LMFDB - Embedded newform 420.2.bv.c.53.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(53,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 9, 8]))

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

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

chi := DirichletCharacter("420.53");

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.bv (of order $12$, degree $4$, 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:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			53.6
Character	$\chi$	$=$	420.53
Dual form			420.2.bv.c.317.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.302208 - 1.70548i) q^{3} +(-1.92665 + 1.13491i) q^{5} +(-0.225753 + 2.63610i) q^{7} +(-2.81734 + 1.03082i) q^{9} +O(q^{10})$	\(q+(-0.302208 - 1.70548i) q^{3} +(-1.92665 + 1.13491i) q^{5} +(-0.225753 + 2.63610i) q^{7} +(-2.81734 + 1.03082i) q^{9} +(1.86244 + 1.07528i) q^{11} +(3.89727 + 3.89727i) q^{13} +(2.51782 + 2.94289i) q^{15} +(-4.10211 + 1.09916i) q^{17} +(-0.631006 + 0.364311i) q^{19} +(4.56405 - 0.411633i) q^{21} +(5.55616 + 1.48877i) q^{23} +(2.42395 - 4.37315i) q^{25} +(2.60947 + 4.49340i) q^{27} -3.95947 q^{29} +(-2.33251 + 4.04003i) q^{31} +(1.27103 - 3.50133i) q^{33} +(-2.55680 - 5.33505i) q^{35} +(2.23265 + 0.598238i) q^{37} +(5.46894 - 7.82450i) q^{39} -4.95231i q^{41} +(3.57830 + 3.57830i) q^{43} +(4.25814 - 5.18346i) q^{45} +(-2.50295 + 9.34112i) q^{47} +(-6.89807 - 1.19022i) q^{49} +(3.11428 + 6.66390i) q^{51} +(1.66848 + 6.22687i) q^{53} +(-4.80863 + 0.0420191i) q^{55} +(0.812022 + 0.966072i) q^{57} +(-4.01205 + 6.94907i) q^{59} +(-6.20108 - 10.7406i) q^{61} +(-2.08132 - 7.65951i) q^{63} +(-11.9317 - 3.08561i) q^{65} +(0.162395 + 0.606066i) q^{67} +(0.859954 - 9.92585i) q^{69} -4.00247i q^{71} +(-10.4387 + 2.79703i) q^{73} +(-8.19087 - 2.81240i) q^{75} +(-3.25501 + 4.66685i) q^{77} +(6.61039 - 3.81651i) q^{79} +(6.87482 - 5.80834i) q^{81} +(-6.56196 + 6.56196i) q^{83} +(6.65587 - 6.77322i) q^{85} +(1.19658 + 6.75282i) q^{87} +(0.656714 + 1.13746i) q^{89} +(-11.1534 + 9.39378i) q^{91} +(7.59510 + 2.75713i) q^{93} +(0.802265 - 1.41804i) q^{95} +(10.0207 - 10.0207i) q^{97} +(-6.35557 - 1.10959i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{3} - 8 q^{7}+O(q^{10}) $ 48 * q - 2 * q^3 - 8 * q^7	$ 48 q - 2 q^{3} - 8 q^{7} + 32 q^{13} - 16 q^{21} + 16 q^{25} - 32 q^{27} - 64 q^{31} + 34 q^{33} - 40 q^{37} - 24 q^{43} + 30 q^{45} + 36 q^{51} + 92 q^{57} - 18 q^{63} + 28 q^{67} - 8 q^{73} - 38 q^{75} + 20 q^{81} - 56 q^{85} - 24 q^{87} - 24 q^{91} + 6 q^{93} + 56 q^{97}+O(q^{100}) $ 48 * q - 2 * q^3 - 8 * q^7 + 32 * q^13 - 16 * q^21 + 16 * q^25 - 32 * q^27 - 64 * q^31 + 34 * q^33 - 40 * q^37 - 24 * q^43 + 30 * q^45 + 36 * q^51 + 92 * q^57 - 18 * q^63 + 28 * q^67 - 8 * q^73 - 38 * q^75 + 20 * q^81 - 56 * q^85 - 24 * q^87 - 24 * q^91 + 6 * q^93 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.302208	−	1.70548i	−0.174480	−	0.984661i
$3$	−0.302208	−	1.70548i	−0.174480	−	0.984661i
$4$		0			0
$5$	−1.92665	+	1.13491i	−0.861623	+	0.507548i
$5$	−1.92665	+	1.13491i	−0.861623	+	0.507548i
$6$		0			0
$7$	−0.225753	+	2.63610i	−0.0853265	+	0.996353i
$7$	−0.225753	+	2.63610i	−0.0853265	+	0.996353i
$8$		0			0
$9$	−2.81734	+	1.03082i	−0.939114	+	0.343607i
$10$		0			0
$11$	1.86244	+	1.07528i	0.561548	+	0.324210i	0.753767	−	0.657142i	$-0.228235\pi$
$11$	1.86244	+	1.07528i	0.561548	+	0.324210i	−0.192218	+	0.981352i	$0.561568\pi$
$12$		0			0
$13$	3.89727	+	3.89727i	1.08091	+	1.08091i	0.996425	+	0.0844823i	$0.0269237\pi$
$13$	3.89727	+	3.89727i	1.08091	+	1.08091i	0.0844823	+	0.996425i	$0.473076\pi$
$14$		0			0
$15$	2.51782	+	2.94289i	0.650099	+	0.759850i
$16$		0			0
$17$	−4.10211	+	1.09916i	−0.994907	+	0.266584i	−0.719310	−	0.694689i	$-0.755542\pi$
$17$	−4.10211	+	1.09916i	−0.994907	+	0.266584i	−0.275596	+	0.961273i	$0.588875\pi$
$18$		0			0
$19$	−0.631006	+	0.364311i	−0.144763	+	0.0835788i	−0.570632	−	0.821206i	$-0.693302\pi$
$19$	−0.631006	+	0.364311i	−0.144763	+	0.0835788i	0.425869	+	0.904785i	$0.359968\pi$
$20$		0			0
$21$	4.56405	−	0.411633i	0.995957	−	0.0898257i
$22$		0			0
$23$	5.55616	+	1.48877i	1.15854	+	0.310430i	0.786382	−	0.617740i	$-0.211952\pi$
$23$	5.55616	+	1.48877i	1.15854	+	0.310430i	0.372157	+	0.928170i	$0.378618\pi$
$24$		0			0
$25$	2.42395	−	4.37315i	0.484790	−	0.874631i
$26$		0			0
$27$	2.60947	+	4.49340i	0.502192	+	0.864756i
$28$		0			0
$29$	−3.95947			−0.735256			−0.367628	−	0.929973i	$-0.619830\pi$
$29$	−3.95947			−0.735256			−0.367628	+	0.929973i	$0.619830\pi$
$30$		0			0
$31$	−2.33251	+	4.04003i	−0.418931	+	0.725610i	−0.995832	−	0.0912037i	$-0.970929\pi$
$31$	−2.33251	+	4.04003i	−0.418931	+	0.725610i	0.576901	+	0.816814i	$0.304262\pi$
$32$		0			0
$33$	1.27103	−	3.50133i	0.221258	−	0.609503i
$34$		0			0
$35$	−2.55680	−	5.33505i	−0.432178	−	0.901788i
$36$		0			0
$37$	2.23265	+	0.598238i	0.367046	+	0.0983497i	0.437628	−	0.899156i	$-0.355819\pi$
$37$	2.23265	+	0.598238i	0.367046	+	0.0983497i	−0.0705816	+	0.997506i	$0.522486\pi$
$38$		0			0
$39$	5.46894	−	7.82450i	0.875731	−	1.25292i
$40$		0			0
$41$		−	4.95231i		−	0.773420i	−0.922201	−	0.386710i	$-0.873611\pi$
$41$		−	4.95231i		−	0.773420i	0.922201	−	0.386710i	$-0.126389\pi$
$42$		0			0
$43$	3.57830	+	3.57830i	0.545686	+	0.545686i	0.925190	−	0.379504i	$-0.123905\pi$
$43$	3.57830	+	3.57830i	0.545686	+	0.545686i	−0.379504	+	0.925190i	$0.623905\pi$
$44$		0			0
$45$	4.25814	−	5.18346i	0.634765	−	0.772705i
$46$		0			0
$47$	−2.50295	+	9.34112i	−0.365092	+	1.36254i	0.502204	+	0.864749i	$0.332523\pi$
$47$	−2.50295	+	9.34112i	−0.365092	+	1.36254i	−0.867296	+	0.497793i	$0.834144\pi$
$48$		0			0
$49$	−6.89807	−	1.19022i	−0.985439	−	0.170031i
$50$		0			0
$51$	3.11428	+	6.66390i	0.436086	+	0.933132i
$52$		0			0
$53$	1.66848	+	6.22687i	0.229184	+	0.855326i	0.980685	+	0.195594i	$0.0626635\pi$
$53$	1.66848	+	6.22687i	0.229184	+	0.855326i	−0.751501	+	0.659732i	$0.770670\pi$
$54$		0			0
$55$	−4.80863	+	0.0420191i	−0.648395	+	0.00566586i
$56$		0			0
$57$	0.812022	+	0.966072i	0.107555	+	0.127959i
$58$		0			0
$59$	−4.01205	+	6.94907i	−0.522324	+	0.904692i	0.477339	+	0.878719i	$0.341601\pi$
$59$	−4.01205	+	6.94907i	−0.522324	+	0.904692i	−0.999663	+	0.0259723i	$0.991732\pi$
$60$		0			0
$61$	−6.20108	−	10.7406i	−0.793967	−	1.37519i	−0.923493	−	0.383615i	$-0.874679\pi$
$61$	−6.20108	−	10.7406i	−0.793967	−	1.37519i	0.129526	−	0.991576i	$-0.458654\pi$
$62$		0			0
$63$	−2.08132	−	7.65951i	−0.262222	−	0.965008i
$64$		0			0
$65$	−11.9317	−	3.08561i	−1.47995	−	0.382722i
$66$		0			0
$67$	0.162395	+	0.606066i	0.0198397	+	0.0740427i	0.975136	−	0.221608i	$-0.0711304\pi$
$67$	0.162395	+	0.606066i	0.0198397	+	0.0740427i	−0.955296	+	0.295650i	$0.904464\pi$
$68$		0			0
$69$	0.859954	−	9.92585i	0.103526	−	1.19493i
$70$		0			0
$71$		−	4.00247i		−	0.475006i	−0.971387	−	0.237503i	$-0.923671\pi$
$71$		−	4.00247i		−	0.475006i	0.971387	−	0.237503i	$-0.0763290\pi$
