LMFDB - Embedded newform 570.2.bi.a.17.9

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			17.9
Character	$\chi$	$=$	570.17
Dual form			570.2.bi.a.503.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.573576 - 0.819152i) q^{2} +(-0.580543 + 1.63186i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(0.846732 - 2.06955i) q^{5} +(1.66973 - 0.460444i) q^{6} +(0.562193 - 2.09813i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-2.32594 - 1.89473i) q^{9} +O(q^{10})$	\(q+(-0.573576 - 0.819152i) q^{2} +(-0.580543 + 1.63186i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(0.846732 - 2.06955i) q^{5} +(1.66973 - 0.460444i) q^{6} +(0.562193 - 2.09813i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-2.32594 - 1.89473i) q^{9} +(-2.18094 + 0.493443i) q^{10} +(-2.25218 - 1.30030i) q^{11} +(-1.33489 - 1.10366i) q^{12} +(-0.252692 + 2.88829i) q^{13} +(-2.04115 + 0.742919i) q^{14} +(2.88566 + 2.58321i) q^{15} +(-0.766044 - 0.642788i) q^{16} +(-1.34476 - 1.92052i) q^{17} +(-0.217968 + 2.99207i) q^{18} +(-3.59309 + 2.46774i) q^{19} +(1.65514 + 1.50350i) q^{20} +(3.09749 + 2.13548i) q^{21} +(0.226657 + 2.59070i) q^{22} +(-2.67592 - 5.73853i) q^{23} +(-0.138405 + 1.72651i) q^{24} +(-3.56609 - 3.50471i) q^{25} +(2.51089 - 1.44966i) q^{26} +(4.44224 - 2.69564i) q^{27} +(1.77932 + 1.24589i) q^{28} +(-0.986495 - 5.59469i) q^{29} +(0.460900 - 3.84546i) q^{30} +(4.45573 + 7.71755i) q^{31} +(-0.0871557 + 0.996195i) q^{32} +(3.42939 - 2.92037i) q^{33} +(-0.801875 + 2.20313i) q^{34} +(-3.86617 - 2.94005i) q^{35} +(2.57598 - 1.53763i) q^{36} +(-8.53429 - 8.53429i) q^{37} +(4.08236 + 1.52785i) q^{38} +(-4.56659 - 2.08913i) q^{39} +(0.282241 - 2.21818i) q^{40} +(3.23906 - 3.86016i) q^{41} +(-0.0273638 - 3.76217i) q^{42} +(3.29646 - 7.06928i) q^{43} +(1.99217 - 1.67163i) q^{44} +(-5.89069 + 3.20932i) q^{45} +(-3.16588 + 5.48347i) q^{46} +(-2.65814 - 1.86125i) q^{47} +(1.49366 - 0.876912i) q^{48} +(1.97607 + 1.14089i) q^{49} +(-0.825469 + 4.93139i) q^{50} +(3.91472 - 1.07952i) q^{51} +(-2.62768 - 1.22531i) q^{52} +(-3.40827 - 7.30907i) q^{53} +(-4.75610 - 2.09272i) q^{54} +(-4.59803 + 3.56000i) q^{55} -2.17215i q^{56} +(-1.94107 - 7.29604i) q^{57} +(-4.01707 + 4.01707i) q^{58} +(-0.302793 + 1.71723i) q^{59} +(-3.41438 + 1.82812i) q^{60} +(-6.68929 - 2.43470i) q^{61} +(3.76615 - 8.07653i) q^{62} +(-5.28303 + 3.81493i) q^{63} +(0.866025 - 0.500000i) q^{64} +(5.76350 + 2.96857i) q^{65} +(-4.35925 - 1.13414i) q^{66} +(1.05816 - 1.51120i) q^{67} +(2.26464 - 0.606808i) q^{68} +(10.9180 - 1.03527i) q^{69} +(-0.190801 + 4.85332i) q^{70} +(4.61510 + 12.6799i) q^{71} +(-2.73708 - 1.22817i) q^{72} +(14.3468 - 1.25518i) q^{73} +(-2.09581 + 11.8859i) q^{74} +(7.78947 - 3.78472i) q^{75} +(-1.09001 - 4.22041i) q^{76} +(-3.99436 + 3.99436i) q^{77} +(0.907968 + 4.93901i) q^{78} +(-7.19735 + 8.57747i) q^{79} +(-1.97892 + 1.04110i) q^{80} +(1.82000 + 8.81406i) q^{81} +(-5.01990 - 0.439185i) q^{82} +(-1.85881 + 6.93717i) q^{83} +(-3.06610 + 2.18031i) q^{84} +(-5.11328 + 1.15689i) q^{85} +(-7.68159 + 1.35447i) q^{86} +(9.70246 + 1.63813i) q^{87} +(-2.51198 - 0.673084i) q^{88} +(0.349266 - 0.293069i) q^{89} +(6.00769 + 2.98458i) q^{90} +(5.91796 + 2.15396i) q^{91} +(6.30767 - 0.551850i) q^{92} +(-15.1807 + 2.79076i) q^{93} +3.24499i q^{94} +(2.06473 + 9.52559i) q^{95} +(-1.57505 - 0.720560i) q^{96} +(2.48935 - 1.74306i) q^{97} +(-0.198869 - 2.27309i) q^{98} +(2.77473 + 7.29169i) 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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.573576	−	0.819152i	−0.405580	−	0.579228i
$2$	−0.573576	−	0.819152i	−0.405580	−	0.579228i
$3$	−0.580543	+	1.63186i	−0.335177	+	0.942155i
$3$	−0.580543	+	1.63186i	−0.335177	+	0.942155i
$4$	−0.342020	+	0.939693i	−0.171010	+	0.469846i
$5$	0.846732	−	2.06955i	0.378670	−	0.925532i
$5$	0.846732	−	2.06955i	0.378670	−	0.925532i
$6$	1.66973	−	0.460444i	0.681664	−	0.187976i
$7$	0.562193	−	2.09813i	0.212489	−	0.793020i	−0.774546	−	0.632517i	$-0.782022\pi$
$7$	0.562193	−	2.09813i	0.212489	−	0.793020i	0.987035	−	0.160503i	$-0.0513116\pi$
$8$	0.965926	−	0.258819i	0.341506	−	0.0915064i
$9$	−2.32594	−	1.89473i	−0.775313	−	0.631577i
$10$	−2.18094	+	0.493443i	−0.689675	+	0.156041i
$11$	−2.25218	−	1.30030i	−0.679059	−	0.392055i	0.120442	−	0.992720i	$-0.461569\pi$
$11$	−2.25218	−	1.30030i	−0.679059	−	0.392055i	−0.799500	+	0.600666i	$0.794902\pi$
$12$	−1.33489	−	1.10366i	−0.385350	−	0.318600i
$13$	−0.252692	+	2.88829i	−0.0700843	+	0.801067i	0.877085	+	0.480334i	$0.159485\pi$
$13$	−0.252692	+	2.88829i	−0.0700843	+	0.801067i	−0.947170	+	0.320733i	$0.896071\pi$
$14$	−2.04115	+	0.742919i	−0.545521	+	0.198553i
$15$	2.88566	+	2.58321i	0.745073	+	0.666983i
$16$	−0.766044	−	0.642788i	−0.191511	−	0.160697i
$17$	−1.34476	−	1.92052i	−0.326153	−	0.465795i	0.622270	−	0.782803i	$-0.286211\pi$
$17$	−1.34476	−	1.92052i	−0.326153	−	0.465795i	−0.948423	+	0.317008i	$0.897322\pi$
$18$	−0.217968	+	2.99207i	−0.0513754	+	0.705238i
$19$	−3.59309	+	2.46774i	−0.824310	+	0.566138i
$19$	−3.59309	+	2.46774i	−0.824310	+	0.566138i
$20$	1.65514	+	1.50350i	0.370101	+	0.336192i
$21$	3.09749	+	2.13548i	0.675927	+	0.466000i
$22$	0.226657	+	2.59070i	0.0483234	+	0.552339i
$23$	−2.67592	−	5.73853i	−0.557968	−	1.19657i	−0.959756	−	0.280834i	$-0.909389\pi$
$23$	−2.67592	−	5.73853i	−0.557968	−	1.19657i	0.401788	−	0.915733i	$-0.368389\pi$
$24$	−0.138405	+	1.72651i	−0.0282517	+	0.352423i
$25$	−3.56609	−	3.50471i	−0.713218	−	0.700943i
$26$	2.51089	−	1.44966i	0.492425	−	0.284302i
$27$	4.44224	−	2.69564i	0.854910	−	0.518776i
$28$	1.77932	+	1.24589i	0.336260	+	0.235452i
$29$	−0.986495	−	5.59469i	−0.183188	−	1.03891i	−0.928262	−	0.371927i	$-0.878697\pi$
$29$	−0.986495	−	5.59469i	−0.183188	−	1.03891i	0.745075	−	0.666981i	$-0.232414\pi$
$30$	0.460900	−	3.84546i	0.0841484	−	0.702082i
$31$	4.45573	+	7.71755i	0.800273	+	1.38611i	0.919436	+	0.393239i	$0.128645\pi$
$31$	4.45573	+	7.71755i	0.800273	+	1.38611i	−0.119163	+	0.992875i	$0.538021\pi$
$32$	−0.0871557	+	0.996195i	−0.0154071	+	0.176104i
$33$	3.42939	−	2.92037i	0.596981	−	0.508371i
$34$	−0.801875	+	2.20313i	−0.137520	+	0.377834i
$35$	−3.86617	−	2.94005i	−0.653502	−	0.496959i
$36$	2.57598	−	1.53763i	0.429330	−	0.256272i
$37$	−8.53429	−	8.53429i	−1.40303	−	1.40303i	−0.790273	−	0.612755i	$-0.790061\pi$
$37$	−8.53429	−	8.53429i	−1.40303	−	1.40303i	−0.612755	−	0.790273i	$-0.709939\pi$
$38$	4.08236	+	1.52785i	0.662247	+	0.247849i
$39$	−4.56659	−	2.08913i	−0.731239	−	0.334529i
$40$	0.282241	−	2.21818i	0.0446263	−	0.350726i
$41$	3.23906	−	3.86016i	0.505856	−	0.602856i	−0.451320	−	0.892362i	$-0.649047\pi$
$41$	3.23906	−	3.86016i	0.505856	−	0.602856i	0.957176	+	0.289507i	$0.0934912\pi$
$42$	−0.0273638	−	3.76217i	−0.00422232	−	0.580516i
$43$	3.29646	−	7.06928i	0.502705	−	1.07806i	−0.477237	−	0.878775i	$-0.658362\pi$
$43$	3.29646	−	7.06928i	0.502705	−	1.07806i	0.979942	−	0.199281i	$-0.0638605\pi$
$44$	1.99217	−	1.67163i	0.300331	−	0.252008i
$45$	−5.89069	+	3.20932i	−0.878132	+	0.478418i
$46$	−3.16588	+	5.48347i	−0.466784	+	0.808494i
$47$	−2.65814	−	1.86125i	−0.387730	−	0.271491i	0.363417	−	0.931627i	$-0.381610\pi$
$47$	−2.65814	−	1.86125i	−0.387730	−	0.271491i	−0.751147	+	0.660135i	$0.770499\pi$
$48$	1.49366	−	0.876912i	0.215591	−	0.126571i
$49$	1.97607	+	1.14089i	0.282296	+	0.162984i
$50$	−0.825469	+	4.93139i	−0.116739	+	0.697404i
$51$	3.91472	−	1.07952i	0.548170	−	0.151164i
$52$	−2.62768	−	1.22531i	−0.364393	−	0.169919i
$53$	−3.40827	−	7.30907i	−0.468162	−	1.00398i	−0.988668	−	0.150119i	$-0.952034\pi$
$53$	−3.40827	−	7.30907i	−0.468162	−	1.00398i	0.520506	−	0.853858i	$-0.325744\pi$
$54$	−4.75610	−	2.09272i	−0.647224	−	0.284783i
$55$	−4.59803	+	3.56000i	−0.619998	+	0.480031i
$56$		−	2.17215i		−	0.290266i
$57$	−1.94107	−	7.29604i	−0.257101	−	0.966385i
$58$	−4.01707	+	4.01707i	−0.527467	+	0.527467i
$59$	−0.302793	+	1.71723i	−0.0394203	+	0.223564i	−0.998153	−	0.0607440i	$-0.980653\pi$
$59$	−0.302793	+	1.71723i	−0.0394203	+	0.223564i	0.958733	+	0.284308i	$0.0917638\pi$
$60$	−3.41438	+	1.82812i	−0.440794	+	0.236009i
$61$	−6.68929	−	2.43470i	−0.856476	−	0.311732i	−0.123798	−	0.992307i	$-0.539508\pi$
$61$	−6.68929	−	2.43470i	−0.856476	−	0.311732i	−0.732678	+	0.680576i	$0.761730\pi$
$62$	3.76615	−	8.07653i	0.478301	−	1.02572i
$63$	−5.28303	+	3.81493i	−0.665599	+	0.480636i
$64$	0.866025	−	0.500000i	0.108253	−	0.0625000i
$65$	5.76350	+	2.96857i	0.714874	+	0.368206i
$66$	−4.35925	−	1.13414i	−0.536586	−	0.139603i
$67$	1.05816	−	1.51120i	0.129274	−	0.184623i	−0.749297	−	0.662234i	$-0.769608\pi$
$67$	1.05816	−	1.51120i	0.129274	−	0.184623i	0.878571	+	0.477611i	$0.158497\pi$
$68$	2.26464	−	0.606808i	0.274628	−	0.0735863i
$69$	10.9180	−	1.03527i	1.31437	−	0.124632i
$70$	−0.190801	+	4.85332i	−0.0228051	+	0.580083i
$71$	4.61510	+	12.6799i	0.547711	+	1.50482i	0.836792	+	0.547520i	$0.184428\pi$
$71$	4.61510	+	12.6799i	0.547711	+	1.50482i	−0.289081	+	0.957305i	$0.593350\pi$
$72$	−2.73708	−	1.22817i	−0.322568	−	0.144741i
$73$	14.3468	−	1.25518i	1.67917	−	0.146908i	0.792673	−	0.609647i	$-0.208689\pi$
$73$	14.3468	−	1.25518i	1.67917	−	0.146908i	0.886495	+	0.462739i	$0.153133\pi$
$74$	−2.09581	+	11.8859i	−0.243633	+	1.38171i
$75$	7.78947	−	3.78472i	0.899451	−	0.437022i
$76$	−1.09001	−	4.22041i	−0.125033	−	0.484115i
$77$	−3.99436	+	3.99436i	−0.455200	+	0.455200i
$78$	0.907968	+	4.93901i	0.102807	+	0.559232i
