LMFDB - Embedded newform 570.2.bi.a.17.13

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			17.13
Character	$\chi$	$=$	570.17
Dual form			570.2.bi.a.503.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.573576 - 0.819152i) q^{2} +(0.721746 + 1.57451i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(-2.18122 - 0.492217i) q^{5} +(0.875787 - 1.49432i) q^{6} +(0.145303 - 0.542278i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-1.95817 + 2.27279i) q^{9} +O(q^{10})$	\(q+(-0.573576 - 0.819152i) q^{2} +(0.721746 + 1.57451i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(-2.18122 - 0.492217i) q^{5} +(0.875787 - 1.49432i) q^{6} +(0.145303 - 0.542278i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-1.95817 + 2.27279i) q^{9} +(0.847896 + 2.06908i) q^{10} +(-3.42129 - 1.97528i) q^{11} +(-1.72641 + 0.139705i) q^{12} +(0.100789 - 1.15202i) q^{13} +(-0.527551 + 0.192013i) q^{14} +(-0.799287 - 3.78961i) q^{15} +(-0.766044 - 0.642788i) q^{16} +(-3.15478 - 4.50549i) q^{17} +(2.98492 + 0.300415i) q^{18} +(1.83509 - 3.95379i) q^{19} +(1.20855 - 1.88133i) q^{20} +(0.958694 - 0.162606i) q^{21} +(0.344314 + 3.93553i) q^{22} +(0.870467 + 1.86672i) q^{23} +(1.10467 + 1.33406i) q^{24} +(4.51545 + 2.14727i) q^{25} +(-1.00149 + 0.578210i) q^{26} +(-4.99183 - 1.44277i) q^{27} +(0.459878 + 0.322010i) q^{28} +(0.343731 + 1.94939i) q^{29} +(-2.64581 + 2.82837i) q^{30} +(-4.41044 - 7.63910i) q^{31} +(-0.0871557 + 0.996195i) q^{32} +(0.640800 - 6.81250i) q^{33} +(-1.88117 + 5.16848i) q^{34} +(-0.583856 + 1.11131i) q^{35} +(-1.46599 - 2.61741i) q^{36} +(-3.81268 - 3.81268i) q^{37} +(-4.29132 + 0.764577i) q^{38} +(1.88661 - 0.672773i) q^{39} +(-2.23429 + 0.0890965i) q^{40} +(2.78046 - 3.31362i) q^{41} +(-0.683084 - 0.692049i) q^{42} +(-3.09155 + 6.62985i) q^{43} +(3.02630 - 2.53937i) q^{44} +(5.38990 - 3.99362i) q^{45} +(1.02985 - 1.78375i) q^{46} +(-4.90003 - 3.43104i) q^{47} +(0.459186 - 1.67007i) q^{48} +(5.78923 + 3.34241i) q^{49} +(-0.831015 - 4.93046i) q^{50} +(4.81699 - 8.21904i) q^{51} +(1.04807 + 0.488724i) q^{52} +(-3.86721 - 8.29327i) q^{53} +(1.68135 + 4.91661i) q^{54} +(6.49031 + 5.99253i) q^{55} -0.561408i q^{56} +(7.54975 + 0.0357464i) q^{57} +(1.39969 - 1.39969i) q^{58} +(-0.585735 + 3.32187i) q^{59} +(3.83444 + 0.545039i) q^{60} +(-5.33263 - 1.94092i) q^{61} +(-3.72786 + 7.99443i) q^{62} +(0.947959 + 1.39211i) q^{63} +(0.866025 - 0.500000i) q^{64} +(-0.786886 + 2.46320i) q^{65} +(-5.94802 + 3.38258i) q^{66} +(-0.769735 + 1.09930i) q^{67} +(5.31277 - 1.42355i) q^{68} +(-2.31092 + 2.71786i) q^{69} +(1.24522 - 0.159153i) q^{70} +(0.994838 + 2.73330i) q^{71} +(-1.30320 + 2.70216i) q^{72} +(-16.1801 + 1.41558i) q^{73} +(-0.936301 + 5.31003i) q^{74} +(-0.121889 + 8.65940i) q^{75} +(3.08770 + 3.07670i) q^{76} +(-1.56827 + 1.56827i) q^{77} +(-1.63322 - 1.15953i) q^{78} +(-0.932998 + 1.11190i) q^{79} +(1.35452 + 1.77912i) q^{80} +(-1.33118 - 8.90101i) q^{81} +(-4.30917 - 0.377003i) q^{82} +(-2.29514 + 8.56557i) q^{83} +(-0.175093 + 0.956493i) q^{84} +(4.66359 + 11.3803i) q^{85} +(7.20410 - 1.27028i) q^{86} +(-2.82125 + 1.94817i) q^{87} +(-3.81595 - 1.02248i) q^{88} +(11.0988 - 9.31298i) q^{89} +(-6.36290 - 2.12450i) q^{90} +(-0.610070 - 0.222047i) q^{91} +(-2.05186 + 0.179515i) q^{92} +(8.84463 - 12.4578i) q^{93} +5.98183i q^{94} +(-5.94887 + 7.72082i) q^{95} +(-1.63142 + 0.581772i) q^{96} +(-13.4055 + 9.38664i) q^{97} +(-0.582621 - 6.65938i) q^{98} +(11.1888 - 3.90795i) 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
$3$	0.721746	+	1.57451i	0.416700	+	0.909044i
$3$	0.721746	+	1.57451i	0.416700	+	0.909044i
$4$	−0.342020	+	0.939693i	−0.171010	+	0.469846i
$5$	−2.18122	−	0.492217i	−0.975471	−	0.220126i
$5$	−2.18122	−	0.492217i	−0.975471	−	0.220126i
$6$	0.875787	−	1.49432i	0.357538	−	0.610054i
$7$	0.145303	−	0.542278i	0.0549194	−	0.204962i	−0.933014	−	0.359839i	$-0.882832\pi$
$7$	0.145303	−	0.542278i	0.0549194	−	0.204962i	0.987934	+	0.154877i	$0.0494982\pi$
$8$	0.965926	−	0.258819i	0.341506	−	0.0915064i
$9$	−1.95817	+	2.27279i	−0.652722	+	0.757598i
$10$	0.847896	+	2.06908i	0.268128	+	0.654299i
$11$	−3.42129	−	1.97528i	−1.03156	−	0.595569i	−0.114126	−	0.993466i	$-0.536407\pi$
$11$	−3.42129	−	1.97528i	−1.03156	−	0.595569i	−0.917430	+	0.397897i	$0.869740\pi$
$12$	−1.72641	+	0.139705i	−0.498371	+	0.0403294i
$13$	0.100789	−	1.15202i	0.0279537	−	0.319513i	−0.969325	−	0.245784i	$-0.920955\pi$
$13$	0.100789	−	1.15202i	0.0279537	−	0.319513i	0.997278	−	0.0737287i	$-0.0234899\pi$
$14$	−0.527551	+	0.192013i	−0.140994	+	0.0513176i
$15$	−0.799287	−	3.78961i	−0.206375	−	0.978473i
$16$	−0.766044	−	0.642788i	−0.191511	−	0.160697i
$17$	−3.15478	−	4.50549i	−0.765146	−	1.09274i	−0.992892	−	0.119021i	$-0.962025\pi$
$17$	−3.15478	−	4.50549i	−0.765146	−	1.09274i	0.227746	−	0.973721i	$-0.426864\pi$
$18$	2.98492	+	0.300415i	0.703553	+	0.0708084i
$19$	1.83509	−	3.95379i	0.421000	−	0.907061i
$19$	1.83509	−	3.95379i	0.421000	−	0.907061i
$20$	1.20855	−	1.88133i	0.270241	−	0.420678i
$21$	0.958694	−	0.162606i	0.209204	−	0.0354835i
$22$	0.344314	+	3.93553i	0.0734080	+	0.839057i
$23$	0.870467	+	1.86672i	0.181505	+	0.389239i	0.975917	−	0.218140i	$-0.0699989\pi$
$23$	0.870467	+	1.86672i	0.181505	+	0.389239i	−0.794413	+	0.607379i	$0.792221\pi$
$24$	1.10467	+	1.33406i	0.225489	+	0.272314i
$25$	4.51545	+	2.14727i	0.903089	+	0.429453i
$26$	−1.00149	+	0.578210i	−0.196408	+	0.113396i
$27$	−4.99183	−	1.44277i	−0.960679	−	0.277662i
$28$	0.459878	+	0.322010i	0.0869088	+	0.0608542i
$29$	0.343731	+	1.94939i	0.0638292	+	0.361993i	0.999947	+	0.0103064i	$0.00328068\pi$
$29$	0.343731	+	1.94939i	0.0638292	+	0.361993i	−0.936118	+	0.351687i	$0.885608\pi$
$30$	−2.64581	+	2.82837i	−0.483057	+	0.516387i
$31$	−4.41044	−	7.63910i	−0.792138	−	1.37202i	−0.924641	−	0.380841i	$-0.875635\pi$
$31$	−4.41044	−	7.63910i	−0.792138	−	1.37202i	0.132502	−	0.991183i	$-0.457699\pi$
$32$	−0.0871557	+	0.996195i	−0.0154071	+	0.176104i
$33$	0.640800	−	6.81250i	0.111549	−	1.18590i
$34$	−1.88117	+	5.16848i	−0.322619	+	0.886387i
$35$	−0.583856	+	1.11131i	−0.0986897	+	0.187845i
$36$	−1.46599	−	2.61741i	−0.244332	−	0.436236i
$37$	−3.81268	−	3.81268i	−0.626801	−	0.626801i	0.320461	−	0.947262i	$-0.396162\pi$
$37$	−3.81268	−	3.81268i	−0.626801	−	0.626801i	−0.947262	+	0.320461i	$0.896162\pi$
$38$	−4.29132	+	0.764577i	−0.696144	+	0.124031i
$39$	1.88661	−	0.672773i	0.302100	−	0.107730i
$40$	−2.23429	+	0.0890965i	−0.353273	+	0.0140874i
$41$	2.78046	−	3.31362i	0.434235	−	0.517501i	−0.503904	−	0.863759i	$-0.668104\pi$
$41$	2.78046	−	3.31362i	0.434235	−	0.517501i	0.938139	+	0.346259i	$0.112548\pi$
$42$	−0.683084	−	0.692049i	−0.105402	−	0.106786i
$43$	−3.09155	+	6.62985i	−0.471457	+	1.01104i	0.516496	+	0.856290i	$0.327236\pi$
$43$	−3.09155	+	6.62985i	−0.471457	+	1.01104i	−0.987953	+	0.154753i	$0.950542\pi$
$44$	3.02630	−	2.53937i	0.456233	−	0.382825i
$45$	5.38990	−	3.99362i	0.803478	−	0.595334i
$46$	1.02985	−	1.78375i	0.151843	−	0.263000i
$47$	−4.90003	−	3.43104i	−0.714743	−	0.500468i	0.158742	−	0.987320i	$-0.449256\pi$
$47$	−4.90003	−	3.43104i	−0.714743	−	0.500468i	−0.873485	+	0.486852i	$0.838145\pi$
$48$	0.459186	−	1.67007i	0.0662778	−	0.241054i
$49$	5.78923	+	3.34241i	0.827032	+	0.477487i
$50$	−0.831015	−	4.93046i	−0.117523	−	0.697272i
$51$	4.81699	−	8.21904i	0.674513	−	1.15090i
$52$	1.04807	+	0.488724i	0.145342	+	0.0677739i
$53$	−3.86721	−	8.29327i	−0.531203	−	1.13917i	−0.970561	−	0.240856i	$-0.922572\pi$
$53$	−3.86721	−	8.29327i	−0.531203	−	1.13917i	0.439358	−	0.898312i	$-0.355206\pi$
$54$	1.68135	+	4.91661i	0.228803	+	0.669066i
$55$	6.49031	+	5.99253i	0.875153	+	0.808033i
$56$		−	0.561408i		−	0.0750213i
$57$	7.54975	+	0.0357464i	0.999989	+	0.00473472i
$58$	1.39969	−	1.39969i	0.183789	−	0.183789i
$59$	−0.585735	+	3.32187i	−0.0762563	+	0.432471i	0.922647	+	0.385646i	$0.126021\pi$
$59$	−0.585735	+	3.32187i	−0.0762563	+	0.432471i	−0.998903	+	0.0468248i	$0.985090\pi$
$60$	3.83444	+	0.545039i	0.495024	+	0.0703642i
$61$	−5.33263	−	1.94092i	−0.682774	−	0.248509i	−0.0227358	−	0.999742i	$-0.507238\pi$
$61$	−5.33263	−	1.94092i	−0.682774	−	0.248509i	−0.660038	+	0.751232i	$0.729460\pi$
$62$	−3.72786	+	7.99443i	−0.473439	+	1.01529i
$63$	0.947959	+	1.39211i	0.119432	+	0.175390i
$64$	0.866025	−	0.500000i	0.108253	−	0.0625000i
$65$	−0.786886	+	2.46320i	−0.0976012	+	0.305522i
$66$	−5.94802	+	3.38258i	−0.732151	+	0.416366i
$67$	−0.769735	+	1.09930i	−0.0940381	+	0.134300i	−0.863414	−	0.504496i	$-0.831678\pi$
$67$	−0.769735	+	1.09930i	−0.0940381	+	0.134300i	0.769376	+	0.638796i	$0.220567\pi$
$68$	5.31277	−	1.42355i	0.644268	−	0.172631i
$69$	−2.31092	+	2.71786i	−0.278202	+	0.327192i
$70$	1.24522	−	0.159153i	0.148832	−	0.0190224i
$71$	0.994838	+	2.73330i	0.118066	+	0.324383i	0.984622	−	0.174696i	$-0.0558942\pi$
$71$	0.994838	+	2.73330i	0.118066	+	0.324383i	−0.866557	+	0.499078i	$0.833672\pi$
$72$	−1.30320	+	2.70216i	−0.153584	+	0.318453i
$73$	−16.1801	+	1.41558i	−1.89374	+	0.165681i	−0.973955	−	0.226741i	$-0.927193\pi$
$73$	−16.1801	+	1.41558i	−1.89374	+	0.165681i	−0.919785	+	0.392422i	$0.871637\pi$
$74$	−0.936301	+	5.31003i	−0.108843	+	0.617278i
$75$	−0.121889	+	8.65940i	−0.0140745	+	0.999901i
$76$	3.08770	+	3.07670i	0.354184	+	0.352922i
$77$	−1.56827	+	1.56827i	−0.178721	+	0.178721i
$78$	−1.63322	−	1.15953i	−0.184926	−	0.131291i
$79$	−0.932998	+	1.11190i	−0.104970	+	0.125099i	−0.815972	−	0.578092i	$-0.803798\pi$
