LMFDB - Embedded newform 740.2.be.a.711.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [740,2,Mod(51,740)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(740, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 11]))

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

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

chi := DirichletCharacter("740.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.be (of order $12$, 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:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$76$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			711.26
Character	$\chi$	$=$	740.711
Dual form			740.2.be.a.51.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.614568 - 1.27370i) q^{2} +(0.450967 - 0.781098i) q^{3} +(-1.24461 + 1.56555i) q^{4} +(0.965926 - 0.258819i) q^{5} +(-1.27203 - 0.0943580i) q^{6} +(-2.84609 - 1.64319i) q^{7} +(2.75893 + 0.623124i) q^{8} +(1.09326 + 1.89358i) q^{9} +(-0.923284 - 1.07124i) q^{10} +2.76913 q^{11} +(0.661567 + 1.67817i) q^{12} +(4.40649 - 1.18072i) q^{13} +(-0.343813 + 4.63491i) q^{14} +(0.233438 - 0.871201i) q^{15} +(-0.901881 - 3.89700i) q^{16} +(0.910419 - 3.39773i) q^{17} +(1.73996 - 2.55621i) q^{18} +(-0.156042 - 0.582356i) q^{19} +(-0.797010 + 1.83433i) q^{20} +(-2.56698 + 1.48205i) q^{21} +(-1.70182 - 3.52704i) q^{22} +(-1.20084 + 1.20084i) q^{23} +(1.73091 - 1.87399i) q^{24} +(0.866025 - 0.500000i) q^{25} +(-4.21196 - 4.88691i) q^{26} +4.67789 q^{27} +(6.11477 - 2.41055i) q^{28} +(-0.280016 + 0.280016i) q^{29} +(-1.25311 + 0.238083i) q^{30} +(-5.98672 - 5.98672i) q^{31} +(-4.40933 + 3.54370i) q^{32} +(1.24879 - 2.16296i) q^{33} +(-4.88720 + 0.928538i) q^{34} +(-3.17440 - 0.850578i) q^{35} +(-4.32517 - 0.645223i) q^{36} +(1.50943 - 5.89251i) q^{37} +(-0.645847 + 0.556647i) q^{38} +(1.06493 - 3.97436i) q^{39} +(2.82620 - 0.112173i) q^{40} +(0.748977 + 0.432422i) q^{41} +(3.46527 + 2.35874i) q^{42} +(0.482448 - 0.482448i) q^{43} +(-3.44649 + 4.33521i) q^{44} +(1.54610 + 1.54610i) q^{45} +(2.26751 + 0.791512i) q^{46} -7.27413i q^{47} +(-3.45066 - 1.05296i) q^{48} +(1.90015 + 3.29116i) q^{49} +(-1.16908 - 0.795771i) q^{50} +(-2.24339 - 2.24339i) q^{51} +(-3.63591 + 8.36811i) q^{52} +(-0.837930 - 1.45134i) q^{53} +(-2.87488 - 5.95822i) q^{54} +(2.67478 - 0.716704i) q^{55} +(-6.82826 - 6.30692i) q^{56} +(-0.525246 - 0.140739i) q^{57} +(0.528745 + 0.184567i) q^{58} +(7.59618 + 2.03539i) q^{59} +(1.07337 + 1.44977i) q^{60} +(3.68670 + 13.7589i) q^{61} +(-3.94603 + 11.3045i) q^{62} -7.18572i q^{63} +(7.22343 + 3.43832i) q^{64} +(3.95075 - 2.28097i) q^{65} +(-3.52242 - 0.261290i) q^{66} +(4.35361 - 7.54067i) q^{67} +(4.18619 + 5.65416i) q^{68} +(0.396435 + 1.47952i) q^{69} +(0.867506 + 4.56597i) q^{70} +(-4.03663 - 2.33055i) q^{71} +(1.83629 + 5.90549i) q^{72} -4.22786i q^{73} +(-8.43292 + 1.69879i) q^{74} -0.901934i q^{75} +(1.10592 + 0.480516i) q^{76} +(-7.88120 - 4.55021i) q^{77} +(-5.71661 + 1.08612i) q^{78} +(-0.270699 - 1.01026i) q^{79} +(-1.87977 - 3.53079i) q^{80} +(-1.17020 + 2.02684i) q^{81} +(0.0904777 - 1.21972i) q^{82} +(-5.63912 + 3.25575i) q^{83} +(0.874681 - 5.86331i) q^{84} -3.51759i q^{85} +(-0.910990 - 0.317996i) q^{86} +(0.0924420 + 0.344998i) q^{87} +(7.63985 + 1.72551i) q^{88} +(-15.9878 - 4.28392i) q^{89} +(1.01908 - 2.91945i) q^{90} +(-14.4814 - 3.88028i) q^{91} +(-0.385393 - 3.37456i) q^{92} +(-7.37603 + 1.97640i) q^{93} +(-9.26505 + 4.47045i) q^{94} +(-0.301449 - 0.522126i) q^{95} +(0.779508 + 5.04221i) q^{96} +(11.7848 + 11.7848i) q^{97} +(3.02417 - 4.44286i) q^{98} +(3.02737 + 5.24356i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q + 4 q^{2} - 12 q^{4} - 8 q^{8} - 152 q^{9} + 16 q^{13} - 24 q^{14} + 20 q^{16} - 60 q^{18} - 16 q^{22} - 24 q^{24} - 32 q^{29} - 56 q^{32} - 32 q^{37} + 40 q^{38} + 20 q^{42} + 12 q^{44} - 8 q^{46}+ \cdots - 36 q^{98}+O(q^{100}) $ 304 * q + 4 * q^2 - 12 * q^4 - 8 * q^8 - 152 * q^9 + 16 * q^13 - 24 * q^14 + 20 * q^16 - 60 * q^18 - 16 * q^22 - 24 * q^24 - 32 * q^29 - 56 * q^32 - 32 * q^37 + 40 * q^38 + 20 * q^42 + 12 * q^44 - 8 * q^46 + 104 * q^49 + 4 * q^50 - 40 * q^52 + 40 * q^54 + 4 * q^56 - 48 * q^57 - 12 * q^58 - 28 * q^60 - 16 * q^61 - 60 * q^62 + 24 * q^65 - 52 * q^66 - 200 * q^68 - 196 * q^72 + 20 * q^74 - 40 * q^76 + 96 * q^77 - 48 * q^78 - 152 * q^81 + 32 * q^82 - 112 * q^84 + 12 * q^88 - 8 * q^89 + 140 * q^92 - 16 * q^93 - 28 * q^94 - 132 * q^96 + 48 * q^97 - 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.614568	−	1.27370i	−0.434565	−	0.900640i
$2$	−0.614568	−	1.27370i	−0.434565	−	0.900640i
$3$	0.450967	−	0.781098i	0.260366	−	0.450967i	−0.705973	−	0.708238i	$-0.749490\pi$
$3$	0.450967	−	0.781098i	0.260366	−	0.450967i	0.966339	+	0.257272i	$0.0828235\pi$
$4$	−1.24461	+	1.56555i	−0.622306	+	0.782774i
$5$	0.965926	−	0.258819i	0.431975	−	0.115747i
$5$	0.965926	−	0.258819i	0.431975	−	0.115747i
$6$	−1.27203	−	0.0943580i	−0.519305	−	0.0385215i
$7$	−2.84609	−	1.64319i	−1.07572	−	0.621068i	−0.145982	−	0.989287i	$-0.546634\pi$
$7$	−2.84609	−	1.64319i	−1.07572	−	0.621068i	−0.929739	+	0.368219i	$0.879967\pi$
$8$	2.75893	+	0.623124i	0.975430	+	0.220308i
$9$	1.09326	+	1.89358i	0.364419	+	0.631193i
$10$	−0.923284	−	1.07124i	−0.291968	−	0.338754i
$11$	2.76913			0.834924			0.417462	−	0.908694i	$-0.362920\pi$
$11$	2.76913			0.834924			0.417462	+	0.908694i	$0.362920\pi$
$12$	0.661567	+	1.67817i	0.190978	+	0.484447i
$13$	4.40649	−	1.18072i	1.22214	−	0.327472i	0.410626	−	0.911804i	$-0.365310\pi$
$13$	4.40649	−	1.18072i	1.22214	−	0.327472i	0.811515	+	0.584332i	$0.198643\pi$
$14$	−0.343813	+	4.63491i	−0.0918878	+	1.23873i
$15$	0.233438	−	0.871201i	0.0602733	−	0.224943i
$16$	−0.901881	−	3.89700i	−0.225470	−	0.974250i
$17$	0.910419	−	3.39773i	0.220809	−	0.824071i	−0.763231	−	0.646125i	$-0.776388\pi$
$17$	0.910419	−	3.39773i	0.220809	−	0.824071i	0.984040	−	0.177945i	$-0.0569450\pi$
$18$	1.73996	−	2.55621i	0.410114	−	0.602505i
$19$	−0.156042	−	0.582356i	−0.0357984	−	0.133602i	0.945714	−	0.325000i	$-0.105364\pi$
$19$	−0.156042	−	0.582356i	−0.0357984	−	0.133602i	−0.981512	+	0.191399i	$0.938698\pi$
$20$	−0.797010	+	1.83433i	−0.178217	+	0.410169i
$21$	−2.56698	+	1.48205i	−0.560162	+	0.323410i
$22$	−1.70182	−	3.52704i	−0.362829	−	0.751967i
$23$	−1.20084	+	1.20084i	−0.250393	+	0.250393i	−0.821132	−	0.570739i	$-0.806657\pi$
$23$	−1.20084	+	1.20084i	−0.250393	+	0.250393i	0.570739	+	0.821132i	$0.306657\pi$
$24$	1.73091	−	1.87399i	0.353320	−	0.382526i
$25$	0.866025	−	0.500000i	0.173205	−	0.100000i
$26$	−4.21196	−	4.88691i	−0.826034	−	0.958401i
$27$	4.67789			0.900261
$28$	6.11477	−	2.41055i	1.15558	−	0.455552i
$29$	−0.280016	+	0.280016i	−0.0519977	+	0.0519977i	−0.732628	−	0.680630i	$-0.761706\pi$
$29$	−0.280016	+	0.280016i	−0.0519977	+	0.0519977i	0.680630	+	0.732628i	$0.261706\pi$
$30$	−1.25311	+	0.238083i	−0.228786	+	0.0434679i
$31$	−5.98672	−	5.98672i	−1.07525	−	1.07525i	−0.996928	−	0.0783182i	$-0.975045\pi$
$31$	−5.98672	−	5.98672i	−1.07525	−	1.07525i	−0.0783182	−	0.996928i	$-0.524955\pi$
$32$	−4.40933	+	3.54370i	−0.779467	+	0.626443i
$33$	1.24879	−	2.16296i	0.217386	−	0.376523i
$34$	−4.88720	+	0.928538i	−0.838147	+	0.159243i
$35$	−3.17440	−	0.850578i	−0.536572	−	0.143774i
$36$	−4.32517	−	0.645223i	−0.720861	−	0.107537i
$37$	1.50943	−	5.89251i	0.248148	−	0.968722i
$37$	1.50943	−	5.89251i	0.248148	−	0.968722i
$38$	−0.645847	+	0.556647i	−0.104770	+	0.0903001i
$39$	1.06493	−	3.97436i	0.170525	−	0.636408i
$40$	2.82620	−	0.112173i	0.446862	−	0.0177361i
$41$	0.748977	+	0.432422i	0.116971	+	0.0675330i	0.557344	−	0.830282i	$-0.311821\pi$
$41$	0.748977	+	0.432422i	0.116971	+	0.0675330i	−0.440373	+	0.897815i	$0.645154\pi$
$42$	3.46527	+	2.35874i	0.534703	+	0.363962i
$43$	0.482448	−	0.482448i	0.0735726	−	0.0735726i	−0.669363	−	0.742936i	$-0.733433\pi$
$43$	0.482448	−	0.482448i	0.0735726	−	0.0735726i	0.742936	+	0.669363i	$0.233433\pi$
$44$	−3.44649	+	4.33521i	−0.519579	+	0.653557i
$45$	1.54610	+	1.54610i	0.230479	+	0.230479i
$46$	2.26751	+	0.791512i	0.334326	+	0.116702i
$47$		−	7.27413i		−	1.06104i	−0.847672	−	0.530521i	$-0.821996\pi$
$47$		−	7.27413i		−	1.06104i	0.847672	−	0.530521i	$-0.178004\pi$
$48$	−3.45066	−	1.05296i	−0.498059	−	0.151982i
$49$	1.90015	+	3.29116i	0.271450	+	0.470166i
$50$	−1.16908	−	0.795771i	−0.165333	−	0.112539i
$51$	−2.24339	−	2.24339i	−0.314138	−	0.314138i
$52$	−3.63591	+	8.36811i	−0.504209	+	1.16045i
$53$	−0.837930	−	1.45134i	−0.115099	−	0.199356i	0.802721	−	0.596355i	$-0.203385\pi$
$53$	−0.837930	−	1.45134i	−0.115099	−	0.199356i	−0.917819	+	0.396999i	$0.870052\pi$
$54$	−2.87488	−	5.95822i	−0.391222	−	0.810811i
$55$	2.67478	−	0.716704i	0.360667	−	0.0966403i
$56$	−6.82826	−	6.30692i	−0.912465	−	0.842798i
$57$	−0.525246	−	0.140739i	−0.0695706	−	0.0186414i
$58$	0.528745	+	0.184567i	0.0694277	+	0.0242348i
$59$	7.59618	+	2.03539i	0.988938	+	0.264985i	0.716805	−	0.697274i	$-0.245604\pi$
$59$	7.59618	+	2.03539i	0.988938	+	0.264985i	0.272134	+	0.962259i	$0.412271\pi$
$60$	1.07337	+	1.44977i	0.138571	+	0.187164i
$61$	3.68670	+	13.7589i	0.472033	+	1.76165i	0.632448	+	0.774603i	$0.282050\pi$
$61$	3.68670	+	13.7589i	0.472033	+	1.76165i	−0.160415	+	0.987050i	$0.551283\pi$
$62$	−3.94603	+	11.3045i	−0.501146	+	1.43568i
$63$		−	7.18572i		−	0.905316i
$64$	7.22343	+	3.43832i	0.902929	+	0.429790i
$65$	3.95075	−	2.28097i	0.490030	−	0.282919i
