LMFDB - Embedded newform 690.2.j.a.643.1

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			643.1
Character	$\chi$	$=$	690.643
Dual form			690.2.j.a.367.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(-2.13084 - 0.677875i) q^{5} -1.00000 q^{6} +(-1.05927 - 1.05927i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(-2.13084 - 0.677875i) q^{5} -1.00000 q^{6} +(-1.05927 - 1.05927i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(1.98606 - 1.02740i) q^{10} -2.05480i q^{11} +(0.707107 - 0.707107i) q^{12} +(2.75307 + 2.75307i) q^{13} +1.49804 q^{14} +(-1.02740 - 1.98606i) q^{15} -1.00000 q^{16} +(4.76291 + 4.76291i) q^{17} +(-0.707107 - 0.707107i) q^{18} +1.85358 q^{19} +(-0.677875 + 2.13084i) q^{20} -1.49804i q^{21} +(1.45297 + 1.45297i) q^{22} +(-3.76456 + 2.97121i) q^{23} +1.00000i q^{24} +(4.08097 + 2.88889i) q^{25} -3.89342 q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.05927 + 1.05927i) q^{28} +7.96345i q^{29} +(2.13084 + 0.677875i) q^{30} +10.3127 q^{31} +(0.707107 - 0.707107i) q^{32} +(1.45297 - 1.45297i) q^{33} -6.73577 q^{34} +(1.53909 + 2.97520i) q^{35} +1.00000 q^{36} +(2.66303 + 2.66303i) q^{37} +(-1.31068 + 1.31068i) q^{38} +3.89342i q^{39} +(-1.02740 - 1.98606i) q^{40} -8.60620 q^{41} +(1.05927 + 1.05927i) q^{42} +(1.45989 - 1.45989i) q^{43} -2.05480 q^{44} +(0.677875 - 2.13084i) q^{45} +(0.560984 - 4.76291i) q^{46} +(1.89984 - 1.89984i) q^{47} +(-0.707107 - 0.707107i) q^{48} -4.75588i q^{49} +(-4.92843 + 0.842929i) q^{50} +6.73577i q^{51} +(2.75307 - 2.75307i) q^{52} +(3.57151 - 3.57151i) q^{53} -1.00000i q^{54} +(-1.39290 + 4.37846i) q^{55} -1.49804i q^{56} +(1.31068 + 1.31068i) q^{57} +(-5.63101 - 5.63101i) q^{58} +3.82027i q^{59} +(-1.98606 + 1.02740i) q^{60} -2.76364i q^{61} +(-7.29215 + 7.29215i) q^{62} +(1.05927 - 1.05927i) q^{63} +1.00000i q^{64} +(-4.00011 - 7.73258i) q^{65} +2.05480i q^{66} +(7.21961 + 7.21961i) q^{67} +(4.76291 - 4.76291i) q^{68} +(-4.76291 - 0.560984i) q^{69} +(-3.19208 - 1.01548i) q^{70} +0.620733 q^{71} +(-0.707107 + 0.707107i) q^{72} +(4.77136 + 4.77136i) q^{73} -3.76610 q^{74} +(0.842929 + 4.92843i) q^{75} -1.85358i q^{76} +(-2.17660 + 2.17660i) q^{77} +(-2.75307 - 2.75307i) q^{78} -16.3891 q^{79} +(2.13084 + 0.677875i) q^{80} -1.00000 q^{81} +(6.08551 - 6.08551i) q^{82} +(5.71805 - 5.71805i) q^{83} -1.49804 q^{84} +(-6.92035 - 13.3777i) q^{85} +2.06459i q^{86} +(-5.63101 + 5.63101i) q^{87} +(1.45297 - 1.45297i) q^{88} +0.705848 q^{89} +(1.02740 + 1.98606i) q^{90} -5.83250i q^{91} +(2.97121 + 3.76456i) q^{92} +(7.29215 + 7.29215i) q^{93} +2.68677i q^{94} +(-3.94968 - 1.25650i) q^{95} +1.00000 q^{96} +(0.564967 + 0.564967i) q^{97} +(3.36292 + 3.36292i) q^{98} +2.05480 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} - 24 q^{16} - 8 q^{23} - 16 q^{25} - 16 q^{26} + 16 q^{31} - 16 q^{35} + 24 q^{36} - 8 q^{46} - 8 q^{47} + 24 q^{50} + 24 q^{55} + 16 q^{58} - 56 q^{62} - 32 q^{70} - 16 q^{71} - 48 q^{73} - 24 q^{81} + 24 q^{82} + 16 q^{87} - 8 q^{92} + 56 q^{93} + 24 q^{95} + 24 q^{96} - 32 q^{98}+O(q^{100}) $ 24 * q - 24 * q^6 - 24 * q^16 - 8 * q^23 - 16 * q^25 - 16 * q^26 + 16 * q^31 - 16 * q^35 + 24 * q^36 - 8 * q^46 - 8 * q^47 + 24 * q^50 + 24 * q^55 + 16 * q^58 - 56 * q^62 - 32 * q^70 - 16 * q^71 - 48 * q^73 - 24 * q^81 + 24 * q^82 + 16 * q^87 - 8 * q^92 + 56 * q^93 + 24 * q^95 + 24 * q^96 - 32 * q^98

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
$5$	−2.13084	−	0.677875i	−0.952941	−	0.303155i
$5$	−2.13084	−	0.677875i	−0.952941	−	0.303155i
$6$	−1.00000			−0.408248
$7$	−1.05927	−	1.05927i	−0.400368	−	0.400368i	0.477995	−	0.878363i	$-0.341364\pi$
$7$	−1.05927	−	1.05927i	−0.400368	−	0.400368i	−0.878363	+	0.477995i	$0.841364\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$			1.00000i			0.333333i
$10$	1.98606	−	1.02740i	0.628048	−	0.324893i
$11$		−	2.05480i		−	0.619547i	−0.950810	−	0.309773i	$-0.899747\pi$
$11$		−	2.05480i		−	0.619547i	0.950810	−	0.309773i	$-0.100253\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	2.75307	+	2.75307i	0.763563	+	0.763563i	0.976965	−	0.213401i	$-0.0684542\pi$
$13$	2.75307	+	2.75307i	0.763563	+	0.763563i	−0.213401	+	0.976965i	$0.568454\pi$
$14$	1.49804			0.400368
$15$	−1.02740	−	1.98606i	−0.265274	−	0.512799i
$16$	−1.00000			−0.250000
$17$	4.76291	+	4.76291i	1.15517	+	1.15517i	0.985500	+	0.169675i	$0.0542718\pi$
$17$	4.76291	+	4.76291i	1.15517	+	1.15517i	0.169675	+	0.985500i	$0.445728\pi$
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	1.85358			0.425240			0.212620	−	0.977135i	$-0.431800\pi$
$19$	1.85358			0.425240			0.212620	+	0.977135i	$0.431800\pi$
$20$	−0.677875	+	2.13084i	−0.151577	+	0.476471i
$21$		−	1.49804i		−	0.326899i
$22$	1.45297	+	1.45297i	0.309773	+	0.309773i
$23$	−3.76456	+	2.97121i	−0.784965	+	0.619540i
$23$	−3.76456	+	2.97121i	−0.784965	+	0.619540i
$24$			1.00000i			0.204124i
$25$	4.08097	+	2.88889i	0.816194	+	0.577778i
$26$	−3.89342			−0.763563
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−1.05927	+	1.05927i	−0.200184	+	0.200184i
$29$			7.96345i			1.47877i	0.673280	+	0.739387i	$0.264885\pi$
$29$			7.96345i			1.47877i	−0.673280	+	0.739387i	$0.735115\pi$
$30$	2.13084	+	0.677875i	0.389037	+	0.123762i
$31$	10.3127			1.85221			0.926105	−	0.377267i	$-0.123136\pi$
$31$	10.3127			1.85221			0.926105	+	0.377267i	$0.123136\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	1.45297	−	1.45297i	0.252929	−	0.252929i
$34$	−6.73577			−1.15517
$35$	1.53909	+	2.97520i	0.260153	+	0.502900i
$36$	1.00000			0.166667
$37$	2.66303	+	2.66303i	0.437800	+	0.437800i	0.891271	−	0.453471i	$-0.149815\pi$
$37$	2.66303	+	2.66303i	0.437800	+	0.437800i	−0.453471	+	0.891271i	$0.649815\pi$
$38$	−1.31068	+	1.31068i	−0.212620	+	0.212620i
$39$			3.89342i			0.623447i
$40$	−1.02740	−	1.98606i	−0.162447	−	0.314024i
$41$	−8.60620			−1.34406			−0.672032	−	0.740522i	$-0.734578\pi$
$41$	−8.60620			−1.34406			−0.672032	+	0.740522i	$0.734578\pi$
$42$	1.05927	+	1.05927i	0.163449	+	0.163449i
$43$	1.45989	−	1.45989i	0.222630	−	0.222630i	−0.586975	−	0.809605i	$-0.699681\pi$
$43$	1.45989	−	1.45989i	0.222630	−	0.222630i	0.809605	+	0.586975i	$0.199681\pi$
$44$	−2.05480			−0.309773
$45$	0.677875	−	2.13084i	0.101052	−	0.317647i
$46$	0.560984	−	4.76291i	0.0827126	−	0.702253i
$47$	1.89984	−	1.89984i	0.277120	−	0.277120i	−0.554838	−	0.831958i	$-0.687220\pi$
$47$	1.89984	−	1.89984i	0.277120	−	0.277120i	0.831958	+	0.554838i	$0.187220\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$		−	4.75588i		−	0.679412i
$50$	−4.92843	+	0.842929i	−0.696986	+	0.119208i
$51$			6.73577i			0.943196i
$52$	2.75307	−	2.75307i	0.381782	−	0.381782i
$53$	3.57151	−	3.57151i	0.490585	−	0.490585i	−0.417906	−	0.908490i	$-0.637236\pi$
$53$	3.57151	−	3.57151i	0.490585	−	0.490585i	0.908490	+	0.417906i	$0.137236\pi$
$54$		−	1.00000i		−	0.136083i
$55$	−1.39290	+	4.37846i	−0.187819	+	0.590392i
$56$		−	1.49804i		−	0.200184i
$57$	1.31068	+	1.31068i	0.173604	+	0.173604i
$58$	−5.63101	−	5.63101i	−0.739387	−	0.739387i
$59$			3.82027i			0.497357i	0.968586	+	0.248679i	$0.0799963\pi$
$59$			3.82027i			0.497357i	−0.968586	+	0.248679i	$0.920004\pi$
$60$	−1.98606	+	1.02740i	−0.256400	+	0.132637i
$61$		−	2.76364i		−	0.353848i	−0.984224	−	0.176924i	$-0.943385\pi$
$61$		−	2.76364i		−	0.353848i	0.984224	−	0.176924i	$-0.0566148\pi$
$62$	−7.29215	+	7.29215i	−0.926105	+	0.926105i
$63$	1.05927	−	1.05927i	0.133456	−	0.133456i
$64$			1.00000i			0.125000i
$65$	−4.00011	−	7.73258i	−0.496153	−	0.959109i
$66$			2.05480i			0.252929i
$67$	7.21961	+	7.21961i	0.882015	+	0.882015i	0.993739	−	0.111724i	$-0.0356372\pi$
$67$	7.21961	+	7.21961i	0.882015	+	0.882015i	−0.111724	+	0.993739i	$0.535637\pi$
$68$	4.76291	−	4.76291i	0.577587	−	0.577587i
$69$	−4.76291	−	0.560984i	−0.573387	−	0.0675345i
$70$	−3.19208	−	1.01548i	−0.381527	−	0.121373i
$71$	0.620733			0.0736675			0.0368337	−	0.999321i	$-0.488273\pi$
$71$	0.620733			0.0736675			0.0368337	+	0.999321i	$0.488273\pi$
$72$	−0.707107	+	0.707107i	−0.0833333	+	0.0833333i
$73$	4.77136	+	4.77136i	0.558446	+	0.558446i	0.928865	−	0.370419i	$-0.120786\pi$
$73$	4.77136	+	4.77136i	0.558446	+	0.558446i	−0.370419	+	0.928865i	$0.620786\pi$
$74$	−3.76610			−0.437800
$75$	0.842929	+	4.92843i	0.0973331	+	0.569087i
