	$0.500482\pi$
$462$	6.10909	−	6.10909i	0.284221	−	0.284221i
$463$	−8.88726	−	8.88726i	−0.413026	−	0.413026i	0.469765	−	0.882791i	$-0.344338\pi$
$463$	−8.88726	−	8.88726i	−0.413026	−	0.413026i	−0.882791	+	0.469765i	$0.844338\pi$
$464$		−	3.23574i		−	0.150215i
$465$	4.00812	−	13.7797i	0.185872	−	0.639018i
$466$	−16.9343			−0.784465
$467$	4.47713	+	4.47713i	0.207177	+	0.207177i	0.803066	−	0.595889i	$-0.203200\pi$
$467$	4.47713	+	4.47713i	0.207177	+	0.207177i	−0.595889	+	0.803066i	$0.703200\pi$
$468$	1.21834	+	1.21834i	0.0563177	+	0.0563177i
$469$			4.03000i			0.186088i
$470$	−25.2358	+	13.8630i	−1.16404	+	0.639454i
$471$			20.0839i			0.925417i
$472$	−7.35964	+	7.35964i	−0.338755	+	0.338755i
$473$	−11.5100	−	11.5100i	−0.529230	−	0.529230i
$474$	6.55768			0.301204
$475$	−6.90565	+	10.8663i	−0.316853	+	0.498579i
$476$	−7.72378			−0.354019
$477$	−6.42643	−	6.42643i	−0.294246	−	0.294246i
$478$	−3.10650	−	3.10650i	−0.142088	−	0.142088i
$479$	−33.4775			−1.52962			−0.764812	−	0.644253i	$-0.777168\pi$
$479$	−33.4775			−1.52962			−0.764812	+	0.644253i	$0.777168\pi$
$480$	−1.07661	−	1.95982i	−0.0491403	−	0.0894533i
$481$		−	0.784258i		−	0.0357591i
$482$	5.26163	+	5.26163i	0.239661	+	0.239661i
$483$	−23.1621	−	2.47910i	−1.05391	−	0.112803i
$484$		−	7.83622i		−	0.356192i
$485$	6.88354	−	23.6652i	0.312566	−	1.07458i
$486$	−1.00000			−0.0453609
$487$	−0.188074	+	0.188074i	−0.00852246	+	0.00852246i	−0.711355	−	0.702833i	$-0.751918\pi$
$487$	−0.188074	+	0.188074i	−0.00852246	+	0.00852246i	0.702833	+	0.711355i	$0.251918\pi$
$488$	−10.2337	+	10.2337i	−0.463259	+	0.463259i
$489$			5.49090i			0.248307i
$490$	10.3625	−	35.6258i	0.468131	−	1.60941i
$491$	−15.9414			−0.719427			−0.359713	−	0.933063i	$-0.617126\pi$
$491$	−15.9414			−0.719427			−0.359713	+	0.933063i	$0.617126\pi$
$492$	−7.23299	+	7.23299i	−0.326088	+	0.326088i
$493$	−3.63831	+	3.63831i	−0.163861	+	0.163861i
$494$	−4.43667			−0.199615
$495$	−1.91497	−	3.48594i	−0.0860715	−	0.156681i
$496$	−6.41786			−0.288171
$497$	45.7335	+	45.7335i	2.05143	+	2.05143i
$498$	2.56461	−	2.56461i	0.114923	−	0.114923i
$499$		−	23.4075i		−	1.04786i	−0.851761	−	0.523931i	$-0.824465\pi$
$499$		−	23.4075i		−	1.04786i	0.851761	−	0.523931i	$-0.175535\pi$
$500$	−0.712667	+	11.1576i	−0.0318714	+	0.498983i
$501$	9.00881			0.402484
$502$	−9.03458	−	9.03458i	−0.403233	−	0.403233i
$503$	11.3295	−	11.3295i	0.505158	−	0.505158i	−0.407878	−	0.913036i	$-0.633731\pi$
$503$	11.3295	−	11.3295i	0.505158	−	0.505158i	0.913036	+	0.407878i	$0.133731\pi$
$504$	4.85722			0.216358
$505$	0.117446	+	0.213794i	0.00522627	+	0.00951372i
$506$	6.63956	−	5.35568i	0.295164	−	0.238089i
$507$	−7.09321	+	7.09321i	−0.315020	+	0.315020i
$508$	−8.30451	−	8.30451i	−0.368453	−	0.368453i
$509$		−	21.9841i		−	0.974429i	−0.873282	−	0.487214i	$-0.838013\pi$
$509$		−	21.9841i		−	0.974429i	0.873282	−	0.487214i	$-0.161987\pi$
$510$	−0.993099	+	3.41421i	−0.0439751	+	0.151184i
$511$		−	26.4249i		−	1.16897i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	1.82079	−	1.82079i	0.0803898	−	0.0803898i
$514$		−	17.3934i		−	0.767192i
$515$	1.37145	+	0.398915i	0.0604332	+	0.0175783i
$516$		−	9.15139i		−	0.402868i
$517$	16.1952	+	16.1952i	0.712266	+	0.712266i
$518$	−1.56333	−	1.56333i	−0.0686886	−	0.0686886i
$519$		−	9.34483i		−	0.410192i
$520$	−3.37676	+	1.85499i	−0.148081	+	0.0813466i
$521$		−	6.76810i		−	0.296516i	−0.988949	−	0.148258i	$-0.952633\pi$
$521$		−	6.76810i		−	0.296516i	0.988949	−	0.148258i	$-0.0473665\pi$
$522$	2.28801	−	2.28801i	0.100144	−	0.100144i
$523$	−12.2965	+	12.2965i	−0.537690	+	0.537690i	−0.922850	−	0.385160i	$-0.874146\pi$
$523$	−12.2965	+	12.2965i	−0.537690	+	0.537690i	0.385160	+	0.922850i	$0.374146\pi$
$524$			12.6605i			0.553077i
$525$	−20.4972	−	13.0262i	−0.894570	−	0.568510i
$526$		−	1.18613i		−	0.0517177i
$527$	7.21634	+	7.21634i	0.314349	+	0.314349i
$528$	−1.25773	+	1.25773i	−0.0547358	+	0.0547358i
$529$	−22.4790	−	4.86773i	−0.977348	−	0.211640i
$530$	17.8116	−	9.78461i	0.773685	−	0.425016i
$531$	−10.4081			−0.451673
$532$	−8.84399	+	8.84399i	−0.383435	+	0.383435i
$533$	12.4624	+	12.4624i	0.539805	+	0.539805i
$534$	3.44952			0.149275
$535$	−4.47682	+	15.3911i	−0.193550	+	0.665413i
$536$		−	0.829692i		−	0.0358372i
$537$	0.478090	−	0.478090i	0.0206311	−	0.0206311i
$538$	18.2770	+	18.2770i	0.787977	+	0.787977i
