LMFDB - Embedded newform 390.2.bl.a.263.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(107,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 4]))

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

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

chi := DirichletCharacter("390.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bl (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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			263.11
Character	$\chi$	$=$	390.263
Dual form			390.2.bl.a.347.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(1.29429 - 1.15100i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.49285 - 1.66475i) q^{5} +(0.776796 + 1.54809i) q^{6} +(1.04151 + 3.88695i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.350385 - 2.97947i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(1.29429 - 1.15100i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.49285 - 1.66475i) q^{5} +(0.776796 + 1.54809i) q^{6} +(1.04151 + 3.88695i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.350385 - 2.97947i) q^{9} +(1.22165 + 1.87285i) q^{10} +(2.62933 - 1.51804i) q^{11} +(-1.69639 + 0.349652i) q^{12} +(-3.59546 + 0.269576i) q^{13} -4.02407 q^{14} +(0.0160570 - 3.87295i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.60451 - 0.429927i) q^{17} +(2.78726 + 1.10959i) q^{18} +(0.154368 + 0.0891245i) q^{19} +(-2.12522 + 0.695289i) q^{20} +(5.82191 + 3.83208i) q^{21} +(0.785797 + 2.93263i) q^{22} +(2.98067 + 0.798669i) q^{23} +(0.101321 - 1.72908i) q^{24} +(-0.542780 - 4.97045i) q^{25} +(0.670183 - 3.54272i) q^{26} +(-2.97588 - 4.25960i) q^{27} +(1.04151 - 3.88695i) q^{28} +(-1.12917 - 1.95578i) q^{29} +(3.73683 + 1.01790i) q^{30} +3.91967 q^{31} +(-0.965926 + 0.258819i) q^{32} +(1.65585 - 4.99115i) q^{33} +1.66111i q^{34} +(8.02562 + 4.06880i) q^{35} +(-1.79318 + 2.40510i) q^{36} +(3.53114 + 0.946165i) q^{37} +(-0.126041 + 0.126041i) q^{38} +(-4.34329 + 4.48729i) q^{39} +(-0.121549 - 2.23276i) q^{40} +(-6.86687 + 3.96459i) q^{41} +(-5.20832 + 4.63172i) q^{42} +(-10.6661 + 2.85798i) q^{43} -3.03609 q^{44} +(-4.43699 - 5.03121i) q^{45} +(-1.54291 + 2.67240i) q^{46} +(6.89581 + 6.89581i) q^{47} +(1.64394 + 0.545389i) q^{48} +(-7.96150 + 4.59658i) q^{49} +(4.94157 + 0.762163i) q^{50} +(1.58186 - 2.40325i) q^{51} +(3.24855 + 1.56427i) q^{52} +(-2.15498 + 2.15498i) q^{53} +(4.88467 - 1.77201i) q^{54} +(1.39804 - 6.64338i) q^{55} +(3.48495 + 2.01204i) q^{56} +(0.302380 - 0.0623250i) q^{57} +(2.18139 - 0.584501i) q^{58} +(4.20931 - 7.29074i) q^{59} +(-1.95038 + 3.34604i) q^{60} +(-6.02607 + 10.4375i) q^{61} +(-1.01449 + 3.78611i) q^{62} +(11.9460 - 1.74120i) q^{63} -1.00000i q^{64} +(-4.91872 + 6.38797i) q^{65} +(4.39252 + 2.89123i) q^{66} +(-13.9303 - 3.73261i) q^{67} +(-1.60451 - 0.429927i) q^{68} +(4.77713 - 2.39705i) q^{69} +(-6.00735 + 6.69907i) q^{70} +(-13.1921 - 7.61644i) q^{71} +(-1.85904 - 2.35456i) q^{72} +(7.83281 + 7.83281i) q^{73} +(-1.82785 + 3.16593i) q^{74} +(-6.42352 - 5.80848i) q^{75} +(-0.0891245 - 0.154368i) q^{76} +(8.63902 + 8.63902i) q^{77} +(-3.21027 - 5.35670i) q^{78} +6.38451i q^{79} +(2.18814 + 0.460474i) q^{80} +(-8.75446 - 2.08792i) q^{81} +(-2.05222 - 7.65900i) q^{82} +(3.82902 - 3.82902i) q^{83} +(-3.12588 - 6.22963i) q^{84} +(1.67958 - 3.31293i) q^{85} -11.0424i q^{86} +(-3.71258 - 1.23167i) q^{87} +(0.785797 - 2.93263i) q^{88} +(-4.34840 - 7.53165i) q^{89} +(6.00816 - 2.98363i) q^{90} +(-4.79252 - 13.6946i) q^{91} +(-2.18200 - 2.18200i) q^{92} +(5.07320 - 4.51156i) q^{93} +(-8.44561 + 4.87608i) q^{94} +(0.378819 - 0.123934i) q^{95} +(-0.952289 + 1.44677i) q^{96} +(2.80156 + 10.4556i) q^{97} +(-2.37936 - 8.87990i) q^{98} +(-3.60168 - 8.36589i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q+O(q^{10}) $ 112 * q	$ 112 q + 24 q^{13} + 56 q^{16} - 16 q^{18} - 16 q^{21} + 24 q^{27} + 12 q^{30} - 80 q^{31} + 52 q^{33} - 8 q^{36} - 8 q^{37} - 16 q^{40} + 12 q^{42} - 8 q^{43} + 20 q^{45} - 8 q^{46} - 80 q^{51} + 24 q^{52} + 8 q^{55} - 96 q^{57} + 8 q^{58} - 32 q^{60} - 16 q^{61} - 16 q^{63} - 32 q^{66} + 40 q^{67} - 32 q^{70} - 8 q^{72} - 80 q^{73} - 64 q^{75} + 16 q^{76} - 36 q^{78} + 8 q^{81} - 16 q^{82} + 96 q^{85} - 8 q^{87} + 24 q^{90} - 32 q^{91} - 68 q^{93} - 40 q^{97}+O(q^{100}) $ 112 * q + 24 * q^13 + 56 * q^16 - 16 * q^18 - 16 * q^21 + 24 * q^27 + 12 * q^30 - 80 * q^31 + 52 * q^33 - 8 * q^36 - 8 * q^37 - 16 * q^40 + 12 * q^42 - 8 * q^43 + 20 * q^45 - 8 * q^46 - 80 * q^51 + 24 * q^52 + 8 * q^55 - 96 * q^57 + 8 * q^58 - 32 * q^60 - 16 * q^61 - 16 * q^63 - 32 * q^66 + 40 * q^67 - 32 * q^70 - 8 * q^72 - 80 * q^73 - 64 * q^75 + 16 * q^76 - 36 * q^78 + 8 * q^81 - 16 * q^82 + 96 * q^85 - 8 * q^87 + 24 * q^90 - 32 * q^91 - 68 * q^93 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	1.29429	−	1.15100i	0.747260	−	0.664532i
$3$	1.29429	−	1.15100i	0.747260	−	0.664532i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	1.49285	−	1.66475i	0.667624	−	0.744498i
$5$	1.49285	−	1.66475i	0.667624	−	0.744498i
$6$	0.776796	+	1.54809i	0.317126	+	0.632006i
$7$	1.04151	+	3.88695i	0.393652	+	1.46913i	0.824063	+	0.566498i	$0.191702\pi$
$7$	1.04151	+	3.88695i	0.393652	+	1.46913i	−0.430411	+	0.902633i	$0.641631\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	0.350385	−	2.97947i	0.116795	−	0.993156i
$10$	1.22165	+	1.87285i	0.386318	+	0.592248i
$11$	2.62933	−	1.51804i	0.792772	−	0.457707i	−0.0481656	−	0.998839i	$-0.515338\pi$
$11$	2.62933	−	1.51804i	0.792772	−	0.457707i	0.840937	+	0.541132i	$0.182004\pi$
$12$	−1.69639	+	0.349652i	−0.489706	+	0.100936i
$13$	−3.59546	+	0.269576i	−0.997201	+	0.0747668i
$13$	−3.59546	+	0.269576i	−0.997201	+	0.0747668i
$14$	−4.02407			−1.07548
$15$	0.0160570	−	3.87295i	0.00414590	−	0.999991i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.60451	−	0.429927i	0.389151	−	0.104273i	−0.0589381	−	0.998262i	$-0.518771\pi$
$17$	1.60451	−	0.429927i	0.389151	−	0.104273i	0.448089	+	0.893989i	$0.352105\pi$
$18$	2.78726	+	1.10959i	0.656963	+	0.261533i
$19$	0.154368	+	0.0891245i	0.0354145	+	0.0204466i	0.517603	−	0.855621i	$-0.326825\pi$
$19$	0.154368	+	0.0891245i	0.0354145	+	0.0204466i	−0.482188	+	0.876068i	$0.660158\pi$
$20$	−2.12522	+	0.695289i	−0.475214	+	0.155471i
$21$	5.82191	+	3.83208i	1.27044	+	0.836228i
$22$	0.785797	+	2.93263i	0.167532	+	0.625239i
$23$	2.98067	+	0.798669i	0.621513	+	0.166534i	0.555815	−	0.831306i	$-0.312406\pi$
$23$	2.98067	+	0.798669i	0.621513	+	0.166534i	0.0656975	+	0.997840i	$0.479073\pi$
$24$	0.101321	−	1.72908i	0.0206820	−	0.352948i
$25$	−0.542780	−	4.97045i	−0.108556	−	0.994090i
$26$	0.670183	−	3.54272i	0.131434	−	0.694784i
$27$	−2.97588	−	4.25960i	−0.572708	−	0.819760i
$28$	1.04151	−	3.88695i	0.196826	−	0.734565i
$29$	−1.12917	−	1.95578i	−0.209682	−	0.363179i	0.741933	−	0.670474i	$-0.233909\pi$
$29$	−1.12917	−	1.95578i	−0.209682	−	0.363179i	−0.951614	+	0.307295i	$0.900576\pi$
$30$	3.73683	+	1.01790i	0.682248	+	0.185843i
$31$	3.91967			0.703994			0.351997	−	0.936001i	$-0.385503\pi$
$31$	3.91967			0.703994			0.351997	+	0.936001i	$0.385503\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	1.65585	−	4.99115i	0.288246	−	0.868848i
$34$			1.66111i			0.284878i
$35$	8.02562	+	4.06880i	1.35658	+	0.687754i
$36$	−1.79318	+	2.40510i	−0.298863	+	0.400850i
$37$	3.53114	+	0.946165i	0.580515	+	0.155549i	0.537115	−	0.843509i	$-0.319514\pi$
$37$	3.53114	+	0.946165i	0.580515	+	0.155549i	0.0434004	+	0.999058i	$0.486181\pi$
$38$	−0.126041	+	0.126041i	−0.0204466	+	0.0204466i
$39$	−4.34329	+	4.48729i	−0.695484	+	0.718542i
$40$	−0.121549	−	2.23276i	−0.0192186	−	0.353031i
$41$	−6.86687	+	3.96459i	−1.07243	+	0.619165i	−0.928843	−	0.370473i	$-0.879196\pi$
$41$	−6.86687	+	3.96459i	−1.07243	+	0.619165i	−0.143582	+	0.989638i	$0.545862\pi$
$42$	−5.20832	+	4.63172i	−0.803662	+	0.714690i
$43$	−10.6661	+	2.85798i	−1.62657	+	0.435838i	−0.952922	−	0.303214i	$-0.901940\pi$
$43$	−10.6661	+	2.85798i	−1.62657	+	0.435838i	−0.673648	+	0.739052i	$0.735274\pi$
$44$	−3.03609			−0.457707
$45$	−4.43699	−	5.03121i	−0.661428	−	0.750009i
$46$	−1.54291	+	2.67240i	−0.227490	+	0.394023i
$47$	6.89581	+	6.89581i	1.00586	+	1.00586i	0.999983	+	0.00587478i	$0.00187001\pi$
$47$	6.89581	+	6.89581i	1.00586	+	1.00586i	0.00587478	+	0.999983i	$0.498130\pi$
$48$	1.64394	+	0.545389i	0.237283	+	0.0787201i
$49$	−7.96150	+	4.59658i	−1.13736	+	0.656654i
$50$	4.94157	+	0.762163i	0.698843	+	0.107786i
$51$	1.58186	−	2.40325i	0.221504	−	0.336522i
$52$	3.24855	+	1.56427i	0.450492	+	0.216925i
$53$	−2.15498	+	2.15498i	−0.296010	+	0.296010i	−0.839449	−	0.543439i	$-0.817122\pi$
$53$	−2.15498	+	2.15498i	−0.296010	+	0.296010i	0.543439	+	0.839449i	$0.317122\pi$
$54$	4.88467	−	1.77201i	0.664719	−	0.241140i
$55$	1.39804	−	6.64338i	0.188511	−	0.895794i
$56$	3.48495	+	2.01204i	0.465696	+	0.268870i
$57$	0.302380	−	0.0623250i	0.0400512	−	0.00825515i
$58$	2.18139	−	0.584501i	0.286430	−	0.0767488i
$59$	4.20931	−	7.29074i	0.548006	−	0.949174i	−0.450405	−	0.892824i	$-0.648721\pi$
$59$	4.20931	−	7.29074i	0.548006	−	0.949174i	0.998411	−	0.0563495i	$-0.0179461\pi$
$60$	−1.95038	+	3.34604i	−0.251793	+	0.431973i
$61$	−6.02607	+	10.4375i	−0.771560	+	1.33638i	0.165148	+	0.986269i	$0.447190\pi$
$61$	−6.02607	+	10.4375i	−0.771560	+	1.33638i	−0.936708	+	0.350112i	$0.886144\pi$
$62$	−1.01449	+	3.78611i	−0.128840	+	0.480837i
$63$	11.9460	−	1.74120i	1.50505	−	0.219371i
$64$		−	1.00000i		−	0.125000i
$65$	−4.91872	+	6.38797i	−0.610092	+	0.792331i
$66$	4.39252	+	2.89123i	0.540682	+	0.355886i
