LMFDB - Embedded newform 462.2.n.e.263.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(65,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 3]))

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

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

chi := DirichletCharacter("462.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.n (of order $6$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			263.7
Character	$\chi$	$=$	462.263
Dual form			462.2.n.e.65.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.301239 - 1.70565i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.38736 + 0.800992i) q^{5} +(-1.62776 + 0.591946i) q^{6} +(0.229478 + 2.63578i) q^{7} +1.00000 q^{8} +(-2.81851 - 1.02762i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.301239 - 1.70565i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.38736 + 0.800992i) q^{5} +(-1.62776 + 0.591946i) q^{6} +(0.229478 + 2.63578i) q^{7} +1.00000 q^{8} +(-2.81851 - 1.02762i) q^{9} +(1.38736 + 0.800992i) q^{10} +(-2.57434 + 2.09111i) q^{11} +(1.32652 + 1.11371i) q^{12} +2.95832i q^{13} +(2.16791 - 1.51662i) q^{14} +(0.948288 + 2.60764i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.22050 + 2.11398i) q^{17} +(0.519310 + 2.95471i) q^{18} +(-2.26479 + 1.30758i) q^{19} -1.60198i q^{20} +(4.56486 + 0.402591i) q^{21} +(3.09813 + 1.18389i) q^{22} +(-0.475699 + 0.274645i) q^{23} +(0.301239 - 1.70565i) q^{24} +(-1.21682 + 2.10760i) q^{25} +(2.56198 - 1.47916i) q^{26} +(-2.60181 + 4.49784i) q^{27} +(-2.39739 - 1.11916i) q^{28} +0.955838 q^{29} +(1.78414 - 2.12506i) q^{30} +(2.87525 - 4.98007i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.79122 + 5.02087i) q^{33} +2.44101 q^{34} +(-2.42961 - 3.47296i) q^{35} +(2.29920 - 1.92709i) q^{36} +(0.653521 + 1.13193i) q^{37} +(2.26479 + 1.30758i) q^{38} +(5.04588 + 0.891163i) q^{39} +(-1.38736 + 0.800992i) q^{40} +1.94074 q^{41} +(-1.93377 - 4.15458i) q^{42} -2.42292i q^{43} +(-0.523783 - 3.27500i) q^{44} +(4.73340 - 0.831927i) q^{45} +(0.475699 + 0.274645i) q^{46} +(5.63833 - 3.25529i) q^{47} +(-1.62776 + 0.591946i) q^{48} +(-6.89468 + 1.20970i) q^{49} +2.43365 q^{50} +(3.23805 + 2.71857i) q^{51} +(-2.56198 - 1.47916i) q^{52} +(-9.07625 - 5.24018i) q^{53} +(5.19615 + 0.00431112i) q^{54} +(1.89658 - 4.96315i) q^{55} +(0.229478 + 2.63578i) q^{56} +(1.54803 + 4.25684i) q^{57} +(-0.477919 - 0.827780i) q^{58} +(11.3873 + 6.57446i) q^{59} +(-2.73243 - 0.482580i) q^{60} +(-2.48802 + 1.43646i) q^{61} -5.75049 q^{62} +(2.06180 - 7.66479i) q^{63} +1.00000 q^{64} +(-2.36959 - 4.10426i) q^{65} +(2.95259 - 4.92770i) q^{66} +(-7.30221 + 12.6478i) q^{67} +(-1.22050 - 2.11398i) q^{68} +(0.325150 + 0.894111i) q^{69} +(-1.79287 + 3.84058i) q^{70} +2.37827i q^{71} +(-2.81851 - 1.02762i) q^{72} +(-10.0056 - 5.77671i) q^{73} +(0.653521 - 1.13193i) q^{74} +(3.22828 + 2.71037i) q^{75} -2.61516i q^{76} +(-6.10247 - 6.30555i) q^{77} +(-1.75117 - 4.81544i) q^{78} +(-11.5543 + 6.67087i) q^{79} +(1.38736 + 0.800992i) q^{80} +(6.88800 + 5.79271i) q^{81} +(-0.970369 - 1.68073i) q^{82} +7.92000 q^{83} +(-2.63108 + 3.75199i) q^{84} -3.91046i q^{85} +(-2.09831 + 1.21146i) q^{86} +(0.287936 - 1.63033i) q^{87} +(-2.57434 + 2.09111i) q^{88} +(-5.89340 + 3.40256i) q^{89} +(-3.08717 - 3.68328i) q^{90} +(-7.79749 + 0.678869i) q^{91} -0.549290i q^{92} +(-7.62814 - 6.40437i) q^{93} +(-5.63833 - 3.25529i) q^{94} +(2.09472 - 3.62816i) q^{95} +(1.32652 + 1.11371i) q^{96} +16.5431 q^{97} +(4.49498 + 5.36612i) q^{98} +(9.40468 - 3.24837i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 8 q^{9}+O(q^{10}) $ 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8 - 8 * q^9	$ 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 8 q^{9} - 4 q^{11} + 4 q^{15} - 12 q^{16} + 4 q^{17} - 8 q^{18} + 8 q^{22} + 20 q^{25} - 12 q^{27} + 40 q^{29} - 2 q^{30} - 28 q^{31} - 12 q^{32} + 32 q^{33} - 8 q^{34} - 32 q^{35} + 16 q^{36} - 16 q^{37} - 8 q^{41} + 6 q^{42} - 4 q^{44} - 28 q^{45} - 8 q^{49} - 40 q^{50} - 34 q^{51} + 6 q^{54} + 8 q^{55} + 40 q^{57} - 20 q^{58} - 2 q^{60} + 56 q^{62} - 14 q^{63} + 24 q^{64} - 44 q^{65} + 32 q^{66} + 4 q^{68} - 20 q^{69} + 64 q^{70} - 8 q^{72} - 16 q^{74} - 26 q^{75} + 24 q^{81} + 4 q^{82} + 144 q^{83} - 6 q^{84} + 8 q^{87} - 4 q^{88} + 56 q^{90} - 32 q^{91} - 22 q^{93} - 44 q^{95} + 64 q^{97} - 8 q^{98} - 52 q^{99}+O(q^{100}) $ 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8 - 8 * q^9 - 4 * q^11 + 4 * q^15 - 12 * q^16 + 4 * q^17 - 8 * q^18 + 8 * q^22 + 20 * q^25 - 12 * q^27 + 40 * q^29 - 2 * q^30 - 28 * q^31 - 12 * q^32 + 32 * q^33 - 8 * q^34 - 32 * q^35 + 16 * q^36 - 16 * q^37 - 8 * q^41 + 6 * q^42 - 4 * q^44 - 28 * q^45 - 8 * q^49 - 40 * q^50 - 34 * q^51 + 6 * q^54 + 8 * q^55 + 40 * q^57 - 20 * q^58 - 2 * q^60 + 56 * q^62 - 14 * q^63 + 24 * q^64 - 44 * q^65 + 32 * q^66 + 4 * q^68 - 20 * q^69 + 64 * q^70 - 8 * q^72 - 16 * q^74 - 26 * q^75 + 24 * q^81 + 4 * q^82 + 144 * q^83 - 6 * q^84 + 8 * q^87 - 4 * q^88 + 56 * q^90 - 32 * q^91 - 22 * q^93 - 44 * q^95 + 64 * q^97 - 8 * q^98 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.301239	−	1.70565i	0.173921	−	0.984760i
$3$	0.301239	−	1.70565i	0.173921	−	0.984760i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.38736	+	0.800992i	−0.620446	+	0.358214i	−0.777042	−	0.629448i	$-0.783281\pi$
$5$	−1.38736	+	0.800992i	−0.620446	+	0.358214i	0.156597	+	0.987663i	$0.449948\pi$
$6$	−1.62776	+	0.591946i	−0.664530	+	0.241661i
$7$	0.229478	+	2.63578i	0.0867344	+	0.996231i
$7$	0.229478	+	2.63578i	0.0867344	+	0.996231i
$8$	1.00000			0.353553
$9$	−2.81851	−	1.02762i	−0.939503	−	0.342540i
$10$	1.38736	+	0.800992i	0.438721	+	0.253296i
$11$	−2.57434	+	2.09111i	−0.776194	+	0.630494i
$11$	−2.57434	+	2.09111i	−0.776194	+	0.630494i
$12$	1.32652	+	1.11371i	0.382933	+	0.321500i
$13$			2.95832i			0.820491i	0.911975	+	0.410246i	$0.134557\pi$
$13$			2.95832i			0.820491i	−0.911975	+	0.410246i	$0.865443\pi$
$14$	2.16791	−	1.51662i	0.579399	−	0.405335i
$15$	0.948288	+	2.60764i	0.244847	+	0.673291i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.22050	+	2.11398i	−0.296016	+	0.512714i	−0.975221	−	0.221234i	$-0.928991\pi$
$17$	−1.22050	+	2.11398i	−0.296016	+	0.512714i	0.679205	+	0.733949i	$0.262325\pi$
$18$	0.519310	+	2.95471i	0.122403	+	0.696432i
$19$	−2.26479	+	1.30758i	−0.519579	+	0.299979i	−0.736762	−	0.676152i	$-0.763646\pi$
$19$	−2.26479	+	1.30758i	−0.519579	+	0.299979i	0.217184	+	0.976131i	$0.430313\pi$
$20$		−	1.60198i		−	0.358214i
$21$	4.56486	+	0.402591i	0.996133	+	0.0878526i
$22$	3.09813	+	1.18389i	0.660523	+	0.252407i
$23$	−0.475699	+	0.274645i	−0.0991901	+	0.0572674i	−0.548774	−	0.835970i	$-0.684905\pi$
$23$	−0.475699	+	0.274645i	−0.0991901	+	0.0572674i	0.449584	+	0.893238i	$0.351572\pi$
$24$	0.301239	−	1.70565i	0.0614902	−	0.348165i
$25$	−1.21682	+	2.10760i	−0.243365	+	0.421520i
$26$	2.56198	−	1.47916i	0.502446	−	0.290087i
$27$	−2.60181	+	4.49784i	−0.500718	+	0.865610i
$28$	−2.39739	−	1.11916i	−0.453064	−	0.211501i
$29$	0.955838			0.177495			0.0887473	−	0.996054i	$-0.471714\pi$
$29$	0.955838			0.177495			0.0887473	+	0.996054i	$0.471714\pi$
$30$	1.78414	−	2.12506i	0.325738	−	0.387982i
$31$	2.87525	−	4.98007i	0.516410	−	0.894448i	−0.483409	−	0.875395i	$-0.660602\pi$
$31$	2.87525	−	4.98007i	0.516410	−	0.894448i	0.999818	−	0.0190529i	$-0.00606510\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	2.79122	+	5.02087i	0.485889	+	0.874021i
$34$	2.44101			0.418630
$35$	−2.42961	−	3.47296i	−0.410678	−	0.587038i
$36$	2.29920	−	1.92709i	0.383200	−	0.321182i
$37$	0.653521	+	1.13193i	0.107438	+	0.186088i	0.914732	−	0.404062i	$-0.132402\pi$
$37$	0.653521	+	1.13193i	0.107438	+	0.186088i	−0.807294	+	0.590150i	$0.799069\pi$
$38$	2.26479	+	1.30758i	0.367398	+	0.212117i
$39$	5.04588	+	0.891163i	0.807987	+	0.142700i
$40$	−1.38736	+	0.800992i	−0.219361	+	0.126648i
$41$	1.94074			0.303092			0.151546	−	0.988450i	$-0.451575\pi$
$41$	1.94074			0.303092			0.151546	+	0.988450i	$0.451575\pi$
$42$	−1.93377	−	4.15458i	−0.298388	−	0.641065i
$43$		−	2.42292i		−	0.369492i	−0.982786	−	0.184746i	$-0.940854\pi$
$43$		−	2.42292i		−	0.369492i	0.982786	−	0.184746i	$-0.0591462\pi$
$44$	−0.523783	−	3.27500i	−0.0789633	−	0.493725i
$45$	4.73340	−	0.831927i	0.705613	−	0.124016i
$46$	0.475699	+	0.274645i	0.0701380	+	0.0404942i
$47$	5.63833	−	3.25529i	0.822436	−	0.474833i	−0.0288200	−	0.999585i	$-0.509175\pi$
$47$	5.63833	−	3.25529i	0.822436	−	0.474833i	0.851256	+	0.524751i	$0.175842\pi$
$48$	−1.62776	+	0.591946i	−0.234947	+	0.0854401i
$49$	−6.89468	+	1.20970i	−0.984954	+	0.172815i
$50$	2.43365			0.344170
$51$	3.23805	+	2.71857i	0.453417	+	0.380676i
$52$	−2.56198	−	1.47916i	−0.355283	−	0.205123i
$53$	−9.07625	−	5.24018i	−1.24672	−	0.719794i	−0.276266	−	0.961081i	$-0.589097\pi$
$53$	−9.07625	−	5.24018i	−1.24672	−	0.719794i	−0.970454	+	0.241287i	$0.922430\pi$
$54$	5.19615	+	0.00431112i	0.707107	+	0.000586669i
$55$	1.89658	−	4.96315i	0.255734	−	0.669231i
$56$	0.229478	+	2.63578i	0.0306652	+	0.352221i
$57$	1.54803	+	4.25684i	0.205042	+	0.563833i
$58$	−0.477919	−	0.827780i	−0.0627538	−	0.108693i
$59$	11.3873	+	6.57446i	1.48250	+	0.855922i	0.999803	−	0.0198655i	$-0.00632381\pi$
$59$	11.3873	+	6.57446i	1.48250	+	0.855922i	0.482697	+	0.875787i	$0.339657\pi$
