LMFDB - Embedded newform 462.2.n.f.65.7

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			65.7
Character	$\chi$	$=$	462.65
Dual form			462.2.n.f.263.7

$q$-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} +(0.523783 + 3.27500i) 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} +(-5.42824 + 1.87995i) 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} +(2.57434 - 2.09111i) 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} +(-1.08603 + 5.64097i) 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} +(-8.75239 + 0.629038i) 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} +(-0.523783 - 3.27500i) 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} +(-4.84175 - 8.69238i) 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} + 24 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} - 24 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} + 28 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 + 24 * 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 - 24 * 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 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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	0.156597	−	0.987663i	$-0.449948\pi$
$5$	−1.38736	−	0.800992i	−0.620446	−	0.358214i	−0.777042	+	0.629448i	$0.783281\pi$
$6$	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
$11$	0.523783	+	3.27500i	0.157927	+	0.987451i
$11$	0.523783	+	3.27500i	0.157927	+	0.987451i
$12$	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	$-0.0710085\pi$
$17$	1.22050	+	2.11398i	0.296016	+	0.512714i	−0.679205	+	0.733949i	$0.737675\pi$
$18$	−0.519310	+	2.95471i	−0.122403	+	0.696432i
$19$	2.26479	+	1.30758i	0.519579	+	0.299979i	0.736762	−	0.676152i	$-0.236354\pi$
$19$	2.26479	+	1.30758i	0.519579	+	0.299979i	−0.217184	+	0.976131i	$0.569687\pi$
$20$			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	0.449584	−	0.893238i	$-0.351572\pi$
$23$	−0.475699	−	0.274645i	−0.0991901	−	0.0572674i	−0.548774	+	0.835970i	$0.684905\pi$
$24$	−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	$-0.528286\pi$
$29$	−0.955838			−0.177495			−0.0887473	+	0.996054i	$0.528286\pi$
$30$	−1.78414	−	2.12506i	−0.325738	−	0.387982i
$31$	2.87525	+	4.98007i	0.516410	+	0.894448i	0.999818	+	0.0190529i	$0.00606510\pi$
$31$	2.87525	+	4.98007i	0.516410	+	0.894448i	−0.483409	+	0.875395i	$0.660602\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−5.42824	+	1.87995i	−0.944935	+	0.327258i
$34$	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	−0.807294	−	0.590150i	$-0.799069\pi$
$37$	0.653521	−	1.13193i	0.107438	−	0.186088i	0.914732	+	0.404062i	$0.132402\pi$
$38$	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	$-0.548425\pi$
$41$	−1.94074			−0.303092			−0.151546	+	0.988450i	$0.548425\pi$
$42$	−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	$-0.0591462\pi$
$44$	2.57434	−	2.09111i	0.388097	−	0.315247i
$45$	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	0.851256	−	0.524751i	$-0.175842\pi$
$47$	5.63833	+	3.25529i	0.822436	+	0.474833i	−0.0288200	+	0.999585i	$0.509175\pi$
$48$	−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	−0.970454	−	0.241287i	$-0.922430\pi$
$53$	−9.07625	+	5.24018i	−1.24672	+	0.719794i	−0.276266	+	0.961081i	$0.589097\pi$
$54$	−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	0.482697	−	0.875787i	$-0.339657\pi$
$59$	11.3873	−	6.57446i	1.48250	−	0.855922i	0.999803	+	0.0198655i	$0.00632381\pi$
$60$	−2.73243	+	0.482580i	−0.352755	+	0.0623008i
$61$	2.48802	+	1.43646i	0.318558	+	0.183920i	0.650750	−	0.759292i	$-0.274455\pi$
$61$	2.48802	+	1.43646i	0.318558	+	0.183920i	−0.332192	+	0.943212i	$0.607788\pi$
$62$	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
$66$	−1.08603	+	5.64097i	−0.133681	+	0.694355i
$67$	−7.30221	−	12.6478i	−0.892106	−	1.54517i	−0.837345	−	0.546674i	$-0.815894\pi$
$67$	−7.30221	−	12.6478i	−0.892106	−	1.54517i	−0.0547609	−	0.998499i	$-0.517440\pi$
$68$	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	$-0.954928\pi$
$71$		−	2.37827i		−	0.282248i	0.989992	−	0.141124i	$-0.0450717\pi$
$72$	2.81851	−	1.02762i	0.332165	−	0.121106i
$73$	10.0056	−	5.77671i	1.17106	−	0.676113i	0.217132	−	0.976142i	$-0.430330\pi$
$73$	10.0056	−	5.77671i	1.17106	−	0.676113i	0.953930	+	0.300029i	$0.0969963\pi$
$74$	−0.653521	−	1.13193i	−0.0759703	−	0.131584i
$75$	3.22828	−	2.71037i	0.372770	−	0.312967i
