LMFDB - Embedded newform 570.2.bi.a.347.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(17,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 9, 20]))

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

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

chi := DirichletCharacter("570.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bi (of order $36$, degree $12$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$40$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			347.14
Character	$\chi$	$=$	570.347
Dual form			570.2.bi.a.23.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.422618 + 0.906308i) q^{2} +(1.13741 + 1.30625i) q^{3} +(-0.642788 - 0.766044i) q^{4} +(2.03932 + 0.917164i) q^{5} +(-1.66456 + 0.478800i) q^{6} +(-1.13371 + 4.23108i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-0.412587 + 2.97149i) q^{9} +O(q^{10})$	\(q+(-0.422618 + 0.906308i) q^{2} +(1.13741 + 1.30625i) q^{3} +(-0.642788 - 0.766044i) q^{4} +(2.03932 + 0.917164i) q^{5} +(-1.66456 + 0.478800i) q^{6} +(-1.13371 + 4.23108i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-0.412587 + 2.97149i) q^{9} +(-1.69309 + 1.46064i) q^{10} +(1.81764 + 1.04941i) q^{11} +(0.269532 - 1.71095i) q^{12} +(-3.84366 - 2.69136i) q^{13} +(-3.35553 - 2.81563i) q^{14} +(1.12150 + 3.70705i) q^{15} +(-0.173648 + 0.984808i) q^{16} +(1.56811 - 3.36282i) q^{17} +(-2.51872 - 1.62974i) q^{18} +(-1.31641 - 4.15537i) q^{19} +(-0.608258 - 2.15175i) q^{20} +(-6.81636 + 3.33157i) q^{21} +(-1.71926 + 1.20384i) q^{22} +(6.58540 + 0.576148i) q^{23} +(1.43674 + 0.967358i) q^{24} +(3.31762 + 3.74078i) q^{25} +(4.06360 - 2.34612i) q^{26} +(-4.35080 + 2.84087i) q^{27} +(3.96993 - 1.85121i) q^{28} +(-7.59687 - 2.76504i) q^{29} +(-3.83370 - 0.550249i) q^{30} +(1.67251 + 2.89688i) q^{31} +(-0.819152 - 0.573576i) q^{32} +(0.696606 + 3.56791i) q^{33} +(2.38504 + 2.84237i) q^{34} +(-6.19260 + 7.58871i) q^{35} +(2.54150 - 1.59398i) q^{36} +(7.16856 + 7.16856i) q^{37} +(4.32238 + 0.563059i) q^{38} +(-0.856232 - 8.08197i) q^{39} +(2.20721 + 0.358099i) q^{40} +(-7.18278 - 1.26652i) q^{41} +(-0.138707 - 7.58570i) q^{42} +(-0.953329 + 0.0834055i) q^{43} +(-0.364458 - 2.06694i) q^{44} +(-3.56674 + 5.68140i) q^{45} +(-3.30528 + 5.72491i) q^{46} +(11.1066 - 5.17910i) q^{47} +(-1.48392 + 0.893304i) q^{48} +(-10.5546 - 6.09368i) q^{49} +(-4.79238 + 1.42586i) q^{50} +(6.17627 - 1.77657i) q^{51} +(0.408956 + 4.67438i) q^{52} +(1.37273 + 0.120098i) q^{53} +(-0.735975 - 5.14377i) q^{54} +(2.74426 + 3.80716i) q^{55} +4.38034i q^{56} +(3.93065 - 6.44593i) q^{57} +(5.71655 - 5.71655i) q^{58} +(-4.99759 + 1.81897i) q^{59} +(2.11888 - 3.24196i) q^{60} +(-1.57675 + 1.32305i) q^{61} +(-3.33229 + 0.291538i) q^{62} +(-12.1049 - 5.11452i) q^{63} +(0.866025 - 0.500000i) q^{64} +(-5.37002 - 9.01380i) q^{65} +(-3.52803 - 0.876526i) q^{66} +(-4.17411 - 8.95141i) q^{67} +(-3.58403 + 0.960337i) q^{68} +(6.73772 + 9.25751i) q^{69} +(-4.26060 - 8.81953i) q^{70} +(6.19315 - 7.38071i) q^{71} +(0.370550 + 2.97703i) q^{72} +(5.21699 + 7.45063i) q^{73} +(-9.52648 + 3.46736i) q^{74} +(-1.11289 + 8.58845i) q^{75} +(-2.33702 + 3.67945i) q^{76} +(-6.50085 + 6.50085i) q^{77} +(7.68661 + 2.63958i) q^{78} +(5.64724 + 0.995761i) q^{79} +(-1.25735 + 1.84907i) q^{80} +(-8.65954 - 2.45200i) q^{81} +(4.18343 - 5.97455i) q^{82} +(-1.61763 + 6.03708i) q^{83} +(6.93360 + 3.08014i) q^{84} +(6.28212 - 5.41963i) q^{85} +(0.327303 - 0.899258i) q^{86} +(-5.02894 - 13.0684i) q^{87} +(2.02731 + 0.543217i) q^{88} +(1.06639 + 6.04779i) q^{89} +(-3.64173 - 5.63363i) q^{90} +(15.7450 - 13.2116i) q^{91} +(-3.79166 - 5.41505i) q^{92} +(-1.88171 + 5.47966i) q^{93} +12.2548i q^{94} +(1.12657 - 9.68147i) q^{95} +(-0.182478 - 1.72241i) q^{96} +(6.95363 + 3.24253i) q^{97} +(9.98330 - 6.99038i) q^{98} +(-3.86826 + 4.96813i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q+O(q^{10}) $ 480 * q	$ 480 q - 36 q^{15} - 48 q^{18} + 24 q^{22} - 24 q^{25} + 72 q^{33} + 24 q^{43} - 36 q^{45} + 24 q^{51} - 120 q^{55} + 108 q^{57} - 48 q^{60} - 48 q^{61} - 36 q^{63} - 24 q^{66} + 48 q^{67} - 48 q^{70} - 48 q^{78} - 144 q^{81} - 48 q^{85} - 96 q^{87} - 168 q^{90} - 144 q^{91} - 228 q^{93} + 48 q^{97}+O(q^{100}) $ 480 * q - 36 * q^15 - 48 * q^18 + 24 * q^22 - 24 * q^25 + 72 * q^33 + 24 * q^43 - 36 * q^45 + 24 * q^51 - 120 * q^55 + 108 * q^57 - 48 * q^60 - 48 * q^61 - 36 * q^63 - 24 * q^66 + 48 * q^67 - 48 * q^70 - 48 * q^78 - 144 * q^81 - 48 * q^85 - 96 * q^87 - 168 * q^90 - 144 * q^91 - 228 * q^93 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.422618	+	0.906308i	−0.298836	+	0.640856i
$2$	−0.422618	+	0.906308i	−0.298836	+	0.640856i
$3$	1.13741	+	1.30625i	0.656685	+	0.754165i
$3$	1.13741	+	1.30625i	0.656685	+	0.754165i
$4$	−0.642788	−	0.766044i	−0.321394	−	0.383022i
$5$	2.03932	+	0.917164i	0.912010	+	0.410168i
$5$	2.03932	+	0.917164i	0.912010	+	0.410168i
$6$	−1.66456	+	0.478800i	−0.679553	+	0.195469i
$7$	−1.13371	+	4.23108i	−0.428504	+	1.59920i	0.327646	+	0.944800i	$0.393745\pi$
$7$	−1.13371	+	4.23108i	−0.428504	+	1.59920i	−0.756150	+	0.654398i	$0.772922\pi$
$8$	0.965926	−	0.258819i	0.341506	−	0.0915064i
$9$	−0.412587	+	2.97149i	−0.137529	+	0.990498i
$10$	−1.69309	+	1.46064i	−0.535401	+	0.461894i
$11$	1.81764	+	1.04941i	0.548039	+	0.316410i	0.748331	−	0.663326i	$-0.230856\pi$
$11$	1.81764	+	1.04941i	0.548039	+	0.316410i	−0.200292	+	0.979736i	$0.564189\pi$
$12$	0.269532	−	1.71095i	0.0778073	−	0.493909i
$13$	−3.84366	−	2.69136i	−1.06604	−	0.746449i	−0.0974812	−	0.995237i	$-0.531079\pi$
$13$	−3.84366	−	2.69136i	−1.06604	−	0.746449i	−0.968558	+	0.248789i	$0.919967\pi$
$14$	−3.35553	−	2.81563i	−0.896804	−	0.752508i
$15$	1.12150	+	3.70705i	0.289569	+	0.957157i
$16$	−0.173648	+	0.984808i	−0.0434120	+	0.246202i
$17$	1.56811	−	3.36282i	0.380322	−	0.815602i	−0.619217	−	0.785220i	$-0.712550\pi$
$17$	1.56811	−	3.36282i	0.380322	−	0.815602i	0.999538	−	0.0303823i	$-0.00967248\pi$
$18$	−2.51872	−	1.62974i	−0.593668	−	0.384133i
$19$	−1.31641	−	4.15537i	−0.302006	−	0.953306i
$19$	−1.31641	−	4.15537i	−0.302006	−	0.953306i
$20$	−0.608258	−	2.15175i	−0.136011	−	0.481146i
$21$	−6.81636	+	3.33157i	−1.48745	+	0.727007i
$22$	−1.71926	+	1.20384i	−0.366548	+	0.256659i
$23$	6.58540	+	0.576148i	1.37315	+	0.120135i	0.749726	−	0.661748i	$-0.230185\pi$
$23$	6.58540	+	0.576148i	1.37315	+	0.120135i	0.623425	+	0.781884i	$0.285741\pi$
$24$	1.43674	+	0.967358i	0.293273	+	0.197461i
$25$	3.31762	+	3.74078i	0.663524	+	0.748155i
$26$	4.06360	−	2.34612i	0.796937	−	0.460112i
$27$	−4.35080	+	2.84087i	−0.837312	+	0.546726i
$28$	3.96993	−	1.85121i	0.750247	−	0.349846i
$29$	−7.59687	−	2.76504i	−1.41070	−	0.513454i	−0.479367	−	0.877614i	$-0.659134\pi$
$29$	−7.59687	−	2.76504i	−1.41070	−	0.513454i	−0.931336	+	0.364160i	$0.881356\pi$
$30$	−3.83370	−	0.550249i	−0.699934	−	0.100461i
$31$	1.67251	+	2.89688i	0.300392	+	0.520294i	0.976225	−	0.216761i	$-0.0695492\pi$
$31$	1.67251	+	2.89688i	0.300392	+	0.520294i	−0.675833	+	0.737055i	$0.736216\pi$
$32$	−0.819152	−	0.573576i	−0.144807	−	0.101395i
$33$	0.696606	+	3.56791i	0.121263	+	0.621094i
$34$	2.38504	+	2.84237i	0.409030	+	0.487463i
$35$	−6.19260	+	7.58871i	−1.04674	+	1.28273i
$36$	2.54150	−	1.59398i	0.423584	−	0.265663i
$37$	7.16856	+	7.16856i	1.17850	+	1.17850i	0.980126	+	0.198378i	$0.0635674\pi$
$37$	7.16856	+	7.16856i	1.17850	+	1.17850i	0.198378	+	0.980126i	$0.436433\pi$
$38$	4.32238	+	0.563059i	0.701183	+	0.0913402i
$39$	−0.856232	−	8.08197i	−0.137107	−	1.29415i
$40$	2.20721	+	0.358099i	0.348990	+	0.0566204i
$41$	−7.18278	−	1.26652i	−1.12176	−	0.197797i	−0.418147	−	0.908379i	$-0.637320\pi$
$41$	−7.18278	−	1.26652i	−1.12176	−	0.197797i	−0.703614	+	0.710583i	$0.748431\pi$
$42$	−0.138707	−	7.58570i	−0.0214030	−	1.17050i
$43$	−0.953329	+	0.0834055i	−0.145381	+	0.0127192i	−0.159614	−	0.987179i	$-0.551025\pi$
$43$	−0.953329	+	0.0834055i	−0.145381	+	0.0127192i	0.0142327	+	0.999899i	$0.495469\pi$
$44$	−0.364458	−	2.06694i	−0.0549441	−	0.311603i
$45$	−3.56674	+	5.68140i	−0.531699	+	0.846934i
$46$	−3.30528	+	5.72491i	−0.487336	+	0.844092i
$47$	11.1066	−	5.17910i	1.62007	−	0.755450i	0.620481	−	0.784221i	$-0.286937\pi$
$47$	11.1066	−	5.17910i	1.62007	−	0.755450i	0.999586	+	0.0287713i	$0.00915946\pi$
$48$	−1.48392	+	0.893304i	−0.214185	+	0.128937i
$49$	−10.5546	−	6.09368i	−1.50780	−	0.870526i
$50$	−4.79238	+	1.42586i	−0.677745	+	0.201648i
$51$	6.17627	−	1.77657i	0.864850	−	0.248769i
$52$	0.408956	+	4.67438i	0.0567120	+	0.648221i
$53$	1.37273	+	0.120098i	0.188558	+	0.0164967i	0.181044	−	0.983475i	$-0.442052\pi$
$53$	1.37273	+	0.120098i	0.188558	+	0.0164967i	0.00751462	+	0.999972i	$0.497608\pi$
$54$	−0.735975	−	5.14377i	−0.100154	−	0.699978i
$55$	2.74426	+	3.80716i	0.370035	+	0.513358i
$56$			4.38034i			0.585347i
$57$	3.93065	−	6.44593i	0.520627	−	0.853784i
$58$	5.71655	−	5.71655i	0.750620	−	0.750620i
$59$	−4.99759	+	1.81897i	−0.650631	+	0.236810i	−0.646186	−	0.763180i	$-0.723637\pi$
$59$	−4.99759	+	1.81897i	−0.650631	+	0.236810i	−0.00444460	+	0.999990i	$0.501415\pi$
$60$	2.11888	−	3.24196i	0.273547	−	0.418536i
$61$	−1.57675	+	1.32305i	−0.201883	+	0.169400i	−0.738124	−	0.674665i	$-0.764288\pi$
$61$	−1.57675	+	1.32305i	−0.201883	+	0.169400i	0.536241	+	0.844065i	$0.319844\pi$
$62$	−3.33229	+	0.291538i	−0.423202	+	0.0370254i
$63$	−12.1049	−	5.11452i	−1.52507	−	0.644369i
$64$	0.866025	−	0.500000i	0.108253	−	0.0625000i
$65$	−5.37002	−	9.01380i	−0.666068	−	1.11802i
$66$	−3.52803	−	0.876526i	−0.434270	−	0.107893i
$67$	−4.17411	−	8.95141i	−0.509949	−	1.09359i	−0.977754	−	0.209757i	$-0.932733\pi$