$79$	−0.932998	+	1.11190i	−0.104970	+	0.125099i	0.711001	+	0.703191i	$0.248242\pi$
$80$	1.35452	+	1.77912i	0.151440	+	0.198912i
$81$	−1.33118	−	8.90101i	−0.147908	−	0.989001i
$82$	−4.30917	−	0.377003i	−0.475868	−	0.0416330i
$83$	−2.29514	+	8.56557i	−0.251924	+	0.940194i	0.717852	+	0.696196i	$0.245126\pi$
$83$	−2.29514	+	8.56557i	−0.251924	+	0.940194i	−0.969776	+	0.243998i	$0.921541\pi$
$84$	−0.175093	+	0.956493i	−0.0191042	+	0.104362i
$85$	4.66359	+	11.3803i	0.505837	+	1.23437i
$86$	7.20410	−	1.27028i	0.776838	−	0.136977i
$87$	−2.82125	+	1.94817i	−0.302470	+	0.208866i
$88$	−3.81595	−	1.02248i	−0.406781	−	0.108997i
$89$	11.0988	−	9.31298i	1.17647	−	0.987174i	0.176472	−	0.984306i	$-0.443532\pi$
$89$	11.0988	−	9.31298i	1.17647	−	0.987174i	0.999996	−	0.00286779i	$-0.000912848\pi$
$90$	−6.36290	−	2.12450i	−0.670709	−	0.223942i
$91$	−0.610070	−	0.222047i	−0.0639527	−	0.0232769i
$92$	−2.05186	+	0.179515i	−0.213921	+	0.0187157i
$93$	8.84463	−	12.4578i	0.917146	−	1.29181i
$94$			5.98183i			0.616979i
$95$	−5.94887	+	7.72082i	−0.610341	+	0.792139i
$96$	−1.63142	+	0.581772i	−0.166506	+	0.0593768i
$97$	−13.4055	+	9.38664i	−1.36112	+	0.953069i	−0.361337	+	0.932435i	$0.617679\pi$
$97$	−13.4055	+	9.38664i	−1.36112	+	0.953069i	−0.999787	+	0.0206337i	$0.993432\pi$
$98$	−0.582621	−	6.65938i	−0.0588536	−	0.672699i
$99$	11.1888	−	3.90795i	1.12452	−	0.392764i
$100$	−3.56214	+	3.50872i	−0.356214	+	0.350872i
$101$	8.19918	+	9.77140i	0.815849	+	0.972291i	0.999944	−	0.0106175i	$-0.00337973\pi$
$101$	8.19918	+	9.77140i	0.815849	+	0.972291i	−0.184095	+	0.982909i	$0.558935\pi$
$102$	−9.49556	+	0.768404i	−0.940200	+	0.0760833i
$103$	2.11727	+	7.90175i	0.208621	+	0.778582i	0.988315	+	0.152423i	$0.0487075\pi$
$103$	2.11727	+	7.90175i	0.208621	+	0.778582i	−0.779695	+	0.626160i	$0.784626\pi$
$104$	−0.200810	−	1.13885i	−0.0196911	−	0.111674i
$105$	−2.17116	−	0.117206i	−0.211884	−	0.0114381i
$106$	−4.57530	+	7.92466i	−0.444393	+	0.769711i
$107$	0.963941	+	0.258287i	0.0931877	+	0.0249696i	0.305112	−	0.952317i	$-0.401306\pi$
$107$	0.963941	+	0.258287i	0.0931877	+	0.0249696i	−0.211924	+	0.977286i	$0.567973\pi$
$108$	3.06307	−	4.19733i	0.294744	−	0.403889i
$109$	−0.629800	−	1.73036i	−0.0603239	−	0.165739i	0.905870	−	0.423557i	$-0.139219\pi$
$109$	−0.629800	−	1.73036i	−0.0603239	−	0.165739i	−0.966193	+	0.257818i	$0.916996\pi$
$110$	1.18611	−	8.75373i	0.113091	−	0.834635i
$111$	3.25132	−	8.75489i	0.308601	−	0.830977i
$112$	−0.459878	+	0.322010i	−0.0434544	+	0.0304271i
$113$	7.99505	+	7.99505i	0.752111	+	0.752111i	0.974873	−	0.222762i	$-0.0715073\pi$
$113$	7.99505	+	7.99505i	0.752111	+	0.752111i	−0.222762	+	0.974873i	$0.571507\pi$
$114$	−4.30108	−	6.20490i	−0.402833	−	0.581142i
$115$	−0.979848	−	4.50019i	−0.0913713	−	0.419645i
$116$	−1.94939	−	0.343731i	−0.180997	−	0.0319146i
$117$	2.42094	+	2.48492i	0.223816	+	0.229731i
$118$	3.05708	−	1.42554i	0.281427	−	0.131232i
$119$	−2.90163	+	1.05611i	−0.265992	+	0.0968130i
$120$	−1.75287	−	3.45361i	−0.160015	−	0.315270i
$121$	2.30346	+	3.98971i	0.209406	+	0.362701i
$122$	1.46876	+	5.48150i	0.132976	+	0.496272i
$123$	7.22412	+	1.98627i	0.651377	+	0.179096i
$124$	8.68687	−	1.53173i	0.780104	−	0.137553i
$125$	−8.79226	−	6.90624i	−0.786404	−	0.617713i
$126$	0.596626	−	1.57501i	0.0531517	−	0.140313i
$127$	−1.42365	−	0.124553i	−0.126329	−	0.0110523i	0.0238160	−	0.999716i	$-0.492418\pi$
$127$	−1.42365	−	0.124553i	−0.126329	−	0.0110523i	−0.150145	+	0.988664i	$0.547974\pi$
$128$	−0.906308	−	0.422618i	−0.0801070	−	0.0373545i
$129$	−12.6701	−	0.0826094i	−1.11554	−	0.00727335i
$130$	2.46907	−	0.768254i	0.216552	−	0.0673803i
$131$	12.3065	+	2.16996i	1.07522	+	0.189591i	0.683101	−	0.730323i	$-0.260631\pi$
$131$	12.3065	+	2.16996i	1.07522	+	0.189591i	0.392120	+	0.919914i	$0.371742\pi$
$132$	6.18249	+	2.93217i	0.538117	+	0.255212i
$133$	−1.87741	−	1.56963i	−0.162792	−	0.136104i
$134$	1.34199			0.115930
$135$	10.1781	+	5.60407i	0.875994	+	0.482321i
$136$	−4.21339	−	3.53545i	−0.361295	−	0.303162i
$137$	15.2494	−	7.11092i	1.30285	−	0.607527i	0.357597	−	0.933876i	$-0.383596\pi$
$137$	15.2494	−	7.11092i	1.30285	−	0.607527i	0.945249	+	0.326349i	$0.105818\pi$
$138$	3.55183	+	0.334093i	0.302352	+	0.0284399i
$139$	−4.31962	−	5.14792i	−0.366385	−	0.436641i	0.551083	−	0.834451i	$-0.314215\pi$
$139$	−4.31962	−	5.14792i	−0.366385	−	0.436641i	−0.917468	+	0.397810i	$0.869770\pi$
$140$	−0.844597	−	0.928735i	−0.0713815	−	0.0784924i
$141$	1.86563	−	10.1915i	0.157114	−	0.858278i
$142$	1.66837	−	2.38268i	0.140006	−	0.199950i
$143$	−2.62039	+	3.74230i	−0.219128	+	0.312947i
$144$	2.96096	−	0.482376i	0.246747	−	0.0401980i
$145$	0.209772	−	4.42125i	0.0174206	−	0.367164i
$146$	10.4401	+	12.4420i	0.864030	+	1.02971i
$147$	−1.08431	+	11.5276i	−0.0894324	+	0.950778i
$148$	4.88676	−	2.27873i	0.401689	−	0.187311i
$149$	−15.4756	−	12.9856i	−1.26781	−	1.06382i	−0.994804	−	0.101807i	$-0.967538\pi$
$149$	−15.4756	−	12.9856i	−1.26781	−	1.06382i	−0.273006	−	0.962012i	$-0.588018\pi$
$150$	7.16327	−	4.86698i	0.584879	−	0.397387i
$151$	16.3453			1.33016			0.665080	−	0.746772i	$-0.268397\pi$
$151$	16.3453			1.33016			0.665080	+	0.746772i	$0.268397\pi$
$152$	0.749250	−	4.29402i	0.0607722	−	0.348291i
$153$	16.4176	+	1.65234i	1.32729	+	0.133583i
$154$	2.18418	+	0.385130i	0.176006	+	0.0310346i
$155$	5.86004	+	18.8335i	0.470690	+	1.51274i
$156$	−0.0130592	+	2.00294i	−0.00104557	+	0.160363i
$157$	2.88769	+	1.34655i	0.230463	+	0.107467i	0.534420	−	0.845219i	$-0.320530\pi$
$157$	2.88769	+	1.34655i	0.230463	+	0.107467i	−0.303957	+	0.952686i	$0.598308\pi$
$158$	1.44596	+	0.126505i	0.115035	+	0.0100642i
$159$	10.2667	−	12.0746i	0.814201	−	0.957578i
$160$	0.680450	−	2.13002i	0.0537943	−	0.168393i
$161$	1.13876	−	0.200795i	0.0897472	−	0.0158249i
$162$	−6.52775	+	6.19584i	−0.512868	+	0.486792i
$163$	−0.834970	−	3.11615i	−0.0653999	−	0.244076i	0.925486	−	0.378783i	$-0.123657\pi$
$163$	−0.834970	−	3.11615i	−0.0653999	−	0.244076i	−0.990885	+	0.134707i	$0.956991\pi$
$164$	2.16281	+	3.74610i	0.168887	+	0.292521i
$165$	−4.75095	+	14.5442i	−0.369861	+	1.13226i
$166$	8.33294	−	3.03294i	0.646762	−	0.235402i
$167$	4.42891	−	2.06524i	0.342719	−	0.159813i	−0.243636	−	0.969867i	$-0.578340\pi$
$167$	4.42891	−	2.06524i	0.342719	−	0.159813i	0.586355	+	0.810054i	$0.300562\pi$
$168$	0.883942	−	0.405194i	0.0681976	−	0.0312614i
$169$	11.4855	+	2.02521i	0.883501	+	0.155785i
$170$	6.64727	−	10.3477i	0.509822	−	0.793629i
$171$	5.39272	+	11.9130i	0.412392	+	0.911007i
$172$	−5.17265	−	5.17265i	−0.394411	−	0.394411i
$173$	−1.21500	+	0.850750i	−0.0923745	+	0.0646813i	−0.618851	−	0.785508i	$-0.712402\pi$
$173$	−1.21500	+	0.850750i	−0.0923745	+	0.0646813i	0.526477	+	0.850190i	$0.323513\pi$
$174$	3.21405	+	1.19361i	0.243657	+	0.0904872i
$175$	1.82052	−	2.13662i	0.137619	−	0.161514i
$176$	1.35117	+	3.71231i	0.101848	+	0.279826i
$177$	−5.65307	+	1.47530i	−0.424911	+	0.110890i
$178$	−13.9947	−	3.74988i	−1.04895	−	0.281065i
$179$	−12.2085	+	21.1457i	−0.912503	+	1.58050i	−0.101988	+	0.994786i	$0.532520\pi$
$179$	−12.2085	+	21.1457i	−0.912503	+	1.58050i	−0.810516	+	0.585717i	$0.800813\pi$
$180$	1.90932	+	6.43075i	0.142312	+	0.479319i
$181$	−2.48656	−	14.1020i	−0.184825	−	1.04819i	−0.926180	−	0.377081i	$-0.876928\pi$
$181$	−2.48656	−	14.1020i	−0.184825	−	1.04819i	0.741355	−	0.671113i	$-0.234183\pi$
$182$	0.168031	+	0.627101i	0.0124553	+	0.0464839i
$183$	−0.792809	−	9.79714i	−0.0586061	−	0.724225i
$184$	1.32395	+	1.57782i	0.0976029	+	0.116319i
$185$	6.43963	+	10.1930i	0.473451	+	0.749401i
$186$	−15.2779	−	0.0996124i	−1.12023	−	0.00730394i
$187$	1.89379	+	21.6461i	0.138488	+	1.58292i
$188$	4.90003	−	3.43104i	0.357371	−	0.250234i
$189$	−1.50771	+	2.49732i	−0.109670	+	0.181654i
$190$	9.73665	+	0.444548i	0.706371	+	0.0322509i
$191$		−	16.2595i		−	1.17650i	−0.808679	−	0.588250i	$-0.799817\pi$
$191$		−	16.2595i		−	1.17650i	0.808679	−	0.588250i	$-0.200183\pi$
$192$	1.41231	+	1.00269i	0.101924	+	0.0723631i
$193$	−21.6247	+	1.89192i	−1.55658	+	0.136183i	−0.832694	−	0.553733i	$-0.813203\pi$
$193$	−21.6247	+	1.89192i	−1.55658	+	0.136183i	−0.723889	+	0.689917i	$0.757647\pi$
$194$	15.3782	+	5.59720i	1.10409	+	0.401855i
$195$	−4.44626	+	0.538844i	−0.318404	+	0.0385875i
$196$	−5.12087	+	4.29692i	−0.365776	+	0.306923i
$197$	−1.11835	−	0.299660i	−0.0796789	−	0.0213499i	0.218759	−	0.975779i	$-0.429799\pi$
$197$	−1.11835	−	0.299660i	−0.0796789	−	0.0213499i	−0.298438	+	0.954429i	$0.596466\pi$
$198$	−9.61886	−	6.92386i	−0.683583	−	0.492057i
$199$	21.7859	−	3.84144i	1.54436	−	0.272312i	0.664407	−	0.747371i	$-0.268684\pi$
$199$	21.7859	−	3.84144i	1.54436	−	0.272312i	0.879954	+	0.475059i	$0.157573\pi$
$200$	4.91734	+	0.905417i	0.347708	+	0.0640226i
$201$	−2.28640	−	0.418544i	−0.161271	−	0.0295218i
$202$	3.30141	−	12.3210i	0.232286	−	0.866904i
$203$	1.10706	+	0.0968550i	0.0777003	+	0.00679789i
$204$	6.07587	+	7.33757i	0.425396	+	0.513732i
$205$	−7.69581	+	5.85915i	−0.537499	+	0.409221i
$206$	5.25832	−	6.26662i	0.366364	−	0.436616i
$207$	−5.94719	−	1.67696i	−0.413358	−	0.116557i
$208$	−0.817713	+	0.817713i	−0.0566982	+	0.0566982i
$209$	−14.0882	+	9.90220i	−0.974502	+	0.684950i
$210$	1.14932	+	1.84574i	0.0793104	+	0.127368i
$211$	−2.64102	+	14.9780i	−0.181815	+	1.03113i	0.748164	+	0.663514i	$0.230936\pi$
$211$	−2.64102	+	14.9780i	−0.181815	+	1.03113i	−0.929979	+	0.367612i	$0.880176\pi$