$76$		−	2.61516i		−	0.299979i
$77$	−8.75239	+	0.629038i	−0.997427	+	0.0716856i
$78$	−1.75117	+	4.81544i	−0.198281	+	0.545241i
$79$	11.5543	+	6.67087i	1.29996	+	0.750532i	0.980397	−	0.197033i	$-0.0631308\pi$
$79$	11.5543	+	6.67087i	1.29996	+	0.750532i	0.319562	+	0.947565i	$0.396464\pi$
$80$	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	$-0.643134\pi$
$83$	−7.92000			−0.869333			−0.434666	+	0.900592i	$0.643134\pi$
$84$	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
$88$	−0.523783	−	3.27500i	−0.0558355	−	0.349117i
$89$	−5.89340	−	3.40256i	−0.624699	−	0.360670i	0.153997	−	0.988071i	$-0.450785\pi$
$89$	−5.89340	−	3.40256i	−0.624699	−	0.360670i	−0.778696	+	0.627401i	$0.784119\pi$
$90$	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
$99$	−4.84175	−	8.69238i	−0.486614	−	0.873617i
$100$	−1.21682	+	2.10760i	−0.121682	+	0.210760i
$101$	7.27257	+	12.5965i	0.723648	+	1.25340i	0.959528	+	0.281613i	$0.0908695\pi$
$101$	7.27257	+	12.5965i	0.723648	+	1.25340i	−0.235880	+	0.971782i	$0.575797\pi$
$102$	0.735328	+	4.16352i	0.0728083	+	0.412250i
$103$	1.39459	−	2.41551i	0.137413	−	0.238007i	−0.789103	−	0.614260i	$-0.789454\pi$
$103$	1.39459	−	2.41551i	0.137413	−	0.238007i	0.926517	+	0.376253i	$0.122788\pi$
$104$		−	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	$-0.899900\pi$
$107$	−2.14746	+	3.71952i	−0.207603	+	0.359579i	0.743356	+	0.668896i	$0.233233\pi$
$108$	−2.59434	+	4.50215i	−0.249641	+	0.433220i
$109$	12.0547	−	6.95977i	1.15463	−	0.666625i	0.204618	−	0.978842i	$-0.434405\pi$
$109$	12.0547	−	6.95977i	1.15463	−	0.666625i	0.950011	+	0.312217i	$0.101072\pi$
$110$	−3.34993	−	4.12406i	−0.319403	−	0.393214i
$111$	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	$0.0516203\pi$
$113$			3.43269i			0.322920i	−0.986879	+	0.161460i	$0.948380\pi$
$114$	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
$121$	−10.4513	+	3.43079i	−0.950118	+	0.311890i
$122$	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	$-0.821259\pi$
$131$	0.434049	−	0.751795i	0.0379230	−	0.0656846i	0.884364	+	0.466798i	$0.154592\pi$
$132$	4.34221	+	3.76102i	0.377941	+	0.327354i
$133$	−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	−0.855233	−	0.518243i	$-0.826586\pi$
$137$	−9.76217	+	5.63619i	−0.834038	+	0.481532i	0.0211950	+	0.999775i	$0.493253\pi$
$138$	−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
$143$	−9.68852	+	1.54952i	−0.810195	+	0.129577i
$144$	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	$-0.718253\pi$
$149$	4.31760	−	7.47830i	0.353712	−	0.612646i	0.986897	+	0.161354i	$0.0515861\pi$
$150$	−0.733110	−	4.15096i	−0.0598582	−	0.338925i
$151$	−15.3180	+	8.84386i	−1.24656	+	0.719703i	−0.970422	−	0.241414i	$-0.922389\pi$
$151$	−15.3180	+	8.84386i	−1.24656	+	0.719703i	−0.276141	+	0.961117i	$0.589056\pi$
$152$	−2.26479	−	1.30758i	−0.183699	−	0.106059i
$153$	−5.61237	−	4.70405i	−0.453733	−	0.380300i
$154$	−3.83143	+	7.89431i	−0.308746	+	0.636142i
$155$		−	9.21220i		−	0.739941i
$156$	3.29471	+	3.92428i	0.263788	+	0.314193i
$157$	−2.63579	−	4.56532i	−0.210359	−	0.364352i	0.741468	−	0.670988i	$-0.234130\pi$
$157$	−2.63579	−	4.56532i	−0.210359	−	0.364352i	−0.951827	+	0.306636i	$0.900797\pi$
$158$	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	−0.978473	−	0.206377i	$-0.933833\pi$
$163$	−3.96431	+	6.86639i	−0.310509	+	0.537817i	0.667964	+	0.744194i	$0.267166\pi$
$164$	0.970369	+	1.68073i	0.0757731	+	0.131243i
$165$	9.03674	+	1.73981i	0.703509	+	0.135444i
$166$	−3.96000	+	6.85892i	−0.307356	+	0.532355i
$167$	−2.29082			−0.177269			−0.0886343	−	0.996064i	$-0.528250\pi$
$167$	−2.29082			−0.177269			−0.0886343	+	0.996064i	$0.528250\pi$
$168$	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	−0.0167600	+	0.999860i	$0.505335\pi$
$173$	−11.4994	+	19.9176i	−0.874284	+	1.51430i	−0.857524	+	0.514444i	$0.827998\pi$
$174$	−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	0.0837308	−	0.996488i	$-0.473316\pi$
$179$	13.2263	−	7.63621i	0.988581	−	0.570757i	0.904850	+	0.425731i	$0.139983\pi$
$180$	−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
$187$	−6.28400	+	5.10442i	−0.459532	+	0.373272i
$188$		−	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	0.978971	−	0.203998i	$-0.0653937\pi$
$191$	17.8529	+	10.3074i	1.29179	+	0.745815i	0.312818	+	0.949813i	$0.398727\pi$
$192$	0.301239	+	1.70565i	0.0217401	+	0.123095i
