LMFDB - Embedded newform 690.2.w.a.7.5

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			7.5
Character	$\chi$	$=$	690.7
Dual form			690.2.w.a.493.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.997452 + 0.0713392i) q^{2} +(0.212565 - 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-0.0140096 + 2.23602i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-0.151445 + 0.277351i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +O(q^{10})$	\(q+(-0.997452 + 0.0713392i) q^{2} +(0.212565 - 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-0.0140096 + 2.23602i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-0.151445 + 0.277351i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +(-0.145542 - 2.23133i) q^{10} +(2.15826 - 1.87014i) q^{11} +(0.0713392 - 0.997452i) q^{12} +(-5.70375 + 3.11448i) q^{13} +(0.131273 - 0.287449i) q^{14} +(2.18195 + 0.488991i) q^{15} +(0.959493 - 0.281733i) q^{16} +(4.45495 + 5.95112i) q^{17} +(0.936950 + 0.349464i) q^{18} +(0.0850417 + 0.591478i) q^{19} +(0.304352 + 2.21526i) q^{20} +(0.238821 + 0.206940i) q^{21} +(-2.01935 + 2.01935i) q^{22} +(3.81594 + 2.90493i) q^{23} +1.00000i q^{24} +(-4.99961 - 0.0626515i) q^{25} +(5.46703 - 3.51345i) q^{26} +(-0.599278 + 0.800541i) q^{27} +(-0.110433 + 0.296081i) q^{28} +(-6.12315 - 0.880376i) q^{29} +(-2.21127 - 0.332086i) q^{30} +(-6.57384 - 4.22475i) q^{31} +(-0.936950 + 0.349464i) q^{32} +(-1.36863 - 2.50646i) q^{33} +(-4.86815 - 5.61814i) q^{34} +(-0.618043 - 0.342521i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(2.33112 + 6.24998i) q^{37} +(-0.127021 - 0.583904i) q^{38} +(1.83089 + 6.23543i) q^{39} +(-0.461612 - 2.18790i) q^{40} +(2.04669 + 4.48162i) q^{41} +(-0.252976 - 0.189375i) q^{42} +(-1.14865 - 0.249873i) 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} +(-0.0713392 - 0.997452i) q^{48} +(3.73050 + 5.80477i) q^{49} +(4.99134 - 0.294176i) q^{50} +(6.76208 - 3.08814i) q^{51} +(-5.20245 + 3.89451i) q^{52} +(2.05560 + 1.12244i) q^{53} +(0.540641 - 0.841254i) q^{54} +(4.15145 + 4.85212i) q^{55} +(0.0890291 - 0.303205i) q^{56} +(0.596038 + 0.0426295i) q^{57} +(6.17035 + 0.441312i) q^{58} +(-0.454415 + 1.54760i) q^{59} +(2.22933 + 0.173490i) q^{60} +(-0.00440909 + 0.00686068i) q^{61} +(6.85848 + 3.74501i) q^{62} +(0.252976 - 0.189375i) q^{63} +(0.909632 - 0.415415i) q^{64} +(-6.88415 - 12.7974i) q^{65} +(1.54395 + 2.40244i) q^{66} +(0.0750776 + 1.04972i) 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} +(0.977147 + 0.212565i) q^{72} +(-4.25243 - 3.18333i) q^{73} +(-2.77105 - 6.06776i) q^{74} +(-1.12396 + 4.87203i) q^{75} +(0.168352 + 0.573355i) q^{76} +(0.191828 + 0.881821i) q^{77} +(-2.27105 - 6.08893i) q^{78} +(11.4407 + 3.35928i) q^{79} +(0.616519 + 2.14940i) q^{80} +(0.654861 + 0.755750i) q^{81} +(-2.36119 - 4.32419i) q^{82} +(8.46989 - 3.15910i) q^{83} +(0.265841 + 0.170846i) q^{84} +(-13.3693 + 9.87800i) q^{85} +(1.16355 + 0.167293i) q^{86} +(-2.16183 + 5.79608i) q^{87} +(-1.71141 + 2.28617i) q^{88} +(7.74342 - 4.97639i) q^{89} +(-0.794537 + 2.09015i) q^{90} -2.05362i q^{91} +(4.19051 + 2.33230i) q^{92} +(-5.52557 + 5.52557i) q^{93} +(-7.66664 - 6.64319i) q^{94} +(-1.32375 + 0.181869i) q^{95} +(0.142315 + 0.989821i) q^{96} +(2.71149 + 1.01133i) q^{97} +(-4.13510 - 5.52385i) 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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{19}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.997452	+	0.0713392i	−0.705305	+	0.0504444i
$2$	−0.997452	+	0.0713392i	−0.705305	+	0.0504444i
$3$	0.212565	−	0.977147i	0.122725	−	0.564156i
$3$	0.212565	−	0.977147i	0.122725	−	0.564156i
$4$	0.989821	−	0.142315i	0.494911	−	0.0711574i
$5$	−0.0140096	+	2.23602i	−0.00626527	+	0.999980i
$5$	−0.0140096	+	2.23602i	−0.00626527	+	0.999980i
$6$	−0.142315	+	0.989821i	−0.0580998	+	0.404093i
$7$	−0.151445	+	0.277351i	−0.0572410	+	0.104829i	−0.904733	−	0.425979i	$-0.859930\pi$
$7$	−0.151445	+	0.277351i	−0.0572410	+	0.104829i	0.847492	+	0.530808i	$0.178112\pi$
$8$	−0.977147	+	0.212565i	−0.345474	+	0.0751532i
$9$	−0.909632	−	0.415415i	−0.303211	−	0.138472i
$10$	−0.145542	−	2.23133i	−0.0460245	−	0.705607i
$11$	2.15826	−	1.87014i	0.650739	−	0.563869i	−0.265693	−	0.964058i	$-0.585601\pi$
$11$	2.15826	−	1.87014i	0.650739	−	0.563869i	0.916433	+	0.400189i	$0.131055\pi$
$12$	0.0713392	−	0.997452i	0.0205938	−	0.287940i
$13$	−5.70375	+	3.11448i	−1.58194	+	0.863802i	−0.583263	+	0.812283i	$0.698224\pi$
$13$	−5.70375	+	3.11448i	−1.58194	+	0.863802i	−0.998672	+	0.0515185i	$0.983594\pi$
$14$	0.131273	−	0.287449i	0.0350843	−	0.0768239i
$15$	2.18195	+	0.488991i	0.563376	+	0.126257i
$16$	0.959493	−	0.281733i	0.239873	−	0.0704331i
$17$	4.45495	+	5.95112i	1.08048	+	1.44336i	0.886718	+	0.462310i	$0.152979\pi$
$17$	4.45495	+	5.95112i	1.08048	+	1.44336i	0.193766	+	0.981048i	$0.437930\pi$
$18$	0.936950	+	0.349464i	0.220841	+	0.0823695i
$19$	0.0850417	+	0.591478i	0.0195099	+	0.135694i	0.997248	−	0.0741329i	$-0.0236189\pi$
$19$	0.0850417	+	0.591478i	0.0195099	+	0.135694i	−0.977738	+	0.209827i	$0.932710\pi$
$20$	0.304352	+	2.21526i	0.0680553	+	0.495347i
$21$	0.238821	+	0.206940i	0.0521150	+	0.0451579i
$22$	−2.01935	+	2.01935i	−0.430526	+	0.430526i
$23$	3.81594	+	2.90493i	0.795678	+	0.605720i
$23$	3.81594	+	2.90493i	0.795678	+	0.605720i
$24$			1.00000i			0.204124i
$25$	−4.99961	−	0.0626515i	−0.999921	−	0.0125303i
$26$	5.46703	−	3.51345i	1.07217	−	0.689044i
$27$	−0.599278	+	0.800541i	−0.115331	+	0.154064i
$28$	−0.110433	+	0.296081i	−0.0208698	+	0.0559541i
$29$	−6.12315	−	0.880376i	−1.13704	−	0.163482i	−0.452021	−	0.892007i	$-0.649297\pi$
$29$	−6.12315	−	0.880376i	−1.13704	−	0.163482i	−0.685019	+	0.728525i	$0.740206\pi$
$30$	−2.21127	−	0.332086i	−0.403721	−	0.0606304i
$31$	−6.57384	−	4.22475i	−1.18070	−	0.758787i	−0.205182	−	0.978724i	$-0.565779\pi$
$31$	−6.57384	−	4.22475i	−1.18070	−	0.758787i	−0.975514	+	0.219936i	$0.929415\pi$
$32$	−0.936950	+	0.349464i	−0.165631	+	0.0617771i
$33$	−1.36863	−	2.50646i	−0.238248	−	0.436319i
$34$	−4.86815	−	5.61814i	−0.834880	−	0.963503i
$35$	−0.618043	−	0.342521i	−0.104468	−	0.0578966i
$36$	−0.959493	−	0.281733i	−0.159915	−	0.0469554i
$37$	2.33112	+	6.24998i	0.383234	+	1.02749i	0.975161	+	0.221499i	$0.0710948\pi$
$37$	2.33112	+	6.24998i	0.383234	+	1.02749i	−0.591926	+	0.805992i	$0.701632\pi$
$38$	−0.127021	−	0.583904i	−0.0206055	−	0.0947218i
$39$	1.83089	+	6.23543i	0.293177	+	0.998468i
$40$	−0.461612	−	2.18790i	−0.0729872	−	0.345938i
$41$	2.04669	+	4.48162i	0.319639	+	0.699911i	0.999439	−	0.0334862i	$-0.0106610\pi$
$41$	2.04669	+	4.48162i	0.319639	+	0.699911i	−0.679801	+	0.733397i	$0.737934\pi$
$42$	−0.252976	−	0.189375i	−0.0390350	−	0.0292212i
$43$	−1.14865	−	0.249873i	−0.175167	−	0.0381052i	0.124126	−	0.992266i	$-0.460387\pi$
$43$	−1.14865	−	0.249873i	−0.175167	−	0.0381052i	−0.299293	+	0.954161i	$0.596751\pi$
$44$	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	$0.484893\pi$
$48$	−0.0713392	−	0.997452i	−0.0102969	−	0.143970i
$49$	3.73050	+	5.80477i	0.532928	+	0.829253i
$50$	4.99134	−	0.294176i	0.705882	−	0.0416028i
$51$	6.76208	−	3.08814i	0.946881	−	0.432426i
$52$	−5.20245	+	3.89451i	−0.721451	+	0.540071i
$53$	2.05560	+	1.12244i	0.282358	+	0.154179i	0.614187	−	0.789160i	$-0.289484\pi$
$53$	2.05560	+	1.12244i	0.282358	+	0.154179i	−0.331829	+	0.943340i	$0.607666\pi$
$54$	0.540641	−	0.841254i	0.0735719	−	0.114480i
$55$	4.15145	+	4.85212i	0.559781	+	0.654259i
$56$	0.0890291	−	0.303205i	0.0118970	−	0.0405175i
$57$	0.596038	+	0.0426295i	0.0789472	+	0.00564641i
$58$	6.17035	+	0.441312i	0.810207	+	0.0579471i
$59$	−0.454415	+	1.54760i	−0.0591598	+	0.201480i	−0.983770	−	0.179435i	$-0.942573\pi$
$59$	−0.454415	+	1.54760i	−0.0591598	+	0.201480i	0.924610	+	0.380915i	$0.124391\pi$
$60$	2.22933	+	0.173490i	0.287805	+	0.0223975i
$61$	−0.00440909	+	0.00686068i	−0.000564526	+	0.000878420i	−0.841536	−	0.540202i	$-0.818348\pi$
$61$	−0.00440909	+	0.00686068i	−0.000564526	+	0.000878420i	0.840971	+	0.541080i	$0.181984\pi$
$62$	6.85848	+	3.74501i	0.871028	+	0.475617i
$63$	0.252976	−	0.189375i	0.0318719	−	0.0238590i
$64$	0.909632	−	0.415415i	0.113704	−	0.0519269i
$65$	−6.88415	−	12.7974i	−0.853874	−	1.58732i
$66$	1.54395	+	2.40244i	0.190048	+	0.295720i
$67$	0.0750776	+	1.04972i	0.00917218	+	0.128244i	0.999975	−	0.00706968i	$-0.00225037\pi$
$67$	0.0750776	+	1.04972i	0.00917218	+	0.128244i	−0.990803	+	0.135314i	$0.956796\pi$
$68$	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	0.117858	+	0.993030i	$0.462397\pi$
$71$	−7.43050	+	8.57525i	−0.881838	+	1.01770i	−0.999696	+	0.0246649i	$0.992148\pi$
$72$	0.977147	+	0.212565i	0.115158	+	0.0250511i
$73$	−4.25243	−	3.18333i	−0.497709	−	0.372580i	0.320733	−	0.947170i	$-0.396071\pi$
$73$	−4.25243	−	3.18333i	−0.497709	−	0.372580i	−0.818442	+	0.574589i	$0.805162\pi$
$74$	−2.77105	−	6.06776i	−0.322128	−	0.705362i
$75$	−1.12396	+	4.87203i	−0.129784	+	0.562574i
$76$	0.168352	+	0.573355i	0.0193113	+	0.0657684i
$77$	0.191828	+	0.881821i	0.0218609	+	0.100493i
$78$	−2.27105	−	6.08893i	−0.257146	−	0.689435i
