LMFDB - Embedded newform 966.2.q.h.547.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(85,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("966.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.q (of order $11$, degree $10$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			547.3
Character	$\chi$	$=$	966.547
Dual form			966.2.q.h.883.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959493 + 0.281733i) q^{2} +(0.654861 - 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.515900 - 3.58816i) q^{5} +(0.841254 - 0.540641i) q^{6} +(0.415415 + 0.909632i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(0.959493 + 0.281733i) q^{2} +(0.654861 - 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.515900 - 3.58816i) q^{5} +(0.841254 - 0.540641i) q^{6} +(0.415415 + 0.909632i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(1.50590 - 3.29747i) q^{10} +(2.78520 - 0.817809i) q^{11} +(0.959493 - 0.281733i) q^{12} +(0.667629 - 1.46190i) q^{13} +(0.142315 + 0.989821i) q^{14} +(-2.37391 - 2.73964i) q^{15} +(0.415415 + 0.909632i) q^{16} +(-1.52682 + 0.981227i) q^{17} +(0.142315 - 0.989821i) q^{18} +(-2.70503 - 1.73842i) q^{19} +(2.37391 - 2.73964i) q^{20} +(0.959493 + 0.281733i) q^{21} +2.90278 q^{22} +(-1.19715 + 4.64401i) q^{23} +1.00000 q^{24} +(-7.81128 - 2.29360i) q^{25} +(1.05245 - 1.21459i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(-0.142315 + 0.989821i) q^{28} +(2.64638 - 1.70073i) q^{29} +(-1.50590 - 3.29747i) q^{30} +(-0.580435 - 0.669858i) q^{31} +(0.142315 + 0.989821i) q^{32} +(1.20586 - 2.64046i) q^{33} +(-1.74142 + 0.511326i) q^{34} +(3.47822 - 1.02130i) q^{35} +(0.415415 - 0.909632i) q^{36} +(0.163573 + 1.13767i) q^{37} +(-2.10569 - 2.43009i) q^{38} +(-0.667629 - 1.46190i) q^{39} +(3.04959 - 1.95985i) q^{40} +(1.03984 - 7.23222i) q^{41} +(0.841254 + 0.540641i) q^{42} +(-2.21557 + 2.55691i) q^{43} +(2.78520 + 0.817809i) q^{44} -3.62506 q^{45} +(-2.45703 + 4.11862i) q^{46} +11.8235 q^{47} +(0.959493 + 0.281733i) q^{48} +(-0.654861 + 0.755750i) q^{49} +(-6.84869 - 4.40138i) q^{50} +(-0.258292 + 1.79646i) q^{51} +(1.35201 - 0.868884i) q^{52} +(2.10629 + 4.61212i) q^{53} +(-0.654861 - 0.755750i) q^{54} +(-1.49754 - 10.4157i) q^{55} +(-0.415415 + 0.909632i) q^{56} +(-3.08523 + 0.905904i) q^{57} +(3.01834 - 0.886264i) q^{58} +(-2.54552 + 5.57391i) q^{59} +(-0.515900 - 3.58816i) q^{60} +(-5.84034 - 6.74011i) q^{61} +(-0.368202 - 0.806251i) q^{62} +(0.841254 - 0.540641i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-4.90111 - 3.14975i) q^{65} +(1.90092 - 2.19378i) q^{66} +(2.26193 + 0.664162i) q^{67} -1.81493 q^{68} +(2.72574 + 3.94593i) q^{69} +3.62506 q^{70} +(-1.22039 - 0.358338i) q^{71} +(0.654861 - 0.755750i) q^{72} +(5.25460 + 3.37692i) q^{73} +(-0.163573 + 1.13767i) q^{74} +(-6.84869 + 4.40138i) q^{75} +(-1.33576 - 2.92490i) q^{76} +(1.90092 + 2.19378i) q^{77} +(-0.228719 - 1.59078i) q^{78} +(-3.96704 + 8.68660i) q^{79} +(3.47822 - 1.02130i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(3.03527 - 6.64631i) q^{82} +(0.755588 + 5.25523i) q^{83} +(0.654861 + 0.755750i) q^{84} +(2.73311 + 5.98469i) q^{85} +(-2.84619 + 1.82913i) q^{86} +(0.447689 - 3.11374i) q^{87} +(2.44198 + 1.56936i) q^{88} +(-1.16313 + 1.34232i) q^{89} +(-3.47822 - 1.02130i) q^{90} +1.60714 q^{91} +(-3.51785 + 3.25956i) q^{92} -0.886349 q^{93} +(11.3446 + 3.33106i) q^{94} +(-7.63324 + 8.80923i) q^{95} +(0.841254 + 0.540641i) q^{96} +(1.93592 - 13.4646i) q^{97} +(-0.841254 + 0.540641i) q^{98} +(-1.20586 - 2.64046i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 10 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 10 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 10 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} - 3 q^{9} + 12 q^{10} + 9 q^{11} + 3 q^{12} - 12 q^{13} + 3 q^{14} + q^{15} - 3 q^{16} + 13 q^{17} + 3 q^{18} - 18 q^{19} - q^{20} + 3 q^{21} + 24 q^{22} + 21 q^{23} + 30 q^{24} - 3 q^{25} + 34 q^{26} + 3 q^{27} - 3 q^{28} - 11 q^{29} - 12 q^{30} + 7 q^{31} + 3 q^{32} + 2 q^{33} - 13 q^{34} - q^{35} - 3 q^{36} + 3 q^{37} - 15 q^{38} + 12 q^{39} + q^{40} + 15 q^{41} - 3 q^{42} + 42 q^{43} + 9 q^{44} + 10 q^{45} + q^{46} + 12 q^{47} + 3 q^{48} - 3 q^{49} - 30 q^{50} + 9 q^{51} - q^{52} - 28 q^{53} - 3 q^{54} + 4 q^{55} + 3 q^{56} - 4 q^{57} - 11 q^{58} + 3 q^{59} - 10 q^{60} - 2 q^{61} + 26 q^{62} - 3 q^{63} - 3 q^{64} - 70 q^{65} - 2 q^{66} + 24 q^{67} + 2 q^{68} + q^{69} - 10 q^{70} - 3 q^{71} + 3 q^{72} - 7 q^{73} - 3 q^{74} - 30 q^{75} - 18 q^{76} - 2 q^{77} + 10 q^{78} - 32 q^{79} - q^{80} - 3 q^{81} - 26 q^{82} + 8 q^{83} + 3 q^{84} - 39 q^{85} + 35 q^{86} - 11 q^{87} + 13 q^{88} + 50 q^{89} + q^{90} + 32 q^{91} - 12 q^{92} + 4 q^{93} + 10 q^{94} + 73 q^{95} - 3 q^{96} + 24 q^{97} + 3 q^{98} - 2 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 10 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 - 3 * q^9 + 12 * q^10 + 9 * q^11 + 3 * q^12 - 12 * q^13 + 3 * q^14 + q^15 - 3 * q^16 + 13 * q^17 + 3 * q^18 - 18 * q^19 - q^20 + 3 * q^21 + 24 * q^22 + 21 * q^23 + 30 * q^24 - 3 * q^25 + 34 * q^26 + 3 * q^27 - 3 * q^28 - 11 * q^29 - 12 * q^30 + 7 * q^31 + 3 * q^32 + 2 * q^33 - 13 * q^34 - q^35 - 3 * q^36 + 3 * q^37 - 15 * q^38 + 12 * q^39 + q^40 + 15 * q^41 - 3 * q^42 + 42 * q^43 + 9 * q^44 + 10 * q^45 + q^46 + 12 * q^47 + 3 * q^48 - 3 * q^49 - 30 * q^50 + 9 * q^51 - q^52 - 28 * q^53 - 3 * q^54 + 4 * q^55 + 3 * q^56 - 4 * q^57 - 11 * q^58 + 3 * q^59 - 10 * q^60 - 2 * q^61 + 26 * q^62 - 3 * q^63 - 3 * q^64 - 70 * q^65 - 2 * q^66 + 24 * q^67 + 2 * q^68 + q^69 - 10 * q^70 - 3 * q^71 + 3 * q^72 - 7 * q^73 - 3 * q^74 - 30 * q^75 - 18 * q^76 - 2 * q^77 + 10 * q^78 - 32 * q^79 - q^80 - 3 * q^81 - 26 * q^82 + 8 * q^83 + 3 * q^84 - 39 * q^85 + 35 * q^86 - 11 * q^87 + 13 * q^88 + 50 * q^89 + q^90 + 32 * q^91 - 12 * q^92 + 4 * q^93 + 10 * q^94 + 73 * q^95 - 3 * q^96 + 24 * q^97 + 3 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{6}{11}\right)$

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 $

$2$	0.959493	+	0.281733i	0.678464	+	0.199215i
$2$	0.959493	+	0.281733i	0.678464	+	0.199215i
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$4$	0.841254	+	0.540641i	0.420627	+	0.270320i
$5$	0.515900	−	3.58816i	0.230717	−	1.60467i	−0.464298	−	0.885679i	$-0.653693\pi$
$5$	0.515900	−	3.58816i	0.230717	−	1.60467i	0.695015	−	0.718995i	$-0.255398\pi$
$6$	0.841254	−	0.540641i	0.343440	−	0.220716i
$7$	0.415415	+	0.909632i	0.157012	+	0.343809i
$7$	0.415415	+	0.909632i	0.157012	+	0.343809i
$8$	0.654861	+	0.755750i	0.231528	+	0.267198i
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$	1.50590	−	3.29747i	0.476209	−	1.04275i
$11$	2.78520	−	0.817809i	0.839769	−	0.246579i	0.166561	−	0.986031i	$-0.446734\pi$
$11$	2.78520	−	0.817809i	0.839769	−	0.246579i	0.673209	+	0.739453i	$0.264916\pi$
$12$	0.959493	−	0.281733i	0.276982	−	0.0813292i
$13$	0.667629	−	1.46190i	0.185167	−	0.405459i	−0.794170	−	0.607696i	$-0.792094\pi$
$13$	0.667629	−	1.46190i	0.185167	−	0.405459i	0.979337	+	0.202237i	$0.0648212\pi$
$14$	0.142315	+	0.989821i	0.0380352	+	0.264541i
$15$	−2.37391	−	2.73964i	−0.612941	−	0.707371i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	−1.52682	+	0.981227i	−0.370308	+	0.237983i	−0.712538	−	0.701634i	$-0.752454\pi$
$17$	−1.52682	+	0.981227i	−0.370308	+	0.237983i	0.342230	+	0.939616i	$0.388818\pi$
$18$	0.142315	−	0.989821i	0.0335439	−	0.233303i
$19$	−2.70503	−	1.73842i	−0.620576	−	0.398820i	0.192234	−	0.981349i	$-0.438427\pi$
$19$	−2.70503	−	1.73842i	−0.620576	−	0.398820i	−0.812810	+	0.582529i	$0.802063\pi$
$20$	2.37391	−	2.73964i	0.530822	−	0.612601i
$21$	0.959493	+	0.281733i	0.209379	+	0.0614791i
$22$	2.90278			0.618875
$23$	−1.19715	+	4.64401i	−0.249623	+	0.968343i
$23$	−1.19715	+	4.64401i	−0.249623	+	0.968343i
$24$	1.00000			0.204124
$25$	−7.81128	−	2.29360i	−1.56226	−	0.458720i
$26$	1.05245	−	1.21459i	0.206403	−	0.238201i
$27$	−0.841254	−	0.540641i	−0.161899	−	0.104046i
$28$	−0.142315	+	0.989821i	−0.0268950	+	0.187059i
$29$	2.64638	−	1.70073i	0.491421	−	0.315817i	−0.271355	−	0.962479i	$-0.587472\pi$
$29$	2.64638	−	1.70073i	0.491421	−	0.315817i	0.762777	+	0.646662i	$0.223836\pi$
$30$	−1.50590	−	3.29747i	−0.274939	−	0.602033i
$31$	−0.580435	−	0.669858i	−0.104249	−	0.120310i	0.701227	−	0.712938i	$-0.252636\pi$
$31$	−0.580435	−	0.669858i	−0.104249	−	0.120310i	−0.805476	+	0.592628i	$0.798090\pi$
$32$	0.142315	+	0.989821i	0.0251579	+	0.174977i
$33$	1.20586	−	2.64046i	0.209913	−	0.459646i
$34$	−1.74142	+	0.511326i	−0.298650	+	0.0876917i
$35$	3.47822	−	1.02130i	0.587926	−	0.172631i
$36$	0.415415	−	0.909632i	0.0692358	−	0.151605i
$37$	0.163573	+	1.13767i	0.0268912	+	0.187032i	0.998840	−	0.0481622i	$-0.0153364\pi$
$37$	0.163573	+	1.13767i	0.0268912	+	0.187032i	−0.971948	+	0.235194i	$0.924427\pi$
$38$	−2.10569	−	2.43009i	−0.341588	−	0.394213i
$39$	−0.667629	−	1.46190i	−0.106906	−	0.234092i
$40$	3.04959	−	1.95985i	0.482183	−	0.309880i
$41$	1.03984	−	7.23222i	0.162395	−	1.12948i	−0.731707	−	0.681619i	$-0.761276\pi$
$41$	1.03984	−	7.23222i	0.162395	−	1.12948i	0.894102	−	0.447863i	$-0.147815\pi$
$42$	0.841254	+	0.540641i	0.129808	+	0.0834227i
$43$	−2.21557	+	2.55691i	−0.337871	+	0.389924i	−0.899105	−	0.437733i	$-0.855781\pi$
$43$	−2.21557	+	2.55691i	−0.337871	+	0.389924i	0.561234	+	0.827657i	$0.310327\pi$
$44$	2.78520	+	0.817809i	0.419885	+	0.123289i
$45$	−3.62506			−0.540392
$46$	−2.45703	+	4.11862i	−0.362269	+	0.607257i
$47$	11.8235			1.72463			0.862317	−	0.506369i	$-0.169013\pi$
$47$	11.8235			1.72463			0.862317	+	0.506369i	$0.169013\pi$
$48$	0.959493	+	0.281733i	0.138491	+	0.0406646i
$49$	−0.654861	+	0.755750i	−0.0935515	+	0.107964i
$50$	−6.84869	−	4.40138i	−0.968551	−	0.622450i
$51$	−0.258292	+	1.79646i	−0.0361681	+	0.251555i
