LMFDB - Embedded newform 425.2.r.a.69.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(69,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([9, 0]))

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

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

chi := DirichletCharacter("425.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.r (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			69.20
Character	$\chi$	$=$	425.69
Dual form			425.2.r.a.154.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.248853 + 0.0808572i) q^{2} +(-0.408373 - 0.562077i) q^{3} +(-1.56264 + 1.13533i) q^{4} +(-1.61719 - 1.54424i) q^{5} +(0.147073 + 0.106855i) q^{6} +1.76904i q^{7} +(0.604668 - 0.832255i) q^{8} +(0.777889 - 2.39410i) q^{9} +(0.527307 + 0.253527i) q^{10} +(1.20206 + 3.69957i) q^{11} +(1.27628 + 0.414689i) q^{12} +(2.08164 + 0.676366i) q^{13} +(-0.143040 - 0.440231i) q^{14} +(-0.207564 + 1.53961i) q^{15} +(1.11057 - 3.41800i) q^{16} +(-0.587785 + 0.809017i) q^{17} +0.658676i q^{18} +(4.31151 + 3.13249i) q^{19} +(4.28032 + 0.577055i) q^{20} +(0.994337 - 0.722428i) q^{21} +(-0.598274 - 0.823454i) q^{22} +(7.61793 - 2.47521i) q^{23} -0.714721 q^{24} +(0.230636 + 4.99468i) q^{25} -0.572712 q^{26} +(-3.64562 + 1.18453i) q^{27} +(-2.00844 - 2.76438i) q^{28} +(-1.72717 + 1.25486i) q^{29} +(-0.0728359 - 0.399920i) q^{30} +(8.32975 + 6.05192i) q^{31} +2.99782i q^{32} +(1.58855 - 2.18646i) q^{33} +(0.0808572 - 0.248853i) q^{34} +(2.73183 - 2.86089i) q^{35} +(1.50252 + 4.62428i) q^{36} +(-3.86926 - 1.25720i) q^{37} +(-1.32622 - 0.430914i) q^{38} +(-0.469916 - 1.44625i) q^{39} +(-2.26307 + 0.412163i) q^{40} +(2.36700 - 7.28488i) q^{41} +(-0.189030 + 0.260178i) q^{42} +4.18236i q^{43} +(-6.07862 - 4.41638i) q^{44} +(-4.95506 + 2.67047i) q^{45} +(-1.69560 + 1.23193i) q^{46} +(-5.92954 - 8.16131i) q^{47} +(-2.37470 + 0.771588i) q^{48} +3.87049 q^{49} +(-0.461250 - 1.22429i) q^{50} +0.694765 q^{51} +(-4.02076 + 1.30642i) q^{52} +(1.99138 + 2.74089i) q^{53} +(0.811444 - 0.589549i) q^{54} +(3.76906 - 7.83920i) q^{55} +(1.47229 + 1.06968i) q^{56} -3.70262i q^{57} +(0.328346 - 0.451930i) q^{58} +(-2.93943 + 9.04665i) q^{59} +(-1.42362 - 2.64152i) q^{60} +(1.67435 + 5.15313i) q^{61} +(-2.56222 - 0.832517i) q^{62} +(4.23526 + 1.37612i) q^{63} +(1.97875 + 6.08997i) q^{64} +(-2.32195 - 4.30837i) q^{65} +(-0.218525 + 0.672552i) q^{66} +(5.25041 - 7.22656i) q^{67} -1.93153i q^{68} +(-4.50221 - 3.27105i) q^{69} +(-0.448500 + 0.932828i) q^{70} +(0.990731 - 0.719808i) q^{71} +(-1.52213 - 2.09504i) q^{72} +(-8.89853 + 2.89131i) q^{73} +1.06453 q^{74} +(2.71321 - 2.16932i) q^{75} -10.2938 q^{76} +(-6.54470 + 2.12650i) q^{77} +(0.233880 + 0.321908i) q^{78} +(-7.05538 + 5.12603i) q^{79} +(-7.07423 + 3.81257i) q^{80} +(-3.95505 - 2.87351i) q^{81} +2.00425i q^{82} +(9.22003 - 12.6903i) q^{83} +(-0.733603 + 2.25780i) q^{84} +(2.19988 - 0.400655i) q^{85} +(-0.338174 - 1.04079i) q^{86} +(1.41066 + 0.458350i) q^{87} +(3.80583 + 1.23659i) q^{88} +(2.92596 + 9.00518i) q^{89} +(1.01715 - 1.06521i) q^{90} +(-1.19652 + 3.68251i) q^{91} +(-9.09393 + 12.5167i) q^{92} -7.15340i q^{93} +(2.13548 + 1.55152i) q^{94} +(-2.13522 - 11.7239i) q^{95} +(1.68501 - 1.22423i) q^{96} +(-0.0568680 - 0.0782721i) q^{97} +(-0.963183 + 0.312957i) q^{98} +9.79220 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) $ 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

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 $

$2$	−0.248853	+	0.0808572i	−0.175966	+	0.0571747i	−0.395675	−	0.918391i	$-0.629489\pi$
$2$	−0.248853	+	0.0808572i	−0.175966	+	0.0571747i	0.219709	+	0.975565i	$0.429489\pi$
$3$	−0.408373	−	0.562077i	−0.235774	−	0.324515i	0.674692	−	0.738100i	$-0.264277\pi$
$3$	−0.408373	−	0.562077i	−0.235774	−	0.324515i	−0.910466	+	0.413585i	$0.864277\pi$
$4$	−1.56264	+	1.13533i	−0.781322	+	0.567664i
$5$	−1.61719	−	1.54424i	−0.723231	−	0.690606i
$5$	−1.61719	−	1.54424i	−0.723231	−	0.690606i
$6$	0.147073	+	0.106855i	0.0600422	+	0.0436232i
$7$			1.76904i			0.668635i	0.942460	+	0.334318i	$0.108506\pi$
$7$			1.76904i			0.668635i	−0.942460	+	0.334318i	$0.891494\pi$
$8$	0.604668	−	0.832255i	0.213783	−	0.294246i
$9$	0.777889	−	2.39410i	0.259296	−	0.798032i
$10$	0.527307	+	0.253527i	0.166749	+	0.0801723i
$11$	1.20206	+	3.69957i	0.362436	+	1.11546i	0.951571	+	0.307428i	$0.0994684\pi$
$11$	1.20206	+	3.69957i	0.362436	+	1.11546i	−0.589135	+	0.808034i	$0.700532\pi$
$12$	1.27628	+	0.414689i	0.368431	+	0.119710i
$13$	2.08164	+	0.676366i	0.577343	+	0.187590i	0.583110	−	0.812393i	$-0.301836\pi$
$13$	2.08164	+	0.676366i	0.577343	+	0.187590i	−0.00576673	+	0.999983i	$0.501836\pi$
$14$	−0.143040	−	0.440231i	−0.0382290	−	0.117657i
$15$	−0.207564	+	1.53961i	−0.0535929	+	0.397526i
$16$	1.11057	−	3.41800i	0.277644	−	0.854499i
$17$	−0.587785	+	0.809017i	−0.142559	+	0.196215i
$17$	−0.587785	+	0.809017i	−0.142559	+	0.196215i
$18$			0.658676i			0.155251i
$19$	4.31151	+	3.13249i	0.989128	+	0.718643i	0.959730	−	0.280925i	$-0.0906411\pi$
$19$	4.31151	+	3.13249i	0.989128	+	0.718643i	0.0293977	+	0.999568i	$0.490641\pi$
$20$	4.28032	+	0.577055i	0.957108	+	0.129033i
$21$	0.994337	−	0.722428i	0.216982	−	0.157647i
$22$	−0.598274	−	0.823454i	−0.127552	−	0.175561i
$23$	7.61793	−	2.47521i	1.58845	−	0.516118i	0.624233	−	0.781239i	$-0.285412\pi$
$23$	7.61793	−	2.47521i	1.58845	−	0.516118i	0.964215	+	0.265121i	$0.0854118\pi$
$24$	−0.714721			−0.145892
$25$	0.230636	+	4.99468i	0.0461272	+	0.998936i
$26$	−0.572712			−0.112318
$27$	−3.64562	+	1.18453i	−0.701599	+	0.227963i
$28$	−2.00844	−	2.76438i	−0.379560	−	0.522419i
$29$	−1.72717	+	1.25486i	−0.320727	+	0.233022i	−0.736486	−	0.676453i	$-0.763516\pi$
$29$	−1.72717	+	1.25486i	−0.320727	+	0.233022i	0.415758	+	0.909475i	$0.363516\pi$
$30$	−0.0728359	−	0.399920i	−0.0132980	−	0.0730151i
$31$	8.32975	+	6.05192i	1.49607	+	1.08696i	0.971915	+	0.235332i	$0.0756178\pi$
$31$	8.32975	+	6.05192i	1.49607	+	1.08696i	0.524152	+	0.851624i	$0.324382\pi$
$32$			2.99782i			0.529945i
$33$	1.58855	−	2.18646i	0.276532	−	0.380613i
$34$	0.0808572	−	0.248853i	0.0138669	−	0.0426779i
$35$	2.73183	−	2.86089i	0.461763	−	0.483578i
$36$	1.50252	+	4.62428i	0.250420	+	0.770713i
$37$	−3.86926	−	1.25720i	−0.636103	−	0.206682i	−0.0268261	−	0.999640i	$-0.508540\pi$
$37$	−3.86926	−	1.25720i	−0.636103	−	0.206682i	−0.609277	+	0.792958i	$0.708540\pi$
$38$	−1.32622	−	0.430914i	−0.215141	−	0.0699034i
$39$	−0.469916	−	1.44625i	−0.0752467	−	0.231586i
$40$	−2.26307	+	0.412163i	−0.357823	+	0.0651688i
$41$	2.36700	−	7.28488i	0.369663	−	1.13771i	−0.577346	−	0.816500i	$-0.695912\pi$
$41$	2.36700	−	7.28488i	0.369663	−	1.13771i	0.947009	−	0.321207i	$-0.104088\pi$
$42$	−0.189030	+	0.260178i	−0.0291680	+	0.0401463i
$43$			4.18236i			0.637805i	0.947788	+	0.318902i	$0.103314\pi$
$43$			4.18236i			0.637805i	−0.947788	+	0.318902i	$0.896686\pi$
$44$	−6.07862	−	4.41638i	−0.916387	−	0.665794i
$45$	−4.95506	+	2.67047i	−0.738657	+	0.398090i
$46$	−1.69560	+	1.23193i	−0.250003	+	0.181638i
$47$	−5.92954	−	8.16131i	−0.864912	−	1.19045i	−0.980376	−	0.197137i	$-0.936835\pi$
$47$	−5.92954	−	8.16131i	−0.864912	−	1.19045i	0.115464	−	0.993312i	$-0.463165\pi$
