LMFDB - Embedded newform 930.2.br.a.11.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(11,930)]

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([15, 0, 23]))

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

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

chi := DirichletCharacter("930.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.br (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:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			11.12
Character	$\chi$	$=$	930.11
Dual form			930.2.br.a.761.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{2} +(-1.69764 - 0.343522i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.72071 + 0.197892i) q^{6} +(-0.487372 - 4.63703i) q^{7} +(0.587785 - 0.809017i) q^{8} +(2.76399 + 1.16636i) q^{9} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{2} +(-1.69764 - 0.343522i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.72071 + 0.197892i) q^{6} +(-0.487372 - 4.63703i) q^{7} +(0.587785 - 0.809017i) q^{8} +(2.76399 + 1.16636i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(-0.793581 - 0.353325i) q^{11} +(-1.57534 + 0.719934i) q^{12} +(0.254594 + 1.19777i) q^{13} +(-1.89644 - 4.25947i) q^{14} +(1.64196 - 0.551323i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.33896 + 1.04137i) q^{17} +(2.98913 + 0.255152i) q^{18} +(-6.87933 - 1.46225i) q^{19} +(-0.406737 + 0.913545i) q^{20} +(-0.765540 + 8.03945i) q^{21} +(-0.863924 - 0.0908021i) q^{22} +(3.09069 + 2.24552i) q^{23} +(-1.27576 + 1.17150i) q^{24} +(0.500000 - 0.866025i) q^{25} +(0.612264 + 1.06047i) q^{26} +(-4.29159 - 2.92955i) q^{27} +(-3.11987 - 3.46497i) q^{28} +(1.73394 + 5.33652i) q^{29} +(1.39123 - 1.03173i) q^{30} +(-4.35158 - 3.47329i) q^{31} -1.00000i q^{32} +(1.22584 + 0.872433i) q^{33} +(-1.90268 + 1.71318i) q^{34} +(2.74059 + 3.77210i) q^{35} +(2.92168 - 0.681028i) q^{36} +(-6.74761 - 3.89573i) q^{37} +(-6.99449 + 0.735150i) q^{38} +(-0.0207491 - 2.12084i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(-3.65338 - 3.28952i) q^{41} +(1.75626 + 7.88254i) q^{42} +(2.00531 - 9.43422i) q^{43} +(-0.849700 + 0.180609i) q^{44} +(-2.97686 + 0.371899i) q^{45} +(3.63333 + 1.18054i) q^{46} +(-8.17122 - 2.65499i) q^{47} +(-0.851310 + 1.50840i) q^{48} +(-14.4175 + 3.06454i) q^{49} +(0.207912 - 0.978148i) q^{50} +(4.32846 - 0.964395i) q^{51} +(0.910001 + 0.819369i) q^{52} +(-0.0119241 + 0.113450i) q^{53} +(-4.98683 - 1.45999i) q^{54} +(0.863924 - 0.0908021i) q^{55} +(-4.03791 - 2.33129i) q^{56} +(11.1763 + 4.84557i) q^{57} +(3.29815 + 4.53951i) q^{58} +(-7.95569 + 7.16334i) q^{59} +(1.00432 - 1.41115i) q^{60} +9.88995i q^{61} +(-5.21190 - 1.95859i) q^{62} +(4.06134 - 13.3851i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-0.819369 - 0.910001i) q^{65} +(1.43544 + 0.450927i) q^{66} +(-0.378654 - 0.655849i) q^{67} +(-1.28016 + 2.21730i) q^{68} +(-4.47551 - 4.87381i) q^{69} +(3.77210 + 2.74059i) q^{70} +(2.04879 + 0.215337i) q^{71} +(2.56823 - 1.55054i) q^{72} +(5.12221 - 11.5047i) q^{73} +(-7.62120 - 1.61994i) q^{74} +(-1.14632 + 1.29844i) q^{75} +(-6.42498 + 2.86059i) q^{76} +(-1.25161 + 3.85206i) q^{77} +(-0.675110 - 2.01063i) q^{78} +(4.61682 + 10.3696i) q^{79} +(0.207912 + 0.978148i) q^{80} +(6.27923 + 6.44758i) q^{81} +(-4.49109 - 1.99956i) q^{82} +(2.31676 - 2.57302i) q^{83} +(4.10614 + 6.95403i) q^{84} +(1.50491 - 2.07134i) q^{85} +(-1.00818 - 9.59215i) q^{86} +(-1.11040 - 9.65515i) q^{87} +(-0.752301 + 0.434341i) q^{88} +(5.10306 - 3.70759i) q^{89} +(-2.71624 + 1.27360i) q^{90} +(5.43001 - 1.76432i) q^{91} +3.82031 q^{92} +(6.19427 + 7.39128i) q^{93} -8.59173 q^{94} +(6.68880 - 2.17332i) q^{95} +(-0.343522 + 1.69764i) q^{96} +(9.19646 - 6.68162i) q^{97} +(-12.7649 + 7.36980i) q^{98} +(-1.78134 - 1.90218i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9	$ 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9} - 22 q^{10} - 38 q^{13} - 44 q^{16} + 12 q^{18} + 8 q^{19} - 18 q^{21} - 4 q^{22} + 88 q^{25} - 90 q^{27} + 36 q^{28} + 24 q^{31} + 18 q^{33} + 14 q^{34} + 4 q^{36} - 42 q^{37} - 42 q^{39} + 22 q^{40} - 12 q^{42} - 34 q^{43} - 8 q^{45} + 10 q^{46} + 22 q^{49} + 26 q^{51} - 2 q^{52} + 4 q^{55} + 114 q^{57} + 32 q^{63} + 44 q^{64} - 42 q^{66} + 20 q^{67} + 16 q^{69} + 8 q^{70} - 12 q^{72} - 28 q^{73} + 12 q^{76} - 92 q^{78} - 56 q^{79} - 124 q^{81} - 32 q^{82} - 12 q^{84} - 36 q^{87} - 6 q^{88} + 24 q^{90} - 140 q^{91} - 104 q^{93} - 36 q^{94} + 88 q^{97} - 60 q^{99}+O(q^{100}) $ 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9 - 22 * q^10 - 38 * q^13 - 44 * q^16 + 12 * q^18 + 8 * q^19 - 18 * q^21 - 4 * q^22 + 88 * q^25 - 90 * q^27 + 36 * q^28 + 24 * q^31 + 18 * q^33 + 14 * q^34 + 4 * q^36 - 42 * q^37 - 42 * q^39 + 22 * q^40 - 12 * q^42 - 34 * q^43 - 8 * q^45 + 10 * q^46 + 22 * q^49 + 26 * q^51 - 2 * q^52 + 4 * q^55 + 114 * q^57 + 32 * q^63 + 44 * q^64 - 42 * q^66 + 20 * q^67 + 16 * q^69 + 8 * q^70 - 12 * q^72 - 28 * q^73 + 12 * q^76 - 92 * q^78 - 56 * q^79 - 124 * q^81 - 32 * q^82 - 12 * q^84 - 36 * q^87 - 6 * q^88 + 24 * q^90 - 140 * q^91 - 104 * q^93 - 36 * q^94 + 88 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{23}{30}\right)$

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 $

$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$3$	−1.69764	−	0.343522i	−0.980135	−	0.198333i
$3$	−1.69764	−	0.343522i	−0.980135	−	0.198333i
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	−1.72071	+	0.197892i	−0.702476	+	0.0807889i
$7$	−0.487372	−	4.63703i	−0.184209	−	1.75263i	−0.562362	−	0.826891i	$-0.690107\pi$
$7$	−0.487372	−	4.63703i	−0.184209	−	1.75263i	0.378153	−	0.925743i	$-0.376559\pi$
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	2.76399	+	1.16636i	0.921328	+	0.388785i
$10$	−0.669131	+	0.743145i	−0.211598	+	0.235003i
$11$	−0.793581	−	0.353325i	−0.239274	−	0.106532i	0.283597	−	0.958944i	$-0.408472\pi$
$11$	−0.793581	−	0.353325i	−0.239274	−	0.106532i	−0.522871	+	0.852412i	$0.675139\pi$
$12$	−1.57534	+	0.719934i	−0.454761	+	0.207827i
$13$	0.254594	+	1.19777i	0.0706115	+	0.332201i	0.999247	−	0.0387915i	$-0.0123508\pi$
$13$	0.254594	+	1.19777i	0.0706115	+	0.332201i	−0.928636	+	0.370993i	$0.879017\pi$
$14$	−1.89644	−	4.25947i	−0.506845	−	1.13839i
$15$	1.64196	−	0.551323i	0.423953	−	0.142351i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−2.33896	+	1.04137i	−0.567282	+	0.252570i	−0.670276	−	0.742112i	$-0.733824\pi$
$17$	−2.33896	+	1.04137i	−0.567282	+	0.252570i	0.102994	+	0.994682i	$0.467158\pi$
$18$	2.98913	+	0.255152i	0.704545	+	0.0601399i
$19$	−6.87933	−	1.46225i	−1.57823	−	0.335462i	−0.666257	−	0.745722i	$-0.732105\pi$
$19$	−6.87933	−	1.46225i	−1.57823	−	0.335462i	−0.911969	+	0.410260i	$0.865438\pi$
$20$	−0.406737	+	0.913545i	−0.0909491	+	0.204275i
$21$	−0.765540	+	8.03945i	−0.167055	+	1.75435i
$22$	−0.863924	−	0.0908021i	−0.184189	−	0.0193591i
$23$	3.09069	+	2.24552i	0.644454	+	0.468223i	0.861377	−	0.507965i	$-0.169602\pi$
$23$	3.09069	+	2.24552i	0.644454	+	0.468223i	−0.216924	+	0.976189i	$0.569602\pi$
$24$	−1.27576	+	1.17150i	−0.260414	+	0.239132i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	0.612264	+	1.06047i	0.120075	+	0.207976i
$27$	−4.29159	−	2.92955i	−0.825917	−	0.563791i
$28$	−3.11987	−	3.46497i	−0.589600	−	0.654818i
$29$	1.73394	+	5.33652i	0.321985	+	0.990967i	0.972783	+	0.231716i	$0.0744341\pi$
$29$	1.73394	+	5.33652i	0.321985	+	0.990967i	−0.650799	+	0.759250i	$0.725566\pi$
$30$	1.39123	−	1.03173i	0.254003	−	0.188368i
$31$	−4.35158	−	3.47329i	−0.781566	−	0.623822i
$31$	−4.35158	−	3.47329i	−0.781566	−	0.623822i
$32$		−	1.00000i		−	0.176777i
$33$	1.22584	+	0.872433i	0.213392	+	0.151871i
$34$	−1.90268	+	1.71318i	−0.326308	+	0.293809i
$35$	2.74059	+	3.77210i	0.463245	+	0.637602i
$36$	2.92168	−	0.681028i	0.486946	−	0.113505i
$37$	−6.74761	−	3.89573i	−1.10930	−	0.640454i	−0.170652	−	0.985331i	$-0.554587\pi$
$37$	−6.74761	−	3.89573i	−1.10930	−	0.640454i	−0.938648	+	0.344877i	$0.887921\pi$
$38$	−6.99449	+	0.735150i	−1.13466	+	0.119257i
$39$	−0.0207491	−	2.12084i	−0.00332251	−	0.339606i
$40$	−0.104528	+	0.994522i	−0.0165274	+	0.157248i
$41$	−3.65338	−	3.28952i	−0.570563	−	0.513737i	0.332581	−	0.943075i	$-0.392080\pi$
$41$	−3.65338	−	3.28952i	−0.570563	−	0.513737i	−0.903144	+	0.429338i	$0.858747\pi$
$42$	1.75626	+	7.88254i	0.270996	+	1.21630i
$43$	2.00531	−	9.43422i	0.305806	−	1.43871i	−0.509897	−	0.860235i	$-0.670317\pi$
$43$	2.00531	−	9.43422i	0.305806	−	1.43871i	0.815704	−	0.578470i	$-0.196350\pi$
$44$	−0.849700	+	0.180609i	−0.128097	+	0.0272279i
$45$	−2.97686	+	0.371899i	−0.443764	+	0.0554394i
$46$	3.63333	+	1.18054i	0.535705	+	0.174061i
$47$	−8.17122	−	2.65499i	−1.19189	−	0.387270i	−0.355122	−	0.934820i	$-0.615561\pi$
$47$	−8.17122	−	2.65499i	−1.19189	−	0.387270i	−0.836773	+	0.547550i	$0.815561\pi$
$48$	−0.851310	+	1.50840i	−0.122876	+	0.217719i
$49$	−14.4175	+	3.06454i	−2.05964	+	0.437791i
$50$	0.207912	−	0.978148i	0.0294032	−	0.138331i
$51$	4.32846	−	0.964395i	0.606106	−	0.135042i
$52$	0.910001	+	0.819369i	0.126194	+	0.113626i
$53$	−0.0119241	+	0.113450i	−0.00163789	+	0.0155835i	−0.995310	−	0.0967335i	$-0.969161\pi$
$53$	−0.0119241	+	0.113450i	−0.00163789	+	0.0155835i	0.993672	+	0.112317i	$0.0358272\pi$
$54$	−4.98683	−	1.45999i	−0.678621	−	0.198679i
$55$	0.863924	−	0.0908021i	0.116491	−	0.0122437i
$56$	−4.03791	−	2.33129i	−0.539588	−	0.311531i
$57$	11.1763	+	4.84557i	1.48034	+	0.641812i
$58$	3.29815	+	4.53951i	0.433068	+	0.596067i
$59$	−7.95569	+	7.16334i	−1.03574	+	0.932587i	−0.997774	−	0.0666921i	$-0.978755\pi$
$59$	−7.95569	+	7.16334i	−1.03574	+	0.932587i	−0.0379690	+	0.999279i	$0.512089\pi$
$60$	1.00432	−	1.41115i	0.129657	−	0.182179i
