LMFDB - Embedded newform 690.2.w.b.37.2

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			37.2
Character	$\chi$	$=$	690.37
Dual form			690.2.w.b.373.2

$q$-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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{21}{22}\right)$

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	−0.973145	−	0.230195i	$-0.926064\pi$
$7$	−1.02771	−	2.75539i	−0.388437	−	1.04144i	0.584708	−	0.811244i	$-0.301209\pi$
$8$	−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	0.567983	+	0.823040i	$0.307724\pi$
$11$	−1.17675	+	4.00765i	−0.354804	+	1.20835i	−0.922787	+	0.385311i	$0.874094\pi$
$12$	0.479249	+	0.877679i	0.138347	+	0.253364i
$13$	−4.57156	−	1.70510i	−1.26792	−	0.472911i	−0.376641	−	0.926360i	$-0.622921\pi$
$13$	−4.57156	−	1.70510i	−1.26792	−	0.472911i	−0.891282	+	0.453449i	$0.850194\pi$
$14$	−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	−0.439239	−	0.898370i	$-0.644752\pi$
$17$	−1.91967	+	0.417599i	−0.465589	+	0.101283i	−0.0263498	+	0.999653i	$0.508388\pi$
$18$	−0.800541	−	0.599278i	−0.188689	−	0.141251i
$19$	0.950931	−	0.611126i	0.218158	−	0.140202i	−0.426998	−	0.904253i	$-0.640429\pi$
$19$	0.950931	−	0.611126i	0.218158	−	0.140202i	0.645156	+	0.764051i	$0.276792\pi$
$20$	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	−0.0299668	+	0.999551i	$0.509540\pi$
$29$	−4.99066	+	7.76561i	−0.926742	+	1.44204i	−0.896775	+	0.442487i	$0.854096\pi$
$30$	0.793745	+	2.09045i	0.144917	+	0.381662i
$31$	2.20533	−	2.54509i	0.396089	−	0.457111i	−0.522316	−	0.852752i	$-0.674932\pi$
$31$	2.20533	−	2.54509i	0.396089	−	0.457111i	0.918405	+	0.395641i	$0.129477\pi$
$32$	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	0.439100	−	0.898438i	$-0.355297\pi$
$37$	−3.32516	−	4.44190i	−0.546654	−	0.730244i	−0.985754	+	0.168194i	$0.946206\pi$
$38$	−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	−0.999983	−	0.00581961i	$-0.998148\pi$
$41$	−0.269866	−	1.87696i	−0.0421459	−	0.293131i	0.957837	−	0.287312i	$-0.0927615\pi$
$42$	−0.625114	+	2.87360i	−0.0964571	+	0.443406i
$43$	−0.294497	+	4.11761i	−0.0449104	+	0.627929i	0.924296	+	0.381677i	$0.124653\pi$
$43$	−0.294497	+	4.11761i	−0.0449104	+	0.627929i	−0.969206	+	0.246252i	$0.920801\pi$
$44$	−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	−0.978615	−	0.205700i	$-0.934053\pi$
$47$	−8.11925	−	8.11925i	−1.18432	−	1.18432i	−0.205700	−	0.978615i	$-0.565947\pi$
$48$	−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	−0.0460107	−	0.998941i	$-0.514651\pi$
$53$	4.17430	−	1.55693i	0.573384	−	0.213861i	0.619395	+	0.785080i	$0.287378\pi$
$54$	−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	−0.840684	−	0.541526i	$-0.817847\pi$
$59$	−7.54255	+	3.44457i	−0.981957	+	0.448445i	−0.141273	+	0.989971i	$0.545119\pi$
$60$	0.305191	−	2.21514i	0.0394000	−	0.285974i
$61$	−10.3951	−	9.00741i	−1.33096	−	1.15328i	−0.975847	−	0.218456i	$-0.929898\pi$
$61$	−10.3951	−	9.00741i	−1.33096	−	1.15328i	−0.355110	−	0.934824i	$-0.615557\pi$
$62$	−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	−0.868544	−	0.495612i	$-0.834944\pi$
$67$	0.147025	−	0.269256i	0.0179619	−	0.0328948i	0.886506	+	0.462717i	$0.153126\pi$
$68$	−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	0.0980177	−	0.995185i	$-0.468750\pi$
$71$	6.05430	−	1.77770i	0.718513	−	0.210974i	0.620495	+	0.784210i	$0.286932\pi$
$72$	0.0713392	−	0.997452i	0.00840740	−	0.117551i
$73$	−1.99970	+	9.19248i	−0.234047	+	1.07590i	0.698713	+	0.715402i	$0.253756\pi$
$73$	−1.99970	+	9.19248i	−0.234047	+	1.07590i	−0.932760	+	0.360497i	$0.882607\pi$
$74$	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	0.910617	−	0.413251i	$-0.135607\pi$
$79$	0.0175589	+	0.0384486i	0.00197553	+	0.00432581i	−0.908642	+	0.417577i	$0.862879\pi$
$80$	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	−0.715981	−	0.698120i	$-0.754020\pi$