$76$		−	1.85358i		−	0.212620i
$77$	−2.17660	+	2.17660i	−0.248047	+	0.248047i
$78$	−2.75307	−	2.75307i	−0.311723	−	0.311723i
$79$	−16.3891			−1.84391			−0.921957	−	0.387292i	$-0.873411\pi$
$79$	−16.3891			−1.84391			−0.921957	+	0.387292i	$0.873411\pi$
$80$	2.13084	+	0.677875i	0.238235	+	0.0757887i
$81$	−1.00000			−0.111111
$82$	6.08551	−	6.08551i	0.672032	−	0.672032i
$83$	5.71805	−	5.71805i	0.627637	−	0.627637i	−0.319836	−	0.947473i	$-0.603628\pi$
$83$	5.71805	−	5.71805i	0.627637	−	0.627637i	0.947473	+	0.319836i	$0.103628\pi$
$84$	−1.49804			−0.163449
$85$	−6.92035	−	13.3777i	−0.750617	−	1.45101i
$86$			2.06459i			0.222630i
$87$	−5.63101	+	5.63101i	−0.603707	+	0.603707i
$88$	1.45297	−	1.45297i	0.154887	−	0.154887i
$89$	0.705848			0.0748197			0.0374099	−	0.999300i	$-0.488089\pi$
$89$	0.705848			0.0748197			0.0374099	+	0.999300i	$0.488089\pi$
$90$	1.02740	+	1.98606i	0.108298	+	0.209349i
$91$		−	5.83250i		−	0.611412i
$92$	2.97121	+	3.76456i	0.309770	+	0.392483i
$93$	7.29215	+	7.29215i	0.756161	+	0.756161i
$94$			2.68677i			0.277120i
$95$	−3.94968	−	1.25650i	−0.405229	−	0.128914i
$96$	1.00000			0.102062
$97$	0.564967	+	0.564967i	0.0573637	+	0.0573637i	0.735207	−	0.677843i	$-0.237085\pi$
$97$	0.564967	+	0.564967i	0.0573637	+	0.0573637i	−0.677843	+	0.735207i	$0.737085\pi$
$98$	3.36292	+	3.36292i	0.339706	+	0.339706i
$99$	2.05480			0.206516
$100$	2.88889	−	4.08097i	0.288889	−	0.408097i
$101$	−14.5606			−1.44883			−0.724416	−	0.689363i	$-0.757890\pi$
$101$	−14.5606			−1.44883			−0.724416	+	0.689363i	$0.757890\pi$
$102$	−4.76291	−	4.76291i	−0.471598	−	0.471598i
$103$	−4.76419	+	4.76419i	−0.469430	+	0.469430i	−0.901730	−	0.432300i	$-0.857702\pi$
$103$	−4.76419	+	4.76419i	−0.469430	+	0.469430i	0.432300	+	0.901730i	$0.357702\pi$
$104$			3.89342i			0.381782i
$105$	−1.01548	+	3.19208i	−0.0991010	+	0.311515i
$106$			5.05088i			0.490585i
$107$	11.8110	+	11.8110i	1.14181	+	1.14181i	0.988119	+	0.153689i	$0.0491155\pi$
$107$	11.8110	+	11.8110i	1.14181	+	1.14181i	0.153689	+	0.988119i	$0.450885\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$	2.85379			0.273343			0.136672	−	0.990616i	$-0.456359\pi$
$109$	2.85379			0.273343			0.136672	+	0.990616i	$0.456359\pi$
$110$	−2.11111	−	4.08097i	−0.201287	−	0.389105i
$111$			3.76610i			0.357462i
$112$	1.05927	+	1.05927i	0.100092	+	0.100092i
$113$	−6.25116	+	6.25116i	−0.588060	+	0.588060i	−0.937106	−	0.349046i	$-0.886506\pi$
$113$	−6.25116	+	6.25116i	−0.588060	+	0.588060i	0.349046	+	0.937106i	$0.386506\pi$
$114$	−1.85358			−0.173604
$115$	10.0358	−	3.77927i	0.935842	−	0.352419i
$116$	7.96345			0.739387
$117$	−2.75307	+	2.75307i	−0.254521	+	0.254521i
$118$	−2.70134	−	2.70134i	−0.248679	−	0.248679i
$119$		−	10.0904i		−	0.924989i
$120$	0.677875	−	2.13084i	0.0618812	−	0.194518i
$121$	6.77778			0.616162
$122$	1.95419	+	1.95419i	0.176924	+	0.176924i
$123$	−6.08551	−	6.08551i	−0.548712	−	0.548712i
$124$		−	10.3127i		−	0.926105i
$125$	−6.73760	−	8.92215i	−0.602629	−	0.798022i
$126$			1.49804i			0.133456i
$127$	5.96063	−	5.96063i	0.528920	−	0.528920i	−0.391330	−	0.920250i	$-0.627985\pi$
$127$	5.96063	−	5.96063i	0.528920	−	0.528920i	0.920250	+	0.391330i	$0.127985\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	2.06459			0.181777
$130$	8.29627	+	2.63925i	0.727631	+	0.231478i
$131$	19.3136			1.68744			0.843718	−	0.536787i	$-0.180362\pi$
$131$	19.3136			1.68744			0.843718	+	0.536787i	$0.180362\pi$
$132$	−1.45297	−	1.45297i	−0.126464	−	0.126464i
$133$	−1.96345	−	1.96345i	−0.170252	−	0.170252i
$134$	−10.2101			−0.882015
$135$	1.98606	−	1.02740i	0.170933	−	0.0884247i
$136$			6.73577i			0.577587i
$137$	11.2806	+	11.2806i	0.963769	+	0.963769i	0.999366	−	0.0355976i	$-0.0113335\pi$
$137$	11.2806	+	11.2806i	0.963769	+	0.963769i	−0.0355976	+	0.999366i	$0.511333\pi$
$138$	3.76456	−	2.97121i	0.320461	−	0.252926i
$139$		−	5.76656i		−	0.489113i	−0.969635	−	0.244557i	$-0.921358\pi$
$139$		−	5.76656i		−	0.489113i	0.969635	−	0.244557i	$-0.0786424\pi$
$140$	2.97520	−	1.53909i	0.251450	−	0.130077i
$141$	2.68677			0.226267
$142$	−0.438925	+	0.438925i	−0.0368337	+	0.0368337i
$143$	5.65701	−	5.65701i	0.473063	−	0.473063i
$144$		−	1.00000i		−	0.0833333i
$145$	5.39822	−	16.9688i	0.448298	−	1.40919i
$146$	−6.74773			−0.558446
$147$	3.36292	−	3.36292i	0.277369	−	0.277369i
$148$	2.66303	−	2.66303i	0.218900	−	0.218900i
$149$	−19.0202			−1.55820			−0.779100	−	0.626900i	$-0.784323\pi$
$149$	−19.0202			−1.55820			−0.779100	+	0.626900i	$0.784323\pi$
$150$	−4.08097	−	2.88889i	−0.333210	−	0.235877i
$151$	−8.07922			−0.657478			−0.328739	−	0.944421i	$-0.606624\pi$
$151$	−8.07922			−0.657478			−0.328739	+	0.944421i	$0.606624\pi$
$152$	1.31068	+	1.31068i	0.106310	+	0.106310i
$153$	−4.76291	+	4.76291i	−0.385058	+	0.385058i
$154$		−	3.07818i		−	0.248047i
$155$	−21.9747	−	6.99070i	−1.76505	−	0.561506i
$156$	3.89342			0.311723
$157$	−5.10732	−	5.10732i	−0.407609	−	0.407609i	0.473295	−	0.880904i	$-0.343064\pi$
$157$	−5.10732	−	5.10732i	−0.407609	−	0.407609i	−0.880904	+	0.473295i	$0.843064\pi$
$158$	11.5888	−	11.5888i	0.921957	−	0.921957i
$159$	5.05088			0.400561
$160$	−1.98606	+	1.02740i	−0.157012	+	0.0812233i
$161$	7.13502	+	0.840376i	0.562318	+	0.0662309i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	3.50613	+	3.50613i	0.274621	+	0.274621i	0.830957	−	0.556336i	$-0.187793\pi$
$163$	3.50613	+	3.50613i	0.274621	+	0.274621i	−0.556336	+	0.830957i	$0.687793\pi$
$164$			8.60620i			0.672032i
$165$	−4.08097	+	2.11111i	−0.317703	+	0.164350i
$166$			8.08654i			0.627637i
$167$	14.5151	−	14.5151i	1.12321	−	1.12321i	0.131958	−	0.991255i	$-0.457874\pi$
$167$	14.5151	−	14.5151i	1.12321	−	1.12321i	0.991255	−	0.131958i	$-0.0421263\pi$
$168$	1.05927	−	1.05927i	0.0817247	−	0.0817247i
$169$			2.15875i			0.166057i
$170$	14.3529	+	4.56601i	1.10081	+	0.350197i
$171$			1.85358i			0.141747i
$172$	−1.45989	−	1.45989i	−0.111315	−	0.111315i
$173$	−17.0914	−	17.0914i	−1.29943	−	1.29943i	−0.928767	−	0.370665i	$-0.879130\pi$
$173$	−17.0914	−	17.0914i	−1.29943	−	1.29943i	−0.370665	−	0.928767i	$-0.620870\pi$
$174$		−	7.96345i		−	0.603707i
$175$	−1.26274	−	7.38298i	−0.0954542	−	0.558101i
$176$			2.05480i			0.154887i
$177$	−2.70134	+	2.70134i	−0.203045	+	0.203045i
$178$	−0.499110	+	0.499110i	−0.0374099	+	0.0374099i
$179$		−	19.5452i		−	1.46088i	−0.682979	−	0.730438i	$-0.739316\pi$
$179$		−	19.5452i		−	1.46088i	0.682979	−	0.730438i	$-0.260684\pi$
$180$	−2.13084	−	0.677875i	−0.158824	−	0.0505258i
$181$			25.0126i			1.85917i	0.368607	+	0.929585i	$0.379835\pi$
$181$			25.0126i			1.85917i	−0.368607	+	0.929585i	$0.620165\pi$
$182$	4.12420	+	4.12420i	0.305706	+	0.305706i
$183$	1.95419	−	1.95419i	0.144458	−	0.144458i
$184$	−4.76291	−	0.560984i	−0.351126	−	0.0413563i
$185$	−3.86930	−	7.47970i	−0.284476	−	0.549919i
$186$	−10.3127			−0.756161
$187$	9.78685	−	9.78685i	0.715685	−	0.715685i
$188$	−1.89984	−	1.89984i	−0.138560	−	0.138560i
$189$	1.49804			0.108966
$190$	3.68132	−	1.90437i	0.267071	−	0.138158i
$191$		−	10.7049i		−	0.774582i	−0.921958	−	0.387291i	$-0.873411\pi$
$191$		−	10.7049i		−	0.774582i	0.921958	−	0.387291i	$-0.126589\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	−7.17660	−	7.17660i	−0.516583	−	0.516583i	0.399953	−	0.916536i	$-0.369027\pi$
$193$	−7.17660	−	7.17660i	−0.516583	−	0.516583i	−0.916536	+	0.399953i	$0.869027\pi$
$194$	−0.798984			−0.0573637
$195$	2.63925	−	8.29627i	0.189001	−	0.594108i
$196$	−4.75588			−0.339706
$197$	2.71278	−	2.71278i	0.193278	−	0.193278i	−0.603833	−	0.797111i	$-0.706361\pi$
$197$	2.71278	−	2.71278i	0.193278	−	0.193278i	0.797111	+	0.603833i	$0.206361\pi$
$198$	−1.45297	+	1.45297i	−0.103258	+	0.103258i
$199$	−19.3755			−1.37350			−0.686748	−	0.726896i	$-0.740962\pi$
$199$	−19.3755			−1.37350			−0.686748	+	0.726896i	$0.740962\pi$
$200$	0.842929	+	4.92843i	0.0596041	+	0.348493i
$201$			10.2101i			0.720163i
$202$	10.2959	−	10.2959i	0.724416	−	0.724416i
$203$	8.43546	−	8.43546i	0.592053	−	0.592053i
$204$	6.73577			0.471598
$205$	18.3385	+	5.83393i	1.28081	+	0.407459i
$206$		−	6.73758i		−	0.469430i
$207$	−2.97121	−	3.76456i	−0.206513	−	0.261655i
$208$	−2.75307	−	2.75307i	−0.190891	−	0.190891i
$209$		−	3.80874i		−	0.263456i
$210$	−1.53909	−	2.97520i	−0.106207	−	0.205308i
