LMFDB - Embedded newform 425.2.q.a.84.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(84,425)]

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([7, 5]))

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

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

chi := DirichletCharacter("425.84");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.q (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:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			84.6
Character	$\chi$	$=$	425.84
Dual form			425.2.q.a.339.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39460 + 1.91951i) q^{2} +(0.152608 + 0.469678i) q^{3} +(-1.12155 - 3.45179i) q^{4} +(-1.97789 + 1.04304i) q^{5} +(-1.11438 - 0.362083i) q^{6} +1.83697 q^{7} +(3.67682 + 1.19467i) q^{8} +(2.22974 - 1.62000i) q^{9} +(0.756252 - 5.25121i) q^{10} +(3.32921 - 4.58227i) q^{11} +(1.45007 - 1.05354i) q^{12} +(-3.63764 - 5.00679i) q^{13} +(-2.56184 + 3.52607i) q^{14} +(-0.791736 - 0.769798i) q^{15} +(-1.54835 + 1.12494i) q^{16} +(-3.84862 + 1.47923i) q^{17} +6.53927i q^{18} +(0.857473 - 2.63903i) q^{19} +(5.81867 + 5.65744i) q^{20} +(0.280336 + 0.862784i) q^{21} +(4.15277 + 12.7809i) q^{22} +(2.77105 + 2.01328i) q^{23} +1.90924i q^{24} +(2.82413 - 4.12605i) q^{25} +14.6836 q^{26} +(2.29975 + 1.67087i) q^{27} +(-2.06026 - 6.34082i) q^{28} +(-4.00911 + 1.30264i) q^{29} +(2.58179 - 0.446180i) q^{30} +(3.14374 + 1.02146i) q^{31} +3.19115i q^{32} +(2.66026 + 0.864370i) q^{33} +(2.52791 - 9.45039i) q^{34} +(-3.63333 + 1.91603i) q^{35} +(-8.09268 - 5.87968i) q^{36} +(2.35482 - 1.71088i) q^{37} +(3.86980 + 5.32633i) q^{38} +(1.79645 - 2.47260i) q^{39} +(-8.51845 + 1.47214i) q^{40} +(0.870046 + 1.19752i) q^{41} +(-2.04708 - 0.665136i) q^{42} -1.83529i q^{43} +(-19.5509 - 6.35248i) q^{44} +(-2.72046 + 5.52991i) q^{45} +(-7.72902 + 2.51131i) q^{46} +(4.47423 - 1.45377i) q^{47} +(-0.764653 - 0.555553i) q^{48} -3.62555 q^{49} +(3.98144 + 11.1751i) q^{50} +(-1.28209 - 1.58187i) q^{51} +(-13.2026 + 18.1718i) q^{52} +(8.15399 - 2.64939i) q^{53} +(-6.41449 + 2.08419i) q^{54} +(-1.80533 + 12.5358i) q^{55} +(6.75420 + 2.19457i) q^{56} +1.37035 q^{57} +(3.09069 - 9.51217i) q^{58} +(4.99085 - 3.62606i) q^{59} +(-1.76920 + 3.59627i) q^{60} +(0.602854 - 0.829757i) q^{61} +(-6.34498 + 4.60990i) q^{62} +(4.09597 - 2.97589i) q^{63} +(-9.22214 - 6.70028i) q^{64} +(12.4172 + 6.10868i) q^{65} +(-5.36917 + 3.90093i) q^{66} +(-3.30684 - 1.07446i) q^{67} +(9.42242 + 11.6256i) q^{68} +(-0.522712 + 1.60874i) q^{69} +(1.38921 - 9.64631i) q^{70} +(-12.9389 + 4.20412i) q^{71} +(10.1337 - 3.29265i) q^{72} +(-10.7422 - 7.80465i) q^{73} +6.90610i q^{74} +(2.36890 + 0.696765i) q^{75} -10.0711 q^{76} +(6.11566 - 8.41749i) q^{77} +(2.24084 + 6.89658i) q^{78} +(10.2175 - 3.31987i) q^{79} +(1.88911 - 3.84002i) q^{80} +(2.12125 - 6.52853i) q^{81} -3.51201 q^{82} +(-8.43322 - 2.74012i) q^{83} +(2.66374 - 1.93532i) q^{84} +(6.06926 - 6.94003i) q^{85} +(3.52286 + 2.55951i) q^{86} +(-1.22364 - 1.68420i) q^{87} +(17.7152 - 12.8709i) q^{88} +(2.02611 + 1.47205i) q^{89} +(-6.82073 - 12.9340i) q^{90} +(-6.68224 - 9.19731i) q^{91} +(3.84155 - 11.8231i) q^{92} +1.63243i q^{93} +(-3.44926 + 10.6157i) q^{94} +(1.05663 + 6.11410i) q^{95} +(-1.49881 + 0.486994i) q^{96} +(-0.152034 - 0.467913i) q^{97} +(5.05620 - 6.95926i) q^{98} -15.6106i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 10 q^{2} + 38 q^{4} - 10 q^{8} - 50 q^{9} - 10 q^{13} + 6 q^{15} - 58 q^{16} - 8 q^{19} - 44 q^{21} - 20 q^{25} - 64 q^{26} + 78 q^{30} - 20 q^{33} - 23 q^{34} - 46 q^{35} + 52 q^{36} - 10 q^{38}+ \cdots - 250 q^{98}+O(q^{100}) $ 176 * q - 10 * q^2 + 38 * q^4 - 10 * q^8 - 50 * q^9 - 10 * q^13 + 6 * q^15 - 58 * q^16 - 8 * q^19 - 44 * q^21 - 20 * q^25 - 64 * q^26 + 78 * q^30 - 20 * q^33 - 23 * q^34 - 46 * q^35 + 52 * q^36 - 10 * q^38 - 20 * q^42 + 40 * q^47 + 164 * q^49 + 84 * q^50 + 20 * q^51 - 30 * q^52 - 40 * q^53 - 18 * q^55 - 18 * q^59 - 48 * q^60 + 66 * q^64 + 80 * q^66 - 50 * q^67 + 68 * q^69 - 152 * q^70 + 60 * q^72 - 72 * q^76 - 40 * q^77 - 38 * q^81 + 50 * q^83 - 52 * q^84 + 47 * q^85 - 94 * q^86 - 120 * q^87 + 60 * q^89 + 50 * q^94 - 250 * q^98

Character values

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

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$

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 $

$2$	−1.39460	+	1.91951i	−0.986133	+	1.35730i	−0.0526745	+	0.998612i	$0.516775\pi$
$2$	−1.39460	+	1.91951i	−0.986133	+	1.35730i	−0.933459	+	0.358684i	$0.883225\pi$
$3$	0.152608	+	0.469678i	0.0881081	+	0.271169i	0.985396	−	0.170276i	$-0.0544660\pi$
$3$	0.152608	+	0.469678i	0.0881081	+	0.271169i	−0.897288	+	0.441445i	$0.854466\pi$
$4$	−1.12155	−	3.45179i	−0.560777	−	1.72589i
$5$	−1.97789	+	1.04304i	−0.884541	+	0.466462i
$5$	−1.97789	+	1.04304i	−0.884541	+	0.466462i
$6$	−1.11438	−	0.362083i	−0.454943	−	0.147820i
$7$	1.83697			0.694309			0.347154	−	0.937808i	$-0.387148\pi$
$7$	1.83697			0.694309			0.347154	+	0.937808i	$0.387148\pi$
$8$	3.67682	+	1.19467i	1.29995	+	0.422380i
$9$	2.22974	−	1.62000i	0.743247	−	0.540001i
$10$	0.756252	−	5.25121i	0.239148	−	1.66058i
$11$	3.32921	−	4.58227i	1.00380	−	1.38161i	0.0808284	−	0.996728i	$-0.474243\pi$
$11$	3.32921	−	4.58227i	1.00380	−	1.38161i	0.922967	−	0.384878i	$-0.125757\pi$
$12$	1.45007	−	1.05354i	0.418600	−	0.304131i
$13$	−3.63764	−	5.00679i	−1.00890	−	1.38863i	−0.919701	−	0.392619i	$-0.871569\pi$
$13$	−3.63764	−	5.00679i	−1.00890	−	1.38863i	−0.0891996	−	0.996014i	$-0.528431\pi$
$14$	−2.56184	+	3.52607i	−0.684681	+	0.942383i
$15$	−0.791736	−	0.769798i	−0.204425	−	0.198761i
$16$	−1.54835	+	1.12494i	−0.387088	+	0.281236i
$17$	−3.84862	+	1.47923i	−0.933428	+	0.358766i
$17$	−3.84862	+	1.47923i	−0.933428	+	0.358766i
$18$			6.53927i			1.54132i
$19$	0.857473	−	2.63903i	0.196718	−	0.605435i	−0.803234	−	0.595663i	$-0.796889\pi$
$19$	0.857473	−	2.63903i	0.196718	−	0.605435i	0.999952	−	0.00977227i	$-0.00311066\pi$
$20$	5.81867	+	5.65744i	1.30109	+	1.26504i
$21$	0.280336	+	0.862784i	0.0611743	+	0.188275i
$22$	4.15277	+	12.7809i	0.885372	+	2.72490i
$23$	2.77105	+	2.01328i	0.577803	+	0.419799i	0.837931	−	0.545775i	$-0.183765\pi$
$23$	2.77105	+	2.01328i	0.577803	+	0.419799i	−0.260128	+	0.965574i	$0.583765\pi$
$24$			1.90924i			0.389722i
$25$	2.82413	−	4.12605i	0.564826	−	0.825210i
$26$	14.6836			2.87970
$27$	2.29975	+	1.67087i	0.442588	+	0.321559i
$28$	−2.06026	−	6.34082i	−0.389352	−	1.19830i
$29$	−4.00911	+	1.30264i	−0.744473	+	0.241894i	−0.656601	−	0.754238i	$-0.728006\pi$
$29$	−4.00911	+	1.30264i	−0.744473	+	0.241894i	−0.0878715	+	0.996132i	$0.528006\pi$
$30$	2.58179	−	0.446180i	0.471368	−	0.0814610i
$31$	3.14374	+	1.02146i	0.564633	+	0.183460i	0.577405	−	0.816458i	$-0.304065\pi$
$31$	3.14374	+	1.02146i	0.564633	+	0.183460i	−0.0127717	+	0.999918i	$0.504065\pi$
$32$			3.19115i			0.564121i
$33$	2.66026	+	0.864370i	0.463091	+	0.150467i
$34$	2.52791	−	9.45039i	0.433533	−	1.62073i
$35$	−3.63333	+	1.91603i	−0.614145	+	0.323869i
$36$	−8.09268	−	5.87968i	−1.34878	−	0.979946i
$37$	2.35482	−	1.71088i	0.387130	−	0.281267i	−0.377148	−	0.926153i	$-0.623095\pi$
$37$	2.35482	−	1.71088i	0.387130	−	0.281267i	0.764279	+	0.644886i	$0.223095\pi$
$38$	3.86980	+	5.32633i	0.627765	+	0.864044i