$79$	11.4407	+	3.35928i	1.28718	+	0.377949i	0.852542	−	0.522659i	$-0.175060\pi$
$79$	11.4407	+	3.35928i	1.28718	+	0.377949i	0.434633	+	0.900608i	$0.356878\pi$
$80$	0.616519	+	2.14940i	0.0689289	+	0.240310i
$81$	0.654861	+	0.755750i	0.0727623	+	0.0839722i
$82$	−2.36119	−	4.32419i	−0.260749	−	0.477527i
$83$	8.46989	−	3.15910i	0.929691	−	0.346757i	0.161423	−	0.986885i	$-0.448392\pi$
$83$	8.46989	−	3.15910i	0.929691	−	0.346757i	0.768268	+	0.640129i	$0.221119\pi$
$84$	0.265841	+	0.170846i	0.0290056	+	0.0186408i
$85$	−13.3693	+	9.87800i	−1.45010	+	1.07142i
$86$	1.16355	+	0.167293i	0.125468	+	0.0180396i
$87$	−2.16183	+	5.79608i	−0.231772	+	0.621405i
$88$	−1.71141	+	2.28617i	−0.182437	+	0.243707i
$89$	7.74342	−	4.97639i	0.820800	−	0.527496i	−0.0615420	−	0.998104i	$-0.519602\pi$
$89$	7.74342	−	4.97639i	0.820800	−	0.527496i	0.882342	+	0.470608i	$0.155965\pi$
$90$	−0.794537	+	2.09015i	−0.0837515	+	0.220321i
$91$		−	2.05362i		−	0.215278i
$92$	4.19051	+	2.33230i	0.436891	+	0.243159i
$93$	−5.52557	+	5.52557i	−0.572975	+	0.572975i
$94$	−7.66664	−	6.64319i	−0.790754	−	0.685192i
$95$	−1.32375	+	0.181869i	−0.135814	+	0.0186594i
$96$	0.142315	+	0.989821i	0.0145249	+	0.101023i
$97$	2.71149	+	1.01133i	0.275310	+	0.102685i	0.483327	−	0.875440i	$-0.339428\pi$
$97$	2.71149	+	1.01133i	0.275310	+	0.102685i	−0.208017	+	0.978125i	$0.566701\pi$
$98$	−4.13510	−	5.52385i	−0.417708	−	0.557993i
$99$	−2.74011	+	0.804568i	−0.275391	+	0.0808621i
$100$	−4.95763	+	0.649505i	−0.495763	+	0.0649505i
$101$	4.25866	−	9.32516i	0.423752	−	0.927888i	−0.570547	−	0.821265i	$-0.693269\pi$
$101$	4.25866	−	9.32516i	0.423752	−	0.927888i	0.994300	−	0.106623i	$-0.0340038\pi$
$102$	−6.52455	+	3.56267i	−0.646027	+	0.352757i
$103$	−0.339452	+	4.74616i	−0.0334472	+	0.467653i	0.952934	+	0.303178i	$0.0980477\pi$
$103$	−0.339452	+	4.74616i	−0.0334472	+	0.467653i	−0.986381	+	0.164475i	$0.947407\pi$
$104$	4.91137	−	4.25573i	0.481599	−	0.417308i
$105$	−0.466068	+	0.531111i	−0.0454836	+	0.0518311i
$106$	−2.13044	−	0.972938i	−0.206926	−	0.0945001i
$107$	−16.6475	+	3.62143i	−1.60937	+	0.350097i	−0.925276	−	0.379295i	$-0.876166\pi$
$107$	−16.6475	+	3.62143i	−1.60937	+	0.350097i	−0.684095	+	0.729393i	$0.739803\pi$
$108$	−0.479249	+	0.877679i	−0.0461158	+	0.0844547i
$109$	1.01545	−	7.06261i	0.0972625	−	0.676475i	−0.881606	−	0.471986i	$-0.843537\pi$
$109$	1.01545	−	7.06261i	0.0972625	−	0.676475i	0.978869	−	0.204490i	$-0.0655535\pi$
$110$	−4.48701	−	4.54359i	−0.427820	−	0.433215i
$111$	6.60267	−	0.949320i	0.626697	−	0.0901055i
$112$	−0.0671718	+	0.308784i	−0.00634714	+	0.0291773i
$113$	−9.70633	+	0.694210i	−0.913094	+	0.0653058i	−0.519975	−	0.854182i	$-0.674059\pi$
$113$	−9.70633	+	0.694210i	−0.913094	+	0.0653058i	−0.393120	+	0.919487i	$0.628604\pi$
$114$	−0.597561			−0.0559667
$115$	−6.54896	+	8.49183i	−0.610694	+	0.791867i
$116$	−6.18611			−0.574366
$117$	6.48211	−	0.463610i	0.599272	−	0.0428608i
$118$	0.342853	−	1.57607i	0.0315622	−	0.145089i
$119$	−2.32523	+	0.334318i	−0.213154	+	0.0306469i
$120$	−2.23602	−	0.0140096i	−0.204120	−	0.00127889i
$121$	−0.404813	+	2.81554i	−0.0368012	+	0.255958i
$122$	0.00390842	−	0.00715774i	0.000353852	−	0.000648031i
$123$	4.81425	−	1.04728i	0.434086	−	0.0944297i
$124$	−7.10817	−	3.24619i	−0.638333	−	0.291517i
$125$	0.210133	−	11.1784i	0.0187948	−	0.999823i
$126$	−0.238821	+	0.206940i	−0.0212759	+	0.0184357i
$127$	0.144739	−	2.02371i	0.0128435	−	0.179575i	−0.986981	−	0.160837i	$-0.948581\pi$
$127$	0.144739	−	2.02371i	0.0128435	−	0.179575i	0.999824	−	0.0187380i	$-0.00596485\pi$
$128$	−0.877679	+	0.479249i	−0.0775766	+	0.0423600i
$129$	−0.488325	+	1.06928i	−0.0429946	+	0.0941450i
$130$	7.77956	+	12.2736i	0.682313	+	1.07647i
$131$	14.1260	−	4.14776i	1.23419	−	0.362392i	0.401362	−	0.915919i	$-0.368537\pi$
$131$	14.1260	−	4.14776i	1.23419	−	0.362392i	0.832831	+	0.553528i	$0.186719\pi$
$132$	−1.71141	−	2.28617i	−0.148959	−	0.198986i
$133$	−0.176927	−	0.0659902i	−0.0153415	−	0.00572208i
$134$	−0.149773	−	1.04169i	−0.0129384	−	0.0899884i
$135$	−1.78163	−	1.35121i	−0.153339	−	0.116294i
$136$	−5.61814	−	4.86815i	−0.481752	−	0.417440i
$137$	2.76278	−	2.76278i	0.236040	−	0.236040i	−0.579168	−	0.815208i	$-0.696623\pi$
$137$	2.76278	−	2.76278i	0.236040	−	0.236040i	0.815208	+	0.579168i	$0.196623\pi$
$138$	−3.41843	+	3.36368i	−0.290996	+	0.286335i
$139$		−	15.6710i		−	1.32920i	−0.747199	−	0.664600i	$-0.768602\pi$
$139$		−	15.6710i		−	1.32920i	0.747199	−	0.664600i	$-0.231398\pi$
$140$	−0.660498	−	0.251078i	−0.0558223	−	0.0212200i
$141$	8.53403	−	5.48449i	0.718695	−	0.461877i
$142$	6.79982	−	9.08349i	0.570628	−	0.762270i
$143$	−6.48564	+	17.3887i	−0.542356	+	1.45411i
$144$	−0.989821	−	0.142315i	−0.0824851	−	0.0118596i
$145$	2.05432	−	13.6792i	0.170602	−	1.13599i
$146$	4.46869	+	2.87185i	0.369831	+	0.237676i
$147$	6.46508	−	2.41135i	0.533231	−	0.198885i
$148$	3.19686	+	5.85461i	0.262780	+	0.481246i
$149$	−4.62619	−	5.33890i	−0.378992	−	0.437380i	0.533921	−	0.845534i	$-0.320718\pi$
$149$	−4.62619	−	5.33890i	−0.378992	−	0.437380i	−0.912913	+	0.408154i	$0.866173\pi$
$150$	0.773532	−	4.93980i	0.0631586	−	0.403333i
$151$	−18.6065	−	5.46337i	−1.51418	−	0.444603i	−0.584012	−	0.811745i	$-0.698518\pi$
$151$	−18.6065	−	5.46337i	−1.51418	−	0.444603i	−0.930165	+	0.367142i	$0.880336\pi$
$152$	−0.208826	−	0.559884i	−0.0169380	−	0.0454126i
$153$	−1.58018	−	7.26398i	−0.127750	−	0.587258i
$154$	−0.254248	−	0.865889i	−0.0204879	−	0.0697753i
$155$	9.53874	−	14.6401i	0.766170	−	1.17592i
$156$	2.69965	+	5.91140i	0.216145	+	0.473291i
$157$	−15.1946	−	11.3746i	−1.21266	−	0.907789i	−0.215034	−	0.976606i	$-0.568986\pi$
$157$	−15.1946	−	11.3746i	−1.21266	−	0.907789i	−0.997629	+	0.0688178i	$0.978077\pi$
$158$	−11.6512	−	2.53456i	−0.926917	−	0.201638i
$159$	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
$163$	−0.766626	−	10.7188i	−0.0600468	−	0.839564i	−0.934840	−	0.355068i	$-0.884458\pi$
$163$	−0.766626	−	10.7188i	−0.0600468	−	0.839564i	0.874794	−	0.484496i	$-0.160997\pi$
$164$	2.66365	+	4.14473i	0.207996	+	0.323649i
$165$	5.62369	−	3.02518i	0.437803	−	0.235510i
$166$	−8.22294	+	3.75529i	−0.638224	+	0.291467i
$167$	7.75350	−	5.80420i	0.599984	−	0.449142i	−0.255617	−	0.966778i	$-0.582279\pi$
$167$	7.75350	−	5.80420i	0.599984	−	0.449142i	0.855601	+	0.517636i	$0.173188\pi$
$168$	−0.277351	−	0.151445i	−0.0213981	−	0.0116843i
$169$	15.8044	−	24.5921i	1.21572	−	1.89170i
$170$	12.6305	−	10.8066i	0.968715	−	0.828827i
$171$	0.168352	−	0.573355i	0.0128742	−	0.0438456i
$172$	−1.17252	−	0.0838599i	−0.0894034	−	0.00639426i
$173$	−21.2416	−	1.51923i	−1.61497	−	0.115505i	−0.765606	−	0.643309i	$-0.777561\pi$
$173$	−21.2416	−	1.51923i	−1.61497	−	0.115505i	−0.849366	+	0.527804i	$0.823015\pi$
$174$	1.74283	−	5.93553i	0.132124	−	0.449972i
$175$	0.774544	−	1.37716i	0.0585500	−	0.104104i
$176$	1.54395	−	2.40244i	0.116380	−	0.181091i
$177$	1.41564	+	0.772996i	0.106406	+	0.0581019i
$178$	−7.36867	+	5.51612i	−0.552305	+	0.413451i
$179$	11.1997	−	5.11472i	0.837104	−	0.382292i	0.0497256	−	0.998763i	$-0.484165\pi$
$179$	11.1997	−	5.11472i	0.837104	−	0.382292i	0.787378	+	0.616471i	$0.211438\pi$
$180$	0.643403	−	2.14150i	0.0479564	−	0.159618i
$181$	9.81107	+	15.2663i	0.729251	+	1.13474i	0.985754	+	0.168193i	$0.0537932\pi$
$181$	9.81107	+	15.2663i	0.729251	+	1.13474i	−0.256503	+	0.966543i	$0.582570\pi$
$182$	0.146503	+	2.04838i	0.0108596	+	0.151836i
$183$	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
$187$	20.7444	+	4.51266i	1.51698	+	0.329998i
$188$	8.12103	+	6.07933i	0.592287	+	0.443381i
$189$	−0.131273	−	0.287449i	−0.00954874	−	0.0209088i
$190$	1.30740	−	0.275841i	0.0948491	−	0.0200116i
$191$	6.03569	+	20.5557i	0.436727	+	1.48736i	0.824639	+	0.565659i	$0.191378\pi$
$191$	6.03569	+	20.5557i	0.436727	+	1.48736i	−0.387912	+	0.921696i	$0.626804\pi$
$192$	−0.212565	−	0.977147i	−0.0153406	−	0.0705195i
$193$	−6.03039	−	16.1681i	−0.434077	−	1.16381i	−0.951384	−	0.308006i	$-0.900338\pi$
$193$	−6.03039	−	16.1681i	−0.434077	−	1.16381i	0.517307	−	0.855800i	$-0.326934\pi$
$194$	−2.77673	−	0.815322i	−0.199358	−	0.0585367i
$195$	−13.9682	+	4.00655i	−1.00029	+	0.286915i
$196$	4.51863	+	5.21478i	0.322759	+	0.372484i
$197$	9.69573	+	17.7564i	0.690793	+	1.26509i	0.953842	+	0.300310i	$0.0970900\pi$
$197$	9.69573	+	17.7564i	0.690793	+	1.26509i	−0.263049	+	0.964782i	$0.584728\pi$
$198$	2.67573	−	0.997995i	0.190156	−	0.0709244i
$199$	−7.21230	−	4.63506i	−0.511266	−	0.328571i	0.259442	−	0.965759i	$-0.416461\pi$
$199$	−7.21230	−	4.63506i	−0.511266	−	0.328571i	−0.770709	+	0.637188i	$0.780098\pi$
$200$	4.89867	−	1.00152i	0.346388	−	0.0708184i
$201$	1.04169	+	0.149773i	0.0734752	+	0.0105641i
$202$	−3.58256	+	9.60521i	−0.252068	+	0.675820i
$203$	1.17150	−	1.56494i	0.0822229	−	0.109837i
$204$	6.25377	−	4.01905i	0.437851	−	0.281390i
$205$	−10.0497	+	4.51365i	−0.701900	+	0.315247i
$206$		−	4.75829i		−	0.331526i
$207$	−2.26434	−	4.22762i	−0.157383	−	0.293840i
$208$	−4.59526	+	4.59526i	−0.318624	+	0.318624i
$209$	1.28969	+	1.11752i	0.0892097	+	0.0773007i
$210$	0.426991	−	0.563006i	0.0294652	−	0.0388511i
