LMFDB - Embedded newform 570.2.bi.a.17.27

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			17.27
Character	$\chi$	$=$	570.17
Dual form			570.2.bi.a.503.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.573576 + 0.819152i) q^{2} +(-0.929621 + 1.46144i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(0.0995518 + 2.23385i) q^{5} +(-1.73035 + 0.0767467i) q^{6} +(-0.252738 + 0.943230i) q^{7} +(-0.965926 + 0.258819i) q^{8} +(-1.27161 - 2.71717i) q^{9} +O(q^{10})$	\(q+(0.573576 + 0.819152i) q^{2} +(-0.929621 + 1.46144i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(0.0995518 + 2.23385i) q^{5} +(-1.73035 + 0.0767467i) q^{6} +(-0.252738 + 0.943230i) q^{7} +(-0.965926 + 0.258819i) q^{8} +(-1.27161 - 2.71717i) q^{9} +(-1.77276 + 1.36283i) q^{10} +(4.69691 + 2.71176i) q^{11} +(-1.05536 - 1.37340i) q^{12} +(-0.275849 + 3.15296i) q^{13} +(-0.917613 + 0.333984i) q^{14} +(-3.35718 - 1.93114i) q^{15} +(-0.766044 - 0.642788i) q^{16} +(-0.477318 - 0.681681i) q^{17} +(1.49641 - 2.60015i) q^{18} +(-4.08584 - 1.51853i) q^{19} +(-2.13318 - 0.670474i) q^{20} +(-1.14352 - 1.24621i) q^{21} +(0.472691 + 5.40289i) q^{22} +(-1.92067 - 4.11888i) q^{23} +(0.519696 - 1.65225i) q^{24} +(-4.98018 + 0.444768i) q^{25} +(-2.74098 + 1.58250i) q^{26} +(5.15309 + 0.667553i) q^{27} +(-0.799904 - 0.560099i) q^{28} +(-0.154429 - 0.875809i) q^{29} +(-0.343700 - 3.85770i) q^{30} +(-2.15711 - 3.73622i) q^{31} +(0.0871557 - 0.996195i) q^{32} +(-8.32942 + 4.34334i) q^{33} +(0.284622 - 0.781993i) q^{34} +(-2.13219 - 0.470678i) q^{35} +(2.98822 - 0.265597i) q^{36} +(6.54753 + 6.54753i) q^{37} +(-1.09964 - 4.21791i) q^{38} +(-4.35143 - 3.33420i) q^{39} +(-0.674323 - 2.13197i) q^{40} +(7.34143 - 8.74918i) q^{41} +(0.364935 - 1.65151i) q^{42} +(-0.862733 + 1.85014i) q^{43} +(-4.15466 + 3.48617i) q^{44} +(5.94316 - 3.11109i) q^{45} +(2.27234 - 3.93581i) q^{46} +(-6.22912 - 4.36168i) q^{47} +(1.65153 - 0.521979i) q^{48} +(5.23637 + 3.02322i) q^{49} +(-3.22085 - 3.82442i) q^{50} +(1.43996 - 0.0638670i) q^{51} +(-2.86847 - 1.33759i) q^{52} +(5.20619 + 11.1647i) q^{53} +(2.40887 + 4.60406i) q^{54} +(-5.59009 + 10.7622i) q^{55} -0.976503i q^{56} +(6.01751 - 4.55955i) q^{57} +(0.628844 - 0.628844i) q^{58} +(0.414295 - 2.34958i) q^{59} +(2.96291 - 2.49423i) q^{60} +(-2.34544 - 0.853669i) q^{61} +(1.82327 - 3.91001i) q^{62} +(2.88430 - 0.512691i) q^{63} +(0.866025 - 0.500000i) q^{64} +(-7.07071 - 0.302321i) q^{65} +(-8.33542 - 4.33182i) q^{66} +(-6.40716 + 9.15037i) q^{67} +(0.803823 - 0.215384i) q^{68} +(7.80499 + 1.02206i) q^{69} +(-0.837420 - 2.01656i) q^{70} +(5.27765 + 14.5002i) q^{71} +(1.93154 + 2.29547i) q^{72} +(-4.10473 + 0.359117i) q^{73} +(-1.60791 + 9.11893i) q^{74} +(3.97968 - 7.69170i) q^{75} +(2.82439 - 3.32007i) q^{76} +(-3.74490 + 3.74490i) q^{77} +(0.235335 - 5.47690i) q^{78} +(-2.85709 + 3.40495i) q^{79} +(1.35963 - 1.77522i) q^{80} +(-5.76601 + 6.91036i) q^{81} +(11.3778 + 0.995427i) q^{82} +(-2.32252 + 8.66776i) q^{83} +(1.56216 - 0.648332i) q^{84} +(1.47526 - 1.13412i) q^{85} +(-2.01039 + 0.354485i) q^{86} +(1.42350 + 0.588482i) q^{87} +(-5.23872 - 1.40371i) q^{88} +(9.51138 - 7.98099i) q^{89} +(5.95731 + 3.08390i) q^{90} +(-2.90425 - 1.05706i) q^{91} +(4.52739 - 0.396095i) q^{92} +(7.46555 + 0.320784i) q^{93} -7.60435i q^{94} +(2.98541 - 9.27833i) q^{95} +(1.37486 + 1.05346i) q^{96} +(4.15309 - 2.90803i) q^{97} +(0.526982 + 6.02343i) q^{98} +(1.39567 - 16.2106i) 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
$3$	−0.929621	+	1.46144i	−0.536717	+	0.843763i
$3$	−0.929621	+	1.46144i	−0.536717	+	0.843763i
$4$	−0.342020	+	0.939693i	−0.171010	+	0.469846i
$5$	0.0995518	+	2.23385i	0.0445209	+	0.999008i
$5$	0.0995518	+	2.23385i	0.0445209	+	0.999008i
$6$	−1.73035	+	0.0767467i	−0.706412	+	0.0313317i
$7$	−0.252738	+	0.943230i	−0.0955258	+	0.356507i	−0.997099	−	0.0761201i	$-0.975747\pi$
$7$	−0.252738	+	0.943230i	−0.0955258	+	0.356507i	0.901573	+	0.432627i	$0.142413\pi$
$8$	−0.965926	+	0.258819i	−0.341506	+	0.0915064i
$9$	−1.27161	−	2.71717i	−0.423870	−	0.905723i
$10$	−1.77276	+	1.36283i	−0.560597	+	0.430965i
$11$	4.69691	+	2.71176i	1.41617	+	0.817627i	0.995960	−	0.0897990i	$-0.0286225\pi$
$11$	4.69691	+	2.71176i	1.41617	+	0.817627i	0.420212	+	0.907426i	$0.361956\pi$
$12$	−1.05536	−	1.37340i	−0.304655	−	0.396466i
$13$	−0.275849	+	3.15296i	−0.0765066	+	0.874475i	0.856860	+	0.515550i	$0.172412\pi$
$13$	−0.275849	+	3.15296i	−0.0765066	+	0.874475i	−0.933366	+	0.358925i	$0.883143\pi$
$14$	−0.917613	+	0.333984i	−0.245242	+	0.0892609i
$15$	−3.35718	−	1.93114i	−0.866821	−	0.498619i
$16$	−0.766044	−	0.642788i	−0.191511	−	0.160697i
$17$	−0.477318	−	0.681681i	−0.115767	−	0.165332i	0.757087	−	0.653314i	$-0.226622\pi$
$17$	−0.477318	−	0.681681i	−0.115767	−	0.165332i	−0.872854	+	0.487982i	$0.837733\pi$
$18$	1.49641	−	2.60015i	0.352707	−	0.612860i
$19$	−4.08584	−	1.51853i	−0.937356	−	0.348374i
$19$	−4.08584	−	1.51853i	−0.937356	−	0.348374i
$20$	−2.13318	−	0.670474i	−0.476994	−	0.149923i
$21$	−1.14352	−	1.24621i	−0.249537	−	0.271944i
$22$	0.472691	+	5.40289i	0.100778	+	1.15190i
$23$	−1.92067	−	4.11888i	−0.400487	−	0.858847i	−0.998360	−	0.0572557i	$-0.981765\pi$
$23$	−1.92067	−	4.11888i	−0.400487	−	0.858847i	0.597873	−	0.801591i	$-0.296013\pi$
$24$	0.519696	−	1.65225i	0.106083	−	0.337263i
$25$	−4.98018	+	0.444768i	−0.996036	+	0.0889535i
$26$	−2.74098	+	1.58250i	−0.537550	+	0.310354i
$27$	5.15309	+	0.667553i	0.991713	+	0.128471i
$28$	−0.799904	−	0.560099i	−0.151168	−	0.105849i
$29$	−0.154429	−	0.875809i	−0.0286767	−	0.162634i	0.967106	−	0.254372i	$-0.0818688\pi$
$29$	−0.154429	−	0.875809i	−0.0286767	−	0.162634i	−0.995783	+	0.0917384i	$0.970758\pi$
$30$	−0.343700	−	3.85770i	−0.0627508	−	0.704317i
$31$	−2.15711	−	3.73622i	−0.387428	−	0.671045i	0.604675	−	0.796472i	$-0.293303\pi$
$31$	−2.15711	−	3.73622i	−0.387428	−	0.671045i	−0.992103	+	0.125428i	$0.959970\pi$
$32$	0.0871557	−	0.996195i	0.0154071	−	0.176104i
$33$	−8.32942	+	4.34334i	−1.44997	+	0.756078i
$34$	0.284622	−	0.781993i	0.0488123	−	0.134111i
$35$	−2.13219	−	0.470678i	−0.360407	−	0.0795591i
$36$	2.98822	−	0.265597i	0.498037	−	0.0442662i
$37$	6.54753	+	6.54753i	1.07641	+	1.07641i	0.996829	+	0.0795791i	$0.0253576\pi$
$37$	6.54753	+	6.54753i	1.07641	+	1.07641i	0.0795791	+	0.996829i	$0.474642\pi$
$38$	−1.09964	−	4.21791i	−0.178385	−	0.684236i
$39$	−4.35143	−	3.33420i	−0.696787	−	0.533898i
$40$	−0.674323	−	2.13197i	−0.106620	−	0.337094i
$41$	7.34143	−	8.74918i	1.14654	−	1.36639i	0.226763	−	0.973950i	$-0.427186\pi$
$41$	7.34143	−	8.74918i	1.14654	−	1.36639i	0.919777	−	0.392442i	$-0.128370\pi$
$42$	0.364935	−	1.65151i	0.0563106	−	0.254834i
$43$	−0.862733	+	1.85014i	−0.131566	+	0.282143i	−0.961044	−	0.276396i	$-0.910860\pi$
$43$	−0.862733	+	1.85014i	−0.131566	+	0.282143i	0.829478	+	0.558539i	$0.188638\pi$
$44$	−4.15466	+	3.48617i	−0.626339	+	0.525561i
$45$	5.94316	−	3.11109i	0.885954	−	0.463774i
$46$	2.27234	−	3.93581i	0.335039	−	0.580304i
$47$	−6.22912	−	4.36168i	−0.908611	−	0.636216i	0.0229757	−	0.999736i	$-0.492686\pi$
$47$	−6.22912	−	4.36168i	−0.908611	−	0.636216i	−0.931586	+	0.363520i	$0.881575\pi$
$48$	1.65153	−	0.521979i	0.238377	−	0.0753412i
$49$	5.23637	+	3.02322i	0.748053	+	0.431889i
$50$	−3.22085	−	3.82442i	−0.455496	−	0.540854i
$51$	1.43996	−	0.0638670i	0.201635	−	0.00894318i
$52$	−2.86847	−	1.33759i	−0.397785	−	0.185490i
$53$	5.20619	+	11.1647i	0.715125	+	1.53359i	0.840697	+	0.541506i	$0.182146\pi$
$53$	5.20619	+	11.1647i	0.715125	+	1.53359i	−0.125571	+	0.992085i	$0.540076\pi$
$54$	2.40887	+	4.60406i	0.327805	+	0.626533i
$55$	−5.59009	+	10.7622i	−0.753767	+	1.45117i
$56$		−	0.976503i		−	0.130491i
$57$	6.01751	−	4.55955i	0.797039	−	0.603928i
$58$	0.628844	−	0.628844i	0.0825713	−	0.0825713i
$59$	0.414295	−	2.34958i	0.0539366	−	0.305890i	−0.945890	−	0.324486i	$-0.894809\pi$
$59$	0.414295	−	2.34958i	0.0539366	−	0.305890i	0.999827	+	0.0185964i	$0.00591977\pi$
$60$	2.96291	−	2.49423i	0.382510	−	0.322004i
$61$	−2.34544	−	0.853669i	−0.300302	−	0.109301i	0.187474	−	0.982269i	$-0.439970\pi$
$61$	−2.34544	−	0.853669i	−0.300302	−	0.109301i	−0.487777	+	0.872968i	$0.662192\pi$
$62$	1.82327	−	3.91001i	0.231555	−	0.496571i
$63$	2.88430	−	0.512691i	0.363387	−	0.0645930i
$64$	0.866025	−	0.500000i	0.108253	−	0.0625000i
$65$	−7.07071	−	0.302321i	−0.877014	−	0.0374984i
$66$	−8.33542	−	4.33182i	−1.02602	−	0.533211i
$67$	−6.40716	+	9.15037i	−0.782759	+	1.11790i	0.207442	+	0.978247i	$0.433486\pi$
$67$	−6.40716	+	9.15037i	−0.782759	+	1.11790i	−0.990201	+	0.139649i	$0.955403\pi$
$68$	0.803823	−	0.215384i	0.0974779	−	0.0261191i
$69$	7.80499	+	1.02206i	0.939611	+	0.123042i
$70$	−0.837420	−	2.01656i	−0.100091	−	0.241025i
$71$	5.27765	+	14.5002i	0.626342	+	1.72086i	0.690903	+	0.722948i	$0.257213\pi$
$71$	5.27765	+	14.5002i	0.626342	+	1.72086i	−0.0645603	+	0.997914i	$0.520564\pi$
$72$	1.93154	+	2.29547i	0.227634	+	0.270523i
$73$	−4.10473	+	0.359117i	−0.480422	+	0.0420315i	−0.324795	−	0.945784i	$-0.605295\pi$
$73$	−4.10473	+	0.359117i	−0.480422	+	0.0420315i	−0.155627	+	0.987816i	$0.549740\pi$
$74$	−1.60791	+	9.11893i	−0.186916	+	1.06005i
$75$	3.97968	−	7.69170i	0.459533	−	0.888161i
$76$	2.82439	−	3.32007i	0.323979	−	0.380838i
$77$	−3.74490	+	3.74490i	−0.426771	+	0.426771i
$78$	0.235335	−	5.47690i	0.0266464	−	0.620137i
$79$	−2.85709	+	3.40495i	−0.321448	+	0.383087i	−0.902435	−	0.430826i	$-0.858222\pi$
