LMFDB - Embedded newform 930.2.bn.b.19.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(19,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 15, 4]))

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

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

chi := DirichletCharacter("930.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bn (of order $30$, degree $8$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.17
Character	$\chi$	$=$	930.19
Dual form			930.2.bn.b.49.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{2} +(0.406737 - 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(2.06638 - 0.854445i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-1.44492 - 1.30102i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +O(q^{10})$	\(q+(0.587785 - 0.809017i) q^{2} +(0.406737 - 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(2.06638 - 0.854445i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-1.44492 - 1.30102i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +(0.523327 - 2.17397i) q^{10} +(-5.64884 - 1.20070i) q^{11} +(-0.994522 - 0.104528i) q^{12} +(-3.28767 + 0.345548i) q^{13} +(-1.90185 + 0.404250i) q^{14} +(0.0598980 - 2.23527i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.0364977 - 0.171708i) q^{17} +(-0.994522 + 0.104528i) q^{18} +(-0.0150665 + 0.143348i) q^{19} +(-1.45117 - 1.70121i) q^{20} +(-1.77624 + 0.790833i) q^{21} +(-4.29169 + 3.86426i) q^{22} +(3.27136 + 1.06293i) q^{23} +(-0.669131 + 0.743145i) q^{24} +(3.53985 - 3.53121i) q^{25} +(-1.65289 + 2.86289i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(-0.790833 + 1.77624i) q^{28} +(-3.04683 - 2.21365i) q^{29} +(-1.77316 - 1.36231i) q^{30} +(-4.47788 - 3.30887i) q^{31} +1.00000i q^{32} +(-3.39448 + 4.67211i) q^{33} +(-0.160368 - 0.0714003i) q^{34} +(-4.09741 - 1.45378i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(5.58998 - 3.22738i) q^{37} +(0.107115 + 0.0964471i) q^{38} +(-1.02154 + 3.14398i) q^{39} +(-2.22928 + 0.174079i) q^{40} +(10.9387 - 4.87021i) q^{41} +(-0.404250 + 1.90185i) q^{42} +(10.6580 + 1.12020i) q^{43} +(0.603656 + 5.74340i) q^{44} +(-2.01765 - 0.963884i) q^{45} +(2.78279 - 2.02181i) q^{46} +(3.74526 + 5.15490i) q^{47} +(0.207912 + 0.978148i) q^{48} +(-0.336535 - 3.20192i) q^{49} +(-0.776142 - 4.93939i) q^{50} +(-0.171708 - 0.0364977i) q^{51} +(1.34458 + 3.01998i) q^{52} +(2.88281 - 2.59569i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-12.6986 + 2.34553i) q^{55} +(0.972168 + 1.68385i) q^{56} +(0.124827 + 0.0720689i) q^{57} +(-3.58176 + 1.16378i) q^{58} +(-11.8032 - 5.25514i) q^{59} +(-2.14437 + 0.633769i) q^{60} +12.0835 q^{61} +(-5.30896 + 1.67777i) q^{62} +1.94434i q^{63} +(0.809017 + 0.587785i) q^{64} +(-6.49831 + 3.52316i) q^{65} +(1.78459 + 5.49239i) q^{66} +(-2.86681 - 1.65515i) q^{67} +(-0.152026 + 0.0877721i) q^{68} +(2.30162 - 2.55621i) q^{69} +(-3.58453 + 2.46036i) q^{70} +(-6.46534 - 7.18049i) q^{71} +(0.406737 + 0.913545i) q^{72} +(-2.81013 + 13.2206i) q^{73} +(0.674705 - 6.41939i) q^{74} +(-1.78614 - 4.67009i) q^{75} +(0.140988 - 0.0299679i) q^{76} +(6.60002 + 9.08415i) q^{77} +(1.94309 + 2.67443i) q^{78} +(0.852468 - 0.181198i) q^{79} +(-1.16951 + 1.90585i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(2.48950 - 11.7122i) q^{82} +(-2.58718 - 5.81090i) q^{83} +(1.30102 + 1.44492i) q^{84} +(-0.222133 - 0.323629i) q^{85} +(7.17087 - 7.96406i) q^{86} +(-3.26152 + 1.88304i) q^{87} +(5.00133 + 2.88752i) q^{88} +(2.52224 + 7.76265i) q^{89} +(-1.96575 + 1.06576i) q^{90} +(5.19999 + 3.77801i) q^{91} -3.43972i q^{92} +(-4.84412 + 2.74490i) q^{93} +6.37181 q^{94} +(0.0913501 + 0.309085i) q^{95} +(0.913545 + 0.406737i) q^{96} +(-11.8413 + 3.84748i) q^{97} +(-2.78822 - 1.60978i) q^{98} +(2.88752 + 5.00133i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9}+O(q^{10}) $ 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9	$ 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9} - 18 q^{11} - 8 q^{14} - 36 q^{16} - 24 q^{19} - 2 q^{20} + 28 q^{21} - 18 q^{24} + 10 q^{25} - 12 q^{26} - 4 q^{30} - 4 q^{31} + 10 q^{34} - 2 q^{35} - 72 q^{36} + 16 q^{39} + 4 q^{41} - 2 q^{44} - 2 q^{45} - 2 q^{46} - 78 q^{49} + 32 q^{50} + 10 q^{51} + 36 q^{54} - 50 q^{55} - 12 q^{56} + 28 q^{59} + 88 q^{61} + 36 q^{64} - 124 q^{65} + 6 q^{66} - 46 q^{69} - 10 q^{70} + 140 q^{71} + 34 q^{74} - 32 q^{75} + 24 q^{76} + 16 q^{79} + 12 q^{80} + 18 q^{81} - 8 q^{84} + 74 q^{85} - 98 q^{86} + 148 q^{89} + 44 q^{91} - 108 q^{94} - 80 q^{95} + 18 q^{96} - 2 q^{99}+O(q^{100}) $ 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9 - 18 * q^11 - 8 * q^14 - 36 * q^16 - 24 * q^19 - 2 * q^20 + 28 * q^21 - 18 * q^24 + 10 * q^25 - 12 * q^26 - 4 * q^30 - 4 * q^31 + 10 * q^34 - 2 * q^35 - 72 * q^36 + 16 * q^39 + 4 * q^41 - 2 * q^44 - 2 * q^45 - 2 * q^46 - 78 * q^49 + 32 * q^50 + 10 * q^51 + 36 * q^54 - 50 * q^55 - 12 * q^56 + 28 * q^59 + 88 * q^61 + 36 * q^64 - 124 * q^65 + 6 * q^66 - 46 * q^69 - 10 * q^70 + 140 * q^71 + 34 * q^74 - 32 * q^75 + 24 * q^76 + 16 * q^79 + 12 * q^80 + 18 * q^81 - 8 * q^84 + 74 * q^85 - 98 * q^86 + 148 * q^89 + 44 * q^91 - 108 * q^94 - 80 * q^95 + 18 * q^96 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{15}\right)$

Coefficient data

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

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

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

$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$3$	0.406737	−	0.913545i	0.234830	−	0.527436i
$3$	0.406737	−	0.913545i	0.234830	−	0.527436i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	2.06638	−	0.854445i	0.924113	−	0.382119i
$5$	2.06638	−	0.854445i	0.924113	−	0.382119i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−1.44492	−	1.30102i	−0.546130	−	0.491738i	0.349257	−	0.937027i	$-0.386434\pi$
$7$	−1.44492	−	1.30102i	−0.546130	−	0.491738i	−0.895387	+	0.445290i	$0.853101\pi$
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$	−0.669131	−	0.743145i	−0.223044	−	0.247715i
$10$	0.523327	−	2.17397i	0.165491	−	0.687468i
$11$	−5.64884	−	1.20070i	−1.70319	−	0.362024i	−0.749311	−	0.662218i	$-0.769615\pi$
$11$	−5.64884	−	1.20070i	−1.70319	−	0.362024i	−0.953878	+	0.300194i	$0.902949\pi$
$12$	−0.994522	−	0.104528i	−0.287094	−	0.0301748i
$13$	−3.28767	+	0.345548i	−0.911834	+	0.0958377i	−0.548815	−	0.835944i	$-0.684921\pi$
$13$	−3.28767	+	0.345548i	−0.911834	+	0.0958377i	−0.363019	+	0.931782i	$0.618254\pi$
$14$	−1.90185	+	0.404250i	−0.508290	+	0.108040i
$15$	0.0598980	−	2.23527i	0.0154656	−	0.577143i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−0.0364977	−	0.171708i	−0.00885199	−	0.0416454i	0.973500	−	0.228687i	$-0.0734433\pi$
$17$	−0.0364977	−	0.171708i	−0.00885199	−	0.0416454i	−0.982352	+	0.187042i	$0.940110\pi$
$18$	−0.994522	+	0.104528i	−0.234411	+	0.0246376i
$19$	−0.0150665	+	0.143348i	−0.00345649	+	0.0328863i	−0.996114	−	0.0880710i	$-0.971930\pi$
$19$	−0.0150665	+	0.143348i	−0.00345649	+	0.0328863i	0.992658	+	0.120957i	$0.0385964\pi$
$20$	−1.45117	−	1.70121i	−0.324492	−	0.380401i
$21$	−1.77624	+	0.790833i	−0.387607	+	0.172574i
$22$	−4.29169	+	3.86426i	−0.914992	+	0.823862i
$23$	3.27136	+	1.06293i	0.682126	+	0.221636i	0.629526	−	0.776979i	$-0.283249\pi$
$23$	3.27136	+	1.06293i	0.682126	+	0.221636i	0.0526004	+	0.998616i	$0.483249\pi$
$24$	−0.669131	+	0.743145i	−0.136586	+	0.151694i
$25$	3.53985	−	3.53121i	0.707970	−	0.706243i
$26$	−1.65289	+	2.86289i	−0.324158	+	0.561458i
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$	−0.790833	+	1.77624i	−0.149453	+	0.335678i
$29$	−3.04683	−	2.21365i	−0.565781	−	0.411064i	0.267789	−	0.963478i	$-0.413707\pi$
$29$	−3.04683	−	2.21365i	−0.565781	−	0.411064i	−0.833570	+	0.552413i	$0.813707\pi$
$30$	−1.77316	−	1.36231i	−0.323733	−	0.248723i
$31$	−4.47788	−	3.30887i	−0.804250	−	0.594291i
$31$	−4.47788	−	3.30887i	−0.804250	−	0.594291i
$32$			1.00000i			0.176777i
$33$	−3.39448	+	4.67211i	−0.590904	+	0.813309i
$34$	−0.160368	−	0.0714003i	−0.0275028	−	0.0122450i
$35$	−4.09741	−	1.45378i	−0.692588	−	0.245734i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	5.58998	−	3.22738i	0.918987	−	0.530577i	0.0356751	−	0.999363i	$-0.488642\pi$
$37$	5.58998	−	3.22738i	0.918987	−	0.530577i	0.883312	+	0.468786i	$0.155309\pi$
$38$	0.107115	+	0.0964471i	0.0173764	+	0.0156458i
$39$	−1.02154	+	3.14398i	−0.163577	+	0.503440i
$40$	−2.22928	+	0.174079i	−0.352480	+	0.0275243i
$41$	10.9387	−	4.87021i	1.70833	−	0.760598i	0.709919	−	0.704283i	$-0.248732\pi$
$41$	10.9387	−	4.87021i	1.70833	−	0.760598i	0.998413	−	0.0563149i	$-0.0179351\pi$
$42$	−0.404250	+	1.90185i	−0.0623772	+	0.293462i
$43$	10.6580	+	1.12020i	1.62533	+	0.170829i	0.872918	−	0.487866i	$-0.162225\pi$
$43$	10.6580	+	1.12020i	1.62533	+	0.170829i	0.752410	+	0.658695i	$0.228891\pi$
$44$	0.603656	+	5.74340i	0.0910046	+	0.865851i
$45$	−2.01765	−	0.963884i	−0.300774	−	0.143687i
$46$	2.78279	−	2.02181i	0.410300	−	0.298100i
$47$	3.74526	+	5.15490i	0.546302	+	0.751920i	0.989505	−	0.144501i	$-0.0461578\pi$
$47$	3.74526	+	5.15490i	0.546302	+	0.751920i	−0.443203	+	0.896421i	$0.646158\pi$
$48$	0.207912	+	0.978148i	0.0300095	+	0.141183i
$49$	−0.336535	−	3.20192i	−0.0480764	−	0.457417i
$50$	−0.776142	−	4.93939i	−0.109763	−	0.698536i
$51$	−0.171708	−	0.0364977i	−0.0240440	−	0.00511070i
$52$	1.34458	+	3.01998i	0.186460	+	0.418795i
$53$	2.88281	−	2.59569i	0.395984	−	0.356545i	−0.446954	−	0.894557i	$-0.647491\pi$
$53$	2.88281	−	2.59569i	0.395984	−	0.356545i	0.842937	+	0.538012i	$0.180824\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$	−12.6986	+	2.34553i	−1.71228	+	0.316271i
$56$	0.972168	+	1.68385i	0.129911	+	0.225013i
$57$	0.124827	+	0.0720689i	0.0165337	+	0.00954576i
$58$	−3.58176	+	1.16378i	−0.470308	+	0.152812i