$539$	−29.5133			−1.27123
$540$	0.624526	−	2.14708i	0.0268753	−	0.0923958i
$541$	−11.2899			−0.485390			−0.242695	−	0.970103i	$-0.578031\pi$
$541$	−11.2899			−0.485390			−0.242695	+	0.970103i	$0.578031\pi$
$542$	22.6580	−	22.6580i	0.973246	−	0.973246i
$543$	−12.6993	+	12.6993i	−0.544977	+	0.544977i
$544$	1.59016			0.0681777
$545$	−8.26332	−	15.0423i	−0.353962	−	0.644339i
$546$		−	8.36895i		−	0.358158i
$547$	3.14045	−	3.14045i	0.134276	−	0.134276i	−0.636774	−	0.771050i	$-0.719732\pi$
$547$	3.14045	−	3.14045i	0.134276	−	0.134276i	0.771050	+	0.636774i	$0.219732\pi$
$548$	1.04108	−	1.04108i	0.0444728	−	0.0444728i
$549$	−14.4727			−0.617678
$550$	8.68056	−	1.93454i	0.370140	−	0.0824889i
$551$			8.33198i			0.354954i
$552$	4.76859	+	0.510395i	0.202965	+	0.0217238i
$553$	−22.5228	−	22.5228i	−0.957769	−	0.957769i
$554$		−	25.7972i		−	1.09602i
$555$	−0.892058	+	0.490044i	−0.0378658	+	0.0208012i
$556$	−8.89535			−0.377247
$557$	11.8068	+	11.8068i	0.500272	+	0.500272i	0.911522	−	0.411251i	$-0.134908\pi$
$557$	11.8068	+	11.8068i	0.500272	+	0.500272i	−0.411251	+	0.911522i	$0.634908\pi$
$558$	−4.53812	−	4.53812i	−0.192114	−	0.192114i
$559$	−15.7677			−0.666905
$560$	−3.03346	+	10.4289i	−0.128187	+	0.440700i
$561$	2.82843			0.119416
$562$	2.25912	+	2.25912i	0.0952954	+	0.0952954i
$563$	28.7684	−	28.7684i	1.21244	−	1.21244i	0.242221	−	0.970221i	$-0.422124\pi$
$563$	28.7684	−	28.7684i	1.21244	−	1.21244i	0.970221	−	0.242221i	$-0.0778758\pi$
$564$			12.8765i			0.542200i
$565$	31.4467	+	9.14696i	1.32297	+	0.384816i
$566$		−	31.9853i		−	1.34444i
$567$	3.43458	+	3.43458i	0.144239	+	0.144239i
$568$	−9.41557	−	9.41557i	−0.395068	−	0.395068i
$569$	21.2280			0.889925			0.444963	−	0.895549i	$-0.353217\pi$
$569$	21.2280			0.889925			0.444963	+	0.895549i	$0.353217\pi$
$570$	2.77226	+	5.04652i	0.116117	+	0.211375i
$571$			22.5582i			0.944030i	0.881591	+	0.472015i	$0.156473\pi$
$571$			22.5582i			0.944030i	−0.881591	+	0.472015i	$0.843527\pi$
$572$	2.16706	+	2.16706i	0.0906093	+	0.0906093i
$573$	−9.00732	+	9.00732i	−0.376286	+	0.376286i
$574$	49.6845			2.07379
$575$	−18.7544	−	14.9423i	−0.782111	−	0.623139i
$576$	−1.00000			−0.0416667
$577$	17.1528	−	17.1528i	0.714078	−	0.714078i	−0.253307	−	0.967386i	$-0.581518\pi$
$577$	17.1528	−	17.1528i	0.714078	−	0.714078i	0.967386	+	0.253307i	$0.0815184\pi$
$578$	10.2328	+	10.2328i	0.425629	+	0.425629i
$579$			2.60779i			0.108376i
$580$	3.48363	+	6.34148i	0.144650	+	0.263316i
$581$	−17.6167			−0.730863
$582$	−7.79375	−	7.79375i	−0.323061	−	0.323061i
$583$	−11.4307	−	11.4307i	−0.473412	−	0.473412i
$584$			5.44033i			0.225122i
$585$	−3.69940	−	1.07605i	−0.152951	−	0.0444893i
$586$			3.20275i			0.132304i
$587$	−18.6292	+	18.6292i	−0.768907	+	0.768907i	−0.977914	−	0.209007i	$-0.932977\pi$
$587$	−18.6292	+	18.6292i	−0.768907	+	0.768907i	0.209007	+	0.977914i	$0.432977\pi$
$588$	−11.7328	−	11.7328i	−0.483851	−	0.483851i
$589$	16.5259			0.680938
$590$	6.50013	−	22.3471i	0.267606	−	0.920014i
$591$	17.2009			0.707550
$592$	0.321856	+	0.321856i	0.0132282	+	0.0132282i
$593$	4.49108	+	4.49108i	0.184427	+	0.184427i	0.793282	−	0.608855i	$-0.208371\pi$
$593$	4.49108	+	4.49108i	0.184427	+	0.184427i	−0.608855	+	0.793282i	$0.708371\pi$
$594$	−1.77870			−0.0729810
$595$	15.1373	−	8.31550i	0.620567	−	0.340902i
$596$		−	11.3358i		−	0.464333i
$597$	−3.79878	−	3.79878i	−0.155474	−	0.155474i
$598$	0.879404	−	8.21624i	0.0359615	−	0.335987i
$599$		−	22.1900i		−	0.906660i	−0.891343	−	0.453330i	$-0.850236\pi$
$599$		−	22.1900i		−	0.906660i	0.891343	−	0.453330i	$-0.149764\pi$
$600$	4.21993	+	2.68182i	0.172278	+	0.109485i
$601$	−15.6107			−0.636776			−0.318388	−	0.947961i	$-0.603141\pi$
$601$	−15.6107			−0.636776			−0.318388	+	0.947961i	$0.603141\pi$
$602$	−31.4312	+	31.4312i	−1.28104	+	1.28104i
$603$	0.586681	−	0.586681i	0.0238915	−	0.0238915i
$604$			8.75190i			0.356110i
$605$	8.43656	+	15.3576i	0.342995	+	0.624376i
$606$	0.109089			0.00443142
$607$	1.06267	−	1.06267i	0.0431325	−	0.0431325i	−0.685212	−	0.728344i	$-0.740290\pi$
$607$	1.06267	−	1.06267i	0.0431325	−	0.0431325i	0.728344	+	0.685212i	$0.240290\pi$
$608$	1.82079	−	1.82079i	0.0738428	−	0.0738428i
$609$	−15.7167			−0.636873
$610$	9.03856	−	31.0740i	0.365960	−	1.25815i
$611$	22.1861			0.897555
$612$	1.12442	+	1.12442i	0.0454518	+	0.0454518i