$193$	−11.0514	+	6.38055i	−0.795500	+	0.459282i	−0.841895	−	0.539641i	$-0.818560\pi$
$193$	−11.0514	+	6.38055i	−0.795500	+	0.459282i	0.0463953	+	0.998923i	$0.485227\pi$
$194$	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	$-0.331046\pi$
$197$	14.2100			1.01242			0.506211	+	0.862410i	$0.331046\pi$
$198$	−9.94870	−	0.153115i	−0.707023	−	0.0108814i
$199$	−2.43346	−	4.21488i	−0.172503	−	0.298785i	0.766791	−	0.641897i	$-0.221852\pi$
$199$	−2.43346	−	4.21488i	−0.172503	−	0.298785i	−0.939294	+	0.343112i	$0.888519\pi$
$200$	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
$220$	−5.24650	+	0.839092i	−0.353719	+	0.0565716i
$221$	−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	$-0.0951525\pi$
$227$	3.35657	+	5.81374i	0.222783	+	0.385872i	−0.732869	+	0.680370i	$0.761819\pi$
$228$	4.46055	−	0.787787i	0.295407	−	0.0521725i
$229$	−3.74069	+	6.47906i	−0.247192	+	0.428149i	−0.962746	−	0.270409i	$-0.912841\pi$
$229$	−3.74069	+	6.47906i	−0.247192	+	0.428149i	0.715554	+	0.698558i	$0.246174\pi$
$230$	0.879953			0.0580224
$231$	−3.70948	−	14.7391i	−0.244066	−	0.969759i
$232$	0.955838			0.0627538
$233$	10.0351	−	17.3813i	0.657421	−	1.13869i	−0.323860	−	0.946105i	$-0.604981\pi$
$233$	10.0351	−	17.3813i	0.657421	−	1.13869i	0.981281	−	0.192582i	$-0.0616861\pi$
$234$	−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	$-0.204238\pi$
$239$	24.7700			1.60224			0.801121	+	0.598503i	$0.204238\pi$
$240$	1.78414	+	2.12506i	0.115166	+	0.137172i
$241$	−14.2602	+	8.23310i	−0.918577	+	0.530341i	−0.883181	−	0.469032i	$-0.844603\pi$
$241$	−14.2602	+	8.23310i	−0.918577	+	0.530341i	−0.0353964	+	0.999373i	$0.511269\pi$
$242$	−2.25450	+	10.7665i	−0.144925	+	0.692096i
$243$	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	$-0.645118\pi$
$251$		−	28.4497i		−	1.79573i	0.440271	−	0.897865i	$-0.354882\pi$
$252$	−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	0.995991	+	0.0894575i	$0.0285133\pi$
$257$	25.1924	+	14.5448i	1.57146	+	0.907282i	0.575468	+	0.817824i	$0.304820\pi$
$258$	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	$-0.305227\pi$
$263$	−6.83853	−	11.8447i	−0.421682	−	0.730374i	−0.996104	+	0.0881850i	$0.971893\pi$
$264$	5.42824	−	1.87995i	0.334085	−	0.115703i
$265$	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	−0.580113	+	0.814536i	$0.696992\pi$
$269$	−25.8414	+	14.9195i	−1.57558	+	0.909661i	−0.995465	+	0.0951245i	$0.969675\pi$
$270$	7.21238	+	4.15609i	0.438931	+	0.252932i
$271$	−10.5988	−	6.11920i	−0.643829	−	0.371715i	0.142259	−	0.989829i	$-0.454563\pi$
$271$	−10.5988	−	6.11920i	−0.643829	−	0.371715i	−0.786088	+	0.618115i	$0.787897\pi$
$272$	−2.44101			−0.148008
$273$	−1.19100	−	13.5043i	−0.0720823	−	0.817319i
$274$			11.2724i			0.680989i
$275$	6.26505	−	5.08903i	0.377797	−	0.306880i
$276$	−0.936898	+	0.165468i	−0.0563946	+	0.00995998i
$277$	−18.1750	+	10.4934i	−1.09203	+	0.630485i	−0.934117	−	0.356968i	$-0.883811\pi$
$277$	−18.1750	+	10.4934i	−1.09203	+	0.630485i	−0.157915	+	0.987453i	$0.550477\pi$
$278$	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	$-0.117535\pi$
$281$	31.2664			1.86520			0.932600	+	0.360913i	$0.117535\pi$
$282$	7.25089	+	8.63643i	0.431784	+	0.514292i
$283$	−21.1922	+	12.2353i	−1.25975	+	0.727314i	−0.973025	−	0.230700i	$-0.925898\pi$
$283$	−21.1922	+	12.2353i	−1.25975	+	0.727314i	−0.286720	+	0.958014i	$0.592565\pi$
$284$	−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	$-0.588817\pi$
$293$	−9.42889			−0.550842			−0.275421	+	0.961324i	$0.588817\pi$
$294$	−10.5068	−	6.05039i	−0.612769	−	0.352866i
$295$	−21.0644			−1.22641
$296$	−0.653521	+	1.13193i	−0.0379851	+	0.0657922i
$297$	13.3677	−	10.8768i	0.775671	−	0.631138i
$298$	−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	$-0.316218\pi$
$308$	4.92096	+	7.26527i	0.280398	+	0.413977i
$309$	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	0.219412	−	0.975632i	$-0.429586\pi$
$311$	20.7044	−	11.9537i	1.17404	−	0.677833i	0.954628	+	0.297800i	$0.0962528\pi$
$312$	5.04588	−	0.891163i	0.285666	−	0.0504522i
$313$	1.63136	−	2.82559i	0.0922098	−	0.159712i	−0.816231	−	0.577726i	$-0.803940\pi$
$313$	1.63136	−	2.82559i	0.0922098	−	0.159712i	0.908441	+	0.418014i	$0.137274\pi$
$314$	−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	−0.000981712	−	1.00000i	$-0.500312\pi$
$317$	−15.4454	−	8.91738i	−0.867498	−	0.500850i	−0.866516	+	0.499150i	$0.833646\pi$
$318$	−17.8759	+	3.15709i	−1.00243	+	0.177041i
