LMFDB - Embedded newform 420.2.i.a.139.17

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			139.17
Character	$\chi$	$=$	420.139
Dual form			420.2.i.a.139.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654401 - 1.25370i) q^{2} -1.00000i q^{3} +(-1.14352 + 1.64084i) q^{4} +(-0.206931 + 2.22647i) q^{5} +(-1.25370 + 0.654401i) q^{6} +(-0.859661 - 2.50220i) q^{7} +(2.80544 + 0.359858i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.654401 - 1.25370i) q^{2} -1.00000i q^{3} +(-1.14352 + 1.64084i) q^{4} +(-0.206931 + 2.22647i) q^{5} +(-1.25370 + 0.654401i) q^{6} +(-0.859661 - 2.50220i) q^{7} +(2.80544 + 0.359858i) q^{8} -1.00000 q^{9} +(2.92674 - 1.19758i) q^{10} -4.14562i q^{11} +(1.64084 + 1.14352i) q^{12} -3.35349 q^{13} +(-2.57443 + 2.71520i) q^{14} +(2.22647 + 0.206931i) q^{15} +(-1.38473 - 3.75267i) q^{16} -3.18809 q^{17} +(0.654401 + 1.25370i) q^{18} -6.52098 q^{19} +(-3.41666 - 2.88555i) q^{20} +(-2.50220 + 0.859661i) q^{21} +(-5.19736 + 2.71290i) q^{22} -1.42902 q^{23} +(0.359858 - 2.80544i) q^{24} +(-4.91436 - 0.921454i) q^{25} +(2.19452 + 4.20426i) q^{26} +1.00000i q^{27} +(5.08875 + 1.45074i) q^{28} +8.88452 q^{29} +(-1.19758 - 2.92674i) q^{30} -2.93809 q^{31} +(-3.79854 + 4.19179i) q^{32} -4.14562 q^{33} +(2.08629 + 3.99690i) q^{34} +(5.74896 - 1.39623i) q^{35} +(1.14352 - 1.64084i) q^{36} -9.54315i q^{37} +(4.26734 + 8.17534i) q^{38} +3.35349i q^{39} +(-1.38175 + 6.17177i) q^{40} +3.55466i q^{41} +(2.71520 + 2.57443i) q^{42} -0.667790 q^{43} +(6.80232 + 4.74060i) q^{44} +(0.206931 - 2.22647i) q^{45} +(0.935154 + 1.79156i) q^{46} -0.693941i q^{47} +(-3.75267 + 1.38473i) q^{48} +(-5.52197 + 4.30208i) q^{49} +(2.06074 + 6.76412i) q^{50} +3.18809i q^{51} +(3.83477 - 5.50254i) q^{52} +4.18410i q^{53} +(1.25370 - 0.654401i) q^{54} +(9.23012 + 0.857859i) q^{55} +(-1.51130 - 7.32912i) q^{56} +6.52098i q^{57} +(-5.81404 - 11.1385i) q^{58} +5.96025 q^{59} +(-2.88555 + 3.41666i) q^{60} -10.3947i q^{61} +(1.92269 + 3.68347i) q^{62} +(0.859661 + 2.50220i) q^{63} +(7.74101 + 2.01912i) q^{64} +(0.693941 - 7.46644i) q^{65} +(2.71290 + 5.19736i) q^{66} -7.05912 q^{67} +(3.64563 - 5.23115i) q^{68} +1.42902i q^{69} +(-5.51258 - 6.29377i) q^{70} -9.50299i q^{71} +(-2.80544 - 0.359858i) q^{72} -7.52091 q^{73} +(-11.9642 + 6.24505i) q^{74} +(-0.921454 + 4.91436i) q^{75} +(7.45686 - 10.6999i) q^{76} +(-10.3732 + 3.56383i) q^{77} +(4.20426 - 2.19452i) q^{78} +12.1118i q^{79} +(8.64176 - 2.30652i) q^{80} +1.00000 q^{81} +(4.45647 - 2.32618i) q^{82} -5.25464i q^{83} +(1.45074 - 5.08875i) q^{84} +(0.659715 - 7.09818i) q^{85} +(0.437003 + 0.837208i) q^{86} -8.88452i q^{87} +(1.49183 - 11.6303i) q^{88} -2.83667i q^{89} +(-2.92674 + 1.19758i) q^{90} +(2.88286 + 8.39108i) q^{91} +(1.63411 - 2.34480i) q^{92} +2.93809i q^{93} +(-0.869993 + 0.454116i) q^{94} +(1.34940 - 14.5188i) q^{95} +(4.19179 + 3.79854i) q^{96} +15.9682 q^{97} +(9.00709 + 4.10759i) q^{98} +4.14562i 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 $

$2$	−0.654401	−	1.25370i	−0.462731	−	0.886499i
$2$	−0.654401	−	1.25370i	−0.462731	−	0.886499i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.14352	+	1.64084i	−0.571759	+	0.820421i
$5$	−0.206931	+	2.22647i	−0.0925425	+	0.995709i
$5$	−0.206931	+	2.22647i	−0.0925425	+	0.995709i
$6$	−1.25370	+	0.654401i	−0.511820	+	0.267158i
$7$	−0.859661	−	2.50220i	−0.324921	−	0.945741i
$7$	−0.859661	−	2.50220i	−0.324921	−	0.945741i
$8$	2.80544	+	0.359858i	0.991873	+	0.127229i
$9$	−1.00000			−0.333333
$10$	2.92674	−	1.19758i	0.925517	−	0.378707i
$11$		−	4.14562i		−	1.24995i	−0.780644	−	0.624976i	$-0.785109\pi$
$11$		−	4.14562i		−	1.24995i	0.780644	−	0.624976i	$-0.214891\pi$
$12$	1.64084	+	1.14352i	0.473671	+	0.330105i
$13$	−3.35349			−0.930089			−0.465045	−	0.885287i	$-0.653962\pi$
$13$	−3.35349			−0.930089			−0.465045	+	0.885287i	$0.653962\pi$
$14$	−2.57443	+	2.71520i	−0.688047	+	0.725666i
$15$	2.22647	+	0.206931i	0.574873	+	0.0534294i
$16$	−1.38473	−	3.75267i	−0.346183	−	0.938167i
$17$	−3.18809			−0.773224			−0.386612	−	0.922242i	$-0.626355\pi$
$17$	−3.18809			−0.773224			−0.386612	+	0.922242i	$0.626355\pi$
$18$	0.654401	+	1.25370i	0.154244	+	0.295500i
$19$	−6.52098			−1.49602			−0.748008	−	0.663690i	$-0.768989\pi$
$19$	−6.52098			−1.49602			−0.748008	+	0.663690i	$0.768989\pi$
$20$	−3.41666	−	2.88555i	−0.763989	−	0.645229i
$21$	−2.50220	+	0.859661i	−0.546024	+	0.187593i
$22$	−5.19736	+	2.71290i	−1.10808	+	0.578392i
$23$	−1.42902			−0.297972			−0.148986	−	0.988839i	$-0.547601\pi$
$23$	−1.42902			−0.297972			−0.148986	+	0.988839i	$0.547601\pi$
$24$	0.359858	−	2.80544i	0.0734556	−	0.572658i
$25$	−4.91436	−	0.921454i	−0.982872	−	0.184291i
$26$	2.19452	+	4.20426i	0.430382	+	0.824523i
$27$			1.00000i			0.192450i
$28$	5.08875	+	1.45074i	0.961683	+	0.274164i
$29$	8.88452			1.64981			0.824907	−	0.565268i	$-0.191227\pi$
$29$	8.88452			1.64981			0.824907	+	0.565268i	$0.191227\pi$
$30$	−1.19758	−	2.92674i	−0.218647	−	0.534347i
$31$	−2.93809			−0.527696			−0.263848	−	0.964564i	$-0.584992\pi$
$31$	−2.93809			−0.527696			−0.263848	+	0.964564i	$0.584992\pi$
$32$	−3.79854	+	4.19179i	−0.671494	+	0.741010i
$33$	−4.14562			−0.721660
$34$	2.08629	+	3.99690i	0.357795	+	0.685462i
$35$	5.74896	−	1.39623i	0.971752	−	0.236006i
$36$	1.14352	−	1.64084i	0.190586	−	0.273474i
$37$		−	9.54315i		−	1.56888i	−0.620202	−	0.784442i	$-0.712950\pi$
$37$		−	9.54315i		−	1.56888i	0.620202	−	0.784442i	$-0.287050\pi$
$38$	4.26734	+	8.17534i	0.692253	+	1.32622i
$39$			3.35349i			0.536987i
$40$	−1.38175	+	6.17177i	−0.218473	+	0.975843i
$41$			3.55466i			0.555145i	0.960705	+	0.277573i	$0.0895299\pi$
$41$			3.55466i			0.555145i	−0.960705	+	0.277573i	$0.910470\pi$
$42$	2.71520	+	2.57443i	0.418964	+	0.397244i
$43$	−0.667790			−0.101837			−0.0509185	−	0.998703i	$-0.516215\pi$
$43$	−0.667790			−0.101837			−0.0509185	+	0.998703i	$0.516215\pi$
$44$	6.80232	+	4.74060i	1.02549	+	0.714672i
$45$	0.206931	−	2.22647i	0.0308475	−	0.331903i
$46$	0.935154	+	1.79156i	0.137881	+	0.264152i
$47$		−	0.693941i		−	0.101222i	−0.998718	−	0.0506109i	$-0.983883\pi$
$47$		−	0.693941i		−	0.101222i	0.998718	−	0.0506109i	$-0.0161168\pi$
$48$	−3.75267	+	1.38473i	−0.541651	+	0.199869i
$49$	−5.52197	+	4.30208i	−0.788852	+	0.614583i
$50$	2.06074	+	6.76412i	0.291432	+	0.956591i
$51$			3.18809i			0.446421i
$52$	3.83477	−	5.50254i	0.531787	−	0.763065i
$53$			4.18410i			0.574731i	0.957821	+	0.287365i	$0.0927794\pi$
$53$			4.18410i			0.574731i	−0.957821	+	0.287365i	$0.907221\pi$
$54$	1.25370	−	0.654401i	0.170607	−	0.0890527i
$55$	9.23012	+	0.857859i	1.24459	+	0.115674i
$56$	−1.51130	−	7.32912i	−0.201955	−	0.979395i
$57$			6.52098i			0.863725i
$58$	−5.81404	−	11.1385i	−0.763421	−	1.46256i
$59$	5.96025			0.775959			0.387980	−	0.921668i	$-0.373173\pi$
$59$	5.96025			0.775959			0.387980	+	0.921668i	$0.373173\pi$
$60$	−2.88555	+	3.41666i	−0.372523	+	0.441089i
$61$		−	10.3947i		−	1.33091i	−0.746439	−	0.665454i	$-0.768238\pi$
$61$		−	10.3947i		−	1.33091i	0.746439	−	0.665454i	$-0.231762\pi$
$62$	1.92269	+	3.68347i	0.244182	+	0.467802i
$63$	0.859661	+	2.50220i	0.108307	+	0.315247i
$64$	7.74101	+	2.01912i	0.967626	+	0.252390i
$65$	0.693941	−	7.46644i	0.0860728	−	0.926098i
$66$	2.71290	+	5.19736i	0.333935	+	0.639751i
$67$	−7.05912			−0.862409			−0.431204	−	0.902254i	$-0.641911\pi$
$67$	−7.05912			−0.862409			−0.431204	+	0.902254i	$0.641911\pi$
$68$	3.64563	−	5.23115i	0.442098	−	0.634370i
$69$			1.42902i			0.172034i
$70$	−5.51258	−	6.29377i	−0.658879	−	0.752249i
$71$		−	9.50299i		−	1.12780i	−0.825844	−	0.563899i	$-0.809301\pi$
$71$		−	9.50299i		−	1.12780i	0.825844	−	0.563899i	$-0.190699\pi$
$72$	−2.80544	−	0.359858i	−0.330624	−	0.0424096i
$73$	−7.52091			−0.880256			−0.440128	−	0.897935i	$-0.645067\pi$
$73$	−7.52091			−0.880256			−0.440128	+	0.897935i	$0.645067\pi$
$74$	−11.9642	+	6.24505i	−1.39081	+	0.725972i
$75$	−0.921454	+	4.91436i	−0.106400	+	0.567461i
$76$	7.45686	−	10.6999i	0.855361	−	1.22736i
$77$	−10.3732	+	3.56383i	−1.18213	+	0.406136i
$78$	4.20426	−	2.19452i	0.476038	−	0.248481i
$79$			12.1118i			1.36269i	0.731964	+	0.681343i	$0.238604\pi$