$79$	−7.19735	+	8.57747i	−0.809765	+	0.965040i	−0.999860	−	0.0167253i	$-0.994676\pi$
$79$	−7.19735	+	8.57747i	−0.809765	+	0.965040i	0.190095	+	0.981766i	$0.439120\pi$
$80$	−1.97892	+	1.04110i	−0.221250	+	0.116398i
$81$	1.82000	+	8.81406i	0.202222	+	0.979340i
$82$	−5.01990	−	0.439185i	−0.554356	−	0.0484998i
$83$	−1.85881	+	6.93717i	−0.204031	+	0.761454i	0.785712	+	0.618593i	$0.212297\pi$
$83$	−1.85881	+	6.93717i	−0.204031	+	0.761454i	−0.989743	+	0.142861i	$0.954370\pi$
$84$	−3.06610	+	2.18031i	−0.334538	+	0.237891i
$85$	−5.11328	+	1.15689i	−0.554613	+	0.125482i
$86$	−7.68159	+	1.35447i	−0.828327	+	0.146056i
$87$	9.70246	+	1.63813i	1.04021	+	0.175626i
$88$	−2.51198	−	0.673084i	−0.267778	−	0.0717510i
$89$	0.349266	−	0.293069i	0.0370221	−	0.0310652i	−0.624089	−	0.781353i	$-0.714530\pi$
$89$	0.349266	−	0.293069i	0.0370221	−	0.0310652i	0.661111	+	0.750288i	$0.270085\pi$
$90$	6.00769	+	2.98458i	0.633266	+	0.314602i
$91$	5.91796	+	2.15396i	0.620370	+	0.225796i
$92$	6.30767	−	0.551850i	0.657621	−	0.0575343i
$93$	−15.1807	+	2.79076i	−1.57417	+	0.289389i
$94$			3.24499i			0.334695i
$95$	2.06473	+	9.52559i	0.211837	+	0.977305i
$96$	−1.57505	−	0.720560i	−0.160753	−	0.0735418i
$97$	2.48935	−	1.74306i	0.252755	−	0.176981i	−0.440331	−	0.897835i	$-0.645139\pi$
$97$	2.48935	−	1.74306i	0.252755	−	0.176981i	0.693087	+	0.720854i	$0.256250\pi$
$98$	−0.198869	−	2.27309i	−0.0200888	−	0.229617i
$99$	2.77473	+	7.29169i	0.278871	+	0.732843i
$100$	4.51303	−	2.15234i	0.451303	−	0.215234i
$101$	1.75004	+	2.08562i	0.174136	+	0.207527i	0.846052	−	0.533100i	$-0.178973\pi$
$101$	1.75004	+	2.08562i	0.174136	+	0.207527i	−0.671917	+	0.740627i	$0.734529\pi$
$102$	−3.12969	−	2.58756i	−0.309885	−	0.256207i
$103$	−0.0193048	−	0.0720466i	−0.00190216	−	0.00709897i	0.964968	−	0.262367i	$-0.0845030\pi$
$103$	−0.0193048	−	0.0720466i	−0.00190216	−	0.00709897i	−0.966870	+	0.255268i	$0.917836\pi$
$104$	0.503462	+	2.85527i	0.0493685	+	0.279983i
$105$	7.04222	−	4.60223i	0.687251	−	0.449132i
$106$	−4.03233	+	6.98420i	−0.391655	+	0.678366i
$107$	11.1967	+	3.00016i	1.08243	+	0.290036i	0.755591	−	0.655044i	$-0.227350\pi$
$107$	11.1967	+	3.00016i	1.08243	+	0.290036i	0.326839	+	0.945080i	$0.394016\pi$
$108$	1.01374	+	5.09631i	0.0975467	+	0.490392i
$109$	−6.96202	−	19.1280i	−0.666841	−	1.83213i	−0.542819	−	0.839850i	$-0.682643\pi$
$109$	−6.96202	−	19.1280i	−0.666841	−	1.83213i	−0.124022	−	0.992279i	$-0.539579\pi$
$110$	5.55351	+	1.72455i	0.529506	+	0.164430i
$111$	18.8813	−	8.97225i	1.79213	−	0.851608i
$112$	−1.77932	+	1.24589i	−0.168130	+	0.117726i
$113$	−2.83693	−	2.83693i	−0.266876	−	0.266876i	0.560964	−	0.827840i	$-0.310430\pi$
$113$	−2.83693	−	2.83693i	−0.266876	−	0.266876i	−0.827840	+	0.560964i	$0.810430\pi$
$114$	−4.86322	+	5.77487i	−0.455482	+	0.540866i
$115$	−14.1420	+	0.678956i	−1.31875	+	0.0633130i
$116$	5.59469	+	0.986495i	0.519454	+	0.0915938i
$117$	6.06027	−	6.23920i	0.560273	−	0.576814i
$118$	1.58034	−	0.736927i	0.145482	−	0.0678396i
$119$	−4.78553	+	1.74179i	−0.438689	+	0.159670i
$120$	3.45591	+	1.74833i	0.315480	+	0.159600i
$121$	−2.11845	−	3.66926i	−0.192586	−	0.333569i
$122$	1.84243	+	6.87603i	0.166806	+	0.622527i
$123$	4.41883	+	7.52668i	0.398433	+	0.678658i
$124$	−8.77608	+	1.54746i	−0.788115	+	0.138966i
$125$	−10.2727	+	4.41265i	−0.918819	+	0.394679i
$126$	6.15523	+	2.13945i	0.548351	+	0.190597i
$127$	3.54487	+	0.310136i	0.314556	+	0.0275201i	0.243341	−	0.969941i	$-0.421757\pi$
$127$	3.54487	+	0.310136i	0.314556	+	0.0275201i	0.0712153	+	0.997461i	$0.477312\pi$
$128$	−0.906308	−	0.422618i	−0.0801070	−	0.0373545i
$129$	9.62235	+	9.48338i	0.847200	+	0.834965i
$130$	−0.874099	−	6.42388i	−0.0766635	−	0.563412i
$131$	−9.36795	−	1.65182i	−0.818482	−	0.144320i	−0.251296	−	0.967910i	$-0.580857\pi$
$131$	−9.36795	−	1.65182i	−0.818482	−	0.144320i	−0.567186	+	0.823590i	$0.691968\pi$
$132$	1.57133	+	4.22140i	0.136767	+	0.367426i
$133$	3.15764	+	8.92612i	0.273802	+	0.773993i
$134$	−1.84484			−0.159370
$135$	−1.81737	−	11.4759i	−0.156414	−	0.987692i
$136$	−1.79601	−	1.50703i	−0.154007	−	0.129227i
$137$	−1.16238	+	0.542028i	−0.0993090	+	0.0463086i	−0.471638	−	0.881792i	$-0.656337\pi$
$137$	−1.16238	+	0.542028i	−0.0993090	+	0.0463086i	0.372329	+	0.928101i	$0.378559\pi$
$138$	−7.11033	−	8.34967i	−0.605272	−	0.710771i
$139$	6.74939	+	8.04362i	0.572476	+	0.682251i	0.972137	−	0.234412i	$-0.0753166\pi$
$139$	6.74939	+	8.04362i	0.572476	+	0.682251i	−0.399661	+	0.916663i	$0.630872\pi$
$140$	4.08505	−	2.62746i	0.345250	−	0.222061i
$141$	4.58046	−	3.25718i	0.385745	−	0.274304i
$142$	7.73964	−	11.0533i	0.649496	−	0.927576i
$143$	4.32475	−	6.17638i	0.361653	−	0.516495i
$144$	0.563865	+	2.94653i	0.0469887	+	0.245544i
$145$	−12.4138	−	2.69560i	−1.03091	−	0.223858i
$146$	−9.25718	−	11.0323i	−0.766130	−	0.913038i
$147$	−3.00896	+	2.56234i	−0.248175	+	0.211338i
$148$	10.9385	−	5.10071i	0.899139	−	0.419276i
$149$	8.91219	+	7.47821i	0.730115	+	0.612639i	0.930163	−	0.367147i	$-0.119665\pi$
$149$	8.91219	+	7.47821i	0.730115	+	0.612639i	−0.200048	+	0.979786i	$0.564110\pi$
$150$	−7.56812	−	4.20993i	−0.617935	−	0.343740i
$151$	8.65440			0.704285			0.352143	−	0.935946i	$-0.385453\pi$
$151$	8.65440			0.704285			0.352143	+	0.935946i	$0.385453\pi$
$152$	−2.83196	+	3.31361i	−0.229702	+	0.268769i
$153$	−0.511031	+	7.01499i	−0.0413144	+	0.567128i
$154$	5.56306	+	0.980918i	0.448284	+	0.0790446i
$155$	19.7447	−	2.68666i	1.58593	−	0.215798i
$156$	3.52501	−	3.57666i	0.282227	−	0.286362i
$157$	9.07132	+	4.23003i	0.723970	+	0.337593i	0.749431	−	0.662083i	$-0.230327\pi$
$157$	9.07132	+	4.23003i	0.723970	+	0.337593i	−0.0254602	+	0.999676i	$0.508105\pi$
$158$	11.1545	+	0.975890i	0.887403	+	0.0776377i
$159$	13.9060	−	1.31860i	1.10282	−	0.104572i
$160$	1.98788	+	1.02388i	0.157156	+	0.0809451i
$161$	−13.5446	+	2.38828i	−1.06746	+	0.188223i
$162$	6.17615	−	6.54639i	0.485244	−	0.514333i
$163$	0.387755	+	1.44712i	0.0303714	+	0.113347i	0.979447	−	0.201699i	$-0.0646464\pi$
$163$	0.387755	+	1.44712i	0.0303714	+	0.113347i	−0.949076	+	0.315047i	$0.897980\pi$
$164$	2.51954	+	4.36397i	0.196743	+	0.340769i
$165$	−3.14008	−	9.57008i	−0.244455	−	0.745030i
$166$	6.74877	−	2.45635i	0.523806	−	0.190650i
$167$	−16.6822	+	7.77903i	−1.29091	+	0.601960i	−0.942130	−	0.335247i	$-0.891180\pi$
$167$	−16.6822	+	7.77903i	−1.29091	+	0.601960i	−0.348776	+	0.937206i	$0.613403\pi$
$168$	3.54464	+	1.26103i	0.273475	+	0.0972902i
$169$	4.52414	+	0.797729i	0.348011	+	0.0613638i
$170$	3.88053	+	3.52499i	0.297623	+	0.270354i
$171$	13.0330	+	1.06811i	0.996659	+	0.0816808i
$172$	5.51550	+	5.51550i	0.420553	+	0.420553i
$173$	9.91968	−	6.94584i	0.754179	−	0.528082i	−0.132098	−	0.991237i	$-0.542171\pi$
$173$	9.91968	−	6.94584i	0.754179	−	0.528082i	0.886278	+	0.463154i	$0.153282\pi$
$174$	−4.22322	−	8.88739i	−0.320162	−	0.673751i
$175$	−9.35819	+	5.51181i	−0.707413	+	0.416653i
$176$	0.889456	+	2.44376i	0.0670453	+	0.184205i
$177$	−2.62649	−	1.49104i	−0.197419	−	0.112073i
$178$	−0.440398	−	0.118004i	−0.0330093	−	0.00884480i
$179$	6.75938	−	11.7076i	0.505220	−	0.875066i	−0.494762	−	0.869028i	$-0.664745\pi$
$179$	6.75938	−	11.7076i	0.505220	−	0.875066i	0.999982	−	0.00603755i	$-0.00192183\pi$
$180$	−1.00104	−	6.63309i	−0.0746133	−	0.494402i
$181$	2.66125	+	15.0927i	0.197809	+	1.12183i	0.908362	+	0.418186i	$0.137334\pi$
$181$	2.66125	+	15.0927i	0.197809	+	1.12183i	−0.710553	+	0.703644i	$0.751555\pi$
$182$	−1.62998	−	6.08317i	−0.120822	−	0.450914i
$183$	7.85651	−	9.50254i	0.580770	−	0.702448i
$184$	−4.06998	−	4.85042i	−0.300043	−	0.357577i
$185$	−24.8884	+	10.4359i	−1.82983	+	0.767262i
$186$	10.9934	+	10.8346i	0.806072	+	0.794431i
$187$	0.531403	+	6.07396i	0.0388600	+	0.444172i
$188$	2.65814	−	1.86125i	0.193865	−	0.135746i
$189$	−3.15841	−	10.8359i	−0.229741	−	0.788195i
$190$	6.61863	−	7.15498i	0.480166	−	0.519077i
$191$		−	1.19747i		−	0.0866457i	−0.999061	−	0.0433229i	$-0.986206\pi$
$191$		−	1.19747i		−	0.0866457i	0.999061	−	0.0433229i	$-0.0137944\pi$
$192$	0.313166	+	1.70350i	0.0226008	+	0.122940i
$193$	6.53935	−	0.572119i	0.470713	−	0.0411821i	0.150668	−	0.988584i	$-0.451858\pi$
$193$	6.53935	−	0.572119i	0.470713	−	0.0411821i	0.320045	+	0.947402i	$0.396302\pi$
$194$	−2.85567	−	1.03938i	−0.205025	−	0.0746230i
$195$	−8.19025	+	7.68185i	−0.586516	+	0.550109i
$196$	−1.74794	+	1.46669i	−0.124853	+	0.104764i
$197$	−20.4069	−	5.46802i	−1.45393	−	0.389580i	−0.556544	−	0.830818i	$-0.687873\pi$
$197$	−20.4069	−	5.46802i	−1.45393	−	0.389580i	−0.897390	+	0.441238i	$0.854539\pi$
$198$	4.38149	−	6.45527i	0.311379	−	0.458756i
$199$	5.51687	−	0.972773i	0.391080	−	0.0689580i	0.0253495	−	0.999679i	$-0.491930\pi$
$199$	5.51687	−	0.972773i	0.391080	−	0.0689580i	0.365731	+	0.930721i	$0.380819\pi$
$200$	−4.35166	−	2.46232i	−0.307709	−	0.174112i
$201$	1.85177	+	2.60408i	0.130614	+	0.183678i
$202$	0.704656	−	2.62981i	0.0495794	−	0.185033i
$203$	−12.2930	−	1.07550i	−0.862800	−	0.0754853i
$204$	−0.324493	+	4.04785i	−0.0227191	+	0.283406i
$205$	−5.24618	−	9.97192i	−0.366409	−	0.696469i
$206$	−0.0479444	+	0.0571379i	−0.00334044	+	0.00398098i
$207$	−4.64894	+	18.4176i	−0.323123	+	1.28011i
$208$	2.05013	−	2.05013i	0.142151	−	0.142151i
$209$	11.3011	−	0.885716i	0.781712	−	0.0612662i
$210$	−7.80918	−	3.12892i	−0.538885	−	0.215916i
$211$	−2.27631	+	12.9096i	−0.156707	+	0.888732i	0.800501	+	0.599332i	$0.204567\pi$