$39$	1.79645	−	2.47260i	0.287662	−	0.395932i
$40$	−8.51845	+	1.47214i	−1.34689	+	0.232766i
$41$	0.870046	+	1.19752i	0.135878	+	0.187020i	0.871534	−	0.490335i	$-0.163126\pi$
$41$	0.870046	+	1.19752i	0.135878	+	0.187020i	−0.735655	+	0.677356i	$0.763126\pi$
$42$	−2.04708	−	0.665136i	−0.315871	−	0.102633i
$43$		−	1.83529i		−	0.279880i	−0.990160	−	0.139940i	$-0.955309\pi$
$43$		−	1.83529i		−	0.279880i	0.990160	−	0.139940i	$-0.0446909\pi$
$44$	−19.5509	−	6.35248i	−2.94741	−	0.957672i
$45$	−2.72046	+	5.52991i	−0.405543	+	0.824350i
$46$	−7.72902	+	2.51131i	−1.13958	+	0.370273i
$47$	4.47423	−	1.45377i	0.652634	−	0.212054i	0.0360587	−	0.999350i	$-0.488520\pi$
$47$	4.47423	−	1.45377i	0.652634	−	0.212054i	0.616575	+	0.787296i	$0.288520\pi$
$48$	−0.764653	−	0.555553i	−0.110368	−	0.0801872i
$49$	−3.62555			−0.517935
$50$	3.98144	+	11.1751i	0.563061	+	1.58040i
$51$	−1.28209	−	1.58187i	−0.179529	−	0.221506i
$52$	−13.2026	+	18.1718i	−1.83086	+	2.51997i
$53$	8.15399	−	2.64939i	1.12004	−	0.363922i	0.310255	−	0.950653i	$-0.399586\pi$
$53$	8.15399	−	2.64939i	1.12004	−	0.363922i	0.809782	+	0.586731i	$0.199586\pi$
$54$	−6.41449	+	2.08419i	−0.872901	+	0.283623i
$55$	−1.80533	+	12.5358i	−0.243431	+	1.69032i
$56$	6.75420	+	2.19457i	0.902568	+	0.293262i
$57$	1.37035			0.181508
$58$	3.09069	−	9.51217i	0.405828	−	1.24901i
$59$	4.99085	−	3.62606i	0.649753	−	0.472073i	−0.213434	−	0.976957i	$-0.568465\pi$
$59$	4.99085	−	3.62606i	0.649753	−	0.472073i	0.863187	+	0.504884i	$0.168465\pi$
$60$	−1.76920	+	3.59627i	−0.228403	+	0.464277i
$61$	0.602854	−	0.829757i	0.0771875	−	0.106240i	−0.768677	−	0.639637i	$-0.779085\pi$
$61$	0.602854	−	0.829757i	0.0771875	−	0.106240i	0.845865	+	0.533397i	$0.179085\pi$
$62$	−6.34498	+	4.60990i	−0.805814	+	0.585458i
$63$	4.09597	−	2.97589i	0.516043	−	0.374927i
$64$	−9.22214	−	6.70028i	−1.15277	−	0.837534i
$65$	12.4172	+	6.10868i	1.54016	+	0.757688i
$66$	−5.36917	+	3.90093i	−0.660899	+	0.480171i
$67$	−3.30684	−	1.07446i	−0.403995	−	0.131266i	0.0999692	−	0.994991i	$-0.468126\pi$
$67$	−3.30684	−	1.07446i	−0.403995	−	0.131266i	−0.503964	+	0.863725i	$0.668126\pi$
$68$	9.42242	+	11.6256i	1.14264	+	1.40981i
$69$	−0.522712	+	1.60874i	−0.0629272	+	0.193670i
$70$	1.38921	−	9.64631i	0.166042	−	1.15295i
$71$	−12.9389	+	4.20412i	−1.53557	+	0.498937i	−0.950150	−	0.311793i	$-0.899070\pi$
$71$	−12.9389	+	4.20412i	−1.53557	+	0.498937i	−0.585420	+	0.810730i	$0.699070\pi$
$72$	10.1337	−	3.29265i	1.19427	−	0.388042i
$73$	−10.7422	−	7.80465i	−1.25728	−	0.913466i	−0.258657	−	0.965969i	$-0.583280\pi$
$73$	−10.7422	−	7.80465i	−1.25728	−	0.913466i	−0.998621	+	0.0525037i	$0.983280\pi$
$74$			6.90610i			0.802817i
$75$	2.36890	+	0.696765i	0.273537	+	0.0804554i
$76$	−10.0711			−1.15523
$77$	6.11566	−	8.41749i	0.696944	−	0.959261i
$78$	2.24084	+	6.89658i	0.253725	+	0.780884i
$79$	10.2175	−	3.31987i	1.14956	−	0.373514i	0.328582	−	0.944476i	$-0.393429\pi$
$79$	10.2175	−	3.31987i	1.14956	−	0.373514i	0.820977	+	0.570961i	$0.193429\pi$
$80$	1.88911	−	3.84002i	0.211209	−	0.429327i
$81$	2.12125	−	6.52853i	0.235694	−	0.725392i
$82$	−3.51201			−0.387836
$83$	−8.43322	−	2.74012i	−0.925666	−	0.300767i	−0.192877	−	0.981223i	$-0.561782\pi$
$83$	−8.43322	−	2.74012i	−0.925666	−	0.300767i	−0.732789	+	0.680456i	$0.761782\pi$
$84$	2.66374	−	1.93532i	0.290638	−	0.211161i
$85$	6.06926	−	6.94003i	0.658304	−	0.752752i
$86$	3.52286	+	2.55951i	0.379880	+	0.275999i
$87$	−1.22364	−	1.68420i	−0.131188	−	0.180565i
$88$	17.7152	−	12.8709i	1.88845	−	1.37204i
$89$	2.02611	+	1.47205i	0.214767	+	0.156037i	0.689968	−	0.723840i	$-0.257625\pi$
$89$	2.02611	+	1.47205i	0.214767	+	0.156037i	−0.475201	+	0.879877i	$0.657625\pi$
$90$	−6.82073	−	12.9340i	−0.718968	−	1.36336i
$91$	−6.68224	−	9.19731i	−0.700489	−	0.964140i
$92$	3.84155	−	11.8231i	0.400509	−	1.23264i
$93$			1.63243i			0.169275i
$94$	−3.44926	+	10.6157i	−0.355764	+	1.09493i
$95$	1.05663	+	6.11410i	0.108408	+	0.627294i
$96$	−1.49881	+	0.486994i	−0.152972	+	0.0497036i
$97$	−0.152034	−	0.467913i	−0.0154367	−	0.0475094i	0.943041	−	0.332675i	$-0.107951\pi$
$97$	−0.152034	−	0.467913i	−0.0154367	−	0.0475094i	−0.958478	+	0.285166i	$0.907951\pi$
$98$	5.05620	−	6.95926i	0.510753	−	0.702992i
$99$		−	15.6106i		−	1.56893i
$100$	−17.4097	−	5.12070i	−1.74097	−	0.512070i
$101$	−9.23212			−0.918631			−0.459315	−	0.888273i	$-0.651905\pi$
$101$	−9.23212			−0.918631			−0.459315	+	0.888273i	$0.651905\pi$
$102$	4.82442	−	0.254899i	0.477689	−	0.0252388i
$103$	13.0941	−	4.25453i	1.29020	−	0.419212i	0.418039	−	0.908429i	$-0.362717\pi$
$103$	13.0941	−	4.25453i	1.29020	−	0.419212i	0.872162	+	0.489217i	$0.162717\pi$
$104$	−7.39350	−	22.7548i	−0.724992	−	2.23130i
$105$	−1.45439	−	1.41409i	−0.141934	−	0.138001i
$106$	−6.28605	+	19.3465i	−0.610556	+	1.87910i
$107$	5.26367			0.508858			0.254429	−	0.967091i	$-0.418113\pi$
$107$	5.26367			0.508858			0.254429	+	0.967091i	$0.418113\pi$
$108$	3.18819	−	9.81223i	0.306783	−	0.944182i
$109$	11.9318	+	16.4228i	1.14286	+	1.57302i	0.760942	+	0.648820i	$0.224737\pi$
$109$	11.9318	+	16.4228i	1.14286	+	1.57302i	0.381921	+	0.924195i	$0.375263\pi$
$110$	−21.5447	−	20.9477i	−2.05421	−	1.99729i
$111$	1.16293	+	0.844916i	0.110380	+	0.0801959i
$112$	−2.84428	+	2.06649i	−0.268759	+	0.195265i
$113$	15.2940	−	11.1117i	1.43874	−	1.04530i	0.450434	−	0.892810i	$-0.351269\pi$
$113$	15.2940	−	11.1117i	1.43874	−	1.04530i	0.988304	−	0.152495i	$-0.0487307\pi$
$114$	−1.91110	+	2.63040i	−0.178991	+	0.246360i
$115$	−7.58077	−	1.09174i	−0.706911	−	0.101806i
$116$	8.99286	+	12.3776i	0.834966	+	1.14923i
$117$	−16.2220	−	5.27085i	−1.49973	−	0.487290i
$118$			14.6369i			1.34743i
$119$	−7.06979	+	2.71730i	−0.648087	+	0.249094i
$120$	−1.99142	−	3.77627i	−0.181791	−	0.344725i
$121$	−6.51434	−	20.0491i	−0.592213	−	1.82264i
$122$	0.751983	+	2.31436i	0.0680813	+	0.209533i
$123$	−0.429671	+	0.591392i	−0.0387422	+	0.0533240i
$124$		−	11.9972i		−	1.07738i
$125$	−1.28218	+	11.1066i	−0.114682	+	0.993402i
$126$			12.0124i			1.07015i
$127$	−8.66968	+	11.9328i	−0.769310	+	1.05886i	0.227072	+	0.973878i	$0.427085\pi$
$127$	−8.66968	+	11.9328i	−0.769310	+	1.05886i	−0.996382	+	0.0849863i	$0.972915\pi$
$128$	19.6525	−	6.38549i	1.73705	−	0.564403i
$129$	0.861998	−	0.280080i	0.0758947	−	0.0246597i
$130$	−29.0427	+	15.3156i	−2.54721	+	1.34327i
$131$	−9.69308	−	3.14947i	−0.846888	−	0.275171i	−0.146746	−	0.989174i	$-0.546880\pi$
$131$	−9.69308	−	3.14947i	−0.846888	−	0.275171i	−0.700142	+	0.714004i	$0.746880\pi$
$132$		−	10.1521i		−	0.883625i
$133$	1.57515	−	4.84782i	0.136583	−	0.420359i
$134$	6.67416	−	4.84906i	0.576559	−	0.418895i
$135$	−6.29145	−	0.906062i	−0.541482	−	0.0779814i
$136$	−15.9179	+	0.841024i	−1.36495	+	0.0721172i
$137$	9.92879	+	13.6658i	0.848273	+	1.16755i	0.984241	+	0.176835i	$0.0565858\pi$
$137$	9.92879	+	13.6658i	0.848273	+	1.16755i	−0.135967	+	0.990713i	$0.543414\pi$
$138$	−2.35902	−	3.24691i	−0.200813	−	0.276395i
$139$	12.5264	−	17.2411i	1.06247	−	1.46237i	0.185001	−	0.982738i	$-0.440771\pi$
$139$	12.5264	−	17.2411i	1.06247	−	1.46237i	0.877471	−	0.479630i	$-0.159229\pi$
$140$	10.6887	+	10.3925i	0.903361	+	0.878330i
$141$	1.36561	+	1.87959i	0.115005	+	0.158290i
$142$	9.97486	−	30.6995i	0.837072	−	2.57624i
$143$	−35.0529			−2.93127
$144$	−1.63002	+	5.01667i	−0.135835	+	0.418056i
$145$	6.57088	−	6.75815i	0.545682	−	0.561233i
