LMFDB - Embedded newform 920.2.bb.a.11.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [920,2,Mod(11,920)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(920, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 11, 0, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("920.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bb (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [480,2,0,-4,-48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.19
Character	$\chi$	$=$	920.11
Dual form			920.2.bb.a.251.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.412411 - 1.35274i) q^{2} +(-0.429309 + 2.98591i) q^{3} +(-1.65983 + 1.11577i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(4.21623 - 0.650679i) q^{6} +(-1.41433 - 1.63223i) q^{7} +(2.19389 + 1.78517i) q^{8} +(-5.85288 - 1.71856i) q^{9} +(0.776818 + 1.18176i) q^{10} +(0.260861 - 0.405908i) q^{11} +(-2.61902 - 5.43513i) q^{12} +(-0.398969 - 0.345709i) q^{13} +(-1.62470 + 2.58638i) q^{14} +(-0.429309 - 2.98591i) q^{15} +(1.51009 - 3.70400i) q^{16} +(1.00123 - 0.457246i) q^{17} +(0.0890221 + 8.62620i) q^{18} +(-2.30954 - 1.05473i) q^{19} +(1.27825 - 1.53821i) q^{20} +(5.48088 - 3.52235i) q^{21} +(-0.656672 - 0.185477i) q^{22} +(-4.73300 - 0.773739i) q^{23} +(-6.27222 + 5.78438i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-0.303116 + 0.682277i) q^{26} +(3.88472 - 8.50636i) q^{27} +(4.16876 + 1.13115i) q^{28} +(7.04860 - 3.21899i) q^{29} +(-3.86212 + 1.81217i) q^{30} +(-4.41035 + 0.634113i) q^{31} +(-5.63334 - 0.515200i) q^{32} +(1.10002 + 0.953169i) q^{33} +(-1.03145 - 1.16583i) q^{34} +(1.81690 + 1.16765i) q^{35} +(11.6323 - 3.67797i) q^{36} +(3.42102 + 1.00450i) q^{37} +(-0.474301 + 3.55920i) q^{38} +(1.20354 - 1.04287i) q^{39} +(-2.60796 - 1.09477i) q^{40} +(5.07992 - 1.49160i) q^{41} +(-7.02521 - 5.96157i) q^{42} +(9.40966 + 1.35291i) q^{43} +(0.0199156 + 0.964802i) q^{44} +6.09997 q^{45} +(0.905274 + 6.72164i) q^{46} +1.55715i q^{47} +(10.4115 + 6.09917i) q^{48} +(0.332374 - 2.31171i) q^{49} +(-1.07829 - 0.915034i) q^{50} +(0.935459 + 3.18588i) q^{51} +(1.04796 + 0.128659i) q^{52} +(-0.419139 - 0.483712i) q^{53} +(-13.1090 - 1.74692i) q^{54} +(-0.135937 + 0.462959i) q^{55} +(-0.189087 - 6.10576i) q^{56} +(4.14084 - 6.44327i) q^{57} +(-7.26139 - 8.20741i) q^{58} +(7.29413 - 8.41787i) q^{59} +(4.04419 + 4.47710i) q^{60} +(-1.47679 - 10.2713i) q^{61} +(2.67667 + 5.70456i) q^{62} +(5.47285 + 11.9839i) q^{63} +(1.62632 + 7.83295i) q^{64} +(0.480205 + 0.219302i) q^{65} +(0.835735 - 1.88114i) q^{66} +(-0.346109 - 0.538557i) q^{67} +(-1.15169 + 1.87610i) q^{68} +(4.34224 - 13.8002i) q^{69} +(0.830220 - 2.93935i) q^{70} +(-3.06304 - 4.76619i) q^{71} +(-9.77266 - 14.2187i) q^{72} +(5.17201 - 11.3251i) q^{73} +(-0.0520336 - 5.04204i) q^{74} +(1.25315 + 2.74401i) q^{75} +(5.01029 - 0.826246i) q^{76} +(-1.03148 + 0.148304i) q^{77} +(-1.90709 - 1.19799i) q^{78} +(1.22567 - 1.41450i) q^{79} +(-0.405388 + 3.97940i) q^{80} +(8.33661 + 5.35761i) q^{81} +(-4.11277 - 6.25668i) q^{82} +(-2.13633 + 7.27566i) q^{83} +(-5.16720 + 11.9619i) q^{84} +(-0.831851 + 0.720803i) q^{85} +(-2.05052 - 13.2868i) q^{86} +(6.58558 + 22.4284i) q^{87} +(1.29692 - 0.424836i) q^{88} +(-17.3851 - 2.49959i) q^{89} +(-2.51570 - 8.25170i) q^{90} +1.14016i q^{91} +(8.71932 - 3.99669i) q^{92} -13.4412i q^{93} +(2.10643 - 0.642187i) q^{94} +(2.51314 + 0.361335i) q^{95} +(3.95679 - 16.5995i) q^{96} +(4.34339 + 14.7922i) q^{97} +(-3.26423 + 0.503760i) q^{98} +(-2.22437 + 1.92743i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 2 q^{2} - 4 q^{4} - 48 q^{5} + 5 q^{6} - q^{8} - 48 q^{9} + 2 q^{10} + 3 q^{12} + 32 q^{16} + 7 q^{18} - 4 q^{20} + 8 q^{21} + 4 q^{23} + 2 q^{24} - 48 q^{25} + 7 q^{26} + 12 q^{27} + 5 q^{30}+ \cdots - 98 q^{98}+O(q^{100}) $ 480 * q + 2 * q^2 - 4 * q^4 - 48 * q^5 + 5 * q^6 - q^8 - 48 * q^9 + 2 * q^10 + 3 * q^12 + 32 * q^16 + 7 * q^18 - 4 * q^20 + 8 * q^21 + 4 * q^23 + 2 * q^24 - 48 * q^25 + 7 * q^26 + 12 * q^27 + 5 * q^30 - 118 * q^32 - 23 * q^34 + 54 * q^36 + 8 * q^37 - 65 * q^38 + 43 * q^40 - 10 * q^42 - q^44 + 480 * q^45 - 184 * q^46 - 44 * q^48 - 48 * q^49 - 9 * q^50 - 7 * q^52 + 32 * q^53 - 27 * q^54 + 67 * q^56 - 40 * q^58 - 12 * q^59 + 14 * q^60 - 8 * q^61 - 128 * q^62 + 59 * q^64 + 88 * q^66 + 10 * q^68 - 20 * q^69 + 3 * q^72 - 11 * q^74 + 110 * q^76 + 118 * q^78 - 144 * q^79 - q^80 - 56 * q^81 - 59 * q^82 - 162 * q^84 - 18 * q^86 - 76 * q^88 + 7 * q^90 - 149 * q^92 + 168 * q^94 + 65 * q^96 - 98 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$-1$	$e\left(\frac{9}{22}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.412411	−	1.35274i	−0.291619	−	0.956535i
$2$	−0.412411	−	1.35274i	−0.291619	−	0.956535i
$3$	−0.429309	+	2.98591i	−0.247862	+	1.72392i	0.362664	+	0.931920i	$0.381867\pi$
$3$	−0.429309	+	2.98591i	−0.247862	+	1.72392i	−0.610525	+	0.791997i	$0.709042\pi$
$4$	−1.65983	+	1.11577i	−0.829917	+	0.557887i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$6$	4.21623	−	0.650679i	1.72127	−	0.265638i
$7$	−1.41433	−	1.63223i	−0.534568	−	0.616925i	0.422650	−	0.906293i	$-0.361100\pi$
$7$	−1.41433	−	1.63223i	−0.534568	−	0.616925i	−0.957218	+	0.289369i	$0.906555\pi$
$8$	2.19389	+	1.78517i	0.775658	+	0.631154i
$9$	−5.85288	−	1.71856i	−1.95096	−	0.572854i
$10$	0.776818	+	1.18176i	0.245651	+	0.373705i
$11$	0.260861	−	0.405908i	0.0786526	−	0.122386i	−0.799699	−	0.600402i	$-0.795007\pi$
$11$	0.260861	−	0.405908i	0.0786526	−	0.122386i	0.878351	+	0.478016i	$0.158644\pi$
$12$	−2.61902	−	5.43513i	−0.756046	−	1.56899i
$13$	−0.398969	−	0.345709i	−0.110654	−	0.0958823i	0.597776	−	0.801663i	$-0.296051\pi$
$13$	−0.398969	−	0.345709i	−0.110654	−	0.0958823i	−0.708431	+	0.705780i	$0.750596\pi$
$14$	−1.62470	+	2.58638i	−0.434219	+	0.691240i
$15$	−0.429309	−	2.98591i	−0.110847	−	0.770959i
$16$	1.51009	−	3.70400i	0.377524	−	0.926000i
$17$	1.00123	−	0.457246i	0.242834	−	0.110898i	−0.290281	−	0.956941i	$-0.593749\pi$
$17$	1.00123	−	0.457246i	0.242834	−	0.110898i	0.533115	+	0.846043i	$0.321021\pi$
$18$	0.0890221	+	8.62620i	0.0209827	+	2.03322i
$19$	−2.30954	−	1.05473i	−0.529844	−	0.241972i	0.132485	−	0.991185i	$-0.457705\pi$
$19$	−2.30954	−	1.05473i	−0.529844	−	0.241972i	−0.662329	+	0.749213i	$0.730432\pi$
$20$	1.27825	−	1.53821i	0.285825	−	0.343954i
$21$	5.48088	−	3.52235i	1.19603	−	0.768639i
$22$	−0.656672	−	0.185477i	−0.140003	−	0.0395439i
$23$	−4.73300	−	0.773739i	−0.986900	−	0.161336i
$23$	−4.73300	−	0.773739i	−0.986900	−	0.161336i
$24$	−6.27222	+	5.78438i	−1.28031	+	1.18073i
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	−0.303116	+	0.682277i	−0.0594459	+	0.133806i
$27$	3.88472	−	8.50636i	0.747615	−	1.63705i
$28$	4.16876	+	1.13115i	0.787821	+	0.213767i
$29$	7.04860	−	3.21899i	1.30889	−	0.597751i	0.365928	−	0.930643i	$-0.380752\pi$
$29$	7.04860	−	3.21899i	1.30889	−	0.597751i	0.942965	+	0.332892i	$0.108024\pi$
$30$	−3.86212	+	1.81217i	−0.705124	+	0.330855i
$31$	−4.41035	+	0.634113i	−0.792123	+	0.113890i	−0.526487	−	0.850183i	$-0.676491\pi$
$31$	−4.41035	+	0.634113i	−0.792123	+	0.113890i	−0.265636	+	0.964073i	$0.585582\pi$
$32$	−5.63334	−	0.515200i	−0.995844	−	0.0910753i
$33$	1.10002	+	0.953169i	0.191488	+	0.165925i
$34$	−1.03145	−	1.16583i	−0.176893	−	0.199939i
$35$	1.81690	+	1.16765i	0.307111	+	0.197369i
$36$	11.6323	−	3.67797i	1.93872	−	0.612995i
$37$	3.42102	+	1.00450i	0.562413	+	0.165139i	0.550568	−	0.834791i	$-0.314411\pi$
$37$	3.42102	+	1.00450i	0.562413	+	0.165139i	0.0118450	+	0.999930i	$0.496230\pi$
$38$	−0.474301	+	3.55920i	−0.0769417	+	0.577378i
$39$	1.20354	−	1.04287i	0.192720	−	0.166993i
$40$	−2.60796	−	1.09477i	−0.412355	−	0.173098i
$41$	5.07992	−	1.49160i	0.793351	−	0.232949i	0.140147	−	0.990131i	$-0.455243\pi$
$41$	5.07992	−	1.49160i	0.793351	−	0.232949i	0.653204	+	0.757182i	$0.273424\pi$
$42$	−7.02521	−	5.96157i	−1.08401	−	0.919890i
$43$	9.40966	+	1.35291i	1.43496	+	0.206316i	0.815521	−	0.578728i	$-0.196451\pi$
$43$	9.40966	+	1.35291i	1.43496	+	0.206316i	0.619440	+	0.785044i	$0.287360\pi$
$44$	0.0199156	+	0.964802i	0.00300238	+	0.145449i
$45$	6.09997			0.909330
$46$	0.905274	+	6.72164i	0.133475	+	0.991052i
$47$			1.55715i			0.227134i	0.993530	+	0.113567i	$0.0362276\pi$
$47$			1.55715i			0.227134i	−0.993530	+	0.113567i	$0.963772\pi$
$48$	10.4115	+	6.09917i	1.50277	+	0.880339i
$49$	0.332374	−	2.31171i	0.0474821	−	0.330245i
$50$	−1.07829	−	0.915034i	−0.152493	−	0.129405i
$51$	0.935459	+	3.18588i	0.130990	+	0.446112i
$52$	1.04796	+	0.128659i	0.145325	+	0.0178418i
$53$	−0.419139	−	0.483712i	−0.0575732	−	0.0664430i	0.726232	−	0.687449i	$-0.241270\pi$
$53$	−0.419139	−	0.483712i	−0.0575732	−	0.0664430i	−0.783806	+	0.621006i	$0.786724\pi$
$54$	−13.1090	−	1.74692i	−1.78391	−	0.237725i
$55$	−0.135937	+	0.462959i	−0.0183297	+	0.0624254i
$56$	−0.189087	−	6.10576i	−0.0252679	−	0.815917i
$57$	4.14084	−	6.44327i	0.548467	−	0.853432i
$58$	−7.26139	−	8.20741i	−0.953468	−	1.07769i
$59$	7.29413	−	8.41787i	0.949615	−	1.09591i	−0.0456737	−	0.998956i	$-0.514543\pi$
$59$	7.29413	−	8.41787i	0.949615	−	1.09591i	0.995289	−	0.0969575i	$-0.0309111\pi$
$60$	4.04419	+	4.47710i	0.522102	+	0.577992i
$61$	−1.47679	−	10.2713i	−0.189084	−	1.31511i	−0.834386	−	0.551181i	$-0.814177\pi$
$61$	−1.47679	−	10.2713i	−0.189084	−	1.31511i	0.645301	−	0.763928i	$-0.276732\pi$
$62$	2.67667	+	5.70456i	0.339938	+	0.724480i
$63$	5.47285	+	11.9839i	0.689514	+	1.50982i
$64$	1.62632	+	7.83295i	0.203290	+	0.979119i
$65$	0.480205	+	0.219302i	0.0595622	+	0.0272011i
$66$	0.835735	−	1.88114i	0.102872	−	0.231552i