$61$			9.88995i			1.26628i	0.774038	+	0.633139i	$0.218234\pi$
$61$			9.88995i			1.26628i	−0.774038	+	0.633139i	$0.781766\pi$
$62$	−5.21190	−	1.95859i	−0.661912	−	0.248741i
$63$	4.06134	−	13.3851i	0.511681	−	1.68637i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−0.819369	−	0.910001i	−0.101630	−	0.112872i
$66$	1.43544	+	0.450927i	0.176691	+	0.0555052i
$67$	−0.378654	−	0.655849i	−0.0462600	−	0.0801247i	0.841968	−	0.539527i	$-0.181397\pi$
$67$	−0.378654	−	0.655849i	−0.0462600	−	0.0801247i	−0.888228	+	0.459402i	$0.848064\pi$
$68$	−1.28016	+	2.21730i	−0.155242	+	0.268887i
$69$	−4.47551	−	4.87381i	−0.538788	−	0.586738i
$70$	3.77210	+	2.74059i	0.450853	+	0.327564i
$71$	2.04879	+	0.215337i	0.243147	+	0.0255558i	0.225318	−	0.974285i	$-0.427658\pi$
$71$	2.04879	+	0.215337i	0.243147	+	0.0255558i	0.0178290	+	0.999841i	$0.494325\pi$
$72$	2.56823	−	1.55054i	0.302669	−	0.182733i
$73$	5.12221	−	11.5047i	0.599510	−	1.34652i	−0.317728	−	0.948182i	$-0.602920\pi$
$73$	5.12221	−	11.5047i	0.599510	−	1.34652i	0.917238	−	0.398339i	$-0.130413\pi$
$74$	−7.62120	−	1.61994i	−0.885947	−	0.188314i
$75$	−1.14632	+	1.29844i	−0.132366	+	0.149931i
$76$	−6.42498	+	2.86059i	−0.736996	+	0.328132i
$77$	−1.25161	+	3.85206i	−0.142634	+	0.438983i
$78$	−0.675110	−	2.01063i	−0.0764411	−	0.227659i
$79$	4.61682	+	10.3696i	0.519433	+	1.16667i	0.962773	+	0.270312i	$0.0871269\pi$
$79$	4.61682	+	10.3696i	0.519433	+	1.16667i	−0.443340	+	0.896354i	$0.646206\pi$
$80$	0.207912	+	0.978148i	0.0232452	+	0.109360i
$81$	6.27923	+	6.44758i	0.697692	+	0.716398i
$82$	−4.49109	−	1.99956i	−0.495958	−	0.220815i
$83$	2.31676	−	2.57302i	0.254297	−	0.282426i	−0.602456	−	0.798152i	$-0.705811\pi$
$83$	2.31676	−	2.57302i	0.254297	−	0.282426i	0.856754	+	0.515726i	$0.172478\pi$
$84$	4.10614	+	6.95403i	0.448016	+	0.758746i
$85$	1.50491	−	2.07134i	0.163231	−	0.224668i
$86$	−1.00818	−	9.59215i	−0.108714	−	1.03435i
$87$	−1.11040	−	9.65515i	−0.119047	−	1.03514i
$88$	−0.752301	+	0.434341i	−0.0801956	+	0.0463009i
$89$	5.10306	−	3.70759i	0.540923	−	0.393004i	−0.283505	−	0.958971i	$-0.591497\pi$
$89$	5.10306	−	3.70759i	0.540923	−	0.393004i	0.824428	+	0.565967i	$0.191497\pi$
$90$	−2.71624	+	1.27360i	−0.286317	+	0.134249i
$91$	5.43001	−	1.76432i	0.569220	−	0.184951i
$92$	3.82031			0.398294
$93$	6.19427	+	7.39128i	0.642316	+	0.766440i
$94$	−8.59173			−0.886169
$95$	6.68880	−	2.17332i	0.686256	−	0.222978i
$96$	−0.343522	+	1.69764i	−0.0350606	+	0.173265i
$97$	9.19646	−	6.68162i	0.933759	−	0.678415i	−0.0131515	−	0.999914i	$-0.504186\pi$
$97$	9.19646	−	6.68162i	0.933759	−	0.678415i	0.946910	+	0.321498i	$0.104186\pi$
$98$	−12.7649	+	7.36980i	−1.28945	+	0.744463i
$99$	−1.78134	−	1.90218i	−0.179032	−	0.191177i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	10.6891	−	14.7123i	1.06361	−	1.46393i	0.187219	−	0.982318i	$-0.440053\pi$
$101$	10.6891	−	14.7123i	1.06361	−	1.46393i	0.876386	−	0.481609i	$-0.159947\pi$
$102$	3.81860	−	2.25476i	0.378097	−	0.223255i
$103$	5.94748	−	6.60535i	0.586023	−	0.650844i	−0.375094	−	0.926987i	$-0.622390\pi$
$103$	5.94748	−	6.60535i	0.586023	−	0.650844i	0.961117	+	0.276143i	$0.0890562\pi$
$104$	1.11866	+	0.498060i	0.109694	+	0.0488388i
$105$	−3.35675	−	7.34514i	−0.327585	−	0.716812i
$106$	0.0237175	+	0.111582i	0.00230364	+	0.0108378i
$107$	1.81808	+	4.08348i	0.175761	+	0.394765i	0.979848	−	0.199747i	$-0.0640119\pi$
$107$	1.81808	+	4.08348i	0.175761	+	0.394765i	−0.804087	+	0.594512i	$0.797345\pi$
$108$	−5.19391	+	0.152481i	−0.499785	+	0.0146725i
$109$	−3.08864	+	9.50587i	−0.295838	+	0.910497i	0.687100	+	0.726563i	$0.258883\pi$
$109$	−3.08864	+	9.50587i	−0.295838	+	0.910497i	−0.982939	+	0.183934i	$0.941117\pi$
$110$	0.793581	−	0.353325i	0.0756650	−	0.0336882i
$111$	10.1168	+	8.93152i	0.960240	+	0.847742i
$112$	−4.56069	−	0.969404i	−0.430944	−	0.0916001i
$113$	−5.40555	+	12.1411i	−0.508512	+	1.14214i	0.458798	+	0.888540i	$0.348280\pi$
$113$	−5.40555	+	12.1411i	−0.508512	+	1.14214i	−0.967310	+	0.253596i	$0.918387\pi$
$114$	12.1267	+	1.15474i	1.13577	+	0.108151i
$115$	−3.79938	−	0.399331i	−0.354294	−	0.0372378i
$116$	4.53951	+	3.29815i	0.421483	+	0.306226i
$117$	−0.693332	+	3.60756i	−0.0640985	+	0.333519i
$118$	−5.35272	+	9.27118i	−0.492758	+	0.853481i
$119$	5.96883	+	10.3383i	0.547162	+	0.947712i
$120$	0.519092	−	1.65244i	0.0473864	−	0.150846i
$121$	−6.85550	−	7.61381i	−0.623228	−	0.692164i
$122$	3.05616	+	9.40590i	0.276692	+	0.851571i
$123$	5.07212	+	6.83945i	0.457337	+	0.616693i
$124$	−5.56205	−	0.252161i	−0.499487	−	0.0226447i
$125$			1.00000i			0.0894427i
$126$	−0.273669	−	13.9850i	−0.0243804	−	1.24589i
$127$	10.7113	−	9.64453i	0.950477	−	0.855814i	−0.0391848	−	0.999232i	$-0.512476\pi$
$127$	10.7113	−	9.64453i	0.950477	−	0.855814i	0.989662	+	0.143418i	$0.0458094\pi$
$128$	−0.587785	−	0.809017i	−0.0519534	−	0.0715077i
$129$	−6.64516	+	15.3271i	−0.585074	+	1.34947i
$130$	−1.06047	−	0.612264i	−0.0930095	−	0.0536991i
$131$	3.50667	−	0.368566i	0.306379	−	0.0322017i	0.0499085	−	0.998754i	$-0.484107\pi$
$131$	3.50667	−	0.368566i	0.306379	−	0.0322017i	0.256470	+	0.966552i	$0.417440\pi$
$132$	1.50453	−	0.0147194i	0.130953	−	0.00128116i
$133$	−3.42769	+	32.6123i	−0.297219	+	2.82785i
$134$	−0.562790	−	0.506739i	−0.0486177	−	0.0437755i
$135$	5.18140	+	0.391266i	0.445944	+	0.0336748i
$136$	−0.532319	+	2.50436i	−0.0456460	+	0.214748i
$137$	11.0103	−	2.34032i	0.940677	−	0.199947i	0.288040	−	0.957618i	$-0.406996\pi$
$137$	11.0103	−	2.34032i	0.940677	−	0.199947i	0.652636	+	0.757671i	$0.273663\pi$
$138$	−5.76255	−	3.25226i	−0.490541	−	0.276851i
$139$	−1.17562	−	0.381982i	−0.0997147	−	0.0323993i	0.258735	−	0.965948i	$-0.416694\pi$
$139$	−1.17562	−	0.381982i	−0.0997147	−	0.0323993i	−0.358449	+	0.933549i	$0.616694\pi$
$140$	4.43437	+	1.44082i	0.374773	+	0.121771i
$141$	12.9598	+	7.31422i	1.09141	+	0.615968i
$142$	2.01506	−	0.428314i	0.169100	−	0.0359434i
$143$	0.221161	−	1.04048i	0.0184944	−	0.0870094i
$144$	1.96339	−	2.26828i	0.163616	−	0.189024i
$145$	−4.16990	−	3.75459i	−0.346291	−	0.311802i
$146$	1.31637	−	12.5245i	0.108944	−	1.03653i
$147$	25.5285	−	0.249756i	2.10556	−	0.0205995i
$148$	−7.74878	+	0.814430i	−0.636946	+	0.0669457i
$149$	−19.6833	−	11.3641i	−1.61252	−	0.930987i	−0.988785	−	0.149348i	$-0.952283\pi$
$149$	−19.6833	−	11.3641i	−1.61252	−	0.930987i	−0.623731	−	0.781639i	$-0.714384\pi$
$150$	−0.688975	+	1.58912i	−0.0562546	+	0.129751i
$151$	−8.07277	−	11.1112i	−0.656952	−	0.904217i	0.342423	−	0.939546i	$-0.388752\pi$
$151$	−8.07277	−	11.1112i	−0.656952	−	0.904217i	−0.999376	+	0.0353283i	$0.988752\pi$
$152$	−5.22655	+	4.70601i	−0.423929	+	0.381707i
$153$	−7.67947	+	0.150277i	−0.620848	+	0.0121492i
$154$			4.05030i			0.326382i
$155$	5.50522	+	0.832172i	0.442190	+	0.0668417i
$156$	−1.26339	−	1.70360i	−0.101152	−	0.136397i
$157$	2.73678	+	8.42296i	0.218419	+	0.672225i	0.998893	+	0.0470368i	$0.0149778\pi$
$157$	2.73678	+	8.42296i	0.218419	+	0.672225i	−0.780474	+	0.625188i	$0.785022\pi$
$158$	7.59523	+	8.43535i	0.604244	+	0.671081i
$159$	0.0592153	−	0.188501i	0.00469608	−	0.0149491i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	8.90623	−	15.4260i	0.701909	−	1.21574i
$162$	7.96431	+	4.19163i	0.625735	+	0.329325i
$163$	4.80008	+	3.48746i	0.375971	+	0.273159i	0.759683	−	0.650294i	$-0.225354\pi$
$163$	4.80008	+	3.48746i	0.375971	+	0.273159i	−0.383711	+	0.923453i	$0.625354\pi$
$164$	−4.88918	−	0.513874i	−0.381781	−	0.0401268i
$165$	−1.49783	−	0.142627i	−0.116606	−	0.0111035i
$166$	1.40826	−	3.16301i	0.109302	−	0.245497i
$167$	−4.33774	−	0.922016i	−0.335665	−	0.0713477i	0.0369960	−	0.999315i	$-0.488221\pi$
$167$	−4.33774	−	0.922016i	−0.335665	−	0.0713477i	−0.372661	+	0.927968i	$0.621554\pi$
$168$	6.05408	+	5.34481i	0.467082	+	0.412361i
$169$	10.5063	−	4.67769i	0.808174	−	0.359822i
$170$	0.791180	−	2.43500i	0.0606808	−	0.186756i
$171$	−17.3089	−	12.0654i	−1.32364	−	0.922662i
$172$	−3.92297	−	8.81114i	−0.299124	−	0.671843i
$173$	−3.16559	−	14.8929i	−0.240675	−	1.13229i	−0.917993	−	0.396597i	$-0.870191\pi$
$173$	−3.16559	−	14.8929i	−0.240675	−	1.13229i	0.677317	−	0.735691i	$-0.263142\pi$
$174$	−4.03966	−	8.83946i	−0.306246	−	0.670118i
$175$	−4.25947	−	1.89644i	−0.321986	−	0.143357i
$176$	−0.581262	+	0.645557i	−0.0438143	+	0.0486607i
$177$	15.9667	−	9.42783i	1.20013	−	0.708639i
$178$	3.70759	−	5.10306i	0.277896	−	0.382491i
$179$	0.392979	+	3.73894i	0.0293726	+	0.279462i	0.999343	+	0.0362392i	$0.0115378\pi$
$179$	0.392979	+	3.73894i	0.0293726	+	0.279462i	−0.969971	+	0.243222i	$0.921795\pi$
$180$	−2.18973	+	2.05063i	−0.163213	+	0.152845i
$181$	−11.8062	+	6.81633i	−0.877550	+	0.506653i	−0.869850	−	0.493317i	$-0.835784\pi$
$181$	−11.8062	+	6.81633i	−0.877550	+	0.506653i	−0.00769990	+	0.999970i	$0.502451\pi$
$182$	4.61904	−	3.35593i	0.342386	−	0.248758i
$183$	3.39742	−	16.7896i	0.251144	−	1.24112i
$184$	3.63333	−	1.18054i	0.267852	−	0.0870305i
$185$	7.79146			0.572840
$186$	8.17513	+	5.11539i	0.599430	+	0.375078i
$187$	2.22410			0.162642
$188$	−8.17122	+	2.65499i	−0.595947	+	0.193635i
$189$	−11.4928	+	21.3280i	−0.835978	+	1.55139i
$190$	5.68983	−	4.13390i	0.412784	−	0.299905i
$191$	2.83469	−	1.63661i	0.205111	−	0.118421i	−0.393926	−	0.919142i	$-0.628883\pi$
$191$	2.83469	−	1.63661i	0.205111	−	0.118421i	0.599037	+	0.800721i	$0.295550\pi$
$192$	0.197892	+	1.72071i	0.0142816	+	0.124181i
$193$	−0.610091	−	5.80463i	−0.0439153	−	0.417826i	−0.994289	−	0.106717i	$-0.965966\pi$
$193$	−0.610091	−	5.80463i	−0.0439153	−	0.417826i	0.950374	−	0.311109i	$-0.100701\pi$
$194$	6.68162	−	9.19646i	0.479712	−	0.660267i
$195$	1.07839	+	1.82633i	0.0772251	+	0.130786i
$196$	−9.86272	+	10.9537i	−0.704480	+	0.782405i
$197$	1.70722	+	0.760102i	0.121634	+	0.0541550i	0.466651	−	0.884441i	$-0.345460\pi$
