LMFDB - Embedded newform 690.2.w.b.373.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, degree $20$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			373.4
Character	$\chi$	$=$	690.373
Dual form			690.2.w.b.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.877679 + 0.479249i) q^{2} +(0.997452 - 0.0713392i) q^{3} +(0.540641 - 0.841254i) q^{4} +(1.06201 - 1.96778i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(-0.702461 + 1.88337i) q^{7} +(-0.0713392 + 0.997452i) q^{8} +(0.989821 - 0.142315i) q^{9} +O(q^{10})$	\(q+(-0.877679 + 0.479249i) q^{2} +(0.997452 - 0.0713392i) q^{3} +(0.540641 - 0.841254i) q^{4} +(1.06201 - 1.96778i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(-0.702461 + 1.88337i) q^{7} +(-0.0713392 + 0.997452i) q^{8} +(0.989821 - 0.142315i) q^{9} +(0.0109547 + 2.23604i) q^{10} +(-1.33698 - 4.55332i) q^{11} +(0.479249 - 0.877679i) q^{12} +(0.596827 - 0.222605i) q^{13} +(-0.286068 - 1.98965i) q^{14} +(0.918920 - 2.03853i) q^{15} +(-0.415415 - 0.909632i) q^{16} +(5.41505 + 1.17797i) q^{17} +(-0.800541 + 0.599278i) q^{18} +(0.936443 + 0.601815i) q^{19} +(-1.08124 - 1.95728i) q^{20} +(-0.566313 + 1.92869i) q^{21} +(3.35561 + 3.35561i) q^{22} +(4.02048 - 2.61452i) q^{23} +1.00000i q^{24} +(-2.74429 - 4.17958i) q^{25} +(-0.417139 + 0.481404i) q^{26} +(0.977147 - 0.212565i) q^{27} +(1.20461 + 1.60918i) q^{28} +(2.61334 + 4.06644i) q^{29} +(0.170444 + 2.22956i) q^{30} +(-6.76992 - 7.81291i) q^{31} +(0.800541 + 0.599278i) q^{32} +(-1.65840 - 4.44634i) q^{33} +(-5.31722 + 1.56128i) q^{34} +(2.96004 + 3.38244i) q^{35} +(0.415415 - 0.909632i) q^{36} +(-2.25509 + 3.01245i) q^{37} +(-1.11032 - 0.0794113i) q^{38} +(0.579426 - 0.264615i) q^{39} +(1.88700 + 1.19968i) q^{40} +(-0.117959 + 0.820422i) q^{41} +(-0.427280 - 1.96417i) q^{42} +(-0.750245 - 10.4898i) q^{43} +(-4.55332 - 1.33698i) q^{44} +(0.771152 - 2.09889i) q^{45} +(-2.27569 + 4.22152i) q^{46} +(9.45887 - 9.45887i) q^{47} +(-0.479249 - 0.877679i) q^{48} +(2.23661 + 1.93803i) q^{49} +(4.41166 + 2.35313i) q^{50} +(5.48529 + 0.788666i) q^{51} +(0.135402 - 0.622432i) q^{52} +(-8.25215 - 3.07789i) q^{53} +(-0.755750 + 0.654861i) q^{54} +(-10.3798 - 2.20478i) q^{55} +(-1.82846 - 0.835030i) q^{56} +(0.976990 + 0.533477i) q^{57} +(-4.24252 - 2.31659i) q^{58} +(0.602627 + 0.275211i) q^{59} +(-1.21811 - 1.87515i) q^{60} +(-0.0336939 + 0.0291959i) q^{61} +(9.68615 + 3.61275i) q^{62} +(-0.427280 + 1.96417i) q^{63} +(-0.989821 - 0.142315i) q^{64} +(0.195797 - 1.41083i) q^{65} +(3.58645 + 3.10767i) q^{66} +(6.80610 + 12.4644i) q^{67} +(3.91857 - 3.91857i) q^{68} +(3.82372 - 2.89468i) q^{69} +(-4.21899 - 1.55010i) q^{70} +(5.99303 + 1.75971i) q^{71} +(0.0713392 + 0.997452i) q^{72} +(3.10030 + 14.2518i) q^{73} +(0.535533 - 3.72472i) q^{74} +(-3.03546 - 3.97316i) q^{75} +(1.01256 - 0.462420i) q^{76} +(9.51477 + 0.680510i) q^{77} +(-0.381734 + 0.509936i) q^{78} +(-2.40182 + 5.25926i) q^{79} +(-2.23113 - 0.148591i) q^{80} +(0.959493 - 0.281733i) q^{81} +(-0.289656 - 0.776598i) q^{82} +(5.71994 + 4.28190i) q^{83} +(1.31634 + 1.51914i) q^{84} +(8.06880 - 9.40460i) q^{85} +(5.68570 + 8.84712i) q^{86} +(2.89678 + 3.86965i) q^{87} +(4.63710 - 1.00874i) q^{88} +(-5.13014 + 5.92050i) q^{89} +(0.329065 + 2.21172i) q^{90} +1.28042i q^{91} +(-0.0258364 - 4.79576i) q^{92} +(-7.31004 - 7.31004i) q^{93} +(-3.76870 + 12.8350i) q^{94} +(2.17875 - 1.20358i) q^{95} +(0.841254 + 0.540641i) q^{96} +(-8.04785 + 6.02455i) q^{97} +(-2.89182 - 0.629078i) q^{98} +(-1.97137 - 4.31670i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{6}+O(q^{10}) $ 240 * q + 24 * q^6	$ 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) $ 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{22}\right)$

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 $

$2$	−0.877679	+	0.479249i	−0.620613	+	0.338880i
$2$	−0.877679	+	0.479249i	−0.620613	+	0.338880i
$3$	0.997452	−	0.0713392i	0.575879	−	0.0411877i
$3$	0.997452	−	0.0713392i	0.575879	−	0.0411877i
$4$	0.540641	−	0.841254i	0.270320	−	0.420627i
$5$	1.06201	−	1.96778i	0.474943	−	0.880016i
$5$	1.06201	−	1.96778i	0.474943	−	0.880016i
$6$	−0.841254	+	0.540641i	−0.343440	+	0.220716i
$7$	−0.702461	+	1.88337i	−0.265505	+	0.711848i	0.733961	+	0.679191i	$0.237669\pi$
$7$	−0.702461	+	1.88337i	−0.265505	+	0.711848i	−0.999467	+	0.0326563i	$0.989603\pi$
$8$	−0.0713392	+	0.997452i	−0.0252222	+	0.352653i
$9$	0.989821	−	0.142315i	0.329940	−	0.0474383i
$10$	0.0109547	+	2.23604i	0.00346418	+	0.707098i
$11$	−1.33698	−	4.55332i	−0.403113	−	1.37288i	−0.871951	−	0.489593i	$-0.837145\pi$
$11$	−1.33698	−	4.55332i	−0.403113	−	1.37288i	0.468838	−	0.883284i	$-0.344673\pi$
$12$	0.479249	−	0.877679i	0.138347	−	0.253364i
$13$	0.596827	−	0.222605i	0.165530	−	0.0617395i	−0.265333	−	0.964157i	$-0.585482\pi$
$13$	0.596827	−	0.222605i	0.165530	−	0.0617395i	0.430863	+	0.902417i	$0.358209\pi$
$14$	−0.286068	−	1.98965i	−0.0764550	−	0.531756i
$15$	0.918920	−	2.03853i	0.237264	−	0.526345i
$16$	−0.415415	−	0.909632i	−0.103854	−	0.227408i
$17$	5.41505	+	1.17797i	1.31334	+	0.285700i	0.814081	−	0.580751i	$-0.197241\pi$
$17$	5.41505	+	1.17797i	1.31334	+	0.285700i	0.499262	+	0.866451i	$0.333605\pi$
$18$	−0.800541	+	0.599278i	−0.188689	+	0.141251i
$19$	0.936443	+	0.601815i	0.214835	+	0.138066i	0.643633	−	0.765335i	$-0.277426\pi$
$19$	0.936443	+	0.601815i	0.214835	+	0.138066i	−0.428798	+	0.903400i	$0.641063\pi$
$20$	−1.08124	−	1.95728i	−0.241772	−	0.437660i
$21$	−0.566313	+	1.92869i	−0.123580	+	0.420874i
$22$	3.35561	+	3.35561i	0.715418	+	0.715418i
$23$	4.02048	−	2.61452i	0.838329	−	0.545165i
$23$	4.02048	−	2.61452i	0.838329	−	0.545165i
$24$			1.00000i			0.204124i
$25$	−2.74429	−	4.17958i	−0.548858	−	0.835916i
$26$	−0.417139	+	0.481404i	−0.0818078	+	0.0944112i
$27$	0.977147	−	0.212565i	0.188052	−	0.0409082i
$28$	1.20461	+	1.60918i	0.227651	+	0.304106i
$29$	2.61334	+	4.06644i	0.485286	+	0.755119i	0.994412	−	0.105573i	$-0.0336676\pi$
$29$	2.61334	+	4.06644i	0.485286	+	0.755119i	−0.509126	+	0.860692i	$0.670031\pi$
$30$	0.170444	+	2.22956i	0.0311187	+	0.407061i
$31$	−6.76992	−	7.81291i	−1.21591	−	1.40324i	−0.888825	−	0.458246i	$-0.848478\pi$
$31$	−6.76992	−	7.81291i	−1.21591	−	1.40324i	−0.327089	−	0.944994i	$-0.606068\pi$
$32$	0.800541	+	0.599278i	0.141517	+	0.105938i
$33$	−1.65840	−	4.44634i	−0.288690	−	0.774008i
$34$	−5.31722	+	1.56128i	−0.911895	+	0.267757i
$35$	2.96004	+	3.38244i	0.500338	+	0.571737i
$36$	0.415415	−	0.909632i	0.0692358	−	0.151605i
$37$	−2.25509	+	3.01245i	−0.370735	+	0.495244i	−0.946649	−	0.322266i	$-0.895555\pi$
$37$	−2.25509	+	3.01245i	−0.370735	+	0.495244i	0.575914	+	0.817510i	$0.304646\pi$
$38$	−1.11032	−	0.0794113i	−0.180117	−	0.0128822i
$39$	0.579426	−	0.264615i	0.0927824	−	0.0423723i
$40$	1.88700	+	1.19968i	0.298361	+	0.189686i
$41$	−0.117959	+	0.820422i	−0.0184221	+	0.128128i	−0.996957	−	0.0779523i	$-0.975162\pi$
$41$	−0.117959	+	0.820422i	−0.0184221	+	0.128128i	0.978535	+	0.206081i	$0.0660709\pi$
$42$	−0.427280	−	1.96417i	−0.0659307	−	0.303078i
$43$	−0.750245	−	10.4898i	−0.114411	−	1.59968i	−0.653165	−	0.757216i	$-0.726559\pi$
$43$	−0.750245	−	10.4898i	−0.114411	−	1.59968i	0.538754	−	0.842463i	$-0.318895\pi$
$44$	−4.55332	−	1.33698i	−0.686439	−	0.201557i
$45$	0.771152	−	2.09889i	0.114957	−	0.312884i
$46$	−2.27569	+	4.22152i	−0.335532	+	0.622429i
$47$	9.45887	−	9.45887i	1.37972	−	1.37972i	0.534635	−	0.845083i	$-0.320449\pi$
$47$	9.45887	−	9.45887i	1.37972	−	1.37972i	0.845083	−	0.534635i	$-0.179551\pi$
$48$	−0.479249	−	0.877679i	−0.0691736	−	0.126682i
$49$	2.23661	+	1.93803i	0.319516	+	0.276862i
$50$	4.41166	+	2.35313i	0.623903	+	0.332783i
$51$	5.48529	+	0.788666i	0.768094	+	0.110435i
$52$	0.135402	−	0.622432i	0.0187769	−	0.0863158i
$53$	−8.25215	−	3.07789i	−1.13352	−	0.422781i	−0.288481	−	0.957486i	$-0.593150\pi$
$53$	−8.25215	−	3.07789i	−1.13352	−	0.422781i	−0.845039	+	0.534704i	$0.820423\pi$
$54$	−0.755750	+	0.654861i	−0.102844	+	0.0891153i
$55$	−10.3798	−	2.20478i	−1.39961	−	0.297293i
$56$	−1.82846	−	0.835030i	−0.244338	−	0.111586i
$57$	0.976990	+	0.533477i	0.129405	+	0.0706607i
$58$	−4.24252	−	2.31659i	−0.557070	−	0.304183i
$59$	0.602627	+	0.275211i	0.0784554	+	0.0358294i	0.454256	−	0.890871i	$-0.349905\pi$
$59$	0.602627	+	0.275211i	0.0784554	+	0.0358294i	−0.375801	+	0.926700i	$0.622632\pi$
$60$	−1.21811	−	1.87515i	−0.157257	−	0.242081i
$61$	−0.0336939	+	0.0291959i	−0.00431406	+	0.00373815i	−0.657015	−	0.753877i	$-0.728181\pi$
$61$	−0.0336939	+	0.0291959i	−0.00431406	+	0.00373815i	0.652701	+	0.757616i	$0.273636\pi$
$62$	9.68615	+	3.61275i	1.23014	+	0.458819i
$63$	−0.427280	+	1.96417i	−0.0538322	+	0.247463i
$64$	−0.989821	−	0.142315i	−0.123728	−	0.0177894i
$65$	0.195797	−	1.41083i	0.0242856	−	0.174992i
$66$	3.58645	+	3.10767i	0.441461	+	0.382528i
$67$	6.80610	+	12.4644i	0.831497	+	1.52277i	0.852338	+	0.522991i	$0.175184\pi$
$67$	6.80610	+	12.4644i	0.831497	+	1.52277i	−0.0208408	+	0.999783i	$0.506634\pi$
$68$	3.91857	−	3.91857i	0.475196	−	0.475196i
$69$	3.82372	−	2.89468i	0.460322	−	0.348478i
$70$	−4.21899	−	1.55010i	−0.504266	−	0.185273i
$71$	5.99303	+	1.75971i	0.711242	+	0.208840i	0.617288	−	0.786737i	$-0.288231\pi$
$71$	5.99303	+	1.75971i	0.711242	+	0.208840i	0.0939539	+	0.995577i	$0.470049\pi$
$72$	0.0713392	+	0.997452i	0.00840740	+	0.117551i
$73$	3.10030	+	14.2518i	0.362862	+	1.66805i	0.690565	+	0.723270i	$0.257362\pi$
$73$	3.10030	+	14.2518i	0.362862	+	1.66805i	−0.327703	+	0.944781i	$0.606274\pi$
