LMFDB - Embedded newform 429.2.s.a.166.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(166,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("429.166");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.s (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:	$3.42558224671$
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			166.7
Character	$\chi$	$=$	429.166
Dual form			429.2.s.a.199.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.219134 - 0.126517i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.967987 + 1.67660i) q^{4} +0.770885i q^{5} +(0.219134 + 0.126517i) q^{6} +(2.38762 + 1.37849i) q^{7} +0.995935i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.219134 - 0.126517i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.967987 + 1.67660i) q^{4} +0.770885i q^{5} +(0.219134 + 0.126517i) q^{6} +(2.38762 + 1.37849i) q^{7} +0.995935i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.0975301 + 0.168927i) q^{10} +(-0.866025 + 0.500000i) q^{11} -1.93597 q^{12} +(-1.10709 - 3.43138i) q^{13} +0.697611 q^{14} +(-0.667606 + 0.385443i) q^{15} +(-1.80997 - 3.13496i) q^{16} +(-3.27942 + 5.68013i) q^{17} +0.253034i q^{18} +(-1.45697 - 0.841182i) q^{19} +(-1.29247 - 0.746207i) q^{20} +2.75699i q^{21} +(-0.126517 + 0.219134i) q^{22} +(0.866534 + 1.50088i) q^{23} +(-0.862505 + 0.497968i) q^{24} +4.40574 q^{25} +(-0.676729 - 0.611864i) q^{26} -1.00000 q^{27} +(-4.62237 + 2.66873i) q^{28} +(1.81033 + 3.13559i) q^{29} +(-0.0975301 + 0.168927i) q^{30} +6.59348i q^{31} +(-2.51826 - 1.45392i) q^{32} +(-0.866025 - 0.500000i) q^{33} +1.65961i q^{34} +(-1.06266 + 1.84058i) q^{35} +(-0.967987 - 1.67660i) q^{36} +(9.18921 - 5.30539i) q^{37} -0.425695 q^{38} +(2.41811 - 2.67446i) q^{39} -0.767752 q^{40} +(1.10512 - 0.638040i) q^{41} +(0.348806 + 0.604149i) q^{42} +(-2.83262 + 4.90624i) q^{43} -1.93597i q^{44} +(-0.667606 - 0.385443i) q^{45} +(0.379774 + 0.219262i) q^{46} -8.64254i q^{47} +(1.80997 - 3.13496i) q^{48} +(0.300488 + 0.520461i) q^{49} +(0.965446 - 0.557400i) q^{50} -6.55885 q^{51} +(6.82471 + 1.46537i) q^{52} -3.28255 q^{53} +(-0.219134 + 0.126517i) q^{54} +(-0.385443 - 0.667606i) q^{55} +(-1.37289 + 2.37792i) q^{56} -1.68236i q^{57} +(0.793410 + 0.458075i) q^{58} +(1.86274 + 1.07546i) q^{59} -1.49241i q^{60} +(5.45634 - 9.45066i) q^{61} +(0.834187 + 1.44485i) q^{62} +(-2.38762 + 1.37849i) q^{63} +6.50410 q^{64} +(2.64520 - 0.853443i) q^{65} -0.253034 q^{66} +(9.08414 - 5.24473i) q^{67} +(-6.34888 - 10.9966i) q^{68} +(-0.866534 + 1.50088i) q^{69} +0.537778i q^{70} +(9.21925 + 5.32274i) q^{71} +(-0.862505 - 0.497968i) q^{72} +0.341831i q^{73} +(1.34244 - 2.32518i) q^{74} +(2.20287 + 3.81548i) q^{75} +(2.82066 - 1.62851i) q^{76} -2.75699 q^{77} +(0.191526 - 0.891997i) q^{78} +3.17820 q^{79} +(2.41670 - 1.39528i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.161446 - 0.279632i) q^{82} +8.70831i q^{83} +(-4.62237 - 2.66873i) q^{84} +(-4.37873 - 2.52806i) q^{85} +1.43350i q^{86} +(-1.81033 + 3.13559i) q^{87} +(-0.497968 - 0.862505i) q^{88} +(-14.2746 + 8.24144i) q^{89} -0.195060 q^{90} +(2.08681 - 9.71895i) q^{91} -3.35517 q^{92} +(-5.71012 + 3.29674i) q^{93} +(-1.09343 - 1.89387i) q^{94} +(0.648455 - 1.12316i) q^{95} -2.90784i q^{96} +(8.47548 + 4.89332i) q^{97} +(0.131694 + 0.0760338i) q^{98} -1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{3} + 14 q^{4} + 6 q^{7} - 12 q^{9}+O(q^{10}) $ 24 * q + 12 * q^3 + 14 * q^4 + 6 * q^7 - 12 * q^9	$ 24 q + 12 q^{3} + 14 q^{4} + 6 q^{7} - 12 q^{9} + 28 q^{12} - 4 q^{13} + 20 q^{14} - 6 q^{15} - 14 q^{16} + 10 q^{17} - 18 q^{20} + 2 q^{22} - 14 q^{23} + 4 q^{25} - 34 q^{26} - 24 q^{27} - 30 q^{28} + 4 q^{29} + 30 q^{32} + 6 q^{35} + 14 q^{36} + 12 q^{38} - 2 q^{39} + 20 q^{40} - 30 q^{41} + 10 q^{42} - 4 q^{43} - 6 q^{45} - 24 q^{46} + 14 q^{48} + 18 q^{49} - 84 q^{50} + 20 q^{51} + 40 q^{52} - 56 q^{53} - 4 q^{55} + 26 q^{56} + 48 q^{58} + 60 q^{59} - 2 q^{61} + 18 q^{62} - 6 q^{63} - 48 q^{64} - 10 q^{65} + 4 q^{66} - 42 q^{67} - 18 q^{68} + 14 q^{69} + 6 q^{71} + 2 q^{75} - 48 q^{76} + 24 q^{77} - 26 q^{78} - 20 q^{79} + 30 q^{80} - 12 q^{81} - 10 q^{82} - 30 q^{84} + 6 q^{85} - 4 q^{87} - 12 q^{88} + 12 q^{89} + 18 q^{91} + 8 q^{92} + 12 q^{93} - 22 q^{94} + 4 q^{95} + 6 q^{97} - 114 q^{98}+O(q^{100}) $ 24 * q + 12 * q^3 + 14 * q^4 + 6 * q^7 - 12 * q^9 + 28 * q^12 - 4 * q^13 + 20 * q^14 - 6 * q^15 - 14 * q^16 + 10 * q^17 - 18 * q^20 + 2 * q^22 - 14 * q^23 + 4 * q^25 - 34 * q^26 - 24 * q^27 - 30 * q^28 + 4 * q^29 + 30 * q^32 + 6 * q^35 + 14 * q^36 + 12 * q^38 - 2 * q^39 + 20 * q^40 - 30 * q^41 + 10 * q^42 - 4 * q^43 - 6 * q^45 - 24 * q^46 + 14 * q^48 + 18 * q^49 - 84 * q^50 + 20 * q^51 + 40 * q^52 - 56 * q^53 - 4 * q^55 + 26 * q^56 + 48 * q^58 + 60 * q^59 - 2 * q^61 + 18 * q^62 - 6 * q^63 - 48 * q^64 - 10 * q^65 + 4 * q^66 - 42 * q^67 - 18 * q^68 + 14 * q^69 + 6 * q^71 + 2 * q^75 - 48 * q^76 + 24 * q^77 - 26 * q^78 - 20 * q^79 + 30 * q^80 - 12 * q^81 - 10 * q^82 - 30 * q^84 + 6 * q^85 - 4 * q^87 - 12 * q^88 + 12 * q^89 + 18 * q^91 + 8 * q^92 + 12 * q^93 - 22 * q^94 + 4 * q^95 + 6 * q^97 - 114 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.219134	−	0.126517i	0.154951	−	0.0894610i	−0.420520	−	0.907283i	$-0.638152\pi$
$2$	0.219134	−	0.126517i	0.154951	−	0.0894610i	0.575471	+	0.817822i	$0.304819\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.967987	+	1.67660i	−0.483993	+	0.838301i
$5$			0.770885i			0.344750i	0.985031	+	0.172375i	$0.0551442\pi$
$5$			0.770885i			0.344750i	−0.985031	+	0.172375i	$0.944856\pi$
$6$	0.219134	+	0.126517i	0.0894610	+	0.0516503i
$7$	2.38762	+	1.37849i	0.902436	+	0.521022i	0.877990	−	0.478680i	$-0.158884\pi$
$7$	2.38762	+	1.37849i	0.902436	+	0.521022i	0.0244461	+	0.999701i	$0.492218\pi$
$8$			0.995935i			0.352116i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.0975301	+	0.168927i	0.0308417	+	0.0534194i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$12$	−1.93597			−0.558868
$13$	−1.10709	−	3.43138i	−0.307053	−	0.951693i
$13$	−1.10709	−	3.43138i	−0.307053	−	0.951693i
$14$	0.697611			0.186444
$15$	−0.667606	+	0.385443i	−0.172375	+	0.0995209i
$16$	−1.80997	−	3.13496i	−0.452493	−	0.783740i
$17$	−3.27942	+	5.68013i	−0.795377	+	1.37763i	0.127223	+	0.991874i	$0.459394\pi$
$17$	−3.27942	+	5.68013i	−0.795377	+	1.37763i	−0.922600	+	0.385759i	$0.873940\pi$
$18$			0.253034i			0.0596407i
$19$	−1.45697	−	0.841182i	−0.334252	−	0.192980i	0.323475	−	0.946237i	$-0.395149\pi$
$19$	−1.45697	−	0.841182i	−0.334252	−	0.192980i	−0.657727	+	0.753256i	$0.728482\pi$
$20$	−1.29247	−	0.746207i	−0.289005	−	0.166857i
$21$			2.75699i			0.601624i
$22$	−0.126517	+	0.219134i	−0.0269735	+	0.0467195i
$23$	0.866534	+	1.50088i	0.180685	+	0.312955i	0.942114	−	0.335293i	$-0.108835\pi$
$23$	0.866534	+	1.50088i	0.180685	+	0.312955i	−0.761429	+	0.648248i	$0.775502\pi$
$24$	−0.862505	+	0.497968i	−0.176058	+	0.101647i
$25$	4.40574			0.881147
$26$	−0.676729	−	0.611864i	−0.132718	−	0.119996i
$27$	−1.00000			−0.192450
$28$	−4.62237	+	2.66873i	−0.873546	+	0.504342i
$29$	1.81033	+	3.13559i	0.336170	+	0.582264i	0.983709	−	0.179769i	$-0.0575350\pi$
$29$	1.81033	+	3.13559i	0.336170	+	0.582264i	−0.647539	+	0.762032i	$0.724202\pi$
$30$	−0.0975301	+	0.168927i	−0.0178065	+	0.0308417i
$31$			6.59348i			1.18422i	0.805856	+	0.592112i	$0.201706\pi$
$31$			6.59348i			1.18422i	−0.805856	+	0.592112i	$0.798294\pi$
$32$	−2.51826	−	1.45392i	−0.445170	−	0.257019i
$33$	−0.866025	−	0.500000i	−0.150756	−	0.0870388i
$34$			1.65961i			0.284621i
$35$	−1.06266	+	1.84058i	−0.179622	+	0.311115i
$36$	−0.967987	−	1.67660i	−0.161331	−	0.279434i
$37$	9.18921	−	5.30539i	1.51070	−	0.872201i	0.510774	−	0.859715i	$-0.329359\pi$
$37$	9.18921	−	5.30539i	1.51070	−	0.872201i	0.999922	−	0.0124858i	$-0.00397447\pi$
$38$	−0.425695			−0.0690569
$39$	2.41811	−	2.67446i	0.387208	−	0.428256i
$40$	−0.767752			−0.121392
$41$	1.10512	−	0.638040i	0.172590	−	0.0996451i	−0.411216	−	0.911538i	$-0.634896\pi$
$41$	1.10512	−	0.638040i	0.172590	−	0.0996451i	0.583807	+	0.811893i	$0.301563\pi$
$42$	0.348806	+	0.604149i	0.0538219	+	0.0932222i
$43$	−2.83262	+	4.90624i	−0.431970	+	0.748194i	−0.997043	−	0.0768468i	$-0.975515\pi$
$43$	−2.83262	+	4.90624i	−0.431970	+	0.748194i	0.565073	+	0.825041i	$0.308848\pi$
$44$		−	1.93597i		−	0.291859i
$45$	−0.667606	−	0.385443i	−0.0995209	−	0.0574584i
$46$	0.379774	+	0.219262i	0.0559946	+	0.0323285i
$47$		−	8.64254i		−	1.26064i	−0.776334	−	0.630322i	$-0.782923\pi$
$47$		−	8.64254i		−	1.26064i	0.776334	−	0.630322i	$-0.217077\pi$
$48$	1.80997	−	3.13496i	0.261247	−	0.452493i
$49$	0.300488	+	0.520461i	0.0429269	+	0.0743516i
$50$	0.965446	−	0.557400i	0.136535	−	0.0788283i
$51$	−6.55885			−0.918422
$52$	6.82471	+	1.46537i	0.946417	+	0.203210i
$53$	−3.28255			−0.450893			−0.225446	−	0.974256i	$-0.572384\pi$
$53$	−3.28255			−0.450893			−0.225446	+	0.974256i	$0.572384\pi$
$54$	−0.219134	+	0.126517i	−0.0298203	+	0.0172168i
$55$	−0.385443	−	0.667606i	−0.0519731	−	0.0900200i