$67$	−0.346109	−	0.538557i	−0.0422840	−	0.0657952i	0.819468	−	0.573125i	$-0.194269\pi$
$67$	−0.346109	−	0.538557i	−0.0422840	−	0.0657952i	−0.861752	+	0.507330i	$0.830633\pi$
$68$	−1.15169	+	1.87610i	−0.139663	+	0.227510i
$69$	4.34224	−	13.8002i	0.522744	−	1.66134i
$70$	0.830220	−	2.93935i	0.0992303	−	0.351319i
$71$	−3.06304	−	4.76619i	−0.363516	−	0.565642i	0.610529	−	0.791994i	$-0.290957\pi$
$71$	−3.06304	−	4.76619i	−0.363516	−	0.565642i	−0.974046	+	0.226351i	$0.927320\pi$
$72$	−9.77266	−	14.2187i	−1.15172	−	1.67569i
$73$	5.17201	−	11.3251i	0.605338	−	1.32551i	−0.320379	−	0.947289i	$-0.603810\pi$
$73$	5.17201	−	11.3251i	0.605338	−	1.32551i	0.925717	−	0.378216i	$-0.123463\pi$
$74$	−0.0520336	−	5.04204i	−0.00604878	−	0.586125i
$75$	1.25315	+	2.74401i	0.144701	+	0.316851i
$76$	5.01029	−	0.826246i	0.574720	−	0.0947769i
$77$	−1.03148	+	0.148304i	−0.117548	+	0.0169009i
$78$	−1.90709	−	1.19799i	−0.215935	−	0.135645i
$79$	1.22567	−	1.41450i	0.137899	−	0.159143i	−0.682600	−	0.730793i	$-0.739151\pi$
$79$	1.22567	−	1.41450i	0.137899	−	0.159143i	0.820498	+	0.571649i	$0.193696\pi$
$80$	−0.405388	+	3.97940i	−0.0453238	+	0.444911i
$81$	8.33661	+	5.35761i	0.926290	+	0.595291i
$82$	−4.11277	−	6.25668i	−0.454180	−	0.690935i
$83$	−2.13633	+	7.27566i	−0.234492	+	0.798607i	0.755212	+	0.655480i	$0.227534\pi$
$83$	−2.13633	+	7.27566i	−0.234492	+	0.798607i	−0.989704	+	0.143127i	$0.954284\pi$
$84$	−5.16720	+	11.9619i	−0.563788	+	1.30515i
$85$	−0.831851	+	0.720803i	−0.0902269	+	0.0781820i
$86$	−2.05052	−	13.2868i	−0.221113	−	1.43275i
$87$	6.58558	+	22.4284i	0.706049	+	2.40458i
$88$	1.29692	−	0.424836i	0.138252	−	0.0452877i
$89$	−17.3851	−	2.49959i	−1.84281	−	0.264956i	−0.869415	−	0.494082i	$-0.835504\pi$
$89$	−17.3851	−	2.49959i	−1.84281	−	0.264956i	−0.973397	+	0.229126i	$0.926413\pi$
$90$	−2.51570	−	8.25170i	−0.265178	−	0.869806i
$91$			1.14016i			0.119521i
$92$	8.71932	−	3.99669i	0.909052	−	0.416683i
$93$		−	13.4412i		−	1.39378i
$94$	2.10643	−	0.642187i	0.217261	−	0.0662365i
$95$	2.51314	+	0.361335i	0.257842	+	0.0370721i
$96$	3.95679	−	16.5995i	0.403838	−	1.69418i
$97$	4.34339	+	14.7922i	0.441005	+	1.50192i	0.817732	+	0.575600i	$0.195231\pi$
$97$	4.34339	+	14.7922i	0.441005	+	1.50192i	−0.376727	+	0.926324i	$0.622951\pi$
$98$	−3.26423	+	0.503760i	−0.329737	+	0.0508875i
$99$	−2.22437	+	1.92743i	−0.223557	+	0.193714i
$100$	−0.793108	+	1.83602i	−0.0793108	+	0.183602i
$101$	3.40016	−	11.5799i	0.338329	−	1.15224i	−0.598111	−	0.801413i	$-0.704082\pi$
$101$	3.40016	−	11.5799i	0.338329	−	1.15224i	0.936440	−	0.350828i	$-0.114100\pi$
$102$	3.92389	−	2.57933i	0.388523	−	0.255392i
$103$	−0.0633518	−	0.0407137i	−0.00624224	−	0.00401164i	0.537516	−	0.843254i	$-0.319363\pi$
$103$	−0.0633518	−	0.0407137i	−0.00624224	−	0.00401164i	−0.543758	+	0.839242i	$0.682999\pi$
$104$	−0.258146	−	1.47068i	−0.0253133	−	0.144212i
$105$	−4.26650	+	4.92381i	−0.416368	+	0.480514i
$106$	−0.481481	+	0.766477i	−0.0467656	+	0.0744468i
$107$	−7.18451	+	1.03298i	−0.694552	+	0.0998616i	−0.480544	−	0.876970i	$-0.659561\pi$
$107$	−7.18451	+	1.03298i	−0.694552	+	0.0998616i	−0.214008	+	0.976832i	$0.568652\pi$
$108$	3.04318	+	18.4536i	0.292830	+	1.77570i
$109$	1.79258	+	3.92520i	0.171698	+	0.375966i	0.975845	−	0.218465i	$-0.0701048\pi$
$109$	1.79258	+	3.92520i	0.171698	+	0.375966i	−0.804147	+	0.594430i	$0.797378\pi$
$110$	0.682327	−	0.00704159i	0.0650573	−	0.000671389i
$111$	−4.46803	+	9.78363i	−0.424087	+	0.928621i
$112$	−8.18155	+	2.77387i	−0.773084	+	0.262106i
$113$	−6.49012	−	10.0988i	−0.610539	−	0.950018i	−0.999585	−	0.0287994i	$-0.990832\pi$
$113$	−6.49012	−	10.0988i	−0.610539	−	0.950018i	0.389046	−	0.921218i	$-0.372805\pi$
$114$	−10.4238	−	2.94422i	−0.976281	−	0.275751i
$115$	4.75927	−	0.591044i	0.443804	−	0.0551151i
$116$	−8.10784	+	13.2076i	−0.752794	+	1.22630i
$117$	1.74100	+	2.70904i	0.160955	+	0.250451i
$118$	−14.3954	−	6.39546i	−1.32521	−	0.588750i
$119$	−2.16240	−	0.987536i	−0.198227	−	0.0905273i
$120$	4.38851	−	7.31716i	0.400614	−	0.667962i
$121$	4.47285	+	9.79418i	0.406623	+	0.890380i
$122$	−13.2854	+	6.23374i	−1.20281	+	0.564376i
$123$	2.27293	+	15.8086i	0.204943	+	1.42541i
$124$	6.61292	−	5.97348i	0.593858	−	0.536434i
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$	13.9540	−	12.3456i	1.24312	−	1.09984i
$127$	−7.73517	+	12.0362i	−0.686385	+	1.06804i	0.306832	+	0.951764i	$0.400731\pi$
$127$	−7.73517	+	12.0362i	−0.686385	+	1.06804i	−0.993217	+	0.116272i	$0.962905\pi$
$128$	9.92526	−	5.43040i	0.877277	−	0.479984i
$129$	−8.07931	+	27.5156i	−0.711344	+	2.42261i
$130$	0.0986179	−	0.740038i	0.00864936	−	0.0649056i
$131$	−4.39184	−	5.06845i	−0.383717	−	0.442833i	0.530729	−	0.847542i	$-0.321918\pi$
$131$	−4.39184	−	5.06845i	−0.383717	−	0.442833i	−0.914446	+	0.404709i	$0.867373\pi$
$132$	−2.88936	−	0.354732i	−0.251487	−	0.0308755i
$133$	1.54490	+	5.26144i	0.133960	+	0.456224i
$134$	−0.585790	+	0.690304i	−0.0506045	+	0.0596332i
$135$	−1.33085	+	9.25624i	−0.114541	+	0.796651i
$136$	3.01285	+	0.784217i	0.258350	+	0.0672461i
$137$		−	10.4500i		−	0.892806i	−0.894832	−	0.446403i	$-0.852705\pi$
$137$		−	10.4500i		−	0.892806i	0.894832	−	0.446403i	$-0.147295\pi$
$138$	−20.4589	−	0.182596i	−1.74157	−	0.0155436i
$139$	5.08260			0.431100			0.215550	−	0.976493i	$-0.430846\pi$
$139$	5.08260			0.431100			0.215550	+	0.976493i	$0.430846\pi$
$140$	−4.31858	+	0.0891446i	−0.364986	+	0.00753409i
$141$	−4.64952	−	0.668499i	−0.391560	−	0.0562978i
$142$	−5.18420	+	6.10914i	−0.435048	+	0.512668i
$143$	−0.244402	+	0.0717628i	−0.0204379	+	0.00600110i
$144$	−15.2040	+	19.0839i	−1.26700	+	1.59032i
$145$	−5.85619	+	5.07442i	−0.486330	+	0.421407i
$146$	−17.4530	−	2.32580i	−1.44442	−	0.192484i
$147$	6.75988	+	1.98488i	0.557546	+	0.163710i
$148$	−6.79913	+	2.14978i	−0.558885	+	0.176711i
$149$	−16.5149	−	10.6135i	−1.35296	−	0.869492i	−0.355093	−	0.934831i	$-0.615551\pi$
$149$	−16.5149	−	10.6135i	−1.35296	−	0.869492i	−0.997863	+	0.0653390i	$0.979187\pi$
$150$	3.19513	−	2.82685i	0.260881	−	0.230811i
$151$	−12.4236	−	10.7651i	−1.01102	−	0.876054i	−0.0187098	−	0.999825i	$-0.505956\pi$
$151$	−12.4236	−	10.7651i	−1.01102	−	0.876054i	−0.992311	+	0.123771i	$0.960501\pi$
$152$	−3.18400	−	6.43689i	−0.258257	−	0.522100i
$153$	−6.64588	+	0.955533i	−0.537287	+	0.0772502i
$154$	0.626012	+	1.33417i	0.0504455	+	0.107510i
$155$	4.05305	−	1.85097i	0.325549	−	0.148673i
$156$	−0.834062	+	3.07387i	−0.0667784	+	0.246106i
$157$	1.97474	−	4.32408i	0.157601	−	0.345099i	−0.814316	−	0.580422i	$-0.802888\pi$
$157$	1.97474	−	4.32408i	0.157601	−	0.345099i	0.971917	+	0.235323i	$0.0756149\pi$
$158$	−2.41893	−	1.07466i	−0.192440	−	0.0854955i
$159$	1.62426	−	1.04385i	0.128812	−	0.0827827i
$160$	5.55030	−	1.09277i	0.438790	−	0.0863907i
$161$	5.43113	+	8.81967i	0.428033	+	0.695088i
$162$	3.80937	−	13.4868i	0.299292	−	1.05963i
$163$	−18.0513	+	11.6009i	−1.41389	+	0.908651i	−0.999999	−	0.00167569i	$-0.999467\pi$
$163$	−18.0513	+	11.6009i	−1.41389	+	0.908651i	−0.413890	+	0.910327i	$0.635830\pi$
$164$	−6.76754	+	8.14386i	−0.528456	+	0.635928i
$165$	−1.32400	−	0.604649i	−0.103073	−	0.0470718i
$166$	10.7231	−	0.110662i	0.832278	−	0.00858907i
$167$	3.02919	−	1.38339i	0.234406	−	0.107050i	−0.294749	−	0.955575i	$-0.595236\pi$
$167$	3.02919	−	1.38339i	0.234406	−	0.107050i	0.529155	+	0.848525i	$0.322509\pi$
$168$	18.3124	+	2.05666i	1.41284	+	0.158675i
$169$	−1.81043	−	12.5918i	−0.139264	−	0.968602i
$170$	1.31813	+	0.828014i	0.101096	+	0.0635058i
$171$	11.7048	+	10.1423i	0.895091	+	0.775601i
$172$	−17.1280	+	8.25347i	−1.30600	+	0.629321i
$173$	1.52566	−	2.37398i	0.115994	−	0.180490i	−0.778402	−	0.627766i	$-0.783969\pi$
$173$	1.52566	−	2.37398i	0.115994	−	0.180490i	0.894396	+	0.447276i	$0.147606\pi$
$174$	27.6240	−	18.1584i	2.09417	−	1.37658i
$175$	−2.07226	−	0.608471i	−0.156648	−	0.0459961i
$176$	−1.10956	−	1.57919i	−0.0836361	−	0.119036i
$177$	22.0036	+	25.3935i	1.65389	+	1.90869i
$178$	3.78849	+	24.5484i	0.283959	+	1.83998i
$179$	−5.50605	+	1.61672i	−0.411541	+	0.120839i	−0.480948	−	0.876749i	$-0.659707\pi$
$179$	−5.50605	+	1.61672i	−0.411541	+	0.120839i	0.0694069	+	0.997588i	$0.477889\pi$
$180$	−10.1249	+	6.80619i	−0.754668	+	0.507304i
$181$	−1.55415	+	10.8094i	−0.115519	+	0.803455i	0.846874	+	0.531794i	$0.178482\pi$
$181$	−1.55415	+	10.8094i	−0.115519	+	0.803455i	−0.962393	+	0.271661i	$0.912427\pi$
$182$	1.54234	−	0.470214i	0.114326	−	0.0348546i
$183$	31.3033			2.31401
$184$	−9.00244	−	10.1467i	−0.663669	−	0.748027i
$185$	−3.56545			−0.262137
$186$	−18.1824	+	5.54329i	−1.33320	+	0.406453i
$187$	0.0755820	−	0.525685i	0.00552711	−	0.0384419i
$188$	−1.73743	−	2.58461i	−0.126715	−	0.188502i
$189$	−19.3786	+	5.69008i	−1.40959	+	0.413892i
$190$	−0.547653	−	3.54865i	−0.0397310	−	0.257446i
$191$	−7.84295	−	9.05125i	−0.567496	−	0.654925i	0.397373	−	0.917657i	$-0.369922\pi$
$191$	−7.84295	−	9.05125i	−0.567496	−	0.654925i	−0.964869	+	0.262732i	$0.915376\pi$
$192$	−24.0867	+	1.49330i	−1.73831	+	0.107769i
$193$	13.3549	+	3.92134i	0.961304	+	0.282264i	0.724486	−	0.689290i	$-0.242077\pi$
$193$	13.3549	+	3.92134i	0.961304	+	0.282264i	0.236818	+	0.971554i	$0.423895\pi$
$194$	18.2188	−	11.9760i	1.30804	−	0.859826i
$195$	−0.860974	+	1.33970i	−0.0616557	+	0.0959381i
$196$	2.02767	+	4.20792i	0.144833	+	0.300565i
$197$	−7.46744	−	6.47057i	−0.532033	−	0.461009i	0.346936	−	0.937889i	$-0.387222\pi$
$197$	−7.46744	−	6.47057i	−0.532033	−	0.461009i	−0.878968	+	0.476880i	$0.841768\pi$
$198$	3.52467	+	2.21411i	0.250487	+	0.157350i
