LMFDB - Embedded newform 420.2.bv.c.317.8

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			317.8
Character	$\chi$	$=$	420.317
Dual form			420.2.bv.c.53.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.591022 - 1.62810i) q^{3} +(1.92665 + 1.13491i) q^{5} +(-0.225753 - 2.63610i) q^{7} +(-2.30139 - 1.92448i) q^{9} +O(q^{10})$	\(q+(0.591022 - 1.62810i) q^{3} +(1.92665 + 1.13491i) q^{5} +(-0.225753 - 2.63610i) q^{7} +(-2.30139 - 1.92448i) q^{9} +(-1.86244 + 1.07528i) q^{11} +(3.89727 - 3.89727i) q^{13} +(2.98644 - 2.46601i) q^{15} +(4.10211 + 1.09916i) q^{17} +(-0.631006 - 0.364311i) q^{19} +(-4.42525 - 1.19045i) q^{21} +(-5.55616 + 1.48877i) q^{23} +(2.42395 + 4.37315i) q^{25} +(-4.49340 + 2.60947i) q^{27} +3.95947 q^{29} +(-2.33251 - 4.04003i) q^{31} +(0.649918 + 3.66775i) q^{33} +(2.55680 - 5.33505i) q^{35} +(2.23265 - 0.598238i) q^{37} +(-4.04175 - 8.64849i) q^{39} -4.95231i q^{41} +(3.57830 - 3.57830i) q^{43} +(-2.24985 - 6.31967i) q^{45} +(2.50295 + 9.34112i) q^{47} +(-6.89807 + 1.19022i) q^{49} +(4.21396 - 6.02899i) q^{51} +(-1.66848 + 6.22687i) q^{53} +(-4.80863 - 0.0420191i) q^{55} +(-0.966072 + 0.812022i) q^{57} +(4.01205 + 6.94907i) q^{59} +(-6.20108 + 10.7406i) q^{61} +(-4.55358 + 6.50115i) q^{63} +(11.9317 - 3.08561i) q^{65} +(0.162395 - 0.606066i) q^{67} +(-0.859954 + 9.92585i) q^{69} -4.00247i q^{71} +(-10.4387 - 2.79703i) q^{73} +(8.55252 - 1.36179i) q^{75} +(3.25501 + 4.66685i) q^{77} +(6.61039 + 3.81651i) q^{79} +(1.59276 + 8.85794i) q^{81} +(6.56196 + 6.56196i) q^{83} +(6.65587 + 6.77322i) q^{85} +(2.34014 - 6.44640i) q^{87} +(-0.656714 + 1.13746i) q^{89} +(-11.1534 - 9.39378i) q^{91} +(-7.95611 + 1.40981i) q^{93} +(-0.802265 - 1.41804i) q^{95} +(10.0207 + 10.0207i) q^{97} +(6.35557 + 1.10959i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.591022	−	1.62810i	0.341226	−	0.939981i
$3$	0.591022	−	1.62810i	0.341226	−	0.939981i
$4$		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
$9$	−2.30139	−	1.92448i	−0.767129	−	0.641493i
$10$		0			0
$11$	−1.86244	+	1.07528i	−0.561548	+	0.324210i	−0.753767	−	0.657142i	$-0.771765\pi$
$11$	−1.86244	+	1.07528i	−0.561548	+	0.324210i	0.192218	+	0.981352i	$0.438432\pi$
$12$		0			0
$13$	3.89727	−	3.89727i	1.08091	−	1.08091i	0.0844823	−	0.996425i	$-0.473076\pi$
$13$	3.89727	−	3.89727i	1.08091	−	1.08091i	0.996425	−	0.0844823i	$-0.0269237\pi$
$14$		0			0
$15$	2.98644	−	2.46601i	0.771094	−	0.636721i
$16$		0			0
$17$	4.10211	+	1.09916i	0.994907	+	0.266584i	0.719310	−	0.694689i	$-0.244458\pi$