$56$	−1.37289	+	2.37792i	−0.183460	+	0.317762i
$57$		−	1.68236i		−	0.222835i
$58$	0.793410	+	0.458075i	0.104180	+	0.0601482i
$59$	1.86274	+	1.07546i	0.242509	+	0.140012i	0.616329	−	0.787489i	$-0.288619\pi$
$59$	1.86274	+	1.07546i	0.242509	+	0.140012i	−0.373821	+	0.927501i	$0.621952\pi$
$60$		−	1.49241i		−	0.192670i
$61$	5.45634	−	9.45066i	0.698613	−	1.21003i	−0.270334	−	0.962766i	$-0.587134\pi$
$61$	5.45634	−	9.45066i	0.698613	−	1.21003i	0.968947	−	0.247267i	$-0.0795324\pi$
$62$	0.834187	+	1.44485i	0.105942	+	0.183497i
$63$	−2.38762	+	1.37849i	−0.300812	+	0.173674i
$64$	6.50410			0.813013
$65$	2.64520	−	0.853443i	0.328096	−	0.105857i
$66$	−0.253034			−0.0311463
$67$	9.08414	−	5.24473i	1.10980	−	0.640746i	0.171026	−	0.985267i	$-0.445292\pi$
$67$	9.08414	−	5.24473i	1.10980	−	0.640746i	0.938779	+	0.344520i	$0.111958\pi$
$68$	−6.34888	−	10.9966i	−0.769914	−	1.33353i
$69$	−0.866534	+	1.50088i	−0.104318	+	0.180685i
$70$			0.537778i			0.0642768i
$71$	9.21925	+	5.32274i	1.09412	+	0.631692i	0.934671	−	0.355513i	$-0.115694\pi$
$71$	9.21925	+	5.32274i	1.09412	+	0.631692i	0.159452	+	0.987206i	$0.449027\pi$
$72$	−0.862505	−	0.497968i	−0.101647	−	0.0586860i
$73$			0.341831i			0.0400083i	0.999800	+	0.0200042i	$0.00636794\pi$
$73$			0.341831i			0.0400083i	−0.999800	+	0.0200042i	$0.993632\pi$
$74$	1.34244	−	2.32518i	0.156056	−	0.270297i
$75$	2.20287	+	3.81548i	0.254365	+	0.440574i
$76$	2.82066	−	1.62851i	0.323551	−	0.186802i
$77$	−2.75699			−0.314188
$78$	0.191526	−	0.891997i	0.0216860	−	0.100999i
$79$	3.17820			0.357576			0.178788	−	0.983888i	$-0.442782\pi$
$79$	3.17820			0.357576			0.178788	+	0.983888i	$0.442782\pi$
$80$	2.41670	−	1.39528i	0.270195	−	0.155997i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.161446	−	0.279632i	0.0178287	−	0.0308802i
$83$			8.70831i			0.955861i	0.878398	+	0.477931i	$0.158613\pi$
$83$			8.70831i			0.955861i	−0.878398	+	0.477931i	$0.841387\pi$
$84$	−4.62237	−	2.66873i	−0.504342	−	0.291182i
$85$	−4.37873	−	2.52806i	−0.474940	−	0.274206i
$86$			1.43350i			0.154578i
$87$	−1.81033	+	3.13559i	−0.194088	+	0.336170i
$88$	−0.497968	−	0.862505i	−0.0530835	−	0.0919433i
$89$	−14.2746	+	8.24144i	−1.51310	+	0.873591i	−0.513222	+	0.858256i	$0.671548\pi$
$89$	−14.2746	+	8.24144i	−1.51310	+	0.873591i	−0.999882	+	0.0153355i	$0.995118\pi$
$90$	−0.195060			−0.0205611
$91$	2.08681	−	9.71895i	0.218757	−	1.01882i
$92$	−3.35517			−0.349801
$93$	−5.71012	+	3.29674i	−0.592112	+	0.341856i
$94$	−1.09343	−	1.89387i	−0.112778	−	0.195338i
$95$	0.648455	−	1.12316i	0.0665301	−	0.115233i
$96$		−	2.90784i		−	0.296780i
$97$	8.47548	+	4.89332i	0.860554	+	0.496841i	0.864198	−	0.503152i	$-0.167826\pi$
$97$	8.47548	+	4.89332i	0.860554	+	0.496841i	−0.00364345	+	0.999993i	$0.501160\pi$
$98$	0.131694	+	0.0760338i	0.0133031	+	0.00768057i
$99$		−	1.00000i		−	0.100504i
$100$	−4.26469	+	7.38667i	−0.426469	+	0.738667i
$101$	−6.82572	−	11.8225i	−0.679185	−	1.17638i	−0.975227	−	0.221208i	$-0.929000\pi$
$101$	−6.82572	−	11.8225i	−0.679185	−	1.17638i	0.296042	−	0.955175i	$-0.404333\pi$
$102$	−1.43726	+	0.829805i	−0.142310	+	0.0821630i
$103$	10.8512			1.06920			0.534602	−	0.845104i	$-0.320461\pi$
$103$	10.8512			1.06920			0.534602	+	0.845104i	$0.320461\pi$
$104$	3.41743	−	1.10259i	0.335106	−	0.108118i
$105$	−2.12532			−0.207410
$106$	−0.719317	+	0.415298i	−0.0698663	+	0.0403373i
$107$	−6.81393	−	11.8021i	−0.658727	−	1.14095i	−0.980945	−	0.194284i	$-0.937762\pi$
$107$	−6.81393	−	11.8021i	−0.658727	−	1.14095i	0.322218	−	0.946666i	$-0.395572\pi$
$108$	0.967987	−	1.67660i	0.0931446	−	0.161331i
$109$			6.89486i			0.660408i	0.943910	+	0.330204i	$0.107118\pi$
$109$			6.89486i			0.660408i	−0.943910	+	0.330204i	$0.892882\pi$
$110$	−0.168927	−	0.0975301i	−0.0161066	−	0.00929913i
$111$	9.18921	+	5.30539i	0.872201	+	0.503565i
$112$		−	9.98013i		−	0.943034i
$113$	8.16212	−	14.1372i	0.767828	−	1.32992i	−0.170911	−	0.985287i	$-0.554671\pi$
$113$	8.16212	−	14.1372i	0.767828	−	1.32992i	0.938738	−	0.344630i	$-0.111996\pi$
$114$	−0.212848	−	0.368663i	−0.0199350	−	0.0345284i
$115$	−1.15701	+	0.667998i	−0.107891	+	0.0622912i
$116$	−7.00951			−0.650816
$117$	3.52521	+	0.756916i	0.325905	+	0.0699770i
$118$	0.544254			0.0501026
$119$	−15.6600	+	9.04133i	−1.43555	+	0.828817i
$120$	−0.383876	−	0.664892i	−0.0350429	−	0.0606961i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$		−	2.76128i		−	0.249995i
$123$	1.10512	+	0.638040i	0.0996451	+	0.0575301i
$124$	−11.0546	−	6.38240i	−0.992736	−	0.573156i
$125$			7.25074i			0.648526i
$126$	−0.348806	+	0.604149i	−0.0310741	+	0.0538219i
$127$	−3.29719	−	5.71090i	−0.292578	−	0.506761i	0.681840	−	0.731501i	$-0.261180\pi$
$127$	−3.29719	−	5.71090i	−0.292578	−	0.506761i	−0.974419	+	0.224740i	$0.927847\pi$
$128$	6.46179	−	3.73072i	0.571147	−	0.329752i
$129$	−5.66524			−0.498796
$130$	0.471677	−	0.521681i	0.0413688	−	0.0457544i
$131$	21.0692			1.84082			0.920412	−	0.390950i	$-0.127853\pi$
$131$	21.0692			1.84082			0.920412	+	0.390950i	$0.127853\pi$
$132$	1.67660	−	0.967987i	0.145930	−	0.0842524i
$133$	−2.31913	−	4.01685i	−0.201094	−	0.348305i
$134$	1.32710	−	2.29860i	0.114644	−	0.198569i
$135$		−	0.770885i		−	0.0663472i
$136$	−5.65704	−	3.26609i	−0.485087	−	0.280065i
$137$	8.69480	+	5.01995i	0.742847	+	0.428883i	0.823104	−	0.567891i	$-0.192241\pi$
$137$	8.69480	+	5.01995i	0.742847	+	0.428883i	−0.0802565	+	0.996774i	$0.525574\pi$
$138$			0.438525i			0.0373297i
$139$	1.62285	−	2.81085i	0.137648	−	0.238413i	−0.788958	−	0.614447i	$-0.789379\pi$
$139$	1.62285	−	2.81085i	0.137648	−	0.238413i	0.926606	+	0.376034i	$0.122712\pi$
$140$	−2.05728	−	3.56332i	−0.173872	−	0.301155i
$141$	7.48466	−	4.32127i	0.630322	−	0.363917i
$142$	2.69367			0.226047
$143$	2.67446	+	2.41811i	0.223650	+	0.202213i
$144$	3.61994			0.301662
$145$	−2.41718	+	1.39556i	−0.200736	+	0.115895i
$146$	0.0432474	+	0.0749068i	0.00357918	+	0.00619933i
$147$	−0.300488	+	0.520461i	−0.0247839	+	0.0429269i
$148$			20.5422i			1.68856i
$149$	−5.76361	−	3.32762i	−0.472173	−	0.272609i	0.244976	−	0.969529i	$-0.421220\pi$
$149$	−5.76361	−	3.32762i	−0.472173	−	0.272609i	−0.717149	+	0.696920i	$0.754553\pi$
$150$	0.965446	+	0.557400i	0.0788283	+	0.0455116i
$151$		−	2.94064i		−	0.239306i	−0.992816	−	0.119653i	$-0.961822\pi$
$151$		−	2.94064i		−	0.239306i	0.992816	−	0.119653i	$-0.0381782\pi$
$152$	0.837762	−	1.45105i	0.0679515	−	0.117695i
$153$	−3.27942	−	5.68013i	−0.265126	−	0.459211i
$154$	−0.604149	+	0.348806i	−0.0486837	+	0.0281076i
$155$	−5.08281			−0.408261
$156$	2.14331	+	6.64305i	0.171602	+	0.531870i
$157$	−7.08541			−0.565477			−0.282739	−	0.959197i	$-0.591243\pi$
$157$	−7.08541			−0.565477			−0.282739	+	0.959197i	$0.591243\pi$
$158$	0.696452	−	0.402097i	0.0554067	−	0.0319891i
$159$	−1.64127	−	2.84277i	−0.130161	−	0.225446i
$160$	1.12080	−	1.94129i	0.0886074	−	0.153473i
$161$			4.77804i			0.376563i
$162$	−0.219134	−	0.126517i	−0.0172168	−	0.00994011i
$163$	−2.05527	−	1.18661i	−0.160981	−	0.0929424i	0.417345	−	0.908748i	$-0.362961\pi$
$163$	−2.05527	−	1.18661i	−0.160981	−	0.0929424i	−0.578326	+	0.815806i	$0.696294\pi$
$164$			2.47046i			0.192910i
$165$	0.385443	−	0.667606i	0.0300067	−	0.0519731i
$166$	1.10175	+	1.90829i	0.0855123	+	0.148112i
$167$	15.4107	−	8.89736i	1.19251	−	0.688498i	0.233638	−	0.972324i	$-0.424937\pi$
$167$	15.4107	−	8.89736i	1.19251	−	0.688498i	0.958876	+	0.283825i	$0.0916036\pi$
$168$	−2.74578			−0.211842
$169$	−10.5487	+	7.59771i	−0.811437	+	0.584439i
$170$	−1.27937			−0.0981232
$171$	1.45697	−	0.841182i	0.111417	−	0.0643268i
$172$	−5.48387	−	9.49835i	−0.418142	−	0.724242i
$173$	−6.89516	+	11.9428i	−0.524229	+	0.907992i	0.475373	+	0.879785i	$0.342313\pi$
$173$	−6.89516	+	11.9428i	−0.524229	+	0.907992i	−0.999602	+	0.0282075i	$0.991020\pi$
$174$			0.916150i			0.0694532i
$175$	10.5192	+	6.07328i	0.795179	+	0.459097i
$176$	3.13496	+	1.80997i	0.236307	+	0.136432i
$177$			2.15091i			0.161672i
$178$	−2.08537	+	3.61196i	−0.156305	+	0.270728i
$179$	−1.22593	−	2.12337i	−0.0916300	−	0.158708i	0.816567	−	0.577250i	$-0.195874\pi$
$179$	−1.22593	−	2.12337i	−0.0916300	−	0.158708i	−0.908197	+	0.418543i	$0.862541\pi$
$180$	1.29247	−	0.746207i	0.0963349	−	0.0556190i
$181$	4.47377			0.332533			0.166266	−	0.986081i	$-0.446829\pi$
$181$	4.47377			0.332533			0.166266	+	0.986081i	$0.446829\pi$
$182$	−0.772321	−	2.39377i	−0.0572483	−	0.177438i
$183$	10.9127			0.806689
$184$	−1.49478	+	0.863011i	−0.110197	+	0.0636220i
$185$	4.08985	+	7.08382i	0.300692	+	0.520813i
$186$	−0.834187	+	1.44485i	−0.0611655	+	0.105942i
$187$		−	6.55885i		−	0.479630i
$188$	14.4901	+	8.36587i	1.05680	+	0.610143i
$189$	−2.38762	−	1.37849i	−0.173674	−	0.100271i
$190$		−	0.328162i		−	0.0238074i
$191$	−0.831713	+	1.44057i	−0.0601806	+	0.104236i	−0.894546	−	0.446976i	$-0.852501\pi$
$191$	−0.831713	+	1.44057i	−0.0601806	+	0.104236i	0.834365	+	0.551212i	$0.185834\pi$
$192$	3.25205	+	5.63272i	0.234697	+	0.406506i
$193$	2.06606	−	1.19284i	0.148718	−	0.0858625i	−0.423794	−	0.905758i	$-0.639302\pi$