$613$	14.1331	−	14.1331i	0.570829	−	0.570829i	−0.361531	−	0.932360i	$-0.617746\pi$
$613$	14.1331	−	14.1331i	0.570829	−	0.570829i	0.932360	+	0.361531i	$0.117746\pi$
$614$			9.00168i			0.363278i
$615$	6.38827	−	21.9625i	0.257600	−	0.885614i
$616$	8.63956			0.348098
$617$	19.3155	+	19.3155i	0.777614	+	0.777614i	0.979425	−	0.201811i	$-0.0646826\pi$
$617$	19.3155	+	19.3155i	0.777614	+	0.777614i	−0.201811	+	0.979425i	$0.564683\pi$
$618$	0.451663	−	0.451663i	0.0181686	−	0.0181686i
$619$	42.0979			1.69206			0.846028	−	0.533138i	$-0.178988\pi$
$619$	42.0979			1.69206			0.846028	+	0.533138i	$0.178988\pi$
$620$	12.5779	−	6.90954i	0.505140	−	0.277494i
$621$	3.01100	+	3.73281i	0.120827	+	0.149792i
$622$	−8.18796	+	8.18796i	−0.328307	+	0.328307i
$623$	−11.8476	−	11.8476i	−0.474666	−	0.474666i
$624$			1.72299i			0.0689748i
$625$	−10.6157	−	22.6342i	−0.424628	−	0.905368i
$626$		−	0.900397i		−	0.0359871i
$627$	3.23864	−	3.23864i	0.129339	−	0.129339i
$628$	−14.2015	+	14.2015i	−0.566700	+	0.566700i
$629$		−	0.723799i		−	0.0288598i
$630$	−9.51930	+	5.22934i	−0.379258	+	0.208342i
$631$			16.9667i			0.675434i	0.941248	+	0.337717i	$0.109655\pi$
$631$			16.9667i			0.675434i	−0.941248	+	0.337717i	$0.890345\pi$
$632$	4.63698	+	4.63698i	0.184449	+	0.184449i
$633$	−5.69442	−	5.69442i	−0.226333	−	0.226333i
$634$			23.8542i			0.947373i
$635$	25.2161	+	7.33465i	1.00067	+	0.291067i
$636$		−	9.08835i		−	0.360376i
$637$	−20.2154	+	20.2154i	−0.800964	+	0.800964i
$638$	4.06969	−	4.06969i	0.161121	−	0.161121i
$639$		−	13.3156i		−	0.526758i
$640$	0.624526	−	2.14708i	0.0246866	−	0.0848709i
$641$			5.44396i			0.215023i	0.994204	+	0.107512i	$0.0342883\pi$
$641$			5.44396i			0.215023i	−0.994204	+	0.107512i	$0.965712\pi$
$642$	5.06879	+	5.06879i	0.200049	+	0.200049i
$643$	−4.81939	+	4.81939i	−0.190058	+	0.190058i	−0.795721	−	0.605663i	$-0.792908\pi$
$643$	−4.81939	+	4.81939i	−0.190058	+	0.190058i	0.605663	+	0.795721i	$0.292908\pi$
$644$	−14.6251	−	18.1311i	−0.576310	−	0.714465i
$645$	9.85249	+	17.9351i	0.387941	+	0.706194i
$646$	−4.09465			−0.161102
$647$	−8.57433	+	8.57433i	−0.337092	+	0.337092i	−0.855272	−	0.518180i	$-0.826610\pi$
$647$	−8.57433	+	8.57433i	−0.337092	+	0.337092i	0.518180	+	0.855272i	$0.326610\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	−18.5129			−0.726696
$650$	4.62075	−	7.27090i	0.181241	−	0.285188i
$651$			31.1730i			1.22177i
$652$	−3.88265	+	3.88265i	−0.152056	+	0.152056i
$653$	11.9157	+	11.9157i	0.466297	+	0.466297i	0.900713	−	0.434416i	$-0.143045\pi$
$653$	11.9157	+	11.9157i	0.466297	+	0.466297i	−0.434416	+	0.900713i	$0.643045\pi$
$654$	−7.67531			−0.300128
$655$	−13.6304	−	24.8124i	−0.532585	−	0.969499i
$656$	−10.2290			−0.399375
$657$	−3.84689	+	3.84689i	−0.150082	+	0.150082i
$658$	44.2255	−	44.2255i	1.72409	−	1.72409i
$659$	−0.738479			−0.0287670			−0.0143835	−	0.999897i	$-0.504579\pi$
$659$	−0.738479			−0.0287670			−0.0143835	+	0.999897i	$0.504579\pi$
$660$	1.11085	−	3.81902i	0.0432396	−	0.148655i
$661$			8.03867i			0.312668i	0.987704	+	0.156334i	$0.0499676\pi$
$661$			8.03867i			0.312668i	−0.987704	+	0.156334i	$0.950032\pi$
$662$	6.71934	−	6.71934i	0.261155	−	0.261155i
$663$	1.93736	−	1.93736i	0.0752407	−	0.0752407i
$664$	3.62690			0.140751
$665$	7.81113	−	26.8542i	0.302902	−	1.04136i
$666$			0.455173i			0.0176376i
$667$	−15.4299	−	1.65150i	−0.597449	−	0.0639465i
$668$	6.37019	+	6.37019i	0.246470	+	0.246470i
$669$		−	11.3073i		−	0.437164i
$670$	0.893255	+	1.62605i	0.0345095	+	0.0628198i
$671$	−25.7426			−0.993780
$672$	3.43458	+	3.43458i	0.132492	+	0.132492i
$673$	−32.1774	−	32.1774i	−1.24035	−	1.24035i	−0.959857	−	0.280488i	$-0.909504\pi$
$673$	−32.1774	−	32.1774i	−1.24035	−	1.24035i	−0.280488	−	0.959857i	$-0.590496\pi$
$674$	−17.8020			−0.685708
$675$	1.08761	+	4.88028i	0.0418622	+	0.187842i
$676$	−10.0313			−0.385820
$677$	−12.9663	−	12.9663i	−0.498335	−	0.498335i	0.412585	−	0.910919i	$-0.364626\pi$
$677$	−12.9663	−	12.9663i	−0.498335	−	0.498335i	−0.910919	+	0.412585i	$0.864626\pi$
$678$	10.3565	−	10.3565i	0.397737	−	0.397737i
$679$			53.5365i			2.05454i
$680$	−3.11644	+	1.71199i	−0.119510	+	0.0656517i
$681$		−	18.6070i		−	0.713020i
$682$	−8.07196	−	8.07196i	−0.309091	−	0.309091i
$683$	27.7204	+	27.7204i	1.06069	+	1.06069i	0.998035	+	0.0626558i	$0.0199570\pi$
$683$	27.7204	+	27.7204i	1.06069	+	1.06069i	0.0626558	+	0.998035i	$0.480043\pi$
