LMFDB - Embedded newform 350.2.r.a.167.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(13,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([19, 10]))

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

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

chi := DirichletCharacter("350.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.r (of order $20$, degree $8$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			167.5
Character	$\chi$	$=$	350.167
Dual form			350.2.r.a.153.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 + 0.891007i) q^{2} +(-0.398173 - 0.0630644i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.91550 + 1.15362i) q^{5} +(0.236957 - 0.326144i) q^{6} +(2.54649 - 0.717909i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.69861 - 0.876830i) q^{9} +O(q^{10})$	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.398173 - 0.0630644i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.91550 + 1.15362i) q^{5} +(0.236957 - 0.326144i) q^{6} +(2.54649 - 0.717909i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.69861 - 0.876830i) q^{9} +(-0.158263 - 2.23046i) q^{10} +(1.65889 + 5.10553i) q^{11} +(0.183020 + 0.359197i) q^{12} +(-4.30091 + 2.19142i) q^{13} +(-0.516420 + 2.59486i) q^{14} +(0.835454 - 0.338540i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(-4.86947 + 0.771249i) q^{17} +(2.00640 - 2.00640i) q^{18} +(-4.51523 - 3.28051i) q^{19} +(2.05920 + 0.871594i) q^{20} +(-1.05922 + 0.125259i) q^{21} +(-5.30218 - 0.839782i) q^{22} +(-4.53568 - 2.31104i) q^{23} -0.403136 q^{24} +(2.33832 - 4.41953i) q^{25} -4.82703i q^{26} +(2.09680 + 1.06838i) q^{27} +(-2.07759 - 1.63818i) q^{28} +(4.32889 + 5.95820i) q^{29} +(-0.0776464 + 0.898089i) q^{30} +(-0.508824 + 0.700336i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.338546 - 2.13750i) q^{33} +(1.52351 - 4.68887i) q^{34} +(-4.04962 + 4.31284i) q^{35} +(0.876830 + 2.69861i) q^{36} +(-7.93401 + 4.04258i) q^{37} +(4.97282 - 2.53378i) q^{38} +(1.85071 - 0.601331i) q^{39} +(-1.71146 + 1.43907i) q^{40} +(5.22278 + 1.69699i) q^{41} +(0.369268 - 1.00064i) q^{42} +(-1.90984 + 1.90984i) q^{43} +(3.15539 - 4.34302i) q^{44} +(6.18072 - 1.43360i) q^{45} +(4.11831 - 2.99213i) q^{46} +(-1.05448 + 6.65770i) q^{47} +(0.183020 - 0.359197i) q^{48} +(5.96921 - 3.65629i) q^{49} +(2.87626 + 4.08988i) q^{50} +1.98753 q^{51} +(4.30091 + 2.19142i) q^{52} +(1.50300 - 9.48959i) q^{53} +(-1.90386 + 1.38323i) q^{54} +(-9.06745 - 7.86593i) q^{55} +(2.40283 - 1.10743i) q^{56} +(1.59096 + 1.59096i) q^{57} +(-7.27407 + 1.15210i) q^{58} +(-1.65773 + 5.10196i) q^{59} +(-0.764952 - 0.476907i) q^{60} +(9.65000 - 3.13548i) q^{61} +(-0.393003 - 0.771311i) q^{62} +(-7.50145 - 0.295485i) q^{63} +(0.951057 - 0.309017i) q^{64} +(5.71034 - 9.15931i) q^{65} +(2.05822 + 0.668757i) q^{66} +(0.608456 + 3.84164i) q^{67} +(3.48616 + 3.48616i) q^{68} +(1.66024 + 1.20623i) q^{69} +(-2.00428 - 5.56622i) q^{70} +(0.834764 - 0.606492i) q^{71} +(-2.80255 - 0.443880i) q^{72} +(-2.22406 + 4.36496i) q^{73} -8.90455i q^{74} +(-1.20977 + 1.61227i) q^{75} +5.58113i q^{76} +(7.88964 + 11.8102i) q^{77} +(-0.304413 + 1.92199i) q^{78} +(-0.739941 - 1.01844i) q^{79} +(-0.505236 - 2.17824i) q^{80} +(6.11920 + 4.44586i) q^{81} +(-3.88312 + 3.88312i) q^{82} +(1.11929 + 7.06692i) q^{83} +(0.723929 + 0.783299i) q^{84} +(8.43777 - 7.09486i) q^{85} +(-0.834631 - 2.56873i) q^{86} +(-1.34789 - 2.64539i) q^{87} +(2.43714 + 4.78316i) q^{88} +(1.15631 + 3.55875i) q^{89} +(-1.52864 + 6.15790i) q^{90} +(-9.37898 + 8.66810i) q^{91} +(0.796331 + 5.02784i) q^{92} +(0.246766 - 0.246766i) q^{93} +(-5.45333 - 3.96208i) q^{94} +(12.4334 + 1.07496i) q^{95} +(0.236957 + 0.326144i) q^{96} +(1.08362 - 6.84171i) q^{97} +(0.547816 + 6.97853i) q^{98} -15.2324i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{7}+O(q^{10}) $ 160 * q + 8 * q^7	$ 160 q + 8 q^{7} + 16 q^{15} + 40 q^{16} - 8 q^{18} - 24 q^{22} - 32 q^{23} + 12 q^{28} - 40 q^{29} - 56 q^{30} + 28 q^{35} + 40 q^{36} - 32 q^{37} + 40 q^{39} - 112 q^{43} - 32 q^{50} + 112 q^{53} - 152 q^{57} + 16 q^{58} + 8 q^{60} - 100 q^{63} - 8 q^{65} - 16 q^{67} - 56 q^{70} - 8 q^{72} - 144 q^{77} + 40 q^{78} + 40 q^{81} - 60 q^{84} + 48 q^{85} - 16 q^{88} + 8 q^{92} + 56 q^{93} - 104 q^{95} - 32 q^{98}+O(q^{100}) $ 160 * q + 8 * q^7 + 16 * q^15 + 40 * q^16 - 8 * q^18 - 24 * q^22 - 32 * q^23 + 12 * q^28 - 40 * q^29 - 56 * q^30 + 28 * q^35 + 40 * q^36 - 32 * q^37 + 40 * q^39 - 112 * q^43 - 32 * q^50 + 112 * q^53 - 152 * q^57 + 16 * q^58 + 8 * q^60 - 100 * q^63 - 8 * q^65 - 16 * q^67 - 56 * q^70 - 8 * q^72 - 144 * q^77 + 40 * q^78 + 40 * q^81 - 60 * q^84 + 48 * q^85 - 16 * q^88 + 8 * q^92 + 56 * q^93 - 104 * q^95 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{13}{20}\right)$

Coefficient data

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

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

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

$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$3$	−0.398173	−	0.0630644i	−0.229885	−	0.0364102i	0.0404290	−	0.999182i	$-0.487128\pi$
$3$	−0.398173	−	0.0630644i	−0.229885	−	0.0364102i	−0.270314	+	0.962772i	$0.587128\pi$
$4$	−0.587785	−	0.809017i	−0.293893	−	0.404508i
$5$	−1.91550	+	1.15362i	−0.856640	+	0.515915i
$5$	−1.91550	+	1.15362i	−0.856640	+	0.515915i
$6$	0.236957	−	0.326144i	0.0967374	−	0.133148i
$7$	2.54649	−	0.717909i	0.962482	−	0.271344i
$7$	2.54649	−	0.717909i	0.962482	−	0.271344i
$8$	0.987688	−	0.156434i	0.349201	−	0.0553079i
$9$	−2.69861	−	0.876830i	−0.899535	−	0.292277i
$10$	−0.158263	−	2.23046i	−0.0500472	−	0.705333i
$11$	1.65889	+	5.10553i	0.500173	+	1.53937i	0.808737	+	0.588171i	$0.200152\pi$
$11$	1.65889	+	5.10553i	0.500173	+	1.53937i	−0.308564	+	0.951204i	$0.599848\pi$
$12$	0.183020	+	0.359197i	0.0528333	+	0.103691i
$13$	−4.30091	+	2.19142i	−1.19286	+	0.607792i	−0.933705	−	0.358045i	$-0.883444\pi$
$13$	−4.30091	+	2.19142i	−1.19286	+	0.607792i	−0.259154	+	0.965836i	$0.583444\pi$
$14$	−0.516420	+	2.59486i	−0.138019	+	0.693506i
$15$	0.835454	−	0.338540i	0.215713	−	0.0874108i
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	−4.86947	+	0.771249i	−1.18102	+	0.187055i	−0.715907	−	0.698196i	$-0.753987\pi$
$17$	−4.86947	+	0.771249i	−1.18102	+	0.187055i	−0.465114	+	0.885251i	$0.653987\pi$
$18$	2.00640	−	2.00640i	0.472914	−	0.472914i
$19$	−4.51523	−	3.28051i	−1.03586	−	0.752600i	−0.0663908	−	0.997794i	$-0.521148\pi$
$19$	−4.51523	−	3.28051i	−1.03586	−	0.752600i	−0.969474	+	0.245194i	$0.921148\pi$
$20$	2.05920	+	0.871594i	0.460452	+	0.194894i
$21$	−1.05922	+	0.125259i	−0.231140	+	0.0273338i
$22$	−5.30218	−	0.839782i	−1.13043	−	0.179042i
$23$	−4.53568	−	2.31104i	−0.945754	−	0.481886i	−0.0880996	−	0.996112i	$-0.528079\pi$
$23$	−4.53568	−	2.31104i	−0.945754	−	0.481886i	−0.857655	+	0.514226i	$0.828079\pi$
$24$	−0.403136			−0.0822898
$25$	2.33832	−	4.41953i	0.467663	−	0.883907i
$26$		−	4.82703i		−	0.946658i
$27$	2.09680	+	1.06838i	0.403530	+	0.205609i
$28$	−2.07759	−	1.63818i	−0.392627	−	0.309586i
$29$	4.32889	+	5.95820i	0.803854	+	1.10641i	0.992243	+	0.124315i	$0.0396734\pi$
$29$	4.32889	+	5.95820i	0.803854	+	1.10641i	−0.188389	+	0.982094i	$0.560327\pi$
$30$	−0.0776464	+	0.898089i	−0.0141762	+	0.163968i
$31$	−0.508824	+	0.700336i	−0.0913874	+	0.125784i	−0.852262	−	0.523114i	$-0.824770\pi$
$31$	−0.508824	+	0.700336i	−0.0913874	+	0.125784i	0.760875	+	0.648898i	$0.224770\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−0.338546	−	2.13750i	−0.0589334	−	0.372091i
$34$	1.52351	−	4.68887i	0.261279	−	0.804135i
$35$	−4.04962	+	4.31284i	−0.684510	+	0.729003i
$36$	0.876830	+	2.69861i	0.146138	+	0.449768i
$37$	−7.93401	+	4.04258i	−1.30434	+	0.664596i	−0.961502	−	0.274797i	$-0.911389\pi$
$37$	−7.93401	+	4.04258i	−1.30434	+	0.664596i	−0.342842	+	0.939393i	$0.611389\pi$
$38$	4.97282	−	2.53378i	0.806699	−	0.411034i
$39$	1.85071	−	0.601331i	0.296350	−	0.0962900i
$40$	−1.71146	+	1.43907i	−0.270605	+	0.227537i
$41$	5.22278	+	1.69699i	0.815662	+	0.265025i	0.686994	−	0.726663i	$-0.258930\pi$
$41$	5.22278	+	1.69699i	0.815662	+	0.265025i	0.128668	+	0.991688i	$0.458930\pi$
$42$	0.369268	−	1.00064i	0.0569793	−	0.154401i
$43$	−1.90984	+	1.90984i	−0.291248	+	0.291248i	−0.837573	−	0.546325i	$-0.816026\pi$
$43$	−1.90984	+	1.90984i	−0.291248	+	0.291248i	0.546325	+	0.837573i	$0.316026\pi$
$44$	3.15539	−	4.34302i	0.475693	−	0.654735i
$45$	6.18072	−	1.43360i	0.921367	−	0.213708i
$46$	4.11831	−	2.99213i	0.607212	−	0.441165i
$47$	−1.05448	+	6.65770i	−0.153811	+	0.971126i	0.783186	+	0.621788i	$0.213593\pi$
$47$	−1.05448	+	6.65770i	−0.153811	+	0.971126i	−0.936997	+	0.349338i	$0.886407\pi$
$48$	0.183020	−	0.359197i	0.0264166	−	0.0518456i
$49$	5.96921	−	3.65629i	0.852745	−	0.522328i
$50$	2.87626	+	4.08988i	0.406765	+	0.578396i
$51$	1.98753			0.278310
$52$	4.30091	+	2.19142i	0.596429	+	0.303896i
$53$	1.50300	−	9.48959i	0.206453	−	1.30350i	−0.638901	−	0.769289i	$-0.720611\pi$
$53$	1.50300	−	9.48959i	0.206453	−	1.30350i	0.845354	−	0.534206i	$-0.179389\pi$
$54$	−1.90386	+	1.38323i	−0.259082	+	0.188234i
$55$	−9.06745	−	7.86593i	−1.22265	−	1.06064i
$56$	2.40283	−	1.10743i	0.321092	−	0.147986i
$57$	1.59096	+	1.59096i	0.210728	+	0.210728i
$58$	−7.27407	+	1.15210i	−0.955132	+	0.151278i
$59$	−1.65773	+	5.10196i	−0.215818	+	0.664218i	0.783277	+	0.621673i	$0.213547\pi$
$59$	−1.65773	+	5.10196i	−0.215818	+	0.664218i	−0.999095	+	0.0425453i	$0.986453\pi$
$60$	−0.764952	−	0.476907i	−0.0987549	−	0.0615685i
$61$	9.65000	−	3.13548i	1.23556	−	0.401457i	0.382832	−	0.923818i	$-0.374949\pi$