$193$	2.06606	−	1.19284i	0.148718	−	0.0858625i	0.572513	+	0.819896i	$0.305969\pi$
$194$	2.47635			0.177792
$195$	2.06170	+	1.86409i	0.147642	+	0.133490i
$196$	−1.16348			−0.0831054
$197$	−22.1495	+	12.7880i	−1.57809	+	0.911109i	−0.582960	+	0.812501i	$0.698106\pi$
$197$	−22.1495	+	12.7880i	−1.57809	+	0.911109i	−0.995126	+	0.0986079i	$0.968561\pi$
$198$	−0.126517	−	0.219134i	−0.00899117	−	0.0155732i
$199$	−11.5588	+	20.0205i	−0.819385	+	1.41922i	0.0867510	+	0.996230i	$0.472352\pi$
$199$	−11.5588	+	20.0205i	−0.819385	+	1.41922i	−0.906136	+	0.422986i	$0.860982\pi$
$200$			4.38783i			0.310266i
$201$	9.08414	+	5.24473i	0.640746	+	0.369935i
$202$	−2.99149	−	1.72714i	−0.210481	−	0.121521i
$203$			9.98212i			0.700607i
$204$	6.34888	−	10.9966i	0.444510	−	0.769914i
$205$	0.491856	+	0.851919i	0.0343527	+	0.0595006i
$206$	2.37787	−	1.37287i	0.165674	−	0.0956522i
$207$	−1.73307			−0.120457
$208$	−8.75343	+	9.68139i	−0.606941	+	0.671284i
$209$	1.68236			0.116372
$210$	−0.465730	+	0.268889i	−0.0321384	+	0.0185551i
$211$	−12.4494	−	21.5630i	−0.857051	−	1.48446i	−0.874729	−	0.484612i	$-0.838961\pi$
$211$	−12.4494	−	21.5630i	−0.857051	−	1.48446i	0.0176783	−	0.999844i	$-0.494373\pi$
$212$	3.17746	−	5.50353i	0.218229	−	0.377984i
$213$			10.6455i			0.729416i
$214$	−2.98632	−	1.72416i	−0.204141	−	0.117861i
$215$	−3.78215	−	2.18362i	−0.257940	−	0.148922i
$216$		−	0.995935i		−	0.0677648i
$217$	−9.08906	+	15.7427i	−0.617006	+	1.06869i
$218$	0.872317	+	1.51090i	0.0590808	+	0.102331i
$219$	−0.296034	+	0.170916i	−0.0200042	+	0.0115494i
$220$	1.49241			0.100619
$221$	23.1213	+	4.96450i	1.55531	+	0.333948i
$222$	2.68489			0.180198
$223$	−13.3723	+	7.72053i	−0.895478	+	0.517005i	−0.875730	−	0.482800i	$-0.839620\pi$
$223$	−13.3723	+	7.72053i	−0.895478	+	0.517005i	−0.0197479	+	0.999805i	$0.506286\pi$
$224$	−4.00844	−	6.94282i	−0.267825	−	0.463886i
$225$	−2.20287	+	3.81548i	−0.146858	+	0.254365i
$226$		−	4.13059i		−	0.274763i
$227$	7.47267	+	4.31435i	0.495979	+	0.286353i	0.727051	−	0.686583i	$-0.240890\pi$
$227$	7.47267	+	4.31435i	0.495979	+	0.286353i	−0.231073	+	0.972936i	$0.574224\pi$
$228$	2.82066	+	1.62851i	0.186802	+	0.107850i
$229$			4.15536i			0.274594i	0.990530	+	0.137297i	$0.0438415\pi$
$229$			4.15536i			0.274594i	−0.990530	+	0.137297i	$0.956159\pi$
$230$	−0.169026	+	0.292762i	−0.0111453	+	0.0193042i
$231$	−1.37849	−	2.38762i	−0.0906982	−	0.157094i
$232$	−3.12284	+	1.80297i	−0.205024	+	0.118371i
$233$	−26.8162			−1.75679			−0.878393	−	0.477939i	$-0.841384\pi$
$233$	−26.8162			−1.75679			−0.878393	+	0.477939i	$0.841384\pi$
$234$	0.868255	−	0.280132i	0.0567596	−	0.0183128i
$235$	6.66241			0.434608
$236$	−3.60622	+	2.08205i	−0.234745	+	0.135530i
$237$	1.58910	+	2.75240i	0.103223	+	0.178788i
$238$	−2.28776	+	3.96252i	−0.148294	+	0.256852i
$239$		−	9.22354i		−	0.596621i	−0.954469	−	0.298311i	$-0.903577\pi$
$239$		−	9.22354i		−	0.596621i	0.954469	−	0.298311i	$-0.0964231\pi$
$240$	2.41670	+	1.39528i	0.155997	+	0.0900649i
$241$	−20.7553	−	11.9831i	−1.33696	−	0.771896i	−0.350608	−	0.936522i	$-0.614025\pi$
$241$	−20.7553	−	11.9831i	−1.33696	−	0.771896i	−0.986356	+	0.164626i	$0.947358\pi$
$242$		−	0.253034i		−	0.0162656i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	10.5633	+	18.2962i	0.676248	+	1.17130i
$245$	−0.401216	+	0.231642i	−0.0256327	+	0.0147991i
$246$	0.322892			0.0205868
$247$	−1.27341	+	5.93068i	−0.0810251	+	0.377360i
$248$	−6.56667			−0.416984
$249$	−7.54162	+	4.35415i	−0.477931	+	0.275933i
$250$	0.917342	+	1.58888i	0.0580178	+	0.100490i
$251$	1.04471	−	1.80949i	0.0659415	−	0.114214i	−0.831170	−	0.556019i	$-0.812328\pi$
$251$	1.04471	−	1.80949i	0.0659415	−	0.114214i	0.897111	+	0.441805i	$0.145662\pi$
$252$		−	5.33745i		−	0.336228i
$253$	−1.50088	−	0.866534i	−0.0943596	−	0.0544785i
$254$	−1.44505	−	0.834301i	−0.0906706	−	0.0523487i
$255$		−	5.05612i		−	0.316626i
$256$	−5.56010	+	9.63038i	−0.347507	+	0.601899i
$257$	−6.28066	−	10.8784i	−0.391777	−	0.678577i	0.600907	−	0.799319i	$-0.294806\pi$
$257$	−6.28066	−	10.8784i	−0.391777	−	0.678577i	−0.992684	+	0.120742i	$0.961473\pi$
$258$	−1.24144	+	0.716749i	−0.0772890	+	0.0446228i
$259$	29.2538			1.81774
$260$	−1.12963	+	5.26107i	−0.0700568	+	0.326277i
$261$	−3.62066			−0.224113
$262$	4.61697	−	2.66561i	0.285238	−	0.164682i
$263$	12.3215	+	21.3414i	0.759774	+	1.31597i	0.942966	+	0.332890i	$0.108024\pi$
$263$	12.3215	+	21.3414i	0.759774	+	1.31597i	−0.183192	+	0.983077i	$0.558643\pi$
$264$	0.497968	−	0.862505i	0.0306478	−	0.0530835i
$265$		−	2.53047i		−	0.155445i
$266$	−1.01640	−	0.586818i	−0.0623194	−	0.0359801i
$267$	−14.2746	−	8.24144i	−0.873591	−	0.504368i
$268$			20.3073i			1.24047i
$269$	12.0072	−	20.7971i	0.732094	−	1.26802i	−0.223892	−	0.974614i	$-0.571876\pi$
$269$	12.0072	−	20.7971i	0.732094	−	1.26802i	0.955987	−	0.293411i	$-0.0947903\pi$
$270$	−0.0975301	−	0.168927i	−0.00593549	−	0.0102806i
$271$	1.03335	−	0.596608i	0.0627718	−	0.0362413i	−0.468286	−	0.883577i	$-0.655128\pi$
$271$	1.03335	−	0.596608i	0.0627718	−	0.0362413i	0.531057	+	0.847336i	$0.321795\pi$
$272$	23.7426			1.43961
$273$	9.46026	−	3.05224i	0.572561	−	0.184730i
$274$	2.54043			0.153473
$275$	−3.81548	+	2.20287i	−0.230082	+	0.132838i
$276$	−1.67759	−	2.90567i	−0.100979	−	0.174901i
$277$	9.57736	−	16.5885i	0.575448	−	0.996705i	−0.420545	−	0.907272i	$-0.638161\pi$
$277$	9.57736	−	16.5885i	0.575448	−	0.996705i	0.995993	−	0.0894330i	$-0.0285055\pi$
$278$		−	0.821270i		−	0.0492565i
$279$	−5.71012	−	3.29674i	−0.341856	−	0.197371i
$280$	−1.83310	−	1.05834i	−0.109549	−	0.0632480i
$281$			7.58373i			0.452407i	0.974080	+	0.226204i	$0.0726315\pi$
$281$			7.58373i			0.452407i	−0.974080	+	0.226204i	$0.927369\pi$
$282$	1.09343	−	1.89387i	0.0651127	−	0.112778i
$283$	0.367235	+	0.636069i	0.0218298	+	0.0378104i	0.876734	−	0.480976i	$-0.159717\pi$
$283$	0.367235	+	0.636069i	0.0218298	+	0.0378104i	−0.854904	+	0.518786i	$0.826384\pi$
$284$	−17.8482	+	10.3047i	−1.05910	+	0.611470i
$285$	1.29691			0.0768223
$286$	0.891997	+	0.191526i	0.0527449	+	0.0113251i
$287$	3.51814			0.207669
$288$	2.51826	−	1.45392i	0.148390	−	0.0856730i
$289$	−13.0092	−	22.5326i	−0.765249	−	1.32545i
$290$	−0.353123	+	0.611628i	−0.0207361	+	0.0359160i
$291$			9.78664i			0.573703i
$292$	−0.573115	−	0.330888i	−0.0335390	−	0.0193638i
$293$	−6.90234	−	3.98507i	−0.403239	−	0.232810i	0.284642	−	0.958634i	$-0.408125\pi$
$293$	−6.90234	−	3.98507i	−0.403239	−	0.232810i	−0.687881	+	0.725824i	$0.741459\pi$
$294$			0.152068i			0.00886876i
$295$	−0.829053	+	1.43596i	−0.0482693	+	0.0836050i
$296$	5.28382	+	9.15185i	0.307116	+	0.531941i
$297$	0.866025	−	0.500000i	0.0502519	−	0.0290129i
$298$	−1.68400			−0.0975517
$299$	4.19075	−	4.63502i	0.242357	−	0.268050i
$300$	−8.52939			−0.492445
$301$	−13.5264	+	7.80949i	−0.779651	+	0.450132i
$302$	−0.372041	−	0.644394i	−0.0214086	−	0.0370807i
$303$	6.82572	−	11.8225i	0.392128	−	0.679185i
$304$			6.09006i			0.349289i
$305$	7.28538	+	4.20621i	0.417159	+	0.240847i
$306$	−1.43726	−	0.829805i	−0.0821630	−	0.0474368i
$307$			14.9141i			0.851194i	0.904913	+	0.425597i	$0.139936\pi$
$307$			14.9141i			0.851194i	−0.904913	+	0.425597i	$0.860064\pi$
$308$	2.66873	−	4.62237i	0.152065	−	0.263384i
$309$	5.42562	+	9.39745i	0.308653	+	0.534602i
$310$	−1.11382	+	0.643062i	−0.0632605	+	0.0365235i
$311$	8.04334			0.456096			0.228048	−	0.973650i	$-0.426766\pi$
$311$	8.04334			0.456096			0.228048	+	0.973650i	$0.426766\pi$
$312$	2.66359	+	2.40828i	0.150796	+	0.136342i
$313$	−32.1892			−1.81944			−0.909721	−	0.415220i	$-0.863705\pi$
$313$	−32.1892			−1.81944			−0.909721	+	0.415220i	$0.863705\pi$
$314$	−1.55265	+	0.896425i	−0.0876213	+	0.0505882i
$315$	−1.06266	−	1.84058i	−0.0598741	−	0.103705i
$316$	−3.07646	+	5.32858i	−0.173064	+	0.299756i
$317$			14.5613i			0.817843i	0.912570	+	0.408921i	$0.134095\pi$
$317$			14.5613i			0.817843i	−0.912570	+	0.408921i	$0.865905\pi$
$318$	−0.719317	−	0.415298i	−0.0403373	−	0.0232888i
$319$	−3.13559	−	1.81033i	−0.175559	−	0.101359i
$320$			5.01392i			0.280287i
$321$	6.81393	−	11.8021i	0.380316	−	0.658727i
$322$	0.604504	+	1.04703i	0.0336877	+	0.0583488i
$323$	9.55604	−	5.51718i	0.531712	−	0.306984i
$324$	1.93597			0.107554
$325$	−4.87756	−	15.1177i	−0.270559	−	0.838581i
$326$	−0.600504			−0.0332589
$327$	−5.97112	+	3.44743i	−0.330204	+	0.190643i
$328$	0.635446	+	1.10063i	0.0350867	+	0.0607719i
$329$	11.9137	−	20.6351i	0.656823	−	1.13765i
$330$		−	0.195060i		−	0.0107377i
$331$	17.1611	+	9.90796i	0.943259	+	0.544591i	0.890980	−	0.454042i	$-0.150018\pi$
$331$	17.1611	+	9.90796i	0.943259	+	0.544591i	0.0522786	+	0.998633i	$0.483352\pi$
$332$	−14.6004	−	8.42953i	−0.801300	−	0.462631i
$333$			10.6108i			0.581467i
$334$	2.25133	−	3.89943i	0.123188	−	0.213367i
$335$	4.04309	+	7.00283i	0.220897	+	0.382606i
$336$	8.64305	−	4.99007i	0.471517	−	0.272230i
$337$	−8.05661			−0.438872			−0.219436	−	0.975627i	$-0.570422\pi$
$337$	−8.05661			−0.438872			−0.219436	+	0.975627i	$0.570422\pi$