$17$	4.10211	+	1.09916i	0.994907	+	0.266584i	0.275596	+	0.961273i	$0.411125\pi$
$18$		0			0
$19$	−0.631006	−	0.364311i	−0.144763	−	0.0835788i	0.425869	−	0.904785i	$-0.359968\pi$
$19$	−0.631006	−	0.364311i	−0.144763	−	0.0835788i	−0.570632	+	0.821206i	$0.693302\pi$
$20$		0			0
$21$	−4.42525	−	1.19045i	−0.965669	−	0.259777i
$22$		0			0
$23$	−5.55616	+	1.48877i	−1.15854	+	0.310430i	−0.786382	−	0.617740i	$-0.788048\pi$
$23$	−5.55616	+	1.48877i	−1.15854	+	0.310430i	−0.372157	+	0.928170i	$0.621382\pi$
$24$		0			0
$25$	2.42395	+	4.37315i	0.484790	+	0.874631i
$26$		0			0
$27$	−4.49340	+	2.60947i	−0.864756	+	0.502192i
$28$		0			0
$29$	3.95947			0.735256			0.367628	−	0.929973i	$-0.380170\pi$
$29$	3.95947			0.735256			0.367628	+	0.929973i	$0.380170\pi$
$30$		0			0
$31$	−2.33251	−	4.04003i	−0.418931	−	0.725610i	0.576901	−	0.816814i	$-0.304262\pi$
$31$	−2.33251	−	4.04003i	−0.418931	−	0.725610i	−0.995832	+	0.0912037i	$0.970929\pi$
$32$		0			0
$33$	0.649918	+	3.66775i	0.113136	+	0.638474i
$34$		0			0
$35$	2.55680	−	5.33505i	0.432178	−	0.901788i
$36$		0			0
$37$	2.23265	−	0.598238i	0.367046	−	0.0983497i	−0.0705816	−	0.997506i	$-0.522486\pi$
$37$	2.23265	−	0.598238i	0.367046	−	0.0983497i	0.437628	+	0.899156i	$0.355819\pi$
$38$		0			0
$39$	−4.04175	−	8.64849i	−0.647198	−	1.38487i
$40$		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	−0.379504	−	0.925190i	$-0.623905\pi$
$43$	3.57830	−	3.57830i	0.545686	−	0.545686i	0.925190	+	0.379504i	$0.123905\pi$
$44$		0			0
$45$	−2.24985	−	6.31967i	−0.335388	−	0.942080i
$46$		0			0
$47$	2.50295	+	9.34112i	0.365092	+	1.36254i	0.867296	+	0.497793i	$0.165856\pi$
$47$	2.50295	+	9.34112i	0.365092	+	1.36254i	−0.502204	+	0.864749i	$0.667477\pi$
$48$		0			0
$49$	−6.89807	+	1.19022i	−0.985439	+	0.170031i
$50$		0			0
$51$	4.21396	−	6.02899i	0.590073	−	0.844228i
$52$		0			0
$53$	−1.66848	+	6.22687i	−0.229184	+	0.855326i	0.751501	+	0.659732i	$0.229330\pi$
$53$	−1.66848	+	6.22687i	−0.229184	+	0.855326i	−0.980685	+	0.195594i	$0.937337\pi$
$54$		0			0
$55$	−4.80863	−	0.0420191i	−0.648395	−	0.00566586i
$56$		0			0
$57$	−0.966072	+	0.812022i	−0.127959	+	0.107555i
$58$		0			0
$59$	4.01205	+	6.94907i	0.522324	+	0.904692i	0.999663	+	0.0259723i	$0.00826815\pi$
$59$	4.01205	+	6.94907i	0.522324	+	0.904692i	−0.477339	+	0.878719i	$0.658399\pi$
$60$		0			0
$61$	−6.20108	+	10.7406i	−0.793967	+	1.37519i	0.129526	+	0.991576i	$0.458654\pi$