$60$	−2.73243	−	0.482580i	−0.352755	−	0.0623008i
$61$	−2.48802	+	1.43646i	−0.318558	+	0.183920i	−0.650750	−	0.759292i	$-0.725545\pi$
$61$	−2.48802	+	1.43646i	−0.318558	+	0.183920i	0.332192	+	0.943212i	$0.392212\pi$
$62$	−5.75049			−0.730313
$63$	2.06180	−	7.66479i	0.259762	−	0.965673i
$64$	1.00000			0.125000
$65$	−2.36959	−	4.10426i	−0.293912	−	0.509070i
$66$	2.95259	−	4.92770i	0.363438	−	0.606558i
$67$	−7.30221	+	12.6478i	−0.892106	+	1.54517i	−0.0547609	+	0.998499i	$0.517440\pi$
$67$	−7.30221	+	12.6478i	−0.892106	+	1.54517i	−0.837345	+	0.546674i	$0.815894\pi$
$68$	−1.22050	−	2.11398i	−0.148008	−	0.256357i
$69$	0.325150	+	0.894111i	0.0391434	+	0.107638i
$70$	−1.79287	+	3.84058i	−0.214289	+	0.459037i
$71$			2.37827i			0.282248i	0.989992	+	0.141124i	$0.0450717\pi$
$71$			2.37827i			0.282248i	−0.989992	+	0.141124i	$0.954928\pi$
$72$	−2.81851	−	1.02762i	−0.332165	−	0.121106i
$73$	−10.0056	−	5.77671i	−1.17106	−	0.676113i	−0.217132	−	0.976142i	$-0.569670\pi$
$73$	−10.0056	−	5.77671i	−1.17106	−	0.676113i	−0.953930	+	0.300029i	$0.903004\pi$
$74$	0.653521	−	1.13193i	0.0759703	−	0.131584i
$75$	3.22828	+	2.71037i	0.372770	+	0.312967i
$76$		−	2.61516i		−	0.299979i
$77$	−6.10247	−	6.30555i	−0.695441	−	0.718584i
$78$	−1.75117	−	4.81544i	−0.198281	−	0.545241i
$79$	−11.5543	+	6.67087i	−1.29996	+	0.750532i	−0.980397	−	0.197033i	$-0.936869\pi$
$79$	−11.5543	+	6.67087i	−1.29996	+	0.750532i	−0.319562	+	0.947565i	$0.603536\pi$
$80$	1.38736	+	0.800992i	0.155111	+	0.0895536i
$81$	6.88800	+	5.79271i	0.765333	+	0.643635i
$82$	−0.970369	−	1.68073i	−0.107159	−	0.185605i
$83$	7.92000			0.869333			0.434666	−	0.900592i	$-0.356866\pi$
$83$	7.92000			0.869333			0.434666	+	0.900592i	$0.356866\pi$
$84$	−2.63108	+	3.75199i	−0.287075	+	0.409375i
$85$		−	3.91046i		−	0.424149i
$86$	−2.09831	+	1.21146i	−0.226267	+	0.130635i
$87$	0.287936	−	1.63033i	0.0308700	−	0.174790i
$88$	−2.57434	+	2.09111i	−0.274426	+	0.222913i
$89$	−5.89340	+	3.40256i	−0.624699	+	0.360670i	−0.778696	−	0.627401i	$-0.784119\pi$
$89$	−5.89340	+	3.40256i	−0.624699	+	0.360670i	0.153997	+	0.988071i	$0.450785\pi$
$90$	−3.08717	−	3.68328i	−0.325416	−	0.388252i
$91$	−7.79749	+	0.678869i	−0.817399	+	0.0711648i
$92$		−	0.549290i		−	0.0572674i
$93$	−7.62814	−	6.40437i	−0.791002	−	0.664102i
$94$	−5.63833	−	3.25529i	−0.581550	−	0.335758i
$95$	2.09472	−	3.62816i	0.214914	−	0.372241i
$96$	1.32652	+	1.11371i	0.135387	+	0.113667i
$97$	16.5431			1.67970			0.839848	−	0.542822i	$-0.182644\pi$
$97$	16.5431			1.67970			0.839848	+	0.542822i	$0.182644\pi$
$98$	4.49498	+	5.36612i	0.454061	+	0.542060i
$99$	9.40468	−	3.24837i	0.945206	−	0.326474i
$100$	−1.21682	−	2.10760i	−0.121682	−	0.210760i
$101$	−7.27257	+	12.5965i	−0.723648	+	1.25340i	0.235880	+	0.971782i	$0.424203\pi$
$101$	−7.27257	+	12.5965i	−0.723648	+	1.25340i	−0.959528	+	0.281613i	$0.909130\pi$
$102$	0.735328	−	4.16352i	0.0728083	−	0.412250i
$103$	1.39459	+	2.41551i	0.137413	+	0.238007i	0.926517	−	0.376253i	$-0.122788\pi$
$103$	1.39459	+	2.41551i	0.137413	+	0.238007i	−0.789103	+	0.614260i	$0.789454\pi$
$104$			2.95832i			0.290087i
$105$	−6.65557	+	3.09787i	−0.649517	+	0.302322i
$106$			10.4804i			1.01794i
$107$	2.14746	+	3.71952i	0.207603	+	0.359579i	0.950959	−	0.309317i	$-0.100100\pi$
$107$	2.14746	+	3.71952i	0.207603	+	0.359579i	−0.743356	+	0.668896i	$0.766767\pi$
$108$	−2.59434	−	4.50215i	−0.249641	−	0.433220i
$109$	−12.0547	−	6.95977i	−1.15463	−	0.666625i	−0.204618	−	0.978842i	$-0.565595\pi$
$109$	−12.0547	−	6.95977i	−1.15463	−	0.666625i	−0.950011	+	0.312217i	$0.898928\pi$
$110$	−5.24650	+	0.839092i	−0.500234	+	0.0800043i
$111$	2.12755	−	0.773698i	0.201938	−	0.0734362i
$112$	2.16791	−	1.51662i	0.204849	−	0.143307i
$113$		−	3.43269i		−	0.322920i	−0.986879	−	0.161460i	$-0.948380\pi$
$113$		−	3.43269i		−	0.322920i	0.986879	−	0.161460i	$-0.0516203\pi$
$114$	2.91252	−	3.46906i	0.272782	−	0.324907i
$115$	0.439977	−	0.762062i	0.0410280	−	0.0710626i
$116$	−0.477919	+	0.827780i	−0.0443736	+	0.0768574i
$117$	3.04003	−	8.33806i	0.281051	−	0.770854i
$118$		−	13.1489i		−	1.21046i
$119$	−5.85206	−	2.73187i	−0.536457	−	0.250430i
$120$	0.948288	+	2.60764i	0.0865665	+	0.238044i
$121$	2.25450	−	10.7665i	0.204955	−	0.978771i
$122$	2.48802	+	1.43646i	0.225255	+	0.130051i
$123$	0.584626	−	3.31023i	0.0527140	−	0.298473i
$124$	2.87525	+	4.98007i	0.258205	+	0.447224i
$125$		−	11.9086i		−	1.06514i
$126$	−7.66880	+	2.04683i	−0.683191	+	0.182346i
$127$		−	11.5546i		−	1.02530i	−0.858597	−	0.512651i	$-0.828663\pi$
$127$		−	11.5546i		−	1.02530i	0.858597	−	0.512651i	$-0.171337\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−4.13266	−	0.729878i	−0.363861	−	0.0642622i
$130$	−2.36959	+	4.10426i	−0.207827	+	0.359967i
$131$	−0.434049	−	0.751795i	−0.0379230	−	0.0656846i	0.846441	−	0.532483i	$-0.178741\pi$
$131$	−0.434049	−	0.751795i	−0.0379230	−	0.0656846i	−0.884364	+	0.466798i	$0.845408\pi$
$132$	−5.74381	−	0.0931664i	−0.499934	−	0.00810909i
$133$	−3.96621	−	5.66943i	−0.343914	−	0.491602i
$134$	14.6044			1.26163
$135$	0.00690634	−	8.32415i	0.000594403	−	0.716429i
$136$	−1.22050	+	2.11398i	−0.104657	+	0.181272i
$137$	−9.76217	−	5.63619i	−0.834038	−	0.481532i	0.0211950	−	0.999775i	$-0.493253\pi$
$137$	−9.76217	−	5.63619i	−0.834038	−	0.481532i	−0.855233	+	0.518243i	$0.826586\pi$
$138$	0.611748	−	0.728644i	0.0520755	−	0.0620263i
$139$			0.232347i			0.0197074i	0.999951	+	0.00985370i	$0.00313658\pi$
$139$			0.232347i			0.0197074i	−0.999951	+	0.00985370i	$0.996863\pi$
$140$	4.22248	−	0.367619i	0.356865	−	0.0310695i
$141$	−3.85392	−	10.5977i	−0.324558	−	0.892485i
$142$	2.05964	−	1.18913i	0.172841	−	0.0997899i
$143$	−6.18619	−	7.61575i	−0.517315	−	0.636861i
$144$	0.519310	+	2.95471i	0.0432759	+	0.246226i
$145$	−1.32609	+	0.765618i	−0.110126	+	0.0635811i
$146$			11.5534i			0.956168i
$147$	−0.0136101	+	12.1243i	−0.00112254	+	0.999999i
$148$	−1.30704			−0.107438
$149$	−4.31760	−	7.47830i	−0.353712	−	0.612646i	0.633185	−	0.774000i	$-0.281747\pi$
$149$	−4.31760	−	7.47830i	−0.353712	−	0.612646i	−0.986897	+	0.161354i	$0.948414\pi$
$150$	0.733110	−	4.15096i	0.0598582	−	0.338925i
$151$	15.3180	+	8.84386i	1.24656	+	0.719703i	0.970422	−	0.241414i	$-0.0776111\pi$
$151$	15.3180	+	8.84386i	1.24656	+	0.719703i	0.276141	+	0.961117i	$0.410944\pi$
$152$	−2.26479	+	1.30758i	−0.183699	+	0.106059i
$153$	5.61237	−	4.70405i	0.453733	−	0.380300i
$154$	−2.40953	+	8.43766i	−0.194165	+	0.679926i
$155$			9.21220i			0.739941i
$156$	−3.29471	+	3.92428i	−0.263788	+	0.314193i
$157$	−2.63579	+	4.56532i	−0.210359	+	0.364352i	−0.951827	−	0.306636i	$-0.900797\pi$
$157$	−2.63579	+	4.56532i	−0.210359	+	0.364352i	0.741468	+	0.670988i	$0.234130\pi$
$158$	11.5543	+	6.67087i	0.919210	+	0.530706i
$159$	−11.6721	+	13.9024i	−0.925654	+	1.10253i
$160$		−	1.60198i		−	0.126648i
$161$	−0.833066	−	1.19081i	−0.0656548	−	0.0938492i
$162$	1.57264	−	8.86154i	0.123558	−	0.696228i
$163$	−3.96431	−	6.86639i	−0.310509	−	0.537817i	0.667964	−	0.744194i	$-0.267166\pi$
$163$	−3.96431	−	6.86639i	−0.310509	−	0.537817i	−0.978473	+	0.206377i	$0.933833\pi$
$164$	−0.970369	+	1.68073i	−0.0757731	+	0.131243i
$165$	−7.89409	−	4.73000i	−0.614554	−	0.368230i
$166$	−3.96000	−	6.85892i	−0.307356	−	0.532355i
$167$	2.29082			0.177269			0.0886343	−	0.996064i	$-0.471750\pi$
$167$	2.29082			0.177269			0.0886343	+	0.996064i	$0.471750\pi$
$168$	4.56486	+	0.402591i	0.352186	+	0.0310606i
$169$	4.24832			0.326794
$170$	−3.38656	+	1.95523i	−0.259737	+	0.149959i
$171$	7.72703	−	1.35808i	0.590901	−	0.103855i
$172$	2.09831	+	1.21146i	0.159995	+	0.0923729i
$173$	11.4994	+	19.9176i	0.874284	+	1.51430i	0.857524	+	0.514444i	$0.172002\pi$
$173$	11.4994	+	19.9176i	0.874284	+	1.51430i	0.0167600	+	0.999860i	$0.494665\pi$
$174$	−1.55587	+	0.565804i	−0.117950	+	0.0428935i
$175$	−5.83441	−	2.72363i	−0.441040	−	0.205887i
$176$	3.09813	+	1.18389i	0.233530	+	0.0892392i
$177$	14.6441	−	17.4423i	1.10071	−	1.31104i
$178$	5.89340	+	3.40256i	0.441729	+	0.255032i
$179$	13.2263	+	7.63621i	0.988581	+	0.570757i	0.904850	−	0.425731i	$-0.139983\pi$
$179$	13.2263	+	7.63621i	0.988581	+	0.570757i	0.0837308	+	0.996488i	$0.473316\pi$
$180$	−1.64623	+	4.51521i	−0.122703	+	0.336544i
$181$	15.9320			1.18422			0.592109	−	0.805858i	$-0.298295\pi$
$181$	15.9320			1.18422			0.592109	+	0.805858i	$0.298295\pi$
$182$	4.48666	+	6.41339i	0.332574	+	0.475392i
$183$	1.70061	+	4.67642i	0.125713	+	0.345691i
$184$	−0.475699	+	0.274645i	−0.0350690	+	0.0202471i
$185$	−1.81334	−	1.04693i	−0.133319	−	0.0769718i
$186$	−1.73227	+	9.80835i	−0.127016	+	0.719183i
$187$	−1.27856	−	7.99431i	−0.0934976	−	0.584602i
$188$			6.51059i			0.474833i
$189$	−12.4524	−	5.82564i	−0.905778	−	0.423753i
$190$	−4.18944			−0.303934
$191$	17.8529	−	10.3074i	1.29179	−	0.745815i	0.312818	−	0.949813i	$-0.398727\pi$
$191$	17.8529	−	10.3074i	1.29179	−	0.745815i	0.978971	+	0.203998i	$0.0653937\pi$
$192$	0.301239	−	1.70565i	0.0217401	−	0.123095i
$193$	11.0514	+	6.38055i	0.795500	+	0.459282i	0.841895	−	0.539641i	$-0.181440\pi$
$193$	11.0514	+	6.38055i	0.795500	+	0.459282i	−0.0463953	+	0.998923i	$0.514773\pi$
$194$	−8.27154	−	14.3267i	−0.593862	−	1.02860i
$195$	−7.71425	+	2.80534i	−0.552429	+	0.200895i
$196$	2.39970	−	6.57582i	0.171407	−	0.469701i
$197$	−14.2100			−1.01242			−0.506211	−	0.862410i	$-0.668954\pi$
