LMFDB - Embedded newform 456.2.bk.a.253.30

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [456,2,Mod(61,456)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("456.61"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(456, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bk (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			253.30
Character	$\chi$	$=$	456.253
Dual form			456.2.bk.a.301.30

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.943660 + 1.05333i) q^{2} +(0.342020 - 0.939693i) q^{3} +(-0.219013 + 1.98797i) q^{4} +(3.30436 - 0.582649i) q^{5} +(1.31256 - 0.526489i) q^{6} +(-1.96330 + 3.40053i) q^{7} +(-2.30067 + 1.64528i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(3.73192 + 2.93077i) q^{10} +(-2.32580 + 1.34280i) q^{11} +(1.79318 + 0.885732i) q^{12} +(1.43956 + 3.95517i) q^{13} +(-5.43457 + 1.14094i) q^{14} +(0.582649 - 3.30436i) q^{15} +(-3.90407 - 0.870784i) q^{16} +(4.40701 - 3.69792i) q^{17} +(-0.0458169 - 1.41347i) q^{18} +(3.87216 - 2.00160i) q^{19} +(0.434590 + 6.69659i) q^{20} +(2.52397 + 3.00795i) q^{21} +(-3.60917 - 1.18269i) q^{22} +(0.958194 - 5.43419i) q^{23} +(0.759179 + 2.72464i) q^{24} +(5.88088 - 2.14047i) q^{25} +(-2.80764 + 5.24867i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(-6.33017 - 4.64774i) q^{28} +(0.439779 - 0.524109i) q^{29} +(4.03041 - 2.50447i) q^{30} +(1.25037 - 2.16570i) q^{31} +(-2.76689 - 4.93400i) q^{32} +(0.466350 + 2.64480i) q^{33} +(8.05386 + 1.15246i) q^{34} +(-4.50614 + 12.3805i) q^{35} +(1.44562 - 1.38210i) q^{36} -4.16521i q^{37} +(5.76234 + 2.18984i) q^{38} +4.20900 q^{39} +(-6.64363 + 6.77707i) q^{40} +(-10.3777 - 3.77718i) q^{41} +(-0.786598 + 5.49705i) q^{42} +(-12.0055 + 2.11689i) q^{43} +(-2.16007 - 4.91771i) q^{44} +(-2.90581 - 1.67767i) q^{45} +(6.62821 - 4.11873i) q^{46} +(4.55811 + 3.82471i) q^{47} +(-2.15354 + 3.37080i) q^{48} +(-4.20907 - 7.29033i) q^{49} +(7.80417 + 4.17465i) q^{50} +(-1.96762 - 5.40600i) q^{51} +(-8.17805 + 1.99558i) q^{52} +(9.75666 + 1.72036i) q^{53} +(-1.34390 - 0.440382i) q^{54} +(-6.90290 + 5.79222i) q^{55} +(-1.07792 - 11.0537i) q^{56} +(-0.556531 - 4.32322i) q^{57} +(0.967062 - 0.0313468i) q^{58} +(5.47945 + 6.53015i) q^{59} +(6.44138 + 1.88199i) q^{60} +(-1.92854 - 0.340054i) q^{61} +(3.46112 - 0.726632i) q^{62} +(3.68979 - 1.34297i) q^{63} +(2.58614 - 7.57046i) q^{64} +(7.06132 + 12.2306i) q^{65} +(-2.34577 + 2.98701i) q^{66} +(2.73629 - 3.26098i) q^{67} +(6.38618 + 9.57092i) q^{68} +(-4.77874 - 2.75901i) q^{69} +(-17.2930 + 6.93653i) q^{70} +(-1.84959 - 10.4895i) q^{71} +(2.81998 + 0.218486i) q^{72} +(-13.9260 - 5.06864i) q^{73} +(4.38735 - 3.93054i) q^{74} -6.25831i q^{75} +(3.13107 + 8.13612i) q^{76} -10.5453i q^{77} +(3.97187 + 4.43347i) q^{78} +(-3.82592 - 1.39252i) q^{79} +(-13.4078 - 0.602690i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-5.81442 - 14.4956i) q^{82} +(1.58055 + 0.912532i) q^{83} +(-6.53250 + 4.35880i) q^{84} +(12.4078 - 14.7870i) q^{85} +(-13.5589 - 10.6481i) q^{86} +(-0.342088 - 0.592513i) q^{87} +(3.14161 - 6.91591i) q^{88} +(-1.91937 + 0.698594i) q^{89} +(-0.974953 - 4.64393i) q^{90} +(-16.2760 - 2.86989i) q^{91} +(10.5932 + 3.09502i) q^{92} +(-1.60744 - 1.91567i) q^{93} +(0.272620 + 8.41043i) q^{94} +(11.6288 - 8.87012i) q^{95} +(-5.58277 + 0.912495i) q^{96} +(8.85598 - 7.43105i) q^{97} +(3.70720 - 11.3131i) q^{98} +(2.64480 + 0.466350i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$	$1$	$1$

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 $

$2$	0.943660	+	1.05333i	0.667268	+	0.744818i
$2$	0.943660	+	1.05333i	0.667268	+	0.744818i
$3$	0.342020	−	0.939693i	0.197465	−	0.542532i
$3$	0.342020	−	0.939693i	0.197465	−	0.542532i
$4$	−0.219013	+	1.98797i	−0.109507	+	0.993986i
$5$	3.30436	−	0.582649i	1.47776	−	0.260568i	0.624075	−	0.781364i	$-0.285476\pi$
$5$	3.30436	−	0.582649i	1.47776	−	0.260568i	0.853681	+	0.520796i	$0.174365\pi$
$6$	1.31256	−	0.526489i	0.535850	−	0.214938i
$7$	−1.96330	+	3.40053i	−0.742057	+	1.28528i	0.209501	+	0.977809i	$0.432816\pi$
$7$	−1.96330	+	3.40053i	−0.742057	+	1.28528i	−0.951557	+	0.307471i	$0.900517\pi$
$8$	−2.30067	+	1.64528i	−0.813409	+	0.581693i
$9$	−0.766044	−	0.642788i	−0.255348	−	0.214263i
$10$	3.73192	+	2.93077i	1.18014	+	0.926790i
$11$	−2.32580	+	1.34280i	−0.701254	+	0.404869i	−0.807814	−	0.589437i	$-0.799350\pi$
$11$	−2.32580	+	1.34280i	−0.701254	+	0.404869i	0.106560	+	0.994306i	$0.466016\pi$
$12$	1.79318	+	0.885732i	0.517645	+	0.255689i
$13$	1.43956	+	3.95517i	0.399263	+	1.09697i	0.962644	+	0.270769i	$0.0872781\pi$
$13$	1.43956	+	3.95517i	0.399263	+	1.09697i	−0.563381	+	0.826197i	$0.690500\pi$
$14$	−5.43457	+	1.14094i	−1.45245	+	0.304929i
$15$	0.582649	−	3.30436i	0.150439	−	0.853183i
$16$	−3.90407	−	0.870784i	−0.976017	−	0.217696i
$17$	4.40701	−	3.69792i	1.06886	−	0.896878i	0.0739095	−	0.997265i	$-0.476452\pi$
$17$	4.40701	−	3.69792i	1.06886	−	0.896878i	0.994949	+	0.100387i	$0.0320079\pi$
$18$	−0.0458169	−	1.41347i	−0.0107992	−	0.333158i
$19$	3.87216	−	2.00160i	0.888334	−	0.459198i
$19$	3.87216	−	2.00160i	0.888334	−	0.459198i
$20$	0.434590	+	6.69659i	0.0971772	+	1.49740i
$21$	2.52397	+	3.00795i	0.550775	+	0.656388i
$22$	−3.60917	−	1.18269i	−0.769479	−	0.252150i
$23$	0.958194	−	5.43419i	0.199797	−	1.13311i	−0.705622	−	0.708588i	$-0.749332\pi$
$23$	0.958194	−	5.43419i	0.199797	−	1.13311i	0.905420	−	0.424518i	$-0.139556\pi$
$24$	0.759179	+	2.72464i	0.154967	+	0.556164i
$25$	5.88088	−	2.14047i	1.17618	−	0.428093i
$26$	−2.80764	+	5.24867i	−0.550624	+	1.02935i
$27$	−0.866025	+	0.500000i	−0.166667	+	0.0962250i
$28$	−6.33017	−	4.64774i	−1.19629	−	0.878341i
$29$	0.439779	−	0.524109i	0.0816650	−	0.0973245i	−0.723665	−	0.690152i	$-0.757544\pi$
$29$	0.439779	−	0.524109i	0.0816650	−	0.0973245i	0.805330	+	0.592827i	$0.201988\pi$
$30$	4.03041	−	2.50447i	0.735849	−	0.457252i
$31$	1.25037	−	2.16570i	0.224573	−	0.388971i	−0.731619	−	0.681714i	$-0.761235\pi$
$31$	1.25037	−	2.16570i	0.224573	−	0.388971i	0.956191	+	0.292743i	$0.0945681\pi$
$32$	−2.76689	−	4.93400i	−0.489121	−	0.872216i
$33$	0.466350	+	2.64480i	0.0811810	+	0.460401i
$34$	8.05386	+	1.15246i	1.38123	+	0.197646i
$35$	−4.50614	+	12.3805i	−0.761676	+	2.09269i
$36$	1.44562	−	1.38210i	0.240936	−	0.230349i
$37$		−	4.16521i		−	0.684757i	−0.939562	−	0.342379i	$-0.888767\pi$
$37$		−	4.16521i		−	0.684757i	0.939562	−	0.342379i	$-0.111233\pi$
$38$	5.76234	+	2.18984i	0.934776	+	0.355239i
$39$	4.20900			0.673980
$40$	−6.64363	+	6.77707i	−1.05045	+	1.07155i
$41$	−10.3777	−	3.77718i	−1.62073	−	0.589897i	−0.637208	−	0.770692i	$-0.719911\pi$
$41$	−10.3777	−	3.77718i	−1.62073	−	0.589897i	−0.983521	+	0.180795i	$0.942133\pi$
$42$	−0.786598	+	5.49705i	−0.121375	+	0.848213i
$43$	−12.0055	+	2.11689i	−1.83082	+	0.322823i	−0.979441	−	0.201730i	$-0.935344\pi$
$43$	−12.0055	+	2.11689i	−1.83082	+	0.322823i	−0.851378	+	0.524553i	$0.824233\pi$
$44$	−2.16007	−	4.91771i	−0.325643	−	0.741373i
$45$	−2.90581	−	1.67767i	−0.433173	−	0.250092i
$46$	6.62821	−	4.11873i	0.977276	−	0.607273i
$47$	4.55811	+	3.82471i	0.664869	+	0.557891i	0.911542	−	0.411207i	$-0.134893\pi$
$47$	4.55811	+	3.82471i	0.664869	+	0.557891i	−0.246673	+	0.969099i	$0.579337\pi$
$48$	−2.15354	+	3.37080i	−0.310837	+	0.486533i
$49$	−4.20907	−	7.29033i	−0.601296	−	1.04148i
$50$	7.80417	+	4.17465i	1.10368	+	0.590384i
$51$	−1.96762	−	5.40600i	−0.275523	−	0.756992i
$52$	−8.17805	+	1.99558i	−1.13409	+	0.276737i
$53$	9.75666	+	1.72036i	1.34018	+	0.236310i	0.797342	−	0.603527i	$-0.206239\pi$
$53$	9.75666	+	1.72036i	1.34018	+	0.236310i	0.542838	+	0.839837i	$0.317350\pi$
$54$	−1.34390	−	0.440382i	−0.182881	−	0.0599284i
$55$	−6.90290	+	5.79222i	−0.930787	+	0.781023i
$56$	−1.07792	−	11.0537i	−0.144043	−	1.47711i
$57$	−0.556531	−	4.32322i	−0.0737143	−	0.572625i
$58$	0.967062	−	0.0313468i	0.126981	−	0.00411604i
$59$	5.47945	+	6.53015i	0.713364	+	0.850154i	0.993968	−	0.109670i	$-0.0349793\pi$
$59$	5.47945	+	6.53015i	0.713364	+	0.850154i	−0.280604	+	0.959824i	$0.590535\pi$
$60$	6.44138	+	1.88199i	0.831578	+	0.242964i
$61$	−1.92854	−	0.340054i	−0.246925	−	0.0435395i	0.0488159	−	0.998808i	$-0.484455\pi$
$61$	−1.92854	−	0.340054i	−0.246925	−	0.0435395i	−0.295740	+	0.955268i	$0.595566\pi$
$62$	3.46112	−	0.726632i	0.439563	−	0.0922824i
$63$	3.68979	−	1.34297i	0.464870	−	0.169199i
$64$	2.58614	−	7.57046i	0.323267	−	0.946308i
$65$	7.06132	+	12.2306i	0.875849	+	1.51701i
$66$	−2.34577	+	2.98701i	−0.288745	+	0.367676i
$67$	2.73629	−	3.26098i	0.334291	−	0.398393i	−0.572547	−	0.819872i	$-0.694045\pi$
$67$	2.73629	−	3.26098i	0.334291	−	0.398393i	0.906838	+	0.421479i	$0.138489\pi$
$68$	6.38618	+	9.57092i	0.774438	+	1.16064i
$69$	−4.77874	−	2.75901i	−0.575293	−	0.332146i
$70$	−17.2930	+	6.93653i	−2.06691	+	0.829074i
$71$	−1.84959	−	10.4895i	−0.219505	−	1.24488i	−0.872915	−	0.487872i	$-0.837773\pi$
$71$	−1.84959	−	10.4895i	−0.219505	−	1.24488i	0.653410	−	0.757005i	$-0.273338\pi$
$72$	2.81998	+	0.218486i	0.332337	+	0.0257488i
$73$	−13.9260	−	5.06864i	−1.62991	−	0.593239i	−0.644677	−	0.764455i	$-0.723008\pi$
$73$	−13.9260	−	5.06864i	−1.62991	−	0.593239i	−0.985234	+	0.171216i	$0.945230\pi$
$74$	4.38735	−	3.93054i	0.510019	−	0.456917i
$75$		−	6.25831i		−	0.722647i