$67$	−4.17411	−	8.95141i	−0.509949	−	1.09359i	0.467805	−	0.883832i	$-0.345045\pi$
$68$	−3.58403	+	0.960337i	−0.434627	+	0.116458i
$69$	6.73772	+	9.25751i	0.811126	+	1.11447i
$70$	−4.26060	−	8.81953i	−0.509239	−	1.05414i
$71$	6.19315	−	7.38071i	0.734991	−	0.875929i	−0.261004	−	0.965338i	$-0.584053\pi$
$71$	6.19315	−	7.38071i	0.734991	−	0.875929i	0.995995	+	0.0894093i	$0.0284979\pi$
$72$	0.370550	+	2.97703i	0.0436698	+	0.350846i
$73$	5.21699	+	7.45063i	0.610602	+	0.872030i	0.998771	−	0.0495579i	$-0.0157812\pi$
$73$	5.21699	+	7.45063i	0.610602	+	0.872030i	−0.388169	+	0.921588i	$0.626892\pi$
$74$	−9.52648	+	3.46736i	−1.10743	+	0.403072i
$75$	−1.11289	+	8.58845i	−0.128506	+	0.991709i
$76$	−2.33702	+	3.67945i	−0.268075	+	0.422062i
$77$	−6.50085	+	6.50085i	−0.740840	+	0.740840i
$78$	7.68661	+	2.63958i	0.870337	+	0.298873i
$79$	5.64724	+	0.995761i	0.635364	+	0.112032i	0.482047	−	0.876145i	$-0.339893\pi$
$79$	5.64724	+	0.995761i	0.635364	+	0.112032i	0.153317	+	0.988177i	$0.451004\pi$
$80$	−1.25735	+	1.84907i	−0.140576	+	0.206732i
$81$	−8.65954	−	2.45200i	−0.962172	−	0.272444i
$82$	4.18343	−	5.97455i	0.461982	−	0.659779i
$83$	−1.61763	+	6.03708i	−0.177558	+	0.662655i	0.818544	+	0.574444i	$0.194782\pi$
$83$	−1.61763	+	6.03708i	−0.177558	+	0.662655i	−0.996102	+	0.0882112i	$0.971885\pi$
$84$	6.93360	+	3.08014i	0.756518	+	0.336071i
$85$	6.28212	−	5.41963i	0.681391	−	0.587842i
$86$	0.327303	−	0.899258i	0.0352940	−	0.0969695i
$87$	−5.02894	−	13.0684i	−0.539159	−	1.40108i
$88$	2.02731	+	0.543217i	0.216112	+	0.0579071i
$89$	1.06639	+	6.04779i	0.113037	+	0.641065i	0.987703	+	0.156339i	$0.0499693\pi$
$89$	1.06639	+	6.04779i	0.113037	+	0.641065i	−0.874666	+	0.484725i	$0.838920\pi$
$90$	−3.64173	−	5.63363i	−0.383872	−	0.593837i
$91$	15.7450	−	13.2116i	1.65052	−	1.38495i
$92$	−3.79166	−	5.41505i	−0.395308	−	0.564558i
$93$	−1.88171	+	5.47966i	−0.195125	+	0.568215i
$94$			12.2548i			1.26399i
$95$	1.12657	−	9.68147i	0.115584	−	0.993298i
$96$	−0.182478	−	1.72241i	−0.0186241	−	0.175793i
$97$	6.95363	+	3.24253i	0.706034	+	0.329229i	0.742258	−	0.670115i	$-0.233755\pi$
$97$	6.95363	+	3.24253i	0.706034	+	0.329229i	−0.0362235	+	0.999344i	$0.511533\pi$
$98$	9.98330	−	6.99038i	1.00847	−	0.706135i
$99$	−3.86826	+	4.96813i	−0.388775	+	0.499316i
$100$	0.733076	−	4.94597i	0.0733076	−	0.494597i
$101$	10.0379	−	1.76996i	0.998811	−	0.176117i	0.349741	−	0.936846i	$-0.386269\pi$
$101$	10.0379	−	1.76996i	0.998811	−	0.176117i	0.649070	+	0.760729i	$0.275158\pi$
$102$	−1.00009	+	6.34841i	−0.0990235	+	0.628586i
$103$	1.22995	+	4.59025i	0.121191	+	0.452291i	0.999675	−	0.0254802i	$-0.00811149\pi$
$103$	1.22995	+	4.59025i	0.121191	+	0.452291i	−0.878484	+	0.477771i	$0.841445\pi$
$104$	−4.40926	−	1.60484i	−0.432364	−	0.157368i
$105$	−16.9563	+	0.542396i	−1.65477	+	0.0529324i
$106$	−0.688985	+	1.19336i	−0.0669201	+	0.115909i
$107$	1.71119	+	0.458513i	0.165427	+	0.0443261i	0.340582	−	0.940215i	$-0.389376\pi$
$107$	1.71119	+	0.458513i	0.165427	+	0.0443261i	−0.175155	+	0.984541i	$0.556043\pi$
$108$	4.97287	+	1.50683i	0.478515	+	0.144995i
$109$	−3.21798	+	3.83504i	−0.308227	+	0.367330i	−0.897814	−	0.440374i	$-0.854846\pi$
$109$	−3.21798	+	3.83504i	−0.308227	+	0.367330i	0.589588	+	0.807704i	$0.299290\pi$
$110$	−4.61023	+	0.878164i	−0.439569	+	0.0837297i
$111$	−1.21034	+	17.5175i	−0.114880	+	1.66269i
$112$	−3.96993	−	1.85121i	−0.375124	−	0.174923i
$113$	1.99985	+	1.99985i	0.188130	+	0.188130i	0.794887	−	0.606757i	$-0.207530\pi$
$113$	1.99985	+	1.99985i	0.188130	+	0.188130i	−0.606757	+	0.794887i	$0.707530\pi$
$114$	4.18083	+	6.28655i	0.391571	+	0.588789i
$115$	12.9013	+	7.21484i	1.20305	+	0.672787i
$116$	2.76504	+	7.59687i	0.256727	+	0.705352i
$117$	9.58320	−	10.3110i	0.885967	−	0.953251i
$118$	0.463522	−	5.29808i	0.0426707	−	0.487728i
$119$	12.4506	+	10.4473i	1.14134	+	0.957699i
$120$	2.04274	+	3.29047i	0.186476	+	0.300378i
$121$	−3.29746	−	5.71136i	−0.299769	−	0.519215i
$122$	−0.532728	−	1.98817i	−0.0482310	−	0.180000i
$123$	−6.51539	−	10.8231i	−0.587473	−	0.975883i
$124$	1.14407	−	3.14329i	0.102740	−	0.282276i
$125$	3.33477	+	10.6714i	0.298271	+	0.954481i
$126$	9.75107	−	8.80925i	0.868694	−	0.784791i
$127$	5.18502	−	7.40498i	0.460096	−	0.657086i	−0.520331	−	0.853964i	$-0.674192\pi$
$127$	5.18502	−	7.40498i	0.460096	−	0.657086i	0.980428	+	0.196879i	$0.0630805\pi$
$128$	0.0871557	+	0.996195i	0.00770355	+	0.0880520i
$129$	−1.19328	−	1.15042i	−0.105062	−	0.101289i
$130$	10.4387	−	1.05749i	0.915538	−	0.0927482i
$131$	4.44041	+	12.1999i	0.387960	+	1.06591i	0.967918	+	0.251266i	$0.0808468\pi$
$131$	4.44041	+	12.1999i	0.387960	+	1.06591i	−0.579958	+	0.814646i	$0.696931\pi$
$132$	2.28541	−	2.82704i	0.198919	−	0.246062i
$133$	19.0741	−	0.858846i	1.65394	−	0.0744714i
$134$	9.87678			0.853224
$135$	−11.4782	+	1.80303i	−0.987886	+	0.155180i
$136$	0.644314	−	3.65409i	0.0552495	−	0.313335i
$137$	1.87464	−	21.4273i	0.160162	−	1.83066i	−0.313085	−	0.949725i	$-0.601362\pi$
$137$	1.87464	−	21.4273i	0.160162	−	1.83066i	0.473246	−	0.880930i	$-0.343082\pi$
$138$	−11.2376	+	2.19406i	−0.956611	+	0.186770i
$139$	−3.25489	+	0.573925i	−0.276076	+	0.0486797i	−0.309972	−	0.950746i	$-0.600320\pi$
$139$	−3.25489	+	0.573925i	−0.276076	+	0.0486797i	0.0338958	+	0.999425i	$0.489209\pi$
$140$	9.79382	−	0.134122i	0.827729	−	0.0113353i
$141$	19.3980	+	8.61727i	1.63361	+	0.725705i
$142$	4.07185	+	8.73212i	0.341702	+	0.732783i
$143$	−4.16203	−	8.92551i	−0.348047	−	0.746389i
$144$	−2.85470	−	0.922313i	−0.237892	−	0.0768595i
$145$	−12.9564	−	12.6064i	−1.07597	−	1.04690i
$146$	−8.95736	+	1.57942i	−0.741316	+	0.130714i
$147$	−4.04501	−	20.7179i	−0.333627	−	1.70879i
$148$	0.883574	−	10.0993i	0.0726293	−	0.830157i
$149$	3.82029	−	21.6659i	0.312970	−	1.77494i	−0.270413	−	0.962745i	$-0.587160\pi$
$149$	3.82029	−	21.6659i	0.312970	−	1.77494i	0.583383	−	0.812197i	$-0.301729\pi$
$150$	−7.31345	−	4.63826i	−0.597141	−	0.378712i
$151$	2.80992			0.228668			0.114334	−	0.993442i	$-0.463527\pi$
$151$	2.80992			0.228668			0.114334	+	0.993442i	$0.463527\pi$
$152$	−2.34704	−	3.67306i	−0.190370	−	0.297925i
$153$	9.34560	+	6.04707i	0.755547	+	0.488877i
$154$	−3.14439	−	8.63914i	−0.253382	−	0.696162i
$155$	0.753869	+	7.44161i	0.0605522	+	0.597725i
$156$	−5.64077	+	5.85090i	−0.451623	+	0.468447i
$157$	−0.118730	−	1.35708i	−0.00947565	−	0.108307i	0.989984	−	0.141180i	$-0.0450898\pi$
$157$	−0.118730	−	1.35708i	−0.00947565	−	0.108307i	−0.999460	+	0.0328733i	$0.989534\pi$
$158$	−3.28909	+	4.69731i	−0.261666	+	0.373698i
$159$	1.40448	+	1.92973i	0.111382	+	0.153037i
$160$	−1.14445	−	1.92100i	−0.0904764	−	0.151868i
$161$	−9.90369	+	27.2102i	−0.780520	+	2.14446i
$162$	5.88195	−	6.81195i	0.462129	−	0.535197i
$163$	2.39491	+	8.93792i	0.187584	+	0.700072i	0.994063	+	0.108809i	$0.0347037\pi$
$163$	2.39491	+	8.93792i	0.187584	+	0.700072i	−0.806479	+	0.591263i	$0.798630\pi$
$164$	3.64679	+	6.31643i	0.284766	+	0.493230i
$165$	−1.85176	+	7.91500i	−0.144160	+	0.616182i
$166$	−4.78781	−	4.01745i	−0.371606	−	0.311815i
$167$	−0.0873362	+	0.998258i	−0.00675828	+	0.0772475i	−0.998825	−	0.0484665i	$-0.984567\pi$
$167$	−0.0873362	+	0.998258i	−0.00675828	+	0.0772475i	0.992067	+	0.125714i	$0.0401222\pi$
$168$	−5.72182	+	4.98225i	−0.441448	+	0.384389i
$169$	3.08404	+	8.47332i	0.237234	+	0.651794i
$170$	2.25692	+	7.98397i	0.173098	+	0.612342i
$171$	12.8908	−	2.19726i	0.985782	−	0.168029i
$172$	0.676680	+	0.676680i	0.0515964	+	0.0515964i
$173$	−0.102979	−	0.0480197i	−0.00782931	−	0.00365087i	0.418700	−	0.908125i	$-0.362486\pi$
$173$	−0.102979	−	0.0480197i	−0.00782931	−	0.00365087i	−0.426529	+	0.904474i	$0.640264\pi$
$174$	13.9693	+	0.965180i	1.05901	+	0.0731701i
$175$	−19.5888	+	9.79615i	−1.48077	+	0.740519i
$176$	−1.34910	+	1.60780i	−0.101692	+	0.121192i
$177$	−8.06036	−	4.45919i	−0.605853	−	0.335173i
$178$	−5.93184	−	1.58943i	−0.444610	−	0.119133i
$179$	0.409048	−	0.708492i	0.0305737	−	0.0529552i	−0.850334	−	0.526244i	$-0.823600\pi$
$179$	0.409048	−	0.708492i	0.0305737	−	0.0529552i	0.880907	+	0.473289i	$0.156933\pi$
$180$	6.64487	−	0.919652i	0.495279	−	0.0685468i
$181$	−13.5223	−	4.92171i	−1.00510	−	0.365827i	−0.213552	−	0.976932i	$-0.568503\pi$
$181$	−13.5223	−	4.92171i	−1.00510	−	0.365827i	−0.791550	+	0.611104i	$0.790726\pi$
$182$	5.31966	+	19.8533i	0.394320	+	1.47162i
$183$	−3.52166	−	0.554780i	−0.260328	−	0.0410105i
$184$	6.51012	−	1.14791i	0.479933	−	0.0846251i
$185$	8.04421	+	21.1937i	0.591422	+	1.55819i
$186$	−4.17101	−	4.02122i	−0.305834	−	0.294850i
$187$	6.37924	−	4.46679i	0.466496	−	0.326644i
$188$	−11.1066	−	5.17910i	−0.810034	−	0.377725i
$189$	−7.08739	−	21.6293i	−0.515531	−	1.57330i
$190$	8.29828	+	5.11259i	0.602020	+	0.370906i
$191$		−	4.13343i		−	0.299085i	−0.988755	−	0.149542i	$-0.952220\pi$
$191$		−	4.13343i		−	0.299085i	0.988755	−	0.149542i	$-0.0477801\pi$
$192$	1.63815	+	0.562541i	0.118224	+	0.0405979i
$193$	−1.17455	−	1.67744i	−0.0845462	−	0.120744i	0.774651	−	0.632389i	$-0.217925\pi$
$193$	−1.17455	−	1.67744i	−0.0845462	−	0.120744i	−0.859197	+	0.511644i	$0.829037\pi$
$194$	−5.87746	+	4.93178i	−0.421977	+	0.354081i
$195$	5.66637	−	17.2670i	0.405777	−	1.23652i
$196$	2.11631	+	12.0022i	0.151165	+	0.857301i
$197$	1.75170	+	0.469367i	0.124804	+	0.0334410i	0.320680	−	0.947188i	$-0.396089\pi$
$197$	1.75170	+	0.469367i	0.124804	+	0.0334410i	−0.195877	+	0.980629i	$0.562755\pi$
$198$	−2.86786	−	5.60546i	−0.203810	−	0.398363i
$199$	6.70157	−	18.4124i	0.475061	−	1.30522i	−0.438577	−	0.898693i	$-0.644517\pi$
$199$	6.70157	−	18.4124i	0.475061	−	1.30522i	0.913639	−	0.406527i	$-0.133260\pi$
$200$	4.17276	+	2.75465i	0.295059	+	0.194783i