$74$	0.535533	−	3.72472i	0.0622545	−	0.432989i
$75$	−3.03546	−	3.97316i	−0.350505	−	0.458780i
$76$	1.01256	−	0.462420i	0.116148	−	0.0530432i
$77$	9.51477	+	0.680510i	1.08431	+	0.0775513i
$78$	−0.381734	+	0.509936i	−0.0432228	+	0.0577389i
$79$	−2.40182	+	5.25926i	−0.270226	+	0.591713i	−0.995287	−	0.0969720i	$-0.969084\pi$
$79$	−2.40182	+	5.25926i	−0.270226	+	0.591713i	0.725061	+	0.688685i	$0.241812\pi$
$80$	−2.23113	−	0.148591i	−0.249447	−	0.0166129i
$81$	0.959493	−	0.281733i	0.106610	−	0.0313036i
$82$	−0.289656	−	0.776598i	−0.0319872	−	0.0857609i
$83$	5.71994	+	4.28190i	0.627845	+	0.469999i	0.865202	−	0.501423i	$-0.167190\pi$
$83$	5.71994	+	4.28190i	0.627845	+	0.469999i	−0.237357	+	0.971423i	$0.576281\pi$
$84$	1.31634	+	1.51914i	0.143625	+	0.165752i
$85$	8.06880	−	9.40460i	0.875184	−	1.02007i
$86$	5.68570	+	8.84712i	0.613105	+	0.954010i
$87$	2.89678	+	3.86965i	0.310568	+	0.414870i
$88$	4.63710	−	1.00874i	0.494316	−	0.107532i
$89$	−5.13014	+	5.92050i	−0.543794	+	0.627572i	−0.959426	−	0.281961i	$-0.909015\pi$
$89$	−5.13014	+	5.92050i	−0.543794	+	0.627572i	0.415632	+	0.909533i	$0.363561\pi$
$90$	0.329065	+	2.21172i	0.0346865	+	0.233136i
$91$			1.28042i			0.134224i
$92$	−0.0258364	−	4.79576i	−0.00269363	−	0.499993i
$93$	−7.31004	−	7.31004i	−0.758016	−	0.758016i
$94$	−3.76870	+	12.8350i	−0.388712	+	1.32383i
$95$	2.17875	−	1.20358i	0.223535	−	0.123485i
$96$	0.841254	+	0.540641i	0.0858601	+	0.0551789i
$97$	−8.04785	+	6.02455i	−0.817136	+	0.611700i	−0.923922	−	0.382582i	$-0.875035\pi$
$97$	−8.04785	+	6.02455i	−0.817136	+	0.611700i	0.106786	+	0.994282i	$0.465944\pi$
$98$	−2.89182	−	0.629078i	−0.292118	−	0.0635465i
$99$	−1.97137	−	4.31670i	−0.198130	−	0.433845i
$100$	−4.99976	+	0.0489904i	−0.499976	+	0.00489904i
$101$	0.269810	+	1.87657i	0.0268471	+	0.186726i	0.998832	−	0.0483176i	$-0.0153860\pi$
$101$	0.269810	+	1.87657i	0.0268471	+	0.186726i	−0.971985	+	0.235043i	$0.924477\pi$
$102$	−5.19229	+	1.93662i	−0.514113	+	0.191754i
$103$	4.99269	−	9.14342i	0.491944	−	0.900928i	−0.507289	−	0.861776i	$-0.669352\pi$
$103$	4.99269	−	9.14342i	0.491944	−	0.900928i	0.999233	−	0.0391523i	$-0.0124658\pi$
$104$	0.179461	+	0.611187i	0.0175976	+	0.0599318i
$105$	3.19380	+	3.16265i	0.311683	+	0.308643i
$106$	8.71782	−	1.25343i	0.846749	−	0.121744i
$107$	1.21349	−	16.9668i	0.117313	−	1.64024i	−0.509067	−	0.860727i	$-0.670010\pi$
$107$	1.21349	−	16.9668i	0.117313	−	1.64024i	0.626380	−	0.779518i	$-0.284536\pi$
$108$	0.349464	−	0.936950i	0.0336272	−	0.0901580i
$109$	−3.47494	+	2.23321i	−0.332839	+	0.213902i	−0.696376	−	0.717677i	$-0.745205\pi$
$109$	−3.47494	+	2.23321i	−0.332839	+	0.213902i	0.363537	+	0.931580i	$0.381569\pi$
$110$	10.1668	−	3.03941i	0.969363	−	0.289797i
$111$	−2.03444	+	3.16565i	−0.193101	+	0.300470i
$112$	2.00499	−	0.143400i	0.189454	−	0.0135500i
$113$	−3.13629	+	1.71254i	−0.295037	+	0.161102i	−0.619950	−	0.784642i	$-0.712847\pi$
$113$	−3.13629	+	1.71254i	−0.295037	+	0.161102i	0.324913	+	0.945744i	$0.394665\pi$
$114$	−1.11315			−0.104256
$115$	−0.875013	−	10.6880i	−0.0815954	−	0.996666i
$116$	4.83379			0.448806
$117$	0.559072	−	0.305277i	0.0516862	−	0.0282228i
$118$	−0.660808	+	0.0472619i	−0.0608323	+	0.00435081i
$119$	−6.02242	+	9.37108i	−0.552075	+	0.859045i
$120$	1.96778	+	1.06201i	0.179633	+	0.0969474i
$121$	−9.69143	+	6.22831i	−0.881039	+	0.566210i
$122$	0.0155803	−	0.0417724i	0.00141057	−	0.00378189i
$123$	−0.0591301	+	0.826746i	−0.00533158	+	0.0745452i
$124$	−10.2327	+	1.47125i	−0.918927	+	0.132122i
$125$	−11.1389	+	0.961407i	−0.996296	+	0.0859908i
$126$	−0.566313	−	1.92869i	−0.0504512	−	0.171821i
$127$	−4.13794	+	7.57808i	−0.367183	+	0.672446i	−0.994316	−	0.106466i	$-0.966046\pi$
$127$	−4.13794	+	7.57808i	−0.367183	+	0.672446i	0.627133	+	0.778912i	$0.284228\pi$
$128$	0.936950	−	0.349464i	0.0828154	−	0.0308886i
$129$	−1.49667	−	10.4095i	−0.131774	−	0.916510i
$130$	0.504292	+	1.33209i	0.0442293	+	0.116832i
$131$	−5.11100	−	11.1915i	−0.446550	−	0.977808i	−0.990349	−	0.138593i	$-0.955742\pi$
$131$	−5.11100	−	11.1915i	−0.446550	−	0.977808i	0.543800	−	0.839215i	$-0.316985\pi$
$132$	−4.63710	−	1.00874i	−0.403608	−	0.0877994i
$133$	−1.79126	+	1.34092i	−0.155322	+	0.116272i
$134$	−11.9471	−	7.67796i	−1.03208	−	0.663275i
$135$	0.619455	−	2.14855i	0.0533142	−	0.184918i
$136$	−1.56128	+	5.31722i	−0.133878	+	0.455948i
$137$	2.08249	+	2.08249i	0.177919	+	0.177919i	0.790448	−	0.612529i	$-0.209848\pi$
$137$	2.08249	+	2.08249i	0.177919	+	0.177919i	−0.612529	+	0.790448i	$0.709848\pi$
$138$	−1.96873	+	4.37311i	−0.167589	+	0.372264i
$139$		−	2.91727i		−	0.247439i	−0.992317	−	0.123720i	$-0.960518\pi$
$139$		−	2.91727i		−	0.247439i	0.992317	−	0.123720i	$-0.0394824\pi$
$140$	4.44581	−	0.661457i	0.375739	−	0.0559033i
$141$	8.75998	−	10.1096i	0.737724	−	0.851378i
$142$	−6.10330	+	1.32769i	−0.512178	+	0.111417i
$143$	−1.81153	−	2.41993i	−0.151488	−	0.202364i
$144$	−0.540641	−	0.841254i	−0.0450534	−	0.0701045i
$145$	10.7772	−	0.823891i	0.895001	−	0.0684204i
$146$	−9.55124	−	11.0227i	−0.790467	−	0.912247i
$147$	2.36917	+	1.77354i	0.195406	+	0.146279i
$148$	1.31504	+	3.52576i	0.108096	+	0.289816i
$149$	−4.89606	+	1.43761i	−0.401101	+	0.117774i	−0.476060	−	0.879413i	$-0.657936\pi$
$149$	−4.89606	+	1.43761i	−0.401101	+	0.117774i	0.0749592	+	0.997187i	$0.476117\pi$
$150$	4.56829	+	2.03241i	0.373000	+	0.165946i
$151$	−8.37239	+	18.3330i	−0.681336	+	1.49192i	0.179886	+	0.983687i	$0.442427\pi$
$151$	−8.37239	+	18.3330i	−0.681336	+	1.49192i	−0.861222	+	0.508230i	$0.830300\pi$
$152$	−0.667087	+	0.891124i	−0.0541079	+	0.0722797i
$153$	5.52758	+	0.395340i	0.446878	+	0.0319613i
$154$	−8.67705	+	3.96267i	−0.699216	+	0.319321i
$155$	−22.5638	+	5.02434i	−1.81236	+	0.403565i
$156$	0.0906530	−	0.630506i	0.00725805	−	0.0504809i
$157$	−2.09074	−	9.61097i	−0.166859	−	0.767039i	−0.982167	−	0.188011i	$-0.939796\pi$
$157$	−2.09074	−	9.61097i	−0.166859	−	0.767039i	0.815308	−	0.579028i	$-0.196568\pi$
$158$	−0.412465	−	5.76701i	−0.0328139	−	0.458799i
$159$	−8.45070	−	2.48135i	−0.670184	−	0.196784i
$160$	2.02942	−	0.938850i	0.160440	−	0.0742226i
$161$	2.09988	+	9.40867i	0.165494	+	0.741507i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	7.75249	+	14.1976i	0.607222	+	1.11204i	0.982699	+	0.185212i	$0.0592971\pi$
$163$	7.75249	+	14.1976i	0.607222	+	1.11204i	−0.375477	+	0.926832i	$0.622521\pi$
$164$	0.626409	+	0.542787i	0.0489143	+	0.0423845i
$165$	−10.5106	−	1.45868i	−0.818252	−	0.113558i
$166$	−7.07237	−	1.01685i	−0.548922	−	0.0789231i
$167$	−5.20304	+	23.9180i	−0.402623	+	1.85083i	0.112413	+	0.993662i	$0.464142\pi$
$167$	−5.20304	+	23.9180i	−0.402623	+	1.85083i	−0.515036	+	0.857168i	$0.672221\pi$
$168$	−1.88337	−	0.702461i	−0.145305	−	0.0541961i
$169$	−9.51809	+	8.24748i	−0.732161	+	0.634421i
$170$	−2.57467	+	12.1212i	−0.197468	+	0.929652i
$171$	1.01256	+	0.462420i	0.0774323	+	0.0353621i
$172$	−9.23019	−	5.04007i	−0.703796	−	0.384301i
$173$	7.96720	+	4.35042i	0.605735	+	0.330756i	0.752678	−	0.658389i	$-0.228762\pi$
$173$	7.96720	+	4.35042i	0.605735	+	0.330756i	−0.146943	+	0.989145i	$0.546943\pi$
$174$	−4.39697	−	2.00803i	−0.333333	−	0.152228i
$175$	9.79946	−	2.23252i	0.740770	−	0.168763i
$176$	−3.58645	+	3.10767i	−0.270339	+	0.234250i
$177$	0.620725	+	0.231518i	0.0466565	+	0.0174020i
$178$	1.66523	−	7.65492i	0.124814	−	0.573760i
$179$	−9.62962	−	1.38453i	−0.719751	−	0.103485i	−0.227300	−	0.973825i	$-0.572990\pi$
$179$	−9.62962	−	1.38453i	−0.719751	−	0.103485i	−0.492451	+	0.870340i	$0.663899\pi$
$180$	−1.34878	−	1.78348i	−0.100532	−	0.132933i
$181$	−7.53837	−	6.53203i	−0.560322	−	0.485522i	0.328041	−	0.944664i	$-0.393612\pi$
$181$	−7.53837	−	6.53203i	−0.560322	−	0.485522i	−0.888363	+	0.459142i	$0.848157\pi$
$182$	−0.613639	−	1.12380i	−0.0454860	−	0.0833014i
$183$	−0.0315252	+	0.0315252i	−0.00233041	+	0.00233041i
$184$	2.32104	+	4.19676i	0.171109	+	0.309389i
$185$	3.53291	+	7.63676i	0.259745	+	0.561466i
$186$	9.91920	+	2.91254i	0.727311	+	0.213558i
$187$	−1.87611	−	26.2314i	−0.137194	−	1.91823i
$188$	−2.84346	−	13.0712i	−0.207380	−	0.953312i
$189$	−0.286068	+	1.98965i	−0.0208084	+	0.144726i
$190$	−1.33542	+	2.10052i	−0.0968819	+	0.152388i
$191$	−19.2920	+	8.81038i	−1.39592	+	0.637497i	−0.964362	−	0.264587i	$-0.914765\pi$
$191$	−19.2920	+	8.81038i	−1.39592	+	0.637497i	−0.431562	+	0.902083i	$0.642037\pi$
$192$	−0.997452	−	0.0713392i	−0.0719849	−	0.00514846i
$193$	0.171593	−	0.229222i	0.0123515	−	0.0164997i	−0.794323	−	0.607496i	$-0.792174\pi$
$193$	0.171593	−	0.229222i	0.0123515	−	0.0164997i	0.806675	+	0.590996i	$0.201265\pi$
$194$	4.17617	−	9.14455i	0.299832	−	0.656540i
$195$	0.0946506	−	1.42120i	0.00677807	−	0.101774i
$196$	2.83958	−	0.833775i	0.202827	−	0.0595554i
$197$	7.79011	+	20.8861i	0.555023	+	1.48807i	0.846971	+	0.531639i	$0.178424\pi$
$197$	7.79011	+	20.8861i	0.555023	+	1.48807i	−0.291948	+	0.956434i	$0.594303\pi$
$198$	3.79901	+	2.84390i	0.269984	+	0.202107i
$199$	−3.15315	−	3.63893i	−0.223521	−	0.257957i	0.632902	−	0.774232i	$-0.281864\pi$
$199$	−3.15315	−	3.63893i	−0.223521	−	0.257957i	−0.856423	+	0.516275i	$0.827318\pi$
$200$	4.36471	−	2.43913i	0.308631	−	0.172472i
$201$	7.67796	+	11.9471i	0.541562	+	0.842686i
$202$	−1.13615	−	1.51772i	−0.0799392	−	0.106786i
$203$	−9.49440	+	2.06538i	−0.666376	+	0.144961i
$204$	3.62904	−	4.18813i	0.254084	−	0.293228i
$205$	1.48913	+	1.10341i	0.104006	+	0.0770654i
$206$			10.4177i			0.725838i
$207$	3.60748	−	3.16008i	0.250737	−	0.219641i