$67$	−13.9303	−	3.73261i	−1.70185	−	0.456011i	−0.728449	−	0.685100i	$-0.759759\pi$
$67$	−13.9303	−	3.73261i	−1.70185	−	0.456011i	−0.973405	+	0.229089i	$0.926425\pi$
$68$	−1.60451	−	0.429927i	−0.194575	−	0.0521363i
$69$	4.77713	−	2.39705i	0.575099	−	0.288571i
$70$	−6.00735	+	6.69907i	−0.718015	+	0.800692i
$71$	−13.1921	−	7.61644i	−1.56561	−	0.903905i	−0.996671	−	0.0815236i	$-0.974021\pi$
$71$	−13.1921	−	7.61644i	−1.56561	−	0.903905i	−0.568937	−	0.822381i	$-0.692645\pi$
$72$	−1.85904	−	2.35456i	−0.219090	−	0.277488i
$73$	7.83281	+	7.83281i	0.916761	+	0.916761i	0.996792	−	0.0800311i	$-0.0255020\pi$
$73$	7.83281	+	7.83281i	0.916761	+	0.916761i	−0.0800311	+	0.996792i	$0.525502\pi$
$74$	−1.82785	+	3.16593i	−0.212483	+	0.368032i
$75$	−6.42352	−	5.80848i	−0.741724	−	0.670705i
$76$	−0.0891245	−	0.154368i	−0.0102233	−	0.0177072i
$77$	8.63902	+	8.63902i	0.984508	+	0.984508i
$78$	−3.21027	−	5.35670i	−0.363491	−	0.606526i
$79$			6.38451i			0.718314i	0.933277	+	0.359157i	$0.116936\pi$
$79$			6.38451i			0.718314i	−0.933277	+	0.359157i	$0.883064\pi$
$80$	2.18814	+	0.460474i	0.244642	+	0.0514826i
$81$	−8.75446	−	2.08792i	−0.972718	−	0.231991i
$82$	−2.05222	−	7.65900i	−0.226630	−	0.845795i
$83$	3.82902	−	3.82902i	0.420290	−	0.420290i	−0.465014	−	0.885304i	$-0.653951\pi$
$83$	3.82902	−	3.82902i	0.420290	−	0.420290i	0.885304	+	0.465014i	$0.153951\pi$
$84$	−3.12588	−	6.22963i	−0.341062	−	0.679709i
$85$	1.67958	−	3.31293i	0.182176	−	0.359337i
$86$		−	11.0424i		−	1.19073i
$87$	−3.71258	−	1.23167i	−0.398031	−	0.132049i
$88$	0.785797	−	2.93263i	0.0837662	−	0.312620i
$89$	−4.34840	−	7.53165i	−0.460930	−	0.798353i	0.538078	−	0.842895i	$-0.319151\pi$
$89$	−4.34840	−	7.53165i	−0.460930	−	0.798353i	−0.999008	+	0.0445417i	$0.985817\pi$
$90$	6.00816	−	2.98363i	0.633315	−	0.314503i
$91$	−4.79252	−	13.6946i	−0.502393	−	1.43559i
$92$	−2.18200	−	2.18200i	−0.227490	−	0.227490i
$93$	5.07320	−	4.51156i	0.526067	−	0.467827i
$94$	−8.44561	+	4.87608i	−0.871098	+	0.502929i
$95$	0.378819	−	0.123934i	0.0388660	−	0.0127154i
$96$	−0.952289	+	1.44677i	−0.0971926	+	0.147660i
$97$	2.80156	+	10.4556i	0.284455	+	1.06160i	0.949237	+	0.314563i	$0.101858\pi$
$97$	2.80156	+	10.4556i	0.284455	+	1.06160i	−0.664782	+	0.747038i	$0.731475\pi$
$98$	−2.37936	−	8.87990i	−0.240352	−	0.897006i
$99$	−3.60168	−	8.36589i	−0.361983	−	0.840804i
$100$	−2.01516	+	4.57593i	−0.201516	+	0.457593i
$101$	−11.8654	+	6.85046i	−1.18065	+	0.681647i	−0.956164	−	0.292831i	$-0.905403\pi$
$101$	−11.8654	+	6.85046i	−1.18065	+	0.681647i	−0.224483	+	0.974478i	$0.572069\pi$
$102$	1.91194	+	2.14996i	0.189311	+	0.212878i
$103$	−1.94971	−	1.94971i	−0.192111	−	0.192111i	0.604497	−	0.796607i	$-0.293374\pi$
$103$	−1.94971	−	1.94971i	−0.192111	−	0.192111i	−0.796607	+	0.604497i	$0.793374\pi$
$104$	−2.35176	+	2.73299i	−0.230609	+	0.267992i
$105$	15.0707	−	3.97129i	1.47075	−	0.387558i
$106$	−1.52380	−	2.63931i	−0.148005	−	0.256352i
$107$	−0.183787	+	0.685903i	−0.0177674	+	0.0663087i	−0.974240	−	0.225512i	$-0.927594\pi$
$107$	−0.183787	+	0.685903i	−0.0177674	+	0.0663087i	0.956473	+	0.291821i	$0.0942611\pi$
$108$	0.447386	+	5.17686i	0.0430497	+	0.498143i
$109$		−	18.4200i		−	1.76432i	−0.470950	−	0.882160i	$-0.656089\pi$
$109$		−	18.4200i		−	1.76432i	0.470950	−	0.882160i	$-0.343911\pi$
$110$	6.05518	+	3.06984i	0.577339	+	0.292697i
$111$	5.65936	−	2.83973i	0.537163	−	0.269536i
$112$	−2.84545	+	2.84545i	−0.268870	+	0.268870i
$113$	2.98005	+	11.1217i	0.280339	+	1.04624i	0.952178	+	0.305544i	$0.0988382\pi$
$113$	2.98005	+	11.1217i	0.280339	+	1.04624i	−0.671839	+	0.740698i	$0.734495\pi$
$114$	−0.0180603	+	0.308207i	−0.00169151	+	0.0288663i
$115$	5.77929	−	3.76978i	0.538921	−	0.351533i
$116$			2.25834i			0.209682i
$117$	−0.456603	+	10.8070i	−0.0422129	+	0.999109i
$118$	5.95286	+	5.95286i	0.548006	+	0.548006i
$119$	3.34222	+	5.78889i	0.306380	+	0.530666i
$120$	−2.72724	−	2.74994i	−0.248961	−	0.251034i
$121$	−0.891093	+	1.54342i	−0.0810085	+	0.140311i
$122$	−8.52215	−	8.52215i	−0.771560	−	0.771560i
$123$	−4.32449	+	13.0351i	−0.389926	+	1.17534i
$124$	−3.39454	−	1.95984i	−0.304838	−	0.175999i
$125$	−9.08485	−	6.51656i	−0.812573	−	0.582859i
$126$	−1.40997	+	11.9896i	−0.125610	+	1.06812i
$127$	11.8537	+	3.17619i	1.05185	+	0.281841i	0.743015	−	0.669275i	$-0.233395\pi$
$127$	11.8537	+	3.17619i	1.05185	+	0.281841i	0.308832	+	0.951117i	$0.400062\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	−10.5156	+	15.9758i	−0.925843	+	1.40659i
$130$	−4.89725	−	6.40445i	−0.429517	−	0.561707i
$131$		−	8.46884i		−	0.739926i	−0.929046	−	0.369963i	$-0.879370\pi$
$131$		−	8.46884i		−	0.739926i	0.929046	−	0.369963i	$-0.120630\pi$
$132$	−3.92958	+	3.49454i	−0.342026	+	0.304161i
$133$	−0.185647	+	0.692845i	−0.0160977	+	0.0600773i
$134$	7.21084	−	12.4895i	0.622922	−	1.07893i
$135$	−11.5337	−	1.40486i	−0.992663	−	0.120911i
$136$	0.830556	−	1.43856i	0.0712196	−	0.123356i
$137$	−1.83033	+	0.490435i	−0.156376	+	0.0419007i	−0.336157	−	0.941806i	$-0.609127\pi$
$137$	−1.83033	+	0.490435i	−0.156376	+	0.0419007i	0.179782	+	0.983706i	$0.442461\pi$
$138$	1.07896	+	5.23476i	0.0918473	+	0.445612i
$139$	−5.71298	−	3.29839i	−0.484569	−	0.279766i	0.237750	−	0.971326i	$-0.423590\pi$
$139$	−5.71298	−	3.29839i	−0.484569	−	0.279766i	−0.722319	+	0.691561i	$0.756924\pi$
$140$	−4.91599	−	7.53650i	−0.415477	−	0.636950i
$141$	16.8623	+	0.988097i	1.42006	+	0.0832127i
$142$	10.7713	−	10.7713i	0.903905	−	0.903905i
$143$	−9.04441	+	6.16686i	−0.756332	+	0.515699i
$144$	2.75549	−	1.18629i	0.229624	−	0.0988577i
$145$	−4.94157	−	1.03991i	−0.410375	−	0.0863595i
$146$	−9.59320	+	5.53863i	−0.793939	+	0.458381i
$147$	−5.01384	+	15.1130i	−0.413534	+	1.24650i
$148$	−2.58497	−	2.58497i	−0.212483	−	0.212483i
$149$	−5.60356	+	9.70565i	−0.459062	+	0.795118i	−0.998912	−	0.0466432i	$-0.985148\pi$
$149$	−5.60356	+	9.70565i	−0.459062	+	0.795118i	0.539850	+	0.841761i	$0.318481\pi$
$150$	7.27309	−	4.70130i	0.593845	−	0.383859i
$151$	−1.03710			−0.0843982			−0.0421991	−	0.999109i	$-0.513436\pi$
$151$	−1.03710			−0.0843982			−0.0421991	+	0.999109i	$0.513436\pi$
$152$	0.172175	−	0.0461342i	0.0139653	−	0.00374198i
$153$	−0.718758	−	4.93123i	−0.0581082	−	0.398666i
$154$	−10.5806	+	6.10871i	−0.852609	+	0.492254i
$155$	5.85150	−	6.52527i	0.470004	−	0.524123i
$156$	6.00505	−	1.71446i	0.480789	−	0.137267i
$157$	2.48883	−	2.48883i	0.198630	−	0.198630i	−0.600782	−	0.799413i	$-0.705144\pi$
$157$	2.48883	−	2.48883i	0.198630	−	0.198630i	0.799413	+	0.600782i	$0.205144\pi$
$158$	−6.16697	−	1.65243i	−0.490618	−	0.131461i
$159$	−0.308786	+	5.26957i	−0.0244883	+	0.417904i
$160$	−1.01112	+	1.99440i	−0.0799358	+	0.157671i
$161$			12.4176i			0.978640i
$162$	4.28260	−	7.91577i	0.336473	−	0.621921i
$163$	0.898187	−	0.240669i	0.0703515	−	0.0188506i	−0.223472	−	0.974710i	$-0.571739\pi$
$163$	0.898187	−	0.240669i	0.0703515	−	0.0188506i	0.293823	+	0.955860i	$0.405072\pi$
$164$	7.92918			0.619165
$165$	−5.83708	−	10.2076i	−0.454416	−	0.794663i
$166$	2.70753	+	4.68958i	0.210145	+	0.363982i
$167$	0.368029	−	1.37350i	0.0284789	−	0.106285i	−0.950223	−	0.311569i	$-0.899145\pi$
$167$	0.368029	−	1.37350i	0.0284789	−	0.106285i	0.978702	+	0.205285i	$0.0658120\pi$
$168$	6.82640	−	1.40702i	0.526668	−	0.108554i
$169$	12.8547	−	1.93850i	0.988820	−	0.149115i
$170$	2.76533	+	2.47980i	0.212091	+	0.190192i
$171$	0.319632	−	0.428707i	0.0244428	−	0.0327840i
$172$	10.6661	+	2.85798i	0.813285	+	0.217919i
$173$	−2.52219	−	9.41293i	−0.191758	−	0.715652i	−0.993082	−	0.117421i	$-0.962537\pi$
$173$	−2.52219	−	9.41293i	−0.191758	−	0.715652i	0.801324	−	0.598231i	$-0.204129\pi$
$174$	2.15059	−	3.26730i	0.163036	−	0.247693i
$175$	18.7546	−	7.28652i	1.41772	−	0.550809i
$176$	2.62933	+	1.51804i	0.198193	+	0.114427i
$177$	−2.94358	−	14.2813i	−0.221253	−	1.07345i
$178$	8.40046	−	2.25090i	0.629641	−	0.168712i
$179$	−2.55218	−	4.42051i	−0.190759	−	0.330405i	0.754743	−	0.656021i	$-0.227762\pi$
$179$	−2.55218	−	4.42051i	−0.190759	−	0.330405i	−0.945502	+	0.325616i	$0.894428\pi$
$180$	1.32694	+	6.57565i	0.0989046	+	0.490120i
$181$	−2.39650			−0.178130			−0.0890650	−	0.996026i	$-0.528388\pi$
$181$	−2.39650			−0.178130			−0.0890650	+	0.996026i	$0.528388\pi$
$182$	14.4684	−	1.08479i	1.07247	−	0.0804101i
$183$	4.21405	+	20.4452i	0.311512	+	1.51135i
$184$	2.67240	−	1.54291i	0.197012	−	0.113745i
$185$	6.84659	−	4.46597i	0.503372	−	0.328345i
$186$	3.04479	+	6.06801i	0.223255	+	0.444928i
$187$	3.56613	−	3.56613i	0.260782	−	0.260782i
$188$	−2.52404	−	9.41985i	−0.184085	−	0.687013i
$189$	13.4575	−	16.0035i	0.978886	−	1.16408i
$190$	0.0216660	+	0.397987i	0.00157181	+	0.0288730i
$191$	22.7817	+	13.1530i	1.64843	+	0.951720i	0.977697	+	0.210020i	$0.0673529\pi$
$191$	22.7817	+	13.1530i	1.64843	+	0.951720i	0.670731	+	0.741701i	$0.265980\pi$
$192$	−1.15100	−	1.29429i	−0.0830665	−	0.0934075i
$193$	−5.79222	+	21.6169i	−0.416933	+	1.55601i	0.363999	+	0.931399i	$0.381411\pi$
$193$	−5.79222	+	21.6169i	−0.416933	+	1.55601i	−0.780932	+	0.624616i	$0.785256\pi$
$194$	−10.8244			−0.777145
$195$	0.986320	+	13.9294i	0.0706319	+	0.997502i
$196$	9.19315			0.656654
$197$	0.225117	−	0.840148i	0.0160389	−	0.0598580i	−0.957443	−	0.288624i	$-0.906802\pi$
$197$	0.225117	−	0.840148i	0.0160389	−	0.0598580i	0.973481	+	0.228766i	$0.0734690\pi$
$198$	9.01302	−	1.31371i	0.640527	−	0.0933610i
$199$	11.2614	+	6.50178i	0.798300	+	0.460899i	0.842876	−	0.538107i	$-0.180860\pi$
$199$	11.2614	+	6.50178i	0.798300	+	0.460899i	−0.0445763	+	0.999006i	$0.514194\pi$