$72$		0			0
$73$	−10.4387	+	2.79703i	−1.22175	+	0.327368i	−0.811364	−	0.584542i	$-0.801274\pi$
$73$	−10.4387	+	2.79703i	−1.22175	+	0.327368i	−0.410391	+	0.911910i	$0.634608\pi$
$74$		0			0
$75$	−8.19087	−	2.81240i	−0.945801	−	0.324748i
$76$		0			0
$77$	−3.25501	+	4.66685i	−0.370943	+	0.531837i
$78$		0			0
$79$	6.61039	−	3.81651i	0.743727	−	0.429391i	−0.0796961	−	0.996819i	$-0.525395\pi$
$79$	6.61039	−	3.81651i	0.743727	−	0.429391i	0.823423	+	0.567428i	$0.192062\pi$
$80$		0			0
$81$	6.87482	−	5.80834i	0.763869	−	0.645371i
$82$		0			0
$83$	−6.56196	+	6.56196i	−0.720268	+	0.720268i	−0.968660	−	0.248392i	$-0.920098\pi$
$83$	−6.56196	+	6.56196i	−0.720268	+	0.720268i	0.248392	+	0.968660i	$0.420098\pi$
$84$		0			0
$85$	6.65587	−	6.77322i	0.721930	−	0.734658i
$86$		0			0
$87$	1.19658	+	6.75282i	0.128287	+	0.723978i
$88$		0			0
$89$	0.656714	+	1.13746i	0.0696116	+	0.120571i	0.898730	−	0.438502i	$-0.144491\pi$
$89$	0.656714	+	1.13746i	0.0696116	+	0.120571i	−0.829119	+	0.559072i	$0.811157\pi$
$90$		0			0
$91$	−11.1534	+	9.39378i	−1.16920	+	0.984735i
$92$		0			0
$93$	7.59510	+	2.75713i	0.787575	+	0.285901i
$94$		0			0
$95$	0.802265	−	1.41804i	0.0823107	−	0.145487i
$96$		0			0
$97$	10.0207	−	10.0207i	1.01745	−	1.01745i	0.0176018	−	0.999845i	$-0.494397\pi$
$97$	10.0207	−	10.0207i	1.01745	−	1.01745i	0.999845	−	0.0176018i	$-0.00560313\pi$
$98$		0			0
$99$	−6.35557	−	1.10959i	−0.638758	−	0.111518i
$100$		0			0
$101$	6.74304	+	3.89310i	0.670958	+	0.387378i	0.796439	−	0.604718i	$-0.206714\pi$
$101$	6.74304	+	3.89310i	0.670958	+	0.387378i	−0.125482	+	0.992096i	$0.540048\pi$
$102$		0			0
$103$	5.15875	−	19.2527i	0.508307	−	1.89703i	0.0715756	−	0.997435i	$-0.477197\pi$
$103$	5.15875	−	19.2527i	0.508307	−	1.89703i	0.436731	−	0.899592i	$-0.356136\pi$
$104$		0			0
$105$	−8.32615	+	5.97287i	−0.812549	+	0.582892i
$106$		0			0
$107$	−1.79006	+	6.68059i	−0.173052	+	0.645837i	0.823824	+	0.566846i	$0.191837\pi$
$107$	−1.79006	+	6.68059i	−0.173052	+	0.645837i	−0.996875	+	0.0789913i	$0.974830\pi$
$108$		0			0
$109$	5.29779	+	3.05868i	0.507436	+	0.292968i	0.731779	−	0.681542i	$-0.238690\pi$
$109$	5.29779	+	3.05868i	0.507436	+	0.292968i	−0.224343	+	0.974510i	$0.572024\pi$
$110$		0			0
$111$	0.345559	−	3.98854i	0.0327990	−	0.378576i
$112$		0			0
$113$	13.8572	−	13.8572i	1.30357	−	1.30357i	0.377605	−	0.925967i	$-0.376748\pi$
$113$	13.8572	−	13.8572i	1.30357	−	1.30357i	0.925967	−	0.377605i	$-0.123252\pi$
$114$		0			0
$115$	−12.3944	+	3.43742i	−1.15578	+	0.320541i
$116$		0			0
$117$	−14.9973	−	6.96255i	−1.38650	−	0.643688i
$118$		0			0
$119$	−1.97143	−	11.0617i	−0.180720	−	1.01403i
$120$		0			0
$121$	−3.18753	−	5.52097i	−0.289776	−	0.501906i
$122$		0			0
$123$	−8.44607	+	1.49663i	−0.761557	+	0.134946i
$124$		0			0
$125$	0.293050	+	11.1765i	0.0262112	+	0.999656i
$126$		0			0
$127$	4.34338	−	4.34338i	0.385412	−	0.385412i	−0.487635	−	0.873047i	$-0.662140\pi$
$127$	4.34338	−	4.34338i	0.385412	−	0.385412i	0.873047	+	0.487635i	$0.162140\pi$
$128$		0			0
$129$	5.02134	−	7.18412i	0.442104	−	0.632527i
$130$		0			0
$131$	18.6405	−	10.7621i	1.62863	−	0.940289i	0.644126	−	0.764919i	$-0.277221\pi$
$131$	18.6405	−	10.7621i	1.62863	−	0.940289i	0.984503	−	0.175370i	$-0.0561121\pi$
$132$		0			0
$133$	−0.817911	−	1.74564i	−0.0709219	−	0.151366i
$134$		0			0
$135$	−10.1271	−	5.69569i	−0.871606	−	0.490207i
$136$		0			0
$137$	−15.3138	+	4.10332i	−1.30835	+	0.350570i	−0.844600	−	0.535397i	$-0.820162\pi$
$137$	−15.3138	+	4.10332i	−1.30835	+	0.350570i	−0.463747	+	0.885968i	$0.653495\pi$
$138$		0			0
$139$			11.4342i			0.969835i	0.874560	+	0.484917i	$0.161150\pi$
$139$			11.4342i			0.969835i	−0.874560	+	0.484917i	$0.838850\pi$
$140$		0			0
$141$	16.6875	+	1.44577i	1.40534	+	0.121756i
$142$		0			0
$143$	3.06778	+	11.4491i	0.256541	+	0.957423i
$144$		0			0
$145$	7.62852	−	4.49366i	0.633514	−	0.373178i
$146$		0			0
$147$	0.0547598	+	12.1242i	0.00451651	+	0.999990i
$148$		0			0
$149$	−4.30668	−	7.45938i	−0.352817	−	0.611096i	0.633925	−	0.773394i	$-0.281443\pi$
$149$	−4.30668	−	7.45938i	−0.352817	−	0.611096i	−0.986742	+	0.162298i	$0.948109\pi$
$150$		0			0
$151$	4.98113	−	8.62757i	0.405358	−	0.702101i	−0.589005	−	0.808130i	$-0.700480\pi$
$151$	4.98113	−	8.62757i	0.405358	−	0.702101i	0.994363	+	0.106028i	$0.0338134\pi$
$152$		0			0
$153$	10.4240	−	7.32523i	0.842730	−	0.592210i
$154$		0			0
$155$	−0.0911482	−	10.4309i	−0.00732120	−	0.837831i
$156$		0			0
$157$	−0.341811	−	1.27566i	−0.0272795	−	0.101808i	0.950944	−	0.309364i	$-0.100116\pi$
$157$	−0.341811	−	1.27566i	−0.0272795	−	0.101808i	−0.978223	+	0.207555i	$0.933449\pi$
$158$		0			0
$159$	10.1156	−	4.72738i	0.802218	−	0.374905i
$160$		0			0
$161$	−5.17886	+	14.3105i	−0.408152	+	1.12783i
$162$		0			0
$163$	−5.77269	+	21.5440i	−0.452152	+	1.68745i	0.244176	+	0.969731i	$0.421483\pi$
$163$	−5.77269	+	21.5440i	−0.452152	+	1.68745i	−0.696328	+	0.717724i	$0.745184\pi$
$164$		0			0
$165$	1.52487	+	8.18833i	0.118711	+	0.637461i
$166$		0			0
$167$	−5.00089	−	5.00089i	−0.386980	−	0.386980i	0.486629	−	0.873609i	$-0.338226\pi$
$167$	−5.00089	−	5.00089i	−0.386980	−	0.386980i	−0.873609	+	0.486629i	$0.838226\pi$
$168$		0			0
$169$			17.3774i			1.33672i
$170$		0			0
$171$	1.40222	−	1.67684i	0.107230	−	0.128231i
$172$		0			0
$173$	2.69465	+	0.722028i	0.204870	+	0.0548948i	0.359795	−	0.933032i	$-0.382847\pi$
$173$	2.69465	+	0.722028i	0.204870	+	0.0548948i	−0.154925	+	0.987926i	$0.549513\pi$
$174$		0			0
$175$	10.9809	+	7.37703i	0.830076	+	0.557651i
$176$		0			0
$177$	13.0640	+	4.74241i	0.981949	+	0.356462i
$178$		0			0
$179$	7.09783	−	12.2938i	0.530517	−	0.918882i	−0.468849	−	0.883278i	$-0.655331\pi$
$179$	7.09783	−	12.2938i	0.530517	−	0.918882i	0.999366	−	0.0356039i	$-0.0113355\pi$
$180$		0			0
$181$	−10.0280			−0.745372			−0.372686	−	0.927958i	$-0.621563\pi$
$181$	−10.0280			−0.745372			−0.372686	+	0.927958i	$0.621563\pi$
$182$		0			0
$183$	−16.4439	+	13.8217i	−1.21557	+	1.02173i
$184$		0			0
$185$	−4.98049	+	1.38127i	−0.366173	+	0.101553i
$186$		0			0
$187$	−8.82185	−	2.36381i	−0.645117	−	0.172859i
$188$		0			0
$189$	−12.4342	+	5.86443i	−0.904453	+	0.426574i
$190$		0			0
$191$	5.89882	−	3.40569i	0.426824	−	0.246427i	−0.271169	−	0.962532i	$-0.587410\pi$
$191$	5.89882	−	3.40569i	0.426824	−	0.246427i	0.697993	+	0.716105i	$0.254077\pi$
$192$		0			0
$193$	8.23125	−	2.20556i	0.592498	−	0.158759i	0.0499036	−	0.998754i	$-0.484109\pi$
$193$	8.23125	−	2.20556i	0.592498	−	0.158759i	0.542595	+	0.839995i	$0.317442\pi$
$194$		0			0
$195$	−1.65659	+	21.2818i	−0.118631	+	1.52402i
$196$		0			0
$197$	15.8809	+	15.8809i	1.13147	+	1.13147i	0.989933	+	0.141537i	$0.0452044\pi$
$197$	15.8809	+	15.8809i	1.13147	+	1.13147i	0.141537	+	0.989933i	$0.454796\pi$
$198$		0			0
$199$	7.68076	+	4.43449i	0.544475	+	0.314353i	0.746891	−	0.664947i	$-0.231546\pi$
$199$	7.68076	+	4.43449i	0.544475	+	0.314353i	−0.202416	+	0.979300i	$0.564879\pi$
