LMFDB - Embedded newform 920.2.bb.a.251.19

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			251.19
Character	$\chi$	$=$	920.251
Dual form			920.2.bb.a.11.19

$q$-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 $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$-1$	$e\left(\frac{13}{22}\right)$	$-1$	$1$

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	−0.610525	−	0.791997i	$-0.709042\pi$
$3$	−0.429309	−	2.98591i	−0.247862	−	1.72392i	0.362664	−	0.931920i	$-0.381867\pi$
$4$	−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	−0.957218	−	0.289369i	$-0.906555\pi$
$7$	−1.41433	+	1.63223i	−0.534568	+	0.616925i	0.422650	+	0.906293i	$0.361100\pi$
$8$	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	0.878351	−	0.478016i	$-0.158644\pi$
$11$	0.260861	+	0.405908i	0.0786526	+	0.122386i	−0.799699	+	0.600402i	$0.795007\pi$
$12$	−2.61902	+	5.43513i	−0.756046	+	1.56899i
$13$	−0.398969	+	0.345709i	−0.110654	+	0.0958823i	−0.708431	−	0.705780i	$-0.750596\pi$
$13$	−0.398969	+	0.345709i	−0.110654	+	0.0958823i	0.597776	+	0.801663i	$0.296051\pi$
$14$	−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	0.533115	−	0.846043i	$-0.321021\pi$
$17$	1.00123	+	0.457246i	0.242834	+	0.110898i	−0.290281	+	0.956941i	$0.593749\pi$
$18$	0.0890221	−	8.62620i	0.0209827	−	2.03322i
$19$	−2.30954	+	1.05473i	−0.529844	+	0.241972i	−0.662329	−	0.749213i	$-0.730432\pi$
$19$	−2.30954	+	1.05473i	−0.529844	+	0.241972i	0.132485	+	0.991185i	$0.457705\pi$
$20$	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	0.942965	−	0.332892i	$-0.108024\pi$
$29$	7.04860	+	3.21899i	1.30889	+	0.597751i	0.365928	+	0.930643i	$0.380752\pi$
$30$	−3.86212	−	1.81217i	−0.705124	−	0.330855i
$31$	−4.41035	−	0.634113i	−0.792123	−	0.113890i	−0.265636	−	0.964073i	$-0.585582\pi$
$31$	−4.41035	−	0.634113i	−0.792123	−	0.113890i	−0.526487	+	0.850183i	$0.676491\pi$
$32$	−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	0.0118450	−	0.999930i	$-0.496230\pi$
$37$	3.42102	−	1.00450i	0.562413	−	0.165139i	0.550568	+	0.834791i	$0.314411\pi$
$38$	−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	0.653204	−	0.757182i	$-0.273424\pi$
$41$	5.07992	+	1.49160i	0.793351	+	0.232949i	0.140147	+	0.990131i	$0.455243\pi$
$42$	−7.02521	+	5.96157i	−1.08401	+	0.919890i
$43$	9.40966	−	1.35291i	1.43496	−	0.206316i	0.619440	−	0.785044i	$-0.287360\pi$
$43$	9.40966	−	1.35291i	1.43496	−	0.206316i	0.815521	+	0.578728i	$0.196451\pi$
$44$	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	$-0.963772\pi$
$47$		−	1.55715i		−	0.227134i	0.993530	−	0.113567i	$-0.0362276\pi$
$48$	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	−0.783806	−	0.621006i	$-0.786724\pi$
$53$	−0.419139	+	0.483712i	−0.0575732	+	0.0664430i	0.726232	+	0.687449i	$0.241270\pi$
$54$	−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	0.995289	+	0.0969575i	$0.0309111\pi$
$59$	7.29413	+	8.41787i	0.949615	+	1.09591i	−0.0456737	+	0.998956i	$0.514543\pi$
$60$	4.04419	−	4.47710i	0.522102	−	0.577992i
$61$	−1.47679	+	10.2713i	−0.189084	+	1.31511i	0.645301	+	0.763928i	$0.276732\pi$
$61$	−1.47679	+	10.2713i	−0.189084	+	1.31511i	−0.834386	+	0.551181i	$0.814177\pi$
$62$	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	−0.861752	−	0.507330i	$-0.830633\pi$
$67$	−0.346109	+	0.538557i	−0.0422840	+	0.0657952i	0.819468	+	0.573125i	$0.194269\pi$
$68$	−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	−0.974046	−	0.226351i	$-0.927320\pi$
$71$	−3.06304	+	4.76619i	−0.363516	+	0.565642i	0.610529	+	0.791994i	$0.290957\pi$
$72$	−9.77266	+	14.2187i	−1.15172	+	1.67569i
$73$	5.17201	+	11.3251i	0.605338	+	1.32551i	0.925717	+	0.378216i	$0.123463\pi$
$73$	5.17201	+	11.3251i	0.605338	+	1.32551i	−0.320379	+	0.947289i	$0.603810\pi$
$74$	−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	0.820498	−	0.571649i	$-0.193696\pi$