$338$	−1.35033	+	2.99950i	−0.0734485	+	0.163151i
$339$	16.3242			0.886611
$340$	8.47710	−	4.89426i	0.459735	−	0.265428i
$341$	−3.29674	−	5.71012i	−0.178528	−	0.309220i
$342$	0.212848	−	0.368663i	0.0115095	−	0.0199350i
$343$		−	17.6420i		−	0.952580i
$344$	−4.88629	−	2.82110i	−0.263451	−	0.152104i
$345$	−1.15701	−	0.667998i	−0.0622912	−	0.0359638i
$346$			3.48942i			0.187592i
$347$	10.3644	−	17.9516i	0.556389	−	0.963694i	−0.441405	−	0.897308i	$-0.645520\pi$
$347$	10.3644	−	17.9516i	0.556389	−	0.963694i	0.997794	−	0.0663864i	$-0.0211470\pi$
$348$	−3.50475	−	6.07041i	−0.187875	−	0.325408i
$349$	13.4969	−	7.79242i	0.722471	−	0.417119i	−0.0931906	−	0.995648i	$-0.529707\pi$
$349$	13.4969	−	7.79242i	0.722471	−	0.417119i	0.815661	+	0.578530i	$0.196373\pi$
$350$	3.07349			0.164285
$351$	1.10709	+	3.43138i	0.0590923	+	0.183153i
$352$	2.90784			0.154988
$353$	−16.8706	+	9.74023i	−0.897930	+	0.518420i	−0.876528	−	0.481351i	$-0.840146\pi$
$353$	−16.8706	+	9.74023i	−0.897930	+	0.518420i	−0.0214021	+	0.999771i	$0.506813\pi$
$354$	0.272127	+	0.471338i	0.0144634	+	0.0250513i
$355$	−4.10322	+	7.10698i	−0.217776	+	0.377200i
$356$		−	31.9104i		−	1.69125i
$357$	−15.6600	−	9.04133i	−0.828817	−	0.478518i
$358$	−0.537284	−	0.310201i	−0.0283963	−	0.0163946i
$359$		−	3.58131i		−	0.189014i	−0.995524	−	0.0945072i	$-0.969872\pi$
$359$		−	3.58131i		−	0.189014i	0.995524	−	0.0945072i	$-0.0301275\pi$
$360$	0.383876	−	0.664892i	0.0202320	−	0.0350429i
$361$	−8.08483	−	14.0033i	−0.425517	−	0.737017i
$362$	0.980355	−	0.566008i	0.0515263	−	0.0297487i
$363$	1.00000			0.0524864
$364$	14.2748	+	12.9066i	0.748203	+	0.676488i
$365$	−0.263513			−0.0137929
$366$	2.39134	−	1.38064i	0.124997	−	0.0721672i
$367$	−5.00746	−	8.67318i	−0.261387	−	0.452736i	0.705223	−	0.708985i	$-0.250847\pi$
$367$	−5.00746	−	8.67318i	−0.261387	−	0.452736i	−0.966611	+	0.256249i	$0.917513\pi$
$368$	3.13680	−	5.43310i	0.163517	−	0.283220i
$369$			1.27608i			0.0664301i
$370$	1.79245	+	1.03487i	0.0931849	+	0.0538003i
$371$	−7.83748	−	4.52497i	−0.406902	−	0.234925i
$372$		−	12.7648i		−	0.661824i
$373$	−7.14574	+	12.3768i	−0.369992	+	0.640845i	−0.989564	−	0.144095i	$-0.953973\pi$
$373$	−7.14574	+	12.3768i	−0.369992	+	0.640845i	0.619572	+	0.784940i	$0.287306\pi$
$374$	−0.829805	−	1.43726i	−0.0429082	−	0.0743192i
$375$	−6.27933	+	3.62537i	−0.324263	+	0.187213i
$376$	8.60741			0.443893
$377$	8.75517	−	9.68332i	0.450914	−	0.498716i
$378$	−0.697611			−0.0358813
$379$	13.6791	−	7.89765i	0.702650	−	0.405675i	−0.105684	−	0.994400i	$-0.533703\pi$
$379$	13.6791	−	7.89765i	0.702650	−	0.405675i	0.808334	+	0.588725i	$0.200370\pi$
$380$	1.25539	+	2.17440i	0.0644002	+	0.111544i
$381$	3.29719	−	5.71090i	0.168920	−	0.292578i
$382$			0.420903i			0.0215353i
$383$	−16.9392	−	9.77985i	−0.865552	−	0.499727i	0.000315280	−	1.00000i	$-0.499900\pi$
$383$	−16.9392	−	9.77985i	−0.865552	−	0.499727i	−0.865868	+	0.500273i	$0.833233\pi$
$384$	6.46179	+	3.73072i	0.329752	+	0.190382i
$385$		−	2.12532i		−	0.108316i
$386$	0.301829	−	0.522783i	0.0153627	−	0.0266090i
$387$	−2.83262	−	4.90624i	−0.143990	−	0.249398i
$388$	−16.4083	+	9.47334i	−0.833005	+	0.480936i
$389$	−1.53775			−0.0779671			−0.0389835	−	0.999240i	$-0.512412\pi$
$389$	−1.53775			−0.0779671			−0.0389835	+	0.999240i	$0.512412\pi$
$390$	0.687627	+	0.147644i	0.0348194	+	0.00747626i
$391$	−11.3669			−0.574850
$392$	−0.518345	+	0.299267i	−0.0261804	+	0.0151153i
$393$	10.5346	+	18.2465i	0.531400	+	0.920412i
$394$	−3.23580	+	5.60458i	−0.163017	+	0.282354i
$395$			2.45003i			0.123274i
$396$	1.67660	+	0.967987i	0.0842524	+	0.0486432i
$397$	−3.26827	−	1.88694i	−0.164030	−	0.0947027i	0.415738	−	0.909484i	$-0.363523\pi$
$397$	−3.26827	−	1.88694i	−0.164030	−	0.0947027i	−0.579768	+	0.814782i	$0.696857\pi$
$398$			5.84956i			0.293212i
$399$	2.31913	−	4.01685i	0.116102	−	0.201094i
$400$	−7.97425	−	13.8118i	−0.398713	−	0.690591i
$401$	21.5767	−	12.4573i	1.07749	−	0.622090i	0.147273	−	0.989096i	$-0.452950\pi$
$401$	21.5767	−	12.4573i	1.07749	−	0.622090i	0.930219	+	0.367006i	$0.119617\pi$
$402$	2.65419			0.132379
$403$	22.6247	−	7.29960i	1.12702	−	0.363619i
$404$	26.4288			1.31488
$405$	0.667606	−	0.385443i	0.0331736	−	0.0191528i
$406$	1.26291	+	2.18742i	0.0626770	+	0.108560i
$407$	−5.30539	+	9.18921i	−0.262978	+	0.455492i
$408$		−	6.53218i		−	0.323391i
$409$	−13.4210	−	7.74859i	−0.663624	−	0.383143i	0.130033	−	0.991510i	$-0.458492\pi$
$409$	−13.4210	−	7.74859i	−0.663624	−	0.383143i	−0.793656	+	0.608366i	$0.791825\pi$
$410$	0.215564	+	0.124456i	0.0106460	+	0.00614645i
$411$			10.0399i			0.495231i
$412$	−10.5039	+	18.1932i	−0.517488	+	0.896316i
$413$	2.96502	+	5.13556i	0.145899	+	0.252704i
$414$	−0.379774	+	0.219262i	−0.0186649	+	0.0107762i
$415$	−6.71311			−0.329534
$416$	−2.20099	+	10.2507i	−0.107912	+	0.502583i
$417$	3.24569			0.158942
$418$	0.368663	−	0.212848i	0.0180319	−	0.0104107i
$419$	−18.9651	−	32.8485i	−0.926504	−	1.60475i	−0.789124	−	0.614235i	$-0.789465\pi$
$419$	−18.9651	−	32.8485i	−0.926504	−	1.60475i	−0.137381	−	0.990518i	$-0.543868\pi$
$420$	2.05728	−	3.56332i	0.100385	−	0.173872i
$421$		−	16.0596i		−	0.782697i	−0.920242	−	0.391349i	$-0.872009\pi$
$421$		−	16.0596i		−	0.782697i	0.920242	−	0.391349i	$-0.127991\pi$
$422$	−5.45616	−	3.15012i	−0.265602	−	0.153345i
$423$	7.48466	+	4.32127i	0.363917	+	0.210107i
$424$		−	3.26920i		−	0.158767i
$425$	−14.4483	+	25.0251i	−0.700844	+	1.21390i
$426$	1.34683	+	2.33278i	0.0652543	+	0.113024i
$427$	26.0554	−	15.0431i	1.26091	−	0.727985i
$428$	26.3832			1.27528
$429$	−0.756916	+	3.52521i	−0.0365443	+	0.170199i
$430$	−1.10506			−0.0532908
$431$	3.88492	−	2.24296i	0.187130	−	0.108040i	−0.403508	−	0.914976i	$-0.632209\pi$
$431$	3.88492	−	2.24296i	0.187130	−	0.108040i	0.590638	+	0.806936i	$0.298876\pi$
$432$	1.80997	+	3.13496i	0.0870823	+	0.150831i
$433$	−14.6172	+	25.3177i	−0.702456	+	1.21669i	0.265145	+	0.964208i	$0.414580\pi$
$433$	−14.6172	+	25.3177i	−0.702456	+	1.21669i	−0.967602	+	0.252482i	$0.918753\pi$
$434$			4.59968i			0.220792i
$435$	−2.41718	−	1.39556i	−0.115895	−	0.0669119i
$436$	−11.5599	−	6.67413i	−0.553621	−	0.319633i
$437$		−	2.91565i		−	0.139474i
$438$	−0.0432474	+	0.0749068i	−0.00206644	+	0.00357918i
$439$	−10.3408	−	17.9107i	−0.493538	−	0.854833i	0.506434	−	0.862279i	$-0.330963\pi$
$439$	−10.3408	−	17.9107i	−0.493538	−	0.854833i	−0.999972	+	0.00744541i	$0.997630\pi$
$440$	0.664892	−	0.383876i	0.0316975	−	0.0183006i
$441$	−0.600977			−0.0286179
$442$	5.69475	−	1.83735i	0.270872	−	0.0873936i
$443$	15.3787			0.730666			0.365333	−	0.930877i	$-0.380955\pi$
$443$	15.3787			0.730666			0.365333	+	0.930877i	$0.380955\pi$
$444$	−17.7901	+	10.2711i	−0.844279	+	0.487445i
$445$	−6.35321	−	11.0041i	−0.301171	−	0.521643i
$446$	−1.95356	+	3.38366i	−0.0925035	+	0.160221i
$447$		−	6.65525i		−	0.314782i
$448$	15.5293	+	8.96586i	0.733692	+	0.423597i
$449$	19.7899	+	11.4257i	0.933945	+	0.539213i	0.888057	−	0.459733i	$-0.152055\pi$
$449$	19.7899	+	11.4257i	0.933945	+	0.539213i	0.0458877	+	0.998947i	$0.485388\pi$
$450$			1.11480i			0.0525522i
$451$	−0.638040	+	1.10512i	−0.0300441	+	0.0520380i
$452$	15.8017	+	27.3693i	0.743247	+	1.28734i
$453$	2.54667	−	1.47032i	0.119653	−	0.0690817i
$454$	2.18335			0.102470
$455$	7.49219	+	1.60869i	0.351239	+	0.0754166i
$456$	1.67552			0.0784636
$457$	−8.15964	+	4.71097i	−0.381692	+	0.220370i	−0.678554	−	0.734550i	$-0.737393\pi$
$457$	−8.15964	+	4.71097i	−0.381692	+	0.220370i	0.296862	+	0.954920i	$0.404060\pi$
$458$	0.525724	+	0.910580i	0.0245655	+	0.0425486i
$459$	3.27942	−	5.68013i	0.153070	−	0.265126i
$460$		−	2.58645i		−	0.120594i
$461$	−23.7332	−	13.7023i	−1.10536	−	0.638182i	−0.167739	−	0.985831i	$-0.553647\pi$
$461$	−23.7332	−	13.7023i	−1.10536	−	0.638182i	−0.937625	+	0.347650i	$0.886980\pi$
$462$	−0.604149	−	0.348806i	−0.0281076	−	0.0162279i
$463$			21.8622i			1.01602i	0.861351	+	0.508010i	$0.169619\pi$
$463$			21.8622i			1.01602i	−0.861351	+	0.508010i	$0.830381\pi$
$464$	6.55329	−	11.3506i	0.304229	−	0.526940i
$465$	−2.54141	−	4.40185i	−0.117855	−	0.204131i
$466$	−5.87633	+	3.39270i	−0.272216	+	0.157164i
$467$	5.33642			0.246940			0.123470	−	0.992348i	$-0.460598\pi$
$467$	5.33642			0.246940			0.123470	+	0.992348i	$0.460598\pi$
$468$	−4.68140	+	5.17768i	−0.216398	+	0.239339i
$469$	28.9193			1.33537
$470$	1.45996	−	0.842908i	0.0673429	−	0.0388804i
$471$	−3.54271	−	6.13615i	−0.163239	−	0.282739i
$472$	−1.07108	+	1.85517i	−0.0493007	+	0.0853912i
$473$		−	5.66524i		−	0.260488i
$474$	0.696452	+	0.402097i	0.0319891	+	0.0184689i
$475$	−6.41902	−	3.70602i	−0.294525	−	0.170044i
$476$		−	35.0075i		−	1.60457i
$477$	1.64127	−	2.84277i	0.0751488	−	0.130161i
$478$	−1.16693	−	2.02119i	−0.0533743	−	0.0924471i
$479$	−33.6696	+	19.4392i	−1.53840	+	0.888198i	−0.539471	+	0.842004i	$0.681376\pi$
$479$	−33.6696	+	19.4392i	−1.53840	+	0.888198i	−0.998932	+	0.0461939i	$0.985291\pi$
$480$	2.24161			0.102315
$481$	−28.3781	−	25.6581i	−1.29393	−	1.16991i
$482$	−6.06424			−0.276219
