LMFDB - Embedded newform 690.2.w.a.217.9

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			217.9
Character	$\chi$	$=$	690.217
Dual form			690.2.w.a.283.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0713392 - 0.997452i) q^{2} +(0.977147 - 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-1.69905 + 1.45370i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(0.277351 - 0.151445i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +O(q^{10})$	\(q+(0.0713392 - 0.997452i) q^{2} +(0.977147 - 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-1.69905 + 1.45370i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(0.277351 - 0.151445i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +(1.32878 + 1.79843i) q^{10} +(2.15826 + 1.87014i) q^{11} +(-0.997452 + 0.0713392i) q^{12} +(-3.11448 + 5.70375i) q^{13} +(-0.131273 - 0.287449i) q^{14} +(-1.35121 + 1.78163i) q^{15} +(0.959493 + 0.281733i) q^{16} +(5.95112 + 4.45495i) q^{17} +(-0.349464 - 0.936950i) q^{18} +(-0.0850417 + 0.591478i) q^{19} +(1.88864 - 1.19710i) q^{20} +(0.238821 - 0.206940i) q^{21} +(2.01935 - 2.01935i) q^{22} +(-2.90493 - 3.81594i) q^{23} +1.00000i q^{24} +(0.773532 - 4.93980i) q^{25} +(5.46703 + 3.51345i) q^{26} +(0.800541 - 0.599278i) q^{27} +(-0.296081 + 0.110433i) q^{28} +(6.12315 - 0.880376i) q^{29} +(1.68070 + 1.47487i) q^{30} +(-6.57384 + 4.22475i) q^{31} +(0.349464 - 0.936950i) q^{32} +(2.50646 + 1.36863i) q^{33} +(4.86815 - 5.61814i) q^{34} +(-0.251078 + 0.660498i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(6.24998 + 2.33112i) q^{37} +(0.583904 + 0.127021i) q^{38} +(-1.83089 + 6.23543i) q^{39} +(-1.05932 - 1.96923i) q^{40} +(2.04669 - 4.48162i) q^{41} +(-0.189375 - 0.252976i) q^{42} +(0.249873 + 1.14865i) q^{43} +(-1.87014 - 2.15826i) q^{44} +(-0.941622 + 2.02814i) q^{45} +(-4.01345 + 2.62531i) q^{46} +(7.17319 + 7.17319i) q^{47} +(0.997452 + 0.0713392i) q^{48} +(-3.73050 + 5.80477i) q^{49} +(-4.87203 - 1.12396i) q^{50} +(6.76208 + 3.08814i) q^{51} +(3.89451 - 5.20245i) q^{52} +(-1.12244 - 2.05560i) q^{53} +(-0.540641 - 0.841254i) q^{54} +(-6.38560 - 0.0400083i) q^{55} +(0.0890291 + 0.303205i) q^{56} +(0.0426295 + 0.596038i) q^{57} +(-0.441312 - 6.17035i) q^{58} +(0.454415 + 1.54760i) q^{59} +(1.59101 - 1.57120i) q^{60} +(-0.00440909 - 0.00686068i) q^{61} +(3.74501 + 6.85848i) q^{62} +(0.189375 - 0.252976i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(-2.99986 - 14.2185i) q^{65} +(1.54395 - 2.40244i) q^{66} +(1.04972 + 0.0750776i) q^{67} +(-5.25654 - 5.25654i) q^{68} +(-3.64968 - 3.11124i) q^{69} +(0.640903 + 0.297558i) q^{70} +(-7.43050 - 8.57525i) q^{71} +(0.212565 + 0.977147i) q^{72} +(3.18333 + 4.25243i) q^{73} +(2.77105 - 6.06776i) q^{74} +(-0.294176 - 4.99134i) q^{75} +(0.168352 - 0.573355i) q^{76} +(0.881821 + 0.191828i) q^{77} +(6.08893 + 2.27105i) q^{78} +(-11.4407 + 3.35928i) q^{79} +(-2.03978 + 0.916134i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-4.32419 - 2.36119i) q^{82} +(3.15910 - 8.46989i) q^{83} +(-0.265841 + 0.170846i) q^{84} +(-16.5874 + 1.08194i) q^{85} +(1.16355 - 0.167293i) q^{86} +(5.79608 - 2.16183i) q^{87} +(-2.28617 + 1.71141i) q^{88} +(-7.74342 - 4.97639i) q^{89} +(1.95580 + 1.08391i) q^{90} +2.05362i q^{91} +(2.33230 + 4.19051i) q^{92} +(-5.52557 + 5.52557i) q^{93} +(7.66664 - 6.64319i) q^{94} +(-0.715340 - 1.12858i) q^{95} +(0.142315 - 0.989821i) q^{96} +(1.01133 + 2.71149i) q^{97} +(5.52385 + 4.13510i) q^{98} +(2.74011 + 0.804568i) 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} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) $ 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.0713392	−	0.997452i	0.0504444	−	0.705305i
$2$	0.0713392	−	0.997452i	0.0504444	−	0.705305i
$3$	0.977147	−	0.212565i	0.564156	−	0.122725i
$3$	0.977147	−	0.212565i	0.564156	−	0.122725i
$4$	−0.989821	−	0.142315i	−0.494911	−	0.0711574i
$5$	−1.69905	+	1.45370i	−0.759838	+	0.650113i
$5$	−1.69905	+	1.45370i	−0.759838	+	0.650113i
$6$	−0.142315	−	0.989821i	−0.0580998	−	0.404093i
$7$	0.277351	−	0.151445i	0.104829	−	0.0572410i	−0.425979	−	0.904733i	$-0.640070\pi$
$7$	0.277351	−	0.151445i	0.104829	−	0.0572410i	0.530808	+	0.847492i	$0.321888\pi$
$8$	−0.212565	+	0.977147i	−0.0751532	+	0.345474i
$9$	0.909632	−	0.415415i	0.303211	−	0.138472i
$10$	1.32878	+	1.79843i	0.420198	+	0.568712i
$11$	2.15826	+	1.87014i	0.650739	+	0.563869i	0.916433	−	0.400189i	$-0.131055\pi$
$11$	2.15826	+	1.87014i	0.650739	+	0.563869i	−0.265693	+	0.964058i	$0.585601\pi$
$12$	−0.997452	+	0.0713392i	−0.287940	+	0.0205938i
$13$	−3.11448	+	5.70375i	−0.863802	+	1.58194i	−0.0515185	+	0.998672i	$0.516406\pi$
$13$	−3.11448	+	5.70375i	−0.863802	+	1.58194i	−0.812283	+	0.583263i	$0.801776\pi$
$14$	−0.131273	−	0.287449i	−0.0350843	−	0.0768239i
$15$	−1.35121	+	1.78163i	−0.348882	+	0.460016i
$16$	0.959493	+	0.281733i	0.239873	+	0.0704331i
$17$	5.95112	+	4.45495i	1.44336	+	1.08048i	0.981048	+	0.193766i	$0.0620702\pi$
$17$	5.95112	+	4.45495i	1.44336	+	1.08048i	0.462310	+	0.886718i	$0.347021\pi$
$18$	−0.349464	−	0.936950i	−0.0823695	−	0.220841i
$19$	−0.0850417	+	0.591478i	−0.0195099	+	0.135694i	−0.997248	−	0.0741329i	$-0.976381\pi$
$19$	−0.0850417	+	0.591478i	−0.0195099	+	0.135694i	0.977738	+	0.209827i	$0.0672902\pi$
$20$	1.88864	−	1.19710i	0.422312	−	0.267680i
$21$	0.238821	−	0.206940i	0.0521150	−	0.0451579i
$22$	2.01935	−	2.01935i	0.430526	−	0.430526i
$23$	−2.90493	−	3.81594i	−0.605720	−	0.795678i
$23$	−2.90493	−	3.81594i	−0.605720	−	0.795678i
$24$			1.00000i			0.204124i
$25$	0.773532	−	4.93980i	0.154706	−	0.987960i
$26$	5.46703	+	3.51345i	1.07217	+	0.689044i
$27$	0.800541	−	0.599278i	0.154064	−	0.115331i
$28$	−0.296081	+	0.110433i	−0.0559541	+	0.0208698i
$29$	6.12315	−	0.880376i	1.13704	−	0.163482i	0.452021	−	0.892007i	$-0.350703\pi$
$29$	6.12315	−	0.880376i	1.13704	−	0.163482i	0.685019	+	0.728525i	$0.259794\pi$
$30$	1.68070	+	1.47487i	0.306852	+	0.269274i
$31$	−6.57384	+	4.22475i	−1.18070	+	0.758787i	−0.975514	−	0.219936i	$-0.929415\pi$
$31$	−6.57384	+	4.22475i	−1.18070	+	0.758787i	−0.205182	+	0.978724i	$0.565779\pi$
$32$	0.349464	−	0.936950i	0.0617771	−	0.165631i
$33$	2.50646	+	1.36863i	0.436319	+	0.238248i
$34$	4.86815	−	5.61814i	0.834880	−	0.963503i
$35$	−0.251078	+	0.660498i	−0.0424399	+	0.111645i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	6.24998	+	2.33112i	1.02749	+	0.383234i	0.805992	−	0.591926i	$-0.201632\pi$
$37$	6.24998	+	2.33112i	1.02749	+	0.383234i	0.221499	+	0.975161i	$0.428905\pi$
$38$	0.583904	+	0.127021i	0.0947218	+	0.0206055i
$39$	−1.83089	+	6.23543i	−0.293177	+	0.998468i
$40$	−1.05932	−	1.96923i	−0.167493	−	0.311362i
$41$	2.04669	−	4.48162i	0.319639	−	0.699911i	−0.679801	−	0.733397i	$-0.737934\pi$
$41$	2.04669	−	4.48162i	0.319639	−	0.699911i	0.999439	+	0.0334862i	$0.0106610\pi$
$42$	−0.189375	−	0.252976i	−0.0292212	−	0.0390350i
$43$	0.249873	+	1.14865i	0.0381052	+	0.175167i	0.992266	−	0.124126i	$-0.0396128\pi$
$43$	0.249873	+	1.14865i	0.0381052	+	0.175167i	−0.954161	+	0.299293i	$0.903249\pi$
$44$	−1.87014	−	2.15826i	−0.281934	−	0.325370i
$45$	−0.941622	+	2.02814i	−0.140369	+	0.302337i
$46$	−4.01345	+	2.62531i	−0.591751	+	0.387080i
$47$	7.17319	+	7.17319i	1.04632	+	1.04632i	0.998874	+	0.0474436i	$0.0151074\pi$
$47$	7.17319	+	7.17319i	1.04632	+	1.04632i	0.0474436	+	0.998874i	$0.484893\pi$
$48$	0.997452	+	0.0713392i	0.143970	+	0.0102969i
$49$	−3.73050	+	5.80477i	−0.532928	+	0.829253i
$50$	−4.87203	−	1.12396i	−0.689010	−	0.158952i
$51$	6.76208	+	3.08814i	0.946881	+	0.432426i
$52$	3.89451	−	5.20245i	0.540071	−	0.721451i
$53$	−1.12244	−	2.05560i	−0.154179	−	0.282358i	0.789160	−	0.614187i	$-0.210516\pi$
$53$	−1.12244	−	2.05560i	−0.154179	−	0.282358i	−0.943340	+	0.331829i	$0.892334\pi$
$54$	−0.540641	−	0.841254i	−0.0735719	−	0.114480i
$55$	−6.38560	−	0.0400083i	−0.861035	−	0.00539472i
$56$	0.0890291	+	0.303205i	0.0118970	+	0.0405175i
$57$	0.0426295	+	0.596038i	0.00564641	+	0.0789472i
$58$	−0.441312	−	6.17035i	−0.0579471	−	0.810207i
$59$	0.454415	+	1.54760i	0.0591598	+	0.201480i	0.983770	−	0.179435i	$-0.0574271\pi$
$59$	0.454415	+	1.54760i	0.0591598	+	0.201480i	−0.924610	+	0.380915i	$0.875609\pi$
$60$	1.59101	−	1.57120i	0.205399	−	0.202841i
$61$	−0.00440909	−	0.00686068i	−0.000564526	−	0.000878420i	0.840971	−	0.541080i	$-0.181984\pi$
$61$	−0.00440909	−	0.00686068i	−0.000564526	−	0.000878420i	−0.841536	+	0.540202i	$0.818348\pi$
$62$	3.74501	+	6.85848i	0.475617	+	0.871028i
$63$	0.189375	−	0.252976i	0.0238590	−	0.0318719i
$64$	−0.909632	−	0.415415i	−0.113704	−	0.0519269i
$65$	−2.99986	−	14.2185i	−0.372087	−	1.76358i
$66$	1.54395	−	2.40244i	0.190048	−	0.295720i
$67$	1.04972	+	0.0750776i	0.128244	+	0.00917218i	0.135314	−	0.990803i	$-0.456796\pi$
$67$	1.04972	+	0.0750776i	0.128244	+	0.00917218i	−0.00706968	+	0.999975i	$0.502250\pi$
$68$	−5.25654	−	5.25654i	−0.637449	−	0.637449i
$69$	−3.64968	−	3.11124i	−0.439370	−	0.374549i
$70$	0.640903	+	0.297558i	0.0766026	+	0.0355649i
$71$	−7.43050	−	8.57525i	−0.881838	−	1.01770i	−0.999696	−	0.0246649i	$-0.992148\pi$
$71$	−7.43050	−	8.57525i	−0.881838	−	1.01770i	0.117858	−	0.993030i	$-0.462397\pi$
$72$	0.212565	+	0.977147i	0.0250511	+	0.115158i
$73$	3.18333	+	4.25243i	0.372580	+	0.497709i	0.947170	−	0.320733i	$-0.103929\pi$
$73$	3.18333	+	4.25243i	0.372580	+	0.497709i	−0.574589	+	0.818442i	$0.694838\pi$
$74$	2.77105	−	6.06776i	0.322128	−	0.705362i
$75$	−0.294176	−	4.99134i	−0.0339685	−	0.576350i
$76$	0.168352	−	0.573355i	0.0193113	−	0.0657684i
