LMFDB - Embedded newform 690.2.w.b.37.5

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			37.5
Character	$\chi$	$=$	690.37
Dual form			690.2.w.b.373.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.877679 - 0.479249i) q^{2} +(0.997452 + 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(2.06085 + 0.867694i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-1.60657 - 4.30737i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +O(q^{10})$	\(q+(-0.877679 - 0.479249i) q^{2} +(0.997452 + 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(2.06085 + 0.867694i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-1.60657 - 4.30737i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +(-1.39292 - 1.74922i) q^{10} +(1.86100 - 6.33797i) q^{11} +(0.479249 + 0.877679i) q^{12} +(-2.47066 - 0.921509i) q^{13} +(-0.654253 + 4.55043i) q^{14} +(1.99370 + 1.01250i) q^{15} +(-0.415415 + 0.909632i) q^{16} +(-5.68433 + 1.23655i) q^{17} +(-0.800541 - 0.599278i) q^{18} +(-2.22074 + 1.42718i) q^{19} +(0.384230 + 2.20281i) q^{20} +(-1.29519 - 4.41100i) q^{21} +(-4.67083 + 4.67083i) q^{22} +(-4.35331 - 2.01214i) q^{23} -1.00000i q^{24} +(3.49422 + 3.57638i) q^{25} +(1.72681 + 1.99285i) q^{26} +(0.977147 + 0.212565i) q^{27} +(2.75501 - 3.68027i) q^{28} +(1.61466 - 2.51246i) q^{29} +(-1.26459 - 1.84413i) q^{30} +(4.46391 - 5.15162i) q^{31} +(0.800541 - 0.599278i) q^{32} +(2.30840 - 6.18906i) q^{33} +(5.58163 + 1.63892i) q^{34} +(0.426584 - 10.2709i) q^{35} +(0.415415 + 0.909632i) q^{36} +(5.71908 + 7.63980i) q^{37} +(2.63308 - 0.188321i) q^{38} +(-2.39863 - 1.09542i) q^{39} +(0.718463 - 2.11750i) q^{40} +(-0.533902 - 3.71337i) q^{41} +(-0.977210 + 4.49216i) q^{42} +(-0.667815 + 9.33728i) q^{43} +(6.33797 - 1.86100i) q^{44} +(1.91639 + 1.15215i) q^{45} +(2.85649 + 3.85233i) q^{46} +(-0.431659 - 0.431659i) q^{47} +(-0.479249 + 0.877679i) q^{48} +(-10.6821 + 9.25611i) q^{49} +(-1.35283 - 4.81351i) q^{50} +(-5.75806 + 0.827884i) q^{51} +(-0.560517 - 2.57666i) q^{52} +(3.32897 - 1.24164i) q^{53} +(-0.755750 - 0.654861i) q^{54} +(9.33466 - 11.4468i) q^{55} +(-4.18178 + 1.90976i) q^{56} +(-2.31690 + 1.26512i) q^{57} +(-2.62124 + 1.43131i) q^{58} +(6.21782 - 2.83958i) q^{59} +(0.226104 + 2.22461i) q^{60} +(8.79747 + 7.62305i) q^{61} +(-6.38679 + 2.38215i) q^{62} +(-0.977210 - 4.49216i) q^{63} +(-0.989821 + 0.142315i) q^{64} +(-4.29208 - 4.04287i) q^{65} +(-4.99214 + 4.32571i) q^{66} +(3.40473 - 6.23529i) q^{67} +(-4.11343 - 4.11343i) q^{68} +(-4.19867 - 2.31757i) q^{69} +(-5.29670 + 8.81007i) q^{70} +(5.72462 - 1.68090i) q^{71} +(0.0713392 - 0.997452i) q^{72} +(2.15880 - 9.92386i) q^{73} +(-1.35815 - 9.44616i) q^{74} +(3.23018 + 3.81654i) q^{75} +(-2.40125 - 1.09661i) q^{76} +(-30.2898 + 2.16637i) q^{77} +(1.58025 + 2.11096i) q^{78} +(0.0599822 + 0.131343i) q^{79} +(-1.64539 + 1.51416i) q^{80} +(0.959493 + 0.281733i) q^{81} +(-1.31103 + 3.51502i) q^{82} +(0.922531 - 0.690598i) q^{83} +(3.01054 - 3.47435i) q^{84} +(-12.7875 - 2.38391i) q^{85} +(5.06101 - 7.87508i) q^{86} +(1.78978 - 2.39087i) q^{87} +(-6.45459 - 1.40411i) q^{88} +(0.183967 + 0.212309i) q^{89} +(-1.12981 - 1.92965i) q^{90} +12.1225i q^{91} +(-0.660856 - 4.75008i) q^{92} +(4.82005 - 4.82005i) q^{93} +(0.171986 + 0.585730i) q^{94} +(-5.81498 + 1.01429i) q^{95} +(0.841254 - 0.540641i) q^{96} +(6.96135 + 5.21120i) q^{97} +(13.8115 - 3.00450i) q^{98} +(2.74404 - 6.00862i) 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
$5$	2.06085	+	0.867694i	0.921641	+	0.388044i
$5$	2.06085	+	0.867694i	0.921641	+	0.388044i
$6$	−0.841254	−	0.540641i	−0.343440	−	0.220716i
$7$	−1.60657	−	4.30737i	−0.607225	−	1.62803i	−0.767566	−	0.640970i	$-0.778532\pi$
$7$	−1.60657	−	4.30737i	−0.607225	−	1.62803i	0.160341	−	0.987062i	$-0.448741\pi$
$8$	−0.0713392	−	0.997452i	−0.0252222	−	0.352653i
$9$	0.989821	+	0.142315i	0.329940	+	0.0474383i
$10$	−1.39292	−	1.74922i	−0.440481	−	0.553151i
$11$	1.86100	−	6.33797i	0.561112	−	1.91097i	0.192954	−	0.981208i	$-0.438193\pi$
$11$	1.86100	−	6.33797i	0.561112	−	1.91097i	0.368157	−	0.929763i	$-0.379989\pi$
$12$	0.479249	+	0.877679i	0.138347	+	0.253364i
$13$	−2.47066	−	0.921509i	−0.685238	−	0.255580i	−0.0173577	−	0.999849i	$-0.505525\pi$
$13$	−2.47066	−	0.921509i	−0.685238	−	0.255580i	−0.667880	+	0.744269i	$0.732798\pi$
$14$	−0.654253	+	4.55043i	−0.174857	+	1.21615i
$15$	1.99370	+	1.01250i	0.514771	+	0.261427i
$16$	−0.415415	+	0.909632i	−0.103854	+	0.227408i
$17$	−5.68433	+	1.23655i	−1.37865	+	0.299908i	−0.839985	−	0.542610i	$-0.817436\pi$
$17$	−5.68433	+	1.23655i	−1.37865	+	0.299908i	−0.538668	+	0.842518i	$0.681072\pi$
$18$	−0.800541	−	0.599278i	−0.188689	−	0.141251i
$19$	−2.22074	+	1.42718i	−0.509473	+	0.327419i	−0.769996	−	0.638049i	$-0.779742\pi$
$19$	−2.22074	+	1.42718i	−0.509473	+	0.327419i	0.260522	+	0.965468i	$0.416105\pi$
$20$	0.384230	+	2.20281i	0.0859164	+	0.492563i
$21$	−1.29519	−	4.41100i	−0.282633	−	0.962560i
$22$	−4.67083	+	4.67083i	−0.995823	+	0.995823i
$23$	−4.35331	−	2.01214i	−0.907728	−	0.419560i
$23$	−4.35331	−	2.01214i	−0.907728	−	0.419560i
$24$		−	1.00000i		−	0.204124i
$25$	3.49422	+	3.57638i	0.698843	+	0.715275i
$26$	1.72681	+	1.99285i	0.338656	+	0.390830i
$27$	0.977147	+	0.212565i	0.188052	+	0.0409082i
$28$	2.75501	−	3.68027i	0.520649	−	0.695505i
$29$	1.61466	−	2.51246i	0.299834	−	0.466551i	−0.658346	−	0.752715i	$-0.728744\pi$
$29$	1.61466	−	2.51246i	0.299834	−	0.466551i	0.958181	+	0.286164i	$0.0923801\pi$
$30$	−1.26459	−	1.84413i	−0.230881	−	0.336691i
$31$	4.46391	−	5.15162i	0.801741	−	0.925259i	−0.196734	−	0.980457i	$-0.563034\pi$
$31$	4.46391	−	5.15162i	0.801741	−	0.925259i	0.998475	+	0.0551980i	$0.0175790\pi$
$32$	0.800541	−	0.599278i	0.141517	−	0.105938i
$33$	2.30840	−	6.18906i	0.401841	−	1.07738i
$34$	5.58163	+	1.63892i	0.957242	+	0.281072i
$35$	0.426584	−	10.2709i	0.0721059	−	1.73609i
$36$	0.415415	+	0.909632i	0.0692358	+	0.151605i
$37$	5.71908	+	7.63980i	0.940212	+	1.25598i	0.966591	+	0.256324i	$0.0825114\pi$
$37$	5.71908	+	7.63980i	0.940212	+	1.25598i	−0.0263792	+	0.999652i	$0.508398\pi$
$38$	2.63308	−	0.188321i	0.427141	−	0.0305497i
$39$	−2.39863	−	1.09542i	−0.384087	−	0.175407i
$40$	0.718463	−	2.11750i	0.113599	−	0.334806i
$41$	−0.533902	−	3.71337i	−0.0833815	−	0.579931i	−0.988087	−	0.153894i	$-0.950818\pi$
$41$	−0.533902	−	3.71337i	−0.0833815	−	0.579931i	0.904706	−	0.426037i	$-0.140091\pi$
$42$	−0.977210	+	4.49216i	−0.150787	+	0.693156i
$43$	−0.667815	+	9.33728i	−0.101841	+	1.42392i	0.647666	+	0.761925i	$0.275745\pi$
$43$	−0.667815	+	9.33728i	−0.101841	+	1.42392i	−0.749507	+	0.661997i	$0.769709\pi$
$44$	6.33797	−	1.86100i	0.955486	−	0.280556i
$45$	1.91639	+	1.15215i	0.285678	+	0.171753i
$46$	2.85649	+	3.85233i	0.421167	+	0.567995i
$47$	−0.431659	−	0.431659i	−0.0629639	−	0.0629639i	0.674924	−	0.737888i	$-0.264177\pi$
$47$	−0.431659	−	0.431659i	−0.0629639	−	0.0629639i	−0.737888	+	0.674924i	$0.764177\pi$
$48$	−0.479249	+	0.877679i	−0.0691736	+	0.126682i
$49$	−10.6821	+	9.25611i	−1.52602	+	1.32230i
$50$	−1.35283	−	4.81351i	−0.191318	−	0.680733i
$51$	−5.75806	+	0.827884i	−0.806290	+	0.115927i
$52$	−0.560517	−	2.57666i	−0.0777298	−	0.357318i
$53$	3.32897	−	1.24164i	0.457269	−	0.170553i	−0.110265	−	0.993902i	$-0.535170\pi$
$53$	3.32897	−	1.24164i	0.457269	−	0.170553i	0.567535	+	0.823350i	$0.307897\pi$
$54$	−0.755750	−	0.654861i	−0.102844	−	0.0891153i
$55$	9.33466	−	11.4468i	1.25869	−	1.54349i
$56$	−4.18178	+	1.90976i	−0.558814	+	0.255202i
$57$	−2.31690	+	1.26512i	−0.306881	+	0.167570i
$58$	−2.62124	+	1.43131i	−0.344186	+	0.187940i
$59$	6.21782	−	2.83958i	0.809491	−	0.369682i	0.0327196	−	0.999465i	$-0.489583\pi$
$59$	6.21782	−	2.83958i	0.809491	−	0.369682i	0.776772	+	0.629782i	$0.216856\pi$
$60$	0.226104	+	2.22461i	0.0291899	+	0.287196i
$61$	8.79747	+	7.62305i	1.12640	+	0.976031i	0.999873	−	0.0159319i	$-0.00507149\pi$
$61$	8.79747	+	7.62305i	1.12640	+	0.976031i	0.126527	+	0.991963i	$0.459617\pi$
$62$	−6.38679	+	2.38215i	−0.811123	+	0.302533i
$63$	−0.977210	−	4.49216i	−0.123117	−	0.565959i
$64$	−0.989821	+	0.142315i	−0.123728	+	0.0177894i
$65$	−4.29208	−	4.04287i	−0.532366	−	0.501456i
$66$	−4.99214	+	4.32571i	−0.614490	+	0.532458i
$67$	3.40473	−	6.23529i	0.415953	−	0.761762i	−0.582751	−	0.812651i	$-0.698024\pi$
$67$	3.40473	−	6.23529i	0.415953	−	0.761762i	0.998704	+	0.0508891i	$0.0162055\pi$
$68$	−4.11343	−	4.11343i	−0.498827	−	0.498827i
$69$	−4.19867	−	2.31757i	−0.505461	−	0.279003i
$70$	−5.29670	+	8.81007i	−0.633077	+	1.05300i
$71$	5.72462	−	1.68090i	0.679387	−	0.199486i	0.0762082	−	0.997092i	$-0.475719\pi$
$71$	5.72462	−	1.68090i	0.679387	−	0.199486i	0.603179	+	0.797606i	$0.293900\pi$
$72$	0.0713392	−	0.997452i	0.00840740	−	0.117551i
$73$	2.15880	−	9.92386i	0.252669	−	1.16150i	−0.659506	−	0.751699i	$-0.729234\pi$
$73$	2.15880	−	9.92386i	0.252669	−	1.16150i	0.912175	−	0.409801i	$-0.134402\pi$
$74$	−1.35815	−	9.44616i	−0.157882	−	1.09809i
$75$	3.23018	+	3.81654i	0.372989	+	0.440696i
$76$	−2.40125	−	1.09661i	−0.275442	−	0.125790i
$77$	−30.2898	+	2.16637i	−3.45184	+	0.246881i
$78$	1.58025	+	2.11096i	0.178928	+	0.239019i
$79$	0.0599822	+	0.131343i	0.00674853	+	0.0147772i	0.912976	−	0.408013i	$-0.133778\pi$
$79$	0.0599822	+	0.131343i	0.00674853	+	0.0147772i	−0.906228	+	0.422790i	$0.861051\pi$
$80$	−1.64539	+	1.51416i	−0.183960	+	0.169289i