$483$	−4.13791	+	2.38902i	−0.188281	+	0.108704i
$484$	0.967987	+	1.67660i	0.0439994	+	0.0762092i
$485$	−3.77219	+	6.53362i	−0.171286	+	0.296677i
$486$		−	0.253034i		−	0.0114779i
$487$	23.8887	+	13.7921i	1.08250	+	0.624981i	0.931569	−	0.363564i	$-0.118440\pi$
$487$	23.8887	+	13.7921i	1.08250	+	0.624981i	0.150929	+	0.988545i	$0.451774\pi$
$488$	9.41225	+	5.43416i	0.426072	+	0.245993i
$489$		−	2.37322i		−	0.107321i
$490$	−0.0586133	+	0.101521i	−0.00264788	+	0.00458626i
$491$	−6.56320	−	11.3678i	−0.296193	−	0.513021i	0.679069	−	0.734075i	$-0.262384\pi$
$491$	−6.56320	−	11.3678i	−0.296193	−	0.513021i	−0.975262	+	0.221053i	$0.929051\pi$
$492$	−2.13948	+	1.23523i	−0.0964551	+	0.0556884i
$493$	−23.7474			−1.06953
$494$	0.471285	+	1.46072i	0.0212041	+	0.0657209i
$495$	0.770885			0.0346487
$496$	20.6703	−	11.9340i	0.928124	−	0.535852i
$497$	14.6747	+	25.4173i	0.658251	+	1.14012i
$498$	−1.10175	+	1.90829i	−0.0493706	+	0.0855123i
$499$		−	31.0636i		−	1.39060i	−0.718721	−	0.695299i	$-0.755272\pi$
$499$		−	31.0636i		−	1.39060i	0.718721	−	0.695299i	$-0.244728\pi$
$500$	−12.1566	−	7.01863i	−0.543660	−	0.313882i
$501$	15.4107	+	8.89736i	0.688498	+	0.397505i
$502$		−	0.528694i		−	0.0235968i
$503$	17.2440	−	29.8675i	0.768873	−	1.33173i	−0.169301	−	0.985564i	$-0.554151\pi$
$503$	17.2440	−	29.8675i	0.768873	−	1.33173i	0.938174	−	0.346163i	$-0.112516\pi$
$504$	−1.37289	−	2.37792i	−0.0611534	−	0.105921i
$505$	9.11379	−	5.26185i	0.405558	−	0.234149i
$506$	−0.438525			−0.0194948
$507$	−11.8542	−	5.33657i	−0.526462	−	0.237006i
$508$	12.7666			0.566424
$509$	9.93499	−	5.73597i	0.440361	−	0.254242i	−0.263390	−	0.964689i	$-0.584841\pi$
$509$	9.93499	−	5.73597i	0.440361	−	0.254242i	0.703751	+	0.710447i	$0.251507\pi$
$510$	−0.639685	−	1.10797i	−0.0283257	−	0.0490616i
$511$	−0.471212	+	0.816163i	−0.0208452	+	0.0361049i
$512$			17.7367i			0.783857i
$513$	1.45697	+	0.841182i	0.0643268	+	0.0371391i
$514$	−2.75261	−	1.58922i	−0.121412	−	0.0700975i
$515$			8.36507i			0.368609i
$516$	5.48387	−	9.49835i	0.241414	−	0.418142i
$517$	4.32127	+	7.48466i	0.190049	+	0.329175i
$518$	6.41049	−	3.70110i	0.281661	−	0.162617i
$519$	−13.7903			−0.605328
$520$	0.849973	+	2.63444i	0.0372738	+	0.115528i
$521$	16.1238			0.706395			0.353198	−	0.935549i	$-0.385094\pi$
$521$	16.1238			0.706395			0.353198	+	0.935549i	$0.385094\pi$
$522$	−0.793410	+	0.458075i	−0.0347266	+	0.0200494i
$523$	−5.37407	−	9.30816i	−0.234992	−	0.407017i	0.724279	−	0.689507i	$-0.242173\pi$
$523$	−5.37407	−	9.30816i	−0.234992	−	0.407017i	−0.959270	+	0.282490i	$0.908840\pi$
$524$	−20.3947	+	35.3247i	−0.890947	+	1.54317i
$525$			12.1466i			0.530119i
$526$	5.40010	+	3.11775i	0.235455	+	0.135940i
$527$	−37.4518	−	21.6228i	−1.63143	−	0.941904i
$528$			3.61994i			0.157538i
$529$	9.99824	−	17.3175i	0.434706	−	0.752933i
$530$	−0.320147	−	0.554511i	−0.0139063	−	0.0240864i
$531$	−1.86274	+	1.07546i	−0.0808362	+	0.0466708i
$532$	8.97954			0.389312
$533$	−3.41282	−	3.08570i	−0.147826	−	0.133657i
$534$	−4.17073			−0.180485
$535$	9.09804	−	5.25276i	0.393343	−	0.227097i
$536$	5.22341	+	9.04722i	0.225617	+	0.390780i
$537$	1.22593	−	2.12337i	0.0529026	−	0.0916300i
$538$		−	6.07648i		−	0.261976i
$539$	−0.520461	−	0.300488i	−0.0224178	−	0.0129430i
$540$	1.29247	+	0.746207i	0.0556190	+	0.0321116i
$541$			4.10687i			0.176568i	0.996095	+	0.0882841i	$0.0281383\pi$
$541$			4.10687i			0.176568i	−0.996095	+	0.0882841i	$0.971862\pi$
$542$	0.150962	−	0.261474i	0.00648437	−	0.0112313i
$543$	2.23689	+	3.87440i	0.0959940	+	0.166266i
$544$	16.5169	−	9.53603i	0.708156	−	0.408854i
$545$	−5.31515			−0.227676
$546$	1.68690	−	1.86573i	0.0721927	−	0.0798460i
$547$	11.1758			0.477843			0.238922	−	0.971039i	$-0.423206\pi$
$547$	11.1758			0.477843			0.238922	+	0.971039i	$0.423206\pi$
$548$	−16.8329	+	9.71849i	−0.719066	+	0.415153i
$549$	5.45634	+	9.45066i	0.232871	+	0.403344i
$550$	−0.557400	+	0.965446i	−0.0237676	+	0.0411667i
$551$		−	6.09127i		−	0.259497i
$552$	−1.49478	−	0.863011i	−0.0636220	−	0.0367322i
$553$	7.58834	+	4.38113i	0.322689	+	0.186305i
$554$		−	4.84679i		−	0.205921i
$555$	−4.08985	+	7.08382i	−0.173604	+	0.300692i
$556$	3.14179	+	5.44173i	0.133241	+	0.230781i
$557$	−22.7520	+	13.1358i	−0.964031	+	0.556584i	−0.897411	−	0.441195i	$-0.854555\pi$
$557$	−22.7520	+	13.1358i	−0.964031	+	0.556584i	−0.0666200	+	0.997778i	$0.521222\pi$
$558$	−1.66837			−0.0706279
$559$	19.9711	+	4.28811i	0.844689	+	0.181368i
$560$	7.69354			0.325111
$561$	5.68013	−	3.27942i	0.239815	−	0.138457i
$562$	0.959470	+	1.66185i	0.0404728	+	0.0701009i
$563$	−9.72708	+	16.8478i	−0.409948	+	0.710050i	−0.994883	−	0.101029i	$-0.967786\pi$
$563$	−9.72708	+	16.8478i	−0.409948	+	0.710050i	0.584936	+	0.811080i	$0.301120\pi$
$564$			16.7317i			0.704533i
$565$	10.8982	+	6.29206i	0.458489	+	0.264709i
$566$	0.160947	+	0.0929228i	0.00676511	+	0.00390584i
$567$		−	2.75699i		−	0.115783i
$568$	−5.30110	+	9.18177i	−0.222429	+	0.385259i
$569$	−16.5819	−	28.7207i	−0.695149	−	1.20403i	−0.970131	−	0.242583i	$-0.922005\pi$
$569$	−16.5819	−	28.7207i	−0.695149	−	1.20403i	0.274982	−	0.961449i	$-0.411328\pi$
$570$	0.284197	−	0.164081i	0.0119037	−	0.00687260i
$571$	13.2190			0.553200			0.276600	−	0.960985i	$-0.410792\pi$
$571$	13.2190			0.553200			0.276600	+	0.960985i	$0.410792\pi$
$572$	−6.64305	+	2.14331i	−0.277760	+	0.0896161i
$573$	−1.66343			−0.0694906
$574$	0.770943	−	0.445104i	0.0321785	−	0.0185783i
$575$	3.81772	+	6.61248i	0.159210	+	0.275760i
$576$	−3.25205	+	5.63272i	−0.135502	+	0.234697i
$577$			8.94979i			0.372584i	0.982494	+	0.186292i	$0.0596471\pi$
$577$			8.94979i			0.372584i	−0.982494	+	0.186292i	$0.940353\pi$
$578$	−5.70152	−	3.29178i	−0.237152	−	0.136920i
$579$	2.06606	+	1.19284i	0.0858625	+	0.0495727i
$580$		−	5.40353i		−	0.224369i
$581$	−12.0043	+	20.7921i	−0.498024	+	0.862603i
$582$	1.23818	+	2.14458i	0.0513241	+	0.0888959i
$583$	2.84277	−	1.64127i	0.117735	−	0.0679746i
$584$	−0.340442			−0.0140876
$585$	−0.583496	+	2.71753i	−0.0241246	+	0.112356i
$586$	−2.01671			−0.0833097
$587$	39.1927	−	22.6279i	1.61766	−	0.933954i	0.630131	−	0.776489i	$-0.283001\pi$
$587$	39.1927	−	22.6279i	1.61766	−	0.933954i	0.987524	−	0.157466i	$-0.0503323\pi$
$588$	−0.581738	−	1.00760i	−0.0239905	−	0.0415527i
$589$	5.54631	−	9.60649i	0.228532	−	0.395829i
$590$			0.419557i			0.0172729i
$591$	−22.1495	−	12.7880i	−0.911109	−	0.526029i
$592$	−33.2644	−	19.2052i	−1.36716	−	0.789329i
$593$			7.85202i			0.322444i	0.986918	+	0.161222i	$0.0515435\pi$
$593$			7.85202i			0.322444i	−0.986918	+	0.161222i	$0.948457\pi$
$594$	0.126517	−	0.219134i	0.00519105	−	0.00899117i
$595$	−6.96983	−	12.0721i	−0.285735	−	0.494907i
$596$	11.1582	−	6.44219i	0.457058	−	0.263882i
$597$	−23.1177			−0.946144
$598$	0.331927	−	1.54589i	0.0135735	−	0.0632162i
$599$	−18.9346			−0.773648			−0.386824	−	0.922154i	$-0.626428\pi$
$599$	−18.9346			−0.773648			−0.386824	+	0.922154i	$0.626428\pi$
$600$	−3.79997	+	2.19391i	−0.155133	+	0.0895661i
$601$	−3.63705	−	6.29955i	−0.148358	−	0.256964i	0.782263	−	0.622949i	$-0.214066\pi$
$601$	−3.63705	−	6.29955i	−0.148358	−	0.256964i	−0.930621	+	0.365985i	$0.880732\pi$
$602$	−1.97607	+	3.42265i	−0.0805385	+	0.139497i
$603$			10.4895i			0.427164i
$604$	4.93028	+	2.84650i	0.200610	+	0.115822i
$605$	0.667606	+	0.385443i	0.0271421	+	0.0156705i
$606$		−	3.45428i		−	0.140321i
$607$	−19.5752	+	33.9052i	−0.794532	+	1.37617i	0.128604	+	0.991696i	$0.458950\pi$
$607$	−19.5752	+	33.9052i	−0.794532	+	1.37617i	−0.923136	+	0.384473i	$0.874383\pi$
$608$	2.44602	+	4.23663i	0.0991992	+	0.171818i
$609$	−8.64477	+	4.99106i	−0.350304	+	0.202248i
$610$	2.12863			0.0861857
$611$	−29.6558	+	9.56810i	−1.19975	+	0.387084i
$612$	12.6978			0.513276
$613$	−26.2280	+	15.1427i	−1.05934	+	0.611609i	−0.925249	−	0.379360i	$-0.876144\pi$
$613$	−26.2280	+	15.1427i	−1.05934	+	0.611609i	−0.134089	+	0.990969i	$0.542811\pi$
$614$	1.88689	+	3.26819i	0.0761487	+	0.131893i
$615$	−0.491856	+	0.851919i	−0.0198335	+	0.0343527i
$616$		−	2.74578i		−	0.110631i
$617$	−10.9723	−	6.33483i	−0.441726	−	0.255031i	0.262603	−	0.964904i	$-0.415419\pi$
$617$	−10.9723	−	6.33483i	−0.441726	−	0.255031i	−0.704330	+	0.709873i	$0.748752\pi$
$618$	2.37787	+	1.37287i	0.0956522	+	0.0552248i
$619$			26.5630i			1.06766i	0.845592	+	0.533829i	$0.179248\pi$
$619$			26.5630i			1.06766i	−0.845592	+	0.533829i	$0.820752\pi$
$620$	4.92010	−	8.52186i	0.197596	−	0.342246i
$621$	−0.866534	−	1.50088i	−0.0347728	−	0.0602283i
$622$	1.76257	−	1.01762i	0.0706726	−	0.0408028i
$623$	−45.4431			−1.82064
$624$	−12.7610	−	2.73999i	−0.510851	−	0.109688i
$625$	16.4392			0.657567
$626$	−7.05375	+	4.07248i	−0.281924	+	0.162769i
$627$	0.841182	+	1.45697i	0.0335936	+	0.0581858i
$628$	6.85859	−	11.8794i	0.273687	−	0.474040i
$629$			69.5945i			2.77491i
$630$	−0.465730	−	0.268889i	−0.0185551	−	0.0107128i
$631$	33.8023	+	19.5158i	1.34565	+	0.776910i	0.987630	−	0.156804i	$-0.0501191\pi$
$631$	33.8023	+	19.5158i	1.34565	+	0.776910i	0.358019	+	0.933714i	$0.383452\pi$
$632$			3.16528i			0.125908i
