LMFDB - Embedded newform 920.2.bb.b.11.37

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(11,920)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			11.37
Character	$\chi$	$=$	920.11
Dual form			920.2.bb.b.251.37

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.05918 + 0.937093i) q^{2} +(-0.429309 + 2.98591i) q^{3} +(0.243714 + 1.98510i) q^{4} +(0.959493 - 0.281733i) q^{5} +(-3.25279 + 2.76031i) q^{6} +(1.41433 + 1.63223i) q^{7} +(-1.60208 + 2.33095i) q^{8} +(-5.85288 - 1.71856i) q^{9} +(1.28028 + 0.600729i) q^{10} +(0.260861 - 0.405908i) q^{11} +(-6.03195 - 0.124512i) q^{12} +(0.398969 + 0.345709i) q^{13} +(-0.0315190 + 3.05418i) q^{14} +(0.429309 + 2.98591i) q^{15} +(-3.88121 + 0.967590i) q^{16} +(1.00123 - 0.457246i) q^{17} +(-4.58879 - 7.30495i) q^{18} +(-2.30954 - 1.05473i) q^{19} +(0.793108 + 1.83602i) 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} +(0.0986179 + 0.740038i) q^{26} +(3.88472 - 8.50636i) q^{27} +(-2.89544 + 3.20539i) q^{28} +(-7.04860 + 3.21899i) q^{29} +(-2.34336 + 3.56491i) q^{30} +(4.41035 - 0.634113i) q^{31} +(-5.01761 - 2.61220i) q^{32} +(1.10002 + 0.953169i) q^{33} +(1.48896 + 0.453940i) q^{34} +(1.81690 + 1.16765i) q^{35} +(1.98508 - 12.0374i) q^{36} +(-3.42102 - 1.00450i) q^{37} +(-1.45783 - 3.28140i) q^{38} +(-1.20354 + 1.04287i) q^{39} +(-0.880482 + 2.68789i) q^{40} +(5.07992 - 1.49160i) q^{41} +(-9.10599 - 1.40530i) q^{42} +(9.40966 + 1.35291i) q^{43} +(0.869342 + 0.418909i) q^{44} -6.09997 q^{45} +(4.28803 + 5.25479i) q^{46} -1.55715i q^{47} +(-1.22290 - 12.0043i) q^{48} +(0.332374 - 2.31171i) q^{49} +(1.39767 + 0.215698i) q^{50} +(0.935459 + 3.18588i) q^{51} +(-0.589030 + 0.876246i) q^{52} +(0.419139 + 0.483712i) q^{53} +(12.0859 - 5.36940i) q^{54} +(0.135937 - 0.462959i) q^{55} +(-6.07053 + 0.681778i) q^{56} +(4.14084 - 6.44327i) q^{57} +(-10.4822 - 3.19571i) q^{58} +(7.29413 - 8.41787i) q^{59} +(-5.82269 + 1.57993i) q^{60} +(1.47679 + 10.2713i) q^{61} +(5.26557 + 3.46127i) q^{62} +(-5.47285 - 11.9839i) q^{63} +(-2.86666 - 7.46875i) q^{64} +(0.480205 + 0.219302i) q^{65} +(0.271904 + 2.04039i) 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} +(13.3827 - 10.8895i) q^{72} +(5.17201 - 11.3251i) q^{73} +(-2.68216 - 4.26976i) q^{74} +(1.25315 + 2.74401i) q^{75} +(1.53087 - 4.84170i) q^{76} +(1.03148 - 0.148304i) q^{77} +(-2.25203 - 0.0232408i) q^{78} +(-1.22567 + 1.41450i) q^{79} +(-3.45139 + 2.02186i) q^{80} +(8.33661 + 5.35761i) q^{81} +(6.77831 + 3.18049i) q^{82} +(-2.13633 + 7.27566i) q^{83} +(-8.32796 - 10.0216i) q^{84} +(0.831851 - 0.720803i) q^{85} +(8.69871 + 10.2507i) q^{86} +(-6.58558 - 22.4284i) q^{87} +(0.528230 + 1.25835i) q^{88} +(-17.3851 - 2.49959i) q^{89} +(-6.46095 - 5.71624i) q^{90} +1.14016i q^{91} +(-0.382448 + 9.58404i) q^{92} +13.4412i q^{93} +(1.45920 - 1.64930i) q^{94} +(-2.51314 - 0.361335i) q^{95} +(9.95391 - 13.8607i) q^{96} +(4.34339 + 14.7922i) q^{97} +(2.51833 - 2.13705i) 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} - 56 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 - 56 * 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 + 102 * q^32 + q^34 + 54 * q^36 - 8 * q^37 - 45 * q^38 + 45 * q^40 + 10 * q^42 + 23 * q^44 - 480 * q^45 + 32 * q^46 + 154 * q^48 - 48 * q^49 - 9 * q^50 - 7 * q^52 - 32 * q^53 - 27 * q^54 + 43 * q^56 - 40 * q^58 - 12 * q^59 + 8 * q^60 + 8 * q^61 + 158 * q^62 - 73 * q^64 - 88 * q^66 - 10 * q^68 + 20 * q^69 + 3 * q^72 - 11 * q^74 - 110 * q^76 - 300 * q^78 + 144 * q^79 + q^80 - 56 * q^81 - 59 * q^82 - 146 * q^84 + 18 * q^86 - 100 * q^88 - 7 * q^90 + 19 * q^92 - 316 * 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 $

$2$	1.05918	+	0.937093i	0.748952	+	0.662625i
$2$	1.05918	+	0.937093i	0.748952	+	0.662625i
$3$	−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	$0.709042\pi$
$4$	0.243714	+	1.98510i	0.121857	+	0.992548i
$5$	0.959493	−	0.281733i	0.429098	−	0.125995i
$5$	0.959493	−	0.281733i	0.429098	−	0.125995i
$6$	−3.25279	+	2.76031i	−1.32795	+	1.12689i
$7$	1.41433	+	1.63223i	0.534568	+	0.616925i	0.957218	−	0.289369i	$-0.0934453\pi$
$7$	1.41433	+	1.63223i	0.534568	+	0.616925i	−0.422650	+	0.906293i	$0.638900\pi$
$8$	−1.60208	+	2.33095i	−0.566422	+	0.824116i
$9$	−5.85288	−	1.71856i	−1.95096	−	0.572854i
$10$	1.28028	+	0.600729i	0.404861	+	0.189967i
$11$	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	$0.158644\pi$
$12$	−6.03195	−	0.124512i	−1.74127	−	0.0359436i
$13$	0.398969	+	0.345709i	0.110654	+	0.0958823i	0.708431	−	0.705780i	$-0.249404\pi$
$13$	0.398969	+	0.345709i	0.110654	+	0.0958823i	−0.597776	+	0.801663i	$0.703949\pi$
$14$	−0.0315190	+	3.05418i	−0.00842382	+	0.816265i
$15$	0.429309	+	2.98591i	0.110847	+	0.770959i
$16$	−3.88121	+	0.967590i	−0.970302	+	0.241898i
$17$	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	$0.321021\pi$
$18$	−4.58879	−	7.30495i	−1.08159	−	1.72179i
$19$	−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	$0.730432\pi$
$20$	0.793108	+	1.83602i	0.177344	+	0.410547i
$21$	−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
$26$	0.0986179	+	0.740038i	0.0193406	+	0.145133i
$27$	3.88472	−	8.50636i	0.747615	−	1.63705i
$28$	−2.89544	+	3.20539i	−0.547186	+	0.605761i
$29$	−7.04860	+	3.21899i	−1.30889	+	0.597751i	−0.942965	−	0.332892i	$-0.891976\pi$
$29$	−7.04860	+	3.21899i	−1.30889	+	0.597751i	−0.365928	+	0.930643i	$0.619248\pi$
$30$	−2.34336	+	3.56491i	−0.427837	+	0.650861i
$31$	4.41035	−	0.634113i	0.792123	−	0.113890i	0.265636	−	0.964073i	$-0.414418\pi$
$31$	4.41035	−	0.634113i	0.792123	−	0.113890i	0.526487	+	0.850183i	$0.323509\pi$
$32$	−5.01761	−	2.61220i	−0.886996	−	0.461776i
$33$	1.10002	+	0.953169i	0.191488	+	0.165925i
$34$	1.48896	+	0.453940i	0.255355	+	0.0778500i
$35$	1.81690	+	1.16765i	0.307111	+	0.197369i
$36$	1.98508	−	12.0374i	0.330847	−	2.00623i
$37$	−3.42102	−	1.00450i	−0.562413	−	0.165139i	−0.0118450	−	0.999930i	$-0.503770\pi$
$37$	−3.42102	−	1.00450i	−0.562413	−	0.165139i	−0.550568	+	0.834791i	$0.685589\pi$
$38$	−1.45783	−	3.28140i	−0.236491	−	0.532313i
$39$	−1.20354	+	1.04287i	−0.192720	+	0.166993i
$40$	−0.880482	+	2.68789i	−0.139216	+	0.424993i
$41$	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	$0.273424\pi$
$42$	−9.10599	−	1.40530i	−1.40508	−	0.216843i
$43$	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	$0.287360\pi$
$44$	0.869342	+	0.418909i	0.131058	+	0.0631529i
$45$	−6.09997			−0.909330
$46$	4.28803	+	5.25479i	0.632235	+	0.774777i
$47$		−	1.55715i		−	0.227134i	−0.993530	−	0.113567i	$-0.963772\pi$
$47$		−	1.55715i		−	0.227134i	0.993530	−	0.113567i	$-0.0362276\pi$
$48$	−1.22290	−	12.0043i	−0.176510	−	1.73268i
$49$	0.332374	−	2.31171i	0.0474821	−	0.330245i
$50$	1.39767	+	0.215698i	0.197660	+	0.0305043i
$51$	0.935459	+	3.18588i	0.130990	+	0.446112i
$52$	−0.589030	+	0.876246i	−0.0816838	+	0.121513i
$53$	0.419139	+	0.483712i	0.0575732	+	0.0664430i	0.783806	−	0.621006i	$-0.213276\pi$
$53$	0.419139	+	0.483712i	0.0575732	+	0.0664430i	−0.726232	+	0.687449i	$0.758730\pi$
$54$	12.0859	−	5.36940i	1.64468	−	0.730682i
$55$	0.135937	−	0.462959i	0.0183297	−	0.0624254i
$56$	−6.07053	+	0.681778i	−0.811208	+	0.0911064i
$57$	4.14084	−	6.44327i	0.548467	−	0.853432i
$58$	−10.4822	−	3.19571i	−1.37638	−	0.419618i
$59$	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	$-0.0309111\pi$
$60$	−5.82269	+	1.57993i	−0.751706	+	0.203968i
$61$	1.47679	+	10.2713i	0.189084	+	1.31511i	0.834386	+	0.551181i	$0.185823\pi$
$61$	1.47679	+	10.2713i	0.189084	+	1.31511i	−0.645301	+	0.763928i	$0.723268\pi$
$62$	5.26557	+	3.46127i	0.668728	+	0.439582i
$63$	−5.47285	−	11.9839i	−0.689514	−	1.50982i
$64$	−2.86666	−	7.46875i	−0.358333	−	0.933594i
$65$	0.480205	+	0.219302i	0.0595622	+	0.0272011i
$66$	0.271904	+	2.04039i	0.0334690	+	0.251155i
$67$	−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	0.974046	−	0.226351i	$-0.0726797\pi$
$71$	3.06304	+	4.76619i	0.363516	+	0.565642i	−0.610529	+	0.791994i	$0.709043\pi$