$200$		0			0
$201$	0.984557	−	0.460119i	0.0694453	−	0.0324543i
$202$		0			0
$203$	0.893863	−	10.4376i	0.0627369	−	0.732575i
$204$		0			0
$205$	5.62043	+	9.54135i	0.392548	+	0.666397i
$206$		0			0
$207$	−17.1882	+	1.53303i	−1.19467	+	0.106553i
$208$		0			0
$209$	−1.56695			−0.108388
$210$		0			0
$211$	14.4567			0.995243			0.497621	−	0.867394i	$-0.334207\pi$
$211$	14.4567			0.995243			0.497621	+	0.867394i	$0.334207\pi$
$212$		0			0
$213$	−6.82615	+	1.20958i	−0.467720	+	0.0828789i
$214$		0			0
$215$	−10.9552	−	2.83307i	−0.747138	−	0.193214i
$216$		0			0
$217$	−10.1234	−	7.06079i	−0.687218	−	0.479317i
$218$		0			0
$219$	7.92494	+	16.9577i	0.535518	+	1.14589i
$220$		0			0
$221$	−20.2707	−	11.7033i	−1.36355	−	0.787249i
$222$		0			0
$223$	17.3260	+	17.3260i	1.16023	+	1.16023i	0.984424	+	0.175810i	$0.0562545\pi$
$223$	17.3260	+	17.3260i	1.16023	+	1.16023i	0.175810	+	0.984424i	$0.443746\pi$
$224$		0			0
$225$	−2.32115	+	14.8193i	−0.154744	+	0.987955i
$226$		0			0
$227$	21.6202	−	5.79310i	1.43498	−	0.384502i	0.544207	−	0.838951i	$-0.316830\pi$
$227$	21.6202	−	5.79310i	1.43498	−	0.384502i	0.890773	+	0.454449i	$0.150164\pi$
$228$		0			0
$229$	−18.9575	+	10.9451i	−1.25274	+	0.723272i	−0.971654	−	0.236409i	$-0.924030\pi$
$229$	−18.9575	+	10.9451i	−1.25274	+	0.723272i	−0.281091	+	0.959681i	$0.590696\pi$
$230$		0			0
$231$	8.94291	+	4.14100i	0.588401	+	0.272458i
$232$		0			0
$233$	−22.6220	−	6.06156i	−1.48202	−	0.397106i	−0.574986	−	0.818163i	$-0.694992\pi$
$233$	−22.6220	−	6.06156i	−1.48202	−	0.397106i	−0.907034	+	0.421058i	$0.861659\pi$
$234$		0			0
$235$	−5.77905	−	20.8377i	−0.376984	−	1.35930i
$236$		0			0
$237$	−8.50670	−	10.1205i	−0.552569	−	0.657398i
$238$		0			0
$239$	19.7365			1.27665			0.638323	−	0.769769i	$-0.279628\pi$
$239$	19.7365			1.27665			0.638323	+	0.769769i	$0.279628\pi$
$240$		0			0
$241$	−6.49458	+	11.2489i	−0.418353	+	0.724608i	−0.995774	−	0.0918384i	$-0.970726\pi$
$241$	−6.49458	+	11.2489i	−0.418353	+	0.724608i	0.577421	+	0.816446i	$0.304059\pi$
$242$		0			0
$243$	−11.9837	−	9.96956i	−0.768752	−	0.639547i
$244$		0			0
$245$	14.6409	−	5.53558i	0.935376	−	0.353655i
$246$		0			0
$247$	−3.87902	−	1.03938i	−0.246816	−	0.0661341i
$248$		0			0
$249$	13.1744	+	9.20823i	0.834892	+	0.583548i
$250$		0			0
$251$			1.84736i			0.116604i	0.998299	+	0.0583022i	$0.0185687\pi$
$251$			1.84736i			0.116604i	−0.998299	+	0.0583022i	$0.981431\pi$
$252$		0			0
$253$	8.74719	+	8.74719i	0.549931	+	0.549931i
$254$		0			0
$255$	−13.5631	−	9.30455i	−0.849352	−	0.582674i
$256$		0			0
$257$	6.42263	−	23.9696i	0.400633	−	1.49518i	−0.411337	−	0.911483i	$-0.634938\pi$
$257$	6.42263	−	23.9696i	0.400633	−	1.49518i	0.811970	−	0.583699i	$-0.198395\pi$
$258$		0			0
$259$	−2.08104	+	5.75045i	−0.129310	+	0.357316i
$260$		0			0
$261$	11.1552	−	4.08151i	0.690489	−	0.252639i
$262$		0			0
$263$	3.10469	+	11.5869i	0.191444	+	0.714477i	0.993159	+	0.116771i	$0.0372544\pi$
$263$	3.10469	+	11.5869i	0.191444	+	0.714477i	−0.801715	+	0.597706i	$0.796079\pi$
$264$		0			0
$265$	−10.2815	−	10.1034i	−0.631589	−	0.620647i
$266$		0			0
$267$	1.74146	−	1.46376i	0.106575	−	0.0895809i
$268$		0			0
$269$	−1.64773	+	2.85395i	−0.100464	+	0.174008i	−0.911876	−	0.410466i	$-0.865366\pi$
$269$	−1.64773	+	2.85395i	−0.100464	+	0.174008i	0.811412	+	0.584474i	$0.198699\pi$
$270$		0			0
$271$	−4.06164	−	7.03497i	−0.246727	−	0.427344i	0.715889	−	0.698215i	$-0.246022\pi$
$271$	−4.06164	−	7.03497i	−0.246727	−	0.427344i	−0.962616	+	0.270870i	$0.912689\pi$
$272$		0			0
$273$	19.3916	+	16.1831i	1.17363	+	0.979444i
$274$		0			0
$275$	9.21685	−	5.53833i	0.555797	−	0.333974i
$276$		0			0
$277$	7.34355	+	27.4065i	0.441231	+	1.64670i	0.725699	+	0.688012i	$0.241517\pi$
$277$	7.34355	+	27.4065i	0.441231	+	1.64670i	−0.284467	+	0.958686i	$0.591817\pi$
$278$		0			0
$279$	2.40694	−	13.7865i	0.144100	−	0.825378i
$280$		0			0
$281$			14.5343i			0.867042i	0.901144	+	0.433521i	$0.142729\pi$
$281$			14.5343i			0.867042i	−0.901144	+	0.433521i	$0.857271\pi$
$282$		0			0
$283$	2.81028	−	0.753013i	0.167054	−	0.0447620i	−0.174323	−	0.984689i	$-0.555774\pi$
$283$	2.81028	−	0.753013i	0.167054	−	0.0447620i	0.341376	+	0.939927i	$0.389107\pi$
$284$		0			0
$285$	−2.66089	−	0.939707i	−0.157617	−	0.0556635i
$286$		0			0
$287$	13.0548	+	1.11800i	0.770600	+	0.0659933i
$288$		0			0
$289$	0.896693	−	0.517706i	0.0527466	−	0.0304533i
$290$		0			0
$291$	−20.1184	−	14.0618i	−1.17936	−	0.824316i
$292$		0			0
$293$	11.9716	−	11.9716i	0.699387	−	0.699387i	−0.264891	−	0.964278i	$-0.585336\pi$
$293$	11.9716	−	11.9716i	0.699387	−	0.699387i	0.964278	+	0.264891i	$0.0853361\pi$
$294$		0			0
$295$	−0.156780	−	17.9417i	−0.00912808	−	1.04461i
$296$		0			0
$297$	0.0283094	+	11.1746i	0.00164268	+	0.648418i
$298$		0			0
$299$	15.8517	+	27.4560i	0.916728	+	1.58782i
$300$		0			0
$301$	−10.2406	+	8.62496i	−0.590257	+	0.497134i
$302$		0			0
$303$	4.60181	−	12.6767i	0.264367	−	0.728255i
$304$		0			0
$305$	24.1369	+	13.6556i	1.38208	+	0.781920i
$306$		0			0
$307$	5.89474	−	5.89474i	0.336431	−	0.336431i	−0.518591	−	0.855022i	$-0.673543\pi$
$307$	5.89474	−	5.89474i	0.336431	−	0.336431i	0.855022	+	0.518591i	$0.173543\pi$
$308$		0			0
$309$	−34.3942	−	2.97984i	−1.95662	−	0.169517i
$310$		0			0
$311$	0.794450	+	0.458676i	0.0450491	+	0.0260091i	0.522355	−	0.852728i	$-0.325053\pi$
$311$	0.794450	+	0.458676i	0.0450491	+	0.0260091i	−0.477306	+	0.878737i	$0.658387\pi$
$312$		0			0
$313$	0.320387	−	1.19570i	0.0181094	−	0.0675850i	−0.956280	−	0.292453i	$-0.905528\pi$
$313$	0.320387	−	1.19570i	0.0181094	−	0.0675850i	0.974389	+	0.224868i	$0.0721951\pi$
$314$		0			0
$315$	12.7029	+	12.3951i	0.715725	+	0.698383i
$316$		0			0
$317$	4.20581	−	15.6963i	0.236222	−	0.881591i	−0.741373	−	0.671093i	$-0.765825\pi$
$317$	4.20581	−	15.6963i	0.236222	−	0.881591i	0.977594	−	0.210498i	$-0.0675084\pi$
$318$		0			0
$319$	−7.37430	−	4.25756i	−0.412882	−	0.238377i
$320$		0			0
$321$	11.9346	+	1.03399i	0.666125	+	0.0577116i
$322$		0			0
$323$	2.18802	−	2.18802i	0.121745	−	0.121745i
$324$		0			0
$325$	26.4901	−	7.59657i	1.46941	−	0.421382i
$326$		0			0
$327$	3.61549	−	9.95964i	0.199937	−	0.550769i
$328$		0			0
$329$	−24.0591	−	8.70680i	−1.32642	−	0.480022i
$330$		0			0
$331$	−5.43665	−	9.41656i	−0.298825	−	0.517581i	0.677042	−	0.735944i	$-0.263261\pi$
$331$	−5.43665	−	9.41656i	−0.298825	−	0.517581i	−0.975868	+	0.218364i	$0.929928\pi$
$332$		0			0
$333$	−6.90682	+	0.616025i	−0.378491	+	0.0337579i
$334$		0			0
$335$	−1.00071	−	0.983371i	−0.0546746	−	0.0537273i
$336$		0			0
$337$	−2.89002	+	2.89002i	−0.157430	+	0.157430i	−0.781427	−	0.623997i	$-0.785508\pi$
$337$	−2.89002	+	2.89002i	−0.157430	+	0.157430i	0.623997	+	0.781427i	$0.285508\pi$
$338$		0			0
$339$	−27.8209	−	19.4454i	−1.51102	−	1.05613i
$340$		0			0
$341$	−8.68835	+	5.01622i	−0.470500	+	0.271643i
$342$		0			0
$343$	4.69479	−	17.9153i	0.253495	−	0.967337i
$344$		0			0