$81$	0.959493	+	0.281733i	0.106610	+	0.0313036i
$82$	−1.31103	+	3.51502i	−0.144780	+	0.388169i
$83$	0.922531	−	0.690598i	0.101261	−	0.0758030i	−0.547447	−	0.836840i	$-0.684400\pi$
$83$	0.922531	−	0.690598i	0.101261	−	0.0758030i	0.648708	+	0.761037i	$0.275309\pi$
$84$	3.01054	−	3.47435i	0.328477	−	0.379083i
$85$	−12.7875	−	2.38391i	−1.38700	−	0.258572i
$86$	5.06101	−	7.87508i	0.545743	−	0.849192i
$87$	1.78978	−	2.39087i	0.191885	−	0.256328i
$88$	−6.45459	−	1.40411i	−0.688061	−	0.149679i
$89$	0.183967	+	0.212309i	0.0195004	+	0.0225047i	0.765416	−	0.643536i	$-0.222533\pi$
$89$	0.183967	+	0.212309i	0.0195004	+	0.0225047i	−0.745916	+	0.666040i	$0.767988\pi$
$90$	−1.12981	−	1.92965i	−0.119092	−	0.203403i
$91$			12.1225i			1.27078i
$92$	−0.660856	−	4.75008i	−0.0688990	−	0.495230i
$93$	4.82005	−	4.82005i	0.499816	−	0.499816i
$94$	0.171986	+	0.585730i	0.0177390	+	0.0604134i
$95$	−5.81498	+	1.01429i	−0.596604	+	0.104064i
$96$	0.841254	−	0.540641i	0.0858601	−	0.0551789i
$97$	6.96135	+	5.21120i	0.706818	+	0.529117i	0.891129	−	0.453751i	$-0.149914\pi$
$97$	6.96135	+	5.21120i	0.706818	+	0.529117i	−0.184311	+	0.982868i	$0.559005\pi$
$98$	13.8115	−	3.00450i	1.39517	−	0.303500i
$99$	2.74404	−	6.00862i	0.275787	−	0.603889i
$100$	−1.11952	+	4.87306i	−0.111952	+	0.487306i
$101$	0.0300202	−	0.208795i	0.00298712	−	0.0207759i	−0.988273	−	0.152695i	$-0.951205\pi$
$101$	0.0300202	−	0.208795i	0.00298712	−	0.0207759i	0.991260	+	0.131919i	$0.0421139\pi$
$102$	5.45049	+	2.03293i	0.539679	+	0.201290i
$103$	3.60612	+	6.60411i	0.355321	+	0.650722i	0.992805	−	0.119742i	$-0.0382066\pi$
$103$	3.60612	+	6.60411i	0.355321	+	0.650722i	−0.637484	+	0.770464i	$0.720025\pi$
$104$	−0.742906	+	2.53010i	−0.0728479	+	0.248097i
$105$	1.15821	−	10.2142i	0.113030	−	0.996809i
$106$	−3.51682	−	0.505643i	−0.341584	−	0.0491124i
$107$	−0.193283	−	2.70245i	−0.0186853	−	0.261255i	−0.998204	−	0.0599029i	$-0.980921\pi$
$107$	−0.193283	−	2.70245i	−0.0186853	−	0.261255i	0.979519	−	0.201352i	$-0.0645336\pi$
$108$	0.349464	+	0.936950i	0.0336272	+	0.0901580i
$109$	12.8725	+	8.27266i	1.23296	+	0.792378i	0.984350	−	0.176225i	$-0.0563887\pi$
$109$	12.8725	+	8.27266i	1.23296	+	0.792378i	0.248614	+	0.968603i	$0.420025\pi$
$110$	−13.6787	+	5.57303i	−1.30422	+	0.531368i
$111$	5.15950	+	8.02833i	0.489718	+	0.762016i
$112$	4.58551	+	0.327962i	0.433290	+	0.0309895i
$113$	−1.43763	−	0.785006i	−0.135241	−	0.0738472i	0.410204	−	0.911994i	$-0.365458\pi$
$113$	−1.43763	−	0.785006i	−0.135241	−	0.0738472i	−0.545445	+	0.838147i	$0.683639\pi$
$114$	2.63980			0.247240
$115$	−7.22560	−	7.92406i	−0.673791	−	0.738922i
$116$	2.98656			0.277295
$117$	−2.31437	−	1.26374i	−0.213963	−	0.116833i
$118$	−6.81812	−	0.487641i	−0.627659	−	0.0448910i
$119$	14.4585	+	22.4979i	1.32541	+	2.06238i
$120$	0.867694	−	2.06085i	0.0792092	−	0.188129i
$121$	−27.4528	−	17.6429i	−2.49571	−	1.60390i
$122$	−4.06801	−	10.9068i	−0.368301	−	0.987452i
$123$	−0.267633	−	3.74200i	−0.0241317	−	0.337405i
$124$	6.74719	+	0.970100i	0.605916	+	0.0871175i
$125$	4.09786	+	10.4023i	0.366524	+	0.930409i
$126$	−1.29519	+	4.41100i	−0.115384	+	0.392963i
$127$	−0.675727	−	1.23750i	−0.0599611	−	0.109811i	0.845979	−	0.533216i	$-0.179017\pi$
$127$	−0.675727	−	1.23750i	−0.0599611	−	0.109811i	−0.905940	+	0.423405i	$0.860835\pi$
$128$	0.936950	+	0.349464i	0.0828154	+	0.0308886i
$129$	−1.33223	+	9.26585i	−0.117296	+	0.815812i
$130$	1.82952	+	5.60531i	0.160460	+	0.491618i
$131$	−2.15901	+	4.72758i	−0.188634	+	0.413051i	−0.980194	−	0.198041i	$-0.936542\pi$
$131$	−2.15901	+	4.72758i	−0.188634	+	0.413051i	0.791560	+	0.611092i	$0.209269\pi$
$132$	6.45459	−	1.40411i	0.561800	−	0.122212i
$133$	9.71518	+	7.27269i	0.842413	+	0.630622i
$134$	−5.97651	+	3.84087i	−0.516292	+	0.331801i
$135$	1.82931	+	1.28593i	0.157442	+	0.110675i
$136$	1.63892	+	5.58163i	0.140536	+	0.478621i
$137$	7.86645	−	7.86645i	0.672077	−	0.672077i	−0.286118	−	0.958194i	$-0.592365\pi$
$137$	7.86645	−	7.86645i	0.672077	−	0.672077i	0.958194	+	0.286118i	$0.0923649\pi$
$138$	2.57439	+	4.04630i	0.219147	+	0.344444i
$139$			3.68232i			0.312330i	0.987731	+	0.156165i	$0.0499132\pi$
$139$			3.68232i			0.312330i	−0.987731	+	0.156165i	$0.950087\pi$
$140$	8.87102	−	5.19398i	0.749738	−	0.438971i
$141$	−0.399765	−	0.461353i	−0.0336663	−	0.0388529i
$142$	−5.82995	−	1.26823i	−0.489238	−	0.106427i
$143$	−10.4384	+	13.9441i	−0.872902	+	1.16606i
$144$	−0.540641	+	0.841254i	−0.0450534	+	0.0701045i
$145$	5.50761	−	3.77677i	0.457382	−	0.313644i
$146$	−6.65074	+	7.67536i	−0.550419	+	0.635218i
$147$	−11.3152	+	8.47047i	−0.933264	+	0.698633i
$148$	−3.33504	+	8.94159i	−0.274139	+	0.734994i
$149$	−0.0518987	−	0.0152388i	−0.00425171	−	0.00124841i	0.279606	−	0.960115i	$-0.409796\pi$
$149$	−0.0518987	−	0.0152388i	−0.00425171	−	0.00124841i	−0.283858	+	0.958866i	$0.591614\pi$
$150$	−1.00599	−	4.89775i	−0.0821385	−	0.399900i
$151$	4.65942	+	10.2027i	0.379179	+	0.830285i	0.998964	+	0.0455138i	$0.0144925\pi$
$151$	4.65942	+	10.2027i	0.379179	+	0.830285i	−0.619785	+	0.784772i	$0.712780\pi$
$152$	1.58197	+	2.11327i	0.128315	+	0.171409i
$153$	−5.80245	+	0.415000i	−0.469101	+	0.0335507i
$154$	27.6230	+	12.6150i	2.22592	+	1.01654i
$155$	13.6695	−	6.74343i	1.09796	−	0.541645i
$156$	−0.375273	−	2.61008i	−0.0300459	−	0.208974i
$157$	0.504810	−	2.32057i	0.0402882	−	0.185202i	−0.952605	−	0.304210i	$-0.901608\pi$
$157$	0.504810	−	2.32057i	0.0402882	−	0.185202i	0.992893	+	0.119008i	$0.0379713\pi$
$158$	0.0103007	−	0.144023i	0.000819483	−	0.0114579i
$159$	3.40907	−	1.00099i	0.270357	−	0.0793839i
$160$	2.16979	−	0.540398i	0.171537	−	0.0427222i
$161$	−1.67315	+	21.9839i	−0.131863	+	1.73258i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	−5.05537	+	9.25821i	−0.395967	+	0.725159i	−0.997268	−	0.0738631i	$-0.976467\pi$
$163$	−5.05537	+	9.25821i	−0.395967	+	0.725159i	0.601302	+	0.799022i	$0.294649\pi$
$164$	2.83524	−	2.45675i	0.221395	−	0.191840i
$165$	10.1275	−	10.7518i	0.788424	−	0.837023i
$166$	−1.14065	+	0.164001i	−0.0885320	+	0.0127290i
$167$	0.583058	+	2.68027i	0.0451184	+	0.207406i	0.994188	−	0.107662i	$-0.0343364\pi$
$167$	0.583058	+	2.68027i	0.0451184	+	0.207406i	−0.949069	+	0.315068i	$0.897973\pi$
$168$	−4.30737	+	1.60657i	−0.332321	+	0.123949i
$169$	−4.56976	−	3.95972i	−0.351520	−	0.304594i
$170$	10.0808	+	8.22071i	0.773165	+	0.630500i
$171$	−2.40125	+	1.09661i	−0.183628	+	0.0838601i
$172$	−8.21607	+	4.48631i	−0.626469	+	0.342078i
$173$	14.7436	−	8.05064i	1.12094	−	0.612079i	0.191661	−	0.981461i	$-0.438613\pi$
$173$	14.7436	−	8.05064i	1.12094	−	0.612079i	0.929277	+	0.369383i	$0.120431\pi$
$174$	−2.71667	+	1.24066i	−0.205950	+	0.0940544i
$175$	9.79108	−	20.7966i	0.740136	−	1.57207i
$176$	4.99214	+	4.32571i	0.376297	+	0.326063i
$177$	6.40455	−	2.38877i	0.481396	−	0.179551i
$178$	−0.0597148	−	0.274505i	−0.00447582	−	0.0205750i
$179$	24.1115	−	3.46671i	1.80218	−	0.259114i	0.842195	−	0.539173i	$-0.181263\pi$
$179$	24.1115	−	3.46671i	1.80218	−	0.259114i	0.959983	+	0.280059i	$0.0903540\pi$
$180$	0.0668266	+	2.23507i	0.00498096	+	0.166592i
$181$	−5.71531	+	4.95235i	−0.424816	+	0.368105i	−0.840872	−	0.541234i	$-0.817957\pi$
$181$	−5.71531	+	4.95235i	−0.424816	+	0.368105i	0.416056	+	0.909339i	$0.363412\pi$
$182$	5.80970	−	10.6397i	0.430643	−	0.788665i
$183$	8.23123	+	8.23123i	0.608470	+	0.608470i
$184$	−1.69645	+	4.48576i	−0.125064	+	0.330695i
$185$	5.15717	+	20.7069i	0.379163	+	1.52240i
$186$	−6.54046	+	1.92045i	−0.479569	+	0.140814i
$187$	−2.74130	+	38.3284i	−0.200464	+	2.80285i
$188$	0.129762	−	0.596507i	0.00946388	−	0.0435047i
$189$	−0.654253	−	4.55043i	−0.0475899	−	0.330995i
$190$	5.58978	+	1.89660i	0.405525	+	0.137594i
$191$	2.23263	+	1.01961i	0.161548	+	0.0737763i	0.494548	−	0.869150i	$-0.335334\pi$
$191$	2.23263	+	1.01961i	0.161548	+	0.0737763i	−0.333000	+	0.942927i	$0.608061\pi$
$192$	−0.997452	+	0.0713392i	−0.0719849	+	0.00514846i
$193$	−12.8252	−	17.1324i	−0.923175	−	1.23322i	−0.972136	−	0.234417i	$-0.924682\pi$
$193$	−12.8252	−	17.1324i	−0.923175	−	1.23322i	0.0489606	−	0.998801i	$-0.484409\pi$
$194$	−3.61237	−	7.90998i	−0.259353	−	0.567904i
$195$	−3.99272	−	4.33876i	−0.285925	−	0.310705i
$196$	−13.5619	−	3.98214i	−0.968709	−	0.284439i
$197$	2.65660	−	7.12261i	0.189275	−	0.507465i	−0.807302	−	0.590139i	$-0.799073\pi$
$197$	2.65660	−	7.12261i	0.189275	−	0.507465i	0.996577	+	0.0826734i	$0.0263458\pi$
$198$	−5.28801	+	3.95856i	−0.375803	+	0.281322i
$199$	−11.3355	+	13.0819i	−0.803553	+	0.927350i	−0.998571	−	0.0534501i	$-0.982978\pi$
$199$	−11.3355	+	13.0819i	−0.803553	+	0.927350i	0.195017	+	0.980800i	$0.437524\pi$
$200$	3.31799	−	3.74045i	0.234617	−	0.264490i
$201$	3.84087	−	5.97651i	0.270914	−	0.421551i
$202$	−0.126413	+	0.168868i	−0.00889437	+	0.0118815i
$203$	−13.4161	−	2.91850i	−0.941627	−	0.204838i
$204$	−3.80950	−	4.39640i	−0.266719	−	0.307810i
$205$	2.12178	−	8.11597i	0.148191	−	0.566844i
$206$		−	7.52451i		−	0.524258i
$207$	−4.02264	−	2.61120i	−0.279593	−	0.181491i
$208$	1.86458	−	1.86458i	0.129286	−	0.129286i
$209$	4.91266	+	16.7310i	0.339816	+	1.15731i
$210$	−5.91171	+	8.40976i	−0.407947	+	0.580329i
$211$	3.84365	−	2.47016i	0.264608	−	0.170053i	−0.401609	−	0.915811i	$-0.631549\pi$
$211$	3.84365	−	2.47016i	0.264608	−	0.170053i	0.666217	+	0.745758i	$0.267913\pi$
$212$	2.84431	+	2.12923i	0.195348	+	0.146236i