$197$	1.70722	+	0.760102i	0.121634	+	0.0541550i	−0.345017	+	0.938596i	$0.612127\pi$
$198$	−2.28197	−	1.25862i	−0.162172	−	0.0894461i
$199$	−3.43227	−	16.1476i	−0.243307	−	1.14467i	−0.914878	−	0.403731i	$-0.867713\pi$
$199$	−3.43227	−	16.1476i	−0.243307	−	1.14467i	0.671570	−	0.740941i	$-0.265620\pi$
$200$	−0.406737	−	0.913545i	−0.0287606	−	0.0645974i
$201$	0.417522	+	1.24347i	0.0294497	+	0.0877078i
$202$	5.61959	−	17.2953i	0.395393	−	1.21690i
$203$	23.9005	−	10.6412i	1.67749	−	0.746866i
$204$	2.93494	−	3.32442i	0.205487	−	0.232756i
$205$	4.80868	+	1.02212i	0.335853	+	0.0713878i
$206$	3.61523	−	8.11993i	0.251885	−	0.565742i
$207$	5.92355	+	9.81143i	0.411715	+	0.681942i
$208$	1.21782	+	0.127998i	0.0844406	+	0.00887506i
$209$	4.94266	+	3.59105i	0.341891	+	0.248398i
$210$	−5.46223	−	5.94835i	−0.376930	−	0.410475i
$211$	3.58995	−	6.21798i	0.247143	−	0.428064i	−0.715589	−	0.698521i	$-0.753842\pi$
$211$	3.58995	−	6.21798i	0.247143	−	0.428064i	0.962732	+	0.270458i	$0.0871750\pi$
$212$	0.0570374	+	0.0987916i	0.00391734	+	0.00678503i
$213$	−3.40415	−	1.06937i	−0.233248	−	0.0732721i
$214$	2.99097	+	3.32180i	0.204458	+	0.227074i
$215$	2.98047	+	9.17293i	0.203266	+	0.625589i
$216$	−4.89259	+	1.75003i	−0.332898	+	0.119074i
$217$	−13.9849	+	21.8712i	−0.949360	+	1.48471i
$218$			9.99506i			0.676951i
$219$	−12.6478	+	17.7713i	−0.854659	+	1.20087i
$220$	0.645557	−	0.581262i	0.0435235	−	0.0391887i
$221$	−1.84281	−	2.53641i	−0.123961	−	0.170617i
$222$	12.3816	+	5.36813i	0.830998	+	0.360285i
$223$	5.94134	+	3.43023i	0.397861	+	0.229705i	0.685561	−	0.728015i	$-0.259557\pi$
$223$	5.94134	+	3.43023i	0.397861	+	0.229705i	−0.287699	+	0.957721i	$0.592890\pi$
$224$	−4.63703	+	0.487372i	−0.309825	+	0.0325639i
$225$	2.39209	−	1.81050i	0.159472	−	0.120700i
$226$	−1.38919	+	13.2173i	−0.0924075	+	0.879199i
$227$	19.7967	+	17.8250i	1.31395	+	1.18309i	0.969724	+	0.244204i	$0.0785267\pi$
$227$	19.7967	+	17.8250i	1.31395	+	1.18309i	0.344230	+	0.938885i	$0.388140\pi$
$228$	11.8900	−	2.64913i	0.787434	−	0.175443i
$229$	3.02261	−	14.2203i	0.199740	−	0.939702i	−0.758042	−	0.652206i	$-0.773844\pi$
$229$	3.02261	−	14.2203i	0.199740	−	0.939702i	0.957782	−	0.287496i	$-0.0928228\pi$
$230$	−3.73682	+	0.794286i	−0.246399	+	0.0523737i
$231$	3.44806	−	6.10947i	0.226866	−	0.401974i
$232$	5.33652	+	1.73394i	0.350360	+	0.113839i
$233$	−21.1716	−	6.87905i	−1.38699	−	0.450662i	−0.482032	−	0.876154i	$-0.660101\pi$
$233$	−21.1716	−	6.87905i	−1.38699	−	0.450662i	−0.904962	+	0.425492i	$0.860101\pi$
$234$	0.455400	+	3.64525i	0.0297704	+	0.238297i
$235$	8.40398	−	1.78632i	0.548215	−	0.116527i
$236$	−2.22579	+	10.4715i	−0.144886	+	0.681636i
$237$	−4.27555	−	19.1898i	−0.277727	−	1.24651i
$238$	8.87141	+	7.98785i	0.575048	+	0.517776i
$239$	2.73910	−	26.0608i	0.177178	−	1.68573i	−0.439284	−	0.898348i	$-0.644768\pi$
$239$	2.73910	−	26.0608i	0.177178	−	1.68573i	0.616461	−	0.787385i	$-0.288566\pi$
$240$	−0.0169445	−	1.73197i	−0.00109377	−	0.111798i
$241$	26.1249	−	2.74583i	1.68285	−	0.176875i	0.785703	−	0.618604i	$-0.212302\pi$
$241$	26.1249	−	2.74583i	1.68285	−	0.176875i	0.897148	+	0.441730i	$0.145635\pi$
$242$	−8.87277	−	5.12270i	−0.570363	−	0.329299i
$243$	−8.44500	−	13.1027i	−0.541747	−	0.840542i
$244$	5.81317	+	8.00114i	0.372150	+	0.512221i
$245$	10.9537	−	9.86272i	0.699804	−	0.630106i
$246$	6.93738	+	4.93733i	0.442311	+	0.314793i
$247$		−	8.61212i		−	0.547976i
$248$	−5.36775	+	1.47895i	−0.340852	+	0.0939134i
$249$	−4.81692	+	3.57222i	−0.305260	+	0.226380i
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	15.7438	+	17.4853i	0.993742	+	1.10366i	0.994613	+	0.103662i	$0.0330562\pi$
$251$	15.7438	+	17.4853i	0.993742	+	1.10366i	−0.000870709		1.00000i	$0.500277\pi$
$252$	−4.58189	−	13.2160i	−0.288632	−	0.832530i
$253$	−1.65932	−	2.87402i	−0.104320	−	0.180688i
$254$	7.20676	−	12.4825i	0.452192	−	0.783220i
$255$	−3.26636	+	2.99942i	−0.204547	+	0.187831i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	13.2187	+	1.38935i	0.824563	+	0.0866650i	0.507405	−	0.861708i	$-0.330605\pi$
$257$	13.2187	+	1.38935i	0.824563	+	0.0866650i	0.317158	+	0.948373i	$0.397271\pi$
$258$	−1.58359	+	16.6304i	−0.0985902	+	1.03536i
$259$	−14.7760	+	33.1875i	−0.918139	+	2.06217i
$260$	−1.19777	−	0.254594i	−0.0742824	−	0.0157892i
$261$	−1.43170	+	16.7724i	−0.0886198	+	1.03819i
$262$	3.22115	−	1.43415i	0.199003	−	0.0886018i
$263$	4.69372	−	14.4458i	0.289427	−	0.890766i	−0.695609	−	0.718420i	$-0.744865\pi$
$263$	4.69372	−	14.4458i	0.289427	−	0.890766i	0.985037	−	0.172345i	$-0.0551345\pi$
$264$	1.42635	−	0.478925i	0.0877855	−	0.0294758i
$265$	−0.0463984	−	0.104212i	−0.00285023	−	0.00640172i
$266$	6.81783	+	32.0754i	0.418028	+	1.96667i
$267$	−9.93682	+	4.54115i	−0.608123	+	0.277914i
$268$	−0.691836	−	0.308025i	−0.0422606	−	0.0188156i
$269$	−0.600537	+	0.666964i	−0.0366154	+	0.0406655i	−0.761174	−	0.648547i	$-0.775377\pi$
$269$	−0.600537	+	0.666964i	−0.0366154	+	0.0406655i	0.724559	+	0.689213i	$0.242044\pi$
$270$	5.04871	−	1.22902i	0.307255	−	0.0747961i
$271$	−7.36133	+	10.1320i	−0.447169	+	0.615475i	−0.971786	−	0.235863i	$-0.924208\pi$
$271$	−7.36133	+	10.1320i	−0.447169	+	0.615475i	0.524618	+	0.851338i	$0.324208\pi$
$272$	0.267626	+	2.54629i	0.0162272	+	0.154391i
$273$	−9.82430	+	1.12985i	−0.594594	+	0.0683818i
$274$	9.74826	−	5.62816i	0.588914	−	0.340010i
$275$	−0.702779	+	0.510599i	−0.0423792	+	0.0307903i
$276$	−6.48552	−	1.31236i	−0.390382	−	0.0789948i
$277$	−13.1497	+	4.27259i	−0.790088	+	0.256715i	−0.676142	−	0.736772i	$-0.736349\pi$
$277$	−13.1497	+	4.27259i	−0.790088	+	0.256715i	−0.113946	+	0.993487i	$0.536349\pi$
$278$	−1.23612			−0.0741375
$279$	−7.97660	−	14.6756i	−0.477546	−	0.878606i
$280$	4.66258			0.278642
$281$	−4.54544	+	1.47690i	−0.271158	+	0.0881047i	−0.441440	−	0.897291i	$-0.645532\pi$
$281$	−4.54544	+	1.47690i	−0.271158	+	0.0881047i	0.170282	+	0.985395i	$0.445532\pi$
$282$	14.5857	+	2.95145i	0.868565	+	0.175756i
$283$	0.129955	−	0.0944175i	0.00772500	−	0.00561254i	−0.583916	−	0.811814i	$-0.698480\pi$
$283$	0.129955	−	0.0944175i	0.00772500	−	0.00561254i	0.591641	+	0.806202i	$0.298480\pi$
$284$	1.78408	−	1.03004i	0.105866	−	0.0611216i
$285$	−12.1018	+	1.39178i	−0.716847	+	0.0824416i
$286$	−0.111190	−	1.05790i	−0.00657478	−	0.0625548i
$287$	−13.4731	+	18.5441i	−0.795290	+	1.09462i
$288$	1.16636	−	2.76399i	0.0687282	−	0.162869i
$289$	−6.98893	+	7.76199i	−0.411114	+	0.456588i
$290$	−5.12604	−	2.28226i	−0.301011	−	0.134019i
$291$	−17.9076	+	8.18382i	−1.04976	+	0.479744i
$292$	−2.61832	−	12.3182i	−0.153226	−	0.720871i
$293$	−9.18876	−	20.6383i	−0.536813	−	1.20570i	−0.954800	−	0.297249i	$-0.903931\pi$
$293$	−9.18876	−	20.6383i	−0.536813	−	1.20570i	0.417987	−	0.908453i	$-0.362736\pi$
$294$	24.2019	−	8.12628i	1.41148	−	0.473934i
$295$	3.30816	−	10.1815i	0.192609	−	0.592788i
$296$	−7.11786	+	3.16907i	−0.413717	+	0.184199i
$297$	2.37064	+	3.84116i	0.137559	+	0.222887i
$298$	−22.2316	−	4.72547i	−1.28784	−	0.273739i
$299$	−1.90274	+	4.27363i	−0.110038	+	0.247150i
$300$	−0.164188	+	1.72425i	−0.00947941	+	0.0995497i
$301$	−44.7241	−	4.70070i	−2.57786	−	0.270944i
$302$	−11.1112	−	8.07277i	−0.639378	−	0.464536i
$303$	−23.2003	+	21.3043i	−1.33282	+	1.22390i
$304$	−3.51651	+	6.09077i	−0.201686	+	0.349330i
$305$	−4.94498	−	8.56495i	−0.283149	−	0.490428i
$306$	−7.25717	+	2.51601i	−0.414865	+	0.143831i
$307$	−7.95513	−	8.83507i	−0.454023	−	0.504244i	0.472058	−	0.881567i	$-0.343511\pi$
$307$	−7.95513	−	8.83507i	−0.454023	−	0.504244i	−0.926082	+	0.377323i	$0.876845\pi$
$308$	1.25161	+	3.85206i	0.0713172	+	0.219492i
$309$	−12.3658	+	9.17043i	−0.703465	+	0.521688i
$310$	5.49293	−	0.909765i	0.311978	−	0.0516712i
$311$			2.78248i			0.157780i	0.996883	+	0.0788900i	$0.0251376\pi$
$311$			2.78248i			0.157780i	−0.996883	+	0.0788900i	$0.974862\pi$
$312$	−1.72799	−	1.22981i	−0.0978283	−	0.0696245i
$313$	−19.7760	+	17.8064i	−1.11781	+	1.00648i	−0.117897	+	0.993026i	$0.537615\pi$
$313$	−19.7760	+	17.8064i	−1.11781	+	1.00648i	−0.999910	+	0.0134518i	$0.995718\pi$
$314$	5.20567	+	7.16499i	0.293773	+	0.404344i
$315$	3.17534	+	13.6225i	0.178910	+	0.767543i
$316$	9.83016	+	5.67544i	0.552990	+	0.319269i
$317$	12.3644	−	1.29955i	0.694453	−	0.0729900i	0.249276	−	0.968432i	$-0.419807\pi$
$317$	12.3644	−	1.29955i	0.694453	−	0.0729900i	0.445177	+	0.895443i	$0.353141\pi$
$318$	−0.00193294	−	0.197574i	−0.000108394	−	0.0110794i
$319$	0.509504	−	4.84761i	0.0285267	−	0.271414i
$320$	0.743145	+	0.669131i	0.0415431	+	0.0374055i
$321$	−1.68369	−	7.55685i	−0.0939745	−	0.421782i
$322$	3.70342	−	17.4232i	0.206384	−	0.970958i
$323$	17.6132	−	3.74381i	0.980027	−	0.208311i
$324$	8.86979	+	1.52537i	0.492766	+	0.0847425i
$325$	1.16459	+	0.378400i	0.0646001	+	0.0209898i
$326$	5.64283	+	1.83347i	0.312528	+	0.101546i
$327$	8.50889	−	15.0766i	0.470543	−	0.833735i
$328$	−4.80868	+	1.02212i	−0.265515	+	0.0564370i
$329$	−8.32886	+	39.1842i	−0.459185	+	2.16029i
$330$	−1.46859	+	0.327207i	−0.0808434	+	0.0180122i
$331$	1.77779	+	1.60073i	0.0977162	+	0.0879841i	0.716541	−	0.697545i	$-0.245724\pi$
$331$	1.77779	+	1.60073i	0.0977162	+	0.0879841i	−0.618825	+	0.785529i	$0.712391\pi$
$332$	0.361913	−	3.44338i	0.0198626	−	0.188980i
$333$	−14.1065	−	18.6379i	−0.773030	−	1.02135i
$334$	−4.41036	+	0.463547i	−0.241324	+	0.0253642i
$335$	0.655849	+	0.378654i	0.0358328	+	0.0206881i
$336$	7.40941	+	3.21240i	0.404216	+	0.175251i
$337$	−7.86275	−	10.8222i	−0.428311	−	0.589520i	0.539253	−	0.842144i	$-0.318707\pi$
$337$	−7.86275	−	10.8222i	−0.428311	−	0.589520i	−0.967565	+	0.252624i	$0.918707\pi$
$338$	8.54656	−	7.69536i	0.464872	−	0.418572i
$339$	13.3474	−	18.7543i	0.724933	−	1.01859i
$340$		−	2.56031i		−	0.138853i