$319$	−0.500652	−	3.13037i	−0.0280311	−	0.175267i
$320$	−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
$330$	6.02509	−	6.95614i	0.331670	−	0.382923i
$331$	0.110394	−	0.191209i	0.00606782	−	0.0105098i	−0.862976	−	0.505246i	$-0.831402\pi$
$331$	0.110394	−	0.191209i	0.00606782	−	0.0105098i	0.869043	+	0.494736i	$0.164735\pi$
$332$	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
$341$	−14.8038	+	12.0249i	−0.801668	+	0.651186i
$342$	−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	$-0.235920\pi$
$347$	−4.02093	−	6.96445i	−0.215855	−	0.373871i	−0.953537	+	0.301277i	$0.902587\pi$
$348$	−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
$352$	−2.57434	+	2.09111i	−0.137213	+	0.111457i
$353$	−0.951398	+	0.549290i	−0.0506378	+	0.0292357i	−0.525105	−	0.851037i	$-0.675974\pi$
$353$	−0.951398	+	0.549290i	−0.0506378	+	0.0292357i	0.474467	+	0.880273i	$0.342641\pi$
$354$	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	−0.174325	+	0.984688i	$0.555774\pi$
$359$	−17.8091	+	30.8462i	−0.939927	+	1.62800i	−0.765603	+	0.643314i	$0.777559\pi$
$360$	−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
$363$	−9.00007	−	16.7928i	−0.472381	−	0.881394i
$364$	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	0.978228	−	0.207533i	$-0.0665436\pi$
$367$	5.92696	+	10.2658i	0.309385	+	0.535870i	−0.668843	+	0.743404i	$0.733210\pi$
$368$	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	$-0.382458\pi$
$373$	−5.14208	−	2.96878i	−0.266247	−	0.153718i	−0.627181	+	0.778874i	$0.715791\pi$
$374$	1.27856	+	7.99431i	0.0661128	+	0.413376i
$375$	−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	0.559766	−	0.828651i	$-0.310891\pi$
$383$	2.38792	+	1.37867i	0.122017	+	0.0704465i	−0.437749	+	0.899097i	$0.644224\pi$
$384$	1.62776	+	0.591946i	0.0830662	+	0.0302076i
$385$	12.6466	+	6.13789i	0.644528	+	0.312816i
$386$			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	−0.608403	−	0.793629i	$-0.708189\pi$
$389$	−4.44364	+	2.56554i	−0.225301	+	0.130078i	0.383101	+	0.923706i	$0.374856\pi$
$390$	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
$396$	−5.10695	+	8.53927i	−0.256634	+	0.429114i
$397$	−12.8199	+	22.2048i	−0.643414	+	1.11443i	0.341251	+	0.939972i	$0.389149\pi$
$397$	−12.8199	+	22.2048i	−0.643414	+	1.11443i	−0.984665	+	0.174454i	$0.944184\pi$
$398$	−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	0.530965	−	0.847394i	$-0.321830\pi$
$401$	1.25322	+	0.723550i	0.0625831	+	0.0361323i	−0.468382	+	0.883526i	$0.655163\pi$
$402$	−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	$-0.586829\pi$
$409$	8.69393	−	5.01945i	0.429887	−	0.248196i	0.699299	+	0.714830i	$0.253496\pi$
$410$	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
$418$	5.46858	+	6.73231i	0.267477	+	0.329288i
$419$		−	19.6066i		−	0.957847i	−0.877857	−	0.478924i	$-0.841027\pi$
$419$		−	19.6066i		−	0.957847i	0.877857	−	0.478924i	$-0.158973\pi$
$420$	−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
$429$	−5.56151	−	16.0585i	−0.268512	−	0.775311i
$430$	1.94074	+	3.36146i	0.0935907	+	0.162104i
$431$	−11.0314	−	19.1069i	−0.531363	−	0.920347i	−0.999330	−	0.0366015i	$-0.988347\pi$
$431$	−11.0314	−	19.1069i	−0.531363	−	0.920347i	0.467967	−	0.883746i	$-0.344987\pi$
$432$	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	$-0.193509\pi$
$439$	15.4336	+	8.91061i	0.736607	+	0.425280i	−0.0842273	+	0.996447i	$0.526842\pi$
$440$	−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	0.455162	−	0.890409i	$-0.349581\pi$
$443$	−1.86006	−	1.07391i	−0.0883744	−	0.0510230i	−0.543536	+	0.839386i	$0.682915\pi$
$444$	−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	$-0.876458\pi$
$449$		−	16.0383i		−	0.756893i	0.925623	−	0.378447i	$-0.123542\pi$
$450$	6.85926	−	2.50086i	0.323349	−	0.117892i
$451$	−1.01653	−	6.35593i	−0.0478664	−	0.299289i
$452$	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	$-0.295032\pi$
$457$	4.44457	+	2.56607i	0.207908	+	0.120036i	−0.392431	+	0.919782i	$0.628366\pi$
$458$	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	$-0.580751\pi$
$461$	−10.7772			−0.501946			−0.250973	+	0.967994i	$0.580751\pi$
$462$	−14.6191	−	4.15702i	−0.680144	−	0.193402i
$463$	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	0.465375	−	0.885114i	$-0.345920\pi$
$467$	−1.47963	−	0.854267i	−0.0684693	−	0.0395308i	−0.533844	+	0.845583i	$0.679253\pi$
$468$	−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