$211$	−2.27631	+	12.9096i	−0.156707	+	0.888732i	−0.957208	+	0.289400i	$0.906544\pi$
$212$	8.03397	−	0.702882i	0.551776	−	0.0482741i
$213$	−23.3711	+	0.169987i	−1.60136	+	0.0116473i
$214$	−3.96460	−	10.8927i	−0.271015	−	0.744607i
$215$	−11.8390	−	12.8080i	−0.807415	−	0.873497i
$216$	3.59320	−	3.75352i	0.244486	−	0.255395i
$217$	18.6974	−	5.00997i	1.26927	−	0.340099i
$218$	−11.6755	+	16.6743i	−0.790764	+	1.12933i
$219$	−6.28065	+	24.1407i	−0.424407	+	1.63128i
$220$	−1.77269	−	5.53833i	−0.119515	−	0.373394i
$221$	5.88684	−	3.39877i	0.395991	−	0.228626i
$222$	−18.1795	−	10.3204i	−1.22013	−	0.692658i
$223$	2.95431	−	6.33554i	0.197835	−	0.424259i	−0.782215	−	0.623008i	$-0.785910\pi$
$223$	2.95431	−	6.33554i	0.197835	−	0.424259i	0.980050	+	0.198749i	$0.0636880\pi$
$224$	2.04115	+	0.742919i	0.136380	+	0.0496383i
$225$	1.65402	+	14.9085i	0.110268	+	0.993902i
$226$	−0.696680	+	3.95107i	−0.0463425	+	0.262821i
$227$	−1.54386	+	1.54386i	−0.102470	+	0.102470i	−0.756483	−	0.654013i	$-0.773084\pi$
$227$	−1.54386	+	1.54386i	−0.102470	+	0.102470i	0.654013	+	0.756483i	$0.273084\pi$
$228$	7.51992	+	0.671388i	0.498019	+	0.0444637i
$229$			13.7017i			0.905435i	0.891654	+	0.452718i	$0.149545\pi$
$229$			13.7017i			0.905435i	−0.891654	+	0.452718i	$0.850455\pi$
$230$	8.66767	+	11.1950i	0.571529	+	0.738176i
$231$	−4.19935	−	8.83714i	−0.276297	−	0.581441i
$232$	−2.40089	−	5.14873i	−0.157626	−	0.338031i
$233$	19.9760	+	9.31497i	1.30867	+	0.610244i	0.946752	−	0.321965i	$-0.104343\pi$
$233$	19.9760	+	9.31497i	1.30867	+	0.610244i	0.361920	+	0.932209i	$0.382121\pi$
$234$	−8.58689	−	1.38563i	−0.561342	−	0.0905813i
$235$	−6.10269	+	3.92518i	−0.398095	+	0.256050i
$236$	−1.51010	−	0.871859i	−0.0982993	−	0.0567532i
$237$	−9.81886	−	16.7247i	−0.637804	−	1.08638i
$238$	4.17166	+	2.92103i	0.270409	+	0.189342i
$239$	10.8475	−	18.7884i	0.701667	−	1.21532i	−0.266214	−	0.963914i	$-0.585773\pi$
$239$	10.8475	−	18.7884i	0.701667	−	1.21532i	0.967881	−	0.251409i	$-0.0808939\pi$
$240$	−0.550084	−	3.83372i	−0.0355077	−	0.247466i
$241$	−15.8632	+	13.3108i	−1.02184	+	0.857422i	−0.989857	−	0.142066i	$-0.954625\pi$
$241$	−15.8632	+	13.3108i	−1.02184	+	0.857422i	−0.0319788	+	0.999489i	$0.510181\pi$
$242$	−1.79059	+	3.83993i	−0.115104	+	0.246840i
$243$	−15.4399	−	2.14696i	−0.990470	−	0.137727i
$244$	4.57574	−	5.45316i	0.292932	−	0.349103i
$245$	4.03432	−	3.12356i	0.257744	−	0.199557i
$246$	3.63096	−	7.93682i	0.231501	−	0.506033i
$247$	−6.21960	−	11.0014i	−0.395743	−	0.700005i
$248$	6.30136	+	6.30136i	0.400136	+	0.400136i
$249$	−10.2414	−	7.06065i	−0.649021	−	0.447450i
$250$	9.50681	+	5.88392i	0.601264	+	0.372132i
$251$	0.782708	−	2.15047i	0.0494041	−	0.135737i	−0.912537	−	0.408995i	$-0.865879\pi$
$251$	0.782708	−	2.15047i	0.0494041	−	0.135737i	0.961941	+	0.273259i	$0.0881015\pi$
$252$	−1.77796	−	6.26920i	−0.112001	−	0.394923i
$253$	−1.43514	+	16.4037i	−0.0902264	+	1.03129i
$254$	−1.77920	−	3.08167i	−0.111637	−	0.193361i
$255$	1.08059	−	9.01578i	0.0676693	−	0.564590i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−4.68676	−	3.28170i	−0.292352	−	0.204707i	0.418194	−	0.908358i	$-0.362663\pi$
$257$	−4.68676	−	3.28170i	−0.292352	−	0.204707i	−0.710546	+	0.703651i	$0.751552\pi$
$258$	2.24918	−	13.3216i	0.140028	−	0.829367i
$259$	−22.7040	+	13.1082i	−1.41076	+	0.814501i
$260$	−4.76077	+	4.40061i	−0.295251	+	0.272914i
$261$	−8.30590	+	14.8821i	−0.514122	+	0.921176i
$262$	4.02014	+	8.62122i	0.248365	+	0.532621i
$263$	−0.789224	−	9.02087i	−0.0486656	−	0.556250i	−0.980915	−	0.194435i	$-0.937713\pi$
$263$	−0.789224	−	9.02087i	−0.0486656	−	0.556250i	0.932250	−	0.361815i	$-0.117843\pi$
$264$	2.55669	−	3.70845i	0.157354	−	0.228240i
$265$	−18.0124	+	0.864774i	−1.10649	+	0.0531227i
$266$	5.50070	−	7.70640i	0.337270	−	0.472510i
$267$	0.275484	+	0.740092i	0.0168593	+	0.0452929i
$268$	1.05816	+	1.51120i	0.0646371	+	0.0923114i
$269$	−4.39791	−	3.69028i	−0.268145	−	0.225001i	0.498794	−	0.866721i	$-0.333777\pi$
$269$	−4.39791	−	3.69028i	−0.268145	−	0.225001i	−0.766939	+	0.641720i	$0.778221\pi$
$270$	−8.35814	+	8.07103i	−0.508660	+	0.491187i
$271$	24.1237	−	8.78030i	1.46541	−	0.533365i	0.518560	−	0.855041i	$-0.326468\pi$
$271$	24.1237	−	8.78030i	1.46541	−	0.533365i	0.946850	+	0.321676i	$0.104246\pi$
$272$	−0.204339	+	2.33560i	−0.0123899	+	0.141617i
$273$	−6.95059	+	8.40681i	−0.420669	+	0.508804i
$274$	1.11072	+	0.641274i	0.0671010	+	0.0387408i
$275$	3.47431	+	12.5302i	0.209509	+	0.755601i
$276$	−2.76133	+	10.6136i	−0.166213	+	0.638865i
$277$	−8.27827	+	2.21816i	−0.497393	+	0.133276i	−0.498790	−	0.866723i	$-0.666222\pi$
$277$	−8.27827	+	2.21816i	−0.497393	+	0.133276i	0.00139686	+	0.999999i	$0.499555\pi$
$278$	2.71765	−	10.1424i	0.162994	−	0.608301i
$279$	4.25892	−	26.3930i	0.254975	−	1.58011i
$280$	−4.49537	−	1.83923i	−0.268650	−	0.109915i
$281$	−3.98212	+	10.9408i	−0.237553	+	0.652672i	0.762431	+	0.647069i	$0.224006\pi$
$281$	−3.98212	+	10.9408i	−0.237553	+	0.652672i	−0.999984	+	0.00560262i	$0.998217\pi$
$282$	−5.29537	−	1.88386i	−0.315335	−	0.112182i
$283$	−5.96047	−	8.51244i	−0.354313	−	0.506012i	0.601944	−	0.798538i	$-0.294393\pi$
$283$	−5.96047	−	8.51244i	−0.354313	−	0.506012i	−0.956257	+	0.292526i	$0.905504\pi$
$284$	−13.4936			−0.800701
$285$	−16.7431	−	2.16066i	−0.991776	−	0.127986i
$286$	−7.53996			−0.445847
$287$	−6.27815	−	8.96613i	−0.370588	−	0.529254i
$288$	2.09024	−	2.15195i	0.123169	−	0.126805i
$289$	3.93433	−	10.8095i	0.231431	−	0.635851i
$290$	4.91215	+	11.7149i	0.288452	+	0.687924i
$291$	1.39926	+	5.07420i	0.0820262	+	0.297455i
$292$	−3.72741	+	13.9109i	−0.218130	+	0.814073i
$293$	22.0135	−	5.89850i	1.28604	−	0.344594i	0.449887	−	0.893086i	$-0.351464\pi$
$293$	22.0135	−	5.89850i	1.28604	−	0.344594i	0.836156	+	0.548491i	$0.184798\pi$
$294$	3.82482	+	0.995097i	0.223068	+	0.0580353i
$295$	3.29750	+	2.08068i	0.191988	+	0.121142i
$296$	−10.4523	−	6.03465i	−0.607529	−	0.350757i
$297$	−13.5099	+	0.294830i	−0.783923	+	0.0171078i
$298$	1.01397	−	11.5898i	0.0587379	−	0.671377i
$299$	17.2507	−	6.27875i	0.997635	−	0.363109i
$300$	0.892321	+	8.61416i	0.0515182	+	0.497339i
$301$	−12.9791	−	10.8907i	−0.748100	−	0.627731i
$302$	−4.96396	−	7.08927i	−0.285644	−	0.407942i
$303$	−4.41941	+	1.64503i	−0.253889	+	0.0945047i
$304$	4.33870	+	0.419193i	0.248841	+	0.0240424i
$305$	−10.7028	+	11.7823i	−0.612839	+	0.674652i
$306$	6.03946	−	3.60502i	0.345253	−	0.206085i
$307$	−0.728504	−	8.32684i	−0.0415779	−	0.475238i	−0.988229	−	0.152979i	$-0.951113\pi$
$307$	−0.728504	−	8.32684i	−0.0415779	−	0.475238i	0.946652	−	0.322259i	$-0.104442\pi$
$308$	−2.38732	−	5.11963i	−0.136030	−	0.291718i
$309$	0.128777	+	0.0103233i	0.00732589	+	0.000587274i
$310$	−13.5259	−	14.6329i	−0.768218	−	0.831093i
$311$	−23.7604	+	13.7181i	−1.34733	+	0.777879i	−0.987870	−	0.155282i	$-0.950371\pi$
$311$	−23.7604	+	13.7181i	−1.34733	+	0.777879i	−0.359457	+	0.933162i	$0.617038\pi$
$312$	−4.95169	−	0.836029i	−0.280334	−	0.0473308i
$313$	−11.7919	−	8.25681i	−0.666520	−	0.466702i	0.190703	−	0.981648i	$-0.438923\pi$
$313$	−11.7919	−	8.25681i	−0.666520	−	0.466702i	−0.857223	+	0.514946i	$0.827812\pi$
$314$	−1.73806	−	9.85704i	−0.0980845	−	0.556265i
$315$	3.42189	+	14.1637i	0.192801	+	0.798035i
$316$	−5.59854	−	9.69696i	−0.314943	−	0.545497i
$317$	−2.42894	+	27.7630i	−0.136423	+	1.55932i	0.551894	+	0.833914i	$0.313905\pi$
$317$	−2.42894	+	27.7630i	−0.136423	+	1.55932i	−0.688318	+	0.725409i	$0.741650\pi$
$318$	−9.05631	−	10.6348i	−0.507852	−	0.596372i
$319$	−5.05300	+	13.8830i	−0.282914	+	0.777299i
$320$	−0.301484	−	2.21565i	−0.0168535	−	0.123859i
$321$	−11.3960	+	16.5298i	−0.636065	+	0.922604i
$322$	9.72522	+	9.72522i	0.541966	+	0.541966i
$323$	9.57121	+	3.58208i	0.532556	+	0.199312i
$324$	−8.90498	−	1.30435i	−0.494721	−	0.0724638i
$325$	11.0237	−	9.41428i	0.611487	−	0.522210i
$326$	0.963006	−	1.14767i	0.0533360	−	0.0635634i
$327$	35.2560	−	0.256431i	1.94966	−	0.0141806i
$328$	2.12961	−	4.56696i	0.117588	−	0.252168i
$329$	−5.39954	+	4.53075i	−0.297686	+	0.249788i
$330$	−6.03828	+	8.06137i	−0.332396	+	0.443764i
$331$	12.1854	−	21.1057i	0.669769	−	1.16007i	−0.308200	−	0.951322i	$-0.599727\pi$
$331$	12.1854	−	21.1057i	0.669769	−	1.16007i	0.977969	−	0.208752i	$-0.0669401\pi$
$332$	−5.88306	−	4.11936i	−0.322875	−	0.226079i
$333$	3.68007	+	36.0204i	0.201667	+	1.97391i
$334$	15.9407	+	9.20338i	0.872237	+	0.503586i
$335$	−2.23154	−	3.46949i	−0.121922	−	0.189559i
$336$	−1.00015	−	3.62690i	−0.0545628	−	0.197863i
$337$	15.2088	+	7.09199i	0.828477	+	0.386325i	0.790130	−	0.612939i	$-0.210013\pi$
$337$	15.2088	+	7.09199i	0.828477	+	0.386325i	0.0383470	+	0.999264i	$0.487791\pi$
$338$	−1.94148	−	4.16352i	−0.105603	−	0.226466i
$339$	6.27643	−	2.98251i	0.340889	−	0.161988i
$340$	0.661722	−	5.20059i	0.0358869	−	0.282042i
$341$		−	23.1751i		−	1.25500i
$342$	−6.60047	−	11.2887i	−0.356913	−	0.610421i
$343$	14.2563	−	14.2563i	0.769765	−	0.769765i
$344$	1.35447	−	7.68159i	0.0730282	−	0.414163i
$345$	7.10206	−	23.4719i	0.382362	−	1.26368i
$346$	−11.3794	−	4.14176i	−0.611760	−	0.222662i
$347$	−3.45793	+	7.41555i	−0.185631	+	0.398087i	−0.976996	−	0.213256i	$-0.931593\pi$
$347$	−3.45793	+	7.41555i	−0.185631	+	0.398087i	0.791365	+	0.611344i	$0.209371\pi$
$348$	−4.85778	+	8.55705i	−0.260404	+	0.458706i
$349$	1.24138	−	0.716712i	0.0664496	−	0.0383647i	−0.466407	−	0.884570i	$-0.654452\pi$
$349$	1.24138	−	0.716712i	0.0664496	−	0.0383647i	0.532857	+	0.846205i	$0.321118\pi$
