LMFDB - Embedded newform 231.2.s.a.8.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(8,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("231.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.s (of order $10$, degree $4$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			8.20
Character	$\chi$	$=$	231.8
Dual form			231.2.s.a.29.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.65450 - 1.20206i) q^{2} +(-0.770590 - 1.55119i) q^{3} +(0.674376 - 2.07552i) q^{4} +(1.12543 - 1.54901i) q^{5} +(-3.13957 - 1.64014i) q^{6} +(0.951057 + 0.309017i) q^{7} +(-0.115224 - 0.354623i) q^{8} +(-1.81238 + 2.39066i) q^{9} +O(q^{10})$	\(q+(1.65450 - 1.20206i) q^{2} +(-0.770590 - 1.55119i) q^{3} +(0.674376 - 2.07552i) q^{4} +(1.12543 - 1.54901i) q^{5} +(-3.13957 - 1.64014i) q^{6} +(0.951057 + 0.309017i) q^{7} +(-0.115224 - 0.354623i) q^{8} +(-1.81238 + 2.39066i) q^{9} -3.91568i q^{10} +(-3.13505 + 1.08235i) q^{11} +(-3.73919 + 0.553287i) q^{12} +(1.36871 + 1.88387i) q^{13} +(1.94498 - 0.631963i) q^{14} +(-3.27006 - 0.552092i) q^{15} +(2.91416 + 2.11726i) q^{16} +(-3.82620 - 2.77990i) q^{17} +(-0.124852 + 6.13395i) q^{18} +(4.14887 - 1.34805i) q^{19} +(-2.45605 - 3.38046i) q^{20} +(-0.253531 - 1.71339i) q^{21} +(-3.88588 + 5.55927i) q^{22} -3.17108i q^{23} +(-0.461297 + 0.452003i) q^{24} +(0.412220 + 1.26868i) q^{25} +(4.52906 + 1.47158i) q^{26} +(5.10498 + 0.969125i) q^{27} +(1.28274 - 1.76554i) q^{28} +(-0.861590 + 2.65170i) q^{29} +(-6.07396 + 3.01738i) q^{30} +(2.58988 - 1.88166i) q^{31} +8.11231 q^{32} +(4.09477 + 4.02901i) q^{33} -9.67207 q^{34} +(1.54901 - 1.12543i) q^{35} +(3.73964 + 5.37383i) q^{36} +(-3.13714 + 9.65512i) q^{37} +(5.24386 - 7.21755i) q^{38} +(1.86752 - 3.57482i) q^{39} +(-0.678991 - 0.220618i) q^{40} +(0.566950 + 1.74489i) q^{41} +(-2.47908 - 2.53005i) q^{42} -5.82583i q^{43} +(0.132234 + 7.23675i) q^{44} +(1.66347 + 5.49792i) q^{45} +(-3.81184 - 5.24655i) q^{46} +(-7.95149 + 2.58359i) q^{47} +(1.03865 - 6.15196i) q^{48} +(0.809017 + 0.587785i) q^{49} +(2.20706 + 1.60352i) q^{50} +(-1.36372 + 8.07733i) q^{51} +(4.83303 - 1.57035i) q^{52} +(4.30637 + 5.92721i) q^{53} +(9.61113 - 4.53309i) q^{54} +(-1.85168 + 6.07434i) q^{55} -0.372872i q^{56} +(-5.28816 - 5.39689i) q^{57} +(1.76201 + 5.42292i) q^{58} +(-6.12265 - 1.98937i) q^{59} +(-3.35113 + 6.41474i) q^{60} +(5.99320 - 8.24893i) q^{61} +(2.02308 - 6.22641i) q^{62} +(-2.46243 + 1.71360i) q^{63} +(7.59349 - 5.51699i) q^{64} +4.45852 q^{65} +(11.6179 + 1.74381i) q^{66} -14.8128 q^{67} +(-8.35003 + 6.06665i) q^{68} +(-4.91895 + 2.44360i) q^{69} +(1.21001 - 3.72403i) q^{70} +(8.76542 - 12.0646i) q^{71} +(1.05661 + 0.367250i) q^{72} +(-8.07191 - 2.62272i) q^{73} +(6.41568 + 19.7454i) q^{74} +(1.65032 - 1.61707i) q^{75} -9.52014i q^{76} +(-3.31607 + 0.0605930i) q^{77} +(-1.20735 - 8.15943i) q^{78} +(-0.424768 - 0.584643i) q^{79} +(6.55934 - 2.13126i) q^{80} +(-2.43055 - 8.66559i) q^{81} +(3.03549 + 2.20541i) q^{82} +(-7.30720 - 5.30899i) q^{83} +(-3.72715 - 0.629265i) q^{84} +(-8.61221 + 2.79828i) q^{85} +(-7.00303 - 9.63884i) q^{86} +(4.77722 - 0.706885i) q^{87} +(0.745058 + 0.987046i) q^{88} +9.47330i q^{89} +(9.36107 + 7.09670i) q^{90} +(0.719574 + 2.21462i) q^{91} +(-6.58163 - 2.13850i) q^{92} +(-4.91455 - 2.56741i) q^{93} +(-10.0501 + 13.8328i) q^{94} +(2.58109 - 7.94379i) q^{95} +(-6.25127 - 12.5837i) q^{96} +(-1.13735 + 0.826332i) q^{97} +2.04507 q^{98} +(3.09437 - 9.45647i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9}+O(q^{10}) $ 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9	$ 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9} - 20 q^{12} - 32 q^{16} - 10 q^{18} - 60 q^{19} + 30 q^{24} + 12 q^{25} - 40 q^{28} + 60 q^{30} + 40 q^{31} - 44 q^{33} + 8 q^{34} + 2 q^{36} + 16 q^{37} - 10 q^{39} - 96 q^{45} - 40 q^{46} + 48 q^{48} + 24 q^{49} - 30 q^{51} - 40 q^{52} + 28 q^{55} - 30 q^{57} + 36 q^{58} - 32 q^{60} + 40 q^{61} - 28 q^{64} + 118 q^{66} - 56 q^{67} + 26 q^{69} + 20 q^{70} + 150 q^{72} + 40 q^{73} + 2 q^{75} - 20 q^{78} - 40 q^{79} + 8 q^{81} - 16 q^{82} + 40 q^{84} - 60 q^{85} - 156 q^{88} + 100 q^{90} + 36 q^{91} - 36 q^{93} + 160 q^{96} - 88 q^{97} - 94 q^{99}+O(q^{100}) $ 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9 - 20 * q^12 - 32 * q^16 - 10 * q^18 - 60 * q^19 + 30 * q^24 + 12 * q^25 - 40 * q^28 + 60 * q^30 + 40 * q^31 - 44 * q^33 + 8 * q^34 + 2 * q^36 + 16 * q^37 - 10 * q^39 - 96 * q^45 - 40 * q^46 + 48 * q^48 + 24 * q^49 - 30 * q^51 - 40 * q^52 + 28 * q^55 - 30 * q^57 + 36 * q^58 - 32 * q^60 + 40 * q^61 - 28 * q^64 + 118 * q^66 - 56 * q^67 + 26 * q^69 + 20 * q^70 + 150 * q^72 + 40 * q^73 + 2 * q^75 - 20 * q^78 - 40 * q^79 + 8 * q^81 - 16 * q^82 + 40 * q^84 - 60 * q^85 - 156 * q^88 + 100 * q^90 + 36 * q^91 - 36 * q^93 + 160 * q^96 - 88 * q^97 - 94 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	1.65450	−	1.20206i	1.16991	−	0.849988i	0.178910	−	0.983865i	$-0.442743\pi$
$2$	1.65450	−	1.20206i	1.16991	−	0.849988i	0.990998	+	0.133878i	$0.0427429\pi$
$3$	−0.770590	−	1.55119i	−0.444901	−	0.895580i
$3$	−0.770590	−	1.55119i	−0.444901	−	0.895580i
$4$	0.674376	−	2.07552i	0.337188	−	1.03776i
$5$	1.12543	−	1.54901i	0.503305	−	0.692740i	−0.479467	−	0.877560i	$-0.659170\pi$
$5$	1.12543	−	1.54901i	0.503305	−	0.692740i	0.982772	+	0.184819i	$0.0591700\pi$
$6$	−3.13957	−	1.64014i	−1.28172	−	0.669586i
$7$	0.951057	+	0.309017i	0.359466	+	0.116797i
$7$	0.951057	+	0.309017i	0.359466	+	0.116797i
$8$	−0.115224	−	0.354623i	−0.0407378	−	0.125378i
$9$	−1.81238	+	2.39066i	−0.604127	+	0.796888i
$10$		−	3.91568i		−	1.23825i
$11$	−3.13505	+	1.08235i	−0.945252	+	0.326341i
$11$	−3.13505	+	1.08235i	−0.945252	+	0.326341i
$12$	−3.73919	+	0.553287i	−1.07941	+	0.159720i
$13$	1.36871	+	1.88387i	0.379612	+	0.522491i	0.955482	−	0.295050i	$-0.0953364\pi$
$13$	1.36871	+	1.88387i	0.379612	+	0.522491i	−0.575870	+	0.817542i	$0.695336\pi$
$14$	1.94498	−	0.631963i	0.519818	−	0.168899i
$15$	−3.27006	−	0.552092i	−0.844325	−	0.142550i
$16$	2.91416	+	2.11726i	0.728541	+	0.529316i
$17$	−3.82620	−	2.77990i	−0.927991	−	0.674225i	0.0175092	−	0.999847i	$-0.494426\pi$
$17$	−3.82620	−	2.77990i	−0.927991	−	0.674225i	−0.945500	+	0.325622i	$0.894426\pi$
$18$	−0.124852	+	6.13395i	−0.0294279	+	1.44579i
$19$	4.14887	−	1.34805i	0.951816	−	0.309264i	0.208363	−	0.978052i	$-0.433187\pi$
$19$	4.14887	−	1.34805i	0.951816	−	0.309264i	0.743453	+	0.668788i	$0.233187\pi$
$20$	−2.45605	−	3.38046i	−0.549188	−	0.755893i
$21$	−0.253531	−	1.71339i	−0.0553250	−	0.373893i
$22$	−3.88588	+	5.55927i	−0.828472	+	1.18524i
$23$		−	3.17108i		−	0.661216i	−0.943768	−	0.330608i	$-0.892746\pi$
$23$		−	3.17108i		−	0.661216i	0.943768	−	0.330608i	$-0.107254\pi$
$24$	−0.461297	+	0.452003i	−0.0941618	+	0.0922647i
$25$	0.412220	+	1.26868i	0.0824440	+	0.253737i
$26$	4.52906	+	1.47158i	0.888222	+	0.288601i
$27$	5.10498	+	0.969125i	0.982453	+	0.186508i
$28$	1.28274	−	1.76554i	0.242415	−	0.333656i
$29$	−0.861590	+	2.65170i	−0.159993	+	0.492408i	−0.998633	−	0.0522787i	$-0.983352\pi$
$29$	−0.861590	+	2.65170i	−0.159993	+	0.492408i	0.838639	+	0.544687i	$0.183352\pi$
$30$	−6.07396	+	3.01738i	−1.10895	+	0.550896i
$31$	2.58988	−	1.88166i	0.465156	−	0.337956i	−0.330394	−	0.943843i	$-0.607182\pi$
$31$	2.58988	−	1.88166i	0.465156	−	0.337956i	0.795551	+	0.605887i	$0.207182\pi$
$32$	8.11231			1.43407
$33$	4.09477	+	4.02901i	0.712807	+	0.701360i
$34$	−9.67207			−1.65875
$35$	1.54901	−	1.12543i	0.261831	−	0.190232i
$36$	3.73964	+	5.37383i	0.623273	+	0.895639i
$37$	−3.13714	+	9.65512i	−0.515742	+	1.58729i	0.266184	+	0.963922i	$0.414237\pi$
$37$	−3.13714	+	9.65512i	−0.515742	+	1.58729i	−0.781927	+	0.623370i	$0.785763\pi$
$38$	5.24386	−	7.21755i	0.850666	−	1.17084i
$39$	1.86752	−	3.57482i	0.299043	−	0.572430i
$40$	−0.678991	−	0.220618i	−0.107358	−	0.0348827i
$41$	0.566950	+	1.74489i	0.0885427	+	0.272506i	0.985517	−	0.169576i	$-0.0542398\pi$
$41$	0.566950	+	1.74489i	0.0885427	+	0.272506i	−0.896974	+	0.442083i	$0.854240\pi$
$42$	−2.47908	−	2.53005i	−0.382530	−	0.390395i
$43$		−	5.82583i		−	0.888431i	−0.895920	−	0.444216i	$-0.853482\pi$
$43$		−	5.82583i		−	0.888431i	0.895920	−	0.444216i	$-0.146518\pi$
$44$	0.132234	+	7.23675i	0.0199350	+	1.09098i
$45$	1.66347	+	5.49792i	0.247976	+	0.819581i
$46$	−3.81184	−	5.24655i	−0.562026	−	0.773562i
$47$	−7.95149	+	2.58359i	−1.15984	+	0.376856i	−0.824843	−	0.565362i	$-0.808737\pi$
$47$	−7.95149	+	2.58359i	−1.15984	+	0.376856i	−0.335001	+	0.942218i	$0.608737\pi$
$48$	1.03865	−	6.15196i	0.149916	−	0.887959i
$49$	0.809017	+	0.587785i	0.115574	+	0.0839693i
$50$	2.20706	+	1.60352i	0.312125	+	0.226772i
$51$	−1.36372	+	8.07733i	−0.190959	+	1.13105i
$52$	4.83303	−	1.57035i	0.670220	−	0.217768i
$53$	4.30637	+	5.92721i	0.591526	+	0.814165i	0.994900	−	0.100870i	$-0.0321626\pi$
$53$	4.30637	+	5.92721i	0.591526	+	0.814165i	−0.403374	+	0.915035i	$0.632163\pi$
$54$	9.61113	−	4.53309i	1.30791	−	0.616876i
$55$	−1.85168	+	6.07434i	−0.249681	+	0.819063i
$56$		−	0.372872i		−	0.0498272i
$57$	−5.28816	−	5.39689i	−0.700434	−	0.714836i
$58$	1.76201	+	5.42292i	0.231364	+	0.712065i
$59$	−6.12265	−	1.98937i	−0.797101	−	0.258994i	−0.117976	−	0.993016i	$-0.537641\pi$
$59$	−6.12265	−	1.98937i	−0.797101	−	0.258994i	−0.679125	+	0.734023i	$0.737641\pi$
$60$	−3.35113	+	6.41474i	−0.432628	+	0.828139i