$211$	0.0865161	+	0.601732i	0.00595601	+	0.0414250i	0.992583	−	0.121571i	$-0.0387933\pi$
$211$	0.0865161	+	0.601732i	0.00595601	+	0.0414250i	−0.986627	+	0.162996i	$0.947884\pi$
$212$	2.19442	+	0.818475i	0.150713	+	0.0562131i
$213$	6.79982	+	9.08349i	0.465916	+	0.622391i
$214$	16.3467	−	4.79982i	1.11744	−	0.328109i
$215$	0.574813	−	2.56490i	0.0392019	−	0.174925i
$216$	0.415415	−	0.909632i	0.0282654	−	0.0618926i
$217$	2.16732	−	1.18345i	0.147127	−	0.0803375i
$218$	−0.509022	+	7.11706i	−0.0344753	+	0.482028i
$219$	−4.01450	+	3.47858i	−0.271275	+	0.235061i
$220$	4.79972	+	4.21192i	0.323597	+	0.283967i
$221$	−43.9446	−	20.0688i	−2.95603	−	1.34997i
$222$	−6.51812	+	1.41793i	−0.437468	+	0.0951652i
$223$	4.41771	−	8.09043i	0.295832	−	0.541775i	−0.686914	−	0.726739i	$-0.741035\pi$
$223$	4.41771	−	8.09043i	0.295832	−	0.541775i	0.982745	+	0.184964i	$0.0592168\pi$
$224$	0.0449723	−	0.312789i	0.00300484	−	0.0208991i
$225$	4.52178	+	2.13390i	0.301452	+	0.142260i
$226$	9.63207	−	1.38488i	0.640716	−	0.0921210i
$227$	1.30546	−	6.00109i	0.0866462	−	0.398306i	−0.913314	−	0.407257i	$-0.866485\pi$
$227$	1.30546	−	6.00109i	0.0866462	−	0.398306i	0.999960	+	0.00895042i	$0.00284905\pi$
$228$	0.596038	−	0.0426295i	0.0394736	−	0.00282321i
$229$	19.5998			1.29519			0.647597	−	0.761983i	$-0.275774\pi$
$229$	19.5998			1.29519			0.647597	+	0.761983i	$0.275774\pi$
$230$	5.92647	−	8.93739i	0.390780	−	0.589314i
$231$	0.902444			0.0593765
$232$	6.17035	−	0.441312i	0.405103	−	0.0289736i
$233$	−0.293691	+	1.35007i	−0.0192403	+	0.0884463i	−0.985766	−	0.168124i	$-0.946229\pi$
$233$	−0.293691	+	1.35007i	−0.0192403	+	0.0884463i	0.966525	+	0.256571i	$0.0825926\pi$
$234$	−6.43252	+	0.924857i	−0.420507	+	0.0604598i
$235$	−16.1399	+	15.9389i	−1.05285	+	1.03974i
$236$	−0.229544	+	1.59651i	−0.0149420	+	0.103924i
$237$	5.71440	−	10.4651i	0.371190	−	0.679784i
$238$	2.29546	−	0.499346i	0.148792	−	0.0323678i
$239$	−16.7244	−	7.63777i	−1.08181	−	0.494046i	−0.206915	−	0.978359i	$-0.566342\pi$
$239$	−16.7244	−	7.63777i	−1.08181	−	0.494046i	−0.874895	+	0.484313i	$0.839070\pi$
$240$	2.23133	−	0.145542i	0.144031	−	0.00939471i
$241$	15.5648	−	13.4870i	1.00262	−	0.868773i	0.0112570	−	0.999937i	$-0.496417\pi$
$241$	15.5648	−	13.4870i	1.00262	−	0.868773i	0.991361	+	0.131163i	$0.0418712\pi$
$242$	0.202924	−	2.83724i	0.0130444	−	0.182385i
$243$	0.877679	−	0.479249i	0.0563031	−	0.0307438i
$244$	−0.00338784	+	0.00741833i	−0.000216884	+	0.000474910i
$245$	−13.0319	+	8.26016i	−0.832575	+	0.527722i
$246$	−4.72727	+	1.38805i	−0.301400	+	0.0884990i
$247$	−2.32721	−	3.10878i	−0.148077	−	0.197807i
$248$	7.32164	+	2.73083i	0.464925	+	0.173408i
$249$	−1.28651	−	8.94784i	−0.0815290	−	0.567046i
$250$	0.587858	+	11.1649i	0.0371794	+	0.706129i
$251$	19.0610	+	16.5165i	1.20312	+	1.04251i	0.997964	+	0.0637798i	$0.0203155\pi$
$251$	19.0610	+	16.5165i	1.20312	+	1.04251i	0.205156	+	0.978729i	$0.434230\pi$
$252$	0.223450	−	0.223450i	0.0140760	−	0.0140760i
$253$	13.6684	−	0.866743i	0.859326	−	0.0544917i
$254$			2.02888i			0.127303i
$255$	6.81042	+	15.1634i	0.426485	+	0.949572i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	14.2713	−	19.0642i	0.890218	−	1.18919i	−0.0909145	−	0.995859i	$-0.528979\pi$
$257$	14.2713	−	19.0642i	0.890218	−	1.18919i	0.981133	−	0.193334i	$-0.0619301\pi$
$258$	0.410799	−	1.10139i	0.0255752	−	0.0685698i
$259$	−2.08648	−	0.299990i	−0.129648	−	0.0186405i
$260$	−8.63533	−	11.6874i	−0.535541	−	0.724820i
$261$	5.20409	+	3.34447i	0.322125	+	0.207017i
$262$	−13.7941	+	5.14493i	−0.852202	+	0.317855i
$263$	−11.3793	−	20.8397i	−0.701678	−	1.28503i	−0.948749	−	0.316030i	$-0.897650\pi$
$263$	−11.3793	−	20.8397i	−0.701678	−	1.28503i	0.247071	−	0.968997i	$-0.420532\pi$
$264$	1.87014	+	2.15826i	0.115099	+	0.132832i
$265$	−2.53861	+	4.58065i	−0.155945	+	0.281387i
$266$	0.181183	+	0.0532003i	0.0111091	+	0.00326192i
$267$	−3.21668	−	8.62426i	−0.196858	−	0.527796i
$268$	0.223704	+	1.02835i	0.0136649	+	0.0628166i
$269$	−0.574956	−	1.95812i	−0.0350557	−	0.119389i	0.940106	−	0.340881i	$-0.110725\pi$
$269$	−0.574956	−	1.95812i	−0.0350557	−	0.119389i	−0.975162	+	0.221492i	$0.928907\pi$
$270$	1.87349	+	1.22067i	0.114017	+	0.0742877i
$271$	7.63048	+	16.7084i	0.463519	+	1.01496i	0.986671	+	0.162726i	$0.0520285\pi$
$271$	7.63048	+	16.7084i	0.463519	+	1.01496i	−0.523152	+	0.852239i	$0.675244\pi$
$272$	5.95112	+	4.45495i	0.360839	+	0.270121i
$273$	−2.00669	−	0.436528i	−0.121450	−	0.0264199i
$274$	−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	$0.813124\pi$
$278$	1.11796	+	15.6311i	0.0670507	+	0.937491i
$279$	4.22475	+	6.57384i	0.252929	+	0.393565i
$280$	0.676727	+	0.203319i	0.0404422	+	0.0121506i
$281$	−18.2152	+	8.31860i	−1.08663	+	0.496246i	−0.876487	−	0.481425i	$-0.840119\pi$
$281$	−18.2152	+	8.31860i	−1.08663	+	0.496246i	−0.210140	+	0.977671i	$0.567392\pi$
$282$	−8.12103	+	6.07933i	−0.483600	+	0.362019i
$283$	1.40178	+	0.765432i	0.0833274	+	0.0455002i	0.520372	−	0.853939i	$-0.325793\pi$
$283$	1.40178	+	0.765432i	0.0833274	+	0.0455002i	−0.437045	+	0.899440i	$0.643975\pi$
$284$	−6.13448	+	9.54544i	−0.364015	+	0.566418i
$285$	−0.103671	+	1.33216i	−0.00614093	+	0.0789102i
$286$	5.22862	−	17.8071i	0.309175	−	1.05295i
$287$	−1.55294	−	0.111069i	−0.0916674	−	0.00655618i
$288$	0.997452	+	0.0713392i	0.0587754	+	0.00420370i
$289$	−10.7798	+	36.7125i	−0.634103	+	2.15956i
$290$	−1.07323	+	13.7909i	−0.0630222	+	0.809828i
$291$	1.56459	−	2.43455i	0.0917179	−	0.142716i
$292$	−4.66218	−	2.54574i	−0.272834	−	0.148978i
$293$	8.83682	−	6.61516i	0.516253	−	0.386462i	−0.309144	−	0.951015i	$-0.600042\pi$
$293$	8.83682	−	6.61516i	0.516253	−	0.386462i	0.825397	+	0.564553i	$0.190952\pi$
$294$	−6.27659	+	2.86642i	−0.366058	+	0.167173i
$295$	−3.45410	−	1.03776i	−0.201105	−	0.0604210i
$296$	−3.60638	−	5.61163i	−0.209616	−	0.326170i
$297$	0.203729	+	2.84851i	0.0118216	+	0.165287i
$298$	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
$302$	18.9489	+	4.12207i	1.09038	+	0.237199i
$303$	−8.20681	−	6.14354i	−0.471469	−	0.352937i
$304$	0.248236	+	0.543560i	0.0142373	+	0.0311753i
$305$	−0.0152789	−	0.00995495i	−0.000874866	−	0.000570019i
$306$	2.09436	+	7.13274i	0.119727	+	0.407752i
$307$	2.63121	+	12.0955i	0.150171	+	0.690326i	0.989240	+	0.146301i	$0.0467367\pi$
$307$	2.63121	+	12.0955i	0.150171	+	0.690326i	−0.839069	+	0.544025i	$0.816900\pi$
$308$	0.315372	+	0.845545i	0.0179700	+	0.0481794i
$309$	4.56554	+	1.34056i	0.259725	+	0.0762621i
$310$	−8.47002	+	15.2833i	−0.481065	+	0.868031i
$311$	14.1074	+	16.2808i	0.799956	+	0.923199i	0.998379	−	0.0569176i	$-0.0181272\pi$
$311$	14.1074	+	16.2808i	0.799956	+	0.923199i	−0.198422	+	0.980117i	$0.563582\pi$
$312$	−3.11448	−	5.70375i	−0.176323	−	0.322911i
$313$	16.7405	−	6.24388i	0.946228	−	0.352925i	0.171475	−	0.985189i	$-0.445147\pi$
$313$	16.7405	−	6.24388i	0.946228	−	0.352925i	0.774753	+	0.632264i	$0.217874\pi$
$314$	15.9674	+	10.2616i	0.901091	+	0.579096i
$315$	0.419903	+	0.568312i	0.0236589	+	0.0320208i
$316$	11.8023	+	1.69691i	0.663931	+	0.0954588i
$317$	−11.6641	+	31.2727i	−0.655121	+	1.75645i	−0.00106910	+	0.999999i	$0.500340\pi$
$317$	−11.6641	+	31.2727i	−0.655121	+	1.75645i	−0.654052	+	0.756449i	$0.726932\pi$
$318$	−1.40356	+	1.87494i	−0.0787078	+	0.105141i
$319$	−14.8618	+	9.55108i	−0.832099	+	0.534758i
$320$	0.916134	+	2.03978i	0.0512135	+	0.114027i
$321$			17.0368i			0.950902i
$322$	1.33595	−	0.715545i	0.0744496	−	0.0398758i
$323$	−3.14110	+	3.14110i	−0.174775	+	0.174775i
$324$	0.755750	+	0.654861i	0.0419861	+	0.0363812i
$325$	28.7116	−	15.2138i	1.59263	−	0.843912i
$326$	1.52935	+	10.6368i	0.0847026	+	0.589119i
$327$	−6.68536	−	2.49351i	−0.369701	−	0.137891i
$328$	−2.95255	−	3.94414i	−0.163027	−	0.217779i
$329$	−3.07584	+	0.903149i	−0.169577	+	0.0497922i
$330$	−5.39354	+	3.41866i	−0.296905	+	0.188191i
$331$	5.99242	−	13.1216i	0.329373	−	0.721226i	−0.670411	−	0.741990i	$-0.733882\pi$
$331$	5.99242	−	13.1216i	0.329373	−	0.721226i	0.999784	+	0.0207633i	$0.00660963\pi$
$332$	7.93409	−	4.33234i	0.435440	−	0.237768i
$333$	0.475872	−	6.65357i	0.0260777	−	0.364613i
$334$	−7.31968	+	6.34254i	−0.400515	+	0.347048i
$335$	−2.34825	+	0.153169i	−0.128299	+	0.00836852i
$336$	0.287449	+	0.131273i	0.0156816	+	0.00716155i
$337$	−17.3460	+	3.77339i	−0.944896	+	0.205550i	−0.658516	−	0.752566i	$-0.728816\pi$
$337$	−17.3460	+	3.77339i	−0.944896	+	0.205550i	−0.286380	+	0.958116i	$0.592452\pi$
$338$	−14.0098	+	25.6570i	−0.762030	+	1.39555i
$339$	−1.38488	+	9.63207i	−0.0752165	+	0.523142i
$340$	−11.8274	+	11.6801i	−0.641430	+	0.633443i
$341$	−22.0889	+	3.17591i	−1.19618	+	0.171985i
$342$	−0.127021	+	0.583904i	−0.00686849	+	0.0315739i
$343$	−4.38133	+	0.313359i	−0.236570	+	0.0169198i
$344$	1.17551			0.0633793
$345$	6.90568	+	8.20436i	0.371789	+	0.441708i
$346$	21.2959			1.14487
$347$	9.31075	−	0.665918i	0.499827	−	0.0357483i	0.180850	−	0.983511i	$-0.442115\pi$
$347$	9.31075	−	0.665918i	0.499827	−	0.0357483i	0.318977	+	0.947762i	$0.396661\pi$
$348$	−1.31495	+	6.04474i	−0.0704889	+	0.324032i
$349$	−7.44268	+	1.07010i	−0.398398	+	0.0572809i	−0.338602	−	0.940930i	$-0.609954\pi$