$341$	2.22613	+	4.29386i	0.120552	+	0.232526i
$342$	−20.1901	−	6.12612i	−1.09176	−	0.331263i
$343$	11.1513	+	34.3203i	0.602116	+	1.85312i
$344$	−6.45376	−	7.16762i	−0.347963	−	0.386452i
$345$	6.31281	+	1.98309i	0.339870	+	0.106766i
$346$	−7.61282	−	13.1858i	−0.409268	−	0.708873i
$347$	6.93837	−	12.0176i	0.372471	−	0.645139i	−0.617474	−	0.786592i	$-0.711844\pi$
$347$	6.93837	−	12.0176i	0.372471	−	0.645139i	0.989945	+	0.141452i	$0.0451771\pi$
$348$	−6.57349	−	7.15851i	−0.352376	−	0.383736i
$349$	4.88477	+	3.54899i	0.261476	+	0.189973i	0.710797	−	0.703397i	$-0.248334\pi$
$349$	4.88477	+	3.54899i	0.261476	+	0.189973i	−0.449322	+	0.893370i	$0.648334\pi$
$350$	−4.63703	−	0.487372i	−0.247860	−	0.0260511i
$351$	2.41631	−	5.88618i	0.128973	−	0.314181i
$352$	−0.353325	+	0.793581i	−0.0188323	+	0.0422980i
$353$	−14.8127	−	3.14853i	−0.788399	−	0.167579i	−0.203919	−	0.978988i	$-0.565368\pi$
$353$	−14.8127	−	3.14853i	−0.788399	−	0.167579i	−0.584480	+	0.811408i	$0.698701\pi$
$354$	12.2719	−	13.9004i	0.652242	−	0.738797i
$355$	−1.88198	+	0.837910i	−0.0998849	+	0.0444716i
$356$	1.94920	−	5.99901i	0.103307	−	0.317947i
$357$	−6.58150	−	19.6012i	−0.348330	−	1.03741i
$358$	1.52914	+	3.43451i	0.0808177	+	0.181519i
$359$	−0.0614367	−	0.289037i	−0.00324251	−	0.0152548i	0.976497	−	0.215533i	$-0.0691488\pi$
$359$	−0.0614367	−	0.289037i	−0.00324251	−	0.0152548i	−0.979739	+	0.200278i	$0.935815\pi$
$360$	−1.44888	+	2.62693i	−0.0763628	+	0.138451i
$361$	27.8296	+	12.3905i	1.46472	+	0.652134i
$362$	−9.12202	+	10.1310i	−0.479443	+	0.532475i
$363$	9.02269	+	15.2805i	0.473568	+	0.802021i
$364$	3.35593	−	4.61904i	0.175899	−	0.242104i
$365$	1.31637	+	12.5245i	0.0689021	+	0.655560i
$366$	−1.95714	−	17.0177i	−0.102301	−	0.889531i
$367$	−4.12072	+	2.37910i	−0.215100	+	0.124188i	−0.603679	−	0.797227i	$-0.706299\pi$
$367$	−4.12072	+	2.37910i	−0.215100	+	0.124188i	0.388580	+	0.921415i	$0.372966\pi$
$368$	3.09069	−	2.24552i	0.161113	−	0.117056i
$369$	−6.26114	−	13.3533i	−0.325942	−	0.695147i
$370$	7.41012	−	2.40769i	0.385234	−	0.125170i
$371$	0.531882			0.0276139
$372$	9.35576	+	2.33877i	0.485073	+	0.121259i
$373$	−2.15281			−0.111468			−0.0557341	−	0.998446i	$-0.517750\pi$
$373$	−2.15281			−0.111468			−0.0557341	+	0.998446i	$0.517750\pi$
$374$	2.11525	−	0.687285i	0.109377	−	0.0355387i
$375$	0.343522	−	1.69764i	0.0177394	−	0.0876659i
$376$	−6.95085	+	5.05009i	−0.358463	+	0.260439i
$377$	−5.95046	+	3.43550i	−0.306464	+	0.176937i
$378$	−4.33958	+	23.8356i	−0.223204	+	1.22597i
$379$	−1.54016	−	14.6537i	−0.0791128	−	0.752708i	−0.960117	−	0.279599i	$-0.909798\pi$
$379$	−1.54016	−	14.6537i	−0.0791128	−	0.752708i	0.881004	−	0.473109i	$-0.156868\pi$
$380$	4.13390	−	5.68983i	0.212065	−	0.291882i
$381$	−21.4971	+	12.6934i	−1.10133	+	0.650302i
$382$	2.19021	−	2.43247i	0.112061	−	0.124456i
$383$	−24.3409	−	10.8373i	−1.24376	−	0.553758i	−0.323933	−	0.946080i	$-0.605005\pi$
$383$	−24.3409	−	10.8373i	−1.24376	−	0.553758i	−0.919828	+	0.392322i	$0.871672\pi$
$384$	0.719934	+	1.57534i	0.0367390	+	0.0803912i
$385$	−0.842105	−	3.96179i	−0.0429176	−	0.201912i
$386$	−2.37396	−	5.33200i	−0.120831	−	0.271392i
$387$	16.5463	−	23.7371i	0.841096	−	1.20663i
$388$	3.51273	−	10.8111i	0.178332	−	0.548850i
$389$	1.52527	−	0.679094i	0.0773343	−	0.0344314i	−0.367705	−	0.929942i	$-0.619856\pi$
$389$	1.52527	−	0.679094i	0.0773343	−	0.0344314i	0.445039	+	0.895511i	$0.353190\pi$
$390$	1.58998	+	1.40370i	0.0805116	+	0.0710791i
$391$	−9.56744	−	2.03362i	−0.483846	−	0.102845i
$392$	−5.99514	+	13.4653i	−0.302800	+	0.680101i
$393$	−6.07968	−	0.578925i	−0.306679	−	0.0292029i
$394$	1.85854	+	0.195341i	0.0936321	+	0.00984113i
$395$	−9.18306	−	6.67188i	−0.462050	−	0.335699i
$396$	−2.55921	−	0.491851i	−0.128605	−	0.0247165i
$397$	−12.5616	+	21.7573i	−0.630447	+	1.09197i	0.357013	+	0.934099i	$0.383795\pi$
$397$	−12.5616	+	21.7573i	−0.630447	+	1.09197i	−0.987460	+	0.157867i	$0.949538\pi$
$398$	−8.25416	−	14.2966i	−0.413744	−	0.716625i
$399$	17.0221	−	54.1866i	0.852169	−	2.71272i
$400$	−0.669131	−	0.743145i	−0.0334565	−	0.0371572i
$401$	11.1442	+	34.2984i	0.556516	+	1.71278i	0.691906	+	0.721987i	$0.256771\pi$
$401$	11.1442	+	34.2984i	0.556516	+	1.71278i	−0.135390	+	0.990792i	$0.543229\pi$
$402$	0.781341	+	1.05359i	0.0389698	+	0.0525484i
$403$	3.05232	−	6.09646i	0.152047	−	0.303686i
$404$		−	18.1854i		−	0.904757i
$405$	−8.66176	−	2.44416i	−0.430406	−	0.121451i
$406$	19.4425	−	17.5061i	0.964913	−	0.868811i
$407$	3.97831	+	5.47568i	0.197198	+	0.271419i
$408$	1.76399	−	4.06865i	0.0873307	−	0.201428i
$409$	16.8910	+	9.75203i	0.835207	+	0.482207i	0.855632	−	0.517584i	$-0.173169\pi$
$409$	16.8910	+	9.75203i	0.835207	+	0.482207i	−0.0204250	+	0.999791i	$0.506502\pi$
$410$	4.88918	−	0.513874i	0.241459	−	0.0253784i
$411$	−19.4956	+	0.190733i	−0.961646	+	0.00940818i
$412$	0.929088	−	8.83968i	0.0457729	−	0.435500i
$413$	37.0940	+	33.3996i	1.82528	+	1.64349i
$414$	8.66553	+	7.50075i	0.425888	+	0.368642i
$415$	−0.719862	+	3.38668i	−0.0353366	+	0.166246i
$416$	1.19777	−	0.254594i	0.0587254	−	0.0124825i
$417$	1.86456	+	1.05232i	0.0913080	+	0.0515323i
$418$	5.81044	+	1.88793i	0.284198	+	0.0923415i
$419$	−34.1565	−	11.0981i	−1.66866	−	0.542179i	−0.685997	−	0.727604i	$-0.740634\pi$
$419$	−34.1565	−	11.0981i	−1.66866	−	0.542179i	−0.982658	+	0.185425i	$0.940634\pi$
$420$	−7.03303	−	3.96930i	−0.343177	−	0.193682i
$421$	37.1038	−	7.88667i	1.80833	−	0.384373i	0.824845	−	0.565359i	$-0.191262\pi$
$421$	37.1038	−	7.88667i	1.80833	−	0.384373i	0.983486	+	0.180986i	$0.0579290\pi$
$422$	1.49279	−	7.02301i	0.0726677	−	0.341875i
$423$	−19.4885	−	16.8689i	−0.947562	−	0.820194i
$424$	0.0847740	+	0.0763309i	0.00411699	+	0.00370696i
$425$	−0.267626	+	2.54629i	−0.0129818	+	0.123513i
$426$	−3.56799	+	0.0349071i	−0.172870	+	0.00169125i
$427$	45.8600	−	4.82008i	2.21932	−	0.233260i
$428$	3.87107	+	2.23496i	0.187115	+	0.108031i
$429$	−0.732881	+	1.69039i	−0.0353838	+	0.0816129i
$430$	5.66918	+	7.80296i	0.273392	+	0.376292i
$431$	−12.3383	+	11.1094i	−0.594314	+	0.535123i	−0.910465	−	0.413586i	$-0.864276\pi$
$431$	−12.3383	+	11.1094i	−0.594314	+	0.535123i	0.316151	+	0.948709i	$0.397609\pi$
$432$	−4.11234	+	3.17627i	−0.197855	+	0.152818i
$433$		−	14.1567i		−	0.680329i	−0.940366	−	0.340165i	$-0.889517\pi$
$433$		−	14.1567i		−	0.680329i	0.940366	−	0.340165i	$-0.110483\pi$
$434$	−6.54190	+	25.1223i	−0.314021	+	1.20591i
$435$	5.78921	+	7.80641i	0.277571	+	0.374289i
$436$	3.08864	+	9.50587i	0.147919	+	0.455249i
$437$	−17.9784	−	19.9670i	−0.860023	−	0.955152i
$438$	−6.53716	+	20.8099i	−0.312358	+	0.994333i
$439$	−4.54416	−	7.87071i	−0.216881	−	0.375649i	0.736972	−	0.675923i	$-0.236255\pi$
$439$	−4.54416	−	7.87071i	−0.216881	−	0.375649i	−0.953853	+	0.300275i	$0.902922\pi$
$440$	0.434341	−	0.752301i	0.0207064	−	0.0358646i
$441$	−43.4241	−	8.34562i	−2.06782	−	0.397410i
$442$	−2.53641	−	1.84281i	−0.120645	−	0.0876535i
$443$	0.986515	+	0.103687i	0.0468707	+	0.00492631i	0.127935	−	0.991783i	$-0.459165\pi$
$443$	0.986515	+	0.103687i	0.0468707	+	0.00492631i	−0.0810641	+	0.996709i	$0.525832\pi$
$444$	13.4344	+	1.27927i	0.637570	+	0.0607113i
$445$	−2.56558	+	5.76240i	−0.121620	+	0.273164i
$446$	6.71055	+	1.42637i	0.317754	+	0.0675406i
$447$	29.5113	+	26.0539i	1.39584	+	1.23231i
$448$	−4.25947	+	1.89644i	−0.201241	+	0.0895984i
$449$	−7.25903	+	22.3410i	−0.342575	+	1.05434i	0.620295	+	0.784369i	$0.287013\pi$
$449$	−7.25903	+	22.3410i	−0.342575	+	1.05434i	−0.962869	+	0.269968i	$0.912987\pi$
$450$	1.71553	−	2.46109i	0.0808710	−	0.116017i
$451$	1.73699	+	3.90133i	0.0817915	+	0.183707i
$452$	2.76316	+	12.9996i	0.129968	+	0.611452i
$453$	9.88773	+	21.6360i	0.464566	+	1.01655i
$454$	24.3360	+	10.8351i	1.14215	+	0.508516i
$455$	−3.82037	+	4.24295i	−0.179102	+	0.198913i
$456$	10.4894	−	6.19368i	0.491213	−	0.290046i
$457$	0.376629	−	0.518385i	0.0176179	−	0.0242490i	−0.800117	−	0.599844i	$-0.795229\pi$
$457$	0.376629	−	0.518385i	0.0176179	−	0.0242490i	0.817735	+	0.575595i	$0.195229\pi$
$458$	−1.51963	−	14.4583i	−0.0710076	−	0.675593i
$459$	13.0886	+	2.38295i	0.610925	+	0.111227i
$460$	−3.30848	+	1.91015i	−0.154259	+	0.0890613i
$461$	28.4844	−	20.6951i	1.32665	−	0.963868i	0.326827	−	0.945084i	$-0.394021\pi$
$461$	28.4844	−	20.6951i	1.32665	−	0.963868i	0.999824	−	0.0187836i	$-0.00597935\pi$
$462$	1.39137	−	6.87596i	0.0647323	−	0.319899i
$463$	5.95894	−	1.93618i	0.276935	−	0.0899817i	−0.167257	−	0.985913i	$-0.553491\pi$
$463$	5.95894	−	1.93618i	0.276935	−	0.0899817i	0.444192	+	0.895932i	$0.353491\pi$
$464$	5.61115			0.260491
$465$	−9.06004	−	3.30390i	−0.420149	−	0.153215i
$466$	−22.2611			−1.03122
$467$	−29.8707	+	9.70556i	−1.38225	+	0.449120i	−0.903408	−	0.428782i	$-0.858943\pi$
$467$	−29.8707	+	9.70556i	−1.38225	+	0.449120i	−0.478841	+	0.877902i	$0.658943\pi$
$468$	1.55955	+	3.32611i	0.0720904	+	0.153749i
$469$	−2.85665	+	2.07548i	−0.131908	+	0.0958366i
$470$	7.44065	−	4.29586i	0.343212	−	0.198153i
$471$	−1.75261	−	15.2393i	−0.0807561	−	0.702191i
$472$	1.11902	+	10.6468i	0.0515072	+	0.490058i
$473$	−4.92472	+	6.77830i	−0.226439	+	0.311666i
$474$	−9.99625	−	16.9293i	−0.459143	−	0.777591i
$475$	−4.70601	+	5.22655i	−0.215926	+	0.239811i
$476$	10.9056	+	4.85548i	0.499857	+	0.222551i
$477$	−0.165281	+	0.299666i	−0.00756769	+	0.0137208i
$478$	−5.44819	−	25.6317i	−0.249195	−	1.17237i
$479$	−1.60604	−	3.60724i	−0.0733821	−	0.164819i	0.873130	−	0.487488i	$-0.162087\pi$
$479$	−1.60604	−	3.60724i	−0.0733821	−	0.164819i	−0.946512	+	0.322669i	$0.895420\pi$
$480$	−0.551323	−	1.64196i	−0.0251643	−	0.0749450i
$481$	2.94829	−	9.07390i	0.134430	−	0.413734i
$482$	23.9977	−	10.6845i	1.09307	−	0.486664i
$483$	−20.4188	+	23.1284i	−0.929087	+	1.05238i