$146$	29.9622	−	9.73530i	2.47969	−	0.805699i
$147$	−0.553287	−	1.70284i	−0.0456343	−	0.140448i
$148$	−8.54665	−	6.20950i	−0.702530	−	0.510418i
$149$	7.52114			0.616156			0.308078	−	0.951361i	$-0.400314\pi$
$149$	7.52114			0.616156			0.308078	+	0.951361i	$0.400314\pi$
$150$	−4.64112	+	3.57541i	−0.378946	+	0.291931i
$151$	12.6866			1.03242			0.516208	−	0.856463i	$-0.327343\pi$
$151$	12.6866			1.03242			0.516208	+	0.856463i	$0.327343\pi$
$152$	6.30555	−	8.67885i	0.511448	−	0.703947i
$153$	−6.18508	+	9.53308i	−0.500034	+	0.770703i
$154$	7.62850	+	23.4781i	0.614722	+	1.89192i
$155$	−7.28342	+	1.25871i	−0.585018	+	0.101102i
$156$	−10.5497	−	3.42780i	−0.844651	−	0.274444i
$157$			9.53607i			0.761061i	0.924768	+	0.380531i	$0.124259\pi$
$157$			9.53607i			0.761061i	−0.924768	+	0.380531i	$0.875741\pi$
$158$	−7.87685	+	24.2425i	−0.626649	+	1.92863i
$159$	2.48872	+	3.42544i	0.197369	+	0.271655i
$160$	−3.32850	−	6.31175i	−0.263141	−	0.498988i
$161$	5.09033	+	3.69834i	0.401174	+	0.291470i
$162$	9.57325	+	13.1765i	0.752146	+	1.03524i
$163$	−8.04278	+	5.84342i	−0.629959	+	0.457692i	−0.856386	−	0.516336i	$-0.827296\pi$
$163$	−8.04278	+	5.84342i	−0.629959	+	0.457692i	0.226427	+	0.974028i	$0.427296\pi$
$164$	3.15776	−	4.34629i	0.246580	−	0.339388i
$165$	−6.16328	+	1.06513i	−0.479811	+	0.0829200i
$166$	17.0207	−	12.3662i	1.32106	−	0.959807i
$167$	−3.70555	+	11.4045i	−0.286744	+	0.882508i	0.699126	+	0.714998i	$0.253573\pi$
$167$	−3.70555	+	11.4045i	−0.286744	+	0.882508i	−0.985870	+	0.167510i	$0.946427\pi$
$168$			3.50721i			0.270587i
$169$	−7.81824	+	24.0621i	−0.601403	+	1.85093i
$170$	4.85722	+	21.3286i	0.372532	+	1.63583i
$171$	−2.36329	−	7.27347i	−0.180726	−	0.556216i
$172$	−6.33504	+	2.05838i	−0.483042	+	0.156950i
$173$	−2.83309	−	2.05836i	−0.215396	−	0.156494i	0.474856	−	0.880064i	$-0.342500\pi$
$173$	−2.83309	−	2.05836i	−0.215396	−	0.156494i	−0.690252	+	0.723569i	$0.742500\pi$
$174$	4.93933			0.374449
$175$	5.18783	−	7.57943i	0.392163	−	0.572951i
$176$			10.8402i			0.817108i
$177$	2.46473	+	1.79073i	0.185260	+	0.134599i
$178$	−5.65123	+	1.83620i	−0.423578	+	0.137629i
$179$	1.03217	+	3.17669i	0.0771479	+	0.237437i	0.982192	−	0.187882i	$-0.0601621\pi$
$179$	1.03217	+	3.17669i	0.0771479	+	0.237437i	−0.905044	+	0.425318i	$0.860162\pi$
$180$	22.1392	+	3.18837i	1.65016	+	0.237647i
$181$	−5.71198	−	1.85593i	−0.424568	−	0.137950i	0.0889368	−	0.996037i	$-0.471653\pi$
$181$	−5.71198	−	1.85593i	−0.424568	−	0.137950i	−0.513505	+	0.858087i	$0.671653\pi$
$182$	26.9734			1.99940
$183$	0.481719	+	0.156520i	0.0356097	+	0.0115703i
$184$	7.78343	+	10.7130i	0.573802	+	0.789771i
$185$	−2.87307	+	5.84012i	−0.211232	+	0.429374i
$186$	−3.13346	−	2.27659i	−0.229757	−	0.166928i
$187$	−6.03465	+	22.5601i	−0.441297	+	1.64976i
$188$	−10.0362	−	13.8136i	−0.731964	−	1.00746i
$189$	4.22457	+	3.06933i	0.307293	+	0.223261i
$190$	−13.2096	−	6.49854i	−0.958328	−	0.471454i
$191$	−1.26784	+	0.921142i	−0.0917379	+	0.0666515i	−0.632709	−	0.774390i	$-0.718057\pi$
$191$	−1.26784	+	0.921142i	−0.0917379	+	0.0666515i	0.540971	+	0.841041i	$0.318057\pi$
$192$	1.73960	−	5.35395i	0.125545	−	0.386388i
$193$	0.178548			0.0128522			0.00642608	−	0.999979i	$-0.497954\pi$
$193$	0.178548			0.0128522			0.00642608	+	0.999979i	$0.497954\pi$
$194$	1.11019	+	0.360723i	0.0797070	+	0.0258984i
$195$	−0.974160	+	6.76430i	−0.0697610	+	0.484402i
$196$	4.06625	+	12.5146i	0.290446	+	0.893901i
$197$	−3.88753	−	11.9646i	−0.276975	−	0.852442i	−0.988690	−	0.149973i	$-0.952081\pi$
$197$	−3.88753	−	11.9646i	−0.276975	−	0.852442i	0.711715	−	0.702468i	$-0.247919\pi$
$198$	29.9647	+	21.7706i	2.12950	+	1.54717i
$199$			9.56075i			0.677744i	0.940833	+	0.338872i	$0.110045\pi$
$199$			9.56075i			0.677744i	−0.940833	+	0.338872i	$0.889955\pi$
$200$	15.3131	−	11.7968i	1.08280	−	0.834163i
$201$		−	1.71712i		−	0.121116i
$202$	12.8751	−	17.7211i	0.905892	−	1.24685i
$203$	−7.36460	+	2.39290i	−0.516894	+	0.167949i
$204$	−4.02235	+	6.19966i	−0.281621	+	0.434063i
$205$	−2.96992	−	1.46106i	−0.207428	−	0.102045i
$206$	−10.0945	+	31.0676i	−0.703316	+	2.16458i
$207$	9.44024			0.656142
$208$	11.2647	+	3.66013i	0.781068	+	0.253784i
$209$	−9.23804	−	12.7151i	−0.639009	−	0.879520i
$210$	4.74267	−	0.819619i	0.327275	−	0.0565591i
$211$	−4.01438	+	5.52532i	−0.276361	+	0.380378i	−0.924524	−	0.381123i	$-0.875537\pi$
$211$	−4.01438	+	5.52532i	−0.276361	+	0.380378i	0.648163	+	0.761501i	$0.275537\pi$
$212$	−18.2903	−	25.1744i	−1.25618	−	1.72898i
$213$	−3.94917	−	5.43556i	−0.270592	−	0.372439i
$214$	−7.34072	+	10.1036i	−0.501802	+	0.690671i
$215$	1.91429	+	3.63002i	0.130553	+	0.247565i
$216$	6.45964	+	8.89093i	0.439523	+	0.604951i
$217$	5.77496	+	1.87640i	0.392030	+	0.127378i
$218$	−48.1638			−3.26206
$219$	2.02634	−	6.23642i	0.136927	−	0.421418i
$220$	45.2955	−	7.82789i	3.05382	−	0.527756i
$221$	21.4061	+	13.8883i	1.43993	+	0.934229i
$222$	−3.24364	+	1.05392i	−0.217699	+	0.0707347i
$223$	−2.80308	+	3.85811i	−0.187708	+	0.258358i	−0.892491	−	0.451065i	$-0.851044\pi$
$223$	−2.80308	+	3.85811i	−0.187708	+	0.258358i	0.704783	+	0.709423i	$0.251044\pi$
$224$			5.86204i			0.391674i
$225$	−0.387136	−	13.7751i	−0.0258091	−	0.918342i
$226$			44.8534i			2.98360i
$227$	−13.5933	−	9.87611i	−0.902219	−	0.655500i	0.0368160	−	0.999322i	$-0.488278\pi$
$227$	−13.5933	−	9.87611i	−0.902219	−	0.655500i	−0.939035	+	0.343822i	$0.888278\pi$
$228$	−1.53692	−	4.73017i	−0.101785	−	0.313263i
$229$	1.36592	+	4.20385i	0.0902622	+	0.277799i	0.985990	−	0.166804i	$-0.0533448\pi$
$229$	1.36592	+	4.20385i	0.0902622	+	0.277799i	−0.895728	+	0.444603i	$0.853345\pi$
$230$	12.6678	−	13.0288i	0.835289	−	0.859094i
$231$	4.88681	+	1.58782i	0.321528	+	0.104471i
$232$	−16.2970			−1.06995
$233$	−0.144613	+	0.445074i	−0.00947394	+	0.0291578i	−0.955682	−	0.294402i	$-0.904880\pi$
$233$	−0.144613	+	0.445074i	−0.00947394	+	0.0291578i	0.946208	+	0.323560i	$0.104880\pi$
$234$	32.7407	−	23.7875i	2.14033	−	1.55504i
$235$	−7.33322	+	7.54220i	−0.478366	+	0.491999i
$236$	−18.1139	−	13.1605i	−1.17911	−	0.856677i
$237$	3.11854	+	4.29230i	0.202571	+	0.278815i
$238$	4.64369	−	17.3601i	0.301006	−	1.12529i
$239$	9.53619	+	6.92845i	0.616845	+	0.448164i	0.851818	−	0.523838i	$-0.175500\pi$
$239$	9.53619	+	6.92845i	0.616845	+	0.448164i	−0.234973	+	0.972002i	$0.575500\pi$
$240$	2.09187	+	0.301260i	0.135029	+	0.0194462i
$241$	11.6789	+	16.0747i	0.752307	+	1.03546i	0.997815	+	0.0660673i	$0.0210452\pi$
$241$	11.6789	+	16.0747i	0.752307	+	1.03546i	−0.245508	+	0.969395i	$0.578955\pi$
$242$	47.5693	+	15.4562i	3.05787	+	0.993562i
$243$	11.9180			0.764539
$244$	−3.54028	−	1.15031i	−0.226643	−	0.0736408i
$245$	7.17095	−	3.78160i	0.458135	−	0.241597i
$246$	−0.535960	−	1.64951i	−0.0341715	−	0.105169i
$247$	−16.3323	+	5.30667i	−1.03920	+	0.337655i
$248$	10.3387	+	7.51148i	0.656506	+	0.476980i
$249$		−	4.37906i		−	0.277512i
$250$	−19.5310	−	17.9504i	−1.23525	−	1.13528i
$251$	−15.2225			−0.960835			−0.480417	−	0.877040i	$-0.659515\pi$
$251$	−15.2225			−0.960835			−0.480417	+	0.877040i	$0.659515\pi$
$252$	−14.8660	−	10.8008i	−0.936470	−	0.680385i
$253$	18.4508	−	5.99503i	1.15999	−	0.376905i
$254$	−10.8143	−	33.2830i	−0.678550	−	2.08836i
$255$	4.18580	+	1.79150i	0.262125	+	0.112188i
$256$	−8.10539	+	24.9458i	−0.506587	+	1.55911i