$79$			12.1118i			1.36269i	−0.731964	+	0.681343i	$0.761396\pi$
$80$	8.64176	−	2.30652i	0.966178	−	0.257877i
$81$	1.00000			0.111111
$82$	4.45647	−	2.32618i	0.492135	−	0.256883i
$83$		−	5.25464i		−	0.576772i	−0.957514	−	0.288386i	$-0.906881\pi$
$83$		−	5.25464i		−	0.576772i	0.957514	−	0.288386i	$-0.0931186\pi$
$84$	1.45074	−	5.08875i	0.158288	−	0.555228i
$85$	0.659715	−	7.09818i	0.0715561	−	0.769906i
$86$	0.437003	+	0.837208i	0.0471232	+	0.0902784i
$87$		−	8.88452i		−	0.952521i
$88$	1.49183	−	11.6303i	0.159030	−	1.23979i
$89$		−	2.83667i		−	0.300686i	−0.988634	−	0.150343i	$-0.951962\pi$
$89$		−	2.83667i		−	0.300686i	0.988634	−	0.150343i	$-0.0480378\pi$
$90$	−2.92674	+	1.19758i	−0.308506	+	0.126236i
$91$	2.88286	+	8.39108i	0.302206	+	0.879624i
$92$	1.63411	−	2.34480i	0.170368	−	0.244463i
$93$			2.93809i			0.304665i
$94$	−0.869993	+	0.454116i	−0.0897329	+	0.0468385i
$95$	1.34940	−	14.5188i	0.138445	−	1.48960i
$96$	4.19179	+	3.79854i	0.427822	+	0.387687i
$97$	15.9682			1.62133			0.810663	−	0.585513i	$-0.199107\pi$
$97$	15.9682			1.62133			0.810663	+	0.585513i	$0.199107\pi$
$98$	9.00709	+	4.10759i	0.909854	+	0.414929i
$99$			4.14562i			0.416651i
$100$	7.13162	−	7.00999i	0.713162	−	0.700999i
$101$		−	1.19853i		−	0.119258i	−0.998221	−	0.0596292i	$-0.981008\pi$
$101$		−	1.19853i		−	0.119258i	0.998221	−	0.0596292i	$-0.0189918\pi$
$102$	3.99690	−	2.08629i	0.395752	−	0.206573i
$103$		−	6.82433i		−	0.672421i	−0.941787	−	0.336210i	$-0.890855\pi$
$103$		−	6.82433i		−	0.672421i	0.941787	−	0.336210i	$-0.109145\pi$
$104$	−9.40801	−	1.20678i	−0.922531	−	0.118334i
$105$	−1.39623	−	5.74896i	−0.136258	−	0.561041i
$106$	5.24560	−	2.73808i	0.509498	−	0.265946i
$107$	−5.09970			−0.493007			−0.246503	−	0.969142i	$-0.579282\pi$
$107$	−5.09970			−0.493007			−0.246503	+	0.969142i	$0.579282\pi$
$108$	−1.64084	−	1.14352i	−0.157890	−	0.110035i
$109$	14.9107			1.42819			0.714093	−	0.700051i	$-0.246840\pi$
$109$	14.9107			1.42819			0.714093	+	0.700051i	$0.246840\pi$
$110$	−4.96470	−	12.1332i	−0.473366	−	1.15685i
$111$	−9.54315			−0.905795
$112$	−8.19951	+	6.69089i	−0.774781	+	0.632230i
$113$			15.0357i			1.41444i	0.706993	+	0.707220i	$0.250051\pi$
$113$			15.0357i			1.41444i	−0.706993	+	0.707220i	$0.749949\pi$
$114$	8.17534	−	4.26734i	0.765691	−	0.399673i
$115$	0.295710	−	3.18168i	0.0275751	−	0.296693i
$116$	−10.1596	+	14.5781i	−0.943297	+	1.35354i
$117$	3.35349			0.310030
$118$	−3.90040	−	7.47236i	−0.359061	−	0.687887i
$119$	2.74067	+	7.97721i	0.251237	+	0.731270i
$120$	6.17177	+	1.38175i	0.563403	+	0.126136i
$121$	−6.18619			−0.562381
$122$	−13.0318	+	6.80232i	−1.17985	+	0.615853i
$123$	3.55466			0.320513
$124$	3.35976	−	4.82094i	0.301715	−	0.432933i
$125$	3.06853	−	10.7510i	0.274457	−	0.961599i
$126$	2.57443	−	2.71520i	0.229349	−	0.241889i
$127$	15.9750			1.41755			0.708774	−	0.705435i	$-0.249248\pi$
$127$	15.9750			1.41755			0.708774	+	0.705435i	$0.249248\pi$
$128$	−2.53436	−	11.0262i	−0.224008	−	0.974587i
$129$			0.667790i			0.0587957i
$130$	−9.81478	+	4.01606i	−0.860813	+	0.352231i
$131$	4.17978			0.365189			0.182595	−	0.983188i	$-0.441550\pi$
$131$	4.17978			0.365189			0.182595	+	0.983188i	$0.441550\pi$
$132$	4.74060	−	6.80232i	0.412616	−	0.592066i
$133$	5.60583	+	16.3168i	0.486087	+	1.41484i
$134$	4.61950	+	8.85001i	0.399064	+	0.764524i
$135$	−2.22647	−	0.206931i	−0.191624	−	0.0178098i
$136$	−8.94399	−	1.14726i	−0.766941	−	0.0983764i
$137$		−	18.3094i		−	1.56428i	−0.623105	−	0.782139i	$-0.714129\pi$
$137$		−	18.3094i		−	1.56428i	0.623105	−	0.782139i	$-0.285871\pi$
$138$	1.79156	−	0.935154i	0.152508	−	0.0796056i
$139$	8.23037			0.698091			0.349046	−	0.937106i	$-0.386506\pi$
$139$	8.23037			0.698091			0.349046	+	0.937106i	$0.386506\pi$
$140$	−4.28305	+	11.0298i	−0.361984	+	0.932184i
$141$	−0.693941			−0.0584404
$142$	−11.9139	+	6.21877i	−0.999791	+	0.521868i
$143$			13.9023i			1.16257i
$144$	1.38473	+	3.75267i	0.115394	+	0.312722i
$145$	−1.83849	+	19.7811i	−0.152678	+	1.64273i
$146$	4.92169	+	9.42895i	0.407322	+	0.780346i
$147$	4.30208	+	5.52197i	0.354830	+	0.455444i
$148$	15.6588	+	10.9128i	1.28715	+	0.897024i
$149$	−2.87574			−0.235590			−0.117795	−	0.993038i	$-0.537583\pi$
$149$	−2.87574			−0.235590			−0.117795	+	0.993038i	$0.537583\pi$
$150$	6.76412	−	2.06074i	0.552288	−	0.168258i
$151$		−	7.47598i		−	0.608386i	−0.952610	−	0.304193i	$-0.901613\pi$
$151$		−	7.47598i		−	0.608386i	0.952610	−	0.304193i	$-0.0983868\pi$
$152$	−18.2942	−	2.34662i	−1.48386	−	0.190336i
$153$	3.18809			0.257741
$154$	11.2562	+	10.6726i	0.907049	+	0.860026i
$155$	0.607982	−	6.54157i	0.0488343	−	0.525432i
$156$	−5.50254	−	3.83477i	−0.440556	−	0.307027i
$157$	1.28235			0.102343			0.0511715	−	0.998690i	$-0.483704\pi$
$157$	1.28235			0.102343			0.0511715	+	0.998690i	$0.483704\pi$
$158$	15.1846	−	7.92599i	1.20802	−	0.630558i
$159$	4.18410			0.331821
$160$	−8.54686	−	9.32476i	−0.675688	−	0.737187i
$161$	1.22848	+	3.57569i	0.0968174	+	0.281804i
$162$	−0.654401	−	1.25370i	−0.0514146	−	0.0984998i
$163$	−21.3376			−1.67129			−0.835646	−	0.549269i	$-0.814906\pi$
$163$	−21.3376			−1.67129			−0.835646	+	0.549269i	$0.814906\pi$
$164$	−5.83264	−	4.06482i	−0.455453	−	0.317409i
$165$	0.857859	−	9.23012i	0.0667843	−	0.718564i
$166$	−6.58774	+	3.43864i	−0.511308	+	0.266891i
$167$			14.6737i			1.13549i	0.823206	+	0.567743i	$0.192183\pi$
$167$			14.6737i			1.13549i	−0.823206	+	0.567743i	$0.807817\pi$
$168$	−7.32912	+	1.51130i	−0.565454	+	0.116599i
$169$	−1.75414			−0.134934
$170$	−9.33070	+	3.81798i	−0.715632	+	0.292825i
$171$	6.52098			0.498672
$172$	0.763631	−	1.09574i	0.0582263	−	0.0835493i
$173$	20.6733			1.57176			0.785882	−	0.618376i	$-0.212209\pi$
$173$	20.6733			1.57176			0.785882	+	0.618376i	$0.212209\pi$
$174$	−11.1385	+	5.81404i	−0.844408	+	0.440761i
$175$	1.91903	+	13.0888i	0.145065	+	0.989422i
$176$	−15.5571	+	5.74057i	−1.17266	+	0.432712i
$177$		−	5.96025i		−	0.448000i
$178$	−3.55633	+	1.85632i	−0.266558	+	0.139137i
$179$		−	19.0127i		−	1.42108i	−0.703659	−	0.710538i	$-0.748452\pi$
$179$		−	19.0127i		−	1.42108i	0.703659	−	0.710538i	$-0.251548\pi$
$180$	3.41666	+	2.88555i	0.254663	+	0.215076i
$181$		−	15.7892i		−	1.17360i	−0.809732	−	0.586800i	$-0.800387\pi$
$181$		−	15.7892i		−	1.17360i	0.809732	−	0.586800i	$-0.199613\pi$
$182$	8.63333	−	9.10537i	0.639945	−	0.674935i
$183$	−10.3947			−0.768400
$184$	−4.00904	−	0.514245i	−0.295550	−	0.0379106i
$185$	21.2476	+	1.97478i	1.56215	+	0.145188i
$186$	3.68347	−	1.92269i	0.270085	−	0.140978i
$187$			13.2166i			0.966494i
$188$	1.13865	+	0.793534i	0.0830445	+	0.0578744i
$189$	2.50220	−	0.859661i	0.182008	−	0.0625312i
$190$	−19.0852	+	7.80937i	−1.38459	+	0.566551i
$191$			1.96830i			0.142421i	0.997461	+	0.0712106i	$0.0226862\pi$
$191$			1.96830i			0.142421i	−0.997461	+	0.0712106i	$0.977314\pi$
$192$	2.01912	−	7.74101i	0.145717	−	0.558659i
$193$			7.34732i			0.528871i	0.964403	+	0.264436i	$0.0851857\pi$
$193$			7.34732i			0.528871i	−0.964403	+	0.264436i	$0.914814\pi$
$194$	−10.4496	−	20.0193i	−0.750239	−	1.43730i
$195$	−7.46644	−	0.693941i	−0.534683	−	0.0496942i
$196$	−0.744571	−	13.9802i	−0.0531836	−	0.998585i
$197$			4.05059i			0.288593i	0.989535	+	0.144296i	$0.0460918\pi$
$197$			4.05059i			0.288593i	−0.989535	+	0.144296i	$0.953908\pi$
$198$	5.19736	−	2.71290i	0.369360	−	0.192797i
$199$	−23.8673			−1.69191			−0.845954	−	0.533256i	$-0.820968\pi$
$199$	−23.8673			−1.69191			−0.845954	+	0.533256i	$0.820968\pi$
$200$	−13.4554	−	4.35355i	−0.951437	−	0.307843i
$201$			7.05912i			0.497912i
$202$	−1.50260	+	0.784320i	−0.105722	+	0.0551846i
$203$	−7.63768	−	22.2308i	−0.536060	−	1.56030i
$204$	−5.23115	−	3.64563i	−0.366254	−	0.255245i
$205$	−7.91436	−	0.735571i	−0.552763	−	0.0513745i
$206$	−8.55565	+	4.46585i	−0.596100	+	0.311150i
$207$	1.42902			0.0993240
$208$	4.64368	+	12.5845i	0.321981	+	0.872579i
$209$			27.0335i			1.86995i
$210$	−6.29377	+	5.51258i	−0.434311	+	0.380404i
$211$		−	6.23257i		−	0.429068i	−0.976717	−	0.214534i	$-0.931177\pi$
$211$		−	6.23257i		−	0.429068i	0.976717	−	0.214534i	$-0.0688233\pi$
$212$	−6.86546	−	4.78460i	−0.471522	−	0.328608i