$66$	−3.52242	−	0.261290i	−0.433580	−	0.0321625i
$67$	4.35361	−	7.54067i	0.531878	−	0.921239i	−0.467430	−	0.884030i	$-0.654820\pi$
$67$	4.35361	−	7.54067i	0.531878	−	0.921239i	0.999308	−	0.0372090i	$-0.0118467\pi$
$68$	4.18619	+	5.65416i	0.507650	+	0.685668i
$69$	0.396435	+	1.47952i	0.0477252	+	0.178113i
$70$	0.867506	+	4.56597i	0.103687	+	0.545737i
$71$	−4.03663	−	2.33055i	−0.479060	−	0.276585i	0.240965	−	0.970534i	$-0.422536\pi$
$71$	−4.03663	−	2.33055i	−0.479060	−	0.276585i	−0.720025	+	0.693948i	$0.755870\pi$
$72$	1.83629	+	5.90549i	0.216409	+	0.695969i
$73$		−	4.22786i		−	0.494833i	−0.968909	−	0.247417i	$-0.920418\pi$
$73$		−	4.22786i		−	0.494833i	0.968909	−	0.247417i	$-0.0795816\pi$
$74$	−8.43292	+	1.69879i	−0.980307	+	0.197480i
$75$		−	0.901934i		−	0.104146i
$76$	1.10592	+	0.480516i	0.126857	+	0.0551190i
$77$	−7.88120	−	4.55021i	−0.898146	−	0.518545i
$78$	−5.71661	+	1.08612i	−0.647278	+	0.122979i
$79$	−0.270699	−	1.01026i	−0.0304560	−	0.113663i	0.949024	−	0.315202i	$-0.102072\pi$
$79$	−0.270699	−	1.01026i	−0.0304560	−	0.113663i	−0.979481	+	0.201539i	$0.935406\pi$
$80$	−1.87977	−	3.53079i	−0.210164	−	0.394754i
$81$	−1.17020	+	2.02684i	−0.130022	+	0.225205i
$82$	0.0904777	−	1.21972i	0.00999159	−	0.134696i
$83$	−5.63912	+	3.25575i	−0.618974	+	0.357365i	−0.776469	−	0.630155i	$-0.782991\pi$
$83$	−5.63912	+	3.25575i	−0.618974	+	0.357365i	0.157496	+	0.987520i	$0.449658\pi$
$84$	0.874681	−	5.86331i	0.0954356	−	0.639740i
$85$		−	3.51759i		−	0.381536i
$86$	−0.910990	−	0.317996i	−0.0982346	−	0.0342904i
$87$	0.0924420	+	0.344998i	0.00991082	+	0.0369877i
$88$	7.63985	+	1.72551i	0.814411	+	0.183940i
$89$	−15.9878	−	4.28392i	−1.69470	−	0.454095i	−0.723107	−	0.690736i	$-0.757287\pi$
$89$	−15.9878	−	4.28392i	−1.69470	−	0.454095i	−0.971597	+	0.236641i	$0.923953\pi$
$90$	1.01908	−	2.91945i	0.107421	−	0.307737i
$91$	−14.4814	−	3.88028i	−1.51806	−	0.406764i
$92$	−0.385393	−	3.37456i	−0.0401800	−	0.351822i
$93$	−7.37603	+	1.97640i	−0.764858	+	0.204943i
$94$	−9.26505	+	4.47045i	−0.955617	+	0.461092i
$95$	−0.301449	−	0.522126i	−0.0309281	−	0.0535690i
$96$	0.779508	+	5.04221i	0.0795582	+	0.514618i
$97$	11.7848	+	11.7848i	1.19657	+	1.19657i	0.975187	+	0.221381i	$0.0710564\pi$
$97$	11.7848	+	11.7848i	1.19657	+	1.19657i	0.221381	+	0.975187i	$0.428944\pi$
$98$	3.02417	−	4.44286i	0.305487	−	0.448797i
$99$	3.02737	+	5.24356i	0.304262	+	0.526998i
$100$	−0.295092	+	1.97811i	−0.0295092	+	0.197811i
$101$		−	1.75774i		−	0.174902i	−0.996169	−	0.0874509i	$-0.972128\pi$
$101$		−	1.75774i		−	0.174902i	0.996169	−	0.0874509i	$-0.0278721\pi$
$102$	−1.47869	+	4.23612i	−0.146412	+	0.419438i
$103$	1.82211	+	1.82211i	0.179537	+	0.179537i	0.791154	−	0.611617i	$-0.209481\pi$
$103$	1.82211	+	1.82211i	0.179537	+	0.179537i	−0.611617	+	0.791154i	$0.709481\pi$
$104$	12.8930	−	0.511725i	1.26426	−	0.0501788i
$105$	−2.09593	+	2.09593i	−0.204542	+	0.204542i
$106$	−1.33360	+	1.95921i	−0.129531	+	0.190296i
$107$	3.23107	+	1.86546i	0.312360	+	0.180341i	0.647982	−	0.761656i	$-0.275613\pi$
$107$	3.23107	+	1.86546i	0.312360	+	0.180341i	−0.335622	+	0.941997i	$0.608947\pi$
$108$	−5.82216	+	7.32347i	−0.560238	+	0.704701i
$109$	0.00991505	−	0.0370035i	0.000949690	−	0.00354429i	−0.965449	−	0.260591i	$-0.916083\pi$
$109$	0.00991505	−	0.0370035i	0.000949690	−	0.00354429i	0.966399	+	0.257046i	$0.0827493\pi$
$110$	−2.55670	−	2.96639i	−0.243771	−	0.282834i
$111$	−3.92192	−	3.83634i	−0.372252	−	0.364129i
$112$	−3.83668	+	12.5732i	−0.362532	+	1.18805i
$113$	5.26403	+	1.41049i	0.495198	+	0.132688i	0.497771	−	0.867309i	$-0.334152\pi$
$113$	5.26403	+	1.41049i	0.495198	+	0.132688i	−0.00257224	+	0.999997i	$0.500819\pi$
$114$	0.143540	+	0.755499i	0.0134438	+	0.0707590i
$115$	−0.849124	+	1.47073i	−0.0791813	+	0.137146i
$116$	−0.0898672	−	0.786891i	−0.00834396	−	0.0730610i
$117$	7.05321	+	7.05321i	0.652069	+	0.652069i
$118$	−2.07590	−	10.9261i	−0.191102	−	1.00583i
$119$	−8.17426	+	8.17426i	−0.749333	+	0.749333i
$120$	1.18691	−	2.25813i	0.108349	−	0.206138i
$121$	−3.33191			−0.302901
$122$	15.2590	−	13.1515i	1.38149	−	1.19068i
$123$	0.675528	−	0.390016i	0.0609103	−	0.0351666i
$124$	16.8236	−	1.92135i	1.51081	−	0.172542i
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$	−9.15244	+	4.41612i	−0.815364	+	0.393419i
$127$	−13.3457	+	7.70516i	−1.18424	+	0.683722i	−0.956992	−	0.290115i	$-0.906307\pi$
$127$	−13.3457	+	7.70516i	−1.18424	+	0.683722i	−0.227249	+	0.973837i	$0.572973\pi$
$128$	−0.0599139	−	11.3135i	−0.00529569	−	0.999986i
$129$	−0.159271	−	0.594407i	−0.0140230	−	0.0523346i
$130$	−5.33327	−	3.63025i	−0.467759	−	0.318394i
$131$	3.26954	−	12.2021i	0.285661	−	1.06610i	−0.662695	−	0.748890i	$-0.730587\pi$
$131$	3.26954	−	12.2021i	0.285661	−	1.06610i	0.948355	−	0.317210i	$-0.102746\pi$
$132$	1.83197	+	4.64708i	0.159452	+	0.404477i
$133$	−0.512813	+	1.91384i	−0.0444665	+	0.165951i
$134$	−12.2801	−	0.910926i	−1.06084	−	0.0786920i
$135$	4.51850	−	1.21073i	0.388890	−	0.104203i
$136$	4.62900	−	8.80681i	0.396933	−	0.755178i
$137$	17.6162			1.50505			0.752526	−	0.658562i	$-0.228835\pi$
$137$	17.6162			1.50505			0.752526	+	0.658562i	$0.228835\pi$
$138$	1.64082	−	1.41420i	0.139676	−	0.120385i
$139$	11.4468	+	19.8264i	0.970903	+	1.68165i	0.692841	+	0.721090i	$0.256359\pi$
$139$	11.4468	+	19.8264i	0.970903	+	1.68165i	0.278062	+	0.960563i	$0.410308\pi$
$140$	5.28252	−	3.91104i	0.446454	−	0.330543i
$141$	−5.68181	−	3.28039i	−0.478495	−	0.276259i
$142$	−0.487632	+	6.57373i	−0.0409212	+	0.551655i
$143$	12.2022	−	3.26956i	1.02040	−	0.273414i
$144$	6.39329	−	5.96821i	0.532774	−	0.497351i
$145$	−0.198001	+	0.342949i	−0.0164431	+	0.0284803i
$146$	−5.38501	+	2.59831i	−0.445667	+	0.215037i
$147$	3.42762			0.282706
$148$	7.34635	+	9.69697i	0.603866	+	0.797086i
$149$	11.8023			0.966879			0.483439	−	0.875378i	$-0.339387\pi$
$149$	11.8023			0.966879			0.483439	+	0.875378i	$0.339387\pi$
$150$	−1.14879	+	0.554300i	−0.0937984	+	0.0452584i
$151$	1.93634	−	3.35383i	0.157577	−	0.272931i	−0.776417	−	0.630219i	$-0.782965\pi$
$151$	1.93634	−	3.35383i	0.157577	−	0.272931i	0.933994	+	0.357288i	$0.116298\pi$
$152$	−0.0676289	−	1.70391i	−0.00548543	−	0.138206i
$153$	7.42919	−	1.99065i	0.600614	−	0.160934i
$154$	−0.952062	+	12.8347i	−0.0767194	+	1.03425i
$155$	−7.33220	−	4.23325i	−0.588937	−	0.340023i
$156$	4.89663	+	6.61374i	0.392045	+	0.529523i
$157$	3.74295	+	6.48298i	0.298720	+	0.517398i	0.975843	−	0.218471i	$-0.0701070\pi$
$157$	3.74295	+	6.48298i	0.298720	+	0.517398i	−0.677123	+	0.735869i	$0.736774\pi$
$158$	−1.12041	+	0.965664i	−0.0891348	+	0.0768241i
$159$	−1.51151			−0.119871
$160$	−3.34191	+	4.56417i	−0.264201	+	0.360829i
$161$	5.39092	−	1.44449i	0.424864	−	0.113842i
$162$	3.30075	+	0.244846i	0.259331	+	0.0192369i
$163$	−2.80498	+	10.4683i	−0.219703	+	0.819942i	0.764755	+	0.644321i	$0.222860\pi$
$163$	−2.80498	+	10.4683i	−0.219703	+	0.819942i	−0.984458	+	0.175621i	$0.943807\pi$
$164$	−1.60916	+	0.634362i	−0.125655	+	0.0495353i
$165$	0.646419	−	2.41247i	0.0503237	−	0.187811i
$166$	7.61246	+	5.18165i	0.590841	+	0.402174i
$167$	1.46877	+	5.48153i	0.113657	+	0.424173i	0.999183	−	0.0404164i	$-0.0128685\pi$
$167$	1.46877	+	5.48153i	0.113657	+	0.424173i	−0.885526	+	0.464590i	$0.846202\pi$
$168$	−8.00564	+	2.48933i	−0.617649	+	0.192056i
$169$	6.76474	−	3.90563i	0.520365	−	0.300433i
$170$	−4.48035	+	2.16180i	−0.343627	+	0.165802i
$171$	0.932142	−	0.932142i	0.0712827	−	0.0712827i
$172$	0.154835	+	1.35576i	0.0118060	+	0.103375i
$173$	−11.7214	+	6.76737i	−0.891163	+	0.514513i	−0.874323	−	0.485345i	$-0.838694\pi$
$173$	−11.7214	+	6.76737i	−0.891163	+	0.514513i	−0.0168404	+	0.999858i	$0.505361\pi$
$174$	0.382612	−	0.329768i	0.0290057	−	0.0249996i
$175$	−3.28638			−0.248427
$176$	−2.49743	−	10.7913i	−0.188251	−	0.813425i
$177$	5.01547	−	5.01547i	0.376985	−	0.376985i
$178$	4.36918	+	22.9964i	0.327484	+	1.72365i
$179$	5.78369	+	5.78369i	0.432294	+	0.432294i	0.889408	−	0.457114i	$-0.151117\pi$
$179$	5.78369	+	5.78369i	0.432294	+	0.432294i	−0.457114	+	0.889408i	$0.651117\pi$
$180$	−4.34479	+	0.496199i	−0.323841	+	0.0369845i
$181$	2.93728	−	5.08752i	0.218327	−	0.378153i	−0.735970	−	0.677014i	$-0.763274\pi$
$181$	2.93728	−	5.08752i	0.218327	−	0.378153i	0.954296	+	0.298862i	$0.0966069\pi$
$182$	3.95751	+	20.8296i	0.293350	+	1.54400i
$183$	12.4097	+	3.32516i	0.917348	+	0.245803i
$184$	−4.06132	+	2.56477i	−0.299405	+	0.189078i
$185$	−0.0670976	−	6.08239i	−0.00493311	−	0.447186i
$186$	7.05041	+	8.18020i	0.516961	+	0.599801i
$187$	2.52107	−	9.40876i	0.184359	−	0.688037i
$188$	11.3880	+	9.05348i	0.830556	+	0.660293i
$189$	−13.3137	−	7.68667i	−0.968430	−	0.559123i
$190$	−0.479769	+	0.704837i	−0.0348061	+	0.0511343i
$191$	10.4883	−	10.4883i	0.758903	−	0.758903i	−0.217219	−	0.976123i	$-0.569699\pi$
$191$	10.4883	−	10.4883i	0.758903	−	0.758903i	0.976123	+	0.217219i	$0.0696987\pi$
$192$	5.94319	−	4.09164i	0.428913	−	0.295289i
$193$	2.11208	+	2.11208i	0.152031	+	0.152031i	0.779025	−	0.626993i	$-0.215715\pi$
$193$	2.11208	+	2.11208i	0.152031	+	0.152031i	−0.626993	+	0.779025i	$0.715715\pi$
$194$	7.76773	−	22.2529i	0.557691	−	1.59766i
$195$		−	4.11456i		−	0.294650i
$196$	−7.51742	−	1.12144i	−0.536959	−	0.0801028i
$197$	−13.8858	−	24.0509i	−0.989320	−	1.71355i	−0.620889	−	0.783898i	$-0.713228\pi$
$197$	−13.8858	−	24.0509i	−0.989320	−	1.71355i	−0.368431	−	0.929655i	$-0.620105\pi$
$198$	4.81819	−	7.07849i	0.342414	−	0.503046i
