LMFDB - Embedded newform 420.2.i.a.139.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(139,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1, 1]))

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

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

chi := DirichletCharacter("420.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.i (of order $2$, degree $1$, 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:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.5
Character	$\chi$	$=$	420.139
Dual form			420.2.i.a.139.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33186 - 0.475542i) q^{2} -1.00000i q^{3} +(1.54772 + 1.26671i) q^{4} +(2.22087 + 0.260295i) q^{5} +(-0.475542 + 1.33186i) q^{6} +(1.17807 - 2.36900i) q^{7} +(-1.45898 - 2.42309i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.33186 - 0.475542i) q^{2} -1.00000i q^{3} +(1.54772 + 1.26671i) q^{4} +(2.22087 + 0.260295i) q^{5} +(-0.475542 + 1.33186i) q^{6} +(1.17807 - 2.36900i) q^{7} +(-1.45898 - 2.42309i) q^{8} -1.00000 q^{9} +(-2.83411 - 1.40279i) q^{10} +0.365940i q^{11} +(1.26671 - 1.54772i) q^{12} +1.72798 q^{13} +(-2.69558 + 2.59496i) q^{14} +(0.260295 - 2.22087i) q^{15} +(0.790878 + 3.92103i) q^{16} -0.146965 q^{17} +(1.33186 + 0.475542i) q^{18} +4.73636 q^{19} +(3.10756 + 3.21606i) q^{20} +(-2.36900 - 1.17807i) q^{21} +(0.174020 - 0.487382i) q^{22} -3.44964 q^{23} +(-2.42309 + 1.45898i) q^{24} +(4.86449 + 1.15616i) q^{25} +(-2.30143 - 0.821724i) q^{26} +1.00000i q^{27} +(4.82416 - 2.17427i) q^{28} -5.29049 q^{29} +(-1.40279 + 2.83411i) q^{30} +6.07392 q^{31} +(0.811273 - 5.59838i) q^{32} +0.365940 q^{33} +(0.195737 + 0.0698879i) q^{34} +(3.23297 - 4.95458i) q^{35} +(-1.54772 - 1.26671i) q^{36} -7.52630i q^{37} +(-6.30819 - 2.25234i) q^{38} -1.72798i q^{39} +(-2.60948 - 5.76113i) q^{40} -7.16300i q^{41} +(2.59496 + 2.69558i) q^{42} -8.65051 q^{43} +(-0.463541 + 0.566373i) q^{44} +(-2.22087 - 0.260295i) q^{45} +(4.59445 + 1.64045i) q^{46} -3.83760i q^{47} +(3.92103 - 0.790878i) q^{48} +(-4.22431 - 5.58168i) q^{49} +(-5.92904 - 3.85312i) q^{50} +0.146965i q^{51} +(2.67442 + 2.18885i) q^{52} +11.5549i q^{53} +(0.475542 - 1.33186i) q^{54} +(-0.0952524 + 0.812704i) q^{55} +(-7.45908 + 0.601749i) q^{56} -4.73636i q^{57} +(7.04621 + 2.51585i) q^{58} +6.18874 q^{59} +(3.21606 - 3.10756i) q^{60} +0.348039i q^{61} +(-8.08963 - 2.88840i) q^{62} +(-1.17807 + 2.36900i) q^{63} +(-3.74277 + 7.07048i) q^{64} +(3.83760 + 0.449783i) q^{65} +(-0.487382 - 0.174020i) q^{66} +12.1623 q^{67} +(-0.227460 - 0.186162i) q^{68} +3.44964i q^{69} +(-6.66198 + 5.06142i) q^{70} -7.78061i q^{71} +(1.45898 + 2.42309i) q^{72} -4.55395 q^{73} +(-3.57907 + 10.0240i) q^{74} +(1.15616 - 4.86449i) q^{75} +(7.33056 + 5.99961i) q^{76} +(0.866911 + 0.431102i) q^{77} +(-0.821724 + 2.30143i) q^{78} +14.2442i q^{79} +(0.735808 + 8.91395i) q^{80} +1.00000 q^{81} +(-3.40630 + 9.54014i) q^{82} +3.53810i q^{83} +(-2.17427 - 4.82416i) q^{84} +(-0.326389 - 0.0382542i) q^{85} +(11.5213 + 4.11367i) q^{86} +5.29049i q^{87} +(0.886707 - 0.533898i) q^{88} +13.6498i q^{89} +(2.83411 + 1.40279i) q^{90} +(2.03567 - 4.09357i) q^{91} +(-5.33907 - 4.36970i) q^{92} -6.07392i q^{93} +(-1.82494 + 5.11116i) q^{94} +(10.5188 + 1.23285i) q^{95} +(-5.59838 - 0.811273i) q^{96} -16.1970 q^{97} +(2.97189 + 9.44288i) q^{98} -0.365940i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{9}+O(q^{10}) $ 48 * q - 48 * q^9	$ 48 q - 48 q^{9} + 20 q^{14} - 16 q^{16} + 8 q^{25} - 16 q^{30} - 40 q^{44} + 16 q^{46} - 16 q^{49} + 48 q^{50} + 28 q^{56} - 32 q^{60} - 112 q^{74} + 48 q^{81} - 28 q^{84} + 56 q^{85} + 8 q^{86}+O(q^{100}) $ 48 * q - 48 * q^9 + 20 * q^14 - 16 * q^16 + 8 * q^25 - 16 * q^30 - 40 * q^44 + 16 * q^46 - 16 * q^49 + 48 * q^50 + 28 * q^56 - 32 * q^60 - 112 * q^74 + 48 * q^81 - 28 * q^84 + 56 * q^85 + 8 * q^86

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

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 $

$2$	−1.33186	−	0.475542i	−0.941770	−	0.336259i
$2$	−1.33186	−	0.475542i	−0.941770	−	0.336259i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.54772	+	1.26671i	0.773860	+	0.633356i
$5$	2.22087	+	0.260295i	0.993202	+	0.116407i
$5$	2.22087	+	0.260295i	0.993202	+	0.116407i
$6$	−0.475542	+	1.33186i	−0.194139	+	0.543731i
$7$	1.17807	−	2.36900i	0.445268	−	0.895397i
$7$	1.17807	−	2.36900i	0.445268	−	0.895397i
$8$	−1.45898	−	2.42309i	−0.515827	−	0.856693i
$9$	−1.00000			−0.333333
$10$	−2.83411	−	1.40279i	−0.896224	−	0.443602i
$11$			0.365940i			0.110335i	0.998477	+	0.0551675i	$0.0175693\pi$
$11$			0.365940i			0.110335i	−0.998477	+	0.0551675i	$0.982431\pi$
$12$	1.26671	−	1.54772i	0.365668	−	0.446788i
$13$	1.72798			0.479254			0.239627	−	0.970865i	$-0.422975\pi$
$13$	1.72798			0.479254			0.239627	+	0.970865i	$0.422975\pi$
$14$	−2.69558	+	2.59496i	−0.720425	+	0.693533i
$15$	0.260295	−	2.22087i	0.0672079	−	0.573425i
$16$	0.790878	+	3.92103i	0.197719	+	0.980259i
$17$	−0.146965			−0.0356442			−0.0178221	−	0.999841i	$-0.505673\pi$
$17$	−0.146965			−0.0356442			−0.0178221	+	0.999841i	$0.505673\pi$
$18$	1.33186	+	0.475542i	0.313923	+	0.112086i
$19$	4.73636			1.08660			0.543298	−	0.839540i	$-0.317175\pi$
$19$	4.73636			1.08660			0.543298	+	0.839540i	$0.317175\pi$
$20$	3.10756	+	3.21606i	0.694872	+	0.719134i
$21$	−2.36900	−	1.17807i	−0.516958	−	0.257075i
$22$	0.174020	−	0.487382i	0.0371011	−	0.103910i
$23$	−3.44964			−0.719299			−0.359650	−	0.933087i	$-0.617104\pi$
$23$	−3.44964			−0.719299			−0.359650	+	0.933087i	$0.617104\pi$
$24$	−2.42309	+	1.45898i	−0.494612	+	0.297813i
$25$	4.86449	+	1.15616i	0.972899	+	0.231232i
$26$	−2.30143	−	0.821724i	−0.451347	−	0.161153i
$27$			1.00000i			0.192450i
$28$	4.82416	−	2.17427i	0.911681	−	0.410899i
$29$	−5.29049			−0.982419			−0.491209	−	0.871042i	$-0.663445\pi$
$29$	−5.29049			−0.982419			−0.491209	+	0.871042i	$0.663445\pi$
$30$	−1.40279	+	2.83411i	−0.256114	+	0.517435i
$31$	6.07392			1.09091			0.545454	−	0.838141i	$-0.316357\pi$
$31$	6.07392			1.09091			0.545454	+	0.838141i	$0.316357\pi$
$32$	0.811273	−	5.59838i	0.143414	−	0.989663i
$33$	0.365940			0.0637020
$34$	0.195737	+	0.0698879i	0.0335686	+	0.0119857i
$35$	3.23297	−	4.95458i	0.546472	−	0.837478i
$36$	−1.54772	−	1.26671i	−0.257953	−	0.211119i
$37$		−	7.52630i		−	1.23732i	−0.785660	−	0.618658i	$-0.787677\pi$
$37$		−	7.52630i		−	1.23732i	0.785660	−	0.618658i	$-0.212323\pi$
$38$	−6.30819	−	2.25234i	−1.02332	−	0.365377i
$39$		−	1.72798i		−	0.276698i
$40$	−2.60948	−	5.76113i	−0.412594	−	0.910915i
$41$		−	7.16300i		−	1.11867i	−0.828941	−	0.559336i	$-0.811056\pi$
$41$		−	7.16300i		−	1.11867i	0.828941	−	0.559336i	$-0.188944\pi$
$42$	2.59496	+	2.69558i	0.400411	+	0.415937i
$43$	−8.65051			−1.31919			−0.659595	−	0.751621i	$-0.729272\pi$
$43$	−8.65051			−1.31919			−0.659595	+	0.751621i	$0.729272\pi$
$44$	−0.463541	+	0.566373i	−0.0698814	+	0.0853839i
$45$	−2.22087	−	0.260295i	−0.331067	−	0.0388025i
$46$	4.59445	+	1.64045i	0.677414	+	0.241871i
$47$		−	3.83760i		−	0.559772i	−0.960033	−	0.279886i	$-0.909703\pi$
$47$		−	3.83760i		−	0.559772i	0.960033	−	0.279886i	$-0.0902967\pi$
$48$	3.92103	−	0.790878i	0.565953	−	0.114153i
$49$	−4.22431	−	5.58168i	−0.603473	−	0.797383i
$50$	−5.92904	−	3.85312i	−0.838493	−	0.544913i
$51$			0.146965i			0.0205792i
$52$	2.67442	+	2.18885i	0.370876	+	0.303539i
$53$			11.5549i			1.58719i	0.608447	+	0.793595i	$0.291793\pi$
$53$			11.5549i			1.58719i	−0.608447	+	0.793595i	$0.708207\pi$
$54$	0.475542	−	1.33186i	0.0647130	−	0.181244i
$55$	−0.0952524	+	0.812704i	−0.0128438	+	0.109585i
$56$	−7.45908	+	0.601749i	−0.996762	+	0.0804120i
$57$		−	4.73636i		−	0.627346i
$58$	7.04621	+	2.51585i	0.925212	+	0.330347i
$59$	6.18874			0.805706			0.402853	−	0.915265i	$-0.368019\pi$
$59$	6.18874			0.805706			0.402853	+	0.915265i	$0.368019\pi$
$60$	3.21606	−	3.10756i	0.415192	−	0.401184i
$61$			0.348039i			0.0445619i	0.999752	+	0.0222809i	$0.00709283\pi$
$61$			0.348039i			0.0445619i	−0.999752	+	0.0222809i	$0.992907\pi$
$62$	−8.08963	−	2.88840i	−1.02738	−	0.366827i
$63$	−1.17807	+	2.36900i	−0.148423	+	0.298466i
$64$	−3.74277	+	7.07048i	−0.467846	+	0.883810i
$65$	3.83760	+	0.449783i	0.475996	+	0.0557888i
$66$	−0.487382	−	0.174020i	−0.0599926	−	0.0214203i
$67$	12.1623			1.48586			0.742929	−	0.669370i	$-0.233436\pi$
$67$	12.1623			1.48586			0.742929	+	0.669370i	$0.233436\pi$