$211$	−9.81831			−0.675921			−0.337960	−	0.941160i	$-0.609737\pi$
$211$	−9.81831			−0.675921			−0.337960	+	0.941160i	$0.609737\pi$
$212$	−3.57151	−	3.57151i	−0.245292	−	0.245292i
$213$	0.438925	+	0.438925i	0.0300746	+	0.0300746i
$214$	−16.7032			−1.14181
$215$	−4.10040	+	2.12116i	−0.279645	+	0.144662i
$216$	−1.00000			−0.0680414
$217$	−10.9239	−	10.9239i	−0.741564	−	0.741564i
$218$	−2.01793	+	2.01793i	−0.136672	+	0.136672i
$219$			6.74773i			0.455969i
$220$	4.37846	+	1.39290i	0.295196	+	0.0939094i
$221$			26.2252i			1.76410i
$222$	−2.66303	−	2.66303i	−0.178731	−	0.178731i
$223$	−11.7320	−	11.7320i	−0.785633	−	0.785633i	0.195142	−	0.980775i	$-0.437483\pi$
$223$	−11.7320	−	11.7320i	−0.785633	−	0.785633i	−0.980775	+	0.195142i	$0.937483\pi$
$224$	−1.49804			−0.100092
$225$	−2.88889	+	4.08097i	−0.192593	+	0.272065i
$226$		−	8.84048i		−	0.588060i
$227$	7.21427	+	7.21427i	0.478828	+	0.478828i	0.904757	−	0.425929i	$-0.140053\pi$
$227$	7.21427	+	7.21427i	0.478828	+	0.478828i	−0.425929	+	0.904757i	$0.640053\pi$
$228$	1.31068	−	1.31068i	0.0868018	−	0.0868018i
$229$	26.7216			1.76582			0.882908	−	0.469547i	$-0.155583\pi$
$229$	26.7216			1.76582			0.882908	+	0.469547i	$0.155583\pi$
$230$	−4.42403	+	9.76873i	−0.291712	+	0.644131i
$231$	−3.07818			−0.202529
$232$	−5.63101	+	5.63101i	−0.369694	+	0.369694i
$233$	7.66479	+	7.66479i	0.502137	+	0.502137i	0.912101	−	0.409965i	$-0.134459\pi$
$233$	7.66479	+	7.66479i	0.502137	+	0.502137i	−0.409965	+	0.912101i	$0.634459\pi$
$234$		−	3.89342i		−	0.254521i
$235$	−5.33610	+	2.76040i	−0.348089	+	0.180069i
$236$	3.82027			0.248679
$237$	−11.5888	−	11.5888i	−0.752775	−	0.752775i
$238$	7.13502	+	7.13502i	0.462495	+	0.462495i
$239$		−	5.19806i		−	0.336235i	−0.985767	−	0.168117i	$-0.946231\pi$
$239$		−	5.19806i		−	0.336235i	0.985767	−	0.168117i	$-0.0537688\pi$
$240$	1.02740	+	1.98606i	0.0663185	+	0.128200i
$241$		−	26.1013i		−	1.68134i	−0.541551	−	0.840668i	$-0.682163\pi$
$241$		−	26.1013i		−	1.68134i	0.541551	−	0.840668i	$-0.317837\pi$
$242$	−4.79261	+	4.79261i	−0.308081	+	0.308081i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−2.76364			−0.176924
$245$	−3.22389	+	10.1340i	−0.205967	+	0.647439i
$246$	8.60620			0.548712
$247$	5.10303	+	5.10303i	0.324698	+	0.324698i
$248$	7.29215	+	7.29215i	0.463052	+	0.463052i
$249$	8.08654			0.512464
$250$	11.0731	+	1.54471i	0.700325	+	0.0976963i
$251$			4.77728i			0.301539i	0.988569	+	0.150770i	$0.0481752\pi$
$251$			4.77728i			0.301539i	−0.988569	+	0.150770i	$0.951825\pi$
$252$	−1.05927	−	1.05927i	−0.0667279	−	0.0667279i
$253$	6.10525	+	7.73544i	0.383834	+	0.486323i
$254$			8.42961i			0.528920i
$255$	4.56601	−	14.3529i	0.285935	−	0.898811i
$256$	1.00000			0.0625000
$257$	3.06500	−	3.06500i	0.191189	−	0.191189i	−0.605021	−	0.796210i	$-0.706835\pi$
$257$	3.06500	−	3.06500i	0.191189	−	0.191189i	0.796210	+	0.605021i	$0.206835\pi$
$258$	−1.45989	+	1.45989i	−0.0908885	+	0.0908885i
$259$		−	5.64176i		−	0.350562i
$260$	−7.73258	+	4.00011i	−0.479554	+	0.248076i
$261$	−7.96345			−0.492925
$262$	−13.6568	+	13.6568i	−0.843718	+	0.843718i
$263$	3.15317	−	3.15317i	0.194433	−	0.194433i	−0.603176	−	0.797608i	$-0.706098\pi$
$263$	3.15317	−	3.15317i	0.194433	−	0.194433i	0.797608	+	0.603176i	$0.206098\pi$
$264$	2.05480			0.126464
$265$	−10.0314	+	5.18929i	−0.616222	+	0.318775i
$266$	2.77673			0.170252
$267$	0.499110	+	0.499110i	0.0305450	+	0.0305450i
$268$	7.21961	−	7.21961i	0.441008	−	0.441008i
$269$			14.0173i			0.854649i	0.904098	+	0.427325i	$0.140544\pi$
$269$			14.0173i			0.854649i	−0.904098	+	0.427325i	$0.859456\pi$
$270$	−0.677875	+	2.13084i	−0.0412542	+	0.129679i
$271$	0.314270			0.0190906			0.00954528	−	0.999954i	$-0.496962\pi$
$271$	0.314270			0.0190906			0.00954528	+	0.999954i	$0.496962\pi$
$272$	−4.76291	−	4.76291i	−0.288794	−	0.288794i
$273$	4.12420	−	4.12420i	0.249608	−	0.249608i
$274$	−15.9532			−0.963769
$275$	5.93610	−	8.38560i	0.357960	−	0.505671i
$276$	−0.560984	+	4.76291i	−0.0337673	+	0.286693i
$277$	−13.1608	+	13.1608i	−0.790754	+	0.790754i	−0.981617	−	0.190862i	$-0.938872\pi$
$277$	−13.1608	+	13.1608i	−0.790754	+	0.790754i	0.190862	+	0.981617i	$0.438872\pi$
$278$	4.07757	+	4.07757i	0.244557	+	0.244557i
$279$			10.3127i			0.617403i
$280$	−1.01548	+	3.19208i	−0.0606867	+	0.190763i
$281$			11.4727i			0.684403i	0.939627	+	0.342201i	$0.111173\pi$
$281$			11.4727i			0.684403i	−0.939627	+	0.342201i	$0.888827\pi$
$282$	−1.89984	+	1.89984i	−0.113134	+	0.113134i
$283$	−3.63921	+	3.63921i	−0.216329	+	0.216329i	−0.806949	−	0.590621i	$-0.798883\pi$
$283$	−3.63921	+	3.63921i	−0.216329	+	0.216329i	0.590621	+	0.806949i	$0.298883\pi$
$284$		−	0.620733i		−	0.0368337i
$285$	−1.90437	−	3.68132i	−0.112805	−	0.218063i
$286$			8.00023i			0.473063i
$287$	9.11632	+	9.11632i	0.538119	+	0.538119i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$			28.3706i			1.66886i
$290$	8.18166	+	15.8159i	0.480444	+	0.928742i
$291$			0.798984i			0.0468373i
$292$	4.77136	−	4.77136i	0.279223	−	0.279223i
$293$	3.00016	−	3.00016i	0.175271	−	0.175271i	−0.614020	−	0.789291i	$-0.710448\pi$
$293$	3.00016	−	3.00016i	0.175271	−	0.175271i	0.789291	+	0.614020i	$0.210448\pi$
$294$			4.75588i			0.277369i
$295$	2.58967	−	8.14040i	0.150776	−	0.473952i
$296$			3.76610i			0.218900i
$297$	1.45297	+	1.45297i	0.0843097	+	0.0843097i
$298$	13.4493	−	13.4493i	0.779100	−	0.779100i
$299$	−18.5440	−	2.18415i	−1.07243	−	0.126313i
$300$	4.92843	−	0.842929i	0.284543	−	0.0486665i
$301$	−3.09283			−0.178268
$302$	5.71287	−	5.71287i	0.328739	−	0.328739i
$303$	−10.2959	−	10.2959i	−0.591483	−	0.591483i
$304$	−1.85358			−0.106310
$305$	−1.87341	+	5.88889i	−0.107271	+	0.337197i
$306$		−	6.73577i		−	0.385058i
$307$	−14.9088	+	14.9088i	−0.850891	+	0.850891i	−0.990243	−	0.139352i	$-0.955498\pi$
$307$	−14.9088	+	14.9088i	−0.850891	+	0.850891i	0.139352	+	0.990243i	$0.455498\pi$
$308$	2.17660	+	2.17660i	0.124023	+	0.124023i
$309$	−6.73758			−0.383288
$310$	20.4816	−	10.5953i	1.16328	−	0.601770i
$311$	10.4912			0.594903			0.297451	−	0.954737i	$-0.403863\pi$
$311$	10.4912			0.594903			0.297451	+	0.954737i	$0.403863\pi$
$312$	−2.75307	+	2.75307i	−0.155862	+	0.155862i
$313$	−13.7256	+	13.7256i	−0.775815	+	0.775815i	−0.979116	−	0.203301i	$-0.934833\pi$
$313$	−13.7256	+	13.7256i	−0.775815	+	0.775815i	0.203301	+	0.979116i	$0.434833\pi$
$314$	7.22285			0.407609
$315$	−2.97520	+	1.53909i	−0.167633	+	0.0867178i
$316$			16.3891i			0.921957i
$317$	−8.37263	+	8.37263i	−0.470254	+	0.470254i	−0.901997	−	0.431743i	$-0.857899\pi$
$317$	−8.37263	+	8.37263i	−0.470254	+	0.470254i	0.431743	+	0.901997i	$0.357899\pi$
$318$	−3.57151	+	3.57151i	−0.200280	+	0.200280i
$319$	16.3633			0.916170
$320$	0.677875	−	2.13084i	0.0378944	−	0.119118i
$321$			16.7032i			0.932283i
$322$	−5.63946	+	4.45099i	−0.314275	+	0.248044i
$323$	8.82843	+	8.82843i	0.491227	+	0.491227i
$324$			1.00000i			0.0555556i
$325$	3.28188	+	19.1885i	0.182046	+	1.06439i
$326$	−4.95842			−0.274621
$327$	2.01793	+	2.01793i	0.111592	+	0.111592i
$328$	−6.08551	−	6.08551i	−0.336016	−	0.336016i
$329$	−4.02489			−0.221899
$330$	1.39290	−	4.37846i	0.0766767	−	0.241026i
$331$	14.8469			0.816059			0.408029	−	0.912969i	$-0.366216\pi$
$331$	14.8469			0.816059			0.408029	+	0.912969i	$0.366216\pi$
$332$	−5.71805	−	5.71805i	−0.313819	−	0.313819i
$333$	−2.66303	+	2.66303i	−0.145933	+	0.145933i
$334$			20.5275i			1.12321i
$335$	−10.4898	−	20.2778i	−0.573122	−	1.10790i
$336$			1.49804i			0.0817247i
$337$	−0.402707	−	0.402707i	−0.0219369	−	0.0219369i	0.696053	−	0.717990i	$-0.254938\pi$
$337$	−0.402707	−	0.402707i	−0.0219369	−	0.0219369i	−0.717990	+	0.696053i	$0.754938\pi$
$338$	−1.52646	−	1.52646i	−0.0830287	−	0.0830287i
$339$	−8.84048			−0.480149
$340$	−13.3777	+	6.92035i	−0.725505	+	0.375308i
$341$		−	21.1905i		−	1.14753i
$342$	−1.31068	−	1.31068i	−0.0708734	−	0.0708734i
$343$	−12.4527	+	12.4527i	−0.672382	+	0.672382i
$344$	2.06459			0.111315
$345$	9.76873	+	4.42403i	0.525931	+	0.238182i
$346$	24.1708			1.29943
$347$	10.0204	−	10.0204i	0.537924	−	0.537924i	−0.384995	−	0.922919i	$-0.625797\pi$
$347$	10.0204	−	10.0204i	0.537924	−	0.537924i	0.922919	+	0.384995i	$0.125797\pi$
$348$	5.63101	+	5.63101i	0.301854	+	0.301854i
$349$			21.1479i			1.13202i	0.824398	+	0.566010i	$0.191514\pi$
