LMFDB - Embedded newform 690.2.w.b.493.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			493.4
Character	$\chi$	$=$	690.493
Dual form			690.2.w.b.7.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.997452 - 0.0713392i) q^{2} +(-0.212565 - 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(1.62532 - 1.53569i) q^{5} +(0.142315 + 0.989821i) q^{6} +(1.83156 + 3.35425i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +O(q^{10})$	\(q+(-0.997452 - 0.0713392i) q^{2} +(-0.212565 - 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(1.62532 - 1.53569i) q^{5} +(0.142315 + 0.989821i) q^{6} +(1.83156 + 3.35425i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +(-1.73074 + 1.41582i) q^{10} +(1.05421 + 0.913477i) q^{11} +(-0.0713392 - 0.997452i) q^{12} +(4.41465 + 2.41058i) q^{13} +(-1.58760 - 3.47637i) q^{14} +(-1.84608 - 1.26174i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-4.62698 + 6.18092i) q^{17} +(0.936950 - 0.349464i) q^{18} +(-0.753219 + 5.23875i) q^{19} +(1.82733 - 1.28875i) q^{20} +(2.88827 - 2.50270i) q^{21} +(-0.986355 - 0.986355i) q^{22} +(4.78172 - 0.367647i) q^{23} +1.00000i q^{24} +(0.283342 - 4.99197i) q^{25} +(-4.23143 - 2.71937i) q^{26} +(0.599278 + 0.800541i) q^{27} +(1.33556 + 3.58077i) q^{28} +(-5.88683 + 0.846398i) q^{29} +(1.75136 + 1.39023i) q^{30} +(-8.20400 + 5.27239i) q^{31} +(-0.936950 - 0.349464i) q^{32} +(0.668513 - 1.22429i) q^{33} +(5.05613 - 5.83508i) q^{34} +(8.12795 + 2.63904i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(0.492162 - 1.31954i) q^{37} +(1.12503 - 5.17167i) q^{38} +(1.41709 - 4.82616i) q^{39} +(-1.91461 + 1.15510i) q^{40} +(2.71326 - 5.94121i) q^{41} +(-3.05945 + 2.29028i) q^{42} +(4.16455 - 0.905943i) q^{43} +(0.913477 + 1.05421i) q^{44} +(-0.840498 + 2.07209i) q^{45} +(-4.79576 + 0.0255868i) q^{46} +(7.10477 - 7.10477i) q^{47} +(0.0713392 - 0.997452i) q^{48} +(-4.11192 + 6.39827i) q^{49} +(-0.638742 + 4.95903i) q^{50} +(7.02320 + 3.20739i) q^{51} +(4.02665 + 3.01431i) q^{52} +(2.49158 - 1.36051i) q^{53} +(-0.540641 - 0.841254i) q^{54} +(3.11624 - 0.134239i) q^{55} +(-1.07671 - 3.66692i) q^{56} +(5.27914 - 0.377572i) q^{57} +(5.93221 - 0.424280i) q^{58} +(-1.11079 - 3.78300i) q^{59} +(-1.64772 - 1.51163i) q^{60} +(-1.03298 - 1.60735i) q^{61} +(8.55923 - 4.67369i) q^{62} +(-3.05945 - 2.29028i) q^{63} +(0.909632 + 0.415415i) q^{64} +(10.8771 - 2.86154i) q^{65} +(-0.754149 + 1.17348i) q^{66} +(-0.824851 + 11.5329i) q^{67} +(-5.45952 + 5.45952i) q^{68} +(-1.37567 - 4.59429i) q^{69} +(-7.91898 - 3.21216i) q^{70} +(-2.57260 - 2.96894i) q^{71} +(0.977147 - 0.212565i) q^{72} +(6.27093 - 4.69436i) q^{73} +(-0.585043 + 1.28107i) q^{74} +(-4.93811 + 0.784252i) q^{75} +(-1.49111 + 5.07824i) q^{76} +(-1.13319 + 5.20917i) q^{77} +(-1.75777 + 4.71277i) q^{78} +(7.27596 - 2.13642i) q^{79} +(1.99214 - 1.01557i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-3.13019 + 5.73251i) q^{82} +(8.24914 + 3.07677i) q^{83} +(3.21505 - 2.06618i) q^{84} +(1.97162 + 17.1516i) q^{85} +(-4.21857 + 0.606539i) q^{86} +(2.07839 + 5.57238i) q^{87} +(-0.835943 - 1.11669i) q^{88} +(-0.749222 - 0.481496i) q^{89} +(0.986178 - 2.00685i) q^{90} +19.2230i q^{91} +(4.78537 + 0.316604i) q^{92} +(6.89579 + 6.89579i) q^{93} +(-7.59352 + 6.57982i) q^{94} +(6.82085 + 9.67137i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(-4.59194 + 1.71270i) q^{97} +(4.55789 - 6.08862i) q^{98} +(-1.33841 - 0.392994i) 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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.997452	−	0.0713392i	−0.705305	−	0.0504444i
$2$	−0.997452	−	0.0713392i	−0.705305	−	0.0504444i
$3$	−0.212565	−	0.977147i	−0.122725	−	0.564156i
$3$	−0.212565	−	0.977147i	−0.122725	−	0.564156i
$4$	0.989821	+	0.142315i	0.494911	+	0.0711574i
$5$	1.62532	−	1.53569i	0.726866	−	0.686779i
$5$	1.62532	−	1.53569i	0.726866	−	0.686779i
$6$	0.142315	+	0.989821i	0.0580998	+	0.404093i
$7$	1.83156	+	3.35425i	0.692265	+	1.26779i	0.953173	+	0.302425i	$0.0977962\pi$
$7$	1.83156	+	3.35425i	0.692265	+	1.26779i	−0.260908	+	0.965364i	$0.584022\pi$
$8$	−0.977147	−	0.212565i	−0.345474	−	0.0751532i
$9$	−0.909632	+	0.415415i	−0.303211	+	0.138472i
$10$	−1.73074	+	1.41582i	−0.547307	+	0.447723i
$11$	1.05421	+	0.913477i	0.317856	+	0.275424i	0.799145	−	0.601138i	$-0.205286\pi$
$11$	1.05421	+	0.913477i	0.317856	+	0.275424i	−0.481289	+	0.876562i	$0.659831\pi$
$12$	−0.0713392	−	0.997452i	−0.0205938	−	0.287940i
$13$	4.41465	+	2.41058i	1.22440	+	0.668574i	0.955613	−	0.294625i	$-0.0951946\pi$
$13$	4.41465	+	2.41058i	1.22440	+	0.668574i	0.268789	+	0.963199i	$0.413376\pi$
$14$	−1.58760	−	3.47637i	−0.424305	−	0.929099i
$15$	−1.84608	−	1.26174i	−0.476655	−	0.325781i
$16$	0.959493	+	0.281733i	0.239873	+	0.0704331i
$17$	−4.62698	+	6.18092i	−1.12221	+	1.49909i	−0.279951	+	0.960014i	$0.590318\pi$
$17$	−4.62698	+	6.18092i	−1.12221	+	1.49909i	−0.842255	+	0.539079i	$0.818773\pi$
$18$	0.936950	−	0.349464i	0.220841	−	0.0823695i
$19$	−0.753219	+	5.23875i	−0.172800	+	1.20185i	0.700133	+	0.714013i	$0.253124\pi$
$19$	−0.753219	+	5.23875i	−0.172800	+	1.20185i	−0.872933	+	0.487840i	$0.837785\pi$
$20$	1.82733	−	1.28875i	0.408603	−	0.288173i
$21$	2.88827	−	2.50270i	0.630273	−	0.546134i
$22$	−0.986355	−	0.986355i	−0.210292	−	0.210292i
$23$	4.78172	−	0.367647i	0.997057	−	0.0766598i
$23$	4.78172	−	0.367647i	0.997057	−	0.0766598i
$24$			1.00000i			0.204124i
$25$	0.283342	−	4.99197i	0.0566683	−	0.998393i
$26$	−4.23143	−	2.71937i	−0.829852	−	0.533313i
$27$	0.599278	+	0.800541i	0.115331	+	0.154064i
$28$	1.33556	+	3.58077i	0.252397	+	0.676702i
$29$	−5.88683	+	0.846398i	−1.09316	+	0.157172i	−0.665228	−	0.746640i	$-0.731666\pi$
$29$	−5.88683	+	0.846398i	−1.09316	+	0.157172i	−0.427928	+	0.903813i	$0.640756\pi$
$30$	1.75136	+	1.39023i	0.319753	+	0.253820i
$31$	−8.20400	+	5.27239i	−1.47348	+	0.946949i	−0.475754	+	0.879578i	$0.657825\pi$
$31$	−8.20400	+	5.27239i	−1.47348	+	0.946949i	−0.997728	+	0.0673712i	$0.978539\pi$
$32$	−0.936950	−	0.349464i	−0.165631	−	0.0617771i
$33$	0.668513	−	1.22429i	0.116373	−	0.213121i
$34$	5.05613	−	5.83508i	0.867119	−	1.00071i
$35$	8.12795	+	2.63904i	1.37388	+	0.446079i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	0.492162	−	1.31954i	0.0809110	−	0.216931i	−0.890195	−	0.455580i	$-0.849432\pi$
$37$	0.492162	−	1.31954i	0.0809110	−	0.216931i	0.971106	+	0.238649i	$0.0767046\pi$
$38$	1.12503	−	5.17167i	0.182504	−	0.838956i
$39$	1.41709	−	4.82616i	0.226916	−	0.772805i
$40$	−1.91461	+	1.15510i	−0.302727	+	0.182638i
$41$	2.71326	−	5.94121i	0.423740	−	0.927860i	−0.570562	−	0.821255i	$-0.693274\pi$
$41$	2.71326	−	5.94121i	0.423740	−	0.927860i	0.994301	−	0.106606i	$-0.0339983\pi$
$42$	−3.05945	+	2.29028i	−0.472084	+	0.353398i
$43$	4.16455	−	0.905943i	0.635088	−	0.138155i	0.116516	−	0.993189i	$-0.462827\pi$
$43$	4.16455	−	0.905943i	0.635088	−	0.138155i	0.518572	+	0.855034i	$0.326464\pi$
$44$	0.913477	+	1.05421i	0.137712	+	0.158928i
$45$	−0.840498	+	2.07209i	−0.125294	+	0.308889i
$46$	−4.79576	+	0.0255868i	−0.707097	+	0.00377256i
$47$	7.10477	−	7.10477i	1.03634	−	1.03634i	0.0370233	−	0.999314i	$-0.488212\pi$
$47$	7.10477	−	7.10477i	1.03634	−	1.03634i	0.999314	−	0.0370233i	$-0.0117876\pi$
$48$	0.0713392	−	0.997452i	0.0102969	−	0.143970i
$49$	−4.11192	+	6.39827i	−0.587417	+	0.914038i
$50$	−0.638742	+	4.95903i	−0.0903318	+	0.701313i
$51$	7.02320	+	3.20739i	0.983445	+	0.449124i
$52$	4.02665	+	3.01431i	0.558396	+	0.418010i
$53$	2.49158	−	1.36051i	0.342245	−	0.186880i	−0.298929	−	0.954275i	$-0.596629\pi$
$53$	2.49158	−	1.36051i	0.342245	−	0.186880i	0.641174	+	0.767395i	$0.278448\pi$
$54$	−0.540641	−	0.841254i	−0.0735719	−	0.114480i
$55$	3.11624	−	0.134239i	0.420194	−	0.0181007i
$56$	−1.07671	−	3.66692i	−0.143881	−	0.490013i
$57$	5.27914	−	0.377572i	0.699239	−	0.0500106i
$58$	5.93221	−	0.424280i	0.778937	−	0.0557107i
$59$	−1.11079	−	3.78300i	−0.144612	−	0.492505i	0.855048	−	0.518548i	$-0.173527\pi$
$59$	−1.11079	−	3.78300i	−0.144612	−	0.492505i	−0.999661	+	0.0260435i	$0.991709\pi$
$60$	−1.64772	−	1.51163i	−0.212720	−	0.195150i
$61$	−1.03298	−	1.60735i	−0.132259	−	0.205800i	0.768807	−	0.639481i	$-0.220851\pi$
$61$	−1.03298	−	1.60735i	−0.132259	−	0.205800i	−0.901066	+	0.433681i	$0.857214\pi$
$62$	8.55923	−	4.67369i	1.08702	−	0.593559i
$63$	−3.05945	−	2.29028i	−0.385455	−	0.288548i
$64$	0.909632	+	0.415415i	0.113704	+	0.0519269i
$65$	10.8771	−	2.86154i	1.34914	−	0.354930i
$66$	−0.754149	+	1.17348i	−0.0928294	+	0.144445i
$67$	−0.824851	+	11.5329i	−0.100772	+	1.40897i	0.655738	+	0.754989i	$0.272358\pi$
$67$	−0.824851	+	11.5329i	−0.100772	+	1.40897i	−0.756510	+	0.653983i	$0.773097\pi$
$68$	−5.45952	+	5.45952i	−0.662064	+	0.662064i
$69$	−1.37567	−	4.59429i	−0.165612	−	0.553088i
$70$	−7.91898	−	3.21216i	−0.946499	−	0.383926i
$71$	−2.57260	−	2.96894i	−0.305312	−	0.352348i	0.582273	−	0.812993i	$-0.302164\pi$
$71$	−2.57260	−	2.96894i	−0.305312	−	0.352348i	−0.887584	+	0.460645i	$0.847618\pi$
$72$	0.977147	−	0.212565i	0.115158	−	0.0250511i
$73$	6.27093	−	4.69436i	0.733957	−	0.549434i	−0.165623	−	0.986189i	$-0.552963\pi$
$73$	6.27093	−	4.69436i	0.733957	−	0.549434i	0.899580	+	0.436756i	$0.143873\pi$
$74$	−0.585043	+	1.28107i	−0.0680099	+	0.148921i
$75$	−4.93811	+	0.784252i	−0.570204	+	0.0905576i
$76$	−1.49111	+	5.07824i	−0.171041	+	0.582514i