$68$	−0.227460	−	0.186162i	−0.0275836	−	0.0225755i
$69$			3.44964i			0.415288i
$70$	−6.66198	+	5.06142i	−0.796259	+	0.604955i
$71$		−	7.78061i		−	0.923388i	−0.887039	−	0.461694i	$-0.847242\pi$
$71$		−	7.78061i		−	0.923388i	0.887039	−	0.461694i	$-0.152758\pi$
$72$	1.45898	+	2.42309i	0.171942	+	0.285564i
$73$	−4.55395			−0.532999			−0.266500	−	0.963835i	$-0.585867\pi$
$73$	−4.55395			−0.532999			−0.266500	+	0.963835i	$0.585867\pi$
$74$	−3.57907	+	10.0240i	−0.416058	+	1.16527i
$75$	1.15616	−	4.86449i	0.133502	−	0.561703i
$76$	7.33056	+	5.99961i	0.840873	+	0.688202i
$77$	0.866911	+	0.431102i	0.0987937	+	0.0491286i
$78$	−0.821724	+	2.30143i	−0.0930419	+	0.260585i
$79$			14.2442i			1.60260i	0.598261	+	0.801301i	$0.295859\pi$
$79$			14.2442i			1.60260i	−0.598261	+	0.801301i	$0.704141\pi$
$80$	0.735808	+	8.91395i	0.0822658	+	0.996610i
$81$	1.00000			0.111111
$82$	−3.40630	+	9.54014i	−0.376163	+	1.05353i
$83$			3.53810i			0.388357i	0.980966	+	0.194179i	$0.0622042\pi$
$83$			3.53810i			0.388357i	−0.980966	+	0.194179i	$0.937796\pi$
$84$	−2.17427	−	4.82416i	−0.237233	−	0.526359i
$85$	−0.326389	−	0.0382542i	−0.0354019	−	0.00414925i
$86$	11.5213	+	4.11367i	1.24237	+	0.443589i
$87$			5.29049i			0.567200i
$88$	0.886707	−	0.533898i	0.0945233	−	0.0569138i
$89$			13.6498i			1.44687i	0.690390	+	0.723437i	$0.257439\pi$
$89$			13.6498i			1.44687i	−0.690390	+	0.723437i	$0.742561\pi$
$90$	2.83411	+	1.40279i	0.298741	+	0.147867i
$91$	2.03567	−	4.09357i	0.213396	−	0.429123i
$92$	−5.33907	−	4.36970i	−0.556637	−	0.455573i
$93$		−	6.07392i		−	0.629836i
$94$	−1.82494	+	5.11116i	−0.188228	+	0.527176i
$95$	10.5188	+	1.23285i	1.07921	+	0.126488i
$96$	−5.59838	−	0.811273i	−0.571382	−	0.0828002i
$97$	−16.1970			−1.64456			−0.822280	−	0.569083i	$-0.807298\pi$
$97$	−16.1970			−1.64456			−0.822280	+	0.569083i	$0.807298\pi$
$98$	2.97189	+	9.44288i	0.300206	+	0.953874i
$99$		−	0.365940i		−	0.0367784i
$100$	6.06435	+	7.95133i	0.606435	+	0.795133i
$101$		−	4.41655i		−	0.439463i	−0.975560	−	0.219732i	$-0.929482\pi$
$101$		−	4.41655i		−	0.439463i	0.975560	−	0.219732i	$-0.0705182\pi$
$102$	0.0698879	−	0.195737i	0.00691993	−	0.0193809i
$103$			12.4670i			1.22841i	0.789147	+	0.614204i	$0.210523\pi$
$103$			12.4670i			1.22841i	−0.789147	+	0.614204i	$0.789477\pi$
$104$	−2.52108	−	4.18705i	−0.247212	−	0.410574i
$105$	−4.95458	−	3.23297i	−0.483518	−	0.315506i
$106$	5.49484	−	15.3896i	0.533706	−	1.49477i
$107$	6.16409			0.595905			0.297953	−	0.954581i	$-0.403696\pi$
$107$	6.16409			0.595905			0.297953	+	0.954581i	$0.403696\pi$
$108$	−1.26671	+	1.54772i	−0.121889	+	0.148929i
$109$	−2.76468			−0.264809			−0.132404	−	0.991196i	$-0.542270\pi$
$109$	−2.76468			−0.264809			−0.132404	+	0.991196i	$0.542270\pi$
$110$	0.513337	−	1.03711i	0.0489448	−	0.0988849i
$111$	−7.52630			−0.714365
$112$	10.2206	+	2.74566i	0.965759	+	0.259440i
$113$			9.60538i			0.903599i	0.892120	+	0.451799i	$0.149218\pi$
$113$			9.60538i			0.903599i	−0.892120	+	0.451799i	$0.850782\pi$
$114$	−2.25234	+	6.30819i	−0.210951	+	0.590816i
$115$	−7.66118	−	0.897923i	−0.714409	−	0.0837318i
$116$	−8.18820	−	6.70153i	−0.760255	−	0.622221i
$117$	−1.72798			−0.159751
$118$	−8.24256	−	2.94300i	−0.758789	−	0.270926i
$119$	−0.173135	+	0.348160i	−0.0158712	+	0.0319157i
$120$	−5.76113	+	2.60948i	−0.525917	+	0.238211i
$121$	10.8661			0.987826
$122$	0.165507	−	0.463541i	0.0149843	−	0.0419670i
$123$	−7.16300			−0.645866
$124$	9.40073	+	7.69391i	0.844210	+	0.690934i
$125$	10.5024	+	3.83388i	0.939367	+	0.342913i
$126$	2.69558	−	2.59496i	0.240142	−	0.231178i
$127$	−8.58236			−0.761561			−0.380781	−	0.924665i	$-0.624345\pi$
$127$	−8.58236			−0.761561			−0.380781	+	0.924665i	$0.624345\pi$
$128$	8.34716	−	7.63707i	0.737792	−	0.675028i
$129$			8.65051i			0.761635i
$130$	−4.89727	−	2.42399i	−0.429519	−	0.212598i
$131$	−18.6036			−1.62540			−0.812702	−	0.582680i	$-0.802004\pi$
$131$	−18.6036			−1.62540			−0.812702	+	0.582680i	$0.802004\pi$
$132$	0.566373	+	0.463541i	0.0492964	+	0.0403460i
$133$	5.57976	−	11.2204i	0.483826	−	0.972935i
$134$	−16.1985	−	5.78367i	−1.39934	−	0.499633i
$135$	−0.260295	+	2.22087i	−0.0224026	+	0.191142i
$136$	0.214418	+	0.356110i	0.0183862	+	0.0305361i
$137$			21.5809i			1.84378i	0.387447	+	0.921892i	$0.373357\pi$
$137$			21.5809i			1.84378i	−0.387447	+	0.921892i	$0.626643\pi$
$138$	1.64045	−	4.59445i	0.139644	−	0.391105i
$139$	−13.1564			−1.11591			−0.557955	−	0.829871i	$-0.688414\pi$
$139$	−13.1564			−1.11591			−0.557955	+	0.829871i	$0.688414\pi$
$140$	11.2798	−	3.57307i	0.953314	−	0.301979i
$141$	−3.83760			−0.323184
$142$	−3.70000	+	10.3627i	−0.310497	+	0.869619i
$143$			0.632335i			0.0528785i
$144$	−0.790878	−	3.92103i	−0.0659065	−	0.326753i
$145$	−11.7495	−	1.37709i	−0.975740	−	0.114361i
$146$	6.06523	+	2.16559i	0.501962	+	0.179226i
$147$	−5.58168	+	4.22431i	−0.460369	+	0.348415i
$148$	9.53366	−	11.6486i	0.783662	−	0.957510i
$149$	10.7665			0.882025			0.441012	−	0.897501i	$-0.354620\pi$
$149$	10.7665			0.882025			0.441012	+	0.897501i	$0.354620\pi$
$150$	−3.85312	+	5.92904i	−0.314606	+	0.484104i
$151$			3.34472i			0.272190i	0.990696	+	0.136095i	$0.0434552\pi$
$151$			3.34472i			0.272190i	−0.990696	+	0.136095i	$0.956545\pi$
$152$	−6.91025	−	11.4766i	−0.560495	−	0.930879i
$153$	0.146965			0.0118814
$154$	−0.949601	−	0.986422i	−0.0765210	−	0.0794881i
$155$	13.4894	+	1.58101i	1.08349	+	0.126990i
$156$	2.18885	−	2.67442i	0.175248	−	0.214125i
$157$	19.3169			1.54166			0.770830	−	0.637041i	$-0.219842\pi$
$157$	19.3169			1.54166			0.770830	+	0.637041i	$0.219842\pi$
$158$	6.77373	−	18.9714i	0.538889	−	1.50928i
$159$	11.5549			0.916364
$160$	3.25896	−	12.2221i	0.257643	−	0.966240i
$161$	−4.06391	+	8.17219i	−0.320281	+	0.644059i
$162$	−1.33186	−	0.475542i	−0.104641	−	0.0373621i
$163$	−17.6321			−1.38106			−0.690528	−	0.723306i	$-0.742622\pi$
$163$	−17.6321			−1.38106			−0.690528	+	0.723306i	$0.742622\pi$
$164$	9.07346	−	11.0863i	0.708518	−	0.865696i
$165$	0.812704	+	0.0952524i	0.0632689	+	0.00741539i
$166$	1.68252	−	4.71227i	0.130589	−	0.365743i
$167$		−	16.7301i		−	1.29461i	−0.762229	−	0.647307i	$-0.775895\pi$
$167$		−	16.7301i		−	1.29461i	0.762229	−	0.647307i	$-0.224105\pi$
$168$	0.601749	+	7.45908i	0.0464259	+	0.575481i
$169$	−10.0141			−0.770315
$170$	0.416514	+	0.206161i	0.0319452	+	0.0158118i
$171$	−4.73636			−0.362199
$172$	−13.3886	−	10.9577i	−1.02087	−	0.835517i
$173$	17.5934			1.33760			0.668802	−	0.743441i	$-0.266807\pi$
$173$	17.5934			1.33760			0.668802	+	0.743441i	$0.266807\pi$
$174$	2.51585	−	7.04621i	0.190726	−	0.534172i
$175$	8.46965	−	10.1619i	0.640245	−	0.768171i
$176$	−1.43486	+	0.289414i	−0.108157	+	0.0218154i
$177$		−	6.18874i		−	0.465175i
$178$	6.49104	−	18.1796i	0.486524	−	1.36262i
$179$			7.52728i			0.562615i	0.959618	+	0.281308i	$0.0907681\pi$
$179$			7.52728i			0.562615i	−0.959618	+	0.281308i	$0.909232\pi$
$180$	−3.10756	−	3.21606i	−0.231624	−	0.239711i
$181$			3.83151i			0.284794i	0.989810	+	0.142397i	$0.0454809\pi$
$181$			3.83151i			0.284794i	−0.989810	+	0.142397i	$0.954519\pi$
$182$	−4.65790	+	4.48403i	−0.345267	+	0.332379i
$183$	0.348039			0.0257278
$184$	5.03294	+	8.35879i	0.371034	+	0.616218i
$185$	1.95906	−	16.7149i	0.144033	−	1.22890i
$186$	−2.88840	+	8.08963i	−0.211788	+	0.593161i
$187$		−	0.0537803i		−	0.00393281i
$188$	4.86114	−	5.93954i	0.354535	−	0.433185i
$189$	2.36900	+	1.17807i	0.172319	+	0.0856918i
$190$	−13.4234	−	6.64413i	−0.973833	−	0.482016i
$191$			20.1200i			1.45583i	0.685665	+	0.727917i	$0.259511\pi$
$191$			20.1200i			1.45583i	−0.685665	+	0.727917i	$0.740489\pi$
$192$	7.07048	+	3.74277i	0.510268	+	0.270111i
$193$			19.6683i			1.41575i	0.706336	+	0.707877i	$0.250347\pi$
$193$			19.6683i			1.41575i	−0.706336	+	0.707877i	$0.749653\pi$
$194$	21.5722	+	7.70237i	1.54880	+	0.552998i
$195$	0.449783	−	3.83760i	0.0322097	−	0.274816i
$196$	0.532333	−	13.9899i	0.0380238	−	0.999277i
$197$			5.44722i			0.388098i	0.980992	+	0.194049i	$0.0621621\pi$
$197$			5.44722i			0.388098i	−0.980992	+	0.194049i	$0.937838\pi$
$198$	−0.174020	+	0.487382i	−0.0123670	+	0.0346367i
$199$	−6.66636			−0.472566			−0.236283	−	0.971684i	$-0.575929\pi$
$199$	−6.66636			−0.472566			−0.236283	+	0.971684i	$0.575929\pi$
$200$	−4.29570	−	13.4739i	−0.303752	−	0.952751i
$201$		−	12.1623i		−	0.857861i
$202$	−2.10025	+	5.88225i	−0.147773	+	0.413873i