$76$	3.13107	+	8.13612i	0.359158	+	0.933277i
$77$		−	10.5453i		−	1.20174i
$78$	3.97187	+	4.43347i	0.449725	+	0.501992i
$79$	−3.82592	−	1.39252i	−0.430450	−	0.156671i	0.117704	−	0.993049i	$-0.462447\pi$
$79$	−3.82592	−	1.39252i	−0.430450	−	0.156671i	−0.548153	+	0.836378i	$0.684669\pi$
$80$	−13.4078	−	0.602690i	−1.49904	−	0.0673828i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	−5.81442	−	14.4956i	−0.642095	−	1.60077i
$83$	1.58055	+	0.912532i	0.173488	+	0.100163i	0.584230	−	0.811588i	$-0.301397\pi$
$83$	1.58055	+	0.912532i	0.173488	+	0.100163i	−0.410741	+	0.911752i	$0.634730\pi$
$84$	−6.53250	+	4.35880i	−0.712754	+	0.475584i
$85$	12.4078	−	14.7870i	1.34581	−	1.60388i
$86$	−13.5589	−	10.6481i	−1.46209	−	1.14822i
$87$	−0.342088	−	0.592513i	−0.0366756	−	0.0635241i
$88$	3.14161	−	6.91591i	0.334897	−	0.737239i
$89$	−1.91937	+	0.698594i	−0.203453	+	0.0740508i	−0.441737	−	0.897145i	$-0.645637\pi$
$89$	−1.91937	+	0.698594i	−0.203453	+	0.0740508i	0.238284	+	0.971196i	$0.423415\pi$
$90$	−0.974953	−	4.64393i	−0.102769	−	0.489513i
$91$	−16.2760	−	2.86989i	−1.70618	−	0.300846i
$92$	10.5932	+	3.09502i	1.10441	+	0.322678i
$93$	−1.60744	−	1.91567i	−0.166684	−	0.198646i
$94$	0.272620	+	8.41043i	0.0281186	+	0.867469i
$95$	11.6288	−	8.87012i	1.19309	−	0.910055i
$96$	−5.58277	+	0.912495i	−0.569789	+	0.0931311i
$97$	8.85598	−	7.43105i	0.899189	−	0.754509i	−0.0708427	−	0.997487i	$-0.522569\pi$
$97$	8.85598	−	7.43105i	0.899189	−	0.754509i	0.970032	+	0.242978i	$0.0781244\pi$
$98$	3.70720	−	11.3131i	0.374484	−	1.14280i
$99$	2.64480	+	0.466350i	0.265812	+	0.0468699i
$100$	2.96720	+	12.1598i	0.296720	+	1.21598i
$101$	4.93980	+	13.5720i	0.491528	+	1.35046i	0.899281	+	0.437371i	$0.144090\pi$
$101$	4.93980	+	13.5720i	0.491528	+	1.35046i	−0.407753	+	0.913092i	$0.633687\pi$
$102$	3.83754	−	7.17399i	0.379974	−	0.710331i
$103$	1.20422	+	2.08577i	0.118655	+	0.205517i	0.919235	−	0.393709i	$-0.128808\pi$
$103$	1.20422	+	2.08577i	0.118655	+	0.205517i	−0.800580	+	0.599226i	$0.795475\pi$
$104$	−9.81930	−	6.73105i	−0.962861	−	0.660034i
$105$	10.0927	+	8.46877i	0.984945	+	0.826467i
$106$	7.39486	+	11.9004i	0.718252	+	1.15587i
$107$	−10.3252	−	5.96125i	−0.998174	−	0.576296i	−0.0904668	−	0.995899i	$-0.528836\pi$
$107$	−10.3252	−	5.96125i	−0.998174	−	0.576296i	−0.907708	+	0.419603i	$0.862169\pi$
$108$	−0.804315	−	1.83114i	−0.0773953	−	0.176202i
$109$	−3.53768	+	0.623789i	−0.338849	+	0.0597482i	−0.340483	−	0.940251i	$-0.610591\pi$
$109$	−3.53768	+	0.623789i	−0.338849	+	0.0597482i	0.00163482	+	0.999999i	$0.499480\pi$
$110$	−12.6151	−	1.80516i	−1.20280	−	0.172115i
$111$	−3.91402	−	1.42459i	−0.371502	−	0.135216i
$112$	10.6260	−	11.5663i	1.00406	−	1.09291i
$113$	3.04887			0.286813			0.143407	−	0.989664i	$-0.454194\pi$
$113$	3.04887			0.286813			0.143407	+	0.989664i	$0.454194\pi$
$114$	4.02861	−	4.66586i	0.377314	−	0.436998i
$115$		−	18.5148i		−	1.72652i
$116$	0.945596	+	0.989056i	0.0877964	+	0.0918315i
$117$	1.43956	−	3.95517i	0.133088	−	0.365655i
$118$	−1.70768	+	11.9339i	−0.157205	+	1.09861i
$119$	3.92263	+	22.2463i	0.359587	+	2.03932i
$120$	4.09611	+	8.56086i	0.373922	+	0.781496i
$121$	−1.89378	+	3.28012i	−0.172161	+	0.298192i
$122$	−1.46170	−	2.35229i	−0.132336	−	0.212966i
$123$	−7.09878	+	8.46000i	−0.640076	+	0.762812i
$124$	4.03150	+	2.96001i	0.362040	+	0.265817i
$125$	3.65640	−	2.11102i	0.327038	−	0.188815i
$126$	4.89650	+	2.61926i	0.436215	+	0.233342i
$127$	12.5136	−	4.55459i	1.11040	−	0.404154i	0.279263	−	0.960215i	$-0.409910\pi$
$127$	12.5136	−	4.55459i	1.11040	−	0.404154i	0.831142	+	0.556060i	$0.187688\pi$
$128$	10.4146	−	4.41988i	0.920533	−	0.390666i
$129$	−2.11689	+	12.0055i	−0.186382	+	1.05702i
$130$	−6.21935	+	18.9794i	−0.545473	+	1.66460i
$131$	2.74268	+	3.26859i	0.239629	+	0.285578i	0.872433	−	0.488733i	$-0.162541\pi$
$131$	2.74268	+	3.26859i	0.239629	+	0.285578i	−0.632805	+	0.774311i	$0.718096\pi$
$132$	−5.35992	+	0.347844i	−0.466522	+	0.0302759i
$133$	−0.795702	+	17.0971i	−0.0689961	+	1.48251i
$134$	6.01702	−	0.195039i	0.519791	−	0.0168488i
$135$	−2.57034	+	2.15677i	−0.221220	+	0.185625i
$136$	−4.05497	+	15.7584i	−0.347711	+	1.35128i
$137$	−1.50846	+	8.55490i	−0.128876	+	0.730894i	0.850053	+	0.526697i	$0.176570\pi$
$137$	−1.50846	+	8.55490i	−0.128876	+	0.730894i	−0.978930	+	0.204198i	$0.934541\pi$
$138$	−1.60336	−	7.63716i	−0.136487	−	0.650119i
$139$	3.05374	+	8.39008i	0.259015	+	0.711638i	0.999229	+	0.0392662i	$0.0125020\pi$
$139$	3.05374	+	8.39008i	0.259015	+	0.711638i	−0.740214	+	0.672372i	$0.765276\pi$
$140$	−23.6252	−	11.6696i	−1.99669	−	0.986258i
$141$	5.15302	−	2.97510i	0.433963	−	0.250548i
$142$	9.30356	−	11.8468i	0.780737	−	0.994158i
$143$	−8.65913	−	7.26588i	−0.724113	−	0.607603i
$144$	2.43096	+	3.17655i	0.202580	+	0.264712i
$145$	1.14782	−	1.98808i	0.0953213	−	0.165101i
$146$	−7.80242	−	19.4517i	−0.645732	−	1.60984i
$147$	−8.29026	+	1.46180i	−0.683769	+	0.120567i
$148$	8.28033	+	0.912237i	0.680639	+	0.0749854i
$149$	−0.906991	+	2.49194i	−0.0743036	+	0.204147i	−0.971284	−	0.237923i	$-0.923534\pi$
$149$	−0.906991	+	2.49194i	−0.0743036	+	0.204147i	0.896981	+	0.442070i	$0.145756\pi$
$150$	6.59207	−	5.90571i	0.538240	−	0.482199i
$151$	−10.4436			−0.849887			−0.424943	−	0.905220i	$-0.639706\pi$
$151$	−10.4436			−0.849887			−0.424943	+	0.905220i	$0.639706\pi$
$152$	−5.61537	+	10.9758i	−0.455466	+	0.890253i
$153$	−5.75295			−0.465098
$154$	11.1077	−	9.95114i	0.895080	−	0.801886i
$155$	2.86983	−	7.88479i	0.230510	−	0.633321i
$156$	−0.921827	+	8.36738i	−0.0738053	+	0.669927i
$157$	10.0499	−	1.77207i	0.802069	−	0.141426i	0.242436	−	0.970167i	$-0.422053\pi$
$157$	10.0499	−	1.77207i	0.802069	−	0.141426i	0.559632	+	0.828741i	$0.310942\pi$
$158$	−2.14358	−	5.34403i	−0.170534	−	0.425148i
$159$	4.95359	−	8.57987i	0.392845	−	0.680428i
$160$	−12.0176	−	14.6916i	−0.950074	−	1.16147i
$161$	16.5979	+	13.9273i	1.30810	+	1.09762i
$162$	−0.873464	+	1.11223i	−0.0686258	+	0.0873852i
$163$	−8.63177	+	4.98356i	−0.676093	+	0.390342i	−0.798381	−	0.602152i	$-0.794310\pi$
$163$	−8.63177	+	4.98356i	−0.676093	+	0.390342i	0.122289	+	0.992495i	$0.460977\pi$
$164$	9.78179	−	19.8034i	0.763830	−	1.54638i
$165$	3.08198	+	8.46766i	0.239932	+	0.659207i
$166$	0.530304	+	2.52596i	0.0411596	+	0.196053i
$167$	0.969007	−	5.49551i	0.0749840	−	0.425255i	−0.924088	−	0.382180i	$-0.875173\pi$
$167$	0.969007	−	5.49551i	0.0749840	−	0.425255i	0.999072	−	0.0430753i	$-0.0137155\pi$
$168$	−10.7557	−	2.76766i	−0.829821	−	0.213530i
$169$	−3.61244	+	3.03120i	−0.277880	+	0.233169i
$170$	27.2844	−	0.884409i	2.09262	−	0.0678310i
$171$	−4.25285	−	0.955662i	−0.325223	−	0.0730813i
$172$	−1.57896	−	24.3302i	−0.120395	−	1.85516i
$173$	7.67404	+	9.14556i	0.583446	+	0.695324i	0.974332	−	0.225115i	$-0.0722757\pi$
$173$	7.67404	+	9.14556i	0.583446	+	0.695324i	−0.390886	+	0.920439i	$0.627831\pi$
$174$	0.301298	−	0.919462i	0.0228414	−	0.0697042i
$175$	−4.26720	+	24.2005i	−0.322570	+	1.82939i
$176$	10.2494	−	3.21711i	0.772574	−	0.242499i
$177$	8.01042	−	2.91555i	0.602100	−	0.219147i
$178$	−2.54708	−	1.36250i	−0.190912	−	0.102124i
$179$	12.7477	−	7.35988i	0.952806	−	0.550103i	0.0588548	−	0.998267i	$-0.481255\pi$
$179$	12.7477	−	7.35988i	0.952806	−	0.550103i	0.893952	+	0.448163i	$0.147922\pi$
$180$	3.97157	−	5.40924i	0.296023	−	0.403181i
$181$	8.94214	−	10.6568i	0.664664	−	0.792116i	−0.323383	−	0.946268i	$-0.604820\pi$
$181$	8.94214	−	10.6568i	0.664664	−	0.792116i	0.988047	+	0.154153i	$0.0492647\pi$
$182$	−12.3360	−	19.8522i	−0.914407	−	1.47154i
$183$	−0.979147	+	1.69593i	−0.0723806	+	0.125367i
$184$	6.73625	+	14.0787i	0.496603	+	1.03790i
$185$	−2.42686	−	13.7634i	−0.178426	−	1.01190i
$186$	0.500962	−	3.50091i	0.0367323	−	0.256699i
$187$	−5.28425	+	14.5184i	−0.386423	+	1.06169i
$188$	−8.60171	+	8.22374i	−0.627344	+	0.599778i
$189$		−	3.92659i		−	0.285618i
$190$	20.3168	+	3.87860i	1.47394	+	0.281383i
$191$	−24.0046			−1.73691			−0.868456	−	0.495766i	$-0.834887\pi$
$191$	−24.0046			−1.73691			−0.868456	+	0.495766i	$0.834887\pi$
$192$	−6.22940	−	5.01942i	−0.449568	−	0.362246i
$193$	−16.5357	−	6.01851i	−1.19027	−	0.433222i	−0.330450	−	0.943824i	$-0.607200\pi$
$193$	−16.5357	−	6.01851i	−1.19027	−	0.433222i	−0.859817	+	0.510602i	$0.829423\pi$
$194$	16.1844	+	2.31590i	1.16197	+	0.166272i
$195$	13.9081	−	2.45237i	0.995978	−	0.175618i
$196$	15.4148	−	6.77084i	1.10106	−	0.483632i
$197$	−1.97709	−	1.14147i	−0.140862	−	0.0813266i	0.427913	−	0.903820i	$-0.359249\pi$
$197$	−1.97709	−	1.14147i	−0.140862	−	0.0813266i	−0.568775	+	0.822493i	$0.692582\pi$
$198$	2.00457	+	3.22593i	0.142459	+	0.229257i
$199$	−1.54567	−	1.29697i	−0.109570	−	0.0919398i	0.586357	−	0.810053i	$-0.300562\pi$
$199$	−1.54567	−	1.29697i	−0.109570	−	0.0919398i	−0.695926	+	0.718113i	$0.745006\pi$
$200$	−10.0083	+	14.6002i	−0.707693	+	1.03239i
$201$	−2.12846	−	3.68659i	−0.150130	−	0.260032i
$202$	−9.63431	+	18.0106i	−0.677868	+	1.26722i
$203$	0.918830	+	2.52446i	0.0644892	+	0.177183i
$204$	11.1779	−	2.72760i	0.782611	−	0.190970i
$205$	−36.4926	−	6.43462i	−2.54875	−	0.449414i
$206$	−1.06063	+	3.23670i	−0.0738978	+	0.225511i
$207$	−4.22705	+	3.54691i	−0.293800	+	0.246527i
$208$	−2.17605	−	16.6948i	−0.150882	−	1.15758i