$199$	19.1849	+	19.1849i	1.35998	+	1.35998i	0.873928	+	0.486056i	$0.161565\pi$
$199$	19.1849	+	19.1849i	1.35998	+	1.35998i	0.486056	+	0.873928i	$0.338435\pi$
$200$	2.70087	−	0.839826i	0.190980	−	0.0593846i
$201$	−3.92667	−	6.80118i	−0.276966	−	0.479719i
$202$	−2.23883	+	1.08025i	−0.157524	+	0.0760062i
$203$	1.25707	−	0.336831i	0.0882292	−	0.0236409i
$204$	6.30429	−	0.719984i	0.441388	−	0.0504090i
$205$	0.835375	+	0.223838i	0.0583451	+	0.0156335i
$206$	1.20100	−	3.44062i	0.0836779	−	0.239719i
$207$	−3.58672	−	0.961059i	−0.249294	−	0.0667982i
$208$	−8.57538	−	16.1072i	−0.594596	−	1.11684i
$209$	−0.432100	−	1.61262i	−0.0298890	−	0.111547i
$210$	3.95768	+	1.38149i	0.273106	+	0.0953321i
$211$			12.1321i			0.835206i	0.908629	+	0.417603i	$0.137130\pi$
$211$			12.1321i			0.835206i	−0.908629	+	0.417603i	$0.862870\pi$
$212$	3.31504	+	0.494533i	0.227678	+	0.0339646i
$213$	−3.64078	+	2.10200i	−0.249462	+	0.144027i
$214$	0.390319	−	5.26187i	0.0266817	−	0.359694i
$215$	0.341142	−	0.590876i	0.0232657	−	0.0402974i
$216$	12.9060	+	2.91491i	0.878142	+	0.198334i
$217$	7.20142	+	26.8761i	0.488864	+	1.82447i
$218$	−0.0532247	+	0.0101124i	−0.00360483	+	0.000684897i
$219$	−3.30237	−	1.90662i	−0.223153	−	0.128838i
$220$	−2.20702	+	5.07951i	−0.148798	+	0.342460i
$221$		−	16.0470i		−	1.07944i
$222$	−2.47605	+	7.35303i	−0.166181	+	0.493503i
$223$			24.5404i			1.64335i	0.569957	+	0.821674i	$0.306960\pi$
$223$			24.5404i			1.64335i	−0.569957	+	0.821674i	$0.693040\pi$
$224$	18.3723	−	2.84030i	1.22755	−	0.189775i
$225$	1.89358	+	1.09326i	0.126239	+	0.0728838i
$226$	−1.43856	−	7.57163i	−0.0956918	−	0.503657i
$227$	4.56378	+	17.0323i	0.302909	+	1.13047i	0.934731	+	0.355357i	$0.115641\pi$
$227$	4.56378	+	17.0323i	0.302909	+	1.13047i	−0.631822	+	0.775114i	$0.717693\pi$
$228$	0.874062	−	0.647132i	0.0578862	−	0.0428574i
$229$	7.07259	−	12.2501i	0.467370	−	0.809508i	−0.531935	−	0.846785i	$-0.678535\pi$
$229$	7.07259	−	12.2501i	0.467370	−	0.809508i	0.999305	+	0.0372770i	$0.0118684\pi$
$230$	2.39511	+	0.177666i	0.157929	+	0.0117150i
$231$	−7.10832	+	4.10399i	−0.467693	+	0.270023i
$232$	−0.947031	+	0.598062i	−0.0621757	+	0.0392647i
$233$		−	3.47650i		−	0.227753i	−0.993495	−	0.113876i	$-0.963673\pi$
$233$		−	3.47650i		−	0.227753i	0.993495	−	0.113876i	$-0.0363268\pi$
$234$	4.64898	−	13.3183i	0.303913	−	0.870646i
$235$	−1.88268	−	7.02627i	−0.122813	−	0.458344i
$236$	−12.6408	+	9.35891i	−0.822846	+	0.609213i
$237$	−0.911191	−	0.244153i	−0.0591882	−	0.0158594i
$238$	15.4352	+	5.38790i	1.00051	+	0.349245i
$239$	−9.52562	−	2.55238i	−0.616161	−	0.165100i	−0.0627791	−	0.998027i	$-0.519996\pi$
$239$	−9.52562	−	2.55238i	−0.616161	−	0.165100i	−0.553382	+	0.832928i	$0.686663\pi$
$240$	−3.60560	−	0.123987i	−0.232741	−	0.00800333i
$241$	−28.0062	+	7.50425i	−1.80404	+	0.483391i	−0.994597	−	0.103807i	$-0.966897\pi$
$241$	−28.0062	+	7.50425i	−1.80404	+	0.483391i	−0.809443	+	0.587199i	$0.800231\pi$
$242$	2.04769	+	4.24385i	0.131630	+	0.272805i
$243$	8.07228	+	13.9816i	0.517837	+	0.896920i
$244$	−26.1288	−	11.3528i	−1.67272	−	0.726792i
$245$	2.68722	+	2.68722i	0.171680	+	0.171680i
$246$	−0.911920	−	0.620727i	−0.0581419	−	0.0395761i
$247$	−1.37519	−	2.38190i	−0.0875014	−	0.151557i
$248$	−12.7865	−	20.2474i	−0.811943	−	1.28571i
$249$			5.87294i			0.372182i
$250$	−1.33521	−	0.466075i	−0.0844458	−	0.0294772i
$251$	0.305893	+	0.305893i	0.0193078	+	0.0193078i	0.716695	−	0.697387i	$-0.245654\pi$
$251$	0.305893	+	0.305893i	0.0193078	+	0.0193078i	−0.697387	+	0.716695i	$0.745654\pi$
$252$	11.2496	+	8.94344i	0.708658	+	0.563384i
$253$	−3.32529	+	3.32529i	−0.209059	+	0.209059i
$254$	18.0159	+	12.2631i	1.13042	+	0.769454i
$255$	−2.74758	−	1.58632i	−0.172060	−	0.0993390i
$256$	−14.3732	+	7.02926i	−0.898326	+	0.439329i
$257$	1.30755	−	4.87986i	0.0815629	−	0.304397i	−0.913078	−	0.407784i	$-0.866301\pi$
$257$	1.30755	−	4.87986i	0.0815629	−	0.304397i	0.994641	+	0.103387i	$0.0329682\pi$
$258$	−0.659212	+	0.568167i	−0.0410408	+	0.0353725i
$259$	−13.9785	+	14.2903i	−0.868580	+	0.887958i
$260$	−1.34619	+	9.02401i	−0.0834872	+	0.559645i
$261$	−0.836363	−	0.224103i	−0.0517696	−	0.0138716i
$262$	−17.5511	+	3.33460i	−1.08431	+	0.206013i
$263$	8.19266	−	14.1901i	0.505181	−	0.874999i	−0.494801	−	0.869006i	$-0.664759\pi$
$263$	8.19266	−	14.1901i	0.505181	−	0.874999i	0.999982	−	0.00599258i	$-0.00190751\pi$
$264$	4.79311	−	5.18932i	0.294996	−	0.319381i
$265$	−1.18501	−	1.18501i	−0.0727947	−	0.0727947i
$266$	2.75282	−	0.523018i	0.168786	−	0.0320683i
$267$	−10.5561	+	10.5561i	−0.646025	+	0.646025i
$268$	6.38672	+	16.2010i	0.390131	+	0.989633i
$269$	−12.5471			−0.765013			−0.382506	−	0.923953i	$-0.624939\pi$
$269$	−12.5471			−0.765013			−0.382506	+	0.923953i	$0.624939\pi$
$270$	−4.31903	−	5.01113i	−0.262848	−	0.304967i
$271$	−6.97894	+	4.02929i	−0.423940	+	0.244762i	−0.696762	−	0.717303i	$-0.745376\pi$
$271$	−6.97894	+	4.02929i	−0.423940	+	0.244762i	0.272821	+	0.962065i	$0.412043\pi$
$272$	−14.0620	−	0.483556i	−0.852637	−	0.0293199i
$273$	−9.56152	+	9.56152i	−0.578689	+	0.578689i
$274$	−10.8263	−	22.4377i	−0.654044	−	1.35551i
$275$	2.39814	−	1.38457i	0.144613	−	0.0834924i
$276$	−2.80966	−	1.22079i	−0.169122	−	0.0734827i
$277$	−6.93088	−	25.8664i	−0.416436	−	1.55416i	−0.781942	−	0.623351i	$-0.785771\pi$
$277$	−6.93088	−	25.8664i	−0.416436	−	1.55416i	0.365506	−	0.930809i	$-0.380896\pi$
$278$	18.2180	−	26.7644i	1.09264	−	1.60522i
$279$	4.79129	−	17.8813i	0.286847	−	1.07053i
$280$	−8.22795	−	4.32473i	−0.491714	−	0.258452i
$281$	−7.90287	+	29.4939i	−0.471445	+	1.75946i	0.163137	+	0.986603i	$0.447839\pi$
$281$	−7.90287	+	29.4939i	−0.471445	+	1.75946i	−0.634583	+	0.772855i	$0.718828\pi$
$282$	−0.686372	+	9.25293i	−0.0408729	+	0.551004i
$283$	−23.2086	+	6.21873i	−1.37961	+	0.369665i	−0.870979	−	0.491320i	$-0.836515\pi$
$283$	−23.2086	+	6.21873i	−1.37961	+	0.369665i	−0.508630	+	0.860985i	$0.669848\pi$
$284$	8.67263	−	3.41891i	0.514626	−	0.202875i
$285$	−0.543775			−0.0322104
$286$	−11.6635	−	13.5325i	−0.689676	−	0.800193i
$287$	−1.42110	−	2.46142i	−0.0838851	−	0.145293i
$288$	−11.5308	−	4.47524i	−0.679459	−	0.263706i
$289$	4.00672	+	2.31328i	0.235689	+	0.136075i
$290$	0.558498	+	0.0414288i	0.0327961	+	0.00243278i
$291$	14.5197	−	3.89053i	0.851158	−	0.228067i
$292$	6.61891	+	5.26204i	0.387343	+	0.307938i
$293$	−8.90709	+	15.4275i	−0.520358	+	0.901286i	0.479362	+	0.877617i	$0.340868\pi$
$293$	−8.90709	+	15.4275i	−0.520358	+	0.901286i	−0.999720	+	0.0236689i	$0.992465\pi$
$294$	−2.10651	−	4.36576i	−0.122854	−	0.254616i
$295$	7.86414			0.457868
$296$	7.83617	−	15.3165i	0.455468	−	0.890252i
$297$	12.9537			0.751650
$298$	−7.25329	−	15.0325i	−0.420172	−	0.870810i
$299$	−3.87365	+	6.70936i	−0.224019	+	0.388012i
$300$	1.41202	+	1.12256i	0.0815231	+	0.0648109i
$301$	−2.16584	+	0.580336i	−0.124837	+	0.0334500i
$302$	−5.46178	−	0.405149i	−0.314290	−	0.0233137i
$303$	−1.37297	−	0.792683i	−0.0788749	−	0.0455384i
$304$	−2.12871	+	1.13331i	−0.122090	+	0.0649998i
$305$	7.12215	+	12.3359i	0.407813	+	0.706353i
$306$	−7.10122	−	8.23916i	−0.405950	−	0.471001i
$307$	−0.521528			−0.0297652			−0.0148826	−	0.999889i	$-0.504737\pi$
$307$	−0.521528			−0.0297652			−0.0148826	+	0.999889i	$0.504737\pi$
$308$	16.9326	−	6.67514i	0.964825	−	0.380352i
$309$	2.24495	−	0.601533i	0.127711	−	0.0342200i
$310$	−0.885743	+	11.9406i	−0.0503068	+	0.678182i
$311$	−3.48662	+	13.0122i	−0.197708	+	0.737856i	0.793841	+	0.608125i	$0.208078\pi$
$311$	−3.48662	+	13.0122i	−0.197708	+	0.737856i	−0.991549	+	0.129731i	$0.958589\pi$
$312$	5.41459	−	10.3014i	0.306541	−	0.583203i
$313$	−4.21541	+	15.7321i	−0.238269	+	0.889233i	0.738379	+	0.674387i	$0.235592\pi$
$313$	−4.21541	+	15.7321i	−0.238269	+	0.889233i	−0.976648	+	0.214847i	$0.931075\pi$
$314$	5.95706	−	8.75162i	0.336176	−	0.493883i
$315$	−1.85980	−	6.94088i	−0.104788	−	0.391074i
$316$	1.91853	+	0.833593i	0.107926	+	0.0468933i
$317$	1.07224	−	0.619060i	0.0602232	−	0.0347699i	−0.469586	−	0.882887i	$-0.655597\pi$
$317$	1.07224	−	0.619060i	0.0602232	−	0.0347699i	0.529809	+	0.848117i	$0.322264\pi$
$318$	0.928929	+	1.92521i	0.0520917	+	0.107961i
$319$	−0.775402	+	0.775402i	−0.0434142	+	0.0434142i
$320$	7.86720	+	1.45160i	0.439790	+	0.0811468i
$321$	2.91422	−	1.68252i	0.162656	−	0.0939093i
$322$	−5.15294	−	5.97867i	−0.287162	−	0.333178i
$323$	−2.12075			−0.118002
$324$	−1.71668	−	4.35463i	−0.0953708	−	0.241924i
$325$	3.22578	−	3.22578i	0.178934	−	0.178934i
$326$	15.0573	−	2.86080i	0.833948	−	0.158445i
$327$	−0.0244320	−	0.0244320i	−0.00135109	−	0.00135109i
$328$	1.79693	+	1.65973i	0.0992186	+	0.0916432i
$329$	−11.9528	+	20.7028i	−0.658979	+	1.14138i
$330$	−3.47003	+	0.659284i	−0.191019	+	0.0362924i
$331$	−10.0566	−	2.69465i	−0.552759	−	0.148111i	−0.0283814	−	0.999597i	$-0.509035\pi$
$331$	−10.0566	−	2.69465i	−0.552759	−	0.148111i	−0.524378	+	0.851486i	$0.675702\pi$
$332$	1.92149	−	12.8805i	0.105455	−	0.706907i
$333$	12.8081	−	3.58381i	0.701880	−	0.196391i
$334$	6.07915	−	5.23954i	0.332636	−	0.286695i
$335$	2.25359	−	8.41052i	0.123127	−	0.459516i
$336$	8.09066	+	8.66691i	0.441382	+	0.472819i
$337$	1.18488	+	0.684093i	0.0645447	+	0.0372649i	0.531925	−	0.846791i	$-0.321469\pi$
$337$	1.18488	+	0.684093i	0.0645447	+	0.0372649i	−0.467380	+	0.884056i	$0.654802\pi$
$338$	−9.13198	−	6.21597i	−0.496714	−	0.338104i
$339$	3.47564	−	3.47564i	0.188771	−	0.188771i
$340$	5.50696	+	4.37804i	0.298657	+	0.237432i