$79$	1.22567	+	1.41450i	0.137899	+	0.159143i	−0.682600	+	0.730793i	$0.739151\pi$
$80$	−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	−0.989704	−	0.143127i	$-0.954284\pi$
$83$	−2.13633	−	7.27566i	−0.234492	−	0.798607i	0.755212	−	0.655480i	$-0.227534\pi$
$84$	−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	−0.973397	−	0.229126i	$-0.926413\pi$
$89$	−17.3851	+	2.49959i	−1.84281	+	0.264956i	−0.869415	+	0.494082i	$0.835504\pi$
$90$	−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	−0.376727	−	0.926324i	$-0.622951\pi$
$97$	4.34339	−	14.7922i	0.441005	−	1.50192i	0.817732	−	0.575600i	$-0.195231\pi$
$98$	−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	0.936440	+	0.350828i	$0.114100\pi$
$101$	3.40016	+	11.5799i	0.338329	+	1.15224i	−0.598111	+	0.801413i	$0.704082\pi$
$102$	3.92389	+	2.57933i	0.388523	+	0.255392i
$103$	−0.0633518	+	0.0407137i	−0.00624224	+	0.00401164i	−0.543758	−	0.839242i	$-0.682999\pi$
$103$	−0.0633518	+	0.0407137i	−0.00624224	+	0.00401164i	0.537516	+	0.843254i	$0.319363\pi$
$104$	−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	−0.214008	−	0.976832i	$-0.568652\pi$
$107$	−7.18451	−	1.03298i	−0.694552	−	0.0998616i	−0.480544	+	0.876970i	$0.659561\pi$
$108$	3.04318	−	18.4536i	0.292830	−	1.77570i
$109$	1.79258	−	3.92520i	0.171698	−	0.375966i	−0.804147	−	0.594430i	$-0.797378\pi$
$109$	1.79258	−	3.92520i	0.171698	−	0.375966i	0.975845	+	0.218465i	$0.0701048\pi$
$110$	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	0.389046	+	0.921218i	$0.372805\pi$
$113$	−6.49012	+	10.0988i	−0.610539	+	0.950018i	−0.999585	+	0.0287994i	$0.990832\pi$
$114$	−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	−0.993217	−	0.116272i	$-0.962905\pi$
$127$	−7.73517	−	12.0362i	−0.686385	−	1.06804i	0.306832	−	0.951764i	$-0.400731\pi$
$128$	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	−0.914446	−	0.404709i	$-0.867373\pi$
$131$	−4.39184	+	5.06845i	−0.383717	+	0.442833i	0.530729	+	0.847542i	$0.321918\pi$
$132$	−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	$0.147295\pi$
$137$			10.4500i			0.892806i	−0.894832	+	0.446403i	$0.852705\pi$
$138$	−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	−0.997863	−	0.0653390i	$-0.979187\pi$
$149$	−16.5149	+	10.6135i	−1.35296	+	0.869492i	−0.355093	+	0.934831i	$0.615551\pi$
$150$	3.19513	+	2.82685i	0.260881	+	0.230811i
$151$	−12.4236	+	10.7651i	−1.01102	+	0.876054i	−0.992311	−	0.123771i	$-0.960501\pi$
$151$	−12.4236	+	10.7651i	−1.01102	+	0.876054i	−0.0187098	+	0.999825i	$0.505956\pi$
$152$	−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	0.971917	−	0.235323i	$-0.0756149\pi$
$157$	1.97474	+	4.32408i	0.157601	+	0.345099i	−0.814316	+	0.580422i	$0.802888\pi$
$158$	−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	−0.413890	−	0.910327i	$-0.635830\pi$
$163$	−18.0513	−	11.6009i	−1.41389	−	0.908651i	−0.999999	+	0.00167569i	$0.999467\pi$
$164$	−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	0.529155	−	0.848525i	$-0.322509\pi$
$167$	3.02919	+	1.38339i	0.234406	+	0.107050i	−0.294749	+	0.955575i	$0.595236\pi$
$168$	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	0.894396	−	0.447276i	$-0.147606\pi$
$173$	1.52566	+	2.37398i	0.115994	+	0.180490i	−0.778402	+	0.627766i	$0.783969\pi$
$174$	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	0.0694069	−	0.997588i	$-0.477889\pi$
$179$	−5.50605	−	1.61672i	−0.411541	−	0.120839i	−0.480948	+	0.876749i	$0.659707\pi$
$180$	−10.1249	−	6.80619i	−0.754668	−	0.507304i
$181$	−1.55415	−	10.8094i	−0.115519	−	0.803455i	−0.962393	−	0.271661i	$-0.912427\pi$
$181$	−1.55415	−	10.8094i	−0.115519	−	0.803455i	0.846874	−	0.531794i	$-0.178482\pi$
$182$	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	−0.964869	−	0.262732i	$-0.915376\pi$
$191$	−7.84295	+	9.05125i	−0.567496	+	0.654925i	0.397373	+	0.917657i	$0.369922\pi$