$208$	−0.450420	−	0.450420i	−0.0312310	−	0.0312310i
$209$	1.48826	−	5.06854i	0.102945	−	0.350598i
$210$	−4.31883	−	1.24517i	−0.298027	−	0.0859250i
$211$	12.1215	+	7.79002i	0.834479	+	0.536287i	0.886698	−	0.462349i	$-0.152993\pi$
$211$	12.1215	+	7.79002i	0.834479	+	0.536287i	−0.0522193	+	0.998636i	$0.516629\pi$
$212$	−7.05074	+	5.27812i	−0.484247	+	0.362503i
$213$	6.10330	+	1.32769i	0.418191	+	0.0909719i
$214$	7.06628	+	15.4730i	0.483041	+	1.05771i
$215$	−21.4383	−	9.66391i	−1.46208	−	0.659073i
$216$	0.142315	+	0.989821i	0.00968330	+	0.0673488i
$217$	19.4702	−	7.26202i	1.32173	−	0.492978i
$218$	1.97962	−	3.62540i	0.134077	−	0.245543i
$219$	4.10911	+	13.9944i	0.277668	+	0.945651i
$220$	−7.46652	+	7.54004i	−0.503393	+	0.508349i
$221$	3.49407	−	0.502372i	0.235037	−	0.0337932i
$222$	0.268451	−	3.75343i	0.0180172	−	0.251914i
$223$	−9.35069	+	25.0702i	−0.626168	+	1.67882i	0.103166	+	0.994664i	$0.467103\pi$
$223$	−9.35069	+	25.0702i	−0.626168	+	1.67882i	−0.729334	+	0.684158i	$0.760170\pi$
$224$	−1.69101	+	1.08675i	−0.112986	+	0.0726114i
$225$	−3.31117	−	3.74648i	−0.220745	−	0.249766i
$226$	1.93192	−	3.00612i	0.128509	−	0.199964i
$227$	8.95513	−	0.640484i	0.594373	−	0.0425104i	0.229087	−	0.973406i	$-0.426426\pi$
$227$	8.95513	−	0.640484i	0.594373	−	0.0425104i	0.365286	+	0.930895i	$0.380971\pi$
$228$	0.976990	−	0.533477i	0.0647027	−	0.0353304i
$229$	5.87869			0.388475			0.194237	−	0.980955i	$-0.437777\pi$
$229$	5.87869			0.388475			0.194237	+	0.980955i	$0.437777\pi$
$230$	5.89022	+	8.96133i	0.388389	+	0.590892i
$231$	9.53907			0.627625
$232$	−4.24252	+	2.31659i	−0.278535	+	0.152091i
$233$	1.30300	−	0.0931925i	0.0853625	−	0.00610524i	−0.0285926	−	0.999591i	$-0.509103\pi$
$233$	1.30300	−	0.0931925i	0.0853625	−	0.00610524i	0.113955	+	0.993486i	$0.463648\pi$
$234$	−0.344382	+	0.535870i	−0.0225130	+	0.0350309i
$235$	−8.56757	−	28.6583i	−0.558886	−	1.86946i
$236$	0.557327	−	0.358172i	0.0362789	−	0.0233150i
$237$	−2.02051	+	5.41720i	−0.131246	+	0.351885i
$238$	0.794677	−	11.1110i	0.0515113	−	0.720222i
$239$	−19.3952	+	2.78861i	−1.25457	+	0.180380i	−0.737372	−	0.675486i	$-0.763934\pi$
$239$	−19.3952	+	2.78861i	−1.25457	+	0.180380i	−0.517197	+	0.855866i	$0.673025\pi$
$240$	−2.23604	+	0.0109547i	−0.144336	+	0.000707123i
$241$	2.32917	+	7.93244i	0.150035	+	0.510973i	0.999871	−	0.0160748i	$-0.00511698\pi$
$241$	2.32917	+	7.93244i	0.150035	+	0.510973i	−0.849836	+	0.527048i	$0.823299\pi$
$242$	5.52106	−	10.1111i	0.354907	−	0.649964i
$243$	0.936950	−	0.349464i	0.0601054	−	0.0224181i
$244$	0.00634487	+	0.0441296i	0.000406189	+	0.00282511i
$245$	6.18891	−	2.34294i	0.395395	−	0.149685i
$246$	−0.344320	−	0.753956i	−0.0219530	−	0.0480705i
$247$	0.692861	+	0.150723i	0.0440857	+	0.00959026i
$248$	8.27596	−	6.19531i	0.525524	−	0.393402i
$249$	6.01084	+	3.86293i	0.380921	+	0.244803i
$250$	9.31565	−	6.18213i	0.589173	−	0.390992i
$251$	3.54466	−	12.0720i	0.223737	−	0.761978i	−0.768742	−	0.639559i	$-0.779117\pi$
$251$	3.54466	−	12.0720i	0.223737	−	0.761978i	0.992479	−	0.122418i	$-0.0390650\pi$
$252$	1.42136	+	1.42136i	0.0895374	+	0.0895374i
$253$	−17.2800	−	14.8110i	−1.08639	−	0.931160i
$254$		−	8.63423i		−	0.541760i
$255$	7.37733	−	9.95626i	0.461986	−	0.623485i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	13.4462	−	2.92503i	0.838748	−	0.182459i	0.227381	−	0.973806i	$-0.426984\pi$
$257$	13.4462	−	2.92503i	0.838748	−	0.182459i	0.611367	+	0.791347i	$0.290620\pi$
$258$	6.30236	+	8.41897i	0.392368	+	0.524142i
$259$	−4.08945	−	6.36331i	−0.254106	−	0.395397i
$260$	−1.08101	−	0.927467i	−0.0670414	−	0.0575191i
$261$	3.16546	+	3.65313i	0.195937	+	0.226123i
$262$	9.84934	+	7.37312i	0.608494	+	0.455513i
$263$	−7.91950	−	21.2330i	−0.488337	−	1.30928i	−0.914481	−	0.404628i	$-0.867401\pi$
$263$	−7.91950	−	21.2330i	−0.488337	−	1.30928i	0.426144	−	0.904655i	$-0.359872\pi$
$264$	4.55332	−	1.33698i	0.280237	−	0.0822852i
$265$	−14.8204	+	12.9696i	−0.910412	+	0.796719i
$266$	0.929515	−	2.03535i	0.0569922	−	0.124796i
$267$	−4.69471	+	6.27140i	−0.287312	+	0.383803i
$268$	14.1654	+	1.01313i	0.865290	+	0.0618868i
$269$	−11.2574	+	5.14109i	−0.686377	+	0.313458i	−0.727904	−	0.685679i	$-0.759505\pi$
$269$	−11.2574	+	5.14109i	−0.686377	+	0.313458i	0.0415265	+	0.999137i	$0.486778\pi$
$270$	0.486009	+	2.18261i	0.0295776	+	0.132830i
$271$	1.44080	−	10.0210i	0.0875221	−	0.608730i	−0.898103	−	0.439785i	$-0.855055\pi$
$271$	1.44080	−	10.0210i	0.0875221	−	0.608730i	0.985625	−	0.168945i	$-0.0540361\pi$
$272$	−1.17797	−	5.41505i	−0.0714251	−	0.328336i
$273$	0.0913440	+	1.27716i	0.00552839	+	0.0772970i
$274$	−2.82579	−	0.829727i	−0.170712	−	0.0501256i
$275$	−15.3619	+	18.0836i	−0.926359	+	1.09048i
$276$	−0.367896	−	4.78170i	−0.0221448	−	0.287825i
$277$	−8.51502	+	8.51502i	−0.511618	+	0.511618i	−0.915022	−	0.403404i	$-0.867827\pi$
$277$	−8.51502	+	8.51502i	−0.511618	+	0.511618i	0.403404	+	0.915022i	$0.367827\pi$
$278$	1.39810	+	2.56043i	0.0838523	+	0.153564i
$279$	−7.81291	−	6.76992i	−0.467747	−	0.405305i
$280$	−3.58499	+	2.71119i	−0.214244	+	0.162025i
$281$	13.5372	+	1.94635i	0.807560	+	0.116110i	0.533715	−	0.845664i	$-0.320796\pi$
$281$	13.5372	+	1.94635i	0.807560	+	0.116110i	0.273845	+	0.961774i	$0.411705\pi$
$282$	−2.84346	+	13.0712i	−0.169325	+	0.778376i
$283$	17.6229	+	6.57299i	1.04757	+	0.390724i	0.813542	−	0.581506i	$-0.197536\pi$
$283$	17.6229	+	6.57299i	1.04757	+	0.390724i	0.234029	+	0.972230i	$0.424809\pi$
$284$	4.72044	−	4.09029i	0.280107	−	0.242714i
$285$	2.08733	−	1.35594i	0.123643	−	0.0803191i
$286$	2.74969	+	1.25574i	0.162593	+	0.0742536i
$287$	−1.46230	−	0.798475i	−0.0863167	−	0.0471325i
$288$	0.877679	+	0.479249i	0.0517177	+	0.0282400i
$289$	12.4714	+	5.69550i	0.733612	+	0.335030i
$290$	−9.06410	+	5.88809i	−0.532263	+	0.345761i
$291$	−7.59756	+	6.58333i	−0.445377	+	0.385921i
$292$	13.6656	+	5.09699i	0.799716	+	0.298279i
$293$	2.27658	−	10.4653i	0.132999	−	0.611388i	−0.861599	−	0.507590i	$-0.830537\pi$
$293$	2.27658	−	10.4653i	0.132999	−	0.611388i	0.994598	−	0.103799i	$-0.0330998\pi$
$294$	−2.92933	−	0.421175i	−0.170842	−	0.0245634i
$295$	1.18155	−	0.893560i	0.0687923	−	0.0520251i
$296$	−2.84390	−	2.46425i	−0.165298	−	0.143232i
$297$	−2.27430	−	4.16507i	−0.131968	−	0.241682i
$298$	3.60819	−	3.60819i	0.209017	−	0.209017i
$299$	1.81753	−	2.45540i	0.105110	−	0.141999i
$300$	−4.98353	+	0.405544i	−0.287724	+	0.0234141i
$301$	20.2832	+	5.95569i	1.16910	+	0.343280i
$302$	−1.43779	−	20.1029i	−0.0827355	−	1.15679i
$303$	0.402995	+	1.85254i	0.0231515	+	0.106426i
$304$	0.158418	−	1.10182i	0.00908589	−	0.0631938i
$305$	0.0216679	+	0.0973082i	0.00124070	+	0.00557185i
$306$	−5.04090	+	2.30210i	−0.288169	+	0.131603i
$307$	−7.73818	−	0.553445i	−0.441641	−	0.0315868i	−0.151252	−	0.988495i	$-0.548330\pi$
$307$	−7.73818	−	0.553445i	−0.441641	−	0.0315868i	−0.290390	+	0.956908i	$0.593785\pi$
$308$	5.71655	−	7.63642i	0.325731	−	0.435126i
$309$	4.32768	−	9.47630i	0.246193	−	0.539088i
$310$	17.3958	−	15.2234i	0.988016	−	0.864632i
$311$	9.80835	−	2.87999i	0.556181	−	0.163309i	0.00845034	−	0.999964i	$-0.497310\pi$
$311$	9.80835	−	2.87999i	0.556181	−	0.163309i	0.547730	+	0.836655i	$0.315492\pi$
$312$	0.222605	+	0.596827i	0.0126025	+	0.0337887i
$313$	6.80047	+	5.09077i	0.384385	+	0.287747i	0.773944	−	0.633255i	$-0.218281\pi$
$313$	6.80047	+	5.09077i	0.384385	+	0.287747i	−0.389558	+	0.921002i	$0.627372\pi$
$314$	6.44105	+	7.43336i	0.363489	+	0.419489i
$315$	3.41128	+	2.92675i	0.192204	+	0.164904i
$316$	3.12585	+	4.86391i	0.175843	+	0.273616i
$317$	−10.8663	−	14.5157i	−0.610313	−	0.815283i	0.383824	−	0.923406i	$-0.374607\pi$
$317$	−10.8663	−	14.5157i	−0.610313	−	0.815283i	−0.994137	+	0.108123i	$0.965516\pi$
$318$	8.60619	−	1.87216i	0.482611	−	0.104986i
$319$	15.0218	−	17.3361i	0.841061	−	0.970637i
$320$	−1.33124	+	1.79661i	−0.0744186	+	0.100433i
$321$		−	17.0102i		−	0.949415i
$322$	−6.35211	−	7.25142i	−0.353989	−	0.404106i
$323$	4.36196	+	4.36196i	0.242706	+	0.242706i
$324$	0.281733	−	0.959493i	0.0156518	−	0.0533052i
$325$	−2.56826	−	1.88359i	−0.142461	−	0.104483i
$326$	−13.6084	−	8.74558i	−0.753699	−	0.484373i
$327$	−3.30677	+	2.47542i	−0.182865	+	0.136891i
$328$	−0.809916	−	0.176186i	−0.0447201	−	0.00972827i
$329$	11.1701	+	24.4591i	0.615827	+	1.34847i
$330$	9.92403	−	3.75696i	0.546300	−	0.206814i
$331$	−1.46380	−	10.1809i	−0.0804576	−	0.559595i	−0.989681	−	0.143287i	$-0.954233\pi$
$331$	−1.46380	−	10.1809i	−0.0804576	−	0.559595i	0.909224	−	0.416308i	$-0.136676\pi$
$332$	6.69459	−	2.49695i	0.367414	−	0.137038i
$333$	−1.80342	+	3.30272i	−0.0988269	+	0.180988i
$334$	−6.89608	−	23.4859i	−0.377336	−	1.28509i
$335$	31.7553	−	0.155574i	1.73498	−	0.00849993i
$336$	1.98965	−	0.286068i	0.108544	−	0.0156063i
$337$	0.163916	−	2.29184i	0.00892905	−	0.124844i	−0.991032	−	0.133622i	$-0.957339\pi$
$337$	0.163916	−	2.29184i	0.00892905	−	0.124844i	0.999961	+	0.00877714i	$0.00279389\pi$
$338$	4.40124	−	11.8002i	0.239396	−	0.641845i
$339$	−3.00612	+	1.93192i	−0.163270	+	0.104927i
$340$	−3.54933	−	11.8724i	−0.192489	−	0.643872i
$341$	−26.5235	+	41.2713i	−1.43633	+	2.23497i
$342$	−1.11032	+	0.0794113i	−0.0600390	+	0.00429407i
$343$	−17.5708	+	9.59438i	−0.948733	+	0.518048i
$344$	10.5166			0.567017
$345$	−1.63526	−	10.5984i	−0.0880395	−	0.570598i
$346$	−9.07758			−0.488014
$347$	−5.09505	+	2.78211i	−0.273517	+	0.149351i	−0.610154	−	0.792283i	$-0.708892\pi$
$347$	−5.09505	+	2.78211i	−0.273517	+	0.149351i	0.336637	+	0.941635i	$0.390710\pi$