$473$	7.93507	−	1.26908i	0.364855	−	0.0583526i
$474$	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	−0.994524	−	0.104512i	$-0.966672\pi$
$479$	−12.8640	−	22.2811i	−0.587772	−	1.01805i	0.406752	−	0.913539i	$-0.366661\pi$
$480$	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	0.968684	−	0.248295i	$-0.0798702\pi$
$487$	5.94321	+	10.2939i	0.269312	+	0.466463i	−0.699372	+	0.714758i	$0.746537\pi$
$488$	−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	$-0.542200\pi$
$491$	−5.85820			−0.264377			−0.132188	+	0.991225i	$0.542200\pi$
$492$	−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
$495$	−0.245287	+	15.9376i	−0.0110248	+	0.716344i
$496$	−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	−0.124931	−	0.992165i	$-0.539871\pi$
$499$	17.7986	−	30.8281i	0.796775	−	1.38005i	0.921706	−	0.387889i	$-0.126796\pi$
$500$	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	$-0.132966\pi$
$503$	40.9984			1.82803			0.914015	+	0.405681i	$0.132966\pi$
$504$	2.06180	+	7.66479i	0.0918397	+	0.341417i
$505$		−	23.3011i		−	1.03688i
$506$	−1.14863	−	1.41406i	−0.0510627	−	0.0628627i
$507$	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	−0.272998	−	0.962015i	$-0.588015\pi$
$509$	−28.0349	−	16.1860i	−1.24263	−	0.717430i	−0.969628	+	0.244585i	$0.921348\pi$
$510$	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	−0.0826899	−	0.996575i	$-0.526351\pi$
$521$	16.8686	−	9.73906i	0.739025	−	0.426676i	0.821715	+	0.569899i	$0.193018\pi$
$522$	0.496376	−	2.82422i	0.0217258	−	0.123613i
$523$	3.52042	+	2.03251i	0.153937	+	0.0888756i	0.574990	−	0.818160i	$-0.305006\pi$
$523$	3.52042	+	2.03251i	0.153937	+	0.0888756i	−0.421053	+	0.907036i	$0.638339\pi$
$524$	−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
$528$	1.08603	−	5.64097i	0.0472635	−	0.245492i
$529$	−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
$539$	0.350469	−	23.2137i	0.0150958	−	0.999886i
$540$	7.20547	−	4.16806i	0.310074	−	0.179365i
$541$	−22.8096	−	13.1691i	−0.980662	−	0.566185i	−0.0781921	−	0.996938i	$-0.524915\pi$
$541$	−22.8096	−	13.1691i	−0.980662	−	0.566185i	−0.902470	+	0.430753i	$0.858248\pi$
$542$	−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
$550$	−1.27470	−	7.97021i	−0.0543536	−	0.339851i
$551$	−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	$-0.261589\pi$
$557$	−6.93413	−	12.0103i	−0.293808	−	0.508891i	−0.974707	+	0.223487i	$0.928256\pi$
$558$	−16.2078	+	5.90932i	−0.686132	+	0.250161i
$559$	7.16778			0.303165
$560$	1.79287	+	3.84058i	0.0757626	+	0.162294i
$561$	−10.5994	−	9.18068i	−0.447506	−	0.387608i
$562$	15.6332	−	27.0775i	0.659448	−	1.14220i
$563$	18.7294	+	32.4402i	0.789348	+	1.36719i	0.926367	+	0.376623i	$0.122915\pi$
$563$	18.7294	+	32.4402i	0.789348	+	1.36719i	−0.137019	+	0.990568i	$0.543752\pi$
$564$	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	$-0.670797\pi$
$569$	11.6578	−	20.1919i	0.488720	−	0.846488i	0.999916	+	0.0129765i	$0.00413068\pi$
$570$	−1.26202	−	7.14573i	−0.0528603	−	0.299302i
$571$	18.9355	−	10.9324i	0.792424	−	0.457506i	−0.0483912	−	0.998828i	$-0.515409\pi$
$571$	18.9355	−	10.9324i	0.792424	−	0.457506i	0.840815	+	0.541322i	$0.182076\pi$
$572$	6.18619	+	7.61575i	0.258657	+	0.318430i
$573$	−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	0.568035	−	0.823004i	$-0.307704\pi$
$577$	−10.2983	−	17.8372i	−0.428725	−	0.742573i	−0.996760	+	0.0804309i	$0.974370\pi$
$578$	−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
$583$	−21.9156	−	26.9801i	−0.907651	−	1.11740i
$584$	−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	$0.0777004\pi$
$587$			11.7112i			0.483372i	−0.970354	+	0.241686i	$0.922300\pi$
$588$	−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	−0.112490	+	0.993653i	$0.535883\pi$
$593$	−22.3249	+	38.6679i	−0.916774	+	1.58790i	−0.804283	+	0.594246i	$0.797451\pi$
$594$	−2.73578	−	17.0152i	−0.112250	−	0.698140i
$595$	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	0.0240271	−	0.999711i	$-0.492351\pi$
$599$	22.0715	−	12.7430i	0.901816	−	0.520664i	0.877789	+	0.479048i	$0.159018\pi$
$600$	−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
$605$	17.2477	+	3.61168i	0.701220	+	0.146836i
$606$	4.38157	+	24.8090i	0.177989	+	1.00780i
$607$	−6.66954	−	3.85066i	−0.270708	−	0.156294i	0.358501	−	0.933529i	$-0.383288\pi$
$607$	−6.66954	−	3.85066i	−0.270708	−	0.156294i	−0.629209	+	0.777236i	$0.716621\pi$