$72$	13.3827	−	10.8895i	1.57716	−	1.28334i
$73$	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	$-0.123463\pi$
$74$	−2.68216	−	4.26976i	−0.311794	−	0.496350i
$75$	1.25315	+	2.74401i	0.144701	+	0.316851i
$76$	1.53087	−	4.84170i	0.175603	−	0.555382i
$77$	1.03148	−	0.148304i	0.117548	−	0.0169009i
$78$	−2.25203	−	0.0232408i	−0.254992	−	0.00263150i
$79$	−1.22567	+	1.41450i	−0.137899	+	0.159143i	−0.820498	−	0.571649i	$-0.806304\pi$
$79$	−1.22567	+	1.41450i	−0.137899	+	0.159143i	0.682600	+	0.730793i	$0.260849\pi$
$80$	−3.45139	+	2.02186i	−0.385877	+	0.226051i
$81$	8.33661	+	5.35761i	0.926290	+	0.595291i
$82$	6.77831	+	3.18049i	0.748539	+	0.351226i
$83$	−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	$0.954284\pi$
$84$	−8.32796	−	10.0216i	−0.908655	−	1.09345i
$85$	0.831851	−	0.720803i	0.0902269	−	0.0781820i
$86$	8.69871	+	10.2507i	0.938006	+	1.10536i
$87$	−6.58558	−	22.4284i	−0.706049	−	2.40458i
$88$	0.528230	+	1.25835i	0.0563096	+	0.134141i
$89$	−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	$0.926413\pi$
$90$	−6.46095	−	5.71624i	−0.681044	−	0.602545i
$91$			1.14016i			0.119521i
$92$	−0.382448	+	9.58404i	−0.0398730	+	0.999205i
$93$			13.4412i			1.39378i
$94$	1.45920	−	1.64930i	0.150505	−	0.170112i
$95$	−2.51314	−	0.361335i	−0.257842	−	0.0370721i
$96$	9.95391	−	13.8607i	1.01592	−	1.41465i
$97$	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	$0.622951\pi$
$98$	2.51833	−	2.13705i	0.254390	−	0.215875i
$99$	−2.22437	+	1.92743i	−0.223557	+	0.193714i
$100$	1.27825	+	1.53821i	0.127825	+	0.153821i
$101$	−3.40016	+	11.5799i	−0.338329	+	1.15224i	0.598111	+	0.801413i	$0.295918\pi$
$101$	−3.40016	+	11.5799i	−0.338329	+	1.15224i	−0.936440	+	0.350828i	$0.885900\pi$
$102$	−1.99465	+	4.25102i	−0.197500	+	0.420914i
$103$	0.0633518	+	0.0407137i	0.00624224	+	0.00401164i	0.543758	−	0.839242i	$-0.317001\pi$
$103$	0.0633518	+	0.0407137i	0.00624224	+	0.00401164i	−0.537516	+	0.843254i	$0.680637\pi$
$104$	−1.44501	+	0.376123i	−0.141695	+	0.0368819i
$105$	−4.26650	+	4.92381i	−0.416368	+	0.480514i
$106$	−0.00934070	+	0.905110i	−0.000907249	+	0.0879120i
$107$	−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	$0.568652\pi$
$108$	17.8327	+	5.63843i	1.71595	+	0.542558i
$109$	−1.79258	−	3.92520i	−0.171698	−	0.375966i	0.804147	−	0.594430i	$-0.202622\pi$
$109$	−1.79258	−	3.92520i	−0.171698	−	0.375966i	−0.975845	+	0.218465i	$0.929895\pi$
$110$	0.577817	−	0.362970i	0.0550927	−	0.0346079i
$111$	4.46803	−	9.78363i	0.424087	−	0.928621i
$112$	−7.06865	−	4.96652i	−0.667925	−	0.469292i
$113$	−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
$118$	15.6141	−	2.08075i	1.43740	−	0.191548i
$119$	2.16240	+	0.987536i	0.198227	+	0.0905273i
$120$	−7.64780	−	3.78298i	−0.698146	−	0.345337i
$121$	4.47285	+	9.79418i	0.406623	+	0.890380i
$122$	−8.06100	+	12.2631i	−0.729809	+	1.11024i
$123$	2.27293	+	15.8086i	0.204943	+	1.42541i
$124$	2.33364	+	8.60043i	0.209567	+	0.772341i
$125$	0.654861	−	0.755750i	0.0585725	−	0.0675963i
$126$	5.43328	−	17.8216i	0.484035	−	1.58767i
$127$	7.73517	−	12.0362i	0.686385	−	1.06804i	−0.306832	−	0.951764i	$-0.599269\pi$
$127$	7.73517	−	12.0362i	0.686385	−	1.06804i	0.993217	−	0.116272i	$-0.0370945\pi$
$128$	3.96261	−	10.5971i	0.350249	−	0.936657i
$129$	−8.07931	+	27.5156i	−0.711344	+	2.42261i
$130$	0.303116	+	0.682277i	0.0265850	+	0.0598397i
$131$	−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	$0.867373\pi$
$132$	−1.62404	+	2.41594i	−0.141355	+	0.210280i
$133$	−1.54490	−	5.26144i	−0.133960	−	0.456224i
$134$	0.138086	−	0.894764i	0.0119288	−	0.0772958i
$135$	1.33085	−	9.25624i	0.114541	−	0.796651i
$136$	−0.538234	+	3.06636i	−0.0461532	+	0.262938i
$137$		−	10.4500i		−	0.892806i	−0.894832	−	0.446403i	$-0.852705\pi$
$137$		−	10.4500i		−	0.892806i	0.894832	−	0.446403i	$-0.147295\pi$
$138$	−17.5312	+	10.5477i	−1.49236	+	0.897883i
$139$	5.08260			0.431100			0.215550	−	0.976493i	$-0.430846\pi$
$139$	5.08260			0.431100			0.215550	+	0.976493i	$0.430846\pi$
$140$	−1.87509	+	3.89128i	−0.158474	+	0.328874i
$141$	4.64952	+	0.668499i	0.391560	+	0.0562978i
$142$	−1.22205	+	7.91859i	−0.102553	+	0.664514i
$143$	0.244402	−	0.0717628i	0.0204379	−	0.00600110i
$144$	24.3791	+	1.00690i	2.03159	+	0.0839085i
$145$	−5.85619	+	5.07442i	−0.486330	+	0.421407i
$146$	16.0908	−	7.14866i	1.33168	−	0.591628i
$147$	6.75988	+	1.98488i	0.557546	+	0.163710i
$148$	1.16028	−	7.03587i	0.0953747	−	0.578345i
$149$	16.5149	+	10.6135i	1.35296	+	0.869492i	0.997863	−	0.0653390i	$-0.0208129\pi$
$149$	16.5149	+	10.6135i	1.35296	+	0.869492i	0.355093	+	0.934831i	$0.384449\pi$
$150$	−1.24409	+	4.08071i	−0.101579	+	0.333189i
$151$	12.4236	+	10.7651i	1.01102	+	0.876054i	0.992311	−	0.123771i	$-0.0394987\pi$
$151$	12.4236	+	10.7651i	1.01102	+	0.876054i	0.0187098	+	0.999825i	$0.494044\pi$
$152$	6.15860	−	3.69365i	0.499528	−	0.299595i
$153$	−6.64588	+	0.955533i	−0.537287	+	0.0772502i
$154$	1.23150	+	0.809512i	0.0992367	+	0.0652323i
$155$	4.05305	−	1.85097i	0.325549	−	0.148673i
$156$	−2.36352	−	2.13497i	−0.189233	−	0.170935i
$157$	−1.97474	+	4.32408i	−0.157601	+	0.345099i	−0.971917	−	0.235323i	$-0.924385\pi$
$157$	−1.97474	+	4.32408i	−0.157601	+	0.345099i	0.814316	+	0.580422i	$0.197112\pi$
$158$	−2.62372	+	0.349638i	−0.208732	+	0.0278157i
$159$	−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	$0.635830\pi$
$164$	4.19902	+	9.72061i	0.327888	+	0.759052i
$165$	1.32400	+	0.604649i	0.103073	+	0.0470718i
$166$	−9.08071	+	5.70428i	−0.704800	+	0.442738i
$167$	−3.02919	+	1.38339i	−0.234406	+	0.107050i	−0.529155	−	0.848525i	$-0.677491\pi$
$167$	−3.02919	+	1.38339i	−0.234406	+	0.107050i	0.294749	+	0.955575i	$0.404764\pi$
$168$	0.570404	−	18.4187i	0.0440076	−	1.42104i
$169$	−1.81043	−	12.5918i	−0.139264	−	0.968602i
$170$	1.55654	+	0.0160634i	0.119381	+	0.00123201i
$171$	11.7048	+	10.1423i	0.895091	+	0.775601i
$172$	−0.392382	+	19.0088i	−0.0299188	+	1.44941i
$173$	−1.52566	+	2.37398i	−0.115994	+	0.180490i	−0.894396	−	0.447276i	$-0.852394\pi$
$173$	−1.52566	+	2.37398i	−0.115994	+	0.180490i	0.778402	+	0.627766i	$0.216031\pi$
$174$	14.0422	−	29.9270i	1.06454	−	2.26876i
$175$	2.07226	+	0.608471i	0.156648	+	0.0459961i
$176$	−0.619704	+	1.82782i	−0.0467120	+	0.137777i
$177$	22.0036	+	25.3935i	1.65389	+	1.90869i
$178$	−16.0715	−	18.9389i	−1.20461	−	1.41953i
$179$	−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	$0.477889\pi$
$180$	−1.48665	−	12.1090i	−0.110808	−	0.902554i
$181$	1.55415	−	10.8094i	0.115519	−	0.803455i	−0.846874	−	0.531794i	$-0.821518\pi$
$181$	1.55415	−	10.8094i	0.115519	−	0.803455i	0.962393	−	0.271661i	$-0.0875728\pi$
$182$	−1.06843	+	1.20763i	−0.0791975	+	0.0895154i
$183$	−31.3033			−2.31401
$184$	−9.38621	+	9.79280i	−0.691961	+	0.721935i
$185$	−3.56545			−0.262137
$186$	−12.5956	+	14.2366i	−0.923555	+	1.04388i
$187$	0.0755820	−	0.525685i	0.00552711	−	0.0384419i
$188$	3.09109	−	0.379499i	0.225441	−	0.0276778i
$189$	19.3786	−	5.69008i	1.40959	−	0.413892i
$190$	−2.32325	−	2.73776i	−0.168547	−	0.198618i
$191$	7.84295	+	9.05125i	0.567496	+	0.654925i	0.964869	−	0.262732i	$-0.0846235\pi$
$191$	7.84295	+	9.05125i	0.567496	+	0.654925i	−0.397373	+	0.917657i	$0.630078\pi$
$192$	23.5317	−	5.35319i	1.69826	−	0.386334i
$193$	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	$0.423895\pi$
$194$	−9.26128	+	19.7378i	−0.664921	+	1.41709i
$195$	−0.860974	+	1.33970i	−0.0616557	+	0.0959381i
$196$	4.66998	+	0.0963982i	0.333570	+	0.00688559i
$197$	7.46744	+	6.47057i	0.532033	+	0.461009i	0.878968	−	0.476880i	$-0.158232\pi$
$197$	7.46744	+	6.47057i	0.532033	+	0.461009i	−0.346936	+	0.937889i	$0.612778\pi$
$198$	−4.16218	−	0.0429535i	−0.295793	−	0.00305257i
$199$	3.50663	+	24.3892i	0.248579	+	1.72890i	0.606441	+	0.795129i	$0.292597\pi$
$199$	3.50663	+	24.3892i	0.248579	+	1.72890i	−0.357862	+	0.933774i	$0.616494\pi$
$200$	−0.0875507	+	2.82707i	−0.00619077	+	0.199904i
$201$	1.75667	−	0.802244i	0.123906	−	0.0565860i
$202$	−14.4528	+	9.07889i	−1.01690	+	0.638788i