$348$	4.82147	−	0.344839i	0.258458	−	0.0184853i
$349$	11.0874	−	17.2524i	0.593496	−	0.923498i	−0.406455	−	0.913671i	$-0.633235\pi$
$349$	11.0874	−	17.2524i	0.593496	−	0.923498i	0.999952	−	0.00982758i	$-0.00312827\pi$
$350$	−7.53085	+	6.65582i	−0.402541	+	0.355768i
$351$	0.535870	−	0.344382i	0.0286026	−	0.0183818i
$352$	1.65840	−	4.44634i	0.0883930	−	0.236991i
$353$	−0.0389063	+	0.543981i	−0.00207077	+	0.0289532i	−0.998382	−	0.0568551i	$-0.981893\pi$
$353$	−0.0389063	+	0.543981i	−0.00207077	+	0.0289532i	0.996312	+	0.0858083i	$0.0273473\pi$
$354$	−0.655752	+	0.0942829i	−0.0348528	+	0.00501108i
$355$	9.82736	−	9.92412i	0.521582	−	0.526718i
$356$	2.20708	+	7.51662i	0.116975	+	0.398380i
$357$	−5.33856	+	9.77683i	−0.282546	+	0.517445i
$358$	9.11525	−	3.39981i	0.481756	−	0.179686i
$359$	−1.86676	−	12.9836i	−0.0985237	−	0.685247i	−0.977893	−	0.209107i	$-0.932944\pi$
$359$	−1.86676	−	12.9836i	−0.0985237	−	0.685247i	0.879369	−	0.476141i	$-0.157965\pi$
$360$	2.03853	+	0.918920i	0.107440	+	0.0484314i
$361$	−7.37814	−	16.1559i	−0.388323	−	0.850309i
$362$	9.74673	+	2.12027i	0.512277	+	0.111439i
$363$	−9.22242	+	6.90382i	−0.484051	+	0.362356i
$364$	1.07716	+	0.692247i	0.0564584	+	0.0362836i
$365$	31.3370	+	9.03484i	1.64025	+	0.472905i
$366$	0.0125606	−	0.0427774i	0.000656552	−	0.00223601i
$367$	19.5724	+	19.5724i	1.02167	+	1.02167i	0.999760	+	0.0219136i	$0.00697588\pi$
$367$	19.5724	+	19.5724i	1.02167	+	1.02167i	0.0219136	+	0.999760i	$0.493024\pi$
$368$	−4.04842	−	2.57105i	−0.211038	−	0.134025i
$369$			0.828858i			0.0431486i
$370$	−6.76067	−	5.00948i	−0.351470	−	0.260430i
$371$	11.5936	−	13.3798i	0.601912	−	0.694643i
$372$	−10.1017	+	2.19749i	−0.523749	+	0.113935i
$373$	0.377831	+	0.504723i	0.0195634	+	0.0261336i	0.810216	−	0.586131i	$-0.199350\pi$
$373$	0.377831	+	0.504723i	0.0195634	+	0.0261336i	−0.790653	+	0.612265i	$0.790259\pi$
$374$	14.2180	+	22.1236i	0.735194	+	1.14398i
$375$	−11.0420	+	1.75360i	−0.570204	+	0.0905555i
$376$	8.75998	+	10.1096i	0.451762	+	0.521361i
$377$	2.46492	+	1.84522i	0.126950	+	0.0950336i
$378$	−0.702461	−	1.88337i	−0.0361307	−	0.0968702i
$379$	−1.18112	+	0.346808i	−0.0606700	+	0.0178143i	−0.311927	−	0.950106i	$-0.600974\pi$
$379$	−1.18112	+	0.346808i	−0.0606700	+	0.0178143i	0.251257	+	0.967920i	$0.419156\pi$
$380$	0.165404	−	2.48358i	0.00848504	−	0.127405i
$381$	−3.58679	+	7.85397i	−0.183757	+	0.402371i
$382$	12.7099	−	16.9784i	0.650293	−	0.868690i
$383$	−25.0665	−	1.79279i	−1.28084	−	0.0916073i	−0.585726	−	0.810509i	$-0.699191\pi$
$383$	−25.0665	−	1.79279i	−1.28084	−	0.0916073i	−0.695112	+	0.718902i	$0.744645\pi$
$384$	0.909632	−	0.415415i	0.0464195	−	0.0211991i
$385$	11.4438	−	18.0002i	0.583232	−	0.917377i
$386$	−0.0407495	+	0.283419i	−0.00207409	+	0.0144256i
$387$	−2.23546	−	10.2763i	−0.113635	−	0.522371i
$388$	0.717174	+	10.0274i	0.0364090	+	0.509064i
$389$	30.7659	+	9.03367i	1.55989	+	0.458025i	0.944038	−	0.329836i	$-0.106993\pi$
$389$	30.7659	+	9.03367i	1.55989	+	0.458025i	0.615853	+	0.787861i	$0.288812\pi$
$390$	0.598037	+	1.29272i	0.0302828	+	0.0654595i
$391$	24.8510	−	9.42174i	1.25677	−	0.476478i
$392$	−2.09265	+	2.09265i	−0.105695	+	0.105695i
$393$	−5.89637	−	10.7984i	−0.297432	−	0.544707i
$394$	−16.8469	−	14.5979i	−0.848733	−	0.735431i
$395$	7.79829	+	10.3116i	0.392375	+	0.518833i
$396$	−4.69725	−	0.675362i	−0.236045	−	0.0339382i
$397$	−2.69067	+	12.3688i	−0.135041	+	0.620774i	0.859019	+	0.511943i	$0.171074\pi$
$397$	−2.69067	+	12.3688i	−0.135041	+	0.620774i	−0.994060	+	0.108830i	$0.965289\pi$
$398$	4.51141	+	1.68267i	0.226137	+	0.0843446i
$399$	−1.69103	+	1.46529i	−0.0846575	+	0.0733562i
$400$	−2.66186	+	4.23255i	−0.133093	+	0.211628i
$401$	12.5643	+	5.73793i	0.627431	+	0.286538i	0.703643	−	0.710553i	$-0.251555\pi$
$401$	12.5643	+	5.73793i	0.627431	+	0.286538i	−0.0762119	+	0.997092i	$0.524283\pi$
$402$	−12.4644	−	6.80610i	−0.621670	−	0.339457i
$403$	−5.77967	−	3.15594i	−0.287906	−	0.157208i
$404$	1.72454	+	0.787571i	0.0857991	+	0.0391831i
$405$	0.464600	−	2.18727i	0.0230862	−	0.108686i
$406$	7.34320	−	6.36292i	0.364437	−	0.315786i
$407$	16.7317	+	6.24059i	0.829357	+	0.309334i
$408$	−1.17797	+	5.41505i	−0.0583183	+	0.268085i
$409$	35.8484	+	5.15422i	1.77259	+	0.254860i	0.949659	−	0.313285i	$-0.101429\pi$
$409$	35.8484	+	5.15422i	1.77259	+	0.254860i	0.822929	+	0.568145i	$0.192339\pi$
$410$	−1.83579	−	0.254773i	−0.0906631	−	0.0125824i
$411$	2.22575	+	1.92862i	0.109788	+	0.0951319i
$412$	−4.99269	−	9.14342i	−0.245972	−	0.450464i
$413$	−0.941646	+	0.941646i	−0.0463354	+	0.0463354i
$414$	−1.65174	+	4.50242i	−0.0811786	+	0.221282i
$415$	14.5004	−	6.70817i	0.711798	−	0.329291i
$416$	0.611187	+	0.179461i	0.0299659	+	0.00879878i
$417$	−0.208116	−	2.90984i	−0.0101915	−	0.142495i
$418$	1.12288	+	5.16179i	0.0549218	+	0.252472i
$419$	2.49713	−	17.3680i	0.121993	−	0.848480i	−0.833300	−	0.552820i	$-0.813552\pi$
$419$	2.49713	−	17.3680i	0.121993	−	0.848480i	0.955293	−	0.295660i	$-0.0955394\pi$
$420$	4.38729	−	0.976932i	0.214078	−	0.0476694i
$421$	−21.9977	+	10.0460i	−1.07210	+	0.489614i	−0.871670	−	0.490093i	$-0.836963\pi$
$421$	−21.9977	+	10.0460i	−1.07210	+	0.489614i	−0.200434	+	0.979707i	$0.564235\pi$
$422$	−14.3721	−	1.02792i	−0.699625	−	0.0500382i
$423$	8.01646	−	10.7087i	0.389773	−	0.520676i
$424$	3.65875	−	8.01155i	0.177685	−	0.389075i
$425$	−9.93703	−	25.8653i	−0.482017	−	1.25465i
$426$	−5.99303	+	1.75971i	−0.290363	+	0.0852584i
$427$	−0.0313181	−	0.0839671i	−0.00151559	−	0.00406345i
$428$	−13.6173	−	10.1938i	−0.658219	−	0.492736i
$429$	−1.97955	−	2.28453i	−0.0955738	−	0.110298i
$430$	23.4474	−	1.79249i	1.13073	−	0.0864416i
$431$	1.51969	+	2.36469i	0.0732010	+	0.113903i	0.875924	−	0.482449i	$-0.160253\pi$
$431$	1.51969	+	2.36469i	0.0732010	+	0.113903i	−0.802723	+	0.596352i	$0.796616\pi$
$432$	−0.599278	−	0.800541i	−0.0288328	−	0.0385161i
$433$	−23.4752	+	5.10672i	−1.12815	+	0.245414i	−0.737645	−	0.675188i	$-0.764062\pi$
$433$	−23.4752	+	5.10672i	−1.12815	+	0.245414i	−0.390502	+	0.920602i	$0.627699\pi$
$434$	−13.6083	+	15.7048i	−0.653219	+	0.753855i
$435$	10.6910	−	1.59063i	0.512594	−	0.0762649i
$436$			4.13067i			0.197823i
$437$	5.33841	−	0.0287598i	0.255371	−	0.00137577i
$438$	−10.3133	−	10.3133i	−0.492787	−	0.492787i
$439$	5.69150	−	19.3835i	0.271641	−	0.925123i	−0.704813	−	0.709394i	$-0.748969\pi$
$439$	5.69150	−	19.3835i	0.271641	−	0.925123i	0.976453	−	0.215729i	$-0.0692129\pi$
$440$	2.93965	−	10.1961i	0.140142	−	0.486078i
$441$	2.48965	+	1.60000i	0.118555	+	0.0761906i
$442$	−2.82591	+	2.11545i	−0.134415	+	0.100622i
$443$	38.7341	+	8.42609i	1.84031	+	0.400336i	0.991689	−	0.128659i	$-0.0410673\pi$
$443$	38.7341	+	8.42609i	1.84031	+	0.400336i	0.848625	+	0.528995i	$0.177431\pi$
$444$	1.56321	+	3.42296i	0.0741869	+	0.162447i
$445$	6.20198	+	16.3826i	0.294002	+	0.776609i
$446$	−3.80795	−	26.4849i	−0.180312	−	1.25409i
$447$	−4.78103	+	1.78323i	−0.226135	+	0.0843439i
$448$	0.963343	−	1.76423i	0.0455137	−	0.0833521i
$449$	4.85943	+	16.5497i	0.229331	+	0.781028i	0.991093	+	0.133172i	$0.0425162\pi$
$449$	4.85943	+	16.5497i	0.229331	+	0.781028i	−0.761762	+	0.647856i	$0.775666\pi$
$450$	4.70164	+	1.70134i	0.221638	+	0.0802017i
$451$	3.89335	−	0.559779i	0.183331	−	0.0263590i
$452$	−0.254922	+	3.56428i	−0.0119905	+	0.167650i
$453$	−7.04320	+	18.8836i	−0.330918	+	0.887227i
$454$	−7.55278	+	4.85388i	−0.354470	+	0.227804i
$455$	2.51958	+	1.35981i	0.118120	+	0.0637490i
$456$	−0.601815	+	0.936443i	−0.0281826	+	0.0438529i
$457$	35.9028	−	2.56782i	1.67946	−	0.120117i	0.801231	−	0.598355i	$-0.204179\pi$
$457$	35.9028	−	2.56782i	1.67946	−	0.120117i	0.878230	+	0.478238i	$0.158724\pi$
$458$	−5.15960	+	2.81735i	−0.241092	+	0.131646i
$459$	5.54170			0.258664
$460$	−9.46443	−	5.04229i	−0.441281	−	0.235098i
$461$	−26.0387			−1.21274			−0.606371	−	0.795182i	$-0.707375\pi$
$461$	−26.0387			−1.21274			−0.606371	+	0.795182i	$0.707375\pi$
$462$	−8.37225	+	4.57159i	−0.389512	+	0.212690i
$463$	16.9619	−	1.21314i	0.788285	−	0.0563792i	0.328609	−	0.944466i	$-0.393420\pi$
$463$	16.9619	−	1.21314i	0.788285	−	0.0563792i	0.459676	+	0.888087i	$0.347966\pi$
$464$	2.61334	−	4.06644i	0.121321	−	0.188780i
$465$	−22.1478	+	6.62122i	−1.02708	+	0.307052i
$466$	−1.09895	+	0.706255i	−0.0509081	+	0.0327166i
$467$	−7.20841	+	19.3265i	−0.333566	+	0.894324i	0.656577	+	0.754259i	$0.272004\pi$
$467$	−7.20841	+	19.3265i	−0.333566	+	0.894324i	−0.990142	+	0.140065i	$0.955269\pi$
$468$	0.0454423	−	0.635366i	0.00210057	−	0.0293698i
$469$	−28.2562	+	4.06263i	−1.30475	+	0.187595i
$470$	21.2540	+	21.0468i	0.980376	+	0.970817i
$471$	−2.77105	−	9.43733i	−0.127683	−	0.434849i
$472$	−0.317500	+	0.581458i	−0.0146141	+	0.0267638i
$473$	−46.7603	+	17.4407i	−2.15004	+	0.801925i
$474$	−0.822828	−	5.72289i	−0.0377937	−	0.262861i
$475$	−0.0545337	−	5.56549i	−0.00250218	−	0.255362i
$476$	4.62748	+	10.1328i	0.212100	+	0.464435i
$477$	−8.60619	−	1.87216i	−0.394050	−	0.0857204i
$478$	15.6863	−	11.7426i	0.717475	−	0.537095i
$479$	−15.2859	−	9.82368i	−0.698433	−	0.448855i	0.142642	−	0.989774i	$-0.454440\pi$
$479$	−15.2859	−	9.82368i	−0.698433	−	0.448855i	−0.841075	+	0.540919i	$0.818077\pi$
$480$	1.95728	−	1.08124i	0.0893370	−	0.0493514i
$481$	−0.675314	+	2.29991i	−0.0307916	+	0.104867i
$482$	−5.84588	−	5.84588i	−0.266273	−	0.266273i
$483$	2.76573	+	9.23489i	0.125845	+	0.420202i
$484$			11.5202i			0.523647i
$485$	3.30810	+	22.2345i	0.150213	+	1.00962i
$486$	−0.654861	+	0.755750i	−0.0297051	+	0.0342815i