$83$	−2.25806	+	1.69037i	−0.247855	+	0.185542i	0.468126	+	0.883662i	$0.344929\pi$
$84$	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	−0.970429	−	0.241388i	$-0.922397\pi$
$89$	−10.1062	−	11.6632i	−1.07125	−	1.23629i	−0.100824	−	0.994904i	$-0.532148\pi$
$90$	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	0.571978	−	0.820269i	$-0.306176\pi$
$97$	−0.531048	−	0.397538i	−0.0539198	−	0.0403638i	−0.625898	+	0.779905i	$0.715267\pi$
$98$	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	0.846326	+	0.532665i	$0.178810\pi$
$101$	−1.16365	+	8.09333i	−0.115787	+	0.805316i	−0.962113	+	0.272651i	$0.912100\pi$
$102$	1.84070	+	0.686547i	0.182257	+	0.0679783i
$103$	−1.02696	−	1.88073i	−0.101189	−	0.185314i	0.822180	−	0.569228i	$-0.192758\pi$
$103$	−1.02696	−	1.88073i	−0.101189	−	0.185314i	−0.923369	+	0.383914i	$0.874576\pi$
$104$	−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	−0.229957	−	0.973201i	$-0.573859\pi$
$107$	−1.45688	−	20.3698i	−0.140842	−	1.96922i	0.0891159	−	0.996021i	$-0.471596\pi$
$108$	0.349464	+	0.936950i	0.0336272	+	0.0901580i
$109$	6.00915	+	3.86185i	0.575573	+	0.369898i	0.795808	−	0.605549i	$-0.207046\pi$
$109$	6.00915	+	3.86185i	0.575573	+	0.369898i	−0.220236	+	0.975447i	$0.570683\pi$
$110$	−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	0.728776	−	0.684753i	$-0.240090\pi$
$113$	5.81183	+	3.17350i	0.546731	+	0.298538i	−0.182045	+	0.983290i	$0.558272\pi$
$114$	−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	0.892306	−	0.451431i	$-0.149086\pi$
$127$	0.339447	+	0.621652i	0.0301211	+	0.0551627i	−0.862185	+	0.506594i	$0.830904\pi$
$128$	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	0.316816	+	0.948487i	$0.397386\pi$
$131$	−6.95284	+	15.2246i	−0.607473	+	1.33018i	−0.924289	+	0.381693i	$0.875341\pi$
$132$	−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	−0.0470390	−	0.998893i	$-0.514978\pi$
$137$	11.1412	−	11.1412i	0.951854	−	0.951854i	0.998893	+	0.0470390i	$0.0149785\pi$
$138$	4.36083	−	1.99578i	0.371219	−	0.169892i
$139$		−	8.61901i		−	0.731055i	−0.930801	−	0.365527i	$-0.880889\pi$
$139$		−	8.61901i		−	0.731055i	0.930801	−	0.365527i	$-0.119111\pi$
$140$	−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	0.602553	−	0.798079i	$-0.294150\pi$
$149$	8.27578	+	2.42999i	0.677978	+	0.199072i	0.0754254	+	0.997151i	$0.475969\pi$
$150$	1.35209	−	4.81372i	0.110397	−	0.393038i
$151$	2.62546	+	5.74895i	0.213657	+	0.467843i	0.985868	−	0.167523i	$-0.0535767\pi$
$151$	2.62546	+	5.74895i	0.213657	+	0.467843i	−0.772211	+	0.635366i	$0.780849\pi$
$152$	−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	−0.865225	−	0.501383i	$-0.832825\pi$
$157$	1.63007	−	7.49330i	0.130094	−	0.598030i	0.995319	−	0.0966469i	$-0.0308118\pi$
$158$	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	−0.267742	−	0.963491i	$-0.586277\pi$
$163$	8.77805	−	16.0758i	0.687550	−	1.25915i	0.955292	−	0.295663i	$-0.0955407\pi$
$164$	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	−0.896653	−	0.442733i	$-0.854009\pi$
$167$	−3.42387	−	15.7393i	−0.264947	−	1.21794i	0.631706	−	0.775208i	$-0.282355\pi$
$168$	−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	−0.891855	−	0.452321i	$-0.850596\pi$
$173$	−13.0676	+	7.13546i	−0.993512	+	0.542499i	−0.101657	+	0.994820i	$0.532414\pi$
$174$	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	0.757178	−	0.653209i	$-0.226578\pi$
$179$	22.3125	−	3.20805i	1.66771	−	0.239781i	0.910537	+	0.413428i	$0.135669\pi$
$180$	0.462440	−	2.18773i	0.0344683	−	0.163064i
$181$	−2.75976	+	2.39134i	−0.205131	+	0.177747i	−0.751368	−	0.659884i	$-0.770605\pi$
$181$	−2.75976	+	2.39134i	−0.205131	+	0.177747i	0.546236	+	0.837631i	$0.316060\pi$
$182$	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	0.158390	−	0.987377i	$-0.449370\pi$
$191$	−6.69034	−	3.05538i	−0.484096	−	0.221079i	−0.642486	+	0.766297i	$0.722097\pi$