$209$	−6.31811	+	9.85485i	−0.437033	+	0.681674i
$210$	0.603641	+	18.6226i	0.0416552	+	1.28508i
$211$	5.93930	+	7.07818i	0.408878	+	0.487282i	0.930706	−	0.365769i	$-0.119194\pi$
$211$	5.93930	+	7.07818i	0.408878	+	0.487282i	−0.521828	+	0.853051i	$0.674750\pi$
$212$	−5.55687	+	19.0192i	−0.381648	+	1.30624i
$213$	−10.4895	−	1.84959i	−0.718730	−	0.126731i
$214$	−3.46429	−	16.5012i	−0.236814	−	1.12800i
$215$	−38.4371	+	13.9900i	−2.62139	+	0.954107i
$216$	1.16980	−	2.57518i	0.0795947	−	0.175219i
$217$	4.90969	+	8.50383i	0.333291	+	0.577277i
$218$	−3.99543	−	3.13771i	−0.270604	−	0.212512i
$219$	−9.52592	+	11.3525i	−0.643702	+	0.767134i
$220$	−10.0030	−	14.9914i	−0.674399	−	1.01072i
$221$	20.9701	+	12.1071i	1.41060	+	0.814411i
$222$	−2.19294	−	5.46709i	−0.147181	−	0.366927i
$223$	0.0241630	+	0.137035i	0.00161807	+	0.00917655i	0.985606	−	0.169058i	$-0.0540725\pi$
$223$	0.0241630	+	0.137035i	0.00161807	+	0.00917655i	−0.983988	+	0.178235i	$0.942961\pi$
$224$	22.2104	+	0.278029i	1.48400	+	0.0185766i
$225$	−5.88088	−	2.14047i	−0.392059	−	0.142698i
$226$	2.87709	+	3.21147i	0.191381	+	0.213623i
$227$		−	8.55037i		−	0.567508i	−0.958897	−	0.283754i	$-0.908420\pi$
$227$		−	8.55037i		−	0.567508i	0.958897	−	0.283754i	$-0.0915799\pi$
$228$	8.71634	−	0.159524i	0.577254	−	0.0105648i
$229$		−	2.88099i		−	0.190381i	−0.995459	−	0.0951907i	$-0.969654\pi$
$229$		−	2.88099i		−	0.190381i	0.995459	−	0.0951907i	$-0.0303461\pi$
$230$	19.5022	−	17.4717i	1.28594	−	1.15205i
$231$	−9.90931	−	3.60669i	−0.651984	−	0.237303i
$232$	−0.149483	+	1.92936i	−0.00981402	+	0.126669i
$233$	1.35989	+	7.71234i	0.0890896	+	0.505252i	0.996399	+	0.0847884i	$0.0270214\pi$
$233$	1.35989	+	7.71234i	0.0890896	+	0.505252i	−0.907309	+	0.420464i	$0.861867\pi$
$234$	5.52456	−	2.21600i	0.361152	−	0.144864i
$235$	17.2901	+	9.98246i	1.12788	+	0.651184i
$236$	−14.1818	+	9.46280i	−0.923159	+	0.615976i
$237$	−2.61708	+	3.11892i	−0.169998	+	0.202595i
$238$	−19.7311	+	25.1248i	−1.27898	+	1.62860i
$239$	0.623181	+	1.07938i	0.0403102	+	0.0698194i	0.885477	−	0.464684i	$-0.153832\pi$
$239$	0.623181	+	1.07938i	0.0403102	+	0.0698194i	−0.845166	+	0.534503i	$0.820499\pi$
$240$	−5.15209	+	12.3931i	−0.332566	+	0.799971i
$241$	−0.0959959	+	0.0349397i	−0.00618364	+	0.00225066i	−0.345110	−	0.938562i	$-0.612158\pi$
$241$	−0.0959959	+	0.0349397i	−0.00618364	+	0.00225066i	0.338926	+	0.940813i	$0.389936\pi$
$242$	−5.24213	+	1.10054i	−0.336977	+	0.0707454i
$243$	0.984808	+	0.173648i	0.0631754	+	0.0111395i
$244$	1.09839	−	3.75941i	0.0703175	−	0.240672i
$245$	−18.1560	−	21.6375i	−1.15995	−	1.38237i
$246$	−15.6100	+	0.505990i	−0.995258	+	0.0322608i
$247$	13.4909	+	12.4336i	0.858404	+	0.791132i
$248$	0.686494	+	7.03975i	0.0435924	+	0.447025i
$249$	1.39808	−	1.17313i	0.0885997	−	0.0743440i
$250$	5.67400	+	1.85931i	0.358855	+	0.117593i
$251$	14.3889	+	2.53715i	0.908220	+	0.160144i	0.608195	−	0.793788i	$-0.291894\pi$
$251$	14.3889	+	2.53715i	0.908220	+	0.160144i	0.300025	+	0.953931i	$0.403005\pi$
$252$	1.86168	+	7.62933i	0.117275	+	0.480603i
$253$	5.06846	+	13.9255i	0.318651	+	0.875487i
$254$	16.6061	+	8.88301i	1.04196	+	0.557370i
$255$	−9.65155	−	16.7170i	−0.604403	−	1.04686i
$256$	14.4835	+	6.79920i	0.905217	+	0.424950i
$257$	−14.8341	−	12.4473i	−0.925326	−	0.776440i	0.0496467	−	0.998767i	$-0.484190\pi$
$257$	−14.8341	−	12.4473i	−0.925326	−	0.776440i	−0.974972	+	0.222326i	$0.928635\pi$
$258$	−14.6434	+	9.09930i	−0.911657	+	0.566498i
$259$	14.1639	+	8.17755i	0.880104	+	0.508129i
$260$	−25.8605	+	11.3590i	−1.60380	+	0.704458i
$261$	−0.673781	+	0.118806i	−0.0417060	+	0.00735389i
$262$	−0.854759	+	5.97338i	−0.0528072	+	0.369037i
$263$	16.7925	+	6.11196i	1.03547	+	0.376880i	0.803160	−	0.595763i	$-0.203150\pi$
$263$	16.7925	+	6.11196i	1.03547	+	0.376880i	0.232308	+	0.972642i	$0.425372\pi$
$264$	−5.42434	−	5.31753i	−0.333845	−	0.327271i
$265$	33.2419			2.04204
$266$	−18.7598	+	15.2957i	−1.15024	+	0.937841i
$267$			2.04255i			0.125002i
$268$	5.88346	+	6.15387i	0.359390	+	0.375907i
$269$	−6.93701	+	19.0593i	−0.422957	+	1.16206i	0.527050	+	0.849834i	$0.323298\pi$
$269$	−6.93701	+	19.0593i	−0.422957	+	1.16206i	−0.950007	+	0.312230i	$0.898924\pi$
$270$	−4.69732	−	0.672161i	−0.285870	−	0.0409064i
$271$	4.40266	+	24.9687i	0.267442	+	1.51674i	0.761989	+	0.647590i	$0.224223\pi$
$271$	4.40266	+	24.9687i	0.267442	+	1.51674i	−0.494547	+	0.869151i	$0.664666\pi$
$272$	−20.4254	+	10.5994i	−1.23847	+	0.642682i
$273$	−8.26352	+	14.3128i	−0.500131	+	0.866253i
$274$	−10.4346	+	6.48401i	−0.630378	+	0.391713i
$275$	−10.8035	+	12.8751i	−0.651477	+	0.776400i
$276$	6.53144	−	8.89575i	0.393146	−	0.535461i
$277$	−27.7246	+	16.0068i	−1.66581	+	0.961757i	−0.695953	+	0.718087i	$0.745018\pi$
$277$	−27.7246	+	16.0068i	−1.66581	+	0.961757i	−0.969858	+	0.243669i	$0.921649\pi$
$278$	−5.95585	+	11.1340i	−0.357208	+	0.667772i
$279$	−2.34992	+	0.855302i	−0.140686	+	0.0512056i
$280$	−10.0022	−	35.8973i	−0.597747	−	2.14527i
$281$	−1.87004	+	10.6055i	−0.111558	+	0.632674i	0.876840	+	0.480783i	$0.159647\pi$
$281$	−1.87004	+	10.6055i	−0.111558	+	0.632674i	−0.988397	+	0.151891i	$0.951464\pi$
$282$	7.99646	+	2.62036i	0.476182	+	0.156040i
$283$	−11.8919	−	14.1723i	−0.706903	−	0.842454i	0.286386	−	0.958114i	$-0.407546\pi$
$283$	−11.8919	−	14.1723i	−0.706903	−	0.842454i	−0.993289	+	0.115661i	$0.963102\pi$
$284$	21.2580	−	1.37958i	1.26143	−	0.0818630i
$285$	−4.35790	−	13.9612i	−0.258140	−	0.826993i
$286$	−0.517901	−	15.9775i	−0.0306241	−	0.944766i
$287$	33.2190	−	27.8740i	1.96086	−	1.64535i
$288$	−1.05196	+	5.55818i	−0.0619871	+	0.327519i
$289$	2.79511	−	15.8519i	0.164419	−	0.932464i
$290$	3.17726	−	0.667038i	0.186575	−	0.0391698i
$291$	−3.95398	−	10.8635i	−0.231786	−	0.636828i
$292$	13.1263	−	26.5743i	0.768157	−	1.55514i
$293$	−7.67346	+	4.43027i	−0.448288	+	0.258819i	−0.707107	−	0.707107i	$-0.750000\pi$
$293$	−7.67346	+	4.43027i	−0.448288	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$294$	−9.36294	−	7.35295i	−0.546058	−	0.428833i
$295$	21.9109	+	18.3854i	1.27570	+	1.07044i
$296$	6.85292	+	9.58277i	0.398318	+	0.556987i
$297$	1.34280	−	2.32580i	0.0779172	−	0.134956i
$298$	−3.48073	+	1.39618i	−0.201633	+	0.0808785i
$299$	22.8725	−	4.03304i	1.32275	−	0.233237i
$300$	12.4413	+	1.37065i	0.718301	+	0.0791346i
$301$	16.3718	−	44.9811i	0.943654	−	2.59267i
$302$	−9.85519	−	11.0006i	−0.567102	−	0.633011i
$303$	14.4430			0.829729
$304$	−16.8601	+	4.44256i	−0.966994	+	0.254798i
$305$	−6.57074			−0.376239
$306$	−5.42883	−	6.05976i	−0.310345	−	0.346413i
$307$	1.16967	−	3.21365i	0.0667568	−	0.183413i	−0.901829	−	0.432094i	$-0.857775\pi$
$307$	1.16967	−	3.21365i	0.0667568	−	0.183413i	0.968585	+	0.248681i	$0.0799971\pi$
$308$	20.9637	+	2.30955i	1.19452	+	0.131599i
$309$	2.37185	−	0.418221i	0.134930	−	0.0237918i
$310$	11.0134	−	4.41768i	0.625521	−	0.250907i
$311$	3.11432	−	5.39416i	0.176597	−	0.305875i	−0.764116	−	0.645079i	$-0.776824\pi$
$311$	3.11432	−	5.39416i	0.176597	−	0.305875i	0.940713	+	0.339204i	$0.110158\pi$
$312$	−9.68351	+	6.92497i	−0.548221	+	0.392049i
$313$	7.63289	+	6.40476i	0.431436	+	0.362018i	0.832493	−	0.554035i	$-0.186913\pi$
$313$	7.63289	+	6.40476i	0.431436	+	0.362018i	−0.401057	+	0.916053i	$0.631357\pi$
$314$	11.3503	+	8.91364i	0.640532	+	0.503026i
$315$	11.4099	−	6.58753i	0.642877	−	0.371165i
$316$	3.60622	−	7.30084i	0.202866	−	0.410704i
$317$	5.91982	+	16.2646i	0.332490	+	0.913509i	0.987462	+	0.157856i	$0.0504582\pi$
$317$	5.91982	+	16.2646i	0.332490	+	0.913509i	−0.654972	+	0.755653i	$0.727320\pi$
$318$	13.7119	−	2.87870i	0.768927	−	0.161430i
$319$	−0.319065	+	1.80951i	−0.0178642	+	0.101313i
$320$	4.13462	−	26.5224i	0.231132	−	1.48265i
$321$	−9.13317	+	7.66364i	−0.509764	+	0.427743i
$322$	0.992716	+	30.6257i	0.0553219	+	1.70670i
$323$	9.66290	−	23.1400i	0.537658	−	1.28755i
$324$	−1.99580	+	0.129522i	−0.110878	+	0.00719566i
$325$	16.9318	+	20.1785i	0.939208	+	1.11930i
$326$	−13.3948	−	4.38934i	−0.741869	−	0.243103i
$327$	−0.623789	+	3.53768i	−0.0344956	+	0.195634i
$328$	30.0902	−	8.38418i	1.66145	−	0.462939i
$329$	−21.9550	+	7.99096i	−1.21042	+	0.440556i
$330$	−6.01092	+	11.2369i	−0.330890	+	0.618573i
$331$	9.98839	−	5.76680i	0.549011	−	0.316972i	−0.199712	−	0.979855i	$-0.564001\pi$
$331$	9.98839	−	5.76680i	0.549011	−	0.316972i	0.748723	+	0.662883i	$0.230667\pi$
$332$	−2.16025	+	2.94224i	−0.118559	+	0.161476i
$333$	−2.67735	+	3.19074i	−0.146718	+	0.174851i
$334$	6.70301	−	4.16521i	0.366772	−	0.227910i
$335$	7.14169	−	12.3698i	0.390192	−	0.675833i
$336$	−7.23446	−	13.9411i	−0.394672	−	0.760547i
$337$	−2.93176	−	16.6269i	−0.159703	−	0.905723i	−0.954359	−	0.298662i	$-0.903460\pi$
$337$	−2.93176	−	16.6269i	−0.159703	−	0.905723i	0.794656	−	0.607061i	$-0.207651\pi$
$338$	−6.60177	−	0.944677i	−0.359089	−	0.0513837i
$339$	1.04277	−	2.86500i	0.0566357	−	0.155605i
$340$	26.6787	+	27.9049i	1.44686	+	1.51336i
$341$			6.71597i			0.363690i
$342$	−3.00661	−	5.38148i	−0.162579	−	0.290997i
$343$	5.56849			0.300670
$344$	24.1378	−	24.6226i	1.30142	−	1.32756i
$345$	−17.3982	−	6.33244i	−0.936690	−	0.340927i
$346$	−2.39163	+	16.7136i	−0.128575	+	0.898529i
$347$	−1.58502	+	0.279482i	−0.0850884	+	0.0150034i	−0.216030	−	0.976387i	$-0.569311\pi$