$349$			21.1479i			1.13202i	−0.824398	+	0.566010i	$0.808486\pi$
$350$	6.11345	+	4.32767i	0.326778	+	0.231323i
$351$	−3.89342			−0.207816
$352$	−1.45297	−	1.45297i	−0.0774434	−	0.0774434i
$353$	−5.85206	−	5.85206i	−0.311474	−	0.311474i	0.534006	−	0.845480i	$-0.320686\pi$
$353$	−5.85206	−	5.85206i	−0.311474	−	0.311474i	−0.845480	+	0.534006i	$0.820686\pi$
$354$		−	3.82027i		−	0.203045i
$355$	−1.32268	−	0.420780i	−0.0702008	−	0.0223327i
$356$		−	0.705848i		−	0.0374099i
$357$	7.13502	−	7.13502i	0.377625	−	0.377625i
$358$	13.8205	+	13.8205i	0.730438	+	0.730438i
$359$	7.29231			0.384874			0.192437	−	0.981309i	$-0.438361\pi$
$359$	7.29231			0.384874			0.192437	+	0.981309i	$0.438361\pi$
$360$	1.98606	−	1.02740i	0.104675	−	0.0541489i
$361$	−15.5642			−0.819171
$362$	−17.6866	−	17.6866i	−0.929585	−	0.929585i
$363$	4.79261	+	4.79261i	0.251547	+	0.251547i
$364$	−5.83250			−0.305706
$365$	−6.93263	−	13.4014i	−0.362871	−	0.701462i
$366$			2.76364i			0.144458i
$367$	4.42844	+	4.42844i	0.231162	+	0.231162i	0.813178	−	0.582015i	$-0.197736\pi$
$367$	4.42844	+	4.42844i	0.231162	+	0.231162i	−0.582015	+	0.813178i	$0.697736\pi$
$368$	3.76456	−	2.97121i	0.196241	−	0.154885i
$369$		−	8.60620i		−	0.448021i
$370$	8.02495	+	2.55294i	0.417197	+	0.132721i
$371$	−7.56641			−0.392829
$372$	7.29215	−	7.29215i	0.378081	−	0.378081i
$373$	−16.7491	+	16.7491i	−0.867237	+	0.867237i	−0.992166	−	0.124929i	$-0.960130\pi$
$373$	−16.7491	+	16.7491i	−0.867237	+	0.867237i	0.124929	+	0.992166i	$0.460130\pi$
$374$			13.8407i			0.715685i
$375$	1.54471	−	11.0731i	0.0797687	−	0.571813i
$376$	2.68677			0.138560
$377$	−21.9239	+	21.9239i	−1.12914	+	1.12914i
$378$	−1.05927	+	1.05927i	−0.0544831	+	0.0544831i
$379$	19.1753			0.984968			0.492484	−	0.870322i	$-0.336089\pi$
$379$	19.1753			0.984968			0.492484	+	0.870322i	$0.336089\pi$
$380$	−1.25650	+	3.94968i	−0.0644568	+	0.202614i
$381$	8.42961			0.431862
$382$	7.56953	+	7.56953i	0.387291	+	0.387291i
$383$	−6.51953	+	6.51953i	−0.333132	+	0.333132i	−0.853775	−	0.520643i	$-0.825692\pi$
$383$	−6.51953	+	6.51953i	−0.333132	+	0.333132i	0.520643	+	0.853775i	$0.325692\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	6.11345	−	3.16253i	0.311570	−	0.161177i
$386$	10.1492			0.516583
$387$	1.45989	+	1.45989i	0.0742102	+	0.0742102i
$388$	0.564967	−	0.564967i	0.0286818	−	0.0286818i
$389$	33.2608			1.68639			0.843195	−	0.537608i	$-0.180672\pi$
$389$	33.2608			1.68639			0.843195	+	0.537608i	$0.180672\pi$
$390$	4.00011	+	7.73258i	0.202554	+	0.391555i
$391$	−32.0819	−	3.77866i	−1.62245	−	0.191095i
$392$	3.36292	−	3.36292i	0.169853	−	0.169853i
$393$	13.6568	+	13.6568i	0.688893	+	0.688893i
$394$			3.83645i			0.193278i
$395$	34.9225	+	11.1097i	1.75714	+	0.558992i
$396$		−	2.05480i		−	0.103258i
$397$	−13.0410	+	13.0410i	−0.654510	+	0.654510i	−0.954076	−	0.299566i	$-0.903158\pi$
$397$	−13.0410	+	13.0410i	−0.654510	+	0.654510i	0.299566	+	0.954076i	$0.403158\pi$
$398$	13.7006	−	13.7006i	0.686748	−	0.686748i
$399$		−	2.77673i		−	0.139010i
$400$	−4.08097	−	2.88889i	−0.204049	−	0.144444i
$401$		−	36.5844i		−	1.82694i	−0.406911	−	0.913468i	$-0.633394\pi$
$401$		−	36.5844i		−	1.82694i	0.406911	−	0.913468i	$-0.366606\pi$
$402$	−7.21961	−	7.21961i	−0.360081	−	0.360081i
$403$	28.3914	+	28.3914i	1.41428	+	1.41428i
$404$			14.5606i			0.724416i
$405$	2.13084	+	0.677875i	0.105882	+	0.0336839i
$406$			11.9295i			0.592053i
$407$	5.47201	−	5.47201i	0.271237	−	0.271237i
$408$	−4.76291	+	4.76291i	−0.235799	+	0.235799i
$409$		−	2.61805i		−	0.129454i	−0.997903	−	0.0647271i	$-0.979382\pi$
$409$		−	2.61805i		−	0.129454i	0.997903	−	0.0647271i	$-0.0206177\pi$
$410$	−17.0925	+	8.84204i	−0.844136	+	0.436677i
$411$			15.9532i			0.786914i
$412$	4.76419	+	4.76419i	0.234715	+	0.234715i
$413$	4.04671	−	4.04671i	0.199126	−	0.199126i
$414$	4.76291	+	0.560984i	0.234084	+	0.0275709i
$415$	−16.0604	+	8.30813i	−0.788373	+	0.407830i
$416$	3.89342			0.190891
$417$	4.07757	−	4.07757i	0.199680	−	0.199680i
$418$	2.69319	+	2.69319i	0.131728	+	0.131728i
$419$	−5.34180			−0.260964			−0.130482	−	0.991451i	$-0.541652\pi$
$419$	−5.34180			−0.260964			−0.130482	+	0.991451i	$0.541652\pi$
$420$	3.19208	+	1.01548i	0.155758	+	0.0495505i
$421$		−	22.4150i		−	1.09244i	−0.837642	−	0.546220i	$-0.816066\pi$
$421$		−	22.4150i		−	1.09244i	0.837642	−	0.546220i	$-0.183934\pi$
$422$	6.94260	−	6.94260i	0.337960	−	0.337960i
$423$	1.89984	+	1.89984i	0.0923732	+	0.0923732i
$424$	5.05088			0.245292
$425$	5.67778	+	33.1968i	0.275413	+	1.61028i
$426$	−0.620733			−0.0300746
$427$	−2.92745	+	2.92745i	−0.141669	+	0.141669i
$428$	11.8110	−	11.8110i	0.570904	−	0.570904i
$429$	8.00023			0.386255
$430$	1.39953	−	4.39931i	0.0674915	−	0.212154i
$431$		−	30.2418i		−	1.45670i	−0.685207	−	0.728348i	$-0.740288\pi$
$431$		−	30.2418i		−	1.45670i	0.685207	−	0.728348i	$-0.259712\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	−11.9248	+	11.9248i	−0.573067	+	0.573067i	−0.932984	−	0.359917i	$-0.882805\pi$
$433$	−11.9248	+	11.9248i	−0.573067	+	0.573067i	0.359917	+	0.932984i	$0.382805\pi$
$434$	15.4488			0.741564
$435$	15.8159	−	8.18166i	0.758314	−	0.392281i
$436$		−	2.85379i		−	0.136672i
$437$	−6.97791	+	5.50737i	−0.333799	+	0.263453i
$438$	−4.77136	−	4.77136i	−0.227985	−	0.227985i
$439$		−	6.91115i		−	0.329851i	−0.986306	−	0.164926i	$-0.947262\pi$
$439$		−	6.91115i		−	0.329851i	0.986306	−	0.164926i	$-0.0527384\pi$
$440$	−4.08097	+	2.11111i	−0.194553	+	0.100643i
$441$	4.75588			0.226471
$442$	−18.5440	−	18.5440i	−0.882049	−	0.882049i
$443$	−10.1194	−	10.1194i	−0.480789	−	0.480789i	0.424594	−	0.905384i	$-0.360417\pi$
$443$	−10.1194	−	10.1194i	−0.480789	−	0.480789i	−0.905384	+	0.424594i	$0.860417\pi$
$444$	3.76610			0.178731
$445$	−1.50405	−	0.478477i	−0.0712988	−	0.0226820i
$446$	16.5915			0.785633
$447$	−13.4493	−	13.4493i	−0.636132	−	0.636132i
$448$	1.05927	−	1.05927i	0.0500459	−	0.0500459i
$449$		−	31.3177i		−	1.47798i	−0.673719	−	0.738988i	$-0.735304\pi$
$449$		−	31.3177i		−	1.47798i	0.673719	−	0.738988i	$-0.264696\pi$
$450$	−0.842929	−	4.92843i	−0.0397361	−	0.232329i
$451$			17.6841i			0.832710i
$452$	6.25116	+	6.25116i	0.294030	+	0.294030i
$453$	−5.71287	−	5.71287i	−0.268414	−	0.268414i
$454$	−10.2025			−0.478828
$455$	−3.95370	+	12.4281i	−0.185353	+	0.582640i
$456$			1.85358i			0.0868018i
$457$	−9.94629	−	9.94629i	−0.465268	−	0.465268i	0.435110	−	0.900378i	$-0.356710\pi$
$457$	−9.94629	−	9.94629i	−0.465268	−	0.465268i	−0.900378	+	0.435110i	$0.856710\pi$
$458$	−18.8950	+	18.8950i	−0.882908	+	0.882908i
$459$	−6.73577			−0.314399
$460$	−3.77927	−	10.0358i	−0.176210	−	0.467921i
$461$	−34.8508			−1.62317			−0.811583	−	0.584237i	$-0.801394\pi$
$461$	−34.8508			−1.62317			−0.811583	+	0.584237i	$0.801394\pi$
$462$	2.17660	−	2.17660i	0.101265	−	0.101265i
$463$	−15.4230	−	15.4230i	−0.716766	−	0.716766i	0.251175	−	0.967942i	$-0.419183\pi$
$463$	−15.4230	−	15.4230i	−0.716766	−	0.716766i	−0.967942	+	0.251175i	$0.919183\pi$
$464$		−	7.96345i		−	0.369694i
$465$	−10.5953	−	20.4816i	−0.491343	−	0.949811i
$466$	−10.8396			−0.502137
$467$	−21.1172	−	21.1172i	−0.977189	−	0.977189i	0.0225568	−	0.999746i	$-0.492819\pi$
$467$	−21.1172	−	21.1172i	−0.977189	−	0.977189i	−0.999746	+	0.0225568i	$0.992819\pi$
$468$	2.75307	+	2.75307i	0.127261	+	0.127261i
$469$		−	15.2951i		−	0.706261i
$470$	1.82130	−	5.72509i	0.0840102	−	0.264079i
$471$		−	7.22285i		−	0.332811i
$472$	−2.70134	+	2.70134i	−0.124339	+	0.124339i
$473$	−2.99978	−	2.99978i	−0.137930	−	0.137930i
$474$	16.3891			0.752775
$475$	7.56440	+	5.35478i	0.347079	+	0.245694i
$476$	−10.0904			−0.462495
$477$	3.57151	+	3.57151i	0.163528	+	0.163528i
$478$	3.67559	+	3.67559i	0.168117	+	0.168117i
$479$	−41.0169			−1.87411			−0.937056	−	0.349180i	$-0.886460\pi$
$479$	−41.0169			−1.87411			−0.937056	+	0.349180i	$0.886460\pi$
$480$	−2.13084	−	0.677875i	−0.0972592	−	0.0309406i
$481$			14.6630i			0.668575i
$482$	18.4564	+	18.4564i	0.840668	+	0.840668i
$483$	4.45099	+	5.63946i	0.202527	+	0.256604i
$484$		−	6.77778i		−	0.308081i
$485$	−0.820878	−	1.58683i	−0.0372741	−	0.0720543i
$486$	1.00000			0.0453609
$487$	4.93023	−	4.93023i	0.223410	−	0.223410i	−0.586523	−	0.809933i	$-0.699504\pi$
$487$	4.93023	−	4.93023i	0.223410	−	0.223410i	0.809933	+	0.586523i	$0.199504\pi$