$684$	2.57499			0.0984571
$685$	−0.919497	+	3.16118i	−0.0351322	+	0.120782i
$686$			46.5936i			1.77895i
$687$	−4.43976	−	4.43976i	−0.169387	−	0.169387i
$688$	6.47101	−	6.47101i	0.246705	−	0.246705i
$689$	−15.6591			−0.596565
$690$	−9.89510	+	4.13364i	−0.376700	+	0.157365i
$691$	23.1360			0.880137			0.440068	−	0.897964i	$-0.354954\pi$
$691$	23.1360			0.880137			0.440068	+	0.897964i	$0.354954\pi$
$692$	6.60779	−	6.60779i	0.251191	−	0.251191i
$693$	6.10909	+	6.10909i	0.232065	+	0.232065i
$694$		−	24.8877i		−	0.944725i
$695$	17.4333	−	9.57683i	0.661284	−	0.363270i
$696$	3.23574			0.122650
$697$	11.5016	+	11.5016i	0.435656	+	0.435656i
$698$	−15.3474	−	15.3474i	−0.580907	−	0.580907i
$699$		−	16.9343i		−	0.640513i
$700$	−5.28277	−	23.7046i	−0.199670	−	0.895950i
$701$		−	27.0938i		−	1.02332i	−0.859189	−	0.511659i	$-0.829031\pi$
$701$		−	27.0938i		−	1.02332i	0.859189	−	0.511659i	$-0.170969\pi$
$702$	−1.21834	+	1.21834i	−0.0459832	+	0.0459832i
$703$	−0.828774	−	0.828774i	−0.0312578	−	0.0312578i
$704$	−1.77870			−0.0670374
$705$	−13.8630	−	25.2358i	−0.522112	−	0.950434i
$706$	−18.7454			−0.705492
$707$	−0.374673	−	0.374673i	−0.0140910	−	0.0140910i
$708$	−7.35964	−	7.35964i	−0.276592	−	0.276592i
$709$	−7.87786			−0.295859			−0.147930	−	0.988998i	$-0.547261\pi$
$709$	−7.87786			−0.295859			−0.147930	+	0.988998i	$0.547261\pi$
$710$	28.5897	+	8.31595i	1.07295	+	0.312092i
$711$			6.55768i			0.245932i
$712$	2.43918	+	2.43918i	0.0914121	+	0.0914121i
$713$	−3.27564	+	30.6042i	−0.122674	+	1.14614i
$714$		−	7.72378i		−	0.289055i
$715$	−6.58013	−	1.91398i	−0.246083	−	0.0715786i
$716$	0.676121			0.0252678
$717$	3.10650	−	3.10650i	0.116014	−	0.116014i
$718$	−6.45016	+	6.45016i	−0.240718	+	0.240718i
$719$		−	18.0186i		−	0.671980i	−0.941865	−	0.335990i	$-0.890929\pi$
$719$		−	18.0186i		−	0.671980i	0.941865	−	0.335990i	$-0.109071\pi$
$720$	1.95982	−	1.07661i	0.0730383	−	0.0401229i
$721$	−3.10255			−0.115545
$722$	8.74652	−	8.74652i	0.325512	−	0.325512i
$723$	−5.26163	+	5.26163i	−0.195682	+	0.195682i
$724$	−17.9595			−0.667458
$725$	−13.6546	−	8.67767i	−0.507119	−	0.322280i
$726$	7.83622			0.290829
$727$	−19.6163	−	19.6163i	−0.727530	−	0.727530i	0.242598	−	0.970127i	$-0.422001\pi$
$727$	−19.6163	−	19.6163i	−0.727530	−	0.727530i	−0.970127	+	0.242598i	$0.922001\pi$
$728$	5.91774	−	5.91774i	0.219326	−	0.219326i
$729$		−	1.00000i		−	0.0370370i
$730$	−5.85711	−	10.6621i	−0.216781	−	0.394621i
$731$	−14.5522			−0.538233
$732$	−10.2337	−	10.2337i	−0.378249	−	0.378249i
$733$	16.5747	−	16.5747i	0.612200	−	0.612200i	−0.331319	−	0.943519i	$-0.607494\pi$
$733$	16.5747	−	16.5747i	0.612200	−	0.612200i	0.943519	+	0.331319i	$0.107494\pi$
$734$	−20.3482			−0.751067
$735$	35.6258	+	10.3625i	1.31408	+	0.382228i
$736$	3.01100	+	3.73281i	0.110987	+	0.137593i
$737$	1.04353	−	1.04353i	0.0384389	−	0.0384389i
$738$	−7.23299	−	7.23299i	−0.266250	−	0.266250i
$739$		−	45.4934i		−	1.67350i	−0.547585	−	0.836750i	$-0.684453\pi$
$739$		−	45.4934i		−	1.67350i	0.547585	−	0.836750i	$-0.315547\pi$
$740$	−0.977294	−	0.284267i	−0.0359260	−	0.0104499i
$741$		−	4.43667i		−	0.162985i
$742$	−31.2146	+	31.2146i	−1.14592	+	1.14592i
$743$	−4.79938	+	4.79938i	−0.176072	+	0.176072i	−0.789641	−	0.613569i	$-0.789733\pi$
$743$	−4.79938	+	4.79938i	−0.176072	+	0.176072i	0.613569	+	0.789641i	$0.289733\pi$
$744$		−	6.41786i		−	0.235290i
$745$	12.2043	+	22.2162i	0.447129	+	0.813938i
$746$			3.27750i			0.119998i
$747$	2.56461	+	2.56461i	0.0938340	+	0.0938340i
$748$	2.00000	+	2.00000i	0.0731272	+	0.0731272i
$749$		−	34.8183i		−	1.27223i
$750$	−11.1576	−	0.712667i	−0.407418	−	0.0260229i
$751$			48.8764i			1.78352i	0.452505	+	0.891762i	$0.350531\pi$
$751$			48.8764i			1.78352i	−0.452505	+	0.891762i	$0.649469\pi$
$752$	−9.10509	+	9.10509i	−0.332029	+	0.332029i
$753$	9.03458	−	9.03458i	0.329238	−	0.329238i
$754$		−	5.57514i		−	0.203035i
$755$	−9.42238	−	17.1522i	−0.342916	−	0.624231i
$756$			4.85722i			0.176656i
$757$	−7.64728	−	7.64728i	−0.277945	−	0.277945i	0.554343	−	0.832288i	$-0.312970\pi$
$757$	−7.64728	−	7.64728i	−0.277945	−	0.277945i	−0.832288	+	0.554343i	$0.812970\pi$
$758$	−20.7884	+	20.7884i	−0.755070	+	0.755070i
$759$	5.35568	+	6.63956i	0.194399	+	0.241001i
$760$	−1.60815	+	5.52871i	−0.0583336	+	0.200547i