$201$	6.94511	−	15.6339i	0.489870	−	1.10273i
$202$	−2.63809	+	9.84547i	−0.185615	+	0.692725i
$203$	20.3118	−	29.0082i	1.42561	−	2.03598i
$204$	−5.33096	−	3.58934i	−0.373242	−	0.251304i
$205$	−13.4863	−	9.17061i	−0.941927	−	0.640503i
$206$	−4.67998	−	0.825207i	−0.326070	−	0.0574949i
$207$	−4.42907	+	19.3308i	−0.307842	+	1.34358i
$208$	3.31791	−	3.31791i	0.230056	−	0.230056i
$209$	1.96794	−	8.93442i	0.136125	−	0.618007i
$210$	6.67447	−	15.5969i	0.460582	−	1.07629i
$211$	6.41447	−	2.33468i	0.441590	−	0.160726i	−0.111650	−	0.993748i	$-0.535613\pi$
$211$	6.41447	−	2.33468i	0.441590	−	0.160726i	0.553240	+	0.833022i	$0.313391\pi$
$212$	−0.790371	−	1.12877i	−0.0542829	−	0.0775240i
$213$	16.6852	−	0.305095i	1.14325	−	0.0209048i
$214$	−1.13874	+	1.35709i	−0.0778424	+	0.0927690i
$215$	−2.02064	−	0.704269i	−0.137806	−	0.0480308i
$216$	−3.46728	+	3.87014i	−0.235918	+	0.263330i
$217$	−14.1531	+	3.79230i	−0.960773	+	0.257438i
$218$	−2.11575	−	4.53724i	−0.143297	−	0.307300i
$219$	−3.79853	+	15.2891i	−0.256681	+	1.03314i
$220$	1.15248	−	4.54942i	0.0777003	−	0.306722i
$221$	−15.0778	+	8.70518i	−1.01424	+	0.585573i
$222$	−15.3648	−	8.50017i	−1.03122	−	0.570494i
$223$	−16.1862	+	1.41611i	−1.08391	+	0.0948295i	−0.615083	−	0.788462i	$-0.710877\pi$
$223$	−16.1862	+	1.41611i	−1.08391	+	0.0948295i	−0.468823	+	0.883292i	$0.655322\pi$
$224$	3.35553	−	2.81563i	0.224201	−	0.188127i
$225$	−12.4845	+	8.31489i	−0.832300	+	0.554326i
$226$	−2.65766	+	0.967308i	−0.176785	+	0.0643444i
$227$	18.8331	−	18.8331i	1.25000	−	1.25000i	0.294276	−	0.955720i	$-0.404921\pi$
$227$	18.8331	−	18.8331i	1.25000	−	1.25000i	0.955720	−	0.294276i	$-0.0950786\pi$
$228$	−7.46444	+	1.13231i	−0.494345	+	0.0749890i
$229$			9.30797i			0.615088i	0.951534	+	0.307544i	$0.0995071\pi$
$229$			9.30797i			0.615088i	−0.951534	+	0.307544i	$0.900493\pi$
$230$	−11.9912	+	8.64341i	−0.790675	+	0.569930i
$231$	−15.8859	−	1.09760i	−1.04521	−	0.0722168i
$232$	−8.05366	−	0.704604i	−0.528749	−	0.0462595i
$233$	−0.208005	−	2.37750i	−0.0136268	−	0.155755i	0.986333	−	0.164767i	$-0.0526871\pi$
$233$	−0.208005	−	2.37750i	−0.0136268	−	0.155755i	−0.999959	+	0.00901131i	$0.997132\pi$
$234$	5.29489	+	13.0429i	0.346138	+	0.852643i
$235$	27.4000	−	0.375230i	1.78738	−	0.0244773i
$236$	4.60580	+	2.65916i	0.299812	+	0.173097i
$237$	5.12253	+	8.50931i	0.332744	+	0.552739i
$238$	−14.7303	+	6.86884i	−0.954821	+	0.445241i
$239$	8.99389	−	15.5779i	0.581766	−	1.00765i	−0.413504	−	0.910502i	$-0.635695\pi$
$239$	8.99389	−	15.5779i	0.581766	−	1.00765i	0.995270	−	0.0971465i	$-0.0309715\pi$
$240$	−3.84548	+	0.460734i	−0.248225	+	0.0297403i
$241$	0.115647	+	0.655866i	0.00744947	+	0.0422480i	0.988306	−	0.152484i	$-0.0487273\pi$
$241$	0.115647	+	0.655866i	0.00744947	+	0.0422480i	−0.980856	+	0.194732i	$0.937616\pi$
$242$	6.56982	−	0.574785i	0.422324	−	0.0369486i
$243$	−6.64654	−	14.1005i	−0.426376	−	0.904546i
$244$	2.02703	+	0.357421i	0.129768	+	0.0228815i
$245$	−15.9352	−	22.1072i	−1.01806	−	1.41238i
$246$	12.5625	−	1.33092i	0.800959	−	0.0848564i
$247$	−6.12374	+	19.5147i	−0.389644	+	1.24169i
$248$	2.36529	+	2.36529i	0.150196	+	0.150196i
$249$	−9.72585	+	4.75361i	−0.616351	+	0.301248i
$250$	−11.0809	−	1.48761i	−0.700820	−	0.0940849i
$251$	−6.40687	−	7.63541i	−0.404398	−	0.481943i	0.524958	−	0.851128i	$-0.324081\pi$
$251$	−6.40687	−	7.63541i	−0.404398	−	0.481943i	−0.929356	+	0.369186i	$0.879637\pi$
$252$	3.86292	+	12.5604i	0.243341	+	0.791232i
$253$	11.3653	+	7.95804i	0.714528	+	0.500318i
$254$	4.51991	+	7.82871i	0.283604	+	0.491217i
$255$	14.2248	+	2.04167i	0.890789	+	0.127855i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−22.7677	+	10.6168i	−1.42021	+	0.662256i	−0.972709	−	0.232027i	$-0.925464\pi$
$257$	−22.7677	+	10.6168i	−1.42021	+	0.662256i	−0.447503	+	0.894283i	$0.647687\pi$
$258$	1.54694	−	0.595287i	0.0963080	−	0.0370609i
$259$	−38.4579	+	22.2037i	−2.38965	+	1.37967i
$260$	−3.45319	+	9.90763i	−0.214158	+	0.614445i
$261$	11.3507	−	21.4332i	0.702588	−	1.32668i
$262$	−12.9335	−	1.13153i	−0.799033	−	0.0699063i
$263$	6.86479	−	4.80677i	0.423301	−	0.296398i	−0.342450	−	0.939536i	$-0.611257\pi$
$263$	6.86479	−	4.80677i	0.423301	−	0.296398i	0.765751	+	0.643138i	$0.222368\pi$
$264$	1.59631	+	3.26604i	0.0982463	+	0.201011i
$265$	2.68927	+	1.50393i	0.165201	+	0.0923858i
$266$	−7.28270	+	17.6500i	−0.446531	+	1.08219i
$267$	−6.68701	+	8.27180i	−0.409239	+	0.506226i
$268$	−4.17411	+	8.95141i	−0.254974	+	0.546794i
$269$	−0.816330	+	4.62964i	−0.0497725	+	0.282274i	−0.999528	−	0.0307187i	$-0.990220\pi$
$269$	−0.816330	+	4.62964i	−0.0497725	+	0.282274i	0.949756	+	0.312993i	$0.101332\pi$
$270$	3.21679	−	11.1648i	0.195768	−	0.679467i
$271$	−7.98675	−	6.70168i	−0.485160	−	0.407098i	0.367128	−	0.930171i	$-0.380341\pi$
$271$	−7.98675	−	6.70168i	−0.485160	−	0.407098i	−0.852288	+	0.523073i	$0.824786\pi$
$272$	3.03943	+	2.12823i	0.184292	+	0.129043i
$273$	35.1662	+	5.53986i	2.12835	+	0.335288i
$274$	18.6274	+	10.7546i	1.12533	+	0.649707i
$275$	2.10461	+	10.2809i	0.126913	+	0.619964i
$276$	2.76074	−	11.1120i	0.166177	−	0.668864i
$277$	7.15227	−	1.91645i	0.429738	−	0.115148i	−0.0374650	−	0.999298i	$-0.511928\pi$
$277$	7.15227	−	1.91645i	0.429738	−	0.115148i	0.467203	+	0.884150i	$0.345262\pi$
$278$	0.855423	−	3.19248i	0.0513049	−	0.191472i
$279$	−9.29810	+	3.77464i	−0.556663	+	0.225982i
$280$	−4.01749	+	8.93289i	−0.240091	+	0.533843i
$281$	3.56978	+	4.25430i	0.212955	+	0.253790i	0.861939	−	0.507012i	$-0.169250\pi$
$281$	3.56978	+	4.25430i	0.212955	+	0.253790i	−0.648984	+	0.760802i	$0.724806\pi$
$282$	−16.0079	+	13.9388i	−0.953254	+	0.830041i
$283$	−13.9417	+	29.8980i	−0.828745	+	1.77725i	−0.236218	+	0.971700i	$0.575908\pi$
$283$	−13.9417	+	29.8980i	−0.828745	+	1.77725i	−0.592527	+	0.805550i	$0.701870\pi$
$284$	−9.63483			−0.571722
$285$	13.9278	−	9.54023i	0.825012	−	0.565115i
$286$	9.84821			0.582337
$287$	13.5020	−	28.9550i	0.796995	−	1.70916i
$288$	2.04235	−	2.19745i	0.120347	−	0.129486i
$289$	2.07782	+	2.47625i	0.122225	+	0.145662i
$290$	16.9009	−	6.41484i	0.992453	−	0.376692i
$291$	3.67358	+	12.7713i	0.215349	+	0.748666i
$292$	2.35410	−	8.78562i	0.137763	−	0.514139i
$293$	−23.9799	+	6.42539i	−1.40092	+	0.375375i	−0.878675	−	0.477420i	$-0.841572\pi$
$293$	−23.9799	+	6.42539i	−1.40092	+	0.375375i	−0.522245	+	0.852796i	$0.674905\pi$
$294$	20.4863	+	5.08976i	1.19479	+	0.296841i
$295$	−11.8600	−	0.874148i	−0.690514	−	0.0508949i
$296$	8.77965	+	5.06894i	0.510307	+	0.294626i
$297$	−10.8894	+	0.597884i	−0.631869	+	0.0346928i
$298$	18.0215	+	12.6188i	1.04396	+	0.730986i
$299$	−23.7614	−	19.9382i	−1.37416	−	1.15305i
$300$	7.29449	−	4.66802i	0.421148	−	0.269508i
$301$	0.727908	−	4.12817i	0.0419559	−	0.237944i
$302$	−1.18752	+	2.54665i	−0.0683342	+	0.146543i
$303$	13.7293	+	11.0989i	0.788726	+	0.637615i
$304$	4.32083	−	0.574841i	0.247817	−	0.0329694i
$305$	−4.42895	+	1.25198i	−0.253601	+	0.0716882i
$306$	−9.43013	+	5.91439i	−0.539085	+	0.338103i
$307$	0.209626	−	0.146782i	0.0119640	−	0.00837727i	−0.567579	−	0.823319i	$-0.692120\pi$
$307$	0.209626	−	0.146782i	0.0119640	−	0.00837727i	0.579543	+	0.814942i	$0.303231\pi$
$308$	9.15860	+	0.801274i	0.521860	+	0.0456568i
$309$	−4.59706	+	6.82764i	−0.261518	+	0.388411i
$310$	−7.06299	−	2.46172i	−0.401151	−	0.139817i
$311$	−9.34655	+	5.39623i	−0.529994	+	0.305992i	−0.741014	−	0.671490i	$-0.765655\pi$
$311$	−9.34655	+	5.39623i	−0.529994	+	0.305992i	0.211020	+	0.977482i	$0.432321\pi$
$312$	−2.91882	−	7.58497i	−0.165246	−	0.429415i
$313$	−7.37474	+	3.43890i	−0.416845	+	0.194378i	−0.619714	−	0.784828i	$-0.712751\pi$
$313$	−7.37474	+	3.43890i	−0.416845	+	0.194378i	0.202869	+	0.979206i	$0.434973\pi$
$314$	1.28011	+	0.465923i	0.0722410	+	0.0262936i
$315$	−19.9948	−	21.5323i	−1.12658	−	1.21321i
$316$	−2.86718	−	4.96610i	−0.161292	−	0.279365i
$317$	−8.31572	−	5.82273i	−0.467057	−	0.327037i	0.316246	−	0.948677i	$-0.397578\pi$
$317$	−8.31572	−	5.82273i	−0.467057	−	0.327037i	−0.783303	+	0.621640i	$0.786467\pi$
$318$	−2.34248	+	0.457351i	−0.131360	+	0.0256470i
$319$	−10.9067	−	12.9981i	−0.610658	−	0.727754i
$320$	2.22468	−	0.225370i	0.124363	−	0.0125986i
$321$	1.34740	+	2.75677i	0.0752045	+	0.153868i
$322$	−20.4753	−	20.4753i	−1.14104	−	1.14104i
$323$	−16.0380	−	2.08921i	−0.892378	−	0.116247i
$324$	3.68791	+	8.20971i	0.204884	+	0.456095i
$325$	−2.68403	−	23.3072i	−0.148883	−	1.29285i
$326$	−9.11264	−	1.60680i	−0.504702	−	0.0889926i
$327$	−8.66970	+	0.158528i	−0.479435	+	0.00876663i
$328$	−7.26583	+	0.635677i	−0.401188	+	0.0350994i
$329$	9.32147	+	52.8647i	0.513909	+	2.91452i
$330$	−6.39084	−	5.02329i	−0.351804	−	0.276523i
$331$	−3.45313	+	5.98099i	−0.189801	+	0.328745i	−0.945184	−	0.326539i	$-0.894118\pi$
$331$	−3.45313	+	5.98099i	−0.189801	+	0.328745i	0.755383	+	0.655284i	$0.227451\pi$
$332$	5.66446	−	2.64138i	0.310878	−	0.144965i
$333$	−24.2590	+	18.3437i	−1.32938	+	1.00523i
$334$	−0.867819	−	0.501035i	−0.0474849	−	0.0274154i
$335$	−0.302417	−	22.0831i	−0.0165228	−	1.20653i
$336$	−2.09730	−	7.29132i	−0.114417	−	0.397774i
$337$	1.72870	+	19.7591i	0.0941683	+	1.07635i	0.885399	+	0.464831i	$0.153885\pi$
$337$	1.72870	+	19.7591i	0.0941683	+	1.07635i	−0.791231	+	0.611517i	$0.790559\pi$
$338$	−8.98281	−	0.785894i	−0.488600	−	0.0427470i
$339$	−0.337654	+	4.88697i	−0.0183389	+	0.265424i
$340$	−8.18975	−	1.32871i	−0.444151	−	0.0720594i
$341$			7.02063i			0.380189i
$342$	−3.45648	+	12.6116i	−0.186905	+	0.681958i
$343$	16.0672	−	16.0672i	0.867546	−	0.867546i
$344$	−0.899258	+	0.327303i	−0.0484848	+	0.0176470i
$345$	5.24968	+	25.0586i	0.282633	+	1.34911i
$346$	0.0870412	−	0.0730362i	0.00467936	−	0.00392645i
