LMFDB - Embedded newform 690.2.w.b.373.2

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			373.2
Character	$\chi$	$=$	690.373
Dual form			690.2.w.b.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.877679 + 0.479249i) q^{2} +(0.997452 - 0.0713392i) q^{3} +(0.540641 - 0.841254i) q^{4} +(-1.79792 + 1.32947i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(-1.02771 + 2.75539i) q^{7} +(-0.0713392 + 0.997452i) q^{8} +(0.989821 - 0.142315i) q^{9} +O(q^{10})$	\(q+(-0.877679 + 0.479249i) q^{2} +(0.997452 - 0.0713392i) q^{3} +(0.540641 - 0.841254i) q^{4} +(-1.79792 + 1.32947i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(-1.02771 + 2.75539i) q^{7} +(-0.0713392 + 0.997452i) q^{8} +(0.989821 - 0.142315i) q^{9} +(0.940853 - 2.02850i) q^{10} +(-1.17675 - 4.00765i) q^{11} +(0.479249 - 0.877679i) q^{12} +(-4.57156 + 1.70510i) q^{13} +(-0.418521 - 2.91087i) q^{14} +(-1.69850 + 1.45434i) q^{15} +(-0.415415 - 0.909632i) q^{16} +(-1.91967 - 0.417599i) q^{17} +(-0.800541 + 0.599278i) q^{18} +(0.950931 + 0.611126i) q^{19} +(0.146387 + 2.23127i) q^{20} +(-0.828521 + 2.82168i) q^{21} +(2.95347 + 2.95347i) q^{22} +(-2.58957 - 4.03660i) q^{23} +1.00000i q^{24} +(1.46504 - 4.78055i) q^{25} +(3.19519 - 3.68745i) q^{26} +(0.977147 - 0.212565i) q^{27} +(1.76236 + 2.35424i) q^{28} +(-4.99066 - 7.76561i) q^{29} +(0.793745 - 2.09045i) q^{30} +(2.20533 + 2.54509i) q^{31} +(0.800541 + 0.599278i) q^{32} +(-1.45966 - 3.91349i) q^{33} +(1.88499 - 0.553483i) q^{34} +(-1.81546 - 6.32027i) q^{35} +(0.415415 - 0.909632i) q^{36} +(-3.32516 + 4.44190i) q^{37} +(-1.12749 - 0.0806399i) q^{38} +(-4.43827 + 2.02689i) q^{39} +(-1.19782 - 1.88818i) q^{40} +(-0.269866 + 1.87696i) q^{41} +(-0.625114 - 2.87360i) q^{42} +(-0.294497 - 4.11761i) q^{43} +(-4.00765 - 1.17675i) q^{44} +(-1.59042 + 1.57180i) q^{45} +(4.20734 + 2.30179i) q^{46} +(-8.11925 + 8.11925i) q^{47} +(-0.479249 - 0.877679i) q^{48} +(-1.24574 - 1.07944i) q^{49} +(1.00523 + 4.89791i) q^{50} +(-1.94457 - 0.279587i) q^{51} +(-1.03715 + 4.76769i) q^{52} +(4.17430 + 1.55693i) q^{53} +(-0.755750 + 0.654861i) q^{54} +(7.44373 + 5.64099i) q^{55} +(-2.67505 - 1.22166i) q^{56} +(0.992105 + 0.541730i) q^{57} +(8.10186 + 4.42395i) q^{58} +(-7.54255 - 3.44457i) q^{59} +(0.305191 + 2.21514i) q^{60} +(-10.3951 + 9.00741i) q^{61} +(-3.15530 - 1.17687i) q^{62} +(-0.625114 + 2.87360i) q^{63} +(-0.989821 - 0.142315i) q^{64} +(5.95243 - 9.14337i) q^{65} +(3.15664 + 2.73525i) q^{66} +(0.147025 + 0.269256i) q^{67} +(-1.38916 + 1.38916i) q^{68} +(-2.87094 - 3.84158i) q^{69} +(4.62237 + 4.67712i) q^{70} +(6.05430 + 1.77770i) q^{71} +(0.0713392 + 0.997452i) q^{72} +(-1.99970 - 9.19248i) q^{73} +(0.789651 - 5.49214i) q^{74} +(1.12027 - 4.87288i) q^{75} +(1.02822 - 0.469574i) q^{76} +(12.2520 + 0.876279i) q^{77} +(2.92399 - 3.90600i) q^{78} +(0.0175589 - 0.0384486i) q^{79} +(1.95621 + 1.08317i) q^{80} +(0.959493 - 0.281733i) q^{81} +(-0.662674 - 1.77670i) q^{82} +(-2.25806 - 1.69037i) q^{83} +(1.92582 + 2.22251i) q^{84} +(4.00661 - 1.80133i) q^{85} +(2.23183 + 3.47280i) q^{86} +(-5.53193 - 7.38980i) q^{87} +(4.08138 - 0.887851i) q^{88} +(-10.1062 + 11.6632i) q^{89} +(0.642592 - 2.14175i) q^{90} -14.3488i q^{91} +(-4.79583 - 0.00386944i) q^{92} +(2.38128 + 2.38128i) q^{93} +(3.23495 - 11.0172i) q^{94} +(-2.52217 + 0.165472i) q^{95} +(0.841254 + 0.540641i) q^{96} +(-0.531048 + 0.397538i) q^{97} +(1.61068 + 0.350381i) q^{98} +(-1.73512 - 3.79939i) 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
$5$	−1.79792	+	1.32947i	−0.804055	+	0.594555i
$5$	−1.79792	+	1.32947i	−0.804055	+	0.594555i
$6$	−0.841254	+	0.540641i	−0.343440	+	0.220716i
$7$	−1.02771	+	2.75539i	−0.388437	+	1.04144i	0.584708	+	0.811244i	$0.301209\pi$
$7$	−1.02771	+	2.75539i	−0.388437	+	1.04144i	−0.973145	+	0.230195i	$0.926064\pi$
$8$	−0.0713392	+	0.997452i	−0.0252222	+	0.352653i
$9$	0.989821	−	0.142315i	0.329940	−	0.0474383i
$10$	0.940853	−	2.02850i	0.297524	−	0.641467i
$11$	−1.17675	−	4.00765i	−0.354804	−	1.20835i	−0.922787	−	0.385311i	$-0.874094\pi$
$11$	−1.17675	−	4.00765i	−0.354804	−	1.20835i	0.567983	−	0.823040i	$-0.307724\pi$
$12$	0.479249	−	0.877679i	0.138347	−	0.253364i
$13$	−4.57156	+	1.70510i	−1.26792	+	0.472911i	−0.891282	−	0.453449i	$-0.850194\pi$
$13$	−4.57156	+	1.70510i	−1.26792	+	0.472911i	−0.376641	+	0.926360i	$0.622921\pi$
$14$	−0.418521	−	2.91087i	−0.111854	−	0.777964i
$15$	−1.69850	+	1.45434i	−0.438550	+	0.375509i
$16$	−0.415415	−	0.909632i	−0.103854	−	0.227408i
$17$	−1.91967	−	0.417599i	−0.465589	−	0.101283i	−0.0263498	−	0.999653i	$-0.508388\pi$
$17$	−1.91967	−	0.417599i	−0.465589	−	0.101283i	−0.439239	+	0.898370i	$0.644752\pi$
$18$	−0.800541	+	0.599278i	−0.188689	+	0.141251i
$19$	0.950931	+	0.611126i	0.218158	+	0.140202i	0.645156	−	0.764051i	$-0.276792\pi$
$19$	0.950931	+	0.611126i	0.218158	+	0.140202i	−0.426998	+	0.904253i	$0.640429\pi$
$20$	0.146387	+	2.23127i	0.0327332	+	0.498927i
$21$	−0.828521	+	2.82168i	−0.180798	+	0.615742i
$22$	2.95347	+	2.95347i	0.629682	+	0.629682i
$23$	−2.58957	−	4.03660i	−0.539962	−	0.841689i
$23$	−2.58957	−	4.03660i	−0.539962	−	0.841689i
$24$			1.00000i			0.204124i
$25$	1.46504	−	4.78055i	0.293009	−	0.956110i
$26$	3.19519	−	3.68745i	0.626629	−	0.723168i
$27$	0.977147	−	0.212565i	0.188052	−	0.0409082i
$28$	1.76236	+	2.35424i	0.333055	+	0.444909i
$29$	−4.99066	−	7.76561i	−0.926742	−	1.44204i	−0.896775	−	0.442487i	$-0.854096\pi$
$29$	−4.99066	−	7.76561i	−0.926742	−	1.44204i	−0.0299668	−	0.999551i	$-0.509540\pi$
$30$	0.793745	−	2.09045i	0.144917	−	0.381662i
$31$	2.20533	+	2.54509i	0.396089	+	0.457111i	0.918405	−	0.395641i	$-0.129477\pi$
$31$	2.20533	+	2.54509i	0.396089	+	0.457111i	−0.522316	+	0.852752i	$0.674932\pi$
$32$	0.800541	+	0.599278i	0.141517	+	0.105938i
$33$	−1.45966	−	3.91349i	−0.254093	−	0.681251i
$34$	1.88499	−	0.553483i	0.323273	−	0.0949216i
$35$	−1.81546	−	6.32027i	−0.306868	−	1.06832i
$36$	0.415415	−	0.909632i	0.0692358	−	0.151605i
$37$	−3.32516	+	4.44190i	−0.546654	+	0.730244i	−0.985754	−	0.168194i	$-0.946206\pi$
$37$	−3.32516	+	4.44190i	−0.546654	+	0.730244i	0.439100	+	0.898438i	$0.355297\pi$
$38$	−1.12749	−	0.0806399i	−0.182904	−	0.0130815i
$39$	−4.43827	+	2.02689i	−0.710692	+	0.324562i
$40$	−1.19782	−	1.88818i	−0.189391	−	0.298548i
$41$	−0.269866	+	1.87696i	−0.0421459	+	0.293131i	0.957837	+	0.287312i	$0.0927615\pi$
$41$	−0.269866	+	1.87696i	−0.0421459	+	0.293131i	−0.999983	+	0.00581961i	$0.998148\pi$
$42$	−0.625114	−	2.87360i	−0.0964571	−	0.443406i
$43$	−0.294497	−	4.11761i	−0.0449104	−	0.627929i	−0.969206	−	0.246252i	$-0.920801\pi$
$43$	−0.294497	−	4.11761i	−0.0449104	−	0.627929i	0.924296	−	0.381677i	$-0.124653\pi$
$44$	−4.00765	−	1.17675i	−0.604175	−	0.177402i
$45$	−1.59042	+	1.57180i	−0.237086	+	0.234311i
$46$	4.20734	+	2.30179i	0.620339	+	0.339381i
$47$	−8.11925	+	8.11925i	−1.18432	+	1.18432i	−0.205700	+	0.978615i	$0.565947\pi$
$47$	−8.11925	+	8.11925i	−1.18432	+	1.18432i	−0.978615	+	0.205700i	$0.934053\pi$
$48$	−0.479249	−	0.877679i	−0.0691736	−	0.126682i
$49$	−1.24574	−	1.07944i	−0.177963	−	0.154205i
$50$	1.00523	+	4.89791i	0.142162	+	0.692669i
$51$	−1.94457	−	0.279587i	−0.272295	−	0.0391501i
$52$	−1.03715	+	4.76769i	−0.143826	+	0.661160i
$53$	4.17430	+	1.55693i	0.573384	+	0.213861i	0.619395	−	0.785080i	$-0.287378\pi$
$53$	4.17430	+	1.55693i	0.573384	+	0.213861i	−0.0460107	+	0.998941i	$0.514651\pi$
$54$	−0.755750	+	0.654861i	−0.102844	+	0.0891153i
$55$	7.44373	+	5.64099i	1.00371	+	0.760630i
$56$	−2.67505	−	1.22166i	−0.357469	−	0.163251i
$57$	0.992105	+	0.541730i	0.131408	+	0.0717539i
$58$	8.10186	+	4.42395i	1.06383	+	0.580893i
$59$	−7.54255	−	3.44457i	−0.981957	−	0.448445i	−0.141273	−	0.989971i	$-0.545119\pi$
$59$	−7.54255	−	3.44457i	−0.981957	−	0.448445i	−0.840684	+	0.541526i	$0.817847\pi$
$60$	0.305191	+	2.21514i	0.0394000	+	0.285974i
$61$	−10.3951	+	9.00741i	−1.33096	+	1.15328i	−0.355110	+	0.934824i	$0.615557\pi$
$61$	−10.3951	+	9.00741i	−1.33096	+	1.15328i	−0.975847	+	0.218456i	$0.929898\pi$
$62$	−3.15530	−	1.17687i	−0.400724	−	0.149462i
$63$	−0.625114	+	2.87360i	−0.0787569	+	0.362040i
$64$	−0.989821	−	0.142315i	−0.123728	−	0.0177894i
$65$	5.95243	−	9.14337i	0.738308	−	1.13410i
$66$	3.15664	+	2.73525i	0.388556	+	0.336686i
$67$	0.147025	+	0.269256i	0.0179619	+	0.0328948i	0.886506	−	0.462717i	$-0.153126\pi$
$67$	0.147025	+	0.269256i	0.0179619	+	0.0328948i	−0.868544	+	0.495612i	$0.834944\pi$
$68$	−1.38916	+	1.38916i	−0.168460	+	0.168460i
$69$	−2.87094	−	3.84158i	−0.345620	−	0.462472i
$70$	4.62237	+	4.67712i	0.552479	+	0.559022i
$71$	6.05430	+	1.77770i	0.718513	+	0.210974i	0.620495	−	0.784210i	$-0.286932\pi$
$71$	6.05430	+	1.77770i	0.718513	+	0.210974i	0.0980177	+	0.995185i	$0.468750\pi$
$72$	0.0713392	+	0.997452i	0.00840740	+	0.117551i
$73$	−1.99970	−	9.19248i	−0.234047	−	1.07590i	−0.932760	−	0.360497i	$-0.882607\pi$
$73$	−1.99970	−	9.19248i	−0.234047	−	1.07590i	0.698713	−	0.715402i	$-0.253756\pi$
$74$	0.789651	−	5.49214i	0.0917951	−	0.638449i
$75$	1.12027	−	4.87288i	0.129358	−	0.562672i
$76$	1.02822	−	0.469574i	0.117945	−	0.0538639i
$77$	12.2520	+	0.876279i	1.39624	+	0.0998612i
$78$	2.92399	−	3.90600i	0.331077	−	0.442267i
$79$	0.0175589	−	0.0384486i	0.00197553	−	0.00432581i	−0.908642	−	0.417577i	$-0.862879\pi$
$79$	0.0175589	−	0.0384486i	0.00197553	−	0.00432581i	0.910617	+	0.413251i	$0.135607\pi$