$341$	−16.5780	−	16.5780i	−0.897750	−	0.897750i
$342$	−1.76013	−	0.614402i	−0.0951770	−	0.0332231i
$343$			10.5154i			0.567779i
$344$	1.63167	−	1.03042i	0.0879736	−	0.0555564i
$345$	0.765854	+	1.32650i	0.0412322	+	0.0714163i
$346$	15.8232	+	10.7705i	0.850660	+	0.579028i
$347$	−17.5712	−	17.5712i	−0.943270	−	0.943270i	0.0552054	−	0.998475i	$-0.482419\pi$
$347$	−17.5712	−	17.5712i	−0.943270	−	0.943270i	−0.998475	+	0.0552054i	$0.982419\pi$
$348$	−0.655166	−	0.284667i	−0.0351206	−	0.0152597i
$349$	2.85173	+	4.93935i	0.152650	+	0.264397i	0.932201	−	0.361942i	$-0.117886\pi$
$349$	2.85173	+	4.93935i	0.152650	+	0.264397i	−0.779551	+	0.626339i	$0.784553\pi$
$350$	2.01971	+	4.18586i	0.107958	+	0.223743i
$351$	20.6131	−	5.52326i	1.10025	−	0.294810i
$352$	−12.2100	+	9.81296i	−0.650796	+	0.523032i
$353$	−22.8139	−	6.11298i	−1.21426	−	0.325361i	−0.405830	−	0.913949i	$-0.633017\pi$
$353$	−22.8139	−	6.11298i	−1.21426	−	0.325361i	−0.808433	+	0.588588i	$0.799684\pi$
$354$	−9.47053	−	3.30584i	−0.503353	−	0.175704i
$355$	−4.50228	−	1.20638i	−0.238956	−	0.0640281i
$356$	26.6053	−	19.6979i	1.41008	−	1.04398i
$357$	2.69857	+	10.0712i	0.142824	+	0.533025i
$358$	3.81220	−	10.9212i	0.201481	−	0.577201i
$359$			31.9778i			1.68772i	0.536560	+	0.843862i	$0.319723\pi$
$359$			31.9778i			1.68772i	−0.536560	+	0.843862i	$0.680277\pi$
$360$	3.30217	+	5.22900i	0.174040	+	0.275592i
$361$	16.1397	−	9.31826i	0.849458	−	0.490435i
$362$	−8.28513	−	0.614582i	−0.435457	−	0.0323017i
$363$	−1.50258	+	2.60255i	−0.0788652	+	0.136598i
$364$	24.0985	−	17.8419i	1.26311	−	0.935169i
$365$	−1.09425	−	4.08380i	−0.0572757	−	0.213756i
$366$	−3.39133	−	17.8497i	−0.177268	−	0.933018i
$367$	12.1558	+	7.01815i	0.634527	+	0.366344i	0.782503	−	0.622647i	$-0.213943\pi$
$367$	12.1558	+	7.01815i	0.634527	+	0.366344i	−0.147976	+	0.988991i	$0.547276\pi$
$368$	5.76270	+	3.59667i	0.300402	+	0.187489i
$369$			1.89099i			0.0984413i
$370$	−7.70589	+	3.82351i	−0.400610	+	0.198775i
$371$			5.50751i			0.285936i
$372$	6.08614	−	14.0074i	0.315552	−	0.726248i
$373$	−7.58014	−	4.37639i	−0.392485	−	0.226601i	0.290751	−	0.956799i	$-0.406095\pi$
$373$	−7.58014	−	4.37639i	−0.392485	−	0.226601i	−0.683236	+	0.730197i	$0.739428\pi$
$374$	−13.5333	+	2.57124i	−0.699790	+	0.132956i
$375$	−0.233438	−	0.871201i	−0.0120547	−	0.0449886i
$376$	4.53269	−	20.0689i	0.233756	−	1.03497i
$377$	−0.903270	+	1.56451i	−0.0465208	+	0.0805763i
$378$	−1.60832	+	21.6816i	−0.0827230	+	1.11518i
$379$	5.25996	−	3.03684i	0.270186	−	0.155992i	−0.358786	−	0.933420i	$-0.616809\pi$
$379$	5.25996	−	3.03684i	0.270186	−	0.155992i	0.628972	+	0.777428i	$0.283476\pi$
$380$	1.19260	+	0.177911i	0.0611791	+	0.00912662i
$381$			13.8991i			0.712072i
$382$	−19.8046	−	6.91312i	−1.01329	−	0.353706i
$383$	−2.34709	−	8.75945i	−0.119931	−	0.447587i	0.879678	−	0.475570i	$-0.157758\pi$
$383$	−2.34709	−	8.75945i	−0.119931	−	0.447587i	−0.999608	+	0.0279831i	$0.991092\pi$
$384$	−8.86401	−	5.05524i	−0.452339	−	0.257974i
$385$	−8.79033	−	2.35536i	−0.447997	−	0.120040i
$386$	1.39214	−	3.98818i	0.0708579	−	0.202993i
$387$	1.44099	+	0.386113i	0.0732498	+	0.0196272i
$388$	−33.1173	+	3.78217i	−1.68127	+	0.192011i
$389$	−33.8403	+	9.06749i	−1.71577	+	0.459740i	−0.976828	−	0.214026i	$-0.931342\pi$
$389$	−33.8403	+	9.06749i	−1.71577	+	0.459740i	−0.738945	+	0.673766i	$0.764676\pi$
$390$	−5.24071	+	2.52868i	−0.265374	+	0.128045i
$391$	2.98687	+	5.17341i	0.151053	+	0.261631i
$392$	3.19159	+	10.2641i	0.161200	+	0.518417i
$393$	−8.05656	−	8.05656i	−0.406400	−	0.406400i
$394$	−22.0998	+	32.4672i	−1.11337	+	1.63567i
$395$	−0.522951	−	0.905777i	−0.0263125	−	0.0455746i
$396$	−11.9770	−	1.78671i	−0.601865	−	0.0897854i
$397$		−	4.77898i		−	0.239850i	−0.992783	−	0.119925i	$-0.961735\pi$
$397$		−	4.77898i		−	0.239850i	0.992783	−	0.119925i	$-0.0382654\pi$
$398$	12.6454	−	36.2262i	0.633855	−	1.81586i
$399$	1.26364	+	1.26364i	0.0632610	+	0.0632610i
$400$	−2.72955	−	2.92396i	−0.136478	−	0.146198i
$401$	20.1158	−	20.1158i	1.00454	−	1.00454i	0.00454755	−	0.999990i	$-0.498552\pi$
$401$	20.1158	−	20.1158i	1.00454	−	1.00454i	0.999990	−	0.00454755i	$-0.00144753\pi$
$402$	−6.24945	+	9.18118i	−0.311694	+	0.457915i
$403$	−33.4490	−	19.3118i	−1.66622	−	0.961990i
$404$	2.75183	+	2.18771i	0.136909	+	0.108842i
$405$	−0.605739	+	2.26065i	−0.0300994	+	0.112332i
$406$	−1.20158	−	1.39412i	−0.0596333	−	0.0691892i
$407$	4.17980	−	16.3171i	0.207185	−	0.808810i
$408$	−4.79146	−	7.58728i	−0.237212	−	0.375626i
$409$	−13.3185	−	3.56868i	−0.658558	−	0.176460i	−0.0859628	−	0.996298i	$-0.527397\pi$
$409$	−13.3185	−	3.56868i	−0.658558	−	0.176460i	−0.572595	+	0.819838i	$0.694063\pi$
$410$	−0.228293	−	1.20158i	−0.0112746	−	0.0593418i
$411$	7.94432	−	13.7600i	0.391864	−	0.678729i
$412$	−5.12041	+	0.584779i	−0.252264	+	0.0288100i
$413$	−18.2749	−	18.2749i	−0.899248	−	0.899248i
$414$	0.980185	+	5.15903i	0.0481735	+	0.253553i
$415$	−4.60432	+	4.60432i	−0.226017	+	0.226017i
$416$	−15.2456	+	20.8214i	−0.747477	+	1.02085i
$417$	20.6485			1.01116
$418$	−1.78843	+	1.54143i	−0.0874752	+	0.0753937i
$419$	−15.3363	+	8.85440i	−0.749226	+	0.432566i	−0.825414	−	0.564528i	$-0.809058\pi$
$419$	−15.3363	+	8.85440i	−0.749226	+	0.432566i	0.0761882	+	0.997093i	$0.475725\pi$
$420$	−0.672660	−	5.88991i	−0.0328225	−	0.287398i
$421$	4.23180	−	4.23180i	0.206245	−	0.206245i	−0.596424	−	0.802669i	$-0.703412\pi$
$421$	4.23180	−	4.23180i	0.206245	−	0.206245i	0.802669	+	0.596424i	$0.203412\pi$
$422$	15.4526	−	7.45599i	0.752221	−	0.362952i
$423$	13.7741	−	7.95250i	0.669722	−	0.386664i
$424$	−1.40743	−	4.52628i	−0.0683508	−	0.219815i
$425$	−0.910419	−	3.39773i	−0.0441618	−	0.164814i
$426$	4.91482	+	3.34542i	0.238124	+	0.162086i
$427$	12.1159	−	45.2171i	0.586329	−	2.18821i
$428$	−6.94191	+	2.73663i	−0.335550	+	0.132280i
$429$	2.94892	−	11.0055i	0.142375	−	0.531352i
$430$	−0.962252	−	0.0713788i	−0.0464039	−	0.00344219i
$431$	−15.9374	+	4.27040i	−0.767675	+	0.205698i	−0.621344	−	0.783538i	$-0.713413\pi$
$431$	−15.9374	+	4.27040i	−0.767675	+	0.205698i	−0.146331	+	0.989236i	$0.546746\pi$
$432$	−4.21890	−	18.2298i	−0.202982	−	0.877079i
$433$	23.0300			1.10675			0.553376	−	0.832932i	$-0.313339\pi$
$433$	23.0300			1.10675			0.553376	+	0.832932i	$0.313339\pi$
$434$	29.8062	−	25.6896i	1.43074	−	1.23314i
$435$	0.178584	+	0.309317i	0.00856246	+	0.0148306i
$436$	0.0455903	+	0.0615775i	0.00218338	+	0.00294903i
$437$	0.886699	+	0.511936i	0.0424166	+	0.0244892i
$438$	−0.398932	+	5.37797i	−0.0190617	+	0.256969i
$439$	29.7892	−	7.98200i	1.42176	−	0.380960i	0.535654	−	0.844438i	$-0.320065\pi$
$439$	29.7892	−	7.98200i	1.42176	−	0.380960i	0.886109	+	0.463478i	$0.153399\pi$
$440$	7.82612	−	0.310621i	0.373096	−	0.0148083i
$441$	−4.15471	+	7.19617i	−0.197843	+	0.342675i
$442$	−20.4391	+	9.86198i	−0.972187	+	0.469087i
$443$	−9.13729			−0.434126			−0.217063	−	0.976158i	$-0.569648\pi$
$443$	−9.13729			−0.434126			−0.217063	+	0.976158i	$0.569648\pi$
$444$	10.8872	−	1.36520i	0.516685	−	0.0647897i
$445$	−16.5518			−0.784630
$446$	31.2571	−	15.0818i	1.48007	−	0.714142i
$447$	5.32243	−	9.21872i	0.251742	−	0.436030i
$448$	−14.9087	−	21.6552i	−0.704371	−	1.02311i
$449$	−17.6764	+	4.73637i	−0.834200	+	0.223523i	−0.650545	−	0.759468i	$-0.725460\pi$
$449$	−17.6764	+	4.73637i	−0.834200	+	0.223523i	−0.183655	+	0.982991i	$0.558793\pi$
$450$	0.228747	−	3.08373i	0.0107833	−	0.145368i
$451$	2.07402	+	1.19743i	0.0976616	+	0.0563849i
$452$	−8.75987	+	6.48558i	−0.412030	+	0.305056i
$453$	−1.74645	−	3.02494i	−0.0820553	−	0.142124i
$454$	18.8892	−	16.2804i	0.886514	−	0.764075i
$455$	−14.9923			−0.702848
$456$	−1.36142	−	0.715584i	−0.0637544	−	0.0335103i
$457$	−7.82346	+	2.09629i	−0.365966	+	0.0980603i	−0.437116	−	0.899405i	$-0.644000\pi$
$457$	−7.82346	+	2.09629i	−0.365966	+	0.0980603i	0.0711495	+	0.997466i	$0.477333\pi$
$458$	−19.9495	−	1.47983i	−0.932178	−	0.0691480i
$459$	4.25884	−	15.8942i	0.198786	−	0.741879i
$460$	−1.24566	−	3.15983i	−0.0580793	−	0.147328i
$461$	0.0198594	−	0.0741162i	0.000924943	−	0.00345194i	−0.965462	−	0.260545i	$-0.916098\pi$
$461$	0.0198594	−	0.0741162i	0.000924943	−	0.00345194i	0.966387	+	0.257093i	$0.0827646\pi$
$462$	9.59579	+	6.53167i	0.446436	+	0.303881i
$463$	0.697388	+	2.60269i	0.0324104	+	0.120957i	0.980236	−	0.197833i	$-0.0633903\pi$
$463$	0.697388	+	2.60269i	0.0324104	+	0.120957i	−0.947825	+	0.318790i	$0.896724\pi$
$464$	1.34377	+	0.838682i	0.0623827	+	0.0389349i
$465$	−6.61316	+	3.81811i	−0.306678	+	0.177061i
$466$	−4.42801	+	2.13654i	−0.205123	+	0.0989735i
$467$	−2.76797	+	2.76797i	−0.128087	+	0.128087i	−0.768244	−	0.640157i	$-0.778869\pi$
$467$	−2.76797	+	2.76797i	−0.128087	+	0.128087i	0.640157	+	0.768244i	$0.278869\pi$
$468$	−19.8206	+	2.26363i	−0.916209	+	0.104636i
$469$	−24.7815	+	14.3076i	−1.14430	+	0.660664i
$470$	−7.79231	+	6.71609i	−0.359433	+	0.309790i
$471$	6.75179			0.311106
$472$	19.6891	+	10.3489i	0.906262	+	0.476345i
$473$	1.33596	−	1.33596i	0.0614276	−	0.0614276i
$474$	0.249012	+	1.31063i	0.0114375	+	0.0601992i
$475$	−0.426314	−	0.426314i	−0.0195606	−	0.0195606i
$476$	−2.62341	−	22.9710i	−0.120244	−	1.05287i
$477$	1.83215	−	3.17337i	0.0838882	−	0.145299i
$478$	2.60318	+	13.7014i	0.119067	+	0.626686i
$479$	−34.2631	−	9.18078i	−1.56552	−	0.419480i	−0.631116	−	0.775689i	$-0.717403\pi$
$479$	−34.2631	−	9.18078i	−1.56552	−	0.419480i	−0.934407	+	0.356208i	$0.884069\pi$
$480$	2.05797	+	4.66865i	0.0939329	+	0.213094i