$61$	5.99320	−	8.24893i	0.767350	−	1.05617i	−0.229217	−	0.973375i	$-0.573616\pi$
$61$	5.99320	−	8.24893i	0.767350	−	1.05617i	0.996567	−	0.0827916i	$-0.0263836\pi$
$62$	2.02308	−	6.22641i	0.256932	−	0.790755i
$63$	−2.46243	+	1.71360i	−0.310237	+	0.215893i
$64$	7.59349	−	5.51699i	0.949186	−	0.689624i
$65$	4.45852			0.553012
$66$	11.6179	+	1.74381i	1.43007	+	0.214649i
$67$	−14.8128			−1.80968			−0.904838	−	0.425757i	$-0.860008\pi$
$67$	−14.8128			−1.80968			−0.904838	+	0.425757i	$0.860008\pi$
$68$	−8.35003	+	6.06665i	−1.01259	+	0.735690i
$69$	−4.91895	+	2.44360i	−0.592172	+	0.294175i
$70$	1.21001	−	3.72403i	0.144624	−	0.445107i
$71$	8.76542	−	12.0646i	1.04026	−	1.43180i	0.143310	−	0.989678i	$-0.454225\pi$
$71$	8.76542	−	12.0646i	1.04026	−	1.43180i	0.896954	−	0.442123i	$-0.145775\pi$
$72$	1.05661	+	0.367250i	0.124523	+	0.0432808i
$73$	−8.07191	−	2.62272i	−0.944745	−	0.306966i	−0.204167	−	0.978936i	$-0.565448\pi$
$73$	−8.07191	−	2.62272i	−0.944745	−	0.306966i	−0.740579	+	0.671970i	$0.765448\pi$
$74$	6.41568	+	19.7454i	0.745808	+	2.29536i
$75$	1.65032	−	1.61707i	0.190562	−	0.186723i
$76$		−	9.52014i		−	1.09203i
$77$	−3.31607	+	0.0605930i	−0.377901	+	0.00690521i
$78$	−1.20735	−	8.15943i	−0.136705	−	0.923873i
$79$	−0.424768	−	0.584643i	−0.0477901	−	0.0657775i	0.784453	−	0.620188i	$-0.212944\pi$
$79$	−0.424768	−	0.584643i	−0.0477901	−	0.0657775i	−0.832243	+	0.554411i	$0.812944\pi$
$80$	6.55934	−	2.13126i	0.733357	−	0.238282i
$81$	−2.43055	−	8.66559i	−0.270061	−	0.962843i
$82$	3.03549	+	2.20541i	0.335214	+	0.243547i
$83$	−7.30720	−	5.30899i	−0.802069	−	0.582737i	0.109451	−	0.993992i	$-0.465091\pi$
$83$	−7.30720	−	5.30899i	−0.802069	−	0.582737i	−0.911520	+	0.411255i	$0.865091\pi$
$84$	−3.72715	−	0.629265i	−0.406666	−	0.0686585i
$85$	−8.61221	+	2.79828i	−0.934126	+	0.303516i
$86$	−7.00303	−	9.63884i	−0.755156	−	1.03938i
$87$	4.77722	−	0.706885i	0.512172	−	0.0757860i
$88$	0.745058	+	0.987046i	0.0794234	+	0.105219i
$89$			9.47330i			1.00417i	0.864819	+	0.502084i	$0.167433\pi$
$89$			9.47330i			1.00417i	−0.864819	+	0.502084i	$0.832567\pi$
$90$	9.36107	+	7.09670i	0.986743	+	0.748058i
$91$	0.719574	+	2.21462i	0.0754319	+	0.232155i
$92$	−6.58163	−	2.13850i	−0.686183	−	0.222954i
$93$	−4.91455	−	2.56741i	−0.509615	−	0.266228i
$94$	−10.0501	+	13.8328i	−1.03659	+	1.42674i
$95$	2.58109	−	7.94379i	0.264815	−	0.815015i
$96$	−6.25127	−	12.5837i	−0.638017	−	1.28432i
$97$	−1.13735	+	0.826332i	−0.115480	+	0.0839013i	−0.644026	−	0.765003i	$-0.722737\pi$
$97$	−1.13735	+	0.826332i	−0.115480	+	0.0839013i	0.528546	+	0.848905i	$0.322737\pi$
$98$	2.04507			0.206584
$99$	3.09437	−	9.45647i	0.310995	−	0.950411i
$100$	2.91116			0.291116
$101$	−4.80264	+	3.48932i	−0.477881	+	0.347201i	−0.800505	−	0.599326i	$-0.795435\pi$
$101$	−4.80264	+	3.48932i	−0.477881	+	0.347201i	0.322624	+	0.946527i	$0.395435\pi$
$102$	7.45320	+	15.0032i	0.737977	+	1.48554i
$103$	−4.41705	+	13.5943i	−0.435225	+	1.33948i	0.457631	+	0.889142i	$0.348698\pi$
$103$	−4.41705	+	13.5943i	−0.435225	+	1.33948i	−0.892856	+	0.450343i	$0.851302\pi$
$104$	0.510354	−	0.702443i	0.0500444	−	0.0688802i
$105$	−2.93940	−	1.53557i	−0.286856	−	0.149857i
$106$	14.2498	+	4.63003i	1.38406	+	0.449709i
$107$	1.01144	+	3.11290i	0.0977798	+	0.300935i	0.987968	−	0.154657i	$-0.0494274\pi$
$107$	1.01144	+	3.11290i	0.0977798	+	0.300935i	−0.890188	+	0.455593i	$0.849427\pi$
$108$	5.45411	−	9.94191i	0.524822	−	0.956661i
$109$			15.3302i			1.46836i	0.678953	+	0.734182i	$0.262434\pi$
$109$			15.3302i			1.46836i	−0.678953	+	0.734182i	$0.737566\pi$
$110$	4.23813	+	12.2758i	0.404090	+	1.17045i
$111$	17.3944	−	2.57384i	1.65100	−	0.244298i
$112$	2.11726	+	2.91416i	0.200063	+	0.275362i
$113$	2.73124	−	0.887434i	0.256933	−	0.0834827i	−0.177718	−	0.984081i	$-0.556872\pi$
$113$	2.73124	−	0.887434i	0.256933	−	0.0834827i	0.434652	+	0.900599i	$0.356872\pi$
$114$	−15.2367	−	2.57245i	−1.42704	−	0.240932i
$115$	−4.91205	−	3.56881i	−0.458051	−	0.332794i
$116$	4.92261	+	3.57649i	0.457053	+	0.332068i
$117$	−6.98432	−	0.142161i	−0.645701	−	0.0131428i
$118$	−12.5213	+	4.06841i	−1.15268	+	0.374527i
$119$	−2.77990	−	3.82620i	−0.254833	−	0.350748i
$120$	0.181004	+	1.22325i	0.0165233	+	0.111667i
$121$	8.65704	−	6.78643i	0.787003	−	0.616949i
$122$		−	20.8521i		−	1.88786i
$123$	2.26977	−	2.22404i	0.204659	−	0.200535i
$124$	−2.15886	−	6.64429i	−0.193871	−	0.596675i
$125$	11.5340	+	3.74763i	1.03163	+	0.335198i
$126$	−2.01424	+	5.79515i	−0.179442	+	0.516273i
$127$	0.767176	−	1.05593i	0.0680759	−	0.0936984i	−0.773621	−	0.633648i	$-0.781557\pi$
$127$	0.767176	−	1.05593i	0.0680759	−	0.0936984i	0.841697	+	0.539950i	$0.181557\pi$
$128$	0.917961	−	2.82519i	0.0811370	−	0.249714i
$129$	−9.03697	+	4.48933i	−0.795661	+	0.395263i
$130$	7.37662	−	5.35943i	0.646973	−	0.470053i
$131$	−19.0969			−1.66850			−0.834250	−	0.551386i	$-0.814099\pi$
$131$	−19.0969			−1.66850			−0.834250	+	0.551386i	$0.814099\pi$
$132$	11.1237	−	5.78169i	0.968192	−	0.503232i
$133$	4.36238			0.378266
$134$	−24.5078	+	17.8060i	−2.11715	+	1.53820i
$135$	7.24646	−	6.81701i	0.623676	−	0.586715i
$136$	−0.544945	+	1.67717i	−0.0467287	+	0.143816i
$137$	0.140144	−	0.192892i	0.0119733	−	0.0164799i	−0.802988	−	0.595995i	$-0.796758\pi$
$137$	0.140144	−	0.192892i	0.0119733	−	0.0164799i	0.814962	+	0.579515i	$0.196758\pi$
$138$	−5.20103	+	9.95584i	−0.442741	+	0.847497i
$139$	−9.69331	−	3.14955i	−0.822176	−	0.267141i	−0.132430	−	0.991192i	$-0.542278\pi$
$139$	−9.69331	−	3.14955i	−0.822176	−	0.267141i	−0.689746	+	0.724051i	$0.742278\pi$
$140$	−1.29122	−	3.97396i	−0.109128	−	0.335861i
$141$	10.1350	+	10.3434i	0.853520	+	0.871069i
$142$		−	30.4974i		−	2.55929i
$143$	−6.32998	−	4.42459i	−0.529339	−	0.370003i
$144$	−10.3432	+	3.12950i	−0.861936	+	0.260791i
$145$	3.13787	+	4.31890i	0.260586	+	0.358666i
$146$	−16.5076	+	5.36366i	−1.36618	+	0.443900i
$147$	0.288346	−	1.70788i	0.0237824	−	0.140864i
$148$	17.9238	+	13.0224i	1.47332	+	1.07043i
$149$	−2.76204	−	2.00674i	−0.226275	−	0.164398i	0.468872	−	0.883266i	$-0.344661\pi$
$149$	−2.76204	−	2.00674i	−0.226275	−	0.164398i	−0.695147	+	0.718868i	$0.744661\pi$
$150$	0.786629	−	4.65922i	0.0642280	−	0.380424i
$151$	4.18561	−	1.35999i	0.340620	−	0.110674i	−0.133712	−	0.991020i	$-0.542690\pi$
$151$	4.18561	−	1.35999i	0.340620	−	0.110674i	0.474332	+	0.880346i	$0.342690\pi$
$152$	−0.956097	−	1.31596i	−0.0775497	−	0.106738i
$153$	13.5803	−	4.10893i	1.09791	−	0.332187i
$154$	−5.41360	+	4.08638i	−0.436240	+	0.329290i
$155$		−	6.12943i		−	0.492328i
$156$	−6.16019	−	6.28685i	−0.493210	−	0.503351i
$157$	−2.47755	−	7.62510i	−0.197730	−	0.608549i	−0.999934	−	0.0114997i	$-0.996339\pi$
$157$	−2.47755	−	7.62510i	−0.197730	−	0.608549i	0.802204	−	0.597050i	$-0.203661\pi$
$158$	−1.40556	−	0.456693i	−0.111820	−	0.0363326i
$159$	5.87578	−	11.2475i	0.465980	−	0.891981i
$160$	9.12980	−	12.5661i	0.721774	−	0.993436i
$161$	0.979918	−	3.01588i	0.0772284	−	0.237684i
$162$	−14.4379	−	11.4155i	−1.13435	−	0.896889i
$163$	15.7685	−	11.4565i	1.23508	−	0.897339i	0.237820	−	0.971309i	$-0.423567\pi$
$163$	15.7685	−	11.4565i	1.23508	−	0.897339i	0.997260	+	0.0739706i	$0.0235671\pi$
$164$	4.00389			0.312651
$165$	10.8493	−	1.80851i	0.844620	−	0.140792i
$166$	−18.4715			−1.43367
$167$	16.5313	−	12.0107i	1.27923	−	0.929416i	0.279702	−	0.960087i	$-0.409764\pi$
$167$	16.5313	−	12.0107i	1.27923	−	0.929416i	0.999530	+	0.0306703i	$0.00976419\pi$
$168$	−0.578396	+	0.287332i	−0.0446242	+	0.0221681i
$169$	2.34163	−	7.20679i	0.180125	−	0.554368i
$170$	−10.8852	+	14.9822i	−0.834856	+	1.14908i
$171$	−4.29660	+	12.3617i	−0.328569	+	0.945325i
$172$	−12.0916	−	3.92880i	−0.921977	−	0.299568i
$173$	−4.19736	−	12.9182i	−0.319120	−	0.982149i	−0.974025	−	0.226439i	$-0.927292\pi$
$173$	−4.19736	−	12.9182i	−0.319120	−	0.982149i	0.654906	−	0.755710i	$-0.272708\pi$
$174$	7.05419	−	6.91207i	0.534777	−	0.524003i
$175$			1.33397i			0.100839i
$176$	−11.4277	−	3.48358i	−0.861392	−	0.262584i
$177$	1.63216	+	11.0304i	0.122681	+	0.829094i
$178$	11.3875	+	15.6736i	0.853531	+	1.17478i
$179$	−0.917320	+	0.298055i	−0.0685637	+	0.0222777i	−0.343098	−	0.939300i	$-0.611476\pi$
$179$	−0.917320	+	0.298055i	−0.0685637	+	0.0222777i	0.274534	+	0.961577i	$0.411476\pi$
$180$	12.5328	+	0.255097i	0.934142	+	0.0190138i
$181$	5.57712	+	4.05201i	0.414544	+	0.301184i	0.775439	−	0.631423i	$-0.217529\pi$
$181$	5.57712	+	4.05201i	0.414544	+	0.301184i	−0.360895	+	0.932607i	$0.617529\pi$
$182$	3.85265	+	2.79912i	0.285578	+	0.207484i
$183$	−17.4140	−	2.94004i	−1.28728	−	0.217334i
$184$	−1.12454	+	0.365384i	−0.0829020	+	0.0269365i
$185$	11.4253	+	15.7256i	0.840005	+	1.15617i
$186$	−11.2173	+	1.65982i	−0.822493	+	0.121704i
$187$	15.0042	+	4.57383i	1.09721	+	0.334471i
$188$			18.2458i			1.33071i
$189$	4.55565	+	2.49922i	0.331374	+	0.181791i
$190$	−5.27853	−	16.2456i	−0.382944	−	1.17858i
$191$	24.3393	+	7.90833i	1.76113	+	0.572227i	0.997317	−	0.0732079i	$-0.0233237\pi$
$191$	24.3393	+	7.90833i	1.76113	+	0.572227i	0.763816	+	0.645434i	$0.223324\pi$
$192$	−14.4094	−	7.52760i	−1.03991	−	0.543258i
$193$	4.01191	−	5.52193i	0.288784	−	0.397477i	−0.639835	−	0.768513i	$-0.720997\pi$
$193$	4.01191	−	5.52193i	0.288784	−	0.397477i	0.928619	+	0.371036i	$0.120997\pi$
$194$	−0.888438	+	2.73433i	−0.0637862	+	0.196314i
$195$	−3.43569	−	6.91602i	−0.246035	−	0.495266i
$196$	1.76554	−	1.28274i	0.126110	−	0.0916243i
$197$	−18.5411			−1.32100			−0.660500	−	0.750826i	$-0.729656\pi$