$77$	−1.13319	+	5.20917i	−0.129138	+	0.593640i
$78$	−1.75777	+	4.71277i	−0.199029	+	0.533616i
$79$	7.27596	−	2.13642i	0.818610	−	0.240366i	0.154493	−	0.987994i	$-0.450626\pi$
$79$	7.27596	−	2.13642i	0.818610	−	0.240366i	0.664117	+	0.747628i	$0.268808\pi$
$80$	1.99214	−	1.01557i	0.222728	−	0.113545i
$81$	0.654861	−	0.755750i	0.0727623	−	0.0839722i
$82$	−3.13019	+	5.73251i	−0.345671	+	0.633049i
$83$	8.24914	+	3.07677i	0.905461	+	0.337720i	0.758691	−	0.651451i	$-0.225839\pi$
$83$	8.24914	+	3.07677i	0.905461	+	0.337720i	0.146771	+	0.989171i	$0.453112\pi$
$84$	3.21505	−	2.06618i	0.350790	−	0.225439i
$85$	1.97162	+	17.1516i	0.213852	+	1.86035i
$86$	−4.21857	+	0.606539i	−0.454900	+	0.0654048i
$87$	2.07839	+	5.57238i	0.222827	+	0.597422i
$88$	−0.835943	−	1.11669i	−0.0891118	−	0.119039i
$89$	−0.749222	−	0.481496i	−0.0794174	−	0.0510384i	0.500330	−	0.865835i	$-0.333212\pi$
$89$	−0.749222	−	0.481496i	−0.0794174	−	0.0510384i	−0.579747	+	0.814797i	$0.696849\pi$
$90$	0.986178	−	2.00685i	0.103952	−	0.211541i
$91$			19.2230i			2.01511i
$92$	4.78537	+	0.316604i	0.498909	+	0.0330083i
$93$	6.89579	+	6.89579i	0.715060	+	0.715060i
$94$	−7.59352	+	6.57982i	−0.783212	+	0.678657i
$95$	6.82085	+	9.67137i	0.699805	+	0.992262i
$96$	−0.142315	+	0.989821i	−0.0145249	+	0.101023i
$97$	−4.59194	+	1.71270i	−0.466241	+	0.173899i	−0.571595	−	0.820536i	$-0.693675\pi$
$97$	−4.59194	+	1.71270i	−0.466241	+	0.173899i	0.105354	+	0.994435i	$0.466402\pi$
$98$	4.55789	−	6.08862i	0.460416	−	0.615044i
$99$	−1.33841	−	0.392994i	−0.134516	−	0.0394973i
$100$	0.990888	−	4.90083i	0.0990888	−	0.490083i
$101$	−6.92270	−	15.1586i	−0.688835	−	1.50834i	−0.853003	−	0.521905i	$-0.825221\pi$
$101$	−6.92270	−	15.1586i	−0.688835	−	1.50834i	0.164169	−	0.986432i	$-0.447506\pi$
$102$	−6.77649	−	3.70024i	−0.670973	−	0.366379i
$103$	−1.30717	−	18.2766i	−0.128799	−	1.80085i	−0.493520	−	0.869734i	$-0.664290\pi$
$103$	−1.30717	−	18.2766i	−0.128799	−	1.80085i	0.364721	−	0.931117i	$-0.381164\pi$
$104$	−3.80135	−	3.29389i	−0.372753	−	0.322993i
$105$	0.851009	−	8.50317i	0.0830500	−	0.829825i
$106$	−2.58229	+	1.17929i	−0.250815	+	0.114543i
$107$	3.50380	+	0.762205i	0.338725	+	0.0736852i	0.378711	−	0.925515i	$-0.376368\pi$
$107$	3.50380	+	0.762205i	0.338725	+	0.0736852i	−0.0399855	+	0.999200i	$0.512731\pi$
$108$	0.479249	+	0.877679i	0.0461158	+	0.0844547i
$109$	−1.71969	−	11.9607i	−0.164717	−	1.14563i	−0.889594	−	0.456752i	$-0.849013\pi$
$109$	−1.71969	−	11.9607i	−0.164717	−	1.14563i	0.724877	−	0.688878i	$-0.241897\pi$
$110$	−3.11788	−	0.0884134i	−0.297278	−	0.00842989i
$111$	−1.39400	−	0.200427i	−0.132313	−	0.0190237i
$112$	0.812368	+	3.73439i	0.0767615	+	0.352867i
$113$	−8.15955	−	0.583582i	−0.767585	−	0.0548988i	−0.317946	−	0.948109i	$-0.602993\pi$
$113$	−8.15955	−	0.583582i	−0.767585	−	0.0548988i	−0.449640	+	0.893210i	$0.648448\pi$
$114$	−5.29263			−0.495700
$115$	7.20724	−	7.94076i	0.672079	−	0.740480i
$116$	−5.94736			−0.552199
$117$	−5.01709	−	0.358830i	−0.463831	−	0.0331738i
$118$	0.838083	+	3.85260i	0.0771518	+	0.354661i
$119$	−29.2070	−	4.19933i	−2.67740	−	0.384952i
$120$	1.53569	+	1.62532i	0.140188	+	0.148371i
$121$	−1.28855	−	8.96205i	−0.117141	−	0.814732i
$122$	0.915681	+	1.67694i	0.0829018	+	0.151823i
$123$	−6.38218	−	1.38836i	−0.575461	−	0.125184i
$124$	−8.87084	+	4.05118i	−0.796625	+	0.363806i
$125$	−7.20557	−	8.54867i	−0.644485	−	0.764617i
$126$	2.88827	+	2.50270i	0.257308	+	0.222958i
$127$	0.356283	+	4.98149i	0.0316150	+	0.442036i	0.988465	+	0.151452i	$0.0483950\pi$
$127$	0.356283	+	4.98149i	0.0316150	+	0.442036i	−0.956850	+	0.290584i	$0.906150\pi$
$128$	−0.877679	−	0.479249i	−0.0775766	−	0.0423600i
$129$	−1.77048	−	3.87681i	−0.155882	−	0.341334i
$130$	−11.0535	+	2.07829i	−0.969459	+	0.182278i
$131$	9.01082	+	2.64582i	0.787279	+	0.231166i	0.650571	−	0.759445i	$-0.274530\pi$
$131$	9.01082	+	2.64582i	0.787279	+	0.231166i	0.136708	+	0.990611i	$0.456348\pi$
$132$	0.835943	−	1.11669i	0.0727595	−	0.0971953i
$133$	−18.9517	+	7.06861i	−1.64332	+	0.612926i
$134$	1.64550	−	11.4447i	0.142149	−	0.988671i
$135$	2.20340	+	0.380835i	0.189638	+	0.0327771i
$136$	5.83508	−	5.05613i	0.500354	−	0.433560i
$137$	1.70416	+	1.70416i	0.145597	+	0.145597i	0.776148	−	0.630551i	$-0.217171\pi$
$137$	1.70416	+	1.70416i	0.145597	+	0.145597i	−0.630551	+	0.776148i	$0.717171\pi$
$138$	1.04441	+	4.68073i	0.0889065	+	0.398450i
$139$		−	10.4039i		−	0.882443i	−0.897398	−	0.441222i	$-0.854545\pi$
$139$		−	10.4039i		−	0.882443i	0.897398	−	0.441222i	$-0.145455\pi$
$140$	7.66965	+	3.76891i	0.648204	+	0.318531i
$141$	−8.45264	−	5.43218i	−0.711840	−	0.457472i
$142$	2.35424	+	3.14490i	0.197564	+	0.263914i
$143$	2.45195	+	6.57393i	0.205042	+	0.549739i
$144$	−0.989821	+	0.142315i	−0.0824851	+	0.0118596i
$145$	−8.26819	+	10.4160i	−0.686636	+	0.865000i
$146$	−6.58985	+	4.23504i	−0.545380	+	0.350494i
$147$	7.12610	+	2.65790i	0.587751	+	0.219220i
$148$	0.674943	−	1.23606i	0.0554799	−	0.101604i
$149$	−9.78309	+	11.2903i	−0.801462	+	0.924936i	−0.998460	−	0.0554674i	$-0.982335\pi$
$149$	−9.78309	+	11.2903i	−0.801462	+	0.924936i	0.196999	+	0.980404i	$0.436881\pi$
$150$	4.98148	−	0.429973i	0.406736	−	0.0351072i
$151$	17.5211	−	5.14465i	1.42585	−	0.418666i	0.524368	−	0.851492i	$-0.324302\pi$
$151$	17.5211	−	5.14465i	1.42585	−	0.418666i	0.901478	+	0.432826i	$0.142483\pi$
$152$	1.84958	−	4.95892i	0.150021	−	0.402222i
$153$	1.64120	−	7.54448i	0.132683	−	0.609935i
$154$	1.50192	−	5.11506i	0.121028	−	0.412183i
$155$	−5.23741	+	21.1681i	−0.420679	+	1.70026i
$156$	2.08950	−	4.57537i	0.167294	−	0.366323i
$157$	−3.50993	+	2.62750i	−0.280123	+	0.209697i	−0.730096	−	0.683345i	$-0.760525\pi$
$157$	−3.50993	+	2.62750i	−0.280123	+	0.209697i	0.449973	+	0.893042i	$0.351434\pi$
$158$	−7.40984	+	1.61191i	−0.589495	+	0.128237i
$159$	−1.85904	−	2.14545i	−0.147431	−	0.170145i
$160$	−2.05951	+	0.870868i	−0.162819	+	0.0688482i
$161$	9.99119	+	15.3657i	0.787416	+	1.21099i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	1.17486	−	16.4267i	0.0920223	−	1.28664i	−0.716255	−	0.697839i	$-0.754145\pi$
$163$	1.17486	−	16.4267i	0.0920223	−	1.28664i	0.808277	−	0.588802i	$-0.200400\pi$
$164$	3.53116	−	5.49460i	0.275737	−	0.429056i
$165$	−0.793575	−	3.01649i	−0.0617797	−	0.234833i
$166$	−8.00863	−	3.65742i	−0.621590	−	0.283871i
$167$	−10.8836	−	8.14738i	−0.842201	−	0.630463i	0.0885689	−	0.996070i	$-0.471771\pi$
$167$	−10.8836	−	8.14738i	−0.842201	−	0.630463i	−0.930769	+	0.365607i	$0.880862\pi$
$168$	−3.35425	+	1.83156i	−0.258786	+	0.141308i
$169$	6.64988	+	10.3474i	0.511529	+	0.795955i
$170$	−0.743016	−	17.2485i	−0.0569867	−	1.32290i
$171$	−1.49111	−	5.07824i	−0.114028	−	0.388343i
$172$	4.25109	−	0.304044i	0.324143	−	0.0231831i
$173$	−11.8848	+	0.850021i	−0.903588	+	0.0646259i	−0.515396	−	0.856952i	$-0.672355\pi$
$173$	−11.8848	+	0.850021i	−0.903588	+	0.0646259i	−0.388193	+	0.921578i	$0.626900\pi$
$174$	−1.67557	−	5.70645i	−0.127024	−	0.432605i
$175$	17.2633	−	8.19269i	1.30498	−	0.619309i
$176$	0.754149	+	1.17348i	0.0568461	+	0.0884543i
$177$	−3.46043	+	1.88954i	−0.260102	+	0.142026i
$178$	0.712964	+	0.533718i	0.0534389	+	0.0400038i
$179$	2.43174	+	1.11054i	0.181757	+	0.0830057i	0.504215	−	0.863578i	$-0.331782\pi$
$179$	2.43174	+	1.11054i	0.181757	+	0.0830057i	−0.322458	+	0.946584i	$0.604509\pi$
$180$	−1.12683	+	1.93139i	−0.0839891	+	0.143957i
$181$	−8.67364	+	13.4965i	−0.644707	+	1.00318i	0.353008	+	0.935620i	$0.385159\pi$
$181$	−8.67364	+	13.4965i	−0.644707	+	1.00318i	−0.997715	+	0.0675630i	$0.978478\pi$
$182$	1.37135	−	19.1740i	0.101651	−	1.42127i
$183$	−1.35104	+	1.35104i	−0.0998717	+	0.0998717i
$184$	−4.75059	−	0.657182i	−0.350218	−	0.0484481i
$185$	−1.22647	−	2.90048i	−0.0901721	−	0.213248i
$186$	−6.38628	−	7.37016i	−0.468265	−	0.540406i
$187$	−10.5239	+	2.28934i	−0.769585	+	0.167413i
$188$	8.04357	−	6.02134i	0.586638	−	0.439152i
$189$	−1.58760	+	3.47637i	−0.115481	+	0.252869i
$190$	−6.11353	−	10.1333i	−0.443522	−	0.735148i
$191$	0.451628	−	1.53810i	0.0326786	−	0.111293i	−0.941539	−	0.336905i	$-0.890620\pi$
$191$	0.451628	−	1.53810i	0.0326786	−	0.111293i	0.974217	+	0.225612i	$0.0724381\pi$
$192$	0.212565	−	0.977147i	0.0153406	−	0.0705195i
$193$	−5.54786	+	14.8744i	−0.399344	+	1.07068i	0.569278	+	0.822145i	$0.307223\pi$
$193$	−5.54786	+	14.8744i	−0.399344	+	1.07068i	−0.968622	+	0.248537i	$0.920050\pi$
$194$	4.70242	−	1.38076i	0.337614	−	0.0991324i
$195$	−5.10824	−	10.0203i	−0.365809	−	0.717566i
$196$	−4.98063	+	5.74796i	−0.355759	+	0.410568i
$197$	2.39927	−	4.39393i	0.170941	−	0.313054i	−0.778138	−	0.628093i	$-0.783836\pi$
$197$	2.39927	−	4.39393i	0.170941	−	0.313054i	0.949079	+	0.315039i	$0.102018\pi$
$198$	1.30697	+	0.487474i	0.0928821	+	0.0346432i
$199$	11.1390	−	7.15862i	0.789625	−	0.507461i	−0.0825900	−	0.996584i	$-0.526319\pi$
$199$	11.1390	−	7.15862i	0.789625	−	0.507461i	0.872215	+	0.489122i	$0.162683\pi$
$200$	−1.33798	+	4.81765i	−0.0946098	+	0.340660i
$201$	11.4447	−	1.64550i	0.807247	−	0.116065i
$202$	5.82366	+	15.6138i	0.409751	+	1.09859i
$203$	−13.6211	−	18.1957i	−0.956015	−	1.27709i
$204$	6.49525	+	4.17425i	0.454759	+	0.292256i
$205$	−4.71391	−	13.8231i	−0.329233	−	0.965446i
$206$			18.3233i			1.27665i
$207$	−4.19688	+	2.32082i	−0.291703	+	0.161308i
$208$	3.55668	+	3.55668i	0.246612	+	0.246612i
$209$	−5.57953	+	4.83469i	−0.385944	+	0.334422i
$210$	−1.45545	+	8.42080i	−0.100436	+	0.581090i