$200$	−3.89844	−	3.13084i	−0.275662	−	0.221384i
$201$	−22.3261	+	11.2027i	−1.57476	+	0.790178i
$202$	−3.54606	−	13.2341i	−0.249500	−	0.931147i
$203$	6.42599	−	6.42599i	0.451016	−	0.451016i
$204$	−2.57155	+	1.29034i	−0.180045	+	0.0903422i
$205$	−3.65118	+	17.3502i	−0.255010	+	1.21179i
$206$	2.38790	−	1.37865i	0.166373	−	0.0960553i
$207$	3.42399	−	8.60097i	0.237984	−	0.597809i
$208$	−2.03119	−	2.97897i	−0.140838	−	0.206555i
$209$	0.541179			0.0374341
$210$	−0.0646145	+	15.5850i	−0.00445883	+	1.07547i
$211$	2.13923	+	3.70526i	0.147271	+	0.255081i	0.930218	−	0.367008i	$-0.119618\pi$
$211$	2.13923	+	3.70526i	0.147271	+	0.255081i	−0.782947	+	0.622089i	$0.786284\pi$
$212$	2.94376	−	0.788779i	0.202178	−	0.0541736i
$213$	−25.8409	+	5.32620i	−1.77059	+	0.364945i
$214$	−0.614964	−	0.355050i	−0.0420381	−	0.0242707i
$215$	−11.1651	+	22.0230i	−0.761457	+	1.50196i
$216$	−5.11625	−	0.907727i	−0.348117	−	0.0617630i
$217$	4.08236	+	15.2356i	0.277129	+	1.03426i
$218$	17.7924	+	4.76746i	1.20505	+	0.322893i
$219$	19.1535	+	1.12236i	1.29428	+	0.0758420i
$220$	−4.53243	+	5.05432i	−0.305576	+	0.340762i
$221$	−5.65305	+	1.97832i	−0.380266	+	0.133076i
$222$	1.27822	+	6.20150i	0.0857886	+	0.416217i
$223$	5.71774	−	21.3389i	0.382888	−	1.42896i	−0.458581	−	0.888653i	$-0.651642\pi$
$223$	5.71774	−	21.3389i	0.382888	−	1.42896i	0.841469	−	0.540305i	$-0.181691\pi$
$224$	−2.01204	−	3.48495i	−0.134435	−	0.232848i
$225$	−14.9995	−	0.124376i	−0.999966	−	0.00829173i
$226$	−11.5140			−0.765902
$227$	26.9999	−	7.23460i	1.79205	−	0.480177i	0.799354	−	0.600860i	$-0.205175\pi$
$227$	26.9999	−	7.23460i	1.79205	−	0.480177i	0.992691	+	0.120683i	$0.0385084\pi$
$228$	−0.293031	−	0.0972149i	−0.0194065	−	0.00643822i
$229$			9.78804i			0.646812i	0.946260	+	0.323406i	$0.104828\pi$
$229$			9.78804i			0.646812i	−0.946260	+	0.323406i	$0.895172\pi$
$230$	2.14553	+	6.55805i	0.141472	+	0.432425i
$231$	21.1250	+	1.23788i	1.38992	+	0.0814465i
$232$	−2.18139	−	0.584501i	−0.143215	−	0.0383744i
$233$	3.61599	−	3.61599i	0.236891	−	0.236891i	−0.578670	−	0.815562i	$-0.696428\pi$
$233$	3.61599	−	3.61599i	0.236891	−	0.236891i	0.815562	+	0.578670i	$0.196428\pi$
$234$	−10.3206	−	3.23810i	−0.674678	−	0.211682i
$235$	21.7742	−	1.18536i	1.42039	−	0.0773246i
$236$	−7.29074	+	4.20931i	−0.474587	+	0.274003i
$237$	7.34859	+	8.26343i	0.477342	+	0.536767i
$238$	−6.45666	+	1.73006i	−0.418523	+	0.112143i
$239$	11.7766			0.761765			0.380882	−	0.924623i	$-0.375620\pi$
$239$	11.7766			0.761765			0.380882	+	0.924623i	$0.375620\pi$
$240$	3.36210	−	1.92257i	0.217023	−	0.124101i
$241$	9.68709	−	16.7785i	0.624000	−	1.08080i	−0.364733	−	0.931112i	$-0.618840\pi$
$241$	9.68709	−	16.7785i	0.624000	−	1.08080i	0.988733	−	0.149688i	$-0.0478269\pi$
$242$	−1.26020	−	1.26020i	−0.0810085	−	0.0810085i
$243$	−13.7340	+	7.37403i	−0.881039	+	0.473044i
$244$	10.4375	−	6.02607i	0.668190	−	0.385780i
$245$	−4.23321	+	20.1159i	−0.270450	+	1.28516i
$246$	−11.4717	−	7.55087i	−0.731410	−	0.481426i
$247$	−0.579050	−	0.278830i	−0.0368441	−	0.0177415i
$248$	2.77163	−	2.77163i	0.175999	−	0.175999i
$249$	0.548658	−	9.36309i	0.0347698	−	0.593362i
$250$	8.64585	−	7.08868i	0.546811	−	0.448327i
$251$	−10.6397	−	6.14282i	−0.671570	−	0.387731i	0.125101	−	0.992144i	$-0.460074\pi$
$251$	−10.6397	−	6.14282i	−0.671570	−	0.387731i	−0.796671	+	0.604413i	$0.793408\pi$
$252$	−11.2161	−	4.46506i	−0.706550	−	0.281273i
$253$	9.04957	−	2.42483i	0.568942	−	0.152447i
$254$	−6.13593	+	10.6277i	−0.385003	+	0.666844i
$255$	−1.63932	−	6.22109i	−0.102658	−	0.389580i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.53609	−	16.9289i	0.282953	−	1.05600i	−0.667369	−	0.744728i	$-0.732579\pi$
$257$	4.53609	−	16.9289i	0.282953	−	1.05600i	0.950322	−	0.311269i	$-0.100754\pi$
$258$	−12.7098	−	14.2921i	−0.791279	−	0.889787i
$259$			14.7108i			0.914085i
$260$	7.45372	−	3.07279i	0.462260	−	0.190566i
$261$	−6.22282	+	2.67905i	−0.385183	+	0.165829i
$262$	8.18027	+	2.19190i	0.505379	+	0.135416i
$263$	−0.0297193	−	0.00796326i	−0.00183257	−	0.000491036i	0.257903	−	0.966171i	$-0.416969\pi$
$263$	−0.0297193	−	0.00796326i	−0.00183257	−	0.000491036i	−0.259735	+	0.965680i	$0.583635\pi$
$264$	−2.35842	−	4.70014i	−0.145151	−	0.289274i
$265$	0.370434	+	6.80458i	0.0227555	+	0.418002i
$266$	−0.621188	−	0.358643i	−0.0380875	−	0.0219898i
$267$	−14.2971	−	4.74314i	−0.874965	−	0.290275i
$268$	10.1977	+	10.1977i	0.622922	+	0.622922i
$269$	0.535944	−	0.928282i	0.0326771	−	0.0565983i	−0.849224	−	0.528032i	$-0.822930\pi$
$269$	0.535944	−	0.928282i	0.0326771	−	0.0565983i	0.881901	+	0.471434i	$0.156263\pi$
$270$	4.34214	−	10.7771i	0.264254	−	0.655873i
$271$	7.45682	+	12.9156i	0.452970	+	0.784567i	0.998569	−	0.0534796i	$-0.0170312\pi$
$271$	7.45682	+	12.9156i	0.452970	+	0.784567i	−0.545599	+	0.838046i	$0.683698\pi$
$272$	1.17458	+	1.17458i	0.0712196	+	0.0712196i
$273$	−21.9655	−	12.2086i	−1.32941	−	0.738900i
$274$		−	1.89490i		−	0.114475i
$275$	−8.97250	−	12.2450i	−0.541062	−	0.738400i
$276$	−5.33564	−	0.312658i	−0.321168	−	0.0188198i
$277$	−2.36575	−	8.82909i	−0.142144	−	0.530489i	−0.999866	−	0.0163747i	$-0.994788\pi$
$277$	−2.36575	−	8.82909i	−0.142144	−	0.530489i	0.857722	−	0.514114i	$-0.171879\pi$
$278$	4.66463	−	4.66463i	0.279766	−	0.279766i
$279$	1.37339	−	11.6785i	0.0822230	−	0.699176i
$280$	8.55205	−	2.79789i	0.511083	−	0.167206i
$281$		−	7.38269i		−	0.440414i	−0.975453	−	0.220207i	$-0.929327\pi$
$281$		−	7.38269i		−	0.440414i	0.975453	−	0.220207i	$-0.0706733\pi$
$282$	−5.31871	+	16.0320i	−0.316725	+	0.954691i
$283$	−1.91633	+	7.15185i	−0.113914	+	0.425133i	−0.999203	−	0.0399074i	$-0.987294\pi$
$283$	−1.91633	+	7.15185i	−0.113914	+	0.425133i	0.885289	+	0.465041i	$0.153960\pi$
$284$	7.61644	+	13.1921i	0.451952	+	0.782804i
$285$	0.347653	−	0.596429i	0.0205932	−	0.0353294i
$286$	−3.61587	−	10.3323i	−0.213811	−	0.610964i
$287$	−22.5621	−	22.5621i	−1.33180	−	1.33180i
$288$	0.432697	+	2.96863i	0.0254969	+	0.174928i
$289$	−12.3328	+	7.12035i	−0.725460	+	0.418844i
$290$	2.28344	−	4.50404i	0.134088	−	0.264486i
$291$	15.6604	+	10.3079i	0.918029	+	0.604262i
$292$	−2.86701	−	10.6998i	−0.167779	−	0.626160i
$293$	−4.92655	−	18.3861i	−0.287812	−	1.07413i	−0.946760	−	0.321941i	$-0.895665\pi$
$293$	−4.92655	−	18.3861i	−0.287812	−	1.07413i	0.658947	−	0.752189i	$-0.271002\pi$
$294$	−13.3004	−	8.75454i	−0.775694	−	0.510575i
$295$	−5.85337	−	17.8915i	−0.340796	−	1.04168i
$296$	3.16593	−	1.82785i	0.184016	−	0.106242i
$297$	−14.2908	−	6.68237i	−0.829236	−	0.387750i
$298$	−7.92463	−	7.92463i	−0.459062	−	0.459062i
$299$	−10.9322	−	2.06806i	−0.632225	−	0.119599i
$300$	2.65869	+	8.24205i	0.153500	+	0.475855i
$301$	−22.2177	−	38.4822i	−1.28061	−	2.21808i
$302$	0.268422	−	1.00176i	0.0154459	−	0.0576450i
$303$	−7.47233	+	22.5236i	−0.429274	+	1.29394i
$304$			0.178249i			0.0102233i
$305$	8.37972	+	25.6135i	0.479821	+	1.46662i
$306$	4.94923	+	0.582028i	0.282929	+	0.0332723i
$307$	−2.13710	+	2.13710i	−0.121971	+	0.121971i	−0.765457	−	0.643487i	$-0.777487\pi$
$307$	−2.13710	+	2.13710i	−0.121971	+	0.121971i	0.643487	+	0.765457i	$0.277487\pi$
$308$	−3.16210	−	11.8011i	−0.180177	−	0.672432i
$309$	−4.76762	−	0.279373i	−0.271220	−	0.0158930i
$310$	4.78845	+	7.34098i	0.271966	+	0.416939i
$311$		−	20.7072i		−	1.17420i	−0.809516	−	0.587098i	$-0.800270\pi$
$311$		−	20.7072i		−	1.17420i	0.809516	−	0.587098i	$-0.199730\pi$
$312$	0.101824	+	6.24417i	0.00576464	+	0.353506i
$313$	−18.8713	−	18.8713i	−1.06667	−	1.06667i	−0.997613	−	0.0690575i	$-0.978001\pi$
$313$	−18.8713	−	18.8713i	−1.06667	−	1.06667i	−0.0690575	−	0.997613i	$-0.521999\pi$
$314$	1.75987	+	3.04818i	0.0993150	+	0.172019i
$315$	14.9349	−	22.4864i	0.841488	−	1.26697i
$316$	3.19226	−	5.52915i	0.179578	−	0.311039i
$317$	16.6405	+	16.6405i	0.934623	+	0.934623i	0.997990	−	0.0633669i	$-0.0201838\pi$
$317$	16.6405	+	16.6405i	0.934623	+	0.934623i	−0.0633669	+	0.997990i	$0.520184\pi$
$318$	−5.01010	−	1.66213i	−0.280952	−	0.0932076i
$319$	−5.93791	−	3.42825i	−0.332459	−	0.191945i
$320$	−1.66475	−	1.49285i	−0.0930623	−	0.0834530i
$321$	0.551602	+	1.09930i	0.0307874	+	0.0613569i
$322$	−11.9944	−	3.21390i	−0.668424	−	0.179104i
$323$	0.286002	+	0.0766341i	0.0159136	+	0.00426403i
$324$	6.53763	+	6.18542i	0.363201	+	0.343635i
$325$	3.29145	+	17.7247i	0.182577	+	0.983192i
$326$			0.929872i			0.0515008i
$327$	−21.2015	−	23.8409i	−1.17245	−	1.31841i
$328$	−2.05222	+	7.65900i	−0.113315	+	0.422898i
$329$	−19.6217	+	33.9857i	−1.08178	+	1.87369i
$330$	11.3706	−	2.99626i	0.625929	−	0.164939i
$331$	1.09896	−	1.90345i	0.0604043	−	0.104623i	−0.834242	−	0.551399i	$-0.814094\pi$
$331$	1.09896	−	1.90345i	0.0604043	−	0.104623i	0.894646	+	0.446775i	$0.147428\pi$
$332$	−5.23054	+	1.40152i	−0.287063	+	0.0769184i
$333$	4.05633	−	10.1894i	0.222285	−	0.558375i
$334$	1.23145	+	0.710977i	0.0673818	+	0.0389029i
$335$	−27.0097	+	17.6182i	−1.47570	+	0.962585i
$336$	−0.407723	+	6.95796i	−0.0222431	+	0.379588i
$337$	−2.77245	+	2.77245i	−0.151025	+	0.151025i	−0.778576	−	0.627551i	$-0.784058\pi$
$337$	−2.77245	+	2.77245i	−0.151025	+	0.151025i	0.627551	+	0.778576i	$0.284058\pi$
$338$	−1.45459	+	12.9184i	−0.0791191	+	0.702666i
$339$	16.6582	+	10.9647i	0.904747	+	0.595520i
$340$	−3.11102	+	2.02929i	−0.168719	+	0.110054i
$341$	10.3061	−	5.95023i	0.558107	−	0.322223i
$342$	0.331372	+	0.419698i	0.0179186	+	0.0226947i
$343$	−6.24050	−	6.24050i	−0.336955	−	0.336955i
$344$	−5.52120	+	9.56300i	−0.297683	+	0.515602i
$345$	3.14106	−	11.5312i	0.169109	−	0.620817i
$346$	9.74499			0.523894