$347$	−1.58502	+	0.279482i	−0.0850884	+	0.0150034i	0.130942	+	0.991390i	$0.458200\pi$
$348$	1.25282	−	0.550292i	0.0671583	−	0.0294988i
$349$	−13.3259	−	7.69374i	−0.713322	−	0.411836i	0.0989681	−	0.995091i	$-0.468446\pi$
$349$	−13.3259	−	7.69374i	−0.713322	−	0.411836i	−0.812290	+	0.583254i	$0.801779\pi$
$350$	−29.5179	+	18.3423i	−1.57780	+	0.980435i
$351$	−3.22428	−	2.70549i	−0.172100	−	0.144409i
$352$	13.0606	+	7.76011i	0.696132	+	0.413615i
$353$	−4.72335	−	8.18108i	−0.251398	−	0.435435i	0.712513	−	0.701659i	$-0.247557\pi$
$353$	−4.72335	−	8.18108i	−0.251398	−	0.435435i	−0.963911	+	0.266224i	$0.914224\pi$
$354$	10.6302	+	5.68634i	0.564986	+	0.302225i
$355$	−12.2234	−	33.5835i	−0.648751	−	1.78243i
$356$	−0.968418	−	3.96866i	−0.0513261	−	0.210339i
$357$	22.2463	+	3.92263i	1.17740	+	0.207607i
$358$	19.7819	+	6.48231i	1.04550	+	0.342601i
$359$	5.65631	−	4.74621i	0.298529	−	0.250495i	−0.481203	−	0.876609i	$-0.659800\pi$
$359$	5.65631	−	4.74621i	0.298529	−	0.250495i	0.779732	+	0.626114i	$0.215355\pi$
$360$	9.44553	−	0.921097i	0.497823	−	0.0485461i
$361$	10.9872	−	15.5010i	0.578274	−	0.815842i
$362$	19.6635	−	0.637382i	1.03349	−	0.0335001i
$363$	2.43459	+	2.90143i	0.127783	+	0.152286i
$364$	9.26992	−	31.7276i	0.485876	−	1.66298i
$365$	−48.9697	−	8.63468i	−2.56319	−	0.451960i
$366$	−2.71036	+	0.569016i	−0.141673	+	0.0297430i
$367$	−3.62034	+	1.31769i	−0.188980	+	0.0687831i	−0.434777	−	0.900538i	$-0.643173\pi$
$367$	−3.62034	+	1.31769i	−0.188980	+	0.0687831i	0.245797	+	0.969321i	$0.420950\pi$
$368$	−8.47286	+	20.3810i	−0.441678	+	1.06244i
$369$	5.52187	+	9.56416i	0.287457	+	0.497890i
$370$	12.2073	−	15.5442i	0.634626	−	0.808106i
$371$	−25.0054	+	29.8003i	−1.29821	+	1.54715i
$372$	4.16036	−	2.77599i	0.215704	−	0.143928i
$373$	2.03091	+	1.17254i	0.105156	+	0.0607121i	0.551656	−	0.834072i	$-0.313996\pi$
$373$	2.03091	+	1.17254i	0.105156	+	0.0607121i	−0.446499	+	0.894784i	$0.647330\pi$
$374$	−20.2792	+	8.13433i	−1.04861	+	0.420616i
$375$	−0.733150	−	4.15790i	−0.0378597	−	0.214713i
$376$	−16.7794	−	1.30003i	−0.865332	−	0.0670442i
$377$	2.70603	+	0.984914i	0.139368	+	0.0507256i
$378$	4.13601	−	3.70537i	0.212733	−	0.190584i
$379$			22.6000i			1.16088i	0.814302	+	0.580442i	$0.197120\pi$
$379$			22.6000i			1.16088i	−0.814302	+	0.580442i	$0.802880\pi$
$380$	15.0867	+	25.0604i	0.773931	+	1.28557i
$381$		−	13.3167i		−	0.682236i
$382$	−22.6522	−	25.2848i	−1.15899	−	1.29368i
$383$	8.67901	+	3.15890i	0.443477	+	0.161412i	0.554100	−	0.832450i	$-0.313063\pi$
$383$	8.67901	+	3.15890i	0.443477	+	0.161412i	−0.110623	+	0.993862i	$0.535285\pi$
$384$	−0.591313	−	11.2982i	−0.0301753	−	0.576561i
$385$	−6.14418	−	34.8454i	−0.313137	−	1.77589i
$386$	−9.26460	−	23.0970i	−0.471556	−	1.17561i
$387$	10.5574	+	6.09534i	0.536665	+	0.309844i
$388$	12.8331	+	19.2329i	0.651504	+	0.976405i
$389$	−9.28178	+	11.0616i	−0.470605	+	0.560845i	−0.948175	−	0.317749i	$-0.897073\pi$
$389$	−9.28178	+	11.0616i	−0.470605	+	0.560845i	0.477570	+	0.878594i	$0.341518\pi$
$390$	15.7077	+	12.3356i	0.795388	+	0.624638i
$391$	−15.8724	−	27.4919i	−0.802704	−	1.39032i
$392$	21.6783	+	9.84754i	1.09492	+	0.497376i
$393$	4.00952	−	1.45935i	0.202254	−	0.0736143i
$394$	−0.663351	−	3.15969i	−0.0334191	−	0.159183i
$395$	−13.4536	−	2.37223i	−0.676923	−	0.119360i
$396$	−1.50634	+	5.15565i	−0.0756962	+	0.259081i
$397$	10.7527	+	12.8146i	0.539662	+	0.643144i	0.965112	−	0.261838i	$-0.0843286\pi$
$397$	10.7527	+	12.8146i	0.539662	+	0.643144i	−0.425450	+	0.904982i	$0.639884\pi$
$398$	−0.0924461	−	2.85200i	−0.00463390	−	0.142958i
$399$	15.7939	+	6.59528i	0.790684	+	0.330177i
$400$	−24.8232	+	3.23554i	−1.24116	+	0.161777i
$401$	−26.3826	+	22.1376i	−1.31748	+	1.10550i	−0.330652	+	0.943753i	$0.607269\pi$
$401$	−26.3826	+	22.1376i	−1.31748	+	1.10550i	−0.986832	+	0.161748i	$0.948287\pi$
$402$	1.87467	−	5.72086i	0.0934999	−	0.285330i
$403$	10.3657	+	1.82775i	0.516352	+	0.0910468i
$404$	−28.0626	+	6.84774i	−1.39617	+	0.340688i
$405$	1.14759	+	3.15299i	0.0570244	+	0.156673i
$406$	−1.79203	+	3.35007i	−0.0889372	+	0.166261i
$407$	5.59305	+	9.68745i	0.277237	+	0.480189i
$408$	13.4212	+	9.20013i	0.664449	+	0.455474i
$409$	14.4081	+	12.0899i	0.712437	+	0.597806i	0.925282	−	0.379280i	$-0.123828\pi$
$409$	14.4081	+	12.0899i	0.712437	+	0.597806i	−0.212845	+	0.977086i	$0.568273\pi$
$410$	−27.6588	−	44.5108i	−1.36597	−	2.19823i
$411$	7.52305	+	4.34344i	0.371085	+	0.214246i
$412$	−4.41019	+	1.93714i	−0.217274	+	0.0954362i
$413$	−32.9638	+	5.81240i	−1.62204	+	0.286010i
$414$	−7.72497	−	1.10540i	−0.379661	−	0.0543275i
$415$	5.75440	+	2.09443i	0.282473	+	0.102812i
$416$	15.5317	−	18.0463i	0.761504	−	0.884793i
$417$	8.92854			0.437233
$418$	−16.3426	+	2.64456i	−0.799341	+	0.129349i
$419$		−	3.15366i		−	0.154066i	−0.997029	−	0.0770331i	$-0.975455\pi$
$419$		−	3.15366i		−	0.154066i	0.997029	−	0.0770331i	$-0.0245447\pi$
$420$	−19.0461	+	18.2092i	−0.929355	+	0.888518i
$421$	−2.10816	+	5.79211i	−0.102745	+	0.282290i	−0.980405	−	0.196995i	$-0.936882\pi$
$421$	−2.10816	+	5.79211i	−0.102745	+	0.282290i	0.877659	+	0.479285i	$0.159104\pi$
$422$	−1.85099	+	12.9354i	−0.0901049	+	0.629687i
$423$	−1.03324	−	5.85980i	−0.0502379	−	0.284913i
$424$	−25.2773	+	12.0944i	−1.22757	+	0.587357i
$425$	18.0019	−	31.1801i	0.873218	−	1.51246i
$426$	−7.95031	−	12.7943i	−0.385194	−	0.619887i
$427$	4.94267	−	5.89044i	0.239192	−	0.285058i
$428$	14.1122	−	19.2206i	0.682137	−	0.929063i
$429$	−9.78929	+	5.65185i	−0.472631	+	0.272874i
$430$	−51.0076	−	27.2852i	−2.45980	−	1.31581i
$431$	25.1995	−	9.17186i	1.21382	−	0.441793i	0.345791	−	0.938312i	$-0.387611\pi$
$431$	25.1995	−	9.17186i	1.21382	−	0.441793i	0.868026	+	0.496518i	$0.165389\pi$
$432$	3.81641	−	1.19791i	0.183617	−	0.0576346i
$433$	4.96039	−	28.1318i	0.238381	−	1.35193i	−0.596994	−	0.802246i	$-0.703638\pi$
$433$	4.96039	−	28.1318i	0.238381	−	1.35193i	0.835375	−	0.549680i	$-0.185250\pi$
$434$	−4.32427	+	13.1962i	−0.207572	+	0.633440i
$435$	−1.47561	−	1.75856i	−0.0707500	−	0.0843166i
$436$	−0.465276	−	7.16943i	−0.0222827	−	0.343354i
$437$	−7.16678	−	22.9599i	−0.342834	−	1.09832i
$438$	−20.9472	+	0.678993i	−1.00090	+	0.0324435i
$439$	−26.0061	+	21.8217i	−1.24120	+	1.04149i	−0.243773	+	0.969832i	$0.578385\pi$
$439$	−26.0061	+	21.8217i	−1.24120	+	1.04149i	−0.997429	+	0.0716602i	$0.977170\pi$
$440$	6.35148	−	24.6832i	0.302795	−	1.17672i
$441$	−1.46180	+	8.29026i	−0.0696093	+	0.394774i
$442$	7.03585	+	33.5134i	0.334661	+	1.59407i
$443$	−4.79305	−	13.1688i	−0.227725	−	0.625669i	0.772228	−	0.635345i	$-0.219142\pi$
$443$	−4.79305	−	13.1688i	−0.227725	−	0.625669i	−0.999953	+	0.00967641i	$0.996920\pi$
$444$	3.68926	−	7.46896i	0.175085	−	0.354461i
$445$	−5.93527	+	3.42673i	−0.281359	+	0.162443i
$446$	−0.121542	+	0.154766i	−0.00575517	+	0.00732839i
$447$	2.03145	+	1.70459i	0.0960841	+	0.0806241i
$448$	20.6662	+	23.6573i	0.976388	+	1.11770i
$449$	−3.35431	+	5.80984i	−0.158300	+	0.274183i	−0.934256	−	0.356604i	$-0.883935\pi$
$449$	−3.35431	+	5.80984i	−0.158300	+	0.274183i	0.775956	+	0.630787i	$0.217268\pi$
$450$	−3.29493	−	8.21439i	−0.155325	−	0.387230i
$451$	29.2085	−	5.15025i	1.37537	−	0.242516i
$452$	−0.667742	+	6.06106i	−0.0314079	+	0.285088i
$453$	−3.57192	+	9.81376i	−0.167823	+	0.461091i
$454$	9.00637	−	8.06864i	0.422690	−	0.378680i
$455$	−55.4539			−2.59972
$456$	8.39329	+	9.03065i	0.393052	+	0.422899i
$457$	−37.7360			−1.76521			−0.882607	−	0.470111i	$-0.844214\pi$
$457$	−37.7360			−1.76521			−0.882607	+	0.470111i	$0.844214\pi$
$458$	3.03464	−	2.71868i	0.141799	−	0.127035i
$459$	−1.96762	+	5.40600i	−0.0918408	+	0.252331i
$460$	36.8070	+	4.05499i	1.71613	+	0.189065i
$461$	−0.871615	+	0.153689i	−0.0405951	+	0.00715802i	−0.193909	−	0.981020i	$-0.562117\pi$
$461$	−0.871615	+	0.153689i	−0.0405951	+	0.00715802i	0.153314	+	0.988178i	$0.451005\pi$
$462$	−5.55197	−	13.8413i	−0.258301	−	0.643954i
$463$	5.04121	−	8.73163i	0.234285	−	0.405793i	−0.724780	−	0.688981i	$-0.758058\pi$
$463$	5.04121	−	8.73163i	0.234285	−	0.405793i	0.959065	+	0.283187i	$0.0913918\pi$
$464$	−2.17331	+	1.66320i	−0.100894	+	0.0772122i
$465$	−6.42774	−	5.39351i	−0.298079	−	0.250118i
$466$	−6.84037	+	8.71024i	−0.316874	+	0.403494i
$467$	−9.14004	+	5.27700i	−0.422951	+	0.244191i	−0.696339	−	0.717713i	$-0.745189\pi$
$467$	−9.14004	+	5.27700i	−0.422951	+	0.244191i	0.273388	+	0.961904i	$0.411856\pi$
$468$	7.54748	+	3.72805i	0.348882	+	0.172329i
$469$	5.71692	+	15.7071i	0.263983	+	0.725287i
$470$	5.80116	+	27.6323i	0.267588	+	1.27458i
$471$	1.77207	−	10.0499i	0.0816525	−	0.463075i
$472$	−23.3503	−	6.00851i	−1.07478	−	0.276564i
$473$	25.0798	−	21.0444i	1.15317	−	0.967624i
$474$	−5.75489	+	0.186542i	−0.264331	+	0.00856814i
$475$	18.4874	−	20.0594i	0.848258	−	0.920388i
$476$	−45.0842	+	2.92583i	−2.06643	+	0.134105i
$477$	−6.36821	−	7.58934i	−0.291580	−	0.347492i
$478$	−0.548875	+	1.67498i	−0.0251050	+	0.0766120i
$479$	−3.25649	+	18.4684i	−0.148793	+	0.843845i	0.815451	+	0.578826i	$0.196489\pi$
$479$	−3.25649	+	18.4684i	−0.148793	+	0.843845i	−0.964243	+	0.265018i	$0.914622\pi$
$480$	−17.9159	+	6.26801i	−0.817743	+	0.286094i
$481$	16.4741	−	5.99609i	0.751155	−	0.273398i
$482$	−0.127391	−	0.0681444i	−0.00580248	−	0.00310389i
$483$	18.7642	−	10.8335i	0.853800	−	0.492942i