$487$	−19.1294	+	4.16135i	−0.866837	+	0.188569i	−0.623929	−	0.781481i	$-0.714465\pi$
$487$	−19.1294	+	4.16135i	−0.866837	+	0.188569i	−0.242907	+	0.970049i	$0.578101\pi$
$488$	−0.0267178	−	0.0356908i	−0.00120946	−	0.00161565i
$489$	8.74558	+	13.6084i	0.395489	+	0.615393i
$490$	−4.30902	+	5.02238i	−0.194662	+	0.226888i
$491$	−27.2556	−	31.4546i	−1.23003	−	1.41953i	−0.874615	−	0.484819i	$-0.838885\pi$
$491$	−27.2556	−	31.4546i	−1.23003	−	1.41953i	−0.355414	−	0.934709i	$-0.615660\pi$
$492$	0.663535	+	0.496716i	0.0299145	+	0.0223937i
$493$	9.36123	+	25.0984i	0.421609	+	1.13038i
$494$	−0.680344	+	0.199767i	−0.0306101	+	0.00898794i
$495$	−10.5879	−	0.705144i	−0.475891	−	0.0316938i
$496$	−4.29454	+	9.40374i	−0.192831	+	0.422240i
$497$	−7.52407	+	10.0510i	−0.337501	+	0.450848i
$498$	−7.12689	−	0.509725i	−0.319364	−	0.0228413i
$499$	0.580749	−	0.265219i	0.0259979	−	0.0118729i	−0.402374	−	0.915476i	$-0.631815\pi$
$499$	0.580749	−	0.265219i	0.0259979	−	0.0118729i	0.428372	+	0.903603i	$0.359087\pi$
$500$	−5.21337	+	9.89044i	−0.233149	+	0.442314i
$501$	−3.48349	+	24.2282i	−0.155631	+	1.08244i
$502$	2.67442	+	12.2941i	0.119365	+	0.548713i
$503$	−0.451763	−	6.31648i	−0.0201431	−	0.281638i	−0.997533	−	0.0701942i	$-0.977638\pi$
$503$	−0.451763	−	6.31648i	−0.0201431	−	0.281638i	0.977390	−	0.211444i	$-0.0678165\pi$
$504$	−1.92869	−	0.566313i	−0.0859105	−	0.0252256i
$505$	3.97921	+	1.46200i	0.177072	+	0.0650582i
$506$	22.2645	+	4.71787i	0.989777	+	0.209735i
$507$	−8.90548	+	8.90548i	−0.395506	+	0.395506i
$508$	4.13794	+	7.57808i	0.183592	+	0.336223i
$509$	6.88009	+	5.96163i	0.304955	+	0.264245i	0.793871	−	0.608086i	$-0.208062\pi$
$509$	6.88009	+	5.96163i	0.304955	+	0.264245i	−0.488917	+	0.872330i	$0.662608\pi$
$510$	−1.70340	+	12.2740i	−0.0754278	+	0.543501i
$511$	−29.0194	−	4.17235i	−1.28374	−	0.184574i
$512$	0.212565	−	0.977147i	0.00939415	−	0.0431842i
$513$	1.04297	+	0.389007i	0.0460481	+	0.0171751i
$514$	−10.3996	+	9.01130i	−0.458706	+	0.397471i
$515$	−12.6899	−	19.5349i	−0.559186	−	0.860809i
$516$	−9.56623	−	4.36875i	−0.421130	−	0.192324i
$517$	−55.7155	−	30.4230i	−2.45037	−	1.33800i
$518$	6.63883	+	3.62508i	0.291694	+	0.159277i
$519$	8.25726	+	3.77096i	0.362453	+	0.165527i
$520$	1.39327	+	0.295946i	0.0610988	+	0.0129781i
$521$	21.9741	−	19.0407i	0.962704	−	0.834188i	−0.0234995	−	0.999724i	$-0.507481\pi$
$521$	21.9741	−	19.0407i	0.962704	−	0.834188i	0.986204	+	0.165536i	$0.0529354\pi$
$522$	−4.52902	−	1.68924i	−0.198230	−	0.0739359i
$523$	−2.47431	+	11.3742i	−0.108194	+	0.497360i	0.890876	+	0.454246i	$0.150091\pi$
$523$	−2.47431	+	11.3742i	−0.108194	+	0.497360i	−0.999070	+	0.0431138i	$0.986272\pi$
$524$	−12.1781	−	1.75095i	−0.532004	−	0.0764906i
$525$	9.61523	−	2.92592i	0.419643	−	0.127698i
$526$	17.1267	+	14.8404i	0.746759	+	0.647070i
$527$	−27.4561	−	50.2821i	−1.19601	−	2.19032i
$528$	−3.35561	+	3.35561i	−0.146034	+	0.146034i
$529$	9.32857	−	21.0233i	0.405590	−	0.914055i
$530$	6.79190	−	18.4859i	0.295021	−	0.802975i
$531$	0.635660	+	0.186647i	0.0275853	+	0.00809977i
$532$	0.159625	+	2.23186i	0.00692064	+	0.0967632i
$533$	0.112229	+	0.515908i	0.00486117	+	0.0223465i
$534$	1.11489	−	7.75421i	0.0482459	−	0.335557i
$535$	−32.0982	−	20.4067i	−1.38773	−	0.882261i
$536$	−12.9182	+	5.89956i	−0.557982	+	0.254822i
$537$	−9.70385	−	0.694033i	−0.418752	−	0.0299498i
$538$	7.41654	−	9.90734i	0.319750	−	0.427136i
$539$	5.83419	−	12.7751i	0.251296	−	0.550262i
$540$	−1.47257	−	1.68271i	−0.0633695	−	0.0724125i
$541$	18.2961	−	5.37221i	0.786609	−	0.230969i	0.136329	−	0.990664i	$-0.456470\pi$
$541$	18.2961	−	5.37221i	0.786609	−	0.230969i	0.650280	+	0.759694i	$0.274652\pi$
$542$	3.53798	+	9.48568i	0.151969	+	0.407445i
$543$	−7.98515	−	5.97761i	−0.342676	−	0.256524i
$544$	3.62904	+	4.18813i	0.155594	+	0.179565i
$545$	0.704048	+	9.20958i	0.0301581	+	0.394495i
$546$	−0.692247	−	1.07716i	−0.0296254	−	0.0460981i
$547$	7.70705	+	10.2954i	0.329530	+	0.440200i	0.934455	−	0.356083i	$-0.115888\pi$
$547$	7.70705	+	10.2954i	0.329530	+	0.440200i	−0.604925	+	0.796282i	$0.706797\pi$
$548$	2.87778	−	0.626023i	0.122933	−	0.0267424i
$549$	−0.0291959	+	0.0336939i	−0.00124605	+	0.00143802i
$550$	4.81628	−	23.2338i	0.205367	−	0.990692i
$551$			5.38074i			0.229227i
$552$	2.61452	+	4.02048i	0.111281	+	0.171123i
$553$	−8.21795	−	8.21795i	−0.349463	−	0.349463i
$554$	3.39264	−	11.5543i	0.144139	−	0.490894i
$555$	4.06871	+	7.36527i	0.172707	+	0.312638i
$556$	−2.45416	−	1.57719i	−0.104080	−	0.0668879i
$557$	21.1488	−	15.8318i	0.896105	−	0.670816i	−0.0485716	−	0.998820i	$-0.515467\pi$
$557$	21.1488	−	15.8318i	0.896105	−	0.670816i	0.944676	+	0.328004i	$0.106376\pi$
$558$	10.1017	+	2.19749i	0.427639	+	0.0930272i
$559$	−2.78285	−	6.09359i	−0.117702	−	0.257731i
$560$	1.84713	−	4.09766i	0.0780555	−	0.173158i
$561$	−3.74265	−	26.0307i	−0.158015	−	1.09902i
$562$	−12.8141	+	4.77940i	−0.540529	+	0.201607i
$563$	−7.20004	+	13.1859i	−0.303446	+	0.555719i	−0.984258	−	0.176739i	$-0.943445\pi$
$563$	−7.20004	+	13.1859i	−0.303446	+	0.555719i	0.680812	+	0.732458i	$0.261627\pi$
$564$	−3.76870	−	12.8350i	−0.158691	−	0.540451i
$565$	0.0391454	+	7.99024i	0.00164686	+	0.336152i
$566$	−18.6173	+	2.67677i	−0.782545	+	0.112513i
$567$	−0.143400	+	2.00499i	−0.00602222	+	0.0842016i
$568$	−2.18277	+	5.85223i	−0.0915869	+	0.245554i
$569$	6.70522	−	4.30919i	0.281098	−	0.180650i	−0.392493	−	0.919755i	$-0.628387\pi$
$569$	6.70522	−	4.30919i	0.281098	−	0.180650i	0.673591	+	0.739104i	$0.264751\pi$
$570$	−1.18217	+	2.19043i	−0.0495158	+	0.0917472i
$571$	5.31856	−	8.27585i	0.222575	−	0.346333i	−0.711950	−	0.702230i	$-0.752188\pi$
$571$	5.31856	−	8.27585i	0.222575	−	0.346333i	0.934525	+	0.355896i	$0.115824\pi$
$572$	−3.01516	+	0.215649i	−0.126070	+	0.00901672i
$573$	−18.6144	+	10.1642i	−0.777626	+	0.424616i
$574$	1.66610			0.0695415
$575$	−21.9610	−	9.62894i	−0.915835	−	0.401554i
$576$	−1.00000			−0.0416667
$577$	−13.2034	+	7.20958i	−0.549663	+	0.300139i	−0.729979	−	0.683470i	$-0.760470\pi$
$577$	−13.2034	+	7.20958i	−0.549663	+	0.300139i	0.180315	+	0.983609i	$0.442288\pi$
$578$	−13.6755	+	0.978088i	−0.568824	+	0.0406831i
$579$	0.154803	−	0.240879i	0.00643341	−	0.0100106i
$580$	5.13351	−	9.51182i	0.213157	−	0.394957i
$581$	−12.0824	+	7.76491i	−0.501264	+	0.322143i
$582$	3.51317	−	9.41917i	0.145626	−	0.390437i
$583$	−2.98171	+	41.6898i	−0.123490	+	1.72661i
$584$	−14.4367	+	2.07568i	−0.597395	+	0.0858924i
$585$	−0.00697803	−	1.42433i	−0.000288506	−	0.0588890i
$586$	3.01737	+	10.2762i	0.124646	+	0.424506i
$587$	1.17888	−	2.15897i	0.0486578	−	0.0891100i	−0.852218	−	0.523186i	$-0.824743\pi$
$587$	1.17888	−	2.15897i	0.0486578	−	0.0891100i	0.900876	+	0.434076i	$0.142925\pi$
$588$	2.77286	−	1.03422i	0.114351	−	0.0426507i
$589$	−1.63772	−	11.3906i	−0.0674810	−	0.469341i
$590$	−0.608781	+	1.35051i	−0.0250631	+	0.0555998i
$591$	9.26026	+	20.2771i	0.380916	+	0.834090i
$592$	3.67702	+	0.799887i	0.151125	+	0.0328752i
$593$	−20.7993	+	15.5702i	−0.854125	+	0.639390i	−0.933944	−	0.357419i	$-0.883657\pi$
$593$	−20.7993	+	15.5702i	−0.854125	+	0.639390i	0.0798191	+	0.996809i	$0.474566\pi$
$594$	3.99221	+	2.56564i	0.163802	+	0.105269i
$595$	12.0443	+	21.8029i	0.493769	+	0.893833i
$596$	−1.43761	+	4.89606i	−0.0588869	+	0.200550i
$597$	−3.40472	−	3.40472i	−0.139346	−	0.139346i
$598$	−0.418460	+	3.02610i	−0.0171121	+	0.123746i
$599$			32.1078i			1.31189i	0.754809	+	0.655945i	$0.227730\pi$
$599$			32.1078i			1.31189i	−0.754809	+	0.655945i	$0.772270\pi$
$600$	4.17958	−	2.74429i	0.170631	−	0.112035i
$601$	13.6523	−	15.7556i	0.556891	−	0.642686i	−0.405584	−	0.914058i	$-0.632932\pi$
$601$	13.6523	−	15.7556i	0.556891	−	0.642686i	0.962475	+	0.271372i	$0.0874772\pi$
$602$	−20.6564	+	4.49353i	−0.841892	+	0.183142i
$603$	8.51070	+	11.3690i	0.346582	+	0.462980i
$604$	10.8962	+	16.9549i	0.443361	+	0.689884i
$605$	1.96356	+	25.6851i	0.0798299	+	1.04425i
$606$	−1.24153	−	1.43280i	−0.0504336	−	0.0582035i
$607$	−14.6526	−	10.9688i	−0.594732	−	0.445211i	0.259034	−	0.965868i	$-0.416596\pi$
$607$	−14.6526	−	10.9688i	−0.594732	−	0.445211i	−0.853766	+	0.520658i	$0.825687\pi$
$608$	0.389007	+	1.04297i	0.0157763	+	0.0422979i
$609$	−9.32286	+	2.73744i	−0.377782	+	0.110927i
$610$	−0.0656523	−	0.0750210i	−0.00265819	−	0.00303751i
$611$	3.53972	−	7.75090i	0.143202	−	0.313568i
$612$	3.32101	−	4.43636i	0.134244	−	0.179329i
$613$	37.4376	+	2.67759i	1.51209	+	0.108147i	0.802579	−	0.596545i	$-0.203460\pi$
$613$	37.4376	+	2.67759i	1.51209	+	0.108147i	0.709513	+	0.704692i	$0.248915\pi$
$614$	7.05688	−	3.22277i	0.284792	−	0.130060i
$615$	1.56406	+	0.994364i	0.0630688	+	0.0400966i
$616$	−1.35755	+	9.44198i	−0.0546973	+	0.380428i
$617$	−4.13932	−	19.0282i	−0.166643	−	0.766045i	−0.982271	−	0.187468i	$-0.939972\pi$
$617$	−4.13932	−	19.0282i	−0.166643	−	0.766045i	0.815628	−	0.578577i	$-0.196392\pi$
$618$	0.743192	+	10.3912i	0.0298956	+	0.417995i
$619$	25.7558	+	7.56258i	1.03521	+	0.303966i	0.754829	−	0.655922i	$-0.227720\pi$
$619$	25.7558	+	7.56258i	1.03521	+	0.303966i	0.280384	+	0.959888i	$0.409538\pi$
$620$	−7.97214	+	21.6982i	−0.320169	+	0.871421i
$621$	3.37285	−	3.40938i	0.135348	−	0.136814i
$622$	−7.22835	+	7.22835i	−0.289831	+	0.289831i
$623$	−7.54678	−	13.8209i	−0.302355	−	0.553723i
$624$	−0.481404	−	0.417139i	−0.0192716	−	0.0166989i
$625$	−9.93777	+	22.9399i	−0.397511	+	0.917597i
$626$	−8.40838	−	1.20894i	−0.336066	−	0.0483190i
$627$	1.12288	−	5.16179i	0.0448435	−	0.206142i