$61$	9.65000	−	3.13548i	1.23556	−	0.401457i	0.852724	+	0.522361i	$0.174949\pi$
$62$	−0.393003	−	0.771311i	−0.0499114	−	0.0979566i
$63$	−7.50145	−	0.295485i	−0.945094	−	0.0372276i
$64$	0.951057	−	0.309017i	0.118882	−	0.0386271i
$65$	5.71034	−	9.15931i	0.708281	−	1.13607i
$66$	2.05822	+	0.668757i	0.253350	+	0.0823183i
$67$	0.608456	+	3.84164i	0.0743347	+	0.469331i	0.996574	+	0.0827104i	$0.0263577\pi$
$67$	0.608456	+	3.84164i	0.0743347	+	0.469331i	−0.922239	+	0.386620i	$0.873642\pi$
$68$	3.48616	+	3.48616i	0.422759	+	0.422759i
$69$	1.66024	+	1.20623i	0.199869	+	0.145214i
$70$	−2.00428	−	5.56622i	−0.239558	−	0.665291i
$71$	0.834764	−	0.606492i	0.0990683	−	0.0719773i	−0.537148	−	0.843488i	$-0.680498\pi$
$71$	0.834764	−	0.606492i	0.0990683	−	0.0719773i	0.636217	+	0.771510i	$0.280498\pi$
$72$	−2.80255	−	0.443880i	−0.330283	−	0.0523117i
$73$	−2.22406	+	4.36496i	−0.260307	+	0.510880i	−0.983759	−	0.179494i	$-0.942554\pi$
$73$	−2.22406	+	4.36496i	−0.260307	+	0.510880i	0.723453	+	0.690374i	$0.242554\pi$
$74$		−	8.90455i		−	1.03513i
$75$	−1.20977	+	1.61227i	−0.139692	+	0.186169i
$76$			5.58113i			0.640200i
$77$	7.88964	+	11.8102i	0.899108	+	1.34590i
$78$	−0.304413	+	1.92199i	−0.0344680	+	0.217622i
$79$	−0.739941	−	1.01844i	−0.0832499	−	0.114584i	0.765361	−	0.643601i	$-0.222561\pi$
$79$	−0.739941	−	1.01844i	−0.0832499	−	0.114584i	−0.848611	+	0.529018i	$0.822561\pi$
$80$	−0.505236	−	2.17824i	−0.0564871	−	0.243535i
$81$	6.11920	+	4.44586i	0.679911	+	0.493984i
$82$	−3.88312	+	3.88312i	−0.428819	+	0.428819i
$83$	1.11929	+	7.06692i	0.122858	+	0.775695i	0.969781	+	0.243979i	$0.0784528\pi$
$83$	1.11929	+	7.06692i	0.122858	+	0.775695i	−0.846922	+	0.531716i	$0.821547\pi$
$84$	0.723929	+	0.783299i	0.0789871	+	0.0854649i
$85$	8.43777	−	7.09486i	0.915204	−	0.769545i
$86$	−0.834631	−	2.56873i	−0.0900005	−	0.276993i
$87$	−1.34789	−	2.64539i	−0.144509	−	0.283616i
$88$	2.43714	+	4.78316i	0.259800	+	0.509887i
$89$	1.15631	+	3.55875i	0.122568	+	0.377226i	0.993450	−	0.114266i	$-0.0364516\pi$
$89$	1.15631	+	3.55875i	0.122568	+	0.377226i	−0.870882	+	0.491492i	$0.836452\pi$
$90$	−1.52864	+	6.15790i	−0.161133	+	0.649100i
$91$	−9.37898	+	8.66810i	−0.983184	+	0.908664i
$92$	0.796331	+	5.02784i	0.0830233	+	0.524188i
$93$	0.246766	−	0.246766i	0.0255884	−	0.0255884i
$94$	−5.45333	−	3.96208i	−0.562468	−	0.408657i
$95$	12.4334	+	1.07496i	1.27564	+	0.110289i
$96$	0.236957	+	0.326144i	0.0241844	+	0.0332869i
$97$	1.08362	−	6.84171i	0.110025	−	0.694671i	−0.869588	−	0.493778i	$-0.835616\pi$
$97$	1.08362	−	6.84171i	0.110025	−	0.694671i	0.979613	−	0.200893i	$-0.0643843\pi$
$98$	0.547816	+	6.97853i	0.0553378	+	0.704938i
$99$		−	15.2324i		−	1.53091i
$100$	−4.94991	+	0.706000i	−0.494991	+	0.0706000i
$101$			5.28997i			0.526372i	0.964745	+	0.263186i	$0.0847732\pi$
$101$			5.28997i			0.526372i	−0.964745	+	0.263186i	$0.915227\pi$
$102$	−0.902319	+	1.77090i	−0.0893429	+	0.175345i
$103$	13.3719	+	2.11789i	1.31757	+	0.208682i	0.775338	−	0.631547i	$-0.217580\pi$
$103$	13.3719	+	2.11789i	1.31757	+	0.208682i	0.542231	+	0.840229i	$0.317580\pi$
$104$	−3.90515	+	2.83725i	−0.382931	+	0.278216i
$105$	1.88443	−	1.46187i	0.183902	−	0.142664i
$106$	7.77294	+	5.64737i	0.754975	+	0.548521i
$107$	−5.29330	−	5.29330i	−0.511722	−	0.511722i	0.403332	−	0.915054i	$-0.367852\pi$
$107$	−5.29330	−	5.29330i	−0.511722	−	0.511722i	−0.915054	+	0.403332i	$0.867852\pi$
$108$	−0.368137	−	2.32433i	−0.0354240	−	0.223658i
$109$	10.4486	+	3.39497i	1.00080	+	0.325179i	0.763184	−	0.646181i	$-0.223635\pi$
$109$	10.4486	+	3.39497i	1.00080	+	0.325179i	0.237614	+	0.971360i	$0.423635\pi$
$110$	11.1251	−	4.50810i	1.06074	−	0.429830i
$111$	3.41405	−	1.10929i	0.324047	−	0.105289i
$112$	−0.104136	+	2.64370i	−0.00983996	+	0.249806i
$113$	−6.53034	−	12.8165i	−0.614323	−	1.20568i	−0.963270	−	0.268534i	$-0.913461\pi$
$113$	−6.53034	−	12.8165i	−0.614323	−	1.20568i	0.348947	−	0.937142i	$-0.386539\pi$
$114$	−2.13983	+	0.695274i	−0.200414	+	0.0651184i
$115$	11.3542	−	0.805641i	1.05878	−	0.0751264i
$116$	2.27583	−	7.00428i	0.211305	−	0.650331i
$117$	13.5280	−	2.14262i	1.25066	−	0.198085i
$118$	−3.79329	−	3.79329i	−0.349200	−	0.349200i
$119$	−11.8464	+	5.45981i	−1.08596	+	0.500500i
$120$	0.772209	−	0.465066i	0.0704927	−	0.0424545i
$121$	−14.4153	+	10.4733i	−1.31048	+	0.952122i
$122$	−1.58728	+	10.0217i	−0.143706	+	0.907321i
$123$	−1.97255	−	1.00506i	−0.177859	−	0.0906236i
$124$	0.865663			0.0777388
$125$	0.619415	+	11.1632i	0.0554021	+	0.998464i
$126$	3.66887	−	6.54970i	0.326849	−	0.583493i
$127$	3.71464	−	7.29039i	0.329621	−	0.646917i	−0.665411	−	0.746477i	$-0.731744\pi$
$127$	3.71464	−	7.29039i	0.329621	−	0.646917i	0.995032	+	0.0995602i	$0.0317436\pi$
$128$	−0.156434	+	0.987688i	−0.0138270	+	0.0873001i
$129$	0.880889	−	0.640003i	0.0775579	−	0.0563491i
$130$	5.56856	+	9.24619i	0.488395	+	0.810944i
$131$	0.566572	−	0.779819i	0.0495016	−	0.0681331i	−0.783549	−	0.621330i	$-0.786592\pi$
$131$	0.566572	−	0.779819i	0.0495016	−	0.0681331i	0.833050	+	0.553197i	$0.186592\pi$
$132$	−1.53028	+	1.53028i	−0.133194	+	0.133194i
$133$	−13.8531	−	5.11225i	−1.20122	−	0.443288i
$134$	−3.69916	−	1.20193i	−0.319559	−	0.103831i
$135$	−5.24894	+	0.372441i	−0.451757	+	0.0320546i
$136$	−4.68887	+	1.52351i	−0.402067	+	0.130640i
$137$	5.44198	−	2.77283i	0.464940	−	0.236899i	−0.205796	−	0.978595i	$-0.565978\pi$
$137$	5.44198	−	2.77283i	0.464940	−	0.236899i	0.670736	+	0.741696i	$0.265978\pi$
$138$	−1.82850	+	0.931665i	−0.155652	+	0.0793086i
$139$	−5.02164	−	15.4550i	−0.425930	−	1.31088i	−0.902101	−	0.431524i	$-0.857976\pi$
$139$	−5.02164	−	15.4550i	−0.425930	−	1.31088i	0.476172	−	0.879352i	$-0.342024\pi$
$140$	5.86947	+	0.741183i	0.496061	+	0.0626414i
$141$	0.839727	−	2.58442i	0.0707178	−	0.217647i
$142$	0.161413	+	1.01912i	0.0135455	+	0.0855228i
$143$	−18.3231	−	18.3231i	−1.53225	−	1.53225i
$144$	1.66783	−	2.29557i	0.138986	−	0.191298i
$145$	−15.1655	−	6.41906i	−1.25943	−	0.533074i
$146$	−2.87951	−	3.96330i	−0.238310	−	0.328005i
$147$	−2.60736	+	1.07939i	−0.215051	+	0.0890268i
$148$	7.93401	+	4.04258i	0.652172	+	0.332298i
$149$			8.58317i			0.703161i	0.936158	+	0.351580i	$0.114356\pi$
$149$			8.58317i			0.703161i	−0.936158	+	0.351580i	$0.885644\pi$
$150$	−0.887323	−	1.80987i	−0.0724496	−	0.147775i
$151$	−19.8284			−1.61362			−0.806808	−	0.590814i	$-0.798807\pi$
$151$	−19.8284			−1.61362			−0.806808	+	0.590814i	$0.798807\pi$
$152$	−4.97282	−	2.53378i	−0.403349	−	0.205517i
$153$	13.8170	+	2.18840i	1.11704	+	0.176922i
$154$	−14.1048	+	1.66798i	−1.13660	+	0.134410i
$155$	0.166732	−	1.92849i	0.0133922	−	0.154900i
$156$	−1.57430	−	1.14380i	−0.126045	−	0.0915772i
$157$	0.702683	−	0.702683i	0.0560802	−	0.0560802i	−0.678511	−	0.734591i	$-0.737374\pi$
$157$	0.702683	−	0.702683i	0.0560802	−	0.0560802i	0.734591	+	0.678511i	$0.237374\pi$
$158$	1.24336	−	0.196930i	0.0989168	−	0.0156669i
$159$	−1.19691	+	3.68371i	−0.0949211	+	0.292137i
$160$	2.17020	+	0.538733i	0.171569	+	0.0425906i
$161$	−13.2092	−	2.62884i	−1.04103	−	0.207182i
$162$	−6.73935	+	3.43387i	−0.529493	+	0.269790i
$163$	0.149556	+	0.293520i	0.0117141	+	0.0229903i	0.896789	−	0.442458i	$-0.145893\pi$
$163$	0.149556	+	0.293520i	0.0117141	+	0.0229903i	−0.885075	+	0.465448i	$0.845893\pi$
$164$	−1.69699	−	5.22278i	−0.132512	−	0.407831i
$165$	3.11435	+	3.70383i	0.242452	+	0.288343i
$166$	−6.80482	−	2.21102i	−0.528156	−	0.171608i
$167$	−13.7526	+	2.17820i	−1.06421	+	0.168554i	−0.663897	−	0.747824i	$-0.731099\pi$
$167$	−13.7526	+	2.17820i	−1.06421	+	0.168554i	−0.400313	+	0.916379i	$0.631099\pi$
$168$	−1.02658	+	0.289415i	−0.0792025	+	0.0223288i
$169$	6.05429	−	8.33302i	0.465715	−	0.641001i
$170$	2.49090	+	10.7391i	0.191043	+	0.823652i
$171$	9.30838	+	12.8119i	0.711829	+	0.979749i
$172$	2.66767	+	0.422517i	0.203408	+	0.0322166i
$173$	−8.76566	+	17.2036i	−0.666441	+	1.30796i	0.271924	+	0.962319i	$0.412340\pi$
$173$	−8.76566	+	17.2036i	−0.666441	+	1.30796i	−0.938365	+	0.345645i	$0.887660\pi$
$174$	2.96899			0.225079
$175$	2.78167	−	12.9330i	0.210275	−	0.977642i
$176$	−5.36827			−0.404648
$177$	0.981813	−	1.92692i	0.0737976	−	0.144836i
$178$	−3.69582	−	0.585360i	−0.277013	−	0.0438746i
$179$	1.83335	+	2.52339i	0.137031	+	0.188607i	0.872017	−	0.489475i	$-0.162812\pi$
$179$	1.83335	+	2.52339i	0.137031	+	0.188607i	−0.734987	+	0.678082i	$0.762812\pi$
$180$	−4.79274	−	4.15766i	−0.357230	−	0.309894i
$181$	6.02339	−	8.29048i	0.447715	−	0.616227i	−0.524190	−	0.851601i	$-0.675632\pi$
$181$	6.02339	−	8.29048i	0.447715	−	0.616227i	0.971905	+	0.235375i	$0.0756317\pi$
$182$	−3.46537	−	12.2920i	−0.256870	−	0.911141i
$183$	−4.04010	+	0.639890i	−0.298653	+	0.0473020i
$184$	−4.84136	−	1.57305i	−0.356910	−	0.115967i
$185$	10.5340	−	16.8964i	0.774477	−	1.24225i
$186$	0.107841	+	0.331899i	0.00790726	+	0.0243360i
$187$	−12.0155	−	23.5818i	−0.878663	−	1.72447i
$188$	6.00600	−	3.06021i	0.438033	−	0.223189i
$189$	6.10649	+	1.21529i	0.444181	+	0.0883994i
$190$	−6.60244	+	10.5902i	−0.478992	+	0.768296i
$191$	−0.652382	+	2.00782i	−0.0472047	+	0.145281i	−0.971881	−	0.235474i	$-0.924336\pi$
$191$	−0.652382	+	2.00782i	−0.0472047	+	0.145281i	0.924676	+	0.380755i	$0.124336\pi$
$192$	−0.398173	+	0.0630644i	−0.0287356	+	0.00455128i
$193$	−11.1600	+	11.1600i	−0.803313	+	0.803313i	−0.983612	−	0.180299i	$-0.942294\pi$
$193$	−11.1600	+	11.1600i	−0.803313	+	0.803313i	0.180299	+	0.983612i	$0.442294\pi$
$194$	5.60406	+	4.07159i	0.402348	+	0.292323i
$195$	−2.85133	+	3.28687i	−0.204188	+	0.235377i
$196$	−6.46662	−	2.68008i	−0.461901	−	0.191434i