$481$	−0.306095	−	27.7475i	−0.0139567	−	1.26518i
$482$	26.7699	+	31.0596i	1.21933	+	1.41473i
$483$	1.30284	−	4.86226i	0.0592812	−	0.221240i
$484$	4.14694	−	5.21627i	0.188497	−	0.237103i
$485$	14.4334	+	8.33313i	0.655387	+	0.378388i
$486$	12.8474	−	18.8743i	0.582769	−	0.856155i
$487$	22.6634	−	22.6634i	1.02698	−	1.02698i	0.0273529	−	0.999626i	$-0.491292\pi$
$487$	22.6634	−	22.6634i	1.02698	−	1.02698i	0.999626	−	0.0273529i	$-0.00870780\pi$
$488$	1.59782	+	40.2573i	0.0723301	+	1.82236i
$489$	6.91183	+	6.91183i	0.312564	+	0.312564i
$490$	1.77123	−	5.07419i	0.0800159	−	0.229228i
$491$			35.0493i			1.58175i	0.611975	+	0.790877i	$0.290375\pi$
$491$			35.0493i			1.58175i	−0.611975	+	0.790877i	$0.709625\pi$
$492$	−0.230181	+	1.54299i	−0.0103774	+	0.0695634i
$493$	0.696488	+	1.20635i	0.0313682	+	0.0543314i
$494$	−2.18868	+	3.21542i	−0.0984732	+	0.144669i
$495$	4.28135	+	4.28135i	0.192432	+	0.192432i
$496$	−17.9309	+	28.7296i	−0.805123	+	1.29000i
$497$	7.65908	+	13.2659i	0.343557	+	0.595058i
$498$	7.48035	−	3.60932i	0.335202	−	0.161737i
$499$	4.03021	−	1.07989i	0.180417	−	0.0483426i	−0.167479	−	0.985876i	$-0.553563\pi$
$499$	4.03021	−	1.07989i	0.180417	−	0.0483426i	0.347896	+	0.937533i	$0.386896\pi$
$500$	0.226936	+	1.98708i	0.0101489	+	0.0888651i
$501$	4.94398	+	1.32473i	0.220881	+	0.0591848i
$502$	0.201623	−	0.577607i	0.00899887	−	0.0257798i
$503$	−28.8191	−	7.72207i	−1.28498	−	0.344310i	−0.449230	−	0.893416i	$-0.648301\pi$
$503$	−28.8191	−	7.72207i	−1.28498	−	0.344310i	−0.835752	+	0.549106i	$0.814968\pi$
$504$	4.47760	−	19.8249i	0.199448	−	0.883073i
$505$	−0.454937	−	1.69785i	−0.0202444	−	0.0755532i
$506$	6.27904	+	2.19180i	0.279137	+	0.0974373i
$507$		−	7.04523i		−	0.312890i
$508$	4.54746	−	30.4833i	0.201761	−	1.35248i
$509$	32.2274	−	18.6065i	1.42845	−	0.824718i	0.431454	−	0.902135i	$-0.358001\pi$
$509$	32.2274	−	18.6065i	1.42845	−	0.824718i	0.996999	+	0.0774174i	$0.0246674\pi$
$510$	−0.331913	+	4.47449i	−0.0146973	+	0.198134i
$511$	−6.94718	+	12.0329i	−0.307325	+	0.532302i
$512$	17.7865	+	13.9872i	0.786059	+	0.618152i
$513$	−0.729947	−	2.72420i	−0.0322279	−	0.120276i
$514$	−7.01904	+	1.33358i	−0.309597	+	0.0588215i
$515$	2.23161	+	1.28842i	0.0983367	+	0.0567747i
$516$	1.12880	+	0.490460i	0.0496928	+	0.0215913i
$517$		−	20.1430i		−	0.885889i
$518$	26.7923	+	9.02198i	1.17719	+	0.396403i
$519$			12.2074i			0.535847i
$520$	12.3212	−	3.83123i	0.540320	−	0.168011i
$521$	21.3107	+	12.3037i	0.933639	+	0.539037i	0.887961	−	0.459920i	$-0.152122\pi$
$521$	21.3107	+	12.3037i	0.933639	+	0.539037i	0.0456783	+	0.998956i	$0.485455\pi$
$522$	0.228563	+	1.20300i	0.0100039	+	0.0526539i
$523$	8.89673	+	33.2031i	0.389027	+	1.45187i	0.831720	+	0.555195i	$0.187357\pi$
$523$	8.89673	+	33.2031i	0.389027	+	1.45187i	−0.442693	+	0.896673i	$0.645977\pi$
$524$	15.0336	+	20.3055i	0.656747	+	0.887048i
$525$	−1.48205	+	2.56698i	−0.0646819	+	0.112032i
$526$	−23.1088	−	1.71419i	−1.00759	−	0.0747422i
$527$	−25.7917	+	14.8908i	−1.12350	+	0.648655i
$528$	−9.55532	−	2.91579i	−0.415842	−	0.126893i
$529$			20.1160i			0.874607i
$530$	−0.781076	+	2.23762i	−0.0339278	+	0.0971959i
$531$	4.45041	+	16.6092i	0.193131	+	0.720776i
$532$	−2.35796	−	3.18483i	−0.102231	−	0.138080i
$533$	3.81093	+	1.02114i	0.165070	+	0.0442303i
$534$	19.9328	+	6.95786i	0.862576	+	0.301096i
$535$	3.60380	+	0.965634i	0.155806	+	0.0417480i
$536$	16.7101	−	18.0914i	0.721766	−	0.781428i
$537$	7.12588	−	1.90937i	0.307505	−	0.0823956i
$538$	7.71107	+	15.9813i	0.332448	+	0.689001i
$539$	5.26177	+	9.11365i	0.226640	+	0.392553i
$540$	−3.72833	+	8.58081i	−0.160442	+	0.369259i
$541$	16.2421	+	16.2421i	0.698302	+	0.698302i	0.964044	−	0.265742i	$-0.0856169\pi$
$541$	16.2421	+	16.2421i	0.698302	+	0.698302i	−0.265742	+	0.964044i	$0.585617\pi$
$542$	9.42113	+	6.41278i	0.404672	+	0.275453i
$543$	−2.64924	−	4.58861i	−0.113690	−	0.196916i
$544$	8.02618	+	18.2080i	0.344120	+	0.780661i
$545$		−	0.0383088i		−	0.00164097i
$546$	18.0547	+	6.30228i	0.772669	+	0.269713i
$547$	11.8048	+	11.8048i	0.504739	+	0.504739i	0.912907	−	0.408168i	$-0.133832\pi$
$547$	11.8048	+	11.8048i	0.504739	+	0.504739i	−0.408168	+	0.912907i	$0.633832\pi$
$548$	−21.9253	+	27.5790i	−0.936604	+	1.17812i
$549$	−22.0231	+	22.0231i	−0.939924	+	0.939924i
$550$	−3.23734	−	2.20359i	−0.138041	−	0.0939615i
$551$	0.206763	+	0.119375i	0.00880841	+	0.00508554i
$552$	0.171816	+	4.32892i	0.00731298	+	0.184251i
$553$	−0.889621	+	3.32011i	−0.0378305	+	0.141185i
$554$	−28.6865	+	24.7245i	−1.21877	+	1.05044i
$555$	−4.78120	−	2.69055i	−0.202951	−	0.114207i
$556$	−45.2860	−	6.75570i	−1.92055	−	0.286506i
$557$	−37.6479	−	10.0877i	−1.59519	−	0.427430i	−0.651605	−	0.758558i	$-0.725904\pi$
$557$	−37.6479	−	10.0877i	−1.59519	−	0.427430i	−0.943586	+	0.331128i	$0.892571\pi$
$558$	−25.7200	+	4.88665i	−1.08881	+	0.206868i
$559$	1.55627	−	2.69554i	0.0658232	−	0.114009i
$560$	−0.451773	+	13.1378i	−0.0190909	+	0.555172i
$561$	−6.21224	−	6.21224i	−0.262281	−	0.262281i
$562$	42.4232	−	8.06014i	1.78951	−	0.339997i
$563$	27.6303	−	27.6303i	1.16448	−	1.16448i	0.180994	−	0.983484i	$-0.442068\pi$
$563$	27.6303	−	27.6303i	1.16448	−	1.16448i	0.983484	−	0.180994i	$-0.0579315\pi$
$564$	12.2073	−	4.81233i	0.514019	−	0.202635i
$565$	5.44973			0.229272
$566$	22.1841	+	25.7389i	0.932466	+	1.08189i
$567$	6.66097	−	3.84572i	0.279735	−	0.161505i
$568$	−9.68458	−	8.94516i	−0.406356	−	0.375330i
$569$	−11.3129	+	11.3129i	−0.474261	+	0.474261i	−0.903290	−	0.429030i	$-0.858856\pi$
$569$	−11.3129	+	11.3129i	−0.474261	+	0.474261i	0.429030	+	0.903290i	$0.358856\pi$
$570$	0.334187	+	0.692605i	0.0139975	+	0.0290100i
$571$	23.0654	−	13.3168i	0.965256	−	0.557291i	0.0674692	−	0.997721i	$-0.478508\pi$
$571$	23.0654	−	13.3168i	0.965256	−	0.557291i	0.897787	+	0.440431i	$0.145174\pi$
$572$	−10.0683	+	23.1724i	−0.420977	+	0.968886i
$573$	−3.46249	−	12.9222i	−0.144648	−	0.539833i
$574$	−2.26175	+	3.32277i	−0.0944034	+	0.138690i
$575$	−0.439539	+	1.64038i	−0.0183300	+	0.0684087i
$576$	1.38635	+	17.4371i	0.0577647	+	0.726546i
$577$	3.18534	−	11.8879i	0.132607	−	0.494898i	−0.867389	−	0.497631i	$-0.834203\pi$
$577$	3.18534	−	11.8879i	0.132607	−	0.494898i	0.999996	+	0.00273331i	$0.000870042\pi$
$578$	0.484019	−	6.52502i	0.0201325	−	0.271405i
$579$	2.60222	−	0.697264i	0.108145	−	0.0289773i
$580$	−0.290467	−	0.736819i	−0.0120610	−	0.0305947i
$581$	21.3992			0.887790
$582$	−13.8787	−	16.1027i	−0.575290	−	0.667477i
$583$	−2.32034	−	4.01894i	−0.0960986	−	0.166448i
$584$	2.63448	−	11.6644i	0.109016	−	0.482675i
$585$	8.63838	+	4.98737i	0.357153	+	0.206202i
$586$	25.1240	+	1.86367i	1.03786	+	0.0769876i
$587$	−8.07569	+	2.16387i	−0.333319	+	0.0893126i	−0.421597	−	0.906783i	$-0.638530\pi$
$587$	−8.07569	+	2.16387i	−0.333319	+	0.0893126i	0.0882778	+	0.996096i	$0.471864\pi$
$588$	−4.26606	+	5.36611i	−0.175929	+	0.221295i
$589$	−2.55222	+	4.42058i	−0.105162	+	0.182147i
$590$	−4.83305	−	10.0165i	−0.198974	−	0.412375i
$591$	−25.0481			−1.03034
$592$	−24.3244	−	0.567903i	−0.999728	−	0.0233407i
$593$	38.7440			1.59102			0.795512	−	0.605938i	$-0.207202\pi$
$593$	38.7440			1.59102			0.795512	+	0.605938i	$0.207202\pi$
$594$	−7.96093	−	16.4991i	−0.326641	−	0.676966i
$595$	−5.78007	+	10.0114i	−0.236960	+	0.410426i
$596$	−14.6892	+	18.4770i	−0.601695	+	0.756848i
$597$	23.6371	−	6.33353i	0.967401	−	0.259214i
$598$	10.9263	+	0.810502i	0.446810	+	0.0331439i
$599$	24.3550	+	14.0614i	0.995118	+	0.574531i	0.906800	−	0.421561i	$-0.138518\pi$
$599$	24.3550	+	14.0614i	0.995118	+	0.574531i	0.0883175	+	0.996092i	$0.471851\pi$
$600$	0.562017	−	2.48838i	0.0229442	−	0.101588i
$601$	17.0938	+	29.6074i	0.697272	+	1.20771i	0.969409	+	0.245451i	$0.0789362\pi$
$601$	17.0938	+	29.6074i	0.697272	+	1.20771i	−0.272137	+	0.962258i	$0.587730\pi$
$602$	2.07023	+	2.40198i	0.0843764	+	0.0978972i
$603$	19.0385			0.775306
$604$	2.84060	+	7.20565i	0.115582	+	0.293194i
$605$	−3.21838	+	0.862363i	−0.130846	+	0.0350600i
$606$	−0.165857	+	2.23590i	−0.00673747	+	0.0908274i
$607$	4.93722	−	18.4259i	0.200395	−	0.747886i	−0.790409	−	0.612580i	$-0.790132\pi$
$607$	4.93722	−	18.4259i	0.200395	−	0.747886i	0.990804	−	0.135306i	$-0.0432016\pi$
$608$	2.75173	+	2.01484i	0.111597	+	0.0817124i
$609$	0.303800	−	1.13380i	0.0123106	−	0.0459437i
$610$	11.3352	−	16.6527i	0.458949	−	0.674250i
$611$	−8.58869	−	32.0534i	−0.347461	−	1.29674i
$612$	−6.13001	+	14.1083i	−0.247791	+	0.570296i
$613$	−33.3706	+	19.2665i	−1.34783	+	0.778168i	−0.987941	−	0.154829i	$-0.950517\pi$
$613$	−33.3706	+	19.2665i	−1.34783	+	0.778168i	−0.359885	+	0.932997i	$0.617184\pi$
$614$	0.320514	+	0.664269i	0.0129349	+	0.0268077i
$615$	0.551566	−	0.551566i	0.0222413	−	0.0222413i
$616$	−18.9084	−	17.4647i	−0.761839	−	0.703673i
$617$	9.02659	−	5.21150i	0.363397	−	0.209807i	−0.307173	−	0.951654i	$-0.599383\pi$
$617$	9.02659	−	5.21150i	0.363397	−	0.209807i	0.670570	+	0.741846i	$0.266050\pi$
$618$	−2.14585	−	2.48971i	−0.0863186	−	0.100151i
$619$	−1.68175			−0.0675954			−0.0337977	−	0.999429i	$-0.510760\pi$
$619$	−1.68175			−0.0675954			−0.0337977	+	0.999429i	$0.510760\pi$
$620$	15.7531	−	6.21016i	0.632660	−	0.249406i
$621$	−5.61742	+	5.61742i	−0.225419	+	0.225419i
$622$	18.7164	−	3.55601i	0.750460	−	0.142583i
$623$	38.4634	+	38.4634i	1.54101	+	1.54101i
$624$	−16.4485	−	0.565621i	−0.658468	−	0.0226430i
$625$	0.500000	−	0.866025i	0.0200000	−	0.0346410i
$626$	22.6287	−	4.29931i	0.904423	−	0.171835i