$197$	−18.5411			−1.32100			−0.660500	+	0.750826i	$0.729656\pi$
$198$	−6.24766	−	19.3654i	−0.444002	−	1.37624i
$199$	4.00645			0.284010			0.142005	−	0.989866i	$-0.454645\pi$
$199$	4.00645			0.284010			0.142005	+	0.989866i	$0.454645\pi$
$200$	0.402406	−	0.292365i	0.0284544	−	0.0206733i
$201$	11.4146	+	22.9775i	0.805125	+	1.62071i
$202$	−3.75158	+	11.5462i	−0.263960	+	0.812386i
$203$	−1.63884	+	2.25567i	−0.115024	+	0.158317i
$204$	15.8450	+	8.27758i	1.10937	+	0.579546i
$205$	3.34092	+	1.08553i	0.233340	+	0.0758168i
$206$	9.03320	+	27.8013i	0.629373	+	1.93701i
$207$	7.58099	+	5.74721i	0.526915	+	0.399459i
$208$			8.38782i			0.581591i
$209$	−11.5478	+	8.71672i	−0.798781	+	0.602948i
$210$	−6.70910	+	0.992745i	−0.462972	+	0.0685059i
$211$	−1.02633	−	1.41263i	−0.0706557	−	0.0972492i	0.772227	−	0.635347i	$-0.219143\pi$
$211$	−1.02633	−	1.41263i	−0.0706557	−	0.0972492i	−0.842882	+	0.538098i	$0.819143\pi$
$212$	15.2061	−	4.94077i	1.04436	−	0.339334i
$213$	−25.4690	−	4.30000i	−1.74511	−	0.294631i
$214$	5.41533	+	3.93447i	0.370185	+	0.268955i
$215$	−9.02430	−	6.55654i	−0.615452	−	0.447152i
$216$	−0.244541	−	1.92201i	−0.0166389	−	0.130776i
$217$	3.04459	−	0.989247i	0.206680	−	0.0671544i
$218$	18.4278	+	25.3637i	1.24809	+	1.71785i
$219$	2.15179	+	14.5421i	0.145405	+	0.982665i
$220$	11.3587	+	7.93959i	0.765800	+	0.535287i
$221$		−	11.0129i		−	0.740811i
$222$	25.6851	−	25.1676i	1.72387	−	1.68914i
$223$	−2.62289	−	8.07243i	−0.175642	−	0.540570i	0.824020	−	0.566560i	$-0.191726\pi$
$223$	−2.62289	−	8.07243i	−0.175642	−	0.540570i	−0.999662	+	0.0259902i	$0.991726\pi$
$224$	7.71527	+	2.50684i	0.515498	+	0.167495i
$225$	−3.78009	−	1.31386i	−0.252006	−	0.0875905i
$226$	3.45208	−	4.75138i	0.229629	−	0.316057i
$227$	0.174826	−	0.538060i	0.0116036	−	0.0357123i	−0.945087	−	0.326819i	$-0.894023\pi$
$227$	0.174826	−	0.538060i	0.0116036	−	0.0357123i	0.956691	+	0.291106i	$0.0940234\pi$
$228$	−14.7675	+	7.33613i	−0.978004	+	0.485847i
$229$	−12.3775	+	8.99279i	−0.817929	+	0.594260i	−0.916118	−	0.400908i	$-0.868695\pi$
$229$	−12.3775	+	8.99279i	−0.817929	+	0.594260i	0.0981897	+	0.995168i	$0.468695\pi$
$230$	−12.4169			−0.818748
$231$	2.64932	+	5.09716i	0.174313	+	0.335369i
$232$	1.03963			0.0682550
$233$	17.7560	−	12.9005i	1.16323	−	0.845138i	0.173049	−	0.984913i	$-0.444638\pi$
$233$	17.7560	−	12.9005i	1.16323	−	0.845138i	0.990183	+	0.139776i	$0.0446381\pi$
$234$	−11.7264	+	8.16040i	−0.766582	+	0.533462i
$235$	−4.94678	+	15.2246i	−0.322692	+	0.993144i
$236$	−8.25793	+	11.3661i	−0.537546	+	0.739868i
$237$	−0.579570	+	1.10942i	−0.0376471	+	0.0720643i
$238$	−9.19869	−	2.98883i	−0.596262	−	0.193737i
$239$	−0.114794	−	0.353299i	−0.00742539	−	0.0228530i	0.947275	−	0.320421i	$-0.103824\pi$
$239$	−0.114794	−	0.353299i	−0.00742539	−	0.0228530i	−0.954701	+	0.297568i	$0.903824\pi$
$240$	−8.36055	−	8.53246i	−0.539671	−	0.550768i
$241$		−	14.7915i		−	0.952807i	−0.879227	−	0.476403i	$-0.841940\pi$
$241$		−	14.7915i		−	0.952807i	0.879227	−	0.476403i	$-0.158060\pi$
$242$	6.16534	−	21.6345i	0.396323	−	1.39072i
$243$	−11.5690	+	10.4479i	−0.742153	+	0.670231i
$244$	−13.0791	−	18.0019i	−0.837305	−	1.15245i
$245$	1.82098	−	0.591671i	0.116338	−	0.0378005i
$246$	1.08190	−	6.40809i	0.0689791	−	0.408565i
$247$	8.21815	+	5.97084i	0.522908	+	0.379915i
$248$	−0.965695	−	0.701619i	−0.0613217	−	0.0445528i
$249$	−2.60440	+	15.4259i	−0.165047	+	0.977577i
$250$	23.5879	−	7.66417i	1.49183	−	0.484725i
$251$	10.0362	+	13.8137i	0.633482	+	0.871913i	0.998247	−	0.0591868i	$-0.0188507\pi$
$251$	10.0362	+	13.8137i	0.633482	+	0.871913i	−0.364765	+	0.931100i	$0.618851\pi$
$252$	1.89600	+	6.26643i	0.119437	+	0.394748i
$253$	3.43222	+	9.94149i	0.215782	+	0.625016i
$254$		−	2.66923i		−	0.167482i
$255$	10.9771	+	11.2029i	0.687416	+	0.701550i
$256$	3.92361	+	12.0756i	0.245226	+	0.754727i
$257$	23.7705	+	7.72350i	1.48276	+	0.481779i	0.934937	−	0.354814i	$-0.115456\pi$
$257$	23.7705	+	7.72350i	1.48276	+	0.481779i	0.547825	+	0.836593i	$0.315456\pi$
$258$	−9.55521	+	18.2906i	−0.594881	+	1.13872i
$259$	−5.96719	+	8.21314i	−0.370783	+	0.510339i
$260$	3.00672	−	9.25374i	0.186469	−	0.573892i
$261$	−4.77780	−	6.86566i	−0.295738	−	0.424974i
$262$	−31.5957	+	22.9557i	−1.95199	+	1.41820i
$263$	−18.0346			−1.11206			−0.556032	−	0.831161i	$-0.687677\pi$
$263$	−18.0346			−1.11206			−0.556032	+	0.831161i	$0.687677\pi$
$264$	0.956961	−	1.91633i	0.0588969	−	0.117942i
$265$	14.0278			0.861723
$266$	7.21755	−	5.24386i	0.442537	−	0.321522i
$267$	14.6949	−	7.30003i	0.899313	−	0.446755i
$268$	−9.98942	+	30.7443i	−0.610201	+	1.87801i
$269$	−8.59989	+	11.8367i	−0.524345	+	0.721698i	−0.986255	−	0.165228i	$-0.947164\pi$
$269$	−8.59989	+	11.8367i	−0.524345	+	0.721698i	0.461911	+	0.886926i	$0.347164\pi$
$270$	3.79478	−	19.9894i	0.230943	−	1.21652i
$271$	−6.03510	−	1.96092i	−0.366606	−	0.119118i	0.119920	−	0.992784i	$-0.461736\pi$
$271$	−6.03510	−	1.96092i	−0.366606	−	0.119118i	−0.486526	+	0.873666i	$0.661736\pi$
$272$	−5.26440	−	16.2022i	−0.319201	−	0.982400i
$273$	2.88080	−	2.82276i	0.174354	−	0.170841i
$274$		−	0.487601i		−	0.0294571i
$275$	−2.66549	−	3.53121i	−0.160735	−	0.212940i
$276$	1.75452	+	11.8573i	0.105610	+	0.713724i
$277$	−16.1142	−	22.1793i	−0.968210	−	1.33263i	−0.942946	−	0.332946i	$-0.891957\pi$
$277$	−16.1142	−	22.1793i	−0.968210	−	1.33263i	−0.0252639	−	0.999681i	$-0.508043\pi$
$278$	−19.8235	+	6.44106i	−1.18894	+	0.386309i
$279$	−0.195438	+	9.60182i	−0.0117006	+	0.574846i
$280$	−0.577585	−	0.419640i	−0.0345173	−	0.0250783i
$281$	25.8335	+	18.7692i	1.54110	+	1.11967i	0.949641	+	0.313339i	$0.101447\pi$
$281$	25.8335	+	18.7692i	1.54110	+	1.11967i	0.591458	+	0.806336i	$0.298553\pi$
$282$	29.2017	+	4.93021i	1.73894	+	0.293589i
$283$	24.9373	−	8.10262i	1.48237	−	0.481651i	0.547549	−	0.836774i	$-0.315561\pi$
$283$	24.9373	−	8.10262i	1.48237	−	0.481651i	0.934820	+	0.355123i	$0.115561\pi$
$284$	−19.1290	−	26.3288i	−1.13510	−	1.56233i
$285$	−14.3113	+	2.11764i	−0.847728	+	0.125438i
$286$	−15.7916	+	0.288552i	−0.933776	+	0.0170625i
$287$			1.83469i			0.108298i
$288$	−14.7026	+	19.3938i	−0.866359	+	1.14279i
$289$	1.65871	+	5.10497i	0.0975709	+	0.300292i
$290$	10.3832	+	3.37371i	0.609723	+	0.198111i
$291$	2.15823	+	1.12748i	0.126518	+	0.0660941i
$292$	−10.8870	+	14.9847i	−0.637114	+	0.876912i
$293$	2.14573	−	6.60389i	0.125355	−	0.385803i	−0.868611	−	0.495495i	$-0.834987\pi$
$293$	2.14573	−	6.60389i	0.125355	−	0.385803i	0.993966	+	0.109692i	$0.0349865\pi$
$294$	−1.57591	−	3.17230i	−0.0919092	−	0.185012i
$295$	−9.97214	+	7.24518i	−0.580600	+	0.421831i
$296$	3.78540			0.220022
$297$	−17.0533	+	2.48712i	−0.989531	+	0.144317i
$298$	−6.98201			−0.404457
$299$	5.97390	−	4.34029i	0.345480	−	0.251006i
$300$	−2.24331	−	4.51577i	−0.129518	−	0.260718i
$301$	1.80028	−	5.54070i	0.103766	−	0.319360i
$302$	5.29030	−	7.28147i	0.304422	−	0.419001i
$303$	9.11348	+	4.76097i	0.523556	+	0.273511i
$304$	14.9447	+	4.85581i	0.857135	+	0.278500i
$305$	−6.03282	−	18.5671i	−0.345438	−	1.06315i
$306$	17.5295	−	23.1227i	1.00209	−	1.32184i
$307$		−	5.05068i		−	0.288258i	−0.989559	−	0.144129i	$-0.953962\pi$
$307$		−	5.05068i		−	0.288258i	0.989559	−	0.144129i	$-0.0460380\pi$
$308$	−2.11052	+	6.92342i	−0.120258	+	0.394499i
$309$	24.4911	−	3.62394i	1.39325	−	0.206159i
$310$	−7.36797	−	10.1411i	−0.418473	−	0.575978i
$311$	25.6119	−	8.32182i	1.45232	−	0.471887i	0.526605	−	0.850110i	$-0.323465\pi$
$311$	25.6119	−	8.32182i	1.45232	−	0.471887i	0.925714	+	0.378223i	$0.123465\pi$
$312$	−1.48290	−	0.250361i	−0.0839525	−	0.0141739i
$313$	−7.09308	−	5.15342i	−0.400925	−	0.291289i	0.368993	−	0.929432i	$-0.379703\pi$
$313$	−7.09308	−	5.15342i	−0.400925	−	0.291289i	−0.769917	+	0.638143i	$0.779703\pi$
$314$	−13.2650	−	9.63756i	−0.748585	−	0.543879i
$315$	−0.116892	+	5.74287i	−0.00658612	+	0.323574i
$316$	−1.49989	+	0.487344i	−0.0843754	+	0.0274152i
$317$	−2.85286	−	3.92663i	−0.160233	−	0.220541i	0.721350	−	0.692570i	$-0.243522\pi$
$317$	−2.85286	−	3.92663i	−0.160233	−	0.220541i	−0.881583	+	0.472029i	$0.843522\pi$
$318$	−3.79868	−	25.6720i	−0.213019	−	1.43961i
$319$	−0.168943	−	9.24575i	−0.00945900	−	0.517662i
$320$		−	17.9714i		−	1.00463i
$321$	4.04929	−	3.96771i	0.226009	−	0.221456i
$322$	−2.00400	−	6.16769i	−0.111679	−	0.343712i
$323$	−19.6219	−	6.37553i	−1.09179	−	0.354744i
$324$	−19.6247	−	0.799224i	−1.09026	−	0.0444013i
$325$	−1.82582	+	2.51303i	−0.101278	+	0.139398i
$326$	12.3175	−	37.9094i	0.682204	−	2.09961i
$327$	23.7800	−	11.8133i	1.31504	−	0.653276i
$328$	0.553452	−	0.402107i	0.0305593	−	0.0222026i
$329$	−8.36069			−0.460940
$330$	15.7763	−	16.0338i	0.868456	−	0.882631i
$331$	−7.55218			−0.415105			−0.207553	−	0.978224i	$-0.566550\pi$
$331$	−7.55218			−0.415105			−0.207553	+	0.978224i	$0.566550\pi$
$332$	−15.9467	+	11.5860i	−0.875189	+	0.635862i
$333$	−17.3965	−	24.9986i	−0.953320	−	1.36992i
$334$	12.9134	−	39.7434i	0.706591	−	2.17466i
$335$	−16.6707	+	22.9453i	−0.910819	+	1.25364i
$336$	2.88888	−	5.52990i	0.157601	−	0.301681i
$337$	−29.6965	−	9.64897i	−1.61767	−	0.525613i	−0.646280	−	0.763100i	$-0.723676\pi$
$337$	−29.6965	−	9.64897i	−1.61767	−	0.525613i	−0.971391	+	0.237487i	$0.923676\pi$
$338$	−4.78880	−	14.7384i	−0.260476	−	0.801664i
$339$	−3.48125	−	3.55282i	−0.189075	−	0.192963i
$340$			19.7619i			1.07174i
$341$	−6.08279	+	8.70225i	−0.329401	+	0.471253i