$488$	1.95419	−	1.95419i	0.0884621	−	0.0884621i
$489$			4.95842i			0.224227i
$490$	−4.88620	−	9.44548i	−0.220736	−	0.426703i
$491$	23.7765			1.07302			0.536509	−	0.843895i	$-0.319743\pi$
$491$	23.7765			1.07302			0.536509	+	0.843895i	$0.319743\pi$
$492$	−6.08551	+	6.08551i	−0.274356	+	0.274356i
$493$	−37.9292	+	37.9292i	−1.70824	+	1.70824i
$494$	−7.21677			−0.324698
$495$	−4.37846	−	1.39290i	−0.196797	−	0.0626062i
$496$	−10.3127			−0.463052
$497$	−0.657526	−	0.657526i	−0.0294941	−	0.0294941i
$498$	−5.71805	+	5.71805i	−0.256232	+	0.256232i
$499$			17.9066i			0.801610i	0.916163	+	0.400805i	$0.131269\pi$
$499$			17.9066i			0.801610i	−0.916163	+	0.400805i	$0.868731\pi$
$500$	−8.92215	+	6.73760i	−0.399011	+	0.301314i
$501$	20.5275			0.917100
$502$	−3.37805	−	3.37805i	−0.150770	−	0.150770i
$503$	−8.64630	+	8.64630i	−0.385519	+	0.385519i	−0.873086	−	0.487567i	$-0.837885\pi$
$503$	−8.64630	+	8.64630i	−0.385519	+	0.385519i	0.487567	+	0.873086i	$0.337885\pi$
$504$	1.49804			0.0667279
$505$	31.0263	+	9.87026i	1.38065	+	0.439221i
$506$	−9.78685	−	1.15271i	−0.435078	−	0.0512443i
$507$	−1.52646	+	1.52646i	−0.0677927	+	0.0677927i
$508$	−5.96063	−	5.96063i	−0.264460	−	0.264460i
$509$			13.9217i			0.617070i	0.951213	+	0.308535i	$0.0998388\pi$
$509$			13.9217i			0.617070i	−0.951213	+	0.308535i	$0.900161\pi$
$510$	6.92035	+	13.3777i	0.306438	+	0.592373i
$511$		−	10.1084i		−	0.447167i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−1.31068	+	1.31068i	−0.0578679	+	0.0578679i
$514$			4.33456i			0.191189i
$515$	13.3813	−	6.92221i	0.589649	−	0.305029i
$516$		−	2.06459i		−	0.0908885i
$517$	−3.90379	−	3.90379i	−0.171689	−	0.171689i
$518$	3.98932	+	3.98932i	0.175281	+	0.175281i
$519$		−	24.1708i		−	1.06098i
$520$	2.63925	−	8.29627i	0.115739	−	0.363815i
$521$			1.76029i			0.0771199i	0.999256	+	0.0385600i	$0.0122771\pi$
$521$			1.76029i			0.0771199i	−0.999256	+	0.0385600i	$0.987723\pi$
$522$	5.63101	−	5.63101i	0.246462	−	0.246462i
$523$	28.5430	−	28.5430i	1.24810	−	1.24810i	0.291540	−	0.956559i	$-0.405832\pi$
$523$	28.5430	−	28.5430i	1.24810	−	1.24810i	0.956559	−	0.291540i	$-0.0941677\pi$
$524$		−	19.3136i		−	0.843718i
$525$	4.32767	−	6.11345i	0.188875	−	0.266813i
$526$			4.45926i			0.194433i
$527$	49.1183	+	49.1183i	2.13963	+	2.13963i
$528$	−1.45297	+	1.45297i	−0.0632322	+	0.0632322i
$529$	5.34383	−	22.3706i	0.232341	−	0.972635i
$530$	3.42387	−	10.7626i	0.148723	−	0.467499i
$531$	−3.82027			−0.165786
$532$	−1.96345	+	1.96345i	−0.0851262	+	0.0851262i
$533$	−23.6935	−	23.6935i	−1.02628	−	1.02628i
$534$	−0.705848			−0.0305450
$535$	−17.1609	−	33.1736i	−0.741932	−	1.43422i
$536$			10.2101i			0.441008i
$537$	13.8205	−	13.8205i	0.596400	−	0.596400i
$538$	−9.91172	−	9.91172i	−0.427325	−	0.427325i
$539$	−9.77241			−0.420927
$540$	−1.02740	−	1.98606i	−0.0442124	−	0.0854665i
$541$	31.2095			1.34180			0.670900	−	0.741548i	$-0.265908\pi$
$541$	31.2095			1.34180			0.670900	+	0.741548i	$0.265908\pi$
$542$	−0.222223	+	0.222223i	−0.00954528	+	0.00954528i
$543$	−17.6866	+	17.6866i	−0.759003	+	0.759003i
$544$	6.73577			0.288794
$545$	−6.08097	−	1.93451i	−0.260480	−	0.0828654i
$546$			5.83250i			0.249608i
$547$	−7.93990	+	7.93990i	−0.339486	+	0.339486i	−0.856174	−	0.516688i	$-0.827165\pi$
$547$	−7.93990	+	7.93990i	−0.339486	+	0.339486i	0.516688	+	0.856174i	$0.327165\pi$
$548$	11.2806	−	11.2806i	0.481884	−	0.481884i
$549$	2.76364			0.117949
$550$	1.73206	+	10.1270i	0.0738551	+	0.431816i
$551$			14.7609i			0.628834i
$552$	−2.97121	−	3.76456i	−0.126463	−	0.160230i
$553$	17.3605	+	17.3605i	0.738243	+	0.738243i
$554$		−	18.6121i		−	0.790754i
$555$	2.55294	−	8.02495i	0.108366	−	0.340640i
$556$	−5.76656			−0.244557
$557$	11.9125	+	11.9125i	0.504749	+	0.504749i	0.912910	−	0.408161i	$-0.133830\pi$
$557$	11.9125	+	11.9125i	0.504749	+	0.504749i	−0.408161	+	0.912910i	$0.633830\pi$
$558$	−7.29215	−	7.29215i	−0.308702	−	0.308702i
$559$	8.03832			0.339985
$560$	−1.53909	−	2.97520i	−0.0650383	−	0.125725i
$561$	13.8407			0.584354
$562$	−8.11241	−	8.11241i	−0.342201	−	0.342201i
$563$	9.93961	−	9.93961i	0.418905	−	0.418905i	−0.465921	−	0.884826i	$-0.654277\pi$
$563$	9.93961	−	9.93961i	0.418905	−	0.418905i	0.884826	+	0.465921i	$0.154277\pi$
$564$		−	2.68677i		−	0.113134i
$565$	17.5577	−	9.08273i	0.738660	−	0.382113i
$566$		−	5.14662i		−	0.216329i
$567$	1.05927	+	1.05927i	0.0444853	+	0.0444853i
$568$	0.438925	+	0.438925i	0.0184169	+	0.0184169i
$569$	21.8062			0.914164			0.457082	−	0.889425i	$-0.348895\pi$
$569$	21.8062			0.914164			0.457082	+	0.889425i	$0.348895\pi$
$570$	3.94968	+	1.25650i	0.165434	+	0.0526288i
$571$		−	4.43149i		−	0.185452i	−0.995692	−	0.0927260i	$-0.970442\pi$
$571$		−	4.43149i		−	0.185452i	0.995692	−	0.0927260i	$-0.0295580\pi$
$572$	−5.65701	−	5.65701i	−0.236532	−	0.236532i
$573$	7.56953	−	7.56953i	0.316222	−	0.316222i
$574$	−12.8924			−0.538119
$575$	−23.9466	+	1.25002i	−0.998640	+	0.0521295i
$576$	−1.00000			−0.0416667
$577$	4.31029	−	4.31029i	0.179440	−	0.179440i	−0.611672	−	0.791112i	$-0.709503\pi$
$577$	4.31029	−	4.31029i	0.179440	−	0.179440i	0.791112	+	0.611672i	$0.209503\pi$
$578$	−20.0610	−	20.0610i	−0.834429	−	0.834429i
$579$		−	10.1492i		−	0.421788i
$580$	−16.9688	−	5.39822i	−0.704593	−	0.224149i
$581$	−12.1139			−0.502571
$582$	−0.564967	−	0.564967i	−0.0234186	−	0.0234186i
$583$	−7.33876	−	7.33876i	−0.303940	−	0.303940i
$584$			6.74773i			0.279223i
$585$	7.73258	−	4.00011i	0.319703	−	0.165384i
$586$			4.24286i			0.175271i
$587$	6.29354	−	6.29354i	0.259762	−	0.259762i	−0.565195	−	0.824957i	$-0.691199\pi$
$587$	6.29354	−	6.29354i	0.259762	−	0.259762i	0.824957	+	0.565195i	$0.191199\pi$
$588$	−3.36292	−	3.36292i	−0.138684	−	0.138684i
$589$	19.1153			0.787634
$590$	3.92496	+	7.58730i	0.161588	+	0.312364i
$591$	3.83645			0.157811
$592$	−2.66303	−	2.66303i	−0.109450	−	0.109450i
$593$	21.5701	+	21.5701i	0.885777	+	0.885777i	0.994114	−	0.108337i	$-0.0345526\pi$
$593$	21.5701	+	21.5701i	0.885777	+	0.885777i	−0.108337	+	0.994114i	$0.534553\pi$
$594$	−2.05480			−0.0843097
$595$	−6.84006	+	21.5011i	−0.280415	+	0.881460i
$596$			19.0202i			0.779100i
$597$	−13.7006	−	13.7006i	−0.560727	−	0.560727i
$598$	14.6570	−	11.5682i	0.599370	−	0.473058i
$599$		−	7.58866i		−	0.310064i	−0.987909	−	0.155032i	$-0.950452\pi$
$599$		−	7.58866i		−	0.310064i	0.987909	−	0.155032i	$-0.0495481\pi$
$600$	−2.88889	+	4.08097i	−0.117938	+	0.166605i
$601$	−21.0502			−0.858656			−0.429328	−	0.903149i	$-0.641250\pi$
$601$	−21.0502			−0.858656			−0.429328	+	0.903149i	$0.641250\pi$
$602$	2.18696	−	2.18696i	0.0891340	−	0.0891340i
$603$	−7.21961	+	7.21961i	−0.294005	+	0.294005i
$604$			8.07922i			0.328739i
$605$	−14.4424	−	4.59449i	−0.587166	−	0.186792i
$606$	14.5606			0.591483
$607$	−4.94638	+	4.94638i	−0.200767	+	0.200767i	−0.800329	−	0.599561i	$-0.795342\pi$
$607$	−4.94638	+	4.94638i	−0.200767	+	0.200767i	0.599561	+	0.800329i	$0.295342\pi$
$608$	1.31068	−	1.31068i	0.0531550	−	0.0531550i
$609$	11.9295			0.483410
$610$	−2.83938	−	5.48877i	−0.114963	−	0.222234i
$611$	10.4608			0.423197
$612$	4.76291	+	4.76291i	0.192529	+	0.192529i
$613$	3.74955	−	3.74955i	0.151443	−	0.151443i	−0.627319	−	0.778762i	$-0.715848\pi$
$613$	3.74955	−	3.74955i	0.151443	−	0.151443i	0.778762	+	0.627319i	$0.215848\pi$
$614$		−	21.0842i		−	0.850891i
$615$	8.84204	+	17.0925i	0.356545	+	0.689235i
$616$	−3.07818			−0.124023
$617$	−19.0364	−	19.0364i	−0.766378	−	0.766378i	0.211089	−	0.977467i	$-0.432299\pi$
$617$	−19.0364	−	19.0364i	−0.766378	−	0.766378i	−0.977467	+	0.211089i	$0.932299\pi$
$618$	4.76419	−	4.76419i	0.191644	−	0.191644i
$619$	46.6096			1.87340			0.936700	−	0.350134i	$-0.113864\pi$
$619$	46.6096			1.87340			0.936700	+	0.350134i	$0.113864\pi$
$620$	−6.99070	+	21.9747i	−0.280753	+	0.882523i
$621$	0.560984	−	4.76291i	0.0225115	−	0.191129i
$622$	−7.41842	+	7.41842i	−0.297451	+	0.297451i
$623$	−0.747686	−	0.747686i	−0.0299554	−	0.0299554i
$624$		−	3.89342i		−	0.155862i
$625$	8.30864	+	23.5789i	0.332346	+	0.943158i
$626$		−	19.4109i		−	0.775815i
$627$	2.69319	−	2.69319i	0.107556	−	0.107556i
$628$	−5.10732	+	5.10732i	−0.203804	+	0.203804i
$629$			25.3676i			1.01147i
$630$	1.01548	−	3.19208i	0.0404578	−	0.127176i
$631$		−	17.2332i		−	0.686042i	−0.939328	−	0.343021i	$-0.888550\pi$