$52$	1.35201	−	0.868884i	0.187490	−	0.120493i
$53$	2.10629	+	4.61212i	0.289321	+	0.633524i	0.997357	−	0.0726517i	$-0.0231462\pi$
$53$	2.10629	+	4.61212i	0.289321	+	0.633524i	−0.708037	+	0.706176i	$0.750419\pi$
$54$	−0.654861	−	0.755750i	−0.0891153	−	0.102844i
$55$	−1.49754	−	10.4157i	−0.201929	−	1.40445i
$56$	−0.415415	+	0.909632i	−0.0555122	+	0.121555i
$57$	−3.08523	+	0.905904i	−0.408648	+	0.119990i
$58$	3.01834	−	0.886264i	0.396327	−	0.116372i
$59$	−2.54552	+	5.57391i	−0.331398	+	0.725661i	−0.999836	−	0.0181069i	$-0.994236\pi$
$59$	−2.54552	+	5.57391i	−0.331398	+	0.725661i	0.668438	+	0.743768i	$0.266963\pi$
$60$	−0.515900	−	3.58816i	−0.0666024	−	0.463230i
$61$	−5.84034	−	6.74011i	−0.747779	−	0.862983i	0.246572	−	0.969124i	$-0.420696\pi$
$61$	−5.84034	−	6.74011i	−0.747779	−	0.862983i	−0.994351	+	0.106142i	$0.966150\pi$
$62$	−0.368202	−	0.806251i	−0.0467618	−	0.102394i
$63$	0.841254	−	0.540641i	0.105988	−	0.0681143i
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	−4.90111	−	3.14975i	−0.607908	−	0.390679i
$66$	1.90092	−	2.19378i	0.233987	−	0.270035i
$67$	2.26193	+	0.664162i	0.276339	+	0.0811403i	0.416965	−	0.908922i	$-0.363094\pi$
$67$	2.26193	+	0.664162i	0.276339	+	0.0811403i	−0.140627	+	0.990063i	$0.544912\pi$
$68$	−1.81493			−0.220093
$69$	2.72574	+	3.94593i	0.328141	+	0.475034i
$70$	3.62506			0.433277
$71$	−1.22039	−	0.358338i	−0.144833	−	0.0425269i	0.208512	−	0.978020i	$-0.433138\pi$
$71$	−1.22039	−	0.358338i	−0.144833	−	0.0425269i	−0.353346	+	0.935493i	$0.614956\pi$
$72$	0.654861	−	0.755750i	0.0771761	−	0.0890659i
$73$	5.25460	+	3.37692i	0.615004	+	0.395239i	0.810731	−	0.585419i	$-0.199070\pi$
$73$	5.25460	+	3.37692i	0.615004	+	0.395239i	−0.195726	+	0.980659i	$0.562706\pi$
$74$	−0.163573	+	1.13767i	−0.0190149	+	0.132252i
$75$	−6.84869	+	4.40138i	−0.790818	+	0.508228i
$76$	−1.33576	−	2.92490i	−0.153222	−	0.335509i
$77$	1.90092	+	2.19378i	0.216630	+	0.250004i
$78$	−0.228719	−	1.59078i	−0.0258974	−	0.180120i
$79$	−3.96704	+	8.68660i	−0.446326	+	0.977318i	0.544067	+	0.839042i	$0.316884\pi$
$79$	−3.96704	+	8.68660i	−0.446326	+	0.977318i	−0.990394	+	0.138277i	$0.955844\pi$
$80$	3.47822	−	1.02130i	0.388877	−	0.114184i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	3.03527	−	6.64631i	0.335189	−	0.733962i
$83$	0.755588	+	5.25523i	0.0829365	+	0.576836i	0.988338	+	0.152279i	$0.0486612\pi$
$83$	0.755588	+	5.25523i	0.0829365	+	0.576836i	−0.905401	+	0.424557i	$0.860430\pi$
$84$	0.654861	+	0.755750i	0.0714512	+	0.0824590i
$85$	2.73311	+	5.98469i	0.296448	+	0.649130i
$86$	−2.84619	+	1.82913i	−0.306912	+	0.197241i
$87$	0.447689	−	3.11374i	0.0479973	−	0.333828i
$88$	2.44198	+	1.56936i	0.260316	+	0.167295i
$89$	−1.16313	+	1.34232i	−0.123291	+	0.142286i	−0.814039	−	0.580810i	$-0.802736\pi$
$89$	−1.16313	+	1.34232i	−0.123291	+	0.142286i	0.690748	+	0.723096i	$0.257281\pi$
$90$	−3.47822	−	1.02130i	−0.366636	−	0.107654i
$91$	1.60714			0.168474
$92$	−3.51785	+	3.25956i	−0.366761	+	0.339833i
$93$	−0.886349			−0.0919101
$94$	11.3446	+	3.33106i	1.17010	+	0.343573i
$95$	−7.63324	+	8.80923i	−0.783154	+	0.903808i
$96$	0.841254	+	0.540641i	0.0858601	+	0.0551789i
$97$	1.93592	−	13.4646i	0.196562	−	1.36712i	−0.617604	−	0.786489i	$-0.711896\pi$
$97$	1.93592	−	13.4646i	0.196562	−	1.36712i	0.814166	−	0.580632i	$-0.197194\pi$
$98$	−0.841254	+	0.540641i	−0.0849794	+	0.0546130i
$99$	−1.20586	−	2.64046i	−0.121193	−	0.265377i
$100$	−5.33125	−	6.15259i	−0.533125	−	0.615259i
$101$	1.25047	+	8.69720i	0.124426	+	0.865404i	0.952447	+	0.304706i	$0.0985581\pi$
$101$	1.25047	+	8.69720i	0.124426	+	0.865404i	−0.828020	+	0.560698i	$0.810533\pi$
$102$	−0.753951	+	1.65092i	−0.0746522	+	0.163466i
$103$	−7.80083	+	2.29053i	−0.768639	+	0.225693i	−0.642464	−	0.766315i	$-0.722088\pi$
$103$	−7.80083	+	2.29053i	−0.768639	+	0.225693i	−0.126174	+	0.992008i	$0.540270\pi$
$104$	1.54204	−	0.452783i	0.151209	−	0.0443990i
$105$	1.50590	−	3.29747i	0.146961	−	0.321800i
$106$	0.721582	+	5.01871i	0.0700862	+	0.487460i
$107$	10.9746	+	12.6653i	1.06095	+	1.22440i	0.973608	+	0.228226i	$0.0732926\pi$
$107$	10.9746	+	12.6653i	1.06095	+	1.22440i	0.0873444	+	0.996178i	$0.472162\pi$
$108$	−0.415415	−	0.909632i	−0.0399733	−	0.0875294i
$109$	−6.49236	+	4.17239i	−0.621856	+	0.399642i	−0.813286	−	0.581864i	$-0.802324\pi$
$109$	−6.49236	+	4.17239i	−0.621856	+	0.399642i	0.191431	+	0.981506i	$0.438687\pi$
$110$	1.49754	−	10.4157i	0.142785	−	0.993094i
$111$	0.966913	+	0.621397i	0.0917753	+	0.0589804i
$112$	−0.654861	+	0.755750i	−0.0618785	+	0.0714116i
$113$	9.67233	+	2.84005i	0.909896	+	0.267170i	0.702997	−	0.711193i	$-0.251845\pi$
$113$	9.67233	+	2.84005i	0.909896	+	0.267170i	0.206899	+	0.978362i	$0.433663\pi$
$114$	−3.21548			−0.301157
$115$	16.0458	+	6.69141i	1.49628	+	0.623977i
$116$	3.14576			0.292077
$117$	−1.54204	−	0.452783i	−0.142561	−	0.0418598i
$118$	−4.01276	+	4.63097i	−0.369404	+	0.426315i
$119$	−1.52682	−	0.981227i	−0.139963	−	0.0899489i
$120$	0.515900	−	3.58816i	0.0470950	−	0.327553i
$121$	−2.16526	+	1.39153i	−0.196842	+	0.126503i
$122$	−3.70486	−	8.11250i	−0.335422	−	0.734472i
$123$	−4.78480	−	5.52195i	−0.431431	−	0.497898i
$124$	−0.126141	−	0.877327i	−0.0113278	−	0.0787863i
$125$	−4.73012	+	10.3575i	−0.423075	+	0.926404i
$126$	0.959493	−	0.281733i	0.0854784	−	0.0250987i
$127$	19.4221	−	5.70285i	1.72344	−	0.506046i	0.737812	−	0.675006i	$-0.235859\pi$
$127$	19.4221	−	5.70285i	1.72344	−	0.506046i	0.985623	+	0.168960i	$0.0540407\pi$
$128$	−0.415415	+	0.909632i	−0.0367178	+	0.0804009i
$129$	0.481490	+	3.34883i	0.0423928	+	0.294848i
$130$	−3.81520	−	4.40297i	−0.334615	−	0.386166i
$131$	5.65894	+	12.3913i	0.494424	+	1.08264i	0.978242	+	0.207468i	$0.0665223\pi$
$131$	5.65894	+	12.3913i	0.494424	+	1.08264i	−0.483818	+	0.875169i	$0.660750\pi$
$132$	2.44198	−	1.56936i	0.212547	−	0.136596i
$133$	0.457610	−	3.18275i	0.0396798	−	0.275979i
$134$	1.98319	+	1.27452i	0.171321	+	0.110102i
$135$	−2.37391	+	2.73964i	−0.204314	+	0.235790i
$136$	−1.74142	−	0.511326i	−0.149325	−	0.0438458i
$137$	−17.4875			−1.49406			−0.747030	−	0.664790i	$-0.768521\pi$
$137$	−17.4875			−1.49406			−0.747030	+	0.664790i	$0.768521\pi$
$138$	1.50363	+	4.55402i	0.127998	+	0.387664i
$139$	15.9171			1.35007			0.675034	−	0.737787i	$-0.264129\pi$
$139$	15.9171			1.35007			0.675034	+	0.737787i	$0.264129\pi$
$140$	3.47822	+	1.02130i	0.293963	+	0.0863154i
$141$	7.74274	−	8.93560i	0.652056	−	0.752513i
$142$	−1.07000	−	0.687645i	−0.0897922	−	0.0577059i
$143$	0.663923	−	4.61769i	0.0555200	−	0.386150i
$144$	0.841254	−	0.540641i	0.0701045	−	0.0450534i
$145$	−4.73722	−	10.3731i	−0.393404	−	0.861436i
$146$	4.09036	+	4.72053i	0.338521	+	0.390674i
$147$	0.142315	+	0.989821i	0.0117379	+	0.0816391i
$148$	−0.477466	+	1.04550i	−0.0392475	+	0.0859400i
$149$	−15.4366	+	4.53259i	−1.26462	+	0.371325i	−0.844210	−	0.536012i	$-0.819930\pi$
$149$	−15.4366	+	4.53259i	−1.26462	+	0.371325i	−0.420405	+	0.907337i	$0.638112\pi$
$150$	−7.81128	+	2.29360i	−0.637788	+	0.187272i
$151$	5.80471	−	12.7105i	0.472381	−	1.03437i	−0.512108	−	0.858921i	$-0.671135\pi$
$151$	5.80471	−	12.7105i	0.472381	−	1.03437i	0.984489	−	0.175448i	$-0.0561375\pi$
$152$	−0.457610	−	3.18275i	−0.0371171	−	0.258155i
$153$	1.18853	+	1.37164i	0.0960868	+	0.110890i
$154$	1.20586	+	2.64046i	0.0971710	+	0.212775i
$155$	−2.70300	+	1.73711i	−0.217110	+	0.139528i
$156$	0.228719	−	1.59078i	0.0183122	−	0.127364i
$157$	16.2289	+	10.4297i	1.29521	+	0.832382i	0.992682	−	0.120759i	$-0.0385327\pi$
$157$	16.2289	+	10.4297i	1.29521	+	0.832382i	0.302529	+	0.953140i	$0.402169\pi$
$158$	−6.25364	+	7.21708i	−0.497513	+	0.574160i
$159$	4.86493	+	1.42847i	0.385814	+	0.113285i
$160$	3.62506			0.286586
$161$	−4.72165	+	0.840225i	−0.372119	+	0.0662190i
$162$	−1.00000			−0.0785674
$163$	−13.2703	−	3.89650i	−1.03941	−	0.305197i	−0.282876	−	0.959156i	$-0.591289\pi$
$163$	−13.2703	−	3.89650i	−1.03941	−	0.305197i	−0.756530	+	0.653959i	$0.773107\pi$
$164$	4.78480	−	5.52195i	0.373630	−	0.431192i
$165$	−8.85231	−	5.68903i	−0.689151	−	0.442891i
$166$	−0.755588	+	5.25523i	−0.0586450	+	0.407885i
$167$	−13.9207	+	8.94628i	−1.07722	+	0.692284i	−0.953912	−	0.300085i	$-0.902985\pi$
$167$	−13.9207	+	8.94628i	−1.07722	+	0.692284i	−0.123303	+	0.992369i	$0.539349\pi$
$168$	0.415415	+	0.909632i	0.0320500	+	0.0701796i
$169$	6.82176	+	7.87273i	0.524751	+	0.605594i
$170$	0.936323	+	6.51227i	0.0718127	+	0.499469i
$171$	−1.33576	+	2.92490i	−0.102148	+	0.223673i
$172$	−3.24622	+	0.953177i	−0.247522	+	0.0726791i
$173$	−6.79932	+	1.99646i	−0.516943	+	0.151788i	−0.529789	−	0.848129i	$-0.677729\pi$
$173$	−6.79932	+	1.99646i	−0.516943	+	0.151788i	0.0128463	+	0.999917i	$0.495911\pi$
$174$	1.30680	−	2.86149i	0.0990681	−	0.216929i
$175$	−1.15859	−	8.05819i	−0.0875813	−	0.609142i
$176$	1.90092	+	2.19378i	0.143287	+	0.165362i
$177$	2.54552	+	5.57391i	0.191333	+	0.418961i
$178$	−1.49419	+	0.960256i	−0.111994	+	0.0719743i
$179$	−1.35907	+	9.45254i	−0.101582	+	0.706516i	0.873847	+	0.486201i	$0.161618\pi$
$179$	−1.35907	+	9.45254i	−0.101582	+	0.706516i	−0.975429	+	0.220315i	$0.929291\pi$
$180$	−3.04959	−	1.95985i	−0.227303	−	0.146079i
$181$	−14.6544	+	16.9120i	−1.08925	+	1.25706i	−0.124974	+	0.992160i	$0.539885\pi$
$181$	−14.6544	+	16.9120i	−1.08925	+	1.25706i	−0.964276	+	0.264901i	$0.914661\pi$
$182$	1.54204	+	0.452783i	0.114303	+	0.0335625i
$183$	−8.91845			−0.659271
$184$	−4.29368	+	2.13643i	−0.316534	+	0.157500i
$185$	4.16654			0.306330
$186$	−0.850445	−	0.249713i	−0.0623577	−	0.0183099i
$187$	−3.45004	+	3.98156i	−0.252292	+	0.291160i
$188$	9.94655	+	6.39226i	0.725427	+	0.466204i
$189$	0.142315	−	0.989821i	0.0103519	−	0.0719989i
$190$	−9.80589	+	6.30186i	−0.711394	+	0.457185i
$191$	−7.45324	−	16.3203i	−0.539298	−	1.18090i	−0.961603	−	0.274443i	$-0.911506\pi$