$197$	−14.2100			−1.01242			−0.506211	+	0.862410i	$0.668954\pi$
$198$	−7.51551	−	6.52051i	−0.534104	−	0.463392i
$199$	−2.43346	+	4.21488i	−0.172503	+	0.298785i	−0.939294	−	0.343112i	$-0.888519\pi$
$199$	−2.43346	+	4.21488i	−0.172503	+	0.298785i	0.766791	+	0.641897i	$0.221852\pi$
$200$	−1.21682	+	2.10760i	−0.0860425	+	0.149030i
$201$	19.3730	+	16.2650i	1.36647	+	1.14725i
$202$	14.5451			1.02339
$203$	0.219343	+	2.51938i	0.0153949	+	0.176826i
$204$	−3.97338	+	1.44495i	−0.278192	+	0.101166i
$205$	−2.69250	+	1.55452i	−0.188052	+	0.108572i
$206$	1.39459	−	2.41551i	0.0971659	−	0.168296i
$207$	1.62299	−	0.285252i	0.112806	−	0.0198264i
$208$	2.56198	−	1.47916i	0.177642	−	0.102561i
$209$	3.09606	−	8.10209i	0.214159	−	0.560433i
$210$	6.01062	+	4.21495i	0.414772	+	0.290859i
$211$			25.6573i			1.76632i	0.469067	+	0.883162i	$0.344590\pi$
$211$			25.6573i			1.76632i	−0.469067	+	0.883162i	$0.655410\pi$
$212$	9.07625	−	5.24018i	0.623360	−	0.359897i
$213$	4.05650	+	0.716427i	0.277947	+	0.0490888i
$214$	2.14746	−	3.71952i	0.146798	−	0.254261i
$215$	1.94074	+	3.36146i	0.132357	+	0.229250i
$216$	−2.60181	+	4.49784i	−0.177031	+	0.306039i
$217$	13.7862	+	6.43571i	0.935867	+	0.436884i
$218$			13.9195i			0.942750i
$219$	−12.8671	+	15.3259i	−0.869481	+	1.03563i
$220$	3.34993	+	4.12406i	0.225852	+	0.278044i
$221$	−6.25383	−	3.61065i	−0.420678	−	0.242878i
$222$	−1.73382	−	1.45566i	−0.116366	−	0.0976977i
$223$	19.9317			1.33472			0.667361	−	0.744734i	$-0.267424\pi$
$223$	19.9317			1.33472			0.667361	+	0.744734i	$0.267424\pi$
$224$	−2.39739	−	1.11916i	−0.160182	−	0.0747768i
$225$	5.59544	−	4.68986i	0.373030	−	0.312658i
$226$	−2.97280	+	1.71634i	−0.197747	+	0.114170i
$227$	−3.35657	+	5.81374i	−0.222783	+	0.385872i	−0.955652	−	0.294498i	$-0.904847\pi$
$227$	−3.35657	+	5.81374i	−0.222783	+	0.385872i	0.732869	+	0.680370i	$0.238181\pi$
$228$	−4.46055	−	0.787787i	−0.295407	−	0.0521725i
$229$	−3.74069	−	6.47906i	−0.247192	−	0.428149i	0.715554	−	0.698558i	$-0.246174\pi$
$229$	−3.74069	−	6.47906i	−0.247192	−	0.428149i	−0.962746	+	0.270409i	$0.912841\pi$
$230$	−0.879953			−0.0580224
$231$	−12.5934	+	8.50922i	−0.828584	+	0.559865i
$232$	0.955838			0.0627538
$233$	−10.0351	−	17.3813i	−0.657421	−	1.13869i	−0.981281	−	0.192582i	$-0.938314\pi$
$233$	−10.0351	−	17.3813i	−0.657421	−	1.13869i	0.323860	−	0.946105i	$-0.395019\pi$
$234$	−8.74099	+	1.53629i	−0.571416	+	0.100430i
$235$	−5.21493	+	9.03252i	−0.340184	+	0.589217i
$236$	−11.3873	+	6.57446i	−0.741250	+	0.427961i
$237$	7.89759	+	21.7171i	0.513004	+	1.41068i
$238$	0.560157	+	6.43397i	0.0363096	+	0.417052i
$239$	−24.7700			−1.60224			−0.801121	−	0.598503i	$-0.795762\pi$
$239$	−24.7700			−1.60224			−0.801121	+	0.598503i	$0.795762\pi$
$240$	1.78414	−	2.12506i	0.115166	−	0.137172i
$241$	14.2602	+	8.23310i	0.918577	+	0.530341i	0.883181	−	0.469032i	$-0.155397\pi$
$241$	14.2602	+	8.23310i	0.918577	+	0.530341i	0.0353964	+	0.999373i	$0.488731\pi$
$242$	−10.4513	+	3.43079i	−0.671835	+	0.220539i
$243$	11.9553	−	10.0035i	0.766933	−	0.641728i
$244$		−	2.87292i		−	0.183920i
$245$	8.59643	−	7.20088i	0.549206	−	0.460047i
$246$	−3.15905	+	1.14881i	−0.201414	+	0.0732456i
$247$	−3.86824	−	6.69999i	−0.246130	−	0.426310i
$248$	2.87525	−	4.98007i	0.182578	−	0.316235i
$249$	2.38581	−	13.5088i	0.151195	−	0.856084i
$250$	−10.3131	+	5.95429i	−0.652260	+	0.376582i
$251$			28.4497i			1.79573i	0.440271	+	0.897865i	$0.354882\pi$
$251$			28.4497i			1.79573i	−0.440271	+	0.897865i	$0.645118\pi$
$252$	5.60701	+	5.61796i	0.353208	+	0.353898i
$253$	0.650300	−	1.70177i	0.0408840	−	0.106989i
$254$	−10.0065	+	5.77728i	−0.627867	+	0.362499i
$255$	−6.66989	−	1.17798i	−0.417684	−	0.0737682i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	25.1924	−	14.5448i	1.57146	−	0.907282i	0.575468	−	0.817824i	$-0.304820\pi$
$257$	25.1924	−	14.5448i	1.57146	−	0.907282i	0.995991	−	0.0894575i	$-0.0285133\pi$
$258$	1.43424	+	3.94393i	0.0892917	+	0.245538i
$259$	−2.83355	+	1.98229i	−0.176068	+	0.123174i
$260$	4.73919			0.293912
$261$	−2.69404	−	0.982237i	−0.166757	−	0.0607990i
$262$	−0.434049	+	0.751795i	−0.0268156	+	0.0464460i
$263$	6.83853	−	11.8447i	0.421682	−	0.730374i	−0.574423	−	0.818559i	$-0.694773\pi$
$263$	6.83853	−	11.8447i	0.421682	−	0.730374i	0.996104	+	0.0881850i	$0.0281067\pi$
$264$	2.79122	+	5.02087i	0.171788	+	0.309013i
$265$	16.7894			1.03136
$266$	−2.92677	+	6.26955i	−0.179452	+	0.384411i
$267$	4.02826	+	11.0771i	0.246526	+	0.677907i
$268$	−7.30221	−	12.6478i	−0.446053	−	0.772587i
$269$	−25.8414	−	14.9195i	−1.57558	−	0.909661i	−0.995465	−	0.0951245i	$-0.969675\pi$
$269$	−25.8414	−	14.9195i	−1.57558	−	0.909661i	−0.580113	−	0.814536i	$-0.696992\pi$
$270$	−7.21238	+	4.15609i	−0.438931	+	0.252932i
$271$	10.5988	−	6.11920i	0.643829	−	0.371715i	−0.142259	−	0.989829i	$-0.545437\pi$
$271$	10.5988	−	6.11920i	0.643829	−	0.371715i	0.786088	+	0.618115i	$0.212103\pi$
$272$	2.44101			0.148008
$273$	−1.19100	+	13.5043i	−0.0720823	+	0.817319i
$274$			11.2724i			0.680989i
$275$	−1.27470	−	7.97021i	−0.0768676	−	0.480622i
$276$	−0.936898	−	0.165468i	−0.0563946	−	0.00995998i
$277$	18.1750	+	10.4934i	1.09203	+	0.630485i	0.934117	−	0.356968i	$-0.116189\pi$
$277$	18.1750	+	10.4934i	1.09203	+	0.630485i	0.157915	+	0.987453i	$0.449523\pi$
$278$	0.201218	−	0.116173i	0.0120683	−	0.00696762i
$279$	−13.2215	+	11.0817i	−0.791552	+	0.663446i
$280$	−2.42961	−	3.47296i	−0.145197	−	0.207549i
$281$	−31.2664			−1.86520			−0.932600	−	0.360913i	$-0.882465\pi$
$281$	−31.2664			−1.86520			−0.932600	+	0.360913i	$0.882465\pi$
$282$	−7.25089	+	8.63643i	−0.431784	+	0.514292i
$283$	21.1922	+	12.2353i	1.25975	+	0.727314i	0.973025	−	0.230700i	$-0.0741016\pi$
$283$	21.1922	+	12.2353i	1.25975	+	0.727314i	0.286720	+	0.958014i	$0.407435\pi$
$284$	−2.05964	−	1.18913i	−0.122217	−	0.0705621i
$285$	−5.55737	−	4.66581i	−0.329190	−	0.276379i
$286$	−3.50234	+	9.16527i	−0.207097	+	0.541954i
$287$	0.445356	+	5.11536i	0.0262885	+	0.301950i
$288$	2.29920	−	1.92709i	0.135482	−	0.113555i
$289$	5.52074	+	9.56220i	0.324749	+	0.562482i
$290$	1.32609	+	0.765618i	0.0778707	+	0.0449586i
$291$	4.98343	−	28.2168i	0.292134	−	1.65410i
$292$	10.0056	−	5.77671i	0.585531	−	0.338057i
$293$	9.42889			0.550842			0.275421	−	0.961324i	$-0.411183\pi$
$293$	9.42889			0.550842			0.275421	+	0.961324i	$0.411183\pi$
$294$	10.5068	−	6.05039i	0.612769	−	0.352866i
$295$	−21.0644			−1.22641
$296$	0.653521	+	1.13193i	0.0379851	+	0.0657922i
$297$	−2.70754	−	17.0197i	−0.157107	−	0.987582i
$298$	−4.31760	+	7.47830i	−0.250112	+	0.433206i
$299$	−0.812488	−	1.40727i	−0.0469874	−	0.0813846i
$300$	−3.96139	+	1.44059i	−0.228711	+	0.0831724i
$301$	6.38628	−	0.556005i	0.368099	−	0.0320476i
$302$		−	17.6877i		−	1.01781i
$303$	19.2944	+	16.1990i	1.10844	+	0.930611i
$304$	2.26479	+	1.30758i	0.129895	+	0.0749947i
$305$	2.30118	−	3.98577i	0.131765	−	0.228224i
$306$	−6.88001	−	2.50843i	−0.393304	−	0.143397i
$307$		−	29.3625i		−	1.67580i	−0.545821	−	0.837902i	$-0.683782\pi$
$307$		−	29.3625i		−	1.67580i	0.545821	−	0.837902i	$-0.316218\pi$
$308$	8.51200	−	2.13212i	0.485016	−	0.121489i
$309$	4.54012	−	1.65105i	0.258279	−	0.0939248i
$310$	7.97800	−	4.60610i	0.453120	−	0.261609i
$311$	20.7044	+	11.9537i	1.17404	+	0.677833i	0.954628	−	0.297800i	$-0.0962528\pi$
$311$	20.7044	+	11.9537i	1.17404	+	0.677833i	0.219412	+	0.975632i	$0.429586\pi$
$312$	5.04588	+	0.891163i	0.285666	+	0.0504522i
$313$	1.63136	+	2.82559i	0.0922098	+	0.159712i	0.908441	−	0.418014i	$-0.137274\pi$
$313$	1.63136	+	2.82559i	0.0922098	+	0.159712i	−0.816231	+	0.577726i	$0.803940\pi$
$314$	5.27158			0.297492
$315$	3.27898	+	12.2853i	0.184750	+	0.692198i
$316$		−	13.3417i		−	0.750532i
$317$	−15.4454	+	8.91738i	−0.867498	+	0.500850i	−0.866516	−	0.499150i	$-0.833646\pi$
$317$	−15.4454	+	8.91738i	−0.867498	+	0.500850i	−0.000981712		1.00000i	$0.500312\pi$
$318$	17.8759	+	3.15709i	1.00243	+	0.177041i
$319$	−2.46066	+	1.99876i	−0.137770	+	0.111909i
$320$	−1.38736	+	0.800992i	−0.0775557	+	0.0447768i
$321$	6.99111	−	2.54237i	0.390205	−	0.141901i
$322$	−0.614741	+	1.31686i	−0.0342582	+	0.0733859i
$323$		−	6.38362i		−	0.355194i
$324$	−8.46063	+	3.06882i	−0.470035	+	0.170490i
$325$	−6.23497	−	3.59976i	−0.345854	−	0.199679i
$326$	−3.96431	+	6.86639i	−0.219563	+	0.380294i
$327$	−15.5023	+	18.4645i	−0.857279	+	1.02109i
$328$	1.94074			0.107159
$329$	9.87411	+	14.1144i	0.544377	+	0.778152i
$330$	−0.149251	+	9.20149i	−0.00821600	+	0.506525i
$331$	0.110394	+	0.191209i	0.00606782	+	0.0105098i	0.869043	−	0.494736i	$-0.164735\pi$
$331$	0.110394	+	0.191209i	0.00606782	+	0.0105098i	−0.862976	+	0.505246i	$0.831402\pi$
$332$	−3.96000	+	6.85892i	−0.217333	+	0.376432i
$333$	−0.678760	−	3.86193i	−0.0371958	−	0.211632i
$334$	−1.14541	−	1.98390i	−0.0626739	−	0.108554i
$335$		−	23.3960i		−	1.27826i
$336$	−1.93377	−	4.15458i	−0.105496	−	0.226651i
$337$		−	21.4000i		−	1.16573i	−0.812569	−	0.582865i	$-0.801932\pi$
$337$		−	21.4000i		−	1.16573i	0.812569	−	0.582865i	$-0.198068\pi$
$338$	−2.12416	−	3.67915i	−0.115539	−	0.200120i
$339$	−5.85498	−	1.03406i	−0.317999	−	0.0561625i
$340$	3.38656	+	1.95523i	0.183662	+	0.106037i
$341$	3.01201	+	18.8329i	0.163110	+	1.01986i
$342$	−5.03964	−	6.01277i	−0.272513	−	0.325133i