$80$	1.95621	+	1.08317i	0.218711	+	0.121102i
$81$	0.959493	−	0.281733i	0.106610	−	0.0313036i
$82$	−0.662674	−	1.77670i	−0.0731801	−	0.196203i
$83$	−2.25806	−	1.69037i	−0.247855	−	0.185542i	0.468126	−	0.883662i	$-0.344929\pi$
$83$	−2.25806	−	1.69037i	−0.247855	−	0.185542i	−0.715981	+	0.698120i	$0.754020\pi$
$84$	1.92582	+	2.22251i	0.210124	+	0.242496i
$85$	4.00661	−	1.80133i	0.434577	−	0.195381i
$86$	2.23183	+	3.47280i	0.240665	+	0.374481i
$87$	−5.53193	−	7.38980i	−0.593085	−	0.792269i
$88$	4.08138	−	0.887851i	0.435077	−	0.0946452i
$89$	−10.1062	+	11.6632i	−1.07125	+	1.23629i	−0.100824	+	0.994904i	$0.532148\pi$
$89$	−10.1062	+	11.6632i	−1.07125	+	1.23629i	−0.970429	+	0.241388i	$0.922397\pi$
$90$	0.642592	−	2.14175i	0.0677351	−	0.225760i
$91$		−	14.3488i		−	1.50416i
$92$	−4.79583	−	0.00386944i	−0.500000	−	0.000403417i
$93$	2.38128	+	2.38128i	0.246927	+	0.246927i
$94$	3.23495	−	11.0172i	0.333660	−	1.13634i
$95$	−2.52217	+	0.165472i	−0.258769	+	0.0169771i
$96$	0.841254	+	0.540641i	0.0858601	+	0.0551789i
$97$	−0.531048	+	0.397538i	−0.0539198	+	0.0403638i	−0.625898	−	0.779905i	$-0.715267\pi$
$97$	−0.531048	+	0.397538i	−0.0539198	+	0.0403638i	0.571978	+	0.820269i	$0.306176\pi$
$98$	1.61068	+	0.350381i	0.162703	+	0.0353939i
$99$	−1.73512	−	3.79939i	−0.174386	−	0.381853i
$100$	−3.22959	−	3.81703i	−0.322959	−	0.381703i
$101$	−1.16365	−	8.09333i	−0.115787	−	0.805316i	−0.962113	−	0.272651i	$-0.912100\pi$
$101$	−1.16365	−	8.09333i	−0.115787	−	0.805316i	0.846326	−	0.532665i	$-0.178810\pi$
$102$	1.84070	−	0.686547i	0.182257	−	0.0679783i
$103$	−1.02696	+	1.88073i	−0.101189	+	0.185314i	−0.923369	−	0.383914i	$-0.874576\pi$
$103$	−1.02696	+	1.88073i	−0.101189	+	0.185314i	0.822180	+	0.569228i	$0.192758\pi$
$104$	−1.37463	−	4.68155i	−0.134793	−	0.459064i
$105$	−2.26171	−	6.17466i	−0.220721	−	0.602585i
$106$	−4.40985	+	0.634041i	−0.428323	+	0.0615835i
$107$	−1.45688	+	20.3698i	−0.140842	+	1.96922i	0.0891159	+	0.996021i	$0.471596\pi$
$107$	−1.45688	+	20.3698i	−0.140842	+	1.96922i	−0.229957	+	0.973201i	$0.573859\pi$
$108$	0.349464	−	0.936950i	0.0336272	−	0.0901580i
$109$	6.00915	−	3.86185i	0.575573	−	0.369898i	−0.220236	−	0.975447i	$-0.570683\pi$
$109$	6.00915	−	3.86185i	0.575573	−	0.369898i	0.795808	+	0.605549i	$0.207046\pi$
$110$	−9.23664	−	1.38357i	−0.880680	−	0.131918i
$111$	−2.99981	+	4.66780i	−0.284729	+	0.443048i
$112$	2.93331	−	0.209795i	0.277172	−	0.0198237i
$113$	5.81183	−	3.17350i	0.546731	−	0.298538i	−0.182045	−	0.983290i	$-0.558272\pi$
$113$	5.81183	−	3.17350i	0.546731	−	0.298538i	0.728776	+	0.684753i	$0.240090\pi$
$114$	−1.13037			−0.105869
$115$	10.0224	+	3.81475i	0.934590	+	0.355728i
$116$	−9.23100			−0.857077
$117$	−4.28237	+	2.33835i	−0.395905	+	0.216180i
$118$	8.27075	−	0.591535i	0.761384	−	0.0544552i
$119$	3.12351	−	4.86028i	0.286332	−	0.445541i
$120$	−1.32947	−	1.79792i	−0.121363	−	0.164127i
$121$	−5.42270	+	3.48496i	−0.492973	+	0.316814i
$122$	4.80677	−	12.8875i	0.435185	−	1.16678i
$123$	−0.135277	+	1.89143i	−0.0121976	+	0.170544i
$124$	3.33336	−	0.479264i	0.299344	−	0.0430392i
$125$	3.72154	+	10.5428i	0.332864	+	0.942975i
$126$	−0.828521	−	2.82168i	−0.0738105	−	0.251376i
$127$	0.339447	−	0.621652i	0.0301211	−	0.0551627i	−0.862185	−	0.506594i	$-0.830904\pi$
$127$	0.339447	−	0.621652i	0.0301211	−	0.0551627i	0.892306	+	0.451431i	$0.149086\pi$
$128$	0.936950	−	0.349464i	0.0828154	−	0.0308886i
$129$	−0.587493	−	4.08610i	−0.0517259	−	0.359761i
$130$	−0.842372	+	10.8776i	−0.0738809	+	0.954033i
$131$	−6.95284	−	15.2246i	−0.607473	−	1.33018i	−0.924289	−	0.381693i	$-0.875341\pi$
$131$	−6.95284	−	15.2246i	−0.607473	−	1.33018i	0.316816	−	0.948487i	$-0.397386\pi$
$132$	−4.08138	−	0.887851i	−0.355239	−	0.0772775i
$133$	−2.66117	+	1.99213i	−0.230753	+	0.172739i
$134$	−0.258081	−	0.165859i	−0.0222948	−	0.0143280i
$135$	−1.47424	+	1.68126i	−0.126882	+	0.144700i
$136$	0.553483	−	1.88499i	0.0474608	−	0.161637i
$137$	11.1412	+	11.1412i	0.951854	+	0.951854i	0.998893	−	0.0470390i	$-0.0149785\pi$
$137$	11.1412	+	11.1412i	0.951854	+	0.951854i	−0.0470390	+	0.998893i	$0.514978\pi$
$138$	4.36083	+	1.99578i	0.371219	+	0.169892i
$139$			8.61901i			0.731055i	0.930801	+	0.365527i	$0.119111\pi$
$139$			8.61901i			0.731055i	−0.930801	+	0.365527i	$0.880889\pi$
$140$	−6.29846	−	1.88974i	−0.532317	−	0.159712i
$141$	−7.51935	+	8.67779i	−0.633243	+	0.730802i
$142$	−6.16569	+	1.34126i	−0.517413	+	0.112556i
$143$	12.2130	+	16.3147i	1.02131	+	1.36431i
$144$	−0.540641	−	0.841254i	−0.0450534	−	0.0701045i
$145$	19.2969	+	7.32706i	1.60252	+	0.608479i
$146$	6.16058	+	7.10969i	0.509854	+	0.588402i
$147$	−1.31957	−	0.987818i	−0.108836	−	0.0814738i
$148$	1.93904	+	5.19878i	0.159388	+	0.427337i
$149$	8.27578	−	2.42999i	0.677978	−	0.199072i	0.0754254	−	0.997151i	$-0.475969\pi$
$149$	8.27578	−	2.42999i	0.677978	−	0.199072i	0.602553	+	0.798079i	$0.294150\pi$
$150$	1.35209	+	4.81372i	0.110397	+	0.393038i
$151$	2.62546	−	5.74895i	0.213657	−	0.467843i	−0.772211	−	0.635366i	$-0.780849\pi$
$151$	2.62546	−	5.74895i	0.213657	−	0.467843i	0.985868	+	0.167523i	$0.0535767\pi$
$152$	−0.677408	+	0.904911i	−0.0549450	+	0.0733979i
$153$	−1.95956	−	0.140151i	−0.158421	−	0.0113305i
$154$	−11.1733	+	5.10266i	−0.900367	+	0.411184i
$155$	−7.34862	−	1.64396i	−0.590255	−	0.132046i
$156$	−0.694382	+	4.82953i	−0.0555950	+	0.386672i
$157$	1.63007	+	7.49330i	0.130094	+	0.598030i	0.995319	+	0.0966469i	$0.0308118\pi$
$157$	1.63007	+	7.49330i	0.130094	+	0.598030i	−0.865225	+	0.501383i	$0.832825\pi$
$158$	0.00301539	+	0.0421606i	0.000239891	+	0.00335412i
$159$	4.27473	+	1.25517i	0.339008	+	0.0995418i
$160$	−2.23603	−	0.0131626i	−0.176774	−	0.00104060i
$161$	13.7837	−	2.98682i	1.08631	−	0.235394i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	8.77805	+	16.0758i	0.687550	+	1.25915i	0.955292	+	0.295663i	$0.0955407\pi$
$163$	8.77805	+	16.0758i	0.687550	+	1.25915i	−0.267742	+	0.963491i	$0.586277\pi$
$164$	1.43310	+	1.24178i	0.111906	+	0.0969671i
$165$	7.82719	+	5.09558i	0.609346	+	0.396691i
$166$	2.79196	+	0.401423i	0.216698	+	0.0311565i
$167$	−3.42387	+	15.7393i	−0.264947	+	1.21794i	0.631706	+	0.775208i	$0.282355\pi$
$167$	−3.42387	+	15.7393i	−0.264947	+	1.21794i	−0.896653	+	0.442733i	$0.854009\pi$
$168$	−2.75539	−	1.02771i	−0.212583	−	0.0792893i
$169$	8.16705	−	7.07678i	0.628234	−	0.544368i
$170$	−2.65323	+	3.50115i	−0.203493	+	0.268526i
$171$	1.02822	+	0.469574i	0.0786303	+	0.0359092i
$172$	−3.62317	−	1.97840i	−0.276264	−	0.150851i
$173$	−13.0676	−	7.13546i	−0.993512	−	0.542499i	−0.101657	−	0.994820i	$-0.532414\pi$
$173$	−13.0676	−	7.13546i	−0.993512	−	0.542499i	−0.891855	+	0.452321i	$0.850596\pi$
$174$	8.39681	+	3.83470i	0.636561	+	0.290708i
$175$	11.6666	+	8.94977i	0.881914	+	0.676539i
$176$	−3.15664	+	2.73525i	−0.237941	+	0.206177i
$177$	−7.76907	−	2.89771i	−0.583959	−	0.217805i
$178$	3.28043	−	15.0799i	0.245878	−	1.13028i
$179$	22.3125	+	3.20805i	1.66771	+	0.239781i	0.910537	−	0.413428i	$-0.135669\pi$
$179$	22.3125	+	3.20805i	1.66771	+	0.239781i	0.757178	+	0.653209i	$0.226578\pi$
$180$	0.462440	+	2.18773i	0.0344683	+	0.163064i
$181$	−2.75976	−	2.39134i	−0.205131	−	0.177747i	0.546236	−	0.837631i	$-0.316060\pi$
$181$	−2.75976	−	2.39134i	−0.205131	−	0.177747i	−0.751368	+	0.659884i	$0.770605\pi$
$182$	6.87664	+	12.5936i	0.509730	+	0.933501i
$183$	−9.72604	+	9.72604i	−0.718969	+	0.718969i
$184$	4.21105	−	2.29500i	0.310443	−	0.169190i
$185$	0.0730345	−	12.4069i	0.00536960	−	0.912172i
$186$	−3.23122	−	0.948772i	−0.236925	−	0.0695673i
$187$	0.585387	+	8.18478i	0.0428078	+	0.598531i
$188$	2.44075	+	11.2200i	0.178010	+	0.818299i
$189$	−0.418521	+	2.91087i	−0.0304429	+	0.211735i
$190$	2.13435	−	1.35398i	0.154842	−	0.0982280i
$191$	−6.69034	+	3.05538i	−0.484096	+	0.221079i	−0.642486	−	0.766297i	$-0.722097\pi$
$191$	−6.69034	+	3.05538i	−0.484096	+	0.221079i	0.158390	+	0.987377i	$0.449370\pi$
$192$	−0.997452	−	0.0713392i	−0.0719849	−	0.00514846i
$193$	10.5340	−	14.0717i	0.758251	−	1.01290i	−0.240852	−	0.970562i	$-0.577427\pi$
$193$	10.5340	−	14.0717i	0.758251	−	1.01290i	0.999103	−	0.0423431i	$-0.0134822\pi$
$194$	0.275570	−	0.603415i	0.0197848	−	0.0433226i
$195$	5.28499	−	9.54472i	0.378466	−	0.683512i
$196$	−1.58158	+	0.464393i	−0.112970	+	0.0331709i
$197$	−5.95498	−	15.9659i	−0.424275	−	1.13752i	−0.956707	−	0.291052i	$-0.905995\pi$
$197$	−5.95498	−	15.9659i	−0.424275	−	1.13752i	0.532433	−	0.846472i	$-0.321278\pi$
$198$	3.34373	+	2.50309i	0.237629	+	0.177887i
$199$	9.96179	+	11.4965i	0.706173	+	0.814967i	0.989573	−	0.144035i	$-0.0460079\pi$
$199$	9.96179	+	11.4965i	0.706173	+	0.814967i	−0.283400	+	0.959002i	$0.591462\pi$
$200$	4.66385	+	1.80235i	0.329784	+	0.127446i
$201$	0.165859	+	0.258081i	0.0116988	+	0.0182036i
$202$	4.90003	+	6.54567i	0.344765	+	0.460552i
$203$	26.5262	−	5.77042i	1.86178	−	0.405004i
$204$	−1.28652	+	1.48472i	−0.0900744	+	0.103951i
$205$	−2.01015	−	3.73340i	−0.140395	−	0.260752i
$206$		−	2.14285i		−	0.149299i
$207$	−3.13768	−	3.62698i	−0.218084	−	0.252093i
$208$	3.45011	+	3.45011i	0.239222	+	0.239222i
$209$	1.33017	−	4.53014i	0.0920097	−	0.313356i
$210$	4.94426	+	4.33544i	0.341186	+	0.299174i
$211$	−15.3518	−	9.86601i	−1.05686	−	0.679204i	−0.107761	−	0.994177i	$-0.534368\pi$
$211$	−15.3518	−	9.86601i	−1.05686	−	0.679204i	−0.949101	+	0.314973i	$0.898005\pi$
$212$	3.56657	−	2.66990i	0.244953	−	0.183370i