$347$	−25.4195	+	2.22392i	−1.36459	+	0.119386i	−0.745800	−	0.666170i	$-0.767933\pi$
$347$	−25.4195	+	2.22392i	−1.36459	+	0.119386i	−0.618791	+	0.785556i	$0.712377\pi$
$348$	−6.77844	+	12.2526i	−0.363363	+	0.656809i
$349$	−10.7611	+	6.21292i	−0.576028	+	0.332570i	−0.759553	−	0.650445i	$-0.774582\pi$
$349$	−10.7611	+	6.21292i	−0.576028	+	0.332570i	0.183525	+	0.983015i	$0.441249\pi$
$350$	−0.599754	−	21.8935i	−0.0320582	−	1.17026i
$351$	24.3688	+	0.790229i	1.30071	+	0.0421793i
$352$	−0.887004	−	1.90219i	−0.0472775	−	0.101387i
$353$	−7.91286	+	2.12024i	−0.421159	+	0.112849i	−0.463173	−	0.886268i	$-0.653289\pi$
$353$	−7.91286	+	2.12024i	−0.421159	+	0.112849i	0.0420141	+	0.999117i	$0.486623\pi$
$354$	7.44785	−	5.42063i	0.395849	−	0.288103i
$355$	19.3991	−	9.37146i	1.02960	−	0.497385i
$356$	3.94742	−	4.70435i	0.209213	−	0.249330i
$357$	0.514666	+	28.1464i	0.0272390	+	1.48967i
$358$	0.469240	+	0.670145i	0.0248001	+	0.0354183i
$359$	14.5326	−	5.28942i	0.767000	−	0.279165i	0.0712587	−	0.997458i	$-0.477298\pi$
$359$	14.5326	−	5.28942i	0.767000	−	0.279165i	0.695741	+	0.718293i	$0.255076\pi$
$360$	−1.97475	+	6.41096i	−0.104079	+	0.337887i
$361$	−15.5341	+	10.9403i	−0.817585	+	0.575808i
$362$	10.1753	−	10.1753i	0.534804	−	0.534804i
$363$	3.70991	−	10.8035i	0.194720	−	0.567036i
$364$	−20.2413	−	3.56910i	−1.06093	−	0.187071i
$365$	3.80563	+	19.9790i	0.199196	+	1.04575i
$366$	1.99112	−	2.95725i	0.104077	−	0.154578i
$367$	2.64084	−	3.77151i	0.137851	−	0.196871i	−0.744291	−	0.667856i	$-0.767212\pi$
$367$	2.64084	−	3.77151i	0.137851	−	0.196871i	0.882141	+	0.470985i	$0.156101\pi$
$368$	−1.71094	+	6.38530i	−0.0891888	+	0.332857i
$369$	6.72697	−	20.8210i	0.350192	−	1.08390i
$370$	−22.6076	−	1.66632i	−1.17532	−	0.0866276i
$371$	−2.06442	+	5.67196i	−0.107180	+	0.294473i
$372$	5.40721	−	2.08078i	0.280351	−	0.107884i
$373$	−12.6986	−	3.40258i	−0.657509	−	0.176179i	−0.0853875	−	0.996348i	$-0.527213\pi$
$373$	−12.6986	−	3.40258i	−0.657509	−	0.176179i	−0.572122	+	0.820169i	$0.693879\pi$
$374$	1.35231	+	7.66930i	0.0699260	+	0.396570i
$375$	−10.1466	+	16.4939i	−0.523966	+	0.851739i
$376$	9.38772	−	7.87724i	0.484135	−	0.406237i
$377$	21.7581	+	31.0738i	1.12060	+	1.60038i
$378$	22.5981	+	2.71760i	1.16232	+	0.139778i
$379$		−	24.9283i		−	1.28048i	−0.768175	−	0.640240i	$-0.778835\pi$
$379$		−	24.9283i		−	1.28048i	0.768175	−	0.640240i	$-0.221165\pi$
$380$	−8.14058	+	5.36012i	−0.417603	+	0.274968i
$381$	15.5703	−	1.64957i	0.797690	−	0.0845100i
$382$	3.74616	+	1.74686i	0.191670	+	0.0893774i
$383$	17.7195	−	12.4073i	0.905426	−	0.633986i	−0.0253096	−	0.999680i	$-0.508057\pi$
$383$	17.7195	−	12.4073i	0.905426	−	0.633986i	0.930735	+	0.365694i	$0.119168\pi$
$384$	−1.20215	+	1.24693i	−0.0613469	+	0.0636322i
$385$	−19.2196	+	7.29493i	−0.979523	+	0.371784i
$386$	2.01666	−	0.355592i	0.102645	−	0.0180991i
$387$	0.145493	−	2.86722i	0.00739580	−	0.145749i
$388$	−1.98578	−	7.41105i	−0.100813	−	0.376239i
$389$	−28.2078	−	10.2668i	−1.43019	−	0.520547i	−0.493204	−	0.869914i	$-0.664174\pi$
$389$	−28.2078	−	10.2668i	−1.43019	−	0.520547i	−0.936986	+	0.349367i	$0.886397\pi$
$390$	13.2545	+	12.4328i	0.671168	+	0.629560i
$391$	12.2641	−	21.2420i	0.620221	−	1.07425i
$392$	−11.7721	−	3.15432i	−0.594580	−	0.159317i
$393$	−10.8856	+	19.6766i	−0.549106	+	0.992555i
$394$	−1.16569	+	1.38922i	−0.0587267	+	0.0699877i
$395$	10.6032	+	7.21012i	0.533507	+	0.362781i
$396$	6.29228	−	0.230190i	0.316199	−	0.0115675i
$397$	2.52229	+	1.17616i	0.126590	+	0.0590300i	0.484881	−	0.874580i	$-0.338863\pi$
$397$	2.52229	+	1.17616i	0.126590	+	0.0590300i	−0.358291	+	0.933610i	$0.616641\pi$
$398$	13.8551	+	13.8551i	0.694493	+	0.694493i
$399$	22.8170	+	23.9387i	1.14228	+	1.19844i
$400$	−4.26004	+	2.61764i	−0.213002	+	0.130882i
$401$	−12.5742	−	34.5472i	−0.627924	−	1.72521i	−0.686705	−	0.726936i	$-0.740944\pi$
$401$	−12.5742	−	34.5472i	−0.627924	−	1.72521i	0.0587816	−	0.998271i	$-0.481278\pi$
$402$	11.2340	+	12.9016i	0.560300	+	0.643472i
$403$	1.36797	−	15.6359i	0.0681433	−	0.778881i
$404$	−7.80812	−	6.55179i	−0.388469	−	0.325964i
$405$	−15.4107	−	12.9426i	−0.765762	−	0.643124i
$406$	17.7063	+	30.6681i	0.878747	+	1.52203i
$407$	5.50707	+	20.5526i	0.272975	+	1.01876i
$408$	5.50601	−	3.31457i	0.272588	−	0.164095i
$409$	8.04259	−	22.0968i	0.397680	−	1.09262i	−0.565731	−	0.824590i	$-0.691406\pi$
$409$	8.04259	−	22.0968i	0.397680	−	1.09262i	0.963411	−	0.268028i	$-0.0863719\pi$
$410$	14.0110	−	8.34711i	0.691953	−	0.412234i
$411$	30.1217	−	21.9229i	1.48579	−	1.08138i
$412$	2.72574	−	3.89276i	0.134287	−	0.191782i
$413$	−2.03038	−	23.2074i	−0.0999087	−	1.14196i
$414$	−15.6478	−	12.1836i	−0.769048	−	0.598793i
$415$	−8.83585	+	10.8279i	−0.433735	+	0.531519i
$416$	1.60484	+	4.40926i	0.0786838	+	0.216182i
$417$	−4.45184	−	3.59892i	−0.218008	−	0.176240i
$418$	7.26565	+	5.55941i	0.355374	+	0.271920i
$419$	−18.5294			−0.905222			−0.452611	−	0.891708i	$-0.649507\pi$
$419$	−18.5294			−0.905222			−0.452611	+	0.891708i	$0.649507\pi$
$420$	11.3148	+	12.6406i	0.552106	+	0.616800i
$421$	−4.84796	+	27.4941i	−0.236275	+	1.33998i	0.603637	+	0.797259i	$0.293718\pi$
$421$	−4.84796	+	27.4941i	−0.236275	+	1.33998i	−0.839912	+	0.542722i	$0.817394\pi$
$422$	−0.594937	+	6.80016i	−0.0289611	+	0.331027i
$423$	10.8072	+	35.1401i	0.525465	+	1.70857i
$424$	1.35703	−	0.239282i	0.0659034	−	0.0116206i
$425$	17.7819	−	5.29061i	0.862550	−	0.256632i
$426$	−6.77497	+	15.2509i	−0.328248	+	0.738908i
$427$	−3.81036	−	8.17134i	−0.184396	−	0.395439i
$428$	−0.748693	−	1.60558i	−0.0361895	−	0.0776085i
$429$	6.92502	−	15.5887i	0.334343	−	0.752627i
$430$	1.49224	−	1.53368i	0.0719623	−	0.0739607i
$431$	26.3543	−	4.64698i	1.26944	−	0.223837i	0.501951	−	0.864896i	$-0.332616\pi$
$431$	26.3543	−	4.64698i	1.26944	−	0.223837i	0.767491	+	0.641059i	$0.221505\pi$
$432$	−2.04220	−	4.77801i	−0.0982555	−	0.229882i
$433$	3.12133	−	35.6769i	0.150001	−	1.71452i	−0.432449	−	0.901658i	$-0.642351\pi$
$433$	3.12133	−	35.6769i	0.150001	−	1.71452i	0.582451	−	0.812866i	$-0.302094\pi$
$434$	2.54435	−	14.4297i	0.122133	−	0.692649i
$435$	1.73028	−	31.2630i	0.0829605	−	1.49895i
$436$	5.00629			0.239758
$437$	−6.27499	−	28.1232i	−0.300174	−	1.34531i
$438$	−12.2513	−	9.90411i	−0.585391	−	0.473237i
$439$	4.24023	+	11.6499i	0.202375	+	0.556021i	0.998814	−	0.0486986i	$-0.0155074\pi$
$439$	4.24023	+	11.6499i	0.202375	+	0.556021i	−0.796438	+	0.604720i	$0.793285\pi$
$440$	3.63611	+	2.96717i	0.173345	+	0.141454i
$441$	22.4620	−	28.8486i	1.06962	−	1.37375i
$442$	−1.51741	−	17.3441i	−0.0721759	−	0.824975i
$443$	0.918202	−	1.31133i	0.0436251	−	0.0623031i	−0.796747	−	0.604313i	$-0.793448\pi$
$443$	0.918202	−	1.31133i	0.0436251	−	0.0623031i	0.840372	+	0.542010i	$0.182337\pi$
$444$	14.1972	−	10.3329i	0.673770	−	0.490377i
$445$	−3.37211	+	13.3114i	−0.159854	+	0.631021i
$446$	5.55714	−	15.2681i	0.263138	−	0.722967i
$447$	32.6464	−	19.6528i	1.54412	−	0.929547i
$448$	1.13371	+	4.23108i	0.0535630	+	0.199900i
$449$	0.105165	+	0.182151i	0.00496304	+	0.00859624i	0.868496	−	0.495696i	$-0.165087\pi$
$449$	0.105165	+	0.182151i	0.00496304	+	0.00859624i	−0.863533	+	0.504292i	$0.831754\pi$
$450$	−2.25967	−	14.8288i	−0.106522	−	0.699037i
$451$	−11.7266	−	9.83978i	−0.552184	−	0.463337i
$452$	0.246496	−	2.81746i	0.0115942	−	0.132522i
$453$	3.19603	+	3.67046i	0.150163	+	0.172453i
$454$	9.10937	+	25.0278i	0.427524	+	1.17461i
$455$	44.2262	−	12.5019i	2.07336	−	0.586098i
$456$	2.12839	−	7.24362i	0.0996709	−	0.339213i
$457$	−18.4185	−	18.4185i	−0.861581	−	0.861581i	0.129941	−	0.991522i	$-0.458521\pi$
$457$	−18.4185	−	18.4185i	−0.861581	−	0.861581i	−0.991522	+	0.129941i	$0.958521\pi$
$458$	−8.43589	−	3.93372i	−0.394183	−	0.183811i
$459$	2.73080	+	19.0857i	0.127463	+	0.890845i
$460$	−2.76590	−	14.5206i	−0.128961	−	0.677025i
$461$	−5.57687	+	6.64625i	−0.259741	+	0.309547i	−0.880116	−	0.474758i	$-0.842536\pi$
$461$	−5.57687	+	6.64625i	−0.259741	+	0.309547i	0.620376	+	0.784305i	$0.286980\pi$
$462$	7.70843	−	13.9336i	0.358628	−	0.648251i
$463$	8.06612	+	2.16131i	0.374865	+	0.100445i	0.441332	−	0.897344i	$-0.354506\pi$
$463$	8.06612	+	2.16131i	0.374865	+	0.100445i	−0.0664673	+	0.997789i	$0.521173\pi$
$464$	4.04221	−	7.00132i	0.187655	−	0.325028i
$465$	−8.86316	+	9.44892i	−0.411019	+	0.438183i
$466$	2.24266	+	0.816260i	0.103889	+	0.0378125i
$467$	2.41122	+	8.99880i	0.111578	+	0.416415i	0.999008	−	0.0445274i	$-0.0141782\pi$
$467$	2.41122	+	8.99880i	0.111578	+	0.416415i	−0.887430	+	0.460942i	$0.847512\pi$
$468$	−14.0586	−	0.713382i	−0.649861	−	0.0329761i
$469$	42.6064	−	7.51265i	1.96738	−	0.346902i
$470$	−11.2397	+	24.9914i	−0.518447	+	1.15277i
$471$	1.63765	−	1.69866i	0.0754589	−	0.0782699i
$472$	−4.35651	+	3.05046i	−0.200525	+	0.140409i
$473$	−1.82034	−	0.848837i	−0.0836991	−	0.0390295i
$474$	−9.87693	+	1.04640i	−0.453662	+	0.0480626i
$475$	11.1769	−	18.7103i	0.512833	−	0.858488i
$476$		−	16.2531i		−	0.744957i
$477$	−0.923239	+	4.02949i	−0.0422722	+	0.184498i
$478$	10.3174	+	14.7347i	0.471905	+	0.673951i
$479$	12.7591	−	10.7061i	0.582977	−	0.489176i	−0.302946	−	0.953008i	$-0.597970\pi$
$479$	12.7591	−	10.7061i	0.582977	−	0.489176i	0.885923	+	0.463832i	$0.153526\pi$
$480$	1.20760	−	3.67990i	0.0551193	−	0.167964i
$481$	−8.26033	−	46.8466i	−0.376639	−	2.13602i
$482$	−0.643291	−	0.172369i	−0.0293011	−	0.00785120i
$483$	−46.8079	+	18.0125i	−2.12983	+	0.819596i
$484$	−2.25559	+	6.19719i	−0.102527	+	0.281691i
$485$	11.2067	+	12.9902i	0.508871	+	0.589853i
$486$	15.5883	−	0.0646922i	0.707101	−	0.00293450i
$487$	0.367578	−	1.37182i	0.0166565	−	0.0621630i	−0.957097	−	0.289767i	$-0.906422\pi$