$191$	−7.45324	−	16.3203i	−0.539298	−	1.18090i	0.422306	−	0.906453i	$-0.361221\pi$
$192$	0.654861	+	0.755750i	0.0472605	+	0.0545415i
$193$	−0.0990489	−	0.688900i	−0.00712970	−	0.0495881i	0.985946	−	0.167064i	$-0.0534287\pi$
$193$	−0.0990489	−	0.688900i	−0.00712970	−	0.0495881i	−0.993076	+	0.117476i	$0.962520\pi$
$194$	5.65091	−	12.3738i	0.405712	−	0.888385i
$195$	−5.58997	+	1.64136i	−0.400306	+	0.117541i
$196$	−0.959493	+	0.281733i	−0.0685352	+	0.0201238i
$197$	−1.88039	+	4.11747i	−0.133972	+	0.293358i	−0.964714	−	0.263300i	$-0.915189\pi$
$197$	−1.88039	+	4.11747i	−0.133972	+	0.293358i	0.830742	+	0.556658i	$0.187916\pi$
$198$	−0.413109	−	2.87324i	−0.0293584	−	0.204192i
$199$	−11.3826	−	13.1362i	−0.806889	−	0.931199i	0.191849	−	0.981424i	$-0.438551\pi$
$199$	−11.3826	−	13.1362i	−0.806889	−	0.931199i	−0.998738	+	0.0502254i	$0.984006\pi$
$200$	−3.38191	−	7.40536i	−0.239137	−	0.523638i
$201$	1.98319	−	1.27452i	0.139883	−	0.0898976i
$202$	−1.25047	+	8.69720i	−0.0879827	+	0.611933i
$203$	2.64638	+	1.70073i	0.185740	+	0.119368i
$204$	−1.18853	+	1.37164i	−0.0832136	+	0.0960337i
$205$	−25.4139	−	7.46220i	−1.77498	−	0.521183i
$206$	−8.13016			−0.566455
$207$	4.76711	+	0.524054i	0.331337	+	0.0364243i
$208$	1.60714			0.111435
$209$	−8.95574	−	2.62964i	−0.619482	−	0.181896i
$210$	2.37391	−	2.73964i	0.163815	−	0.189053i
$211$	−2.47952	−	1.59349i	−0.170697	−	0.109700i	0.452503	−	0.891763i	$-0.350531\pi$
$211$	−2.47952	−	1.59349i	−0.170697	−	0.109700i	−0.623200	+	0.782063i	$0.714168\pi$
$212$	−0.721582	+	5.01871i	−0.0495584	+	0.344686i
$213$	−1.07000	+	0.687645i	−0.0733150	+	0.0471167i
$214$	6.96179	+	15.2442i	0.475898	+	1.04207i
$215$	8.03157	+	9.26893i	0.547749	+	0.632136i
$216$	−0.142315	−	0.989821i	−0.00968330	−	0.0673488i
$217$	0.368202	−	0.806251i	0.0249952	−	0.0547319i
$218$	−7.40487	+	2.17427i	−0.501521	+	0.147260i
$219$	5.99314	−	1.75974i	0.404979	−	0.118913i
$220$	4.37131	−	9.57184i	0.294714	−	0.645333i
$221$	0.415111	+	2.88716i	0.0279234	+	0.194211i
$222$	0.752678	+	0.868637i	0.0505165	+	0.0582991i
$223$	−7.92971	−	17.3636i	−0.531012	−	1.16276i	−0.965099	−	0.261884i	$-0.915656\pi$
$223$	−7.92971	−	17.3636i	−0.531012	−	1.16276i	0.434087	−	0.900871i	$-0.357071\pi$
$224$	−0.841254	+	0.540641i	−0.0562086	+	0.0361231i
$225$	−1.15859	+	8.05819i	−0.0772395	+	0.537212i
$226$	8.48040	+	5.45002i	0.564108	+	0.362530i
$227$	9.95398	−	11.4875i	0.660669	−	0.762453i	−0.322217	−	0.946666i	$-0.604428\pi$
$227$	9.95398	−	11.4875i	0.660669	−	0.762453i	0.982886	+	0.184213i	$0.0589736\pi$
$228$	−3.08523	−	0.905904i	−0.204324	−	0.0599950i
$229$	−19.7611			−1.30585			−0.652924	−	0.757424i	$-0.726458\pi$
$229$	−19.7611			−1.30585			−0.652924	+	0.757424i	$0.726458\pi$
$230$	13.5107	+	10.9410i	0.890868	+	0.721428i
$231$	2.90278			0.190989
$232$	3.01834	+	0.886264i	0.198164	+	0.0581861i
$233$	1.87462	−	2.16342i	0.122810	−	0.141731i	−0.691015	−	0.722841i	$-0.742836\pi$
$233$	1.87462	−	2.16342i	0.122810	−	0.141731i	0.813825	+	0.581110i	$0.197381\pi$
$234$	−1.35201	−	0.868884i	−0.0883836	−	0.0568007i
$235$	6.09973	−	42.4246i	0.397903	−	2.76747i
$236$	−5.15491	+	3.31286i	−0.335556	+	0.215649i
$237$	3.96704	+	8.68660i	0.257687	+	0.564255i
$238$	−1.18853	−	1.37164i	−0.0770409	−	0.0889099i
$239$	1.79786	+	12.5044i	0.116294	+	0.808842i	0.961579	+	0.274527i	$0.0885213\pi$
$239$	1.79786	+	12.5044i	0.116294	+	0.808842i	−0.845285	+	0.534315i	$0.820570\pi$
$240$	1.50590	−	3.29747i	0.0972057	−	0.212851i
$241$	8.60854	−	2.52770i	0.554525	−	0.162823i	0.00754893	−	0.999972i	$-0.497597\pi$
$241$	8.60854	−	2.52770i	0.554525	−	0.162823i	0.546976	+	0.837148i	$0.315779\pi$
$242$	−2.46959	+	0.725137i	−0.158751	+	0.0466136i
$243$	−0.415415	+	0.909632i	−0.0266489	+	0.0583529i
$244$	−1.26923	−	8.82767i	−0.0812540	−	0.565134i
$245$	2.37391	+	2.73964i	0.151663	+	0.175029i
$246$	−3.03527	−	6.64631i	−0.193522	−	0.423753i
$247$	−4.34735	+	2.79387i	−0.276615	+	0.177770i
$248$	0.126141	−	0.877327i	0.00800993	−	0.0557103i
$249$	4.46644	+	2.87041i	0.283049	+	0.181905i
$250$	−7.45656	+	8.60533i	−0.471595	+	0.544249i
$251$	22.1126	+	6.49284i	1.39573	+	0.409825i	0.891217	−	0.453577i	$-0.149852\pi$
$251$	22.1126	+	6.49284i	1.39573	+	0.409825i	0.504517	+	0.863402i	$0.331670\pi$
$252$	1.00000			0.0629941
$253$	0.463607	+	13.9135i	0.0291467	+	0.874737i
$254$	20.2421			1.27010
$255$	6.31273	+	1.85359i	0.395319	+	0.116076i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	9.90524	+	6.36571i	0.617872	+	0.397082i	0.811802	−	0.583933i	$-0.198487\pi$
$257$	9.90524	+	6.36571i	0.617872	+	0.397082i	−0.193930	+	0.981015i	$0.562123\pi$
$258$	−0.481490	+	3.34883i	−0.0299762	+	0.208489i
$259$	−0.966913	+	0.621397i	−0.0600810	+	0.0386117i
$260$	−2.42019	−	5.29948i	−0.150094	−	0.328660i
$261$	−2.06004	−	2.37741i	−0.127513	−	0.147158i
$262$	1.93867	+	13.4837i	0.119771	+	0.833027i
$263$	6.77805	−	14.8419i	0.417952	−	0.915188i	−0.577178	−	0.816619i	$-0.695846\pi$
$263$	6.77805	−	14.8419i	0.417952	−	0.915188i	0.995130	−	0.0985695i	$-0.0314267\pi$
$264$	2.78520	−	0.817809i	0.171417	−	0.0503326i
$265$	17.6357	−	5.17830i	1.08335	−	0.318100i
$266$	1.33576	−	2.92490i	0.0819005	−	0.179337i
$267$	0.252772	+	1.75807i	0.0154694	+	0.107592i
$268$	1.54378	+	1.78162i	0.0943015	+	0.108830i
$269$	10.1740	+	22.2778i	0.620317	+	1.35830i	0.915289	+	0.402798i	$0.131962\pi$
$269$	10.1740	+	22.2778i	0.620317	+	1.35830i	−0.294972	+	0.955506i	$0.595310\pi$
$270$	−3.04959	+	1.95985i	−0.185592	+	0.119273i
$271$	−3.47737	+	24.1856i	−0.211235	+	1.46917i	0.557805	+	0.829972i	$0.311644\pi$
$271$	−3.47737	+	24.1856i	−0.211235	+	1.46917i	−0.769040	+	0.639200i	$0.779265\pi$
$272$	−1.52682	−	0.981227i	−0.0925770	−	0.0594956i
$273$	1.05245	−	1.21459i	0.0636972	−	0.0735105i
$274$	−16.7792	−	4.92680i	−1.01367	−	0.297639i
$275$	−23.6317			−1.42505
$276$	0.159711	+	4.79317i	0.00961349	+	0.288515i
$277$	−11.7434			−0.705590			−0.352795	−	0.935701i	$-0.614769\pi$
$277$	−11.7434			−0.705590			−0.352795	+	0.935701i	$0.614769\pi$
$278$	15.2723	+	4.48435i	0.915972	+	0.268954i
$279$	−0.580435	+	0.669858i	−0.0347497	+	0.0401033i
$280$	3.04959	+	1.95985i	0.182248	+	0.117124i
$281$	2.70439	−	18.8094i	0.161330	−	1.12208i	−0.734800	−	0.678284i	$-0.762724\pi$
$281$	2.70439	−	18.8094i	0.161330	−	1.12208i	0.896130	−	0.443792i	$-0.146367\pi$
$282$	9.94655	−	6.39226i	0.592309	−	0.380654i
$283$	−1.44866	−	3.17211i	−0.0861136	−	0.188562i	0.861676	−	0.507459i	$-0.169415\pi$
$283$	−1.44866	−	3.17211i	−0.0861136	−	0.188562i	−0.947790	+	0.318896i	$0.896688\pi$
$284$	−0.832923	−	0.961244i	−0.0494249	−	0.0570393i
$285$	1.65886	+	11.5376i	0.0982625	+	0.683431i
$286$	1.93798	−	4.24359i	0.114595	−	0.250929i
$287$	7.01062	−	2.05850i	0.413824	−	0.121510i
$288$	0.959493	−	0.281733i	0.0565387	−	0.0166013i
$289$	−5.69369	+	12.4674i	−0.334923	+	0.733378i
$290$	−1.62290	−	11.2875i	−0.0952999	−	0.662825i
$291$	−8.90810	−	10.2805i	−0.522202	−	0.602653i
$292$	2.59475	+	5.68170i	0.151846	+	0.332496i
$293$	−10.0169	+	6.43744i	−0.585191	+	0.376080i	−0.799482	−	0.600690i	$-0.794892\pi$
$293$	−10.0169	+	6.43744i	−0.585191	+	0.376080i	0.214291	+	0.976770i	$0.431256\pi$
$294$	−0.142315	+	0.989821i	−0.00829997	+	0.0577276i
$295$	18.6869	+	12.0093i	1.08799	+	0.699209i
$296$	−0.752678	+	0.868637i	−0.0437485	+	0.0504885i
$297$	−2.78520	−	0.817809i	−0.161614	−	0.0474541i
$298$	−16.0883			−0.931970
$299$	5.98984	+	4.85059i	0.346401	+	0.280517i
$300$	−8.14105			−0.470024
$301$	−3.24622	−	0.953177i	−0.187109	−	0.0549402i
$302$	9.15055	−	10.5603i	0.526555	−	0.607677i
$303$	7.39179	+	4.75041i	0.424647	+	0.272904i
$304$	0.457610	−	3.18275i	0.0262457	−	0.182543i
$305$	−27.1976	+	17.4789i	−1.55733	+	1.00084i
$306$	0.753951	+	1.65092i	0.0431005	+	0.0943769i
$307$	−12.6421	−	14.5898i	−0.721523	−	0.832682i	0.269966	−	0.962870i	$-0.412987\pi$
$307$	−12.6421	−	14.5898i	−0.721523	−	0.832682i	−0.991489	+	0.130188i	$0.958442\pi$
$308$	0.413109	+	2.87324i	0.0235391	+	0.163718i
$309$	−3.37739	+	7.39545i	−0.192133	+	0.420713i
$310$	−3.08291	+	0.905225i	−0.175098	+	0.0514133i
$311$	22.7367	−	6.67609i	1.28928	−	0.378566i	0.435965	−	0.899964i	$-0.356407\pi$
$311$	22.7367	−	6.67609i	1.28928	−	0.378566i	0.853314	+	0.521397i	$0.174589\pi$
$312$	0.667629	−	1.46190i	0.0377970	−	0.0827640i
$313$	−0.915990	−	6.37085i	−0.0517748	−	0.360102i	−0.999195	−	0.0401104i	$-0.987229\pi$
$313$	−0.915990	−	6.37085i	−0.0517748	−	0.360102i	0.947420	−	0.319992i	$-0.103680\pi$
$314$	12.6332	+	14.5795i	0.712931	+	0.822766i
$315$	−1.50590	−	3.29747i	−0.0848481	−	0.185791i
$316$	−8.03361	+	5.16289i	−0.451926	+	0.290435i
$317$	2.41566	−	16.8013i	0.135677	−	0.943652i	−0.802292	−	0.596932i	$-0.796386\pi$
$317$	2.41566	−	16.8013i	0.135677	−	0.943652i	0.937969	−	0.346720i	$-0.112705\pi$
$318$	4.26542	+	2.74122i	0.239193	+	0.153720i
$319$	5.97984	−	6.90110i	0.334807	−	0.386388i
$320$	3.47822	+	1.02130i	0.194438	+	0.0570922i
$321$	16.7586			0.935376
$322$	−4.76711	−	0.524054i	−0.265661	−	0.0292044i
$323$	5.83587			0.324717
$324$	−0.959493	−	0.281733i	−0.0533052	−	0.0156518i
$325$	−8.56805	+	9.88806i	−0.475270	+	0.548491i
$326$	−11.6349	−	7.47732i	−0.644400	−	0.414131i
$327$	−1.09831	+	7.63893i	−0.0607368	+	0.422434i
$328$	6.14669	−	3.95024i	0.339394	−	0.218116i
$329$	4.91166	+	10.7550i	0.270788	+	0.592944i
$330$	−6.89094	−	7.95257i	−0.379334	−	0.437775i
$331$	−3.39812	−	23.6344i	−0.186777	−	1.29907i	−0.840285	−	0.542146i	$-0.817612\pi$
$331$	−3.39812	−	23.6344i	−0.186777	−	1.29907i	0.653507	−	0.756920i	$-0.273297\pi$
$332$	−2.20555	+	4.82948i	−0.121045	+	0.265052i
$333$	1.10281	−	0.323815i	0.0604338	−	0.0177450i
$334$	−15.8773	+	4.66198i	−0.868765	+	0.255092i
$335$	3.55005	−	7.77352i	0.193960	−	0.424713i
$336$	0.142315	+	0.989821i	0.00776391	+	0.0539992i