$61$	−6.20108	+	10.7406i	−0.793967	+	1.37519i	−0.923493	+	0.383615i	$0.874679\pi$
$62$		0			0
$63$	−4.55358	+	6.50115i	−0.573697	+	0.819068i
$64$		0			0
$65$	11.9317	−	3.08561i	1.47995	−	0.382722i
$66$		0			0
$67$	0.162395	−	0.606066i	0.0198397	−	0.0740427i	−0.955296	−	0.295650i	$-0.904464\pi$
$67$	0.162395	−	0.606066i	0.0198397	−	0.0740427i	0.975136	+	0.221608i	$0.0711304\pi$
$68$		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	−0.410391	−	0.911910i	$-0.634608\pi$
$73$	−10.4387	−	2.79703i	−1.22175	−	0.327368i	−0.811364	+	0.584542i	$0.801274\pi$
$74$		0			0
$75$	8.55252	−	1.36179i	0.987559	−	0.157246i
$76$		0			0
$77$	3.25501	+	4.66685i	0.370943	+	0.531837i
$78$		0			0
$79$	6.61039	+	3.81651i	0.743727	+	0.429391i	0.823423	−	0.567428i	$-0.192062\pi$
$79$	6.61039	+	3.81651i	0.743727	+	0.429391i	−0.0796961	+	0.996819i	$0.525395\pi$
$80$		0			0
$81$	1.59276	+	8.85794i	0.176974	+	0.984216i
$82$		0			0
$83$	6.56196	+	6.56196i	0.720268	+	0.720268i	0.968660	−	0.248392i	$-0.0799020\pi$
$83$	6.56196	+	6.56196i	0.720268	+	0.720268i	−0.248392	+	0.968660i	$0.579902\pi$
$84$		0			0
$85$	6.65587	+	6.77322i	0.721930	+	0.734658i
$86$		0			0
$87$	2.34014	−	6.44640i	0.250889	−	0.691127i
$88$		0			0
$89$	−0.656714	+	1.13746i	−0.0696116	+	0.120571i	−0.898730	−	0.438502i	$-0.855509\pi$
$89$	−0.656714	+	1.13746i	−0.0696116	+	0.120571i	0.829119	+	0.559072i	$0.188843\pi$
$90$		0			0
$91$	−11.1534	−	9.39378i	−1.16920	−	0.984735i
$92$		0			0
$93$	−7.95611	+	1.40981i	−0.825011	+	0.146190i
$94$		0			0
$95$	−0.802265	−	1.41804i	−0.0823107	−	0.145487i
$96$		0			0
$97$	10.0207	+	10.0207i	1.01745	+	1.01745i	0.999845	+	0.0176018i	$0.00560313\pi$
$97$	10.0207	+	10.0207i	1.01745	+	1.01745i	0.0176018	+	0.999845i	$0.494397\pi$
$98$		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	$-0.793286\pi$
$101$	−6.74304	+	3.89310i	−0.670958	+	0.387378i	0.125482	+	0.992096i	$0.459952\pi$
$102$		0			0
$103$	5.15875	+	19.2527i	0.508307	+	1.89703i	0.436731	+	0.899592i	$0.356136\pi$
$103$	5.15875	+	19.2527i	0.508307	+	1.89703i	0.0715756	+	0.997435i	$0.477197\pi$
$104$		0			0
$105$	−7.17485	−	7.31584i	−0.700194	−	0.713953i
$106$		0			0
$107$	1.79006	+	6.68059i	0.173052	+	0.645837i	0.996875	+	0.0789913i	$0.0251699\pi$
$107$	1.79006	+	6.68059i	0.173052	+	0.645837i	−0.823824	+	0.566846i	$0.808163\pi$
$108$		0			0
$109$	5.29779	−	3.05868i	0.507436	−	0.292968i	−0.224343	−	0.974510i	$-0.572024\pi$
$109$	5.29779	−	3.05868i	0.507436	−	0.292968i	0.731779	+	0.681542i	$0.238690\pi$
$110$		0			0