$197$	15.0741	+	2.38751i	1.07399	+	0.170103i	0.668288	−	0.743903i	$-0.267028\pi$
$197$	15.0741	+	2.38751i	1.07399	+	0.170103i	0.405701	+	0.914006i	$0.367028\pi$
$198$	13.5721	+	6.91535i	0.964530	+	0.491452i
$199$	14.3413			1.01663			0.508315	−	0.861171i	$-0.330269\pi$
$199$	14.3413			1.01663			0.508315	+	0.861171i	$0.330269\pi$
$200$	1.61816	−	4.73092i	0.114421	−	0.334526i
$201$		−	1.56801i		−	0.110599i
$202$	−4.71340	−	2.40160i	−0.331634	−	0.168976i
$203$	15.3009	+	12.0647i	1.07391	+	0.846779i
$204$	−1.16824	−	1.60795i	−0.0817932	−	0.112579i
$205$	−11.9619	+	2.77453i	−0.835458	+	0.193782i
$206$	−7.95776	+	10.9529i	−0.554443	+	0.763125i
$207$	10.2136	+	10.2136i	0.709895	+	0.709895i
$208$	−0.755113	−	4.76760i	−0.0523577	−	0.330573i
$209$	9.25846	−	28.4946i	0.640421	−	1.97101i
$210$	0.447020	+	2.34272i	0.0308473	+	0.161663i
$211$	4.75168	+	14.6242i	0.327119	+	1.00677i	0.970475	+	0.241202i	$0.0775417\pi$
$211$	4.75168	+	14.6242i	0.327119	+	1.00677i	−0.643356	+	0.765568i	$0.722458\pi$
$212$	−8.56068	+	4.36189i	−0.587950	+	0.299576i
$213$	−0.370628	+	0.188845i	−0.0253950	+	0.0129394i
$214$	7.11947	−	2.31325i	0.486677	−	0.158131i
$215$	1.45507	−	5.86154i	0.0992353	−	0.399754i
$216$	2.23812	+	0.727209i	0.152285	+	0.0494803i
$217$	−0.792937	+	2.14869i	−0.0538281	+	0.145862i
$218$	−7.76852	+	7.76852i	−0.526151	+	0.526151i
$219$	1.16083	−	1.59775i	0.0784419	−	0.107966i
$220$	−1.03396	+	11.9592i	−0.0697096	+	0.806289i
$221$	19.2530	−	13.9882i	1.29510	−	0.940945i
$222$	−0.561560	+	3.54555i	−0.0376894	+	0.237962i
$223$	−10.8656	+	21.3250i	−0.727618	+	1.42803i	0.169178	+	0.985585i	$0.445889\pi$
$223$	−10.8656	+	21.3250i	−0.727618	+	1.42803i	−0.896796	+	0.442444i	$0.854111\pi$
$224$	−2.30828	−	1.29300i	−0.154228	−	0.0863923i
$225$	−10.1854	+	9.87627i	−0.679025	+	0.658418i
$226$	14.3843			0.956831
$227$	−2.94229	−	1.49917i	−0.195287	−	0.0995035i	0.353613	−	0.935392i	$-0.384953\pi$
$227$	−2.94229	−	1.49917i	−0.195287	−	0.0995035i	−0.548900	+	0.835888i	$0.684953\pi$
$228$	0.351970	−	2.22225i	0.0233098	−	0.147172i
$229$	−24.2328	+	17.6061i	−1.60135	+	1.16345i	−0.716474	+	0.697614i	$0.754245\pi$
$229$	−24.2328	+	17.6061i	−1.60135	+	1.16345i	−0.884873	+	0.465833i	$0.845755\pi$
$230$	−4.43686	+	10.4824i	−0.292558	+	0.691189i
$231$	−2.39663	−	5.20007i	−0.157687	−	0.342139i
$232$	5.20766	+	5.20766i	0.341899	+	0.341899i
$233$	−8.90708	+	1.41074i	−0.583522	+	0.0924208i	−0.441214	−	0.897402i	$-0.645452\pi$
$233$	−8.90708	+	1.41074i	−0.583522	+	0.0924208i	−0.142308	+	0.989822i	$0.545452\pi$
$234$	−4.23248	+	13.0262i	−0.276686	+	0.851552i
$235$	−5.66061	−	13.9693i	−0.369258	−	0.911258i
$236$	5.10196	−	1.65773i	0.332109	−	0.107909i
$237$	0.230397	+	0.452180i	0.0149659	+	0.0293722i
$238$	0.513410	−	13.0339i	0.0332794	−	0.844862i
$239$	−15.4506	+	5.02019i	−0.999414	+	0.324729i	−0.762632	−	0.646833i	$-0.776093\pi$
$239$	−15.4506	+	5.02019i	−0.999414	+	0.324729i	−0.236783	+	0.971563i	$0.576093\pi$
$240$	0.0638016	+	0.899179i	0.00411838	+	0.0580417i
$241$	−17.1012	−	5.55651i	−1.10158	−	0.357927i	−0.298872	−	0.954293i	$-0.596611\pi$
$241$	−17.1012	−	5.55651i	−1.10158	−	0.357927i	−0.802712	+	0.596366i	$0.796611\pi$
$242$	−2.78740	−	17.5989i	−0.179181	−	1.13130i
$243$	−7.14822	−	7.14822i	−0.458559	−	0.458559i
$244$	−8.20878	−	5.96403i	−0.525513	−	0.381808i
$245$	−7.21608	+	13.8899i	−0.461018	+	0.887391i
$246$	1.79104	−	1.30127i	0.114192	−	0.0829657i
$247$	26.6086	+	4.21439i	1.69306	+	0.268155i
$248$	−0.393003	+	0.771311i	−0.0249557	+	0.0489783i
$249$		−	2.88444i		−	0.182794i
$250$	−10.2277	−	4.51607i	−0.646854	−	0.285621i
$251$		−	6.20662i		−	0.391758i	−0.980628	−	0.195879i	$-0.937244\pi$
$251$		−	6.20662i		−	0.391758i	0.980628	−	0.195879i	$-0.0627560\pi$
$252$	4.17019	+	6.24248i	0.262697	+	0.393240i
$253$	4.27492	−	26.9908i	0.268762	−	1.69690i
$254$	4.80937	+	6.61953i	0.301767	+	0.415346i
$255$	−3.80712	+	2.29286i	−0.238411	+	0.143584i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	11.7952	−	11.7952i	0.735765	−	0.735765i	−0.235990	−	0.971755i	$-0.575833\pi$
$257$	11.7952	−	11.7952i	0.735765	−	0.735765i	0.971755	+	0.235990i	$0.0758334\pi$
$258$	0.170332	+	1.07543i	0.0106044	+	0.0669535i
$259$	−17.3017	+	15.9903i	−1.07507	+	0.993588i
$260$	−10.7665	+	0.763941i	−0.667709	+	0.0473776i
$261$	−6.45762	−	19.8745i	−0.399717	−	1.23020i
$262$	0.437606	+	0.858849i	0.0270354	+	0.0530599i
$263$	8.39366	+	16.4735i	0.517575	+	1.01580i	0.990861	+	0.134890i	$0.0430680\pi$
$263$	8.39366	+	16.4735i	0.517575	+	1.01580i	−0.473285	+	0.880909i	$0.656932\pi$
$264$	−0.668757	−	2.05822i	−0.0411591	−	0.126675i
$265$	8.06839	+	19.9113i	0.495637	+	1.22314i
$266$	10.8442	−	10.0223i	0.664902	−	0.614505i
$267$	−0.235980	−	1.48992i	−0.0144417	−	0.0911814i
$268$	2.75031	−	2.75031i	0.168002	−	0.168002i
$269$	10.5644	+	7.67549i	0.644123	+	0.467983i	0.861264	−	0.508158i	$-0.169673\pi$
$269$	10.5644	+	7.67549i	0.644123	+	0.467983i	−0.217141	+	0.976140i	$0.569673\pi$
$270$	2.05112	−	4.84592i	0.124827	−	0.294914i
$271$	15.5724	+	21.4335i	0.945954	+	1.30199i	0.953301	+	0.302021i	$0.0976613\pi$
$271$	15.5724	+	21.4335i	0.945954	+	1.30199i	−0.00734722	+	0.999973i	$0.502339\pi$
$272$	0.771249	−	4.86947i	0.0467638	−	0.295255i
$273$	4.28110	−	2.85992i	0.259104	−	0.173090i
$274$			6.10768i			0.368978i
$275$	26.4431	+	4.60683i	1.59458	+	0.277802i
$276$		−	2.05217i		−	0.123526i
$277$	2.45787	−	4.82385i	0.147679	−	0.289837i	−0.805303	−	0.592864i	$-0.797997\pi$
$277$	2.45787	−	4.82385i	0.147679	−	0.289837i	0.952982	+	0.303027i	$0.0979972\pi$
$278$	16.0503	+	2.54212i	0.962632	+	0.152466i
$279$	1.98719	−	1.44378i	0.118970	−	0.0864367i
$280$	−3.32508	+	4.89324i	−0.198712	+	0.292427i
$281$	−18.0478	−	13.1125i	−1.07664	−	0.782226i	−0.0995472	−	0.995033i	$-0.531739\pi$
$281$	−18.0478	−	13.1125i	−1.07664	−	0.782226i	−0.977094	+	0.212807i	$0.931739\pi$
$282$	1.92150	+	1.92150i	0.114424	+	0.114424i
$283$	−3.90149	−	24.6330i	−0.231919	−	1.46428i	−0.778907	−	0.627140i	$-0.784225\pi$
$283$	−3.90149	−	24.6330i	−0.231919	−	1.46428i	0.546987	−	0.837141i	$-0.315775\pi$
$284$	−0.981324	−	0.318852i	−0.0582309	−	0.0189204i
$285$	−4.88285	−	1.21212i	−0.289235	−	0.0718001i
$286$	24.6445	−	8.00749i	1.45726	−	0.473493i
$287$	14.5180	+	0.571871i	0.856973	+	0.0337565i
$288$	1.28819	+	2.52821i	0.0759073	+	0.148976i
$289$	6.94898	−	2.25786i	0.408764	−	0.132815i
$290$	12.6044	−	10.5984i	0.740157	−	0.622358i
$291$	−0.862936	+	2.65584i	−0.0505862	+	0.155688i
$292$	4.83860	−	0.766359i	0.283158	−	0.0448478i
$293$	12.4004	+	12.4004i	0.724441	+	0.724441i	0.969507	−	0.245065i	$-0.0788095\pi$
$293$	12.4004	+	12.4004i	0.724441	+	0.724441i	−0.245065	+	0.969507i	$0.578809\pi$
$294$	0.221971	−	2.81321i	0.0129456	−	0.164070i
$295$	−2.71034	−	11.6852i	−0.157802	−	0.680339i
$296$	−7.20393	+	5.23396i	−0.418720	+	0.304218i
$297$	−1.97626	+	12.4776i	−0.114674	+	0.724024i
$298$	−7.64766	−	3.89668i	−0.443017	−	0.225728i
$299$	24.5720			1.42104
$300$	2.01544	+	0.0310528i	0.116362	+	0.00179283i
$301$	−3.49229	+	6.23448i	−0.201293	+	0.359349i
$302$	9.00192	−	17.6673i	0.518002	−	1.01664i
$303$	0.333609	−	2.10632i	0.0191653	−	0.121005i
$304$	4.51523	−	3.28051i	0.258966	−	0.188150i
$305$	−14.8675	+	17.1385i	−0.851309	+	0.981346i
$306$	−8.22269	+	11.3176i	−0.470060	+	0.646982i
$307$	−12.3860	+	12.3860i	−0.706909	+	0.706909i	−0.965884	−	0.258975i	$-0.916615\pi$
$307$	−12.3860	+	12.3860i	−0.706909	+	0.706909i	0.258975	+	0.965884i	$0.416615\pi$
$308$	4.91727	−	13.3247i	0.280188	−	0.759247i
$309$	−5.19075	−	1.68658i	−0.295291	−	0.0959459i
$310$	1.64260	+	1.02407i	0.0932934	+	0.0581635i
$311$	−20.5345	+	6.67207i	−1.16441	+	0.378339i	−0.826552	−	0.562860i	$-0.809701\pi$
$311$	−20.5345	+	6.67207i	−1.16441	+	0.378339i	−0.337854	+	0.941198i	$0.609701\pi$
$312$	1.73385	−	0.883442i	0.0981600	−	0.0500150i
$313$	−0.442358	+	0.225393i	−0.0250035	+	0.0127399i	−0.466448	−	0.884549i	$-0.654466\pi$
$313$	−0.442358	+	0.225393i	−0.0250035	+	0.0127399i	0.441444	+	0.897289i	$0.354466\pi$
$314$	0.307084	+	0.945106i	0.0173297	+	0.0533354i
$315$	14.7099	−	8.08783i	0.828812	−	0.455698i
$316$	−0.389010	+	1.19725i	−0.0218835	+	0.0673506i
$317$	0.464296	+	2.93145i	0.0260774	+	0.164647i	0.997290	−	0.0735669i	$-0.0234382\pi$
$317$	0.464296	+	2.93145i	0.0260774	+	0.164647i	−0.971213	+	0.238213i	$0.923438\pi$
$318$	−2.73882	−	2.73882i	−0.153586	−	0.153586i
$319$	−23.2386	+	31.9852i	−1.30111	+	1.79083i
$320$	−1.46526	+	1.68908i	−0.0819108	+	0.0944226i
$321$	1.77383	+	2.44146i	0.0990054	+	0.136269i
$322$	8.33916	−	10.5760i	0.464723	−	0.589377i
$323$	24.5169	+	12.4920i	1.36416	+	0.695072i
$324$		−	7.56374i		−	0.420208i
$325$	−0.371816	+	24.1323i	−0.0206246	+	1.33862i
$326$	−0.329425			−0.0182452
$327$	−3.94626	−	2.01072i	−0.218229	−	0.111193i
$328$	5.42395	+	0.859069i	0.299487	+	0.0474342i
$329$	2.09441	+	17.7108i	0.115469	+	0.976427i
$330$	−4.71402	+	1.09340i	−0.259499	+	0.0601898i
$331$	−1.53731	−	1.11692i	−0.0844983	−	0.0613916i	0.544734	−	0.838609i	$-0.316631\pi$
$331$	−1.53731	−	1.11692i	−0.0844983	−	0.0613916i	−0.629232	+	0.777217i	$0.716631\pi$
$332$	5.05936	−	5.05936i	0.277668	−	0.277668i
$333$	24.9554	−	3.95255i	1.36755	−	0.216598i
$334$	4.30277	−	13.2426i	0.235437	−	0.724600i
$335$	−5.59730	−	6.65675i	−0.305813	−	0.363697i
$336$	0.208188	−	1.04608i	0.0113576	−	0.0570685i
$337$	4.47915	−	2.28224i	0.243995	−	0.124322i	−0.327717	−	0.944776i	$-0.606279\pi$
$337$	4.47915	−	2.28224i	0.243995	−	0.124322i	0.571712	+	0.820454i	$0.306279\pi$
$338$	4.67618	+	9.17752i	0.254351	+	0.499191i
$339$	1.79194	+	5.51502i	0.0973248	+	0.299535i