$59$	−11.8032	−	5.25514i	−1.53665	−	0.684161i	−0.548290	−	0.836288i	$-0.684721\pi$
$59$	−11.8032	−	5.25514i	−1.53665	−	0.684161i	−0.988361	+	0.152127i	$0.951388\pi$
$60$	−2.14437	+	0.633769i	−0.276837	+	0.0818192i
$61$	12.0835			1.54713			0.773567	−	0.633715i	$-0.218471\pi$
$61$	12.0835			1.54713			0.773567	+	0.633715i	$0.218471\pi$
$62$	−5.30896	+	1.67777i	−0.674239	+	0.213077i
$63$			1.94434i			0.244963i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	−6.49831	+	3.52316i	−0.806017	+	0.436994i
$66$	1.78459	+	5.49239i	0.219667	+	0.676066i
$67$	−2.86681	−	1.65515i	−0.350236	−	0.202209i	0.314553	−	0.949240i	$-0.398145\pi$
$67$	−2.86681	−	1.65515i	−0.350236	−	0.202209i	−0.664789	+	0.747031i	$0.731479\pi$
$68$	−0.152026	+	0.0877721i	−0.0184358	+	0.0106439i
$69$	2.30162	−	2.55621i	0.277082	−	0.307731i
$70$	−3.58453	+	2.46036i	−0.428433	+	0.294069i
$71$	−6.46534	−	7.18049i	−0.767295	−	0.852168i	0.225218	−	0.974308i	$-0.427691\pi$
$71$	−6.46534	−	7.18049i	−0.767295	−	0.852168i	−0.992513	+	0.122141i	$0.961024\pi$
$72$	0.406737	+	0.913545i	0.0479344	+	0.107662i
$73$	−2.81013	+	13.2206i	−0.328901	+	1.54736i	0.434042	+	0.900893i	$0.357087\pi$
$73$	−2.81013	+	13.2206i	−0.328901	+	1.54736i	−0.762943	+	0.646466i	$0.776246\pi$
$74$	0.674705	−	6.41939i	0.0784329	−	0.746239i
$75$	−1.78614	−	4.67009i	−0.206246	−	0.539255i
$76$	0.140988	−	0.0299679i	0.0161724	−	0.00343756i
$77$	6.60002	+	9.08415i	0.752142	+	1.03523i
$78$	1.94309	+	2.67443i	0.220011	+	0.302819i
$79$	0.852468	−	0.181198i	0.0959102	−	0.0203863i	−0.159707	−	0.987165i	$-0.551055\pi$
$79$	0.852468	−	0.181198i	0.0959102	−	0.0203863i	0.255617	+	0.966778i	$0.417721\pi$
$80$	−1.16951	+	1.90585i	−0.130755	+	0.213080i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	2.48950	−	11.7122i	0.274920	−	1.29340i
$83$	−2.58718	−	5.81090i	−0.283980	−	0.637829i	0.714082	−	0.700062i	$-0.246844\pi$
$83$	−2.58718	−	5.81090i	−0.283980	−	0.637829i	−0.998062	+	0.0622331i	$0.980178\pi$
$84$	1.30102	+	1.44492i	0.141952	+	0.157654i
$85$	−0.222133	−	0.323629i	−0.0240937	−	0.0351025i
$86$	7.17087	−	7.96406i	0.773255	−	0.858787i
$87$	−3.26152	+	1.88304i	−0.349672	+	0.201883i
$88$	5.00133	+	2.88752i	0.533144	+	0.307811i
$89$	2.52224	+	7.76265i	0.267357	+	0.822839i	0.991141	+	0.132813i	$0.0424010\pi$
$89$	2.52224	+	7.76265i	0.267357	+	0.822839i	−0.723784	+	0.690026i	$0.757599\pi$
$90$	−1.96575	+	1.06576i	−0.207208	+	0.112341i
$91$	5.19999	+	3.77801i	0.545107	+	0.396043i
$92$		−	3.43972i		−	0.358615i
$93$	−4.84412	+	2.74490i	−0.502312	+	0.284633i
$94$	6.37181			0.657202
$95$	0.0913501	+	0.309085i	0.00937232	+	0.0317115i
$96$	0.913545	+	0.406737i	0.0932383	+	0.0415124i
$97$	−11.8413	+	3.84748i	−1.20231	+	0.390653i	−0.840609	−	0.541643i	$-0.817802\pi$
$97$	−11.8413	+	3.84748i	−1.20231	+	0.390653i	−0.361697	+	0.932296i	$0.617802\pi$
$98$	−2.78822	−	1.60978i	−0.281652	−	0.162612i
$99$	2.88752	+	5.00133i	0.290207	+	0.502653i
$100$	−4.45226	−	2.27539i	−0.445226	−	0.227539i
$101$	4.69999	−	14.4651i	0.467667	−	1.43933i	−0.387931	−	0.921689i	$-0.626810\pi$
$101$	4.69999	−	14.4651i	0.467667	−	1.43933i	0.855597	−	0.517642i	$-0.173190\pi$
$102$	−0.130455	+	0.117462i	−0.0129170	+	0.0116305i
$103$	0.923234	+	2.07362i	0.0909690	+	0.204320i	0.953300	−	0.302026i	$-0.0976628\pi$
$103$	0.923234	+	2.07362i	0.0909690	+	0.204320i	−0.862331	+	0.506345i	$0.830996\pi$
$104$	3.23354	+	0.687309i	0.317074	+	0.0673962i
$105$	−2.99466	+	3.15186i	−0.292249	+	0.307590i
$106$	−0.405487	−	3.85795i	−0.0393843	−	0.374717i
$107$	0.262963	+	1.23714i	0.0254216	+	0.119599i	0.989029	−	0.147723i	$-0.0471945\pi$
$107$	0.262963	+	1.23714i	0.0254216	+	0.119599i	−0.963607	+	0.267322i	$0.913861\pi$
$108$	0.587785	+	0.809017i	0.0565597	+	0.0778477i
$109$	−15.1988	+	11.0426i	−1.45578	+	1.05769i	−0.471342	+	0.881951i	$0.656230\pi$
$109$	−15.1988	+	11.0426i	−1.45578	+	1.05769i	−0.984438	+	0.175735i	$0.943770\pi$
$110$	−5.56647	+	11.6520i	−0.530742	+	1.11098i
$111$	−0.674705	−	6.41939i	−0.0640402	−	0.609302i
$112$	1.93369	+	0.203239i	0.182716	+	0.0192042i
$113$	2.66837	−	12.5537i	0.251019	−	1.18095i	−0.654305	−	0.756231i	$-0.727039\pi$
$113$	2.66837	−	12.5537i	0.251019	−	1.18095i	0.905324	−	0.424721i	$-0.139628\pi$
$114$	0.131676	−	0.0586262i	0.0123326	−	0.00549084i
$115$	7.66809	−	0.598782i	0.715053	−	0.0558367i
$116$	−1.16378	+	3.58176i	−0.108055	+	0.332558i
$117$	2.45667	+	2.21200i	0.227119	+	0.204499i
$118$	−11.1893	+	6.46013i	−1.03006	+	0.594703i
$119$	−0.170659	+	0.295589i	−0.0156442	+	0.0270966i
$120$	−0.747701	+	2.10735i	−0.0682555	+	0.192374i
$121$	20.4187	+	9.09101i	1.85625	+	0.826455i
$122$	7.10250	−	9.77576i	0.643031	−	0.885056i
$123$		−	11.9739i		−	1.07965i
$124$	−1.76318	+	5.28121i	−0.158339	+	0.474267i
$125$	4.29744	−	10.3214i	0.384375	−	0.923177i
$126$	1.57300	+	1.14285i	0.140134	+	0.101813i
$127$	−5.29126	+	11.8844i	−0.469524	+	1.05457i	0.511252	+	0.859431i	$0.329182\pi$
$127$	−5.29126	+	11.8844i	−0.469524	+	1.05457i	−0.980776	+	0.195137i	$0.937485\pi$
$128$	0.951057	−	0.309017i	0.0840623	−	0.0273135i
$129$	5.35835	−	9.28093i	0.471776	−	0.817141i
$130$	−0.969315	+	7.32811i	−0.0850146	+	0.642718i
$131$	7.07388	−	7.85634i	0.618048	−	0.686412i	−0.350122	−	0.936704i	$-0.613860\pi$
$131$	7.07388	−	7.85634i	0.618048	−	0.686412i	0.968170	+	0.250292i	$0.0805267\pi$
$132$	5.49239	+	1.78459i	0.478051	+	0.155328i
$133$	0.208268	−	0.187526i	0.0180591	−	0.0162605i
$134$	−3.02411	+	1.34642i	−0.261244	+	0.116313i
$135$	−1.70121	+	1.45117i	−0.146416	+	0.124897i
$136$	−0.0183494	+	0.174583i	−0.00157345	+	0.0149703i
$137$	14.7000	−	1.54503i	1.25590	−	0.132001i	0.546895	−	0.837201i	$-0.315810\pi$
$137$	14.7000	−	1.54503i	1.25590	−	0.132001i	0.709008	+	0.705201i	$0.249143\pi$
$138$	−0.715157	−	3.36455i	−0.0608782	−	0.286409i
$139$	−0.354604	+	0.257635i	−0.0300771	+	0.0218523i	−0.602722	−	0.797951i	$-0.705917\pi$
$139$	−0.354604	+	0.257635i	−0.0300771	+	0.0218523i	0.572645	+	0.819803i	$0.305917\pi$
$140$	−0.116462	+	4.34611i	−0.00984282	+	0.367313i
$141$	6.23257	−	1.32477i	0.524877	−	0.111566i
$142$	−9.60937	+	1.00999i	−0.806401	+	0.0847561i
$143$	18.9864	+	1.99555i	1.58772	+	0.166876i
$144$	0.978148	+	0.207912i	0.0815123	+	0.0173260i
$145$	−8.18734	−	1.97089i	−0.679921	−	0.163674i
$146$	9.04397	+	10.0443i	0.748484	+	0.831276i
$147$	−3.06198	−	0.994897i	−0.252548	−	0.0820577i
$148$	−4.79682	−	4.31907i	−0.394296	−	0.355026i
$149$	−3.27716	−	5.67620i	−0.268475	−	0.465012i	0.699993	−	0.714149i	$-0.253186\pi$
$149$	−3.27716	−	5.67620i	−0.268475	−	0.465012i	−0.968468	+	0.249137i	$0.919853\pi$
$150$	−4.82805	−	1.29999i	−0.394208	−	0.106144i
$151$	2.23955	+	6.89263i	0.182252	+	0.560915i	0.999890	−	0.0148180i	$-0.00471690\pi$
$151$	2.23955	+	6.89263i	0.182252	+	0.560915i	−0.817638	+	0.575733i	$0.804717\pi$
$152$	0.0586262	−	0.131676i	0.00475521	−	0.0106804i
$153$	−0.103182	+	0.142018i	−0.00834180	+	0.0114815i
$154$	11.2286			0.904828
$155$	−12.0802	−	3.01128i	−0.970308	−	0.241872i
$156$	3.30578			0.264674
$157$	10.0791	−	13.8726i	0.804396	−	1.10716i	−0.187768	−	0.982213i	$-0.560125\pi$
$157$	10.0791	−	13.8726i	0.804396	−	1.10716i	0.992164	−	0.124942i	$-0.0398746\pi$
$158$	0.354476	−	0.796167i	0.0282006	−	0.0633396i
$159$	−1.19874	−	3.68934i	−0.0950661	−	0.292583i
$160$	0.854445	+	2.06638i	0.0675498	+	0.163362i
$161$	−3.34398	−	5.79195i	−0.263543	−	0.456469i
$162$	0.743145	+	0.669131i	0.0583870	+	0.0525719i
$163$	7.00022	+	2.27451i	0.548300	+	0.178153i	0.570050	−	0.821610i	$-0.306924\pi$
$163$	7.00022	+	2.27451i	0.548300	+	0.178153i	−0.0217501	+	0.999763i	$0.506924\pi$
$164$	−8.01207	−	8.89831i	−0.625638	−	0.694841i
$165$	−3.02223	+	12.5547i	−0.235281	+	0.977385i
$166$	−6.22182	−	1.32249i	−0.482907	−	0.102645i
$167$	0.583853	+	0.0613655i	0.0451799	+	0.00474860i	0.127091	−	0.991891i	$-0.459436\pi$
$167$	0.583853	+	0.0613655i	0.0451799	+	0.00474860i	−0.0819115	+	0.996640i	$0.526102\pi$
$168$	1.93369	−	0.203239i	0.149187	−	0.0156802i
$169$	−2.02658	+	0.430762i	−0.155890	+	0.0331355i
$170$	−0.392388	−	0.0105147i	−0.0300948	−	0.000806444i
$171$	0.116610	−	0.0847221i	0.00891739	−	0.00647886i
$172$	−2.22813	−	10.4825i	−0.169893	−	0.799284i
$173$	17.5295	−	1.84242i	1.33274	−	0.140077i	0.588777	−	0.808295i	$-0.299610\pi$
$173$	17.5295	−	1.84242i	1.33274	−	0.140077i	0.743965	+	0.668219i	$0.232943\pi$
$174$	−0.393663	+	3.74545i	−0.0298435	+	0.283942i
$175$	−9.70897	+	0.496940i	−0.733929	+	0.0375651i
$176$	5.27576	−	2.34892i	0.397675	−	0.177057i
$177$	−9.60162	+	8.64534i	−0.721702	+	0.649823i
$178$	7.76265	+	2.52224i	0.581835	+	0.189050i
$179$	−7.43947	+	8.26237i	−0.556052	+	0.617559i	−0.953984	−	0.299856i	$-0.903061\pi$
$179$	−7.43947	+	8.26237i	−0.556052	+	0.617559i	0.397932	+	0.917415i	$0.369728\pi$
$180$	−0.293219	+	2.21676i	−0.0218552	+	0.165227i
$181$	−3.75852	+	6.50995i	−0.279369	+	0.483881i	−0.971228	−	0.238152i	$-0.923458\pi$
$181$	−3.75852	+	6.50995i	−0.279369	+	0.483881i	0.691859	+	0.722032i	$0.256792\pi$
$182$	6.11295	−	1.98622i	0.453122	−	0.147228i
$183$	4.91480	−	11.0388i	0.363313	−	0.816014i
$184$	−2.78279	−	2.02181i	−0.205150	−	0.149050i
$185$	8.79340	−	11.4453i	0.646504	−	0.841476i
$186$	−0.626628	+	5.53239i	−0.0459466	+	0.405655i
$187$			1.01378i			0.0741346i
$188$	3.74526	−	5.15490i	0.273151	−	0.375960i
$189$	1.77624	+	0.790833i	0.129202	+	0.0575246i
$190$	0.303750	+	0.107772i	0.0220363	+	0.00781861i
$191$	3.47708	−	6.02248i	0.251593	−	0.435771i	−0.712372	−	0.701802i	$-0.752379\pi$
$191$	3.47708	−	6.02248i	0.251593	−	0.435771i	0.963964	+	0.266031i	$0.0857124\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	10.1136	+	9.10634i	0.727994	+	0.655489i	0.947366	−	0.320153i	$-0.103734\pi$
$193$	10.1136	+	9.10634i	0.727994	+	0.655489i	−0.219372	+	0.975641i	$0.570401\pi$