$203$	−6.23255	+	12.5332i	−0.437439	+	0.879655i
$204$	−0.186162	+	0.227460i	−0.0130340	+	0.0159254i
$205$	1.86449	−	15.9081i	0.130222	−	1.11107i
$206$	5.92857	−	16.6043i	0.413063	−	1.15688i
$207$	3.44964			0.239766
$208$	1.36662	+	6.77545i	0.0947579	+	0.469793i
$209$			1.73322i			0.119890i
$210$	5.06142	+	6.66198i	0.349271	+	0.459721i
$211$		−	8.81673i		−	0.606969i	−0.952836	−	0.303484i	$-0.901850\pi$
$211$		−	8.81673i		−	0.606969i	0.952836	−	0.303484i	$-0.0981500\pi$
$212$	−14.6368	+	17.8838i	−1.00526	+	1.22826i
$213$	−7.78061			−0.533118
$214$	−8.20973	−	2.93128i	−0.561205	−	0.200378i
$215$	−19.2116	−	2.25168i	−1.31022	−	0.153564i
$216$	2.42309	−	1.45898i	0.164871	−	0.0992709i
$217$	7.15549	−	14.3891i	0.485746	−	0.976796i
$218$	3.68218	+	1.31472i	0.249389	+	0.0890442i
$219$			4.55395i			0.307727i
$220$	−1.17689	+	1.13718i	−0.0793456	+	0.0766687i
$221$	−0.253952			−0.0170826
$222$	10.0240	+	3.57907i	0.672767	+	0.240211i
$223$			7.18662i			0.481252i	0.970618	+	0.240626i	$0.0773527\pi$
$223$			7.18662i			0.481252i	−0.970618	+	0.240626i	$0.922647\pi$
$224$	−12.3068	−	8.51717i	−0.822284	−	0.569078i
$225$	−4.86449	−	1.15616i	−0.324300	−	0.0770774i
$226$	4.56776	−	12.7931i	0.303843	−	0.850982i
$227$		−	4.76468i		−	0.316243i	−0.987420	−	0.158122i	$-0.949456\pi$
$227$		−	4.76468i		−	0.316243i	0.987420	−	0.158122i	$-0.0505438\pi$
$228$	5.99961	−	7.33056i	0.397334	−	0.485479i
$229$		−	15.4673i		−	1.02211i	−0.859548	−	0.511055i	$-0.829255\pi$
$229$		−	15.4673i		−	1.02211i	0.859548	−	0.511055i	$-0.170745\pi$
$230$	9.77665	+	4.83912i	0.644653	+	0.319082i
$231$	0.431102	−	0.866911i	0.0283644	−	0.0570386i
$232$	7.71870	+	12.8193i	0.506758	+	0.841631i
$233$		−	13.7907i		−	0.903461i	−0.892155	−	0.451730i	$-0.850807\pi$
$233$		−	13.7907i		−	0.903461i	0.892155	−	0.451730i	$-0.149193\pi$
$234$	2.30143	+	0.821724i	0.150449	+	0.0537178i
$235$	0.998909	−	8.52280i	0.0651616	−	0.555966i
$236$	9.57845	+	7.83936i	0.623504	+	0.510299i
$237$	14.2442			0.925263
$238$	0.396156	−	0.381368i	0.0256790	−	0.0247204i
$239$		−	1.39679i		−	0.0903506i	−0.998979	−	0.0451753i	$-0.985615\pi$
$239$		−	1.39679i		−	0.0903506i	0.998979	−	0.0451753i	$-0.0143846\pi$
$240$	8.91395	−	0.735808i	0.575393	−	0.0474962i
$241$			18.9796i			1.22258i	0.791406	+	0.611290i	$0.209349\pi$
$241$			18.9796i			1.22258i	−0.791406	+	0.611290i	$0.790651\pi$
$242$	−14.4721	−	5.16728i	−0.930305	−	0.332165i
$243$		−	1.00000i		−	0.0641500i
$244$	−0.440866	+	0.538668i	−0.0282235	+	0.0344847i
$245$	−7.92875	−	13.4957i	−0.506549	−	0.862211i
$246$	9.54014	+	3.40630i	0.608257	+	0.217178i
$247$	8.18432			0.520756
$248$	−8.86171	−	14.7177i	−0.562719	−	0.934573i
$249$	3.53810			0.224218
$250$	−12.1647	−	10.1006i	−0.769360	−	0.638815i
$251$	10.9949			0.693994			0.346997	−	0.937866i	$-0.387201\pi$
$251$	10.9949			0.693994			0.346997	+	0.937866i	$0.387201\pi$
$252$	−4.82416	+	2.17427i	−0.303894	+	0.136966i
$253$		−	1.26236i		−	0.0793639i
$254$	11.4305	+	4.08127i	0.717215	+	0.256081i
$255$	−0.0382542	+	0.326389i	−0.00239557	+	0.0204393i
$256$	−14.7490	+	6.20212i	−0.921814	+	0.387632i
$257$	−18.1739			−1.13366			−0.566828	−	0.823836i	$-0.691830\pi$
$257$	−18.1739			−1.13366			−0.566828	+	0.823836i	$0.691830\pi$
$258$	4.11367	−	11.5213i	0.256106	−	0.717284i
$259$	−17.8298	−	8.86649i	−1.10789	−	0.550937i
$260$	5.36979	+	5.55728i	0.333020	+	0.344648i
$261$	5.29049			0.327473
$262$	24.7775	+	8.84678i	1.53076	+	0.546556i
$263$	−9.67183			−0.596390			−0.298195	−	0.954505i	$-0.596385\pi$
$263$	−9.67183			−0.596390			−0.298195	+	0.954505i	$0.596385\pi$
$264$	−0.533898	−	0.886707i	−0.0328592	−	0.0545730i
$265$	−3.00769	+	25.6619i	−0.184761	+	1.57640i
$266$	−12.7673	+	12.2907i	−0.782811	+	0.753590i
$267$	13.6498			0.835353
$268$	18.8238	+	15.4061i	1.14985	+	0.941078i
$269$		−	1.72109i		−	0.104937i	−0.998623	−	0.0524684i	$-0.983291\pi$
$269$		−	1.72109i		−	0.104937i	0.998623	−	0.0524684i	$-0.0167089\pi$
$270$	1.40279	−	2.83411i	0.0853712	−	0.172478i
$271$	8.11648			0.493041			0.246521	−	0.969138i	$-0.420713\pi$
$271$	8.11648			0.493041			0.246521	+	0.969138i	$0.420713\pi$
$272$	−0.116231	−	0.576254i	−0.00704755	−	0.0349405i
$273$	−4.09357	−	2.03567i	−0.247754	−	0.123205i
$274$	10.2626	−	28.7429i	0.619988	−	1.73642i
$275$	−0.423085	+	1.78011i	−0.0255130	+	0.107345i
$276$	−4.36970	+	5.33907i	−0.263025	+	0.321375i
$277$		−	1.12611i		−	0.0676615i	−0.999428	−	0.0338307i	$-0.989229\pi$
$277$		−	1.12611i		−	0.0676615i	0.999428	−	0.0338307i	$-0.0107707\pi$
$278$	17.5225	+	6.25640i	1.05093	+	0.375234i
$279$	−6.07392			−0.363636
$280$	−16.7223	−	0.605158i	−0.999346	−	0.0361651i
$281$	14.3818			0.857944			0.428972	−	0.903318i	$-0.358876\pi$
$281$	14.3818			0.857944			0.428972	+	0.903318i	$0.358876\pi$
$282$	5.11116	+	1.82494i	0.304365	+	0.108674i
$283$		−	23.4832i		−	1.39593i	−0.716132	−	0.697965i	$-0.754089\pi$
$283$		−	23.4832i		−	1.39593i	0.716132	−	0.697965i	$-0.245911\pi$
$284$	9.85579	−	12.0422i	0.584834	−	0.714573i
$285$	1.23285	−	10.5188i	0.0730278	−	0.623081i
$286$	0.300702	−	0.842184i	0.0177809	−	0.0497994i
$287$	−16.9691	−	8.43850i	−1.00166	−	0.498109i
$288$	−0.811273	+	5.59838i	−0.0478047	+	0.329888i
$289$	−16.9784			−0.998729
$290$	14.9938	+	7.42145i	0.880467	+	0.435803i
$291$			16.1970i			0.949487i
$292$	−7.04824	−	5.76854i	−0.412467	−	0.337578i
$293$	13.3608			0.780544			0.390272	−	0.920700i	$-0.372381\pi$
$293$	13.3608			0.780544			0.390272	+	0.920700i	$0.372381\pi$
$294$	9.44288	−	2.97189i	0.550720	−	0.173324i
$295$	13.7444	+	1.61090i	0.800228	+	0.0937902i
$296$	−18.2369	+	10.9807i	−1.06000	+	0.638241i
$297$	−0.365940			−0.0212340
$298$	−14.3395	−	5.11991i	−0.830664	−	0.296588i
$299$	−5.96089			−0.344727
$300$	7.95133	−	6.06435i	0.459070	−	0.350126i
$301$	−10.1909	+	20.4930i	−0.587393	+	1.18120i
$302$	1.59055	−	4.45471i	0.0915261	−	0.256340i
$303$	−4.41655			−0.253724
$304$	3.74588	+	18.5714i	0.214841	+	1.06515i
$305$	−0.0905929	+	0.772949i	−0.00518733	+	0.0442589i
$306$	−0.195737	−	0.0698879i	−0.0111895	−	0.00399522i
$307$			27.7860i			1.58583i	0.609333	+	0.792914i	$0.291437\pi$
$307$			27.7860i			1.58583i	−0.609333	+	0.792914i	$0.708563\pi$
$308$	0.795654	+	1.76535i	0.0453366	+	0.100590i
$309$	12.4670			0.709222
$310$	−17.2142	−	8.52044i	−0.977698	−	0.483929i
$311$	−4.53917			−0.257393			−0.128696	−	0.991684i	$-0.541079\pi$
$311$	−4.53917			−0.257393			−0.128696	+	0.991684i	$0.541079\pi$
$312$	−4.18705	+	2.52108i	−0.237045	+	0.142728i
$313$	−2.86576			−0.161982			−0.0809911	−	0.996715i	$-0.525809\pi$
$313$	−2.86576			−0.161982			−0.0809911	+	0.996715i	$0.525809\pi$
$314$	−25.7275	−	9.18601i	−1.45189	−	0.518396i
$315$	−3.23297	+	4.95458i	−0.182157	+	0.279159i
$316$	−18.0434	+	22.0461i	−1.01502	+	1.24019i
$317$		−	16.3518i		−	0.918411i	−0.888330	−	0.459206i	$-0.848134\pi$
$317$		−	16.3518i		−	0.918411i	0.888330	−	0.459206i	$-0.151866\pi$
$318$	−15.3896	−	5.49484i	−0.863004	−	0.308135i
$319$		−	1.93600i		−	0.108395i
$320$	−10.1526	+	14.7284i	−0.567547	+	0.823341i
$321$		−	6.16409i		−	0.344046i
$322$	9.29878	−	8.95168i	0.518201	−	0.498858i
$323$	−0.696079			−0.0387308
$324$	1.54772	+	1.26671i	0.0859845	+	0.0703729i
$325$	8.40573	+	1.99782i	0.466266	+	0.110819i
$326$	23.4836	+	8.38481i	1.30064	+	0.464392i
$327$			2.76468i			0.152887i
$328$	−17.3566	+	10.4507i	−0.958359	+	0.577041i
$329$	−9.09128	−	4.52096i	−0.501218	−	0.249248i
$330$	−1.03711	−	0.513337i	−0.0570912	−	0.0282583i
$331$		−	16.4160i		−	0.902306i	−0.892447	−	0.451153i	$-0.851013\pi$
$331$		−	16.4160i		−	0.902306i	0.892447	−	0.451153i	$-0.148987\pi$
$332$	−4.48176	+	5.47600i	−0.245969	+	0.300534i
$333$			7.52630i			0.412439i
$334$	−7.95586	+	22.2822i	−0.435325	+	1.21923i
$335$	27.0108	+	3.16578i	1.47576	+	0.172965i
$336$	2.74566	−	10.2206i	0.149788	−	0.557581i
$337$			35.3369i			1.92492i	0.271415	+	0.962462i	$0.412508\pi$
$337$			35.3369i			1.92492i	−0.271415	+	0.962462i	$0.587492\pi$
$338$	13.3374	+	4.76212i	0.725460	+	0.259025i
$339$	9.60538			0.521693
$340$	−0.456702	−	0.472648i	−0.0247682	−	0.0256329i
$341$			2.22269i			0.120365i
$342$	6.30819	+	2.25234i	0.341108	+	0.121792i
$343$	−18.1995	+	3.43179i	−0.982682	+	0.185299i
$344$	12.6209	+	20.9610i	0.680473	+	1.13014i
$345$	−0.897923	+	7.66118i	−0.0483426	+	0.412464i
$346$	−23.4321	−	8.36641i	−1.25971	−	0.449781i