$192$	−24.0867	−	1.49330i	−1.73831	−	0.107769i
$193$	13.3549	−	3.92134i	0.961304	−	0.282264i	0.236818	−	0.971554i	$-0.423895\pi$
$193$	13.3549	−	3.92134i	0.961304	−	0.282264i	0.724486	+	0.689290i	$0.242077\pi$
$194$	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	−0.878968	−	0.476880i	$-0.841768\pi$
$197$	−7.46744	+	6.47057i	−0.532033	+	0.461009i	0.346936	+	0.937889i	$0.387222\pi$
$198$	3.52467	−	2.21411i	0.250487	−	0.157350i
$199$	−3.50663	+	24.3892i	−0.248579	+	1.72890i	0.357862	+	0.933774i	$0.383506\pi$
$199$	−3.50663	+	24.3892i	−0.248579	+	1.72890i	−0.606441	+	0.795129i	$0.707403\pi$
$200$	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	0.888753	−	0.458386i	$-0.151572\pi$
$211$	−0.576404	−	1.26215i	−0.0396813	−	0.0868899i	−0.928435	+	0.371496i	$0.878845\pi$
$212$	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	0.980894	+	0.194542i	$0.0623221\pi$
$223$	19.6080	+	16.9905i	1.31305	+	1.13777i	0.332158	+	0.943224i	$0.392223\pi$
$224$	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	0.213116	−	0.977027i	$-0.431639\pi$
$227$	10.4390	−	1.50090i	0.692860	−	0.0996182i	0.479744	+	0.877409i	$0.340730\pi$
$228$	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	0.792182	+	0.610285i	$0.208945\pi$
$233$	3.11432	+	21.6606i	0.204026	+	1.41903i	−0.588156	+	0.808748i	$0.700146\pi$
$234$	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	0.944821	−	0.327587i	$-0.106235\pi$
$239$	−0.419264	−	1.42788i	−0.0271199	−	0.0923621i	−0.971941	+	0.235225i	$0.924417\pi$
$240$	−11.7081	+	2.91885i	−0.755755	+	0.188411i
$241$	4.37954	+	6.81469i	0.282111	+	0.438973i	0.953172	−	0.302429i	$-0.0977976\pi$
$241$	4.37954	+	6.81469i	0.282111	+	0.438973i	−0.671061	+	0.741402i	$0.734161\pi$
$242$	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	−0.944171	−	0.329455i	$-0.893135\pi$
$251$	−3.99664	+	6.21890i	−0.252266	+	0.392533i	0.691906	+	0.721988i	$0.256771\pi$
$252$	−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	0.866367	+	0.499409i	$0.166449\pi$
$257$	10.8442	+	23.7456i	0.676445	+	1.48121i	−0.189922	+	0.981799i	$0.560823\pi$
$258$	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	−0.911286	−	0.411774i	$-0.864909\pi$
$263$	−19.2852	−	22.2564i	−1.18918	−	1.37239i	−0.277893	−	0.960612i	$-0.589636\pi$
$264$	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	0.862385	−	0.506253i	$-0.168970\pi$
$269$	7.93844	+	6.87870i	0.484016	+	0.419402i	−0.378370	+	0.925655i	$0.623515\pi$
$270$	13.0702	+	2.01709i	0.795426	+	0.122756i
$271$	7.19233	−	24.4948i	0.436903	−	1.48796i	−0.387456	−	0.921888i	$-0.626646\pi$
$271$	7.19233	−	24.4948i	0.436903	−	1.48796i	0.824359	−	0.566067i	$-0.191536\pi$
$272$	−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	$-0.865647\pi$
$277$		−	13.6362i		−	0.819319i	0.912238	−	0.409660i	$-0.134353\pi$
$278$	−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	0.484476	+	0.874805i	$0.339010\pi$
$281$	−6.63895	+	22.6102i	−0.396046	+	1.34881i	−0.880522	+	0.474005i	$0.842808\pi$
$282$	1.01320	−	6.56530i	0.0603355	−	0.390958i
$283$	0.179403	+	0.155454i	0.0106644	+	0.00924078i	0.660177	−	0.751110i	$-0.270481\pi$
$283$	0.179403	+	0.155454i	0.0106644	+	0.00924078i	−0.649512	+	0.760351i	$0.725027\pi$
$284$	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	−0.266649	−	0.963794i	$-0.585916\pi$
$293$	10.8927	−	23.8516i	0.636356	−	1.39342i	0.903005	−	0.429631i	$-0.141356\pi$
$294$	−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	0.958088	+	0.286475i	$0.0924834\pi$
$307$	−0.734146	+	5.10610i	−0.0418999	+	0.291420i	−0.999988	+	0.00494582i	$0.998426\pi$
$308$	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	0.709493	−	0.704713i	$-0.248924\pi$
$311$	−3.99032	−	6.20906i	−0.226270	−	0.352084i	−0.935763	+	0.352629i	$0.885288\pi$
$312$	4.50213	+	0.139425i	0.254883	+	0.00789339i