$627$	−1.45448	−	0.389726i	−0.0580862	−	0.0155641i
$628$	−14.8079	−	2.20903i	−0.590901	−	0.0881498i
$629$	−18.6469	−	10.4933i	−0.743502	−	0.418395i
$630$	−7.69760	+	6.63447i	−0.306680	+	0.264323i
$631$	−6.66054	+	24.8575i	−0.265152	+	0.989560i	0.697005	+	0.717066i	$0.254515\pi$
$631$	−6.66054	+	24.8575i	−0.265152	+	0.989560i	−0.962157	+	0.272494i	$0.912151\pi$
$632$	−0.117322	−	2.95593i	−0.00466681	−	0.117581i
$633$	9.47634	+	5.47116i	0.376651	+	0.217459i
$634$	−1.44746	−	0.985260i	−0.0574861	−	0.0391297i
$635$	−10.8967	+	10.8967i	−0.432424	+	0.432424i
$636$	1.88125	−	2.36635i	0.0745964	−	0.0938318i
$637$	12.2589	+	12.2589i	0.485716	+	0.485716i
$638$	1.46416	+	0.511090i	0.0579668	+	0.0202343i
$639$		−	10.1916i		−	0.403172i
$640$	−2.98603	−	10.9125i	−0.118033	−	0.431356i
$641$	−5.90271	−	10.2238i	−0.233143	−	0.403815i	0.725588	−	0.688129i	$-0.241568\pi$
$641$	−5.90271	−	10.2238i	−0.233143	−	0.403815i	−0.958731	+	0.284314i	$0.908234\pi$
$642$	−3.93401	−	2.67781i	−0.155263	−	0.105685i
$643$	9.46191	+	9.46191i	0.373141	+	0.373141i	0.868620	−	0.495479i	$-0.165007\pi$
$643$	9.46191	+	9.46191i	0.373141	+	0.373141i	−0.495479	+	0.868620i	$0.665007\pi$
$644$	−4.44818	+	10.2376i	−0.175283	+	0.403417i
$645$	−0.307688	−	0.532931i	−0.0121152	−	0.0209841i
$646$	1.30335	+	2.70120i	0.0512795	+	0.106277i
$647$	−44.8687	+	12.0225i	−1.76397	+	0.472655i	−0.987516	−	0.157517i	$-0.949651\pi$
$647$	−44.8687	+	12.0225i	−1.76397	+	0.472655i	−0.776455	+	0.630172i	$0.782984\pi$
$648$	−4.49147	+	4.86274i	−0.176442	+	0.191027i
$649$	21.0348	+	5.63626i	0.825689	+	0.221243i
$650$	−6.09112	−	2.12620i	−0.238913	−	0.0833966i
$651$	24.2404	+	6.49520i	0.950058	+	0.254567i
$652$	−12.8975	−	17.4203i	−0.505107	−	0.682233i
$653$	−3.78754	−	14.1353i	−0.148218	−	0.553157i	−0.999591	−	0.0285965i	$-0.990896\pi$
$653$	−3.78754	−	14.1353i	−0.148218	−	0.553157i	0.851373	−	0.524561i	$-0.175770\pi$
$654$	−0.0161038	+	0.0461341i	−0.000629710	+	0.00180398i
$655$		−	12.6325i		−	0.493593i
$656$	1.00966	−	3.30876i	0.0394206	−	0.129185i
$657$	8.00578	−	4.62214i	0.312335	−	0.180327i
$658$	33.7150	+	2.50094i	1.31435	+	0.0974968i
$659$	−13.9118	+	24.0960i	−0.541928	+	0.938647i	0.456865	+	0.889536i	$0.348972\pi$
$659$	−13.9118	+	24.0960i	−0.541928	+	0.938647i	−0.998793	+	0.0491110i	$0.984361\pi$
$660$	2.97230	+	4.01459i	0.115696	+	0.156268i
$661$	1.63132	+	6.08817i	0.0634510	+	0.236802i	0.990367	−	0.138466i	$-0.0442172\pi$
$661$	1.63132	+	6.08817i	0.0634510	+	0.236802i	−0.926916	+	0.375268i	$0.877551\pi$
$662$	2.74828	+	14.4651i	0.106815	+	0.562201i
$663$	−12.5343	−	7.23667i	−0.486791	−	0.281049i
$664$	−17.5867	+	5.46852i	−0.682496	+	0.212220i
$665$			1.98136i			0.0768337i
$666$	−12.4361	−	14.1112i	−0.481891	−	0.546797i
$667$		−	0.672511i		−	0.0260397i
$668$	−10.4096	−	4.52295i	−0.402761	−	0.174998i
$669$	19.1685	+	11.0669i	0.741096	+	0.427872i
$670$	−12.0974	+	2.29844i	−0.467365	+	0.0887966i
$671$	10.2089	+	38.1003i	0.394112	+	1.47085i
$672$	6.06676	−	15.6315i	0.234030	−	0.602997i
$673$	0.618248	−	1.07084i	0.0238317	−	0.0412777i	−0.853864	−	0.520497i	$-0.825747\pi$
$673$	0.618248	−	1.07084i	0.0238317	−	0.0412777i	0.877695	+	0.479219i	$0.159080\pi$
$674$	0.143136	−	1.92960i	0.00551339	−	0.0743256i
$675$	4.05117	−	2.33895i	0.155930	−	0.0900261i
$676$	−2.30504	+	15.4515i	−0.0886553	+	0.594289i
$677$		−	27.5120i		−	1.05737i	−0.848817	−	0.528686i	$-0.822685\pi$
$677$		−	27.5120i		−	1.05737i	0.848817	−	0.528686i	$-0.177315\pi$
$678$	−6.56293	−	2.29090i	−0.252048	−	0.0879813i
$679$	−14.1760	−	52.9054i	−0.544023	−	2.03032i
$680$	2.19190	−	9.70480i	0.0840554	−	0.372162i
$681$	15.3620	+	4.11623i	0.588672	+	0.157734i
$682$	−10.9271	+	31.3037i	−0.418419	+	1.19868i
$683$	−10.8568	−	2.90907i	−0.415423	−	0.111312i	0.0450524	−	0.998985i	$-0.485655\pi$
$683$	−10.8568	−	2.90907i	−0.415423	−	0.111312i	−0.460476	+	0.887672i	$0.652321\pi$
$684$	0.299158	+	2.61947i	0.0114386	+	0.100158i
$685$	17.0159	−	4.55941i	0.650145	−	0.174206i
$686$	13.3935	−	6.46244i	0.511365	−	0.246737i
$687$	−6.37901	−	11.0488i	−0.243374	−	0.421537i
$688$	−2.31521	−	1.44499i	−0.0882666	−	0.0550897i
$689$	−5.40595	−	5.40595i	−0.205950	−	0.205950i
$690$	1.21889	−	1.79069i	0.0464023	−	0.0681704i
$691$	10.6357	+	18.4216i	0.404601	+	0.700790i	0.994275	−	0.106852i	$-0.0340770\pi$
$691$	10.6357	+	18.4216i	0.404601	+	0.700790i	−0.589674	+	0.807641i	$0.700744\pi$
$692$	3.99399	−	26.7732i	0.151829	−	1.01776i
$693$		−	19.8982i		−	0.755870i
$694$	−11.5817	+	33.1790i	−0.439635	+	1.25946i
$695$	16.1882	+	16.1882i	0.614053	+	0.614053i
$696$	0.0400646	+	1.00943i	0.00151865	+	0.0382623i
$697$	2.15114	−	2.15114i	0.0814801	−	0.0814801i
$698$	4.53865	−	6.66781i	0.171791	−	0.252380i
$699$	−2.71548	−	1.56779i	−0.102709	−	0.0592991i
$700$	4.09027	−	5.14499i	0.154598	−	0.194462i
$701$	4.67314	−	17.4404i	0.176502	−	0.658714i	−0.819789	−	0.572666i	$-0.805909\pi$
$701$	4.67314	−	17.4404i	0.176502	−	0.658714i	0.996291	−	0.0860484i	$-0.0274240\pi$
$702$	−19.7031	−	22.8604i	−0.743646	−	0.862812i
$703$	−3.66707	+	0.0404531i	−0.138306	+	0.00152572i
$704$	20.0026	+	9.52115i	0.753877	+	0.358842i
$705$	−6.33723	−	1.69806i	−0.238674	−	0.0639525i
$706$	6.23463	+	32.8149i	0.234643	+	1.23500i
$707$	−2.88830	+	5.00269i	−0.108626	+	0.188145i
$708$	1.60964	+	14.0943i	0.0604940	+	0.529695i
$709$	−31.2445	−	31.2445i	−1.17341	−	1.17341i	−0.981390	−	0.192023i	$-0.938495\pi$
$709$	−31.2445	−	31.2445i	−1.17341	−	1.17341i	−0.192023	−	0.981390i	$-0.561505\pi$
$710$	1.23039	+	6.47595i	0.0461757	+	0.243038i
$711$	1.61707	−	1.61707i	0.0606448	−	0.0606448i
$712$	−41.4399	−	21.7814i	−1.55303	−	0.816294i
$713$	14.3782			0.538469
$714$	11.1692	−	9.62661i	0.417998	−	0.360267i
$715$	10.9401	−	6.31630i	0.409138	−	0.236216i
$716$	−16.2531	+	1.85619i	−0.607407	+	0.0693692i
$717$	−6.28940	+	6.28940i	−0.234882	+	0.234882i
$718$	40.7301	−	19.6525i	1.52003	−	0.733426i
$719$	−1.61058	+	0.929866i	−0.0600643	+	0.0346782i	−0.529731	−	0.848165i	$-0.677707\pi$
$719$	−1.61058	+	0.929866i	−0.0600643	+	0.0346782i	0.469667	+	0.882844i	$0.344374\pi$
$720$	4.63075	−	7.41955i	0.172578	−	0.276510i
$721$	−2.19181	−	8.17994i	−0.0816272	−	0.304637i
$722$	−21.7876	−	14.8304i	−0.810850	−	0.551930i
$723$	−6.76834	+	25.2598i	−0.251717	+	0.939421i
$724$	4.30898	+	10.9305i	0.160142	+	0.406227i
$725$	−0.102493	+	0.382509i	−0.00380650	+	0.0142060i
$726$	4.23830	+	0.314393i	0.157298	+	0.0116682i
$727$	−50.4341	+	13.5138i	−1.87050	+	0.501198i	−0.870539	+	0.492100i	$0.836229\pi$
$727$	−50.4341	+	13.5138i	−1.87050	+	0.501198i	−0.999959	+	0.00909798i	$0.997104\pi$
$728$	−37.5354	−	19.7292i	−1.39115	−	0.731211i
$729$	7.54014			0.279265
$730$	−4.52903	+	3.90351i	−0.167627	+	0.144476i
$731$	−1.20000	−	2.07846i	−0.0443836	−	0.0768746i
$732$	−20.6509	+	15.2894i	−0.763279	+	0.565112i
$733$	−5.01033	−	2.89271i	−0.185061	−	0.106845i	0.404608	−	0.914490i	$-0.367408\pi$
$733$	−5.01033	−	2.89271i	−0.185061	−	0.106845i	−0.589668	+	0.807646i	$0.700741\pi$
$734$	1.46844	−	19.7959i	0.0542011	−	0.730681i
$735$	3.31083	−	0.887134i	0.122122	−	0.0327224i
$736$	1.03950	−	9.55034i	0.0383163	−	0.352030i
$737$	12.0557	−	20.8811i	0.444078	−	0.769165i
$738$	2.40856	−	1.16215i	0.0886602	−	0.0427792i
$739$	26.1700			0.962679			0.481339	−	0.876534i	$-0.340151\pi$
$739$	26.1700			0.962679			0.481339	+	0.876534i	$0.340151\pi$
$740$	9.60579	+	7.46518i	0.353116	+	0.274425i
$741$	−2.48067			−0.0911295
$742$	7.01491	−	3.38474i	0.257525	−	0.124258i
$743$	24.8838	−	43.1001i	0.912899	−	1.58119i	0.102952	−	0.994686i	$-0.467171\pi$
$743$	24.8838	−	43.1001i	0.912899	−	1.58119i	0.809948	−	0.586502i	$-0.199495\pi$
$744$	−21.5815	+	0.856577i	−0.791217	+	0.0314036i
$745$	11.4001	−	3.05465i	0.417668	−	0.111914i
$746$	−0.915694	+	12.3444i	−0.0335259	+	0.451960i
$747$	−12.3300	−	7.11874i	−0.451132	−	0.260461i
$748$	11.5921	+	15.6571i	0.423850	+	0.572481i
$749$	−6.13062	−	10.6185i	−0.224008	−	0.387993i
$750$	−0.966184	+	0.832741i	−0.0352800	+	0.0304074i
$751$	21.6095			0.788541			0.394271	−	0.918994i	$-0.370997\pi$
$751$	21.6095			0.788541			0.394271	+	0.918994i	$0.370997\pi$
$752$	−28.3473	+	6.56040i	−1.03372	+	0.239233i
$753$	0.376880	−	0.100985i	0.0137343	−	0.00368008i
$754$	2.54783	+	0.188995i	0.0927866	+	0.00688281i
$755$	1.00232	−	3.74072i	0.0364782	−	0.136139i
$756$	28.6043	−	11.2763i	1.04033	−	0.410116i
$757$	−10.9313	+	40.7960i	−0.397303	+	1.48276i	0.420519	+	0.907284i	$0.361848\pi$
$757$	−10.9313	+	40.7960i	−0.397303	+	1.48276i	−0.817822	+	0.575471i	$0.804819\pi$
$758$	−7.10062	−	4.83325i	−0.257906	−	0.175552i
$759$	1.09778	+	4.09697i	0.0398469	+	0.148711i
$760$	−0.506330	−	1.62835i	−0.0183665	−	0.0590665i
$761$	1.20559	−	0.696050i	0.0437028	−	0.0252318i	−0.477989	−	0.878366i	$-0.658634\pi$
$761$	1.20559	−	0.696050i	0.0437028	−	0.0252318i	0.521692	+	0.853134i	$0.325301\pi$
$762$	17.7032	−	8.54193i	0.641320	−	0.309442i
$763$	−0.0890229	+	0.0890229i	−0.00322285	+	0.00322285i
$764$	3.36605	+	29.4737i	0.121780	+	1.06632i
$765$	6.66083	−	3.84563i	0.240823	−	0.139039i
$766$	−9.71445	+	8.37276i	−0.350997	+	0.302520i
$767$	35.8757			1.29540
$768$	−0.991311	+	14.3969i	−0.0357709	+	0.519502i
$769$	32.9246	−	32.9246i	1.18729	−	1.18729i	0.209480	−	0.977813i	$-0.432823\pi$
$769$	32.9246	−	32.9246i	1.18729	−	1.18729i	0.977813	−	0.209480i	$-0.0671771\pi$
$770$	2.40224	+	12.6438i	0.0865706	+	0.455649i
$771$	−3.22198	−	3.22198i	−0.116037	−	0.116037i