$628$	−9.21560	−	3.43724i	−0.367743	−	0.137161i
$629$	−15.7600	+	13.6561i	−0.628393	+	0.544506i
$630$	−4.39665	−	0.933898i	−0.175167	−	0.0372074i
$631$	−13.0249	−	5.94827i	−0.518513	−	0.236797i	0.138929	−	0.990302i	$-0.455634\pi$
$631$	−13.0249	−	5.94827i	−0.518513	−	0.236797i	−0.657442	+	0.753506i	$0.728361\pi$
$632$	−5.07451	−	2.77089i	−0.201853	−	0.110220i
$633$	12.6464	+	6.90543i	0.502648	+	0.274466i
$634$	16.4938	+	7.53245i	0.655051	+	0.299152i
$635$	10.5174	+	16.1905i	0.417372	+	0.642501i
$636$	−6.65624	+	5.76766i	−0.263937	+	0.228703i
$637$	1.76628	+	0.658790i	0.0699827	+	0.0261022i
$638$	−4.87603	+	22.4148i	−0.193044	+	0.887409i
$639$	6.18247	+	0.888904i	0.244575	+	0.0351645i
$640$	0.307379	−	2.21484i	0.0121502	−	0.0875493i
$641$	−16.1348	−	13.9809i	−0.637287	−	0.552212i	0.275164	−	0.961397i	$-0.411268\pi$
$641$	−16.1348	−	13.9809i	−0.637287	−	0.552212i	−0.912452	+	0.409185i	$0.865813\pi$
$642$	8.15210	+	14.9295i	0.321738	+	0.589219i
$643$	19.1539	−	19.1539i	0.755355	−	0.755355i	−0.220118	−	0.975473i	$-0.570644\pi$
$643$	19.1539	−	19.1539i	0.755355	−	0.755355i	0.975473	+	0.220118i	$0.0706443\pi$
$644$	9.05035	+	3.32018i	0.356634	+	0.130833i
$645$	−22.0731	−	8.10989i	−0.869129	−	0.319327i
$646$	−5.91887	−	1.73794i	−0.232875	−	0.0683782i
$647$	2.96504	+	41.4567i	0.116568	+	1.62983i	0.633456	+	0.773778i	$0.281636\pi$
$647$	2.96504	+	41.4567i	0.116568	+	1.62983i	−0.516889	+	0.856053i	$0.672910\pi$
$648$	0.212565	+	0.977147i	0.00835035	+	0.0383860i
$649$	0.447424	−	3.11190i	0.0175629	−	0.122153i
$650$	3.15682	+	0.422355i	0.123821	+	0.0165661i
$651$	18.9026	−	8.63251i	0.740849	−	0.338335i
$652$	16.1351	+	1.15401i	0.631900	+	0.0451944i
$653$	22.0520	−	29.4580i	0.862961	−	1.15278i	−0.124073	−	0.992273i	$-0.539596\pi$
$653$	22.0520	−	29.4580i	0.862961	−	1.15278i	0.987035	−	0.160508i	$-0.0513133\pi$
$654$	1.71594	−	3.75739i	0.0670986	−	0.146925i
$655$	−27.4503	−	1.82816i	−1.07257	−	0.0714322i
$656$	0.795284	−	0.233516i	0.0310506	−	0.00911728i
$657$	5.09699	+	13.6656i	0.198852	+	0.533144i
$658$	−21.5257	−	16.1140i	−0.839160	−	0.628188i
$659$	−6.70149	−	7.73393i	−0.261053	−	0.301271i	0.610059	−	0.792356i	$-0.291146\pi$
$659$	−6.70149	−	7.73393i	−0.261053	−	0.301271i	−0.871112	+	0.491085i	$0.836600\pi$
$660$	−6.90960	+	8.05348i	−0.268956	+	0.313481i
$661$	−20.5051	−	31.9066i	−0.797557	−	1.24102i	−0.966822	−	0.255452i	$-0.917776\pi$
$661$	−20.5051	−	31.9066i	−0.797557	−	1.24102i	0.169265	−	0.985571i	$-0.445861\pi$
$662$	6.16395	+	8.23407i	0.239569	+	0.320026i
$663$	3.44933	−	0.750356i	0.133961	−	0.0291414i
$664$	−4.67904	+	5.39990i	−0.181582	+	0.209557i
$665$	0.736302	+	4.94886i	0.0285526	+	0.191908i
$666$		−	3.76302i		−	0.145814i
$667$	21.1387	+	9.51643i	0.818494	+	0.368477i
$668$	17.3081	+	17.3081i	0.669671	+	0.669671i
$669$	−7.53838	+	25.6734i	−0.291450	+	0.992589i
$670$	−27.7964	+	15.3553i	−1.07387	+	0.593226i
$671$	0.177986	+	0.114385i	0.00687108	+	0.00441577i
$672$	−1.60918	+	1.20461i	−0.0620753	+	0.0464690i
$673$	−19.3318	−	4.20538i	−0.745188	−	0.162106i	−0.176088	−	0.984374i	$-0.556344\pi$
$673$	−19.3318	−	4.20538i	−0.745188	−	0.162106i	−0.569099	+	0.822269i	$0.692708\pi$
$674$	0.954496	+	2.09006i	0.0367658	+	0.0805059i
$675$	−3.57001	−	3.50072i	−0.137410	−	0.134743i
$676$	1.79235	+	12.4661i	0.0689365	+	0.479464i
$677$	48.1061	−	17.9426i	1.84887	−	0.689592i	0.867504	−	0.497430i	$-0.165723\pi$
$677$	48.1061	−	17.9426i	1.84887	−	0.689592i	0.981363	−	0.192162i	$-0.0615500\pi$
$678$	1.71254	−	3.13629i	0.0657698	−	0.120448i
$679$	−5.69316	−	19.3891i	−0.218483	−	0.744086i
$680$	8.80501	+	8.71916i	0.337657	+	0.334364i
$681$	8.88663	−	1.27770i	0.340536	−	0.0489617i
$682$	3.49985	−	48.9343i	0.134016	−	1.87379i
$683$	4.81007	−	12.8963i	0.184052	−	0.493463i	−0.811854	−	0.583861i	$-0.801541\pi$
$683$	4.81007	−	12.8963i	0.184052	−	0.493463i	0.995906	+	0.0903983i	$0.0288140\pi$
$684$	0.936443	−	0.601815i	0.0358058	−	0.0230110i
$685$	6.30949	−	1.88626i	0.241073	−	0.0720702i
$686$	10.8234	−	16.8416i	0.413240	−	0.643014i
$687$	5.86371	−	0.419381i	0.223714	−	0.0160004i
$688$	−9.23019	+	5.04007i	−0.351898	+	0.192151i
$689$	−5.61026			−0.213734
$690$	6.51450	+	8.51829i	0.248003	+	0.324286i
$691$	34.2962			1.30469			0.652345	−	0.757922i	$-0.273785\pi$
$691$	34.2962			1.30469			0.652345	+	0.757922i	$0.273785\pi$
$692$	7.96720	−	4.35042i	0.302868	−	0.165378i
$693$	9.51477	−	0.680510i	0.361436	−	0.0258504i
$694$	3.13850	−	4.88360i	0.119136	−	0.185379i
$695$	−5.74053	−	3.09816i	−0.217751	−	0.117520i
$696$	−4.06644	+	2.61334i	−0.154138	+	0.0990585i
$697$	−1.60519	+	4.30367i	−0.0608008	+	0.163013i
$698$	−1.46302	+	20.4557i	−0.0553761	+	0.774259i
$699$	1.29303	−	0.185910i	0.0489070	−	0.00703177i
$700$	3.41987	−	9.45082i	0.129259	−	0.357208i
$701$	−0.780204	−	2.65713i	−0.0294679	−	0.100358i	0.943446	−	0.331526i	$-0.107564\pi$
$701$	−0.780204	−	2.65713i	−0.0294679	−	0.100358i	−0.972914	+	0.231168i	$0.925745\pi$
$702$	−0.305277	+	0.559072i	−0.0115219	+	0.0211008i
$703$	−3.92470	+	1.46384i	−0.148023	+	0.0552097i
$704$	0.675362	+	4.69725i	0.0254537	+	0.177034i
$705$	−10.5902	−	27.9741i	−0.398850	−	1.05357i
$706$	−0.226555	−	0.496087i	−0.00852652	−	0.0186705i
$707$	−3.72381	−	0.810065i	−0.140048	−	0.0304656i
$708$	0.530355	−	0.397019i	0.0199320	−	0.0149209i
$709$	0.869917	+	0.559062i	0.0326704	+	0.0209960i	0.556874	−	0.830597i	$-0.312001\pi$
$709$	0.869917	+	0.559062i	0.0326704	+	0.0209960i	−0.524204	+	0.851593i	$0.675637\pi$
$710$	−3.86914	+	13.4199i	−0.145206	+	0.503642i
$711$	−1.62890	+	5.54754i	−0.0610887	+	0.208049i
$712$	−5.53944	−	5.53944i	−0.207599	−	0.207599i
$713$	−47.6454	−	13.7116i	−1.78433	−	0.513502i
$714$		−	11.1394i		−	0.416882i
$715$	−6.68574	+	0.994719i	−0.250032	+	0.0372004i
$716$	−6.37091	+	7.35242i	−0.238092	+	0.274773i
$717$	−19.1468	+	4.16514i	−0.715051	+	0.155550i
$718$	7.86078	+	10.5008i	0.293362	+	0.391886i
$719$	17.5785	+	27.3527i	0.655567	+	1.02008i	0.996787	+	0.0800986i	$0.0255235\pi$
$719$	17.5785	+	27.3527i	0.655567	+	1.02008i	−0.341220	+	0.939983i	$0.610840\pi$
$720$	−2.22956	+	0.170444i	−0.0830909	+	0.00635208i
$721$	13.7133	+	15.8260i	0.510710	+	0.589391i
$722$	14.2183	+	10.6437i	0.529151	+	0.396118i
$723$	2.88913	+	7.74607i	0.107448	+	0.288079i
$724$	−9.57064	+	2.81019i	−0.355690	+	0.104440i
$725$	9.82425	−	22.0822i	0.364864	−	0.820111i
$726$	4.78568	−	10.4792i	0.177613	−	0.388918i
$727$	−30.5586	+	40.8216i	−1.13336	+	1.51399i	−0.306244	+	0.951953i	$0.599072\pi$
$727$	−30.5586	+	40.8216i	−1.13336	+	1.51399i	−0.827114	+	0.562035i	$0.810019\pi$
$728$	−1.27716	−	0.0913440i	−0.0473346	−	0.00338544i
$729$	0.909632	−	0.415415i	0.0336901	−	0.0153857i
$730$	−31.8337	+	7.08852i	−1.17822	+	0.262358i
$731$	8.29407	−	57.6866i	0.306767	−	2.13361i
$732$	0.00947688	+	0.0435645i	0.000350275	+	0.00161019i
$733$	0.437055	+	6.11082i	0.0161430	+	0.225708i	0.999119	+	0.0419731i	$0.0133644\pi$
$733$	0.437055	+	6.11082i	0.0161430	+	0.225708i	−0.982976	+	0.183735i	$0.941181\pi$
$734$	−26.5584	−	7.79825i	−0.980289	−	0.287839i
$735$	6.00599	−	2.77849i	0.221534	−	0.102486i
$736$	4.78539	+	0.316355i	0.176392	+	0.0116610i
$737$	47.6550	−	47.6550i	1.75539	−	1.75539i
$738$	−0.397229	−	0.727471i	−0.0146222	−	0.0267786i
$739$	12.9401	+	11.2127i	0.476010	+	0.412465i	0.859544	−	0.511062i	$-0.170748\pi$
$739$	12.9401	+	11.2127i	0.476010	+	0.412465i	−0.383534	+	0.923527i	$0.625293\pi$
$740$	8.33448	+	1.15667i	0.306382	+	0.0425201i
$741$	0.701848	+	0.100911i	0.0257830	+	0.00370704i
$742$	−3.76325	+	17.2994i	−0.138153	+	0.635080i
$743$	−44.8130	−	16.7144i	−1.64403	−	0.613191i	−0.654312	−	0.756225i	$-0.727042\pi$
$743$	−44.8130	−	16.7144i	−1.64403	−	0.613191i	−0.989718	+	0.143034i	$0.954314\pi$
$744$	7.81291	−	6.76992i	0.286435	−	0.248197i
$745$	−2.37074	+	11.1611i	−0.0868573	+	0.408911i
$746$	−0.573503	−	0.261910i	−0.0209974	−	0.00958920i
$747$	6.27110	+	3.42428i	0.229448	+	0.125288i
$748$	−23.0815	−	12.6035i	−0.843945	−	0.460829i
$749$	31.1024	+	14.2040i	1.13646	+	0.519003i
$750$	8.85089	−	6.83095i	0.323189	−	0.249431i
$751$	13.2567	−	11.4870i	0.483743	−	0.419166i	−0.378546	−	0.925583i	$-0.623576\pi$
$751$	13.2567	−	11.4870i	0.483743	−	0.419166i	0.862289	+	0.506417i	$0.169030\pi$
$752$	−12.5334	−	4.67473i	−0.457048	−	0.170470i
$753$	2.67442	−	12.2941i	0.0974613	−	0.448022i
$754$	−3.04773	−	0.438198i	−0.110992	−	0.0159582i
$755$	27.1837	+	35.9447i	0.989316	+	1.30816i
$756$	1.51914	+	1.31634i	0.0552506	+	0.0478749i
$757$	−6.55421	−	12.0031i	−0.238217	−	0.436261i	0.731032	−	0.682343i	$-0.239039\pi$
$757$	−6.55421	−	12.0031i	−0.238217	−	0.436261i	−0.969249	+	0.246081i	$0.920857\pi$
$758$	0.870436	−	0.870436i	0.0316157	−	0.0316157i
$759$	−18.2926	−	13.5405i	−0.663980	−	0.491490i
$760$	1.04508	+	2.25906i	0.0379091	+	0.0819446i
$761$	0.614378	+	0.180398i	0.0222712	+	0.00653941i	0.292849	−	0.956159i	$-0.405397\pi$
$761$	0.614378	+	0.180398i	0.0222712	+	0.00653941i	−0.270578	+	0.962698i	$0.587215\pi$
$762$	−0.615959	−	8.61223i	−0.0223138	−	0.311988i
$763$	−1.76495	−	8.11334i	−0.0638955	−	0.293723i
$764$	−3.01830	+	20.9928i	−0.109198	+	0.759491i
$765$	6.64826	−	10.4572i	0.240368	−	0.378080i
$766$	22.8595	−	10.4396i	0.825948	−	0.377198i
$767$	0.420927	+	0.0301053i	0.0151988	+	0.00108704i
$768$	−0.599278	+	0.800541i	−0.0216246	+	0.0288870i
$769$	11.4769	−	25.1310i	0.413868	−	0.906246i	−0.581805	−	0.813328i	$-0.697653\pi$
$769$	11.4769	−	25.1310i	0.413868	−	0.906246i	0.995674	−	0.0929175i	$-0.0296193\pi$