$213$	5.82995	−	1.26823i	0.399461	−	0.0868975i
$214$	−1.12550	+	2.46451i	−0.0769379	+	0.168470i
$215$	−9.47816	+	18.6633i	−0.646405	+	1.27283i
$216$	0.142315	−	0.989821i	0.00968330	−	0.0673488i
$217$	−29.3615	−	10.9513i	−1.99319	−	0.743421i
$218$	−7.33327	−	13.4299i	−0.496672	−	0.909587i
$219$	2.86126	−	9.74457i	0.193346	−	0.658477i
$220$	14.6764	+	1.66418i	0.989483	+	0.112199i
$221$	15.1835	+	2.18306i	1.02136	+	0.146849i
$222$	−0.680811	−	9.51898i	−0.0456930	−	0.638872i
$223$	−2.76645	−	7.41714i	−0.185255	−	0.496689i	0.810810	−	0.585309i	$-0.199027\pi$
$223$	−2.76645	−	7.41714i	−0.185255	−	0.496689i	−0.996065	+	0.0886206i	$0.971754\pi$
$224$	−3.86743	−	2.48545i	−0.258404	−	0.166066i
$225$	2.94968	+	4.03725i	0.196645	+	0.269150i
$226$	0.885566	+	1.37797i	0.0589070	+	0.0916610i
$227$	−4.65874	−	0.333200i	−0.309212	−	0.0221152i	−0.0841288	−	0.996455i	$-0.526811\pi$
$227$	−4.65874	−	0.333200i	−0.309212	−	0.0221152i	−0.225083	+	0.974340i	$0.572265\pi$
$228$	−2.31690	−	1.26512i	−0.153440	−	0.0837848i
$229$	18.2568			1.20644			0.603220	−	0.797575i	$-0.293884\pi$
$229$	18.2568			1.20644			0.603220	+	0.797575i	$0.293884\pi$
$230$	2.54416	+	10.4176i	0.167757	+	0.686919i
$231$	−30.3672			−1.99801
$232$	−2.62124	−	1.43131i	−0.172093	−	0.0939699i
$233$	11.3358	+	0.810752i	0.742632	+	0.0531141i	0.437528	−	0.899205i	$-0.355854\pi$
$233$	11.3358	+	0.810752i	0.742632	+	0.0531141i	0.305104	+	0.952319i	$0.401309\pi$
$234$	1.42563	+	2.21832i	0.0931961	+	0.145016i
$235$	−0.515037	−	1.26413i	−0.0335973	−	0.0824629i
$236$	5.75042	+	3.69557i	0.374320	+	0.240561i
$237$	0.0504595	+	0.135287i	0.00327770	+	0.00878785i
$238$	−1.90785	−	26.6752i	−0.123667	−	1.72909i
$239$	−26.8261	−	3.85701i	−1.73524	−	0.249489i	−0.799118	−	0.601174i	$-0.794700\pi$
$239$	−26.8261	−	3.85701i	−1.73524	−	0.249489i	−0.936118	+	0.351685i	$0.885609\pi$
$240$	−1.74922	+	1.39292i	−0.112911	+	0.0899129i
$241$	−2.87903	+	9.80509i	−0.185455	+	0.631601i	0.813306	+	0.581836i	$0.197666\pi$
$241$	−2.87903	+	9.80509i	−0.185455	+	0.631601i	−0.998761	+	0.0497653i	$0.984153\pi$
$242$	15.6394	+	28.6415i	1.00534	+	1.84115i
$243$	0.936950	+	0.349464i	0.0601054	+	0.0224181i
$244$	−1.65665	+	11.5222i	−0.106056	+	0.737635i
$245$	−30.0457	+	9.80666i	−1.91955	+	0.626524i
$246$	−1.55845	+	3.41254i	−0.0993633	+	0.217575i
$247$	6.80186	−	1.47965i	0.432792	−	0.0941482i
$248$	−5.45695	−	4.08502i	−0.346517	−	0.259399i
$249$	0.969447	−	0.623026i	0.0614362	−	0.0394827i
$250$	1.38868	−	11.0938i	0.0878278	−	0.701631i
$251$	6.24779	+	21.2780i	0.394357	+	1.34306i	0.882508	+	0.470297i	$0.155853\pi$
$251$	6.24779	+	21.2780i	0.394357	+	1.34306i	−0.488151	+	0.872759i	$0.662329\pi$
$252$	3.25073	−	3.25073i	0.204777	−	0.204777i
$253$	−20.8544	+	23.8466i	−1.31110	+	1.49922i
$254$			1.40997i			0.0884695i
$255$	−12.5849	−	3.29009i	−0.788095	−	0.206033i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	−16.3242	−	3.55111i	−1.01827	−	0.221512i	−0.327706	−	0.944780i	$-0.606276\pi$
$257$	−16.3242	−	3.55111i	−1.01827	−	0.221512i	−0.690568	+	0.723268i	$0.742639\pi$
$258$	5.60992	−	7.49397i	0.349258	−	0.466554i
$259$	23.7194	−	36.9080i	1.47385	−	2.29335i
$260$	1.08061	−	5.79646i	0.0670163	−	0.359481i
$261$	1.95578	−	2.25709i	0.121060	−	0.139711i
$262$	4.16061	−	3.11459i	0.257043	−	0.192420i
$263$	5.44339	−	14.5943i	0.335654	−	0.899923i	−0.654006	−	0.756489i	$-0.726913\pi$
$263$	5.44339	−	14.5943i	0.335654	−	0.899923i	0.989660	−	0.143434i	$-0.0458143\pi$
$264$	−6.33797	−	1.86100i	−0.390075	−	0.114536i
$265$	7.93788	+	0.329688i	0.487620	+	0.0202526i
$266$	−5.04138	−	11.0391i	−0.309107	−	0.676849i
$267$	0.168352	+	0.224892i	0.0103030	+	0.0137632i
$268$	7.08619	−	0.506814i	0.432858	−	0.0309586i
$269$	−22.2705	−	10.1706i	−1.35786	−	0.620113i	−0.402460	−	0.915437i	$-0.631845\pi$
$269$	−22.2705	−	10.1706i	−1.35786	−	0.620113i	−0.955397	+	0.295325i	$0.904572\pi$
$270$	−0.989269	−	2.00533i	−0.0602050	−	0.122040i
$271$	−1.22298	−	8.50602i	−0.0742908	−	0.516704i	−0.992656	−	0.120970i	$-0.961399\pi$
$271$	−1.22298	−	8.50602i	−0.0742908	−	0.516704i	0.918365	−	0.395734i	$-0.129510\pi$
$272$	1.23655	−	5.68433i	0.0749769	−	0.344663i
$273$	−0.864810	+	12.0916i	−0.0523407	+	0.731818i
$274$	−10.6742	+	3.13423i	−0.644853	+	0.189346i
$275$	29.1697	−	15.4906i	1.75900	−	0.934120i
$276$	−0.320305	−	4.78512i	−0.0192801	−	0.288031i
$277$	7.66273	+	7.66273i	0.460409	+	0.460409i	0.898789	−	0.438381i	$-0.144448\pi$
$277$	7.66273	+	7.66273i	0.460409	+	0.460409i	−0.438381	+	0.898789i	$0.644448\pi$
$278$	1.76475	−	3.23190i	0.105843	−	0.193836i
$279$	5.15162	−	4.46391i	0.308420	−	0.267247i
$280$	−10.2751	+	0.307217i	−0.614055	+	0.0183597i
$281$	−25.9882	+	3.73654i	−1.55033	+	0.222903i	−0.863662	−	0.504071i	$-0.831835\pi$
$281$	−25.9882	+	3.73654i	−1.55033	+	0.222903i	−0.686665	+	0.726974i	$0.740926\pi$
$282$	0.129762	+	0.596507i	0.00772722	+	0.0355215i
$283$	−4.54288	+	1.69441i	−0.270046	+	0.100722i	−0.480839	−	0.876809i	$-0.659668\pi$
$283$	−4.54288	+	1.69441i	−0.270046	+	0.100722i	0.210793	+	0.977531i	$0.432395\pi$
$284$	4.50902	+	3.90709i	0.267561	+	0.231843i
$285$	−5.87252	+	0.596871i	−0.347858	+	0.0353556i
$286$	15.8442	−	7.23582i	0.936889	−	0.427863i
$287$	−15.1371	+	8.26549i	−0.893515	+	0.487896i
$288$	0.877679	−	0.479249i	0.0517177	−	0.0282400i
$289$	15.3188	−	6.99587i	0.901107	−	0.411522i
$290$	−6.64393	+	0.675275i	−0.390145	+	0.0396535i
$291$	6.57185	+	5.69454i	0.385249	+	0.333820i
$292$	9.51562	−	3.54914i	0.556860	−	0.207698i
$293$	4.78434	+	21.9932i	0.279504	+	1.28486i	0.876027	+	0.482263i	$0.160185\pi$
$293$	4.78434	+	21.9932i	0.279504	+	1.28486i	−0.596523	+	0.802596i	$0.703451\pi$
$294$	13.9906	−	2.01154i	0.815948	−	0.117316i
$295$	15.2779	−	0.456796i	0.889513	−	0.0265957i
$296$	7.21234	−	6.24953i	0.419209	−	0.363247i
$297$	3.16570	−	5.79755i	0.183693	−	0.336408i
$298$	0.0382472	+	0.0382472i	0.00221560	+	0.00221560i
$299$	8.90134	+	8.98293i	0.514778	+	0.519496i
$300$	−1.46431	+	4.78077i	−0.0845420	+	0.276018i
$301$	41.2920	−	12.1244i	2.38003	−	0.698840i
$302$	0.800163	−	11.1877i	0.0460442	−	0.643782i
$303$	0.0448389	−	0.206121i	0.00257593	−	0.0118414i
$304$	−0.375683	−	2.61293i	−0.0215469	−	0.149862i
$305$	11.5158	+	23.3435i	0.659393	+	1.33664i
$306$	5.29158	+	2.41658i	0.302499	+	0.138147i
$307$	7.09824	−	0.507676i	0.405118	−	0.0289746i	0.132706	−	0.991155i	$-0.457633\pi$
$307$	7.09824	−	0.507676i	0.405118	−	0.0289746i	0.272412	+	0.962181i	$0.412179\pi$
$308$	−18.1984	−	24.3102i	−1.03695	−	1.38520i
$309$	3.12580	+	6.84454i	0.177820	+	0.389372i
$310$	−15.2292	−	0.632521i	−0.864960	−	0.0359248i
$311$	9.88363	+	2.90209i	0.560449	+	0.164563i	0.549674	−	0.835379i	$-0.314752\pi$
$311$	9.88363	+	2.90209i	0.560449	+	0.164563i	0.0107750	+	0.999942i	$0.496570\pi$
$312$	−0.921509	+	2.47066i	−0.0521701	+	0.139874i
$313$	−6.43220	+	4.81509i	−0.363569	+	0.272165i	−0.765407	−	0.643546i	$-0.777462\pi$
$313$	−6.43220	+	4.81509i	−0.363569	+	0.272165i	0.401838	+	0.915711i	$0.368372\pi$
$314$	−1.55519	+	1.79479i	−0.0877646	+	0.101286i
$315$	1.88394	−	10.1056i	0.106148	−	0.569386i
$316$	−0.0780637	+	0.121470i	−0.00439143	+	0.00683319i
$317$	−18.0844	+	24.1579i	−1.01572	+	1.35684i	−0.0828766	+	0.996560i	$0.526411\pi$
$317$	−18.0844	+	24.1579i	−1.01572	+	1.35684i	−0.932843	+	0.360283i	$0.882680\pi$
$318$	−3.47179	−	0.755242i	−0.194688	−	0.0423519i
$319$	−12.9190	−	14.9093i	−0.723326	−	0.834762i
$320$	−2.16336	−	0.565572i	−0.120936	−	0.0316164i
$321$		−	2.70935i		−	0.151221i
$322$	12.0043	−	18.4930i	0.668972	−	1.03057i
$323$	10.8587	−	10.8587i	0.604191	−	0.604191i
$324$	0.281733	+	0.959493i	0.0156518	+	0.0533052i
$325$	−5.33736	−	12.0560i	−0.296063	−	0.668744i
$326$	8.87398	−	5.70296i	0.491484	−	0.315858i
$327$	12.2496	+	9.16990i	0.677402	+	0.507097i
$328$	−3.66582	+	0.797451i	−0.202411	+	0.0440319i
$329$	−1.16583	+	2.55280i	−0.0642740	+	0.140740i
$330$	−14.0414	+	4.58300i	−0.772956	+	0.252286i
$331$	1.41134	−	9.81612i	0.0775745	−	0.539543i	−0.913562	−	0.406699i	$-0.866680\pi$
$331$	1.41134	−	9.81612i	0.0775745	−	0.539543i	0.991137	−	0.132844i	$-0.0424110\pi$
$332$	1.07973	+	0.402717i	0.0592577	+	0.0221020i
$333$	4.57362	+	8.37595i	0.250633	+	0.458999i
$334$	0.772781	−	2.63185i	0.0422847	−	0.144008i
$335$	12.4270	−	9.89574i	0.678957	−	0.540662i
$336$	4.55043	+	0.654253i	0.248246	+	0.0356924i
$337$	0.0139026	+	0.194384i	0.000757324	+	0.0105888i	0.997817	−	0.0660438i	$-0.0210377\pi$
$337$	0.0139026	+	0.194384i	0.000757324	+	0.0105888i	−0.997059	+	0.0766326i	$0.975583\pi$
$338$	2.11309	+	5.66542i	0.114937	+	0.308158i
$339$	−1.37797	−	0.885566i	−0.0748409	−	0.0480973i
$340$	−4.90798	−	12.0464i	−0.266172	−	0.653307i
$341$	−24.3435	−	37.8793i	−1.31828	−	2.05128i
$342$	2.63308	+	0.188321i	0.142380	+	0.0101832i
$343$	28.7868	+	15.7188i	1.55434	+	0.848734i
$344$	9.36113			0.504718
$345$	−6.64189	−	8.41934i	−0.357588	−	0.453282i
$346$	−16.7984			−0.903090
$347$	−20.4595	−	11.1717i	−1.09832	−	0.599729i	−0.175315	−	0.984512i	$-0.556094\pi$
$347$	−20.4595	−	11.1717i	−1.09832	−	0.599729i	−0.923007	+	0.384783i	$0.874276\pi$
$348$	2.97895	+	0.213059i	0.159689	+	0.0114212i
$349$	−9.68031	−	15.0629i	−0.518175	−	0.806297i	0.479275	−	0.877665i	$-0.340900\pi$
$349$	−9.68031	−	15.0629i	−0.518175	−	0.806297i	−0.997450	+	0.0713684i	$0.977263\pi$
$350$	−18.5601	+	13.5603i	−0.992082	+	0.724830i