$257$		−	15.6890i		−	0.978650i	−0.872101	−	0.489325i	$-0.837243\pi$
$257$		−	15.6890i		−	0.978650i	0.872101	−	0.489325i	$-0.162757\pi$
$258$	−0.664529	+	2.04521i	−0.0413718	+	0.127329i
$259$	4.32574	−	3.14283i	0.268788	−	0.195286i
$260$	7.15935	−	49.7126i	0.444004	−	3.08305i
$261$	−6.82900	+	9.39931i	−0.422704	+	0.581803i
$262$	19.5634	−	14.2137i	1.20863	−	0.878123i
$263$	−18.1350	−	24.9607i	−1.11825	−	1.53914i	−0.808666	−	0.588268i	$-0.799810\pi$
$263$	−18.1350	−	24.9607i	−1.11825	−	1.53914i	−0.309584	−	0.950872i	$-0.600190\pi$
$264$	8.74865	+	6.35627i	0.538442	+	0.391201i
$265$	−13.3643	+	13.7452i	−0.820962	+	0.844359i
$266$	7.10871	+	9.78430i	0.435863	+	0.599914i
$267$	−0.382192	+	1.17627i	−0.0233898	+	0.0719863i
$268$			12.6196i			0.770863i
$269$	−15.6676	−	5.09071i	−0.955269	−	0.310386i	−0.210414	−	0.977612i	$-0.567481\pi$
$269$	−15.6676	−	5.09071i	−0.955269	−	0.310386i	−0.744855	+	0.667226i	$0.767481\pi$
$270$	10.5133	−	10.8129i	0.639817	−	0.658052i
$271$	0.231585	+	0.712745i	0.0140678	+	0.0432962i	0.957844	−	0.287289i	$-0.0927540\pi$
$271$	0.231585	+	0.712745i	0.0140678	+	0.0432962i	−0.943776	+	0.330585i	$0.892754\pi$
$272$	4.29497	−	6.61986i	0.260421	−	0.401388i
$273$	3.30002	−	4.54208i	0.199726	−	0.274899i
$274$	−40.0783			−2.42122
$275$	−9.50455	−	26.6774i	−0.573146	−	1.60871i
$276$	6.13929			0.369542
$277$	11.6172	+	8.44037i	0.698008	+	0.507133i	0.879283	−	0.476300i	$-0.158022\pi$
$277$	11.6172	+	8.44037i	0.698008	+	0.507133i	−0.181275	+	0.983432i	$0.558022\pi$
$278$	15.6250	+	48.0889i	0.937127	+	2.88418i
$279$	8.66451	−	2.81527i	0.518731	−	0.168546i
$280$	−15.6481	+	2.70428i	−0.935155	+	0.161612i
$281$	−1.04632	+	3.22025i	−0.0624185	+	0.192104i	−0.977403	−	0.211385i	$-0.932203\pi$
$281$	−1.04632	+	3.22025i	−0.0624185	+	0.192104i	0.914984	+	0.403489i	$0.132203\pi$
$282$	−5.51237			−0.328257
$283$	−5.92302	+	18.2292i	−0.352087	+	1.08361i	0.605592	+	0.795775i	$0.292936\pi$
$283$	−5.92302	+	18.2292i	−0.352087	+	1.08361i	−0.957679	+	0.287838i	$0.907064\pi$
$284$	29.0234	+	39.9473i	1.72222	+	2.37044i
$285$	−2.71041	+	1.42934i	−0.160551	+	0.0846665i
$286$	48.8849	−	67.2844i	2.89063	−	3.97861i
$287$	1.59825	+	2.19980i	0.0943415	+	0.129850i
$288$	5.16967	+	7.11544i	0.304626	+	0.419281i
$289$	12.6238	−	11.3860i	0.742574	−	0.669764i
$290$	3.80853	+	22.0378i	0.223645	+	1.29410i
$291$	0.196567	−	0.142814i	0.0115230	−	0.00837193i
$292$	−14.8921	+	45.8331i	−0.871492	+	2.68218i
$293$			8.56093i			0.500135i	0.968228	+	0.250067i	$0.0804527\pi$
$293$			8.56093i			0.500135i	−0.968228	+	0.250067i	$0.919547\pi$
$294$	4.04023	+	1.31275i	0.235631	+	0.0765612i
$295$	−6.08923	+	12.3776i	−0.354529	+	0.720653i
$296$	10.7022	−	3.47735i	0.622053	−	0.202117i
$297$	15.3127	−	4.97541i	0.888535	−	0.288703i
$298$	−10.4890	+	14.4369i	−0.607612	+	0.836306i
$299$		−	21.1976i		−	1.22589i
$300$	−0.251767	−	8.95840i	−0.0145358	−	0.517214i
$301$		−	3.37138i		−	0.194323i
$302$	−17.6927	+	24.3519i	−1.01810	+	1.40130i
$303$	−1.40889	−	4.33613i	−0.0809388	−	0.249104i
$304$	1.64109	+	5.05076i	0.0941231	+	0.289681i
$305$	−0.326910	+	2.26997i	−0.0187188	+	0.129978i
$306$	−9.67308	−	25.1672i	−0.552973	−	1.43871i
$307$		−	33.0695i		−	1.88738i	−0.330834	−	0.943689i	$-0.607330\pi$
$307$		−	33.0695i		−	1.88738i	0.330834	−	0.943689i	$-0.392670\pi$
$308$	−35.9144	−	11.6693i	−2.04641	−	0.664920i
$309$	3.99653	+	5.50075i	0.227354	+	0.312927i
$310$	7.74138	−	15.7360i	0.439681	−	0.893743i
$311$	−17.1966	+	23.6690i	−0.975127	+	1.34215i	−0.0357138	+	0.999362i	$0.511370\pi$
$311$	−17.1966	+	23.6690i	−0.975127	+	1.34215i	−0.939414	+	0.342786i	$0.888630\pi$
$312$	9.55915	−	6.94513i	0.541181	−	0.393191i
$313$	−23.1607	+	16.8272i	−1.30912	+	0.951131i	−0.309119	+	0.951023i	$0.600034\pi$
$313$	−23.1607	+	16.8272i	−1.30912	+	0.951131i	−1.00000		0.000107577i	$0.999966\pi$
$314$	−18.3045	−	13.2990i	−1.03299	−	0.750508i
$315$	−4.99741	+	10.1583i	−0.281572	+	0.572353i
$316$	−22.9189	−	31.5452i	−1.28929	−	1.77456i
$317$	3.74922	−	11.5389i	0.210577	−	0.648090i	−0.788861	−	0.614572i	$-0.789329\pi$
$317$	3.74922	−	11.5389i	0.210577	−	0.648090i	0.999438	−	0.0335180i	$-0.0106711\pi$
$318$	−10.0459			−0.563348
$319$	−7.37814	+	22.7076i	−0.413096	+	1.27138i
$320$	25.2291	+	3.63336i	1.41035	+	0.203111i
$321$	0.803276	+	2.47223i	0.0448345	+	0.137986i
$322$	−14.1980	+	4.61320i	−0.791222	+	0.257084i
$323$	0.603644	+	11.4250i	0.0335876	+	0.635706i
$324$	−24.9142			−1.38412
$325$	−30.9314	+	0.869297i	−1.71577	+	0.0482199i
$326$		−	23.5874i		−	1.30639i
$327$	−5.89253	+	8.11037i	−0.325857	+	0.448504i
$328$	1.76836	+	5.44247i	0.0976416	+	0.300510i
$329$	8.21902	−	2.67052i	0.453129	−	0.147231i
$330$	6.55081	−	13.3159i	0.360610	−	0.733015i
$331$	−3.15958	+	9.72419i	−0.173666	+	0.534490i	−0.999570	−	0.0293214i	$-0.990665\pi$
$331$	−3.15958	+	9.72419i	−0.173666	+	0.534490i	0.825904	+	0.563811i	$0.190665\pi$
$332$			32.1829i			1.76626i
$333$	2.47902	−	7.62964i	0.135849	−	0.418102i
$334$	−16.7233	−	23.0176i	−0.915057	−	1.25947i
$335$	7.66128	−	1.32401i	0.418581	−	0.0723384i
$336$	−1.40464	−	1.02053i	−0.0766296	−	0.0556747i
$337$	−10.1417	+	7.36836i	−0.552453	+	0.401380i	−0.828689	−	0.559709i	$-0.810913\pi$
$337$	−10.1417	+	7.36836i	−0.552453	+	0.401380i	0.276236	+	0.961090i	$0.410913\pi$
$338$	−35.2840	−	48.5642i	−1.91919	−	2.64155i
$339$	7.55293	+	5.48752i	0.410219	+	0.298041i
$340$	−30.7625	−	13.1662i	−1.66833	−	0.714037i
$341$	15.1468	−	11.0048i	0.820246	−	0.595944i
$342$	17.2573	+	5.60725i	0.933170	+	0.303205i
$343$	−19.5188			−1.05392
$344$	2.19257	−	6.74804i	0.118216	−	0.363830i
$345$	−0.644117	−	3.72713i	−0.0346781	−	0.200662i
$346$	7.90207	−	2.56754i	0.424818	−	0.138032i
$347$	−7.60056	−	23.3921i	−0.408020	−	1.25576i	−0.918347	−	0.395775i	$-0.870476\pi$
$347$	−7.60056	−	23.3921i	−0.408020	−	1.25576i	0.510328	−	0.859980i	$-0.329524\pi$
$348$	−4.44112	+	6.11267i	−0.238069	+	0.327674i
$349$	28.7364			1.53822			0.769112	−	0.639114i	$-0.220699\pi$
$349$	28.7364			1.53822			0.769112	+	0.639114i	$0.220699\pi$
$350$	7.31379	+	20.5284i	0.390938	+	1.09729i
$351$		−	17.5924i		−	0.939013i
$352$	14.6227	+	10.6240i	0.779393	+	0.566262i
$353$	−2.23064	+	0.724777i	−0.118725	+	0.0385760i	−0.367777	−	0.929914i	$-0.619881\pi$
$353$	−2.23064	+	0.724777i	−0.118725	+	0.0385760i	0.249052	+	0.968490i	$0.419881\pi$
$354$	−6.87463	+	2.23370i	−0.365382	+	0.118720i
$355$	21.2068	−	21.8112i	1.12554	−	1.15762i
$356$	2.80883	−	8.64468i	0.148868	−	0.458167i
$357$	−2.35516	−	2.90585i	−0.124648	−	0.153794i
$358$	−7.53714	−	2.44896i	−0.398350	−	0.129432i
$359$	−24.5241	+	17.8178i	−1.29433	+	0.940387i	−0.999883	−	0.0152803i	$-0.995136\pi$
$359$	−24.5241	+	17.8178i	−1.29433	+	0.940387i	−0.294449	+	0.955667i	$0.595136\pi$
$360$	−16.6091	+	17.0824i	−0.875375	+	0.900322i
$361$	9.14210	+	6.64212i	0.481163	+	0.349585i
$362$	11.5284	−	8.37588i	0.605920	−	0.440227i
$363$	8.42249	−	6.11929i	0.442066	−	0.321180i
$364$	−24.2527	+	33.3809i	−1.27119	+	1.74964i
$365$	29.3875	+	4.23223i	1.53821	+	0.221525i
$366$	−0.972249	+	0.706380i	−0.0508202	+	0.0369231i
$367$	−1.29660	+	3.99052i	−0.0676819	+	0.208303i	−0.979177	−	0.203007i	$-0.934929\pi$
$367$	−1.29660	+	3.99052i	−0.0676819	+	0.208303i	0.911495	+	0.411310i	$0.134929\pi$
$368$	−6.55539			−0.341723
$369$	3.87996	+	1.26067i	0.201982	+	0.0656281i