$761$	31.0826			1.12674			0.563372	−	0.826203i	$-0.309504\pi$
$761$	31.0826			1.12674			0.563372	+	0.826203i	$0.309504\pi$
$762$	8.30451	−	8.30451i	0.300841	−	0.300841i
$763$	26.3614	+	26.3614i	0.954348	+	0.954348i
$764$	−12.7383			−0.460855
$765$	−3.41421	−	0.993099i	−0.123441	−	0.0359056i
$766$		−	12.7264i		−	0.459824i
$767$	−12.6806	+	12.6806i	−0.457869	+	0.457869i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	−13.6176			−0.491062			−0.245531	−	0.969389i	$-0.578962\pi$
$769$	−13.6176			−0.491062			−0.245531	+	0.969389i	$0.578962\pi$
$770$	−16.9320	+	9.30144i	−0.610187	+	0.335201i
$771$	17.3934			0.626409
$772$	−1.84399	+	1.84399i	−0.0663665	+	0.0663665i
$773$	−6.20764	+	6.20764i	−0.223273	+	0.223273i	−0.809875	−	0.586602i	$-0.800465\pi$
$773$	−6.20764	+	6.20764i	−0.223273	+	0.223273i	0.586602	+	0.809875i	$0.300465\pi$
$774$	9.15139			0.328940
$775$	−17.2116	+	27.0830i	−0.618257	+	0.972849i
$776$		−	11.0220i		−	0.395668i
$777$	1.56333	−	1.56333i	0.0560840	−	0.0560840i
$778$	−19.9581	+	19.9581i	−0.715534	+	0.715534i
$779$	26.3395			0.943711
$780$	−1.85499	−	3.37676i	−0.0664192	−	0.120907i
$781$		−	23.6845i		−	0.847499i
$782$	0.811611	−	7.58285i	0.0290231	−	0.271162i
$783$	2.28801	+	2.28801i	0.0817669	+	0.0817669i
$784$		−	16.5926i		−	0.592594i
$785$	12.5429	−	43.1218i	0.447676	−	1.53908i
$786$	−12.6605			−0.451585
$787$	−6.14851	−	6.14851i	−0.219171	−	0.219171i	0.588978	−	0.808149i	$-0.299530\pi$
$787$	−6.14851	−	6.14851i	−0.219171	−	0.219171i	−0.808149	+	0.588978i	$0.799530\pi$
$788$	12.1629	+	12.1629i	0.433284	+	0.433284i
$789$	1.18613			0.0422274
$790$	−14.0799	−	4.09544i	−0.500940	−	0.145709i
$791$	−71.1401			−2.52945
$792$	−1.25773	−	1.25773i	−0.0446916	−	0.0446916i
$793$	−17.6326	+	17.6326i	−0.626152	+	0.626152i
$794$			12.0881i			0.428992i
$795$	9.78461	+	17.8116i	0.347024	+	0.631711i
$796$		−	5.37229i		−	0.190416i
$797$	−16.7828	−	16.7828i	−0.594476	−	0.594476i	0.344361	−	0.938837i	$-0.388096\pi$
$797$	−16.7828	−	16.7828i	−0.594476	−	0.594476i	−0.938837	+	0.344361i	$0.888096\pi$
$798$	−8.84399	−	8.84399i	−0.313074	−	0.313074i
$799$	20.4758			0.724382
$800$	1.08761	+	4.88028i	0.0384529	+	0.172544i
$801$			3.44952i			0.121883i
$802$	−27.0641	−	27.0641i	−0.955667	−	0.955667i
$803$	−6.84247	+	6.84247i	−0.241466	+	0.241466i
$804$	0.829692			0.0292610
$805$	48.1828	+	19.7882i	1.69822	+	0.697442i
$806$	−11.0579			−0.389498
$807$	−18.2770	+	18.2770i	−0.643381	+	0.643381i
$808$	0.0771372	+	0.0771372i	0.00271368	+	0.00271368i
$809$		−	17.9358i		−	0.630588i	−0.948994	−	0.315294i	$-0.897897\pi$
$809$		−	17.9358i		−	0.630588i	0.948994	−	0.315294i	$-0.102103\pi$
$810$	2.14708	+	0.624526i	0.0754408	+	0.0219436i
$811$	43.1441			1.51500			0.757498	−	0.652838i	$-0.226422\pi$
$811$	43.1441			1.51500			0.757498	+	0.652838i	$0.226422\pi$
$812$	−11.1134	−	11.1134i	−0.390004	−	0.390004i
$813$	22.6580	+	22.6580i	0.794652	+	0.794652i
$814$			0.809617i			0.0283770i
$815$	3.42921	−	11.7894i	0.120120	−	0.412965i
$816$			1.59016i			0.0556669i
$817$	−16.6628	+	16.6628i	−0.582956	+	0.582956i
$818$	−23.2631	−	23.2631i	−0.813376	−	0.813376i
$819$	8.36895			0.292435
$820$	20.0470	−	11.0126i	0.700072	−	0.384578i
$821$	5.77627			0.201593			0.100797	−	0.994907i	$-0.467861\pi$
$821$	5.77627			0.201593			0.100797	+	0.994907i	$0.467861\pi$
$822$	1.04108	+	1.04108i	0.0363119	+	0.0363119i
$823$	−27.2467	−	27.2467i	−0.949762	−	0.949762i	0.0490353	−	0.998797i	$-0.484385\pi$
$823$	−27.2467	−	27.2467i	−0.949762	−	0.949762i	−0.998797	+	0.0490353i	$0.984385\pi$
$824$	0.638749			0.0222519
$825$	1.93454	+	8.68056i	0.0673519	+	0.302218i
$826$			50.5545i			1.75902i
$827$	12.7737	+	12.7737i	0.444186	+	0.444186i	0.893416	−	0.449230i	$-0.148302\pi$
$827$	12.7737	+	12.7737i	0.444186	+	0.444186i	−0.449230	+	0.893416i	$0.648302\pi$
$828$	−0.510395	+	4.76859i	−0.0177374	+	0.165720i
$829$		−	3.68926i		−	0.128133i	−0.997946	−	0.0640667i	$-0.979593\pi$
$829$		−	3.68926i		−	0.128133i	0.997946	−	0.0640667i	$-0.0204070\pi$
$830$	−7.10809	+	3.90476i	−0.246725	+	0.135536i
$831$	25.7972			0.894896
$832$	−1.21834	+	1.21834i	−0.0422382	+	0.0422382i
$833$	−18.6570	+	18.6570i	−0.646427	+	0.646427i
$834$		−	8.89535i		−	0.308021i
$835$	−19.3427	−	5.62624i	−0.669381	−	0.194704i
$836$	4.58013			0.158407
$837$	4.53812	−	4.53812i	0.156860	−	0.156860i
$838$	15.5925	−	15.5925i	0.538634	−	0.538634i