$194$	−3.84748	+	11.8413i	−0.276233	+	0.850158i
$195$	0.575466	+	7.36950i	0.0412100	+	0.527741i
$196$	−2.94121	+	1.30951i	−0.210086	+	0.0935365i
$197$	−1.66806	+	7.84760i	−0.118844	+	0.559118i	0.877925	+	0.478798i	$0.158928\pi$
$197$	−1.66806	+	7.84760i	−0.118844	+	0.559118i	−0.996769	+	0.0803199i	$0.974406\pi$
$198$	5.74340	+	0.603656i	0.408166	+	0.0429000i
$199$	−1.70844	−	16.2547i	−0.121108	−	1.15227i	−0.871198	−	0.490931i	$-0.836657\pi$
$199$	−1.70844	−	16.2547i	−0.121108	−	1.15227i	0.750090	−	0.661335i	$-0.230010\pi$
$200$	−4.45780	+	2.26451i	−0.315214	+	0.160125i
$201$	−2.67809	+	1.94575i	−0.188898	+	0.137243i
$202$	−8.93992	−	12.3047i	−0.629010	−	0.865759i
$203$	1.52244	+	7.16252i	0.106854	+	0.502710i
$204$	0.0183494	+	0.174583i	0.00128471	+	0.0122232i
$205$	18.4421	−	19.4102i	1.28805	−	1.35567i
$206$	2.22026	+	0.471930i	0.154693	+	0.0328809i
$207$	−1.39906	−	3.14234i	−0.0972413	−	0.218407i
$208$	2.45667	−	2.21200i	0.170339	−	0.153374i
$209$	0.257226	−	0.791661i	0.0177927	−	0.0547604i
$210$	0.789690	+	4.27535i	0.0544938	+	0.295027i
$211$	10.8717	+	18.8304i	0.748441	+	1.29634i	0.948570	+	0.316568i	$0.102530\pi$
$211$	10.8717	+	18.8304i	0.748441	+	1.29634i	−0.200129	+	0.979769i	$0.564136\pi$
$212$	−3.35948	−	1.93960i	−0.230730	−	0.133212i
$213$	−9.18940	+	2.98582i	−0.629647	+	0.204585i
$214$	1.15544	+	0.514433i	0.0789840	+	0.0351659i
$215$	22.9806	−	6.79191i	1.56726	−	0.463204i
$216$	1.00000			0.0680414
$217$	2.16530	+	10.6069i	0.146990	+	0.720040i
$218$			18.7867i			1.27240i
$219$	10.9347	+	7.94450i	0.738896	+	0.536840i
$220$	6.15480	+	11.3523i	0.414957	+	0.765369i
$221$	0.179326	+	0.551907i	0.0120627	+	0.0371253i
$222$	−5.58998	−	3.22738i	−0.375175	−	0.216607i
$223$	11.9041	−	6.87282i	0.797156	−	0.460238i	−0.0453199	−	0.998973i	$-0.514431\pi$
$223$	11.9041	−	6.87282i	0.797156	−	0.460238i	0.842476	+	0.538734i	$0.181097\pi$
$224$	1.30102	−	1.44492i	0.0869277	−	0.0965430i
$225$	−4.99282	−	0.267776i	−0.332855	−	0.0178517i
$226$	−8.58772	−	9.53763i	−0.571247	−	0.634434i
$227$	−9.96585	−	22.3837i	−0.661457	−	1.48566i	−0.862491	−	0.506072i	$-0.831097\pi$
$227$	−9.96585	−	22.3837i	−0.661457	−	1.48566i	0.201035	−	0.979584i	$-0.435570\pi$
$228$	0.0299679	−	0.140988i	0.00198468	−	0.00933717i
$229$	−2.13774	+	20.3392i	−0.141266	+	1.34405i	0.662479	+	0.749080i	$0.269504\pi$
$229$	−2.13774	+	20.3392i	−0.141266	+	1.34405i	−0.803745	+	0.594974i	$0.797162\pi$
$230$	4.02277	−	6.55557i	0.265253	−	0.432262i
$231$	10.9832	−	2.33456i	0.722645	−	0.153603i
$232$	2.21365	+	3.04683i	0.145333	+	0.200034i
$233$	−8.28790	−	11.4073i	−0.542958	−	0.747318i	0.446078	−	0.894994i	$-0.352821\pi$
$233$	−8.28790	−	11.4073i	−0.542958	−	0.747318i	−0.989036	+	0.147676i	$0.952821\pi$
$234$	3.23354	−	0.687309i	0.211383	−	0.0449308i
$235$	12.1437	+	7.45187i	0.792168	+	0.486107i
$236$	−1.35053	+	12.8495i	−0.0879123	+	0.836430i
$237$	0.181198	−	0.852468i	0.0117701	−	0.0553738i
$238$	0.138826	+	0.311809i	0.00899877	+	0.0202116i
$239$	4.89385	+	5.43517i	0.316557	+	0.351572i	0.880334	−	0.474355i	$-0.157319\pi$
$239$	4.89385	+	5.43517i	0.316557	+	0.351572i	−0.563777	+	0.825927i	$0.690652\pi$
$240$	1.26540	+	1.84358i	0.0816811	+	0.119002i
$241$	10.0555	−	11.1677i	0.647729	−	0.719376i	−0.326434	−	0.945220i	$-0.605847\pi$
$241$	10.0555	−	11.1677i	0.647729	−	0.719376i	0.974164	+	0.225844i	$0.0725138\pi$
$242$	19.3566	−	11.1755i	1.24429	−	0.718391i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−3.73401	−	11.4921i	−0.239045	−	0.735706i
$245$	−3.43127	−	6.32883i	−0.219216	−	0.404334i
$246$	−9.68705	−	7.03806i	−0.617624	−	0.448730i
$247$		−	0.476487i		−	0.0303182i
$248$	3.23622	+	4.53066i	0.205500	+	0.287697i
$249$	−6.36082			−0.403101
$250$	−5.82424	−	9.54349i	−0.368358	−	0.603583i
$251$	1.67504	+	0.745774i	0.105727	+	0.0470728i	0.458919	−	0.888478i	$-0.348237\pi$
$251$	1.67504	+	0.745774i	0.105727	+	0.0470728i	−0.353191	+	0.935551i	$0.614904\pi$
$252$	1.84917	−	0.600833i	0.116487	−	0.0378489i
$253$	−17.2032	−	9.93225i	−1.08155	−	0.624435i
$254$	6.50453	+	11.2662i	0.408131	+	0.706903i
$255$	−0.386000	+	0.0712971i	−0.0241722	+	0.00446480i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−18.0562	+	16.2579i	−1.12632	+	1.01414i	−0.126564	+	0.991958i	$0.540395\pi$
$257$	−18.0562	+	16.2579i	−1.12632	+	1.01414i	−0.999754	+	0.0221825i	$0.992939\pi$
$258$	−4.35887	−	9.79019i	−0.271372	−	0.609511i
$259$	−12.2760	−	2.60934i	−0.762791	−	0.162136i
$260$	5.35882	+	5.09155i	0.332340	+	0.315764i
$261$	0.393663	+	3.74545i	0.0243671	+	0.231838i
$262$	−2.19799	−	10.3407i	−0.135792	−	0.638853i
$263$	−12.5395	−	17.2592i	−0.773220	−	1.06425i	−0.995998	−	0.0893765i	$-0.971513\pi$
$263$	−12.5395	−	17.2592i	−0.773220	−	1.06425i	0.222778	−	0.974869i	$-0.428487\pi$
$264$	4.67211	−	3.39448i	0.287548	−	0.208916i
$265$	3.73910	−	7.82688i	0.229691	−	0.480801i
$266$	−0.0292944	−	0.278717i	−0.00179615	−	0.0170893i
$267$	8.11742	+	0.853175i	0.496778	+	0.0522135i
$268$	−0.688251	+	3.23797i	−0.0420416	+	0.197790i
$269$	−6.39326	+	2.84646i	−0.389804	+	0.173552i	−0.592274	−	0.805736i	$-0.701770\pi$
$269$	−6.39326	+	2.84646i	−0.389804	+	0.173552i	0.202470	+	0.979288i	$0.435103\pi$
$270$	0.174079	+	2.22928i	0.0105941	+	0.135670i
$271$	−3.68868	+	11.3526i	−0.224071	+	0.689620i	0.774313	+	0.632802i	$0.218095\pi$
$271$	−3.68868	+	11.3526i	−0.224071	+	0.689620i	−0.998385	+	0.0568180i	$0.981905\pi$
$272$	0.130455	+	0.117462i	0.00790998	+	0.00712218i
$273$	5.56641	−	3.21377i	0.336895	−	0.194506i
$274$	7.39047	−	12.8007i	0.446475	−	0.773317i
$275$	−24.2360	+	15.6970i	−1.46148	+	0.946564i
$276$	−3.14234	−	1.39906i	−0.189146	−	0.0842134i
$277$	−1.76407	+	2.42803i	−0.105993	+	0.145886i	−0.858718	−	0.512448i	$-0.828739\pi$
$277$	−1.76407	+	2.42803i	−0.105993	+	0.145886i	0.752726	+	0.658334i	$0.228739\pi$
$278$			0.438315i			0.0262884i
$279$	0.537314	+	5.54178i	0.0321681	+	0.331778i
$280$	3.44762	+	2.64880i	0.206035	+	0.158296i
$281$	10.1153	+	7.34920i	0.603428	+	0.438416i	0.847094	−	0.531443i	$-0.178350\pi$
$281$	10.1153	+	7.34920i	0.603428	+	0.438416i	−0.243666	+	0.969859i	$0.578350\pi$
$282$	2.59165	−	5.82094i	0.154330	−	0.346632i
$283$	−14.7004	+	4.77644i	−0.873847	+	0.283930i	−0.711400	−	0.702787i	$-0.751939\pi$
$283$	−14.7004	+	4.77644i	−0.873847	+	0.283930i	−0.162447	+	0.986717i	$0.551939\pi$
$284$	−4.83115	+	8.36780i	−0.286676	+	0.496538i
$285$	0.319519	+	0.0422639i	0.0189267	+	0.00250350i
$286$	12.7744	−	14.1874i	0.755364	−	0.838916i
$287$	−22.1417	−	7.19429i	−1.30699	−	0.424665i
$288$	0.743145	−	0.669131i	0.0437902	−	0.0394289i
$289$	15.5021	−	6.90199i	0.911889	−	0.405999i
$290$	−6.40688	+	5.46523i	−0.376225	+	0.320930i
$291$	−1.30145	+	12.3825i	−0.0762926	+	0.725876i
$292$	13.4420	−	1.41281i	0.786631	−	0.0826782i
$293$	2.61389	+	12.2974i	0.152705	+	0.718422i	0.986155	+	0.165826i	$0.0530292\pi$
$293$	2.61389	+	12.2974i	0.152705	+	0.718422i	−0.833450	+	0.552595i	$0.813638\pi$
$294$	−2.60467	+	1.89241i	−0.151908	+	0.110367i
$295$	−28.8802	−	0.773897i	−1.68147	−	0.0450580i
$296$	−6.31370	+	1.34202i	−0.366976	+	0.0780032i
$297$	5.74340	−	0.603656i	0.333266	−	0.0350277i
$298$	−6.51840	−	0.685112i	−0.377601	−	0.0396875i
$299$	−11.1224	−	2.36415i	−0.643228	−	0.136722i
$300$	−3.88957	+	3.14186i	−0.224564	+	0.181395i
$301$	−13.9426	−	15.4848i	−0.803637	−	0.892530i
$302$	6.89263	+	2.23955i	0.396627	+	0.128872i
$303$	−11.3029	−	10.1771i	−0.649332	−	0.584661i
$304$	−0.0720689	−	0.124827i	−0.00413344	−	0.00715932i
$305$	24.9691	−	10.3247i	1.42973	−	0.591190i
$306$	0.0542462	+	0.166953i	0.00310105	+	0.00954404i
$307$	0.263545	−	0.591932i	0.0150413	−	0.0337834i	−0.905869	−	0.423559i	$-0.860781\pi$
$307$	0.263545	−	0.591932i	0.0150413	−	0.0337834i	0.920910	+	0.389775i	$0.127447\pi$
$308$	6.60002	−	9.08415i	0.376071	−	0.517617i
$309$	2.26986			0.129128
$310$	−9.53677	+	8.00313i	−0.541652	+	0.454547i
$311$	18.5407			1.05135			0.525674	−	0.850686i	$-0.323813\pi$
$311$	18.5407			1.05135			0.525674	+	0.850686i	$0.323813\pi$
$312$	1.94309	−	2.67443i	0.110006	−	0.151410i
$313$	−7.78626	+	17.4882i	−0.440106	+	0.988494i	0.548248	+	0.836316i	$0.315295\pi$
$313$	−7.78626	+	17.4882i	−0.440106	+	0.988494i	−0.988353	+	0.152177i	$0.951371\pi$
$314$	−5.29887	−	16.3082i	−0.299033	−	0.920328i
$315$	1.66133	+	4.01774i	0.0936053	+	0.226374i
$316$	−0.435756	−	0.754752i	−0.0245132	−	0.0424581i
$317$	−3.76044	−	3.38591i	−0.211207	−	0.190172i	0.556737	−	0.830689i	$-0.312053\pi$
$317$	−3.76044	−	3.38591i	−0.211207	−	0.190172i	−0.767944	+	0.640517i	$0.778720\pi$
$318$	−3.68934	−	1.19874i	−0.206888	−	0.0672219i
$319$	14.5531	+	16.1629i	0.814818	+	0.904947i
$320$	2.17397	+	0.523327i	0.121528	+	0.0292549i
$321$	1.23714	+	0.262963i	0.0690506	+	0.0146772i
$322$	−6.65133	−	0.699083i	−0.370664	−	0.0389584i
$323$	0.0251640	−	0.00264484i	0.00140016	−	0.000147163i
$324$	0.978148	−	0.207912i	0.0543415	−	0.0115506i
$325$	−10.4176	+	12.8326i	−0.577866	+	0.711827i
$326$	5.95475	−	4.32638i	0.329803	−	0.239616i
$327$	3.90598	+	18.3762i	0.216001	+	1.01621i
$328$	−11.9083	+	1.25161i	−0.657524	+	0.0691085i
$329$	1.29500	−	12.3211i	0.0713955	−	0.679283i
$330$	8.38057	+	9.82453i	0.461335	+	0.540823i
$331$	−1.98110	+	0.882040i	−0.108891	+	0.0484813i	−0.460459	−	0.887681i	$-0.652315\pi$
$331$	−1.98110	+	0.882040i	−0.108891	+	0.0484813i	0.351568	+	0.936162i	$0.385649\pi$
$332$	−4.72701	+	4.25622i	−0.259429	+	0.233590i
$333$	−6.13883	−	1.99463i	−0.336406	−	0.109305i
$334$	0.392826	−	0.436278i	0.0214945	−	0.0238721i
$335$	−7.33815	−	0.970644i	−0.400926	−	0.0530319i
$336$	0.972168	−	1.68385i	0.0530361	−	0.0918613i
$337$	15.0591	−	4.89301i	0.820323	−	0.266539i	0.131359	−	0.991335i	$-0.458066\pi$
$337$	15.0591	−	4.89301i	0.820323	−	0.266539i	0.688964	+	0.724796i	$0.258066\pi$