$203$	−15.2232	−	6.95221i	−1.06846	−	0.487949i
$204$	−6.09629	+	2.63342i	−0.426826	+	0.184376i
$205$	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
$210$	−9.13305	+	1.21708i	−0.630240	+	0.0839862i
$211$	−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	$0.151572\pi$
$212$	−0.858065	+	0.949919i	−0.0589322	+	0.0652407i
$213$	−15.5464	+	7.09981i	−1.06522	+	0.486471i
$214$	−8.57766	−	5.63844i	−0.586357	−	0.385436i
$215$	9.40966	−	1.35291i	0.641734	−	0.0922674i
$216$	13.6043	+	22.6830i	0.925652	+	1.54338i
$217$	7.27273	+	6.30186i	0.493705	+	0.427798i
$218$	1.77962	−	5.83729i	0.120531	−	0.395351i
$219$	31.5954	+	20.3052i	2.13502	+	1.37210i
$220$	0.952148	+	0.157019i	0.0641938	+	0.0105862i
$221$	0.557533	+	0.163706i	0.0375037	+	0.0110121i
$222$	13.9006	−	6.17563i	0.932948	−	0.414481i
$223$	−19.6080	+	16.9905i	−1.31305	+	1.13777i	−0.332158	+	0.943224i	$0.607777\pi$
$223$	−19.6080	+	16.9905i	−1.31305	+	1.13777i	−0.980894	+	0.194542i	$0.937678\pi$
$224$	−2.83286	−	11.8844i	−0.189279	−	0.794061i
$225$	−5.85288	+	1.71856i	−0.390192	+	0.114571i
$226$	2.58935	−	16.7783i	0.172241	−	1.11608i
$227$	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	$0.431639\pi$
$228$	13.7997	+	6.64964i	0.913906	+	0.440383i
$229$	−4.84212			−0.319976			−0.159988	−	0.987119i	$-0.551146\pi$
$229$	−4.84212			−0.319976			−0.159988	+	0.987119i	$0.551146\pi$
$230$	5.59478	+	3.83386i	0.368909	+	0.252797i
$231$			3.14358i			0.206832i
$232$	3.78914	−	21.5870i	0.248769	−	1.41726i
$233$	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	$-0.208945\pi$
$234$	0.694601	−	4.50084i	0.0454075	−	0.294229i
$235$	−0.438700	−	1.49408i	−0.0286176	−	0.0974627i
$236$	18.4880	+	12.4280i	1.20346	+	0.808993i
$237$	−3.69738	−	4.26700i	−0.240170	−	0.277171i
$238$	1.36495	+	3.07235i	0.0884769	+	0.199151i
$239$	0.419264	−	1.42788i	0.0271199	−	0.0923621i	−0.944821	−	0.327587i	$-0.893765\pi$
$239$	0.419264	−	1.42788i	0.0271199	−	0.0923621i	0.971941	+	0.235225i	$0.0755827\pi$
$240$	−4.55538	−	11.1735i	−0.294048	−	0.721249i
$241$	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	$0.0977976\pi$
$242$	−4.44051	+	14.5653i	−0.285447	+	0.936290i
$243$	−1.20470	+	1.39030i	−0.0772814	+	0.0891875i
$244$	−20.0297	+	5.43484i	−1.28227	+	0.347930i
$245$	−0.332374	−	2.31171i	−0.0212346	−	0.147690i
$246$	−12.4067	+	18.8740i	−0.791019	+	1.20336i
$247$	−0.556805	−	1.21923i	−0.0354286	−	0.0775779i
$248$	−5.58766	+	11.2962i	−0.354817	+	0.717310i
$249$	−20.8073	−	9.50238i	−1.31861	−	0.602189i
$250$	1.40182	−	0.186808i	0.0886590	−	0.0118147i
$251$	−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
$256$	14.1275	−	7.51083i	0.882971	−	0.469427i
$257$	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	$-0.166449\pi$
$258$	−34.3421	+	21.5728i	−2.13805	+	1.34307i
$259$	−3.19889	−	7.00459i	−0.198769	−	0.435244i
$260$	−0.318304	+	1.00670i	−0.0197404	+	0.0624329i
$261$	46.7867	−	6.72691i	2.89602	−	0.416385i
$262$	0.0978741	−	9.48396i	0.00604668	−	0.585921i
$263$	19.2852	−	22.2564i	1.18918	−	1.37239i	0.277893	−	0.960612i	$-0.410364\pi$
$263$	19.2852	−	22.2564i	1.18918	−	1.37239i	0.911286	−	0.411774i	$-0.135091\pi$
$264$	−3.98411	+	1.03703i	−0.245205	+	0.0638246i
$265$	0.538439	+	0.346034i	0.0330760	+	0.0212567i
$266$	3.29413	−	7.02051i	0.201976	−	0.430455i
$267$	14.9271	−	50.8371i	0.913526	−	3.11118i
$268$	0.984735	−	0.818314i	0.0601522	−	0.0499865i
$269$	−7.93844	+	6.87870i	−0.484016	+	0.419402i	−0.862385	−	0.506253i	$-0.831030\pi$
$269$	−7.93844	+	6.87870i	−0.484016	+	0.419402i	0.378370	+	0.925655i	$0.376485\pi$
$270$	10.0836	−	8.55688i	0.613666	−	0.520755i
$271$	−7.19233	−	24.4948i	−0.436903	−	1.48796i	−0.824359	−	0.566067i	$-0.808464\pi$
$271$	−7.19233	−	24.4948i	−0.436903	−	1.48796i	0.387456	−	0.921888i	$-0.373354\pi$
$272$	−3.44355	+	2.74344i	−0.208796	+	0.166346i
$273$	−3.40441	−	0.489480i	−0.206044	−	0.0296247i
$274$	9.79265	−	11.0684i	0.591596	−	0.668669i
$275$		−	0.482504i		−	0.0290961i
$276$	−28.4529	−	5.25647i	−1.71266	−	0.316402i
$277$		−	13.6362i		−	0.819319i	−0.912238	−	0.409660i	$-0.865647\pi$
$277$		−	13.6362i		−	0.819319i	0.912238	−	0.409660i	$-0.134353\pi$
$278$	5.38337	+	4.76287i	0.322873	+	0.285658i
$279$	−26.9030	−	3.86807i	−1.61064	−	0.231575i
$280$	−5.63255	+	2.36443i	−0.336609	+	0.141301i
$281$	−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	$-0.339010\pi$
$282$	4.29822	+	5.06509i	0.255955	+	0.301622i
$283$	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	$0.270481\pi$
$284$	−8.71483	+	7.24202i	−0.517130	+	0.429735i
$285$	2.15783	−	7.34888i	0.127819	−	0.435310i
$286$	0.326113	+	0.153017i	0.0192835	+	0.00904811i
$287$	9.61934	+	6.18198i	0.567812	+	0.364911i
$288$	24.8782	+	23.9120i	1.46596	+	1.40903i
$289$	−10.3392	+	11.9321i	−0.608191	+	0.701890i
$290$	−10.9579	−	0.113086i	−0.643473	−	0.00664061i
$291$	−46.0330	+	6.61854i	−2.69850	+	0.387986i
$292$	23.7419	+	7.50685i	1.38939	+	0.439305i
$293$	−10.8927	−	23.8516i	−0.636356	−	1.39342i	−0.903005	−	0.429631i	$-0.858644\pi$
$293$	−10.8927	−	23.8516i	−0.636356	−	1.39342i	0.266649	−	0.963794i	$-0.414084\pi$
$294$	5.29990	+	8.43698i	0.309096	+	0.492055i
$295$	4.62708	−	10.1319i	0.269399	−	0.589901i
$296$	7.82221	−	6.36494i	0.454657	−	0.369954i
$297$	−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
$302$	3.07090	+	23.0443i	0.176710	+	1.32605i
$303$	−33.1168	−	15.1239i	−1.90251	−	0.868847i
$304$	9.98434	+	1.85894i	0.572641	+	0.106618i
$305$	4.31074	+	9.43921i	0.246832	+	0.540488i
$306$	−7.93459	−	5.21572i	−0.453590	−	0.298163i
$307$	−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	$-0.0924834\pi$
$308$	0.545784	+	2.01144i	0.0310990	+	0.114613i
$309$	−0.148765	+	0.171684i	−0.00846295	+	0.00976676i
$310$	6.02743	+	1.83758i	0.342335	+	0.104368i
$311$	3.99032	−	6.20906i	0.226270	−	0.352084i	−0.709493	−	0.704713i	$-0.751076\pi$
$311$	3.99032	−	6.20906i	0.226270	−	0.352084i	0.935763	+	0.352629i	$0.114712\pi$
$312$	−0.502714	−	4.47615i	−0.0284606	−	0.253412i
$313$	−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	$0.678004\pi$
$314$	−6.14366	+	2.72945i	−0.346707	+	0.154032i
$315$	−8.62740	−	9.95655i	−0.486099	−	0.560988i
$316$	−3.10663	−	2.08834i	−0.174761	−	0.117478i
$317$	2.83066	+	9.64035i	0.158986	+	0.541456i	1.00000		0.000442633i	$0.000140895\pi$
$317$	2.83066	+	9.64035i	0.158986	+	0.541456i	−0.841014	+	0.541013i	$0.818041\pi$
$318$	−2.69857	−	0.416462i	−0.151328	−	0.0233541i
$319$	−0.532094	+	3.70079i	−0.0297915	+	0.207205i
$320$	−4.85473	−	6.35858i	−0.271388	−	0.355456i
$321$		−	21.8958i		−	1.22210i
$322$	−2.51232	+	14.4311i	−0.140006	+	0.804212i
$323$	−2.79465			−0.155498
$324$	−8.60363	+	17.8547i	−0.477979	+	0.991927i
$325$	0.522538	+	0.0751297i	0.0289852	+	0.00416744i
$326$	−29.9907	−	4.62838i	−1.66103	−	0.256342i
$327$	12.4899	−	3.66735i	0.690691	−	0.202805i
$328$	−4.66161	+	14.2307i	−0.257394	+	0.785760i
$329$	2.54163	−	2.20233i	0.140124	−	0.121419i
$330$	0.835735	+	1.88114i	0.0460057	+	0.103553i
$331$	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	$0.398875\pi$
$332$	−14.9635	−	2.46763i	−0.821230	−	0.135429i
$333$	18.2965	+	11.7585i	1.00264	+	0.644360i
$334$	−4.50481	−	1.37338i	−0.246492	−	0.0751482i
$335$	−0.483818	−	0.419231i	−0.0264338	−	0.0229050i
$336$	17.8642	−	18.9742i	0.974574	−	1.03513i
$337$	−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	$0.653985\pi$
$338$	9.88214	−	15.0335i	0.537518	−	0.817716i
$339$	32.9405	−	15.0434i	1.78908	−	0.817046i
$340$	1.63360	+	1.47563i	0.0885942	+	0.0800275i
$341$	0.893099	−	1.95561i	0.0483640	−	0.105902i
$342$	2.89322	+	21.7110i	0.156447	+	1.17400i
$343$	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	$0.156712\pi$
$348$	42.9176	−	18.5391i	2.30062	−	0.993802i
$349$	−19.6330	−	8.96610i	−1.05093	−	0.479944i	−0.186375	−	0.982479i	$-0.559674\pi$
$349$	−19.6330	−	8.96610i	−1.05093	−	0.479944i	−0.864557	+	0.502534i	$0.832401\pi$
$350$	1.62470	+	2.58638i	0.0868439	+	0.138248i