$347$	−9.02951	+	2.41945i	−0.484729	+	0.129883i	−0.492904	−	0.870084i	$-0.664065\pi$
$347$	−9.02951	+	2.41945i	−0.484729	+	0.129883i	0.00817449	+	0.999967i	$0.497398\pi$
$348$	2.59935	+	2.92295i	0.139340	+	0.156687i
$349$	7.17814	−	4.14430i	0.384237	−	0.221839i	−0.295423	−	0.955366i	$-0.595461\pi$
$349$	7.17814	−	4.14430i	0.384237	−	0.221839i	0.679660	+	0.733527i	$0.262127\pi$
$350$	2.18418	+	20.0015i	0.116750	+	1.06912i
$351$	11.8479	+	14.5130i	0.632395	+	0.774646i
$352$	−2.14684	+	2.14684i	−0.114427	+	0.114427i
$353$	−19.2293	−	5.15249i	−1.02347	−	0.274239i	−0.292225	−	0.956349i	$-0.594396\pi$
$353$	−19.2293	−	5.15249i	−1.02347	−	0.274239i	−0.731249	+	0.682110i	$0.761062\pi$
$354$	14.5565	+	0.852982i	0.773670	+	0.0453355i
$355$	−32.3733	+	10.5912i	−1.71819	+	0.562125i
$356$			8.69680i			0.460930i
$357$	10.9888	+	3.64561i	0.581590	+	0.192946i
$358$	4.93044	−	1.32111i	0.260582	−	0.0698227i
$359$	36.7484			1.93951			0.969754	−	0.244085i	$-0.0784877\pi$
$359$	36.7484			1.93951			0.969754	+	0.244085i	$0.0784877\pi$
$360$	−6.69503	−	0.420175i	−0.352859	−	0.0221452i
$361$	−9.48411	−	16.4270i	−0.499164	−	0.864577i
$362$	0.620259	−	2.31484i	0.0326001	−	0.121665i
$363$	0.623144	+	3.02329i	0.0327066	+	0.158681i
$364$	−2.69687	+	14.2562i	−0.141354	+	0.747225i
$365$	24.7329	−	1.34643i	1.29458	−	0.0704754i
$366$	−20.8392	−	1.22113i	−1.08928	−	0.0638297i
$367$	−17.7857	−	4.76567i	−0.928407	−	0.248766i	−0.237232	−	0.971453i	$-0.576240\pi$
$367$	−17.7857	−	4.76567i	−0.928407	−	0.248766i	−0.691175	+	0.722687i	$0.742907\pi$
$368$	0.798669	+	2.98067i	0.0416335	+	0.155378i
$369$	9.40633	+	21.8488i	0.489674	+	1.13740i
$370$	2.54177	+	7.76918i	0.132140	+	0.403900i
$371$	−10.6208	−	6.13190i	−0.551402	−	0.318352i
$372$	−6.64930	+	1.37052i	−0.344750	+	0.0710582i
$373$	7.69106	−	2.06081i	0.398228	−	0.106705i	−0.0541464	−	0.998533i	$-0.517244\pi$
$373$	7.69106	−	2.06081i	0.398228	−	0.106705i	0.452374	+	0.891828i	$0.350577\pi$
$374$	2.52164	+	4.36760i	0.130391	+	0.225843i
$375$	−19.2590	+	2.02235i	−0.994532	+	0.104434i
$376$	9.75215			0.502929
$377$	4.58711	+	6.72753i	0.236248	+	0.346485i
$378$	11.9751	+	17.1409i	0.615935	+	0.881634i
$379$	31.8216	−	18.3722i	1.63457	−	0.943718i	0.651909	−	0.758297i	$-0.273968\pi$
$379$	31.8216	−	18.3722i	1.63457	−	0.943718i	0.982659	−	0.185421i	$-0.0593649\pi$
$380$	−0.390034	−	0.0820790i	−0.0200083	−	0.00421056i
$381$	18.9980	−	9.53273i	0.973296	−	0.488377i
$382$	−18.6012	+	18.6012i	−0.951720	+	0.951720i
$383$	−3.67900	−	13.7302i	−0.187988	−	0.701582i	−0.993971	−	0.109643i	$-0.965029\pi$
$383$	−3.67900	−	13.7302i	−0.187988	−	0.701582i	0.805983	−	0.591939i	$-0.201637\pi$
$384$	1.54809	−	0.776796i	0.0790007	−	0.0396407i
$385$	27.2786	−	1.48502i	1.39025	−	0.0756834i
$386$	−19.3811	−	11.1897i	−0.986474	−	0.569541i
$387$	4.77802	+	32.7808i	0.242880	+	1.66634i
$388$	2.80156	−	10.4556i	0.142227	−	0.530800i
$389$	−2.22827			−0.112978			−0.0564888	−	0.998403i	$-0.517991\pi$
$389$	−2.22827			−0.112978			−0.0564888	+	0.998403i	$0.517991\pi$
$390$	−13.7100	−	2.65247i	−0.694233	−	0.134313i
$391$	5.12589			0.259227
$392$	−2.37936	+	8.87990i	−0.120176	+	0.448503i
$393$	−9.74766	−	10.9612i	−0.491704	−	0.552917i
$394$	0.753256	+	0.434892i	0.0379485	+	0.0219096i
$395$	10.6286	+	9.53114i	0.534784	+	0.479564i
$396$	−1.06380	+	9.04592i	−0.0534579	+	0.454575i
$397$	−2.04648	−	7.63758i	−0.102710	−	0.383319i	0.895365	−	0.445333i	$-0.146915\pi$
$397$	−2.04648	−	7.63758i	−0.102710	−	0.383319i	−0.998075	+	0.0620133i	$0.980248\pi$
$398$	−9.19490	+	9.19490i	−0.460899	+	0.460899i
$399$	0.557185	+	1.11043i	0.0278941	+	0.0555908i
$400$	4.03315	−	2.95529i	0.201657	−	0.147764i
$401$	−0.0188718	+	0.0108957i	−0.000942414	+	0.000544103i	−0.500471	−	0.865753i	$-0.666840\pi$
$401$	−0.0188718	+	0.0108957i	−0.000942414	+	0.000544103i	0.499529	+	0.866297i	$0.333507\pi$
$402$	−5.04257	−	24.4648i	−0.251500	−	1.22019i
$403$	−14.0930	+	1.05665i	−0.702024	+	0.0526354i
$404$	13.7009			0.681647
$405$	−16.5450	+	11.4570i	−0.822127	+	0.569304i
$406$	4.54386	+	7.87019i	0.225508	+	0.390591i
$407$	10.7208	−	2.87264i	0.531412	−	0.142391i
$408$	−0.580810	−	2.81789i	−0.0287544	−	0.139507i
$409$	−6.43392	−	3.71463i	−0.318137	−	0.183676i	0.332425	−	0.943130i	$-0.392133\pi$
$409$	−6.43392	−	3.71463i	−0.318137	−	0.183676i	−0.650562	+	0.759453i	$0.725467\pi$
$410$	−15.8140	−	8.01733i	−0.780997	−	0.395948i
$411$	−1.80449	+	2.74148i	−0.0890088	+	0.135227i
$412$	0.713643	+	2.66335i	0.0351587	+	0.131214i
$413$	32.7228	+	8.76805i	1.61018	+	0.431447i
$414$	7.42171	+	5.53342i	0.364757	+	0.271953i
$415$	−0.658194	−	12.0905i	−0.0323095	−	0.593501i
$416$	3.40318	−	1.19096i	0.166854	−	0.0583918i
$417$	−11.1907	+	2.30658i	−0.548012	+	0.112954i
$418$	−0.140067	+	0.522739i	−0.00685092	+	0.0255680i
$419$	−5.63488	−	9.75989i	−0.275282	−	0.476802i	0.694924	−	0.719083i	$-0.255438\pi$
$419$	−5.63488	−	9.75989i	−0.275282	−	0.476802i	−0.970206	+	0.242281i	$0.922104\pi$
$420$	−15.0373	−	4.09611i	−0.733743	−	0.199870i
$421$	37.0417			1.80530			0.902651	−	0.430373i	$-0.141618\pi$
$421$	37.0417			1.80530			0.902651	+	0.430373i	$0.141618\pi$
$422$	−4.13268	+	1.10735i	−0.201176	+	0.0539049i
$423$	22.9620	−	18.1297i	1.11645	−	0.881494i
$424$			3.04761i			0.148005i
$425$	−3.00783	−	7.74179i	−0.145901	−	0.375532i
$426$	1.54341	−	26.3389i	0.0747784	−	1.27613i
$427$	−46.8461	−	12.5524i	−2.26704	−	0.607453i
$428$	0.502116	−	0.502116i	0.0242707	−	0.0242707i
$429$	−4.60803	+	18.3919i	−0.222478	+	0.887968i
$430$	−18.3828	−	16.4847i	−0.886498	−	0.794962i
$431$	22.0645	−	12.7389i	1.06281	−	0.613612i	0.136600	−	0.990626i	$-0.456383\pi$
$431$	22.0645	−	12.7389i	1.06281	−	0.613612i	0.926207	+	0.377014i	$0.123049\pi$
$432$	2.20098	−	4.70698i	0.105895	−	0.226465i
$433$	35.6427	−	9.55042i	1.71288	−	0.458964i	0.736750	−	0.676165i	$-0.236359\pi$
$433$	35.6427	−	9.55042i	1.71288	−	0.458964i	0.976127	+	0.217201i	$0.0696926\pi$
$434$	−15.7730			−0.757130
$435$	−7.59276	+	4.34181i	−0.364045	+	0.208174i
$436$	−9.21002	+	15.9522i	−0.441080	+	0.763973i
$437$	0.388940	+	0.388940i	0.0186055	+	0.0186055i
$438$	−6.04142	+	18.2104i	−0.288670	+	0.870127i
$439$	−2.36564	+	1.36580i	−0.112906	+	0.0651862i	−0.555389	−	0.831590i	$-0.687431\pi$
$439$	−2.36564	+	1.36580i	−0.112906	+	0.0651862i	0.442484	+	0.896777i	$0.354097\pi$
$440$	−3.70902	−	5.68614i	−0.176821	−	0.271076i
$441$	10.9058	+	25.3316i	0.519322	+	1.20627i
$442$	−0.447795	−	5.97246i	−0.0212994	−	0.284081i
$443$	−13.3374	+	13.3374i	−0.633679	+	0.633679i	−0.948989	−	0.315310i	$-0.897892\pi$
$443$	−13.3374	+	13.3374i	−0.633679	+	0.633679i	0.315310	+	0.948989i	$0.397892\pi$
$444$	−6.32102	−	0.370399i	−0.299982	−	0.0175784i
$445$	−19.0298	−	4.00465i	−0.902101	−	0.189839i
$446$	19.1319	+	11.0458i	0.905923	+	0.523035i
$447$	3.91859	+	19.0117i	0.185343	+	0.899221i
$448$	3.88695	−	1.04151i	0.183641	−	0.0492065i
$449$	−11.8159	+	20.4658i	−0.557629	+	0.965841i	0.440065	+	0.897966i	$0.354955\pi$
$449$	−11.8159	+	20.4658i	−0.557629	+	0.965841i	−0.997694	+	0.0678755i	$0.978378\pi$
$450$	4.00229	−	14.4562i	0.188670	−	0.681472i
$451$	−12.0368	+	20.8484i	−0.566793	+	0.981714i
$452$	2.98005	−	11.1217i	0.140170	−	0.523121i
$453$	−1.34231	+	1.19371i	−0.0630674	+	0.0560853i
$454$			27.9523i			1.31187i
$455$	−29.9526	−	12.4657i	−1.40420	−	0.584402i
$456$	0.169744	−	0.257885i	0.00794901	−	0.0120766i
$457$	20.5609	+	5.50929i	0.961800	+	0.257714i	0.705362	−	0.708847i	$-0.250784\pi$
$457$	20.5609	+	5.50929i	0.961800	+	0.257714i	0.256438	+	0.966561i	$0.417451\pi$
$458$	−9.45452	−	2.53333i	−0.441781	−	0.118375i
$459$	−6.60614	−	5.55516i	−0.308348	−	0.259292i
$460$	−6.88990	+	0.375078i	−0.321243	+	0.0174881i
$461$	−13.9530	−	8.05574i	−0.649854	−	0.375193i	0.138546	−	0.990356i	$-0.455757\pi$
$461$	−13.9530	−	8.05574i	−0.649854	−	0.375193i	−0.788400	+	0.615163i	$0.789090\pi$
$462$	−6.66324	+	20.0848i	−0.310002	+	0.934428i
$463$	23.6278	+	23.6278i	1.09808	+	1.09808i	0.994635	+	0.103443i	$0.0329858\pi$
$463$	23.6278	+	23.6278i	1.09808	+	1.09808i	0.103443	+	0.994635i	$0.467014\pi$
$464$	1.12917	−	1.95578i	0.0524204	−	0.0907948i
$465$	0.0629382	−	15.1807i	0.00291869	−	0.703988i
$466$	2.55689	+	4.42866i	0.118446	+	0.205154i
$467$	13.9127	+	13.9127i	0.643803	+	0.643803i	0.951488	−	0.307685i	$-0.0995544\pi$
$467$	13.9127	+	13.9127i	0.643803	+	0.643803i	−0.307685	+	0.951488i	$0.599554\pi$
$468$	5.79894	−	9.13085i	0.268056	−	0.422073i
$469$		−	58.0339i		−	2.67976i
$470$	−4.49061	+	21.3391i	−0.207136	+	0.984299i
$471$	0.356623	−	6.08592i	0.0164323	−	0.280424i
$472$	−2.17890	−	8.13176i	−0.100292	−	0.374295i
$473$	−23.7062	+	23.7062i	−1.09001	+	1.09001i
$474$	−9.88381	+	4.95946i	−0.453979	+	0.227796i
$475$	0.359201	−	0.815654i	0.0164813	−	0.0374248i
$476$		−	6.68443i		−	0.306380i
$477$	5.66563	+	7.17578i	0.259411	+	0.328556i
$478$	−3.04801	+	11.3753i	−0.139413	+	0.520295i
$479$	−16.0013	−	27.7150i	−0.731117	−	1.26633i	−0.956406	−	0.292040i	$-0.905666\pi$
$479$	−16.0013	−	27.7150i	−0.731117	−	1.26633i	0.225289	−	0.974292i	$-0.427667\pi$
$480$	0.986883	+	3.74514i	0.0450449	+	0.170941i
$481$	−12.9511	−	2.44999i	−0.590520	−	0.111710i
$482$	13.6996	+	13.6996i	0.624000	+	0.624000i
$483$	14.2926	+	16.0719i	0.650338	+	0.731299i
$484$	1.54342	−	0.891093i	0.0701554	−	0.0405042i
$485$	21.5882	+	10.9447i	0.980269	+	0.496974i
$486$	−3.56814	−	15.1746i	−0.161854	−	0.688334i
$487$	0.835382	+	3.11769i	0.0378548	+	0.141276i	0.982267	−	0.187488i	$-0.0600346\pi$