$345$	9.60814	+	20.0996i	0.517285	+	1.08213i
$346$		0			0
$347$	1.08593	−	0.290975i	0.0582960	−	0.0156204i	−0.229553	−	0.973296i	$-0.573726\pi$
$347$	1.08593	−	0.290975i	0.0582960	−	0.0156204i	0.287849	+	0.957676i	$0.407060\pi$
$348$		0			0
$349$		−	33.7351i		−	1.80580i	−0.429852	−	0.902899i	$-0.641434\pi$
$349$		−	33.7351i		−	1.80580i	0.429852	−	0.902899i	$-0.358566\pi$
$350$		0			0
$351$	−7.34220	+	27.6818i	−0.391898	+	1.47754i
$352$		0			0
$353$	−1.77829	−	6.63668i	−0.0946489	−	0.353235i	0.902317	−	0.431073i	$-0.141865\pi$
$353$	−1.77829	−	6.63668i	−0.0946489	−	0.353235i	−0.996966	+	0.0778384i	$0.975198\pi$
$354$		0			0
$355$	4.54245	+	7.71136i	0.241088	+	0.409276i
$356$		0			0
$357$	−18.2698	+	6.70517i	−0.966939	+	0.354875i
$358$		0			0
$359$	−1.02137	−	1.76907i	−0.0539060	−	0.0933680i	0.837813	−	0.545957i	$-0.183834\pi$
$359$	−1.02137	−	1.76907i	−0.0539060	−	0.0933680i	−0.891719	+	0.452589i	$0.850500\pi$
$360$		0			0
$361$	−9.23455	+	15.9947i	−0.486029	+	0.841827i
$362$		0			0
$363$	−8.45262	+	7.10476i	−0.443647	+	0.372903i
$364$		0			0
$365$	16.9373	−	17.2359i	0.886537	−	0.902167i
$366$		0			0
$367$	−1.94879	−	7.27299i	−0.101726	−	0.379647i	0.896227	−	0.443596i	$-0.146297\pi$
$367$	−1.94879	−	7.27299i	−0.101726	−	0.379647i	−0.997953	+	0.0639485i	$0.979631\pi$
$368$		0			0
$369$	5.10494	+	13.9523i	0.265752	+	0.726329i
$370$		0			0
$371$	−16.7913	+	2.99256i	−0.871762	+	0.155366i
$372$		0			0
$373$	−0.374011	+	1.39583i	−0.0193655	+	0.0722732i	−0.974932	−	0.222501i	$-0.928578\pi$
$373$	−0.374011	+	1.39583i	−0.0193655	+	0.0722732i	0.955567	+	0.294774i	$0.0952445\pi$
$374$		0			0
$375$	18.9728	−	3.87742i	0.979749	−	0.200229i
$376$		0			0
$377$	−15.4311	−	15.4311i	−0.794744	−	0.794744i
$378$		0			0
$379$		−	1.83298i		−	0.0941538i	−0.998891	−	0.0470769i	$-0.985009\pi$
$379$		−	1.83298i		−	0.0941538i	0.998891	−	0.0470769i	$-0.0149906\pi$
$380$		0			0
$381$	−8.72015	−	6.09495i	−0.446747	−	0.312254i
$382$		0			0
$383$	−16.8876	−	4.52502i	−0.862916	−	0.231218i	−0.199894	−	0.979817i	$-0.564060\pi$
$383$	−16.8876	−	4.52502i	−0.862916	−	0.231218i	−0.663022	+	0.748600i	$0.730726\pi$
$384$		0			0
$385$	0.974795	−	12.6855i	0.0496801	−	0.646514i
$386$		0			0
$387$	−13.7699	−	6.39271i	−0.699962	−	0.324960i
$388$		0			0
$389$	11.9965	−	20.7786i	0.608249	−	1.05352i	−0.383280	−	0.923632i	$-0.625206\pi$
$389$	11.9965	−	20.7786i	0.608249	−	1.05352i	0.991529	−	0.129886i	$-0.0414610\pi$
$390$		0			0
$391$	−24.4283			−1.23539
$392$		0			0
$393$	−23.9879	−	28.5387i	−1.21003	−	1.43959i
$394$		0			0
$395$	−8.40449	+	14.8553i	−0.422876	+	0.747450i
$396$		0			0
$397$	22.9338	+	6.14509i	1.15101	+	0.308413i	0.783372	−	0.621554i	$-0.213498\pi$
$397$	22.9338	+	6.14509i	1.15101	+	0.308413i	0.367643	+	0.929967i	$0.380165\pi$
$398$		0			0
$399$	−2.72998	+	1.92248i	−0.136670	+	0.0962443i
$400$		0			0
$401$	−2.79781	+	1.61532i	−0.139716	+	0.0806650i	−0.568229	−	0.822871i	$-0.692371\pi$
$401$	−2.79781	+	1.61532i	−0.139716	+	0.0806650i	0.428513	+	0.903536i	$0.359038\pi$
$402$		0			0
$403$	−24.8355	+	6.65465i	−1.23714	+	0.331492i
$404$		0			0
$405$	−6.65340	+	18.9930i	−0.330610	+	0.943767i
$406$		0			0
$407$	3.51492	+	3.51492i	0.174228	+	0.174228i
$408$		0			0
$409$	4.14956	+	2.39575i	0.205183	+	0.118462i	0.599071	−	0.800696i	$-0.295537\pi$
$409$	4.14956	+	2.39575i	0.205183	+	0.118462i	−0.393888	+	0.919158i	$0.628870\pi$
$410$		0			0
$411$	11.6261	+	24.8774i	0.573473	+	1.22711i
$412$		0			0
$413$	−17.4127	−	12.1449i	−0.856824	−	0.597613i
$414$		0			0
$415$	5.19534	−	20.0898i	0.255029	−	0.986171i
$416$		0			0
$417$	19.5008	−	3.45550i	0.954958	−	0.169217i
$418$		0			0
$419$	20.3805			0.995651			0.497826	−	0.867277i	$-0.334132\pi$
$419$	20.3805			0.995651			0.497826	+	0.867277i	$0.334132\pi$
$420$		0			0
$421$	−33.9866			−1.65641			−0.828203	−	0.560428i	$-0.810637\pi$
$421$	−33.9866			−1.65641			−0.828203	+	0.560428i	$0.810637\pi$
$422$		0			0
$423$	−2.57736	−	28.8972i	−0.125316	−	1.40503i
$424$		0			0
$425$	−5.13651	+	20.6034i	−0.249158	+	0.999413i
$426$		0			0
$427$	29.7132	−	13.9220i	1.43792	−	0.673731i
$428$		0			0
$429$	18.5991	−	8.69205i	0.897975	−	0.419656i
$430$		0			0
$431$	1.88165	+	1.08637i	0.0906357	+	0.0523285i	0.544633	−	0.838675i	$-0.316669\pi$
$431$	1.88165	+	1.08637i	0.0906357	+	0.0523285i	−0.453997	+	0.891003i	$0.650002\pi$
$432$		0			0
$433$	1.81661	+	1.81661i	0.0873009	+	0.0873009i	0.749409	−	0.662108i	$-0.230338\pi$
$433$	1.81661	+	1.81661i	0.0873009	+	0.0873009i	−0.662108	+	0.749409i	$0.730338\pi$
$434$		0			0
$435$	−9.96925	−	11.6523i	−0.477989	−	0.558684i
$436$		0			0
$437$	−4.04834	+	1.08475i	−0.193659	+	0.0518907i
$438$		0			0
$439$	8.95736	−	5.17153i	0.427511	−	0.246824i	−0.270775	−	0.962643i	$-0.587280\pi$
$439$	8.95736	−	5.17153i	0.427511	−	0.246824i	0.698286	+	0.715819i	$0.253946\pi$
$440$		0			0
$441$	20.6611	−	3.75743i	0.983863	−	0.178925i
$442$		0			0
$443$	−19.6578	−	5.26730i	−0.933971	−	0.250257i	−0.240424	−	0.970668i	$-0.577286\pi$
$443$	−19.6578	−	5.26730i	−0.933971	−	0.250257i	−0.693547	+	0.720411i	$0.743953\pi$
$444$		0			0
$445$	−2.55618	−	1.44618i	−0.121174	−	0.0685554i
$446$		0			0
$447$	−11.4203	+	9.59925i	−0.540163	+	0.454029i
$448$		0			0
$449$	−14.6156			−0.689754			−0.344877	−	0.938648i	$-0.612079\pi$
$449$	−14.6156			−0.689754			−0.344877	+	0.938648i	$0.612079\pi$
$450$		0			0
$451$	5.32513	−	9.22340i	0.250751	−	0.434313i
$452$		0			0
$453$	−16.2195	−	5.88791i	−0.762058	−	0.276638i
$454$		0			0
$455$	10.8276	−	30.7566i	0.507605	−	1.44189i
$456$		0			0
$457$	6.40237	+	1.71551i	0.299490	+	0.0802481i	0.405435	−	0.914124i	$-0.367120\pi$
$457$	6.40237	+	1.71551i	0.299490	+	0.0802481i	−0.105945	+	0.994372i	$0.533787\pi$
$458$		0			0
$459$	−15.6433	−	15.5642i	−0.730165	−	0.726475i
$460$		0			0
$461$			29.3424i			1.36661i	0.730132	+	0.683306i	$0.239459\pi$
$461$			29.3424i			1.36661i	−0.730132	+	0.683306i	$0.760541\pi$
$462$		0			0
$463$	−3.11379	−	3.11379i	−0.144710	−	0.144710i	0.631040	−	0.775750i	$-0.282628\pi$
$463$	−3.11379	−	3.11379i	−0.144710	−	0.144710i	−0.775750	+	0.631040i	$0.782628\pi$
$464$		0			0
$465$	−17.7622	+	3.30775i	−0.823702	+	0.153393i
$466$		0			0
$467$	6.99718	−	26.1138i	0.323791	−	1.20840i	−0.591731	−	0.806135i	$-0.701555\pi$
$467$	6.99718	−	26.1138i	0.323791	−	1.20840i	0.915522	−	0.402268i	$-0.131778\pi$
$468$		0			0
$469$	−1.63431	+	0.291268i	−0.0754655	+	0.0134495i
$470$		0			0
$471$	−2.07231	+	0.968466i	−0.0954871	+	0.0446246i
$472$		0			0
$473$	2.81670	+	10.5121i	0.129512	+	0.483346i
$474$		0			0
$475$	0.0636642	+	3.64256i	0.00292112	+	0.167132i
$476$		0			0
$477$	−11.1195	−	15.8233i	−0.509125	−	0.724499i
$478$		0			0
$479$	−18.8746	+	32.6918i	−0.862404	+	1.49373i	0.00719862	+	0.999974i	$0.497709\pi$
$479$	−18.8746	+	32.6918i	−0.862404	+	1.49373i	−0.869602	+	0.493753i	$0.835625\pi$
$480$		0			0
$481$	6.36975	+	11.0327i	0.290436	+	0.503050i