$211$	−0.908813	+	6.32093i	−0.0625653	+	0.435151i	0.934330	+	0.356410i	$0.115999\pi$
$211$	−0.908813	+	6.32093i	−0.0625653	+	0.435151i	−0.996895	+	0.0787414i	$0.974910\pi$
$212$	2.65984	−	0.992071i	0.182679	−	0.0681357i
$213$	−2.35424	+	3.14490i	−0.161310	+	0.215485i
$214$	−3.44050	−	1.01022i	−0.235188	−	0.0690573i
$215$	5.37749	−	7.86789i	0.366742	−	0.536586i
$216$	−0.415415	−	0.909632i	−0.0282654	−	0.0618926i
$217$	−32.7111	−	17.8616i	−2.22057	−	1.21252i
$218$	0.862043	+	12.0529i	0.0583849	+	0.816328i
$219$	−5.92006	−	5.12976i	−0.400041	−	0.346637i
$220$	3.10363	+	0.310615i	0.209246	+	0.0209417i
$221$	−35.3261	+	16.1329i	−2.37629	+	1.08521i
$222$	1.37615	+	0.299363i	0.0923611	+	0.0200919i
$223$	12.1577	+	22.2653i	0.814143	+	1.49099i	0.870274	+	0.492568i	$0.163942\pi$
$223$	12.1577	+	22.2653i	0.814143	+	1.49099i	−0.0561306	+	0.998423i	$0.517876\pi$
$224$	−0.543889	−	3.78283i	−0.0363401	−	0.252751i
$225$	1.81600	+	4.65856i	0.121067	+	0.310570i
$226$	8.09712	+	1.16419i	0.538613	+	0.0774408i
$227$	3.85164	+	17.7057i	0.255642	+	1.17517i	0.908565	+	0.417744i	$0.137179\pi$
$227$	3.85164	+	17.7057i	0.255642	+	1.17517i	−0.652923	+	0.757425i	$0.726457\pi$
$228$	5.27914	+	0.377572i	0.349620	+	0.0250053i
$229$	0.366279			0.0242044			0.0121022	−	0.999927i	$-0.496148\pi$
$229$	0.366279			0.0242044			0.0121022	+	0.999927i	$0.496148\pi$
$230$	−7.75537	+	7.40637i	−0.511374	+	0.488362i
$231$	5.33100			0.350754
$232$	5.93221	+	0.424280i	0.389469	+	0.0278553i
$233$	−4.60301	−	21.1597i	−0.301553	−	1.38622i	−0.839555	−	0.543275i	$-0.817184\pi$
$233$	−4.60301	−	21.1597i	−0.301553	−	1.38622i	0.538001	−	0.842944i	$-0.319180\pi$
$234$	4.97871	+	0.715831i	0.325469	+	0.0467953i
$235$	0.636847	−	22.4582i	0.0415433	−	1.46501i
$236$	−0.561106	−	3.90258i	−0.0365249	−	0.254036i
$237$	−3.63421	−	6.65556i	−0.236067	−	0.432325i
$238$	28.8330	+	6.27223i	1.86896	+	0.406568i
$239$	13.2378	−	6.04551i	0.856284	−	0.391052i	0.0616189	−	0.998100i	$-0.480374\pi$
$239$	13.2378	−	6.04551i	0.856284	−	0.391052i	0.794665	+	0.607048i	$0.207646\pi$
$240$	−1.41582	−	1.73074i	−0.0913910	−	0.111718i
$241$	−17.1441	−	14.8555i	−1.10435	−	0.956926i	−0.105056	−	0.994466i	$-0.533502\pi$
$241$	−17.1441	−	14.8555i	−1.10435	−	0.956926i	−0.999295	+	0.0375404i	$0.988048\pi$
$242$	0.645920	+	9.03114i	0.0415213	+	0.580543i
$243$	−0.877679	−	0.479249i	−0.0563031	−	0.0307438i
$244$	−0.793716	−	1.73800i	−0.0508124	−	0.111264i
$245$	3.14254	+	16.7139i	0.200769	+	1.06781i
$246$	6.26687	+	1.84012i	0.399561	+	0.117322i
$247$	−15.9536	+	21.3116i	−1.01511	+	1.35602i
$248$	9.13724	−	3.40801i	0.580215	−	0.216409i
$249$	1.25298	−	8.71464i	0.0794041	−	0.552268i
$250$	6.57735	+	9.04093i	0.415988	+	0.571799i
$251$	−15.6793	+	13.5862i	−0.989668	+	0.857552i	−0.989802	−	0.142448i	$-0.954503\pi$
$251$	−15.6793	+	13.5862i	−0.989668	+	0.857552i	0.000134070		1.00000i	$0.499957\pi$
$252$	−2.70237	−	2.70237i	−0.170233	−	0.170233i
$253$	5.37676	+	3.98041i	0.338034	+	0.250246i
$254$		−	4.99422i		−	0.313365i
$255$	16.3405	−	5.57239i	1.02328	−	0.348956i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	−0.528538	−	0.706045i	−0.0329693	−	0.0440419i	0.783754	−	0.621072i	$-0.213302\pi$
$257$	−0.528538	−	0.706045i	−0.0329693	−	0.0440419i	−0.816723	+	0.577030i	$0.804212\pi$
$258$	1.48940	+	3.99323i	0.0927259	+	0.248608i
$259$	5.32749	−	0.765977i	0.331034	−	0.0475955i
$260$	11.1736	−	1.28444i	0.692960	−	0.0796576i
$261$	5.00324	−	3.21539i	0.309693	−	0.199027i
$262$	−8.79911	−	3.28190i	−0.543611	−	0.202756i
$263$	−9.83056	+	18.0033i	−0.606178	+	1.11013i	0.376780	+	0.926303i	$0.377031\pi$
$263$	−9.83056	+	18.0033i	−0.606178	+	1.11013i	−0.982958	+	0.183829i	$0.941151\pi$
$264$	−0.913477	+	1.05421i	−0.0562206	+	0.0648820i
$265$	1.96031	−	6.03755i	0.120421	−	0.370884i
$266$	19.4077	−	5.69860i	1.18996	−	0.349404i
$267$	−0.311233	+	0.834449i	−0.0190472	+	0.0510675i
$268$	−2.45776	+	11.2981i	−0.150132	+	0.690144i
$269$	−5.70171	+	19.4183i	−0.347640	+	1.18395i	0.581290	+	0.813696i	$0.302548\pi$
$269$	−5.70171	+	19.4183i	−0.347640	+	1.18395i	−0.928930	+	0.370256i	$0.879270\pi$
$270$	−2.17062	−	0.537054i	−0.132099	−	0.0326840i
$271$	−0.723593	+	1.58445i	−0.0439552	+	0.0962484i	−0.930336	−	0.366709i	$-0.880484\pi$
$271$	−0.723593	+	1.58445i	−0.0439552	+	0.0962484i	0.886381	+	0.462957i	$0.153212\pi$
$272$	−6.18092	+	4.62698i	−0.374773	+	0.280552i
$273$	18.7837	−	4.08614i	1.13684	−	0.247304i
$274$	−1.57825	−	1.82140i	−0.0953455	−	0.110035i
$275$	4.85874	−	5.00374i	0.292993	−	0.301737i
$276$	−0.707835	−	4.74331i	−0.0426066	−	0.285514i
$277$	18.8888	−	18.8888i	1.13492	−	1.13492i	0.145567	−	0.989348i	$-0.453499\pi$
$277$	18.8888	−	18.8888i	1.13492	−	1.13492i	0.989348	−	0.145567i	$-0.0465008\pi$
$278$	−0.742202	+	10.3773i	−0.0445143	+	0.622392i
$279$	5.27239	−	8.20400i	0.315650	−	0.491161i
$280$	−7.38124	−	4.30645i	−0.441113	−	0.257360i
$281$	27.0868	+	12.3701i	1.61586	+	0.737939i	0.998800	−	0.0489760i	$-0.0155958\pi$
$281$	27.0868	+	12.3701i	1.61586	+	0.737939i	0.617061	+	0.786915i	$0.288323\pi$
$282$	8.04357	+	6.02134i	0.478988	+	0.358566i
$283$	11.5498	−	6.30665i	0.686562	−	0.374891i	−0.0977901	−	0.995207i	$-0.531177\pi$
$283$	11.5498	−	6.30665i	0.686562	−	0.374891i	0.784352	+	0.620316i	$0.212996\pi$
$284$	−2.12389	−	3.30484i	−0.126030	−	0.196106i
$285$	8.00047	−	8.72077i	0.473907	−	0.516574i
$286$	−1.97672	−	6.73210i	−0.116886	−	0.398077i
$287$	24.8978	−	1.78073i	1.46967	−	0.105113i
$288$	0.997452	−	0.0713392i	0.0587754	−	0.00420370i
$289$	−12.0054	−	40.8866i	−0.706199	−	2.40509i
$290$	8.99019	−	9.79960i	0.527922	−	0.575452i
$291$	2.64965	+	4.12294i	0.155325	+	0.241691i
$292$	6.87518	−	3.75413i	0.402340	−	0.219694i
$293$	1.66489	+	1.24632i	0.0972637	+	0.0728107i	0.646803	−	0.762657i	$-0.276106\pi$
$293$	1.66489	+	1.24632i	0.0972637	+	0.0728107i	−0.549539	+	0.835468i	$0.685197\pi$
$294$	−6.91833	−	3.15950i	−0.403485	−	0.184265i
$295$	−7.61489	−	4.44277i	−0.443356	−	0.258668i
$296$	−0.761403	+	1.18477i	−0.0442556	+	0.0688631i
$297$	−0.0995123	+	1.39136i	−0.00577429	+	0.0807351i
$298$	10.5636	−	10.5636i	0.611933	−	0.611933i
$299$	21.9958	+	9.90368i	1.27205	+	0.572745i
$300$	−4.99946	+	0.0735031i	−0.288644	+	0.00424370i
$301$	10.6664	+	12.3097i	0.614801	+	0.709518i
$302$	−17.8435	+	3.88161i	−1.02678	+	0.223361i
$303$	−13.3407	+	9.98669i	−0.766401	+	0.573720i
$304$	−2.19864	+	4.81434i	−0.126100	+	0.276121i
$305$	−4.14730	−	1.02613i	−0.237474	−	0.0587558i
$306$	−2.17524	+	7.40817i	−0.124350	+	0.423497i
$307$	−1.27353	+	5.85432i	−0.0726841	+	0.334123i	−0.999102	−	0.0423738i	$-0.986508\pi$
$307$	−1.27353	+	5.85432i	−0.0726841	+	0.334123i	0.926418	+	0.376497i	$0.122872\pi$
$308$	−1.86299	+	4.99488i	−0.106154	+	0.284610i
$309$	−17.5811	+	5.16228i	−1.00015	+	0.293672i
$310$	6.73418	−	20.7405i	0.382476	−	1.17798i
$311$	12.3051	−	14.2008i	0.697758	−	0.805256i	−0.290690	−	0.956817i	$-0.593885\pi$
$311$	12.3051	−	14.2008i	0.697758	−	0.805256i	0.988448	+	0.151562i	$0.0484302\pi$
$312$	−2.41058	+	4.41465i	−0.136472	+	0.249930i
$313$	9.08601	+	3.38891i	0.513572	+	0.191552i	0.592869	−	0.805299i	$-0.297995\pi$
$313$	9.08601	+	3.38891i	0.513572	+	0.191552i	−0.0792976	+	0.996851i	$0.525268\pi$
$314$	3.68843	−	2.37041i	0.208150	−	0.133770i
$315$	−8.48974	+	0.975919i	−0.478343	+	0.0549868i
$316$	7.50595	−	1.07919i	0.422243	−	0.0607093i
$317$	4.77226	+	12.7949i	0.268037	+	0.718634i	0.999331	+	0.0365721i	$0.0116439\pi$
$317$	4.77226	+	12.7949i	0.268037	+	0.718634i	−0.731294	+	0.682062i	$0.761083\pi$
$318$	1.70125	+	2.27260i	0.0954013	+	0.127441i
$319$	−6.97911	−	4.48520i	−0.390755	−	0.251123i
$320$	2.11639	−	0.721725i	0.118310	−	0.0403457i
$321$		−	3.58575i		−	0.200137i
$322$	−8.86956	−	16.0393i	−0.494281	−	0.893838i
$323$	−28.8952	−	28.8952i	−1.60777	−	1.60777i
$324$	0.755750	−	0.654861i	0.0419861	−	0.0363812i
$325$	13.2844	−	21.3547i	0.736885	−	1.18455i
$326$	−2.34374	+	16.3011i	−0.129808	+	0.902832i
$327$	−11.3218	+	4.22283i	−0.626099	+	0.233523i
$328$	−3.91415	+	5.22869i	−0.216123	+	0.288706i
$329$	36.8440	+	10.8184i	2.03128	+	0.596437i
$330$	0.576359	+	3.06542i	0.0317275	+	0.168746i
$331$	−6.46452	−	14.1553i	−0.355322	−	0.778047i	−0.999909	−	0.0135156i	$-0.995698\pi$
$331$	−6.46452	−	14.1553i	−0.355322	−	0.778047i	0.644586	−	0.764531i	$-0.277030\pi$
$332$	7.72731	+	4.21943i	0.424091	+	0.231571i
$333$	0.100469	+	1.40475i	0.00550569	+	0.0769796i
$334$	10.2747	+	8.90305i	0.562205	+	0.487153i
$335$	16.3703	+	20.0114i	0.894405	+	1.09334i
$336$	3.47637	−	1.58760i	0.189652	−	0.0866109i
$337$	9.37096	+	2.03853i	0.510469	+	0.111046i	0.460420	−	0.887701i	$-0.347699\pi$
$337$	9.37096	+	2.03853i	0.510469	+	0.111046i	0.0500486	+	0.998747i	$0.484062\pi$
$338$	−5.89476	−	10.7954i	−0.320633	−	0.587195i
$339$	1.16419	+	8.09712i	0.0632302	+	0.439775i
$340$	−0.489372	+	17.2576i	−0.0265399	+	0.935923i
$341$	−13.4649	−	1.93596i	−0.729167	−	0.104838i
$342$	1.12503	+	5.17167i	0.0608346	+	0.279652i
$343$	−2.30868	−	0.165120i	−0.124657	−	0.00891564i
$344$	−4.26195			−0.229789
$345$	−9.29130	−	5.35460i	−0.500227	−	0.288282i
$346$	11.9152			0.640565
$347$	4.10504	+	0.293598i	0.220370	+	0.0157612i	0.181087	−	0.983467i	$-0.442038\pi$
$347$	4.10504	+	0.293598i	0.220370	+	0.0157612i	0.0392823	+	0.999228i	$0.487493\pi$
$348$	1.26420	+	5.81145i	0.0677684	+	0.311526i