$212$	9.11579	−	0.797528i	0.626075	−	0.0547744i
$213$	−3.58558	+	3.53913i	−0.245680	+	0.242497i
$214$	−0.341317	−	0.937761i	−0.0233320	−	0.0641040i
$215$	10.0067	−	12.9395i	0.682450	−	0.882463i
$216$	−5.19516	−	0.101629i	−0.353486	−	0.00691501i
$217$	−4.78337	+	1.28170i	−0.324716	+	0.0870075i
$218$	−1.05619	+	1.50840i	−0.0715343	+	0.102162i
$219$	−13.9068	−	24.4541i	−0.939733	−	1.65245i
$220$	−7.85096	+	4.04933i	−0.529311	+	0.273006i
$221$	−5.50838	+	3.18026i	−0.370533	+	0.213928i
$222$	−9.03647	+	2.35828i	−0.606488	+	0.158277i
$223$	5.76454	−	12.3621i	0.386022	−	0.827827i	−0.613258	−	0.789883i	$-0.710141\pi$
$223$	5.76454	−	12.3621i	0.386022	−	0.827827i	0.999280	−	0.0379443i	$-0.0120809\pi$
$224$	0.527551	+	0.192013i	0.0352485	+	0.0128294i
$225$	−13.7223	+	6.05797i	−0.914819	+	0.403865i
$226$	1.96339	−	11.1349i	0.130603	−	0.740684i
$227$	4.26201	−	4.26201i	0.282880	−	0.282880i	−0.551377	−	0.834256i	$-0.685897\pi$
$227$	4.26201	−	4.26201i	0.282880	−	0.282880i	0.834256	+	0.551377i	$0.185897\pi$
$228$	−2.61576	+	7.08222i	−0.173233	+	0.469031i
$229$		−	14.4695i		−	0.956171i	−0.878313	−	0.478086i	$-0.841331\pi$
$229$		−	14.4695i		−	0.956171i	0.878313	−	0.478086i	$-0.158669\pi$
$230$	−3.12432	+	3.38385i	−0.206012	+	0.223124i
$231$	−3.60116	−	1.33737i	−0.236939	−	0.0879924i
$232$	0.836558	+	1.79400i	0.0549227	+	0.117782i
$233$	−21.7270	−	10.1315i	−1.42338	−	0.663735i	−0.450024	−	0.893016i	$-0.648585\pi$
$233$	−21.7270	−	10.1315i	−1.42338	−	0.663735i	−0.973360	+	0.229281i	$0.926363\pi$
$234$	0.646930	−	3.40841i	0.0422911	−	0.222815i
$235$	8.99923	+	9.89573i	0.587045	+	0.645526i
$236$	−2.92120	−	1.68656i	−0.190154	−	0.109786i
$237$	−2.42409	−	0.666503i	−0.157462	−	0.0432940i
$238$	2.52941	+	1.77112i	0.163958	+	0.114804i
$239$	−1.56147	+	2.70454i	−0.101003	+	0.174942i	−0.912098	−	0.409972i	$-0.865539\pi$
$239$	−1.56147	+	2.70454i	−0.101003	+	0.174942i	0.811095	+	0.584914i	$0.198872\pi$
$240$	−1.82362	+	3.41678i	−0.117714	+	0.220552i
$241$	7.68174	−	6.44574i	0.494824	−	0.415207i	−0.360927	−	0.932594i	$-0.617540\pi$
$241$	7.68174	−	6.44574i	0.494824	−	0.415207i	0.855751	+	0.517387i	$0.173095\pi$
$242$	1.94697	−	4.17529i	0.125156	−	0.268398i
$243$	13.0540	−	8.52022i	0.837412	−	0.546572i
$244$	3.64774	−	4.34720i	0.233522	−	0.278301i
$245$	−10.9824	−	10.1401i	−0.701639	−	0.647826i
$246$	−2.51653	−	7.05693i	−0.160448	−	0.449933i
$247$	−4.36988	−	2.51256i	−0.278049	−	0.159871i
$248$	−6.23730	−	6.23730i	−0.396069	−	0.396069i
$249$	−15.1431	+	2.56845i	−0.959654	+	0.162769i
$250$	−0.614226	+	11.1635i	−0.0388471	+	0.706039i
$251$	−2.39889	+	6.59088i	−0.151416	+	0.416013i	−0.992090	−	0.125529i	$-0.959937\pi$
$251$	−2.39889	+	6.59088i	−0.151416	+	0.416013i	0.840674	+	0.541542i	$0.182159\pi$
$252$	−1.63238	+	0.414659i	−0.102830	+	0.0261210i
$253$	0.709184	−	8.10601i	0.0445860	−	0.509620i
$254$	0.714545	+	1.23763i	0.0448346	+	0.0776557i
$255$	−14.5525	+	15.5565i	−0.911311	+	0.974189i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−13.4850	−	9.44227i	−0.841169	−	0.588993i	0.0716166	−	0.997432i	$-0.477184\pi$
$257$	−13.4850	−	9.44227i	−0.841169	−	0.588993i	−0.912785	+	0.408440i	$0.866073\pi$
$258$	7.19959	+	10.4261i	0.448227	+	0.649101i
$259$	−2.62153	+	1.51354i	−0.162894	+	0.0940467i
$260$	−2.04552	−	1.58189i	−0.126858	−	0.0981049i
$261$	−5.10365	−	3.03601i	−0.315908	−	0.187924i
$262$	−5.28117	−	11.3255i	−0.326272	−	0.699692i
$263$	0.409479	+	4.68037i	0.0252496	+	0.288604i	0.998313	+	0.0580654i	$0.0184932\pi$
$263$	0.409479	+	4.68037i	0.0252496	+	0.288604i	−0.973063	+	0.230538i	$0.925951\pi$
$264$	−1.14424	−	6.74622i	−0.0704231	−	0.415201i
$265$	4.35316	+	19.9929i	0.267413	+	1.22816i
$266$	−0.208928	+	2.43818i	−0.0128102	+	0.149495i
$267$	22.6739	+	10.7535i	1.38762	+	0.658105i
$268$	−0.769735	−	1.09930i	−0.0470190	−	0.0671502i
$269$	−13.2753	−	11.1393i	−0.809411	−	0.679176i	0.141056	−	0.990002i	$-0.454950\pi$
$269$	−13.2753	−	11.1393i	−0.809411	−	0.679176i	−0.950467	+	0.310825i	$0.899395\pi$
$270$	−1.24735	−	11.5518i	−0.0759115	−	0.703020i
$271$	19.9449	−	7.25935i	1.21157	−	0.440974i	0.344320	−	0.938852i	$-0.388109\pi$
$271$	19.9449	−	7.25935i	1.21157	−	0.440974i	0.867247	+	0.497878i	$0.165887\pi$
$272$	−0.479373	+	5.47925i	−0.0290662	+	0.332229i
$273$	−0.0906998	−	1.12082i	−0.00548940	−	0.0678353i
$274$	−14.5716	−	8.41294i	−0.880305	−	0.508244i
$275$	−11.2072	−	16.2657i	−0.675818	−	0.980857i
$276$	−1.76357	−	3.10111i	−0.106155	−	0.186665i
$277$	−20.7542	+	5.56106i	−1.24700	+	0.334132i	−0.821176	−	0.570675i	$-0.806681\pi$
$277$	−20.7542	+	5.56106i	−1.24700	+	0.334132i	−0.425821	+	0.904807i	$0.640015\pi$
$278$	−1.73930	+	6.49115i	−0.104316	+	0.389313i
$279$	25.9985	+	4.93462i	1.55649	+	0.295428i
$280$	−0.276334	+	1.22455i	−0.0165141	+	0.0731811i
$281$	−5.82185	+	15.9954i	−0.347303	+	0.954206i	0.635913	+	0.771761i	$0.280624\pi$
$281$	−5.82185	+	15.9954i	−0.347303	+	0.954206i	−0.983216	+	0.182446i	$0.941599\pi$
$282$	−9.41846	+	4.31736i	−0.560861	+	0.257095i
$283$	−9.87901	−	14.1087i	−0.587246	−	0.838675i	0.410057	−	0.912060i	$-0.365509\pi$
$283$	−9.87901	−	14.1087i	−0.587246	−	0.838675i	−0.997304	+	0.0733852i	$0.976620\pi$
$284$	−2.90871			−0.172600
$285$	−16.4501	−	3.79408i	−0.974418	−	0.224742i
$286$	4.56851			0.270142
$287$	−1.39290	−	1.98926i	−0.0822200	−	0.117422i
$288$	−2.09348	−	2.14880i	−0.123359	−	0.126619i
$289$	−4.53246	+	12.4528i	−0.266615	+	0.732519i
$290$	−3.74199	+	2.36409i	−0.219737	+	0.138824i
$291$	−24.4547	−	14.3323i	−1.43356	−	0.840177i
$292$	4.20372	−	15.6885i	0.246004	−	0.918100i
$293$	−9.81116	+	2.62889i	−0.573174	+	0.153582i	−0.533752	−	0.845641i	$-0.679218\pi$
$293$	−9.81116	+	2.62889i	−0.573174	+	0.153582i	−0.0394223	+	0.999223i	$0.512552\pi$
$294$	10.0648	−	5.72373i	0.586989	−	0.333814i
$295$	2.91270	−	6.95742i	0.169584	−	0.405077i
$296$	−4.66956	−	2.69597i	−0.271413	−	0.156700i
$297$	14.2286	+	14.7964i	0.825628	+	0.858575i
$298$	−1.76072	+	20.1251i	−0.101996	+	1.16581i
$299$	2.23823	−	0.814651i	0.129440	−	0.0471125i
$300$	−8.09548	−	3.07623i	−0.467393	−	0.177606i
$301$	3.14601	+	2.63982i	0.181333	+	0.152157i
$302$	−9.37527	−	13.3893i	−0.539486	−	0.770466i
$303$	−9.46745	+	19.9622i	−0.543891	+	1.14680i
$304$	−3.94721	+	1.84920i	−0.226388	+	0.106059i
$305$	10.6763	+	6.85839i	0.611323	+	0.392710i
$306$	−8.06324	−	14.3963i	−0.460945	−	0.822979i
$307$	0.555627	+	6.35085i	0.0317113	+	0.362462i	0.995427	+	0.0955297i	$0.0304545\pi$
$307$	0.555627	+	6.35085i	0.0317113	+	0.362462i	−0.963715	+	0.266932i	$0.913990\pi$
$308$	−0.937314	−	2.01008i	−0.0534084	−	0.114535i
$309$	−10.9133	+	9.03671i	−0.620833	+	0.514081i
$310$	12.0663	−	15.6027i	0.685319	−	0.886174i
$311$	10.5504	−	6.09127i	0.598258	−	0.345404i	−0.170098	−	0.985427i	$-0.554408\pi$
$311$	10.5504	−	6.09127i	0.598258	−	0.345404i	0.768356	+	0.640023i	$0.221075\pi$
$312$	1.64820	−	1.13814i	0.0933109	−	0.0644345i
$313$	−9.67372	−	6.77361i	−0.546791	−	0.382867i	0.267292	−	0.963616i	$-0.413871\pi$
$313$	−9.67372	−	6.77361i	−0.546791	−	0.382867i	−0.814083	+	0.580748i	$0.802760\pi$
$314$	−0.553280	−	3.13781i	−0.0312234	−	0.177077i
$315$	−1.38249	−	3.50311i	−0.0778942	−	0.197378i
$316$	−0.725744	−	1.25702i	−0.0408263	−	0.0707132i
$317$	2.53962	−	29.0280i	0.142639	−	1.63037i	−0.501283	−	0.865283i	$-0.667139\pi$
$317$	2.53962	−	29.0280i	0.142639	−	1.63037i	0.643923	−	0.765091i	$-0.277306\pi$
$318$	−15.7797	−	1.48427i	−0.884879	−	0.0832339i
$319$	2.67460	−	7.34839i	0.149749	−	0.411431i
$320$	−2.13510	+	0.664338i	−0.119356	+	0.0371376i
$321$	0.289045	+	1.70415i	0.0161329	+	0.0951165i
$322$	−0.817650	−	0.817650i	−0.0455658	−	0.0455658i
$323$	−23.6030	+	4.20531i	−1.31331	+	0.233990i
$324$	8.81950	+	1.79343i	0.489972	+	0.0996349i
$325$	2.92880	−	4.98546i	0.162461	−	0.276544i
$326$	−2.07368	+	2.47132i	−0.114851	+	0.136874i
$327$	2.26992	−	2.24051i	0.125527	−	0.123900i
$328$	1.82809	−	3.92035i	0.100939	−	0.216465i
$329$	−2.57257	+	2.15864i	−0.141830	+	0.119010i
$330$	14.6389	−	4.45043i	0.805845	−	0.244988i
$331$	−10.2001	+	17.6672i	−0.560650	+	0.971075i	0.436789	+	0.899564i	$0.356116\pi$
$331$	−10.2001	+	17.6672i	−0.560650	+	0.971075i	−0.997440	+	0.0715112i	$0.977218\pi$
$332$	−7.26402	−	5.08632i	−0.398665	−	0.279148i
$333$	16.1313	−	1.19957i	0.883989	−	0.0657363i
$334$	−4.23206	−	2.44338i	−0.231568	−	0.133696i
$335$	2.22005	−	2.01893i	0.121294	−	0.110306i
$336$	−0.838924	−	0.491673i	−0.0457670	−	0.0268230i
$337$	22.0947	+	10.3029i	1.20357	+	0.561236i	0.917793	−	0.397059i	$-0.129969\pi$
$337$	22.0947	+	10.3029i	1.20357	+	0.561236i	0.285781	+	0.958295i	$0.407747\pi$
$338$	−4.92887	−	10.5700i	−0.268095	−	0.574932i
$339$	−6.81789	+	18.3587i	−0.370297	+	0.997106i
$340$	−12.2890	+	0.490047i	−0.666466	+	0.0265765i
$341$			34.8474i			1.88709i
$342$	6.66539	−	11.2504i	0.360423	−	0.608355i
$343$	5.43253	−	5.43253i	0.293329	−	0.293329i
$344$	−1.27028	+	7.20410i	−0.0684887	+	0.388419i
$345$	6.37840	−	4.79078i	0.343401	−	0.257927i
$346$	1.39379	+	0.507297i	0.0749304	+	0.0272724i
$347$	−0.518883	+	1.11275i	−0.0278551	+	0.0597354i	−0.919743	−	0.392521i	$-0.871603\pi$
$347$	−0.518883	+	1.11275i	−0.0278551	+	0.0597354i	0.891888	+	0.452256i	$0.149381\pi$
$348$	−0.865759	−	3.31743i	−0.0464096	−	0.177833i
$349$	−0.926879	+	0.535134i	−0.0496147	+	0.0286451i	−0.524602	−	0.851347i	$-0.675786\pi$
$349$	−0.926879	+	0.535134i	−0.0496147	+	0.0286451i	0.474987	+	0.879993i	$0.342453\pi$