$213$	6.16569	+	1.34126i	0.422466	+	0.0919019i
$214$	−8.48353	−	18.5763i	−0.579922	−	1.26985i
$215$	6.00370	+	7.01161i	0.409449	+	0.478188i
$216$	0.142315	+	0.989821i	0.00968330	+	0.0673488i
$217$	−9.27914	+	3.46094i	−0.629909	+	0.234944i
$218$	−3.42332	+	6.26934i	−0.231857	+	0.424614i
$219$	−2.65039	−	9.02640i	−0.179097	−	0.609948i
$220$	8.76988	−	3.21232i	0.591265	−	0.216575i
$221$	9.48795	−	1.36416i	0.638229	−	0.0917635i
$222$	0.395834	−	5.53448i	0.0265666	−	0.371450i
$223$	−5.05509	+	13.5532i	−0.338514	+	0.907592i	0.650465	+	0.759536i	$0.274574\pi$
$223$	−5.05509	+	13.5532i	−0.338514	+	0.907592i	−0.988979	+	0.148055i	$0.952699\pi$
$224$	−2.47396	+	1.58992i	−0.165299	+	0.106231i
$225$	0.769790	−	4.94039i	0.0513193	−	0.329359i
$226$	−3.58002	+	5.57062i	−0.238140	+	0.370552i
$227$	−19.5042	+	1.39497i	−1.29454	+	0.0925873i	−0.701549	−	0.712622i	$-0.747508\pi$
$227$	−19.5042	+	1.39497i	−1.29454	+	0.0925873i	−0.592991	+	0.805209i	$0.702053\pi$
$228$	0.992105	−	0.541730i	0.0657038	−	0.0358770i
$229$	−14.2367			−0.940787			−0.470394	−	0.882457i	$-0.655888\pi$
$229$	−14.2367			−0.940787			−0.470394	+	0.882457i	$0.655888\pi$
$230$	−10.6246	+	1.45508i	−0.700567	+	0.0959448i
$231$	12.2833			0.808180
$232$	8.10186	−	4.42395i	0.531913	−	0.290446i
$233$	14.4386	−	1.03267i	0.945903	−	0.0676523i	0.410142	−	0.912022i	$-0.365479\pi$
$233$	14.4386	−	1.03267i	0.945903	−	0.0676523i	0.535761	+	0.844370i	$0.320025\pi$
$234$	2.63789	−	4.10464i	0.172444	−	0.268329i
$235$	3.80352	−	25.3921i	0.248114	−	1.65639i
$236$	−6.97557	+	4.48292i	−0.454071	+	0.291814i
$237$	0.0147713	−	0.0396033i	0.000959497	−	0.00257251i
$238$	−0.412157	+	5.76270i	−0.0267161	+	0.373540i
$239$	−19.8725	+	2.85723i	−1.28544	+	0.184819i	−0.750954	−	0.660355i	$-0.770406\pi$
$239$	−19.8725	+	2.85723i	−1.28544	+	0.184819i	−0.534491	+	0.845174i	$0.679497\pi$
$240$	2.02850	+	0.940853i	0.130939	+	0.0607318i
$241$	8.08122	+	27.5221i	0.520557	+	1.77285i	0.627530	+	0.778592i	$0.284066\pi$
$241$	8.08122	+	27.5221i	0.520557	+	1.77285i	−0.106973	+	0.994262i	$0.534116\pi$
$242$	3.08923	−	5.65750i	0.198583	−	0.363678i
$243$	0.936950	−	0.349464i	0.0601054	−	0.0224181i
$244$	1.95750	+	13.6147i	0.125316	+	0.871591i
$245$	3.67481	+	0.284580i	0.234775	+	0.0181811i
$246$	−0.787734	−	1.72490i	−0.0502241	−	0.109975i
$247$	−5.38927	−	1.17236i	−0.342911	−	0.0745958i
$248$	−2.69593	+	2.01815i	−0.171192	+	0.128152i
$249$	−2.37290	−	1.52497i	−0.150376	−	0.0966411i
$250$	−8.31893	−	7.46963i	−0.526135	−	0.472421i
$251$	−7.60012	+	25.8836i	−0.479716	+	1.63376i	0.263464	+	0.964669i	$0.415135\pi$
$251$	−7.60012	+	25.8836i	−0.479716	+	1.63376i	−0.743180	+	0.669092i	$0.766683\pi$
$252$	2.07946	+	2.07946i	0.130994	+	0.130994i
$253$	−13.1300	+	15.1281i	−0.825476	+	0.951098i
$254$			0.708290i			0.0444421i
$255$	3.86789	−	2.08257i	0.242217	−	0.130415i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	15.1402	−	3.29355i	0.944420	−	0.205446i	0.286114	−	0.958196i	$-0.407637\pi$
$257$	15.1402	−	3.29355i	0.944420	−	0.205446i	0.658307	+	0.752750i	$0.271273\pi$
$258$	2.47389	+	3.30473i	0.154018	+	0.205744i
$259$	−8.82186	−	13.7271i	−0.548164	−	0.852960i
$260$	−4.47377	−	9.95079i	−0.277451	−	0.617122i
$261$	−6.04502	−	6.97633i	−0.374177	−	0.431824i
$262$	13.3987	+	10.0302i	0.827777	+	0.619666i
$263$	3.71154	+	9.95103i	0.228864	+	0.613607i	0.999726	−	0.0233944i	$-0.00744734\pi$
$263$	3.71154	+	9.95103i	0.228864	+	0.613607i	−0.770863	+	0.637001i	$0.780175\pi$
$264$	4.00765	−	1.17675i	0.246654	−	0.0724240i
$265$	−9.57495	+	2.75034i	−0.588185	+	0.168952i
$266$	1.38093	−	3.02381i	0.0846701	−	0.185402i
$267$	−9.24839	+	12.3544i	−0.565992	+	0.756077i
$268$	0.306000	+	0.0218856i	0.0186919	+	0.00133687i
$269$	0.941270	−	0.429863i	0.0573902	−	0.0262092i	−0.386513	−	0.922284i	$-0.626321\pi$
$269$	0.941270	−	0.429863i	0.0573902	−	0.0262092i	0.443903	+	0.896075i	$0.353593\pi$
$270$	0.488164	−	2.18213i	0.0297087	−	0.132800i
$271$	1.67158	−	11.6261i	0.101541	−	0.706235i	−0.873921	−	0.486068i	$-0.838431\pi$
$271$	1.67158	−	11.6261i	0.101541	−	0.706235i	0.975462	−	0.220167i	$-0.0706602\pi$
$272$	0.417599	+	1.91967i	0.0253207	+	0.116397i
$273$	−1.02363	−	14.3122i	−0.0619529	−	0.866215i
$274$	−15.1178	−	4.43898i	−0.913297	−	0.268168i
$275$	−20.8827	−	0.245866i	−1.25928	−	0.0148263i
$276$	−4.78389	+	0.338271i	−0.287956	+	0.0203615i
$277$	16.3457	−	16.3457i	0.982119	−	0.982119i	−0.0177239	−	0.999843i	$-0.505642\pi$
$277$	16.3457	−	16.3457i	0.982119	−	0.982119i	0.999843	+	0.0177239i	$0.00564199\pi$
$278$	−4.13065	−	7.56472i	−0.247740	−	0.453702i
$279$	2.54509	+	2.20533i	0.152370	+	0.132030i
$280$	6.43368	−	1.35995i	0.384486	−	0.0812724i
$281$	9.15255	+	1.31594i	0.545995	+	0.0785022i	0.409793	−	0.912179i	$-0.365601\pi$
$281$	9.15255	+	1.31594i	0.545995	+	0.0785022i	0.136203	+	0.990681i	$0.456510\pi$
$282$	2.44075	−	11.2200i	0.145345	−	0.668138i
$283$	−22.0328	−	8.21782i	−1.30972	−	0.488499i	−0.404923	−	0.914351i	$-0.632702\pi$
$283$	−22.0328	−	8.21782i	−1.30972	−	0.488499i	−0.904793	+	0.425852i	$0.859974\pi$
$284$	4.76870	−	4.13210i	0.282970	−	0.245195i
$285$	−2.50394	+	0.344980i	−0.148321	+	0.0204349i
$286$	−18.5379	−	8.46600i	−1.09617	−	0.500605i
$287$	−4.89440	−	2.67254i	−0.288907	−	0.157755i
$288$	0.877679	+	0.479249i	0.0517177	+	0.0282400i
$289$	−11.9530	−	5.45875i	−0.703117	−	0.321103i
$290$	−20.4480	+	2.81722i	−1.20075	+	0.165433i
$291$	−0.501335	+	0.434409i	−0.0293888	+	0.0254655i
$292$	−8.81433	−	3.28757i	−0.515820	−	0.192391i
$293$	3.63437	−	16.7069i	0.212322	−	0.976030i	−0.740395	−	0.672172i	$-0.765362\pi$
$293$	3.63437	−	16.7069i	0.212322	−	0.976030i	0.952717	−	0.303858i	$-0.0982748\pi$
$294$	1.63157	+	0.234584i	0.0951551	+	0.0136812i
$295$	18.1404	−	3.83450i	1.05617	−	0.223253i
$296$	−4.19337	−	3.63357i	−0.243735	−	0.211197i
$297$	−2.00175	−	3.66592i	−0.116153	−	0.212718i
$298$	−6.09891	+	6.09891i	−0.353300	+	0.353300i
$299$	18.7212	+	14.0381i	1.08267	+	0.811844i
$300$	−3.49367	−	3.57691i	−0.201707	−	0.206513i
$301$	11.6483	+	3.42024i	0.671394	+	0.197139i
$302$	0.450870	+	6.30398i	0.0259446	+	0.362753i
$303$	−1.73805	−	7.98969i	−0.0998485	−	0.458996i
$304$	0.160869	−	1.11887i	0.00922647	−	0.0641715i
$305$	6.71455	−	30.0145i	0.384474	−	1.71863i
$306$	1.78704	−	0.816112i	0.102158	−	0.0466540i
$307$	11.3045	+	0.808513i	0.645181	+	0.0461443i	0.390096	−	0.920774i	$-0.372442\pi$
$307$	11.3045	+	0.808513i	0.645181	+	0.0461443i	0.255085	+	0.966919i	$0.417896\pi$
$308$	7.36109	−	9.83327i	0.419437	−	0.560302i
$309$	−0.890171	+	1.94920i	−0.0506401	+	0.110886i
$310$	7.23759	−	2.07895i	0.411068	−	0.118076i
$311$	−0.966571	+	0.283811i	−0.0548092	+	0.0160934i	−0.309022	−	0.951055i	$-0.600002\pi$
$311$	−0.966571	+	0.283811i	−0.0548092	+	0.0160934i	0.254213	+	0.967148i	$0.418184\pi$
$312$	−1.70510	−	4.57156i	−0.0965325	−	0.258814i
$313$	−11.5735	−	8.66383i	−0.654174	−	0.489709i	0.219887	−	0.975525i	$-0.429431\pi$
$313$	−11.5735	−	8.66383i	−0.654174	−	0.489709i	−0.874061	+	0.485817i	$0.838522\pi$
$314$	−5.02183	−	5.79550i	−0.283398	−	0.327059i
$315$	−2.69645	−	5.99758i	−0.151928	−	0.337925i
$316$	−0.0228520	−	0.0355584i	−0.00128552	−	0.00200032i
$317$	4.75034	+	6.34571i	0.266806	+	0.356411i	0.913857	−	0.406036i	$-0.133089\pi$
$317$	4.75034	+	6.34571i	0.266806	+	0.356411i	−0.647052	+	0.762446i	$0.723998\pi$
$318$	−4.35338	+	0.947021i	−0.244126	+	0.0531063i
$319$	−25.2491	+	29.1390i	−1.41368	+	1.63147i
$320$	1.96882	−	1.06006i	0.110061	−	0.0592593i
$321$			20.4218i			1.13984i
$322$	−10.6663	+	9.22730i	−0.594407	+	0.514217i
$323$	−1.57027	−	1.57027i	−0.0873722	−	0.0873722i
$324$	0.281733	−	0.959493i	0.0156518	−	0.0533052i
$325$	1.45379	+	24.3526i	0.0806418	+	1.35084i
$326$	−15.4086	−	9.90252i	−0.853405	−	0.548450i
$327$	5.71834	−	4.28070i	0.316225	−	0.236723i
$328$	−1.85292	−	0.403078i	−0.102310	−	0.0222563i
$329$	−14.0275	−	30.7159i	−0.773360	−	1.69342i
$330$	−9.31181	−	0.721113i	−0.512598	−	0.0396959i
$331$	−0.552413	−	3.84211i	−0.0303633	−	0.211182i	0.968992	−	0.247094i	$-0.0794755\pi$
$331$	−0.552413	−	3.84211i	−0.0303633	−	0.211182i	−0.999355	+	0.0359119i	$0.988566\pi$
$332$	−2.64283	+	0.985724i	−0.145044	+	0.0540986i
$333$	−2.65917	+	4.86991i	−0.145722	+	0.266869i
$334$	−4.53797	−	15.4549i	−0.248307	−	0.845655i
$335$	−0.622305	−	0.288637i	−0.0340002	−	0.0157699i
$336$	2.91087	−	0.418521i	0.158801	−	0.0228322i
$337$	1.78694	−	24.9847i	0.0973409	−	1.36100i	−0.680595	−	0.732660i	$-0.738278\pi$
$337$	1.78694	−	24.9847i	0.0973409	−	1.36100i	0.777936	−	0.628344i	$-0.216267\pi$
$338$	−3.77650	+	10.1252i	−0.205415	+	0.550738i
$339$	5.57062	−	3.58002i	0.302555	−	0.194440i
$340$	0.650761	−	4.34444i	0.0352925	−	0.235610i
$341$	7.60468	−	11.8331i	0.411817	−	0.640799i
$342$	−1.12749	+	0.0806399i	−0.0609679	+	0.00436051i
$343$	−13.8131	+	7.54251i	−0.745836	+	0.407257i
$344$	4.12812			0.222573
$345$	10.2690	+	3.09005i	0.552862	+	0.166363i
$346$	14.8888			0.800428
$347$	−27.6067	+	15.0744i	−1.48200	+	0.809235i	−0.997837	−	0.0657402i	$-0.979059\pi$
$347$	−27.6067	+	15.0744i	−1.48200	+	0.809235i	−0.484167	+	0.874976i	$0.660877\pi$
$348$	−9.20748	+	0.658532i	−0.493573	+	0.0353010i
$349$	13.7531	−	21.4003i	0.736188	−	1.14553i	−0.248061	−	0.968744i	$-0.579793\pi$
$349$	13.7531	−	21.4003i	0.736188	−	1.14553i	0.984249	−	0.176787i	$-0.0565704\pi$