$351$	−2.21832	−	1.42563i	−0.118405	−	0.0760943i
$352$	−2.30840	−	6.18906i	−0.123038	−	0.329878i
$353$	−1.52690	−	21.3489i	−0.0812687	−	1.13628i	−0.860467	−	0.509507i	$-0.829828\pi$
$353$	−1.52690	−	21.3489i	−0.0812687	−	1.13628i	0.779198	−	0.626778i	$-0.215627\pi$
$354$	−6.76596	−	0.972798i	−0.359607	−	0.0517036i
$355$	13.2561	+	1.50313i	0.703560	+	0.0797779i
$356$	−0.0791456	+	0.269545i	−0.00419471	+	0.0142859i
$357$	12.8167	+	23.4720i	0.678332	+	1.24227i
$358$	−22.8236	−	8.51275i	−1.20626	−	0.449913i
$359$	1.54171	−	10.7228i	0.0813683	−	0.565929i	−0.907829	−	0.419340i	$-0.862262\pi$
$359$	1.54171	−	10.7228i	0.0813683	−	0.565929i	0.989198	−	0.146589i	$-0.0468294\pi$
$360$	1.01250	−	1.99370i	0.0533636	−	0.105077i
$361$	−4.99804	+	10.9442i	−0.263055	+	0.576010i
$362$	7.38962	−	1.60751i	0.388390	−	0.0844890i
$363$	−26.1242	−	19.5564i	−1.37117	−	1.02644i
$364$	−10.1981	+	6.55392i	−0.534526	+	0.343519i
$365$	13.0599	−	18.5784i	0.683584	−	0.972439i
$366$	−3.27957	−	11.1692i	−0.171426	−	0.583823i
$367$	−17.7638	+	17.7638i	−0.927263	+	0.927263i	−0.997528	−	0.0702658i	$-0.977615\pi$
$367$	−17.7638	+	17.7638i	−0.927263	+	0.927263i	0.0702658	+	0.997528i	$0.477615\pi$
$368$	3.63874	−	3.12404i	0.189682	−	0.162852i
$369$		−	3.75156i		−	0.195298i
$370$	5.39742	−	20.6456i	0.280599	−	1.07331i
$371$	−10.6964	−	12.3443i	−0.555330	−	0.640885i
$372$	6.66079	+	1.44897i	0.345346	+	0.0751255i
$373$	−2.76255	+	3.69033i	−0.143039	+	0.191078i	−0.866339	−	0.499456i	$-0.833533\pi$
$373$	−2.76255	+	3.69033i	−0.143039	+	0.191078i	0.723300	+	0.690534i	$0.242624\pi$
$374$	20.7748	−	32.3262i	1.07424	−	1.67155i
$375$	3.34533	+	10.6681i	0.172752	+	0.550899i
$376$	−0.399765	+	0.461353i	−0.0206163	+	0.0237925i
$377$	−6.30452	+	4.71950i	−0.324699	+	0.243067i
$378$	−1.60657	+	4.30737i	−0.0826328	+	0.221547i
$379$	−30.9791	−	9.09628i	−1.59129	−	0.467244i	−0.638183	−	0.769885i	$-0.720314\pi$
$379$	−30.9791	−	9.09628i	−1.59129	−	0.467244i	−0.953105	+	0.302640i	$0.902132\pi$
$380$	−3.99709	−	4.34350i	−0.205046	−	0.222817i
$381$	−0.585723	−	1.28256i	−0.0300075	−	0.0657073i
$382$	−1.47089	−	1.96488i	−0.0752572	−	0.100532i
$383$	−1.32167	+	0.0945275i	−0.0675340	+	0.00483013i	−0.105065	−	0.994465i	$-0.533505\pi$
$383$	−1.32167	+	0.0945275i	−0.0675340	+	0.00483013i	0.0375313	+	0.999295i	$0.488051\pi$
$384$	0.909632	+	0.415415i	0.0464195	+	0.0211991i
$385$	−64.3025	−	21.8177i	−3.27716	−	1.11193i
$386$	3.04568	+	21.1832i	0.155021	+	1.07820i
$387$	−1.98985	+	9.14720i	−0.101150	+	0.464978i
$388$	−0.620352	+	8.67365i	−0.0314936	+	0.440338i
$389$	−24.8409	+	7.29394i	−1.25948	+	0.369818i	−0.842302	−	0.539006i	$-0.818800\pi$
$389$	−24.8409	+	7.29394i	−1.25948	+	0.369818i	−0.417181	+	0.908823i	$0.636982\pi$
$390$	1.42498	+	5.72155i	0.0721569	+	0.289722i
$391$	27.2338	+	6.05459i	1.37727	+	0.306194i
$392$	9.99458	+	9.99458i	0.504802	+	0.504802i
$393$	−2.49077	+	4.56151i	−0.125643	+	0.230098i
$394$	−5.74514	+	4.97820i	−0.289436	+	0.250798i
$395$	0.00964917	+	0.322724i	0.000485502	+	0.0162380i
$396$	6.53831	−	0.940067i	0.328562	−	0.0472402i
$397$	−4.61693	−	21.2237i	−0.231717	−	1.06519i	−0.935103	−	0.354377i	$-0.884693\pi$
$397$	−4.61693	−	21.2237i	−0.231717	−	1.06519i	0.703386	−	0.710808i	$-0.251671\pi$
$398$	16.2184	−	6.04916i	0.812956	−	0.303217i
$399$	9.17160	+	7.94723i	0.459154	+	0.397859i
$400$	−4.70473	+	1.69277i	−0.235237	+	0.0846385i
$401$	−34.1587	+	15.5997i	−1.70580	+	0.779014i	−0.708493	+	0.705718i	$0.750624\pi$
$401$	−34.1587	+	15.5997i	−1.70580	+	0.779014i	−0.997310	+	0.0732959i	$0.976648\pi$
$402$	−6.23529	+	3.40473i	−0.310988	+	0.169812i
$403$	−15.7761	+	8.61438i	−0.785862	+	0.429113i
$404$	0.191880	−	0.0876284i	0.00954636	−	0.00435968i
$405$	1.73291	+	1.41315i	0.0861092	+	0.0702202i
$406$	10.3764	+	8.99117i	0.514970	+	0.446224i
$407$	59.0641	−	22.0298i	2.92770	−	1.09197i
$408$	1.23655	+	5.68433i	0.0612184	+	0.281416i
$409$	−20.4260	+	2.93681i	−1.01000	+	0.145216i	−0.627399	−	0.778698i	$-0.715881\pi$
$409$	−20.4260	+	2.93681i	−1.01000	+	0.145216i	−0.382601	+	0.923914i	$0.624972\pi$
$410$	−5.75181	+	6.10636i	−0.284062	+	0.301571i
$411$	8.40760	−	7.28523i	0.414716	−	0.359354i
$412$	−3.60612	+	6.60411i	−0.177661	+	0.325361i
$413$	−22.2205	−	22.2205i	−1.09340	−	1.09340i
$414$	2.27917	+	4.21964i	0.112015	+	0.207384i
$415$	2.50043	−	0.622746i	0.122741	−	0.0305694i
$416$	−2.53010	+	0.742906i	−0.124049	+	0.0364240i
$417$	−0.262694	+	3.67294i	−0.0128642	+	0.179865i
$418$	3.70657	−	17.0388i	0.181294	−	0.833397i
$419$	−0.138226	−	0.961386i	−0.00675281	−	0.0469668i	0.986166	−	0.165758i	$-0.0530071\pi$
$419$	−0.138226	−	0.961386i	−0.00675281	−	0.0469668i	−0.992919	+	0.118791i	$0.962098\pi$
$420$	9.21895	−	4.54789i	0.449839	−	0.221914i
$421$	30.7197	+	14.0292i	1.49719	+	0.683743i	0.984589	−	0.174885i	$-0.0559554\pi$
$421$	30.7197	+	14.0292i	1.49719	+	0.683743i	0.512599	+	0.858628i	$0.328683\pi$
$422$	−4.55731	+	0.325945i	−0.221846	+	0.0158668i
$423$	−0.365834	−	0.488697i	−0.0177874	−	0.0237612i
$424$	−1.47596	−	3.23191i	−0.0716792	−	0.156956i
$425$	−24.2846	−	16.0085i	−1.17798	−	0.776528i
$426$	−5.72462	−	1.68090i	−0.277359	−	0.0814398i
$427$	18.7016	−	50.1408i	0.905032	−	2.42649i
$428$	2.16895	−	1.62365i	0.104840	−	0.0784822i
$429$	−11.4066	+	13.1639i	−0.550713	+	0.635557i
$430$	17.2631	−	11.8380i	0.832503	−	0.570878i
$431$	6.14843	−	9.56714i	0.296159	−	0.460833i	−0.661004	−	0.750383i	$-0.729869\pi$
$431$	6.14843	−	9.56714i	0.296159	−	0.460833i	0.957163	+	0.289550i	$0.0935055\pi$
$432$	−0.599278	+	0.800541i	−0.0288328	+	0.0385161i
$433$	10.0778	+	2.19230i	0.484310	+	0.105355i	0.448090	−	0.893989i	$-0.352105\pi$
$433$	10.0778	+	2.19230i	0.484310	+	0.105355i	0.0362203	+	0.999344i	$0.488468\pi$
$434$	20.5216	+	23.6832i	0.985067	+	1.13683i
$435$	5.76301	−	3.37424i	0.276315	−	0.161782i
$436$			15.3016i			0.732813i
$437$	12.5393	−	1.74453i	0.599835	−	0.0834521i
$438$	−7.18135	+	7.18135i	−0.343138	+	0.343138i
$439$	0.994162	+	3.38580i	0.0474487	+	0.161596i	0.979809	−	0.199934i	$-0.0640728\pi$
$439$	0.994162	+	3.38580i	0.0474487	+	0.161596i	−0.932361	+	0.361530i	$0.882255\pi$
$440$	−12.0836	−	8.49427i	−0.576063	−	0.404948i
$441$	−11.8907	+	7.64167i	−0.566222	+	0.363889i
$442$	−12.2800	−	9.19273i	−0.584102	−	0.437253i
$443$	22.6969	−	4.93741i	1.07836	−	0.234584i	0.361906	−	0.932215i	$-0.382126\pi$
$443$	22.6969	−	4.93741i	1.07836	−	0.234584i	0.716457	+	0.697631i	$0.245762\pi$
$444$	−3.96443	+	8.68089i	−0.188143	+	0.411977i
$445$	0.194909	+	0.597163i	0.00923956	+	0.0283083i
$446$	−1.12660	+	7.83569i	−0.0533461	+	0.371031i
$447$	−0.0506794	−	0.0189024i	−0.00239705	−	0.000894054i
$448$	2.20321	+	4.03489i	0.104092	+	0.190630i
$449$	−1.74942	+	5.95799i	−0.0825604	+	0.281175i	−0.990418	−	0.138104i	$-0.955899\pi$
$449$	−1.74942	+	5.95799i	−0.0825604	+	0.281175i	0.907857	+	0.419279i	$0.137717\pi$
$450$	−0.654022	−	4.95704i	−0.0308309	−	0.233677i
$451$	−24.5288	−	3.52672i	−1.15502	−	0.166067i
$452$	−0.116853	−	1.63382i	−0.00549631	−	0.0768484i
$453$	3.91970	+	10.5091i	0.184164	+	0.493762i
$454$	3.92919	+	2.52514i	0.184406	+	0.118511i
$455$	−10.5186	+	24.9827i	−0.493121	+	1.17121i
$456$	1.42718	+	2.22074i	0.0668340	+	0.103996i
$457$	28.5264	+	2.04025i	1.33441	+	0.0954388i	0.720234	−	0.693731i	$-0.244034\pi$
$457$	28.5264	+	2.04025i	1.33441	+	0.0954388i	0.614175	+	0.789170i	$0.289489\pi$
$458$	−16.0236	−	8.74953i	−0.748732	−	0.408839i
$459$	−5.81727			−0.271527
$460$	2.75969	−	10.3626i	0.128671	−	0.483160i
$461$	18.5368			0.863346			0.431673	−	0.902030i	$-0.357923\pi$
$461$	18.5368			0.863346			0.431673	+	0.902030i	$0.357923\pi$
$462$	26.6526	+	14.5534i	1.23999	+	0.677087i
$463$	31.9294	+	2.28363i	1.48388	+	0.106129i	0.789622	−	0.613594i	$-0.210277\pi$
$463$	31.9294	+	2.28363i	1.48388	+	0.106129i	0.694261	+	0.719723i	$0.255731\pi$
$464$	1.61466	+	2.51246i	0.0749586	+	0.116638i
$465$	14.1157	−	5.75107i	0.654601	−	0.266700i
$466$	−9.56063	−	6.14424i	−0.442888	−	0.284627i
$467$	−9.55043	−	25.6057i	−0.441941	−	1.18489i	−0.946838	−	0.321710i	$-0.895742\pi$
$467$	−9.55043	−	25.6057i	−0.441941	−	1.18489i	0.504897	−	0.863180i	$-0.331530\pi$
$468$	−0.188116	−	2.63020i	−0.00869565	−	0.121581i
$469$	−32.3276	−	4.64801i	−1.49275	−	0.214625i
$470$	−0.153797	+	1.35633i	−0.00709412	+	0.0625630i
$471$	0.669071	−	2.27865i	0.0308292	−	0.104995i
$472$	−3.27592	−	5.99940i	−0.150787	−	0.276145i
$473$	57.9366	+	21.6092i	2.66393	+	0.993594i
$474$	0.0205490	−	0.142921i	0.000943847	−	0.00656460i
$475$	−12.8639	−	2.95532i	−0.590236	−	0.135599i
$476$	−11.1096	+	24.3266i	−0.509207	+	1.11501i
$477$	3.47179	−	0.755242i	0.158962	−	0.0345802i
$478$	21.6962	+	16.2416i	0.992363	+	0.742874i
$479$	1.62976	−	1.04738i	0.0744655	−	0.0478561i	−0.502878	−	0.864357i	$-0.667726\pi$
$479$	1.62976	−	1.04738i	0.0744655	−	0.0478561i	0.577344	+	0.816501i	$0.304089\pi$
$480$	2.20281	−	0.384230i	0.100544	−	0.0175376i
$481$	−7.08977	−	24.1455i	−0.323266	−	1.10094i
$482$	7.22595	−	7.22595i	0.329133	−	0.329133i
$483$	−3.23721	+	21.8086i	−0.147298	+	0.992324i
$484$		−	32.6332i		−	1.48333i
$485$	9.82458	+	16.7798i	0.446111	+	0.761933i
$486$	−0.654861	−	0.755750i	−0.0297051	−	0.0342815i
$487$	1.86185	+	0.405021i	0.0843685	+	0.0183532i	0.254551	−	0.967059i	$-0.418072\pi$
$487$	1.86185	+	0.405021i	0.0843685	+	0.0183532i	−0.170183	+	0.985412i	$0.554436\pi$