$340$	−10.6995	−	2.65605i	−0.580260	−	0.144044i
$341$	−4.41966	−	1.43604i	−0.239338	−	0.0777657i
$342$	−15.6414	+	2.47735i	−0.845789	+	0.133960i
$343$	12.5756	−	13.5961i	0.679021	−	0.734119i
$344$	−1.58756	+	2.18509i	−0.0855956	+	0.117812i
$345$	−4.57173	−	0.395260i	−0.246134	−	0.0212801i
$346$	−11.3490	−	15.6205i	−0.610125	−	0.839765i
$347$	−29.0122	−	4.59507i	−1.55745	−	0.246677i	−0.682501	−	0.730884i	$-0.739108\pi$
$347$	−29.0122	−	4.59507i	−1.55745	−	0.246677i	−0.874953	+	0.484208i	$0.839108\pi$
$348$	−1.34789	+	2.64539i	−0.0722547	+	0.141808i
$349$	29.5425			1.58137			0.790687	−	0.612221i	$-0.209724\pi$
$349$	29.5425			1.58137			0.790687	+	0.612221i	$0.209724\pi$
$350$	10.2605	+	8.34994i	0.548448	+	0.446323i
$351$	−11.3594			−0.606322
$352$	2.43714	−	4.78316i	0.129900	−	0.254943i
$353$	−4.10847	−	0.650718i	−0.218672	−	0.0346342i	0.0461371	−	0.998935i	$-0.485309\pi$
$353$	−4.10847	−	0.650718i	−0.218672	−	0.0346342i	−0.264809	+	0.964301i	$0.585309\pi$
$354$	1.27116	+	1.74960i	0.0675615	+	0.0929904i
$355$	−0.899333	+	2.12474i	−0.0477316	+	0.112769i
$356$	2.19943	−	3.02725i	0.116569	−	0.160444i
$357$	5.06122	−	1.42687i	0.267868	−	0.0755177i
$358$	−3.08068	+	0.487931i	−0.162819	+	0.0257880i
$359$	9.20237	+	2.99003i	0.485683	+	0.157808i	0.541615	−	0.840627i	$-0.317813\pi$
$359$	9.20237	+	2.99003i	0.485683	+	0.157808i	−0.0559323	+	0.998435i	$0.517813\pi$
$360$	5.88036	−	2.38282i	0.309922	−	0.125586i
$361$	3.75426	+	11.5544i	0.197592	+	0.608127i
$362$	4.65231	+	9.13068i	0.244520	+	0.479898i
$363$	6.40028	−	3.26111i	0.335928	−	0.171164i
$364$	12.5255	+	2.49277i	0.656513	+	0.130657i
$365$	−0.775318	−	10.9268i	−0.0405820	−	0.571937i
$366$	1.26402	−	3.89026i	0.0660715	−	0.203347i
$367$	21.5367	−	3.41108i	1.12421	−	0.178057i	0.433473	−	0.901167i	$-0.357288\pi$
$367$	21.5367	−	3.41108i	1.12421	−	0.178057i	0.690733	+	0.723110i	$0.257288\pi$
$368$	3.59954	−	3.59954i	0.187639	−	0.187639i
$369$	−12.6063	−	9.15899i	−0.656256	−	0.476798i
$370$	10.2725	+	17.0567i	0.534041	+	0.886736i
$371$	−2.98528	−	25.2442i	−0.154988	−	1.31061i
$372$	−0.344683	−	0.0545925i	−0.0178710	−	0.00283049i
$373$	16.9773	+	8.65034i	0.879049	+	0.447898i	0.834435	−	0.551107i	$-0.185794\pi$
$373$	16.9773	+	8.65034i	0.879049	+	0.447898i	0.0446140	+	0.999004i	$0.485794\pi$
$374$	26.4665			1.36855
$375$	0.457364	−	4.48393i	0.0236182	−	0.231549i
$376$			6.74069i			0.347625i
$377$	−31.6751	−	16.1393i	−1.63135	−	0.831214i
$378$	−3.85512	+	4.88919i	−0.198286	+	0.251473i
$379$	6.92886	+	9.53676i	0.355912	+	0.489871i	0.949004	−	0.315264i	$-0.102093\pi$
$379$	6.92886	+	9.53676i	0.355912	+	0.489871i	−0.593092	+	0.805135i	$0.702093\pi$
$380$	−6.43851	−	10.6907i	−0.330289	−	0.548420i
$381$	−1.93883	+	2.66857i	−0.0993293	+	0.136715i
$382$	−1.49281	−	1.49281i	−0.0763788	−	0.0763788i
$383$	0.116187	+	0.733573i	0.00593686	+	0.0374839i	0.990479	−	0.137664i	$-0.0439595\pi$
$383$	0.116187	+	0.733573i	0.00593686	+	0.0374839i	−0.984542	+	0.175148i	$0.943960\pi$
$384$	0.124576	−	0.383405i	0.00635724	−	0.0195656i
$385$	−28.7372	−	13.5209i	−1.46458	−	0.689089i
$386$	−4.87709	−	15.0101i	−0.248237	−	0.763996i
$387$	6.82851	−	3.47930i	0.347113	−	0.176863i
$388$	−6.17200	+	3.14479i	−0.313336	+	0.159653i
$389$	−2.33587	+	0.758970i	−0.118433	+	0.0384813i	−0.367634	−	0.929971i	$-0.619832\pi$
$389$	−2.33587	+	0.758970i	−0.118433	+	0.0384813i	0.249201	+	0.968452i	$0.419832\pi$
$390$	−1.63414	−	4.03276i	−0.0827481	−	0.204207i
$391$	23.8688	+	7.75543i	1.20709	+	0.392209i
$392$	5.32375	−	4.54507i	0.268890	−	0.229561i
$393$	−0.274772	+	0.274772i	−0.0138604	+	0.0138604i
$394$	−8.97080	+	12.3473i	−0.451943	+	0.622046i
$395$	2.59226	+	1.09722i	0.130431	+	0.0552070i
$396$	−12.3232	+	8.95336i	−0.619266	+	0.449923i
$397$	2.12959	−	13.4457i	0.106881	−	0.674820i	−0.874828	−	0.484433i	$-0.839026\pi$
$397$	2.12959	−	13.4457i	0.106881	−	0.674820i	0.981709	−	0.190387i	$-0.0609742\pi$
$398$	−6.51083	+	12.7782i	−0.326358	+	0.640514i
$399$	5.19352	+	2.90919i	0.260001	+	0.145642i
$400$	3.48065	+	3.58958i	0.174032	+	0.179479i
$401$	24.3399			1.21547			0.607737	−	0.794138i	$-0.292077\pi$
$401$	24.3399			1.21547			0.607737	+	0.794138i	$0.292077\pi$
$402$	1.39711	+	0.711861i	0.0696813	+	0.0355044i
$403$	0.653673	−	4.12713i	0.0325618	−	0.205587i
$404$	4.27968	−	3.10937i	0.212922	−	0.154697i
$405$	−16.8502	−	1.45682i	−0.837293	−	0.0723901i
$406$	−17.6962	+	8.15593i	−0.878249	+	0.404772i
$407$	−33.8011	−	33.8011i	−1.67546	−	1.67546i
$408$	1.96306	−	0.310918i	0.0971859	−	0.0153927i
$409$	10.2987	−	31.6961i	0.509237	−	1.56727i	−0.284291	−	0.958738i	$-0.591758\pi$
$409$	10.2987	−	31.6961i	0.509237	−	1.56727i	0.793528	−	0.608534i	$-0.208242\pi$
$410$	2.95848	−	11.9178i	0.146109	−	0.588577i
$411$	−2.34171	+	0.760869i	−0.115508	+	0.0375309i
$412$	−6.14637	−	12.0629i	−0.302810	−	0.594298i
$413$	−0.558641	+	14.1822i	−0.0274889	+	0.697859i
$414$	−13.7373	+	4.46351i	−0.675151	+	0.219370i
$415$	−10.2966	−	12.2455i	−0.505438	−	0.601107i
$416$	4.59077	+	1.49163i	0.225081	+	0.0731333i
$417$	1.02482	+	6.47045i	0.0501856	+	0.316859i
$418$	21.1856	+	21.1856i	1.03622	+	1.03622i
$419$	−11.2237	−	8.15448i	−0.548313	−	0.398372i	0.278850	−	0.960335i	$-0.410047\pi$
$419$	−11.2237	−	8.15448i	−0.548313	−	0.398372i	−0.827163	+	0.561962i	$0.810047\pi$
$420$	−2.29032	−	0.665273i	−0.111756	−	0.0324620i
$421$	21.5365	−	15.6472i	1.04962	−	0.762597i	0.0774833	−	0.996994i	$-0.475312\pi$
$421$	21.5365	−	15.6472i	1.04962	−	0.762597i	0.972141	+	0.234397i	$0.0753116\pi$
$422$	−15.1875	−	2.40546i	−0.739314	−	0.117096i
$423$	8.68329	−	17.0419i	0.422196	−	0.828606i
$424$		−	9.60788i		−	0.466600i
$425$	−7.97780	+	23.3242i	−0.386980	+	1.13139i
$426$		−	0.415966i		−	0.0201536i
$427$	22.3226	−	14.9123i	1.08027	−	0.721656i
$428$	−1.17104	+	7.39369i	−0.0566046	+	0.357387i
$429$	6.14022	+	8.45129i	0.296453	+	0.408032i
$430$	4.56208	+	3.95756i	0.220003	+	0.190851i
$431$	−17.6470	−	12.8213i	−0.850028	−	0.617582i	0.0751254	−	0.997174i	$-0.476064\pi$
$431$	−17.6470	−	12.8213i	−0.850028	−	0.617582i	−0.925154	+	0.379592i	$0.876064\pi$
$432$	−1.66403	+	1.66403i	−0.0800608	+	0.0800608i
$433$	−0.111444	−	0.703630i	−0.00535566	−	0.0338143i	0.984866	−	0.173319i	$-0.0554491\pi$
$433$	−0.111444	−	0.703630i	−0.00535566	−	0.0338143i	−0.990221	+	0.139504i	$0.955449\pi$
$434$	−1.55451	−	1.68200i	−0.0746188	−	0.0807383i
$435$	5.63368	+	3.51230i	0.270114	+	0.168402i
$436$	−3.39497	−	10.4486i	−0.162590	−	0.500399i
$437$	12.8982	+	25.3142i	0.617007	+	1.21094i
$438$	0.896599	+	1.75967i	0.0428411	+	0.0840805i
$439$	5.27761	+	16.2428i	0.251887	+	0.775228i	0.994427	+	0.105426i	$0.0336208\pi$
$439$	5.27761	+	16.2428i	0.251887	+	0.775228i	−0.742540	+	0.669801i	$0.766379\pi$
$440$	−10.1863	−	6.35063i	−0.485614	−	0.302754i
$441$	−19.3145	+	4.63291i	−0.919738	+	0.220615i
$442$	3.72284	+	23.5051i	0.177077	+	1.11802i
$443$	−19.5817	+	19.5817i	−0.930356	+	0.930356i	−0.997728	−	0.0673715i	$-0.978539\pi$
$443$	−19.5817	+	19.5817i	−0.930356	+	0.930356i	0.0673715	+	0.997728i	$0.478539\pi$
$444$	−2.90416	−	2.11000i	−0.137826	−	0.100136i
$445$	−6.32036	−	5.48285i	−0.299614	−	0.259912i
$446$	−14.0678	−	19.3627i	−0.666132	−	0.916852i
$447$	0.541292	−	3.41758i	0.0256022	−	0.161646i
$448$	2.20001	−	1.46968i	0.103941	−	0.0694359i
$449$			37.0518i			1.74858i	0.485402	+	0.874291i	$0.338673\pi$
$449$			37.0518i			1.74858i	−0.485402	+	0.874291i	$0.661327\pi$
$450$	−4.17576	−	13.5590i	−0.196847	−	0.639176i
$451$			29.4802i			1.38817i
$452$	−6.53034	+	12.8165i	−0.307162	+	0.602838i
$453$	7.89514	+	1.25047i	0.370946	+	0.0587521i
$454$	2.67154	−	1.94099i	0.125382	−	0.0910952i
$455$	7.96578	−	27.4236i	0.373441	−	1.28564i
$456$	1.82025	+	1.32249i	0.0852411	+	0.0619313i
$457$	4.75817	+	4.75817i	0.222578	+	0.222578i	0.809583	−	0.587005i	$-0.199693\pi$
$457$	4.75817	+	4.75817i	0.222578	+	0.222578i	−0.587005	+	0.809583i	$0.699693\pi$
$458$	−4.68574	−	29.5846i	−0.218950	−	1.38240i
$459$	−11.0343	−	3.58527i	−0.515038	−	0.167346i
$460$	−7.32560	−	8.71218i	−0.341558	−	0.406208i
$461$	−29.5143	+	9.58979i	−1.37462	+	0.446641i	−0.900897	−	0.434033i	$-0.857090\pi$
$461$	−29.5143	+	9.58979i	−1.37462	+	0.446641i	−0.473723	+	0.880674i	$0.657090\pi$
$462$	5.72135	+	0.225366i	0.266181	+	0.0104850i
$463$	11.4054	+	22.3844i	0.530055	+	1.04029i	0.988451	+	0.151543i	$0.0484242\pi$
$463$	11.4054	+	22.3844i	0.530055	+	1.04029i	−0.458396	+	0.888748i	$0.651576\pi$
$464$	−7.00428	+	2.27583i	−0.325166	+	0.105653i
$465$	−0.188007	+	0.757356i	−0.00871861	+	0.0351215i
$466$	2.78675	−	8.57673i	0.129094	−	0.397309i
$467$	−20.8304	+	3.29921i	−0.963916	+	0.152669i	−0.618504	−	0.785782i	$-0.712261\pi$
$467$	−20.8304	+	3.29921i	−0.963916	+	0.152669i	−0.345412	+	0.938451i	$0.612261\pi$
$468$	−9.68496	−	9.68496i	−0.447687	−	0.447687i
$469$	4.30737	+	9.34588i	0.198896	+	0.431552i
$470$	15.0166	+	1.29830i	0.692665	+	0.0598860i
$471$	−0.324103	+	0.235475i	−0.0149339	+	0.0108501i
$472$	−0.839195	+	5.29847i	−0.0386271	+	0.243882i
$473$	−12.9189	−	6.58253i	−0.594014	−	0.302665i
$474$	−0.507493			−0.0233099
$475$	−25.0563	+	12.2844i	−1.14966	+	0.563645i
$476$	11.3802	+	6.37472i	0.521611	+	0.292185i
$477$	−12.3768	+	24.2908i	−0.566693	+	1.11220i
$478$	2.54139	−	16.0457i	0.116240	−	0.733912i
$479$	−32.6108	+	23.6932i	−1.49003	+	1.08257i	−0.515878	+	0.856662i	$0.672534\pi$
$479$	−32.6108	+	23.6932i	−1.49003	+	1.08257i	−0.974149	+	0.225906i	$0.927466\pi$
$480$	−0.830139	−	0.351371i	−0.0378905	−	0.0160378i
$481$	25.2645	−	34.7736i	1.15196	−	1.58554i