$350$	9.88264	+	4.50434i	0.528250	+	0.240767i
$351$	6.66326	+	13.5116i	0.355659	+	0.721198i
$352$	1.49164	−	2.13028i	0.0795047	−	0.113545i
$353$	7.14944	−	1.91569i	0.380526	−	0.101962i	−0.0634854	−	0.997983i	$-0.520222\pi$
$353$	7.14944	−	1.91569i	0.380526	−	0.101962i	0.444011	+	0.896021i	$0.353555\pi$
$354$	0.285104	+	3.00672i	0.0151531	+	0.159805i
$355$	30.1494	+	1.18528i	1.60016	+	0.0629082i
$356$	0.155939	+	0.428438i	0.00826473	+	0.0227072i
$357$	−0.0641551	−	8.82051i	−0.00339545	−	0.466831i
$358$	−13.4673	+	1.17824i	−0.711770	+	0.0622718i
$359$	0.704206	−	3.99375i	0.0371666	−	0.210782i	−0.960569	−	0.278042i	$-0.910315\pi$
$359$	0.704206	−	3.99375i	0.0371666	−	0.210782i	0.997735	+	0.0672599i	$0.0214257\pi$
$360$	−4.85934	+	4.62459i	−0.256110	+	0.243737i
$361$	6.82053	−	17.7336i	0.358975	−	0.933347i
$362$	10.8368	−	10.8368i	0.569568	−	0.569568i
$363$	7.21757	−	1.32685i	0.378824	−	0.0696416i
$364$	−4.04812	+	4.82436i	−0.212179	+	0.252865i
$365$	9.55025	−	30.7543i	0.499883	−	1.60975i
$366$	−12.2903	−	0.985246i	−0.642426	−	0.0514996i
$367$	−0.307540	−	0.0269063i	−0.0160535	−	0.00140450i	0.0791262	−	0.996865i	$-0.474787\pi$
$367$	−0.307540	−	0.0269063i	−0.0160535	−	0.00140450i	−0.0951797	+	0.995460i	$0.530343\pi$
$368$	−1.63878	+	6.11602i	−0.0854274	+	0.318820i
$369$	−14.8478	+	2.84136i	−0.772946	+	0.147915i
$370$	22.8240	+	14.4016i	1.18656	+	0.748704i
$371$	−17.2515	+	3.04191i	−0.895654	+	0.157928i
$372$	2.56965	−	15.2197i	0.133230	−	0.789105i
$373$	−25.5425	−	6.84410i	−1.32254	−	0.354374i	−0.472612	−	0.881270i	$-0.656689\pi$
$373$	−25.5425	−	6.84410i	−1.32254	−	0.354374i	−0.849930	+	0.526896i	$0.823356\pi$
$374$	4.67070	−	3.91918i	0.241516	−	0.202656i
$375$	−1.23708	−	19.3254i	−0.0638827	−	0.997957i
$376$	−3.04929	−	1.10985i	−0.157255	−	0.0572362i
$377$	16.4084	−	1.43555i	0.845074	−	0.0739344i
$378$	−7.06465	+	8.80243i	−0.363367	+	0.452748i
$379$		−	26.2505i		−	1.34840i	−0.738549	−	0.674200i	$-0.764489\pi$
$379$		−	26.2505i		−	1.34840i	0.738549	−	0.674200i	$-0.235511\pi$
$380$	−9.65731	−	1.31773i	−0.495409	−	0.0675982i
$381$	−2.56404	+	5.60468i	−0.131360	+	0.287137i
$382$	−0.980908	+	0.686839i	−0.0501876	+	0.0351418i
$383$	−1.66681	−	19.0517i	−0.0851699	−	0.973497i	−0.911768	−	0.410705i	$-0.865283\pi$
$383$	−1.66681	−	19.0517i	−0.0851699	−	0.973497i	0.826598	−	0.562792i	$-0.190273\pi$
$384$	1.21580	−	1.23362i	0.0620438	−	0.0629529i
$385$	4.88438	+	11.6487i	0.248931	+	0.593673i
$386$	−4.21947	−	5.02857i	−0.214766	−	0.255948i
$387$	−21.0617	+	10.1968i	−1.07063	+	0.518334i
$388$	0.786535	+	2.93539i	0.0399303	+	0.149022i
$389$	−6.21080	−	35.2232i	−0.314900	−	1.78589i	−0.572780	−	0.819709i	$-0.694135\pi$
$389$	−6.21080	−	35.2232i	−0.314900	−	1.78589i	0.257880	−	0.966177i	$-0.416976\pi$
$390$	10.9903	+	2.30293i	0.556517	+	0.116613i
$391$	−7.42250	+	12.8561i	−0.375372	+	0.650163i
$392$	2.20402	+	0.590566i	0.111320	+	0.0298281i
$393$	8.13404	−	14.3282i	0.410308	−	0.722764i
$394$	7.22580	+	19.8527i	0.364030	+	1.00017i
$395$	11.6573	+	22.1581i	0.586541	+	1.11490i
$396$	−7.80096	+	0.113485i	−0.392013	+	0.00570284i
$397$	8.61546	−	6.03261i	0.432397	−	0.302768i	−0.337040	−	0.941490i	$-0.609426\pi$
$397$	8.61546	−	6.03261i	0.432397	−	0.302768i	0.769437	+	0.638722i	$0.220537\pi$
$398$	−3.96119	−	3.96119i	−0.198557	−	0.198557i
$399$	−16.3993	−	0.0291688i	−0.820994	−	0.00146027i
$400$	0.478996	+	4.97700i	0.0239498	+	0.248850i
$401$	22.0628	+	3.89027i	1.10176	+	0.194271i	0.694821	−	0.719182i	$-0.255483\pi$
$401$	22.0628	+	3.89027i	1.10176	+	0.194271i	0.406943	+	0.913453i	$0.366595\pi$
$402$	1.07101	−	3.01052i	0.0534170	−	0.150151i
$403$	−23.4164	+	10.9193i	−1.16646	+	0.543928i
$404$	−2.55839	+	0.931178i	−0.127285	+	0.0463278i
$405$	19.7822	+	3.69657i	0.982985	+	0.183684i
$406$	6.16999	+	10.6867i	0.306211	+	0.530373i
$407$	8.12365	+	30.3179i	0.402675	+	1.50280i
$408$	3.50193	−	2.05594i	0.173371	−	0.101784i
$409$	4.54384	−	0.801202i	0.224678	−	0.0396169i	−0.0601755	−	0.998188i	$-0.519166\pi$
$409$	4.54384	−	0.801202i	0.224678	−	0.0396169i	0.284854	+	0.958571i	$0.408055\pi$
$410$	−5.15943	+	10.0171i	−0.254806	+	0.494708i
$411$	−0.209701	−	2.21152i	−0.0103438	−	0.109086i
$412$	0.0743043	+	0.00650079i	0.00366071	+	0.000320271i
$413$	3.43274	+	1.60071i	0.168914	+	0.0787660i
$414$	17.7534	−	6.75573i	0.872530	−	0.332026i
$415$	12.7829	+	9.72083i	0.627489	+	0.477177i
$416$	−2.85527	−	0.503462i	−0.139991	−	0.0246842i
$417$	−17.0444	+	6.34441i	−0.834667	+	0.310687i
$418$	−7.20757	−	8.74928i	−0.352534	−	0.427941i
$419$	2.80237			0.136905			0.0684523	−	0.997654i	$-0.478194\pi$
$419$	2.80237			0.136905			0.0684523	+	0.997654i	$0.478194\pi$
$420$	1.91610	+	8.19158i	0.0934960	+	0.399708i
$421$	2.54127	+	2.13238i	0.123854	+	0.103926i	0.702611	−	0.711574i	$-0.252018\pi$
$421$	2.54127	+	2.13238i	0.123854	+	0.103926i	−0.578757	+	0.815500i	$0.696462\pi$
$422$	11.8805	−	5.53999i	0.578336	−	0.269682i
$423$	2.65611	+	9.36561i	0.129144	+	0.455372i
$424$	−5.18386	−	6.17789i	−0.251751	−	0.300025i
$425$	−1.93533	+	11.5618i	−0.0938774	+	0.560828i
$426$	13.5443	+	19.0470i	0.656225	+	0.922828i
$427$	−8.86901	+	12.6663i	−0.429201	+	0.612963i
$428$	−6.64874	+	9.49539i	−0.321379	+	0.458977i
$429$	7.56829	+	10.6430i	0.365400	+	0.513851i
$430$	−3.70110	+	17.0443i	−0.178483	+	0.821950i
$431$	−23.9311	−	28.5199i	−1.15272	−	1.37376i	−0.915509	−	0.402298i	$-0.868212\pi$
$431$	−23.9311	−	28.5199i	−1.15272	−	1.37376i	−0.237210	−	0.971458i	$-0.576233\pi$
$432$	−5.13568	−	0.790440i	−0.247090	−	0.0380301i
$433$	33.1655	−	15.4653i	1.59383	−	0.743215i	0.595634	−	0.803256i	$-0.296901\pi$
$433$	33.1655	−	15.4653i	1.59383	−	0.743215i	0.998196	+	0.0600405i	$0.0191230\pi$
$434$	−14.8283	−	12.4425i	−0.711783	−	0.597257i
$435$	11.6056	−	18.6927i	0.556446	−	0.896245i
$436$	20.3556			0.974856
$437$	23.7760	+	14.0156i	1.13736	+	0.670455i
$438$	23.3773	−	8.70172i	1.11701	−	0.415784i
$439$	35.6338	+	6.28320i	1.70071	+	0.299881i	0.937942	−	0.346793i	$-0.112729\pi$
$439$	35.6338	+	6.28320i	1.70071	+	0.299881i	0.762766	+	0.646674i	$0.223841\pi$
$440$	−3.51996	+	4.62876i	−0.167808	+	0.220667i
$441$	−2.43455	−	6.39775i	−0.115931	−	0.304655i
$442$	−6.16066	−	2.87276i	−0.293033	−	0.136643i
$443$	−6.39763	−	0.559720i	−0.303961	−	0.0265931i	−0.0658447	−	0.997830i	$-0.520974\pi$
$443$	−6.39763	−	0.559720i	−0.303961	−	0.0265931i	−0.238116	+	0.971237i	$0.576530\pi$
$444$	1.97338	+	20.8113i	0.0936523	+	0.987660i
$445$	−0.310786	−	0.970974i	−0.0147327	−	0.0460286i
$446$	−6.88429	+	1.21389i	−0.325981	+	0.0574792i
$447$	−17.3773	+	10.2020i	−0.821919	+	0.482539i
$448$	−0.562193	−	2.09813i	−0.0265611	−	0.0991275i
$449$	2.20685	+	3.82237i	0.104148	+	0.180389i	0.913390	−	0.407087i	$-0.133455\pi$
$449$	2.20685	+	3.82237i	0.104148	+	0.180389i	−0.809242	+	0.587475i	$0.800122\pi$
$450$	11.2636	−	9.90608i	0.530973	−	0.466977i
$451$	−12.3143	+	4.48204i	−0.579858	+	0.211051i
$452$	3.63613	−	1.69555i	0.171029	−	0.0797521i
$453$	−5.02425	+	14.1228i	−0.236060	+	0.663546i
$454$	2.15018	+	0.379135i	0.100913	+	0.0177937i
$455$	9.46866	−	10.4237i	0.443897	−	0.488670i
$456$	−3.76328	−	6.54505i	−0.176232	−	0.306500i
$457$	−3.51929	−	3.51929i	−0.164625	−	0.164625i	0.619987	−	0.784612i	$-0.287138\pi$
$457$	−3.51929	−	3.51929i	−0.164625	−	0.164625i	−0.784612	+	0.619987i	$0.787138\pi$
$458$	11.2238	−	7.85899i	0.524454	−	0.367226i
$459$	−11.1508	−	4.90643i	−0.520475	−	0.229013i
$460$	4.19883	−	13.5213i	0.195771	−	0.630435i
$461$	−13.6328	−	37.4557i	−0.634941	−	1.74449i	−0.667063	−	0.745001i	$-0.732449\pi$
$461$	−13.6328	−	37.4557i	−0.634941	−	1.74449i	0.0321222	−	0.999484i	$-0.489773\pi$
$462$	−4.83032	+	8.50868i	−0.224727	+	0.395860i
$463$	27.9595	+	7.49172i	1.29939	+	0.348170i	0.841219	−	0.540695i	$-0.181839\pi$
$463$	27.9595	+	7.49172i	1.29939	+	0.348170i	0.458169	+	0.888865i	$0.348505\pi$
$464$	−2.84050	+	4.91989i	−0.131867	+	0.228400i
$465$	−7.07837	+	33.7803i	−0.328252	+	1.56652i
$466$	−3.82739	−	21.7062i	−0.177301	−	1.00552i
$467$	7.48354	+	27.9290i	0.346297	+	1.29240i	0.891090	+	0.453827i	$0.149942\pi$
$467$	7.48354	+	27.9290i	0.346297	+	1.29240i	−0.544792	+	0.838571i	$0.683392\pi$
$468$	3.79020	+	7.82873i	0.175202	+	0.361883i
$469$	−2.57582	−	3.06974i	−0.118940	−	0.141747i
$470$	6.71567	+	2.74764i	0.309771	+	0.126739i
$471$	−12.1691	+	12.3474i	−0.560723	+	0.568939i
$472$	0.151975	+	1.73708i	0.00699521	+	0.0799557i
$473$	−16.6164	+	11.6349i	−0.764023	+	0.534975i
$474$	−8.06817	+	17.6360i	−0.370583	+	0.810049i
$475$	21.4620	+	3.79256i	0.984743	+	0.174015i
$476$		−	5.09266i		−	0.233422i
$477$	−5.92127	+	23.4582i	−0.271116	+	1.07408i
$478$	−21.6125	+	1.89085i	−0.988531	+	0.0864853i
$479$	−25.9950	−	9.46142i	−1.18774	−	0.432303i	−0.328813	−	0.944395i	$-0.606648\pi$
$479$	−25.9950	−	9.46142i	−1.18774	−	0.432303i	−0.858931	+	0.512092i	$0.828871\pi$
$480$	−2.82488	+	2.64953i	−0.128938	+	0.120934i
$481$	26.8060	−	22.4929i	1.22225	−	1.02559i
$482$	20.0023	+	5.35959i	0.911079	+	0.244123i
$483$	3.96588	−	23.4894i	0.180454	−	1.06880i
$484$	4.17253	−	0.735730i	0.189660	−	0.0334423i
$485$	−1.49954	−	6.62775i	−0.0680908	−	0.300951i
$486$	7.09728	+	13.8791i	0.321939	+	0.629567i
$487$	1.62423	−	6.06171i	0.0736009	−	0.274682i	−0.919311	−	0.393531i	$-0.871254\pi$
$487$	1.62423	−	6.06171i	0.0736009	−	0.274682i	0.992912	+	0.118848i	$0.0379202\pi$
$488$	−7.09151	−	0.620426i	−0.321017	−	0.0280854i