$351$	4.49061	−	2.05079i	0.239691	−	0.109463i
$352$	−2.36921	+	1.35527i	−0.126280	+	0.0722359i
$353$	−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	$-0.129115\pi$
$354$	−0.490359	+	47.5156i	−0.0260623	+	2.52543i
$355$	4.28176	+	3.71016i	0.227252	+	0.196915i
$356$	0.724955	−	35.1202i	0.0384225	−	1.86137i
$357$	−3.87703	+	6.03278i	−0.205194	+	0.319289i
$358$	−7.34690	−	3.44728i	−0.388296	−	0.182195i
$359$	−12.9111	−	3.79103i	−0.681419	−	0.200083i	−0.0773373	−	0.997005i	$-0.524642\pi$
$359$	−12.9111	−	3.79103i	−0.681419	−	0.200083i	−0.604082	+	0.796922i	$0.706460\pi$
$360$	9.77266	−	14.2187i	0.515064	−	0.749393i
$361$	−8.22085	−	9.48736i	−0.432676	−	0.499335i
$362$	11.7755	−	9.99266i	0.618907	−	0.525203i
$363$	−31.1648	+	9.15081i	−1.63573	+	0.480293i
$364$	−2.26332	+	0.277872i	−0.118630	+	0.0145644i
$365$	1.77185	−	12.3235i	0.0927430	−	0.645042i
$366$	−33.1557	−	29.3341i	−1.73308	−	1.53332i
$367$	−2.48501			−0.129716			−0.0648581	−	0.997894i	$-0.520659\pi$
$367$	−2.48501			−0.129716			−0.0648581	+	0.997894i	$0.520659\pi$
$368$	−19.1184	+	1.57656i	−0.996617	+	0.0821841i
$369$	−32.2956			−1.68124
$370$	−3.77644	−	3.34116i	−0.196328	−	0.173698i
$371$	−0.196726	+	1.36826i	−0.0102135	+	0.0710366i
$372$	−26.6820	+	3.27579i	−1.38340	+	0.169842i
$373$	33.3038	−	9.77889i	1.72441	−	0.506332i	0.738590	−	0.674155i	$-0.235492\pi$
$373$	33.3038	−	9.77889i	1.72441	−	0.506332i	0.985817	+	0.167824i	$0.0536739\pi$
$374$	0.572670	−	0.485966i	0.0296121	−	0.0251287i
$375$	1.97546	+	2.27981i	0.102012	+	0.117729i
$376$	3.62964	+	2.49468i	0.187185	+	0.128654i
$377$	−3.92501	−	1.15249i	−0.202148	−	0.0593561i
$378$	25.8575	+	12.1328i	1.32997	+	0.624042i
$379$	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	$-0.125155\pi$
$380$	0.104798	−	5.07688i	0.00537600	−	0.260438i
$381$	32.6181	+	28.2638i	1.67108	+	1.44800i
$382$	−0.174783	+	16.9364i	−0.00894270	+	0.866544i
$383$	−1.09135	−	7.59048i	−0.0557652	−	0.387855i	−0.998521	−	0.0543709i	$-0.982685\pi$
$383$	−1.09135	−	7.59048i	−0.0557652	−	0.387855i	0.942756	−	0.333484i	$-0.108224\pi$
$384$	29.9407	+	16.3814i	1.52791	+	0.835961i
$385$	0.947916	−	0.432899i	0.0483103	−	0.0220626i
$386$	10.4705	+	16.6681i	0.532935	+	0.848386i
$387$	−52.7486	−	24.0895i	−2.68136	−	1.22454i
$388$	−28.3055	+	12.2271i	−1.43699	+	0.620738i
$389$	9.40313	−	6.04302i	0.476757	−	0.306393i	−0.280103	−	0.959970i	$-0.590369\pi$
$389$	9.40313	−	6.04302i	0.476757	−	0.306393i	0.756860	+	0.653577i	$0.226732\pi$
$390$	−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
$394$	1.84581	+	13.8512i	0.0929908	+	0.697812i
$395$	−0.777511	+	1.70251i	−0.0391208	+	0.0856627i
$396$	−4.36823	−	3.94584i	−0.219512	−	0.198286i
$397$	−22.0159	+	10.0543i	−1.10495	+	0.504612i	−0.882490	−	0.470331i	$-0.844134\pi$
$397$	−22.0159	+	10.0543i	−1.10495	+	0.504612i	−0.222456	+	0.974943i	$0.571407\pi$
$398$	−19.1408	+	29.1185i	−0.959441	+	1.45958i
$399$	16.3734	−	2.35414i	0.819696	−	0.117855i
$400$	−2.74196	+	2.91233i	−0.137098	+	0.145616i
$401$	−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	$0.918929\pi$
$402$	2.61240	+	0.796444i	0.130295	+	0.0397230i
$403$	1.97881	+	1.27171i	0.0985717	+	0.0633482i
$404$	−23.8158	−	3.92747i	−1.18488	−	0.195399i
$405$	9.50833	+	2.79190i	0.472473	+	0.138731i
$406$	−9.60922	−	21.6292i	−0.476897	−	1.07344i
$407$	−1.30015	+	1.12658i	−0.0644460	+	0.0558427i
$408$	−8.92481	−	2.92353i	−0.441844	−	0.144737i
$409$	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	$0.152196\pi$
$410$	7.39979	+	1.14199i	0.365449	+	0.0563988i
$411$	31.2029	+	4.48629i	1.53912	+	0.221293i
$412$	−0.0653809	+	0.135682i	−0.00322109	+	0.00668456i
$413$	24.0562			1.18373
$414$	−16.0666	−	38.1249i	−0.789631	−	1.87374i
$415$			7.58281i			0.372226i
$416$	−1.09881	−	2.77682i	−0.0538736	−	0.136145i
$417$	−2.18201	+	15.1762i	−0.106853	+	0.743181i
$418$	−1.71224	−	0.264245i	−0.0837483	−	0.0129246i
$419$	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	$0.893567\pi$
$420$	−10.8140	−	7.26942i	−0.527671	−	0.354711i
$421$	−0.532308	−	0.614316i	−0.0259431	−	0.0299399i	0.742630	−	0.669702i	$-0.233578\pi$
$421$	−0.532308	−	0.614316i	−0.0259431	−	0.0299399i	−0.768573	+	0.639762i	$0.779033\pi$
$422$	−1.79326	+	0.796695i	−0.0872947	+	0.0387825i
$423$	−2.67606	+	9.11382i	−0.130114	+	0.443129i
$424$	−1.79901	+	0.202045i	−0.0873674	+	0.00981220i
$425$	0.595081	−	0.925965i	0.0288657	−	0.0449159i
$426$	−23.1196	−	7.04847i	−1.12015	−	0.341500i
$427$	−14.6765	+	16.9376i	−0.710245	+	0.819666i
$428$	−3.80152	−	14.0102i	−0.183753	−	0.677208i
$429$	0.109353	+	0.760570i	0.00527963	+	0.0367207i
$430$	11.2343	+	7.38476i	0.541766	+	0.356125i
$431$	5.50933	+	12.0638i	0.265375	+	0.581091i	0.994670	−	0.103109i	$-0.0328790\pi$
$431$	5.50933	+	12.0638i	0.265375	+	0.581091i	−0.729295	+	0.684199i	$0.760152\pi$
$432$	−6.84675	+	36.7738i	−0.329414	+	1.76928i
$433$	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	$0.247966\pi$
$434$	1.79769	+	13.4900i	0.0862917	+	0.647541i
$435$	−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	$-0.131199\pi$
$439$	3.58757	+	5.58236i	0.171225	+	0.266432i	−0.745026	+	0.667035i	$0.767563\pi$
$440$	0.861352	+	1.05856i	0.0410634	+	0.0504649i
$441$	−5.91817	+	12.9590i	−0.281818	+	0.617095i
$442$	0.437118	+	0.695855i	0.0207916	+	0.0330984i
$443$	−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	$-0.308136\pi$
$444$	20.5104	+	6.48507i	0.973378	+	0.307768i
$445$	−17.3851	+	2.49959i	−0.824131	+	0.118492i
$446$	−36.6900	−	0.378640i	−1.73732	−	0.0179291i
$447$	−38.7810	+	44.7556i	−1.83428	+	2.11687i
$448$	8.13629	−	15.2424i	0.384404	−	0.720134i
$449$	−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	$0.720352\pi$
$450$	−7.80969	−	3.66443i	−0.368152	−	0.172743i
$451$	0.719703	−	2.45108i	0.0338895	−	0.115417i
$452$	18.4654	−	15.3447i	0.868540	−	0.721756i
$453$	−37.4773	+	32.4743i	−1.76084	+	1.52577i
$454$	9.65026	+	11.3720i	0.452909	+	0.533715i
$455$	0.321219	+	1.09397i	0.0150590	+	0.0512862i
$456$	8.38498	+	19.9747i	0.392663	+	0.935403i
$457$	−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	$0.603998\pi$
$458$	−5.12866	−	4.53752i	−0.239647	−	0.212024i
$459$		−	10.2931i		−	0.480440i
$460$	2.33318	+	9.30356i	0.108785	+	0.433781i
$461$		−	10.1583i		−	0.473120i	−0.971617	−	0.236560i	$-0.923980\pi$
$461$		−	10.1583i		−	0.473120i	0.971617	−	0.236560i	$-0.0760200\pi$
$462$	−2.94582	+	3.32961i	−0.137052	+	0.154907i
$463$	36.0086	+	5.17726i	1.67346	+	0.240608i	0.912761	−	0.408494i	$-0.133946\pi$
$463$	36.0086	+	5.17726i	1.67346	+	0.240608i	0.760701	+	0.649102i	$0.224855\pi$
$464$	24.2424	−	19.3137i	1.12543	−	0.896617i
$465$	3.78681	+	12.8967i	0.175609	+	0.598070i
$466$	23.5966	−	20.0240i	1.09309	−	0.927594i
$467$	−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	$0.288729\pi$
$468$	4.95341	−	4.11628i	0.228971	−	0.190275i
$469$	0.389533	−	1.32663i	0.0179870	−	0.0612580i
$470$	0.935426	−	1.99359i	0.0431480	−	0.0919576i
$471$	−12.0635	−	7.75276i	−0.555858	−	0.357228i
$472$	7.93585	+	30.4884i	0.365277	+	1.40334i
$473$	3.00377	−	3.46654i	0.138114	−	0.159392i
$474$	0.0823976	−	7.98429i	0.00378465	−	0.366731i
$475$	−2.51314	+	0.361335i	−0.115311	+	0.0165792i
$476$	−1.43335	+	4.53325i	−0.0656973	+	0.207781i
$477$	−1.62188	−	3.55143i	−0.0742609	−	0.162609i
$478$	1.78213	−	1.11949i	0.0815129	−	0.0512044i
$479$	9.93263	−	21.7494i	0.453834	−	0.993757i	−0.535016	−	0.844842i	$-0.679695\pi$
$479$	9.93263	−	21.7494i	0.453834	−	0.993757i	0.988850	−	0.148915i	$-0.0475781\pi$
$480$	5.64570	−	16.1036i	0.257690	−	0.735024i
$481$	−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
$486$	−2.57883	+	0.343656i	−0.116978	+	0.0155885i
$487$	3.00977	+	1.37452i	0.136386	+	0.0622852i	0.482439	−	0.875930i	$-0.339751\pi$
$487$	3.00977	+	1.37452i	0.136386	+	0.0622852i	−0.346053	+	0.938215i	$0.612478\pi$
$488$	−26.3079	−	13.0132i	−1.19090	−	0.589079i
$489$	−26.8896	−	58.8800i	−1.21599	−	2.66265i
$490$	1.81425	−	2.75998i	0.0819594	−	0.124683i