$484$	−10.0215	−	2.13014i	−0.455523	−	0.0968244i
$485$	−4.62356	+	10.3847i	−0.209945	+	0.471544i
$486$	−12.0806	−	9.85180i	−0.547989	−	0.446887i
$487$	0.431094	+	0.0453098i	0.0195347	+	0.00205318i	0.114291	−	0.993447i	$-0.463540\pi$
$487$	0.431094	+	0.0453098i	0.0195347	+	0.00205318i	−0.0947561	+	0.995501i	$0.530207\pi$
$488$	8.00114	+	5.81317i	0.362195	+	0.263150i
$489$	−6.95080	−	7.56940i	−0.314326	−	0.342300i
$490$	7.36980	−	12.7649i	0.332934	−	0.576658i
$491$	20.5882	+	35.6598i	0.929132	+	1.60930i	0.784777	+	0.619778i	$0.212777\pi$
$491$	20.5882	+	35.6598i	0.929132	+	1.60930i	0.144355	+	0.989526i	$0.453889\pi$
$492$	8.12356	+	2.55192i	0.366238	+	0.115049i
$493$	−9.61293	−	10.6762i	−0.432945	−	0.480834i
$494$	−2.66129	−	8.19061i	−0.119737	−	0.368513i
$495$	2.49378	+	0.756667i	0.112087	+	0.0340097i
$496$	−4.64801	+	3.06529i	−0.208702	+	0.137636i
$497$		−	9.60527i		−	0.430855i
$498$	−3.47729	+	4.88589i	−0.155821	+	0.218942i
$499$	3.81835	−	3.43806i	0.170933	−	0.153909i	−0.579224	−	0.815168i	$-0.696645\pi$
$499$	3.81835	−	3.43806i	0.170933	−	0.153909i	0.750157	+	0.661260i	$0.229978\pi$
$500$	0.587785	+	0.809017i	0.0262866	+	0.0361803i
$501$	7.04721	+	3.05536i	0.314846	+	0.136504i
$502$	20.3765	+	11.7644i	0.909449	+	0.525071i
$503$	14.5269	−	1.52684i	0.647724	−	0.0680785i	0.225031	−	0.974352i	$-0.427752\pi$
$503$	14.5269	−	1.52684i	0.647724	−	0.0680785i	0.422693	+	0.906273i	$0.361085\pi$
$504$	−8.44161	−	11.1533i	−0.376019	−	0.496807i
$505$	−1.90089	+	18.0858i	−0.0845885	+	0.804806i
$506$	−2.46623	−	2.22060i	−0.109637	−	0.0987177i
$507$	−19.4428	+	4.33191i	−0.863484	+	0.192387i
$508$	2.99674	−	14.0986i	0.132959	−	0.625522i
$509$	6.02541	−	1.28074i	0.267072	−	0.0567678i	−0.0724293	−	0.997374i	$-0.523075\pi$
$509$	6.02541	−	1.28074i	0.267072	−	0.0567678i	0.339501	+	0.940606i	$0.389742\pi$
$510$	−2.17962	+	3.86198i	−0.0965152	+	0.171011i
$511$	−55.8440	−	18.1448i	−2.47039	−	0.802680i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	25.2395	+	26.4287i	1.11435	+	1.16685i
$514$	13.0011	−	2.76347i	0.573454	−	0.121891i
$515$	−1.84800	+	8.69414i	−0.0814324	+	0.383109i
$516$	3.63298	+	16.3058i	0.159933	+	0.717822i
$517$	5.54645	+	4.99405i	0.243933	+	0.219638i
$518$	−3.79734	+	36.1293i	−0.166846	+	1.58743i
$519$	0.257992	+	26.3703i	0.0113246	+	1.15753i
$520$	−1.21782	+	0.127998i	−0.0534049	+	0.00561308i
$521$	−16.4739	−	9.51122i	−0.721735	−	0.416694i	0.0936558	−	0.995605i	$-0.470145\pi$
$521$	−16.4739	−	9.51122i	−0.721735	−	0.416694i	−0.815391	+	0.578911i	$0.803478\pi$
$522$	3.82135	+	16.3940i	0.167256	+	0.717544i
$523$	1.91090	+	2.63012i	0.0835576	+	0.115007i	0.848750	−	0.528795i	$-0.177356\pi$
$523$	1.91090	+	2.63012i	0.0835576	+	0.115007i	−0.765192	+	0.643802i	$0.777356\pi$
$524$	2.62032	−	2.35934i	0.114469	−	0.103068i
$525$	6.57960	+	4.68270i	0.287157	+	0.204370i
$526$		−	15.1892i		−	0.662281i
$527$	13.7952	+	3.59229i	0.600927	+	0.156483i
$528$	1.20854	−	0.896249i	0.0525949	−	0.0390042i
$529$	−2.59737	−	7.99388i	−0.112929	−	0.347560i
$530$	−0.0763309	−	0.0847740i	−0.00331560	−	0.00368235i
$531$	−30.3444	+	10.5202i	−1.31684	+	0.456537i
$532$	16.3960	+	28.3987i	0.710856	+	1.23124i
$533$	3.00996	−	5.21340i	0.130376	−	0.225817i
$534$	−8.04718	+	7.38954i	−0.348236	+	0.319777i
$535$	−3.61625	−	2.62736i	−0.156344	−	0.113591i
$536$	−0.753160	−	0.0791603i	−0.0325316	−	0.00341921i
$537$	0.617272	−	6.48239i	0.0266372	−	0.279736i
$538$	−0.365041	+	0.819896i	−0.0157381	+	0.0353482i
$539$	12.5242	+	2.66211i	0.539457	+	0.114665i
$540$	4.42182	−	2.72901i	0.190285	−	0.117438i
$541$	0.493101	−	0.219543i	0.0212001	−	0.00943888i	−0.396109	−	0.918203i	$-0.629640\pi$
$541$	0.493101	−	0.219543i	0.0212001	−	0.00943888i	0.417309	+	0.908765i	$0.362973\pi$
$542$	−3.87008	+	11.9109i	−0.166234	+	0.511616i
$543$	22.3843	−	7.51599i	0.960603	−	0.322542i
$544$	1.04137	+	2.33896i	0.0446485	+	0.100282i
$545$	−2.07809	−	9.77665i	−0.0890156	−	0.418785i
$546$	−8.99432	+	4.11043i	−0.384921	+	0.175910i
$547$	−35.1596	−	15.6541i	−1.50332	−	0.669320i	−0.520494	−	0.853865i	$-0.674252\pi$
$547$	−35.1596	−	15.6541i	−1.50332	−	0.669320i	−0.982824	+	0.184545i	$0.940919\pi$
$548$	7.53195	−	8.36507i	0.321749	−	0.357338i
$549$	−11.5352	+	27.3357i	−0.492311	+	1.16666i
$550$	−0.510599	+	0.702779i	−0.0217720	+	0.0299666i
$551$	−4.12504	−	39.2471i	−0.175732	−	1.67198i
$552$	−6.57363	+	0.756007i	−0.279792	+	0.0321778i
$553$	45.8339	−	26.4622i	1.94905	−	1.12529i
$554$	−11.1858	+	8.12695i	−0.475239	+	0.345281i
$555$	−13.2271	−	2.67654i	−0.561460	−	0.113613i
$556$	−1.17562	+	0.381982i	−0.0498574	+	0.0161996i
$557$	−28.1529			−1.19288			−0.596439	−	0.802659i	$-0.703418\pi$
$557$	−28.1529			−1.19288			−0.596439	+	0.802659i	$0.703418\pi$
$558$	−12.1212	−	11.4924i	−0.513132	−	0.486514i
$559$	11.8106			0.499533
$560$	4.43437	−	1.44082i	0.187386	−	0.0608855i
$561$	−3.77573	−	0.764028i	−0.159411	−	0.0322573i
$562$	−3.86658	+	2.80924i	−0.163102	+	0.118501i
$563$	−31.6236	+	18.2579i	−1.33278	+	0.769478i	−0.985724	−	0.168368i	$-0.946150\pi$
$563$	−31.6236	+	18.2579i	−1.33278	+	0.769478i	−0.347051	+	0.937846i	$0.612817\pi$
$564$	14.7839	−	1.70023i	0.622513	−	0.0715927i
$565$	−1.38919	−	13.2173i	−0.0584436	−	0.556054i
$566$	0.0944175	−	0.129955i	0.00396866	−	0.00546240i
$567$	26.8373	−	32.2594i	1.12706	−	1.35477i
$568$	1.37846	−	1.53094i	0.0578390	−	0.0642367i
$569$	−22.7409	−	10.1249i	−0.953348	−	0.424458i	−0.129696	−	0.991554i	$-0.541400\pi$
$569$	−22.7409	−	10.1249i	−0.953348	−	0.424458i	−0.823652	+	0.567096i	$0.808067\pi$
$570$	−11.0794	+	5.06331i	−0.464064	+	0.212079i
$571$	4.02840	+	18.9522i	0.168583	+	0.793123i	0.978446	+	0.206503i	$0.0662084\pi$
$571$	4.02840	+	18.9522i	0.168583	+	0.793123i	−0.809862	+	0.586620i	$0.800458\pi$
$572$	−0.432656	−	0.971762i	−0.0180903	−	0.0406314i
$573$	−5.37450	+	1.80460i	−0.224523	+	0.0753882i
$574$	−7.08321	+	21.7999i	−0.295647	+	0.909909i
$575$	3.49002	−	1.55386i	0.145544	−	0.0648004i
$576$	0.255152	−	2.98913i	0.0106313	−	0.124547i
$577$	5.27651	+	1.12156i	0.219664	+	0.0466911i	0.316429	−	0.948616i	$-0.397516\pi$
$577$	5.27651	+	1.12156i	0.219664	+	0.0466911i	−0.0967648	+	0.995307i	$0.530849\pi$
$578$	−4.24828	+	9.54179i	−0.176705	+	0.396886i
$579$	−0.958301	+	10.0638i	−0.0398256	+	0.418236i
$580$	−5.58041	−	0.586525i	−0.231714	−	0.0243541i
$581$	−13.0603	−	9.48887i	−0.541833	−	0.393665i
$582$	−14.5022	+	13.3170i	−0.601135	+	0.552008i
$583$	0.0495474	−	0.0858186i	0.00205204	−	0.00355424i
$584$	−6.29672	−	10.9062i	−0.260560	−	0.451303i
$585$	−1.20334	−	3.47090i	−0.0497519	−	0.143504i
$586$	−15.1166	−	16.7887i	−0.624461	−	0.693535i
$587$	−1.11231	−	3.42333i	−0.0459098	−	0.141296i	0.925474	−	0.378811i	$-0.123667\pi$
$587$	−1.11231	−	3.42333i	−0.0459098	−	0.141296i	−0.971384	+	0.237515i	$0.923667\pi$
$588$	20.5062	−	15.2074i	0.845662	−	0.627141i
$589$	24.8571	+	30.2570i	1.02422	+	1.24672i
$590$		−	10.7054i		−	0.440736i
$591$	−2.63713	−	1.87685i	−0.108477	−	0.0772032i
$592$	−5.79019	+	5.21351i	−0.237975	+	0.214274i
$593$	2.48623	+	3.42200i	0.102097	+	0.140525i	0.857009	−	0.515302i	$-0.172320\pi$
$593$	2.48623	+	3.42200i	0.102097	+	0.140525i	−0.754911	+	0.655827i	$0.772320\pi$
$594$	3.44160	+	2.92059i	0.141211	+	0.119833i
$595$	−10.3383	−	5.96883i	−0.423830	−	0.244698i
$596$	−22.6038	+	2.37575i	−0.925887	+	0.0973146i
$597$	0.279726	+	28.5919i	0.0114484	+	1.17019i
$598$	−0.488991	+	4.65244i	−0.0199963	+	0.190252i
$599$	5.23221	+	4.71111i	0.213782	+	0.192491i	0.769064	−	0.639172i	$-0.220723\pi$
$599$	5.23221	+	4.71111i	0.213782	+	0.192491i	−0.555281	+	0.831663i	$0.687389\pi$
$600$	0.376671	+	1.69060i	0.0153775	+	0.0690183i
$601$	−3.39396	+	15.9673i	−0.138443	+	0.651321i	0.853122	+	0.521711i	$0.174706\pi$
$601$	−3.39396	+	15.9673i	−0.138443	+	0.651321i	−0.991565	+	0.129610i	$0.958627\pi$
$602$	−43.9878	+	9.34989i	−1.79281	+	0.381073i
$603$	−0.281642	−	2.25440i	−0.0114694	−	0.0918063i
$604$	−13.0620	−	4.24410i	−0.531486	−	0.172690i
$605$	9.74395	+	3.16600i	0.396148	+	0.128716i
$606$	−15.4814	+	27.4308i	−0.628889	+	1.11430i
$607$	5.01573	−	1.06613i	0.203582	−	0.0432728i	−0.104992	−	0.994473i	$-0.533482\pi$
$607$	5.01573	−	1.06613i	0.203582	−	0.0432728i	0.308574	+	0.951200i	$0.400148\pi$
$608$	−1.46225	+	6.87933i	−0.0593019	+	0.278994i
$609$	−44.2301	+	9.85461i	−1.79229	+	0.399329i
$610$	−7.34967	−	6.61767i	−0.297579	−	0.267942i
$611$	1.09972	−	10.4632i	0.0444901	−	0.423295i
$612$	−6.12449	+	4.63546i	−0.247568	+	0.187377i
$613$	43.8992	−	4.61399i	1.77307	−	0.186357i	0.839166	−	0.543875i	$-0.183043\pi$
$613$	43.8992	−	4.61399i	1.77307	−	0.186357i	0.933907	+	0.357517i	$0.116377\pi$
$614$	−10.2960	−	5.94438i	−0.415511	−	0.239896i
$615$	−7.81231	−	3.38708i	−0.315023	−	0.136580i
$616$	2.38071	+	3.27676i	0.0959214	+	0.132024i
$617$	20.2178	−	18.2042i	0.813938	−	0.732873i	−0.152906	−	0.988241i	$-0.548863\pi$
$617$	20.2178	−	18.2042i	0.813938	−	0.732873i	0.966844	+	0.255368i	$0.0821965\pi$
$618$	−8.92674	+	12.5428i	−0.359086	+	0.504547i
$619$		−	26.1180i		−	1.04977i	−0.851173	−	0.524885i	$-0.824108\pi$
$619$		−	26.1180i		−	1.04977i	0.851173	−	0.524885i	$-0.175892\pi$
$620$	4.94296	−	2.56265i	0.198514	−	0.102918i
$621$	−6.68564	−	18.6912i	−0.268285	−	0.750051i
$622$	0.859834	+	2.64630i	0.0344762	+	0.106107i
$623$	−19.6793	−	21.8561i	−0.788435	−	0.875646i
$624$	−2.02345	−	0.635643i	−0.0810029	−	0.0254461i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−13.3056	+	23.0460i	−0.531800	+	0.921104i
$627$	−7.15726	−	7.79423i	−0.285834	−	0.311272i
$628$	7.16499	+	5.20567i	0.285914	+	0.207729i
$629$	19.8393	+	2.08520i	0.791045	+	0.0831422i
$630$	7.22953	+	11.9746i	0.288031	+	0.477078i
$631$	7.18246	−	16.1321i	0.285929	−	0.642207i	−0.712288	−	0.701887i	$-0.752341\pi$