$489$	−2.58661	−	0.207354i	−0.116971	−	0.00937687i
$490$	−4.87266	−	1.51313i	−0.220124	−	0.0683561i
$491$	−8.45195	+	10.0726i	−0.381431	+	0.454572i	−0.922265	−	0.386557i	$-0.873664\pi$
$491$	−8.45195	+	10.0726i	−0.381431	+	0.454572i	0.540834	+	0.841129i	$0.318109\pi$
$492$	−8.58409	+	1.57807i	−0.387001	+	0.0711447i
$493$	−9.41813	+	9.41813i	−0.424171	+	0.424171i
$494$	−5.44444	+	11.4050i	−0.244957	+	0.513134i
$495$	17.4400	+	0.431672i	0.783869	+	0.0194022i
$496$	1.54746	−	8.77608i	0.0694830	−	0.394058i
$497$	29.1987	−	2.55455i	1.30974	−	0.114587i
$498$	0.0904743	+	12.4391i	0.00405425	+	0.557408i
$499$	−6.14121	−	16.8728i	−0.274918	−	0.755331i	−0.997919	−	0.0644840i	$-0.979460\pi$
$499$	−6.14121	−	16.8728i	−0.274918	−	0.755331i	0.723001	−	0.690847i	$-0.242762\pi$
$500$	−0.633061	−	11.1624i	−0.0283113	−	0.499198i
$501$	−3.00957	−	31.7391i	−0.134458	−	1.41800i
$502$	−2.21051	+	0.592303i	−0.0986597	+	0.0264358i
$503$	−13.3789	+	19.1070i	−0.596535	+	0.851941i	−0.997953	−	0.0639544i	$-0.979629\pi$
$503$	−13.3789	+	19.1070i	−0.596535	+	0.851941i	0.401417	+	0.915895i	$0.368518\pi$
$504$	−4.11564	+	5.05229i	−0.183325	+	0.225047i
$505$	5.79811	−	1.85584i	0.258013	−	0.0825838i
$506$	14.2603	−	8.23319i	0.633948	−	0.366010i
$507$	−3.92824	+	6.91966i	−0.174459	+	0.307313i
$508$	−1.50385	+	3.22501i	−0.0667225	+	0.143087i
$509$	−0.963495	−	0.350684i	−0.0427062	−	0.0155438i	0.320579	−	0.947222i	$-0.396123\pi$
$509$	−0.963495	−	0.350684i	−0.0427062	−	0.0155438i	−0.363285	+	0.931678i	$0.618345\pi$
$510$	−8.00510	+	4.28607i	−0.354472	+	0.189790i
$511$	5.43214	−	30.8072i	0.240304	−	1.36283i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−9.30923	+	20.6480i	−0.411012	+	0.911630i
$514$			5.72148i			0.252364i
$515$	−0.165450	−	0.0210519i	−0.00729061	−	0.000927656i
$516$	−12.2025	+	5.79854i	−0.537185	+	0.255266i
$517$	3.56644	+	7.64825i	0.156852	+	0.336370i
$518$	23.7601	+	11.0795i	1.04396	+	0.486805i
$519$	5.57584	+	20.2199i	0.244752	+	0.887555i
$520$	6.33543	+	1.37571i	0.277827	+	0.0603290i
$521$	3.60995	+	2.08420i	0.158155	+	0.0913106i	0.576989	−	0.816752i	$-0.304228\pi$
$521$	3.60995	+	2.08420i	0.158155	+	0.0913106i	−0.418834	+	0.908063i	$0.637561\pi$
$522$	16.9547	−	1.73220i	0.742089	−	0.0758164i
$523$	−7.96602	−	5.57787i	−0.348330	−	0.243903i	0.386297	−	0.922374i	$-0.373754\pi$
$523$	−7.96602	−	5.57787i	−0.348330	−	0.243903i	−0.734627	+	0.678471i	$0.762643\pi$
$524$	4.75623	−	8.23804i	0.207777	−	0.359880i
$525$	−3.56167	−	18.4711i	−0.155444	−	0.806145i
$526$	−6.93678	+	5.82065i	−0.302458	+	0.253792i
$527$	8.82983	−	18.9356i	0.384633	−	0.824849i
$528$	−4.50425	+	0.0327612i	−0.196022	+	0.00142575i
$529$	−10.9861	+	13.0927i	−0.477655	+	0.569248i
$530$	11.0399	+	14.2589i	0.479541	+	0.619366i
$531$	3.95796	−	3.42045i	0.171761	−	0.148435i
$532$	−9.46779	−	0.0857040i	−0.410481	−	0.00371574i
$533$	10.3308	+	10.3308i	0.447475	+	0.447475i
$534$	0.448237	−	0.650162i	0.0193971	−	0.0281353i
$535$	15.6896	−	20.6319i	0.678322	−	0.891995i
$536$	0.630972	−	1.73358i	0.0272538	−	0.0748793i
$537$	15.1810	+	17.8271i	0.655110	+	0.769297i
$538$	−0.500367	+	5.71922i	−0.0215723	+	0.246573i
$539$	−2.96698	−	5.13896i	−0.127797	−	0.221351i
$540$	11.4054	+	2.21723i	0.490812	+	0.0954144i
$541$	4.92882	+	27.9527i	0.211907	+	1.20178i	0.886195	+	0.463313i	$0.153339\pi$
$541$	4.92882	+	27.9527i	0.211907	+	1.20178i	−0.674288	+	0.738468i	$0.735549\pi$
$542$	−21.0292	−	14.7248i	−0.903281	−	0.632484i
$543$	−26.1741	−	4.41916i	−1.12324	−	0.189644i
$544$	2.03042	−	1.17226i	0.0870535	−	0.0502604i
$545$	−45.4813	−	1.78803i	−1.94821	−	0.0765909i
$546$	10.8732	+	0.871638i	0.465328	+	0.0373027i
$547$	2.03912	+	4.37290i	0.0871863	+	0.186972i	0.945067	−	0.326878i	$-0.105997\pi$
$547$	2.03912	+	4.37290i	0.0871863	+	0.186972i	−0.857880	+	0.513850i	$0.828219\pi$
$548$	−0.111781	−	1.27767i	−0.00477506	−	0.0545792i
$549$	10.9458	+	18.3374i	0.467155	+	0.782620i
$550$	8.27138	−	10.0330i	0.352693	−	0.427810i
$551$	17.3508	+	17.6678i	0.739169	+	0.752673i
$552$	10.2780	−	3.82577i	0.437461	−	0.162836i
$553$	13.9504	+	19.9232i	0.593230	+	0.847221i
$554$	6.56523	+	5.50888i	0.278930	+	0.234050i
$555$	−2.58114	−	46.6729i	−0.109563	−	1.98115i
$556$	−9.86696	+	3.59128i	−0.418452	+	0.152304i
$557$	1.41851	−	16.2137i	0.0601043	−	0.686995i	−0.905049	−	0.425308i	$-0.860166\pi$
$557$	1.41851	−	16.2137i	0.0601043	−	0.686995i	0.965153	−	0.261687i	$-0.0842787\pi$
$558$	−24.0627	+	11.6497i	−1.01865	+	0.493171i
$559$	19.5851	+	11.3075i	0.828363	+	0.478255i
$560$	1.07183	+	4.73733i	0.0452932	+	0.200189i
$561$	−10.2204	−	2.65902i	−0.431504	−	0.112264i
$562$	11.2462	−	3.01341i	0.474393	−	0.127113i
$563$	−4.38880	+	16.3792i	−0.184966	+	0.690302i	0.809672	+	0.586882i	$0.199645\pi$
$563$	−4.38880	+	16.3792i	−0.184966	+	0.690302i	−0.994638	+	0.103419i	$0.967022\pi$
$564$	1.49414	+	5.41825i	0.0629145	+	0.228149i
$565$	−8.27329	+	3.46905i	−0.348060	+	0.145944i
$566$	−3.55419	+	9.76507i	−0.149394	+	0.410456i
$567$	19.5163	+	1.13661i	0.819606	+	0.0477331i
$568$	7.73964	+	11.0533i	0.324748	+	0.463788i
$569$	15.5246			0.650824			0.325412	−	0.945572i	$-0.394497\pi$
$569$	15.5246			0.650824			0.325412	+	0.945572i	$0.394497\pi$
$570$	7.83354	+	14.9545i	0.328111	+	0.626373i
$571$	−34.2466			−1.43318			−0.716588	−	0.697497i	$-0.754297\pi$
$571$	−34.2466			−1.43318			−0.716588	+	0.697497i	$0.754297\pi$
$572$	4.32475	+	6.17638i	0.180827	+	0.258247i
$573$	1.95410	+	0.695181i	0.0816337	+	0.0290416i
$574$	−3.74363	+	10.2855i	−0.156256	+	0.429310i
$575$	−10.5693	+	29.8424i	−0.440772	+	1.24452i
$576$	−2.96169	−	0.477914i	−0.123404	−	0.0199131i
$577$	0.541132	−	2.01953i	0.0225276	−	0.0840743i	−0.953747	−	0.300611i	$-0.902809\pi$
$577$	0.541132	−	2.01953i	0.0225276	−	0.0840743i	0.976274	+	0.216537i	$0.0694761\pi$
$578$	−11.1112	+	2.97725i	−0.462166	+	0.123837i
$579$	−2.86276	+	11.0035i	−0.118972	+	0.457288i
$580$	6.77881	−	10.7432i	0.281475	−	0.446087i
$581$	13.5101	+	7.80007i	0.560494	+	0.323601i
$582$	3.35396	−	4.05665i	0.139026	−	0.168154i
$583$	−1.82791	+	20.8931i	−0.0757044	+	0.865305i
$584$	13.5331	−	4.92564i	0.560003	−	0.203825i
$585$	−7.78092	−	17.8250i	−0.321701	−	0.736972i
$586$	−17.4582	−	14.6492i	−0.721192	−	0.605152i
$587$	−6.64431	−	9.48906i	−0.274240	−	0.391656i	0.658280	−	0.752773i	$-0.271284\pi$
$587$	−6.64431	−	9.48906i	−0.274240	−	0.391656i	−0.932520	+	0.361117i	$0.882395\pi$
$588$	−1.37869	−	3.70387i	−0.0568561	−	0.152745i
$589$	−35.0547	−	16.7342i	−1.44440	−	0.689523i
$590$	−0.186979	−	3.89458i	−0.00769780	−	0.160337i
$591$	20.7701	−	30.1269i	0.854370	−	1.23925i
$592$	1.05191	+	12.0234i	0.0432332	+	0.494158i
$593$	−13.5659	−	29.0922i	−0.557086	−	1.19468i	−0.960145	−	0.279501i	$-0.909831\pi$
$593$	−13.5659	−	29.0922i	−0.557086	−	1.19468i	0.403059	−	0.915174i	$-0.367947\pi$
$594$	7.99046	+	10.8975i	0.327852	+	0.447131i
$595$	−0.447339	+	11.3787i	−0.0183391	+	0.466483i
$596$	−10.0754	+	5.81702i	−0.412703	+	0.238274i
$597$	−1.61535	+	9.56750i	−0.0661118	+	0.391572i
$598$	−15.0379	−	10.5296i	−0.614944	−	0.430588i
$599$	8.01234	+	45.4402i	0.327375	+	1.85664i	0.492428	+	0.870353i	$0.336110\pi$
$599$	8.01234	+	45.4402i	0.327375	+	1.85664i	−0.165052	+	0.986285i	$0.552779\pi$
$600$	6.54449	−	5.67183i	0.267178	−	0.231551i
$601$	−15.6832	−	27.1642i	−0.639733	−	1.10805i	−0.985491	−	0.169726i	$-0.945712\pi$
$601$	−15.6832	−	27.1642i	−0.639733	−	1.10805i	0.345758	−	0.938324i	$-0.387622\pi$
$602$	−1.47668	+	16.8785i	−0.0601848	+	0.687915i
$603$	−5.32453	+	1.51005i	−0.216832	+	0.0614939i
$604$	−2.95998	+	8.13248i	−0.120440	+	0.330906i
$605$	−9.38748	+	1.27736i	−0.381656	+	0.0519319i
$606$	3.88240	+	2.67662i	0.157712	+	0.108730i
$607$	−30.2517	−	30.2517i	−1.22788	−	1.22788i	−0.964765	−	0.263112i	$-0.915251\pi$
$607$	−30.2517	−	30.2517i	−1.22788	−	1.22788i	−0.263112	−	0.964765i	$-0.584749\pi$
$608$	−2.14519	−	3.79449i	−0.0869990	−	0.153887i
$609$	8.89169	−	19.4361i	0.360309	−	0.787591i
$610$	15.7903	+	2.00916i	0.639333	+	0.0813486i
$611$	6.04752	−	7.20715i	0.244656	−	0.291570i
$612$	−6.41715	−	2.87948i	−0.259398	−	0.116396i
$613$	16.1219	−	34.5736i	0.651159	−	1.39642i	−0.252261	−	0.967659i	$-0.581174\pi$
$613$	16.1219	−	34.5736i	0.651159	−	1.39642i	0.903420	−	0.428756i	$-0.141048\pi$
$614$	−6.40309	+	5.37283i	−0.258408	+	0.216830i
$615$	19.3184	−	2.77191i	0.778994	−	0.111774i
$616$	−2.82444	+	4.89208i	−0.113800	+	0.197107i
$617$	12.7476	+	8.92594i	0.513198	+	0.359345i	0.801308	−	0.598252i	$-0.204138\pi$
$617$	12.7476	+	8.92594i	0.513198	+	0.359345i	−0.288110	+	0.957597i	$0.593027\pi$
$618$	−0.0654073	−	0.111409i	−0.00263107	−	0.00448155i
$619$	15.2646	+	8.81303i	0.613537	+	0.354225i	0.774348	−	0.632760i	$-0.218078\pi$
$619$	15.2646	+	8.81303i	0.613537	+	0.354225i	−0.160812	+	0.986985i	$0.551411\pi$
$620$	−4.22844	+	19.4728i	−0.169818	+	0.782048i
$621$	−27.3561	−	18.2786i	−1.09776	−	0.733496i
$622$	24.8656	+	11.5950i	0.997018	+	0.464917i
$623$	−0.418543	−	0.897568i	−0.0167686	−	0.0359603i
$624$	2.15534	+	4.53571i	0.0862826	+	0.181574i
$625$	0.433970	+	24.9962i	0.0173588	+	0.999849i
$626$			14.3953i			0.575352i
$627$	−5.11540	+	18.9560i	−0.204289	+	0.757029i
$628$	−7.07750	+	7.07750i	−0.282423	+	0.282423i
$629$	−4.91369	+	27.8669i	−0.195922	+	1.11113i
$630$	9.63953	−	10.9270i	0.384048	−	0.435343i
$631$	35.8068	+	13.0326i	1.42544	+	0.518819i	0.935622	−	0.353003i	$-0.114839\pi$