$213$	−9.50299			−0.651134
$214$	3.33725	+	6.39349i	0.228130	+	0.437050i
$215$	0.138187	−	1.48682i	0.00942426	−	0.101400i
$216$	−0.359858	+	2.80544i	−0.0244852	+	0.190886i
$217$	2.52576	+	7.35167i	0.171460	+	0.499064i
$218$	−9.75757	−	18.6935i	−0.660866	−	1.26608i
$219$			7.52091i			0.508216i
$220$	−11.9624	+	14.1642i	−0.806506	+	0.954950i
$221$	10.6912			0.719168
$222$	6.24505	+	11.9642i	0.419140	+	0.802986i
$223$			10.0483i			0.672885i	0.941704	+	0.336443i	$0.109224\pi$
$223$			10.0483i			0.672885i	−0.941704	+	0.336443i	$0.890776\pi$
$224$	13.7541	+	5.90118i	0.918986	+	0.394289i
$225$	4.91436	+	0.921454i	0.327624	+	0.0614303i
$226$	18.8502	−	9.83938i	1.25390	−	0.654506i
$227$			12.9107i			0.856913i	0.903562	+	0.428456i	$0.140942\pi$
$227$			12.9107i			0.856913i	−0.903562	+	0.428456i	$0.859058\pi$
$228$	−10.6999	−	7.45686i	−0.708619	−	0.493843i
$229$		−	20.2148i		−	1.33583i	−0.744235	−	0.667917i	$-0.767186\pi$
$229$		−	20.2148i		−	1.33583i	0.744235	−	0.667917i	$-0.232814\pi$
$230$	−4.18238	+	1.71136i	−0.275778	+	0.112844i
$231$	3.56383	+	10.3732i	0.234483	+	0.682504i
$232$	24.9250	+	3.19716i	1.63641	+	0.209904i
$233$			11.8552i			0.776658i	0.921521	+	0.388329i	$0.126948\pi$
$233$			11.8552i			0.776658i	−0.921521	+	0.388329i	$0.873052\pi$
$234$	−2.19452	−	4.20426i	−0.143461	−	0.274841i
$235$	1.54504	+	0.143598i	0.100787	+	0.00936731i
$236$	−6.81566	+	9.77984i	−0.443662	+	0.636613i
$237$	12.1118			0.786747
$238$	8.20752	−	8.65627i	0.532014	−	0.561103i
$239$			3.95455i			0.255799i	0.991787	+	0.127899i	$0.0408234\pi$
$239$			3.95455i			0.255799i	−0.991787	+	0.127899i	$0.959177\pi$
$240$	−2.30652	−	8.64176i	−0.148885	−	0.557823i
$241$			21.4716i			1.38311i	0.722324	+	0.691555i	$0.243074\pi$
$241$			21.4716i			1.38311i	−0.722324	+	0.691555i	$0.756926\pi$
$242$	4.04825	+	7.75562i	0.260231	+	0.498550i
$243$		−	1.00000i		−	0.0641500i
$244$	17.0561	+	11.8866i	1.09191	+	0.760959i
$245$	−8.43580	−	13.1847i	−0.538943	−	0.842342i
$246$	−2.32618	−	4.45647i	−0.148312	−	0.284134i
$247$	21.8680			1.39143
$248$	−8.24263	−	1.05729i	−0.523408	−	0.0671382i
$249$	−5.25464			−0.333000
$250$	−15.4866	+	3.18846i	−0.979456	+	0.201656i
$251$	−24.2390			−1.52995			−0.764975	−	0.644060i	$-0.777249\pi$
$251$	−24.2390			−1.52995			−0.764975	+	0.644060i	$0.777249\pi$
$252$	−5.08875	−	1.45074i	−0.320561	−	0.0913879i
$253$			5.92419i			0.372451i
$254$	−10.4540	−	20.0278i	−0.655944	−	1.25665i
$255$	−7.09818	−	0.659715i	−0.444506	−	0.0413129i
$256$	−12.1650	+	10.3929i	−0.760315	+	0.649555i
$257$	6.84349			0.426885			0.213443	−	0.976956i	$-0.431532\pi$
$257$	6.84349			0.426885			0.213443	+	0.976956i	$0.431532\pi$
$258$	0.837208	−	0.437003i	0.0521223	−	0.0272066i
$259$	−23.8788	+	8.20387i	−1.48376	+	0.509764i
$260$	11.4577	+	9.67666i	0.710578	+	0.600121i
$261$	−8.88452			−0.549938
$262$	−2.73526	−	5.24019i	−0.168985	−	0.323740i
$263$	−26.0905			−1.60881			−0.804403	−	0.594083i	$-0.797515\pi$
$263$	−26.0905			−1.60881			−0.804403	+	0.594083i	$0.797515\pi$
$264$	−11.6303	−	1.49183i	−0.715796	−	0.0918160i
$265$	−9.31579	−	0.865822i	−0.572265	−	0.0531870i
$266$	16.7878	−	17.7057i	1.02933	−	1.08561i
$267$	−2.83667			−0.173601
$268$	8.07223	−	11.5829i	0.493090	−	0.707539i
$269$		−	8.74121i		−	0.532961i	−0.963840	−	0.266481i	$-0.914139\pi$
$269$		−	8.74121i		−	0.532961i	0.963840	−	0.266481i	$-0.0858608\pi$
$270$	1.19758	+	2.92674i	0.0728822	+	0.178116i
$271$	14.8967			0.904911			0.452456	−	0.891787i	$-0.350548\pi$
$271$	14.8967			0.904911			0.452456	+	0.891787i	$0.350548\pi$
$272$	4.41464	+	11.9638i	0.267677	+	0.725414i
$273$	8.39108	−	2.88286i	0.507851	−	0.174479i
$274$	−22.9545	+	11.9817i	−1.38673	+	0.723840i
$275$	−3.82000	+	20.3731i	−0.230355	+	1.22854i
$276$	−2.34480	−	1.63411i	−0.141140	−	0.0983621i
$277$			8.86971i			0.532929i	0.963845	+	0.266465i	$0.0858555\pi$
$277$			8.86971i			0.532929i	−0.963845	+	0.266465i	$0.914144\pi$
$278$	−5.38597	−	10.3184i	−0.323029	−	0.618857i
$279$	2.93809			0.175899
$280$	16.6308	−	1.84823i	0.993881	−	0.110453i
$281$	−7.14815			−0.426423			−0.213211	−	0.977006i	$-0.568392\pi$
$281$	−7.14815			−0.426423			−0.213211	+	0.977006i	$0.568392\pi$
$282$	0.454116	+	0.869993i	0.0270422	+	0.0518073i
$283$		−	2.57635i		−	0.153148i	−0.997064	−	0.0765742i	$-0.975602\pi$
$283$		−	2.57635i		−	0.153148i	0.997064	−	0.0765742i	$-0.0243982\pi$
$284$	15.5929	+	10.8668i	0.925270	+	0.644829i
$285$	−14.5188	−	1.34940i	−0.860018	−	0.0799313i
$286$	17.4293	−	9.09767i	1.03061	−	0.537957i
$287$	8.89446	−	3.05581i	0.525023	−	0.180379i
$288$	3.79854	−	4.19179i	0.223831	−	0.247003i
$289$	−6.83611			−0.402124
$290$	26.0027	−	10.6399i	1.52693	−	0.624796i
$291$		−	15.9682i		−	0.936073i
$292$	8.60030	−	12.3406i	0.503294	−	0.722181i
$293$	−25.4873			−1.48898			−0.744491	−	0.667633i	$-0.767308\pi$
$293$	−25.4873			−1.48898			−0.744491	+	0.667633i	$0.767308\pi$
$294$	4.10759	−	9.00709i	0.239560	−	0.525304i
$295$	−1.23336	+	13.2703i	−0.0718092	+	0.772629i
$296$	3.43417	−	26.7727i	0.199607	−	1.55613i
$297$	4.14562			0.240553
$298$	1.88189	+	3.60531i	0.109015	+	0.208850i
$299$	4.79221			0.277140
$300$	−7.00999	−	7.13162i	−0.404722	−	0.411744i
$301$	0.574074	+	1.67094i	0.0330891	+	0.0963115i
$302$	−9.37262	+	4.89229i	−0.539334	+	0.281520i
$303$	−1.19853			−0.0688538
$304$	9.02981	+	24.4711i	0.517895	+	1.40351i
$305$	23.1436	+	2.15099i	1.32520	+	0.123166i
$306$	−2.08629	−	3.99690i	−0.119265	−	0.228487i
$307$		−	19.5890i		−	1.11800i	−0.829167	−	0.559001i	$-0.811185\pi$
$307$		−	19.5890i		−	1.11800i	0.829167	−	0.559001i	$-0.188815\pi$
$308$	6.01421	−	21.0960i	0.342691	−	1.20206i
$309$	−6.82433			−0.388222
$310$	−8.59902	+	3.51858i	−0.488391	+	0.199842i
$311$	25.9353			1.47066			0.735329	−	0.677710i	$-0.237028\pi$
$311$	25.9353			1.47066			0.735329	+	0.677710i	$0.237028\pi$
$312$	−1.20678	+	9.40801i	−0.0683203	+	0.532623i
$313$	−8.23386			−0.465405			−0.232703	−	0.972548i	$-0.574757\pi$
$313$	−8.23386			−0.465405			−0.232703	+	0.972548i	$0.574757\pi$
$314$	−0.839174	−	1.60769i	−0.0473573	−	0.0907269i
$315$	−5.74896	+	1.39623i	−0.323917	+	0.0786686i
$316$	−19.8736	−	13.8501i	−1.11798	−	0.779128i
$317$		−	27.9672i		−	1.57080i	−0.618992	−	0.785398i	$-0.712459\pi$
$317$		−	27.9672i		−	1.57080i	0.618992	−	0.785398i	$-0.287541\pi$
$318$	−2.73808	−	5.24560i	−0.153544	−	0.294159i
$319$		−	36.8319i		−	2.06219i
$320$	−6.09737	+	16.8173i	−0.340853	+	0.940117i
$321$			5.09970i			0.284638i
$322$	3.67893	−	3.88008i	0.205019	−	0.216228i
$323$	20.7894			1.15676
$324$	−1.14352	+	1.64084i	−0.0635288	+	0.0911579i
$325$	16.4802	+	3.09008i	0.914159	+	0.171407i
$326$	13.9634	+	26.7509i	0.773359	+	1.48160i
$327$		−	14.9107i		−	0.824563i
$328$	−1.27917	+	9.97240i	−0.0706305	+	0.550634i
$329$	−1.73638	+	0.596554i	−0.0957295	+	0.0328891i
$330$	−12.1332	+	4.96470i	−0.667909	+	0.273298i
$331$			23.3019i			1.28079i	0.768046	+	0.640395i	$0.221229\pi$
$331$			23.3019i			1.28079i	−0.768046	+	0.640395i	$0.778771\pi$
$332$	8.62205	+	6.00878i	0.473196	+	0.329775i
$333$			9.54315i			0.522961i
$334$	18.3964	−	9.60249i	1.00661	−	0.525425i
$335$	1.46075	−	15.7169i	0.0798095	−	0.858708i
$336$	6.69089	+	8.19951i	0.365018	+	0.447320i
$337$			1.27455i			0.0694292i	0.999397	+	0.0347146i	$0.0110522\pi$
$337$			1.27455i			0.0694292i	−0.999397	+	0.0347146i	$0.988948\pi$
$338$	1.14791	+	2.19916i	0.0624381	+	0.119619i
$339$	15.0357			0.816627
$340$	10.8926	+	9.19939i	0.590735	+	0.498907i
$341$			12.1802i			0.659595i
$342$	−4.26734	−	8.17534i	−0.230751	−	0.442072i
$343$	15.5117	+	10.1187i	0.837551	+	0.546359i
$344$	−1.87345	−	0.240309i	−0.101010	−	0.0129566i
$345$	−3.18168	−	0.295710i	−0.171296	−	0.0159205i
$346$	−13.5286	−	25.9181i	−0.727305	−	1.39337i
$347$	22.6794			1.21750			0.608748	−	0.793363i	$-0.291672\pi$
$347$	22.6794			1.21750			0.608748	+	0.793363i	$0.291672\pi$
$348$	14.5781	+	10.1596i	0.781469	+	0.544613i
$349$		−	14.8204i		−	0.793317i	−0.917966	−	0.396658i	$-0.870170\pi$
$349$		−	14.8204i		−	0.793317i	0.917966	−	0.396658i	$-0.129830\pi$
$350$	15.1536	−	10.9712i	0.809995	−	0.586436i