$488$	6.97602	−	9.31887i	0.315790	−	0.421846i
$489$	−5.70296	+	8.87398i	−0.257897	+	0.401295i
$490$	31.0703	+	5.79229i	1.40361	+	0.261669i
$491$	12.5772	−	14.5149i	0.567602	−	0.655048i	−0.397290	−	0.917693i	$-0.630049\pi$
$491$	12.5772	−	14.5149i	0.567602	−	0.655048i	0.964893	+	0.262645i	$0.0845948\pi$
$492$	3.00328	−	2.24822i	0.135398	−	0.101358i
$493$	−6.07147	+	16.2782i	−0.273445	+	0.733135i
$494$	−6.67897	−	1.96112i	−0.300501	−	0.0882351i
$495$	10.8687	−	10.0019i	0.488512	−	0.449551i
$496$	2.83171	+	6.20057i	0.127147	+	0.278414i
$497$	−16.4372	−	21.9576i	−0.737310	−	0.984931i
$498$	−1.14945	+	0.0822102i	−0.0515080	+	0.00368393i
$499$	−22.4298	−	10.2433i	−1.00409	−	0.458554i	−0.155635	−	0.987815i	$-0.549742\pi$
$499$	−22.4298	−	10.2433i	−1.00409	−	0.458554i	−0.848460	+	0.529260i	$0.822470\pi$
$500$	−6.53549	+	9.07124i	−0.292276	+	0.405678i
$501$	0.390364	+	2.71504i	0.0174402	+	0.121299i
$502$	4.71391	−	21.6695i	0.210392	−	0.967157i
$503$	−1.37217	+	19.1855i	−0.0611822	+	0.855438i	0.870501	+	0.492167i	$0.163795\pi$
$503$	−1.37217	+	19.1855i	−0.0611822	+	0.855438i	−0.931683	+	0.363272i	$0.881660\pi$
$504$	−4.41100	+	1.29519i	−0.196482	+	0.0576922i
$505$	0.243037	−	0.404247i	0.0108150	−	0.0179887i
$506$	29.7319	−	10.9352i	1.32174	−	0.486128i
$507$	−4.27563	−	4.27563i	−0.189888	−	0.189888i
$508$	0.675727	−	1.23750i	0.0299806	−	0.0549053i
$509$	−6.08706	+	5.27447i	−0.269804	+	0.233787i	−0.779246	−	0.626719i	$-0.784398\pi$
$509$	−6.08706	+	5.27447i	−0.269804	+	0.233787i	0.509441	+	0.860505i	$0.329852\pi$
$510$	9.46870	+	8.91892i	0.419281	+	0.394937i
$511$	−46.2140	+	6.64457i	−2.04439	+	0.293938i
$512$	0.212565	+	0.977147i	0.00939415	+	0.0431842i
$513$	−2.47336	+	0.922516i	−0.109202	+	0.0407301i
$514$	12.6255	+	10.9401i	0.556888	+	0.482546i
$515$	1.70133	+	16.7391i	0.0749693	+	0.737612i
$516$	−8.51518	+	3.88875i	−0.374860	+	0.171193i
$517$	−3.53916	+	1.93253i	−0.155652	+	0.0849924i
$518$	−38.5061	+	21.0259i	−1.69186	+	0.923827i
$519$	15.2804	−	6.97832i	0.670735	−	0.306314i
$520$	−3.72637	+	4.56955i	−0.163412	+	0.200388i
$521$	4.32484	+	3.74750i	0.189475	+	0.164181i	0.744432	−	0.667698i	$-0.232720\pi$
$521$	4.32484	+	3.74750i	0.189475	+	0.164181i	−0.554958	+	0.831879i	$0.687266\pi$
$522$	−2.79826	+	1.04370i	−0.122476	+	0.0456814i
$523$	5.34614	+	24.5758i	0.233770	+	1.07462i	0.933042	+	0.359768i	$0.117144\pi$
$523$	5.34614	+	24.5758i	0.233770	+	1.07462i	−0.699272	+	0.714856i	$0.746492\pi$
$524$	−5.14434	+	0.739645i	−0.224732	+	0.0323115i
$525$	11.2497	−	20.0451i	0.490979	−	0.874839i
$526$	−11.7719	+	10.2004i	−0.513277	+	0.444757i
$527$	−19.0041	+	34.8034i	−0.827831	+	1.51606i
$528$	4.67083	+	4.67083i	0.203272	+	0.203272i
$529$	14.9026	+	17.5189i	0.647938	+	0.761693i
$530$	−6.80891	−	4.09358i	−0.295760	−	0.177814i
$531$	6.55865	−	1.92579i	0.284621	−	0.0835723i
$532$	−0.865755	+	12.1048i	−0.0375352	+	0.524811i
$533$	−2.10281	+	9.66647i	−0.0910829	+	0.418701i
$534$	−0.0399798	−	0.278065i	−0.00173009	−	0.0120331i
$535$	1.94657	−	5.73705i	0.0841575	−	0.248034i
$536$	−6.46229	−	2.95123i	−0.279129	−	0.127474i
$537$	24.2974	−	1.73778i	1.04851	−	0.0749909i
$538$	14.6721	+	19.5996i	0.632560	+	0.845001i
$539$	38.7856	+	84.9286i	1.67061	+	3.65813i
$540$	−0.0927917	+	2.23414i	−0.00399312	+	0.0961422i
$541$	−3.26182	−	0.957758i	−0.140237	−	0.0411772i	0.210861	−	0.977516i	$-0.432373\pi$
$541$	−3.26182	−	0.957758i	−0.140237	−	0.0411772i	−0.351098	+	0.936339i	$0.614191\pi$
$542$	−3.00312	+	8.05166i	−0.128995	+	0.345849i
$543$	−6.05405	+	4.53200i	−0.259804	+	0.194487i
$544$	−3.80950	+	4.39640i	−0.163331	+	0.188494i
$545$	19.3502	+	28.2181i	0.828872	+	1.20873i
$546$	6.55392	−	10.1981i	0.280482	−	0.436438i
$547$	−4.87119	+	6.50715i	−0.208277	+	0.278226i	−0.892500	−	0.451047i	$-0.851051\pi$
$547$	−4.87119	+	6.50715i	−0.208277	+	0.278226i	0.684223	+	0.729273i	$0.260142\pi$
$548$	10.8706	+	2.36476i	0.464369	+	0.101017i
$549$	7.62305	+	8.79747i	0.325344	+	0.375467i
$550$	−33.0255	−	0.383754i	−1.40821	−	0.0163633i
$551$			7.88393i			0.335867i
$552$	−2.01214	+	4.35331i	−0.0856424	+	0.185289i
$553$	0.469376	−	0.469376i	0.0199599	−	0.0199599i
$554$	−3.05306	−	10.3978i	−0.129712	−	0.441759i
$555$	3.66682	+	21.0221i	0.155648	+	0.892337i
$556$	−3.09776	+	1.99081i	−0.131374	+	0.0844293i
$557$	13.0932	+	9.80143i	0.554775	+	0.415300i	0.839540	−	0.543298i	$-0.182825\pi$
$557$	13.0932	+	9.80143i	0.554775	+	0.415300i	−0.284765	+	0.958597i	$0.591915\pi$
$558$	−6.66079	+	1.44897i	−0.281974	+	0.0613397i
$559$	10.2543	−	22.4538i	0.433712	−	0.949696i
$560$	9.16548	+	4.65470i	0.387312	+	0.196697i
$561$	−5.46863	+	38.0351i	−0.230886	+	1.60585i
$562$	24.6000	+	9.17534i	1.03769	+	0.387038i
$563$	8.91765	+	16.3315i	0.375834	+	0.688289i	0.995311	−	0.0967258i	$-0.0308370\pi$
$563$	8.91765	+	16.3315i	0.375834	+	0.688289i	−0.619477	+	0.785015i	$0.712655\pi$
$564$	0.171986	−	0.585730i	0.00724191	−	0.0246637i
$565$	−2.28160	−	2.86521i	−0.0959876	−	0.120540i
$566$	4.79923	+	0.690026i	0.201727	+	0.0290039i
$567$	−0.327962	−	4.58551i	−0.0137731	−	0.192573i
$568$	−2.08501	−	5.59012i	−0.0874849	−	0.234556i
$569$	−26.2311	−	16.8577i	−1.09966	−	0.706711i	−0.140647	−	0.990060i	$-0.544918\pi$
$569$	−26.2311	−	16.8577i	−1.09966	−	0.706711i	−0.959017	+	0.283349i	$0.908555\pi$
$570$	5.44024	+	2.29054i	0.227867	+	0.0959401i
$571$	−12.1631	−	18.9261i	−0.509008	−	0.792032i	0.487708	−	0.873007i	$-0.337833\pi$
$571$	−12.1631	−	18.9261i	−0.509008	−	0.792032i	−0.996716	+	0.0809750i	$0.974197\pi$
$572$	−17.3739	−	1.24261i	−0.726439	−	0.0519560i
$573$	2.15421	+	1.17629i	0.0899932	+	0.0491400i
$574$	17.2467			0.719865
$575$	−8.01523	−	22.5999i	−0.334258	−	0.942482i
$576$	−1.00000			−0.0416667
$577$	26.5413	+	14.4927i	1.10493	+	0.603338i	0.924857	−	0.380315i	$-0.124185\pi$
$577$	26.5413	+	14.4927i	1.10493	+	0.603338i	0.180074	+	0.983653i	$0.442366\pi$
$578$	−16.7978	−	1.20140i	−0.698695	−	0.0499717i
$579$	−11.5703	−	18.0037i	−0.480844	−	0.748208i
$580$	6.15486	+	2.59142i	0.255567	+	0.107603i
$581$	−4.45677	−	2.86419i	−0.184898	−	0.118827i
$582$	−3.03887	−	8.14753i	−0.125965	−	0.337726i
$583$	−1.67429	−	23.4096i	−0.0693420	−	0.969528i
$584$	−10.0526	−	1.44534i	−0.415979	−	0.0598088i
$585$	−3.67303	−	4.61254i	−0.151861	−	0.190705i
$586$	6.34113	−	21.5959i	0.261949	−	0.892118i
$587$	−1.20576	−	2.20818i	−0.0497669	−	0.0911413i	0.851612	−	0.524173i	$-0.175626\pi$
$587$	−1.20576	−	2.20818i	−0.0497669	−	0.0911413i	−0.901379	+	0.433032i	$0.857444\pi$
$588$	−13.2433	−	4.93949i	−0.546144	−	0.203701i
$589$	−2.56087	+	17.8112i	−0.105519	+	0.733900i
$590$	−13.6280	−	6.92099i	−0.561056	−	0.284933i
$591$	3.15795	−	6.91495i	0.129901	−	0.284443i
$592$	−9.32520	+	2.02857i	−0.383263	+	0.0833739i
$593$	−2.05329	−	1.53708i	−0.0843187	−	0.0631202i	0.556287	−	0.830990i	$-0.312226\pi$
$593$	−2.05329	−	1.53708i	−0.0843187	−	0.0631202i	−0.640605	+	0.767870i	$0.721317\pi$
$594$	−5.55694	+	3.57123i	−0.228004	+	0.146529i
$595$	10.2756	+	58.9104i	0.421258	+	2.41509i
$596$	−0.0152388	−	0.0518987i	−0.000624207	−	0.00212585i
$597$	−12.2399	+	12.2399i	−0.500945	+	0.500945i
$598$	−3.50746	−	12.1501i	−0.143431	−	0.496854i
$599$			25.7133i			1.05062i	0.850912	+	0.525309i	$0.176050\pi$
$599$			25.7133i			1.05062i	−0.850912	+	0.525309i	$0.823950\pi$
$600$	3.57638	−	3.49422i	0.146005	−	0.142651i
$601$	17.7538	+	20.4890i	0.724193	+	0.835763i	0.991805	−	0.127764i	$-0.0407799\pi$
$601$	17.7538	+	20.4890i	0.724193	+	0.835763i	−0.267612	+	0.963527i	$0.586234\pi$
$602$	−42.0517	−	9.14779i	−1.71390	−	0.372836i
$603$	4.25744	−	5.68728i	0.173377	−	0.231604i
$604$	−6.06400	+	9.43576i	−0.246741	+	0.383936i
$605$	−41.2676	−	60.1799i	−1.67777	−	2.44666i
$606$	−0.138138	+	0.159419i	−0.00561146	+	0.00647597i
$607$	−15.8184	+	11.8415i	−0.642048	+	0.480631i	−0.870007	−	0.493040i	$-0.835886\pi$
$607$	−15.8184	+	11.8415i	−0.642048	+	0.480631i	0.227959	+	0.973671i	$0.426795\pi$
$608$	−0.922516	+	2.47336i	−0.0374130	+	0.100308i
$609$	−13.1737	−	3.86816i	−0.533827	−	0.156746i
$610$	1.08016	−	26.0070i	0.0437345	−	1.05299i
$611$	0.668705	+	1.46426i	0.0270529	+	0.0592376i
$612$	−3.48616	−	4.65697i	−0.140920	−	0.188247i
$613$	30.5600	−	2.18570i	1.23431	−	0.0882794i	0.561109	−	0.827742i	$-0.310375\pi$
$613$	30.5600	−	2.18570i	1.23431	−	0.0882794i	0.673198	+	0.739462i	$0.264920\pi$
$614$	−6.47328	−	2.95625i	−0.261240	−	0.119305i
$615$	2.69536	−	7.94393i	0.108687	−	0.320330i
$616$	4.32170	+	30.0581i	0.174126	+	1.21107i
$617$	7.21410	−	33.1627i	0.290429	−	1.33508i	−0.568373	−	0.822771i	$-0.692427\pi$
$617$	7.21410	−	33.1627i	0.290429	−	1.33508i	0.858802	−	0.512308i	$-0.171209\pi$
$618$	0.536793	−	7.50534i	0.0215930	−	0.301909i
$619$	−5.50073	+	1.61516i	−0.221093	+	0.0649188i	−0.390403	−	0.920644i	$-0.627664\pi$
$619$	−5.50073	+	1.61516i	−0.221093	+	0.0649188i	0.169310	+	0.985563i	$0.445846\pi$
$620$	13.0632	+	7.85373i	0.524631	+	0.315413i
$621$	−3.82611	−	2.89152i	−0.153537	−	0.116033i
$622$	−7.28382	−	7.28382i	−0.292055	−	0.292055i
$623$	0.618938	−	1.13350i	0.0247972	−	0.0454127i
$624$	1.99285	−	1.72681i	0.0797778	−	0.0691279i
$625$	−0.580918	+	24.9932i	−0.0232367	+	0.999730i
$626$	7.95303	−	1.14347i	0.317867	−	0.0457024i
$627$	3.70657	+	17.0388i	0.148026	+	0.680465i
$628$	2.22511	−	0.829923i	0.0887916	−	0.0331176i
$629$	−41.9562	−	36.3552i	−1.67290	−	1.44958i