$313$	−9.59787	−	32.6874i	−0.542504	−	1.84760i	−0.530523	−	0.847670i	$-0.678004\pi$
$313$	−9.59787	−	32.6874i	−0.542504	−	1.84760i	−0.0119808	−	0.999928i	$-0.503814\pi$
$314$	−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	0.841014	+	0.541013i	$0.181959\pi$
$317$	−2.83066	+	9.64035i	−0.158986	+	0.541456i	−1.00000		0.000442633i	$0.999859\pi$
$318$	−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	0.312376	−	0.949959i	$-0.398875\pi$
$331$	19.8081	−	5.81617i	1.08875	−	0.319686i	0.776374	+	0.630273i	$0.217057\pi$
$332$	−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	−0.465109	−	0.885253i	$-0.653985\pi$
$337$	−21.3091	−	3.06379i	−1.16078	−	0.166895i	−0.695674	+	0.718358i	$0.744894\pi$
$338$	−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	0.881236	−	0.472677i	$-0.156712\pi$
$347$	15.2256	+	9.78488i	0.817352	+	0.525280i	−0.0638838	+	0.997957i	$0.520349\pi$
$348$	−35.9561	+	29.8795i	−1.92745	+	1.60171i
$349$	19.6330	−	8.96610i	1.05093	−	0.479944i	0.186375	−	0.982479i	$-0.440326\pi$
$349$	19.6330	−	8.96610i	1.05093	−	0.479944i	0.864557	+	0.502534i	$0.167599\pi$
$350$	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	0.918855	+	0.394595i	$0.129115\pi$
$353$	−1.38940	+	9.66346i	−0.0739501	+	0.514334i	−0.992805	+	0.119739i	$0.961794\pi$
$354$	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	0.0773373	−	0.997005i	$-0.475358\pi$
$359$	12.9111	−	3.79103i	0.681419	−	0.200083i	0.604082	+	0.796922i	$0.293540\pi$
$360$	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	−0.738590	−	0.674155i	$-0.764508\pi$
$373$	−33.3038	−	9.77889i	−1.72441	−	0.506332i	−0.985817	+	0.167824i	$0.946326\pi$
$374$	−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	0.923693	+	0.383132i	$0.125155\pi$
$379$	17.2970	+	26.9146i	0.888487	+	1.38251i	−0.0352067	+	0.999380i	$0.511209\pi$
$380$	−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	−0.942756	−	0.333484i	$-0.891776\pi$
$383$	1.09135	−	7.59048i	0.0557652	−	0.387855i	0.998521	−	0.0543709i	$-0.0173153\pi$
$384$	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	0.280103	−	0.959970i	$-0.409631\pi$
$389$	−9.40313	−	6.04302i	−0.476757	−	0.306393i	−0.756860	+	0.653577i	$0.773268\pi$
$390$	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	0.882490	−	0.470331i	$-0.155866\pi$
$397$	22.0159	+	10.0543i	1.10495	+	0.504612i	0.222456	+	0.974943i	$0.428593\pi$
$398$	−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	−0.967741	−	0.251946i	$-0.918929\pi$
$401$	−17.1431	+	14.8545i	−0.856083	+	0.741800i	0.111658	+	0.993747i	$0.464384\pi$
$402$	−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	0.887853	−	0.460128i	$-0.152196\pi$
$409$	28.0301	+	8.23037i	1.38600	+	0.406966i	0.498145	+	0.867094i	$0.334015\pi$
$410$	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	−0.944617	−	0.328174i	$-0.893567\pi$
$419$	0.562285	−	1.91497i	0.0274694	−	0.0935522i	0.972087	+	0.234621i	$0.0753851\pi$
$420$	1.58783	+	12.9332i	0.0774780	+	0.631074i
$421$	0.532308	−	0.614316i	0.0259431	−	0.0299399i	−0.742630	−	0.669702i	$-0.766422\pi$
$421$	0.532308	−	0.614316i	0.0259431	−	0.0299399i	0.768573	+	0.639762i	$0.220967\pi$
$422$	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	−0.994670	−	0.103109i	$-0.967121\pi$
$431$	−5.50933	+	12.0638i	−0.265375	+	0.581091i	0.729295	+	0.684199i	$0.239848\pi$
$432$	−25.6412	+	27.2344i	−1.23367	+	1.31032i
$433$	35.5534	−	16.2367i	1.70859	−	0.780285i	0.711610	−	0.702574i	$-0.247966\pi$
$433$	35.5534	−	16.2367i	1.70859	−	0.780285i	0.996976	−	0.0777109i	$-0.0247611\pi$
$434$	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	−0.916252	−	0.400603i	$-0.868801\pi$
$439$	−3.58757	+	5.58236i	−0.171225	+	0.266432i	0.745026	+	0.667035i	$0.232437\pi$
$440$	−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	0.566918	+	0.823775i	$0.308136\pi$