$349$	16.7696	+	2.41111i	0.897658	+	0.129064i	0.575672	−	0.817681i	$-0.304741\pi$
$349$	16.7696	+	2.41111i	0.897658	+	0.129064i	0.321986	+	0.946745i	$0.395650\pi$
$350$	−17.8038	+	6.94027i	−0.951651	+	0.370973i
$351$	0.715831	+	4.97871i	0.0382082	+	0.265744i
$352$	−0.668513	−	1.22429i	−0.0356318	−	0.0652549i
$353$	9.16815	+	1.99441i	0.487971	+	0.106152i	0.449818	−	0.893120i	$-0.351489\pi$
$353$	9.16815	+	1.99441i	0.487971	+	0.106152i	0.0381533	+	0.999272i	$0.487852\pi$
$354$	3.58641	−	1.63786i	0.190616	−	0.0870513i
$355$	−8.74066	−	0.874777i	−0.463906	−	0.0464283i
$356$	−0.673072	−	0.583220i	−0.0356727	−	0.0309106i
$357$	2.10503	+	29.4321i	0.111410	+	1.55771i
$358$	−2.34632	−	1.28119i	−0.124007	−	0.0677130i
$359$	9.75099	+	21.3517i	0.514638	+	1.12690i	0.971430	+	0.237326i	$0.0762710\pi$
$359$	9.75099	+	21.3517i	0.514638	+	1.12690i	−0.456792	+	0.889573i	$0.651002\pi$
$360$	1.26174	−	1.84608i	0.0664998	−	0.0972968i
$361$	−8.64684	−	2.53894i	−0.455097	−	0.133629i
$362$	9.61437	−	12.8433i	0.505320	−	0.675028i
$363$	−8.48334	+	3.16412i	−0.445260	+	0.166073i
$364$	−2.73571	+	19.0273i	−0.143390	+	0.997302i
$365$	2.98322	−	17.2600i	0.156149	−	0.903431i
$366$	1.44398	−	1.25121i	0.0754780	−	0.0654020i
$367$	6.63213	+	6.63213i	0.346194	+	0.346194i	0.858690	−	0.512496i	$-0.171279\pi$
$367$	6.63213	+	6.63213i	0.346194	+	0.346194i	−0.512496	+	0.858690i	$0.671279\pi$
$368$	4.69160	+	0.994411i	0.244567	+	0.0518372i
$369$			6.53144i			0.340013i
$370$	1.01643	+	2.98059i	0.0528417	+	0.154953i
$371$	9.12698	+	5.86555i	0.473849	+	0.304524i
$372$	5.84422	+	7.80697i	0.303009	+	0.404773i
$373$	2.57103	+	6.89321i	0.133123	+	0.356917i	0.986359	−	0.164608i	$-0.0526360\pi$
$373$	2.57103	+	6.89321i	0.133123	+	0.356917i	−0.853236	+	0.521525i	$0.825363\pi$
$374$	10.6604	−	1.53274i	0.551238	−	0.0792560i
$375$	−6.82166	+	8.85805i	−0.352269	+	0.457428i
$376$	−8.45264	+	5.43218i	−0.435911	+	0.280143i
$377$	−28.0286	−	10.4541i	−1.44354	−	0.538414i
$378$	1.83156	−	3.35425i	0.0942053	−	0.172524i
$379$	−1.91720	+	2.21257i	−0.0984800	+	0.113652i	−0.802850	−	0.596181i	$-0.796684\pi$
$379$	−1.91720	+	2.21257i	−0.0984800	+	0.113652i	0.704370	+	0.709833i	$0.251230\pi$
$380$	5.37505	+	10.5436i	0.275734	+	0.540877i
$381$	4.79192	−	1.40703i	0.245497	−	0.0720845i
$382$	−0.560204	+	1.50196i	−0.0286625	+	0.0768472i
$383$	2.75654	−	12.6716i	0.140852	−	0.647488i	−0.851531	−	0.524304i	$-0.824326\pi$
$383$	2.75654	−	12.6716i	0.140852	−	0.647488i	0.992384	−	0.123184i	$-0.0393107\pi$
$384$	−0.281733	+	0.959493i	−0.0143771	+	0.0489639i
$385$	6.15785	+	10.2068i	0.313833	+	0.520186i
$386$	6.59485	−	14.4407i	0.335669	−	0.735013i
$387$	−3.41187	+	2.55409i	−0.173435	+	0.129832i
$388$	−4.78894	+	1.04177i	−0.243122	+	0.0528879i
$389$	−12.1918	−	14.0701i	−0.618148	−	0.713381i	0.357206	−	0.934026i	$-0.383729\pi$
$389$	−12.1918	−	14.0701i	−0.618148	−	0.713381i	−0.975354	+	0.220645i	$0.929184\pi$
$390$	4.38039	+	10.3592i	0.221810	+	0.524556i
$391$	−19.8525	+	31.2565i	−1.00398	+	1.58071i
$392$	5.37800	−	5.37800i	0.271630	−	0.271630i
$393$	0.669963	−	9.36731i	0.0337952	−	0.472518i
$394$	−2.70661	+	4.21157i	−0.136357	+	0.212176i
$395$	8.54492	−	14.6460i	0.429942	−	0.736918i
$396$	−1.26886	−	0.579470i	−0.0637627	−	0.0291194i
$397$	5.79943	+	4.34140i	0.291065	+	0.217889i	0.734824	−	0.678257i	$-0.237265\pi$
$397$	5.79943	+	4.34140i	0.291065	+	0.217889i	−0.443759	+	0.896146i	$0.646356\pi$
$398$	−11.6213	+	6.34573i	−0.582525	+	0.318083i
$399$	10.9355	+	17.0160i	0.547462	+	0.851867i
$400$	1.67826	−	4.70993i	0.0839132	−	0.235496i
$401$	−3.07335	−	10.4669i	−0.153476	−	0.522690i	0.846477	−	0.532425i	$-0.178719\pi$
$401$	−3.07335	−	10.4669i	−0.153476	−	0.522690i	−0.999953	+	0.00973520i	$0.996901\pi$
$402$	−11.5329	+	0.824851i	−0.575210	+	0.0411398i
$403$	−48.9273	+	3.49935i	−2.43724	+	0.174315i
$404$	−4.69495	−	15.9895i	−0.233582	−	0.795508i
$405$	−0.0962341	−	2.23400i	−0.00478191	−	0.111008i
$406$	12.2883	+	19.1210i	0.609860	+	0.948961i
$407$	1.72421	−	0.941489i	0.0854658	−	0.0466679i
$408$	−6.18092	−	4.62698i	−0.306001	−	0.229070i
$409$	32.8264	+	14.9913i	1.62316	+	0.741272i	0.999193	−	0.0401786i	$-0.0127927\pi$
$409$	32.8264	+	14.9913i	1.62316	+	0.741272i	0.623967	+	0.781451i	$0.285520\pi$
$410$	3.71577	+	14.1241i	0.183509	+	0.697542i
$411$	1.30297	−	2.02746i	0.0642709	−	0.100007i
$412$	1.30717	−	18.2766i	0.0643997	−	0.900426i
$413$	10.6547	−	10.6547i	0.524282	−	0.524282i
$414$	4.35175	−	2.01551i	0.213877	−	0.0990567i
$415$	18.1325	−	7.66735i	0.890088	−	0.376375i
$416$	−3.29389	−	3.80135i	−0.161496	−	0.186377i
$417$	−10.1661	+	2.21150i	−0.497836	+	0.108297i
$418$	5.91022	−	4.42433i	0.289078	−	0.216401i
$419$	−6.92937	+	15.1732i	−0.338522	+	0.741259i	−0.999962	−	0.00873890i	$-0.997218\pi$
$419$	−6.92937	+	15.1732i	−0.338522	+	0.741259i	0.661440	+	0.749998i	$0.269946\pi$
$420$	2.05247	−	8.29551i	0.100151	−	0.404780i
$421$	10.3965	−	35.4072i	0.506694	−	1.72564i	−0.166377	−	0.986062i	$-0.553207\pi$
$421$	10.3965	−	35.4072i	0.506694	−	1.72564i	0.673071	−	0.739578i	$-0.264975\pi$
$422$	1.35743	−	6.24000i	0.0660786	−	0.303758i
$423$	−3.51130	+	9.41416i	−0.170725	+	0.457732i
$424$	−2.72384	+	0.799792i	−0.132281	+	0.0388413i
$425$	29.5439	+	24.8490i	1.43309	+	1.20535i
$426$	2.57260	−	2.96894i	0.124643	−	0.143846i
$427$	3.49949	−	6.40883i	0.169352	−	0.310145i
$428$	3.35966	+	1.25309i	0.162395	+	0.0605704i
$429$	5.90249	−	3.79330i	0.284975	−	0.183142i
$430$	−5.92508	+	7.46422i	−0.285733	+	0.359957i
$431$	−19.0513	+	2.73916i	−0.917667	+	0.131941i	−0.584934	−	0.811081i	$-0.698880\pi$
$431$	−19.0513	+	2.73916i	−0.917667	+	0.131941i	−0.332733	+	0.943021i	$0.607971\pi$
$432$	0.349464	+	0.936950i	0.0168136	+	0.0450790i
$433$	−6.34554	−	8.47665i	−0.304947	−	0.407362i	0.621723	−	0.783237i	$-0.286433\pi$
$433$	−6.34554	−	8.47665i	−0.304947	−	0.407362i	−0.926670	+	0.375875i	$0.877342\pi$
$434$	31.3535	+	20.1497i	1.50502	+	0.967215i
$435$	11.9355	+	5.86516i	0.572262	+	0.281213i
$436$		−	12.0837i		−	0.578706i
$437$	−1.67567	+	25.3272i	−0.0801581	+	1.21156i
$438$	5.53903	+	5.53903i	0.264665	+	0.264665i
$439$	−15.0857	+	13.0718i	−0.720002	+	0.623885i	−0.935791	−	0.352555i	$-0.885313\pi$
$439$	−15.0857	+	13.0718i	−0.720002	+	0.623885i	0.215789	+	0.976440i	$0.430768\pi$
$440$	−3.07356	−	0.531234i	−0.146526	−	0.0253256i
$441$	1.08239	−	7.52822i	0.0515426	−	0.358487i
$442$	36.3870	−	13.5716i	1.73075	−	0.645537i
$443$	−2.64784	+	3.53709i	−0.125802	+	0.168052i	−0.859020	−	0.511941i	$-0.828927\pi$
$443$	−2.64784	+	3.53709i	−0.125802	+	0.168052i	0.733218	+	0.679994i	$0.238017\pi$
$444$	−1.35129	−	0.396773i	−0.0641292	−	0.0188300i
$445$	−1.95715	+	0.367984i	−0.0927779	+	0.0174441i
$446$	−10.5384	−	23.0759i	−0.499007	−	1.09267i
$447$	13.1118	+	7.15959i	0.620168	+	0.338637i
$448$	0.272639	+	3.81199i	0.0128810	+	0.180100i
$449$	−18.6300	−	16.1430i	−0.879206	−	0.761837i	0.0930729	−	0.995659i	$-0.470331\pi$
$449$	−18.6300	−	16.1430i	−0.879206	−	0.761837i	−0.972279	+	0.233823i	$0.924877\pi$
$450$	−1.47904	−	4.77624i	−0.0697224	−	0.225154i
$451$	8.28749	−	3.78477i	0.390243	−	0.178218i
$452$	−7.99344	−	1.73887i	−0.375980	−	0.0817894i
$453$	−8.75146	−	16.0271i	−0.411179	−	0.753019i
$454$	−2.57872	−	17.9354i	−0.121025	−	0.841748i
$455$	29.5204	+	31.2435i	1.38394	+	1.46472i
$456$	−5.23875	−	0.753219i	−0.245327	−	0.0352727i
$457$	−1.00485	−	4.61921i	−0.0470048	−	0.216078i	0.947653	−	0.319301i	$-0.103448\pi$
$457$	−1.00485	−	4.61921i	−0.0470048	−	0.216078i	−0.994658	+	0.103223i	$0.967084\pi$
$458$	−0.365346	−	0.0261300i	−0.0170715	−	0.00122098i
$459$	−7.72092			−0.360382
$460$	8.26397	−	6.83424i	0.385310	−	0.318648i
$461$	−12.8598			−0.598939			−0.299469	−	0.954106i	$-0.596810\pi$
$461$	−12.8598			−0.598939			−0.299469	+	0.954106i	$0.596810\pi$
$462$	−5.31742	−	0.380309i	−0.247389	−	0.0176936i
$463$	4.81774	+	22.1468i	0.223899	+	1.02925i	0.942599	+	0.333927i	$0.108374\pi$
$463$	4.81774	+	22.1468i	0.223899	+	1.02925i	−0.718700	+	0.695321i	$0.755262\pi$
$464$	−5.88683	−	0.846398i	−0.273289	−	0.0392930i
$465$	21.7976	+	0.618114i	1.01084	+	0.0286644i
$466$	3.08177	+	21.4342i	0.142760	+	0.992919i
$467$	−19.3978	−	35.5244i	−0.897622	−	1.64387i	−0.756613	−	0.653863i	$-0.773147\pi$
$467$	−19.3978	−	35.5244i	−0.897622	−	1.64387i	−0.141009	−	0.990008i	$-0.545035\pi$
$468$	−4.91496	−	1.06918i	−0.227194	−	0.0494231i
$469$	−40.1951	+	18.3565i	−1.85604	+	0.847624i
$470$	−2.23738	+	22.3556i	−0.103202	+	1.03119i
$471$	3.31354	+	2.87120i	0.152680	+	0.132298i
$472$	0.281270	+	3.93266i	0.0129465	+	0.181015i
$473$	5.21786	+	2.84917i	0.239918	+	0.131005i
$474$	3.15015	+	6.89786i	0.144691	+	0.316829i
$475$	25.9383	+	5.24440i	1.19013	+	0.240630i
$476$	−28.3120	−	8.31317i	−1.29768	−	0.381033i
$477$	−1.70125	+	2.27260i	−0.0778949	+	0.104055i
$478$	−13.6354	+	5.08574i	−0.623668	+	0.232616i
$479$	0.331832	−	2.30795i	0.0151618	−	0.105453i	−0.980835	−	0.194839i	$-0.937582\pi$
$479$	0.331832	−	2.30795i	0.0151618	−	0.105453i	0.995997	+	0.0893864i	$0.0284906\pi$
$480$	1.28875	+	1.82733i	0.0588230	+	0.0834058i
$481$	5.35357	−	4.63890i	0.244102	−	0.211515i
$482$	16.0407	+	16.0407i	0.730633	+	0.730633i
$483$	12.8908	−	13.0291i	0.586551	−	0.592844i
$484$		−	9.05421i		−	0.411555i
$485$	−4.83320	+	9.83547i	−0.219464	+	0.446605i
$486$	0.841254	+	0.540641i	0.0381600	+	0.0245240i