$343$	−4.77069	−	17.8953i	−0.257593	−	0.966253i
$344$		−	2.42292i		−	0.130635i
$345$	−1.16728	−	0.980010i	−0.0628440	−	0.0527620i
$346$	11.4994	−	19.9176i	0.618212	−	1.07077i
$347$	4.02093	−	6.96445i	0.215855	−	0.373871i	−0.737682	−	0.675148i	$-0.764080\pi$
$347$	4.02093	−	6.96445i	0.215855	−	0.373871i	0.953537	+	0.301277i	$0.0974129\pi$
$348$	1.26794	+	1.06452i	0.0679686	+	0.0570645i
$349$			8.20020i			0.438947i	0.975618	+	0.219473i	$0.0704339\pi$
$349$			8.20020i			0.438947i	−0.975618	+	0.219473i	$0.929566\pi$
$350$	0.558468	+	6.41456i	0.0298513	+	0.342873i
$351$	−13.3061	−	7.69699i	−0.710226	−	0.410835i
$352$	−0.523783	−	3.27500i	−0.0279177	−	0.174558i
$353$	−0.951398	−	0.549290i	−0.0506378	−	0.0292357i	0.474467	−	0.880273i	$-0.342641\pi$
$353$	−0.951398	−	0.549290i	−0.0506378	−	0.0292357i	−0.525105	+	0.851037i	$0.675974\pi$
$354$	−22.4275	−	3.96097i	−1.19201	−	0.210523i
$355$	−1.90497	−	3.29951i	−0.101105	−	0.175120i
$356$		−	6.80511i		−	0.360670i
$357$	−6.42250	+	9.15863i	−0.339915	+	0.484726i
$358$		−	15.2724i		−	0.807173i
$359$	17.8091	+	30.8462i	0.939927	+	1.62800i	0.765603	+	0.643314i	$0.222441\pi$
$359$	17.8091	+	30.8462i	0.939927	+	1.62800i	0.174325	+	0.984688i	$0.444226\pi$
$360$	4.73340	−	0.831927i	0.249472	−	0.0438464i
$361$	−6.08048	+	10.5317i	−0.320025	+	0.554300i
$362$	−7.96601	−	13.7975i	−0.418684	−	0.725183i
$363$	−17.6848	−	7.08869i	−0.928209	−	0.372060i
$364$	3.31083	−	7.09226i	0.173535	−	0.371735i
$365$	18.5084			0.968774
$366$	3.19959	−	3.81098i	0.167245	−	0.199203i
$367$	5.92696	−	10.2658i	0.309385	−	0.535870i	−0.668843	−	0.743404i	$-0.733210\pi$
$367$	5.92696	−	10.2658i	0.309385	−	0.535870i	0.978228	+	0.207533i	$0.0665436\pi$
$368$	0.475699	+	0.274645i	0.0247975	+	0.0143169i
$369$	−5.46999	−	1.99434i	−0.284756	−	0.103821i
$370$			2.09386i			0.108855i
$371$	11.7292	−	25.1255i	0.608948	−	1.30445i
$372$	9.36042	−	3.40398i	0.485315	−	0.176488i
$373$	5.14208	−	2.96878i	0.266247	−	0.153718i	−0.360934	−	0.932591i	$-0.617542\pi$
$373$	5.14208	−	2.96878i	0.266247	−	0.153718i	0.627181	+	0.778874i	$0.284209\pi$
$374$	−6.28400	+	5.10442i	−0.324938	+	0.263943i
$375$	−20.3119	−	3.58733i	−1.04890	−	0.185249i
$376$	5.63833	−	3.25529i	0.290775	−	0.167879i
$377$			2.82768i			0.145633i
$378$	1.18104	+	13.6969i	0.0607460	+	0.704493i
$379$	−13.3391			−0.685183			−0.342591	−	0.939484i	$-0.611305\pi$
$379$	−13.3391			−0.685183			−0.342591	+	0.939484i	$0.611305\pi$
$380$	2.09472	+	3.62816i	0.107457	+	0.186121i
$381$	−19.7081	−	3.48069i	−1.00968	−	0.178321i
$382$	−17.8529	−	10.3074i	−0.913433	−	0.527371i
$383$	2.38792	−	1.37867i	0.122017	−	0.0704465i	−0.437749	−	0.899097i	$-0.644224\pi$
$383$	2.38792	−	1.37867i	0.122017	−	0.0704465i	0.559766	+	0.828651i	$0.310891\pi$
$384$	−1.62776	+	0.591946i	−0.0830662	+	0.0302076i
$385$	13.5170	+	3.86003i	0.688890	+	0.196725i
$386$		−	12.7611i		−	0.649523i
$387$	−2.48984	+	6.82902i	−0.126566	+	0.347139i
$388$	−8.27154	+	14.3267i	−0.419924	+	0.727330i
$389$	−4.44364	−	2.56554i	−0.225301	−	0.130078i	0.383101	−	0.923706i	$-0.374856\pi$
$389$	−4.44364	−	2.56554i	−0.225301	−	0.130078i	−0.608403	+	0.793629i	$0.708189\pi$
$390$	6.28662	+	5.27807i	0.318336	+	0.267265i
$391$		−	1.34082i		−	0.0678082i
$392$	−6.89468	+	1.20970i	−0.348234	+	0.0610993i
$393$	−1.41305	+	0.513867i	−0.0712792	+	0.0259212i
$394$	7.10500	+	12.3062i	0.357945	+	0.619979i
$395$	10.6866	−	18.5098i	0.537703	−	0.931328i
$396$	−1.88917	+	9.76888i	−0.0949343	+	0.490905i
$397$	−12.8199	−	22.2048i	−0.643414	−	1.11443i	−0.984665	−	0.174454i	$-0.944184\pi$
$397$	−12.8199	−	22.2048i	−0.643414	−	1.11443i	0.341251	−	0.939972i	$-0.389149\pi$
$398$	4.86692			0.243957
$399$	−10.8649	+	5.05712i	−0.543924	+	0.253173i
$400$	2.43365			0.121682
$401$	1.25322	−	0.723550i	0.0625831	−	0.0361323i	−0.468382	−	0.883526i	$-0.655163\pi$
$401$	1.25322	−	0.723550i	0.0625831	−	0.0361323i	0.530965	+	0.847394i	$0.321830\pi$
$402$	4.39942	−	24.9101i	0.219423	−	1.24240i
$403$	14.7327	+	8.50591i	0.733886	+	0.423710i
$404$	−7.27257	−	12.5965i	−0.361824	−	0.626698i
$405$	−14.1960	−	2.51934i	−0.705407	−	0.125187i
$406$	2.07217	−	1.44965i	0.102840	−	0.0719447i
$407$	−4.04938	−	1.54740i	−0.200720	−	0.0767016i
$408$	3.23805	+	2.71857i	0.160307	+	0.134589i
$409$	−8.69393	−	5.01945i	−0.429887	−	0.248196i	0.269411	−	0.963025i	$-0.413171\pi$
$409$	−8.69393	−	5.01945i	−0.429887	−	0.248196i	−0.699299	+	0.714830i	$0.746504\pi$
$410$	2.69250	+	1.55452i	0.132973	+	0.0767721i
$411$	−12.5541	+	14.9530i	−0.619250	+	0.737579i
$412$	−2.78919			−0.137413
$413$	−14.7157	+	31.5231i	−0.724113	+	1.55115i
$414$	−1.05853	−	1.26293i	−0.0520240	−	0.0620695i
$415$	−10.9879	+	6.34385i	−0.539374	+	0.311408i
$416$	−2.56198	−	1.47916i	−0.125612	−	0.0725219i
$417$	0.396303	+	0.0699919i	0.0194070	+	0.00342752i
$418$	−8.56465	+	1.36978i	−0.418911	+	0.0669979i
$419$			19.6066i			0.957847i	0.877857	+	0.478924i	$0.158973\pi$
$419$			19.6066i			0.957847i	−0.877857	+	0.478924i	$0.841027\pi$
$420$	0.644945	−	7.31283i	0.0314701	−	0.356829i
$421$	−24.3393			−1.18622			−0.593112	−	0.805120i	$-0.702101\pi$
$421$	−24.3393			−1.18622			−0.593112	+	0.805120i	$0.702101\pi$
$422$	22.2199	−	12.8287i	1.08165	−	0.624490i
$423$	−19.2369	+	3.38102i	−0.935330	+	0.164391i
$424$	−9.07625	−	5.24018i	−0.440782	−	0.254486i
$425$	−2.97028	−	5.14467i	−0.144080	−	0.249553i
$426$	−1.40781	−	3.87125i	−0.0682084	−	0.187563i
$427$	−4.35713	−	6.22824i	−0.210856	−	0.301406i
$428$	−4.29493			−0.207603
$429$	−14.8533	+	8.25733i	−0.717126	+	0.398668i
$430$	1.94074	−	3.36146i	0.0935907	−	0.162104i
$431$	11.0314	−	19.1069i	0.531363	−	0.920347i	−0.467967	−	0.883746i	$-0.655013\pi$
$431$	11.0314	−	19.1069i	0.531363	−	0.920347i	0.999330	−	0.0366015i	$-0.0116532\pi$
$432$	5.19615	+	0.00431112i	0.250000	+	0.000207419i
$433$	−27.5968			−1.32622			−0.663108	−	0.748523i	$-0.730763\pi$
$433$	−27.5968			−1.32622			−0.663108	+	0.748523i	$0.730763\pi$
$434$	−1.31961	−	15.1570i	−0.0633433	−	0.727561i
$435$	0.906409	+	2.49248i	0.0434590	+	0.119505i
$436$	12.0547	−	6.95977i	0.577314	−	0.333312i
$437$	0.718239	−	1.24403i	0.0343580	−	0.0595099i
$438$	19.7061	+	3.48035i	0.941596	+	0.166297i
$439$	−15.4336	+	8.91061i	−0.736607	+	0.425280i	−0.820834	−	0.571166i	$-0.806491\pi$
$439$	−15.4336	+	8.91061i	−0.736607	+	0.425280i	0.0842273	+	0.996447i	$0.473158\pi$
$440$	1.89658	−	4.96315i	0.0904157	−	0.236609i
$441$	20.6758	+	3.67554i	0.984564	+	0.175026i
$442$			7.22130i			0.343482i
$443$	−1.86006	+	1.07391i	−0.0883744	+	0.0510230i	−0.543536	−	0.839386i	$-0.682915\pi$
$443$	−1.86006	+	1.07391i	−0.0883744	+	0.0510230i	0.455162	+	0.890409i	$0.349581\pi$
$444$	−0.393732	+	2.22936i	−0.0186857	+	0.105801i
$445$	5.45084	−	9.44113i	0.258395	−	0.447553i
$446$	−9.96583	−	17.2613i	−0.471896	−	0.817347i
$447$	−14.0560	+	5.11157i	−0.664827	+	0.241769i
$448$	0.229478	+	2.63578i	0.0108418	+	0.124529i
$449$			16.0383i			0.756893i	0.925623	+	0.378447i	$0.123542\pi$
$449$			16.0383i			0.756893i	−0.925623	+	0.378447i	$0.876458\pi$
$450$	−6.85926	−	2.50086i	−0.323349	−	0.117892i
$451$	−4.99613	+	4.05830i	−0.235259	+	0.191098i
$452$	2.97280	+	1.71634i	0.139829	+	0.0807301i
$453$	19.6990	−	23.4631i	0.925538	−	1.10239i
$454$	6.71313			0.315063
$455$	10.2741	−	7.18756i	0.481660	−	0.336958i
$456$	1.54803	+	4.25684i	0.0724932	+	0.199345i
$457$	−4.44457	+	2.56607i	−0.207908	+	0.120036i	−0.600339	−	0.799746i	$-0.704968\pi$
$457$	−4.44457	+	2.56607i	−0.207908	+	0.120036i	0.392431	+	0.919782i	$0.371634\pi$
$458$	−3.74069	+	6.47906i	−0.174791	+	0.302747i
$459$	−6.33281	−	10.9898i	−0.295590	−	0.512960i
$460$	0.439977	+	0.762062i	0.0205140	+	0.0355313i
$461$	10.7772			0.501946			0.250973	−	0.967994i	$-0.419249\pi$
$461$	10.7772			0.501946			0.250973	+	0.967994i	$0.419249\pi$
$462$	13.6659	+	6.65158i	0.635795	+	0.309459i
$463$	31.4934			1.46362			0.731811	−	0.681507i	$-0.238675\pi$
$463$	31.4934			1.46362			0.731811	+	0.681507i	$0.238675\pi$
$464$	−0.477919	−	0.827780i	−0.0221868	−	0.0384287i
$465$	15.7128	+	2.77507i	0.728665	+	0.128691i
$466$	−10.0351	+	17.3813i	−0.464867	+	0.805173i
$467$	−1.47963	+	0.854267i	−0.0684693	+	0.0395308i	−0.533844	−	0.845583i	$-0.679253\pi$
$467$	−1.47963	+	0.854267i	−0.0684693	+	0.0395308i	0.465375	+	0.885114i	$0.345920\pi$
$468$	5.70096	+	6.80178i	0.263527	+	0.314412i
$469$	−35.0125	−	16.3446i	−1.61673	−	0.754725i
$470$	10.4299			0.481093
$471$	6.99286	+	5.87100i	0.322214	+	0.270521i
$472$	11.3873	+	6.57446i	0.524143	+	0.302614i
$473$	5.06659	+	6.23743i	0.232962	+	0.286797i
$474$	14.8588	−	17.6981i	0.682487	−	0.812900i
$475$		−	6.36437i		−	0.292017i
$476$	5.29190	−	3.70209i	0.242554	−	0.169685i
$477$	20.1966	+	24.0964i	0.924739	+	1.10330i
$478$	12.3850	+	21.4515i	0.566478	+	0.981168i
$479$	12.8640	−	22.2811i	0.587772	−	1.01805i	−0.406752	−	0.913539i	$-0.633339\pi$
$479$	12.8640	−	22.2811i	0.587772	−	1.01805i	0.994524	−	0.104512i	$-0.0333279\pi$
$480$	−2.73243	−	0.482580i	−0.124718	−	0.0220267i
$481$	−3.34862	+	1.93333i	−0.152684	+	0.0881521i
$482$		−	16.4662i		−	0.750015i
$483$	−2.28207	+	1.06220i	−0.103838	+	0.0483319i
$484$	8.19680	+	7.33570i	0.372582	+	0.333441i
$485$	−22.9512	+	13.2509i	−1.04216	+	0.601691i
$486$	−14.6410	−	5.35182i	−0.664128	−	0.242763i
$487$	5.94321	−	10.2939i	0.269312	−	0.466463i	−0.699372	−	0.714758i	$-0.746537\pi$