$443$	−8.98524	+	19.6749i	−0.426902	+	0.934784i	−0.993819	+	0.111010i	$0.964591\pi$
$444$	−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	−0.638277	−	0.769807i	$-0.720352\pi$
$449$	−4.30542	+	2.76693i	−0.203185	+	0.130579i	0.435091	+	0.900386i	$0.356716\pi$
$450$	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	−0.320939	−	0.947100i	$-0.603998\pi$
$457$	−7.73970	+	1.11280i	−0.362048	+	0.0520546i	−0.0411094	+	0.999155i	$0.513089\pi$
$458$	−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	$-0.923980\pi$
$461$		−	10.1583i		−	0.473120i	0.971617	−	0.236560i	$-0.0760200\pi$
$462$	−4.25245	−	1.29645i	−0.197842	−	0.0603162i
$463$	−36.0086	+	5.17726i	−1.67346	+	0.240608i	−0.912761	−	0.408494i	$-0.866054\pi$
$463$	−36.0086	+	5.17726i	−1.67346	+	0.240608i	−0.760701	+	0.649102i	$0.775145\pi$
$464$	−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	0.616058	−	0.787701i	$-0.288729\pi$
$467$	−1.64133	−	1.42222i	−0.0759517	−	0.0658125i	−0.692009	+	0.721889i	$0.743274\pi$
$468$	−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	−0.988850	−	0.148915i	$-0.952422\pi$
$479$	−9.93263	−	21.7494i	−0.453834	−	0.993757i	0.535016	−	0.844842i	$-0.320305\pi$
$480$	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	−0.482439	−	0.875930i	$-0.660249\pi$
$487$	−3.00977	+	1.37452i	−0.136386	+	0.0622852i	0.346053	+	0.938215i	$0.387522\pi$
$488$	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	−0.996727	−	0.0808398i	$-0.974240\pi$
$491$	−0.389973	+	2.71232i	−0.0175993	+	0.122405i	0.979128	+	0.203245i	$0.0651489\pi$
$492$	−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	−0.599201	−	0.800599i	$-0.704515\pi$
$499$	6.22175	−	7.18028i	0.278524	−	0.321433i	0.877725	+	0.479165i	$0.159060\pi$
$500$	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	0.970527	−	0.240993i	$-0.0774732\pi$
$503$	−0.641039	−	4.45852i	−0.0285825	−	0.198796i	−0.999109	+	0.0421976i	$0.986564\pi$
$504$	−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	0.669685	−	0.742646i	$-0.266429\pi$
$509$	34.3259	−	4.93532i	1.52147	−	0.218754i	0.851785	+	0.523891i	$0.175520\pi$
$510$	−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	−0.249650	−	0.968336i	$-0.580315\pi$
$521$	−17.3929	−	2.50073i	−0.761998	−	0.109559i	−0.512349	+	0.858777i	$0.671225\pi$
$522$	28.3951	−	60.5161i	1.24282	−	2.64872i
$523$	−4.36905	−	1.99528i	−0.191045	−	0.0872474i	0.317596	−	0.948226i	$-0.397125\pi$
$523$	−4.36905	−	1.99528i	−0.191045	−	0.0872474i	−0.508641	+	0.860979i	$0.669852\pi$
$524$	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	0.680210	−	0.733018i	$-0.261889\pi$
$541$	−6.25994	−	9.74066i	−0.269136	−	0.418784i	−0.949346	+	0.314234i	$0.898252\pi$
$542$	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	−0.542192	−	0.840254i	$-0.682406\pi$
$547$	−33.9732	−	9.97543i	−1.45259	−	0.426519i	−0.910397	+	0.413736i	$0.864224\pi$
$548$	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	0.491677	−	0.870778i	$-0.336384\pi$
$557$	10.2551	+	3.01117i	0.434523	+	0.127588i	−0.0571534	+	0.998365i	$0.518202\pi$
$558$	−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	0.764474	−	0.644654i	$-0.222999\pi$
$563$	−3.30995	−	5.15038i	−0.139498	−	0.217063i	−0.903972	+	0.427591i	$0.859362\pi$
$564$	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	0.509128	−	0.860691i	$-0.329968\pi$
$569$	4.58157	+	2.09233i	0.192069	+	0.0877151i	−0.317059	+	0.948406i	$0.602695\pi$
$570$	10.8311	+	0.111776i	0.453663	+	0.00468179i
$571$	1.14558	−	0.523169i	0.0479411	−	0.0218939i	−0.391300	−	0.920263i	$-0.627975\pi$
$571$	1.14558	−	0.523169i	0.0479411	−	0.0218939i	0.439241	+	0.898369i	$0.355247\pi$
$572$	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	0.981049	−	0.193759i	$-0.0620680\pi$
$577$	29.1215	+	18.7152i	1.21234	+	0.779125i	0.231293	+	0.972884i	$0.425704\pi$
$578$	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	−0.873348	−	0.487098i	$-0.838056\pi$