$770$	−1.41742	+	21.2829i	−0.0510801	+	0.766981i
$771$	13.2032	−	3.87682i	0.475503	−	0.139620i
$772$	−0.100063	−	0.268280i	−0.00360135	−	0.00965560i
$773$	9.77394	+	7.31668i	0.351544	+	0.263163i	0.760426	−	0.649425i	$-0.224990\pi$
$773$	9.77394	+	7.31668i	0.351544	+	0.263163i	−0.408882	+	0.912587i	$0.634081\pi$
$774$	6.88690	+	7.94791i	0.247545	+	0.285682i
$775$	−14.0761	+	49.7363i	−0.505627	+	1.78658i
$776$	−5.43507	−	8.45714i	−0.195108	−	0.303593i
$777$	−4.53298	−	6.05536i	−0.162620	−	0.217235i
$778$	−31.3319	+	6.81584i	−1.12330	+	0.244360i
$779$	−0.604204	+	0.697288i	−0.0216478	+	0.0249829i
$780$	−1.14442	−	0.847986i	−0.0409768	−	0.0303628i
$781$		−	29.6409i		−	1.06063i
$782$	−17.2958	+	20.1791i	−0.618497	+	0.721602i
$783$	3.41801	+	3.41801i	0.122150	+	0.122150i
$784$	0.833775	−	2.83958i	0.0297777	−	0.101414i
$785$	−21.1326	−	6.09280i	−0.754256	−	0.217461i
$786$	10.3502	+	6.65169i	0.369181	+	0.237258i
$787$	−16.3028	+	12.2041i	−0.581132	+	0.435030i	−0.848975	−	0.528432i	$-0.822780\pi$
$787$	−16.3028	+	12.2041i	−0.581132	+	0.435030i	0.267843	+	0.963463i	$0.413689\pi$
$788$	21.7822	+	4.73842i	0.775957	+	0.168799i
$789$	−9.41407	−	20.6139i	−0.335150	−	0.733876i
$790$	−11.7862	−	5.31296i	−0.419335	−	0.189027i
$791$	−1.02223	−	7.10979i	−0.0363464	−	0.252795i
$792$	4.44634	−	1.65840i	0.157994	−	0.0589286i
$793$	−0.0136103	+	0.0249253i	−0.000483314	+	0.000885124i
$794$	−3.56620	−	12.1454i	−0.126560	−	0.431023i
$795$	−13.8574	+	13.9939i	−0.491472	+	0.496312i
$796$	−4.76599	+	0.685246i	−0.168926	+	0.0242879i
$797$	−0.462695	+	6.46932i	−0.0163895	+	0.229155i	0.982655	+	0.185445i	$0.0593725\pi$
$797$	−0.462695	+	6.46932i	−0.0163895	+	0.229155i	−0.999044	+	0.0437106i	$0.986082\pi$
$798$	0.781946	−	2.09648i	0.0276806	−	0.0742145i
$799$	62.3626	−	40.0780i	2.20623	−	1.41786i
$800$	0.307813	−	4.99052i	0.0108828	−	0.176441i
$801$	−4.23535	+	6.59034i	−0.149649	+	0.232858i
$802$	−13.7773	+	0.985374i	−0.486494	+	0.0347947i
$803$	60.7482	−	33.1710i	2.14376	−	1.17058i
$804$	14.2016			0.500852
$805$	20.7442	+	5.85997i	0.731138	+	0.206537i
$806$	6.58517			0.231953
$807$	−10.8620	+	5.93109i	−0.382360	+	0.208784i
$808$	−1.89104	+	0.135250i	−0.0665264	+	0.00475806i
$809$	−2.42777	+	3.77769i	−0.0853560	+	0.132816i	−0.881306	−	0.472545i	$-0.843335\pi$
$809$	−2.42777	+	3.77769i	−0.0853560	+	0.132816i	0.795950	+	0.605362i	$0.206972\pi$
$810$	0.640477	+	2.14238i	0.0225041	+	0.0752755i
$811$	−44.0147	+	28.2865i	−1.54556	+	0.993274i	−0.559137	+	0.829075i	$0.688867\pi$
$811$	−44.0147	+	28.2865i	−1.54556	+	0.993274i	−0.986427	+	0.164199i	$0.947496\pi$
$812$	−3.39555	+	9.10382i	−0.119160	+	0.319482i
$813$	0.722238	−	10.0982i	0.0253300	−	0.354160i
$814$	−17.6758	+	2.54140i	−0.619537	+	0.0890760i
$815$	36.1709	−	0.177207i	1.26701	−	0.00620729i
$816$	−1.56128	−	5.31722i	−0.0546556	−	0.186140i
$817$	5.61036	−	10.2746i	0.196282	−	0.359463i
$818$	−33.9335	+	12.6565i	−1.18646	+	0.442526i
$819$	0.182223	+	1.26739i	0.00636737	+	0.0442860i
$820$	1.73333	−	0.656191i	0.0605306	−	0.0229152i
$821$	−7.44783	−	16.3085i	−0.259931	−	0.569169i	0.734003	−	0.679146i	$-0.237650\pi$
$821$	−7.44783	−	16.3085i	−0.259931	−	0.569169i	−0.993934	+	0.109977i	$0.964922\pi$
$822$	−2.87778	−	0.626023i	−0.100374	−	0.0218351i
$823$	−10.8157	+	8.09655i	−0.377013	+	0.282228i	−0.770933	−	0.636917i	$-0.780210\pi$
$823$	−10.8157	+	8.09655i	−0.377013	+	0.282228i	0.393920	+	0.919145i	$0.371119\pi$
$824$	8.76395	+	5.63225i	0.305307	+	0.196209i
$825$	−14.0327	+	19.1334i	−0.488556	+	0.666141i
$826$	0.375180	−	1.27775i	0.0130542	−	0.0444585i
$827$	−1.32447	−	1.32447i	−0.0460565	−	0.0460565i	0.683703	−	0.729760i	$-0.260368\pi$
$827$	−1.32447	−	1.32447i	−0.0460565	−	0.0460565i	−0.729760	+	0.683703i	$0.760368\pi$
$828$	−0.708081	−	4.74327i	−0.0246075	−	0.164840i
$829$			2.00144i			0.0695129i	0.999396	+	0.0347565i	$0.0110656\pi$
$829$			2.00144i			0.0695129i	−0.999396	+	0.0347565i	$0.988934\pi$
$830$	−9.51183	+	12.8369i	−0.330161	+	0.445577i
$831$	−7.88587	+	9.10078i	−0.273558	+	0.315702i
$832$	−0.622432	+	0.135402i	−0.0215790	+	0.00469421i
$833$	9.82840	+	13.1292i	0.340534	+	0.454900i
$834$	1.57719	+	2.45416i	0.0546138	+	0.0849807i
$835$	41.5396	+	35.6395i	1.43754	+	1.23335i
$836$	−3.45931	−	3.99226i	−0.119643	−	0.138075i
$837$	−8.27596	−	6.19531i	−0.286059	−	0.214141i
$838$	6.13189	+	16.4402i	0.211823	+	0.567919i
$839$	−5.80506	+	1.70452i	−0.200413	+	0.0588466i	−0.380398	−	0.924823i	$-0.624213\pi$
$839$	−5.80506	+	1.70452i	−0.200413	+	0.0588466i	0.179985	+	0.983669i	$0.442395\pi$
$840$	−3.38244	+	2.96004i	−0.116705	+	0.102131i
$841$	2.34065	−	5.12530i	0.0807120	−	0.176735i
$842$	14.4924	−	19.3596i	0.499441	−	0.667175i
$843$	13.6415	+	0.975661i	0.469839	+	0.0336036i
$844$	13.1068	−	5.98566i	0.451153	−	0.206035i
$845$	6.12092	+	27.4883i	0.210566	+	0.945628i
$846$	−1.90373	+	13.2407i	−0.0654515	+	0.455225i
$847$	−4.92236	−	22.6277i	−0.169134	−	0.777498i
$848$	0.628317	+	8.78502i	0.0215765	+	0.301679i
$849$	18.0469	+	5.29904i	0.619368	+	0.181863i
$850$	21.1175	+	17.9391i	0.724323	+	0.615308i
$851$	−1.19045	+	18.0075i	−0.0408081	+	0.617289i
$852$	4.41662	−	4.41662i	0.151311	−	0.151311i
$853$	−11.1306	−	20.3841i	−0.381104	−	0.697940i	0.614768	−	0.788708i	$-0.289250\pi$
$853$	−11.1306	−	20.3841i	−0.381104	−	0.697940i	−0.995872	+	0.0907681i	$0.971068\pi$
$854$	0.0677284	+	0.0586870i	0.00231762	+	0.00200823i
$855$	1.98528	−	1.50140i	0.0678952	−	0.0513466i
$856$	16.8370	+	2.42080i	0.575478	+	0.0827412i
$857$	−0.175079	+	0.804825i	−0.00598059	+	0.0274923i	−0.980040	−	0.198798i	$-0.936296\pi$
$857$	−0.175079	+	0.804825i	−0.00598059	+	0.0274923i	0.974060	+	0.226290i	$0.0726598\pi$
$858$	2.83227	+	1.05638i	0.0966922	+	0.0360643i
$859$	−29.6080	+	25.6555i	−1.01021	+	0.875353i	−0.992221	−	0.124485i	$-0.960272\pi$
$859$	−29.6080	+	25.6555i	−1.01021	+	0.875353i	−0.0179900	+	0.999838i	$0.505727\pi$
$860$	−19.7202	+	12.8104i	−0.672455	+	0.436830i
$861$	−1.51553	−	0.692121i	−0.0516493	−	0.0235874i
$862$	−2.46707	−	1.34712i	−0.0840289	−	0.0458832i
$863$	−31.7186	−	17.3197i	−1.07971	−	0.589569i	−0.161992	−	0.986792i	$-0.551792\pi$
$863$	−31.7186	−	17.3197i	−1.07971	−	0.589569i	−0.917722	+	0.397223i	$0.869974\pi$
$864$	0.909632	+	0.415415i	0.0309463	+	0.0141327i
$865$	17.0219	−	11.0575i	0.578761	−	0.375966i
$866$	18.1563	−	15.7325i	0.616977	−	0.534614i
$867$	12.8459	+	4.79129i	0.436271	+	0.162721i
$868$	4.41720	−	20.3055i	0.149930	−	0.689215i
$869$	27.1583	+	3.90477i	0.921281	+	0.132460i
$870$	−8.62096	+	6.51971i	−0.292278	+	0.221039i
$871$	6.83671	+	5.92404i	0.231653	+	0.200729i
$872$	−1.97962	−	3.62540i	−0.0670383	−	0.122772i
$873$	−7.10856	+	7.10856i	−0.240588	+	0.240588i
$874$	−4.67163	+	2.58367i	−0.158020	+	0.0873939i
$875$	6.01398	−	21.6541i	0.203310	−	0.732042i
$876$	13.9944	+	4.10911i	0.472825	+	0.138834i
$877$	−1.86145	−	26.0265i	−0.0628568	−	0.878853i	−0.926870	−	0.375383i	$-0.877511\pi$
$877$	−1.86145	−	26.0265i	−0.0628568	−	0.878853i	0.864013	−	0.503470i	$-0.167944\pi$
$878$	4.29420	+	19.7401i	0.144922	+	0.666197i
$879$	1.52420	−	10.6010i	0.0514099	−	0.357564i
$880$	2.30638	+	10.3577i	0.0777480	+	0.349158i
$881$	−26.1302	+	11.9333i	−0.880349	+	0.402042i	−0.803713	−	0.595017i	$-0.797145\pi$
$881$	−26.1302	+	11.9333i	−0.880349	+	0.402042i	−0.0766361	+	0.997059i	$0.524418\pi$
$882$	−2.95192	−	0.211125i	−0.0993962	−	0.00710896i
$883$	−9.02199	+	12.0520i	−0.303614	+	0.405581i	−0.926237	−	0.376941i	$-0.876976\pi$
$883$	−9.02199	+	12.0520i	−0.303614	+	0.405581i	0.622623	+	0.782522i	$0.286067\pi$
$884$	1.46642	−	3.21100i	0.0493209	−	0.107998i
$885$	1.11479	−	0.975574i	0.0374733	−	0.0327936i
$886$	−38.0343	+	11.1679i	−1.27779	+	0.375192i
$887$	13.7914	+	36.9761i	0.463069	+	1.24154i	0.933333	+	0.359011i	$0.116886\pi$
$887$	13.7914	+	36.9761i	0.463069	+	1.24154i	−0.470264	+	0.882526i	$0.655841\pi$
$888$	−3.01245	−	2.25509i	−0.101091	−	0.0756759i
$889$	−11.3656	−	13.1166i	−0.381190	−	0.439917i
$890$	−13.2947	−	11.4064i	−0.445639	−	0.382342i
$891$	−2.56564	−	3.99221i	−0.0859521	−	0.133744i
$892$	16.0350	+	21.4202i	0.536891	+	0.717203i
$893$	14.5502	−	3.16520i	0.486903	−	0.105919i
$894$	3.34160	−	3.85641i	0.111760	−	0.128978i
$895$	−12.9512	+	17.4786i	−0.432909	+	0.584244i
$896$			2.01011i			0.0671531i
$897$	1.63773	−	2.57880i	0.0546823	−	0.0861036i
$898$	−12.1964	−	12.1964i	−0.407000	−	0.407000i
$899$	14.0786	−	47.9473i	0.469548	−	1.59913i
$900$	−4.94190	+	0.760032i	−0.164730	+	0.0253344i
$901$	−41.0601	−	26.3878i	−1.36791	−	0.879103i
$902$	−3.14884	+	2.35719i	−0.104845	+	0.0784859i
$903$	20.6564	+	4.49353i	0.687402	+	0.149535i
$904$	−1.48444	−	3.25047i	−0.0493717	−	0.108109i
$905$	−20.8594	+	7.89676i	−0.693389	+	0.262497i
$906$	−2.86825	−	19.9491i	−0.0952914	−	0.662766i
$907$	−22.3254	+	8.32696i	−0.741304	+	0.276492i	−0.691609	−	0.722272i	$-0.743098\pi$
$907$	−22.3254	+	8.32696i	−0.741304	+	0.276492i	−0.0496951	+	0.998764i	$0.515825\pi$
$908$	4.30270	−	7.87981i	0.142790	−	0.261501i
$909$	0.534127	+	1.81907i	0.0177159	+	0.0603347i
$910$	−2.86307	+	0.0140266i	−0.0949098	+	0.000464978i
$911$	−14.9395	+	2.14797i	−0.494966	+	0.0711654i	−0.385278	−	0.922801i	$-0.625894\pi$
$911$	−14.9395	+	2.14797i	−0.494966	+	0.0711654i	−0.109688	+	0.993966i	$0.534985\pi$
$912$	0.0794113	−	1.11032i	0.00262957	−	0.0367662i
$913$	11.8494	−	31.7695i	0.392159	−	1.05142i
$914$	−30.2805	+	19.4601i	−1.00159	+	0.643683i