$484$	−6.10602	−	4.48316i	−0.277546	−	0.203780i
$485$	24.9337	−	29.7148i	1.13218	−	1.34928i
$486$	0.746414	+	1.20119i	0.0338580	+	0.0544872i
$487$	−8.28900	+	14.3570i	−0.375610	+	0.650576i	−0.990418	−	0.138101i	$-0.955900\pi$
$487$	−8.28900	+	14.3570i	−0.375610	+	0.650576i	0.614808	+	0.788677i	$0.289234\pi$
$488$	4.99642	−	2.39063i	0.226177	−	0.108219i
$489$	1.73077	+	9.81569i	0.0782682	+	0.443881i
$490$	5.65835	−	39.5427i	0.255618	−	1.78636i
$491$	13.7826	−	37.8674i	0.622000	−	1.70893i	−0.0800381	−	0.996792i	$-0.525504\pi$
$491$	13.7826	−	37.8674i	0.622000	−	1.70893i	0.702038	−	0.712139i	$-0.252274\pi$
$492$	−15.2635	−	15.9650i	−0.688132	−	0.719759i
$493$		−	3.93602i		−	0.177270i
$494$	−0.365915	+	25.9435i	−0.0164633	+	1.16725i
$495$	9.01110			0.405019
$496$	−6.76737	+	7.36624i	−0.303864	+	0.330754i
$497$	39.3012	+	14.3045i	1.76290	+	0.641643i
$498$	2.55500	+	0.365607i	0.114492	+	0.0163833i
$499$	−34.0851	+	6.01012i	−1.52586	+	0.269050i	−0.872733	−	0.488199i	$-0.837654\pi$
$499$	−34.0851	+	6.01012i	−1.52586	+	0.269050i	−0.653127	+	0.757249i	$0.726543\pi$
$500$	3.39585	+	7.73115i	0.151867	+	0.345748i
$501$	−4.83267	−	2.79014i	−0.215908	−	0.124654i
$502$	10.9058	+	17.5505i	0.486748	+	0.783317i
$503$	−8.18395	−	6.86715i	−0.364904	−	0.306191i	0.441837	−	0.897095i	$-0.354327\pi$
$503$	−8.18395	−	6.86715i	−0.364904	−	0.306191i	−0.806742	+	0.590904i	$0.798771\pi$
$504$	−6.27942	+	9.16046i	−0.279708	+	0.408039i
$505$	24.2306	+	41.9686i	1.07825	+	1.86758i
$506$	−9.88524	+	18.4797i	−0.439453	+	0.821522i
$507$	1.61287	+	4.43131i	0.0716299	+	0.196801i
$508$	6.31374	+	25.8743i	0.280127	+	1.14798i
$509$	33.2370	+	5.86057i	1.47320	+	0.259765i	0.851858	−	0.523773i	$-0.175476\pi$
$509$	33.2370	+	5.86057i	1.47320	+	0.259765i	0.621344	+	0.783538i	$0.286587\pi$
$510$	8.50073	−	25.9414i	0.376419	−	1.14870i
$511$	44.5769	−	37.4044i	1.97196	−	1.65467i
$512$	6.50565	+	21.6720i	0.287512	+	0.957777i
$513$	−2.35259	+	3.66951i	−0.103869	+	0.162013i
$514$	−0.887224	−	27.3712i	−0.0391338	−	1.20729i
$515$	5.19445	+	6.19050i	0.228895	+	0.272786i
$516$	−23.4029	−	6.83768i	−1.03026	−	0.301012i
$517$	−15.7371	−	2.77487i	−0.692116	−	0.122039i
$518$	4.75226	+	22.6361i	0.208803	+	0.994575i
$519$	11.2187	−	4.08327i	0.492446	−	0.179236i
$520$	−36.3684	−	16.5206i	−1.59486	−	0.724478i
$521$	−2.74892	−	4.76127i	−0.120432	−	0.208595i	0.799506	−	0.600658i	$-0.205095\pi$
$521$	−2.74892	−	4.76127i	−0.120432	−	0.208595i	−0.919938	+	0.392063i	$0.871761\pi$
$522$	−0.760962	−	0.597602i	−0.0333064	−	0.0261563i
$523$	19.1994	−	22.8809i	0.839531	−	1.00051i	−0.160379	−	0.987056i	$-0.551272\pi$
$523$	19.1994	−	22.8809i	0.839531	−	1.00051i	0.999909	−	0.0134581i	$-0.00428398\pi$
$524$	−7.09855	+	4.73650i	−0.310102	+	0.206915i
$525$	21.2816	+	12.2869i	0.928803	+	0.536245i
$526$	9.40846	+	23.4556i	0.410228	+	1.02271i
$527$	−2.49821	−	14.1680i	−0.108824	−	0.617169i
$528$	0.482391	−	10.7316i	0.0209934	−	0.467031i
$529$	−6.99931	−	2.54754i	−0.304318	−	0.110763i
$530$	31.3691	+	35.0148i	1.36259	+	1.52094i
$531$		−	8.52451i		−	0.369932i
$532$	−33.8143	−	5.32633i	−1.46604	−	0.230926i
$533$		−	46.4832i		−	2.01341i
$534$	−2.15148	+	1.92747i	−0.0931039	+	0.0834100i
$535$	−37.5915	−	13.6822i	−1.62522	−	0.591533i
$536$	−0.930076	+	12.0044i	−0.0401732	+	0.518511i
$537$	−2.55606	−	14.4961i	−0.110302	−	0.625554i
$538$	−26.6219	+	10.6785i	−1.14775	+	0.460383i
$539$	19.5789	+	11.3039i	0.843323	+	0.486893i
$540$	−3.72466	−	5.58212i	−0.160284	−	0.240216i
$541$	−21.1941	+	25.2581i	−0.911205	+	1.08593i	0.0847789	+	0.996400i	$0.472982\pi$
$541$	−21.1941	+	25.2581i	−0.911205	+	1.08593i	−0.995984	+	0.0895321i	$0.971463\pi$
$542$	−22.1457	+	28.1994i	−0.951240	+	1.21127i
$543$	−6.95575	−	12.0477i	−0.298500	−	0.517017i
$544$	−30.4393	−	11.5125i	−1.30507	−	0.493593i
$545$	−11.3263	+	4.12245i	−0.485167	+	0.176586i
$546$	−22.8741	+	4.80222i	−0.978922	+	0.205516i
$547$	−9.54968	−	1.68387i	−0.408315	−	0.0719969i	−0.0342816	−	0.999412i	$-0.510914\pi$
$547$	−9.54968	−	1.68387i	−0.408315	−	0.0719969i	−0.374033	+	0.927415i	$0.622025\pi$
$548$	−16.6765	−	4.87241i	−0.712386	−	0.208139i
$549$	1.25877	+	1.50014i	0.0537229	+	0.0640244i
$550$	−23.7566	+	0.770059i	−1.01299	+	0.0328354i
$551$	0.653840	−	2.90969i	0.0278545	−	0.123957i
$552$	15.5336	−	1.51479i	0.661155	−	0.0644737i
$553$	12.2467	−	10.2762i	0.520784	−	0.436990i
$554$	−43.0231	−	14.0982i	−1.82788	−	0.598976i
$555$	−13.7634	−	2.42686i	−0.584223	−	0.103014i
$556$	−17.3481	+	4.23321i	−0.735722	+	0.179528i
$557$	−13.2236	−	36.3314i	−0.560300	−	1.53941i	−0.819200	−	0.573509i	$-0.805582\pi$
$557$	−13.2236	−	36.3314i	−0.560300	−	1.53941i	0.258899	−	0.965904i	$-0.416640\pi$
$558$	−3.11844	−	1.66813i	−0.132014	−	0.0706177i
$559$	−25.6553	−	44.4363i	−1.08510	−	1.87946i
$560$	28.3730	−	44.4104i	1.19898	−	1.87668i
$561$	11.8355	+	9.93115i	0.499694	+	0.419293i
$562$	−12.9358	+	8.03825i	−0.545666	+	0.339073i
$563$	19.1200	+	11.0390i	0.805813	+	0.465237i	0.845500	−	0.533976i	$-0.179303\pi$
$563$	19.1200	+	11.0390i	0.805813	+	0.465237i	−0.0396864	+	0.999212i	$0.512636\pi$
$564$	4.78583	+	10.8956i	0.201520	+	0.458789i
$565$	10.0746	−	1.77642i	0.423840	−	0.0747344i
$566$	3.70614	−	25.8999i	0.155781	−	1.08866i
$567$	−3.68979	−	1.34297i	−0.154957	−	0.0563996i
$568$	21.5134	+	21.0898i	0.902683	+	0.884909i
$569$	46.8208			1.96283			0.981415	−	0.191900i	$-0.0614648\pi$
$569$	46.8208			1.96283			0.981415	+	0.191900i	$0.0614648\pi$
$570$	10.5934	−	17.7650i	0.443711	−	0.744093i
$571$			17.1255i			0.716682i	0.933591	+	0.358341i	$0.116657\pi$
$571$			17.1255i			0.716682i	−0.933591	+	0.358341i	$0.883343\pi$
$572$	16.3408	−	15.6228i	0.683244	−	0.653222i
$573$	−8.21006	+	22.5569i	−0.342980	+	0.942330i
$574$	60.7080	+	8.68699i	2.53390	+	0.362588i
$575$	−5.99667	−	34.0088i	−0.250078	−	1.41826i
$576$	−6.84730	+	4.13697i	−0.285304	+	0.172374i
$577$	−11.7435	+	20.3404i	−0.488890	+	0.846782i	−0.999918	−	0.0127818i	$-0.995931\pi$
$577$	−11.7435	+	20.3404i	−0.488890	+	0.846782i	0.511029	+	0.859564i	$0.329265\pi$
$578$	19.3349	−	12.0146i	0.804227	−	0.499741i
$579$	−11.3111	+	13.4800i	−0.470073	+	0.560211i
$580$	3.70086	+	2.71725i	0.153670	+	0.112828i
$581$	−6.20619	+	3.58314i	−0.257476	+	0.148654i
$582$	7.71162	−	14.4163i	0.319657	−	0.597574i
$583$	−25.0021	+	9.10003i	−1.03548	+	0.376885i
$584$	40.3783	−	11.2508i	1.67087	−	0.465561i
$585$	2.45237	−	13.9081i	0.101393	−	0.575028i
$586$	−11.9077	−	3.90202i	−0.491902	−	0.161191i
$587$	−18.3963	−	21.9238i	−0.759295	−	0.904893i	0.238508	−	0.971141i	$-0.423342\pi$
$587$	−18.3963	−	21.9238i	−0.759295	−	0.904893i	−0.997803	+	0.0662476i	$0.978897\pi$
$588$	−1.09033	−	16.8010i	−0.0449646	−	0.692860i
$589$	0.506759	−	10.8887i	0.0208807	−	0.448660i
$590$	1.31048	+	40.4290i	0.0539518	+	1.66444i
$591$	−1.74884	+	1.46745i	−0.0719376	+	0.0603628i
$592$	−3.62700	+	16.2613i	−0.149069	+	0.668334i
$593$	1.43245	−	8.12384i	0.0588238	−	0.333606i	−0.941167	−	0.337942i	$-0.890269\pi$
$593$	1.43245	−	8.12384i	0.0588238	−	0.333606i	0.999991	+	0.00433617i	$0.00138025\pi$
$594$	3.71698	−	0.780348i	0.152510	−	0.0320181i
$595$	25.9236	+	71.2244i	1.06276	+	2.91992i
$596$	−4.75526	−	2.34884i	−0.194783	−	0.0962122i
$597$	−1.74740	+	1.00886i	−0.0715165	+	0.0412900i
$598$	25.8320	+	20.2865i	1.05635	+	0.829577i
$599$	19.0326	+	15.9703i	0.777651	+	0.652527i	0.942656	−	0.333766i	$-0.108320\pi$
$599$	19.0326	+	15.9703i	0.777651	+	0.652527i	−0.165005	+	0.986293i	$0.552764\pi$
$600$	10.2966	+	14.3983i	0.420358	+	0.587807i
$601$	13.0666	−	22.6320i	0.532998	−	0.923180i	−0.466259	−	0.884648i	$-0.654398\pi$
$601$	13.0666	−	22.6320i	0.532998	−	0.923180i	0.999257	−	0.0385321i	$-0.0122682\pi$
$602$	62.8294	−	25.2019i	2.56073	−	1.02715i
$603$	−4.19224	+	0.739205i	−0.170721	+	0.0301028i
$604$	2.28728	−	20.7616i	0.0930682	−	0.844776i
$605$	−4.34657	+	11.9421i	−0.176713	+	0.485516i
$606$	13.6293	+	15.2133i	0.553652	+	0.617997i
$607$	25.4042			1.03112			0.515562	−	0.856853i	$-0.327583\pi$
$607$	25.4042			1.03112			0.515562	+	0.856853i	$0.327583\pi$
$608$	−20.5897	−	13.5670i	−0.835023	−	0.550216i
$609$	2.68648			0.108862
$610$	−6.20054	−	6.92116i	−0.251053	−	0.280230i
$611$	−8.56568	+	23.5340i	−0.346530	+	0.952085i
$612$	1.25997	−	11.4367i	0.0509313	−	0.462301i
$613$	−12.8156	+	2.25974i	−0.517619	+	0.0912702i	−0.426354	−	0.904556i	$-0.640202\pi$
$613$	−12.8156	+	2.25974i	−0.517619	+	0.0912702i	−0.0912652	+	0.995827i	$0.529091\pi$
$614$	4.48882	−	1.80054i	0.181154	−	0.0726639i
$615$	−18.5278	+	32.0910i	−0.747111	+	1.29403i
$616$	17.3499	+	24.2611i	0.699046	+	0.977509i
$617$	−16.1716	−	13.5696i	−0.651044	−	0.546291i	0.256344	−	0.966586i	$-0.417482\pi$
$617$	−16.1716	−	13.5696i	−0.651044	−	0.546291i	−0.907388	+	0.420295i	$0.861927\pi$
$618$	2.67874	+	2.10368i	0.107755	+	0.0846226i
$619$	30.9165	−	17.8497i	1.24264	−	0.717439i	0.273009	−	0.962011i	$-0.411981\pi$
$619$	30.9165	−	17.8497i	1.24264	−	0.717439i	0.969631	+	0.244573i	$0.0786478\pi$
$620$	15.0462	+	7.43201i	0.604270	+	0.298477i
$621$	1.88727	+	5.18524i	0.0757337	+	0.208077i
$622$	8.62070	−	1.80984i	0.345658	−	0.0725680i
$623$	1.39271	−	7.89843i	0.0557976	−	0.316444i
$624$	−16.4322	−	3.66513i	−0.657816	−	0.146723i