$839$	−36.6605			−1.26566			−0.632831	−	0.774290i	$-0.718107\pi$
$839$	−36.6605			−1.26566			−0.632831	+	0.774290i	$0.718107\pi$
$840$	−10.4289	−	3.03346i	−0.359830	−	0.104664i
$841$	18.5300			0.638965
$842$	26.0531	+	26.0531i	0.897848	+	0.897848i
$843$	−2.25912	+	2.25912i	−0.0778084	+	0.0778084i
$844$		−	8.05312i		−	0.277200i
$845$	19.6596	−	10.7998i	0.676311	−	0.371525i
$846$	−12.8765			−0.442705
$847$	−26.9141	−	26.9141i	−0.924779	−	0.924779i
$848$	6.42643	−	6.42643i	0.220685	−	0.220685i
$849$	31.9853			1.09773
$850$	4.26453	−	6.71039i	0.146272	−	0.230164i
$851$	1.69907	−	1.37053i	0.0582435	−	0.0469810i
$852$	9.41557	−	9.41557i	0.322572	−	0.322572i
$853$	25.4890	+	25.4890i	0.872727	+	0.872727i	0.992769	−	0.120042i	$-0.0383029\pi$
$853$	25.4890	+	25.4890i	0.872727	+	0.872727i	−0.120042	+	0.992769i	$0.538303\pi$
$854$			70.2970i			2.40551i
$855$	−5.04652	+	2.77226i	−0.172587	+	0.0948092i
$856$			7.16835i			0.245009i
$857$	29.0469	−	29.0469i	0.992223	−	0.992223i	−0.00774669	−	0.999970i	$-0.502466\pi$
$857$	29.0469	−	29.0469i	0.992223	−	0.992223i	0.999970	+	0.00774669i	$0.00246587\pi$
$858$	−2.16706	+	2.16706i	−0.0739822	+	0.0739822i
$859$			50.9359i			1.73791i	0.494892	+	0.868954i	$0.335208\pi$
$859$			50.9359i			1.73791i	−0.494892	+	0.868954i	$0.664792\pi$
$860$	−5.71528	+	19.6488i	−0.194890	+	0.670019i
$861$			49.6845i			1.69324i
$862$	22.9145	+	22.9145i	0.780471	+	0.780471i
$863$	4.14395	+	4.14395i	0.141062	+	0.141062i	0.774111	−	0.633050i	$-0.218197\pi$
$863$	4.14395	+	4.14395i	0.141062	+	0.141062i	−0.633050	+	0.774111i	$0.718197\pi$
$864$		−	1.00000i		−	0.0340207i
$865$	−5.83609	+	20.0641i	−0.198433	+	0.682201i
$866$			2.40359i			0.0816773i
$867$	−10.2328	+	10.2328i	−0.347524	+	0.347524i
$868$	−22.0426	+	22.0426i	−0.748176	+	0.748176i
$869$			11.6642i			0.395679i
$870$	−6.34148	+	3.48363i	−0.214996	+	0.118106i
$871$		−	1.42955i		−	0.0484385i
$872$	−5.42726	−	5.42726i	−0.183790	−	0.183790i
$873$	7.79375	−	7.79375i	0.263778	−	0.263778i
$874$	−7.75329	−	9.61193i	−0.262259	−	0.325128i
$875$	35.8739	+	40.7694i	1.21276	+	1.37826i
$876$	−5.44033			−0.183812
$877$	−16.3814	+	16.3814i	−0.553162	+	0.553162i	−0.927352	−	0.374190i	$-0.877921\pi$
$877$	−16.3814	+	16.3814i	−0.553162	+	0.553162i	0.374190	+	0.927352i	$0.377921\pi$
$878$	23.9656	+	23.9656i	0.808799	+	0.808799i
$879$	−3.20275			−0.108026
$880$	3.48594	−	1.91497i	0.117511	−	0.0645536i
$881$		−	47.5503i		−	1.60201i	−0.598657	−	0.801005i	$-0.704299\pi$
$881$		−	47.5503i		−	1.60201i	0.598657	−	0.801005i	$-0.295701\pi$
$882$	11.7328	−	11.7328i	0.395063	−	0.395063i
$883$	15.3437	+	15.3437i	0.516357	+	0.516357i	0.916467	−	0.400110i	$-0.131028\pi$
$883$	15.3437	+	15.3437i	0.516357	+	0.516357i	−0.400110	+	0.916467i	$0.631028\pi$
$884$	2.73983			0.0921506
$885$	22.3471	+	6.50013i	0.751188	+	0.218500i
$886$	−3.46036			−0.116253
$887$	−19.8747	+	19.8747i	−0.667327	+	0.667327i	−0.957096	−	0.289770i	$-0.906421\pi$
$887$	−19.8747	+	19.8747i	−0.667327	+	0.667327i	0.289770	+	0.957096i	$0.406421\pi$
$888$	−0.321856	+	0.321856i	−0.0108008	+	0.0108008i
$889$	−57.0449			−1.91323
$890$	−7.40641	−	2.15431i	−0.248263	−	0.0722128i
$891$		−	1.77870i		−	0.0595888i
$892$	7.99544	−	7.99544i	0.267707	−	0.267707i
$893$	23.4455	−	23.4455i	0.784573	−	0.784573i
$894$	11.3358			0.379126
$895$	−1.32508	+	0.727919i	−0.0442925	+	0.0243317i
$896$			4.85722i			0.162268i
$897$	8.21624	+	0.879404i	0.274332	+	0.0293625i
$898$	−3.17708	−	3.17708i	−0.106021	−	0.106021i
$899$			20.7665i			0.692603i
$900$	−2.68182	+	4.21993i	−0.0893940	+	0.140664i
$901$	−14.4520			−0.481465
$902$	−12.8653	−	12.8653i	−0.428369	−	0.428369i
$903$	−31.4312	−	31.4312i	−1.04596	−	1.04596i
$904$	14.6462			0.487127
$905$	35.1974	−	19.3353i	1.17000	−	0.642729i
$906$	−8.75190			−0.290762
$907$	−28.1205	−	28.1205i	−0.933726	−	0.933726i	0.0642101	−	0.997936i	$-0.479547\pi$
$907$	−28.1205	−	28.1205i	−0.933726	−	0.933726i	−0.997936	+	0.0642101i	$0.979547\pi$
$908$	13.1571	−	13.1571i	0.436634	−	0.436634i
$909$			0.109089i			0.00361824i
$910$	−5.22662	+	17.9688i	−0.173261	+	0.595661i
$911$			51.4776i			1.70553i	0.522296	+	0.852764i	$0.325075\pi$
$911$			51.4776i			1.70553i	−0.522296	+	0.852764i	$0.674925\pi$
$912$	1.82079	+	1.82079i	0.0602924	+	0.0602924i
$913$	4.56167	+	4.56167i	0.150969	+	0.150969i