$347$	0.819726			0.0440052			0.0220026	−	0.999758i	$-0.492996\pi$
$347$	0.819726			0.0440052			0.0220026	+	0.999758i	$0.492996\pi$
$348$	−6.70153	+	8.18820i	−0.359240	+	0.438933i
$349$		−	18.9508i		−	1.01441i	−0.861825	−	0.507206i	$-0.830678\pi$
$349$		−	18.9508i		−	1.01441i	0.861825	−	0.507206i	$-0.169322\pi$
$350$	−16.1128	+	9.50665i	−0.861267	+	0.508152i
$351$			1.72798i			0.0922325i
$352$	2.04867	+	0.296877i	0.109194	+	0.0158236i
$353$	−18.6922			−0.994888			−0.497444	−	0.867496i	$-0.665728\pi$
$353$	−18.6922			−0.994888			−0.497444	+	0.867496i	$0.665728\pi$
$354$	−2.94300	+	8.24256i	−0.156419	+	0.438087i
$355$	2.02525	−	17.2797i	0.107489	−	0.917111i
$356$	−17.2904	+	21.1260i	−0.916387	+	1.11968i
$357$	0.348160	+	0.173135i	0.0184266	+	0.00916325i
$358$	3.57953	−	10.0253i	0.189184	−	0.529854i
$359$		−	20.3800i		−	1.07562i	−0.843067	−	0.537808i	$-0.819253\pi$
$359$		−	20.3800i		−	1.07562i	0.843067	−	0.537808i	$-0.180747\pi$
$360$	2.60948	+	5.76113i	0.137531	+	0.303638i
$361$	3.43313			0.180691
$362$	1.82204	−	5.10305i	0.0957644	−	0.268210i
$363$		−	10.8661i		−	0.570322i
$364$	8.33603	−	3.75709i	0.436927	−	0.196925i
$365$	−10.1137	−	1.18537i	−0.529375	−	0.0620451i
$366$	−0.463541	−	0.165507i	−0.0242297	−	0.00865120i
$367$			2.16777i			0.113157i	0.998398	+	0.0565783i	$0.0180191\pi$
$367$			2.16777i			0.113157i	−0.998398	+	0.0565783i	$0.981981\pi$
$368$	−2.72824	−	13.5261i	−0.142219	−	0.705099i
$369$			7.16300i			0.372891i
$370$	−10.5578	+	21.3304i	−0.548876	+	1.10891i
$371$	27.3736	+	13.6125i	1.42117	+	0.706724i
$372$	7.69391	−	9.40073i	0.398911	−	0.487405i
$373$			9.91788i			0.513528i	0.966474	+	0.256764i	$0.0826564\pi$
$373$			9.91788i			0.513528i	−0.966474	+	0.256764i	$0.917344\pi$
$374$	−0.0255748	+	0.0716280i	−0.00132244	+	0.00370380i
$375$	3.83388	−	10.5024i	0.197981	−	0.542344i
$376$	−9.29887	+	5.59898i	−0.479553	+	0.288745i
$377$	−9.14183			−0.470828
$378$	−2.59496	−	2.69558i	−0.133470	−	0.138646i
$379$			0.146790i			0.00754011i	0.999993	+	0.00377005i	$0.00120005\pi$
$379$			0.146790i			0.00754011i	−0.999993	+	0.00377005i	$0.998800\pi$
$380$	14.7185	+	15.2324i	0.755045	+	0.781408i
$381$			8.58236i			0.439688i
$382$	9.56791	−	26.7971i	0.489537	−	1.37106i
$383$			34.9127i			1.78395i	0.452081	+	0.891977i	$0.350682\pi$
$383$			34.9127i			1.78395i	−0.452081	+	0.891977i	$0.649318\pi$
$384$	−7.63707	−	8.34716i	−0.389728	−	0.425964i
$385$	1.81308	+	1.18307i	0.0924031	+	0.0602950i
$386$	9.35309	−	26.1955i	0.476060	−	1.33331i
$387$	8.65051			0.439730
$388$	−25.0685	−	20.5170i	−1.27266	−	1.04159i
$389$	27.6435			1.40158			0.700790	−	0.713368i	$-0.252831\pi$
$389$	27.6435			1.40158			0.700790	+	0.713368i	$0.252831\pi$
$390$	−2.42399	+	4.89727i	−0.122743	+	0.247983i
$391$	0.506975			0.0256388
$392$	−7.36176	+	18.3795i	−0.371825	+	0.928303i
$393$			18.6036i			0.938427i
$394$	2.59038	−	7.25495i	0.130501	−	0.365499i
$395$	−3.70771	+	31.6346i	−0.186555	+	1.59171i
$396$	0.463541	−	0.566373i	0.0232938	−	0.0284613i
$397$	9.62119			0.482874			0.241437	−	0.970417i	$-0.422381\pi$
$397$	9.62119			0.482874			0.241437	+	0.970417i	$0.422381\pi$
$398$	8.87869	+	3.17013i	0.445048	+	0.158904i
$399$	−11.2204	−	5.57976i	−0.561724	−	0.279337i
$400$	−0.686127	+	19.9882i	−0.0343063	+	0.999411i
$401$	−21.8030			−1.08879			−0.544395	−	0.838829i	$-0.683241\pi$
$401$	−21.8030			−1.08879			−0.544395	+	0.838829i	$0.683241\pi$
$402$	−5.78367	+	16.1985i	−0.288463	+	0.807907i
$403$	10.4956			0.522822
$404$	5.59450	−	6.83559i	0.278337	−	0.340083i
$405$	2.22087	+	0.260295i	0.110356	+	0.0129342i
$406$	14.2609	−	13.7286i	0.707759	−	0.681340i
$407$	2.75417			0.136519
$408$	0.356110	−	0.214418i	0.0176300	−	0.0106153i
$409$		−	30.1429i		−	1.49047i	−0.666801	−	0.745236i	$-0.732337\pi$
$409$		−	30.1429i		−	1.49047i	0.666801	−	0.745236i	$-0.267663\pi$
$410$	−10.0482	+	20.3007i	−0.496245	+	1.00258i
$411$	21.5809			1.06451
$412$	−15.7921	+	19.2954i	−0.778020	+	0.950616i
$413$	7.29076	−	14.6611i	0.358755	−	0.721427i
$414$	−4.59445	−	1.64045i	−0.225805	−	0.0806235i
$415$	−0.920951	+	7.85766i	−0.0452077	+	0.385717i
$416$	1.40186	−	9.67386i	0.0687319	−	0.474300i
$417$			13.1564i			0.644271i
$418$	0.824220	−	2.30842i	0.0403139	−	0.112908i
$419$	24.2208			1.18327			0.591633	−	0.806208i	$-0.298484\pi$
$419$	24.2208			1.18327			0.591633	+	0.806208i	$0.298484\pi$
$420$	−3.57307	−	11.2798i	−0.174348	−	0.550396i
$421$	5.72899			0.279214			0.139607	−	0.990207i	$-0.455416\pi$
$421$	5.72899			0.279214			0.139607	+	0.990207i	$0.455416\pi$
$422$	−4.19272	+	11.7427i	−0.204099	+	0.571625i
$423$			3.83760i			0.186591i
$424$	27.9986	−	16.8584i	1.35973	−	0.818715i
$425$	−0.714909	−	0.169915i	−0.0346782	−	0.00824209i
$426$	10.3627	+	3.70000i	0.502075	+	0.179266i
$427$	0.824505	+	0.410014i	0.0399006	+	0.0198420i
$428$	9.54029	+	7.80813i	0.461147	+	0.377420i
$429$	0.632335			0.0305294
$430$	24.5165	+	12.1349i	1.18229	+	0.585195i
$431$		−	34.1933i		−	1.64703i	−0.567293	−	0.823516i	$-0.692009\pi$
$431$		−	34.1933i		−	1.64703i	0.567293	−	0.823516i	$-0.307991\pi$
$432$	−3.92103	+	0.790878i	−0.188651	+	0.0380511i
$433$	−32.7841			−1.57550			−0.787751	−	0.615994i	$-0.788755\pi$
$433$	−32.7841			−1.57550			−0.787751	+	0.615994i	$0.788755\pi$
$434$	−16.3728	+	15.7616i	−0.785917	+	0.756581i
$435$	−1.37709	+	11.7495i	−0.0660263	+	0.563344i
$436$	−4.27896	−	3.50206i	−0.204925	−	0.167718i
$437$	−16.3387			−0.781587
$438$	2.16559	−	6.06523i	0.103476	−	0.289808i
$439$	32.1286			1.53342			0.766708	−	0.641996i	$-0.221894\pi$
$439$	32.1286			1.53342			0.766708	+	0.641996i	$0.221894\pi$
$440$	2.10823	−	0.954911i	0.100506	−	0.0455236i
$441$	4.22431	+	5.58168i	0.201158	+	0.265794i
$442$	0.338229	+	0.120765i	0.0160879	+	0.00574418i
$443$	−12.4260			−0.590377			−0.295189	−	0.955439i	$-0.595382\pi$
$443$	−12.4260			−0.590377			−0.295189	+	0.955439i	$0.595382\pi$
$444$	−11.6486	−	9.53366i	−0.552819	−	0.452448i
$445$	−3.55297	+	30.3143i	−0.168427	+	1.43704i
$446$	3.41754	−	9.57160i	0.161825	−	0.453228i
$447$		−	10.7665i		−	0.509237i
$448$	12.3407	+	17.1961i	0.583045	+	0.812440i
$449$	3.27542			0.154577			0.0772883	−	0.997009i	$-0.475374\pi$
$449$	3.27542			0.154577			0.0772883	+	0.997009i	$0.475374\pi$
$450$	5.92904	+	3.85312i	0.279498	+	0.181638i
$451$	2.62123			0.123429
$452$	−12.1673	+	14.8665i	−0.572300	+	0.699259i
$453$	3.34472			0.157149
$454$	−2.26581	+	6.34591i	−0.106340	+	0.297828i
$455$	5.58649	−	8.56140i	0.261899	−	0.401365i
$456$	−11.4766	+	6.91025i	−0.537443	+	0.323602i
$457$		−	17.9017i		−	0.837406i	−0.908123	−	0.418703i	$-0.862485\pi$
$457$		−	17.9017i		−	0.837406i	0.908123	−	0.418703i	$-0.137515\pi$
$458$	−7.35535	+	20.6004i	−0.343693	+	0.962591i
$459$		−	0.146965i		−	0.00685973i
$460$	−10.7200	−	11.0943i	−0.499821	−	0.517272i
$461$		−	40.2381i		−	1.87408i	−0.349226	−	0.937039i	$-0.613555\pi$
$461$		−	40.2381i		−	1.87408i	0.349226	−	0.937039i	$-0.386445\pi$
$462$	−0.986422	+	0.949601i	−0.0458925	+	0.0441794i
$463$	25.8834			1.20290			0.601451	−	0.798910i	$-0.294589\pi$
$463$	25.8834			1.20290			0.601451	+	0.798910i	$0.294589\pi$
$464$	−4.18413	−	20.7442i	−0.194243	−	0.963025i
$465$	1.58101	−	13.4894i	0.0733176	−	0.625554i
$466$	−6.55806	+	18.3674i	−0.303796	+	0.850852i
$467$		−	20.8217i		−	0.963511i	−0.876306	−	0.481756i	$-0.839999\pi$
$467$		−	20.8217i		−	0.963511i	0.876306	−	0.481756i	$-0.160001\pi$
$468$	−2.67442	−	2.18885i	−0.123625	−	0.101180i
$469$	14.3280	−	28.8124i	0.661605	−	1.33043i
$470$	−5.38336	+	10.8762i	−0.248316	+	0.501681i
$471$		−	19.3169i		−	0.890078i
$472$	−9.02924	−	14.9959i	−0.415605	−	0.690243i
$473$		−	3.16557i		−	0.145553i
$474$	−18.9714	−	6.77373i	−0.871385	−	0.311128i
$475$	23.0400	+	5.47600i	1.05715	+	0.251256i
$476$	−0.708982	+	0.319542i	−0.0324961	+	0.0146462i
$477$		−	11.5549i		−	0.529063i
$478$	−0.664230	+	1.86033i	−0.0303812	+	0.0850895i
$479$	−6.30716			−0.288181			−0.144091	−	0.989564i	$-0.546026\pi$
$479$	−6.30716			−0.288181			−0.144091	+	0.989564i	$0.546026\pi$
$480$	−12.2221	−	3.25896i	−0.557859	−	0.148750i
$481$		−	13.0053i		−	0.592989i
$482$	9.02557	−	25.2782i	0.411103	−	1.15139i
$483$	8.17219	+	4.06391i	0.371847	+	0.184914i
$484$	16.8177	+	13.7642i	0.764439	+	0.625646i
$485$	−35.9715	−	4.21601i	−1.63338	−	0.191439i
$486$	−0.475542	+	1.33186i	−0.0215710	+	0.0604146i
$487$	2.04829			0.0928167			0.0464083	−	0.998923i	$-0.485222\pi$