$487$	0.367578	−	1.37182i	0.0166565	−	0.0621630i	0.973754	+	0.227604i	$0.0730890\pi$
$488$	−1.18060	+	1.68606i	−0.0534430	+	0.0763246i
$489$	−8.95117	+	13.2944i	−0.404786	+	0.601196i
$490$	26.7704	−	5.09927i	1.20937	−	0.230362i
$491$	−3.30283	−	0.582378i	−0.149055	−	0.0262824i	0.0986229	−	0.995125i	$-0.468556\pi$
$491$	−3.30283	−	0.582378i	−0.149055	−	0.0262824i	−0.247678	+	0.968843i	$0.579667\pi$
$492$	−4.10294	+	11.9480i	−0.184975	+	0.538658i
$493$	−21.2110	+	21.2110i	−0.955296	+	0.955296i
$494$	−15.0984	−	13.7973i	−0.679307	−	0.620769i
$495$	−12.4452	+	6.58375i	−0.559370	+	0.295918i
$496$	−3.14329	+	1.14407i	−0.141138	+	0.0513701i
$497$	24.2071	+	34.5713i	1.08584	+	1.55074i
$498$	−0.197913	−	10.8236i	−0.00886868	−	0.485016i
$499$	−11.5592	+	13.7757i	−0.517459	+	0.616684i	−0.959978	−	0.280076i	$-0.909640\pi$
$499$	−11.5592	+	13.7757i	−0.517459	+	0.616684i	0.442519	+	0.896759i	$0.354085\pi$
$500$	6.03124	−	9.41404i	0.269725	−	0.421009i
$501$	−1.40331	+	1.02135i	−0.0626954	+	0.0456304i
$502$	9.62769	−	2.57973i	0.429705	−	0.115139i
$503$	11.4992	+	24.6600i	0.512722	+	1.09954i	0.976881	+	0.213784i	$0.0685787\pi$
$503$	11.4992	+	24.6600i	0.512722	+	1.09954i	−0.464159	+	0.885752i	$0.653643\pi$
$504$	−13.0161	−	1.80727i	−0.579785	−	0.0805023i
$505$	22.0938	+	5.59693i	0.983163	+	0.249060i
$506$	−12.0156	+	6.93721i	−0.534159	+	0.308397i
$507$	−7.56047	+	13.6662i	−0.335772	+	0.606937i
$508$	−9.00541	+	0.787872i	−0.399551	+	0.0349561i
$509$	10.0691	−	8.44897i	0.446304	−	0.374494i	−0.391758	−	0.920068i	$-0.628133\pi$
$509$	10.0691	−	8.44897i	0.446304	−	0.374494i	0.838062	+	0.545574i	$0.183688\pi$
$510$	−7.86203	+	12.0292i	−0.348136	+	0.532660i
$511$	−37.4388	+	13.6266i	−1.65619	+	0.602806i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	17.5323	+	14.3394i	0.774070	+	0.633100i
$514$		−	25.1214i		−	1.10806i
$515$	−1.70175	+	10.4890i	−0.0749880	+	0.462202i
$516$	−0.114250	+	1.65358i	−0.00502959	+	0.0727948i
$517$	25.6229	+	2.24171i	1.12689	+	0.0985903i
$518$	−3.87035	−	44.2383i	−0.170053	−	1.94372i
$519$	−0.0544032	−	0.189134i	−0.00238804	−	0.00830206i
$520$	−7.51998	−	7.31680i	−0.329773	−	0.320863i
$521$	0.941262	+	0.543438i	0.0412374	+	0.0238084i	0.520477	−	0.853876i	$-0.325754\pi$
$521$	0.941262	+	0.543438i	0.0412374	+	0.0238084i	−0.479240	+	0.877684i	$0.659087\pi$
$522$	14.6281	+	19.3453i	0.640255	+	0.846719i
$523$	−21.8377	+	10.1831i	−0.954895	+	0.445275i	−0.836667	−	0.547711i	$-0.815499\pi$
$523$	−21.8377	+	10.1831i	−0.954895	+	0.445275i	−0.118228	+	0.992986i	$0.537721\pi$
$524$	6.49144	−	11.2435i	0.283580	−	0.491175i
$525$	−35.0767	−	14.4456i	−1.53087	−	0.630458i
$526$	1.45523	+	8.25304i	0.0634512	+	0.359850i
$527$	12.3643	−	1.08174i	0.538599	−	0.0471213i
$528$	−3.63467	+	0.0664612i	−0.158179	+	0.00289235i
$529$	20.3849	+	3.59442i	0.886302	+	0.156279i
$530$	−2.49956	+	1.80172i	−0.108574	+	0.0782616i
$531$	−3.34313	−	15.6008i	−0.145079	−	0.677016i
$532$	−12.9185	−	14.0596i	−0.560089	−	0.609560i
$533$	24.1995	+	24.1995i	1.04820	+	1.04820i
$534$	−4.67075	−	9.55631i	−0.202123	−	0.413542i
$535$	3.06913	+	2.50450i	0.132690	+	0.108279i
$536$	−6.34867	−	7.56606i	−0.274221	−	0.326804i
$537$	1.39072	−	0.271528i	0.0600142	−	0.0117173i
$538$	−3.85088	−	2.69641i	−0.166023	−	0.116251i
$539$	−12.7896	−	22.1522i	−0.550887	−	0.954164i
$540$	8.75925	+	7.63384i	0.376938	+	0.328508i
$541$	−20.3075	−	7.39133i	−0.873088	−	0.317778i	−0.133671	−	0.991026i	$-0.542677\pi$
$541$	−20.3075	−	7.39133i	−0.873088	−	0.317778i	−0.739417	+	0.673248i	$0.764899\pi$
$542$	9.44913	−	4.40620i	0.405875	−	0.189263i
$543$	−8.95141	−	23.2615i	−0.384142	−	0.998247i
$544$	−3.21335	+	1.85523i	−0.137771	+	0.0795422i
$545$	−10.0798	+	4.86944i	−0.431773	+	0.208584i
$546$	−19.8827	+	29.5302i	−0.850901	+	1.26377i
$547$	24.9512	+	2.18295i	1.06684	+	0.0933362i	0.607027	−	0.794681i	$-0.292362\pi$
$547$	24.9512	+	2.18295i	1.06684	+	0.0933362i	0.459810	+	0.888017i	$0.347917\pi$
$548$	−17.6192	+	12.3371i	−0.752657	+	0.527016i
$549$	−3.28089	−	5.23119i	−0.140025	−	0.223262i
$550$	−10.2071	−	2.43749i	−0.435234	−	0.103935i
$551$	−1.48912	+	35.2077i	−0.0634387	+	1.49990i
$552$	8.90415	+	7.19821i	0.378986	+	0.306376i
$553$	−10.6155	+	22.7650i	−0.451417	+	0.968068i
$554$	−1.28579	+	7.29209i	−0.0546280	+	0.309811i
$555$	−18.5347	+	34.6137i	−0.786755	+	1.46927i
$556$	2.53186	+	2.12448i	0.107375	+	0.0900980i
$557$	25.9956	+	18.2023i	1.10147	+	0.771257i	0.975329	−	0.220755i	$-0.0708522\pi$
$557$	25.9956	+	18.2023i	1.10147	+	0.771257i	0.126140	+	0.992012i	$0.459741\pi$
$558$	0.508559	−	10.0222i	0.0215290	−	0.424273i
$559$	3.88875	+	2.24517i	0.164476	+	0.0949605i
$560$	−6.39809	−	7.41629i	−0.270369	−	0.313395i
$561$	13.0906	+	3.25231i	0.552685	+	0.137313i
$562$	−5.36436	+	1.43738i	−0.226282	+	0.0606321i
$563$	2.49742	−	9.32050i	0.105254	−	0.392812i	−0.893120	−	0.449818i	$-0.851489\pi$
$563$	2.49742	−	9.32050i	0.105254	−	0.392812i	0.998374	+	0.0570059i	$0.0181554\pi$
$564$	−5.86760	−	20.3988i	−0.247070	−	0.858945i
$565$	2.24414	+	5.91253i	0.0944116	+	0.248742i
$566$	−21.2048	−	25.2709i	−0.891303	−	1.06221i
$567$	20.1921	−	33.8594i	0.847987	−	1.42196i
$568$	4.07185	−	8.73212i	0.170851	−	0.366392i
$569$	−41.2198			−1.72802			−0.864011	−	0.503473i	$-0.832055\pi$
$569$	−41.2198			−1.72802			−0.864011	+	0.503473i	$0.832055\pi$
$570$	2.76024	+	16.6548i	0.115614	+	0.697591i
$571$	28.6992			1.20102			0.600511	−	0.799616i	$-0.294964\pi$
$571$	28.6992			1.20102			0.600511	+	0.799616i	$0.294964\pi$
$572$	−4.16203	+	8.92551i	−0.174023	+	0.373194i
$573$	5.39931	−	4.70142i	0.225559	−	0.196405i
$574$	20.5360	+	24.4739i	0.857156	+	1.02152i
$575$	19.6926	+	26.5459i	0.821238	+	1.10704i
$576$	1.12844	+	2.77968i	0.0470182	+	0.115820i
$577$	0.982927	−	3.66833i	0.0409198	−	0.152715i	−0.942443	−	0.334366i	$-0.891478\pi$
$577$	0.982927	−	3.66833i	0.0409198	−	0.152715i	0.983363	+	0.181652i	$0.0581444\pi$
$578$	−3.12237	+	0.836637i	−0.129873	+	0.0347995i
$579$	0.855202	−	3.44220i	0.0355410	−	0.143053i
$580$	−1.32880	+	18.0284i	−0.0551754	+	0.748589i
$581$	−23.7094	−	13.6886i	−0.983633	−	0.567901i
$582$	−13.1272	−	2.06798i	−0.544142	−	0.0857206i
$583$	2.36909	+	1.65885i	0.0981176	+	0.0687027i
$584$	6.96759	+	5.84650i	0.288321	+	0.241930i
$585$	29.0000	−	12.2380i	1.19900	−	0.505979i
$586$	4.31096	−	24.4486i	0.178084	−	1.00996i
$587$	−8.46664	+	18.1568i	−0.349456	+	0.749410i	−0.999949	−	0.0101021i	$-0.996784\pi$
$587$	−8.46664	+	18.1568i	−0.349456	+	0.749410i	0.650493	+	0.759512i	$0.274562\pi$
$588$	−13.2708	+	16.4159i	−0.547278	+	0.676980i
$589$	9.83586	−	10.7634i	0.405280	−	0.443497i
$590$	5.80448	−	10.3793i	0.238967	−	0.427311i
$591$	1.37929	+	2.82203i	0.0567366	+	0.116083i
$592$	−8.30446	+	5.81484i	−0.341311	+	0.238989i
$593$	−28.0627	−	2.45516i	−1.15240	−	0.100822i	−0.505100	−	0.863061i	$-0.668544\pi$
$593$	−28.0627	−	2.45516i	−1.15240	−	0.100822i	−0.647295	+	0.762239i	$0.724100\pi$
$594$	4.06021	−	10.1219i	0.166592	−	0.415305i
$595$	15.8088	+	32.7245i	0.648096	+	1.34157i
$596$	−19.0527	+	11.0001i	−0.780429	+	0.450581i
$597$	31.6737	−	12.1886i	1.29632	−	0.498844i
$598$	28.1121	−	13.1089i	1.14959	−	0.536063i
$599$	−18.7130	−	6.81097i	−0.764592	−	0.278289i	−0.0698597	−	0.997557i	$-0.522255\pi$
$599$	−18.7130	−	6.81097i	−0.764592	−	0.278289i	−0.694733	+	0.719268i	$0.744477\pi$
$600$	1.14788	+	8.58384i	0.0468620	+	0.350434i
$601$	−6.79544	−	11.7701i	−0.277192	−	0.480110i	0.693494	−	0.720463i	$-0.256070\pi$
$601$	−6.79544	−	11.7701i	−0.277192	−	0.480110i	−0.970686	+	0.240352i	$0.922737\pi$
$602$	3.43377	+	2.40435i	0.139950	+	0.0979940i
$603$	28.3212	−	8.71010i	1.15333	−	0.354703i
$604$	−1.80618	−	2.15252i	−0.0734924	−	0.0875849i
$605$	−1.48630	−	14.6716i	−0.0604266	−	0.596485i
$606$	−15.8613	+	7.75235i	−0.644319	+	0.314918i
$607$	22.9974	+	22.9974i	0.933434	+	0.933434i	0.997919	−	0.0644843i	$-0.0205402\pi$
$607$	22.9974	+	22.9974i	0.933434	+	0.933434i	−0.0644843	+	0.997919i	$0.520540\pi$
$608$	−1.30508	+	4.15894i	−0.0529279	+	0.168667i
$609$	60.9949	−	6.46201i	2.47164	−	0.261854i
$610$	0.737077	−	4.54311i	0.0298434	−	0.183945i
$611$	−56.6289	−	9.98520i	−2.29096	−	0.403958i
$612$	−1.37491	−	11.0461i	−0.0555775	−	0.446513i
$613$	37.9294	−	3.31839i	1.53195	−	0.134028i	0.710252	−	0.703948i	$-0.248581\pi$
$613$	37.9294	−	3.31839i	1.53195	−	0.134028i	0.821701	+	0.569919i	$0.193026\pi$
$614$	0.0444376	+	0.252018i	0.00179336	+	0.0101706i
$615$	−3.36040	−	28.0473i	−0.135504	−	1.13098i
$616$	−4.59679	+	7.96188i	−0.185210	+	0.320793i
$617$	−19.5706	+	9.12590i	−0.787881	+	0.367395i	−0.774547	−	0.632516i	$-0.782022\pi$
$617$	−19.5706	+	9.12590i	−0.787881	+	0.367395i	−0.0133339	+	0.999911i	$0.504244\pi$
$618$	−4.24514	−	7.05183i	−0.170765	−	0.283666i
$619$	−30.0247	−	17.3348i	−1.20679	−	0.696743i	−0.244737	−	0.969589i	$-0.578702\pi$
$619$	−30.0247	−	17.3348i	−1.20679	−	0.696743i	−0.962058	+	0.272846i	$0.912035\pi$
$620$	5.21603	−	5.36087i	0.209481	−	0.215298i
$621$	−30.2885	+	16.2016i	−1.21544	+	0.650146i
$622$	−0.940625	−	10.7514i	−0.0377156	−	0.431092i
$623$	−26.7977	−	2.34449i	−1.07363	−	0.0939301i
$624$	8.10787	+	0.560195i	0.324575	+	0.0224258i
$625$	−2.98681	+	24.8209i	−0.119472	+	0.992838i
$626$		−	8.13712i		−	0.325225i
$627$	13.9090	−	7.59149i	0.555470	−	0.303175i
$628$	−0.963269	+	0.963269i	−0.0384386	+	0.0384386i
$629$	35.3476	−	12.8655i	1.40940	−	0.512980i
$630$	27.9650	−	9.02152i	1.11415	−	0.359426i
$631$	5.68332	−	4.76888i	0.226250	−	0.189846i	−0.522615	−	0.852569i	$-0.675044\pi$
$631$	5.68332	−	4.76888i	0.226250	−	0.189846i	0.748865	+	0.662723i	$0.230599\pi$
$632$	5.71254	−	0.499782i	0.227233	−	0.0198803i