$914$	−2.09645			−0.0693445
$915$	31.0740	+	9.03856i	1.02728	+	0.298805i
$916$		−	6.27877i		−	0.207456i
$917$	43.4835	+	43.4835i	1.43595	+	1.43595i
$918$	−1.12442	+	1.12442i	−0.0371112	+	0.0371112i
$919$	52.5111			1.73218			0.866090	−	0.499888i	$-0.166625\pi$
$919$	52.5111			1.73218			0.866090	+	0.499888i	$0.166625\pi$
$920$	−9.91982	−	4.07397i	−0.327047	−	0.134315i
$921$	−9.00168			−0.296616
$922$	0.0460180	−	0.0460180i	0.00151552	−	0.00151552i
$923$	−16.2229	−	16.2229i	−0.533984	−	0.533984i
$924$			8.63956i			0.284221i
$925$	2.22137	−	0.495051i	0.0730381	−	0.0162772i
$926$	12.5685			0.413026
$927$	0.451663	+	0.451663i	0.0148346	+	0.0148346i
$928$	2.28801	+	2.28801i	0.0751077	+	0.0751077i
$929$		−	10.7225i		−	0.351793i	−0.984409	−	0.175897i	$-0.943718\pi$
$929$		−	10.7225i		−	0.351793i	0.984409	−	0.175897i	$-0.0562825\pi$
$930$	6.90954	+	12.5779i	0.226573	+	0.412445i
$931$			42.7258i			1.40028i
$932$	11.9743	−	11.9743i	0.392232	−	0.392232i
$933$	−8.18796	−	8.18796i	−0.268062	−	0.268062i
$934$	−6.33162			−0.207177
$935$	−6.07287	−	1.76643i	−0.198604	−	0.0577683i
$936$	−1.72299			−0.0563177
$937$	6.98650	+	6.98650i	0.228239	+	0.228239i	0.811957	−	0.583718i	$-0.198403\pi$
$937$	6.98650	+	6.98650i	0.228239	+	0.228239i	−0.583718	+	0.811957i	$0.698403\pi$
$938$	−2.84964	−	2.84964i	−0.0930440	−	0.0930440i
$939$	0.900397			0.0293834
$940$	8.04174	−	27.6470i	0.262293	−	0.901746i
$941$		−	29.7146i		−	0.968667i	−0.874883	−	0.484333i	$-0.839062\pi$
$941$		−	29.7146i		−	0.968667i	0.874883	−	0.484333i	$-0.160938\pi$
$942$	−14.2015	−	14.2015i	−0.462708	−	0.462708i
$943$	−5.22082	+	48.7779i	−0.170013	+	1.58843i
$944$		−	10.4081i		−	0.338755i
$945$	−5.22934	−	9.51930i	−0.170110	−	0.309663i
$946$	16.2776			0.529230
$947$	18.3257	−	18.3257i	0.595506	−	0.595506i	−0.343608	−	0.939113i	$-0.611649\pi$
$947$	18.3257	−	18.3257i	0.595506	−	0.595506i	0.939113	+	0.343608i	$0.111649\pi$
$948$	−4.63698	+	4.63698i	−0.150602	+	0.150602i
$949$			9.37362i			0.304281i
$950$	−2.80059	−	12.5666i	−0.0908630	−	0.407716i
$951$	−23.8542			−0.773527
$952$	5.46154	−	5.46154i	0.177009	−	0.177009i
$953$	−13.5507	+	13.5507i	−0.438952	+	0.438952i	−0.891659	−	0.452707i	$-0.850458\pi$
$953$	−13.5507	+	13.5507i	−0.438952	+	0.438952i	0.452707	+	0.891659i	$0.350458\pi$
$954$	9.08835			0.294246
$955$	24.9648	−	13.7142i	0.807841	−	0.443780i
$956$	4.39325			0.142088
$957$	4.06969	+	4.06969i	0.131555	+	0.131555i
$958$	23.6721	−	23.6721i	0.764812	−	0.764812i
$959$		−	7.15135i		−	0.230929i
$960$	2.14708	+	0.624526i	0.0692968	+	0.0201565i
$961$	10.1890			0.328677
$962$	0.554554	+	0.554554i	0.0178795	+	0.0178795i
$963$	−5.06879	+	5.06879i	−0.163339	+	0.163339i
$964$	−7.44107			−0.239661
$965$	1.62863	−	5.59914i	0.0524276	−	0.180243i
$966$	18.1311	−	14.6251i	0.583358	−	0.470555i
$967$	40.6269	−	40.6269i	1.30647	−	1.30647i	0.382529	−	0.923943i	$-0.375053\pi$
$967$	40.6269	−	40.6269i	1.30647	−	1.30647i	0.923943	−	0.382529i	$-0.124947\pi$
$968$	5.54104	+	5.54104i	0.178096	+	0.178096i
$969$		−	4.09465i		−	0.131539i
$970$	11.8664	+	21.6012i	0.381008	+	0.693574i
$971$		−	35.7932i		−	1.14866i	−0.818624	−	0.574330i	$-0.805263\pi$
$971$		−	35.7932i		−	1.14866i	0.818624	−	0.574330i	$-0.194737\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	−30.5518	+	30.5518i	−0.979445	+	0.979445i
$974$		−	0.265977i		−	0.00852246i
$975$	7.27090	+	4.62075i	0.232855	+	0.147982i
$976$		−	14.4727i		−	0.463259i
$977$	−7.74791	−	7.74791i	−0.247878	−	0.247878i	0.572221	−	0.820099i	$-0.306082\pi$
$977$	−7.74791	−	7.74791i	−0.247878	−	0.247878i	−0.820099	+	0.572221i	$0.806082\pi$
$978$	−3.88265	−	3.88265i	−0.124154	−	0.124154i
$979$			6.13567i			0.196097i
$980$	17.8638	+	32.5186i	0.570638	+	1.03877i
$981$		−	7.67531i		−	0.245054i
$982$	11.2723	−	11.2723i	0.359713	−	0.359713i
$983$	−25.9694	+	25.9694i	−0.828296	+	0.828296i	−0.987281	−	0.158985i	$-0.949178\pi$
$983$	−25.9694	+	25.9694i	−0.828296	+	0.828296i	0.158985	+	0.987281i	$0.449178\pi$
$984$		−	10.2290i		−	0.326088i
$985$	−36.9317	−	10.7424i	−1.17674	−	0.342281i
$986$		−	5.14535i		−	0.163861i
$987$	44.2255	+	44.2255i	1.40771	+	1.40771i
$988$	3.13720	−	3.13720i	0.0998077	−	0.0998077i
$989$	−27.5549	−	34.1604i	−0.876194	−	1.08624i
$990$	3.81902	+	1.11085i	0.121376	+	0.0353050i
$991$	−52.9168			−1.68096			−0.840478	−	0.541846i	$-0.817726\pi$