$199$	−3.50663	−	24.3892i	−0.248579	−	1.72890i	−0.606441	−	0.795129i	$-0.707403\pi$
$199$	−3.50663	−	24.3892i	−0.248579	−	1.72890i	0.357862	−	0.933774i	$-0.383506\pi$
$200$	2.81076	+	0.315675i	0.198750	+	0.0223216i
$201$	1.75667	−	0.802244i	0.123906	−	0.0565860i
$202$	−17.0669	+	0.176130i	−1.20082	+	0.0123924i
$203$	−15.2232	−	6.95221i	−1.06846	−	0.487949i
$204$	−5.10743	−	4.24427i	−0.357592	−	0.297158i
$205$	−4.45392	+	2.86236i	−0.311075	+	0.199916i
$206$	−0.0289482	+	0.102490i	−0.00201692	+	0.00714079i
$207$	26.3720	+	12.6626i	1.83298	+	0.880109i
$208$	−1.88299	+	0.955729i	−0.130562	+	0.0662679i
$209$	−1.03059	+	0.662322i	−0.0712876	+	0.0458138i
$210$	8.42021	+	3.74085i	0.581050	+	0.258143i
$211$	−0.576404	+	1.26215i	−0.0396813	+	0.0868899i	−0.928435	−	0.371496i	$-0.878845\pi$
$211$	−0.576404	+	1.26215i	−0.0396813	+	0.0868899i	0.888753	+	0.458386i	$0.151572\pi$
$212$	1.23542	+	0.335217i	0.0848487	+	0.0230228i
$213$	15.5464	−	7.09981i	1.06522	−	0.486471i
$214$	4.36032	+	9.29279i	0.298066	+	0.635242i
$215$	−9.40966	+	1.35291i	−0.641734	+	0.0922674i
$216$	23.7080	−	11.7271i	1.61312	−	0.797930i
$217$	7.27273	+	6.30186i	0.493705	+	0.427798i
$218$	4.57051	−	4.04370i	0.309554	−	0.273874i
$219$	31.5954	+	20.3052i	2.13502	+	1.37210i
$220$	−0.290925	−	0.920110i	−0.0196142	−	0.0620338i
$221$	−0.557533	−	0.163706i	−0.0375037	−	0.0110121i
$222$	15.0774	+	2.00922i	1.01193	+	0.134850i
$223$	19.6080	−	16.9905i	1.31305	−	1.13777i	0.332158	−	0.943224i	$-0.392223\pi$
$223$	19.6080	−	16.9905i	1.31305	−	1.13777i	0.980894	−	0.194542i	$-0.0623221\pi$
$224$	7.12651	+	9.92357i	0.476160	+	0.663047i
$225$	−5.85288	+	1.71856i	−0.390192	+	0.114571i
$226$	−10.9845	+	12.9443i	−0.730680	+	0.861045i
$227$	10.4390	+	1.50090i	0.692860	+	0.0996182i	0.479744	−	0.877409i	$-0.340730\pi$
$227$	10.4390	+	1.50090i	0.692860	+	0.0996182i	0.213116	+	0.977027i	$0.431639\pi$
$228$	0.316134	+	15.3150i	0.0209365	+	1.01426i
$229$	4.84212			0.319976			0.159988	−	0.987119i	$-0.448854\pi$
$229$	4.84212			0.319976			0.159988	+	0.987119i	$0.448854\pi$
$230$	−2.76231	−	6.19432i	−0.182141	−	0.408442i
$231$		−	3.14358i		−	0.206832i
$232$	21.2103	+	5.52085i	1.39253	+	0.362462i
$233$	3.11432	−	21.6606i	0.204026	−	1.41903i	−0.588156	−	0.808748i	$-0.700146\pi$
$233$	3.11432	−	21.6606i	0.204026	−	1.41903i	0.792182	−	0.610285i	$-0.208945\pi$
$234$	2.94664	−	3.47236i	0.192628	−	0.226996i
$235$	−0.438700	−	1.49408i	−0.0286176	−	0.0974627i
$236$	−2.71459	+	22.1109i	−0.176705	+	1.43930i
$237$	3.69738	+	4.26700i	0.240170	+	0.277171i
$238$	−0.444084	+	3.33245i	−0.0287857	+	0.216010i
$239$	−0.419264	+	1.42788i	−0.0271199	+	0.0923621i	−0.971941	−	0.235225i	$-0.924417\pi$
$239$	−0.419264	+	1.42788i	−0.0271199	+	0.0923621i	0.944821	+	0.327587i	$0.106235\pi$
$240$	−11.7081	−	2.91885i	−0.755755	−	0.188411i
$241$	4.37954	−	6.81469i	0.282111	−	0.438973i	−0.671061	−	0.741402i	$-0.734161\pi$
$241$	4.37954	−	6.81469i	0.282111	−	0.438973i	0.953172	+	0.302429i	$0.0977976\pi$
$242$	11.4044	−	10.0899i	0.733100	−	0.648601i
$243$	−1.20470	+	1.39030i	−0.0772814	+	0.0891875i
$244$	13.9117	+	15.4009i	0.890607	+	0.985943i
$245$	0.332374	+	2.31171i	0.0212346	+	0.147690i
$246$	20.4476	−	9.59432i	1.30369	−	0.611712i
$247$	0.556805	+	1.21923i	0.0354286	+	0.0775779i
$248$	−10.8078	−	6.48206i	−0.686298	−	0.411611i
$249$	−20.8073	−	9.50238i	−1.31861	−	0.602189i
$250$	1.29241	+	0.574179i	0.0817391	+	0.0363143i
$251$	−3.99664	−	6.21890i	−0.252266	−	0.392533i	0.691906	−	0.721988i	$-0.256771\pi$
$251$	−3.99664	−	6.21890i	−0.252266	−	0.392533i	−0.944171	+	0.329455i	$0.893135\pi$
$252$	−22.4553	−	13.7848i	−1.41455	−	0.868358i
$253$	−1.54872	+	1.71933i	−0.0973675	+	0.108093i
$254$	19.4719	+	5.49985i	1.22178	+	0.345091i
$255$	−1.79513	−	2.79328i	−0.112416	−	0.174922i
$256$	−11.4392	−	11.1868i	−0.714952	−	0.699174i
$257$	10.8442	−	23.7456i	0.676445	−	1.48121i	−0.189922	−	0.981799i	$-0.560823\pi$
$257$	10.8442	−	23.7456i	0.676445	−	1.48121i	0.866367	−	0.499409i	$-0.166449\pi$
$258$	40.5536	−	0.418511i	2.52476	−	0.0260554i
$259$	−3.19889	−	7.00459i	−0.198769	−	0.435244i
$260$	−1.04175	+	0.171795i	−0.0646068	+	0.0106543i
$261$	−46.7867	+	6.72691i	−2.89602	+	0.416385i
$262$	−5.04508	+	8.03133i	−0.311686	+	0.496177i
$263$	−19.2852	+	22.2564i	−1.18918	+	1.37239i	−0.277893	+	0.960612i	$0.589636\pi$
$263$	−19.2852	+	22.2564i	−1.18918	+	1.37239i	−0.911286	+	0.411774i	$0.864909\pi$
$264$	0.711745	+	4.05487i	0.0438049	+	0.249560i
$265$	0.538439	+	0.346034i	0.0330760	+	0.0212567i
$266$	6.48024	−	4.25973i	0.397329	−	0.261181i
$267$	14.9271	−	50.8371i	0.913526	−	3.11118i
$268$	1.17539	+	0.507734i	0.0717985	+	0.0310148i
$269$	7.93844	−	6.87870i	0.484016	−	0.419402i	−0.378370	−	0.925655i	$-0.623515\pi$
$269$	7.93844	−	6.87870i	0.484016	−	0.419402i	0.862385	+	0.506253i	$0.168970\pi$
$270$	13.0702	−	2.01709i	0.795426	−	0.122756i
$271$	7.19233	+	24.4948i	0.436903	+	1.48796i	0.824359	+	0.566067i	$0.191536\pi$
$271$	7.19233	+	24.4948i	0.436903	+	1.48796i	−0.387456	+	0.921888i	$0.626646\pi$
$272$	−0.181688	−	4.39903i	−0.0110165	−	0.266731i
$273$	−3.40441	−	0.489480i	−0.206044	−	0.0296247i
$274$	−14.1362	+	4.30971i	−0.854000	+	0.260359i
$275$		−	0.482504i		−	0.0290961i
$276$	8.19047	+	27.7509i	0.493008	+	1.67041i
$277$			13.6362i			0.819319i	0.912238	+	0.409660i	$0.134353\pi$
$277$			13.6362i			0.819319i	−0.912238	+	0.409660i	$0.865647\pi$
$278$	−2.09612	−	6.87545i	−0.125717	−	0.412362i
$279$	26.9030	+	3.86807i	1.61064	+	0.231575i
$280$	1.90162	+	5.80517i	0.113644	+	0.346925i
$281$	−6.63895	−	22.6102i	−0.396046	−	1.34881i	−0.880522	−	0.474005i	$-0.842808\pi$
$281$	−6.63895	−	22.6102i	−0.396046	−	1.34881i	0.484476	−	0.874805i	$-0.339010\pi$
$282$	1.01320	+	6.56530i	0.0603355	+	0.390958i
$283$	0.179403	−	0.155454i	0.0106644	−	0.00924078i	−0.649512	−	0.760351i	$-0.725027\pi$
$283$	0.179403	−	0.155454i	0.0106644	−	0.00924078i	0.660177	+	0.751110i	$0.270481\pi$
$284$	10.4021	+	4.49341i	0.617253	+	0.266635i
$285$	−2.15783	+	7.34888i	−0.127819	+	0.435310i
$286$	0.197871	+	0.301017i	0.0117003	+	0.0177995i
$287$	−9.61934	−	6.18198i	−0.567812	−	0.364911i
$288$	32.0859	+	12.6966i	1.89068	+	0.748157i
$289$	−10.3392	+	11.9321i	−0.608191	+	0.701890i
$290$	9.27955	+	5.82918i	0.544914	+	0.342301i
$291$	−46.0330	+	6.61854i	−2.69850	+	0.387986i
$292$	4.05161	+	24.5686i	0.237102	+	1.43777i
$293$	10.8927	+	23.8516i	0.636356	+	1.39342i	0.903005	+	0.429631i	$0.141356\pi$
$293$	10.8927	+	23.8516i	0.636356	+	1.39342i	−0.266649	+	0.963794i	$0.585916\pi$
$294$	−0.102818	−	9.96298i	−0.00599644	−	0.581053i
$295$	−4.62708	+	10.1319i	−0.269399	+	0.589901i
$296$	5.71214	+	8.31088i	0.332012	+	0.483060i
$297$	−2.43943	−	3.79582i	−0.141550	−	0.220256i
$298$	−7.54641	+	26.7176i	−0.437152	+	1.54771i
$299$	1.62083	+	1.94494i	0.0937352	+	0.112479i
$300$	−5.14171	−	3.15637i	−0.296857	−	0.182233i
$301$	−11.1002	−	17.2722i	−0.639803	−	0.995552i
$302$	−9.43883	+	21.2457i	−0.543144	+	1.22255i
$303$	33.1168	+	15.1239i	1.90251	+	0.868847i
$304$	−7.39434	+	6.96178i	−0.424095	+	0.399286i
$305$	4.31074	+	9.43921i	0.246832	+	0.540488i
$306$	4.03343	+	8.59610i	0.230576	+	0.491406i
$307$	−0.734146	−	5.10610i	−0.0418999	−	0.291420i	−0.999988	−	0.00494582i	$-0.998426\pi$
$307$	−0.734146	−	5.10610i	−0.0418999	−	0.291420i	0.958088	−	0.286475i	$-0.0924834\pi$
$308$	1.54661	−	1.39706i	0.0881263	−	0.0796049i
$309$	0.148765	−	0.171684i	0.00846295	−	0.00976676i
$310$	−4.17541	−	4.71938i	−0.237147	−	0.268043i
$311$	−3.99032	+	6.20906i	−0.226270	+	0.352084i	−0.935763	−	0.352629i	$-0.885288\pi$
$311$	−3.99032	+	6.20906i	−0.226270	+	0.352084i	0.709493	+	0.704713i	$0.248924\pi$
$312$	4.50213	−	0.139425i	0.254883	−	0.00789339i
$313$	−9.59787	+	32.6874i	−0.542504	+	1.84760i	−0.0119808	+	0.999928i	$0.503814\pi$
$313$	−9.59787	+	32.6874i	−0.542504	+	1.84760i	−0.530523	+	0.847670i	$0.678004\pi$
$314$	−6.66377	−	0.888019i	−0.376059	−	0.0501138i
$315$	−8.62740	−	9.95655i	−0.486099	−	0.560988i
$316$	−0.456147	+	3.71540i	−0.0256603	+	0.209008i
$317$	−2.83066	−	9.64035i	−0.158986	−	0.541456i	−1.00000		0.000442633i	$-0.999859\pi$
$317$	−2.83066	−	9.64035i	−0.158986	−	0.541456i	0.841014	−	0.541013i	$-0.181959\pi$
$318$	−2.08193	−	1.76672i	−0.116749	−	0.0990725i
$319$	0.532094	−	3.70079i	0.0297915	−	0.207205i
$320$	−3.76724	−	7.05747i	−0.210595	−	0.394525i
$321$		−	21.8958i		−	1.22210i
$322$	9.69090	−	10.9843i	0.540053	−	0.612129i
$323$	−2.79465			−0.155498
$324$	−19.8153	+	0.409029i	−1.10085	+	0.0227238i
$325$	−0.522538	−	0.0751297i	−0.0289852	−	0.00416744i
$326$	23.1376	+	19.6345i	1.28147	+	1.08745i
$327$	−12.4899	+	3.66735i	−0.690691	+	0.202805i
$328$	13.8076	+	5.79613i	0.762395	+	0.320038i
$329$	2.54163	−	2.20233i	0.140124	−	0.121419i
$330$	−0.271904	+	2.04039i	−0.0149678	+	0.112320i
$331$	19.8081	+	5.81617i	1.08875	+	0.319686i	0.776374	−	0.630273i	$-0.217057\pi$
$331$	19.8081	+	5.81617i	1.08875	+	0.319686i	0.312376	+	0.949959i	$0.398875\pi$
$332$	−4.57205	−	14.4600i	−0.250924	−	0.793598i
$333$	−18.2965	−	11.7585i	−1.00264	−	0.644360i
$334$	−3.12064	−	3.52720i	−0.170754	−	0.193000i
$335$	0.483818	+	0.419231i	0.0264338	+	0.0229050i
$336$	−4.77013	−	25.6202i	−0.260232	−	1.39770i
$337$	−21.3091	+	3.06379i	−1.16078	+	0.166895i	−0.695674	−	0.718358i	$-0.744894\pi$
$337$	−21.3091	+	3.06379i	−1.16078	+	0.166895i	−0.465109	+	0.885253i	$0.653985\pi$
$338$	−16.2869	+	7.64206i	−0.885889	+	0.415673i
$339$	32.9405	−	15.0434i	1.78908	−	0.817046i
$340$	0.576480	−	2.12457i	0.0312640	−	0.115221i
$341$	−0.893099	+	1.95561i	−0.0483640	+	0.105902i