$349$	−7.44268	+	1.07010i	−0.398398	+	0.0572809i	−0.0597957	+	0.998211i	$0.519045\pi$
$350$	−0.674325	+	1.42891i	−0.0360442	+	0.0763783i
$351$	0.924857	−	6.43252i	0.0493652	−	0.343343i
$352$	−1.36863	+	2.50646i	−0.0729483	+	0.133595i
$353$	−7.03123	+	1.52955i	−0.374235	+	0.0814098i	−0.395749	−	0.918359i	$-0.629515\pi$
$353$	−7.03123	+	1.52955i	−0.374235	+	0.0814098i	0.0215142	+	0.999769i	$0.493151\pi$
$354$	−1.46717	−	0.670036i	−0.0779794	−	0.0356120i
$355$	−19.0704	−	16.7349i	−1.01215	−	0.888197i
$356$	6.95638	−	6.02774i	0.368688	−	0.319470i
$357$	−0.167586	+	2.34316i	−0.00886959	+	0.124013i
$358$	−10.8063	+	5.90067i	−0.571129	+	0.311860i
$359$	2.66346	−	5.83215i	0.140572	−	0.307809i	−0.826232	−	0.563330i	$-0.809520\pi$
$359$	2.66346	−	5.83215i	0.140572	−	0.307809i	0.966803	+	0.255521i	$0.0822471\pi$
$360$	−0.488991	+	2.18195i	−0.0257721	+	0.114999i
$361$	17.8878	−	5.25232i	0.941461	−	0.276438i
$362$	−10.8752	−	14.5275i	−0.571585	−	0.763549i
$363$	2.66514	+	0.994047i	0.139884	+	0.0521740i
$364$	−0.292260	−	2.03271i	−0.0153186	−	0.106543i
$365$	7.17757	−	9.46394i	0.375691	−	0.495365i
$366$	−0.00616337	−	0.00534059i	−0.000322164	−	0.000279157i
$367$	−24.7441	+	24.7441i	−1.29163	+	1.29163i	−0.357856	+	0.933777i	$0.616492\pi$
$367$	−24.7441	+	24.7441i	−1.29163	+	1.29163i	−0.933777	+	0.357856i	$0.883508\pi$
$368$	4.47978	+	1.71219i	0.233525	+	0.0892541i
$369$		−	4.92684i		−	0.256481i
$370$	13.6065	−	6.11113i	0.707367	−	0.317703i
$371$	−0.622622	+	0.400135i	−0.0323249	+	0.0207740i
$372$	−4.68296	+	6.25570i	−0.242800	+	0.324343i
$373$	1.78905	−	4.79662i	0.0926333	−	0.248360i	−0.882367	−	0.470561i	$-0.844052\pi$
$373$	1.78905	−	4.79662i	0.0926333	−	0.248360i	0.975001	+	0.222202i	$0.0713243\pi$
$374$	−21.0134	−	3.02128i	−1.08658	−	0.156227i
$375$	−10.8782	−	2.58146i	−0.561750	−	0.133306i
$376$	−8.53403	−	5.48449i	−0.440109	−	0.282841i
$377$	37.6668	−	14.0490i	1.93994	−	0.723560i
$378$	0.151445	+	0.277351i	0.00778951	+	0.0142654i
$379$	13.5146	+	15.5967i	0.694199	+	0.801149i	0.987957	−	0.154731i	$-0.0494512\pi$
$379$	13.5146	+	15.5967i	0.694199	+	0.801149i	−0.293757	+	0.955880i	$0.594906\pi$
$380$	−1.28439	+	0.368407i	−0.0658881	+	0.0188989i
$381$	−1.94669	−	0.571601i	−0.0997322	−	0.0292840i
$382$	−7.48673	−	20.0727i	−0.383055	−	1.02701i
$383$	2.19458	+	10.0883i	0.112138	+	0.515489i	0.998610	+	0.0527074i	$0.0167851\pi$
$383$	2.19458	+	10.0883i	0.112138	+	0.515489i	−0.886472	+	0.462782i	$0.846851\pi$
$384$	0.281733	+	0.959493i	0.0143771	+	0.0489639i
$385$	−1.97446	+	0.416579i	−0.100628	+	0.0212308i
$386$	7.16845	+	15.6967i	0.364864	+	0.798942i
$387$	0.941044	+	0.704457i	0.0478360	+	0.0358096i
$388$	2.82782	+	0.615155i	0.143561	+	0.0312297i
$389$	12.8836	−	14.8684i	0.653222	−	0.753859i	−0.328432	−	0.944528i	$-0.606520\pi$
$389$	12.8836	−	14.8684i	0.653222	−	0.753859i	0.981654	+	0.190669i	$0.0610657\pi$
$390$	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
$393$	−1.05028	−	14.6848i	−0.0529796	−	0.740752i
$394$	−10.9378	−	17.0195i	−0.551036	−	0.857429i
$395$	−7.67171	+	25.5345i	−0.386006	+	1.28478i
$396$	−2.59771	+	1.18634i	−0.130540	+	0.0596156i
$397$	24.7543	−	18.5308i	1.24238	−	0.930034i	0.243179	−	0.969982i	$-0.421810\pi$
$397$	24.7543	−	18.5308i	1.24238	−	0.930034i	0.999202	+	0.0399473i	$0.0127190\pi$
$398$	7.52458	+	4.10873i	0.377173	+	0.205952i
$399$	−0.102091	+	0.158856i	−0.00511092	+	0.00795275i
$400$	−4.81474	+	1.34844i	−0.240737	+	0.0674219i
$401$	5.30438	−	18.0651i	0.264888	−	0.902127i	−0.714414	−	0.699723i	$-0.753307\pi$
$401$	5.30438	−	18.0651i	0.264888	−	0.902127i	0.979302	−	0.202403i	$-0.0648752\pi$
$402$	−1.04972	−	0.0750776i	−0.0523553	−	0.00374453i
$403$	50.6534	+	3.62280i	2.52323	+	0.180465i
$404$	2.88820	−	9.83631i	0.143693	−	0.489375i
$405$	−1.69905	+	1.45370i	−0.0844264	+	0.0722348i
$406$	−1.05687	+	1.64452i	−0.0524516	+	0.0816162i
$407$	16.7195	+	9.12955i	0.828756	+	0.452535i
$408$	−5.95112	+	4.45495i	−0.294624	+	0.220553i
$409$	16.0876	−	7.34694i	0.795479	−	0.363283i	0.0241407	−	0.999709i	$-0.492315\pi$
$409$	16.0876	−	7.34694i	0.795479	−	0.363283i	0.771338	+	0.636426i	$0.219588\pi$
$410$	9.70207	−	5.21909i	0.479151	−	0.257752i
$411$	−2.11237	−	3.28691i	−0.104195	−	0.162131i
$412$	0.339452	+	4.74616i	0.0167236	+	0.233827i
$413$	−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
$417$	−15.3129	−	3.33112i	−0.749876	−	0.163126i
$418$	−1.36613	−	1.02267i	−0.0668195	−	0.0500204i
$419$	−11.4539	−	25.0806i	−0.559562	−	1.22527i	−0.952172	−	0.305564i	$-0.901155\pi$
$419$	−11.4539	−	25.0806i	−0.559562	−	1.22527i	0.392610	−	0.919705i	$-0.371572\pi$
$420$	−0.385739	+	0.592033i	−0.0188221	+	0.0288883i
$421$	−1.61265	−	5.49218i	−0.0785957	−	0.267672i	0.910815	−	0.412815i	$-0.135454\pi$
$421$	−1.61265	−	5.49218i	−0.0785957	−	0.267672i	−0.989411	+	0.145142i	$0.953636\pi$
$422$	−0.129223	−	0.594027i	−0.00629046	−	0.0289168i
$423$	−3.54511	−	9.50482i	−0.172369	−	0.462140i
$424$	−2.24722	−	0.659842i	−0.109134	−	0.0320448i
$425$	−21.9002	−	30.0324i	−1.06231	−	1.45678i
$426$	−7.43050	−	8.57525i	−0.360009	−	0.415472i
$427$	−0.00123508	−	0.00226189i	−5.97699e−5	−	0.000109460i
$428$	−15.9626	+	5.95375i	−0.771583	+	0.287786i
$429$	15.6127	+	10.0337i	0.753787	+	0.484429i
$430$	−0.390371	+	2.59937i	−0.0188254	+	0.125353i
$431$	16.4971	+	2.37193i	0.794639	+	0.114252i	0.527666	−	0.849452i	$-0.323067\pi$
$431$	16.4971	+	2.37193i	0.794639	+	0.114252i	0.266973	+	0.963704i	$0.413976\pi$
$432$	−0.349464	+	0.936950i	−0.0168136	+	0.0450790i
$433$	−6.26122	+	8.36402i	−0.300895	+	0.401949i	−0.925351	−	0.379111i	$-0.876230\pi$
$433$	−6.26122	+	8.36402i	−0.300895	+	0.401949i	0.624456	+	0.781060i	$0.285321\pi$
$434$	−2.07737	+	1.33504i	−0.0997169	+	0.0640842i
$435$	−12.9299	−	4.91509i	−0.619940	−	0.235661i
$436$		−	7.13524i		−	0.341716i
$437$	−1.39369	+	2.50408i	−0.0666693	+	0.119787i
$438$	3.75611	−	3.75611i	0.179474	−	0.179474i
$439$	20.3160	+	17.6039i	0.969629	+	0.840188i	0.987172	−	0.159658i	$-0.0510392\pi$
$439$	20.3160	+	17.6039i	0.969629	+	0.840188i	−0.0175437	+	0.999846i	$0.505585\pi$
$440$	−5.08796	−	3.85878i	−0.242559	−	0.183960i
$441$	−0.981992	−	6.82991i	−0.0467615	−	0.325234i
$442$	45.2643	+	16.8827i	2.15300	+	0.803028i
$443$	9.96682	+	13.3141i	0.473538	+	0.632573i	0.972180	−	0.234235i	$-0.0752586\pi$
$443$	9.96682	+	13.3141i	0.473538	+	0.632573i	−0.498642	+	0.866808i	$0.666168\pi$
$444$	6.40036	−	1.87931i	0.303748	−	0.0891883i
$445$	11.0188	+	17.3842i	0.522343	+	0.824089i
$446$	−3.82929	+	8.38497i	−0.181322	+	0.397040i
$447$	−6.20026	+	3.38560i	−0.293262	+	0.160133i
$448$	−0.0225436	+	0.315200i	−0.00106508	+	0.0148918i
$449$	10.8195	−	9.37516i	0.510604	−	0.442441i	−0.361061	−	0.932542i	$-0.617586\pi$
$449$	10.8195	−	9.37516i	0.510604	−	0.442441i	0.871666	+	0.490101i	$0.163040\pi$
$450$	−4.66249	−	1.80588i	−0.219792	−	0.0851302i
$451$	12.7985	+	5.84489i	0.602659	+	0.275225i
$452$	−9.50873	+	2.06850i	−0.447253	+	0.0972940i
$453$	−9.29361	+	17.0200i	−0.436652	+	0.799668i
$454$	−0.874018	+	6.07893i	−0.0410197	+	0.285298i
$455$	4.59194	+	0.0287703i	0.215273	+	0.00134877i
$456$	−0.591478	+	0.0850417i	−0.0276985	+	0.00398244i
$457$	−9.07072	+	41.6974i	−0.424310	+	1.95052i	−0.151482	+	0.988460i	$0.548405\pi$
$457$	−9.07072	+	41.6974i	−0.424310	+	1.95052i	−0.272828	+	0.962063i	$0.587959\pi$
$458$	−19.5499	+	1.39824i	−0.913507	+	0.0653353i
$459$	−7.43387			−0.346983
$460$	−5.27379	+	9.33741i	−0.245892	+	0.435359i
$461$	−19.2052			−0.894477			−0.447239	−	0.894415i	$-0.647593\pi$
$461$	−19.2052			−0.894477			−0.447239	+	0.894415i	$0.647593\pi$
$462$	−0.900145	+	0.0643796i	−0.0418785	+	0.00299521i
$463$	2.89567	−	13.3112i	0.134573	−	0.618623i	−0.859613	−	0.510946i	$-0.829295\pi$
$463$	2.89567	−	13.3112i	0.134573	−	0.618623i	0.994186	−	0.107677i	$-0.0343412\pi$
$464$	−6.12315	+	0.880376i	−0.284260	+	0.0408704i
$465$	−12.2779	−	12.4327i	−0.569374	−	0.576554i
$466$	0.196629	−	1.36759i	0.00910867	−	0.0633522i
$467$	0.688118	−	1.26019i	0.0318423	−	0.0583148i	−0.861273	−	0.508142i	$-0.830333\pi$
$467$	0.688118	−	1.26019i	0.0318423	−	0.0583148i	0.893116	+	0.449827i	$0.148514\pi$
$468$	6.35016	−	1.38139i	0.293536	−	0.0638549i
$469$	−0.302512	−	0.138153i	−0.0139687	−	0.00637929i
$470$	14.9617	−	17.0497i	0.690133	−	0.786446i
$471$	−14.3445	+	12.4296i	−0.660958	+	0.572723i
$472$	0.115065	−	1.60882i	0.00529631	−	0.0740520i
$473$	−2.94637	+	1.60884i	−0.135474	+	0.0739746i
$474$	−4.95327	+	10.8461i	−0.227511	+	0.498180i
$475$	−0.388118	−	2.96249i	−0.0178081	−	0.135928i
$476$	−2.25399	+	0.661830i	−0.103311	+	0.0303349i
$477$	−1.40356	−	1.87494i	−0.0642646	−	0.0858475i
$478$	17.2266	+	6.42520i	0.787928	+	0.293882i
$479$	1.96015	+	13.6331i	0.0895615	+	0.622914i	0.984324	+	0.176371i	$0.0564359\pi$
$479$	1.96015	+	13.6331i	0.0895615	+	0.622914i	−0.894762	+	0.446543i	$0.852655\pi$
$480$	−2.21526	+	0.304352i	−0.101112	+	0.0138917i
$481$	−32.7616	−	28.3881i	−1.49380	−	1.29439i
$482$	−14.5630	+	14.5630i	−0.663327	+	0.663327i
$483$	0.310180	+	1.48343i	0.0141137	+	0.0674983i
$484$			2.84449i			0.129295i