$487$	2.04829			0.0928167			0.0464083	+	0.998923i	$0.485222\pi$
$488$	0.843332	−	0.507782i	0.0381758	−	0.0229862i
$489$			17.6321i			0.797353i
$490$	4.14223	+	21.7449i	0.187127	+	0.982336i
$491$			2.63143i			0.118755i	0.998236	+	0.0593774i	$0.0189115\pi$
$491$			2.63143i			0.118755i	−0.998236	+	0.0593774i	$0.981088\pi$
$492$	−11.0863	−	9.07346i	−0.499810	−	0.409063i
$493$	0.777515			0.0350175
$494$	−10.9004	−	3.89198i	−0.490432	−	0.175109i
$495$	0.0952524	−	0.812704i	0.00428127	−	0.0365283i
$496$	4.80373	+	23.8160i	0.215694	+	1.06937i
$497$	−18.4323	−	9.16608i	−0.826799	−	0.411155i
$498$	−4.71227	−	1.68252i	−0.211162	−	0.0753953i
$499$		−	26.3951i		−	1.18161i	−0.806815	−	0.590804i	$-0.798810\pi$
$499$		−	26.3951i		−	1.18161i	0.806815	−	0.590804i	$-0.201190\pi$
$500$	11.3984	+	19.2374i	0.509753	+	0.860321i
$501$	−16.7301			−0.747446
$502$	−14.6437	−	5.22855i	−0.653582	−	0.233361i
$503$		−	25.3043i		−	1.12826i	−0.825685	−	0.564132i	$-0.809211\pi$
$503$		−	25.3043i		−	1.12826i	0.825685	−	0.564132i	$-0.190789\pi$
$504$	7.45908	−	0.601749i	0.332254	−	0.0268040i
$505$	1.14961	−	9.80857i	0.0511568	−	0.436476i
$506$	−0.600305	+	1.68129i	−0.0266868	+	0.0747425i
$507$			10.0141i			0.444742i
$508$	−13.2831	−	10.8714i	−0.589342	−	0.482340i
$509$			32.2172i			1.42800i	0.700145	+	0.714001i	$0.253119\pi$
$509$			32.2172i			1.42800i	−0.700145	+	0.714001i	$0.746881\pi$
$510$	0.206161	−	0.416514i	0.00912896	−	0.0184436i
$511$	−5.36486	+	10.7883i	−0.237327	+	0.477246i
$512$	22.5931	−	1.24660i	0.998481	−	0.0550925i
$513$			4.73636i			0.209115i
$514$	24.2051	+	8.64244i	1.06764	+	0.381201i
$515$	−3.24509	+	27.6875i	−0.142996	+	1.22006i
$516$	−10.9577	+	13.3886i	−0.482386	+	0.589399i
$517$	1.40433			0.0617625
$518$	19.5305	+	20.2878i	0.858120	+	0.891393i
$519$		−	17.5934i		−	0.772266i
$520$	−4.50911	−	9.95510i	−0.197738	−	0.436560i
$521$			31.1683i			1.36551i	0.730649	+	0.682753i	$0.239218\pi$
$521$			31.1683i			1.36551i	−0.730649	+	0.682753i	$0.760782\pi$
$522$	−7.04621	−	2.51585i	−0.308404	−	0.110116i
$523$		−	6.94386i		−	0.303634i	−0.988409	−	0.151817i	$-0.951488\pi$
$523$		−	6.94386i		−	0.303634i	0.988409	−	0.151817i	$-0.0485124\pi$
$524$	−28.7932	−	23.5654i	−1.25784	−	1.02946i
$525$	−10.1619	−	8.46965i	−0.443504	−	0.369646i
$526$	12.8816	+	4.59935i	0.561662	+	0.200541i
$527$	−0.892652			−0.0388846
$528$	0.289414	+	1.43486i	0.0125951	+	0.0624444i
$529$	−11.1000			−0.482609
$530$	16.2091	−	32.7479i	0.704080	−	1.42248i
$531$	−6.18874			−0.268569
$532$	22.8490	−	10.2982i	0.990629	−	0.446482i
$533$		−	12.3775i		−	0.536129i
$534$	−18.1796	−	6.49104i	−0.786710	−	0.280895i
$535$	13.6896	+	1.60448i	0.591854	+	0.0693678i
$536$	−17.7445	−	29.4703i	−0.766445	−	1.27292i
$537$	7.52728			0.324826
$538$	−0.818451	+	2.29226i	−0.0352859	+	0.0988263i
$539$	2.04256	−	1.54584i	0.0879793	−	0.0665843i
$540$	−3.21606	+	3.10756i	−0.138397	+	0.133728i
$541$	−14.0032			−0.602044			−0.301022	−	0.953617i	$-0.597328\pi$
$541$	−14.0032			−0.602044			−0.301022	+	0.953617i	$0.597328\pi$
$542$	−10.8100	−	3.85972i	−0.464331	−	0.165789i
$543$	3.83151			0.164426
$544$	−0.119229	+	0.822765i	−0.00511189	+	0.0352757i
$545$	−6.13999	−	0.719634i	−0.263008	−	0.0308257i
$546$	4.48403	+	4.65790i	0.191899	+	0.199340i
$547$	−15.3265			−0.655313			−0.327656	−	0.944797i	$-0.606259\pi$
$547$	−15.3265			−0.655313			−0.327656	+	0.944797i	$0.606259\pi$
$548$	−27.3368	+	33.4013i	−1.16777	+	1.42683i
$549$		−	0.348039i		−	0.0148540i
$550$	1.41001	−	2.16967i	0.0601230	−	0.0925151i
$551$	−25.0577			−1.06749
$552$	8.35879	−	5.03294i	0.355774	−	0.214216i
$553$	33.7446	+	16.7807i	1.43497	+	0.713587i
$554$	−0.535513	+	1.49983i	−0.0227517	+	0.0637215i
$555$	−16.7149	−	1.95906i	−0.709508	−	0.0831574i
$556$	−20.3624	−	16.6654i	−0.863558	−	0.706768i
$557$		−	14.6903i		−	0.622448i	−0.950337	−	0.311224i	$-0.899261\pi$
$557$		−	14.6903i		−	0.622448i	0.950337	−	0.311224i	$-0.100739\pi$
$558$	8.08963	+	2.88840i	0.342461	+	0.122276i
$559$	−14.9479			−0.632227
$560$	21.9840	+	8.75811i	0.928993	+	0.370098i
$561$	−0.0537803			−0.00227061
$562$	−19.1545	−	6.83913i	−0.807986	−	0.288491i
$563$		−	25.5127i		−	1.07523i	−0.843190	−	0.537616i	$-0.819325\pi$
$563$		−	25.5127i		−	1.07523i	0.843190	−	0.537616i	$-0.180675\pi$
$564$	−5.93954	−	4.86114i	−0.250100	−	0.204691i
$565$	−2.50023	+	21.3323i	−0.105186	+	0.897456i
$566$	−11.1672	+	31.2764i	−0.469393	+	1.31464i
$567$	1.17807	−	2.36900i	0.0494742	−	0.0994886i
$568$	−18.8531	+	11.3517i	−0.791060	+	0.476308i
$569$	18.8877			0.791815			0.395908	−	0.918290i	$-0.370430\pi$
$569$	18.8877			0.791815			0.395908	+	0.918290i	$0.370430\pi$
$570$	−6.64413	+	13.4234i	−0.278292	+	0.562243i
$571$			16.5940i			0.694436i	0.937784	+	0.347218i	$0.112874\pi$
$571$			16.5940i			0.694436i	−0.937784	+	0.347218i	$0.887126\pi$
$572$	−0.800987	+	0.978679i	−0.0334910	+	0.0409206i
$573$	20.1200			0.840526
$574$	18.5877	+	19.3085i	0.775836	+	0.805919i
$575$	−16.7807	−	3.98834i	−0.699805	−	0.166325i
$576$	3.74277	−	7.07048i	0.155949	−	0.294603i
$577$	12.4355			0.517695			0.258848	−	0.965918i	$-0.416657\pi$
$577$	12.4355			0.517695			0.258848	+	0.965918i	$0.416657\pi$
$578$	22.6129	+	8.07393i	0.940573	+	0.335831i
$579$	19.6683			0.817386
$580$	−16.4405	−	17.0145i	−0.682655	−	0.706490i
$581$	8.38176	+	4.16813i	0.347734	+	0.172923i
$582$	7.70237	−	21.5722i	0.319273	−	0.894199i
$583$	−4.22840			−0.175123
$584$	6.64411	+	11.0346i	0.274935	+	0.456617i
$585$	−3.83760	−	0.449783i	−0.158665	−	0.0185963i
$586$	−17.7947	−	6.35359i	−0.735092	−	0.262465i
$587$		−	6.89502i		−	0.284588i	−0.989824	−	0.142294i	$-0.954552\pi$
$587$		−	6.89502i		−	0.284588i	0.989824	−	0.142294i	$-0.0454478\pi$
$588$	−13.9899	−	0.532333i	−0.576933	−	0.0219531i
$589$	28.7683			1.18538
$590$	−17.5396	−	8.68152i	−0.722093	−	0.357412i
$591$	5.44722			0.224069
$592$	29.5109	−	5.95239i	1.21289	−	0.244642i
$593$	7.25097			0.297762			0.148881	−	0.988855i	$-0.452433\pi$
$593$	7.25097			0.297762			0.148881	+	0.988855i	$0.452433\pi$
$594$	0.487382	+	0.174020i	0.0199975	+	0.00714011i
$595$	−0.475133	+	0.728150i	−0.0194785	+	0.0298512i
$596$	16.6635	+	13.6380i	0.682564	+	0.558636i
$597$			6.66636i			0.272836i
$598$	7.93909	+	2.83465i	0.324654	+	0.115917i
$599$		−	30.0293i		−	1.22696i	−0.789709	−	0.613482i	$-0.789768\pi$
$599$		−	30.0293i		−	1.22696i	0.789709	−	0.613482i	$-0.210232\pi$
$600$	−13.4739	+	4.29570i	−0.550071	+	0.175371i
$601$		−	36.6770i		−	1.49609i	−0.663650	−	0.748043i	$-0.730994\pi$
$601$		−	36.6770i		−	1.49609i	0.663650	−	0.748043i	$-0.269006\pi$
$602$	23.3182	−	22.4477i	0.950377	−	0.914902i
$603$	−12.1623			−0.495286
$604$	−4.23680	+	5.17670i	−0.172393	+	0.210637i
$605$	24.1321	+	2.82839i	0.981110	+	0.114990i
$606$	5.88225	+	2.10025i	0.238950	+	0.0853170i
$607$		−	13.3370i		−	0.541332i	−0.962673	−	0.270666i	$-0.912756\pi$
$607$		−	13.3370i		−	0.541332i	0.962673	−	0.270666i	$-0.0872439\pi$
$608$	3.84248	−	26.5159i	0.155833	−	1.07536i
$609$	12.5332	+	6.23255i	0.507869	+	0.252556i
$610$	0.488227	−	0.986381i	0.0197677	−	0.0399374i
$611$		−	6.63128i		−	0.268273i
$612$	0.227460	+	0.186162i	0.00919454	+	0.00752516i
$613$		−	1.93442i		−	0.0781304i	−0.999237	−	0.0390652i	$-0.987562\pi$
$613$		−	1.93442i		−	0.0781304i	0.999237	−	0.0390652i	$-0.0124380\pi$
$614$	13.2134	−	37.0071i	0.533248	−	1.49348i
$615$	−15.9081	−	1.86449i	−0.641475	−	0.0751836i
$616$	−0.220204	−	2.72958i	−0.00887227	−	0.109978i
$617$		−	25.8246i		−	1.03966i	−0.854270	−	0.519829i	$-0.825996\pi$
$617$		−	25.8246i		−	1.03966i	0.854270	−	0.519829i	$-0.174004\pi$
$618$	−16.6043	−	5.92857i	−0.667924	−	0.238482i
$619$	−7.45062			−0.299466			−0.149733	−	0.988726i	$-0.547841\pi$
$619$	−7.45062			−0.299466			−0.149733	+	0.988726i	$0.547841\pi$
$620$	18.8751	+	19.5341i	0.758041	+	0.784509i
$621$		−	3.44964i		−	0.138429i
$622$	6.04556	+	2.15857i	0.242405	+	0.0865506i
$623$	32.3363	+	16.0804i	1.29553	+	0.644246i
$624$	6.77545	−	1.36662i	0.271235	−	0.0547085i
$625$	22.3266	+	11.2483i	0.893063	+	0.449931i
$626$	3.81680	+	1.36279i	0.152550	+	0.0544679i
$627$	1.73322			0.0692183
$628$	29.8972	+	24.4690i	1.19303	+	0.976420i
$629$			1.10610i			0.0441032i
$630$	6.66198	−	5.06142i	0.265420	−	0.201652i
$631$			33.3176i			1.32635i	0.748463	+	0.663176i	$0.230792\pi$
$631$			33.3176i			1.32635i	−0.748463	+	0.663176i	$0.769208\pi$