$342$	8.89272	−	20.0164i	0.480863	−	1.08237i
$343$	−16.9616	+	10.9006i	−0.915841	+	0.588575i
$344$	18.2286	+	19.7660i	0.982821	+	1.06571i
$345$	−0.278395	+	14.4645i	−0.0149883	+	0.778743i
$346$	−3.84059	−	1.08478i	−0.206471	−	0.0583179i
$347$	15.2256	−	9.78488i	0.817352	−	0.525280i	−0.0638838	−	0.997957i	$-0.520349\pi$
$347$	15.2256	−	9.78488i	0.817352	−	0.525280i	0.881236	+	0.472677i	$0.156712\pi$
$348$	−35.9561	−	29.8795i	−1.92745	−	1.60171i
$349$	19.6330	+	8.96610i	1.05093	+	0.479944i	0.864557	−	0.502534i	$-0.167599\pi$
$349$	19.6330	+	8.96610i	1.05093	+	0.479944i	0.186375	+	0.982479i	$0.440326\pi$
$350$	0.0315190	+	3.05418i	0.00168476	+	0.163253i
$351$	−4.49061	+	2.05079i	−0.239691	+	0.109463i
$352$	−1.67865	+	2.15222i	−0.0894721	+	0.114714i
$353$	−1.38940	−	9.66346i	−0.0739501	−	0.514334i	−0.992805	−	0.119739i	$-0.961794\pi$
$353$	−1.38940	−	9.66346i	−0.0739501	−	0.514334i	0.918855	−	0.394595i	$-0.129115\pi$
$354$	25.2764	−	40.2378i	1.34342	−	2.13861i
$355$	4.28176	+	3.71016i	0.227252	+	0.196915i
$356$	31.6453	−	15.2489i	1.67720	−	0.808190i
$357$	3.87703	−	6.03278i	0.205194	−	0.319289i
$358$	4.45777	+	6.78152i	0.235600	+	0.358414i
$359$	12.9111	+	3.79103i	0.681419	+	0.200083i	0.604082	−	0.796922i	$-0.293540\pi$
$359$	12.9111	+	3.79103i	0.681419	+	0.200083i	0.0773373	+	0.997005i	$0.475358\pi$
$360$	13.3827	+	10.8895i	0.705329	+	0.573927i
$361$	−8.22085	−	9.48736i	−0.432676	−	0.499335i
$362$	15.2633	−	2.35554i	0.802220	−	0.123804i
$363$	−31.1648	+	9.15081i	−1.63573	+	0.480293i
$364$	−1.27216	−	1.89247i	−0.0666792	−	0.0991924i
$365$	−1.77185	+	12.3235i	−0.0927430	+	0.645042i
$366$	−12.9098	−	42.3453i	−0.674808	−	2.21343i
$367$	2.48501			0.129716			0.0648581	−	0.997894i	$-0.479341\pi$
$367$	2.48501			0.129716			0.0648581	+	0.997894i	$0.479341\pi$
$368$	−10.0132	+	16.3626i	−0.521975	+	0.852961i
$369$	−32.2956			−1.68124
$370$	1.47043	+	4.82314i	0.0764441	+	0.250743i
$371$	−0.196726	+	1.36826i	−0.0102135	+	0.0710366i
$372$	14.9973	+	22.3101i	0.777574	+	1.15672i
$373$	−33.3038	+	9.77889i	−1.72441	+	0.506332i	−0.985817	−	0.167824i	$-0.946326\pi$
$373$	−33.3038	+	9.77889i	−1.72441	+	0.506332i	−0.738590	+	0.674155i	$0.764508\pi$
$374$	−0.742288	+	0.114555i	−0.0383828	+	0.00592351i
$375$	−1.97546	−	2.27981i	−0.102012	−	0.117729i
$376$	−2.77978	+	3.41622i	−0.143356	+	0.176178i
$377$	−3.92501	−	1.15249i	−0.202148	−	0.0593561i
$378$	15.6892	+	23.8677i	0.806965	+	1.22762i
$379$	17.2970	−	26.9146i	0.888487	−	1.38251i	−0.0352067	−	0.999380i	$-0.511209\pi$
$379$	17.2970	−	26.9146i	0.888487	−	1.38251i	0.923693	−	0.383132i	$-0.125155\pi$
$380$	−4.57456	+	2.20434i	−0.234670	+	0.113080i
$381$	−32.6181	−	28.2638i	−1.67108	−	1.44800i
$382$	−9.00950	+	14.3423i	−0.460966	+	0.733818i
$383$	1.09135	+	7.59048i	0.0557652	+	0.387855i	0.998521	+	0.0543709i	$0.0173153\pi$
$383$	1.09135	+	7.59048i	0.0557652	+	0.387855i	−0.942756	+	0.333484i	$0.891776\pi$
$384$	11.9537	+	31.9673i	0.610008	+	1.63132i
$385$	0.947916	−	0.432899i	0.0483103	−	0.0220626i
$386$	−0.203127	−	19.6829i	−0.0103389	−	1.00183i
$387$	−52.7486	−	24.0895i	−2.68136	−	1.22454i
$388$	−23.7141	−	19.7064i	−1.20390	−	1.00044i
$389$	−9.40313	+	6.04302i	−0.476757	+	0.306393i	−0.756860	−	0.653577i	$-0.773268\pi$
$389$	−9.40313	+	6.04302i	−0.476757	+	0.306393i	0.280103	+	0.959970i	$0.409631\pi$
$390$	2.16735	+	0.612169i	0.109748	+	0.0309984i
$391$	−5.09261	+	1.38946i	−0.257544	+	0.0702678i
$392$	4.85600	−	4.47831i	0.245265	−	0.226189i
$393$	17.0194	−	10.9377i	0.858516	−	0.551735i
$394$	−5.67337	+	12.7701i	−0.285820	+	0.643347i
$395$	−0.777511	+	1.70251i	−0.0391208	+	0.0856627i
$396$	1.54151	−	5.68110i	0.0774637	−	0.285486i
$397$	22.0159	−	10.0543i	1.10495	−	0.504612i	0.222456	−	0.974943i	$-0.428593\pi$
$397$	22.0159	−	10.0543i	1.10495	−	0.504612i	0.882490	+	0.470331i	$0.155866\pi$
$398$	−31.5461	+	14.8020i	−1.58127	+	0.741955i
$399$	−16.3734	+	2.35414i	−0.819696	+	0.117855i
$400$	−0.732161	−	3.93242i	−0.0366080	−	0.196621i
$401$	−17.1431	−	14.8545i	−0.856083	−	0.741800i	0.111658	−	0.993747i	$-0.464384\pi$
$401$	−17.1431	−	14.8545i	−0.856083	−	0.741800i	−0.967741	+	0.251946i	$0.918929\pi$
$402$	−1.80970	−	2.04547i	−0.0902597	−	0.102019i
$403$	1.97881	+	1.27171i	0.0985717	+	0.0633482i
$404$	7.27684	+	23.0145i	0.362036	+	1.14501i
$405$	−9.50833	−	2.79190i	−0.472473	−	0.138731i
$406$	−3.12633	+	23.4603i	−0.155157	+	1.16431i
$407$	1.30015	−	1.12658i	0.0644460	−	0.0558427i
$408$	−3.63505	+	8.65943i	−0.179962	+	0.428706i
$409$	28.0301	−	8.23037i	1.38600	−	0.406966i	0.498145	−	0.867094i	$-0.334015\pi$
$409$	28.0301	−	8.23037i	1.38600	−	0.406966i	0.887853	+	0.460128i	$0.152196\pi$
$410$	5.70889	+	4.84454i	0.281942	+	0.239255i
$411$	31.2029	+	4.48629i	1.53912	+	0.221293i
$412$	0.150581	−	0.00310831i	0.00741858	−	0.000153135i
$413$	−24.0562			−1.18373
$414$	6.25309	−	40.8967i	0.307323	−	2.00997i
$415$		−	7.58281i		−	0.372226i
$416$	2.06942	+	2.15305i	0.101462	+	0.105562i
$417$	−2.18201	+	15.1762i	−0.106853	+	0.743181i
$418$	1.32098	+	1.12098i	0.0646113	+	0.0548289i
$419$	0.562285	+	1.91497i	0.0274694	+	0.0935522i	0.972087	−	0.234621i	$-0.0753851\pi$
$419$	0.562285	+	1.91497i	0.0274694	+	0.0935522i	−0.944617	+	0.328174i	$0.893567\pi$
$420$	1.58783	−	12.9332i	0.0774780	−	0.631074i
$421$	0.532308	+	0.614316i	0.0259431	+	0.0299399i	0.768573	−	0.639762i	$-0.220967\pi$
$421$	0.532308	+	0.614316i	0.0259431	+	0.0299399i	−0.742630	+	0.669702i	$0.766422\pi$
$422$	1.94508	+	0.259202i	0.0946850	+	0.0126178i
$423$	2.67606	−	9.11382i	0.130114	−	0.443129i
$424$	−0.0560362	−	1.80945i	−0.00272136	−	0.0878746i
$425$	0.595081	−	0.925965i	0.0288657	−	0.0449159i
$426$	−16.0157	−	18.1023i	−0.775965	−	0.877058i
$427$	−14.6765	+	16.9376i	−0.710245	+	0.819666i
$428$	10.7725	−	9.73086i	0.520709	−	0.470359i
$429$	−0.109353	−	0.760570i	−0.00527963	−	0.0367207i
$430$	5.71079	+	12.1709i	0.275399	+	0.586934i
$431$	−5.50933	−	12.0638i	−0.265375	−	0.581091i	0.729295	−	0.684199i	$-0.239848\pi$
$431$	−5.50933	−	12.0638i	−0.265375	−	0.581091i	−0.994670	+	0.103109i	$0.967121\pi$
$432$	−25.6412	−	27.2344i	−1.23367	−	1.31032i
$433$	35.5534	+	16.2367i	1.70859	+	0.780285i	0.996976	+	0.0777109i	$0.0247611\pi$
$433$	35.5534	+	16.2367i	1.70859	+	0.780285i	0.711610	+	0.702574i	$0.247966\pi$
$434$	5.52544	−	12.4371i	0.265230	−	0.597000i
$435$	−12.6376	−	19.6646i	−0.605929	−	0.942843i
$436$	−7.35502	−	4.51506i	−0.352241	−	0.216232i
$437$	10.1150	+	6.77902i	0.483864	+	0.324285i
$438$	14.4374	−	51.1146i	0.689844	−	2.44235i
$439$	−3.58757	−	5.58236i	−0.171225	−	0.266432i	0.745026	−	0.667035i	$-0.232437\pi$
$439$	−3.58757	−	5.58236i	−0.171225	−	0.266432i	−0.916252	+	0.400603i	$0.868801\pi$
$440$	−1.12469	+	0.773011i	−0.0536176	+	0.0368519i
$441$	−5.91817	+	12.9590i	−0.281818	+	0.617095i
$442$	0.00848006	+	0.821714i	0.000403355	+	0.0390850i
$443$	−8.98524	−	19.6749i	−0.426902	−	0.934784i	−0.993819	−	0.111010i	$-0.964591\pi$
$443$	−8.98524	−	19.6749i	−0.426902	−	0.934784i	0.566918	−	0.823775i	$-0.308136\pi$
$444$	−3.50013	−	21.2245i	−0.166109	−	1.00727i
$445$	17.3851	−	2.49959i	0.824131	−	0.118492i
$446$	−31.0703	−	19.5176i	−1.47122	−	0.924185i
$447$	38.7810	−	44.7556i	1.83428	−	2.11687i
$448$	10.4850	−	13.7329i	0.495370	−	0.648820i
$449$	−4.30542	−	2.76693i	−0.203185	−	0.130579i	0.435091	−	0.900386i	$-0.356716\pi$
$449$	−4.30542	−	2.76693i	−0.203185	−	0.130579i	−0.638277	+	0.769807i	$0.720352\pi$
$450$	4.73857	+	7.20870i	0.223378	+	0.339821i
$451$	0.719703	−	2.45108i	0.0338895	−	0.115417i
$452$	22.0405	+	9.52086i	1.03670	+	0.447824i
$453$	37.4773	−	32.4743i	1.76084	−	1.52577i
$454$	−2.27482	−	14.7403i	−0.106763	−	0.691795i
$455$	−0.321219	−	1.09397i	−0.0150590	−	0.0512862i
$456$	20.5869	−	6.74373i	0.964070	−	0.315804i
$457$	−7.73970	−	1.11280i	−0.362048	−	0.0520546i	−0.0411094	−	0.999155i	$-0.513089\pi$
$457$	−7.73970	−	1.11280i	−0.362048	−	0.0520546i	−0.320939	+	0.947100i	$0.603998\pi$
$458$	−1.99695	−	6.55015i	−0.0933112	−	0.306068i
$459$		−	10.2931i		−	0.480440i
$460$	−7.24013	+	6.29131i	−0.337573	+	0.293334i
$461$			10.1583i			0.473120i	0.971617	+	0.236560i	$0.0760200\pi$
$461$			10.1583i			0.473120i	−0.971617	+	0.236560i	$0.923980\pi$
$462$	−4.25245	+	1.29645i	−0.197842	+	0.0603162i
$463$	−36.0086	−	5.17726i	−1.67346	−	0.240608i	−0.760701	−	0.649102i	$-0.775145\pi$
$463$	−36.0086	−	5.17726i	−1.67346	−	0.240608i	−0.912761	+	0.408494i	$0.866054\pi$
$464$	−1.27908	−	30.9690i	−0.0593796	−	1.43770i
$465$	3.78681	+	12.8967i	0.175609	+	0.598070i
$466$	−30.5856	+	4.72020i	−1.41685	+	0.218659i
$467$	−1.64133	+	1.42222i	−0.0759517	+	0.0658125i	−0.692009	−	0.721889i	$-0.743274\pi$
$467$	−1.64133	+	1.42222i	−0.0759517	+	0.0658125i	0.616058	+	0.787701i	$0.288729\pi$
$468$	−5.91245	−	2.55400i	−0.273303	−	0.118059i
$469$	−0.389533	+	1.32663i	−0.0179870	+	0.0612580i
$470$	−1.84018	+	1.20962i	−0.0848810	+	0.0557957i
$471$	12.0635	+	7.75276i	0.555858	+	0.357228i
$472$	31.0299	−	5.44663i	1.42827	−	0.250701i
$473$	3.00377	−	3.46654i	0.138114	−	0.159392i
$474$	4.24732	−	6.76136i	0.195086	−	0.310560i
$475$	−2.51314	+	0.361335i	−0.115311	+	0.0165792i
$476$	4.69109	−	0.773608i	0.215016	−	0.0354582i
$477$	1.62188	+	3.55143i	0.0742609	+	0.162609i
$478$	2.10447	−	0.0217180i	0.0962562	−	0.000993360i
$479$	−9.93263	+	21.7494i	−0.453834	+	0.993757i	0.535016	+	0.844842i	$0.320305\pi$
$479$	−9.93263	+	21.7494i	−0.453834	+	0.993757i	−0.988850	+	0.148915i	$0.952422\pi$
$480$	0.880106	+	17.0418i	0.0401712	+	0.777850i
$481$	−1.01762	−	1.58344i	−0.0463993	−	0.0721988i