$338$	−0.842698	+	1.89273i	−0.0458367	+	0.102951i
$339$	−10.3830	−	7.54372i	−0.563930	−	0.409719i
$340$	−0.239147	+	0.311268i	−0.0129695	+	0.0168809i
$341$	21.3219	+	24.0679i	1.15464	+	1.30335i
$342$		−	0.144138i		−	0.00779408i
$343$	−11.6794	+	16.0754i	−0.630631	+	0.867989i
$344$	−9.79019	−	4.35887i	−0.527852	−	0.235015i
$345$	2.57188	−	7.24870i	0.138465	−	0.390257i
$346$	8.81302	−	15.2646i	0.473791	−	0.820630i
$347$	13.4728	−	7.77852i	0.723257	−	0.417573i	−0.0926931	−	0.995695i	$-0.529548\pi$
$347$	13.4728	−	7.77852i	0.723257	−	0.417573i	0.815950	+	0.578122i	$0.196214\pi$
$348$	2.79875	+	2.52000i	0.150028	+	0.135086i
$349$	9.34704	−	28.7672i	0.500335	−	1.53987i	−0.308138	−	0.951342i	$-0.599706\pi$
$349$	9.34704	−	28.7672i	0.500335	−	1.53987i	0.808474	−	0.588533i	$-0.200294\pi$
$350$	−5.30476	+	8.14682i	−0.283551	+	0.435466i
$351$	3.01998	−	1.34458i	0.161194	−	0.0717684i
$352$	1.20070	−	5.64884i	0.0639974	−	0.301084i
$353$	−2.24328	−	0.235778i	−0.119398	−	0.0125492i	0.0446412	−	0.999003i	$-0.485786\pi$
$353$	−2.24328	−	0.235778i	−0.119398	−	0.0125492i	−0.164039	+	0.986454i	$0.552452\pi$
$354$	1.35053	+	12.8495i	0.0717801	+	0.682942i
$355$	−19.4952	−	9.31334i	−1.03470	−	0.494301i
$356$	6.60330	−	4.79758i	0.349974	−	0.254271i
$357$	0.200621	+	0.276131i	0.0106180	+	0.0146144i
$358$	2.31159	+	10.8752i	0.122171	+	0.574770i
$359$	1.04923	+	9.98273i	0.0553761	+	0.526868i	0.986686	+	0.162639i	$0.0520007\pi$
$359$	1.04923	+	9.98273i	0.0553761	+	0.526868i	−0.931309	+	0.364229i	$0.881333\pi$
$360$	1.62105	+	1.54020i	0.0854367	+	0.0811755i
$361$	18.5645	+	3.94600i	0.977078	+	0.207684i
$362$	3.05746	+	6.86716i	0.160696	+	0.360930i
$363$	16.6101	−	14.9558i	0.871804	−	0.784976i
$364$	1.98622	−	6.11295i	0.104106	−	0.320406i
$365$	5.48950	+	29.7200i	0.287334	+	1.55561i
$366$	−6.04175	−	10.4646i	−0.315807	−	0.546994i
$367$	6.33470	+	3.65734i	0.330669	+	0.190912i	0.656138	−	0.754641i	$-0.272189\pi$
$367$	6.33470	+	3.65734i	0.330669	+	0.190912i	−0.325469	+	0.945553i	$0.605522\pi$
$368$	−3.27136	+	1.06293i	−0.170532	+	0.0554091i
$369$	−10.9387	−	4.87021i	−0.569444	−	0.253533i
$370$	−4.09082	−	13.8414i	−0.212672	−	0.719580i
$371$	−7.54247			−0.391585
$372$	4.10747	+	3.75881i	0.212963	+	0.194885i
$373$			24.7965i			1.28391i	0.766741	+	0.641956i	$0.221877\pi$
$373$			24.7965i			1.28391i	−0.766741	+	0.641956i	$0.778123\pi$
$374$	0.820161	+	0.595882i	0.0424095	+	0.0308123i
$375$	−7.68117	−	8.12401i	−0.396654	−	0.419522i
$376$	−1.96900	−	6.05995i	−0.101543	−	0.312518i
$377$	10.7819	+	6.22491i	0.555294	+	0.320599i
$378$	1.68385	−	0.972168i	0.0866076	−	0.0500029i
$379$	−6.76918	+	7.51794i	−0.347709	+	0.386171i	−0.891477	−	0.453065i	$-0.850331\pi$
$379$	−6.76918	+	7.51794i	−0.347709	+	0.386171i	0.543768	+	0.839236i	$0.316997\pi$
$380$	0.265729	−	0.182392i	0.0136316	−	0.00935650i
$381$	8.70476	+	9.66762i	0.445959	+	0.495287i
$382$	−2.82851	−	6.35294i	−0.144719	−	0.325045i
$383$	−0.359268	+	1.69022i	−0.0183577	+	0.0863664i	−0.986373	−	0.164526i	$-0.947391\pi$
$383$	−0.359268	+	1.69022i	−0.0183577	+	0.0863664i	0.968015	+	0.250892i	$0.0807240\pi$
$384$	0.104528	−	0.994522i	0.00533420	−	0.0507515i
$385$	21.4000	+	13.1319i	1.09065	+	0.669266i
$386$	13.3118	−	2.82951i	0.677554	−	0.144018i
$387$	−6.29912	−	8.66999i	−0.320202	−	0.440720i
$388$	7.31835	+	10.0728i	0.371533	+	0.511371i
$389$	−22.5482	+	4.79277i	−1.14324	+	0.243003i	−0.740334	−	0.672239i	$-0.765333\pi$
$389$	−22.5482	+	4.79277i	−1.14324	+	0.243003i	−0.402905	+	0.915242i	$0.631999\pi$
$390$	6.30030	+	3.86612i	0.319028	+	0.195769i
$391$	0.0631166	−	0.600514i	0.00319194	−	0.0303693i
$392$	−0.669383	+	3.14920i	−0.0338089	+	0.159059i
$393$	−4.29992	−	9.65778i	−0.216902	−	0.487170i
$394$	5.36838	+	5.96219i	0.270455	+	0.300371i
$395$	1.60670	−	1.10281i	0.0808418	−	0.0554884i
$396$	3.86426	−	4.29169i	0.194186	−	0.215666i
$397$	−29.1497	+	16.8296i	−1.46298	+	0.844653i	−0.999148	−	0.0412688i	$-0.986860\pi$
$397$	−29.1497	+	16.8296i	−1.46298	+	0.844653i	−0.463834	+	0.885922i	$0.653527\pi$
$398$	−14.1545	−	8.17213i	−0.709503	−	0.409632i
$399$	−0.0866028	−	0.266536i	−0.00433556	−	0.0133435i
$400$	−0.788201	+	4.93748i	−0.0394101	+	0.246874i
$401$	−22.2440	−	16.1612i	−1.11081	−	0.807054i	−0.128023	−	0.991771i	$-0.540863\pi$
$401$	−22.2440	−	16.1612i	−1.11081	−	0.807054i	−0.982792	+	0.184717i	$0.940863\pi$
$402$			3.31031i			0.165103i
$403$	15.8651	+	9.33114i	0.790299	+	0.464817i
$404$	−15.2095			−0.756701
$405$	0.633769	+	2.14437i	0.0314922	+	0.106555i
$406$	6.68947	+	2.97834i	0.331993	+	0.147813i
$407$	−35.4520	+	11.5191i	−1.75729	+	0.570978i
$408$	0.152026	+	0.0877721i	0.00752640	+	0.00434537i
$409$	10.0610	+	17.4262i	0.497485	+	0.861669i	0.999996	−	0.00290176i	$-0.000923660\pi$
$409$	10.0610	+	17.4262i	0.497485	+	0.861669i	−0.502511	+	0.864571i	$0.667590\pi$
$410$	−4.86317	−	26.3290i	−0.240175	−	1.30030i
$411$	4.56756	−	14.0575i	0.225301	−	0.693406i
$412$	1.68683	−	1.51883i	0.0831043	−	0.0748275i
$413$	10.2178	+	22.9495i	0.502783	+	1.12927i
$414$	−3.36455	−	0.715157i	−0.165359	−	0.0351481i
$415$	−10.3112	−	9.79692i	−0.506156	−	0.480912i
$416$	−0.345548	−	3.28767i	−0.0169419	−	0.161191i
$417$	0.0911308	+	0.428737i	0.00446270	+	0.0209953i
$418$	−0.489274	−	0.673427i	−0.0239312	−	0.0329384i
$419$	16.5918	−	12.0546i	0.810562	−	0.588908i	−0.103431	−	0.994637i	$-0.532982\pi$
$419$	16.5918	−	12.0546i	0.810562	−	0.588908i	0.913994	+	0.405729i	$0.132982\pi$
$420$	3.92300	+	1.87412i	0.191423	+	0.0914474i
$421$	−2.20130	−	20.9439i	−0.107285	−	1.02075i	−0.907219	−	0.420658i	$-0.861799\pi$
$421$	−2.20130	−	20.9439i	−0.107285	−	1.02075i	0.799935	−	0.600087i	$-0.204867\pi$
$422$	21.6243	+	2.27281i	1.05266	+	0.110639i
$423$	1.32477	−	6.23257i	0.0644127	−	0.303038i
$424$	−3.54382	+	1.57781i	−0.172103	+	0.0766253i
$425$	−0.735535	−	0.478940i	−0.0356787	−	0.0232320i
$426$	−2.98582	+	9.18940i	−0.144663	+	0.445228i
$427$	−17.4597	−	15.7208i	−0.844936	−	0.760784i
$428$	1.09533	−	0.632391i	0.0529449	−	0.0305678i
$429$	9.54549	−	16.5333i	0.460861	−	0.798234i
$430$	8.01289	−	22.5839i	0.386416	−	1.08909i
$431$	21.5123	+	9.57788i	1.03621	+	0.461350i	0.853103	−	0.521743i	$-0.174718\pi$
$431$	21.5123	+	9.57788i	1.03621	+	0.461350i	0.183107	+	0.983093i	$0.441385\pi$
$432$	0.587785	−	0.809017i	0.0282798	−	0.0389238i
$433$		−	23.7804i		−	1.14281i	−0.820668	−	0.571406i	$-0.806398\pi$
$433$		−	23.7804i		−	1.14281i	0.820668	−	0.571406i	$-0.193602\pi$
$434$	9.85385	+	4.48279i	0.473000	+	0.215181i
$435$	−5.13059	+	6.67787i	−0.245993	+	0.320179i
$436$	15.1988	+	11.0426i	0.727890	+	0.528843i
$437$	−0.201657	+	0.452930i	−0.00964658	+	0.0216666i
$438$	12.8545	−	4.17667i	0.614211	−	0.199569i
$439$	−0.984088	+	1.70449i	−0.0469680	+	0.0813509i	−0.888554	−	0.458773i	$-0.848289\pi$
$439$	−0.984088	+	1.70449i	−0.0469680	+	0.0813509i	0.841586	+	0.540124i	$0.181623\pi$
$440$	12.8019	+	1.69335i	0.610305	+	0.0807273i
$441$	−2.15430	+	2.39260i	−0.102586	+	0.113933i
$442$	0.551907	+	0.179326i	0.0262516	+	0.00852965i
$443$	11.1308	−	10.0222i	0.528839	−	0.476169i	−0.360922	−	0.932596i	$-0.617538\pi$
$443$	11.1308	−	10.0222i	0.528839	−	0.476169i	0.889761	+	0.456427i	$0.150871\pi$
$444$	−5.89671	+	2.62538i	−0.279845	+	0.124595i
$445$	11.8447	+	13.8855i	0.561490	+	0.658234i
$446$	1.43681	−	13.6703i	0.0680350	−	0.647309i
$447$	−6.51840	+	0.685112i	−0.308310	+	0.0324047i
$448$	−0.404250	−	1.90185i	−0.0190990	−	0.0898539i
$449$	−15.1555	+	11.0111i	−0.715231	+	0.519646i	−0.884857	−	0.465863i	$-0.845744\pi$
$449$	−15.1555	+	11.0111i	−0.715231	+	0.519646i	0.169626	+	0.985509i	$0.445744\pi$
$450$	−3.15134	+	3.88189i	−0.148556	+	0.182994i
$451$	−67.6384	+	14.3770i	−3.18497	+	0.676986i
$452$	−12.7638	+	1.34153i	−0.600361	+	0.0631005i
$453$	7.20764	+	0.757554i	0.338645	+	0.0355930i
$454$	−23.9665	−	5.09425i	−1.12481	−	0.239085i
$455$	13.9733	+	3.36370i	0.655076	+	0.157693i
$456$	−0.0964471	−	0.107115i	−0.00451655	−	0.00501613i
$457$	21.7190	+	7.05695i	1.01597	+	0.330110i	0.769231	−	0.638971i	$-0.220640\pi$
$457$	21.7190	+	7.05695i	1.01597	+	0.330110i	0.246743	+	0.969081i	$0.420640\pi$
$458$	15.1983	+	13.6846i	0.710168	+	0.639438i
$459$	0.0877721	+	0.152026i	0.00409685	+	0.00709596i
$460$	−2.93905	−	7.10776i	−0.137034	−	0.331401i
$461$	7.32911	+	22.5567i	0.341351	+	1.05057i	0.963508	+	0.267678i	$0.0862563\pi$
$461$	7.32911	+	22.5567i	0.341351	+	1.05057i	−0.622158	+	0.782892i	$0.713744\pi$
$462$	4.56709	−	10.2579i	0.212480	−	0.477239i
$463$	−10.4931	+	14.4424i	−0.487653	+	0.671197i	−0.979953	−	0.199228i	$-0.936156\pi$
$463$	−10.4931	+	14.4424i	−0.487653	+	0.671197i	0.492300	+	0.870426i	$0.336156\pi$
$464$	3.76608			0.174836
$465$	−7.66442	+	9.81105i	−0.355429	+	0.454976i
$466$	−14.1002			−0.653180
$467$	0.342044	−	0.470783i	0.0158279	−	0.0217852i	−0.801030	−	0.598625i	$-0.795714\pi$
$467$	0.342044	−	0.470783i	0.0158279	−	0.0217852i	0.816858	+	0.576839i	$0.195714\pi$
$468$	1.34458	−	3.01998i	0.0621532	−	0.139598i
$469$	1.98894	+	6.12133i	0.0918408	+	0.282657i
$470$	13.1666	−	5.44436i	0.607329	−	0.251130i
$471$	−8.57375	−	14.8502i	−0.395058	−	0.684260i
$472$	9.60162	+	8.64534i	0.441950	+	0.397934i
$473$	−58.8603	−	19.1249i	−2.70640	−	0.879362i
$474$	−0.583156	−	0.647660i	−0.0267852	−	0.0297480i
$475$	0.452860	+	0.560634i	0.0207787	+	0.0257237i
$476$	0.333859	+	0.0709638i	0.0153024	+	0.00325262i
$477$	−3.85795	−	0.405487i	−0.176643	−	0.0185660i
$478$	7.27368	−	0.764495i	0.332690	−	0.0349672i
$479$	13.6379	−	2.89882i	0.623130	−	0.132450i	0.114482	−	0.993425i	$-0.463479\pi$
$479$	13.6379	−	2.89882i	0.623130	−	0.132450i	0.508647	+	0.860975i	$0.330146\pi$
$480$	2.23527	+	0.0598980i	0.102025	+	0.00273396i
$481$	−17.2628	+	12.5421i	−0.787115	+	0.571872i
$482$	−3.12442	−	14.6993i	−0.142314	−	0.669533i