$487$	0.835382	+	3.11769i	0.0378548	+	0.141276i	−0.944412	+	0.328764i	$0.893368\pi$
$488$	3.11932	+	11.6415i	0.141205	+	0.526985i
$489$	0.885507	−	1.34531i	0.0400440	−	0.0608371i
$490$	−18.3348	−	9.29535i	−0.828284	−	0.419921i
$491$	15.5320	−	8.96741i	0.700950	−	0.404694i	−0.106751	−	0.994286i	$-0.534045\pi$
$491$	15.5320	−	8.96741i	0.700950	−	0.404694i	0.807701	+	0.589592i	$0.200711\pi$
$492$	10.2627	−	9.12651i	0.462677	−	0.411455i
$493$	−2.65261	−	2.65261i	−0.119467	−	0.119467i
$494$	0.419198	−	0.487153i	0.0188606	−	0.0219180i
$495$	−19.3039	−	6.49315i	−0.867646	−	0.291845i
$496$	1.95984	+	3.39454i	0.0879993	+	0.152419i
$497$	15.8651	−	59.2095i	0.711648	−	2.65591i
$498$	8.90205	+	2.95331i	0.398910	+	0.132341i
$499$		−	7.18865i		−	0.321808i	−0.986970	−	0.160904i	$-0.948559\pi$
$499$		−	7.18865i		−	0.321808i	0.986970	−	0.160904i	$-0.0514410\pi$
$500$	4.60943	+	10.1859i	0.206140	+	0.455529i
$501$	−1.10457	−	2.20131i	−0.0493484	−	0.0983475i
$502$	8.68725	−	8.68725i	0.387731	−	0.387731i
$503$	−4.86305	−	18.1491i	−0.216833	−	0.809231i	−0.985513	−	0.169598i	$-0.945753\pi$
$503$	−4.86305	−	18.1491i	−0.216833	−	0.809231i	0.768681	−	0.639633i	$-0.220914\pi$
$504$	7.21587	−	9.67831i	0.321420	−	0.431106i
$505$	−6.30892	+	29.9796i	−0.280743	+	1.33407i
$506$			9.36881i			0.416494i
$507$	14.4065	−	17.3047i	0.639814	−	0.768530i
$508$	−8.67752	−	8.67752i	−0.385003	−	0.385003i
$509$	3.92213	+	6.79332i	0.173845	+	0.301109i	0.939761	−	0.341832i	$-0.111047\pi$
$509$	3.92213	+	6.79332i	0.173845	+	0.301109i	−0.765916	+	0.642941i	$0.777714\pi$
$510$	6.43340	+	0.0266725i	0.284876	+	0.00118108i
$511$	−22.2879	+	38.6037i	−0.985957	+	1.70773i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−0.0797461	−	0.922769i	−0.00352087	−	0.0407413i
$514$	15.1780	+	8.76305i	0.669475	+	0.386521i
$515$	−6.15641	+	0.335148i	−0.271284	+	0.0147684i
$516$	17.0946	−	8.57769i	0.752550	−	0.377612i
$517$	28.5995	+	7.66321i	1.25780	+	0.337027i
$518$	−14.2095	−	3.80744i	−0.624332	−	0.167289i
$519$	−14.0988	−	9.28004i	−0.618867	−	0.407349i
$520$	1.03892	+	7.99504i	0.0455598	+	0.350606i
$521$		−	25.7690i		−	1.12896i	−0.825447	−	0.564480i	$-0.809077\pi$
$521$		−	25.7690i		−	1.12896i	0.825447	−	0.564480i	$-0.190923\pi$
$522$	−0.977177	−	6.70418i	−0.0427699	−	0.293434i
$523$	−8.34249	+	31.1346i	−0.364792	+	1.36142i	0.502911	+	0.864338i	$0.332262\pi$
$523$	−8.34249	+	31.1346i	−0.364792	+	1.36142i	−0.867703	+	0.497083i	$0.834404\pi$
$524$	−4.23442	+	7.33423i	−0.184981	+	0.320397i
$525$	15.8871	−	31.0175i	0.693372	−	1.35371i
$526$	0.0153838	−	0.0266456i	0.000670767	−	0.00116180i
$527$	6.28916	−	1.68517i	0.273960	−	0.0734074i
$528$	5.15039	−	1.06157i	0.224142	−	0.0461990i
$529$	−11.6721	−	6.73886i	−0.507481	−	0.292994i
$530$	−6.66860	−	1.40334i	−0.289665	−	0.0609574i
$531$	−20.2477	−	15.0961i	−0.878673	−	0.655114i
$532$	0.507198	−	0.507198i	0.0219898	−	0.0219898i
$533$	23.6208	−	16.1057i	1.02313	−	0.697614i
$534$	8.28187	−	12.5823i	0.358391	−	0.544488i
$535$	0.867489	+	1.32991i	0.0375048	+	0.0574971i
$536$	−12.4895	+	7.21084i	−0.539466	+	0.311461i
$537$	−8.39129	−	2.78386i	−0.362111	−	0.120133i
$538$	0.757939	+	0.757939i	0.0326771	+	0.0326771i
$539$	−13.9556	+	24.1718i	−0.601110	+	1.04115i
$540$	9.28605	+	6.98350i	0.399608	+	0.300522i
$541$	−12.7264			−0.547153			−0.273576	−	0.961850i	$-0.588207\pi$
$541$	−12.7264			−0.547153			−0.273576	+	0.961850i	$0.588207\pi$
$542$	−14.4055	+	3.85994i	−0.618768	+	0.165798i
$543$	−3.10177	+	2.75837i	−0.133109	+	0.118373i
$544$	−1.43856	+	0.830556i	−0.0616779	+	0.0356098i
$545$	−30.6647	−	27.4984i	−1.31353	−	1.17790i
$546$	17.4777	−	18.0572i	0.747977	−	0.772776i
$547$	−20.4407	+	20.4407i	−0.873982	+	0.873982i	−0.992904	−	0.118921i	$-0.962056\pi$
$547$	−20.4407	+	20.4407i	−0.873982	+	0.873982i	0.118921	+	0.992904i	$0.462056\pi$
$548$	1.83033	+	0.490435i	0.0781878	+	0.0209503i
$549$	28.9866	+	21.6116i	1.23712	+	0.922362i
$550$	14.1500	−	5.49754i	0.603358	−	0.234416i
$551$		−	0.402546i		−	0.0171491i
$552$	1.68297	−	5.07291i	0.0716320	−	0.215917i
$553$	−24.8163	+	6.64951i	−1.05530	+	0.282766i
$554$	9.14055			0.388345
$555$	3.72115	−	13.6607i	0.157954	−	0.579865i
$556$	3.29839	+	5.71298i	0.139883	+	0.242284i
$557$	4.05050	−	15.1167i	0.171625	−	0.640513i	−0.825477	−	0.564436i	$-0.809094\pi$
$557$	4.05050	−	15.1167i	0.171625	−	0.640513i	0.997102	−	0.0760773i	$-0.0242396\pi$
$558$	10.9251	+	4.34923i	0.462498	+	0.184117i
$559$	37.5792	−	13.1511i	1.58943	−	0.556232i
$560$	0.489122	+	8.98479i	0.0206692	+	0.379677i
$561$	0.510989	−	8.72025i	0.0215740	−	0.368169i
$562$	7.13113	+	1.91078i	0.300808	+	0.0806014i
$563$	−10.7871	−	40.2581i	−0.454624	−	1.69668i	−0.689192	−	0.724579i	$-0.742034\pi$
$563$	−10.7871	−	40.2581i	−0.454624	−	1.69668i	0.234569	−	0.972100i	$-0.424632\pi$
$564$	−14.1091	−	9.28686i	−0.594101	−	0.391048i
$565$	22.9636	+	11.6420i	0.966086	+	0.489784i
$566$	−6.41217	−	3.70207i	−0.269524	−	0.155610i
$567$	−1.00217	−	36.2028i	−0.0420873	−	1.52037i
$568$	−14.7138	+	3.94256i	−0.617378	+	0.165426i
$569$	5.02299	+	8.70008i	0.210575	+	0.364726i	0.951895	−	0.306426i	$-0.0991331\pi$
$569$	5.02299	+	8.70008i	0.210575	+	0.364726i	−0.741320	+	0.671152i	$0.765800\pi$
$570$	0.486127	+	0.490174i	0.0203616	+	0.0205311i
$571$	3.87977			0.162363			0.0811816	−	0.996699i	$-0.474131\pi$
$571$	3.87977			0.162363			0.0811816	+	0.996699i	$0.474131\pi$
$572$	10.9161	−	0.818454i	0.456426	−	0.0342213i
$573$	44.6254	−	9.19796i	1.86425	−	0.384250i
$574$	27.6328	−	15.9538i	1.15337	−	0.665899i
$575$	2.35190	−	15.2488i	0.0980808	−	0.635918i
$576$	−2.97947	−	0.350385i	−0.124145	−	0.0145994i
$577$	−28.6819	+	28.6819i	−1.19404	+	1.19404i	−0.218120	+	0.975922i	$0.569992\pi$
$577$	−28.6819	+	28.6819i	−1.19404	+	1.19404i	−0.975922	+	0.218120i	$0.930008\pi$
$578$	−3.68577	−	13.7555i	−0.153308	−	0.572152i
$579$	17.3842	+	34.6454i	0.722464	+	1.43981i
$580$	3.75957	+	3.37137i	0.156108	+	0.139988i
$581$	18.8712	+	10.8953i	0.782909	+	0.452013i
$582$	−14.0099	+	12.4589i	−0.580730	+	0.516438i
$583$	−2.39480	+	8.93751i	−0.0991825	+	0.370154i
$584$	11.0773			0.458381
$585$	17.3093	+	16.8934i	0.715652	+	0.698457i
$586$	19.0347			0.786318
$587$	−4.68645	+	17.4901i	−0.193430	+	0.721892i	0.799237	+	0.601016i	$0.205237\pi$
$587$	−4.68645	+	17.4901i	−0.193430	+	0.721892i	−0.992668	+	0.120876i	$0.961430\pi$
$588$	11.8986	−	10.5813i	0.490691	−	0.436367i
$589$	0.605073	+	0.349339i	0.0249316	+	0.0143943i
$590$	18.7968	−	1.02327i	0.773851	−	0.0421276i
$591$	−0.675645	−	1.34651i	−0.0277923	−	0.0553879i
$592$	0.946165	+	3.53114i	0.0388871	+	0.145129i
$593$	−31.5321	+	31.5321i	−1.29487	+	1.29487i	−0.363132	+	0.931738i	$0.618293\pi$
$593$	−31.5321	+	31.5321i	−1.29487	+	1.29487i	−0.931738	+	0.363132i	$0.881707\pi$
$594$	10.1534	−	12.0743i	0.416599	−	0.495416i
$595$	14.6265	+	3.07801i	0.599627	+	0.126186i
$596$	9.70565	−	5.60356i	0.397559	−	0.229531i
$597$	22.0591	−	4.54671i	0.902820	−	0.186085i
$598$	4.82705	−	10.0244i	0.197393	−	0.409929i
$599$	6.02851			0.246318			0.123159	−	0.992387i	$-0.460697\pi$
$599$	6.02851			0.246318			0.123159	+	0.992387i	$0.460697\pi$
$600$	−8.64933	+	0.434902i	−0.353107	+	0.0177548i
$601$	−4.49709	−	7.78920i	−0.183440	−	0.317728i	0.759610	−	0.650379i	$-0.225390\pi$
$601$	−4.49709	−	7.78920i	−0.183440	−	0.317728i	−0.943050	+	0.332651i	$0.892057\pi$
$602$	42.9213	−	11.5007i	1.74934	−	0.468735i
$603$	−16.0021	+	40.1970i	−0.651658	+	1.63695i
$604$	0.898157	+	0.518551i	0.0365455	+	0.0210995i
$605$	1.23913	+	3.78754i	0.0503780	+	0.153986i
$606$	−19.8221	−	13.0472i	−0.805218	−	0.530008i
$607$	−0.0708808	−	0.264531i	−0.00287696	−	0.0107370i	0.964472	−	0.264184i	$-0.0851025\pi$
$607$	−0.0708808	−	0.264531i	−0.00287696	−	0.0107370i	−0.967349	+	0.253447i	$0.918436\pi$
$608$	−0.172175	−	0.0461342i	−0.00698263	−	0.00187099i
$609$	0.920776	−	15.7134i	0.0373117	−	0.636740i
$610$	−26.9096	+	1.46493i	−1.08954	+	0.0593131i
$611$	−26.6526	−	22.9347i	−1.07825	−	0.927837i
$612$	−1.84315	+	4.62995i	−0.0745049	+	0.187155i
$613$	−10.8646	+	40.5474i	−0.438819	+	1.63769i	0.292941	+	0.956130i	$0.405366\pi$
$613$	−10.8646	+	40.5474i	−0.438819	+	1.63769i	−0.731760	+	0.681563i	$0.761301\pi$
$614$	−1.51116	−	2.61740i	−0.0609853	−	0.105630i
$615$	15.2444	+	26.6587i	0.614714	+	1.07498i
$616$	12.2174			0.492254
$617$	13.4091	−	3.59297i	0.539832	−	0.144647i	0.0214071	−	0.999771i	$-0.493185\pi$
$617$	13.4091	−	3.59297i	0.539832	−	0.144647i	0.518425	+	0.855123i	$0.326519\pi$
$618$	1.50380	−	4.53286i	0.0604918	−	0.182338i
$619$		−	3.66171i		−	0.147176i	−0.997289	−	0.0735882i	$-0.976555\pi$
$619$		−	3.66171i		−	0.147176i	0.997289	−	0.0735882i	$-0.0234451\pi$
$620$	−8.33018	+	2.72530i	−0.334548	+	0.109451i
$621$	−5.46810	−	15.0732i	−0.219427	−	0.604867i
$622$	20.0016	+	5.35941i	0.801991	+	0.214893i
$623$	24.7463	−	24.7463i	0.991439	−	0.991439i
$624$	−6.05776	−	1.51776i	−0.242504	−	0.0607588i
$625$	−24.4108	+	5.39572i	−0.976431	+	0.215829i
$626$	23.1126	−	13.3440i	0.923763	−	0.533335i
$627$	0.700444	−	0.622898i	0.0279730	−	0.0248762i
$628$	−3.39980	+	0.910974i	−0.135667	+	0.0363518i
$629$	6.07253			0.242127
$630$	17.8548	+	20.2460i	0.711352	+	0.806618i
$631$	−18.4049	+	31.8783i	−0.732689	+	1.26905i	0.223041	+	0.974809i	$0.428402\pi$
$631$	−18.4049	+	31.8783i	−0.732689	+	1.26905i	−0.955730	+	0.294245i	$0.904932\pi$
$632$	4.51453	+	4.51453i	0.179578	+	0.179578i
$633$	7.03356	+	2.33343i	0.279559	+	0.0927455i
$634$	−20.3804	+	11.7666i	−0.809408	+	0.467312i
$635$	22.9834	−	14.9919i	0.912069	−	0.594934i