$482$	−11.0247	−	3.11394i	−0.502162	−	0.141836i
$483$	−28.6664	+	12.4305i	−1.30437	+	0.565608i
$484$	−18.3523	−	11.2660i	−0.834195	−	0.512092i
$485$	−8.33491	−	12.9694i	−0.378469	−	0.588909i
$486$	2.37755	+	1.05627i	0.107848	+	0.0479136i
$487$	−3.00977	−	1.37452i	−0.136386	−	0.0622852i	0.346053	−	0.938215i	$-0.387522\pi$
$487$	−3.00977	−	1.37452i	−0.136386	−	0.0622852i	−0.482439	+	0.875930i	$0.660249\pi$
$488$	15.0962	−	25.1705i	0.683371	−	1.13942i
$489$	−26.8896	−	58.8800i	−1.21599	−	2.66265i
$490$	2.99008	−	1.40300i	0.135078	−	0.0633809i
$491$	−0.389973	−	2.71232i	−0.0175993	−	0.122405i	0.979128	−	0.203245i	$-0.0651489\pi$
$491$	−0.389973	−	2.71232i	−0.0175993	−	0.122405i	−0.996727	+	0.0808398i	$0.974240\pi$
$492$	−21.4115	−	23.7035i	−0.965304	−	1.06864i
$493$	5.58539	−	6.44589i	0.251553	−	0.290308i
$494$	1.41968	−	1.25604i	0.0638743	−	0.0565119i
$495$	1.59125	−	2.47603i	0.0715212	−	0.111289i
$496$	−4.31130	+	17.2935i	−0.193583	+	0.776502i
$497$	−3.44734	+	11.7406i	−0.154634	+	0.526637i
$498$	−4.27312	+	32.0659i	−0.191483	+	1.43691i
$499$	6.22175	+	7.18028i	0.278524	+	0.321433i	0.877725	−	0.479165i	$-0.159060\pi$
$499$	6.22175	+	7.18028i	0.278524	+	0.321433i	−0.599201	+	0.800599i	$0.704515\pi$
$500$	0.243714	−	1.98510i	0.0108992	−	0.0887762i
$501$	2.83021	+	9.63880i	0.126444	+	0.430630i
$502$	−6.76431	+	7.97118i	−0.301906	+	0.355771i
$503$	−0.641039	+	4.45852i	−0.0285825	+	0.198796i	−0.999109	−	0.0421976i	$-0.986564\pi$
$503$	−0.641039	+	4.45852i	−0.0285825	+	0.198796i	0.970527	+	0.240993i	$0.0774732\pi$
$504$	−9.38642	+	36.0613i	−0.418104	+	1.60630i
$505$			12.0688i			0.537052i
$506$	2.96452	+	1.38596i	0.131789	+	0.0616134i
$507$	38.3753			1.70431
$508$	−0.590544	−	28.6087i	−0.0262012	−	1.26931i
$509$	34.3259	+	4.93532i	1.52147	+	0.218754i	0.851785	−	0.523891i	$-0.175520\pi$
$509$	34.3259	+	4.93532i	1.52147	+	0.218754i	0.669685	+	0.742646i	$0.266429\pi$
$510$	−3.03826	+	3.58034i	−0.134536	+	0.158540i
$511$	−25.8002	+	7.57561i	−1.14133	+	0.335125i
$512$	−10.4152	+	20.0879i	−0.460290	+	0.887768i
$513$	−17.9438	+	15.5484i	−0.792239	+	0.686479i
$514$	−36.5940	−	4.87653i	−1.61409	−	0.215095i
$515$	0.0722560	+	0.0212163i	0.00318398	+	0.000934900i
$516$	−17.2909	−	54.6860i	−0.761189	−	2.40742i
$517$	0.632060	+	0.406200i	0.0277980	+	0.0178647i
$518$	−8.15616	+	7.21606i	−0.358361	+	0.317055i
$519$	6.43351	+	5.57467i	0.282400	+	0.244701i
$520$	0.662026	+	1.33838i	0.0290318	+	0.0586916i
$521$	−17.3929	+	2.50073i	−0.761998	+	0.109559i	−0.512349	−	0.858777i	$-0.671225\pi$
$521$	−17.3929	+	2.50073i	−0.761998	+	0.109559i	−0.249650	+	0.968336i	$0.580315\pi$
$522$	28.3951	+	60.5161i	1.24282	+	2.64872i
$523$	−4.36905	+	1.99528i	−0.191045	+	0.0872474i	−0.508641	−	0.860979i	$-0.669852\pi$
$523$	−4.36905	+	1.99528i	−0.191045	+	0.0872474i	0.317596	+	0.948226i	$0.397125\pi$
$524$	12.9450	+	3.51249i	0.565504	+	0.153444i
$525$	2.70648	−	5.92637i	0.118121	−	0.258648i
$526$	38.0606	+	16.9092i	1.65952	+	0.737277i
$527$	−4.12583	+	2.65151i	−0.179724	+	0.115501i
$528$	5.19166	−	2.63508i	0.225938	−	0.114677i
$529$	21.8027	+	7.32422i	0.947942	+	0.318445i
$530$	0.246037	−	0.871078i	0.0106871	−	0.0378372i
$531$	−57.1583	+	36.7334i	−2.48046	+	1.59409i
$532$	−8.43485	−	7.00935i	−0.365697	−	0.303894i
$533$	−2.54239	−	1.16107i	−0.110123	−	0.0502916i
$534$	−74.9258	+	0.773231i	−3.24235	+	0.0334610i
$535$	6.60246	−	3.01524i	0.285449	−	0.130360i
$536$	0.202090	−	1.79940i	0.00872895	−	0.0777222i
$537$	−2.46359	−	17.1346i	−0.106312	−	0.739414i
$538$	−12.5790	−	7.90183i	−0.542320	−	0.340672i
$539$	−0.851640	−	0.737950i	−0.0366827	−	0.0317858i
$540$	−8.11890	−	16.8487i	−0.349382	−	0.725055i
$541$	−6.25994	+	9.74066i	−0.269136	+	0.418784i	−0.949346	−	0.314234i	$-0.898252\pi$
$541$	−6.25994	+	9.74066i	−0.269136	+	0.418784i	0.680210	+	0.733018i	$0.261889\pi$
$542$	30.1691	−	19.8313i	1.29587	−	0.851829i
$543$	−31.6086	−	9.28113i	−1.35646	−	0.398291i
$544$	−5.87584	+	2.05999i	−0.251924	+	0.0883213i
$545$	−2.82582	−	3.26117i	−0.121045	−	0.139693i
$546$	0.741876	+	4.80716i	0.0317493	+	0.205727i
$547$	−33.9732	+	9.97543i	−1.45259	+	0.426519i	−0.910397	−	0.413736i	$-0.864224\pi$
$547$	−33.9732	+	9.97543i	−1.45259	+	0.426519i	−0.542192	+	0.840254i	$0.682406\pi$
$548$	11.6599	+	17.3453i	0.498085	+	0.740955i
$549$	−9.00841	+	62.6548i	−0.384469	+	2.67404i
$550$	−0.652704	+	0.198990i	−0.0278314	+	0.00848497i
$551$	−19.6742			−0.838148
$552$	34.1621	−	22.5244i	1.45403	−	0.958702i
$553$	−4.04229			−0.171896
$554$	18.4463	−	5.62372i	0.783707	−	0.238929i
$555$	1.53068	−	10.6461i	0.0649737	−	0.451902i
$556$	−8.43626	+	5.67103i	−0.357777	+	0.240505i
$557$	10.2551	−	3.01117i	0.434523	−	0.127588i	−0.0571534	−	0.998365i	$-0.518202\pi$
$557$	10.2551	−	3.01117i	0.434523	−	0.127588i	0.491677	+	0.870778i	$0.336384\pi$
$558$	−5.86261	−	37.9882i	−0.248184	−	1.60817i
$559$	−3.28645	−	3.79277i	−0.139002	−	0.160417i
$560$	7.06865	−	4.96652i	0.298705	−	0.209874i
$561$	1.53720	+	0.451362i	0.0649006	+	0.0190565i
$562$	−27.8478	+	18.3055i	−1.17469	+	0.772171i
$563$	−3.30995	+	5.15038i	−0.139498	+	0.217063i	−0.903972	−	0.427591i	$-0.859362\pi$
$563$	−3.30995	+	5.15038i	−0.139498	+	0.217063i	0.764474	+	0.644654i	$0.222999\pi$
$564$	8.46332	−	4.07821i	0.356370	−	0.171724i
$565$	9.07240	+	7.86128i	0.381679	+	0.330726i
$566$	−0.284278	−	0.178576i	−0.0119491	−	0.00750611i
$567$	−3.04590	−	21.1847i	−0.127916	−	0.889674i
$568$	1.78848	−	15.9246i	0.0750429	−	0.668180i
$569$	4.58157	−	2.09233i	0.192069	−	0.0877151i	−0.317059	−	0.948406i	$-0.602695\pi$
$569$	4.58157	−	2.09233i	0.192069	−	0.0877151i	0.509128	+	0.860691i	$0.329968\pi$
$570$	10.8311	−	0.111776i	0.453663	−	0.00468179i
$571$	1.14558	+	0.523169i	0.0479411	+	0.0218939i	0.439241	−	0.898369i	$-0.355247\pi$
$571$	1.14558	+	0.523169i	0.0479411	+	0.0218939i	−0.391300	+	0.920263i	$0.627975\pi$
$572$	0.325595	−	0.391811i	0.0136138	−	0.0163825i
$573$	30.3933	−	19.5326i	1.26970	−	0.815985i
$574$	−4.39551	+	15.5620i	−0.183465	+	0.649547i
$575$	−4.39997	+	1.90794i	−0.183491	+	0.0795668i
$576$	3.94273	−	48.6402i	0.164280	−	2.02668i
$577$	29.1215	−	18.7152i	1.21234	−	0.779125i	0.231293	−	0.972884i	$-0.425704\pi$
$577$	29.1215	−	18.7152i	1.21234	−	0.779125i	0.981049	+	0.193759i	$0.0620680\pi$
$578$	20.4051	+	9.06541i	0.848742	+	0.377071i
$579$	−17.4421	+	38.1930i	−0.724871	+	1.58725i
$580$	4.05840	−	14.9569i	0.168516	−	0.621050i
$581$	14.8970	−	6.80324i	0.618032	−	0.282246i
$582$	27.9377	+	59.5413i	1.15806	+	2.46806i
$583$	−0.305680	+	0.0439501i	−0.0126600	+	0.00182023i
$584$	31.5641	−	15.6132i	1.30613	−	0.646078i
$585$	−2.43370	−	2.10881i	−0.100621	−	0.0871887i
$586$	27.7728	−	24.5716i	1.14729	−	1.01505i
$587$	−19.2146	−	12.3484i	−0.793070	−	0.509675i	0.0802778	−	0.996773i	$-0.474419\pi$
$587$	−19.2146	−	12.3484i	−0.793070	−	0.509675i	−0.873348	+	0.487098i	$0.838056\pi$
$588$	−13.4350	+	4.24793i	−0.554048	+	0.175182i
$589$	10.8547	+	3.18723i	0.447260	+	0.131327i
$590$	15.6141	+	2.08075i	0.642823	+	0.0856629i
$591$	22.5264	−	19.5192i	0.926612	−	0.802914i
$592$	8.88675	−	11.1546i	0.365243	−	0.458450i
$593$	2.90921	−	0.854220i	0.119467	−	0.0350786i	−0.221453	−	0.975171i	$-0.571080\pi$
$593$	2.90921	−	0.854220i	0.119467	−	0.0350786i	0.340919	+	0.940092i	$0.389262\pi$
$594$	−4.12873	+	4.86536i	−0.169404	+	0.199628i
$595$	2.35303	+	0.338315i	0.0964648	+	0.0138696i
$596$	39.2543	−	0.810292i	1.60792	−	0.0331909i
$597$	74.3294			3.04210
$598$	1.96255	−	2.99469i	0.0802548	−	0.122462i
$599$			16.2467i			0.663823i	0.943311	+	0.331911i	$0.107694\pi$
$599$			16.2467i			0.663823i	−0.943311	+	0.331911i	$0.892306\pi$
$600$	−2.14926	+	8.25715i	−0.0877432	+	0.337097i
$601$	−4.84423	+	33.6924i	−0.197600	+	1.37434i	0.613621	+	0.789601i	$0.289712\pi$
$601$	−4.84423	+	33.6924i	−0.197600	+	1.37434i	−0.811221	+	0.584740i	$0.801197\pi$
$602$	−18.7870	+	22.1389i	−0.765702	+	0.902315i
$603$	1.10019	+	3.74692i	0.0448034	+	0.152586i
$604$	32.6326	+	4.00637i	1.32780	+	0.163017i
$605$	−7.05101	−	8.13730i	−0.286664	−	0.330828i
$606$	6.80106	−	51.0358i	0.276274	−	2.07319i
$607$	6.33804	−	21.5854i	0.257253	−	0.876123i	−0.725030	−	0.688718i	$-0.758174\pi$
$607$	6.33804	−	21.5854i	0.257253	−	0.876123i	0.982283	−	0.187405i	$-0.0600078\pi$
$608$	12.4670	+	7.13153i	0.505605	+	0.289222i
$609$	27.2941	−	42.4705i	1.10601	−	1.72099i
$610$	10.9910	−	9.72417i	0.445014	−	0.393720i
$611$	0.538321	−	0.621255i	0.0217781	−	0.0251333i
$612$	9.96489	−	9.00132i	0.402807	−	0.363857i
$613$	5.45865	+	37.9657i	0.220473	+	1.53342i	0.736256	+	0.676703i	$0.236592\pi$
$613$	5.45865	+	37.9657i	0.220473	+	1.53342i	−0.515783	+	0.856719i	$0.672499\pi$
$614$	−6.60447	+	3.09893i	−0.266535	+	0.125062i
$615$	−6.63464	−	14.5278i	−0.267535	−	0.585819i
$616$	−2.52770	−	1.51601i	−0.101844	−	0.0610816i
$617$	28.7781	+	13.1425i	1.15856	+	0.529098i	0.899568	−	0.436780i	$-0.143881\pi$
$617$	28.7781	+	13.1425i	1.15856	+	0.529098i	0.258995	+	0.965879i	$0.416609\pi$
$618$	−0.293597	−	0.130437i	−0.0118102	−	0.00524693i
$619$	16.2315	+	25.2568i	0.652401	+	1.01516i	0.997075	+	0.0764327i	$0.0243530\pi$
$619$	16.2315	+	25.2568i	0.652401	+	1.01516i	−0.344674	+	0.938722i	$0.612011\pi$
$620$	−4.66213	+	7.59459i	−0.187236	+	0.305006i
$621$	−24.9681	+	37.2549i	−1.00194	+	1.49499i
$622$	10.0449	+	2.83720i	0.402765	+	0.113761i
$623$	20.5084	+	31.9117i	0.821651	+	1.27851i
$624$	−2.04534	−	6.03273i	−0.0818790	−	0.241503i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	48.1759	−	0.497173i	1.92550	−	0.0198710i
$627$	−1.53519	−	3.36160i	−0.0613096	−	0.134249i