$608$			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	$-0.769252\pi$
$613$	−13.5825	+	7.84188i	−0.548593	+	0.316730i	0.199961	+	0.979804i	$0.435918\pi$
$614$	−25.4286	−	14.6812i	−1.02622	−	0.592486i
$615$	−1.84038	+	5.06075i	−0.0742112	+	0.204069i
$616$	8.75239	−	0.629038i	0.352644	−	0.0253447i
$617$		−	38.7271i		−	1.55909i	−0.626344	−	0.779547i	$-0.715449\pi$
$617$		−	38.7271i		−	1.55909i	0.626344	−	0.779547i	$-0.284551\pi$
$618$	3.69991	−	3.10634i	0.148832	−	0.124955i
$619$	−2.51690	−	4.35939i	−0.101163	−	0.175219i	0.811001	−	0.585044i	$-0.198923\pi$
$619$	−2.51690	−	4.35939i	−0.101163	−	0.175219i	−0.912164	+	0.409826i	$0.865590\pi$
$620$	−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
$627$	−14.7520	−	2.84014i	−0.589139	−	0.113424i
$628$	−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	0.151545	−	0.988450i	$-0.451575\pi$
$641$	27.4280	−	15.8356i	1.08334	−	0.625467i	0.931796	+	0.362983i	$0.118242\pi$
$642$	−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	−0.563862	−	0.825869i	$-0.690685\pi$
$647$	−3.32120	+	1.91749i	−0.130570	+	0.0753844i	0.433292	+	0.901253i	$0.357352\pi$
$648$	−6.88800	+	5.79271i	−0.270586	+	0.227559i
$649$	27.4959	+	33.8499i	1.07931	+	1.32872i
$650$		−	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	−0.213714	−	0.976896i	$-0.568556\pi$
$653$	−29.8108	−	17.2113i	−1.16659	−	0.673530i	−0.952874	+	0.303367i	$0.901889\pi$
$654$	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	$-0.373629\pi$
$659$	19.8519			0.773320			0.386660	+	0.922222i	$0.373629\pi$
$660$	−3.01165	−	8.69595i	−0.117228	−	0.338489i
$661$	6.37648	+	11.0444i	0.248016	+	0.429577i	0.962975	−	0.269590i	$-0.0868880\pi$
$661$	6.37648	+	11.0444i	0.248016	+	0.429577i	−0.714959	+	0.699166i	$0.753555\pi$
$662$	−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	$-0.701202\pi$
$677$	10.4931	−	18.1746i	0.403283	−	0.698507i	0.994120	+	0.108284i	$0.0345356\pi$
$678$	−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
$682$	3.01201	+	18.8329i	0.115336	+	0.721149i
$683$	−10.1814	+	5.87823i	−0.389580	+	0.224924i	−0.681978	−	0.731372i	$-0.738880\pi$
$683$	−10.1814	+	5.87823i	−0.389580	+	0.224924i	0.292398	+	0.956297i	$0.405547\pi$
$684$	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	−0.674168	−	0.738578i	$-0.735497\pi$
$691$	7.95293	−	13.7749i	0.302544	−	0.524021i	0.976711	+	0.214557i	$0.0688308\pi$
$692$	22.9988			0.874284
$693$	24.0223	−	10.7671i	0.912531	−	0.409007i
$694$	−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	$-0.683916\pi$
$701$	−28.9214			−1.09235			−0.546174	+	0.837672i	$0.683916\pi$
$702$	−0.0127537	−	15.3719i	−0.000481357	−	0.580175i
$703$	2.96018	−	1.70906i	0.111645	−	0.0644584i
$704$	0.523783	+	3.27500i	0.0197408	+	0.123431i
$705$	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	−0.487152	−	0.873317i	$-0.661964\pi$
$709$	13.6527	−	23.6472i	0.512738	−	0.888089i	0.999891	−	0.0147720i	$-0.00470226\pi$
$710$	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	0.889963	−	0.456032i	$-0.150730\pi$
$719$	25.2056	+	14.5524i	0.940009	+	0.542714i	0.0500459	+	0.998747i	$0.484063\pi$
$720$	−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
$726$	−19.0430	−	0.602115i	−0.706754	−	0.0223466i
$727$	−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	$-0.0985889\pi$
$733$	31.5321	+	18.2050i	1.16466	+	0.672419i	0.212246	+	0.977216i	$0.431922\pi$
$734$	11.8539			0.437536
$735$	−9.69262	+	16.8317i	−0.357518	+	0.620847i
$736$		−	0.549290i		−	0.0202471i
$737$	37.5968	−	30.5395i	1.38490	−	1.12494i
$738$	1.00785	−	5.73432i	0.0370993	−	0.211083i
$739$	39.1857	−	22.6239i	1.44147	−	0.832234i	0.443523	−	0.896263i	$-0.353729\pi$
$739$	39.1857	−	22.6239i	1.44147	−	0.832234i	0.997948	+	0.0640296i	$0.0203952\pi$
$740$	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	$-0.185294\pi$
$743$	45.5372			1.67060			0.835299	+	0.549795i	$0.185294\pi$
$744$	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	0.251790	−	0.967782i	$-0.418981\pi$
$751$	26.4183	−	45.7579i	0.964019	−	1.66973i	0.712229	−	0.701947i	$-0.247686\pi$
$752$	−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
$759$	3.09853	+	0.596546i	0.112469	+	0.0216533i
$760$	2.09472	+	3.62816i	0.0759834	+	0.131607i
$761$	−9.62701	+	16.6745i	−0.348979	+	0.604449i	−0.986068	−	0.166341i	$-0.946805\pi$
$761$	−9.62701	+	16.6745i	−0.348979	+	0.604449i	0.637089	+	0.770790i	$0.280138\pi$