$370$	−7.20334	−	13.6595i	−0.374484	−	0.710125i
$371$	14.9786	−	4.86685i	0.777651	−	0.252674i
$372$	5.63481	−	1.83086i	0.292151	−	0.0949257i
$373$	13.4309	−	18.4861i	0.695428	−	0.957174i	−0.304562	−	0.952493i	$-0.598510\pi$
$373$	13.4309	−	18.4861i	0.695428	−	0.957174i	0.999989	−	0.00468122i	$-0.00149008\pi$
$374$	−34.8883	−	43.0459i	−1.80403	−	2.22585i
$375$	−5.41219	+	1.09274i	−0.279484	+	0.0564287i
$376$	18.1877			0.937960
$377$	21.1057	+	15.3342i	1.08700	+	0.789752i
$378$	−11.7832	+	3.82860i	−0.606063	+	0.196922i
$379$	32.4100	−	10.5307i	1.66479	−	0.540924i	0.682924	−	0.730489i	$-0.260708\pi$
$379$	32.4100	−	10.5307i	1.66479	−	0.540924i	0.981868	+	0.189565i	$0.0607079\pi$
$380$	19.9195	−	10.5046i	1.02185	−	0.538872i
$381$	−6.92764	−	2.25093i	−0.354914	−	0.115318i
$382$		−	3.71826i		−	0.190243i
$383$	25.1986	+	8.18752i	1.28759	+	0.418363i	0.871247	−	0.490845i	$-0.163312\pi$
$383$	25.1986	+	8.18752i	1.28759	+	0.418363i	0.416342	+	0.909208i	$0.363312\pi$
$384$	5.99826	+	8.25589i	0.306097	+	0.421307i
$385$	−3.31634	+	23.0278i	−0.169016	+	1.17360i
$386$	−0.249004	+	0.342724i	−0.0126740	+	0.0174442i
$387$	−2.97318	−	4.09223i	−0.151135	−	0.208020i
$388$	−1.44462	+	1.04958i	−0.0733396	+	0.0532843i
$389$	5.75689	+	4.18263i	0.291886	+	0.212068i	0.724085	−	0.689711i	$-0.242262\pi$
$389$	5.75689	+	4.18263i	0.291886	+	0.212068i	−0.432199	+	0.901778i	$0.642262\pi$
$390$	−11.6256	−	11.3034i	−0.588683	−	0.572371i
$391$	−13.6428	−	3.64935i	−0.689947	−	0.184556i
$392$	−13.3305	−	4.33134i	−0.673291	−	0.218766i
$393$		−	5.03326i		−	0.253894i
$394$	28.3877	+	9.22372i	1.43015	+	0.464684i
$395$	−16.7464	+	17.2236i	−0.842601	+	0.866614i
$396$	−53.8845	+	17.5081i	−2.70780	+	0.879817i
$397$	1.76792	+	5.44110i	0.0887294	+	0.273081i	0.985569	−	0.169275i	$-0.0541427\pi$
$397$	1.76792	+	5.44110i	0.0887294	+	0.273081i	−0.896839	+	0.442356i	$0.854143\pi$
$398$	−18.3519	−	13.3335i	−0.919899	−	0.668346i
$399$	2.51730			0.126022
$400$	0.268831	+	9.56558i	0.0134415	+	0.478279i
$401$		−	1.98245i		−	0.0989990i	−0.998774	−	0.0494995i	$-0.984237\pi$
$401$		−	1.98245i		−	0.0989990i	0.998774	−	0.0494995i	$-0.0157626\pi$
$402$	3.29603	+	2.39470i	0.164391	+	0.119437i
$403$	−6.32157	−	19.4558i	−0.314900	−	0.969161i
$404$	10.3543	+	31.8673i	0.515147	+	1.58546i
$405$	2.61392	+	15.1253i	0.129887	+	0.751581i
$406$	5.67750	−	17.4736i	0.281770	−	0.867198i
$407$		−	16.4863i		−	0.817196i
$408$	−2.82420	−	7.34794i	−0.139819	−	0.363777i
$409$	11.8804	−	8.63163i	0.587449	−	0.426807i	−0.253953	−	0.967217i	$-0.581731\pi$
$409$	11.8804	−	8.63163i	0.587449	−	0.426807i	0.841402	+	0.540410i	$0.181731\pi$
$410$	6.94638	−	3.66317i	0.343057	−	0.180911i
$411$	−4.90332	+	6.74884i	−0.241863	+	0.332896i
$412$	−29.3715	−	40.4264i	−1.44703	−	1.99167i
$413$	9.16803	−	6.66096i	0.451129	−	0.327765i
$414$	−13.1654	+	18.1206i	−0.647044	+	0.890579i
$415$	19.5381	−	3.37653i	0.959086	−	0.165748i
$416$	15.9774	−	11.6083i	0.783356	−	0.569142i
$417$	10.0094	+	3.25224i	0.490161	+	0.159263i
$418$	37.2901			1.82392
$419$	−5.02206	−	1.63177i	−0.245344	−	0.0797171i	0.183764	−	0.982970i	$-0.441172\pi$
$419$	−5.02206	−	1.63177i	−0.245344	−	0.0797171i	−0.429108	+	0.903253i	$0.641172\pi$
$420$	−3.24997	+	6.60624i	−0.158582	+	0.322352i
$421$	−9.25378	−	28.4802i	−0.451002	−	1.38804i	−0.875766	−	0.482736i	$-0.839643\pi$
$421$	−9.25378	−	28.4802i	−0.451002	−	1.38804i	0.424764	−	0.905304i	$-0.360357\pi$
$422$	−5.00742	−	15.4112i	−0.243757	−	0.750208i
$423$	7.62128	−	10.4898i	0.370559	−	0.510031i
$424$	33.1459			1.60971
$425$	−4.76562	+	20.0571i	−0.231167	+	0.972914i
$426$	15.9411			0.772350
$427$	1.10742	−	1.52424i	0.0535920	−	0.0737630i
$428$	−5.90348	−	18.1691i	−0.285356	−	0.878234i
$429$	−5.34935	−	16.4636i	−0.258269	−	0.794871i
$430$	−9.63751	−	1.38794i	−0.464762	−	0.0669326i
$431$	−4.99934	−	1.62438i	−0.240810	−	0.0782438i	0.186126	−	0.982526i	$-0.440407\pi$
$431$	−4.99934	−	1.62438i	−0.240810	−	0.0782438i	−0.426935	+	0.904282i	$0.640407\pi$
$432$	−5.44047			−0.261755
$433$	12.4097	+	4.03215i	0.596371	+	0.193773i	0.591621	−	0.806216i	$-0.298488\pi$
$433$	12.4097	+	4.03215i	0.596371	+	0.193773i	0.00474994	+	0.999989i	$0.498488\pi$
$434$	−11.6555	+	8.46824i	−0.559483	+	0.406489i
$435$	4.17692	+	2.05486i	0.200268	+	0.0985228i
$436$	43.3057	−	59.6052i	2.07397	−	2.85457i
$437$	7.68922	−	5.58654i	0.367825	−	0.267241i
$438$	9.14492	+	12.5869i	0.436961	+	0.601425i
$439$	−17.4308	+	23.9914i	−0.831926	+	1.14505i	0.155635	+	0.987815i	$0.450258\pi$
$439$	−17.4308	+	23.9914i	−0.831926	+	1.14505i	−0.987561	+	0.157234i	$0.949742\pi$
$440$	−21.6140	+	43.9349i	−1.03041	+	2.09452i
$441$	−8.08404	+	5.87340i	−0.384954	+	0.279685i
$442$	−56.5117	+	21.7205i	−2.68799	+	1.03314i
$443$			5.82302i			0.276660i	0.990386	+	0.138330i	$0.0441735\pi$
$443$			5.82302i			0.276660i	−0.990386	+	0.138330i	$0.955827\pi$
$444$	1.61219	−	4.96180i	0.0765109	−	0.235476i
$445$	−5.54284	−	0.798251i	−0.262756	−	0.0378407i
$446$	−3.49648	−	10.7611i	−0.165563	−	0.509551i
$447$	1.14778	+	3.53252i	0.0542883	+	0.167082i
$448$	−16.9408	−	12.3082i	−0.800376	−	0.581508i
$449$			41.4716i			1.95717i	0.205848	+	0.978584i	$0.434005\pi$
$449$			41.4716i			1.95717i	−0.205848	+	0.978584i	$0.565995\pi$
$450$	26.9813	+	18.4677i	1.27191	+	0.870577i
$451$	8.38391			0.394783
$452$	−55.5084	−	40.3292i	−2.61090	−	1.89693i
$453$	1.93607	+	5.95860i	0.0909643	+	0.279959i
$454$	37.9145	−	12.3192i	1.77942	−	0.578167i
$455$	22.8099	+	11.2215i	1.06935	+	0.526070i
$456$	5.03854	+	1.63712i	0.235951	+	0.0766653i
$457$			17.3542i			0.811796i	0.913918	+	0.405898i	$0.133041\pi$
$457$			17.3542i			0.811796i	−0.913918	+	0.405898i	$0.866959\pi$
$458$	−9.97424	−	3.24083i	−0.466066	−	0.151434i
$459$	−11.3225	−	3.02868i	−0.528488	−	0.141367i
$460$	4.73378	+	27.3917i	0.220714	+	1.27714i
$461$	3.74798	+	2.72307i	0.174561	+	0.126826i	0.671635	−	0.740882i	$-0.265592\pi$
$461$	3.74798	+	2.72307i	0.174561	+	0.126826i	−0.497074	+	0.867708i	$0.665592\pi$
$462$	−9.86299	+	7.16588i	−0.458868	+	0.333387i
$463$	11.4754	+	15.7946i	0.533308	+	0.734035i	0.987630	−	0.156802i	$-0.0501185\pi$
$463$	11.4754	+	15.7946i	0.533308	+	0.734035i	−0.454322	+	0.890837i	$0.650118\pi$
$464$	4.74212	−	6.52697i	0.220147	−	0.303007i
$465$	−1.70269	−	3.22878i	−0.0789606	−	0.149731i
$466$	−0.652645	−	0.898288i	−0.0302332	−	0.0416124i
$467$	−3.30937	−	1.07528i	−0.153140	−	0.0497581i	0.231444	−	0.972848i	$-0.425655\pi$
$467$	−3.30937	−	1.07528i	−0.153140	−	0.0497581i	−0.384584	+	0.923090i	$0.625655\pi$
$468$			61.9065i			2.86163i
$469$	−6.07456	−	1.97374i	−0.280497	−	0.0911391i
$470$	−4.25038	−	24.5945i	−0.196056	−	1.13446i
$471$	−4.47889	+	1.45528i	−0.206376	+	0.0670557i
$472$	22.6824	−	7.36996i	1.04404	−	0.339230i
$473$	−8.40981	−	6.11008i	−0.386683	−	0.280942i
$474$	−12.5882			−0.578196
$475$	−8.46717	−	10.9909i	−0.388500	−	0.504299i
$476$	17.3087	+	21.3558i	0.793342	+	0.978843i
$477$	13.8893	−	19.1169i	0.635946	−	0.875305i
$478$	−26.5984	+	8.64234i	−1.21658	+	0.395292i
$479$	6.70481	−	2.17853i	0.306351	−	0.0995394i	−0.151807	−	0.988410i	$-0.548509\pi$
$479$	6.70481	−	2.17853i	0.306351	−	0.0995394i	0.458158	+	0.888871i	$0.348509\pi$
$480$	2.45654	−	2.52655i	0.112125	−	0.115321i
$481$	−17.1320	−	5.56653i	−0.781152	−	0.253812i
$482$	−47.1430			−2.14730