$192$	−0.997452	+	0.0713392i	−0.0719849	+	0.00514846i
$193$	10.5340	+	14.0717i	0.758251	+	1.01290i	0.999103	+	0.0423431i	$0.0134822\pi$
$193$	10.5340	+	14.0717i	0.758251	+	1.01290i	−0.240852	+	0.970562i	$0.577427\pi$
$194$	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	0.532433	+	0.846472i	$0.321278\pi$
$197$	−5.95498	+	15.9659i	−0.424275	+	1.13752i	−0.956707	+	0.291052i	$0.905995\pi$
$198$	3.34373	−	2.50309i	0.237629	−	0.177887i
$199$	9.96179	−	11.4965i	0.706173	−	0.814967i	−0.283400	−	0.959002i	$-0.591462\pi$
$199$	9.96179	−	11.4965i	0.706173	−	0.814967i	0.989573	+	0.144035i	$0.0460079\pi$
$200$	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	−0.949101	−	0.314973i	$-0.898005\pi$
$211$	−15.3518	+	9.86601i	−1.05686	+	0.679204i	−0.107761	+	0.994177i	$0.534368\pi$
$212$	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	−0.988979	−	0.148055i	$-0.952699\pi$
$223$	−5.05509	−	13.5532i	−0.338514	−	0.907592i	0.650465	−	0.759536i	$-0.274574\pi$
$224$	−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	−0.592991	−	0.805209i	$-0.702053\pi$
$227$	−19.5042	−	1.39497i	−1.29454	−	0.0925873i	−0.701549	+	0.712622i	$0.747508\pi$
$228$	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	0.535761	−	0.844370i	$-0.320025\pi$
$233$	14.4386	+	1.03267i	0.945903	+	0.0676523i	0.410142	+	0.912022i	$0.365479\pi$
$234$	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	−0.534491	−	0.845174i	$-0.679497\pi$
$239$	−19.8725	−	2.85723i	−1.28544	−	0.184819i	−0.750954	+	0.660355i	$0.770406\pi$
$240$	2.02850	−	0.940853i	0.130939	−	0.0607318i
$241$	8.08122	−	27.5221i	0.520557	−	1.77285i	−0.106973	−	0.994262i	$-0.534116\pi$
$241$	8.08122	−	27.5221i	0.520557	−	1.77285i	0.627530	−	0.778592i	$-0.284066\pi$
$242$	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	−0.743180	−	0.669092i	$-0.766683\pi$
$251$	−7.60012	−	25.8836i	−0.479716	−	1.63376i	0.263464	−	0.964669i	$-0.415135\pi$
$252$	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	0.658307	−	0.752750i	$-0.271273\pi$
$257$	15.1402	+	3.29355i	0.944420	+	0.205446i	0.286114	+	0.958196i	$0.407637\pi$
$258$	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	−0.770863	−	0.637001i	$-0.780175\pi$
$263$	3.71154	−	9.95103i	0.228864	−	0.613607i	0.999726	+	0.0233944i	$0.00744734\pi$
$264$	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	0.443903	−	0.896075i	$-0.353593\pi$
$269$	0.941270	+	0.429863i	0.0573902	+	0.0262092i	−0.386513	+	0.922284i	$0.626321\pi$
$270$	0.488164	+	2.18213i	0.0297087	+	0.132800i
$271$	1.67158	+	11.6261i	0.101541	+	0.706235i	0.975462	+	0.220167i	$0.0706602\pi$
$271$	1.67158	+	11.6261i	0.101541	+	0.706235i	−0.873921	+	0.486068i	$0.838431\pi$
$272$	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	0.999843	−	0.0177239i	$-0.00564199\pi$
$277$	16.3457	+	16.3457i	0.982119	+	0.982119i	−0.0177239	+	0.999843i	$0.505642\pi$
$278$	−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	0.136203	−	0.990681i	$-0.456510\pi$
$281$	9.15255	−	1.31594i	0.545995	−	0.0785022i	0.409793	+	0.912179i	$0.365601\pi$
$282$	2.44075	+	11.2200i	0.145345	+	0.668138i
$283$	−22.0328	+	8.21782i	−1.30972	+	0.488499i	−0.904793	−	0.425852i	$-0.859974\pi$
$283$	−22.0328	+	8.21782i	−1.30972	+	0.488499i	−0.404923	+	0.914351i	$0.632702\pi$
$284$	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	0.952717	+	0.303858i	$0.0982748\pi$
$293$	3.63437	+	16.7069i	0.212322	+	0.976030i	−0.740395	+	0.672172i	$0.765362\pi$
$294$	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	0.255085	−	0.966919i	$-0.417896\pi$
$307$	11.3045	−	0.808513i	0.645181	−	0.0461443i	0.390096	+	0.920774i	$0.372442\pi$
$308$	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	0.254213	−	0.967148i	$-0.418184\pi$
$311$	−0.966571	−	0.283811i	−0.0548092	−	0.0160934i	−0.309022	+	0.951055i	$0.600002\pi$
$312$	−1.70510	+	4.57156i	−0.0965325	+	0.258814i