$350$	−2.79443	−	0.265769i	−0.149368	−	0.0142059i
$351$	−2.16522	+	5.60528i	−0.115571	+	0.299188i
$352$	2.26595	−	3.23611i	0.120775	−	0.172485i
$353$	4.89654	−	1.31202i	0.260617	−	0.0698320i	−0.126145	−	0.992012i	$-0.540260\pi$
$353$	4.89654	−	1.31202i	0.260617	−	0.0698320i	0.386761	+	0.922180i	$0.373594\pi$
$354$	4.45096	+	3.78453i	0.236566	+	0.201145i
$355$	−0.824588	−	6.45160i	−0.0437646	−	0.342415i
$356$	4.95533	+	13.6147i	0.262632	+	0.721576i
$357$	−3.75708	−	3.80640i	−0.198846	−	0.201456i
$358$	24.3240	−	2.12808i	1.28556	−	0.112472i
$359$	−4.52558	+	25.6658i	−0.238851	+	1.35459i	0.595499	+	0.803356i	$0.296954\pi$
$359$	−4.52558	+	25.6658i	−0.238851	+	1.35459i	−0.834350	+	0.551235i	$0.814157\pi$
$360$	4.17262	−	5.25255i	0.219916	−	0.276834i
$361$	−12.2649	−	14.5111i	−0.645519	−	0.763745i
$362$	−10.1255	+	10.1255i	−0.532182	+	0.532182i
$363$	−4.61933	+	6.50638i	−0.242452	+	0.341497i
$364$	0.417313	−	0.497334i	0.0218731	−	0.0260674i
$365$	35.9892	+	4.87644i	1.88376	+	0.255245i
$366$	−7.57061	+	6.26884i	−0.395722	+	0.327677i
$367$	19.4005	+	1.69733i	1.01270	+	0.0885997i	0.581407	−	0.813613i	$-0.302502\pi$
$367$	19.4005	+	1.69733i	1.01270	+	0.0885997i	0.431292	+	0.902212i	$0.358058\pi$
$368$	0.533090	−	1.98952i	0.0277892	−	0.103711i
$369$	2.08658	+	12.8080i	0.108623	+	0.666759i
$370$	4.65596	−	11.1215i	0.242052	−	0.578178i
$371$	−5.05917	+	0.892069i	−0.262659	+	0.0463139i
$372$	8.68144	+	12.5720i	0.450112	+	0.651830i
$373$	14.5237	+	3.89160i	0.752006	+	0.201499i	0.614408	−	0.788989i	$-0.289395\pi$
$373$	14.5237	+	3.89160i	0.752006	+	0.201499i	0.137599	+	0.990488i	$0.456062\pi$
$374$	16.6452	−	13.9670i	0.860704	−	0.722217i
$375$	4.52817	−	18.8281i	0.233833	−	0.972277i
$376$	−5.62108	−	2.04591i	−0.289885	−	0.105510i
$377$	2.28038	−	0.199508i	0.117446	−	0.0102752i
$378$	2.91048	−	0.197360i	0.149699	−	0.0101511i
$379$		−	32.5690i		−	1.67296i	−0.548000	−	0.836478i	$-0.684611\pi$
$379$		−	32.5690i		−	1.67296i	0.548000	−	0.836478i	$-0.315389\pi$
$380$	−5.22056	−	8.23078i	−0.267809	−	0.422230i
$381$	−0.831405	−	2.33145i	−0.0425942	−	0.119444i
$382$	−13.3190	+	9.32609i	−0.681461	+	0.477164i
$383$	1.64927	+	18.8512i	0.0842735	+	0.963251i	0.914169	+	0.405332i	$0.132844\pi$
$383$	1.64927	+	18.8512i	0.0842735	+	0.963251i	−0.829896	+	0.557918i	$0.811600\pi$
$384$	0.0112928	−	1.73201i	0.000576283	−	0.0883865i
$385$	4.19268	−	2.64882i	0.213679	−	0.134996i
$386$	13.9532	+	16.6288i	0.710200	+	0.846383i
$387$	−9.01451	−	20.0088i	−0.458233	−	1.01710i
$388$	−4.23560	−	15.8075i	−0.215030	−	0.802503i
$389$	−5.08228	−	28.8230i	−0.257682	−	1.46139i	−0.789094	−	0.614273i	$-0.789449\pi$
$389$	−5.08228	−	28.8230i	−0.257682	−	1.46139i	0.531412	−	0.847114i	$-0.321662\pi$
$390$	2.99167	+	3.33310i	0.151489	+	0.168778i
$391$	5.66437	−	9.81097i	0.286459	−	0.496162i
$392$	6.45704	+	1.73016i	0.326130	+	0.0873862i
$393$	5.46552	+	20.9428i	0.275699	+	1.05643i
$394$	0.395990	+	1.08797i	0.0199497	+	0.0548114i
$395$	2.58237	−	1.96607i	0.129933	−	0.0989237i
$396$	−0.154540	+	11.8507i	−0.00776594	+	0.595519i
$397$	24.3620	−	17.0585i	1.22269	−	0.856139i	0.229580	−	0.973290i	$-0.426265\pi$
$397$	24.3620	−	17.0585i	1.22269	−	0.856139i	0.993114	+	0.117150i	$0.0373760\pi$
$398$	−15.6426	−	15.6426i	−0.784092	−	0.784092i
$399$	1.11639	−	4.08887i	0.0558892	−	0.204700i
$400$	−2.07880	−	4.54737i	−0.103940	−	0.227369i
$401$	14.2236	+	2.50801i	0.710294	+	0.125244i	0.517110	−	0.855919i	$-0.327008\pi$
$401$	14.2236	+	2.50801i	0.710294	+	0.125244i	0.193183	+	0.981163i	$0.438119\pi$
$402$	0.968577	+	2.11298i	0.0483082	+	0.105386i
$403$	−9.24492	+	4.31098i	−0.460522	+	0.214745i
$404$	−11.9864	+	4.36269i	−0.596346	+	0.217052i
$405$	−1.47764	+	20.0703i	−0.0734244	+	0.997301i
$406$	−0.555643	−	0.962403i	−0.0275761	−	0.0477632i
$407$	5.51316	+	20.5754i	0.273277	+	1.01988i
$408$	2.52561	−	9.18572i	0.125036	−	0.454761i
$409$	−12.5261	+	2.20869i	−0.619376	+	0.109213i	−0.474527	−	0.880241i	$-0.657381\pi$
$409$	−12.5261	+	2.20869i	−0.619376	+	0.109213i	−0.144849	+	0.989454i	$0.546270\pi$
$410$	9.21367	+	2.94337i	0.455031	+	0.145363i
$411$	22.2024	+	18.8781i	1.09517	+	0.931188i
$412$	−8.14936	−	0.712977i	−0.401490	−	0.0351258i
$413$	1.71627	+	0.800309i	0.0844521	+	0.0393806i
$414$	2.03748	+	5.83352i	0.100137	+	0.286702i
$415$	9.22232	−	17.5537i	0.452706	−	0.861677i
$416$	1.13885	+	0.200810i	0.0558368	+	0.00984553i
$417$	4.98778	−	10.5168i	0.244253	−	0.515008i
$418$	16.1921	+	5.86072i	0.791981	+	0.286657i
$419$	−24.4915			−1.19649			−0.598244	−	0.801314i	$-0.704135\pi$
$419$	−24.4915			−1.19649			−0.598244	+	0.801314i	$0.704135\pi$
$420$	0.852718	−	2.00014i	0.0416084	−	0.0975967i
$421$	−4.07576	−	3.41997i	−0.198640	−	0.166679i	0.538042	−	0.842918i	$-0.319164\pi$
$421$	−4.07576	−	3.41997i	−0.198640	−	0.166679i	−0.736682	+	0.676239i	$0.763609\pi$
$422$	13.7841	−	6.42761i	0.670997	−	0.312891i
$423$	17.3931	−	4.41821i	0.845682	−	0.214821i
$424$	−5.88190	−	7.00977i	−0.285650	−	0.340425i
$425$	−4.57074	−	27.1184i	−0.221713	−	1.31544i
$426$	4.95569	+	0.907176i	0.240104	+	0.0439528i
$427$	−1.82737	+	2.60975i	−0.0884325	+	0.126295i
$428$	−0.572398	+	0.817468i	−0.0276679	+	0.0395138i
$429$	−7.78355	−	1.42484i	−0.375793	−	0.0687918i
$430$	−16.3390	−	0.775224i	−0.787935	−	0.0373846i
$431$	−16.0139	−	19.0846i	−0.771361	−	0.919273i	0.227148	−	0.973860i	$-0.427060\pi$
$431$	−16.0139	−	19.0846i	−0.771361	−	0.919273i	−0.998509	+	0.0545877i	$0.982616\pi$
$432$	2.89657	+	4.31392i	0.139361	+	0.207553i
$433$	25.4794	−	11.8812i	1.22446	−	0.570976i	0.300617	−	0.953745i	$-0.402807\pi$
$433$	25.4794	−	11.8812i	1.22446	−	0.570976i	0.923844	+	0.382769i	$0.125030\pi$
$434$	3.79354	+	3.18315i	0.182096	+	0.152796i
$435$	7.11270	−	2.86073i	0.341028	−	0.137161i
$436$	1.84141			0.0881876
$437$	8.97801	−	0.0160276i	0.429477	−	0.000766706i
$438$	−12.0550	+	25.4181i	−0.576011	+	1.21452i
$439$	−29.2317	−	5.15433i	−1.39515	−	0.246003i	−0.575002	−	0.818152i	$-0.694999\pi$
$439$	−29.2317	−	5.15433i	−1.39515	−	0.246003i	−0.820149	+	0.572149i	$0.806110\pi$
$440$	7.82014	+	4.10853i	0.372811	+	0.195866i
$441$	−18.9329	+	6.61272i	−0.901565	+	0.314891i
$442$	5.76459	+	2.68807i	0.274194	+	0.127859i
$443$	−4.63435	−	0.405453i	−0.220185	−	0.0192637i	−0.0234705	−	0.999725i	$-0.507472\pi$
$443$	−4.63435	−	0.405453i	−0.220185	−	0.0192637i	−0.196714	+	0.980461i	$0.563027\pi$
$444$	7.11489	+	6.04959i	0.337658	+	0.287101i
$445$	−28.7929	+	14.8507i	−1.36491	+	0.703988i
$446$	−13.4328	+	2.36857i	−0.636063	+	0.112155i
$447$	9.27646	−	33.7388i	0.438762	−	1.59579i
$448$	−0.145303	−	0.542278i	−0.00686492	−	0.0256202i
$449$	7.42966	+	12.8686i	0.350627	+	0.607305i	0.986360	−	0.164605i	$-0.0526350\pi$
$449$	7.42966	+	12.8686i	0.350627	+	0.607305i	−0.635732	+	0.771910i	$0.719302\pi$
$450$	12.8332	+	7.76593i	0.604962	+	0.366089i
$451$	−16.0581	+	5.84466i	−0.756145	+	0.275214i
$452$	−10.2474	+	4.77842i	−0.481995	+	0.224758i
$453$	11.7971	+	25.7358i	0.554278	+	1.20917i
$454$	−5.93583	−	1.04665i	−0.278582	−	0.0491216i
$455$	1.22140	+	0.784621i	0.0572602	+	0.0367836i
$456$	7.30175	−	1.91949i	0.341936	−	0.0898884i
$457$	−12.4726	−	12.4726i	−0.583445	−	0.583445i	0.352403	−	0.935848i	$-0.385365\pi$
$457$	−12.4726	−	12.4726i	−0.583445	−	0.583445i	−0.935848	+	0.352403i	$0.885365\pi$
$458$	−11.8527	+	8.29936i	−0.553841	+	0.387804i
$459$	9.24773	+	27.0423i	0.431647	+	1.26222i
$460$	4.56392	+	0.618400i	0.212794	+	0.0288330i
$461$	−2.69429	−	7.40250i	−0.125486	−	0.344769i	0.861003	−	0.508600i	$-0.169837\pi$
$461$	−2.69429	−	7.40250i	−0.125486	−	0.344769i	−0.986488	+	0.163831i	$0.947615\pi$
$462$	0.970032	+	3.71698i	0.0451300	+	0.172930i
$463$	13.4807	+	3.61214i	0.626501	+	0.167871i	0.558082	−	0.829786i	$-0.311538\pi$
$463$	13.4807	+	3.61214i	0.626501	+	0.167871i	0.0684198	+	0.997657i	$0.478204\pi$
$464$	0.989733	−	1.71427i	0.0459472	−	0.0795829i
$465$	−25.4240	+	22.8197i	−1.17901	+	1.05824i
$466$	4.16289	+	23.6089i	0.192842	+	1.09366i
$467$	0.716204	+	2.67291i	0.0331420	+	0.123688i	0.980515	−	0.196444i	$-0.0629395\pi$
$467$	0.716204	+	2.67291i	0.0331420	+	0.123688i	−0.947373	+	0.320132i	$0.896273\pi$
$468$	−3.16307	+	1.42505i	−0.146213	+	0.0658729i
$469$	0.484279	+	0.577141i	0.0223619	+	0.0266499i
$470$	2.94436	−	13.0477i	0.135813	−	0.601845i
$471$	−0.0359813	+	5.51857i	−0.00165793	+	0.254282i
$472$	0.293986	+	3.36028i	0.0135318	+	0.154669i
$473$	23.6729	−	16.5759i	1.08848	−	0.762162i
$474$	0.844434	+	2.36799i	0.0387862	+	0.108765i
$475$	16.7761	−	13.9127i	0.769740	−	0.638357i
$476$		−	3.08785i		−	0.141531i
$477$	26.4215	+	7.45021i	1.20976	+	0.341122i
$478$	3.11105	−	0.272182i	0.142296	−	0.0124493i
$479$	29.8211	+	10.8540i	1.36256	+	0.495932i	0.916846	−	0.399241i	$-0.130726\pi$
$479$	29.8211	+	10.8540i	1.36256	+	0.495932i	0.445717	+	0.895174i	$0.352949\pi$
$480$	3.84485	−	0.465959i	0.175493	−	0.0212680i
$481$	−4.77656	+	4.00801i	−0.217792	+	0.182749i
$482$	−9.68611	−	2.59539i	−0.441190	−	0.118217i
$483$	1.13805	+	1.64807i	0.0517832	+	0.0749899i
$484$	−4.53693	+	0.799984i	−0.206224	+	0.0363629i
$485$	33.8606	−	13.8759i	1.53753	−	0.630073i
$486$	−14.4668	−	5.80618i	−0.656227	−	0.263374i
$487$	7.09555	−	26.4809i	0.321530	−	1.19997i	−0.596225	−	0.802818i	$-0.703333\pi$
$487$	7.09555	−	26.4809i	0.321530	−	1.19997i	0.917754	−	0.397148i	$-0.130000\pi$
$488$	−5.65328	−	0.494598i	−0.255912	−	0.0223894i
$489$	4.30378	−	3.56374i	0.194623	−	0.161158i