$483$	−6.65133	+	0.699083i	−0.302646	+	0.0318094i
$484$	2.33632	−	22.2286i	0.106197	−	1.01039i
$485$	−21.1812	+	18.0681i	−0.961790	+	0.820431i
$486$	0.913545	−	0.406737i	0.0414393	−	0.0184499i
$487$	−19.6211	+	17.6669i	−0.889115	+	0.800563i	−0.980758	−	0.195229i	$-0.937455\pi$
$487$	−19.6211	+	17.6669i	−0.889115	+	0.800563i	0.0916428	+	0.995792i	$0.470788\pi$
$488$	−11.4921	−	3.73401i	−0.520223	−	0.169031i
$489$	4.92512	−	5.46990i	0.222721	−	0.247357i
$490$	−7.13698	−	0.944034i	−0.322416	−	0.0426471i
$491$	9.08073	−	15.7283i	0.409808	−	0.709808i	−0.585060	−	0.810990i	$-0.698929\pi$
$491$	9.08073	−	15.7283i	0.409808	−	0.709808i	0.994868	+	0.101182i	$0.0322624\pi$
$492$	−11.3878	+	3.70012i	−0.513402	+	0.166815i
$493$	−0.268899	+	0.603958i	−0.0121106	+	0.0272009i
$494$	−0.385486	−	0.280072i	−0.0173439	−	0.0126010i
$495$	10.2401	+	7.86742i	0.460257	+	0.353614i
$496$	5.56758	+	0.0449032i	0.249992	+	0.00201621i
$497$			18.7868i			0.842702i
$498$	−3.73880	+	5.14601i	−0.167540	+	0.230598i
$499$	−14.4273	−	6.42344i	−0.645853	−	0.287552i	0.0575507	−	0.998343i	$-0.481671\pi$
$499$	−14.4273	−	6.42344i	−0.645853	−	0.287552i	−0.703404	+	0.710790i	$0.748338\pi$
$500$	−11.1442	−	0.897610i	−0.498386	−	0.0401424i
$501$	0.293535	−	0.508417i	0.0131142	−	0.0227144i
$502$	1.58790	−	0.916777i	0.0708716	−	0.0409178i
$503$	−12.1269	−	10.9191i	−0.540713	−	0.486861i	0.352923	−	0.935652i	$-0.385188\pi$
$503$	−12.1269	−	10.9191i	−0.540713	−	0.486861i	−0.893636	+	0.448792i	$0.851854\pi$
$504$	0.600833	−	1.84917i	0.0267632	−	0.0823688i
$505$	−2.64765	−	33.9063i	−0.117819	−	1.50881i
$506$	−18.1471	+	8.07962i	−0.806738	+	0.359183i
$507$	−0.430762	+	2.02658i	−0.0191308	+	0.0900034i
$508$	12.9378	+	1.35982i	0.574022	+	0.0603321i
$509$	0.739161	+	7.03265i	0.0327627	+	0.311717i	0.998615	+	0.0526215i	$0.0167577\pi$
$509$	0.739161	+	7.03265i	0.0327627	+	0.311717i	−0.965852	+	0.259095i	$0.916576\pi$
$510$	−0.169204	+	0.354188i	−0.00749249	+	0.0156837i
$511$	21.2607	−	15.4468i	0.940517	−	0.683326i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$	−0.0299679	−	0.140988i	−0.00132312	−	0.00622478i
$514$	2.53974	+	24.1640i	0.112023	+	1.06583i
$515$	3.67955	+	3.49603i	0.162140	+	0.154053i
$516$	−10.4825	−	2.22813i	−0.461467	−	0.0980878i
$517$	−14.9669	−	33.6162i	−0.658243	−	1.47844i
$518$	−9.32662	+	8.39773i	−0.409788	+	0.368975i
$519$	5.44675	−	16.7634i	0.239086	−	0.735830i
$520$	7.26898	−	1.34264i	0.318766	−	0.0588785i
$521$	−12.0303	−	20.8371i	−0.527056	−	0.912888i	−0.999503	−	0.0315289i	$-0.989962\pi$
$521$	−12.0303	−	20.8371i	−0.527056	−	0.912888i	0.472447	−	0.881359i	$-0.343371\pi$
$522$	3.26152	+	1.88304i	0.142753	+	0.0824185i
$523$	−0.709332	+	0.230476i	−0.0310169	+	0.0100780i	−0.324484	−	0.945891i	$-0.605191\pi$
$523$	−0.709332	+	0.230476i	−0.0310169	+	0.0100780i	0.293467	+	0.955969i	$0.405191\pi$
$524$	−9.65778	−	4.29992i	−0.421902	−	0.187843i
$525$	−3.49502	+	9.07171i	−0.152535	+	0.395922i
$526$	−21.3335			−0.930185
$527$	−0.404728	+	0.889654i	−0.0176302	+	0.0387539i
$528$		−	5.77504i		−	0.251326i
$529$	−9.03539	−	6.56460i	−0.392843	−	0.285417i
$530$	−4.13429	−	7.62552i	−0.179582	−	0.331231i
$531$	3.99258	+	12.2879i	0.173263	+	0.533249i
$532$	−0.242706	−	0.140126i	−0.0105226	−	0.00607524i
$533$	−34.2798	+	19.7914i	−1.48482	+	0.857262i
$534$	5.46153	−	6.06565i	0.236344	−	0.262486i
$535$	1.60045	+	2.33172i	0.0691936	+	0.100809i
$536$	2.21503	+	2.46004i	0.0956746	+	0.106257i
$537$	4.52215	+	10.1569i	0.195145	+	0.438303i
$538$	−1.45503	+	6.84537i	−0.0627307	+	0.295125i
$539$	−1.94350	+	18.4912i	−0.0837126	+	0.796472i
$540$	1.90585	+	1.16951i	0.0820146	+	0.0503275i
$541$	30.7246	−	6.53071i	1.32095	−	0.280777i	0.507119	−	0.861876i	$-0.330710\pi$
$541$	30.7246	−	6.53071i	1.32095	−	0.280777i	0.813833	+	0.581099i	$0.197377\pi$
$542$	7.01628	+	9.65709i	0.301375	+	0.414807i
$543$	4.41841	+	6.08141i	0.189612	+	0.260978i
$544$	0.171708	−	0.0364977i	0.00736193	−	0.00156483i
$545$	−21.9712	+	35.8046i	−0.941142	+	1.53370i
$546$	0.671861	−	6.39233i	0.0287530	−	0.273566i
$547$	0.858769	−	4.04019i	0.0367183	−	0.172746i	−0.955967	−	0.293473i	$-0.905189\pi$
$547$	0.858769	−	4.04019i	0.0367183	−	0.172746i	0.992686	+	0.120726i	$0.0385224\pi$
$548$	−6.01195	−	13.5031i	−0.256818	−	0.576822i
$549$	−8.08544	−	8.97979i	−0.345078	−	0.383248i
$550$	−1.54642	+	28.8338i	−0.0659394	+	1.22948i
$551$	0.363228	−	0.403405i	0.0154740	−	0.0171856i
$552$	−2.97888	+	1.71986i	−0.126790	+	0.0732020i
$553$	−1.46749	−	0.847257i	−0.0624041	−	0.0360290i
$554$	0.927427	+	2.85433i	0.0394026	+	0.121269i
$555$	−6.87921	−	12.6884i	−0.292006	−	0.538593i
$556$	0.354604	+	0.257635i	0.0150386	+	0.0109262i
$557$			40.2089i			1.70370i	0.523782	+	0.851852i	$0.324521\pi$
$557$			40.2089i			1.70370i	−0.523782	+	0.851852i	$0.675479\pi$
$558$	4.79922	+	2.82268i	0.203167	+	0.119494i
$559$	−35.4270			−1.49840
$560$	4.16938	−	1.23226i	0.176189	−	0.0520725i
$561$	0.926130	+	0.412339i	0.0391012	+	0.0174090i
$562$	11.8913	−	3.86370i	0.501602	−	0.162980i
$563$	−27.8312	−	16.0683i	−1.17294	−	0.677200i	−0.218572	−	0.975821i	$-0.570140\pi$
$563$	−27.8312	−	16.0683i	−1.17294	−	0.677200i	−0.954372	+	0.298621i	$0.903473\pi$
$564$	−3.18591	−	5.51815i	−0.134151	−	0.232356i
$565$	−5.21257	−	28.2207i	−0.219295	−	1.18725i
$566$	−4.77644	+	14.7004i	−0.200769	+	0.617903i
$567$	1.44492	−	1.30102i	0.0606811	−	0.0546375i
$568$	3.93001	+	8.82695i	0.164900	+	0.370371i
$569$	12.2656	+	2.60714i	0.514201	+	0.109297i	0.457702	−	0.889106i	$-0.348673\pi$
$569$	12.2656	+	2.60714i	0.514201	+	0.109297i	0.0564995	+	0.998403i	$0.482006\pi$
$570$	0.222001	−	0.233654i	0.00929859	−	0.00978670i
$571$	−3.85647	−	36.6919i	−0.161388	−	1.53551i	−0.712856	−	0.701310i	$-0.752599\pi$
$571$	−3.85647	−	36.6919i	−0.161388	−	1.53551i	0.551468	−	0.834196i	$-0.314068\pi$
$572$	−3.96924	−	18.6738i	−0.165962	−	0.780791i
$573$	−4.08755	−	5.62603i	−0.170760	−	0.235031i
$574$	−18.8349	+	13.6844i	−0.786153	+	0.571174i
$575$	15.3336	−	7.78928i	0.639454	−	0.324835i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	38.6529	+	4.06259i	1.60914	+	0.169128i	0.866014	−	0.500020i	$-0.166674\pi$
$577$	38.6529	+	4.06259i	1.60914	+	0.169128i	0.743129	+	0.669148i	$0.233341\pi$
$578$	3.52809	−	16.5984i	0.146749	−	0.690401i
$579$	12.4326	−	5.53536i	0.516683	−	0.230042i
$580$	0.655596	+	8.39566i	0.0272221	+	0.348611i
$581$	−3.82179	+	11.7623i	−0.158555	+	0.487981i
$582$	9.25268	+	8.33115i	0.383536	+	0.345337i
$583$	−19.4012	+	11.2013i	−0.803514	+	0.463909i
$584$	6.75800	−	11.7052i	0.279648	−	0.484364i
$585$	6.96644	+	2.47173i	0.288027	+	0.102194i
$586$	11.4852	+	5.11355i	0.474450	+	0.211239i
$587$	−13.0913	+	18.0187i	−0.540337	+	0.743711i	−0.988662	−	0.150160i	$-0.952021\pi$
$587$	−13.0913	+	18.0187i	−0.540337	+	0.743711i	0.448324	+	0.893871i	$0.352021\pi$
$588$			3.21955i			0.132772i
$589$	0.541787	−	0.592043i	0.0223239	−	0.0243947i
$590$	−17.6015	+	22.9097i	−0.724640	+	0.943177i
$591$	6.49068	+	4.71575i	0.266991	+	0.193980i
$592$	−2.62538	+	5.89671i	−0.107903	+	0.242353i
$593$	19.1266	−	6.21462i	0.785437	−	0.255204i	0.111277	−	0.993789i	$-0.464506\pi$
$593$	19.1266	−	6.21462i	0.785437	−	0.255204i	0.674160	+	0.738586i	$0.264506\pi$
$594$	2.88752	−	5.00133i	0.118476	−	0.205207i
$595$	−0.100081	+	0.756618i	−0.00410290	+	0.0310183i
$596$	−4.38569	+	4.87080i	−0.179645	+	0.199516i
$597$	−15.5443	−	5.05065i	−0.636186	−	0.206709i
$598$	−8.45024	+	7.60863i	−0.345556	+	0.311140i
$599$	−14.6733	+	6.53295i	−0.599533	+	0.266929i	−0.683982	−	0.729499i	$-0.739753\pi$
$599$	−14.6733	+	6.53295i	−0.599533	+	0.266929i	0.0844496	+	0.996428i	$0.473087\pi$
$600$	0.255583	+	4.99346i	0.0104341	+	0.203857i
$601$	−1.80468	+	17.1704i	−0.0736145	+	0.700395i	0.894018	+	0.448031i	$0.147875\pi$
$601$	−1.80468	+	17.1704i	−0.0736145	+	0.700395i	−0.967632	+	0.252364i	$0.918792\pi$
$602$	−20.7227	+	2.17805i	−0.844595	+	0.0887705i
$603$	0.688251	+	3.23797i	0.0280278	+	0.131860i
$604$	5.86323	−	4.25988i	0.238571	−	0.173332i
$605$	49.9606	+	1.33879i	2.03119	+	0.0544294i
$606$	−14.8771	+	3.16223i	−0.604342	+	0.128457i
$607$	25.1110	−	2.63927i	1.01923	−	0.107125i	0.419850	−	0.907593i	$-0.362083\pi$
$607$	25.1110	−	2.63927i	1.01923	−	0.107125i	0.599375	+	0.800469i	$0.295416\pi$
$608$	−0.143348	−	0.0150665i	−0.00581354	−	0.000611028i
$609$	7.16252	+	1.52244i	0.290240	+	0.0616924i
$610$	6.32362	−	26.2691i	0.256036	−	1.06361i
$611$	−14.0944	−	15.6534i	−0.570199	−	0.633270i
$612$	0.166953	+	0.0542462i	0.00674866	+	0.00219277i
$613$	−10.8172	−	9.73983i	−0.436902	−	0.393388i	0.421117	−	0.907006i	$-0.361638\pi$
$613$	−10.8172	−	9.73983i	−0.436902	−	0.393388i	−0.858019	+	0.513618i	$0.828305\pi$
$614$	−0.323975	−	0.561142i	−0.0130746	−	0.0226458i
$615$	−10.2310	−	24.7425i	−0.412554	−	0.997715i
$616$	−3.46984	−	10.6791i	−0.139804	−	0.430271i
$617$	−0.247973	+	0.556956i	−0.00998300	+	0.0224222i	−0.918468	−	0.395495i	$-0.870573\pi$
$617$	−0.247973	+	0.556956i	−0.00998300	+	0.0224222i	0.908485	+	0.417917i	$0.137240\pi$
$618$	1.33419	−	1.83635i	0.0536690	−	0.0738690i
$619$	7.41722			0.298123			0.149062	−	0.988828i	$-0.452375\pi$
$619$	7.41722			0.298123			0.149062	+	0.988828i	$0.452375\pi$
$620$	0.869098	+	12.4195i	0.0349038	+	0.498780i
$621$	−3.43972			−0.138031
$622$	10.8980	−	14.9998i	0.436969	−	0.601436i
$623$	6.45488	−	14.4979i	0.258609	−	0.580846i
$624$	−1.02154	−	3.14398i	−0.0408944	−	0.125860i
$625$	0.0610462	−	24.9999i	0.00244185	−	0.999997i
$626$	9.57163	+	16.5785i	0.382559	+	0.662612i
$627$	−0.618595	−	0.556986i	−0.0247043	−	0.0222439i
$628$	−16.3082	−	5.29887i	−0.650770	−	0.211448i
$629$	−0.758188	−	0.842053i	−0.0302309	−	0.0335749i
$630$	4.22692	+	1.01752i	0.168405	+	0.0405391i
$631$	−10.5370	−	2.23971i	−0.419472	−	0.0891615i	−0.00666013	−	0.999978i	$-0.502120\pi$