$337$	6.78332	+	7.82837i	0.369511	+	0.426438i	0.909804	−	0.415039i	$-0.136232\pi$
$337$	6.78332	+	7.82837i	0.369511	+	0.426438i	−0.540293	+	0.841477i	$0.681687\pi$
$338$	4.32742	+	9.47574i	0.235381	+	0.515412i
$339$	8.48040	−	5.45002i	0.460592	−	0.296004i
$340$	−0.936323	+	6.51227i	−0.0507793	+	0.353178i
$341$	−2.16444	−	1.39100i	−0.117211	−	0.0753270i
$342$	−2.10569	+	2.43009i	−0.113863	+	0.131404i
$343$	−0.959493	−	0.281733i	−0.0518078	−	0.0152121i
$344$	−3.38327			−0.182414
$345$	15.5648	−	7.74470i	0.837982	−	0.416961i
$346$	−7.08637			−0.380966
$347$	7.05089	+	2.07033i	0.378512	+	0.111141i	0.465453	−	0.885072i	$-0.345891\pi$
$347$	7.05089	+	2.07033i	0.378512	+	0.111141i	−0.0869418	+	0.996213i	$0.527709\pi$
$348$	2.06004	−	2.37741i	0.110430	−	0.127443i
$349$	−3.67066	−	2.35899i	−0.196486	−	0.126274i	0.438699	−	0.898634i	$-0.355440\pi$
$349$	−3.67066	−	2.35899i	−0.196486	−	0.126274i	−0.635184	+	0.772360i	$0.719076\pi$
$350$	1.15859	−	8.05819i	0.0619294	−	0.430728i
$351$	−1.35201	+	0.868884i	−0.0721649	+	0.0463776i
$352$	1.20586	+	2.64046i	0.0642725	+	0.140737i
$353$	−2.40901	−	2.78015i	−0.128219	−	0.147972i	0.688010	−	0.725701i	$-0.258485\pi$
$353$	−2.40901	−	2.78015i	−0.128219	−	0.147972i	−0.816229	+	0.577729i	$0.803939\pi$
$354$	0.872056	+	6.06528i	0.0463493	+	0.322366i
$355$	−1.91537	+	4.19408i	−0.101657	+	0.222599i
$356$	−1.70420	+	0.500398i	−0.0903223	+	0.0265210i
$357$	−1.74142	+	0.511326i	−0.0921655	+	0.0270622i
$358$	−3.96711	+	8.68675i	−0.209668	+	0.459109i
$359$	−3.26004	−	22.6741i	−0.172058	−	1.19669i	−0.874527	−	0.484978i	$-0.838828\pi$
$359$	−3.26004	−	22.6741i	−0.172058	−	1.19669i	0.702468	−	0.711715i	$-0.252081\pi$
$360$	−2.37391	−	2.73964i	−0.125116	−	0.144392i
$361$	−3.59779	−	7.87807i	−0.189357	−	0.414635i
$362$	−18.8254	+	12.0984i	−0.989442	+	0.635876i
$363$	−0.366297	+	2.54765i	−0.0192256	+	0.133717i
$364$	1.35201	+	0.868884i	0.0708646	+	0.0455419i
$365$	14.8278	−	17.1122i	0.776122	−	0.895693i
$366$	−8.55719	−	2.51262i	−0.447291	−	0.131337i
$367$	−9.51987			−0.496933			−0.248467	−	0.968640i	$-0.579927\pi$
$367$	−9.51987			−0.496933			−0.248467	+	0.968640i	$0.579927\pi$
$368$	−4.72165	+	0.840225i	−0.246133	+	0.0437998i
$369$	−7.30659			−0.380366
$370$	3.99776	+	1.17385i	0.207834	+	0.0610255i
$371$	−3.32035	+	3.83189i	−0.172384	+	0.198942i
$372$	−0.745644	−	0.479196i	−0.0386598	−	0.0248452i
$373$	0.629718	−	4.37978i	0.0326055	−	0.226777i	−0.967003	−	0.254766i	$-0.918001\pi$
$373$	0.629718	−	4.37978i	0.0326055	−	0.226777i	0.999608	+	0.0279897i	$0.00891057\pi$
$374$	−4.43203	+	2.84829i	−0.229175	+	0.147282i
$375$	4.73012	+	10.3575i	0.244262	+	0.534860i
$376$	7.74274	+	8.93560i	0.399301	+	0.460818i
$377$	−0.719497	−	5.00421i	−0.0370560	−	0.257730i
$378$	0.415415	−	0.909632i	0.0213666	−	0.0467864i
$379$	7.36767	−	2.16334i	0.378452	−	0.111123i	−0.0869735	−	0.996211i	$-0.527720\pi$
$379$	7.36767	−	2.16334i	0.378452	−	0.111123i	0.465425	+	0.885087i	$0.345901\pi$
$380$	−11.1841	+	3.28396i	−0.573733	+	0.168463i
$381$	8.40886	−	18.4128i	0.430799	−	0.943318i
$382$	−2.55337	−	17.7591i	−0.130642	−	0.908632i
$383$	−16.3847	−	18.9089i	−0.837218	−	0.966201i	0.162572	−	0.986697i	$-0.448021\pi$
$383$	−16.3847	−	18.9089i	−0.837218	−	0.966201i	−0.999790	+	0.0204960i	$0.993475\pi$
$384$	0.415415	+	0.909632i	0.0211991	+	0.0464195i
$385$	8.85231	−	5.68903i	0.451155	−	0.289940i
$386$	0.0990489	−	0.688900i	0.00504146	−	0.0350641i
$387$	2.84619	+	1.82913i	0.144680	+	0.0929801i
$388$	8.90810	−	10.2805i	0.452240	−	0.521913i
$389$	−34.7718	−	10.2099i	−1.76300	−	0.517663i	−0.770237	−	0.637758i	$-0.779862\pi$
$389$	−34.7718	−	10.2099i	−1.76300	−	0.517663i	−0.992762	+	0.120095i	$0.961680\pi$
$390$	−5.82597			−0.295009
$391$	−2.72900	−	8.26524i	−0.138011	−	0.417991i
$392$	−1.00000			−0.0505076
$393$	13.0706	+	3.83786i	0.659323	+	0.193595i
$394$	−2.96425	+	3.42092i	−0.149337	+	0.172344i
$395$	29.1223	+	18.7158i	1.46530	+	0.941693i
$396$	0.413109	−	2.87324i	0.0207595	−	0.144386i
$397$	−15.7999	+	10.1539i	−0.792972	+	0.509612i	−0.873315	−	0.487155i	$-0.838035\pi$
$397$	−15.7999	+	10.1539i	−0.792972	+	0.509612i	0.0803436	+	0.996767i	$0.474398\pi$
$398$	−7.22060	−	15.8109i	−0.361936	−	0.792529i
$399$	−2.10569	−	2.43009i	−0.105416	−	0.121657i
$400$	−1.15859	−	8.05819i	−0.0579296	−	0.402909i
$401$	−13.8125	+	30.2451i	−0.689762	+	1.51037i	0.162197	+	0.986758i	$0.448142\pi$
$401$	−13.8125	+	30.2451i	−0.689762	+	1.51037i	−0.851959	+	0.523609i	$0.824585\pi$
$402$	2.26193	−	0.664162i	0.112815	−	0.0331254i
$403$	−1.36678	+	0.401323i	−0.0680843	+	0.0199913i
$404$	−3.65010	+	7.99260i	−0.181599	+	0.397647i
$405$	0.515900	+	3.58816i	0.0256353	+	0.178297i
$406$	2.06004	+	2.37741i	0.102238	+	0.117989i
$407$	1.38598	+	3.03487i	0.0687005	+	0.150433i
$408$	−1.52682	+	0.981227i	−0.0755888	+	0.0485780i
$409$	1.56903	−	10.9129i	0.0775836	−	0.539606i	−0.913549	−	0.406729i	$-0.866669\pi$
$409$	1.56903	−	10.9129i	0.0775836	−	0.539606i	0.991133	−	0.132877i	$-0.0424215\pi$
$410$	−22.2821	−	14.3199i	−1.10044	−	0.707207i
$411$	−11.4519	+	13.2162i	−0.564880	+	0.651906i
$412$	−7.80083	−	2.29053i	−0.384319	−	0.112846i
$413$	−6.12765			−0.301522
$414$	4.42637	+	1.84588i	0.217544	+	0.0907199i
$415$	19.2464			0.944769
$416$	1.54204	+	0.452783i	0.0756046	+	0.0221995i
$417$	10.4235	−	12.0293i	0.510439	−	0.589078i
$418$	−7.85212	−	5.04625i	−0.384060	−	0.246820i
$419$	−0.306044	+	2.12858i	−0.0149512	+	0.103988i	−0.995931	−	0.0901244i	$-0.971274\pi$
$419$	−0.306044	+	2.12858i	−0.0149512	+	0.103988i	0.980979	+	0.194112i	$0.0621826\pi$
$420$	3.04959	−	1.95985i	0.148805	−	0.0956311i
$421$	−1.63211	−	3.57383i	−0.0795444	−	0.174178i	0.865681	−	0.500596i	$-0.166886\pi$
$421$	−1.63211	−	3.57383i	−0.0795444	−	0.174178i	−0.945226	+	0.326418i	$0.894158\pi$
$422$	−1.93014	−	2.22751i	−0.0939580	−	0.108433i
$423$	−1.68266	−	11.7031i	−0.0818136	−	0.569026i
$424$	−2.10629	+	4.61212i	−0.102290	+	0.223985i
$425$	14.1770	−	4.16273i	0.687683	−	0.201922i
$426$	−1.22039	+	0.358338i	−0.0591279	+	0.0173615i
$427$	3.70486	−	8.11250i	0.179291	−	0.392592i
$428$	2.38500	+	16.5881i	0.115284	+	0.801814i
$429$	−3.05504	−	3.52570i	−0.147499	−	0.170222i
$430$	5.09488	+	11.1562i	0.245697	+	0.538001i
$431$	−14.1811	+	9.11367i	−0.683082	+	0.438990i	−0.835620	−	0.549307i	$-0.814892\pi$
$431$	−14.1811	+	9.11367i	−0.683082	+	0.438990i	0.152538	+	0.988298i	$0.451255\pi$
$432$	0.142315	−	0.989821i	0.00684713	−	0.0476228i
$433$	2.83547	+	1.82224i	0.136264	+	0.0875715i	0.606997	−	0.794704i	$-0.292374\pi$
$433$	2.83547	+	1.82224i	0.136264	+	0.0875715i	−0.470733	+	0.882276i	$0.656010\pi$
$434$	0.580435	−	0.669858i	0.0278618	−	0.0321542i
$435$	−10.9417	−	3.21276i	−0.524612	−	0.154040i
$436$	−7.71749			−0.369601
$437$	11.3116	−	10.4810i	0.541105	−	0.501376i
$438$	6.24615			0.298453
$439$	−18.9025	−	5.55029i	−0.902169	−	0.264901i	−0.202428	−	0.979297i	$-0.564883\pi$
$439$	−18.9025	−	5.55029i	−0.902169	−	0.264901i	−0.699741	+	0.714397i	$0.746701\pi$
$440$	6.89094	−	7.95257i	0.328513	−	0.379124i
$441$	0.841254	+	0.540641i	0.0400597	+	0.0257448i
$442$	−0.415111	+	2.88716i	−0.0197448	+	0.137328i
$443$	14.2191	−	9.13809i	0.675572	−	0.434164i	−0.157358	−	0.987542i	$-0.550298\pi$
$443$	14.2191	−	9.13809i	0.675572	−	0.434164i	0.832930	+	0.553378i	$0.186661\pi$
$444$	0.477466	+	1.04550i	0.0226595	+	0.0496175i
$445$	4.21641	+	4.86599i	0.199877	+	0.230670i
$446$	−2.71660	−	18.8943i	−0.128635	−	0.894673i
$447$	−6.68332	+	14.6344i	−0.316110	+	0.692184i
$448$	−0.959493	+	0.281733i	−0.0453318	+	0.0133106i
$449$	17.6754	−	5.18996i	0.834153	−	0.244930i	0.163353	−	0.986568i	$-0.447769\pi$
$449$	17.6754	−	5.18996i	0.834153	−	0.244930i	0.670800	+	0.741638i	$0.265951\pi$
$450$	−3.38191	+	7.40536i	−0.159425	+	0.349092i
$451$	−3.01842	−	20.9936i	−0.142132	−	0.988548i
$452$	6.60143	+	7.61846i	0.310505	+	0.358342i
$453$	−5.80471	−	12.7105i	−0.272729	−	0.597194i
$454$	12.7872	−	8.21782i	0.600132	−	0.385681i
$455$	0.829121	−	5.76667i	0.0388698	−	0.270345i
$456$	−2.70503	−	1.73842i	−0.126675	−	0.0814088i
$457$	8.82606	−	10.1858i	0.412866	−	0.476472i	−0.510785	−	0.859709i	$-0.670645\pi$
$457$	8.82606	−	10.1858i	0.412866	−	0.476472i	0.923650	+	0.383236i	$0.125191\pi$
$458$	−18.9606	−	5.56733i	−0.885970	−	0.260144i
$459$	1.81493			0.0847138
$460$	9.88097	+	14.3042i	0.460703	+	0.666937i
$461$	20.0062			0.931781			0.465891	−	0.884842i	$-0.345734\pi$
$461$	20.0062			0.931781			0.465891	+	0.884842i	$0.345734\pi$
$462$	2.78520	+	0.817809i	0.129579	+	0.0380479i
$463$	12.9974	−	14.9998i	0.604042	−	0.697101i	−0.368554	−	0.929607i	$-0.620147\pi$
$463$	12.9974	−	14.9998i	0.604042	−	0.697101i	0.972595	+	0.232505i	$0.0746923\pi$
$464$	2.64638	+	1.70073i	0.122855	+	0.0789543i
$465$	−0.457267	+	3.18036i	−0.0212052	+	0.147486i
$466$	2.40819	−	1.54765i	0.111557	−	0.0716934i
$467$	−9.48399	−	20.7670i	−0.438867	−	0.960984i	−0.991805	−	0.127762i	$-0.959221\pi$
$467$	−9.48399	−	20.7670i	−0.438867	−	0.960984i	0.552938	−	0.833222i	$-0.313507\pi$
$468$	−1.05245	−	1.21459i	−0.0486496	−	0.0561446i
$469$	0.335496	+	2.33343i	0.0154918	+	0.107748i
$470$	17.8050	−	38.9876i	0.821285	−	1.79836i
$471$	18.5099	−	5.43501i	0.852893	−	0.250432i
$472$	−5.87944	+	1.72636i	−0.270623	+	0.0794621i
$473$	−4.07975	+	8.93341i	−0.187587	+	0.410758i
$474$	1.35905	+	9.45237i	0.0624230	+	0.434162i
$475$	17.1425	+	19.7835i	0.786553	+	0.907730i
$476$	−0.753951	−	1.65092i	−0.0345573	−	0.0756699i
$477$	4.26542	−	2.74122i	0.195300	−	0.125512i
$478$	−1.79786	+	12.5044i	−0.0822323	+	0.571938i
$479$	4.25641	+	2.73543i	0.194480	+	0.124985i	0.634257	−	0.773122i	$-0.281306\pi$
$479$	4.25641	+	2.73543i	0.194480	+	0.124985i	−0.439777	+	0.898107i	$0.644942\pi$
$480$	2.37391	−	2.73964i	0.108354	−	0.125047i