$636$	2.90220	−	4.40919i	0.115080	−	0.174836i
$637$	27.3861	−	18.6730i	1.08508	−	0.739852i
$638$	4.84828	−	4.84828i	0.191945	−	0.191945i
$639$	−27.3152	+	36.6366i	−1.08057	+	1.44932i
$640$	1.87285	−	1.22165i	0.0740311	−	0.0482898i
$641$	−11.7524	−	6.78528i	−0.464194	−	0.268002i	0.249612	−	0.968346i	$-0.419697\pi$
$641$	−11.7524	−	6.78528i	−0.464194	−	0.268002i	−0.713806	+	0.700344i	$0.753030\pi$
$642$	−1.20461	+	0.248287i	−0.0475420	+	0.00979912i
$643$	3.51116	−	0.940814i	0.138467	−	0.0371021i	−0.188920	−	0.981992i	$-0.560499\pi$
$643$	3.51116	−	0.940814i	0.138467	−	0.0371021i	0.327387	+	0.944890i	$0.393832\pi$
$644$	6.20878	−	10.7539i	0.244660	−	0.423764i
$645$	10.8976	+	41.3553i	0.429091	+	1.62836i
$646$	−0.148046	+	0.256423i	−0.00582478	+	0.0100888i
$647$	−10.6020	+	39.5673i	−0.416809	+	1.55555i	0.364375	+	0.931252i	$0.381283\pi$
$647$	−10.6020	+	39.5673i	−0.416809	+	1.55555i	−0.781184	+	0.624300i	$0.785384\pi$
$648$	−7.66672	+	4.71396i	−0.301177	+	0.185182i
$649$		−	25.5597i		−	1.00330i
$650$	−17.9727	−	1.40820i	−0.704946	−	0.0552341i
$651$	22.8200	+	15.0205i	0.894386	+	0.588700i
$652$	−0.898187	−	0.240669i	−0.0351757	−	0.00942531i
$653$	15.2714	+	4.09197i	0.597617	+	0.160131i	0.544932	−	0.838480i	$-0.316555\pi$
$653$	15.2714	+	4.09197i	0.597617	+	0.160131i	0.0526851	+	0.998611i	$0.483222\pi$
$654$	28.5159	−	14.3086i	1.11506	−	0.559511i
$655$	−14.0985	−	12.6427i	−0.550874	−	0.493992i
$656$	−6.86687	−	3.96459i	−0.268106	−	0.154791i
$657$	26.0821	−	20.5931i	1.01756	−	0.803414i
$658$	−27.7492	−	27.7492i	−1.08178	−	1.08178i
$659$	7.83920	−	13.5779i	0.305372	−	0.528920i	−0.671972	−	0.740576i	$-0.734553\pi$
$659$	7.83920	−	13.5779i	0.305372	−	0.528920i	0.977344	+	0.211657i	$0.0678859\pi$
$660$	−0.0487504	+	11.7586i	−0.00189761	+	0.457703i
$661$	13.5670	+	23.4988i	0.527696	+	0.913997i	0.999479	+	0.0322820i	$0.0102775\pi$
$661$	13.5670	+	23.4988i	0.527696	+	0.913997i	−0.471782	+	0.881715i	$0.656389\pi$
$662$	1.55416	+	1.55416i	0.0604043	+	0.0604043i
$663$	−5.03965	+	9.06721i	−0.195724	+	0.352141i
$664$		−	5.41506i		−	0.210145i
$665$	0.876270	+	1.34337i	0.0339803	+	0.0520938i
$666$	8.79234	+	6.55532i	0.340696	+	0.254013i
$667$	−1.80366	−	6.73137i	−0.0698382	−	0.260640i
$668$	−1.00547	+	1.00547i	−0.0389029	+	0.0389029i
$669$	−17.1607	−	34.1999i	−0.663471	−	1.32224i
$670$	−10.0272	−	30.6493i	−0.387386	−	1.18409i
$671$			36.5913i			1.41259i
$672$	−6.61535	−	2.19468i	−0.255193	−	0.0846617i
$673$	9.46827	−	35.3361i	0.364975	−	1.36211i	−0.502480	−	0.864589i	$-0.667579\pi$
$673$	9.46827	−	35.3361i	0.364975	−	1.36211i	0.867455	−	0.497516i	$-0.165755\pi$
$674$	−1.96042	−	3.39555i	−0.0755126	−	0.130792i
$675$	−19.5569	+	17.1035i	−0.752744	+	0.658313i
$676$	−12.1017	−	4.74854i	−0.465450	−	0.182636i
$677$	−14.0072	−	14.0072i	−0.538342	−	0.538342i	0.384700	−	0.923042i	$-0.374305\pi$
$677$	−14.0072	−	14.0072i	−0.538342	−	0.538342i	−0.923042	+	0.384700i	$0.874305\pi$
$678$	−14.9025	+	13.2527i	−0.572328	+	0.508966i
$679$	−37.7224	+	21.7790i	−1.44765	+	0.835803i
$680$	−1.15495	−	3.53023i	−0.0442904	−	0.135378i
$681$	26.6187	−	40.4406i	1.02003	−	1.54969i
$682$	3.08007	+	11.4950i	0.117942	+	0.440165i
$683$	8.71791	+	32.5357i	0.333582	+	1.24494i	0.905399	+	0.424562i	$0.139572\pi$
$683$	8.71791	+	32.5357i	0.333582	+	1.24494i	−0.571817	+	0.820381i	$0.693761\pi$
$684$	−0.491163	+	0.211455i	−0.0187801	+	0.00808519i
$685$	−1.91596	+	3.77919i	−0.0732051	+	0.144395i
$686$	7.64302	−	4.41270i	0.291812	−	0.168478i
$687$	11.2661	+	12.6686i	0.429827	+	0.483337i
$688$	−7.80815	−	7.80815i	−0.297683	−	0.297683i
$689$	7.16723	−	8.32909i	0.273050	−	0.317313i
$690$	10.3253	+	6.01852i	0.393077	+	0.229121i
$691$	11.6788	+	20.2283i	0.444283	+	0.769520i	0.998002	−	0.0631833i	$-0.0201253\pi$
$691$	11.6788	+	20.2283i	0.444283	+	0.769520i	−0.553719	+	0.832703i	$0.686792\pi$
$692$	−2.52219	+	9.41293i	−0.0958792	+	0.357826i
$693$	28.7667	−	22.7127i	1.09276	−	0.862785i
$694$		−	9.34804i		−	0.354847i
$695$	−14.0196	+	4.58667i	−0.531795	+	0.173982i
$696$	−3.49612	+	1.75427i	−0.132520	+	0.0664954i
$697$	−9.31348	+	9.31348i	−0.352773	+	0.352773i
$698$	2.14525	+	8.00617i	0.0811988	+	0.303038i
$699$	0.518132	−	8.84215i	0.0195976	−	0.334441i
$700$	−19.8852	−	3.06700i	−0.751591	−	0.115922i
$701$			38.6101i			1.45828i	0.684362	+	0.729142i	$0.260081\pi$
$701$			38.6101i			1.45828i	−0.684362	+	0.729142i	$0.739919\pi$
$702$	−17.0849	+	7.68798i	−0.644829	+	0.290164i
$703$	0.460768	+	0.460768i	0.0173782	+	0.0173782i
$704$	−1.51804	−	2.62933i	−0.0572134	−	0.0990965i
$705$	26.8179	−	26.5964i	1.01002	−	1.00168i
$706$	9.95384	−	17.2406i	0.374618	−	0.648857i
$707$	−38.9853	−	38.9853i	−1.46619	−	1.46619i
$708$	−4.59142	+	13.8397i	−0.172556	+	0.520129i
$709$	13.7827	+	7.95743i	0.517619	+	0.298847i	0.735960	−	0.677025i	$-0.236731\pi$
$709$	13.7827	+	7.95743i	0.517619	+	0.298847i	−0.218341	+	0.975873i	$0.570064\pi$
$710$	−1.85154	−	34.0114i	−0.0694870	−	1.27642i
$711$	19.0225	+	2.23704i	0.713398	+	0.0838954i
$712$	−8.40046	−	2.25090i	−0.314821	−	0.0843560i
$713$	11.6833	+	3.13052i	0.437541	+	0.117239i
$714$	−6.36551	+	9.67084i	−0.238223	+	0.361922i
$715$	−3.23570	+	24.2629i	−0.121008	+	0.907381i
$716$			5.10437i			0.190759i
$717$	15.2424	−	13.5549i	0.569236	−	0.506217i
$718$	−9.51119	+	35.4962i	−0.354955	+	1.32471i
$719$	−4.56047	+	7.89896i	−0.170077	+	0.294582i	−0.938447	−	0.345425i	$-0.887735\pi$
$719$	−4.56047	+	7.89896i	−0.170077	+	0.294582i	0.768370	+	0.640006i	$0.221068\pi$
$720$	2.13866	−	6.35816i	0.0797031	−	0.236954i
$721$	5.54780	−	9.60907i	0.206611	−	0.357860i
$722$	18.3219	−	4.90934i	0.681871	−	0.182707i
$723$	−6.77421	−	32.8662i	−0.251936	−	1.22231i
$724$	2.07543	+	1.19825i	0.0771326	+	0.0445325i
$725$	−9.10821	+	6.67404i	−0.338271	+	0.247868i
$726$	−3.08155	−	0.180573i	−0.114367	−	0.00670168i
$727$	−1.93836	+	1.93836i	−0.0718898	+	0.0718898i	−0.742137	−	0.670248i	$-0.766188\pi$
$727$	−1.93836	+	1.93836i	−0.0718898	+	0.0718898i	0.670248	+	0.742137i	$0.266188\pi$
$728$	−13.0724	−	6.29474i	−0.484495	−	0.233298i
$729$	−9.28832	+	25.3521i	−0.344012	+	0.938965i
$730$	−5.10079	+	24.2386i	−0.188789	+	0.897112i
$731$	−15.8852	+	9.17132i	−0.587535	+	0.339214i
$732$	6.57310	−	19.8131i	0.242949	−	0.732311i
$733$	−2.03312	−	2.03312i	−0.0750951	−	0.0750951i	0.668562	−	0.743657i	$-0.266910\pi$
$733$	−2.03312	−	2.03312i	−0.0750951	−	0.0750951i	−0.743657	+	0.668562i	$0.766910\pi$
$734$	9.20656	−	15.9462i	0.339821	−	0.588586i
$735$	17.6745	+	30.9083i	0.651933	+	1.14007i
$736$	−3.08582			−0.113745
$737$	−42.2935	+	11.3325i	−1.55790	+	0.417439i
$738$	−23.5388	+	3.43094i	−0.866476	+	0.126295i
$739$	14.8800	−	8.59100i	0.547371	−	0.316025i	−0.200690	−	0.979655i	$-0.564318\pi$
$739$	14.8800	−	8.59100i	0.547371	−	0.316025i	0.748061	+	0.663630i	$0.230985\pi$
$740$	−8.16231	+	0.444347i	−0.300053	+	0.0163345i
$741$	−1.07039	+	0.305601i	−0.0393219	+	0.0112265i
$742$	8.67181	−	8.67181i	0.318352	−	0.318352i
$743$	−41.6735	−	11.1664i	−1.52885	−	0.409655i	−0.606207	−	0.795307i	$-0.707310\pi$
$743$	−41.6735	−	11.1664i	−1.52885	−	0.409655i	−0.922644	+	0.385652i	$0.873976\pi$
$744$	0.397145	−	6.77745i	0.0145600	−	0.248473i
$745$	7.79218	+	23.8176i	0.285484	+	0.872611i
$746$			7.96237i			0.291523i
$747$	−10.0668	−	12.7501i	−0.368326	−	0.466501i
$748$	−4.87143	+	1.30530i	−0.178117	+	0.0477263i
$749$	−2.85749			−0.104410
$750$	3.03116	−	19.1262i	0.110682	−	0.698391i
$751$	−12.6049	−	21.8323i	−0.459959	−	0.796673i	0.538999	−	0.842306i	$-0.318803\pi$
$751$	−12.6049	−	21.8323i	−0.459959	−	0.796673i	−0.998958	+	0.0456337i	$0.985469\pi$
$752$	−2.52404	+	9.41985i	−0.0920424	+	0.343507i
$753$	−20.8412	+	4.29569i	−0.759497	+	0.156544i
$754$	−7.68552	+	2.68960i	−0.279890	+	0.0979494i
$755$	−1.54824	+	1.72651i	−0.0563463	+	0.0628343i
$756$	−19.6563	+	7.13070i	−0.714891	+	0.259341i
$757$	4.21427	+	1.12921i	0.153170	+	0.0410418i	0.334589	−	0.942364i	$-0.391402\pi$
$757$	4.21427	+	1.12921i	0.153170	+	0.0410418i	−0.181419	+	0.983406i	$0.558069\pi$
$758$	9.51017	+	35.4924i	0.345425	+	1.28914i
$759$	8.92181	−	13.5545i	0.323841	−	0.491998i
$760$	0.180230	−	0.355500i	0.00653764	−	0.0128953i
$761$	8.76613	+	5.06113i	0.317772	+	0.183466i	0.650399	−	0.759593i	$-0.274602\pi$
$761$	8.76613	+	5.06113i	0.317772	+	0.183466i	−0.332627	+	0.943058i	$0.607935\pi$
$762$	4.29088	+	20.8179i	0.155442	+	0.754152i
$763$	71.5979	−	19.1846i	2.59202	−	0.694529i
$764$	−13.1530	−	22.7817i	−0.475860	−	0.824214i
$765$	−9.28226	−	6.16505i	−0.335601	−	0.222898i
$766$	14.2146			0.513593
$767$	−13.1690	+	27.3483i	−0.475505	+	0.987489i
$768$	0.349652	+	1.69639i	0.0126170	+	0.0612133i
$769$	−19.8822	+	11.4790i	−0.716972	+	0.413944i	−0.813637	−	0.581373i	$-0.802516\pi$
$769$	−19.8822	+	11.4790i	−0.716972	+	0.413944i	0.0966652	+	0.995317i	$0.469182\pi$
$770$	−5.62581	+	26.7335i	−0.202740	+	0.963407i
$771$	−13.6142	−	27.1320i	−0.490303	−	0.977135i
$772$	15.8246	−	15.8246i	0.569541	−	0.569541i
$773$	1.28054	+	4.77905i	0.0460579	+	0.171891i	0.985124	−	0.171847i	$-0.0549735\pi$
$773$	1.28054	+	4.77905i	0.0460579	+	0.171891i	−0.939066	+	0.343738i	$0.888307\pi$
$774$	−32.9005	−	3.86909i	−1.18258	−	0.139072i
$775$	−2.12752	−	19.4825i	−0.0764228	−	0.699834i
$776$	9.37419	+	5.41219i	0.336514	+	0.194286i
$777$	16.9322	+	19.0401i	0.607438	+	0.683059i
$778$	0.576718	−	2.15234i	0.0206764	−	0.0771652i
$779$	−1.41337			−0.0506392
$780$	6.11050	−	12.5563i	0.218791	−	0.449589i
$781$	−46.2483			−1.65489
$782$	−1.32668	+	4.95123i	−0.0474419	+	0.177056i