$633$	12.4494	−	21.5630i	0.494819	−	0.857051i
$634$	1.84225	+	3.19087i	0.0731651	+	0.126726i
$635$	4.40245	−	2.54176i	0.174706	−	0.100867i
$636$	6.35493			0.251989
$637$	1.45323	−	1.60729i	0.0575790	−	0.0636831i
$638$	−0.916150			−0.0362707
$639$	−9.21925	+	5.32274i	−0.364708	+	0.210564i
$640$	2.87596	+	4.98130i	0.113682	+	0.196903i
$641$	9.12142	−	15.7988i	0.360275	−	0.624014i	−0.627731	−	0.778430i	$-0.716016\pi$
$641$	9.12142	−	15.7988i	0.360275	−	0.624014i	0.988006	+	0.154416i	$0.0493497\pi$
$642$		−	3.44831i		−	0.136094i
$643$	28.4616	+	16.4323i	1.12241	+	0.648026i	0.942016	−	0.335567i	$-0.108928\pi$
$643$	28.4616	+	16.4323i	1.12241	+	0.648026i	0.180398	+	0.983594i	$0.442261\pi$
$644$	−8.01088	−	4.62508i	−0.315673	−	0.182254i
$645$		−	4.36725i		−	0.171960i
$646$	1.39603	−	2.41800i	0.0549262	−	0.0951350i
$647$	4.38651	+	7.59765i	0.172451	+	0.298695i	0.939276	−	0.343162i	$-0.111498\pi$
$647$	4.38651	+	7.59765i	0.172451	+	0.298695i	−0.766825	+	0.641856i	$0.778165\pi$
$648$	0.862505	−	0.497968i	0.0338824	−	0.0195620i
$649$	−2.15091			−0.0844307
$650$	−2.98149	−	2.69571i	−0.116944	−	0.105735i
$651$	−18.1781			−0.712457
$652$	3.97894	−	2.29724i	0.155827	−	0.0899670i
$653$	16.9758	+	29.4030i	0.664314	+	1.15063i	0.979471	+	0.201587i	$0.0646097\pi$
$653$	16.9758	+	29.4030i	0.664314	+	1.15063i	−0.315156	+	0.949040i	$0.602057\pi$
$654$	−0.872317	+	1.51090i	−0.0341103	+	0.0590808i
$655$			16.2419i			0.634625i
$656$	−4.00046	−	2.30967i	−0.156192	−	0.0901774i
$657$	−0.296034	−	0.170916i	−0.0115494	−	0.00666805i
$658$		−	6.02913i		−	0.235040i
$659$	−3.85572	+	6.67830i	−0.150197	+	0.260150i	−0.931300	−	0.364253i	$-0.881324\pi$
$659$	−3.85572	+	6.67830i	−0.150197	+	0.260150i	0.781103	+	0.624403i	$0.214658\pi$
$660$	0.746207	+	1.29247i	0.0290461	+	0.0503093i
$661$	−22.8531	+	13.1942i	−0.888882	+	0.513196i	−0.873577	−	0.486686i	$-0.838205\pi$
$661$	−22.8531	+	13.1942i	−0.888882	+	0.513196i	−0.0153056	+	0.999883i	$0.504872\pi$
$662$	5.01410			0.194879
$663$	7.26126	+	22.5059i	0.282004	+	0.874055i
$664$	−8.67291			−0.336574
$665$	3.09653	−	1.78778i	0.120078	−	0.0693272i
$666$	1.34244	+	2.32518i	0.0520186	+	0.0900989i
$667$	−3.13743	+	5.43418i	−0.121482	+	0.210412i
$668$			34.4501i			1.33291i
$669$	−13.3723	−	7.72053i	−0.517005	−	0.298493i
$670$	1.77195	+	1.02304i	0.0684566	+	0.0395234i
$671$			10.9127i			0.421280i
$672$	4.00844	−	6.94282i	0.154629	−	0.267825i
$673$	13.8379	+	23.9679i	0.533411	+	0.923895i	0.999238	+	0.0390195i	$0.0124235\pi$
$673$	13.8379	+	23.9679i	0.533411	+	0.923895i	−0.465827	+	0.884876i	$0.654243\pi$
$674$	−1.76548	+	1.01930i	−0.0680036	+	0.0392619i
$675$	−4.40574			−0.169577
$676$	−2.52735	−	25.0404i	−0.0972060	−	0.963094i
$677$	−4.97778			−0.191312			−0.0956559	−	0.995414i	$-0.530495\pi$
$677$	−4.97778			−0.191312			−0.0956559	+	0.995414i	$0.530495\pi$
$678$	3.57719	−	2.06529i	0.137381	−	0.0793171i
$679$	13.4908	+	23.3668i	0.517730	+	0.896735i
$680$	2.51778	−	4.36093i	0.0965525	−	0.167234i
$681$			8.62870i			0.330652i
$682$	−1.44485	−	0.834187i	−0.0553263	−	0.0319427i
$683$	23.9947	+	13.8534i	0.918133	+	0.530085i	0.883039	−	0.469299i	$-0.155494\pi$
$683$	23.9947	+	13.8534i	0.918133	+	0.530085i	0.0350942	+	0.999384i	$0.488827\pi$
$684$			3.25701i			0.124535i
$685$	−3.86980	+	6.70270i	−0.147858	+	0.256097i
$686$	−2.23202	−	3.86596i	−0.0852187	−	0.147603i
$687$	−3.59865	+	2.07768i	−0.137297	+	0.0792685i
$688$	20.5078			0.781854
$689$	3.63409	+	11.2637i	0.138448	+	0.429111i
$690$	−0.338052			−0.0128694
$691$	13.8058	−	7.97079i	0.525198	−	0.303223i	−0.213861	−	0.976864i	$-0.568604\pi$
$691$	13.8058	−	7.97079i	0.525198	−	0.303223i	0.739059	+	0.673641i	$0.235271\pi$
$692$	−13.3489	−	23.1209i	−0.507447	−	0.878924i
$693$	1.37849	−	2.38762i	0.0523646	−	0.0906982i
$694$		−	5.24508i		−	0.199101i
$695$	2.16684	+	1.25103i	0.0821930	+	0.0474542i
$696$	−3.12284	−	1.80297i	−0.118371	−	0.0683415i
$697$			8.36961i			0.317022i
$698$	1.97175	−	3.41517i	0.0746317	−	0.129266i
$699$	−13.4081	−	23.2235i	−0.507141	−	0.878393i
$700$	−20.3649	+	11.7577i	−0.769723	+	0.444400i
$701$	9.33293			0.352500			0.176250	−	0.984345i	$-0.443603\pi$
$701$	9.33293			0.352500			0.176250	+	0.984345i	$0.443603\pi$
$702$	0.676729	+	0.611864i	0.0255415	+	0.0230933i
$703$	−17.8512			−0.673270
$704$	−5.63272	+	3.25205i	−0.212291	+	0.122566i
$705$	3.33120	+	5.76981i	0.125460	+	0.217304i
$706$	−2.46461	+	4.26883i	−0.0927568	+	0.160659i
$707$		−	37.6369i		−	1.41548i
$708$	−3.60622	−	2.08205i	−0.135530	−	0.0782484i
$709$	26.0213	+	15.0234i	0.977249	+	0.564215i	0.901439	−	0.432907i	$-0.142512\pi$
$709$	26.0213	+	15.0234i	0.977249	+	0.564215i	0.0758108	+	0.997122i	$0.475845\pi$
$710$			2.07651i			0.0779299i
$711$	−1.58910	+	2.75240i	−0.0595960	+	0.103223i
$712$	−8.20794	−	14.2166i	−0.307606	−	0.532789i
$713$	−9.89602	+	5.71347i	−0.370609	+	0.213971i
$714$	−4.57552			−0.171235
$715$	−1.86409	+	2.06170i	−0.0697129	+	0.0771033i
$716$	4.74672			0.177393
$717$	7.98782	−	4.61177i	0.298311	−	0.172230i
$718$	−0.453097	−	0.784786i	−0.0169094	−	0.0292880i
$719$	4.99997	−	8.66020i	0.186467	−	0.322971i	−0.757603	−	0.652716i	$-0.773629\pi$
$719$	4.99997	−	8.66020i	0.186467	−	0.322971i	0.944070	+	0.329745i	$0.106963\pi$
$720$			2.79056i			0.103998i
$721$	25.9087	+	14.9584i	0.964889	+	0.557079i
$722$	−3.54332	−	2.04574i	−0.131869	−	0.0761344i
$723$		−	23.9661i		−	0.891309i
$724$	−4.33055	+	7.50074i	−0.160944	+	0.278763i
$725$	7.97584	+	13.8146i	0.296215	+	0.513060i
$726$	0.219134	−	0.126517i	0.00813282	−	0.00469549i
$727$	−28.3562			−1.05167			−0.525837	−	0.850585i	$-0.676248\pi$
$727$	−28.3562			−1.05167			−0.525837	+	0.850585i	$0.676248\pi$
$728$	9.67944	+	2.07833i	0.358744	+	0.0770279i
$729$	1.00000			0.0370370
$730$	−0.0577445	+	0.0333388i	−0.00213722	+	0.00123392i
$731$	−18.5787	−	32.1793i	−0.687158	−	1.19019i
$732$	−10.5633	+	18.2962i	−0.390432	+	0.676248i
$733$		−	41.7359i		−	1.54155i	−0.637108	−	0.770775i	$-0.719869\pi$
$733$		−	41.7359i		−	1.54155i	0.637108	−	0.770775i	$-0.280131\pi$
$734$	−2.19461	−	1.26706i	−0.0810045	−	0.0467680i
$735$	−0.401216	−	0.231642i	−0.0147991	−	0.00854425i
$736$		−	5.03948i		−	0.185758i
$737$	−5.24473	+	9.08414i	−0.193192	+	0.334619i
$738$	0.161446	+	0.279632i	0.00594290	+	0.0102934i
$739$	32.5054	−	18.7670i	1.19573	−	0.690355i	0.236129	−	0.971722i	$-0.424121\pi$
$739$	32.5054	−	18.7670i	1.19573	−	0.690355i	0.959600	+	0.281367i	$0.0907878\pi$
$740$	−15.8357			−0.582131
$741$	−5.77282	+	1.86253i	−0.212070	+	0.0684219i
$742$	−2.28994			−0.0840664
$743$	−31.4226	+	18.1418i	−1.15278	+	0.665559i	−0.949564	−	0.313574i	$-0.898474\pi$
$743$	−31.4226	+	18.1418i	−1.15278	+	0.665559i	−0.203219	+	0.979133i	$0.565140\pi$
$744$	−3.28334	−	5.68691i	−0.120373	−	0.208492i
$745$	2.56522	−	4.44308i	0.0939822	−	0.162782i
$746$			3.61623i			0.132400i
$747$	−7.54162	−	4.35415i	−0.275933	−	0.159310i
$748$	10.9966	+	6.34888i	0.402075	+	0.232138i
$749$		−	37.5718i		−	1.37284i
$750$	−0.917342	+	1.58888i	−0.0334966	+	0.0580178i
$751$	15.1877	+	26.3058i	0.554206	+	0.959912i	0.997965	+	0.0637662i	$0.0203112\pi$
$751$	15.1877	+	26.3058i	0.554206	+	0.959912i	−0.443759	+	0.896146i	$0.646355\pi$
$752$	−27.0940	+	15.6427i	−0.988018	+	0.570432i
$753$	2.08942			0.0761427
$754$	0.693449	−	3.22962i	0.0252539	−	0.117616i
$755$	2.26690			0.0825008
$756$	4.62237	−	2.66873i	0.168114	−	0.0970607i
$757$	7.23262	+	12.5273i	0.262874	+	0.455311i	0.967004	−	0.254759i	$-0.0819963\pi$
$757$	7.23262	+	12.5273i	0.262874	+	0.455311i	−0.704130	+	0.710071i	$0.748663\pi$
$758$	1.99837	−	3.46128i	0.0725842	−	0.125720i
$759$		−	1.73307i		−	0.0629064i
$760$	1.11859	+	0.645819i	0.0405756	+	0.0234263i
$761$	−20.7326	−	11.9700i	−0.751555	−	0.433910i	0.0747006	−	0.997206i	$-0.476200\pi$
$761$	−20.7326	−	11.9700i	−0.751555	−	0.433910i	−0.826255	+	0.563296i	$0.809533\pi$
$762$		−	1.66860i		−	0.0604471i
$763$	−9.50452	+	16.4623i	−0.344087	+	0.595976i
$764$	−1.61017	−	2.78890i	−0.0582541	−	0.100899i
$765$	4.37873	−	2.52806i	0.158313	−	0.0914022i
$766$	−4.94927			−0.178824
$767$	1.62806	−	7.58241i	0.0587859	−	0.273785i
$768$	−11.1202			−0.401266
$769$	15.6190	−	9.01766i	0.563237	−	0.325185i	−0.191207	−	0.981550i	$-0.561240\pi$
$769$	15.6190	−	9.01766i	0.563237	−	0.325185i	0.754444	+	0.656365i	$0.227907\pi$
$770$	−0.268889	−	0.465730i	−0.00969009	−	0.0167837i
$771$	6.28066	−	10.8784i	0.226192	−	0.391777i
$772$			4.61861i			0.166228i
$773$	30.2703	+	17.4766i	1.08875	+	0.628589i	0.933243	−	0.359246i	$-0.116966\pi$
$773$	30.2703	+	17.4766i	1.08875	+	0.628589i	0.155505	+	0.987835i	$0.450299\pi$
$774$	−1.24144	−	0.716749i	−0.0446228	−	0.0257630i
$775$			29.0491i			1.04347i
$776$	−4.87343	+	8.44103i	−0.174946	+	0.303015i
$777$	14.6269	+	25.3345i	0.524737	+	0.908871i
$778$	−0.336973	+	0.194552i	−0.0120811	+	0.00697501i
$779$	−2.14683			−0.0769182
$780$	−5.12103	+	1.65224i	−0.183362	+	0.0591598i
$781$	−10.6455			−0.380925
$782$	−2.49088	+	1.43811i	−0.0890736	+	0.0514267i