$630$	−6.49659	+	7.96660i	−0.258830	+	0.317397i
$631$	40.9219	−	18.6884i	1.62908	−	0.743974i	0.629618	−	0.776905i	$-0.283211\pi$
$631$	40.9219	−	18.6884i	1.62908	−	0.743974i	0.999458	+	0.0329310i	$0.0104842\pi$
$632$	0.126729	−	0.0691993i	0.00504101	−	0.00275260i
$633$	4.01007	−	2.18967i	0.159386	−	0.0870314i
$634$	27.4499	−	12.5360i	1.09018	−	0.497867i
$635$	−0.318801	−	3.13663i	−0.0126512	−	0.124473i
$636$	2.68517	+	2.32671i	0.106474	+	0.0922601i
$637$	34.9215	−	13.0250i	1.38364	−	0.516071i
$638$	4.19346	+	19.2770i	0.166021	+	0.763185i
$639$	5.90557	−	0.849092i	0.233621	−	0.0335896i
$640$	1.62769	+	1.53318i	0.0643399	+	0.0606042i
$641$	19.6128	−	16.9946i	0.774660	−	0.671247i	−0.174986	−	0.984571i	$-0.555988\pi$
$641$	19.6128	−	16.9946i	0.774660	−	0.671247i	0.949646	+	0.313324i	$0.101443\pi$
$642$	−1.29845	+	2.37794i	−0.0512458	+	0.0938497i
$643$	−14.8531	−	14.8531i	−0.585749	−	0.585749i	0.350728	−	0.936477i	$-0.385934\pi$
$643$	−14.8531	−	14.8531i	−0.585749	−	0.585749i	−0.936477	+	0.350728i	$0.885934\pi$
$644$	−19.3986	+	10.4779i	−0.764413	+	0.412886i
$645$	−10.7854	+	17.9396i	−0.424676	+	0.706370i
$646$	−14.7344	+	4.32641i	−0.579717	+	0.170220i
$647$	−2.22405	+	31.0963i	−0.0874363	+	1.22252i	0.744490	+	0.667634i	$0.232693\pi$
$647$	−2.22405	+	31.0963i	−0.0874363	+	1.22252i	−0.831926	+	0.554886i	$0.812762\pi$
$648$	0.212565	−	0.977147i	0.00835035	−	0.0383860i
$649$	−6.42586	−	44.6928i	−0.252237	−	1.75435i
$650$	−1.09332	+	13.1392i	−0.0428835	+	0.515361i
$651$	−28.5054	−	13.0180i	−1.11722	−	0.510215i
$652$	−10.5216	+	0.752522i	−0.412059	+	0.0294711i
$653$	12.1487	+	16.2287i	0.475414	+	0.635079i	0.972578	−	0.232578i	$-0.0747160\pi$
$653$	12.1487	+	16.2287i	0.475414	+	0.635079i	−0.497164	+	0.867657i	$0.665625\pi$
$654$	−6.35651	−	13.9188i	−0.248559	−	0.544269i
$655$	−8.55150	+	7.86948i	−0.334135	+	0.307486i
$656$	3.59959	+	1.05694i	0.140540	+	0.0412664i
$657$	3.54914	−	9.51562i	0.138465	−	0.371240i
$658$	2.24665	−	1.68182i	0.0875834	−	0.0655641i
$659$	16.8572	−	19.4543i	0.656664	−	0.757831i	−0.325564	−	0.945520i	$-0.605554\pi$
$659$	16.8572	−	19.4543i	0.656664	−	0.757831i	0.982228	+	0.187689i	$0.0600997\pi$
$660$	14.5203	+	2.70694i	0.565201	+	0.105368i
$661$	0.118718	−	0.184729i	0.00461760	−	0.00718512i	−0.838937	−	0.544228i	$-0.816822\pi$
$661$	0.118718	−	0.184729i	0.00461760	−	0.00718512i	0.843555	+	0.537043i	$0.180459\pi$
$662$	−5.94307	+	7.93902i	−0.230984	+	0.308559i
$663$	14.9891	+	3.26068i	0.582129	+	0.126634i
$664$	−0.754651	−	0.870914i	−0.0292862	−	0.0337980i
$665$	13.7111	+	23.4177i	0.531692	+	0.908101i
$666$		−	9.54330i		−	0.369795i
$667$	−12.0845	+	7.68858i	−0.467914	+	0.297703i
$668$	−1.93956	+	1.93956i	−0.0750440	+	0.0750440i
$669$	−2.23027	−	7.59560i	−0.0862272	−	0.293663i
$670$	−15.6494	+	2.72968i	−0.604589	+	0.105457i
$671$	64.6867	−	41.5716i	2.49720	−	1.60486i
$672$	−3.68027	−	2.75501i	−0.141969	−	0.106277i
$673$	5.48956	−	1.19418i	0.211607	−	0.0460322i	−0.105512	−	0.994418i	$-0.533648\pi$
$673$	5.48956	−	1.19418i	0.211607	−	0.0460322i	0.317119	+	0.948386i	$0.397285\pi$
$674$	0.0809564	−	0.177270i	0.00311832	−	0.00682817i
$675$	2.65415	+	4.23739i	0.102158	+	0.163097i
$676$	0.860530	−	5.98511i	0.0330973	−	0.230197i
$677$	32.2533	+	12.0299i	1.23959	+	0.462345i	0.881875	−	0.471484i	$-0.156281\pi$
$677$	32.2533	+	12.0299i	1.23959	+	0.462345i	0.357720	+	0.933829i	$0.383554\pi$
$678$	0.785006	+	1.43763i	0.0301480	+	0.0552119i
$679$	11.2627	−	38.3572i	0.432223	−	1.47202i
$680$	−1.46559	+	12.9250i	−0.0562027	+	0.495651i
$681$	−4.62310	−	0.664702i	−0.177158	−	0.0254714i
$682$	3.21220	+	44.9125i	0.123002	+	1.71979i
$683$	−1.39662	−	3.74449i	−0.0534403	−	0.143279i	0.907487	−	0.420081i	$-0.137998\pi$
$683$	−1.39662	−	3.74449i	−0.0534403	−	0.143279i	−0.960927	+	0.276802i	$0.910725\pi$
$684$	−2.22074	−	1.42718i	−0.0849122	−	0.0545698i
$685$	23.0373	−	9.38592i	0.880209	−	0.358618i
$686$	−17.7323	−	27.5921i	−0.677024	−	1.05347i
$687$	18.2102	+	1.30242i	0.694764	+	0.0496905i
$688$	−8.21607	−	4.48631i	−0.313235	−	0.171039i
$689$	−9.36894			−0.356928
$690$	1.79449	+	10.5726i	0.0683151	+	0.402492i
$691$	−24.5812			−0.935114			−0.467557	−	0.883963i	$-0.654866\pi$
$691$	−24.5812			−0.935114			−0.467557	+	0.883963i	$0.654866\pi$
$692$	14.7436	+	8.05064i	0.560469	+	0.306039i
$693$	−30.2898	−	2.16637i	−1.15061	−	0.0822936i
$694$	12.6028	+	19.6104i	0.478396	+	0.744399i
$695$	−3.19513	+	7.58871i	−0.121198	+	0.287856i
$696$	−2.51246	−	1.61466i	−0.0952344	−	0.0612034i
$697$	7.62665	+	20.4478i	0.288880	+	0.774517i
$698$	1.27735	+	17.8596i	0.0483483	+	0.675997i
$699$	11.2491	+	1.61737i	0.425479	+	0.0611746i
$700$	22.7886	−	3.00668i	0.861329	−	0.113642i
$701$	−2.69099	+	9.16466i	−0.101637	+	0.346145i	−0.994573	−	0.104039i	$-0.966823\pi$
$701$	−2.69099	+	9.16466i	−0.101637	+	0.346145i	0.892936	+	0.450184i	$0.148641\pi$
$702$	1.26374	+	2.31437i	0.0476968	+	0.0873502i
$703$	−23.6040	−	8.80385i	−0.890243	−	0.332043i
$704$	−0.940067	+	6.53831i	−0.0354301	+	0.246422i
$705$	−0.423543	−	1.29765i	−0.0159515	−	0.0488725i
$706$	−8.89129	+	19.4692i	−0.334628	+	0.732733i
$707$	−0.947586	+	0.206135i	−0.0356376	+	0.00775249i
$708$	5.47213	+	4.09638i	0.205655	+	0.153952i
$709$	12.1850	−	7.83080i	0.457616	−	0.294092i	−0.291451	−	0.956586i	$-0.594138\pi$
$709$	12.1850	−	7.83080i	0.457616	−	0.294092i	0.749068	+	0.662494i	$0.230502\pi$
$710$	−10.9142	−	7.67224i	−0.409603	−	0.287934i
$711$	0.0406797	+	0.138542i	0.00152561	+	0.00519574i
$712$	0.198644	−	0.198644i	0.00744449	−	0.00744449i
$713$	−29.7986	+	13.4446i	−1.11596	+	0.503504i
$714$		−	26.7433i		−	1.00084i
$715$	−33.6111	+	19.6793i	−1.25699	+	0.735964i
$716$	15.9520	+	18.4096i	0.596156	+	0.688000i
$717$	−26.4826	−	5.76094i	−0.989011	−	0.215146i
$718$	−6.49203	+	8.67233i	−0.242280	+	0.323649i
$719$	15.0784	−	23.4625i	0.562331	−	0.875004i	−0.437374	−	0.899280i	$-0.644091\pi$
$719$	15.0784	−	23.4625i	0.562331	−	0.875004i	0.999705	+	0.0242754i	$0.00772785\pi$
$720$	−1.84413	+	1.26459i	−0.0687267	+	0.0471284i
$721$	22.6529	−	26.1428i	0.843637	−	0.973608i
$722$	9.63167	−	7.21018i	0.358454	−	0.268335i
$723$	−3.57119	+	9.57472i	−0.132814	+	0.356088i
$724$	−7.25611	−	2.13059i	−0.269671	−	0.0791826i
$725$	14.6274	−	3.00444i	0.543250	−	0.111582i
$726$	13.5563	+	29.6842i	0.503123	+	1.10169i
$727$	14.8360	+	19.8186i	0.550236	+	0.735030i	0.986314	−	0.164880i	$-0.0527236\pi$
$727$	14.8360	+	19.8186i	0.550236	+	0.735030i	−0.436078	+	0.899909i	$0.643633\pi$
$728$	12.0916	−	0.864810i	0.448145	−	0.0320520i
$729$	0.909632	+	0.415415i	0.0336901	+	0.0153857i
$730$	−20.3660	+	10.0470i	−0.753781	+	0.371855i
$731$	−7.74993	−	53.9020i	−0.286642	−	1.99364i
$732$	−2.47441	+	11.3747i	−0.0914569	+	0.420421i
$733$	−3.15722	+	44.1436i	−0.116614	+	1.63048i	0.516403	+	0.856346i	$0.327271\pi$
$733$	−3.15722	+	44.1436i	−0.116614	+	1.63048i	−0.633018	+	0.774137i	$0.718184\pi$
$734$	24.1042	−	7.07763i	0.889702	−	0.261240i
$735$	−30.6688	+	7.63823i	−1.13123	+	0.281740i
$736$	−4.69083	+	0.998039i	−0.172906	+	0.0367882i
$737$	−33.1829	−	33.1829i	−1.22231	−	1.22231i
$738$	−1.79793	+	3.29266i	−0.0661827	+	0.121205i
$739$	−4.98217	+	4.31708i	−0.183272	+	0.158806i	−0.741665	−	0.670770i	$-0.765964\pi$
$739$	−4.98217	+	4.31708i	−0.183272	+	0.158806i	0.558393	+	0.829577i	$0.311418\pi$
$740$	−14.6316	+	15.5335i	−0.537868	+	0.571023i
$741$	6.89009	−	0.990645i	0.253114	−	0.0363923i
$742$	3.47202	+	15.9606i	0.127462	+	0.585932i
$743$	25.0534	−	9.34444i	0.919120	−	0.342814i	0.155020	−	0.987911i	$-0.450456\pi$
$743$	25.0534	−	9.34444i	0.919120	−	0.342814i	0.764100	+	0.645097i	$0.223183\pi$
$744$	−5.15162	−	4.46391i	−0.188868	−	0.163655i
$745$	−0.0937329	−	0.0764372i	−0.00343411	−	0.00280044i
$746$	4.19322	−	1.91498i	0.153525	−	0.0701123i
$747$	1.01142	−	0.552279i	0.0370061	−	0.0202068i
$748$	−33.7259	+	18.4158i	−1.23314	+	0.673347i
$749$	−11.3299	+	5.17419i	−0.413986	+	0.189061i
$750$	2.17656	−	10.9664i	0.0794768	−	0.400437i
$751$	−28.4783	−	24.6766i	−1.03919	−	0.900462i	−0.0440579	−	0.999029i	$-0.514029\pi$
$751$	−28.4783	−	24.6766i	−1.03919	−	0.900462i	−0.995130	+	0.0985672i	$0.968574\pi$
$752$	0.571968	−	0.213333i	0.0208575	−	0.00777946i
$753$	4.71391	+	21.6695i	0.171785	+	0.789681i
$754$	7.79516	−	1.12078i	0.283883	−	0.0408162i
$755$	0.749548	+	25.0692i	0.0272788	+	0.912363i
$756$	3.47435	−	3.01054i	0.126361	−	0.109492i
$757$	7.82301	−	14.3268i	0.284332	−	0.520716i	−0.696007	−	0.718035i	$-0.745042\pi$
$757$	7.82301	−	14.3268i	0.284332	−	0.520716i	0.980339	+	0.197319i	$0.0632236\pi$
$758$	22.8303	+	22.8303i	0.829234	+	0.829234i
$759$	−22.5024	+	22.2981i	−0.816787	+	0.809369i
$760$	1.42654	+	5.72780i	0.0517461	+	0.207769i
$761$	10.8518	−	3.18637i	0.393376	−	0.115506i	−0.0790614	−	0.996870i	$-0.525192\pi$
$761$	10.8518	−	3.18637i	0.393376	−	0.115506i	0.472438	+	0.881364i	$0.343374\pi$
$762$	−0.100586	+	1.40638i	−0.00364385	+	0.0509477i
$763$	14.9529	−	68.7372i	0.541330	−	2.48846i
$764$	0.349303	+	2.42945i	0.0126373	+	0.0878945i
$765$	−12.3181	−	4.17950i	−0.445361	−	0.151110i
$766$	1.20530	+	0.550443i	0.0435493	+	0.0198883i
$767$	−17.9788	+	1.28587i	−0.649178	+	0.0464301i
$768$	−0.599278	−	0.800541i	−0.0216246	−	0.0288870i
$769$	20.1807	+	44.1895i	0.727733	+	1.59351i	0.802739	+	0.596331i	$0.203375\pi$