$772$	−5.93530	+	0.677843i	−0.213616	+	0.0243961i
$773$	11.8502	−	20.5251i	0.426221	−	0.738237i	−0.570312	−	0.821428i	$-0.693178\pi$
$773$	11.8502	−	20.5251i	0.426221	−	0.738237i	0.996534	+	0.0831911i	$0.0265112\pi$
$774$	−0.393797	−	2.07268i	−0.0141547	−	0.0745010i
$775$	−8.17801	−	2.19129i	−0.293763	−	0.0787135i
$776$	25.1702	+	39.8570i	0.903556	+	1.43078i
$777$	4.85831	+	17.3630i	0.174291	+	0.622895i
$778$	32.3464	+	37.5298i	1.15968	+	1.34551i
$779$	0.134952	−	0.503647i	0.00483515	−	0.0180450i
$780$	6.44155	+	5.12104i	0.230644	+	0.183363i
$781$	−11.1780	−	6.45360i	−0.399979	−	0.230928i
$782$	4.75373	−	6.98379i	0.169993	−	0.249740i
$783$	−1.30989	+	1.30989i	−0.0468115	+	0.0468115i
$784$	11.1119	−	10.3731i	0.396855	−	0.370469i
$785$	5.29333	+	5.29333i	0.188927	+	0.188927i
$786$	−5.31032	+	15.2129i	−0.189413	+	0.542627i
$787$		−	53.7851i		−	1.91723i	−0.284705	−	0.958615i	$-0.591896\pi$
$787$		−	53.7851i		−	1.91723i	0.284705	−	0.958615i	$-0.408104\pi$
$788$	54.9352	+	8.19516i	1.95699	+	0.291940i
$789$	−7.38923	−	12.7985i	−0.263064	−	0.455640i
$790$	−0.832298	+	1.22274i	−0.0296118	+	0.0435032i
$791$	−12.6642	−	12.6642i	−0.450287	−	0.450287i
$792$	5.08493	+	16.3531i	0.180685	+	0.581081i
$793$	32.4908	+	56.2757i	1.15378	+	1.99841i
$794$	−6.08697	+	2.93701i	−0.216019	+	0.104230i
$795$	−1.46001	+	0.391209i	−0.0517813	+	0.0138747i
$796$	−53.9127	+	6.15713i	−1.91089	+	0.218234i
$797$	29.4049	+	7.87902i	1.04158	+	0.279089i	0.738766	−	0.673962i	$-0.235409\pi$
$797$	29.4049	+	7.87902i	1.04158	+	0.279089i	0.302809	+	0.953051i	$0.402075\pi$
$798$	0.832901	−	2.38608i	0.0294844	−	0.0844664i
$799$	−24.7156	−	6.62251i	−0.874373	−	0.234288i
$800$	−2.04675	+	5.27360i	−0.0723634	+	0.186450i
$801$	−9.36686	−	34.9576i	−0.330962	−	1.23517i
$802$	−37.9841	−	13.2590i	−1.34126	−	0.468190i
$803$		−	11.7075i		−	0.413148i
$804$	15.5348	+	2.31745i	0.547869	+	0.0817303i
$805$	4.83337	−	2.79055i	0.170354	−	0.0983538i
$806$	−4.04070	+	54.4724i	−0.142328	+	1.91871i
$807$	−5.65835	+	9.80054i	−0.199183	+	0.344995i
$808$	1.09529	−	4.84949i	0.0385322	−	0.170604i
$809$	4.05753	+	15.1429i	0.142655	+	0.532396i	0.999849	+	0.0174014i	$0.00553933\pi$
$809$	4.05753	+	15.1429i	0.142655	+	0.532396i	−0.857194	+	0.514994i	$0.827794\pi$
$810$	3.25165	−	0.617794i	0.114251	−	0.0217071i
$811$	19.3187	+	11.1537i	0.678371	+	0.391658i	0.799241	−	0.601011i	$-0.205235\pi$
$811$	19.3187	+	11.1537i	0.678371	+	0.391658i	−0.120870	+	0.992668i	$0.538568\pi$
$812$	−1.03724	+	2.38723i	−0.0364000	+	0.0837754i
$813$			7.26831i			0.254911i
$814$	−23.3519	+	4.70417i	−0.818482	+	0.164881i
$815$			10.8376i			0.379625i
$816$	−6.71922	+	10.7658i	−0.235220	+	0.376877i
$817$	−0.356238	−	0.205674i	−0.0124632	−	0.00719563i
$818$	3.63971	+	19.1570i	0.127259	+	0.669807i
$819$	−8.48430	−	31.6638i	−0.296465	−	1.10642i
$820$	−1.39015	+	1.02923i	−0.0485461	+	0.0359422i
$821$	−7.30066	+	12.6451i	−0.254795	+	0.441318i	−0.964840	−	0.262839i	$-0.915341\pi$
$821$	−7.30066	+	12.6451i	−0.254795	+	0.441318i	0.710045	+	0.704156i	$0.248675\pi$
$822$	−22.4084	−	1.66223i	−0.781581	−	0.0579769i
$823$	11.0673	−	6.38973i	0.385783	−	0.222732i	−0.294548	−	0.955637i	$-0.595169\pi$
$823$	11.0673	−	6.38973i	0.385783	−	0.222732i	0.680331	+	0.732905i	$0.261836\pi$
$824$	3.89167	+	6.16247i	0.135573	+	0.214680i
$825$		−	2.49757i		−	0.0869543i
$826$	−12.0455	+	34.5078i	−0.419117	+	1.20068i
$827$	−13.0765	−	48.8020i	−0.454713	−	1.69701i	−0.688930	−	0.724828i	$-0.741919\pi$
$827$	−13.0765	−	48.8020i	−0.454713	−	1.69701i	0.234217	−	0.972184i	$-0.424747\pi$
$828$	5.96866	−	4.41904i	0.207425	−	0.153572i
$829$	8.19774	+	2.19658i	0.284719	+	0.0762903i	0.398352	−	0.917232i	$-0.369582\pi$
$829$	8.19774	+	2.19658i	0.284719	+	0.0762903i	−0.113633	+	0.993523i	$0.536249\pi$
$830$	8.69418	+	3.03484i	0.301779	+	0.105341i
$831$	−23.3298	−	6.25119i	−0.809301	−	0.216851i
$832$	35.8897	+	6.62209i	1.24425	+	0.229580i
$833$	12.9124	−	3.45987i	0.447389	−	0.119877i
$834$	−12.6899	−	26.2999i	−0.439415	−	0.910692i
$835$	2.83745	+	4.91460i	0.0981939	+	0.170077i
$836$	3.06243	+	1.33061i	0.105916	+	0.0460202i
$837$	−28.0052	−	28.0052i	−0.968003	−	0.968003i
$838$	20.7030	+	14.0921i	0.715174	+	0.486805i
$839$	−6.86045	−	11.8826i	−0.236849	−	0.410234i	0.722959	−	0.690890i	$-0.242781\pi$
$839$	−6.86045	−	11.8826i	−0.236849	−	0.410234i	−0.959808	+	0.280656i	$0.909448\pi$
$840$	−7.08857	+	4.47652i	−0.244579	+	0.154455i
$841$			28.8432i			0.994592i
$842$	−7.99076	−	2.78930i	−0.275380	−	0.0961258i
$843$	19.4737	+	19.4737i	0.670709	+	0.670709i
$844$	−18.9933	−	15.0997i	−0.653778	−	0.519754i
$845$	5.52339	−	5.52339i	0.190010	−	0.190010i
$846$	−18.5942	−	12.6567i	−0.639283	−	0.435148i
$847$	9.48293	+	5.47497i	0.325837	+	0.188122i
$848$	−4.90015	+	4.57435i	−0.168272	+	0.157084i
$849$	−5.60889	+	20.9326i	−0.192496	+	0.718407i
$850$	−3.76817	+	3.24774i	−0.129247	+	0.111396i
$851$	5.26339	+	8.88856i	0.180427	+	0.304696i
$852$	1.24057	−	8.31599i	0.0425011	−	0.284901i
$853$	18.5117	+	4.96019i	0.633828	+	0.169834i	0.561406	−	0.827540i	$-0.310261\pi$
$853$	18.5117	+	4.96019i	0.633828	+	0.169834i	0.0724216	+	0.997374i	$0.476927\pi$
$854$	−65.0390	+	12.3570i	−2.22559	+	0.422848i
$855$	0.659124	−	1.14164i	0.0225416	−	0.0390431i
$856$	7.75191	+	7.16005i	0.264955	+	0.244725i
$857$	29.0047	+	29.0047i	0.990780	+	0.990780i	0.999958	−	0.00917752i	$-0.00292134\pi$
$857$	29.0047	+	29.0047i	0.990780	+	0.990780i	−0.00917752	+	0.999958i	$0.502921\pi$
$858$	−15.8300	+	3.00761i	−0.540429	+	0.102678i
$859$	5.71944	−	5.71944i	0.195145	−	0.195145i	−0.602770	−	0.797915i	$-0.705936\pi$
$859$	5.71944	−	5.71944i	0.195145	−	0.195145i	0.797915	+	0.602770i	$0.205936\pi$
$860$	0.500454	+	1.26949i	0.0170654	+	0.0432891i
$861$	−2.56348			−0.0873633
$862$	15.2338	+	17.6749i	0.518865	+	0.602010i
$863$	−6.50639	+	3.75646i	−0.221480	+	0.127872i	−0.606635	−	0.794980i	$-0.707481\pi$
$863$	−6.50639	+	3.75646i	−0.221480	+	0.127872i	0.385155	+	0.922852i	$0.374148\pi$
$864$	−20.6264	+	16.5770i	−0.701724	+	0.563962i
$865$	−9.57050	+	9.57050i	−0.325407	+	0.325407i
$866$	−14.1535	−	29.3333i	−0.480956	−	0.996785i
$867$	3.61380	−	2.08643i	0.122731	−	0.0708587i
$868$	−51.0387	−	22.1761i	−1.73237	−	0.752706i
$869$	−0.749601	−	2.79755i	−0.0254285	−	0.0949004i
$870$	0.284224	−	0.417559i	0.00963610	−	0.0141566i
$871$	10.2807	−	38.3683i	0.348350	−	1.30006i
$872$	0.0504127	−	0.0959119i	0.00170719	−	0.00324799i
$873$	−9.43164	+	35.1993i	−0.319213	+	1.19132i
$874$	0.107115	−	1.44401i	0.00362321	−	0.0488443i
$875$	−3.17440	+	0.850578i	−0.107314	+	0.0287548i
$876$	7.09508	−	2.79701i	0.239721	−	0.0945022i
$877$	−33.0892			−1.11734			−0.558672	−	0.829389i	$-0.688689\pi$
$877$	−33.0892			−1.11734			−0.558672	+	0.829389i	$0.688689\pi$
$878$	−28.4742	−	33.0370i	−0.960957	−	1.11494i
$879$	8.03361	+	13.9146i	0.270967	+	0.469328i
$880$	−5.20532	−	9.77722i	−0.175471	−	0.329590i
$881$	−45.4308	−	26.2295i	−1.53060	−	0.883694i	−0.999334	−	0.0364900i	$-0.988382\pi$
$881$	−45.4308	−	26.2295i	−1.53060	−	0.883694i	−0.531268	−	0.847204i	$-0.678284\pi$
$882$	11.7191	+	0.869310i	0.394603	+	0.0292712i
$883$	−10.0426	+	2.69090i	−0.337960	+	0.0905560i	−0.423808	−	0.905752i	$-0.639307\pi$
$883$	−10.0426	+	2.69090i	−0.337960	+	0.0905560i	0.0858480	+	0.996308i	$0.472640\pi$
$884$	25.1224	+	19.9723i	0.844957	+	0.671742i
$885$	3.54647	−	6.14267i	0.119213	−	0.206483i
$886$	5.61549	+	11.6382i	0.188656	+	0.390991i
$887$	−7.86354			−0.264032			−0.132016	−	0.991248i	$-0.542145\pi$
$887$	−7.86354			−0.264032			−0.132016	+	0.991248i	$0.542145\pi$
$888$	−8.42981	−	13.0280i	−0.282886	−	0.437192i
$889$	50.6442			1.69855
$890$	10.1722	+	21.0820i	0.340973	+	0.706670i
$891$	−3.24043	+	5.61259i	−0.108558	+	0.188029i
$892$	−38.4192	−	30.5433i	−1.28637	−	1.02267i
$893$	−4.23613	+	1.13507i	−0.141757	+	0.0379836i
$894$	−15.0129	−	1.11364i	−0.502105	−	0.0372456i
$895$	7.08355	+	4.08969i	0.236777	+	0.136703i
$896$	−18.4198	+	32.2978i	−0.615362	+	1.07899i
$897$	3.49378	+	6.05140i	0.116654	+	0.202050i
$898$	16.8960	+	19.6035i	0.563828	+	0.654179i
$899$	3.35276			0.111821
$900$	−4.06832	+	1.60380i	−0.135611	+	0.0534602i
$901$	−5.69412	+	1.52573i	−0.189699	+	0.0508296i
$902$	0.250545	−	3.37757i	0.00834223	−	0.112461i
$903$	−0.523425	+	1.95345i	−0.0174185	+	0.0650067i
$904$	13.6442	+	7.17160i	0.453799	+	0.238524i
$905$	1.52045	−	5.67440i	0.0505415	−	0.188623i
$906$	−2.77954	+	4.08348i	−0.0923442	+	0.135664i
$907$	−10.6078	−	39.5887i	−0.352225	−	1.31452i	−0.883941	−	0.467599i	$-0.845119\pi$
$907$	−10.6078	−	39.5887i	−0.352225	−	1.31452i	0.531716	−	0.846923i	$-0.321547\pi$
$908$	−32.3450	−	14.0537i	−1.07341	−	0.466390i
$909$	3.32842	−	1.92166i	0.110397	−	0.0637376i
$910$	9.21376	+	19.0956i	0.305433	+	0.633013i
$911$	4.05910	−	4.05910i	0.134484	−	0.134484i	−0.636660	−	0.771144i	$-0.719685\pi$
$911$	4.05910	−	4.05910i	0.134484	−	0.134484i	0.771144	+	0.636660i	$0.219685\pi$
$912$	−0.0747517	+	2.17381i	−0.00247528	+	0.0719822i
$913$	−15.6155	+	9.01559i	−0.516796	+	0.298372i
$914$	7.47809	+	8.67641i	0.247353	+	0.286990i
$915$	12.8474			0.424723
$916$	10.3755	+	26.3191i	0.342815	+	0.869607i
$917$	−29.3557	+	29.3557i	−0.969412	+	0.969412i
$918$	−22.8618	+	4.34360i	−0.754552	+	0.143360i
$919$	10.3504	+	10.3504i	0.341427	+	0.341427i	0.856904	−	0.515476i	$-0.172385\pi$
$919$	10.3504	+	10.3504i	0.341427	+	0.341427i	−0.515476	+	0.856904i	$0.672385\pi$