$631$	−10.5370	−	2.23971i	−0.419472	−	0.0891615i	−0.412812	+	0.910816i	$0.635453\pi$
$632$	−0.866739	−	0.0910979i	−0.0344770	−	0.00362368i
$633$	21.6243	−	2.27281i	0.859490	−	0.0903361i
$634$	−4.94959	+	1.05207i	−0.196573	+	0.0417830i
$635$	−0.779217	+	29.0787i	−0.0309223	+	1.15395i
$636$	−3.13834	+	2.28014i	−0.124443	+	0.0904132i
$637$	2.21283	+	10.4105i	0.0876755	+	0.412481i
$638$	21.6301	−	2.27342i	0.856345	−	0.0900055i
$639$	−1.00999	+	9.60937i	−0.0399544	+	0.380141i
$640$	1.70121	−	1.45117i	0.0672461	−	0.0573626i
$641$	−28.8667	+	12.8523i	−1.14016	+	0.507634i	−0.887906	−	0.460026i	$-0.847840\pi$
$641$	−28.8667	+	12.8523i	−1.14016	+	0.507634i	−0.252259	+	0.967660i	$0.581174\pi$
$642$	0.939916	−	0.846304i	0.0370955	−	0.0334010i
$643$	7.83620	+	2.54614i	0.309030	+	0.100410i	0.459426	−	0.888216i	$-0.348055\pi$
$643$	7.83620	+	2.54614i	0.309030	+	0.100410i	−0.150397	+	0.988626i	$0.548055\pi$
$644$	−4.47512	+	4.97013i	−0.176345	+	0.195850i
$645$	3.14234	−	23.7563i	0.123729	−	0.935405i
$646$	0.0126513	−	0.0219127i	0.000497758	−	0.000862143i
$647$	−7.68834	+	2.49809i	−0.302260	+	0.0982102i	−0.456220	−	0.889867i	$-0.650797\pi$
$647$	−7.68834	+	2.49809i	−0.302260	+	0.0982102i	0.153961	+	0.988077i	$0.450797\pi$
$648$	0.406737	−	0.913545i	0.0159781	−	0.0358875i
$649$	60.3648	+	43.8576i	2.36953	+	1.72156i
$650$	4.25849	+	15.9709i	0.167032	+	0.626429i
$651$	10.5705	+	2.33610i	0.414292	+	0.0915588i
$652$		−	7.36047i		−	0.288258i
$653$	18.2913	−	25.1758i	0.715793	−	0.985204i	−0.283860	−	0.958866i	$-0.591615\pi$
$653$	18.2913	−	25.1758i	0.715793	−	0.985204i	0.999653	−	0.0263386i	$-0.00838481\pi$
$654$	17.1625	+	7.64125i	0.671108	+	0.298797i
$655$	7.90451	−	22.2784i	0.308855	−	0.870490i
$656$	−5.98693	+	10.3697i	−0.233750	+	0.404867i
$657$	11.7052	−	6.75800i	0.456663	−	0.263655i
$658$	−9.20678	−	8.28983i	−0.358918	−	0.323171i
$659$	8.87429	−	27.3122i	0.345693	−	1.06393i	−0.615519	−	0.788122i	$-0.711053\pi$
$659$	8.87429	−	27.3122i	0.345693	−	1.06393i	0.961212	−	0.275812i	$-0.0889466\pi$
$660$	12.8742	−	1.00531i	0.501127	−	0.0391318i
$661$	−16.6539	+	7.41481i	−0.647763	+	0.288403i	−0.704198	−	0.710004i	$-0.748693\pi$
$661$	−16.6539	+	7.41481i	−0.647763	+	0.288403i	0.0564350	+	0.998406i	$0.482027\pi$
$662$	−0.450873	+	2.12119i	−0.0175237	+	0.0824424i
$663$	0.577131	+	0.0606589i	0.0224139	+	0.00235580i
$664$	0.664887	+	6.32598i	0.0258026	+	0.245496i
$665$	0.270131	−	0.565453i	0.0104752	−	0.0219273i
$666$	−5.22200	+	3.79401i	−0.202349	+	0.147015i
$667$	−7.61432	−	10.4802i	−0.294828	−	0.405795i
$668$	−0.122059	−	0.574241i	−0.00472259	−	0.0222180i
$669$	−1.43681	−	13.6703i	−0.0555503	−	0.528526i
$670$	−5.09852	+	5.36616i	−0.196973	+	0.207313i
$671$	−68.2578	−	14.5086i	−2.63506	−	0.560100i
$672$	−0.790833	−	1.77624i	−0.0305070	−	0.0685199i
$673$	31.3346	−	28.2138i	1.20786	−	1.08756i	0.214008	−	0.976832i	$-0.431348\pi$
$673$	31.3346	−	28.2138i	1.20786	−	1.08756i	0.993851	−	0.110729i	$-0.0353186\pi$
$674$	4.89301	−	15.0591i	0.188472	−	0.580056i
$675$	−2.27539	+	4.45226i	−0.0875798	+	0.171367i
$676$	1.03593	+	1.79428i	0.0398433	+	0.0690106i
$677$	−13.9210	−	8.03730i	−0.535028	−	0.308898i	0.208034	−	0.978122i	$-0.433294\pi$
$677$	−13.9210	−	8.03730i	−0.535028	−	0.308898i	−0.743061	+	0.669223i	$0.766627\pi$
$678$	−12.2060	+	3.96597i	−0.468769	+	0.152312i
$679$	22.1155	+	9.84644i	0.848713	+	0.377872i
$680$	0.111254	+	0.376432i	0.00426641	+	0.0144355i
$681$	−24.5020			−0.938917
$682$	32.0040	−	3.10301i	1.22550	−	0.118820i
$683$		−	9.32698i		−	0.356887i	−0.983950	−	0.178444i	$-0.942894\pi$
$683$		−	9.32698i		−	0.356887i	0.983950	−	0.178444i	$-0.0571062\pi$
$684$	−0.116610	−	0.0847221i	−0.00445869	−	0.00323943i
$685$	29.0556	−	15.7529i	1.11016	−	0.601888i
$686$	6.14025	+	18.8977i	0.234436	+	0.721519i
$687$	17.7113	+	10.2256i	0.675729	+	0.390132i
$688$	−9.28093	+	5.35835i	−0.353832	+	0.204285i
$689$	−8.58077	+	9.52991i	−0.326901	+	0.363061i
$690$	−4.35261	−	6.34137i	−0.165701	−	0.241412i
$691$	−20.7882	−	23.0876i	−0.790820	−	0.878295i	0.204101	−	0.978950i	$-0.434573\pi$
$691$	−20.7882	−	23.0876i	−0.790820	−	0.878295i	−0.994921	+	0.100655i	$0.967906\pi$
$692$	−7.16916	−	16.1022i	−0.272530	−	0.612113i
$693$	2.33456	−	10.9832i	0.0886827	−	0.417219i
$694$	1.62615	−	15.4718i	0.0617279	−	0.587302i
$695$	−0.512612	+	0.835362i	−0.0194445	+	0.0316871i
$696$	3.68379	−	0.783013i	0.139634	−	0.0296800i
$697$	−1.23549	−	1.70051i	−0.0467975	−	0.0644113i
$698$	−17.7791	−	24.4709i	−0.672950	−	0.926236i
$699$	−13.7921	+	2.93160i	−0.521665	+	0.110883i
$700$	3.47286	+	9.08022i	0.131262	+	0.343200i
$701$	0.468628	−	4.45870i	0.0176998	−	0.168403i	−0.982101	−	0.188354i	$-0.939685\pi$
$701$	0.468628	−	4.45870i	0.0176998	−	0.168403i	0.999801	+	0.0199518i	$0.00635128\pi$
$702$	0.687309	−	3.23354i	0.0259408	−	0.122042i
$703$	0.378417	+	0.849939i	0.0142723	+	0.0320561i
$704$	−3.86426	−	4.29169i	−0.145640	−	0.161749i
$705$	11.7469	−	8.06288i	0.442414	−	0.303666i
$706$	−1.50931	+	1.67626i	−0.0568038	+	0.0630870i
$707$	−25.6104	+	14.7862i	−0.963180	+	0.556092i
$708$	11.1893	+	6.46013i	0.420518	+	0.242786i
$709$	1.45667	+	4.48316i	0.0547063	+	0.168369i	0.974676	−	0.223620i	$-0.0717874\pi$
$709$	1.45667	+	4.48316i	0.0547063	+	0.168369i	−0.919970	+	0.391988i	$0.871787\pi$
$710$	−18.9936	+	10.2977i	−0.712818	+	0.386466i
$711$	−0.705069	−	0.512262i	−0.0264421	−	0.0192113i
$712$		−	8.16213i		−	0.305889i
$713$	−11.1317	−	15.5842i	−0.416884	−	0.583633i
$714$	0.341317			0.0127735
$715$	40.9382	−	12.0993i	1.53100	−	0.452487i
$716$	10.1569	+	4.52215i	0.379581	+	0.169001i
$717$	6.95579	−	2.26007i	0.259769	−	0.0844039i
$718$	8.69292	+	5.01886i	0.324417	+	0.187302i
$719$	23.7687	+	41.1687i	0.886425	+	1.53533i	0.844072	+	0.536230i	$0.180152\pi$
$719$	23.7687	+	41.1687i	0.886425	+	1.53533i	0.0423528	+	0.999103i	$0.486515\pi$
$720$	2.19887	−	0.406149i	0.0819472	−	0.0151363i
$721$	1.36381	−	4.19736i	0.0507908	−	0.156318i
$722$	14.1043	−	12.6996i	0.524908	−	0.472629i
$723$	−6.11230	−	13.7284i	−0.227319	−	0.510566i
$724$	7.35278	+	1.56288i	0.273264	+	0.0580840i
$725$	−18.6022	+	2.92302i	−0.690867	+	0.108558i
$726$	−2.33632	−	22.2286i	−0.0867091	−	0.824982i
$727$	7.81567	+	36.7699i	0.289867	+	1.36372i	0.846247	+	0.532790i	$0.178857\pi$
$727$	7.81567	+	36.7699i	0.289867	+	1.36372i	−0.556380	+	0.830928i	$0.687810\pi$
$728$	−3.77801	−	5.19999i	−0.140022	−	0.192724i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	27.2706	+	13.0279i	1.00933	+	0.482182i
$731$	−0.196645	−	1.87095i	−0.00727317	−	0.0691996i
$732$	−12.0173	−	1.26307i	−0.444172	−	0.0466844i
$733$	−8.58415	+	40.3853i	−0.317063	+	1.49166i	0.474325	+	0.880350i	$0.342692\pi$
$733$	−8.58415	+	40.3853i	−0.317063	+	1.49166i	−0.791388	+	0.611314i	$0.790641\pi$
$734$	6.68230	−	2.97515i	0.246648	−	0.109815i
$735$	−7.17729	+	0.560457i	−0.264738	+	0.0206728i
$736$	−1.06293	+	3.27136i	−0.0391801	+	0.120584i
$737$	14.2068	+	12.7919i	0.523314	+	0.471194i
$738$	−10.3697	+	5.98693i	−0.381713	+	0.220382i
$739$	18.4191	−	31.9027i	0.677556	−	1.17356i	−0.298159	−	0.954516i	$-0.596373\pi$
$739$	18.4191	−	31.9027i	0.677556	−	1.17356i	0.975715	−	0.219045i	$-0.0702941\pi$
$740$	−13.6024	−	4.82623i	−0.500036	−	0.177416i
$741$	−0.435293	−	0.193805i	−0.0159909	−	0.00711960i
$742$	−4.43335	+	6.10198i	−0.162753	+	0.224011i
$743$			33.6073i			1.23293i	0.787381	+	0.616466i	$0.211436\pi$
$743$			33.6073i			1.23293i	−0.787381	+	0.616466i	$0.788564\pi$
$744$	5.45525	−	1.11364i	0.199999	−	0.0408282i
$745$	−11.6218	−	8.92903i	−0.425791	−	0.327134i
$746$	20.0608	+	14.5750i	0.734477	+	0.533628i
$747$	−2.58718	+	5.81090i	−0.0946599	+	0.212610i
$748$	0.964157	−	0.313274i	0.0352531	−	0.0114544i
$749$	1.22958	−	2.12970i	0.0449279	−	0.0778174i
$750$	−11.0873	+	1.43902i	−0.404853	+	0.0525457i
$751$	9.92756	−	11.0257i	0.362262	−	0.402332i	−0.534269	−	0.845315i	$-0.679413\pi$
$751$	9.92756	−	11.0257i	0.362262	−	0.402332i	0.896530	+	0.442982i	$0.146080\pi$
$752$	−6.05995	−	1.96900i	−0.220984	−	0.0718020i
$753$	1.36260	−	1.22689i	0.0496558	−	0.0447103i
$754$	11.3735	−	5.06380i	0.414198	−	0.184413i
$755$	10.5171	+	12.3292i	0.382758	+	0.448706i
$756$	0.203239	−	1.93369i	0.00739171	−	0.0703275i
$757$	−10.4354	+	1.09681i	−0.379283	+	0.0398642i	−0.292252	−	0.956341i	$-0.594405\pi$
$757$	−10.4354	+	1.09681i	−0.379283	+	0.0398642i	−0.0870309	+	0.996206i	$0.527738\pi$
$758$	2.10331	+	9.89532i	0.0763958	+	0.359414i
$759$	−16.0707	+	11.6761i	−0.583330	+	0.423814i
$760$	0.00863357	−	0.322186i	0.000313172	−	0.0116869i
$761$	−16.6468	+	3.53839i	−0.603446	+	0.128267i	−0.499496	−	0.866316i	$-0.666482\pi$
$761$	−16.6468	+	3.53839i	−0.603446	+	0.128267i	−0.103950	+	0.994583i	$0.533148\pi$
$762$	12.9378	−	1.35982i	0.468687	−	0.0492610i
$763$	36.3276	+	3.81819i	1.31515	+	0.138228i
$764$	−6.80219	−	1.44585i	−0.246095	−	0.0523090i
$765$	−0.0918670	+	0.381627i	−0.00332146	+	0.0137978i
$766$	1.15625	+	1.28414i	0.0417769	+	0.0463979i
$767$	40.6210	+	13.1986i	1.46674	+	0.476573i
$768$	−0.743145	−	0.669131i	−0.0268159	−	0.0241452i
$769$	−5.78942	−	10.0276i	−0.208772	−	0.361604i	0.742556	−	0.669784i	$-0.233613\pi$
$769$	−5.78942	−	10.0276i	−0.208772	−	0.361604i	−0.951328	+	0.308180i	$0.900280\pi$
$770$	23.2026	−	9.59424i	0.836163	−	0.345752i
$771$	7.50821	+	23.1079i	0.270402	+	0.832210i
$772$	5.53536	−	12.4326i	0.199222	−	0.447460i
$773$	11.9608	−	16.4627i	0.430201	−	0.592121i	−0.537798	−	0.843073i	$-0.680744\pi$
$773$	11.9608	−	16.4627i	0.430201	−	0.592121i	0.967999	+	0.250953i	$0.0807438\pi$
$774$	−10.7167			−0.385204
$775$	−27.5353	+	4.09944i	−0.989098	+	0.147256i
$776$	12.4507			0.446955
$777$	−7.37683	+	10.1533i	−0.264642	+	0.364249i
$778$	−9.37607	+	21.0590i	−0.336148	+	0.755001i