$351$		−	3.35349i		−	0.178996i
$352$	17.3776	+	15.7473i	0.926227	+	0.839336i
$353$	−15.4022			−0.819778			−0.409889	−	0.912135i	$-0.634433\pi$
$353$	−15.4022			−0.819778			−0.409889	+	0.912135i	$0.634433\pi$
$354$	−7.47236	+	3.90040i	−0.397151	+	0.207304i
$355$	21.1582	+	1.96647i	1.12296	+	0.104369i
$356$	4.65453	+	3.24378i	0.246689	+	0.171920i
$357$	7.97721	−	2.74067i	0.422199	−	0.145052i
$358$	−23.8362	+	12.4419i	−1.25978	+	0.657576i
$359$			6.40783i			0.338192i	0.985600	+	0.169096i	$0.0540848\pi$
$359$			6.40783i			0.338192i	−0.985600	+	0.169096i	$0.945915\pi$
$360$	1.38175	−	6.17177i	0.0728244	−	0.325281i
$361$	23.5232			1.23806
$362$	−19.7949	+	10.3325i	−1.04040	+	0.543062i
$363$			6.18619i			0.324691i
$364$	−17.0650	−	4.86503i	−0.894451	−	0.254997i
$365$	1.55631	−	16.7451i	0.0814611	−	0.876479i
$366$	6.80232	+	13.0318i	0.355563	+	0.681185i
$367$		−	20.1613i		−	1.05241i	−0.850357	−	0.526206i	$-0.823614\pi$
$367$		−	20.1613i		−	1.05241i	0.850357	−	0.526206i	$-0.176386\pi$
$368$	1.97881	+	5.36265i	0.103153	+	0.279547i
$369$		−	3.55466i		−	0.185048i
$370$	−11.4286	−	27.9303i	−0.594147	−	1.45203i
$371$	10.4694	−	3.59691i	0.543547	−	0.186742i
$372$	−4.82094	−	3.35976i	−0.249954	−	0.174195i
$373$			6.48276i			0.335664i	0.985816	+	0.167832i	$0.0536767\pi$
$373$			6.48276i			0.335664i	−0.985816	+	0.167832i	$0.946323\pi$
$374$	16.5696	−	8.64896i	0.856795	−	0.447227i
$375$	−10.7510	−	3.06853i	−0.555180	−	0.158458i
$376$	0.249720	−	1.94681i	0.0128783	−	0.100399i
$377$	−29.7941			−1.53448
$378$	−2.71520	−	2.57443i	−0.139655	−	0.132415i
$379$		−	23.4767i		−	1.20592i	−0.797773	−	0.602958i	$-0.793989\pi$
$379$		−	23.4767i		−	1.20592i	0.797773	−	0.602958i	$-0.206011\pi$
$380$	22.2800	+	18.8166i	1.14294	+	0.965273i
$381$		−	15.9750i		−	0.818422i
$382$	2.46765	−	1.28806i	0.126256	−	0.0659027i
$383$		−	11.2009i		−	0.572342i	−0.958179	−	0.286171i	$-0.907617\pi$
$383$		−	11.2009i		−	0.572342i	0.958179	−	0.286171i	$-0.0923825\pi$
$384$	−11.0262	+	2.53436i	−0.562678	+	0.129331i
$385$	−5.78824	−	23.8330i	−0.294996	−	1.21464i
$386$	9.21132	−	4.80809i	0.468844	−	0.244725i
$387$	0.667790			0.0339457
$388$	−18.2599	+	26.2013i	−0.927008	+	1.33017i
$389$	3.23587			0.164065			0.0820326	−	0.996630i	$-0.473859\pi$
$389$	3.23587			0.164065			0.0820326	+	0.996630i	$0.473859\pi$
$390$	4.01606	+	9.81478i	0.203361	+	0.496991i
$391$	4.55585			0.230399
$392$	−17.0397	+	10.0821i	−0.860634	+	0.509224i
$393$		−	4.17978i		−	0.210842i
$394$	5.07822	−	2.65071i	0.255837	−	0.133541i
$395$	−26.9666	−	2.50631i	−1.35684	−	0.126106i
$396$	−6.80232	−	4.74060i	−0.341829	−	0.238224i
$397$	−26.5118			−1.33059			−0.665295	−	0.746581i	$-0.731694\pi$
$397$	−26.5118			−1.33059			−0.665295	+	0.746581i	$0.731694\pi$
$398$	15.6188	+	29.9224i	0.782899	+	1.49987i
$399$	16.3168	−	5.60583i	0.816860	−	0.280643i
$400$	3.34716	+	19.7179i	0.167358	+	0.985896i
$401$	−4.93093			−0.246239			−0.123119	−	0.992392i	$-0.539290\pi$
$401$	−4.93093			−0.246239			−0.123119	+	0.992392i	$0.539290\pi$
$402$	8.85001	−	4.61950i	0.441398	−	0.230400i
$403$	9.85283			0.490805
$404$	1.96660	+	1.37054i	0.0978421	+	0.0681870i
$405$	−0.206931	+	2.22647i	−0.0102825	+	0.110634i
$406$	−22.8726	+	24.1232i	−1.13515	+	1.19722i
$407$	−39.5623			−1.96103
$408$	−1.14726	+	8.94399i	−0.0567977	+	0.442793i
$409$		−	12.8675i		−	0.636256i	−0.948048	−	0.318128i	$-0.896946\pi$
$409$		−	12.8675i		−	0.636256i	0.948048	−	0.318128i	$-0.103054\pi$
$410$	4.25698	+	10.4036i	0.210237	+	0.513796i
$411$	−18.3094			−0.903136
$412$	11.1976	+	7.80374i	0.551669	+	0.384463i
$413$	−5.12380	−	14.9137i	−0.252126	−	0.733856i
$414$	−0.935154	−	1.79156i	−0.0459603	−	0.0880505i
$415$	11.6993	+	1.08735i	0.574297	+	0.0533759i
$416$	12.7384	−	14.0571i	0.624549	−	0.689206i
$417$		−	8.23037i		−	0.403043i
$418$	33.8919	−	17.6908i	1.65771	−	0.865284i
$419$	5.88793			0.287644			0.143822	−	0.989604i	$-0.454061\pi$
$419$	5.88793			0.287644			0.143822	+	0.989604i	$0.454061\pi$
$420$	11.0298	+	4.28305i	0.538197	+	0.208991i
$421$	−13.8287			−0.673970			−0.336985	−	0.941510i	$-0.609407\pi$
$421$	−13.8287			−0.673970			−0.336985	+	0.941510i	$0.609407\pi$
$422$	−7.81376	+	4.07860i	−0.380368	+	0.198543i
$423$			0.693941i			0.0337406i
$424$	−1.50568	+	11.7383i	−0.0731223	+	0.570060i
$425$	15.6674	+	2.93767i	0.759980	+	0.142498i
$426$	6.21877	+	11.9139i	0.301300	+	0.577230i
$427$	−26.0096	+	8.93594i	−1.25869	+	0.432440i
$428$	5.83160	−	8.36781i	0.281881	−	0.404474i
$429$	13.9023			0.671209
$430$	−1.95445	+	0.799730i	−0.0942519	+	0.0385664i
$431$			26.3127i			1.26744i	0.773563	+	0.633719i	$0.218473\pi$
$431$			26.3127i			1.26744i	−0.773563	+	0.633719i	$0.781527\pi$
$432$	3.75267	−	1.38473i	0.180550	−	0.0666229i
$433$	−1.12270			−0.0539536			−0.0269768	−	0.999636i	$-0.508588\pi$
$433$	−1.12270			−0.0539536			−0.0269768	+	0.999636i	$0.508588\pi$
$434$	7.56391	−	7.97748i	0.363079	−	0.382931i
$435$	19.7811	+	1.83849i	0.948433	+	0.0881487i
$436$	−17.0507	+	24.4661i	−0.816578	+	1.17171i
$437$	9.31863			0.445771
$438$	9.42895	−	4.92169i	0.450533	−	0.235168i
$439$	−7.08181			−0.337996			−0.168998	−	0.985616i	$-0.554053\pi$
$439$	−7.08181			−0.337996			−0.168998	+	0.985616i	$0.554053\pi$
$440$	25.5858	+	5.72820i	1.21976	+	0.273081i
$441$	5.52197	−	4.30208i	0.262951	−	0.204861i
$442$	−6.99633	−	13.4035i	−0.332782	−	0.637541i
$443$	13.4718			0.640066			0.320033	−	0.947406i	$-0.396306\pi$
$443$	13.4718			0.640066			0.320033	+	0.947406i	$0.396306\pi$
$444$	10.9128	−	15.6588i	0.517897	−	0.743134i
$445$	6.31576	+	0.586995i	0.299396	+	0.0278263i
$446$	12.5976	−	6.57563i	0.596512	−	0.311365i
$447$			2.87574i			0.136018i
$448$	−1.60241	−	21.1053i	−0.0757069	−	0.997130i
$449$	−21.1302			−0.997195			−0.498598	−	0.866834i	$-0.666151\pi$
$449$	−21.1302			−0.997195			−0.498598	+	0.866834i	$0.666151\pi$
$450$	−2.06074	−	6.76412i	−0.0971441	−	0.318864i
$451$	14.7363			0.693905
$452$	−24.6712	−	17.1936i	−1.16044	−	0.808719i
$453$	−7.47598			−0.351252
$454$	16.1861	−	8.44877i	0.759652	−	0.396520i
$455$	−19.2791	+	4.68223i	−0.903816	+	0.219507i
$456$	−2.34662	+	18.2942i	−0.109891	+	0.856706i
$457$			6.69819i			0.313328i	0.987652	+	0.156664i	$0.0500740\pi$
$457$			6.69819i			0.313328i	−0.987652	+	0.156664i	$0.949926\pi$
$458$	−25.3433	+	13.2286i	−1.18422	+	0.618133i
$459$		−	3.18809i		−	0.148807i
$460$	4.88249	+	4.12352i	0.227647	+	0.192260i
$461$		−	38.8726i		−	1.81048i	−0.424904	−	0.905238i	$-0.639692\pi$
$461$		−	38.8726i		−	1.81048i	0.424904	−	0.905238i	$-0.360308\pi$
$462$	10.6726	−	11.2562i	0.496536	−	0.523685i
$463$	−14.6394			−0.680350			−0.340175	−	0.940362i	$-0.610486\pi$
$463$	−14.6394			−0.680350			−0.340175	+	0.940362i	$0.610486\pi$
$464$	−12.3027	−	33.3407i	−0.571138	−	1.54780i
$465$	−6.54157	−	0.607982i	−0.303358	−	0.0281945i
$466$	14.8628	−	7.75804i	0.688506	−	0.359384i
$467$			24.6710i			1.14164i	0.821077	+	0.570818i	$0.193374\pi$
$467$			24.6710i			1.14164i	−0.821077	+	0.570818i	$0.806626\pi$
$468$	−3.83477	+	5.50254i	−0.177262	+	0.254355i
$469$	6.06845	+	17.6633i	0.280215	+	0.815615i
$470$	−0.831048	−	2.03099i	−0.0383334	−	0.0936824i
$471$		−	1.28235i		−	0.0590878i
$472$	16.7211	+	2.14484i	0.769653	+	0.0987244i
$473$			2.76841i			0.127292i
$474$	−7.92599	−	15.1846i	−0.364053	−	0.697450i
$475$	32.0464	+	6.00878i	1.47039	+	0.275702i
$476$	−16.2234	−	4.62507i	−0.743597	−	0.211990i
$477$		−	4.18410i		−	0.191577i
$478$	4.95781	−	2.58786i	0.226765	−	0.118366i
$479$	10.2736			0.469411			0.234705	−	0.972067i	$-0.424587\pi$
$479$	10.2736			0.469411			0.234705	+	0.972067i	$0.424587\pi$
$480$	−9.32476	+	8.54686i	−0.425615	+	0.390109i
$481$			32.0028i			1.45920i
$482$	26.9190	−	14.0511i	1.22613	−	0.640009i
$483$	3.57569	−	1.22848i	0.162700	−	0.0558976i
$484$	7.07402	−	10.1506i	0.321547	−	0.461389i
$485$	−3.30432	+	35.5528i	−0.150042	+	1.61437i
$486$	−1.25370	+	0.654401i	−0.0568689	+	0.0296842i
$487$	−15.3745			−0.696683			−0.348342	−	0.937368i	$-0.613255\pi$
$487$	−15.3745			−0.696683			−0.348342	+	0.937368i	$0.613255\pi$
$488$	3.74062	−	29.1618i	0.169330	−	1.32009i
$489$			21.3376i			0.964920i