$481$	1.77237	+	0.520416i	0.0808132	+	0.0237289i
$482$	8.97197			0.408662
$483$	−2.45703	+	4.11862i	−0.111799	+	0.187404i
$484$	−2.57385			−0.116993
$485$	−47.3144	−	13.8927i	−2.14843	−	0.630837i
$486$	−0.654861	+	0.755750i	−0.0297051	+	0.0342815i
$487$	10.5367	+	6.77156i	0.477466	+	0.306849i	0.757147	−	0.653244i	$-0.226593\pi$
$487$	10.5367	+	6.77156i	0.477466	+	0.306849i	−0.279682	+	0.960093i	$0.590229\pi$
$488$	1.26923	−	8.82767i	0.0574552	−	0.399610i
$489$	−11.6349	+	7.47732i	−0.526150	+	0.338136i
$490$	1.50590	+	3.29747i	0.0680298	+	0.148964i
$491$	19.9392	+	23.0110i	0.899842	+	1.03847i	0.999057	+	0.0434075i	$0.0138214\pi$
$491$	19.9392	+	23.0110i	0.899842	+	1.03847i	−0.0992150	+	0.995066i	$0.531633\pi$
$492$	−1.03984	−	7.23222i	−0.0468794	−	0.326054i
$493$	−2.37175	+	5.19341i	−0.106818	+	0.233899i
$494$	−4.95838	+	1.45591i	−0.223088	+	0.0655046i
$495$	−10.0965	+	2.96460i	−0.453805	+	0.133249i
$496$	0.368202	−	0.806251i	0.0165328	−	0.0362017i
$497$	−0.181011	−	1.25896i	−0.00811947	−	0.0564722i
$498$	3.47683	+	4.01248i	0.155801	+	0.179803i
$499$	3.94635	+	8.64130i	0.176663	+	0.386838i	0.977162	−	0.212496i	$-0.0681594\pi$
$499$	3.94635	+	8.64130i	0.176663	+	0.386838i	−0.800499	+	0.599334i	$0.795432\pi$
$500$	−9.57892	+	6.15600i	−0.428382	+	0.275305i
$501$	−2.35496	+	16.3791i	−0.105212	+	0.731765i
$502$	19.3876	+	12.4597i	0.865312	+	0.556102i
$503$	21.3698	−	24.6621i	0.952832	−	1.09963i	−0.0421039	−	0.999113i	$-0.513406\pi$
$503$	21.3698	−	24.6621i	0.952832	−	1.09963i	0.994936	−	0.100513i	$-0.0320485\pi$
$504$	0.959493	+	0.281733i	0.0427392	+	0.0125494i
$505$	31.8521			1.41740
$506$	−3.47507	+	13.4806i	−0.154486	+	0.599284i
$507$	10.4171			0.462640
$508$	19.4221	+	5.70285i	0.861718	+	0.253023i
$509$	19.9903	−	23.0701i	0.886055	−	1.02256i	−0.113524	−	0.993535i	$-0.536214\pi$
$509$	19.9903	−	23.0701i	0.886055	−	1.02256i	0.999579	−	0.0290268i	$-0.00924082\pi$
$510$	5.53481	+	3.55701i	0.245085	+	0.157507i
$511$	−0.888920	+	6.18258i	−0.0393235	+	0.273501i
$512$	−0.841254	+	0.540641i	−0.0371785	+	0.0238932i
$513$	1.33576	+	2.92490i	0.0589751	+	0.129137i
$514$	7.71058	+	8.89848i	0.340099	+	0.392495i
$515$	4.19435	+	29.1723i	0.184825	+	1.28549i
$516$	−1.40546	+	3.07753i	−0.0618720	+	0.135481i
$517$	32.9308	−	9.66935i	1.44829	−	0.425258i
$518$	−1.10281	+	0.323815i	−0.0484549	+	0.0142276i
$519$	−2.94378	+	6.44599i	−0.129218	+	0.282947i
$520$	−0.829121	−	5.76667i	−0.0363594	−	0.252885i
$521$	−9.85746	−	11.3761i	−0.431863	−	0.498397i	0.497551	−	0.867435i	$-0.334233\pi$
$521$	−9.85746	−	11.3761i	−0.431863	−	0.498397i	−0.929414	+	0.369038i	$0.879687\pi$
$522$	−1.30680	−	2.86149i	−0.0571970	−	0.125244i
$523$	−22.0306	+	14.1582i	−0.963329	+	0.619094i	−0.924917	−	0.380168i	$-0.875866\pi$
$523$	−22.0306	+	14.1582i	−0.963329	+	0.619094i	−0.0384114	+	0.999262i	$0.512230\pi$
$524$	−1.93867	+	13.4837i	−0.0846910	+	0.589039i
$525$	−6.84869	−	4.40138i	−0.298901	−	0.192092i
$526$	10.6849	−	12.3311i	0.465885	−	0.537660i
$527$	1.54350	+	0.453213i	0.0672360	+	0.0197423i
$528$	2.90278			0.126327
$529$	−20.1337	−	11.1192i	−0.875377	−	0.483442i
$530$	18.3802			0.798385
$531$	5.87944	+	1.72636i	0.255146	+	0.0749176i
$532$	2.10569	−	2.43009i	0.0912932	−	0.105358i
$533$	−9.87858	−	6.34858i	−0.427889	−	0.274987i
$534$	−0.252772	+	1.75807i	−0.0109385	+	0.0760790i
$535$	51.1070	−	32.8445i	2.20955	−	1.41999i
$536$	0.979308	+	2.14439i	0.0422997	+	0.0926233i
$537$	6.25375	+	7.21721i	0.269869	+	0.311446i
$538$	3.48544	+	24.2418i	0.150268	+	1.04514i
$539$	−1.20586	+	2.64046i	−0.0519401	+	0.113733i
$540$	−3.47822	+	1.02130i	−0.149679	+	0.0439496i
$541$	5.56612	−	1.63436i	0.239306	−	0.0702666i	−0.159880	−	0.987136i	$-0.551111\pi$
$541$	5.56612	−	1.63436i	0.239306	−	0.0702666i	0.399186	+	0.916870i	$0.369293\pi$
$542$	−10.1504	+	22.2263i	−0.435997	+	0.954699i
$543$	3.18470	+	22.1500i	0.136668	+	0.950549i
$544$	−1.18853	−	1.37164i	−0.0509577	−	0.0588084i
$545$	11.6218	+	25.4482i	0.497823	+	1.09008i
$546$	1.35201	−	0.868884i	0.0578607	−	0.0371848i
$547$	−2.60822	+	18.1406i	−0.111520	+	0.775635i	0.854923	+	0.518754i	$0.173604\pi$
$547$	−2.60822	+	18.1406i	−0.111520	+	0.775635i	−0.966443	+	0.256881i	$0.917305\pi$
$548$	−14.7114	−	9.45447i	−0.628441	−	0.403875i
$549$	−5.84034	+	6.74011i	−0.249260	+	0.287661i
$550$	−22.6745	−	6.65782i	−0.966842	−	0.283890i
$551$	−10.1151			−0.430919
$552$	−1.19715	+	4.64401i	−0.0509541	+	0.197662i
$553$	−9.54957			−0.406089
$554$	−11.2677	−	3.30848i	−0.478717	−	0.140564i
$555$	2.72850	−	3.14886i	0.115818	−	0.133662i
$556$	13.3903	+	8.60541i	0.567875	+	0.364951i
$557$	0.562676	−	3.91350i	0.0238413	−	0.165820i	−0.974422	−	0.224725i	$-0.927852\pi$
$557$	0.562676	−	3.91350i	0.0238413	−	0.165820i	0.998264	+	0.0589046i	$0.0187608\pi$
$558$	−0.745644	+	0.479196i	−0.0315656	+	0.0202860i
$559$	2.25877	+	4.94601i	0.0955357	+	0.209194i
$560$	2.37391	+	2.73964i	0.100316	+	0.115771i
$561$	0.749766	+	5.21473i	0.0316551	+	0.220166i
$562$	7.89407	−	17.2856i	0.332991	−	0.729149i
$563$	−13.6214	+	3.99959i	−0.574072	+	0.168563i	−0.555867	−	0.831271i	$-0.687614\pi$
$563$	−13.6214	+	3.99959i	−0.574072	+	0.168563i	−0.0182055	+	0.999834i	$0.505795\pi$
$564$	11.3446	−	3.33106i	0.477692	−	0.140263i
$565$	15.1805	−	33.2407i	0.638649	−	1.39845i
$566$	−0.496287	−	3.45175i	−0.0208605	−	0.145088i
$567$	−0.654861	−	0.755750i	−0.0275016	−	0.0317385i
$568$	−0.528370	−	1.15697i	−0.0221699	−	0.0485453i
$569$	12.1424	−	7.80342i	0.509034	−	0.327136i	−0.260787	−	0.965396i	$-0.583982\pi$
$569$	12.1424	−	7.80342i	0.509034	−	0.327136i	0.769821	+	0.638260i	$0.220346\pi$
$570$	−1.65886	+	11.5376i	−0.0694821	+	0.483259i
$571$	6.46928	+	4.15755i	0.270731	+	0.173988i	0.668961	−	0.743297i	$-0.266739\pi$
$571$	6.46928	+	4.15755i	0.270731	+	0.173988i	−0.398230	+	0.917285i	$0.630376\pi$
$572$	3.05504	−	3.52570i	0.127738	−	0.147417i
$573$	−17.2149	−	5.05475i	−0.719163	−	0.211165i
$574$	7.30659			0.304971
$575$	20.0028	−	33.5299i	0.834173	−	1.39829i
$576$	1.00000			0.0416667
$577$	−40.3157	−	11.8378i	−1.67836	−	0.492812i	−0.702590	−	0.711595i	$-0.747973\pi$
$577$	−40.3157	−	11.8378i	−1.67836	−	0.492812i	−0.975774	+	0.218783i	$0.929791\pi$
$578$	−8.97553	+	10.3583i	−0.373333	+	0.430849i
$579$	−0.585499	−	0.376278i	−0.0243325	−	0.0156376i
$580$	1.62290	−	11.2875i	0.0673872	−	0.468688i
$581$	−4.46644	+	2.87041i	−0.185299	+	0.119085i
$582$	−5.65091	−	12.3738i	−0.234238	−	0.512909i
$583$	9.63826	+	11.1231i	0.399176	+	0.460674i
$584$	0.888920	+	6.18258i	0.0367838	+	0.255837i
$585$	−2.42019	+	5.29948i	−0.100063	+	0.219107i
$586$	−11.4247	+	3.35461i	−0.471952	+	0.138578i
$587$	25.2753	−	7.42150i	1.04322	−	0.306318i	0.285147	−	0.958484i	$-0.407958\pi$
$587$	25.2753	−	7.42150i	1.04322	−	0.306318i	0.758076	+	0.652166i	$0.226139\pi$
$588$	−0.415415	+	0.909632i	−0.0171314	+	0.0375126i
$589$	0.405602	+	2.82102i	0.0167125	+	0.116238i
$590$	14.5465	+	16.7875i	0.598869	+	0.691132i
$591$	1.88039	+	4.11747i	0.0773488	+	0.169370i
$592$	−0.966913	+	0.621397i	−0.0397399	+	0.0255393i
$593$	6.71533	−	46.7061i	0.275765	−	1.91799i	−0.107218	−	0.994236i	$-0.534194\pi$
$593$	6.71533	−	46.7061i	0.275765	−	1.91799i	0.382983	−	0.923755i	$-0.374897\pi$
$594$	−2.44198	−	1.56936i	−0.100196	−	0.0643918i
$595$	−4.30849	+	4.97226i	−0.176631	+	0.203843i
$596$	−15.4366	−	4.53259i	−0.632308	−	0.185662i
$597$	−17.3817			−0.711384
$598$	4.38064	+	6.34164i	0.179138	+	0.259329i
$599$	−15.3773			−0.628301			−0.314151	−	0.949373i	$-0.601720\pi$
$599$	−15.3773			−0.628301			−0.314151	+	0.949373i	$0.601720\pi$
$600$	−7.81128	−	2.29360i	−0.318894	−	0.0936358i
$601$	18.2304	−	21.0390i	0.743635	−	0.858200i	−0.250300	−	0.968168i	$-0.580529\pi$
$601$	18.2304	−	21.0390i	0.743635	−	0.858200i	0.993935	+	0.109968i	$0.0350748\pi$
$602$	−2.84619	−	1.82913i	−0.116002	−	0.0745499i
$603$	0.335496	−	2.33343i	0.0136625	−	0.0950244i
$604$	11.7551	−	7.55453i	0.478307	−	0.307389i
$605$	3.87597	+	8.48719i	0.157581	+	0.345053i
$606$	5.75402	+	6.64049i	0.233741	+	0.269752i
$607$	−0.195547	−	1.36006i	−0.00793700	−	0.0552030i	0.985468	−	0.169861i	$-0.0543319\pi$
$607$	−0.195547	−	1.36006i	−0.00793700	−	0.0552030i	−0.993405	+	0.114658i	$0.963423\pi$
$608$	1.33576	−	2.92490i	0.0541721	−	0.118620i
$609$	3.01834	−	0.886264i	0.122309	−	0.0359132i
$610$	−31.0203	+	9.10838i	−1.25598	+	0.368788i
$611$	7.89370	−	17.2848i	0.319345	−	0.699268i
$612$	0.258292	+	1.79646i	0.0104408	+	0.0726176i
$613$	7.28316	+	8.40522i	0.294164	+	0.339483i	0.883523	−	0.468388i	$-0.155165\pi$
$613$	7.28316	+	8.40522i	0.294164	+	0.339483i	−0.589359	+	0.807871i	$0.700620\pi$
$614$	−8.01960	−	17.5605i	−0.323645	−	0.708683i
$615$	−22.2821	+	14.3199i	−0.898502	+	0.577432i
$616$	−0.413109	+	2.87324i	−0.0166446	+	0.115766i
$617$	−36.9948	−	23.7751i	−1.48936	−	0.957151i	−0.996189	−	0.0872168i	$-0.972203\pi$
$617$	−36.9948	−	23.7751i	−1.48936	−	0.957151i	−0.493167	−	0.869935i	$-0.664161\pi$
$618$	−5.32412	+	6.14436i	−0.214168	+	0.247163i
$619$	−2.76404	−	0.811594i	−0.111096	−	0.0326207i	0.225712	−	0.974194i	$-0.427529\pi$
$619$	−2.76404	−	0.811594i	−0.111096	−	0.0326207i	−0.336808	+	0.941573i	$0.609347\pi$
$620$	−3.21307			−0.129040
$621$	3.51785	−	3.25956i	0.141166	−	0.130802i
$622$	23.6966			0.950145
$623$	−1.70420	−	0.500398i	−0.0682773	−	0.0200480i
$624$	1.05245	−	1.21459i	0.0421318	−	0.0486226i
$625$	0.480724	+	0.308943i	0.0192290	+	0.0123577i
$626$	0.915990	−	6.37085i	0.0366103	−	0.254631i
$627$	−7.85212	+	5.04625i	−0.313583	+	0.201528i
$628$	8.01393	+	17.5481i	0.319791	+	0.700244i
$629$	−1.36606	−	1.57652i	−0.0544684	−	0.0628599i
$630$	−0.515900	−	3.58816i	−0.0205539	−	0.142956i
$631$	17.4952	−	38.3092i	0.696474	−	1.52507i	−0.147720	−	0.989029i	$-0.547194\pi$
$631$	17.4952	−	38.3092i	0.696474	−	1.52507i	0.844195	−	0.536037i	$-0.180079\pi$