$482$	12.7147	−	12.7147i	0.579137	−	0.579137i
$483$	5.09375	+	1.87976i	0.231774	+	0.0855321i
$484$	16.9462	+	5.50616i	0.770283	+	0.250280i
$485$	5.81706	+	14.3554i	0.264139	+	0.651846i
$486$	9.61434	−	3.12389i	0.436115	−	0.141702i
$487$	4.51086	−	2.29840i	0.204407	−	0.104150i	−0.348791	−	0.937201i	$-0.613408\pi$
$487$	4.51086	−	2.29840i	0.204407	−	0.104150i	0.553197	+	0.833050i	$0.313408\pi$
$488$	9.04070	−	4.60647i	0.409253	−	0.208525i
$489$	−0.0410384	−	0.126303i	−0.00185582	−	0.00571163i
$490$	−9.09993	−	12.7354i	−0.411093	−	0.575328i
$491$	4.54163	−	13.9777i	0.204961	−	0.630804i	−0.794754	−	0.606931i	$-0.792400\pi$
$491$	4.54163	−	13.9777i	0.204961	−	0.630804i	0.999715	−	0.0238729i	$-0.00759970\pi$
$492$	0.346322	+	2.18659i	0.0156134	+	0.0985790i
$493$	−25.6746	−	25.6746i	−1.15633	−	1.15633i
$494$	−15.8351	+	21.7951i	−0.712454	+	0.980609i
$495$	17.5724	+	29.1777i	0.789820	+	1.31144i
$496$	−0.508824	−	0.700336i	−0.0228469	−	0.0314460i
$497$	1.69031	−	2.14371i	0.0758209	−	0.0961585i
$498$	2.57006	+	1.30951i	0.115167	+	0.0586805i
$499$		−	9.97880i		−	0.446712i	−0.974737	−	0.223356i	$-0.928299\pi$
$499$		−	9.97880i		−	0.446712i	0.974737	−	0.223356i	$-0.0717013\pi$
$500$	8.66711	−	7.06266i	0.387605	−	0.315852i
$501$	5.61328			0.250783
$502$	5.53014	+	2.81775i	0.246822	+	0.125762i
$503$	32.1297	+	5.08885i	1.43259	+	0.226901i	0.824004	−	0.566584i	$-0.191736\pi$
$503$	32.1297	+	5.08885i	1.43259	+	0.226901i	0.608590	+	0.793485i	$0.291736\pi$
$504$	−7.45532	+	0.881639i	−0.332086	+	0.0392713i
$505$	−6.10262	−	10.1330i	−0.271563	−	0.450911i
$506$	22.1082	+	16.0625i	0.982829	+	0.714067i
$507$	−2.93617	+	2.93617i	−0.130400	+	0.130400i
$508$	−8.08146	+	1.27998i	−0.358557	+	0.0567898i
$509$	2.07657	−	6.39102i	0.0920422	−	0.283277i	−0.894429	−	0.447209i	$-0.852418\pi$
$509$	2.07657	−	6.39102i	0.0920422	−	0.283277i	0.986472	+	0.163932i	$0.0524179\pi$
$510$	−0.314553	−	4.43311i	−0.0139286	−	0.196301i
$511$	−2.52990	+	12.7120i	−0.111916	+	0.562346i
$512$	0.891007	−	0.453990i	0.0393773	−	0.0200637i
$513$	−5.96274	−	11.7025i	−0.263262	−	0.516680i
$514$	5.15470	+	15.8645i	0.227364	+	0.699754i
$515$	−28.0571	+	11.3692i	−1.23634	+	0.500988i
$516$	−1.03555	−	0.336470i	−0.0455874	−	0.0148122i
$517$	−35.7403	+	5.66071i	−1.57186	+	0.248958i
$518$	−6.39266	−	22.6753i	−0.280877	−	0.996297i
$519$	4.57518	−	6.29720i	0.200828	−	0.276416i
$520$	4.20721	−	9.93983i	0.184498	−	0.435891i
$521$	−5.53515	−	7.61849i	−0.242500	−	0.333772i	0.670367	−	0.742029i	$-0.266137\pi$
$521$	−5.53515	−	7.61849i	−0.242500	−	0.333772i	−0.912867	+	0.408257i	$0.866137\pi$
$522$	20.6400	+	3.26906i	0.903390	+	0.143083i
$523$	2.11204	−	4.14511i	0.0923530	−	0.181253i	−0.840209	−	0.542263i	$-0.817568\pi$
$523$	2.11204	−	4.14511i	0.0923530	−	0.181253i	0.932562	+	0.361010i	$0.117568\pi$
$524$	−0.963909			−0.0421086
$525$	−1.92320	+	4.97414i	−0.0839352	+	0.217089i
$526$	−18.4886			−0.806142
$527$	1.93757	−	3.80270i	0.0844019	−	0.165648i
$528$	2.13750	+	0.338546i	0.0930227	+	0.0147333i
$529$	1.71240	+	2.35692i	0.0744522	+	0.102475i
$530$	−21.4040	−	1.85054i	−0.929732	−	0.0803822i
$531$	8.94710	−	12.3146i	0.388271	−	0.534409i
$532$	4.00674	+	14.2123i	0.173714	+	0.616181i
$533$	−26.1815	+	4.14675i	−1.13405	+	0.179616i
$534$	1.43466	+	0.466149i	0.0620837	+	0.0201722i
$535$	16.2458	+	4.03287i	0.702367	+	0.174356i
$536$	1.20193	+	3.69916i	0.0519154	+	0.159779i
$537$	−0.570853	−	1.12036i	−0.0246341	−	0.0483472i
$538$	−11.6350	+	5.92835i	−0.501622	+	0.255589i
$539$	28.5696	+	24.4106i	1.23058	+	1.05144i
$540$	3.38656	+	4.02757i	0.145734	+	0.173319i
$541$	1.17846	−	3.62691i	0.0506658	−	0.155933i	−0.922522	−	0.385943i	$-0.873876\pi$
$541$	1.17846	−	3.62691i	0.0506658	−	0.155933i	0.973188	+	0.230010i	$0.0738760\pi$
$542$	−26.1671	+	4.14446i	−1.12397	+	0.178020i
$543$	−2.92118	+	2.92118i	−0.125360	+	0.125360i
$544$	3.98859	+	2.89788i	0.171009	+	0.124246i
$545$	−23.9309	+	5.55070i	−1.02509	+	0.237766i
$546$	0.604629	+	5.11287i	0.0258757	+	0.218810i
$547$	7.31494	+	1.15857i	0.312764	+	0.0495370i	0.310843	−	0.950461i	$-0.399389\pi$
$547$	7.31494	+	1.15857i	0.312764	+	0.0495370i	0.00192102	+	0.999998i	$0.499389\pi$
$548$	−5.44198	−	2.77283i	−0.232470	−	0.118449i
$549$	−28.7908			−1.22876
$550$	−16.1096	+	21.4695i	−0.686916	+	0.915461i
$551$		−	41.1036i		−	1.75107i
$552$	1.82850	+	0.931665i	0.0778259	+	0.0396543i
$553$	−2.61540	−	2.06224i	−0.111218	−	0.0876954i
$554$	3.18223	+	4.37996i	0.135200	+	0.186087i
$555$	−5.25993	+	6.06338i	−0.223271	+	0.257376i
$556$	−9.55172	+	13.1468i	−0.405083	+	0.557549i
$557$	3.18995	+	3.18995i	0.135163	+	0.135163i	0.771451	−	0.636289i	$-0.219531\pi$
$557$	3.18995	+	3.18995i	0.135163	+	0.135163i	−0.636289	+	0.771451i	$0.719531\pi$
$558$	0.384250	+	2.42606i	0.0162666	+	0.102703i
$559$	4.02878	−	12.3993i	0.170399	−	0.524435i
$560$	−2.85036	−	5.18416i	−0.120450	−	0.219071i
$561$	3.29709	+	10.1474i	0.139203	+	0.428423i
$562$	19.8768	−	10.1278i	0.838454	−	0.427214i
$563$	−5.90123	+	3.00683i	−0.248707	+	0.126723i	−0.573901	−	0.818925i	$-0.694571\pi$
$563$	−5.90123	+	3.00683i	−0.248707	+	0.126723i	0.325194	+	0.945647i	$0.394571\pi$
$564$	−2.58442	+	0.839727i	−0.108824	+	0.0353589i
$565$	27.2943	+	17.0166i	1.14828	+	0.715892i
$566$	23.7194	+	7.70691i	0.997002	+	0.323945i
$567$	18.7742	+	6.92830i	0.788442	+	0.290961i
$568$	0.729611	−	0.729611i	0.0306138	−	0.0306138i
$569$	4.61715	−	6.35496i	0.193561	−	0.266414i	−0.701195	−	0.712970i	$-0.747350\pi$
$569$	4.61715	−	6.35496i	0.193561	−	0.266414i	0.894756	+	0.446556i	$0.147350\pi$
$570$	3.29678	−	3.80036i	0.138087	−	0.159180i
$571$	−29.9260	+	21.7425i	−1.25236	+	0.909895i	−0.998357	−	0.0573070i	$-0.981749\pi$
$571$	−29.9260	+	21.7425i	−1.25236	+	0.909895i	−0.254007	+	0.967202i	$0.581749\pi$
$572$	−4.05365	+	25.5937i	−0.169492	+	1.07013i
$573$	0.386383	−	0.758319i	0.0161414	−	0.0316792i
$574$	−7.10059	+	12.6760i	−0.296373	+	0.529088i
$575$	−20.8196	+	14.6416i	−0.868237	+	0.610599i
$576$	−2.83748			−0.118228
$577$	16.0919	+	8.19924i	0.669915	+	0.341339i	0.755647	−	0.654980i	$-0.227323\pi$
$577$	16.0919	+	8.19924i	0.669915	+	0.341339i	−0.0857316	+	0.996318i	$0.527323\pi$
$578$	−1.14300	+	7.21663i	−0.0475426	+	0.300172i
$579$	5.14740	−	3.73980i	0.213918	−	0.155421i
$580$	3.72093	+	16.0422i	0.154503	+	0.666115i
$581$	7.92367	+	17.1923i	0.328729	+	0.713256i
$582$	−1.97461	−	1.97461i	−0.0818502	−	0.0818502i
$583$	50.9427	−	8.06853i	2.10983	−	0.334164i
$584$	−1.51385	+	4.65914i	−0.0626435	+	0.192797i
$585$	−23.4411	+	19.7103i	−0.969171	+	0.814923i
$586$	−16.6785	+	5.41919i	−0.688984	+	0.223865i
$587$	−7.27499	−	14.2780i	−0.300271	−	0.589315i	0.690739	−	0.723104i	$-0.257285\pi$
$587$	−7.27499	−	14.2780i	−0.300271	−	0.589315i	−0.991010	+	0.133789i	$0.957285\pi$
$588$	2.40581	+	1.47495i	0.0992141	+	0.0608258i
$589$	4.59491	−	1.49298i	0.189330	−	0.0615171i
$590$	11.6421	+	2.89004i	0.479296	+	0.118981i
$591$	−5.85154	−	1.90128i	−0.240700	−	0.0782083i
$592$	−1.39298	−	8.79492i	−0.0572511	−	0.361469i
$593$	−16.0691	−	16.0691i	−0.659880	−	0.659880i	0.295472	−	0.955351i	$-0.404523\pi$
$593$	−16.0691	−	16.0691i	−0.659880	−	0.659880i	−0.955351	+	0.295472i	$0.904523\pi$
$594$	−10.2204	−	7.42557i	−0.419349	−	0.304675i
$595$	16.3932	−	24.1245i	0.672057	−	0.989009i
$596$	6.94393	−	5.04506i	0.284434	−	0.206654i
$597$	−5.71033	−	0.904427i	−0.233708	−	0.0370157i
$598$	−11.1555	+	21.8938i	−0.456181	+	0.895306i
$599$		−	34.6391i		−	1.41532i	−0.706556	−	0.707658i	$-0.749752\pi$
$599$		−	34.6391i		−	1.41532i	0.706556	−	0.707658i	$-0.250248\pi$
$600$	−0.942659	+	1.78167i	−0.0384839	+	0.0727365i
$601$		−	0.329209i		−	0.0134287i	−0.999977	−	0.00671435i	$-0.997863\pi$
$601$		−	0.329209i		−	0.0134287i	0.999977	−	0.00671435i	$-0.00213726\pi$
$602$	−3.96949	−	5.94205i	−0.161784	−	0.242180i
$603$	1.72648	−	10.9006i	0.0703078	−	0.443906i
$604$	11.6549	+	16.0415i	0.474230	+	0.652721i
$605$	15.5303	−	36.6915i	0.631398	−	1.49172i
$606$	1.72529	+	1.25350i	0.0700852	+	0.0509198i
$607$	−1.81497	+	1.81497i	−0.0736675	+	0.0736675i	−0.742981	−	0.669313i	$-0.766589\pi$
$607$	−1.81497	+	1.81497i	−0.0736675	+	0.0736675i	0.669313	+	0.742981i	$0.266589\pi$
$608$	0.873081	+	5.51242i	0.0354081	+	0.223558i
$609$	−5.33155	−	5.76879i	−0.216045	−	0.233763i
$610$	−8.52080	−	21.0277i	−0.344997	−	0.851387i
$611$	−10.0546	−	30.9450i	−0.406767	−	1.25190i
$612$	−6.35100	−	12.4645i	−0.256724	−	0.503849i
$613$	−1.08836	−	2.13602i	−0.0439584	−	0.0862732i	0.867983	−	0.496595i	$-0.165416\pi$
$613$	−1.08836	−	2.13602i	−0.0439584	−	0.0862732i	−0.911941	+	0.410322i	$0.865416\pi$
$614$	−5.41290	−	16.6592i	−0.218447	−	0.672310i
$615$	4.93789	−	0.350370i	0.199115	−	0.0141283i
$616$	9.64003	+	10.4306i	0.388408	+	0.420262i
$617$	−0.577531	−	3.64638i	−0.0232505	−	0.146798i	0.973332	−	0.229401i	$-0.0736767\pi$
$617$	−0.577531	−	3.64638i	−0.0232505	−	0.146798i	−0.996583	+	0.0826029i	$0.973677\pi$
$618$	3.85930	−	3.85930i	0.155244	−	0.155244i
$619$	−5.59908	−	4.06797i	−0.225046	−	0.163505i	0.469549	−	0.882906i	$-0.344416\pi$
$619$	−5.59908	−	4.06797i	−0.225046	−	0.163505i	−0.694595	+	0.719401i	$0.744416\pi$
$620$	−1.65818	+	0.998647i	−0.0665941	+	0.0401066i
$621$	−7.04137	−	9.69161i	−0.282560	−	0.388911i
$622$	3.37762	−	21.3255i	0.135430	−	0.855073i
$623$	5.49938	+	8.23218i	0.220328	+	0.329815i
$624$			1.94595i			0.0779002i
$625$	−14.0646	−	20.6685i	−0.562582	−	0.826741i
$626$		−	0.496470i		−	0.0198429i
$627$	−5.48346	+	10.7619i	−0.218988	+	0.429789i
$628$	−0.981509	−	0.155456i	−0.0391665	−	0.00620336i
$629$	35.5166	−	25.8043i	1.41614	−	1.02889i