$79$	−2.85709	+	3.40495i	−0.321448	+	0.383087i	0.580987	+	0.813913i	$0.302667\pi$
$80$	1.35963	−	1.77522i	0.152011	−	0.198476i
$81$	−5.76601	+	6.91036i	−0.640668	+	0.767818i
$82$	11.3778	+	0.995427i	1.25647	+	0.109927i
$83$	−2.32252	+	8.66776i	−0.254930	+	0.951411i	0.713200	+	0.700961i	$0.247245\pi$
$83$	−2.32252	+	8.66776i	−0.254930	+	0.951411i	−0.968130	+	0.250450i	$0.919421\pi$
$84$	1.56216	−	0.648332i	0.170445	−	0.0707389i
$85$	1.47526	−	1.13412i	0.160014	−	0.123013i
$86$	−2.01039	+	0.354485i	−0.216786	+	0.0382251i
$87$	1.42350	+	0.588482i	0.152615	+	0.0630919i
$88$	−5.23872	−	1.40371i	−0.558450	−	0.149636i
$89$	9.51138	−	7.98099i	1.00820	−	0.845983i	0.0201041	−	0.999798i	$-0.493600\pi$
$89$	9.51138	−	7.98099i	1.00820	−	0.845983i	0.988100	+	0.153814i	$0.0491558\pi$
$90$	5.95731	+	3.08390i	0.627956	+	0.325072i
$91$	−2.90425	−	1.05706i	−0.304448	−	0.110810i
$92$	4.52739	−	0.396095i	0.472013	−	0.0412958i
$93$	7.46555	+	0.320784i	0.774142	+	0.0332638i
$94$		−	7.60435i		−	0.784329i
$95$	2.98541	−	9.27833i	0.306296	−	0.951936i
$96$	1.37486	+	1.05346i	0.140321	+	0.107518i
$97$	4.15309	−	2.90803i	0.421683	−	0.295265i	−0.343410	−	0.939186i	$-0.611582\pi$
$97$	4.15309	−	2.90803i	0.421683	−	0.295265i	0.765093	+	0.643920i	$0.222693\pi$
$98$	0.526982	+	6.02343i	0.0532332	+	0.608459i
$99$	1.39567	−	16.2106i	0.140270	−	1.62923i
$100$	1.28538	−	4.83196i	0.128538	−	0.483196i
$101$	−1.20001	−	1.43012i	−0.119406	−	0.142302i	0.703030	−	0.711160i	$-0.251830\pi$
$101$	−1.20001	−	1.43012i	−0.119406	−	0.142302i	−0.822436	+	0.568858i	$0.807385\pi$
$102$	0.878245	+	1.14291i	0.0869592	+	0.113165i
$103$	−0.274756	−	1.02540i	−0.0270725	−	0.101036i	0.951068	−	0.308983i	$-0.0999886\pi$
$103$	−0.274756	−	1.02540i	−0.0270725	−	0.101036i	−0.978140	+	0.207947i	$0.933322\pi$
$104$	−0.549598	−	3.11692i	−0.0538925	−	0.305639i
$105$	2.67000	−	2.67852i	0.260565	−	0.261397i
$106$	−6.15945	+	10.6685i	−0.598258	+	1.03621i
$107$	16.1151	+	4.31802i	1.55790	+	0.417439i	0.931999	−	0.362462i	$-0.118064\pi$
$107$	16.1151	+	4.31802i	1.55790	+	0.417439i	0.625903	+	0.779901i	$0.284730\pi$
$108$	−2.38976	+	4.61401i	−0.229954	+	0.443983i
$109$	−0.548567	−	1.50718i	−0.0525432	−	0.144361i	0.910645	−	0.413190i	$-0.135586\pi$
$109$	−0.548567	−	1.50718i	−0.0525432	−	0.144361i	−0.963188	+	0.268829i	$0.913363\pi$
$110$	−12.0222	+	1.59379i	−1.14627	+	0.151962i
$111$	−15.6555	+	3.48210i	−1.48596	+	0.330507i
$112$	0.799904	−	0.560099i	0.0755839	−	0.0529244i
$113$	9.37756	+	9.37756i	0.882167	+	0.882167i	0.993755	−	0.111588i	$-0.0355937\pi$
$113$	9.37756	+	9.37756i	0.882167	+	0.882167i	−0.111588	+	0.993755i	$0.535594\pi$
$114$	7.18647	+	2.31401i	0.673075	+	0.216726i
$115$	9.00977	−	4.70053i	0.840165	−	0.438326i
$116$	0.875809	+	0.154429i	0.0813168	+	0.0143383i
$117$	8.91790	−	3.25982i	0.824460	−	0.301370i
$118$	2.16230	−	1.00829i	0.199055	−	0.0928211i
$119$	0.763618	−	0.277934i	0.0700008	−	0.0254782i
$120$	3.74261	+	0.996440i	0.341652	+	0.0909621i
$121$	9.20731	+	15.9475i	0.837028	+	1.44978i
$122$	−0.646003	−	2.41091i	−0.0584863	−	0.218274i
$123$	5.96165	+	18.8625i	0.537544	+	1.70077i
$124$	4.24867	−	0.749156i	0.381542	−	0.0672762i
$125$	−1.48933	−	11.0807i	−0.133210	−	0.991088i
$126$	2.07434	+	2.06861i	0.184797	+	0.184287i
$127$	−4.43701	−	0.388188i	−0.393721	−	0.0344461i	−0.111423	−	0.993773i	$-0.535541\pi$
$127$	−4.43701	−	0.388188i	−0.393721	−	0.0344461i	−0.282297	+	0.959327i	$0.591096\pi$
$128$	0.906308	+	0.422618i	0.0801070	+	0.0373545i
$129$	−1.90185	−	2.98076i	−0.167448	−	0.262441i
$130$	−3.80795	−	5.96539i	−0.333979	−	0.523199i
$131$	−0.165185	−	0.0291266i	−0.0144323	−	0.00254481i	0.166427	−	0.986054i	$-0.446777\pi$
$131$	−0.165185	−	0.0291266i	−0.0144323	−	0.00254481i	−0.180860	+	0.983509i	$0.557888\pi$
$132$	−1.23258	−	9.31260i	−0.107282	−	0.810558i
$133$	2.46496	−	3.47010i	0.213739	−	0.300895i
$134$	−11.1705			−0.964988
$135$	−0.978213	+	11.5777i	−0.0841912	+	0.996450i
$136$	0.637486	+	0.534914i	0.0546640	+	0.0458685i
$137$	11.2892	−	5.26423i	0.964499	−	0.449753i	0.124428	−	0.992229i	$-0.460291\pi$
$137$	11.2892	−	5.26423i	0.964499	−	0.449753i	0.840072	+	0.542475i	$0.182513\pi$
$138$	3.63954	+	6.97970i	0.309818	+	0.594152i
$139$	−8.45969	−	10.0819i	−0.717542	−	0.855133i	0.276848	−	0.960914i	$-0.410710\pi$
$139$	−8.45969	−	10.0819i	−0.717542	−	0.855133i	−0.994389	+	0.105781i	$0.966266\pi$
$140$	1.17155	−	1.84263i	0.0990137	−	0.155730i
$141$	12.1650	−	5.04878i	1.02448	−	0.425184i
$142$	−8.85076	+	12.6402i	−0.742739	+	1.06074i
$143$	−9.84572	+	14.0611i	−0.823341	+	1.17585i
$144$	−0.772451	+	2.89885i	−0.0643710	+	0.241571i
$145$	1.94105	−	0.432159i	0.161196	−	0.0358889i
$146$	−2.64855	−	3.15641i	−0.219195	−	0.261227i
$147$	−9.28609	+	4.84219i	−0.765904	+	0.399377i
$148$	−8.39206	+	3.91328i	−0.689823	+	0.321670i
$149$	8.34480	+	7.00212i	0.683633	+	0.573636i	0.917065	−	0.398737i	$-0.130551\pi$
$149$	8.34480	+	7.00212i	0.683633	+	0.573636i	−0.233433	+	0.972373i	$0.574996\pi$
$150$	8.58332	−	1.15182i	0.700825	−	0.0940454i
$151$	−21.3819			−1.74003			−0.870016	−	0.493024i	$-0.835891\pi$
$151$	−21.3819			−1.74003			−0.870016	+	0.493024i	$0.835891\pi$
$152$	4.33964	+	0.409290i	0.351991	+	0.0331978i
$153$	−1.24528	+	2.16379i	−0.100675	+	0.174932i
$154$	−5.21563	−	0.919656i	−0.420287	−	0.0741080i
$155$	8.13141	−	5.19060i	0.653131	−	0.416919i
$156$	4.62140	−	2.94865i	0.370008	−	0.236081i
$157$	13.2633	+	6.18477i	1.05852	+	0.493598i	0.872331	−	0.488915i	$-0.162607\pi$
$157$	13.2633	+	6.18477i	1.05852	+	0.493598i	0.186193	+	0.982513i	$0.440385\pi$
$158$	−4.42793	−	0.387394i	−0.352267	−	0.0308194i
$159$	−21.1563	−	2.77041i	−1.67781	−	0.219708i
$160$	2.23403	+	0.0955200i	0.176615	+	0.00755152i
$161$	4.37048	−	0.770633i	0.344442	−	0.0607344i
$162$	−8.96789	−	0.759616i	−0.704584	−	0.0596811i
$163$	−4.63271	−	17.2895i	−0.362862	−	1.35422i	−0.870296	−	0.492529i	$-0.836073\pi$
$163$	−4.63271	−	17.2895i	−0.362862	−	1.35422i	0.507434	−	0.861690i	$-0.330594\pi$
$164$	5.71062	+	9.89109i	0.445925	+	0.772364i
$165$	−10.5316	−	18.1743i	−0.819883	−	1.41487i
$166$	−8.43236	+	3.06913i	−0.654478	+	0.238211i
$167$	15.5157	−	7.23507i	1.20064	−	0.559866i	0.283706	−	0.958911i	$-0.408436\pi$
$167$	15.5157	−	7.23507i	1.20064	−	0.559866i	0.916931	+	0.399045i	$0.130658\pi$
$168$	1.42710	+	0.907777i	0.110103	+	0.0700365i
$169$	2.93742	+	0.517946i	0.225955	+	0.0398420i
$170$	1.77519	+	0.557954i	0.136151	+	0.0427932i
$171$	1.06951	+	13.0329i	0.0817875	+	0.996650i
$172$	−1.44349	−	1.44349i	−0.110065	−	0.110065i
$173$	−4.75142	+	3.32698i	−0.361244	+	0.252946i	−0.740081	−	0.672518i	$-0.765213\pi$
$173$	−4.75142	+	3.32698i	−0.361244	+	0.252946i	0.378837	+	0.925463i	$0.376324\pi$
$174$	0.334431	+	1.50360i	0.0253532	+	0.113988i
$175$	0.839160	−	4.80986i	0.0634346	−	0.363591i
$176$	−1.85495	−	5.09645i	−0.139822	−	0.384159i
$177$	3.04864	+	2.78969i	0.229150	+	0.209686i
$178$	11.9931	+	3.21355i	0.898924	+	0.240866i
$179$	−3.38097	+	5.85601i	−0.252706	+	0.437699i	−0.964270	−	0.264922i	$-0.914654\pi$
$179$	−3.38097	+	5.85601i	−0.252706	+	0.437699i	0.711564	+	0.702621i	$0.247987\pi$
$180$	0.890788	+	6.64880i	0.0663954	+	0.495572i
$181$	−1.36290	−	7.72937i	−0.101303	−	0.574519i	−0.992633	−	0.121163i	$-0.961338\pi$
$181$	−1.36290	−	7.72937i	−0.101303	−	0.574519i	0.891329	−	0.453356i	$-0.149773\pi$
$182$	−0.799916	−	2.98533i	−0.0592937	−	0.221287i
$183$	3.42795	−	2.63413i	0.253402	−	0.194720i
$184$	2.92127	+	3.48143i	0.215359	+	0.256655i
$185$	−13.9744	+	15.2780i	−1.02742	+	1.12326i
$186$	4.01929	+	6.29942i	0.294709	+	0.461896i
$187$	−0.393364	−	4.49617i	−0.0287656	−	0.328792i
$188$	6.22912	−	4.36168i	0.454305	−	0.318108i
$189$	−1.93204	+	4.69183i	−0.140535	+	0.341281i
$190$	9.31272	−	2.87633i	0.675616	−	0.208671i
$191$		−	14.8936i		−	1.07767i	−0.842412	−	0.538833i	$-0.818865\pi$
$191$		−	14.8936i		−	1.07767i	0.842412	−	0.538833i	$-0.181135\pi$
$192$	−0.0743552	+	1.73045i	−0.00536613	+	0.124885i
$193$	−3.17373	+	0.277666i	−0.228450	+	0.0199868i	−0.200806	−	0.979631i	$-0.564356\pi$
$193$	−3.17373	+	0.277666i	−0.228450	+	0.0199868i	−0.0276443	+	0.999618i	$0.508801\pi$
$194$	4.76423	+	1.73404i	0.342052	+	0.124497i
$195$	7.01490	−	10.0524i	0.502348	−	0.719865i
$196$	−4.63184	+	3.88658i	−0.330846	+	0.277613i
$197$	−17.4760	−	4.68268i	−1.24511	−	0.333627i	−0.424666	−	0.905350i	$-0.639608\pi$
$197$	−17.4760	−	4.68268i	−1.24511	−	0.333627i	−0.820446	+	0.571723i	$0.806275\pi$
$198$	14.0795	−	8.15475i	1.00058	−	0.579533i
$199$	10.1460	−	1.78901i	0.719228	−	0.126819i	0.197957	−	0.980211i	$-0.436569\pi$
$199$	10.1460	−	1.78901i	0.719228	−	0.126819i	0.521271	+	0.853391i	$0.325458\pi$
$200$	4.69537	−	1.71858i	0.332013	−	0.121522i
$201$	−7.41649	−	17.8701i	−0.523119	−	1.26046i
$202$	0.483186	−	1.80328i	0.0339969	−	0.126878i
$203$	0.865119	+	0.0756881i	0.0607194	+	0.00531226i
$204$	−0.432480	+	1.37496i	−0.0302797	+	0.0962668i
$205$	20.2752	+	15.5287i	1.41608	+	1.08457i
$206$	0.682367	−	0.813213i	0.0475428	−	0.0566593i
$207$	−8.74936	+	10.4564i	−0.608123	+	0.726770i
$208$	2.23800	−	2.23800i	0.155177	−	0.155177i
$209$	−15.0729	−	18.2122i	−1.04262	−	1.25976i
$210$	3.72557	+	0.650798i	0.257088	+	0.0449094i
$211$	0.425310	−	2.41205i	0.0292795	−	0.166053i	−0.966662	−	0.256056i	$-0.917577\pi$
$211$	0.425310	−	2.41205i	0.0292795	−	0.166053i	0.995941	+	0.0900037i	$0.0286879\pi$