$762$	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	$0.876576\pi$
$770$	11.6388	−	7.88329i	0.419435	−	0.284094i
$771$	−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	−0.928186	−	0.372116i	$-0.878632\pi$
$773$	−29.7496	+	17.1759i	−1.07002	+	0.617775i	−0.141831	+	0.989891i	$0.545299\pi$
$774$	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
$781$	7.78884	−	1.24570i	0.278706	−	0.0445745i
$782$	−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	$-0.701759\pi$
$787$	−5.34606	+	3.08655i	−0.190567	+	0.110024i	0.401681	+	0.915780i	$0.368426\pi$
$788$	−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
$792$	4.84175	+	8.69238i	0.172044	+	0.308870i
$793$	−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	$-0.836678\pi$
$797$		−	27.7159i		−	0.981746i	0.871231	−	0.490873i	$-0.163322\pi$
$798$	−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
$803$	24.1595	+	29.7425i	0.852571	+	1.04959i
$804$	−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	$-0.00795201\pi$
$809$	13.6017	+	23.5589i	0.478211	+	0.828286i	−0.521477	+	0.853265i	$0.674619\pi$
$810$	−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
$814$	3.36478	−	2.73317i	0.117935	−	0.0957976i
$815$	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	$-0.869060\pi$
$821$	−3.20923	+	5.55856i	−0.112003	+	0.193995i	0.804575	+	0.593851i	$0.202393\pi$
$822$	−19.2268	+	3.39568i	−0.670611	+	0.118438i
$823$	5.02394	+	8.70171i	0.175123	+	0.303323i	0.940204	−	0.340612i	$-0.110634\pi$
$823$	5.02394	+	8.70171i	0.175123	+	0.303323i	−0.765081	+	0.643935i	$0.777301\pi$
$824$	−1.39459	+	2.41551i	−0.0485829	+	0.0841481i
$825$	10.5674	+	9.15299i	0.367910	+	0.318666i
$826$	34.6577	+	3.01738i	1.20589	+	0.104988i
$827$	−49.0759			−1.70654			−0.853269	−	0.521471i	$-0.825383\pi$
$827$	−49.0759			−1.70654			−0.853269	+	0.521471i	$0.825383\pi$
$828$	−0.564461	−	1.54818i	−0.0196164	−	0.0538029i
$829$	−1.55350	−	2.69074i	−0.0539553	−	0.0934534i	0.837786	−	0.545998i	$-0.183850\pi$
$829$	−1.55350	−	2.69074i	−0.0539553	−	0.0934534i	−0.891742	+	0.452545i	$0.850516\pi$
$830$	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
$836$	8.56465	−	1.36978i	0.296214	−	0.0473747i
$837$	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	$0.0656576\pi$
$839$			11.8648i			0.409620i	−0.978802	+	0.204810i	$0.934342\pi$
$840$	−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
$847$	−6.64446	−	28.3346i	−0.228306	−	0.973589i
$848$		−	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	−0.981938	−	0.189201i	$-0.939410\pi$
$857$	−19.1696	−	33.2028i	−0.654822	−	1.13419i	0.327116	−	0.944984i	$-0.393923\pi$
$858$	−16.6878	−	3.21284i	−0.569713	−	0.109684i
$859$	−7.98719	+	13.8342i	−0.272519	+	0.472018i	−0.969506	−	0.245066i	$-0.921190\pi$
$859$	−7.98719	+	13.8342i	−0.272519	+	0.472018i	0.696987	+	0.717084i	$0.254524\pi$
$860$	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	0.973801	−	0.227400i	$-0.0730224\pi$
$863$	37.1255	+	21.4344i	1.26377	+	0.729637i	0.289967	+	0.957037i	$0.406356\pi$
$864$	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	$-0.543581\pi$
$877$	−31.4695	−	18.1689i	−1.06265	−	0.613521i	−0.926164	+	0.377121i	$0.876914\pi$
$878$	15.4336	−	8.91061i	0.520860	−	0.300719i
$879$	−2.84035	−	16.0824i	−0.0958027	−	0.542447i
$880$	3.34993	+	4.12406i	0.112926	+	0.139022i
$881$		−	14.6701i		−	0.494247i	−0.968984	−	0.247123i	$-0.920515\pi$
$881$		−	14.6701i		−	0.494247i	0.968984	−	0.247123i	$-0.0794853\pi$
$882$	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	$-0.725140\pi$
$887$	9.92929	−	17.1980i	0.333393	−	0.577454i	0.983175	+	0.182667i	$0.0584731\pi$
$888$	−2.12755	−	0.773698i	−0.0713959	−	0.0259636i
$889$	30.4553	+	2.65151i	1.02144	+	0.0889289i
$890$	10.9017			0.365425
$891$	22.5790	+	19.5241i	0.756424	+	0.654082i
$892$	−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	0.884747	−	0.466072i	$-0.154331\pi$
$907$	1.16681	+	2.02098i	0.0387434	+	0.0671056i	−0.846003	+	0.533177i	$0.820998\pi$
$908$	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	$0.0616827\pi$
$911$			11.6247i			0.385143i	−0.981283	+	0.192571i	$0.938317\pi$
$912$	−2.91252	−	3.46906i	−0.0964432	−	0.114872i
$913$	−4.14836	−	25.9380i	−0.137291	−	0.858423i
$914$	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	$-0.291539\pi$
$919$	6.87450	+	3.96900i	0.226769	+	0.130925i	−0.382312	+	0.924033i	$0.624872\pi$