$313$	−11.5735	+	8.66383i	−0.654174	+	0.489709i	−0.874061	−	0.485817i	$-0.838522\pi$
$313$	−11.5735	+	8.66383i	−0.654174	+	0.489709i	0.219887	+	0.975525i	$0.429431\pi$
$314$	−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	−0.647052	−	0.762446i	$-0.723998\pi$
$317$	4.75034	−	6.34571i	0.266806	−	0.356411i	0.913857	+	0.406036i	$0.133089\pi$
$318$	−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	−0.999355	−	0.0359119i	$-0.988566\pi$
$331$	−0.552413	+	3.84211i	−0.0303633	+	0.211182i	0.968992	+	0.247094i	$0.0794755\pi$
$332$	−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	0.777936	+	0.628344i	$0.216267\pi$
$337$	1.78694	+	24.9847i	0.0973409	+	1.36100i	−0.680595	+	0.732660i	$0.738278\pi$
$338$	−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	−0.484167	−	0.874976i	$-0.660877\pi$
$347$	−27.6067	−	15.0744i	−1.48200	−	0.809235i	−0.997837	+	0.0657402i	$0.979059\pi$
$348$	−9.20748	−	0.658532i	−0.493573	−	0.0353010i
$349$	13.7531	+	21.4003i	0.736188	+	1.14553i	0.984249	+	0.176787i	$0.0565704\pi$
$349$	13.7531	+	21.4003i	0.736188	+	1.14553i	−0.248061	+	0.968744i	$0.579793\pi$
$350$	−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	0.882510	+	0.470293i	$0.155852\pi$
$353$	1.42626	+	19.9418i	0.0759123	+	1.06139i	−0.806598	+	0.591100i	$0.798694\pi$
$354$	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	0.480206	+	0.877156i	$0.340562\pi$
$359$	−4.31376	+	30.0029i	−0.227672	+	1.58349i	−0.707878	+	0.706335i	$0.750347\pi$
$360$	−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	−0.132205	+	0.991222i	$0.542206\pi$
$367$	−21.5218	+	21.5218i	−1.12343	+	1.12343i	−0.991222	+	0.132205i	$0.957794\pi$
$368$	−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	−0.774697	−	0.632333i	$-0.782098\pi$
$373$	0.971049	−	1.29717i	0.0502790	−	0.0671649i	0.824976	+	0.565168i	$0.191189\pi$
$374$	−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	0.175237	−	0.984526i	$-0.443931\pi$
$379$	−4.08087	−	1.19825i	−0.209620	−	0.0615500i	−0.384857	+	0.922976i	$0.625749\pi$
$380$	−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	−0.0287290	−	0.999587i	$-0.509146\pi$
$383$	1.66525	−	0.119101i	0.0850904	−	0.00608579i	0.113819	+	0.993501i	$0.463691\pi$
$384$	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	−0.0973375	−	0.995251i	$-0.531033\pi$
$389$	7.07764	−	2.07818i	0.358851	−	0.105368i	0.456188	+	0.889883i	$0.349214\pi$
$390$	−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	0.935675	+	0.352864i	$0.114792\pi$
$397$	4.60543	+	21.1708i	0.231140	+	1.06253i	−0.704534	+	0.709670i	$0.748844\pi$
$398$	−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	−0.797209	−	0.603703i	$-0.793691\pi$
$401$	−17.2820	+	7.89242i	−0.863021	+	0.394129i	−0.0658124	+	0.997832i	$0.520964\pi$
$402$	−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	0.282042	−	0.959402i	$-0.408988\pi$
$409$	16.6432	−	2.39293i	0.822954	−	0.118323i	0.540912	+	0.841079i	$0.318079\pi$
$410$	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	−0.905652	−	0.424022i	$-0.860618\pi$
$419$	−3.19623	−	22.2303i	−0.156146	−	1.08602i	0.749506	−	0.661998i	$-0.230291\pi$
$420$	−6.41723	+	1.43560i	−0.313129	+	0.0700499i
$421$	10.3462	+	4.72496i	0.504244	+	0.230280i	0.651261	−	0.758854i	$-0.274240\pi$
$421$	10.3462	+	4.72496i	0.504244	+	0.230280i	−0.147018	+	0.989134i	$0.546967\pi$
$422$	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	−0.571693	−	0.820468i	$-0.693713\pi$
$431$	8.55585	−	13.3132i	0.412121	−	0.641273i	0.983814	+	0.179195i	$0.0573494\pi$
$432$	−0.599278	+	0.800541i	−0.0288328	+	0.0385161i
$433$	−31.5157	−	6.85582i	−1.51455	−	0.329470i	−0.622937	−	0.782272i	$-0.714061\pi$
$433$	−31.5157	−	6.85582i	−1.51455	−	0.329470i	−0.891611	+	0.452802i	$0.850424\pi$
$434$	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	0.954879	−	0.296994i	$-0.0959840\pi$
$439$	−0.188218	−	0.641010i	−0.00898314	−	0.0305938i	−0.963863	+	0.266400i	$0.914166\pi$