$350$	−14.5287	−	2.26380i	−0.776593	−	0.121005i
$351$	−4.10464	+	2.63789i	−0.219090	+	0.140800i
$352$	1.45966	−	3.91349i	0.0777999	−	0.208590i
$353$	1.42626	−	19.9418i	0.0759123	−	1.06139i	−0.806598	−	0.591100i	$-0.798694\pi$
$353$	1.42626	−	19.9418i	0.0759123	−	1.06139i	0.882510	−	0.470293i	$-0.155852\pi$
$354$	8.20747	−	1.18006i	0.436222	−	0.0627193i
$355$	−13.2485	+	4.85281i	−0.703160	+	0.257560i
$356$	4.34786	+	14.8074i	0.230436	+	0.784793i
$357$	2.76882	−	5.07072i	0.146542	−	0.268371i
$358$	−21.1207	+	7.87760i	−1.11626	+	0.416344i
$359$	−4.31376	−	30.0029i	−0.227672	−	1.58349i	−0.707878	−	0.706335i	$-0.750347\pi$
$359$	−4.31376	−	30.0029i	−0.227672	−	1.58349i	0.480206	−	0.877156i	$-0.340562\pi$
$360$	−1.45434	−	1.69850i	−0.0766505	−	0.0895187i
$361$	−7.36209	−	16.1207i	−0.387478	−	0.848460i
$362$	3.56823	+	0.776221i	0.187542	+	0.0407973i
$363$	−5.16027	+	3.86293i	−0.270844	+	0.202751i
$364$	−12.0710	−	7.75753i	−0.632690	−	0.406605i
$365$	15.8164	+	13.8688i	0.827868	+	0.725928i
$366$	3.87515	−	13.1975i	0.202557	−	0.689846i
$367$	−21.5218	−	21.5218i	−1.12343	−	1.12343i	−0.991222	−	0.132205i	$-0.957794\pi$
$367$	−21.5218	−	21.5218i	−1.12343	−	1.12343i	−0.132205	−	0.991222i	$-0.542206\pi$
$368$	−2.59608	+	4.03242i	−0.135330	+	0.210204i
$369$			1.89626i			0.0987152i
$370$	5.88188	+	10.9243i	0.305784	+	0.567925i
$371$	−8.57991	+	9.90174i	−0.445447	+	0.514073i
$372$	3.29067	−	0.715842i	0.170613	−	0.0371147i
$373$	0.971049	+	1.29717i	0.0502790	+	0.0671649i	0.824976	−	0.565168i	$-0.191189\pi$
$373$	0.971049	+	1.29717i	0.0502790	+	0.0671649i	−0.774697	+	0.632333i	$0.782098\pi$
$374$	−4.43633	−	6.90307i	−0.229397	−	0.356949i
$375$	4.46417	+	10.2504i	0.230529	+	0.529330i
$376$	−7.51935	−	8.67779i	−0.387781	−	0.447523i
$377$	36.0563	+	26.9914i	1.85699	+	1.39013i
$378$	−1.02771	−	2.75539i	−0.0528595	−	0.141722i
$379$	−4.08087	+	1.19825i	−0.209620	+	0.0615500i	−0.384857	−	0.922976i	$-0.625749\pi$
$379$	−4.08087	+	1.19825i	−0.209620	+	0.0615500i	0.175237	+	0.984526i	$0.443931\pi$
$380$	−1.22438	+	2.21125i	−0.0628096	+	0.113435i
$381$	0.294234	−	0.644284i	0.0150741	−	0.0330076i
$382$	4.40768	−	5.88798i	0.225517	−	0.301255i
$383$	1.66525	+	0.119101i	0.0850904	+	0.00608579i	0.113819	−	0.993501i	$-0.463691\pi$
$383$	1.66525	+	0.119101i	0.0850904	+	0.00608579i	−0.0287290	+	0.999587i	$0.509146\pi$
$384$	0.909632	−	0.415415i	0.0464195	−	0.0211991i
$385$	−23.1931	+	14.7131i	−1.18203	+	0.749849i
$386$	−2.50158	+	17.3988i	−0.127327	+	0.885578i
$387$	−0.877496	−	4.03378i	−0.0446056	−	0.205049i
$388$	0.0473236	+	0.661671i	0.00240249	+	0.0335913i
$389$	7.07764	+	2.07818i	0.358851	+	0.105368i	0.456188	−	0.889883i	$-0.349214\pi$
$389$	7.07764	+	2.07818i	0.358851	+	0.105368i	−0.0973375	+	0.995251i	$0.531033\pi$
$390$	−0.0642231	+	10.9100i	−0.00325206	+	0.552451i
$391$	3.28544	+	8.83036i	0.166152	+	0.446570i
$392$	1.16556	−	1.16556i	0.0588695	−	0.0588695i
$393$	−8.02124	−	14.6898i	−0.404618	−	0.741003i
$394$	12.8782	+	11.1590i	0.648795	+	0.562184i
$395$	0.0195466	+	0.0924716i	0.000983495	+	0.00465275i
$396$	−4.13432	−	0.594426i	−0.207758	−	0.0298710i
$397$	4.60543	−	21.1708i	0.231140	−	1.06253i	−0.704534	−	0.709670i	$-0.748844\pi$
$397$	4.60543	−	21.1708i	0.231140	−	1.06253i	0.935675	−	0.352864i	$-0.114792\pi$
$398$	−14.2529	−	5.31607i	−0.714436	−	0.266471i
$399$	−2.51227	+	2.17690i	−0.125771	+	0.108981i
$400$	−4.95714	+	0.653260i	−0.247857	+	0.0326630i
$401$	−17.2820	−	7.89242i	−0.863021	−	0.394129i	−0.0658124	−	0.997832i	$-0.520964\pi$
$401$	−17.2820	−	7.89242i	−0.863021	−	0.394129i	−0.797209	+	0.603703i	$0.793691\pi$
$402$	−0.269256	−	0.147025i	−0.0134293	−	0.00733293i
$403$	−14.4214	−	7.87470i	−0.718383	−	0.392267i
$404$	−7.43766	−	3.39666i	−0.370037	−	0.168990i
$405$	−1.35054	+	1.78215i	−0.0671089	+	0.0885555i
$406$	−20.5160	+	17.7772i	−1.01819	+	0.882270i
$407$	21.7145	+	8.09907i	1.07635	+	0.401456i
$408$	0.417599	−	1.91967i	0.0206742	−	0.0950380i
$409$	16.6432	+	2.39293i	0.822954	+	0.118323i	0.540912	−	0.841079i	$-0.318079\pi$
$409$	16.6432	+	2.39293i	0.822954	+	0.118323i	0.282042	+	0.959402i	$0.408988\pi$
$410$	3.55349	+	2.31336i	0.175495	+	0.114249i
$411$	11.9076	+	10.3180i	0.587358	+	0.508948i
$412$	1.02696	+	1.88073i	0.0505946	+	0.0926571i
$413$	17.2427	−	17.2427i	0.848456	−	0.848456i
$414$	4.49210	+	1.67960i	0.220775	+	0.0825477i
$415$	6.30710	+	0.0371275i	0.309604	+	0.00182252i
$416$	−4.68155	−	1.37463i	−0.229532	−	0.0673967i
$417$	0.614873	+	8.59705i	0.0301105	+	0.420999i
$418$	1.00360	+	4.61349i	0.0490878	+	0.225653i
$419$	−3.19623	+	22.2303i	−0.156146	+	1.08602i	0.749506	+	0.661998i	$0.230291\pi$
$419$	−3.19623	+	22.2303i	−0.156146	+	1.08602i	−0.905652	+	0.424022i	$0.860618\pi$
$420$	−6.41723	−	1.43560i	−0.313129	−	0.0700499i
$421$	10.3462	−	4.72496i	0.504244	−	0.230280i	−0.147018	−	0.989134i	$-0.546967\pi$
$421$	10.3462	−	4.72496i	0.504244	−	0.230280i	0.651261	+	0.758854i	$0.274240\pi$
$422$	18.2022	+	1.30185i	0.886071	+	0.0633730i
$423$	−6.88112	+	9.19210i	−0.334572	+	0.446935i
$424$	−1.85076	+	4.05259i	−0.0898807	+	0.196811i
$425$	−4.80876	+	8.56529i	−0.233259	+	0.415478i
$426$	−6.05430	+	1.77770i	−0.293332	+	0.0861299i
$427$	−14.1358	−	37.8995i	−0.684079	−	1.83409i
$428$	16.3485	+	12.2383i	0.790235	+	0.591563i
$429$	13.3458	+	15.4019i	0.644342	+	0.743610i
$430$	−8.62962	−	3.27668i	−0.416157	−	0.158015i
$431$	8.55585	+	13.3132i	0.412121	+	0.641273i	0.983814	−	0.179195i	$-0.0573494\pi$
$431$	8.55585	+	13.3132i	0.412121	+	0.641273i	−0.571693	+	0.820468i	$0.693713\pi$
$432$	−0.599278	−	0.800541i	−0.0288328	−	0.0385161i
$433$	−31.5157	+	6.85582i	−1.51455	+	0.329470i	−0.891611	−	0.452802i	$-0.850424\pi$
$433$	−31.5157	+	6.85582i	−1.51455	+	0.329470i	−0.622937	+	0.782272i	$0.714061\pi$
$434$	6.48545	−	7.48461i	0.311312	−	0.359273i
$435$	19.7705	+	5.93177i	0.947921	+	0.284406i
$436$		−	7.14309i		−	0.342092i
$437$	0.00437391	−	5.42108i	0.000209233	−	0.259325i
$438$	6.65209	+	6.65209i	0.317849	+	0.317849i
$439$	−0.188218	+	0.641010i	−0.00898314	+	0.0305938i	−0.963863	−	0.266400i	$-0.914166\pi$
$439$	−0.188218	+	0.641010i	−0.00898314	+	0.0305938i	0.954879	+	0.296994i	$0.0959840\pi$
$440$	−6.15764	+	7.02234i	−0.293554	+	0.334777i
$441$	−1.38668	−	0.891164i	−0.0660323	−	0.0424364i
$442$	−7.67360	+	5.74439i	−0.364996	+	0.273233i
$443$	−4.19362	−	0.912265i	−0.199245	−	0.0433430i	0.111835	−	0.993727i	$-0.464327\pi$
$443$	−4.19362	−	0.912265i	−0.199245	−	0.0433430i	−0.311080	+	0.950384i	$0.600691\pi$
$444$	2.30498	+	5.04720i	0.109390	+	0.239530i
$445$	2.66436	−	34.4053i	0.126303	−	1.63097i
$446$	−2.05862	−	14.3180i	−0.0974786	−	0.677979i
$447$	8.08134	−	3.01418i	0.382234	−	0.142566i
$448$	1.40938	−	2.58108i	0.0665869	−	0.121945i
$449$	9.26593	+	31.5569i	0.437286	+	1.48926i	0.823749	+	0.566955i	$0.191879\pi$
$449$	9.26593	+	31.5569i	0.437286	+	1.48926i	−0.386462	+	0.922305i	$0.626303\pi$
$450$	1.69205	+	4.70499i	0.0797639	+	0.221796i
$451$	7.83974	−	1.12718i	0.369159	−	0.0530770i
$452$	0.472395	−	6.60494i	0.0222196	−	0.310670i
$453$	2.20864	−	5.92160i	0.103771	−	0.278221i
$454$	16.4499	−	10.5717i	0.772032	−	0.496155i
$455$	19.0762	+	25.7980i	0.894306	+	1.20943i
$456$	−0.611126	+	0.950931i	−0.0286186	+	0.0445314i
$457$	−7.45946	+	0.533511i	−0.348939	+	0.0249566i	−0.244709	−	0.969597i	$-0.578692\pi$
$457$	−7.45946	+	0.533511i	−0.348939	+	0.0249566i	−0.104230	+	0.994553i	$0.533238\pi$
$458$	12.4952	−	6.82292i	0.583865	−	0.318814i
$459$	−1.96457			−0.0916983
$460$	8.62767	−	6.36893i	0.402267	−	0.296953i
$461$	−39.8167			−1.85445			−0.927224	−	0.374506i	$-0.877812\pi$
$461$	−39.8167			−1.85445			−0.927224	+	0.374506i	$0.877812\pi$
$462$	−10.7808	+	5.88675i	−0.501567	+	0.273876i
$463$	−18.1404	+	1.29742i	−0.843054	+	0.0602964i	−0.486183	−	0.873857i	$-0.661611\pi$
$463$	−18.1404	+	1.29742i	−0.843054	+	0.0602964i	−0.356871	+	0.934153i	$0.616157\pi$
$464$	−4.99066	+	7.76561i	−0.231685	+	0.360510i
$465$	−7.44717	−	1.11552i	−0.345354	−	0.0517312i
$466$	−12.1775	+	7.82603i	−0.564113	+	0.362534i
$467$	7.43623	−	19.9373i	0.344108	−	0.922589i	−0.643472	−	0.765470i	$-0.722507\pi$
$467$	7.43623	−	19.9373i	0.344108	−	0.922589i	0.987580	−	0.157119i	$-0.0502206\pi$
$468$	−0.348078	+	4.86676i	−0.0160899	+	0.224966i
$469$	−0.893003	+	0.128394i	−0.0412350	+	0.00592870i
$470$	8.83085	+	24.1089i	0.407337	+	1.11206i
$471$	2.16048	+	7.35792i	0.0995497	+	0.339035i
$472$	3.97387	−	7.27760i	0.182912	−	0.334979i
$473$	−16.1554	+	6.02564i	−0.742824	+	0.277059i
$474$	0.00601541	+	0.0418381i	0.000276297	+	0.00192169i
$475$	4.31467	−	3.65064i	0.197971	−	0.167503i
$476$	−2.40003	−	5.25533i	−0.110005	−	0.240878i
$477$	4.35338	+	0.947021i	0.199328	+	0.0433611i
$478$	16.0723	−	12.0316i	0.735132	−	0.550313i
$479$	1.10188	+	0.708132i	0.0503460	+	0.0323554i	0.565572	−	0.824699i	$-0.308656\pi$
$479$	1.10188	+	0.708132i	0.0503460	+	0.0323554i	−0.515226	+	0.857055i	$0.672292\pi$
$480$	−2.23127	+	0.146387i	−0.101843	+	0.00668164i
$481$	7.62729	−	25.9762i	0.347774	−	1.18441i
$482$	−20.2827	−	20.2827i	−0.923850	−	0.923850i
$483$	13.5355	−	3.96253i	0.615888	−	0.180301i
$484$			6.44598i			0.292999i
$485$	0.426270	−	1.42075i	0.0193559	−	0.0645130i
$486$	−0.654861	+	0.755750i	−0.0297051	+	0.0342815i
$487$	−24.9696	+	5.43181i	−1.13148	+	0.246139i	−0.739055	−	0.673645i	$-0.764728\pi$
$487$	−24.9696	+	5.43181i	−1.13148	+	0.246139i	−0.392426	+	0.919784i	$0.628364\pi$