$490$	−2.00704	+	14.8124i	−0.0906687	+	0.669154i
$491$	18.0305	−	21.4879i	0.813704	−	0.969735i	−0.186214	−	0.982509i	$-0.559622\pi$
$491$	18.0305	−	21.4879i	0.813704	−	0.969735i	0.999918	+	0.0127743i	$0.00406629\pi$
$492$	−4.33728	+	6.10911i	−0.195539	+	0.275420i
$493$	7.69857	−	7.69857i	0.346726	−	0.346726i
$494$	0.448291	+	5.02075i	0.0201696	+	0.225894i
$495$	−26.3289	+	3.01676i	−1.18340	+	0.135593i
$496$	−1.53173	+	8.68687i	−0.0687767	+	0.390052i
$497$	1.62676	−	0.142323i	0.0729701	−	0.00638406i
$498$	10.7897	+	10.9313i	0.483497	+	0.489843i
$499$	8.85695	+	24.3343i	0.396492	+	1.08935i	0.963981	+	0.265971i	$0.0856926\pi$
$499$	8.85695	+	24.3343i	0.396492	+	1.08935i	−0.567489	+	0.823381i	$0.692085\pi$
$500$	9.49687	−	5.89995i	0.424713	−	0.263854i
$501$	6.44828	+	5.48279i	0.288088	+	0.244953i
$502$	6.77488	−	1.81532i	0.302378	−	0.0810219i
$503$	23.8046	−	33.9965i	1.06139	−	1.51583i	0.219931	−	0.975515i	$-0.429417\pi$
$503$	23.8046	−	33.9965i	1.06139	−	1.51583i	0.841464	−	0.540313i	$-0.181694\pi$
$504$	1.27596	+	1.09933i	0.0568359	+	0.0489680i
$505$	−13.0746	−	25.3494i	−0.581811	−	1.12803i
$506$	−7.04682	+	4.06848i	−0.313269	+	0.180866i
$507$	5.10091	+	19.5457i	0.226540	+	0.868057i
$508$	0.603960	−	1.29520i	0.0267964	−	0.0574650i
$509$	−36.7968	−	13.3929i	−1.63099	−	0.593632i	−0.645559	−	0.763710i	$-0.723376\pi$
$509$	−36.7968	−	13.3929i	−1.63099	−	0.593632i	−0.985430	+	0.170079i	$0.945598\pi$
$510$	21.0901	+	2.99781i	0.933886	+	0.132745i
$511$	−1.58338	+	8.97982i	−0.0700448	+	0.397244i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−14.8649	+	17.0890i	−0.656302	+	0.754499i
$514$			16.4621i			0.726112i
$515$	−0.728853	−	18.2776i	−0.0321171	−	0.805408i
$516$	4.41105	−	11.8777i	0.194186	−	0.522888i
$517$	9.98714	+	21.4175i	0.439234	+	0.941940i
$518$	2.74346	+	1.27930i	0.120541	+	0.0562092i
$519$	−2.21643	−	1.29900i	−0.0972906	−	0.0570197i
$520$	−0.122550	+	2.58293i	−0.00537419	+	0.113269i
$521$	9.06734	+	5.23503i	0.397247	+	0.229351i	0.685296	−	0.728265i	$-0.259673\pi$
$521$	9.06734	+	5.23503i	0.397247	+	0.229351i	−0.288048	+	0.957616i	$0.593006\pi$
$522$	0.440382	+	5.92204i	0.0192750	+	0.259201i
$523$	20.1882	+	14.1359i	0.882769	+	0.618122i	0.924573	−	0.381004i	$-0.124422\pi$
$523$	20.1882	+	14.1359i	0.882769	+	0.618122i	−0.0418043	+	0.999126i	$0.513311\pi$
$524$	−6.24816	+	10.8221i	−0.272952	+	0.472767i
$525$	4.67809	+	1.32433i	0.204169	+	0.0577987i
$526$	3.59907	−	3.01998i	0.156927	−	0.131677i
$527$	−20.5039	+	43.9708i	−0.893166	+	1.91540i
$528$	−4.86987	+	4.80678i	−0.211934	+	0.209188i
$529$	12.0572	−	14.3692i	0.524225	−	0.624747i
$530$	13.8804	−	15.0334i	0.602926	−	0.653008i
$531$	−6.40296	−	7.83603i	−0.277865	−	0.340055i
$532$	2.11708	−	1.22734i	0.0917870	−	0.0532120i
$533$	−3.53712	−	3.53712i	−0.153210	−	0.153210i
$534$	−4.19642	−	24.7413i	−0.181597	−	1.07066i
$535$	−1.97543	−	1.03785i	−0.0854054	−	0.0448701i
$536$	−0.458988	+	1.26106i	−0.0198253	+	0.0544695i
$537$	−42.1055	−	3.96054i	−1.81699	−	0.170910i
$538$	−1.51038	+	17.2638i	−0.0651172	+	0.744293i
$539$	−13.2044	−	22.8707i	−0.568754	−	0.985110i
$540$	−8.74723	+	7.64761i	−0.376421	+	0.329101i
$541$	−2.23160	−	12.6560i	−0.0959440	−	0.544125i	−0.994454	−	0.105172i	$-0.966461\pi$
$541$	−2.23160	−	12.6560i	−0.0959440	−	0.544125i	0.898510	−	0.438953i	$-0.144651\pi$
$542$	−17.3864	−	12.1741i	−0.746812	−	0.522923i
$543$	20.4091	−	14.0932i	0.875838	−	0.604797i
$544$	4.76330	−	2.75009i	0.204225	−	0.117909i
$545$	0.522020	+	4.08430i	0.0223609	+	0.174952i
$546$	−0.866102	+	0.717175i	−0.0370657	+	0.0306923i
$547$	14.3677	+	30.8116i	0.614317	+	1.31741i	0.929656	+	0.368429i	$0.120104\pi$
$547$	14.3677	+	30.8116i	0.614317	+	1.31741i	−0.315339	+	0.948979i	$0.602118\pi$
$548$	1.46647	+	16.7618i	0.0626446	+	0.716031i
$549$	14.8535	−	8.31933i	0.633932	−	0.355060i
$550$	−6.89589	+	18.5100i	−0.294042	+	0.789269i
$551$	8.33826	+	2.21828i	0.355222	+	0.0945021i
$552$	−1.52874	+	3.22336i	−0.0650676	+	0.137195i
$553$	0.467394	+	0.667507i	0.0198756	+	0.0283853i
$554$	16.4595	+	13.8111i	0.699295	+	0.586778i
$555$	−11.4011	+	17.4960i	−0.483952	+	0.742664i
$556$	6.31486	−	2.29842i	0.267810	−	0.0974747i
$557$	1.62420	−	18.5647i	0.0688195	−	0.786610i	−0.880858	−	0.473381i	$-0.843033\pi$
$557$	1.62420	−	18.5647i	0.0688195	−	0.786610i	0.949677	−	0.313230i	$-0.101411\pi$
$558$	−10.8699	−	24.1271i	−0.460160	−	1.02138i
$559$	7.32613	+	4.22974i	0.309862	+	0.178899i
$560$	1.16159	−	0.476015i	0.0490863	−	0.0201153i
$561$	−32.7152	+	18.6048i	−1.38124	+	0.785495i
$562$	16.4420	−	4.40561i	0.693562	−	0.185839i
$563$	−7.53163	+	28.1084i	−0.317420	+	1.18463i	0.604295	+	0.796761i	$0.293455\pi$
$563$	−7.53163	+	28.1084i	−0.317420	+	1.18463i	−0.921715	+	0.387868i	$0.873212\pi$
$564$	8.93878	+	5.23881i	0.376391	+	0.220594i
$565$	−13.5037	−	21.3743i	−0.568103	−	0.899222i
$566$	−5.89079	+	16.1848i	−0.247609	+	0.680299i
$567$	−5.02025	−	0.571476i	−0.210831	−	0.0239997i
$568$	1.66837	+	2.38268i	0.0700032	+	0.0999749i
$569$	22.6332			0.948834			0.474417	−	0.880300i	$-0.342659\pi$
$569$	22.6332			0.948834			0.474417	+	0.880300i	$0.342659\pi$
$570$	6.32744	+	15.6513i	0.265027	+	0.655561i
$571$	−19.2333			−0.804888			−0.402444	−	0.915445i	$-0.631839\pi$
$571$	−19.2333			−0.804888			−0.402444	+	0.915445i	$0.631839\pi$
$572$	−2.62039	−	3.74230i	−0.109564	−	0.156474i
$573$	25.6008	−	11.7353i	1.06949	−	0.490247i
$574$	−0.830575	+	2.28199i	−0.0346675	+	0.0952483i
$575$	−0.0778046	+	10.2982i	−0.00324468	+	0.429465i
$576$	−0.559425	+	2.94738i	−0.0233094	+	0.122807i
$577$	8.15687	−	30.4419i	0.339575	−	1.26731i	−0.559248	−	0.829000i	$-0.688910\pi$
$577$	8.15687	−	30.4419i	0.339575	−	1.26731i	0.898823	−	0.438311i	$-0.144423\pi$
$578$	12.8005	−	3.42988i	0.532429	−	0.142664i
$579$	−18.5864	−	32.6829i	−0.772425	−	1.35825i
$580$	4.08287	+	1.70928i	0.169532	+	0.0709738i
$581$	4.31143	+	2.48921i	0.178868	+	0.103270i
$582$	2.28629	+	28.2528i	0.0947698	+	1.17112i
$583$	−3.15068	+	36.0125i	−0.130488	+	1.49148i
$584$	−15.2624	+	5.55507i	−0.631564	+	0.229870i
$585$	−4.05749	−	6.61178i	−0.167757	−	0.273363i
$586$	7.78092	+	6.52896i	0.321427	+	0.269709i
$587$	−9.73649	−	13.9051i	−0.401868	−	0.573927i	0.566309	−	0.824193i	$-0.308371\pi$
$587$	−9.73649	−	13.9051i	−0.401868	−	0.573927i	−0.968177	+	0.250266i	$0.919482\pi$
$588$	−10.4615	−	4.96158i	−0.431426	−	0.204612i
$589$	−38.2970	+	3.41945i	−1.57800	+	0.140896i
$590$	−7.36984	+	1.60467i	−0.303412	+	0.0660633i
$591$	−0.335344	−	1.97713i	−0.0137942	−	0.0813282i
$592$	0.469939	+	5.37143i	0.0193144	+	0.220764i
$593$	−1.78274	−	3.82310i	−0.0732084	−	0.156996i	0.866298	−	0.499528i	$-0.166493\pi$
$593$	−1.78274	−	3.82310i	−0.0732084	−	0.156996i	−0.939506	+	0.342532i	$0.888715\pi$
$594$	3.95931	−	20.1423i	0.162453	−	0.826447i
$595$	6.84892	−	0.875370i	0.280778	−	0.0358867i
$596$	17.4954	−	10.1010i	0.716640	−	0.413752i
$597$	21.7723	+	31.5296i	0.891079	+	1.29042i
$598$	−1.95112	−	1.36619i	−0.0797873	−	0.0558677i
$599$	6.16947	+	34.9888i	0.252078	+	1.42960i	0.803464	+	0.595353i	$0.202988\pi$
$599$	6.16947	+	34.9888i	0.252078	+	1.42960i	−0.551387	+	0.834250i	$0.685901\pi$
$600$	2.12348	+	8.39588i	0.0866908	+	0.342760i
$601$	6.95994	+	12.0550i	0.283902	+	0.491733i	0.972342	−	0.233560i	$-0.0750377\pi$
$601$	6.95994	+	12.0550i	0.283902	+	0.491733i	−0.688440	+	0.725293i	$0.741704\pi$
$602$	0.357934	−	4.09120i	0.0145883	−	0.166745i
$603$	−0.991203	−	3.90205i	−0.0403649	−	0.158904i
$604$	−5.59041	+	15.3595i	−0.227471	+	0.624971i
$605$	−3.06055	−	9.83625i	−0.124429	−	0.399900i
$606$	21.7824	−	3.69455i	0.884848	−	0.150081i
$607$	−18.4329	−	18.4329i	−0.748170	−	0.748170i	0.225965	−	0.974135i	$-0.427446\pi$
$607$	−18.4329	−	18.4329i	−0.748170	−	0.748170i	−0.974135	+	0.225965i	$0.927446\pi$
$608$	3.77880	+	2.17271i	0.153251	+	0.0881149i
$609$	0.646516	+	1.81298i	0.0261981	+	0.0734656i
$610$	−0.505611	−	12.6793i	−0.0204716	−	0.513371i
$611$	−4.44649	+	5.29912i	−0.179886	+	0.214380i
$612$	−7.16784	+	14.8624i	−0.289743	+	0.600776i
$613$	−1.92331	+	4.12454i	−0.0776816	+	0.166589i	−0.941313	−	0.337535i	$-0.890407\pi$
$613$	−1.92331	+	4.12454i	−0.0776816	+	0.166589i	0.863631	+	0.504124i	$0.168185\pi$
$614$	4.88362	−	4.09784i	0.197087	−	0.165375i
$615$	−14.7797	−	7.88832i	−0.595976	−	0.318088i
$616$	−1.10894	+	1.92074i	−0.0446804	+	0.0773886i
$617$	34.2075	+	23.9524i	1.37714	+	0.964287i	0.999261	+	0.0384333i	$0.0122367\pi$
$617$	34.2075	+	23.9524i	1.37714	+	0.964287i	0.377883	+	0.925853i	$0.376652\pi$
$618$	13.6620	+	3.75637i	0.549567	+	0.151103i
$619$	0.186785	+	0.107840i	0.00750752	+	0.00433447i	0.503749	−	0.863850i	$-0.331954\pi$
$619$	0.186785	+	0.107840i	0.00750752	+	0.00433447i	−0.496242	+	0.868185i	$0.665287\pi$
$620$	−19.7019	−	0.934783i	−0.791248	−	0.0375418i
$621$	−1.65197	−	10.5743i	−0.0662913	−	0.424330i
$622$	−11.0411	−	5.14856i	−0.442709	−	0.206439i
$623$	−3.43754	−	7.37183i	−0.137722	−	0.295346i
$624$	−1.87768	−	0.697316i	−0.0751673	−	0.0279150i
$625$	15.7785	+	19.3917i	0.631140	+	0.775669i
$626$			11.8094i			0.472000i
$627$	−25.7592	−	15.0352i	−1.02872	−	0.600447i
$628$	−2.25299	+	2.25299i	−0.0899042	+	0.0899042i
$629$	−5.14983	+	29.2061i	−0.205337	+	1.16452i
$630$	−2.07662	+	3.14177i	−0.0827344	+	0.125171i
$631$	−37.3969	−	13.6113i	−1.48875	−	0.541859i	−0.535627	−	0.844455i	$-0.679925\pi$
$631$	−37.3969	−	13.6113i	−1.48875	−	0.541859i	−0.953119	+	0.302595i	$0.902147\pi$