$631$		−	17.2332i		−	0.686042i	0.939328	−	0.343021i	$-0.111450\pi$
$632$	−11.5888	−	11.5888i	−0.460979	−	0.460979i
$633$	−6.94260	−	6.94260i	−0.275943	−	0.275943i
$634$		−	11.8407i		−	0.470254i
$635$	−16.7417	+	8.66060i	−0.664375	+	0.343685i
$636$		−	5.05088i		−	0.200280i
$637$	13.0933	−	13.0933i	0.518774	−	0.518774i
$638$	−11.5706	+	11.5706i	−0.458085	+	0.458085i
$639$			0.620733i			0.0245558i
$640$	1.02740	+	1.98606i	0.0406116	+	0.0785060i
$641$		−	37.3431i		−	1.47496i	−0.675367	−	0.737482i	$-0.736015\pi$
$641$		−	37.3431i		−	1.47496i	0.675367	−	0.737482i	$-0.263985\pi$
$642$	−11.8110	−	11.8110i	−0.466141	−	0.466141i
$643$	−9.61594	+	9.61594i	−0.379215	+	0.379215i	−0.870819	−	0.491604i	$-0.836411\pi$
$643$	−9.61594	+	9.61594i	−0.379215	+	0.379215i	0.491604	+	0.870819i	$0.336411\pi$
$644$	0.840376	−	7.13502i	0.0331154	−	0.281159i
$645$	−4.39931	−	1.39953i	−0.173223	−	0.0551066i
$646$	−12.4853			−0.491227
$647$	31.9140	−	31.9140i	1.25467	−	1.25467i	0.301064	−	0.953604i	$-0.402658\pi$
$647$	31.9140	−	31.9140i	1.25467	−	1.25467i	0.953604	−	0.301064i	$-0.0973416\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	7.84992			0.308136
$650$	−15.8889	−	11.2477i	−0.623216	−	0.441170i
$651$		−	15.4488i		−	0.605485i
$652$	3.50613	−	3.50613i	0.137311	−	0.137311i
$653$	12.0188	+	12.0188i	0.470332	+	0.470332i	0.902022	−	0.431690i	$-0.142082\pi$
$653$	12.0188	+	12.0188i	0.470332	+	0.470332i	−0.431690	+	0.902022i	$0.642082\pi$
$654$	−2.85379			−0.111592
$655$	−41.1542	−	13.0922i	−1.60803	−	0.511554i
$656$	8.60620			0.336016
$657$	−4.77136	+	4.77136i	−0.186149	+	0.186149i
$658$	2.84603	−	2.84603i	0.110950	−	0.110950i
$659$	−5.65904			−0.220445			−0.110222	−	0.993907i	$-0.535156\pi$
$659$	−5.65904			−0.220445			−0.110222	+	0.993907i	$0.535156\pi$
$660$	2.11111	+	4.08097i	0.0821749	+	0.158852i
$661$		−	21.4115i		−	0.832811i	−0.909179	−	0.416406i	$-0.863290\pi$
$661$		−	21.4115i		−	0.832811i	0.909179	−	0.416406i	$-0.136710\pi$
$662$	−10.4983	+	10.4983i	−0.408029	+	0.408029i
$663$	−18.5440	+	18.5440i	−0.720190	+	0.720190i
$664$	8.08654			0.313819
$665$	2.85282	+	5.51476i	0.110628	+	0.213853i
$666$		−	3.76610i		−	0.145933i
$667$	−23.6611	−	29.9789i	−0.916160	−	1.16079i
$668$	−14.5151	−	14.5151i	−0.561606	−	0.561606i
$669$		−	16.5915i		−	0.641466i
$670$	21.7560	+	6.92115i	0.840509	+	0.267387i
$671$	−5.67875			−0.219226
$672$	−1.05927	−	1.05927i	−0.0408623	−	0.0408623i
$673$	0.273515	+	0.273515i	0.0105432	+	0.0105432i	0.712359	−	0.701816i	$-0.247627\pi$
$673$	0.273515	+	0.273515i	0.0105432	+	0.0105432i	−0.701816	+	0.712359i	$0.747627\pi$
$674$	0.569514			0.0219369
$675$	−4.92843	+	0.842929i	−0.189696	+	0.0324444i
$676$	2.15875			0.0830287
$677$	3.62366	+	3.62366i	0.139268	+	0.139268i	0.773304	−	0.634035i	$-0.218603\pi$
$677$	3.62366	+	3.62366i	0.139268	+	0.139268i	−0.634035	+	0.773304i	$0.718603\pi$
$678$	6.25116	−	6.25116i	0.240074	−	0.240074i
$679$		−	1.19691i		−	0.0459331i
$680$	4.56601	−	14.3529i	0.175099	−	0.550407i
$681$			10.2025i			0.390962i
$682$	14.9840	+	14.9840i	0.573765	+	0.573765i
$683$	22.0303	+	22.0303i	0.842968	+	0.842968i	0.989244	−	0.146276i	$-0.0467288\pi$
$683$	22.0303	+	22.0303i	0.842968	+	0.842968i	−0.146276	+	0.989244i	$0.546729\pi$
$684$	1.85358			0.0708734
$685$	−16.3904	−	31.6841i	−0.626244	−	1.21059i
$686$		−	17.6108i		−	0.672382i
$687$	18.8950	+	18.8950i	0.720891	+	0.720891i
$688$	−1.45989	+	1.45989i	−0.0556576	+	0.0556576i
$689$	19.6652			0.749185
$690$	−10.0358	+	3.77927i	−0.382056	+	0.143875i
$691$	11.8861			0.452167			0.226083	−	0.974108i	$-0.427408\pi$
$691$	11.8861			0.452167			0.226083	+	0.974108i	$0.427408\pi$
$692$	−17.0914	+	17.0914i	−0.649716	+	0.649716i
$693$	−2.17660	−	2.17660i	−0.0826822	−	0.0826822i
$694$			14.1710i			0.537924i
$695$	−3.90901	+	12.2876i	−0.148277	+	0.466096i
$696$	−7.96345			−0.301854
$697$	−40.9906	−	40.9906i	−1.55263	−	1.55263i
$698$	−14.9538	−	14.9538i	−0.566010	−	0.566010i
$699$			10.8396i			0.409993i
$700$	−7.38298	+	1.26274i	−0.279051	+	0.0477271i
$701$			18.1192i			0.684353i	0.939636	+	0.342177i	$0.111164\pi$
$701$			18.1192i			0.684353i	−0.939636	+	0.342177i	$0.888836\pi$
$702$	2.75307	−	2.75307i	0.103908	−	0.103908i
$703$	4.93614	+	4.93614i	0.186170	+	0.186170i
$704$	2.05480			0.0774434
$705$	−5.72509	−	1.82130i	−0.215619	−	0.0685940i
$706$	8.27607			0.311474
$707$	15.4236	+	15.4236i	0.580065	+	0.580065i
$708$	2.70134	+	2.70134i	0.101523	+	0.101523i
$709$	27.9725			1.05053			0.525266	−	0.850938i	$-0.323966\pi$
$709$	27.9725			1.05053			0.525266	+	0.850938i	$0.323966\pi$
$710$	1.23282	−	0.637743i	0.0462667	−	0.0239341i
$711$		−	16.3891i		−	0.614638i
$712$	0.499110	+	0.499110i	0.0187049	+	0.0187049i
$713$	−38.8226	+	30.6411i	−1.45392	+	1.14752i
$714$			10.0904i			0.377625i
$715$	−15.8889	+	8.21945i	−0.594213	+	0.307390i
$716$	−19.5452			−0.730438
$717$	3.67559	−	3.67559i	0.137267	−	0.137267i
$718$	−5.15644	+	5.15644i	−0.192437	+	0.192437i
$719$			30.4764i			1.13658i	0.822829	+	0.568289i	$0.192394\pi$
$719$			30.4764i			1.13658i	−0.822829	+	0.568289i	$0.807606\pi$
$720$	−0.677875	+	2.13084i	−0.0252629	+	0.0794118i
$721$	10.0932			0.375889
$722$	11.0056	−	11.0056i	0.409585	−	0.409585i
$723$	18.4564	−	18.4564i	0.686402	−	0.686402i
$724$	25.0126			0.929585
$725$	−23.0055	+	32.4986i	−0.854403	+	1.20697i
$726$	−6.77778			−0.251547
$727$	34.3280	+	34.3280i	1.27316	+	1.27316i	0.944423	+	0.328732i	$0.106621\pi$
$727$	34.3280	+	34.3280i	1.27316	+	1.27316i	0.328732	+	0.944423i	$0.393379\pi$
$728$	4.12420	−	4.12420i	0.152853	−	0.152853i
$729$		−	1.00000i		−	0.0370370i
$730$	14.3783	+	4.57412i	0.532166	+	0.169296i
$731$	13.9066			0.514354
$732$	−1.95419	−	1.95419i	−0.0722290	−	0.0722290i
$733$	−21.2431	+	21.2431i	−0.784630	+	0.784630i	−0.980608	−	0.195978i	$-0.937212\pi$
$733$	−21.2431	+	21.2431i	−0.784630	+	0.784630i	0.195978	+	0.980608i	$0.437212\pi$
$734$	−6.26275			−0.231162
$735$	−9.44548	+	4.88620i	−0.348402	+	0.180230i
$736$	−0.560984	+	4.76291i	−0.0206781	+	0.175563i
$737$	14.8349	−	14.8349i	0.546450	−	0.546450i
$738$	6.08551	+	6.08551i	0.224011	+	0.224011i
$739$			13.7089i			0.504289i	0.967690	+	0.252144i	$0.0811358\pi$
$739$			13.7089i			0.504289i	−0.967690	+	0.252144i	$0.918864\pi$
$740$	−7.47970	+	3.86930i	−0.274959	+	0.142238i
$741$			7.21677i			0.265115i
$742$	5.35026	−	5.35026i	0.196414	−	0.196414i
$743$	4.39312	−	4.39312i	0.161168	−	0.161168i	−0.621916	−	0.783084i	$-0.713645\pi$
$743$	4.39312	−	4.39312i	0.161168	−	0.161168i	0.783084	+	0.621916i	$0.213645\pi$
$744$			10.3127i			0.378081i
$745$	40.5291	+	12.8934i	1.48487	+	0.472376i
$746$		−	23.6868i		−	0.867237i
$747$	5.71805	+	5.71805i	0.209212	+	0.209212i
$748$	−9.78685	−	9.78685i	−0.357843	−	0.357843i
$749$		−	25.0221i		−	0.914286i
$750$	6.73760	+	8.92215i	0.246022	+	0.325791i
$751$		−	34.4080i		−	1.25557i	−0.778388	−	0.627783i	$-0.783962\pi$
$751$		−	34.4080i		−	1.25557i	0.778388	−	0.627783i	$-0.216038\pi$
$752$	−1.89984	+	1.89984i	−0.0692799	+	0.0692799i
$753$	−3.37805	+	3.37805i	−0.123103	+	0.123103i
$754$		−	31.0051i		−	1.12914i
$755$	17.2155	+	5.47670i	0.626538	+	0.199318i
$756$		−	1.49804i		−	0.0544831i
$757$	−14.8002	−	14.8002i	−0.537924	−	0.537924i	0.384995	−	0.922919i	$-0.374203\pi$
$757$	−14.8002	−	14.8002i	−0.537924	−	0.537924i	−0.922919	+	0.384995i	$0.874203\pi$
$758$	−13.5590	+	13.5590i	−0.492484	+	0.492484i
$759$	−1.15271	+	9.78685i	−0.0418408	+	0.355240i
$760$	−1.90437	−	3.68132i	−0.0690788	−	0.133536i
$761$	−25.2096			−0.913849			−0.456924	−	0.889506i	$-0.651049\pi$
$761$	−25.2096			−0.913849			−0.456924	+	0.889506i	$0.651049\pi$
$762$	−5.96063	+	5.96063i	−0.215931	+	0.215931i
$763$	−3.02294	−	3.02294i	−0.109438	−	0.109438i
$764$	−10.7049			−0.387291
$765$	13.3777	−	6.92035i	0.483670	−	0.250206i
$766$		−	9.22000i		−	0.333132i
$767$	−10.5175	+	10.5175i	−0.379764	+	0.379764i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	−7.92654			−0.285838			−0.142919	−	0.989734i	$-0.545649\pi$
$769$	−7.92654			−0.285838			−0.142919	+	0.989734i	$0.545649\pi$
$770$	−2.08662	+	6.55911i	−0.0751965	+	0.236374i
$771$	4.33456			0.156105
$772$	−7.17660	+	7.17660i	−0.258291	+	0.258291i
$773$	36.0701	−	36.0701i	1.29735	−	1.29735i	0.367215	−	0.930136i	$-0.380311\pi$