$77$	0.881821	+	0.191828i	0.100493	+	0.0218609i
$78$	6.08893	+	2.27105i	0.689435	+	0.257146i
$79$	−11.4407	+	3.35928i	−1.28718	+	0.377949i	−0.852542	−	0.522659i	$-0.824940\pi$
$79$	−11.4407	+	3.35928i	−1.28718	+	0.377949i	−0.434633	+	0.900608i	$0.643122\pi$
$80$	−2.03978	+	0.916134i	−0.228054	+	0.102427i
$81$	0.654861	−	0.755750i	0.0727623	−	0.0839722i
$82$	−4.32419	−	2.36119i	−0.477527	−	0.260749i
$83$	3.15910	−	8.46989i	0.346757	−	0.929691i	−0.640129	−	0.768268i	$-0.721119\pi$
$83$	3.15910	−	8.46989i	0.346757	−	0.929691i	0.986885	−	0.161423i	$-0.0516084\pi$
$84$	−0.265841	+	0.170846i	−0.0290056	+	0.0186408i
$85$	−16.5874	+	1.08194i	−1.79915	+	0.117353i
$86$	1.16355	−	0.167293i	0.125468	−	0.0180396i
$87$	5.79608	−	2.16183i	0.621405	−	0.231772i
$88$	−2.28617	+	1.71141i	−0.243707	+	0.182437i
$89$	−7.74342	−	4.97639i	−0.820800	−	0.527496i	0.0615420	−	0.998104i	$-0.480398\pi$
$89$	−7.74342	−	4.97639i	−0.820800	−	0.527496i	−0.882342	+	0.470608i	$0.844035\pi$
$90$	1.95580	+	1.08391i	0.206159	+	0.114254i
$91$			2.05362i			0.215278i
$92$	2.33230	+	4.19051i	0.243159	+	0.436891i
$93$	−5.52557	+	5.52557i	−0.572975	+	0.572975i
$94$	7.66664	−	6.64319i	0.790754	−	0.685192i
$95$	−0.715340	−	1.12858i	−0.0733923	−	0.115789i
$96$	0.142315	−	0.989821i	0.0145249	−	0.101023i
$97$	1.01133	+	2.71149i	0.102685	+	0.275310i	0.978125	−	0.208017i	$-0.0667009\pi$
$97$	1.01133	+	2.71149i	0.102685	+	0.275310i	−0.875440	+	0.483327i	$0.839428\pi$
$98$	5.52385	+	4.13510i	0.557993	+	0.417708i
$99$	2.74011	+	0.804568i	0.275391	+	0.0808621i
$100$	−1.46867	+	4.77944i	−0.146867	+	0.477944i
$101$	4.25866	+	9.32516i	0.423752	+	0.927888i	0.994300	+	0.106623i	$0.0340038\pi$
$101$	4.25866	+	9.32516i	0.423752	+	0.927888i	−0.570547	+	0.821265i	$0.693269\pi$
$102$	3.56267	−	6.52455i	0.352757	−	0.646027i
$103$	−4.74616	+	0.339452i	−0.467653	+	0.0334472i	−0.303178	−	0.952934i	$-0.598048\pi$
$103$	−4.74616	+	0.339452i	−0.467653	+	0.0334472i	−0.164475	+	0.986381i	$0.552593\pi$
$104$	−4.91137	−	4.25573i	−0.481599	−	0.417308i
$105$	−0.104941	+	0.698774i	−0.0102412	+	0.0681934i
$106$	−2.13044	+	0.972938i	−0.206926	+	0.0945001i
$107$	3.62143	−	16.6475i	0.350097	−	1.60937i	−0.379295	−	0.925276i	$-0.623834\pi$
$107$	3.62143	−	16.6475i	0.350097	−	1.60937i	0.729393	−	0.684095i	$-0.239803\pi$
$108$	−0.877679	+	0.479249i	−0.0844547	+	0.0461158i
$109$	−1.01545	−	7.06261i	−0.0972625	−	0.676475i	−0.978869	−	0.204490i	$-0.934447\pi$
$109$	−1.01545	−	7.06261i	−0.0972625	−	0.676475i	0.881606	−	0.471986i	$-0.156463\pi$
$110$	−0.495450	+	6.36648i	−0.0472393	+	0.607020i
$111$	6.60267	+	0.949320i	0.626697	+	0.0901055i
$112$	0.308784	−	0.0671718i	0.0291773	−	0.00634714i
$113$	−0.694210	+	9.70633i	−0.0653058	+	0.913094i	0.854182	+	0.519975i	$0.174059\pi$
$113$	−0.694210	+	9.70633i	−0.0653058	+	0.913094i	−0.919487	+	0.393120i	$0.871396\pi$
$114$	0.597561			0.0559667
$115$	10.4828	+	2.26057i	0.977529	+	0.210799i
$116$	−6.18611			−0.574366
$117$	−0.463610	+	6.48211i	−0.0428608	+	0.599272i
$118$	1.57607	−	0.342853i	0.145089	−	0.0315622i
$119$	2.32523	+	0.334318i	0.213154	+	0.0306469i
$120$	−1.45370	−	1.69905i	−0.132704	−	0.155101i
$121$	−0.404813	−	2.81554i	−0.0368012	−	0.255958i
$122$	−0.00715774	+	0.00390842i	−0.000648031	+	0.000353852i
$123$	1.04728	−	4.81425i	0.0944297	−	0.434086i
$124$	7.10817	−	3.24619i	0.638333	−	0.291517i
$125$	5.86671	+	9.51745i	0.524734	+	0.851266i
$126$	−0.238821	−	0.206940i	−0.0212759	−	0.0184357i
$127$	−2.02371	+	0.144739i	−0.179575	+	0.0128435i	−0.160837	−	0.986981i	$-0.551419\pi$
$127$	−2.02371	+	0.144739i	−0.179575	+	0.0128435i	−0.0187380	+	0.999824i	$0.505965\pi$
$128$	−0.479249	+	0.877679i	−0.0423600	+	0.0775766i
$129$	0.488325	+	1.06928i	0.0429946	+	0.0941450i
$130$	−14.3962	+	1.97789i	−1.26263	+	0.173472i
$131$	14.1260	+	4.14776i	1.23419	+	0.362392i	0.832831	−	0.553528i	$-0.186719\pi$
$131$	14.1260	+	4.14776i	1.23419	+	0.362392i	0.401362	+	0.915919i	$0.368537\pi$
$132$	−2.28617	−	1.71141i	−0.198986	−	0.148959i
$133$	0.0659902	+	0.176927i	0.00572208	+	0.0153415i
$134$	0.149773	−	1.04169i	0.0129384	−	0.0899884i
$135$	−0.488991	+	2.18195i	−0.0420856	+	0.187792i
$136$	−5.61814	+	4.86815i	−0.481752	+	0.417440i
$137$	−2.76278	+	2.76278i	−0.236040	+	0.236040i	−0.815208	−	0.579168i	$-0.803377\pi$
$137$	−2.76278	+	2.76278i	−0.236040	+	0.236040i	0.579168	+	0.815208i	$0.303377\pi$
$138$	−3.36368	+	3.41843i	−0.286335	+	0.290996i
$139$		−	15.6710i		−	1.32920i	−0.747199	−	0.664600i	$-0.768602\pi$
$139$		−	15.6710i		−	1.32920i	0.747199	−	0.664600i	$-0.231398\pi$
$140$	0.342521	−	0.618043i	0.0289483	−	0.0522342i
$141$	8.53403	+	5.48449i	0.718695	+	0.461877i
$142$	−9.08349	+	6.79982i	−0.762270	+	0.570628i
$143$	−17.3887	+	6.48564i	−1.45411	+	0.542356i
$144$	0.989821	−	0.142315i	0.0824851	−	0.0118596i
$145$	−9.12373	+	10.3970i	−0.757684	+	0.863424i
$146$	4.46869	−	2.87185i	0.369831	−	0.237676i
$147$	−2.41135	+	6.46508i	−0.198885	+	0.533231i
$148$	−5.85461	−	3.19686i	−0.481246	−	0.262780i
$149$	4.62619	−	5.33890i	0.378992	−	0.437380i	−0.533921	−	0.845534i	$-0.679282\pi$
$149$	4.62619	−	5.33890i	0.378992	−	0.437380i	0.912913	+	0.408154i	$0.133827\pi$
$150$	−4.99961	−	0.0626515i	−0.408216	−	0.00511547i
$151$	−18.6065	+	5.46337i	−1.51418	+	0.444603i	−0.930165	−	0.367142i	$-0.880336\pi$
$151$	−18.6065	+	5.46337i	−1.51418	+	0.444603i	−0.584012	+	0.811745i	$0.698518\pi$
$152$	−0.559884	−	0.208826i	−0.0454126	−	0.0169380i
$153$	7.26398	+	1.58018i	0.587258	+	0.127750i
$154$	0.254248	−	0.865889i	0.0204879	−	0.0697753i
$155$	5.02777	−	16.7344i	0.403840	−	1.34414i
$156$	2.69965	−	5.91140i	0.216145	−	0.473291i
$157$	−11.3746	−	15.1946i	−0.907789	−	1.21266i	−0.976606	−	0.215034i	$-0.931014\pi$
$157$	−11.3746	−	15.1946i	−0.907789	−	1.21266i	0.0688178	−	0.997629i	$-0.478077\pi$
$158$	2.53456	+	11.6512i	0.201638	+	0.926917i
$159$	−1.53374	−	1.77003i	−0.121634	−	0.140373i
$160$	0.768284	+	2.09994i	0.0607382	+	0.166015i
$161$	−1.38359	−	0.618417i	−0.109042	−	0.0487381i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	10.7188	+	0.766626i	0.839564	+	0.0600468i	0.484496	−	0.874794i	$-0.339003\pi$
$163$	10.7188	+	0.766626i	0.839564	+	0.0600468i	0.355068	+	0.934840i	$0.384458\pi$
$164$	−2.66365	+	4.14473i	−0.207996	+	0.323649i
$165$	−6.24818	+	1.31826i	−0.486420	+	0.102627i
$166$	−8.22294	−	3.75529i	−0.638224	−	0.291467i
$167$	−5.80420	+	7.75350i	−0.449142	+	0.599984i	−0.966778	−	0.255617i	$-0.917721\pi$
$167$	−5.80420	+	7.75350i	−0.449142	+	0.599984i	0.517636	+	0.855601i	$0.326812\pi$
$168$	0.151445	+	0.277351i	0.0116843	+	0.0213981i
$169$	−15.8044	−	24.5921i	−1.21572	−	1.89170i
$170$	−0.104145	+	16.6223i	−0.00798758	+	1.27487i
$171$	0.168352	+	0.573355i	0.0128742	+	0.0438456i
$172$	−0.0838599	−	1.17252i	−0.00639426	−	0.0894034i
$173$	1.51923	+	21.2416i	0.115505	+	1.61497i	0.643309	+	0.765606i	$0.277561\pi$
$173$	1.51923	+	21.2416i	0.115505	+	1.61497i	−0.527804	+	0.849366i	$0.676985\pi$
$174$	−1.74283	−	5.93553i	−0.132124	−	0.449972i
$175$	−0.533570	−	1.48721i	−0.0403341	−	0.112422i
$176$	1.54395	+	2.40244i	0.116380	+	0.181091i
$177$	0.772996	+	1.41564i	0.0581019	+	0.106406i
$178$	−5.51612	+	7.36867i	−0.413451	+	0.552305i
$179$	−11.1997	−	5.11472i	−0.837104	−	0.382292i	−0.0497256	−	0.998763i	$-0.515835\pi$
$179$	−11.1997	−	5.11472i	−0.837104	−	0.382292i	−0.787378	+	0.616471i	$0.788562\pi$
$180$	1.22067	−	1.87349i	0.0909835	−	0.139642i
$181$	9.81107	−	15.2663i	0.729251	−	1.13474i	−0.256503	−	0.966543i	$-0.582570\pi$
$181$	9.81107	−	15.2663i	0.729251	−	1.13474i	0.985754	−	0.168193i	$-0.0537932\pi$
$182$	2.04838	+	0.146503i	0.151836	+	0.0108596i
$183$	−0.00576667	−	0.00576667i	−0.000426285	−	0.000426285i
$184$	4.34622	−	2.02741i	0.320407	−	0.149463i
$185$	−14.0078	+	5.12489i	−1.02987	+	0.376789i
$186$	5.11730	+	5.90568i	0.375219	+	0.433026i
$187$	4.51266	+	20.7444i	0.329998	+	1.51698i
$188$	−6.07933	−	8.12103i	−0.443381	−	0.592287i
$189$	0.131273	−	0.287449i	0.00954874	−	0.0209088i
$190$	−1.17673	+	0.633006i	−0.0853691	+	0.0459231i
$191$	6.03569	−	20.5557i	0.436727	−	1.48736i	−0.387912	−	0.921696i	$-0.626804\pi$
$191$	6.03569	−	20.5557i	0.436727	−	1.48736i	0.824639	−	0.565659i	$-0.191378\pi$
$192$	−0.977147	−	0.212565i	−0.0705195	−	0.0153406i
$193$	16.1681	+	6.03039i	1.16381	+	0.434077i	0.855800	−	0.517307i	$-0.173066\pi$
$193$	16.1681	+	6.03039i	1.16381	+	0.434077i	0.308006	+	0.951384i	$0.400338\pi$
$194$	2.77673	−	0.815322i	0.199358	−	0.0585367i
$195$	−5.95366	−	13.2559i	−0.426350	−	0.949271i
$196$	4.51863	−	5.21478i	0.322759	−	0.372484i
$197$	17.7564	+	9.69573i	1.26509	+	0.690793i	0.964782	−	0.263049i	$-0.0847282\pi$
$197$	17.7564	+	9.69573i	1.26509	+	0.690793i	0.300310	+	0.953842i	$0.402910\pi$
$198$	0.997995	−	2.67573i	0.0709244	−	0.190156i
$199$	7.21230	−	4.63506i	0.511266	−	0.328571i	−0.259442	−	0.965759i	$-0.583539\pi$
$199$	7.21230	−	4.63506i	0.511266	−	0.328571i	0.770709	+	0.637188i	$0.219902\pi$
$200$	4.66249	+	1.80588i	0.329688	+	0.127695i
$201$	1.04169	−	0.149773i	0.0734752	−	0.0105641i
$202$	9.60521	−	3.58256i	0.675820	−	0.252068i
$203$	1.56494	−	1.17150i	0.109837	−	0.0822229i
$204$	−6.25377	−	4.01905i	−0.437851	−	0.281390i
$205$	3.03749	+	10.5897i	0.212148	+	0.739620i
$206$			4.75829i			0.331526i
$207$	−4.22762	−	2.26434i	−0.293840	−	0.157383i
$208$	−4.59526	+	4.59526i	−0.318624	+	0.318624i
$209$	−1.28969	+	1.11752i	−0.0892097	+	0.0773007i
$210$	0.689507	+	0.154524i	0.0475805	+	0.0106632i