$487$	−9.54385	−	12.7491i	−0.432473	−	0.577717i	0.530374	−	0.847764i	$-0.322052\pi$
$487$	−9.54385	−	12.7491i	−0.432473	−	0.577717i	−0.962847	+	0.270047i	$0.912961\pi$
$488$	0.667706	+	1.79019i	0.0302256	+	0.0810381i
$489$	−16.3011	+	2.34374i	−0.737159	+	0.105988i
$490$	−1.94218	−	16.8955i	−0.0877386	−	0.763259i
$491$	−31.8873	+	20.4927i	−1.43905	+	0.924823i	−0.439405	+	0.898289i	$0.644811\pi$
$491$	−31.8873	+	20.4927i	−1.43905	+	0.924823i	−0.999648	+	0.0265345i	$0.991553\pi$
$492$	−6.11963	−	2.28250i	−0.275894	−	0.102903i
$493$	22.0067	−	40.3023i	0.991132	−	1.81512i
$494$	17.4333	−	20.1191i	0.784363	−	0.905203i
$495$	−2.77887	+	1.41664i	−0.124901	+	0.0636733i
$496$	−9.35709	+	2.74749i	−0.420146	+	0.123366i
$497$	5.24670	−	14.0670i	0.235347	−	0.630989i
$498$	−1.87148	+	8.60305i	−0.0838630	+	0.385512i
$499$	1.34884	−	4.59374i	0.0603826	−	0.205644i	−0.923776	−	0.382932i	$-0.874914\pi$
$499$	1.34884	−	4.59374i	0.0603826	−	0.205644i	0.984159	+	0.177288i	$0.0567324\pi$
$500$	−5.91562	−	9.48712i	−0.264555	−	0.424277i
$501$	−5.64771	+	12.3668i	−0.252321	+	0.552506i
$502$	16.6086	−	12.4330i	0.741277	−	0.554913i
$503$	9.99707	−	2.17473i	0.445748	−	0.0969664i	0.0159115	−	0.999873i	$-0.494935\pi$
$503$	9.99707	−	2.17473i	0.445748	−	0.0969664i	0.429836	+	0.902907i	$0.358571\pi$
$504$	2.50270	+	2.88827i	0.111479	+	0.128654i
$505$	−34.5305	−	14.0065i	−1.53659	−	0.623282i
$506$	−5.07911	−	4.35384i	−0.225794	−	0.193552i
$507$	8.69741	−	8.69741i	0.386265	−	0.386265i
$508$	−0.356283	+	4.98149i	−0.0158075	+	0.221018i
$509$	−15.0692	+	23.4482i	−0.667932	+	1.03932i	0.327593	+	0.944819i	$0.393763\pi$
$509$	−15.0692	+	23.4482i	−0.667932	+	1.03932i	−0.995525	+	0.0945033i	$0.969874\pi$
$510$	−16.6964	+	4.39247i	−0.739329	+	0.194502i
$511$	27.2317	+	12.4363i	1.20466	+	0.550149i
$512$	−0.800541	−	0.599278i	−0.0353793	−	0.0264846i
$513$	−4.64523	+	2.53649i	−0.205092	+	0.111989i
$514$	0.476823	+	0.741951i	0.0210318	+	0.0327261i
$515$	−30.1917	−	27.6980i	−1.33041	−	1.22052i
$516$	−1.20073	−	4.08931i	−0.0528592	−	0.180022i
$517$	13.9800	−	0.999866i	0.614838	−	0.0439741i
$518$	−5.36856	+	0.383967i	−0.235881	+	0.0168705i
$519$	3.35690	+	11.4326i	0.147352	+	0.501833i
$520$	−11.2368	+	0.484049i	−0.492766	+	0.0212269i
$521$	5.91309	+	9.20095i	0.259057	+	0.403101i	0.946281	−	0.323345i	$-0.104807\pi$
$521$	5.91309	+	9.20095i	0.259057	+	0.403101i	−0.687224	+	0.726446i	$0.741171\pi$
$522$	−5.21987	+	2.85027i	−0.228468	+	0.124753i
$523$	−5.42156	−	4.05853i	−0.237068	−	0.177467i	0.474138	−	0.880451i	$-0.342760\pi$
$523$	−5.42156	−	4.05853i	−0.237068	−	0.177467i	−0.711206	+	0.702983i	$0.751851\pi$
$524$	8.54257	+	3.90126i	0.373184	+	0.170427i
$525$	−11.6750	−	15.1273i	−0.509540	−	0.660208i
$526$	11.0899	−	17.2561i	0.483540	−	0.752404i
$527$	5.37151	−	75.1035i	0.233987	−	3.27156i
$528$	0.986355	−	0.986355i	0.0429256	−	0.0429256i
$529$	22.7297	−	3.51597i	0.988247	−	0.152868i
$530$	−2.38603	+	5.88232i	−0.103643	+	0.255512i
$531$	2.58192	+	2.97970i	0.112046	+	0.129308i
$532$	−19.7647	+	4.29956i	−0.856910	+	0.186409i
$533$	26.2998	−	19.6878i	1.13917	−	0.852773i
$534$	0.369969	−	0.810120i	0.0160101	−	0.0350573i
$535$	6.86531	−	4.14191i	0.296813	−	0.179070i
$536$	3.25750	−	11.0940i	0.140703	−	0.479189i
$537$	0.568257	−	2.61223i	0.0245221	−	0.112726i
$538$	7.07247	−	18.9620i	0.304916	−	0.817511i
$539$	−10.1795	+	2.98897i	−0.438461	+	0.128744i
$540$	2.12677	+	0.690535i	0.0915217	+	0.0297159i
$541$	18.6433	−	21.5155i	0.801538	−	0.925024i	−0.196927	−	0.980418i	$-0.563096\pi$
$541$	18.6433	−	21.5155i	0.801538	−	0.925024i	0.998465	+	0.0553944i	$0.0176416\pi$
$542$	0.834783	−	1.52879i	0.0358570	−	0.0656672i
$543$	15.0317	+	5.60655i	0.645073	+	0.240600i
$544$	6.49525	−	4.17425i	0.278482	−	0.178969i
$545$	−21.1630	−	16.7991i	−0.906522	−	0.719596i
$546$	−19.0273	+	2.73571i	−0.814293	+	0.117078i
$547$	−8.33951	−	22.3591i	−0.356572	−	0.956006i	−0.984132	−	0.177438i	$-0.943219\pi$
$547$	−8.33951	−	22.3591i	−0.356572	−	0.956006i	0.627560	−	0.778568i	$-0.284054\pi$
$548$	1.44429	+	1.92935i	0.0616970	+	0.0824176i
$549$	1.60735	+	1.03298i	0.0685999	+	0.0440865i
$550$	−5.20333	+	4.64438i	−0.221871	+	0.198037i
$551$		−	31.4772i		−	1.34097i
$552$	0.367647	+	4.78172i	0.0156481	+	0.203523i
$553$	20.4925	+	20.4925i	0.871428	+	0.871428i
$554$	−20.1881	+	17.4931i	−0.857712	+	0.743212i
$555$	−2.57349	+	1.81499i	−0.109239	+	0.0770418i
$556$	1.48062	−	10.2980i	0.0627924	−	0.436731i
$557$	15.8337	−	5.90566i	0.670894	−	0.250231i	0.00914772	−	0.999958i	$-0.497088\pi$
$557$	15.8337	−	5.90566i	0.670894	−	0.250231i	0.661747	+	0.749727i	$0.269815\pi$
$558$	−5.84422	+	7.80697i	−0.247406	+	0.330495i
$559$	20.5689	+	6.03956i	0.869970	+	0.255446i
$560$	7.05521	+	4.82205i	0.298137	+	0.203769i
$561$	4.47404	+	9.79678i	0.188894	+	0.413620i
$562$	−26.1353	−	14.2709i	−1.10245	−	0.601983i
$563$	1.49737	+	20.9360i	0.0631068	+	0.882348i	0.926135	+	0.377192i	$0.123110\pi$
$563$	1.49737	+	20.9360i	0.0631068	+	0.882348i	−0.863028	+	0.505156i	$0.831435\pi$
$564$	−7.59352	−	6.57982i	−0.319745	−	0.277061i
$565$	−14.1581	+	11.5820i	−0.595635	+	0.487258i
$566$	−11.9702	+	5.46663i	−0.503147	+	0.229779i
$567$	3.73439	+	0.812368i	0.156830	+	0.0341162i
$568$	1.88272	+	3.44794i	0.0789970	+	0.144672i
$569$	1.18212	+	8.22183i	0.0495571	+	0.344677i	0.999482	+	0.0321973i	$0.0102505\pi$
$569$	1.18212	+	8.22183i	0.0495571	+	0.344677i	−0.949924	+	0.312480i	$0.898840\pi$
$570$	−8.60222	+	8.12781i	−0.360307	+	0.340436i
$571$	−1.91743	−	0.275685i	−0.0802420	−	0.0115371i	0.102077	−	0.994777i	$-0.467451\pi$
$571$	−1.91743	−	0.275685i	−0.0802420	−	0.0115371i	−0.182319	+	0.983239i	$0.558360\pi$
$572$	1.49142	+	6.85596i	0.0623596	+	0.286662i
$573$	−1.59895	−	0.114359i	−0.0667972	−	0.00477743i
$574$	−24.9614			−1.04187
$575$	−0.480423	−	23.9743i	−0.0200350	−	0.999799i
$576$	−1.00000			−0.0416667
$577$	−6.39062	−	0.457066i	−0.266045	−	0.0190279i	−0.0623206	−	0.998056i	$-0.519850\pi$
$577$	−6.39062	−	0.457066i	−0.266045	−	0.0190279i	−0.203724	+	0.979028i	$0.565305\pi$
$578$	9.05797	+	41.6388i	0.376762	+	1.73195i
$579$	15.7137	+	2.25930i	0.653041	+	0.0938931i
$580$	−9.66638	+	9.13328i	−0.401374	+	0.379239i
$581$	4.78854	+	33.3050i	0.198662	+	1.38173i
$582$	−2.34877	−	4.30145i	−0.0973597	−	0.178301i
$583$	3.86944	+	0.841745i	0.160256	+	0.0348615i
$584$	−7.12548	+	3.25410i	−0.294855	+	0.134656i
$585$	−8.70544	+	7.12146i	−0.359926	+	0.294436i
$586$	−1.57173	−	1.36191i	−0.0649277	−	0.0562602i
$587$	2.26704	+	31.6974i	0.0935709	+	1.30829i	0.799782	+	0.600291i	$0.204949\pi$
$587$	2.26704	+	31.6974i	0.0935709	+	1.30829i	−0.706211	+	0.708002i	$0.749597\pi$
$588$	6.67531	+	3.64499i	0.275285	+	0.150317i
$589$	−21.4414	−	46.9500i	−0.883476	−	1.93454i
$590$	7.27854	+	4.97469i	0.299653	+	0.204805i
$591$	−4.80351	−	1.41044i	−0.197590	−	0.0580177i
$592$	0.843983	−	1.12743i	0.0346875	−	0.0463371i
$593$	−44.5759	+	16.6259i	−1.83051	+	0.682745i	−0.840490	+	0.541827i	$0.817733\pi$
$593$	−44.5759	+	16.6259i	−1.83051	+	0.682745i	−0.990021	+	0.140918i	$0.954995\pi$
$594$	0.198517	−	1.38072i	0.00814527	−	0.0566516i
$595$	−53.9196	+	38.0274i	−2.21049	+	1.55897i
$596$	−11.2903	+	9.78309i	−0.462468	+	0.400731i
$597$	−9.36280	−	9.36280i	−0.383194	−	0.383194i
$598$	−21.2333	−	11.4476i	−0.868293	−	0.468128i
$599$		−	2.85376i		−	0.116601i	−0.998299	−	0.0583007i	$-0.981432\pi$
$599$		−	2.85376i		−	0.116601i	0.998299	−	0.0583007i	$-0.0185682\pi$
$600$	4.99197	+	0.283342i	0.203796	+	0.0115674i
$601$	−31.1743	−	20.0345i	−1.27163	−	0.817225i	−0.281796	−	0.959474i	$-0.590930\pi$
$601$	−31.1743	−	20.0345i	−1.27163	−	0.817225i	−0.989831	+	0.142250i	$0.954566\pi$
$602$	−9.76105	−	13.0392i	−0.397831	−	0.531440i
$603$	−4.04064	−	10.8334i	−0.164548	−	0.441169i
$604$	18.0749	−	2.59878i	0.735457	−	0.105743i
$605$	−15.8572	−	12.5874i	−0.644686	−	0.511751i
$606$	14.0191	−	9.00953i	0.569487	−	0.365987i
$607$	−21.1461	−	7.88709i	−0.858294	−	0.320127i	−0.118494	−	0.992955i	$-0.537807\pi$
$607$	−21.1461	−	7.88709i	−0.858294	−	0.320127i	−0.739799	+	0.672828i	$0.765080\pi$
$608$	2.53649	−	4.64523i	0.102868	−	0.188389i
$609$	−14.8845	+	17.1776i	−0.603149	+	0.696072i
$610$	4.06353	+	1.31938i	0.164528	+	0.0534200i
$611$	48.4917	−	14.2384i	1.96176	−	0.576026i
$612$	2.69819	−	7.23412i	0.109068	−	0.292422i
$613$	5.85724	−	26.9253i	0.236572	−	1.08750i	−0.693595	−	0.720365i	$-0.743974\pi$
$613$	5.85724	−	26.9253i	0.236572	−	1.08750i	0.930167	−	0.367137i	$-0.119662\pi$
$614$	1.68793	−	5.74855i	0.0681191	−	0.231992i
$615$	−12.5052	+	7.54448i	−0.504257	+	0.304223i
$616$	2.21458	−	4.84925i	0.0892279	−	0.195382i
$617$	18.1044	−	13.5528i	0.728858	−	0.545616i	−0.169153	−	0.985590i	$-0.554103\pi$
$617$	18.1044	−	13.5528i	0.728858	−	0.545616i	0.898011	+	0.439974i	$0.145012\pi$
$618$	17.9046	−	3.89490i	0.720228	−	0.156676i
$619$	3.75792	+	4.33687i	0.151044	+	0.174314i	0.826229	−	0.563335i	$-0.190482\pi$
$619$	3.75792	+	4.33687i	0.151044	+	0.174314i	−0.675185	+	0.737648i	$0.735936\pi$
$620$	−8.19663	+	20.2073i	−0.329185	+	0.811544i
$621$	3.15989	+	3.60764i	0.126802	+	0.144770i
$622$	−13.2868	+	13.2868i	−0.532753	+	0.532753i
$623$	0.242813	−	3.39497i	0.00972810	−	0.136017i
$624$	2.71937	−	4.23143i	0.108862	−	0.169393i
$625$	−24.8394	−	2.82886i	−0.993577	−	0.113155i
$626$	−8.82110	−	4.02846i	−0.352562	−	0.161010i
$627$	5.91022	+	4.42433i	0.236031	+	0.176691i