$342$	7.75087	+	25.6173i	0.419119	+	1.38522i
$343$	0.587785	+	0.809017i	0.0317374	+	0.0436828i
$344$	−2.06597	+	0.671275i	−0.111390	+	0.0361927i
$345$	−1.75073	+	10.3696i	−0.0942561	+	0.558282i
$346$	−22.4730	−	16.3276i	−1.20816	−	0.877776i
$347$	20.8416	+	15.1423i	1.11884	+	0.812883i	0.984032	−	0.177989i	$-0.0569593\pi$
$347$	20.8416	+	15.1423i	1.11884	+	0.812883i	0.134805	+	0.990872i	$0.456959\pi$
$348$	1.75449	−	10.3919i	0.0940508	−	0.557065i
$349$	−0.498247	+	0.161890i	−0.0266705	+	0.00866578i	−0.322322	−	0.946630i	$-0.604463\pi$
$349$	−0.498247	+	0.161890i	−0.0266705	+	0.00866578i	0.295651	+	0.955296i	$0.404463\pi$
$350$	1.60352	+	2.20706i	0.0857118	+	0.117972i
$351$	5.16153	+	10.9436i	0.275502	+	0.584124i
$352$	−25.4325	+	8.78036i	−1.35556	+	0.467995i
$353$		−	11.4993i		−	0.612045i	−0.952024	−	0.306023i	$-0.901002\pi$
$353$		−	11.4993i		−	0.612045i	0.952024	−	0.306023i	$-0.0989983\pi$
$354$	15.9596	+	16.2878i	0.848245	+	0.865686i
$355$	−8.82337	−	27.1555i	−0.468296	−	1.44127i
$356$	19.6620	+	6.38857i	1.04208	+	0.338593i
$357$	−3.79301	+	7.26059i	−0.200747	+	0.384271i
$358$	−1.15942	+	1.59581i	−0.0612774	+	0.0843412i
$359$	−2.58731	+	7.96293i	−0.136553	+	0.420268i	−0.995828	−	0.0912460i	$-0.970915\pi$
$359$	−2.58731	+	7.96293i	−0.136553	+	0.420268i	0.859275	+	0.511514i	$0.170915\pi$
$360$	1.75801	−	1.22340i	0.0926555	−	0.0644787i
$361$	0.0245531	−	0.0178389i	0.00129227	−	0.000938887i
$362$	14.0981			0.740981
$363$	−17.1981	−	8.19915i	−0.902665	−	0.430344i
$364$	5.08175			0.266356
$365$	−13.1470	+	9.55183i	−0.688143	+	0.499965i
$366$	−32.3455	+	16.0684i	−1.69073	+	0.839908i
$367$	6.81278	−	20.9676i	0.355624	−	1.09450i	−0.600022	−	0.799983i	$-0.704842\pi$
$367$	6.81278	−	20.9676i	0.355624	−	1.09450i	0.955647	−	0.294516i	$-0.0951584\pi$
$368$	6.71401	−	9.24105i	0.349992	−	0.481723i
$369$	−5.19898	−	1.80702i	−0.270648	−	0.0940699i
$370$	37.8063	+	12.2840i	1.96546	+	0.638616i
$371$	2.26399	+	6.96786i	0.117541	+	0.361753i
$372$	−8.64296	+	8.46883i	−0.448116	+	0.439088i
$373$		−	16.8147i		−	0.870633i	−0.900278	−	0.435316i	$-0.856637\pi$
$373$		−	16.8147i		−	0.870633i	0.900278	−	0.435316i	$-0.143363\pi$
$374$	30.3224	−	10.4686i	1.56793	−	0.541317i
$375$	−3.07471	−	20.7793i	−0.158778	−	1.07304i
$376$	1.83240	+	2.52209i	0.0944989	+	0.130067i
$377$	−6.17472	+	2.00629i	−0.318014	+	0.103329i
$378$	10.5415	−	1.34122i	0.542198	−	0.0689851i
$379$	22.2624	+	16.1746i	1.14354	+	0.830833i	0.987609	−	0.156935i	$-0.0501612\pi$
$379$	22.2624	+	16.1746i	1.14354	+	0.830833i	0.155934	+	0.987767i	$0.450161\pi$
$380$	−14.7468	−	10.7142i	−0.756497	−	0.549627i
$381$	−2.22912	−	0.376349i	−0.114201	−	0.0192809i
$382$	49.7757	−	16.1731i	2.54675	−	0.827489i
$383$	−21.6763	−	29.8348i	−1.10761	−	1.52449i	−0.824897	−	0.565284i	$-0.808767\pi$
$383$	−21.6763	−	29.8348i	−1.10761	−	1.52449i	−0.282710	−	0.959206i	$-0.591233\pi$
$384$	−5.08978	+	0.753134i	−0.259737	+	0.0384332i
$385$	−3.63813	+	5.20484i	−0.185416	+	0.265263i
$386$		−	13.9586i		−	0.710474i
$387$	13.9276	+	10.5586i	0.707980	+	0.536725i
$388$	0.948065	+	2.91784i	0.0481307	+	0.148131i
$389$	−8.41798	−	2.73517i	−0.426809	−	0.138679i	0.0877329	−	0.996144i	$-0.472038\pi$
$389$	−8.41798	−	2.73517i	−0.426809	−	0.138679i	−0.514541	+	0.857466i	$0.672038\pi$
$390$	−13.9978	−	7.31262i	−0.708809	−	0.370289i
$391$	−8.81529	+	12.1332i	−0.445808	+	0.613603i
$392$	0.115224	−	0.354623i	0.00581968	−	0.0179111i
$393$	14.7159	+	29.6229i	0.742317	+	1.49428i
$394$	−30.6763	+	22.2876i	−1.54545	+	1.12283i
$395$	−1.38367			−0.0696197
$396$	−17.5403	−	12.7996i	−0.881433	−	0.643205i
$397$	15.0685			0.756264			0.378132	−	0.925752i	$-0.376567\pi$
$397$	15.0685			0.756264			0.378132	+	0.925752i	$0.376567\pi$
$398$	6.62867	−	4.81601i	0.332265	−	0.241405i
$399$	−3.36161	−	6.76688i	−0.168291	−	0.338768i
$400$	−1.48486	+	4.56993i	−0.0742430	+	0.228496i
$401$	9.25386	−	12.7368i	0.462116	−	0.636048i	−0.512830	−	0.858490i	$-0.671403\pi$
$401$	9.25386	−	12.7368i	0.462116	−	0.636048i	0.974946	+	0.222442i	$0.0714029\pi$
$402$	46.5059	+	24.2952i	2.31951	+	1.21173i
$403$	7.08960	+	2.30355i	0.353158	+	0.114748i
$404$	4.00336	+	12.3211i	0.199175	+	0.612997i
$405$	−16.1585	−	5.98752i	−0.802924	−	0.297522i
$406$			5.70200i			0.282985i
$407$	−0.615140	−	33.6647i	−0.0304913	−	1.66870i
$408$	3.02154	−	0.447097i	0.149588	−	0.0221346i
$409$	−7.54185	−	10.3805i	−0.372921	−	0.513281i	0.580771	−	0.814067i	$-0.302751\pi$
$409$	−7.54185	−	10.3805i	−0.372921	−	0.513281i	−0.953692	+	0.300786i	$0.902751\pi$
$410$	6.83244	−	2.21999i	0.337430	−	0.109638i
$411$	−0.407205	−	0.0687496i	−0.0200860	−	0.00339117i
$412$	25.2364	+	18.3353i	1.24331	+	0.903317i
$413$	−5.20823	−	3.78400i	−0.256280	−	0.186199i
$414$	19.4513	+	0.395916i	0.955977	+	0.0194582i
$415$	−16.4474	+	5.34409i	−0.807372	+	0.262331i
$416$	11.1034	+	15.2825i	0.544389	+	0.749288i
$417$	2.58402	+	17.4632i	0.126540	+	0.855176i
$418$	−8.62783	+	28.3031i	−0.422001	+	1.38435i
$419$			16.1104i			0.787043i	0.919315	+	0.393522i	$0.128743\pi$
$419$			16.1104i			0.787043i	−0.919315	+	0.393522i	$0.871257\pi$
$420$	−5.16937	+	5.06523i	−0.252240	+	0.247158i
$421$	2.57766	+	7.93323i	0.125628	+	0.386642i	0.994015	−	0.109245i	$-0.0348432\pi$
$421$	2.57766	+	7.93323i	0.125628	+	0.386642i	−0.868387	+	0.495887i	$0.834843\pi$
$422$	−3.39614	−	1.10347i	−0.165321	−	0.0537162i
$423$	8.23462	−	23.6918i	0.400381	−	1.15193i
$424$	1.60573	−	2.21009i	0.0779810	−	0.107332i
$425$	1.94957	−	6.00017i	0.0945682	−	0.291051i
$426$	−47.3073	+	23.5010i	−2.29205	+	1.13863i
$427$	8.24893	−	5.99320i	0.399194	−	0.290031i
$428$	7.14296			0.345268
$429$	−1.98557	+	13.2285i	−0.0958641	+	0.638680i
$430$	−22.8121			−1.10010
$431$	−12.3819	+	8.99597i	−0.596415	+	0.433321i	−0.844604	−	0.535391i	$-0.820164\pi$
$431$	−12.3819	+	8.99597i	−0.596415	+	0.433321i	0.248190	+	0.968711i	$0.420164\pi$
$432$	12.8248	+	13.6328i	0.617035	+	0.655907i
$433$	−8.49151	+	26.1342i	−0.408076	+	1.25593i	0.510224	+	0.860042i	$0.329563\pi$
$433$	−8.49151	+	26.1342i	−0.408076	+	1.25593i	−0.918299	+	0.395887i	$0.870437\pi$
$434$	3.84813	−	5.29650i	0.184716	−	0.254240i
$435$	4.28143	−	8.19554i	0.205279	−	0.392946i
$436$	31.8180	+	10.3383i	1.52381	+	0.495115i
$437$	−4.27477	−	13.1564i	−0.204490	−	0.629356i
$438$	21.0407	+	21.4733i	1.00536	+	1.02603i
$439$		−	2.31895i		−	0.110678i	−0.998468	−	0.0553388i	$-0.982376\pi$
$439$		−	2.31895i		−	0.110678i	0.998468	−	0.0553388i	$-0.0176239\pi$
$440$	2.36746	−	0.0432594i	0.112864	−	0.00206231i
$441$	−2.87144	+	0.868797i	−0.136735	+	0.0413713i
$442$	−13.2383	−	18.2209i	−0.629680	−	0.866681i
$443$	6.83189	−	2.21982i	0.324593	−	0.105467i	−0.142188	−	0.989840i	$-0.545414\pi$
$443$	6.83189	−	2.21982i	0.324593	−	0.105467i	0.466781	+	0.884373i	$0.345414\pi$
$444$	6.38830	−	37.8381i	0.303175	−	1.79571i
$445$	14.6743	+	10.6615i	0.695628	+	0.505403i
$446$	−14.0432	−	10.2029i	−0.664963	−	0.483124i
$447$	−0.984432	+	5.83081i	−0.0465620	+	0.275788i
$448$	8.92668	−	2.90045i	0.421746	−	0.137034i
$449$	6.92065	+	9.52546i	0.326606	+	0.449534i	0.940470	−	0.339878i	$-0.110386\pi$
$449$	6.92065	+	9.52546i	0.326606	+	0.449534i	−0.613864	+	0.789412i	$0.710386\pi$
$450$	−7.83351	+	2.37014i	−0.369275	+	0.111729i
$451$	−3.66600	−	4.85668i	−0.172625	−	0.228692i
$452$		−	6.26720i		−	0.294784i
$453$	−5.33499	−	5.44468i	−0.250660	−	0.255814i
$454$	−0.357533	−	1.10037i	−0.0167798	−	0.0516430i
$455$	4.24031	+	1.37776i	0.198789	+	0.0645903i
$456$	−1.30454	+	2.49715i	−0.0610906	+	0.116940i
$457$	−16.4686	+	22.6671i	−0.770371	+	1.06032i	0.225909	+	0.974148i	$0.427465\pi$
$457$	−16.4686	+	22.6671i	−0.770371	+	1.06032i	−0.996280	+	0.0861761i	$0.972535\pi$
$458$	−9.66867	+	29.7571i	−0.451787	+	1.39046i
$459$	−16.8386	−	17.8994i	−0.785959	−	0.835472i
$460$	−10.7197	+	7.78832i	−0.499809	+	0.363132i
$461$	18.6344			0.867889			0.433945	−	0.900940i	$-0.357121\pi$
$461$	18.6344			0.867889			0.433945	+	0.900940i	$0.357121\pi$
$462$	10.5104	+	5.24860i	0.488989	+	0.244187i
$463$	0.357479			0.0166135			0.00830674	−	0.999965i	$-0.497356\pi$
$463$	0.357479			0.0166135			0.00830674	+	0.999965i	$0.497356\pi$
$464$	−8.12516	+	5.90327i	−0.377201	+	0.274053i
$465$	−9.50791	+	4.72328i	−0.440919	+	0.219037i
$466$	13.8701	−	42.6876i	0.642518	−	1.97747i
$467$	−23.0115	+	31.6726i	−1.06485	+	1.46564i	−0.189660	+	0.981850i	$0.560738\pi$
$467$	−23.0115	+	31.6726i	−1.06485	+	1.46564i	−0.875187	+	0.483785i	$0.839262\pi$
$468$	−5.00512	+	14.4002i	−0.231362	+	0.665650i
$469$	−14.0878	−	4.57742i	−0.650516	−	0.211365i
$470$	10.1165	+	31.1355i	0.466640	+	1.43617i
$471$	−9.91881	+	9.71898i	−0.457035	+	0.447827i
$472$			2.40045i			0.110490i
$473$	6.30559	+	18.2643i	0.289931	+	0.839792i
$474$	0.374691	+	2.53221i	0.0172101	+	0.116308i
$475$	3.42049	+	4.70791i	0.156943	+	0.216014i
$476$	−9.81605	+	3.18943i	−0.449918	+	0.146187i
$477$	−21.9748	−	0.447281i	−1.00616	−	0.0204796i
$478$	−0.614614	−	0.446544i	−0.0281118	−	0.0204244i
$479$	−21.6302	−	15.7153i	−0.988309	−	0.718048i	−0.0287587	−	0.999586i	$-0.509155\pi$
$479$	−21.6302	−	15.7153i	−0.988309	−	0.718048i	−0.959550	+	0.281538i	$0.909155\pi$
$480$	−26.5277	−	4.47875i	−1.21082	−	0.204426i
$481$	−22.4828	+	7.30511i	−1.02513	+	0.333084i
$482$	−17.7804	−	24.4726i	−0.809874	−	1.11470i
$483$	−5.43331	+	0.803967i	−0.247224	+	0.0365818i
$484$	−8.24726	−	22.5444i	−0.374875	−	1.02475i