$48$	−2.37470	+	0.771588i	−0.342759	+	0.111369i
$49$	3.87049			0.552927
$50$	−0.461250	−	1.22429i	−0.0652306	−	0.173141i
$51$	0.694765			0.0972866
$52$	−4.02076	+	1.30642i	−0.557579	+	0.181168i
$53$	1.99138	+	2.74089i	0.273536	+	0.376491i	0.923580	−	0.383407i	$-0.125249\pi$
$53$	1.99138	+	2.74089i	0.273536	+	0.376491i	−0.650043	+	0.759897i	$0.725249\pi$
$54$	0.811444	−	0.589549i	0.110424	−	0.0802274i
$55$	3.76906	−	7.83920i	0.508220	−	1.05704i
$56$	1.47229	+	1.06968i	0.196743	+	0.142942i
$57$		−	3.70262i		−	0.490424i
$58$	0.328346	−	0.451930i	0.0431140	−	0.0593413i
$59$	−2.93943	+	9.04665i	−0.382682	+	1.17777i	0.555466	+	0.831539i	$0.312540\pi$
$59$	−2.93943	+	9.04665i	−0.382682	+	1.17777i	−0.938148	+	0.346234i	$0.887460\pi$
$60$	−1.42362	−	2.64152i	−0.183788	−	0.341019i
$61$	1.67435	+	5.15313i	0.214379	+	0.659791i	0.999197	+	0.0400646i	$0.0127564\pi$
$61$	1.67435	+	5.15313i	0.214379	+	0.659791i	−0.784818	+	0.619726i	$0.787244\pi$
$62$	−2.56222	−	0.832517i	−0.325403	−	0.105730i
$63$	4.23526	+	1.37612i	0.533592	+	0.173375i
$64$	1.97875	+	6.08997i	0.247344	+	0.761247i
$65$	−2.32195	−	4.30837i	−0.288002	−	0.534388i
$66$	−0.218525	+	0.672552i	−0.0268986	+	0.0827854i
$67$	5.25041	−	7.22656i	0.641439	−	0.882865i	−0.357252	−	0.934008i	$-0.616286\pi$
$67$	5.25041	−	7.22656i	0.641439	−	0.882865i	0.998691	+	0.0511428i	$0.0162864\pi$
$68$		−	1.93153i		−	0.234233i
$69$	−4.50221	−	3.27105i	−0.542003	−	0.393788i
$70$	−0.448500	+	0.932828i	−0.0536060	+	0.111494i
$71$	0.990731	−	0.719808i	0.117578	−	0.0854255i	−0.527442	−	0.849591i	$-0.676849\pi$
$71$	0.990731	−	0.719808i	0.117578	−	0.0854255i	0.645020	+	0.764165i	$0.276849\pi$
$72$	−1.52213	−	2.09504i	−0.179385	−	0.246902i
$73$	−8.89853	+	2.89131i	−1.04149	+	0.338402i	−0.779325	−	0.626620i	$-0.784438\pi$
$73$	−8.89853	+	2.89131i	−1.04149	+	0.338402i	−0.262169	+	0.965022i	$0.584438\pi$
$74$	1.06453			0.123749
$75$	2.71321	−	2.16932i	0.313294	−	0.250492i
$76$	−10.2938			−1.18077
$77$	−6.54470	+	2.12650i	−0.745837	+	0.242337i
$78$	0.233880	+	0.321908i	0.0264817	+	0.0364489i
$79$	−7.05538	+	5.12603i	−0.793792	+	0.576724i	−0.909086	−	0.416608i	$-0.863219\pi$
$79$	−7.05538	+	5.12603i	−0.793792	+	0.576724i	0.115294	+	0.993331i	$0.463219\pi$
$80$	−7.07423	+	3.81257i	−0.790922	+	0.426258i
$81$	−3.95505	−	2.87351i	−0.439450	−	0.319279i
$82$			2.00425i			0.221333i
$83$	9.22003	−	12.6903i	1.01203	−	1.39294i	0.0943865	−	0.995536i	$-0.469911\pi$
$83$	9.22003	−	12.6903i	1.01203	−	1.39294i	0.917644	−	0.397404i	$-0.130089\pi$
$84$	−0.733603	+	2.25780i	−0.0800426	+	0.246346i
$85$	2.19988	−	0.400655i	0.238611	−	0.0434572i
$86$	−0.338174	−	1.04079i	−0.0364663	−	0.112232i
$87$	1.41066	+	0.458350i	0.151238	+	0.0491403i
$88$	3.80583	+	1.23659i	0.405703	+	0.131821i
$89$	2.92596	+	9.00518i	0.310151	+	0.954547i	0.977705	+	0.209985i	$0.0673415\pi$
$89$	2.92596	+	9.00518i	0.310151	+	0.954547i	−0.667554	+	0.744562i	$0.732658\pi$
$90$	1.01715	−	1.06521i	0.107217	−	0.112283i
$91$	−1.19652	+	3.68251i	−0.125429	+	0.386032i
$92$	−9.09393	+	12.5167i	−0.948108	+	1.30496i
$93$		−	7.15340i		−	0.741773i
$94$	2.13548	+	1.55152i	0.220258	+	0.160027i
$95$	−2.13522	−	11.7239i	−0.219069	−	1.20284i
$96$	1.68501	−	1.22423i	0.171975	−	0.124947i
$97$	−0.0568680	−	0.0782721i	−0.00577407	−	0.00794733i	0.806120	−	0.591752i	$-0.201563\pi$
$97$	−0.0568680	−	0.0782721i	−0.00577407	−	0.00794733i	−0.811894	+	0.583804i	$0.801563\pi$
$98$	−0.963183	+	0.312957i	−0.0972962	+	0.0316134i
$99$	9.79220			0.984153
$100$	−6.03100	−	7.54306i	−0.603100	−	0.754306i
$101$	17.4908			1.74040			0.870200	−	0.492699i	$-0.163990\pi$
$101$	17.4908			1.74040			0.870200	+	0.492699i	$0.163990\pi$
$102$	−0.172894	+	0.0561768i	−0.0171191	+	0.00556233i
$103$	−8.09807	−	11.1460i	−0.797927	−	1.09825i	−0.993075	−	0.117478i	$-0.962519\pi$
$103$	−8.09807	−	11.1460i	−0.797927	−	1.09825i	0.195149	−	0.980774i	$-0.437481\pi$
$104$	1.82161	−	1.32348i	0.178624	−	0.129778i
$105$	−2.72364	−	0.367190i	−0.265800	−	0.0358341i
$106$	−0.717181	−	0.521062i	−0.0696587	−	0.0506100i
$107$			7.79549i			0.753618i	0.926291	+	0.376809i	$0.122979\pi$
$107$			7.79549i			0.753618i	−0.926291	+	0.376809i	$0.877021\pi$
$108$	4.35197	−	5.98997i	0.418768	−	0.576385i
$109$	−2.65064	+	8.15785i	−0.253886	+	0.781380i	0.740161	+	0.672429i	$0.234749\pi$
$109$	−2.65064	+	8.15785i	−0.253886	+	0.781380i	−0.994047	+	0.108951i	$0.965251\pi$
$110$	−0.304086	+	2.25556i	−0.0289934	+	0.215060i
$111$	0.873458	+	2.68823i	0.0829050	+	0.255155i
$112$	6.04658	+	1.96465i	0.571348	+	0.185642i
$113$	−3.07440	−	0.998933i	−0.289215	−	0.0939717i	0.160816	−	0.986984i	$-0.448587\pi$
$113$	−3.07440	−	0.998933i	−0.289215	−	0.0939717i	−0.450032	+	0.893013i	$0.648587\pi$
$114$	0.299384	+	0.921408i	0.0280399	+	0.0862978i
$115$	−16.1420	−	7.76102i	−1.50525	−	0.723719i
$116$	1.27427	−	3.92180i	0.118313	−	0.364130i
$117$	3.23857	−	4.45751i	0.299406	−	0.412097i
$118$		−	2.48896i		−	0.229127i
$119$	−1.43119	−	1.03982i	−0.131197	−	0.0953199i
$120$	1.15584	+	1.10370i	0.105514	+	0.100754i
$121$	−3.34268	+	2.42860i	−0.303880	+	0.220782i
$122$	−0.833336	−	1.14699i	−0.0754467	−	0.103843i
$123$	−5.06128	+	1.64451i	−0.456360	+	0.148280i
$124$	−19.8873			−1.78594
$125$	7.34001	−	8.43352i	0.656510	−	0.754317i
$126$	−1.16523			−0.103807
$127$	−2.69660	+	0.876179i	−0.239285	+	0.0777483i	−0.426204	−	0.904627i	$-0.640150\pi$
$127$	−2.69660	+	0.876179i	−0.239285	+	0.0777483i	0.186920	+	0.982375i	$0.440150\pi$
$128$	−4.50899	−	6.20609i	−0.398542	−	0.548546i
$129$	2.35081	−	1.70796i	0.206977	−	0.150378i
$130$	0.926186	+	0.884405i	0.0812319	+	0.0775675i
$131$	−5.66636	−	4.11685i	−0.495072	−	0.359691i	0.312060	−	0.950063i	$-0.398981\pi$
$131$	−5.66636	−	4.11685i	−0.495072	−	0.359691i	−0.807131	+	0.590372i	$0.798981\pi$
$132$			5.22018i			0.454358i
$133$	−5.54151	+	7.62724i	−0.480510	+	0.661365i
$134$	−0.722259	+	2.22288i	−0.0623937	+	0.192028i
$135$	7.72488	+	3.71409i	0.664851	+	0.319658i
$136$	0.317893	+	0.978374i	0.0272591	+	0.0838949i
$137$	4.25940	+	1.38396i	0.363905	+	0.118240i	0.485262	−	0.874369i	$-0.338724\pi$
$137$	4.25940	+	1.38396i	0.363905	+	0.118240i	−0.121356	+	0.992609i	$0.538724\pi$
$138$	1.38488	+	0.449974i	0.117889	+	0.0383043i
$139$	5.31946	+	16.3716i	0.451190	+	1.38862i	0.875550	+	0.483127i	$0.160499\pi$
$139$	5.31946	+	16.3716i	0.451190	+	1.38862i	−0.424360	+	0.905494i	$0.639501\pi$
$140$	−1.02083	+	7.57206i	−0.0862762	+	0.639956i
$141$	−2.16582	+	6.66571i	−0.182395	+	0.561354i
$142$	−0.188345	+	0.259234i	−0.0158055	+	0.0217545i
$143$			8.51421i			0.711994i
$144$	−7.31911	−	5.31764i	−0.609926	−	0.443137i
$145$	4.73098	+	0.637811i	0.392886	+	0.0529673i
$146$	1.98064	−	1.43902i	0.163919	−	0.119094i
$147$	−1.58060	−	2.17551i	−0.130366	−	0.179433i
$148$	7.47361	−	2.42832i	0.614327	−	0.199607i
$149$	−1.20858			−0.0990107			−0.0495053	−	0.998774i	$-0.515764\pi$
$149$	−1.20858			−0.0990107			−0.0495053	+	0.998774i	$0.515764\pi$
$150$	−0.499784	+	0.759225i	−0.0408072	+	0.0619905i
$151$	−18.4900			−1.50470			−0.752349	−	0.658765i	$-0.771079\pi$
$151$	−18.4900			−1.50470			−0.752349	+	0.658765i	$0.771079\pi$