$491$	−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	$0.974240\pi$
$492$	−30.8276	+	8.36474i	−1.38981	+	0.377112i
$493$	−5.58539	+	6.44589i	−0.251553	+	0.290308i
$494$	0.552779	−	1.81316i	0.0248707	−	0.0815780i
$495$	−1.59125	+	2.47603i	−0.0715212	+	0.111289i
$496$	−16.5039	+	6.72854i	−0.741048	+	0.302120i
$497$	−3.44734	+	11.7406i	−0.154634	+	0.526637i
$498$	−13.1340	−	29.5631i	−0.588550	−	1.32475i
$499$	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	$0.704515\pi$
$500$	1.65983	+	1.11577i	0.0742300	+	0.0498990i
$501$	−2.83021	−	9.63880i	−0.126444	−	0.430630i
$502$	1.59453	−	10.3321i	0.0711674	−	0.461146i
$503$	0.641039	−	4.45852i	0.0285825	−	0.198796i	−0.970527	−	0.240993i	$-0.922527\pi$
$503$	0.641039	−	4.45852i	0.0285825	−	0.198796i	0.999109	+	0.0421976i	$0.0134359\pi$
$504$	36.7017	+	6.44220i	1.63483	+	0.286959i
$505$			12.0688i			0.537052i
$506$	3.25154	−	0.369772i	0.144549	−	0.0164384i
$507$	38.3753			1.70431
$508$	25.7781	+	12.4217i	1.14372	+	0.551122i
$509$	−34.3259	−	4.93532i	−1.52147	−	0.218754i	−0.669685	−	0.742646i	$-0.733571\pi$
$509$	−34.3259	−	4.93532i	−1.52147	−	0.218754i	−0.851785	+	0.523891i	$0.824480\pi$
$510$	−0.716199	+	4.64078i	−0.0317138	+	0.205497i
$511$	25.8002	−	7.57561i	1.14133	−	0.335125i
$512$	22.0019	+	5.28351i	0.972357	+	0.233500i
$513$	−17.9438	+	15.5484i	−0.792239	+	0.686479i
$514$	33.7378	−	14.9887i	1.48811	−	0.661124i
$515$	0.0722560	+	0.0212163i	0.00318398	+	0.000934900i
$516$	−56.5901	−	9.33227i	−2.49124	−	0.410830i
$517$	−0.632060	−	0.406200i	−0.0277980	−	0.0178647i
$518$	3.17576	−	10.4168i	0.139535	−	0.457686i
$519$	−6.43351	−	5.57467i	−0.282400	−	0.244701i
$520$	−1.28051	+	0.767995i	−0.0561542	+	0.0336788i
$521$	−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	$0.580315\pi$
$522$	55.8591	+	36.7185i	2.44489	+	1.60712i
$523$	−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	$0.397125\pi$
$524$	8.99101	−	9.95348i	0.392774	−	0.434820i
$525$	−2.70648	+	5.92637i	−0.118121	+	0.258648i
$526$	41.2828	−	5.50137i	1.80001	−	0.239871i
$527$	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
$532$	10.0679	−	4.34905i	0.436501	−	0.188555i
$533$	2.54239	+	1.16107i	0.110123	+	0.0502916i
$534$	63.4496	−	39.8574i	2.74573	−	1.72480i
$535$	−6.60246	+	3.01524i	−0.285449	+	0.130360i
$536$	1.80984	+	0.0560485i	0.0781734	+	0.00242093i
$537$	−2.46359	−	17.1346i	−0.106312	−	0.739414i
$538$	−14.8542	−	0.153295i	−0.640410	−	0.00660901i
$539$	−0.851640	−	0.737950i	−0.0366827	−	0.0317858i
$540$	18.6989	+	0.385984i	0.804671	+	0.0166101i
$541$	6.25994	−	9.74066i	0.269136	−	0.418784i	−0.680210	−	0.733018i	$-0.738111\pi$
$541$	6.25994	−	9.74066i	0.269136	−	0.418784i	0.949346	+	0.314234i	$0.101748\pi$
$542$	15.3360	−	32.6843i	0.658737	−	1.40391i
$543$	31.6086	+	9.28113i	1.35646	+	0.398291i
$544$	−6.21819	−	0.321131i	−0.266603	−	0.0137684i
$545$	−2.82582	−	3.26117i	−0.121045	−	0.139693i
$546$	−3.14718	−	3.70869i	−0.134687	−	0.158717i
$547$	−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	$0.682406\pi$
$548$	20.7443	−	2.54682i	0.886153	−	0.108795i
$549$	9.00841	−	62.6548i	0.384469	−	2.67404i
$550$	0.452151	−	0.511057i	0.0192798	−	0.0217916i
$551$	19.6742			0.838148
$552$	−25.2109	−	32.2305i	−1.07305	−	1.37182i
$553$	−4.04229			−0.171896
$554$	12.7784	−	14.4431i	0.542901	−	0.613630i
$555$	1.53068	−	10.6461i	0.0649737	−	0.451902i
$556$	1.23870	+	10.0894i	0.0525325	+	0.427888i
$557$	−10.2551	+	3.01117i	−0.434523	+	0.127588i	−0.491677	−	0.870778i	$-0.663616\pi$
$557$	−10.2551	+	3.01117i	−0.434523	+	0.127588i	0.0571534	+	0.998365i	$0.481798\pi$
$558$	−24.8703	−	29.3076i	−1.05285	−	1.24069i
$559$	3.28645	+	3.79277i	0.139002	+	0.160417i
$560$	−8.18155	−	2.77387i	−0.345734	−	0.117218i
$561$	1.53720	+	0.451362i	0.0649006	+	0.0190565i
$562$	14.1560	−	30.1695i	0.597135	−	1.27262i
$563$	−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	$0.222999\pi$
$564$	−0.193884	+	9.39265i	−0.00816400	+	0.395502i
$565$	−9.07240	−	7.86128i	−0.381679	−	0.330726i
$566$	0.335695	+	0.00346436i	0.0141103	+	0.000145618i
$567$	3.04590	+	21.1847i	0.127916	+	0.889674i
$568$	−16.0170	−	0.496025i	−0.672058	−	0.0208128i
$569$	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	$0.329968\pi$
$570$	9.17210	−	5.76168i	0.384177	−	0.241330i
$571$	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	$0.627975\pi$
$572$	0.202020	+	0.467671i	0.00844688	+	0.0195543i
$573$	−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	$0.0620680\pi$
$578$	−22.1326	+	2.94940i	−0.920595	+	0.122679i
$579$	−17.4421	+	38.1930i	−0.724871	+	1.58725i
$580$	−11.5004	−	10.3884i	−0.477530	−	0.431354i
$581$	−14.8970	+	6.80324i	−0.618032	+	0.282246i
$582$	−54.9593	−	36.1270i	−2.27813	−	1.49751i
$583$	0.305680	−	0.0439501i	0.0126600	−	0.00182023i
$584$	18.1123	+	30.1995i	0.749493	+	1.24966i
$585$	−2.43370	−	2.10881i	−0.100621	−	0.0871887i
$586$	10.8139	−	35.4705i	0.446718	−	1.46527i
$587$	−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	$0.838056\pi$
$588$	−2.29270	+	13.9028i	−0.0945494	+	0.573340i
$589$	−10.8547	−	3.18723i	−0.447260	−	0.131327i
$590$	14.3954	−	6.39546i	0.592650	−	0.263297i
$591$	−22.5264	+	19.5192i	−0.926612	+	0.802914i
$592$	14.2496	+	0.588536i	0.585657	+	0.0241887i
$593$	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	$0.389262\pi$
$594$	0.973252	−	6.30642i	0.0399330	−	0.258755i
$595$	2.35303	+	0.338315i	0.0964648	+	0.0138696i
$596$	−17.0439	+	35.3704i	−0.698145	+	1.44883i
$597$	−74.3294			−3.04210
$598$	−0.105838	+	3.57891i	−0.00432802	+	0.146352i
$599$		−	16.2467i		−	0.663823i	−0.943311	−	0.331911i	$-0.892306\pi$
$599$		−	16.2467i		−	0.663823i	0.943311	−	0.331911i	$-0.107694\pi$
$600$	−8.40380	−	1.47511i	−0.343084	−	0.0602210i
$601$	−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	$0.801197\pi$
$602$	−4.42860	+	28.6962i	−0.180496	+	1.16957i
$603$	1.10019	+	3.74692i	0.0448034	+	0.152586i
$604$	−18.3420	+	27.2857i	−0.746326	+	1.11024i
$605$	7.05101	+	8.13730i	0.286664	+	0.330828i
$606$	−20.9040	−	47.0524i	−0.849168	−	1.91137i
$607$	−6.33804	+	21.5854i	−0.257253	+	0.876123i	0.725030	+	0.688718i	$0.241826\pi$
$607$	−6.33804	+	21.5854i	−0.257253	+	0.876123i	−0.982283	+	0.187405i	$0.939992\pi$
$608$	8.83319	+	11.3252i	0.358233	+	0.459298i
$609$	27.2941	−	42.4705i	1.10601	−	1.72099i
$610$	−4.27957	+	14.0374i	−0.173275	+	0.568356i
$611$	0.538321	−	0.621255i	0.0217781	−	0.0251333i
$612$	−3.51652	−	12.9598i	−0.142147	−	0.523870i
$613$	−5.45865	−	37.9657i	−0.220473	−	1.53342i	−0.736256	−	0.676703i	$-0.763408\pi$
$613$	−5.45865	−	37.9657i	−0.220473	−	1.53342i	0.515783	−	0.856719i	$-0.327501\pi$
$614$	4.00730	−	6.09623i	0.161721	−	0.246024i
$615$	6.63464	+	14.5278i	0.267535	+	0.585819i
$616$	−1.30683	+	2.64193i	−0.0526535	+	0.106446i
$617$	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	$0.416609\pi$
$618$	−0.318452	+	0.0424372i	−0.0128100	+	0.00170707i
$619$	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
$624$	3.66210	−	5.21213i	0.146601	−	0.208652i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	−40.7969	+	25.6276i	−1.63057	+	1.02429i
$627$	−1.53519	−	3.36160i	−0.0613096	−	0.134249i
$628$	−9.06498	−	2.86621i	−0.361732	−	0.114374i
$629$	−3.88453	+	0.558511i	−0.154886	+	0.0222693i
$630$	0.192265	−	18.6304i	0.00766003	−	0.742254i
$631$	−25.8865	+	29.8746i	−1.03052	+	1.18929i	−0.0488334	+	0.998807i	$0.515550\pi$
$631$	−25.8865	+	29.8746i	−1.03052	+	1.18929i	−0.981691	+	0.190481i	$0.938995\pi$
$632$	−1.33350	−	5.12312i	−0.0530438	−	0.203787i
$633$	−3.52121	−	2.26294i	−0.139955	−	0.0899439i
$634$	−6.03573	+	12.8634i	−0.239709	+	0.510872i
$635$	4.03086	−	13.7279i	0.159960	−	0.544773i
$636$	−2.46800	−	2.96992i	−0.0978625	−	0.117765i
$637$	0.931787	−	0.807398i	0.0369187	−	0.0319903i
$638$	−4.03157	+	3.42118i	−0.159611	+	0.135446i
$639$	−9.73664	−	33.1600i	−0.385176	−	1.31179i
$640$	0.816560	−	11.2842i	0.0322774	−	0.446047i
$641$	−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	$0.740209\pi$