$632$	34.5151	−	20.7820i	1.37294	−	0.826665i
$633$	−8.81673			−0.350434
$634$	−7.77598	+	21.7784i	−0.308824	+	0.864932i
$635$	−19.0603	−	2.23394i	−0.756384	−	0.0886514i
$636$	17.8838	+	14.6368i	0.709138	+	0.580385i
$637$	−7.29951	−	9.64501i	−0.289217	−	0.382149i
$638$	−0.920649	+	2.57849i	−0.0364488	+	0.102083i
$639$			7.78061i			0.307796i
$640$	20.5258	−	14.7882i	0.811354	−	0.584555i
$641$	−7.97123			−0.314845			−0.157422	−	0.987531i	$-0.550318\pi$
$641$	−7.97123			−0.314845			−0.157422	+	0.987531i	$0.550318\pi$
$642$	−2.93128	+	8.20973i	−0.115688	+	0.324012i
$643$			17.9282i			0.707019i	0.935431	+	0.353510i	$0.115012\pi$
$643$			17.9282i			0.707019i	−0.935431	+	0.353510i	$0.884988\pi$
$644$	−16.6416	+	7.50046i	−0.655771	+	0.295560i
$645$	−2.25168	+	19.2116i	−0.0886600	+	0.756457i
$646$	0.927082	+	0.331014i	0.0364755	+	0.0130236i
$647$			32.2608i			1.26830i	0.773208	+	0.634152i	$0.218651\pi$
$647$			32.2608i			1.26830i	−0.773208	+	0.634152i	$0.781349\pi$
$648$	−1.45898	−	2.42309i	−0.0573141	−	0.0951881i
$649$			2.26471i			0.0888976i
$650$	−10.2452	−	6.65809i	−0.401851	−	0.261152i
$651$	−14.3891	−	7.15549i	−0.563954	−	0.280446i
$652$	−27.2896	−	22.3349i	−1.06874	−	0.874700i
$653$		−	8.09685i		−	0.316854i	−0.987371	−	0.158427i	$-0.949358\pi$
$653$		−	8.09685i		−	0.316854i	0.987371	−	0.158427i	$-0.0506423\pi$
$654$	1.31472	−	3.68218i	0.0514097	−	0.143985i
$655$	−41.3161	−	4.84242i	−1.61435	−	0.189209i
$656$	28.0864	−	5.66506i	1.09659	−	0.221183i
$657$	4.55395			0.177666
$658$	9.95844	+	10.3446i	0.388220	+	0.403274i
$659$			39.2582i			1.52928i	0.644456	+	0.764641i	$0.277084\pi$
$659$			39.2582i			1.52928i	−0.644456	+	0.764641i	$0.722916\pi$
$660$	1.13718	+	1.17689i	0.0442647	+	0.0458102i
$661$			14.5952i			0.567688i	0.958870	+	0.283844i	$0.0916099\pi$
$661$			14.5952i			0.567688i	−0.958870	+	0.283844i	$0.908390\pi$
$662$	−7.80650	+	21.8639i	−0.303408	+	0.849764i
$663$			0.253952i			0.00986266i
$664$	8.57316	−	5.16202i	0.332703	−	0.200325i
$665$	15.3125	−	23.4667i	0.593794	−	0.910000i
$666$	3.57907	−	10.0240i	0.138686	−	0.388422i
$667$	18.2503			0.706653
$668$	21.1922	−	25.8935i	0.819952	−	1.00185i
$669$	7.18662			0.277851
$670$	−34.4692	−	17.0611i	−1.33166	−	0.659129i
$671$	−0.127361			−0.00491674
$672$	−8.51717	+	12.3068i	−0.328557	+	0.474746i
$673$		−	32.3547i		−	1.24718i	−0.781751	−	0.623591i	$-0.785673\pi$
$673$		−	32.3547i		−	1.24718i	0.781751	−	0.623591i	$-0.214327\pi$
$674$	16.8042	−	47.0640i	0.647273	−	1.81284i
$675$	−1.15616	+	4.86449i	−0.0445006	+	0.187234i
$676$	−15.4990	−	12.6850i	−0.596116	−	0.487884i
$677$	6.45779			0.248193			0.124097	−	0.992270i	$-0.460397\pi$
$677$	6.45779			0.248193			0.124097	+	0.992270i	$0.460397\pi$
$678$	−12.7931	−	4.56776i	−0.491315	−	0.175424i
$679$	−19.0812	+	38.3708i	−0.732270	+	1.47254i
$680$	0.383501	+	0.846684i	0.0147066	+	0.0324688i
$681$	−4.76468			−0.182583
$682$	1.05698	−	2.96032i	0.0404739	−	0.113356i
$683$	16.8904			0.646292			0.323146	−	0.946349i	$-0.395259\pi$
$683$	16.8904			0.646292			0.323146	+	0.946349i	$0.395259\pi$
$684$	−7.33056	−	5.99961i	−0.280291	−	0.229401i
$685$	−5.61741	+	47.9284i	−0.214630	+	1.83125i
$686$	25.8712	+	4.08395i	0.987769	+	0.155926i
$687$	−15.4673			−0.590115
$688$	−6.84149	−	33.9189i	−0.260829	−	1.29315i
$689$			19.9666i			0.760667i
$690$	4.83912	−	9.77665i	0.184222	−	0.372191i
$691$	−0.330330			−0.0125663			−0.00628317	−	0.999980i	$-0.502000\pi$
$691$	−0.330330			−0.0125663			−0.00628317	+	0.999980i	$0.502000\pi$
$692$	27.2297	+	22.2858i	1.03512	+	0.847180i
$693$	−0.866911	−	0.431102i	−0.0329312	−	0.0163762i
$694$	−1.09176	−	0.389814i	−0.0414428	−	0.0147971i
$695$	−29.2186	−	3.42454i	−1.10832	−	0.129900i
$696$	12.8193	−	7.71870i	0.485916	−	0.292577i
$697$			1.05271i			0.0398742i
$698$	−9.01189	+	25.2399i	−0.341105	+	0.955343i
$699$	−13.7907			−0.521613
$700$	25.9809	−	4.99924i	0.981986	−	0.188954i
$701$	−22.4214			−0.846846			−0.423423	−	0.905932i	$-0.639172\pi$
$701$	−22.4214			−0.846846			−0.423423	+	0.905932i	$0.639172\pi$
$702$	0.821724	−	2.30143i	0.0310140	−	0.0868618i
$703$		−	35.6473i		−	1.34446i
$704$	−2.58737	−	1.36963i	−0.0975152	−	0.0516198i
$705$	−8.52280	−	0.998909i	−0.320987	−	0.0376211i
$706$	24.8955	+	8.88894i	0.936955	+	0.334540i
$707$	−10.4628	−	5.20300i	−0.393494	−	0.195679i
$708$	7.83936	−	9.57845i	0.294621	−	0.359980i
$709$	−15.6572			−0.588018			−0.294009	−	0.955803i	$-0.594990\pi$
$709$	−15.6572			−0.588018			−0.294009	+	0.955803i	$0.594990\pi$
$710$	−10.9146	+	22.0511i	−0.409616	+	0.827563i
$711$		−	14.2442i		−	0.534201i
$712$	33.0747	−	19.9147i	1.23953	−	0.746336i
$713$	−20.9528			−0.784689
$714$	−0.381368	−	0.396156i	−0.0142723	−	0.0148258i
$715$	−0.164594	+	1.40433i	−0.00615546	+	0.0525191i
$716$	−9.53490	+	11.6501i	−0.356336	+	0.435385i
$717$	−1.39679			−0.0521640
$718$	−9.69154	+	27.1434i	−0.361685	+	1.01298i
$719$	−32.0066			−1.19365			−0.596823	−	0.802373i	$-0.703571\pi$
$719$	−32.0066			−1.19365			−0.596823	+	0.802373i	$0.703571\pi$
$720$	−0.735808	−	8.91395i	−0.0274219	−	0.332203i
$721$	29.5343	+	14.6870i	1.09991	+	0.546971i
$722$	−4.57245	−	1.63259i	−0.170169	−	0.0607588i
$723$	18.9796			0.705857
$724$	−4.85342	+	5.93011i	−0.180376	+	0.220391i
$725$	−25.7355	−	6.11665i	−0.955794	−	0.227167i
$726$	−5.16728	+	14.4721i	−0.191776	+	0.537112i
$727$			3.20369i			0.118818i	0.998234	+	0.0594091i	$0.0189216\pi$
$727$			3.20369i			0.118818i	−0.998234	+	0.0594091i	$0.981078\pi$
$728$	−12.8891	+	1.03981i	−0.477702	+	0.0385378i
$729$	−1.00000			−0.0370370
$730$	12.9064	+	6.38824i	0.477687	+	0.236439i
$731$	1.27132			0.0470215
$732$	0.538668	+	0.440866i	0.0199097	+	0.0162949i
$733$	32.3886			1.19630			0.598150	−	0.801384i	$-0.295903\pi$
$733$	32.3886			1.19630			0.598150	+	0.801384i	$0.295903\pi$
$734$	1.03086	−	2.88717i	0.0380499	−	0.106568i
$735$	−13.4957	+	7.92875i	−0.497798	+	0.292456i
$736$	−2.79860	+	19.3124i	−0.103158	+	0.711863i
$737$			4.45066i			0.163942i
$738$	3.40630	−	9.54014i	0.125388	−	0.351177i
$739$			4.75067i			0.174756i	0.996175	+	0.0873781i	$0.0278488\pi$
$739$			4.75067i			0.174756i	−0.996175	+	0.0873781i	$0.972151\pi$
$740$	24.2051	−	23.3884i	0.889796	−	0.859776i
$741$		−	8.18432i		−	0.300658i
$742$	−29.9846	−	31.1472i	−1.10077	−	1.14345i
$743$	−12.4260			−0.455866			−0.227933	−	0.973677i	$-0.573197\pi$
$743$	−12.4260			−0.455866			−0.227933	+	0.973677i	$0.573197\pi$
$744$	−14.7177	+	8.86171i	−0.539576	+	0.324886i
$745$	23.9109	+	2.80246i	0.876028	+	0.102674i
$746$	4.71636	−	13.2093i	0.172678	−	0.483625i
$747$		−	3.53810i		−	0.129452i
$748$	0.0681242	−	0.0832369i	0.00249087	−	0.00304344i
$749$	7.26172	−	14.6027i	0.265337	−	0.533572i
$750$	−10.1006	+	12.1647i	−0.368820	+	0.444190i
$751$			15.8621i			0.578816i	0.957206	+	0.289408i	$0.0934585\pi$
$751$			15.8621i			0.578816i	−0.957206	+	0.289408i	$0.906542\pi$
$752$	15.0474	−	3.03507i	0.548721	−	0.110678i
$753$		−	10.9949i		−	0.400678i
$754$	12.1757	+	4.34732i	0.443412	+	0.158320i
$755$	−0.870615	+	7.42818i	−0.0316849	+	0.270339i
$756$	2.17427	+	4.82416i	0.0790776	+	0.175453i
$757$			9.98543i			0.362927i	0.983398	+	0.181463i	$0.0580834\pi$
$757$			9.98543i			0.362927i	−0.983398	+	0.181463i	$0.941917\pi$
$758$	0.0698048	−	0.195504i	0.00253543	−	0.00710104i
$759$	−1.26236			−0.0458208
$760$	−12.3594	−	27.2868i	−0.448323	−	0.989796i
$761$		−	8.89622i		−	0.322488i	−0.986915	−	0.161244i	$-0.948449\pi$
$761$		−	8.89622i		−	0.322488i	0.986915	−	0.161244i	$-0.0515506\pi$
$762$	4.08127	−	11.4305i	0.147849	−	0.414084i
$763$	−3.25699	+	6.54953i	−0.117911	+	0.237109i
$764$	−25.4863	+	31.1402i	−0.922062	+	1.12661i
$765$	0.326389	+	0.0382542i	0.0118006	+	0.00138308i
$766$	16.6024	−	46.4989i	0.599870	−	1.68007i
$767$	10.6940			0.386138
$768$	6.20212	+	14.7490i	0.223800	+	0.532210i
$769$			10.0175i			0.361242i	0.983553	+	0.180621i	$0.0578107\pi$
$769$			10.0175i			0.361242i	−0.983553	+	0.180621i	$0.942189\pi$
$770$	−1.85218	−	2.43789i	−0.0667478	−	0.0878553i
$771$			18.1739i			0.654516i
$772$	−24.9141	+	30.4410i	−0.896677	+	1.09560i
$773$	−41.9683			−1.50949			−0.754747	−	0.656016i	$-0.772240\pi$
$773$	−41.9683			−1.50949			−0.754747	+	0.656016i	$0.772240\pi$
$774$	−11.5213	−	4.11367i	−0.414124	−	0.147863i
$775$	29.5465	+	7.02243i	1.06134	+	0.252253i
$776$	23.6311	+	39.2470i	0.848308	+	1.40888i