$487$	5.94321	−	10.2939i	0.269312	−	0.466463i	0.968684	+	0.248295i	$0.0798702\pi$
$488$	−2.48802	+	1.43646i	−0.112627	+	0.0650254i
$489$	−12.9059	+	4.69332i	−0.583624	+	0.212239i
$490$	−10.5344	−	3.84429i	−0.475894	−	0.173667i
$491$	5.85820			0.264377			0.132188	−	0.991225i	$-0.457800\pi$
$491$	5.85820			0.264377			0.132188	+	0.991225i	$0.457800\pi$
$492$	2.57443	+	2.16142i	0.116064	+	0.0974441i
$493$	−1.16660	+	2.02062i	−0.0525412	+	0.0910041i
$494$	−3.86824	+	6.69999i	−0.174040	+	0.301447i
$495$	−10.4457	+	12.0397i	−0.469502	+	0.541146i
$496$	−5.75049			−0.258205
$497$	−6.26859	+	0.545759i	−0.281185	+	0.0244806i
$498$	−12.8918	+	4.68821i	−0.577698	+	0.210084i
$499$	17.7986	+	30.8281i	0.796775	+	1.38005i	0.921706	+	0.387889i	$0.126796\pi$
$499$	17.7986	+	30.8281i	0.796775	+	1.38005i	−0.124931	+	0.992165i	$0.539871\pi$
$500$	10.3131	+	5.95429i	0.461217	+	0.266284i
$501$	0.690084	−	3.90734i	0.0308307	−	0.174567i
$502$	24.6382	−	14.2249i	1.09966	−	0.634886i
$503$	−40.9984			−1.82803			−0.914015	−	0.405681i	$-0.867034\pi$
$503$	−40.9984			−1.82803			−0.914015	+	0.405681i	$0.867034\pi$
$504$	2.06180	−	7.66479i	0.0918397	−	0.341417i
$505$		−	23.3011i		−	1.03688i
$506$	−1.79893	+	0.287709i	−0.0799720	+	0.0127902i
$507$	1.27976	−	7.24617i	0.0568362	−	0.321814i
$508$	10.0065	+	5.77728i	0.443969	+	0.256326i
$509$	−28.0349	+	16.1860i	−1.24263	+	0.717430i	−0.969628	−	0.244585i	$-0.921348\pi$
$509$	−28.0349	+	16.1860i	−1.24263	+	0.717430i	−0.272998	+	0.962015i	$0.588015\pi$
$510$	2.31478	+	6.36528i	0.102500	+	0.281859i
$511$	12.9301	−	27.6981i	0.571994	−	1.22529i
$512$	1.00000			0.0441942
$513$	0.0112742	−	13.5887i	0.000497770	−	0.599958i
$514$	−25.1924	−	14.5448i	−1.11119	−	0.641545i
$515$	−3.86960	−	2.23412i	−0.170515	−	0.0984469i
$516$	2.69842	−	3.21405i	0.118791	−	0.141491i
$517$	−7.70783	+	20.1706i	−0.338990	+	0.887104i
$518$	3.13349	+	1.46278i	0.137678	+	0.0642711i
$519$	37.4365	−	13.6141i	1.64328	−	0.597591i
$520$	−2.36959	−	4.10426i	−0.103914	−	0.179984i
$521$	16.8686	+	9.73906i	0.739025	+	0.426676i	0.821715	−	0.569899i	$-0.193018\pi$
$521$	16.8686	+	9.73906i	0.739025	+	0.426676i	−0.0826899	+	0.996575i	$0.526351\pi$
$522$	0.496376	+	2.82422i	0.0217258	+	0.123613i
$523$	−3.52042	+	2.03251i	−0.153937	+	0.0888756i	−0.574990	−	0.818160i	$-0.694994\pi$
$523$	−3.52042	+	2.03251i	−0.153937	+	0.0888756i	0.421053	+	0.907036i	$0.361661\pi$
$524$	0.868098			0.0379230
$525$	−6.40313	+	9.13102i	−0.279455	+	0.398510i
$526$	−13.6771			−0.596348
$527$	7.01850	+	12.1564i	0.305731	+	0.529541i
$528$	2.95259	−	4.92770i	0.128495	−	0.214451i
$529$	−11.3491	+	19.6573i	−0.493441	+	0.854665i
$530$	−8.39468	−	14.5400i	−0.364642	−	0.631578i
$531$	−25.3392	−	30.2320i	−1.09963	−	1.31196i
$532$	6.89298	−	0.600120i	0.298848	−	0.0260185i
$533$			5.74133i			0.248685i
$534$	7.57891	−	9.02712i	0.327971	−	0.390642i
$535$	−5.95860	−	3.44020i	−0.257613	−	0.148733i
$536$	−7.30221	+	12.6478i	−0.315407	+	0.546301i
$537$	17.0090	−	20.2592i	0.733993	−	0.874248i
$538$			29.8391i			1.28645i
$539$	15.2197	−	17.5317i	0.655557	−	0.755146i
$540$	7.20547	+	4.16806i	0.310074	+	0.179365i
$541$	22.8096	−	13.1691i	0.980662	−	0.566185i	0.0781921	−	0.996938i	$-0.475085\pi$
$541$	22.8096	−	13.1691i	0.980662	−	0.566185i	0.902470	+	0.430753i	$0.141752\pi$
$542$	−10.5988	−	6.11920i	−0.455256	−	0.262842i
$543$	4.79935	−	27.1745i	0.205960	−	1.16617i
$544$	−1.22050	−	2.11398i	−0.0523287	−	0.0906360i
$545$	22.2989			0.955179
$546$	12.2906	−	5.72073i	0.525989	−	0.244825i
$547$			22.9709i			0.982163i	0.871114	+	0.491081i	$0.163398\pi$
$547$			22.9709i			0.982163i	−0.871114	+	0.491081i	$0.836602\pi$
$548$	9.76217	−	5.63619i	0.417019	−	0.240766i
$549$	8.48864	−	1.49194i	0.362286	−	0.0636742i
$550$	−6.26505	+	5.08903i	−0.267143	+	0.216997i
$551$	−2.16477	+	1.24983i	−0.0922224	+	0.0532446i
$552$	0.325150	+	0.894111i	0.0138393	+	0.0380559i
$553$	−20.2344	−	28.9238i	−0.860454	−	1.22996i
$554$		−	20.9867i		−	0.891640i
$555$	−2.33195	+	2.77755i	−0.0989857	+	0.117900i
$556$	−0.201218	−	0.116173i	−0.00853355	−	0.00492685i
$557$	6.93413	−	12.0103i	0.293808	−	0.508891i	−0.680899	−	0.732378i	$-0.738411\pi$
$557$	6.93413	−	12.0103i	0.293808	−	0.508891i	0.974707	+	0.223487i	$0.0717439\pi$
$558$	16.2078	+	5.90932i	0.686132	+	0.250161i
$559$	7.16778			0.303165
$560$	−1.79287	+	3.84058i	−0.0757626	+	0.162294i
$561$	−14.0207	−	0.227420i	−0.591954	−	0.00960168i
$562$	15.6332	+	27.0775i	0.659448	+	1.14220i
$563$	−18.7294	+	32.4402i	−0.789348	+	1.36719i	0.137019	+	0.990568i	$0.456248\pi$
$563$	−18.7294	+	32.4402i	−0.789348	+	1.36719i	−0.926367	+	0.376623i	$0.877085\pi$
$564$	11.1048	+	1.96124i	0.467597	+	0.0825833i
$565$	2.74956	+	4.76237i	0.115675	+	0.200354i
$566$		−	24.4706i		−	1.02858i
$567$	−13.6877	+	19.4845i	−0.574828	+	0.818274i
$568$			2.37827i			0.0997899i
$569$	−11.6578	−	20.1919i	−0.488720	−	0.846488i	0.511196	−	0.859464i	$-0.329203\pi$
$569$	−11.6578	−	20.1919i	−0.488720	−	0.846488i	−0.999916	+	0.0129765i	$0.995869\pi$
$570$	−1.26202	+	7.14573i	−0.0528603	+	0.299302i
$571$	−18.9355	−	10.9324i	−0.792424	−	0.457506i	0.0483912	−	0.998828i	$-0.484591\pi$
$571$	−18.9355	−	10.9324i	−0.792424	−	0.457506i	−0.840815	+	0.541322i	$0.817924\pi$
$572$	9.68852	−	1.54952i	0.405097	−	0.0647887i
$573$	−12.2028	−	33.5558i	−0.509780	−	1.40181i
$574$	4.20735	−	2.94337i	0.175612	−	0.122854i
$575$		−	1.33678i		−	0.0557475i
$576$	−2.81851	−	1.02762i	−0.117438	−	0.0428175i
$577$	−10.2983	+	17.8372i	−0.428725	+	0.742573i	−0.996760	−	0.0804309i	$-0.974370\pi$
$577$	−10.2983	+	17.8372i	−0.428725	+	0.742573i	0.568035	+	0.823004i	$0.307704\pi$
$578$	5.52074	−	9.56220i	0.229632	−	0.397735i
$579$	14.2121	−	16.9279i	0.590636	−	0.703498i
$580$		−	1.53124i		−	0.0635811i
$581$	1.81746	+	20.8754i	0.0754010	+	0.866057i
$582$	−26.9282	+	9.79261i	−1.11621	+	0.405917i
$583$	34.3232	−	5.48944i	1.42152	−	0.227349i
$584$	−10.0056	−	5.77671i	−0.414033	−	0.239042i
$585$	2.46111	+	14.0029i	0.101754	+	0.578950i
$586$	−4.71445	−	8.16566i	−0.194752	−	0.337320i
$587$		−	11.7112i		−	0.483372i	−0.970354	−	0.241686i	$-0.922300\pi$
$587$		−	11.7112i		−	0.483372i	0.970354	−	0.241686i	$-0.0777004\pi$
$588$	−10.4932	−	6.07396i	−0.432732	−	0.250486i
$589$			15.0384i			0.619648i
$590$	10.5322	+	18.2423i	0.433603	+	0.751022i
$591$	−4.28061	+	24.2374i	−0.176081	+	0.996991i
$592$	0.653521	−	1.13193i	0.0268595	−	0.0465221i
$593$	22.3249	+	38.6679i	0.916774	+	1.58790i	0.804283	+	0.594246i	$0.202549\pi$
$593$	22.3249	+	38.6679i	0.916774	+	1.58790i	0.112490	+	0.993653i	$0.464117\pi$
$594$	−13.3857	+	10.8546i	−0.549222	+	0.445371i
$595$	10.3071	−	0.897362i	0.422550	−	0.0367883i
$596$	8.63520			0.353712
$597$	6.45607	+	5.42033i	0.264229	+	0.221839i
$598$	−0.812488	+	1.40727i	−0.0332251	+	0.0575476i
$599$	22.0715	+	12.7430i	0.901816	+	0.520664i	0.877789	−	0.479048i	$-0.159018\pi$
$599$	22.0715	+	12.7430i	0.901816	+	0.520664i	0.0240271	+	0.999711i	$0.492351\pi$
$600$	3.22828	+	2.71037i	0.131794	+	0.110651i
$601$		−	3.69212i		−	0.150605i	−0.997161	−	0.0753024i	$-0.976008\pi$
$601$		−	3.69212i		−	0.150605i	0.997161	−	0.0753024i	$-0.0239922\pi$
$602$	−3.67466	−	5.25268i	−0.149768	−	0.214083i
$603$	33.5785	−	28.1440i	1.36742	−	1.14611i
$604$	−15.3180	+	8.84386i	−0.623281	+	0.359852i
$605$	5.49606	+	16.7428i	0.223447	+	0.680692i
$606$	4.38157	−	24.8090i	0.177989	−	1.00780i
$607$	6.66954	−	3.85066i	0.270708	−	0.156294i	−0.358501	−	0.933529i	$-0.616712\pi$
$607$	6.66954	−	3.85066i	0.270708	−	0.156294i	0.629209	+	0.777236i	$0.283379\pi$
$608$		−	2.61516i		−	0.106059i
$609$	4.36326	+	0.384812i	0.176808	+	0.0155934i
$610$	−4.60237			−0.186344
$611$	9.63021	+	16.6800i	0.389597	+	0.674801i
$612$	1.26764	+	7.21248i	0.0512414	+	0.291547i
$613$	13.5825	+	7.84188i	0.548593	+	0.316730i	0.748554	−	0.663073i	$-0.230748\pi$
$613$	13.5825	+	7.84188i	0.548593	+	0.316730i	−0.199961	+	0.979804i	$0.564082\pi$
$614$	−25.4286	+	14.6812i	−1.02622	+	0.592486i
$615$	1.84038	+	5.06075i	0.0742112	+	0.204069i
$616$	−6.10247	−	6.30555i	−0.245875	−	0.254058i
$617$			38.7271i			1.55909i	0.626344	+	0.779547i	$0.284551\pi$
$617$			38.7271i			1.55909i	−0.626344	+	0.779547i	$0.715449\pi$
$618$	−3.69991	−	3.10634i	−0.148832	−	0.124955i
$619$	−2.51690	+	4.35939i	−0.101163	+	0.175219i	−0.912164	−	0.409826i	$-0.865590\pi$
$619$	−2.51690	+	4.35939i	−0.101163	+	0.175219i	0.811001	+	0.585044i	$0.198923\pi$
$620$	−7.97800	−	4.60610i	−0.320404	−	0.184985i
$621$	0.00236805	−	2.85419i	9.50267e−5	−	0.114535i
$622$		−	23.9074i		−	0.958600i
$623$	−10.3208	−	14.7529i	−0.413494	−	0.591063i
$624$	−1.75117	−	4.81544i	−0.0701028	−	0.192772i
$625$	3.45456	+	5.98347i	0.138182	+	0.239339i
$626$	1.63136	−	2.82559i	0.0652022	−	0.112933i
$627$	−12.8867	−	7.72148i	−0.514645	−	0.308366i
$628$	−2.63579	−	4.56532i	−0.105179	−	0.182176i
$629$	−3.19050			−0.127214
$630$	8.99988	−	8.98233i	0.358564	−	0.357865i
$631$	−21.0058			−0.836228			−0.418114	−	0.908395i	$-0.637309\pi$
$631$	−21.0058			−0.836228			−0.418114	+	0.908395i	$0.637309\pi$
$632$	−11.5543	+	6.67087i	−0.459605	+	0.265353i
$633$	43.7626	+	7.72900i	1.73941	+	0.307200i
$634$	15.4454	+	8.91738i	0.613413	+	0.354154i
$635$	9.25511	+	16.0303i	0.367278	+	0.636144i