$212$	−12.2720	+	1.07366i	−0.842846	+	0.0737394i
$213$	−26.0974	−	5.76674i	−1.78817	−	0.395131i
$214$	5.70611	+	15.6774i	0.390061	+	1.07169i
$215$	−4.21882	−	1.74303i	−0.287721	−	0.118874i
$216$	−5.15028	+	0.688913i	−0.350432	+	0.0468746i
$217$	4.06930	−	1.09036i	0.276242	−	0.0740188i
$218$	0.919961	−	1.31384i	0.0623076	−	0.0889845i
$219$	3.29101	−	6.33265i	0.222386	−	0.427921i
$220$	−8.20120	−	8.93384i	−0.552925	−	0.602319i
$221$	2.28098	−	1.31693i	0.153436	−	0.0885861i
$222$	−11.8320	−	10.8270i	−0.794113	−	0.726662i
$223$	−7.62237	+	16.3462i	−0.510432	+	1.09462i	0.467171	+	0.884167i	$0.345273\pi$
$223$	−7.62237	+	16.3462i	−0.510432	+	1.09462i	−0.977603	+	0.210458i	$0.932505\pi$
$224$	0.917613	+	0.333984i	0.0613106	+	0.0223152i
$225$	7.54136	+	12.9664i	0.502757	+	0.864428i
$226$	−2.30290	+	13.0604i	−0.153187	+	0.868765i
$227$	0.914162	−	0.914162i	0.0606751	−	0.0606751i	−0.676118	−	0.736793i	$-0.736339\pi$
$227$	0.914162	−	0.914162i	0.0606751	−	0.0606751i	0.736793	+	0.676118i	$0.236339\pi$
$228$	2.22647	+	7.21407i	0.147452	+	0.477764i
$229$			10.6406i			0.703150i	0.936160	+	0.351575i	$0.114354\pi$
$229$			10.6406i			0.703150i	−0.936160	+	0.351575i	$0.885646\pi$
$230$	9.01824	+	4.68426i	0.594645	+	0.308871i
$231$	−1.99161	−	8.95428i	−0.131038	−	0.589148i
$232$	0.375843	+	0.805997i	0.0246753	+	0.0529163i
$233$	1.42467	+	0.664336i	0.0933334	+	0.0435221i	0.468724	−	0.883344i	$-0.344714\pi$
$233$	1.42467	+	0.664336i	0.0933334	+	0.0435221i	−0.375391	+	0.926867i	$0.622492\pi$
$234$	7.78538	+	5.43537i	0.508947	+	0.355321i
$235$	9.12322	−	14.3491i	0.595133	−	0.936035i
$236$	2.06619	+	1.19291i	0.134497	+	0.0776521i
$237$	−2.32012	−	7.34078i	−0.150708	−	0.476835i
$238$	0.665664	+	0.466103i	0.0431486	+	0.0302130i
$239$	−3.42796	+	5.93741i	−0.221736	+	0.384059i	−0.955335	−	0.295524i	$-0.904506\pi$
$239$	−3.42796	+	5.93741i	−0.221736	+	0.384059i	0.733599	+	0.679583i	$0.237839\pi$
$240$	1.33044	+	3.63730i	0.0858793	+	0.234787i
$241$	−1.69527	+	1.42250i	−0.109202	+	0.0916313i	−0.695754	−	0.718280i	$-0.744929\pi$
$241$	−1.69527	+	1.42250i	−0.109202	+	0.0916313i	0.586552	+	0.809912i	$0.300485\pi$
$242$	−7.78235	+	16.6893i	−0.500269	+	1.07283i
$243$	−4.73888	−	14.8507i	−0.303999	−	0.952672i
$244$	1.60437	−	1.91202i	0.102709	−	0.122404i
$245$	−6.23213	+	11.9982i	−0.398156	+	0.766540i
$246$	−12.0318	+	15.7026i	−0.767118	+	1.00116i
$247$	5.91493	−	12.4636i	0.376358	−	0.793041i
$248$	3.05061	+	3.05061i	0.193714	+	0.193714i
$249$	−10.5084	−	11.4520i	−0.665940	−	0.725738i
$250$	8.22253	−	7.57562i	0.520039	−	0.479124i
$251$	6.52244	−	17.9203i	0.411693	−	1.13112i	−0.544598	−	0.838698i	$-0.683318\pi$
$251$	6.52244	−	17.9203i	0.411693	−	1.13112i	0.956290	−	0.292419i	$-0.0944602\pi$
$252$	−0.504716	+	2.88570i	−0.0317941	+	0.181782i
$253$	2.14823	−	24.5544i	0.135058	−	1.54372i
$254$	−2.22698	−	3.85724i	−0.139733	−	0.242025i
$255$	0.286020	+	3.21030i	0.0179113	+	0.201037i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−18.2701	−	12.7929i	−1.13966	−	0.797998i	−0.157774	−	0.987475i	$-0.550432\pi$
$257$	−18.2701	−	12.7929i	−1.13966	−	0.797998i	−0.981885	+	0.189478i	$0.939321\pi$
$258$	1.35084	−	3.26759i	0.0840995	−	0.203432i
$259$	−7.83063	+	4.52102i	−0.486572	+	0.280922i
$260$	2.70241	−	6.54089i	0.167597	−	0.405649i
$261$	−2.18335	+	1.53330i	−0.135146	+	0.0949087i
$262$	−0.0708873	−	0.152018i	−0.00437943	−	0.00939172i
$263$	−0.820684	−	9.38046i	−0.0506055	−	0.578424i	−0.978592	−	0.205810i	$-0.934017\pi$
$263$	−0.820684	−	9.38046i	−0.0506055	−	0.578424i	0.927986	−	0.372614i	$-0.121538\pi$
$264$	6.92146	−	6.35116i	0.425987	−	0.390887i
$265$	−24.4220	+	12.7413i	−1.50023	+	0.782693i
$266$	4.25638	+	0.0288145i	0.260975	+	0.00176673i
$267$	2.82177	+	21.3196i	0.172689	+	1.30474i
$268$	−6.40716	−	9.15037i	−0.391380	−	0.558948i
$269$	9.11644	+	7.64961i	0.555839	+	0.466405i	0.876913	−	0.480650i	$-0.159599\pi$
$269$	9.11644	+	7.64961i	0.555839	+	0.466405i	−0.321073	+	0.947054i	$0.604044\pi$
$270$	−10.0450	+	5.83939i	−0.611318	+	0.355374i
$271$	21.0937	−	7.67748i	1.28135	−	0.466374i	0.390472	−	0.920615i	$-0.372312\pi$
$271$	21.0937	−	7.67748i	1.28135	−	0.466374i	0.890879	+	0.454241i	$0.150089\pi$
$272$	−0.0725292	+	0.829013i	−0.00439773	+	0.0502663i
$273$	4.24468	−	3.26172i	0.256900	−	0.197408i
$274$	10.7874	+	6.22811i	0.651691	+	0.376254i
$275$	−24.5976	−	11.4160i	−1.48329	−	0.688412i
$276$	−3.62989	+	6.98473i	−0.218494	+	0.420431i
$277$	2.87316	−	0.769861i	0.172631	−	0.0462564i	−0.171468	−	0.985190i	$-0.554851\pi$
$277$	2.87316	−	0.769861i	0.172631	−	0.0462564i	0.344099	+	0.938933i	$0.388184\pi$
$278$	3.40630	−	12.7125i	0.204297	−	0.762445i
$279$	−7.40894	+	10.6122i	−0.443561	+	0.635338i
$280$	2.18136	−	0.0972126i	0.130361	−	0.00580956i
$281$	−8.60404	+	23.6394i	−0.513274	+	1.41021i	0.364531	+	0.931191i	$0.381229\pi$
$281$	−8.60404	+	23.6394i	−0.513274	+	1.41021i	−0.877805	+	0.479018i	$0.840993\pi$
$282$	11.1133	+	7.06916i	0.661788	+	0.420963i
$283$	−2.59168	−	3.70130i	−0.154059	−	0.220019i	0.734702	−	0.678390i	$-0.237322\pi$
$283$	−2.59168	−	3.70130i	−0.154059	−	0.220019i	−0.888761	+	0.458371i	$0.848433\pi$
$284$	−15.4308			−0.915651
$285$	10.7844	+	12.9883i	0.638814	+	0.769361i
$286$	−17.1655			−1.01502
$287$	6.39703	+	9.13590i	0.377605	+	0.539275i
$288$	−2.81766	+	1.02996i	−0.166032	+	0.0606907i
$289$	5.57749	−	15.3240i	0.328087	−	0.901413i
$290$	1.46735	+	1.34214i	0.0861655	+	0.0788132i
$291$	0.389105	+	8.77285i	0.0228097	+	0.514274i
$292$	1.06644	−	3.98001i	0.0624086	−	0.232912i
$293$	27.7288	−	7.42990i	1.61993	−	0.434060i	0.668951	−	0.743307i	$-0.266744\pi$
$293$	27.7288	−	7.42990i	1.61993	−	0.434060i	0.950982	+	0.309247i	$0.100077\pi$
$294$	−9.29278	−	4.82935i	−0.541966	−	0.281654i
$295$	5.28986	+	0.691568i	0.307988	+	0.0402646i
$296$	−8.01906	−	4.62980i	−0.466098	−	0.269102i
$297$	22.3934	+	17.1094i	1.29940	+	0.992788i
$298$	−0.949419	+	10.8519i	−0.0549984	+	0.628634i
$299$	13.5165	−	4.91960i	0.781680	−	0.284508i
$300$	5.86670	+	6.37039i	0.338714	+	0.367794i
$301$	−1.52706	−	1.28135i	−0.0880182	−	0.0738560i
$302$	−12.2641	−	17.5150i	−0.705721	−	1.00787i
$303$	3.20559	−	0.424278i	0.184156	−	0.0243741i
$304$	2.15384	+	3.78958i	0.123531	+	0.217348i
$305$	1.67348	−	5.32434i	0.0958231	−	0.304871i
$306$	−2.48673	+	0.221025i	−0.142157	+	0.0126351i
$307$	−1.24589	−	14.2406i	−0.0711069	−	0.812756i	−0.945092	−	0.326804i	$-0.894028\pi$
$307$	−1.24589	−	14.2406i	−0.0711069	−	0.812756i	0.873985	−	0.485952i	$-0.161527\pi$
$308$	−2.23822	−	4.79989i	−0.127535	−	0.273499i
$309$	1.75398	+	0.551696i	0.0997806	+	0.0313849i
$310$	8.91588	+	3.68366i	0.506388	+	0.209218i
$311$	−0.756960	+	0.437031i	−0.0429233	+	0.0247818i	−0.521308	−	0.853369i	$-0.674556\pi$
$311$	−0.756960	+	0.437031i	−0.0429233	+	0.0247818i	0.478385	+	0.878150i	$0.341222\pi$
$312$	5.06611	+	2.09435i	0.286812	+	0.118569i
$313$	−2.17917	−	1.52587i	−0.123174	−	0.0862472i	0.510366	−	0.859957i	$-0.329510\pi$
$313$	−2.17917	−	1.52587i	−0.123174	−	0.0862472i	−0.633540	+	0.773710i	$0.718399\pi$
$314$	2.54124	+	14.4121i	0.143410	+	0.813320i
$315$	1.43241	+	6.39205i	0.0807072	+	0.360151i
$316$	−2.22242	−	3.84935i	−0.125021	−	0.216543i
$317$	0.291798	−	3.33527i	0.0163890	−	0.187327i	−0.983587	−	0.180433i	$-0.942250\pi$
$317$	0.291798	−	3.33527i	0.0163890	−	0.187327i	0.999976	−	0.00689398i	$-0.00219444\pi$
$318$	−9.86539	−	18.9193i	−0.553223	−	1.06094i
$319$	1.64965	−	4.53237i	0.0923625	−	0.253764i
$320$	1.20314	+	1.88480i	0.0672576	+	0.105363i
$321$	−21.2914	+	19.5371i	−1.18837	+	1.09045i
$322$	3.13807	+	3.13807i	0.174878	+	0.174878i
$323$	0.915096	+	3.51006i	0.0509173	+	0.195305i
$324$	−4.52153	−	7.78176i	−0.251196	−	0.432320i
$325$	−0.0285607	−	15.8250i	−0.00158427	−	0.877814i
$326$	11.5055	−	13.7118i	0.637232	−	0.759424i
$327$	2.71261	+	0.599404i	0.150007	+	0.0331471i
$328$	−4.82683	+	10.3512i	−0.266517	+	0.571547i
$329$	5.68840	−	4.77313i	0.313611	−	0.263151i
$330$	8.84684	−	19.0513i	0.487003	−	1.04874i
$331$	3.79766	−	6.57774i	0.208738	−	0.361545i	−0.742579	−	0.669758i	$-0.766398\pi$
$331$	3.79766	−	6.57774i	0.208738	−	0.361545i	0.951317	+	0.308213i	$0.0997310\pi$
$332$	−7.35069	−	5.14701i	−0.403421	−	0.282479i
$333$	9.46483	−	26.1167i	0.518670	−	1.43118i
$334$	14.8260	+	8.55982i	0.811245	+	0.468372i
$335$	−21.0784	−	13.4017i	−1.15164	−	0.732213i
$336$	0.0749434	+	1.68969i	0.00408850	+	0.0921802i
$337$	18.3611	+	8.56192i	1.00019	+	0.466398i	0.852551	−	0.522643i	$-0.175054\pi$
$337$	18.3611	+	8.56192i	1.00019	+	0.466398i	0.147641	+	0.989041i	$0.452832\pi$
$338$	1.26056	+	2.70327i	0.0685653	+	0.147039i
$339$	−22.4223	+	4.98717i	−1.21781	+	0.270866i
$340$	0.561157	+	1.77418i	0.0304330	+	0.0962184i
$341$		−	23.3983i		−	1.26709i
$342$	−10.0625	+	8.35145i	−0.544116	+	0.451595i
$343$	−9.00846	+	9.00846i	−0.486411	+	0.486411i
$344$	0.354485	−	2.01039i	0.0191126	−	0.108393i
$345$	−1.50613	+	17.5369i	−0.0810873	+	0.944157i
$346$	−5.45060	−	1.98386i	−0.293026	−	0.106653i
$347$	−4.44646	+	9.53547i	−0.238699	+	0.511891i	−0.988766	−	0.149470i	$-0.952243\pi$
$347$	−4.44646	+	9.53547i	−0.238699	+	0.511891i	0.750067	+	0.661361i	$0.230021\pi$
$348$	−1.03986	+	1.13638i	−0.0557423	+	0.0609165i
$349$	−26.8791	+	15.5186i	−1.43880	+	0.830694i	−0.997767	−	0.0667952i	$-0.978723\pi$
$349$	−26.8791	+	15.5186i	−1.43880	+	0.830694i	−0.441037	+	0.897489i	$0.645389\pi$
$350$	4.42133	−	2.07142i	0.236330	−	0.110722i