$632$	−9.16275	+	2.69043i	−0.364474	+	0.107019i
$633$	−2.82802	+	0.830382i	−0.112404	+	0.0330047i
$634$	7.05126	−	15.4401i	0.280041	−	0.613205i
$635$	−10.4429	−	72.6318i	−0.414413	−	2.88231i
$636$	3.32035	+	3.83189i	0.131661	+	0.151944i
$637$	0.667629	+	1.46190i	0.0264524	+	0.0579227i
$638$	7.68188	−	4.93685i	0.304129	−	0.195452i
$639$	−0.181011	+	1.25896i	−0.00716070	+	0.0498038i
$640$	3.04959	+	1.95985i	0.120546	+	0.0774701i
$641$	1.64201	−	1.89498i	0.0648556	−	0.0748474i	−0.722395	−	0.691481i	$-0.756959\pi$
$641$	1.64201	−	1.89498i	0.0648556	−	0.0748474i	0.787250	+	0.616634i	$0.211504\pi$
$642$	16.0798	+	4.72146i	0.634619	+	0.186341i
$643$	6.73416			0.265569			0.132785	−	0.991145i	$-0.457608\pi$
$643$	6.73416			0.265569			0.132785	+	0.991145i	$0.457608\pi$
$644$	−4.42637	−	1.84588i	−0.174423	−	0.0727377i
$645$	12.2646			0.482916
$646$	5.59948	+	1.64416i	0.220309	+	0.0646884i
$647$	−13.7658	+	15.8866i	−0.541190	+	0.624566i	−0.958808	−	0.284056i	$-0.908320\pi$
$647$	−13.7658	+	15.8866i	−0.541190	+	0.624566i	0.417618	+	0.908623i	$0.362865\pi$
$648$	−0.841254	−	0.540641i	−0.0330476	−	0.0212384i
$649$	−2.53139	+	17.6062i	−0.0993657	+	0.691104i
$650$	−11.0068	+	7.07363i	−0.431721	+	0.277450i
$651$	−0.368202	−	0.806251i	−0.0144310	−	0.0315995i
$652$	−9.05704	−	10.4524i	−0.354701	−	0.409347i
$653$	−0.330891	−	2.30140i	−0.0129488	−	0.0900606i	0.982322	−	0.187198i	$-0.0599405\pi$
$653$	−0.330891	−	2.30140i	−0.0129488	−	0.0900606i	−0.995271	+	0.0971372i	$0.969031\pi$
$654$	−3.20596	+	7.02007i	−0.125363	+	0.274507i
$655$	47.3816	−	13.9125i	1.85135	−	0.543606i
$656$	7.01062	−	2.05850i	0.273719	−	0.0803711i
$657$	2.59475	−	5.68170i	0.101231	−	0.221664i
$658$	1.68266	+	11.7031i	0.0655968	+	0.456236i
$659$	31.0607	+	35.8460i	1.20995	+	1.39636i	0.894288	+	0.447492i	$0.147683\pi$
$659$	31.0607	+	35.8460i	1.20995	+	1.39636i	0.315667	+	0.948870i	$0.397772\pi$
$660$	−4.37131	−	9.57184i	−0.170153	−	0.372583i
$661$	−19.9230	+	12.8037i	−0.774915	+	0.498008i	−0.867343	−	0.497712i	$-0.834174\pi$
$661$	−19.9230	+	12.8037i	−0.774915	+	0.498008i	0.0924272	+	0.995719i	$0.470537\pi$
$662$	3.39812	−	23.6344i	0.132072	−	0.918578i
$663$	2.45381	+	1.57697i	0.0952980	+	0.0612443i
$664$	−3.47683	+	4.01248i	−0.134927	+	0.155714i
$665$	−11.1841	−	3.28396i	−0.433702	−	0.127346i
$666$	1.14937			0.0445372
$667$	4.73008	+	14.3259i	0.183149	+	0.554700i
$668$	−16.5476			−0.640244
$669$	−18.3154	−	5.37789i	−0.708115	−	0.207921i
$670$	5.59630	−	6.45848i	0.216204	−	0.249513i
$671$	−21.7786	−	13.9963i	−0.840755	−	0.540320i
$672$	−0.142315	+	0.989821i	−0.00548991	+	0.0381832i
$673$	−27.2532	+	17.5146i	−1.05053	+	0.675137i	−0.947570	−	0.319548i	$-0.896469\pi$
$673$	−27.2532	+	17.5146i	−1.05053	+	0.675137i	−0.102964	+	0.994685i	$0.532833\pi$
$674$	4.30304	+	9.42235i	0.165747	+	0.362935i
$675$	5.33125	+	6.15259i	0.205200	+	0.236813i
$676$	1.48251	+	10.3111i	0.0570196	+	0.396580i
$677$	12.6832	−	27.7724i	0.487456	−	1.06738i	−0.492889	−	0.870092i	$-0.664059\pi$
$677$	12.6832	−	27.7724i	0.487456	−	1.06738i	0.980346	−	0.197288i	$-0.0632134\pi$
$678$	9.67233	−	2.84005i	0.371464	−	0.109072i
$679$	13.0520	−	3.83242i	0.500891	−	0.147075i
$680$	−2.73311	+	5.98469i	−0.104810	+	0.229502i
$681$	−2.16321	−	15.0454i	−0.0828943	−	0.576542i
$682$	−1.68488	−	1.94445i	−0.0645173	−	0.0744569i
$683$	13.6304	+	29.8465i	0.521554	+	1.14204i	0.968848	+	0.247657i	$0.0796605\pi$
$683$	13.6304	+	29.8465i	0.521554	+	1.14204i	−0.447294	+	0.894387i	$0.647612\pi$
$684$	−2.70503	+	1.73842i	−0.103429	+	0.0664700i
$685$	−9.02181	+	62.7480i	−0.344705	+	2.39748i
$686$	−0.841254	−	0.540641i	−0.0321192	−	0.0206418i
$687$	−12.9407	+	14.9344i	−0.493720	+	0.569783i
$688$	−3.24622	−	0.953177i	−0.123761	−	0.0363395i
$689$	8.14870			0.310441
$690$	17.1163	−	3.04587i	0.651605	−	0.115954i
$691$	−25.8129			−0.981969			−0.490985	−	0.871168i	$-0.663363\pi$
$691$	−25.8129			−0.981969			−0.490985	+	0.871168i	$0.663363\pi$
$692$	−6.79932	−	1.99646i	−0.258471	−	0.0758941i
$693$	1.90092	−	2.19378i	0.0722099	−	0.0833347i
$694$	6.18200	+	3.97293i	0.234666	+	0.150810i
$695$	8.21161	−	57.1130i	0.311484	−	2.16642i
$696$	2.64638	−	1.70073i	0.100311	−	0.0644659i
$697$	5.50881	+	12.0626i	0.208661	+	0.456904i
$698$	−2.85737	−	3.29758i	−0.108153	−	0.124815i
$699$	−0.407393	−	2.83348i	−0.0154090	−	0.107172i
$700$	3.38191	−	7.40536i	0.127824	−	0.279896i
$701$	4.76545	−	1.39926i	0.179989	−	0.0528494i	−0.190496	−	0.981688i	$-0.561010\pi$
$701$	4.76545	−	1.39926i	0.179989	−	0.0528494i	0.370485	+	0.928838i	$0.379192\pi$
$702$	−1.54204	+	0.452783i	−0.0582004	+	0.0170892i
$703$	1.53528	−	3.36180i	0.0579042	−	0.126793i
$704$	0.413109	+	2.87324i	0.0155696	+	0.108289i
$705$	−28.0679	−	32.3921i	−1.05710	−	1.21996i
$706$	−1.52817	−	3.34623i	−0.0575135	−	0.125937i
$707$	−7.39179	+	4.75041i	−0.277997	+	0.178658i
$708$	−0.872056	+	6.06528i	−0.0327739	+	0.227947i
$709$	−1.19165	−	0.765826i	−0.0447533	−	0.0287612i	0.518073	−	0.855336i	$-0.326650\pi$
$709$	−1.19165	−	0.765826i	−0.0447533	−	0.0287612i	−0.562826	+	0.826575i	$0.690286\pi$
$710$	−3.01939	+	3.48457i	−0.113316	+	0.130773i
$711$	9.16275	+	2.69043i	0.343630	+	0.100899i
$712$	−1.77614			−0.0665638
$713$	3.80569	−	1.89363i	0.142524	−	0.0709168i
$714$	−1.81493			−0.0679222
$715$	−16.2265	−	4.76452i	−0.606836	−	0.178183i
$716$	−6.25375	+	7.21721i	−0.233714	+	0.269720i
$717$	10.6275	+	6.82991i	0.396893	+	0.255068i
$718$	3.26004	−	22.6741i	0.121664	−	0.846190i
$719$	−29.9921	+	19.2748i	−1.11852	+	0.718828i	−0.963133	−	0.269026i	$-0.913298\pi$
$719$	−29.9921	+	19.2748i	−1.11852	+	0.718828i	−0.155385	+	0.987854i	$0.549662\pi$
$720$	−1.50590	−	3.29747i	−0.0561217	−	0.122889i
$721$	−5.32412	−	6.14436i	−0.198281	−	0.228828i
$722$	−1.23255	−	8.57256i	−0.0458707	−	0.319038i
$723$	3.72709	−	8.16119i	0.138612	−	0.303518i
$724$	−21.4714	+	6.30456i	−0.797977	+	0.234307i
$725$	−24.5724	+	7.21512i	−0.912598	+	0.267963i
$726$	−1.06922	+	2.34126i	−0.0396823	+	0.0868921i
$727$	−2.79542	−	19.4426i	−0.103676	−	0.721085i	−0.973660	−	0.228005i	$-0.926780\pi$
$727$	−2.79542	−	19.4426i	−0.103676	−	0.721085i	0.869984	−	0.493081i	$-0.164129\pi$
$728$	1.05245	+	1.21459i	0.0390064	+	0.0450158i
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$	19.0482	−	12.2416i	0.705006	−	0.453080i
$731$	0.873872	−	6.07791i	0.0323213	−	0.224800i
$732$	−7.50267	−	4.82168i	−0.277307	−	0.178214i
$733$	−22.2262	+	25.6504i	−0.820944	+	0.947420i	−0.999332	−	0.0365406i	$-0.988366\pi$
$733$	−22.2262	+	25.6504i	−0.820944	+	0.947420i	0.178388	+	0.983960i	$0.442912\pi$
$734$	−9.13425	−	2.68206i	−0.337151	−	0.0989965i
$735$	3.62506			0.133712
$736$	−4.76711	−	0.524054i	−0.175718	−	0.0193169i
$737$	6.84308			0.252068
$738$	−7.01062	−	2.05850i	−0.258065	−	0.0757746i
$739$	−4.11201	+	4.74551i	−0.151263	+	0.174566i	−0.826324	−	0.563195i	$-0.809572\pi$
$739$	−4.11201	+	4.74551i	−0.151263	+	0.174566i	0.675061	+	0.737762i	$0.264117\pi$
$740$	3.50512	+	2.25260i	0.128851	+	0.0828072i
$741$	−0.735442	+	5.11511i	−0.0270171	+	0.187908i
$742$	−4.26542	+	2.74122i	−0.156589	+	0.100633i
$743$	6.33418	+	13.8699i	0.232379	+	0.508838i	0.989517	−	0.144416i	$-0.0461304\pi$
$743$	6.33418	+	13.8699i	0.232379	+	0.508838i	−0.757138	+	0.653255i	$0.773403\pi$
$744$	−0.580435	−	0.669858i	−0.0212798	−	0.0245582i
$745$	8.29994	+	57.7274i	0.304086	+	2.11497i
$746$	1.83814	−	4.02496i	0.0672990	−	0.147364i
$747$	5.09421	−	1.49579i	0.186387	−	0.0547282i
$748$	−5.05495	+	1.48427i	−0.184827	+	0.0542702i
$749$	−6.96179	+	15.2442i	−0.254378	+	0.557011i
$750$	1.62047	+	11.2706i	0.0591711	+	0.411544i
$751$	21.1175	+	24.3709i	0.770589	+	0.889307i	0.996392	−	0.0848662i	$-0.0270463\pi$
$751$	21.1175	+	24.3709i	0.770589	+	0.889307i	−0.225804	+	0.974173i	$0.572501\pi$
$752$	4.91166	+	10.7550i	0.179110	+	0.392195i
$753$	19.3876	−	12.4597i	0.706524	−	0.454056i
$754$	0.719497	−	5.00421i	0.0262025	−	0.182243i
$755$	−42.6128	−	27.3856i	−1.55084	−	0.996664i
$756$	0.654861	−	0.755750i	0.0238171	−	0.0274863i
$757$	−35.0572	−	10.2937i	−1.27418	−	0.374132i	−0.426423	−	0.904524i	$-0.640227\pi$
$757$	−35.0572	−	10.2937i	−1.27418	−	0.374132i	−0.847753	+	0.530392i	$0.822045\pi$
$758$	7.67871			0.278903
$759$	10.8187	+	8.76106i	0.392696	+	0.318006i
$760$	−11.6563			−0.422818
$761$	−30.0428	−	8.82138i	−1.08905	−	0.319775i	−0.312558	−	0.949899i	$-0.601186\pi$
$761$	−30.0428	−	8.82138i	−1.08905	−	0.319775i	−0.776494	+	0.630124i	$0.783004\pi$
$762$	13.2557	−	15.2979i	0.480205	−	0.554186i
$763$	−6.49236	−	4.17239i	−0.235039	−	0.151051i
$764$	2.55337	−	17.7591i	0.0923776	−	0.642500i
$765$	5.53481	−	3.55701i	0.200111	−	0.128604i
$766$	−10.3937	−	22.7591i	−0.375540	−	0.822319i
$767$	6.44905	+	7.44261i	0.232862	+	0.268737i
$768$	0.142315	+	0.989821i	0.00513534	+	0.0357171i
$769$	−10.1510	+	22.2277i	−0.366056	+	0.801550i	0.633557	+	0.773696i	$0.281594\pi$
$769$	−10.1510	+	22.2277i	−0.366056	+	0.801550i	−0.999612	+	0.0278533i	$0.991133\pi$
$770$	10.0965	−	2.96460i	0.363853	−	0.106837i
$771$	11.2974	−	3.31723i	0.406867	−	0.119467i
$772$	0.289122	−	0.633090i	0.0104057	−	0.0227854i
$773$	−7.47904	−	52.0179i	−0.269002	−	1.87095i	−0.457968	−	0.888969i	$-0.651423\pi$
$773$	−7.47904	−	52.0179i	−0.269002	−	1.87095i	0.188966	−	0.981984i	$-0.439487\pi$
$774$	2.21557	+	2.55691i	0.0796371	+	0.0919061i
$775$	2.99755	+	6.56373i	0.107675	+	0.235776i
$776$	11.4436	−	7.35436i	0.410802	−	0.264006i
$777$	−0.163573	+	1.13767i	−0.00586813	+	0.0408138i
$778$	−30.4868	−	19.5927i	−1.09301	−	0.702432i
$779$	−15.3854	+	17.7557i	−0.551239	+	0.636164i
$780$	−5.58997	−	1.64136i	−0.200153	−	0.0587703i
$781$	−3.69207			−0.132113
$782$	−0.289865	−	8.69929i	−0.0103656	−	0.311086i
$783$	−3.14576			−0.112420
$784$	−0.959493	−	0.281733i	−0.0342676	−	0.0100619i