$628$	−3.84814	+	2.10124i	−0.153557	+	0.0838487i
$629$	5.87873	+	9.14749i	0.234400	+	0.364734i
$630$	8.53773	−	0.367781i	0.340151	−	0.0146527i
$631$	6.51467	+	22.1869i	0.259345	+	0.883248i	0.981491	+	0.191507i	$0.0613375\pi$
$631$	6.51467	+	22.1869i	0.259345	+	0.883248i	−0.722146	+	0.691740i	$0.756844\pi$
$632$	−7.56381	+	0.540975i	−0.300872	+	0.0215188i
$633$	6.36966	−	0.455567i	0.253171	−	0.0181072i
$634$	−3.84732	−	13.1028i	−0.152797	−	0.520377i
$635$	8.22908	+	7.54939i	0.326561	+	0.299588i
$636$	−1.53479	−	2.38818i	−0.0608583	−	0.0946974i
$637$	−33.5762	+	18.3340i	−1.33034	+	0.726419i
$638$	6.64135	+	4.97165i	0.262934	+	0.196830i
$639$	3.57346	+	1.63195i	0.141364	+	0.0645588i
$640$	−2.16249	+	0.568905i	−0.0854798	+	0.0224879i
$641$	6.27206	−	9.75951i	0.247731	−	0.385477i	−0.695011	−	0.718999i	$-0.744601\pi$
$641$	6.27206	−	9.75951i	0.247731	−	0.385477i	0.942742	+	0.333521i	$0.108237\pi$
$642$	−0.255804	+	3.57661i	−0.0100958	+	0.141158i
$643$	−4.24802	+	4.24802i	−0.167526	+	0.167526i	−0.785891	−	0.618365i	$-0.787795\pi$
$643$	−4.24802	+	4.24802i	−0.167526	+	0.167526i	0.618365	+	0.785891i	$0.287795\pi$
$644$	7.70273	+	16.6312i	0.303530	+	0.655362i
$645$	−8.83115	−	3.58216i	−0.347726	−	0.141047i
$646$	26.7602	+	30.8829i	1.05287	+	1.21507i
$647$	−16.4665	+	3.58206i	−0.647364	+	0.140825i	−0.524246	−	0.851567i	$-0.675653\pi$
$647$	−16.4665	+	3.58206i	−0.647364	+	0.140825i	−0.123118	+	0.992392i	$0.539289\pi$
$648$	−0.800541	+	0.599278i	−0.0314482	+	0.0235419i
$649$	2.28468	−	5.00275i	0.0896815	−	0.196375i
$650$	−14.7740	+	20.3526i	−0.579482	+	0.798296i
$651$	−10.5002	+	35.7603i	−0.411534	+	1.40156i
$652$	3.50067	−	16.0923i	0.137097	−	0.630224i
$653$	−2.77851	+	7.44947i	−0.108731	+	0.291520i	−0.979908	−	0.199449i	$-0.936085\pi$
$653$	−2.77851	+	7.44947i	−0.108731	+	0.291520i	0.871177	+	0.490970i	$0.163357\pi$
$654$	11.5943	−	3.40438i	0.453371	−	0.133122i
$655$	18.7086	−	9.53749i	0.731007	−	0.372660i
$656$	4.27718	−	4.93613i	0.166996	−	0.192724i
$657$	−3.75413	+	6.87518i	−0.146463	+	0.268226i
$658$	−35.9784	−	13.4192i	−1.40258	−	0.523137i
$659$	1.93175	−	1.24146i	0.0752505	−	0.0483605i	−0.502475	−	0.864592i	$-0.667577\pi$
$659$	1.93175	−	1.24146i	0.0752505	−	0.0483605i	0.577725	+	0.816231i	$0.303941\pi$
$660$	−0.356207	−	3.09872i	−0.0138653	−	0.120618i
$661$	−5.92726	+	0.852211i	−0.230544	+	0.0331472i	−0.256618	−	0.966513i	$-0.582608\pi$
$661$	−5.92726	+	0.852211i	−0.230544	+	0.0331472i	0.0260746	+	0.999660i	$0.491699\pi$
$662$	5.43822	+	14.5804i	0.211362	+	0.566685i
$663$	23.2733	+	31.0895i	0.903859	+	1.20741i
$664$	−7.40661	−	4.75994i	−0.287432	−	0.184721i
$665$	−19.9474	+	40.5926i	−0.773528	+	1.57411i
$666$		−	1.40833i		−	0.0545718i
$667$	−27.8380	+	6.21151i	−1.07789	+	0.240511i
$668$	−9.61336	−	9.61336i	−0.371952	−	0.371952i
$669$	19.1721	−	16.6127i	0.741237	−	0.642285i
$670$	−14.9010	−	21.1283i	−0.575675	−	0.816257i
$671$	0.379299	−	2.63808i	0.0146427	−	0.101842i
$672$	−3.58077	+	1.33556i	−0.138131	+	0.0515203i
$673$	−26.7091	+	35.6792i	−1.02956	+	1.37533i	−0.104926	+	0.994480i	$0.533460\pi$
$673$	−26.7091	+	35.6792i	−1.02956	+	1.37533i	−0.924636	+	0.380853i	$0.875630\pi$
$674$	−9.20166	−	2.70185i	−0.354435	−	0.104071i
$675$	4.16607	−	2.76475i	0.160352	−	0.106415i
$676$	5.10960	+	11.1885i	0.196523	+	0.430326i
$677$	23.7938	+	12.9924i	0.914468	+	0.499337i	0.866313	−	0.499502i	$-0.166484\pi$
$677$	23.7938	+	12.9924i	0.914468	+	0.499337i	0.0481557	+	0.998840i	$0.484666\pi$
$678$	−0.583582	−	8.15955i	−0.0224123	−	0.313365i
$679$	−14.1553	−	12.2656i	−0.543229	−	0.470711i
$680$	1.71927	−	17.1787i	0.0659309	−	0.658773i
$681$	16.4823	−	7.52723i	0.631605	−	0.288444i
$682$	13.2925	+	2.89161i	0.508997	+	0.110725i
$683$	−8.68739	−	15.9098i	−0.332414	−	0.608770i	0.657000	−	0.753890i	$-0.271825\pi$
$683$	−8.68739	−	15.9098i	−0.332414	−	0.608770i	−0.989414	+	0.145120i	$0.953643\pi$
$684$	−0.753219	−	5.23875i	−0.0288001	−	0.200309i
$685$	5.38687	+	0.152755i	0.205822	+	0.00583648i
$686$	2.29102	+	0.329398i	0.0874714	+	0.0125765i
$687$	−0.0778582	−	0.357908i	−0.00297047	−	0.0136550i
$688$	4.25109	+	0.304044i	0.162071	+	0.0115916i
$689$	14.2791			0.543989
$690$	8.88563	+	6.00379i	0.338270	+	0.228561i
$691$	34.8359			1.32522			0.662609	−	0.748965i	$-0.269449\pi$
$691$	34.8359			1.32522			0.662609	+	0.748965i	$0.269449\pi$
$692$	−11.8848	−	0.850021i	−0.451794	−	0.0323129i
$693$	−1.13319	−	5.20917i	−0.0430462	−	0.197880i
$694$	−4.07363	−	0.585700i	−0.154633	−	0.0222329i
$695$	−15.9770	−	16.9096i	−0.606044	−	0.641418i
$696$	−0.846398	−	5.88683i	−0.0320826	−	0.223140i
$697$	24.1679	+	44.2602i	0.915425	+	1.67648i
$698$	−16.5549	−	3.60130i	−0.626612	−	0.136311i
$699$	−19.6977	+	8.99564i	−0.745036	+	0.340246i
$700$	18.2535	−	5.65248i	0.689918	−	0.213644i
$701$	−14.5710	−	12.6258i	−0.550337	−	0.476870i	0.334742	−	0.942310i	$-0.391351\pi$
$701$	−14.5710	−	12.6258i	−0.550337	−	0.476870i	−0.885080	+	0.465440i	$0.845896\pi$
$702$	−0.358830	−	5.01709i	−0.0135432	−	0.189358i
$703$	6.54203	+	3.57222i	0.246737	+	0.134729i
$704$	0.579470	+	1.26886i	0.0218396	+	0.0478220i
$705$	−22.0804	+	4.15155i	−0.831595	+	0.156356i
$706$	−9.00251	−	2.64338i	−0.338814	−	0.0994847i
$707$	38.1665	−	50.9844i	1.43540	−	1.91747i
$708$	−3.69412	+	1.37784i	−0.138833	+	0.0517822i
$709$	3.17038	−	22.0505i	0.119066	−	0.828123i	−0.839522	−	0.543326i	$-0.817165\pi$
$709$	3.17038	−	22.0505i	0.119066	−	0.828123i	0.958588	−	0.284797i	$-0.0919262\pi$
$710$	8.65599	+	1.49610i	0.324853	+	0.0561476i
$711$	−5.73095	+	4.96590i	−0.214927	+	0.186236i
$712$	0.629751	+	0.629751i	0.0236009	+	0.0236009i
$713$	−37.2908	+	28.2273i	−1.39655	+	1.05712i
$714$		−	29.5073i		−	1.10428i
$715$	14.0807	+	6.91933i	0.526588	+	0.258768i
$716$	2.24895	+	1.44531i	0.0840471	+	0.0540138i
$717$	−8.72126	−	11.6502i	−0.325701	−	0.435086i
$718$	−8.20294	−	21.9929i	−0.306131	−	0.820769i
$719$	−19.5296	+	2.80793i	−0.728331	+	0.104718i	−0.496499	−	0.868038i	$-0.665381\pi$
$719$	−19.5296	+	2.80793i	−0.728331	+	0.104718i	−0.231832	+	0.972756i	$0.574472\pi$
$720$	−1.39023	+	1.75136i	−0.0518107	+	0.0652694i
$721$	58.9103	−	37.8594i	2.19394	−	1.40996i
$722$	8.44369	+	3.14933i	0.314241	+	0.117206i
$723$	−10.8717	+	19.9101i	−0.404324	+	0.740465i
$724$	−10.5061	+	12.1247i	−0.390456	+	0.450610i
$725$	2.55721	+	29.6267i	0.0949723	+	1.10031i
$726$	8.68745	−	2.55086i	0.322421	−	0.0946715i
$727$	8.34024	−	22.3610i	0.309322	−	0.829325i	−0.685535	−	0.728040i	$-0.740432\pi$
$727$	8.34024	−	22.3610i	0.309322	−	0.829325i	0.994857	−	0.101286i	$-0.0322956\pi$
$728$	4.08614	−	18.7837i	0.151442	−	0.696169i
$729$	−0.281733	+	0.959493i	−0.0104345	+	0.0355368i
$730$	−4.20694	+	17.0032i	−0.155706	+	0.629318i
$731$	−13.6697	+	29.9325i	−0.505593	+	1.10709i
$732$	−1.52956	+	1.14501i	−0.0565342	+	0.0423209i
$733$	24.0969	−	5.24195i	0.890038	−	0.193616i	0.255778	−	0.966736i	$-0.417668\pi$
$733$	24.0969	−	5.24195i	0.890038	−	0.193616i	0.634260	+	0.773120i	$0.281305\pi$
$734$	−6.14210	−	7.08836i	−0.226709	−	0.261636i
$735$	15.6639	−	6.62351i	0.577771	−	0.244312i
$736$	−4.60871	−	1.32657i	−0.169879	−	0.0488981i
$737$	−11.4046	+	11.4046i	−0.420095	+	0.420095i
$738$	0.465948	−	6.51480i	0.0171518	−	0.239813i
$739$	−12.3075	+	19.1509i	−0.452740	+	0.704477i	−0.990330	−	0.138729i	$-0.955698\pi$
$739$	−12.3075	+	19.1509i	−0.452740	+	0.704477i	0.537590	+	0.843206i	$0.319335\pi$
$740$	−0.801208	−	3.04550i	−0.0294530	−	0.111955i
$741$	24.2157	+	11.0589i	0.889586	+	0.406260i
$742$	−8.68528	−	6.50172i	−0.318847	−	0.238686i
$743$	−28.1704	+	15.3822i	−1.03347	+	0.564319i	−0.904119	−	0.427280i	$-0.859472\pi$
$743$	−28.1704	+	15.3822i	−1.03347	+	0.564319i	−0.129353	+	0.991599i	$0.541290\pi$
$744$	−5.27239	−	8.20400i	−0.193295	−	0.300773i
$745$	1.43766	+	33.3741i	0.0526718	+	1.22273i
$746$	−2.07273	−	7.05906i	−0.0758880	−	0.258451i
$747$	−8.78182	+	0.628088i	−0.321310	+	0.0229806i
$748$	−10.7426	+	0.768327i	−0.392789	+	0.0280928i
$749$	3.86080	+	13.1487i	0.141070	+	0.480442i
$750$	7.43620	−	8.34883i	0.271532	−	0.304856i
$751$	11.5537	+	17.9778i	0.421599	+	0.656020i	0.985471	−	0.169841i	$-0.0543255\pi$
$751$	11.5537	+	17.9778i	0.421599	+	0.656020i	−0.563873	+	0.825862i	$0.690689\pi$
$752$	8.81863	−	4.81533i	0.321582	−	0.175597i
$753$	16.6086	+	12.4330i	0.605250	+	0.453085i
$754$	27.2114	+	12.4270i	0.990979	+	0.452565i
$755$	20.5768	−	35.2686i	0.748867	−	1.28356i
$756$	−2.06618	+	3.21505i	−0.0751464	+	0.116930i
$757$	1.84542	−	25.8024i	0.0670730	−	0.937803i	−0.846828	−	0.531866i	$-0.821491\pi$
$757$	1.84542	−	25.8024i	0.0670730	−	0.937803i	0.913901	−	0.405937i	$-0.133055\pi$
$758$	2.07016	−	2.07016i	0.0751916	−	0.0751916i
$759$	2.74653	−	6.09999i	0.0996928	−	0.221415i
$760$	−4.60918	−	10.9002i	−0.167193	−	0.395393i
$761$	−25.2040	−	29.0870i	−0.913645	−	1.05440i	−0.998317	−	0.0579935i	$-0.981530\pi$
$761$	−25.2040	−	29.0870i	−0.913645	−	1.05440i	0.0846721	−	0.996409i	$-0.473016\pi$
$762$	−4.88008	+	1.06160i	−0.176787	+	0.0384576i
$763$	36.9696	−	27.6751i	1.33839	−	1.00191i
$764$	0.665925	−	1.45817i	0.0240923	−	0.0527549i
$765$	−8.91846	−	14.7826i	−0.322448	−	0.534465i
$766$	−3.65349	+	12.4427i	−0.132006	+	0.449571i
$767$	4.21548	−	19.3783i	0.152212	−	0.699708i
$768$	0.349464	−	0.936950i	0.0126102	−	0.0338093i
$769$	−3.15622	+	0.926749i	−0.113816	+	0.0334194i	−0.338145	−	0.941094i	$-0.609799\pi$