$351$	−3.52624	+	16.0634i	−0.188217	+	0.857399i
$352$	3.11081	−	4.44269i	0.165807	−	0.236796i
$353$	−13.7093	+	3.67339i	−0.729671	+	0.195515i	−0.604483	−	0.796618i	$-0.706620\pi$
$353$	−13.7093	+	3.67339i	−0.729671	+	0.195515i	−0.125188	+	0.992133i	$0.539953\pi$
$354$	−0.536552	+	4.09740i	−0.0285174	+	0.217774i
$355$	−31.8660	+	13.2330i	−1.69127	+	0.702336i
$356$	4.24660	+	11.6674i	0.225069	+	0.618373i
$357$	−0.303691	+	1.37436i	−0.0160730	+	0.0727386i
$358$	−6.73621	+	0.589342i	−0.356020	+	0.0311477i
$359$	1.03486	−	5.86897i	0.0546177	−	0.309752i	−0.945244	−	0.326364i	$-0.894177\pi$
$359$	1.03486	−	5.86897i	0.0546177	−	0.309752i	0.999862	+	0.0166112i	$0.00528775\pi$
$360$	−4.93544	+	4.54328i	−0.260121	+	0.239452i
$361$	14.3882	+	12.4089i	0.757272	+	0.653100i
$362$	5.54980	−	5.54980i	0.291691	−	0.291691i
$363$	−31.8656	−	1.36922i	−1.67251	−	0.0718656i
$364$	1.98662	−	2.36757i	0.104127	−	0.124094i
$365$	−1.21085	−	9.13359i	−0.0633786	−	0.478074i
$366$	4.12394	+	1.29714i	0.215562	+	0.0678027i
$367$	−17.5851	−	1.53850i	−0.917934	−	0.0803088i	−0.381612	−	0.924322i	$-0.624631\pi$
$367$	−17.5851	−	1.53850i	−0.917934	−	0.0803088i	−0.536322	+	0.844014i	$0.680187\pi$
$368$	−1.17625	+	4.38983i	−0.0613163	+	0.228836i
$369$	−33.1084	−	8.82236i	−1.72356	−	0.459274i
$370$	−20.5304	−	2.68403i	−1.06733	−	0.139536i
$371$	−11.8467	+	2.08889i	−0.615049	+	0.108450i
$372$	−2.85481	+	6.90561i	−0.148015	+	0.358039i
$373$	11.9406	+	3.19947i	0.618259	+	0.165662i	0.554336	−	0.832293i	$-0.312972\pi$
$373$	11.9406	+	3.19947i	0.618259	+	0.165662i	0.0639230	+	0.997955i	$0.479639\pi$
$374$	3.45742	−	2.90112i	0.178779	−	0.150013i
$375$	17.5783	+	8.12428i	0.907739	+	0.419536i
$376$	7.14575	+	2.60084i	0.368514	+	0.134128i
$377$	2.80399	−	0.245318i	0.144413	−	0.0126345i
$378$	−4.95150	+	1.10849i	−0.254677	+	0.0570148i
$379$			10.0904i			0.518309i	0.965836	+	0.259155i	$0.0834440\pi$
$379$			10.0904i			0.518309i	−0.965836	+	0.259155i	$0.916556\pi$
$380$	7.69771	+	5.97874i	0.394884	+	0.306703i
$381$	4.69204	−	6.12355i	0.240381	−	0.313719i
$382$	12.2002	−	8.54265i	0.624215	−	0.437080i
$383$	−1.00240	−	11.4574i	−0.0512201	−	0.585448i	−0.977827	−	0.209416i	$-0.932844\pi$
$383$	−1.00240	−	11.4574i	−0.0512201	−	0.585448i	0.926607	−	0.376032i	$-0.122712\pi$
$384$	−1.46015	+	0.931639i	−0.0745131	+	0.0475425i
$385$	−8.73836	−	7.99274i	−0.445348	−	0.407348i
$386$	−2.04783	−	2.44051i	−0.104232	−	0.124219i
$387$	6.12419	−	0.00846406i	0.311310	−	0.000430252i
$388$	1.31221	+	4.89723i	0.0666174	+	0.248619i
$389$	0.0809062	+	0.458842i	0.00410211	+	0.0232642i	0.986790	−	0.162004i	$-0.0517957\pi$
$389$	0.0809062	+	0.458842i	0.00410211	+	0.0232642i	−0.982688	+	0.185268i	$0.940685\pi$
$390$	12.2580	−	0.0195322i	0.620708	−	0.000989053i
$391$	−1.89100	+	3.27530i	−0.0956318	+	0.165639i
$392$	−5.84041	−	1.56493i	−0.294985	−	0.0790411i
$393$	0.196126	−	0.214332i	0.00989327	−	0.0108116i
$394$	−6.18799	−	17.0014i	−0.311746	−	0.856516i
$395$	−7.89058	−	6.04335i	−0.397018	−	0.304074i
$396$	14.7556	+	6.85585i	0.741499	+	0.344520i
$397$	1.03868	−	0.727290i	0.0521297	−	0.0365016i	−0.547221	−	0.836988i	$-0.684314\pi$
$397$	1.03868	−	0.727290i	0.0521297	−	0.0365016i	0.599351	+	0.800486i	$0.295425\pi$
$398$	7.28495	+	7.28495i	0.365162	+	0.365162i
$399$	2.77985	+	6.82827i	0.139167	+	0.341841i
$400$	4.10093	+	2.86049i	0.205046	+	0.143024i
$401$	6.13890	+	1.08245i	0.306562	+	0.0540552i	0.324813	−	0.945778i	$-0.394699\pi$
$401$	6.13890	+	1.08245i	0.306562	+	0.0540552i	−0.0182509	+	0.999833i	$0.505810\pi$
$402$	10.3844	−	16.3251i	0.517925	−	0.814221i
$403$	12.3752	−	5.77065i	0.616453	−	0.287457i
$404$	1.75430	−	0.638513i	0.0872797	−	0.0317672i
$405$	−16.0107	−	12.1925i	−0.795580	−	0.605848i
$406$	0.434212	+	0.752077i	0.0215496	+	0.0373249i
$407$	12.9978	+	48.5085i	0.644278	+	2.40448i
$408$	−1.37437	+	0.434380i	−0.0680412	+	0.0215050i
$409$	11.5683	−	2.03980i	0.572015	−	0.100862i	0.119844	−	0.992793i	$-0.461761\pi$
$409$	11.5683	−	2.03980i	0.572015	−	0.100862i	0.452171	+	0.891931i	$0.350650\pi$
$410$	−1.09096	+	25.5154i	−0.0538785	+	1.26011i
$411$	−2.80130	+	21.3922i	−0.138178	+	1.05520i
$412$	1.05754	+	0.0925223i	0.0521010	+	0.00455825i
$413$	2.11149	+	0.984603i	0.103900	+	0.0484491i
$414$	−13.5838	−	1.16951i	−0.667608	−	0.0574785i
$415$	−19.5937	−	4.32527i	−0.961817	−	0.212319i
$416$	3.11692	+	0.549598i	0.152820	+	0.0269462i
$417$	22.5984	−	2.99102i	1.10665	−	0.146471i
$418$	6.27308	−	22.7931i	0.306826	−	1.11485i
$419$	−22.2294			−1.08598			−0.542989	−	0.839740i	$-0.682707\pi$
$419$	−22.2294			−1.08598			−0.542989	+	0.839740i	$0.682707\pi$
$420$	1.60379	+	3.42509i	0.0782571	+	0.167127i
$421$	−28.6542	−	24.0437i	−1.39652	−	1.17182i	−0.962619	−	0.270859i	$-0.912692\pi$
$421$	−28.6542	−	24.0437i	−1.39652	−	1.17182i	−0.433901	−	0.900960i	$-0.642863\pi$
$422$	2.21979	−	1.03510i	0.108057	−	0.0503880i
$423$	−3.93039	+	22.4719i	−0.191102	+	1.09262i
$424$	−7.91843	−	9.43682i	−0.384553	−	0.458293i
$425$	2.68032	+	3.18260i	0.130015	+	0.154379i
$426$	−10.2450	−	24.6854i	−0.496374	−	1.19601i
$427$	1.39799	−	1.99653i	0.0676533	−	0.0966189i
$428$	−9.56929	+	13.6664i	−0.462549	+	0.660588i
$429$	−11.3967	−	27.4605i	−0.550239	−	1.32580i
$430$	−0.992005	−	4.45561i	−0.0478387	−	0.214869i
$431$	13.8538	+	16.5103i	0.667314	+	0.795274i	0.988416	−	0.151771i	$-0.0484975\pi$
$431$	13.8538	+	16.5103i	0.667314	+	0.795274i	−0.321102	+	0.947045i	$0.604053\pi$
$432$	−3.51840	−	3.82372i	−0.169279	−	0.183969i
$433$	27.7229	−	12.9274i	1.33228	−	0.621252i	0.379578	−	0.925160i	$-0.376069\pi$
$433$	27.7229	−	12.9274i	1.33228	−	0.621252i	0.952702	+	0.303908i	$0.0982914\pi$
$434$	3.22723	+	2.70796i	0.154912	+	0.129986i
$435$	−1.17287	+	3.23848i	−0.0562347	+	0.155273i
$436$	1.60390			0.0768130
$437$	1.59291	+	19.7457i	0.0761991	+	0.944564i
$438$	7.07505	−	0.936422i	0.338059	−	0.0447440i
$439$	38.1351	+	6.72425i	1.82009	+	0.320931i	0.976411	−	0.215920i	$-0.0692749\pi$
$439$	38.1351	+	6.72425i	1.82009	+	0.320931i	0.843678	+	0.536850i	$0.180386\pi$
$440$	2.61416	−	11.8423i	0.124625	−	0.564558i
$441$	1.55597	−	18.0725i	0.0740938	−	0.860594i
$442$	2.38708	+	1.11311i	0.113542	+	0.0529454i
$443$	−25.4937	−	2.23041i	−1.21124	−	0.105970i	−0.536420	−	0.843951i	$-0.680224\pi$
$443$	−25.4937	−	2.23041i	−1.21124	−	0.105970i	−0.674821	+	0.737982i	$0.735779\pi$
$444$	2.08241	−	15.9023i	0.0988266	−	0.754692i
$445$	18.7752	+	20.4525i	0.890031	+	0.969540i
$446$	−17.7621	+	3.13193i	−0.841058	+	0.148301i
$447$	−17.9907	+	5.68611i	−0.850930	+	0.268944i
$448$	0.252738	+	0.943230i	0.0119407	+	0.0445634i
$449$	−2.30404	−	3.99072i	−0.108735	−	0.188334i	0.806523	−	0.591202i	$-0.201347\pi$
$449$	−2.30404	−	3.99072i	−0.108735	−	0.188334i	−0.915258	+	0.402869i	$0.868013\pi$
$450$	−6.29592	+	13.6148i	−0.296792	+	0.641805i
$451$	58.2077	−	21.1859i	2.74090	−	0.997604i
$452$	−12.0193	+	5.60471i	−0.565342	+	0.263623i
$453$	19.8770	−	31.2483i	0.933904	−	1.46817i
$454$	1.27318	+	0.224496i	0.0597533	+	0.0105361i
$455$	2.07219	−	6.59289i	0.0971459	−	0.309080i
$456$	−4.63237	+	5.96164i	−0.216931	+	0.279179i
$457$	−28.7087	−	28.7087i	−1.34294	−	1.34294i	−0.893122	−	0.449815i	$-0.851490\pi$
$457$	−28.7087	−	28.7087i	−1.34294	−	1.34294i	−0.449815	−	0.893122i	$-0.648510\pi$
$458$	−8.71626	+	6.10319i	−0.407284	+	0.285183i
$459$	−2.00461	−	3.83140i	−0.0935671	−	0.178835i
$460$	1.33553	+	10.0741i	0.0622693	+	0.469707i
$461$	6.98898	+	19.2021i	0.325509	+	0.894330i	0.989233	+	0.146351i	$0.0467530\pi$
$461$	6.98898	+	19.2021i	0.325509	+	0.894330i	−0.663723	+	0.747978i	$0.731025\pi$
$462$	6.19258	−	6.76740i	0.288105	−	0.314848i
$463$	16.4644	+	4.41162i	0.765166	+	0.205026i	0.620235	−	0.784416i	$-0.287037\pi$
$463$	16.4644	+	4.41162i	0.765166	+	0.205026i	0.144931	+	0.989442i	$0.453704\pi$
$464$	−0.444660	+	0.770173i	−0.0206428	+	0.0357544i
$465$	0.0266244	+	16.7089i	0.00123468	+	0.774855i
$466$	0.272967	+	1.54807i	0.0126449	+	0.0717130i
$467$	−3.73914	−	13.9547i	−0.173027	−	0.645744i	−0.996879	−	0.0789404i	$-0.974846\pi$
$467$	−3.73914	−	13.9547i	−0.173027	−	0.645744i	0.823853	−	0.566804i	$-0.191820\pi$
$468$	0.0131228	+	9.49501i	0.000606600	+	0.438907i
$469$	−7.01157	−	8.35607i	−0.323764	−	0.385847i
$470$	16.9870	−	0.757027i	0.783551	−	0.0349190i
$471$	−21.3685	+	13.6340i	−0.984607	+	0.628221i
$472$	0.207939	+	2.37675i	0.00957115	+	0.109399i
$473$	−9.06931	+	6.35040i	−0.417007	+	0.291992i
$474$	4.68245	−	6.11102i	0.215072	−	0.280689i
$475$	21.0236	+	5.74528i	0.964629	+	0.263612i
$476$			0.812626i			0.0372466i
$477$	23.7162	−	28.3433i	1.08589	−	1.29775i
$478$	−6.82984	+	0.597533i	−0.312389	+	0.0273305i
$479$	39.1699	+	14.2567i	1.78972	+	0.651404i	0.999243	+	0.0389099i	$0.0123885\pi$
$479$	39.1699	+	14.2567i	1.78972	+	0.651404i	0.790475	+	0.612494i	$0.209834\pi$
$480$	−2.21639	+	3.17610i	−0.101164	+	0.144968i
$481$	−22.4503	+	18.8380i	−1.02364	+	0.858939i
$482$	−2.13761	−	0.572771i	−0.0973655	−	0.0260890i
$483$	−2.93665	+	7.10359i	−0.133622	+	0.323224i
$484$	−18.1349	+	3.19766i	−0.824312	+	0.145348i
$485$	6.90954	+	8.98789i	0.313746	+	0.408119i
$486$	9.44686	−	12.3999i	0.428518	−	0.562469i
$487$	0.0779555	−	0.290934i	0.00353250	−	0.0131835i	−0.964137	−	0.265405i	$-0.914494\pi$
$487$	0.0779555	−	0.290934i	0.00353250	−	0.0131835i	0.967670	+	0.252221i	$0.0811611\pi$
$488$	2.48646	+	0.217537i	0.112557	+	0.00984746i
$489$	29.5742	+	9.30226i	1.33739	+	0.420663i