$152$	5.21406	−	1.69415i	0.422916	−	0.137414i
$153$	1.47963	+	2.03654i	0.119621	+	0.164644i
$154$	1.45672	−	1.05837i	0.117386	−	0.0852860i
$155$	−4.12520	−	22.6503i	−0.331344	−	1.81931i
$156$	2.37628	+	1.72647i	0.190255	+	0.138228i
$157$		−	10.8964i		−	0.869629i	−0.900520	−	0.434814i	$-0.856814\pi$
$157$		−	10.8964i		−	0.869629i	0.900520	−	0.434814i	$-0.143186\pi$
$158$	1.34127	−	1.84611i	0.106706	−	0.146868i
$159$	0.727369	−	2.23861i	0.0576841	−	0.177533i
$160$	4.62936	−	4.84806i	0.365983	−	0.383273i
$161$	4.37876	+	13.4764i	0.345095	+	1.06209i
$162$	1.21657	+	0.395288i	0.0955828	+	0.0310567i
$163$	2.08101	+	0.676162i	0.162998	+	0.0529611i	0.389379	−	0.921078i	$-0.372690\pi$
$163$	2.08101	+	0.676162i	0.162998	+	0.0529611i	−0.226382	+	0.974039i	$0.572690\pi$
$164$	4.57194	+	14.0710i	0.357009	+	1.09876i
$165$	−5.94541	+	1.08281i	−0.462850	+	0.0842970i
$166$	−1.26833	+	3.90352i	−0.0984416	+	0.302972i
$167$	1.98166	−	2.72752i	0.153346	−	0.211062i	−0.725432	−	0.688294i	$-0.758360\pi$
$167$	1.98166	−	2.72752i	0.153346	−	0.211062i	0.878777	+	0.477232i	$0.158360\pi$
$168$		−	1.26437i		−	0.0975484i
$169$	−6.64146	−	4.82530i	−0.510882	−	0.371177i
$170$	−0.515051	+	0.277581i	−0.0395026	+	0.0212895i
$171$	10.8534	−	7.88543i	0.829977	−	0.603014i
$172$	−4.74835	−	6.53555i	−0.362059	−	0.498331i
$173$	8.47569	−	2.75392i	0.644395	−	0.209377i	0.0314538	−	0.999505i	$-0.489986\pi$
$173$	8.47569	−	2.75392i	0.644395	−	0.209377i	0.612941	+	0.790129i	$0.289986\pi$
$174$	−0.388107			−0.0294223
$175$	−8.83580	+	0.408005i	−0.667923	+	0.0308423i
$176$	13.9801			1.05379
$177$	6.28529	−	2.04222i	0.472432	−	0.153502i
$178$	−1.45627	−	2.00438i	−0.109152	−	0.150235i
$179$	14.8930	−	10.8204i	1.11315	−	0.808753i	0.129996	−	0.991515i	$-0.458504\pi$
$179$	14.8930	−	10.8204i	1.11315	−	0.808753i	0.983157	+	0.182762i	$0.0585037\pi$
$180$	4.71114	−	9.79861i	0.351147	−	0.730345i
$181$	8.77133	+	6.37274i	0.651968	+	0.473682i	0.863941	−	0.503593i	$-0.167989\pi$
$181$	8.77133	+	6.37274i	0.651968	+	0.473682i	−0.211973	+	0.977275i	$0.567989\pi$
$182$		−	1.01315i		−	0.0750997i
$183$	2.21269	−	3.04551i	0.163567	−	0.225131i
$184$	2.54631	−	7.83674i	0.187717	−	0.577732i
$185$	4.31593	+	8.00821i	0.317313	+	0.588775i
$186$	0.578404	+	1.78014i	0.0424106	+	0.130526i
$187$	−3.69957	−	1.20206i	−0.270539	−	0.0879036i
$188$	18.5315	+	6.02125i	1.35155	+	0.439145i
$189$	−2.09549	−	6.44925i	−0.152424	−	0.469114i
$190$	1.47931	+	2.74487i	0.107321	+	0.199134i
$191$	2.82238	−	8.68639i	0.204220	−	0.628525i	−0.795524	−	0.605922i	$-0.792805\pi$
$191$	2.82238	−	8.68639i	0.204220	−	0.628525i	0.999745	−	0.0226033i	$-0.00719548\pi$
$192$	2.61496	−	3.59919i	0.188719	−	0.259749i
$193$			13.9103i			1.00128i	0.865654	+	0.500642i	$0.166903\pi$
$193$			13.9103i			1.00128i	−0.865654	+	0.500642i	$0.833097\pi$
$194$	0.0204806	+	0.0148801i	0.00147042	+	0.00106833i
$195$	−1.47342	+	3.06453i	−0.105514	+	0.219456i
$196$	−6.04820	+	4.39427i	−0.432014	+	0.313877i
$197$	11.4710	+	15.7884i	0.817273	+	1.12488i	0.990160	+	0.139938i	$0.0446905\pi$
$197$	11.4710	+	15.7884i	0.817273	+	1.12488i	−0.172887	+	0.984942i	$0.555310\pi$
$198$	−2.43682	+	0.791770i	−0.173177	+	0.0562687i
$199$	4.57777			0.324510			0.162255	−	0.986749i	$-0.448123\pi$
$199$	4.57777			0.324510			0.162255	+	0.986749i	$0.448123\pi$
$200$	4.29630	+	2.82818i	0.303794	+	0.199982i
$201$	−6.20600			−0.437738
$202$	−4.35264	+	1.41426i	−0.306250	+	0.0995068i
$203$	−2.21990	−	3.05544i	−0.155807	−	0.214449i
$204$	−1.08567	+	0.788786i	−0.0760121	+	0.0552260i
$205$	−15.0775	+	8.12584i	−1.05306	+	0.567533i
$206$	2.91647	+	2.11894i	0.203200	+	0.147633i
$207$		−	20.1635i		−	1.40146i
$208$	4.62363	−	6.36389i	0.320591	−	0.441256i
$209$	−6.40618	+	19.7162i	−0.443124	+	1.36380i
$210$	0.707476	−	0.128850i	0.0488205	−	0.00889148i
$211$	2.91290	+	8.96498i	0.200532	+	0.617175i	0.999867	+	0.0162893i	$0.00518529\pi$
$211$	2.91290	+	8.96498i	0.200532	+	0.617175i	−0.799335	+	0.600886i	$0.794815\pi$
$212$	−6.22362	−	2.02218i	−0.427440	−	0.138884i
$213$	−0.809175	−	0.262917i	−0.0554438	−	0.0180148i
$214$	−0.630321	−	1.93993i	−0.0430879	−	0.132611i
$215$	6.45858	−	6.76370i	0.440472	−	0.461280i
$216$	−1.21856	+	3.75033i	−0.0829122	+	0.255178i
$217$	−10.7061	+	14.7357i	−0.726777	+	1.00032i
$218$		−	2.24443i		−	0.152012i
$219$	5.25905	+	3.82093i	0.355374	+	0.258194i
$220$	3.01036	+	16.5290i	0.202958	+	1.11439i
$221$	−1.77075	+	1.28652i	−0.119114	+	0.0865410i
$222$	−0.434725	−	0.598348i	−0.0291768	−	0.0401585i
$223$	22.1596	−	7.20010i	1.48392	−	0.482154i	0.548638	−	0.836060i	$-0.315147\pi$
$223$	22.1596	−	7.20010i	1.48392	−	0.482154i	0.935281	+	0.353906i	$0.115147\pi$
$224$	−5.30327			−0.354340
$225$	12.1371	+	3.33314i	0.809143	+	0.222209i
$226$	0.845844			0.0562647
$227$	−7.83482	+	2.54569i	−0.520015	+	0.168963i	−0.557252	−	0.830343i	$-0.688144\pi$
$227$	−7.83482	+	2.54569i	−0.520015	+	0.168963i	0.0372371	+	0.999306i	$0.488144\pi$
$228$	4.20369	+	5.78588i	0.278396	+	0.383179i
$229$	14.6013	−	10.6085i	0.964881	−	0.701027i	0.0106017	−	0.999944i	$-0.496625\pi$
$229$	14.6013	−	10.6085i	0.964881	−	0.701027i	0.954279	+	0.298917i	$0.0966253\pi$
$230$	4.64452	+	0.626155i	0.306250	+	0.0412874i
$231$	3.86793	+	2.81022i	0.254491	+	0.184899i
$232$			2.19622i			0.144189i
$233$	−12.2724	+	16.8915i	−0.803990	+	1.10660i	0.188233	+	0.982124i	$0.439724\pi$
$233$	−12.2724	+	16.8915i	−0.803990	+	1.10660i	−0.992223	+	0.124473i	$0.960276\pi$
$234$	−0.445506	+	1.37113i	−0.0291236	+	0.0896333i
$235$	−3.01382	+	22.3551i	−0.196600	+	1.45828i
$236$	−5.67762	−	17.4739i	−0.369581	−	1.13745i
$237$	5.76245	+	1.87233i	0.374311	+	0.121621i
$238$	0.440231	+	0.143040i	0.0285360	+	0.00927189i
$239$	3.52008	+	10.8337i	0.227695	+	0.700773i	0.998007	+	0.0631055i	$0.0201005\pi$
$239$	3.52008	+	10.8337i	0.227695	+	0.700773i	−0.770312	+	0.637667i	$0.779900\pi$
$240$	5.03188	+	2.41931i	0.324806	+	0.156166i
$241$	3.99934	−	12.3087i	0.257620	−	0.792873i	−0.735682	−	0.677327i	$-0.763138\pi$
$241$	3.99934	−	12.3087i	0.257620	−	0.792873i	0.993302	−	0.115546i	$-0.0368618\pi$
$242$	0.635466	−	0.874645i	0.0408493	−	0.0562243i
$243$			14.8962i			0.955591i
$244$	−8.46691	−	6.15157i	−0.542038	−	0.393814i
$245$	−6.25934	−	5.97697i	−0.399894	−	0.381855i
$246$	1.12654	−	0.818481i	0.0718258	−	0.0521845i
$247$	6.85630	+	9.43688i	0.436256	+	0.600455i
$248$	10.0735	−	3.27307i	0.639666	−	0.207840i
$249$	−10.8981			−0.690641
$250$	−1.14467	+	2.69220i	−0.0723953	+	0.170270i
$251$	−0.618916			−0.0390657			−0.0195328	−	0.999809i	$-0.506218\pi$
$251$	−0.618916			−0.0390657			−0.0195328	+	0.999809i	$0.506218\pi$
$252$	−8.18054	+	2.65802i	−0.515326	+	0.167440i
$253$	18.3145	+	25.2077i	1.15142	+	1.58479i
$254$	0.600212	−	0.436079i	0.0376606	−	0.0273620i
$255$	−1.12357	−	1.07288i	−0.0703607	−	0.0671867i
$256$	−8.73700	−	6.34780i	−0.546063	−	0.396738i
$257$			17.1392i			1.06912i	0.845132	+	0.534558i	$0.179522\pi$
$257$			17.1392i			1.06912i	−0.845132	+	0.534558i	$0.820478\pi$
$258$	−0.446905	+	0.615112i	−0.0278231	+	0.0382952i
$259$	2.22404	−	6.84489i	0.138195	−	0.425321i
$260$	8.51979	+	4.09628i	0.528375	+	0.254041i