$779$	0.533328	+	1.64142i	0.0191085	+	0.0588098i
$780$	6.83099	−	2.82460i	0.244589	−	0.101137i
$781$	27.9001	+	48.3244i	0.998344	+	1.72918i
$782$	−0.448727	−	0.404036i	−0.0160465	−	0.0144483i
$783$	3.58176	+	1.16378i	0.128002	+	0.0415902i
$784$	2.15430	+	2.39260i	0.0769394	+	0.0854498i
$785$	8.97375	−	37.2781i	0.320287	−	1.33051i
$786$	−10.3407	−	2.19799i	−0.368842	−	0.0783997i
$787$	44.8913	+	4.71826i	1.60020	+	0.168188i	0.862184	−	0.506595i	$-0.169096\pi$
$787$	44.8913	+	4.71826i	1.60020	+	0.168188i	0.738016	+	0.674783i	$0.235763\pi$
$788$	7.97897	−	0.838623i	0.284239	−	0.0298747i
$789$	−20.8673	+	4.43548i	−0.742896	+	0.157907i
$790$	0.0522019	−	1.94806i	0.00185726	−	0.0693090i
$791$	−20.1881	+	14.6675i	−0.717808	+	0.521518i
$792$	−1.20070	−	5.64884i	−0.0426650	−	0.200723i
$793$	−39.7265	+	4.17543i	−1.41073	+	0.148274i
$794$	−3.51834	+	33.4748i	−0.124861	+	1.18798i
$795$	−5.62938	−	6.59931i	−0.199654	−	0.234054i
$796$	−14.9312	+	6.64781i	−0.529223	+	0.235625i
$797$	7.10308	−	6.39564i	0.251604	−	0.226545i	−0.533671	−	0.845692i	$-0.679188\pi$
$797$	7.10308	−	6.39564i	0.251604	−	0.226545i	0.785275	+	0.619147i	$0.212521\pi$
$798$	−0.266536	−	0.0866028i	−0.00943527	−	0.00306571i
$799$	0.748446	−	0.831234i	0.0264781	−	0.0294069i
$800$	3.53121	+	3.53985i	0.124847	+	0.125153i
$801$	4.08107	−	7.06861i	0.144197	−	0.249757i
$802$	−26.1494	+	8.49647i	−0.923369	+	0.300021i
$803$	31.7480	−	71.3072i	1.12036	−	2.51638i
$804$	2.67809	+	1.94575i	0.0944491	+	0.0686213i
$805$	−11.8588	−	9.11111i	−0.417969	−	0.321125i
$806$	16.8743	−	7.35045i	0.594373	−	0.258909i
$807$			6.99830i			0.246352i
$808$	−8.93992	+	12.3047i	−0.314505	+	0.432879i
$809$	−2.71364	−	1.20819i	−0.0954065	−	0.0424777i	0.358479	−	0.933538i	$-0.383296\pi$
$809$	−2.71364	−	1.20819i	−0.0954065	−	0.0424777i	−0.453885	+	0.891060i	$0.649962\pi$
$810$	2.10735	+	0.747701i	0.0740449	+	0.0262716i
$811$	−6.09689	+	10.5601i	−0.214091	+	0.370816i	−0.952991	−	0.302999i	$-0.902012\pi$
$811$	−6.09689	+	10.5601i	−0.214091	+	0.370816i	0.738900	+	0.673815i	$0.235346\pi$
$812$	6.34150	−	3.66127i	0.222543	−	0.128485i
$813$	8.87078	+	7.98729i	0.311112	+	0.280126i
$814$	−11.5191	+	35.4520i	−0.403743	+	1.24259i
$815$	16.4086	−	1.28130i	0.574767	−	0.0448821i
$816$	0.160368	−	0.0714003i	0.00561399	−	0.00249951i
$817$	−0.321157	+	1.51093i	−0.0112359	+	0.0528606i
$818$	20.0118	+	2.10332i	0.699696	+	0.0735410i
$819$	−0.671861	−	6.39233i	−0.0234767	−	0.223366i
$820$	−24.1591	−	11.5414i	−0.843672	−	0.403043i
$821$	25.5574	−	18.5685i	0.891959	−	0.648046i	−0.0444290	−	0.999013i	$-0.514147\pi$
$821$	25.5574	−	18.5685i	0.891959	−	0.648046i	0.936388	+	0.350966i	$0.114147\pi$
$822$	−8.68802	−	11.9580i	−0.303029	−	0.417084i
$823$	−6.02995	−	28.3687i	−0.210191	−	0.988870i	−0.949078	−	0.315041i	$-0.897982\pi$
$823$	−6.02995	−	28.3687i	−0.210191	−	0.988870i	0.738887	−	0.673829i	$-0.235352\pi$
$824$	−0.237265	−	2.25742i	−0.00826551	−	0.0786411i
$825$	4.48225	+	28.5252i	0.156052	+	0.993120i
$826$	24.5724	+	5.22302i	0.854982	+	0.181732i
$827$	−9.23323	−	20.7382i	−0.321071	−	0.721137i	0.678843	−	0.734284i	$-0.262482\pi$
$827$	−9.23323	−	20.7382i	−0.321071	−	0.721137i	−0.999914	+	0.0131466i	$0.995815\pi$
$828$	−2.55621	+	2.30162i	−0.0888343	+	0.0799868i
$829$	−0.723792	+	2.22760i	−0.0251383	+	0.0773678i	−0.962839	−	0.270077i	$-0.912951\pi$
$829$	−0.723792	+	2.22760i	−0.0251383	+	0.0773678i	0.937700	+	0.347445i	$0.112951\pi$
$830$	−13.9866	+	2.58344i	−0.485483	+	0.0896725i
$831$	1.50061	+	2.59913i	0.0520555	+	0.0901628i
$832$	−2.86289	−	1.65289i	−0.0992527	−	0.0573036i
$833$	−0.537513	+	0.174648i	−0.0186237	+	0.00605121i
$834$	0.400421	+	0.178279i	0.0138654	+	0.00617329i
$835$	1.25890	−	0.372066i	0.0435659	−	0.0128759i
$836$	−0.832402			−0.0287892
$837$	5.28121	+	1.76318i	0.182545	+	0.0609445i
$838$		−	20.5086i		−	0.708458i
$839$	38.9099	+	28.2697i	1.34332	+	0.975979i	0.999315	+	0.0370107i	$0.0117836\pi$
$839$	38.9099	+	28.2697i	1.34332	+	0.975979i	0.344005	+	0.938968i	$0.388216\pi$
$840$	3.82207	−	2.07220i	0.131874	−	0.0714975i
$841$	−4.57859	−	14.0914i	−0.157882	−	0.485912i
$842$	−18.2379	−	10.5297i	−0.628519	−	0.362876i
$843$	10.8281	−	6.25160i	0.372939	−	0.215317i
$844$	14.5492	−	16.1585i	0.500804	−	0.556200i
$845$	−3.81961	+	2.62172i	−0.131399	+	0.0901898i
$846$	−4.26357	−	4.73518i	−0.146585	−	0.162799i
$847$	−17.6760	−	39.7009i	−0.607354	−	1.36414i
$848$	−0.806531	+	3.79443i	−0.0276964	+	0.130301i
$849$	−1.61568	+	15.3722i	−0.0554502	+	0.527573i
$850$	−0.819807	+	0.313546i	−0.0281191	+	0.0107546i
$851$	21.7173	−	4.61616i	0.744460	−	0.158240i
$852$	5.67936	+	7.81697i	0.194572	+	0.267805i
$853$	12.0482	+	16.5829i	0.412521	+	0.567786i	0.963831	−	0.266514i	$-0.0858719\pi$
$853$	12.0482	+	16.5829i	0.412521	+	0.567786i	−0.551310	+	0.834300i	$0.685872\pi$
$854$	−22.9810	+	4.88476i	−0.786393	+	0.167153i
$855$	0.168570	−	0.274705i	0.00576498	−	0.00939471i
$856$	0.132206	−	1.25785i	0.00451870	−	0.0429925i
$857$	−1.84053	+	8.65902i	−0.0628714	+	0.295787i	−0.998338	−	0.0576282i	$-0.981646\pi$
$857$	−1.84053	+	8.65902i	−0.0628714	+	0.295787i	0.935467	+	0.353415i	$0.114980\pi$
$858$	−7.76500	−	17.4405i	−0.265093	−	0.595408i
$859$	−11.4154	−	12.6780i	−0.389487	−	0.432569i	0.516231	−	0.856449i	$-0.327334\pi$
$859$	−11.4154	−	12.6780i	−0.389487	−	0.432569i	−0.905718	+	0.423880i	$0.860668\pi$
$860$	−13.5609	−	19.7570i	−0.462422	−	0.673709i
$861$	−15.5782	+	17.3013i	−0.530903	+	0.589627i
$862$	20.3933	−	11.7741i	0.694597	−	0.401026i
$863$	−26.6428	−	15.3822i	−0.906931	−	0.523617i	−0.0274886	−	0.999622i	$-0.508751\pi$
$863$	−26.6428	−	15.3822i	−0.906931	−	0.523617i	−0.879442	+	0.476005i	$0.842084\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	34.6483	−	18.7851i	1.17808	−	0.638713i
$866$	−19.2387	−	13.9777i	−0.653758	−	0.474983i
$867$		−	16.9692i		−	0.576304i
$868$	9.41860	−	5.33702i	0.319688	−	0.181150i
$869$	−5.03302			−0.170734
$870$	2.38683	+	8.07589i	0.0809210	+	0.273798i
$871$	9.99704	+	4.45097i	0.338737	+	0.150815i
$872$	17.8672	−	5.80542i	0.605061	−	0.196596i
$873$	10.7826	+	6.22536i	0.364937	+	0.210696i
$874$	0.247897	+	0.429370i	0.00838523	+	0.0145236i
$875$	−19.6378	+	9.32265i	−0.663879	+	0.315163i
$876$	4.17667	−	12.8545i	0.141117	−	0.434312i
$877$	14.7740	−	13.3026i	0.498883	−	0.449196i	−0.380869	−	0.924629i	$-0.624375\pi$
$877$	14.7740	−	13.3026i	0.498883	−	0.449196i	0.879752	+	0.475433i	$0.157708\pi$
$878$	0.800530	+	1.79802i	0.0270166	+	0.0606802i
$879$	12.2974	+	2.61389i	0.414781	+	0.0881644i
$880$	8.89470	−	9.36161i	0.299840	−	0.315580i
$881$	−0.430942	−	4.10013i	−0.0145188	−	0.138137i	0.984861	−	0.173345i	$-0.0554574\pi$
$881$	−0.430942	−	4.10013i	−0.0145188	−	0.138137i	−0.999380	+	0.0352076i	$0.988791\pi$
$882$	0.669383	+	3.14920i	0.0225393	+	0.106039i
$883$	10.2341	+	14.0861i	0.344406	+	0.474034i	0.945722	−	0.324977i	$-0.105357\pi$
$883$	10.2341	+	14.0861i	0.344406	+	0.474034i	−0.601316	+	0.799011i	$0.705357\pi$
$884$	0.469481	−	0.341098i	0.0157903	−	0.0114724i
$885$	−12.4536	+	26.0686i	−0.418624	+	0.876286i
$886$	−1.56562	−	14.8959i	−0.0525981	−	0.500437i
$887$	2.84764	+	0.299299i	0.0956144	+	0.0100495i	0.152215	−	0.988347i	$-0.451359\pi$
$887$	2.84764	+	0.299299i	0.0956144	+	0.0100495i	−0.0566004	+	0.998397i	$0.518026\pi$
$888$	−1.34202	+	6.31370i	−0.0450352	+	0.211874i
$889$	23.1072	−	10.2880i	0.774991	−	0.345048i
$890$	18.1957	−	1.42086i	0.609921	−	0.0476272i
$891$	1.78459	−	5.49239i	0.0597859	−	0.184002i
$892$	−10.2150	−	9.19763i	−0.342024	−	0.307959i
$893$	−0.795375	+	0.459210i	−0.0266162	+	0.0153669i
$894$	−3.27716	+	5.67620i	−0.109604	+	0.189840i
$895$	−8.31303	+	23.4298i	−0.277874	+	0.783173i
$896$	−1.77624	−	0.790833i	−0.0593400	−	0.0264199i
$897$	−6.68366	+	9.19927i	−0.223161	+	0.307155i
$898$			18.7332i			0.625135i
$899$	6.31863	+	19.9940i	0.210738	+	0.666837i
$900$	1.28820	+	4.83121i	0.0429399	+	0.161040i
$901$	−0.550917	−	0.400265i	−0.0183537	−	0.0133347i
$902$	−28.1256	+	63.1712i	−0.936481	+	2.10337i
$903$	−19.8170	+	6.43895i	−0.659470	+	0.214275i
$904$	−6.41708	+	11.1147i	−0.213429	+	0.369669i
$905$	−2.20414	+	16.6635i	−0.0732680	+	0.553913i
$906$	4.84942	−	5.38583i	0.161111	−	0.178932i
$907$	33.8853	+	11.0100i	1.12514	+	0.365581i	0.811728	−	0.584036i	$-0.198527\pi$
$907$	33.8853	+	11.0100i	1.12514	+	0.365581i	0.313414	+	0.949617i	$0.398527\pi$
$908$	−18.2085	+	16.3950i	−0.604271	+	0.544088i
$909$	−13.8946	+	6.18626i	−0.460854	+	0.205185i
$910$	10.9346	−	9.32746i	0.362477	−	0.309202i
$911$	−2.20040	+	20.9354i	−0.0729025	+	0.693621i	0.895641	+	0.444777i	$0.146717\pi$
$911$	−2.20040	+	20.9354i	−0.0729025	+	0.693621i	−0.968544	+	0.248844i	$0.919949\pi$
$912$	−0.143348	+	0.0150665i	−0.00474674	+	0.000498902i
$913$	7.63743	+	35.9313i	0.252762	+	1.18915i
$914$	18.4753	−	13.4231i	0.611109	−	0.443997i
$915$	0.723778	−	27.0098i	0.0239273	−	0.892918i
$916$	20.0044	−	4.25206i	0.660963	−	0.140492i
$917$	−20.4424	+	2.14859i	−0.675069	+	0.0709526i
$918$	0.174583	+	0.0183494i	0.00576208	+	0.000605620i
$919$	−23.9122	−	5.08270i	−0.788792	−	0.167663i	−0.204134	−	0.978943i	$-0.565438\pi$
$919$	−23.9122	−	5.08270i	−0.788792	−	0.167663i	−0.584658	+	0.811280i	$0.698771\pi$
$920$	−7.47782	−	1.80010i	−0.246537	−	0.0593474i
$921$	−0.433564	−	0.481521i	−0.0142864	−	0.0158667i
$922$	22.5567	+	7.32911i	0.742865	+	0.241371i
$923$	23.7371	+	21.3730i	0.781316	+	0.703500i
$924$	−5.61431	−	9.72427i	−0.184697	−	0.319905i
$925$	8.39112	−	31.1638i	0.275898	−	1.02466i
$926$	5.51652	+	16.9781i	0.181284	+	0.557935i
$927$	0.923234	−	2.07362i	0.0303230	−	0.0681066i
$928$	2.21365	−	3.04683i	0.0726666	−	0.100017i
$929$	42.6093			1.39797			0.698983	−	0.715138i	$-0.253636\pi$
$929$	42.6093			1.39797			0.698983	+	0.715138i	$0.253636\pi$