$631$	7.18246	−	16.1321i	0.285929	−	0.642207i	0.998218	+	0.0596794i	$0.0190078\pi$
$632$	11.1028	+	2.35998i	0.441647	+	0.0938751i
$633$	−8.23048	+	9.32269i	−0.327132	+	0.370544i
$634$	11.3576	−	5.05675i	0.451070	−	0.200829i
$635$	−4.45402	+	13.7081i	−0.176753	+	0.543988i
$636$	−0.0628920	−	0.187306i	−0.00249383	−	0.00742719i
$637$	−7.34121	−	16.4886i	−0.290869	−	0.653303i
$638$	−1.01343	−	4.76779i	−0.0401219	−	0.188759i
$639$	5.41168	+	2.98481i	0.214083	+	0.118077i
$640$	0.913545	+	0.406737i	0.0361111	+	0.0160777i
$641$	32.0977	−	35.6481i	1.26778	−	1.40802i	0.395908	−	0.918290i	$-0.370430\pi$
$641$	32.0977	−	35.6481i	1.26778	−	1.40802i	0.871876	−	0.489727i	$-0.162903\pi$
$642$	−3.93648	−	6.66670i	−0.155360	−	0.263114i
$643$	12.9807	−	17.8665i	0.511910	−	0.704584i	−0.472330	−	0.881422i	$-0.656587\pi$
$643$	12.9807	−	17.8665i	0.511910	−	0.704584i	0.984240	+	0.176838i	$0.0565868\pi$
$644$	−1.86191	−	17.7149i	−0.0733695	−	0.698064i
$645$	−1.90866	−	16.5962i	−0.0751535	−	0.653475i
$646$	15.5943	−	9.00336i	0.613549	−	0.354233i
$647$	−14.8380	+	10.7805i	−0.583343	+	0.423824i	−0.839928	−	0.542698i	$-0.817403\pi$
$647$	−14.8380	+	10.7805i	−0.583343	+	0.423824i	0.256585	+	0.966522i	$0.417403\pi$
$648$	8.90704	−	1.29021i	0.349902	−	0.0506842i
$649$	8.84447	−	2.87374i	0.347176	−	0.112804i
$650$	1.22453			0.0480299
$651$	31.2547	−	32.3254i	1.22497	−	1.26693i
$652$	5.93322			0.232363
$653$	−28.3984	+	9.22720i	−1.11131	+	0.361088i	−0.806447	−	0.591307i	$-0.798612\pi$
$653$	−28.3984	+	9.22720i	−1.11131	+	0.361088i	−0.304868	+	0.952395i	$0.598612\pi$
$654$	3.43352	−	16.9680i	0.134261	−	0.663503i
$655$	−2.85258	+	2.07252i	−0.111460	+	0.0809801i
$656$	−4.25748	+	2.45806i	−0.166227	+	0.0959710i
$657$	27.5763	−	25.8244i	1.07585	−	1.00751i
$658$	4.18737	+	39.8401i	0.163241	+	1.55313i
$659$	−1.00751	+	1.38673i	−0.0392472	+	0.0540191i	−0.828190	−	0.560448i	$-0.810629\pi$
$659$	−1.00751	+	1.38673i	−0.0392472	+	0.0540191i	0.788942	+	0.614467i	$0.210629\pi$
$660$	−1.29560	+	0.765013i	−0.0504312	+	0.0297781i
$661$	15.1732	−	16.8515i	0.590169	−	0.655449i	−0.371894	−	0.928275i	$-0.621292\pi$
$661$	15.1732	−	16.8515i	0.590169	−	0.655449i	0.962063	+	0.272826i	$0.0879583\pi$
$662$	2.18543	+	0.973017i	0.0849392	+	0.0378174i
$663$	2.25712	+	4.93896i	0.0876593	+	0.191813i
$664$	−0.719862	−	3.38668i	−0.0279361	−	0.131429i
$665$	−13.3377	−	29.9570i	−0.517214	−	1.16168i
$666$	−19.1755	−	13.3665i	−0.743034	−	0.517942i
$667$	−6.62418	+	20.3871i	−0.256489	+	0.789393i
$668$	−4.05126	+	1.80373i	−0.156748	+	0.0697886i
$669$	−8.90791	−	7.86429i	−0.344400	−	0.304051i
$670$	0.740760	+	0.157453i	0.0286181	+	0.00608295i
$671$	3.49437	−	7.84848i	0.134899	−	0.302987i
$672$	8.03945	+	0.765540i	0.310129	+	0.0295313i
$673$	−26.5778	−	2.79344i	−1.02450	−	0.107679i	−0.422652	−	0.906292i	$-0.638901\pi$
$673$	−26.5778	−	2.79344i	−1.02450	−	0.107679i	−0.601845	+	0.798613i	$0.705568\pi$
$674$	−10.8222	−	7.86275i	−0.416854	−	0.302862i
$675$	−4.68286	+	2.25185i	−0.180243	+	0.0866739i
$676$	5.75027	−	9.95975i	0.221164	−	0.383067i
$677$	2.26108	+	3.91630i	0.0869002	+	0.150516i	0.906199	−	0.422851i	$-0.138971\pi$
$677$	2.26108	+	3.91630i	0.0869002	+	0.150516i	−0.819299	+	0.573366i	$0.805637\pi$
$678$	6.89877	−	21.9610i	0.264946	−	0.843406i
$679$	−35.4650	−	39.3878i	−1.36102	−	1.51157i
$680$	−0.791180	−	2.43500i	−0.0303404	−	0.0933781i
$681$	−27.4845	−	37.0612i	−1.05321	−	1.42019i
$682$	3.44405	+	3.39579i	0.131879	+	0.130032i
$683$		−	46.0641i		−	1.76260i	−0.472562	−	0.881298i	$-0.656671\pi$
$683$		−	46.0641i		−	1.76260i	0.472562	−	0.881298i	$-0.343329\pi$
$684$	−21.0950	+	0.412802i	−0.806588	+	0.0157839i
$685$	−8.36507	+	7.53195i	−0.319613	+	0.287781i
$686$	21.2111	+	29.1946i	0.809844	+	1.11466i
$687$	−10.0163	+	23.1026i	−0.382145	+	0.881419i
$688$	−8.35280	−	4.82249i	−0.318448	−	0.183856i
$689$	−0.138922	+	0.0146013i	−0.00529252	+	0.000556266i
$690$	6.61665	−	0.0647334i	0.251891	−	0.00246436i
$691$	−2.98625	+	28.4123i	−0.113602	+	1.08085i	0.778072	+	0.628175i	$0.216198\pi$
$691$	−2.98625	+	28.4123i	−0.113602	+	1.08085i	−0.891674	+	0.452678i	$0.850469\pi$
$692$	−11.3149	−	10.1879i	−0.430126	−	0.387287i
$693$	−7.95231	+	9.18722i	−0.302083	+	0.348994i
$694$	2.88514	−	13.5735i	0.109518	−	0.515243i
$695$	1.20911	−	0.257004i	0.0458641	−	0.00974870i
$696$	−8.46386	−	4.77682i	−0.320822	−	0.181065i
$697$	11.9707	+	3.88953i	0.453424	+	0.147327i
$698$	5.74239	+	1.86581i	0.217353	+	0.0706221i
$699$	33.5786	+	18.9511i	1.27006	+	0.716796i
$700$	−4.56069	+	0.969404i	−0.172378	+	0.0366400i
$701$	6.25875	−	29.4451i	0.236390	−	1.11213i	−0.686520	−	0.727111i	$-0.740863\pi$
$701$	6.25875	−	29.4451i	0.236390	−	1.11213i	0.922910	−	0.385016i	$-0.125804\pi$
$702$	0.479116	−	6.34477i	0.0180831	−	0.239468i
$703$	40.7225	+	36.6667i	1.53588	+	1.38291i
$704$	−0.0908021	+	0.863924i	−0.00342223	+	0.0325604i
$705$	−14.8806	+	0.145583i	−0.560436	+	0.00548297i
$706$	−15.0606	+	1.58294i	−0.566815	+	0.0595746i
$707$	−73.4309	−	42.3954i	−2.76165	−	1.59444i
$708$	7.37578	−	17.0123i	0.277199	−	0.639360i
$709$	30.1045	+	41.4352i	1.13060	+	1.55613i	0.786930	+	0.617042i	$0.211669\pi$
$709$	30.1045	+	41.4352i	1.13060	+	1.55613i	0.343667	+	0.939092i	$0.388331\pi$
$710$	−1.53094	+	1.37846i	−0.0574550	+	0.0517327i
$711$	0.666238	+	34.0461i	0.0249859	+	1.27683i
$712$		−	6.30773i		−	0.236392i
$713$	−5.65004	−	20.5064i	−0.211596	−	0.767972i
$714$	−12.3165	−	16.6080i	−0.460933	−	0.621541i
$715$	0.328709	+	1.01166i	0.0122930	+	0.0378341i
$716$	2.51562	+	2.79388i	0.0940132	+	0.104412i
$717$	−13.6025	+	43.3010i	−0.507994	+	1.61711i
$718$	−0.147747	−	0.255906i	−0.00551388	−	0.00955031i
$719$	−8.08232	+	13.9990i	−0.301420	+	0.522075i	−0.976458	−	0.215709i	$-0.930794\pi$
$719$	−8.08232	+	13.9990i	−0.301420	+	0.522075i	0.675038	+	0.737783i	$0.264127\pi$
$720$	−0.566203	+	2.94608i	−0.0211012	+	0.109794i
$721$	−33.5278	−	24.3594i	−1.24864	−	0.907192i
$722$	30.2964	+	3.18428i	1.12752	+	0.118507i
$723$	−45.2940	−	4.31302i	−1.68450	−	0.160403i
$724$	−5.54490	+	12.4540i	−0.206075	+	0.462851i
$725$	5.48853	+	1.16662i	0.203839	+	0.0433273i
$726$	13.3030	+	11.7445i	0.493722	+	0.435879i
$727$	30.3896	−	13.5303i	1.12709	−	0.501812i	0.243417	−	0.969922i	$-0.421732\pi$
$727$	30.3896	−	13.5303i	1.12709	−	0.501812i	0.883670	+	0.468110i	$0.155065\pi$
$728$	1.76432	−	5.43001i	0.0653899	−	0.201250i
$729$	9.83552	+	25.1448i	0.364278	+	0.931290i
$730$	5.12221	+	11.5047i	0.189582	+	0.425807i
$731$	5.13421	+	24.1546i	0.189896	+	0.893389i
$732$	−7.12012	−	15.5800i	−0.263167	−	0.575855i
$733$	20.5968	+	9.17027i	0.760759	+	0.338712i	0.750181	−	0.661232i	$-0.229966\pi$
$733$	20.5968	+	9.17027i	0.760759	+	0.338712i	0.0105777	+	0.999944i	$0.496633\pi$
$734$	−3.18385	+	3.53603i	−0.117518	+	0.130517i
$735$	−21.9835	+	12.9806i	−0.810873	+	0.478795i
$736$	2.24552	−	3.09069i	0.0827710	−	0.113924i
$737$	0.0687652	+	0.654257i	0.00253300	+	0.0240999i
$738$	−10.0811	−	10.7650i	−0.371091	−	0.396264i
$739$	−29.8678	+	17.2442i	−1.09871	+	0.634338i	−0.935881	−	0.352317i	$-0.885394\pi$
$739$	−29.8678	+	17.2442i	−1.09871	+	0.634338i	−0.162825	+	0.986655i	$0.552060\pi$
$740$	6.30343	−	4.57971i	0.231719	−	0.168353i
$741$	−2.95845	+	14.6203i	−0.108681	+	0.537090i
$742$	0.505850	−	0.164361i	0.0185703	−	0.00603387i
$743$	12.5487			0.460368			0.230184	−	0.973147i	$-0.426067\pi$
$743$	12.5487			0.460368			0.230184	+	0.973147i	$0.426067\pi$
$744$	9.62057	−	0.666788i	0.352707	−	0.0244456i
$745$	22.7283			0.832700
$746$	−2.04744	+	0.665255i	−0.0749622	+	0.0243567i
$747$	9.40455	−	4.40963i	0.344095	−	0.161340i
$748$	1.79934	−	1.30729i	0.0657902	−	0.0477994i
$749$	18.0492	−	10.4207i	0.659502	−	0.380764i
$750$	−0.197892	−	1.72071i	−0.00722598	−	0.0628314i
$751$	2.15160	+	20.4711i	0.0785129	+	0.747000i	0.960978	+	0.276623i	$0.0892154\pi$
$751$	2.15160	+	20.4711i	0.0785129	+	0.747000i	−0.882466	+	0.470377i	$0.844118\pi$
$752$	−5.05009	+	6.95085i	−0.184158	+	0.253472i
$753$	−20.7208	−	35.0921i	−0.755109	−	1.27883i
$754$	−4.59760	+	5.10615i	−0.167435	+	0.185955i
$755$	12.5468	+	5.58621i	0.456626	+	0.203303i
$756$	3.23843	+	24.0100i	0.117781	+	0.873237i
$757$	4.76628	+	22.4236i	0.173233	+	0.814999i	0.975839	+	0.218490i	$0.0701130\pi$
$757$	4.76628	+	22.4236i	0.173233	+	0.814999i	−0.802606	+	0.596510i	$0.796554\pi$
$758$	−5.99301	−	13.4605i	−0.217676	−	0.488908i
$759$	1.82964	+	5.44908i	0.0664117	+	0.197789i
$760$	2.17332	−	6.68880i	0.0788346	−	0.242628i
$761$	−41.4014	+	18.4331i	−1.50080	+	0.668199i	−0.982375	−	0.186923i	$-0.940148\pi$
$761$	−41.4014	+	18.4331i	−1.50080	+	0.668199i	−0.518426	+	0.855123i	$0.673482\pi$
$762$	−16.5225	+	18.7151i	−0.598548	+	0.677977i
$763$	45.5843	+	9.68925i	1.65026	+	0.350774i
$764$	1.33134	−	2.99023i	0.0481661	−	0.108183i
$765$	6.57548	−	3.96988i	0.237737	−	0.143531i
$766$	−26.4985	−	2.78510i	−0.957428	−	0.100630i
$767$	−10.6055	−	7.70533i	−0.382942	−	0.278224i
$768$	1.17150	+	1.27576i	0.0422730	+	0.0460352i
$769$	7.46653	−	12.9324i	0.269250	−	0.466355i	−0.699418	−	0.714713i	$-0.746558\pi$
$769$	7.46653	−	12.9324i	0.269250	−	0.466355i	0.968668	+	0.248358i	$0.0798908\pi$
$770$	−2.02515	−	3.50766i	−0.0729813	−	0.126407i
$771$	−21.9634	−	6.89955i	−0.790994	−	0.248481i
$772$	−3.90545	−	4.33744i	−0.140560	−	0.156108i
$773$	11.0966	+	34.1517i	0.399116	+	1.22835i	0.925710	+	0.378235i	$0.123469\pi$
$773$	11.0966	+	34.1517i	0.399116	+	1.22835i	−0.526594	+	0.850117i	$0.676531\pi$
$774$	8.40128	−	27.6885i	0.301978	−	0.995241i
$775$	−5.18375	+	2.03193i	−0.186206	+	0.0729891i
$776$		−	11.3674i		−	0.408068i
$777$	36.4851	−	51.2647i	1.30890	−	1.83911i
$778$	1.24077	−	1.11719i	0.0444836	−	0.0400533i