$783$	−4.97056	+	10.6300i	−0.177633	+	0.379884i
$784$	−7.96150	−	4.59658i	−0.284339	−	0.164163i
$785$	−0.427820	−	7.85873i	−0.0152696	−	0.280490i
$786$	13.1105	−	6.57856i	0.467638	−	0.234649i
$787$	−4.98461	−	18.6028i	−0.177682	−	0.663119i	−0.996079	−	0.0884656i	$-0.971804\pi$
$787$	−4.98461	−	18.6028i	−0.177682	−	0.663119i	0.818397	−	0.574653i	$-0.194863\pi$
$788$	−0.615031	+	0.615031i	−0.0219096	+	0.0219096i
$789$	−0.0476312	+	0.0239002i	−0.00169571	+	0.000850870i
$790$	−11.9573	+	7.79961i	−0.425420	+	0.277498i
$791$	−40.1258	+	23.1666i	−1.42671	+	0.823711i
$792$	−8.46236	−	3.36881i	−0.300697	−	0.119705i
$793$	18.8528	−	39.1520i	0.669483	−	1.39033i
$794$	7.90701			0.280609
$795$	8.31154	+	8.38075i	0.294780	+	0.297234i
$796$	−6.50178	−	11.2614i	−0.230449	−	0.399150i
$797$	−46.3862	+	12.4291i	−1.64308	+	0.440263i	−0.957665	−	0.287886i	$-0.907048\pi$
$797$	−46.3862	+	12.4291i	−1.64308	+	0.440263i	−0.685419	+	0.728149i	$0.740381\pi$
$798$	−1.21680	+	0.250800i	−0.0430742	+	0.00887824i
$799$	14.0291	+	8.09970i	0.496314	+	0.286547i
$800$	1.81073	+	4.66061i	0.0640191	+	0.164777i
$801$	−23.9639	+	10.3169i	−0.846724	+	0.364531i
$802$	−0.00564001	−	0.0210488i	−0.000199156	−	0.000743259i
$803$	32.4856	+	8.70448i	1.14639	+	0.307174i
$804$	24.9363	+	1.46122i	0.879436	+	0.0515332i
$805$	20.6721	+	18.5376i	0.728596	+	0.653364i
$806$	2.62690	−	13.8863i	0.0925286	−	0.489124i
$807$	−0.374787	−	1.81834i	−0.0131931	−	0.0640086i
$808$	−3.54606	+	13.2341i	−0.124750	+	0.465573i
$809$	11.7727	+	20.3910i	0.413907	+	0.716909i	0.995313	−	0.0967052i	$-0.0308304\pi$
$809$	11.7727	+	20.3910i	0.413907	+	0.716909i	−0.581406	+	0.813614i	$0.697497\pi$
$810$	−6.78448	−	18.9465i	−0.238382	−	0.665713i
$811$	−5.41319			−0.190083			−0.0950414	−	0.995473i	$-0.530298\pi$
$811$	−5.41319			−0.190083			−0.0950414	+	0.995473i	$0.530298\pi$
$812$	−8.77806	+	2.35207i	−0.308050	+	0.0825416i
$813$	24.5172	+	8.13373i	0.859856	+	0.285262i
$814$			11.0990i			0.389020i
$815$	0.940209	−	1.85454i	0.0329341	−	0.0649617i
$816$	2.87220	+	0.168305i	0.100547	+	0.00589186i
$817$	−1.90123	−	0.509432i	−0.0665155	−	0.0178228i
$818$	5.25327	−	5.25327i	0.183676	−	0.183676i
$819$	−42.4819	+	9.48078i	−1.48444	+	0.331285i
$820$	11.8371	−	13.2001i	0.413370	−	0.460968i
$821$	25.2564	−	14.5818i	0.881454	−	0.508908i	0.0103164	−	0.999947i	$-0.496716\pi$
$821$	25.2564	−	14.5818i	0.881454	−	0.508908i	0.871138	+	0.491039i	$0.163383\pi$
$822$	−2.18103	−	2.45255i	−0.0760722	−	0.0855425i
$823$	−12.4079	+	3.32469i	−0.432512	+	0.115891i	−0.468505	−	0.883461i	$-0.655207\pi$
$823$	−12.4079	+	3.32469i	−0.432512	+	0.115891i	0.0359931	+	0.999352i	$0.488541\pi$
$824$	−2.75731			−0.0960553
$825$	−25.7070	−	5.52121i	−0.895005	−	0.192224i
$826$	−16.9386	+	29.3385i	−0.589368	+	1.02082i
$827$	16.4462	+	16.4462i	0.571889	+	0.571889i	0.932656	−	0.360767i	$-0.117485\pi$
$827$	16.4462	+	16.4462i	0.571889	+	0.571889i	−0.360767	+	0.932656i	$0.617485\pi$
$828$	−7.26575	+	5.73667i	−0.252502	+	0.199363i
$829$	−38.5742	+	22.2708i	−1.33974	+	0.773498i	−0.986768	−	0.162137i	$-0.948161\pi$
$829$	−38.5742	+	22.2708i	−1.33974	+	0.773498i	−0.352969	+	0.935635i	$0.614828\pi$
$830$	11.8489	+	2.49349i	0.411282	+	0.0865504i
$831$	−13.2243	−	8.70444i	−0.458745	−	0.301954i
$832$	0.269576	+	3.59546i	0.00934585	+	0.124650i
$833$	−10.7981	+	10.7981i	−0.374133	+	0.374133i
$834$	0.668392	−	11.4064i	0.0231445	−	0.394971i
$835$	−1.73712	−	2.66311i	−0.0601156	−	0.0921607i
$836$	−0.468675	−	0.270589i	−0.0162095	−	0.00935853i
$837$	−11.6645	−	16.6962i	−0.403183	−	0.577106i
$838$	10.8857	−	2.91683i	0.376042	−	0.100760i
$839$	4.11460	−	7.12669i	0.142052	−	0.246041i	−0.786217	−	0.617950i	$-0.787963\pi$
$839$	4.11460	−	7.12669i	0.142052	−	0.246041i	0.928269	+	0.371909i	$0.121297\pi$
$840$	7.84847	−	13.4647i	0.270798	−	0.464577i
$841$	11.9500	−	20.6979i	0.412067	−	0.713722i
$842$	−9.58710	+	35.7795i	−0.330393	+	1.23304i
$843$	−8.49749	−	9.55535i	−0.292669	−	0.329104i
$844$		−	4.27847i		−	0.147271i
$845$	15.9630	−	24.2937i	0.549144	−	0.835728i
$846$	11.5689	+	26.8719i	0.397747	+	0.923876i
$847$	−6.92728	−	1.85616i	−0.238024	−	0.0637784i
$848$	−2.94376	−	0.788779i	−0.101089	−	0.0270868i
$849$	5.75151	+	11.4623i	0.197391	+	0.393385i
$850$	8.25647	−	0.901618i	0.283195	−	0.0309252i
$851$	9.76948	+	5.64041i	0.334894	+	0.193351i
$852$	25.0420	+	8.30783i	0.857924	+	0.284622i
$853$	−2.44288	−	2.44288i	−0.0836428	−	0.0836428i	0.664048	−	0.747690i	$-0.268837\pi$
$853$	−2.44288	−	2.44288i	−0.0836428	−	0.0836428i	−0.747690	+	0.664048i	$0.768837\pi$
$854$	24.2493	−	42.0011i	0.829796	−	1.43725i
$855$	−0.236526	−	1.17210i	−0.00808903	−	0.0400851i
$856$	0.355050	+	0.614964i	0.0121353	+	0.0210190i
$857$	−10.4488	−	10.4488i	−0.356925	−	0.356925i	0.505754	−	0.862678i	$-0.331215\pi$
$857$	−10.4488	−	10.4488i	−0.356925	−	0.356925i	−0.862678	+	0.505754i	$0.831215\pi$
$858$	−16.5725	−	9.21118i	−0.565777	−	0.314465i
$859$		−	23.2186i		−	0.792209i	−0.918205	−	0.396104i	$-0.870362\pi$
$859$		−	23.2186i		−	0.792209i	0.918205	−	0.396104i	$-0.129638\pi$
$860$	20.6808	−	13.4899i	0.705209	−	0.460002i
$861$	−55.1709	−	3.23291i	−1.88022	−	0.110177i
$862$	6.59415	+	24.6097i	0.224598	+	0.838210i
$863$	7.52681	−	7.52681i	0.256216	−	0.256216i	−0.567297	−	0.823513i	$-0.692011\pi$
$863$	7.52681	−	7.52681i	0.256216	−	0.256216i	0.823513	+	0.567297i	$0.192011\pi$
$864$	3.97694	+	3.34424i	0.135298	+	0.113773i
$865$	−19.4354	−	9.85332i	−0.660825	−	0.335023i
$866$			36.9000i			1.25391i
$867$	−7.76672	+	23.4109i	−0.263772	+	0.795077i
$868$	4.08236	−	15.2356i	0.138564	−	0.517130i
$869$	9.69196	+	16.7870i	0.328777	+	0.569459i
$870$	−2.22872	−	8.45779i	−0.0755606	−	0.286746i
$871$	51.0920	+	9.66518i	1.73119	+	0.327492i
$872$	−13.0249	−	13.0249i	−0.441080	−	0.441080i
$873$	32.1336	−	4.68368i	1.08756	−	0.158519i
$874$	−0.476352	+	0.275022i	−0.0161128	+	0.00930275i
$875$	15.8677	−	42.0994i	0.536425	−	1.42322i
$876$	−16.0263	−	10.5488i	−0.541477	−	0.356410i
$877$	−5.09752	−	19.0242i	−0.172131	−	0.642401i	−0.997023	−	0.0771104i	$-0.975431\pi$
$877$	−5.09752	−	19.0242i	−0.172131	−	0.642401i	0.824892	−	0.565291i	$-0.191236\pi$
$878$	−0.706991	−	2.63853i	−0.0238598	−	0.0890460i
$879$	−27.5389	−	18.1266i	−0.928864	−	0.611394i
$880$	6.45236	−	2.11096i	0.217509	−	0.0711603i
$881$	30.7601	−	17.7593i	1.03633	−	0.598327i	0.117540	−	0.993068i	$-0.462499\pi$
$881$	30.7601	−	17.7593i	1.03633	−	0.598327i	0.918792	+	0.394741i	$0.129166\pi$
$882$	−27.2911	+	3.97785i	−0.918938	+	0.133941i
$883$	−3.40418	−	3.40418i	−0.114560	−	0.114560i	0.647503	−	0.762063i	$-0.275813\pi$
$883$	−3.40418	−	3.40418i	−0.114560	−	0.114560i	−0.762063	+	0.647503i	$0.775813\pi$
$884$	5.88485	+	1.11325i	0.197929	+	0.0374426i
$885$	−28.1691	−	16.4195i	−0.946893	−	0.551936i
$886$	−9.43097	−	16.3349i	−0.316840	−	0.548782i
$887$	−12.3366	+	46.0409i	−0.414223	+	1.54590i	0.372164	+	0.928167i	$0.378616\pi$
$887$	−12.3366	+	46.0409i	−0.414223	+	1.54590i	−0.786387	+	0.617735i	$0.788051\pi$
$888$	1.99378	−	6.00977i	0.0669068	−	0.201675i
$889$			49.3829i			1.65625i
$890$	8.79348	−	17.3449i	0.294758	−	0.581403i
$891$	−26.1879	+	7.79982i	−0.877327	+	0.261304i
$892$	−15.6212	+	15.6212i	−0.523035	+	0.523035i
$893$	0.449908	+	1.67908i	0.0150556	+	0.0561882i
$894$	−19.3781	−	1.13552i	−0.648099	−	0.0379773i
$895$	−11.1691	−	2.35043i	−0.373341	−	0.0785662i
$896$			4.02407i			0.134435i
$897$	−16.5298	+	9.90630i	−0.551914	+	0.330762i
$898$	−16.7103	−	16.7103i	−0.557629	−	0.557629i
$899$	−4.42598	−	7.66601i	−0.147615	−	0.255676i
$900$	12.9277	+	7.60745i	0.430925	+	0.253582i
$901$	−2.53121	+	4.38418i	−0.0843268	+	0.146058i
$902$	−17.0227	−	17.0227i	−0.566793	−	0.566793i
$903$	−73.0493	−	24.2346i	−2.43093	−	0.806475i
$904$	9.97144	+	5.75701i	0.331645	+	0.191475i
$905$	−3.57762	+	3.98956i	−0.118924	+	0.132618i
$906$	−0.805617	−	1.60553i	−0.0267648	−	0.0533401i
$907$	7.22077	+	1.93480i	0.239762	+	0.0642440i	0.376699	−	0.926336i	$-0.377059\pi$
$907$	7.22077	+	1.93480i	0.239762	+	0.0642440i	−0.136937	+	0.990580i	$0.543726\pi$
$908$	−26.9999	−	7.23460i	−0.896023	−	0.240089i
$909$	16.2533	+	37.7527i	0.539088	+	1.25218i
$910$	19.7933	−	25.7057i	0.656140	−	0.852135i
$911$			46.1829i			1.53011i	0.643966	+	0.765054i	$0.277288\pi$
$911$			46.1829i			1.53011i	−0.643966	+	0.765054i	$0.722712\pi$
$912$	0.205165	+	0.230706i	0.00679369	+	0.00763945i
$913$	4.25513	−	15.8804i	0.140824	−	0.525564i
$914$	−10.6431	+	18.4344i	−0.352043	+	0.609757i
$915$	40.3270	+	23.5063i	1.33317	+	0.777093i
$916$	4.89402	−	8.47669i	0.161703	−	0.280078i
$917$	32.9180	−	8.82035i	1.08705	−	0.291274i
$918$	7.07566	−	4.94326i	0.233532	−	0.163152i
$919$	−8.58169	−	4.95464i	−0.283084	−	0.163438i	0.351735	−	0.936100i	$-0.385592\pi$
$919$	−8.58169	−	4.95464i	−0.283084	−	0.163438i	−0.634819	+	0.772661i	$0.718925\pi$
$920$	1.42094	−	6.75221i	0.0468470	−	0.222614i
$921$	−0.306223	+	5.22583i	−0.0100904	+	0.172197i
$922$	11.3925	−	11.3925i	0.375193	−	0.375193i
$923$	49.4847	+	23.8283i	1.62881	+	0.784319i
$924$	−17.6758	−	11.6345i	−0.581492	−	0.382747i
$925$	2.78624	−	18.0649i	0.0916110	−	0.593970i
$926$	−28.9381	+	16.7074i	−0.950964	+	0.549039i
$927$	−6.49225	+	5.12595i	−0.213233	+	0.168358i
$928$	1.59689	+	1.59689i	0.0524204	+	0.0524204i
$929$	11.4641	−	19.8564i	0.376124	−	0.651466i	−0.614371	−	0.789018i	$-0.710590\pi$
$929$	11.4641	−	19.8564i	0.376124	−	0.651466i	0.990495	+	0.137552i	$0.0439233\pi$
$930$	14.6471	+	3.98985i	0.480299	+	0.130832i
$931$	−1.63867			−0.0537052