$440$	−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	−0.311080	−	0.950384i	$-0.600691\pi$
$443$	−4.19362	+	0.912265i	−0.199245	+	0.0433430i	0.111835	+	0.993727i	$0.464327\pi$
$444$	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	−0.386462	−	0.922305i	$-0.626303\pi$
$449$	9.26593	−	31.5569i	0.437286	−	1.48926i	0.823749	−	0.566955i	$-0.191879\pi$
$450$	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	−0.104230	−	0.994553i	$-0.533238\pi$
$457$	−7.45946	−	0.533511i	−0.348939	−	0.0249566i	−0.244709	+	0.969597i	$0.578692\pi$
$458$	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	−0.356871	−	0.934153i	$-0.616157\pi$
$463$	−18.1404	−	1.29742i	−0.843054	−	0.0602964i	−0.486183	+	0.873857i	$0.661611\pi$
$464$	−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	0.987580	+	0.157119i	$0.0502206\pi$
$467$	7.43623	+	19.9373i	0.344108	+	0.922589i	−0.643472	+	0.765470i	$0.722507\pi$
$468$	−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	−0.515226	−	0.857055i	$-0.672292\pi$
$479$	1.10188	−	0.708132i	0.0503460	−	0.0323554i	0.565572	+	0.824699i	$0.308656\pi$
$480$	−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	−0.392426	−	0.919784i	$-0.628364\pi$
$487$	−24.9696	−	5.43181i	−1.13148	−	0.246139i	−0.739055	+	0.673645i	$0.764728\pi$
$488$	−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	−0.686301	−	0.727317i	$-0.740767\pi$
$491$	2.90906	−	3.35724i	0.131284	−	0.151510i	0.817585	+	0.575808i	$0.195312\pi$
$492$	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	0.508624	−	0.860989i	$-0.330154\pi$
$499$	4.26686	+	1.94861i	0.191011	+	0.0872317i	−0.317614	+	0.948220i	$0.602881\pi$
$500$	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	−0.866242	−	0.499624i	$-0.833471\pi$
$503$	1.39695	−	19.5319i	0.0622869	−	0.870884i	0.928529	−	0.371260i	$-0.121074\pi$
$504$	−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	−0.546235	−	0.837632i	$-0.683939\pi$
$509$	4.62803	−	4.01021i	0.205134	−	0.177749i	0.751369	+	0.659883i	$0.229394\pi$
$510$	−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	0.998387	+	0.0567754i	$0.0180819\pi$
$521$	27.3145	+	23.6681i	1.19667	+	1.03692i	0.198283	+	0.980145i	$0.436464\pi$
$522$	8.64898	−	3.22590i	0.378556	−	0.141194i
$523$	−0.521821	−	2.39877i	−0.0228177	−	0.104891i	0.964330	−	0.264704i	$-0.0852744\pi$
$523$	−0.521821	−	2.39877i	−0.0228177	−	0.104891i	−0.987147	+	0.159813i	$0.948911\pi$
$524$	−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	0.930425	−	0.366482i	$-0.119438\pi$
$541$	35.2383	+	10.3469i	1.51501	+	0.444848i	0.584588	+	0.811330i	$0.301256\pi$
$542$	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	0.0580698	+	0.998313i	$0.481505\pi$
$547$	−21.4273	+	28.6235i	−0.916164	+	1.22385i	−0.974234	+	0.225540i	$0.927585\pi$
$548$	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	0.673292	−	0.739376i	$-0.264880\pi$
$557$	3.62401	+	2.71290i	0.153554	+	0.114949i	−0.519738	+	0.854326i	$0.673970\pi$
$558$	−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	0.872808	+	0.488064i	$0.162297\pi$
$563$	19.2554	+	35.2636i	0.811518	+	1.48618i	−0.0612897	+	0.998120i	$0.519521\pi$
$564$	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	−0.0798934	−	0.996803i	$-0.525458\pi$
$569$	−24.3262	−	15.6335i	−1.01981	−	0.655390i	−0.939913	+	0.341414i	$0.889094\pi$
$570$	2.03232	+	1.50279i	0.0851247	+	0.0629450i
$571$	−19.4960	−	30.3363i	−0.815882	−	1.26954i	−0.960007	−	0.279977i	$-0.909673\pi$
$571$	−19.4960	−	30.3363i	−0.815882	−	1.26954i	0.144125	−	0.989559i	$-0.453963\pi$
$572$	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	−0.999729	−	0.0232671i	$-0.992593\pi$
$577$	−37.4676	−	20.4589i	−1.55980	−	0.851714i	−0.560068	−	0.828447i	$-0.689225\pi$
$578$	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	−0.988629	−	0.150376i	$-0.951952\pi$