$485$			2.69174i			0.122226i
$486$	−6.58194	+	31.1927i	−0.298563	+	1.41493i
$487$	0.329561	+	1.01429i	0.0149338	+	0.0459616i	0.958246	−	0.285946i	$-0.0923078\pi$
$487$	0.329561	+	1.01429i	0.0149338	+	0.0459616i	−0.943312	+	0.331908i	$0.892308\pi$
$488$	−3.61582	−	1.17485i	−0.163680	−	0.0531830i
$489$	−29.9222	−	15.6316i	−1.35313	−	0.706887i
$490$	2.30158	−	3.16785i	0.103975	−	0.143109i
$491$	−0.728991	+	2.24360i	−0.0328989	+	0.101252i	−0.966158	−	0.257953i	$-0.916952\pi$
$491$	−0.728991	+	2.24360i	−0.0328989	+	0.101252i	0.933259	+	0.359205i	$0.116952\pi$
$492$	−3.08536	−	6.21080i	−0.139099	−	0.280004i
$493$	10.6681	−	7.75081i	0.480466	−	0.349079i
$494$	20.7743			0.934678
$495$	−11.1657	−	15.4358i	−0.501863	−	0.693786i
$496$	11.5313			0.517771
$497$	12.0646	−	8.76542i	0.541170	−	0.393183i
$498$	14.2340	+	28.6528i	0.637839	+	1.28396i
$499$	−4.61901	+	14.2159i	−0.206775	+	0.636389i	0.792860	+	0.609403i	$0.208591\pi$
$499$	−4.61901	+	14.2159i	−0.206775	+	0.636389i	−0.999636	+	0.0269860i	$0.991409\pi$
$500$	15.5565	−	21.4117i	0.695709	−	0.957561i
$501$	−31.3698	−	16.3879i	−1.40150	−	0.732157i
$502$	33.2099	+	10.7906i	1.48223	+	0.481606i
$503$	8.03167	+	24.7189i	0.358115	+	1.10216i	0.954181	+	0.299228i	$0.0967293\pi$
$503$	8.03167	+	24.7189i	0.358115	+	1.10216i	−0.596067	+	0.802935i	$0.703271\pi$
$504$	0.891412	+	0.675787i	0.0397067	+	0.0301019i
$505$			11.3663i			0.505795i
$506$	17.6289	+	12.3224i	0.783701	+	0.547799i
$507$	−12.9835	+	1.92117i	−0.576619	+	0.0853222i
$508$	−1.67423	−	2.30438i	−0.0742819	−	0.102240i
$509$	17.9518	−	5.83289i	0.795699	−	0.258538i	0.117170	−	0.993112i	$-0.462618\pi$
$509$	17.9518	−	5.83289i	0.795699	−	0.258538i	0.678529	+	0.734573i	$0.262618\pi$
$510$	31.6282	+	5.33988i	1.40052	+	0.236454i
$511$	−6.86638	−	4.98871i	−0.303751	−	0.220688i
$512$	25.8138	+	18.7548i	1.14082	+	0.828854i
$513$	22.4863	−	2.86099i	0.992795	−	0.126316i
$514$	48.6124	−	15.7951i	2.14420	−	0.696693i
$515$	16.0867	+	22.1414i	0.708864	+	0.975668i
$516$	3.22336	+	21.7839i	0.141900	+	0.958982i
$517$	22.1319	−	16.7060i	0.973361	−	0.734728i
$518$			20.7616i			0.912211i
$519$	−16.8041	+	16.4655i	−0.737617	+	0.722756i
$520$	−0.513728	−	1.58109i	−0.0225285	−	0.0693355i
$521$	18.2126	+	5.91763i	0.797908	+	0.259256i	0.679468	−	0.733705i	$-0.262211\pi$
$521$	18.2126	+	5.91763i	0.797908	+	0.259256i	0.118440	+	0.992961i	$0.462211\pi$
$522$	−16.1578	−	5.61602i	−0.707209	−	0.245806i
$523$	20.5867	−	28.3352i	0.900195	−	1.23901i	−0.0702107	−	0.997532i	$-0.522367\pi$
$523$	20.5867	−	28.3352i	0.900195	−	1.23901i	0.970406	−	0.241480i	$-0.0776328\pi$
$524$	−12.8785	+	39.6358i	−0.562598	+	1.73150i
$525$	2.06924	−	1.02795i	0.0903092	−	0.0448632i
$526$	−29.8383	+	21.6788i	−1.30101	+	0.945240i
$527$	−15.1402			−0.659519
$528$	3.40235	+	20.4109i	0.148068	+	0.888269i
$529$	12.9442			0.562793
$530$	23.2091	−	16.8624i	1.00814	−	0.732454i
$531$	15.8525	−	11.0317i	0.687939	−	0.478735i
$532$	2.94188	−	9.05419i	0.127547	−	0.392549i
$533$	−2.51116	+	3.45631i	−0.108770	+	0.149710i
$534$	15.5376	−	29.7421i	0.672377	−	1.28707i
$535$	5.96023	+	1.93659i	0.257683	+	0.0837263i
$536$	1.70679	+	5.25296i	0.0737222	+	0.226893i
$537$	1.16922	+	1.19326i	0.0504555	+	0.0514929i
$538$			29.9215i			1.29001i
$539$	−3.17250	−	0.967095i	−0.136649	−	0.0416557i
$540$	−9.26197	−	19.6374i	−0.398572	−	0.845058i
$541$	−19.6810	−	27.0885i	−0.846151	−	1.16463i	−0.984698	−	0.174271i	$-0.944243\pi$
$541$	−19.6810	−	27.0885i	−0.846151	−	1.16463i	0.138547	−	0.990356i	$-0.455757\pi$
$542$	−12.3422	+	4.01023i	−0.530144	+	0.172254i
$543$	1.98777	−	11.7736i	0.0853034	−	0.505254i
$544$	−31.0394	−	22.5514i	−1.33080	−	0.966884i
$545$	23.7466	+	17.2529i	1.01719	+	0.739035i
$546$	1.37314	−	8.13317i	0.0587651	−	0.348067i
$547$	−20.8376	+	6.77055i	−0.890952	+	0.289488i	−0.718498	−	0.695530i	$-0.755170\pi$
$547$	−20.8376	+	6.77055i	−0.890952	+	0.289488i	−0.172455	+	0.985017i	$0.555170\pi$
$548$	−0.305840	−	0.420953i	−0.0130648	−	0.0179822i
$549$	8.85846	+	29.2779i	0.378070	+	1.24955i
$550$	−8.65480	−	2.63830i	−0.369042	−	0.112498i
$551$			12.1630i			0.518162i
$552$	1.43334	+	1.46281i	0.0610069	+	0.0622613i
$553$	−0.223314	−	0.687289i	−0.00949627	−	0.0292265i
$554$	−53.3220	−	17.3254i	−2.26543	−	0.736084i
$555$	15.5891	−	29.8408i	0.661722	−	1.26667i
$556$	−13.0739	+	17.9946i	−0.554456	+	0.763143i
$557$	−2.16755	+	6.67103i	−0.0918421	+	0.282661i	−0.986418	−	0.164256i	$-0.947478\pi$
$557$	−2.16755	+	6.67103i	−0.0918421	+	0.282661i	0.894576	+	0.446916i	$0.147478\pi$
$558$	11.2187	+	16.1211i	0.474923	+	0.682462i
$559$	10.9751	−	7.97388i	0.464198	−	0.337259i
$560$	6.89690			0.291447
$561$	−4.46718	−	26.7988i	−0.188605	−	1.13145i
$562$	65.3033			2.75465
$563$	−32.1893	+	23.3869i	−1.35662	+	0.985641i	−0.357967	+	0.933734i	$0.616530\pi$
$563$	−32.1893	+	23.3869i	−1.35662	+	0.985641i	−0.998652	+	0.0519073i	$0.983470\pi$
$564$	28.3026	−	14.0600i	1.19176	−	0.592033i
$565$	1.69916	−	5.22947i	0.0714841	−	0.220006i
$566$	31.5189	−	43.3820i	1.32484	−	1.82348i
$567$	0.366225	−	8.99255i	0.0153800	−	0.377651i
$568$	−5.28835	−	1.71829i	−0.221894	−	0.0720979i
$569$	−3.54084	−	10.8976i	−0.148440	−	0.456851i	0.848997	−	0.528397i	$-0.177207\pi$
$569$	−3.54084	−	10.8976i	−0.148440	−	0.456851i	−0.997437	+	0.0715461i	$0.977207\pi$
$570$	−21.1325	+	20.7067i	−0.885142	+	0.867309i
$571$			3.38303i			0.141576i	0.997491	+	0.0707878i	$0.0225513\pi$
$571$			3.38303i			0.141576i	−0.997491	+	0.0707878i	$0.977449\pi$
$572$	−13.4521	+	10.1541i	−0.562461	+	0.424566i
$573$	−6.48833	−	43.8490i	−0.271054	−	1.83182i
$574$	2.20541	+	3.03549i	0.0920522	+	0.126699i
$575$	4.02310	−	1.30718i	0.167775	−	0.0545133i
$576$	−0.573021	+	28.1524i	−0.0238759	+	1.17302i
$577$	9.44022	+	6.85872i	0.393002	+	0.285532i	0.766684	−	0.642024i	$-0.221905\pi$
$577$	9.44022	+	6.85872i	0.393002	+	0.285532i	−0.373683	+	0.927557i	$0.621905\pi$
$578$	8.88083	+	6.45230i	0.369394	+	0.268380i
$579$	−11.6571	−	1.96810i	−0.484453	−	0.0817914i
$580$	11.0801	−	3.60013i	0.460074	−	0.149487i
$581$	−5.30899	−	7.30720i	−0.220254	−	0.303154i
$582$	4.92609	−	0.728913i	0.204193	−	0.0302144i
$583$	−19.9160	−	13.9211i	−0.824836	−	0.576553i
$584$			3.16468i			0.130955i
$585$	−8.08054	+	10.6588i	−0.334089	+	0.440688i
$586$	−4.38818	−	13.5054i	−0.181274	−	0.557904i
$587$	−37.1892	−	12.0835i	−1.53496	−	0.498739i	−0.584980	−	0.811048i	$-0.698898\pi$
$587$	−37.1892	−	12.0835i	−1.53496	−	0.498739i	−0.949981	+	0.312309i	$0.898898\pi$
$588$	−3.35028	−	1.75022i	−0.138163	−	0.0721779i
$589$	8.20851	−	11.2980i	0.338226	−	0.465528i
$590$	−7.78972	+	23.9743i	−0.320698	+	0.987007i
$591$	14.2876	+	28.7608i	0.587713	+	1.18306i
$592$	−29.5846	+	21.4944i	−1.21592	+	0.883416i
$593$	30.5451			1.25434			0.627169	−	0.778883i	$-0.284213\pi$
$593$	30.5451			1.25434			0.627169	+	0.778883i	$0.284213\pi$
$594$	−25.2250	+	24.6141i	−1.03499	+	1.00993i
$595$	−9.05542			−0.371236
$596$	−6.02767	+	4.37936i	−0.246903	+	0.179385i
$597$	−3.08733	−	6.21477i	−0.126356	−	0.254354i
$598$	4.66651	−	14.3620i	0.190828	−	0.587307i
$599$	16.7269	−	23.0226i	0.683442	−	0.940677i	−0.316527	−	0.948583i	$-0.602517\pi$
$599$	16.7269	−	23.0226i	0.683442	−	0.940677i	0.999969	+	0.00790670i	$0.00251681\pi$
$600$	−0.763604	−	0.398915i	−0.0311740	−	0.0162856i
$601$	4.48576	+	1.45751i	0.182978	+	0.0594532i	0.399073	−	0.916919i	$-0.369332\pi$
$601$	4.48576	+	1.45751i	0.182978	+	0.0594532i	−0.216095	+	0.976372i	$0.569332\pi$
$602$	−3.68171	−	11.3311i	−0.150055	−	0.461822i
$603$	26.8465	−	35.4125i	1.09327	−	1.44211i
$604$		−	9.60444i		−	0.390799i
$605$	−0.769439	−	21.0475i	−0.0312821	−	0.855703i
$606$	20.8012	−	3.07796i	0.844993	−	0.125033i
$607$	20.5713	+	28.3139i	0.834961	+	1.14923i	0.986979	+	0.160848i	$0.0514229\pi$
$607$	20.5713	+	28.3139i	0.834961	+	1.14923i	−0.152018	+	0.988378i	$0.548577\pi$
$608$	33.6569	−	10.9358i	1.36497	−	0.443505i
$609$	4.76185	+	0.803956i	0.192960	+	0.0325779i
$610$	−32.3001	−	23.4674i	−1.30779	−	0.950168i
$611$	−15.7504	−	11.4434i	−0.637195	−	0.462949i
$612$	0.630112	−	30.9572i	0.0254708	−	1.25137i
$613$	7.12779	−	2.31596i	0.287889	−	0.0935407i	−0.161513	−	0.986871i	$-0.551637\pi$
$613$	7.12779	−	2.31596i	0.287889	−	0.0935407i	0.449401	+	0.893330i	$0.351637\pi$
$614$	−6.07125	−	8.35636i	−0.245016	−	0.337235i
$615$	−0.890617	−	6.01891i	−0.0359131	−	0.242706i
$616$	0.403578	+	1.16897i	0.0162606	+	0.0470992i
$617$			14.4093i			0.580098i	0.957012	+	0.290049i	$0.0936717\pi$
$617$			14.4093i			0.580098i	−0.957012	+	0.290049i	$0.906328\pi$
$618$	36.1642	−	35.4356i	1.45474	−	1.42543i
$619$	5.46633	+	16.8236i	0.219710	+	0.676199i	0.998786	+	0.0492685i	$0.0156890\pi$
$619$	5.46633	+	16.8236i	0.219710	+	0.676199i	−0.779075	+	0.626930i	$0.784311\pi$
$620$	−12.7217	−	4.13354i	−0.510917	−	0.166007i
$621$	3.07318	−	16.1883i	0.123322	−	0.649614i
$622$	32.3716	−	44.5556i	1.29798	−	1.78652i
$623$	−2.92741	+	9.00965i	−0.117284	+	0.360964i
$624$	13.0111	−	6.46357i	0.520861	−	0.258750i
$625$	13.3898	−	9.72823i	0.535591	−	0.389129i
$626$	−17.9302			−0.716637
$627$	22.4199	+	11.1959i	0.895366	+	0.447120i
$628$	−17.4968			−0.698199
$629$	38.8436	−	28.2215i	1.54880	−	1.12527i
$630$	6.70990	+	9.64209i	0.267329	+	0.384150i
$631$	0.691637	−	2.12864i	0.0275336	−	0.0847398i	−0.936345	−	0.351080i	$-0.885814\pi$
$631$	0.691637	−	2.12864i	0.0275336	−	0.0847398i	0.963879	+	0.266340i	$0.0858145\pi$