$482$		0			0
$483$	25.9714	+	4.50771i	1.18174	+	0.205108i
$484$		0			0
$485$	−7.93374	+	30.6790i	−0.360253	+	1.39306i
$486$		0			0
$487$	−7.63106	−	28.4795i	−0.345796	−	1.29053i	−0.891679	−	0.452668i	$-0.850472\pi$
$487$	−7.63106	−	28.4795i	−0.345796	−	1.29053i	0.545883	−	0.837861i	$-0.316194\pi$
$488$		0			0
$489$	38.4874	+	3.33447i	1.74046	+	0.150790i
$490$		0			0
$491$		−	31.9025i		−	1.43974i	−0.694110	−	0.719869i	$-0.744202\pi$
$491$		−	31.9025i		−	1.43974i	0.694110	−	0.719869i	$-0.255798\pi$
$492$		0			0
$493$	16.2422	−	4.35208i	0.731511	−	0.196008i
$494$		0			0
$495$	13.5042	−	5.07521i	0.606970	−	0.228114i
$496$		0			0
$497$	10.5509	+	0.903569i	0.473274	+	0.0405306i
$498$		0			0
$499$	−13.9880	+	8.07598i	−0.626189	+	0.361531i	−0.779275	−	0.626682i	$-0.784412\pi$
$499$	−13.9880	+	8.07598i	−0.626189	+	0.361531i	0.153086	+	0.988213i	$0.451079\pi$
$500$		0			0
$501$	−7.01762	+	10.0402i	−0.313524	+	0.448565i
$502$		0			0
$503$	−25.0418	+	25.0418i	−1.11656	+	1.11656i	−0.124316	+	0.992243i	$0.539674\pi$
$503$	−25.0418	+	25.0418i	−1.11656	+	1.11656i	−0.992243	+	0.124316i	$0.960326\pi$
$504$		0			0
$505$	−17.4098	+	0.152132i	−0.774726	+	0.00676977i
$506$		0			0
$507$	29.6368	−	5.25158i	1.31622	−	0.233231i
$508$		0			0
$509$	21.6658	+	37.5262i	0.960319	+	1.66332i	0.721698	+	0.692208i	$0.243362\pi$
$509$	21.6658	+	37.5262i	0.960319	+	1.66332i	0.238621	+	0.971113i	$0.423305\pi$
$510$		0			0
$511$	−5.01671	−	28.1488i	−0.221926	−	1.24523i
$512$		0			0
$513$	−3.28359	−	1.88471i	−0.144974	−	0.0832118i
$514$		0			0
$515$	11.9111	+	42.9480i	0.524864	+	1.89251i
$516$		0			0
$517$	−14.7059	+	14.7059i	−0.646767	+	0.646767i
$518$		0			0
$519$	0.417063	−	4.81387i	0.0183071	−	0.211306i
$520$		0			0
$521$	21.1824	+	12.2297i	0.928018	+	0.535791i	0.886184	−	0.463333i	$-0.153347\pi$
$521$	21.1824	+	12.2297i	0.928018	+	0.535791i	0.0418336	+	0.999125i	$0.486680\pi$
$522$		0			0
$523$	−7.55434	+	28.1932i	−0.330328	+	1.23280i	0.578518	+	0.815670i	$0.303631\pi$
$523$	−7.55434	+	28.1932i	−0.330328	+	1.23280i	−0.908846	+	0.417132i	$0.863035\pi$
$524$		0			0
$525$	9.26289	−	20.9571i	0.404266	−	0.914642i
$526$		0			0
$527$	5.12759	−	19.1364i	0.223361	−	0.833595i
$528$		0			0
$529$	8.73588	+	5.04366i	0.379821	+	0.219290i
$530$		0			0
$531$	4.14006	−	23.7136i	0.179663	−	1.02908i
$532$		0			0
$533$	19.3005	−	19.3005i	0.835996	−	0.835996i
$534$		0			0
$535$	−4.13307	−	14.9027i	−0.178688	−	0.644301i
$536$		0			0
$537$	−23.1119	−	8.38994i	−0.997352	−	0.362053i
$538$		0			0
$539$	−11.5675	−	9.63409i	−0.498246	−	0.414970i
$540$		0			0
$541$	4.55156	+	7.88354i	0.195687	+	0.338940i	0.947125	−	0.320863i	$-0.103973\pi$
$541$	4.55156	+	7.88354i	0.195687	+	0.338940i	−0.751439	+	0.659803i	$0.770640\pi$
$542$		0			0
$543$	3.03053	+	17.1025i	0.130052	+	0.733938i
$544$		0			0
$545$	−13.6783	+	0.119525i	−0.585914	+	0.00511988i
$546$		0			0
$547$	−17.5854	+	17.5854i	−0.751900	+	0.751900i	−0.974834	−	0.222934i	$-0.928437\pi$
$547$	−17.5854	+	17.5854i	−0.751900	+	0.751900i	0.222934	+	0.974834i	$0.428437\pi$
$548$		0			0
$549$	28.5422	+	23.8677i	1.21815	+	1.01865i
$550$		0			0
$551$	2.49845	−	1.44248i	0.106438	−	0.0614518i
$552$		0			0
$553$	8.56839	+	18.2872i	0.364365	+	0.777653i
$554$		0			0
$555$	3.86088	+	8.07670i	0.163885	+	0.342837i
$556$		0			0
$557$	−10.3211	+	2.76552i	−0.437318	+	0.117179i	−0.470759	−	0.882262i	$-0.656020\pi$
$557$	−10.3211	+	2.76552i	−0.437318	+	0.117179i	0.0334413	+	0.999441i	$0.489353\pi$
$558$		0			0
$559$			27.8912i			1.17967i
$560$		0			0
$561$	−1.36540	+	15.7599i	−0.0576473	+	0.665382i
$562$		0			0
$563$	0.963101	+	3.59434i	0.0405898	+	0.151483i	0.983247	−	0.182280i	$-0.0583479\pi$
$563$	0.963101	+	3.59434i	0.0405898	+	0.151483i	−0.942657	+	0.333764i	$0.891681\pi$
$564$		0			0
$565$	−10.9712	+	42.4245i	−0.461562	+	1.78481i
$566$		0			0
$567$	13.7594	+	19.4340i	0.577840	+	0.816150i
$568$		0			0
$569$	1.12664	+	1.95139i	0.0472311	+	0.0818066i	0.888674	−	0.458539i	$-0.151627\pi$
$569$	1.12664	+	1.95139i	0.0472311	+	0.0818066i	−0.841443	+	0.540345i	$0.818294\pi$
$570$		0			0
$571$	2.03062	−	3.51713i	0.0849787	−	0.147187i	−0.820403	−	0.571785i	$-0.806251\pi$
$571$	2.03062	−	3.51713i	0.0849787	−	0.147187i	0.905382	+	0.424598i	$0.139584\pi$
$572$		0			0
$573$	−7.59101	−	9.03111i	−0.317119	−	0.377280i
$574$		0			0
$575$	19.9785	−	20.6892i	0.833159	−	0.862801i
$576$		0			0
$577$	−4.34025	−	16.1980i	−0.180687	−	0.674332i	−0.995513	−	0.0946268i	$-0.969834\pi$
$577$	−4.34025	−	16.1980i	−0.180687	−	0.674332i	0.814826	−	0.579706i	$-0.196832\pi$
$578$		0			0
$579$	−6.24909	−	13.3717i	−0.259703	−	0.555710i
$580$		0			0
$581$	−15.8166	−	18.7794i	−0.656183	−	0.779099i
$582$		0			0
$583$	−3.58818	+	13.3913i	−0.148607	+	0.554610i
$584$		0			0
$585$	36.7964	−	3.60625i	1.52134	−	0.149100i
$586$		0			0
$587$	11.2728	+	11.2728i	0.465279	+	0.465279i	0.900381	−	0.435102i	$-0.143288\pi$
$587$	11.2728	+	11.2728i	0.465279	+	0.465279i	−0.435102	+	0.900381i	$0.643288\pi$
$588$		0			0
$589$		−	3.39904i		−	0.140055i
$590$		0			0
$591$	22.2853	−	31.8840i	0.916696	−	1.31153i
$592$		0			0
$593$	15.1364	+	4.05578i	0.621577	+	0.166551i	0.555844	−	0.831286i	$-0.312395\pi$
$593$	15.1364	+	4.05578i	0.621577	+	0.166551i	0.0657322	+	0.997837i	$0.479062\pi$
$594$		0			0
$595$	16.3523	+	19.0746i	0.670379	+	0.781983i
$596$		0			0
$597$	5.24176	−	14.4395i	0.214531	−	0.590971i
$598$		0			0
$599$	16.5463	−	28.6589i	0.676062	−	1.17097i	−0.300096	−	0.953909i	$-0.597019\pi$
$599$	16.5463	−	28.6589i	0.676062	−	1.17097i	0.976157	−	0.217064i	$-0.0696480\pi$
$600$		0			0
$601$	25.2056			1.02816			0.514079	−	0.857743i	$-0.328134\pi$
$601$	25.2056			1.02816			0.514079	+	0.857743i	$0.328134\pi$
$602$		0			0
$603$	−1.08227	−	1.54009i	−0.0440733	−	0.0627175i
$604$		0			0
$605$	12.4071	+	7.01940i	0.504419	+	0.285379i
$606$		0			0
$607$	33.2974	+	8.92202i	1.35150	+	0.362134i	0.860689	−	0.509132i	$-0.170033\pi$
$607$	33.2974	+	8.92202i	1.35150	+	0.362134i	0.490812	+	0.871265i	$0.336700\pi$
$608$		0			0
$609$	−18.0712	+	1.62985i	−0.732284	+	0.0660449i
$610$		0			0
$611$	−46.1595	+	26.6502i	−1.86741	+	1.07815i
$612$		0			0
$613$	19.2254	−	5.15144i	0.776509	−	0.208065i	0.151264	−	0.988493i	$-0.451666\pi$
$613$	19.2254	−	5.15144i	0.776509	−	0.208065i	0.625245	+	0.780429i	$0.284999\pi$
$614$		0			0
$615$	14.5741	−	12.4690i	0.587683	−	0.502799i
$616$		0			0
$617$	−12.3161	−	12.3161i	−0.495829	−	0.495829i	0.414308	−	0.910137i	$-0.364024\pi$
$617$	−12.3161	−	12.3161i	−0.495829	−	0.495829i	−0.910137	+	0.414308i	$0.864024\pi$
$618$		0			0
$619$	23.0037	+	13.2812i	0.924597	+	0.533816i	0.885099	−	0.465404i	$-0.154091\pi$
$619$	23.0037	+	13.2812i	0.924597	+	0.533816i	0.0394980	+	0.999220i	$0.487424\pi$
$620$		0			0
$621$	7.80898	+	28.8510i	0.313364	+	1.15775i
$622$		0			0
$623$	−3.14672	+	1.47438i	−0.126071	+	0.0590698i
$624$		0			0
$625$	−13.2489	−	21.2006i	−0.529958	−	0.848024i