$261$	1.66071	+	5.11115i	0.102796	+	0.316372i
$262$	1.74297	+	0.566324i	0.107681	+	0.0349876i
$263$	−29.7603	−	9.66972i	−1.83510	−	0.596261i	−0.998852	−	0.0479126i	$-0.984743\pi$
$263$	−29.7603	−	9.66972i	−1.83510	−	0.596261i	−0.836250	−	0.548348i	$-0.815257\pi$
$264$	−0.859140	−	2.64416i	−0.0528764	−	0.162737i
$265$	1.01216	−	7.50772i	0.0621765	−	0.461196i
$266$	0.762304	−	2.34613i	0.0467399	−	0.143851i
$267$	3.86672	−	5.32208i	0.236639	−	0.325706i
$268$			17.2535i			1.05392i
$269$	−12.9135	−	9.38223i	−0.787352	−	0.572044i	0.119825	−	0.992795i	$-0.461767\pi$
$269$	−12.9135	−	9.38223i	−0.787352	−	0.572044i	−0.907176	+	0.420751i	$0.861767\pi$
$270$	−2.22267	−	0.299651i	−0.135267	−	0.0182362i
$271$	20.4457	−	14.8547i	1.24199	−	0.902358i	0.244260	−	0.969710i	$-0.421455\pi$
$271$	20.4457	−	14.8547i	1.24199	−	0.902358i	0.997729	+	0.0673513i	$0.0214548\pi$
$272$	2.11244	+	2.90752i	0.128085	+	0.176294i
$273$	2.55848	−	0.831300i	0.154846	−	0.0503126i
$274$	−1.17187			−0.0707951
$275$	−18.2009	+	6.85717i	−1.09756	+	0.413503i
$276$	10.7491			0.647018
$277$	−23.1202	+	7.51222i	−1.38916	+	0.451365i	−0.905670	−	0.423984i	$-0.860631\pi$
$277$	−23.1202	+	7.51222i	−1.38916	+	0.451365i	−0.483490	+	0.875350i	$0.660631\pi$
$278$	−2.64752	−	3.64400i	−0.158788	−	0.218553i
$279$	20.9685	−	15.2345i	1.25535	−	0.912066i
$280$	−0.729135	−	4.00346i	−0.0435741	−	0.239253i
$281$	−12.3212	−	8.95187i	−0.735021	−	0.534024i	0.156127	−	0.987737i	$-0.450099\pi$
$281$	−12.3212	−	8.95187i	−0.735021	−	0.534024i	−0.891148	+	0.453713i	$0.850099\pi$
$282$		−	1.83390i		−	0.109207i
$283$	−9.72607	+	13.3868i	−0.578155	+	0.795762i	−0.993492	−	0.113906i	$-0.963664\pi$
$283$	−9.72607	+	13.3868i	−0.578155	+	0.795762i	0.415337	+	0.909668i	$0.363664\pi$
$284$	−0.730942	+	2.24961i	−0.0433734	+	0.133490i
$285$	−5.71774	+	5.98786i	−0.338690	+	0.354690i
$286$	−0.688436	−	2.11879i	−0.0407081	−	0.125287i
$287$	12.8873	+	4.18732i	0.760710	+	0.247170i
$288$	7.17708	+	2.33197i	0.422913	+	0.137413i
$289$	−0.309017	−	0.951057i	−0.0181775	−	0.0559445i
$290$	−1.22889	+	0.223813i	−0.0721629	+	0.0131427i
$291$	−0.0207716	+	0.0639284i	−0.00121765	+	0.00374755i
$292$	10.6227	−	14.6208i	0.621644	−	0.855620i
$293$		−	30.8808i		−	1.80408i	−0.431655	−	0.902039i	$-0.642070\pi$
$293$		−	30.8808i		−	1.80408i	0.431655	−	0.902039i	$-0.357930\pi$
$294$	0.569243	+	0.413580i	0.0331989	+	0.0241204i
$295$	18.7238	−	10.0910i	1.09014	−	0.587520i
$296$	−3.38593	+	2.46002i	−0.196803	+	0.142986i
$297$	−8.76453	−	12.0633i	−0.508569	−	0.699986i
$298$	0.300758	−	0.0977223i	0.0174225	−	0.00566090i
$299$	17.5319			1.01390
$300$	−1.77688	+	6.47026i	−0.102588	+	0.373561i
$301$	−7.39878			−0.426459
$302$	4.60130	−	1.49505i	0.264775	−	0.0860306i
$303$	−7.14276	−	9.83117i	−0.410341	−	0.564786i
$304$	15.4951	−	11.2578i	0.888705	−	0.645682i
$305$	5.24992	−	10.9192i	0.300610	−	0.625233i
$306$	−0.532880	−	0.387160i	−0.0304627	−	0.0221325i
$307$			13.9036i			0.793520i	0.917922	+	0.396760i	$0.129865\pi$
$307$			13.9036i			0.793520i	−0.917922	+	0.396760i	$0.870135\pi$
$308$	7.81276	−	10.7533i	0.445173	−	0.612728i
$309$	−2.95790	+	9.10347i	−0.168269	+	0.517879i
$310$	2.85801	+	5.30304i	0.162324	+	0.301192i
$311$	−6.70274	−	20.6289i	−0.380078	−	1.16976i	−0.939988	−	0.341206i	$-0.889165\pi$
$311$	−6.70274	−	20.6289i	−0.380078	−	1.16976i	0.559911	−	0.828553i	$-0.310835\pi$
$312$	−1.48779	−	0.483413i	−0.0842297	−	0.0273679i
$313$	−22.4900	−	7.30745i	−1.27121	−	0.413042i	−0.405735	−	0.913991i	$-0.632984\pi$
$313$	−22.4900	−	7.30745i	−1.27121	−	0.413042i	−0.865477	+	0.500949i	$0.832984\pi$
$314$	0.881054	+	2.71160i	0.0497207	+	0.153025i
$315$	−4.72417	−	8.76571i	−0.266177	−	0.493892i
$316$	5.20532	−	16.0203i	0.292822	−	0.901214i
$317$	11.5775	−	15.9351i	0.650258	−	0.895004i	−0.348852	−	0.937178i	$-0.613428\pi$
$317$	11.5775	−	15.9351i	0.650258	−	0.895004i	0.999110	+	0.0421739i	$0.0134284\pi$
$318$			0.615898i			0.0345378i
$319$	−6.71862	−	4.88136i	−0.376170	−	0.273304i
$320$	6.20436	−	12.9043i	0.346834	−	0.721375i
$321$	4.38166	−	3.18346i	0.244560	−	0.177684i
$322$	−2.17933	−	2.99960i	−0.121450	−	0.167161i
$323$	−5.06848	+	1.64685i	−0.282018	+	0.0916331i
$324$	9.44272			0.524595
$325$	−2.89813	+	10.5531i	−0.160759	+	0.585382i
$326$	−0.572539			−0.0317100
$327$	5.66779	−	1.84158i	0.313429	−	0.101839i
$328$	−4.63162	−	6.37488i	−0.255738	−	0.351994i
$329$	14.4377	−	10.4896i	0.795976	−	0.578310i
$330$	1.39198	−	0.750191i	0.0766260	−	0.0412967i
$331$	7.53231	+	5.47254i	0.414013	+	0.300798i	0.775225	−	0.631686i	$-0.217637\pi$
$331$	7.53231	+	5.47254i	0.414013	+	0.300798i	−0.361211	+	0.932484i	$0.617637\pi$
$332$			30.2982i			1.66283i
$333$	−6.01971	+	8.28542i	−0.329878	+	0.454038i
$334$	−0.272602	+	0.838984i	−0.0149161	+	0.0459071i
$335$	−19.6505	+	3.57886i	−1.07362	+	0.195534i
$336$	−1.36497	−	4.20095i	−0.0744653	−	0.229181i
$337$	−18.8848	−	6.13605i	−1.02872	−	0.334252i	−0.254437	−	0.967089i	$-0.581890\pi$
$337$	−18.8848	−	6.13605i	−1.02872	−	0.334252i	−0.774285	+	0.632837i	$0.781890\pi$
$338$	2.04291	+	0.663781i	0.111120	+	0.0361049i
$339$	0.694024	+	2.13598i	0.0376942	+	0.116011i
$340$	−2.98276	+	3.12367i	−0.161763	+	0.169405i
$341$	−12.3766	+	38.0913i	−0.670231	+	2.06276i
$342$	−2.06330	+	2.83989i	−0.111570	+	0.153563i
$343$			19.2304i			1.03834i
$344$	3.48079	+	2.52894i	0.187672	+	0.136351i
$345$	2.22966	+	12.2424i	0.120041	+	0.659110i
$346$	−1.88653	+	1.37064i	−0.101420	+	0.0736861i
$347$	−9.46684	−	13.0300i	−0.508207	−	0.699487i	0.475409	−	0.879765i	$-0.342300\pi$
$347$	−9.46684	−	13.0300i	−0.508207	−	0.699487i	−0.983616	+	0.180278i	$0.942300\pi$
$348$	−2.72473	+	0.885319i	−0.146061	+	0.0474581i
$349$	−15.3305			−0.820623			−0.410312	−	0.911945i	$-0.634580\pi$
$349$	−15.3305			−0.820623			−0.410312	+	0.911945i	$0.634580\pi$
$350$	2.16582	−	0.815971i	0.115768	−	0.0436155i
$351$	−8.39004			−0.447827
$352$	−11.0907	+	3.60357i	−0.591134	+	0.192071i
$353$	0.0340891	+	0.0469196i	0.00181438	+	0.00249728i	0.809923	−	0.586536i	$-0.199509\pi$
$353$	0.0340891	+	0.0469196i	0.00181438	+	0.00249728i	−0.808109	+	0.589033i	$0.799509\pi$
$354$	−1.39899	+	1.01642i	−0.0743553	+	0.0540223i
$355$	−2.71376	−	0.365858i	−0.144032	−	0.0194177i
$356$	−14.7961	−	10.7500i	−0.784189	−	0.569747i
$357$			1.22907i			0.0650492i
$358$	−2.83125	+	3.89689i	−0.149636	+	0.205957i
$359$	5.74049	−	17.6674i	0.302971	−	0.932450i	−0.677455	−	0.735564i	$-0.736917\pi$
$359$	5.74049	−	17.6674i	0.302971	−	0.932450i	0.980426	−	0.196886i	$-0.0630828\pi$
$360$	−0.773657	+	5.73862i	−0.0407753	+	0.302452i
$361$	2.90526	+	8.94146i	0.152908	+	0.470603i
$362$	−2.69805	−	0.876651i	−0.141807	−	0.0460757i
$363$	2.73012	+	0.887070i	0.143294	+	0.0465591i
$364$	−2.31112	−	7.11290i	−0.121136	−	0.372817i
$365$	18.8555	+	9.06568i	0.986944	+	0.474519i
$366$	−0.304384	+	0.936797i	−0.0159104	+	0.0489672i
$367$	21.1524	−	29.1138i	1.10415	−	1.51973i	0.274377	−	0.961622i	$-0.411529\pi$
$367$	21.1524	−	29.1138i	1.10415	−	1.51973i	0.829770	−	0.558105i	$-0.188471\pi$
$368$		−	28.7870i		−	1.50062i
$369$	−15.5994	−	11.3336i	−0.812074	−	0.590006i
$370$	−1.72155	−	1.64389i	−0.0894993	−	0.0854619i