$485$	−2.29935	+	6.04879i	−0.104408	+	0.274661i
$486$	−0.841254	+	0.540641i	−0.0381600	+	0.0245240i
$487$	11.5769	−	15.4649i	0.524600	−	0.700783i	−0.457486	−	0.889217i	$-0.651250\pi$
$487$	11.5769	−	15.4649i	0.524600	−	0.700783i	0.982086	+	0.188433i	$0.0603410\pi$
$488$	0.00284999	−	0.00764111i	0.000129013	−	0.000345897i
$489$	−10.6368	−	1.52935i	−0.481014	−	0.0691594i
$490$	12.4094	−	9.16880i	0.560599	−	0.414204i
$491$	13.7121	+	8.81223i	0.618818	+	0.397690i	0.812155	−	0.583442i	$-0.198294\pi$
$491$	13.7121	+	8.81223i	0.618818	+	0.397690i	−0.193336	+	0.981133i	$0.561931\pi$
$492$	4.61621	−	1.72176i	0.208115	−	0.0776227i
$493$	−22.0391	−	40.3616i	−0.992591	−	1.81780i
$494$	2.54305	+	2.93484i	0.114417	+	0.132045i
$495$	−1.76065	−	6.13821i	−0.0791351	−	0.275892i
$496$	−7.49780	−	2.20155i	−0.336661	−	0.0988527i
$497$	−1.25304	−	3.35954i	−0.0562067	−	0.150696i
$498$	1.92156	+	8.83326i	0.0861071	+	0.395828i
$499$	−0.291137	−	0.991521i	−0.0130331	−	0.0443866i	0.952720	−	0.303850i	$-0.0982723\pi$
$499$	−0.291137	−	0.991521i	−0.0130331	−	0.0443866i	−0.965753	+	0.259464i	$0.916454\pi$
$500$	−1.38285	−	11.0945i	−0.0618431	−	0.496161i
$501$	−4.02343	−	8.81008i	−0.179754	−	0.393605i
$502$	−20.1907	−	15.1146i	−0.901155	−	0.674596i
$503$	38.0147	+	8.26959i	1.69499	+	0.368723i	0.953302	−	0.302020i	$-0.0976610\pi$
$503$	38.0147	+	8.26959i	1.69499	+	0.368723i	0.741690	+	0.670743i	$0.234025\pi$
$504$	−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
$508$	−0.144739	−	2.02371i	−0.00642173	−	0.0897876i
$509$	0.500788	+	0.779241i	0.0221970	+	0.0345392i	0.852175	−	0.523257i	$-0.175283\pi$
$509$	0.500788	+	0.779241i	0.0221970	+	0.0345392i	−0.829978	+	0.557797i	$0.811647\pi$
$510$	−7.87482	−	14.6390i	−0.348703	−	0.648224i
$511$	1.52691	−	0.697317i	0.0675466	−	0.0308475i
$512$	−0.800541	+	0.599278i	−0.0353793	+	0.0264846i
$513$	−0.524466	−	0.286380i	−0.0231558	−	0.0126440i
$514$	−12.8749	+	20.0337i	−0.567888	+	0.883650i
$515$	−10.6078	−	0.825515i	−0.467435	−	0.0363766i
$516$	−0.331179	+	1.12789i	−0.0145794	+	0.0496527i
$517$	28.8965	+	2.06672i	1.27087	+	0.0908941i
$518$	2.10256	+	0.150378i	0.0923814	+	0.00660725i
$519$	−5.99975	+	20.4333i	−0.263360	+	0.896921i
$520$	9.44710	+	11.0416i	0.414283	+	0.484204i
$521$	−1.65838	+	2.58048i	−0.0726547	+	0.113053i	−0.875680	−	0.482892i	$-0.839586\pi$
$521$	−1.65838	+	2.58048i	−0.0726547	+	0.113053i	0.803025	+	0.595945i	$0.203223\pi$
$522$	−5.42942	−	2.96469i	−0.237639	−	0.129761i
$523$	1.30987	−	0.980555i	0.0572765	−	0.0428767i	−0.570256	−	0.821467i	$-0.693156\pi$
$523$	1.30987	−	0.980555i	0.0572765	−	0.0428767i	0.627532	+	0.778590i	$0.284065\pi$
$524$	13.3919	−	6.11588i	0.585028	−	0.267173i
$525$	−1.18105	−	1.04958i	−0.0515451	−	0.0458074i
$526$	12.8370	+	19.9748i	0.559720	+	0.870941i
$527$	−4.14415	−	57.9427i	−0.180522	−	2.52403i
$528$	−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
$532$	−0.184517	−	0.0401392i	−0.00799983	−	0.00174026i
$533$	−25.6317	−	19.1876i	−1.11023	−	0.831109i
$534$	3.82374	+	8.37281i	0.165469	+	0.362327i
$535$	−7.86439	−	37.2749i	−0.340007	−	1.61153i
$536$	−0.296496	−	1.00977i	−0.0128067	−	0.0436156i
$537$	−2.61717	−	12.0309i	−0.112939	−	0.519174i
$538$	0.713182	+	1.91212i	0.0307475	+	0.0824372i
$539$	18.9071	+	5.55163i	0.814387	+	0.239126i
$540$	−1.95580	−	1.08391i	−0.0841641	−	0.0466440i
$541$	−10.7986	−	12.4623i	−0.464269	−	0.535794i	0.474540	−	0.880234i	$-0.342614\pi$
$541$	−10.7986	−	12.4623i	−0.464269	−	0.535794i	−0.938809	+	0.344440i	$0.888069\pi$
$542$	−8.80301	−	16.1215i	−0.378122	−	0.692478i
$543$	17.0029	−	6.34176i	0.729665	−	0.272151i
$544$	−6.25377	−	4.01905i	−0.268128	−	0.172315i
$545$	15.7779	+	2.36951i	0.675853	+	0.101499i
$546$	2.03271	+	0.292260i	0.0869921	+	0.0125076i
$547$	−1.88065	+	5.04221i	−0.0804106	+	0.215589i	−0.970934	−	0.239349i	$-0.923066\pi$
$547$	−1.88065	+	5.04221i	−0.0804106	+	0.215589i	0.890523	+	0.454938i	$0.150339\pi$
$548$	2.34147	−	3.12784i	0.100023	−	0.133615i
$549$	0.00686068	−	0.00440909i	0.000292807	−	0.000188175i
$550$	10.2224	−	9.96942i	0.435887	−	0.425097i
$551$		−	3.69658i		−	0.157480i
$552$	−2.90493	+	3.81594i	−0.123642	+	0.162417i
$553$	−2.66434	+	2.66434i	−0.113299	+	0.113299i
$554$	4.95614	+	4.29452i	0.210566	+	0.182457i
$555$	2.03020	+	14.7770i	0.0861773	+	0.627250i
$556$	−2.23022	−	15.5115i	−0.0945824	−	0.657835i
$557$	0.179318	+	0.0668822i	0.00759795	+	0.00283389i	0.353260	−	0.935525i	$-0.385073\pi$
$557$	0.179318	+	0.0668822i	0.00759795	+	0.00283389i	−0.345662	+	0.938359i	$0.612346\pi$
$558$	−4.68296	−	6.25570i	−0.198245	−	0.264825i
$559$	7.32981	−	2.15223i	0.310018	−	0.0910295i
$560$	−0.689507	−	0.154524i	−0.0291370	−	0.00652982i
$561$	8.81907	−	19.3111i	0.372341	−	0.815314i
$562$	17.5753	−	9.59686i	0.741371	−	0.404819i
$563$	−1.26730	+	17.7192i	−0.0534105	+	0.746776i	0.898223	+	0.439540i	$0.144859\pi$
$563$	−1.26730	+	17.7192i	−0.0534105	+	0.746776i	−0.951633	+	0.307236i	$0.900596\pi$
$564$	7.66664	−	6.64319i	0.322824	−	0.279729i
$565$	−1.41629	−	21.7133i	−0.0595837	−	0.913486i
$566$	−1.45282	−	0.663479i	−0.0610664	−	0.0278881i
$567$	−0.308784	+	0.0671718i	−0.0129677	+	0.00282095i
$568$	5.43789	−	9.95875i	0.228169	−	0.417860i
$569$	−3.73091	+	25.9490i	−0.156408	+	1.08784i	0.748777	+	0.662822i	$0.230641\pi$
$569$	−3.73091	+	25.9490i	−0.156408	+	1.08784i	−0.905185	+	0.425018i	$0.860268\pi$
$570$	0.00837157	−	1.33616i	0.000350646	−	0.0559656i
$571$	−9.51794	+	1.36847i	−0.398313	+	0.0572688i	−0.338561	−	0.940944i	$-0.609940\pi$
$571$	−9.51794	+	1.36847i	−0.398313	+	0.0572688i	−0.0597523	+	0.998213i	$0.519031\pi$
$572$	−3.94496	+	18.1347i	−0.164947	+	0.758249i
$573$	21.3689	−	1.52833i	0.892698	−	0.0638470i
$574$	1.55691			0.0649842
$575$	−18.8962	−	14.7626i	−0.788025	−	0.615643i
$576$	−1.00000			−0.0416667
$577$	−36.3774	+	2.60176i	−1.51441	+	0.108313i	−0.803642	−	0.595113i	$-0.797107\pi$
$577$	−36.3774	+	2.60176i	−1.51441	+	0.108313i	−0.710768	+	0.703426i	$0.751653\pi$
$578$	8.13325	−	37.3880i	0.338299	−	1.55513i
$579$	−17.0805	+	2.45580i	−0.709840	+	0.102060i
$580$	0.0866648	−	13.8323i	0.00359856	−	0.574355i
$581$	−0.406543	+	2.82757i	−0.0168662	+	0.117307i
$582$	−1.38693	+	2.53996i	−0.0574899	+	0.105285i
$583$	6.53564	−	1.42174i	0.270679	−	0.0588826i
$584$	4.83191	+	2.20666i	0.199946	+	0.0913123i
$585$	0.945831	+	14.5007i	0.0391053	+	0.599528i
$586$	−8.34239	+	7.22872i	−0.344621	+	0.298616i
$587$	1.37176	−	19.1797i	0.0566186	−	0.791632i	−0.887245	−	0.461298i	$-0.847384\pi$
$587$	1.37176	−	19.1797i	0.0566186	−	0.791632i	0.943864	−	0.330334i	$-0.107161\pi$
$588$	6.05611	−	3.30689i	0.249750	−	0.136374i
$589$	1.93980	−	4.24756i	0.0799279	−	0.175018i
$590$	3.51933	+	0.788708i	0.144888	+	0.0324706i
$591$	19.4116	−	5.69976i	0.798487	−	0.234457i
$592$	3.99752	+	5.34006i	0.164297	+	0.219475i
$593$	13.8585	+	5.16897i	0.569102	+	0.212264i	0.617509	−	0.786564i	$-0.288142\pi$
$593$	13.8585	+	5.16897i	0.569102	+	0.212264i	−0.0484071	+	0.998828i	$0.515414\pi$
$594$	−0.406421	−	2.82672i	−0.0166756	−	0.115982i
$595$	−0.714968	−	5.20396i	−0.0293108	−	0.213342i
$596$	−5.33890	−	4.62619i	−0.218690	−	0.189496i
$597$	−6.06222	+	6.06222i	−0.248110	+	0.248110i
$598$	31.0682	+	2.47427i	1.27047	+	0.101180i
$599$			24.7711i			1.01212i	0.862498	+	0.506061i	$0.168899\pi$
$599$			24.7711i			1.01212i	−0.862498	+	0.506061i	$0.831101\pi$
$600$	0.0626515	−	4.99961i	0.00255774	−	0.204108i
$601$	−24.1401	+	15.5139i	−0.984694	+	0.632824i	−0.930726	−	0.365718i	$-0.880823\pi$
$601$	−24.1401	+	15.5139i	−0.984694	+	0.632824i	−0.0539682	+	0.998543i	$0.517187\pi$
$602$	−0.222612	+	0.297375i	−0.00907300	+	0.0121201i
$603$	0.367777	−	0.986048i	0.0149770	−	0.0401550i
$604$	−19.1947	−	2.75977i	−0.781019	−	0.112294i
$605$	−6.28994	−	0.944616i	−0.255722	−	0.0384041i
$606$	8.62417	+	5.54242i	0.350333	+	0.225145i
$607$	25.0130	−	9.32938i	1.01525	−	0.378668i	0.213893	−	0.976857i	$-0.431386\pi$
$607$	25.0130	−	9.32938i	1.01525	−	0.378668i	0.801355	+	0.598189i	$0.204113\pi$
$608$	−0.286380	−	0.524466i	−0.0116143	−	0.0212699i
$609$	−1.28015	−	1.47737i	−0.0518744	−	0.0598662i
$610$	0.0159501	+	0.00883960i	0.000645802	+	0.000357905i
$611$	−63.2549	−	18.5733i	−2.55902	−	0.751395i
$612$	−2.59787	−	6.96516i	−0.105013	−	0.281550i
$613$	−2.18101	−	10.0259i	−0.0880901	−	0.404944i	0.911895	−	0.410424i	$-0.134619\pi$
$613$	−2.18101	−	10.0259i	−0.0880901	−	0.404944i	−0.999985	+	0.00548023i	$0.998256\pi$
$614$	−3.48739	−	11.8770i	−0.140740	−	0.479315i
$615$	2.27429	+	10.7795i	0.0917082	+	0.434669i
$616$	−0.374889	−	0.820892i	−0.0151047	−	0.0330747i
$617$	28.6843	+	21.4728i	1.15479	+	0.864462i	0.992496	−	0.122281i	$-0.0390209\pi$
$617$	28.6843	+	21.4728i	1.15479	+	0.864462i	0.162291	+	0.986743i	$0.448112\pi$
$618$	−4.64955	−	1.01145i	−0.187032	−	0.0406864i
$619$	8.59028	−	9.91371i	0.345272	−	0.398466i	−0.556379	−	0.830928i	$-0.687810\pi$
$619$	8.59028	−	9.91371i	0.345272	−	0.398466i	0.901652	+	0.432463i	$0.142355\pi$
$620$	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
$623$	0.207505	+	2.90130i	0.00831351	+	0.116238i
$624$	3.51345	+	5.46703i	0.140650	+	0.218856i