$636$	−6.20381	−	17.0595i	−0.245997	−	0.676453i
$637$	−3.57870	−	20.3967i	−0.141793	−	0.808146i
$638$	2.96131	+	1.13161i	0.117239	+	0.0448008i
$639$	2.44395	−	6.70317i	0.0966813	−	0.265173i
$640$	1.38736	+	0.800992i	0.0548402	+	0.0316620i
$641$	27.4280	+	15.8356i	1.08334	+	0.625467i	0.931796	−	0.362983i	$-0.118242\pi$
$641$	27.4280	+	15.8356i	1.08334	+	0.625467i	0.151545	+	0.988450i	$0.451575\pi$
$642$	−5.69731	−	4.78329i	−0.224855	−	0.188782i
$643$	−4.82297			−0.190199			−0.0950997	−	0.995468i	$-0.530317\pi$
$643$	−4.82297			−0.190199			−0.0950997	+	0.995468i	$0.530317\pi$
$644$	1.44781	−	0.126050i	0.0570516	−	0.00496705i
$645$	6.31811	−	2.29763i	0.248775	−	0.0904689i
$646$	−5.52838	+	3.19181i	−0.217511	+	0.125580i
$647$	−3.32120	−	1.91749i	−0.130570	−	0.0753844i	0.433292	−	0.901253i	$-0.357352\pi$
$647$	−3.32120	−	1.91749i	−0.130570	−	0.0753844i	−0.563862	+	0.825869i	$0.690685\pi$
$648$	6.88800	+	5.79271i	0.270586	+	0.227559i
$649$	−43.0628	+	6.88719i	−1.69036	+	0.270346i
$650$			7.19952i			0.282388i
$651$	15.1300	−	21.5758i	0.592992	−	0.845621i
$652$	7.92862			0.310509
$653$	−29.8108	+	17.2113i	−1.16659	+	0.673530i	−0.952874	−	0.303367i	$-0.901889\pi$
$653$	−29.8108	+	17.2113i	−1.16659	+	0.673530i	−0.213714	+	0.976896i	$0.568556\pi$
$654$	23.7419	+	4.19311i	0.928382	+	0.163964i
$655$	1.20436	+	0.695339i	0.0470584	+	0.0271692i
$656$	−0.970369	−	1.68073i	−0.0378866	−	0.0656214i
$657$	22.2645	+	26.5636i	0.868621	+	1.03635i
$658$	7.28637	−	15.6084i	0.284052	−	0.608480i
$659$	−19.8519			−0.773320			−0.386660	−	0.922222i	$-0.626371\pi$
$659$	−19.8519			−0.773320			−0.386660	+	0.922222i	$0.626371\pi$
$660$	8.04335	−	4.47149i	0.313087	−	0.174052i
$661$	6.37648	−	11.0444i	0.248016	−	0.429577i	−0.714959	−	0.699166i	$-0.753555\pi$
$661$	6.37648	−	11.0444i	0.248016	−	0.429577i	0.962975	+	0.269590i	$0.0868880\pi$
$662$	0.110394	−	0.191209i	0.00429060	−	0.00743153i
$663$	−8.04241	+	9.57919i	−0.312341	+	0.372025i
$664$	7.92000			0.307356
$665$	10.0437	+	4.68864i	0.389479	+	0.181818i
$666$	−3.00515	+	2.51879i	−0.116447	+	0.0976011i
$667$	−0.454691	+	0.262516i	−0.0176057	+	0.0101647i
$668$	−1.14541	+	1.98390i	−0.0443172	+	0.0767596i
$669$	6.00419	−	33.9965i	0.232136	−	1.31438i
$670$	−20.2616	+	11.6980i	−0.782772	+	0.451934i
$671$	3.40122	−	8.90066i	0.131303	−	0.343606i
$672$	−2.63108	+	3.75199i	−0.101496	+	0.144736i
$673$			29.4006i			1.13331i	0.823955	+	0.566655i	$0.191763\pi$
$673$			29.4006i			1.13331i	−0.823955	+	0.566655i	$0.808237\pi$
$674$	−18.5329	+	10.7000i	−0.713861	+	0.412148i
$675$	−6.31372	−	10.9567i	−0.243015	−	0.421722i
$676$	−2.12416	+	3.67915i	−0.0816985	+	0.141506i
$677$	−10.4931	−	18.1746i	−0.403283	−	0.698507i	0.590837	−	0.806791i	$-0.298798\pi$
$677$	−10.4931	−	18.1746i	−0.403283	−	0.698507i	−0.994120	+	0.108284i	$0.965464\pi$
$678$	2.03197	+	5.58759i	0.0780372	+	0.214590i
$679$	3.79627	+	43.6039i	0.145687	+	1.67337i
$680$		−	3.91046i		−	0.149959i
$681$	8.90510	+	7.47647i	0.341244	+	0.286499i
$682$	14.8038	−	12.0249i	0.566865	−	0.460458i
$683$	−10.1814	−	5.87823i	−0.389580	−	0.224924i	0.292398	−	0.956297i	$-0.405547\pi$
$683$	−10.1814	−	5.87823i	−0.389580	−	0.224924i	−0.681978	+	0.731372i	$0.738880\pi$
$684$	−2.68739	+	7.37084i	−0.102755	+	0.281831i
$685$	18.0582			0.689967
$686$	−13.1124	+	13.0792i	−0.500634	+	0.499365i
$687$	−12.1779	+	4.42857i	−0.464615	+	0.168961i
$688$	−2.09831	+	1.21146i	−0.0799973	+	0.0461865i
$689$	15.5021	−	26.8505i	0.590585	−	1.02292i
$690$	−0.265076	+	1.50090i	−0.0100913	+	0.0571381i
$691$	7.95293	+	13.7749i	0.302544	+	0.524021i	0.976711	−	0.214557i	$-0.0688308\pi$
$691$	7.95293	+	13.7749i	0.302544	+	0.524021i	−0.674168	+	0.738578i	$0.735497\pi$
$692$	−22.9988			−0.874284
$693$	10.7202	+	24.0433i	0.407225	+	0.913328i
$694$	−8.04185			−0.305264
$695$	−0.186108	−	0.322348i	−0.00705947	−	0.0122274i
$696$	0.287936	−	1.63033i	0.0109142	−	0.0617974i
$697$	−2.36868	+	4.10267i	−0.0897202	+	0.155400i
$698$	7.10158	−	4.10010i	0.268799	−	0.155191i
$699$	−32.6695	+	11.8805i	−1.23567	+	0.449361i
$700$	5.27594	−	3.69093i	0.199412	−	0.139504i
$701$	28.9214			1.09235			0.546174	−	0.837672i	$-0.316084\pi$
$701$	28.9214			1.09235			0.546174	+	0.837672i	$0.316084\pi$
$702$	−0.0127537	+	15.3719i	−0.000481357	+	0.580175i
$703$	−2.96018	−	1.70906i	−0.111645	−	0.0644584i
$704$	−2.57434	+	2.09111i	−0.0970243	+	0.0788117i
$705$	13.8354	+	11.6158i	0.521072	+	0.437477i
$706$			1.09858i			0.0413456i
$707$	−34.8704	−	16.2783i	−1.31144	−	0.612209i
$708$	7.78345	+	21.4033i	0.292520	+	0.804384i
$709$	13.6527	+	23.6472i	0.512738	+	0.888089i	0.999891	+	0.0147720i	$0.00470226\pi$
$709$	13.6527	+	23.6472i	0.512738	+	0.888089i	−0.487152	+	0.873317i	$0.661964\pi$
$710$	−1.90497	+	3.29951i	−0.0714924	+	0.123828i
$711$	39.4210	−	6.92851i	1.47840	−	0.259839i
$712$	−5.89340	+	3.40256i	−0.220865	+	0.127516i
$713$			3.15869i			0.118294i
$714$	11.1429	+	0.982729i	0.417011	+	0.0367777i
$715$	14.6826	+	5.61069i	0.549098	+	0.209828i
$716$	−13.2263	+	7.63621i	−0.494290	+	0.285379i
$717$	−7.46171	+	42.2491i	−0.278663	+	1.57782i
$718$	17.8091	−	30.8462i	0.664629	−	1.15117i
$719$	25.2056	−	14.5524i	0.940009	−	0.542714i	0.0500459	−	0.998747i	$-0.484063\pi$
$719$	25.2056	−	14.5524i	0.940009	−	0.542714i	0.889963	+	0.456032i	$0.150730\pi$
$720$	−3.08717	−	3.68328i	−0.115052	−	0.137268i
$721$	−6.04672	+	4.23015i	−0.225191	+	0.157539i
$722$	12.1610			0.452584
$723$	18.3385	−	21.8428i	0.682018	−	0.812341i
$724$	−7.96601	+	13.7975i	−0.296055	+	0.512782i
$725$	−1.16309	+	2.01452i	−0.0431959	+	0.0748176i
$726$	2.70339	+	18.8598i	0.100332	+	0.699952i
$727$	−22.2294			−0.824443			−0.412222	−	0.911084i	$-0.635247\pi$
$727$	−22.2294			−0.824443			−0.412222	+	0.911084i	$0.635247\pi$
$728$	−7.79749	+	0.678869i	−0.288994	+	0.0251606i
$729$	−13.4612	−	23.4051i	−0.498562	−	0.866854i
$730$	−9.25420	−	16.0287i	−0.342513	−	0.593251i
$731$	5.12199	+	2.95718i	0.189444	+	0.109375i
$732$	−4.90020	−	0.865435i	−0.181117	−	0.0319874i
$733$	−31.5321	+	18.2050i	−1.16466	+	0.672419i	−0.952417	−	0.304798i	$-0.901411\pi$
$733$	−31.5321	+	18.2050i	−1.16466	+	0.672419i	−0.212246	+	0.977216i	$0.568078\pi$
$734$	−11.8539			−0.437536
$735$	−9.69262	−	16.8317i	−0.357518	−	0.620847i
$736$		−	0.549290i		−	0.0202471i
$737$	−7.64955	−	47.8295i	−0.281775	−	1.76182i
$738$	1.00785	+	5.73432i	0.0370993	+	0.211083i
$739$	−39.1857	−	22.6239i	−1.44147	−	0.832234i	−0.443523	−	0.896263i	$-0.646271\pi$
$739$	−39.1857	−	22.6239i	−1.44147	−	0.832234i	−0.997948	+	0.0640296i	$0.979605\pi$
$740$	1.81334	−	1.04693i	0.0666595	−	0.0384859i
$741$	−12.5931	+	4.57958i	−0.462620	+	0.168235i
$742$	−27.6239	+	2.40501i	−1.01411	+	0.0882906i
$743$	−45.5372			−1.67060			−0.835299	−	0.549795i	$-0.814706\pi$
$743$	−45.5372			−1.67060			−0.835299	+	0.549795i	$0.814706\pi$
$744$	−7.62814	−	6.40437i	−0.279661	−	0.234796i
$745$	11.9801	+	6.91673i	0.438918	+	0.253409i
$746$	−5.14208	−	2.96878i	−0.188265	−	0.108695i
$747$	−22.3226	−	8.13875i	−0.816741	−	0.297781i
$748$	7.56256	+	2.88989i	0.276515	+	0.105665i
$749$	−9.31103	+	6.51379i	−0.340218	+	0.238009i
$750$	7.04924	+	19.3843i	0.257402	+	0.707815i
$751$	26.4183	+	45.7579i	0.964019	+	1.66973i	0.712229	+	0.701947i	$0.247686\pi$
$751$	26.4183	+	45.7579i	0.964019	+	1.66973i	0.251790	+	0.967782i	$0.418981\pi$
$752$	−5.63833	−	3.25529i	−0.205609	−	0.118708i
$753$	48.5254	+	8.57017i	1.76836	+	0.312314i
$754$	2.44884	−	1.41384i	0.0891815	−	0.0514890i
$755$	−28.3354			−1.03123
$756$	11.2713	−	7.87126i	0.409935	−	0.286275i
$757$	−4.44272			−0.161473			−0.0807366	−	0.996735i	$-0.525727\pi$
$757$	−4.44272			−0.161473			−0.0807366	+	0.996735i	$0.525727\pi$
$758$	6.66954	+	11.5520i	0.242249	+	0.419587i
$759$	−2.70673	−	1.62183i	−0.0982482	−	0.0588686i
$760$	2.09472	−	3.62816i	0.0759834	−	0.131607i
$761$	9.62701	+	16.6745i	0.348979	+	0.604449i	0.986068	−	0.166341i	$-0.0531951\pi$
$761$	9.62701	+	16.6745i	0.348979	+	0.604449i	−0.637089	+	0.770790i	$0.719862\pi$
$762$	6.83968	+	18.8081i	0.247776	+	0.681344i
$763$	15.5781	−	33.3706i	0.563967	−	1.20810i
$764$			20.6147i			0.745815i
$765$	−4.01846	+	11.0217i	−0.145288	+	0.398489i
$766$	−2.38792	−	1.37867i	−0.0862790	−	0.0498132i
$767$	−19.4494	+	33.6873i	−0.702276	+	1.21638i
$768$	1.32652	+	1.11371i	0.0478667	+	0.0401875i
$769$			20.9702i			0.756206i	0.925763	+	0.378103i	$0.123424\pi$
$769$			20.9702i			0.756206i	−0.925763	+	0.378103i	$0.876576\pi$
$770$	−3.41562	−	13.6361i	−0.123090	−	0.491410i
$771$	−17.2195	−	47.3510i	−0.620146	−	1.70530i
$772$	−11.0514	+	6.38055i	−0.397750	+	0.229641i
$773$	−29.7496	−	17.1759i	−1.07002	−	0.617775i	−0.141831	−	0.989891i	$-0.545299\pi$
$773$	−29.7496	−	17.1759i	−1.07002	−	0.617775i	−0.928186	+	0.372116i	$0.878632\pi$
$774$	7.15903	−	1.25825i	0.257326	−	0.0452267i
$775$	6.99734	+	12.1197i	0.251352	+	0.435354i
$776$	16.5431			0.593862
$777$	2.52752	+	5.43021i	0.0906744	+	0.194808i
$778$			5.13107i			0.183958i
$779$	−4.39537	+	2.53767i	−0.157480	+	0.0909214i
$780$	1.42763	−	8.08341i	0.0511173	−	0.289433i
$781$	−4.97322	−	6.12248i	−0.177956	−	0.219080i
$782$	−1.16119	+	0.670411i	−0.0415239	+	0.0239738i
$783$	−2.48691	+	4.29921i	−0.0888748	+	0.153641i
$784$	4.49498	+	5.36612i	0.160535	+	0.191647i
$785$		−	8.44498i		−	0.301414i