$211$	0.0865161	−	0.601732i	0.00595601	−	0.0414250i	−0.986627	−	0.162996i	$-0.947884\pi$
$211$	0.0865161	−	0.601732i	0.00595601	−	0.0414250i	0.992583	+	0.121571i	$0.0387933\pi$
$212$	0.818475	+	2.19442i	0.0562131	+	0.150713i
$213$	−9.08349	−	6.79982i	−0.622391	−	0.465916i
$214$	−16.3467	−	4.79982i	−1.11744	−	0.328109i
$215$	−2.09433	−	1.58837i	−0.142832	−	0.108326i
$216$	0.415415	+	0.909632i	0.0282654	+	0.0618926i
$217$	−1.18345	+	2.16732i	−0.0803375	+	0.147127i
$218$	−7.11706	+	0.509022i	−0.482028	+	0.0344753i
$219$	4.01450	+	3.47858i	0.271275	+	0.235061i
$220$	6.31491	+	0.948367i	0.425751	+	0.0639389i
$221$	−43.9446	+	20.0688i	−2.95603	+	1.34997i
$222$	1.41793	−	6.51812i	0.0951652	−	0.437468i
$223$	8.09043	−	4.41771i	0.541775	−	0.295832i	−0.184964	−	0.982745i	$-0.559217\pi$
$223$	8.09043	−	4.41771i	0.541775	−	0.295832i	0.726739	+	0.686914i	$0.241035\pi$
$224$	−0.0449723	−	0.312789i	−0.00300484	−	0.0208991i
$225$	−1.34844	−	4.81474i	−0.0898959	−	0.320983i
$226$	9.63207	+	1.38488i	0.640716	+	0.0921210i
$227$	−6.00109	+	1.30546i	−0.398306	+	0.0866462i	−0.407257	−	0.913314i	$-0.633515\pi$
$227$	−6.00109	+	1.30546i	−0.398306	+	0.0866462i	0.00895042	+	0.999960i	$0.497151\pi$
$228$	0.0426295	−	0.596038i	0.00282321	−	0.0394736i
$229$	−19.5998			−1.29519			−0.647597	−	0.761983i	$-0.724226\pi$
$229$	−19.5998			−1.29519			−0.647597	+	0.761983i	$0.724226\pi$
$230$	3.00265	−	10.2949i	0.197989	−	0.678823i
$231$	0.902444			0.0593765
$232$	−0.441312	+	6.17035i	−0.0289736	+	0.405103i
$233$	−1.35007	+	0.293691i	−0.0884463	+	0.0192403i	−0.256571	−	0.966525i	$-0.582593\pi$
$233$	−1.35007	+	0.293691i	−0.0884463	+	0.0192403i	0.168124	+	0.985766i	$0.446229\pi$
$234$	6.43252	+	0.924857i	0.420507	+	0.0604598i
$235$	−22.6152	−	1.75996i	−1.47526	−	0.114807i
$236$	−0.229544	−	1.59651i	−0.0149420	−	0.103924i
$237$	−10.4651	+	5.71440i	−0.679784	+	0.371190i
$238$	0.499346	−	2.29546i	0.0323678	−	0.148792i
$239$	16.7244	−	7.63777i	1.08181	−	0.494046i	0.206915	−	0.978359i	$-0.433658\pi$
$239$	16.7244	−	7.63777i	1.08181	−	0.494046i	0.874895	+	0.484313i	$0.160930\pi$
$240$	−1.79843	+	1.32878i	−0.116088	+	0.0857726i
$241$	15.5648	+	13.4870i	1.00262	+	0.868773i	0.991361	−	0.131163i	$-0.0418712\pi$
$241$	15.5648	+	13.4870i	1.00262	+	0.868773i	0.0112570	+	0.999937i	$0.496417\pi$
$242$	−2.83724	+	0.202924i	−0.182385	+	0.0130444i
$243$	0.479249	−	0.877679i	0.0307438	−	0.0563031i
$244$	0.00338784	+	0.00741833i	0.000216884	+	0.000474910i
$245$	−2.10007	−	15.2856i	−0.134169	−	0.976561i
$246$	−4.72727	−	1.38805i	−0.301400	−	0.0884990i
$247$	−3.10878	−	2.32721i	−0.197807	−	0.148077i
$248$	−2.73083	−	7.32164i	−0.173408	−	0.464925i
$249$	1.28651	−	8.94784i	0.0815290	−	0.567046i
$250$	9.91172	−	5.17279i	0.626872	−	0.327156i
$251$	19.0610	−	16.5165i	1.20312	−	1.04251i	0.205156	−	0.978729i	$-0.434230\pi$
$251$	19.0610	−	16.5165i	1.20312	−	1.04251i	0.997964	−	0.0637798i	$-0.0203155\pi$
$252$	−0.223450	+	0.223450i	−0.0140760	+	0.0140760i
$253$	0.866743	−	13.6684i	0.0544917	−	0.859326i
$254$			2.02888i			0.127303i
$255$	−15.9783	+	4.58312i	−1.00060	+	0.287006i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	−19.0642	+	14.2713i	−1.18919	+	0.890218i	−0.995859	−	0.0909145i	$-0.971021\pi$
$257$	−19.0642	+	14.2713i	−1.18919	+	0.890218i	−0.193334	+	0.981133i	$0.561930\pi$
$258$	1.10139	−	0.410799i	0.0685698	−	0.0255752i
$259$	2.08648	−	0.299990i	0.129648	−	0.0186405i
$260$	0.945831	+	14.5007i	0.0586580	+	0.899293i
$261$	5.20409	−	3.34447i	0.322125	−	0.207017i
$262$	5.14493	−	13.7941i	0.317855	−	0.852202i
$263$	20.8397	+	11.3793i	1.28503	+	0.701678i	0.968997	−	0.247071i	$-0.0794680\pi$
$263$	20.8397	+	11.3793i	1.28503	+	0.701678i	0.316030	+	0.948749i	$0.397650\pi$
$264$	−1.87014	+	2.15826i	−0.115099	+	0.132832i
$265$	4.89530	+	1.86087i	0.300716	+	0.114313i
$266$	0.181183	−	0.0532003i	0.0111091	−	0.00326192i
$267$	−8.62426	−	3.21668i	−0.527796	−	0.196858i
$268$	−1.02835	−	0.223704i	−0.0628166	−	0.0136649i
$269$	0.574956	−	1.95812i	0.0350557	−	0.119389i	−0.940106	−	0.340881i	$-0.889275\pi$
$269$	0.574956	−	1.95812i	0.0350557	−	0.119389i	0.975162	+	0.221492i	$0.0710928\pi$
$270$	2.14150	+	0.643403i	0.130328	+	0.0391563i
$271$	7.63048	−	16.7084i	0.463519	−	1.01496i	−0.523152	−	0.852239i	$-0.675244\pi$
$271$	7.63048	−	16.7084i	0.463519	−	1.01496i	0.986671	−	0.162726i	$-0.0520285\pi$
$272$	4.45495	+	5.95112i	0.270121	+	0.360839i
$273$	0.436528	+	2.00669i	0.0264199	+	0.121450i
$274$	2.55864	+	2.95283i	0.154573	+	0.178387i
$275$	10.9076	−	9.21476i	0.657754	−	0.555671i
$276$	3.16976	+	3.59898i	0.190797	+	0.216633i
$277$	−4.63714	−	4.63714i	−0.278619	−	0.278619i	0.553939	−	0.832558i	$-0.313124\pi$
$277$	−4.63714	−	4.63714i	−0.278619	−	0.278619i	−0.832558	+	0.553939i	$0.813124\pi$
$278$	−15.6311	−	1.11796i	−0.937491	−	0.0670507i
$279$	−4.22475	+	6.57384i	−0.252929	+	0.393565i
$280$	−0.592033	−	0.385739i	−0.0353807	−	0.0230523i
$281$	−18.2152	−	8.31860i	−1.08663	−	0.496246i	−0.210140	−	0.977671i	$-0.567392\pi$
$281$	−18.2152	−	8.31860i	−1.08663	−	0.496246i	−0.876487	+	0.481425i	$0.840119\pi$
$282$	6.07933	−	8.12103i	0.362019	−	0.483600i
$283$	−0.765432	−	1.40178i	−0.0455002	−	0.0833274i	0.853939	−	0.520372i	$-0.174207\pi$
$283$	−0.765432	−	1.40178i	−0.0455002	−	0.0833274i	−0.899440	+	0.437045i	$0.856025\pi$
$284$	6.13448	+	9.54544i	0.364015	+	0.566418i
$285$	−0.938888	−	0.950727i	−0.0556149	−	0.0563162i
$286$	5.22862	+	17.8071i	0.309175	+	1.05295i
$287$	−0.111069	−	1.55294i	−0.00655618	−	0.0916674i
$288$	−0.0713392	−	0.997452i	−0.00420370	−	0.0587754i
$289$	10.7798	+	36.7125i	0.634103	+	2.15956i
$290$	9.71963	+	9.84219i	0.570756	+	0.577954i
$291$	1.56459	+	2.43455i	0.0917179	+	0.142716i
$292$	−2.54574	−	4.66218i	−0.148978	−	0.272834i
$293$	6.61516	−	8.83682i	0.386462	−	0.516253i	−0.564553	−	0.825397i	$-0.690952\pi$
$293$	6.61516	−	8.83682i	0.386462	−	0.516253i	0.951015	+	0.309144i	$0.100042\pi$
$294$	6.27659	+	2.86642i	0.366058	+	0.167173i
$295$	−3.02181	−	1.96886i	−0.175937	−	0.114631i
$296$	−3.60638	+	5.61163i	−0.209616	+	0.326170i
$297$	2.84851	+	0.203729i	0.165287	+	0.0118216i
$298$	−4.99527	−	4.99527i	−0.289368	−	0.289368i
$299$	30.8125	−	4.68434i	1.78193	−	0.270903i
$300$	−0.419160	+	4.98240i	−0.0242002	+	0.287659i
$301$	0.243260	+	0.280737i	0.0140213	+	0.0161814i
$302$	4.12207	+	18.9489i	0.237199	+	1.09038i
$303$	6.14354	+	8.20681i	0.352937	+	0.471469i
$304$	−0.248236	+	0.543560i	−0.0142373	+	0.0311753i
$305$	0.0174646	+	0.00524715i	0.00100002	+	0.000300451i
$306$	2.09436	−	7.13274i	0.119727	−	0.407752i
$307$	12.0955	+	2.63121i	0.690326	+	0.150171i	0.544025	−	0.839069i	$-0.316900\pi$
$307$	12.0955	+	2.63121i	0.690326	+	0.150171i	0.146301	+	0.989240i	$0.453263\pi$
$308$	−0.845545	−	0.315372i	−0.0481794	−	0.0179700i
$309$	−4.56554	+	1.34056i	−0.259725	+	0.0762621i
$310$	−16.3331	−	6.20878i	−0.927658	−	0.352635i
$311$	14.1074	−	16.2808i	0.799956	−	0.923199i	−0.198422	−	0.980117i	$-0.563582\pi$
$311$	14.1074	−	16.2808i	0.799956	−	0.923199i	0.998379	+	0.0569176i	$0.0181272\pi$
$312$	−5.70375	−	3.11448i	−0.322911	−	0.176323i
$313$	6.24388	−	16.7405i	0.352925	−	0.946228i	−0.632264	−	0.774753i	$-0.717874\pi$
$313$	6.24388	−	16.7405i	0.352925	−	0.946228i	0.985189	−	0.171475i	$-0.0548532\pi$
$314$	−15.9674	+	10.2616i	−0.901091	+	0.579096i
$315$	0.0459922	+	0.705112i	0.00259137	+	0.0397285i
$316$	11.8023	−	1.69691i	0.663931	−	0.0954588i
$317$	31.2727	−	11.6641i	1.75645	−	0.655121i	0.756449	−	0.654052i	$-0.226932\pi$
$317$	31.2727	−	11.6641i	1.75645	−	0.655121i	0.999999	−	0.00106910i	$-0.000340304\pi$
$318$	−1.87494	+	1.40356i	−0.105141	+	0.0787078i
$319$	14.8618	+	9.55108i	0.832099	+	0.534758i
$320$	2.14940	−	0.616519i	0.120155	−	0.0344644i
$321$		−	17.0368i		−	0.950902i
$322$	−0.715545	+	1.33595i	−0.0398758	+	0.0744496i
$323$	−3.14110	+	3.14110i	−0.174775	+	0.174775i
$324$	−0.755750	+	0.654861i	−0.0419861	+	0.0363812i
$325$	25.7662	+	19.7970i	1.42925	+	1.09814i
$326$	1.52935	−	10.6368i	0.0847026	−	0.589119i
$327$	−2.49351	−	6.68536i	−0.137891	−	0.369701i
$328$	3.94414	+	2.95255i	0.217779	+	0.163027i
$329$	3.07584	+	0.903149i	0.169577	+	0.0497922i
$330$	0.869165	+	6.32630i	0.0478460	+	0.348251i
$331$	5.99242	+	13.1216i	0.329373	+	0.721226i	0.999784	−	0.0207633i	$-0.00660963\pi$
$331$	5.99242	+	13.1216i	0.329373	+	0.721226i	−0.670411	+	0.741990i	$0.733882\pi$
$332$	−4.33234	+	7.93409i	−0.237768	+	0.435440i
$333$	6.65357	−	0.475872i	0.364613	−	0.0260777i
$334$	7.31968	+	6.34254i	0.400515	+	0.347048i
$335$	−1.89267	+	1.39842i	−0.103407	+	0.0764036i
$336$	0.287449	−	0.131273i	0.0156816	−	0.00716155i
$337$	3.77339	−	17.3460i	0.205550	−	0.944896i	−0.752566	−	0.658516i	$-0.771184\pi$
$337$	3.77339	−	17.3460i	0.205550	−	0.944896i	0.958116	−	0.286380i	$-0.0924520\pi$
$338$	−25.6570	+	14.0098i	−1.39555	+	0.762030i
$339$	1.38488	+	9.63207i	0.0752165	+	0.523142i
$340$	16.5725	+	1.28970i	0.898771	+	0.0699439i
$341$	−22.0889	−	3.17591i	−1.19618	−	0.171985i
$342$	0.583904	−	0.127021i	0.0315739	−	0.00686849i
$343$	−0.313359	+	4.38133i	−0.0169198	+	0.236570i
$344$	−1.17551			−0.0633793
$345$	10.7238	−	0.0193800i	0.577349	−	0.00104338i
$346$	21.2959			1.14487
$347$	−0.665918	+	9.31075i	−0.0357483	+	0.499827i	0.947762	+	0.318977i	$0.103339\pi$
$347$	−0.665918	+	9.31075i	−0.0357483	+	0.499827i	−0.983511	+	0.180850i	$0.942115\pi$
$348$	−6.04474	+	1.31495i	−0.324032	+	0.0704889i
$349$	7.44268	+	1.07010i	0.398398	+	0.0572809i	0.338602	−	0.940930i	$-0.390046\pi$