$783$	−1.81033	−	3.13559i	−0.0646960	−	0.112057i
$784$	1.08775	−	1.88404i	0.0388482	−	0.0672871i
$785$		−	5.46204i		−	0.194949i
$786$	4.61697	+	2.66561i	0.164682	+	0.0950792i
$787$	39.0772	+	22.5613i	1.39295	+	0.804222i	0.993641	−	0.112593i	$-0.0359157\pi$
$787$	39.0772	+	22.5613i	1.39295	+	0.804222i	0.399312	+	0.916815i	$0.369249\pi$
$788$		−	49.5145i		−	1.76388i
$789$	−12.3215	+	21.3414i	−0.438656	+	0.759774i
$790$	0.309970	+	0.536884i	0.0110282	+	0.0191015i
$791$	38.9761	−	22.5029i	1.38583	−	0.800110i
$792$	0.995935			0.0353890
$793$	−38.4695	−	8.25999i	−1.36609	−	0.293321i
$794$	−0.954918			−0.0338888
$795$	2.19145	−	1.26523i	0.0777227	−	0.0448732i
$796$	−22.3776	−	38.7592i	−0.793154	−	1.37378i
$797$	23.7227	−	41.0890i	0.840302	−	1.45545i	−0.0493379	−	0.998782i	$-0.515711\pi$
$797$	23.7227	−	41.0890i	0.840302	−	1.45545i	0.889640	−	0.456663i	$-0.150956\pi$
$798$		−	1.17364i		−	0.0415463i
$799$	49.0907	+	28.3425i	1.73670	+	1.00269i
$800$	−11.0948	−	6.40558i	−0.392260	−	0.226472i
$801$		−	16.4829i		−	0.582394i
$802$	3.15213	−	5.45965i	0.111306	−	0.192787i
$803$	−0.170916	−	0.296034i	−0.00603148	−	0.0104468i
$804$	−17.5867	+	10.1537i	−0.620234	+	0.358092i
$805$	−3.68332			−0.129820
$806$	4.03431	−	4.46200i	0.142103	−	0.157167i
$807$	24.0145			0.845350
$808$	11.7744	−	6.79798i	0.414223	−	0.239152i
$809$	11.6537	+	20.1848i	0.409722	+	0.709659i	0.994858	−	0.101276i	$-0.0322924\pi$
$809$	11.6537	+	20.1848i	0.409722	+	0.709659i	−0.585137	+	0.810935i	$0.698959\pi$
$810$	0.0975301	−	0.168927i	0.00342686	−	0.00593549i
$811$			3.05914i			0.107421i	0.998557	+	0.0537104i	$0.0171048\pi$
$811$			3.05914i			0.107421i	−0.998557	+	0.0537104i	$0.982895\pi$
$812$	−16.7360	−	9.66256i	−0.587320	−	0.339089i
$813$	1.03335	+	0.596608i	0.0362413	+	0.0209239i
$814$			2.68489i			0.0941053i
$815$	0.914739	−	1.58437i	0.0320419	−	0.0554982i
$816$	11.8713	+	20.5617i	0.415579	+	0.719805i
$817$	8.25408	−	4.76549i	0.288774	−	0.166724i
$818$	−3.92131			−0.137106
$819$	7.37345	+	6.66670i	0.257649	+	0.232953i
$820$	−1.90444			−0.0665059
$821$	31.1717	−	17.9970i	1.08790	−	0.628099i	0.154883	−	0.987933i	$-0.450500\pi$
$821$	31.1717	−	17.9970i	1.08790	−	0.628099i	0.933016	+	0.359834i	$0.117167\pi$
$822$	1.27022	+	2.20008i	0.0443039	+	0.0767366i
$823$	10.7035	−	18.5390i	0.373100	−	0.646228i	−0.616941	−	0.787009i	$-0.711628\pi$
$823$	10.7035	−	18.5390i	0.373100	−	0.646228i	0.990041	+	0.140782i	$0.0449616\pi$
$824$			10.8071i			0.376484i
$825$	−3.81548	−	2.20287i	−0.132838	−	0.0766940i
$826$	1.29947	+	0.750250i	0.0452144	+	0.0261045i
$827$		−	20.1533i		−	0.700798i	−0.936601	−	0.350399i	$-0.886046\pi$
$827$		−	20.1533i		−	0.700798i	0.936601	−	0.350399i	$-0.113954\pi$
$828$	1.67759	−	2.90567i	0.0583002	−	0.100979i
$829$	0.718920	+	1.24521i	0.0249691	+	0.0432478i	0.878240	−	0.478220i	$-0.158718\pi$
$829$	0.718920	+	1.24521i	0.0249691	+	0.0432478i	−0.853271	+	0.521468i	$0.825385\pi$
$830$	−1.47107	+	0.849322i	−0.0510616	+	0.0294804i
$831$	19.1547			0.664470
$832$	−7.20065	−	22.3180i	−0.249638	−	0.773738i
$833$	−3.94171			−0.136572
$834$	0.711241	−	0.410635i	0.0246282	−	0.0142191i
$835$	6.85884	+	11.8799i	0.237360	+	0.411120i
$836$	−1.62851	+	2.82066i	−0.0563231	+	0.0975544i
$837$		−	6.59348i		−	0.227904i
$838$	−8.31178	−	4.79881i	−0.287126	−	0.165772i
$839$	40.0491	+	23.1224i	1.38265	+	0.798273i	0.992473	−	0.122468i	$-0.0390807\pi$
$839$	40.0491	+	23.1224i	1.38265	+	0.798273i	0.390176	+	0.920740i	$0.372414\pi$
$840$		−	2.11668i		−	0.0730324i
$841$	7.94540	−	13.7618i	0.273979	−	0.474546i
$842$	−2.03181	−	3.51920i	−0.0700209	−	0.121280i
$843$	−6.56770	+	3.79186i	−0.226204	+	0.130599i
$844$	48.2034			1.65923
$845$	−5.85697	−	8.13183i	−0.201486	−	0.279743i
$846$	2.18686			0.0751857
$847$	2.38762	−	1.37849i	0.0820396	−	0.0473656i
$848$	5.94132	+	10.2907i	0.204026	+	0.353383i
$849$	−0.367235	+	0.636069i	−0.0126035	+	0.0218298i
$850$			7.31181i			0.250793i
$851$	15.9255	+	9.19460i	0.545920	+	0.315187i
$852$	−17.8482	−	10.3047i	−0.611470	−	0.353032i
$853$			2.07988i			0.0712137i	0.999366	+	0.0356068i	$0.0113364\pi$
$853$			2.07988i			0.0712137i	−0.999366	+	0.0356068i	$0.988664\pi$
$854$	3.80641	−	6.59289i	0.130253	−	0.225604i
$855$	0.648455	+	1.12316i	0.0221767	+	0.0384111i
$856$	11.7541	−	6.78623i	0.401747	−	0.231949i
$857$	−38.6745			−1.32110			−0.660548	−	0.750784i	$-0.729676\pi$
$857$	−38.6745			−1.32110			−0.660548	+	0.750784i	$0.729676\pi$
$858$	0.280132	+	0.868255i	0.00956356	+	0.0296417i
$859$	−33.3547			−1.13805			−0.569024	−	0.822321i	$-0.692679\pi$
$859$	−33.3547			−1.13805			−0.569024	+	0.822321i	$0.692679\pi$
$860$	7.32214	−	4.22744i	0.249683	−	0.144154i
$861$	1.75907	+	3.04679i	0.0599489	+	0.103834i
$862$	0.567545	−	0.983016i	0.0193307	−	0.0334817i
$863$			1.51642i			0.0516197i	0.999667	+	0.0258098i	$0.00821644\pi$
$863$			1.51642i			0.0516197i	−0.999667	+	0.0258098i	$0.991784\pi$
$864$	2.51826	+	1.45392i	0.0856730	+	0.0494633i
$865$	−9.20651	−	5.31538i	−0.313031	−	0.180728i
$866$			7.39728i			0.251370i
$867$	13.0092	−	22.5326i	0.441817	−	0.765249i
$868$	−17.5962	−	30.4775i	−0.597254	−	1.03447i
$869$	−2.75240	+	1.58910i	−0.0933689	+	0.0539066i
$870$	−0.706247			−0.0239440
$871$	−28.0537	−	25.3647i	−0.950562	−	0.859450i
$872$	−6.86683			−0.232540
$873$	−8.47548	+	4.89332i	−0.286851	+	0.165614i
$874$	−0.368879	−	0.638918i	−0.0124775	−	0.0216117i
$875$	−9.99510	+	17.3120i	−0.337896	+	0.585253i
$876$		−	0.661776i		−	0.0223593i
$877$	−21.9403	−	12.6672i	−0.740870	−	0.427741i	0.0815158	−	0.996672i	$-0.474024\pi$
$877$	−21.9403	−	12.6672i	−0.740870	−	0.427741i	−0.822385	+	0.568931i	$0.807357\pi$
$878$	−4.53203	−	2.61657i	−0.152949	−	0.0883049i
$879$		−	7.97013i		−	0.268826i
$880$	−1.39528	+	2.41670i	−0.0470349	+	0.0814668i
$881$	−27.7933	−	48.1393i	−0.936379	−	1.62186i	−0.772157	−	0.635432i	$-0.780822\pi$
$881$	−27.7933	−	48.1393i	−0.936379	−	1.62186i	−0.164222	−	0.986423i	$-0.552511\pi$
$882$	−0.131694	+	0.0760338i	−0.00443438	+	0.00256019i
$883$	−35.2667			−1.18682			−0.593409	−	0.804901i	$-0.702218\pi$
$883$	−35.2667			−1.18682			−0.593409	+	0.804901i	$0.702218\pi$
$884$	−30.7046	+	33.9596i	−1.03271	+	1.14219i
$885$	−1.65811			−0.0557366
$886$	3.37000	−	1.94567i	0.113217	−	0.0653661i
$887$	28.5777	+	49.4981i	0.959547	+	1.66198i	0.723603	+	0.690217i	$0.242485\pi$
$887$	28.5777	+	49.4981i	0.959547	+	1.66198i	0.235944	+	0.971767i	$0.424182\pi$
$888$	−5.28382	+	9.15185i	−0.177314	+	0.307116i
$889$		−	18.1806i		−	0.609759i
$890$	−2.78441	−	1.60758i	−0.0933335	−	0.0538861i
$891$	0.866025	+	0.500000i	0.0290129	+	0.0167506i
$892$		−	29.8935i		−	1.00091i
$893$	−7.26995	+	12.5919i	−0.243280	+	0.421372i
$894$	−0.842002	−	1.45839i	−0.0281607	−	0.0487758i
$895$	1.63687	−	0.945048i	0.0547146	−	0.0315895i
$896$	20.5711			0.687232
$897$	6.10942	+	1.31179i	0.203988	+	0.0437993i
$898$	5.78219			0.192954
$899$	−20.6744	+	11.9364i	−0.689530	+	0.398100i
$900$	−4.26469	−	7.38667i	−0.142156	−	0.246222i
$901$	10.7649	−	18.6453i	0.358630	−	0.621165i
$902$			0.322892i			0.0107511i
$903$	−13.5264	−	7.80949i	−0.450132	−	0.259884i
$904$	14.0797	+	8.12894i	0.468285	+	0.270365i
$905$			3.44876i			0.114641i
$906$	0.372041	−	0.644394i	0.0123602	−	0.0214086i
$907$	−12.1361	−	21.0204i	−0.402973	−	0.697970i	0.591110	−	0.806591i	$-0.298690\pi$
$907$	−12.1361	−	21.0204i	−0.402973	−	0.697970i	−0.994083	+	0.108621i	$0.965356\pi$
$908$	−14.4669	+	8.35246i	−0.480101	+	0.277186i
$909$	13.6514			0.452790
$910$	1.84532	−	0.595371i	0.0611718	−	0.0197364i
$911$	0.660537			0.0218846			0.0109423	−	0.999940i	$-0.496517\pi$
$911$	0.660537			0.0218846			0.0109423	+	0.999940i	$0.496517\pi$
$912$	−5.27415	+	3.04503i	−0.174644	+	0.100831i
$913$	−4.35415	−	7.54162i	−0.144101	−	0.249591i
$914$	−1.19204	+	2.06467i	−0.0394290	+	0.0682931i
$915$			8.41243i			0.278106i
$916$	−6.96689	−	4.02234i	−0.230193	−	0.132902i
$917$	50.3052	+	29.0437i	1.66123	+	0.959109i
$918$		−	1.65961i		−	0.0547753i
$919$	14.3886	−	24.9218i	0.474637	−	0.822095i	−0.524942	−	0.851138i	$-0.675913\pi$
$919$	14.3886	−	24.9218i	0.474637	−	0.822095i	0.999578	+	0.0290436i	$0.00924615\pi$
$920$	−0.665283	−	1.15230i	−0.0219337	−	0.0379903i
$921$	−12.9160	+	7.45706i	−0.425597	+	0.245719i
$922$	−6.93432			−0.228370
$923$	8.05773	−	37.5275i	0.265224	−	1.23523i
$924$	5.33745			0.175589
$925$	40.4852	−	23.3741i	1.33115	−	0.768537i
$926$	2.76593	+	4.79074i	0.0908942	+	0.157433i
$927$	−5.42562	+	9.39745i	−0.178201	+	0.308653i
$928$		−	10.5283i		−	0.345608i
$929$	−35.7513	−	20.6410i	−1.17296	−	0.677210i	−0.218586	−	0.975818i	$-0.570144\pi$
$929$	−35.7513	−	20.6410i	−1.17296	−	0.677210i	−0.954376	+	0.298608i	$0.903478\pi$
$930$	−1.11382	−	0.643062i	−0.0365235	−	0.0210868i
$931$		−	1.01106i		−	0.0331362i
$932$	25.9577	−	44.9601i	0.850273	−	1.47272i
$933$	4.02167	+	6.96574i	0.131664	+	0.228048i
$934$	1.16939	−	0.675148i	0.0382636	−	0.0220915i
$935$	5.05612			0.165353
$936$	−0.753840	+	3.51088i	−0.0246400	+	0.114757i