$632$	−0.613425	+	1.31549i	−0.0244007	+	0.0523275i
$633$	−25.4891	+	6.65197i	−1.01310	+	0.264392i
$634$	−25.2350	+	14.5694i	−1.00221	+	0.578626i
$635$	3.04399	+	0.972424i	0.120797	+	0.0385895i
$636$	7.83500	+	13.7773i	0.310678	+	0.546305i
$637$	4.43401	−	6.33242i	0.175682	−	0.250900i
$638$	−7.55354	+	2.02396i	−0.299047	+	0.0801295i
$639$	−8.16027	−	3.09118i	−0.322815	−	0.122285i
$640$	1.76884	+	1.36792i	0.0699194	+	0.0540719i
$641$	−1.30133	−	3.57536i	−0.0513993	−	0.141218i	0.911336	−	0.411662i	$-0.135052\pi$
$641$	−1.30133	−	3.57536i	−0.0513993	−	0.141218i	−0.962736	+	0.270444i	$0.912829\pi$
$642$	1.23017	−	1.21423i	0.0485510	−	0.0479219i
$643$	−41.2968	+	3.61300i	−1.62859	+	0.142483i	−0.864501	−	0.502631i	$-0.832366\pi$
$643$	−41.2968	+	3.61300i	−1.62859	+	0.142483i	−0.764087	+	0.645114i	$0.776810\pi$
$644$	−0.200795	+	1.13876i	−0.00791243	+	0.0448736i
$645$	27.5956	+	6.41662i	1.08658	+	0.252654i
$646$	16.9829	+	16.9224i	0.668185	+	0.665803i
$647$	11.7286	−	11.7286i	0.461098	−	0.461098i	−0.437917	−	0.899015i	$-0.644284\pi$
$647$	11.7286	−	11.7286i	0.461098	−	0.461098i	0.899015	+	0.437917i	$0.144284\pi$
$648$	−3.58957	−	8.25318i	−0.141012	−	0.324216i
$649$	8.56559	−	10.2081i	0.336229	−	0.400702i
$650$	−5.76374	+	0.460412i	−0.226073	+	0.0180588i
$651$	−5.47043	−	6.60640i	−0.214403	−	0.258925i
$652$	3.21380	+	0.281171i	0.125862	+	0.0110115i
$653$	0.0182548	−	0.0681278i	0.000714365	−	0.00266605i	−0.965568	−	0.260152i	$-0.916227\pi$
$653$	0.0182548	−	0.0681278i	0.000714365	−	0.00266605i	0.966282	+	0.257486i	$0.0828941\pi$
$654$	−3.13729	−	0.574304i	−0.122678	−	0.0224571i
$655$	−25.7750	−	10.7906i	−1.00711	−	0.421624i
$656$	−4.25991	+	0.751137i	−0.166322	+	0.0293270i
$657$	28.4660	−	39.5460i	1.11057	−	1.54284i
$658$	3.24382	+	0.869178i	0.126457	+	0.0338841i
$659$	16.7583	−	14.0619i	0.652810	−	0.547773i	−0.255112	−	0.966911i	$-0.582112\pi$
$659$	16.7583	−	14.0619i	0.652810	−	0.547773i	0.907922	+	0.419139i	$0.137668\pi$
$660$	−12.0421	−	9.43883i	−0.468738	−	0.367406i
$661$	14.1616	+	5.15439i	0.550822	+	0.200483i	0.602412	−	0.798186i	$-0.294207\pi$
$661$	14.1616	+	5.15439i	0.550822	+	0.200483i	−0.0515898	+	0.998668i	$0.516429\pi$
$662$	20.3227	−	1.77800i	0.789862	−	0.0691040i
$663$	−8.98300	−	6.37765i	−0.348871	−	0.247687i
$664$			8.86773i			0.344135i
$665$	3.32244	+	4.34780i	0.128839	+	0.168600i
$666$	−10.2352	−	12.5259i	−0.396604	−	0.485370i
$667$	−3.33977	+	2.33853i	−0.129316	+	0.0905483i
$668$	0.425909	+	4.86817i	0.0164789	+	0.188355i
$669$	23.6248	+	0.154034i	0.913387	+	0.00595532i
$670$	−2.92718	−	0.660551i	−0.113087	−	0.0255193i
$671$	14.4106	+	17.1739i	0.556315	+	0.662991i
$672$	0.0784315	+	0.969218i	0.00302556	+	0.0373884i
$673$	1.14044	+	4.25617i	0.0439606	+	0.164063i	0.984417	−	0.175852i	$-0.0562682\pi$
$673$	1.14044	+	4.25617i	0.0439606	+	0.164063i	−0.940456	+	0.339916i	$0.889601\pi$
$674$	−4.23333	−	24.0084i	−0.163062	−	0.924770i
$675$	−19.4423	−	17.2336i	−0.748336	−	0.663320i
$676$	−5.83135	+	10.1002i	−0.224283	+	0.388469i
$677$	−11.6456	−	3.12042i	−0.447576	−	0.119928i	0.0279891	−	0.999608i	$-0.491090\pi$
$677$	−11.6456	−	3.12042i	−0.447576	−	0.119928i	−0.475565	+	0.879681i	$0.657756\pi$
$678$	18.9491	−	4.94521i	0.727737	−	0.189920i
$679$	3.14231	+	8.63342i	0.120591	+	0.331320i
$680$	7.45011	+	9.78549i	0.285699	+	0.375257i
$681$	9.78668	+	3.63449i	0.375026	+	0.139274i
$682$	28.5453	−	19.9877i	1.09306	−	0.765367i
$683$	−4.49971	−	4.49971i	−0.172177	−	0.172177i	0.615758	−	0.787935i	$-0.288850\pi$
$683$	−4.49971	−	4.49971i	−0.172177	−	0.172177i	−0.787935	+	0.615758i	$0.788850\pi$
$684$	−13.0389	+	0.993026i	−0.498556	+	0.0379693i
$685$	−36.7625	+	8.00447i	−1.40462	+	0.305835i
$686$	−7.56604	−	1.33410i	−0.288873	−	0.0509361i
$687$	22.7824	−	10.4433i	0.869202	−	0.398437i
$688$	6.62985	−	3.09155i	0.252761	−	0.117864i
$689$	−9.94378	+	3.61924i	−0.378828	+	0.137882i
$690$	−7.58287	−	2.47700i	−0.288675	−	0.0942978i
$691$	23.1931	+	40.1716i	0.882307	+	1.52820i	0.848769	+	0.528763i	$0.177344\pi$
$691$	23.1931	+	40.1716i	0.882307	+	1.52820i	0.0335379	+	0.999437i	$0.489323\pi$
$692$	−0.383890	−	1.43270i	−0.0145933	−	0.0544630i
$693$	−0.493422	−	6.63530i	−0.0187436	−	0.252054i
$694$	1.20913	−	0.213202i	0.0458979	−	0.00809303i
$695$	6.88814	+	13.3549i	0.261282	+	0.506581i
$696$	−2.22090	+	2.61199i	−0.0841829	+	0.0990071i
$697$	−23.7012	−	2.07359i	−0.897747	−	0.0785427i
$698$	0.969992	+	0.452315i	0.0367147	+	0.0171204i
$699$	0.270724	−	41.5218i	0.0102397	−	1.57050i
$700$	1.38511	+	2.44150i	0.0523524	+	0.0922800i
$701$	−33.9650	−	5.98894i	−1.28284	−	0.226199i	−0.509655	−	0.860379i	$-0.670227\pi$
$701$	−33.9650	−	5.98894i	−1.28284	−	0.226199i	−0.773186	+	0.634180i	$0.781338\pi$
$702$	5.83349	−	1.44141i	0.220171	−	0.0544024i
$703$	−22.0712	+	8.07789i	−0.832429	+	0.304663i
$704$	−3.95056			−0.148892
$705$	−9.08576	+	21.3116i	−0.342190	+	0.802641i
$706$	−3.88329	−	3.25847i	−0.146150	−	0.122634i
$707$	6.49018	−	3.02642i	0.244088	−	0.113820i
$708$	0.547136	−	5.81673i	0.0205626	−	0.218606i
$709$	5.64348	+	6.72563i	0.211945	+	0.252586i	0.861535	−	0.507699i	$-0.169504\pi$
$709$	5.64348	+	6.72563i	0.211945	+	0.252586i	−0.649589	+	0.760285i	$0.725059\pi$
$710$	−4.81187	+	4.37595i	−0.180586	+	0.164226i
$711$	−0.700162	−	4.29780i	−0.0262581	−	0.161180i
$712$	8.31022	−	11.8682i	0.311439	−	0.444780i
$713$	10.4209	−	14.8827i	0.390268	−	0.557360i
$714$	−0.963044	+	5.26088i	−0.0360410	+	0.196884i
$715$	7.55767	−	6.87299i	0.282641	−	0.257035i
$716$	−15.6949	−	18.7045i	−0.586546	−	0.699018i
$717$	−5.38532	−	0.506555i	−0.201118	−	0.0189177i
$718$	23.6200	−	11.0142i	0.881490	−	0.411046i
$719$	35.8866	+	30.1124i	1.33834	+	1.12300i	0.982048	+	0.188631i	$0.0604050\pi$
$719$	35.8866	+	30.1124i	1.33834	+	1.12300i	0.356296	+	0.934373i	$0.384039\pi$
$720$	−6.69595	−	0.405268i	−0.249543	−	0.0151035i
$721$	4.59259			0.171037
$722$	−4.85200	+	18.3700i	−0.180573	+	0.683662i
$723$	15.6932	+	7.44279i	0.583635	+	0.276800i
$724$	14.1020	+	2.48656i	0.524097	+	0.0924124i
$725$	−2.63377	+	9.54046i	−0.0978157	+	0.354324i
$726$	7.97926	+	0.0520251i	0.296138	+	0.00193083i
$727$	20.5442	+	9.57994i	0.761944	+	0.355300i	0.764438	−	0.644697i	$-0.223016\pi$
$727$	20.5442	+	9.57994i	0.761944	+	0.355300i	−0.00249479	+	0.999997i	$0.500794\pi$
$728$	−0.646753	−	0.0565835i	−0.0239702	−	0.00209713i
$729$	22.8368	+	14.4042i	0.845808	+	0.533487i
$730$	−16.6480	−	32.2776i	−0.616170	−	1.19465i
$731$	39.6239	−	6.98675i	1.46554	−	0.258414i
$732$	9.47746	+	2.60582i	0.350297	+	0.0963140i
$733$	−8.42042	−	31.4254i	−0.311015	−	1.16073i	−0.927642	−	0.373470i	$-0.878168\pi$
$733$	−8.42042	−	31.4254i	−0.311015	−	1.16073i	0.616627	−	0.787256i	$-0.288499\pi$
$734$	−9.73732	−	16.8655i	−0.359411	−	0.622518i
$735$	8.03918	−	24.6104i	0.296530	−	0.907770i
$736$	−1.93549	+	0.704459i	−0.0713429	+	0.0259667i
$737$	4.80490	−	2.24056i	0.176991	−	0.0825321i
$738$	9.29491	−	9.05561i	0.342150	−	0.333342i
$739$	−8.55194	−	1.50794i	−0.314588	−	0.0554704i	0.0141248	−	0.999900i	$-0.495504\pi$
$739$	−8.55194	−	1.50794i	−0.314588	−	0.0554704i	−0.328713	+	0.944430i	$0.606615\pi$
$740$	−11.7807	+	2.56508i	−0.433068	+	0.0942941i
$741$	0.802110	−	8.69386i	0.0294662	−	0.319377i
$742$	3.63256	+	3.63256i	0.133356	+	0.133356i
$743$	−41.8963	+	29.3361i	−1.53703	+	1.07624i	−0.569972	+	0.821664i	$0.693046\pi$
$743$	−41.8963	+	29.3361i	−1.53703	+	1.07624i	−0.967054	+	0.254573i	$0.918065\pi$
$744$	5.31895	−	14.3224i	0.195002	−	0.525086i
$745$	27.3640	+	35.9417i	1.00254	+	1.31680i
$746$	−5.14261	−	14.1292i	−0.188284	−	0.517307i
$747$	−14.9735	−	21.9892i	−0.547852	−	0.804542i
$748$	−20.9884	−	5.62383i	−0.767412	−	0.205628i
$749$	0.280127	−	0.485194i	0.0102356	−	0.0177286i
$750$	−18.0203	+	7.09007i	−0.658008	+	0.258893i
$751$	−3.76031	−	21.3258i	−0.137216	−	0.778189i	−0.973291	−	0.229574i	$-0.926267\pi$
$751$	−3.76031	−	21.3258i	−0.137216	−	0.778189i	0.836075	−	0.548614i	$-0.184845\pi$
$752$	1.54821	+	5.77801i	0.0564575	+	0.210702i
$753$	−12.1088	+	0.979874i	−0.441269	+	0.0357086i
$754$	−1.47140	−	1.75355i	−0.0535853	−	0.0638604i
$755$	−35.6527	−	8.04542i	−1.29753	−	0.292803i
$756$	−1.83105	−	2.27092i	−0.0665946	−	0.0825926i
$757$	−2.53545	−	28.9804i	−0.0921526	−	1.05331i	−0.891676	−	0.452674i	$-0.850470\pi$
$757$	−2.53545	−	28.9804i	−0.0921526	−	1.05331i	0.799523	−	0.600635i	$-0.205085\pi$
$758$	−26.6790	+	18.6808i	−0.969023	+	0.678517i
$759$	13.2748	−	4.73386i	0.481846	−	0.171828i
$760$	−3.74787	+	8.99741i	−0.135950	+	0.326371i
$761$			3.65790i			0.132599i	0.997800	+	0.0662994i	$0.0211192\pi$
$761$			3.65790i			0.132599i	−0.997800	+	0.0662994i	$0.978881\pi$
$762$	−1.43294	+	2.01831i	−0.0519099	+	0.0731157i
$763$	−1.02985	+	0.0901001i	−0.0372830	+	0.00326184i
$764$	15.2790	+	5.56109i	0.552774	+	0.201193i
$765$	−34.9971	−	11.6851i	−1.26532	−	0.422477i
$766$	14.4960	−	12.1636i	0.523762	−	0.439489i
$767$	3.76783	+	1.00959i	0.136048	+	0.0364540i
$768$	−1.42526	+	0.984192i	−0.0514296	+	0.0355140i
$769$	43.7322	−	7.71117i	1.57702	−	0.278072i	0.684480	−	0.729031i	$-0.260029\pi$
$769$	43.7322	−	7.71117i	1.57702	−	0.278072i	0.892544	+	0.450960i	$0.148918\pi$
$770$	−4.57461	−	1.91514i	−0.164858	−	0.0690170i
$771$	5.13424	−	28.0471i	0.184905	−	1.01009i
$772$	5.61827	−	20.9677i	0.202206	−	0.754643i
$773$	24.9989	+	2.18712i	0.899148	+	0.0786653i	0.527350	−	0.849648i	$-0.323186\pi$