$490$	−11.0093	+	19.2041i	−0.497349	+	0.867551i
$491$			14.8168i			0.668671i	0.942454	+	0.334336i	$0.108512\pi$
$491$			14.8168i			0.668671i	−0.942454	+	0.334336i	$0.891488\pi$
$492$	−4.06482	+	5.83264i	−0.183256	+	0.262956i
$493$	−28.3246			−1.27568
$494$	−14.3104	−	27.4159i	−0.643858	−	1.23350i
$495$	−9.23012	−	0.857859i	−0.414863	−	0.0385579i
$496$	4.06846	+	11.0257i	0.182679	+	0.495067i
$497$	−23.7784	+	8.16936i	−1.06660	+	0.366446i
$498$	3.43864	+	6.58774i	0.154089	+	0.295204i
$499$		−	17.7914i		−	0.796453i	−0.917287	−	0.398226i	$-0.869626\pi$
$499$		−	17.7914i		−	0.796453i	0.917287	−	0.398226i	$-0.130374\pi$
$500$	14.1318	+	17.3289i	0.631993	+	0.774974i
$501$	14.6737			0.655573
$502$	15.8620	+	30.3883i	0.707956	+	1.35630i
$503$		−	9.60325i		−	0.428188i	−0.976813	−	0.214094i	$-0.931320\pi$
$503$		−	9.60325i		−	0.428188i	0.976813	−	0.214094i	$-0.0686798\pi$
$504$	1.51130	+	7.32912i	0.0673185	+	0.326465i
$505$	2.66850	+	0.248014i	0.118747	+	0.0110365i
$506$	7.42715	−	3.87680i	0.330177	−	0.172345i
$507$			1.75414i			0.0779040i
$508$	−18.2677	+	26.2124i	−0.810496	+	1.16299i
$509$		−	26.5301i		−	1.17593i	−0.808887	−	0.587964i	$-0.799930\pi$
$509$		−	26.5301i		−	1.17593i	0.808887	−	0.587964i	$-0.200070\pi$
$510$	3.81798	+	9.33070i	0.169063	+	0.413170i
$511$	6.46543	+	18.8188i	0.286014	+	0.832494i
$512$	20.9903	+	8.45018i	0.927651	+	0.373449i
$513$		−	6.52098i		−	0.287908i
$514$	−4.47839	−	8.57967i	−0.197533	−	0.378433i
$515$	15.1942	+	1.41217i	0.669535	+	0.0622275i
$516$	−1.09574	−	0.763631i	−0.0482372	−	0.0336170i
$517$	−2.87682			−0.126522
$518$	25.9115	+	24.5682i	1.13849	+	1.07947i
$519$		−	20.6733i		−	0.907458i
$520$	4.63367	−	20.6969i	0.203200	−	0.907621i
$521$		−	0.626926i		−	0.0274661i	−0.999906	−	0.0137331i	$-0.995628\pi$
$521$		−	0.626926i		−	0.0274661i	0.999906	−	0.0137331i	$-0.00437150\pi$
$522$	5.81404	+	11.1385i	0.254474	+	0.487519i
$523$		−	20.3037i		−	0.887818i	−0.896072	−	0.443909i	$-0.853591\pi$
$523$		−	20.3037i		−	0.887818i	0.896072	−	0.443909i	$-0.146409\pi$
$524$	−4.77966	+	6.85837i	−0.208800	+	0.299609i
$525$	13.0888	−	1.91903i	0.571243	−	0.0837532i
$526$	17.0736	+	32.7096i	0.744446	+	1.42620i
$527$	9.36687			0.408027
$528$	5.74057	+	15.5571i	0.249826	+	0.677038i
$529$	−20.9579			−0.911213
$530$	5.01079	+	12.2458i	0.217655	+	0.531923i
$531$	−5.96025			−0.258653
$532$	−33.1836	−	9.46023i	−1.43869	−	0.410153i
$533$		−	11.9205i		−	0.516335i
$534$	1.85632	+	3.55633i	0.0803308	+	0.153897i
$535$	1.05529	−	11.3543i	0.0456241	−	0.490891i
$536$	−19.8040	−	2.54028i	−0.855400	−	0.109723i
$537$	−19.0127			−0.820458
$538$	−10.9588	+	5.72026i	−0.472469	+	0.246618i
$539$	17.8348	+	22.8920i	0.768200	+	0.986028i
$540$	2.88555	−	3.41666i	0.124174	−	0.147030i
$541$	0.543665			0.0233740			0.0116870	−	0.999932i	$-0.496280\pi$
$541$	0.543665			0.0233740			0.0116870	+	0.999932i	$0.496280\pi$
$542$	−9.74843	−	18.6760i	−0.418731	−	0.802202i
$543$	−15.7892			−0.677579
$544$	12.1101	−	13.3638i	0.519215	−	0.572967i
$545$	−3.08549	+	33.1982i	−0.132168	+	1.42206i
$546$	−9.10537	−	8.63333i	−0.389674	−	0.369472i
$547$	−4.59239			−0.196357			−0.0981783	−	0.995169i	$-0.531302\pi$
$547$	−4.59239			−0.196357			−0.0981783	+	0.995169i	$0.531302\pi$
$548$	30.0428	+	20.9371i	1.28337	+	0.894390i
$549$			10.3947i			0.443636i
$550$	28.0415	−	8.54304i	1.19569	−	0.364276i
$551$	−57.9358			−2.46815
$552$	−0.514245	+	4.00904i	−0.0218877	+	0.170636i
$553$	30.3061	−	10.4121i	1.28875	−	0.442766i
$554$	11.1199	−	5.80435i	0.472441	−	0.246603i
$555$	1.97478	−	21.2476i	0.0838246	−	0.901908i
$556$	−9.41158	+	13.5047i	−0.399140	+	0.572729i
$557$			26.7881i			1.13505i	0.823357	+	0.567523i	$0.192098\pi$
$557$			26.7881i			1.13505i	−0.823357	+	0.567523i	$0.807902\pi$
$558$	−1.92269	−	3.68347i	−0.0813939	−	0.155934i
$559$	2.23943			0.0947176
$560$	−13.2004	−	19.6405i	−0.557817	−	0.829964i
$561$	13.2166			0.558005
$562$	4.67776	+	8.96162i	0.197319	+	0.378023i
$563$			17.7277i			0.747135i	0.927603	+	0.373567i	$0.121866\pi$
$563$			17.7277i			0.747135i	−0.927603	+	0.373567i	$0.878134\pi$
$564$	0.793534	−	1.13865i	0.0334138	−	0.0479457i
$565$	−33.4766	−	3.11136i	−1.40837	−	0.130896i
$566$	−3.22997	+	1.68597i	−0.135766	+	0.0708666i
$567$	−0.859661	−	2.50220i	−0.0361024	−	0.105082i
$568$	3.41972	−	26.6601i	0.143488	−	1.11863i
$569$	−42.8231			−1.79524			−0.897620	−	0.440770i	$-0.854705\pi$
$569$	−42.8231			−1.79524			−0.897620	+	0.440770i	$0.854705\pi$
$570$	7.80937	+	19.0852i	0.327099	+	0.799392i
$571$		−	29.5932i		−	1.23844i	−0.785219	−	0.619219i	$-0.787449\pi$
$571$		−	29.5932i		−	1.23844i	0.785219	−	0.619219i	$-0.212551\pi$
$572$	−22.8115	−	15.8975i	−0.953795	−	0.664709i
$573$	1.96830			0.0822269
$574$	−9.65160	−	9.15125i	−0.402850	−	0.381966i
$575$	7.02273	+	1.31678i	0.292868	+	0.0549135i
$576$	−7.74101	−	2.01912i	−0.322542	−	0.0841299i
$577$	19.1483			0.797152			0.398576	−	0.917135i	$-0.369504\pi$
$577$	19.1483			0.797152			0.398576	+	0.917135i	$0.369504\pi$
$578$	4.47356	+	8.57042i	0.186076	+	0.356483i
$579$	7.34732			0.305344
$580$	−30.3554	−	25.6368i	−1.26044	−	1.06451i
$581$	−13.1481	+	4.51721i	−0.545477	+	0.187406i
$582$	−20.0193	+	10.4496i	−0.829827	+	0.433150i
$583$	17.3457			0.718386
$584$	−21.0995	−	2.70646i	−0.873102	−	0.111994i
$585$	−0.693941	+	7.46644i	−0.0286909	+	0.308699i
$586$	16.6789	+	31.9533i	0.688999	+	1.31998i
$587$		−	35.7778i		−	1.47671i	−0.674413	−	0.738355i	$-0.735603\pi$
$587$		−	35.7778i		−	1.47671i	0.674413	−	0.738355i	$-0.264397\pi$
$588$	−13.9802	+	0.744571i	−0.576533	+	0.0307056i
$589$	19.1592			0.789441
$590$	17.4441	−	7.13786i	0.718163	−	0.293861i
$591$	4.05059			0.166619
$592$	−35.8123	+	13.2147i	−1.47188	+	0.543121i
$593$	43.1401			1.77155			0.885775	−	0.464115i	$-0.153628\pi$
$593$	43.1401			1.77155			0.885775	+	0.464115i	$0.153628\pi$
$594$	−2.71290	−	5.19736i	−0.111312	−	0.213250i
$595$	−18.3282	+	4.45130i	−0.751382	+	0.182485i
$596$	3.28846	−	4.71864i	0.134701	−	0.193283i
$597$			23.8673i			0.976823i
$598$	−3.13603	−	6.00798i	−0.128242	−	0.245685i
$599$			0.774502i			0.0316453i	0.999875	+	0.0158227i	$0.00503672\pi$
$599$			0.774502i			0.0316453i	−0.999875	+	0.0158227i	$0.994963\pi$
$600$	−4.35355	+	13.4554i	−0.177733	+	0.549313i
$601$		−	12.2670i		−	0.500381i	−0.968197	−	0.250190i	$-0.919507\pi$
$601$		−	12.2670i		−	0.500381i	0.968197	−	0.250190i	$-0.0804932\pi$
$602$	1.71918	−	1.81318i	0.0700687	−	0.0738998i
$603$	7.05912			0.287470
$604$	12.2669	+	8.54892i	0.499133	+	0.347851i
$605$	1.28012	−	13.7734i	0.0520441	−	0.559968i
$606$	0.784320	+	1.50260i	0.0318608	+	0.0610388i
$607$		−	24.9016i		−	1.01072i	−0.862908	−	0.505362i	$-0.831359\pi$
$607$		−	24.9016i		−	1.01072i	0.862908	−	0.505362i	$-0.168641\pi$
$608$	24.7702	−	27.3346i	1.00457	−	1.10856i
$609$	−22.2308	+	7.63768i	−0.900838	+	0.309494i
$610$	−12.4485	−	30.4227i	−0.504024	−	1.23178i
$611$			2.32712i			0.0941452i
$612$	−3.64563	+	5.23115i	−0.147366	+	0.211457i
$613$		−	46.8111i		−	1.89068i	−0.326085	−	0.945340i	$-0.605730\pi$
$613$		−	46.8111i		−	1.89068i	0.326085	−	0.945340i	$-0.394270\pi$
$614$	−24.5587	+	12.8191i	−0.991107	+	0.517335i
$615$	−0.735571	+	7.91436i	−0.0296611	+	0.319138i
$616$	−30.3838	+	6.26526i	−1.22420	+	0.252435i
$617$		−	14.9253i		−	0.600868i	−0.953803	−	0.300434i	$-0.902868\pi$
$617$		−	14.9253i		−	0.600868i	0.953803	−	0.300434i	$-0.0971315\pi$
$618$	4.46585	+	8.55565i	0.179643	+	0.344159i
$619$	−36.9017			−1.48321			−0.741603	−	0.670839i	$-0.765934\pi$
$619$	−36.9017			−1.48321			−0.741603	+	0.670839i	$0.765934\pi$
$620$	10.0385	+	8.47801i	0.403154	+	0.340485i
$621$		−	1.42902i		−	0.0573447i
$622$	−16.9721	−	32.5151i	−0.680520	−	1.30374i
$623$	−7.09790	+	2.43857i	−0.284371	+	0.0976994i
$624$	12.5845	−	4.64368i	0.503784	−	0.185896i
$625$	23.3018	+	9.05671i	0.932074	+	0.362268i
$626$	5.38825	+	10.3228i	0.215358	+	0.412581i
$627$	27.0335			1.07962
$628$	−1.46640	+	2.10414i	−0.0585156	+	0.0839644i
$629$			30.4244i			1.21310i
$630$	5.51258	+	6.29377i	0.219626	+	0.250750i
$631$		−	2.54553i		−	0.101336i	−0.998716	−	0.0506679i	$-0.983865\pi$