$769$	−3.15622	+	0.926749i	−0.113816	+	0.0334194i	0.224329	+	0.974514i	$0.427981\pi$
$770$	−5.41402	−	10.6201i	−0.195108	−	0.382721i
$771$	−0.577560	+	0.666540i	−0.0208003	+	0.0240049i
$772$	−7.60824	+	13.9335i	−0.273827	+	0.501476i
$773$	−45.5467	−	16.9880i	−1.63820	−	0.611018i	−0.649426	−	0.760425i	$-0.724991\pi$
$773$	−45.5467	−	16.9880i	−1.63820	−	0.611018i	−0.988776	+	0.149407i	$0.952263\pi$
$774$	3.58538	−	2.30418i	0.128874	−	0.0828222i
$775$	23.9951	+	42.4480i	0.861928	+	1.52478i
$776$	4.85106	−	0.697477i	0.174143	−	0.0250380i
$777$	−1.88091	−	5.04292i	−0.0674773	−	0.180914i
$778$	11.1570	+	14.9040i	0.399997	+	0.534333i
$779$	29.0808	+	18.6891i	1.04193	+	0.669607i
$780$	−3.63021	−	10.6453i	−0.129982	−	0.381161i
$781$		−	5.47989i		−	0.196086i
$782$	22.0317	−	29.7606i	0.787853	−	1.06424i
$783$	−4.20542	−	4.20542i	−0.150289	−	0.150289i
$784$	−5.74796	+	4.98063i	−0.205284	+	0.177880i
$785$	−1.66975	+	9.66068i	−0.0595960	+	0.344805i
$786$	−1.33651	+	9.29565i	−0.0476718	+	0.331565i
$787$	−15.8822	+	5.92375i	−0.566139	+	0.211159i	−0.616203	−	0.787587i	$-0.711330\pi$
$787$	−15.8822	+	5.92375i	−0.566139	+	0.211159i	0.0500646	+	0.998746i	$0.484057\pi$
$788$	3.00017	−	4.00775i	0.106876	−	0.142770i
$789$	19.6815	+	5.77902i	0.700681	+	0.205738i
$790$	−9.56798	+	13.9991i	−0.340413	+	0.498064i
$791$	−12.9872	−	28.4381i	−0.461773	−	1.01114i
$792$	1.22429	+	0.668513i	0.0435032	+	0.0237546i
$793$	−0.685601	−	9.58595i	−0.0243464	−	0.340407i
$794$	−5.47494	−	4.74406i	−0.194298	−	0.168360i
$795$	−6.31627	−	0.632141i	−0.224015	−	0.0224197i
$796$	12.0444	−	5.50051i	0.426904	−	0.194960i
$797$	34.1645	+	7.43203i	1.21017	+	0.263256i	0.771992	−	0.635633i	$-0.219261\pi$
$797$	34.1645	+	7.43203i	1.21017	+	0.263256i	0.438177	+	0.898889i	$0.355624\pi$
$798$	−9.69377	−	17.7528i	−0.343156	−	0.628443i
$799$	11.0404	+	76.7876i	0.390581	+	2.71655i
$800$	−2.00999	+	4.57820i	−0.0710639	+	0.161864i
$801$	0.881537	+	0.126746i	0.0311476	+	0.00447834i
$802$	2.31882	+	10.6594i	0.0818804	+	0.376398i
$803$	10.8991	+	0.779516i	0.384619	+	0.0275085i
$804$	11.5624			0.407774
$805$	39.8358	+	9.63093i	1.40403	+	0.339446i
$806$	49.0523			1.72779
$807$	20.1865	+	1.44377i	0.710598	+	0.0508229i
$808$	3.54230	+	16.2837i	0.124618	+	0.572859i
$809$	38.3326	+	5.51140i	1.34770	+	0.193770i	0.778095	−	0.628147i	$-0.216186\pi$
$809$	38.3326	+	5.51140i	1.34770	+	0.193770i	0.569607	+	0.821917i	$0.307095\pi$
$810$	−0.0633826	+	2.23517i	−0.00222704	+	0.0785359i
$811$	−3.63626	−	25.2907i	−0.127686	−	0.888077i	−0.948476	−	0.316848i	$-0.897376\pi$
$811$	−3.63626	−	25.2907i	−0.127686	−	0.888077i	0.820790	−	0.571230i	$-0.193533\pi$
$812$	−10.8930	−	19.9490i	−0.382268	−	0.700071i
$813$	1.70205	+	0.370258i	0.0596935	+	0.0129855i
$814$	−1.78698	+	0.816087i	−0.0626336	+	0.0286038i
$815$	−23.3168	−	28.5029i	−0.816750	−	0.998414i
$816$	5.83508	+	5.05613i	0.204269	+	0.177000i
$817$	1.60919	+	22.4994i	0.0562985	+	0.787156i
$818$	−31.6733	−	17.2949i	−1.10743	−	0.604702i
$819$	−7.98551	−	17.4858i	−0.279036	−	0.611004i
$820$	−2.69869	−	14.3532i	−0.0942425	−	0.501237i
$821$	38.4407	+	11.2872i	1.34159	+	0.393926i	0.872236	−	0.489085i	$-0.162669\pi$
$821$	38.4407	+	11.2872i	1.34159	+	0.393926i	0.469353	+	0.883011i	$0.344487\pi$
$822$	−1.44429	+	1.92935i	−0.0503754	+	0.0672937i
$823$	−31.6314	+	11.7979i	−1.10260	+	0.411249i	−0.833867	−	0.551966i	$-0.813878\pi$
$823$	−31.6314	+	11.7979i	−1.10260	+	0.411249i	−0.268734	+	0.963215i	$0.586605\pi$
$824$	−2.60768	+	18.1368i	−0.0908429	+	0.631826i
$825$	−5.92219	−	3.68408i	−0.206184	−	0.128263i
$826$	−11.3876	+	9.86742i	−0.396226	+	0.343332i
$827$	−5.47322	−	5.47322i	−0.190323	−	0.190323i	0.605513	−	0.795835i	$-0.292968\pi$
$827$	−5.47322	−	5.47322i	−0.190323	−	0.190323i	−0.795835	+	0.605513i	$0.792968\pi$
$828$	−4.48445	+	1.69992i	−0.155845	+	0.0590763i
$829$		−	5.14955i		−	0.178851i	−0.995993	−	0.0894257i	$-0.971497\pi$
$829$		−	5.14955i		−	0.178851i	0.995993	−	0.0894257i	$-0.0285031\pi$
$830$	−18.6333	+	6.35425i	−0.646770	+	0.220559i
$831$	−22.4722	−	14.4420i	−0.779552	−	0.500987i
$832$	3.01431	+	4.02665i	0.104502	+	0.139599i
$833$	−20.5214	−	55.0201i	−0.711025	−	1.90633i
$834$	10.2980	−	1.48062i	0.356589	−	0.0512698i
$835$	−30.2012	+	3.47171i	−1.04516	+	0.120144i
$836$	−6.21079	+	3.99143i	−0.214805	+	0.138046i
$837$	−9.13724	−	3.40801i	−0.315829	−	0.117798i
$838$	7.99415	−	14.6402i	0.276153	−	0.505737i
$839$	−25.6253	+	29.5732i	−0.884683	+	1.02098i	0.114936	+	0.993373i	$0.463334\pi$
$839$	−25.6253	+	29.5732i	−0.884683	+	1.02098i	−0.999619	+	0.0276059i	$0.991212\pi$
$840$	−2.63904	+	8.12795i	−0.0910555	+	0.280441i
$841$	6.11304	−	1.79495i	0.210795	−	0.0618949i
$842$	−12.8959	+	34.5753i	−0.444423	+	1.19154i
$843$	6.32971	−	29.0972i	0.218007	−	1.00216i
$844$	−1.79913	+	6.12726i	−0.0619285	+	0.210909i
$845$	26.6986	+	6.60575i	0.918458	+	0.227245i
$846$	4.17395	−	9.13968i	0.143503	−	0.314229i
$847$	27.7009	−	20.7367i	0.951815	−	0.712520i
$848$	2.77396	−	0.603437i	0.0952581	−	0.0207221i
$849$	−8.61760	−	9.94524i	−0.295755	−	0.341320i
$850$	−27.6959	−	26.8933i	−0.949963	−	0.922434i
$851$	1.86826	−	6.49060i	0.0640430	−	0.222495i
$852$	−2.77785	+	2.77785i	−0.0951675	+	0.0951675i
$853$	−3.59373	+	50.2469i	−0.123047	+	1.72042i	0.443402	+	0.896323i	$0.353771\pi$
$853$	−3.59373	+	50.2469i	−0.123047	+	1.72042i	−0.566449	+	0.824097i	$0.691683\pi$
$854$	−3.94777	+	6.14285i	−0.135090	+	0.210204i
$855$	−10.2221	−	5.96390i	−0.349588	−	0.203961i
$856$	−3.26171	−	1.48957i	−0.111483	−	0.0509126i
$857$	−4.19021	−	3.13675i	−0.143135	−	0.107149i	0.525311	−	0.850911i	$-0.323949\pi$
$857$	−4.19021	−	3.13675i	−0.143135	−	0.107149i	−0.668446	+	0.743761i	$0.733040\pi$
$858$	−6.15807	+	3.36256i	−0.210233	+	0.114796i
$859$	0.870484	+	1.35450i	0.0297005	+	0.0462149i	0.855786	−	0.517329i	$-0.173074\pi$
$859$	0.870484	+	1.35450i	0.0297005	+	0.0462149i	−0.826086	+	0.563544i	$0.809437\pi$
$860$	6.44248	−	7.02251i	0.219687	−	0.239466i
$861$	−7.03244	−	23.9503i	−0.239665	−	0.816224i
$862$	19.1981	−	1.37308i	0.653891	−	0.0467672i
$863$	42.5330	−	3.04202i	1.44784	−	0.103552i	0.674843	−	0.737961i	$-0.264211\pi$
$863$	42.5330	−	3.04202i	1.44784	−	0.103552i	0.772997	+	0.634409i	$0.218757\pi$
$864$	−0.281733	−	0.959493i	−0.00958474	−	0.0326426i
$865$	−18.0113	+	19.6329i	−0.612404	+	0.667540i
$866$	5.72465	+	8.90774i	0.194532	+	0.302697i
$867$	−37.4002	+	20.4221i	−1.27018	+	0.693570i
$868$	−29.8361	−	22.3351i	−1.01270	−	0.758101i
$869$	9.62195	+	4.39420i	0.326402	+	0.149063i
$870$	−11.4866	−	6.70168i	−0.389434	−	0.227208i
$871$	−31.4425	+	48.9254i	−1.06539	+	1.65777i
$872$	−0.862043	+	12.0529i	−0.0291925	+	0.408164i
$873$	3.46549	−	3.46549i	0.117289	−	0.117289i
$874$	3.47822	−	25.1431i	0.117652	−	0.850478i
$875$	15.4770	−	39.8267i	0.523218	−	1.34639i
$876$	−5.12976	−	5.92006i	−0.173319	−	0.200020i
$877$	−4.11673	+	0.895540i	−0.139012	+	0.0302402i	−0.281533	−	0.959552i	$-0.590843\pi$
$877$	−4.11673	+	0.895540i	−0.139012	+	0.0302402i	0.142521	+	0.989792i	$0.454479\pi$
$878$	15.9798	−	11.9623i	0.539293	−	0.403709i
$879$	0.863939	−	1.89176i	0.0291399	−	0.0638075i
$880$	3.02783	+	0.749145i	0.102068	+	0.0252537i
$881$	1.79177	−	6.10220i	0.0603662	−	0.205588i	−0.923788	−	0.382905i	$-0.874924\pi$
$881$	1.79177	−	6.10220i	0.0603662	−	0.205588i	0.984154	+	0.177317i	$0.0567417\pi$
$882$	−1.61669	+	7.43182i	−0.0544369	+	0.250242i
$883$	−0.404560	+	1.08467i	−0.0136145	+	0.0365020i	−0.943579	−	0.331147i	$-0.892564\pi$
$883$	−0.404560	+	1.08467i	−0.0136145	+	0.0365020i	0.929965	+	0.367649i	$0.119837\pi$
$884$	−37.2624	+	10.9412i	−1.25327	+	0.367994i
$885$	−2.72258	+	8.38524i	−0.0915185	+	0.281867i
$886$	2.89342	−	3.33919i	0.0972064	−	0.112182i
$887$	7.65067	−	14.0111i	0.256884	−	0.470448i	−0.717129	−	0.696941i	$-0.754544\pi$
$887$	7.65067	−	14.0111i	0.256884	−	0.470448i	0.974013	+	0.226492i	$0.0727258\pi$
$888$	1.31954	+	0.492162i	0.0442808	+	0.0165159i
$889$	−16.0566	+	10.3190i	−0.538522	+	0.346087i
$890$	1.97842	−	0.227424i	0.0663167	−	0.00762328i
$891$	1.38072	−	0.198517i	0.0462558	−	0.00665058i
$892$	8.86532	+	23.7689i	0.296833	+	0.795840i
$893$	31.8687	+	42.5716i	1.06645	+	1.42460i
$894$	−12.5676	−	8.07674i	−0.420325	−	0.270126i
$895$	5.65781	−	1.92941i	0.189120	−	0.0644930i
$896$		−	3.82173i		−	0.127675i
$897$	5.00180	−	23.5983i	0.167005	−	0.787926i
$898$	17.4310	+	17.4310i	0.581678	+	0.581678i
$899$	43.8330	−	37.9815i	1.46191	−	1.26675i
$900$	1.13453	+	4.86958i	0.0378178	+	0.162319i
$901$	−3.11932	+	21.6953i	−0.103919	+	0.722776i
$902$	−8.53638	+	3.18390i	−0.284230	+	0.106012i
$903$	9.76105	−	13.0392i	0.324828	−	0.433919i
$904$	7.84903	+	2.30468i	0.261055	+	0.0766526i
$905$	6.62884	+	35.2561i	0.220350	+	1.17195i
$906$	7.58580	+	16.6106i	0.252021	+	0.551850i
$907$	−23.6872	−	12.9342i	−0.786521	−	0.429473i	0.0351876	−	0.999381i	$-0.488797\pi$
$907$	−23.6872	−	12.9342i	−0.786521	−	0.429473i	−0.821709	+	0.569908i	$0.806979\pi$
$908$	1.29265	+	18.0736i	0.0428981	+	0.599794i
$909$	12.5942	+	10.9130i	0.417724	+	0.361960i
$910$	−27.2163	−	33.2699i	−0.902212	−	1.10289i
$911$	13.5044	−	6.16726i	0.447421	−	0.204330i	−0.178945	−	0.983859i	$-0.557269\pi$
$911$	13.5044	−	6.16726i	0.447421	−	0.204330i	0.626367	+	0.779529i	$0.284541\pi$
$912$	5.17167	+	1.12503i	0.171251	+	0.0372534i