$625$	−13.1186	+	11.0078i	−0.524745	+	0.440313i
$626$	0.456521	+	14.0839i	0.0182463	+	0.562905i
$627$	7.09960	+	9.30764i	0.283531	+	0.371711i
$628$	1.32176	+	20.3670i	0.0527440	+	0.812732i
$629$	−15.4026	−	18.3562i	−0.614144	−	0.731908i
$630$	17.7059	+	5.80206i	0.705422	+	0.231159i
$631$	−7.18915	+	40.7717i	−0.286196	+	1.62310i	0.414788	+	0.909918i	$0.363856\pi$
$631$	−7.18915	+	40.7717i	−0.286196	+	1.62310i	−0.700983	+	0.713178i	$0.747255\pi$
$632$	11.0932	−	3.09096i	0.441266	−	0.122952i
$633$	8.68267	−	3.16023i	0.345105	−	0.125608i
$634$	−11.5457	+	21.5837i	−0.458538	+	0.857200i
$635$	38.6959	−	22.3411i	1.53560	−	0.886578i
$636$	15.9716	+	11.7267i	0.633316	+	0.464994i
$637$	22.7753	−	27.1425i	0.902389	−	1.07542i
$638$	−2.20710	+	1.37148i	−0.0873798	+	0.0542973i
$639$	−5.32567	+	9.22433i	−0.210680	+	0.364909i
$640$	31.8385	−	20.6730i	1.25853	−	0.817171i
$641$	−7.08963	−	40.2073i	−0.280024	−	1.58809i	−0.722537	−	0.691332i	$-0.757024\pi$
$641$	−7.08963	−	40.2073i	−0.280024	−	1.58809i	0.442514	−	0.896762i	$-0.354087\pi$
$642$	−16.6910	−	2.38839i	−0.658740	−	0.0942621i
$643$	−14.5677	+	40.0246i	−0.574496	+	1.57841i	0.222825	+	0.974859i	$0.428472\pi$
$643$	−14.5677	+	40.0246i	−0.574496	+	1.57841i	−0.797321	+	0.603556i	$0.793750\pi$
$644$	−31.3222	+	29.9459i	−1.23427	+	1.18003i
$645$			40.9039i			1.61059i
$646$	33.4926	−	11.6581i	1.31775	−	0.458681i
$647$	−9.54743			−0.375348			−0.187674	−	0.982231i	$-0.560095\pi$
$647$	−9.54743			−0.375348			−0.187674	+	0.982231i	$0.560095\pi$
$648$	−2.01979	−	1.98002i	−0.0793447	−	0.0777824i
$649$	−21.5128	−	7.83001i	−0.844451	−	0.307355i
$650$	−5.27683	+	36.8765i	−0.206974	+	1.44641i
$651$	9.67019	−	1.70512i	0.379005	−	0.0668288i
$652$	−8.01670	−	18.2512i	−0.313958	−	0.714772i
$653$	3.53609	+	2.04156i	0.138378	+	0.0798926i	0.567591	−	0.823311i	$-0.307876\pi$
$653$	3.53609	+	2.04156i	0.138378	+	0.0798926i	−0.429213	+	0.903203i	$0.641209\pi$
$654$	−4.31500	+	2.68131i	−0.168730	+	0.104848i
$655$	10.9672	+	9.20261i	0.428526	+	0.359576i
$656$	37.2262	+	23.7831i	1.45344	+	0.928575i
$657$	7.40985	+	12.8342i	0.289086	+	0.500711i
$658$	−29.1352	−	15.5851i	−1.13581	−	0.607571i
$659$	−3.58781	−	9.85743i	−0.139761	−	0.383991i	0.849989	−	0.526801i	$-0.176609\pi$
$659$	−3.58781	−	9.85743i	−0.139761	−	0.383991i	−0.989750	+	0.142810i	$0.954386\pi$
$660$	−17.5085	+	4.27236i	−0.681516	+	0.166301i
$661$	−38.6472	−	6.81455i	−1.50320	−	0.265055i	−0.639396	−	0.768877i	$-0.720816\pi$
$661$	−38.6472	−	6.81455i	−1.50320	−	0.265055i	−0.863807	+	0.503822i	$0.831927\pi$
$662$	15.5000	+	5.07919i	0.602424	+	0.197408i
$663$	18.5491	−	15.5646i	0.720389	−	0.604478i
$664$	−5.13769	+	0.501011i	−0.199381	+	0.0194430i
$665$	7.33233	+	56.9587i	0.284335	+	2.20877i
$666$	−5.88741	+	0.190837i	−0.228133	+	0.00739480i
$667$	−2.42671	−	2.89204i	−0.0939626	−	0.111980i
$668$	10.7127	+	3.12995i	0.414487	+	0.121101i
$669$	0.137035	+	0.0241630i	0.00529808	+	0.000934195i
$670$	19.7688	−	4.15029i	0.763735	−	0.160340i
$671$	4.94202	−	1.79875i	0.190785	−	0.0694400i
$672$	7.85768	−	20.7759i	0.303117	−	0.801447i
$673$	2.17339	+	3.76442i	0.0837780	+	0.145108i	0.904870	−	0.425688i	$-0.139968\pi$
$673$	2.17339	+	3.76442i	0.0837780	+	0.145108i	−0.821092	+	0.570796i	$0.806635\pi$
$674$	14.7470	−	18.7782i	0.568033	−	0.723310i
$675$	−4.02276	+	4.79414i	−0.154836	+	0.184527i
$676$	−5.23476	−	7.84530i	−0.201337	−	0.301742i
$677$	−12.5037	−	7.21903i	−0.480557	−	0.277450i	0.240091	−	0.970750i	$-0.422823\pi$
$677$	−12.5037	−	7.21903i	−0.480557	−	0.277450i	−0.720649	+	0.693300i	$0.756156\pi$
$678$	4.00181	−	1.60520i	0.153689	−	0.0616472i
$679$	7.88260	+	44.7044i	0.302506	+	1.71560i
$680$	−4.21746	+	54.4343i	−0.161732	+	2.08746i
$681$	−8.03472	−	2.92440i	−0.307891	−	0.112063i
$682$	−7.07414	+	6.33759i	−0.270883	+	0.242679i
$683$		−	3.35870i		−	0.128517i	−0.997933	−	0.0642585i	$-0.979532\pi$
$683$		−	3.35870i		−	0.128517i	0.997933	−	0.0642585i	$-0.0204682\pi$
$684$	2.83126	−	8.24524i	0.108256	−	0.315265i
$685$			29.1474i			1.11367i
$686$	5.25476	+	5.86547i	0.200628	+	0.223945i
$687$	−2.70725	−	0.985357i	−0.103288	−	0.0375937i
$688$	48.7136	+	2.18971i	1.85719	+	0.0834818i
$689$	7.24101	+	41.0658i	0.275861	+	1.56448i
$690$	−9.74786	−	24.3018i	−0.371095	−	0.925153i
$691$	−27.8912	−	16.1030i	−1.06103	−	0.612586i	−0.135313	−	0.990803i	$-0.543204\pi$
$691$	−27.8912	−	16.1030i	−1.06103	−	0.612586i	−0.925717	+	0.378217i	$0.876537\pi$
$692$	−19.8618	+	13.2528i	−0.755034	+	0.503795i
$693$	−6.77836	+	8.07814i	−0.257489	+	0.306863i
$694$	−1.79011	−	1.40582i	−0.0679515	−	0.0533640i
$695$	14.9791	+	25.9446i	0.568191	+	0.984136i
$696$	1.76188	+	0.800347i	0.0667838	+	0.0303371i
$697$	−59.7025	+	21.7299i	−2.26139	+	0.823080i
$698$	−4.47110	−	21.2969i	−0.169234	−	0.806100i
$699$	7.71234	+	1.35989i	0.291707	+	0.0514359i
$700$	−47.1753	−	13.7833i	−1.78306	−	0.520960i
$701$	27.4511	+	32.7149i	1.03681	+	1.23563i	0.971321	+	0.237773i	$0.0764173\pi$
$701$	27.4511	+	32.7149i	1.03681	+	1.23563i	0.0654921	+	0.997853i	$0.479138\pi$
$702$	−0.192844	−	5.94930i	−0.00727841	−	0.224542i
$703$	−8.33708	−	16.1284i	−0.314439	−	0.608293i
$704$	4.15078	+	21.0800i	0.156439	+	0.794483i
$705$	15.2940	−	12.8332i	0.576006	−	0.483326i
$706$	4.16015	−	12.6954i	0.156569	−	0.477798i
$707$	−55.8503	−	9.84791i	−2.10047	−	0.370369i
$708$	4.04165	+	16.5630i	0.151895	+	0.622477i
$709$	16.6710	+	45.8032i	0.626092	+	1.72017i	0.691560	+	0.722319i	$0.256924\pi$
$709$	16.6710	+	45.8032i	0.626092	+	1.72017i	−0.0654678	+	0.997855i	$0.520854\pi$
$710$	23.8399	−	44.5667i	0.894694	−	1.67256i
$711$	2.03573	+	3.52599i	0.0763458	+	0.132235i
$712$	3.26646	−	4.76513i	0.122416	−	0.178581i
$713$	−10.5707	−	8.86989i	−0.395877	−	0.332180i
$714$	16.8611	+	27.1344i	0.631012	+	1.01548i
$715$	−32.8464	−	18.9639i	−1.22839	−	0.709209i
$716$	11.8393	+	26.9539i	0.442456	+	1.00732i
$717$	1.22743	−	0.216429i	0.0458391	−	0.00808267i
$718$	10.3370	+	1.47916i	0.385772	+	0.0552019i
$719$	48.6000	+	17.6890i	1.81247	+	0.659687i	0.996687	+	0.0813346i	$0.0259182\pi$
$719$	48.6000	+	17.6890i	1.81247	+	0.659687i	0.815787	+	0.578352i	$0.196304\pi$
$720$	9.88358	+	9.08007i	0.368339	+	0.338394i
$721$	−9.45696			−0.352196
$722$	26.6959	−	3.05450i	0.993518	−	0.113677i
$723$			0.102157i			0.00379925i
$724$	19.2270	+	20.1107i	0.714567	+	0.747409i
$725$	1.46445	−	4.02355i	0.0543885	−	0.149431i
$726$	−0.758745	+	5.30240i	−0.0281597	+	0.196790i
$727$	−5.86279	−	33.2496i	−0.217439	−	1.23316i	−0.876624	−	0.481177i	$-0.840210\pi$
$727$	−5.86279	−	33.2496i	−0.217439	−	1.23316i	0.659185	−	0.751981i	$-0.270902\pi$
$728$	42.1673	−	20.1758i	1.56283	−	0.747764i
$729$	0.500000	−	0.866025i	0.0185185	−	0.0320750i
$730$	−37.1155	−	59.7295i	−1.37371	−	2.21069i
$731$	−45.0802	+	53.7245i	−1.66735	+	1.98707i
$732$	−3.15702	−	2.31795i	−0.116687	−	0.0856738i
$733$	18.8833	−	10.9023i	0.697472	−	0.402686i	−0.108933	−	0.994049i	$-0.534743\pi$
$733$	18.8833	−	10.9023i	0.697472	−	0.402686i	0.806405	+	0.591363i	$0.201410\pi$
$734$	−4.80433	−	2.56996i	−0.177331	−	0.0948589i
$735$	−26.5423	+	9.66061i	−0.979028	+	0.356337i
$736$	−29.4635	+	10.3080i	−1.08604	+	0.379959i
$737$	−1.98521	+	11.2587i	−0.0731261	+	0.414719i
$738$	−4.86346	+	14.8417i	−0.179027	+	0.546330i
$739$	−4.10736	−	4.89496i	−0.151092	−	0.180064i	0.685190	−	0.728365i	$-0.259719\pi$
$739$	−4.10736	−	4.89496i	−0.151092	−	0.180064i	−0.836281	+	0.548301i	$0.815275\pi$
$740$	27.8927	−	1.81016i	1.02536	−	0.0665428i
$741$	16.2979	−	8.42473i	0.598719	−	0.309490i
$742$	−54.9861	+	1.78235i	−2.01860	+	0.0654320i
$743$	19.1037	−	16.0299i	0.700847	−	0.588080i	−0.221168	−	0.975236i	$-0.570987\pi$
$743$	19.1037	−	16.0299i	0.700847	−	0.588080i	0.922014	+	0.387156i	$0.126542\pi$
$744$	6.85000	+	1.76264i	0.251133	+	0.0646217i
$745$	−1.54511	+	8.76273i	−0.0566083	+	0.321041i
$746$	0.681407	+	3.24570i	0.0249481	+	0.118834i
$747$	−0.624209	−	1.71500i	−0.0228386	−	0.0627485i
$748$	−27.7048	−	13.6847i	−1.01299	−	0.500361i
$749$	40.5429	−	23.4074i	1.48140	−	0.855289i
$750$	3.68780	−	4.69589i	0.134659	−	0.171470i
$751$	−24.3713	−	20.4499i	−0.889321	−	0.746229i	0.0787530	−	0.996894i	$-0.474906\pi$
$751$	−24.3713	−	20.4499i	−0.889321	−	0.746229i	−0.968074	+	0.250665i	$0.919351\pi$
$752$	−14.4647	−	18.9011i	−0.527473	−	0.689251i
$753$	7.30544	−	12.6534i	0.266225	−	0.461115i
$754$	1.51613	+	3.77977i	0.0552142	+	0.137651i
$755$	−34.5094	+	6.08494i	−1.25593	+	0.221454i
$756$	7.80596	+	0.859976i	0.283900	+	0.0312770i
$757$	−2.52743	+	6.94406i	−0.0918610	+	0.252386i	−0.977111	−	0.212729i	$-0.931765\pi$
$757$	−2.52743	+	6.94406i	−0.0918610	+	0.252386i	0.885250	+	0.465115i	$0.153987\pi$
$758$	−23.8053	+	21.3267i	−0.864646	+	0.774620i
$759$	14.8192			0.537902
$760$	−12.1602	+	39.5398i	−0.441097	+	1.43426i
$761$	−20.7690			−0.752875			−0.376437	−	0.926442i	$-0.622851\pi$
$761$	−20.7690			−0.752875			−0.376437	+	0.926442i	$0.622851\pi$
$762$	14.0269	−	12.5665i	0.508142	−	0.455234i
$763$	4.82431	−	13.2547i	0.174652	−	0.479852i
$764$	5.25733	−	47.7205i	0.190203	−	1.72647i
$765$	−19.0098	+	3.35195i	−0.687302	+	0.121190i
$766$	4.86266	+	12.1228i	0.175695	+	0.438014i
$767$	−17.9398	+	31.0727i	−0.647770	+	1.12197i