$773$	24.9989	+	2.18712i	0.899148	+	0.0786653i	0.371798	+	0.928313i	$0.378741\pi$
$774$	−11.2197	+	18.8608i	−0.403285	+	0.677939i
$775$	−3.51190	−	43.9643i	−0.126151	−	1.57925i
$776$	−10.5193	+	12.5364i	−0.377621	+	0.450031i
$777$	−4.27516	−	3.03523i	−0.153370	−	0.108888i
$778$	−20.6954	+	20.6954i	−0.741965	+	0.741965i
$779$	−7.99895	−	17.0742i	−0.286592	−	0.611745i
$780$	1.01436	−	4.36242i	0.0363200	−	0.156200i
$781$	1.99540	−	11.3165i	0.0714010	−	0.404935i
$782$	−11.2856	+	0.987364i	−0.403573	+	0.0353081i
$783$	1.09668	−	10.2270i	0.0391923	−	0.365482i
$784$	−2.28634	−	6.28168i	−0.0816551	−	0.224346i
$785$	−5.63589	−	4.35850i	−0.201154	−	0.155561i
$786$	14.0205	−	16.4894i	0.500094	−	0.588158i
$787$	−20.6843	+	5.54233i	−0.737314	+	0.197563i	−0.607884	−	0.794026i	$-0.707981\pi$
$787$	−20.6843	+	5.54233i	−0.737314	+	0.197563i	−0.129430	+	0.991589i	$0.541315\pi$
$788$	0.664086	−	0.948413i	0.0236571	−	0.0337858i
$789$	−7.07375	+	4.02277i	−0.251832	+	0.143214i
$790$	−3.09170	−	0.987664i	−0.109998	−	0.0351395i
$791$	5.49724	−	3.17383i	0.195459	−	0.112849i
$792$	9.79614	−	6.67067i	0.348091	−	0.237032i
$793$	−2.77345	+	5.94768i	−0.0984880	+	0.211208i
$794$	−27.9469	−	10.1719i	−0.991800	−	0.360986i
$795$	−28.3372	+	21.2839i	−1.00502	+	0.754863i
$796$	−3.84144	+	21.7859i	−0.136156	+	0.772180i
$797$	16.2826	−	16.2826i	0.576759	−	0.576759i	−0.357250	−	0.934009i	$-0.616286\pi$
$797$	16.2826	−	16.2826i	0.576759	−	0.576759i	0.934009	+	0.357250i	$0.116286\pi$
$798$	−3.98974	+	1.43079i	−0.141235	+	0.0506494i
$799$			32.9012i			1.16396i
$800$	−2.53264	+	4.31112i	−0.0895424	+	0.152421i
$801$	−0.566766	+	43.4616i	−0.0200257	+	1.53564i
$802$	−6.10389	−	13.0898i	−0.215536	−	0.462218i
$803$	58.1530	+	27.1172i	2.05217	+	0.956945i
$804$	1.17530	−	2.00537i	0.0414496	−	0.0707239i
$805$	−2.58273	−	0.122541i	−0.0910293	−	0.00431900i
$806$	8.83402	+	5.10032i	0.311165	+	0.179651i
$807$	7.95756	−	28.9419i	0.280119	−	1.01880i
$808$	10.4488	+	7.31635i	0.367588	+	0.257388i
$809$	11.2420	−	19.4718i	0.395249	−	0.684591i	−0.597884	−	0.801582i	$-0.703992\pi$
$809$	11.2420	−	19.4718i	0.395249	−	0.684591i	0.993133	+	0.116992i	$0.0373251\pi$
$810$	17.2882	−	10.3014i	0.607444	−	0.361956i
$811$	7.49946	−	6.29279i	0.263342	−	0.220970i	−0.501550	−	0.865128i	$-0.667237\pi$
$811$	7.49946	−	6.29279i	0.263342	−	0.220970i	0.764892	+	0.644159i	$0.222792\pi$
$812$	−0.469650	+	1.00717i	−0.0164815	+	0.0353447i
$813$	25.8251	+	26.1641i	0.905725	+	0.917614i
$814$	13.6921	−	16.3177i	0.479909	−	0.571934i
$815$	0.287432	+	7.20800i	0.0100683	+	0.252485i
$816$	−8.97313	+	3.19985i	−0.314122	+	0.112017i
$817$	20.5397	+	24.3897i	0.718594	+	0.853289i
$818$	8.99393	+	8.99393i	0.314466	+	0.314466i
$819$	1.69929	−	0.951758i	0.0593779	−	0.0332571i
$820$	−2.87368	−	9.23565i	−0.100353	−	0.322523i
$821$	4.72460	−	12.9807i	0.164890	−	0.453030i	−0.829538	−	0.558450i	$-0.811396\pi$
$821$	4.72460	−	12.9807i	0.164890	−	0.453030i	0.994428	+	0.105419i	$0.0336185\pi$
$822$	2.72924	−	29.0152i	0.0951931	−	1.01202i
$823$	−2.91578	+	33.3275i	−0.101638	+	1.16172i	0.758504	+	0.651669i	$0.225931\pi$
$823$	−2.91578	+	33.3275i	−0.101638	+	1.16172i	−0.860141	+	0.510056i	$0.829625\pi$
$824$	4.09025	+	7.08451i	0.142490	+	0.246801i
$825$	17.5217	−	29.3855i	0.610029	−	1.02307i
$826$	−0.328836	−	1.86492i	−0.0114417	−	0.0648890i
$827$	10.2441	+	7.17301i	0.356223	+	0.249430i	0.737965	−	0.674839i	$-0.235787\pi$
$827$	10.2441	+	7.17301i	0.356223	+	0.249430i	−0.381742	+	0.924269i	$0.624676\pi$
$828$	3.60989	−	5.01498i	0.125452	−	0.174283i
$829$	23.5814	−	13.6147i	0.819017	−	0.472859i	−0.0310606	−	0.999518i	$-0.509888\pi$
$829$	23.5814	−	13.6147i	0.819017	−	0.472859i	0.850077	+	0.526658i	$0.176555\pi$
$830$	−19.6689	+	2.51390i	−0.682716	+	0.0872589i
$831$	−23.7352	−	28.6640i	−0.823364	−	0.994342i
$832$	−0.488724	−	1.04807i	−0.0169435	−	0.0363354i
$833$	−3.20452	−	36.6278i	−0.111030	−	1.26908i
$834$	−11.4757	+	1.94642i	−0.397371	+	0.0673989i
$835$	−10.6770	+	2.32475i	−0.369492	+	0.0804513i
$836$	−4.48657	−	16.6253i	−0.155171	−	0.575000i
$837$	10.9947	+	44.4964i	0.380032	+	1.53802i
$838$	14.0477	+	20.0623i	0.485271	+	0.693039i
$839$	3.56351	+	2.99014i	0.123026	+	0.103231i	0.702225	−	0.711955i	$-0.252190\pi$
$839$	3.56351	+	2.99014i	0.123026	+	0.103231i	−0.579199	+	0.815186i	$0.696635\pi$
$840$	−2.12752	+	0.448726i	−0.0734063	+	0.0154825i
$841$	23.5691	−	8.57845i	0.812728	−	0.295809i
$842$	−0.463714	+	5.30028i	−0.0159807	+	0.182660i
$843$	−29.3868	+	2.37806i	−1.01214	+	0.0819046i
$844$	−13.1714	−	7.60451i	−0.453378	−	0.261758i
$845$	−24.0556	−	10.0708i	−0.827537	−	0.346445i
$846$	−13.5955	−	11.7134i	−0.467422	−	0.402716i
$847$	2.49823	−	0.669400i	0.0858403	−	0.0230008i
$848$	−2.36835	+	8.83881i	−0.0813295	+	0.303526i
$849$	15.0841	−	25.7375i	0.517686	−	0.883308i
$850$	−19.5924	+	19.2986i	−0.672015	+	0.661937i
$851$	3.79840	−	10.4360i	0.130208	−	0.357742i
$852$	−2.09935	−	4.57980i	−0.0719226	−	0.156901i
$853$	31.3692	+	44.7998i	1.07406	+	1.53392i	0.824754	+	0.565492i	$0.191314\pi$
$853$	31.3692	+	44.7998i	1.07406	+	1.53392i	0.249307	+	0.968425i	$0.419797\pi$
$854$	3.18592			0.109020
$855$	−5.89895	−	28.6392i	−0.201740	−	0.979439i
$856$	0.997945			0.0341090
$857$	−18.1363	−	25.9014i	−0.619526	−	0.884774i	0.379660	−	0.925126i	$-0.376041\pi$
$857$	−18.1363	−	25.9014i	−0.619526	−	0.884774i	−0.999186	+	0.0403517i	$0.987152\pi$
$858$	3.29730	+	7.19316i	0.112568	+	0.245571i
$859$	−10.1196	+	27.8033i	−0.345276	+	0.948638i	0.638561	+	0.769571i	$0.279530\pi$
$859$	−10.1196	+	27.8033i	−0.345276	+	0.948638i	−0.983837	+	0.179067i	$0.942692\pi$
$860$	8.73662	+	13.8288i	0.297916	+	0.471557i
$861$	2.12680	−	3.62887i	0.0724810	−	0.123672i
$862$	−6.44800	+	24.0643i	−0.219620	+	0.819632i
$863$	−53.5707	+	14.3542i	−1.82357	+	0.488623i	−0.997218	−	0.0745347i	$-0.976253\pi$
$863$	−53.5707	+	14.3542i	−1.82357	+	0.488623i	−0.826349	+	0.563158i	$0.809586\pi$
$864$	1.87235	−	4.84709i	0.0636986	−	0.164901i
$865$	3.06893	−	1.25763i	0.104347	−	0.0427607i
$866$	−24.3469	−	14.0567i	−0.827342	−	0.477666i
$867$	−22.8784	+	1.85138i	−0.776991	+	0.0628760i
$868$	0.431605	−	4.93326i	0.0146496	−	0.167446i
$869$	5.38837	−	1.96121i	0.182788	−	0.0665294i
$870$	−6.42305	−	4.18554i	−0.217762	−	0.141903i
$871$	1.18883	+	0.997546i	0.0402819	+	0.0338006i
$872$	−1.05619	−	1.50840i	−0.0357671	−	0.0510808i
$873$	4.91632	−	48.8486i	0.166392	−	1.65327i
$874$	−5.16270	−	7.34516i	−0.174631	−	0.248454i
$875$	−5.02264	+	3.76435i	−0.169796	+	0.127258i
$876$	27.7357	−	4.70431i	0.937103	−	0.158944i
$877$	3.35573	+	38.3562i	0.113315	+	1.29520i	0.813638	+	0.581371i	$0.197484\pi$
$877$	3.35573	+	38.3562i	0.113315	+	1.29520i	−0.700323	+	0.713826i	$0.746961\pi$
$878$	12.5444	+	26.9016i	0.423353	+	0.907884i
$879$	−11.2204	−	13.5504i	−0.378454	−	0.457043i
$880$	−1.11994	−	8.76244i	−0.0377532	−	0.295382i
$881$	−29.6381	+	17.1116i	−0.998532	+	0.576503i	−0.907814	−	0.419374i	$-0.862250\pi$
$881$	−29.6381	+	17.1116i	−0.998532	+	0.576503i	−0.0907186	+	0.995877i	$0.528916\pi$
$882$	16.2763	+	11.7160i	0.548050	+	0.394498i
$883$	−12.3925	−	8.67730i	−0.417040	−	0.292014i	0.346162	−	0.938175i	$-0.387485\pi$
$883$	−12.3925	−	8.67730i	−0.417040	−	0.292014i	−0.763202	+	0.646161i	$0.776374\pi$
$884$	−1.10449	−	6.26389i	−0.0371481	−	0.210678i
$885$	13.0568	−	0.435419i	0.438898	−	0.0146364i
$886$	2.32603	+	4.02880i	0.0781444	+	0.135350i
$887$	−2.42879	+	27.7612i	−0.0815508	+	0.932130i	0.839672	+	0.543094i	$0.182747\pi$
$887$	−2.42879	+	27.7612i	−0.0815508	+	0.932130i	−0.921223	+	0.389036i	$0.872808\pi$
$888$	0.874599	−	9.29808i	0.0293496	−	0.312023i
$889$	−0.274404	+	0.753918i	−0.00920320	+	0.0252856i
$890$	28.6799	+	15.0678i	0.961351	+	0.505072i
$891$	−13.0277	+	33.0823i	−0.436443	+	1.10830i
$892$	9.64498	+	9.64498i	0.322938	+	0.322938i
$893$	−22.5576	+	13.0774i	−0.754862	+	0.437618i
$894$	−32.9579	+	11.7529i	−1.10228	+	0.393077i
$895$	37.0376	−	40.1142i	1.23803	−	1.34087i
$896$	−0.360866	+	0.430063i	−0.0120557	+	0.0143674i
$897$	2.89811	+	2.93615i	0.0967652	+	0.0980353i
$898$	6.27982	−	13.4671i	0.209560	−	0.449404i
$899$	13.3756	−	11.2235i	0.446102	−	0.374324i
$900$	−0.999333	−	14.9667i	−0.0333111	−	0.498889i
$901$	−25.1650	+	43.5871i	−0.838368	+	1.45210i
$902$	13.9982	+	9.80164i	0.466089	+	0.326359i
$903$	−1.88580	+	6.85871i	−0.0627554	+	0.228243i
$904$	9.79189	+	5.65335i	0.325673	+	0.188028i
$905$	−1.51750	+	31.9835i	−0.0504434	+	1.06317i
$906$	14.3150	−	24.4251i	0.475583	−	0.811470i
$907$	−3.37528	−	1.57392i	−0.112074	−	0.0522611i	0.365773	−	0.930704i	$-0.380805\pi$
$907$	−3.37528	−	1.57392i	−0.112074	−	0.0522611i	−0.477847	+	0.878443i	$0.658583\pi$
$908$	2.54729	+	5.46268i	0.0845347	+	0.181285i
$909$	−38.2637	−	0.498983i	−1.26913	−	0.0165502i
$910$	−0.0578435	−	1.45055i	−0.00191749	−	0.0480854i
$911$		−	5.30180i		−	0.175657i	−0.996136	−	0.0878283i	$-0.972007\pi$
$911$		−	5.30180i		−	0.175657i	0.996136	−	0.0878283i	$-0.0279927\pi$
$912$	−5.76047	−	4.88027i	−0.190748	−	0.161602i
$913$	24.7717	−	24.7717i	0.819825	−	0.819825i
$914$	−3.06298	+	17.3710i	−0.101314	+	0.574581i
$915$	−3.09303	+	21.7600i	−0.102252	+	0.719362i
$916$	13.5969	+	4.94886i	0.449254	+	0.163515i
$917$	2.96489	−	6.35823i	0.0979093	−	0.209967i
$918$	16.8475	−	23.0861i	0.556049	−	0.761955i
$919$	−11.3853	+	6.57332i	−0.375567	+	0.216834i	−0.675888	−	0.737004i	$-0.736240\pi$
$919$	−11.3853	+	6.57332i	−0.375567	+	0.216834i	0.300321	+	0.953838i	$0.402906\pi$