$626$		0			0
$627$	0.473545	+	2.67241i	0.0189116	+	0.106726i
$628$		0			0
$629$	−9.81614			−0.391395
$630$		0			0
$631$	8.52290			0.339291			0.169646	−	0.985505i	$-0.445738\pi$
$631$	8.52290			0.339291			0.169646	+	0.985505i	$0.445738\pi$
$632$		0			0
$633$	−4.36894	−	24.6557i	−0.173650	−	0.979977i
$634$		0			0
$635$	−3.43881	+	13.2975i	−0.136465	+	0.527696i
$636$		0			0
$637$	−22.2450	−	31.5222i	−0.881381	−	1.24896i
$638$		0			0
$639$	4.12583	+	11.2763i	0.163215	+	0.446085i
$640$		0			0
$641$	−28.8842	−	16.6763i	−1.14086	−	0.658674i	−0.194214	−	0.980959i	$-0.562216\pi$
$641$	−28.8842	−	16.6763i	−1.14086	−	0.658674i	−0.946643	+	0.322286i	$0.895549\pi$
$642$		0			0
$643$	−6.59026	−	6.59026i	−0.259895	−	0.259895i	0.565117	−	0.825011i	$-0.308831\pi$
$643$	−6.59026	−	6.59026i	−0.259895	−	0.259895i	−0.825011	+	0.565117i	$0.808831\pi$
$644$		0			0
$645$	−1.52101	+	19.5401i	−0.0598897	+	0.769389i
$646$		0			0
$647$	−24.4118	+	6.54113i	−0.959729	+	0.257159i	−0.704485	−	0.709718i	$-0.748822\pi$
$647$	−24.4118	+	6.54113i	−0.959729	+	0.257159i	−0.255243	+	0.966877i	$0.582156\pi$
$648$		0			0
$649$	−14.9444	+	8.62817i	−0.586620	+	0.338685i
$650$		0			0
$651$	−8.98269	+	19.3990i	−0.352059	+	0.760308i
$652$		0			0
$653$	12.7291	+	3.41075i	0.498129	+	0.133473i	0.499131	−	0.866526i	$-0.333653\pi$
$653$	12.7291	+	3.41075i	0.498129	+	0.133473i	−0.00100275	+	0.999999i	$0.500319\pi$
$654$		0			0
$655$	−23.6997	+	41.8901i	−0.926022	+	1.63678i
$656$		0			0
$657$	26.5261	−	18.6406i	1.03488	−	0.727239i
$658$		0			0
$659$	−34.5112			−1.34437			−0.672183	−	0.740385i	$-0.734643\pi$
$659$	−34.5112			−1.34437			−0.672183	+	0.740385i	$0.734643\pi$
$660$		0			0
$661$	5.75162	−	9.96211i	0.223712	−	0.387481i	−0.732220	−	0.681068i	$-0.761516\pi$
$661$	5.75162	−	9.96211i	0.223712	−	0.387481i	0.955932	+	0.293587i	$0.0948491\pi$
$662$		0			0
$663$	−13.8338	+	38.1082i	−0.537260	+	1.48000i
$664$		0			0
$665$	3.55698	+	2.43498i	0.137934	+	0.0944244i
$666$		0			0
$667$	−21.9995	−	5.89474i	−0.851823	−	0.228245i
$668$		0			0
$669$	24.3131	−	34.7852i	0.940000	−	1.34487i
$670$		0			0
$671$		−	26.6717i		−	1.02965i
$672$		0			0
$673$	2.07846	+	2.07846i	0.0801187	+	0.0801187i	0.746030	−	0.665912i	$-0.231957\pi$
$673$	2.07846	+	2.07846i	0.0801187	+	0.0801187i	−0.665912	+	0.746030i	$0.731957\pi$
$674$		0			0
$675$	25.9756	−	0.519827i	0.999800	−	0.0200081i
$676$		0			0
$677$	4.59302	−	17.1414i	0.176524	−	0.658797i	−0.819763	−	0.572703i	$-0.805895\pi$
$677$	4.59302	−	17.1414i	0.176524	−	0.658797i	0.996287	−	0.0860941i	$-0.0274386\pi$
$678$		0			0
$679$	24.1534	+	28.6778i	0.926921	+	1.10055i
$680$		0			0
$681$	−16.4138	−	35.1221i	−0.628979	−	1.34588i
$682$		0			0
$683$	2.97965	+	11.1202i	0.114013	+	0.425503i	0.999211	−	0.0397112i	$-0.0126438\pi$
$683$	2.97965	+	11.1202i	0.114013	+	0.425503i	−0.885198	+	0.465215i	$0.845977\pi$
$684$		0			0
$685$	24.8474	−	25.2855i	0.949371	−	0.966109i
$686$		0			0
$687$	24.3958	+	29.0239i	0.930757	+	1.10733i
$688$		0			0
$689$	−17.7652	+	30.7703i	−0.676801	+	1.17225i
$690$		0			0
$691$	−2.37495	−	4.11354i	−0.0903475	−	0.156486i	0.817310	−	0.576198i	$-0.195464\pi$
$691$	−2.37495	−	4.11354i	−0.0903475	−	0.156486i	−0.907657	+	0.419712i	$0.862131\pi$
$692$		0			0
$693$	4.35979	−	16.5034i	0.165615	−	0.626913i
$694$		0			0
$695$	−12.9768	−	22.0297i	−0.492238	−	0.835632i
$696$		0			0
$697$	5.44336	+	20.3149i	0.206182	+	0.769481i
$698$		0			0
$699$	−3.50132	+	40.4134i	−0.132432	+	1.52857i
$700$		0			0
$701$			29.9516i			1.13126i	0.824660	+	0.565628i	$0.191366\pi$
$701$			29.9516i			1.13126i	−0.824660	+	0.565628i	$0.808634\pi$
$702$		0			0
$703$	−1.62676	+	0.435890i	−0.0613545	+	0.0164399i
$704$		0			0
$705$	−33.7918	+	16.1534i	−1.27267	+	0.608372i
$706$		0			0
$707$	−11.7849	+	16.8965i	−0.443215	+	0.635457i
$708$		0			0
$709$	4.99216	−	2.88222i	0.187484	−	0.108244i	−0.403320	−	0.915059i	$-0.632144\pi$
$709$	4.99216	−	2.88222i	0.187484	−	0.108244i	0.590804	+	0.806815i	$0.298811\pi$
$710$		0			0
$711$	−14.6896	+	17.5665i	−0.550902	+	0.658796i
$712$		0			0
$713$	−18.9745	+	18.9745i	−0.710599	+	0.710599i
$714$		0			0
$715$	−18.9043	−	18.5767i	−0.706979	−	0.694731i
$716$		0			0
$717$	−5.96451	−	33.6602i	−0.222749	−	1.25706i
$718$		0			0
$719$	18.4248	+	31.9127i	0.687129	+	1.19014i	0.972763	+	0.231804i	$0.0744627\pi$
$719$	18.4248	+	31.9127i	0.687129	+	1.19014i	−0.285633	+	0.958339i	$0.592204\pi$
$720$		0			0
$721$	49.5875	+	17.9454i	1.84674	+	0.668320i
$722$		0			0
$723$	21.1476	+	7.67687i	0.786487	+	0.285506i
$724$		0			0
$725$	−9.59756	+	17.3154i	−0.356445	+	0.643078i
$726$		0			0
$727$	−5.34727	+	5.34727i	−0.198319	+	0.198319i	−0.799279	−	0.600960i	$-0.794785\pi$
$727$	−5.34727	+	5.34727i	−0.198319	+	0.198319i	0.600960	+	0.799279i	$0.294785\pi$
$728$		0			0
$729$	−13.3814	+	23.4508i	−0.495606	+	0.868548i
$730$		0			0
$731$	−18.6117	−	10.7455i	−0.688378	−	0.397435i
$732$		0			0
$733$	−4.79803	+	17.9065i	−0.177219	+	0.661391i	0.818944	+	0.573874i	$0.194560\pi$
$733$	−4.79803	+	17.9065i	−0.177219	+	0.661391i	−0.996163	+	0.0875174i	$0.972107\pi$
$734$		0			0
$735$	−13.8654	−	23.2970i	−0.511435	−	0.859322i
$736$		0			0
$737$	−0.349241	+	1.30338i	−0.0128644	+	0.0480108i
$738$		0			0
$739$	6.24688	+	3.60664i	0.229795	+	0.132672i	0.610478	−	0.792034i	$-0.290978\pi$
$739$	6.24688	+	3.60664i	0.229795	+	0.132672i	−0.380682	+	0.924706i	$0.624311\pi$
$740$		0			0
$741$	−0.600375	+	6.92971i	−0.0220553	+	0.254569i
$742$		0			0
$743$	9.61154	−	9.61154i	0.352613	−	0.352613i	−0.508468	−	0.861081i	$-0.669788\pi$
$743$	9.61154	−	9.61154i	0.352613	−	0.352613i	0.861081	+	0.508468i	$0.169788\pi$
$744$		0			0
$745$	16.7632	+	9.48391i	0.614156	+	0.347464i
$746$		0			0
$747$	11.7231	−	25.2515i	0.428925	−	0.923903i
$748$		0			0
$749$	−17.2066	−	6.22694i	−0.628716	−	0.227528i
$750$		0			0
$751$	8.51460	+	14.7477i	0.310702	+	0.538152i	0.978515	−	0.206178i	$-0.0661025\pi$
$751$	8.51460	+	14.7477i	0.310702	+	0.538152i	−0.667812	+	0.744330i	$0.732769\pi$
$752$		0			0
$753$	3.15064	−	0.558287i	0.114816	−	0.0203451i
$754$		0			0
$755$	0.194649	+	22.2754i	0.00708400	+	0.810686i
$756$		0			0
$757$	−18.5494	+	18.5494i	−0.674191	+	0.674191i	−0.958679	−	0.284488i	$-0.908176\pi$
$757$	−18.5494	+	18.5494i	−0.674191	+	0.674191i	0.284488	+	0.958679i	$0.408176\pi$
$758$		0			0
$759$	12.2747	−	17.5616i	0.445544	−	0.637447i
$760$		0			0
$761$	33.0626	−	19.0887i	1.19852	−	0.691965i	0.238294	−	0.971193i	$-0.423412\pi$
$761$	33.0626	−	19.0887i	1.19852	−	0.691965i	0.960225	+	0.279228i	$0.0900784\pi$
$762$		0			0
$763$	−9.25898	+	13.2750i	−0.335198	+	0.480587i
$764$		0			0
$765$	−11.7699	+	25.9435i	−0.425541	+	0.937988i
$766$		0			0
$767$	−42.7184	+	11.4464i	−1.54247	+	0.413304i
$768$		0			0
$769$		−	16.7248i		−	0.603110i	−0.953449	−	0.301555i	$-0.902494\pi$
$769$		−	16.7248i		−	0.603110i	0.953449	−	0.301555i	$-0.0975057\pi$
$770$		0			0