$632$	−0.158384	+	0.217997i	−0.00630019	+	0.00867146i
$633$	−1.40037	+	2.68059i	−0.0556597	+	0.106544i
$634$	−9.44012	−	3.06728i	−0.374915	−	0.121817i
$635$	−0.772248	−	2.37674i	−0.0306457	−	0.0943179i
$636$	−19.3818	−	19.7803i	−0.768538	−	0.784340i
$637$			2.32859i			0.0922621i
$638$	−11.3935	−	15.0940i	−0.451073	−	0.597577i
$639$	12.9560	+	42.8208i	0.512533	+	1.69396i
$640$	−3.34317	−	4.60148i	−0.132150	−	0.181889i
$641$	−36.4500	+	11.8433i	−1.43969	+	0.467783i	−0.921800	−	0.387666i	$-0.873282\pi$
$641$	−36.4500	+	11.8433i	−1.43969	+	0.467783i	−0.517888	+	0.855449i	$0.673282\pi$
$642$	1.93011	−	11.4321i	0.0761753	−	0.451188i
$643$	0.684915	+	0.497620i	0.0270104	+	0.0196242i	0.601209	−	0.799092i	$-0.294686\pi$
$643$	0.684915	+	0.497620i	0.0270104	+	0.0196242i	−0.574198	+	0.818716i	$0.694686\pi$
$644$	−5.59867	−	4.06767i	−0.220619	−	0.160289i
$645$	−3.21640	+	19.0508i	−0.126646	+	0.750125i
$646$	−40.1282	+	13.0384i	−1.57882	+	0.512990i
$647$	7.90060	+	10.8742i	0.310605	+	0.427511i	0.935570	−	0.353142i	$-0.114887\pi$
$647$	7.90060	+	10.8742i	0.310605	+	0.427511i	−0.624965	+	0.780653i	$0.714887\pi$
$648$	−2.79296	+	1.86041i	−0.109718	+	0.0730838i
$649$	21.3480	−	0.390081i	0.837981	−	0.0153120i
$650$			6.35256i			0.249168i
$651$	−3.88064	−	3.96043i	−0.152094	−	0.155222i
$652$	−13.1442	−	40.4536i	−0.514766	−	1.58429i
$653$	−8.21564	−	2.66942i	−0.321503	−	0.104463i	0.143819	−	0.989604i	$-0.454062\pi$
$653$	−8.21564	−	2.66942i	−0.321503	−	0.104463i	−0.465322	+	0.885141i	$0.654062\pi$
$654$	25.1437	−	48.1301i	0.983196	−	1.88204i
$655$	−21.4921	+	29.5813i	−0.839765	+	1.15584i
$656$	−2.04221	+	6.28528i	−0.0797350	+	0.245399i
$657$	20.8994	−	14.5438i	0.815364	−	0.567410i
$658$	−13.8328	+	10.0501i	−0.539257	+	0.391793i
$659$	−2.48853			−0.0969394			−0.0484697	−	0.998825i	$-0.515434\pi$
$659$	−2.48853			−0.0969394			−0.0484697	+	0.998825i	$0.515434\pi$
$660$	3.56294	−	23.7376i	0.138687	−	0.923985i
$661$	16.0004			0.622345			0.311172	−	0.950354i	$-0.399278\pi$
$661$	16.0004			0.622345			0.311172	+	0.950354i	$0.399278\pi$
$662$	−12.4951	+	9.07821i	−0.485635	+	0.352835i
$663$	−17.0832	+	8.48647i	−0.663456	+	0.329587i
$664$	−1.04072	+	3.20302i	−0.0403879	+	0.124301i
$665$	4.90953	−	6.75739i	0.190383	−	0.262040i
$666$	−58.8324	−	20.4485i	−2.27971	−	0.792364i
$667$	8.40876	+	2.73217i	0.325588	+	0.105790i
$668$	−13.7801	−	42.4108i	−0.533168	−	1.64092i
$669$	−10.5007	+	10.2891i	−0.405980	+	0.397801i
$670$			58.0023i			2.24082i
$671$	−9.86073	+	32.3475i	−0.380669	+	1.24876i
$672$	−2.05672	−	13.8996i	−0.0793397	−	0.536188i
$673$	19.7163	+	27.1372i	0.760008	+	1.04606i	0.997213	+	0.0746015i	$0.0237685\pi$
$673$	19.7163	+	27.1372i	0.760008	+	1.04606i	−0.237206	+	0.971459i	$0.576232\pi$
$674$	−60.7315	+	19.7329i	−2.33929	+	0.760081i
$675$	0.874861	+	6.87609i	0.0336734	+	0.264661i
$676$	−13.3787	−	9.72017i	−0.514564	−	0.373853i
$677$	−25.2529	−	18.3473i	−0.970546	−	0.705143i	−0.0149702	−	0.999888i	$-0.504765\pi$
$677$	−25.2529	−	18.3473i	−0.970546	−	0.705143i	−0.955576	+	0.294745i	$0.904765\pi$
$678$	−10.0304	−	1.69347i	−0.385217	−	0.0650372i
$679$	−1.33703	+	0.434429i	−0.0513106	+	0.0166718i
$680$	1.98466	+	2.73166i	0.0761084	+	0.104754i
$681$	−0.969353	+	0.143435i	−0.0371457	+	0.00549644i
$682$	0.396692	+	21.7098i	0.0151901	+	0.831310i
$683$			31.8256i			1.21777i	0.793258	+	0.608886i	$0.208383\pi$
$683$			31.8256i			1.21777i	−0.793258	+	0.608886i	$0.791617\pi$
$684$	22.7594	+	17.2541i	0.870229	+	0.659728i
$685$	−0.141071	−	0.434170i	−0.00539003	−	0.0165888i
$686$	1.94498	+	0.631963i	0.0742597	+	0.0241284i
$687$	23.4875	+	12.2701i	0.896104	+	0.468134i
$688$	12.3348	−	16.9774i	0.470261	−	0.647258i
$689$	−5.27191	+	16.2253i	−0.200844	+	0.618134i
$690$	9.56837	+	19.2610i	0.364261	+	0.733255i
$691$	−12.7695	+	9.27758i	−0.485774	+	0.352936i	−0.803557	−	0.595228i	$-0.797062\pi$
$691$	−12.7695	+	9.27758i	−0.485774	+	0.352936i	0.317783	+	0.948164i	$0.397062\pi$
$692$	−29.6424			−1.12684
$693$	5.86513	−	8.03743i	0.222798	−	0.305317i
$694$	52.6845			1.99988
$695$	−15.7878	+	11.4705i	−0.598865	+	0.435101i
$696$	−0.801128	−	1.61266i	−0.0303667	−	0.0611278i
$697$	2.68136	−	8.25238i	0.101564	−	0.312581i
$698$	−0.629747	+	0.866772i	−0.0238363	+	0.0328078i
$699$	−33.6936	−	17.6019i	−1.27441	−	0.665765i
$700$	2.76868	+	0.899599i	0.104646	+	0.0340016i
$701$	9.14423	+	28.1431i	0.345373	+	1.06295i	0.961384	+	0.275211i	$0.0887477\pi$
$701$	9.14423	+	28.1431i	0.345373	+	1.06295i	−0.616011	+	0.787738i	$0.711252\pi$
$702$	21.6946	+	11.9016i	0.818811	+	0.449198i
$703$			44.2869i			1.67031i
$704$	−17.8346	+	25.5148i	−0.672168	+	0.961627i
$705$	27.4282	−	4.05855i	1.03301	−	0.152854i
$706$	−13.8229	−	19.0256i	−0.520231	−	0.716037i
$707$	−5.64585	+	1.83445i	−0.212334	+	0.0689915i
$708$	23.9944	+	4.05104i	0.901766	+	0.152247i
$709$	7.19412	+	5.22683i	0.270181	+	0.196298i	0.714623	−	0.699510i	$-0.246598\pi$
$709$	7.19412	+	5.22683i	0.270181	+	0.196298i	−0.444442	+	0.895807i	$0.646598\pi$
$710$	−47.2410	−	34.3226i	−1.77292	−	1.28810i
$711$	2.16753	+	0.0441185i	0.0812886	+	0.00165457i
$712$	3.35945	−	1.09155i	0.125901	−	0.0409076i
$713$	−5.96689	−	8.21273i	−0.223462	−	0.307569i
$714$	2.45217	+	16.5721i	0.0917701	+	0.620194i
$715$	−13.9777	+	4.82568i	−0.522735	+	0.180470i
$716$			2.10491i			0.0786643i
$717$	−0.459575	+	0.450316i	−0.0171631	+	0.0168174i
$718$	5.29125	+	16.2848i	0.197468	+	0.607743i
$719$	−6.68952	−	2.17356i	−0.249477	−	0.0810600i	0.181609	−	0.983371i	$-0.441869\pi$
$719$	−6.68952	−	2.17356i	−0.249477	−	0.0810600i	−0.431086	+	0.902311i	$0.641869\pi$
$720$	−6.79290	+	19.5438i	−0.253157	+	0.728356i
$721$	−8.40173	+	11.5640i	−0.312897	+	0.430666i
$722$	0.0191796	−	0.0590287i	0.000713791	−	0.00219682i
$723$	−22.9445	+	11.3982i	−0.853314	+	0.423904i
$724$	12.1711	−	8.84282i	0.452335	−	0.328641i
$725$	−3.71933			−0.138133
$726$	−38.3101	+	7.10770i	−1.42182	+	0.263792i
$727$	−38.1389			−1.41449			−0.707247	−	0.706966i	$-0.750063\pi$
$727$	−38.1389			−1.41449			−0.707247	+	0.706966i	$0.750063\pi$
$728$	0.702443	−	0.510354i	0.0260343	−	0.0189150i
$729$	25.1216	+	9.89473i	0.930429	+	0.366471i
$730$	−10.2697	+	31.6070i	−0.380100	+	1.16983i
$731$	−16.1952	+	22.2908i	−0.599002	+	0.824456i
$732$	−17.8457	+	34.1603i	−0.659595	+	1.26260i
$733$	−40.1631	−	13.0498i	−1.48346	−	0.482005i	−0.548314	−	0.836272i	$-0.684730\pi$
$733$	−40.1631	−	13.0498i	−1.48346	−	0.482005i	−0.935144	+	0.354267i	$0.884730\pi$
$734$	−13.9326	−	42.8803i	−0.514263	−	1.58274i
$735$	−2.32102	−	2.36874i	−0.0856121	−	0.0873724i
$736$		−	25.7248i		−	0.948229i
$737$	46.4389	−	16.0327i	1.71060	−	0.590571i
$738$	−10.7739	+	3.25979i	−0.396592	+	0.119995i
$739$	24.2160	+	33.3305i	0.890801	+	1.22608i	0.973311	+	0.229492i	$0.0737065\pi$
$739$	24.2160	+	33.3305i	0.890801	+	1.22608i	−0.0825095	+	0.996590i	$0.526293\pi$
$740$	40.3437	−	13.1085i	1.48306	−	0.481876i
$741$	2.92907	−	17.3490i	0.107602	−	0.637331i
$742$	12.1216	+	8.80685i	0.444997	+	0.323310i
$743$	14.3348	+	10.4148i	0.525892	+	0.382083i	0.818819	−	0.574052i	$-0.194629\pi$
$743$	14.3348	+	10.4148i	0.525892	+	0.382083i	−0.292927	+	0.956135i	$0.594629\pi$
$744$	−0.344188	+	2.03864i	−0.0126186	+	0.0747401i
$745$	−6.21693	+	2.02000i	−0.227771	+	0.0740072i
$746$	−20.2124	−	27.8199i	−0.740027	−	1.01856i
$747$	25.9354	−	7.84714i	0.948928	−	0.287112i
$748$	19.6115	−	28.0569i	0.717067	−	1.02586i
$749$			3.27309i			0.119596i
$750$	−30.0652	−	30.6834i	−1.09783	−	1.12040i
$751$	−16.1246	−	49.6264i	−0.588394	−	1.81089i	−0.585190	−	0.810896i	$-0.698980\pi$
$751$	−16.1246	−	49.6264i	−0.588394	−	1.81089i	−0.00320464	−	0.999995i	$-0.501020\pi$
$752$	−28.6421	−	9.30637i	−1.04447	−	0.339369i
$753$	13.6938	−	26.2128i	0.499031	−	0.955248i
$754$	−7.80439	+	10.7418i	−0.284219	+	0.391194i
$755$	2.60395	−	8.01413i	0.0947674	−	0.291664i
$756$	8.25939	−	7.76990i	0.300391	−	0.282589i
$757$	−7.30961	+	5.31074i	−0.265672	+	0.193022i	−0.712644	−	0.701526i	$-0.752502\pi$
$757$	−7.30961	+	5.31074i	−0.265672	+	0.193022i	0.446972	+	0.894548i	$0.352502\pi$
$758$	56.2760			2.04404
$759$	12.7763	−	12.9848i	0.463750	−	0.471320i
$760$	−3.11445			−0.112973
$761$	18.4897	−	13.4335i	0.670249	−	0.486965i	−0.199859	−	0.979825i	$-0.564048\pi$
$761$	18.4897	−	13.4335i	0.670249	−	0.486965i	0.870109	+	0.492860i	$0.164048\pi$
$762$	−4.14048	+	2.05688i	−0.149994	+	0.0745129i
$763$	−4.73728	+	14.5799i	−0.171501	+	0.527826i
$764$	32.8277	−	45.1835i	1.18767	−	1.63468i
$765$	8.91887	−	25.6604i	0.322462	−	0.927756i
$766$	−71.7268	−	23.3054i	−2.59159	−	0.842060i
$767$	−4.63242	−	14.2571i	−0.167267	−	0.514795i
$768$	15.7081	−	15.3916i	0.566818	−	0.555398i
$769$			35.3883i			1.27614i	0.769980	+	0.638068i	$0.220266\pi$
$769$			35.3883i			1.27614i	−0.769980	+	0.638068i	$0.779734\pi$
$770$	0.237263	+	12.9847i	0.00855035	+	0.467935i
$771$	−6.33669	−	42.8242i	−0.228210	−	1.54228i
$772$	−8.75531	−	12.0507i	−0.315111	−	0.433712i
$773$	16.6912	−	5.42330i	0.600341	−	0.195063i	0.00694837	−	0.999976i	$-0.497788\pi$
$773$	16.6912	−	5.42330i	0.600341	−	0.195063i	0.593392	+	0.804913i	$0.297788\pi$
$774$	35.7354	+	0.727368i	1.28448	+	0.0261447i
$775$	3.45483	+	2.51008i	0.124101	+	0.0901648i
$776$	0.424086	+	0.308116i	0.0152238	+	0.0110607i
$777$	17.3384	+	2.92729i	0.622012	+	0.105016i
$778$	−17.2154	+	5.59362i	−0.617202	+	0.200541i