$913$	5.88576	+	10.7790i	0.194790	+	0.356731i
$914$	0.672757	+	4.67913i	0.0222528	+	0.154772i
$915$	−0.121102	+	4.27064i	−0.00400352	+	0.141183i
$916$	0.362551	+	0.0521269i	0.0119790	+	0.00172232i
$917$	7.62913	+	35.0706i	0.251936	+	1.15813i
$918$	7.70125	+	0.550804i	0.254179	+	0.0181793i
$919$	51.5573			1.70072			0.850359	−	0.526203i	$-0.176385\pi$
$919$	51.5573			1.70072			0.850359	+	0.526203i	$0.176385\pi$
$920$	−8.73046	+	6.22728i	−0.287835	+	0.205307i
$921$	5.99123			0.197418
$922$	12.8270	+	0.917405i	0.422435	+	0.0302131i
$923$	−4.20026	−	19.3083i	−0.138253	−	0.635540i
$924$	5.27674	+	0.758680i	0.173592	+	0.0249588i
$925$	−6.44764	−	2.83074i	−0.211997	−	0.0930740i
$926$	−3.22553	−	22.4340i	−0.105997	−	0.737229i
$927$	8.78144	+	16.0820i	0.288420	+	0.528202i
$928$	5.81145	+	1.26420i	0.190770	+	0.0414995i
$929$	−2.92603	+	1.33627i	−0.0960000	+	0.0438417i	−0.462836	−	0.886444i	$-0.653168\pi$
$929$	−2.92603	+	1.33627i	−0.0960000	+	0.0438417i	0.366836	+	0.930286i	$0.380441\pi$
$930$	−21.6980	−	2.17156i	−0.711505	−	0.0712084i
$931$	−30.4218	−	26.3606i	−0.997034	−	0.863934i
$932$	−1.54482	−	21.5994i	−0.0506023	−	0.707512i
$933$	−16.4919	−	9.00528i	−0.539922	−	0.294820i
$934$	16.8141	+	36.8177i	0.550173	+	1.20471i
$935$	−13.5891	+	19.8823i	−0.444410	+	0.650222i
$936$	4.82616	+	1.41709i	0.157748	+	0.0463190i
$937$	−20.3483	+	27.1822i	−0.664750	+	0.888003i	−0.998505	−	0.0546574i	$-0.982593\pi$
$937$	−20.3483	+	27.1822i	−0.664750	+	0.888003i	0.333755	+	0.942660i	$0.391684\pi$
$938$	41.4023	−	15.4422i	1.35183	−	0.504207i
$939$	1.38009	−	9.59873i	0.0450375	−	0.313243i
$940$	3.82651	−	22.1390i	0.124807	−	0.722095i
$941$	18.0952	−	15.6796i	0.589888	−	0.511141i	−0.307987	−	0.951390i	$-0.599655\pi$
$941$	18.0952	−	15.6796i	0.589888	−	0.511141i	0.897875	+	0.440249i	$0.145110\pi$
$942$	−3.10027	−	3.10027i	−0.101012	−	0.101012i
$943$	10.7898	−	29.4067i	0.351363	−	0.957614i
$944$		−	3.94271i		−	0.128324i
$945$	2.75824	+	8.08828i	0.0897256	+	0.263112i
$946$	−5.00131	−	3.21415i	−0.162607	−	0.104501i
$947$	−8.58935	−	11.4740i	−0.279117	−	0.372856i	0.638973	−	0.769229i	$-0.279360\pi$
$947$	−8.58935	−	11.4740i	−0.279117	−	0.372856i	−0.918089	+	0.396373i	$0.870269\pi$
$948$	−2.65003	−	7.10502i	−0.0860691	−	0.230760i
$949$	39.0001	−	5.60737i	1.26600	−	0.182023i
$950$	−25.4980	−	7.08145i	−0.827266	−	0.229753i
$951$	11.4881	−	7.38295i	0.372527	−	0.239409i
$952$	27.6469	+	10.3117i	0.896040	+	0.334206i
$953$	13.9946	−	25.6292i	0.453330	−	0.830211i	−0.546645	−	0.837365i	$-0.684095\pi$
$953$	13.9946	−	25.6292i	0.453330	−	0.830211i	0.999974	+	0.00715329i	$0.00227698\pi$
$954$	1.85904	−	2.14545i	0.0601887	−	0.0694614i
$955$	−1.62800	−	3.19347i	−0.0526809	−	0.103338i
$956$	13.9635	−	4.10004i	0.451610	−	0.132605i
$957$	−2.89918	+	7.77301i	−0.0937173	+	0.251266i
$958$	−0.495634	+	2.27839i	−0.0160132	+	0.0736115i
$959$	−2.59492	+	8.83748i	−0.0837943	+	0.285377i
$960$	−1.15510	−	1.91461i	−0.0372808	−	0.0617938i
$961$	26.6297	−	58.3108i	0.859021	−	1.88099i
$962$	−5.67087	+	4.24516i	−0.182836	+	0.136869i
$963$	−3.50380	+	0.762205i	−0.112908	+	0.0245617i
$964$	−14.8555	−	17.1441i	−0.478463	−	0.552176i
$965$	13.8253	+	32.6954i	0.445053	+	1.05250i
$966$	−13.7874	+	12.0763i	−0.443603	+	0.388548i
$967$	−7.77763	+	7.77763i	−0.250112	+	0.250112i	−0.821016	−	0.570905i	$-0.806593\pi$
$967$	−7.77763	+	7.77763i	−0.250112	+	0.250112i	0.570905	+	0.821016i	$0.306593\pi$
$968$	−0.645920	+	9.03114i	−0.0207606	+	0.290272i
$969$	−22.0927	+	34.3770i	−0.709721	+	1.10435i
$970$	5.52254	−	9.46561i	0.177318	−	0.303922i
$971$	−34.8195	−	15.9015i	−1.11741	−	0.510304i	−0.230883	−	0.972982i	$-0.574161\pi$
$971$	−34.8195	−	15.9015i	−1.11741	−	0.510304i	−0.886527	+	0.462678i	$0.846889\pi$
$972$	−0.800541	−	0.599278i	−0.0256774	−	0.0192218i
$973$	34.8972	−	19.0553i	1.11875	−	0.610885i
$974$	8.61002	+	13.3975i	0.275883	+	0.429282i
$975$	−23.6905	−	8.44151i	−0.758704	−	0.270345i
$976$	−0.538294	−	1.83326i	−0.0172304	−	0.0586813i
$977$	39.9418	−	2.85669i	1.27785	−	0.0913937i	0.584144	−	0.811650i	$-0.301430\pi$
$977$	39.9418	−	2.85669i	1.27785	−	0.0913937i	0.693708	+	0.720256i	$0.255976\pi$
$978$	16.4267	−	1.17486i	0.525269	−	0.0375680i
$979$	−0.350001	−	1.19199i	−0.0111861	−	0.0380963i
$980$	0.731921	+	16.9910i	0.0233804	+	0.542756i
$981$	6.53296	+	10.1655i	0.208581	+	0.324559i
$982$	33.2680	−	18.1657i	1.06162	−	0.579691i
$983$	40.4115	+	30.2517i	1.28893	+	0.964878i	0.999972	+	0.00753557i	$0.00239867\pi$
$983$	40.4115	+	30.2517i	1.28893	+	0.964878i	0.288955	+	0.957343i	$0.406692\pi$
$984$	5.94121	+	2.71326i	0.189399	+	0.0864955i
$985$	−2.84811	−	10.8261i	−0.0907483	−	0.344947i
$986$	−24.8258	+	38.6296i	−0.790613	+	1.23022i
$987$	2.73939	−	38.3017i	0.0871957	−	1.21916i
$988$	−18.8242	+	18.8242i	−0.598877	+	0.598877i
$989$	19.5806	−	5.86305i	0.622628	−	0.186434i
$990$	2.87285	−	1.21479i	0.0913051	−	0.0386085i
$991$	−27.5733	−	31.8212i	−0.875893	−	1.01083i	−0.999828	−	0.0185444i	$-0.994097\pi$
$991$	−27.5733	−	31.8212i	−0.875893	−	1.01083i	0.123935	−	0.992290i	$-0.460449\pi$
$992$	9.52925	−	2.07296i	0.302554	−	0.0658166i
$993$	−12.4577	+	9.32572i	−0.395333	+	0.295943i
$994$	−6.23686	+	13.6568i	−0.197821	+	0.433168i
$995$	7.11112	−	28.7411i	0.225438	−	0.911155i
$996$	2.48045	−	8.44762i	0.0785959	−	0.267673i
$997$	−4.64348	+	21.3457i	−0.147060	+	0.676026i	0.843292	+	0.537455i	$0.180614\pi$
$997$	−4.64348	+	21.3457i	−0.147060	+	0.676026i	−0.990353	+	0.138570i	$0.955749\pi$
$998$	−1.67312	+	4.48581i	−0.0529617	+	0.141996i
$999$	1.35129	−	0.396773i	0.0427528	−	0.0125534i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.b.493.4	yes	240
5.2	odd	4	inner	690.2.w.b.217.9	yes	240
23.7	odd	22	inner	690.2.w.b.283.9	yes	240
115.7	even	44	inner	690.2.w.b.7.4	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.b.7.4	✓	240	115.7	even	44	inner
690.2.w.b.217.9	yes	240	5.2	odd	4	inner
690.2.w.b.283.9	yes	240	23.7	odd	22	inner
690.2.w.b.493.4	yes	240	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.997452 - 0.0713392i) q^{2} +(-0.212565 - 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(1.62532 - 1.53569i) q^{5} +(0.142315 + 0.989821i) q^{6} +(1.83156 + 3.35425i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +O(q^{10})\)	\(q+(-0.997452 - 0.0713392i) q^{2} +(-0.212565 - 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(1.62532 - 1.53569i) q^{5} +(0.142315 + 0.989821i) q^{6} +(1.83156 + 3.35425i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +(-1.73074 + 1.41582i) q^{10} +(1.05421 + 0.913477i) q^{11} +(-0.0713392 - 0.997452i) q^{12} +(4.41465 + 2.41058i) q^{13} +(-1.58760 - 3.47637i) q^{14} +(-1.84608 - 1.26174i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-4.62698 + 6.18092i) q^{17} +(0.936950 - 0.349464i) q^{18} +(-0.753219 + 5.23875i) q^{19} +(1.82733 - 1.28875i) q^{20} +(2.88827 - 2.50270i) q^{21} +(-0.986355 - 0.986355i) q^{22} +(4.78172 - 0.367647i) q^{23} +1.00000i q^{24} +(0.283342 - 4.99197i) q^{25} +(-4.23143 - 2.71937i) q^{26} +(0.599278 + 0.800541i) q^{27} +(1.33556 + 3.58077i) q^{28} +(-5.88683 + 0.846398i) q^{29} +(1.75136 + 1.39023i) q^{30} +(-8.20400 + 5.27239i) q^{31} +(-0.936950 - 0.349464i) q^{32} +(0.668513 - 1.22429i) q^{33} +(5.05613 - 5.83508i) q^{34} +(8.12795 + 2.63904i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(0.492162 - 1.31954i) q^{37} +(1.12503 - 5.17167i) q^{38} +(1.41709 - 4.82616i) q^{39} +(-1.91461 + 1.15510i) q^{40} +(2.71326 - 5.94121i) q^{41} +(-3.05945 + 2.29028i) q^{42} +(4.16455 - 0.905943i) q^{43} +(0.913477 + 1.05421i) q^{44} +(-0.840498 + 2.07209i) q^{45} +(-4.79576 + 0.0255868i) q^{46} +(7.10477 - 7.10477i) q^{47} +(0.0713392 - 0.997452i) q^{48} +(-4.11192 + 6.39827i) q^{49} +(-0.638742 + 4.95903i) q^{50} +(7.02320 + 3.20739i) q^{51} +(4.02665 + 3.01431i) q^{52} +(2.49158 - 1.36051i) q^{53} +(-0.540641 - 0.841254i) q^{54} +(3.11624 - 0.134239i) q^{55} +(-1.07671 - 3.66692i) q^{56} +(5.27914 - 0.377572i) q^{57} +(5.93221 - 0.424280i) q^{58} +(-1.11079 - 3.78300i) q^{59} +(-1.64772 - 1.51163i) q^{60} +(-1.03298 - 1.60735i) q^{61} +(8.55923 - 4.67369i) q^{62} +(-3.05945 - 2.29028i) q^{63} +(0.909632 + 0.415415i) q^{64} +(10.8771 - 2.86154i) q^{65} +(-0.754149 + 1.17348i) q^{66} +(-0.824851 + 11.5329i) q^{67} +(-5.45952 + 5.45952i) q^{68} +(-1.37567 - 4.59429i) q^{69} +(-7.91898 - 3.21216i) q^{70} +(-2.57260 - 2.96894i) q^{71} +(0.977147 - 0.212565i) q^{72} +(6.27093 - 4.69436i) q^{73} +(-0.585043 + 1.28107i) q^{74} +(-4.93811 + 0.784252i) q^{75} +(-1.49111 + 5.07824i) q^{76} +(-1.13319 + 5.20917i) q^{77} +(-1.75777 + 4.71277i) q^{78} +(7.27596 - 2.13642i) q^{79} +(1.99214 - 1.01557i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-3.13019 + 5.73251i) q^{82} +(8.24914 + 3.07677i) q^{83} +(3.21505 - 2.06618i) q^{84} +(1.97162 + 17.1516i) q^{85} +(-4.21857 + 0.606539i) q^{86} +(2.07839 + 5.57238i) q^{87} +(-0.835943 - 1.11669i) q^{88} +(-0.749222 - 0.481496i) q^{89} +(0.986178 - 2.00685i) q^{90} +19.2230i q^{91} +(4.78537 + 0.316604i) q^{92} +(6.89579 + 6.89579i) q^{93} +(-7.59352 + 6.57982i) q^{94} +(6.82085 + 9.67137i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(-4.59194 + 1.71270i) q^{97} +(4.55789 - 6.08862i) q^{98} +(-1.33841 - 0.392994i) 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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