$633$	10.3456	+	5.72342i	0.411200	+	0.227486i
$634$	8.79156	−	5.07581i	0.349157	−	0.201586i
$635$	17.3655	−	10.3456i	0.689128	−	0.410552i
$636$	0.575476	−	2.31630i	0.0228191	−	0.0918471i
$637$	24.1679	+	51.8282i	0.957566	+	2.05351i
$638$	16.3897	−	4.39160i	0.648873	−	0.173865i
$639$	19.3765	+	21.4481i	0.766523	+	0.848473i
$640$	−0.735936	+	2.11149i	−0.0290904	+	0.0834640i
$641$	−1.32095	+	1.57424i	−0.0521742	+	0.0621788i	−0.791500	−	0.611169i	$-0.790700\pi$
$641$	−1.32095	+	1.57424i	−0.0521742	+	0.0621788i	0.739326	+	0.673347i	$0.235144\pi$
$642$	−3.06792	+	0.0560979i	−0.121081	+	0.00221401i
$643$	−7.68442	−	10.9745i	−0.303044	−	0.432791i	0.638531	−	0.769596i	$-0.279543\pi$
$643$	−7.68442	−	10.9745i	−0.303044	−	0.432791i	−0.941574	+	0.336805i	$0.890654\pi$
$644$	27.2102	−	9.90369i	1.07223	−	0.390260i
$645$	−1.37834	−	3.44050i	−0.0542722	−	0.135470i
$646$	8.67142	−	13.6524i	0.341172	−	0.537148i
$647$	−33.8233	+	33.8233i	−1.32973	+	1.32973i	−0.424127	+	0.905603i	$0.639419\pi$
$647$	−33.8233	+	33.8233i	−1.32973	+	1.32973i	−0.905603	+	0.424127i	$0.860581\pi$
$648$	−8.99910	−	0.127195i	−0.353518	−	0.00499670i
$649$	−10.9927	−	1.93831i	−0.431500	−	0.0760851i
$650$	22.2578	+	7.41748i	0.873022	+	0.290938i
$651$	−21.0516	−	14.1741i	−0.825076	−	0.555525i
$652$	5.30743	−	7.57979i	0.207855	−	0.296847i
$653$	3.26158	−	12.1724i	0.127635	−	0.476342i	−0.872285	−	0.488999i	$-0.837362\pi$
$653$	3.26158	−	12.1724i	0.127635	−	0.476342i	0.999920	+	0.0126570i	$0.00402895\pi$
$654$	3.52030	−	7.92441i	0.137654	−	0.309869i
$655$	−2.13394	+	28.9521i	−0.0833798	+	1.13125i
$656$	2.49455	−	6.85372i	0.0973959	−	0.267593i
$657$	−24.2920	+	12.4282i	−0.947719	+	0.484871i
$658$	−51.8511	−	13.8935i	−2.02137	−	0.541623i
$659$	6.82837	+	38.7256i	0.265996	+	1.50854i	0.766185	+	0.642620i	$0.222153\pi$
$659$	6.82837	+	38.7256i	0.265996	+	1.50854i	−0.500190	+	0.865916i	$0.666736\pi$
$660$	7.25353	−	3.66913i	0.282343	−	0.142821i
$661$	−12.0048	+	10.0733i	−0.466934	+	0.391805i	−0.845675	−	0.533698i	$-0.820802\pi$
$661$	−12.0048	+	10.0733i	−0.466934	+	0.391805i	0.378740	+	0.925503i	$0.376357\pi$
$662$	−3.96127	−	5.65727i	−0.153959	−	0.219876i
$663$	−28.5208	−	9.79404i	−1.10766	−	0.380369i
$664$			6.25004i			0.242549i
$665$	39.6859	+	15.7427i	1.53895	+	0.610474i
$666$	−6.37272	−	29.7385i	−0.246938	−	1.15234i
$667$	−48.4354	−	22.5858i	−1.87542	−	0.874525i
$668$	0.820848	−	0.574764i	0.0317596	−	0.0222383i
$669$	−20.2601	−	19.5325i	−0.783302	−	0.755171i
$670$	20.1419	+	9.05863i	0.778149	+	0.349966i
$671$	−4.25440	+	0.750166i	−0.164239	+	0.0289598i
$672$	7.49454	+	1.18064i	0.289108	+	0.0455443i
$673$	−1.35016	−	5.03885i	−0.0520447	−	0.194233i	0.935009	−	0.354624i	$-0.115391\pi$
$673$	−1.35016	−	5.03885i	−0.0520447	−	0.194233i	−0.987054	+	0.160391i	$0.948725\pi$
$674$	−18.6384	−	6.78384i	−0.717926	−	0.261304i
$675$	−25.0614	−	6.85044i	−0.964612	−	0.263674i
$676$	4.50856	−	7.80905i	0.173406	−	0.300348i
$677$	17.3845	+	4.65816i	0.668140	+	0.179028i	0.576917	−	0.816803i	$-0.304256\pi$
$677$	17.3845	+	4.65816i	0.668140	+	0.179028i	0.0912231	+	0.995830i	$0.470922\pi$
$678$	−4.28640	−	2.37134i	−0.164618	−	0.0910708i
$679$	−21.6028	+	25.7453i	−0.829041	+	0.988013i
$680$	4.66536	−	6.86089i	0.178908	−	0.263103i
$681$	46.0218	+	3.17977i	1.76356	+	0.121849i
$682$	−6.36286	−	2.96705i	−0.243646	−	0.113614i
$683$	−5.66231	−	5.66231i	−0.216662	−	0.216662i	0.590428	−	0.807090i	$-0.298959\pi$
$683$	−5.66231	−	5.66231i	−0.216662	−	0.216662i	−0.807090	+	0.590428i	$0.798959\pi$
$684$	−9.96923	−	8.46254i	−0.381183	−	0.323573i
$685$	23.4753	−	41.9776i	0.896946	−	1.60388i
$686$	7.77152	+	21.3521i	0.296718	+	0.815226i
$687$	−12.1586	+	10.5870i	−0.463878	+	0.403919i
$688$	0.0834055	−	0.953329i	0.00317980	−	0.0363453i
$689$	−4.95306	−	4.15611i	−0.188697	−	0.158335i
$690$	−24.9294	−	5.83238i	−0.949046	−	0.222035i
$691$	6.55925	+	11.3610i	0.249526	+	0.432191i	0.963394	−	0.268088i	$-0.0863920\pi$
$691$	6.55925	+	11.3610i	0.249526	+	0.432191i	−0.713869	+	0.700280i	$0.753059\pi$
$692$	0.0294081	+	0.109753i	0.00111793	+	0.00417217i
$693$	−16.6351	−	21.9994i	−0.631913	−	0.835688i
$694$	8.72720	−	23.9778i	0.331280	−	0.910184i
$695$	−7.16413	−	1.81485i	−0.271751	−	0.0688414i
$696$	−8.23994	−	11.3215i	−0.312334	−	0.429142i
$697$	−15.5224	+	22.1683i	−0.587954	+	0.839685i
$698$	−1.08298	−	12.3786i	−0.0409915	−	0.468535i
$699$	2.86903	−	2.97591i	0.108517	−	0.112559i
$700$	20.0957	+	8.70902i	0.759546	+	0.329170i
$701$	−17.6244	−	48.4225i	−0.665663	−	1.82889i	−0.549187	−	0.835699i	$-0.685063\pi$
$701$	−17.6244	−	48.4225i	−0.665663	−	1.82889i	−0.116475	−	0.993194i	$-0.537160\pi$
$702$	−11.0149	+	21.7517i	−0.415730	+	0.820963i
$703$	20.3512	−	39.2247i	0.767560	−	1.47939i
$704$	2.09883			0.0791026
$705$	31.6552	+	35.3645i	1.19221	+	1.33190i
$706$	1.42253	−	8.06754i	0.0535374	−	0.303626i
$707$	−3.89131	+	44.4779i	−0.146348	+	1.67276i
$708$	1.76516	+	9.04090i	0.0663388	+	0.339778i
$709$	−8.07605	+	1.42403i	−0.303302	+	0.0534804i	−0.323228	−	0.946321i	$-0.604768\pi$
$709$	−8.07605	+	1.42403i	−0.303302	+	0.0534804i	0.0199257	+	0.999801i	$0.493657\pi$
$710$	0.295009	+	21.5421i	0.0110715	+	0.808461i
$711$	−5.28888	+	16.3699i	−0.198348	+	0.613919i
$712$	2.59534	+	5.56572i	0.0972643	+	0.208584i
$713$	9.34513	+	20.0407i	0.349978	+	0.750530i
$714$	−25.7268	−	11.4287i	−0.962802	−	0.427710i
$715$	−0.301542	−	22.0192i	−0.0112770	−	0.823472i
$716$	−0.805667	+	0.142061i	−0.0301092	+	0.00530906i
$717$	30.5784	−	5.97018i	1.14197	−	0.222960i
$718$	−1.34788	+	15.4064i	−0.0503026	+	0.574961i
$719$	3.20851	−	18.1964i	0.119657	−	0.678610i	−0.864681	−	0.502321i	$-0.832480\pi$
$719$	3.20851	−	18.1964i	0.119657	−	0.678610i	0.984338	−	0.176289i	$-0.0564093\pi$
$720$	−4.97573	−	4.49912i	−0.185435	−	0.167672i
$721$	−20.8161			−0.775234
$722$	−3.35031	−	18.7023i	−0.124686	−	0.696027i
$723$	−0.725188	+	0.897054i	−0.0269700	+	0.0333618i
$724$	4.92171	+	13.5223i	0.182914	+	0.502551i
$725$	−14.8602	−	37.5915i	−0.551892	−	1.39611i
$726$	8.22340	+	7.92807i	0.305199	+	0.294238i
$727$	−2.09289	−	23.9218i	−0.0776210	−	0.887212i	−0.930784	−	0.365568i	$-0.880875\pi$
$727$	−2.09289	−	23.9218i	−0.0776210	−	0.887212i	0.853163	−	0.521644i	$-0.174681\pi$
$728$	11.7891	−	16.8365i	0.436932	−	0.624003i
$729$	10.8589	−	24.7201i	0.402182	−	0.915560i
$730$	−19.7155	−	4.99442i	−0.729702	−	0.184852i
$731$	−1.21444	+	3.33666i	−0.0449178	+	0.123411i
$732$	1.83869	+	3.05435i	0.0679600	+	0.112892i
$733$	−7.09469	−	26.4777i	−0.262048	−	0.977977i	−0.964032	−	0.265785i	$-0.914369\pi$
$733$	−7.09469	−	26.4777i	−0.262048	−	0.977977i	0.701984	−	0.712193i	$-0.252298\pi$
$734$	2.30208	+	3.98732i	0.0849713	+	0.147175i
$735$	10.7527	−	45.9604i	0.396620	−	1.69527i
$736$	−5.06398	−	4.24918i	−0.186661	−	0.156627i
$737$	1.80671	−	20.6508i	0.0665511	−	0.760682i
$738$	16.0273	+	14.8960i	0.589974	+	0.548331i
$739$	12.4940	+	34.3270i	0.459600	+	1.26274i	0.925784	+	0.378053i	$0.123406\pi$
$739$	12.4940	+	34.3270i	0.459600	+	1.26274i	−0.466184	+	0.884688i	$0.654371\pi$
$740$	11.0646	−	19.7853i	0.406743	−	0.727321i
$741$	−32.4564	+	14.1972i	−1.19231	+	0.521546i
$742$	−4.26808	−	4.26808i	−0.156686	−	0.156686i
$743$	−3.43717	−	1.60278i	−0.126098	−	0.0588003i	0.358546	−	0.933512i	$-0.383273\pi$
$743$	−3.43717	−	1.60278i	−0.126098	−	0.0588003i	−0.484643	+	0.874712i	$0.661051\pi$
$744$	−0.399354	+	5.77997i	−0.0146410	+	0.211904i
$745$	27.6620	−	40.6798i	1.01346	−	1.49039i
$746$	8.45045	−	10.0709i	0.309393	−	0.368720i
$747$	−17.2717	−	7.29760i	−0.631939	−	0.267005i
$748$	−7.52226	−	2.01558i	−0.275041	−	0.0736970i
$749$	−3.88001	+	6.72038i	−0.141773	+	0.245557i
$750$	−10.6604	−	16.1665i	−0.389262	−	0.590318i
$751$	17.5546	+	6.38934i	0.640575	+	0.233150i	0.641828	−	0.766849i	$-0.278177\pi$
$751$	17.5546	+	6.38934i	0.640575	+	0.233150i	−0.00125265	+	0.999999i	$0.500399\pi$
$752$	3.17178	+	11.8372i	0.115663	+	0.431659i
$753$	2.68652	−	17.0536i	0.0979021	−	0.621467i
$754$	−37.3577	+	6.58718i	−1.36049	+	0.239891i
$755$	5.73031	+	2.57716i	0.208547	+	0.0937923i
$756$	−12.0133	+	19.3323i	−0.436921	+	0.703110i
$757$	14.1258	−	9.89101i	0.513412	−	0.359495i	−0.287978	−	0.957637i	$-0.592983\pi$
$757$	14.1258	−	9.89101i	0.513412	−	0.359495i	0.801390	+	0.598142i	$0.204094\pi$
$758$	22.5927	+	10.5352i	0.820604	+	0.382654i
$759$	2.53178	+	23.8975i	0.0918978	+	0.867423i
$760$	−1.41756	−	9.64316i	−0.0514204	−	0.349794i
$761$			6.10102i			0.221162i	0.993867	+	0.110581i	$0.0352711\pi$
$761$			6.10102i			0.221162i	−0.993867	+	0.110581i	$0.964729\pi$
$762$	−5.08527	+	14.8086i	−0.184220	+	0.536459i
$763$	−12.5781	−	17.9634i	−0.455357	−	0.650318i
$764$	−3.16639	+	2.65692i	−0.114556	+	0.0961240i
$765$	13.5125	+	20.9033i	0.488545	+	0.755762i
$766$	3.75628	+	21.3029i	0.135720	+	0.769706i
$767$	24.1045	+	6.45879i	0.870364	+	0.233213i
$768$	−0.622053	−	1.61649i	−0.0224464	−	0.0583302i
$769$	11.5187	−	31.6473i	0.415373	−	1.14123i	−0.538920	−	0.842357i	$-0.681167\pi$
$769$	11.5187	−	31.6473i	0.415373	−	1.14123i	0.954293	−	0.298872i	$-0.0966104\pi$
$770$	1.51111	−	20.5019i	0.0544565	−	0.738836i
$771$	−39.7645	−	17.6647i	−1.43208	−	0.636180i
$772$	−0.530002	+	1.97799i	−0.0190752	+	0.0711896i
$773$	−12.2291	+	17.4650i	−0.439851	+	0.628173i	−0.976470	−	0.215652i	$-0.930812\pi$
$773$	−12.2291	+	17.4650i	−0.439851	+	0.628173i	0.536619	+	0.843825i	$0.319701\pi$
$774$	2.53710	+	1.34360i	0.0911941	+	0.0482948i
$775$	−5.28780	+	15.8672i	−0.189944	+	0.569967i
$776$	7.55592	+	1.33231i	0.271242	+	0.0478272i
$777$	−72.7460	−	24.9809i	−2.60975	−	0.896186i
$778$	21.2260	−	21.2260i	0.760988	−	0.760988i