$915$	0.0285546	+	0.0955145i	0.000943986	+	0.00315761i
$916$	3.17826	−	4.94547i	0.105013	−	0.163403i
$917$	24.6681	−	1.76430i	0.814612	−	0.0582622i
$918$	−4.86383	+	2.65585i	−0.160530	+	0.0876562i
$919$	−17.6712			−0.582921			−0.291460	−	0.956583i	$-0.594141\pi$
$919$	−17.6712			−0.582921			−0.291460	+	0.956583i	$0.594141\pi$
$920$	10.7232	−	0.110307i	0.353535	−	0.00363673i
$921$	−7.75795			−0.255633
$922$	22.8536	−	12.4790i	0.752643	−	0.410974i
$923$	3.96853	−	0.283835i	0.130626	−	0.00934253i
$924$	5.15721	−	8.02478i	0.169660	−	0.263996i
$925$	18.7794	+	1.15831i	0.617463	+	0.0380849i
$926$	−14.3057	+	9.19370i	−0.470114	+	0.302124i
$927$	3.64062	−	9.76089i	0.119574	−	0.320590i
$928$	−0.344839	+	4.82147i	−0.0113199	+	0.158273i
$929$	35.5587	−	5.11256i	1.16664	−	0.167738i	0.468345	−	0.883546i	$-0.344851\pi$
$929$	35.5587	−	5.11256i	1.16664	−	0.167738i	0.698297	+	0.715808i	$0.253942\pi$
$930$	16.2655	−	16.4256i	0.533366	−	0.538618i
$931$	0.928118	+	3.16088i	0.0304179	+	0.103594i
$932$	0.626057	−	1.14654i	0.0205072	−	0.0375561i
$933$	9.57791	−	3.57237i	0.313567	−	0.116954i
$934$	−2.93554	−	20.4171i	−0.0960536	−	0.668068i
$935$	−53.6099	−	24.1661i	−1.75323	−	0.790317i
$936$	0.264615	+	0.579426i	0.00864921	+	0.0189391i
$937$	0.714505	+	0.155431i	0.0233419	+	0.00507771i	0.224221	−	0.974538i	$-0.428016\pi$
$937$	0.714505	+	0.155431i	0.0233419	+	0.00507771i	−0.200879	+	0.979616i	$0.564380\pi$
$938$	22.8529	−	17.1074i	0.746172	−	0.558578i
$939$	7.14632	+	4.59266i	0.233211	+	0.149876i
$940$	−28.7409	−	8.28636i	−0.937424	−	0.270271i
$941$	−3.08868	+	10.5191i	−0.100688	+	0.342912i	−0.994394	−	0.105742i	$-0.966278\pi$
$941$	−3.08868	+	10.5191i	−0.100688	+	0.342912i	0.893705	+	0.448654i	$0.148097\pi$
$942$	6.95493	+	6.95493i	0.226604	+	0.226604i
$943$	1.67076	+	3.60690i	0.0544073	+	0.117457i
$944$		−	0.662495i		−	0.0215624i
$945$	3.61138	+	2.67594i	0.117478	+	0.0870483i
$946$	32.6821	−	37.7172i	1.06259	−	1.22629i
$947$	−27.3633	+	5.95253i	−0.889188	+	0.193431i	−0.633883	−	0.773429i	$-0.718540\pi$
$947$	−27.3633	+	5.95253i	−0.889188	+	0.193431i	−0.255306	+	0.966860i	$0.582176\pi$
$948$	3.46487	+	4.62852i	0.112534	+	0.150327i
$949$	5.02287	+	7.81574i	0.163049	+	0.253710i
$950$	2.71512	+	4.85858i	0.0880901	+	0.157633i
$951$	−11.8742	−	13.7035i	−0.385046	−	0.444367i
$952$	−8.91756	−	6.67560i	−0.289020	−	0.216358i
$953$	18.1573	+	48.6815i	0.588171	+	1.57695i	0.800231	+	0.599691i	$0.204710\pi$
$953$	18.1573	+	48.6815i	0.588171	+	1.57695i	−0.212060	+	0.977257i	$0.568017\pi$
$954$	8.45070	−	2.48135i	0.273602	−	0.0803367i
$955$	−3.15140	+	47.3191i	−0.101977	+	1.53121i
$956$	−8.13990	+	17.8239i	−0.263263	+	0.576466i
$957$	13.7468	−	18.3636i	0.444372	−	0.593611i
$958$	18.1241	+	1.29626i	0.585564	+	0.0418804i
$959$	−5.38497	+	2.45924i	−0.173890	+	0.0794129i
$960$	−1.19968	+	1.88700i	−0.0387195	+	0.0609027i
$961$	−10.7979	+	75.1011i	−0.348320	+	2.42262i
$962$	−0.509519	−	2.34222i	−0.0164276	−	0.0755163i
$963$	−1.21349	−	16.9668i	−0.0391042	−	0.546748i
$964$	7.93244	+	2.32917i	0.255487	+	0.0750176i
$965$	−0.268824	−	0.581092i	−0.00865375	−	0.0187060i
$966$	−6.85324	−	6.77979i	−0.220499	−	0.218136i
$967$	−11.5517	+	11.5517i	−0.371477	+	0.371477i	−0.868015	−	0.496538i	$-0.834604\pi$
$967$	−11.5517	+	11.5517i	−0.371477	+	0.371477i	0.496538	+	0.868015i	$0.334604\pi$
$968$	−5.52106	−	10.1111i	−0.177454	−	0.324982i
$969$	4.66203	+	4.03967i	0.149766	+	0.129773i
$970$	−13.5593	−	17.9293i	−0.435363	−	0.575676i
$971$	0.670859	+	0.0964549i	0.0215289	+	0.00309539i	0.153071	−	0.988215i	$-0.451084\pi$
$971$	0.670859	+	0.0964549i	0.0215289	+	0.00309539i	−0.131542	+	0.991311i	$0.541993\pi$
$972$	0.212565	−	0.977147i	0.00681803	−	0.0313420i
$973$	5.49430	+	2.04927i	0.176139	+	0.0656965i
$974$	14.7952	−	12.8201i	0.474068	−	0.410782i
$975$	−2.69609	−	1.69558i	−0.0863440	−	0.0543019i
$976$	0.0405545	+	0.0185206i	0.00129812	+	0.000592830i
$977$	−44.5648	−	24.3342i	−1.42576	−	0.778521i	−0.433314	−	0.901243i	$-0.642656\pi$
$977$	−44.5648	−	24.3342i	−1.42576	−	0.778521i	−0.992441	+	0.122722i	$0.960838\pi$
$978$	−14.1976	−	7.75249i	−0.453990	−	0.247897i
$979$	33.8168	+	15.4436i	1.08079	+	0.493580i
$980$	1.37497	−	6.47313i	0.0439216	−	0.206777i
$981$	−3.12175	+	2.70501i	−0.0996698	+	0.0863644i
$982$	38.9963	+	14.5449i	1.24442	+	0.464145i
$983$	11.0537	−	50.8130i	0.352558	−	1.62068i	−0.369764	−	0.929126i	$-0.620562\pi$
$983$	11.0537	−	50.8130i	0.352558	−	1.62068i	0.722322	−	0.691557i	$-0.243075\pi$
$984$	−0.820422	−	0.117959i	−0.0261541	−	0.00376039i
$985$	49.3723	+	6.85196i	1.57313	+	0.218322i
$986$	−20.2446	−	17.5420i	−0.644718	−	0.558651i
$987$	12.8865	+	23.5999i	0.410182	+	0.751193i
$988$	0.501385	−	0.501385i	0.0159512	−	0.0159512i
$989$	−30.4421	−	40.2125i	−0.968003	−	1.27868i
$990$	9.63073	−	4.45536i	0.306085	−	0.141601i
$991$	33.3518	+	9.79297i	1.05945	+	0.311084i	0.764631	−	0.644468i	$-0.222921\pi$
$991$	33.3518	+	9.79297i	1.05945	+	0.311084i	0.294823	+	0.955552i	$0.404739\pi$
$992$	−0.737502	−	10.3116i	−0.0234157	−	0.327394i
$993$	−2.18637	−	10.0506i	−0.0693823	−	0.318945i
$994$	1.78680	−	12.4274i	0.0566737	−	0.394174i
$995$	−10.5093	+	2.34013i	−0.333166	+	0.0741872i
$996$	6.49941	−	2.96818i	0.205942	−	0.0940504i
$997$	−42.7513	−	3.05764i	−1.35395	−	0.0968363i	−0.624582	−	0.780960i	$-0.714730\pi$
$997$	−42.7513	−	3.05764i	−1.35395	−	0.0968363i	−0.729366	+	0.684123i	$0.760185\pi$
$998$	−0.382605	+	0.511101i	−0.0121112	+	0.0161786i
$999$	−1.56321	+	3.42296i	−0.0494579	+	0.108298i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.b.373.4	yes	240
5.2	odd	4	inner	690.2.w.b.97.3	yes	240
23.14	odd	22	inner	690.2.w.b.313.3	yes	240
115.37	even	44	inner	690.2.w.b.37.4	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.b.37.4	✓	240	115.37	even	44	inner
690.2.w.b.97.3	yes	240	5.2	odd	4	inner
690.2.w.b.313.3	yes	240	23.14	odd	22	inner
690.2.w.b.373.4	yes	240	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.877679 + 0.479249i) q^{2} +(0.997452 - 0.0713392i) q^{3} +(0.540641 - 0.841254i) q^{4} +(1.06201 - 1.96778i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(-0.702461 + 1.88337i) q^{7} +(-0.0713392 + 0.997452i) q^{8} +(0.989821 - 0.142315i) q^{9} +O(q^{10})\)	\(q+(-0.877679 + 0.479249i) q^{2} +(0.997452 - 0.0713392i) q^{3} +(0.540641 - 0.841254i) q^{4} +(1.06201 - 1.96778i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(-0.702461 + 1.88337i) q^{7} +(-0.0713392 + 0.997452i) q^{8} +(0.989821 - 0.142315i) q^{9} +(0.0109547 + 2.23604i) q^{10} +(-1.33698 - 4.55332i) q^{11} +(0.479249 - 0.877679i) q^{12} +(0.596827 - 0.222605i) q^{13} +(-0.286068 - 1.98965i) q^{14} +(0.918920 - 2.03853i) q^{15} +(-0.415415 - 0.909632i) q^{16} +(5.41505 + 1.17797i) q^{17} +(-0.800541 + 0.599278i) q^{18} +(0.936443 + 0.601815i) q^{19} +(-1.08124 - 1.95728i) q^{20} +(-0.566313 + 1.92869i) q^{21} +(3.35561 + 3.35561i) q^{22} +(4.02048 - 2.61452i) q^{23} +1.00000i q^{24} +(-2.74429 - 4.17958i) q^{25} +(-0.417139 + 0.481404i) q^{26} +(0.977147 - 0.212565i) q^{27} +(1.20461 + 1.60918i) q^{28} +(2.61334 + 4.06644i) q^{29} +(0.170444 + 2.22956i) q^{30} +(-6.76992 - 7.81291i) q^{31} +(0.800541 + 0.599278i) q^{32} +(-1.65840 - 4.44634i) q^{33} +(-5.31722 + 1.56128i) q^{34} +(2.96004 + 3.38244i) q^{35} +(0.415415 - 0.909632i) q^{36} +(-2.25509 + 3.01245i) q^{37} +(-1.11032 - 0.0794113i) q^{38} +(0.579426 - 0.264615i) q^{39} +(1.88700 + 1.19968i) q^{40} +(-0.117959 + 0.820422i) q^{41} +(-0.427280 - 1.96417i) q^{42} +(-0.750245 - 10.4898i) q^{43} +(-4.55332 - 1.33698i) q^{44} +(0.771152 - 2.09889i) q^{45} +(-2.27569 + 4.22152i) q^{46} +(9.45887 - 9.45887i) q^{47} +(-0.479249 - 0.877679i) q^{48} +(2.23661 + 1.93803i) q^{49} +(4.41166 + 2.35313i) q^{50} +(5.48529 + 0.788666i) q^{51} +(0.135402 - 0.622432i) q^{52} +(-8.25215 - 3.07789i) q^{53} +(-0.755750 + 0.654861i) q^{54} +(-10.3798 - 2.20478i) q^{55} +(-1.82846 - 0.835030i) q^{56} +(0.976990 + 0.533477i) q^{57} +(-4.24252 - 2.31659i) q^{58} +(0.602627 + 0.275211i) q^{59} +(-1.21811 - 1.87515i) q^{60} +(-0.0336939 + 0.0291959i) q^{61} +(9.68615 + 3.61275i) q^{62} +(-0.427280 + 1.96417i) q^{63} +(-0.989821 - 0.142315i) q^{64} +(0.195797 - 1.41083i) q^{65} +(3.58645 + 3.10767i) q^{66} +(6.80610 + 12.4644i) q^{67} +(3.91857 - 3.91857i) q^{68} +(3.82372 - 2.89468i) q^{69} +(-4.21899 - 1.55010i) q^{70} +(5.99303 + 1.75971i) q^{71} +(0.0713392 + 0.997452i) q^{72} +(3.10030 + 14.2518i) q^{73} +(0.535533 - 3.72472i) q^{74} +(-3.03546 - 3.97316i) q^{75} +(1.01256 - 0.462420i) q^{76} +(9.51477 + 0.680510i) q^{77} +(-0.381734 + 0.509936i) q^{78} +(-2.40182 + 5.25926i) q^{79} +(-2.23113 - 0.148591i) q^{80} +(0.959493 - 0.281733i) q^{81} +(-0.289656 - 0.776598i) q^{82} +(5.71994 + 4.28190i) q^{83} +(1.31634 + 1.51914i) q^{84} +(8.06880 - 9.40460i) q^{85} +(5.68570 + 8.84712i) q^{86} +(2.89678 + 3.86965i) q^{87} +(4.63710 - 1.00874i) q^{88} +(-5.13014 + 5.92050i) q^{89} +(0.329065 + 2.21172i) q^{90} +1.28042i q^{91} +(-0.0258364 - 4.79576i) q^{92} +(-7.31004 - 7.31004i) q^{93} +(-3.76870 + 12.8350i) q^{94} +(2.17875 - 1.20358i) q^{95} +(0.841254 + 0.540641i) q^{96} +(-8.04785 + 6.02455i) q^{97} +(-2.89182 - 0.629078i) q^{98} +(-1.97137 - 4.31670i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{6}+O(q^{10}) \) 240 * q + 24 * q^6	\( 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) \) 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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