$628$	1.54696	+	9.38061i	0.0617302	+	0.374327i
$629$	3.88453	−	0.558511i	0.154886	−	0.0222693i
$630$	−9.91063	+	15.7769i	−0.394849	+	0.628565i
$631$	25.8865	−	29.8746i	1.03052	−	1.18929i	0.0488334	−	0.998807i	$-0.484450\pi$
$631$	25.8865	−	29.8746i	1.03052	−	1.18929i	0.981691	−	0.190481i	$-0.0610049\pi$
$632$	5.21411	−	0.915225i	0.207406	−	0.0364057i
$633$	−3.52121	−	2.26294i	−0.139955	−	0.0899439i
$634$	−11.8735	+	7.80495i	−0.471558	+	0.309974i
$635$	4.03086	−	13.7279i	0.159960	−	0.544773i
$636$	−1.53130	+	3.54493i	−0.0607202	+	0.140566i
$637$	−0.931787	+	0.807398i	−0.0369187	+	0.0319903i
$638$	−5.22567	+	0.806463i	−0.206886	+	0.0319282i
$639$	9.73664	+	33.1600i	0.385176	+	1.31179i
$640$	−7.99330	+	8.00670i	−0.315963	+	0.316492i
$641$	−28.7879	−	4.13908i	−1.13705	−	0.163484i	−0.452029	−	0.892003i	$-0.649300\pi$
$641$	−28.7879	−	4.13908i	−1.13705	−	0.163484i	−0.685025	+	0.728520i	$0.740209\pi$
$642$	−29.6194	+	9.03006i	−1.16898	+	0.356388i
$643$		−	27.9770i		−	1.10330i	−0.834075	−	0.551652i	$-0.813998\pi$
$643$		−	27.9770i		−	1.10330i	0.834075	−	0.551652i	$-0.186002\pi$
$644$	−18.8555	−	8.57927i	−0.743012	−	0.338071i
$645$		−	28.6772i		−	1.12917i
$646$	1.15254	+	3.78044i	0.0453462	+	0.148739i
$647$	−32.3132	−	4.64594i	−1.27036	−	0.182651i	−0.526034	−	0.850464i	$-0.676322\pi$
$647$	−32.3132	−	4.64594i	−1.27036	−	0.182651i	−0.744329	+	0.667813i	$0.767231\pi$
$648$	8.72536	+	26.6363i	0.342764	+	1.04637i
$649$	−1.51413	−	5.15664i	−0.0594347	−	0.202416i
$650$	0.113870	+	0.737845i	0.00446633	+	0.0289407i
$651$	−21.9390	+	19.0103i	−0.859859	+	0.745072i
$652$	17.0182	−	39.3967i	0.666485	−	1.54290i
$653$	−13.4885	+	45.9377i	−0.527847	+	1.79768i	0.0718044	+	0.997419i	$0.477124\pi$
$653$	−13.4885	+	45.9377i	−0.527847	+	1.79768i	−0.599651	+	0.800262i	$0.704694\pi$
$654$	10.1120	+	15.3831i	0.395409	+	0.601528i
$655$	5.64189	+	3.62582i	0.220447	+	0.141673i
$656$	2.14628	−	21.0685i	0.0837981	−	0.822586i
$657$	−49.7341	+	57.3962i	−1.94031	+	2.23924i
$658$	−4.02739	−	2.52990i	−0.157004	−	0.0986259i
$659$	1.37730	−	0.198026i	0.0536522	−	0.00771402i	−0.115436	−	0.993315i	$-0.536827\pi$
$659$	1.37730	−	0.198026i	0.0536522	−	0.00771402i	0.169089	+	0.985601i	$0.445918\pi$
$660$	2.87226	−	0.473665i	0.111803	−	0.0184374i
$661$	2.23170	+	4.88675i	0.0868032	+	0.190072i	0.948055	−	0.318105i	$-0.103047\pi$
$661$	2.23170	+	4.88675i	0.0868032	+	0.190072i	−0.861252	+	0.508178i	$0.830319\pi$
$662$	−0.301280	−	29.1939i	−0.0117096	−	1.13465i
$663$	0.728167	−	1.59446i	0.0282797	−	0.0619238i
$664$	−17.6752	+	12.1483i	−0.685929	+	0.471445i
$665$	−2.96464	−	4.61306i	−0.114964	−	0.178887i
$666$	−8.36050	+	29.5999i	−0.323963	+	1.14697i
$667$	−35.8517	+	9.78171i	−1.38818	+	0.378749i
$668$	−3.48441	+	5.67608i	−0.134816	+	0.219614i
$669$	42.3141	+	65.8421i	1.63596	+	2.54560i
$670$	0.367580	−	0.827378i	0.0142009	−	0.0319644i
$671$	−4.55446	−	2.07995i	−0.175823	−	0.0802956i
$672$	−32.6904	+	17.0188i	−1.26106	+	0.656516i
$673$	−18.8281	−	41.2279i	−0.725772	−	1.58922i	−0.805635	−	0.592412i	$-0.798176\pi$
$673$	−18.8281	−	41.2279i	−0.725772	−	1.58922i	0.0798633	−	0.996806i	$-0.474552\pi$
$674$	12.9327	+	27.5623i	0.498147	+	1.06166i
$675$	−1.33085	−	9.25624i	−0.0512243	−	0.356273i
$676$	17.0547	+	18.8803i	0.655948	+	0.726165i
$677$	22.1074	−	25.5134i	0.849658	−	0.980558i	−0.150309	−	0.988639i	$-0.548027\pi$
$677$	22.1074	−	25.5134i	0.849658	−	0.980558i	0.999967	+	0.00808129i	$0.00257238\pi$
$678$	−33.9349	−	38.3560i	−1.30326	−	1.47305i
$679$	18.0013	−	28.0106i	0.690827	−	1.07495i
$680$	−3.11175	+	0.0963667i	−0.119330	+	0.00369549i
$681$	−8.96311	+	30.5255i	−0.343467	+	1.16974i
$682$	3.01377	+	0.401617i	0.115403	+	0.0153787i
$683$	15.2167	+	17.5610i	0.582252	+	0.671954i	0.968087	−	0.250613i	$-0.0806323\pi$
$683$	15.2167	+	17.5610i	0.582252	+	0.671954i	−0.385836	+	0.922568i	$0.626087\pi$
$684$	−30.7446	−	3.77457i	−1.17555	−	0.144324i
$685$	2.94411	+	10.0267i	0.112489	+	0.383102i
$686$	21.7408	+	18.4492i	0.830069	+	0.704394i
$687$	−2.07877	+	14.4581i	−0.0793099	+	0.551612i
$688$	19.2206	−	32.8104i	0.732780	−	1.25088i
$689$			0.337886i			0.0128724i
$690$	19.6816	−	5.58873i	0.749265	−	0.212759i
$691$	19.9812			0.760121			0.380061	−	0.924962i	$-0.375903\pi$
$691$	19.9812			0.760121			0.380061	+	0.924962i	$0.375903\pi$
$692$	0.116477	+	5.64270i	0.00442781	+	0.214503i
$693$	6.29200	+	0.904653i	0.239013	+	0.0343649i
$694$	−19.5156	−	16.5609i	−0.740804	−	0.628644i
$695$	−4.87672	+	1.43193i	−0.184984	+	0.0543163i
$696$	−25.5906	+	60.9620i	−0.970008	+	2.31076i
$697$	4.40414	−	3.81621i	0.166819	−	0.144549i
$698$	4.03196	−	30.2562i	0.152612	−	1.14521i
$699$	63.3396	+	18.5982i	2.39572	+	0.703448i
$700$	4.11853	−	1.30222i	0.155666	−	0.0492192i
$701$	31.8196	+	20.4492i	1.20181	+	0.772357i	0.979269	−	0.202566i	$-0.0649281\pi$
$701$	31.8196	+	20.4492i	1.20181	+	0.772357i	0.222542	+	0.974923i	$0.428564\pi$
$702$	4.62617	+	5.22887i	0.174604	+	0.197351i
$703$	−6.84150	−	5.92819i	−0.258032	−	0.223586i
$704$	3.60370	+	1.38318i	0.135820	+	0.0521304i
$705$	4.64952	−	0.668499i	0.175111	−	0.0251771i
$706$	−12.4992	+	5.86482i	−0.470413	+	0.220725i
$707$	−23.7100	+	10.8280i	−0.891706	+	0.407228i
$708$	−64.8557	−	17.5979i	−2.43743	−	0.661371i
$709$	−3.51131	+	7.68869i	−0.131870	+	0.288755i	−0.964036	−	0.265772i	$-0.914373\pi$
$709$	−3.51131	+	7.68869i	−0.131870	+	0.288755i	0.832166	+	0.554526i	$0.187101\pi$
$710$	3.25306	−	7.32224i	0.122085	−	0.274799i
$711$	−9.60460	+	6.17250i	−0.360201	+	0.231487i
$712$	−33.6787	−	36.5192i	−1.26216	−	1.36861i
$713$	21.3649	+	0.411204i	0.800120	+	0.0153997i
$714$	−9.75974	−	2.75665i	−0.365249	−	0.103165i
$715$	0.214284	−	0.137712i	0.00801376	−	0.00515013i
$716$	7.33522	−	8.82699i	0.274130	−	0.329880i
$717$	−4.08354	−	1.86489i	−0.152503	−	0.0696456i
$718$	−0.196377	−	19.0288i	−0.00732871	−	0.710149i
$719$	14.8438	−	6.77892i	0.553579	−	0.252811i	−0.118927	−	0.992903i	$-0.537945\pi$
$719$	14.8438	−	6.77892i	0.553579	−	0.252811i	0.672506	+	0.740092i	$0.265218\pi$
$720$	9.21154	−	22.5943i	0.343294	−	0.842040i
$721$	0.0231465	+	0.160987i	0.000862021	+	0.00599548i
$722$	−9.44360	+	15.0334i	−0.351454	+	0.559485i
$723$	18.4679	+	16.0025i	0.686828	+	0.595140i
$724$	−9.48119	−	19.6758i	−0.352366	−	0.731247i
$725$	4.18934	−	6.51875i	0.155588	−	0.242100i
$726$	25.2314	+	38.3841i	0.936426	+	1.42457i
$727$	−46.3222	−	13.6014i	−1.71799	−	0.504449i	−0.733474	−	0.679718i	$-0.762102\pi$
$727$	−46.3222	−	13.6014i	−1.71799	−	0.504449i	−0.984521	+	0.175269i	$0.943921\pi$
$728$	−2.03538	+	2.50138i	−0.0754360	+	0.0927073i
$729$	15.8344	+	18.2739i	0.586459	+	0.676810i
$730$	17.4013	−	2.68549i	0.644050	−	0.0993945i
$731$	10.0398	−	2.94796i	0.371337	−	0.109034i
$732$	−51.9582	+	34.9274i	−1.92043	+	1.29095i
$733$	3.43211	−	23.8708i	0.126768	−	0.881689i	−0.822846	−	0.568265i	$-0.807615\pi$
$733$	3.43211	−	23.8708i	0.126768	−	0.881689i	0.949613	−	0.313424i	$-0.101476\pi$
$734$	−1.02484	−	3.36158i	−0.0378277	−	0.124078i
$735$	−7.04527			−0.259869
$736$	26.2640	+	6.79718i	0.968104	+	0.250548i
$737$	−0.308891			−0.0113781
$738$	13.3191	+	43.6877i	0.490282	+	1.60817i
$739$	−2.53589	+	17.6375i	−0.0932841	+	0.648805i	0.888510	+	0.458857i	$0.151741\pi$
$739$	−2.53589	+	17.6375i	−0.0932841	+	0.648805i	−0.981794	+	0.189948i	$0.939168\pi$
$740$	5.91805	−	3.97824i	0.217552	−	0.146243i
$741$	−3.87956	+	1.13914i	−0.142519	+	0.0418474i
$742$	1.93204	−	0.298167i	0.0709275	−	0.0109460i
$743$	−9.61820	−	11.1000i	−0.352858	−	0.407220i	0.551376	−	0.834257i	$-0.314103\pi$
$743$	−9.61820	−	11.1000i	−0.352858	−	0.407220i	−0.904234	+	0.427037i	$0.859557\pi$
$744$	23.9948	−	29.4884i	0.879691	−	1.08110i
$745$	18.8361	+	5.53079i	0.690102	+	0.202632i
$746$	26.9632	+	41.0186i	0.987193	+	1.50180i
$747$	25.0073	−	38.9121i	0.914970	−	1.42372i
$748$	0.461092	+	0.956881i	0.0168592	+	0.0349870i
$749$	11.8473	+	10.2658i	0.432893	+	0.375104i
$750$	−2.26929	+	3.61251i	−0.0828628	+	0.131910i
$751$	−3.93244	−	27.3507i	−0.143497	−	0.998042i	−0.926573	−	0.376116i	$-0.877259\pi$
$751$	−3.93244	−	27.3507i	−0.143497	−	0.998042i	0.783076	−	0.621926i	$-0.213650\pi$
$752$	5.76769	+	2.35145i	0.210326	+	0.0857484i
$753$	20.2849	−	9.26379i	0.739222	−	0.337591i
$754$	0.0596992	+	5.78483i	0.00217412	+	0.210671i
$755$	14.9533	+	6.82893i	0.544205	+	0.248530i
$756$	25.8164	−	31.0668i	0.938935	−	1.12989i
$757$	−15.5677	+	10.0047i	−0.565817	+	0.363629i	−0.792061	−	0.610442i	$-0.790992\pi$
$757$	−15.5677	+	10.0047i	−0.565817	+	0.363629i	0.226244	+	0.974071i	$0.427355\pi$
$758$	−43.5421	−	12.2985i	−1.58152	−	0.446701i
$759$	−4.46887	−	5.36248i	−0.162210	−	0.194646i
$760$	4.86851	+	5.27911i	0.176599	+	0.191493i
$761$	11.1789	−	7.18426i	0.405236	−	0.260429i	−0.322107	−	0.946703i	$-0.604391\pi$
$761$	11.1789	−	7.18426i	0.405236	−	0.260429i	0.727343	+	0.686274i	$0.240755\pi$
$762$	−24.7815	+	55.7802i	−0.897741	+	2.02071i
$763$	3.87152	−	8.47744i	0.140158	−	0.306904i
$764$	23.1171	+	6.27260i	0.836349	+	0.226935i
$765$	6.10747	−	2.78919i	0.220816	−	0.100843i
$766$	9.81789	−	4.60671i	0.354735	−	0.166447i
$767$	−5.82026	+	0.836828i	−0.210158	+	0.0302161i
$768$	38.3137	−	29.3539i	1.38253	−	1.05922i
$769$	−20.0940	−	17.4116i	−0.724610	−	0.627878i	0.212399	−	0.977183i	$-0.431872\pi$
$769$	−20.0940	−	17.4116i	−0.724610	−	0.627878i	−0.937009	+	0.349305i	$0.886418\pi$
$770$	−0.976532	−	1.10376i	−0.0351918	−	0.0397766i
$771$	66.2466	+	42.5741i	2.38581	+	1.53327i
$772$	−26.5422	+	8.39224i	−0.955274	+	0.302043i
$773$	31.0683	+	9.12246i	1.11745	+	0.328112i	0.787763	−	0.615979i	$-0.211239\pi$