$920$	−2.11120	−	4.09325i	−0.0696041	−	0.134950i
$921$	−9.59845	+	5.45854i	−0.316280	+	0.179865i
$922$	−4.51839	+	6.45294i	−0.148805	+	0.212516i
$923$	3.24908	−	0.870588i	0.106945	−	0.0286558i
$924$	2.48838	−	2.92658i	0.0818618	−	0.0962773i
$925$	−9.02911	−	25.4028i	−0.296875	−	0.835239i
$926$	−4.77332	−	13.1146i	−0.156861	−	0.430972i
$927$	−22.1050	−	10.6608i	−0.726023	−	0.350147i
$928$	−1.97193	+	0.172522i	−0.0647319	+	0.00566330i
$929$	8.71101	−	49.4026i	0.285799	−	1.62085i	−0.416619	−	0.909081i	$-0.636785\pi$
$929$	8.71101	−	49.4026i	0.285799	−	1.62085i	0.702418	−	0.711765i	$-0.252104\pi$
$930$	33.2754	+	7.73731i	1.09114	+	0.253716i
$931$	23.8390	−	16.7557i	0.781290	−	0.549147i
$932$	16.9516	−	16.9516i	0.555267	−	0.555267i
$933$	17.2055	+	12.2153i	0.563282	+	0.399912i
$934$	1.77872	−	2.11980i	0.0582016	−	0.0693619i
$935$	6.52381	−	48.1471i	0.213351	−	1.57458i
$936$	2.98159	+	1.77366i	0.0974564	+	0.0579739i
$937$	11.5380	+	1.00945i	0.376931	+	0.0329772i	0.274047	−	0.961716i	$-0.411638\pi$
$937$	11.5380	+	1.00945i	0.376931	+	0.0329772i	0.102884	+	0.994693i	$0.467193\pi$
$938$	0.194995	−	0.727733i	0.00636683	−	0.0237613i
$939$	3.68315	−	20.1202i	0.120195	−	0.656598i
$940$	−12.3769	+	5.07197i	−0.403689	+	0.165430i
$941$	−8.32443	+	1.46782i	−0.271369	+	0.0478496i	−0.307676	−	0.951491i	$-0.599551\pi$
$941$	−8.32443	+	1.46782i	−0.271369	+	0.0478496i	0.0363078	+	0.999341i	$0.488440\pi$
$942$	4.54118	−	3.13584i	0.147960	−	0.102171i
$943$	8.60591	+	2.30595i	0.280247	+	0.0750920i
$944$	2.58396	−	2.16820i	0.0841006	−	0.0705688i
$945$	4.51788	−	4.70509i	0.146967	−	0.153057i
$946$	−27.1564	−	9.88413i	−0.882931	−	0.321361i
$947$	−24.1974	+	2.11700i	−0.786311	+	0.0687933i	−0.473237	−	0.880935i	$-0.656914\pi$
$947$	−24.1974	+	2.11700i	−0.786311	+	0.0687933i	−0.313074	+	0.949729i	$0.601359\pi$
$948$	1.45540	−	2.04994i	0.0472691	−	0.0665791i
$949$			18.7825i			0.609706i
$950$	−21.0190	−	5.76220i	−0.681945	−	0.186950i
$951$	47.5378	−	16.9522i	1.54152	−	0.549712i
$952$	−2.52941	+	1.77112i	−0.0819788	+	0.0574022i
$953$	1.02123	+	11.6727i	0.0330808	+	0.378116i	0.994631	+	0.103486i	$0.0329997\pi$
$953$	1.02123	+	11.6727i	0.0330808	+	0.378116i	−0.961550	+	0.274630i	$0.911445\pi$
$954$	−9.05191	−	25.9165i	−0.293066	−	0.839078i
$955$	−8.00322	+	35.4656i	−0.258978	+	1.14764i
$956$	−2.00739	−	2.39231i	−0.0649235	−	0.0773728i
$957$	13.5005	−	1.09249i	0.436409	−	0.0353153i
$958$	−8.21362	−	30.6537i	−0.265370	−	0.990375i
$959$	−1.64031	−	9.30267i	−0.0529684	−	0.300399i
$960$	−2.58701	−	2.88225i	−0.0834953	−	0.0930244i
$961$	−23.4039	+	40.5368i	−0.754966	+	1.30764i
$962$	6.02289	+	1.61383i	0.194186	+	0.0520319i
$963$	−2.47459	+	1.68507i	−0.0797425	+	0.0543006i
$964$	3.42971	+	9.42305i	0.110463	+	0.303496i
$965$	48.0996	+	6.51737i	1.54838	+	0.209801i
$966$	0.697263	−	1.87753i	0.0224341	−	0.0604087i
$967$	−29.0680	+	20.3536i	−0.934763	+	0.654528i	−0.938431	−	0.345465i	$-0.887721\pi$
$967$	−29.0680	+	20.3536i	−0.934763	+	0.654528i	0.00366880	+	0.999993i	$0.498832\pi$
$968$	3.25759	+	3.25759i	0.104703	+	0.104703i
$969$	−23.6567	−	34.1281i	−0.759963	−	1.09635i
$970$	−30.7882	−	19.7781i	−0.988548	−	0.635037i
$971$	18.1853	+	3.20656i	0.583594	+	0.102903i	0.457648	−	0.889134i	$-0.348692\pi$
$971$	18.1853	+	3.20656i	0.583594	+	0.102903i	0.125947	+	0.992037i	$0.459803\pi$
$972$	3.54167	+	15.1808i	0.113599	+	0.486924i
$973$	−3.41926	+	1.59443i	−0.109616	+	0.0511149i
$974$	−25.7618	+	9.37651i	−0.825460	+	0.300443i
$975$	9.96351	+	1.01319i	0.319088	+	0.0324480i
$976$	2.83744	+	4.91458i	0.0908241	+	0.157312i
$977$	−0.678199	−	2.53107i	−0.0216975	−	0.0809762i	0.954228	−	0.299080i	$-0.0966796\pi$
$977$	−0.678199	−	2.53107i	−0.0216975	−	0.0809762i	−0.975926	+	0.218103i	$0.930013\pi$
$978$	−5.38779	−	1.48137i	−0.172282	−	0.0473690i
$979$	−56.3678	+	9.93916i	−1.80152	+	0.317657i
$980$	13.2848	−	6.85195i	0.424366	−	0.218878i
$981$	5.16601	+	1.95693i	0.164938	+	0.0624799i
$982$	−27.9437	−	2.44476i	−0.891720	−	0.0780153i
$983$	−12.7343	−	5.93810i	−0.406161	−	0.189396i	0.208791	−	0.977960i	$-0.433047\pi$
$983$	−12.7343	−	5.93810i	−0.406161	−	0.189396i	−0.614952	+	0.788564i	$0.710825\pi$
$984$	7.49205	+	0.0488484i	0.238838	+	0.00155723i
$985$	2.29186	+	1.20409i	0.0730249	+	0.0383656i
$986$	−10.7220	−	1.89058i	−0.341459	−	0.0602084i
$987$	−5.25554	−	2.49254i	−0.167286	−	0.0793385i
$988$	3.85562	−	3.24700i	0.122664	−	0.103301i
$989$	−15.0672			−0.479109
$990$	17.5728	+	19.8370i	0.558501	+	0.630462i
$991$	−18.0623	−	15.1561i	−0.573768	−	0.481448i	0.309126	−	0.951021i	$-0.399963\pi$
$991$	−18.0623	−	15.1561i	−0.573768	−	0.481448i	−0.882894	+	0.469573i	$0.844408\pi$
$992$	7.99443	−	3.72786i	0.253823	−	0.118360i
$993$	−35.1790	−	3.30902i	−1.11637	−	0.105009i
$994$	−1.04966	−	1.25093i	−0.0332930	−	0.0396771i
$995$	−49.4106	−	2.34435i	−1.56642	−	0.0743209i
$996$	2.76569	−	15.1083i	0.0876342	−	0.478725i
$997$	10.4036	−	14.8579i	0.329487	−	0.470556i	−0.619893	−	0.784686i	$-0.712824\pi$
$997$	10.4036	−	14.8579i	0.329487	−	0.470556i	0.949380	+	0.314130i	$0.101713\pi$
$998$	14.8533	−	21.2128i	0.470174	−	0.671478i
$999$	13.5314	+	24.5331i	0.428116	+	0.776193i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bi.a.17.13	✓	480
3.2	odd	2	inner	570.2.bi.a.17.33	yes	480
5.3	odd	4	inner	570.2.bi.a.473.3	yes	480
15.8	even	4	inner	570.2.bi.a.473.39	yes	480
19.9	even	9	inner	570.2.bi.a.47.39	yes	480
57.47	odd	18	inner	570.2.bi.a.47.3	yes	480
95.28	odd	36	inner	570.2.bi.a.503.33	yes	480
285.218	even	36	inner	570.2.bi.a.503.13	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bi.a.17.13	✓	480	1.1	even	1	trivial
570.2.bi.a.17.33	yes	480	3.2	odd	2	inner
570.2.bi.a.47.3	yes	480	57.47	odd	18	inner
570.2.bi.a.47.39	yes	480	19.9	even	9	inner
570.2.bi.a.473.3	yes	480	5.3	odd	4	inner
570.2.bi.a.473.39	yes	480	15.8	even	4	inner
570.2.bi.a.503.13	yes	480	285.218	even	36	inner
570.2.bi.a.503.33	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)

\(f(q)\)	\(=\)	\(q+(-0.573576 - 0.819152i) q^{2} +(0.721746 + 1.57451i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(-2.18122 - 0.492217i) q^{5} +(0.875787 - 1.49432i) q^{6} +(0.145303 - 0.542278i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-1.95817 + 2.27279i) q^{9} +O(q^{10})\)	\(q+(-0.573576 - 0.819152i) q^{2} +(0.721746 + 1.57451i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(-2.18122 - 0.492217i) q^{5} +(0.875787 - 1.49432i) q^{6} +(0.145303 - 0.542278i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-1.95817 + 2.27279i) q^{9} +(0.847896 + 2.06908i) q^{10} +(-3.42129 - 1.97528i) q^{11} +(-1.72641 + 0.139705i) q^{12} +(0.100789 - 1.15202i) q^{13} +(-0.527551 + 0.192013i) q^{14} +(-0.799287 - 3.78961i) q^{15} +(-0.766044 - 0.642788i) q^{16} +(-3.15478 - 4.50549i) q^{17} +(2.98492 + 0.300415i) q^{18} +(1.83509 - 3.95379i) q^{19} +(1.20855 - 1.88133i) q^{20} +(0.958694 - 0.162606i) q^{21} +(0.344314 + 3.93553i) q^{22} +(0.870467 + 1.86672i) q^{23} +(1.10467 + 1.33406i) q^{24} +(4.51545 + 2.14727i) q^{25} +(-1.00149 + 0.578210i) q^{26} +(-4.99183 - 1.44277i) q^{27} +(0.459878 + 0.322010i) q^{28} +(0.343731 + 1.94939i) q^{29} +(-2.64581 + 2.82837i) q^{30} +(-4.41044 - 7.63910i) q^{31} +(-0.0871557 + 0.996195i) q^{32} +(0.640800 - 6.81250i) q^{33} +(-1.88117 + 5.16848i) q^{34} +(-0.583856 + 1.11131i) q^{35} +(-1.46599 - 2.61741i) q^{36} +(-3.81268 - 3.81268i) q^{37} +(-4.29132 + 0.764577i) q^{38} +(1.88661 - 0.672773i) q^{39} +(-2.23429 + 0.0890965i) q^{40} +(2.78046 - 3.31362i) q^{41} +(-0.683084 - 0.692049i) q^{42} +(-3.09155 + 6.62985i) q^{43} +(3.02630 - 2.53937i) q^{44} +(5.38990 - 3.99362i) q^{45} +(1.02985 - 1.78375i) q^{46} +(-4.90003 - 3.43104i) q^{47} +(0.459186 - 1.67007i) q^{48} +(5.78923 + 3.34241i) q^{49} +(-0.831015 - 4.93046i) q^{50} +(4.81699 - 8.21904i) q^{51} +(1.04807 + 0.488724i) q^{52} +(-3.86721 - 8.29327i) q^{53} +(1.68135 + 4.91661i) q^{54} +(6.49031 + 5.99253i) q^{55} -0.561408i q^{56} +(7.54975 + 0.0357464i) q^{57} +(1.39969 - 1.39969i) q^{58} +(-0.585735 + 3.32187i) q^{59} +(3.83444 + 0.545039i) q^{60} +(-5.33263 - 1.94092i) q^{61} +(-3.72786 + 7.99443i) q^{62} +(0.947959 + 1.39211i) q^{63} +(0.866025 - 0.500000i) q^{64} +(-0.786886 + 2.46320i) q^{65} +(-5.94802 + 3.38258i) q^{66} +(-0.769735 + 1.09930i) q^{67} +(5.31277 - 1.42355i) q^{68} +(-2.31092 + 2.71786i) q^{69} +(1.24522 - 0.159153i) q^{70} +(0.994838 + 2.73330i) q^{71} +(-1.30320 + 2.70216i) q^{72} +(-16.1801 + 1.41558i) q^{73} +(-0.936301 + 5.31003i) q^{74} +(-0.121889 + 8.65940i) q^{75} +(3.08770 + 3.07670i) q^{76} +(-1.56827 + 1.56827i) q^{77} +(-1.63322 - 1.15953i) q^{78} +(-0.932998 + 1.11190i) q^{79} +(1.35452 + 1.77912i) q^{80} +(-1.33118 - 8.90101i) q^{81} +(-4.30917 - 0.377003i) q^{82} +(-2.29514 + 8.56557i) q^{83} +(-0.175093 + 0.956493i) q^{84} +(4.66359 + 11.3803i) q^{85} +(7.20410 - 1.27028i) q^{86} +(-2.82125 + 1.94817i) q^{87} +(-3.81595 - 1.02248i) q^{88} +(11.0988 - 9.31298i) q^{89} +(-6.36290 - 2.12450i) q^{90} +(-0.610070 - 0.222047i) q^{91} +(-2.05186 + 0.179515i) q^{92} +(8.84463 - 12.4578i) q^{93} +5.98183i q^{94} +(-5.94887 + 7.72082i) q^{95} +(-1.63142 + 0.581772i) q^{96} +(-13.4055 + 9.38664i) q^{97} +(-0.582621 - 6.65938i) q^{98} +(11.1888 - 3.90795i) 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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