$349$	7.44268	+	1.07010i	0.398398	+	0.0572809i	0.0597957	+	0.998211i	$0.480955\pi$
$350$	−1.52148	+	0.426114i	−0.0813268	+	0.0227768i
$351$	0.924857	+	6.43252i	0.0493652	+	0.343343i
$352$	2.50646	−	1.36863i	0.133595	−	0.0729483i
$353$	−1.52955	+	7.03123i	−0.0814098	+	0.374235i	−0.999769	−	0.0215142i	$-0.993151\pi$
$353$	−1.52955	+	7.03123i	−0.0814098	+	0.374235i	0.918359	+	0.395749i	$0.129515\pi$
$354$	1.46717	−	0.670036i	0.0779794	−	0.0356120i
$355$	25.0906	+	3.76808i	1.33167	+	0.199989i
$356$	6.95638	+	6.02774i	0.368688	+	0.319470i
$357$	2.34316	−	0.167586i	0.124013	−	0.00886959i
$358$	−5.90067	+	10.8063i	−0.311860	+	0.571129i
$359$	−2.66346	−	5.83215i	−0.140572	−	0.307809i	0.826232	−	0.563330i	$-0.190480\pi$
$359$	−2.66346	−	5.83215i	−0.140572	−	0.307809i	−0.966803	+	0.255521i	$0.917753\pi$
$360$	−1.78163	−	1.35121i	−0.0939004	−	0.0712153i
$361$	17.8878	+	5.25232i	0.941461	+	0.276438i
$362$	−14.5275	−	10.8752i	−0.763549	−	0.571585i
$363$	−0.994047	−	2.66514i	−0.0521740	−	0.139884i
$364$	0.292260	−	2.03271i	0.0153186	−	0.106543i
$365$	−11.5904	−	2.59749i	−0.606668	−	0.135959i
$366$	−0.00616337	+	0.00534059i	−0.000322164	+	0.000279157i
$367$	24.7441	−	24.7441i	1.29163	−	1.29163i	0.357856	−	0.933777i	$-0.383508\pi$
$367$	24.7441	−	24.7441i	1.29163	−	1.29163i	0.933777	−	0.357856i	$-0.116492\pi$
$368$	−1.71219	−	4.47978i	−0.0892541	−	0.233525i
$369$		−	4.92684i		−	0.256481i
$370$	4.11253	+	14.3377i	0.213800	+	0.745381i
$371$	−0.622622	−	0.400135i	−0.0323249	−	0.0207740i
$372$	6.25570	−	4.68296i	0.324343	−	0.242800i
$373$	4.79662	−	1.78905i	0.248360	−	0.0926333i	−0.222202	−	0.975001i	$-0.571324\pi$
$373$	4.79662	−	1.78905i	0.248360	−	0.0926333i	0.470561	+	0.882367i	$0.344052\pi$
$374$	21.0134	−	3.02128i	1.08658	−	0.156227i
$375$	7.75571	+	8.05288i	0.400503	+	0.415849i
$376$	−8.53403	+	5.48449i	−0.440109	+	0.282841i
$377$	−14.0490	+	37.6668i	−0.723560	+	1.93994i
$378$	−0.277351	−	0.151445i	−0.0142654	−	0.00778951i
$379$	−13.5146	+	15.5967i	−0.694199	+	0.801149i	−0.987957	−	0.154731i	$-0.950549\pi$
$379$	−13.5146	+	15.5967i	−0.694199	+	0.801149i	0.293757	+	0.955880i	$0.405094\pi$
$380$	0.547446	+	1.21889i	0.0280834	+	0.0625278i
$381$	−1.94669	+	0.571601i	−0.0997322	+	0.0292840i
$382$	−20.0727	−	7.48673i	−1.02701	−	0.383055i
$383$	−10.0883	−	2.19458i	−0.515489	−	0.112138i	−0.0527074	−	0.998610i	$-0.516785\pi$
$383$	−10.0883	−	2.19458i	−0.515489	−	0.112138i	−0.462782	+	0.886472i	$0.653149\pi$
$384$	−0.281733	+	0.959493i	−0.0143771	+	0.0489639i
$385$	−1.77712	+	0.955974i	−0.0905702	+	0.0487209i
$386$	7.16845	−	15.6967i	0.364864	−	0.798942i
$387$	0.704457	+	0.941044i	0.0358096	+	0.0478360i
$388$	−0.615155	−	2.82782i	−0.0312297	−	0.143561i
$389$	−12.8836	−	14.8684i	−0.653222	−	0.753859i	0.328432	−	0.944528i	$-0.393480\pi$
$389$	−12.8836	−	14.8684i	−0.653222	−	0.753859i	−0.981654	+	0.190669i	$0.938934\pi$
$390$	−13.6468	+	4.99283i	−0.691033	+	0.252822i
$391$	−0.287794	−	35.6504i	−0.0145544	−	1.80292i
$392$	−4.87914	−	4.87914i	−0.246434	−	0.246434i
$393$	14.6848	+	1.05028i	0.740752	+	0.0529796i
$394$	10.9378	−	17.0195i	0.551036	−	0.857429i
$395$	14.5549	−	22.3388i	0.732335	−	1.12399i
$396$	−2.59771	−	1.18634i	−0.130540	−	0.0596156i
$397$	−18.5308	+	24.7543i	−0.930034	+	1.24238i	0.0399473	+	0.999202i	$0.487281\pi$
$397$	−18.5308	+	24.7543i	−0.930034	+	1.24238i	−0.969982	+	0.243179i	$0.921810\pi$
$398$	−4.10873	−	7.52458i	−0.205952	−	0.377173i
$399$	0.102091	+	0.158856i	0.00511092	+	0.00795275i
$400$	2.13390	−	4.52178i	0.106695	−	0.226089i
$401$	5.30438	+	18.0651i	0.264888	+	0.902127i	0.979302	+	0.202403i	$0.0648752\pi$
$401$	5.30438	+	18.0651i	0.264888	+	0.902127i	−0.714414	+	0.699723i	$0.753307\pi$
$402$	−0.0750776	−	1.04972i	−0.00374453	−	0.0523553i
$403$	−3.62280	−	50.6534i	−0.180465	−	2.52323i
$404$	−2.88820	−	9.83631i	−0.143693	−	0.489375i
$405$	−0.0140096	+	2.23602i	−0.000696141	+	0.111109i
$406$	−1.05687	−	1.64452i	−0.0524516	−	0.0816162i
$407$	9.12955	+	16.7195i	0.452535	+	0.828756i
$408$	−4.45495	+	5.95112i	−0.220553	+	0.294624i
$409$	−16.0876	−	7.34694i	−0.795479	−	0.363283i	−0.0241407	−	0.999709i	$-0.507685\pi$
$409$	−16.0876	−	7.34694i	−0.795479	−	0.363283i	−0.771338	+	0.636426i	$0.780412\pi$
$410$	10.7795	−	2.27429i	0.532359	−	0.112319i
$411$	−2.11237	+	3.28691i	−0.104195	+	0.162131i
$412$	4.74616	+	0.339452i	0.233827	+	0.0167236i
$413$	0.360409	+	0.360409i	0.0177346	+	0.0177346i
$414$	−2.56017	+	4.05531i	−0.125825	+	0.199308i
$415$	6.94517	+	18.9831i	0.340925	+	0.931845i
$416$	4.25573	+	4.91137i	0.208654	+	0.240800i
$417$	−3.33112	−	15.3129i	−0.163126	−	0.749876i
$418$	1.02267	+	1.36613i	0.0500204	+	0.0668195i
$419$	11.4539	−	25.0806i	0.559562	−	1.22527i	−0.392610	−	0.919705i	$-0.628428\pi$
$419$	11.4539	−	25.0806i	0.559562	−	1.22527i	0.952172	−	0.305564i	$-0.0988450\pi$
$420$	0.203319	−	0.676727i	0.00992095	−	0.0330209i
$421$	−1.61265	+	5.49218i	−0.0785957	+	0.267672i	−0.989411	−	0.145142i	$-0.953636\pi$
$421$	−1.61265	+	5.49218i	−0.0785957	+	0.267672i	0.910815	+	0.412815i	$0.135454\pi$
$422$	−0.594027	−	0.129223i	−0.0289168	−	0.00629046i
$423$	9.50482	+	3.54511i	0.462140	+	0.172369i
$424$	2.24722	−	0.659842i	0.109134	−	0.0320448i
$425$	26.6100	−	25.9513i	1.29077	−	1.25882i
$426$	−7.43050	+	8.57525i	−0.360009	+	0.415472i
$427$	−0.00226189	−	0.00123508i	−0.000109460	−	5.97699e-5i
$428$	−5.95375	+	15.9626i	−0.287786	+	0.771583i
$429$	−15.6127	+	10.0337i	−0.753787	+	0.484429i
$430$	−1.73373	+	1.97568i	−0.0836077	+	0.0952757i
$431$	16.4971	−	2.37193i	0.794639	−	0.114252i	0.266973	−	0.963704i	$-0.413976\pi$
$431$	16.4971	−	2.37193i	0.794639	−	0.114252i	0.527666	+	0.849452i	$0.323067\pi$
$432$	0.936950	−	0.349464i	0.0450790	−	0.0168136i
$433$	−8.36402	+	6.26122i	−0.401949	+	0.300895i	−0.781060	−	0.624456i	$-0.785321\pi$
$433$	−8.36402	+	6.26122i	−0.401949	+	0.300895i	0.379111	+	0.925351i	$0.376230\pi$
$434$	2.07737	+	1.33504i	0.0997169	+	0.0640842i
$435$	−6.70518	+	12.0988i	−0.321489	+	0.580092i
$436$			7.13524i			0.341716i
$437$	2.50408	−	1.39369i	0.119787	−	0.0666693i
$438$	3.75611	−	3.75611i	0.179474	−	0.179474i
$439$	−20.3160	+	17.6039i	−0.969629	+	0.840188i	−0.987172	−	0.159658i	$-0.948961\pi$
$439$	−20.3160	+	17.6039i	−0.969629	+	0.840188i	0.0175437	+	0.999846i	$0.494415\pi$
$440$	1.39645	−	6.23117i	0.0665732	−	0.297059i
$441$	−0.981992	+	6.82991i	−0.0467615	+	0.325234i
$442$	16.8827	+	45.2643i	0.803028	+	2.15300i
$443$	−13.3141	−	9.96682i	−0.632573	−	0.473538i	0.234235	−	0.972180i	$-0.424741\pi$
$443$	−13.3141	−	9.96682i	−0.632573	−	0.473538i	−0.866808	+	0.498642i	$0.833832\pi$
$444$	−6.40036	−	1.87931i	−0.303748	−	0.0891883i
$445$	20.3906	−	2.80145i	0.966607	−	0.132801i
$446$	−3.82929	−	8.38497i	−0.181322	−	0.397040i
$447$	3.38560	−	6.20026i	0.160133	−	0.293262i
$448$	−0.315200	+	0.0225436i	−0.0148918	+	0.00106508i
$449$	−10.8195	−	9.37516i	−0.510604	−	0.442441i	0.361061	−	0.932542i	$-0.382414\pi$
$449$	−10.8195	−	9.37516i	−0.510604	−	0.442441i	−0.871666	+	0.490101i	$0.836960\pi$
$450$	−4.89867	+	1.00152i	−0.230925	+	0.0472123i
$451$	12.7985	−	5.84489i	0.602659	−	0.275225i
$452$	2.06850	−	9.50873i	0.0972940	−	0.447253i
$453$	−17.0200	+	9.29361i	−0.799668	+	0.436652i
$454$	0.874018	+	6.07893i	0.0410197	+	0.285298i
$455$	−2.98534	−	3.48919i	−0.139955	−	0.163576i
$456$	−0.591478	−	0.0850417i	−0.0276985	−	0.00398244i
$457$	41.6974	−	9.07072i	1.95052	−	0.424310i	0.962063	−	0.272828i	$-0.0879590\pi$
$457$	41.6974	−	9.07072i	1.95052	−	0.424310i	0.988460	−	0.151482i	$-0.0484046\pi$
$458$	−1.39824	+	19.5499i	−0.0653353	+	0.913507i
$459$	7.43387			0.346983
$460$	−10.0544	−	3.72942i	−0.468790	−	0.173885i
$461$	−19.2052			−0.894477			−0.447239	−	0.894415i	$-0.647593\pi$
$461$	−19.2052			−0.894477			−0.447239	+	0.894415i	$0.647593\pi$
$462$	0.0643796	−	0.900145i	0.00299521	−	0.0418785i
$463$	13.3112	−	2.89567i	0.618623	−	0.134573i	0.107677	−	0.994186i	$-0.465659\pi$
$463$	13.3112	−	2.89567i	0.618623	−	0.134573i	0.510946	+	0.859613i	$0.329295\pi$
$464$	6.12315	+	0.880376i	0.284260	+	0.0408704i
$465$	1.35571	−	17.4207i	0.0628695	−	0.807866i
$466$	0.196629	+	1.36759i	0.00910867	+	0.0633522i
$467$	−1.26019	+	0.688118i	−0.0583148	+	0.0318423i	−0.508142	−	0.861273i	$-0.669667\pi$
$467$	−1.26019	+	0.688118i	−0.0583148	+	0.0318423i	0.449827	+	0.893116i	$0.351486\pi$
$468$	1.38139	−	6.35016i	0.0638549	−	0.293536i
$469$	0.302512	−	0.138153i	0.0139687	−	0.00637929i
$470$	−3.36883	+	22.4321i	−0.155392	+	1.03471i
$471$	−14.3445	−	12.4296i	−0.660958	−	0.572723i
$472$	−1.60882	+	0.115065i	−0.0740520	+	0.00529631i
$473$	−1.60884	+	2.94637i	−0.0739746	+	0.135474i
$474$	4.95327	+	10.8461i	0.227511	+	0.498180i
$475$	2.85600	+	0.877617i	0.131042	+	0.0402678i
$476$	−2.25399	−	0.661830i	−0.103311	−	0.0303349i
$477$	−1.87494	−	1.40356i	−0.0858475	−	0.0642646i
$478$	−6.42520	−	17.2266i	−0.293882	−	0.787928i
$479$	−1.96015	+	13.6331i	−0.0895615	+	0.622914i	0.894762	+	0.446543i	$0.147345\pi$
$479$	−1.96015	+	13.6331i	−0.0895615	+	0.622914i	−0.984324	+	0.176371i	$0.943564\pi$
$480$	1.19710	+	1.88864i	0.0546399	+	0.0862041i
$481$	−32.7616	+	28.3881i	−1.49380	+	1.29439i
$482$	14.5630	−	14.5630i	0.663327	−	0.663327i
$483$	−1.48343	−	0.310180i	−0.0674983	−	0.0141137i
$484$			2.84449i			0.129295i
$485$	−5.65999	−	3.13678i	−0.257007	−	0.142434i
$486$	−0.841254	−	0.540641i	−0.0381600	−	0.0245240i
$487$	−15.4649	+	11.5769i	−0.700783	+	0.524600i	−0.889217	−	0.457486i	$-0.848750\pi$