$630$	0.528137	+	16.7785i	0.0210415	+	0.668470i
$631$	−0.150808	−	0.109568i	−0.00600356	−	0.00436184i	0.584779	−	0.811192i	$-0.301181\pi$
$631$	−0.150808	−	0.109568i	−0.00600356	−	0.00436184i	−0.590783	+	0.806831i	$0.701181\pi$
$632$	−0.890151	−	0.890151i	−0.0354083	−	0.0354083i
$633$	−0.969726	−	6.12261i	−0.0385431	−	0.243352i
$634$	−2.82273	−	0.917159i	−0.112105	−	0.0364250i
$635$	1.29494	+	18.2501i	0.0513882	+	0.724231i
$636$	3.68371	−	1.19691i	0.146069	−	0.0474606i
$637$	−17.6606	+	28.8065i	−0.699737	+	1.14135i
$638$	−17.9489	−	35.2267i	−0.710605	−	1.39464i
$639$	−2.78449	+	0.904736i	−0.110153	+	0.0357908i
$640$	−0.839767	−	2.07239i	−0.0331947	−	0.0819183i
$641$	4.94731	−	15.2263i	0.195407	−	0.601401i	−0.804565	−	0.593865i	$-0.797601\pi$
$641$	4.94731	−	15.2263i	0.195407	−	0.601401i	0.999972	−	0.00753569i	$-0.00239871\pi$
$642$	−2.98066	+	0.472090i	−0.117637	+	0.0186319i
$643$	12.7593	+	12.7593i	0.503177	+	0.503177i	0.912424	−	0.409247i	$-0.134208\pi$
$643$	12.7593	+	12.7593i	0.503177	+	0.503177i	−0.409247	+	0.912424i	$0.634208\pi$
$644$	5.63738	+	12.2316i	0.222144	+	0.481994i
$645$	−0.949025	+	2.24214i	−0.0373678	+	0.0882842i
$646$	−22.2609	+	16.1735i	−0.875842	+	0.636336i
$647$	4.15741	−	26.2488i	0.163445	−	1.03195i	−0.760476	−	0.649366i	$-0.775035\pi$
$647$	4.15741	−	26.2488i	0.163445	−	1.03195i	0.923921	−	0.382583i	$-0.124965\pi$
$648$	6.73935	+	3.43387i	0.264747	+	0.134895i
$649$	−28.7982			−1.13043
$650$	−21.3332	−	11.2871i	−0.836757	−	0.442717i
$651$	0.451231	−	0.805542i	0.0176851	−	0.0315717i
$652$	0.149556	−	0.293520i	0.00585706	−	0.0114951i
$653$	5.12978	−	32.3882i	0.200744	−	1.26745i	−0.657205	−	0.753712i	$-0.728261\pi$
$653$	5.12978	−	32.3882i	0.200744	−	1.26745i	0.857949	−	0.513735i	$-0.171739\pi$
$654$	3.58313	−	2.60330i	0.140111	−	0.101797i
$655$	−0.185655	+	2.14736i	−0.00725413	+	0.0839041i
$656$	−3.22786	+	4.44276i	−0.126027	+	0.173461i
$657$	9.82919	−	9.82919i	0.383473	−	0.383473i
$658$	−16.7313	−	6.17439i	−0.652253	−	0.240703i
$659$	−15.7370	−	5.11325i	−0.613025	−	0.199184i	−0.0139841	−	0.999902i	$-0.504451\pi$
$659$	−15.7370	−	5.11325i	−0.613025	−	0.199184i	−0.599041	+	0.800718i	$0.704451\pi$
$660$	1.16589	−	4.69662i	0.0453824	−	0.182816i
$661$	−13.3613	+	4.34134i	−0.519693	+	0.168858i	−0.557106	−	0.830441i	$-0.688088\pi$
$661$	−13.3613	+	4.34134i	−0.519693	+	0.168858i	0.0374131	+	0.999300i	$0.488088\pi$
$662$	1.69311	−	0.862683i	0.0658046	−	0.0335291i
$663$	−8.54819	+	4.35552i	−0.331984	+	0.169154i
$664$	2.21102	+	6.80482i	0.0858042	+	0.264078i
$665$	32.4333	−	6.18868i	1.25771	−	0.239987i
$666$	−7.80778	+	24.0299i	−0.302545	+	0.931139i
$667$	−5.86477	−	37.0287i	−0.227085	−	1.43376i
$668$	9.84579	+	9.84579i	0.380945	+	0.380945i
$669$	5.67125	−	7.80581i	0.219263	−	0.301790i
$670$	8.47233	−	1.96513i	0.327315	−	0.0759195i
$671$	32.0165	+	44.0670i	1.23598	+	1.70119i
$672$	0.837551	+	0.660408i	0.0323092	+	0.0254758i
$673$	19.9933	+	10.1871i	0.770686	+	0.392684i	0.794680	−	0.607028i	$-0.207638\pi$
$673$	19.9933	+	10.1871i	0.770686	+	0.392684i	−0.0239947	+	0.999712i	$0.507638\pi$
$674$			5.02707i			0.193635i
$675$	9.62471	−	6.76870i	0.370455	−	0.260527i
$676$	−10.3002			−0.396161
$677$	11.9136	+	6.07029i	0.457877	+	0.233300i	0.667687	−	0.744442i	$-0.267284\pi$
$677$	11.9136	+	6.07029i	0.457877	+	0.233300i	−0.209810	+	0.977742i	$0.567284\pi$
$678$	−5.72744	−	0.907138i	−0.219961	−	0.0348384i
$679$	−2.15230	−	18.2003i	−0.0825976	−	0.698463i
$680$	7.22401	−	8.32747i	0.277028	−	0.319344i
$681$	1.07700	+	0.782483i	0.0412706	+	0.0299848i
$682$	3.28600	−	3.28600i	0.125828	−	0.125828i
$683$	−43.2489	+	6.84996i	−1.65487	+	0.262106i	−0.912858	−	0.408276i	$-0.866130\pi$
$683$	−43.2489	+	6.84996i	−1.65487	+	0.262106i	−0.742016	+	0.670382i	$0.766130\pi$
$684$	4.89370	−	15.0613i	0.187115	−	0.575882i
$685$	−7.22534	+	11.5893i	−0.276066	+	0.442806i
$686$	6.40496	+	17.3775i	0.244542	+	0.663475i
$687$	10.7591	−	5.48206i	0.410487	−	0.209154i
$688$	−1.22619	−	2.40654i	−0.0467482	−	0.0917484i
$689$	14.3314	+	44.1076i	0.545984	+	1.68037i
$690$	2.42770	−	3.89400i	0.0924211	−	0.148242i
$691$	11.9645	+	3.88751i	0.455152	+	0.147888i	0.527616	−	0.849483i	$-0.323086\pi$
$691$	11.9645	+	3.88751i	0.455152	+	0.147888i	−0.0724634	+	0.997371i	$0.523086\pi$
$692$	19.0703	−	3.02044i	0.724945	−	0.114820i
$693$	−10.9355	−	38.7890i	−0.415403	−	1.47347i
$694$	17.2655	−	23.7639i	0.655389	−	0.902065i
$695$	27.4482	+	23.8111i	1.04117	+	0.903205i
$696$	−1.74513	−	2.40196i	−0.0661490	−	0.0910462i
$697$	−26.7410	−	4.23536i	−1.01289	−	0.160426i
$698$	−13.4120	+	26.3226i	−0.507652	+	0.996324i
$699$	3.63552			0.137508
$700$	−12.0980	+	5.35140i	−0.457263	+	0.202264i
$701$	10.3366			0.390406			0.195203	−	0.980763i	$-0.437463\pi$
$701$	10.3366			0.390406			0.195203	+	0.980763i	$0.437463\pi$
$702$	5.15707	−	10.1213i	0.194641	−	0.382005i
$703$	49.0856	+	7.77440i	1.85130	+	0.293217i
$704$	3.15539	+	4.34302i	0.118923	+	0.163684i
$705$	1.37293	+	5.91919i	0.0517077	+	0.222929i
$706$	2.44500	−	3.36525i	0.0920188	−	0.126653i
$707$	3.79772	+	13.4709i	0.142828	+	0.506623i
$708$	−2.13600	+	0.338310i	−0.0802759	+	0.0127145i
$709$	−30.6777	−	9.96777i	−1.15212	−	0.374348i	−0.330181	−	0.943918i	$-0.607110\pi$
$709$	−30.6777	−	9.96777i	−1.15212	−	0.374348i	−0.821943	+	0.569570i	$0.807110\pi$
$710$	−1.48487	−	1.76592i	−0.0557261	−	0.0662739i
$711$	1.10381	+	3.39717i	0.0413961	+	0.127404i
$712$	1.69878	+	3.33405i	0.0636645	+	0.124949i
$713$	3.92637	−	2.00058i	0.147044	−	0.0749225i
$714$	−1.02640	+	5.15736i	−0.0384121	+	0.193010i
$715$	56.2359	+	13.9601i	2.10310	+	0.522077i
$716$	0.963848	−	2.96642i	0.0360207	−	0.110860i
$717$	6.46859	−	1.02452i	0.241574	−	0.0382616i
$718$	−6.84193	+	6.84193i	−0.255338	+	0.255338i
$719$	−28.5967	−	20.7767i	−1.06648	−	0.774840i	−0.0912006	−	0.995833i	$-0.529070\pi$
$719$	−28.5967	−	20.7767i	−1.06648	−	0.774840i	−0.975276	+	0.220992i	$0.929070\pi$
$720$	−0.546516	+	6.32122i	−0.0203675	+	0.235578i
$721$	35.5718	−	4.20658i	1.32476	−	0.156661i
$722$	−11.9995	−	1.90053i	−0.446573	−	0.0707303i
$723$	6.45881	+	3.29093i	0.240206	+	0.122391i
$724$	−10.2476			−0.380849
$725$	36.4548	−	5.19950i	1.35390	−	0.193105i
$726$			7.18320i			0.266594i
$727$	2.75226	+	1.40235i	0.102076	+	0.0520102i	0.504283	−	0.863538i	$-0.331757\pi$
$727$	2.75226	+	1.40235i	0.102076	+	0.0520102i	−0.402207	+	0.915549i	$0.631757\pi$
$728$	−7.90752	+	10.0286i	−0.293072	+	0.371684i
$729$	−10.9421	−	15.0606i	−0.405265	−	0.557799i
$730$	10.0879	+	4.26986i	0.373369	+	0.158035i
$731$	7.82695	−	10.7729i	0.289490	−	0.398449i
$732$	2.89240	+	2.89240i	0.106906	+	0.106906i
$733$	0.971857	+	6.13606i	0.0358963	+	0.226641i	0.999114	−	0.0420811i	$-0.0133988\pi$
$733$	0.971857	+	6.13606i	0.0358963	+	0.226641i	−0.963218	+	0.268722i	$0.913399\pi$
$734$	−6.73816	+	20.7379i	−0.248710	+	0.765451i
$735$	3.74920	−	5.07549i	0.138291	−	0.187212i
$736$	1.57305	+	4.84136i	0.0579836	+	0.178455i
$737$	−18.6042	+	9.47933i	−0.685296	+	0.349176i
$738$	13.8838	−	7.07417i	0.511071	−	0.260404i
$739$	−7.75708	+	2.52043i	−0.285349	+	0.0927155i	−0.448194	−	0.893936i	$-0.647933\pi$
$739$	−7.75708	+	2.52043i	−0.285349	+	0.0927155i	0.162846	+	0.986652i	$0.447933\pi$
$740$	−19.8612	+	1.40926i	−0.730114	+	0.0518056i
$741$	−10.3290	−	3.35611i	−0.379447	−	0.123290i
$742$	23.8480	+	8.80071i	0.875488	+	0.323084i
$743$	−25.7873	+	25.7873i	−0.946045	+	0.946045i	−0.998617	−	0.0525717i	$-0.983258\pi$
$743$	−25.7873	+	25.7873i	−0.946045	+	0.946045i	0.0525717	+	0.998617i	$0.483258\pi$
$744$	0.205125	−	0.282331i	0.00752025	−	0.0103507i
$745$	−9.90173	−	16.4411i	−0.362771	−	0.602355i
$746$	−15.4150	+	11.1997i	−0.564384	+	0.410049i
$747$	3.17597	−	20.0523i	0.116202	−	0.733674i
$748$	−12.0155	+	23.5818i	−0.439331	+	0.862236i
$749$	−17.2794	−	9.67921i	−0.631376	−	0.353671i
$750$	3.78757	+	2.44318i	0.138303	+	0.0892122i
$751$	18.9699			0.692220			0.346110	−	0.938194i	$-0.387502\pi$
$751$	18.9699			0.692220			0.346110	+	0.938194i	$0.387502\pi$
$752$	−6.00600	−	3.06021i	−0.219016	−	0.111594i
$753$	−0.391416	+	2.47131i	−0.0142640	+	0.0900594i
$754$	28.7604	−	20.8956i	1.04739	−	0.760974i
$755$	37.9815	−	22.8745i	1.38229	−	0.832489i
$756$	−2.60611	−	5.65458i	−0.0947833	−	0.205655i
$757$	24.9353	+	24.9353i	0.906289	+	0.906289i	0.995970	−	0.0896815i	$-0.0285849\pi$
$757$	24.9353	+	24.9353i	0.906289	+	0.906289i	−0.0896815	+	0.995970i	$0.528585\pi$
$758$	−11.6430	+	1.84406i	−0.422891	+	0.0669794i
$759$	−3.40431	+	10.4774i	−0.123569	+	0.380306i
$760$	12.4485	−	0.883288i	0.451554	−	0.0320402i
$761$	26.1310	−	8.49048i	0.947249	−	0.307780i	0.205652	−	0.978625i	$-0.434069\pi$
$761$	26.1310	−	8.49048i	0.947249	−	0.307780i	0.741597	+	0.670846i	$0.234069\pi$
$762$	−1.49750	−	2.93902i	−0.0542488	−	0.106469i
$763$	29.0446	+	1.14408i	1.05149	+	0.0414184i
$764$	2.00782	−	0.652382i	0.0726405	−	0.0236023i
$765$	−28.9912	+	11.7477i	−1.04818	+	0.424740i
$766$	−0.706366	−	0.229512i	−0.0255221	−	0.00829262i
$767$	−4.05082	−	25.5758i	−0.146266	−	0.923490i
$768$	0.285060	+	0.285060i	0.0102862	+	0.0102862i
$769$	−22.1153	−	16.0677i	−0.797497	−	0.579416i	0.112682	−	0.993631i	$-0.464056\pi$
$769$	−22.1153	−	16.0677i	−0.797497	−	0.579416i	−0.910179	+	0.414215i	$0.864056\pi$
$770$	25.0936	−	19.4667i	0.904312	−	0.701530i
$771$	−5.44039	+	3.95267i	−0.195931	+	0.142352i
$772$	15.5883	+	2.46894i	0.561035	+	0.0888592i
$773$	−6.09623	+	11.9645i	−0.219266	+	0.430334i	−0.974269	−	0.225387i	$-0.927635\pi$
$773$	−6.09623	+	11.9645i	−0.219266	+	0.430334i	0.755003	+	0.655721i	$0.227635\pi$