$488$	−8.24288	−	11.0112i	−0.373138	−	0.498454i
$489$	9.90252	+	15.4086i	0.447808	+	0.696802i
$490$	−3.36169	+	1.51138i	−0.151866	+	0.0682772i
$491$	2.90906	+	3.35724i	0.131284	+	0.151510i	0.817585	−	0.575808i	$-0.195312\pi$
$491$	2.90906	+	3.35724i	0.131284	+	0.151510i	−0.686301	+	0.727317i	$0.740767\pi$
$492$	1.51803	+	1.13638i	0.0684382	+	0.0512322i
$493$	6.33751	+	16.9915i	0.285427	+	0.765260i
$494$	5.29190	−	1.55384i	0.238094	−	0.0699107i
$495$	8.17076	+	4.52421i	0.367248	+	0.203348i
$496$	1.39897	−	3.06331i	0.0628154	−	0.137547i
$497$	−11.1203	+	14.8550i	−0.498814	+	0.666337i
$498$	2.81349	+	0.201224i	0.126075	+	0.00901708i
$499$	4.26686	−	1.94861i	0.191011	−	0.0872317i	−0.317614	−	0.948220i	$-0.602881\pi$
$499$	4.26686	−	1.94861i	0.191011	−	0.0872317i	0.508624	+	0.860989i	$0.330154\pi$
$500$	10.8812	+	2.56910i	0.486620	+	0.114894i
$501$	−2.29232	+	15.9434i	−0.102413	+	0.712300i
$502$	−5.73424	−	26.3599i	−0.255932	−	1.17650i
$503$	1.39695	+	19.5319i	0.0622869	+	0.870884i	0.928529	+	0.371260i	$0.121074\pi$
$503$	1.39695	+	19.5319i	0.0622869	+	0.870884i	−0.866242	+	0.499624i	$0.833471\pi$
$504$	−2.82168	−	0.828521i	−0.125688	−	0.0369053i
$505$	12.8519	+	13.0041i	0.571904	+	0.578677i
$506$	4.27377	−	19.5702i	0.189992	−	0.870001i
$507$	7.64138	−	7.64138i	0.339366	−	0.339366i
$508$	−0.339447	−	0.621652i	−0.0150605	−	0.0275813i
$509$	4.62803	+	4.01021i	0.205134	+	0.177749i	0.751369	−	0.659883i	$-0.229394\pi$
$509$	4.62803	+	4.01021i	0.205134	+	0.177749i	−0.546235	+	0.837632i	$0.683939\pi$
$510$	−2.39670	+	3.68151i	−0.106128	+	0.163020i
$511$	27.3840	+	3.93722i	1.21140	+	0.174172i
$512$	0.212565	−	0.977147i	0.00939415	−	0.0431842i
$513$	1.05910	+	0.395025i	0.0467605	+	0.0174408i
$514$	−11.7098	+	10.1466i	−0.516498	+	0.447548i
$515$	−0.653979	−	4.74672i	−0.0288178	−	0.209165i
$516$	−3.75507	−	1.71488i	−0.165308	−	0.0754936i
$517$	42.0934	+	22.9848i	1.85127	+	1.01087i
$518$	14.3215	+	7.82011i	0.629249	+	0.343596i
$519$	−13.5434	−	6.18504i	−0.594487	−	0.271493i
$520$	8.69544	+	6.58955i	0.381320	+	0.288971i
$521$	27.3145	−	23.6681i	1.19667	−	1.03692i	0.198283	−	0.980145i	$-0.436464\pi$
$521$	27.3145	−	23.6681i	1.19667	−	1.03692i	0.998387	−	0.0567754i	$-0.0180819\pi$
$522$	8.64898	+	3.22590i	0.378556	+	0.141194i
$523$	−0.521821	+	2.39877i	−0.0228177	+	0.104891i	−0.987147	−	0.159813i	$-0.948911\pi$
$523$	−0.521821	+	2.39877i	−0.0228177	+	0.104891i	0.964330	+	0.264704i	$0.0852744\pi$
$524$	−16.5667	−	2.38194i	−0.723722	−	0.104055i
$525$	12.2754	+	8.09468i	0.535741	+	0.353281i
$526$	−8.02656	−	6.95506i	−0.349975	−	0.303255i
$527$	−3.17069	−	5.80668i	−0.138117	−	0.252943i
$528$	−2.95347	+	2.95347i	−0.128533	+	0.128533i
$529$	−9.58829	+	20.9061i	−0.416882	+	0.908960i
$530$	7.08563	−	7.00270i	0.307780	−	0.304178i
$531$	−7.95599	−	2.33609i	−0.345261	−	0.101378i
$532$	0.237146	+	3.31574i	0.0102816	+	0.143756i
$533$	−1.96670	−	9.04077i	−0.0851872	−	0.391599i
$534$	2.19628	−	15.2755i	0.0950425	−	0.661035i
$535$	−24.4616	−	38.5602i	−1.05757	−	1.66710i
$536$	−0.279058	+	0.127442i	−0.0120535	+	0.00550464i
$537$	22.4845	+	1.60812i	0.970278	+	0.0693957i
$538$	−0.620121	+	0.828385i	−0.0267353	+	0.0357142i
$539$	−2.86008	+	6.26271i	−0.123192	+	0.269754i
$540$	0.617333	+	2.14916i	0.0265658	+	0.0924852i
$541$	35.2383	−	10.3469i	1.51501	−	0.444848i	0.584588	−	0.811330i	$-0.301256\pi$
$541$	35.2383	−	10.3469i	1.51501	−	0.444848i	0.930425	+	0.366482i	$0.119438\pi$
$542$	4.10468	+	11.0051i	0.176311	+	0.472709i
$543$	−2.92332	−	2.18837i	−0.125452	−	0.0939120i
$544$	−1.28652	−	1.48472i	−0.0551591	−	0.0636570i
$545$	−5.66979	+	14.9323i	−0.242867	+	0.639628i
$546$	7.75753	+	12.0710i	0.331992	+	0.516589i
$547$	−21.4273	−	28.6235i	−0.916164	−	1.22385i	−0.974234	−	0.225540i	$-0.927585\pi$
$547$	−21.4273	−	28.6235i	−0.916164	−	1.22385i	0.0580698	−	0.998313i	$-0.481505\pi$
$548$	15.3959	−	3.34918i	0.657681	−	0.143070i
$549$	−9.00741	+	10.3951i	−0.384427	+	0.443652i
$550$	18.4462	−	9.79224i	0.786548	−	0.417543i
$551$		−	10.4345i		−	0.444524i
$552$	4.03660	−	2.58957i	0.171809	−	0.110219i
$553$	0.0878955	+	0.0878955i	0.00373770	+	0.00373770i
$554$	−6.51262	+	22.1800i	−0.276695	+	0.942336i
$555$	−0.812248	−	12.3805i	−0.0344780	−	0.525522i
$556$	7.25077	+	4.65979i	0.307501	+	0.197619i
$557$	3.62401	−	2.71290i	0.153554	−	0.114949i	−0.519738	−	0.854326i	$-0.673970\pi$
$557$	3.62401	−	2.71290i	0.153554	−	0.114949i	0.673292	+	0.739376i	$0.264880\pi$
$558$	−3.29067	−	0.715842i	−0.139305	−	0.0303040i
$559$	8.36726	+	18.3217i	0.353897	+	0.774927i
$560$	−4.99495	+	4.27693i	−0.211075	+	0.180733i
$561$	1.16779	+	8.12217i	0.0493042	+	0.342918i
$562$	−8.66366	+	3.23138i	−0.365454	+	0.136307i
$563$	19.2554	−	35.2636i	0.811518	−	1.48618i	−0.0612897	−	0.998120i	$-0.519521\pi$
$563$	19.2554	−	35.2636i	0.811518	−	1.48618i	0.872808	−	0.488064i	$-0.162297\pi$
$564$	3.23495	+	11.0172i	0.136216	+	0.463910i
$565$	−6.23016	+	13.4323i	−0.262105	+	0.565102i
$566$	23.2761	−	3.34660i	0.978369	−	0.140668i
$567$	−0.209795	+	2.93331i	−0.00881055	+	0.123188i
$568$	−2.20508	+	5.91205i	−0.0925232	+	0.248064i
$569$	−24.3262	+	15.6335i	−1.01981	+	0.655390i	−0.939913	−	0.341414i	$-0.889094\pi$
$569$	−24.3262	+	15.6335i	−1.01981	+	0.655390i	−0.0798934	+	0.996803i	$0.525458\pi$
$570$	2.03232	−	1.50279i	0.0851247	−	0.0629450i
$571$	−19.4960	+	30.3363i	−0.815882	+	1.26954i	0.144125	+	0.989559i	$0.453963\pi$
$571$	−19.4960	+	30.3363i	−0.815882	+	1.26954i	−0.960007	+	0.279977i	$0.909673\pi$
$572$	20.3277	−	1.45386i	0.849943	−	0.0607891i
$573$	−6.45533	+	3.52487i	−0.269675	+	0.147254i
$574$	5.57653			0.232760
$575$	−23.0910	+	6.46575i	−0.962961	+	0.269640i
$576$	−1.00000			−0.0416667
$577$	−37.4676	+	20.4589i	−1.55980	+	0.851714i	−0.560068	+	0.828447i	$0.689225\pi$
$577$	−37.4676	+	20.4589i	−1.55980	+	0.851714i	−0.999729	+	0.0232671i	$0.992593\pi$
$578$	13.1070	−	0.937430i	0.545179	−	0.0389919i
$579$	9.50326	−	14.7874i	0.394942	−	0.614542i
$580$	16.5966	−	12.2723i	0.689137	−	0.509579i
$581$	6.97824	−	4.48464i	0.289506	−	0.186054i
$582$	0.231821	−	0.621536i	0.00960929	−	0.0257635i
$583$	1.32753	−	18.5612i	0.0549805	−	0.768728i
$584$	9.31172	−	1.33882i	0.385322	−	0.0554009i
$585$	4.59061	−	9.89743i	0.189798	−	0.409208i
$586$	4.81697	+	16.4051i	0.198987	+	0.677688i
$587$	−14.0678	+	25.7632i	−0.580640	+	1.06336i	0.407989	+	0.912987i	$0.366230\pi$
$587$	−14.0678	+	25.7632i	−0.580640	+	1.06336i	−0.988629	+	0.150376i	$0.951952\pi$
$588$	−1.54442	+	0.576038i	−0.0636907	+	0.0237554i
$589$	0.541748	+	3.76794i	0.0223223	+	0.155255i
$590$	−14.0837	+	12.0592i	−0.579818	+	0.496469i
$591$	−7.07880	−	15.5004i	−0.291183	−	0.637602i
$592$	5.42182	+	1.17944i	0.222835	+	0.0484748i
$593$	−25.0137	+	18.7250i	−1.02719	+	0.768945i	−0.973285	−	0.229601i	$-0.926258\pi$
$593$	−25.0137	+	18.7250i	−1.02719	+	0.768945i	−0.0539059	+	0.998546i	$0.517167\pi$
$594$	3.51378	+	2.25817i	0.144172	+	0.0926538i
$595$	0.845742	+	12.8910i	0.0346720	+	0.528479i
$596$	2.42999	−	8.27578i	0.0995362	−	0.338989i
$597$	10.7566	+	10.7566i	0.440237	+	0.440237i
$598$	−23.1589	−	3.34883i	−0.947039	−	0.136944i
$599$			29.5757i			1.20843i	0.796821	+	0.604215i	$0.206513\pi$
$599$			29.5757i			1.20843i	−0.796821	+	0.604215i	$0.793487\pi$
$600$	4.78055	+	1.46504i	0.195165	+	0.0598102i
$601$	−14.8029	+	17.0834i	−0.603822	+	0.696848i	−0.972551	−	0.232689i	$-0.925248\pi$
$601$	−14.8029	+	17.0834i	−0.603822	+	0.696848i	0.368729	+	0.929537i	$0.379793\pi$
$602$	−11.8626	+	2.58055i	−0.483483	+	0.105175i
$603$	0.183847	+	0.245591i	0.00748685	+	0.0100013i
$604$	−3.41690	−	5.31679i	−0.139032	−	0.216337i
$605$	5.11646	−	13.4750i	0.208014	−	0.547835i
$606$	5.35450	+	6.17943i	0.217512	+	0.251022i
$607$	20.8409	+	15.6013i	0.845906	+	0.633238i	0.931762	−	0.363070i	$-0.118271\pi$
$607$	20.8409	+	15.6013i	0.845906	+	0.633238i	−0.0858555	+	0.996308i	$0.527362\pi$
$608$	0.395025	+	1.05910i	0.0160204	+	0.0429523i
$609$	26.0470	−	7.64808i	1.05548	−	0.309916i
$610$	8.49122	+	29.5611i	0.343800	+	1.19689i
$611$	23.2735	−	50.9618i	0.941545	−	2.06170i
$612$	−1.17732	+	1.57272i	−0.0475905	+	0.0635734i
$613$	−7.07221	−	0.505814i	−0.285644	−	0.0204297i	−0.0722179	−	0.997389i	$-0.523008\pi$
$613$	−7.07221	−	0.505814i	−0.285644	−	0.0204297i	−0.213426	+	0.976959i	$0.568462\pi$
$614$	−10.3092	+	4.70805i	−0.416045	+	0.190001i
$615$	−2.27137	−	3.58048i	−0.0915903	−	0.144379i
$616$	−1.74809	+	12.1582i	−0.0704326	+	0.489870i
$617$	−6.14359	−	28.2416i	−0.247332	−	1.13697i	−0.918426	−	0.395594i	$-0.870539\pi$
$617$	−6.14359	−	28.2416i	−0.247332	−	1.13697i	0.671094	−	0.741372i	$-0.265825\pi$
$618$	−0.152869	−	2.13739i	−0.00614930	−	0.0859784i
$619$	30.0118	+	8.81225i	1.20627	+	0.354194i	0.822249	−	0.569128i	$-0.192719\pi$
$619$	30.0118	+	8.81225i	1.20627	+	0.354194i	0.384026	+	0.923322i	$0.374537\pi$
$620$	−5.35595	+	5.29326i	−0.215100	+	0.212582i
$621$	−3.38843	−	3.39390i	−0.135973	−	0.136193i
$622$	0.712323	−	0.712323i	0.0285615	−	0.0285615i
$623$	−21.7503	−	39.8328i	−0.871409	−	1.59587i
$624$	3.68745	+	3.19519i	0.147616	+	0.127910i
$625$	−20.7073	−	14.0074i	−0.828291	−	0.560297i
$626$	14.3100	+	2.05746i	0.571941	+	0.0822327i
$627$	1.00360	−	4.61349i	0.0400800	−	0.184245i
$628$	7.18505	+	2.67988i	0.286715	+	0.106939i
$629$	8.23816	−	7.13841i	0.328477	−	0.284627i