$779$	4.19265	+	31.5143i	0.150217	+	1.12912i
$780$	−16.8696	+	6.75832i	−0.604027	+	0.241987i
$781$	19.0023	−	6.91628i	0.679957	−	0.247484i
$782$	14.0688	+	20.0923i	0.503099	+	0.718499i
$783$	40.9076	−	9.55161i	1.46192	−	0.341347i
$784$	7.83389	−	9.33606i	0.279782	−	0.333431i
$785$	1.00254	−	2.87642i	0.0357823	−	0.102664i
$786$	−13.2326	−	18.1814i	−0.471992	−	0.648509i
$787$	−31.8785	+	8.54183i	−1.13635	+	0.304483i	−0.777481	−	0.628906i	$-0.783503\pi$
$787$	−31.8785	+	8.54183i	−1.13635	+	0.304483i	−0.358866	+	0.933389i	$0.616836\pi$
$788$	−0.766416	−	1.64358i	−0.0273024	−	0.0585502i
$789$	14.0869	+	3.49985i	0.501509	+	0.124598i
$790$	−11.0157	+	6.56267i	−0.391921	+	0.233489i
$791$	−10.7288	+	6.19428i	−0.381472	+	0.220243i
$792$	−2.45061	+	5.80002i	−0.0870786	+	0.206095i
$793$	9.62131	−	0.841755i	0.341663	−	0.0298916i
$794$	−2.13193	+	1.78890i	−0.0756595	+	0.0634859i
$795$	1.09430	+	5.22346i	0.0388107	+	0.185257i
$796$	−18.4124	+	6.70157i	−0.652610	+	0.237531i
$797$	−0.312200	+	0.312200i	−0.0110587	+	0.0110587i	−0.712615	−	0.701556i	$-0.752489\pi$
$797$	−0.312200	+	0.312200i	−0.0110587	+	0.0110587i	0.701556	+	0.712615i	$0.252489\pi$
$798$	−31.3388	+	10.5623i	−1.10938	+	0.373901i
$799$		−	45.4709i		−	1.60865i
$800$	−0.572014	−	4.96717i	−0.0202237	−	0.175616i
$801$	−18.4109	+	0.673526i	−0.650519	+	0.0237979i
$802$	36.6245	+	3.20423i	1.29326	+	0.113145i
$803$	1.66380	+	19.0173i	0.0587143	+	0.671108i
$804$	−16.4405	+	4.72900i	−0.579811	+	0.166779i
$805$	−45.1530	+	46.4068i	−1.59143	+	1.63563i
$806$	13.5928	+	7.84783i	0.478787	+	0.276428i
$807$	−6.97597	+	4.19947i	−0.245566	+	0.147828i
$808$	9.23780	−	4.30765i	0.324985	−	0.151543i
$809$	0.790370	−	1.36896i	0.0277879	−	0.0481301i	−0.851797	−	0.523872i	$-0.824487\pi$
$809$	0.790370	−	1.36896i	0.0277879	−	0.0481301i	0.879585	+	0.475742i	$0.157820\pi$
$810$	18.2428	−	8.49701i	0.640988	−	0.298554i
$811$	7.36583	+	41.7737i	0.258649	+	1.46687i	0.786529	+	0.617553i	$0.211876\pi$
$811$	7.36583	+	41.7737i	0.258649	+	1.46687i	−0.527880	+	0.849319i	$0.677013\pi$
$812$	−35.2777	+	3.08640i	−1.23801	+	0.108312i
$813$	−0.330147	−	18.0553i	−0.0115787	−	0.633226i
$814$	−20.9544	−	3.69483i	−0.734452	−	0.129504i
$815$	−3.31357	+	20.4238i	−0.116069	+	0.715413i
$816$	0.677078	+	6.39093i	0.0237025	+	0.223727i
$817$	1.60155	+	3.85163i	0.0560313	+	0.134752i
$818$	16.6276	+	16.6276i	0.581370	+	0.581370i
$819$	32.7620	+	52.2370i	1.14480	+	1.82531i
$820$	1.64376	+	16.2259i	0.0574025	+	0.566633i
$821$	−2.04382	−	2.43573i	−0.0713299	−	0.0850076i	0.729199	−	0.684301i	$-0.239893\pi$
$821$	−2.04382	−	2.43573i	−0.0713299	−	0.0850076i	−0.800529	+	0.599294i	$0.795448\pi$
$822$	7.13892	+	36.5645i	0.248998	+	1.27533i
$823$	−2.15631	−	1.50986i	−0.0751642	−	0.0526305i	0.535390	−	0.844605i	$-0.320165\pi$
$823$	−2.15631	−	1.50986i	−0.0751642	−	0.0526305i	−0.610555	+	0.791974i	$0.709053\pi$
$824$	2.37609	+	4.11551i	0.0827750	+	0.143370i
$825$	−11.0357	+	14.4428i	−0.384213	+	0.502834i
$826$	21.8911	+	7.96772i	0.761690	+	0.277232i
$827$	−9.54227	+	4.44963i	−0.331817	+	0.154729i	−0.581385	−	0.813628i	$-0.697489\pi$
$827$	−9.54227	+	4.44963i	−0.331817	+	0.154729i	0.249568	+	0.968357i	$0.419711\pi$
$828$	17.6552	−	9.03271i	0.613560	−	0.313908i
$829$	29.2847	−	16.9075i	1.01710	−	0.587223i	0.103838	−	0.994594i	$-0.466888\pi$
$829$	29.2847	−	16.9075i	1.01710	−	0.587223i	0.913263	+	0.407371i	$0.133554\pi$
$830$	−6.07919	−	12.5841i	−0.211012	−	0.436799i
$831$	10.6384	+	7.16288i	0.369043	+	0.248478i
$832$	−4.67438	−	0.408956i	−0.162055	−	0.0141780i
$833$	−37.0426	+	25.9375i	−1.28345	+	0.898682i
$834$	5.14316	−	2.51377i	0.178093	−	0.0870448i
$835$	−1.09367	+	1.95566i	−0.0378481	+	0.0676784i
$836$	−8.10913	+	4.23540i	−0.280460	+	0.146485i
$837$	−15.5064	−	7.85234i	−0.535980	−	0.271416i
$838$	7.83088	−	16.7934i	0.270513	−	0.580118i
$839$	1.88005	−	10.6623i	0.0649066	−	0.368104i	−0.935003	−	0.354640i	$-0.884603\pi$
$839$	1.88005	−	10.6623i	0.0649066	−	0.368104i	0.999909	−	0.0134632i	$-0.00428560\pi$
$840$	−16.2381	+	4.91253i	−0.560269	+	0.169498i
$841$	27.8518	+	23.3704i	0.960405	+	0.805876i
$842$	−22.8693	−	16.0133i	−0.788128	−	0.551853i
$843$	−1.49687	+	9.50193i	−0.0515551	+	0.327264i
$844$	−5.91161	−	3.41307i	−0.203486	−	0.117483i
$845$	−1.48210	+	20.1083i	−0.0509859	+	0.691748i
$846$	−36.4151	−	5.05617i	−1.25198	−	0.173835i
$847$	27.9036	−	7.47675i	0.958780	−	0.256904i
$848$	−0.356645	+	1.33102i	−0.0122472	+	0.0457073i
$849$	−54.9117	+	15.7950i	−1.88456	+	0.542083i
$850$	−2.72005	+	18.3518i	−0.0932968	+	0.629461i
$851$	43.0777	+	51.3380i	1.47668	+	1.75984i
$852$	−10.9588	−	12.5855i	−0.375441	−	0.431172i
$853$	−20.4632	+	43.8834i	−0.700645	+	1.50254i	0.156618	+	0.987659i	$0.449941\pi$
$853$	−20.4632	+	43.8834i	−0.700645	+	1.50254i	−0.857263	+	0.514879i	$0.827837\pi$
$854$	9.01607			0.308524
$855$	28.3036	+	7.34205i	0.967963	+	0.251093i
$856$	1.77156			0.0605506
$857$	9.15934	−	19.6423i	0.312877	−	0.670967i	−0.685491	−	0.728081i	$-0.740412\pi$
$857$	9.15934	−	19.6423i	0.312877	−	0.670967i	0.998368	+	0.0571145i	$0.0181900\pi$
$858$	11.2015	+	12.8642i	0.382412	+	0.439178i
$859$	−3.99676	−	4.76315i	−0.136368	−	0.162517i	0.693539	−	0.720419i	$-0.256051\pi$
$859$	−3.99676	−	4.76315i	−0.136368	−	0.162517i	−0.829906	+	0.557903i	$0.811606\pi$
$860$	0.759338	+	2.00059i	0.0258932	+	0.0682196i
$861$	53.1799	−	15.2969i	1.81236	−	0.521316i
$862$	−6.92622	+	25.8490i	−0.235908	+	0.880421i
$863$	28.5625	−	7.65329i	0.972278	−	0.260521i	0.262489	−	0.964935i	$-0.415457\pi$
$863$	28.5625	−	7.65329i	0.972278	−	0.260521i	0.709789	+	0.704414i	$0.248790\pi$
$864$	5.19342	+	0.168412i	0.176684	+	0.00572949i
$865$	−0.165964	−	0.192375i	−0.00564294	−	0.00654096i
$866$	31.0152	+	17.9066i	1.05394	+	0.608491i
$867$	−0.871268	+	5.53067i	−0.0295898	+	0.187832i
$868$	12.0025	+	8.40423i	0.407391	+	0.285258i
$869$	9.21969	+	7.73624i	0.312756	+	0.262434i
$870$	27.6026	+	14.7805i	0.935817	+	0.501105i
$871$	−8.04759	+	45.6402i	−0.272682	+	1.54646i
$872$	−2.11575	+	4.53724i	−0.0716483	+	0.153650i
$873$	−12.5041	+	19.3248i	−0.423201	+	0.654047i
$874$	28.1402	+	6.19830i	0.951856	+	0.209661i
$875$	−48.9324	+	2.01132i	−1.65422	+	0.0679951i
$876$	14.1538	−	6.91782i	0.478213	−	0.233732i
$877$	18.2456	−	12.7757i	0.616109	−	0.431404i	−0.223418	−	0.974723i	$-0.571721\pi$
$877$	18.2456	−	12.7757i	0.616109	−	0.431404i	0.839526	+	0.543319i	$0.182833\pi$
$878$	−12.3504	−	1.08052i	−0.416807	−	0.0364659i
$879$	−35.6682	−	24.0155i	−1.20306	−	0.810021i
$880$	−4.22586	+	2.04146i	−0.142454	+	0.0688175i
$881$	13.4679	−	7.77570i	0.453745	−	0.261970i	−0.255665	−	0.966765i	$-0.582295\pi$
$881$	13.4679	−	7.77570i	0.453745	−	0.261970i	0.709411	+	0.704795i	$0.248961\pi$
$882$	16.6529	+	32.5495i	0.560732	+	1.09600i
$883$	−1.45426	+	0.678132i	−0.0489397	+	0.0228210i	−0.446934	−	0.894567i	$-0.647484\pi$
$883$	−1.45426	+	0.678132i	−0.0489397	+	0.0228210i	0.397994	+	0.917388i	$0.369706\pi$
$884$	16.3604	+	5.95469i	0.550259	+	0.200278i
$885$	−12.3478	−	16.4864i	−0.415067	−	0.554183i
$886$	0.800418	+	1.38636i	0.0268906	+	0.0465758i
$887$	1.83309	+	1.28355i	0.0615492	+	0.0430972i	0.603946	−	0.797025i	$-0.293594\pi$
$887$	1.83309	+	1.28355i	0.0615492	+	0.0430972i	−0.542397	+	0.840122i	$0.682483\pi$
$888$	3.36478	+	17.2339i	0.112915	+	0.578332i
$889$	25.4527	+	30.3334i	0.853658	+	1.01735i
$890$	−10.6391	−	8.68182i	−0.356624	−	0.291015i
$891$	−13.1668	−	13.5443i	−0.441103	−	0.453751i
$892$	11.4891	+	11.4891i	0.384683	+	0.384683i
$893$	−36.1420	−	39.3342i	−1.20944	−	1.31627i
$894$	4.01455	+	37.8933i	0.134267	+	1.26734i
$895$	1.48398	−	1.06967i	0.0496040	−	0.0357553i
$896$	−4.31379	−	0.760638i	−0.144114	−	0.0254111i
$897$	−0.982221	−	53.7163i	−0.0327954	−	1.79354i
$898$	−0.209530	+	0.0183315i	−0.00699209	+	0.000611729i
$899$	−4.69590	−	26.6317i	−0.156617	−	0.888218i
$900$	14.3945	+	4.21897i	0.479815	+	0.140632i
$901$	2.55645	−	4.42790i	0.0851676	−	0.147515i
$902$	13.8737	−	6.46943i	0.461945	−	0.215409i
$903$	6.22036	−	3.74460i	0.207001	−	0.124613i
$904$	2.44931	+	1.41411i	0.0814628	+	0.0470326i
$905$	−23.0622	−	22.4391i	−0.766613	−	0.745900i
$906$	−4.67727	+	1.34539i	−0.155392	+	0.0446975i
$907$	−0.274096	−	3.13293i	−0.00910120	−	0.104027i	0.990285	−	0.139050i	$-0.0444050\pi$
$907$	−0.274096	−	3.13293i	−0.00910120	−	0.104027i	−0.999386	+	0.0350233i	$0.988849\pi$
$908$	−26.5327	−	2.32131i	−0.880518	−	0.0770353i
$909$	1.11790	+	30.5579i	0.0370783	+	1.01354i
$910$	−7.36022	+	45.3661i	−0.243989	+	1.50387i
$911$		−	11.3276i		−	0.375301i	−0.982236	−	0.187651i	$-0.939913\pi$
$911$		−	11.3276i		−	0.375301i	0.982236	−	0.187651i	$-0.0600873\pi$
$912$	5.66545	+	4.99026i	0.187602	+	0.165244i
$913$	−9.27567	+	9.27567i	−0.306980	+	0.306980i
$914$	24.4768	−	8.90883i	0.809621	−	0.294678i
$915$	−6.67295	−	4.36131i	−0.220601	−	0.144180i
$916$	7.13032	−	5.98305i	0.235592	−	0.197685i
$917$	−56.6530	+	4.95650i	−1.87085	+	0.163678i
$918$	−18.4516	−	5.59103i	−0.608994	−	0.184531i
$919$	−28.7859	+	16.6195i	−0.949558	+	0.548228i	−0.892944	−	0.450169i	$-0.851364\pi$
$919$	−28.7859	+	16.6195i	−0.949558	+	0.548228i	−0.0566144	+	0.998396i	$0.518031\pi$
$920$	14.3290	+	3.62990i	0.472414	+	0.119674i
$921$	0.430165	+	0.106873i	0.0141744	+	0.00352158i
$922$	−3.66666	−	7.86319i	−0.120755	−	0.258960i
$923$	−43.6685	+	11.7009i	−1.43737	+	0.385141i
$924$	9.37044	+	12.8748i	0.308265	+	0.423550i
$925$	−3.03342	+	50.5985i	−0.0997383	+	1.66367i
$926$	−5.36770	+	6.39698i	−0.176394	+	0.210218i
$927$	−14.1474	+	1.76092i	−0.464660	+	0.0578363i
$928$	4.63703	+	6.62237i	0.152218	+	0.217390i