$642$	20.5184	−	23.1915i	0.809795	−	0.915295i
$643$		−	27.9770i		−	1.10330i	−0.834075	−	0.551652i	$-0.813998\pi$
$643$		−	27.9770i		−	1.10330i	0.834075	−	0.551652i	$-0.186002\pi$
$644$	−16.1843	+	12.9308i	−0.637749	+	0.509544i
$645$			28.6772i			1.12917i
$646$	−2.96003	−	2.61884i	−0.116461	−	0.103037i
$647$	32.3132	+	4.64594i	1.27036	+	0.182651i	0.744329	−	0.667813i	$-0.232769\pi$
$647$	32.3132	+	4.64594i	1.27036	+	0.182651i	0.526034	+	0.850464i	$0.323678\pi$
$648$	−25.8443	+	10.8489i	−1.01526	+	0.426185i
$649$	−1.51413	−	5.15664i	−0.0594347	−	0.202416i
$650$	0.483057	+	0.569243i	0.0189471	+	0.0223275i
$651$	−21.9390	+	19.0103i	−0.859859	+	0.745072i
$652$	−27.4282	−	33.0063i	−1.07417	−	1.29263i
$653$	13.4885	−	45.9377i	0.527847	−	1.79768i	−0.0718044	−	0.997419i	$-0.522876\pi$
$653$	13.4885	−	45.9377i	0.527847	−	1.79768i	0.599651	−	0.800262i	$-0.295306\pi$
$654$	16.6656	+	7.81978i	0.651678	+	0.305778i
$655$	−5.64189	−	3.62582i	−0.220447	−	0.141673i
$656$	−18.2730	+	10.7045i	−0.713440	+	0.417940i
$657$	−49.7341	+	57.3962i	−1.94031	+	2.23924i
$658$	4.75582	+	0.0490799i	0.185401	+	0.00191333i
$659$	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	$0.445918\pi$
$660$	−0.877609	+	2.77562i	−0.0341609	+	0.108041i
$661$	−2.23170	−	4.88675i	−0.0868032	−	0.190072i	0.861252	−	0.508178i	$-0.169681\pi$
$661$	−2.23170	−	4.88675i	−0.0868032	−	0.190072i	−0.948055	+	0.318105i	$0.896953\pi$
$662$	15.5300	+	24.7224i	0.603589	+	0.960862i
$663$	−0.728167	+	1.59446i	−0.0282797	+	0.0619238i
$664$	−13.5366	−	16.6359i	−0.525323	−	0.645597i
$665$	−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
$670$	−0.119591	−	0.897423i	−0.00462021	−	0.0346705i
$671$	4.55446	+	2.07995i	0.175823	+	0.0802956i
$672$	36.7020	−	3.35659i	1.41581	−	0.129483i
$673$	−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	$-0.474552\pi$
$674$	−25.4412	−	16.7235i	−0.979959	−	0.644167i
$675$	−1.33085	−	9.25624i	−0.0512243	−	0.356273i
$676$	24.5547	−	6.66268i	0.944413	−	0.256257i
$677$	−22.1074	+	25.5134i	−0.849658	+	0.980558i	−0.999967	−	0.00808129i	$-0.997428\pi$
$677$	−22.1074	+	25.5134i	−0.849658	+	0.980558i	0.150309	+	0.988639i	$0.451973\pi$
$678$	48.9869	+	14.9346i	1.88133	+	0.573562i
$679$	−18.0013	+	28.0106i	−0.690827	+	1.07495i
$680$	0.347462	+	3.09379i	0.0133246	+	0.118641i
$681$	−8.96311	+	30.5255i	−0.343467	+	1.16974i
$682$	2.77854	−	1.23443i	0.106396	−	0.0472686i
$683$	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	$0.626087\pi$
$684$	−17.2808	+	25.7070i	−0.660748	+	0.982933i
$685$	−2.94411	−	10.0267i	−0.112489	−	0.383102i
$686$	28.1802	+	4.34897i	1.07592	+	0.166045i
$687$	2.07877	−	14.4581i	0.0793099	−	0.551612i
$688$	−37.8299	+	3.85379i	−1.44225	+	0.146924i
$689$			0.337886i			0.0128724i
$690$	−13.8495	+	15.0596i	−0.527240	+	0.573309i
$691$	19.9812			0.760121			0.380061	−	0.924962i	$-0.375903\pi$
$691$	19.9812			0.760121			0.380061	+	0.924962i	$0.375903\pi$
$692$	−5.08440	−	2.45002i	−0.193280	−	0.0931356i
$693$	−6.29200	−	0.904653i	−0.239013	−	0.0343649i
$694$	25.2959	+	3.90385i	0.960220	+	0.148188i
$695$	4.87672	−	1.43193i	0.184984	−	0.0543163i
$696$	62.8302	+	20.5815i	2.38157	+	0.780142i
$697$	4.40414	−	3.81621i	0.166819	−	0.144549i
$698$	−12.3928	−	27.8947i	−0.469074	−	1.05583i
$699$	63.3396	+	18.5982i	2.39572	+	0.703448i
$700$	−0.702835	+	4.26193i	−0.0265647	+	0.161086i
$701$	−31.8196	−	20.4492i	−1.20181	−	0.772357i	−0.222542	−	0.974923i	$-0.571436\pi$
$701$	−31.8196	−	20.4492i	−1.20181	−	0.772357i	−0.979269	+	0.202566i	$0.935072\pi$
$702$	6.67813	+	2.03596i	0.252050	+	0.0768425i
$703$	6.84150	+	5.92819i	0.258032	+	0.223586i
$704$	−3.77943	−	0.784707i	−0.142443	−	0.0295748i
$705$	4.64952	−	0.668499i	0.175111	−	0.0251771i
$706$	7.58394	−	11.5373i	0.285425	−	0.434212i
$707$	−23.7100	+	10.8280i	−0.891706	+	0.407228i
$708$	−45.0459	+	49.8680i	−1.69293	+	1.87415i
$709$	3.51131	−	7.68869i	0.131870	−	0.288755i	−0.832166	−	0.554526i	$-0.812899\pi$
$709$	3.51131	−	7.68869i	0.131870	−	0.288755i	0.964036	+	0.265772i	$0.0856267\pi$
$710$	1.05837	+	7.94213i	0.0397200	+	0.298063i
$711$	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
$716$	−4.55124	−	10.5360i	−0.170088	−	0.393749i
$717$	4.08354	+	1.86489i	0.152503	+	0.0696456i
$718$	−10.1226	−	16.1142i	−0.377770	−	0.601378i
$719$	−14.8438	+	6.77892i	−0.553579	+	0.252811i	−0.672506	−	0.740092i	$-0.734782\pi$
$719$	−14.8438	+	6.77892i	−0.553579	+	0.252811i	0.118927	+	0.992903i	$0.462055\pi$
$720$	23.6753	−	5.90227i	0.882325	−	0.219965i
$721$	0.0231465	+	0.160987i	0.000862021	+	0.00599548i
$722$	0.183205	−	17.7525i	0.00681819	−	0.660680i
$723$	18.4679	+	16.0025i	0.686828	+	0.595140i
$724$	21.8364	+	0.450750i	0.811544	+	0.0167520i
$725$	−4.18934	+	6.51875i	−0.155588	+	0.242100i
$726$	−41.5842	−	19.5120i	−1.54333	−	0.724157i
$727$	46.3222	+	13.6014i	1.71799	+	0.504449i	0.984521	−	0.175269i	$-0.0560795\pi$
$727$	46.3222	+	13.6014i	1.71799	+	0.504449i	0.733474	+	0.679718i	$0.237898\pi$
$728$	−2.65765	−	1.82663i	−0.0984990	−	0.0676992i
$729$	15.8344	+	18.2739i	0.586459	+	0.676810i
$730$	13.4250	−	11.3924i	0.496881	−	0.421651i
$731$	10.0398	−	2.94796i	0.371337	−	0.109034i
$732$	−7.62904	−	62.1400i	−0.281977	−	2.29676i
$733$	−3.43211	+	23.8708i	−0.126768	+	0.881689i	0.822846	+	0.568265i	$0.192385\pi$
$733$	−3.43211	+	23.8708i	−0.126768	+	0.881689i	−0.949613	+	0.313424i	$0.898524\pi$
$734$	−2.63206	−	2.32868i	−0.0971512	−	0.0859532i
$735$	7.04527			0.259869
$736$	−21.7272	−	16.2459i	−0.800875	−	0.598831i
$737$	−0.308891			−0.0113781
$738$	−34.2068	−	30.2640i	−1.25917	−	1.11403i
$739$	−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	$0.939168\pi$
$740$	−0.868949	−	7.07775i	−0.0319432	−	0.260183i
$741$	3.87956	−	1.13914i	0.142519	−	0.0418474i
$742$	−1.49056	+	1.26488i	−0.0547201	+	0.0464353i
$743$	9.61820	+	11.1000i	0.352858	+	0.407220i	0.904234	−	0.427037i	$-0.140443\pi$
$743$	9.61820	+	11.1000i	0.352858	+	0.407220i	−0.551376	+	0.834257i	$0.685897\pi$
$744$	−31.3307	−	21.5338i	−1.14864	−	0.789469i
$745$	18.8361	+	5.53079i	0.690102	+	0.202632i
$746$	44.4384	+	20.8512i	1.62701	+	0.763417i
$747$	25.0073	−	38.9121i	0.914970	−	1.42372i
$748$	1.06195	+	0.0219210i	0.0388289	+	0.000801511i
$749$	−11.8473	−	10.2658i	−0.432893	−	0.375104i
$750$	−0.0440240	+	4.26591i	−0.00160753	+	0.155769i
$751$	3.93244	+	27.3507i	0.143497	+	0.998042i	0.926573	+	0.376116i	$0.122741\pi$
$751$	3.93244	+	27.3507i	0.143497	+	0.998042i	−0.783076	+	0.621926i	$0.786350\pi$
$752$	1.50668	+	6.04363i	0.0549431	+	0.220388i
$753$	20.2849	−	9.26379i	0.739222	−	0.337591i
$754$	−3.07729	−	4.89878i	−0.112068	−	0.178403i
$755$	14.9533	+	6.82893i	0.544205	+	0.248530i
$756$	16.0182	+	37.0817i	0.582576	+	1.34865i
$757$	15.5677	−	10.0047i	0.565817	−	0.363629i	−0.226244	−	0.974071i	$-0.572645\pi$
$757$	15.5677	−	10.0047i	0.565817	−	0.363629i	0.792061	+	0.610442i	$0.209008\pi$
$758$	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	$0.240755\pi$
$762$	8.06260	+	60.5025i	0.292077	+	2.19178i
$763$	3.87152	−	8.47744i	0.140158	−	0.306904i
$764$	−16.0562	+	17.7749i	−0.580891	+	0.643074i
$765$	−6.10747	+	2.78919i	−0.220816	+	0.100843i
$766$	5.95705	−	9.06235i	0.215237	−	0.327436i
$767$	5.82026	−	0.836828i	0.210158	−	0.0302161i
$768$	16.3616	+	45.4080i	0.590399	+	1.63852i
$769$	−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	$0.886418\pi$
$770$	1.40968	+	0.429769i	0.0508012	+	0.0154878i
$771$	66.2466	+	42.5741i	2.38581	+	1.53327i
$772$	−4.52947	+	27.4664i	−0.163019	+	0.988536i
$773$	−31.0683	−	9.12246i	−1.11745	−	0.328112i	−0.329685	−	0.944091i	$-0.606942\pi$
$773$	−31.0683	−	9.12246i	−1.11745	−	0.328112i	−0.787763	+	0.615979i	$0.788761\pi$
$774$	−33.2960	−	74.9454i	−1.19680	−	2.69386i
$775$	3.36740	−	2.91787i	0.120960	−	0.104813i
$776$	−41.4384	−	13.5742i	−1.48755	−	0.487284i
$777$	22.2884	−	6.54447i	0.799592	−	0.234781i
$778$	15.6225	+	2.41097i	0.560092	+	0.0864375i