$769$	20.1807	+	44.1895i	0.727733	+	1.59351i	−0.0750054	+	0.997183i	$0.523897\pi$
$770$	45.9809	+	49.9659i	1.65704	+	1.80064i
$771$	−16.0293	−	4.70661i	−0.577279	−	0.169505i
$772$	7.47890	−	20.0517i	0.269171	−	0.721676i
$773$	−18.0536	+	13.5147i	−0.649343	+	0.486092i	−0.872451	−	0.488702i	$-0.837471\pi$
$773$	−18.0536	+	13.5147i	−0.649343	+	0.486092i	0.223108	+	0.974794i	$0.428380\pi$
$774$	6.13024	−	7.07467i	0.220347	−	0.254294i
$775$	34.0220	−	2.03628i	1.22211	−	0.0731452i
$776$	4.70131	−	7.31538i	0.168767	−	0.262607i
$777$	26.2919	−	35.1219i	0.943217	−	1.25999i
$778$	25.2979	+	5.50323i	0.906975	+	0.197300i
$779$	6.48533	+	7.48446i	0.232361	+	0.268159i
$780$	1.49137	−	5.70461i	0.0533995	−	0.204258i
$781$		−	39.4106i		−	1.41022i
$782$	−21.0008	−	18.3657i	−0.750989	−	0.656757i
$783$	2.11182	−	2.11182i	0.0754702	−	0.0754702i
$784$	−3.98214	−	13.5619i	−0.142219	−	0.484354i
$785$	3.05388	−	4.34434i	0.108998	−	0.155056i
$786$	4.37220	−	2.80984i	0.155951	−	0.100224i
$787$	−34.6473	−	25.9366i	−1.23504	−	0.924541i	−0.236155	−	0.971715i	$-0.575887\pi$
$787$	−34.6473	−	25.9366i	−1.23504	−	0.924541i	−0.998887	+	0.0471748i	$0.984978\pi$
$788$	7.42819	−	1.61590i	0.264618	−	0.0575642i
$789$	6.47067	−	14.1688i	0.230362	−	0.504422i
$790$	0.146196	−	0.287872i	0.00520143	−	0.0102420i
$791$	−1.07166	+	7.45357i	−0.0381039	+	0.265019i
$792$	−6.18906	−	2.30840i	−0.219919	−	0.0820255i
$793$	−14.7108	−	26.9409i	−0.522397	−	0.956699i
$794$	−6.11924	+	20.8402i	−0.217164	+	0.739592i
$795$	7.89413	+	0.895130i	0.279976	+	0.0317470i
$796$	−17.1336	−	2.46344i	−0.607285	−	0.0873144i
$797$	−0.133443	−	1.86578i	−0.00472680	−	0.0660892i	0.994541	−	0.104345i	$-0.0332745\pi$
$797$	−0.133443	−	1.86578i	−0.00472680	−	0.0660892i	−0.999268	+	0.0382554i	$0.987820\pi$
$798$	−4.24101	−	11.3706i	−0.150130	−	0.402515i
$799$	2.98746	+	1.91992i	0.105689	+	0.0679220i
$800$	4.94051	+	0.769031i	0.174673	+	0.0271893i
$801$	0.151879	+	0.236329i	0.00536639	+	0.00835027i
$802$	37.4565	+	2.67894i	1.32264	+	0.0945968i
$803$	−58.8797	−	32.1507i	−2.07782	−	1.13457i
$804$	7.10429			0.250549
$805$	−22.5234	+	43.8538i	−0.793847	+	1.54564i
$806$	17.9748			0.633134
$807$	−21.4882	−	11.7335i	−0.756421	−	0.413037i
$808$	−0.210404	−	0.0150484i	−0.00740200	−	0.000529402i
$809$	10.3024	+	16.0309i	0.362215	+	0.563617i	0.973756	−	0.227596i	$-0.0730864\pi$
$809$	10.3024	+	16.0309i	0.362215	+	0.563617i	−0.611541	+	0.791213i	$0.709450\pi$
$810$	−0.843690	−	2.07079i	−0.0296442	−	0.0727603i
$811$	11.5553	+	7.42614i	0.405761	+	0.260767i	0.727564	−	0.686040i	$-0.240652\pi$
$811$	11.5553	+	7.42614i	0.405761	+	0.260767i	−0.321803	+	0.946807i	$0.604289\pi$
$812$	−4.79811	−	12.8642i	−0.168381	−	0.451446i
$813$	−0.613052	−	8.57159i	−0.0215007	−	0.300619i
$814$	−62.3970	−	8.97134i	−2.18702	−	0.314445i
$815$	−18.4516	+	14.6933i	−0.646333	+	0.514683i
$816$	1.63892	−	5.58163i	0.0573735	−	0.195396i
$817$	−11.8430	−	21.6888i	−0.414333	−	0.758795i
$818$	19.3349	+	7.21156i	0.676030	+	0.252146i
$819$	−1.72521	+	11.9991i	−0.0602838	+	0.419283i
$820$	7.97471	−	2.60287i	0.278489	−	0.0908963i
$821$	−11.9737	+	26.2187i	−0.417884	+	0.915039i	0.577255	+	0.816564i	$0.304124\pi$
$821$	−11.9737	+	26.2187i	−0.417884	+	0.915039i	−0.995140	+	0.0984751i	$0.968604\pi$
$822$	−10.8706	+	2.36476i	−0.379156	+	0.0824804i
$823$	10.7913	+	8.07829i	0.376162	+	0.281591i	0.770585	−	0.637338i	$-0.219964\pi$
$823$	10.7913	+	8.07829i	0.376162	+	0.281591i	−0.394422	+	0.918929i	$0.629055\pi$
$824$	6.33002	−	4.06806i	0.220517	−	0.141718i
$825$	30.2005	−	13.3702i	1.05145	−	0.465491i
$826$	8.85330	+	30.1516i	0.308046	+	1.04911i
$827$	−7.93863	+	7.93863i	−0.276053	+	0.276053i	−0.831531	−	0.555478i	$-0.812535\pi$
$827$	−7.93863	+	7.93863i	−0.276053	+	0.276053i	0.555478	+	0.831531i	$0.312535\pi$
$828$	0.0218775	−	4.79578i	0.000760296	−	0.166665i
$829$		−	27.7712i		−	0.964535i	−0.876024	−	0.482267i	$-0.839813\pi$
$829$		−	27.7712i		−	0.964535i	0.876024	−	0.482267i	$-0.160187\pi$
$830$	−2.49302	−	0.651756i	−0.0865341	−	0.0226228i
$831$	7.09656	+	8.18986i	0.246177	+	0.284103i
$832$	2.57666	+	0.560517i	0.0893295	+	0.0194324i
$833$	49.2751	−	65.8238i	1.70728	−	2.28066i
$834$	1.99081	−	3.09776i	0.0689362	−	0.107267i
$835$	−1.12406	+	6.02956i	−0.0388997	+	0.208662i
$836$	−11.4190	+	13.1783i	−0.394935	+	0.455779i
$837$	5.45695	−	4.08502i	0.188620	−	0.141199i
$838$	−0.339425	+	0.910033i	−0.0117252	+	0.0314366i
$839$	−12.9647	−	3.80678i	−0.447591	−	0.131425i	0.0501662	−	0.998741i	$-0.484025\pi$
$839$	−12.9647	−	3.80678i	−0.447591	−	0.131425i	−0.497758	+	0.867316i	$0.665843\pi$
$840$	−10.2709	−	0.426584i	−0.354378	−	0.0147185i
$841$	8.34172	+	18.2658i	0.287645	+	0.629856i
$842$	−20.2386	−	27.0356i	−0.697467	−	0.931707i
$843$	−26.1886	+	1.87304i	−0.901982	+	0.0645110i
$844$	4.15606	+	1.89801i	0.143058	+	0.0653322i
$845$	−5.98177	−	12.1255i	−0.205779	−	0.417132i
$846$	0.0868772	+	0.604244i	0.00298690	+	0.0207743i
$847$	−31.8895	+	146.594i	−1.09574	+	5.03702i
$848$	−0.253467	+	3.54394i	−0.00870410	+	0.121699i
$849$	−4.65218	+	1.36600i	−0.159663	+	0.0468811i
$850$	13.6421	+	25.6887i	0.467919	+	0.881117i
$851$	−9.52458	−	44.7660i	−0.326499	−	1.53456i
$852$	4.21881	+	4.21881i	0.144534	+	0.144534i
$853$	−11.7856	+	21.5837i	−0.403531	+	0.739013i	−0.997872	−	0.0652007i	$-0.979231\pi$
$853$	−11.7856	+	21.5837i	−0.403531	+	0.739013i	0.594341	+	0.804213i	$0.297413\pi$
$854$	−40.4439	+	35.0449i	−1.38396	+	1.19921i
$855$	−5.90014	+	0.176409i	−0.201781	+	0.00603306i
$856$	−2.68177	+	0.385581i	−0.0916611	+	0.0131789i
$857$	−2.83329	−	13.0244i	−0.0967835	−	0.444906i	−0.999880	−	0.0154695i	$-0.995076\pi$
$857$	−2.83329	−	13.0244i	−0.0967835	−	0.444906i	0.903097	−	0.429437i	$-0.141288\pi$
$858$	16.3201	−	6.08707i	0.557158	−	0.207809i
$859$	−39.9381	−	34.6066i	−1.36267	−	1.18076i	−0.964696	−	0.263366i	$-0.915167\pi$
$859$	−39.9381	−	34.6066i	−1.36267	−	1.18076i	−0.397976	−	0.917396i	$-0.630287\pi$
$860$	−20.8248	+	2.11659i	−0.710121	+	0.0721752i
$861$	−15.6882	+	7.16456i	−0.534652	+	0.244167i
$862$	−9.98139	+	5.45025i	−0.339968	+	0.185636i
$863$	4.00372	−	2.18620i	0.136288	−	0.0744190i	−0.409658	−	0.912239i	$-0.634352\pi$
$863$	4.00372	−	2.18620i	0.136288	−	0.0744190i	0.545946	+	0.837820i	$0.316170\pi$
$864$	0.909632	−	0.415415i	0.0309463	−	0.0141327i
$865$	37.3699	−	3.79820i	1.27062	−	0.129143i
$866$	−7.79445	−	6.75393i	−0.264866	−	0.229508i
$867$	15.7789	−	5.88522i	0.535879	−	0.199872i
$868$	−6.66123	−	30.6212i	−0.226097	−	1.03935i
$869$	0.944074	−	0.135737i	0.0320255	−	0.00460457i
$870$	−6.67517	+	0.199582i	−0.226310	+	0.00676646i
$871$	−14.1578	+	12.2678i	−0.479718	+	0.415678i
$872$	7.33327	−	13.4299i	0.248336	−	0.454793i
$873$	6.14886	+	6.14886i	0.208108	+	0.208108i
$874$	−11.8415	−	4.47830i	−0.400545	−	0.151481i
$875$	38.2230	−	34.3629i	1.29217	−	1.16168i
$876$	9.74457	−	2.86126i	0.329239	−	0.0966732i
$877$	3.79708	−	53.0901i	0.128218	−	1.79272i	−0.373436	−	0.927656i	$-0.621820\pi$
$877$	3.79708	−	53.0901i	0.128218	−	1.79272i	0.501654	−	0.865068i	$-0.332725\pi$
$878$	0.750088	−	3.44810i	0.0253142	−	0.116368i
$879$	3.20317	+	22.2785i	0.108040	+	0.751436i
$880$	6.53466	+	13.2463i	0.220283	+	0.446533i
$881$	−18.5997	−	8.49420i	−0.626640	−	0.286177i	0.0766740	−	0.997056i	$-0.475570\pi$
$881$	−18.5997	−	8.49420i	−0.626640	−	0.286177i	−0.703314	+	0.710879i	$0.748297\pi$
$882$	14.0985	−	1.00834i	0.474720	−	0.0339526i
$883$	13.5457	+	18.0949i	0.455848	+	0.608941i	0.968305	−	0.249772i	$-0.0803556\pi$
$883$	13.5457	+	18.0949i	0.455848	+	0.608941i	−0.512457	+	0.858713i	$0.671265\pi$
$884$	6.37233	+	13.9535i	0.214325	+	0.469306i
$885$	15.2716	+	0.634281i	0.513348	+	0.0213211i
$886$	−22.2869	−	6.54401i	−0.748742	−	0.219850i
$887$	2.25284	−	6.04009i	0.0756429	−	0.202806i	−0.893625	−	0.448815i	$-0.851846\pi$
$887$	2.25284	−	6.04009i	0.0756429	−	0.202806i	0.969268	+	0.246008i	$0.0791190\pi$
$888$	7.63980	−	5.71908i	0.256375	−	0.191920i
$889$	−4.24478	+	4.89873i	−0.142365	+	0.164298i
$890$	0.115123	−	0.617528i	0.00385892	−	0.0206996i
$891$	3.57123	−	5.55694i	0.119641	−	0.186164i
$892$	4.74404	−	6.33730i	0.158842	−	0.212188i
$893$	1.57466	+	0.342546i	0.0526940	+	0.0114629i
$894$	0.0354212	+	0.0408783i	0.00118466	+	0.00136717i
$895$	52.6983	+	13.7770i	1.76151	+	0.460515i
$896$		−	4.59722i		−	0.153582i
$897$	8.23783	+	9.59505i	0.275053	+	0.320369i
$898$	4.39079	−	4.39079i	0.146523	−	0.146523i
$899$	−5.73555	−	19.5335i	−0.191291	−	0.651478i
$900$	−1.80164	+	4.66413i	−0.0600545	+	0.155471i
$901$	−17.3876	+	11.1743i	−0.579266	+	0.372271i
$902$	19.8383	+	14.8507i	0.660542	+	0.494476i
$903$	42.0517	−	9.14779i	1.39939	−	0.304419i
$904$	−0.680447	+	1.48997i	−0.0226313	+	0.0495557i
$905$	−16.0755	+	5.24691i	−0.534369	+	0.174413i
$906$	1.59625	−	11.1021i	0.0530318	−	0.368844i
$907$	1.08936	+	0.406311i	0.0361717	+	0.0134913i	0.367485	−	0.930029i	$-0.380219\pi$
$907$	1.08936	+	0.406311i	0.0361717	+	0.0134913i	−0.331313	+	0.943521i	$0.607492\pi$
$908$	−2.23840	−	4.09932i	−0.0742839	−	0.136041i
$909$	0.0594292	−	0.202397i	0.00197114	−	0.00671309i
$910$	21.2049	−	16.8857i	0.702935	−	0.559757i
$911$	12.3307	+	1.77289i	0.408534	+	0.0587384i	0.343519	−	0.939146i	$-0.388381\pi$
$911$	12.3307	+	1.77289i	0.408534	+	0.0587384i	0.0650157	+	0.997884i	$0.479290\pi$
$912$	−0.188321	−	2.63308i	−0.00623594	−	0.0871898i