$483$	−0.960206	+	2.95521i	−0.0436909	+	0.134467i
$484$	−61.8990	+	44.9723i	−2.81359	+	2.04419i
$485$	0.788761	+	0.766905i	0.0358158	+	0.0348233i
$486$	−16.6209	+	22.8766i	−0.753937	+	1.03771i
$487$	−30.3284	+	22.0349i	−1.37431	+	0.998496i	−0.376925	+	0.926244i	$0.623019\pi$
$487$	−30.3284	+	22.0349i	−1.37431	+	0.998496i	−0.997386	+	0.0722521i	$0.976981\pi$
$488$	3.20787	−	2.33066i	0.145214	−	0.105504i
$489$	−3.97192	−	2.88577i	−0.179617	−	0.130499i
$490$	−2.74183	+	19.0385i	−0.123863	+	0.860072i
$491$	3.01312	−	2.18916i	0.135980	−	0.0987953i	−0.517716	−	0.855553i	$-0.673218\pi$
$491$	3.01312	−	2.18916i	0.135980	−	0.0987953i	0.653696	+	0.756757i	$0.273218\pi$
$492$	2.52326	+	0.819856i	0.113757	+	0.0369620i
$493$	13.5026	−	10.9437i	0.608128	−	0.492882i
$494$	12.5908	−	38.7506i	0.566488	−	1.74347i
$495$	16.2825	+	30.8761i	0.731845	+	1.38778i
$496$	−6.01672	+	1.95495i	−0.270159	+	0.0877799i
$497$	−23.7684	+	7.72283i	−1.06616	+	0.346416i
$498$	8.40564	+	6.10706i	0.376666	+	0.273664i
$499$			15.9917i			0.715889i	0.933743	+	0.357944i	$0.116522\pi$
$499$			15.9917i			0.715889i	−0.933743	+	0.357944i	$0.883478\pi$
$500$	39.7756	−	8.03080i	1.77882	−	0.359148i
$501$	−5.92195			−0.264573
$502$	21.2293	−	29.2197i	0.947511	−	1.30414i
$503$	1.87813	+	5.78029i	0.0837417	+	0.257731i	0.984157	−	0.177302i	$-0.0567369\pi$
$503$	1.87813	+	5.78029i	0.0837417	+	0.257731i	−0.900415	+	0.435032i	$0.856737\pi$
$504$	18.6153	−	6.04849i	0.829193	−	0.269421i
$505$	18.2602	−	9.62949i	0.812566	−	0.428507i
$506$	−14.2241	+	43.7772i	−0.632337	+	1.94613i
$507$	−12.4946			−0.554903
$508$	50.9130	+	16.5426i	2.25890	+	0.733961i
$509$	11.7236	−	8.51767i	0.519638	−	0.377539i	−0.296830	−	0.954930i	$-0.595929\pi$
$509$	11.7236	−	8.51767i	0.519638	−	0.377539i	0.816467	+	0.577391i	$0.195929\pi$
$510$	−9.27633	+	5.53624i	−0.410763	+	0.245149i
$511$	−19.7331	−	14.3369i	−0.872939	−	0.634227i
$512$	−12.2880	−	16.9130i	−0.543059	−	0.747457i
$513$	6.38145	−	4.63640i	0.281748	−	0.204702i
$514$	30.1151	+	21.8799i	1.32832	+	0.965080i
$515$	−21.4611	+	22.0727i	−0.945689	+	0.972640i
$516$	−1.93355	−	2.66131i	−0.0851199	−	0.117158i
$517$	8.23413	−	25.3420i	0.362136	−	1.11454i
$518$			12.6863i			0.557403i
$519$	0.534416	−	1.64476i	0.0234582	−	0.0721971i
$520$	38.3578	+	37.2949i	1.68210	+	1.63549i
$521$	−14.2672	+	4.63569i	−0.625056	+	0.203093i	−0.604384	−	0.796693i	$-0.706581\pi$
$521$	−14.2672	+	4.63569i	−0.625056	+	0.203093i	−0.0206724	+	0.999786i	$0.506581\pi$
$522$	−8.51830	−	26.2166i	−0.372836	−	1.14747i
$523$	−10.3296	+	14.2175i	−0.451682	+	0.621687i	−0.972758	−	0.231823i	$-0.925531\pi$
$523$	−10.3296	+	14.2175i	−0.451682	+	0.621687i	0.521076	+	0.853510i	$0.325531\pi$
$524$			36.9907i			1.61595i
$525$	4.35160	+	1.27993i	0.189919	+	0.0558609i
$526$	73.2032			3.19181
$527$	−13.6101	+	0.719090i	−0.592863	+	0.0313241i
$528$	−5.09139	+	1.65429i	−0.221574	+	0.0719938i
$529$	−3.48200	−	10.7165i	−0.151391	−	0.465935i
$530$	−7.74604	−	44.8219i	−0.336467	−	1.94694i
$531$	5.25407	−	16.1704i	0.228007	−	0.701734i
$532$	−18.5003			−0.802088
$533$	2.83079	−	8.71227i	0.122615	−	0.377370i
$534$	−1.72484	−	2.37404i	−0.0746413	−	0.102735i
$535$	−10.4110	+	5.49022i	−0.450106	+	0.237363i
$536$	−10.8750	−	7.90117i	−0.469730	−	0.341279i
$537$	−1.33450	+	0.969574i	−0.0575881	+	0.0418402i
$538$	31.6217	−	22.9745i	1.36331	−	0.990502i
$539$	−12.0702	+	16.6132i	−0.519901	+	0.715583i
$540$	3.92867	+	22.7330i	0.169063	+	0.978271i
$541$	13.4755	+	18.5475i	0.579359	+	0.797419i	0.993625	−	0.112737i	$-0.0359618\pi$
$541$	13.4755	+	18.5475i	0.579359	+	0.797419i	−0.414266	+	0.910156i	$0.635962\pi$
$542$	−1.69109	−	0.549468i	−0.0726385	−	0.0236017i
$543$		−	2.96602i		−	0.127284i
$544$	−4.72044	−	12.2815i	−0.202387	−	0.526566i
$545$	−40.7295	−	20.0371i	−1.74466	−	0.858294i
$546$	4.11635	+	12.6688i	0.176163	+	0.542175i
$547$	5.62351	+	17.3074i	0.240444	+	0.740010i	0.996353	+	0.0853328i	$0.0271954\pi$
$547$	5.62351	+	17.3074i	0.240444	+	0.740010i	−0.755909	+	0.654677i	$0.772805\pi$
$548$	36.0358	−	49.5990i	1.53937	−	2.11876i
$549$		−	2.82677i		−	0.120644i
$550$	64.4626	+	18.9604i	2.74869	+	0.808473i
$551$			11.6971i			0.498315i
$552$	−3.84384	+	5.29059i	−0.163605	+	0.225183i
$553$	18.7692	−	6.09849i	0.798149	−	0.259334i
$554$	−32.4027	+	10.5283i	−1.37666	+	0.447303i
$555$	−3.18143	−	0.458173i	−0.135044	−	0.0194484i
$556$	−73.5615	−	23.9016i	−3.11970	−	1.01365i
$557$			21.9560i			0.930304i	0.885231	+	0.465152i	$0.154000\pi$
$557$			21.9560i			0.930304i	−0.885231	+	0.465152i	$0.846000\pi$
$558$	−6.67963	+	20.5578i	−0.282771	+	0.870280i
$559$	−9.18892	+	6.67614i	−0.388650	+	0.282371i
$560$	3.47024	−	7.05399i	0.146645	−	0.298086i
$561$	−11.5169	+	0.608499i	−0.486245	+	0.0256908i
$562$	−4.72209	−	6.49940i	−0.199189	−	0.274161i
$563$	10.3210	+	14.2056i	0.434979	+	0.598697i	0.969087	−	0.246719i	$-0.0793526\pi$
$563$	10.3210	+	14.2056i	0.434979	+	0.598697i	−0.534108	+	0.845416i	$0.679353\pi$
$564$	4.95636	−	6.82184i	0.208700	−	0.287251i
$565$	−18.6599	+	37.9301i	−0.785028	+	1.59573i
$566$	−26.7308	−	36.7918i	−1.12358	−	1.54647i
$567$	3.89666	−	11.9927i	0.163644	−	0.503646i
$568$	−52.5967			−2.20691
$569$	11.2660	−	34.6731i	0.472295	−	1.45357i	−0.377277	−	0.926101i	$-0.623139\pi$
$569$	11.2660	−	34.6731i	0.472295	−	1.45357i	0.849572	−	0.527473i	$-0.176861\pi$
$570$	1.03633	−	7.19601i	0.0434072	−	0.301408i
$571$	27.0728	−	8.79647i	1.13296	−	0.368121i	0.318260	−	0.948004i	$-0.396902\pi$
$571$	27.0728	−	8.79647i	1.13296	−	0.368121i	0.814700	+	0.579883i	$0.196902\pi$
$572$	39.3138	+	120.995i	1.64379	+	5.05907i
$573$	−0.626123	−	0.454905i	−0.0261567	−	0.0190039i
$574$	−6.45145			−0.269278
$575$	16.1327	−	5.74771i	0.672780	−	0.239696i
$576$	−31.4175			−1.30906
$577$	18.1062	−	24.9210i	0.753770	−	1.03748i	−0.243937	−	0.969791i	$-0.578439\pi$
$577$	18.1062	−	24.9210i	0.753770	−	1.03748i	0.997707	−	0.0676844i	$-0.0215611\pi$
$578$	4.25034	+	40.1103i	0.176791	+	1.66837i
$579$	0.0272478	+	0.0838602i	0.00113238	+	0.00348511i
$580$	−30.6973	−	15.1017i	−1.27464	−	0.627063i
$581$	−15.4916	−	5.03351i	−0.642698	−	0.208825i
$582$			0.576481i			0.0238959i
$583$	15.0061	−	46.1842i	0.621491	−	1.91275i
$584$	−30.1731	−	41.5297i	−1.24857	−	1.71851i
$585$	37.5831	−	6.49505i	1.55387	−	0.268537i
$586$	−16.4328	−	11.9391i	−0.678831	−	0.493199i
$587$	−11.2222	−	15.4460i	−0.463188	−	0.637523i	0.511978	−	0.858998i	$-0.328913\pi$
$587$	−11.2222	−	15.4460i	−0.463188	−	0.637523i	−0.975166	+	0.221475i	$0.928913\pi$
$588$	−5.25730	+	3.81966i	−0.216808	+	0.157520i
$589$	5.39135	−	7.42056i	0.222147	−	0.305759i
$590$	−15.2669	−	28.9502i	−0.628527	−	1.19186i
$591$	5.02624	−	3.65178i	0.206752	−	0.150214i
$592$	−1.72145	+	5.29809i	−0.0707513	+	0.217750i
$593$			35.4210i			1.45457i	0.686337	+	0.727284i	$0.259217\pi$
$593$			35.4210i			1.45457i	−0.686337	+	0.727284i	$0.740783\pi$
$594$	−11.8049	+	36.3316i	−0.484359	+	1.49070i
$595$	11.1490	−	12.7486i	0.457066	−	0.522642i
$596$	−8.43536	−	25.9614i	−0.345526	−	1.06342i
$597$	−4.49048	+	1.45905i	−0.183783	+	0.0597147i
$598$	40.6890	+	29.5623i	1.66390	+	1.20889i
$599$	−9.15527			−0.374074			−0.187037	−	0.982353i	$-0.559888\pi$
$599$	−9.15527			−0.374074			−0.187037	+	0.982353i	$0.559888\pi$
$600$	7.87762	+	5.39194i	0.321602	+	0.220125i