$371$	−4.84875	+	3.52283i	−0.251735	+	0.182896i
$372$	8.12145	+	11.1782i	0.421077	+	0.579563i
$373$	−22.2606	+	7.23290i	−1.15261	+	0.374505i	−0.822125	−	0.569306i	$-0.807212\pi$
$373$	−22.2606	+	7.23290i	−1.15261	+	0.374505i	−0.330484	+	0.943812i	$0.607212\pi$
$374$	1.01784			0.0526315
$375$	−7.73774	−	0.681626i	−0.399575	−	0.0351990i
$376$	−10.3777			−0.535188
$377$	−4.44409	+	1.44397i	−0.228882	+	0.0743684i
$378$	1.04294	+	1.43548i	0.0536429	+	0.0738331i
$379$	−7.05230	+	5.12380i	−0.362252	+	0.263192i	−0.753991	−	0.656885i	$-0.771874\pi$
$379$	−7.05230	+	5.12380i	−0.362252	+	0.263192i	0.391739	+	0.920077i	$0.371874\pi$
$380$	16.6470	+	15.8960i	0.853973	+	0.815450i
$381$	1.59370	+	1.15789i	0.0816476	+	0.0593204i
$382$			2.38984i			0.122275i
$383$	6.81187	−	9.37574i	0.348070	−	0.479078i	−0.598706	−	0.800969i	$-0.704318\pi$
$383$	6.81187	−	9.37574i	0.348070	−	0.479078i	0.946777	+	0.321891i	$0.104318\pi$
$384$	−1.64695	+	5.06879i	−0.0840456	+	0.258666i
$385$	13.8679	+	6.66763i	0.706773	+	0.339814i
$386$	−1.12475	−	3.46161i	−0.0572481	−	0.176192i
$387$	10.0130	+	3.25342i	0.508989	+	0.165380i
$388$	0.177729	+	0.0577476i	0.00902282	+	0.00293169i
$389$	−3.68404	−	11.3383i	−0.186788	−	0.574875i	0.813186	−	0.582003i	$-0.197731\pi$
$389$	−3.68404	−	11.3383i	−0.186788	−	0.574875i	−0.999975	+	0.00712836i	$0.997731\pi$
$390$	0.118874	−	0.881754i	0.00601944	−	0.0446494i
$391$	−2.47521	+	7.61793i	−0.125177	+	0.385255i
$392$	2.34036	−	3.22123i	0.118206	−	0.162697i
$393$			4.86613i			0.245464i
$394$	−4.13120	−	3.00149i	−0.208127	−	0.151213i
$395$	19.3258	+	2.60542i	0.972384	+	0.131093i
$396$	−15.3017	+	11.1174i	−0.768941	+	0.558668i
$397$	−13.3611	−	18.3899i	−0.670572	−	0.922963i	0.329201	−	0.944260i	$-0.393221\pi$
$397$	−13.3611	−	18.3899i	−0.670572	−	0.922963i	−0.999773	+	0.0212965i	$0.993221\pi$
$398$	−1.13919	+	0.370146i	−0.0571025	+	0.0185537i
$399$	6.55009			0.327915
$400$	17.3279	+	4.75865i	0.866396	+	0.237932i
$401$	−22.9853			−1.14783			−0.573916	−	0.818914i	$-0.694576\pi$
$401$	−22.9853			−1.14783			−0.573916	+	0.818914i	$0.694576\pi$
$402$	1.54438	−	0.501800i	0.0770268	−	0.0250275i
$403$	13.2462	+	18.2319i	0.659842	+	0.908195i
$404$	−27.3319	+	19.8578i	−1.35981	+	0.987961i
$405$	1.95869	+	10.7546i	0.0973280	+	0.534400i
$406$	0.799483	+	0.580859i	0.0396777	+	0.0288275i
$407$		−	15.8258i		−	0.784458i
$408$	0.420102	−	0.578221i	0.0207982	−	0.0286262i
$409$	5.84501	−	17.9891i	0.289017	−	0.889503i	−0.696149	−	0.717898i	$-0.745105\pi$
$409$	5.84501	−	17.9891i	0.289017	−	0.889503i	0.985166	−	0.171605i	$-0.0548954\pi$
$410$	3.09505	−	3.24126i	0.152854	−	0.160075i
$411$	−0.961529	−	2.95928i	−0.0474288	−	0.145971i
$412$	25.3088	+	8.22333i	1.24688	+	0.405134i
$413$	−16.0039	−	5.19998i	−0.787500	−	0.255874i
$414$	1.63036	+	5.01774i	0.0801280	+	0.246609i
$415$	−34.5075	+	6.28470i	−1.69390	+	0.308504i
$416$	−2.02763	+	6.24039i	−0.0994125	+	0.305960i
$417$	7.02977	−	9.67565i	0.344250	−	0.473819i
$418$		−	5.42442i		−	0.265317i
$419$	−23.8802	−	17.3500i	−1.16662	−	0.847602i	−0.176023	−	0.984386i	$-0.556323\pi$
$419$	−23.8802	−	17.3500i	−1.16662	−	0.847602i	−0.990601	+	0.136784i	$0.956323\pi$
$420$	4.67296	−	2.51844i	0.228017	−	0.122887i
$421$	−19.8702	+	14.4365i	−0.968412	+	0.703593i	−0.955089	−	0.296319i	$-0.904241\pi$
$421$	−19.8702	+	14.4365i	−0.968412	+	0.703593i	−0.0133230	+	0.999911i	$0.504241\pi$
$422$	−1.44977	−	1.99543i	−0.0705736	−	0.0971362i
$423$	−24.1515	+	7.84729i	−1.17428	+	0.381548i
$424$	3.48524			0.169258
$425$	−4.17634	−	2.74921i	−0.202582	−	0.133356i
$426$	0.222624			0.0107862
$427$	−9.11611	+	2.96200i	−0.441159	+	0.143341i
$428$	−8.85043	−	12.1816i	−0.427802	−	0.588818i
$429$	4.78564	−	3.47697i	0.231053	−	0.167870i
$430$	−1.06034	+	2.20539i	−0.0511343	+	0.106353i
$431$	−8.27343	−	6.01100i	−0.398517	−	0.289540i	0.370420	−	0.928865i	$-0.379214\pi$
$431$	−8.27343	−	6.01100i	−0.398517	−	0.289540i	−0.768937	+	0.639325i	$0.779214\pi$
$432$			13.7762i			0.662808i
$433$	−16.4225	+	22.6036i	−0.789215	+	1.08626i	0.204991	+	0.978764i	$0.434284\pi$
$433$	−16.4225	+	22.6036i	−0.789215	+	1.08626i	−0.994205	+	0.107497i	$0.965716\pi$
$434$	1.47276	−	4.53268i	0.0706946	−	0.217576i
$435$	−1.57350	−	2.91964i	−0.0754437	−	0.139986i
$436$	−5.11981	−	15.7572i	−0.245194	−	0.754631i
$437$	40.5983	+	13.1912i	1.94208	+	0.631021i
$438$	−1.61768	−	0.525616i	−0.0772958	−	0.0251149i
$439$	−3.26488	−	10.0483i	−0.155824	−	0.479577i	0.842419	−	0.538823i	$-0.181131\pi$
$439$	−3.26488	−	10.0483i	−0.155824	−	0.479577i	−0.998243	+	0.0592451i	$0.981131\pi$
$440$	−4.24518	−	7.87694i	−0.202381	−	0.375518i
$441$	3.01081	−	9.26632i	0.143372	−	0.441254i
$442$	0.336631	−	0.463333i	0.0160119	−	0.0220385i
$443$		−	4.10520i		−	0.195044i	−0.995233	−	0.0975219i	$-0.968908\pi$
$443$		−	4.10520i		−	0.195044i	0.995233	−	0.0975219i	$-0.0310916\pi$
$444$	−4.41692	−	3.20908i	−0.209618	−	0.152296i
$445$	9.17432	−	19.0815i	0.434905	−	0.904550i
$446$	−4.93231	+	3.58353i	−0.233552	+	0.169685i
$447$	0.493551	+	0.679314i	0.0233441	+	0.0321305i
$448$	−10.7734	+	3.50050i	−0.508996	+	0.165383i
$449$	−24.3079			−1.14716			−0.573580	−	0.819149i	$-0.694446\pi$
$449$	−24.3079			−1.14716			−0.573580	+	0.819149i	$0.694446\pi$
$450$	−3.28987	+	0.151914i	−0.155086	+	0.00716131i
$451$	29.7962			1.40305
$452$	5.93831	−	1.92947i	0.279314	−	0.0907548i
$453$	7.55082	+	10.3928i	0.354769	+	0.488297i
$454$	1.74388	−	1.26700i	0.0818444	−	0.0594634i
$455$	7.62169	−	4.10762i	0.357310	−	0.192568i
$456$	−3.08152	−	2.23886i	−0.144306	−	0.104844i
$457$		−	0.0269860i		−	0.00126235i	−1.00000		0.000631177i	$-0.999799\pi$
$457$		−	0.0269860i		−	0.00126235i	1.00000		0.000631177i	$-0.000200910\pi$
$458$	−2.77580	+	3.82057i	−0.129705	+	0.178523i
$459$	1.18453	−	3.64562i	0.0552892	−	0.170163i
$460$	34.0355	−	6.19875i	1.58691	−	0.289018i
$461$	−0.782321	−	2.40774i	−0.0364363	−	0.112139i	0.931184	−	0.364549i	$-0.118777\pi$
$461$	−0.782321	−	2.40774i	−0.0364363	−	0.112139i	−0.967620	+	0.252410i	$0.918777\pi$
$462$	−1.18977	−	0.386581i	−0.0553532	−	0.0179854i
$463$	−9.85254	−	3.20128i	−0.457886	−	0.148776i	0.0709866	−	0.997477i	$-0.477385\pi$
$463$	−9.85254	−	3.20128i	−0.457886	−	0.148776i	−0.528873	+	0.848701i	$0.677385\pi$
$464$	2.37096	+	7.29707i	0.110069	+	0.338758i
$465$	−11.0466	+	11.5684i	−0.512273	+	0.536473i
$466$	1.68822	−	5.19581i	0.0782053	−	0.240691i
$467$	−14.1348	+	19.4549i	−0.654080	+	0.900263i	−0.999267	−	0.0382703i	$-0.987815\pi$
$467$	−14.1348	+	19.4549i	−0.654080	+	0.900263i	0.345188	+	0.938534i	$0.387815\pi$
$468$			10.6423i			0.491942i
$469$	12.7841	+	9.28819i	0.590315	+	0.428889i
$470$	−1.05757	−	5.80681i	−0.0487821	−	0.267848i
$471$	−6.12462	+	4.44980i	−0.282208	+	0.205036i
$472$	5.75173	+	7.91658i	0.264745	+	0.364390i
$473$	−15.4730	+	5.02747i	−0.711447	+	0.231163i
$474$	−1.58539			−0.0728195
$475$	−14.6514	+	22.2571i	−0.672253	+	1.02122i
$476$	3.41697			0.156616
$477$	8.11103	−	2.63543i	0.371379	−	0.120668i
$478$	−1.75196	−	2.41137i	−0.0801329	−	0.110293i
$479$	0.649375	−	0.471799i	0.0296707	−	0.0215570i	−0.572851	−	0.819659i	$-0.694163\pi$