$920$	−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
$924$	−10.9097	+	10.5820i	−0.358901	+	0.348123i
$925$	−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	0.990834	+	0.135088i	$0.0431317\pi$
$929$	48.8660	+	28.2128i	1.60324	+	0.925631i	0.612406	+	0.790543i	$0.290202\pi$
$930$	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
$935$	12.8068	−	2.04823i	0.418826	−	0.0669844i
$936$	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	$-0.326946\pi$
$941$	−14.8017	−	25.6374i	−0.482523	−	0.835754i	−0.999799	+	0.0200646i	$0.993613\pi$
$942$	−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	0.833562	−	0.552426i	$-0.186298\pi$
$947$	23.7548	+	13.7149i	0.771929	+	0.445673i	−0.0616334	+	0.998099i	$0.519631\pi$
$948$	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	$-0.496803\pi$
$953$	0.620095			0.0200868			0.0100434	+	0.999950i	$0.496803\pi$
$954$	−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
$957$	5.18852	−	1.79693i	0.167721	−	0.0580865i
$958$	−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	$-0.166091\pi$
$968$	10.4513	−	3.43079i	0.335918	−	0.110270i
$969$	−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	0.249029	−	0.968496i	$-0.419889\pi$
$971$	−14.4960	−	8.36927i	−0.465199	−	0.268583i	−0.714228	+	0.699913i	$0.753222\pi$
$972$	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	−0.357757	−	0.933815i	$-0.616458\pi$
$977$	8.50414	−	4.90987i	0.272072	−	0.157081i	0.629829	+	0.776734i	$0.283125\pi$
$978$	−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	−0.992855	−	0.119327i	$-0.961926\pi$
$983$	−43.4532	+	25.0877i	−1.38594	+	0.800174i	−0.393088	+	0.919501i	$0.628593\pi$
$984$	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
$990$	13.6798	+	8.18125i	0.434771	+	0.260017i
$991$	−6.24721	−	10.8205i	−0.198449	−	0.343724i	0.749577	−	0.661918i	$-0.230257\pi$
$991$	−6.24721	−	10.8205i	−0.198449	−	0.343724i	−0.948026	+	0.318194i	$0.896924\pi$
$992$	−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	$-0.580269\pi$
$997$	14.6628	−	8.46554i	0.464374	−	0.268106i	0.713882	+	0.700266i	$0.246935\pi$
$998$	−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.f.65.7	yes	24
3.2	odd	2		462.2.n.e.65.10	yes	24
7.4	even	3	inner	462.2.n.f.263.10	yes	24
11.10	odd	2		462.2.n.e.65.7	✓	24
21.11	odd	6		462.2.n.e.263.7	yes	24
33.32	even	2	inner	462.2.n.f.65.10	yes	24
77.32	odd	6		462.2.n.e.263.10	yes	24
231.32	even	6	inner	462.2.n.f.263.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.n.e.65.7	✓	24	11.10	odd	2
462.2.n.e.65.10	yes	24	3.2	odd	2
462.2.n.e.263.7	yes	24	21.11	odd	6
462.2.n.e.263.10	yes	24	77.32	odd	6
462.2.n.f.65.7	yes	24	1.1	even	1	trivial
462.2.n.f.65.10	yes	24	33.32	even	2	inner
462.2.n.f.263.7	yes	24	231.32	even	6	inner
462.2.n.f.263.10	yes	24	7.4	even	3	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
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} +(0.523783 + 3.27500i) 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} +(-5.42824 + 1.87995i) 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} +(2.57434 - 2.09111i) 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} +(-1.08603 + 5.64097i) 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} +(-8.75239 + 0.629038i) 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} +(-0.523783 - 3.27500i) 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} +(-4.84175 - 8.69238i) 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	\( 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} - 8 q^{9} + 4 q^{11} + 4 q^{15} - 12 q^{16} - 4 q^{17} + 8 q^{18} + 8 q^{22} + 20 q^{25} - 12 q^{27} - 40 q^{29} + 2 q^{30} - 28 q^{31} + 12 q^{32} + 24 q^{33} - 8 q^{34} + 32 q^{35} + 16 q^{36} - 16 q^{37} + 8 q^{41} + 6 q^{42} + 4 q^{44} - 28 q^{45} - 8 q^{49} + 40 q^{50} + 34 q^{51} - 6 q^{54} + 8 q^{55} - 40 q^{57} - 20 q^{58} - 2 q^{60} - 56 q^{62} + 14 q^{63} + 24 q^{64} + 44 q^{65} - 24 q^{66} - 4 q^{68} - 20 q^{69} + 64 q^{70} + 8 q^{72} + 16 q^{74} - 26 q^{75} + 24 q^{81} + 4 q^{82} - 144 q^{83} + 6 q^{84} - 8 q^{87} - 4 q^{88} - 56 q^{90} - 32 q^{91} - 22 q^{93} + 44 q^{95} + 64 q^{97} + 8 q^{98} + 28 q^{99}+O(q^{100}) \) 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 + 24 * 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 - 24 * 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 + 28 * q^99

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