$490$	−13.4030	+	1.77684i	−0.605485	+	0.0802696i
$491$	19.0557	−	22.7097i	0.859973	−	1.02488i	−0.139427	−	0.990232i	$-0.544526\pi$
$491$	19.0557	−	22.7097i	0.859973	−	1.02488i	0.999400	−	0.0346437i	$-0.0110297\pi$
$492$	−19.7639	−	0.849229i	−0.891027	−	0.0382862i
$493$	−0.523311	+	0.523311i	−0.0235687	+	0.0235687i
$494$	13.6023	−	2.30361i	0.611995	−	0.103644i
$495$	36.3510	+	1.50393i	1.63386	+	0.0675965i
$496$	−0.749156	+	4.24867i	−0.0336381	+	0.190771i
$497$	−15.0109	+	1.31328i	−0.673331	+	0.0589089i
$498$	3.35355	−	15.1765i	0.150276	−	0.680076i
$499$	−7.60533	−	20.8955i	−0.340461	−	0.935410i	−0.985261	−	0.171058i	$-0.945281\pi$
$499$	−7.60533	−	20.8955i	−0.340461	−	0.935410i	0.644800	−	0.764352i	$-0.276941\pi$
$500$	10.9218	+	2.39031i	0.488439	+	0.106898i
$501$	−3.85006	+	29.4011i	−0.172008	+	1.31354i
$502$	18.4205	−	4.93577i	0.822149	−	0.220294i
$503$	−14.4417	+	20.6249i	−0.643925	+	0.919620i	−0.999889	−	0.0148793i	$-0.995264\pi$
$503$	−14.4417	+	20.6249i	−0.643925	+	0.919620i	0.355964	+	0.934500i	$0.384152\pi$
$504$	−2.65332	+	1.24173i	−0.118188	+	0.0553112i
$505$	3.07521	−	2.82302i	0.136845	−	0.125623i
$506$	21.3460	−	12.3241i	0.948945	−	0.547873i
$507$	−3.48763	+	3.81137i	−0.154891	+	0.169269i
$508$	1.88232	−	4.03665i	0.0835146	−	0.179098i
$509$	27.3556	+	9.95663i	1.21252	+	0.441320i	0.867576	−	0.497305i	$-0.165677\pi$
$509$	27.3556	+	9.95663i	1.21252	+	0.441320i	0.344941	+	0.938625i	$0.387899\pi$
$510$	−2.46567	+	2.07565i	−0.109182	+	0.0919112i
$511$	0.698689	−	3.96246i	0.0309082	−	0.175289i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−20.0410	−	10.5526i	−0.884832	−	0.465909i
$514$		−	22.3037i		−	0.983774i
$515$	2.26324	−	0.715844i	0.0997304	−	0.0315439i
$516$	3.45147	−	0.767674i	0.151942	−	0.0337950i
$517$	−17.4298	−	37.3783i	−0.766561	−	1.64390i
$518$	−8.19487	−	3.82133i	−0.360062	−	0.167900i
$519$	−0.445163	−	10.0367i	−0.0195405	−	0.440564i
$520$	6.90803	−	1.53801i	0.302937	−	0.0674464i
$521$	26.2672	+	15.1654i	1.15079	+	0.664407i	0.949079	−	0.315038i	$-0.102017\pi$
$521$	26.2672	+	15.1654i	1.15079	+	0.664407i	0.201708	+	0.979446i	$0.435351\pi$
$522$	−2.50832	−	0.909030i	−0.109786	−	0.0397872i
$523$	2.02122	+	1.41528i	0.0883819	+	0.0618857i	0.616932	−	0.787016i	$-0.288375\pi$
$523$	2.02122	+	1.41528i	0.0883819	+	0.0618857i	−0.528550	+	0.848902i	$0.677264\pi$
$524$	0.0838668	−	0.145262i	0.00366374	−	0.00634578i
$525$	6.24922	+	5.69773i	0.272738	+	0.248669i
$526$	7.21330	−	6.05267i	0.314515	−	0.263909i
$527$	−1.51728	+	3.25383i	−0.0660939	+	0.141739i
$528$	9.17255	+	2.02686i	0.399184	+	0.0882076i
$529$	1.50787	−	1.79701i	0.0655596	−	0.0781309i
$530$	−24.4450	−	12.6972i	−1.06182	−	0.551532i
$531$	−6.91103	+	1.86205i	−0.299913	+	0.0808060i
$532$	2.41776	+	3.50315i	0.104823	+	0.151881i
$533$	25.5607	+	25.5607i	1.10716	+	1.10716i
$534$	−15.8455	+	14.5399i	−0.685701	+	0.629202i
$535$	−8.04153	+	36.4285i	−0.347665	+	1.57494i
$536$	3.82055	−	10.4969i	0.165023	−	0.453396i
$537$	−5.41519	−	10.3850i	−0.233683	−	0.448144i
$538$	−1.03721	+	11.8554i	−0.0447174	+	0.511122i
$539$	16.3965	+	28.3996i	0.706248	+	1.22326i
$540$	−10.5449	−	4.87903i	−0.453781	−	0.209960i
$541$	−6.25817	−	35.4918i	−0.269060	−	1.52591i	−0.757220	−	0.653160i	$-0.773443\pi$
$541$	−6.25817	−	35.4918i	−0.269060	−	1.52591i	0.488160	−	0.872754i	$-0.337668\pi$
$542$	18.3879	+	12.8753i	0.789827	+	0.553043i
$543$	12.5630	+	5.19359i	0.539129	+	0.222878i
$544$	−0.720688	+	0.416090i	−0.0308993	+	0.0178397i
$545$	3.31219	−	1.37546i	0.141879	−	0.0589182i
$546$	5.10649	+	1.60619i	0.218538	+	0.0687387i
$547$	7.39188	+	15.8519i	0.316054	+	0.677780i	0.998591	−	0.0530715i	$-0.0169011\pi$
$547$	7.39188	+	15.8519i	0.316054	+	0.677780i	−0.682537	+	0.730851i	$0.739123\pi$
$548$	1.08563	+	12.4088i	0.0463759	+	0.530079i
$549$	0.662921	+	7.45848i	0.0282928	+	0.318320i
$550$	−4.75712	−	26.6971i	−0.202844	−	1.13837i
$551$	−0.698967	+	3.81292i	−0.0297770	+	0.162436i
$552$	−7.80357	+	1.03285i	−0.332142	+	0.0439609i
$553$	−2.48955	−	3.55545i	−0.105867	−	0.151193i
$554$	2.27861	+	1.91198i	0.0968088	+	0.0812322i
$555$	−9.33703	−	34.6255i	−0.396335	−	1.46977i
$556$	12.3672	−	4.50131i	0.524488	−	0.190898i
$557$	−2.74812	+	31.4112i	−0.116442	+	1.33094i	0.683100	+	0.730325i	$0.260631\pi$
$557$	−2.74812	+	31.4112i	−0.116442	+	1.33094i	−0.799542	+	0.600611i	$0.794924\pi$
$558$	−12.9426	+	0.0178876i	−0.547905	+	0.000757243i
$559$	−5.59543	−	3.23052i	−0.236661	−	0.136637i
$560$	1.33081	+	1.73111i	0.0562370	+	0.0731527i
$561$	6.93656	+	3.60485i	0.292862	+	0.152197i
$562$	−24.2993	+	6.51099i	−1.02501	+	0.274650i
$563$	7.03111	−	26.2405i	0.296326	−	1.10590i	−0.643833	−	0.765166i	$-0.722657\pi$
$563$	7.03111	−	26.2405i	0.296326	−	1.10590i	0.940159	−	0.340737i	$-0.110677\pi$
$564$	0.583609	+	13.1582i	0.0245744	+	0.554060i
$565$	−20.0145	+	21.8816i	−0.842017	+	0.920567i
$566$	1.54540	−	4.24596i	0.0649581	−	0.178471i
$567$	−5.06077	−	7.18518i	−0.212532	−	0.301749i
$568$	−8.85076	−	12.6402i	−0.371370	−	0.530371i
$569$	8.02284			0.336335			0.168168	−	0.985758i	$-0.446215\pi$
$569$	8.02284			0.336335			0.168168	+	0.985758i	$0.446215\pi$
$570$	−4.45372	+	16.2839i	−0.186546	+	0.682056i
$571$	26.6225			1.11412			0.557059	−	0.830473i	$-0.311930\pi$
$571$	26.6225			1.11412			0.557059	+	0.830473i	$0.311930\pi$
$572$	−9.84572	−	14.0611i	−0.411670	−	0.587926i
$573$	21.7662	+	13.8454i	0.909295	+	0.578402i
$574$	−3.81451	+	10.4803i	−0.159215	+	0.437438i
$575$	11.3972	+	19.6585i	0.475297	+	0.819817i
$576$	−2.45983	−	1.71733i	−0.102493	−	0.0715555i
$577$	−5.13515	+	19.1647i	−0.213779	+	0.797835i	0.772814	+	0.634633i	$0.218849\pi$
$577$	−5.13515	+	19.1647i	−0.213779	+	0.797835i	−0.986593	+	0.163202i	$0.947818\pi$
$578$	15.7518	−	4.22069i	0.655189	−	0.175557i
$579$	2.54458	−	4.89634i	0.105749	−	0.203485i
$580$	−0.257782	+	1.97180i	−0.0107038	+	0.0818745i
$581$	−7.58870	−	4.38134i	−0.314832	−	0.181769i
$582$	−6.96312	+	5.35064i	−0.288631	+	0.221791i
$583$	−5.82304	+	66.5576i	−0.241165	+	2.75653i
$584$	3.87191	−	1.40926i	0.160221	−	0.0583157i
$585$	8.16974	+	19.5967i	0.337777	+	0.810226i
$586$	21.9908	+	18.4525i	0.908431	+	0.762264i
$587$	−21.5550	−	30.7838i	−0.889672	−	1.27058i	−0.961958	−	0.273199i	$-0.911918\pi$
$587$	−21.5550	−	30.7838i	−0.889672	−	1.27058i	0.0722858	−	0.997384i	$-0.476971\pi$
$588$	−1.37414	−	10.3822i	−0.0566687	−	0.428155i
$589$	3.14005	+	18.5412i	0.129383	+	0.763978i
$590$	2.46764	+	4.72987i	0.101591	+	0.194726i
$591$	23.0895	−	21.1870i	0.949774	−	0.871516i
$592$	−0.807028	−	9.22437i	−0.0331687	−	0.379119i
$593$	0.142521	+	0.305637i	0.00585263	+	0.0125510i	0.909212	−	0.416333i	$-0.136685\pi$
$593$	0.142521	+	0.305637i	0.00585263	+	0.0125510i	−0.903360	+	0.428884i	$0.858907\pi$
$594$	−1.17089	+	28.1571i	−0.0480421	+	1.15530i
$595$	0.696883	+	1.67814i	0.0285694	+	0.0687970i
$596$	−9.43393	+	5.44668i	−0.386429	+	0.223105i
$597$	−6.81737	+	16.4908i	−0.279016	+	0.674924i
$598$	11.7827	+	8.25030i	0.481828	+	0.337380i
$599$	0.461204	+	2.61562i	0.0188443	+	0.106871i	0.992779	−	0.119957i	$-0.0382756\pi$
$599$	0.461204	+	2.61562i	0.0188443	+	0.106871i	−0.973935	+	0.226828i	$0.927164\pi$
$600$	−1.85331	+	8.45962i	−0.0756612	+	0.345363i
$601$	−11.3512	−	19.6609i	−0.463025	−	0.801983i	0.536085	−	0.844164i	$-0.319903\pi$
$601$	−11.3512	−	19.6609i	−0.463025	−	0.801983i	−0.999110	+	0.0421811i	$0.986569\pi$
$602$	0.173739	−	1.98585i	0.00708108	−	0.0809371i
$603$	33.0105	+	5.77362i	1.34429	+	0.235120i
$604$	7.31303	−	20.0924i	0.297563	−	0.817547i
$605$	−34.7078	+	22.1554i	−1.41107	+	0.900743i
$606$	2.18620	+	2.38251i	0.0888082	+	0.0967828i
$607$	−10.1732	−	10.1732i	−0.412918	−	0.412918i	0.469836	−	0.882754i	$-0.344313\pi$
$607$	−10.1732	−	10.1732i	−0.412918	−	0.412918i	−0.882754	+	0.469836i	$0.844313\pi$
$608$	−1.86885	+	3.93794i	−0.0757919	+	0.159705i
$609$	−0.914846	+	1.19396i	−0.0370714	+	0.0483816i
$610$	5.32131	−	1.68308i	0.215454	−	0.0681461i
$611$	15.4705	−	18.4370i	0.625870	−	0.745882i
$612$	−1.60739	−	1.91024i	−0.0649747	−	0.0772168i
$613$	12.0553	−	25.8527i	0.486910	−	1.04418i	−0.497365	−	0.867541i	$-0.665699\pi$
$613$	12.0553	−	25.8527i	0.486910	−	1.04418i	0.984275	−	0.176641i	$-0.0565231\pi$
$614$	10.9506	−	9.18867i	0.441931	−	0.370824i
$615$	−41.5425	+	15.1952i	−1.67515	+	0.612731i
$616$	2.64804	−	4.58655i	0.106693	−	0.184797i
$617$	−11.2340	−	7.86614i	−0.452264	−	0.316679i	0.325156	−	0.945660i	$-0.394583\pi$
$617$	−11.2340	−	7.86614i	−0.452264	−	0.316679i	−0.777420	+	0.628982i	$0.783472\pi$
$618$	0.554120	+	1.75322i	0.0222900	+	0.0705248i
$619$	15.7747	+	9.10752i	0.634038	+	0.366062i	0.782314	−	0.622884i	$-0.214039\pi$
$619$	15.7747	+	9.10752i	0.634038	+	0.366062i	−0.148276	+	0.988946i	$0.547372\pi$
$620$	2.09646	+	9.41632i	0.0841961	+	0.378169i
$621$	−7.14781	−	22.5071i	−0.286832	−	0.903181i
$622$	−0.792169	−	0.369395i	−0.0317631	−	0.0148114i
$623$	5.12403	+	10.9885i	0.205290	+	0.440245i
$624$	1.19021	+	5.35119i	0.0476465	+	0.214219i
$625$	24.6044	−	4.43004i	0.984175	−	0.177202i
$626$		−	2.66027i		−	0.106326i
$627$	40.6281	−	5.09775i	1.62253	−	0.203585i
$628$	−10.3481	+	10.3481i	−0.412934	+	0.412934i
$629$	1.33807	−	7.58859i	0.0533525	−	0.302577i
$630$	−4.41446	+	4.83969i	−0.175876	+	0.192818i
$631$	−1.29808	−	0.472463i	−0.0516758	−	0.0188085i	0.316053	−	0.948742i	$-0.397642\pi$
$631$	−1.29808	−	0.472463i	−0.0516758	−	0.0188085i	−0.367729	+	0.929933i	$0.619865\pi$