$920$	−3.25912	+	3.52853i	−0.107450	+	0.116332i
$921$	−0.235192	+	0.407364i	−0.00774983	+	0.0134231i
$922$	−0.106607	+	0.0202546i	−0.00351090	+	0.000667050i
$923$	−20.5391	−	5.50344i	−0.676053	−	0.181148i
$924$	2.42211	−	16.2363i	0.0796815	−	0.534135i
$925$	−1.63905	−	5.85777i	−0.0538916	−	0.192602i
$926$	2.88645	−	2.48779i	0.0948545	−	0.0817539i
$927$	−1.45827	+	5.44233i	−0.0478958	+	0.178750i
$928$	0.242393	−	2.22698i	0.00795694	−	0.0731041i
$929$	31.1807	+	18.0022i	1.02301	+	0.590633i	0.914973	−	0.403514i	$-0.132211\pi$
$929$	31.1807	+	18.0022i	1.02301	+	0.590633i	0.108033	+	0.994147i	$0.465545\pi$
$930$	8.92736	+	6.07668i	0.292740	+	0.199262i
$931$	1.62012	−	1.62012i	0.0530974	−	0.0530974i
$932$	5.44262	+	4.32689i	0.178279	+	0.141732i
$933$	8.59148	+	8.59148i	0.281272	+	0.281272i
$934$	5.22667	+	1.82445i	0.171022	+	0.0596979i
$935$		−	9.74067i		−	0.318554i
$936$	15.0643	+	23.8544i	0.492392	+	0.779704i
$937$	−28.1349	−	48.7312i	−0.919129	−	1.59198i	−0.800741	−	0.599010i	$-0.795561\pi$
$937$	−28.1349	−	48.7312i	−0.919129	−	1.59198i	−0.118387	−	0.992967i	$-0.537772\pi$
$938$	33.4535	+	22.7712i	1.09230	+	0.743505i
$939$	10.3873	+	10.3873i	0.338978	+	0.338978i
$940$	13.3432	+	5.79755i	0.435207	+	0.189095i
$941$	−4.59103	−	7.95190i	−0.149663	−	0.259225i	0.781440	−	0.623981i	$-0.214486\pi$
$941$	−4.59103	−	7.95190i	−0.149663	−	0.259225i	−0.931103	+	0.364756i	$0.881152\pi$
$942$	−4.14943	−	8.59974i	−0.135196	−	0.280195i
$943$	−1.41868	+	0.380133i	−0.0461984	+	0.0123788i
$944$	1.08107	−	31.4380i	0.0351858	−	1.02322i
$945$	−14.8495	−	3.97891i	−0.483055	−	0.129434i
$946$	−2.52265	−	0.880572i	−0.0820185	−	0.0286299i
$947$	12.5313	+	3.35774i	0.407211	+	0.109112i	0.456609	−	0.889667i	$-0.349064\pi$
$947$	12.5313	+	3.35774i	0.407211	+	0.109112i	−0.0493983	+	0.998779i	$0.515730\pi$
$948$	1.51631	−	1.12264i	0.0492475	−	0.0364616i
$949$	−4.99190	−	18.6300i	−0.162044	−	0.604756i
$950$	−0.280996	+	0.804994i	−0.00911672	+	0.0261175i
$951$		−	1.11670i		−	0.0362116i
$952$	−27.6458	+	17.4587i	−0.896006	+	0.565838i
$953$	−24.2661	+	14.0100i	−0.786056	+	0.453830i	−0.838572	−	0.544790i	$-0.816609\pi$
$953$	−24.2661	+	14.0100i	−0.786056	+	0.453830i	0.0525160	+	0.998620i	$0.483276\pi$
$954$	−5.16789	−	0.383349i	−0.167317	−	0.0124114i
$955$	7.41631	−	12.8454i	0.239986	−	0.415668i
$956$	15.8516	−	11.7361i	0.512677	−	0.379572i
$957$	0.255984	+	0.955345i	0.00827479	+	0.0308819i
$958$	9.36349	+	49.2831i	0.302521	+	1.59226i
$959$	−50.1373	−	28.9468i	−1.61902	−	0.934740i
$960$	4.68169	−	5.49043i	0.151101	−	0.177203i
$961$			40.6816i			1.31231i
$962$	−35.1538	+	17.4426i	−1.13340	+	0.562372i
$963$			8.15772i			0.262879i
$964$	23.1086	−	53.1850i	0.744279	−	1.71297i
$965$	2.58676	+	1.49347i	0.0832709	+	0.0480765i
$966$	−6.99373	+	1.32877i	−0.225019	+	0.0427523i
$967$	6.54936	+	24.4425i	0.210613	+	0.786019i	0.987665	+	0.156582i	$0.0500477\pi$
$967$	6.54936	+	24.4425i	0.210613	+	0.786019i	−0.777052	+	0.629437i	$0.783286\pi$
$968$	−9.19253	−	2.07620i	−0.295459	−	0.0667315i
$969$	−0.956389	+	1.65651i	−0.0307236	+	0.0532149i
$970$	1.74358	−	23.5051i	0.0559830	−	0.754703i
$971$	−19.9647	+	11.5266i	−0.640699	+	0.369908i	−0.784884	−	0.619643i	$-0.787277\pi$
$971$	−19.9647	+	11.5266i	−0.640699	+	0.369908i	0.144185	+	0.989551i	$0.453944\pi$
$972$	−31.9357	−	4.76413i	−1.02434	−	0.152810i
$973$		−	75.2370i		−	2.41199i
$974$	−42.7946	−	14.9382i	−1.37123	−	0.478649i
$975$	−1.06493	−	3.97436i	−0.0341050	−	0.127282i
$976$	50.2936	−	26.7760i	1.60986	−	0.857078i
$977$	−24.7139	−	6.62207i	−0.790668	−	0.211859i	−0.159185	−	0.987249i	$-0.550887\pi$
$977$	−24.7139	−	6.62207i	−0.790668	−	0.211859i	−0.631483	+	0.775390i	$0.717553\pi$
$978$	4.55579	−	13.0514i	0.145678	−	0.417337i
$979$	−44.2723	−	11.8627i	−1.41495	−	0.379135i
$980$	−7.55152	+	0.862425i	−0.241224	+	0.0275492i
$981$	0.0809087	−	0.0216794i	0.00258322	−	0.000692170i
$982$	44.6422	−	21.5402i	1.42459	−	0.687375i
$983$	24.4688	+	42.3812i	0.780434	+	1.35175i	0.931689	+	0.363256i	$0.118335\pi$
$983$	24.4688	+	42.3812i	0.780434	+	1.35175i	−0.151256	+	0.988495i	$0.548332\pi$
$984$	2.10676	−	0.655091i	0.0671612	−	0.0208835i
$985$	−19.6375	−	19.6375i	−0.625701	−	0.625701i
$986$	1.10849	−	1.62850i	0.0353015	−	0.0518620i
$987$	10.7806	+	18.6726i	0.343151	+	0.594355i
$988$	5.44057	+	0.811616i	0.173087	+	0.0258210i
$989$			1.15869i			0.0368442i
$990$	2.82197	−	8.08433i	0.0896880	−	0.256937i
$991$	33.4028	+	33.4028i	1.06108	+	1.06108i	0.998009	+	0.0630670i	$0.0200882\pi$
$991$	33.4028	+	33.4028i	1.06108	+	1.06108i	0.0630670	+	0.998009i	$0.479912\pi$
$992$	47.6126	+	5.18234i	1.51170	+	0.164539i
$993$	−6.63996	+	6.63996i	−0.210713	+	0.210713i
$994$	12.1897	−	17.9082i	0.386635	−	0.568012i
$995$	23.4966	+	13.5658i	0.744894	+	0.430065i
$996$	−9.19436	−	7.30953i	−0.291335	−	0.231611i
$997$	−5.51393	+	20.5783i	−0.174628	+	0.651721i	0.821987	+	0.569507i	$0.192866\pi$
$997$	−5.51393	+	20.5783i	−0.174628	+	0.651721i	−0.996615	+	0.0822140i	$0.973801\pi$
$998$	−3.85230	−	4.46961i	−0.121942	−	0.141483i
$999$	7.06094	−	27.5645i	0.223398	−	0.872103i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.be.a.711.26	yes	304
4.3	odd	2	inner	740.2.be.a.711.14	yes	304
37.14	odd	12	inner	740.2.be.a.51.14	✓	304
148.51	even	12	inner	740.2.be.a.51.26	yes	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.be.a.51.14	✓	304	37.14	odd	12	inner
740.2.be.a.51.26	yes	304	148.51	even	12	inner
740.2.be.a.711.14	yes	304	4.3	odd	2	inner
740.2.be.a.711.26	yes	304	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.614568 - 1.27370i) q^{2} +(0.450967 - 0.781098i) q^{3} +(-1.24461 + 1.56555i) q^{4} +(0.965926 - 0.258819i) q^{5} +(-1.27203 - 0.0943580i) q^{6} +(-2.84609 - 1.64319i) q^{7} +(2.75893 + 0.623124i) q^{8} +(1.09326 + 1.89358i) q^{9} +(-0.923284 - 1.07124i) q^{10} +2.76913 q^{11} +(0.661567 + 1.67817i) q^{12} +(4.40649 - 1.18072i) q^{13} +(-0.343813 + 4.63491i) q^{14} +(0.233438 - 0.871201i) q^{15} +(-0.901881 - 3.89700i) q^{16} +(0.910419 - 3.39773i) q^{17} +(1.73996 - 2.55621i) q^{18} +(-0.156042 - 0.582356i) q^{19} +(-0.797010 + 1.83433i) q^{20} +(-2.56698 + 1.48205i) q^{21} +(-1.70182 - 3.52704i) q^{22} +(-1.20084 + 1.20084i) q^{23} +(1.73091 - 1.87399i) q^{24} +(0.866025 - 0.500000i) q^{25} +(-4.21196 - 4.88691i) q^{26} +4.67789 q^{27} +(6.11477 - 2.41055i) q^{28} +(-0.280016 + 0.280016i) q^{29} +(-1.25311 + 0.238083i) q^{30} +(-5.98672 - 5.98672i) q^{31} +(-4.40933 + 3.54370i) q^{32} +(1.24879 - 2.16296i) q^{33} +(-4.88720 + 0.928538i) q^{34} +(-3.17440 - 0.850578i) q^{35} +(-4.32517 - 0.645223i) q^{36} +(1.50943 - 5.89251i) q^{37} +(-0.645847 + 0.556647i) q^{38} +(1.06493 - 3.97436i) q^{39} +(2.82620 - 0.112173i) q^{40} +(0.748977 + 0.432422i) q^{41} +(3.46527 + 2.35874i) q^{42} +(0.482448 - 0.482448i) q^{43} +(-3.44649 + 4.33521i) q^{44} +(1.54610 + 1.54610i) q^{45} +(2.26751 + 0.791512i) q^{46} -7.27413i q^{47} +(-3.45066 - 1.05296i) q^{48} +(1.90015 + 3.29116i) q^{49} +(-1.16908 - 0.795771i) q^{50} +(-2.24339 - 2.24339i) q^{51} +(-3.63591 + 8.36811i) q^{52} +(-0.837930 - 1.45134i) q^{53} +(-2.87488 - 5.95822i) q^{54} +(2.67478 - 0.716704i) q^{55} +(-6.82826 - 6.30692i) q^{56} +(-0.525246 - 0.140739i) q^{57} +(0.528745 + 0.184567i) q^{58} +(7.59618 + 2.03539i) q^{59} +(1.07337 + 1.44977i) q^{60} +(3.68670 + 13.7589i) q^{61} +(-3.94603 + 11.3045i) q^{62} -7.18572i q^{63} +(7.22343 + 3.43832i) q^{64} +(3.95075 - 2.28097i) q^{65} +(-3.52242 - 0.261290i) q^{66} +(4.35361 - 7.54067i) q^{67} +(4.18619 + 5.65416i) q^{68} +(0.396435 + 1.47952i) q^{69} +(0.867506 + 4.56597i) q^{70} +(-4.03663 - 2.33055i) q^{71} +(1.83629 + 5.90549i) q^{72} -4.22786i q^{73} +(-8.43292 + 1.69879i) q^{74} -0.901934i q^{75} +(1.10592 + 0.480516i) q^{76} +(-7.88120 - 4.55021i) q^{77} +(-5.71661 + 1.08612i) q^{78} +(-0.270699 - 1.01026i) q^{79} +(-1.87977 - 3.53079i) q^{80} +(-1.17020 + 2.02684i) q^{81} +(0.0904777 - 1.21972i) q^{82} +(-5.63912 + 3.25575i) q^{83} +(0.874681 - 5.86331i) q^{84} -3.51759i q^{85} +(-0.910990 - 0.317996i) q^{86} +(0.0924420 + 0.344998i) q^{87} +(7.63985 + 1.72551i) q^{88} +(-15.9878 - 4.28392i) q^{89} +(1.01908 - 2.91945i) q^{90} +(-14.4814 - 3.88028i) q^{91} +(-0.385393 - 3.37456i) q^{92} +(-7.37603 + 1.97640i) q^{93} +(-9.26505 + 4.47045i) q^{94} +(-0.301449 - 0.522126i) q^{95} +(0.779508 + 5.04221i) q^{96} +(11.7848 + 11.7848i) q^{97} +(3.02417 - 4.44286i) q^{98} +(3.02737 + 5.24356i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q + 4 q^{2} - 12 q^{4} - 8 q^{8} - 152 q^{9} + 16 q^{13} - 24 q^{14} + 20 q^{16} - 60 q^{18} - 16 q^{22} - 24 q^{24} - 32 q^{29} - 56 q^{32} - 32 q^{37} + 40 q^{38} + 20 q^{42} + 12 q^{44} - 8 q^{46}+ \cdots - 36 q^{98}+O(q^{100}) \) 304 * q + 4 * q^2 - 12 * q^4 - 8 * q^8 - 152 * q^9 + 16 * q^13 - 24 * q^14 + 20 * q^16 - 60 * q^18 - 16 * q^22 - 24 * q^24 - 32 * q^29 - 56 * q^32 - 32 * q^37 + 40 * q^38 + 20 * q^42 + 12 * q^44 - 8 * q^46 + 104 * q^49 + 4 * q^50 - 40 * q^52 + 40 * q^54 + 4 * q^56 - 48 * q^57 - 12 * q^58 - 28 * q^60 - 16 * q^61 - 60 * q^62 + 24 * q^65 - 52 * q^66 - 200 * q^68 - 196 * q^72 + 20 * q^74 - 40 * q^76 + 96 * q^77 - 48 * q^78 - 152 * q^81 + 32 * q^82 - 112 * q^84 + 12 * q^88 - 8 * q^89 + 140 * q^92 - 16 * q^93 - 28 * q^94 - 132 * q^96 + 48 * q^97 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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