$991$	−52.9168			−1.68096			−0.840478	+	0.541846i	$0.817726\pi$
$992$	4.53812	−	4.53812i	0.144085	−	0.144085i
$993$	6.71934	+	6.71934i	0.213232	+	0.213232i
$994$	−64.6770			−2.05143
$995$	5.78386	+	10.5287i	0.183361	+	0.333784i
$996$			3.62690i			0.114923i
$997$	20.1714	−	20.1714i	0.638835	−	0.638835i	−0.311433	−	0.950268i	$-0.600809\pi$
$997$	20.1714	−	20.1714i	0.638835	−	0.638835i	0.950268	+	0.311433i	$0.100809\pi$
$998$	16.5516	+	16.5516i	0.523931	+	0.523931i
$999$	−0.455173			−0.0144010

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.j.b.643.5	yes	24
5.2	odd	4	inner	690.2.j.b.367.2	✓	24
23.22	odd	2	inner	690.2.j.b.643.2	yes	24
115.22	even	4	inner	690.2.j.b.367.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.j.b.367.2	✓	24	5.2	odd	4	inner
690.2.j.b.367.5	yes	24	115.22	even	4	inner
690.2.j.b.643.2	yes	24	23.22	odd	2	inner
690.2.j.b.643.5	yes	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(1.07661 + 1.95982i) q^{5} +1.00000 q^{6} +(-3.43458 - 3.43458i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(1.07661 + 1.95982i) q^{5} +1.00000 q^{6} +(-3.43458 - 3.43458i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(-2.14708 - 0.624526i) q^{10} +1.77870i q^{11} +(-0.707107 + 0.707107i) q^{12} +(1.21834 + 1.21834i) q^{13} +4.85722 q^{14} +(0.624526 - 2.14708i) q^{15} -1.00000 q^{16} +(1.12442 + 1.12442i) q^{17} +(-0.707107 - 0.707107i) q^{18} +2.57499 q^{19} +(1.95982 - 1.07661i) q^{20} +4.85722i q^{21} +(-1.25773 - 1.25773i) q^{22} +(-0.510395 + 4.76859i) q^{23} -1.00000i q^{24} +(-2.68182 + 4.21993i) q^{25} -1.72299 q^{26} +(0.707107 - 0.707107i) q^{27} +(-3.43458 + 3.43458i) q^{28} +3.23574i q^{29} +(1.07661 + 1.95982i) q^{30} +6.41786 q^{31} +(0.707107 - 0.707107i) q^{32} +(1.25773 - 1.25773i) q^{33} -1.59016 q^{34} +(3.03346 - 10.4289i) q^{35} +1.00000 q^{36} +(-0.321856 - 0.321856i) q^{37} +(-1.82079 + 1.82079i) q^{38} -1.72299i q^{39} +(-0.624526 + 2.14708i) q^{40} +10.2290 q^{41} +(-3.43458 - 3.43458i) q^{42} +(-6.47101 + 6.47101i) q^{43} +1.77870 q^{44} +(-1.95982 + 1.07661i) q^{45} +(-3.01100 - 3.73281i) q^{46} +(9.10509 - 9.10509i) q^{47} +(0.707107 + 0.707107i) q^{48} +16.5926i q^{49} +(-1.08761 - 4.88028i) q^{50} -1.59016i q^{51} +(1.21834 - 1.21834i) q^{52} +(-6.42643 + 6.42643i) q^{53} +1.00000i q^{54} +(-3.48594 + 1.91497i) q^{55} -4.85722i q^{56} +(-1.82079 - 1.82079i) q^{57} +(-2.28801 - 2.28801i) q^{58} +10.4081i q^{59} +(-2.14708 - 0.624526i) q^{60} +14.4727i q^{61} +(-4.53812 + 4.53812i) q^{62} +(3.43458 - 3.43458i) q^{63} +1.00000i q^{64} +(-1.07605 + 3.69940i) q^{65} +1.77870i q^{66} +(-0.586681 - 0.586681i) q^{67} +(1.12442 - 1.12442i) q^{68} +(3.73281 - 3.01100i) q^{69} +(5.22934 + 9.51930i) q^{70} -13.3156 q^{71} +(-0.707107 + 0.707107i) q^{72} +(3.84689 + 3.84689i) q^{73} +0.455173 q^{74} +(4.88028 - 1.08761i) q^{75} -2.57499i q^{76} +(6.10909 - 6.10909i) q^{77} +(1.21834 + 1.21834i) q^{78} +6.55768 q^{79} +(-1.07661 - 1.95982i) q^{80} -1.00000 q^{81} +(-7.23299 + 7.23299i) q^{82} +(2.56461 - 2.56461i) q^{83} +4.85722 q^{84} +(-0.993099 + 3.41421i) q^{85} -9.15139i q^{86} +(2.28801 - 2.28801i) q^{87} +(-1.25773 + 1.25773i) q^{88} +3.44952 q^{89} +(0.624526 - 2.14708i) q^{90} -8.36895i q^{91} +(4.76859 + 0.510395i) q^{92} +(-4.53812 - 4.53812i) q^{93} +12.8765i q^{94} +(2.77226 + 5.04652i) q^{95} -1.00000 q^{96} +(-7.79375 - 7.79375i) q^{97} +(-11.7328 - 11.7328i) q^{98} -1.77870 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{6}+O(q^{10}) \) 24 * q + 24 * q^6	\( 24 q + 24 q^{6} + 16 q^{13} - 24 q^{16} + 16 q^{23} - 16 q^{25} + 16 q^{31} + 24 q^{36} + 8 q^{46} + 40 q^{47} - 8 q^{50} + 16 q^{52} - 56 q^{55} - 16 q^{58} - 8 q^{62} + 32 q^{70} + 64 q^{71} - 16 q^{73} + 32 q^{75} + 16 q^{77} + 16 q^{78} - 24 q^{81} + 24 q^{82} - 48 q^{85} + 16 q^{87} + 16 q^{92} - 8 q^{93} + 24 q^{95} - 24 q^{96}+O(q^{100}) \) 24 * q + 24 * q^6 + 16 * q^13 - 24 * q^16 + 16 * q^23 - 16 * q^25 + 16 * q^31 + 24 * q^36 + 8 * q^46 + 40 * q^47 - 8 * q^50 + 16 * q^52 - 56 * q^55 - 16 * q^58 - 8 * q^62 + 32 * q^70 + 64 * q^71 - 16 * q^73 + 32 * q^75 + 16 * q^77 + 16 * q^78 - 24 * q^81 + 24 * q^82 - 48 * q^85 + 16 * q^87 + 16 * q^92 - 8 * q^93 + 24 * q^95 - 24 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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