$632$	1.87847	−	4.02840i	0.0747216	−	0.160241i
$633$	3.12969	+	2.86386i	0.124394	+	0.113828i
$634$	2.89946	−	1.67400i	0.115152	−	0.0664832i
$635$	0.425442	−	9.95025i	0.0168831	−	0.394864i
$636$	9.83923	−	18.9329i	0.390151	−	0.750739i
$637$	−10.9765	+	15.6761i	−0.434907	+	0.621111i
$638$	4.65890	−	1.24835i	0.184448	−	0.0494226i
$639$	32.6885	−	32.7789i	1.29314	−	1.29671i
$640$	−0.853842	+	2.06663i	−0.0337511	+	0.0816907i
$641$	−11.0270	−	30.2964i	−0.435540	−	1.19664i	−0.942365	−	0.334587i	$-0.891403\pi$
$641$	−11.0270	−	30.2964i	−0.435540	−	1.19664i	0.506825	−	0.862049i	$-0.330819\pi$
$642$	−28.2161	−	6.23490i	−1.11360	−	0.246072i
$643$	9.16392	−	0.801739i	0.361390	−	0.0316175i	0.0949848	−	0.995479i	$-0.469720\pi$
$643$	9.16392	−	0.801739i	0.361390	−	0.0316175i	0.266405	+	0.963861i	$0.414164\pi$
$644$	−0.770633	+	4.37048i	−0.0303672	+	0.172221i
$645$	6.46923	−	4.54519i	0.254726	−	0.178966i
$646$	−2.35040	+	2.76289i	−0.0924751	+	0.108704i
$647$	13.5416	−	13.5416i	0.532377	−	0.532377i	−0.388902	−	0.921279i	$-0.627146\pi$
$647$	13.5416	−	13.5416i	0.532377	−	0.532377i	0.921279	+	0.388902i	$0.127146\pi$
$648$	3.78100	−	8.16725i	0.148532	−	0.320840i
$649$	8.31742	−	9.91231i	0.326487	−	0.389092i
$650$	12.9467	−	9.10025i	0.507812	−	0.356941i
$651$	−2.18940	+	6.96065i	−0.0858093	+	0.272810i
$652$	17.8313	+	1.56004i	0.698328	+	0.0610958i
$653$	12.1801	−	45.4569i	0.476646	−	1.77887i	−0.138403	−	0.990376i	$-0.544197\pi$
$653$	12.1801	−	45.4569i	0.476646	−	1.77887i	0.615048	−	0.788489i	$-0.289137\pi$
$654$	1.06488	+	2.56584i	0.0416402	+	0.100332i
$655$	0.0486201	−	0.371899i	0.00189974	−	0.0145313i
$656$	−11.2477	+	1.98328i	−0.439150	+	0.0774340i
$657$	6.19540	+	10.6966i	0.241705	+	0.417313i
$658$	7.17265	+	1.92191i	0.279619	+	0.0749237i
$659$	18.3160	−	15.3689i	0.713489	−	0.598689i	−0.212087	−	0.977251i	$-0.568026\pi$
$659$	18.3160	−	15.3689i	0.713489	−	0.598689i	0.925576	+	0.378562i	$0.123581\pi$
$660$	20.6803	−	3.68048i	0.804978	−	0.143262i
$661$	22.8096	+	8.30203i	0.887192	+	0.322912i	0.745109	−	0.666943i	$-0.232398\pi$
$661$	22.8096	+	8.30203i	0.887192	+	0.322912i	0.142084	+	0.989855i	$0.454620\pi$
$662$	7.56642	−	0.661976i	0.294077	−	0.0257284i
$663$	−0.195841	+	4.55776i	−0.00760582	+	0.177009i
$664$		−	8.97353i		−	0.348240i
$665$	7.99707	+	5.16091i	0.310113	+	0.200131i
$666$	26.8223	−	7.22677i	1.03934	−	0.280032i
$667$	−3.31075	+	2.31821i	−0.128193	+	0.0897615i
$668$	1.49207	+	17.0545i	0.0577301	+	0.659858i
$669$	−16.8031	−	26.3354i	−0.649646	−	1.01819i
$670$	−1.11205	−	24.9533i	−0.0429621	−	0.964031i
$671$	−8.70136	−	10.3699i	−0.335912	−	0.400325i
$672$	−1.34113	+	1.03056i	−0.0517352	+	0.0397546i
$673$	−5.43375	−	20.2790i	−0.209456	−	0.781699i	−0.988045	−	0.154165i	$-0.950731\pi$
$673$	−5.43375	−	20.2790i	−0.209456	−	0.781699i	0.778589	−	0.627534i	$-0.215936\pi$
$674$	3.51798	+	19.9514i	0.135507	+	0.768501i
$675$	−25.9602	−	1.03260i	−0.999210	−	0.0397449i
$676$	−1.49137	+	2.58312i	−0.0573602	+	0.0993508i
$677$	−10.4983	−	2.81301i	−0.403482	−	0.108113i	0.0513702	−	0.998680i	$-0.483641\pi$
$677$	−10.4983	−	2.81301i	−0.403482	−	0.108113i	−0.454852	+	0.890567i	$0.650308\pi$
$678$	−16.9462	−	15.5068i	−0.650813	−	0.595534i
$679$	1.69329	+	4.65229i	0.0649827	+	0.178538i
$680$	−1.13146	+	1.47730i	−0.0433894	+	0.0566519i
$681$	0.486169	+	2.18582i	0.0186300	+	0.0837606i
$682$	19.1667	−	13.4207i	0.733932	−	0.513905i
$683$	−15.9176	−	15.9176i	−0.609068	−	0.609068i	0.333634	−	0.942703i	$-0.391725\pi$
$683$	−15.9176	−	15.9176i	−0.609068	−	0.609068i	−0.942703	+	0.333634i	$0.891725\pi$
$684$	−12.6127	−	3.45250i	−0.482259	−	0.132010i
$685$	12.8834	+	24.6943i	0.492248	+	0.943520i
$686$	−12.5463	−	2.21226i	−0.479022	−	0.0844644i
$687$	−15.5506	−	9.89171i	−0.593291	−	0.377392i
$688$	1.85014	−	0.862733i	0.0705358	−	0.0328914i
$689$	−36.6380	+	13.3352i	−1.39580	+	0.508029i
$690$	−15.2293	+	8.82502i	−0.579769	+	0.335963i
$691$	18.0471	+	31.2585i	0.686544	+	1.18913i	0.972949	+	0.231020i	$0.0742064\pi$
$691$	18.0471	+	31.2585i	0.686544	+	1.18913i	−0.286405	+	0.958109i	$0.592460\pi$
$692$	−1.50126	−	5.60277i	−0.0570692	−	0.212985i
$693$	14.9376	+	5.41347i	0.567432	+	0.205641i
$694$	−10.3614	+	1.82699i	−0.393313	+	0.0693517i
$695$	21.6792	−	19.9014i	0.822340	−	0.754902i
$696$	−1.52731	−	0.200000i	−0.0578924	−	0.00758099i
$697$	−9.46835	−	0.828374i	−0.358639	−	0.0313769i
$698$	−28.1293	−	13.1169i	−1.06471	−	0.496483i
$699$	−2.29529	+	1.46449i	−0.0868159	+	0.0553922i
$700$	4.23278	+	2.43362i	0.159984	+	0.0919823i
$701$	4.39747	+	0.775393i	0.166090	+	0.0292862i	0.256075	−	0.966657i	$-0.417571\pi$
$701$	4.39747	+	0.775393i	0.166090	+	0.0292862i	−0.0899845	+	0.995943i	$0.528682\pi$
$702$	−15.1809	+	6.32504i	−0.572967	+	0.238723i
$703$	−16.8096	−	36.6948i	−0.633985	−	1.38397i
$704$	5.42352			0.204407
$705$	12.4893	+	26.6723i	0.470373	+	1.00454i
$706$	−10.8724	−	9.12301i	−0.409187	−	0.343349i
$707$	1.65222	−	0.770442i	0.0621381	−	0.0289755i
$708$	−3.66414	+	1.91065i	−0.137707	+	0.0718067i
$709$	18.2120	+	21.7043i	0.683967	+	0.815120i	0.990612	−	0.136704i	$-0.0436508\pi$
$709$	18.2120	+	21.7043i	0.683967	+	0.815120i	−0.306645	+	0.951824i	$0.599206\pi$
$710$	−29.1174	−	18.5129i	−1.09276	−	0.694778i
$711$	12.8849	+	3.43343i	0.483223	+	0.128764i
$712$	−7.12165	+	10.1708i	−0.266895	+	0.381166i
$713$	−11.2460	+	16.0609i	−0.421165	+	0.601486i
$714$	−1.30000	+	0.539529i	−0.0486511	+	0.0201914i
$715$	−32.3907	−	20.5941i	−1.21134	−	0.770174i
$716$	−4.34649	−	5.17995i	−0.162436	−	0.193584i
$717$	−5.49046	−	10.5293i	−0.205045	−	0.393224i
$718$	5.40115	−	2.51860i	0.201569	−	0.0939932i
$719$	1.35864	+	1.14003i	0.0506686	+	0.0425160i	0.667770	−	0.744367i	$-0.267249\pi$
$719$	1.35864	+	1.14003i	0.0506686	+	0.0425160i	−0.617102	+	0.786883i	$0.711693\pi$
$720$	−6.55249	−	1.43696i	−0.244197	−	0.0535522i
$721$	1.03663			0.0386062
$722$	−1.91207	+	18.9035i	−0.0711597	+	0.703517i
$723$	−0.502941	−	3.79992i	−0.0187046	−	0.141321i
$724$	7.72937	+	1.36290i	0.287260	+	0.0506516i
$725$	1.15861	+	4.29300i	0.0430299	+	0.159438i
$726$	−17.1558	−	26.8882i	−0.636711	−	0.997913i
$727$	−11.6307	−	5.42347i	−0.431358	−	0.201145i	0.194798	−	0.980843i	$-0.437595\pi$
$727$	−11.6307	−	5.42347i	−0.431358	−	0.201145i	−0.626156	+	0.779698i	$0.715373\pi$
$728$	3.07888	+	0.269367i	0.114111	+	0.00998340i
$729$	26.1087	+	6.87992i	0.966991	+	0.254812i
$730$	6.78729	−	6.23068i	0.251209	−	0.230608i
$731$	1.67300	−	0.294995i	0.0618782	−	0.0109108i
$732$	1.30284	+	4.12215i	0.0481544	+	0.152359i
$733$	9.77526	+	36.4818i	0.361058	+	1.34749i	0.872687	+	0.488279i	$0.162375\pi$
$733$	9.77526	+	36.4818i	0.361058	+	1.34749i	−0.511630	+	0.859206i	$0.670958\pi$
$734$	−8.82613	−	15.2873i	−0.325778	−	0.564265i
$735$	−11.7412	−	20.2617i	−0.433080	−	0.747364i
$736$	−4.27061	+	1.55437i	−0.157417	+	0.0572950i
$737$	−54.9075	+	25.6038i	−2.02254	+	0.943127i
$738$	−11.7634	−	32.1811i	−0.433016	−	1.18460i
$739$	−36.4384	−	6.42507i	−1.34041	−	0.236350i	−0.542970	−	0.839752i	$-0.682700\pi$
$739$	−36.4384	−	6.42507i	−1.34041	−	0.236350i	−0.797437	+	0.603402i	$0.793812\pi$
$740$	−9.57713	−	18.3570i	−0.352062	−	0.674818i
$741$	12.7162	+	20.2307i	0.467141	+	0.743195i
$742$	−8.50610	−	8.50610i	−0.312269	−	0.312269i
$743$	6.69895	−	4.69065i	0.245760	−	0.172083i	−0.444206	−	0.895925i	$-0.646514\pi$
$743$	6.69895	−	4.69065i	0.245760	−	0.172083i	0.689966	+	0.723841i	$0.257625\pi$
$744$	−7.29419	+	1.62237i	−0.267418	+	0.0594791i
$745$	−14.8109	+	19.3381i	−0.542631	+	0.708494i
$746$	4.22798	+	11.6163i	0.154797	+	0.425302i
$747$	26.5051	−	4.71135i	0.969772	−	0.172379i
$748$	4.35956	+	1.16814i	0.159401	+	0.0427114i
$749$	−8.14576	+	14.1089i	−0.297640	+	0.515527i
$750$	3.42747	+	19.0592i	0.125153	+	0.695943i
$751$	2.68206	+	15.2107i	0.0978696	+	0.555046i	0.993830	+	0.110912i	$0.0353773\pi$
$751$	2.68206	+	15.2107i	0.0978696	+	0.555046i	−0.895961	+	0.444134i	$0.853512\pi$
$752$	1.96815	+	7.34524i	0.0717711	+	0.267853i
$753$	20.1260	+	26.1912i	0.733431	+	0.954460i
$754$	1.80926	+	2.15619i	0.0658892	+	0.0785237i
$755$	−2.12860	−	47.7639i	−0.0774678	−	1.73831i
$756$	−3.74809	−	3.42022i	−0.136317	−	0.124392i
$757$	−2.76437	−	31.5968i	−0.100473	−	1.14841i	−0.864297	−	0.502982i	$-0.832236\pi$
$757$	−2.76437	−	31.5968i	−0.100473	−	1.14841i	0.763824	−	0.645424i	$-0.223319\pi$
$758$	−8.26558	+	5.78762i	−0.300219	+	0.210216i
$759$	33.8878	+	25.9658i	1.23005	+	0.942499i
$760$	−0.482274	+	9.73486i	−0.0174939	+	0.353120i
$761$		−	40.2179i		−	1.45790i	−0.684568	−	0.728949i	$-0.740009\pi$
$761$		−	40.2179i		−	1.45790i	0.684568	−	0.728949i	$-0.259991\pi$
$762$	7.70736	+	0.331175i	0.279208	+	0.0119972i
$763$	1.56026	−	0.136505i	0.0564851	−	0.00494180i
$764$	13.9955	+	5.09393i	0.506338	+	0.184292i
$765$	−4.95755	−	2.56636i	−0.179241	−	0.0927869i
$766$	8.81044	−	7.39284i	0.318334	−	0.267114i
$767$	7.29386	+	1.95439i	0.263366	+	0.0705688i
$768$	−1.60066	−	0.661721i	−0.0577590	−	0.0238778i
$769$	−30.3644	+	5.35406i	−1.09497	+	0.193072i	−0.691825	−	0.722065i	$-0.743193\pi$
$769$	−30.3644	+	5.35406i	−1.09497	+	0.193072i	−0.403143	+	0.915137i	$0.632082\pi$
$770$	1.53515	−	11.7425i	0.0553229	−	0.423170i
$771$	35.6803	−	14.8082i	1.28499	−	0.533303i
$772$	0.824561	−	3.07730i	0.0296766	−	0.110755i
$773$	−28.8302	−	2.52232i	−1.03695	−	0.0907215i	−0.444055	−	0.896000i	$-0.646460\pi$