$625$	24.9921	+	0.626465i	0.999686	+	0.0250586i
$626$	−16.2524	+	7.42222i	−0.649576	+	0.296652i
$627$	1.36613	−	1.02267i	0.0545579	−	0.0408415i
$628$	−16.6587	−	9.09636i	−0.664756	−	0.362984i
$629$	−26.8093	+	41.7161i	−1.06896	+	1.66333i
$630$	−0.459376	−	0.536909i	−0.0183020	−	0.0213910i
$631$	2.55860	−	8.71378i	0.101856	−	0.346890i	−0.892758	−	0.450536i	$-0.851233\pi$
$631$	2.55860	−	8.71378i	0.101856	−	0.346890i	0.994614	+	0.103646i	$0.0330510\pi$
$632$	−11.8933	−	0.850624i	−0.473089	−	0.0338360i
$633$	0.606371	+	0.0433685i	0.0241011	+	0.00172374i
$634$	9.40342	−	32.0251i	0.373458	−	1.27188i
$635$	4.52304	+	0.351990i	0.179491	+	0.0139683i
$636$	1.26623	−	1.97029i	0.0502092	−	0.0781270i
$637$	−39.3567	−	21.4904i	−1.55937	−	0.851479i
$638$	14.1425	−	10.5870i	0.559908	−	0.419142i
$639$	10.3213	−	4.71358i	0.408305	−	0.186466i
$640$	−1.05932	−	1.96923i	−0.0418732	−	0.0778405i
$641$	7.08983	+	11.0320i	0.280031	+	0.435737i	0.952568	−	0.304327i	$-0.0984315\pi$
$641$	7.08983	+	11.0320i	0.280031	+	0.435737i	−0.672536	+	0.740064i	$0.734795\pi$
$642$	−1.21539	−	16.9934i	−0.0479677	−	0.670676i
$643$	−29.8773	−	29.8773i	−1.17825	−	1.17825i	−0.980191	−	0.198055i	$-0.936537\pi$
$643$	−29.8773	−	29.8773i	−1.17825	−	1.17825i	−0.198055	−	0.980191i	$-0.563463\pi$
$644$	−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
$647$	20.8599	+	4.53780i	0.820088	+	0.178399i	0.602988	−	0.797750i	$-0.293977\pi$
$647$	20.8599	+	4.53780i	0.820088	+	0.178399i	0.217100	+	0.976149i	$0.430340\pi$
$648$	−0.800541	−	0.599278i	−0.0314482	−	0.0235419i
$649$	1.91348	+	4.18993i	0.0751106	+	0.164469i
$650$	−27.5531	+	17.2233i	−1.08072	+	0.675555i
$651$	−0.695703	−	2.36935i	−0.0272668	−	0.0928620i
$652$	−2.28427	−	10.5006i	−0.0894590	−	0.411236i
$653$	15.6762	+	42.0295i	0.613457	+	1.64474i	0.755705	+	0.654912i	$0.227294\pi$
$653$	15.6762	+	42.0295i	0.613457	+	1.64474i	−0.142248	+	0.989831i	$0.545433\pi$
$654$	6.84621	+	2.01023i	0.267708	+	0.0786061i
$655$	9.07660	+	31.6441i	0.354652	+	1.23644i
$656$	3.22640	+	3.72346i	0.125970	+	0.145377i
$657$	2.54574	+	4.66218i	0.0993189	+	0.181889i
$658$	3.00358	−	1.12028i	0.117092	−	0.0436729i
$659$	−17.7000	−	11.3751i	−0.689495	−	0.443111i	0.148412	−	0.988926i	$-0.452584\pi$
$659$	−17.7000	−	11.3751i	−0.689495	−	0.443111i	−0.837906	+	0.545814i	$0.816220\pi$
$660$	5.13592	−	3.79472i	0.199915	−	0.147709i
$661$	38.3163	+	5.50905i	1.49033	+	0.214277i	0.838839	−	0.544379i	$-0.183235\pi$
$661$	38.3163	+	5.50905i	1.49033	+	0.214277i	0.651491	+	0.758656i	$0.274144\pi$
$662$	−5.04107	+	13.5156i	−0.195927	+	0.525300i
$663$	−28.9513	+	38.6744i	−1.12437	+	1.50199i
$664$	−7.60481	+	4.88731i	−0.295124	+	0.189665i
$665$	0.150034	−	0.394688i	0.00581808	−	0.0153053i
$666$			6.67056i			0.258479i
$667$	−20.8081	−	21.1468i	−0.805693	−	0.818807i
$668$	6.84856	−	6.84856i	0.264979	−	0.264979i
$669$	−6.96649	−	6.03650i	−0.269340	−	0.233384i
$670$	2.33134	−	0.320301i	0.0900677	−	0.0123743i
$671$	0.00331448	+	0.0230527i	0.000127954	+	0.000889941i
$672$	−0.296081	−	0.110433i	−0.0114216	−	0.00426003i
$673$	23.5254	+	31.4263i	0.906839	+	1.21139i	0.976867	+	0.213850i	$0.0686003\pi$
$673$	23.5254	+	31.4263i	0.906839	+	1.21139i	−0.0700277	+	0.997545i	$0.522309\pi$
$674$	17.0326	−	5.00122i	0.656071	−	0.192640i
$675$	3.04631	−	3.96485i	0.117252	−	0.152607i
$676$	12.1437	−	26.5910i	0.467066	−	1.02273i
$677$	−3.99422	+	2.18101i	−0.153510	+	0.0838229i	−0.554168	−	0.832405i	$-0.686963\pi$
$677$	−3.99422	+	2.18101i	−0.153510	+	0.0838229i	0.400658	+	0.916228i	$0.368782\pi$
$678$	0.694210	−	9.70633i	0.0266610	−	0.372769i
$679$	−0.691138	+	0.598874i	−0.0265234	+	0.0229827i
$680$	10.9640	−	12.4941i	0.420450	−	0.479127i
$681$	−5.58645	−	2.55125i	−0.214073	−	0.0977640i
$682$	21.8061	−	4.74362i	0.834998	−	0.181643i
$683$	16.4962	−	30.2105i	0.631210	−	1.15597i	−0.344888	−	0.938644i	$-0.612083\pi$
$683$	16.4962	−	30.2105i	0.631210	−	1.15597i	0.976098	−	0.217331i	$-0.0697350\pi$
$684$	0.0850417	−	0.591478i	0.00325165	−	0.0226157i
$685$	6.13893	+	6.21634i	0.234556	+	0.237514i
$686$	4.34781	−	0.625121i	0.166000	−	0.0238672i
$687$	4.16625	−	19.1519i	0.158952	−	0.730692i
$688$	−1.17252	+	0.0838599i	−0.0447017	+	0.00319713i
$689$	−15.2205			−0.579853
$690$	−7.47338	−	7.69081i	−0.284507	−	0.292784i
$691$	−24.9945			−0.950836			−0.475418	−	0.879760i	$-0.657703\pi$
$691$	−24.9945			−0.950836			−0.475418	+	0.879760i	$0.657703\pi$
$692$	−21.2416	+	1.51923i	−0.807486	+	0.0577526i
$693$	0.191828	−	0.881821i	0.00728695	−	0.0334976i
$694$	−9.23952	+	1.32844i	−0.350727	+	0.0504270i
$695$	35.0408	+	0.219544i	1.32917	+	0.00832779i
$696$	0.880376	−	6.12315i	0.0333706	−	0.232097i
$697$	−17.5527	+	32.1454i	−0.664857	+	1.21760i
$698$	7.34738	−	1.59832i	0.278102	−	0.0604975i
$699$	1.25679	+	0.573958i	0.0475362	+	0.0217091i
$700$	0.570670	−	1.47337i	0.0215693	−	0.0556882i
$701$	−26.2849	+	22.7760i	−0.992768	+	0.860239i	−0.990186	−	0.139758i	$-0.955368\pi$
$701$	−26.2849	+	22.7760i	−0.992768	+	0.860239i	−0.00258268	+	0.999997i	$0.500822\pi$
$702$	−0.463610	+	6.48211i	−0.0174978	+	0.244652i
$703$	−3.49849	+	1.91032i	−0.131948	+	0.0720490i
$704$	1.18634	−	2.59771i	0.0447117	−	0.0979050i
$705$	12.1439	+	19.1591i	0.457366	+	0.721575i
$706$	6.90420	−	2.02726i	0.259843	−	0.0762968i
$707$	1.94139	+	2.59340i	0.0730136	+	0.0975347i
$708$	1.51124	+	0.563662i	0.0567957	+	0.0211837i
$709$	−2.10748	−	14.6579i	−0.0791482	−	0.550487i	−0.990357	−	0.138542i	$-0.955758\pi$
$709$	−2.10748	−	14.6579i	−0.0791482	−	0.550487i	0.911208	−	0.411946i	$-0.135151\pi$
$710$	20.2156	+	15.3318i	0.758679	+	0.575392i
$711$	−9.01130	−	7.80833i	−0.337950	−	0.292835i
$712$	−6.50865	+	6.50865i	−0.243922	+	0.243922i
$713$	−12.8127	−	35.2179i	−0.479840	−	1.31892i
$714$		−	2.34914i		−	0.0879145i
$715$	−38.7906	−	14.7457i	−1.45069	−	0.551456i
$716$	10.3578	−	6.65654i	0.387089	−	0.248767i
$717$	−11.0182	+	14.7186i	−0.411484	+	0.549678i
$718$	−2.24061	+	6.00730i	−0.0836187	+	0.224191i
$719$	31.2195	+	4.48869i	1.16429	+	0.167400i	0.697245	−	0.716833i	$-0.254409\pi$
$719$	31.2195	+	4.48869i	1.16429	+	0.167400i	0.467046	+	0.884233i	$0.345318\pi$
$720$	0.332086	−	2.21127i	0.0123761	−	0.0824092i
$721$	−1.26495	−	0.812932i	−0.0471091	−	0.0302752i
$722$	−17.4675	+	6.51503i	−0.650072	+	0.242464i
$723$	−9.87023	−	18.0760i	−0.367078	−	0.672253i
$724$	11.8838	+	13.7147i	0.441659	+	0.509702i
$725$	30.5582	+	4.78516i	1.13490	+	0.177716i
$726$	−2.72927	−	0.801385i	−0.101293	−	0.0297422i
$727$	−0.0741853	−	0.198899i	−0.00275138	−	0.00737674i	0.935567	−	0.353150i	$-0.114889\pi$
$727$	−0.0741853	−	0.198899i	−0.00275138	−	0.00737674i	−0.938318	+	0.345773i	$0.887617\pi$
$728$	0.436528	+	2.00669i	0.0161788	+	0.0743727i
$729$	−0.281733	−	0.959493i	−0.0104345	−	0.0355368i
$730$	−6.48414	+	9.95187i	−0.239989	+	0.368335i
$731$	−3.63014	−	7.94890i	−0.134266	−	0.294001i
$732$	0.00652866	+	0.00488729i	0.000241306	+	0.000180640i
$733$	−21.4421	−	4.66444i	−0.791981	−	0.172285i	−0.201662	−	0.979455i	$-0.564634\pi$
$733$	−21.4421	−	4.66444i	−0.791981	−	0.172285i	−0.590319	+	0.807170i	$0.700998\pi$
$734$	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
$738$	0.351477	+	4.91429i	0.0129380	+	0.180898i
$739$	−9.44901	−	14.7029i	−0.347587	−	0.540856i	0.622809	−	0.782374i	$-0.285991\pi$
$739$	−9.44901	−	14.7029i	−0.347587	−	0.540856i	−0.970397	+	0.241517i	$0.922355\pi$
$740$	−13.1358	+	7.06624i	−0.482883	+	0.259760i
$741$	−3.53242	+	1.61320i	−0.129767	+	0.0592625i
$742$	0.592491	−	0.443533i	0.0217510	−	0.0162826i
$743$	31.9834	+	17.4643i	1.17336	+	0.640701i	0.943126	−	0.332435i	$-0.107870\pi$
$743$	31.9834	+	17.4643i	1.17336	+	0.640701i	0.230230	+	0.973136i	$0.426052\pi$
$744$	4.22475	−	6.57384i	0.154887	−	0.241009i
$745$	12.0027	−	10.2695i	0.439746	−	0.376244i
$746$	−1.44230	+	4.91203i	−0.0528064	+	0.179842i
$747$	−9.01682	−	0.644896i	−0.329908	−	0.0235955i
$748$	21.1754	+	1.51450i	0.774251	+	0.0553755i
$749$	1.51677	−	5.16565i	0.0554216	−	0.188749i
$750$	11.0347	+	1.79884i	0.402930	+	0.0656844i
$751$	−3.89299	+	6.05762i	−0.142057	+	0.221046i	−0.904990	−	0.425432i	$-0.860122\pi$
$751$	−3.89299	+	6.05762i	−0.142057	+	0.221046i	0.762933	+	0.646477i	$0.223759\pi$
$752$	8.90355	+	4.86171i	0.324679	+	0.177288i
$753$	20.1907	−	15.1146i	0.735790	−	0.550806i
$754$	−36.5686	+	16.7003i	−1.33175	+	0.608190i
$755$	12.4769	−	41.5281i	0.454081	−	1.51136i
$756$	−0.170846	−	0.265841i	−0.00621359	−	0.00966854i
$757$	−0.702363	−	9.82032i	−0.0255278	−	0.356926i	−0.994121	−	0.108275i	$-0.965467\pi$
$757$	−0.702363	−	9.82032i	−0.0255278	−	0.356926i	0.968593	−	0.248651i	$-0.0799872\pi$
$758$	−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	−0.493076	−	0.869986i	$-0.664127\pi$
$761$	12.0890	−	13.9515i	0.438227	−	0.505741i	0.931303	+	0.364245i	$0.118673\pi$
$762$	1.98251	+	0.431269i	0.0718188	+	0.0156232i
$763$	1.80504	+	1.35124i	0.0653468	+	0.0489180i
$764$	8.89963	+	19.4875i	0.321977	+	0.705032i
$765$	16.2646	−	3.43156i	0.588047	−	0.124068i
$766$	−2.90868	−	9.90606i	−0.105095	−	0.357921i
$767$	−2.22809	−	10.2424i	−0.0804517	−	0.369830i