$786$	1.15155	+	0.966807i	0.0410744	+	0.0344849i
$787$	5.34606	+	3.08655i	0.190567	+	0.110024i	0.592248	−	0.805756i	$-0.298241\pi$
$787$	5.34606	+	3.08655i	0.190567	+	0.110024i	−0.401681	+	0.915780i	$0.631574\pi$
$788$	7.10500	−	12.3062i	0.253105	−	0.438391i
$789$	−18.1429	−	15.2322i	−0.645904	−	0.542282i
$790$	−21.3733			−0.760426
$791$	9.04782	−	0.787725i	0.321703	−	0.0280083i
$792$	9.40468	−	3.24837i	0.334181	−	0.115426i
$793$	−4.24951	−	7.36036i	−0.150904	−	0.261374i
$794$	−12.8199	+	22.2048i	−0.454962	+	0.788018i
$795$	5.05761	−	28.6368i	0.179375	−	1.01564i
$796$	−2.43346	−	4.21488i	−0.0862517	−	0.149392i
$797$			27.7159i			0.981746i	0.871231	+	0.490873i	$0.163322\pi$
$797$			27.7159i			0.981746i	−0.871231	+	0.490873i	$0.836678\pi$
$798$	9.81203	+	6.88069i	0.347342	+	0.243574i
$799$			15.8924i			0.562233i
$800$	−1.21682	−	2.10760i	−0.0430212	−	0.0745150i
$801$	20.1071	−	3.53397i	0.710451	−	0.124867i
$802$	−1.25322	−	0.723550i	−0.0442529	−	0.0255494i
$803$	37.8375	−	6.05149i	1.33526	−	0.213553i
$804$	−23.7725	+	8.64502i	−0.838390	+	0.304887i
$805$	2.10959	+	0.984806i	0.0743534	+	0.0347098i
$806$		−	17.0118i		−	0.599216i
$807$	−33.2320	+	39.5821i	−1.16982	+	1.39336i
$808$	−7.27257	+	12.5965i	−0.255848	+	0.443142i
$809$	−13.6017	+	23.5589i	−0.478211	+	0.828286i	−0.999688	−	0.0249794i	$-0.992048\pi$
$809$	−13.6017	+	23.5589i	−0.478211	+	0.828286i	0.521477	+	0.853265i	$0.325381\pi$
$810$	4.91621	+	13.5538i	0.172738	+	0.476232i
$811$		−	25.8669i		−	0.908310i	−0.890923	−	0.454155i	$-0.849941\pi$
$811$		−	25.8669i		−	0.908310i	0.890923	−	0.454155i	$-0.150059\pi$
$812$	−2.29152	−	1.06973i	−0.0804165	−	0.0375402i
$813$	−7.24447	−	19.9212i	−0.254075	−	0.698666i
$814$	0.684607	+	4.28057i	0.0239955	+	0.150034i
$815$	10.9998	+	6.35076i	0.385308	+	0.222458i
$816$	0.735328	−	4.16352i	0.0257416	−	0.145752i
$817$	3.16816	+	5.48741i	0.110840	+	0.191980i
$818$			10.0389i			0.351002i
$819$	22.6749	+	6.09946i	0.792326	+	0.213132i
$820$		−	3.10903i		−	0.108572i
$821$	3.20923	+	5.55856i	0.112003	+	0.193995i	0.916578	−	0.399856i	$-0.130940\pi$
$821$	3.20923	+	5.55856i	0.112003	+	0.193995i	−0.804575	+	0.593851i	$0.797607\pi$
$822$	19.2268	+	3.39568i	0.670611	+	0.118438i
$823$	5.02394	−	8.70171i	0.175123	−	0.303323i	−0.765081	−	0.643935i	$-0.777301\pi$
$823$	5.02394	−	8.70171i	0.175123	−	0.303323i	0.940204	+	0.340612i	$0.110634\pi$
$824$	1.39459	+	2.41551i	0.0485829	+	0.0841481i
$825$	−13.9784	−	0.226734i	−0.486666	−	0.00789387i
$826$	34.6577	−	3.01738i	1.20589	−	0.104988i
$827$	49.0759			1.70654			0.853269	−	0.521471i	$-0.174617\pi$
$827$	49.0759			1.70654			0.853269	+	0.521471i	$0.174617\pi$
$828$	−0.564461	+	1.54818i	−0.0196164	+	0.0538029i
$829$	−1.55350	+	2.69074i	−0.0539553	+	0.0934534i	−0.891742	−	0.452545i	$-0.850516\pi$
$829$	−1.55350	+	2.69074i	−0.0539553	+	0.0934534i	0.837786	+	0.545998i	$0.183850\pi$
$830$	10.9879	+	6.34385i	0.381395	+	0.220198i
$831$	23.3731	−	27.8393i	0.810803	−	0.965734i
$832$			2.95832i			0.102561i
$833$	5.85770	−	16.0516i	0.202957	−	0.556156i
$834$	−0.137537	−	0.378205i	−0.00476251	−	0.0130962i
$835$	−3.17818	+	1.83492i	−0.109986	+	0.0635002i
$836$	5.46858	+	6.73231i	0.189135	+	0.232842i
$837$	14.9187	+	25.8896i	0.515667	+	0.894876i
$838$	16.9799	−	9.80332i	0.586559	−	0.338650i
$839$		−	11.8648i		−	0.409620i	−0.978802	−	0.204810i	$-0.934342\pi$
$839$		−	11.8648i		−	0.409620i	0.978802	−	0.204810i	$-0.0656576\pi$
$840$	−6.65557	+	3.09787i	−0.229639	+	0.106887i
$841$	−28.0864			−0.968496
$842$	12.1696	+	21.0784i	0.419393	+	0.726410i
$843$	−9.41868	+	53.3297i	−0.324396	+	1.83677i
$844$	−22.2199	−	12.8287i	−0.764841	−	0.441581i
$845$	−5.89395	+	3.40287i	−0.202758	+	0.117062i
$846$	12.5465	+	14.9691i	0.431358	+	0.514650i
$847$	28.8955	+	3.47171i	0.992860	+	0.119289i
$848$			10.4804i			0.359897i
$849$	27.2531	−	32.4608i	0.935325	−	1.11405i
$850$	−2.97028	+	5.14467i	−0.101880	+	0.176461i
$851$	−0.621758	−	0.358972i	−0.0213136	−	0.0123054i
$852$	−2.64869	+	3.15482i	−0.0907428	+	0.108082i
$853$		−	0.133149i		−	0.00455892i	−0.999997	−	0.00227946i	$-0.999274\pi$
$853$		−	0.133149i		−	0.00455892i	0.999997	−	0.00227946i	$-0.000725576\pi$
$854$	−3.21524	+	6.88751i	−0.110023	+	0.235686i
$855$	−9.63235	+	8.07343i	−0.329420	+	0.276105i
$856$	2.14746	+	3.71952i	0.0733988	+	0.127130i
$857$	19.1696	−	33.2028i	0.654822	−	1.13419i	−0.327116	−	0.944984i	$-0.606077\pi$
$857$	19.1696	−	33.2028i	0.654822	−	1.13419i	0.981938	−	0.189201i	$-0.0605898\pi$
$858$	14.5777	+	8.73471i	0.497675	+	0.298198i
$859$	−7.98719	−	13.8342i	−0.272519	−	0.472018i	0.696987	−	0.717084i	$-0.254524\pi$
$859$	−7.98719	−	13.8342i	−0.272519	−	0.472018i	−0.969506	+	0.245066i	$0.921190\pi$
$860$	−3.88148			−0.132357
$861$	8.85919	+	0.781324i	0.301921	+	0.0266275i
$862$	−22.0628			−0.751460
$863$	37.1255	−	21.4344i	1.26377	−	0.729637i	0.289967	−	0.957037i	$-0.406356\pi$
$863$	37.1255	−	21.4344i	1.26377	−	0.729637i	0.973801	+	0.227400i	$0.0730224\pi$
$864$	−2.59434	−	4.50215i	−0.0882613	−	0.153166i
$865$	−31.9076	−	18.4219i	−1.08489	−	0.626362i
$866$	13.7984	+	23.8995i	0.468888	+	0.812139i
$867$	17.9729	−	6.53596i	0.610390	−	0.221973i
$868$	−12.4666	+	8.72133i	−0.423143	+	0.296021i
$869$	15.7952	−	41.3344i	0.535815	−	1.40217i
$870$	1.70535	−	2.03122i	0.0578168	−	0.0688647i
$871$	−37.4163	−	21.6023i	−1.26780	−	0.731966i
$872$	−12.0547	−	6.95977i	−0.408223	−	0.235688i
$873$	−46.6268	−	17.0000i	−1.57808	−	0.575363i
$874$	−1.43648			−0.0485896
$875$	31.3884	−	2.73275i	1.06112	−	0.0923839i
$876$	−6.83901	−	18.8062i	−0.231069	−	0.635403i
$877$	31.4695	−	18.1689i	1.06265	−	0.613521i	0.136485	−	0.990642i	$-0.456419\pi$
$877$	31.4695	−	18.1689i	1.06265	−	0.613521i	0.926164	+	0.377121i	$0.123086\pi$
$878$	15.4336	+	8.91061i	0.520860	+	0.300719i
$879$	2.84035	−	16.0824i	0.0958027	−	0.542447i
$880$	−5.24650	+	0.839092i	−0.176860	+	0.0282858i
$881$			14.6701i			0.494247i	0.968984	+	0.247123i	$0.0794853\pi$
$881$			14.6701i			0.494247i	−0.968984	+	0.247123i	$0.920515\pi$
$882$	−7.15481	−	19.7436i	−0.240915	−	0.664801i
$883$	3.13019			0.105339			0.0526697	−	0.998612i	$-0.483227\pi$
$883$	3.13019			0.105339			0.0526697	+	0.998612i	$0.483227\pi$
$884$	6.25383	−	3.61065i	0.210339	−	0.121439i
$885$	−6.34541	+	35.9285i	−0.213299	+	1.20772i
$886$	1.86006	+	1.07391i	0.0624901	+	0.0360787i
$887$	−9.92929	−	17.1980i	−0.333393	−	0.577454i	0.649782	−	0.760121i	$-0.274860\pi$
$887$	−9.92929	−	17.1980i	−0.333393	−	0.577454i	−0.983175	+	0.182667i	$0.941527\pi$
$888$	2.12755	−	0.773698i	0.0713959	−	0.0259636i
$889$	30.4553	−	2.65151i	1.02144	−	0.0889289i
$890$	−10.9017			−0.365425
$891$	−29.8453	−	0.508869i	−0.999855	−	0.0170477i
$892$	−9.96583	+	17.2613i	−0.333681	+	0.577952i
$893$	−8.51310	+	14.7451i	−0.284880	+	0.493427i
$894$	11.4548	+	9.61709i	0.383105	+	0.321644i
$895$	−24.4662			−0.817814
$896$	2.16791	−	1.51662i	0.0724249	−	0.0506668i
$897$	−2.64507	+	0.961899i	−0.0883163	+	0.0321169i
$898$	13.8896	−	8.01914i	0.463500	−	0.267602i
$899$	2.74827	−	4.76014i	0.0916599	−	0.158760i
$900$	1.26382	+	7.19073i	0.0421273	+	0.239691i
$901$	22.1552	−	12.7913i	0.738097	−	0.426141i
$902$	6.01266	+	2.29763i	0.200200	+	0.0765025i
$903$	0.975446	−	11.0603i	0.0324608	−	0.368063i
$904$		−	3.43269i		−	0.114170i
$905$	−22.1034	+	12.7614i	−0.734743	+	0.424204i
$906$	−30.1691	−	5.32824i	−1.00230	−	0.177019i
$907$	1.16681	−	2.02098i	0.0387434	−	0.0671056i	−0.846003	−	0.533177i	$-0.820998\pi$
$907$	1.16681	−	2.02098i	0.0387434	−	0.0671056i	0.884747	+	0.466072i	$0.154331\pi$
$908$	−3.35657	−	5.81374i	−0.111392	−	0.192936i
$909$	33.4422	−	28.0298i	1.10921	−	0.929691i
$910$	−11.3617	−	5.30389i	−0.376636	−	0.175822i
$911$		−	11.6247i		−	0.385143i	−0.981283	−	0.192571i	$-0.938317\pi$
$911$		−	11.6247i		−	0.385143i	0.981283	−	0.192571i	$-0.0616827\pi$
$912$	2.91252	−	3.46906i	0.0964432	−	0.114872i
$913$	−20.3888	+	16.5616i	−0.674771	+	0.548109i
$914$	4.44457	+	2.56607i	0.147013	+	0.0848781i
$915$	−6.10513	−	5.12569i	−0.201829	−	0.169450i
$916$	7.48138			0.247192
$917$	1.88196	−	1.31658i	0.0621479	−	0.0434772i
$918$	−6.35104	+	10.9793i	−0.209616	+	0.362370i
$919$	−6.87450	+	3.96900i	−0.226769	+	0.130925i	−0.609081	−	0.793108i	$-0.708461\pi$
$919$	−6.87450	+	3.96900i	−0.226769	+	0.130925i	0.382312	+	0.924033i	$0.375128\pi$
$920$	0.439977	−	0.762062i	0.0145056	−	0.0251244i
$921$	−50.0822	−	8.84512i	−1.65026	−	0.291457i
$922$	−5.38862	−	9.33337i	−0.177465	−	0.307378i
$923$	−7.03568			−0.231582
$924$	−1.07251	−	15.1608i	−0.0352829	−	0.498754i
$925$	−3.18088			−0.104587
$926$	−15.7467	−	27.2741i	−0.517469	−	0.896282i
$927$	−1.44845	−	8.24124i	−0.0475734	−	0.270678i
$928$	−0.477919	+	0.827780i	−0.0156885	+	0.0271732i
$929$	48.8660	−	28.2128i	1.60324	−	0.925631i	0.612406	−	0.790543i	$-0.290202\pi$
$929$	48.8660	−	28.2128i	1.60324	−	0.925631i	0.990834	−	0.135088i	$-0.0431317\pi$
$930$	−5.45312	−	14.9952i	−0.178815	−	0.491713i
$931$	14.0332	−	11.7551i	0.459921	−	0.385257i
$932$	20.0702			0.657421
$933$	26.6259	−	31.7137i	0.871692	−	1.03826i
$934$	1.47963	+	0.854267i	0.0484151	+	0.0279525i
$935$	8.17720	+	10.0669i	0.267423	+	0.329222i
$936$	3.04003	−	8.33806i	0.0993665	−	0.272538i
$937$		−	9.76744i		−	0.319088i	−0.987191	−	0.159544i	$-0.948998\pi$