$630$	5.24095	+	3.97168i	0.208804	+	0.158235i
$631$	39.6649	+	18.1143i	1.57903	+	0.721120i	0.995832	−	0.0912073i	$-0.0290726\pi$
$631$	39.6649	+	18.1143i	1.57903	+	0.721120i	0.583201	+	0.812328i	$0.301800\pi$
$632$	0.0370980	+	0.0202571i	0.00147568	+	0.000805782i
$633$	−16.0165	−	8.74569i	−0.636600	−	0.347610i
$634$	−7.21045	−	3.29290i	−0.286364	−	0.130778i
$635$	0.216164	+	1.56896i	0.00857821	+	0.0622625i
$636$	3.36702	−	2.91754i	0.133511	−	0.115688i
$637$	7.53552	+	2.81060i	0.298568	+	0.111360i
$638$	8.19575	−	37.6753i	0.324473	−	1.49158i
$639$	6.24567	+	0.897991i	0.247075	+	0.0355240i
$640$	−1.21996	+	1.87395i	−0.0482232	+	0.0740744i
$641$	−26.0004	−	22.5295i	−1.02696	−	0.889862i	−0.0329795	−	0.999456i	$-0.510500\pi$
$641$	−26.0004	−	22.5295i	−1.02696	−	0.889862i	−0.993976	+	0.109594i	$0.965045\pi$
$642$	−9.78714	−	17.9238i	−0.386268	−	0.707396i
$643$	13.9539	−	13.9539i	0.550288	−	0.550288i	−0.376236	−	0.926524i	$-0.622782\pi$
$643$	13.9539	−	13.9539i	0.550288	−	0.550288i	0.926524	+	0.376236i	$0.122782\pi$
$644$	4.93937	−	13.2104i	0.194638	−	0.520563i
$645$	6.48860	+	6.56544i	0.255488	+	0.258514i
$646$	2.13074	+	0.625643i	0.0838330	+	0.0246156i
$647$	0.612820	+	8.56834i	0.0240924	+	0.336856i	0.995175	+	0.0981133i	$0.0312808\pi$
$647$	0.612820	+	8.56834i	0.0240924	+	0.336856i	−0.971083	+	0.238743i	$0.923265\pi$
$648$	0.212565	+	0.977147i	0.00835035	+	0.0383860i
$649$	−4.92890	+	34.2813i	−0.193476	+	1.34566i
$650$	−12.9469	−	20.6771i	−0.507820	−	0.811021i
$651$	−9.00859	+	4.11409i	−0.353075	+	0.161244i
$652$	18.2696	+	1.30667i	0.715493	+	0.0511731i
$653$	5.07903	−	6.78479i	0.198758	−	0.265509i	−0.690078	−	0.723735i	$-0.742424\pi$
$653$	5.07903	−	6.78479i	0.198758	−	0.265509i	0.888836	+	0.458226i	$0.151515\pi$
$654$	−2.96735	+	6.49759i	−0.116033	+	0.254076i
$655$	32.7413	+	18.1291i	1.27931	+	0.708362i
$656$	1.81945	−	0.534237i	0.0710374	−	0.0208585i
$657$	−3.28757	−	8.81433i	−0.128261	−	0.343880i
$658$	27.0322	+	20.2361i	1.05382	+	0.788883i
$659$	8.17213	+	9.43114i	0.318341	+	0.367385i	0.892256	−	0.451530i	$-0.149122\pi$
$659$	8.17213	+	9.43114i	0.318341	+	0.367385i	−0.573915	+	0.818915i	$0.694576\pi$
$660$	8.51838	−	3.82977i	0.331577	−	0.149074i
$661$	−14.9083	−	23.1978i	−0.579866	−	0.902289i	0.420121	−	0.907468i	$-0.361988\pi$
$661$	−14.9083	−	23.1978i	−0.579866	−	0.902289i	−0.999987	+	0.00517936i	$0.998351\pi$
$662$	2.32617	+	3.10740i	0.0904092	+	0.120772i
$663$	9.36646	−	2.03755i	0.363763	−	0.0791318i
$664$	1.84715	−	2.13172i	0.0716832	−	0.0827268i
$665$	2.13611	−	7.11962i	0.0828348	−	0.276087i
$666$		−	5.54862i		−	0.215005i
$667$	−18.4230	+	40.2549i	−0.713343	+	1.55867i
$668$	11.3896	+	11.3896i	0.440678	+	0.440678i
$669$	−4.07534	+	13.8793i	−0.157562	+	0.536606i
$670$	0.684513	−	0.0449090i	0.0264450	−	0.00173498i
$671$	48.3310	+	31.0604i	1.86580	+	1.19907i
$672$	−2.35424	+	1.76236i	−0.0908167	+	0.0679845i
$673$	16.4176	+	3.57143i	0.632853	+	0.137669i	0.517538	−	0.855660i	$-0.326849\pi$
$673$	16.4176	+	3.57143i	0.632853	+	0.137669i	0.115315	+	0.993329i	$0.463212\pi$
$674$	10.4055	+	22.7849i	0.400806	+	0.877643i
$675$	0.415385	−	4.98272i	0.0159882	−	0.191785i
$676$	−1.53793	−	10.6966i	−0.0591512	−	0.411406i
$677$	−33.2702	+	12.4091i	−1.27868	+	0.476922i	−0.894802	−	0.446463i	$-0.852683\pi$
$677$	−33.2702	+	12.4091i	−1.27868	+	0.476922i	−0.383875	+	0.923385i	$0.625411\pi$
$678$	−3.17350	+	5.81183i	−0.121877	+	0.223202i
$679$	−0.549609	−	1.87180i	−0.0210920	−	0.0718329i
$680$	1.51091	+	4.12490i	0.0579408	+	0.158183i
$681$	−19.3550	+	2.78283i	−0.741685	+	0.106638i
$682$	−1.00346	+	14.0302i	−0.0384245	+	0.537245i
$683$	−3.16567	+	8.48750i	−0.121131	+	0.324765i	−0.983337	−	0.181793i	$-0.941810\pi$
$683$	−3.16567	+	8.48750i	−0.121131	+	0.324765i	0.862206	+	0.506558i	$0.169083\pi$
$684$	0.950931	−	0.611126i	0.0363597	−	0.0233670i
$685$	−34.8427	−	5.21915i	−1.33127	−	0.199414i
$686$	8.50870	−	13.2398i	0.324864	−	0.505498i
$687$	−14.2004	+	1.01563i	−0.541780	+	0.0387489i
$688$	−3.62317	+	1.97840i	−0.138132	+	0.0754257i
$689$	−21.7378			−0.828144
$690$	−10.4938	+	2.20932i	−0.399490	+	0.0841074i
$691$	−11.9313			−0.453889			−0.226944	−	0.973908i	$-0.572874\pi$
$691$	−11.9313			−0.453889			−0.226944	+	0.973908i	$0.572874\pi$
$692$	−13.0676	+	7.13546i	−0.496756	+	0.271249i
$693$	12.2520	−	0.876279i	0.465414	−	0.0332871i
$694$	17.0054	−	26.4609i	0.645517	−	1.00444i
$695$	−11.4587	−	15.4963i	−0.434652	−	0.587808i
$696$	7.76561	−	4.99066i	0.294355	−	0.189170i
$697$	1.30187	−	3.49045i	0.0493118	−	0.132210i
$698$	−1.81477	+	25.3738i	−0.0686900	+	0.960411i
$699$	14.3281	−	2.06007i	0.541939	−	0.0779191i
$700$	13.8365	−	4.97598i	0.522970	−	0.188075i
$701$	3.31204	+	11.2798i	0.125094	+	0.426031i	0.998096	−	0.0616864i	$-0.0196479\pi$
$701$	3.31204	+	11.2798i	0.125094	+	0.426031i	−0.873002	+	0.487717i	$0.837830\pi$
$702$	2.33835	−	4.28237i	0.0882553	−	0.161628i
$703$	−5.87656	+	2.19184i	−0.221639	+	0.0826670i
$704$	0.594426	+	4.13432i	0.0224033	+	0.155818i
$705$	1.98238	−	25.5987i	0.0746607	−	0.964103i
$706$	8.30527	+	18.1860i	0.312573	+	0.684439i
$707$	23.4962	+	5.11127i	0.883664	+	0.192229i
$708$	−6.63799	+	4.96913i	−0.249471	+	0.186751i
$709$	30.6740	+	19.7130i	1.15199	+	0.740336i	0.970034	−	0.242971i	$-0.0781220\pi$
$709$	30.6740	+	19.7130i	1.15199	+	0.740336i	0.181952	+	0.983307i	$0.441758\pi$
$710$	9.30227	−	10.6086i	0.349108	−	0.398132i
$711$	0.0119084	−	0.0405562i	0.000446599	−	0.00152097i
$712$	−10.9125	−	10.9125i	−0.408962	−	0.408962i
$713$	4.56265	−	15.4927i	0.170873	−	0.580207i
$714$			5.77742i			0.216215i
$715$	−43.6479	−	13.0958i	−1.63234	−	0.489754i
$716$	14.7618	−	17.0361i	0.551676	−	0.636668i
$717$	−19.6180	+	4.26764i	−0.732649	+	0.159378i
$718$	18.1649	+	24.2655i	0.677910	+	0.905581i
$719$	−18.4260	−	28.6714i	−0.687173	−	1.06926i	−0.993107	−	0.117210i	$-0.962605\pi$
$719$	−18.4260	−	28.6714i	−0.687173	−	1.06926i	0.305934	−	0.952053i	$-0.401031\pi$
$720$	2.09045	+	0.793745i	0.0779064	+	0.0295811i
$721$	−4.12674	−	4.76251i	−0.153688	−	0.177365i
$722$	14.1874	+	10.6206i	0.528000	+	0.395256i
$723$	10.0240	+	26.8755i	0.372798	+	0.999509i
$724$	−3.50376	+	1.02880i	−0.130216	+	0.0382350i
$725$	−44.4354	+	12.4811i	−1.65029	+	0.463537i
$726$	2.67775	−	5.86347i	0.0993808	−	0.217614i
$727$	11.9448	−	15.9564i	0.443009	−	0.591791i	−0.522345	−	0.852734i	$-0.674943\pi$
$727$	11.9448	−	15.9564i	0.443009	−	0.591791i	0.965354	+	0.260943i	$0.0840336\pi$
$728$	14.3122	+	1.02363i	0.530446	+	0.0379382i
$729$	0.909632	−	0.415415i	0.0336901	−	0.0153857i
$730$	−20.5283	−	4.59239i	−0.759788	−	0.169972i
$731$	−1.15417	+	8.02744i	−0.0426886	+	0.296906i
$732$	2.92377	+	13.4404i	0.108066	+	0.496770i
$733$	−0.0548473	−	0.766865i	−0.00202583	−	0.0283248i	0.996339	−	0.0854944i	$-0.0272470\pi$
$733$	−0.0548473	−	0.766865i	−0.00202583	−	0.0283248i	−0.998364	+	0.0571696i	$0.981792\pi$
$734$	29.2035	+	8.57492i	1.07792	+	0.316506i
$735$	3.68575	+	0.0216966i	0.135951	+	0.000800291i
$736$	0.345990	−	4.78333i	0.0127534	−	0.176316i
$737$	0.906071	−	0.906071i	0.0333755	−	0.0333755i
$738$	−0.908779	−	1.66431i	−0.0334526	−	0.0612639i
$739$	9.04099	+	7.83406i	0.332578	+	0.288181i	0.805101	−	0.593138i	$-0.202111\pi$
$739$	9.04099	+	7.83406i	0.332578	+	0.288181i	−0.472523	+	0.881318i	$0.656657\pi$
$740$	−10.3978	−	6.76910i	−0.382232	−	0.248837i
$741$	−5.45918	−	0.784911i	−0.200548	−	0.0288344i
$742$	2.78501	−	12.8025i	0.102241	−	0.469993i
$743$	17.0609	+	6.36340i	0.625905	+	0.233451i	0.642347	−	0.766414i	$-0.277961\pi$
$743$	17.0609	+	6.36340i	0.625905	+	0.233451i	−0.0164414	+	0.999865i	$0.505234\pi$
$744$	−2.54509	+	2.20533i	−0.0933074	+	0.0808513i
$745$	−11.6486	+	15.3713i	−0.426772	+	0.563160i
$746$	−1.47394	−	0.673124i	−0.0539646	−	0.0246448i
$747$	−2.47564	−	1.35180i	−0.0905791	−	0.0494599i
$748$	7.20196	+	3.93257i	0.263330	+	0.143789i
$749$	−54.6294	−	24.9484i	−1.99612	−	0.911596i
$750$	−8.83061	−	6.85713i	−0.322448	−	0.250387i
$751$	−15.7348	+	13.6343i	−0.574172	+	0.497523i	−0.892859	−	0.450337i	$-0.851304\pi$
$751$	−15.7348	+	13.6343i	−0.574172	+	0.497523i	0.318686	+	0.947860i	$0.396758\pi$
$752$	10.7584	+	4.01267i	0.392318	+	0.146327i
$753$	−5.73424	+	26.3599i	−0.208967	+	0.960608i
$754$	−44.5814	−	6.40984i	−1.62356	−	0.233433i
$755$	2.92266	+	13.8266i	0.106367	+	0.503202i
$756$	2.22251	+	1.92582i	0.0808320	+	0.0700414i
$757$	−12.3660	−	22.6466i	−0.449449	−	0.823104i	0.550482	−	0.834847i	$-0.314444\pi$
$757$	−12.3660	−	22.6466i	−0.449449	−	0.823104i	−0.999931	+	0.0117429i	$0.996262\pi$
$758$	3.00743	−	3.00743i	0.109235	−	0.109235i
$759$	−12.0173	+	16.0263i	−0.436201	+	0.581717i
$760$	0.0148787	−	2.52755i	0.000539707	−	0.0916838i
$761$	35.0956	+	10.3050i	1.27221	+	0.373555i	0.847027	−	0.531550i	$-0.178390\pi$
$761$	35.0956	+	10.3050i	1.27221	+	0.373555i	0.425186	+	0.905106i	$0.360209\pi$
$762$	0.0505289	+	0.706486i	0.00183047	+	0.0255933i
$763$	4.46525	+	20.5264i	0.161653	+	0.743106i
$764$	−1.04673	+	7.28013i	−0.0378692	+	0.263386i
$765$	3.70947	−	2.35319i	0.134116	−	0.0850798i
$766$	−1.51864	+	0.693538i	−0.0548706	+	0.0250585i
$767$	40.3546	+	2.88622i	1.45712	+	0.104215i
$768$	−0.599278	+	0.800541i	−0.0216246	+	0.0288870i
$769$	−0.116265	+	0.254584i	−0.00419261	+	0.00918054i	−0.911717	−	0.410819i	$-0.865243\pi$
$769$	−0.116265	+	0.254584i	−0.00419261	+	0.00918054i	0.907524	+	0.420000i	$0.137970\pi$