$768$	−0.349464	−	0.936950i	−0.0126102	−	0.0338093i
$769$	3.48057	+	1.02199i	0.125513	+	0.0368538i	0.343886	−	0.939012i	$-0.388257\pi$
$769$	3.48057	+	1.02199i	0.125513	+	0.0368538i	−0.218373	+	0.975865i	$0.570075\pi$
$770$	1.93971	−	0.556374i	0.0699023	−	0.0200503i
$771$	−15.5950	−	17.9975i	−0.561638	−	0.648165i
$772$	−8.26997	−	15.1453i	−0.297643	−	0.545092i
$773$	−43.6297	+	16.2730i	−1.56925	+	0.585301i	−0.975626	−	0.219440i	$-0.929577\pi$
$773$	−43.6297	+	16.2730i	−1.56925	+	0.585301i	−0.593626	+	0.804741i	$0.702304\pi$
$774$	−0.988902	−	0.635529i	−0.0355453	−	0.0228436i
$775$	32.6019	+	21.5340i	1.17110	+	0.773522i
$776$	−2.86450	−	0.411853i	−0.102830	−	0.0147847i
$777$	−0.736648	+	1.97503i	−0.0264271	+	0.0708538i
$778$	−11.7900	+	15.7496i	−0.422693	+	0.564652i
$779$	−2.47672	+	1.59169i	−0.0887379	+	0.0570284i
$780$	−13.2559	+	5.95366i	−0.474636	+	0.213175i
$781$			32.4037i			1.15950i
$782$	−2.25621	−	35.5801i	−0.0806819	−	1.27234i
$783$	4.37424	−	4.37424i	0.156323	−	0.156323i
$784$	5.21478	+	4.51863i	0.186242	+	0.161380i
$785$	25.6467	−	33.8162i	0.915368	−	1.20695i
$786$	2.09521	+	14.5725i	0.0747336	+	0.519783i
$787$	−14.3571	−	5.35494i	−0.511777	−	0.190883i	0.0802903	−	0.996772i	$-0.474415\pi$
$787$	−14.3571	−	5.35494i	−0.511777	−	0.190883i	−0.592067	+	0.805889i	$0.701688\pi$
$788$	12.1240	+	16.1958i	0.431901	+	0.576953i
$789$	−22.7822	+	6.68947i	−0.811069	+	0.238151i
$790$	5.83055	−	26.0168i	0.207442	−	0.925635i
$791$	1.27744	−	2.79720i	0.0454205	−	0.0994569i
$792$	2.50646	−	1.36863i	0.0890633	−	0.0486322i
$793$	0.00378088	−	0.0528636i	0.000134263	−	0.00187724i
$794$	−23.3692	+	20.2495i	−0.829342	+	0.718629i
$795$	3.93635	+	3.45428i	0.139608	+	0.122511i
$796$	−7.79852	−	3.56147i	−0.276411	−	0.126233i
$797$	2.55817	−	0.556496i	0.0906151	−	0.0197121i	−0.167029	−	0.985952i	$-0.553417\pi$
$797$	2.55817	−	0.556496i	0.0906151	−	0.0197121i	0.257644	+	0.966240i	$0.417054\pi$
$798$	0.0904978	−	0.165734i	0.00320359	−	0.00586693i
$799$	−10.7323	+	74.6447i	−0.379681	+	2.64074i
$800$	4.70628	−	1.68848i	0.166392	−	0.0596969i
$801$	−9.11093	+	1.30995i	−0.321919	+	0.0462849i
$802$	−4.00212	+	18.3975i	−0.141320	+	0.649637i
$803$	−15.1311	+	1.08220i	−0.533966	+	0.0381900i
$804$	1.05240			0.0371154
$805$	−1.36341	−	3.10241i	−0.0480539	−	0.109346i
$806$	−50.7828			−1.78875
$807$	−2.03559	+	0.145588i	−0.0716561	+	0.00512495i
$808$	−2.17913	+	10.0173i	−0.0766615	+	0.352407i
$809$	15.6113	−	2.24456i	0.548864	−	0.0789147i	0.137696	−	0.990475i	$-0.456030\pi$
$809$	15.6113	−	2.24456i	0.548864	−	0.0789147i	0.411168	+	0.911560i	$0.365121\pi$
$810$	1.59101	−	1.57120i	0.0559025	−	0.0552064i
$811$	0.846281	−	5.88601i	0.0297169	−	0.206686i	−0.969553	−	0.244880i	$-0.921251\pi$
$811$	0.846281	−	5.88601i	0.0297169	−	0.206686i	0.999270	+	0.0381941i	$0.0121605\pi$
$812$	0.936858	−	1.71573i	0.0328773	−	0.0602102i
$813$	17.9486	−	3.90447i	0.629484	−	0.136936i
$814$	−17.3282	−	7.91353i	−0.607354	−	0.277369i
$815$	23.9783	−	1.56403i	0.839923	−	0.0547855i
$816$	5.61814	−	4.86815i	0.196674	−	0.170419i
$817$	0.0501114	−	0.700649i	0.00175318	−	0.0245126i
$818$	−15.5224	+	8.47590i	−0.542730	+	0.296353i
$819$	−0.853103	+	1.86804i	−0.0298098	+	0.0652744i
$820$	−9.30502	+	5.89793i	−0.324945	+	0.205965i
$821$	−27.6943	+	8.13178i	−0.966538	+	0.283801i	−0.726656	−	0.687001i	$-0.758927\pi$
$821$	−27.6943	+	8.13178i	−0.966538	+	0.283801i	−0.239881	+	0.970802i	$0.577109\pi$
$822$	2.34147	+	3.12784i	0.0816682	+	0.109096i
$823$	−0.767246	−	0.286168i	−0.0267445	−	0.00997519i	0.336056	−	0.941842i	$-0.390907\pi$
$823$	−0.767246	−	0.286168i	−0.0267445	−	0.00997519i	−0.362801	+	0.931867i	$0.618179\pi$
$824$	−0.677175	−	4.70986i	−0.0235905	−	0.164076i
$825$	6.68559	+	12.6171i	0.232762	+	0.439270i
$826$	0.385202	+	0.333779i	0.0134029	+	0.0116137i
$827$	28.9067	−	28.9067i	1.00518	−	1.00518i	0.00519842	−	0.999986i	$-0.498345\pi$
$827$	28.9067	−	28.9067i	1.00518	−	1.00518i	0.999986	−	0.00519842i	$-0.00165472\pi$
$828$	−2.84295	−	3.86234i	−0.0987993	−	0.134225i
$829$			5.56990i			0.193451i	0.995311	+	0.0967253i	$0.0308368\pi$
$829$			5.56990i			0.193451i	−0.995311	+	0.0967253i	$0.969163\pi$
$830$	−8.28172	−	18.4393i	−0.287463	−	0.640037i
$831$	−5.51687	+	3.54547i	−0.191378	+	0.122991i
$832$	−3.89451	+	5.20245i	−0.135018	+	0.180363i
$833$	−17.9257	+	48.0606i	−0.621088	+	1.66520i
$834$	15.5115	+	2.23022i	0.537120	+	0.0772262i
$835$	12.8697	+	17.4183i	0.445374	+	0.602786i
$836$	1.43560	+	0.922606i	0.0496514	+	0.0319090i
$837$	7.32164	−	2.73083i	0.253073	−	0.0943913i
$838$	13.2140	+	24.1996i	0.456470	+	0.835962i
$839$	−3.45860	−	3.99143i	−0.119404	−	0.137800i	0.692900	−	0.721033i	$-0.256333\pi$
$839$	−3.45860	−	3.99143i	−0.119404	−	0.137800i	−0.812304	+	0.583234i	$0.801787\pi$
$840$	0.342521	−	0.618043i	0.0118181	−	0.0213245i
$841$	8.89258	+	2.61110i	0.306641	+	0.0900378i
$842$	2.00035	+	5.36314i	0.0689365	+	0.184826i
$843$	4.25658	+	19.5672i	0.146604	+	0.673929i
$844$	0.171271	+	0.583295i	0.00589539	+	0.0200778i
$845$	54.7672	+	35.6836i	1.88405	+	1.22755i
$846$	4.21415	+	9.22769i	0.144885	+	0.317255i
$847$	−0.719586	−	0.538676i	−0.0247253	−	0.0185091i
$848$	2.28856	+	0.497846i	0.0785896	+	0.0170961i
$849$	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
$853$	0.0385150	+	0.538510i	0.00131873	+	0.0184382i	0.998069	−	0.0621170i	$-0.0197852\pi$
$853$	0.0385150	+	0.538510i	0.00131873	+	0.0184382i	−0.996750	+	0.0805553i	$0.974331\pi$
$854$	0.00139330	+	0.00216801i	4.76777e−5	+	7.41879e-5i
$855$	1.27968	+	0.384472i	0.0437640	+	0.0131487i
$856$	15.4972	−	7.07735i	0.529684	−	0.241899i
$857$	−28.4761	+	21.3169i	−0.972723	+	0.728172i	−0.962361	−	0.271775i	$-0.912389\pi$
$857$	−28.4761	+	21.3169i	−0.972723	+	0.728172i	−0.0103626	+	0.999946i	$0.503299\pi$
$858$	−16.2887	−	8.89429i	−0.556086	−	0.303646i
$859$	−21.1124	+	32.8515i	−0.720346	+	1.12088i	0.267214	+	0.963637i	$0.413897\pi$
$859$	−21.1124	+	32.8515i	−0.720346	+	1.12088i	−0.987560	+	0.157243i	$0.949740\pi$
$860$	0.203939	−	2.62060i	0.00695427	−	0.0893616i
$861$	−0.438632	+	1.49384i	−0.0149486	+	0.0509101i
$862$	−16.6243	−	1.18899i	−0.566227	−	0.0404973i
$863$	−22.6363	−	1.61898i	−0.770550	−	0.0551108i	−0.319472	−	0.947596i	$-0.603506\pi$
$863$	−22.6363	−	1.61898i	−0.770550	−	0.0551108i	−0.451078	+	0.892485i	$0.648960\pi$
$864$	0.281733	−	0.959493i	0.00958474	−	0.0326426i
$865$	3.69463	−	47.4755i	0.125621	−	1.61422i
$866$	5.64859	−	8.78938i	0.191947	−	0.298675i
$867$	33.5821	+	18.3372i	1.14051	+	0.622764i
$868$	1.97684	−	1.47984i	0.0670982	−	0.0502291i
$869$	30.9742	−	14.1455i	1.05073	−	0.479852i
$870$	13.2476	+	3.98016i	0.449135	+	0.134940i
$871$	−3.69756	−	5.75352i	−0.125287	−	0.194951i
$872$	0.509022	+	7.11706i	0.0172377	+	0.241014i
$873$	−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
$877$	1.20335	+	0.261773i	0.0406343	+	0.00883944i	0.232836	−	0.972516i	$-0.425199\pi$
$877$	1.20335	+	0.261773i	0.0406343	+	0.00883944i	−0.192202	+	0.981355i	$0.561563\pi$
$878$	−21.5201	−	16.1097i	−0.726267	−	0.543677i
$879$	−4.58558	−	10.0410i	−0.154668	−	0.338675i
$880$	5.35028	+	3.48598i	0.180358	+	0.117512i
$881$	−9.70310	−	33.0457i	−0.326906	−	1.11334i	−0.944955	−	0.327199i	$-0.893895\pi$
$881$	−9.70310	−	33.0457i	−0.326906	−	1.11334i	0.618050	−	0.786139i	$-0.287923\pi$
$882$	1.46673	+	6.74245i	0.0493874	+	0.227030i
$883$	−11.1200	−	29.8139i	−0.374218	−	1.00332i	−0.978445	−	0.206506i	$-0.933791\pi$
$883$	−11.1200	−	29.8139i	−0.374218	−	1.00332i	0.604227	−	0.796812i	$-0.293482\pi$
$884$	−46.3534	−	13.6106i	−1.55903	−	0.457773i
$885$	−1.74827	+	3.15457i	−0.0587674	+	0.106040i
$886$	−10.8912	−	12.5692i	−0.365899	−	0.422270i
$887$	18.7522	+	34.3420i	0.629636	+	1.15309i	0.976570	+	0.215202i	$0.0690410\pi$
$887$	18.7522	+	34.3420i	0.629636	+	1.15309i	−0.346934	+	0.937890i	$0.612777\pi$
$888$	−6.24998	+	2.33112i	−0.209736	+	0.0782274i
$889$	0.539359	+	0.346625i	0.0180895	+	0.0116254i
$890$	−12.2309	−	16.5538i	−0.409982	−	0.554885i
$891$	2.82672	+	0.406421i	0.0946986	+	0.0136156i
$892$	3.22136	−	8.63679i	0.107859	−	0.289181i
$893$	−3.63277	+	4.85281i	−0.121566	+	0.162393i
$894$	5.94294	−	3.81929i	0.198762	−	0.127736i
$895$	11.2797	+	25.1144i	0.377040	+	0.839482i
$896$		−	0.316006i		−	0.0105570i
$897$	−11.1270	+	29.1126i	−0.371518	+	0.972042i
$898$	−10.1231	+	10.1231i	−0.337813	+	0.337813i
$899$	36.5332	+	31.6562i	1.21845	+	1.05579i
$900$	4.77944	+	1.46867i	0.159315	+	0.0489555i
$901$	2.47781	+	17.2335i	0.0825478	+	0.574133i
$902$	−13.1829	−	4.91696i	−0.438942	−	0.163717i
$903$	−0.222612	−	0.297375i	−0.00740807	−	0.00989603i
$904$	9.33694	−	2.74157i	0.310542	−	0.0911834i
$905$	−34.2733	+	21.7239i	−1.13928	+	0.722127i
$906$	8.05574	−	17.6396i	0.267634	−	0.586037i
$907$	7.01023	−	3.82787i	0.232771	−	0.127102i	−0.358631	−	0.933479i	$-0.616756\pi$
$907$	7.01023	−	3.82787i	0.232771	−	0.127102i	0.591402	+	0.806377i	$0.298575\pi$
$908$	0.438125	−	6.12579i	0.0145397	−	0.203292i
$909$	−7.74762	+	6.71335i	−0.256972	+	0.222668i
$910$	−4.58229	+	0.298888i	−0.151901	+	0.00990804i