$779$	−13.3055	−	1.91304i	−0.476719	−	0.0685419i
$780$	−2.86927	−	1.38261i	−0.102736	−	0.0495055i
$781$	2.73366			0.0978182
$782$	6.69602	+	3.30057i	0.239449	+	0.118028i
$783$			72.4628i			2.58961i
$784$	0.946778	+	9.29385i	0.0338135	+	0.331923i
$785$	−0.676516	+	4.70527i	−0.0241459	+	0.167938i
$786$	28.2762	+	4.36379i	1.00858	+	0.155651i
$787$	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	$0.806685\pi$
$788$	−11.0248	+	16.4005i	−0.392742	+	0.584245i
$789$	58.1762	+	67.1389i	2.07113	+	2.39021i
$790$	−2.41893	+	1.07466i	−0.0860618	+	0.0382348i
$791$	7.30440	−	24.8765i	0.259714	−	0.884506i
$792$	−0.929113	−	8.27279i	−0.0330146	−	0.293961i
$793$	−2.96169	+	4.60848i	−0.105173	+	0.163652i
$794$	−32.7406	−	9.98162i	−1.16192	−	0.354235i
$795$	−1.26438	+	1.45917i	−0.0448430	+	0.0517516i
$796$	−47.5602	+	12.9050i	−1.68573	+	0.457405i
$797$	7.31696	+	50.8906i	0.259180	+	1.80264i	0.538700	+	0.842498i	$0.318916\pi$
$797$	7.31696	+	50.8906i	0.259180	+	1.80264i	−0.279520	+	0.960140i	$0.590175\pi$
$798$	19.5484	+	12.8500i	0.692006	+	0.454884i
$799$	−0.712001	−	1.55906i	−0.0251888	−	0.0551557i
$800$	−5.63334	+	0.515200i	−0.199169	+	0.0182151i
$801$	97.4570	+	44.5071i	3.44347	+	1.57258i
$802$	−4.23745	−	31.7982i	−0.149630	−	1.12283i
$803$	−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
$808$	−21.5448	−	26.4775i	−0.757943	−	0.931477i
$809$	−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	$0.175463\pi$
$810$	7.45474	+	11.8673i	0.261933	+	0.416975i
$811$	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	$0.689231\pi$
$812$	10.0907	−	31.9139i	0.354114	−	1.11996i
$813$	76.2272	−	10.9598i	2.67340	−	0.384377i
$814$	−2.43280	−	0.0251064i	−0.0852697	−	0.000879980i
$815$	−14.0518	+	16.2166i	−0.492212	+	0.568043i
$816$	−6.71333	−	11.4599i	−0.235014	−	0.401177i
$817$	−20.3050	−	13.0492i	−0.710383	−	0.456535i
$818$	37.4014	+	17.5494i	1.30771	+	0.613599i
$819$	1.95943	−	6.67320i	0.0684680	−	0.233181i
$820$	6.76754	+	8.14386i	0.236333	+	0.284396i
$821$	−19.8523	+	17.2021i	−0.692851	+	0.600359i	−0.928435	−	0.371495i	$-0.878845\pi$
$821$	−19.8523	+	17.2021i	−0.692851	+	0.600359i	0.235584	+	0.971854i	$0.424300\pi$
$822$	28.8453	+	33.9918i	1.00610	+	1.18560i
$823$	9.50782	+	32.3806i	0.331422	+	1.12872i	0.941678	+	0.336515i	$0.109248\pi$
$823$	9.50782	+	32.3806i	0.331422	+	1.12872i	−0.610257	+	0.792204i	$0.708934\pi$
$824$	−0.196396	+	0.0824431i	−0.00684179	+	0.00287204i
$825$	1.44071	+	0.207143i	0.0501592	+	0.00721181i
$826$	25.4798	+	22.5429i	0.886556	+	0.784369i
$827$		−	5.58209i		−	0.194108i	−0.995279	−	0.0970541i	$-0.969058\pi$
$827$		−	5.58209i		−	0.194108i	0.995279	−	0.0970541i	$-0.0309420\pi$
$828$	18.7092	−	55.4370i	0.650189	−	1.92657i
$829$			3.72702i			0.129445i	0.997903	+	0.0647224i	$0.0206162\pi$
$829$			3.72702i			0.129445i	−0.997903	+	0.0647224i	$0.979384\pi$
$830$	−7.10580	+	8.03154i	−0.246646	+	0.278779i
$831$	40.7164	+	5.85414i	1.41244	+	0.203078i
$832$	1.43830	−	3.97083i	0.0498642	−	0.137664i
$833$	−0.724239	−	2.46653i	−0.0250934	−	0.0854603i
$834$	−16.5326	+	14.0295i	−0.572478	+	0.485803i
$835$	−2.51674	+	2.18077i	−0.0870955	+	0.0754687i
$836$	−1.56594	−	1.88441i	−0.0541592	−	0.0651736i
$837$	11.7390	−	39.9794i	0.405760	−	1.38189i
$838$	−1.19894	+	2.55520i	−0.0414168	+	0.0882680i
$839$	−28.2402	−	18.1489i	−0.974960	−	0.626569i	−0.0468605	−	0.998901i	$-0.514922\pi$
$839$	−28.2402	−	18.1489i	−0.974960	−	0.626569i	−0.928099	+	0.372333i	$0.878558\pi$
$840$	−4.64186	−	17.8334i	−0.160159	−	0.615309i
$841$	20.3299	−	23.4620i	0.701033	−	0.809035i
$842$	0.0118627	−	1.14949i	0.000408816	−	0.0396141i
$843$	70.3622	−	10.1166i	2.42340	−	0.348433i
$844$	−2.64596	−	0.836614i	−0.0910778	−	0.0287974i
$845$	−5.28462	−	11.5717i	−0.181797	−	0.398079i
$846$	−11.3749	+	7.14544i	−0.391078	+	0.245665i
$847$	−9.66024	+	21.1530i	−0.331930	+	0.726825i
$848$	−2.09480	−	1.47183i	−0.0719358	−	0.0505430i
$849$	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	$-0.327535\pi$
$853$	−13.9572	−	21.7178i	−0.477885	−	0.743603i	−0.993575	+	0.113172i	$0.963899\pi$
$854$	−31.4171	+	4.18666i	−1.07507	+	0.143264i
$855$	14.0881	+	6.43383i	0.481803	+	0.220032i
$856$	9.10236	−	18.4016i	0.311112	−	0.628955i
$857$	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	$0.831390\pi$
$858$	−0.596900	+	0.908053i	−0.0203778	+	0.0310004i
$859$	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	$0.609802\pi$
$860$	4.97891	+	18.3494i	0.169779	+	0.625708i
$861$	−22.5885	+	26.0685i	−0.769814	+	0.888413i
$862$	−5.46950	+	17.9404i	−0.186292	+	0.611053i
$863$	25.8137	−	40.1668i	0.878707	−	1.36730i	−0.0508847	−	0.998705i	$-0.516204\pi$
$863$	25.8137	−	40.1668i	0.878707	−	1.36730i	0.929592	−	0.368590i	$-0.120160\pi$
$864$	−41.7123	+	32.5339i	−1.41908	+	1.10683i
$865$	−0.795036	+	2.70764i	−0.0270320	+	0.0920627i
$866$	22.4421	+	50.5143i	0.762612	+	1.71655i
$867$	−31.1895	−	35.9946i	−1.05925	−	1.22244i
$868$	−10.7373	+	15.9729i	−0.364449	+	0.542156i
$869$	0.254427	+	0.866497i	0.00863083	+	0.0293939i
$870$	5.04201	−	32.6709i	0.170940	−	1.10765i
$871$	0.0480968	−	0.334520i	0.00162970	−	0.0113348i
$872$	12.0213	+	2.11008i	0.407093	+	0.0714564i
$873$		−	94.0416i		−	3.18283i
$874$	−4.36097	−	16.6589i	−0.147512	−	0.563494i
$875$	2.15975			0.0730128
$876$	−32.6074	+	67.6686i	−1.10170	+	2.28631i
$877$	29.2485	+	4.20530i	0.987652	+	0.142003i	0.617164	−	0.786834i	$-0.288281\pi$
$877$	29.2485	+	4.20530i	0.987652	+	0.142003i	0.370488	+	0.928837i	$0.379190\pi$
$878$	−1.43132	+	9.27459i	−0.0483048	+	0.313002i
$879$	75.8950	−	22.2848i	2.55988	−	0.751647i
$880$	−0.0796453	+	1.92837i	−0.00268484	+	0.0650054i
$881$	−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	$0.928896\pi$
$882$	−18.4122	+	8.17999i	−0.619970	+	0.275435i
$883$	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	$0.341366\pi$
$884$	−0.189095	+	1.14665i	−0.00635994	+	0.0385661i
$885$	28.2665	+	18.1658i	0.950167	+	0.610635i
$886$	8.92028	−	29.2593i	0.299683	−	0.982984i
$887$	8.68381	+	7.52457i	0.291574	+	0.252650i	0.788348	−	0.615230i	$-0.210937\pi$
$887$	8.68381	+	7.52457i	0.291574	+	0.252650i	−0.496774	+	0.867880i	$0.665482\pi$
$888$	15.6470	+	26.0889i	0.525079	+	0.875488i
$889$	30.5859	−	4.39758i	1.02582	−	0.147490i
$890$	−20.7562	−	13.6439i	−0.695750	−	0.457345i
$891$	4.34940	−	1.98630i	0.145710	−	0.0665437i
$892$	−38.5065	−	34.7830i	−1.28929	−	1.16462i
$893$	−1.64237	+	3.59630i	−0.0549600	+	0.120346i
$894$	−83.0162	+	11.0628i	−2.77648	+	0.369995i
$895$	−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
$900$	−4.83793	−	11.1997i	−0.161264	−	0.373323i
$901$	0.640830	+	0.292657i	0.0213491	+	0.00974982i
$902$	3.05919	−	1.92170i	0.101860	−	0.0639857i
$903$	−56.3386	+	25.7290i	−1.87483	+	0.856207i
$904$	33.9376	+	1.05100i	1.12875	+	0.0349558i
$905$	−1.55415	−	10.8094i	−0.0516618	−	0.359316i
$906$	−70.1266	−	0.723703i	−2.32980	−	0.0240434i
$907$	−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	$0.974856\pi$
$908$	−0.435305	+	21.0882i	−0.0144461	+	0.699836i
$909$	39.8015	−	61.9323i	1.32013	−	2.05416i
$910$	−0.684926	+	1.45972i	−0.0227051	+	0.0483894i
$911$	−45.0086	−	13.2157i	−1.49120	−	0.437856i	−0.568277	−	0.822837i	$-0.692390\pi$
$911$	−45.0086	−	13.2157i	−1.49120	−	0.437856i	−0.922925	+	0.384981i	$0.874208\pi$
$912$	−9.83701	+	29.0143i	−0.325736	+	0.960759i
$913$	2.39596	+	2.76509i	0.0792948	+	0.0915111i
$914$	−7.15492	−	8.43147i	−0.236664	−	0.278888i
$915$	−30.0353	+	8.81915i	−0.992936	+	0.291552i
$916$	−1.18009	−	9.61207i	−0.0389913	−	0.317592i
$917$	2.06135	−	14.3370i	0.0680717	−	0.473449i
$918$	9.64557	−	10.9022i	0.318351	−	0.359826i
$919$	−36.6864			−1.21017			−0.605086	−	0.796160i	$-0.706861\pi$
$919$	−36.6864			−1.21017			−0.605086	+	0.796160i	$0.706861\pi$
$920$	−6.24705	+	12.0405i	−0.205959	+	0.396964i
$921$	15.5615			0.512770
$922$	9.51929	−	10.7595i	0.313501	−	0.354344i
$923$	−0.425653	+	2.96048i	−0.0140105	+	0.0974455i
$924$	−6.24030	+	0.766133i	−0.205291	+	0.0252039i