$479$	0.649375	−	0.471799i	0.0296707	−	0.0215570i	0.602522	+	0.798102i	$0.294163\pi$
$480$	−4.61549	−	0.622241i	−0.210667	−	0.0284013i
$481$	−7.20409	−	5.23408i	−0.328478	−	0.238653i
$482$			3.38643i			0.154248i
$483$	5.78662	−	7.96461i	0.263301	−	0.362402i
$484$	2.46617	−	7.59008i	0.112098	−	0.345004i
$485$	−0.0289044	+	0.214399i	−0.00131248	+	0.00973536i
$486$	−1.20446	−	3.70696i	−0.0546356	−	0.168151i
$487$	11.3312	+	3.68172i	0.513464	+	0.166835i	0.554277	−	0.832332i	$-0.312995\pi$
$487$	11.3312	+	3.68172i	0.513464	+	0.166835i	−0.0408128	+	0.999167i	$0.512995\pi$
$488$	5.30115	+	1.72245i	0.239972	+	0.0779715i
$489$	−0.469774	−	1.44582i	−0.0212439	−	0.0653820i
$490$	2.04094	+	0.981274i	0.0922001	+	0.0443295i
$491$	−3.85177	+	11.8545i	−0.173828	+	0.534988i	−0.999578	−	0.0290484i	$-0.990752\pi$
$491$	−3.85177	+	11.8545i	−0.173828	+	0.534988i	0.825750	+	0.564037i	$0.190752\pi$
$492$	6.04192	−	8.31599i	0.272391	−	0.374914i
$493$		−	2.13490i		−	0.0961510i
$494$	−2.46925	−	1.79402i	−0.111097	−	0.0807166i
$495$	−15.8359	−	15.1215i	−0.711770	−	0.679662i
$496$	29.9362	−	21.7499i	1.34418	−	0.976602i
$497$	1.27337	+	1.75265i	0.0571185	+	0.0786169i
$498$	2.71203	−	0.881192i	0.121529	−	0.0394872i
$499$	21.1115			0.945080			0.472540	−	0.881309i	$-0.343337\pi$
$499$	21.1115			0.945080			0.472540	+	0.881309i	$0.343337\pi$
$500$	−1.89501	+	21.5119i	−0.0847473	+	0.962042i
$501$	−2.34233			−0.104648
$502$	0.154019	−	0.0500439i	0.00687421	−	0.00223357i
$503$	12.7079	+	17.4909i	0.566617	+	0.779881i	0.992149	−	0.125062i	$-0.0399130\pi$
$503$	12.7079	+	17.4909i	0.566617	+	0.779881i	−0.425532	+	0.904943i	$0.639913\pi$
$504$	3.70621	−	2.69272i	0.165088	−	0.119943i
$505$	−28.2860	−	27.0100i	−1.25871	−	1.20193i
$506$	−6.59583	−	4.79215i	−0.293221	−	0.213037i
$507$			5.70353i			0.253303i
$508$	3.21908	−	4.43068i	0.142823	−	0.196580i
$509$	−3.33666	+	10.2692i	−0.147895	+	0.455174i	−0.997372	−	0.0724520i	$-0.976918\pi$
$509$	−3.33666	+	10.2692i	−0.147895	+	0.455174i	0.849477	+	0.527626i	$0.176918\pi$
$510$	0.366354	+	0.176142i	0.0162224	+	0.00779969i
$511$	−5.11485	−	15.7419i	−0.226268	−	0.696380i
$512$	17.2789	+	5.61425i	0.763626	+	0.248117i
$513$	−19.4286	−	6.31275i	−0.857796	−	0.278715i
$514$	−1.38583	−	4.26514i	−0.0611263	−	0.188127i
$515$	−4.11602	+	30.5307i	−0.181374	+	1.34534i
$516$	−1.73438	+	5.33788i	−0.0763519	+	0.234987i
$517$	23.0657	−	31.7472i	1.01443	−	1.39624i
$518$			1.88320i			0.0827430i
$519$	−5.00915	−	3.63936i	−0.219877	−	0.159750i
$520$	−4.98967	−	0.672686i	−0.218811	−	0.0294992i
$521$	−14.8221	+	10.7689i	−0.649369	+	0.471794i	−0.863056	−	0.505108i	$-0.831453\pi$
$521$	−14.8221	+	10.7689i	−0.649369	+	0.471794i	0.213687	+	0.976902i	$0.431453\pi$
$522$	−0.826547	−	1.13764i	−0.0361770	−	0.0497933i
$523$	24.8110	−	8.06159i	1.08491	−	0.352509i	0.288632	−	0.957440i	$-0.406800\pi$
$523$	24.8110	−	8.06159i	1.08491	−	0.352509i	0.796278	+	0.604932i	$0.206800\pi$
$524$	13.5285			0.590994
$525$	3.83763	+	4.79978i	0.167488	+	0.209479i
$526$	8.18782			0.357006
$527$	−9.79221	+	3.18168i	−0.426555	+	0.138596i
$528$	−5.70909	−	7.85789i	−0.248456	−	0.341971i
$529$	33.2987	−	24.1930i	1.44777	−	1.05187i
$530$	0.355175	+	1.95016i	0.0154278	+	0.0847095i
$531$	19.3720	+	14.0746i	0.840673	+	0.610784i
$532$		−	18.2101i		−	0.789507i
$533$	9.85449	−	13.5635i	0.426845	−	0.587502i
$534$	−0.531916	+	1.63707i	−0.0230182	+	0.0708428i
$535$	12.0381	−	12.6068i	0.520453	−	0.545040i
$536$	−2.83959	−	8.73935i	−0.122651	−	0.377482i
$537$	−12.1638	−	3.95225i	−0.524905	−	0.170552i
$538$	3.97219	+	1.29064i	0.171253	+	0.0556436i
$539$	4.65257	+	14.3192i	0.200401	+	0.616770i
$540$	−16.2879	+	2.96646i	−0.700921	+	0.127656i
$541$	−4.71642	+	14.5157i	−0.202775	+	0.624077i	0.797023	+	0.603949i	$0.206407\pi$
$541$	−4.71642	+	14.5157i	−0.202775	+	0.624077i	−0.999797	+	0.0201273i	$0.993593\pi$
$542$	−3.88687	+	5.34982i	−0.166955	+	0.229794i
$543$		−	7.53261i		−	0.323255i
$544$	−2.42529	−	1.76208i	−0.103983	−	0.0755484i
$545$	16.8843	−	9.09959i	0.723244	−	0.389783i
$546$	−0.569469	+	0.413743i	−0.0243710	+	0.0177066i
$547$	13.5726	+	18.6811i	0.580323	+	0.798747i	0.993731	−	0.111800i	$-0.0356615\pi$
$547$	13.5726	+	18.6811i	0.580323	+	0.798747i	−0.413407	+	0.910546i	$0.635661\pi$
$548$	−8.22718	+	2.67317i	−0.351448	+	0.114192i
$549$	13.6396			0.582122
$550$	3.97490	−	3.17810i	0.169490	−	0.135515i
$551$	−11.3775			−0.484700
$552$	−5.44469	+	1.76909i	−0.231741	+	0.0752974i
$553$	−9.06817	−	12.4813i	−0.385618	−	0.530757i
$554$	5.14612	−	3.73888i	0.218638	−	0.158850i
$555$	2.73872	−	5.69622i	0.116252	−	0.241791i
$556$	−26.8995	−	19.5437i	−1.14079	−	0.828836i
$557$		−	6.96026i		−	0.294916i	−0.989068	−	0.147458i	$-0.952891\pi$
$557$		−	6.96026i		−	0.294916i	0.989068	−	0.147458i	$-0.0471091\pi$
$558$	−3.98625	+	5.48661i	−0.168751	+	0.232267i
$559$	−2.82881	+	8.70618i	−0.119646	+	0.368232i
$560$	−6.74460	−	12.5146i	−0.285011	−	0.528839i
$561$	0.835152	+	2.57033i	0.0352601	+	0.108520i
$562$	3.78999	+	1.23144i	0.159871	+	0.0519452i
$563$	11.9467	+	3.88170i	0.503491	+	0.163594i	0.549740	−	0.835336i	$-0.314727\pi$
$563$	11.9467	+	3.88170i	0.503491	+	0.163594i	−0.0462488	+	0.998930i	$0.514727\pi$
$564$	−4.18336	−	12.8750i	−0.176151	−	0.542137i
$565$	3.42931	+	6.36308i	0.144272	+	0.267697i
$566$	1.33794	−	4.11776i	0.0562379	−	0.173083i
$567$	5.08337	−	6.99665i	0.213481	−	0.293832i
$568$		−	1.25979i		−	0.0528594i
$569$	−5.58962	−	4.06110i	−0.234329	−	0.170250i	0.464424	−	0.885613i	$-0.346261\pi$
$569$	−5.58962	−	4.06110i	−0.234329	−	0.170250i	−0.698753	+	0.715363i	$0.746261\pi$
$570$	0.938715	−	1.95242i	0.0393185	−	0.0817778i
$571$	−10.4440	+	7.58804i	−0.437069	+	0.317549i	−0.784469	−	0.620168i	$-0.787065\pi$
$571$	−10.4440	+	7.58804i	−0.437069	+	0.317549i	0.347400	+	0.937717i	$0.387065\pi$
$572$	−9.66642	−	13.3047i	−0.404173	−	0.556297i
$573$	−6.03500	+	1.96089i	−0.252116	+	0.0819173i
$574$	−3.54561			−0.147991
$575$	14.1199	+	37.4782i	0.588839	+	1.56295i
$576$	16.1192			0.671635
$577$	31.6933	−	10.2978i	1.31941	−	0.428703i	0.437119	−	0.899404i	$-0.355999\pi$
$577$	31.6933	−	10.2978i	1.31941	−	0.428703i	0.882293	+	0.470701i	$0.155999\pi$
$578$	0.153800	+	0.211687i	0.00639722	+	0.00880502i
$579$	7.81865	−	5.68058i	0.324932	−	0.236077i
$580$	−8.11696	+	4.37454i	−0.337038	+	0.181643i
$581$	22.4497	+	16.3106i	0.931369	+	0.676679i
$582$		−	0.0175883i		−	0.000729058i
$583$	−7.74637	+	10.6620i	−0.320822	+	0.441573i
$584$	−2.97436	+	9.15413i	−0.123080	+	0.378800i
$585$	−12.1209	+	2.20753i	−0.501136	+	0.0912700i
$586$	2.49694	+	7.68478i	0.103148	+	0.317456i
$587$	0.0929701	+	0.0302078i	0.00383729	+	0.00124681i	0.310935	−	0.950431i	$-0.399358\pi$
$587$	0.0929701	+	0.0302078i	0.00383729	+	0.00124681i	−0.307098	+	0.951678i	$0.599358\pi$
$588$	4.93984	+	1.60505i	0.203715	+	0.0661912i
$589$	16.9562	+	52.1858i	0.698668	+	2.15028i
$590$	−3.84355	+	4.02513i	−0.158237	+	0.165712i
$591$	4.18988	−	12.8951i	0.172349	−	0.530435i
$592$	−8.59420	+	11.8289i	−0.353220	+	0.486165i
$593$			15.4663i			0.635124i	0.948237	+	0.317562i	$0.102864\pi$
$593$			15.4663i			0.635124i	−0.948237	+	0.317562i	$0.897136\pi$
$594$	3.15649	+	2.29332i	0.129512	+	0.0940961i