$773$	31.0683	+	9.12246i	1.11745	+	0.328112i	0.329685	+	0.944091i	$0.393058\pi$
$774$	−10.8328	+	81.2901i	−0.389376	+	2.92191i
$775$	−3.36740	+	2.91787i	−0.120960	+	0.104813i
$776$	−16.8778	+	40.2063i	−0.605876	+	1.44332i
$777$	22.2884	−	6.54447i	0.799592	−	0.234781i
$778$	12.0526	+	10.2278i	0.432107	+	0.366685i
$779$	−13.3055	−	1.91304i	−0.476719	−	0.0685419i
$780$	−0.0657314	−	3.18434i	−0.00235356	−	0.114018i
$781$	−2.73366			−0.0978182
$782$	3.97983	+	6.31597i	0.142318	+	0.225859i
$783$		−	72.4628i		−	2.58961i
$784$	−8.06067	−	4.72202i	−0.287881	−	0.168644i
$785$	−0.676516	+	4.70527i	−0.0241459	+	0.167938i
$786$	−21.8149	−	18.5121i	−0.778113	−	0.660304i
$787$	4.99819	+	17.0223i	0.178166	+	0.606778i	0.999348	+	0.0361113i	$0.0114971\pi$
$787$	4.99819	+	17.0223i	0.178166	+	0.606778i	−0.821182	+	0.570667i	$0.806685\pi$
$788$	19.6144	+	2.40810i	0.698734	+	0.0857848i
$789$	−58.1762	−	67.1389i	−2.07113	−	2.39021i
$790$	2.62372	+	0.349638i	0.0933477	+	0.0124396i
$791$	−7.30440	+	24.8765i	−0.259714	+	0.884506i
$792$	−8.32081	+	0.257684i	−0.295667	+	0.00915642i
$793$	−2.96169	+	4.60848i	−0.105173	+	0.163652i
$794$	−22.6805	−	25.6353i	−0.804902	−	0.909764i
$795$	−1.26438	+	1.45917i	−0.0448430	+	0.0517516i
$796$	33.0333	+	36.5694i	1.17083	+	1.29617i
$797$	−7.31696	−	50.8906i	−0.259180	−	1.80264i	−0.538700	−	0.842498i	$-0.681084\pi$
$797$	−7.31696	−	50.8906i	−0.259180	−	1.80264i	0.279520	−	0.960140i	$-0.409825\pi$
$798$	9.93714	+	21.1782i	0.351771	+	0.749699i
$799$	0.712001	+	1.55906i	0.0251888	+	0.0551557i
$800$	−5.01761	+	2.61220i	−0.177399	+	0.0923553i
$801$	97.4570	+	44.5071i	3.44347	+	1.57258i
$802$	−13.0244	+	29.3164i	−0.459908	+	1.03520i
$803$	−3.24778	−	5.05365i	−0.114612	−	0.178339i
$804$	−2.02066	+	3.29164i	−0.0712630	+	0.116087i
$805$	−7.69592	−	6.93229i	−0.271246	−	0.244331i
$806$	0.904208	−	3.20129i	0.0318494	−	0.112761i
$807$	17.1311	+	26.6566i	0.603045	+	0.938356i
$808$	28.1317	−	19.3351i	0.989669	−	0.680208i
$809$	−2.89540	+	6.34003i	−0.101797	+	0.222904i	−0.953677	−	0.300833i	$-0.902735\pi$
$809$	−2.89540	+	6.34003i	−0.101797	+	0.222904i	0.851880	+	0.523737i	$0.175463\pi$
$810$	0.144621	+	14.0138i	0.00508148	+	0.492393i
$811$	12.3249	+	26.9877i	0.432784	+	0.947665i	0.992867	+	0.119229i	$0.0380421\pi$
$811$	12.3249	+	26.9877i	0.432784	+	0.947665i	−0.560083	+	0.828437i	$0.689231\pi$
$812$	33.0251	−	5.44616i	1.15895	−	0.191123i
$813$	−76.2272	+	10.9598i	−2.67340	+	0.384377i
$814$	−2.06018	−	1.29415i	−0.0722092	−	0.0453600i
$815$	14.0518	−	16.2166i	0.492212	−	0.568043i
$816$	13.2131	+	1.34604i	0.462552	+	0.0471209i
$817$	−20.3050	−	13.0492i	−0.710383	−	0.456535i
$818$	−22.6935	−	34.5232i	−0.793460	−	1.20708i
$819$	1.95943	−	6.67320i	0.0684680	−	0.233181i
$820$	4.19902	−	9.72061i	0.146636	−	0.339458i
$821$	19.8523	−	17.2021i	0.692851	−	0.600359i	−0.235584	−	0.971854i	$-0.575700\pi$
$821$	19.8523	−	17.2021i	0.692851	−	0.600359i	0.928435	+	0.371495i	$0.121155\pi$
$822$	−6.79961	−	44.0597i	−0.237164	−	1.53676i
$823$	−9.50782	−	32.3806i	−0.331422	−	1.12872i	−0.941678	−	0.336515i	$-0.890752\pi$
$823$	−9.50782	−	32.3806i	−0.331422	−	1.12872i	0.610257	−	0.792204i	$-0.291066\pi$
$824$	−0.0663060	−	0.202415i	−0.00230988	−	0.00705147i
$825$	1.44071	+	0.207143i	0.0501592	+	0.00721181i
$826$	9.92107	+	32.5419i	0.345198	+	1.13228i
$827$		−	5.58209i		−	0.194108i	−0.995279	−	0.0970541i	$-0.969058\pi$
$827$		−	5.58209i		−	0.194108i	0.995279	−	0.0970541i	$-0.0309420\pi$
$828$	−57.9017	+	8.40745i	−2.01222	+	0.292179i
$829$		−	3.72702i		−	0.129445i	−0.997903	−	0.0647224i	$-0.979384\pi$
$829$		−	3.72702i		−	0.129445i	0.997903	−	0.0647224i	$-0.0206162\pi$
$830$	−10.2576	+	3.12724i	−0.356047	+	0.108548i
$831$	−40.7164	−	5.85414i	−1.41244	−	0.203078i
$832$	2.05907	−	3.68734i	0.0713853	−	0.127835i
$833$	−0.724239	−	2.46653i	−0.0250934	−	0.0854603i
$834$	21.4294	−	3.30714i	0.742039	−	0.114517i
$835$	−2.51674	+	2.18077i	−0.0870955	+	0.0754687i
$836$	0.971611	−	2.24925i	0.0336039	−	0.0777920i
$837$	−11.7390	+	39.9794i	−0.405760	+	1.38189i
$838$	2.35857	−	1.55038i	0.0814753	−	0.0535570i
$839$	28.2402	+	18.1489i	0.974960	+	0.626569i	0.928099	−	0.372333i	$-0.121442\pi$
$839$	28.2402	+	18.1489i	0.974960	+	0.626569i	0.0468605	+	0.998901i	$0.485078\pi$
$840$	−18.1501	+	3.18586i	−0.626238	+	0.109923i
$841$	20.3299	−	23.4620i	0.701033	−	0.809035i
$842$	0.611483	−	0.973428i	0.0210731	−	0.0335465i
$843$	70.3622	−	10.1166i	2.42340	−	0.348433i
$844$	−0.451538	−	2.73809i	−0.0155426	−	0.0942490i
$845$	5.28462	+	11.5717i	0.181797	+	0.398079i
$846$	−13.4323	+	0.138621i	−0.461812	+	0.00476588i
$847$	9.66024	−	21.1530i	0.331930	−	0.726825i
$848$	−2.42461	+	0.822040i	−0.0832615	+	0.0282290i
$849$	0.387152	+	0.602421i	0.0132870	+	0.0206750i
$850$	−1.49801	−	0.423114i	−0.0513814	−	0.0145127i
$851$	−15.4145	−	7.40130i	−0.528402	−	0.253713i
$852$	−17.8827	+	29.1308i	−0.612650	+	0.998004i
$853$	13.9572	+	21.7178i	0.477885	+	0.743603i	0.993575	−	0.113172i	$-0.0361010\pi$
$853$	13.9572	+	21.7178i	0.477885	+	0.743603i	−0.515691	+	0.856775i	$0.672465\pi$
$854$	28.9649	+	12.8683i	0.991160	+	0.440343i
$855$	−14.0881	−	6.43383i	−0.481803	−	0.220032i
$856$	−17.6061	−	10.5593i	−0.601763	−	0.360911i
$857$	2.45977	+	5.38615i	0.0840243	+	0.183988i	0.946980	−	0.321291i	$-0.104117\pi$
$857$	2.45977	+	5.38615i	0.0840243	+	0.183988i	−0.862956	+	0.505279i	$0.831390\pi$
$858$	−0.983758	+	0.461595i	−0.0335849	+	0.0157586i
$859$	7.36933	+	51.2548i	0.251438	+	1.74879i	0.589592	+	0.807701i	$0.299289\pi$
$859$	7.36933	+	51.2548i	0.251438	+	1.74879i	−0.338154	+	0.941091i	$0.609802\pi$
$860$	14.1089	−	12.7447i	0.481111	−	0.434589i
$861$	22.5885	−	26.0685i	0.769814	−	0.888413i
$862$	−14.0471	+	12.4279i	−0.478445	+	0.423298i
$863$	−25.8137	+	40.1668i	−0.878707	+	1.36730i	0.0508847	+	0.998705i	$0.483796\pi$
$863$	−25.8137	+	40.1668i	−0.878707	+	1.36730i	−0.929592	+	0.368590i	$0.879840\pi$
$864$	−26.2665	+	45.9178i	−0.893603	+	1.56216i
$865$	−0.795036	+	2.70764i	−0.0270320	+	0.0920627i
$866$	7.30146	−	54.7908i	0.248114	−	1.86187i
$867$	−31.1895	−	35.9946i	−1.05925	−	1.22244i
$868$	−19.1030	−	2.34531i	−0.648397	−	0.0796049i
$869$	−0.254427	−	0.866497i	−0.00863083	−	0.0293939i
$870$	−21.3892	+	25.2054i	−0.725162	+	0.854543i
$871$	−0.0480968	+	0.334520i	−0.00162970	+	0.0113348i
$872$	−3.07443	+	11.8115i	−0.104113	+	0.399989i
$873$		−	94.0416i		−	3.18283i
$874$	4.99876	−	16.4787i	0.169086	−	0.557401i
$875$	2.15975			0.0730128
$876$	−75.0991	+	1.55021i	−2.53736	+	0.0523766i
$877$	−29.2485	−	4.20530i	−0.987652	−	0.142003i	−0.370488	−	0.928837i	$-0.620810\pi$
$877$	−29.2485	−	4.20530i	−0.987652	−	0.142003i	−0.617164	+	0.786834i	$0.711719\pi$
$878$	−6.07195	+	7.15529i	−0.204919	+	0.241479i
$879$	−75.8950	+	22.2848i	−2.55988	+	0.751647i
$880$	1.50952	+	1.20262i	0.0508860	+	0.0405404i
$881$	−39.5717	+	34.2891i	−1.33321	+	1.15523i	−0.358052	+	0.933702i	$0.616559\pi$
$881$	−39.5717	+	34.2891i	−1.33321	+	1.15523i	−0.975154	+	0.221528i	$0.928896\pi$
$882$	19.9709	+	2.66134i	0.672456	+	0.0896118i
$883$	40.2636	+	11.8225i	1.35498	+	0.397858i	0.876990	−	0.480508i	$-0.159548\pi$
$883$	40.2636	+	11.8225i	1.35498	+	0.397858i	0.477989	+	0.878366i	$0.341366\pi$
$884$	1.10807	−	0.350356i	0.0372685	−	0.0117837i
$885$	−28.2665	−	18.1658i	−0.950167	−	0.610635i
$886$	−22.9095	+	20.2689i	−0.769661	+	0.680947i
$887$	−8.68381	−	7.52457i	−0.291574	−	0.252650i	0.496774	−	0.867880i	$-0.334518\pi$
$887$	−8.68381	−	7.52457i	−0.291574	−	0.252650i	−0.788348	+	0.615230i	$0.789063\pi$
$888$	−27.2678	+	13.4880i	−0.915049	+	0.452628i
$889$	30.5859	−	4.39758i	1.02582	−	0.147490i
$890$	−10.5511	−	22.4867i	−0.353674	−	0.753755i
$891$	4.34940	−	1.98630i	0.145710	−	0.0665437i
$892$	−13.5886	+	50.0795i	−0.454979	+	1.67679i
$893$	1.64237	−	3.59630i	0.0549600	−	0.120346i
$894$	−76.5367	−	34.0030i	−2.55977	−	1.13723i
$895$	4.82753	−	3.10247i	0.161367	−	0.103704i
$896$	−22.9013	−	8.51990i	−0.765078	−	0.284630i
$897$	−6.50325	+	4.00469i	−0.217137	+	0.133713i
$898$	−1.96734	+	6.96525i	−0.0656509	+	0.232433i
$899$	−29.0456	+	18.6665i	−0.968726	+	0.622562i
$900$	7.79728	−	9.38302i	0.259909	−	0.312767i
$901$	−0.640830	−	0.292657i	−0.0213491	−	0.00974982i
$902$	−3.61250	+	0.0372809i	−0.120283	+	0.00124132i
$903$	56.3386	−	25.7290i	1.87483	−	0.856207i
$904$	3.78952	−	33.7417i	0.126037	−	1.12223i
$905$	−1.55415	−	10.8094i	−0.0516618	−	0.359316i
$906$	−59.3855	−	37.3045i	−1.97295	−	1.23936i
$907$	−31.9429	−	27.6787i	−1.06065	−	0.919055i	−0.0637648	−	0.997965i	$-0.520311\pi$
$907$	−31.9429	−	27.6787i	−1.06065	−	0.919055i	−0.996882	+	0.0789095i	$0.974856\pi$
$908$	−19.0016	+	9.15631i	−0.630592	+	0.303863i
$909$	−39.8015	+	61.9323i	−1.32013	+	2.05416i
$910$	−1.34739	+	0.885694i	−0.0446655	+	0.0293605i
$911$	45.0086	+	13.2157i	1.49120	+	0.437856i	0.922925	−	0.384981i	$-0.125792\pi$
$911$	45.0086	+	13.2157i	1.49120	+	0.437856i	0.568277	+	0.822837i	$0.307610\pi$
$912$	−17.6128	−	25.0676i	−0.583218	−	0.830071i
$913$	2.39596	+	2.76509i	0.0792948	+	0.0915111i
$914$	1.68661	+	10.9288i	0.0557880	+	0.361492i
$915$	−30.0353	+	8.81915i	−0.992936	+	0.291552i
$916$	−8.03711	+	5.40271i	−0.265554	+	0.178511i
$917$	−2.06135	+	14.3370i	−0.0680717	+	0.473449i
$918$	−13.9239	+	4.24499i	−0.459557	+	0.140105i
$919$	36.6864			1.21017			0.605086	−	0.796160i	$-0.293139\pi$
$919$	36.6864			1.21017			0.605086	+	0.796160i	$0.293139\pi$
$920$	11.4964	+	7.19943i	0.379026	+	0.237358i
$921$	15.5615			0.512770
$922$	13.7416	−	4.18941i	0.452556	−	0.137971i