$631$	35.8068	+	13.0326i	1.42544	+	0.518819i	0.489822	+	0.871822i	$0.337062\pi$
$632$	−4.73209	+	10.1480i	−0.188233	+	0.403666i
$633$	−19.7451	−	11.2092i	−0.784799	−	0.445525i
$634$	24.1353	−	13.9345i	0.958534	−	0.553410i
$635$	3.64340	−	7.07368i	0.144584	−	0.280711i
$636$	−3.51706	+	13.5184i	−0.139461	+	0.536039i
$637$	−3.79454	+	5.41917i	−0.150345	+	0.214715i
$638$	14.2706	−	3.82379i	0.564977	−	0.151385i
$639$	13.2905	−	38.2370i	0.525764	−	1.51263i
$640$	−1.64203	+	1.51781i	−0.0649070	+	0.0599966i
$641$	12.5898	+	34.5902i	0.497268	+	1.36623i	0.893905	+	0.448256i	$0.147955\pi$
$641$	12.5898	+	34.5902i	0.497268	+	1.36623i	−0.396637	+	0.917975i	$0.629823\pi$
$642$	20.0769	−	0.146027i	0.792373	−	0.00576324i
$643$	−37.5346	+	3.28386i	−1.48022	+	0.129503i	−0.798450	−	0.602062i	$-0.794346\pi$
$643$	−37.5346	+	3.28386i	−1.48022	+	0.129503i	−0.681772	+	0.731564i	$0.738791\pi$
$644$	2.38828	−	13.5446i	0.0941113	−	0.533732i
$645$	27.7739	−	11.8841i	1.09360	−	0.467934i
$646$	−2.55555	−	9.89487i	−0.100547	−	0.389308i
$647$	29.7444	−	29.7444i	1.16937	−	1.16937i	0.187015	−	0.982357i	$-0.440119\pi$
$647$	29.7444	−	29.7444i	1.16937	−	1.16937i	0.982357	−	0.187015i	$-0.0598814\pi$
$648$	4.03923	+	8.04268i	0.158676	+	0.315946i
$649$	2.91485	−	3.47379i	0.114418	−	0.136358i
$650$	−14.0347	−	3.63032i	−0.550486	−	0.142393i
$651$	−2.67910	+	33.4201i	−0.105002	+	1.30984i
$652$	−1.49247	−	0.130574i	−0.0584497	−	0.00511368i
$653$	−4.80116	+	17.9182i	−0.187884	+	0.701192i	0.806111	+	0.591764i	$0.201568\pi$
$653$	−4.80116	+	17.9182i	−0.187884	+	0.701192i	−0.993995	+	0.109428i	$0.965098\pi$
$654$	−20.4321	−	28.7329i	−0.798956	−	1.12355i
$655$	−11.3507	+	17.9888i	−0.443508	+	0.702881i
$656$	−4.96252	+	0.875027i	−0.193754	+	0.0341641i
$657$	−35.7481	−	24.2639i	−1.39466	−	0.946623i
$658$	6.80843	+	1.82431i	0.265420	+	0.0711191i
$659$	−16.7820	+	14.0817i	−0.653733	+	0.548547i	−0.908201	−	0.418534i	$-0.862544\pi$
$659$	−16.7820	+	14.0817i	−0.653733	+	0.548547i	0.254468	+	0.967081i	$0.418100\pi$
$660$	10.0669	+	0.322453i	0.391854	+	0.0125515i
$661$	2.78248	+	1.01274i	0.108226	+	0.0393910i	0.395566	−	0.918438i	$-0.370549\pi$
$661$	2.78248	+	1.01274i	0.108226	+	0.0393910i	−0.287340	+	0.957829i	$0.592771\pi$
$662$	−24.2780	+	2.12405i	−0.943592	+	0.0825536i
$663$	2.12875	+	11.5796i	0.0826740	+	0.449716i
$664$			7.18189i			0.278711i
$665$	21.1467	+	1.02314i	0.820036	+	0.0396757i
$666$	27.3954	−	23.6750i	1.06155	−	0.917387i
$667$	−29.4655	+	20.6320i	−1.14091	+	0.798874i
$668$	−1.60425	−	18.3367i	−0.0620705	−	0.709469i
$669$	8.62361	+	8.49907i	0.333408	+	0.328593i
$670$	−1.56208	+	3.81799i	−0.0603486	+	0.147502i
$671$	11.8997	+	14.1815i	0.459381	+	0.547469i
$672$	−2.39732	+	2.89958i	−0.0924785	+	0.111854i
$673$	−6.53299	−	24.3814i	−0.251828	−	0.939836i	−0.969828	−	0.243792i	$-0.921609\pi$
$673$	−6.53299	−	24.3814i	−0.251828	−	0.939836i	0.717999	−	0.696044i	$-0.245058\pi$
$674$	−2.91400	−	16.5261i	−0.112243	−	0.636563i
$675$	−25.2889	−	5.95590i	−0.973369	−	0.229243i
$676$	−2.29697	+	3.97847i	−0.0883449	+	0.153018i
$677$	3.89189	+	1.04283i	0.149578	+	0.0400792i	0.332831	−	0.942987i	$-0.391996\pi$
$677$	3.89189	+	1.04283i	0.149578	+	0.0400792i	−0.183253	+	0.983066i	$0.558663\pi$
$678$	−6.04314	−	3.43065i	−0.232085	−	0.131753i
$679$	−2.25768	−	6.20294i	−0.0866419	−	0.238047i
$680$	−4.63962	+	2.44088i	−0.177921	+	0.0936036i
$681$	−1.62309	−	3.41565i	−0.0621971	−	0.130888i
$682$	−18.9839	+	13.2927i	−0.726933	+	0.509004i
$683$	2.48258	+	2.48258i	0.0949933	+	0.0949933i	0.753006	−	0.658013i	$-0.228603\pi$
$683$	2.48258	+	2.48258i	0.0949933	+	0.0949933i	−0.658013	+	0.753006i	$0.728603\pi$
$684$	−5.46125	+	11.8817i	−0.208816	+	0.454308i
$685$	0.137528	+	2.86456i	0.00525466	+	0.109449i
$686$	−19.8551	−	3.50099i	−0.758071	−	0.133668i
$687$	−22.3593	−	7.95444i	−0.853061	−	0.303481i
$688$	−7.06928	+	3.29646i	−0.269514	+	0.125676i
$689$	21.9719	−	7.99713i	0.837064	−	0.304666i
$690$	−23.3006	+	7.64526i	−0.887040	+	0.291050i
$691$	6.24786	+	10.8216i	0.237680	+	0.411674i	0.960048	−	0.279835i	$-0.0902797\pi$
$691$	6.24786	+	10.8216i	0.237680	+	0.411674i	−0.722368	+	0.691509i	$0.756946\pi$
$692$	3.13422	+	11.6971i	0.119145	+	0.444656i
$693$	16.8589	−	1.72241i	0.640416	−	0.0654289i
$694$	8.05785	−	1.42082i	0.305872	−	0.0539334i
$695$	22.3616	−	7.15743i	0.848224	−	0.271497i
$696$	9.79584	−	0.928865i	0.371310	−	0.0352085i
$697$	−11.7693	−	1.02968i	−0.445794	−	0.0390019i
$698$	−1.29912	−	0.605791i	−0.0491725	−	0.0229295i
$699$	−26.7977	+	27.1903i	−1.01358	+	1.02843i
$700$	−1.97871	−	10.6790i	−0.0747883	−	0.403627i
$701$	−47.6373	−	8.39974i	−1.79924	−	0.317254i	−0.828970	−	0.559293i	$-0.811073\pi$
$701$	−47.6373	−	8.39974i	−1.79924	−	0.317254i	−0.970267	+	0.242039i	$0.922184\pi$
$702$	7.24620	−	13.2082i	0.273490	−	0.498511i
$703$	51.7248	+	9.60403i	1.95084	+	0.362223i
$704$	−2.60060			−0.0980137
$705$	−2.86247	−	12.2375i	−0.107807	−	0.460890i
$706$	−5.66999	−	4.75768i	−0.213393	−	0.179058i
$707$	5.35977	−	2.49930i	0.201575	−	0.0939959i
$708$	2.29943	−	1.95813i	0.0864179	−	0.0735909i
$709$	−7.82531	−	9.32584i	−0.293886	−	0.350239i	0.598817	−	0.800886i	$-0.295638\pi$
$709$	−7.82531	−	9.32584i	−0.293886	−	0.350239i	−0.892702	+	0.450647i	$0.851193\pi$
$710$	−16.3221	−	25.3768i	−0.612556	−	0.952375i
$711$	32.9926	−	6.31364i	1.23732	−	0.236780i
$712$	0.261513	−	0.373479i	0.00980061	−	0.0139967i
$713$	32.3642	−	46.2209i	1.21205	−	1.73099i
$714$	−7.18854	+	5.11179i	−0.269024	+	0.191304i
$715$	−9.12043	−	14.1800i	−0.341085	−	0.530303i
$716$	8.68969	+	10.3560i	0.324749	+	0.387021i
$717$	24.3627	+	28.6091i	0.909841	+	1.06843i
$718$	−3.67541	+	1.71387i	−0.137165	+	0.0639611i
$719$	−11.1167	−	9.32805i	−0.414584	−	0.347877i	0.411514	−	0.911403i	$-0.365000\pi$
$719$	−11.1167	−	9.32805i	−0.414584	−	0.347877i	−0.826098	+	0.563526i	$0.809445\pi$
$720$	6.57544	+	1.32798i	0.245052	+	0.0494908i
$721$	−0.162017			−0.00603381
$722$	−18.4386	+	4.58452i	−0.686214	+	0.170618i
$723$	−12.5121	−	33.6139i	−0.465329	−	1.25012i
$724$	−15.0927	−	2.66125i	−0.560915	−	0.0989044i
$725$	−16.0899	+	23.4085i	−0.597562	+	0.869371i
$726$	−5.22672	−	5.15124i	−0.193982	−	0.191180i
$727$	−33.5073	−	15.6247i	−1.24272	−	0.579488i	−0.313699	−	0.949523i	$-0.601568\pi$
$727$	−33.5073	−	15.6247i	−1.24272	−	0.579488i	−0.929018	+	0.370034i	$0.879346\pi$
$728$	6.27379	+	0.548886i	0.232522	+	0.0203431i
$729$	12.4671	−	23.9494i	0.461743	−	0.887014i
$730$	−30.6702	+	9.81683i	−1.13516	+	0.363337i
$731$	−18.0097	+	3.17559i	−0.666112	+	0.117454i
$732$	6.24238	+	10.6328i	0.230725	+	0.392998i
$733$	5.55307	+	20.7244i	0.205107	+	0.765471i	0.989417	+	0.145101i	$0.0463508\pi$
$733$	5.55307	+	20.7244i	0.205107	+	0.765471i	−0.784309	+	0.620370i	$0.786982\pi$
$734$	0.154358	+	0.267355i	0.00569744	+	0.00986826i
$735$	2.75511	+	8.39682i	0.101624	+	0.309721i
$736$	5.94992	−	2.16559i	0.219317	−	0.0798248i
$737$	−4.34817	+	2.02759i	−0.160167	+	0.0746871i
$738$	10.8439	+	10.5329i	0.399168	+	0.387721i
$739$	3.52287	+	0.621178i	0.129591	+	0.0228504i	0.238067	−	0.971249i	$-0.423486\pi$
$739$	3.52287	+	0.621178i	0.129591	+	0.0228504i	−0.108476	+	0.994099i	$0.534597\pi$
$740$	−1.29419	−	26.9567i	−0.0475755	−	0.990949i
$741$	21.5636	−	3.76271i	0.792158	−	0.138226i
$742$	12.3868	+	12.3868i	0.454735	+	0.454735i
$743$	−19.8355	+	13.8890i	−0.727694	+	0.509537i	−0.877737	−	0.479143i	$-0.840948\pi$
$743$	−19.8355	+	13.8890i	−0.727694	+	0.509537i	0.150043	+	0.988679i	$0.452059\pi$
$744$	−13.9411	+	6.62473i	−0.511107	+	0.242874i
$745$	23.0228	−	12.1122i	0.843490	−	0.443756i
$746$	9.04423	+	24.8488i	0.331133	+	0.909780i
$747$	17.4676	−	12.6135i	0.639104	−	0.461504i
$748$	−5.88941	−	1.57806i	−0.215338	−	0.0576997i
$749$	12.5895	−	21.8056i	0.460009	−	0.796760i
$750$	−15.1208	+	12.0979i	−0.552135	+	0.441754i
$751$	3.49041	+	19.7951i	0.127367	+	0.722334i	0.979874	+	0.199618i	$0.0639701\pi$
$751$	3.49041	+	19.7951i	0.127367	+	0.722334i	−0.852507	+	0.522716i	$0.824919\pi$
$752$	0.839865	+	3.13442i	0.0306267	+	0.114301i
$753$	3.05487	+	2.52571i	0.111326	+	0.0920420i
$754$	−10.5874	−	12.6175i	−0.385570	−	0.459504i
$755$	7.32796	−	17.9107i	0.266692	−	0.651838i
$756$	11.2627	+	0.738157i	0.409619	+	0.0268465i
$757$	2.17079	+	24.8122i	0.0788986	+	0.901815i	0.927755	+	0.373191i	$0.121736\pi$
$757$	2.17079	+	24.8122i	0.0788986	+	0.901815i	−0.848856	+	0.528624i	$0.822708\pi$
$758$	−21.5032	+	15.0567i	−0.781031	+	0.546884i
$759$	−25.9354	−	11.8650i	−0.941396	−	0.430672i
$760$	4.45978	+	8.66662i	0.161773	+	0.314371i
$761$		−	18.6056i		−	0.674454i	−0.941423	−	0.337227i	$-0.890511\pi$
$761$		−	18.6056i		−	0.674454i	0.941423	−	0.337227i	$-0.109489\pi$
$762$	6.06176	−	1.11437i	0.219594	−	0.0403694i
$763$	−44.0471	+	3.85362i	−1.59461	+	0.139510i
$764$	1.12525	+	0.409558i	0.0407102	+	0.0148173i
$765$	14.0852	+	6.99742i	0.509251	+	0.252992i
$766$	−14.6502	+	12.2930i	−0.529333	+	0.444163i
$767$	−4.88333	−	1.30848i	−0.176327	−	0.0472466i
$768$	−1.70788	−	0.288353i	−0.0616278	−	0.0104051i
$769$	−27.0529	+	4.77016i	−0.975554	+	0.172016i	−0.638629	−	0.769515i	$-0.720498\pi$
$769$	−27.0529	+	4.77016i	−0.975554	+	0.172016i	−0.336925	+	0.941531i	$0.609387\pi$
$770$	6.74049	−	10.6825i	0.242910	−	0.384970i
$771$	8.07615	−	5.74297i	0.290855	−	0.206828i
$772$	−1.69897	+	6.34066i	−0.0611474	+	0.228205i
$773$	45.0341	+	3.93998i	1.61977	+	0.141711i	0.860633	−	0.509226i	$-0.170068\pi$