$587$	−19.2146	+	12.3484i	−0.793070	+	0.509675i	0.0802778	+	0.996773i	$0.474419\pi$
$588$	−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	0.340919	−	0.940092i	$-0.389262\pi$
$593$	2.90921	+	0.854220i	0.119467	+	0.0350786i	−0.221453	+	0.975171i	$0.571080\pi$
$594$	−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	$-0.892306\pi$
$599$		−	16.2467i		−	0.663823i	0.943311	−	0.331911i	$-0.107694\pi$
$600$	−2.14926	−	8.25715i	−0.0877432	−	0.337097i
$601$	−4.84423	−	33.6924i	−0.197600	−	1.37434i	−0.811221	−	0.584740i	$-0.801197\pi$
$601$	−4.84423	−	33.6924i	−0.197600	−	1.37434i	0.613621	−	0.789601i	$-0.289712\pi$
$602$	−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	0.982283	+	0.187405i	$0.0600078\pi$
$607$	6.33804	+	21.5854i	0.257253	+	0.876123i	−0.725030	+	0.688718i	$0.758174\pi$
$608$	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	−0.515783	−	0.856719i	$-0.672499\pi$
$613$	5.45865	−	37.9657i	0.220473	−	1.53342i	0.736256	−	0.676703i	$-0.236592\pi$
$614$	−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	0.258995	−	0.965879i	$-0.416609\pi$
$617$	28.7781	−	13.1425i	1.15856	−	0.529098i	0.899568	+	0.436780i	$0.143881\pi$
$618$	−0.293597	+	0.130437i	−0.0118102	+	0.00524693i
$619$	16.2315	−	25.2568i	0.652401	−	1.01516i	−0.344674	−	0.938722i	$-0.612011\pi$
$619$	16.2315	−	25.2568i	0.652401	−	1.01516i	0.997075	−	0.0764327i	$-0.0243530\pi$
$620$	−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	0.981691	+	0.190481i	$0.0610049\pi$
$631$	25.8865	+	29.8746i	1.03052	+	1.18929i	0.0488334	+	0.998807i	$0.484450\pi$
$632$	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	−0.685025	−	0.728520i	$-0.740209\pi$
$641$	−28.7879	+	4.13908i	−1.13705	+	0.163484i	−0.452029	+	0.892003i	$0.649300\pi$
$642$	−29.6194	−	9.03006i	−1.16898	−	0.356388i
$643$			27.9770i			1.10330i	0.834075	+	0.551652i	$0.186002\pi$
$643$			27.9770i			1.10330i	−0.834075	+	0.551652i	$0.813998\pi$
$644$	−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	−0.744329	−	0.667813i	$-0.767231\pi$
$647$	−32.3132	+	4.64594i	−1.27036	+	0.182651i	−0.526034	+	0.850464i	$0.676322\pi$
$648$	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	−0.599651	−	0.800262i	$-0.704694\pi$
$653$	−13.4885	−	45.9377i	−0.527847	−	1.79768i	0.0718044	−	0.997419i	$-0.477124\pi$
$654$	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	0.169089	−	0.985601i	$-0.445918\pi$
$659$	1.37730	+	0.198026i	0.0536522	+	0.00771402i	−0.115436	+	0.993315i	$0.536827\pi$
$660$	2.87226	+	0.473665i	0.111803	+	0.0184374i
$661$	2.23170	−	4.88675i	0.0868032	−	0.190072i	−0.861252	−	0.508178i	$-0.830319\pi$
$661$	2.23170	−	4.88675i	0.0868032	−	0.190072i	0.948055	+	0.318105i	$0.103047\pi$
$662$	−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	0.0798633	+	0.996806i	$0.474552\pi$
$673$	−18.8281	+	41.2279i	−0.725772	+	1.58922i	−0.805635	+	0.592412i	$0.798176\pi$
$674$	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	0.999967	−	0.00808129i	$-0.00257238\pi$
$677$	22.1074	+	25.5134i	0.849658	+	0.980558i	−0.150309	+	0.988639i	$0.548027\pi$
$678$	−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	−0.385836	−	0.922568i	$-0.626087\pi$
$683$	15.2167	−	17.5610i	0.582252	−	0.671954i	0.968087	+	0.250613i	$0.0806323\pi$
$684$	−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	0.222542	−	0.974923i	$-0.428564\pi$
$701$	31.8196	−	20.4492i	1.20181	−	0.772357i	0.979269	+	0.202566i	$0.0649281\pi$
$702$	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	0.832166	−	0.554526i	$-0.187101\pi$
$709$	−3.51131	−	7.68869i	−0.131870	−	0.288755i	−0.964036	+	0.265772i	$0.914373\pi$
$710$	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	0.672506	−	0.740092i	$-0.265218\pi$
$719$	14.8438	+	6.77892i	0.553579	+	0.252811i	−0.118927	+	0.992903i	$0.537945\pi$