$587$	−14.0678	−	25.7632i	−0.580640	−	1.06336i	0.407989	−	0.912987i	$-0.366230\pi$
$588$	−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	−0.0539059	−	0.998546i	$-0.517167\pi$
$593$	−25.0137	−	18.7250i	−1.02719	−	0.768945i	−0.973285	+	0.229601i	$0.926258\pi$
$594$	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	$-0.793487\pi$
$599$		−	29.5757i		−	1.20843i	0.796821	−	0.604215i	$-0.206513\pi$
$600$	4.78055	−	1.46504i	0.195165	−	0.0598102i
$601$	−14.8029	−	17.0834i	−0.603822	−	0.696848i	0.368729	−	0.929537i	$-0.379793\pi$
$601$	−14.8029	−	17.0834i	−0.603822	−	0.696848i	−0.972551	+	0.232689i	$0.925248\pi$
$602$	−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	−0.0858555	−	0.996308i	$-0.527362\pi$
$607$	20.8409	−	15.6013i	0.845906	−	0.633238i	0.931762	+	0.363070i	$0.118271\pi$
$608$	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	−0.213426	−	0.976959i	$-0.568462\pi$
$613$	−7.07221	+	0.505814i	−0.285644	+	0.0204297i	−0.0722179	+	0.997389i	$0.523008\pi$
$614$	−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	0.671094	+	0.741372i	$0.265825\pi$
$617$	−6.14359	+	28.2416i	−0.247332	+	1.13697i	−0.918426	+	0.395594i	$0.870539\pi$
$618$	−0.152869	+	2.13739i	−0.00614930	+	0.0859784i
$619$	30.0118	−	8.81225i	1.20627	−	0.354194i	0.384026	−	0.923322i	$-0.374537\pi$
$619$	30.0118	−	8.81225i	1.20627	−	0.354194i	0.822249	+	0.569128i	$0.192719\pi$
$620$	−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	0.583201	−	0.812328i	$-0.301800\pi$
$631$	39.6649	−	18.1143i	1.57903	−	0.721120i	0.995832	+	0.0912073i	$0.0290726\pi$
$632$	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	−0.993976	−	0.109594i	$-0.965045\pi$
$641$	−26.0004	+	22.5295i	−1.02696	+	0.889862i	−0.0329795	+	0.999456i	$0.510500\pi$
$642$	−9.78714	+	17.9238i	−0.386268	+	0.707396i
$643$	13.9539	+	13.9539i	0.550288	+	0.550288i	0.926524	−	0.376236i	$-0.122782\pi$
$643$	13.9539	+	13.9539i	0.550288	+	0.550288i	−0.376236	+	0.926524i	$0.622782\pi$
$644$	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	−0.971083	−	0.238743i	$-0.923265\pi$
$647$	0.612820	−	8.56834i	0.0240924	−	0.336856i	0.995175	−	0.0981133i	$-0.0312808\pi$
$648$	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	0.888836	−	0.458226i	$-0.151515\pi$
$653$	5.07903	+	6.78479i	0.198758	+	0.265509i	−0.690078	+	0.723735i	$0.742424\pi$
$654$	−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	−0.573915	−	0.818915i	$-0.694576\pi$
$659$	8.17213	−	9.43114i	0.318341	−	0.367385i	0.892256	+	0.451530i	$0.149122\pi$
$660$	8.51838	+	3.82977i	0.331577	+	0.149074i
$661$	−14.9083	+	23.1978i	−0.579866	+	0.902289i	−0.999987	−	0.00517936i	$-0.998351\pi$
$661$	−14.9083	+	23.1978i	−0.579866	+	0.902289i	0.420121	+	0.907468i	$0.361988\pi$
$662$	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	0.115315	−	0.993329i	$-0.463212\pi$
$673$	16.4176	−	3.57143i	0.632853	−	0.137669i	0.517538	+	0.855660i	$0.326849\pi$
$674$	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	−0.383875	−	0.923385i	$-0.625411\pi$
$677$	−33.2702	−	12.4091i	−1.27868	−	0.476922i	−0.894802	+	0.446463i	$0.852683\pi$
$678$	−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	0.862206	−	0.506558i	$-0.169083\pi$
$683$	−3.16567	−	8.48750i	−0.121131	−	0.324765i	−0.983337	+	0.181793i	$0.941810\pi$
$684$	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	−0.873002	−	0.487717i	$-0.837830\pi$
$701$	3.31204	−	11.2798i	0.125094	−	0.426031i	0.998096	+	0.0616864i	$0.0196479\pi$
$702$	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	0.181952	−	0.983307i	$-0.441758\pi$
$709$	30.6740	−	19.7130i	1.15199	−	0.740336i	0.970034	+	0.242971i	$0.0781220\pi$
$710$	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	0.305934	+	0.952053i	$0.401031\pi$
$719$	−18.4260	+	28.6714i	−0.687173	+	1.06926i	−0.993107	+	0.117210i	$0.962605\pi$
$720$	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	0.965354	−	0.260943i	$-0.0840336\pi$