$770$	13.3048	−	24.0286i	0.479473	−	0.865932i
$771$	14.8667	−	4.36525i	0.535410	−	0.157211i
$772$	−6.14280	−	16.4695i	−0.221084	−	0.592750i
$773$	−9.72929	−	7.28325i	−0.349938	−	0.261960i	0.409820	−	0.912167i	$-0.365592\pi$
$773$	−9.72929	−	7.28325i	−0.349938	−	0.261960i	−0.759758	+	0.650206i	$0.774683\pi$
$774$	2.70335	+	3.11983i	0.0971698	+	0.112140i
$775$	15.3978	−	6.81402i	0.553106	−	0.244767i
$776$	−0.358640	−	0.558055i	−0.0128744	−	0.0200330i
$777$	−9.77867	−	13.0628i	−0.350808	−	0.468624i
$778$	−7.20786	+	1.56797i	−0.258414	+	0.0562146i
$779$	−1.40368	+	1.61993i	−0.0502921	+	0.0580401i
$780$	−5.17225	−	9.60628i	−0.185196	−	0.343960i
$781$		−	26.3554i		−	0.943070i
$782$	−7.11550	−	6.17567i	−0.254450	−	0.220842i
$783$	−6.52730	−	6.52730i	−0.233267	−	0.233267i
$784$	−0.464393	+	1.58158i	−0.0165855	+	0.0564849i
$785$	−12.8928	−	11.3052i	−0.460164	−	0.403502i
$786$	14.0801	+	9.04876i	0.502222	+	0.322759i
$787$	8.59363	−	6.43311i	0.306330	−	0.229316i	−0.435042	−	0.900410i	$-0.643266\pi$
$787$	8.59363	−	6.43311i	0.306330	−	0.229316i	0.741372	+	0.671095i	$0.234176\pi$
$788$	−16.6509	−	3.62218i	−0.593163	−	0.129035i
$789$	4.41198	+	9.66090i	0.157071	+	0.343937i
$790$	−0.0614725	−	0.0717927i	−0.00218709	−	0.00255427i
$791$	2.77137	+	19.2753i	0.0985384	+	0.685350i
$792$	3.91349	−	1.45966i	0.139060	−	0.0518666i
$793$	32.1633	−	58.9027i	1.14215	−	2.09169i
$794$	6.10401	+	20.7884i	0.216623	+	0.737751i
$795$	−9.35435	+	3.42640i	−0.331765	+	0.121522i
$796$	15.0572	−	2.16490i	0.533690	−	0.0767330i
$797$	−2.70583	+	37.8324i	−0.0958453	+	1.34009i	0.690961	+	0.722892i	$0.257188\pi$
$797$	−2.70583	+	37.8324i	−0.0958453	+	1.34009i	−0.786806	+	0.617200i	$0.788267\pi$
$798$	1.16169	−	3.11462i	0.0411235	−	0.110256i
$799$	18.9769	−	12.1957i	0.671355	−	0.431454i
$800$	4.03770	−	2.94906i	0.142754	−	0.104265i
$801$	−8.34347	+	12.9827i	−0.294802	+	0.458721i
$802$	18.9505	−	1.35536i	0.669165	−	0.0478596i
$803$	−34.4871	+	18.8314i	−1.21702	+	0.664544i
$804$	0.306782			0.0108194
$805$	−20.8112	+	23.6950i	−0.733498	+	0.835140i
$806$	16.4313			0.578769
$807$	0.908205	−	0.495918i	0.0319703	−	0.0174571i
$808$	8.15572	−	0.583309i	0.286917	−	0.0205207i
$809$	−2.94763	+	4.58661i	−0.103633	+	0.161257i	−0.889197	−	0.457524i	$-0.848737\pi$
$809$	−2.94763	+	4.58661i	−0.103633	+	0.161257i	0.785564	+	0.618780i	$0.212373\pi$
$810$	0.331249	−	2.21140i	0.0116389	−	0.0777006i
$811$	24.7659	−	15.9161i	0.869650	−	0.558890i	−0.0279957	−	0.999608i	$-0.508912\pi$
$811$	24.7659	−	15.9161i	0.869650	−	0.558890i	0.897646	+	0.440718i	$0.145276\pi$
$812$	9.48676	−	25.4350i	0.332920	−	0.892593i
$813$	0.837925	−	11.7157i	0.0293873	−	0.410888i
$814$	−22.9398	+	3.29824i	−0.804039	+	0.115603i
$815$	−37.1545	−	17.2329i	−1.30146	−	0.603643i
$816$	0.553483	+	1.88499i	0.0193758	+	0.0659879i
$817$	2.23633	−	4.09553i	0.0782393	−	0.143285i
$818$	−15.7542	+	5.87602i	−0.550833	+	0.205450i
$819$	−2.04204	−	14.2027i	−0.0713548	−	0.496283i
$820$	−4.22750	−	0.327380i	−0.147631	−	0.0114326i
$821$	−5.32982	−	11.6707i	−0.186012	−	0.407310i	0.793535	−	0.608525i	$-0.208238\pi$
$821$	−5.32982	−	11.6707i	−0.186012	−	0.407310i	−0.979547	+	0.201215i	$0.935511\pi$
$822$	−15.3959	−	3.34918i	−0.536994	−	0.116816i
$823$	5.41243	−	4.05169i	0.188665	−	0.141233i	−0.500770	−	0.865581i	$-0.666950\pi$
$823$	5.41243	−	4.05169i	0.188665	−	0.141233i	0.689435	+	0.724347i	$0.257859\pi$
$824$	−1.80268	−	1.15851i	−0.0627993	−	0.0403587i
$825$	−20.8471	+	1.24452i	−0.725802	+	0.0433286i
$826$	−6.86999	+	23.3970i	−0.239038	+	0.814087i
$827$	−23.6998	−	23.6998i	−0.824123	−	0.824123i	0.162574	−	0.986696i	$-0.448020\pi$
$827$	−23.6998	−	23.6998i	−0.824123	−	0.824123i	−0.986696	+	0.162574i	$0.948020\pi$
$828$	−4.74757	+	0.678688i	−0.164989	+	0.0235860i
$829$		−	1.23232i		−	0.0428003i	−0.999771	−	0.0214001i	$-0.993188\pi$
$829$		−	1.23232i		−	0.0428003i	0.999771	−	0.0214001i	$-0.00681239\pi$
$830$	−5.55341	+	2.99009i	−0.192762	+	0.103787i
$831$	15.1380	−	17.4702i	0.525131	−	0.606033i
$832$	4.76769	−	1.03715i	0.165290	−	0.0359566i
$833$	1.94064	+	2.59239i	0.0672391	+	0.0898209i
$834$	−4.65979	−	7.25077i	−0.161355	−	0.251074i
$835$	−14.7690	−	32.8499i	−0.511101	−	1.13682i
$836$	−3.09185	−	3.56819i	−0.106934	−	0.123408i
$837$	2.69593	+	2.01815i	0.0931849	+	0.0697574i
$838$	−7.84858	−	21.0428i	−0.271125	−	0.726913i
$839$	31.5338	−	9.25915i	1.08867	−	0.319661i	0.312326	−	0.949975i	$-0.398892\pi$
$839$	31.5338	−	9.25915i	1.08867	−	0.319661i	0.776341	+	0.630314i	$0.217074\pi$
$840$	6.32027	−	1.81546i	0.218070	−	0.0626392i
$841$	−23.3511	+	51.1317i	−0.805209	+	1.76316i
$842$	−6.81622	+	9.10541i	−0.234903	+	0.313793i
$843$	9.22310	+	0.659649i	0.317661	+	0.0227195i
$844$	−16.5996	+	7.58080i	−0.571383	+	0.260942i
$845$	−5.27537	+	23.5813i	−0.181478	+	0.811222i
$846$	1.63411	−	11.3655i	0.0561819	−	0.390753i
$847$	−4.02947	−	18.5232i	−0.138454	−	0.636463i
$848$	−0.317830	−	4.44385i	−0.0109143	−	0.152602i
$849$	−22.5629	−	6.62508i	−0.774358	−	0.227372i
$850$	0.115643	−	9.82217i	0.00396651	−	0.336898i
$851$	26.5409	+	1.91977i	0.909810	+	0.0658088i
$852$	4.46177	−	4.46177i	0.152858	−	0.152858i
$853$	9.29497	+	17.0225i	0.318254	+	0.582838i	0.987013	−	0.160641i	$-0.0513561\pi$
$853$	9.29497	+	17.0225i	0.318254	+	0.582838i	−0.668759	+	0.743479i	$0.733174\pi$
$854$	30.5700	+	26.4891i	1.04608	+	0.906437i
$855$	−2.47295	+	0.522730i	−0.0845731	+	0.0178770i
$856$	−20.2140	−	2.90633i	−0.690899	−	0.0993363i
$857$	6.39131	−	29.3804i	0.218323	−	1.00362i	−0.729292	−	0.684202i	$-0.760151\pi$
$857$	6.39131	−	29.3804i	0.218323	−	1.00362i	0.947616	−	0.319413i	$-0.103486\pi$
$858$	−19.0947	−	7.12194i	−0.651881	−	0.243139i
$859$	17.4472	−	15.1181i	0.595292	−	0.515823i	−0.304288	−	0.952580i	$-0.598418\pi$
$859$	17.4472	−	15.1181i	0.595292	−	0.515823i	0.899580	+	0.436757i	$0.143873\pi$
$860$	9.14438	−	1.25987i	0.311821	−	0.0429611i
$861$	−5.07259	−	2.31657i	−0.172873	−	0.0789486i
$862$	−13.8896	−	7.58430i	−0.473082	−	0.258322i
$863$	3.78975	+	2.06936i	0.129005	+	0.0704419i	0.542455	−	0.840085i	$-0.317495\pi$
$863$	3.78975	+	2.06936i	0.129005	+	0.0704419i	−0.413451	+	0.910527i	$0.635677\pi$
$864$	0.909632	+	0.415415i	0.0309463	+	0.0141327i
$865$	32.9809	−	4.54394i	1.12138	−	0.154499i
$866$	24.3750	−	21.1211i	0.828297	−	0.717723i
$867$	−12.3120	−	4.59212i	−0.418136	−	0.155957i
$868$	−2.10515	+	9.67723i	−0.0714535	+	0.328467i
$869$	−0.174751	−	0.0251254i	−0.00592802	−	0.000852321i
$870$	−20.1949	+	4.26879i	−0.684672	+	0.144725i
$871$	−1.13124	−	0.980227i	−0.0383307	−	0.0332137i
$872$	3.42332	+	6.26934i	0.115928	+	0.212307i
$873$	−0.469067	+	0.469067i	−0.0158755	+	0.0158755i
$874$	2.59421	+	4.76006i	0.0877504	+	0.161012i
$875$	−32.8741	−	0.580605i	−1.11135	−	0.0196280i
$876$	−9.02640	−	2.65039i	−0.304974	−	0.0895484i
$877$	−2.87237	−	40.1609i	−0.0969929	−	1.35614i	−0.780024	−	0.625749i	$-0.784793\pi$
$877$	−2.87237	−	40.1609i	−0.0969929	−	1.35614i	0.683031	−	0.730389i	$-0.260661\pi$
$878$	−0.142009	−	0.652804i	−0.00479257	−	0.0220311i
$879$	2.43325	−	16.9236i	0.0820716	−	0.570820i
$880$	2.03898	−	9.11441i	0.0687341	−	0.307247i
$881$	20.6337	−	9.42310i	0.695168	−	0.317472i	−0.0363074	−	0.999341i	$-0.511560\pi$
$881$	20.6337	−	9.42310i	0.695168	−	0.317472i	0.731475	+	0.681868i	$0.238832\pi$
$882$	1.64415	+	0.117592i	0.0553613	+	0.00395952i
$883$	18.6638	−	24.9320i	0.628088	−	0.839028i	−0.367773	−	0.929916i	$-0.619880\pi$
$883$	18.6638	−	24.9320i	0.628088	−	0.839028i	0.995861	+	0.0908881i	$0.0289706\pi$
$884$	3.98197	−	8.71930i	0.133928	−	0.293262i
$885$	17.8206	−	5.11884i	0.599032	−	0.172068i
$886$	4.11785	−	1.20911i	0.138342	−	0.0406209i
$887$	7.68450	+	20.6030i	0.258020	+	0.691779i	0.999777	+	0.0211105i	$0.00672017\pi$
$887$	7.68450	+	20.6030i	0.258020	+	0.691779i	−0.741757	+	0.670669i	$0.766007\pi$
$888$	−4.44190	−	3.32516i	−0.149060	−	0.111585i
$889$	1.36404	+	1.57419i	0.0457484	+	0.0527965i
$890$	14.1502	+	31.4737i	0.474317	+	1.05500i
$891$	−2.25817	−	3.51378i	−0.0756515	−	0.117716i
$892$	8.66871	+	11.5800i	0.290250	+	0.387729i
$893$	−12.6827	+	2.75896i	−0.424412	+	0.0923251i
$894$	−5.64828	+	6.51846i	−0.188907	+	0.218010i
$895$	−44.3811	+	23.8959i	−1.48350	+	0.798750i
$896$			2.94081i			0.0982455i
$897$	19.6750	+	12.6668i	0.656927	+	0.422931i
$898$	−23.2561	−	23.2561i	−0.776066	−	0.776066i
$899$	8.75811	−	29.8274i	0.292099	−	0.994799i
$900$	−3.73994	−	3.31856i	−0.124665	−	0.110619i
$901$	−7.36312	−	4.73199i	−0.245301	−	0.157645i
$902$	−6.34057	+	4.74649i	−0.211118	+	0.158041i
$903$	11.8626	+	2.58055i	0.394762	+	0.0858752i
$904$	2.75080	+	6.02341i	0.0914903	+	0.200336i
$905$	8.14104	+	0.630447i	0.270617	+	0.0209568i
$906$	0.899442	+	6.25576i	0.0298820	+	0.207834i
$907$	23.3927	−	8.72503i	0.776742	−	0.289710i	0.0703425	−	0.997523i	$-0.477591\pi$
$907$	23.3927	−	8.72503i	0.776742	−	0.289710i	0.706400	+	0.707813i	$0.250318\pi$
$908$	−9.37125	+	17.1622i	−0.310996	+	0.569546i
$909$	−2.30360	−	7.84535i	−0.0764056	−	0.260214i
$910$	−29.1064	−	13.5001i	−0.964869	−	0.447524i
$911$	−20.8824	+	3.00244i	−0.691865	+	0.0994752i	−0.479273	−	0.877666i	$-0.659100\pi$
$911$	−20.8824	+	3.00244i	−0.691865	+	0.0994752i	−0.212592	+	0.977141i	$0.568191\pi$
$912$	0.0806399	−	1.12749i	0.00267025	−	0.0373350i
$913$	−4.11721	+	11.0387i	−0.136260	+	0.365326i
$914$	6.29132	−	4.04319i	0.208098	−	0.133737i