$720$	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	−0.984521	−	0.175269i	$-0.943921\pi$
$727$	−46.3222	+	13.6014i	−1.71799	+	0.504449i	−0.733474	+	0.679718i	$0.762102\pi$
$728$	−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	0.949613	+	0.313424i	$0.101476\pi$
$733$	3.43211	+	23.8708i	0.126768	+	0.881689i	−0.822846	+	0.568265i	$0.807615\pi$
$734$	−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	−0.981794	−	0.189948i	$-0.939168\pi$
$739$	−2.53589	−	17.6375i	−0.0932841	−	0.648805i	0.888510	−	0.458857i	$-0.151741\pi$
$740$	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	−0.904234	−	0.427037i	$-0.859557\pi$
$743$	−9.61820	+	11.1000i	−0.352858	+	0.407220i	0.551376	+	0.834257i	$0.314103\pi$
$744$	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	0.783076	+	0.621926i	$0.213650\pi$
$751$	−3.93244	+	27.3507i	−0.143497	+	0.998042i	−0.926573	+	0.376116i	$0.877259\pi$
$752$	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	0.226244	−	0.974071i	$-0.427355\pi$
$757$	−15.5677	−	10.0047i	−0.565817	−	0.363629i	−0.792061	+	0.610442i	$0.790992\pi$
$758$	−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	0.727343	−	0.686274i	$-0.240755\pi$
$761$	11.1789	+	7.18426i	0.405236	+	0.260429i	−0.322107	+	0.946703i	$0.604391\pi$
$762$	−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	−0.937009	−	0.349305i	$-0.886418\pi$
$769$	−20.0940	+	17.4116i	−0.724610	+	0.627878i	0.212399	+	0.977183i	$0.431872\pi$
$770$	−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	0.329685	−	0.944091i	$-0.393058\pi$
$773$	31.0683	−	9.12246i	1.11745	−	0.328112i	0.787763	+	0.615979i	$0.211239\pi$
$774$	−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	−0.821182	−	0.570667i	$-0.806685\pi$
$787$	4.99819	−	17.0223i	0.178166	−	0.606778i	0.999348	−	0.0361113i	$-0.0114971\pi$
$788$	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	0.279520	+	0.960140i	$0.409825\pi$
$797$	−7.31696	+	50.8906i	−0.259180	+	1.80264i	−0.538700	+	0.842498i	$0.681084\pi$
$798$	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	0.851880	−	0.523737i	$-0.175463\pi$
$809$	−2.89540	−	6.34003i	−0.101797	−	0.222904i	−0.953677	+	0.300833i	$0.902735\pi$
$810$	0.144621	−	14.0138i	0.00508148	−	0.492393i
$811$	12.3249	−	26.9877i	0.432784	−	0.947665i	−0.560083	−	0.828437i	$-0.689231\pi$
$811$	12.3249	−	26.9877i	0.432784	−	0.947665i	0.992867	−	0.119229i	$-0.0380421\pi$
$812$	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	0.928435	−	0.371495i	$-0.121155\pi$
$821$	19.8523	+	17.2021i	0.692851	+	0.600359i	−0.235584	+	0.971854i	$0.575700\pi$
$822$	−6.79961	+	44.0597i	−0.237164	+	1.53676i
$823$	−9.50782	+	32.3806i	−0.331422	+	1.12872i	0.610257	+	0.792204i	$0.291066\pi$
$823$	−9.50782	+	32.3806i	−0.331422	+	1.12872i	−0.941678	+	0.336515i	$0.890752\pi$
$824$	−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	$0.0309420\pi$
$827$			5.58209i			0.194108i	−0.995279	+	0.0970541i	$0.969058\pi$
$828$	−57.9017	−	8.40745i	−2.01222	−	0.292179i
$829$			3.72702i			0.129445i	0.997903	+	0.0647224i	$0.0206162\pi$
$829$			3.72702i			0.129445i	−0.997903	+	0.0647224i	$0.979384\pi$
$830$	−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	0.0468605	−	0.998901i	$-0.485078\pi$
$839$	28.2402	−	18.1489i	0.974960	−	0.626569i	0.928099	+	0.372333i	$0.121442\pi$
$840$	−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	−0.515691	−	0.856775i	$-0.672465\pi$
$853$	13.9572	−	21.7178i	0.477885	−	0.743603i	0.993575	+	0.113172i	$0.0361010\pi$
$854$	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	−0.862956	−	0.505279i	$-0.831390\pi$
$857$	2.45977	−	5.38615i	0.0840243	−	0.183988i	0.946980	+	0.321291i	$0.104117\pi$
$858$	−0.983758	−	0.461595i	−0.0335849	−	0.0157586i
$859$	7.36933	−	51.2548i	0.251438	−	1.74879i	−0.338154	−	0.941091i	$-0.609802\pi$