$785$	45.7960	−	52.8514i	1.63453	−	1.88635i
$786$	11.4599	+	7.36481i	0.408760	+	0.262694i
$787$	4.04308	−	28.1202i	0.144120	−	1.00238i	−0.781495	−	0.623912i	$-0.785542\pi$
$787$	4.04308	−	28.1202i	0.144120	−	1.00238i	0.925615	−	0.378466i	$-0.123548\pi$
$788$	−3.80796	+	2.44723i	−0.135653	+	0.0871788i
$789$	−6.77805	−	14.8419i	−0.241305	−	0.528384i
$790$	22.6698	+	26.1624i	0.806556	+	0.930815i
$791$	1.43463	+	9.97806i	0.0510095	+	0.354779i
$792$	1.20586	−	2.64046i	0.0428484	−	0.0938248i
$793$	−13.7526	+	4.03812i	−0.488368	+	0.143398i
$794$	−18.0205	+	5.29131i	−0.639525	+	0.187782i
$795$	7.63541	−	16.7192i	0.270800	−	0.592970i
$796$	−2.47367	−	17.2047i	−0.0876768	−	0.609806i
$797$	−24.0178	−	27.7180i	−0.850755	−	0.981823i	0.149221	−	0.988804i	$-0.452323\pi$
$797$	−24.0178	−	27.7180i	−0.850755	−	0.981823i	−0.999976	+	0.00698071i	$0.997778\pi$
$798$	−1.33576	−	2.92490i	−0.0472853	−	0.103540i
$799$	−18.0523	+	11.6015i	−0.638646	+	0.410433i
$800$	1.15859	−	8.05819i	0.0409624	−	0.284900i
$801$	1.49419	+	0.960256i	0.0527945	+	0.0339290i
$802$	−21.7740	+	25.1285i	−0.768866	+	0.887319i
$803$	17.3968	+	5.10816i	0.613919	+	0.180263i
$804$	2.35742			0.0831398
$805$	0.578963	+	17.3755i	0.0204058	+	0.612407i
$806$	−1.42448			−0.0501753
$807$	23.4990	+	6.89993i	0.827204	+	0.242889i
$808$	−5.75402	+	6.64049i	−0.202426	+	0.233612i
$809$	5.65610	+	3.63496i	0.198858	+	0.127798i	0.636280	−	0.771458i	$-0.280472\pi$
$809$	5.65610	+	3.63496i	0.198858	+	0.127798i	−0.437422	+	0.899256i	$0.644109\pi$
$810$	−0.515900	+	3.58816i	−0.0181269	+	0.126075i
$811$	31.0306	−	19.9421i	1.08963	−	0.700263i	0.132869	−	0.991134i	$-0.457581\pi$
$811$	31.0306	−	19.9421i	1.08963	−	0.700263i	0.956763	+	0.290870i	$0.0939448\pi$
$812$	1.30680	+	2.86149i	0.0458596	+	0.100419i
$813$	16.0011	+	18.4662i	0.561183	+	0.647639i
$814$	0.474816	+	3.30242i	0.0166423	+	0.115750i
$815$	−20.8274	+	45.6056i	−0.729551	+	1.59749i
$816$	−1.74142	+	0.511326i	−0.0609617	+	0.0179000i
$817$	10.4382	−	3.06492i	0.365185	−	0.107228i
$818$	4.57998	−	10.0288i	0.160135	−	0.350647i
$819$	−0.228719	−	1.59078i	−0.00799210	−	0.0555863i
$820$	−17.3452	−	20.0174i	−0.605720	−	0.699038i
$821$	8.08423	+	17.7020i	0.282142	+	0.617804i	0.996647	−	0.0818265i	$-0.0260753\pi$
$821$	8.08423	+	17.7020i	0.282142	+	0.617804i	−0.714505	+	0.699630i	$0.753348\pi$
$822$	−14.7114	+	9.45447i	−0.513120	+	0.329762i
$823$	−4.97448	+	34.5983i	−0.173400	+	1.20602i	0.698236	+	0.715867i	$0.253968\pi$
$823$	−4.97448	+	34.5983i	−0.173400	+	1.20602i	−0.871636	+	0.490154i	$0.836941\pi$
$824$	−6.83952	−	4.39550i	−0.238266	−	0.153124i
$825$	−15.4755	+	17.8596i	−0.538787	+	0.621793i
$826$	−5.87944	−	1.72636i	−0.204572	−	0.0600677i
$827$	−17.7901			−0.618624			−0.309312	−	0.950961i	$-0.600099\pi$
$827$	−17.7901			−0.618624			−0.309312	+	0.950961i	$0.600099\pi$
$828$	3.72703	+	3.01816i	0.129523	+	0.104888i
$829$	−8.53694			−0.296500			−0.148250	−	0.988950i	$-0.547364\pi$
$829$	−8.53694			−0.296500			−0.148250	+	0.988950i	$0.547364\pi$
$830$	18.4668	+	5.42234i	0.640992	+	0.188212i
$831$	−7.69026	+	8.87503i	−0.266772	+	0.307872i
$832$	1.35201	+	0.868884i	0.0468725	+	0.0301231i
$833$	0.258292	−	1.79646i	0.00894929	−	0.0622436i
$834$	13.3903	−	8.60541i	0.463668	−	0.297981i
$835$	24.9190	+	54.5650i	0.862358	+	1.88830i
$836$	−6.11236	−	7.05404i	−0.211400	−	0.243969i
$837$	0.126141	+	0.877327i	0.00436006	+	0.0303248i
$838$	−0.893337	+	1.95614i	−0.0308598	+	0.0675736i
$839$	−28.9381	+	8.49698i	−0.999053	+	0.293348i	−0.740067	−	0.672533i	$-0.765206\pi$
$839$	−28.9381	+	8.49698i	−0.999053	+	0.293348i	−0.258986	+	0.965881i	$0.583388\pi$
$840$	3.47822	−	1.02130i	0.120010	−	0.0352381i
$841$	−7.93616	+	17.3778i	−0.273661	+	0.599233i
$842$	−0.559137	−	3.88889i	−0.0192691	−	0.134020i
$843$	−12.4442	−	14.3614i	−0.428602	−	0.494633i
$844$	−1.22440	−	2.68106i	−0.0421456	−	0.0922859i
$845$	31.7680	−	20.4160i	1.09285	−	0.702333i
$846$	1.68266	−	11.7031i	0.0578510	−	0.402362i
$847$	−2.16526	−	1.39153i	−0.0743992	−	0.0478135i
$848$	−3.32035	+	3.83189i	−0.114021	+	0.131588i
$849$	−3.34599	−	0.982471i	−0.114834	−	0.0337183i
$850$	14.7755			0.506794
$851$	−5.47918	−	0.602332i	−0.187824	−	0.0206477i
$852$	−1.27191			−0.0435749
$853$	−31.2934	−	9.18856i	−1.07146	−	0.314610i	−0.302005	−	0.953306i	$-0.597656\pi$
$853$	−31.2934	−	9.18856i	−1.07146	−	0.314610i	−0.769459	+	0.638696i	$0.779474\pi$
$854$	5.84034	−	6.74011i	0.199852	−	0.230642i
$855$	9.80589	+	6.30186i	0.335354	+	0.215519i
$856$	−2.38500	+	16.5881i	−0.0815177	+	0.566968i
$857$	36.1117	−	23.2076i	1.23355	−	0.792757i	0.249113	−	0.968474i	$-0.419861\pi$
$857$	36.1117	−	23.2076i	1.23355	−	0.792757i	0.984441	+	0.175718i	$0.0562247\pi$
$858$	−1.93798	−	4.24359i	−0.0661616	−	0.144874i
$859$	9.38592	+	10.8319i	0.320243	+	0.369581i	0.892931	−	0.450193i	$-0.148645\pi$
$859$	9.38592	+	10.8319i	0.320243	+	0.369581i	−0.572688	+	0.819773i	$0.694099\pi$
$860$	1.74543	+	12.1397i	0.0595186	+	0.413961i
$861$	3.03527	−	6.64631i	0.103442	−	0.226506i
$862$	−16.1743	+	4.74921i	−0.550900	+	0.161759i
$863$	−55.3231	+	16.2443i	−1.88322	+	0.552964i	−0.887472	+	0.460862i	$0.847540\pi$
$863$	−55.3231	+	16.2443i	−1.88322	+	0.552964i	−0.995750	+	0.0921017i	$0.970642\pi$
$864$	0.415415	−	0.909632i	0.0141327	−	0.0309463i
$865$	3.65586	+	25.4270i	0.124303	+	0.864545i
$866$	2.20723	+	2.54728i	0.0750046	+	0.0865599i
$867$	5.69369	+	12.4674i	0.193368	+	0.423416i
$868$	0.745644	−	0.479196i	0.0253088	−	0.0162650i
$869$	−3.94502	+	27.4382i	−0.133825	+	0.930777i
$870$	−9.59330	−	6.16524i	−0.325243	−	0.209021i
$871$	2.48107	−	2.86331i	0.0840678	−	0.0970195i
$872$	−7.40487	−	2.17427i	−0.250761	−	0.0736300i
$873$	−13.6030			−0.460393
$874$	13.8062	−	6.86965i	0.467002	−	0.232369i
$875$	−11.3865			−0.384934
$876$	5.99314	+	1.75974i	0.202489	+	0.0594563i
$877$	−7.54498	+	8.70737i	−0.254776	+	0.294027i	−0.868701	−	0.495338i	$-0.835044\pi$
$877$	−7.54498	+	8.70737i	−0.254776	+	0.294027i	0.613925	+	0.789365i	$0.289590\pi$
$878$	−16.5732	−	10.6509i	−0.559317	−	0.359451i
$879$	−1.69455	+	11.7859i	−0.0571558	+	0.397527i
$880$	8.85231	−	5.68903i	0.298411	−	0.191777i
$881$	16.7628	+	36.7053i	0.564752	+	1.23663i	0.949545	+	0.313631i	$0.101545\pi$
$881$	16.7628	+	36.7053i	0.564752	+	1.23663i	−0.384793	+	0.923003i	$0.625727\pi$
$882$	0.654861	+	0.755750i	0.0220503	+	0.0254474i
$883$	6.91276	+	48.0793i	0.232633	+	1.61800i	0.686639	+	0.726999i	$0.259085\pi$
$883$	6.91276	+	48.0793i	0.232633	+	1.61800i	−0.454006	+	0.890999i	$0.650005\pi$
$884$	−1.21170	+	2.65326i	−0.0407539	+	0.0892387i
$885$	21.3133	−	6.25815i	0.716439	−	0.210366i
$886$	16.2177	−	4.76194i	0.544843	−	0.159980i
$887$	5.64257	−	12.3555i	0.189459	−	0.414857i	−0.790936	−	0.611898i	$-0.790406\pi$
$887$	5.64257	−	12.3555i	0.189459	−	0.414857i	0.980395	+	0.197042i	$0.0631334\pi$
$888$	0.163573	+	1.13767i	0.00548914	+	0.0381778i
$889$	13.2557	+	15.2979i	0.444583	+	0.513076i
$890$	2.67470	+	5.85678i	0.0896563	+	0.196320i
$891$	−2.44198	+	1.56936i	−0.0818093	+	0.0525756i
$892$	2.71660	−	18.8943i	0.0909584	−	0.632629i
$893$	−31.9829	−	20.5542i	−1.07027	−	0.687819i
$894$	−10.5356	+	12.1587i	−0.352363	+	0.406648i
$895$	33.2161	+	9.75312i	1.11029	+	0.326011i
$896$	−1.00000			−0.0334077
$897$	7.58835	−	1.35036i	0.253367	−	0.0450871i
$898$	18.4216			0.614737
$899$	−2.67530	−	0.785539i	−0.0892262	−	0.0261992i
$900$	−5.33125	+	6.15259i	−0.177708	+	0.205086i
$901$	−7.74146	−	4.97513i	−0.257905	−	0.165746i
$902$	3.01842	−	20.9936i	0.100502	−	0.699009i
$903$	−2.84619	+	1.82913i	−0.0947152	+	0.0608698i
$904$	4.18766	+	9.16970i	0.139279	+	0.304980i
$905$	53.1229	+	61.3071i	1.76586	+	2.03792i
$906$	−1.98861	−	13.8311i	−0.0660670	−	0.459506i
$907$	−1.23214	+	2.69801i	−0.0409126	+	0.0895861i	−0.928985	−	0.370118i	$-0.879317\pi$
$907$	−1.23214	+	2.69801i	−0.0409126	+	0.0895861i	0.888072	+	0.459704i	$0.152045\pi$
$908$	14.5844	−	4.28238i	0.484002	−	0.142116i
$909$	8.43071	−	2.47548i	0.279629	−	0.0821065i
$910$	2.42019	−	5.29948i	0.0802286	−	0.175676i
$911$	1.44550	+	10.0537i	0.0478915	+	0.333092i	0.999655	+	0.0262603i	$0.00835989\pi$
$911$	1.44550	+	10.0537i	0.0478915	+	0.333092i	−0.951764	+	0.306832i	$0.900731\pi$
$912$	−2.10569	−	2.43009i	−0.0697263	−	0.0804685i
$913$	6.40223	+	14.0189i	0.211883	+	0.463959i
$914$	11.3382	−	7.28663i	0.375035	−	0.241020i
$915$	−4.60102	+	32.0008i	−0.152105	+	1.05791i
$916$	−16.6241	−	10.6836i	−0.549274	−	0.352997i
$917$	−8.92075	+	10.2951i	−0.294589	+	0.339974i
$918$	1.74142	+	0.511326i	0.0574753	+	0.0168763i
$919$	−19.6259			−0.647400			−0.323700	−	0.946160i	$-0.604927\pi$
$919$	−19.6259			−0.647400			−0.323700	+	0.946160i	$0.604927\pi$
$920$	5.45076	+	16.5086i	0.179706	+	0.544272i
$921$	−19.3050			−0.636122
$922$	19.1958	+	5.63640i	0.632180	+	0.185625i
$923$	−1.33862	+	1.54485i	−0.0440612	+	0.0508494i
$924$	2.44198	+	1.56936i	0.0803351	+	0.0516283i
$925$	1.33165	−	9.26185i	0.0437845	−	0.304528i
$926$	16.6969	−	10.7304i	0.548693	−	0.352624i
$927$	3.37739	+	7.39545i	0.110928	+	0.242899i
$928$	2.06004	+	2.37741i	0.0676240	+	0.0780423i
$929$	2.53475	+	17.6296i	0.0831626	+	0.578408i	0.988211	+	0.153099i	$0.0489255\pi$
$929$	2.53475	+	17.6296i	0.0831626	+	0.578408i	−0.905048	+	0.425309i	$0.860165\pi$
$930$	−1.33476	+	2.92271i	−0.0437684	+	0.0958393i
$931$	3.08523	−	0.905904i	0.101114	−	0.0296898i
$932$	2.74666	−	0.806493i	0.0899699	−	0.0264176i
$933$	9.84390	−	21.5551i	0.322275	−	0.705684i
$934$	−3.24907	−	22.5978i	−0.106313	−	0.739422i
$935$	12.5066	+	14.4334i	0.409010	+	0.472022i
$936$	−0.667629	−	1.46190i	−0.0218221	−	0.0477838i
$937$	−10.8548	+	6.97594i	−0.354610	+	0.227894i	−0.705802	−	0.708410i	$-0.749413\pi$
$937$	−10.8548	+	6.97594i	−0.354610	+	0.227894i	0.351191	+	0.936304i	$0.385777\pi$