$773$	45.0341	+	3.93998i	1.61977	+	0.141711i	0.759132	+	0.650937i	$0.225624\pi$
$774$	20.4333	+	11.4041i	0.734459	+	0.409912i
$775$	11.1583	−	43.1375i	0.400817	−	1.54955i
$776$	1.95339	−	2.32796i	0.0701227	−	0.0835690i
$777$	−8.21005	−	44.6596i	−0.294534	−	1.60215i
$778$	−25.2908	+	25.2908i	−0.906718	+	0.906718i
$779$	−2.11235	+	21.8630i	−0.0756827	+	0.783324i
$780$	−4.41735	−	10.3237i	−0.158166	−	0.369646i
$781$	6.09358	−	34.5584i	0.218045	−	1.23660i
$782$	14.7885	−	1.29383i	0.528836	−	0.0462671i
$783$	−19.4635	−	22.1937i	−0.695569	−	0.793140i
$784$	−0.780412	−	2.14416i	−0.0278718	−	0.0765773i
$785$	16.4352	−	15.1919i	0.586599	−	0.542221i
$786$	−16.4025	+	1.55532i	−0.585058	+	0.0554766i
$787$	28.5491	−	7.64970i	1.01766	−	0.272682i	0.288836	−	0.957379i	$-0.406732\pi$
$787$	28.5491	−	7.64970i	1.01766	−	0.272682i	0.728828	+	0.684696i	$0.240065\pi$
$788$	12.1178	−	17.3061i	0.431680	−	0.616503i
$789$	15.1790	+	3.94910i	0.540386	+	0.140592i
$790$	11.4645	−	22.2585i	0.407889	−	0.791920i
$791$	−7.54716	+	4.35735i	−0.268346	+	0.154930i
$792$	4.56741	+	6.32508i	0.162296	+	0.224752i
$793$	8.72246	−	18.7054i	0.309743	−	0.664247i
$794$	−9.88325	−	3.59721i	−0.350743	−	0.127660i
$795$	9.04577	−	29.8957i	0.320820	−	1.06029i
$796$	−0.972773	+	5.51687i	−0.0344790	+	0.195540i
$797$	−0.838849	+	0.838849i	−0.0297135	+	0.0297135i	−0.721807	−	0.692094i	$-0.756688\pi$
$797$	−0.838849	+	0.838849i	−0.0297135	+	0.0297135i	0.692094	+	0.721807i	$0.256688\pi$
$798$	9.38238	+	13.4503i	0.332133	+	0.476135i
$799$			7.60796i			0.269150i
$800$	3.80218	−	3.24706i	0.134427	−	0.114801i
$801$	−1.36766	+	0.0198961i	−0.0483238	+	0.000702993i
$802$	−9.46799	−	20.3042i	−0.334326	−	0.716965i
$803$	−33.9438	−	15.8282i	−1.19785	−	0.558566i
$804$	−3.08038	+	0.849445i	−0.108637	+	0.0299576i
$805$	−6.52599	+	30.0535i	−0.230011	+	1.05925i
$806$	22.3757	+	12.9186i	0.788149	+	0.455038i
$807$	8.57521	−	5.03441i	0.301862	−	0.177220i
$808$	2.23021	+	1.56161i	0.0784584	+	0.0549372i
$809$	−2.51647	+	4.35865i	−0.0884742	+	0.153242i	−0.906866	−	0.421418i	$-0.861532\pi$
$809$	−2.51647	+	4.35865i	−0.0884742	+	0.153242i	0.818392	+	0.574660i	$0.194866\pi$
$810$	−8.31855	−	18.3249i	−0.292284	−	0.643871i
$811$	−10.3112	+	8.65213i	−0.362076	+	0.303817i	−0.805617	−	0.592436i	$-0.798166\pi$
$811$	−10.3112	+	8.65213i	−0.362076	+	0.303817i	0.443542	+	0.896254i	$0.353722\pi$
$812$	5.21510	−	11.1838i	0.183014	−	0.392475i
$813$	0.323403	+	44.4638i	0.0113422	+	1.55942i
$814$	20.1754	−	24.0441i	0.707148	−	0.842746i
$815$	3.32322	+	0.422846i	0.116407	+	0.0148117i
$816$	−3.69275	−	1.68937i	−0.129272	−	0.0591398i
$817$	5.60068	+	33.5353i	0.195943	+	1.17325i
$818$	−3.26255	−	3.26255i	−0.114072	−	0.114072i
$819$	−9.68364	−	16.2229i	−0.338374	−	0.566874i
$820$	11.1648	−	1.51920i	0.389893	−	0.0530528i
$821$	6.66053	−	18.2997i	0.232454	−	0.638662i	−0.767543	−	0.640997i	$-0.778521\pi$
$821$	6.66053	−	18.2997i	0.232454	−	0.638662i	0.999997	+	0.00233490i	$0.000743222\pi$
$822$	−1.69129	+	1.44025i	−0.0589905	+	0.0502345i
$823$	0.172661	−	1.97353i	0.00601859	−	0.0687928i	−0.992591	−	0.121500i	$-0.961229\pi$
$823$	0.172661	−	1.97353i	0.00601859	−	0.0687928i	0.998610	+	0.0527074i	$0.0167851\pi$
$824$	−0.0372941	−	0.0645953i	−0.00129920	−	0.00225028i
$825$	−22.4646	−	1.60475i	−0.782116	−	0.0558701i
$826$	−0.657712	−	3.73007i	−0.0228847	−	0.129786i
$827$	−28.9164	−	20.2475i	−1.00552	−	0.704075i	−0.0499263	−	0.998753i	$-0.515899\pi$
$827$	−28.9164	−	20.2475i	−1.00552	−	0.704075i	−0.955597	+	0.294678i	$0.904788\pi$
$828$	−15.7169	−	10.6678i	−0.546199	−	0.370731i
$829$	24.3941	−	14.0840i	0.847243	−	0.489156i	−0.0124764	−	0.999922i	$-0.503971\pi$
$829$	24.3941	−	14.0840i	0.847243	−	0.489156i	0.859720	+	0.510766i	$0.170638\pi$
$830$	0.630857	−	16.0468i	0.0218974	−	0.556993i
$831$	1.18617	−	14.7967i	0.0411477	−	0.513292i
$832$	1.22531	+	2.62768i	0.0424798	+	0.0910983i
$833$	−0.466255	−	5.32931i	−0.0161548	−	0.184650i
$834$	14.9733	+	10.3229i	0.518483	+	0.357454i
$835$	1.97376	+	41.1114i	0.0683047	+	1.42272i
$836$	−3.03290	+	10.9225i	−0.104895	+	0.377762i
$837$	40.5972	+	22.2722i	1.40324	+	0.769840i
$838$	−1.60737	−	2.29556i	−0.0555257	−	0.0792990i
$839$	−31.8437	−	26.7200i	−1.09937	−	0.922478i	−0.101984	−	0.994786i	$-0.532519\pi$
$839$	−31.8437	−	26.7200i	−1.09937	−	0.922478i	−0.997382	+	0.0723079i	$0.976964\pi$
$840$	5.61112	−	6.26807i	0.193602	−	0.216269i
$841$	−3.07631	+	1.11968i	−0.106080	+	0.0386098i
$842$	0.289130	−	3.30477i	0.00996407	−	0.113890i
$843$	−15.5420	−	12.8498i	−0.535296	−	0.442572i
$844$	−11.3525	−	6.55436i	−0.390769	−	0.225610i
$845$	5.48168	−	8.68749i	0.188576	−	0.298859i
$846$	6.14838	−	7.54765i	0.211386	−	0.259494i
$847$	−8.88958	+	2.38196i	−0.305450	+	0.0818450i
$848$	−2.08729	+	7.78987i	−0.0716778	+	0.267505i
$849$	17.3514	−	4.78483i	0.595499	−	0.164215i
$850$	10.5809	−	5.04623i	0.362922	−	0.173084i
$851$	−26.1372	+	71.8113i	−0.895971	+	2.46166i
$852$	7.83364	−	22.0198i	0.268376	−	0.754384i
$853$	−0.819696	−	1.17065i	−0.0280659	−	0.0400822i	0.804874	−	0.593446i	$-0.202233\pi$
$853$	−0.819696	−	1.17065i	−0.0280659	−	0.0400822i	−0.832940	+	0.553364i	$0.813344\pi$
$854$	15.4626			0.529121
$855$	13.2460	−	26.0681i	0.453003	−	0.891509i
$856$	11.5917			0.396197
$857$	8.33035	+	11.8970i	0.284559	+	0.406393i	0.935829	−	0.352453i	$-0.114652\pi$
$857$	8.33035	+	11.8970i	0.284559	+	0.406393i	−0.651270	+	0.758846i	$0.725764\pi$
$858$	4.37727	−	12.3042i	0.149438	−	0.420058i
$859$	−1.95250	+	5.36445i	−0.0666185	+	0.183033i	−0.968535	−	0.248878i	$-0.919938\pi$
$859$	−1.95250	+	5.36445i	−0.0666185	+	0.183033i	0.901916	+	0.431911i	$0.142160\pi$
$860$	16.0848	−	6.74445i	0.548485	−	0.229984i
$861$	18.2762	−	5.03985i	0.622852	−	0.171758i
$862$	−9.63586	+	35.9615i	−0.328199	+	1.22485i
$863$	2.53083	−	0.678133i	0.0861503	−	0.0230839i	−0.215486	−	0.976507i	$-0.569134\pi$
$863$	2.53083	−	0.678133i	0.0861503	−	0.0230839i	0.301637	+	0.953423i	$0.402467\pi$
$864$	2.29821	+	4.66028i	0.0781868	+	0.158546i
$865$	−5.97545	−	26.4106i	−0.203171	−	0.897986i
$866$	−31.6914	−	18.2970i	−1.07692	−	0.621758i
$867$	15.3555	+	12.6956i	0.521500	+	0.431166i
$868$	−1.68708	+	19.2834i	−0.0572631	+	0.654520i
$869$	27.3630	−	9.95932i	0.928226	−	0.337847i
$870$	−21.9688	+	1.21494i	−0.744813	+	0.0411902i
$871$	4.09740	+	3.43813i	0.138835	+	0.116497i
$872$	−11.6755	−	16.6743i	−0.395382	−	0.564664i
$873$	−9.09272	−	0.662390i	−0.307742	−	0.0224185i
$874$	−2.15649	−	27.5152i	−0.0729442	−	0.930714i
$875$	3.48308	+	24.0343i	0.117750	+	0.812507i
$876$	−20.5367	−	14.1585i	−0.693872	−	0.478371i
$877$	−0.0844227	−	0.964956i	−0.00285075	−	0.0325843i	0.994636	−	0.103436i	$-0.0329838\pi$
$877$	−0.0844227	−	0.964956i	−0.00285075	−	0.0325843i	−0.997487	+	0.0708520i	$0.977428\pi$
$878$	−15.2918	−	32.7934i	−0.516073	−	1.10672i
$879$	−3.15425	+	39.3473i	−0.106390	+	1.32715i
$880$	5.81062	+	0.228436i	0.195876	+	0.00770058i
$881$	47.3202	−	27.3203i	1.59426	−	0.920445i	0.601693	−	0.798728i	$-0.294493\pi$
$881$	47.3202	−	27.3203i	1.59426	−	0.920445i	0.992565	−	0.121717i	$-0.0388401\pi$
$882$	−3.84433	+	5.66387i	−0.129445	+	0.190712i
$883$	−42.3215	−	29.6339i	−1.42423	−	0.997259i	−0.995593	−	0.0937841i	$-0.970104\pi$
$883$	−42.3215	−	29.6339i	−1.42423	−	0.997259i	−0.428641	−	0.903475i	$-0.641007\pi$
$884$	1.18038	+	6.69426i	0.0397005	+	0.225152i
$885$	−5.30972	+	4.17314i	−0.178484	+	0.140279i
$886$	3.21103	+	5.56167i	0.107877	+	0.186848i
$887$	1.23614	−	14.1291i	0.0415054	−	0.474409i	−0.946790	−	0.321853i	$-0.895694\pi$
$887$	1.23614	−	14.1291i	0.0415054	−	0.474409i	0.988295	−	0.152555i	$-0.0487502\pi$
$888$	15.9157	−	13.5534i	0.534097	−	0.454821i
$889$	2.64361	−	7.26325i	0.0886637	−	0.243602i
$890$	−0.617116	+	0.811509i	−0.0206858	+	0.0272019i
$891$	7.36194	−	22.2174i	0.246634	−	0.744311i
$892$	4.94303	+	4.94303i	0.165505	+	0.165505i
$893$	14.1440	+	0.128034i	0.473311	+	0.00428449i
$894$	18.3242	+	8.38302i	0.612854	+	0.280370i
$895$	−18.5061	−	23.9021i	−0.618590	−	0.798958i
$896$	−1.39623	+	1.66396i	−0.0466448	+	0.0555891i
$897$	0.231264	+	31.7959i	0.00772168	+	1.06163i
$898$	1.86531	−	4.00016i	0.0622461	−	0.133487i
$899$	38.7818	−	32.5418i	1.29344	−	1.08533i
$900$	−14.5751	−	3.54474i	−0.485838	−	0.118158i
$901$	−9.45390	+	16.3746i	−0.314955	+	0.545518i
$902$	10.7347	+	7.51650i	0.357425	+	0.250272i
$903$	25.3070	−	14.8575i	0.842165	−	0.494426i
$904$	−3.47451	−	2.00601i	−0.115561	−	0.0667189i
$905$	33.4884	+	7.27187i	1.11319	+	0.241725i
$906$	14.4505	−	3.98487i	0.480086	−	0.132388i
$907$	5.83412	+	2.72049i	0.193719	+	0.0903325i	0.517057	−	0.855951i	$-0.327027\pi$
$907$	5.83412	+	2.72049i	0.193719	+	0.0903325i	−0.323338	+	0.946283i	$0.604805\pi$
$908$	−0.922725	−	1.97879i	−0.0306217	−	0.0656685i
$909$	−0.118808	−	8.16688i	−0.00394062	−	0.270878i
$910$	−13.9696	−	1.77749i	−0.463087	−	0.0589231i
$911$			31.9485i			1.05850i	0.848466	+	0.529250i	$0.177527\pi$
$911$			31.9485i			1.05850i	−0.848466	+	0.529250i	$0.822473\pi$
$912$	−3.20286	+	6.83679i	−0.106057	+	0.226389i
$913$	13.2068	−	13.2068i	0.437080	−	0.437080i
$914$	−0.864251	+	4.90141i	−0.0285869	+	0.162124i
$915$	−13.0136	−	24.3056i	−0.430218	−	0.803517i
$916$	−12.8754	−	4.68627i	−0.425415	−	0.154839i
$917$	−8.73235	+	18.7266i	−0.288368	+	0.618406i
$918$	2.37673	+	11.9484i	0.0784437	+	0.394357i
$919$	23.4413	−	13.5339i	0.773258	−	0.446441i	−0.0607774	−	0.998151i	$-0.519358\pi$