$930$	3.43227	+	11.9674i	0.112549	+	0.392428i
$931$	0.464060			0.0152089
$932$	−8.28790	+	11.4073i	−0.271479	+	0.373659i
$933$	7.54119	−	16.9378i	0.246888	−	0.554519i
$934$	−0.179823	−	0.553438i	−0.00588399	−	0.0181091i
$935$	0.866215	+	2.09484i	0.0283283	+	0.0685087i
$936$	−1.65289	−	2.86289i	−0.0540263	−	0.0935763i
$937$	−20.1050	−	18.1026i	−0.656801	−	0.591387i	0.271850	−	0.962340i	$-0.412364\pi$
$937$	−20.1050	−	18.1026i	−0.656801	−	0.591387i	−0.928652	+	0.370953i	$0.879031\pi$
$938$	6.12133	+	1.98894i	0.199869	+	0.0649412i
$939$	12.8093	+	14.2262i	0.418017	+	0.464255i
$940$	3.33454	−	13.8521i	0.108761	−	0.451806i
$941$	−52.9092	−	11.2462i	−1.72479	−	0.366616i	−0.764287	−	0.644877i	$-0.776909\pi$
$941$	−52.9092	−	11.2462i	−1.72479	−	0.366616i	−0.960506	+	0.278261i	$0.910242\pi$
$942$	−17.0536	−	1.79240i	−0.555635	−	0.0583996i
$943$	40.9610	−	4.30518i	1.33387	−	0.140196i
$944$	12.6379	−	2.68627i	0.411329	−	0.0874307i
$945$	4.34611	+	0.116462i	0.141379	+	0.00378850i
$946$	−50.0695	+	36.3777i	−1.62790	+	1.18274i
$947$	−5.13303	−	24.1490i	−0.166801	−	0.784738i	−0.979402	−	0.201918i	$-0.935283\pi$
$947$	−5.13303	−	24.1490i	−0.166801	−	0.784738i	0.812601	−	0.582820i	$-0.198051\pi$
$948$	−0.866739	+	0.0910979i	−0.0281504	+	0.00295872i
$949$	4.67042	−	44.4361i	0.151608	−	1.44246i
$950$	0.719747	−	0.0368392i	0.0233517	−	0.00119522i
$951$	−4.62269	+	2.05816i	−0.149901	+	0.0667403i
$952$	0.253648	−	0.228386i	0.00822078	−	0.00740202i
$953$	23.8048	+	7.73466i	0.771114	+	0.250550i	0.668042	−	0.744124i	$-0.267133\pi$
$953$	23.8048	+	7.73466i	0.771114	+	0.250550i	0.103072	+	0.994674i	$0.467133\pi$
$954$	−2.59569	+	2.88281i	−0.0840386	+	0.0933343i
$955$	2.03909	−	15.4157i	0.0659834	−	0.498840i
$956$	3.65687	−	6.33389i	0.118272	−	0.204853i
$957$	20.6848	−	6.72090i	0.668644	−	0.217256i
$958$	5.67094	−	12.7371i	0.183220	−	0.411518i
$959$	−23.2504	−	16.8924i	−0.750796	−	0.545485i
$960$	1.36231	−	1.77316i	0.0439685	−	0.0572285i
$961$	9.10275	+	29.6334i	0.293637	+	0.955917i
$962$			21.3380i			0.687963i
$963$	0.743420	−	1.02323i	0.0239564	−	0.0329731i
$964$	−13.7284	−	6.11230i	−0.442163	−	0.196864i
$965$	28.6794	+	10.1756i	0.923223	+	0.327565i
$966$	−3.34398	+	5.79195i	−0.107591	+	0.186353i
$967$	10.9296	−	6.31024i	0.351474	−	0.202923i	−0.313860	−	0.949469i	$-0.601622\pi$
$967$	10.9296	−	6.31024i	0.351474	−	0.202923i	0.665334	+	0.746546i	$0.268289\pi$
$968$	−16.6101	−	14.9558i	−0.533869	−	0.480697i
$969$	0.00781893	−	0.0240642i	0.000251180	−	0.000773053i
$970$	2.16741	+	27.7562i	0.0695913	+	0.891196i
$971$	−1.98998	+	0.885995i	−0.0638614	+	0.0284329i	−0.438419	−	0.898771i	$-0.644461\pi$
$971$	−1.98998	+	0.885995i	−0.0638614	+	0.0284329i	0.374557	+	0.927204i	$0.377795\pi$
$972$	0.207912	−	0.978148i	0.00666877	−	0.0313741i
$973$	0.847563	+	0.0890825i	0.0271716	+	0.00285585i
$974$	2.75984	+	26.2581i	0.0884309	+	0.841364i
$975$	7.48597	+	14.7365i	0.239743	+	0.471945i
$976$	−9.77576	+	7.10250i	−0.312914	+	0.227346i
$977$	30.9891	+	42.6528i	0.991429	+	1.36458i	0.930439	+	0.366446i	$0.119426\pi$
$977$	30.9891	+	42.6528i	0.991429	+	1.36458i	0.0609896	+	0.998138i	$0.480574\pi$
$978$	−1.53033	−	7.19963i	−0.0489345	−	0.230219i
$979$	−4.92712	−	46.8784i	−0.157471	−	1.49824i
$980$	−4.95875	+	5.21905i	−0.158401	+	0.166716i
$981$	18.3762	+	3.90598i	0.586707	+	0.124708i
$982$	−7.38693	−	16.5913i	−0.235727	−	0.529450i
$983$	−33.4828	+	30.1481i	−1.06794	+	0.961575i	−0.999349	−	0.0360706i	$-0.988516\pi$
$983$	−33.4828	+	30.1481i	−1.06794	+	0.961575i	−0.0685875	+	0.997645i	$0.521849\pi$
$984$	−3.70012	+	11.3878i	−0.117956	+	0.363030i
$985$	3.25850	+	17.6414i	0.103824	+	0.562101i
$986$	0.330557	+	0.572542i	0.0105271	+	0.0182334i
$987$	−10.7291	−	6.19447i	−0.341512	−	0.197172i
$988$	−0.453166	+	0.147243i	−0.0144171	+	0.00468441i
$989$	33.6755	+	14.9933i	1.07082	+	0.476759i
$990$	12.3838	−	3.66004i	0.393584	−	0.116324i
$991$	41.0607			1.30434			0.652169	−	0.758074i	$-0.273859\pi$
$991$	41.0607			1.30434			0.652169	+	0.758074i	$0.273859\pi$
$992$	3.30887	−	4.47788i	0.105057	−	0.142173i
$993$			2.16858i			0.0688178i
$994$	15.1988	+	11.0426i	0.482077	+	0.350250i
$995$	−17.4190	−	32.1287i	−0.552221	−	1.01855i
$996$	1.96560	+	6.04950i	0.0622825	+	0.191686i
$997$	9.28338	+	5.35976i	0.294008	+	0.169745i	0.639748	−	0.768585i	$-0.279039\pi$
$997$	9.28338	+	5.35976i	0.294008	+	0.169745i	−0.345740	+	0.938330i	$0.612372\pi$
$998$	−13.6768	+	7.89631i	−0.432932	+	0.249953i
$999$	−4.31907	+	4.79682i	−0.136649	+	0.151765i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bn.b.19.17	yes	144
5.4	even	2	inner	930.2.bn.b.19.5	✓	144
31.18	even	15	inner	930.2.bn.b.49.5	yes	144
155.49	even	30	inner	930.2.bn.b.49.17	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bn.b.19.5	✓	144	5.4	even	2	inner
930.2.bn.b.19.17	yes	144	1.1	even	1	trivial
930.2.bn.b.49.5	yes	144	31.18	even	15	inner
930.2.bn.b.49.17	yes	144	155.49	even	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bn (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{2} +(0.406737 - 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(2.06638 - 0.854445i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-1.44492 - 1.30102i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +O(q^{10})\)	\(q+(0.587785 - 0.809017i) q^{2} +(0.406737 - 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(2.06638 - 0.854445i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-1.44492 - 1.30102i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +(0.523327 - 2.17397i) q^{10} +(-5.64884 - 1.20070i) q^{11} +(-0.994522 - 0.104528i) q^{12} +(-3.28767 + 0.345548i) q^{13} +(-1.90185 + 0.404250i) q^{14} +(0.0598980 - 2.23527i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.0364977 - 0.171708i) q^{17} +(-0.994522 + 0.104528i) q^{18} +(-0.0150665 + 0.143348i) q^{19} +(-1.45117 - 1.70121i) q^{20} +(-1.77624 + 0.790833i) q^{21} +(-4.29169 + 3.86426i) q^{22} +(3.27136 + 1.06293i) q^{23} +(-0.669131 + 0.743145i) q^{24} +(3.53985 - 3.53121i) q^{25} +(-1.65289 + 2.86289i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(-0.790833 + 1.77624i) q^{28} +(-3.04683 - 2.21365i) q^{29} +(-1.77316 - 1.36231i) q^{30} +(-4.47788 - 3.30887i) q^{31} +1.00000i q^{32} +(-3.39448 + 4.67211i) q^{33} +(-0.160368 - 0.0714003i) q^{34} +(-4.09741 - 1.45378i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(5.58998 - 3.22738i) q^{37} +(0.107115 + 0.0964471i) q^{38} +(-1.02154 + 3.14398i) q^{39} +(-2.22928 + 0.174079i) q^{40} +(10.9387 - 4.87021i) q^{41} +(-0.404250 + 1.90185i) q^{42} +(10.6580 + 1.12020i) q^{43} +(0.603656 + 5.74340i) q^{44} +(-2.01765 - 0.963884i) q^{45} +(2.78279 - 2.02181i) q^{46} +(3.74526 + 5.15490i) q^{47} +(0.207912 + 0.978148i) q^{48} +(-0.336535 - 3.20192i) q^{49} +(-0.776142 - 4.93939i) q^{50} +(-0.171708 - 0.0364977i) q^{51} +(1.34458 + 3.01998i) q^{52} +(2.88281 - 2.59569i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-12.6986 + 2.34553i) q^{55} +(0.972168 + 1.68385i) q^{56} +(0.124827 + 0.0720689i) q^{57} +(-3.58176 + 1.16378i) q^{58} +(-11.8032 - 5.25514i) q^{59} +(-2.14437 + 0.633769i) q^{60} +12.0835 q^{61} +(-5.30896 + 1.67777i) q^{62} +1.94434i q^{63} +(0.809017 + 0.587785i) q^{64} +(-6.49831 + 3.52316i) q^{65} +(1.78459 + 5.49239i) q^{66} +(-2.86681 - 1.65515i) q^{67} +(-0.152026 + 0.0877721i) q^{68} +(2.30162 - 2.55621i) q^{69} +(-3.58453 + 2.46036i) q^{70} +(-6.46534 - 7.18049i) q^{71} +(0.406737 + 0.913545i) q^{72} +(-2.81013 + 13.2206i) q^{73} +(0.674705 - 6.41939i) q^{74} +(-1.78614 - 4.67009i) q^{75} +(0.140988 - 0.0299679i) q^{76} +(6.60002 + 9.08415i) q^{77} +(1.94309 + 2.67443i) q^{78} +(0.852468 - 0.181198i) q^{79} +(-1.16951 + 1.90585i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(2.48950 - 11.7122i) q^{82} +(-2.58718 - 5.81090i) q^{83} +(1.30102 + 1.44492i) q^{84} +(-0.222133 - 0.323629i) q^{85} +(7.17087 - 7.96406i) q^{86} +(-3.26152 + 1.88304i) q^{87} +(5.00133 + 2.88752i) q^{88} +(2.52224 + 7.76265i) q^{89} +(-1.96575 + 1.06576i) q^{90} +(5.19999 + 3.77801i) q^{91} -3.43972i q^{92} +(-4.84412 + 2.74490i) q^{93} +6.37181 q^{94} +(0.0913501 + 0.309085i) q^{95} +(0.913545 + 0.406737i) q^{96} +(-11.8413 + 3.84748i) q^{97} +(-2.78822 - 1.60978i) q^{98} +(2.88752 + 5.00133i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9}+O(q^{10}) \) 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9	\( 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9} - 18 q^{11} - 8 q^{14} - 36 q^{16} - 24 q^{19} - 2 q^{20} + 28 q^{21} - 18 q^{24} + 10 q^{25} - 12 q^{26} - 4 q^{30} - 4 q^{31} + 10 q^{34} - 2 q^{35} - 72 q^{36} + 16 q^{39} + 4 q^{41} - 2 q^{44} - 2 q^{45} - 2 q^{46} - 78 q^{49} + 32 q^{50} + 10 q^{51} + 36 q^{54} - 50 q^{55} - 12 q^{56} + 28 q^{59} + 88 q^{61} + 36 q^{64} - 124 q^{65} + 6 q^{66} - 46 q^{69} - 10 q^{70} + 140 q^{71} + 34 q^{74} - 32 q^{75} + 24 q^{76} + 16 q^{79} + 12 q^{80} + 18 q^{81} - 8 q^{84} + 74 q^{85} - 98 q^{86} + 148 q^{89} + 44 q^{91} - 108 q^{94} - 80 q^{95} + 18 q^{96} - 2 q^{99}+O(q^{100}) \) 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9 - 18 * q^11 - 8 * q^14 - 36 * q^16 - 24 * q^19 - 2 * q^20 + 28 * q^21 - 18 * q^24 + 10 * q^25 - 12 * q^26 - 4 * q^30 - 4 * q^31 + 10 * q^34 - 2 * q^35 - 72 * q^36 + 16 * q^39 + 4 * q^41 - 2 * q^44 - 2 * q^45 - 2 * q^46 - 78 * q^49 + 32 * q^50 + 10 * q^51 + 36 * q^54 - 50 * q^55 - 12 * q^56 + 28 * q^59 + 88 * q^61 + 36 * q^64 - 124 * q^65 + 6 * q^66 - 46 * q^69 - 10 * q^70 + 140 * q^71 + 34 * q^74 - 32 * q^75 + 24 * q^76 + 16 * q^79 + 12 * q^80 + 18 * q^81 - 8 * q^84 + 74 * q^85 - 98 * q^86 + 148 * q^89 + 44 * q^91 - 108 * q^94 - 80 * q^95 + 18 * q^96 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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