$727$	11.9448	+	15.9564i	0.443009	+	0.591791i	−0.522345	+	0.852734i	$0.674943\pi$
$728$	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	−0.998364	−	0.0571696i	$-0.981792\pi$
$733$	−0.0548473	+	0.766865i	−0.00202583	+	0.0283248i	0.996339	+	0.0854944i	$0.0272470\pi$
$734$	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	−0.472523	−	0.881318i	$-0.656657\pi$
$739$	9.04099	−	7.83406i	0.332578	−	0.288181i	0.805101	+	0.593138i	$0.202111\pi$
$740$	−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	−0.0164414	−	0.999865i	$-0.505234\pi$
$743$	17.0609	−	6.36340i	0.625905	−	0.233451i	0.642347	+	0.766414i	$0.277961\pi$
$744$	−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	0.318686	−	0.947860i	$-0.396758\pi$
$751$	−15.7348	−	13.6343i	−0.574172	−	0.497523i	−0.892859	+	0.450337i	$0.851304\pi$
$752$	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	−0.999931	−	0.0117429i	$-0.996262\pi$
$757$	−12.3660	+	22.6466i	−0.449449	+	0.823104i	0.550482	+	0.834847i	$0.314444\pi$
$758$	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	0.425186	−	0.905106i	$-0.360209\pi$
$761$	35.0956	−	10.3050i	1.27221	−	0.373555i	0.847027	+	0.531550i	$0.178390\pi$
$762$	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	0.907524	−	0.420000i	$-0.137970\pi$
$769$	−0.116265	−	0.254584i	−0.00419261	−	0.00918054i	−0.911717	+	0.410819i	$0.865243\pi$
$770$	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	−0.759758	−	0.650206i	$-0.774683\pi$
$773$	−9.72929	+	7.28325i	−0.349938	+	0.261960i	0.409820	+	0.912167i	$0.365592\pi$
$774$	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	0.741372	−	0.671095i	$-0.234176\pi$
$787$	8.59363	+	6.43311i	0.306330	+	0.229316i	−0.435042	+	0.900410i	$0.643266\pi$
$788$	−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	−0.786806	−	0.617200i	$-0.788267\pi$
$797$	−2.70583	−	37.8324i	−0.0958453	−	1.34009i	0.690961	−	0.722892i	$-0.257188\pi$
$798$	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	0.785564	−	0.618780i	$-0.212373\pi$
$809$	−2.94763	−	4.58661i	−0.103633	−	0.161257i	−0.889197	+	0.457524i	$0.848737\pi$
$810$	0.331249	+	2.21140i	0.0116389	+	0.0777006i
$811$	24.7659	+	15.9161i	0.869650	+	0.558890i	0.897646	−	0.440718i	$-0.145276\pi$
$811$	24.7659	+	15.9161i	0.869650	+	0.558890i	−0.0279957	+	0.999608i	$0.508912\pi$
$812$	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	−0.979547	−	0.201215i	$-0.935511\pi$
$821$	−5.32982	+	11.6707i	−0.186012	+	0.407310i	0.793535	+	0.608525i	$0.208238\pi$
$822$	−15.3959	+	3.34918i	−0.536994	+	0.116816i
$823$	5.41243	+	4.05169i	0.188665	+	0.141233i	0.689435	−	0.724347i	$-0.257859\pi$
$823$	5.41243	+	4.05169i	0.188665	+	0.141233i	−0.500770	+	0.865581i	$0.666950\pi$
$824$	−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	−0.986696	−	0.162574i	$-0.948020\pi$
$827$	−23.6998	+	23.6998i	−0.824123	+	0.824123i	0.162574	+	0.986696i	$0.448020\pi$
$828$	−4.74757	−	0.678688i	−0.164989	−	0.0235860i
$829$			1.23232i			0.0428003i	0.999771	+	0.0214001i	$0.00681239\pi$
$829$			1.23232i			0.0428003i	−0.999771	+	0.0214001i	$0.993188\pi$
$830$	−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	0.776341	−	0.630314i	$-0.217074\pi$
$839$	31.5338	+	9.25915i	1.08867	+	0.319661i	0.312326	+	0.949975i	$0.398892\pi$
$840$	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	−0.668759	−	0.743479i	$-0.733174\pi$
$853$	9.29497	−	17.0225i	0.318254	−	0.582838i	0.987013	+	0.160641i	$0.0513561\pi$
$854$	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	0.947616	+	0.319413i	$0.103486\pi$
$857$	6.39131	+	29.3804i	0.218323	+	1.00362i	−0.729292	+	0.684202i	$0.760151\pi$
$858$	−19.0947	+	7.12194i	−0.651881	+	0.243139i
$859$	17.4472	+	15.1181i	0.595292	+	0.515823i	0.899580	−	0.436757i	$-0.143873\pi$
$859$	17.4472	+	15.1181i	0.595292	+	0.515823i	−0.304288	+	0.952580i	$0.598418\pi$