$938$	−0.335496	+	2.33343i	−0.0109543	+	0.0761890i
$939$	−5.41462	−	3.47976i	−0.176699	−	0.113558i
$940$	28.0679	−	32.3921i	0.915474	−	1.05651i
$941$	−21.1380	−	6.20668i	−0.689079	−	0.202332i	−0.0815971	−	0.996665i	$-0.526002\pi$
$941$	−21.1380	−	6.20668i	−0.689079	−	0.202332i	−0.607482	+	0.794334i	$0.707820\pi$
$942$	19.2914			0.628547
$943$	32.3417	+	13.4871i	1.05319	+	0.439199i
$944$	−6.12765			−0.199438
$945$	−3.47822	−	1.02130i	−0.113146	−	0.0332228i
$946$	−6.43132	+	7.42214i	−0.209100	+	0.241315i
$947$	17.2827	+	11.1069i	0.561612	+	0.360926i	0.790439	−	0.612541i	$-0.209852\pi$
$947$	17.2827	+	11.1069i	0.561612	+	0.360926i	−0.228827	+	0.973467i	$0.573489\pi$
$948$	−1.35905	+	9.45237i	−0.0441398	+	0.306999i
$949$	8.44486	−	5.42718i	0.274132	−	0.176174i
$950$	10.8745	+	23.8117i	0.352814	+	0.772555i
$951$	−11.1156	−	12.8281i	−0.360449	−	0.415980i
$952$	−0.258292	−	1.79646i	−0.00837129	−	0.0582236i
$953$	9.82758	−	21.5194i	0.318347	−	0.697082i	−0.681035	−	0.732251i	$-0.738470\pi$
$953$	9.82758	−	21.5194i	0.318347	−	0.697082i	0.999381	+	0.0351691i	$0.0111970\pi$
$954$	4.86493	−	1.42847i	0.157508	−	0.0462485i
$955$	−62.4051	+	18.3238i	−2.01938	+	0.592944i
$956$	−5.24793	+	11.4914i	−0.169730	+	0.371657i
$957$	−1.29954	−	9.03853i	−0.0420083	−	0.292174i
$958$	3.31334	+	3.82380i	0.107049	+	0.123541i
$959$	−7.26458	−	15.9072i	−0.234585	−	0.513671i
$960$	3.04959	−	1.95985i	0.0984252	−	0.0632540i
$961$	4.29996	−	29.9068i	0.138708	−	0.964737i
$962$	1.55396	+	0.998670i	0.0501017	+	0.0321984i
$963$	10.9746	−	12.6653i	0.353651	−	0.408135i
$964$	8.60854	+	2.52770i	0.277262	+	0.0814116i
$965$	−2.52298			−0.0812177
$966$	−3.51785	+	3.25956i	−0.113185	+	0.104875i
$967$	−13.0311			−0.419051			−0.209525	−	0.977803i	$-0.567192\pi$
$967$	−13.0311			−0.419051			−0.209525	+	0.977803i	$0.567192\pi$
$968$	−2.46959	−	0.725137i	−0.0793756	−	0.0233068i
$969$	3.82168	−	4.41046i	0.122770	−	0.141684i
$970$	−41.4838	−	26.6600i	−1.33196	−	0.856001i
$971$	−5.75552	+	40.0305i	−0.184703	+	1.28464i	0.660756	+	0.750600i	$0.270236\pi$
$971$	−5.75552	+	40.0305i	−0.184703	+	1.28464i	−0.845460	+	0.534039i	$0.820673\pi$
$972$	−0.841254	+	0.540641i	−0.0269832	+	0.0173411i
$973$	6.61219	+	14.4787i	0.211977	+	0.464165i
$974$	8.20217	+	9.46581i	0.262814	+	0.303304i
$975$	1.86202	+	12.9506i	0.0596322	+	0.414751i
$976$	3.70486	−	8.11250i	0.118590	−	0.259675i
$977$	31.6487	−	9.29291i	1.01253	−	0.297307i	0.266944	−	0.963712i	$-0.413986\pi$
$977$	31.6487	−	9.29291i	1.01253	−	0.297307i	0.745589	+	0.666406i	$0.232168\pi$
$978$	−13.2703	+	3.89650i	−0.424336	+	0.124596i
$979$	−2.14178	+	4.68985i	−0.0684516	+	0.149888i
$980$	0.515900	+	3.58816i	0.0164798	+	0.114620i
$981$	5.05388	+	5.83249i	0.161358	+	0.186217i
$982$	12.6485	+	27.6964i	0.403631	+	0.883829i
$983$	−46.7334	+	30.0337i	−1.49056	+	0.957927i	−0.494509	+	0.869172i	$0.664652\pi$
$983$	−46.7334	+	30.0337i	−1.49056	+	0.957927i	−0.996054	+	0.0887544i	$0.971711\pi$
$984$	1.03984	−	7.23222i	0.0331488	−	0.230555i
$985$	13.8041	+	8.87134i	0.439834	+	0.282664i
$986$	−3.73883	+	4.31484i	−0.119069	+	0.137412i
$987$	11.3446	+	3.33106i	0.361101	+	0.106029i
$988$	−5.16771			−0.164407
$989$	−9.22192	−	13.3501i	−0.293240	−	0.424510i
$990$	−10.5228			−0.334435
$991$	−34.7725	−	10.2101i	−1.10458	−	0.324335i	−0.321913	−	0.946769i	$-0.604326\pi$
$991$	−34.7725	−	10.2101i	−1.10458	−	0.324335i	−0.782672	+	0.622434i	$0.786144\pi$
$992$	0.580435	−	0.669858i	0.0184288	−	0.0212680i
$993$	−20.0870	−	12.9091i	−0.637442	−	0.409659i
$994$	0.181011	−	1.25896i	0.00574133	−	0.0399318i
$995$	−53.0070	+	34.0655i	−1.68043	+	1.07995i
$996$	2.20555	+	4.82948i	0.0698855	+	0.153028i
$997$	3.94591	+	4.55383i	0.124968	+	0.144221i	0.814786	−	0.579762i	$-0.196855\pi$
$997$	3.94591	+	4.55383i	0.124968	+	0.144221i	−0.689817	+	0.723983i	$0.742309\pi$
$998$	1.35196	+	9.40308i	0.0427955	+	0.297649i
$999$	0.477466	−	1.04550i	0.0151064	−	0.0330783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.h.547.3	✓	30
23.9	even	11	inner	966.2.q.h.883.3	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.h.547.3	✓	30	1.1	even	1	trivial
966.2.q.h.883.3	yes	30	23.9	even	11	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.959493 + 0.281733i) q^{2} +(0.654861 - 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.515900 - 3.58816i) q^{5} +(0.841254 - 0.540641i) q^{6} +(0.415415 + 0.909632i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.959493 + 0.281733i) q^{2} +(0.654861 - 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.515900 - 3.58816i) q^{5} +(0.841254 - 0.540641i) q^{6} +(0.415415 + 0.909632i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(1.50590 - 3.29747i) q^{10} +(2.78520 - 0.817809i) q^{11} +(0.959493 - 0.281733i) q^{12} +(0.667629 - 1.46190i) q^{13} +(0.142315 + 0.989821i) q^{14} +(-2.37391 - 2.73964i) q^{15} +(0.415415 + 0.909632i) q^{16} +(-1.52682 + 0.981227i) q^{17} +(0.142315 - 0.989821i) q^{18} +(-2.70503 - 1.73842i) q^{19} +(2.37391 - 2.73964i) q^{20} +(0.959493 + 0.281733i) q^{21} +2.90278 q^{22} +(-1.19715 + 4.64401i) q^{23} +1.00000 q^{24} +(-7.81128 - 2.29360i) q^{25} +(1.05245 - 1.21459i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(-0.142315 + 0.989821i) q^{28} +(2.64638 - 1.70073i) q^{29} +(-1.50590 - 3.29747i) q^{30} +(-0.580435 - 0.669858i) q^{31} +(0.142315 + 0.989821i) q^{32} +(1.20586 - 2.64046i) q^{33} +(-1.74142 + 0.511326i) q^{34} +(3.47822 - 1.02130i) q^{35} +(0.415415 - 0.909632i) q^{36} +(0.163573 + 1.13767i) q^{37} +(-2.10569 - 2.43009i) q^{38} +(-0.667629 - 1.46190i) q^{39} +(3.04959 - 1.95985i) q^{40} +(1.03984 - 7.23222i) q^{41} +(0.841254 + 0.540641i) q^{42} +(-2.21557 + 2.55691i) q^{43} +(2.78520 + 0.817809i) q^{44} -3.62506 q^{45} +(-2.45703 + 4.11862i) q^{46} +11.8235 q^{47} +(0.959493 + 0.281733i) q^{48} +(-0.654861 + 0.755750i) q^{49} +(-6.84869 - 4.40138i) q^{50} +(-0.258292 + 1.79646i) q^{51} +(1.35201 - 0.868884i) q^{52} +(2.10629 + 4.61212i) q^{53} +(-0.654861 - 0.755750i) q^{54} +(-1.49754 - 10.4157i) q^{55} +(-0.415415 + 0.909632i) q^{56} +(-3.08523 + 0.905904i) q^{57} +(3.01834 - 0.886264i) q^{58} +(-2.54552 + 5.57391i) q^{59} +(-0.515900 - 3.58816i) q^{60} +(-5.84034 - 6.74011i) q^{61} +(-0.368202 - 0.806251i) q^{62} +(0.841254 - 0.540641i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-4.90111 - 3.14975i) q^{65} +(1.90092 - 2.19378i) q^{66} +(2.26193 + 0.664162i) q^{67} -1.81493 q^{68} +(2.72574 + 3.94593i) q^{69} +3.62506 q^{70} +(-1.22039 - 0.358338i) q^{71} +(0.654861 - 0.755750i) q^{72} +(5.25460 + 3.37692i) q^{73} +(-0.163573 + 1.13767i) q^{74} +(-6.84869 + 4.40138i) q^{75} +(-1.33576 - 2.92490i) q^{76} +(1.90092 + 2.19378i) q^{77} +(-0.228719 - 1.59078i) q^{78} +(-3.96704 + 8.68660i) q^{79} +(3.47822 - 1.02130i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(3.03527 - 6.64631i) q^{82} +(0.755588 + 5.25523i) q^{83} +(0.654861 + 0.755750i) q^{84} +(2.73311 + 5.98469i) q^{85} +(-2.84619 + 1.82913i) q^{86} +(0.447689 - 3.11374i) q^{87} +(2.44198 + 1.56936i) q^{88} +(-1.16313 + 1.34232i) q^{89} +(-3.47822 - 1.02130i) q^{90} +1.60714 q^{91} +(-3.51785 + 3.25956i) q^{92} -0.886349 q^{93} +(11.3446 + 3.33106i) q^{94} +(-7.63324 + 8.80923i) q^{95} +(0.841254 + 0.540641i) q^{96} +(1.93592 - 13.4646i) q^{97} +(-0.841254 + 0.540641i) q^{98} +(-1.20586 - 2.64046i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 10 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 10 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 10 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} - 3 q^{9} + 12 q^{10} + 9 q^{11} + 3 q^{12} - 12 q^{13} + 3 q^{14} + q^{15} - 3 q^{16} + 13 q^{17} + 3 q^{18} - 18 q^{19} - q^{20} + 3 q^{21} + 24 q^{22} + 21 q^{23} + 30 q^{24} - 3 q^{25} + 34 q^{26} + 3 q^{27} - 3 q^{28} - 11 q^{29} - 12 q^{30} + 7 q^{31} + 3 q^{32} + 2 q^{33} - 13 q^{34} - q^{35} - 3 q^{36} + 3 q^{37} - 15 q^{38} + 12 q^{39} + q^{40} + 15 q^{41} - 3 q^{42} + 42 q^{43} + 9 q^{44} + 10 q^{45} + q^{46} + 12 q^{47} + 3 q^{48} - 3 q^{49} - 30 q^{50} + 9 q^{51} - q^{52} - 28 q^{53} - 3 q^{54} + 4 q^{55} + 3 q^{56} - 4 q^{57} - 11 q^{58} + 3 q^{59} - 10 q^{60} - 2 q^{61} + 26 q^{62} - 3 q^{63} - 3 q^{64} - 70 q^{65} - 2 q^{66} + 24 q^{67} + 2 q^{68} + q^{69} - 10 q^{70} - 3 q^{71} + 3 q^{72} - 7 q^{73} - 3 q^{74} - 30 q^{75} - 18 q^{76} - 2 q^{77} + 10 q^{78} - 32 q^{79} - q^{80} - 3 q^{81} - 26 q^{82} + 8 q^{83} + 3 q^{84} - 39 q^{85} + 35 q^{86} - 11 q^{87} + 13 q^{88} + 50 q^{89} + q^{90} + 32 q^{91} - 12 q^{92} + 4 q^{93} + 10 q^{94} + 73 q^{95} - 3 q^{96} + 24 q^{97} + 3 q^{98} - 2 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 10 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 - 3 * q^9 + 12 * q^10 + 9 * q^11 + 3 * q^12 - 12 * q^13 + 3 * q^14 + q^15 - 3 * q^16 + 13 * q^17 + 3 * q^18 - 18 * q^19 - q^20 + 3 * q^21 + 24 * q^22 + 21 * q^23 + 30 * q^24 - 3 * q^25 + 34 * q^26 + 3 * q^27 - 3 * q^28 - 11 * q^29 - 12 * q^30 + 7 * q^31 + 3 * q^32 + 2 * q^33 - 13 * q^34 - q^35 - 3 * q^36 + 3 * q^37 - 15 * q^38 + 12 * q^39 + q^40 + 15 * q^41 - 3 * q^42 + 42 * q^43 + 9 * q^44 + 10 * q^45 + q^46 + 12 * q^47 + 3 * q^48 - 3 * q^49 - 30 * q^50 + 9 * q^51 - q^52 - 28 * q^53 - 3 * q^54 + 4 * q^55 + 3 * q^56 - 4 * q^57 - 11 * q^58 + 3 * q^59 - 10 * q^60 - 2 * q^61 + 26 * q^62 - 3 * q^63 - 3 * q^64 - 70 * q^65 - 2 * q^66 + 24 * q^67 + 2 * q^68 + q^69 - 10 * q^70 - 3 * q^71 + 3 * q^72 - 7 * q^73 - 3 * q^74 - 30 * q^75 - 18 * q^76 - 2 * q^77 + 10 * q^78 - 32 * q^79 - q^80 - 3 * q^81 - 26 * q^82 + 8 * q^83 + 3 * q^84 - 39 * q^85 + 35 * q^86 - 11 * q^87 + 13 * q^88 + 50 * q^89 + q^90 + 32 * q^91 - 12 * q^92 + 4 * q^93 + 10 * q^94 + 73 * q^95 - 3 * q^96 + 24 * q^97 + 3 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more