$937$		−	9.76744i		−	0.319088i	0.987191	−	0.159544i	$-0.0510025\pi$
$938$	3.35138	+	38.4940i	0.109427	+	1.25687i
$939$	5.31091	−	1.93135i	0.173315	−	0.0630273i
$940$	−5.21493	−	9.03252i	−0.170092	−	0.294608i
$941$	14.8017	−	25.6374i	0.482523	−	0.835754i	−0.517276	−	0.855819i	$-0.673054\pi$
$941$	14.8017	−	25.6374i	0.482523	−	0.835754i	0.999799	+	0.0200646i	$0.00638720\pi$
$942$	1.58801	−	8.99149i	0.0517400	−	0.292959i
$943$	−0.923207	+	0.533014i	−0.0300638	+	0.0173573i
$944$		−	13.1489i		−	0.427961i
$945$	21.9422	−	1.89200i	0.713780	−	0.0615468i
$946$	2.86848	−	7.50651i	0.0932622	−	0.244058i
$947$	23.7548	−	13.7149i	0.771929	−	0.445673i	−0.0616334	−	0.998099i	$-0.519631\pi$
$947$	23.7548	−	13.7149i	0.771929	−	0.445673i	0.833562	+	0.552426i	$0.186298\pi$
$948$	−22.7564	−	4.01906i	−0.739093	−	0.130533i
$949$	17.0894	−	29.5997i	0.554745	−	0.960847i
$950$	−5.51171	+	3.18218i	−0.178823	+	0.103244i
$951$	10.5572	+	29.0307i	0.342341	+	0.941385i
$952$	−5.85206	−	2.73187i	−0.189666	−	0.0885405i
$953$	−0.620095			−0.0200868			−0.0100434	−	0.999950i	$-0.503197\pi$
$953$	−0.620095			−0.0200868			−0.0100434	+	0.999950i	$0.503197\pi$
$954$	10.7698	−	29.5390i	0.348686	−	0.956360i
$955$	−16.5122	+	28.6000i	−0.534323	+	0.925475i
$956$	12.3850	−	21.4515i	0.400560	−	0.693791i
$957$	2.66795	+	4.79913i	0.0862427	+	0.155134i
$958$	−25.7280			−0.831234
$959$	12.6156	−	27.0243i	0.407378	−	0.872661i
$960$	0.948288	+	2.60764i	0.0306059	+	0.0841613i
$961$	−1.03409	−	1.79109i	−0.0333577	−	0.0577772i
$962$	3.34862	+	1.93333i	0.107964	+	0.0623329i
$963$	−2.23040	−	12.6903i	−0.0718736	−	0.408938i
$964$	−14.2602	+	8.23310i	−0.459289	+	0.265170i
$965$	−20.4431			−0.658086
$966$	2.06093	+	1.44523i	0.0663093	+	0.0464994i
$967$		−	30.9991i		−	0.996864i	−0.866929	−	0.498432i	$-0.833909\pi$
$967$		−	30.9991i		−	0.996864i	0.866929	−	0.498432i	$-0.166091\pi$
$968$	2.25450	−	10.7665i	0.0724625	−	0.346048i
$969$	−10.8882	−	1.92300i	−0.349781	−	0.0617755i
$970$	22.9512	+	13.2509i	0.736918	+	0.425460i
$971$	−14.4960	+	8.36927i	−0.465199	+	0.268583i	−0.714228	−	0.699913i	$-0.753222\pi$
$971$	−14.4960	+	8.36927i	−0.465199	+	0.268583i	0.249029	+	0.968496i	$0.419889\pi$
$972$	2.68568	+	15.3554i	0.0861431	+	0.492523i
$973$	−0.612415	+	0.0533184i	−0.0196331	+	0.00170931i
$974$	−11.8864			−0.380865
$975$	−8.01816	+	9.55031i	−0.256787	+	0.305855i
$976$	2.48802	+	1.43646i	0.0796395	+	0.0459799i
$977$	8.50414	+	4.90987i	0.272072	+	0.157081i	0.629829	−	0.776734i	$-0.283125\pi$
$977$	8.50414	+	4.90987i	0.272072	+	0.157081i	−0.357757	+	0.933815i	$0.616458\pi$
$978$	10.5175	+	8.83017i	0.336312	+	0.282358i
$979$	8.05652	−	21.0831i	0.257488	−	0.673819i
$980$	1.93793	+	11.0452i	0.0619048	+	0.352825i
$981$	26.8242	+	32.0038i	0.856431	+	1.02180i
$982$	−2.92910	−	5.07335i	−0.0934713	−	0.161897i
$983$	−43.4532	−	25.0877i	−1.38594	−	0.800174i	−0.393088	−	0.919501i	$-0.628593\pi$
$983$	−43.4532	−	25.0877i	−1.38594	−	0.800174i	−0.992855	+	0.119327i	$0.961926\pi$
$984$	0.584626	−	3.31023i	0.0186372	−	0.105526i
$985$	19.7144	−	11.3821i	0.628152	−	0.362664i
$986$	2.33321			0.0743045
$987$	27.0487	−	12.5900i	0.860971	−	0.400744i
$988$	7.73648			0.246130
$989$	0.665442	+	1.15258i	0.0211598	+	0.0366499i
$990$	15.6496	+	3.02642i	0.497377	+	0.0961859i
$991$	−6.24721	+	10.8205i	−0.198449	+	0.343724i	−0.948026	−	0.318194i	$-0.896924\pi$
$991$	−6.24721	+	10.8205i	−0.198449	+	0.343724i	0.749577	+	0.661918i	$0.230257\pi$
$992$	2.87525	+	4.98007i	0.0912892	+	0.158117i
$993$	0.359391	−	0.130695i	0.0114049	−	0.00414748i
$994$	3.60694	+	5.15588i	0.114405	+	0.163535i
$995$		−	7.79673i		−	0.247173i
$996$	10.5060	+	8.82056i	0.332896	+	0.279490i
$997$	−14.6628	−	8.46554i	−0.464374	−	0.268106i	0.249508	−	0.968373i	$-0.419731\pi$
$997$	−14.6628	−	8.46554i	−0.464374	−	0.268106i	−0.713882	+	0.700266i	$0.753065\pi$
$998$	17.7986	−	30.8281i	0.563405	−	0.975846i
$999$	−6.79159	−	0.00563481i	−0.214876	−	0.000178278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.n.e.263.7	yes	24
3.2	odd	2		462.2.n.f.263.10	yes	24
7.2	even	3	inner	462.2.n.e.65.10	yes	24
11.10	odd	2		462.2.n.f.263.7	yes	24
21.2	odd	6		462.2.n.f.65.7	yes	24
33.32	even	2	inner	462.2.n.e.263.10	yes	24
77.65	odd	6		462.2.n.f.65.10	yes	24
231.65	even	6	inner	462.2.n.e.65.7	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.n.e.65.7	✓	24	231.65	even	6	inner
462.2.n.e.65.10	yes	24	7.2	even	3	inner
462.2.n.e.263.7	yes	24	1.1	even	1	trivial
462.2.n.e.263.10	yes	24	33.32	even	2	inner
462.2.n.f.65.7	yes	24	21.2	odd	6
462.2.n.f.65.10	yes	24	77.65	odd	6
462.2.n.f.263.7	yes	24	11.10	odd	2
462.2.n.f.263.10	yes	24	3.2	odd	2

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.301239 - 1.70565i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.38736 + 0.800992i) q^{5} +(-1.62776 + 0.591946i) q^{6} +(0.229478 + 2.63578i) q^{7} +1.00000 q^{8} +(-2.81851 - 1.02762i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.301239 - 1.70565i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.38736 + 0.800992i) q^{5} +(-1.62776 + 0.591946i) q^{6} +(0.229478 + 2.63578i) q^{7} +1.00000 q^{8} +(-2.81851 - 1.02762i) q^{9} +(1.38736 + 0.800992i) q^{10} +(-2.57434 + 2.09111i) q^{11} +(1.32652 + 1.11371i) q^{12} +2.95832i q^{13} +(2.16791 - 1.51662i) q^{14} +(0.948288 + 2.60764i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.22050 + 2.11398i) q^{17} +(0.519310 + 2.95471i) q^{18} +(-2.26479 + 1.30758i) q^{19} -1.60198i q^{20} +(4.56486 + 0.402591i) q^{21} +(3.09813 + 1.18389i) q^{22} +(-0.475699 + 0.274645i) q^{23} +(0.301239 - 1.70565i) q^{24} +(-1.21682 + 2.10760i) q^{25} +(2.56198 - 1.47916i) q^{26} +(-2.60181 + 4.49784i) q^{27} +(-2.39739 - 1.11916i) q^{28} +0.955838 q^{29} +(1.78414 - 2.12506i) q^{30} +(2.87525 - 4.98007i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.79122 + 5.02087i) q^{33} +2.44101 q^{34} +(-2.42961 - 3.47296i) q^{35} +(2.29920 - 1.92709i) q^{36} +(0.653521 + 1.13193i) q^{37} +(2.26479 + 1.30758i) q^{38} +(5.04588 + 0.891163i) q^{39} +(-1.38736 + 0.800992i) q^{40} +1.94074 q^{41} +(-1.93377 - 4.15458i) q^{42} -2.42292i q^{43} +(-0.523783 - 3.27500i) q^{44} +(4.73340 - 0.831927i) q^{45} +(0.475699 + 0.274645i) q^{46} +(5.63833 - 3.25529i) q^{47} +(-1.62776 + 0.591946i) q^{48} +(-6.89468 + 1.20970i) q^{49} +2.43365 q^{50} +(3.23805 + 2.71857i) q^{51} +(-2.56198 - 1.47916i) q^{52} +(-9.07625 - 5.24018i) q^{53} +(5.19615 + 0.00431112i) q^{54} +(1.89658 - 4.96315i) q^{55} +(0.229478 + 2.63578i) q^{56} +(1.54803 + 4.25684i) q^{57} +(-0.477919 - 0.827780i) q^{58} +(11.3873 + 6.57446i) q^{59} +(-2.73243 - 0.482580i) q^{60} +(-2.48802 + 1.43646i) q^{61} -5.75049 q^{62} +(2.06180 - 7.66479i) q^{63} +1.00000 q^{64} +(-2.36959 - 4.10426i) q^{65} +(2.95259 - 4.92770i) q^{66} +(-7.30221 + 12.6478i) q^{67} +(-1.22050 - 2.11398i) q^{68} +(0.325150 + 0.894111i) q^{69} +(-1.79287 + 3.84058i) q^{70} +2.37827i q^{71} +(-2.81851 - 1.02762i) q^{72} +(-10.0056 - 5.77671i) q^{73} +(0.653521 - 1.13193i) q^{74} +(3.22828 + 2.71037i) q^{75} -2.61516i q^{76} +(-6.10247 - 6.30555i) q^{77} +(-1.75117 - 4.81544i) q^{78} +(-11.5543 + 6.67087i) q^{79} +(1.38736 + 0.800992i) q^{80} +(6.88800 + 5.79271i) q^{81} +(-0.970369 - 1.68073i) q^{82} +7.92000 q^{83} +(-2.63108 + 3.75199i) q^{84} -3.91046i q^{85} +(-2.09831 + 1.21146i) q^{86} +(0.287936 - 1.63033i) q^{87} +(-2.57434 + 2.09111i) q^{88} +(-5.89340 + 3.40256i) q^{89} +(-3.08717 - 3.68328i) q^{90} +(-7.79749 + 0.678869i) q^{91} -0.549290i q^{92} +(-7.62814 - 6.40437i) q^{93} +(-5.63833 - 3.25529i) q^{94} +(2.09472 - 3.62816i) q^{95} +(1.32652 + 1.11371i) q^{96} +16.5431 q^{97} +(4.49498 + 5.36612i) q^{98} +(9.40468 - 3.24837i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 8 q^{9}+O(q^{10}) \) 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8 - 8 * q^9	\( 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 8 q^{9} - 4 q^{11} + 4 q^{15} - 12 q^{16} + 4 q^{17} - 8 q^{18} + 8 q^{22} + 20 q^{25} - 12 q^{27} + 40 q^{29} - 2 q^{30} - 28 q^{31} - 12 q^{32} + 32 q^{33} - 8 q^{34} - 32 q^{35} + 16 q^{36} - 16 q^{37} - 8 q^{41} + 6 q^{42} - 4 q^{44} - 28 q^{45} - 8 q^{49} - 40 q^{50} - 34 q^{51} + 6 q^{54} + 8 q^{55} + 40 q^{57} - 20 q^{58} - 2 q^{60} + 56 q^{62} - 14 q^{63} + 24 q^{64} - 44 q^{65} + 32 q^{66} + 4 q^{68} - 20 q^{69} + 64 q^{70} - 8 q^{72} - 16 q^{74} - 26 q^{75} + 24 q^{81} + 4 q^{82} + 144 q^{83} - 6 q^{84} + 8 q^{87} - 4 q^{88} + 56 q^{90} - 32 q^{91} - 22 q^{93} - 44 q^{95} + 64 q^{97} - 8 q^{98} - 52 q^{99}+O(q^{100}) \) 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8 - 8 * q^9 - 4 * q^11 + 4 * q^15 - 12 * q^16 + 4 * q^17 - 8 * q^18 + 8 * q^22 + 20 * q^25 - 12 * q^27 + 40 * q^29 - 2 * q^30 - 28 * q^31 - 12 * q^32 + 32 * q^33 - 8 * q^34 - 32 * q^35 + 16 * q^36 - 16 * q^37 - 8 * q^41 + 6 * q^42 - 4 * q^44 - 28 * q^45 - 8 * q^49 - 40 * q^50 - 34 * q^51 + 6 * q^54 + 8 * q^55 + 40 * q^57 - 20 * q^58 - 2 * q^60 + 56 * q^62 - 14 * q^63 + 24 * q^64 - 44 * q^65 + 32 * q^66 + 4 * q^68 - 20 * q^69 + 64 * q^70 - 8 * q^72 - 16 * q^74 - 26 * q^75 + 24 * q^81 + 4 * q^82 + 144 * q^83 - 6 * q^84 + 8 * q^87 - 4 * q^88 + 56 * q^90 - 32 * q^91 - 22 * q^93 - 44 * q^95 + 64 * q^97 - 8 * q^98 - 52 * q^99

Introduction

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