$773$	36.0701	−	36.0701i	1.29735	−	1.29735i	0.930136	−	0.367215i	$-0.119689\pi$
$774$	−2.06459			−0.0742102
$775$	42.0857	+	29.7921i	1.51176	+	1.07017i
$776$			0.798984i			0.0286818i
$777$	3.98932	−	3.98932i	0.143116	−	0.143116i
$778$	−23.5189	+	23.5189i	−0.843195	+	0.843195i
$779$	−15.9523			−0.571550
$780$	−8.29627	−	2.63925i	−0.297054	−	0.0945005i
$781$		−	1.27549i		−	0.0456405i
$782$	25.3572	−	20.0134i	0.906772	−	0.715677i
$783$	−5.63101	−	5.63101i	−0.201236	−	0.201236i
$784$			4.75588i			0.169853i
$785$	7.42077	+	14.3450i	0.264859	+	0.511996i
$786$	−19.3136			−0.688893
$787$	−14.2261	−	14.2261i	−0.507105	−	0.507105i	0.406532	−	0.913637i	$-0.366738\pi$
$787$	−14.2261	−	14.2261i	−0.507105	−	0.507105i	−0.913637	+	0.406532i	$0.866738\pi$
$788$	−2.71278	−	2.71278i	−0.0966388	−	0.0966388i
$789$	4.45926			0.158754
$790$	−32.5497	+	16.8382i	−1.15807	+	0.599075i
$791$	13.2434			0.470880
$792$	1.45297	+	1.45297i	0.0516289	+	0.0516289i
$793$	7.60850	−	7.60850i	0.270186	−	0.270186i
$794$		−	18.4428i		−	0.654510i
$795$	−10.7626	−	3.42387i	−0.381711	−	0.121432i
$796$			19.3755i			0.686748i
$797$	−20.2378	−	20.2378i	−0.716859	−	0.716859i	0.251101	−	0.967961i	$-0.419207\pi$
$797$	−20.2378	−	20.2378i	−0.716859	−	0.716859i	−0.967961	+	0.251101i	$0.919207\pi$
$798$	1.96345	+	1.96345i	0.0695052	+	0.0695052i
$799$	18.0975			0.640243
$800$	4.92843	−	0.842929i	0.174246	−	0.0298021i
$801$			0.705848i			0.0249399i
$802$	25.8690	+	25.8690i	0.913468	+	0.913468i
$803$	9.80422	−	9.80422i	0.345983	−	0.345983i
$804$	10.2101			0.360081
$805$	−14.6339	−	6.62736i	−0.515778	−	0.233584i
$806$	−40.1516			−1.41428
$807$	−9.91172	+	9.91172i	−0.348909	+	0.348909i
$808$	−10.2959	−	10.2959i	−0.362208	−	0.362208i
$809$			3.05536i			0.107421i	0.998557	+	0.0537103i	$0.0171048\pi$
$809$			3.05536i			0.107421i	−0.998557	+	0.0537103i	$0.982895\pi$
$810$	−1.98606	+	1.02740i	−0.0697831	+	0.0360992i
$811$	−16.0121			−0.562262			−0.281131	−	0.959669i	$-0.590710\pi$
$811$	−16.0121			−0.562262			−0.281131	+	0.959669i	$0.590710\pi$
$812$	−8.43546	−	8.43546i	−0.296027	−	0.296027i
$813$	0.222223	+	0.222223i	0.00779369	+	0.00779369i
$814$			7.73859i			0.271237i
$815$	−5.09429	−	9.84773i	−0.178445	−	0.344951i
$816$		−	6.73577i		−	0.235799i
$817$	2.70601	−	2.70601i	0.0946714	−	0.0946714i
$818$	1.85124	+	1.85124i	0.0647271	+	0.0647271i
$819$	5.83250			0.203804
$820$	5.83393	−	18.3385i	0.203730	−	0.640407i
$821$	14.8907			0.519690			0.259845	−	0.965650i	$-0.416329\pi$
$821$	14.8907			0.519690			0.259845	+	0.965650i	$0.416329\pi$
$822$	−11.2806	−	11.2806i	−0.393457	−	0.393457i
$823$	−14.0644	−	14.0644i	−0.490254	−	0.490254i	0.418132	−	0.908386i	$-0.362685\pi$
$823$	−14.0644	−	14.0644i	−0.490254	−	0.490254i	−0.908386	+	0.418132i	$0.862685\pi$
$824$	−6.73758			−0.234715
$825$	10.1270	−	1.73206i	0.352576	−	0.0603024i
$826$			5.72292i			0.199126i
$827$	31.3242	+	31.3242i	1.08925	+	1.08925i	0.995606	+	0.0936432i	$0.0298513\pi$
$827$	31.3242	+	31.3242i	1.08925	+	1.08925i	0.0936432	+	0.995606i	$0.470149\pi$
$828$	−3.76456	+	2.97121i	−0.130828	+	0.103257i
$829$		−	39.2942i		−	1.36474i	−0.731005	−	0.682372i	$-0.760949\pi$
$829$		−	39.2942i		−	1.36474i	0.731005	−	0.682372i	$-0.239051\pi$
$830$	5.48166	−	17.2311i	0.190271	−	0.598101i
$831$	−18.6121			−0.645648
$832$	−2.75307	+	2.75307i	−0.0954454	+	0.0954454i
$833$	22.6518	−	22.6518i	0.784839	−	0.784839i
$834$			5.76656i			0.199680i
$835$	−40.7688	+	21.0900i	−1.41086	+	0.729848i
$836$	−3.80874			−0.131728
$837$	−7.29215	+	7.29215i	−0.252054	+	0.252054i
$838$	3.77722	−	3.77722i	0.130482	−	0.130482i
$839$	15.4816			0.534483			0.267241	−	0.963630i	$-0.413888\pi$
$839$	15.4816			0.534483			0.267241	+	0.963630i	$0.413888\pi$
$840$	−2.97520	+	1.53909i	−0.102654	+	0.0531036i
$841$	−34.4165			−1.18678
$842$	15.8498	+	15.8498i	0.546220	+	0.546220i
$843$	−8.11241	+	8.11241i	−0.279406	+	0.279406i
$844$			9.81831i			0.337960i
$845$	1.46336	−	4.59995i	0.0503411	−	0.158243i
$846$	−2.68677			−0.0923732
$847$	−7.17952	−	7.17952i	−0.246691	−	0.246691i
$848$	−3.57151	+	3.57151i	−0.122646	+	0.122646i
$849$	−5.14662			−0.176632
$850$	−27.4885	−	19.4589i	−0.942847	−	0.667434i
$851$	−17.9376	−	2.11272i	−0.614892	−	0.0724231i
$852$	0.438925	−	0.438925i	0.0150373	−	0.0150373i
$853$	−14.2518	−	14.2518i	−0.487972	−	0.487972i	0.419694	−	0.907666i	$-0.362137\pi$
$853$	−14.2518	−	14.2518i	−0.487972	−	0.487972i	−0.907666	+	0.419694i	$0.862137\pi$
$854$		−	4.14005i		−	0.141669i
$855$	1.25650	−	3.94968i	0.0429712	−	0.135076i
$856$			16.7032i			0.570904i
$857$	−2.26492	+	2.26492i	−0.0773682	+	0.0773682i	−0.744732	−	0.667364i	$-0.767423\pi$
$857$	−2.26492	+	2.26492i	−0.0773682	+	0.0773682i	0.667364	+	0.744732i	$0.267423\pi$
$858$	−5.65701	+	5.65701i	−0.193127	+	0.193127i
$859$		−	19.8900i		−	0.678637i	−0.940671	−	0.339319i	$-0.889804\pi$
$859$		−	19.8900i		−	0.678637i	0.940671	−	0.339319i	$-0.110196\pi$
$860$	2.12116	+	4.10040i	0.0723311	+	0.139823i
$861$			12.8924i			0.439373i
$862$	21.3842	+	21.3842i	0.728348	+	0.728348i
$863$	4.59473	+	4.59473i	0.156406	+	0.156406i	0.780972	−	0.624566i	$-0.214724\pi$
$863$	4.59473	+	4.59473i	0.156406	+	0.156406i	−0.624566	+	0.780972i	$0.714724\pi$
$864$			1.00000i			0.0340207i
$865$	24.8332	+	48.0048i	0.844353	+	1.63221i
$866$		−	16.8641i		−	0.573067i
$867$	−20.0610	+	20.0610i	−0.681309	+	0.681309i
$868$	−10.9239	+	10.9239i	−0.370782	+	0.370782i
$869$			33.6763i			1.14239i
$870$	−5.39822	+	16.9688i	−0.183017	+	0.575298i
$871$			39.7521i			1.34695i
$872$	2.01793	+	2.01793i	0.0683358	+	0.0683358i
$873$	−0.564967	+	0.564967i	−0.0191212	+	0.0191212i
$874$	1.03983	−	8.82843i	0.0351727	−	0.298626i
$875$	−2.31404	+	16.5879i	−0.0782289	+	0.560775i
$876$	6.74773			0.227985
$877$	37.2514	−	37.2514i	1.25789	−	1.25789i	0.305792	−	0.952098i	$-0.401079\pi$
$877$	37.2514	−	37.2514i	1.25789	−	1.25789i	0.952098	−	0.305792i	$-0.0989212\pi$
$878$	4.88692	+	4.88692i	0.164926	+	0.164926i
$879$	4.24286			0.143108
$880$	1.39290	−	4.37846i	0.0469547	−	0.147598i
$881$			23.4711i			0.790761i	0.918517	+	0.395380i	$0.129387\pi$
$881$			23.4711i			0.790761i	−0.918517	+	0.395380i	$0.870613\pi$
$882$	−3.36292	+	3.36292i	−0.113235	+	0.113235i
$883$	1.67549	+	1.67549i	0.0563848	+	0.0563848i	0.734737	−	0.678352i	$-0.237306\pi$
$883$	1.67549	+	1.67549i	0.0563848	+	0.0563848i	−0.678352	+	0.734737i	$0.737306\pi$
$884$	26.2252			0.882049
$885$	7.58730	−	3.92496i	0.255044	−	0.131936i
$886$	14.3111			0.480789
$887$	−37.1049	+	37.1049i	−1.24586	+	1.24586i	−0.288328	+	0.957532i	$0.593099\pi$
$887$	−37.1049	+	37.1049i	−1.24586	+	1.24586i	−0.957532	+	0.288328i	$0.906901\pi$
$888$	−2.66303	+	2.66303i	−0.0893655	+	0.0893655i
$889$	−12.6279			−0.423525
$890$	1.40186	−	0.725190i	0.0469904	−	0.0243084i
$891$			2.05480i			0.0688385i
$892$	−11.7320	+	11.7320i	−0.392816	+	0.392816i
$893$	3.52150	−	3.52150i	0.117842	−	0.117842i
$894$	19.0202			0.636132
$895$	−13.2492	+	41.6477i	−0.442872	+	1.39213i
$896$			1.49804i			0.0500459i
$897$	−11.5682	−	14.6570i	−0.386250	−	0.489384i
$898$	22.1450	+	22.1450i	0.738988	+	0.738988i
$899$			82.1243i			2.73900i
$900$	4.08097	+	2.88889i	0.136032	+	0.0962963i
$901$	34.0216			1.13342
$902$	−12.5045	−	12.5045i	−0.416355	−	0.416355i
$903$	−2.18696	−	2.18696i	−0.0727776	−	0.0727776i
$904$	−8.84048			−0.294030
$905$	16.9554	−	53.2978i	0.563617	−	1.77168i
$906$	8.07922			0.268414
$907$	−9.36706	−	9.36706i	−0.311028	−	0.311028i	0.534280	−	0.845308i	$-0.320583\pi$
$907$	−9.36706	−	9.36706i	−0.311028	−	0.311028i	−0.845308	+	0.534280i	$0.820583\pi$
$908$	7.21427	−	7.21427i	0.239414	−	0.239414i
$909$		−	14.5606i		−	0.482944i
$910$	−5.99232	−	11.5837i	−0.198644	−	0.383996i
$911$		−	43.8286i		−	1.45210i	−0.687639	−	0.726052i	$-0.741353\pi$
$911$		−	43.8286i		−	1.45210i	0.687639	−	0.726052i	$-0.258647\pi$
$912$	−1.31068	−	1.31068i	−0.0434009	−	0.0434009i
$913$	−11.7495	−	11.7495i	−0.388851	−	0.388851i
$914$	14.0662			0.465268
$915$	−5.48877	+	2.83938i	−0.181453	+	0.0938668i
$916$		−	26.7216i		−	0.882908i
$917$	−20.4584	−	20.4584i	−0.675594	−	0.675594i
$918$	4.76291	−	4.76291i	0.157199	−	0.157199i
$919$	39.5657			1.30515			0.652575	−	0.757724i	$-0.273689\pi$
$919$	39.5657			1.30515			0.652575	+	0.757724i	$0.273689\pi$
$920$	9.76873	+	4.42403i	0.322065	+	0.145856i