$779$	20.3227	+	27.9718i	0.728137	+	1.00220i
$780$	1.94592	+	0.843669i	0.0696753	+	0.0302082i
$781$	−1.54980	−	0.894777i	−0.0554562	−	0.0320177i
$782$	−9.72760	+	1.02241i	−0.347858	+	0.0365614i
$783$	8.19222	−	27.9818i	0.292766	−	0.999989i
$784$	−1.54071	+	14.6589i	−0.0550253	+	0.523531i
$785$	−6.58160	−	5.92610i	−0.234907	−	0.211512i
$786$	−5.96102	+	1.32813i	−0.212622	+	0.0473730i
$787$	−7.34405	+	34.5510i	−0.261787	+	1.23161i	0.629078	+	0.777343i	$0.283433\pi$
$787$	−7.34405	+	34.5510i	−0.261787	+	1.23161i	−0.890865	+	0.454269i	$0.849901\pi$
$788$	1.82794	−	0.388541i	0.0651178	−	0.0138412i
$789$	−12.9307	+	22.9114i	−0.460346	+	0.815668i
$790$	−10.7953	−	3.50762i	−0.384081	−	0.124795i
$791$	58.9331	+	19.1485i	2.09542	+	0.680843i
$792$	−2.58595	+	0.323062i	−0.0918876	+	0.0114795i
$793$	−11.8459	+	2.51792i	−0.420659	+	0.0894139i
$794$	−5.22340	+	24.5741i	−0.185371	+	0.872104i
$795$	0.0429686	+	0.192854i	0.00152394	+	0.00683984i
$796$	−12.2681	−	11.0462i	−0.434830	−	0.391523i
$797$	−4.70756	+	44.7894i	−0.166750	+	1.58652i	0.516466	+	0.856308i	$0.327247\pi$
$797$	−4.70756	+	44.7894i	−0.166750	+	1.58652i	−0.683217	+	0.730216i	$0.739420\pi$
$798$	−0.555645	−	56.7946i	−0.0196696	−	2.01051i
$799$	21.8770	−	2.29937i	0.773953	−	0.0813458i
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$	18.4292	−	4.29574i	0.651162	−	0.151782i
$802$	21.1976	+	29.1760i	0.748512	+	1.03024i
$803$	−8.12979	+	7.32009i	−0.286894	+	0.258320i
$804$	1.06868	+	0.760578i	0.0376893	+	0.0268235i
$805$			17.8125i			0.627807i
$806$	1.01902	−	6.74130i	0.0358934	−	0.237452i
$807$	1.24861	−	0.925969i	0.0439533	−	0.0325956i
$808$	−5.61959	−	17.2953i	−0.197697	−	0.608448i
$809$	32.1695	+	35.7279i	1.13102	+	1.25612i	0.962753	+	0.270384i	$0.0871505\pi$
$809$	32.1695	+	35.7279i	1.13102	+	1.25612i	0.168267	+	0.985741i	$0.446183\pi$
$810$	−8.99311	+	0.352102i	−0.315986	+	0.0123716i
$811$	24.0154	+	41.5959i	0.843294	+	1.46063i	0.887095	+	0.461588i	$0.152720\pi$
$811$	24.0154	+	41.5959i	0.843294	+	1.46063i	−0.0438005	+	0.999040i	$0.513947\pi$
$812$	13.0812	−	22.6573i	0.459060	−	0.795115i
$813$	15.9775	−	14.6717i	0.560354	−	0.514560i
$814$	5.47568	+	3.97831i	0.191922	+	0.139440i
$815$	−5.90072	−	0.620191i	−0.206693	−	0.0217243i
$816$	0.420373	−	4.41462i	0.0147160	−	0.154543i
$817$	−27.5903	+	61.9689i	−0.965263	+	2.16802i
$818$	19.0779	+	4.05512i	0.667042	+	0.141784i
$819$	17.0663	+	1.45678i	0.596344	+	0.0509039i
$820$	4.49109	−	1.99956i	0.156836	−	0.0698278i
$821$	5.74811	−	17.6908i	0.200610	−	0.617415i	−0.799255	−	0.600992i	$-0.794772\pi$
$821$	5.74811	−	17.6908i	0.200610	−	0.617415i	0.999865	−	0.0164227i	$-0.00522774\pi$
$822$	−18.4825	+	6.20586i	−0.644650	+	0.216454i
$823$	−11.7137	−	26.3095i	−0.408315	−	0.917091i	−0.994285	−	0.106758i	$-0.965953\pi$
$823$	−11.7137	−	26.3095i	−0.408315	−	0.917091i	0.585970	−	0.810333i	$-0.300714\pi$
$824$	−1.84800	−	8.69414i	−0.0643780	−	0.302875i
$825$	1.36847	−	0.625395i	0.0476440	−	0.0217734i
$826$	45.5995	+	20.3022i	1.58661	+	0.706405i
$827$	−16.7835	+	18.6399i	−0.583619	+	0.648174i	−0.960563	−	0.278062i	$-0.910308\pi$
$827$	−16.7835	+	18.6399i	−0.583619	+	0.648174i	0.376945	+	0.926236i	$0.376975\pi$
$828$	10.5593	+	4.45584i	0.366960	+	0.154851i
$829$	12.3367	−	16.9800i	0.428472	−	0.589741i	−0.539130	−	0.842223i	$-0.681247\pi$
$829$	12.3367	−	16.9800i	0.428472	−	0.589741i	0.967602	+	0.252482i	$0.0812468\pi$
$830$	0.361913	+	3.44338i	0.0125622	+	0.119521i
$831$	23.7912	−	2.73613i	0.825308	−	0.0949153i
$832$	1.06047	−	0.612264i	0.0367652	−	0.0212264i
$833$	30.5307	−	22.1819i	1.05783	−	0.768556i
$834$	2.09849	+	0.424634i	0.0726648	+	0.0147039i
$835$	4.21760	−	1.37038i	0.145956	−	0.0474240i
$836$	6.10946			0.211300
$837$	8.50002	+	27.6541i	0.293804	+	0.955866i
$838$	−35.9143			−1.24064
$839$	−39.7085	+	12.9021i	−1.37089	+	0.445429i	−0.899664	−	0.436583i	$-0.856189\pi$
$839$	−39.7085	+	12.9021i	−1.37089	+	0.445429i	−0.471227	+	0.882012i	$0.656189\pi$
$840$	−7.91539	−	1.60170i	−0.273107	−	0.0552638i
$841$	−2.01039	+	1.46063i	−0.0693238	+	0.0503667i
$842$	32.8507	−	18.9664i	1.13211	−	0.653625i
$843$	8.22389	−	0.945795i	0.283246	−	0.0325749i
$844$	−0.750505	−	7.14058i	−0.0258334	−	0.245789i
$845$	−6.75984	+	9.30413i	−0.232546	+	0.320072i
$846$	−23.7474	−	10.0210i	−0.816453	−	0.344530i
$847$	−31.9643	+	35.5000i	−1.09831	+	1.21979i
$848$	0.104212	+	0.0463984i	0.00357867	+	0.00159333i
$849$	−0.253051	+	0.115645i	−0.00868469	+	0.00396893i
$850$	0.532319	+	2.50436i	0.0182584	+	0.0858990i
$851$	−12.1068	−	27.1924i	−0.415017	−	0.932143i
$852$	−3.38257	+	1.13577i	−0.115885	+	0.0389108i
$853$	7.29158	−	22.4412i	0.249659	−	0.768371i	−0.745176	−	0.666867i	$-0.767635\pi$
$853$	7.29158	−	22.4412i	0.249659	−	0.768371i	0.994835	−	0.101503i	$-0.0323653\pi$
$854$	42.1260	−	18.7557i	1.44152	−	0.641807i
$855$	21.0226	+	1.79449i	0.718958	+	0.0613702i
$856$	4.37225	+	0.929351i	0.149440	+	0.0317645i
$857$	12.5525	−	28.1933i	0.428784	−	0.963064i	−0.561941	−	0.827177i	$-0.689945\pi$
$857$	12.5525	−	28.1933i	0.428784	−	0.963064i	0.990724	−	0.135886i	$-0.0433882\pi$
$858$	−0.174651	+	1.83413i	−0.00596249	+	0.0626162i
$859$	−18.6364	−	1.95876i	−0.635865	−	0.0668321i	−0.218889	−	0.975750i	$-0.570243\pi$
$859$	−18.6364	−	1.95876i	−0.635865	−	0.0668321i	−0.416976	+	0.908918i	$0.636910\pi$
$860$	7.80296	+	5.66918i	0.266079	+	0.193318i
$861$	29.2428	−	26.8529i	0.996590	−	0.915146i
$862$	−8.30140	+	14.3784i	−0.282747	+	0.489732i
$863$	−3.47493	−	6.01875i	−0.118288	−	0.204881i	0.800801	−	0.598930i	$-0.204407\pi$
$863$	−3.47493	−	6.01875i	−0.118288	−	0.204881i	−0.919089	+	0.394049i	$0.871074\pi$
$864$	−2.92955	+	4.29159i	−0.0996652	+	0.146003i
$865$	10.1879	+	11.3149i	0.346400	+	0.384717i
$866$	−4.37467	−	13.4639i	−0.148657	−	0.457520i
$867$	14.5311	−	10.7762i	0.493503	−	0.365980i
$868$	1.54151	+	25.9143i	0.0523222	+	0.879589i
$869$		−	9.86032i		−	0.334488i
$870$	7.91818	+	5.63537i	0.268451	+	0.191057i
$871$	0.689152	−	0.620515i	0.0233510	−	0.0210254i
$872$	5.87495	+	8.08617i	0.198951	+	0.273832i
$873$	33.2120	−	7.74155i	1.12406	−	0.262012i
$874$	−23.2686	−	13.4341i	−0.787072	−	0.454416i
$875$	4.63703	−	0.487372i	0.156760	−	0.0164762i
$876$	0.213390	+	21.8114i	0.00720979	+	0.736940i
$877$	5.13297	−	48.8370i	0.173328	−	1.64911i	−0.469380	−	0.882996i	$-0.655522\pi$
$877$	5.13297	−	48.8370i	0.173328	−	1.64911i	0.642708	−	0.766111i	$-0.277811\pi$
$878$	−6.75393	−	6.08127i	−0.227934	−	0.205233i
$879$	8.50952	+	38.1930i	0.287019	+	1.28822i
$880$	0.180609	−	0.849700i	0.00608834	−	0.0286434i
$881$	34.3766	−	7.30696i	1.15818	−	0.246178i	0.411528	−	0.911397i	$-0.364995\pi$
$881$	34.3766	−	7.30696i	1.15818	−	0.246178i	0.746648	+	0.665219i	$0.231662\pi$
$882$	−43.8777	+	5.48164i	−1.47744	+	0.184576i
$883$	−8.71119	−	2.83044i	−0.293155	−	0.0952518i	0.158747	−	0.987319i	$-0.449254\pi$
$883$	−8.71119	−	2.83044i	−0.293155	−	0.0952518i	−0.451902	+	0.892067i	$0.649254\pi$
$884$	−2.98173	−	0.968822i	−0.100286	−	0.0325850i
$885$	−9.11364	+	16.1481i	−0.306352	+	0.542812i
$886$	0.970272	−	0.206238i	0.0325969	−	0.00692869i
$887$	−3.40174	+	16.0039i	−0.114219	+	0.537359i	0.883414	+	0.468594i	$0.155239\pi$
$887$	−3.40174	+	16.0039i	−0.114219	+	0.537359i	−0.997633	+	0.0687650i	$0.978094\pi$
$888$	13.1722	−	2.93482i	0.442031	−	0.0984860i
$889$	−49.9424	−	44.9684i	−1.67501	−	1.50819i
$890$	−0.659337	+	6.27318i	−0.0221010	+	0.210277i
$891$	−2.70498	−	7.33529i	−0.0906204	−	0.245741i
$892$	6.82289	−	0.717114i	0.228447	−	0.0240108i
$893$	52.3302	+	30.2129i	1.75116	+	1.01104i
$894$	36.1180	+	15.6592i	1.20797	+	0.523723i
$895$	−2.20980	−	3.04153i	−0.0738655	−	0.101667i
$896$	−3.46497	+	3.11987i	−0.115756	+	0.104228i
$897$	4.69826	−	6.60146i	0.156870	−	0.220416i
$898$			23.4907i			0.783895i
$899$	10.9899	−	29.2448i	0.366534	−	0.975367i
$900$	0.871051	−	2.87076i	0.0290350	−	0.0956920i
$901$	−0.0902537	−	0.277772i	−0.00300679	−	0.00925394i
$902$	2.85755	+	3.17363i	0.0951460	+	0.105670i
$903$	74.3108	+	23.3438i	2.47291	+	0.776834i
$904$	6.64503	+	11.5095i	0.221010	+	0.382801i
$905$	6.81633	−	11.8062i	0.226582	−	0.392452i
$906$	16.0897	+	17.5216i	0.534544	+	0.582117i
$907$	−19.3507	−	14.0591i	−0.642530	−	0.466826i	0.218188	−	0.975907i	$-0.429985\pi$
$907$	−19.3507	−	14.0591i	−0.642530	−	0.466826i	−0.860719	+	0.509081i	$0.829985\pi$
$908$	26.4932	+	2.78454i	0.879207	+	0.0924084i
$909$	46.7043	−	28.1972i	1.54908	−	0.935243i
$910$	−2.32224	+	5.21584i	−0.0769816	+	0.172904i
$911$	−7.14472	−	1.51866i	−0.236715	−	0.0503153i	0.0880265	−	0.996118i	$-0.471944\pi$
$911$	−7.14472	−	1.51866i	−0.236715	−	0.0503153i	−0.324742	+	0.945803i	$0.605277\pi$
$912$	8.06209	−	9.13196i	0.266962	−	0.302389i
$913$	−2.74765	+	1.22333i	−0.0909340	+	0.0404864i
$914$	0.198005	−	0.609398i	0.00654944	−	0.0201571i
$915$	5.45256	+	16.2389i	0.180256	+	0.536843i
$916$	−5.91312	−	13.2811i	−0.195375	−	0.438819i
$917$	−3.41810	−	16.0809i	−0.112876	−	0.531038i
$918$	13.1844	−	1.77829i	0.435150	−	0.0586922i
$919$	−12.1067	−	5.39023i	−0.399362	−	0.177807i	0.197221	−	0.980359i	$-0.436808\pi$
$919$	−12.1067	−	5.39023i	−0.399362	−	0.177807i	−0.596583	+	0.802552i	$0.703475\pi$
$920$	−2.55628	+	2.83904i	−0.0842782	+	0.0936004i
$921$	10.4699	+	17.7316i	0.344996	+	0.584275i
$922$	20.6951	−	28.4844i	0.681557	−	0.938083i
$923$	0.263686	+	2.50880i	0.00867933	+	0.0825783i
$924$	−0.801520	−	6.96939i	−0.0263681	−	0.229276i
$925$	−6.74761	+	3.89573i	−0.221860	+	0.128091i
$926$	5.06897	−	3.68283i	0.166577	−	0.121025i
$927$	24.1429	−	11.3202i	0.792958	−	0.371804i
$928$	5.33652	−	1.73394i	0.175180	−	0.0569194i
$929$	−43.2109			−1.41770			−0.708852	−	0.705357i	$-0.750787\pi$
$929$	−43.2109			−1.41770			−0.708852	+	0.705357i	$0.750787\pi$