$859$	7.36933	−	51.2548i	0.251438	−	1.74879i	0.589592	−	0.807701i	$-0.299289\pi$
$860$	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	−0.929592	−	0.368590i	$-0.879840\pi$
$863$	−25.8137	−	40.1668i	−0.878707	−	1.36730i	0.0508847	−	0.998705i	$-0.483796\pi$
$864$	−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	−0.617164	−	0.786834i	$-0.711719\pi$
$877$	−29.2485	+	4.20530i	−0.987652	+	0.142003i	−0.370488	+	0.928837i	$0.620810\pi$
$878$	−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	−0.975154	−	0.221528i	$-0.928896\pi$
$881$	−39.5717	−	34.2891i	−1.33321	−	1.15523i	−0.358052	−	0.933702i	$-0.616559\pi$
$882$	19.9709	−	2.66134i	0.672456	−	0.0896118i
$883$	40.2636	−	11.8225i	1.35498	−	0.397858i	0.477989	−	0.878366i	$-0.341366\pi$
$883$	40.2636	−	11.8225i	1.35498	−	0.397858i	0.876990	+	0.480508i	$0.159548\pi$
$884$	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	−0.788348	−	0.615230i	$-0.789063\pi$
$887$	−8.68381	+	7.52457i	−0.291574	+	0.252650i	0.496774	+	0.867880i	$0.334518\pi$
$888$	−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	−0.996882	−	0.0789095i	$-0.974856\pi$
$907$	−31.9429	+	27.6787i	−1.06065	+	0.919055i	−0.0637648	+	0.997965i	$0.520311\pi$
$908$	−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	0.568277	−	0.822837i	$-0.307610\pi$
$911$	45.0086	−	13.2157i	1.49120	−	0.437856i	0.922925	+	0.384981i	$0.125792\pi$
$912$	−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	−0.0892137	−	0.996013i	$-0.528435\pi$
$929$	11.4060	−	3.34911i	0.374220	−	0.109881i	0.463434	+	0.886132i	$0.346617\pi$
$930$	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	−0.0711760	−	0.997464i	$-0.522675\pi$
$937$	−26.6807	−	12.1846i	−0.871619	−	0.398055i	−0.800443	+	0.599409i	$0.795402\pi$
$938$	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	0.857962	−	0.513713i	$-0.171730\pi$
$941$	22.9173	+	14.7281i	0.747083	+	0.480121i	−0.110879	+	0.993834i	$0.535367\pi$
$942$	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	0.549374	+	0.835577i	$0.314866\pi$
$947$	25.2679	+	55.3290i	0.821097	+	1.79795i	0.271723	+	0.962375i	$0.412406\pi$
$948$	−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	−0.994172	−	0.107807i	$-0.965617\pi$
$953$	−31.7643	+	27.5239i	−1.02895	+	0.891588i	−0.0347756	+	0.999395i	$0.511072\pi$
$954$	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	$-0.886683\pi$
$967$		−	21.6758i		−	0.697046i	0.937300	−	0.348523i	$-0.113317\pi$
$968$	−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	−0.989040	−	0.147647i	$-0.952830\pi$
$971$	−2.40507	+	8.19093i	−0.0771825	+	0.262859i	0.911858	+	0.410507i	$0.134648\pi$
$972$	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	0.975482	−	0.220077i	$-0.0706310\pi$
$977$	11.5671	+	17.9987i	0.370063	+	0.575829i	−0.605420	+	0.795907i	$0.706995\pi$
$978$	−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	0.635165	+	0.772377i	$0.280932\pi$
$983$	−11.4282	+	25.0243i	−0.364503	+	0.798150i	−0.999668	+	0.0257736i	$0.991795\pi$
$984$	−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	−0.716637	−	0.697446i	$-0.754320\pi$
$991$	6.78346	−	10.5553i	0.215484	−	0.335299i	0.932121	+	0.362147i	$0.117956\pi$
$992$	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	0.235236	−	0.971938i	$-0.424414\pi$
$997$	5.90824	+	0.849477i	0.187116	+	0.0269032i	−0.0481198	+	0.998842i	$0.515323\pi$
$998$	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.251.19	yes	480
8.3	odd	2		920.2.bb.b.251.37	yes	480
23.11	odd	22		920.2.bb.b.11.37	yes	480
184.11	even	22	inner	920.2.bb.a.11.19	✓	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bb.a.11.19	✓	480	184.11	even	22	inner
920.2.bb.a.251.19	yes	480	1.1	even	1	trivial
920.2.bb.b.11.37	yes	480	23.11	odd	22
920.2.bb.b.251.37	yes	480	8.3	odd	2

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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