$768$	11.3428	−	11.2845i	0.409298	−	0.407196i
$769$	1.18409	+	0.993567i	0.0426993	+	0.0358289i	0.663888	−	0.747832i	$-0.268905\pi$
$769$	1.18409	+	0.993567i	0.0426993	+	0.0358289i	−0.621188	+	0.783661i	$0.713350\pi$
$770$	30.9057	−	39.3541i	1.11377	−	1.41822i
$771$	−16.7702	+	9.68227i	−0.603963	+	0.348698i
$772$	15.5862	−	31.5544i	0.560958	−	1.13567i
$773$	−1.17978	−	3.24141i	−0.0424336	−	0.116585i	0.916666	−	0.399654i	$-0.130870\pi$
$773$	−1.17978	−	3.24141i	−0.0424336	−	0.116585i	−0.959100	+	0.283069i	$0.908648\pi$
$774$	3.54222	+	16.8724i	0.127322	+	0.606466i
$775$	2.71766	−	15.4126i	0.0976211	−	0.553637i
$776$	−8.14854	+	31.6669i	−0.292516	+	1.13678i
$777$	12.5287	−	10.5129i	0.449466	−	0.377147i
$778$	−20.4104	+	0.661591i	−0.731747	+	0.0237192i
$779$	−47.7446	+	6.14619i	−1.71063	+	0.220210i
$780$	1.82919	+	28.1860i	0.0654955	+	1.00922i
$781$	18.3871	+	21.9129i	0.657942	+	0.784104i
$782$	13.9799	−	42.6619i	0.499919	−	1.52559i
$783$	−0.118806	+	0.673781i	−0.00424577	+	0.0240790i
$784$	10.0842	+	32.1271i	0.360150	+	1.14740i
$785$	32.1760	−	11.7111i	1.14841	−	0.417988i
$786$	5.32080	+	2.84623i	0.189787	+	0.101522i
$787$	10.2117	−	5.89571i	0.364007	−	0.210160i	−0.306830	−	0.951764i	$-0.599268\pi$
$787$	10.2117	−	5.89571i	0.364007	−	0.210160i	0.670837	+	0.741605i	$0.265935\pi$
$788$	2.70223	−	3.68040i	0.0962629	−	0.131109i
$789$	11.4867	−	13.6893i	0.408938	−	0.487354i
$790$	−10.1969	−	16.4097i	−0.362788	−	0.583829i
$791$	−5.98583	+	10.3678i	−0.212832	+	0.368635i
$792$	−6.85208	+	3.27851i	−0.243478	+	0.116497i
$793$	−1.43129	−	8.11724i	−0.0508265	−	0.288252i
$794$	−3.35109	+	23.4187i	−0.118926	+	0.831099i
$795$	11.3694	−	31.2372i	0.403232	−	1.10787i
$796$	2.91686	−	2.78869i	0.103385	−	0.0988426i
$797$			5.04623i			0.178747i	0.995998	+	0.0893733i	$0.0284864\pi$
$797$			5.04623i			0.178747i	−0.995998	+	0.0893733i	$0.971514\pi$
$798$	7.95705	+	22.8599i	0.281677	+	0.809232i
$799$	34.2312			1.21101
$800$	−26.8328	−	23.0938i	−0.948682	−	0.816491i
$801$	1.91937	+	0.698594i	0.0678177	+	0.0246836i
$802$	−48.2145	−	6.89923i	−1.70251	−	0.243620i
$803$	39.1951	−	6.91116i	1.38317	−	0.243890i
$804$	7.79500	−	3.42390i	0.274909	−	0.120752i
$805$	62.9602	+	36.3501i	2.21906	+	1.28117i
$806$	7.85646	+	12.6433i	0.276732	+	0.445341i
$807$	15.5373	+	13.0373i	0.546938	+	0.458935i
$808$	−33.6945	−	23.0973i	−1.18537	−	0.812560i
$809$	−14.5521	−	25.2050i	−0.511626	−	0.886162i	−0.999909	−	0.0134765i	$-0.995710\pi$
$809$	−14.5521	−	25.2050i	−0.511626	−	0.886162i	0.488284	−	0.872685i	$-0.337623\pi$
$810$	−2.23820	+	4.18414i	−0.0786424	+	0.147016i
$811$	15.7759	+	43.3441i	0.553968	+	1.52202i	0.828246	+	0.560365i	$0.189339\pi$
$811$	15.7759	+	43.3441i	0.553968	+	1.52202i	−0.274277	+	0.961651i	$0.588439\pi$
$812$	−5.21980	+	1.27372i	−0.183179	+	0.0446987i
$813$	24.9687	+	4.40266i	0.875691	+	0.154408i
$814$	−4.92615	+	15.0330i	−0.172662	+	0.526906i
$815$	−25.6189	+	21.4968i	−0.897390	+	0.752999i
$816$	2.97427	+	22.8188i	0.104120	+	0.798817i
$817$	−42.2500	+	32.2271i	−1.47814	+	1.12748i
$818$	0.861748	+	26.5853i	0.0301303	+	0.929532i
$819$	10.6234	+	12.6605i	0.371211	+	0.442392i
$820$	20.7842	−	71.1369i	0.725816	−	2.48421i
$821$	0.208800	+	0.0368171i	0.00728718	+	0.00128493i	0.177291	−	0.984159i	$-0.443267\pi$
$821$	0.208800	+	0.0368171i	0.00728718	+	0.00128493i	−0.170003	+	0.985443i	$0.554378\pi$
$822$	2.52412	+	12.0230i	0.0880389	+	0.419350i
$823$	38.3979	−	13.9757i	1.33847	−	0.487163i	0.429138	−	0.903239i	$-0.358817\pi$
$823$	38.3979	−	13.9757i	1.33847	−	0.487163i	0.909330	+	0.416076i	$0.136595\pi$
$824$	−6.20217	−	2.81739i	−0.216063	−	0.0981483i
$825$	8.40365	+	14.5556i	0.292578	+	0.506759i
$826$	−37.2290	−	29.2369i	−1.29536	−	1.01728i
$827$	12.7163	−	15.1547i	0.442190	−	0.526982i	−0.498208	−	0.867058i	$-0.666008\pi$
$827$	12.7163	−	15.1547i	0.442190	−	0.526982i	0.940398	+	0.340076i	$0.110453\pi$
$828$	−6.12539	−	9.18007i	−0.212872	−	0.319030i
$829$	−20.4848	−	11.8269i	−0.711465	−	0.410764i	0.100138	−	0.994974i	$-0.468071\pi$
$829$	−20.4848	−	11.8269i	−0.711465	−	0.410764i	−0.811603	+	0.584209i	$0.801405\pi$
$830$	3.22407	+	8.03772i	0.111909	+	0.278993i
$831$	5.55911	+	31.5273i	0.192843	+	1.09367i
$832$	33.6654	−	0.669552i	1.16714	−	0.0232125i
$833$	−45.5085	−	16.5638i	−1.57678	−	0.573900i
$834$	8.42550	+	9.40471i	0.291751	+	0.325659i
$835$		−	18.7238i		−	0.647963i
$836$	−18.2074	−	14.7186i	−0.629716	−	0.509052i
$837$			2.50073i			0.0864380i
$838$	3.32185	−	2.97598i	0.114751	−	0.102803i
$839$	−9.38141	−	3.41455i	−0.323882	−	0.117883i	0.174962	−	0.984575i	$-0.444020\pi$
$839$	−9.38141	−	3.41455i	−0.323882	−	0.117883i	−0.498844	+	0.866692i	$0.666242\pi$
$840$	−37.1534	−	2.87857i	−1.28191	−	0.0993200i
$841$	4.95451	+	28.0984i	0.170845	+	0.968912i
$842$	−8.09040	+	3.24520i	−0.278813	+	0.111837i
$843$	9.32636	+	5.38458i	0.321217	+	0.185455i
$844$	−15.3720	+	10.2569i	−0.529126	+	0.353058i
$845$	−10.1707	+	12.1210i	−0.349882	+	0.416974i
$846$	5.19728	−	6.61800i	0.178686	−	0.227531i
$847$	−7.43609	−	12.8797i	−0.255507	−	0.442551i
$848$	−36.5926	−	15.2124i	−1.25659	−	0.522395i
$849$	−17.3849	+	6.32757i	−0.596647	+	0.217162i
$850$	49.8306	−	10.4615i	1.70918	−	0.358827i
$851$	−22.6346	−	3.99108i	−0.775902	−	0.136813i
$852$	5.97427	−	20.4478i	0.204675	−	0.700530i
$853$	−9.43067	−	11.2390i	−0.322900	−	0.384817i	0.580037	−	0.814590i	$-0.303038\pi$
$853$	−9.43067	−	11.2390i	−0.322900	−	0.384817i	−0.902937	+	0.429773i	$0.858594\pi$
$854$	10.8688	−	0.352306i	0.371922	−	0.0120557i
$855$	−14.6098	−	0.679940i	−0.499644	−	0.0232535i
$856$	33.5627	−	3.27293i	1.14715	−	0.111866i
$857$	−33.6219	+	28.2121i	−1.14850	+	0.963707i	−0.999684	−	0.0251574i	$-0.991991\pi$
$857$	−33.6219	+	28.2121i	−1.14850	+	0.963707i	−0.148818	+	0.988865i	$0.547547\pi$
$858$	−15.1910	−	4.97794i	−0.518613	−	0.169944i
$859$	−12.7107	−	2.24124i	−0.433683	−	0.0764700i	−0.0474551	−	0.998873i	$-0.515111\pi$
$859$	−12.7107	−	2.24124i	−0.433683	−	0.0764700i	−0.386228	+	0.922403i	$0.626222\pi$
$860$	−19.3934	−	79.4759i	−0.661310	−	2.71010i
$861$	−14.8315	−	40.7491i	−0.505455	−	1.38873i
$862$	33.4408	+	17.8883i	1.13900	+	0.609278i
$863$	−6.55360	−	11.3512i	−0.223087	−	0.386398i	0.732657	−	0.680598i	$-0.238280\pi$
$863$	−6.55360	−	11.3512i	−0.223087	−	0.386398i	−0.955744	+	0.294200i	$0.904947\pi$
$864$	4.86319	+	2.88953i	0.165449	+	0.0983037i
$865$	30.6865	+	25.7490i	1.04337	+	0.875493i
$866$	34.3130	−	21.3219i	1.16600	−	0.724547i
$867$	−13.9399	−	8.04821i	−0.473424	−	0.273332i
$868$	−17.9807	+	7.89787i	−0.610303	+	0.268071i
$869$	10.7682	−	1.89872i	0.365286	−	0.0644098i
$870$	0.459876	−	3.21379i	0.0155913	−	0.108958i
$871$	16.8368	+	6.12810i	0.570493	+	0.207643i
$872$	7.11273	−	7.25559i	0.240867	−	0.245705i
$873$	−11.5607			−0.391269
$874$	17.4214	−	29.2154i	0.589289	−	0.988224i
$875$			16.5782i			0.560447i
$876$	−20.4822	−	21.4236i	−0.692031	−	0.723837i
$877$	14.0533	−	38.6112i	0.474547	−	1.30381i	−0.439515	−	0.898235i	$-0.644850\pi$
$877$	14.0533	−	38.6112i	0.474547	−	1.30381i	0.914063	−	0.405573i	$-0.132928\pi$
$878$	−47.5264	−	6.80077i	−1.60394	−	0.229515i
$879$	1.53862	+	8.72594i	0.0518963	+	0.294318i
$880$	31.9932	−	16.6023i	1.07849	−	0.559663i
$881$	11.4126	−	19.7671i	0.384499	−	0.665972i	−0.607201	−	0.794548i	$-0.707708\pi$
$881$	11.4126	−	19.7671i	0.384499	−	0.665972i	0.991700	+	0.128577i	$0.0410409\pi$
$882$	−10.1118	+	6.28343i	−0.340483	+	0.211574i
$883$	15.1560	−	18.0622i	0.510041	−	0.607843i	−0.448155	−	0.893956i	$-0.647919\pi$
$883$	15.1560	−	18.0622i	0.510041	−	0.607843i	0.958196	+	0.286113i	$0.0923632\pi$
$884$	−28.6613	+	39.0363i	−0.963983	+	1.31293i
$885$	24.7706	−	14.3013i	0.832655	−	0.480734i
$886$	9.34810	−	17.4755i	0.314056	−	0.587102i
$887$	−17.4520	+	6.35201i	−0.585981	+	0.213280i	−0.617961	−	0.786209i	$-0.712041\pi$
$887$	−17.4520	+	6.35201i	−0.585981	+	0.213280i	0.0319798	+	0.999489i	$0.489819\pi$
$888$	11.3487	−	3.16214i	0.380837	−	0.106115i
$889$	−9.07995	+	51.4950i	−0.304532	+	1.72709i
$890$	−9.21036	−	3.01814i	−0.308732	−	0.101168i
$891$	−1.72627	−	2.05729i	−0.0578322	−	0.0689218i
$892$	−0.277714	+	0.0180228i	−0.00929855	+	0.000603450i
$893$	25.3053	+	5.68637i	0.846808	+	0.190287i
$894$	0.121500	+	3.74833i	0.00406358	+	0.125363i
$895$	37.8348	−	31.7471i	1.26468	−	1.06119i
$896$	−5.41709	+	44.0928i	−0.180972	+	1.47304i
$897$	4.03304	−	22.8725i	0.134659	−	0.763691i
$898$	−9.28501	+	1.94931i	−0.309845	+	0.0650493i
$899$	−0.585176	−	1.60776i	−0.0195167	−	0.0536217i
$900$	5.54318	−	11.2222i	0.184773	−	0.374075i
$901$	49.3595	−	28.4977i	1.64440	−	0.949397i
$902$	32.9878	+	25.9061i	1.09837	+	0.862580i
$903$	−36.6689	−	30.7689i	−1.22027	−	1.02392i
$904$	−7.01442	+	5.01622i	−0.233296	+	0.166837i
$905$	23.3389	−	40.4242i	0.775811	−	1.34374i
$906$	−13.7078	+	5.49844i	−0.455412	+	0.182673i
$907$	2.09717	−	0.369787i	0.0696353	−	0.0122786i	−0.138722	−	0.990331i	$-0.544299\pi$
$907$	2.09717	−	0.369787i	0.0696353	−	0.0122786i	0.208357	+	0.978053i	$0.433188\pi$
$908$	16.9979	+	1.87264i	0.564095	+	0.0621459i
$909$	4.93980	−	13.5720i	0.163843	−	0.450154i
$910$	−52.3296	−	58.4113i	−1.73471	−	1.93632i
$911$	−30.4406			−1.00854			−0.504270	−	0.863546i	$-0.668239\pi$