$921$	−21.0842			−0.694750
$922$	24.6433	−	24.6433i	0.811583	−	0.811583i
$923$	1.70892	+	1.70892i	0.0562498	+	0.0562498i
$924$			3.07818i			0.101265i
$925$	3.17455	+	18.5610i	0.104379	+	0.610281i
$926$	21.8114			0.716766
$927$	−4.76419	−	4.76419i	−0.156477	−	0.156477i
$928$	5.63101	+	5.63101i	0.184847	+	0.184847i
$929$		−	31.1896i		−	1.02330i	−0.859195	−	0.511648i	$-0.829035\pi$
$929$		−	31.1896i		−	1.02330i	0.859195	−	0.511648i	$-0.170965\pi$
$930$	21.9747	+	6.99070i	0.720577	+	0.229234i
$931$		−	8.81540i		−	0.288913i
$932$	7.66479	−	7.66479i	0.251068	−	0.251068i
$933$	7.41842	+	7.41842i	0.242868	+	0.242868i
$934$	29.8643			0.977189
$935$	−27.4885	+	14.2200i	−0.898969	+	0.465042i
$936$	−3.89342			−0.127261
$937$	−15.7182	−	15.7182i	−0.513491	−	0.513491i	0.402104	−	0.915594i	$-0.368279\pi$
$937$	−15.7182	−	15.7182i	−0.513491	−	0.513491i	−0.915594	+	0.402104i	$0.868279\pi$
$938$	10.8152	+	10.8152i	0.353130	+	0.353130i
$939$	−19.4109			−0.633450
$940$	2.76040	+	5.33610i	0.0900343	+	0.174044i
$941$			53.2666i			1.73644i	0.496178	+	0.868221i	$0.334736\pi$
$941$			53.2666i			1.73644i	−0.496178	+	0.868221i	$0.665264\pi$
$942$	5.10732	+	5.10732i	0.166406	+	0.166406i
$943$	32.3986	−	25.5708i	1.05504	−	0.832701i
$944$		−	3.82027i		−	0.124339i
$945$	−3.19208	−	1.01548i	−0.103838	−	0.0330337i
$946$	4.24233			0.137930
$947$	−24.9909	+	24.9909i	−0.812094	+	0.812094i	−0.984947	−	0.172854i	$-0.944701\pi$
$947$	−24.9909	+	24.9909i	−0.812094	+	0.812094i	0.172854	+	0.984947i	$0.444701\pi$
$948$	−11.5888	+	11.5888i	−0.376387	+	0.376387i
$949$			26.2718i			0.852817i
$950$	−9.13524	+	1.56244i	−0.296386	+	0.0506921i
$951$	−11.8407			−0.383961
$952$	7.13502	−	7.13502i	0.231247	−	0.231247i
$953$	−6.28850	+	6.28850i	−0.203705	+	0.203705i	−0.801585	−	0.597881i	$-0.796010\pi$
$953$	−6.28850	+	6.28850i	−0.203705	+	0.203705i	0.597881	+	0.801585i	$0.296010\pi$
$954$	−5.05088			−0.163528
$955$	−7.25661	+	22.8105i	−0.234818	+	0.738131i
$956$	−5.19806			−0.168117
$957$	11.5706	+	11.5706i	0.374025	+	0.374025i
$958$	29.0033	−	29.0033i	0.937056	−	0.937056i
$959$		−	23.8985i		−	0.771723i
$960$	1.98606	−	1.02740i	0.0640999	−	0.0331593i
$961$	75.3510			2.43068
$962$	−10.3683	−	10.3683i	−0.334288	−	0.334288i
$963$	−11.8110	+	11.8110i	−0.380603	+	0.380603i
$964$	−26.1013			−0.840668
$965$	10.4274	+	20.1570i	0.335669	+	0.648878i
$966$	−7.13502	−	0.840376i	−0.229565	−	0.0270386i
$967$	−18.5697	+	18.5697i	−0.597160	+	0.597160i	−0.939556	−	0.342395i	$-0.888762\pi$
$967$	−18.5697	+	18.5697i	−0.597160	+	0.597160i	0.342395	+	0.939556i	$0.388762\pi$
$968$	4.79261	+	4.79261i	0.154040	+	0.154040i
$969$			12.4853i			0.401085i
$970$	1.70251	+	0.541611i	0.0546642	+	0.0173901i
$971$		−	46.2938i		−	1.48564i	−0.669492	−	0.742819i	$-0.733488\pi$
$971$		−	46.2938i		−	1.48564i	0.669492	−	0.742819i	$-0.266512\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	−6.10836	+	6.10836i	−0.195825	+	0.195825i
$974$			6.97239i			0.223410i
$975$	−11.2477	+	15.8889i	−0.360214	+	0.508854i
$976$			2.76364i			0.0884621i
$977$	14.5578	+	14.5578i	0.465745	+	0.465745i	0.900533	−	0.434788i	$-0.143177\pi$
$977$	14.5578	+	14.5578i	0.465745	+	0.465745i	−0.434788	+	0.900533i	$0.643177\pi$
$978$	−3.50613	−	3.50613i	−0.112114	−	0.112114i
$979$		−	1.45038i		−	0.0463543i
$980$	10.1340	+	3.22389i	0.323720	+	0.102983i
$981$			2.85379i			0.0911145i
$982$	−16.8125	+	16.8125i	−0.536509	+	0.536509i
$983$	22.8319	−	22.8319i	0.728225	−	0.728225i	−0.242041	−	0.970266i	$-0.577817\pi$
$983$	22.8319	−	22.8319i	0.728225	−	0.728225i	0.970266	+	0.242041i	$0.0778168\pi$
$984$		−	8.60620i		−	0.274356i
$985$	−7.61943	+	3.94158i	−0.242775	+	0.125589i
$986$		−	53.6399i		−	1.70824i
$987$	−2.84603	−	2.84603i	−0.0905901	−	0.0905901i
$988$	5.10303	−	5.10303i	0.162349	−	0.162349i
$989$	−1.15820	+	9.83345i	−0.0368287	+	0.312686i
$990$	4.08097	−	2.11111i	0.129702	−	0.0670955i
$991$	−19.0826			−0.606180			−0.303090	−	0.952962i	$-0.598018\pi$
$991$	−19.0826			−0.606180			−0.303090	+	0.952962i	$0.598018\pi$
$992$	7.29215	−	7.29215i	0.231526	−	0.231526i
$993$	10.4983	+	10.4983i	0.333155	+	0.333155i
$994$	0.929882			0.0294941
$995$	41.2862	+	13.1342i	1.30886	+	0.416382i
$996$		−	8.08654i		−	0.256232i
$997$	−29.5084	+	29.5084i	−0.934540	+	0.934540i	−0.997985	−	0.0634454i	$-0.979791\pi$
$997$	−29.5084	+	29.5084i	−0.934540	+	0.934540i	0.0634454	+	0.997985i	$0.479791\pi$
$998$	−12.6619	−	12.6619i	−0.400805	−	0.400805i
$999$	−3.76610			−0.119154

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.j.a.643.1	yes	24
5.2	odd	4	inner	690.2.j.a.367.6	yes	24
23.22	odd	2	inner	690.2.j.a.643.6	yes	24
115.22	even	4	inner	690.2.j.a.367.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.j.a.367.1	✓	24	115.22	even	4	inner
690.2.j.a.367.6	yes	24	5.2	odd	4	inner
690.2.j.a.643.1	yes	24	1.1	even	1	trivial
690.2.j.a.643.6	yes	24	23.22	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(-2.13084 - 0.677875i) q^{5} -1.00000 q^{6} +(-1.05927 - 1.05927i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(-2.13084 - 0.677875i) q^{5} -1.00000 q^{6} +(-1.05927 - 1.05927i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(1.98606 - 1.02740i) q^{10} -2.05480i q^{11} +(0.707107 - 0.707107i) q^{12} +(2.75307 + 2.75307i) q^{13} +1.49804 q^{14} +(-1.02740 - 1.98606i) q^{15} -1.00000 q^{16} +(4.76291 + 4.76291i) q^{17} +(-0.707107 - 0.707107i) q^{18} +1.85358 q^{19} +(-0.677875 + 2.13084i) q^{20} -1.49804i q^{21} +(1.45297 + 1.45297i) q^{22} +(-3.76456 + 2.97121i) q^{23} +1.00000i q^{24} +(4.08097 + 2.88889i) q^{25} -3.89342 q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.05927 + 1.05927i) q^{28} +7.96345i q^{29} +(2.13084 + 0.677875i) q^{30} +10.3127 q^{31} +(0.707107 - 0.707107i) q^{32} +(1.45297 - 1.45297i) q^{33} -6.73577 q^{34} +(1.53909 + 2.97520i) q^{35} +1.00000 q^{36} +(2.66303 + 2.66303i) q^{37} +(-1.31068 + 1.31068i) q^{38} +3.89342i q^{39} +(-1.02740 - 1.98606i) q^{40} -8.60620 q^{41} +(1.05927 + 1.05927i) q^{42} +(1.45989 - 1.45989i) q^{43} -2.05480 q^{44} +(0.677875 - 2.13084i) q^{45} +(0.560984 - 4.76291i) q^{46} +(1.89984 - 1.89984i) q^{47} +(-0.707107 - 0.707107i) q^{48} -4.75588i q^{49} +(-4.92843 + 0.842929i) q^{50} +6.73577i q^{51} +(2.75307 - 2.75307i) q^{52} +(3.57151 - 3.57151i) q^{53} -1.00000i q^{54} +(-1.39290 + 4.37846i) q^{55} -1.49804i q^{56} +(1.31068 + 1.31068i) q^{57} +(-5.63101 - 5.63101i) q^{58} +3.82027i q^{59} +(-1.98606 + 1.02740i) q^{60} -2.76364i q^{61} +(-7.29215 + 7.29215i) q^{62} +(1.05927 - 1.05927i) q^{63} +1.00000i q^{64} +(-4.00011 - 7.73258i) q^{65} +2.05480i q^{66} +(7.21961 + 7.21961i) q^{67} +(4.76291 - 4.76291i) q^{68} +(-4.76291 - 0.560984i) q^{69} +(-3.19208 - 1.01548i) q^{70} +0.620733 q^{71} +(-0.707107 + 0.707107i) q^{72} +(4.77136 + 4.77136i) q^{73} -3.76610 q^{74} +(0.842929 + 4.92843i) q^{75} -1.85358i q^{76} +(-2.17660 + 2.17660i) q^{77} +(-2.75307 - 2.75307i) q^{78} -16.3891 q^{79} +(2.13084 + 0.677875i) q^{80} -1.00000 q^{81} +(6.08551 - 6.08551i) q^{82} +(5.71805 - 5.71805i) q^{83} -1.49804 q^{84} +(-6.92035 - 13.3777i) q^{85} +2.06459i q^{86} +(-5.63101 + 5.63101i) q^{87} +(1.45297 - 1.45297i) q^{88} +0.705848 q^{89} +(1.02740 + 1.98606i) q^{90} -5.83250i q^{91} +(2.97121 + 3.76456i) q^{92} +(7.29215 + 7.29215i) q^{93} +2.68677i q^{94} +(-3.94968 - 1.25650i) q^{95} +1.00000 q^{96} +(0.564967 + 0.564967i) q^{97} +(3.36292 + 3.36292i) q^{98} +2.05480 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{6}+O(q^{10}) \) 24 * q - 24 * q^6	\( 24 q - 24 q^{6} - 24 q^{16} - 8 q^{23} - 16 q^{25} - 16 q^{26} + 16 q^{31} - 16 q^{35} + 24 q^{36} - 8 q^{46} - 8 q^{47} + 24 q^{50} + 24 q^{55} + 16 q^{58} - 56 q^{62} - 32 q^{70} - 16 q^{71} - 48 q^{73} - 24 q^{81} + 24 q^{82} + 16 q^{87} - 8 q^{92} + 56 q^{93} + 24 q^{95} + 24 q^{96} - 32 q^{98}+O(q^{100}) \) 24 * q - 24 * q^6 - 24 * q^16 - 8 * q^23 - 16 * q^25 - 16 * q^26 + 16 * q^31 - 16 * q^35 + 24 * q^36 - 8 * q^46 - 8 * q^47 + 24 * q^50 + 24 * q^55 + 16 * q^58 - 56 * q^62 - 32 * q^70 - 16 * q^71 - 48 * q^73 - 24 * q^81 + 24 * q^82 + 16 * q^87 - 8 * q^92 + 56 * q^93 + 24 * q^95 + 24 * q^96 - 32 * q^98

Introduction

L-functions

Modular forms

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