$919$	23.4413	−	13.5339i	0.773258	−	0.446441i	0.834036	+	0.551710i	$0.186025\pi$
$920$	−13.4844	+	4.31603i	−0.444567	+	0.142295i
$921$	14.0112	+	3.64527i	0.461684	+	0.120116i
$922$	−22.8625	+	32.6510i	−0.752936	+	1.07530i
$923$	−37.7893	+	10.1256i	−1.24385	+	0.333289i
$924$	9.74046	−	0.923614i	0.320438	−	0.0303847i
$925$	0.523791	+	60.3442i	0.0172222	+	1.98411i
$926$	−9.90004	−	27.2001i	−0.325336	−	0.893852i
$927$	−0.0916070	+	0.204154i	−0.00300877	+	0.00670529i
$928$	5.65938	−	0.495132i	0.185778	−	0.0162535i
$929$	−4.47775	+	25.3946i	−0.146910	+	0.833170i	0.818903	+	0.573932i	$0.194582\pi$
$929$	−4.47775	+	25.3946i	−0.146910	+	0.833170i	−0.965813	+	0.259238i	$0.916529\pi$
$930$	31.7312	−	13.5773i	1.04051	−	0.445218i
$931$	−9.91560	+	0.777129i	−0.324971	+	0.0254694i
$932$	−15.5854	+	15.5854i	−0.510517	+	0.510517i
$933$	−8.59205	−	46.7375i	−0.281291	−	1.53012i
$934$	18.5857	−	22.1496i	0.608142	−	0.724756i
$935$	13.0203	+	4.04326i	0.425811	+	0.132229i
$936$	4.23895	−	7.59512i	0.138554	−	0.248254i
$937$	−28.4283	−	2.48715i	−0.928712	−	0.0812517i	−0.387248	−	0.921976i	$-0.626574\pi$
$937$	−28.4283	−	2.48715i	−0.928712	−	0.0812517i	−0.541464	+	0.840724i	$0.682130\pi$
$938$	−1.03716	+	3.87072i	−0.0338643	+	0.126383i
$939$	20.3197	−	14.4494i	0.663108	−	0.471538i
$940$	−1.60122	−	7.07714i	−0.0522260	−	0.230831i
$941$	−24.8784	+	4.38673i	−0.811012	+	0.143003i	−0.563750	−	0.825945i	$-0.690642\pi$
$941$	−24.8784	+	4.38673i	−0.811012	+	0.143003i	−0.247262	+	0.968949i	$0.579531\pi$
$942$	17.0943	+	2.88616i	0.556963	+	0.0940361i
$943$	−30.8191	−	8.25795i	−1.00361	−	0.268916i
$944$	1.33576	−	1.12084i	0.0434754	−	0.0364802i
$945$	−25.0998	−	2.63861i	−0.816496	−	0.0858339i
$946$	19.0616	+	6.93784i	0.619745	+	0.225569i
$947$	−26.0022	+	2.27490i	−0.844959	+	0.0739243i	−0.501409	−	0.865210i	$-0.667185\pi$
$947$	−26.0022	+	2.27490i	−0.844959	+	0.0739243i	−0.343549	+	0.939135i	$0.611629\pi$
$948$	19.0743	−	3.50654i	0.619504	−	0.113887i
$949$			41.7549i			1.35542i
$950$	−9.20340	−	19.7559i	−0.298598	−	0.640968i
$951$	−43.8952	−	20.0813i	−1.42340	−	0.651180i
$952$	−4.17166	+	2.92103i	−0.135204	+	0.0946711i
$953$	4.26418	+	48.7398i	0.138130	+	1.57884i	0.676701	+	0.736258i	$0.263409\pi$
$953$	4.26418	+	48.7398i	0.138130	+	1.57884i	−0.538571	+	0.842580i	$0.681036\pi$
$954$	22.6121	−	8.60466i	0.732095	−	0.278586i
$955$	−2.47822	−	1.01393i	−0.0801934	−	0.0328102i
$956$	13.9453	+	16.6193i	0.451023	+	0.537508i
$957$	−19.7216	−	16.3055i	−0.637510	−	0.527081i
$958$	7.15980	+	26.7207i	0.231323	+	0.863308i
$959$	0.483763	+	2.74356i	0.0156215	+	0.0885941i
$960$	3.79066	+	0.794300i	0.122343	+	0.0256359i
$961$	−24.2071	+	41.9279i	−0.780874	+	1.35251i
$962$	−33.8004	−	9.05680i	−1.08977	−	0.292003i
$963$	−20.3585	−	28.1930i	−0.656043	−	0.908507i
$964$	−7.08251	−	19.4590i	−0.228112	−	0.626734i
$965$	4.35305	−	14.0180i	0.140130	−	0.451254i
$966$	−21.5161	+	10.2243i	−0.692270	+	0.328962i
$967$	2.44428	−	1.71151i	0.0786029	−	0.0550383i	−0.533614	−	0.845728i	$-0.679167\pi$
$967$	2.44428	−	1.71151i	0.0786029	−	0.0550383i	0.612217	+	0.790690i	$0.290278\pi$
$968$	−2.99594	−	2.99594i	−0.0962931	−	0.0962931i
$969$	−11.4019	+	13.5393i	−0.366283	+	0.434946i
$970$	−4.56903	+	5.02988i	−0.146703	+	0.161500i
$971$	−3.21877	−	0.567557i	−0.103295	−	0.0182138i	0.121762	−	0.992559i	$-0.461146\pi$
$971$	−3.21877	−	0.567557i	−0.103295	−	0.0182138i	−0.225057	+	0.974346i	$0.572257\pi$
$972$	7.29824	−	13.7745i	0.234091	−	0.441816i
$973$	20.6711	−	9.63907i	0.662683	−	0.309014i
$974$	−5.89709	+	2.14636i	−0.188955	+	0.0687739i
$975$	8.96303	+	23.4546i	0.287047	+	0.751149i
$976$	3.55930	+	6.16488i	0.113930	+	0.197333i
$977$	−12.3994	−	46.2751i	−0.396691	−	1.48047i	−0.818881	−	0.573964i	$-0.805405\pi$
$977$	−12.3994	−	46.2751i	−0.396691	−	1.48047i	0.422190	−	0.906508i	$-0.361262\pi$
$978$	1.31377	+	2.23776i	0.0420096	+	0.0715557i
$979$	−1.16769	+	0.205895i	−0.0373194	+	0.00658042i
$980$	1.55536	+	4.85934i	0.0496843	+	0.155226i
$981$	−20.0491	+	57.6817i	−0.640120	+	1.84164i
$982$	13.0989	+	1.14600i	0.418002	+	0.0365704i
$983$	55.6339	+	25.9425i	1.77445	+	0.827438i	0.973495	+	0.228709i	$0.0734503\pi$
$983$	55.6339	+	25.9425i	1.77445	+	0.827438i	0.800951	+	0.598729i	$0.204327\pi$
$984$	6.21631	+	6.12654i	0.198169	+	0.195307i
$985$	−28.5956	+	37.6033i	−0.911130	+	1.19814i
$986$	13.1169	+	2.31286i	0.417727	+	0.0736566i
$987$	−4.25889	−	11.4416i	−0.135562	−	0.364190i
$988$	12.4652	−	2.08179i	0.396571	−	0.0662306i
$989$	−49.3884			−1.57046
$990$	−9.64956	−	14.5336i	−0.306683	−	0.461908i
$991$	0.247060	+	0.207308i	0.00784813	+	0.00658536i	0.646703	−	0.762742i	$-0.276147\pi$
$991$	0.247060	+	0.207308i	0.00784813	+	0.00658536i	−0.638855	+	0.769327i	$0.720592\pi$
$992$	−8.07653	+	3.76615i	−0.256430	+	0.119575i
$993$	27.3674	+	32.1376i	0.868479	+	1.01986i
$994$	−18.8402	−	22.4529i	−0.597576	−	0.712163i
$995$	2.65811	−	12.2411i	0.0842677	−	0.388070i
$996$	10.1376	−	7.20887i	0.321222	−	0.228422i
$997$	−21.0064	+	30.0003i	−0.665280	+	0.950118i	0.334690	+	0.942328i	$0.391369\pi$
$997$	−21.0064	+	30.0003i	−0.665280	+	0.950118i	−0.999970	+	0.00778985i	$0.997520\pi$
$998$	−10.2990	+	14.7084i	−0.326008	+	0.465587i
$999$	−60.9167	−	14.9060i	−1.92732	−	0.471606i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bi.a.17.9	✓	480
3.2	odd	2	inner	570.2.bi.a.17.28	yes	480
5.3	odd	4	inner	570.2.bi.a.473.2	yes	480
15.8	even	4	inner	570.2.bi.a.473.38	yes	480
19.9	even	9	inner	570.2.bi.a.47.38	yes	480
57.47	odd	18	inner	570.2.bi.a.47.2	yes	480
95.28	odd	36	inner	570.2.bi.a.503.28	yes	480
285.218	even	36	inner	570.2.bi.a.503.9	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bi.a.17.9	✓	480	1.1	even	1	trivial
570.2.bi.a.17.28	yes	480	3.2	odd	2	inner
570.2.bi.a.47.2	yes	480	57.47	odd	18	inner
570.2.bi.a.47.38	yes	480	19.9	even	9	inner
570.2.bi.a.473.2	yes	480	5.3	odd	4	inner
570.2.bi.a.473.38	yes	480	15.8	even	4	inner
570.2.bi.a.503.9	yes	480	285.218	even	36	inner
570.2.bi.a.503.28	yes	480	95.28	odd	36	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)

\(f(q)\)	\(=\)	\(q+(-0.573576 - 0.819152i) q^{2} +(-0.580543 + 1.63186i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(0.846732 - 2.06955i) q^{5} +(1.66973 - 0.460444i) q^{6} +(0.562193 - 2.09813i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-2.32594 - 1.89473i) q^{9} +O(q^{10})\)	\(q+(-0.573576 - 0.819152i) q^{2} +(-0.580543 + 1.63186i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(0.846732 - 2.06955i) q^{5} +(1.66973 - 0.460444i) q^{6} +(0.562193 - 2.09813i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-2.32594 - 1.89473i) q^{9} +(-2.18094 + 0.493443i) q^{10} +(-2.25218 - 1.30030i) q^{11} +(-1.33489 - 1.10366i) q^{12} +(-0.252692 + 2.88829i) q^{13} +(-2.04115 + 0.742919i) q^{14} +(2.88566 + 2.58321i) q^{15} +(-0.766044 - 0.642788i) q^{16} +(-1.34476 - 1.92052i) q^{17} +(-0.217968 + 2.99207i) q^{18} +(-3.59309 + 2.46774i) q^{19} +(1.65514 + 1.50350i) q^{20} +(3.09749 + 2.13548i) q^{21} +(0.226657 + 2.59070i) q^{22} +(-2.67592 - 5.73853i) q^{23} +(-0.138405 + 1.72651i) q^{24} +(-3.56609 - 3.50471i) q^{25} +(2.51089 - 1.44966i) q^{26} +(4.44224 - 2.69564i) q^{27} +(1.77932 + 1.24589i) q^{28} +(-0.986495 - 5.59469i) q^{29} +(0.460900 - 3.84546i) q^{30} +(4.45573 + 7.71755i) q^{31} +(-0.0871557 + 0.996195i) q^{32} +(3.42939 - 2.92037i) q^{33} +(-0.801875 + 2.20313i) q^{34} +(-3.86617 - 2.94005i) q^{35} +(2.57598 - 1.53763i) q^{36} +(-8.53429 - 8.53429i) q^{37} +(4.08236 + 1.52785i) q^{38} +(-4.56659 - 2.08913i) q^{39} +(0.282241 - 2.21818i) q^{40} +(3.23906 - 3.86016i) q^{41} +(-0.0273638 - 3.76217i) q^{42} +(3.29646 - 7.06928i) q^{43} +(1.99217 - 1.67163i) q^{44} +(-5.89069 + 3.20932i) q^{45} +(-3.16588 + 5.48347i) q^{46} +(-2.65814 - 1.86125i) q^{47} +(1.49366 - 0.876912i) q^{48} +(1.97607 + 1.14089i) q^{49} +(-0.825469 + 4.93139i) q^{50} +(3.91472 - 1.07952i) q^{51} +(-2.62768 - 1.22531i) q^{52} +(-3.40827 - 7.30907i) q^{53} +(-4.75610 - 2.09272i) q^{54} +(-4.59803 + 3.56000i) q^{55} -2.17215i q^{56} +(-1.94107 - 7.29604i) q^{57} +(-4.01707 + 4.01707i) q^{58} +(-0.302793 + 1.71723i) q^{59} +(-3.41438 + 1.82812i) q^{60} +(-6.68929 - 2.43470i) q^{61} +(3.76615 - 8.07653i) q^{62} +(-5.28303 + 3.81493i) q^{63} +(0.866025 - 0.500000i) q^{64} +(5.76350 + 2.96857i) q^{65} +(-4.35925 - 1.13414i) q^{66} +(1.05816 - 1.51120i) q^{67} +(2.26464 - 0.606808i) q^{68} +(10.9180 - 1.03527i) q^{69} +(-0.190801 + 4.85332i) q^{70} +(4.61510 + 12.6799i) q^{71} +(-2.73708 - 1.22817i) q^{72} +(14.3468 - 1.25518i) q^{73} +(-2.09581 + 11.8859i) q^{74} +(7.78947 - 3.78472i) q^{75} +(-1.09001 - 4.22041i) q^{76} +(-3.99436 + 3.99436i) q^{77} +(0.907968 + 4.93901i) q^{78} +(-7.19735 + 8.57747i) q^{79} +(-1.97892 + 1.04110i) q^{80} +(1.82000 + 8.81406i) q^{81} +(-5.01990 - 0.439185i) q^{82} +(-1.85881 + 6.93717i) q^{83} +(-3.06610 + 2.18031i) q^{84} +(-5.11328 + 1.15689i) q^{85} +(-7.68159 + 1.35447i) q^{86} +(9.70246 + 1.63813i) q^{87} +(-2.51198 - 0.673084i) q^{88} +(0.349266 - 0.293069i) q^{89} +(6.00769 + 2.98458i) q^{90} +(5.91796 + 2.15396i) q^{91} +(6.30767 - 0.551850i) q^{92} +(-15.1807 + 2.79076i) q^{93} +3.24499i q^{94} +(2.06473 + 9.52559i) q^{95} +(-1.57505 - 0.720560i) q^{96} +(2.48935 - 1.74306i) q^{97} +(-0.198869 - 2.27309i) q^{98} +(2.77473 + 7.29169i) 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

Related objects

Downloads

Learn more