$631$		−	2.54553i		−	0.101336i	0.998716	−	0.0506679i	$-0.0161350\pi$
$632$	−4.35853	+	33.9790i	−0.173373	+	1.35161i
$633$	−6.23257			−0.247723
$634$	−35.0624	+	18.3018i	−1.39251	+	0.726856i
$635$	−3.30572	+	35.5678i	−0.131183	+	1.41147i
$636$	−4.78460	+	6.86546i	−0.189722	+	0.272233i
$637$	18.5178	−	14.4270i	0.733703	−	0.571617i
$638$	−46.1761	+	24.1028i	−1.82813	+	0.954240i
$639$			9.50299i			0.375933i
$640$	25.0740	−	3.36101i	0.991135	−	0.132856i
$641$	−19.2685			−0.761062			−0.380531	−	0.924768i	$-0.624259\pi$
$641$	−19.2685			−0.761062			−0.380531	+	0.924768i	$0.624259\pi$
$642$	6.39349	−	3.33725i	0.252331	−	0.131711i
$643$		−	8.44962i		−	0.333220i	−0.986023	−	0.166610i	$-0.946718\pi$
$643$		−	8.44962i		−	0.333220i	0.986023	−	0.166610i	$-0.0532821\pi$
$644$	−7.27194	−	2.07314i	−0.286554	−	0.0816930i
$645$	−1.48682	−	0.138187i	−0.0585434	−	0.00544110i
$646$	−13.6046	−	26.0637i	−0.535267	−	1.02546i
$647$		−	2.73522i		−	0.107532i	−0.998554	−	0.0537662i	$-0.982877\pi$
$647$		−	2.73522i		−	0.107532i	0.998554	−	0.0537662i	$-0.0171226\pi$
$648$	2.80544	+	0.359858i	0.110208	+	0.0141365i
$649$		−	24.7090i		−	0.969912i
$650$	−6.91065	−	22.6834i	−0.271058	−	0.889716i
$651$	7.35167	−	2.52576i	0.288135	−	0.0989923i
$652$	24.4000	−	35.0117i	0.955576	−	1.37116i
$653$			11.3268i			0.443253i	0.975132	+	0.221627i	$0.0711366\pi$
$653$			11.3268i			0.443253i	−0.975132	+	0.221627i	$0.928863\pi$
$654$	−18.6935	+	9.75757i	−0.730974	+	0.381551i
$655$	−0.864928	+	9.30617i	−0.0337955	+	0.363622i
$656$	13.3395	−	4.92225i	0.520819	−	0.192182i
$657$	7.52091			0.293419
$658$	1.88419	+	1.78651i	0.0734532	+	0.0696453i
$659$			29.0409i			1.13127i	0.824654	+	0.565637i	$0.191370\pi$
$659$			29.0409i			1.13127i	−0.824654	+	0.565637i	$0.808630\pi$
$660$	14.1642	+	11.9624i	0.551340	+	0.465637i
$661$			40.7524i			1.58508i	0.609818	+	0.792541i	$0.291242\pi$
$661$			40.7524i			1.58508i	−0.609818	+	0.792541i	$0.708758\pi$
$662$	29.2136	−	15.2488i	1.13542	−	0.592662i
$663$		−	10.6912i		−	0.415212i
$664$	1.89092	−	14.7416i	0.0733820	−	0.572085i
$665$	−37.4889	+	9.10478i	−1.45376	+	0.353068i
$666$	11.9642	−	6.24505i	0.463604	−	0.241991i
$667$	−12.6962			−0.491598
$668$	−24.0772	−	16.7796i	−0.931576	−	0.649224i
$669$	10.0483			0.388491
$670$	−20.6602	+	8.45384i	−0.798174	+	0.326600i
$671$	−43.0926			−1.66357
$672$	5.90118	−	13.7541i	0.227643	−	0.530577i
$673$		−	35.8470i		−	1.38180i	−0.722950	−	0.690901i	$-0.757214\pi$
$673$		−	35.8470i		−	1.38180i	0.722950	−	0.690901i	$-0.242786\pi$
$674$	1.59790	−	0.834068i	0.0615489	−	0.0321271i
$675$	0.921454	−	4.91436i	0.0354668	−	0.189154i
$676$	2.00589	−	2.87827i	0.0771496	−	0.110703i
$677$	20.0017			0.768726			0.384363	−	0.923182i	$-0.374421\pi$
$677$	20.0017			0.768726			0.384363	+	0.923182i	$0.374421\pi$
$678$	−9.83938	−	18.8502i	−0.377879	−	0.723939i
$679$	−13.7273	−	39.9556i	−0.526804	−	1.53335i
$680$	4.40513	−	19.6761i	0.168929	−	0.754545i
$681$	12.9107			0.494739
$682$	15.2703	−	7.97074i	0.584730	−	0.305215i
$683$	11.9025			0.455438			0.227719	−	0.973727i	$-0.426873\pi$
$683$	11.9025			0.455438			0.227719	+	0.973727i	$0.426873\pi$
$684$	−7.45686	+	10.6999i	−0.285120	+	0.409121i
$685$	40.7654	+	3.78879i	1.55756	+	0.144762i
$686$	2.53495	−	26.0686i	0.0967848	−	0.995305i
$687$	−20.2148			−0.771245
$688$	0.924710	+	2.50600i	0.0352543	+	0.0955402i
$689$		−	14.0313i		−	0.534551i
$690$	1.71136	+	4.18238i	0.0651505	+	0.159220i
$691$	−10.6264			−0.404246			−0.202123	−	0.979360i	$-0.564784\pi$
$691$	−10.6264			−0.404246			−0.202123	+	0.979360i	$0.564784\pi$
$692$	−23.6403	+	33.9217i	−0.898671	+	1.28951i
$693$	10.3732	−	3.56383i	0.394044	−	0.135379i
$694$	−14.8415	−	28.4332i	−0.563374	−	1.07931i
$695$	−1.70312	+	18.3247i	−0.0646031	+	0.695095i
$696$	3.19716	−	24.9250i	0.121188	−	0.944780i
$697$		−	11.3326i		−	0.429252i
$698$	−18.5803	+	9.69848i	−0.703274	+	0.367093i
$699$	11.8552			0.448404
$700$	−23.6711	−	11.8185i	−0.894685	−	0.446697i
$701$	13.4641			0.508532			0.254266	−	0.967134i	$-0.418166\pi$
$701$	13.4641			0.508532			0.254266	+	0.967134i	$0.418166\pi$
$702$	−4.20426	+	2.19452i	−0.158679	+	0.0828270i
$703$			62.2307i			2.34707i
$704$	8.37050	−	32.0913i	0.315475	−	1.20949i
$705$	0.143598	−	1.54504i	0.00540822	−	0.0581896i
$706$	10.0792	+	19.3097i	0.379337	+	0.726732i
$707$	−2.99896	+	1.03033i	−0.112787	+	0.0387496i
$708$	9.77984	+	6.81566i	0.367549	+	0.256148i
$709$	30.2783			1.13713			0.568563	−	0.822639i	$-0.307499\pi$
$709$	30.2783			1.13713			0.568563	+	0.822639i	$0.307499\pi$
$710$	−11.3806	−	27.8128i	−0.427105	−	1.04380i
$711$		−	12.1118i		−	0.454229i
$712$	1.02080	−	7.95811i	0.0382560	−	0.298243i
$713$	4.19859			0.157239
$714$	−8.65627	−	8.20752i	−0.323953	−	0.307159i
$715$	−30.9531	−	2.87682i	−1.15758	−	0.107587i
$716$	31.1969	+	21.7414i	1.16588	+	0.812513i
$717$	3.95455			0.147685
$718$	8.03348	−	4.19329i	0.299807	−	0.156492i
$719$	16.9891			0.633586			0.316793	−	0.948495i	$-0.397394\pi$
$719$	16.9891			0.633586			0.316793	+	0.948495i	$0.397394\pi$
$720$	−8.64176	+	2.30652i	−0.322059	+	0.0859590i
$721$	−17.0758	+	5.86661i	−0.635936	+	0.218484i
$722$	−15.3936	−	29.4910i	−0.572890	−	1.09754i
$723$	21.4716			0.798539
$724$	25.9076	+	18.0552i	0.962847	+	0.671017i
$725$	−43.6617	−	8.18668i	−1.62156	−	0.304046i
$726$	7.75562	−	4.04825i	0.287838	−	0.150245i
$727$			36.5682i			1.35624i	0.734951	+	0.678120i	$0.237205\pi$
$727$			36.5682i			1.35624i	−0.734951	+	0.678120i	$0.762795\pi$
$728$	5.06811	+	24.5781i	0.187837	+	0.910925i
$729$	−1.00000			−0.0370370
$730$	−22.0118	+	9.00687i	−0.814691	+	0.333359i
$731$	2.12897			0.0787429
$732$	11.8866	−	17.0561i	0.439340	−	0.630412i
$733$	38.7859			1.43259			0.716295	−	0.697797i	$-0.245836\pi$
$733$	38.7859			1.43259			0.716295	+	0.697797i	$0.245836\pi$
$734$	−25.2762	+	13.1936i	−0.932962	+	0.486984i
$735$	−13.1847	+	8.43580i	−0.486326	+	0.311159i
$736$	5.42821	−	5.99016i	0.200086	−	0.220800i
$737$			29.2645i			1.07797i
$738$	−4.45647	+	2.32618i	−0.164045	+	0.0856277i
$739$			41.8959i			1.54116i	0.637341	+	0.770582i	$0.280034\pi$
$739$			41.8959i			1.54116i	−0.637341	+	0.770582i	$0.719966\pi$
$740$	−27.5373	+	32.6057i	−1.01229	+	1.19861i
$741$		−	21.8680i		−	0.803341i
$742$	−11.3607	−	10.7717i	−0.417063	−	0.395442i
$743$	13.4718			0.494233			0.247117	−	0.968986i	$-0.420517\pi$
$743$	13.4718			0.494233			0.247117	+	0.968986i	$0.420517\pi$
$744$	−1.05729	+	8.24263i	−0.0387622	+	0.302190i
$745$	0.595081	−	6.40276i	0.0218021	−	0.234579i
$746$	8.12742	−	4.24232i	0.297566	−	0.155322i
$747$			5.25464i			0.192257i
$748$	−21.6864	−	15.1134i	−0.792932	−	0.552602i
$749$	4.38402	+	12.7605i	0.160189	+	0.466257i
$750$	3.18846	+	15.4866i	0.116426	+	0.565489i
$751$		−	21.3020i		−	0.777320i	−0.921381	−	0.388660i	$-0.872938\pi$
$751$		−	21.3020i		−	0.777320i	0.921381	−	0.388660i	$-0.127062\pi$
$752$	−2.60413	+	0.960922i	−0.0949629	+	0.0350412i
$753$			24.2390i			0.883317i
$754$	19.4973	+	37.3528i	0.710050	+	1.36031i
$755$	16.6451	+	1.54701i	0.605776	+	0.0563016i
$756$	−1.45074	+	5.08875i	−0.0527628	+	0.185076i
$757$			12.6260i			0.458898i	0.973321	+	0.229449i	$0.0736925\pi$
$757$			12.6260i			0.458898i	−0.973321	+	0.229449i	$0.926308\pi$
$758$	−29.4327	+	15.3632i	−1.06904	+	0.558015i
$759$	5.92419			0.215034
$760$	9.01034	−	40.2460i	0.326839	−	1.45988i
$761$		−	23.4789i		−	0.851108i	−0.904933	−	0.425554i	$-0.860079\pi$
$761$		−	23.4789i		−	0.851108i	0.904933	−	0.425554i	$-0.139921\pi$
$762$	−20.0278	+	10.4540i	−0.725530	+	0.378710i
$763$	−12.8181	−	37.3095i	−0.464048	−	1.35069i
$764$	−3.22967	−	2.25079i	−0.116845	−	0.0814306i
$765$	−0.659715	+	7.09818i	−0.0238520	+	0.256635i
$766$	−14.0426	+	7.32991i	−0.507380	+	0.264841i
$767$	−19.9876			−0.721711
$768$	10.3929	+	12.1650i	0.375021	+	0.438968i
$769$		−	5.99496i		−	0.216184i	−0.994141	−	0.108092i	$-0.965526\pi$
$769$		−	5.99496i		−	0.216184i	0.994141	−	0.108092i	$-0.0344741\pi$
$770$	−26.0916	+	22.8531i	−0.940276	+	0.823567i
$771$		−	6.84349i		−	0.246462i
$772$	−12.0558	−	8.40179i	−0.433897	−	0.302387i
$773$	4.98453			0.179281			0.0896406	−	0.995974i	$-0.471428\pi$