$595$	0.708776	+	3.89168i	0.0290570	+	0.159543i
$596$	1.88858	−	1.37213i	0.0773592	−	0.0562048i
$597$	−1.86944	−	2.57306i	−0.0765109	−	0.105308i
$598$	−4.36288	+	1.41758i	−0.178411	+	0.0579693i
$599$	16.3238			0.666974			0.333487	−	0.942755i	$-0.391775\pi$
$599$	16.3238			0.666974			0.333487	+	0.942755i	$0.391775\pi$
$600$	−0.164840	−	3.56980i	−0.00672958	−	0.145736i
$601$	5.47691			0.223408			0.111704	−	0.993742i	$-0.464369\pi$
$601$	5.47691			0.223408			0.111704	+	0.993742i	$0.464369\pi$
$602$	1.84121	−	0.598245i	0.0750420	−	0.0243826i
$603$	−13.2169	−	18.1914i	−0.538232	−	0.740813i
$604$	28.8933	−	20.9922i	1.17565	−	0.854162i
$605$	9.15611	+	1.23439i	0.372249	+	0.0501851i
$606$	2.57242	+	1.86897i	0.104497	+	0.0759218i
$607$			1.92569i			0.0781613i	0.999236	+	0.0390807i	$0.0124429\pi$
$607$			1.92569i			0.0781613i	−0.999236	+	0.0390807i	$0.987557\pi$
$608$	−9.39066	+	12.9251i	−0.380842	+	0.524183i
$609$	−0.810841	+	2.49551i	−0.0328569	+	0.101123i
$610$	−0.423561	+	3.14177i	−0.0171495	+	0.127207i
$611$	−6.82314	−	20.9995i	−0.276035	−	0.849547i
$612$	−4.62428	−	1.50252i	−0.186925	−	0.0607357i
$613$	−11.7845	−	3.82902i	−0.475972	−	0.154653i	0.0611998	−	0.998126i	$-0.480507\pi$
$613$	−11.7845	−	3.82902i	−0.475972	−	0.154653i	−0.537172	+	0.843473i	$0.680507\pi$
$614$	−1.12421	−	3.45995i	−0.0453693	−	0.139632i
$615$	10.7246	+	5.15634i	0.432457	+	0.207924i
$616$	−2.18758	+	6.73268i	−0.0881401	+	0.271267i
$617$	22.6540	−	31.1805i	0.912015	−	1.25528i	−0.0544591	−	0.998516i	$-0.517343\pi$
$617$	22.6540	−	31.1805i	0.912015	−	1.25528i	0.966474	−	0.256765i	$-0.0826565\pi$
$618$		−	2.50459i		−	0.100750i
$619$	18.7144	+	13.5968i	0.752194	+	0.546501i	0.896506	−	0.443031i	$-0.146097\pi$
$619$	18.7144	+	13.5968i	0.752194	+	0.546501i	−0.144312	+	0.989532i	$0.546097\pi$
$620$	32.1617	+	30.7109i	1.29165	+	1.23338i
$621$	−24.8401	+	18.0474i	−0.996798	+	0.724216i
$622$	3.33600	+	4.59160i	0.133761	+	0.184107i
$623$	−15.9305	+	5.17615i	−0.638244	+	0.207378i
$624$	−5.46516			−0.218781
$625$	−24.8936	+	2.30390i	−0.995745	+	0.0921562i
$626$	6.18757			0.247305
$627$	13.6981	−	4.45079i	0.547050	−	0.177747i
$628$	12.3710	+	17.0272i	0.493657	+	0.679460i
$629$	3.29139	−	2.39134i	0.131236	−	0.0953488i
$630$	1.88440	+	1.79939i	0.0750761	+	0.0716894i
$631$	−1.05428	−	0.765983i	−0.0419704	−	0.0304933i	0.566602	−	0.823991i	$-0.308258\pi$
$631$	−1.05428	−	0.765983i	−0.0419704	−	0.0304933i	−0.608573	+	0.793498i	$0.708258\pi$
$632$			8.97142i			0.356864i
$633$	3.84946	−	5.29833i	0.153002	−	0.210590i
$634$	−1.59263	+	4.90162i	−0.0632515	+	0.194668i
$635$	5.71396	+	2.74725i	0.226752	+	0.109021i
$636$	1.40494	+	4.32395i	0.0557094	+	0.171456i
$637$	8.05697	+	2.61787i	0.319229	+	0.103724i
$638$	2.06664	+	0.671492i	0.0818191	+	0.0265846i
$639$	−0.952612	−	2.93184i	−0.0376847	−	0.115982i
$640$	−2.29179	+	16.9994i	−0.0905910	+	0.671961i
$641$	12.2024	−	37.5552i	0.481967	−	1.48334i	−0.354358	−	0.935110i	$-0.615301\pi$
$641$	12.2024	−	37.5552i	0.481967	−	1.48334i	0.836326	−	0.548233i	$-0.184699\pi$
$642$	−0.832983	+	1.14650i	−0.0328752	+	0.0452489i
$643$		−	18.2810i		−	0.720934i	−0.932772	−	0.360467i	$-0.882617\pi$
$643$		−	18.2810i		−	0.720934i	0.932772	−	0.360467i	$-0.117383\pi$
$644$	−22.1426	−	16.0875i	−0.872541	−	0.633938i
$645$	−6.43922	−	0.868109i	−0.253544	−	0.0341818i
$646$	1.12815	−	0.819647i	0.0443863	−	0.0322486i
$647$	1.50536	+	2.07195i	0.0591818	+	0.0814567i	0.837582	−	0.546312i	$-0.183969\pi$
$647$	1.50536	+	2.07195i	0.0591818	+	0.0814567i	−0.778400	+	0.627768i	$0.783969\pi$
$648$	−4.78299	+	1.55409i	−0.187894	+	0.0610503i
$649$	−37.0021			−1.45246
$650$	−0.132088	−	2.86051i	−0.00518091	−	0.112198i
$651$	12.6547			0.495975
$652$	−4.01955	+	1.30603i	−0.157418	+	0.0511481i
$653$	12.1606	+	16.7377i	0.475882	+	0.654996i	0.977707	−	0.209974i	$-0.0673378\pi$
$653$	12.1606	+	16.7377i	0.475882	+	0.654996i	−0.501825	+	0.864969i	$0.667338\pi$
$654$	−1.26154	+	0.916563i	−0.0493301	+	0.0358404i
$655$	2.80619	+	15.4080i	0.109647	+	0.602039i
$656$	−22.2709	−	16.1808i	−0.869534	−	0.631754i
$657$			23.5531i			0.918892i
$658$	−2.74470	+	3.77776i	−0.107000	+	0.147272i
$659$	−11.9913	+	36.9054i	−0.467115	+	1.43763i	0.389189	+	0.921158i	$0.372755\pi$
$659$	−11.9913	+	36.9054i	−0.467115	+	1.43763i	−0.856303	+	0.516473i	$0.827245\pi$
$660$	8.06122	−	8.44205i	0.313782	−	0.328606i
$661$	−1.46535	−	4.50990i	−0.0569957	−	0.175415i	0.918506	−	0.395407i	$-0.129397\pi$
$661$	−1.46535	−	4.50990i	−0.0569957	−	0.175415i	−0.975501	+	0.219993i	$0.929397\pi$
$662$	−2.31693	−	0.752817i	−0.0900501	−	0.0292591i
$663$	1.44625	+	0.469916i	0.0561677	+	0.0182500i
$664$	−4.98649	−	15.3468i	−0.193513	−	0.595572i
$665$	20.7400	−	3.77729i	0.804263	−	0.146477i
$666$	0.828087	−	2.54859i	0.0320877	−	0.0987558i
$667$	−10.0514	+	13.8346i	−0.389192	+	0.535676i
$668$			6.51198i			0.251956i
$669$	−13.0964	−	9.51509i	−0.506336	−	0.367875i
$670$	4.60070	−	2.47949i	0.177741	−	0.0957912i
$671$	−17.0517	+	12.3888i	−0.658273	+	0.478264i
$672$	2.16571	+	2.98085i	0.0835442	+	0.114989i
$673$	39.8480	−	12.9474i	1.53603	−	0.499086i	0.585751	−	0.810491i	$-0.300800\pi$
$673$	39.8480	−	12.9474i	1.53603	−	0.499086i	0.950277	+	0.311405i	$0.100800\pi$
$674$	5.19569			0.200131
$675$	−6.75717	−	17.9355i	−0.260084	−	0.690337i
$676$	15.8565			0.609867
$677$	−26.6690	+	8.66530i	−1.02497	+	0.333034i	−0.772802	−	0.634648i	$-0.781145\pi$
$677$	−26.6690	+	8.66530i	−1.02497	+	0.333034i	−0.252173	+	0.967682i	$0.581145\pi$
$678$	−0.345420	−	0.475429i	−0.0132658	−	0.0182588i
$679$	0.138467	−	0.100602i	0.00531386	−	0.00386075i
$680$	0.996751	−	2.07312i	0.0382237	−	0.0795007i
$681$	4.63040	+	3.36418i	0.177437	+	0.128916i
$682$		−	10.4799i		−	0.401295i
$683$	−6.64883	+	9.15133i	−0.254410	+	0.350166i	−0.917050	−	0.398773i	$-0.869436\pi$
$683$	−6.64883	+	9.15133i	−0.254410	+	0.350166i	0.662639	+	0.748939i	$0.269436\pi$
$684$	−8.00740	+	24.6442i	−0.306171	+	0.942296i
$685$	−4.75111	−	8.81568i	−0.181530	−	0.336830i
$686$	−1.55491	−	4.78553i	−0.0593669	−	0.182712i
$687$	−11.9255	−	3.87484i	−0.454988	−	0.147834i
$688$	14.2953	+	4.64483i	0.545003	+	0.177082i
$689$	2.29148	+	7.05245i	0.0872985	+	0.268677i
$690$	−1.54475	−	2.86628i	−0.0588075	−	0.109117i
$691$	7.83568	−	24.1157i	0.298083	−	0.917406i	−0.684085	−	0.729402i	$-0.739798\pi$
$691$	7.83568	−	24.1157i	0.298083	−	0.917406i	0.982168	−	0.188004i	$-0.0602016\pi$
$692$	−10.1179	+	13.9261i	−0.384624	+	0.529390i
$693$			17.3228i			0.658039i
$694$	3.40942	+	2.47709i	0.129420	+	0.0940290i
$695$	16.6791	−	34.6906i	0.632675	−	1.31589i
$696$	1.23444	−	0.896876i	0.0467915	−	0.0339960i
$697$	4.50230	+	6.19689i	0.170537	+	0.234724i
$698$	3.81504	−	1.23958i	0.144401	−	0.0469189i
$699$	14.5060			0.548668
$700$	13.3440	−	10.6691i	0.504355	−	0.403254i
$701$	−8.54625			−0.322787			−0.161394	−	0.986890i	$-0.551599\pi$
$701$	−8.54625			−0.322787			−0.161394	+	0.986890i	$0.551599\pi$
$702$	2.08789	−	0.678396i	0.0788022	−	0.0256044i
$703$	−12.7442	−	17.5409i	−0.480656	−	0.661566i
$704$	−20.1517	+	14.6411i	−0.759496	+	0.551806i
$705$	13.7960	−	7.43520i	0.519588	−	0.280026i