$779$	4.70440	+	6.47505i	0.168553	+	0.231993i
$780$	−16.6713	+	2.46684i	−0.596927	+	0.0883272i
$781$	−14.4219	+	47.3102i	−0.516057	+	1.69289i
$782$			30.6709i			1.09679i
$783$	−6.96823	+	12.7019i	−0.249024	+	0.453928i
$784$	1.11311	+	3.42580i	0.0397540	+	0.122350i
$785$	−14.5997	−	4.74373i	−0.521085	−	0.169311i
$786$	59.9559	+	31.3216i	2.13856	+	1.11720i
$787$	−10.2242	+	14.0724i	−0.364452	+	0.501626i	−0.951383	−	0.308012i	$-0.900336\pi$
$787$	−10.2242	+	14.0724i	−0.364452	+	0.501626i	0.586930	+	0.809638i	$0.300336\pi$
$788$	−12.5037	+	38.4824i	−0.445425	+	1.37088i
$789$	13.8973	+	27.9752i	0.494758	+	0.995942i
$790$	−2.28927	+	1.66325i	−0.0814487	+	0.0591759i
$791$	2.87180			0.102109
$792$	−3.71002	−	0.00772051i	−0.131830	−	0.000274337i
$793$	23.7429			0.843134
$794$	24.9307	−	18.1132i	0.884759	−	0.642815i
$795$	−10.8097	−	21.7598i	−0.383381	−	0.771742i
$796$	2.70186	−	8.31546i	0.0957647	−	0.294734i
$797$	−18.9733	+	26.1145i	−0.672069	+	0.925024i	−0.999805	−	0.0197456i	$-0.993714\pi$
$797$	−18.9733	+	26.1145i	−0.672069	+	0.925024i	0.327736	+	0.944769i	$0.393714\pi$
$798$	−13.6960	−	7.15493i	−0.484833	−	0.253282i
$799$	37.6062	+	12.2190i	1.33041	+	0.432276i
$800$	3.34406	+	10.2920i	0.118230	+	0.363875i
$801$	−22.6475	−	17.1692i	−0.800209	−	0.606645i
$802$		−	32.1968i		−	1.13691i
$803$	28.1445	−	0.514271i	0.993198	−	0.0181482i
$804$	55.3880	−	8.19575i	1.95338	−	0.289042i
$805$	−3.56881	−	4.91205i	−0.125784	−	0.173127i
$806$	14.4988	−	4.71093i	0.510697	−	0.165935i
$807$	24.9880	+	4.21879i	0.879620	+	0.148509i
$808$	1.79077	+	1.30107i	0.0629992	+	0.0457716i
$809$	27.9277	+	20.2906i	0.981884	+	0.713381i	0.958129	−	0.286337i	$-0.0924377\pi$
$809$	27.9277	+	20.2906i	0.981884	+	0.713381i	0.0237555	+	0.999718i	$0.492438\pi$
$810$	−33.9316	+	9.51724i	−1.19224	+	0.334402i
$811$	19.7143	−	6.40558i	0.692264	−	0.224930i	0.0583073	−	0.998299i	$-0.481430\pi$
$811$	19.7143	−	6.40558i	0.692264	−	0.224930i	0.633957	+	0.773368i	$0.281430\pi$
$812$	3.57649	+	4.92261i	0.125510	+	0.172750i
$813$	1.60883	+	10.8727i	0.0564240	+	0.381321i
$814$	−41.4849	−	54.9589i	−1.45405	−	1.92631i
$815$		−	37.3189i		−	1.30723i
$816$	−21.0759	+	20.6513i	−0.737805	+	0.722941i
$817$	−7.85351	−	24.1706i	−0.274760	−	0.845623i
$818$	−24.9560	−	8.10869i	−0.872565	−	0.283514i
$819$	−6.59856	−	2.29348i	−0.230572	−	0.0801406i
$820$	4.50608	−	6.20209i	0.157359	−	0.216586i
$821$	7.08559	−	21.8072i	0.247289	−	0.761077i	−0.747963	−	0.663741i	$-0.768968\pi$
$821$	7.08559	−	21.8072i	0.247289	−	0.761077i	0.995252	−	0.0973361i	$-0.0310322\pi$
$822$	−0.756363	+	0.375741i	−0.0263812	+	0.0131055i
$823$	34.1536	−	24.8141i	1.19052	−	0.864964i	0.197201	−	0.980363i	$-0.436815\pi$
$823$	34.1536	−	24.8141i	1.19052	−	0.864964i	0.993319	+	0.115399i	$0.0368147\pi$
$824$	5.32979			0.185672
$825$	−3.42359	+	6.85580i	−0.119194	+	0.238688i
$826$	−13.1656			−0.458091
$827$	41.6894	−	30.2892i	1.44968	−	1.05326i	0.463779	−	0.885951i	$-0.346493\pi$
$827$	41.6894	−	30.2892i	1.44968	−	1.05326i	0.985905	−	0.167306i	$-0.0535069\pi$
$828$	17.0409	−	11.8587i	0.592211	−	0.412118i
$829$	−4.43168	+	13.6393i	−0.153919	+	0.473713i	−0.998050	−	0.0624238i	$-0.980117\pi$
$829$	−4.43168	+	13.6393i	−0.153919	+	0.473713i	0.844131	+	0.536137i	$0.180117\pi$
$830$	−20.7883	+	28.6126i	−0.721572	+	0.993159i
$831$	−21.9869	+	42.0874i	−0.762717	+	1.46000i
$832$	20.7866	+	6.75397i	0.720645	+	0.234152i
$833$	−1.46148	−	4.49797i	−0.0506373	−	0.155846i
$834$	25.2671	+	25.7867i	0.874929	+	0.892919i
$835$		−	39.1244i		−	1.35396i
$836$	10.3041	+	29.8461i	0.356375	+	1.03225i
$837$	15.0449	−	7.09591i	0.520026	−	0.245270i
$838$	19.3657	+	26.6546i	0.668977	+	0.920768i
$839$	−9.41289	+	3.05843i	−0.324969	+	0.105589i	−0.466958	−	0.884279i	$-0.654650\pi$
$839$	−9.41289	+	3.05843i	−0.324969	+	0.105589i	0.141989	+	0.989868i	$0.454650\pi$
$840$	−0.205860	+	1.21931i	−0.00710284	+	0.0420703i
$841$	17.1723	+	12.4764i	0.592149	+	0.430221i
$842$	13.8010	+	10.0270i	0.475614	+	0.345554i
$843$	9.20747	−	54.5361i	0.317122	−	1.87832i
$844$	−3.62406	+	1.17753i	−0.124745	+	0.0405323i
$845$	−8.52810	−	11.7379i	−0.293375	−	0.403797i
$846$	−14.8549	−	49.0966i	−0.510721	−	1.68798i
$847$	10.3305	−	3.77911i	0.354959	−	0.129852i
$848$			26.3906i			0.906256i
$849$	−31.7851	−	32.4387i	−1.09086	−	1.11329i
$850$	−3.98702	−	12.2708i	−0.136754	−	0.420885i
$851$	30.6172	+	9.94812i	1.04954	+	0.341017i
$852$	−26.1004	+	49.9615i	−0.894185	+	1.71165i
$853$	14.6135	−	20.1138i	0.500357	−	0.688682i	−0.481899	−	0.876227i	$-0.660053\pi$
$853$	14.6135	−	20.1138i	0.500357	−	0.688682i	0.982256	+	0.187544i	$0.0600529\pi$
$854$	6.44364	−	19.8315i	0.220497	−	0.678619i
$855$	14.3130	+	20.5677i	0.489494	+	0.703400i
$856$	0.987362	−	0.717360i	0.0337473	−	0.0245189i
$857$	18.9660			0.647868			0.323934	−	0.946080i	$-0.394994\pi$
$857$	18.9660			0.647868			0.323934	+	0.946080i	$0.394994\pi$
$858$	12.6164	+	24.2734i	0.430718	+	0.828680i
$859$	−48.5611			−1.65689			−0.828443	−	0.560074i	$-0.810773\pi$
$859$	−48.5611			−1.65689			−0.828443	+	0.560074i	$0.810773\pi$
$860$	−19.6940	+	14.3085i	−0.671559	+	0.487916i
$861$	2.84595	−	1.41379i	0.0969897	−	0.0481819i
$862$	−9.67210	+	29.7677i	−0.329433	+	1.01389i
$863$	−22.9581	+	31.5991i	−0.781503	+	1.07565i	0.213611	+	0.976919i	$0.431477\pi$
$863$	−22.9581	+	31.5991i	−0.781503	+	1.07565i	−0.995114	+	0.0987281i	$0.968523\pi$
$864$	41.4132	+	7.86185i	1.40890	+	0.267465i
$865$	−24.7342	−	8.03664i	−0.840989	−	0.273254i
$866$	17.3658	+	53.4463i	0.590113	+	1.81618i
$867$	6.64060	−	6.50681i	0.225527	−	0.220983i
$868$		−	6.98622i		−	0.237128i
$869$	1.96446	+	1.37314i	0.0666396	+	0.0465804i
$870$	−2.76793	−	18.7061i	−0.0938418	−	0.634195i
$871$	−20.2745	−	27.9054i	−0.686975	−	0.945540i
$872$	5.43642	−	1.76640i	0.184100	−	0.0598179i
$873$	0.0858268	−	4.21665i	0.00290480	−	0.142712i
$874$	−22.8875	−	16.6287i	−0.774180	−	0.562474i
$875$	9.81142	+	7.12841i	0.331686	+	0.240984i
$876$	31.6335	+	5.34077i	1.06880	+	0.180448i
$877$	23.7627	−	7.72096i	0.802409	−	0.260718i	0.121029	−	0.992649i	$-0.461380\pi$
$877$	23.7627	−	7.72096i	0.802409	−	0.260718i	0.681379	+	0.731931i	$0.261380\pi$
$878$	−2.78753	−	3.83671i	−0.0940746	−	0.129483i
$879$	−11.8974	+	1.76045i	−0.401288	+	0.0593785i
$880$	−18.2571	+	13.7811i	−0.615446	+	0.464561i
$881$		−	17.7617i		−	0.598408i	−0.954189	−	0.299204i	$-0.903279\pi$
$881$		−	17.7617i		−	0.598408i	0.954189	−	0.299204i	$-0.0967211\pi$
$882$	−3.70645	+	4.88908i	−0.124803	+	0.164624i
$883$	0.200890	+	0.618275i	0.00676047	+	0.0208066i	0.954380	−	0.298595i	$-0.0965180\pi$
$883$	0.200890	+	0.618275i	0.00676047	+	0.0208066i	−0.947619	+	0.319402i	$0.896518\pi$
$884$	−22.8576	−	7.42687i	−0.768783	−	0.249793i
$885$	18.9231	+	9.88562i	0.636093	+	0.332301i
$886$	8.63500	−	11.8851i	0.290099	−	0.399286i
$887$	−8.00886	+	24.6487i	−0.268911	+	0.827624i	0.721855	+	0.692044i	$0.243290\pi$
$887$	−8.00886	+	24.6487i	−0.268911	+	0.827624i	−0.990766	+	0.135580i	$0.956710\pi$
$888$	−2.91699	−	5.87187i	−0.0978878	−	0.197047i
$889$	1.05593	−	0.767176i	0.0354147	−	0.0257303i
$890$	37.0944			1.24341
$891$	16.9991	+	24.5363i	0.569491	+	0.821998i
$892$	−18.5233			−0.620205
$893$	−29.5069	+	21.4380i	−0.987410	+	0.717395i
$894$	5.38027	+	10.8304i	0.179943	+	0.362224i
$895$	−0.570683	+	1.75638i	−0.0190758	+	0.0587093i
$896$	1.74606	−	2.40325i	0.0583319	−	0.0802870i
$897$	−11.3361	−	5.92207i	−0.378500	−	0.197732i
$898$	22.9004	+	7.44080i	0.764197	+	0.248303i
$899$	2.75818	+	8.48881i	0.0919905	+	0.283118i
$900$	−5.27614	+	6.95961i	−0.175871	+	0.231987i
$901$		−	34.6500i		−	1.15436i
$902$	−11.9034	−	3.62861i	−0.396341	−	0.120820i
$903$	−9.98195	+	1.47703i	−0.332179	+	0.0491524i
$904$	−0.629408	−	0.866306i	−0.0209338	−	0.0288129i
$905$	12.5533	−	4.07880i	0.417284	−	0.135584i
$906$	−15.3716	−	2.59523i	−0.510687	−	0.0862206i
$907$	−7.23925	−	5.25962i	−0.240375	−	0.174643i	0.461075	−	0.887361i	$-0.347464\pi$
$907$	−7.23925	−	5.25962i	−0.240375	−	0.174643i	−0.701451	+	0.712718i	$0.747464\pi$
$908$	−0.998854	−	0.725710i	−0.0331481	−	0.0240835i
$909$	0.362418	−	17.8055i	0.0120206	−	0.590571i
$910$	8.67174	−	2.81762i	0.287465	−	0.0934032i
$911$	−5.36966	−	7.39071i	−0.177905	−	0.244865i	0.710747	−	0.703448i	$-0.248357\pi$
$911$	−5.36966	−	7.39071i	−0.177905	−	0.244865i	−0.888652	+	0.458583i	$0.848357\pi$
$912$	−3.98392	−	26.9238i	−0.131921	−	0.891537i
$913$	28.6546	+	8.73499i	0.948329	+	0.289086i
$914$			57.2992i			1.89529i
$915$	−24.1523	+	23.6657i	−0.798450	+	0.782363i
$916$	10.3176	+	31.7542i	0.340902	+	1.04919i
$917$	−18.1622	−	5.90125i	−0.599768	−	0.194877i
$918$	−49.3757	−	9.37345i	−1.62964	−	0.309370i
$919$	−13.9990	+	19.2679i	−0.461783	+	0.635590i	−0.974877	−	0.222742i	$-0.928499\pi$
$919$	−13.9990	+	19.2679i	−0.461783	+	0.635590i	0.513094	+	0.858332i	$0.328499\pi$
$920$	−0.699597	+	2.15314i	−0.0230650	+	0.0709868i
$921$	−7.83457	+	3.89201i	−0.258158	+	0.128246i
$922$	30.8306	−	22.3997i	1.01535	−	0.737695i
$923$	34.7254			1.14300
$924$	12.3659	−	2.06131i	0.406808	−	0.0678121i
$925$	−13.5425			−0.445274
$926$	0.591450	−	0.429713i	0.0194362	−	0.0141213i
$927$	−24.4940	−	35.1977i	−0.804488	−	1.15604i
$928$	−6.98948	+	21.5114i	−0.229441	+	0.706147i
$929$	12.1898	−	16.7779i	0.399935	−	0.550464i	−0.560792	−	0.827956i	$-0.689503\pi$
$929$	12.1898	−	16.7779i	0.399935	−	0.550464i	0.960728	+	0.277493i	$0.0895034\pi$