$487$	−15.4649	+	11.5769i	−0.700783	+	0.524600i	0.188433	+	0.982086i	$0.439659\pi$
$488$	0.00764111	−	0.00284999i	0.000345897	−	0.000129013i
$489$	10.6368	−	1.52935i	0.481014	−	0.0691594i
$490$	−15.3965	+	1.00426i	−0.695541	+	0.0453679i
$491$	13.7121	−	8.81223i	0.618818	−	0.397690i	−0.193336	−	0.981133i	$-0.561931\pi$
$491$	13.7121	−	8.81223i	0.618818	−	0.397690i	0.812155	+	0.583442i	$0.198294\pi$
$492$	−1.72176	+	4.61621i	−0.0776227	+	0.208115i
$493$	40.3616	+	22.0391i	1.81780	+	0.992591i
$494$	−2.54305	+	2.93484i	−0.114417	+	0.132045i
$495$	−5.82517	+	2.61628i	−0.261822	+	0.117593i
$496$	−7.49780	+	2.20155i	−0.336661	+	0.0988527i
$497$	−3.35954	−	1.25304i	−0.150696	−	0.0562067i
$498$	−8.83326	−	1.92156i	−0.395828	−	0.0861071i
$499$	0.291137	−	0.991521i	0.0130331	−	0.0443866i	−0.952720	−	0.303850i	$-0.901728\pi$
$499$	0.291137	−	0.991521i	0.0130331	−	0.0443866i	0.965753	+	0.259464i	$0.0835459\pi$
$500$	−4.45252	−	10.2555i	−0.199123	−	0.458639i
$501$	−4.02343	+	8.81008i	−0.179754	+	0.393605i
$502$	−15.1146	−	20.1907i	−0.674596	−	0.901155i
$503$	−8.26959	−	38.0147i	−0.368723	−	1.69499i	−0.670743	−	0.741690i	$-0.734025\pi$
$503$	−8.26959	−	38.0147i	−0.368723	−	1.69499i	0.302020	−	0.953302i	$-0.402339\pi$
$504$	0.206940	+	0.238821i	0.00921783	+	0.0106379i
$505$	−20.7916	−	9.65310i	−0.925215	−	0.429557i
$506$	−13.5718	−	1.83963i	−0.603338	−	0.0817814i
$507$	−20.6707	−	20.6707i	−0.918017	−	0.918017i
$508$	2.02371	+	0.144739i	0.0897876	+	0.00642173i
$509$	−0.500788	+	0.779241i	−0.0221970	+	0.0345392i	−0.852175	−	0.523257i	$-0.824717\pi$
$509$	−0.500788	+	0.779241i	−0.0221970	+	0.0345392i	0.829978	+	0.557797i	$0.188353\pi$
$510$	3.43156	+	16.2646i	0.151952	+	0.720207i
$511$	1.52691	+	0.697317i	0.0675466	+	0.0308475i
$512$	0.599278	−	0.800541i	0.0264846	−	0.0353793i
$513$	0.286380	+	0.524466i	0.0126440	+	0.0231558i
$514$	12.8749	+	20.0337i	0.567888	+	0.883650i
$515$	7.57050	−	7.47623i	0.333596	−	0.329442i
$516$	−0.331179	−	1.12789i	−0.0145794	−	0.0496527i
$517$	2.06672	+	28.8965i	0.0908941	+	1.27087i
$518$	−0.150378	−	2.10256i	−0.00660725	−	0.0923814i
$519$	5.99975	+	20.4333i	0.263360	+	0.896921i
$520$	14.5312	+	0.0910436i	0.637235	+	0.00399253i
$521$	−1.65838	−	2.58048i	−0.0726547	−	0.113053i	0.803025	−	0.595945i	$-0.203223\pi$
$521$	−1.65838	−	2.58048i	−0.0726547	−	0.113053i	−0.875680	+	0.482892i	$0.839586\pi$
$522$	−2.96469	−	5.42942i	−0.129761	−	0.237639i
$523$	0.980555	−	1.30987i	0.0428767	−	0.0572765i	−0.778590	−	0.627532i	$-0.784065\pi$
$523$	0.980555	−	1.30987i	0.0428767	−	0.0572765i	0.821467	+	0.570256i	$0.193156\pi$
$524$	−13.3919	−	6.11588i	−0.585028	−	0.267173i
$525$	−0.837505	−	1.33980i	−0.0365517	−	0.0584738i
$526$	12.8370	−	19.9748i	0.559720	−	0.870941i
$527$	−57.9427	−	4.14415i	−2.52403	−	0.180522i
$528$	2.01935	+	2.01935i	0.0878807	+	0.0878807i
$529$	−6.12273	+	22.1701i	−0.266205	+	0.963916i
$530$	2.20536	−	4.75008i	0.0957947	−	0.206330i
$531$	1.05625	+	1.21897i	0.0458371	+	0.0528989i
$532$	−0.0401392	−	0.184517i	−0.00174026	−	0.00799983i
$533$	19.1876	+	25.6317i	0.831109	+	1.11023i
$534$	−3.82374	+	8.37281i	−0.165469	+	0.362327i
$535$	18.0474	+	33.5493i	0.780256	+	1.45046i
$536$	−0.296496	+	1.00977i	−0.0128067	+	0.0436156i
$537$	−12.0309	−	2.61717i	−0.519174	−	0.112939i
$538$	−1.91212	−	0.713182i	−0.0824372	−	0.0307475i
$539$	−18.9071	+	5.55163i	−0.814387	+	0.239126i
$540$	0.794537	−	2.09015i	0.0341914	−	0.0899456i
$541$	−10.7986	+	12.4623i	−0.464269	+	0.535794i	−0.938809	−	0.344440i	$-0.888069\pi$
$541$	−10.7986	+	12.4623i	−0.464269	+	0.535794i	0.474540	+	0.880234i	$0.342614\pi$
$542$	−16.1215	−	8.80301i	−0.692478	−	0.378122i
$543$	6.34176	−	17.0029i	0.272151	−	0.729665i
$544$	6.25377	−	4.01905i	0.268128	−	0.172315i
$545$	11.9922	+	10.5236i	0.513689	+	0.450780i
$546$	2.03271	−	0.292260i	0.0869921	−	0.0125076i
$547$	5.04221	−	1.88065i	0.215589	−	0.0804106i	−0.239349	−	0.970934i	$-0.576934\pi$
$547$	5.04221	−	1.88065i	0.215589	−	0.0804106i	0.454938	+	0.890523i	$0.349661\pi$
$548$	3.12784	−	2.34147i	0.133615	−	0.100023i
$549$	−0.00686068	−	0.00440909i	−0.000292807	−	0.000188175i
$550$	−8.41314	−	11.5372i	−0.358737	−	0.491948i
$551$			3.69658i			0.157480i
$552$	3.81594	−	2.90493i	0.162417	−	0.123642i
$553$	−2.66434	+	2.66434i	−0.113299	+	0.113299i
$554$	−4.95614	+	4.29452i	−0.210566	+	0.182457i
$555$	−12.5983	+	7.98533i	−0.534767	+	0.338958i
$556$	−2.23022	+	15.5115i	−0.0945824	+	0.657835i
$557$	0.0668822	+	0.179318i	0.00283389	+	0.00759795i	0.938359	−	0.345662i	$-0.112346\pi$
$557$	0.0668822	+	0.179318i	0.00283389	+	0.00759795i	−0.935525	+	0.353260i	$0.885073\pi$
$558$	6.25570	+	4.68296i	0.264825	+	0.198245i
$559$	−7.32981	−	2.15223i	−0.310018	−	0.0910295i
$560$	−0.426991	+	0.563006i	−0.0180437	+	0.0237914i
$561$	8.81907	+	19.3111i	0.372341	+	0.815314i
$562$	−9.59686	+	17.5753i	−0.404819	+	0.741371i
$563$	−17.7192	+	1.26730i	−0.746776	+	0.0534105i	−0.439540	−	0.898223i	$-0.644859\pi$
$563$	−17.7192	+	1.26730i	−0.746776	+	0.0534105i	−0.307236	+	0.951633i	$0.599404\pi$
$564$	−7.66664	−	6.64319i	−0.322824	−	0.279729i
$565$	−12.9306	−	17.5007i	−0.543993	−	0.736260i
$566$	−1.45282	+	0.663479i	−0.0610664	+	0.0278881i
$567$	0.0671718	−	0.308784i	0.00282095	−	0.0129677i
$568$	9.95875	−	5.43789i	0.417860	−	0.228169i
$569$	3.73091	+	25.9490i	0.156408	+	1.08784i	0.905185	+	0.425018i	$0.139732\pi$
$569$	3.73091	+	25.9490i	0.156408	+	1.08784i	−0.748777	+	0.662822i	$0.769359\pi$
$570$	−1.01528	+	0.868672i	−0.0425256	+	0.0363847i
$571$	−9.51794	−	1.36847i	−0.398313	−	0.0572688i	−0.0597523	−	0.998213i	$-0.519031\pi$
$571$	−9.51794	−	1.36847i	−0.398313	−	0.0572688i	−0.338561	+	0.940944i	$0.609940\pi$
$572$	18.1347	−	3.94496i	0.758249	−	0.164947i
$573$	1.52833	−	21.3689i	0.0638470	−	0.892698i
$574$	−1.55691			−0.0649842
$575$	−21.0970	+	11.3980i	−0.879807	+	0.475331i
$576$	−1.00000			−0.0416667
$577$	2.60176	−	36.3774i	0.108313	−	1.51441i	−0.595113	−	0.803642i	$-0.702893\pi$
$577$	2.60176	−	36.3774i	0.108313	−	1.51441i	0.703426	−	0.710768i	$-0.251653\pi$
$578$	37.3880	−	8.13325i	1.55513	−	0.338299i
$579$	17.0805	+	2.45580i	0.709840	+	0.102060i
$580$	10.5105	−	8.99273i	0.436425	−	0.373403i
$581$	−0.406543	−	2.82757i	−0.0168662	−	0.117307i
$582$	2.53996	−	1.38693i	0.105285	−	0.0574899i
$583$	1.42174	−	6.53564i	0.0588826	−	0.270679i
$584$	−4.83191	+	2.20666i	−0.199946	+	0.0913123i
$585$	−8.63533	−	11.6874i	−0.357027	−	0.483213i
$586$	−8.34239	−	7.22872i	−0.344621	−	0.298616i
$587$	−19.1797	+	1.37176i	−0.791632	+	0.0566186i	−0.461298	−	0.887245i	$-0.652616\pi$
$587$	−19.1797	+	1.37176i	−0.791632	+	0.0566186i	−0.330334	+	0.943864i	$0.607161\pi$
$588$	3.30689	−	6.05611i	0.136374	−	0.249750i
$589$	−1.93980	−	4.24756i	−0.0799279	−	0.175018i
$590$	−2.17942	+	2.87365i	−0.0897251	+	0.118306i
$591$	19.4116	+	5.69976i	0.798487	+	0.234457i
$592$	5.34006	+	3.99752i	0.219475	+	0.164297i
$593$	−5.16897	−	13.8585i	−0.212264	−	0.569102i	0.786564	−	0.617509i	$-0.211858\pi$
$593$	−5.16897	−	13.8585i	−0.212264	−	0.569102i	−0.998828	+	0.0484071i	$0.984586\pi$
$594$	0.406421	−	2.82672i	0.0166756	−	0.115982i
$595$	−4.43668	+	2.81216i	−0.181886	+	0.115287i
$596$	−5.33890	+	4.62619i	−0.218690	+	0.189496i
$597$	6.06222	−	6.06222i	0.248110	−	0.248110i
$598$	−2.47427	−	31.0682i	−0.101180	−	1.27047i
$599$			24.7711i			1.01212i	0.862498	+	0.506061i	$0.168899\pi$
$599$			24.7711i			1.01212i	−0.862498	+	0.506061i	$0.831101\pi$
$600$	4.93980	+	0.773532i	0.201667	+	0.0315793i
$601$	−24.1401	−	15.5139i	−0.984694	−	0.632824i	−0.0539682	−	0.998543i	$-0.517187\pi$
$601$	−24.1401	−	15.5139i	−0.984694	−	0.632824i	−0.930726	+	0.365718i	$0.880823\pi$
$602$	0.297375	−	0.222612i	0.0121201	−	0.00907300i
$603$	0.986048	−	0.367777i	0.0401550	−	0.0149770i
$604$	19.1947	−	2.75977i	0.781019	−	0.112294i
$605$	4.78073	+	4.19526i	0.194364	+	0.170562i
$606$	8.62417	−	5.54242i	0.350333	−	0.225145i
$607$	−9.32938	+	25.0130i	−0.378668	+	1.01525i	0.598189	+	0.801355i	$0.295887\pi$
$607$	−9.32938	+	25.0130i	−0.378668	+	1.01525i	−0.976857	+	0.213893i	$0.931386\pi$
$608$	0.524466	+	0.286380i	0.0212699	+	0.0116143i
$609$	1.28015	−	1.47737i	0.0518744	−	0.0598662i
$610$	0.00647969	−	0.0170458i	0.000262355	−	0.000690163i
$611$	−63.2549	+	18.5733i	−2.55902	+	0.751395i
$612$	−6.96516	−	2.59787i	−0.281550	−	0.105013i
$613$	10.0259	+	2.18101i	0.404944	+	0.0880901i	0.410424	−	0.911895i	$-0.365381\pi$
$613$	10.0259	+	2.18101i	0.404944	+	0.0880901i	−0.00548023	+	0.999985i	$0.501744\pi$
$614$	3.48739	−	11.8770i	0.140740	−	0.479315i
$615$	5.21909	+	9.70207i	0.210454	+	0.391225i
$616$	−0.374889	+	0.820892i	−0.0151047	+	0.0330747i
$617$	21.4728	+	28.6843i	0.864462	+	1.15479i	0.986743	+	0.162291i	$0.0518882\pi$
$617$	21.4728	+	28.6843i	0.864462	+	1.15479i	−0.122281	+	0.992496i	$0.539021\pi$
$618$	1.01145	+	4.64955i	0.0406864	+	0.187032i
$619$	−8.59028	−	9.91371i	−0.345272	−	0.398466i	0.556379	−	0.830928i	$-0.312190\pi$
$619$	−8.59028	−	9.91371i	−0.345272	−	0.398466i	−0.901652	+	0.432463i	$0.857645\pi$
$620$	−7.35815	+	15.8486i	−0.295510	+	0.636494i
$621$	−4.61232	−	1.31395i	−0.185086	−	0.0527271i
$622$	−15.2329	−	15.2329i	−0.610784	−	0.610784i
$623$	−2.90130	−	0.207505i	−0.116238	−	0.00831351i
$624$	−3.51345	+	5.46703i	−0.140650	+	0.218856i
$625$	−23.8033	−	7.64219i	−0.952132	−	0.305688i
$626$	−16.2524	−	7.42222i	−0.649576	−	0.296652i
$627$	−1.02267	+	1.36613i	−0.0408415	+	0.0545579i
$628$	9.09636	+	16.6587i	0.362984	+	0.664756i
$629$	26.8093	+	41.7161i	1.06896	+	1.66333i