$930$	−9.63757	−	0.342488i	−0.316028	−	0.0112306i
$931$	103.664			3.39745
$932$	−21.1716	+	6.87905i	−0.693497	+	0.225331i
$933$	0.955843	−	4.72366i	0.0312929	−	0.154646i
$934$	−25.4095	+	18.4611i	−0.831424	+	0.604065i
$935$	−1.92613	+	1.11205i	−0.0629911	+	0.0363679i
$936$	2.51105	+	2.68139i	0.0820762	+	0.0876439i
$937$	−2.04339	−	19.4416i	−0.0667548	−	0.635129i	−0.975835	−	0.218508i	$-0.929881\pi$
$937$	−2.04339	−	19.4416i	−0.0667548	−	0.635129i	0.909080	−	0.416621i	$-0.136786\pi$
$938$	−2.07548	+	2.85665i	−0.0677667	+	0.0932728i
$939$	39.6895	−	23.4354i	1.29522	−	0.764786i
$940$	5.74899	−	6.38490i	0.187511	−	0.208252i
$941$	15.2392	+	6.78494i	0.496784	+	0.221183i	0.639805	−	0.768537i	$-0.279015\pi$
$941$	15.2392	+	6.78494i	0.496784	+	0.221183i	−0.143021	+	0.989720i	$0.545682\pi$
$942$	−6.37604	−	13.9519i	−0.207743	−	0.454576i
$943$	−3.90480	−	18.3706i	−0.127158	−	0.598230i
$944$	4.35429	+	9.77990i	0.141720	+	0.318309i
$945$	−0.710956	−	24.2170i	−0.0231274	−	0.787780i
$946$	−2.58908	+	7.96837i	−0.0841782	+	0.259074i
$947$	22.6375	−	10.0789i	0.735620	−	0.327519i	−0.00450372	−	0.999990i	$-0.501434\pi$
$947$	22.6375	−	10.0789i	0.735620	−	0.327519i	0.740124	+	0.672471i	$0.234767\pi$
$948$	−14.7385	−	13.0118i	−0.478683	−	0.422602i
$949$	15.0840	+	3.20621i	0.489648	+	0.104078i
$950$	−2.86059	+	6.42498i	−0.0928096	+	0.208454i
$951$	−21.4367	−	2.04127i	−0.695134	−	0.0661927i
$952$	11.8723	+	1.24782i	0.384782	+	0.0404422i
$953$	5.90735	+	4.29194i	0.191358	+	0.139030i	0.679339	−	0.733824i	$-0.262267\pi$
$953$	5.90735	+	4.29194i	0.191358	+	0.139030i	−0.487981	+	0.872854i	$0.662267\pi$
$954$	−0.0645895	+	0.336074i	−0.00209116	+	0.0108808i
$955$	−1.63661	+	2.83469i	−0.0529594	+	0.0917284i
$956$	−13.1022	−	22.6936i	−0.423755	−	0.733965i
$957$	−2.53022	+	8.05448i	−0.0817902	+	0.260364i
$958$	−2.64214	−	2.93439i	−0.0853635	−	0.0948058i
$959$	−16.2183	−	49.9147i	−0.523715	−	1.61183i
$960$	−1.03173	−	1.39123i	−0.0332991	−	0.0449018i
$961$	6.87246	+	30.2286i	0.221692	+	0.975117i
$962$		−	9.54086i		−	0.307610i
$963$	0.262362	+	13.4072i	0.00845449	+	0.432042i
$964$	19.5215	−	17.5772i	0.628745	−	0.566125i
$965$	3.43067	+	4.72191i	0.110437	+	0.152004i
$966$	−12.2723	+	28.3062i	−0.394856	+	0.910737i
$967$	19.5399	+	11.2813i	0.628360	+	0.362784i	0.780117	−	0.625634i	$-0.215160\pi$
$967$	19.5399	+	11.2813i	0.628360	+	0.362784i	−0.151757	+	0.988418i	$0.548493\pi$
$968$	−10.1893	+	1.07093i	−0.327495	+	0.0344212i
$969$	−31.1871	+	0.305116i	−1.00187	+	0.00980173i
$970$	−1.18822	+	11.3052i	−0.0381515	+	0.362987i
$971$	37.4116	+	33.6855i	1.20059	+	1.08102i	0.994739	+	0.102437i	$0.0326641\pi$
$971$	37.4116	+	33.6855i	1.20059	+	1.08102i	0.205855	+	0.978583i	$0.434003\pi$
$972$	−14.5338	−	5.63650i	−0.466170	−	0.180791i
$973$	−1.19830	+	5.63755i	−0.0384157	+	0.180732i
$974$	0.423996	−	0.0901231i	0.0135857	−	0.00288773i
$975$	−1.84708	−	1.04245i	−0.0591538	−	0.0333852i
$976$	9.40590	+	3.05616i	0.301076	+	0.0978254i
$977$	19.8816	+	6.45994i	0.636070	+	0.206672i	0.609262	−	0.792969i	$-0.291466\pi$
$977$	19.8816	+	6.45994i	0.636070	+	0.206672i	0.0268079	+	0.999641i	$0.491466\pi$
$978$	−8.94968	−	5.05101i	−0.286179	−	0.161514i
$979$	−5.35968	+	1.13923i	−0.171296	+	0.0364101i
$980$	3.06454	−	14.4175i	0.0978931	−	0.460551i
$981$	−19.6242	+	22.6716i	−0.626552	+	0.723849i
$982$	30.6000	+	27.5524i	0.976486	+	0.879232i
$983$	−5.92454	+	56.3682i	−0.188964	+	1.79787i	0.330949	+	0.943649i	$0.392631\pi$
$983$	−5.92454	+	56.3682i	−0.188964	+	1.79787i	−0.519913	+	0.854219i	$0.674036\pi$
$984$	8.51455	−	0.0833013i	0.271434	−	0.00265555i
$985$	−1.85854	+	0.195341i	−0.0592181	+	0.00622407i
$986$	−12.4416	−	7.18315i	−0.396221	−	0.228758i
$987$	27.6001	−	63.6596i	0.878520	−	2.02631i
$988$	−5.06208	−	6.96735i	−0.161046	−	0.221661i
$989$	27.3825	−	24.6553i	0.870713	−	0.783994i
$990$	2.60555	−	0.0509872i	0.0828098	−	0.00162048i
$991$		−	11.0220i		−	0.350125i	−0.984557	−	0.175063i	$-0.943987\pi$
$991$		−	11.0220i		−	0.350125i	0.984557	−	0.175063i	$-0.0560128\pi$
$992$	−3.47329	+	4.35158i	−0.110277	+	0.138163i
$993$	−2.46817	−	3.32818i	−0.0783249	−	0.105617i
$994$	−2.96819	−	9.13516i	−0.0941453	−	0.289750i
$995$	11.0462	+	12.2681i	0.350189	+	0.388924i
$996$	−1.79728	+	5.72130i	−0.0569489	+	0.181286i
$997$	−26.4098	−	45.7431i	−0.836406	−	1.44870i	−0.892880	−	0.450294i	$-0.851319\pi$
$997$	−26.4098	−	45.7431i	−0.836406	−	1.44870i	0.0564744	−	0.998404i	$-0.482014\pi$
$998$	2.56905	−	4.44972i	0.0813218	−	0.140853i
$999$	17.5452	+	36.4863i	0.555107	+	1.15438i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.a.11.12	yes	176
3.2	odd	2	inner	930.2.br.a.11.6	✓	176
31.17	odd	30	inner	930.2.br.a.761.6	yes	176
93.17	even	30	inner	930.2.br.a.761.12	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.a.11.6	✓	176	3.2	odd	2	inner
930.2.br.a.11.12	yes	176	1.1	even	1	trivial
930.2.br.a.761.6	yes	176	31.17	odd	30	inner
930.2.br.a.761.12	yes	176	93.17	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.br (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(-1.69764 - 0.343522i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.72071 + 0.197892i) q^{6} +(-0.487372 - 4.63703i) q^{7} +(0.587785 - 0.809017i) q^{8} +(2.76399 + 1.16636i) q^{9} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{2} +(-1.69764 - 0.343522i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.72071 + 0.197892i) q^{6} +(-0.487372 - 4.63703i) q^{7} +(0.587785 - 0.809017i) q^{8} +(2.76399 + 1.16636i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(-0.793581 - 0.353325i) q^{11} +(-1.57534 + 0.719934i) q^{12} +(0.254594 + 1.19777i) q^{13} +(-1.89644 - 4.25947i) q^{14} +(1.64196 - 0.551323i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.33896 + 1.04137i) q^{17} +(2.98913 + 0.255152i) q^{18} +(-6.87933 - 1.46225i) q^{19} +(-0.406737 + 0.913545i) q^{20} +(-0.765540 + 8.03945i) q^{21} +(-0.863924 - 0.0908021i) q^{22} +(3.09069 + 2.24552i) q^{23} +(-1.27576 + 1.17150i) q^{24} +(0.500000 - 0.866025i) q^{25} +(0.612264 + 1.06047i) q^{26} +(-4.29159 - 2.92955i) q^{27} +(-3.11987 - 3.46497i) q^{28} +(1.73394 + 5.33652i) q^{29} +(1.39123 - 1.03173i) q^{30} +(-4.35158 - 3.47329i) q^{31} -1.00000i q^{32} +(1.22584 + 0.872433i) q^{33} +(-1.90268 + 1.71318i) q^{34} +(2.74059 + 3.77210i) q^{35} +(2.92168 - 0.681028i) q^{36} +(-6.74761 - 3.89573i) q^{37} +(-6.99449 + 0.735150i) q^{38} +(-0.0207491 - 2.12084i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(-3.65338 - 3.28952i) q^{41} +(1.75626 + 7.88254i) q^{42} +(2.00531 - 9.43422i) q^{43} +(-0.849700 + 0.180609i) q^{44} +(-2.97686 + 0.371899i) q^{45} +(3.63333 + 1.18054i) q^{46} +(-8.17122 - 2.65499i) q^{47} +(-0.851310 + 1.50840i) q^{48} +(-14.4175 + 3.06454i) q^{49} +(0.207912 - 0.978148i) q^{50} +(4.32846 - 0.964395i) q^{51} +(0.910001 + 0.819369i) q^{52} +(-0.0119241 + 0.113450i) q^{53} +(-4.98683 - 1.45999i) q^{54} +(0.863924 - 0.0908021i) q^{55} +(-4.03791 - 2.33129i) q^{56} +(11.1763 + 4.84557i) q^{57} +(3.29815 + 4.53951i) q^{58} +(-7.95569 + 7.16334i) q^{59} +(1.00432 - 1.41115i) q^{60} +9.88995i q^{61} +(-5.21190 - 1.95859i) q^{62} +(4.06134 - 13.3851i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-0.819369 - 0.910001i) q^{65} +(1.43544 + 0.450927i) q^{66} +(-0.378654 - 0.655849i) q^{67} +(-1.28016 + 2.21730i) q^{68} +(-4.47551 - 4.87381i) q^{69} +(3.77210 + 2.74059i) q^{70} +(2.04879 + 0.215337i) q^{71} +(2.56823 - 1.55054i) q^{72} +(5.12221 - 11.5047i) q^{73} +(-7.62120 - 1.61994i) q^{74} +(-1.14632 + 1.29844i) q^{75} +(-6.42498 + 2.86059i) q^{76} +(-1.25161 + 3.85206i) q^{77} +(-0.675110 - 2.01063i) q^{78} +(4.61682 + 10.3696i) q^{79} +(0.207912 + 0.978148i) q^{80} +(6.27923 + 6.44758i) q^{81} +(-4.49109 - 1.99956i) q^{82} +(2.31676 - 2.57302i) q^{83} +(4.10614 + 6.95403i) q^{84} +(1.50491 - 2.07134i) q^{85} +(-1.00818 - 9.59215i) q^{86} +(-1.11040 - 9.65515i) q^{87} +(-0.752301 + 0.434341i) q^{88} +(5.10306 - 3.70759i) q^{89} +(-2.71624 + 1.27360i) q^{90} +(5.43001 - 1.76432i) q^{91} +3.82031 q^{92} +(6.19427 + 7.39128i) q^{93} -8.59173 q^{94} +(6.68880 - 2.17332i) q^{95} +(-0.343522 + 1.69764i) q^{96} +(9.19646 - 6.68162i) q^{97} +(-12.7649 + 7.36980i) q^{98} +(-1.78134 - 1.90218i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9	\( 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9} - 22 q^{10} - 38 q^{13} - 44 q^{16} + 12 q^{18} + 8 q^{19} - 18 q^{21} - 4 q^{22} + 88 q^{25} - 90 q^{27} + 36 q^{28} + 24 q^{31} + 18 q^{33} + 14 q^{34} + 4 q^{36} - 42 q^{37} - 42 q^{39} + 22 q^{40} - 12 q^{42} - 34 q^{43} - 8 q^{45} + 10 q^{46} + 22 q^{49} + 26 q^{51} - 2 q^{52} + 4 q^{55} + 114 q^{57} + 32 q^{63} + 44 q^{64} - 42 q^{66} + 20 q^{67} + 16 q^{69} + 8 q^{70} - 12 q^{72} - 28 q^{73} + 12 q^{76} - 92 q^{78} - 56 q^{79} - 124 q^{81} - 32 q^{82} - 12 q^{84} - 36 q^{87} - 6 q^{88} + 24 q^{90} - 140 q^{91} - 104 q^{93} - 36 q^{94} + 88 q^{97} - 60 q^{99}+O(q^{100}) \) 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9 - 22 * q^10 - 38 * q^13 - 44 * q^16 + 12 * q^18 + 8 * q^19 - 18 * q^21 - 4 * q^22 + 88 * q^25 - 90 * q^27 + 36 * q^28 + 24 * q^31 + 18 * q^33 + 14 * q^34 + 4 * q^36 - 42 * q^37 - 42 * q^39 + 22 * q^40 - 12 * q^42 - 34 * q^43 - 8 * q^45 + 10 * q^46 + 22 * q^49 + 26 * q^51 - 2 * q^52 + 4 * q^55 + 114 * q^57 + 32 * q^63 + 44 * q^64 - 42 * q^66 + 20 * q^67 + 16 * q^69 + 8 * q^70 - 12 * q^72 - 28 * q^73 + 12 * q^76 - 92 * q^78 - 56 * q^79 - 124 * q^81 - 32 * q^82 - 12 * q^84 - 36 * q^87 - 6 * q^88 + 24 * q^90 - 140 * q^91 - 104 * q^93 - 36 * q^94 + 88 * q^97 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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