$773$	−28.8302	−	2.52232i	−1.03695	−	0.0907215i	−0.592897	+	0.805278i	$0.702016\pi$
$774$	3.51963	+	5.01179i	0.126510	+	0.180145i
$775$	12.4045	+	17.6476i	0.445584	+	0.633922i
$776$	−3.25893	+	3.88384i	−0.116989	+	0.139422i
$777$	0.672323	−	15.6468i	0.0241194	−	0.561327i
$778$	−0.329456	+	0.329456i	−0.0118116	+	0.0118116i
$779$	−43.2818	+	24.5996i	−1.55073	+	0.881372i
$780$	7.04690	+	10.0300i	0.252320	+	0.359130i
$781$	−14.5325	+	82.4181i	−0.520015	+	2.94915i
$782$	−3.76760	+	0.329622i	−0.134729	+	0.0117873i
$783$	−0.211137	−	4.61621i	−0.00754543	−	0.164970i
$784$	−2.06800	−	5.68180i	−0.0738573	−	0.202921i
$785$	−12.4955	+	30.2439i	−0.445982	+	1.07945i
$786$	0.288064	+	0.0377218i	0.0102749	+	0.00134549i
$787$	−50.0568	+	13.4127i	−1.78433	+	0.478110i	−0.991362	−	0.131152i	$-0.958132\pi$
$787$	−50.0568	+	13.4127i	−1.78433	+	0.478110i	−0.792969	+	0.609262i	$0.791466\pi$
$788$	10.3774	−	14.8205i	0.369680	−	0.527958i
$789$	14.4719	+	7.52089i	0.515213	+	0.267751i
$790$	0.424572	−	9.92990i	0.0151056	−	0.353290i
$791$	−11.2153	+	6.47513i	−0.398769	+	0.230229i
$792$	2.84750	+	16.0195i	0.101181	+	0.569227i
$793$	3.33857	−	7.15959i	0.118556	−	0.254245i
$794$	1.19152	+	0.433678i	0.0422855	+	0.0153907i
$795$	4.08254	−	47.5359i	0.144793	−	1.68592i
$796$	−1.78901	+	10.1460i	−0.0634096	+	0.359614i
$797$	−3.57028	+	3.57028i	−0.126466	+	0.126466i	−0.767507	−	0.641041i	$-0.778503\pi$
$797$	−3.57028	+	3.57028i	−0.126466	+	0.126466i	0.641041	+	0.767507i	$0.278503\pi$
$798$	−3.99893	+	6.19366i	−0.141561	+	0.219253i
$799$			6.32818i			0.223875i
$800$	0.00902391	+	4.99999i	0.000319044	+	0.176776i
$801$	−33.7805	−	15.6953i	−1.19357	−	0.554566i
$802$	2.63443	+	5.64956i	0.0930251	+	0.199493i
$803$	−20.2534	−	9.44430i	−0.714726	−	0.333282i
$804$	19.3289	−	0.857303i	0.681679	−	0.0302347i
$805$	2.15657	+	9.68628i	0.0760090	+	0.341396i
$806$	11.8252	+	6.82726i	0.416524	+	0.240480i
$807$	−19.6543	+	6.21190i	−0.691863	+	0.218669i
$808$	1.52927	+	1.07080i	0.0537994	+	0.0376707i
$809$	−2.38403	+	4.12927i	−0.0838182	+	0.145177i	−0.904887	−	0.425652i	$-0.860045\pi$
$809$	−2.38403	+	4.12927i	−0.0838182	+	0.145177i	0.821069	+	0.570829i	$0.193378\pi$
$810$	0.804100	−	20.1085i	0.0282532	−	0.706542i
$811$	9.06439	−	7.60593i	0.318294	−	0.267080i	−0.469616	−	0.882871i	$-0.655608\pi$
$811$	9.06439	−	7.60593i	0.318294	−	0.267080i	0.787910	+	0.615790i	$0.211163\pi$
$812$	−0.367012	+	0.787059i	−0.0128796	+	0.0276204i
$813$	−8.38897	+	37.9643i	−0.294214	+	1.33147i
$814$	−32.2806	+	38.4705i	−1.13143	+	1.34839i
$815$	38.1610	−	12.0700i	1.33672	−	0.422793i
$816$	−1.14413	−	0.876664i	−0.0400525	−	0.0306894i
$817$	6.33447	−	6.24928i	0.221615	−	0.218635i
$818$	8.30621	+	8.30621i	0.290420	+	0.290420i
$819$	0.820866	+	9.23551i	0.0286834	+	0.322715i
$820$	−21.5267	+	13.7414i	−0.751745	+	0.479869i
$821$	−3.70057	+	10.1672i	−0.129151	+	0.354839i	−0.987367	−	0.158449i	$-0.949351\pi$
$821$	−3.70057	+	10.1672i	−0.129151	+	0.354839i	0.858216	+	0.513288i	$0.171573\pi$
$822$	−19.1302	+	9.97536i	−0.667243	+	0.347931i
$823$	2.52746	−	28.8890i	0.0881018	−	1.00701i	−0.815535	−	0.578708i	$-0.803557\pi$
$823$	2.52746	−	28.8890i	0.0881018	−	1.00701i	0.903637	−	0.428300i	$-0.140887\pi$
$824$	0.530787	+	0.919351i	0.0184909	+	0.0320271i
$825$	39.5502	−	25.3353i	1.37696	−	0.882061i
$826$	0.404560	+	2.29437i	0.0140764	+	0.0798315i
$827$	−20.9597	−	14.6762i	−0.728841	−	0.510340i	0.149270	−	0.988796i	$-0.452307\pi$
$827$	−20.9597	−	14.6762i	−0.728841	−	0.510340i	−0.878111	+	0.478457i	$0.841196\pi$
$828$	−6.83334	−	11.7980i	−0.237475	−	0.410009i
$829$	−34.8837	+	20.1401i	−1.21156	+	0.699495i	−0.963099	−	0.269147i	$-0.913258\pi$
$829$	−34.8837	+	20.1401i	−1.21156	+	0.699495i	−0.248461	+	0.968642i	$0.579925\pi$
$830$	−7.69543	−	18.5311i	−0.267112	−	0.643224i
$831$	−1.54584	+	4.91463i	−0.0536247	+	0.170486i
$832$	1.33759	+	2.86847i	0.0463726	+	0.0994463i
$833$	−0.438544	−	5.01258i	−0.0151946	−	0.173675i
$834$	15.4120	+	16.7959i	0.533673	+	0.581595i
$835$	17.7067	+	33.9394i	0.612765	+	1.17452i
$836$	22.2691	−	7.93499i	0.770194	−	0.274437i
$837$	−8.62165	−	20.6931i	−0.298008	−	0.715257i
$838$	−12.7503	−	18.2093i	−0.440451	−	0.629029i
$839$	−27.5663	−	23.1308i	−0.951693	−	0.798565i	0.0278890	−	0.999611i	$-0.491122\pi$
$839$	−27.5663	−	23.1308i	−0.951693	−	0.798565i	−0.979582	+	0.201046i	$0.935566\pi$
$840$	−1.88577	+	3.27830i	−0.0650652	+	0.113112i
$841$	26.5079	−	9.64808i	0.914065	−	0.332693i
$842$	3.26010	−	37.2631i	0.112350	−	1.28417i
$843$	−26.5491	−	34.5500i	−0.914399	−	1.18996i
$844$	2.12112	+	1.22463i	0.0730121	+	0.0421536i
$845$	−0.864589	+	6.61332i	−0.0297428	+	0.227505i
$846$	−20.6623	+	9.66978i	−0.710385	+	0.332454i
$847$	−17.3692	+	4.65407i	−0.596813	+	0.159916i
$848$	3.18836	−	11.8991i	0.109489	−	0.408618i
$849$	7.81850	−	0.346777i	0.268330	−	0.0119013i
$850$	−1.06966	+	4.02105i	−0.0366892	+	0.137921i
$851$	14.3929	−	39.5442i	0.493382	−	1.35556i
$852$	14.3448	−	22.5512i	0.491445	−	0.772592i
$853$	−6.90255	−	9.85786i	−0.236339	−	0.337527i	0.683410	−	0.730035i	$-0.260496\pi$
$853$	−6.90255	−	9.85786i	−0.236339	−	0.337527i	−0.919748	+	0.392508i	$0.871607\pi$
$854$	2.43731			0.0834032
$855$	−29.0071	+	3.68657i	−0.992020	+	0.126078i
$856$	−16.6835			−0.570232
$857$	4.98476	+	7.11898i	0.170276	+	0.243180i	0.895216	−	0.445633i	$-0.147021\pi$
$857$	4.98476	+	7.11898i	0.170276	+	0.243180i	−0.724940	+	0.688812i	$0.758132\pi$
$858$	15.9574	−	25.0863i	0.544776	−	0.856433i
$859$	−10.7552	+	29.5498i	−0.366964	+	1.00823i	0.609546	+	0.792751i	$0.291352\pi$
$859$	−10.7552	+	29.5498i	−0.366964	+	1.00823i	−0.976510	+	0.215474i	$0.930870\pi$
$860$	3.08083	−	3.36824i	0.105056	−	0.114856i
$861$	−19.2984	+	0.855947i	−0.657687	+	0.0291706i
$862$	−5.57825	+	20.8183i	−0.189996	+	0.709074i
$863$	−20.3606	+	5.45560i	−0.693082	+	0.185711i	−0.588130	−	0.808767i	$-0.700136\pi$
$863$	−20.3606	+	5.45560i	−0.693082	+	0.185711i	−0.104952	+	0.994477i	$0.533469\pi$
$864$	1.11413	−	5.07530i	0.0379036	−	0.172665i
$865$	−7.90499	−	10.2828i	−0.268778	−	0.349624i
$866$	26.4907	+	15.2944i	0.900192	+	0.519726i
$867$	17.2102	+	22.3967i	0.584488	+	0.760631i
$868$	−0.367174	+	4.19681i	−0.0124627	+	0.142449i
$869$	−22.6529	+	8.24499i	−0.768447	+	0.279692i
$870$	−3.32553	+	0.896756i	−0.112746	+	0.0304029i
$871$	−27.0834	−	22.7257i	−0.917685	−	0.770029i
$872$	0.919961	+	1.31384i	0.0311538	+	0.0444922i
$873$	−13.1827	−	7.58677i	−0.446167	−	0.256773i
$874$	−15.2611	+	12.6305i	−0.516213	+	0.427233i
$875$	10.8281	+	1.39573i	0.366055	+	0.0471843i
$876$	4.82515	+	5.25843i	0.163027	+	0.177666i
$877$	0.938070	+	10.7222i	0.0316764	+	0.362062i	0.995446	+	0.0953266i	$0.0303896\pi$
$877$	0.938070	+	10.7222i	0.0316764	+	0.362062i	−0.963770	+	0.266736i	$0.914055\pi$
$878$	16.3652	+	35.0953i	0.552299	+	1.18441i
$879$	−14.9189	+	47.4309i	−0.503202	+	1.59981i
$880$	11.2000	−	4.65105i	0.377553	−	0.156787i
$881$	5.02543	−	2.90144i	0.169311	−	0.0977519i	−0.412950	−	0.910754i	$-0.635502\pi$
$881$	5.02543	−	2.90144i	0.169311	−	0.0977519i	0.582261	+	0.813002i	$0.302168\pi$
$882$	15.6966	−	9.09137i	0.528531	−	0.306122i
$883$	39.2700	+	27.4972i	1.32154	+	0.925354i	0.999770	−	0.0214635i	$-0.00683256\pi$
$883$	39.2700	+	27.4972i	1.32154	+	0.925354i	0.321772	+	0.946817i	$0.395721\pi$
$884$	0.457364	+	2.59384i	0.0153828	+	0.0872402i
$885$	−5.92825	+	7.08792i	−0.199276	+	0.238258i
$886$	−12.7955	−	22.1625i	−0.429874	−	0.744564i
$887$	3.65787	−	41.8096i	0.122819	−	1.40383i	−0.645499	−	0.763761i	$-0.723351\pi$
$887$	3.65787	−	41.8096i	0.122819	−	1.40383i	0.768318	−	0.640068i	$-0.221094\pi$
$888$	14.2209	−	7.41541i	0.477221	−	0.248845i
$889$	1.48755	−	4.08701i	0.0498908	−	0.137074i
$890$	−5.98466	+	27.1108i	−0.200606	+	0.908757i
$891$	−45.8217	+	16.8213i	−1.53508	+	0.563535i
$892$	−12.7534	−	12.7534i	−0.427016	−	0.427016i
$893$	18.8279	+	27.2802i	0.630051	+	0.912897i
$894$	−14.9768	−	11.4757i	−0.500900	−	0.383804i
$895$	−13.4180	−	6.96961i	−0.448516	−	0.232968i
$896$	−0.627684	+	0.748045i	−0.0209695	+	0.0249904i
$897$	−5.37551	+	24.3269i	−0.179483	+	0.812252i
$898$	1.94746	−	4.17634i	0.0649876	−	0.139366i
$899$	−2.93910	+	2.46619i	−0.0980243	+	0.0822522i
$900$	−14.7637	+	2.65179i	−0.492125	+	0.0883929i
$901$	5.12576	−	8.87808i	0.170764	−	0.295772i
$902$	50.7411	+	35.5293i	1.68949	+	1.18300i
$903$	3.29221	−	1.04053i	0.109558	−	0.0346267i
$904$	−11.4851	−	6.63094i	−0.381989	−	0.220542i
$905$	17.1306	−	3.81398i	0.569440	−	0.126781i
$906$	36.9981	−	1.64099i	1.22918	−	0.0545182i
$907$	12.1632	+	5.67181i	0.403873	+	0.188329i	0.613931	−	0.789360i	$-0.289587\pi$
$907$	12.1632	+	5.67181i	0.403873	+	0.188329i	−0.210057	+	0.977689i	$0.567365\pi$
$908$	0.546369	+	1.17169i	0.0181319	+	0.0388840i
$909$	−2.35993	+	5.07919i	−0.0782738	+	0.168466i
$910$	6.58914	−	2.08409i	0.218428	−	0.0690868i
$911$		−	8.61946i		−	0.285575i	−0.989753	−	0.142788i	$-0.954393\pi$
$911$		−	8.61946i		−	0.285575i	0.989753	−	0.142788i	$-0.0456066\pi$
$912$	−7.54051	−	0.375161i	−0.249691	−	0.0124228i
$913$	−34.4136	+	34.4136i	−1.13892	+	1.13892i
$914$	7.05016	−	39.9834i	0.233198	−	1.32253i
$915$	6.22550	+	7.39530i	0.205809	+	0.244481i
$916$	−9.99888	−	3.63929i	−0.330372	−	0.120246i
$917$	0.0692216	−	0.148446i	0.00228590	−	0.00490213i
$918$	1.98871	−	3.83968i	0.0656371	−	0.126728i
$919$	−28.1299	+	16.2408i	−0.927921	+	0.535736i	−0.886154	−	0.463392i	$-0.846632\pi$