$630$	0.706596	+	0.00442710i	0.0281515	+	0.000176380i
$631$	2.55860	+	8.71378i	0.101856	+	0.346890i	0.994614	−	0.103646i	$-0.0330510\pi$
$631$	2.55860	+	8.71378i	0.101856	+	0.346890i	−0.892758	+	0.450536i	$0.851233\pi$
$632$	−0.850624	−	11.8933i	−0.0338360	−	0.473089i
$633$	−0.0433685	−	0.606371i	−0.00172374	−	0.0241011i
$634$	−9.40342	−	32.0251i	−0.373458	−	1.27188i
$635$	3.22797	−	3.18778i	0.128098	−	0.126503i
$636$	1.26623	+	1.97029i	0.0502092	+	0.0781270i
$637$	−21.4904	−	39.3567i	−0.851479	−	1.55937i
$638$	10.5870	−	14.1425i	0.419142	−	0.559908i
$639$	−10.3213	−	4.71358i	−0.408305	−	0.186466i
$640$	−0.461612	−	2.18790i	−0.0182468	−	0.0864844i
$641$	7.08983	−	11.0320i	0.280031	−	0.435737i	−0.672536	−	0.740064i	$-0.734795\pi$
$641$	7.08983	−	11.0320i	0.280031	−	0.435737i	0.952568	+	0.304327i	$0.0984315\pi$
$642$	−16.9934	−	1.21539i	−0.670676	−	0.0479677i
$643$	29.8773	+	29.8773i	1.17825	+	1.17825i	0.980191	+	0.198055i	$0.0634625\pi$
$643$	29.8773	+	29.8773i	1.17825	+	1.17825i	0.198055	+	0.980191i	$0.436537\pi$
$644$	1.28150	+	0.809028i	0.0504982	+	0.0318802i
$645$	−2.38410	−	1.10689i	−0.0938738	−	0.0435836i
$646$	2.90901	+	3.35718i	0.114454	+	0.132086i
$647$	4.53780	+	20.8599i	0.178399	+	0.820088i	0.976149	+	0.217100i	$0.0696598\pi$
$647$	4.53780	+	20.8599i	0.178399	+	0.820088i	−0.797750	+	0.602988i	$0.793977\pi$
$648$	0.599278	+	0.800541i	0.0235419	+	0.0314482i
$649$	−1.91348	+	4.18993i	−0.0751106	+	0.164469i
$650$	21.5847	−	24.2883i	0.846620	−	0.952665i
$651$	−0.695703	+	2.36935i	−0.0272668	+	0.0928620i
$652$	−10.5006	−	2.28427i	−0.411236	−	0.0894590i
$653$	−42.0295	−	15.6762i	−1.64474	−	0.613457i	−0.654912	−	0.755705i	$-0.727294\pi$
$653$	−42.0295	−	15.6762i	−1.64474	−	0.613457i	−0.989831	+	0.142248i	$0.954567\pi$
$654$	−6.84621	+	2.01023i	−0.267708	+	0.0786061i
$655$	−30.0303	+	13.4876i	−1.17338	+	0.527006i
$656$	3.22640	−	3.72346i	0.125970	−	0.145377i
$657$	4.66218	+	2.54574i	0.181889	+	0.0993189i
$658$	1.12028	−	3.00358i	0.0436729	−	0.117092i
$659$	17.7000	−	11.3751i	0.689495	−	0.443111i	−0.148412	−	0.988926i	$-0.547416\pi$
$659$	17.7000	−	11.3751i	0.689495	−	0.443111i	0.837906	+	0.545814i	$0.183780\pi$
$660$	6.37219	−	0.415637i	0.248037	−	0.0161787i
$661$	38.3163	−	5.50905i	1.49033	−	0.214277i	0.651491	−	0.758656i	$-0.274144\pi$
$661$	38.3163	−	5.50905i	1.49033	−	0.214277i	0.838839	+	0.544379i	$0.183235\pi$
$662$	13.5156	−	5.04107i	0.525300	−	0.195927i
$663$	−38.6744	+	28.9513i	−1.50199	+	1.12437i
$664$	7.60481	+	4.88731i	0.295124	+	0.189665i
$665$	−0.369318	−	0.204677i	−0.0143215	−	0.00793704i
$666$		−	6.67056i		−	0.258479i
$667$	−21.1468	−	20.8081i	−0.818807	−	0.805693i
$668$	6.84856	−	6.84856i	0.264979	−	0.264979i
$669$	6.96649	−	6.03650i	0.269340	−	0.233384i
$670$	1.25983	+	1.98761i	0.0486715	+	0.0767880i
$671$	0.00331448	−	0.0230527i	0.000127954	−	0.000889941i
$672$	−0.110433	−	0.296081i	−0.00426003	−	0.0114216i
$673$	−31.4263	−	23.5254i	−1.21139	−	0.906839i	−0.213850	−	0.976867i	$-0.568600\pi$
$673$	−31.4263	−	23.5254i	−1.21139	−	0.906839i	−0.997545	+	0.0700277i	$0.977691\pi$
$674$	−17.0326	−	5.00122i	−0.656071	−	0.192640i
$675$	−2.34107	−	4.41808i	−0.0901078	−	0.170052i
$676$	12.1437	+	26.5910i	0.467066	+	1.02273i
$677$	2.18101	−	3.99422i	0.0838229	−	0.153510i	−0.832405	−	0.554168i	$-0.813037\pi$
$677$	2.18101	−	3.99422i	0.0838229	−	0.153510i	0.916228	+	0.400658i	$0.131218\pi$
$678$	9.70633	−	0.694210i	0.372769	−	0.0266610i
$679$	0.691138	+	0.598874i	0.0265234	+	0.0229827i
$680$	2.46869	−	16.4383i	0.0946698	−	0.630380i
$681$	−5.58645	+	2.55125i	−0.214073	+	0.0977640i
$682$	−4.74362	+	21.8061i	−0.181643	+	0.834998i
$683$	30.2105	−	16.4962i	1.15597	−	0.631210i	0.217331	−	0.976098i	$-0.430265\pi$
$683$	30.2105	−	16.4962i	1.15597	−	0.631210i	0.938644	+	0.344888i	$0.112083\pi$
$684$	−0.0850417	−	0.591478i	−0.00325165	−	0.0226157i
$685$	0.677852	−	8.71033i	0.0258994	−	0.332805i
$686$	4.34781	+	0.625121i	0.166000	+	0.0238672i
$687$	−19.1519	+	4.16625i	−0.730692	+	0.158952i
$688$	−0.0838599	+	1.17252i	−0.00319713	+	0.0447017i
$689$	15.2205			0.579853
$690$	0.745696	−	10.6978i	0.0283881	−	0.407260i
$691$	−24.9945			−0.950836			−0.475418	−	0.879760i	$-0.657703\pi$
$691$	−24.9945			−0.950836			−0.475418	+	0.879760i	$0.657703\pi$
$692$	1.51923	−	21.2416i	0.0577526	−	0.807486i
$693$	0.881821	−	0.191828i	0.0334976	−	0.00728695i
$694$	9.23952	+	1.32844i	0.350727	+	0.0504270i
$695$	22.7809	+	26.6258i	0.864130	+	1.00998i
$696$	0.880376	+	6.12315i	0.0333706	+	0.232097i
$697$	32.1454	−	17.5527i	1.21760	−	0.664857i
$698$	1.59832	−	7.34738i	0.0604975	−	0.278102i
$699$	−1.25679	+	0.573958i	−0.0475362	+	0.0217091i
$700$	0.316487	+	1.54801i	0.0119621	+	0.0585092i
$701$	−26.2849	−	22.7760i	−0.992768	−	0.860239i	−0.00258268	−	0.999997i	$-0.500822\pi$
$701$	−26.2849	−	22.7760i	−0.992768	−	0.860239i	−0.990186	+	0.139758i	$0.955368\pi$
$702$	6.48211	−	0.463610i	0.244652	−	0.0174978i
$703$	−1.91032	+	3.49849i	−0.0720490	+	0.131948i
$704$	−1.18634	−	2.59771i	−0.0447117	−	0.0979050i
$705$	−22.4725	+	3.08748i	−0.846364	+	0.116281i
$706$	6.90420	+	2.02726i	0.259843	+	0.0762968i
$707$	2.59340	+	1.94139i	0.0975347	+	0.0730136i
$708$	−0.563662	−	1.51124i	−0.0211837	−	0.0567957i
$709$	2.10748	−	14.6579i	0.0791482	−	0.550487i	−0.911208	−	0.411946i	$-0.864849\pi$
$709$	2.10748	−	14.6579i	0.0791482	−	0.550487i	0.990357	−	0.138542i	$-0.0442415\pi$
$710$	5.54842	−	24.7579i	0.208229	−	0.929146i
$711$	−9.01130	+	7.80833i	−0.337950	+	0.292835i
$712$	6.50865	−	6.50865i	0.243922	−	0.243922i
$713$	35.2179	+	12.8127i	1.31892	+	0.479840i
$714$		−	2.34914i		−	0.0879145i
$715$	20.1160	−	36.2973i	0.752298	−	1.35744i
$716$	10.3578	+	6.65654i	0.387089	+	0.248767i
$717$	14.7186	−	11.0182i	0.549678	−	0.411484i
$718$	−6.00730	+	2.24061i	−0.224191	+	0.0836187i
$719$	−31.2195	+	4.48869i	−1.16429	+	0.167400i	−0.697245	−	0.716833i	$-0.745591\pi$
$719$	−31.2195	+	4.48869i	−1.16429	+	0.167400i	−0.467046	+	0.884233i	$0.654682\pi$
$720$	−1.47487	+	1.68070i	−0.0549652	+	0.0626360i
$721$	−1.26495	+	0.812932i	−0.0471091	+	0.0302752i
$722$	6.51503	−	17.4675i	0.242464	−	0.650072i
$723$	18.0760	+	9.87023i	0.672253	+	0.367078i
$724$	−11.8838	+	13.7147i	−0.441659	+	0.509702i
$725$	0.387569	−	30.9281i	0.0143940	−	1.14864i
$726$	−2.72927	+	0.801385i	−0.101293	+	0.0297422i
$727$	−0.198899	−	0.0741853i	−0.00737674	−	0.00275138i	0.345773	−	0.938318i	$-0.387617\pi$
$727$	−0.198899	−	0.0741853i	−0.00737674	−	0.00275138i	−0.353150	+	0.935567i	$0.614889\pi$
$728$	−2.00669	−	0.436528i	−0.0743727	−	0.0161788i
$729$	0.281733	−	0.959493i	0.0104345	−	0.0355368i
$730$	−3.41772	+	11.3755i	−0.126495	+	0.421028i
$731$	−3.63014	+	7.94890i	−0.134266	+	0.294001i
$732$	0.00488729	+	0.00652866i	0.000180640	+	0.000241306i
$733$	4.66444	+	21.4421i	0.172285	+	0.791981i	0.979455	+	0.201662i	$0.0646343\pi$
$733$	4.66444	+	21.4421i	0.172285	+	0.791981i	−0.807170	+	0.590319i	$0.799002\pi$
$734$	−22.9159	−	26.4463i	−0.845839	−	0.976151i
$735$	−5.30127	−	14.4899i	−0.195540	−	0.534467i
$736$	−4.59051	+	1.38824i	−0.169208	+	0.0511713i
$737$	2.12516	+	2.12516i	0.0782814	+	0.0782814i
$738$	−4.91429	−	0.351477i	−0.180898	−	0.0129380i
$739$	9.44901	−	14.7029i	0.347587	−	0.540856i	−0.622809	−	0.782374i	$-0.714009\pi$
$739$	9.44901	−	14.7029i	0.347587	−	0.540856i	0.970397	+	0.241517i	$0.0776451\pi$
$740$	14.5945	−	3.07921i	0.536506	−	0.113194i
$741$	−3.53242	−	1.61320i	−0.129767	−	0.0592625i
$742$	−0.443533	+	0.592491i	−0.0162826	+	0.0217510i
$743$	−17.4643	−	31.9834i	−0.640701	−	1.17336i	−0.973136	−	0.230230i	$-0.926052\pi$
$743$	−17.4643	−	31.9834i	−0.640701	−	1.17336i	0.332435	−	0.943126i	$-0.392130\pi$
$744$	−4.22475	−	6.57384i	−0.154887	−	0.241009i
$745$	−0.0989689	+	15.7961i	−0.00362594	+	0.578725i
$746$	−1.44230	−	4.91203i	−0.0528064	−	0.179842i
$747$	−0.644896	−	9.01682i	−0.0235955	−	0.329908i
$748$	−1.51450	−	21.1754i	−0.0553755	−	0.774251i
$749$	−1.51677	−	5.16565i	−0.0554216	−	0.188749i
$750$	8.58565	−	7.16146i	0.313504	−	0.261500i
$751$	−3.89299	−	6.05762i	−0.142057	−	0.221046i	0.762933	−	0.646477i	$-0.223759\pi$
$751$	−3.89299	−	6.05762i	−0.142057	−	0.221046i	−0.904990	+	0.425432i	$0.860122\pi$
$752$	4.86171	+	8.90355i	0.177288	+	0.324679i
$753$	15.1146	−	20.1907i	0.550806	−	0.735790i
$754$	36.5686	+	16.7003i	1.33175	+	0.608190i
$755$	23.6713	−	36.3308i	0.861487	−	1.32221i
$756$	−0.170846	+	0.265841i	−0.00621359	+	0.00966854i
$757$	−9.82032	−	0.702363i	−0.356926	−	0.0255278i	−0.108275	−	0.994121i	$-0.534533\pi$
$757$	−9.82032	−	0.702363i	−0.356926	−	0.0255278i	−0.248651	+	0.968593i	$0.579987\pi$
$758$	14.5928	+	14.5928i	0.530036	+	0.530036i
$759$	−2.05849	−	13.5403i	−0.0747186	−	0.491481i
$760$	1.25484	−	0.459096i	0.0455178	−	0.0166532i
$761$	12.0890	+	13.9515i	0.438227	+	0.505741i	0.931303	−	0.364245i	$-0.118673\pi$
$761$	12.0890	+	13.9515i	0.438227	+	0.505741i	−0.493076	+	0.869986i	$0.664127\pi$
$762$	0.431269	+	1.98251i	0.0156232	+	0.0718188i
$763$	−1.35124	−	1.80504i	−0.0489180	−	0.0653468i
$764$	−8.89963	+	19.4875i	−0.321977	+	0.705032i
$765$	−14.6390	+	7.87482i	−0.529273	+	0.284715i
$766$	−2.90868	+	9.90606i	−0.105095	+	0.357921i
$767$	−10.2424	−	2.22809i	−0.369830	−	0.0804517i
$768$	0.936950	+	0.349464i	0.0338093	+	0.0126102i
$769$	−3.48057	+	1.02199i	−0.125513	+	0.0368538i	−0.343886	−	0.939012i	$-0.611743\pi$
$769$	−3.48057	+	1.02199i	−0.125513	+	0.0368538i	0.218373	+	0.975865i	$0.429925\pi$