$771$	−42.8207	−	3.70989i	−1.54215	−	0.133608i
$772$		0			0
$773$	1.57137	+	5.86442i	0.0565182	+	0.210929i	0.988410	−	0.151807i	$-0.0485093\pi$
$773$	1.57137	+	5.86442i	0.0565182	+	0.210929i	−0.931892	+	0.362736i	$0.881843\pi$
$774$		0			0
$775$	12.0138	+	19.9932i	0.431548	+	0.718179i
$776$		0			0
$777$	10.4362	+	1.81135i	0.374397	+	0.0649819i
$778$		0			0
$779$	1.80418	+	3.12493i	0.0646415	+	0.111962i
$780$		0			0
$781$	4.30379	−	7.45438i	0.154002	−	0.266739i
$782$		0			0
$783$	−10.3321	−	17.7915i	−0.369240	−	0.635817i
$784$		0			0
$785$	2.10631	+	2.06982i	0.0751774	+	0.0738749i
$786$		0			0
$787$	−3.20956	−	11.9782i	−0.114409	−	0.426978i	0.884833	−	0.465907i	$-0.154272\pi$
$787$	−3.20956	−	11.9782i	−0.114409	−	0.426978i	−0.999242	+	0.0389290i	$0.987605\pi$
$788$		0			0
$789$	18.8229	−	8.79664i	0.670115	−	0.313169i
$790$		0			0
$791$	33.4006	+	39.6572i	1.18759	+	1.41005i
$792$		0			0
$793$	17.6917	−	66.0262i	0.628249	−	2.34466i
$794$		0			0
$795$	−14.1240	+	20.5883i	−0.500927	+	0.730191i
$796$		0			0
$797$	−17.2195	−	17.2195i	−0.609945	−	0.609945i	0.332986	−	0.942932i	$-0.391944\pi$
$797$	−17.2195	−	17.2195i	−0.609945	−	0.609945i	−0.942932	+	0.332986i	$0.891944\pi$
$798$		0			0
$799$		−	41.0694i		−	1.45293i
$800$		0			0
$801$	−3.02271	−	2.52766i	−0.106802	−	0.0893106i
$802$		0			0
$803$	−22.4491	−	6.01521i	−0.792210	−	0.212272i
$804$		0			0
$805$	−6.26332	−	33.4489i	−0.220753	−	1.17892i
$806$		0			0
$807$	5.36531	+	1.94768i	0.188868	+	0.0685617i
$808$		0			0
$809$	−0.599532	+	1.03842i	−0.0210784	+	0.0365089i	−0.876372	−	0.481634i	$-0.840043\pi$
$809$	−0.599532	+	1.03842i	−0.0210784	+	0.0365089i	0.855294	+	0.518143i	$0.173377\pi$
$810$		0			0
$811$	−24.0455			−0.844353			−0.422176	−	0.906514i	$-0.638734\pi$
$811$	−24.0455			−0.844353			−0.422176	+	0.906514i	$0.638734\pi$
$812$		0			0
$813$	−10.7706	+	9.05309i	−0.377740	+	0.317506i
$814$		0			0
$815$	−13.3286	−	48.0592i	−0.466880	−	1.68344i
$816$		0			0
$817$	−3.56155	−	0.954314i	−0.124603	−	0.0333872i
$818$		0			0
$819$	21.7397	−	37.9626i	0.759646	−	1.32652i
$820$		0			0
$821$	33.8794	−	19.5603i	1.18240	−	0.682659i	0.225831	−	0.974166i	$-0.427490\pi$
$821$	33.8794	−	19.5603i	1.18240	−	0.682659i	0.956568	+	0.291508i	$0.0941569\pi$
$822$		0			0
$823$	1.79793	−	0.481753i	0.0626718	−	0.0167929i	−0.227347	−	0.973814i	$-0.573005\pi$
$823$	1.79793	−	0.481753i	0.0626718	−	0.0167929i	0.290019	+	0.957021i	$0.406338\pi$
$824$		0			0
$825$	−12.2309	−	14.0454i	−0.425826	−	0.489000i
$826$		0			0
$827$	23.1571	+	23.1571i	0.805251	+	0.805251i	0.983911	−	0.178660i	$-0.0571763\pi$
$827$	23.1571	+	23.1571i	0.805251	+	0.805251i	−0.178660	+	0.983911i	$0.557176\pi$
$828$		0			0
$829$	−27.5833	−	15.9252i	−0.958008	−	0.553106i	−0.0624485	−	0.998048i	$-0.519891\pi$
$829$	−27.5833	−	15.9252i	−0.958008	−	0.553106i	−0.895559	+	0.444942i	$0.853224\pi$
$830$		0			0
$831$	44.5221	−	20.8068i	1.54445	−	0.721779i
$832$		0			0
$833$	29.6048	−	2.69967i	1.02575	−	0.0935379i
$834$		0			0
$835$	15.3105	+	3.95938i	0.529842	+	0.137020i
$836$		0			0
$837$	−24.2401	+	0.0614089i	−0.837860	+	0.00212260i
$838$		0			0
$839$	25.9027			0.894262			0.447131	−	0.894469i	$-0.352446\pi$
$839$	25.9027			0.894262			0.447131	+	0.894469i	$0.352446\pi$
$840$		0			0
$841$	−13.3226			−0.459399
$842$		0			0
$843$	24.7879	−	4.39237i	0.853742	−	0.151281i
$844$		0			0
$845$	−19.7218	−	33.4801i	−0.678450	−	1.15175i
$846$		0			0
$847$	15.2734	−	7.15629i	0.524801	−	0.245893i
$848$		0			0
$849$	−2.13354	−	4.56532i	−0.0732229	−	0.156681i
$850$		0			0
$851$	11.5143	+	6.64781i	0.394706	+	0.227884i
$852$		0			0
$853$	−25.9730	−	25.9730i	−0.889299	−	0.889299i	0.105157	−	0.994456i	$-0.466465\pi$
$853$	−25.9730	−	25.9730i	−0.889299	−	0.889299i	−0.994456	+	0.105157i	$0.966465\pi$
$854$		0			0
$855$	−0.798514	+	4.82208i	−0.0273086	+	0.164912i
$856$		0			0
$857$	17.0839	−	4.57762i	0.583575	−	0.156368i	0.0450600	−	0.998984i	$-0.485652\pi$
$857$	17.0839	−	4.57762i	0.583575	−	0.156368i	0.538515	+	0.842616i	$0.318985\pi$
$858$		0			0
$859$	14.7883	−	8.53804i	0.504571	−	0.291314i	−0.226028	−	0.974121i	$-0.572574\pi$
$859$	14.7883	−	8.53804i	0.504571	−	0.291314i	0.730599	+	0.682806i	$0.239241\pi$
$860$		0			0
$861$	−2.03853	−	22.6026i	−0.0694730	−	0.770294i
$862$		0			0
$863$	4.54605	+	1.21811i	0.154749	+	0.0414650i	0.335362	−	0.942089i	$-0.391141\pi$
$863$	4.54605	+	1.21811i	0.154749	+	0.0414650i	−0.180613	+	0.983554i	$0.557808\pi$
$864$		0			0
$865$	−6.01107	+	1.66709i	−0.204383	+	0.0566828i
$866$		0			0
$867$	−1.15393	−	1.37284i	−0.0391894	−	0.0466241i
$868$		0			0
$869$	16.4153			0.556851
$870$		0			0
$871$	−1.72910	+	2.99489i	−0.0585884	+	0.101478i
$872$		0			0
$873$	−17.9022	+	38.5612i	−0.605897	+	1.30510i
$874$		0			0
$875$	−29.5286	−	1.75062i	−0.998247	−	0.0591817i
$876$		0			0
$877$	21.3601	+	5.72343i	0.721281	+	0.193267i	0.600743	−	0.799442i	$-0.294872\pi$
$877$	21.3601	+	5.72343i	0.721281	+	0.193267i	0.120538	+	0.992709i	$0.461538\pi$
$878$		0			0
$879$	−24.0352	−	16.7994i	−0.810688	−	0.566630i
$880$		0			0
$881$		−	49.8630i		−	1.67993i	−0.542642	−	0.839964i	$-0.682576\pi$
$881$		−	49.8630i		−	1.67993i	0.542642	−	0.839964i	$-0.317424\pi$
$882$		0			0
$883$	−17.7492	−	17.7492i	−0.597308	−	0.597308i	0.342287	−	0.939595i	$-0.388798\pi$
$883$	−17.7492	−	17.7492i	−0.597308	−	0.597308i	−0.939595	+	0.342287i	$0.888798\pi$
$884$		0			0
$885$	−30.5519	+	5.68952i	−1.02699	+	0.191251i
$886$		0			0
$887$	−6.64206	+	24.7885i	−0.223019	+	0.832316i	0.760170	+	0.649724i	$0.225116\pi$
$887$	−6.64206	+	24.7885i	−0.223019	+	0.832316i	−0.983189	+	0.182592i	$0.941551\pi$
$888$		0			0
$889$	10.4691	+	12.4301i	0.351121	+	0.416893i
$890$		0			0
$891$	19.0496	−	3.42534i	0.638185	−	0.114753i
$892$		0			0
$893$	−1.82370	−	6.80615i	−0.0610279	−	0.227759i
$894$		0			0
$895$	0.277364	+	31.7413i	0.00927125	+	1.06099i
$896$		0			0
$897$	42.0351	−	35.3322i	1.40351	−	1.17971i
$898$		0			0
$899$	9.23552	−	15.9964i	0.308022	−	0.533509i
$900$		0			0
$901$	−13.6886	−	23.7093i	−0.456033	−	0.789872i
$902$		0			0
$903$	17.8045	+	14.8586i	0.592497	+	0.494463i
$904$		0			0
$905$	19.3203	−	11.3808i	0.642230	−	0.378312i
$906$		0			0
$907$	0.432502	+	1.61412i	0.0143610	+	0.0535960i	0.972735	−	0.231921i	$-0.0745012\pi$
$907$	0.432502	+	1.61412i	0.0143610	+	0.0535960i	−0.958374	+	0.285517i	$0.907835\pi$
$908$		0			0
$909$	−23.0105	−	4.01732i	−0.763211	−	0.133246i
$910$		0			0
$911$			40.8752i			1.35426i	0.735865	+	0.677129i	$0.236776\pi$
$911$			40.8752i			1.35426i	−0.735865	+	0.677129i	$0.763224\pi$
$912$		0			0
$913$	−19.2772	+	5.16532i	−0.637983	+	0.170947i
$914$		0			0
$915$	15.9951	−	45.2919i	0.528782	−	1.49731i
$916$		0			0
$917$	24.1619	+	51.5679i	0.797895	+	1.70292i
$918$		0			0
$919$	−17.0980	+	9.87155i	−0.564012	+	0.325632i	−0.754754	−	0.656008i	$-0.772244\pi$
$919$	−17.0980	+	9.87155i	−0.564012	+	0.325632i	0.190742	+	0.981640i	$0.438911\pi$