$601$			4.04517i			0.165006i	0.996591	+	0.0825030i	$0.0262914\pi$
$601$			4.04517i			0.165006i	−0.996591	+	0.0825030i	$0.973709\pi$
$602$	6.47138	+	4.70173i	0.263754	+	0.191628i
$603$	−9.11403	+	2.96133i	−0.371152	+	0.120595i
$604$	−14.2286	−	43.7913i	−0.578955	−	1.78184i
$605$	33.7967	+	32.8602i	1.37403	+	1.33596i
$606$	10.2881	+	3.34280i	0.417925	+	0.135792i
$607$	−1.30899			−0.0531303			−0.0265651	−	0.999647i	$-0.508457\pi$
$607$	−1.30899			−0.0531303			−0.0265651	+	0.999647i	$0.508457\pi$
$608$	8.42154	+	2.73632i	0.341539	+	0.110973i
$609$	−2.24779	−	3.09382i	−0.0910851	−	0.125368i
$610$	−3.90132	−	3.79322i	−0.157960	−	0.153583i
$611$	−23.5544	−	17.1132i	−0.952907	−	0.692328i
$612$	39.8430	+	10.6577i	1.61056	+	0.430812i
$613$	−11.7773	−	16.2100i	−0.475679	−	0.654716i	0.501988	−	0.864874i	$-0.332602\pi$
$613$	−11.7773	−	16.2100i	−0.475679	−	0.654716i	−0.977667	+	0.210158i	$0.932602\pi$
$614$	63.4772	+	46.1189i	2.56173	+	1.86121i
$615$	0.232998	−	1.61788i	0.00939538	−	0.0652390i
$616$	32.5423	−	23.6434i	1.31117	−	0.952619i
$617$	−3.43451	+	10.5703i	−0.138268	+	0.425546i	−0.996084	−	0.0884112i	$-0.971821\pi$
$617$	−3.43451	+	10.5703i	−0.138268	+	0.425546i	0.857816	+	0.513957i	$0.171821\pi$
$618$	−16.1323			−0.648936
$619$	26.9523	+	8.75732i	1.08330	+	0.351986i	0.795655	−	0.605750i	$-0.207127\pi$
$619$	26.9523	+	8.75732i	1.08330	+	0.351986i	0.287647	+	0.957736i	$0.407127\pi$
$620$	12.5135	+	23.7291i	0.502556	+	0.952984i
$621$	3.00879	+	9.26011i	0.120739	+	0.371595i
$622$	−21.4505	−	66.0178i	−0.860086	−	2.64707i
$623$	3.72190	+	2.70412i	0.149115	+	0.108338i
$624$			5.84936i			0.234162i
$625$	−9.04860	−	23.3050i	−0.361944	−	0.932200i
$626$		−	67.9244i		−	2.71480i
$627$	4.56220	−	6.27933i	0.182197	−	0.250772i
$628$	32.9165	−	10.6952i	1.31351	−	0.426785i
$629$	−6.53204	+	10.0678i	−0.260449	+	0.401431i
$630$	−12.5295	−	23.7593i	−0.499186	−	0.946593i
$631$	−1.43239	+	4.40845i	−0.0570226	+	0.175497i	−0.975511	−	0.219950i	$-0.929411\pi$
$631$	−1.43239	+	4.40845i	−0.0570226	+	0.175497i	0.918489	+	0.395448i	$0.129411\pi$
$632$	41.5341			1.65214
$633$	−3.20775	−	1.04226i	−0.127496	−	0.0414261i
$634$	16.9203	+	23.2888i	0.671992	+	0.924918i
$635$	4.70131	−	32.6446i	0.186566	−	1.29546i
$636$	9.03264	−	12.4324i	0.358167	−	0.492975i
$637$	13.1884	+	18.1523i	0.522545	+	0.719222i
$638$	−33.2978	−	45.8304i	−1.31827	−	1.81444i
$639$	−22.0398	+	30.3352i	−0.871882	+	1.20004i
$640$	−32.2103	+	33.1282i	−1.27322	+	1.30951i
$641$	25.7935	+	35.5017i	1.01878	+	1.40223i	0.913054	+	0.407838i	$0.133717\pi$
$641$	25.7935	+	35.5017i	1.01878	+	1.40223i	0.105728	+	0.994395i	$0.466283\pi$
$642$	−5.86571	−	1.90589i	−0.231501	−	0.0752193i
$643$	29.7483			1.17316			0.586579	−	0.809892i	$-0.300474\pi$
$643$	29.7483			1.17316			0.586579	+	0.809892i	$0.300474\pi$
$644$	7.05680	−	21.7186i	0.278077	−	0.855833i
$645$	−1.41280	+	1.45307i	−0.0556291	+	0.0572145i
$646$	−22.7723	−	14.7747i	−0.895963	−	0.581302i
$647$	19.7524	−	6.41794i	0.776546	−	0.252315i	0.106181	−	0.994347i	$-0.466138\pi$
$647$	19.7524	−	6.41794i	0.776546	−	0.252315i	0.670365	+	0.742032i	$0.266138\pi$
$648$	15.5989	−	21.4700i	0.612782	−	0.843422i
$649$		−	34.9413i		−	1.37157i
$650$	41.4685	−	60.5854i	1.62653	−	2.37636i
$651$			2.99873i			0.117529i
$652$	29.1907	+	21.2083i	1.14320	+	0.830580i
$653$	−5.60039	−	17.2362i	−0.219160	−	0.674506i	−0.998832	−	0.0483176i	$-0.984614\pi$
$653$	−5.60039	−	17.2362i	−0.219160	−	0.674506i	0.779672	−	0.626189i	$-0.215386\pi$
$654$	−7.35017	−	22.6215i	−0.287414	−	0.884570i
$655$	22.4569	−	3.88096i	0.877464	−	0.151642i
$656$	−2.69428	−	0.875424i	−0.105194	−	0.0341796i
$657$	−36.5959			−1.42774
$658$	−6.33619	+	19.5008i	−0.247010	+	0.760220i
$659$	3.01244	−	2.18867i	0.117348	−	0.0852584i	−0.527563	−	0.849516i	$-0.676894\pi$
$659$	3.01244	−	2.18867i	0.117348	−	0.0852584i	0.644911	+	0.764257i	$0.276894\pi$
$660$	10.5890	+	20.0797i	0.412178	+	0.781603i
$661$	27.1159	+	19.7009i	1.05469	+	0.766275i	0.973098	−	0.230391i	$-0.0740006\pi$
$661$	27.1159	+	19.7009i	1.05469	+	0.766275i	0.0815886	+	0.996666i	$0.474001\pi$
$662$	−14.2593	−	19.6262i	−0.554203	−	0.762795i
$663$	−3.25630	+	12.1734i	−0.126464	+	0.472777i
$664$	−27.7339	−	20.1499i	−1.07628	−	0.781966i
$665$	1.94099	+	11.2314i	0.0752685	+	0.435536i
$666$	11.1879	+	15.3988i	0.433522	+	0.596692i
$667$	−13.7320	−	4.46180i	−0.531705	−	0.172762i
$668$	43.5220			1.68391
$669$	−2.23984	−	0.727769i	−0.0865974	−	0.0281372i
$670$	−8.14301	+	16.5524i	−0.314592	+	0.639473i
$671$	−1.79514	−	5.52488i	−0.0693007	−	0.213286i
$672$	−2.75327	+	0.894593i	−0.106210	+	0.0345097i
$673$	−9.13231	−	6.63501i	−0.352025	−	0.255761i	0.397693	−	0.917518i	$-0.369811\pi$
$673$	−9.13231	−	6.63501i	−0.352025	−	0.255761i	−0.749718	+	0.661758i	$0.769811\pi$
$674$		−	29.7430i		−	1.14566i
$675$	13.3889	−	4.77015i	0.515339	−	0.183603i
$676$	91.8257			3.53176
$677$	−8.59060	−	6.24144i	−0.330164	−	0.239878i	0.410336	−	0.911934i	$-0.365411\pi$
$677$	−8.59060	−	6.24144i	−0.330164	−	0.239878i	−0.740500	+	0.672056i	$0.765411\pi$
$678$	−21.0667	+	6.84498i	−0.809061	+	0.262880i
$679$	−0.279282	−	0.859542i	−0.0107179	−	0.0329862i
$680$	30.6067	−	18.2665i	1.17371	−	0.700487i
$681$	2.56415	−	7.89165i	0.0982585	−	0.302409i
$682$			44.4218i			1.70100i
$683$	0.750481	−	2.30974i	0.0287163	−	0.0883798i	−0.935671	−	0.352873i	$-0.885205\pi$
$683$	0.750481	−	2.30974i	0.0287163	−	0.0883798i	0.964388	+	0.264493i	$0.0852047\pi$
$684$	−22.4559	+	16.3152i	−0.858623	+	0.623826i
$685$	−33.8921	−	16.6734i	−1.29495	−	0.637057i
$686$	27.2210	−	37.4665i	1.03930	−	1.43048i
$687$	−1.76601	+	1.28308i	−0.0673775	+	0.0489526i
$688$	2.06460	+	2.84168i	0.0787123	+	0.108338i
$689$	−42.9262	−	31.1877i	−1.63536	−	1.18816i
$690$	8.05255	+	3.96149i	0.306555	+	0.150811i
$691$	−11.0938	−	15.2693i	−0.422027	−	0.580870i	0.544074	−	0.839038i	$-0.316881\pi$
$691$	−11.0938	−	15.2693i	−0.422027	−	0.580870i	−0.966100	+	0.258168i	$0.916881\pi$
$692$	−3.92756	+	12.0878i	−0.149303	+	0.459508i
$693$		−	28.6762i		−	1.08932i
$694$	55.5011	+	18.0334i	2.10679	+	0.684539i
$695$	−6.79267	+	47.1665i	−0.257661	+	1.78913i
$696$	−2.48705	−	7.65435i	−0.0942713	−	0.290137i
$697$	−5.11988	−	3.32178i	−0.193929	−	0.125822i
$698$	−40.0759	+	55.1597i	−1.51689	+	2.08783i
$699$	−0.231111			−0.00874142
$700$	−31.9810	−	9.40657i	−1.20877	−	0.355535i
$701$	−29.7258			−1.12273			−0.561365	−	0.827569i	$-0.689723\pi$
$701$	−29.7258			−1.12273			−0.561365	+	0.827569i	$0.689723\pi$
$702$	33.7687	+	24.5344i	1.27452	+	0.925992i
$703$	−2.49587	−	7.68148i	−0.0941334	−	0.289713i
$704$	−61.4049	+	19.9517i	−2.31429	+	0.751957i
$705$	−4.66152	−	2.29325i	−0.175563	−	0.0863690i
$706$	1.71964	−	5.29250i	0.0647194	−	0.199186i
$707$	−16.9591			−0.637813
$708$	3.41689	−	10.5161i	0.128415	−	0.395219i
$709$	−16.2412	−	22.3541i	−0.609950	−	0.839525i	0.386623	−	0.922238i	$-0.373641\pi$
$709$	−16.2412	−	22.3541i	−0.609950	−	0.839525i	−0.996573	+	0.0827133i	$0.973641\pi$
$710$	12.2916	+	71.1245i	0.461296	+	2.66925i
$711$	17.4042	−	23.9548i	0.652708	−	0.898376i
$712$	5.69101	+	7.83301i	0.213280	+	0.293554i
$713$	6.65496	+	9.15977i	0.249230	+	0.343036i
$714$	8.86231	−	0.468242i	0.331664	−	0.0175235i
$715$	69.3310	−	36.5617i	2.59283	−	1.36733i
$716$	9.80761	−	7.12565i	0.366528	−	0.266298i