$773$	4.98453			0.179281			0.0896406	+	0.995974i	$0.471428\pi$
$774$	−0.437003	−	0.837208i	−0.0157077	−	0.0300928i
$775$	14.4388	+	2.70731i	0.518658	+	0.0972495i
$776$	44.7979	+	5.74628i	1.60815	+	0.206279i
$777$	8.20387	+	23.8788i	0.294312	+	0.856648i
$778$	−2.11756	−	4.05680i	−0.0759181	−	0.145444i
$779$		−	23.1799i		−	0.830506i
$780$	9.67666	−	11.4577i	0.346480	−	0.410252i
$781$	−39.3958			−1.40969
$782$	−2.98135	−	5.71166i	−0.106613	−	0.204248i
$783$			8.88452i			0.317507i
$784$	23.7907	+	14.7649i	0.849669	+	0.527317i
$785$	−0.265359	+	2.85513i	−0.00947108	+	0.101904i
$786$	−5.24019	+	2.73526i	−0.186911	+	0.0975633i
$787$			9.43059i			0.336164i	0.985773	+	0.168082i	$0.0537573\pi$
$787$			9.43059i			0.336164i	−0.985773	+	0.168082i	$0.946243\pi$
$788$	−6.64638	−	4.63192i	−0.236768	−	0.165005i
$789$			26.0905i			0.928845i
$790$	14.5048	+	35.4481i	0.516059	+	1.26119i
$791$	37.6223	−	12.9256i	1.33769	−	0.459582i
$792$	−1.49183	+	11.6303i	−0.0530100	+	0.413265i
$793$			34.8585i			1.23786i
$794$	17.3494	+	33.2378i	0.615706	+	1.17957i
$795$	−0.865822	+	9.31579i	−0.0307076	+	0.330397i
$796$	27.2927	−	39.1625i	0.967364	−	1.38808i
$797$	−20.0949			−0.711797			−0.355898	−	0.934525i	$-0.615825\pi$
$797$	−20.0949			−0.711797			−0.355898	+	0.934525i	$0.615825\pi$
$798$	−17.7057	−	16.7878i	−0.626776	−	0.594283i
$799$			2.21234i			0.0782671i
$800$	22.5299	−	17.0998i	0.796554	−	0.604568i
$801$			2.83667i			0.100229i
$802$	3.22681	+	6.18190i	0.113943	+	0.218290i
$803$			31.1789i			1.10028i
$804$	−11.5829	−	8.07223i	−0.408498	−	0.284686i
$805$	−8.21540	+	1.99524i	−0.289555	+	0.0703231i
$806$	−6.44770	−	12.3525i	−0.227111	−	0.435097i
$807$	−8.74121			−0.307705
$808$	0.431300	−	3.36241i	0.0151731	−	0.118289i
$809$	−1.73923			−0.0611480			−0.0305740	−	0.999533i	$-0.509734\pi$
$809$	−1.73923			−0.0611480			−0.0305740	+	0.999533i	$0.509734\pi$
$810$	2.92674	−	1.19758i	0.102835	−	0.0420786i
$811$	−17.6292			−0.619044			−0.309522	−	0.950892i	$-0.600169\pi$
$811$	−17.6292			−0.619044			−0.309522	+	0.950892i	$0.600169\pi$
$812$	45.2111	+	12.8891i	1.58660	+	0.452319i
$813$		−	14.8967i		−	0.522451i
$814$	25.8896	+	49.5992i	0.907430	+	1.73845i
$815$	4.41542	−	47.5076i	0.154665	−	1.66412i
$816$	11.9638	−	4.41464i	0.418818	−	0.154543i
$817$	4.35465			0.152350
$818$	−16.1319	+	8.42049i	−0.564040	+	0.294416i
$819$	−2.88286	−	8.39108i	−0.100735	−	0.293208i
$820$	10.2572	−	12.1451i	0.358196	−	0.424125i
$821$	41.3089			1.44169			0.720846	−	0.693095i	$-0.243753\pi$
$821$	41.3089			1.44169			0.720846	+	0.693095i	$0.243753\pi$
$822$	11.9817	+	22.9545i	0.417909	+	0.800629i
$823$	38.9835			1.35888			0.679440	−	0.733731i	$-0.262223\pi$
$823$	38.9835			1.35888			0.679440	+	0.733731i	$0.262223\pi$
$824$	2.45579	−	19.1452i	0.0855513	−	0.666956i
$825$	20.3731	+	3.82000i	0.709300	+	0.132995i
$826$	−15.3443	+	16.1833i	−0.533896	+	0.563087i
$827$	3.65170			0.126982			0.0634911	−	0.997982i	$-0.479777\pi$
$827$	3.65170			0.126982			0.0634911	+	0.997982i	$0.479777\pi$
$828$	−1.63411	+	2.34480i	−0.0567894	+	0.0814875i
$829$		−	18.9941i		−	0.659693i	−0.944035	−	0.329846i	$-0.893003\pi$
$829$		−	18.9941i		−	0.659693i	0.944035	−	0.329846i	$-0.106997\pi$
$830$	−6.29284	−	15.3790i	−0.218428	−	0.533812i
$831$	8.86971			0.307687
$832$	−25.9593	−	6.77108i	−0.899978	−	0.234745i
$833$	17.6045	−	13.7154i	0.609960	−	0.475210i
$834$	−10.3184	+	5.38597i	−0.357297	+	0.186501i
$835$	−32.6706	−	3.03645i	−1.13061	−	0.105081i
$836$	−44.3578	−	30.9133i	−1.53415	−	1.06916i
$837$		−	2.93809i		−	0.101555i
$838$	−3.85306	−	7.38168i	−0.133102	−	0.254996i
$839$	36.3049			1.25339			0.626693	−	0.779266i	$-0.284408\pi$
$839$	36.3049			1.25339			0.626693	+	0.779266i	$0.284408\pi$
$840$	−1.84823	−	16.6308i	−0.0637701	−	0.573818i
$841$	49.9348			1.72189
$842$	9.04953	+	17.3370i	0.311867	+	0.597474i
$843$			7.14815i			0.246195i
$844$	10.2267	+	7.12706i	0.352017	+	0.245324i
$845$	0.362986	−	3.90554i	0.0124871	−	0.134355i
$846$	0.869993	−	0.454116i	0.0299110	−	0.0156128i
$847$	5.31803	+	15.4791i	0.182730	+	0.531867i
$848$	15.7016	−	5.79386i	0.539194	−	0.198962i
$849$	−2.57635			−0.0884202
$850$	−6.56980	−	21.5646i	−0.225342	−	0.739660i
$851$			13.6374i			0.467483i
$852$	10.8668	−	15.5929i	0.372292	−	0.534205i
$853$	17.8797			0.612189			0.306094	−	0.952001i	$-0.400978\pi$
$853$	17.8797			0.612189			0.306094	+	0.952001i	$0.400978\pi$
$854$	28.2237	+	26.7605i	0.965795	+	0.915727i
$855$	−1.34940	+	14.5188i	−0.0461483	+	0.496532i
$856$	−14.3069	−	1.83517i	−0.489000	−	0.0627247i
$857$	36.5307			1.24786			0.623932	−	0.781478i	$-0.285534\pi$
$857$	36.5307			1.24786			0.623932	+	0.781478i	$0.285534\pi$
$858$	−9.09767	−	17.4293i	−0.310589	−	0.595025i
$859$	−10.2299			−0.349038			−0.174519	−	0.984654i	$-0.555837\pi$
$859$	−10.2299			−0.349038			−0.174519	+	0.984654i	$0.555837\pi$
$860$	2.28161	+	1.92695i	0.0778024	+	0.0657083i
$861$	−3.05581	−	8.89446i	−0.104142	−	0.303122i
$862$	32.9882	−	17.2191i	1.12358	−	0.586484i
$863$	31.2788			1.06474			0.532372	−	0.846511i	$-0.321301\pi$
$863$	31.2788			1.06474			0.532372	+	0.846511i	$0.321301\pi$
$864$	−4.19179	−	3.79854i	−0.142607	−	0.129229i
$865$	−4.27796	+	46.0286i	−0.145455	+	1.56502i
$866$	0.734697	+	1.40753i	0.0249660	+	0.0478298i
$867$			6.83611i			0.232167i
$868$	−14.9512	−	4.26239i	−0.507476	−	0.144675i
$869$	50.2110			1.70329
$870$	−10.6399	−	26.0027i	−0.360726	−	0.881574i
$871$	23.6727			0.802117
$872$	41.8311	+	5.36572i	1.41658	+	0.181706i
$873$	−15.9682			−0.540442
$874$	−6.09812	−	11.6827i	−0.206272	−	0.395175i
$875$	−29.5390	+	1.56417i	−0.998601	+	0.0528786i
$876$	−12.3406	−	8.60030i	−0.416951	−	0.290577i
$877$		−	9.19346i		−	0.310441i	−0.987880	−	0.155220i	$-0.950391\pi$
$877$		−	9.19346i		−	0.310441i	0.987880	−	0.155220i	$-0.0496088\pi$
$878$	4.63434	+	8.87845i	0.156401	+	0.299633i
$879$			25.4873i			0.859664i
$880$	−9.56197	−	35.8255i	−0.322334	−	1.20768i
$881$		−	7.56097i		−	0.254736i	−0.991856	−	0.127368i	$-0.959347\pi$
$881$		−	7.56097i		−	0.254736i	0.991856	−	0.127368i	$-0.0406528\pi$
$882$	−9.00709	−	4.10759i	−0.303285	−	0.138310i
$883$	−33.5250			−1.12821			−0.564103	−	0.825705i	$-0.690778\pi$
$883$	−33.5250			−1.12821			−0.564103	+	0.825705i	$0.690778\pi$
$884$	−12.2256	+	17.5426i	−0.411191	+	0.590021i
$885$	13.2703	+	1.23336i	0.446078	+	0.0414591i
$886$	−8.81598	−	16.8896i	−0.296179	−	0.567418i
$887$			45.8345i			1.53897i	0.638663	+	0.769486i	$0.279488\pi$
$887$			45.8345i			1.53897i	−0.638663	+	0.769486i	$0.720512\pi$
$888$	−26.7727	−	3.43417i	−0.898434	−	0.115243i
$889$	−13.7331	−	39.9725i	−0.460592	−	1.34063i
$890$	−3.39713	−	8.30219i	−0.113872	−	0.278290i
$891$		−	4.14562i		−	0.138884i
$892$	−16.4877	−	11.4904i	−0.552050	−	0.384728i
$893$			4.52518i			0.151429i
$894$	3.60531	−	1.88189i	0.120580	−	0.0629398i
$895$	42.3312	+	3.93432i	1.41498	+	0.131510i
$896$	−25.4110	+	15.8203i	−0.848922	+	0.528518i
$897$		−	4.79221i		−	0.160007i
$898$	13.8276	+	26.4909i	0.461434	+	0.884012i
$899$	−26.1035			−0.870601
$900$	−7.13162	+	7.00999i	−0.237721	+	0.233666i
$901$		−	13.3393i		−	0.444396i
$902$	−9.64345	−	18.4749i	−0.321092	−	0.615146i
$903$	1.67094	−	0.574074i	0.0556055	−	0.0191040i
$904$	−5.41071	+	42.1818i	−0.179958	+	1.40295i
$905$	35.1542	+	3.26728i	1.16856	+	0.108608i
$906$	4.89229	+	9.37262i	0.162535	+	0.311384i
$907$	−10.4401			−0.346658			−0.173329	−	0.984864i	$-0.555452\pi$
$907$	−10.4401			−0.346658			−0.173329	+	0.984864i	$0.555452\pi$
$908$	−21.1844	−	14.7636i	−0.703030	−	0.489948i
$909$			1.19853i			0.0397528i
$910$	18.4863	+	21.1061i	0.612816	+	0.699659i
$911$		−	7.71906i		−	0.255744i	−0.991791	−	0.127872i	$-0.959185\pi$
$911$		−	7.71906i		−	0.255744i	0.991791	−	0.127872i	$-0.0408146\pi$
$912$	24.4711	−	9.02981i	0.810318	−	0.299007i
$913$	−21.7838			−0.720938
$914$	8.39751	−	4.38330i	0.277765	−	0.144987i
$915$	2.15099	−	23.1436i	0.0711096	−	0.765102i
$916$	33.1694	+	23.1160i	1.09595	+	0.763776i
$917$	−3.59320	−	10.4586i	−0.118658	−	0.345375i
$918$	−3.99690	+	2.08629i	−0.131917	+	0.0688577i
$919$			2.09031i			0.0689530i	0.999406	+	0.0344765i	$0.0109764\pi$