$770$	0.826760	+	1.84079i	0.0297944	+	0.0663373i
$771$	−15.5950	+	17.9975i	−0.561638	+	0.648165i
$772$	−15.1453	−	8.26997i	−0.545092	−	0.297643i
$773$	−16.2730	+	43.6297i	−0.585301	+	1.56925i	0.219440	+	0.975626i	$0.429577\pi$
$773$	−16.2730	+	43.6297i	−0.585301	+	1.56925i	−0.804741	+	0.593626i	$0.797696\pi$
$774$	0.988902	−	0.635529i	0.0355453	−	0.0228436i
$775$	15.7844	+	35.7414i	0.566991	+	1.28387i
$776$	−2.86450	+	0.411853i	−0.102830	+	0.0147847i
$777$	1.97503	−	0.736648i	0.0708538	−	0.0264271i
$778$	−15.7496	+	11.7900i	−0.564652	+	0.422693i
$779$	2.47672	+	1.59169i	0.0887379	+	0.0570284i
$780$	4.00655	+	13.9682i	0.143458	+	0.500143i
$781$		−	32.4037i		−	1.15950i
$782$	−35.5801	−	2.25621i	−1.27234	−	0.0806819i
$783$	4.37424	−	4.37424i	0.156323	−	0.156323i
$784$	−5.21478	+	4.51863i	−0.186242	+	0.161380i
$785$	41.4143	+	9.28126i	1.47814	+	0.331262i
$786$	2.09521	−	14.5725i	0.0747336	−	0.519783i
$787$	−5.35494	−	14.3571i	−0.190883	−	0.511777i	0.805889	−	0.592067i	$-0.201688\pi$
$787$	−5.35494	−	14.3571i	−0.190883	−	0.511777i	−0.996772	+	0.0802903i	$0.974415\pi$
$788$	−16.1958	−	12.1240i	−0.576953	−	0.431901i
$789$	22.7822	+	6.68947i	0.811069	+	0.238151i
$790$	−21.2436	−	16.1114i	−0.755813	−	0.573218i
$791$	1.27744	+	2.79720i	0.0454205	+	0.0994569i
$792$	−1.36863	+	2.50646i	−0.0486322	+	0.0890633i
$793$	0.0528636	−	0.00378088i	0.00187724	−	0.000134263i
$794$	23.3692	+	20.2495i	0.829342	+	0.718629i
$795$	5.17899	+	0.777775i	0.183680	+	0.0275848i
$796$	−7.79852	+	3.56147i	−0.276411	+	0.126233i
$797$	−0.556496	+	2.55817i	−0.0197121	+	0.0906151i	−0.985952	−	0.167029i	$-0.946583\pi$
$797$	−0.556496	+	2.55817i	−0.0197121	+	0.0906151i	0.966240	+	0.257644i	$0.0829463\pi$
$798$	0.165734	−	0.0904978i	0.00586693	−	0.00320359i
$799$	10.7323	+	74.6447i	0.379681	+	2.64074i
$800$	−4.35802	−	2.45104i	−0.154079	−	0.0866575i
$801$	−9.11093	−	1.30995i	−0.321919	−	0.0462849i
$802$	18.3975	−	4.00212i	0.649637	−	0.141320i
$803$	−1.08220	+	15.1311i	−0.0381900	+	0.533966i
$804$	−1.05240			−0.0371154
$805$	3.24978	−	0.960605i	0.114540	−	0.0338569i
$806$	−50.7828			−1.78875
$807$	0.145588	−	2.03559i	0.00512495	−	0.0716561i
$808$	−10.0173	+	2.17913i	−0.352407	+	0.0766615i
$809$	−15.6113	−	2.24456i	−0.548864	−	0.0789147i	−0.137696	−	0.990475i	$-0.543970\pi$
$809$	−15.6113	−	2.24456i	−0.548864	−	0.0789147i	−0.411168	+	0.911560i	$0.634879\pi$
$810$	2.22933	+	0.173490i	0.0783306	+	0.00609582i
$811$	0.846281	+	5.88601i	0.0297169	+	0.206686i	0.999270	−	0.0381941i	$-0.0121605\pi$
$811$	0.846281	+	5.88601i	0.0297169	+	0.206686i	−0.969553	+	0.244880i	$0.921251\pi$
$812$	−1.71573	+	0.936858i	−0.0602102	+	0.0328773i
$813$	3.90447	−	17.9486i	0.136936	−	0.629484i
$814$	17.3282	−	7.91353i	0.607354	−	0.277369i
$815$	−19.3263	+	14.2794i	−0.676969	+	0.500185i
$816$	5.61814	+	4.86815i	0.196674	+	0.170419i
$817$	−0.700649	+	0.0501114i	−0.0245126	+	0.00175318i
$818$	−8.47590	+	15.5224i	−0.296353	+	0.542730i
$819$	0.853103	+	1.86804i	0.0298098	+	0.0652744i
$820$	−1.49950	−	10.9142i	−0.0523647	−	0.381142i
$821$	−27.6943	−	8.13178i	−0.966538	−	0.283801i	−0.239881	−	0.970802i	$-0.577109\pi$
$821$	−27.6943	−	8.13178i	−0.966538	−	0.283801i	−0.726656	+	0.687001i	$0.758927\pi$
$822$	3.12784	+	2.34147i	0.109096	+	0.0816682i
$823$	0.286168	+	0.767246i	0.00997519	+	0.0267445i	0.941842	−	0.336056i	$-0.109093\pi$
$823$	0.286168	+	0.767246i	0.00997519	+	0.0267445i	−0.931867	+	0.362801i	$0.881821\pi$
$824$	0.677175	−	4.70986i	0.0235905	−	0.164076i
$825$	8.69960	−	11.3228i	0.302881	−	0.394208i
$826$	0.385202	−	0.333779i	0.0134029	−	0.0116137i
$827$	−28.9067	+	28.9067i	−1.00518	+	1.00518i	−0.00519842	+	0.999986i	$0.501655\pi$
$827$	−28.9067	+	28.9067i	−1.00518	+	1.00518i	−0.999986	+	0.00519842i	$0.998345\pi$
$828$	3.86234	+	2.84295i	0.134225	+	0.0987993i
$829$			5.56990i			0.193451i	0.995311	+	0.0967253i	$0.0308368\pi$
$829$			5.56990i			0.193451i	−0.995311	+	0.0967253i	$0.969163\pi$
$830$	19.4302	−	5.57324i	0.674433	−	0.193450i
$831$	−5.51687	−	3.54547i	−0.191378	−	0.122991i
$832$	5.20245	−	3.89451i	0.180363	−	0.135018i
$833$	−48.0606	+	17.9257i	−1.66520	+	0.621088i
$834$	−15.5115	+	2.23022i	−0.537120	+	0.0772262i
$835$	−1.40962	−	21.6111i	−0.0487820	−	0.747884i
$836$	1.43560	−	0.922606i	0.0496514	−	0.0319090i
$837$	−2.73083	+	7.32164i	−0.0943913	+	0.253073i
$838$	−24.1996	−	13.2140i	−0.835962	−	0.456470i
$839$	3.45860	−	3.99143i	0.119404	−	0.137800i	−0.692900	−	0.721033i	$-0.743667\pi$
$839$	3.45860	−	3.99143i	0.119404	−	0.137800i	0.812304	+	0.583234i	$0.198213\pi$
$840$	−0.660498	−	0.251078i	−0.0227893	−	0.00866301i
$841$	8.89258	−	2.61110i	0.306641	−	0.0900378i
$842$	5.36314	+	2.00035i	0.184826	+	0.0689365i
$843$	−19.5672	−	4.25658i	−0.673929	−	0.146604i
$844$	−0.171271	+	0.583295i	−0.00589539	+	0.0200778i
$845$	62.6020	+	18.8084i	2.15357	+	0.647030i
$846$	4.21415	−	9.22769i	0.144885	−	0.317255i
$847$	−0.538676	−	0.719586i	−0.0185091	−	0.0247253i
$848$	−0.497846	−	2.28856i	−0.0170961	−	0.0785896i
$849$	−1.04591	−	1.20704i	−0.0358955	−	0.0414256i
$850$	−23.9868	−	28.3935i	−0.822742	−	0.973889i
$851$	−9.26037	−	30.6213i	−0.317441	−	1.04968i
$852$	8.02332	+	8.02332i	0.274874	+	0.274874i
$853$	−0.538510	−	0.0385150i	−0.0184382	−	0.00131873i	0.0621170	−	0.998069i	$-0.480215\pi$
$853$	−0.538510	−	0.0385150i	−0.0184382	−	0.00131873i	−0.0805553	+	0.996750i	$0.525669\pi$
$854$	−0.00139330	+	0.00216801i	−4.76777e−5	+	7.41879e-5i
$855$	−1.11952	−	0.729425i	−0.0382869	−	0.0249458i
$856$	15.4972	+	7.07735i	0.529684	+	0.241899i
$857$	21.3169	−	28.4761i	0.728172	−	0.972723i	−0.271775	−	0.962361i	$-0.587611\pi$
$857$	21.3169	−	28.4761i	0.728172	−	0.972723i	0.999946	−	0.0103626i	$-0.00329857\pi$
$858$	8.89429	+	16.2887i	0.303646	+	0.556086i
$859$	21.1124	+	32.8515i	0.720346	+	1.12088i	0.987560	+	0.157243i	$0.0502605\pi$
$859$	21.1124	+	32.8515i	0.720346	+	1.12088i	−0.267214	+	0.963637i	$0.586103\pi$
$860$	1.84696	+	1.87025i	0.0629809	+	0.0637751i
$861$	−0.438632	−	1.49384i	−0.0149486	−	0.0509101i
$862$	−1.18899	−	16.6243i	−0.0404973	−	0.566227i
$863$	1.61898	+	22.6363i	0.0551108	+	0.770550i	0.947596	+	0.319472i	$0.103506\pi$
$863$	1.61898	+	22.6363i	0.0551108	+	0.770550i	−0.892485	+	0.451078i	$0.851040\pi$
$864$	−0.281733	−	0.959493i	−0.00958474	−	0.0326426i
$865$	−33.4602	−	33.8821i	−1.13768	−	1.15203i
$866$	5.64859	+	8.78938i	0.191947	+	0.298675i
$867$	18.3372	+	33.5821i	0.622764	+	1.14051i
$868$	1.47984	−	1.97684i	0.0502291	−	0.0670982i
$869$	−30.9742	−	14.1455i	−1.05073	−	0.479852i
$870$	11.5896	+	7.55121i	0.392925	+	0.256010i
$871$	−3.69756	+	5.75352i	−0.125287	+	0.194951i
$872$	7.11706	+	0.509022i	0.241014	+	0.0172377i
$873$	2.04634	+	2.04634i	0.0692580	+	0.0692580i
$874$	−1.21150	−	2.59713i	−0.0409796	−	0.0878492i
$875$	3.06851	+	1.75119i	0.103735	+	0.0592011i
$876$	−3.47858	−	4.01450i	−0.117530	−	0.135637i
$877$	0.261773	+	1.20335i	0.00883944	+	0.0406343i	0.981355	−	0.192202i	$-0.0615629\pi$
$877$	0.261773	+	1.20335i	0.00883944	+	0.0406343i	−0.972516	+	0.232836i	$0.925199\pi$
$878$	16.1097	+	21.5201i	0.543677	+	0.726267i
$879$	4.58558	−	10.0410i	0.154668	−	0.338675i
$880$	−6.11567	−	1.83742i	−0.206159	−	0.0619394i
$881$	−9.70310	+	33.0457i	−0.326906	+	1.11334i	0.618050	+	0.786139i	$0.287923\pi$
$881$	−9.70310	+	33.0457i	−0.326906	+	1.11334i	−0.944955	+	0.327199i	$0.893895\pi$
$882$	6.74245	+	1.46673i	0.227030	+	0.0493874i
$883$	29.8139	+	11.1200i	1.00332	+	0.374218i	0.796812	−	0.604227i	$-0.206518\pi$
$883$	29.8139	+	11.1200i	1.00332	+	0.374218i	0.206506	+	0.978445i	$0.433791\pi$
$884$	46.3534	−	13.6106i	1.55903	−	0.457773i
$885$	−3.37126	−	1.28153i	−0.113324	−	0.0430783i
$886$	−10.8912	+	12.5692i	−0.365899	+	0.422270i
$887$	34.3420	+	18.7522i	1.15309	+	0.629636i	0.937890	−	0.346934i	$-0.112777\pi$
$887$	34.3420	+	18.7522i	1.15309	+	0.629636i	0.215202	+	0.976570i	$0.430959\pi$
$888$	−2.33112	+	6.24998i	−0.0782274	+	0.209736i
$889$	−0.539359	+	0.346625i	−0.0180895	+	0.0116254i
$890$	−1.33966	−	20.5385i	−0.0449055	−	0.688452i
$891$	2.82672	−	0.406421i	0.0946986	−	0.0136156i
$892$	−8.63679	+	3.22136i	−0.289181	+	0.107859i
$893$	−4.85281	+	3.63277i	−0.162393	+	0.121566i
$894$	−5.94294	−	3.81929i	−0.198762	−	0.127736i
$895$	26.4641	−	7.59078i	0.884596	−	0.253732i
$896$			0.316006i			0.0105570i
$897$	29.1126	−	11.1270i	0.972042	−	0.371518i
$898$	−10.1231	+	10.1231i	−0.337813	+	0.337813i
$899$	−36.5332	+	31.6562i	−1.21845	+	1.05579i
$900$	0.649505	+	4.95763i	0.0216502	+	0.165254i
$901$	2.47781	−	17.2335i	0.0825478	−	0.574133i
$902$	−4.91696	−	13.1829i	−0.163717	−	0.438942i
$903$	0.297375	+	0.222612i	0.00989603	+	0.00740807i
$904$	−9.33694	−	2.74157i	−0.310542	−	0.0911834i
$905$	5.52312	+	40.2005i	0.183595	+	1.33631i
$906$	8.05574	+	17.6396i	0.267634	+	0.586037i
$907$	−3.82787	+	7.01023i	−0.127102	+	0.232771i	−0.933479	−	0.358631i	$-0.883244\pi$
$907$	−3.82787	+	7.01023i	−0.127102	+	0.232771i	0.806377	+	0.591402i	$0.201425\pi$
$908$	6.12579	−	0.438125i	0.203292	−	0.0145397i
$909$	7.74762	+	6.71335i	0.256972	+	0.222668i
$910$	−3.69328	+	2.72881i	−0.122431	+	0.0904593i
$911$	−25.3550	+	11.5792i	−0.840049	+	0.383637i	−0.788501	−	0.615033i	$-0.789143\pi$
$911$	−25.3550	+	11.5792i	−0.840049	+	0.383637i	−0.0515474	+	0.998671i	$0.516415\pi$
$912$	−0.127021	+	0.583904i	−0.00420607	+	0.0193350i
$913$	22.6581	−	12.3722i	0.749872	−	0.409461i
$914$	−6.07295	−	42.2383i	−0.200875	−	1.39712i
$915$	0.0181808	+	0.00141486i	0.000601040	+	4.67740e-5i