$913$	−2.66017	−	7.13218i	−0.0880386	−	0.236041i
$914$	−24.0592	−	15.4619i	−0.795809	−	0.511435i
$915$	9.82115	+	24.1055i	0.324677	+	0.796904i
$916$	9.87035	+	15.3586i	0.326125	+	0.507461i
$917$	23.8320	+	1.70450i	0.787003	+	0.0562875i
$918$	5.10570	+	2.78792i	0.168513	+	0.0920152i
$919$	5.11126			0.168605			0.0843025	−	0.996440i	$-0.473134\pi$
$919$	5.11126			0.168605			0.0843025	+	0.996440i	$0.473134\pi$
$920$	−7.38840	+	7.77249i	−0.243588	+	0.256251i
$921$	7.11638			0.234493
$922$	−16.2694	−	8.88376i	−0.535804	−	0.292571i
$923$	−15.6925	−	1.12235i	−0.516527	−	0.0369427i
$924$	−16.4177	−	25.5465i	−0.540104	−	0.840418i
$925$	−7.33909	+	47.1487i	−0.241308	+	1.55024i
$926$	−26.9293	−	17.3064i	−0.884952	−	0.568724i
$927$	2.62955	+	7.05009i	0.0863657	+	0.231555i
$928$	−0.213059	−	2.97895i	−0.00699400	−	0.0977889i
$929$	42.6479	+	6.13184i	1.39923	+	0.201179i	0.800290	−	0.599613i	$-0.204679\pi$
$929$	42.6479	+	6.13184i	1.39923	+	0.201179i	0.598942	+	0.800792i	$0.295588\pi$
$930$	−15.1453	−	1.71735i	−0.496633	−	0.0563141i
$931$	10.5121	−	35.8008i	0.344519	−	1.17332i
$932$	5.44654	+	9.97460i	0.178407	+	0.326729i
$933$	9.65141	+	3.59979i	0.315973	+	0.117852i
$934$	−3.88929	+	27.0506i	−0.127261	+	0.885123i
$935$	−38.9067	+	76.6105i	−1.27238	+	2.50543i
$936$	−1.09542	+	2.39863i	−0.0358048	+	0.0784015i
$937$	54.2446	−	11.8002i	1.77209	−	0.385495i	0.796423	−	0.604740i	$-0.206723\pi$
$937$	54.2446	−	11.8002i	1.77209	−	0.385495i	0.975670	+	0.219245i	$0.0703595\pi$
$938$	26.1457	+	19.5724i	0.853687	+	0.639062i
$939$	−6.75932	+	4.34395i	−0.220582	+	0.141759i
$940$	0.785006	−	1.11672i	0.0256041	−	0.0364233i
$941$	16.1989	+	55.1682i	0.528068	+	1.79843i	0.598752	+	0.800935i	$0.295664\pi$
$941$	16.1989	+	55.1682i	0.528068	+	1.79843i	−0.0706841	+	0.997499i	$0.522518\pi$
$942$	−1.67927	+	1.67927i	−0.0547136	+	0.0547136i
$943$	−5.14758	+	17.2397i	−0.167628	+	0.561403i
$944$			6.83553i			0.222478i
$945$	2.60006	−	9.94545i	0.0845800	−	0.323526i
$946$	−40.4935	−	46.7320i	−1.31656	−	1.51939i
$947$	−34.1360	−	7.42583i	−1.10927	−	0.241307i	−0.379630	−	0.925138i	$-0.623949\pi$
$947$	−34.1360	−	7.42583i	−1.10927	−	0.241307i	−0.729640	+	0.683831i	$0.760312\pi$
$948$	−0.0865304	+	0.115591i	−0.00281038	+	0.00375422i
$949$	−14.4786	+	22.5291i	−0.469995	+	0.731327i
$950$	9.87404	+	8.75883i	0.320356	+	0.284174i
$951$	−19.7617	+	22.8062i	−0.640817	+	0.739542i
$952$	21.4091	−	16.0267i	0.693874	−	0.519427i
$953$	16.7951	−	45.0293i	0.544046	−	1.45864i	−0.316165	−	0.948704i	$-0.602395\pi$
$953$	16.7951	−	45.0293i	0.544046	−	1.45864i	0.860211	−	0.509939i	$-0.170332\pi$
$954$	−3.40907	−	1.00099i	−0.110373	−	0.0324083i
$955$	3.71642	+	4.03850i	0.120260	+	0.130683i
$956$	−11.2586	−	24.6528i	−0.364128	−	0.797329i
$957$	−11.8225	−	15.7930i	−0.382166	−	0.510514i
$958$	−1.93236	+	0.138205i	−0.0624317	+	0.00446521i
$959$	−46.5217	−	21.2457i	−1.50226	−	0.686061i
$960$	−2.11750	−	0.718463i	−0.0683420	−	0.0231883i
$961$	−2.20100	−	15.3083i	−0.0709999	−	0.493815i
$962$	−5.34918	+	24.5898i	−0.172465	+	0.792807i
$963$	0.193283	−	2.70245i	0.00622845	−	0.0870851i
$964$	−9.80509	+	2.87903i	−0.315801	+	0.0927275i
$965$	−11.5651	−	46.4357i	−0.372293	−	1.49482i
$966$	13.2930	−	17.5895i	0.427694	−	0.565932i
$967$	24.1752	+	24.1752i	0.777422	+	0.777422i	0.979392	−	0.201969i	$-0.0647342\pi$
$967$	24.1752	+	24.1752i	0.777422	+	0.777422i	−0.201969	+	0.979392i	$0.564734\pi$
$968$	−15.6394	+	28.6415i	−0.502671	+	0.920573i
$969$	11.6056	−	10.0563i	0.372827	−	0.323056i
$970$	−0.581111	−	19.4357i	−0.0186584	−	0.624044i
$971$	44.8937	−	6.45473i	1.44071	−	0.207142i	0.622749	−	0.782422i	$-0.286016\pi$
$971$	44.8937	−	6.45473i	1.44071	−	0.207142i	0.817957	+	0.575279i	$0.195107\pi$
$972$	0.212565	+	0.977147i	0.00681803	+	0.0313420i
$973$	15.8611	−	5.91589i	0.508484	−	0.189655i
$974$	−1.44000	−	1.24777i	−0.0461406	−	0.0399811i
$975$	−4.46370	−	12.4060i	−0.142953	−	0.397310i
$976$	−10.5888	+	4.83573i	−0.338938	+	0.154788i
$977$	11.1775	−	6.10340i	0.357601	−	0.195265i	−0.290398	−	0.956906i	$-0.593788\pi$
$977$	11.1775	−	6.10340i	0.357601	−	0.195265i	0.647999	+	0.761641i	$0.275606\pi$
$978$	9.25821	−	5.05537i	0.296045	−	0.161653i
$979$	1.68797	−	0.770869i	0.0539477	−	0.0246371i
$980$	−24.4938	−	19.9742i	−0.782427	−	0.638052i
$981$	11.5642	+	10.0204i	0.369216	+	0.319927i
$982$	−17.9950	+	6.71180i	−0.574244	+	0.214182i
$983$	−8.16030	−	37.5123i	−0.260273	−	1.19646i	−0.902755	−	0.430155i	$-0.858459\pi$
$983$	−8.16030	−	37.5123i	−0.260273	−	1.19646i	0.642482	−	0.766301i	$-0.277905\pi$
$984$	−3.71337	+	0.533902i	−0.118378	+	0.0170202i
$985$	11.6551	−	12.3735i	0.371362	−	0.394253i
$986$	13.1301	−	11.3773i	0.418149	−	0.362328i
$987$	−1.34497	+	2.46313i	−0.0428109	+	0.0784022i
$988$	4.92213	+	4.92213i	0.156594	+	0.156594i
$989$	21.6951	−	39.3043i	0.689865	−	1.24980i
$990$	−14.3326	+	3.56962i	−0.455521	+	0.113450i
$991$	−23.5757	+	6.92245i	−0.748906	+	0.219899i	−0.633846	−	0.773460i	$-0.718525\pi$
$991$	−23.5757	+	6.92245i	−0.748906	+	0.219899i	−0.115061	+	0.993358i	$0.536706\pi$
$992$	0.486289	−	6.79921i	0.0154397	−	0.215875i
$993$	2.10802	−	9.69042i	0.0668961	−	0.307516i
$994$	3.90347	+	27.1492i	0.123810	+	0.861121i
$995$	−34.7119	+	17.1241i	−1.10044	+	0.542869i
$996$	1.04825	+	0.478718i	0.0332149	+	0.0151688i
$997$	18.7343	−	1.33990i	0.593321	−	0.0424352i	0.228550	−	0.973532i	$-0.426602\pi$
$997$	18.7343	−	1.33990i	0.593321	−	0.0424352i	0.364772	+	0.931097i	$0.381147\pi$
$998$	14.7770	+	19.7398i	0.467759	+	0.624852i
$999$	3.96443	+	8.68089i	0.125429	+	0.274651i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.b.37.5	✓	240
5.3	odd	4	inner	690.2.w.b.313.5	yes	240
23.5	odd	22	inner	690.2.w.b.97.5	yes	240
115.28	even	44	inner	690.2.w.b.373.5	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.b.37.5	✓	240	1.1	even	1	trivial
690.2.w.b.97.5	yes	240	23.5	odd	22	inner
690.2.w.b.313.5	yes	240	5.3	odd	4	inner
690.2.w.b.373.5	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)

\(f(q)\)	\(=\)	\(q+(-0.877679 - 0.479249i) q^{2} +(0.997452 + 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(2.06085 + 0.867694i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-1.60657 - 4.30737i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +O(q^{10})\)	\(q+(-0.877679 - 0.479249i) q^{2} +(0.997452 + 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(2.06085 + 0.867694i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-1.60657 - 4.30737i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +(-1.39292 - 1.74922i) q^{10} +(1.86100 - 6.33797i) q^{11} +(0.479249 + 0.877679i) q^{12} +(-2.47066 - 0.921509i) q^{13} +(-0.654253 + 4.55043i) q^{14} +(1.99370 + 1.01250i) q^{15} +(-0.415415 + 0.909632i) q^{16} +(-5.68433 + 1.23655i) q^{17} +(-0.800541 - 0.599278i) q^{18} +(-2.22074 + 1.42718i) q^{19} +(0.384230 + 2.20281i) q^{20} +(-1.29519 - 4.41100i) q^{21} +(-4.67083 + 4.67083i) q^{22} +(-4.35331 - 2.01214i) q^{23} -1.00000i q^{24} +(3.49422 + 3.57638i) q^{25} +(1.72681 + 1.99285i) q^{26} +(0.977147 + 0.212565i) q^{27} +(2.75501 - 3.68027i) q^{28} +(1.61466 - 2.51246i) q^{29} +(-1.26459 - 1.84413i) q^{30} +(4.46391 - 5.15162i) q^{31} +(0.800541 - 0.599278i) q^{32} +(2.30840 - 6.18906i) q^{33} +(5.58163 + 1.63892i) q^{34} +(0.426584 - 10.2709i) q^{35} +(0.415415 + 0.909632i) q^{36} +(5.71908 + 7.63980i) q^{37} +(2.63308 - 0.188321i) q^{38} +(-2.39863 - 1.09542i) q^{39} +(0.718463 - 2.11750i) q^{40} +(-0.533902 - 3.71337i) q^{41} +(-0.977210 + 4.49216i) q^{42} +(-0.667815 + 9.33728i) q^{43} +(6.33797 - 1.86100i) q^{44} +(1.91639 + 1.15215i) q^{45} +(2.85649 + 3.85233i) q^{46} +(-0.431659 - 0.431659i) q^{47} +(-0.479249 + 0.877679i) q^{48} +(-10.6821 + 9.25611i) q^{49} +(-1.35283 - 4.81351i) q^{50} +(-5.75806 + 0.827884i) q^{51} +(-0.560517 - 2.57666i) q^{52} +(3.32897 - 1.24164i) q^{53} +(-0.755750 - 0.654861i) q^{54} +(9.33466 - 11.4468i) q^{55} +(-4.18178 + 1.90976i) q^{56} +(-2.31690 + 1.26512i) q^{57} +(-2.62124 + 1.43131i) q^{58} +(6.21782 - 2.83958i) q^{59} +(0.226104 + 2.22461i) q^{60} +(8.79747 + 7.62305i) q^{61} +(-6.38679 + 2.38215i) q^{62} +(-0.977210 - 4.49216i) q^{63} +(-0.989821 + 0.142315i) q^{64} +(-4.29208 - 4.04287i) q^{65} +(-4.99214 + 4.32571i) q^{66} +(3.40473 - 6.23529i) q^{67} +(-4.11343 - 4.11343i) q^{68} +(-4.19867 - 2.31757i) q^{69} +(-5.29670 + 8.81007i) q^{70} +(5.72462 - 1.68090i) q^{71} +(0.0713392 - 0.997452i) q^{72} +(2.15880 - 9.92386i) q^{73} +(-1.35815 - 9.44616i) q^{74} +(3.23018 + 3.81654i) q^{75} +(-2.40125 - 1.09661i) q^{76} +(-30.2898 + 2.16637i) q^{77} +(1.58025 + 2.11096i) q^{78} +(0.0599822 + 0.131343i) q^{79} +(-1.64539 + 1.51416i) q^{80} +(0.959493 + 0.281733i) q^{81} +(-1.31103 + 3.51502i) q^{82} +(0.922531 - 0.690598i) q^{83} +(3.01054 - 3.47435i) q^{84} +(-12.7875 - 2.38391i) q^{85} +(5.06101 - 7.87508i) q^{86} +(1.78978 - 2.39087i) q^{87} +(-6.45459 - 1.40411i) q^{88} +(0.183967 + 0.212309i) q^{89} +(-1.12981 - 1.92965i) q^{90} +12.1225i q^{91} +(-0.660856 - 4.75008i) q^{92} +(4.82005 - 4.82005i) q^{93} +(0.171986 + 0.585730i) q^{94} +(-5.81498 + 1.01429i) q^{95} +(0.841254 - 0.540641i) q^{96} +(6.96135 + 5.21120i) q^{97} +(13.8115 - 3.00450i) q^{98} +(2.74404 - 6.00862i) 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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