$929$	−28.8618	+	10.5048i	−0.946926	+	0.344653i	−0.768897	−	0.639373i	$-0.779194\pi$
$929$	−28.8618	+	10.5048i	−0.946926	+	0.344653i	−0.178029	+	0.984025i	$0.556972\pi$
$930$	−4.81790	−	12.0260i	−0.157985	−	0.394349i
$931$	−11.4273	+	51.8799i	−0.374515	+	1.70029i
$932$	−1.68757	+	1.68757i	−0.0552782	+	0.0552782i
$933$	−17.6797	−	6.07120i	−0.578808	−	0.198762i
$934$	−9.17471	−	1.61775i	−0.300206	−	0.0529343i
$935$	17.1061	−	3.25839i	0.559428	−	0.106561i
$936$	6.58798	−	12.4400i	0.215335	−	0.406613i
$937$	−27.5131	+	39.2927i	−0.898813	+	1.28364i	0.0595916	+	0.998223i	$0.481020\pi$
$937$	−27.5131	+	39.2927i	−0.898813	+	1.28364i	−0.958404	+	0.285415i	$0.907869\pi$
$938$	−11.1975	+	41.7895i	−0.365610	+	1.36447i
$939$	−12.8802	−	5.72182i	−0.420329	−	0.186725i
$940$	−17.8998	−	20.7484i	−0.583828	−	0.676739i
$941$	−0.641256	+	1.76184i	−0.0209043	+	0.0574342i	−0.949706	−	0.313143i	$-0.898618\pi$
$941$	−0.641256	+	1.76184i	−0.0209043	+	0.0574342i	0.928802	+	0.370577i	$0.120840\pi$
$942$	0.847404	+	2.20210i	0.0276099	+	0.0717482i
$943$	−46.5717	−	12.4789i	−1.51658	−	0.406368i
$944$	−0.923517	−	5.23753i	−0.0300579	−	0.170467i
$945$	5.38423	−	50.6093i	0.175149	−	1.64632i
$946$	1.53861	−	1.29105i	0.0500247	−	0.0419757i
$947$	−3.55819	−	5.08162i	−0.115626	−	0.165130i	0.757168	−	0.653221i	$-0.226583\pi$
$947$	−3.55819	−	5.08162i	−0.115626	−	0.165130i	−0.872793	+	0.488090i	$0.837694\pi$
$948$	3.22581	−	9.39376i	0.104770	−	0.305095i
$949$		−	42.6785i		−	1.38540i
$950$	12.2337	+	18.0371i	0.396915	+	0.585200i
$951$	−1.85245	−	17.4853i	−0.0600698	−	0.566999i
$952$	14.7303	+	6.86884i	0.477411	+	0.222620i
$953$	45.2107	−	31.6568i	1.46452	−	1.02547i	0.475169	−	0.879894i	$-0.342387\pi$
$953$	45.2107	−	31.6568i	1.46452	−	1.02547i	0.989348	−	0.145572i	$-0.0465021\pi$
$954$	−3.26178	−	2.53968i	−0.105604	−	0.0822251i
$955$	3.79104	−	8.42938i	0.122675	−	0.272768i
$956$	−17.7145	+	3.12355i	−0.572928	+	0.101023i
$957$	4.57338	−	29.0311i	0.147836	−	0.938443i
$958$	4.31084	+	16.0883i	0.139277	+	0.519788i
$959$	88.5352	+	32.2242i	2.85895	+	1.04057i
$960$	2.82477	+	2.64966i	0.0911691	+	0.0855173i
$961$	9.90541	−	17.1567i	0.319529	−	0.553441i
$962$	45.9484	+	12.3118i	1.48144	+	0.396950i
$963$	−2.06849	+	4.89563i	−0.0666560	+	0.157759i
$964$	0.428086	−	0.510173i	0.0137877	−	0.0164316i
$965$	−0.856801	−	4.49808i	−0.0275814	−	0.144798i
$966$	3.45704	−	50.0348i	0.111229	−	1.60984i
$967$	36.9185	+	17.2154i	1.18722	+	0.553610i	0.912961	−	0.408046i	$-0.133790\pi$
$967$	36.9185	+	17.2154i	1.18722	+	0.553610i	0.274259	+	0.961656i	$0.411567\pi$
$968$	−4.66331	−	4.66331i	−0.149884	−	0.149884i
$969$	−15.5128	−	23.3260i	−0.498342	−	0.749338i
$970$	−16.5093	+	4.66685i	−0.530080	+	0.149844i
$971$	13.3235	+	36.6061i	0.427573	+	1.17475i	0.947281	+	0.320403i	$0.103818\pi$
$971$	13.3235	+	36.6061i	0.427573	+	1.17475i	−0.519708	+	0.854344i	$0.673959\pi$
$972$	−6.52928	+	14.1552i	−0.209427	+	0.454027i
$973$	1.26179	−	14.4224i	0.0404513	−	0.462360i
$974$	1.08794	+	0.912894i	0.0348600	+	0.0292510i
$975$	27.3922	−	30.0159i	0.877252	−	0.961277i
$976$	−1.02915	−	1.78254i	−0.0329424	−	0.0570579i
$977$	−6.71138	−	25.0472i	−0.214716	−	0.801331i	−0.986266	−	0.165163i	$-0.947185\pi$
$977$	−6.71138	−	25.0472i	−0.214716	−	0.801331i	0.771550	−	0.636168i	$-0.219482\pi$
$978$	−8.26593	−	13.7310i	−0.264315	−	0.439069i
$979$	−4.40833	+	12.1118i	−0.140891	+	0.387095i
$980$	−6.69217	+	26.4173i	−0.213773	+	0.843870i
$981$	−10.0681	−	11.1445i	−0.321450	−	0.355816i
$982$	1.92365	−	2.74726i	0.0613862	−	0.0876685i
$983$	−1.31028	−	14.9766i	−0.0417916	−	0.477680i	−0.988036	−	0.154226i	$-0.950712\pi$
$983$	−1.31028	−	14.9766i	−0.0417916	−	0.477680i	0.946244	−	0.323454i	$-0.104844\pi$
$984$	−9.09459	−	8.76797i	−0.289925	−	0.279513i
$985$	3.14178	+	2.56378i	0.100106	+	0.0816890i
$986$	−10.2595	−	28.1879i	−0.326730	−	0.897684i
$987$	−58.4522	+	72.3051i	−1.86055	+	2.30150i
$988$	18.8854	−	7.85278i	0.600825	−	0.249830i
$989$	−6.32611			−0.201158
$990$	−0.707335	−	14.0616i	−0.0224806	−	0.446907i
$991$	3.57098	−	20.2520i	0.113436	−	0.643327i	−0.874077	−	0.485788i	$-0.838533\pi$
$991$	3.57098	−	20.2520i	0.113436	−	0.643327i	0.987513	−	0.157539i	$-0.0503561\pi$
$992$	0.291538	−	3.33229i	0.00925634	−	0.105800i
$993$	−11.7403	+	2.29220i	−0.372568	+	0.0727408i
$994$	−41.5626	+	7.32861i	−1.31829	+	0.232449i
$995$	30.5538	−	31.4023i	0.968621	−	0.995519i
$996$	9.89314	+	4.39487i	0.313476	+	0.139257i
$997$	2.06437	+	4.42705i	0.0653792	+	0.140206i	0.936282	−	0.351249i	$-0.114243\pi$
$997$	2.06437	+	4.42705i	0.0653792	+	0.140206i	−0.870903	+	0.491455i	$0.836465\pi$
$998$	−7.59988	−	16.2980i	−0.240570	−	0.515904i
$999$	−51.5539	−	10.8240i	−1.63109	−	0.342457i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bi.a.347.14	yes	480
3.2	odd	2	inner	570.2.bi.a.347.34	yes	480
5.3	odd	4	inner	570.2.bi.a.233.24	yes	480
15.8	even	4	inner	570.2.bi.a.233.5	yes	480
19.4	even	9	inner	570.2.bi.a.137.5	yes	480
57.23	odd	18	inner	570.2.bi.a.137.24	yes	480
95.23	odd	36	inner	570.2.bi.a.23.34	yes	480
285.23	even	36	inner	570.2.bi.a.23.14	✓	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bi.a.23.14	✓	480	285.23	even	36	inner
570.2.bi.a.23.34	yes	480	95.23	odd	36	inner
570.2.bi.a.137.5	yes	480	19.4	even	9	inner
570.2.bi.a.137.24	yes	480	57.23	odd	18	inner
570.2.bi.a.233.5	yes	480	15.8	even	4	inner
570.2.bi.a.233.24	yes	480	5.3	odd	4	inner
570.2.bi.a.347.14	yes	480	1.1	even	1	trivial
570.2.bi.a.347.34	yes	480	3.2	odd	2	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bi (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.422618 + 0.906308i) q^{2} +(1.13741 + 1.30625i) q^{3} +(-0.642788 - 0.766044i) q^{4} +(2.03932 + 0.917164i) q^{5} +(-1.66456 + 0.478800i) q^{6} +(-1.13371 + 4.23108i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-0.412587 + 2.97149i) q^{9} +O(q^{10})\)	\(q+(-0.422618 + 0.906308i) q^{2} +(1.13741 + 1.30625i) q^{3} +(-0.642788 - 0.766044i) q^{4} +(2.03932 + 0.917164i) q^{5} +(-1.66456 + 0.478800i) q^{6} +(-1.13371 + 4.23108i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-0.412587 + 2.97149i) q^{9} +(-1.69309 + 1.46064i) q^{10} +(1.81764 + 1.04941i) q^{11} +(0.269532 - 1.71095i) q^{12} +(-3.84366 - 2.69136i) q^{13} +(-3.35553 - 2.81563i) q^{14} +(1.12150 + 3.70705i) q^{15} +(-0.173648 + 0.984808i) q^{16} +(1.56811 - 3.36282i) q^{17} +(-2.51872 - 1.62974i) q^{18} +(-1.31641 - 4.15537i) q^{19} +(-0.608258 - 2.15175i) q^{20} +(-6.81636 + 3.33157i) q^{21} +(-1.71926 + 1.20384i) q^{22} +(6.58540 + 0.576148i) q^{23} +(1.43674 + 0.967358i) q^{24} +(3.31762 + 3.74078i) q^{25} +(4.06360 - 2.34612i) q^{26} +(-4.35080 + 2.84087i) q^{27} +(3.96993 - 1.85121i) q^{28} +(-7.59687 - 2.76504i) q^{29} +(-3.83370 - 0.550249i) q^{30} +(1.67251 + 2.89688i) q^{31} +(-0.819152 - 0.573576i) q^{32} +(0.696606 + 3.56791i) q^{33} +(2.38504 + 2.84237i) q^{34} +(-6.19260 + 7.58871i) q^{35} +(2.54150 - 1.59398i) q^{36} +(7.16856 + 7.16856i) q^{37} +(4.32238 + 0.563059i) q^{38} +(-0.856232 - 8.08197i) q^{39} +(2.20721 + 0.358099i) q^{40} +(-7.18278 - 1.26652i) q^{41} +(-0.138707 - 7.58570i) q^{42} +(-0.953329 + 0.0834055i) q^{43} +(-0.364458 - 2.06694i) q^{44} +(-3.56674 + 5.68140i) q^{45} +(-3.30528 + 5.72491i) q^{46} +(11.1066 - 5.17910i) q^{47} +(-1.48392 + 0.893304i) q^{48} +(-10.5546 - 6.09368i) q^{49} +(-4.79238 + 1.42586i) q^{50} +(6.17627 - 1.77657i) q^{51} +(0.408956 + 4.67438i) q^{52} +(1.37273 + 0.120098i) q^{53} +(-0.735975 - 5.14377i) q^{54} +(2.74426 + 3.80716i) q^{55} +4.38034i q^{56} +(3.93065 - 6.44593i) q^{57} +(5.71655 - 5.71655i) q^{58} +(-4.99759 + 1.81897i) q^{59} +(2.11888 - 3.24196i) q^{60} +(-1.57675 + 1.32305i) q^{61} +(-3.33229 + 0.291538i) q^{62} +(-12.1049 - 5.11452i) q^{63} +(0.866025 - 0.500000i) q^{64} +(-5.37002 - 9.01380i) q^{65} +(-3.52803 - 0.876526i) q^{66} +(-4.17411 - 8.95141i) q^{67} +(-3.58403 + 0.960337i) q^{68} +(6.73772 + 9.25751i) q^{69} +(-4.26060 - 8.81953i) q^{70} +(6.19315 - 7.38071i) q^{71} +(0.370550 + 2.97703i) q^{72} +(5.21699 + 7.45063i) q^{73} +(-9.52648 + 3.46736i) q^{74} +(-1.11289 + 8.58845i) q^{75} +(-2.33702 + 3.67945i) q^{76} +(-6.50085 + 6.50085i) q^{77} +(7.68661 + 2.63958i) q^{78} +(5.64724 + 0.995761i) q^{79} +(-1.25735 + 1.84907i) q^{80} +(-8.65954 - 2.45200i) q^{81} +(4.18343 - 5.97455i) q^{82} +(-1.61763 + 6.03708i) q^{83} +(6.93360 + 3.08014i) q^{84} +(6.28212 - 5.41963i) q^{85} +(0.327303 - 0.899258i) q^{86} +(-5.02894 - 13.0684i) q^{87} +(2.02731 + 0.543217i) q^{88} +(1.06639 + 6.04779i) q^{89} +(-3.64173 - 5.63363i) q^{90} +(15.7450 - 13.2116i) q^{91} +(-3.79166 - 5.41505i) q^{92} +(-1.88171 + 5.47966i) q^{93} +12.2548i q^{94} +(1.12657 - 9.68147i) q^{95} +(-0.182478 - 1.72241i) q^{96} +(6.95363 + 3.24253i) q^{97} +(9.98330 - 6.99038i) q^{98} +(-3.86826 + 4.96813i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q+O(q^{10}) \) 480 * q	\( 480 q - 36 q^{15} - 48 q^{18} + 24 q^{22} - 24 q^{25} + 72 q^{33} + 24 q^{43} - 36 q^{45} + 24 q^{51} - 120 q^{55} + 108 q^{57} - 48 q^{60} - 48 q^{61} - 36 q^{63} - 24 q^{66} + 48 q^{67} - 48 q^{70} - 48 q^{78} - 144 q^{81} - 48 q^{85} - 96 q^{87} - 168 q^{90} - 144 q^{91} - 228 q^{93} + 48 q^{97}+O(q^{100}) \) 480 * q - 36 * q^15 - 48 * q^18 + 24 * q^22 - 24 * q^25 + 72 * q^33 + 24 * q^43 - 36 * q^45 + 24 * q^51 - 120 * q^55 + 108 * q^57 - 48 * q^60 - 48 * q^61 - 36 * q^63 - 24 * q^66 + 48 * q^67 - 48 * q^70 - 48 * q^78 - 144 * q^81 - 48 * q^85 - 96 * q^87 - 168 * q^90 - 144 * q^91 - 228 * q^93 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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