$916$	19.4003	+	2.78935i	0.641006	+	0.0921627i
$917$	4.54602	−	0.988926i	0.150123	−	0.0326572i
$918$	0.530326	−	7.41493i	0.0175034	−	0.244729i
$919$	1.64745			0.0543443			0.0271721	−	0.999631i	$-0.491350\pi$
$919$	1.64745			0.0543443			0.0271721	+	0.999631i	$0.491350\pi$
$920$	−4.43719	+	9.76275i	−0.146290	+	0.321868i
$921$	12.3784			0.407881
$922$	−1.37009	+	19.1563i	−0.0451214	+	0.630879i
$923$	72.0532	−	15.6742i	2.37166	−	0.515923i
$924$	−0.893259	−	0.128431i	−0.0293861	−	0.00422508i
$925$	16.3498	−	29.0705i	0.537580	−	0.955831i
$926$	−1.93868	−	13.4838i	−0.0637091	−	0.443106i
$927$	−4.17625	+	2.28040i	−0.137166	+	0.0748983i
$928$	1.31495	−	6.04474i	0.0431654	−	0.198428i
$929$	1.84139	−	0.840936i	0.0604142	−	0.0275902i	−0.384979	−	0.922925i	$-0.625791\pi$
$929$	1.84139	−	0.840936i	0.0604142	−	0.0275902i	0.445393	+	0.895335i	$0.353064\pi$
$930$	−17.2796	−	2.59503i	−0.566621	−	0.0850945i
$931$	−3.11615	−	2.70016i	−0.102128	−	0.0884940i
$932$	1.37813	−	0.0985657i	0.0451421	−	0.00322863i
$933$	10.3243	−	18.9075i	0.338001	−	0.619003i
$934$	0.596463	+	1.30607i	0.0195169	+	0.0427360i
$935$	−37.8232	−	28.6856i	−1.23695	−	0.938121i
$936$	−6.23543	−	1.83089i	−0.203811	−	0.0598444i
$937$	−3.66964	−	2.74706i	−0.119882	−	0.0897425i	0.537654	−	0.843165i	$-0.319311\pi$
$937$	−3.66964	−	2.74706i	−0.119882	−	0.0897425i	−0.657536	+	0.753423i	$0.728401\pi$
$938$	−0.116220	−	0.311597i	−0.00379470	−	0.0101740i
$939$	2.54274	−	17.6851i	0.0829792	−	0.577133i
$940$	22.1346	+	4.96053i	0.721951	+	0.161795i
$941$	−8.46421	+	7.33428i	−0.275925	+	0.239091i	−0.781819	−	0.623505i	$-0.785708\pi$
$941$	−8.46421	+	7.33428i	−0.275925	+	0.239091i	0.505894	+	0.862596i	$0.331163\pi$
$942$	−13.4212	+	13.4212i	−0.437286	+	0.437286i
$943$	−23.0470	+	5.20877i	−0.750515	+	0.169621i
$944$			1.61293i			0.0524964i
$945$	0.194823	+	0.679221i	0.00633760	+	0.0220951i
$946$	2.82409	+	1.81493i	0.0918191	+	0.0590086i
$947$	12.5687	−	9.40881i	0.408428	−	0.305745i	−0.375237	−	0.926929i	$-0.622439\pi$
$947$	12.5687	−	9.40881i	0.408428	−	0.305745i	0.783665	+	0.621183i	$0.213348\pi$
$948$	11.1719	−	4.16689i	0.362845	−	0.135334i
$949$	−34.1692	+	4.91279i	−1.10918	+	0.159476i
$950$	1.07913	−	2.78612i	0.0350115	−	0.0903936i
$951$	28.0786	−	18.0450i	0.910512	−	0.585150i
$952$	−0.820942	+	2.20103i	−0.0266069	+	0.0713358i
$953$	−26.0585	−	14.2290i	−0.844119	−	0.460924i	−0.00186056	−	0.999998i	$-0.500592\pi$
$953$	−26.0585	−	14.2290i	−0.844119	−	0.460924i	−0.842258	+	0.539075i	$0.818774\pi$
$954$	−1.53374	+	1.77003i	−0.0496567	+	0.0573069i
$955$	19.6268	+	43.6991i	0.635107	+	1.41407i
$956$	−17.6411	+	5.17990i	−0.570554	+	0.167530i
$957$	16.5524	+	6.17371i	0.535062	+	0.199568i
$958$	13.4586	+	2.92773i	0.434827	+	0.0945907i
$959$	−0.347850	+	1.18467i	−0.0112327	+	0.0382550i
$960$	1.96923	−	1.05932i	0.0635565	−	0.0341893i
$961$	12.4890	−	27.3471i	0.402870	−	0.882163i
$962$	25.9786	+	34.7033i	0.837583	+	1.11888i
$963$	−3.62143	−	16.6475i	−0.116699	−	0.536457i
$964$	−13.4870	−	15.5648i	−0.434387	−	0.501309i
$965$	−36.2368	+	13.2576i	−1.16650	+	0.426777i
$966$	−0.415216	+	1.45752i	−0.0133594	+	0.0468949i
$967$	−40.3353	−	40.3353i	−1.29710	−	1.29710i	−0.930302	−	0.366795i	$-0.880455\pi$
$967$	−40.3353	−	40.3353i	−1.29710	−	1.29710i	−0.366795	−	0.930302i	$-0.619545\pi$
$968$	2.83724	+	0.202924i	0.0911924	+	0.00652221i
$969$	−2.40163	+	3.73700i	−0.0771514	+	0.120050i
$970$	−3.53257	+	5.42179i	−0.113424	+	0.174083i
$971$	35.4837	+	16.2049i	1.13873	+	0.520039i	0.893338	−	0.449386i	$-0.148357\pi$
$971$	35.4837	+	16.2049i	1.13873	+	0.520039i	0.245388	+	0.969425i	$0.421084\pi$
$972$	−0.599278	+	0.800541i	−0.0192218	+	0.0256774i
$973$	−2.37331	−	4.34638i	−0.0760847	−	0.139339i
$974$	10.4442	+	16.2514i	0.334652	+	0.520729i
$975$	29.3855	+	13.8675i	0.941091	+	0.444116i
$976$	−0.00229761	−	0.00782496i	−7.35449e−5	−	0.000250471i
$977$	0.368872	+	5.15751i	0.0118013	+	0.165003i	0.999935	+	0.0114069i	$0.00363102\pi$
$977$	0.368872	+	5.15751i	0.0118013	+	0.165003i	−0.988134	+	0.153596i	$0.950914\pi$
$978$	−0.766626	−	10.7188i	−0.0245140	−	0.342750i
$979$	−7.40574	−	25.2216i	−0.236688	−	0.806087i
$980$	−0.0966680	+	15.4289i	−0.00308795	+	0.492858i
$981$	−3.85760	−	6.00254i	−0.123164	−	0.191646i
$982$	−7.81157	−	14.3058i	−0.249277	−	0.456517i
$983$	27.0375	−	36.1179i	0.862363	−	1.15198i	−0.124787	−	0.992184i	$-0.539825\pi$
$983$	27.0375	−	36.1179i	0.862363	−	1.15198i	0.987150	−	0.159798i	$-0.0510843\pi$
$984$	4.48162	+	2.04669i	0.142869	+	0.0652459i
$985$	−44.2637	+	9.33891i	−1.41036	+	0.297563i
$986$	24.8623	−	38.6865i	0.791777	−	1.23203i
$987$	3.19753	+	0.228692i	0.101778	+	0.00727934i
$988$	2.74594	+	2.74594i	0.0873601	+	0.0873601i
$989$	3.65730	−	4.29024i	0.116295	−	0.136422i
$990$	2.19405	+	5.99697i	0.0697316	+	0.190596i
$991$	3.90677	+	4.50866i	0.124103	+	0.143222i	0.814401	−	0.580303i	$-0.197066\pi$
$991$	3.90677	+	4.50866i	0.124103	+	0.143222i	−0.690298	+	0.723525i	$0.742520\pi$
$992$	1.66106	+	7.63576i	0.0527386	+	0.242435i
$993$	8.64466	+	11.5479i	0.274330	+	0.366462i
$994$	−1.48952	+	3.26159i	−0.0472447	+	0.103451i
$995$	−5.51607	+	18.3597i	−0.174871	+	0.582041i
$996$	−2.54682	+	8.67368i	−0.0806991	+	0.274836i
$997$	−13.8588	−	3.01480i	−0.438913	−	0.0954798i	−0.0123217	−	0.999924i	$-0.503922\pi$
$997$	−13.8588	−	3.01480i	−0.438913	−	0.0954798i	−0.426592	+	0.904444i	$0.640286\pi$
$998$	−0.968225	−	0.361129i	−0.0306486	−	0.0114313i
$999$	6.40036	−	1.87931i	0.202498	−	0.0594589i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.a.217.9	yes	240
5.3	odd	4	inner	690.2.w.a.493.5	yes	240
23.7	odd	22	inner	690.2.w.a.7.5	✓	240
115.53	even	44	inner	690.2.w.a.283.9	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.a.7.5	✓	240	23.7	odd	22	inner
690.2.w.a.217.9	yes	240	1.1	even	1	trivial
690.2.w.a.283.9	yes	240	115.53	even	44	inner
690.2.w.a.493.5	yes	240	5.3	odd	4	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)

\(f(q)\)	\(=\)	\(q+(0.0713392 - 0.997452i) q^{2} +(0.977147 - 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-1.69905 + 1.45370i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(0.277351 - 0.151445i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +O(q^{10})\)	\(q+(0.0713392 - 0.997452i) q^{2} +(0.977147 - 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-1.69905 + 1.45370i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(0.277351 - 0.151445i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +(1.32878 + 1.79843i) q^{10} +(2.15826 + 1.87014i) q^{11} +(-0.997452 + 0.0713392i) q^{12} +(-3.11448 + 5.70375i) q^{13} +(-0.131273 - 0.287449i) q^{14} +(-1.35121 + 1.78163i) q^{15} +(0.959493 + 0.281733i) q^{16} +(5.95112 + 4.45495i) q^{17} +(-0.349464 - 0.936950i) q^{18} +(-0.0850417 + 0.591478i) q^{19} +(1.88864 - 1.19710i) q^{20} +(0.238821 - 0.206940i) q^{21} +(2.01935 - 2.01935i) q^{22} +(-2.90493 - 3.81594i) q^{23} +1.00000i q^{24} +(0.773532 - 4.93980i) q^{25} +(5.46703 + 3.51345i) q^{26} +(0.800541 - 0.599278i) q^{27} +(-0.296081 + 0.110433i) q^{28} +(6.12315 - 0.880376i) q^{29} +(1.68070 + 1.47487i) q^{30} +(-6.57384 + 4.22475i) q^{31} +(0.349464 - 0.936950i) q^{32} +(2.50646 + 1.36863i) q^{33} +(4.86815 - 5.61814i) q^{34} +(-0.251078 + 0.660498i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(6.24998 + 2.33112i) q^{37} +(0.583904 + 0.127021i) q^{38} +(-1.83089 + 6.23543i) q^{39} +(-1.05932 - 1.96923i) q^{40} +(2.04669 - 4.48162i) q^{41} +(-0.189375 - 0.252976i) q^{42} +(0.249873 + 1.14865i) q^{43} +(-1.87014 - 2.15826i) q^{44} +(-0.941622 + 2.02814i) q^{45} +(-4.01345 + 2.62531i) q^{46} +(7.17319 + 7.17319i) q^{47} +(0.997452 + 0.0713392i) q^{48} +(-3.73050 + 5.80477i) q^{49} +(-4.87203 - 1.12396i) q^{50} +(6.76208 + 3.08814i) q^{51} +(3.89451 - 5.20245i) q^{52} +(-1.12244 - 2.05560i) q^{53} +(-0.540641 - 0.841254i) q^{54} +(-6.38560 - 0.0400083i) q^{55} +(0.0890291 + 0.303205i) q^{56} +(0.0426295 + 0.596038i) q^{57} +(-0.441312 - 6.17035i) q^{58} +(0.454415 + 1.54760i) q^{59} +(1.59101 - 1.57120i) q^{60} +(-0.00440909 - 0.00686068i) q^{61} +(3.74501 + 6.85848i) q^{62} +(0.189375 - 0.252976i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(-2.99986 - 14.2185i) q^{65} +(1.54395 - 2.40244i) q^{66} +(1.04972 + 0.0750776i) q^{67} +(-5.25654 - 5.25654i) q^{68} +(-3.64968 - 3.11124i) q^{69} +(0.640903 + 0.297558i) q^{70} +(-7.43050 - 8.57525i) q^{71} +(0.212565 + 0.977147i) q^{72} +(3.18333 + 4.25243i) q^{73} +(2.77105 - 6.06776i) q^{74} +(-0.294176 - 4.99134i) q^{75} +(0.168352 - 0.573355i) q^{76} +(0.881821 + 0.191828i) q^{77} +(6.08893 + 2.27105i) q^{78} +(-11.4407 + 3.35928i) q^{79} +(-2.03978 + 0.916134i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-4.32419 - 2.36119i) q^{82} +(3.15910 - 8.46989i) q^{83} +(-0.265841 + 0.170846i) q^{84} +(-16.5874 + 1.08194i) q^{85} +(1.16355 - 0.167293i) q^{86} +(5.79608 - 2.16183i) q^{87} +(-2.28617 + 1.71141i) q^{88} +(-7.74342 - 4.97639i) q^{89} +(1.95580 + 1.08391i) q^{90} +2.05362i q^{91} +(2.33230 + 4.19051i) q^{92} +(-5.52557 + 5.52557i) q^{93} +(7.66664 - 6.64319i) q^{94} +(-0.715340 - 1.12858i) q^{95} +(0.142315 - 0.989821i) q^{96} +(1.01133 + 2.71149i) q^{97} +(5.52385 + 4.13510i) q^{98} +(2.74011 + 0.804568i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{6}+O(q^{10}) \) 240 * q - 24 * q^6	\( 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) \) 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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