$930$	−10.0532	+	19.2438i	−0.329656	+	0.631029i
$931$	4.14887	+	1.34805i	0.135974	+	0.0441805i
$932$	−14.8009	−	45.5526i	−0.484820	−	1.49212i
$933$	−32.6450	−	33.3163i	−1.06875	−	1.09073i
$934$			80.0637i			2.61976i
$935$	23.9710	−	18.0942i	0.783935	−	0.591742i
$936$	0.754347	+	2.49318i	0.0246566	+	0.0814921i
$937$	−20.1119	−	27.6817i	−0.657028	−	0.904321i	0.342351	−	0.939572i	$-0.388777\pi$
$937$	−20.1119	−	27.6817i	−0.657028	−	0.904321i	−0.999378	+	0.0352512i	$0.988777\pi$
$938$	−28.8107	+	9.36115i	−0.940702	+	0.305653i
$939$	−2.52808	+	14.9739i	−0.0825008	+	0.488655i
$940$	28.2629	+	20.5342i	0.921836	+	0.669753i
$941$	21.9408	+	15.9409i	0.715249	+	0.519659i	0.884863	−	0.465852i	$-0.154252\pi$
$941$	21.9408	+	15.9409i	0.715249	+	0.519659i	−0.169614	+	0.985511i	$0.554252\pi$
$942$	−4.72784	+	28.0031i	−0.154041	+	0.912390i
$943$	5.53320	−	1.79784i	0.180186	−	0.0585459i
$944$	−13.6304	−	18.7606i	−0.443631	−	0.610605i
$945$	8.99836	−	4.24408i	0.292717	−	0.138060i
$946$	32.3874	+	22.6385i	1.05301	+	0.736041i
$947$			25.0438i			0.813813i	0.913470	+	0.406907i	$0.133393\pi$
$947$			25.0438i			0.813813i	−0.913470	+	0.406907i	$0.866607\pi$
$948$	1.91176	+	1.95107i	0.0620912	+	0.0633679i
$949$	−6.10725	−	18.7962i	−0.198250	−	0.610149i
$950$	11.3184	+	3.67757i	0.367218	+	0.119316i
$951$	−3.89256	+	7.45115i	−0.126225	+	0.241620i
$952$	−1.03655	+	1.42669i	−0.0335947	+	0.0462391i
$953$	16.4388	−	50.5933i	0.532504	−	1.63888i	−0.216477	−	0.976288i	$-0.569457\pi$
$953$	16.4388	−	50.5933i	0.532504	−	1.63888i	0.748981	−	0.662591i	$-0.230543\pi$
$954$	−36.8949	+	25.6750i	−1.19452	+	0.831260i
$955$	39.6422	−	28.8018i	1.28279	−	0.932003i
$956$	−0.810692			−0.0262197
$957$	−14.2117	+	7.38674i	−0.459400	+	0.238780i
$958$	−54.6779			−1.76656
$959$	0.192892	−	0.140144i	0.00622880	−	0.00452549i
$960$	−27.8770	+	13.8486i	−0.899728	+	0.446961i
$961$	−6.41268	+	19.7362i	−0.206861	+	0.636652i
$962$	−28.4166	+	39.1121i	−0.916188	+	1.26102i
$963$	−9.27501	−	3.22374i	−0.298883	−	0.103884i
$964$	−30.7001	−	9.97506i	−0.988783	−	0.321275i
$965$	−4.03844	−	12.4290i	−0.130002	−	0.400105i
$966$	−8.02300	+	7.86136i	−0.258136	+	0.252935i
$967$			5.63352i			0.181162i	0.995889	+	0.0905809i	$0.0288724\pi$
$967$			5.63352i			0.181162i	−0.995889	+	0.0905809i	$0.971128\pi$
$968$	−3.40412	−	2.28802i	−0.109413	−	0.0735398i
$969$	5.23076	+	35.3502i	0.168036	+	1.13561i
$970$	3.23565	+	4.45349i	0.103890	+	0.142993i
$971$	−15.6245	+	5.07669i	−0.501413	+	0.162919i	−0.548793	−	0.835958i	$-0.684913\pi$
$971$	−15.6245	+	5.07669i	−0.501413	+	0.162919i	0.0473807	+	0.998877i	$0.484913\pi$
$972$	13.8828	+	31.0575i	0.445292	+	0.996169i
$973$	−8.24562	−	5.99080i	−0.264343	−	0.192056i
$974$	1.76449	+	1.28198i	0.0565381	+	0.0410773i
$975$	5.30515	+	0.895682i	0.169901	+	0.0286848i
$976$	34.9303	−	11.3495i	1.11809	−	0.363290i
$977$	7.44164	+	10.2425i	0.238079	+	0.327688i	0.911292	−	0.411761i	$-0.135086\pi$
$977$	7.44164	+	10.2425i	0.238079	+	0.327688i	−0.673213	+	0.739449i	$0.735086\pi$
$978$	−68.2964	+	10.1058i	−2.18388	+	0.323148i
$979$	−10.2534	−	29.6992i	−0.327701	−	0.949192i
$980$		−	4.17847i		−	0.133476i
$981$	−36.6493	−	27.7841i	−1.17012	−	0.887078i
$982$	1.49084	+	4.58833i	0.0475746	+	0.146420i
$983$	9.82729	+	3.19308i	0.313442	+	0.101843i	0.461513	−	0.887133i	$-0.347307\pi$
$983$	9.82729	+	3.19308i	0.313442	+	0.101843i	−0.148072	+	0.988977i	$0.547307\pi$
$984$	−1.05023	−	0.548650i	−0.0334801	−	0.0174903i
$985$	−20.8666	+	28.7204i	−0.664866	+	0.915110i
$986$	8.33336	−	25.6474i	0.265388	−	0.816781i
$987$	6.44267	+	12.9690i	0.205072	+	0.412808i
$988$	17.9347	−	13.0303i	0.570579	−	0.414550i
$989$	−18.4742			−0.587445
$990$	−37.0285	−	12.1165i	−1.17684	−	0.385089i
$991$	−1.62734			−0.0516942			−0.0258471	−	0.999666i	$-0.508228\pi$
$991$	−1.62734			−0.0516942			−0.0258471	+	0.999666i	$0.508228\pi$
$992$	21.0099	−	15.2646i	0.667066	−	0.484652i
$993$	5.81964	+	11.7149i	0.184681	+	0.371760i
$994$	9.42422	−	29.0048i	0.298918	−	0.919976i
$995$	4.50896	−	6.20605i	0.142944	−	0.196745i
$996$	30.2604	+	15.8083i	0.958837	+	0.500906i
$997$	−20.1842	−	6.55823i	−0.639239	−	0.207701i	−0.0285755	−	0.999592i	$-0.509097\pi$
$997$	−20.1842	−	6.55823i	−0.639239	−	0.207701i	−0.610663	+	0.791890i	$0.709097\pi$
$998$	9.44622	+	29.0725i	0.299015	+	0.920274i
$999$	−25.3720	+	46.2489i	−0.802736	+	1.46325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.s.a.8.20	yes	96
3.2	odd	2	inner	231.2.s.a.8.5	✓	96
11.7	odd	10	inner	231.2.s.a.29.5	yes	96
33.29	even	10	inner	231.2.s.a.29.20	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.s.a.8.5	✓	96	3.2	odd	2	inner
231.2.s.a.8.20	yes	96	1.1	even	1	trivial
231.2.s.a.29.5	yes	96	11.7	odd	10	inner
231.2.s.a.29.20	yes	96	33.29	even	10	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.s (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.65450 - 1.20206i) q^{2} +(-0.770590 - 1.55119i) q^{3} +(0.674376 - 2.07552i) q^{4} +(1.12543 - 1.54901i) q^{5} +(-3.13957 - 1.64014i) q^{6} +(0.951057 + 0.309017i) q^{7} +(-0.115224 - 0.354623i) q^{8} +(-1.81238 + 2.39066i) q^{9} +O(q^{10})\)	\(q+(1.65450 - 1.20206i) q^{2} +(-0.770590 - 1.55119i) q^{3} +(0.674376 - 2.07552i) q^{4} +(1.12543 - 1.54901i) q^{5} +(-3.13957 - 1.64014i) q^{6} +(0.951057 + 0.309017i) q^{7} +(-0.115224 - 0.354623i) q^{8} +(-1.81238 + 2.39066i) q^{9} -3.91568i q^{10} +(-3.13505 + 1.08235i) q^{11} +(-3.73919 + 0.553287i) q^{12} +(1.36871 + 1.88387i) q^{13} +(1.94498 - 0.631963i) q^{14} +(-3.27006 - 0.552092i) q^{15} +(2.91416 + 2.11726i) q^{16} +(-3.82620 - 2.77990i) q^{17} +(-0.124852 + 6.13395i) q^{18} +(4.14887 - 1.34805i) q^{19} +(-2.45605 - 3.38046i) q^{20} +(-0.253531 - 1.71339i) q^{21} +(-3.88588 + 5.55927i) q^{22} -3.17108i q^{23} +(-0.461297 + 0.452003i) q^{24} +(0.412220 + 1.26868i) q^{25} +(4.52906 + 1.47158i) q^{26} +(5.10498 + 0.969125i) q^{27} +(1.28274 - 1.76554i) q^{28} +(-0.861590 + 2.65170i) q^{29} +(-6.07396 + 3.01738i) q^{30} +(2.58988 - 1.88166i) q^{31} +8.11231 q^{32} +(4.09477 + 4.02901i) q^{33} -9.67207 q^{34} +(1.54901 - 1.12543i) q^{35} +(3.73964 + 5.37383i) q^{36} +(-3.13714 + 9.65512i) q^{37} +(5.24386 - 7.21755i) q^{38} +(1.86752 - 3.57482i) q^{39} +(-0.678991 - 0.220618i) q^{40} +(0.566950 + 1.74489i) q^{41} +(-2.47908 - 2.53005i) q^{42} -5.82583i q^{43} +(0.132234 + 7.23675i) q^{44} +(1.66347 + 5.49792i) q^{45} +(-3.81184 - 5.24655i) q^{46} +(-7.95149 + 2.58359i) q^{47} +(1.03865 - 6.15196i) q^{48} +(0.809017 + 0.587785i) q^{49} +(2.20706 + 1.60352i) q^{50} +(-1.36372 + 8.07733i) q^{51} +(4.83303 - 1.57035i) q^{52} +(4.30637 + 5.92721i) q^{53} +(9.61113 - 4.53309i) q^{54} +(-1.85168 + 6.07434i) q^{55} -0.372872i q^{56} +(-5.28816 - 5.39689i) q^{57} +(1.76201 + 5.42292i) q^{58} +(-6.12265 - 1.98937i) q^{59} +(-3.35113 + 6.41474i) q^{60} +(5.99320 - 8.24893i) q^{61} +(2.02308 - 6.22641i) q^{62} +(-2.46243 + 1.71360i) q^{63} +(7.59349 - 5.51699i) q^{64} +4.45852 q^{65} +(11.6179 + 1.74381i) q^{66} -14.8128 q^{67} +(-8.35003 + 6.06665i) q^{68} +(-4.91895 + 2.44360i) q^{69} +(1.21001 - 3.72403i) q^{70} +(8.76542 - 12.0646i) q^{71} +(1.05661 + 0.367250i) q^{72} +(-8.07191 - 2.62272i) q^{73} +(6.41568 + 19.7454i) q^{74} +(1.65032 - 1.61707i) q^{75} -9.52014i q^{76} +(-3.31607 + 0.0605930i) q^{77} +(-1.20735 - 8.15943i) q^{78} +(-0.424768 - 0.584643i) q^{79} +(6.55934 - 2.13126i) q^{80} +(-2.43055 - 8.66559i) q^{81} +(3.03549 + 2.20541i) q^{82} +(-7.30720 - 5.30899i) q^{83} +(-3.72715 - 0.629265i) q^{84} +(-8.61221 + 2.79828i) q^{85} +(-7.00303 - 9.63884i) q^{86} +(4.77722 - 0.706885i) q^{87} +(0.745058 + 0.987046i) q^{88} +9.47330i q^{89} +(9.36107 + 7.09670i) q^{90} +(0.719574 + 2.21462i) q^{91} +(-6.58163 - 2.13850i) q^{92} +(-4.91455 - 2.56741i) q^{93} +(-10.0501 + 13.8328i) q^{94} +(2.58109 - 7.94379i) q^{95} +(-6.25127 - 12.5837i) q^{96} +(-1.13735 + 0.826332i) q^{97} +2.04507 q^{98} +(3.09437 - 9.45647i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9}+O(q^{10}) \) 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9	\( 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9} - 20 q^{12} - 32 q^{16} - 10 q^{18} - 60 q^{19} + 30 q^{24} + 12 q^{25} - 40 q^{28} + 60 q^{30} + 40 q^{31} - 44 q^{33} + 8 q^{34} + 2 q^{36} + 16 q^{37} - 10 q^{39} - 96 q^{45} - 40 q^{46} + 48 q^{48} + 24 q^{49} - 30 q^{51} - 40 q^{52} + 28 q^{55} - 30 q^{57} + 36 q^{58} - 32 q^{60} + 40 q^{61} - 28 q^{64} + 118 q^{66} - 56 q^{67} + 26 q^{69} + 20 q^{70} + 150 q^{72} + 40 q^{73} + 2 q^{75} - 20 q^{78} - 40 q^{79} + 8 q^{81} - 16 q^{82} + 40 q^{84} - 60 q^{85} - 156 q^{88} + 100 q^{90} + 36 q^{91} - 36 q^{93} + 160 q^{96} - 88 q^{97} - 94 q^{99}+O(q^{100}) \) 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9 - 20 * q^12 - 32 * q^16 - 10 * q^18 - 60 * q^19 + 30 * q^24 + 12 * q^25 - 40 * q^28 + 60 * q^30 + 40 * q^31 - 44 * q^33 + 8 * q^34 + 2 * q^36 + 16 * q^37 - 10 * q^39 - 96 * q^45 - 40 * q^46 + 48 * q^48 + 24 * q^49 - 30 * q^51 - 40 * q^52 + 28 * q^55 - 30 * q^57 + 36 * q^58 - 32 * q^60 + 40 * q^61 - 28 * q^64 + 118 * q^66 - 56 * q^67 + 26 * q^69 + 20 * q^70 + 150 * q^72 + 40 * q^73 + 2 * q^75 - 20 * q^78 - 40 * q^79 + 8 * q^81 - 16 * q^82 + 40 * q^84 - 60 * q^85 - 156 * q^88 + 100 * q^90 + 36 * q^91 - 36 * q^93 + 160 * q^96 - 88 * q^97 - 94 * q^99

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