$919$	−28.1299	+	16.2408i	−0.927921	+	0.535736i	−0.0417677	+	0.999127i	$0.513299\pi$
$920$	−7.48618	+	6.87226i	−0.246812	+	0.226572i
$921$	21.9700	+	11.4176i	0.723937	+	0.376222i
$922$	−11.7207	+	16.7389i	−0.386001	+	0.551266i
$923$	−47.1745	+	12.6404i	−1.55277	+	0.416063i
$924$	9.09544	+	1.19104i	0.299218	+	0.0391825i
$925$	−35.5200	−	29.6958i	−1.16789	−	0.976390i
$926$	5.82980	+	16.0173i	0.191579	+	0.526360i
$927$	−2.43681	+	2.05047i	−0.0800353	+	0.0673463i
$928$	−0.885936	+	0.0775093i	−0.0290823	+	0.00254437i
$929$	5.96024	−	33.8022i	0.195549	−	1.10901i	−0.716085	−	0.698013i	$-0.754068\pi$
$929$	5.96024	−	33.8022i	0.195549	−	1.10901i	0.911635	−	0.411002i	$-0.134821\pi$
$930$	−13.6718	+	9.60562i	−0.448317	+	0.314981i
$931$	−16.8041	−	20.3040i	−0.550733	−	0.665435i
$932$	−1.11154	+	1.11154i	−0.0364097	+	0.0364097i
$933$	0.0649911	−	1.51252i	0.00212771	−	0.0495178i
$934$	9.28630	−	11.0670i	0.303857	−	0.362123i
$935$	10.0046	−	1.32632i	0.327186	−	0.0433752i
$936$	−7.77033	+	5.45686i	−0.253981	+	0.178363i
$937$	−31.4158	−	2.74853i	−1.02631	−	0.0897904i	−0.438451	−	0.898755i	$-0.644473\pi$
$937$	−31.4158	−	2.74853i	−1.02631	−	0.0897904i	−0.587858	+	0.808964i	$0.700028\pi$
$938$	2.82322	−	10.5364i	0.0921813	−	0.344025i
$939$	4.25576	−	1.76624i	0.138882	−	0.0576391i
$940$	10.3635	+	13.4807i	0.338019	+	0.439692i
$941$	−42.5921	+	7.51014i	−1.38846	+	0.244824i	−0.817395	−	0.576078i	$-0.804582\pi$
$941$	−42.5921	+	7.51014i	−1.38846	+	0.244824i	−0.571069	+	0.820902i	$0.693471\pi$
$942$	−23.4248	−	9.68390i	−0.763220	−	0.315518i
$943$	−50.1373	−	13.4343i	−1.63270	−	0.437479i
$944$	−1.82765	+	1.53358i	−0.0594850	+	0.0499138i
$945$	−10.6732	−	3.84880i	−0.347199	−	0.125201i
$946$	−10.4039	−	3.78670i	−0.338259	−	0.123116i
$947$	−34.7878	+	3.04354i	−1.13045	+	0.0989016i	−0.636994	−	0.770869i	$-0.719822\pi$
$947$	−34.7878	+	3.04354i	−1.13045	+	0.0989016i	−0.493457	+	0.869770i	$0.664267\pi$
$948$	7.69160	+	0.330497i	0.249812	+	0.0107341i
$949$		−	13.0411i		−	0.423332i
$950$	7.35238	+	20.5169i	0.238543	+	0.665656i
$951$	4.60303	+	3.52698i	0.149263	+	0.114370i
$952$	−0.665664	+	0.466103i	−0.0215743	+	0.0151065i
$953$	−3.56771	−	40.7792i	−0.115570	−	1.32097i	−0.803550	−	0.595237i	$-0.797058\pi$
$953$	−3.56771	−	40.7792i	−0.115570	−	1.32097i	0.687980	−	0.725729i	$-0.258497\pi$
$954$	36.8205	+	3.17010i	1.19211	+	0.102636i
$955$	33.2702	−	1.48269i	1.07660	−	0.0479787i
$956$	−4.40690	−	5.25194i	−0.142529	−	0.169860i
$957$	5.09024	+	6.62424i	0.164544	+	0.214131i
$958$	10.7885	+	40.2634i	0.348562	+	1.30085i
$959$	2.11218	+	11.9788i	0.0682058	+	0.386814i
$960$	−3.87298	+	0.00617131i	−0.125000	+	0.000199178i
$961$	6.19377	−	10.7279i	0.199799	−	0.346062i
$962$	−28.3081	−	7.58514i	−0.912690	−	0.244555i
$963$	−8.75931	−	49.2782i	−0.282265	−	1.58797i
$964$	−0.756897	−	2.07956i	−0.0243780	−	0.0669780i
$965$	−0.936215	−	7.06201i	−0.0301378	−	0.227334i
$966$	−7.50331	+	1.66888i	−0.241415	+	0.0536955i
$967$	−19.0537	+	13.3416i	−0.612727	+	0.429036i	−0.838315	−	0.545187i	$-0.816459\pi$
$967$	−19.0537	+	13.3416i	−0.612727	+	0.429036i	0.225588	+	0.974223i	$0.427570\pi$
$968$	−13.0211	−	13.0211i	−0.418514	−	0.418514i
$969$	−5.98043	−	1.92567i	−0.192119	−	0.0618613i
$970$	−3.39930	+	10.8152i	−0.109145	+	0.347255i
$971$	56.8375	+	10.0220i	1.82400	+	0.321621i	0.977527	−	0.210808i	$-0.0676095\pi$
$971$	56.8375	+	10.0220i	1.82400	+	0.321621i	0.846475	+	0.532429i	$0.178721\pi$
$972$	15.5759	+	0.626145i	0.499596	+	0.0200836i
$973$	11.6476	−	5.43137i	0.373405	−	0.174122i
$974$	0.283033	−	0.103015i	0.00906895	−	0.00330083i
$975$	23.1538	+	14.6695i	0.741516	+	0.469800i
$976$	1.24798	+	2.16157i	0.0399469	+	0.0691901i
$977$	9.84561	+	36.7443i	0.314989	+	1.17555i	0.924000	+	0.382393i	$0.124900\pi$
$977$	9.84561	+	36.7443i	0.314989	+	1.17555i	−0.609011	+	0.793162i	$0.708433\pi$
$978$	9.34312	+	29.5614i	0.298760	+	0.945268i
$979$	66.3166	−	11.6934i	2.11949	−	0.373723i
$980$	−9.14314	−	9.95993i	−0.292067	−	0.318158i
$981$	−3.39769	+	3.40709i	−0.108480	+	0.108780i
$982$	29.5326	+	2.58377i	0.942425	+	0.0824515i
$983$	36.6305	+	17.0811i	1.16833	+	0.544802i	0.907282	−	0.420523i	$-0.138153\pi$
$983$	36.6305	+	17.0811i	1.16833	+	0.544802i	0.261050	+	0.965325i	$0.415931\pi$
$984$	−10.6405	−	16.6768i	−0.339206	−	0.531636i
$985$	8.72063	−	39.5049i	0.277863	−	1.25873i
$986$	−0.728830	−	0.128512i	−0.0232107	−	0.00409267i
$987$	1.68759	+	12.7504i	0.0537167	+	0.405851i
$988$	9.68894	+	9.82102i	0.308246	+	0.312448i
$989$	9.27752			0.295008
$990$	19.6181	+	30.6396i	0.623505	+	0.973791i
$991$	21.3418	+	17.9079i	0.677944	+	0.568862i	0.915405	−	0.402535i	$-0.131871\pi$
$991$	21.3418	+	17.9079i	0.677944	+	0.568862i	−0.237461	+	0.971397i	$0.576315\pi$
$992$	−3.91001	+	1.82327i	−0.124143	+	0.0578888i
$993$	6.08259	+	11.6649i	0.193025	+	0.370173i
$994$	−9.68569	−	11.5430i	−0.307211	−	0.366120i
$995$	5.00642	+	22.4865i	0.158714	+	0.712869i
$996$	14.3554	−	5.95782i	0.454868	−	0.188781i
$997$	−24.5609	+	35.0766i	−0.777852	+	1.11089i	0.213147	+	0.977020i	$0.431629\pi$
$997$	−24.5609	+	35.0766i	−0.777852	+	1.11089i	−0.990999	+	0.133868i	$0.957260\pi$
$998$	12.7543	−	18.2151i	0.403731	−	0.576588i
$999$	29.3692	+	38.1109i	0.929201	+	1.20577i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bi.a.17.27	yes	480
3.2	odd	2	inner	570.2.bi.a.17.5	✓	480
5.3	odd	4	inner	570.2.bi.a.473.24	yes	480
15.8	even	4	inner	570.2.bi.a.473.14	yes	480
19.9	even	9	inner	570.2.bi.a.47.14	yes	480
57.47	odd	18	inner	570.2.bi.a.47.24	yes	480
95.28	odd	36	inner	570.2.bi.a.503.5	yes	480
285.218	even	36	inner	570.2.bi.a.503.27	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bi.a.17.5	✓	480	3.2	odd	2	inner
570.2.bi.a.17.27	yes	480	1.1	even	1	trivial
570.2.bi.a.47.14	yes	480	19.9	even	9	inner
570.2.bi.a.47.24	yes	480	57.47	odd	18	inner
570.2.bi.a.473.14	yes	480	15.8	even	4	inner
570.2.bi.a.473.24	yes	480	5.3	odd	4	inner
570.2.bi.a.503.5	yes	480	95.28	odd	36	inner
570.2.bi.a.503.27	yes	480	285.218	even	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)

\(f(q)\)	\(=\)	\(q+(0.573576 + 0.819152i) q^{2} +(-0.929621 + 1.46144i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(0.0995518 + 2.23385i) q^{5} +(-1.73035 + 0.0767467i) q^{6} +(-0.252738 + 0.943230i) q^{7} +(-0.965926 + 0.258819i) q^{8} +(-1.27161 - 2.71717i) q^{9} +O(q^{10})\)	\(q+(0.573576 + 0.819152i) q^{2} +(-0.929621 + 1.46144i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(0.0995518 + 2.23385i) q^{5} +(-1.73035 + 0.0767467i) q^{6} +(-0.252738 + 0.943230i) q^{7} +(-0.965926 + 0.258819i) q^{8} +(-1.27161 - 2.71717i) q^{9} +(-1.77276 + 1.36283i) q^{10} +(4.69691 + 2.71176i) q^{11} +(-1.05536 - 1.37340i) q^{12} +(-0.275849 + 3.15296i) q^{13} +(-0.917613 + 0.333984i) q^{14} +(-3.35718 - 1.93114i) q^{15} +(-0.766044 - 0.642788i) q^{16} +(-0.477318 - 0.681681i) q^{17} +(1.49641 - 2.60015i) q^{18} +(-4.08584 - 1.51853i) q^{19} +(-2.13318 - 0.670474i) q^{20} +(-1.14352 - 1.24621i) q^{21} +(0.472691 + 5.40289i) q^{22} +(-1.92067 - 4.11888i) q^{23} +(0.519696 - 1.65225i) q^{24} +(-4.98018 + 0.444768i) q^{25} +(-2.74098 + 1.58250i) q^{26} +(5.15309 + 0.667553i) q^{27} +(-0.799904 - 0.560099i) q^{28} +(-0.154429 - 0.875809i) q^{29} +(-0.343700 - 3.85770i) q^{30} +(-2.15711 - 3.73622i) q^{31} +(0.0871557 - 0.996195i) q^{32} +(-8.32942 + 4.34334i) q^{33} +(0.284622 - 0.781993i) q^{34} +(-2.13219 - 0.470678i) q^{35} +(2.98822 - 0.265597i) q^{36} +(6.54753 + 6.54753i) q^{37} +(-1.09964 - 4.21791i) q^{38} +(-4.35143 - 3.33420i) q^{39} +(-0.674323 - 2.13197i) q^{40} +(7.34143 - 8.74918i) q^{41} +(0.364935 - 1.65151i) q^{42} +(-0.862733 + 1.85014i) q^{43} +(-4.15466 + 3.48617i) q^{44} +(5.94316 - 3.11109i) q^{45} +(2.27234 - 3.93581i) q^{46} +(-6.22912 - 4.36168i) q^{47} +(1.65153 - 0.521979i) q^{48} +(5.23637 + 3.02322i) q^{49} +(-3.22085 - 3.82442i) q^{50} +(1.43996 - 0.0638670i) q^{51} +(-2.86847 - 1.33759i) q^{52} +(5.20619 + 11.1647i) q^{53} +(2.40887 + 4.60406i) q^{54} +(-5.59009 + 10.7622i) q^{55} -0.976503i q^{56} +(6.01751 - 4.55955i) q^{57} +(0.628844 - 0.628844i) q^{58} +(0.414295 - 2.34958i) q^{59} +(2.96291 - 2.49423i) q^{60} +(-2.34544 - 0.853669i) q^{61} +(1.82327 - 3.91001i) q^{62} +(2.88430 - 0.512691i) q^{63} +(0.866025 - 0.500000i) q^{64} +(-7.07071 - 0.302321i) q^{65} +(-8.33542 - 4.33182i) q^{66} +(-6.40716 + 9.15037i) q^{67} +(0.803823 - 0.215384i) q^{68} +(7.80499 + 1.02206i) q^{69} +(-0.837420 - 2.01656i) q^{70} +(5.27765 + 14.5002i) q^{71} +(1.93154 + 2.29547i) q^{72} +(-4.10473 + 0.359117i) q^{73} +(-1.60791 + 9.11893i) q^{74} +(3.97968 - 7.69170i) q^{75} +(2.82439 - 3.32007i) q^{76} +(-3.74490 + 3.74490i) q^{77} +(0.235335 - 5.47690i) q^{78} +(-2.85709 + 3.40495i) q^{79} +(1.35963 - 1.77522i) q^{80} +(-5.76601 + 6.91036i) q^{81} +(11.3778 + 0.995427i) q^{82} +(-2.32252 + 8.66776i) q^{83} +(1.56216 - 0.648332i) q^{84} +(1.47526 - 1.13412i) q^{85} +(-2.01039 + 0.354485i) q^{86} +(1.42350 + 0.588482i) q^{87} +(-5.23872 - 1.40371i) q^{88} +(9.51138 - 7.98099i) q^{89} +(5.95731 + 3.08390i) q^{90} +(-2.90425 - 1.05706i) q^{91} +(4.52739 - 0.396095i) q^{92} +(7.46555 + 0.320784i) q^{93} -7.60435i q^{94} +(2.98541 - 9.27833i) q^{95} +(1.37486 + 1.05346i) q^{96} +(4.15309 - 2.90803i) q^{97} +(0.526982 + 6.02343i) q^{98} +(1.39567 - 16.2106i) 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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