$932$	−4.93953	+	1.32354i	−0.161800	+	0.0433541i
$933$	−23.8340	−	26.8011i	−0.780291	−	0.877430i
$934$	−17.0395	+	9.83776i	−0.557550	+	0.321901i
$935$	−0.613005	−	11.2604i	−0.0200474	−	0.368256i
$936$	7.31884	+	7.96458i	0.239224	+	0.260330i
$937$	−19.3039	+	19.3039i	−0.630630	+	0.630630i	−0.948226	−	0.317596i	$-0.897124\pi$
$937$	−19.3039	+	19.3039i	−0.630630	+	0.630630i	0.317596	+	0.948226i	$0.397124\pi$
$938$	56.0565	+	15.0203i	1.83031	+	0.490430i
$939$	−46.1460	−	2.70406i	−1.50592	−	0.0882437i
$940$	−19.4497	−	9.86056i	−0.634380	−	0.321616i
$941$			18.7355i			0.610759i	0.952231	+	0.305379i	$0.0987833\pi$
$941$			18.7355i			0.610759i	−0.952231	+	0.305379i	$0.901217\pi$
$942$	5.78625	+	1.91962i	0.188526	+	0.0625447i
$943$	−23.6343	+	6.33279i	−0.769638	+	0.206224i
$944$	8.41862			0.274003
$945$	−6.55178	−	46.2942i	−0.213130	−	1.50595i
$946$	−16.7628	−	29.0341i	−0.545007	−	0.943979i
$947$	11.5653	−	43.1622i	0.375821	−	1.40258i	−0.476321	−	0.879272i	$-0.658030\pi$
$947$	11.5653	−	43.1622i	0.375821	−	1.40258i	0.852142	−	0.523311i	$-0.175304\pi$
$948$	−2.23236	−	10.8306i	−0.0725035	−	0.351763i
$949$	−30.2741	−	26.0510i	−0.982739	−	0.845652i
$950$	0.694893	+	0.558068i	0.0225453	+	0.0181061i
$951$	40.6909	+	2.38441i	1.31949	+	0.0773197i
$952$	6.45666	+	1.73006i	0.209262	+	0.0560715i
$953$	0.675576	+	2.52128i	0.0218841	+	0.0816724i	0.976004	−	0.217751i	$-0.0698722\pi$
$953$	0.675576	+	2.52128i	0.0218841	+	0.0816724i	−0.954120	+	0.299424i	$0.903206\pi$
$954$	−8.39764	+	3.61535i	−0.271884	+	0.117051i
$955$	55.9063	−	18.2903i	1.80908	−	0.591861i
$956$	−10.1988	−	5.88830i	−0.329854	−	0.190441i
$957$	−11.6313	+	2.39739i	−0.375987	+	0.0774966i
$958$	30.9121	−	8.28287i	0.998725	−	0.267608i
$959$	−3.81260	−	6.60361i	−0.123115	−	0.213242i
$960$	−3.87295	−	0.0160570i	−0.124999	−	0.000518238i
$961$	−15.6362			−0.504392
$962$	5.71851	−	11.8757i	0.184372	−	0.382888i
$963$	1.97923	+	0.787918i	0.0637798	+	0.0253903i
$964$	−16.7785	+	9.68709i	−0.540400	+	0.312000i
$965$	27.3397	+	41.9134i	0.880096	+	1.34924i
$966$	−19.2235	+	9.64590i	−0.618506	+	0.310352i
$967$	32.1174	−	32.1174i	1.03283	−	1.03283i	0.0333843	−	0.999443i	$-0.489371\pi$
$967$	32.1174	−	32.1174i	1.03283	−	1.03283i	0.999443	−	0.0333843i	$-0.0106285\pi$
$968$	0.461264	+	1.72146i	0.0148256	+	0.0553298i
$969$	0.458376	−	0.230002i	0.0147252	−	0.00738874i
$970$	−16.1592	+	18.0199i	−0.518841	+	0.578584i
$971$	30.8451	+	17.8084i	0.989868	+	0.571500i	0.905235	−	0.424912i	$-0.139695\pi$
$971$	30.8451	+	17.8084i	0.989868	+	0.571500i	0.0846329	+	0.996412i	$0.473028\pi$
$972$	15.5810	+	0.480920i	0.499762	+	0.0154255i
$973$	6.87059	−	25.6414i	0.220261	−	0.822025i
$974$	−3.22767			−0.103421
$975$	24.6613	+	19.1525i	0.789795	+	0.613371i
$976$	−12.0521			−0.385780
$977$	−4.17726	+	15.5897i	−0.133642	+	0.498760i	−1.00000		0.000664463i	$-0.999788\pi$
$977$	−4.17726	+	15.5897i	−0.133642	+	0.498760i	0.866357	+	0.499424i	$0.166455\pi$
$978$	1.07029	+	1.20353i	0.0342240	+	0.0384845i
$979$	−22.8667	−	13.2021i	−0.730824	−	0.421941i
$980$	13.7240	−	15.3043i	0.438398	−	0.488878i
$981$	−54.8819	−	6.45410i	−1.75224	−	0.206064i
$982$	4.64187	+	17.3237i	0.148128	+	0.552822i
$983$	21.9610	−	21.9610i	0.700448	−	0.700448i	−0.264059	−	0.964507i	$-0.585061\pi$
$983$	21.9610	−	21.9610i	0.700448	−	0.700448i	0.964507	+	0.264059i	$0.0850612\pi$
$984$	6.15936	+	12.2751i	0.196353	+	0.391316i
$985$	−1.06257	−	1.62898i	−0.0338562	−	0.0519036i
$986$	3.24877	−	1.87568i	0.103462	−	0.0597337i
$987$	13.7215	+	66.5721i	0.436760	+	2.11901i
$988$	0.362057	+	0.530998i	0.0115186	+	0.0168933i
$989$	−34.0748			−1.08352
$990$	11.2681	−	16.9656i	0.358124	−	0.539202i
$991$	23.5580	+	40.8036i	0.748344	+	1.29617i	0.948616	+	0.316429i	$0.102484\pi$
$991$	23.5580	+	40.8036i	0.748344	+	1.29617i	−0.200272	+	0.979740i	$0.564183\pi$
$992$	−3.78611	+	1.01449i	−0.120209	+	0.0322100i
$993$	−0.768506	−	3.72853i	−0.0243878	−	0.118321i
$994$	53.0858	+	30.6491i	1.68378	+	0.972130i
$995$	27.6355	−	9.04122i	0.876103	−	0.286626i
$996$	−5.15670	+	7.83435i	−0.163396	+	0.248241i
$997$	−5.14454	−	19.1997i	−0.162929	−	0.608060i	−0.998295	−	0.0583659i	$-0.981411\pi$
$997$	−5.14454	−	19.1997i	−0.162929	−	0.608060i	0.835366	−	0.549694i	$-0.185256\pi$
$998$	6.94370	+	1.86056i	0.219799	+	0.0588950i
$999$	−6.47794	−	17.8569i	−0.204953	−	0.564967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bl.a.263.11	yes	112
3.2	odd	2	inner	390.2.bl.a.263.20	yes	112
5.2	odd	4	inner	390.2.bl.a.107.4	✓	112
13.9	even	3	inner	390.2.bl.a.113.16	yes	112
15.2	even	4	inner	390.2.bl.a.107.16	yes	112
39.35	odd	6	inner	390.2.bl.a.113.4	yes	112
65.22	odd	12	inner	390.2.bl.a.347.20	yes	112
195.152	even	12	inner	390.2.bl.a.347.11	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bl.a.107.4	✓	112	5.2	odd	4	inner
390.2.bl.a.107.16	yes	112	15.2	even	4	inner
390.2.bl.a.113.4	yes	112	39.35	odd	6	inner
390.2.bl.a.113.16	yes	112	13.9	even	3	inner
390.2.bl.a.263.11	yes	112	1.1	even	1	trivial
390.2.bl.a.263.20	yes	112	3.2	odd	2	inner
390.2.bl.a.347.11	yes	112	195.152	even	12	inner
390.2.bl.a.347.20	yes	112	65.22	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bl (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(1.29429 - 1.15100i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.49285 - 1.66475i) q^{5} +(0.776796 + 1.54809i) q^{6} +(1.04151 + 3.88695i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.350385 - 2.97947i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(1.29429 - 1.15100i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.49285 - 1.66475i) q^{5} +(0.776796 + 1.54809i) q^{6} +(1.04151 + 3.88695i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.350385 - 2.97947i) q^{9} +(1.22165 + 1.87285i) q^{10} +(2.62933 - 1.51804i) q^{11} +(-1.69639 + 0.349652i) q^{12} +(-3.59546 + 0.269576i) q^{13} -4.02407 q^{14} +(0.0160570 - 3.87295i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.60451 - 0.429927i) q^{17} +(2.78726 + 1.10959i) q^{18} +(0.154368 + 0.0891245i) q^{19} +(-2.12522 + 0.695289i) q^{20} +(5.82191 + 3.83208i) q^{21} +(0.785797 + 2.93263i) q^{22} +(2.98067 + 0.798669i) q^{23} +(0.101321 - 1.72908i) q^{24} +(-0.542780 - 4.97045i) q^{25} +(0.670183 - 3.54272i) q^{26} +(-2.97588 - 4.25960i) q^{27} +(1.04151 - 3.88695i) q^{28} +(-1.12917 - 1.95578i) q^{29} +(3.73683 + 1.01790i) q^{30} +3.91967 q^{31} +(-0.965926 + 0.258819i) q^{32} +(1.65585 - 4.99115i) q^{33} +1.66111i q^{34} +(8.02562 + 4.06880i) q^{35} +(-1.79318 + 2.40510i) q^{36} +(3.53114 + 0.946165i) q^{37} +(-0.126041 + 0.126041i) q^{38} +(-4.34329 + 4.48729i) q^{39} +(-0.121549 - 2.23276i) q^{40} +(-6.86687 + 3.96459i) q^{41} +(-5.20832 + 4.63172i) q^{42} +(-10.6661 + 2.85798i) q^{43} -3.03609 q^{44} +(-4.43699 - 5.03121i) q^{45} +(-1.54291 + 2.67240i) q^{46} +(6.89581 + 6.89581i) q^{47} +(1.64394 + 0.545389i) q^{48} +(-7.96150 + 4.59658i) q^{49} +(4.94157 + 0.762163i) q^{50} +(1.58186 - 2.40325i) q^{51} +(3.24855 + 1.56427i) q^{52} +(-2.15498 + 2.15498i) q^{53} +(4.88467 - 1.77201i) q^{54} +(1.39804 - 6.64338i) q^{55} +(3.48495 + 2.01204i) q^{56} +(0.302380 - 0.0623250i) q^{57} +(2.18139 - 0.584501i) q^{58} +(4.20931 - 7.29074i) q^{59} +(-1.95038 + 3.34604i) q^{60} +(-6.02607 + 10.4375i) q^{61} +(-1.01449 + 3.78611i) q^{62} +(11.9460 - 1.74120i) q^{63} -1.00000i q^{64} +(-4.91872 + 6.38797i) q^{65} +(4.39252 + 2.89123i) q^{66} +(-13.9303 - 3.73261i) q^{67} +(-1.60451 - 0.429927i) q^{68} +(4.77713 - 2.39705i) q^{69} +(-6.00735 + 6.69907i) q^{70} +(-13.1921 - 7.61644i) q^{71} +(-1.85904 - 2.35456i) q^{72} +(7.83281 + 7.83281i) q^{73} +(-1.82785 + 3.16593i) q^{74} +(-6.42352 - 5.80848i) q^{75} +(-0.0891245 - 0.154368i) q^{76} +(8.63902 + 8.63902i) q^{77} +(-3.21027 - 5.35670i) q^{78} +6.38451i q^{79} +(2.18814 + 0.460474i) q^{80} +(-8.75446 - 2.08792i) q^{81} +(-2.05222 - 7.65900i) q^{82} +(3.82902 - 3.82902i) q^{83} +(-3.12588 - 6.22963i) q^{84} +(1.67958 - 3.31293i) q^{85} -11.0424i q^{86} +(-3.71258 - 1.23167i) q^{87} +(0.785797 - 2.93263i) q^{88} +(-4.34840 - 7.53165i) q^{89} +(6.00816 - 2.98363i) q^{90} +(-4.79252 - 13.6946i) q^{91} +(-2.18200 - 2.18200i) q^{92} +(5.07320 - 4.51156i) q^{93} +(-8.44561 + 4.87608i) q^{94} +(0.378819 - 0.123934i) q^{95} +(-0.952289 + 1.44677i) q^{96} +(2.80156 + 10.4556i) q^{97} +(-2.37936 - 8.87990i) q^{98} +(-3.60168 - 8.36589i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q+O(q^{10}) \) 112 * q	\( 112 q + 24 q^{13} + 56 q^{16} - 16 q^{18} - 16 q^{21} + 24 q^{27} + 12 q^{30} - 80 q^{31} + 52 q^{33} - 8 q^{36} - 8 q^{37} - 16 q^{40} + 12 q^{42} - 8 q^{43} + 20 q^{45} - 8 q^{46} - 80 q^{51} + 24 q^{52} + 8 q^{55} - 96 q^{57} + 8 q^{58} - 32 q^{60} - 16 q^{61} - 16 q^{63} - 32 q^{66} + 40 q^{67} - 32 q^{70} - 8 q^{72} - 80 q^{73} - 64 q^{75} + 16 q^{76} - 36 q^{78} + 8 q^{81} - 16 q^{82} + 96 q^{85} - 8 q^{87} + 24 q^{90} - 32 q^{91} - 68 q^{93} - 40 q^{97}+O(q^{100}) \) 112 * q + 24 * q^13 + 56 * q^16 - 16 * q^18 - 16 * q^21 + 24 * q^27 + 12 * q^30 - 80 * q^31 + 52 * q^33 - 8 * q^36 - 8 * q^37 - 16 * q^40 + 12 * q^42 - 8 * q^43 + 20 * q^45 - 8 * q^46 - 80 * q^51 + 24 * q^52 + 8 * q^55 - 96 * q^57 + 8 * q^58 - 32 * q^60 - 16 * q^61 - 16 * q^63 - 32 * q^66 + 40 * q^67 - 32 * q^70 - 8 * q^72 - 80 * q^73 - 64 * q^75 + 16 * q^76 - 36 * q^78 + 8 * q^81 - 16 * q^82 + 96 * q^85 - 8 * q^87 + 24 * q^90 - 32 * q^91 - 68 * q^93 - 40 * q^97

Introduction

L-functions

Modular forms

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