$860$	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	−0.413451	−	0.910527i	$-0.635677\pi$
$863$	3.78975	−	2.06936i	0.129005	−	0.0704419i	0.542455	+	0.840085i	$0.317495\pi$
$864$	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	0.683031	+	0.730389i	$0.260661\pi$
$877$	−2.87237	+	40.1609i	−0.0969929	+	1.35614i	−0.780024	+	0.625749i	$0.784793\pi$
$878$	−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	0.731475	−	0.681868i	$-0.238832\pi$
$881$	20.6337	+	9.42310i	0.695168	+	0.317472i	−0.0363074	+	0.999341i	$0.511560\pi$
$882$	1.64415	−	0.117592i	0.0553613	−	0.00395952i
$883$	18.6638	+	24.9320i	0.628088	+	0.839028i	0.995861	−	0.0908881i	$-0.0289706\pi$
$883$	18.6638	+	24.9320i	0.628088	+	0.839028i	−0.367773	+	0.929916i	$0.619880\pi$
$884$	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	−0.741757	−	0.670669i	$-0.766007\pi$
$887$	7.68450	−	20.6030i	0.258020	−	0.691779i	0.999777	−	0.0211105i	$-0.00672017\pi$
$888$	−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	0.706400	−	0.707813i	$-0.250318\pi$
$907$	23.3927	+	8.72503i	0.776742	+	0.289710i	0.0703425	+	0.997523i	$0.477591\pi$
$908$	−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	−0.212592	−	0.977141i	$-0.568191\pi$
$911$	−20.8824	−	3.00244i	−0.691865	−	0.0994752i	−0.479273	+	0.877666i	$0.659100\pi$
$912$	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	−0.199972	−	0.979802i	$-0.564085\pi$
$929$	−20.3568	−	2.92687i	−0.667885	−	0.0960274i	−0.467913	+	0.883774i	$0.654994\pi$
$930$	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	0.499058	−	0.866568i	$-0.333679\pi$
$937$	40.1916	−	8.74315i	1.31300	−	0.285626i	0.813945	+	0.580942i	$0.197316\pi$
$938$	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	0.992190	−	0.124732i	$-0.0398071\pi$
$941$	2.76301	+	9.40994i	0.0900715	+	0.306755i	−0.902119	+	0.431487i	$0.857989\pi$
$942$	−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	−0.739615	−	0.673030i	$-0.764992\pi$
$947$	−52.0679	−	11.3267i	−1.69198	−	0.368067i	−0.952364	+	0.304963i	$0.901356\pi$
$948$	−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	−0.208924	−	0.977932i	$-0.566996\pi$
$953$	18.1945	−	48.7815i	0.589379	−	1.58019i	0.798304	−	0.602255i	$-0.205731\pi$
$954$	−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	0.0633102	−	0.997994i	$-0.479834\pi$
$967$	−29.0655	−	29.0655i	−0.934684	−	0.934684i	−0.997994	+	0.0633102i	$0.979834\pi$
$968$	−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	−0.417986	−	0.908454i	$-0.637264\pi$
$971$	−17.5467	+	2.52283i	−0.563099	+	0.0809614i	−0.145113	+	0.989415i	$0.546355\pi$
$972$	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	−0.369640	−	0.929175i	$-0.620519\pi$
$977$	6.63242	−	3.62158i	0.212190	−	0.115864i	0.581830	+	0.813311i	$0.302337\pi$
$978$	−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	0.997959	−	0.0638619i	$-0.0203417\pi$
$983$	1.99574	+	9.17429i	0.0636543	+	0.292614i	−0.934304	+	0.356476i	$0.883978\pi$
$984$	−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	0.101131	−	0.994873i	$-0.467754\pi$
$991$	22.7941	−	6.69294i	0.724078	−	0.212608i	0.622946	+	0.782265i	$0.285936\pi$
$992$	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	−0.672774	−	0.739848i	$-0.734897\pi$
$997$	−38.9453	+	2.78542i	−1.23341	+	0.0882152i	−0.560635	+	0.828063i	$0.689443\pi$
$998$	−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.37.2	✓	240
5.3	odd	4	inner	690.2.w.b.313.2	yes	240
23.5	odd	22	inner	690.2.w.b.97.2	yes	240
115.28	even	44	inner	690.2.w.b.373.2	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.b.37.2	✓	240	1.1	even	1	trivial
690.2.w.b.97.2	yes	240	23.5	odd	22	inner
690.2.w.b.313.2	yes	240	5.3	odd	4	inner
690.2.w.b.373.2	yes	240	115.28	even	44	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
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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