$923$	−0.425653	+	2.96048i	−0.0140105	+	0.0974455i
$924$	3.50752	+	5.21781i	0.115389	+	0.171653i
$925$	3.42102	−	1.00450i	0.112483	−	0.0330278i
$926$	7.84686	+	50.8456i	0.257864	+	1.67089i
$927$	0.300821	+	0.347166i	0.00988027	+	0.0114024i
$928$	−41.3656	+	14.5022i	−1.35789	+	0.476059i
$929$	11.4060	+	3.34911i	0.374220	+	0.109881i	0.463434	−	0.886132i	$-0.346617\pi$
$929$	11.4060	+	3.34911i	0.374220	+	0.109881i	−0.0892137	+	0.996013i	$0.528435\pi$
$930$	15.8842	−	10.4413i	0.520863	−	0.342385i
$931$	−3.20587	+	4.98843i	−0.105068	+	0.163489i
$932$	18.9991	+	39.4279i	0.622336	+	1.29150i
$933$	−16.8266	−	14.5804i	−0.550879	−	0.477339i
$934$	2.60080	+	1.63376i	0.0851009	+	0.0534583i
$935$	0.0755820	+	0.525685i	0.00247180	+	0.0171917i
$936$	−1.01655	+	9.05133i	−0.0332270	+	0.295852i
$937$	−26.6807	+	12.1846i	−0.871619	+	0.398055i	−0.800443	−	0.599409i	$-0.795402\pi$
$937$	−26.6807	+	12.1846i	−0.871619	+	0.398055i	−0.0711760	+	0.997464i	$0.522675\pi$
$938$	1.95524	−	0.0201780i	0.0638408	−	0.000658834i
$939$	−93.4811	−	42.6914i	−3.05064	−	1.39318i
$940$	2.39522	+	1.99043i	0.0781235	+	0.0649205i
$941$	22.9173	−	14.7281i	0.747083	−	0.480121i	−0.110879	−	0.993834i	$-0.535367\pi$
$941$	22.9173	−	14.7281i	0.747083	−	0.480121i	0.857962	+	0.513713i	$0.171730\pi$
$942$	5.51236	−	19.5162i	0.179603	−	0.635872i
$943$	−25.1974	+	3.12921i	−0.820541	+	0.101901i
$944$	−20.1650	−	39.7292i	−0.656314	−	1.29308i
$945$	16.9906	−	10.9192i	0.552703	−	0.355201i
$946$	−5.92813	−	2.63370i	−0.192740	−	0.0856288i
$947$	25.2679	−	55.3290i	0.821097	−	1.79795i	0.271723	−	0.962375i	$-0.412406\pi$
$947$	25.2679	−	55.3290i	0.821097	−	1.79795i	0.549374	−	0.835577i	$-0.314866\pi$
$948$	−10.8980	−	2.95707i	−0.353952	−	0.0960412i
$949$	−5.97867	+	2.73037i	−0.194076	+	0.0886314i
$950$	1.52524	+	3.25061i	0.0494853	+	0.105464i
$951$	30.0004	−	4.31341i	0.972831	−	0.139872i
$952$	−2.98115	−	6.02681i	−0.0966198	−	0.195330i
$953$	−31.7643	−	27.5239i	−1.02895	−	0.891588i	−0.0347756	−	0.999395i	$-0.511072\pi$
$953$	−31.7643	−	27.5239i	−1.02895	−	0.891588i	−0.994172	+	0.107807i	$0.965617\pi$
$954$	4.13529	−	3.65864i	0.133885	−	0.118453i
$955$	10.0753	+	6.47499i	0.326029	+	0.209526i
$956$	−0.897286	−	2.83785i	−0.0290203	−	0.0917827i
$957$	10.8218	+	3.17757i	0.349819	+	0.102716i
$958$	33.5177	+	4.46659i	1.08291	+	0.144309i
$959$	−17.0568	+	14.7798i	−0.550794	+	0.477266i
$960$	22.6903	−	8.21881i	0.732326	−	0.265261i
$961$	−10.6952	+	3.14038i	−0.345005	+	0.101303i
$962$	−1.72232	+	2.02961i	−0.0555297	+	0.0654371i
$963$	43.8253	+	6.30113i	1.41225	+	0.203051i
$964$	0.334358	+	16.1978i	0.0107689	+	0.521697i
$965$	−13.9187			−0.448058
$966$	28.6376	+	33.6518i	0.921401	+	1.08273i
$967$			21.6758i			0.697046i	0.937300	+	0.348523i	$0.113317\pi$
$967$			21.6758i			0.697046i	−0.937300	+	0.348523i	$0.886683\pi$
$968$	−7.67134	+	29.4722i	−0.246566	+	0.947272i
$969$	1.19977	−	8.34457i	0.0385421	−	0.268066i
$970$	−14.1068	+	16.6237i	−0.452943	+	0.533755i
$971$	−2.40507	−	8.19093i	−0.0771825	−	0.262859i	0.911858	−	0.410507i	$-0.134648\pi$
$971$	−2.40507	−	8.19093i	−0.0771825	−	0.262859i	−0.989040	+	0.147647i	$0.952830\pi$
$972$	0.448342	−	3.65183i	0.0143806	−	0.117133i
$973$	−7.18849	−	8.29596i	−0.230452	−	0.265956i
$974$	−0.618105	+	4.63831i	−0.0198053	+	0.148621i
$975$	0.448661	−	1.52800i	0.0143687	−	0.0489351i
$976$	−40.2751	−	10.0406i	−1.28917	−	0.321393i
$977$	11.5671	−	17.9987i	0.370063	−	0.575829i	−0.605420	−	0.795907i	$-0.706995\pi$
$977$	11.5671	−	17.9987i	0.370063	−	0.575829i	0.975482	+	0.220077i	$0.0706310\pi$
$978$	−68.5600	+	60.6575i	−2.19231	+	1.93961i
$979$	−5.54969	+	6.40469i	−0.177369	+	0.204695i
$980$	−3.13104	−	3.46621i	−0.100017	−	0.110724i
$981$	−3.74605	−	26.0544i	−0.119602	−	0.831852i
$982$	−3.50825	+	1.64613i	−0.111953	+	0.0525301i
$983$	−11.4282	−	25.0243i	−0.364503	−	0.798150i	−0.999668	−	0.0257736i	$-0.991795\pi$
$983$	−11.4282	−	25.0243i	−0.364503	−	0.798150i	0.635165	−	0.772377i	$-0.280932\pi$
$984$	−23.2344	+	38.7398i	−0.740687	+	1.23498i
$985$	8.98792	+	4.10465i	0.286379	+	0.130785i
$986$	−11.0231	−	4.89725i	−0.351048	−	0.155960i
$987$	5.48483	+	8.53456i	0.174584	+	0.271658i
$988$	−2.28459	−	1.40245i	−0.0726825	−	0.0446180i
$989$	−43.4892	−	13.6839i	−1.38288	−	0.435124i
$990$	−4.00568	−	1.13141i	−0.127309	−	0.0359585i
$991$	6.78346	+	10.5553i	0.215484	+	0.335299i	0.932121	−	0.362147i	$-0.117956\pi$
$991$	6.78346	+	10.5553i	0.215484	+	0.335299i	−0.716637	+	0.697446i	$0.754320\pi$
$992$	25.1717	−	1.29996i	0.799203	−	0.0412739i
$993$	−25.8704	+	56.6482i	−0.820971	+	1.79768i
$994$	17.3037	−	0.178574i	0.548840	−	0.00566401i
$995$	10.2358	+	22.4133i	0.324497	+	0.710550i
$996$	45.1392	−	7.44390i	1.43029	−	0.235869i
$997$	5.90824	−	0.849477i	0.187116	−	0.0269032i	−0.0481198	−	0.998842i	$-0.515323\pi$
$997$	5.90824	−	0.849477i	0.187116	−	0.0269032i	0.235236	+	0.971938i	$0.424414\pi$
$998$	7.14716	−	11.3777i	0.226239	−	0.360154i
$999$	21.8344	−	25.1982i	0.690809	−	0.797236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bb.a.11.19	✓	480
8.3	odd	2		920.2.bb.b.11.37	yes	480
23.21	odd	22		920.2.bb.b.251.37	yes	480
184.67	even	22	inner	920.2.bb.a.251.19	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bb.a.11.19	✓	480	1.1	even	1	trivial
920.2.bb.a.251.19	yes	480	184.67	even	22	inner
920.2.bb.b.11.37	yes	480	8.3	odd	2
920.2.bb.b.251.37	yes	480	23.21	odd	22

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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.412411 - 1.35274i) q^{2} +(-0.429309 + 2.98591i) q^{3} +(-1.65983 + 1.11577i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(4.21623 - 0.650679i) q^{6} +(-1.41433 - 1.63223i) q^{7} +(2.19389 + 1.78517i) q^{8} +(-5.85288 - 1.71856i) q^{9} +(0.776818 + 1.18176i) q^{10} +(0.260861 - 0.405908i) q^{11} +(-2.61902 - 5.43513i) q^{12} +(-0.398969 - 0.345709i) q^{13} +(-1.62470 + 2.58638i) q^{14} +(-0.429309 - 2.98591i) q^{15} +(1.51009 - 3.70400i) q^{16} +(1.00123 - 0.457246i) q^{17} +(0.0890221 + 8.62620i) q^{18} +(-2.30954 - 1.05473i) q^{19} +(1.27825 - 1.53821i) q^{20} +(5.48088 - 3.52235i) q^{21} +(-0.656672 - 0.185477i) q^{22} +(-4.73300 - 0.773739i) q^{23} +(-6.27222 + 5.78438i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-0.303116 + 0.682277i) q^{26} +(3.88472 - 8.50636i) q^{27} +(4.16876 + 1.13115i) q^{28} +(7.04860 - 3.21899i) q^{29} +(-3.86212 + 1.81217i) q^{30} +(-4.41035 + 0.634113i) q^{31} +(-5.63334 - 0.515200i) q^{32} +(1.10002 + 0.953169i) q^{33} +(-1.03145 - 1.16583i) q^{34} +(1.81690 + 1.16765i) q^{35} +(11.6323 - 3.67797i) q^{36} +(3.42102 + 1.00450i) q^{37} +(-0.474301 + 3.55920i) q^{38} +(1.20354 - 1.04287i) q^{39} +(-2.60796 - 1.09477i) q^{40} +(5.07992 - 1.49160i) q^{41} +(-7.02521 - 5.96157i) q^{42} +(9.40966 + 1.35291i) q^{43} +(0.0199156 + 0.964802i) q^{44} +6.09997 q^{45} +(0.905274 + 6.72164i) q^{46} +1.55715i q^{47} +(10.4115 + 6.09917i) q^{48} +(0.332374 - 2.31171i) q^{49} +(-1.07829 - 0.915034i) q^{50} +(0.935459 + 3.18588i) q^{51} +(1.04796 + 0.128659i) q^{52} +(-0.419139 - 0.483712i) q^{53} +(-13.1090 - 1.74692i) q^{54} +(-0.135937 + 0.462959i) q^{55} +(-0.189087 - 6.10576i) q^{56} +(4.14084 - 6.44327i) q^{57} +(-7.26139 - 8.20741i) q^{58} +(7.29413 - 8.41787i) q^{59} +(4.04419 + 4.47710i) q^{60} +(-1.47679 - 10.2713i) q^{61} +(2.67667 + 5.70456i) q^{62} +(5.47285 + 11.9839i) q^{63} +(1.62632 + 7.83295i) q^{64} +(0.480205 + 0.219302i) q^{65} +(0.835735 - 1.88114i) q^{66} +(-0.346109 - 0.538557i) q^{67} +(-1.15169 + 1.87610i) q^{68} +(4.34224 - 13.8002i) q^{69} +(0.830220 - 2.93935i) q^{70} +(-3.06304 - 4.76619i) q^{71} +(-9.77266 - 14.2187i) q^{72} +(5.17201 - 11.3251i) q^{73} +(-0.0520336 - 5.04204i) q^{74} +(1.25315 + 2.74401i) q^{75} +(5.01029 - 0.826246i) q^{76} +(-1.03148 + 0.148304i) q^{77} +(-1.90709 - 1.19799i) q^{78} +(1.22567 - 1.41450i) q^{79} +(-0.405388 + 3.97940i) q^{80} +(8.33661 + 5.35761i) q^{81} +(-4.11277 - 6.25668i) q^{82} +(-2.13633 + 7.27566i) q^{83} +(-5.16720 + 11.9619i) q^{84} +(-0.831851 + 0.720803i) q^{85} +(-2.05052 - 13.2868i) q^{86} +(6.58558 + 22.4284i) q^{87} +(1.29692 - 0.424836i) q^{88} +(-17.3851 - 2.49959i) q^{89} +(-2.51570 - 8.25170i) q^{90} +1.14016i q^{91} +(8.71932 - 3.99669i) q^{92} -13.4412i q^{93} +(2.10643 - 0.642187i) q^{94} +(2.51314 + 0.361335i) q^{95} +(3.95679 - 16.5995i) q^{96} +(4.34339 + 14.7922i) q^{97} +(-3.26423 + 0.503760i) q^{98} +(-2.22437 + 1.92743i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 2 q^{2} - 4 q^{4} - 48 q^{5} + 5 q^{6} - q^{8} - 48 q^{9} + 2 q^{10} + 3 q^{12} + 32 q^{16} + 7 q^{18} - 4 q^{20} + 8 q^{21} + 4 q^{23} + 2 q^{24} - 48 q^{25} + 7 q^{26} + 12 q^{27} + 5 q^{30}+ \cdots - 98 q^{98}+O(q^{100}) \) 480 * q + 2 * q^2 - 4 * q^4 - 48 * q^5 + 5 * q^6 - q^8 - 48 * q^9 + 2 * q^10 + 3 * q^12 + 32 * q^16 + 7 * q^18 - 4 * q^20 + 8 * q^21 + 4 * q^23 + 2 * q^24 - 48 * q^25 + 7 * q^26 + 12 * q^27 + 5 * q^30 - 118 * q^32 - 23 * q^34 + 54 * q^36 + 8 * q^37 - 65 * q^38 + 43 * q^40 - 10 * q^42 - q^44 + 480 * q^45 - 184 * q^46 - 44 * q^48 - 48 * q^49 - 9 * q^50 - 7 * q^52 + 32 * q^53 - 27 * q^54 + 67 * q^56 - 40 * q^58 - 12 * q^59 + 14 * q^60 - 8 * q^61 - 128 * q^62 + 59 * q^64 + 88 * q^66 + 10 * q^68 - 20 * q^69 + 3 * q^72 - 11 * q^74 + 110 * q^76 + 118 * q^78 - 144 * q^79 - q^80 - 56 * q^81 - 59 * q^82 - 162 * q^84 - 18 * q^86 - 76 * q^88 + 7 * q^90 - 149 * q^92 + 168 * q^94 + 65 * q^96 - 98 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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