$919$			2.09031i			0.0689530i	−0.999406	+	0.0344765i	$0.989024\pi$
$920$	1.97455	−	8.81960i	0.0650989	−	0.290774i
$921$	−19.5890			−0.645479
$922$	−48.7345	+	25.4383i	−1.60498	+	0.837764i
$923$			31.8681i			1.04895i
$924$	−21.0960	−	6.01421i	−0.694009	−	0.197853i
$925$	−8.79357	+	46.8985i	−0.289131	+	1.54201i
$926$	9.58003	+	18.3534i	0.314819	+	0.603129i
$927$			6.82433i			0.224140i
$928$	−33.7483	+	37.2420i	−1.10784	+	1.22253i
$929$			37.8995i			1.24344i	0.783238	+	0.621722i	$0.213566\pi$
$929$			37.8995i			1.24344i	−0.783238	+	0.621722i	$0.786434\pi$
$930$	3.51858	+	8.59902i	0.115379	+	0.281973i
$931$	36.0086	−	28.0538i	1.18014	−	0.919426i
$932$	−19.4525	−	13.5566i	−0.637187	−	0.444061i
$933$		−	25.9353i		−	0.849085i
$934$	30.9299	−	16.1447i	1.01206	−	0.528271i
$935$	−29.4264	−	2.73493i	−0.962346	−	0.0894417i
$936$	9.40801	+	1.20678i	0.307510	+	0.0394447i
$937$	−6.24587			−0.204044			−0.102022	−	0.994782i	$-0.532531\pi$
$937$	−6.24587			−0.204044			−0.102022	+	0.994782i	$0.532531\pi$
$938$	18.1732	−	19.1669i	0.593378	−	0.625821i
$939$			8.23386i			0.268702i
$940$	−2.00240	+	2.37096i	−0.0653112	+	0.0773323i
$941$			21.7262i			0.708253i	0.935197	+	0.354127i	$0.115222\pi$
$941$			21.7262i			0.708253i	−0.935197	+	0.354127i	$0.884778\pi$
$942$	−1.60769	+	0.839174i	−0.0523812	+	0.0273418i
$943$		−	5.07969i		−	0.165418i
$944$	−8.25335	−	22.3669i	−0.268624	−	0.727979i
$945$	1.39623	+	5.74896i	0.0454193	+	0.187014i
$946$	3.47075	−	1.81165i	0.112844	−	0.0589018i
$947$	11.2143			0.364415			0.182208	−	0.983260i	$-0.441676\pi$
$947$	11.2143			0.364415			0.182208	+	0.983260i	$0.441676\pi$
$948$	−13.8501	+	19.8736i	−0.449830	+	0.645464i
$949$	25.2213			0.818717
$950$	−13.4380	−	44.1087i	−0.435987	−	1.43108i
$951$	−27.9672			−0.906899
$952$	4.81814	+	23.3659i	0.156157	+	0.757292i
$953$		−	30.9796i		−	1.00353i	−0.865005	−	0.501764i	$-0.832685\pi$
$953$		−	30.9796i		−	1.00353i	0.865005	−	0.501764i	$-0.167315\pi$
$954$	−5.24560	+	2.73808i	−0.169833	+	0.0886487i
$955$	−4.38236	−	0.407303i	−0.141810	−	0.0131800i
$956$	−6.48879	−	4.52210i	−0.209863	−	0.146255i
$957$	−36.8319			−1.19061
$958$	−6.72302	−	12.8799i	−0.217211	−	0.416132i
$959$	−45.8137	+	15.7399i	−1.47940	+	0.508267i
$960$	16.8173	+	6.09737i	0.542777	+	0.196792i
$961$	−22.3676			−0.721537
$962$	40.1219	−	20.9427i	1.29358	−	0.675219i
$963$	5.09970			0.164336
$964$	−35.2316	−	24.5532i	−1.13473	−	0.790806i
$965$	−16.3586	−	1.52039i	−0.526602	−	0.0489431i
$966$	−3.88008	−	3.67893i	−0.124839	−	0.118368i
$967$	48.5226			1.56038			0.780190	−	0.625542i	$-0.215122\pi$
$967$	48.5226			1.56038			0.780190	+	0.625542i	$0.215122\pi$
$968$	−17.3550	−	2.22615i	−0.557811	−	0.0715511i
$969$		−	20.7894i		−	0.667853i
$970$	46.7348	−	19.1232i	1.50056	−	0.614008i
$971$	55.7545			1.78925			0.894624	−	0.446820i	$-0.147444\pi$
$971$	55.7545			1.78925			0.894624	+	0.446820i	$0.147444\pi$
$972$	1.64084	+	1.14352i	0.0526301	+	0.0366784i
$973$	−7.07533	−	20.5940i	−0.226825	−	0.660213i
$974$	10.0611	+	19.2749i	0.322377	+	0.617609i
$975$	3.09008	−	16.4802i	0.0989618	−	0.527790i
$976$	−39.0079	+	14.3939i	−1.24861	+	0.460737i
$977$			15.4305i			0.493667i	0.969058	+	0.246833i	$0.0793900\pi$
$977$			15.4305i			0.493667i	−0.969058	+	0.246833i	$0.920610\pi$
$978$	26.7509	−	13.9634i	0.855400	−	0.446499i
$979$	−11.7598			−0.375843
$980$	31.2806	+	1.23517i	0.999221	+	0.0394561i
$981$	−14.9107			−0.476062
$982$	18.5757	−	9.69611i	0.592776	−	0.309415i
$983$		−	29.4115i		−	0.938081i	−0.883177	−	0.469040i	$-0.844600\pi$
$983$		−	29.4115i		−	0.938081i	0.883177	−	0.469040i	$-0.155400\pi$
$984$	9.97240	+	1.27917i	0.317908	+	0.0407785i
$985$	−9.01853	−	0.838194i	−0.287354	−	0.0267071i
$986$	18.5357	+	35.5105i	0.590296	+	1.13089i
$987$	0.596554	+	1.73638i	0.0189885	+	0.0552695i
$988$	−25.0065	+	35.8820i	−0.795562	+	1.14156i
$989$	0.954288			0.0303446
$990$	4.96470	+	12.1332i	0.157789	+	0.385617i
$991$			37.8845i			1.20344i	0.798707	+	0.601720i	$0.205518\pi$
$991$			37.8845i			1.20344i	−0.798707	+	0.601720i	$0.794482\pi$
$992$	11.1605	−	12.3158i	0.354345	−	0.391028i
$993$	23.3019			0.739464
$994$	25.8025	+	24.4648i	0.818405	+	0.775978i
$995$	4.93889	−	53.1399i	0.156573	−	1.68465i
$996$	6.00878	−	8.62205i	0.190396	−	0.273200i
$997$	3.24991			0.102926			0.0514629	−	0.998675i	$-0.483612\pi$
$997$	3.24991			0.102926			0.0514629	+	0.998675i	$0.483612\pi$
$998$	−22.3051	+	11.6427i	−0.706054	+	0.368544i
$999$	9.54315			0.301932

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.i.a.139.17	✓	48
4.3	odd	2	inner	420.2.i.a.139.30	yes	48
5.4	even	2	inner	420.2.i.a.139.32	yes	48
7.6	odd	2	inner	420.2.i.a.139.18	yes	48
20.19	odd	2	inner	420.2.i.a.139.19	yes	48
28.27	even	2	inner	420.2.i.a.139.29	yes	48
35.34	odd	2	inner	420.2.i.a.139.31	yes	48
140.139	even	2	inner	420.2.i.a.139.20	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.i.a.139.17	✓	48	1.1	even	1	trivial
420.2.i.a.139.18	yes	48	7.6	odd	2	inner
420.2.i.a.139.19	yes	48	20.19	odd	2	inner
420.2.i.a.139.20	yes	48	140.139	even	2	inner
420.2.i.a.139.29	yes	48	28.27	even	2	inner
420.2.i.a.139.30	yes	48	4.3	odd	2	inner
420.2.i.a.139.31	yes	48	35.34	odd	2	inner
420.2.i.a.139.32	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)

\(f(q)\)	\(=\)	\(q+(-0.654401 - 1.25370i) q^{2} -1.00000i q^{3} +(-1.14352 + 1.64084i) q^{4} +(-0.206931 + 2.22647i) q^{5} +(-1.25370 + 0.654401i) q^{6} +(-0.859661 - 2.50220i) q^{7} +(2.80544 + 0.359858i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.654401 - 1.25370i) q^{2} -1.00000i q^{3} +(-1.14352 + 1.64084i) q^{4} +(-0.206931 + 2.22647i) q^{5} +(-1.25370 + 0.654401i) q^{6} +(-0.859661 - 2.50220i) q^{7} +(2.80544 + 0.359858i) q^{8} -1.00000 q^{9} +(2.92674 - 1.19758i) q^{10} -4.14562i q^{11} +(1.64084 + 1.14352i) q^{12} -3.35349 q^{13} +(-2.57443 + 2.71520i) q^{14} +(2.22647 + 0.206931i) q^{15} +(-1.38473 - 3.75267i) q^{16} -3.18809 q^{17} +(0.654401 + 1.25370i) q^{18} -6.52098 q^{19} +(-3.41666 - 2.88555i) q^{20} +(-2.50220 + 0.859661i) q^{21} +(-5.19736 + 2.71290i) q^{22} -1.42902 q^{23} +(0.359858 - 2.80544i) q^{24} +(-4.91436 - 0.921454i) q^{25} +(2.19452 + 4.20426i) q^{26} +1.00000i q^{27} +(5.08875 + 1.45074i) q^{28} +8.88452 q^{29} +(-1.19758 - 2.92674i) q^{30} -2.93809 q^{31} +(-3.79854 + 4.19179i) q^{32} -4.14562 q^{33} +(2.08629 + 3.99690i) q^{34} +(5.74896 - 1.39623i) q^{35} +(1.14352 - 1.64084i) q^{36} -9.54315i q^{37} +(4.26734 + 8.17534i) q^{38} +3.35349i q^{39} +(-1.38175 + 6.17177i) q^{40} +3.55466i q^{41} +(2.71520 + 2.57443i) q^{42} -0.667790 q^{43} +(6.80232 + 4.74060i) q^{44} +(0.206931 - 2.22647i) q^{45} +(0.935154 + 1.79156i) q^{46} -0.693941i q^{47} +(-3.75267 + 1.38473i) q^{48} +(-5.52197 + 4.30208i) q^{49} +(2.06074 + 6.76412i) q^{50} +3.18809i q^{51} +(3.83477 - 5.50254i) q^{52} +4.18410i q^{53} +(1.25370 - 0.654401i) q^{54} +(9.23012 + 0.857859i) q^{55} +(-1.51130 - 7.32912i) q^{56} +6.52098i q^{57} +(-5.81404 - 11.1385i) q^{58} +5.96025 q^{59} +(-2.88555 + 3.41666i) q^{60} -10.3947i q^{61} +(1.92269 + 3.68347i) q^{62} +(0.859661 + 2.50220i) q^{63} +(7.74101 + 2.01912i) q^{64} +(0.693941 - 7.46644i) q^{65} +(2.71290 + 5.19736i) q^{66} -7.05912 q^{67} +(3.64563 - 5.23115i) q^{68} +1.42902i q^{69} +(-5.51258 - 6.29377i) q^{70} -9.50299i q^{71} +(-2.80544 - 0.359858i) q^{72} -7.52091 q^{73} +(-11.9642 + 6.24505i) q^{74} +(-0.921454 + 4.91436i) q^{75} +(7.45686 - 10.6999i) q^{76} +(-10.3732 + 3.56383i) q^{77} +(4.20426 - 2.19452i) q^{78} +12.1118i q^{79} +(8.64176 - 2.30652i) q^{80} +1.00000 q^{81} +(4.45647 - 2.32618i) q^{82} -5.25464i q^{83} +(1.45074 - 5.08875i) q^{84} +(0.659715 - 7.09818i) q^{85} +(0.437003 + 0.837208i) q^{86} -8.88452i q^{87} +(1.49183 - 11.6303i) q^{88} -2.83667i q^{89} +(-2.92674 + 1.19758i) q^{90} +(2.88286 + 8.39108i) q^{91} +(1.63411 - 2.34480i) q^{92} +2.93809i q^{93} +(-0.869993 + 0.454116i) q^{94} +(1.34940 - 14.5188i) q^{95} +(4.19179 + 3.79854i) q^{96} +15.9682 q^{97} +(9.00709 + 4.10759i) q^{98} +4.14562i 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

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