$925$	−3.42102	+	1.00450i	−0.112483	+	0.0330278i
$926$	33.2879	+	39.2271i	1.09391	+	1.28908i
$927$	−0.300821	−	0.347166i	−0.00988027	−	0.0114024i
$928$	43.7758	+	2.26075i	1.43701	+	0.0742127i
$929$	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	$0.528435\pi$
$930$	−8.07449	+	17.2085i	−0.264773	+	0.564288i
$931$	−3.20587	+	4.98843i	−0.105068	+	0.163489i
$932$	43.7574	+	0.903245i	1.43332	+	0.0295868i
$933$	16.8266	+	14.5804i	0.550879	+	0.477339i
$934$	−3.07121	−	0.0316948i	−0.100493	−	0.00103709i
$935$	−0.0755820	−	0.525685i	−0.00247180	−	0.0171917i
$936$	9.10387	+	0.281935i	0.297569	+	0.00921533i
$937$	−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	$0.522675\pi$
$938$	1.65576	−	1.04011i	0.0540625	−	0.0339607i
$939$	−93.4811	−	42.6914i	−3.05064	−	1.39318i
$940$	2.85897	−	1.23499i	0.0932492	−	0.0402809i
$941$	−22.9173	+	14.7281i	−0.747083	+	0.480121i	−0.857962	−	0.513713i	$-0.828270\pi$
$941$	−22.9173	+	14.7281i	−0.747083	+	0.480121i	0.110879	+	0.993834i	$0.464633\pi$
$942$	−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
$946$	6.43000	−	0.856865i	0.209057	−	0.0278591i
$947$	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	$-0.314866\pi$
$948$	7.56930	−	8.37957i	0.245839	−	0.272156i
$949$	5.97867	−	2.73037i	0.194076	−	0.0886314i
$950$	−3.00046	−	1.97233i	−0.0973479	−	0.0639907i
$951$	−30.0004	+	4.31341i	−0.972831	+	0.139872i
$952$	−5.76624	+	3.45834i	−0.186885	+	0.112085i
$953$	−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	$0.965617\pi$
$954$	1.61016	−	5.28145i	0.0521307	−	0.170993i
$955$	10.0753	+	6.47499i	0.326029	+	0.209526i
$956$	2.93666	+	0.484285i	0.0949785	+	0.0156629i
$957$	−10.8218	−	3.17757i	−0.349819	−	0.102716i
$958$	30.9017	−	13.7287i	0.998387	−	0.443554i
$959$	17.0568	−	14.7798i	0.550794	−	0.477266i
$960$	21.0703	−	11.7660i	0.680042	−	0.379746i
$961$	−10.6952	+	3.14038i	−0.345005	+	0.101303i
$962$	0.405996	−	2.63075i	0.0130898	−	0.0848187i
$963$	43.8253	+	6.30113i	1.41225	+	0.203051i
$964$	14.5952	+	7.03296i	0.470079	+	0.226517i
$965$	13.9187			0.448058
$966$	−42.0113	−	13.6970i	−1.35169	−	0.440693i
$967$		−	21.6758i		−	0.697046i	−0.937300	−	0.348523i	$-0.886683\pi$
$967$		−	21.6758i		−	0.697046i	0.937300	−	0.348523i	$-0.113317\pi$
$968$	−29.9956	−	5.26509i	−0.964096	−	0.169226i
$969$	1.19977	−	8.34457i	0.0385421	−	0.268066i
$970$	−3.32536	+	21.5474i	−0.106771	+	0.691847i
$971$	−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	$0.952830\pi$
$972$	−3.05347	−	2.05261i	−0.0979401	−	0.0658374i
$973$	7.18849	+	8.29596i	0.230452	+	0.265956i
$974$	1.89983	+	4.27629i	0.0608745	+	0.137021i
$975$	−0.448661	+	1.52800i	−0.0143687	+	0.0489351i
$976$	−15.6702	−	38.4362i	−0.501590	−	1.23031i
$977$	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	$0.0706310\pi$
$978$	26.6952	−	87.5624i	0.853618	−	2.79994i
$979$	−5.54969	+	6.40469i	−0.177369	+	0.204695i
$980$	4.50797	−	1.22319i	0.144002	−	0.0390734i
$981$	3.74605	+	26.0544i	0.119602	+	0.831852i
$982$	2.12865	−	3.23827i	0.0679279	−	0.103337i
$983$	11.4282	+	25.0243i	0.364503	+	0.798150i	0.999668	+	0.0257736i	$0.00820491\pi$
$983$	11.4282	+	25.0243i	0.364503	+	0.798150i	−0.635165	+	0.772377i	$0.719068\pi$
$984$	−40.4904	−	20.0285i	−1.29079	−	0.638486i
$985$	8.98792	+	4.10465i	0.286379	+	0.130785i
$986$	−11.9563	+	1.59331i	−0.380767	+	0.0507412i
$987$	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	$-0.245680\pi$
$991$	−6.78346	−	10.5553i	−0.215484	−	0.335299i	−0.932121	+	0.362147i	$0.882044\pi$
$992$	−23.7859	−	8.33900i	−0.755202	−	0.264764i
$993$	−25.8704	+	56.6482i	−0.820971	+	1.79768i
$994$	−14.6534	+	9.20487i	−0.464776	+	0.291961i
$995$	10.2358	+	22.4133i	0.324497	+	0.710550i
$996$	13.7921	−	43.6204i	0.437020	−	1.38216i
$997$	−5.90824	+	0.849477i	−0.187116	+	0.0269032i	−0.235236	−	0.971938i	$-0.575586\pi$
$997$	−5.90824	+	0.849477i	−0.187116	+	0.0269032i	0.0481198	+	0.998842i	$0.484677\pi$
$998$	−0.138654	+	13.4355i	−0.00438903	+	0.425295i
$999$	−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.b.11.37	yes	480
8.3	odd	2		920.2.bb.a.11.19	✓	480
23.21	odd	22		920.2.bb.a.251.19	yes	480
184.67	even	22	inner	920.2.bb.b.251.37	yes	480

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.05918 + 0.937093i) q^{2} +(-0.429309 + 2.98591i) q^{3} +(0.243714 + 1.98510i) q^{4} +(0.959493 - 0.281733i) q^{5} +(-3.25279 + 2.76031i) q^{6} +(1.41433 + 1.63223i) q^{7} +(-1.60208 + 2.33095i) q^{8} +(-5.85288 - 1.71856i) q^{9} +(1.28028 + 0.600729i) q^{10} +(0.260861 - 0.405908i) q^{11} +(-6.03195 - 0.124512i) q^{12} +(0.398969 + 0.345709i) q^{13} +(-0.0315190 + 3.05418i) q^{14} +(0.429309 + 2.98591i) q^{15} +(-3.88121 + 0.967590i) q^{16} +(1.00123 - 0.457246i) q^{17} +(-4.58879 - 7.30495i) q^{18} +(-2.30954 - 1.05473i) q^{19} +(0.793108 + 1.83602i) 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} +(0.0986179 + 0.740038i) q^{26} +(3.88472 - 8.50636i) q^{27} +(-2.89544 + 3.20539i) q^{28} +(-7.04860 + 3.21899i) q^{29} +(-2.34336 + 3.56491i) q^{30} +(4.41035 - 0.634113i) q^{31} +(-5.01761 - 2.61220i) q^{32} +(1.10002 + 0.953169i) q^{33} +(1.48896 + 0.453940i) q^{34} +(1.81690 + 1.16765i) q^{35} +(1.98508 - 12.0374i) q^{36} +(-3.42102 - 1.00450i) q^{37} +(-1.45783 - 3.28140i) q^{38} +(-1.20354 + 1.04287i) q^{39} +(-0.880482 + 2.68789i) q^{40} +(5.07992 - 1.49160i) q^{41} +(-9.10599 - 1.40530i) q^{42} +(9.40966 + 1.35291i) q^{43} +(0.869342 + 0.418909i) q^{44} -6.09997 q^{45} +(4.28803 + 5.25479i) q^{46} -1.55715i q^{47} +(-1.22290 - 12.0043i) q^{48} +(0.332374 - 2.31171i) q^{49} +(1.39767 + 0.215698i) q^{50} +(0.935459 + 3.18588i) q^{51} +(-0.589030 + 0.876246i) q^{52} +(0.419139 + 0.483712i) q^{53} +(12.0859 - 5.36940i) q^{54} +(0.135937 - 0.462959i) q^{55} +(-6.07053 + 0.681778i) q^{56} +(4.14084 - 6.44327i) q^{57} +(-10.4822 - 3.19571i) q^{58} +(7.29413 - 8.41787i) q^{59} +(-5.82269 + 1.57993i) q^{60} +(1.47679 + 10.2713i) q^{61} +(5.26557 + 3.46127i) q^{62} +(-5.47285 - 11.9839i) q^{63} +(-2.86666 - 7.46875i) q^{64} +(0.480205 + 0.219302i) q^{65} +(0.271904 + 2.04039i) 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} +(13.3827 - 10.8895i) q^{72} +(5.17201 - 11.3251i) q^{73} +(-2.68216 - 4.26976i) q^{74} +(1.25315 + 2.74401i) q^{75} +(1.53087 - 4.84170i) q^{76} +(1.03148 - 0.148304i) q^{77} +(-2.25203 - 0.0232408i) q^{78} +(-1.22567 + 1.41450i) q^{79} +(-3.45139 + 2.02186i) q^{80} +(8.33661 + 5.35761i) q^{81} +(6.77831 + 3.18049i) q^{82} +(-2.13633 + 7.27566i) q^{83} +(-8.32796 - 10.0216i) q^{84} +(0.831851 - 0.720803i) q^{85} +(8.69871 + 10.2507i) q^{86} +(-6.58558 - 22.4284i) q^{87} +(0.528230 + 1.25835i) q^{88} +(-17.3851 - 2.49959i) q^{89} +(-6.46095 - 5.71624i) q^{90} +1.14016i q^{91} +(-0.382448 + 9.58404i) q^{92} +13.4412i q^{93} +(1.45920 - 1.64930i) q^{94} +(-2.51314 - 0.361335i) q^{95} +(9.95391 - 13.8607i) q^{96} +(4.34339 + 14.7922i) q^{97} +(2.51833 - 2.13705i) q^{98} +(-2.22437 + 1.92743i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 2 q^{2} - 4 q^{4} + 48 q^{5} + 5 q^{6} - q^{8} - 48 q^{9} - 2 q^{10} + 3 q^{12} - 56 q^{16} + 7 q^{18} + 4 q^{20} - 8 q^{21} - 4 q^{23} + 2 q^{24} - 48 q^{25} + 7 q^{26} + 12 q^{27} - 5 q^{30}+ \cdots - 98 q^{98}+O(q^{100}) \) 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 - 56 * 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 + 102 * q^32 + q^34 + 54 * q^36 - 8 * q^37 - 45 * q^38 + 45 * q^40 + 10 * q^42 + 23 * q^44 - 480 * q^45 + 32 * q^46 + 154 * q^48 - 48 * q^49 - 9 * q^50 - 7 * q^52 - 32 * q^53 - 27 * q^54 + 43 * q^56 - 40 * q^58 - 12 * q^59 + 8 * q^60 + 8 * q^61 + 158 * q^62 - 73 * q^64 - 88 * q^66 - 10 * q^68 + 20 * q^69 + 3 * q^72 - 11 * q^74 - 110 * q^76 - 300 * q^78 + 144 * q^79 + q^80 - 56 * q^81 - 59 * q^82 - 146 * q^84 + 18 * q^86 - 100 * q^88 - 7 * q^90 + 19 * q^92 - 316 * q^94 + 65 * q^96 - 98 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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