$920$		0			0
$921$	−11.8348	−	8.27194i	−0.389970	−	0.272570i
$922$		0			0
$923$	15.5987	−	15.5987i	0.513437	−	0.513437i
$924$		0			0
$925$	8.02802	−	8.31364i	0.263960	−	0.273351i
$926$		0			0
$927$	5.31213	+	59.5592i	0.174473	+	1.95618i
$928$		0			0
$929$	−25.3654	−	43.9342i	−0.832212	−	1.44143i	−0.896281	−	0.443487i	$-0.853741\pi$
$929$	−25.3654	−	43.9342i	−0.832212	−	1.44143i	0.0640690	−	0.997945i	$-0.479592\pi$
$930$		0			0
$931$	4.78633	−	1.76201i	0.156866	−	0.0577477i
$932$		0			0
$933$	0.542175	−	1.49354i	0.0177500	−	0.0488962i
$934$		0			0
$935$	19.6793	−	5.45780i	0.643582	−	0.178489i
$936$		0			0
$937$	−26.5787	+	26.5787i	−0.868287	+	0.868287i	−0.992283	−	0.123995i	$-0.960429\pi$
$937$	−26.5787	+	26.5787i	−0.868287	+	0.868287i	0.123995	+	0.992283i	$0.460429\pi$
$938$		0			0
$939$	−2.13607	−	0.185065i	−0.0697080	−	0.00603935i
$940$		0			0
$941$	23.6212	+	13.6377i	0.770030	+	0.444577i	0.832885	−	0.553446i	$-0.186687\pi$
$941$	23.6212	+	13.6377i	0.770030	+	0.444577i	−0.0628556	+	0.998023i	$0.520021\pi$
$942$		0			0
$943$	7.37283	−	27.5158i	0.240093	−	0.896037i
$944$		0			0
$945$	17.3007	−	25.4104i	0.562790	−	0.826600i
$946$		0			0
$947$	0.412833	−	1.54071i	0.0134153	−	0.0500664i	−0.958894	−	0.283765i	$-0.908416\pi$
$947$	0.412833	−	1.54071i	0.0134153	−	0.0500664i	0.972309	+	0.233699i	$0.0750830\pi$
$948$		0			0
$949$	−51.5831	−	29.7815i	−1.67446	−	0.966748i
$950$		0			0
$951$	−28.0408	−	2.42939i	−0.909284	−	0.0787784i
$952$		0			0
$953$	−17.6192	+	17.6192i	−0.570741	+	0.570741i	−0.932336	−	0.361594i	$-0.882233\pi$
$953$	−17.6192	+	17.6192i	−0.570741	+	0.570741i	0.361594	+	0.932336i	$0.382233\pi$
$954$		0			0
$955$	−7.49980	+	13.2562i	−0.242688	+	0.428961i
$956$		0			0
$957$	−5.03262	+	13.8634i	−0.162681	+	0.448140i
$958$		0			0
$959$	−7.35964	−	41.2951i	−0.237655	−	1.33349i
$960$		0			0
$961$	4.61878	+	7.99997i	0.148993	+	0.258063i
$962$		0			0
$963$	−1.84328	−	20.6667i	−0.0593989	−	0.665976i
$964$		0			0
$965$	−13.3556	+	13.5911i	−0.429932	+	0.437512i
$966$		0			0
$967$	−8.13992	+	8.13992i	−0.261762	+	0.261762i	−0.825770	−	0.564007i	$-0.809259\pi$
$967$	−8.13992	+	8.13992i	−0.261762	+	0.261762i	0.564007	+	0.825770i	$0.309259\pi$
$968$		0			0
$969$	−4.39286	−	3.07039i	−0.141119	−	0.0986351i
$970$		0			0
$971$	3.45490	−	1.99469i	0.110873	−	0.0640125i	−0.443538	−	0.896256i	$-0.646277\pi$
$971$	3.45490	−	1.99469i	0.110873	−	0.0640125i	0.554411	+	0.832243i	$0.312944\pi$
$972$		0			0
$973$	−30.1417	−	2.58130i	−0.966298	−	0.0827527i
$974$		0			0
$975$	−20.9613	−	42.8827i	−0.671300	−	1.37335i
$976$		0			0
$977$	−45.5422	+	12.2030i	−1.45702	+	0.390408i	−0.898461	−	0.439054i	$-0.855314\pi$
$977$	−45.5422	+	12.2030i	−1.45702	+	0.390408i	−0.558563	+	0.829462i	$0.688647\pi$
$978$		0			0
$979$			2.82461i			0.0902751i
$980$		0			0
$981$	−18.0786	−	3.15627i	−0.577206	−	0.100772i
$982$		0			0
$983$	9.41853	+	35.1504i	0.300404	+	1.12112i	0.936830	+	0.349786i	$0.113746\pi$
$983$	9.41853	+	35.1504i	0.300404	+	1.12112i	−0.636425	+	0.771338i	$0.719588\pi$
$984$		0			0
$985$	−48.6205	−	12.5735i	−1.54918	−	0.400625i
$986$		0			0
$987$	−7.57845	+	43.6636i	−0.241225	+	1.38983i
$988$		0			0
$989$	14.5543	+	25.2089i	0.462801	+	0.801596i
$990$		0			0
$991$	−7.14153	+	12.3695i	−0.226858	+	0.392930i	−0.956875	−	0.290499i	$-0.906179\pi$
$991$	−7.14153	+	12.3695i	−0.226858	+	0.392930i	0.730017	+	0.683429i	$0.239512\pi$
$992$		0			0
$993$	−14.4168	+	12.1179i	−0.457503	+	0.384549i
$994$		0			0
$995$	−19.8309	+	0.173288i	−0.628681	+	0.00549359i
$996$		0			0
$997$	−9.15638	−	34.1721i	−0.289985	−	1.08224i	−0.945119	−	0.326727i	$-0.894054\pi$
$997$	−9.15638	−	34.1721i	−0.289985	−	1.08224i	0.655133	−	0.755513i	$-0.272612\pi$
$998$		0			0
$999$	3.13791	+	11.5933i	0.0992792	+	0.366796i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.bv.c.53.6	✓	48
3.2	odd	2	inner	420.2.bv.c.53.8	yes	48
5.2	odd	4	inner	420.2.bv.c.137.1	yes	48
7.2	even	3	inner	420.2.bv.c.233.11	yes	48
15.2	even	4	inner	420.2.bv.c.137.11	yes	48
21.2	odd	6	inner	420.2.bv.c.233.1	yes	48
35.2	odd	12	inner	420.2.bv.c.317.8	yes	48
105.2	even	12	inner	420.2.bv.c.317.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bv.c.53.6	✓	48	1.1	even	1	trivial
420.2.bv.c.53.8	yes	48	3.2	odd	2	inner
420.2.bv.c.137.1	yes	48	5.2	odd	4	inner
420.2.bv.c.137.11	yes	48	15.2	even	4	inner
420.2.bv.c.233.1	yes	48	21.2	odd	6	inner
420.2.bv.c.233.11	yes	48	7.2	even	3	inner
420.2.bv.c.317.6	yes	48	105.2	even	12	inner
420.2.bv.c.317.8	yes	48	35.2	odd	12	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.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.302208 - 1.70548i) q^{3} +(-1.92665 + 1.13491i) q^{5} +(-0.225753 + 2.63610i) q^{7} +(-2.81734 + 1.03082i) q^{9} +O(q^{10})\)	\(q+(-0.302208 - 1.70548i) q^{3} +(-1.92665 + 1.13491i) q^{5} +(-0.225753 + 2.63610i) q^{7} +(-2.81734 + 1.03082i) q^{9} +(1.86244 + 1.07528i) q^{11} +(3.89727 + 3.89727i) q^{13} +(2.51782 + 2.94289i) q^{15} +(-4.10211 + 1.09916i) q^{17} +(-0.631006 + 0.364311i) q^{19} +(4.56405 - 0.411633i) q^{21} +(5.55616 + 1.48877i) q^{23} +(2.42395 - 4.37315i) q^{25} +(2.60947 + 4.49340i) q^{27} -3.95947 q^{29} +(-2.33251 + 4.04003i) q^{31} +(1.27103 - 3.50133i) q^{33} +(-2.55680 - 5.33505i) q^{35} +(2.23265 + 0.598238i) q^{37} +(5.46894 - 7.82450i) q^{39} -4.95231i q^{41} +(3.57830 + 3.57830i) q^{43} +(4.25814 - 5.18346i) q^{45} +(-2.50295 + 9.34112i) q^{47} +(-6.89807 - 1.19022i) q^{49} +(3.11428 + 6.66390i) q^{51} +(1.66848 + 6.22687i) q^{53} +(-4.80863 + 0.0420191i) q^{55} +(0.812022 + 0.966072i) q^{57} +(-4.01205 + 6.94907i) q^{59} +(-6.20108 - 10.7406i) q^{61} +(-2.08132 - 7.65951i) q^{63} +(-11.9317 - 3.08561i) q^{65} +(0.162395 + 0.606066i) q^{67} +(0.859954 - 9.92585i) q^{69} -4.00247i q^{71} +(-10.4387 + 2.79703i) q^{73} +(-8.19087 - 2.81240i) q^{75} +(-3.25501 + 4.66685i) q^{77} +(6.61039 - 3.81651i) q^{79} +(6.87482 - 5.80834i) q^{81} +(-6.56196 + 6.56196i) q^{83} +(6.65587 - 6.77322i) q^{85} +(1.19658 + 6.75282i) q^{87} +(0.656714 + 1.13746i) q^{89} +(-11.1534 + 9.39378i) q^{91} +(7.59510 + 2.75713i) q^{93} +(0.802265 - 1.41804i) q^{95} +(10.0207 - 10.0207i) q^{97} +(-6.35557 - 1.10959i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{3} - 8 q^{7}+O(q^{10}) \) 48 * q - 2 * q^3 - 8 * q^7	\( 48 q - 2 q^{3} - 8 q^{7} + 32 q^{13} - 16 q^{21} + 16 q^{25} - 32 q^{27} - 64 q^{31} + 34 q^{33} - 40 q^{37} - 24 q^{43} + 30 q^{45} + 36 q^{51} + 92 q^{57} - 18 q^{63} + 28 q^{67} - 8 q^{73} - 38 q^{75} + 20 q^{81} - 56 q^{85} - 24 q^{87} - 24 q^{91} + 6 q^{93} + 56 q^{97}+O(q^{100}) \) 48 * q - 2 * q^3 - 8 * q^7 + 32 * q^13 - 16 * q^21 + 16 * q^25 - 32 * q^27 - 64 * q^31 + 34 * q^33 - 40 * q^37 - 24 * q^43 + 30 * q^45 + 36 * q^51 + 92 * q^57 - 18 * q^63 + 28 * q^67 - 8 * q^73 - 38 * q^75 + 20 * q^81 - 56 * q^85 - 24 * q^87 - 24 * q^91 + 6 * q^93 + 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more