$777$	−8.86649	+	17.8298i	−0.318084	+	0.639641i
$778$	−36.8173	−	13.1456i	−1.31997	−	0.471293i
$779$		−	33.9266i		−	1.21555i
$780$	5.55728	−	5.36979i	0.198983	−	0.192269i
$781$	2.84724			0.101882
$782$	−0.675222	−	0.241088i	−0.0241459	−	0.00862128i
$783$		−	5.29049i		−	0.189067i
$784$	18.5451	−	20.9781i	0.662323	−	0.749218i
$785$	42.9003	+	5.02810i	1.53118	+	0.179461i
$786$	8.84678	−	24.7775i	0.315554	−	0.883782i
$787$			0.375554i			0.0133871i	0.999978	+	0.00669353i	$0.00213063\pi$
$787$			0.375554i			0.0133871i	−0.999978	+	0.00669353i	$0.997869\pi$
$788$	−6.90006	+	8.43077i	−0.245805	+	0.300334i
$789$			9.67183i			0.344326i
$790$	19.9817	−	40.3697i	0.710917	−	1.43629i
$791$	22.7551	+	11.3158i	0.809080	+	0.402343i
$792$	−0.886707	+	0.533898i	−0.0315078	+	0.0189713i
$793$			0.601403i			0.0213565i
$794$	−12.8141	−	4.57528i	−0.454756	−	0.162370i
$795$	25.6619	+	3.00769i	0.910134	+	0.106672i
$796$	−10.3177	−	8.44437i	−0.365700	−	0.299303i
$797$	42.5573			1.50746			0.753728	−	0.657187i	$-0.228254\pi$
$797$	42.5573			1.50746			0.753728	+	0.657187i	$0.228254\pi$
$798$	12.2907	+	12.7673i	0.435086	+	0.451956i
$799$			0.563993i			0.0199526i
$800$	10.4191	−	26.2953i	0.368369	−	0.929680i
$801$		−	13.6498i		−	0.482291i
$802$	29.0386	+	10.3682i	1.02539	+	0.366115i
$803$		−	1.66647i		−	0.0588085i
$804$	15.4061	−	18.8238i	0.543332	−	0.663864i
$805$	−11.1526	+	17.0915i	−0.393077	+	0.602397i
$806$	−13.9787	−	4.99109i	−0.492378	−	0.175804i
$807$	−1.72109			−0.0605853
$808$	−10.7017	+	6.44365i	−0.376485	+	0.226687i
$809$	−46.6092			−1.63869			−0.819346	−	0.573300i	$-0.805663\pi$
$809$	−46.6092			−1.63869			−0.819346	+	0.573300i	$0.805663\pi$
$810$	−2.83411	−	1.40279i	−0.0995805	−	0.0492891i
$811$	−55.4019			−1.94542			−0.972711	−	0.232019i	$-0.925467\pi$
$811$	−55.4019			−1.94542			−0.972711	+	0.232019i	$0.925467\pi$
$812$	−25.5222	+	11.5030i	−0.895652	+	0.403675i
$813$		−	8.11648i		−	0.284657i
$814$	−3.66818	−	1.30972i	−0.128570	−	0.0459058i
$815$	−39.1586	−	4.58956i	−1.37167	−	0.160765i
$816$	−0.576254	+	0.116231i	−0.0201729	+	0.00406891i
$817$	−40.9719			−1.43343
$818$	−14.3342	+	40.1463i	−0.501184	+	1.40368i
$819$	−2.03567	+	4.09357i	−0.0711322	+	0.143041i
$820$	23.0367	−	22.2595i	0.804475	−	0.777334i
$821$	1.12596			0.0392961			0.0196481	−	0.999807i	$-0.493745\pi$
$821$	1.12596			0.0392961			0.0196481	+	0.999807i	$0.493745\pi$
$822$	−28.7429	−	10.2626i	−1.00252	−	0.357950i
$823$	44.2302			1.54177			0.770884	−	0.636976i	$-0.219815\pi$
$823$	44.2302			1.54177			0.770884	+	0.636976i	$0.219815\pi$
$824$	30.2087	−	18.1891i	1.05237	−	0.633646i
$825$	1.78011	+	0.423085i	0.0619756	+	0.0147299i
$826$	−16.6823	+	16.0596i	−0.580451	+	0.558784i
$827$	−28.2414			−0.982048			−0.491024	−	0.871146i	$-0.663377\pi$
$827$	−28.2414			−0.982048			−0.491024	+	0.871146i	$0.663377\pi$
$828$	5.33907	+	4.36970i	0.185546	+	0.151858i
$829$		−	38.0736i		−	1.32235i	−0.750231	−	0.661175i	$-0.770058\pi$
$829$		−	38.0736i		−	1.32235i	0.750231	−	0.661175i	$-0.229942\pi$
$830$	4.96322	−	10.0274i	0.172276	−	0.348055i
$831$	−1.12611			−0.0390644
$832$	−6.46741	+	12.2176i	−0.224217	+	0.423570i
$833$	0.620825	+	0.820311i	0.0215103	+	0.0284221i
$834$	6.25640	−	17.5225i	0.216642	−	0.606754i
$835$	4.35476	−	37.1553i	0.150703	−	1.28581i
$836$	−2.19550	+	2.68255i	−0.0759329	+	0.0927778i
$837$			6.07392i			0.209945i
$838$	−32.2589	−	11.5180i	−1.11436	−	0.397883i
$839$	10.9246			0.377160			0.188580	−	0.982058i	$-0.439612\pi$
$839$	10.9246			0.377160			0.188580	+	0.982058i	$0.439612\pi$
$840$	−0.605158	+	16.7223i	−0.0208800	+	0.576973i
$841$	−1.01075			−0.0348533
$842$	−7.63023	−	2.72437i	−0.262955	−	0.0938880i
$843$		−	14.3818i		−	0.495334i
$844$	11.1683	−	13.6458i	0.384428	−	0.469709i
$845$	−22.2400	−	2.60662i	−0.765078	−	0.0896705i
$846$	1.82494	−	5.11116i	0.0627427	−	0.175725i
$847$	12.8010	−	25.7418i	0.439847	−	0.884497i
$848$	−45.3072	+	9.13852i	−1.55586	+	0.313818i
$849$	−23.4832			−0.805940
$850$	0.871360	+	0.566273i	0.0298874	+	0.0194230i
$851$			25.9630i			0.890001i
$852$	−12.0422	−	9.85579i	−0.412559	−	0.337654i
$853$	−23.7748			−0.814035			−0.407017	−	0.913420i	$-0.633431\pi$
$853$	−23.7748			−0.814035			−0.407017	+	0.913420i	$0.633431\pi$
$854$	−0.903149	−	0.938169i	−0.0309051	−	0.0321035i
$855$	−10.5188	−	1.23285i	−0.359736	−	0.0421626i
$856$	−8.99327	−	14.9362i	−0.307384	−	0.510508i
$857$	19.0201			0.649715			0.324857	−	0.945763i	$-0.394684\pi$
$857$	19.0201			0.649715			0.324857	+	0.945763i	$0.394684\pi$
$858$	−0.842184	−	0.300702i	−0.0287517	−	0.0102658i
$859$	−12.9659			−0.442390			−0.221195	−	0.975230i	$-0.570996\pi$
$859$	−12.9659			−0.442390			−0.221195	+	0.975230i	$0.570996\pi$
$860$	−26.8820	−	27.8206i	−0.916668	−	0.948674i
$861$	−8.43850	+	16.9691i	−0.287583	+	0.578307i
$862$	−16.2603	+	45.5408i	−0.553829	+	1.55112i
$863$	39.2414			1.33579			0.667896	−	0.744255i	$-0.267195\pi$
$863$	39.2414			1.33579			0.667896	+	0.744255i	$0.267195\pi$
$864$	5.59838	+	0.811273i	0.190461	+	0.0276001i
$865$	39.0727	+	4.57948i	1.32851	+	0.155707i
$866$	43.6639	+	15.5902i	1.48376	+	0.529776i
$867$			16.9784i			0.576617i
$868$	29.3016	−	13.2064i	0.994560	−	0.448253i
$869$	−5.21254			−0.176823
$870$	7.42145	−	14.9938i	0.251611	−	0.508338i
$871$	21.0161			0.712104
$872$	4.03361	+	6.69909i	0.136595	+	0.226860i
$873$	16.1970			0.548187
$874$	21.7610	+	7.76974i	0.736075	+	0.262816i
$875$	21.4551	−	20.3637i	0.725313	−	0.688419i
$876$	−5.76854	+	7.04824i	−0.194901	+	0.238138i
$877$			46.1400i			1.55804i	0.627000	+	0.779019i	$0.284283\pi$
$877$			46.1400i			1.55804i	−0.627000	+	0.779019i	$0.715717\pi$
$878$	−42.7909	−	15.2785i	−1.44412	−	0.515624i
$879$		−	13.3608i		−	0.450647i
$880$	−3.26197	+	0.269262i	−0.109961	+	0.00907681i
$881$		−	25.7227i		−	0.866619i	−0.901245	−	0.433309i	$-0.857346\pi$
$881$		−	25.7227i		−	0.866619i	0.901245	−	0.433309i	$-0.142654\pi$
$882$	−2.97189	−	9.44288i	−0.100069	−	0.317958i
$883$	48.0270			1.61624			0.808119	−	0.589020i	$-0.200486\pi$
$883$	48.0270			1.61624			0.808119	+	0.589020i	$0.200486\pi$
$884$	−0.393046	−	0.321684i	−0.0132196	−	0.0108194i
$885$	1.61090	−	13.7444i	0.0541498	−	0.462012i
$886$	16.5497	+	5.90908i	0.555999	+	0.198519i
$887$			40.6595i			1.36521i	0.730787	+	0.682606i	$0.239153\pi$
$887$			40.6595i			1.36521i	−0.730787	+	0.682606i	$0.760847\pi$
$888$	10.9807	+	18.2369i	0.368488	+	0.611991i
$889$	−10.1106	+	20.3316i	−0.339099	+	0.681900i
$890$	19.1478	−	38.6850i	0.641836	−	1.29672i
$891$			0.365940i			0.0122595i
$892$	−9.10339	+	11.1229i	−0.304804	+	0.372422i
$893$		−	18.1763i		−	0.608246i
$894$	−5.11991	+	14.3395i	−0.171235	+	0.479584i
$895$	−1.95931	+	16.7171i	−0.0654926	+	0.558790i
$896$	−8.25870	−	28.7714i	−0.275904	−	0.961185i
$897$			5.96089i			0.199028i
$898$	−4.36241	−	1.55760i	−0.145575	−	0.0519777i
$899$	−32.1340			−1.07173
$900$	−6.06435	−	7.95133i	−0.202145	−	0.265044i
$901$		−	1.69817i		−	0.0565741i
$902$	−3.49112	−	1.24650i	−0.116242	−	0.0415040i
$903$	20.4930	+	10.1909i	0.681966	+	0.339131i
$904$	23.2747	−	14.0140i	0.774107	−	0.466100i
$905$	−0.997323	+	8.50927i	−0.0331521	+	0.282858i
$906$	−4.45471	−	1.59055i	−0.147998	−	0.0528426i
$907$	−28.5510			−0.948021			−0.474010	−	0.880519i	$-0.657194\pi$
$907$	−28.5510			−0.948021			−0.474010	+	0.880519i	$0.657194\pi$
$908$	6.03549	−	7.37440i	0.200295	−	0.244728i
$909$			4.41655i			0.146488i
$910$	−11.5117	+	8.74601i	−0.381611	+	0.289927i
$911$		−	11.7799i		−	0.390286i	−0.980775	−	0.195143i	$-0.937483\pi$
$911$		−	11.7799i		−	0.390286i	0.980775	−	0.195143i	$-0.0625171\pi$
$912$	18.5714	−	3.74588i	0.614962	−	0.124039i
$913$	−1.29473			−0.0428494
$914$	−8.51300	+	23.8426i	−0.281585	+	0.788644i
$915$	0.772949	+	0.0905929i	0.0255529	+	0.00299491i
$916$	19.5926	−	23.9391i	0.647359	−	0.790970i
$917$	−21.9163	+	44.0719i	−0.723740	+	1.45538i
$918$	−0.0698879	+	0.195737i	−0.00230664	+	0.00646029i
$919$			50.9066i			1.67925i	0.543164	+	0.839626i	$0.317226\pi$
$919$			50.9066i			1.67925i	−0.543164	+	0.839626i	$0.682774\pi$
$920$	9.00174	+	19.8738i	0.296779	+	0.655220i
$921$	27.7860			0.915578
$922$	−19.1349	+	53.5917i	−0.630175	+	1.76495i
$923$		−	13.4447i		−	0.442538i
$924$	1.76535	−	0.795654i	0.0580759	−	0.0261751i
$925$	8.70162	−	36.6116i	0.286107	−	1.20378i
$926$	−34.4731	−	12.3086i	−1.13286	−	0.404486i
$927$		−	12.4670i		−	0.409469i