$911$	−25.3550	−	11.5792i	−0.840049	−	0.383637i	−0.0515474	−	0.998671i	$-0.516415\pi$
$911$	−25.3550	−	11.5792i	−0.840049	−	0.383637i	−0.788501	+	0.615033i	$0.789143\pi$
$912$	0.583904	−	0.127021i	0.0193350	−	0.00420607i
$913$	12.3722	−	22.6581i	0.409461	−	0.749872i
$914$	6.07295	−	42.2383i	0.200875	−	1.39712i
$915$	−0.0129752	+	0.0128136i	−0.000428947	+	0.000423605i
$916$	19.4003	−	2.78935i	0.641006	−	0.0921627i
$917$	−0.988926	+	4.54602i	−0.0326572	+	0.150123i
$918$	7.41493	−	0.530326i	0.244729	−	0.0175034i
$919$	−1.64745			−0.0543443			−0.0271721	−	0.999631i	$-0.508650\pi$
$919$	−1.64745			−0.0543443			−0.0271721	+	0.999631i	$0.508650\pi$
$920$	4.59423	−	9.68984i	0.151467	−	0.319465i
$921$	12.3784			0.407881
$922$	19.1563	−	1.37009i	0.630879	−	0.0451214i
$923$	15.6742	−	72.0532i	0.515923	−	2.37166i
$924$	0.893259	−	0.128431i	0.0293861	−	0.00422508i
$925$	−11.2631	−	31.3935i	−0.370329	−	1.03221i
$926$	−1.93868	+	13.4838i	−0.0637091	+	0.443106i
$927$	2.28040	−	4.17625i	0.0748983	−	0.137166i
$928$	6.04474	−	1.31495i	0.198428	−	0.0431654i
$929$	−1.84139	−	0.840936i	−0.0604142	−	0.0275902i	0.384979	−	0.922925i	$-0.374209\pi$
$929$	−1.84139	−	0.840936i	−0.0604142	−	0.0275902i	−0.445393	+	0.895335i	$0.646936\pi$
$930$	13.1336	+	11.5251i	0.430666	+	0.377924i
$931$	−3.11615	+	2.70016i	−0.102128	+	0.0884940i
$932$	−0.0985657	+	1.37813i	−0.00322863	+	0.0451421i
$933$	18.9075	−	10.3243i	0.619003	−	0.338001i
$934$	−0.596463	+	1.30607i	−0.0195169	+	0.0427360i
$935$	−10.3810	+	46.3217i	−0.339496	+	1.51488i
$936$	−6.23543	+	1.83089i	−0.203811	+	0.0598444i
$937$	−2.74706	−	3.66964i	−0.0897425	−	0.119882i	0.753423	−	0.657536i	$-0.228401\pi$
$937$	−2.74706	−	3.66964i	−0.0897425	−	0.119882i	−0.843165	+	0.537654i	$0.819311\pi$
$938$	0.311597	+	0.116220i	0.0101740	+	0.00379470i
$939$	−2.54274	−	17.6851i	−0.0829792	−	0.577133i
$940$	−13.7073	+	18.0737i	−0.447083	+	0.589498i
$941$	−8.46421	−	7.33428i	−0.275925	−	0.239091i	0.505894	−	0.862596i	$-0.331163\pi$
$941$	−8.46421	−	7.33428i	−0.275925	−	0.239091i	−0.781819	+	0.623505i	$0.785708\pi$
$942$	13.4212	−	13.4212i	0.437286	−	0.437286i
$943$	−5.20877	+	23.0470i	−0.169621	+	0.750515i
$944$			1.61293i			0.0524964i
$945$	0.644582	−	0.289504i	0.0209682	−	0.00941755i
$946$	2.82409	−	1.81493i	0.0918191	−	0.0590086i
$947$	−9.40881	+	12.5687i	−0.305745	+	0.408428i	−0.926929	−	0.375237i	$-0.877561\pi$
$947$	−9.40881	+	12.5687i	−0.305745	+	0.408428i	0.621183	+	0.783665i	$0.286652\pi$
$948$	4.16689	−	11.1719i	0.135334	−	0.362845i
$949$	34.1692	+	4.91279i	1.10918	+	0.159476i
$950$	0.598471	+	2.92725i	0.0194170	+	0.0949726i
$951$	28.0786	+	18.0450i	0.910512	+	0.585150i
$952$	2.20103	−	0.820942i	0.0713358	−	0.0266069i
$953$	14.2290	+	26.0585i	0.460924	+	0.844119i	0.999998	+	0.00186056i	$0.000592235\pi$
$953$	14.2290	+	26.0585i	0.460924	+	0.844119i	−0.539075	+	0.842258i	$0.681226\pi$
$954$	1.53374	+	1.77003i	0.0496567	+	0.0573069i
$955$	−46.0475	+	13.2080i	−1.49006	+	0.427400i
$956$	−17.6411	−	5.17990i	−0.570554	−	0.167530i
$957$	6.17371	+	16.5524i	0.199568	+	0.535062i
$958$	−2.92773	−	13.4586i	−0.0945907	−	0.434827i
$959$	0.347850	+	1.18467i	0.0112327	+	0.0382550i
$960$	2.18790	−	0.461612i	0.0706142	−	0.0148985i
$961$	12.4890	+	27.3471i	0.402870	+	0.882163i
$962$	34.7033	+	25.9786i	1.11888	+	0.837583i
$963$	16.6475	+	3.62143i	0.536457	+	0.116699i
$964$	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	$-0.619545\pi$
$968$	−0.202924	−	2.83724i	−0.00652221	−	0.0911924i
$969$	2.40163	+	3.73700i	0.0771514	+	0.120050i
$970$	1.86198	−	6.19741i	0.0597846	−	0.198987i
$971$	35.4837	−	16.2049i	1.13873	−	0.520039i	0.245388	−	0.969425i	$-0.421084\pi$
$971$	35.4837	−	16.2049i	1.13873	−	0.520039i	0.893338	+	0.449386i	$0.148357\pi$
$972$	0.800541	−	0.599278i	0.0256774	−	0.0192218i
$973$	4.34638	+	2.37331i	0.139339	+	0.0760847i
$974$	−10.4442	+	16.2514i	−0.334652	+	0.520729i
$975$	−8.76306	−	31.2894i	−0.280643	−	1.00206i
$976$	−0.00229761	+	0.00782496i	−7.35449e−5	+	0.000250471i
$977$	5.15751	+	0.368872i	0.165003	+	0.0118013i	0.153596	−	0.988134i	$-0.450914\pi$
$977$	5.15751	+	0.368872i	0.165003	+	0.0118013i	0.0114069	+	0.999935i	$0.496369\pi$
$978$	10.7188	+	0.766626i	0.342750	+	0.0245140i
$979$	7.40574	−	25.2216i	0.236688	−	0.806087i
$980$	−11.7237	+	10.0307i	−0.374499	+	0.320419i
$981$	−3.85760	+	6.00254i	−0.123164	+	0.191646i
$982$	−14.3058	−	7.81157i	−0.456517	−	0.249277i
$983$	36.1179	−	27.0375i	1.15198	−	0.862363i	0.159798	−	0.987150i	$-0.448916\pi$
$983$	36.1179	−	27.0375i	1.15198	−	0.862363i	0.992184	+	0.124787i	$0.0398248\pi$
$984$	−4.48162	+	2.04669i	−0.142869	+	0.0652459i
$985$	−39.8396	+	21.4311i	−1.26940	+	0.682853i
$986$	24.8623	+	38.6865i	0.791777	+	1.23203i
$987$	0.228692	+	3.19753i	0.00727934	+	0.101778i
$988$	−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	−0.690298	−	0.723525i	$-0.742520\pi$
$991$	3.90677	−	4.50866i	0.124103	−	0.143222i	0.814401	+	0.580303i	$0.197066\pi$
$992$	7.63576	+	1.66106i	0.242435	+	0.0527386i
$993$	−11.5479	−	8.64466i	−0.366462	−	0.274330i
$994$	1.48952	+	3.26159i	0.0472447	+	0.103451i
$995$	10.4651	−	16.0619i	0.331768	−	0.509197i
$996$	−2.54682	−	8.67368i	−0.0806991	−	0.274836i
$997$	−3.01480	−	13.8588i	−0.0954798	−	0.438913i	−0.999924	−	0.0123217i	$-0.996078\pi$
$997$	−3.01480	−	13.8588i	−0.0954798	−	0.438913i	0.904444	−	0.426592i	$-0.140286\pi$
$998$	0.361129	+	0.968225i	0.0114313	+	0.0306486i
$999$	−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.7.5	✓	240
5.3	odd	4	inner	690.2.w.a.283.9	yes	240
23.10	odd	22	inner	690.2.w.a.217.9	yes	240
115.33	even	44	inner	690.2.w.a.493.5	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.a.7.5	✓	240	1.1	even	1	trivial
690.2.w.a.217.9	yes	240	23.10	odd	22	inner
690.2.w.a.283.9	yes	240	5.3	odd	4	inner
690.2.w.a.493.5	yes	240	115.33	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)

\(f(q)\)	\(=\)	\(q+(-0.997452 + 0.0713392i) q^{2} +(0.212565 - 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-0.0140096 + 2.23602i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-0.151445 + 0.277351i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +O(q^{10})\)	\(q+(-0.997452 + 0.0713392i) q^{2} +(0.212565 - 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-0.0140096 + 2.23602i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-0.151445 + 0.277351i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +(-0.145542 - 2.23133i) q^{10} +(2.15826 - 1.87014i) q^{11} +(0.0713392 - 0.997452i) q^{12} +(-5.70375 + 3.11448i) q^{13} +(0.131273 - 0.287449i) q^{14} +(2.18195 + 0.488991i) q^{15} +(0.959493 - 0.281733i) q^{16} +(4.45495 + 5.95112i) q^{17} +(0.936950 + 0.349464i) q^{18} +(0.0850417 + 0.591478i) q^{19} +(0.304352 + 2.21526i) q^{20} +(0.238821 + 0.206940i) q^{21} +(-2.01935 + 2.01935i) q^{22} +(3.81594 + 2.90493i) q^{23} +1.00000i q^{24} +(-4.99961 - 0.0626515i) q^{25} +(5.46703 - 3.51345i) q^{26} +(-0.599278 + 0.800541i) q^{27} +(-0.110433 + 0.296081i) q^{28} +(-6.12315 - 0.880376i) q^{29} +(-2.21127 - 0.332086i) q^{30} +(-6.57384 - 4.22475i) q^{31} +(-0.936950 + 0.349464i) q^{32} +(-1.36863 - 2.50646i) q^{33} +(-4.86815 - 5.61814i) q^{34} +(-0.618043 - 0.342521i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(2.33112 + 6.24998i) q^{37} +(-0.127021 - 0.583904i) q^{38} +(1.83089 + 6.23543i) q^{39} +(-0.461612 - 2.18790i) q^{40} +(2.04669 + 4.48162i) q^{41} +(-0.252976 - 0.189375i) q^{42} +(-1.14865 - 0.249873i) 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} +(-0.0713392 - 0.997452i) q^{48} +(3.73050 + 5.80477i) q^{49} +(4.99134 - 0.294176i) q^{50} +(6.76208 - 3.08814i) q^{51} +(-5.20245 + 3.89451i) q^{52} +(2.05560 + 1.12244i) q^{53} +(0.540641 - 0.841254i) q^{54} +(4.15145 + 4.85212i) q^{55} +(0.0890291 - 0.303205i) q^{56} +(0.596038 + 0.0426295i) q^{57} +(6.17035 + 0.441312i) q^{58} +(-0.454415 + 1.54760i) q^{59} +(2.22933 + 0.173490i) q^{60} +(-0.00440909 + 0.00686068i) q^{61} +(6.85848 + 3.74501i) q^{62} +(0.252976 - 0.189375i) q^{63} +(0.909632 - 0.415415i) q^{64} +(-6.88415 - 12.7974i) q^{65} +(1.54395 + 2.40244i) q^{66} +(0.0750776 + 1.04972i) 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} +(0.977147 + 0.212565i) q^{72} +(-4.25243 - 3.18333i) q^{73} +(-2.77105 - 6.06776i) q^{74} +(-1.12396 + 4.87203i) q^{75} +(0.168352 + 0.573355i) q^{76} +(0.191828 + 0.881821i) q^{77} +(-2.27105 - 6.08893i) q^{78} +(11.4407 + 3.35928i) q^{79} +(0.616519 + 2.14940i) q^{80} +(0.654861 + 0.755750i) q^{81} +(-2.36119 - 4.32419i) q^{82} +(8.46989 - 3.15910i) q^{83} +(0.265841 + 0.170846i) q^{84} +(-13.3693 + 9.87800i) q^{85} +(1.16355 + 0.167293i) q^{86} +(-2.16183 + 5.79608i) q^{87} +(-1.71141 + 2.28617i) q^{88} +(7.74342 - 4.97639i) q^{89} +(-0.794537 + 2.09015i) q^{90} -2.05362i q^{91} +(4.19051 + 2.33230i) q^{92} +(-5.52557 + 5.52557i) q^{93} +(-7.66664 - 6.64319i) q^{94} +(-1.32375 + 0.181869i) q^{95} +(0.142315 + 0.989821i) q^{96} +(2.71149 + 1.01133i) q^{97} +(-4.13510 - 5.52385i) 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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