$717$	−1.79885	+	5.53628i	−0.0671791	+	0.206756i
$718$		−	71.9229i		−	2.68414i
$719$	27.6323	+	8.97827i	1.03051	+	0.334833i	0.774992	−	0.631971i	$-0.217754\pi$
$719$	27.6323	+	8.97827i	1.03051	+	0.334833i	0.255518	+	0.966804i	$0.417754\pi$
$720$	−2.00860	−	11.6226i	−0.0748561	−	0.433150i
$721$	24.0535	−	7.81545i	0.895798	−	0.291062i
$722$	−25.4992	+	8.28519i	−0.948982	+	0.308343i
$723$	−5.76764	+	7.93847i	−0.214501	+	0.295235i
$724$			21.7981i			0.810118i
$725$	−5.94748	+	20.2206i	−0.220884	+	0.750974i
$726$			24.7010i			0.916740i
$727$	15.3230	−	21.0902i	0.568297	−	0.782194i	−0.424055	−	0.905637i	$-0.639394\pi$
$727$	15.3230	−	21.0902i	0.568297	−	0.782194i	0.992352	+	0.123443i	$0.0393936\pi$
$728$	−13.5816	−	41.7999i	−0.503368	−	1.54921i
$729$	−4.54496	−	13.9880i	−0.168332	−	0.518073i
$730$	−49.1077	+	50.5072i	−1.81756	+	1.86935i
$731$	2.71482	+	7.06335i	0.100411	+	0.261247i
$732$		−	1.83834i		−	0.0679469i
$733$	20.7886	+	6.75463i	0.767845	+	0.249488i	0.666642	−	0.745378i	$-0.267731\pi$
$733$	20.7886	+	6.75463i	0.767845	+	0.249488i	0.101203	+	0.994866i	$0.467731\pi$
$734$	−5.85159	−	8.05402i	−0.215986	−	0.297279i
$735$	2.87048	+	2.79094i	0.105879	+	0.102945i
$736$	−6.42469	+	8.84282i	−0.236817	+	0.325951i
$737$	−15.9326	+	11.5757i	−0.586886	+	0.426398i
$738$	−7.83087	+	5.68946i	−0.288258	+	0.209432i
$739$	18.4134	+	13.3781i	0.677347	+	0.492121i	0.872476	−	0.488656i	$-0.162513\pi$
$739$	18.4134	+	13.3781i	0.677347	+	0.492121i	−0.195130	+	0.980777i	$0.562513\pi$
$740$	23.3811	+	3.36723i	0.859508	+	0.123782i
$741$	−4.98486	−	6.86107i	−0.183123	−	0.252048i
$742$	−11.5473	+	35.5389i	−0.423914	+	1.30467i
$743$	−2.53114			−0.0928584			−0.0464292	−	0.998922i	$-0.514784\pi$
$743$	−2.53114			−0.0928584			−0.0464292	+	0.998922i	$0.514784\pi$
$744$	−1.95022	+	6.00216i	−0.0714985	+	0.220050i
$745$	−14.8760	+	7.84486i	−0.545015	+	0.287414i
$746$	16.7534	+	51.5615i	0.613384	+	1.88780i
$747$	−23.2429	+	7.55208i	−0.850413	+	0.276316i
$748$	84.6408	−	4.47201i	3.09477	−	0.163513i
$749$	9.66919			0.353304
$750$	5.45034	−	11.9127i	0.199018	−	0.434989i
$751$			12.2153i			0.445744i	0.974848	+	0.222872i	$0.0715432\pi$
$751$			12.2153i			0.445744i	−0.974848	+	0.222872i	$0.928457\pi$
$752$	−5.29229	+	7.28421i	−0.192990	+	0.265628i
$753$	−2.32307	−	7.14967i	−0.0846574	−	0.260549i
$754$	−58.8683	+	19.1275i	−2.14386	+	0.696581i
$755$	−25.0926	+	13.2326i	−0.913215	+	0.481584i
$756$	5.85660	−	18.0248i	0.213002	−	0.655554i
$757$		−	11.1991i		−	0.407037i	−0.979071	−	0.203519i	$-0.934762\pi$
$757$		−	11.1991i		−	0.407037i	0.979071	−	0.203519i	$-0.0652378\pi$
$758$	−24.9855	+	76.8974i	−0.907513	+	2.79304i
$759$	5.63148	+	7.75106i	0.204410	+	0.281346i
$760$	−3.41931	+	23.7428i	−0.124031	+	0.861241i
$761$	21.1755	+	15.3849i	0.767613	+	0.557703i	0.901236	−	0.433329i	$-0.142661\pi$
$761$	21.1755	+	15.3849i	0.767613	+	0.557703i	−0.133623	+	0.991032i	$0.542661\pi$
$762$	13.9820	−	10.1585i	0.506513	−	0.368004i
$763$	21.9184	+	30.1681i	0.793499	+	1.09216i
$764$	4.60154	+	3.34322i	0.166478	+	0.120953i
$765$	2.29003	−	25.3067i	0.0827962	−	0.914966i
$766$	−50.8581	+	36.9505i	−1.83758	+	1.33508i
$767$	−36.3098	−	11.7978i	−1.31107	−	0.425993i
$768$	−12.9535			−0.467418
$769$	−12.8454	+	39.5340i	−0.463216	+	1.42563i	0.397996	+	0.917387i	$0.369706\pi$
$769$	−12.8454	+	39.5340i	−0.463216	+	1.42563i	−0.861212	+	0.508246i	$0.830294\pi$
$770$	−39.5770	−	38.4804i	−1.42626	−	1.38674i
$771$	7.36876	−	2.39426i	0.265380	−	0.0862271i

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.q (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39460 + 1.91951i) q^{2} +(0.152608 + 0.469678i) q^{3} +(-1.12155 - 3.45179i) q^{4} +(-1.97789 + 1.04304i) q^{5} +(-1.11438 - 0.362083i) q^{6} +1.83697 q^{7} +(3.67682 + 1.19467i) q^{8} +(2.22974 - 1.62000i) q^{9} +(0.756252 - 5.25121i) q^{10} +(3.32921 - 4.58227i) q^{11} +(1.45007 - 1.05354i) q^{12} +(-3.63764 - 5.00679i) q^{13} +(-2.56184 + 3.52607i) q^{14} +(-0.791736 - 0.769798i) q^{15} +(-1.54835 + 1.12494i) q^{16} +(-3.84862 + 1.47923i) q^{17} +6.53927i q^{18} +(0.857473 - 2.63903i) q^{19} +(5.81867 + 5.65744i) q^{20} +(0.280336 + 0.862784i) q^{21} +(4.15277 + 12.7809i) q^{22} +(2.77105 + 2.01328i) q^{23} +1.90924i q^{24} +(2.82413 - 4.12605i) q^{25} +14.6836 q^{26} +(2.29975 + 1.67087i) q^{27} +(-2.06026 - 6.34082i) q^{28} +(-4.00911 + 1.30264i) q^{29} +(2.58179 - 0.446180i) q^{30} +(3.14374 + 1.02146i) q^{31} +3.19115i q^{32} +(2.66026 + 0.864370i) q^{33} +(2.52791 - 9.45039i) q^{34} +(-3.63333 + 1.91603i) q^{35} +(-8.09268 - 5.87968i) q^{36} +(2.35482 - 1.71088i) q^{37} +(3.86980 + 5.32633i) q^{38} +(1.79645 - 2.47260i) q^{39} +(-8.51845 + 1.47214i) q^{40} +(0.870046 + 1.19752i) q^{41} +(-2.04708 - 0.665136i) q^{42} -1.83529i q^{43} +(-19.5509 - 6.35248i) q^{44} +(-2.72046 + 5.52991i) q^{45} +(-7.72902 + 2.51131i) q^{46} +(4.47423 - 1.45377i) q^{47} +(-0.764653 - 0.555553i) q^{48} -3.62555 q^{49} +(3.98144 + 11.1751i) q^{50} +(-1.28209 - 1.58187i) q^{51} +(-13.2026 + 18.1718i) q^{52} +(8.15399 - 2.64939i) q^{53} +(-6.41449 + 2.08419i) q^{54} +(-1.80533 + 12.5358i) q^{55} +(6.75420 + 2.19457i) q^{56} +1.37035 q^{57} +(3.09069 - 9.51217i) q^{58} +(4.99085 - 3.62606i) q^{59} +(-1.76920 + 3.59627i) q^{60} +(0.602854 - 0.829757i) q^{61} +(-6.34498 + 4.60990i) q^{62} +(4.09597 - 2.97589i) q^{63} +(-9.22214 - 6.70028i) q^{64} +(12.4172 + 6.10868i) q^{65} +(-5.36917 + 3.90093i) q^{66} +(-3.30684 - 1.07446i) q^{67} +(9.42242 + 11.6256i) q^{68} +(-0.522712 + 1.60874i) q^{69} +(1.38921 - 9.64631i) q^{70} +(-12.9389 + 4.20412i) q^{71} +(10.1337 - 3.29265i) q^{72} +(-10.7422 - 7.80465i) q^{73} +6.90610i q^{74} +(2.36890 + 0.696765i) q^{75} -10.0711 q^{76} +(6.11566 - 8.41749i) q^{77} +(2.24084 + 6.89658i) q^{78} +(10.2175 - 3.31987i) q^{79} +(1.88911 - 3.84002i) q^{80} +(2.12125 - 6.52853i) q^{81} -3.51201 q^{82} +(-8.43322 - 2.74012i) q^{83} +(2.66374 - 1.93532i) q^{84} +(6.06926 - 6.94003i) q^{85} +(3.52286 + 2.55951i) q^{86} +(-1.22364 - 1.68420i) q^{87} +(17.7152 - 12.8709i) q^{88} +(2.02611 + 1.47205i) q^{89} +(-6.82073 - 12.9340i) q^{90} +(-6.68224 - 9.19731i) q^{91} +(3.84155 - 11.8231i) q^{92} +1.63243i q^{93} +(-3.44926 + 10.6157i) q^{94} +(1.05663 + 6.11410i) q^{95} +(-1.49881 + 0.486994i) q^{96} +(-0.152034 - 0.467913i) q^{97} +(5.05620 - 6.95926i) q^{98} -15.6106i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 10 q^{2} + 38 q^{4} - 10 q^{8} - 50 q^{9} - 10 q^{13} + 6 q^{15} - 58 q^{16} - 8 q^{19} - 44 q^{21} - 20 q^{25} - 64 q^{26} + 78 q^{30} - 20 q^{33} - 23 q^{34} - 46 q^{35} + 52 q^{36} - 10 q^{38}+ \cdots - 250 q^{98}+O(q^{100}) \) 176 * q - 10 * q^2 + 38 * q^4 - 10 * q^8 - 50 * q^9 - 10 * q^13 + 6 * q^15 - 58 * q^16 - 8 * q^19 - 44 * q^21 - 20 * q^25 - 64 * q^26 + 78 * q^30 - 20 * q^33 - 23 * q^34 - 46 * q^35 + 52 * q^36 - 10 * q^38 - 20 * q^42 + 40 * q^47 + 164 * q^49 + 84 * q^50 + 20 * q^51 - 30 * q^52 - 40 * q^53 - 18 * q^55 - 18 * q^59 - 48 * q^60 + 66 * q^64 + 80 * q^66 - 50 * q^67 + 68 * q^69 - 152 * q^70 + 60 * q^72 - 72 * q^76 - 40 * q^77 - 38 * q^81 + 50 * q^83 - 52 * q^84 + 47 * q^85 - 94 * q^86 - 120 * q^87 + 60 * q^89 + 50 * q^94 - 250 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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