$928$	−4.29203	+	29.6181i	−0.140893	+	0.972263i
$929$			7.20396i			0.236354i	0.992993	+	0.118177i	$0.0377051\pi$
$929$			7.20396i			0.236354i	−0.992993	+	0.118177i	$0.962295\pi$
$930$	−8.52044	+	17.2142i	−0.279396	+	0.564474i
$931$	−20.0079	−	26.4369i	−0.655732	−	0.866433i
$932$	17.4689	−	21.3442i	0.572212	−	0.699152i
$933$			4.53917i			0.148606i
$934$	−9.90156	+	27.7316i	−0.323989	+	0.907406i
$935$	0.0139987	−	0.119439i	0.000457808	−	0.00390607i
$936$	2.52108	+	4.18705i	0.0824040	+	0.136858i
$937$	43.7398			1.42892			0.714458	−	0.699678i	$-0.246673\pi$
$937$	43.7398			1.42892			0.714458	+	0.699678i	$0.246673\pi$
$938$	−32.7844	+	31.5607i	−1.07045	+	1.03049i
$939$			2.86576i			0.0935205i
$940$	12.3420	−	11.9256i	0.402551	−	0.388970i
$941$			44.8849i			1.46320i	0.681732	+	0.731602i	$0.261227\pi$
$941$			44.8849i			1.46320i	−0.681732	+	0.731602i	$0.738773\pi$
$942$	−9.18601	+	25.7275i	−0.299296	+	0.838248i
$943$			24.7097i			0.804660i
$944$	4.89454	+	24.2663i	0.159304	+	0.789800i
$945$	4.95458	+	3.23297i	0.161173	+	0.105169i
$946$	−1.50536	+	4.21610i	−0.0489434	+	0.137077i
$947$	−25.8593			−0.840316			−0.420158	−	0.907451i	$-0.638025\pi$
$947$	−25.8593			−0.840316			−0.420158	+	0.907451i	$0.638025\pi$
$948$	22.0461	+	18.0434i	0.716024	+	0.586021i
$949$	−7.86911			−0.255442
$950$	−28.0821	−	18.2498i	−0.911103	−	0.592100i
$951$	−16.3518			−0.530245
$952$	1.09622	−	0.0884359i	0.0355288	−	0.00286622i
$953$		−	3.07479i		−	0.0996022i	−0.998759	−	0.0498011i	$-0.984141\pi$
$953$		−	3.07479i		−	0.0996022i	0.998759	−	0.0498011i	$-0.0158587\pi$
$954$	−5.49484	+	15.3896i	−0.177902	+	0.498256i
$955$	−5.23714	+	44.6839i	−0.169470	+	1.44594i
$956$	1.76933	−	2.16184i	0.0572241	−	0.0699188i
$957$	−1.93600			−0.0625820
$958$	8.40027	+	2.99932i	0.271401	+	0.0969035i
$959$	51.1252	+	25.4238i	1.65092	+	0.820977i
$960$	14.7284	+	10.1526i	0.475356	+	0.327674i
$961$	5.89250			0.190081
$962$	−6.18454	+	17.3212i	−0.199398	+	0.558459i
$963$	−6.16409			−0.198635
$964$	−24.0416	+	29.3750i	−0.774329	+	0.946107i
$965$	−5.11956	+	43.6806i	−0.164804	+	1.40613i
$966$	−8.95168	−	9.29878i	−0.288016	−	0.299183i
$967$	−20.0103			−0.643488			−0.321744	−	0.946827i	$-0.604269\pi$
$967$	−20.0103			−0.643488			−0.321744	+	0.946827i	$0.604269\pi$
$968$	−15.8534	−	26.3295i	−0.509547	−	0.846264i
$969$			0.696079i			0.0223613i
$970$	45.9042	+	22.7211i	1.47389	+	0.729530i
$971$	−40.3382			−1.29451			−0.647257	−	0.762272i	$-0.724084\pi$
$971$	−40.3382			−1.29451			−0.647257	+	0.762272i	$0.724084\pi$
$972$	1.26671	−	1.54772i	0.0406298	−	0.0496432i
$973$	−15.4991	+	31.1674i	−0.496878	+	0.999182i
$974$	−2.72804	−	0.974045i	−0.0874119	−	0.0312104i
$975$	1.99782	−	8.40573i	0.0639814	−	0.269199i
$976$	−1.36467	+	0.275257i	−0.0436822	+	0.00881075i
$977$		−	2.19619i		−	0.0702622i	−0.999383	−	0.0351311i	$-0.988815\pi$
$977$		−	2.19619i		−	0.0702622i	0.999383	−	0.0351311i	$-0.0111849\pi$
$978$	8.38481	−	23.4836i	0.268117	−	0.750923i
$979$	−4.99500			−0.159641
$980$	4.82374	−	30.9311i	0.154089	−	0.988057i
$981$	2.76468			0.0882696
$982$	1.25135	−	3.50471i	0.0399323	−	0.111840i
$983$		−	20.0116i		−	0.638272i	−0.947709	−	0.319136i	$-0.896607\pi$
$983$		−	20.0116i		−	0.638272i	0.947709	−	0.319136i	$-0.103393\pi$
$984$	10.4507	+	17.3566i	0.333155	+	0.553309i
$985$	−1.41788	+	12.0975i	−0.0451775	+	0.385460i
$986$	−1.03554	−	0.369741i	−0.0329785	−	0.0117749i
$987$	−4.52096	+	9.09128i	−0.143904	+	0.289379i
$988$	12.6670	+	10.3672i	0.402992	+	0.329824i
$989$	29.8411			0.948892
$990$	−0.513337	+	1.03711i	−0.0163149	+	0.0329616i
$991$		−	17.3259i		−	0.550374i	−0.961391	−	0.275187i	$-0.911260\pi$
$991$		−	17.3259i		−	0.550374i	0.961391	−	0.275187i	$-0.0887398\pi$
$992$	4.92761	−	34.0041i	0.156452	−	1.07963i
$993$	−16.4160			−0.520947
$994$	20.1904	+	20.9733i	0.640400	+	0.665232i
$995$	−14.8051	−	1.73522i	−0.469353	−	0.0550102i
$996$	5.47600	+	4.48176i	0.173514	+	0.142010i
$997$	−38.4882			−1.21893			−0.609467	−	0.792812i	$-0.708616\pi$
$997$	−38.4882			−1.21893			−0.609467	+	0.792812i	$0.708616\pi$
$998$	−12.5520	+	35.1547i	−0.397326	+	1.11280i
$999$	7.52630			0.238122

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.i.a.139.5	✓	48
4.3	odd	2	inner	420.2.i.a.139.42	yes	48
5.4	even	2	inner	420.2.i.a.139.44	yes	48
7.6	odd	2	inner	420.2.i.a.139.6	yes	48
20.19	odd	2	inner	420.2.i.a.139.7	yes	48
28.27	even	2	inner	420.2.i.a.139.41	yes	48
35.34	odd	2	inner	420.2.i.a.139.43	yes	48
140.139	even	2	inner	420.2.i.a.139.8	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.i.a.139.5	✓	48	1.1	even	1	trivial
420.2.i.a.139.6	yes	48	7.6	odd	2	inner
420.2.i.a.139.7	yes	48	20.19	odd	2	inner
420.2.i.a.139.8	yes	48	140.139	even	2	inner
420.2.i.a.139.41	yes	48	28.27	even	2	inner
420.2.i.a.139.42	yes	48	4.3	odd	2	inner
420.2.i.a.139.43	yes	48	35.34	odd	2	inner
420.2.i.a.139.44	yes	48	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33186 - 0.475542i) q^{2} -1.00000i q^{3} +(1.54772 + 1.26671i) q^{4} +(2.22087 + 0.260295i) q^{5} +(-0.475542 + 1.33186i) q^{6} +(1.17807 - 2.36900i) q^{7} +(-1.45898 - 2.42309i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.33186 - 0.475542i) q^{2} -1.00000i q^{3} +(1.54772 + 1.26671i) q^{4} +(2.22087 + 0.260295i) q^{5} +(-0.475542 + 1.33186i) q^{6} +(1.17807 - 2.36900i) q^{7} +(-1.45898 - 2.42309i) q^{8} -1.00000 q^{9} +(-2.83411 - 1.40279i) q^{10} +0.365940i q^{11} +(1.26671 - 1.54772i) q^{12} +1.72798 q^{13} +(-2.69558 + 2.59496i) q^{14} +(0.260295 - 2.22087i) q^{15} +(0.790878 + 3.92103i) q^{16} -0.146965 q^{17} +(1.33186 + 0.475542i) q^{18} +4.73636 q^{19} +(3.10756 + 3.21606i) q^{20} +(-2.36900 - 1.17807i) q^{21} +(0.174020 - 0.487382i) q^{22} -3.44964 q^{23} +(-2.42309 + 1.45898i) q^{24} +(4.86449 + 1.15616i) q^{25} +(-2.30143 - 0.821724i) q^{26} +1.00000i q^{27} +(4.82416 - 2.17427i) q^{28} -5.29049 q^{29} +(-1.40279 + 2.83411i) q^{30} +6.07392 q^{31} +(0.811273 - 5.59838i) q^{32} +0.365940 q^{33} +(0.195737 + 0.0698879i) q^{34} +(3.23297 - 4.95458i) q^{35} +(-1.54772 - 1.26671i) q^{36} -7.52630i q^{37} +(-6.30819 - 2.25234i) q^{38} -1.72798i q^{39} +(-2.60948 - 5.76113i) q^{40} -7.16300i q^{41} +(2.59496 + 2.69558i) q^{42} -8.65051 q^{43} +(-0.463541 + 0.566373i) q^{44} +(-2.22087 - 0.260295i) q^{45} +(4.59445 + 1.64045i) q^{46} -3.83760i q^{47} +(3.92103 - 0.790878i) q^{48} +(-4.22431 - 5.58168i) q^{49} +(-5.92904 - 3.85312i) q^{50} +0.146965i q^{51} +(2.67442 + 2.18885i) q^{52} +11.5549i q^{53} +(0.475542 - 1.33186i) q^{54} +(-0.0952524 + 0.812704i) q^{55} +(-7.45908 + 0.601749i) q^{56} -4.73636i q^{57} +(7.04621 + 2.51585i) q^{58} +6.18874 q^{59} +(3.21606 - 3.10756i) q^{60} +0.348039i q^{61} +(-8.08963 - 2.88840i) q^{62} +(-1.17807 + 2.36900i) q^{63} +(-3.74277 + 7.07048i) q^{64} +(3.83760 + 0.449783i) q^{65} +(-0.487382 - 0.174020i) q^{66} +12.1623 q^{67} +(-0.227460 - 0.186162i) q^{68} +3.44964i q^{69} +(-6.66198 + 5.06142i) q^{70} -7.78061i q^{71} +(1.45898 + 2.42309i) q^{72} -4.55395 q^{73} +(-3.57907 + 10.0240i) q^{74} +(1.15616 - 4.86449i) q^{75} +(7.33056 + 5.99961i) q^{76} +(0.866911 + 0.431102i) q^{77} +(-0.821724 + 2.30143i) q^{78} +14.2442i q^{79} +(0.735808 + 8.91395i) q^{80} +1.00000 q^{81} +(-3.40630 + 9.54014i) q^{82} +3.53810i q^{83} +(-2.17427 - 4.82416i) q^{84} +(-0.326389 - 0.0382542i) q^{85} +(11.5213 + 4.11367i) q^{86} +5.29049i q^{87} +(0.886707 - 0.533898i) q^{88} +13.6498i q^{89} +(2.83411 + 1.40279i) q^{90} +(2.03567 - 4.09357i) q^{91} +(-5.33907 - 4.36970i) q^{92} -6.07392i q^{93} +(-1.82494 + 5.11116i) q^{94} +(10.5188 + 1.23285i) q^{95} +(-5.59838 - 0.811273i) q^{96} -16.1970 q^{97} +(2.97189 + 9.44288i) q^{98} -0.365940i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{9}+O(q^{10}) \) 48 * q - 48 * q^9	\( 48 q - 48 q^{9} + 20 q^{14} - 16 q^{16} + 8 q^{25} - 16 q^{30} - 40 q^{44} + 16 q^{46} - 16 q^{49} + 48 q^{50} + 28 q^{56} - 32 q^{60} - 112 q^{74} + 48 q^{81} - 28 q^{84} + 56 q^{85} + 8 q^{86}+O(q^{100}) \) 48 * q - 48 * q^9 + 20 * q^14 - 16 * q^16 + 8 * q^25 - 16 * q^30 - 40 * q^44 + 16 * q^46 - 16 * q^49 + 48 * q^50 + 28 * q^56 - 32 * q^60 - 112 * q^74 + 48 * q^81 - 28 * q^84 + 56 * q^85 + 8 * q^86

Introduction

L-functions

Modular forms

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Database

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