$911$	−30.4406			−1.00854			−0.504270	+	0.863546i	$0.668239\pi$
$912$	−1.59186	+	17.3628i	−0.0527119	+	0.574939i
$913$	−4.90139			−0.162212
$914$	−35.6099	−	39.7485i	−1.17787	−	1.31476i
$915$	−2.24733	+	6.17448i	−0.0742943	+	0.204122i
$916$	5.72733	+	0.630975i	0.189236	+	0.0208480i
$917$	−16.4996	+	2.90933i	−0.544866	+	0.0960746i
$918$	−7.55108	+	3.02887i	−0.249223	+	0.0999675i
$919$	−13.8182	+	23.9339i	−0.455821	+	0.789505i	−0.998735	−	0.0502829i	$-0.983988\pi$
$919$	−13.8182	+	23.9339i	−0.455821	+	0.789505i	0.542914	+	0.839788i	$0.317321\pi$
$920$	30.4620	+	42.5964i	1.00430	+	1.40436i
$921$	−2.61979	−	2.19827i	−0.0863252	−	0.0724354i
$922$	−0.984393	−	0.773069i	−0.0324193	−	0.0254597i
$923$	38.8252	−	22.4158i	1.27795	−	0.737823i
$924$	9.34027	−	18.9095i	0.307272	−	0.622077i
$925$	−8.91550	−	24.4951i	−0.293140	−	0.805395i
$926$	13.9545	−	2.92962i	0.458573	−	0.0962734i
$927$	0.418221	−	2.37185i	0.0137362	−	0.0779017i
$928$	−3.80277	−	0.719722i	−0.124832	−	0.0236260i
$929$	3.70922	−	3.11241i	0.121696	−	0.102115i	−0.579909	−	0.814681i	$-0.696912\pi$
$929$	3.70922	−	3.11241i	0.121696	−	0.102115i	0.701604	+	0.712567i	$0.252467\pi$
$930$	−0.384441	−	11.8602i	−0.0126063	−	0.388910i
$931$	−30.8905	−	19.8044i	−1.01240	−	0.649064i
$932$	−15.6297	+	1.01433i	−0.511969	+	0.0332253i
$933$	−4.00369	−	4.77142i	−0.131075	−	0.156209i
$934$	−14.1835	−	4.64779i	−0.464099	−	0.152080i
$935$	−9.00199	+	51.0528i	−0.294397	+	1.66961i
$936$	3.19539	+	11.4680i	0.104444	+	0.374843i
$937$	−37.1284	+	13.5136i	−1.21293	+	0.441471i	−0.867720	−	0.497053i	$-0.834415\pi$
$937$	−37.1284	+	13.5136i	−1.21293	+	0.441471i	−0.345213	+	0.938525i	$0.612193\pi$
$938$	−11.1500	+	20.8440i	−0.364059	+	0.680580i
$939$	8.62910	−	4.98202i	0.281600	−	0.162582i
$940$	−23.6316	+	32.1860i	−0.770779	+	1.04979i
$941$	6.28939	−	7.49540i	0.205028	−	0.244343i	−0.653725	−	0.756732i	$-0.726795\pi$
$941$	6.28939	−	7.49540i	0.205028	−	0.244343i	0.858754	+	0.512389i	$0.171239\pi$
$942$	12.2581	−	7.61710i	0.399390	−	0.248179i
$943$	−30.4698	+	52.7752i	−0.992233	+	1.71860i
$944$	−15.7058	−	30.2656i	−0.511180	−	0.985061i
$945$	−2.28783	−	12.9749i	−0.0744230	−	0.422074i
$946$	45.8335	+	6.55853i	1.49018	+	0.213236i
$947$	9.95349	−	27.3470i	0.323445	−	0.888657i	−0.666284	−	0.745698i	$-0.732116\pi$
$947$	9.95349	−	27.3470i	0.323445	−	0.888657i	0.989729	−	0.142959i	$-0.0456617\pi$
$948$	−5.62715	−	5.88577i	−0.182761	−	0.191161i
$949$		−	62.3762i		−	2.02482i
$950$	38.5749	+	0.544074i	1.25154	+	0.0176521i
$951$	17.3084			0.561263
$952$	−45.6260	−	44.7276i	−1.47875	−	1.44963i
$953$	48.3929	+	17.6136i	1.56760	+	0.570559i	0.972461	−	0.233065i	$-0.0748755\pi$
$953$	48.3929	+	17.6136i	1.56760	+	0.570559i	0.595137	+	0.803624i	$0.297098\pi$
$954$	1.98466	−	13.8696i	0.0642558	−	0.449044i
$955$	−79.3200	+	13.9862i	−2.56673	+	0.452584i
$956$	−2.28226	+	1.00247i	−0.0738137	+	0.0324221i
$957$	1.59125	+	0.918710i	0.0514379	+	0.0296977i
$958$	−22.5264	+	13.9978i	−0.727795	+	0.452247i
$959$	−26.1296	−	21.9254i	−0.843770	−	0.708007i
$960$	−23.5088	−	12.9565i	−0.758742	−	0.418168i
$961$	12.3732	+	21.4309i	0.399134	+	0.691321i
$962$	21.8618	+	11.6944i	0.704854	+	0.377044i
$963$	4.07774	+	11.2035i	0.131403	+	0.361028i
$964$	−0.0484347	−	0.198490i	−0.00155998	−	0.00639292i
$965$	−58.1467	−	10.2528i	−1.87181	−	0.330050i
$966$	29.1183	+	9.54176i	0.936865	+	0.307001i
$967$	−21.0088	+	17.6284i	−0.675596	+	0.566892i	−0.914716	−	0.404098i	$-0.867586\pi$
$967$	−21.0088	+	17.6284i	−0.675596	+	0.566892i	0.239120	+	0.970990i	$0.423141\pi$
$968$	−1.03975	−	10.6622i	−0.0334187	−	0.342697i
$969$	−18.4396	−	16.9945i	−0.592365	−	0.545942i
$970$	54.8285	−	1.77724i	1.76044	−	0.0570636i
$971$	10.7243	+	12.7807i	0.344158	+	0.410151i	0.910163	−	0.414251i	$-0.135956\pi$
$971$	10.7243	+	12.7807i	0.344158	+	0.410151i	−0.566005	+	0.824402i	$0.691512\pi$
$972$	−0.560894	+	1.91974i	−0.0179907	+	0.0615757i
$973$	−34.5261	−	6.08789i	−1.10686	−	0.195169i
$974$	−22.9446	+	4.81703i	−0.735193	+	0.154348i
$975$	24.7527	−	9.00923i	0.792719	−	0.288526i
$976$	7.23304	+	3.00694i	0.231524	+	0.0962498i
$977$	−10.9005	−	18.8803i	−0.348739	−	0.604034i	0.637287	−	0.770627i	$-0.280057\pi$
$977$	−10.9005	−	18.8803i	−0.348739	−	0.604034i	−0.986026	+	0.166593i	$0.946723\pi$
$978$	−8.70592	+	11.0857i	−0.278384	+	0.354483i
$979$	3.52600	−	4.20212i	0.112691	−	0.134300i
$980$	46.9912	−	31.3548i	1.50108	−	1.00159i
$981$	3.11099	+	1.79613i	0.0993262	+	0.0573460i
$982$	52.8930	−	21.2163i	1.68788	−	0.677039i
$983$	−1.55555	−	8.82199i	−0.0496145	−	0.281378i	0.949899	−	0.312556i	$-0.101185\pi$
$983$	−1.55555	−	8.82199i	−0.0496145	−	0.281378i	−0.999514	+	0.0311782i	$0.990074\pi$
$984$	2.41291	−	31.1431i	0.0769206	−	0.992806i
$985$	−7.19811	−	2.61990i	−0.229351	−	0.0834768i
$986$	4.14594	−	3.71427i	0.132034	−	0.118286i
$987$			23.3640i			0.743684i
$988$	−27.6724	+	24.0964i	−0.880375	+	0.766607i
$989$			67.2684i			2.13901i
$990$	8.50341	+	9.49167i	0.270256	+	0.301665i
$991$	20.8997	+	7.60687i	0.663901	+	0.241640i	0.651920	−	0.758288i	$-0.273964\pi$
$991$	20.8997	+	7.60687i	0.663901	+	0.241640i	0.0119811	+	0.999928i	$0.496186\pi$
$992$	−14.1452	−	0.177069i	−0.449110	−	0.00562193i
$993$	−2.00279	−	11.3584i	−0.0635566	−	0.360447i
$994$	22.0196	+	54.8958i	0.698420	+	1.74119i
$995$	−5.86313	−	3.38508i	−0.185874	−	0.107314i
$996$	2.02595	+	3.03627i	0.0641946	+	0.0962080i
$997$	18.5043	−	22.0526i	0.586038	−	0.698413i	−0.388801	−	0.921322i	$-0.627111\pi$
$997$	18.5043	−	22.0526i	0.586038	−	0.698413i	0.974839	+	0.222909i	$0.0715552\pi$
$998$	−38.4954	−	30.2314i	−1.21855	−	0.956958i
$999$	2.08261	+	3.60718i	0.0658908	+	0.114126i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.bk.a.253.30	yes	240
8.5	even	2	inner	456.2.bk.a.253.13	✓	240
19.16	even	9	inner	456.2.bk.a.301.13	yes	240
152.149	even	18	inner	456.2.bk.a.301.30	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bk.a.253.13	✓	240	8.5	even	2	inner
456.2.bk.a.253.30	yes	240	1.1	even	1	trivial
456.2.bk.a.301.13	yes	240	19.16	even	9	inner
456.2.bk.a.301.30	yes	240	152.149	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bk (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.943660 + 1.05333i) q^{2} +(0.342020 - 0.939693i) q^{3} +(-0.219013 + 1.98797i) q^{4} +(3.30436 - 0.582649i) q^{5} +(1.31256 - 0.526489i) q^{6} +(-1.96330 + 3.40053i) q^{7} +(-2.30067 + 1.64528i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(3.73192 + 2.93077i) q^{10} +(-2.32580 + 1.34280i) q^{11} +(1.79318 + 0.885732i) q^{12} +(1.43956 + 3.95517i) q^{13} +(-5.43457 + 1.14094i) q^{14} +(0.582649 - 3.30436i) q^{15} +(-3.90407 - 0.870784i) q^{16} +(4.40701 - 3.69792i) q^{17} +(-0.0458169 - 1.41347i) q^{18} +(3.87216 - 2.00160i) q^{19} +(0.434590 + 6.69659i) q^{20} +(2.52397 + 3.00795i) q^{21} +(-3.60917 - 1.18269i) q^{22} +(0.958194 - 5.43419i) q^{23} +(0.759179 + 2.72464i) q^{24} +(5.88088 - 2.14047i) q^{25} +(-2.80764 + 5.24867i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(-6.33017 - 4.64774i) q^{28} +(0.439779 - 0.524109i) q^{29} +(4.03041 - 2.50447i) q^{30} +(1.25037 - 2.16570i) q^{31} +(-2.76689 - 4.93400i) q^{32} +(0.466350 + 2.64480i) q^{33} +(8.05386 + 1.15246i) q^{34} +(-4.50614 + 12.3805i) q^{35} +(1.44562 - 1.38210i) q^{36} -4.16521i q^{37} +(5.76234 + 2.18984i) q^{38} +4.20900 q^{39} +(-6.64363 + 6.77707i) q^{40} +(-10.3777 - 3.77718i) q^{41} +(-0.786598 + 5.49705i) q^{42} +(-12.0055 + 2.11689i) q^{43} +(-2.16007 - 4.91771i) q^{44} +(-2.90581 - 1.67767i) q^{45} +(6.62821 - 4.11873i) q^{46} +(4.55811 + 3.82471i) q^{47} +(-2.15354 + 3.37080i) q^{48} +(-4.20907 - 7.29033i) q^{49} +(7.80417 + 4.17465i) q^{50} +(-1.96762 - 5.40600i) q^{51} +(-8.17805 + 1.99558i) q^{52} +(9.75666 + 1.72036i) q^{53} +(-1.34390 - 0.440382i) q^{54} +(-6.90290 + 5.79222i) q^{55} +(-1.07792 - 11.0537i) q^{56} +(-0.556531 - 4.32322i) q^{57} +(0.967062 - 0.0313468i) q^{58} +(5.47945 + 6.53015i) q^{59} +(6.44138 + 1.88199i) q^{60} +(-1.92854 - 0.340054i) q^{61} +(3.46112 - 0.726632i) q^{62} +(3.68979 - 1.34297i) q^{63} +(2.58614 - 7.57046i) q^{64} +(7.06132 + 12.2306i) q^{65} +(-2.34577 + 2.98701i) q^{66} +(2.73629 - 3.26098i) q^{67} +(6.38618 + 9.57092i) q^{68} +(-4.77874 - 2.75901i) q^{69} +(-17.2930 + 6.93653i) q^{70} +(-1.84959 - 10.4895i) q^{71} +(2.81998 + 0.218486i) q^{72} +(-13.9260 - 5.06864i) q^{73} +(4.38735 - 3.93054i) q^{74} -6.25831i q^{75} +(3.13107 + 8.13612i) q^{76} -10.5453i q^{77} +(3.97187 + 4.43347i) q^{78} +(-3.82592 - 1.39252i) q^{79} +(-13.4078 - 0.602690i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-5.81442 - 14.4956i) q^{82} +(1.58055 + 0.912532i) q^{83} +(-6.53250 + 4.35880i) q^{84} +(12.4078 - 14.7870i) q^{85} +(-13.5589 - 10.6481i) q^{86} +(-0.342088 - 0.592513i) q^{87} +(3.14161 - 6.91591i) q^{88} +(-1.91937 + 0.698594i) q^{89} +(-0.974953 - 4.64393i) q^{90} +(-16.2760 - 2.86989i) q^{91} +(10.5932 + 3.09502i) q^{92} +(-1.60744 - 1.91567i) q^{93} +(0.272620 + 8.41043i) q^{94} +(11.6288 - 8.87012i) q^{95} +(-5.58277 + 0.912495i) q^{96} +(8.85598 - 7.43105i) q^{97} +(3.70720 - 11.3131i) q^{98} +(2.64480 + 0.466350i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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