$774$			7.66381i			0.275470i
$775$	1.90537	+	3.88637i	0.0684428	+	0.139603i
$776$		−	6.92699i		−	0.248665i
$777$	7.89747	−	5.27578i	0.283320	−	0.189267i
$778$	0.384215	−	2.42584i	0.0137748	−	0.0869705i
$779$	−18.0151	−	24.7957i	−0.645458	−	0.888397i
$780$	4.33510	+	0.374801i	0.155221	+	0.0134200i
$781$	4.48124	+	3.25581i	0.160351	+	0.116502i
$782$	−17.7463	+	17.7463i	−0.634607	+	0.634607i
$783$	2.71123	+	17.1181i	0.0968916	+	0.611749i
$784$	1.63275	+	6.80692i	0.0583127	+	0.243104i
$785$	−0.535362	+	2.15662i	−0.0191079	+	0.0769731i
$786$	−0.120080	−	0.369568i	−0.00428311	−	0.0131820i
$787$	16.5473	+	32.4758i	0.589846	+	1.15764i	0.972316	+	0.233670i	$0.0750735\pi$
$787$	16.5473	+	32.4758i	0.589846	+	1.15764i	−0.382470	+	0.923968i	$0.624927\pi$
$788$	−6.92882	−	13.5986i	−0.246829	−	0.484429i
$789$	−2.30324	−	7.08863i	−0.0819974	−	0.252362i
$790$	−2.15449	+	1.81159i	−0.0766532	+	0.0644535i
$791$	−25.8305	−	27.9489i	−0.918428	−	0.993750i
$792$	−2.38287	−	15.0448i	−0.0846715	−	0.534595i
$793$	−34.6327	+	34.6327i	−1.22984	+	1.22984i
$794$	11.0134	+	8.00170i	0.390851	+	0.283970i
$795$	−1.95692	−	8.43694i	−0.0694048	−	0.299228i
$796$	−8.42963	−	11.6024i	−0.298780	−	0.411236i
$797$	−8.05677	+	50.8685i	−0.285386	+	1.80185i	0.262102	+	0.965040i	$0.415584\pi$
$797$	−8.05677	+	50.8685i	−0.285386	+	1.80185i	−0.547488	+	0.836814i	$0.684416\pi$
$798$	−4.94992	+	3.30671i	−0.175225	+	0.117056i
$799$		−	33.2328i		−	1.17569i
$800$	−4.77852	+	1.47164i	−0.168946	+	0.0520305i
$801$		−	10.6175i		−	0.375152i
$802$	−11.0501	+	21.6870i	−0.390191	+	0.765794i
$803$	−25.9749	−	4.11402i	−0.916635	−	0.145181i
$804$	−1.26854	+	0.921652i	−0.0447381	+	0.0325042i
$805$	28.3349	−	10.2028i	0.998675	−	0.359602i
$806$	3.38054	+	2.45611i	0.119074	+	0.0865126i
$807$	−3.72241	−	3.72241i	−0.131035	−	0.131035i
$808$	0.827534	+	5.22484i	0.0291125	+	0.183809i
$809$	25.0785	+	8.14851i	0.881714	+	0.286486i	0.714669	−	0.699463i	$-0.246577\pi$
$809$	25.0785	+	8.14851i	0.881714	+	0.286486i	0.167045	+	0.985949i	$0.446577\pi$
$810$	8.94786	−	14.3522i	0.314396	−	0.504286i
$811$	53.1040	−	17.2545i	1.86473	−	0.605888i	0.871405	−	0.490564i	$-0.163209\pi$
$811$	53.1040	−	17.2545i	1.86473	−	0.605888i	0.993328	−	0.115324i	$-0.0367907\pi$
$812$	0.766937	−	19.4702i	0.0269142	−	0.683269i
$813$	−4.84880	−	9.51631i	−0.170055	−	0.333751i
$814$	45.4624	−	14.7716i	1.59346	−	0.517746i
$815$	−0.625086	−	0.389708i	−0.0218958	−	0.0136509i
$816$	−0.614180	+	1.89025i	−0.0215006	+	0.0661721i
$817$	14.8886	−	2.35812i	0.520886	−	0.0825003i
$818$	23.5659	+	23.5659i	0.823963	+	0.823963i
$819$	32.9106	−	15.1680i	1.14999	−	0.530013i
$820$	9.27570	+	8.04659i	0.323921	+	0.280999i
$821$	4.45501	−	3.23676i	0.155481	−	0.112964i	−0.507325	−	0.861755i	$-0.669366\pi$
$821$	4.45501	−	3.23676i	0.155481	−	0.112964i	0.662806	+	0.748791i	$0.269366\pi$
$822$	0.385177	−	2.43191i	0.0134346	−	0.0848226i
$823$	−15.5449	−	7.92051i	−0.541860	−	0.276092i	0.161564	−	0.986862i	$-0.448346\pi$
$823$	−15.5449	−	7.92051i	−0.541860	−	0.276092i	−0.703424	+	0.710771i	$0.748346\pi$
$824$	13.5385			0.471637
$825$	−10.2384	−	3.50193i	−0.356454	−	0.121921i
$826$	−12.3828	−	6.93633i	−0.430852	−	0.241346i
$827$	−17.3558	+	34.0626i	−0.603519	+	1.18447i	0.363934	+	0.931425i	$0.381433\pi$
$827$	−17.3558	+	34.0626i	−0.603519	+	1.18447i	−0.967454	+	0.253049i	$0.918567\pi$
$828$	2.25958	−	14.2664i	0.0785257	−	0.495792i
$829$	−15.8571	+	11.5209i	−0.550741	+	0.400137i	−0.828059	−	0.560642i	$-0.810555\pi$
$829$	−15.8571	+	11.5209i	−0.550741	+	0.400137i	0.277318	+	0.960778i	$0.410555\pi$
$830$	15.5853	−	3.61497i	0.540975	−	0.125477i
$831$	−1.28287	+	1.76572i	−0.0445023	+	0.0612522i
$832$	−3.41322	+	3.41322i	−0.118332	+	0.118332i
$833$	−26.2470	+	22.4080i	−0.909405	+	0.776390i
$834$	−6.23047	−	2.02440i	−0.215743	−	0.0700993i
$835$	23.8304	−	20.0377i	0.824684	−	0.693432i
$836$	−28.4946	+	9.25846i	−0.985507	+	0.320211i
$837$	−1.81513	+	0.924853i	−0.0627399	+	0.0319676i
$838$	12.3611	−	6.29832i	0.427009	−	0.217572i
$839$	−9.95145	−	30.6274i	−0.343562	−	1.05738i	−0.962349	−	0.271817i	$-0.912376\pi$
$839$	−9.95145	−	30.6274i	−0.343562	−	1.05738i	0.618787	−	0.785559i	$-0.287624\pi$
$840$	1.63255	−	1.73866i	0.0563282	−	0.0599895i
$841$	−7.79940	+	24.0041i	−0.268945	+	0.827727i
$842$	4.16437	+	26.2928i	0.143514	+	0.906110i
$843$	6.35921	+	6.35921i	0.219023	+	0.219023i
$844$	9.03824	−	12.4401i	0.311109	−	0.428205i
$845$	−1.98388	+	22.9463i	−0.0682474	+	0.789376i
$846$	11.2423	+	15.4737i	0.386519	+	0.531998i
$847$	−29.1895	+	37.0191i	−1.00296	+	1.27199i
$848$	8.56068	+	4.36189i	0.293975	+	0.149788i
$849$			10.0542i			0.345061i
$850$	−17.1602	−	17.6973i	−0.588590	−	0.607011i
$851$	45.3287			1.55385
$852$	0.370628	+	0.188845i	0.0126975	+	0.00646971i
$853$	41.0465	+	6.50113i	1.40541	+	0.222594i	0.812633	−	0.582776i	$-0.198033\pi$
$853$	41.0465	+	6.50113i	1.40541	+	0.222594i	0.592772	+	0.805370i	$0.298033\pi$
$854$	3.15267	+	26.6597i	0.107882	+	0.912275i
$855$	−32.6103	−	13.8029i	−1.11525	−	0.472048i
$856$	−6.05618	−	4.40007i	−0.206996	−	0.150391i
$857$	10.8955	−	10.8955i	0.372183	−	0.372183i	−0.496089	−	0.868272i	$-0.665231\pi$
$857$	10.8955	−	10.8955i	0.372183	−	0.372183i	0.868272	+	0.496089i	$0.165231\pi$
$858$	−10.3178	+	1.63417i	−0.352242	+	0.0557897i
$859$	−9.07920	+	27.9429i	−0.309778	+	0.953399i	0.668072	+	0.744096i	$0.267120\pi$
$859$	−9.07920	+	27.9429i	−0.309778	+	0.953399i	−0.977851	+	0.209303i	$0.932880\pi$
$860$	−5.59736	+	2.26815i	−0.190868	+	0.0773431i
$861$	−5.74462	−	1.14327i	−0.195776	−	0.0389627i
$862$	19.4355	−	9.90287i	0.661975	−	0.337293i
$863$	6.11364	+	11.9987i	0.208111	+	0.408440i	0.971342	−	0.237685i	$-0.0763885\pi$
$863$	6.11364	+	11.9987i	0.208111	+	0.408440i	−0.763232	+	0.646125i	$0.776388\pi$
$864$	−0.727209	−	2.23812i	−0.0247402	−	0.0761424i
$865$	−3.05575	−	43.0658i	−0.103899	−	1.46428i
$866$	0.677533	+	0.220144i	0.0230235	+	0.00748079i
$867$	−2.90928	+	0.460785i	−0.0988045	+	0.0156491i
$868$	2.20440	−	0.621467i	0.0748222	−	0.0210940i
$869$	3.97220	−	5.46727i	0.134748	−	0.185464i
$870$	−5.68712	+	3.42509i	−0.192811	+	0.116121i
$871$	−11.0356	−	15.1892i	−0.373926	−	0.514665i
$872$	10.8511	+	1.71864i	0.367464	+	0.0582006i
$873$	−8.92328	+	17.5129i	−0.302007	+	0.592723i
$874$	−28.4108			−0.961010
$875$	9.59147	+	27.9822i	0.324251	+	0.945971i
$876$	−1.97493			−0.0667266
$877$	−8.93545	+	17.5368i	−0.301729	+	0.592176i	−0.991236	−	0.132103i	$-0.957827\pi$
$877$	−8.93545	+	17.5368i	−0.301729	+	0.592176i	0.689507	+	0.724279i	$0.257827\pi$
$878$	−16.8685	−	2.67170i	−0.569283	−	0.0901655i
$879$	−4.15549	−	5.71954i	−0.140161	−	0.192915i
$880$	10.2829	−	6.19295i	0.346638	−	0.208764i
$881$	−1.31624	+	1.81165i	−0.0443452	+	0.0610359i	−0.830614	−	0.556849i	$-0.812010\pi$
$881$	−1.31624	+	1.81165i	−0.0443452	+	0.0610359i	0.786269	+	0.617885i	$0.212010\pi$
$882$	4.64065	−	19.3126i	0.156259	−	0.650290i
$883$	7.94331	−	1.25810i	0.267314	−	0.0423383i	−0.0213387	−	0.999772i	$-0.506793\pi$
$883$	7.94331	−	1.25810i	0.267314	−	0.0423383i	0.288652	+	0.957434i	$0.406793\pi$
$884$	−22.6333	−	7.35401i	−0.761240	−	0.247342i
$885$	0.342265	+	4.82366i	0.0115051	+	0.162145i
$886$	−8.55753	−	26.3374i	−0.287496	−	0.884822i
$887$	5.67272	+	11.1333i	0.190471	+	0.373821i	0.966417	−	0.256979i	$-0.0827270\pi$
$887$	5.67272	+	11.1333i	0.190471	+	0.373821i	−0.775946	+	0.630800i	$0.782727\pi$
$888$	3.19849	−	1.62971i	0.107334	−	0.0546895i
$889$	4.22545	−	21.2317i	0.141717	−	0.712087i
$890$	7.75464	−	3.14231i	0.259936	−	0.105331i
$891$	−12.5474	+	38.6169i	−0.420353	+	1.29371i
$892$	23.6390	−	3.74405i	0.791492	−	0.125360i
$893$	26.6018	−	26.6018i	0.890197	−	0.890197i
$894$	2.79935	+	2.03384i	0.0936242	+	0.0680219i
$895$	−6.42282	−	2.71857i	−0.214691	−	0.0908717i
$896$	0.310712	+	2.62744i	0.0103801	+	0.0877767i
$897$	−9.78391	−	1.54962i	−0.326675	−	0.0517403i
$898$	−33.0134	−	16.8212i	−1.10167	−	0.561329i
$899$	−6.37538			−0.212631
$900$	13.9769	+	2.43501i	0.465896	+	0.0811670i
$901$			47.3685i			1.57807i
$902$	−26.2670	−	13.3837i	−0.874596	−	0.445629i
$903$	1.78371	−	2.26216i	0.0593581	−	0.0752799i
$904$	−8.45489	−	11.6372i	−0.281205	−	0.387046i
$905$	−1.97375	+	22.8292i	−0.0656097	+	0.758867i
$906$	−4.69849	+	6.46692i	−0.156097	+	0.214849i
$907$	−6.05614	−	6.05614i	−0.201091	−	0.201091i	0.599376	−	0.800467i	$-0.295415\pi$
$907$	−6.05614	−	6.05614i	−0.201091	−	0.201091i	−0.800467	+	0.599376i	$0.795415\pi$
$908$	0.516579	+	3.26155i	0.0171433	+	0.108238i
$909$	4.63840	−	14.2755i	0.153846	−	0.473490i
$910$	20.8182	+	19.5476i	0.690117	+	0.647997i
$911$	13.0373	+	40.1246i	0.431944	+	1.32939i	0.896186	+	0.443679i	$0.146327\pi$
$911$	13.0373	+	40.1246i	0.431944	+	1.32939i	−0.464242	+	0.885709i	$0.653673\pi$
$912$	−2.00472	+	1.02146i	−0.0663831	+	0.0338239i
$913$	−34.2236	+	17.4378i	−1.13264	+	0.577106i
$914$	−6.39972	+	2.07940i	−0.211684	+	0.0687803i
$915$	7.00065	−	5.88646i	0.231434	−	0.194600i
$916$	28.4873	+	9.25610i	0.941248	+	0.305830i
$917$	0.882929	−	2.39255i	0.0291569	−	0.0790089i
$918$	8.20397	−	8.20397i	0.270771	−	0.270771i
$919$	20.8268	−	28.6657i	0.687014	−	0.945594i	−0.312977	−	0.949761i	$-0.601326\pi$
$919$	20.8268	−	28.6657i	0.687014	−	0.945594i	0.999991	+	0.00416677i	$0.00132633\pi$
$920$	11.0884	−	2.57191i	0.365573	−	0.0847933i
$921$	5.71290	−	4.15067i	0.188247	−	0.136769i
$922$	4.85466	−	30.6511i	0.159880	−	1.00944i
$923$	−2.26117	+	4.43779i	−0.0744272	+	0.146072i
$924$	−2.79824	+	4.99544i	−0.0920553	+	0.164338i
$925$	−0.685900	+	44.5175i	−0.0225522	+	1.46373i
$926$	−25.1226			−0.825580