$915$	4.55623	−	30.4171i	0.150624	−	1.00556i
$916$	−7.69694	+	11.9767i	−0.254314	+	0.395720i
$917$	49.0952	−	3.51136i	1.62127	−	0.115955i
$918$	1.72426	−	0.941518i	0.0569091	−	0.0310747i
$919$	27.5281			0.908068			0.454034	−	0.890984i	$-0.349984\pi$
$919$	27.5281			0.908068			0.454034	+	0.890984i	$0.349984\pi$
$920$	−4.52002	+	9.72468i	−0.149021	+	0.320613i
$921$	11.3334			0.373447
$922$	34.9463	−	19.0821i	1.15089	−	0.628436i
$923$	−30.7088	+	2.19633i	−1.01079	+	0.0722932i
$924$	6.64084	−	10.3333i	0.218468	−	0.339942i
$925$	16.3632	+	22.4037i	0.538019	+	0.736629i
$926$	15.2996	−	9.83248i	0.502777	−	0.323115i
$927$	−0.748849	+	2.00774i	−0.0245954	+	0.0659429i
$928$	0.658532	−	9.20748i	0.0216174	−	0.302250i
$929$	−20.3568	+	2.92687i	−0.667885	+	0.0960274i	−0.467913	−	0.883774i	$-0.654994\pi$
$929$	−20.3568	+	2.92687i	−0.667885	+	0.0960274i	−0.199972	+	0.979802i	$0.564085\pi$
$930$	7.07084	−	2.58998i	0.231862	−	0.0849287i
$931$	−0.524938	−	1.78777i	−0.0172041	−	0.0585919i
$932$	6.93735	−	12.7048i	0.227240	−	0.416160i
$933$	−0.943861	+	0.352042i	−0.0309006	+	0.0115253i
$934$	3.02831	+	21.0624i	0.0990894	+	0.689182i
$935$	−11.9339	−	13.9373i	−0.390279	−	0.455800i
$936$	−2.02689	−	4.43827i	−0.0662510	−	0.145069i
$937$	40.1916	+	8.74315i	1.31300	+	0.285626i	0.813945	−	0.580942i	$-0.197316\pi$
$937$	40.1916	+	8.74315i	1.31300	+	0.285626i	0.499058	+	0.866568i	$0.333679\pi$
$938$	0.722237	−	0.540660i	0.0235819	−	0.0176532i
$939$	−12.1621	−	7.81611i	−0.396895	−	0.255069i
$940$	−19.3048	−	16.9277i	−0.629654	−	0.552121i
$941$	2.76301	−	9.40994i	0.0900715	−	0.306755i	−0.902119	−	0.431487i	$-0.857989\pi$
$941$	2.76301	−	9.40994i	0.0900715	−	0.306755i	0.992190	+	0.124732i	$0.0398071\pi$
$942$	−5.42248	−	5.42248i	−0.176674	−	0.176674i
$943$	8.27536	−	3.77116i	0.269483	−	0.122806i
$944$			8.29187i			0.269877i
$945$	−3.11744	−	5.78993i	−0.101410	−	0.188347i
$946$	11.2914	−	13.0310i	0.367116	−	0.423675i
$947$	−52.0679	+	11.3267i	−1.69198	+	0.368067i	−0.952364	−	0.304963i	$-0.901356\pi$
$947$	−52.0679	+	11.3267i	−1.69198	+	0.368067i	−0.739615	+	0.673030i	$0.764992\pi$
$948$	−0.0253305	−	0.0338375i	−0.000822695	−	0.00109899i
$949$	24.8159	+	38.6143i	0.805558	+	1.25347i
$950$	−2.03733	+	5.27190i	−0.0660998	+	0.171043i
$951$	5.19093	+	5.99066i	0.168328	+	0.194260i
$952$	4.62506	+	3.46228i	0.149899	+	0.112213i
$953$	18.1945	+	48.7815i	0.589379	+	1.58019i	0.798304	+	0.602255i	$0.205731\pi$
$953$	18.1945	+	48.7815i	0.589379	+	1.58019i	−0.208924	+	0.977932i	$0.566996\pi$
$954$	−4.27473	+	1.25517i	−0.138400	+	0.0406378i
$955$	7.96669	−	14.3879i	0.257796	−	0.465581i
$956$	−8.34022	+	18.2625i	−0.269742	+	0.590653i
$957$	−23.1060	+	30.8660i	−0.746911	+	0.997756i
$958$	−1.30646	−	0.0934402i	−0.0422100	−	0.00301892i
$959$	−42.1481	+	19.2484i	−1.36103	+	0.621563i
$960$	1.88818	−	1.19782i	0.0609409	−	0.0386593i
$961$	2.79777	−	19.4589i	0.0902508	−	0.627708i
$962$	5.75474	+	26.4541i	0.185540	+	0.852914i
$963$	1.45688	+	20.3698i	0.0469472	+	0.656407i
$964$	27.5221	+	8.08122i	0.886427	+	0.260279i
$965$	−0.231370	+	39.3044i	−0.00744806	+	1.26525i
$966$	−9.98081	+	9.96471i	−0.321127	+	0.320609i
$967$	−29.0655	+	29.0655i	−0.934684	+	0.934684i	−0.997994	−	0.0633102i	$-0.979834\pi$
$967$	−29.0655	+	29.0655i	−0.934684	+	0.934684i	0.0633102	+	0.997994i	$0.479834\pi$
$968$	−3.08923	−	5.65750i	−0.0992915	−	0.181839i
$969$	−1.67829	−	1.45425i	−0.0539145	−	0.0467172i
$970$	0.306765	+	1.45125i	0.00984963	+	0.0465969i
$971$	−17.5467	−	2.52283i	−0.563099	−	0.0809614i	−0.145113	−	0.989415i	$-0.546355\pi$
$971$	−17.5467	−	2.52283i	−0.563099	−	0.0809614i	−0.417986	+	0.908454i	$0.637264\pi$
$972$	0.212565	−	0.977147i	0.00681803	−	0.0313420i
$973$	−23.7487	−	8.85781i	−0.761349	−	0.283968i
$974$	19.3121	−	16.7340i	0.618800	−	0.536193i
$975$	3.18738	+	24.1869i	0.102078	+	0.774600i
$976$	12.5117	+	5.71391i	0.400490	+	0.182898i
$977$	6.63242	+	3.62158i	0.212190	+	0.115864i	0.581830	−	0.813311i	$-0.302337\pi$
$977$	6.63242	+	3.62158i	0.212190	+	0.115864i	−0.369640	+	0.929175i	$0.620519\pi$
$978$	−16.0758	−	8.77805i	−0.514048	−	0.280691i
$979$	58.6343	+	26.7774i	1.87396	+	0.855808i
$980$	2.22616	−	2.93759i	0.0711120	−	0.0938380i
$981$	5.39839	−	4.67773i	0.172357	−	0.149348i
$982$	−4.16217	−	1.55241i	−0.132820	−	0.0495394i
$983$	1.99574	−	9.17429i	0.0636543	−	0.292614i	−0.934304	−	0.356476i	$-0.883978\pi$
$983$	1.99574	−	9.17429i	0.0636543	−	0.292614i	0.997959	+	0.0638619i	$0.0203417\pi$
$984$	−1.87696	−	0.269866i	−0.0598352	−	0.00860300i
$985$	31.9327	+	20.7885i	1.01746	+	0.662377i
$986$	−13.7055	−	11.8759i	−0.436471	−	0.378205i
$987$	−16.1830	−	29.6369i	−0.515110	−	0.943354i
$988$	−3.89992	+	3.89992i	−0.124073	+	0.124073i
$989$	−15.8585	+	11.8516i	−0.504271	+	0.376858i
$990$	−9.33953	−	0.0549782i	−0.296830	−	0.00174732i
$991$	22.7941	+	6.69294i	0.724078	+	0.212608i	0.622946	−	0.782265i	$-0.285936\pi$
$991$	22.7941	+	6.69294i	0.724078	+	0.212608i	0.101131	+	0.994873i	$0.467754\pi$
$992$	0.240244	+	3.35905i	0.00762776	+	0.106650i
$993$	−0.825098	−	3.79292i	−0.0261837	−	0.120365i
$994$	2.64082	−	18.3673i	0.0837617	−	0.582575i
$995$	−33.1947	−	7.42599i	−1.05234	−	0.235420i
$996$	−2.56577	+	1.17175i	−0.0812996	+	0.0371283i
$997$	−38.9453	−	2.78542i	−1.23341	−	0.0882152i	−0.560635	−	0.828063i	$-0.689443\pi$
$997$	−38.9453	−	2.78542i	−1.23341	−	0.0882152i	−0.672774	+	0.739848i	$0.734897\pi$
$998$	−2.81106	+	3.75514i	−0.0889826	+	0.118867i
$999$	−2.30498	+	5.04720i	−0.0729263	+	0.159686i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.b.373.2	yes	240
5.2	odd	4	inner	690.2.w.b.97.2	yes	240
23.14	odd	22	inner	690.2.w.b.313.2	yes	240
115.37	even	44	inner	690.2.w.b.37.2	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.b.37.2	✓	240	115.37	even	44	inner
690.2.w.b.97.2	yes	240	5.2	odd	4	inner
690.2.w.b.313.2	yes	240	23.14	odd	22	inner
690.2.w.b.373.2	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)

\(f(q)\)	\(=\)	\(q+(-0.877679 + 0.479249i) q^{2} +(0.997452 - 0.0713392i) q^{3} +(0.540641 - 0.841254i) q^{4} +(-1.79792 + 1.32947i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(-1.02771 + 2.75539i) q^{7} +(-0.0713392 + 0.997452i) q^{8} +(0.989821 - 0.142315i) q^{9} +O(q^{10})\)	\(q+(-0.877679 + 0.479249i) q^{2} +(0.997452 - 0.0713392i) q^{3} +(0.540641 - 0.841254i) q^{4} +(-1.79792 + 1.32947i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(-1.02771 + 2.75539i) q^{7} +(-0.0713392 + 0.997452i) q^{8} +(0.989821 - 0.142315i) q^{9} +(0.940853 - 2.02850i) q^{10} +(-1.17675 - 4.00765i) q^{11} +(0.479249 - 0.877679i) q^{12} +(-4.57156 + 1.70510i) q^{13} +(-0.418521 - 2.91087i) q^{14} +(-1.69850 + 1.45434i) q^{15} +(-0.415415 - 0.909632i) q^{16} +(-1.91967 - 0.417599i) q^{17} +(-0.800541 + 0.599278i) q^{18} +(0.950931 + 0.611126i) q^{19} +(0.146387 + 2.23127i) q^{20} +(-0.828521 + 2.82168i) q^{21} +(2.95347 + 2.95347i) q^{22} +(-2.58957 - 4.03660i) q^{23} +1.00000i q^{24} +(1.46504 - 4.78055i) q^{25} +(3.19519 - 3.68745i) q^{26} +(0.977147 - 0.212565i) q^{27} +(1.76236 + 2.35424i) q^{28} +(-4.99066 - 7.76561i) q^{29} +(0.793745 - 2.09045i) q^{30} +(2.20533 + 2.54509i) q^{31} +(0.800541 + 0.599278i) q^{32} +(-1.45966 - 3.91349i) q^{33} +(1.88499 - 0.553483i) q^{34} +(-1.81546 - 6.32027i) q^{35} +(0.415415 - 0.909632i) q^{36} +(-3.32516 + 4.44190i) q^{37} +(-1.12749 - 0.0806399i) q^{38} +(-4.43827 + 2.02689i) q^{39} +(-1.19782 - 1.88818i) q^{40} +(-0.269866 + 1.87696i) q^{41} +(-0.625114 - 2.87360i) q^{42} +(-0.294497 - 4.11761i) q^{43} +(-4.00765 - 1.17675i) q^{44} +(-1.59042 + 1.57180i) q^{45} +(4.20734 + 2.30179i) q^{46} +(-8.11925 + 8.11925i) q^{47} +(-0.479249 - 0.877679i) q^{48} +(-1.24574 - 1.07944i) q^{49} +(1.00523 + 4.89791i) q^{50} +(-1.94457 - 0.279587i) q^{51} +(-1.03715 + 4.76769i) q^{52} +(4.17430 + 1.55693i) q^{53} +(-0.755750 + 0.654861i) q^{54} +(7.44373 + 5.64099i) q^{55} +(-2.67505 - 1.22166i) q^{56} +(0.992105 + 0.541730i) q^{57} +(8.10186 + 4.42395i) q^{58} +(-7.54255 - 3.44457i) q^{59} +(0.305191 + 2.21514i) q^{60} +(-10.3951 + 9.00741i) q^{61} +(-3.15530 - 1.17687i) q^{62} +(-0.625114 + 2.87360i) q^{63} +(-0.989821 - 0.142315i) q^{64} +(5.95243 - 9.14337i) q^{65} +(3.15664 + 2.73525i) q^{66} +(0.147025 + 0.269256i) q^{67} +(-1.38916 + 1.38916i) q^{68} +(-2.87094 - 3.84158i) q^{69} +(4.62237 + 4.67712i) q^{70} +(6.05430 + 1.77770i) q^{71} +(0.0713392 + 0.997452i) q^{72} +(-1.99970 - 9.19248i) q^{73} +(0.789651 - 5.49214i) q^{74} +(1.12027 - 4.87288i) q^{75} +(1.02822 - 0.469574i) q^{76} +(12.2520 + 0.876279i) q^{77} +(2.92399 - 3.90600i) q^{78} +(0.0175589 - 0.0384486i) q^{79} +(1.95621 + 1.08317i) q^{80} +(0.959493 - 0.281733i) q^{81} +(-0.662674 - 1.77670i) q^{82} +(-2.25806 - 1.69037i) q^{83} +(1.92582 + 2.22251i) q^{84} +(4.00661 - 1.80133i) q^{85} +(2.23183 + 3.47280i) q^{86} +(-5.53193 - 7.38980i) q^{87} +(4.08138 - 0.887851i) q^{88} +(-10.1062 + 11.6632i) q^{89} +(0.642592 - 2.14175i) q^{90} -14.3488i q^{91} +(-4.79583 - 0.00386944i) q^{92} +(2.38128 + 2.38128i) q^{93} +(3.23495 - 11.0172i) q^{94} +(-2.52217 + 0.165472i) q^{95} +(0.841254 + 0.540641i) q^{96} +(-0.531048 + 0.397538i) q^{97} +(1.61068 + 0.350381i) q^{98} +(-1.73512 - 3.79939i) 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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