$937$	−10.0860			−0.329495			−0.164747	−	0.986336i	$-0.552681\pi$
$937$	−10.0860			−0.329495			−0.164747	+	0.986336i	$0.552681\pi$
$938$	6.33720	−	3.65878i	0.206917	−	0.119464i
$939$	−16.0946	−	27.8767i	−0.525228	−	0.909721i
$940$	−6.44912	+	11.1702i	−0.210347	+	0.364332i
$941$			6.21148i			0.202488i	0.994862	+	0.101244i	$0.0322823\pi$
$941$			6.21148i			0.202488i	−0.994862	+	0.101244i	$0.967718\pi$
$942$	−1.55265	−	0.896425i	−0.0505882	−	0.0292071i
$943$	1.91524	+	1.10577i	0.0623689	+	0.0360087i
$944$		−	7.78618i		−	0.253418i
$945$	1.06266	−	1.84058i	0.0345683	−	0.0598741i
$946$	−0.716749	−	1.24144i	−0.0233035	−	0.0403629i
$947$	−8.16032	+	4.71136i	−0.265175	+	0.153099i	−0.626693	−	0.779266i	$-0.715592\pi$
$947$	−8.16032	+	4.71136i	−0.265175	+	0.153099i	0.361518	+	0.932365i	$0.382259\pi$
$948$	−6.15292			−0.199837
$949$	1.17295	−	0.378439i	0.0380756	−	0.0122847i
$950$	−1.87550			−0.0608493
$951$	−12.6104	+	7.28064i	−0.408921	+	0.236091i
$952$	−9.00457	−	15.5964i	−0.291840	−	0.505481i
$953$	7.02878	−	12.1742i	0.227684	−	0.394361i	−0.729437	−	0.684048i	$-0.760218\pi$
$953$	7.02878	−	12.1742i	0.227684	−	0.394361i	0.957121	+	0.289687i	$0.0935512\pi$
$954$		−	0.830596i		−	0.0268915i
$955$	−1.11051	−	0.641155i	−0.0359354	−	0.0207473i
$956$	15.4642	+	8.92827i	0.500148	+	0.288761i
$957$		−	3.62066i		−	0.117039i
$958$	−4.91877	+	8.51956i	−0.158918	+	0.275254i
$959$	13.8399	+	23.9715i	0.446915	+	0.774079i
$960$	−4.34218	+	2.50696i	−0.140143	+	0.0809117i
$961$	−12.4739			−0.402385
$962$	−9.46478	−	2.03224i	−0.305157	−	0.0655219i
$963$	13.6279			0.439152
$964$	40.1816	−	23.1989i	1.29416	−	0.747186i
$965$	0.919543	+	1.59269i	0.0296011	+	0.0512707i
$966$	−0.604504	+	1.04703i	−0.0194496	+	0.0336877i
$967$			25.7205i			0.827117i	0.910478	+	0.413558i	$0.135714\pi$
$967$			25.7205i			0.827117i	−0.910478	+	0.413558i	$0.864286\pi$
$968$	0.862505	+	0.497968i	0.0277220	+	0.0160053i
$969$	9.55604	+	5.51718i	0.306984	+	0.177237i
$970$			1.90898i			0.0612938i
$971$	−22.9586	+	39.7654i	−0.736776	+	1.27613i	0.217163	+	0.976135i	$0.430320\pi$
$971$	−22.9586	+	39.7654i	−0.736776	+	1.27613i	−0.953940	+	0.299999i	$0.903014\pi$
$972$	0.967987	+	1.67660i	0.0310482	+	0.0537771i
$973$	7.74948	−	4.47416i	0.248437	−	0.143435i
$974$	6.97975			0.223646
$975$	10.6536	−	11.7830i	0.341187	−	0.377357i
$976$	−39.5033			−1.26447
$977$	45.5590	−	26.3035i	1.45756	−	0.841524i	0.458671	−	0.888606i	$-0.348325\pi$
$977$	45.5590	−	26.3035i	1.45756	−	0.841524i	0.998891	+	0.0470818i	$0.0149922\pi$
$978$	−0.300252	−	0.520052i	−0.00960101	−	0.0166294i
$979$	8.24144	−	14.2746i	0.263398	−	0.456218i
$980$		−	0.896906i		−	0.0286506i
$981$	−5.97112	−	3.44743i	−0.190643	−	0.110068i
$982$	−2.87644	−	1.66071i	−0.0917908	−	0.0529955i
$983$		−	2.69450i		−	0.0859412i	−0.999076	−	0.0429706i	$-0.986318\pi$
$983$		−	2.69450i		−	0.0859412i	0.999076	−	0.0429706i	$-0.0136822\pi$
$984$	−0.635446	+	1.10063i	−0.0202573	+	0.0350867i
$985$	−9.85810	−	17.0747i	−0.314105	−	0.544046i
$986$	−5.20385	+	3.00444i	−0.165724	+	0.0956810i
$987$	23.8274			0.758433
$988$	−8.71075	−	7.87582i	−0.277126	−	0.250563i
$989$	−9.81824			−0.312202
$990$	0.168927	−	0.0975301i	0.00536885	−	0.00309971i
$991$	−7.97924	−	13.8205i	−0.253469	−	0.439021i	0.711010	−	0.703182i	$-0.248238\pi$
$991$	−7.97924	−	13.8205i	−0.253469	−	0.439021i	−0.964479	+	0.264161i	$0.914905\pi$
$992$	9.58638	−	16.6041i	0.304368	−	0.527181i
$993$			19.8159i			0.628839i
$994$	6.43145	+	3.71320i	0.203993	+	0.117776i
$995$	−15.4335	−	8.91055i	−0.489275	−	0.282483i
$996$		−	16.8591i		−	0.534200i
$997$	−21.4084	+	37.0804i	−0.678010	+	1.17435i	0.297570	+	0.954700i	$0.403824\pi$
$997$	−21.4084	+	37.0804i	−0.678010	+	1.17435i	−0.975579	+	0.219647i	$0.929509\pi$
$998$	−3.93007	−	6.80708i	−0.124404	−	0.215474i
$999$	−9.18921	+	5.30539i	−0.290734	+	0.167855i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.s.a.166.7	✓	24
13.2	odd	12		5577.2.a.z.1.7		12
13.4	even	6	inner	429.2.s.a.199.7	yes	24
13.11	odd	12		5577.2.a.be.1.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.s.a.166.7	✓	24	1.1	even	1	trivial
429.2.s.a.199.7	yes	24	13.4	even	6	inner
5577.2.a.z.1.7		12	13.2	odd	12
5577.2.a.be.1.6		12	13.11	odd	12

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.219134 - 0.126517i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.967987 + 1.67660i) q^{4} +0.770885i q^{5} +(0.219134 + 0.126517i) q^{6} +(2.38762 + 1.37849i) q^{7} +0.995935i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.219134 - 0.126517i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.967987 + 1.67660i) q^{4} +0.770885i q^{5} +(0.219134 + 0.126517i) q^{6} +(2.38762 + 1.37849i) q^{7} +0.995935i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.0975301 + 0.168927i) q^{10} +(-0.866025 + 0.500000i) q^{11} -1.93597 q^{12} +(-1.10709 - 3.43138i) q^{13} +0.697611 q^{14} +(-0.667606 + 0.385443i) q^{15} +(-1.80997 - 3.13496i) q^{16} +(-3.27942 + 5.68013i) q^{17} +0.253034i q^{18} +(-1.45697 - 0.841182i) q^{19} +(-1.29247 - 0.746207i) q^{20} +2.75699i q^{21} +(-0.126517 + 0.219134i) q^{22} +(0.866534 + 1.50088i) q^{23} +(-0.862505 + 0.497968i) q^{24} +4.40574 q^{25} +(-0.676729 - 0.611864i) q^{26} -1.00000 q^{27} +(-4.62237 + 2.66873i) q^{28} +(1.81033 + 3.13559i) q^{29} +(-0.0975301 + 0.168927i) q^{30} +6.59348i q^{31} +(-2.51826 - 1.45392i) q^{32} +(-0.866025 - 0.500000i) q^{33} +1.65961i q^{34} +(-1.06266 + 1.84058i) q^{35} +(-0.967987 - 1.67660i) q^{36} +(9.18921 - 5.30539i) q^{37} -0.425695 q^{38} +(2.41811 - 2.67446i) q^{39} -0.767752 q^{40} +(1.10512 - 0.638040i) q^{41} +(0.348806 + 0.604149i) q^{42} +(-2.83262 + 4.90624i) q^{43} -1.93597i q^{44} +(-0.667606 - 0.385443i) q^{45} +(0.379774 + 0.219262i) q^{46} -8.64254i q^{47} +(1.80997 - 3.13496i) q^{48} +(0.300488 + 0.520461i) q^{49} +(0.965446 - 0.557400i) q^{50} -6.55885 q^{51} +(6.82471 + 1.46537i) q^{52} -3.28255 q^{53} +(-0.219134 + 0.126517i) q^{54} +(-0.385443 - 0.667606i) q^{55} +(-1.37289 + 2.37792i) q^{56} -1.68236i q^{57} +(0.793410 + 0.458075i) q^{58} +(1.86274 + 1.07546i) q^{59} -1.49241i q^{60} +(5.45634 - 9.45066i) q^{61} +(0.834187 + 1.44485i) q^{62} +(-2.38762 + 1.37849i) q^{63} +6.50410 q^{64} +(2.64520 - 0.853443i) q^{65} -0.253034 q^{66} +(9.08414 - 5.24473i) q^{67} +(-6.34888 - 10.9966i) q^{68} +(-0.866534 + 1.50088i) q^{69} +0.537778i q^{70} +(9.21925 + 5.32274i) q^{71} +(-0.862505 - 0.497968i) q^{72} +0.341831i q^{73} +(1.34244 - 2.32518i) q^{74} +(2.20287 + 3.81548i) q^{75} +(2.82066 - 1.62851i) q^{76} -2.75699 q^{77} +(0.191526 - 0.891997i) q^{78} +3.17820 q^{79} +(2.41670 - 1.39528i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.161446 - 0.279632i) q^{82} +8.70831i q^{83} +(-4.62237 - 2.66873i) q^{84} +(-4.37873 - 2.52806i) q^{85} +1.43350i q^{86} +(-1.81033 + 3.13559i) q^{87} +(-0.497968 - 0.862505i) q^{88} +(-14.2746 + 8.24144i) q^{89} -0.195060 q^{90} +(2.08681 - 9.71895i) q^{91} -3.35517 q^{92} +(-5.71012 + 3.29674i) q^{93} +(-1.09343 - 1.89387i) q^{94} +(0.648455 - 1.12316i) q^{95} -2.90784i q^{96} +(8.47548 + 4.89332i) q^{97} +(0.131694 + 0.0760338i) q^{98} -1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{3} + 14 q^{4} + 6 q^{7} - 12 q^{9}+O(q^{10}) \) 24 * q + 12 * q^3 + 14 * q^4 + 6 * q^7 - 12 * q^9	\( 24 q + 12 q^{3} + 14 q^{4} + 6 q^{7} - 12 q^{9} + 28 q^{12} - 4 q^{13} + 20 q^{14} - 6 q^{15} - 14 q^{16} + 10 q^{17} - 18 q^{20} + 2 q^{22} - 14 q^{23} + 4 q^{25} - 34 q^{26} - 24 q^{27} - 30 q^{28} + 4 q^{29} + 30 q^{32} + 6 q^{35} + 14 q^{36} + 12 q^{38} - 2 q^{39} + 20 q^{40} - 30 q^{41} + 10 q^{42} - 4 q^{43} - 6 q^{45} - 24 q^{46} + 14 q^{48} + 18 q^{49} - 84 q^{50} + 20 q^{51} + 40 q^{52} - 56 q^{53} - 4 q^{55} + 26 q^{56} + 48 q^{58} + 60 q^{59} - 2 q^{61} + 18 q^{62} - 6 q^{63} - 48 q^{64} - 10 q^{65} + 4 q^{66} - 42 q^{67} - 18 q^{68} + 14 q^{69} + 6 q^{71} + 2 q^{75} - 48 q^{76} + 24 q^{77} - 26 q^{78} - 20 q^{79} + 30 q^{80} - 12 q^{81} - 10 q^{82} - 30 q^{84} + 6 q^{85} - 4 q^{87} - 12 q^{88} + 12 q^{89} + 18 q^{91} + 8 q^{92} + 12 q^{93} - 22 q^{94} + 4 q^{95} + 6 q^{97} - 114 q^{98}+O(q^{100}) \) 24 * q + 12 * q^3 + 14 * q^4 + 6 * q^7 - 12 * q^9 + 28 * q^12 - 4 * q^13 + 20 * q^14 - 6 * q^15 - 14 * q^16 + 10 * q^17 - 18 * q^20 + 2 * q^22 - 14 * q^23 + 4 * q^25 - 34 * q^26 - 24 * q^27 - 30 * q^28 + 4 * q^29 + 30 * q^32 + 6 * q^35 + 14 * q^36 + 12 * q^38 - 2 * q^39 + 20 * q^40 - 30 * q^41 + 10 * q^42 - 4 * q^43 - 6 * q^45 - 24 * q^46 + 14 * q^48 + 18 * q^49 - 84 * q^50 + 20 * q^51 + 40 * q^52 - 56 * q^53 - 4 * q^55 + 26 * q^56 + 48 * q^58 + 60 * q^59 - 2 * q^61 + 18 * q^62 - 6 * q^63 - 48 * q^64 - 10 * q^65 + 4 * q^66 - 42 * q^67 - 18 * q^68 + 14 * q^69 + 6 * q^71 + 2 * q^75 - 48 * q^76 + 24 * q^77 - 26 * q^78 - 20 * q^79 + 30 * q^80 - 12 * q^81 - 10 * q^82 - 30 * q^84 + 6 * q^85 - 4 * q^87 - 12 * q^88 + 12 * q^89 + 18 * q^91 + 8 * q^92 + 12 * q^93 - 22 * q^94 + 4 * q^95 + 6 * q^97 - 114 * q^98

Introduction

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