$927$	−34.2283	−	17.4402i	−1.12421	−	0.572812i
$928$	1.15210	−	7.27407i	0.0378195	−	0.238783i
$929$	20.6794	−	15.0245i	0.678470	−	0.492938i	−0.194380	−	0.980926i	$-0.562269\pi$
$929$	20.6794	−	15.0245i	0.678470	−	0.492938i	0.872850	+	0.487989i	$0.162269\pi$
$930$	−0.589456	−	0.511348i	−0.0193290	−	0.0167677i
$931$	−38.9469	−	3.07303i	−1.27643	−	0.100715i
$932$	6.37676	+	6.37676i	0.208878	+	0.208878i
$933$	8.59706	−	1.36164i	0.281455	−	0.0445781i
$934$	6.51719	−	20.0578i	0.213249	−	0.656313i
$935$	50.2203	+	31.3097i	1.64238	+	1.02394i
$936$	13.0262	−	4.23248i	0.425776	−	0.138343i
$937$	−19.1054	−	37.4964i	−0.624145	−	1.22495i	−0.959193	−	0.282752i	$-0.908753\pi$
$937$	−19.1054	−	37.4964i	−0.624145	−	1.22495i	0.335048	−	0.942201i	$-0.391247\pi$
$938$	−10.2827	−	0.405041i	−0.335743	−	0.0132251i
$939$	0.190349	−	0.0618481i	0.00621181	−	0.00201834i
$940$	−7.97420	+	12.7905i	−0.260090	+	0.417180i
$941$	5.71905	+	1.85823i	0.186436	+	0.0605767i	0.400747	−	0.916189i	$-0.368751\pi$
$941$	5.71905	+	1.85823i	0.186436	+	0.0605767i	−0.214311	+	0.976765i	$0.568751\pi$
$942$	−0.0626698	−	0.395681i	−0.00204189	−	0.0128920i
$943$	−19.7671	−	19.7671i	−0.643704	−	0.643704i
$944$	−4.33998	−	3.15318i	−0.141254	−	0.102627i
$945$	−13.0990	+	4.71668i	−0.426110	+	0.153434i
$946$	11.7302	−	8.52246i	0.381380	−	0.277089i
$947$	7.93496	+	1.25677i	0.257852	+	0.0408397i	0.284022	−	0.958818i	$-0.408331\pi$
$947$	7.93496	+	1.25677i	0.257852	+	0.0408397i	−0.0261702	+	0.999658i	$0.508331\pi$
$948$	0.230397	−	0.452180i	0.00748295	−	0.0146861i
$949$		−	23.6472i		−	0.767620i
$950$	0.429903	−	27.9023i	0.0139479	−	0.905272i
$951$		−	1.19650i		−	0.0387993i
$952$	−10.8464	+	7.24578i	−0.351535	+	0.234837i
$953$	−3.96848	+	25.0560i	−0.128552	+	0.811643i	0.836189	+	0.548441i	$0.184778\pi$
$953$	−3.96848	+	25.0560i	−0.128552	+	0.811643i	−0.964741	+	0.263202i	$0.915222\pi$
$954$	−16.0243	−	22.0556i	−0.518806	−	0.714075i
$955$	−1.06663	−	4.59860i	−0.0345153	−	0.148807i
$956$	13.1430	+	9.54898i	0.425076	+	0.308836i
$957$	11.2701	−	11.2701i	0.364311	−	0.364311i
$958$	−6.30575	−	39.8129i	−0.203730	−	1.28630i
$959$	11.8673	−	10.9678i	0.383215	−	0.354169i
$960$	0.689949	−	0.580141i	0.0222680	−	0.0187240i
$961$	9.34796	+	28.7701i	0.301547	+	0.928066i
$962$	19.5136	+	38.2977i	0.629145	+	1.23477i
$963$	9.64319	+	18.9258i	0.310748	+	0.609876i
$964$	5.55651	+	17.1012i	0.178963	+	0.550792i
$965$	8.50260	−	34.2514i	0.273708	−	1.10259i
$966$	−3.98739	+	3.68517i	−0.128292	+	0.118568i
$967$	−0.962688	−	6.07817i	−0.0309579	−	0.195461i	0.967362	−	0.253397i	$-0.0815479\pi$
$967$	−0.962688	−	6.07817i	−0.0309579	−	0.195461i	−0.998320	+	0.0579364i	$0.981548\pi$
$968$	−12.5994	+	12.5994i	−0.404962	+	0.404962i
$969$	−8.97415	−	6.52010i	−0.288291	−	0.209456i
$970$	−15.4317	−	1.33418i	−0.495481	−	0.0428380i
$971$	20.3632	+	28.0276i	0.653488	+	0.899449i	0.999244	−	0.0388757i	$-0.0123776\pi$
$971$	20.3632	+	28.0276i	0.653488	+	0.899449i	−0.345756	+	0.938324i	$0.612378\pi$
$972$	−1.58141	+	9.98465i	−0.0507239	+	0.320258i
$973$	−23.8828	−	35.7509i	−0.765648	−	1.14612i
$974$			5.06266i			0.162218i
$975$	1.66993	−	9.58536i	0.0534806	−	0.306977i
$976$			10.1466i			0.324785i
$977$	5.76533	−	11.3151i	0.184449	−	0.362002i	−0.780204	−	0.625525i	$-0.784885\pi$
$977$	5.76533	−	11.3151i	0.184449	−	0.362002i	0.964653	+	0.263523i	$0.0848847\pi$
$978$	0.131168	+	0.0207750i	0.00419429	+	0.000664311i
$979$	−16.2511	+	11.8071i	−0.519387	+	0.377357i
$980$	15.4786	−	2.32633i	0.494447	−	0.0743118i
$981$	−25.2199	−	18.3234i	−0.805211	−	0.585020i
$982$	10.3924	+	10.3924i	0.331633	+	0.331633i
$983$	−0.650101	−	4.10458i	−0.0207350	−	0.130916i	0.975149	−	0.221548i	$-0.0711111\pi$
$983$	−0.650101	−	4.10458i	−0.0207350	−	0.130916i	−0.995884	+	0.0906327i	$0.971111\pi$
$984$	−2.10549	−	0.684116i	−0.0671206	−	0.0218088i
$985$	−31.6289	+	12.8166i	−1.00778	+	0.408370i
$986$	34.5323	−	11.2202i	1.09973	−	0.357325i
$987$	0.282982	−	7.18403i	0.00900741	−	0.228670i
$988$	−12.2306	−	24.0040i	−0.389108	−	0.763667i
$989$	13.0761	−	4.24870i	0.415797	−	0.135101i
$990$	−33.9752	+	2.41072i	−1.07980	+	0.0766178i
$991$	−12.3053	+	37.8720i	−0.390892	+	1.20304i	0.541222	+	0.840880i	$0.317962\pi$
$991$	−12.3053	+	37.8720i	−0.390892	+	1.20304i	−0.932115	+	0.362163i	$0.882038\pi$
$992$	0.855005	−	0.135419i	0.0271464	−	0.00429957i
$993$	0.541678	+	0.541678i	0.0171896	+	0.0171896i
$994$	1.14267	+	2.47930i	0.0362434	+	0.0786387i
$995$	−27.4709	+	16.5445i	−0.870886	+	0.524495i
$996$	−2.33356	+	1.69543i	−0.0739418	+	0.0537218i
$997$	1.56294	−	9.86802i	0.0494988	−	0.312523i	−0.950500	−	0.310726i	$-0.899428\pi$
$997$	1.56294	−	9.86802i	0.0494988	−	0.312523i	0.999998	−	0.00179733i	$-0.000572109\pi$
$998$	8.89118	+	4.53028i	0.281445	+	0.143404i
$999$	−20.9551			−0.662989

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.r.a.167.5	yes	160
7.6	odd	2	inner	350.2.r.a.167.6	yes	160
25.3	odd	20	inner	350.2.r.a.153.6	yes	160
175.153	even	20	inner	350.2.r.a.153.5	✓	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.r.a.153.5	✓	160	175.153	even	20	inner
350.2.r.a.153.6	yes	160	25.3	odd	20	inner
350.2.r.a.167.5	yes	160	1.1	even	1	trivial
350.2.r.a.167.6	yes	160	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.r (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.398173 - 0.0630644i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.91550 + 1.15362i) q^{5} +(0.236957 - 0.326144i) q^{6} +(2.54649 - 0.717909i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.69861 - 0.876830i) q^{9} +O(q^{10})\)	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.398173 - 0.0630644i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.91550 + 1.15362i) q^{5} +(0.236957 - 0.326144i) q^{6} +(2.54649 - 0.717909i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.69861 - 0.876830i) q^{9} +(-0.158263 - 2.23046i) q^{10} +(1.65889 + 5.10553i) q^{11} +(0.183020 + 0.359197i) q^{12} +(-4.30091 + 2.19142i) q^{13} +(-0.516420 + 2.59486i) q^{14} +(0.835454 - 0.338540i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(-4.86947 + 0.771249i) q^{17} +(2.00640 - 2.00640i) q^{18} +(-4.51523 - 3.28051i) q^{19} +(2.05920 + 0.871594i) q^{20} +(-1.05922 + 0.125259i) q^{21} +(-5.30218 - 0.839782i) q^{22} +(-4.53568 - 2.31104i) q^{23} -0.403136 q^{24} +(2.33832 - 4.41953i) q^{25} -4.82703i q^{26} +(2.09680 + 1.06838i) q^{27} +(-2.07759 - 1.63818i) q^{28} +(4.32889 + 5.95820i) q^{29} +(-0.0776464 + 0.898089i) q^{30} +(-0.508824 + 0.700336i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.338546 - 2.13750i) q^{33} +(1.52351 - 4.68887i) q^{34} +(-4.04962 + 4.31284i) q^{35} +(0.876830 + 2.69861i) q^{36} +(-7.93401 + 4.04258i) q^{37} +(4.97282 - 2.53378i) q^{38} +(1.85071 - 0.601331i) q^{39} +(-1.71146 + 1.43907i) q^{40} +(5.22278 + 1.69699i) q^{41} +(0.369268 - 1.00064i) q^{42} +(-1.90984 + 1.90984i) q^{43} +(3.15539 - 4.34302i) q^{44} +(6.18072 - 1.43360i) q^{45} +(4.11831 - 2.99213i) q^{46} +(-1.05448 + 6.65770i) q^{47} +(0.183020 - 0.359197i) q^{48} +(5.96921 - 3.65629i) q^{49} +(2.87626 + 4.08988i) q^{50} +1.98753 q^{51} +(4.30091 + 2.19142i) q^{52} +(1.50300 - 9.48959i) q^{53} +(-1.90386 + 1.38323i) q^{54} +(-9.06745 - 7.86593i) q^{55} +(2.40283 - 1.10743i) q^{56} +(1.59096 + 1.59096i) q^{57} +(-7.27407 + 1.15210i) q^{58} +(-1.65773 + 5.10196i) q^{59} +(-0.764952 - 0.476907i) q^{60} +(9.65000 - 3.13548i) q^{61} +(-0.393003 - 0.771311i) q^{62} +(-7.50145 - 0.295485i) q^{63} +(0.951057 - 0.309017i) q^{64} +(5.71034 - 9.15931i) q^{65} +(2.05822 + 0.668757i) q^{66} +(0.608456 + 3.84164i) q^{67} +(3.48616 + 3.48616i) q^{68} +(1.66024 + 1.20623i) q^{69} +(-2.00428 - 5.56622i) q^{70} +(0.834764 - 0.606492i) q^{71} +(-2.80255 - 0.443880i) q^{72} +(-2.22406 + 4.36496i) q^{73} -8.90455i q^{74} +(-1.20977 + 1.61227i) q^{75} +5.58113i q^{76} +(7.88964 + 11.8102i) q^{77} +(-0.304413 + 1.92199i) q^{78} +(-0.739941 - 1.01844i) q^{79} +(-0.505236 - 2.17824i) q^{80} +(6.11920 + 4.44586i) q^{81} +(-3.88312 + 3.88312i) q^{82} +(1.11929 + 7.06692i) q^{83} +(0.723929 + 0.783299i) q^{84} +(8.43777 - 7.09486i) q^{85} +(-0.834631 - 2.56873i) q^{86} +(-1.34789 - 2.64539i) q^{87} +(2.43714 + 4.78316i) q^{88} +(1.15631 + 3.55875i) q^{89} +(-1.52864 + 6.15790i) q^{90} +(-9.37898 + 8.66810i) q^{91} +(0.796331 + 5.02784i) q^{92} +(0.246766 - 0.246766i) q^{93} +(-5.45333 - 3.96208i) q^{94} +(12.4334 + 1.07496i) q^{95} +(0.236957 + 0.326144i) q^{96} +(1.08362 - 6.84171i) q^{97} +(0.547816 + 6.97853i) q^{98} -15.2324i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{7}+O(q^{10}) \) 160 * q + 8 * q^7	\( 160 q + 8 q^{7} + 16 q^{15} + 40 q^{16} - 8 q^{18} - 24 q^{22} - 32 q^{23} + 12 q^{28} - 40 q^{29} - 56 q^{30} + 28 q^{35} + 40 q^{36} - 32 q^{37} + 40 q^{39} - 112 q^{43} - 32 q^{50} + 112 q^{53} - 152 q^{57} + 16 q^{58} + 8 q^{60} - 100 q^{63} - 8 q^{65} - 16 q^{67} - 56 q^{70} - 8 q^{72} - 144 q^{77} + 40 q^{78} + 40 q^{81} - 60 q^{84} + 48 q^{85} - 16 q^{88} + 8 q^{92} + 56 q^{93} - 104 q^{95} - 32 q^{98}+O(q^{100}) \) 160 * q + 8 * q^7 + 16 * q^15 + 40 * q^16 - 8 * q^18 - 24 * q^22 - 32 * q^23 + 12 * q^28 - 40 * q^29 - 56 * q^30 + 28 * q^35 + 40 * q^36 - 32 * q^37 + 40 * q^39 - 112 * q^43 - 32 * q^50 + 112 * q^53 - 152 * q^57 + 16 * q^58 + 8 * q^60 - 100 * q^63 - 8 * q^65 - 16 * q^67 - 56 * q^70 - 8 * q^72 - 144 * q^77 + 40 * q^78 + 40 * q^81 - 60 * q^84 + 48 * q^85 - 16 * q^88 + 8 * q^92 + 56 * q^93 - 104 * q^95 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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