$706$	−0.0122770	−	0.00891974i	−0.000462050	−	0.000335699i
$707$			30.9420i			1.16369i
$708$	−7.50309	+	10.3271i	−0.281984	+	0.388117i
$709$	0.911087	−	2.80404i	0.0342166	−	0.105308i	−0.932490	−	0.361197i	$-0.882368\pi$
$709$	0.911087	−	2.80404i	0.0342166	−	0.105308i	0.966706	+	0.255889i	$0.0823682\pi$
$710$	0.704910	−	0.128382i	0.0264548	−	0.00481811i
$711$	6.78391	+	20.8787i	0.254417	+	0.783014i
$712$	9.26383	+	3.01000i	0.347177	+	0.112805i
$713$	78.4352	+	25.4852i	2.93742	+	0.954427i
$714$	−0.0993791	−	0.305857i	−0.00371917	−	0.0114464i
$715$	13.1480	−	13.7691i	0.491707	−	0.514937i
$716$	−10.9877	+	33.8168i	−0.410631	+	1.26379i
$717$	4.65186	−	6.40273i	0.173727	−	0.239114i
$718$			4.86074i			0.181401i
$719$	−0.930260	−	0.675874i	−0.0346929	−	0.0252058i	0.570304	−	0.821434i	$-0.306826\pi$
$719$	−0.930260	−	0.675874i	−0.0346929	−	0.0252058i	−0.604997	+	0.796228i	$0.706826\pi$
$720$	3.62469	+	19.9021i	0.135084	+	0.741709i
$721$	19.7178	−	14.3258i	0.734330	−	0.533522i
$722$	−1.44596	−	1.99020i	−0.0538132	−	0.0740675i
$723$	−8.55165	+	2.77860i	−0.318039	+	0.103337i
$724$	−20.9416			−0.778289
$725$	−6.66598	−	8.33724i	−0.247568	−	0.309637i
$726$	−0.751124			−0.0278768
$727$	43.4907	−	14.1310i	1.61298	−	0.524090i	0.642711	−	0.766109i	$-0.277810\pi$
$727$	43.4907	−	14.1310i	1.61298	−	0.524090i	0.970271	+	0.242019i	$0.0778097\pi$
$728$	2.34129	+	3.22251i	0.0867739	+	0.119434i
$729$	−3.49235	+	2.53734i	−0.129346	+	0.0939756i
$730$	−5.42528	−	0.731414i	−0.200799	−	0.0270708i
$731$	−3.38360	−	2.45833i	−0.125147	−	0.0909247i
$732$			7.27119i			0.268751i
$733$	−12.9906	+	17.8801i	−0.479820	+	0.660415i	−0.978470	−	0.206388i	$-0.933829\pi$
$733$	−12.9906	+	17.8801i	−0.479820	+	0.660415i	0.498651	+	0.866803i	$0.333829\pi$
$734$	−2.90978	+	8.95538i	−0.107402	+	0.330549i
$735$	−0.803375	+	5.95906i	−0.0296329	+	0.219803i
$736$	7.42025	+	22.8372i	0.273514	+	0.841790i
$737$	33.0465	+	10.7375i	1.21728	+	0.395519i
$738$	4.79837	+	1.55909i	0.176630	+	0.0573907i
$739$	−9.77634	−	30.0885i	−0.359629	−	1.10682i	−0.953277	−	0.302098i	$-0.902313\pi$
$739$	−9.77634	−	30.0885i	−0.359629	−	1.10682i	0.593648	−	0.804725i	$-0.297687\pi$
$740$	−15.8362	−	7.61399i	−0.582150	−	0.279896i
$741$	2.50433	−	7.70753i	0.0919988	−	0.283143i
$742$	0.921781	−	1.26872i	0.0338396	−	0.0465763i
$743$		−	29.5982i		−	1.08585i	−0.839780	−	0.542927i	$-0.817316\pi$
$743$		−	29.5982i		−	1.08585i	0.839780	−	0.542927i	$-0.182684\pi$
$744$	−5.95345	−	4.32543i	−0.218264	−	0.158578i
$745$	1.95451	+	1.86634i	0.0716076	+	0.0683773i
$746$	4.95478	−	3.59986i	0.181407	−	0.131800i
$747$	−23.2096	−	31.9453i	−0.849195	−	1.16882i
$748$	7.14585	−	2.32183i	0.261278	−	0.0848944i
$749$	−13.7905			−0.503895
$750$	1.98067	−	0.456028i	0.0723240	−	0.0166518i
$751$	1.92870			0.0703791			0.0351896	−	0.999381i	$-0.488796\pi$
$751$	1.92870			0.0703791			0.0351896	+	0.999381i	$0.488796\pi$
$752$	−34.4805	+	11.2034i	−1.25737	+	0.408546i
$753$	0.252749	+	0.347879i	0.00921067	+	0.0126774i
$754$	0.989170	−	0.718674i	0.0360234	−	0.0261726i
$755$	29.9020	+	28.5531i	1.08824	+	1.03915i
$756$	10.5965	+	7.69882i	0.385391	+	0.280003i
$757$		−	40.7460i		−	1.48094i	−0.672089	−	0.740470i	$-0.734603\pi$
$757$		−	40.7460i		−	1.48094i	0.672089	−	0.740470i	$-0.265397\pi$
$758$	1.34069	−	1.84530i	0.0486961	−	0.0670244i
$759$	6.68953	−	20.5883i	0.242815	−	0.747307i
$760$	−11.0483	−	5.31200i	−0.400765	−	0.192687i
$761$	−11.4943	−	35.3758i	−0.416668	−	1.28237i	−0.910750	−	0.412958i	$-0.864496\pi$
$761$	−11.4943	−	35.3758i	−0.416668	−	1.28237i	0.494082	−	0.869415i	$-0.335504\pi$
$762$	−0.490220	−	0.159282i	−0.0177588	−	0.00577018i
$763$	−14.4316	−	4.68910i	−0.522458	−	0.169757i
$764$	5.45152	+	16.7781i	0.197229	+	0.607009i
$765$	0.752055	−	5.57839i	0.0271906	−	0.201687i
$766$	−0.937058	+	2.88397i	−0.0338573	+	0.104202i
$767$	−12.2377	+	16.8437i	−0.441877	+	0.608192i
$768$			7.50313i			0.270746i
$769$	−15.0402	−	10.9273i	−0.542363	−	0.394050i	0.282599	−	0.959238i	$-0.408803\pi$
$769$	−15.0402	−	10.9273i	−0.542363	−	0.394050i	−0.824962	+	0.565188i	$0.808803\pi$
$770$	−3.99019	−	0.537941i	−0.143796	−	0.0193860i
$771$	9.63356	−	6.99919i

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.248853 + 0.0808572i) q^{2} +(-0.408373 - 0.562077i) q^{3} +(-1.56264 + 1.13533i) q^{4} +(-1.61719 - 1.54424i) q^{5} +(0.147073 + 0.106855i) q^{6} +1.76904i q^{7} +(0.604668 - 0.832255i) q^{8} +(0.777889 - 2.39410i) q^{9} +(0.527307 + 0.253527i) q^{10} +(1.20206 + 3.69957i) q^{11} +(1.27628 + 0.414689i) q^{12} +(2.08164 + 0.676366i) q^{13} +(-0.143040 - 0.440231i) q^{14} +(-0.207564 + 1.53961i) q^{15} +(1.11057 - 3.41800i) q^{16} +(-0.587785 + 0.809017i) q^{17} +0.658676i q^{18} +(4.31151 + 3.13249i) q^{19} +(4.28032 + 0.577055i) q^{20} +(0.994337 - 0.722428i) q^{21} +(-0.598274 - 0.823454i) q^{22} +(7.61793 - 2.47521i) q^{23} -0.714721 q^{24} +(0.230636 + 4.99468i) q^{25} -0.572712 q^{26} +(-3.64562 + 1.18453i) q^{27} +(-2.00844 - 2.76438i) q^{28} +(-1.72717 + 1.25486i) q^{29} +(-0.0728359 - 0.399920i) q^{30} +(8.32975 + 6.05192i) q^{31} +2.99782i q^{32} +(1.58855 - 2.18646i) q^{33} +(0.0808572 - 0.248853i) q^{34} +(2.73183 - 2.86089i) q^{35} +(1.50252 + 4.62428i) q^{36} +(-3.86926 - 1.25720i) q^{37} +(-1.32622 - 0.430914i) q^{38} +(-0.469916 - 1.44625i) q^{39} +(-2.26307 + 0.412163i) q^{40} +(2.36700 - 7.28488i) q^{41} +(-0.189030 + 0.260178i) q^{42} +4.18236i q^{43} +(-6.07862 - 4.41638i) q^{44} +(-4.95506 + 2.67047i) q^{45} +(-1.69560 + 1.23193i) q^{46} +(-5.92954 - 8.16131i) q^{47} +(-2.37470 + 0.771588i) q^{48} +3.87049 q^{49} +(-0.461250 - 1.22429i) q^{50} +0.694765 q^{51} +(-4.02076 + 1.30642i) q^{52} +(1.99138 + 2.74089i) q^{53} +(0.811444 - 0.589549i) q^{54} +(3.76906 - 7.83920i) q^{55} +(1.47229 + 1.06968i) q^{56} -3.70262i q^{57} +(0.328346 - 0.451930i) q^{58} +(-2.93943 + 9.04665i) q^{59} +(-1.42362 - 2.64152i) q^{60} +(1.67435 + 5.15313i) q^{61} +(-2.56222 - 0.832517i) q^{62} +(4.23526 + 1.37612i) q^{63} +(1.97875 + 6.08997i) q^{64} +(-2.32195 - 4.30837i) q^{65} +(-0.218525 + 0.672552i) q^{66} +(5.25041 - 7.22656i) q^{67} -1.93153i q^{68} +(-4.50221 - 3.27105i) q^{69} +(-0.448500 + 0.932828i) q^{70} +(0.990731 - 0.719808i) q^{71} +(-1.52213 - 2.09504i) q^{72} +(-8.89853 + 2.89131i) q^{73} +1.06453 q^{74} +(2.71321 - 2.16932i) q^{75} -10.2938 q^{76} +(-6.54470 + 2.12650i) q^{77} +(0.233880 + 0.321908i) q^{78} +(-7.05538 + 5.12603i) q^{79} +(-7.07423 + 3.81257i) q^{80} +(-3.95505 - 2.87351i) q^{81} +2.00425i q^{82} +(9.22003 - 12.6903i) q^{83} +(-0.733603 + 2.25780i) q^{84} +(2.19988 - 0.400655i) q^{85} +(-0.338174 - 1.04079i) q^{86} +(1.41066 + 0.458350i) q^{87} +(3.80583 + 1.23659i) q^{88} +(2.92596 + 9.00518i) q^{89} +(1.01715 - 1.06521i) q^{90} +(-1.19652 + 3.68251i) q^{91} +(-9.09393 + 12.5167i) q^{92} -7.15340i q^{93} +(2.13548 + 1.55152i) q^{94} +(-2.13522 - 11.7239i) q^{95} +(1.68501 - 1.22423i) q^{96} +(-0.0568680 - 0.0782721i) q^{97} +(-0.963183 + 0.312957i) q^{98} +9.79220 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) \) 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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