$111$	0.345559	−	3.98854i	0.0327990	−	0.378576i
$112$		0			0
$113$	−13.8572	−	13.8572i	−1.30357	−	1.30357i	−0.925967	−	0.377605i	$-0.876748\pi$
$113$	−13.8572	−	13.8572i	−1.30357	−	1.30357i	−0.377605	−	0.925967i	$-0.623252\pi$
$114$		0			0
$115$	−12.3944	−	3.43742i	−1.15578	−	0.320541i
$116$		0			0
$117$	−16.4693	+	1.46891i	−1.52259	+	0.135801i
$118$		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
$123$	−8.06282	−	2.92692i	−0.727000	−	0.263911i
$124$		0			0
$125$	−0.293050	+	11.1765i	−0.0262112	+	0.999656i
$126$		0			0
$127$	4.34338	+	4.34338i	0.385412	+	0.385412i	0.873047	−	0.487635i	$-0.162140\pi$
$127$	4.34338	+	4.34338i	0.385412	+	0.385412i	−0.487635	+	0.873047i	$0.662140\pi$
$128$		0			0
$129$	−3.71096	−	7.94067i	−0.326732	−	0.699137i
$130$		0			0
$131$	−18.6405	−	10.7621i	−1.62863	−	0.940289i	−0.984503	−	0.175370i	$-0.943888\pi$
$131$	−18.6405	−	10.7621i	−1.62863	−	0.940289i	−0.644126	−	0.764919i	$-0.722779\pi$
$132$		0			0
$133$	−0.817911	+	1.74564i	−0.0709219	+	0.151366i
$134$		0			0
$135$	−11.6187	−	0.0720916i	−0.999981	−	0.00620466i
$136$		0			0
$137$	15.3138	+	4.10332i	1.30835	+	0.350570i	0.844600	−	0.535397i	$-0.179838\pi$
$137$	15.3138	+	4.10332i	1.30835	+	0.350570i	0.463747	+	0.885968i	$0.346505\pi$
$138$		0			0
$139$		−	11.4342i		−	0.969835i	−0.874560	−	0.484917i	$-0.838850\pi$
$139$		−	11.4342i		−	0.969835i	0.874560	−	0.484917i	$-0.161150\pi$
$140$		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
$147$	−2.13913	+	11.9342i	−0.176432	+	0.984313i
$148$		0			0
$149$	4.30668	−	7.45938i	0.352817	−	0.611096i	−0.633925	−	0.773394i	$-0.718557\pi$
$149$	4.30668	−	7.45938i	0.352817	−	0.611096i	0.986742	+	0.162298i	$0.0518906\pi$
$150$		0			0
$151$	4.98113	+	8.62757i	0.405358	+	0.702101i	0.994363	−	0.106028i	$-0.0338134\pi$
$151$	4.98113	+	8.62757i	0.405358	+	0.702101i	−0.589005	+	0.808130i	$0.700480\pi$
$152$		0			0
$153$	−7.32523	−	10.4240i	−0.592210	−	0.842730i
$154$		0			0
$155$	0.0911482	−	10.4309i	0.00732120	−	0.837831i
$156$		0			0
$157$	−0.341811	+	1.27566i	−0.0272795	+	0.101808i	−0.978223	−	0.207555i	$-0.933449\pi$
$157$	−0.341811	+	1.27566i	−0.0272795	+	0.101808i	0.950944	+	0.309364i	$0.100116\pi$
$158$		0			0
$159$	9.15182	+	6.39666i	0.725786	+	0.507288i
$160$		0			0
$161$	5.17886	+	14.3105i	0.408152	+	1.12783i
$162$		0			0
$163$	−5.77269	−	21.5440i	−0.452152	−	1.68745i	−0.696328	−	0.717724i	$-0.745184\pi$
$163$	−5.77269	−	21.5440i	−0.452152	−	1.68745i	0.244176	−	0.969731i	$-0.421483\pi$
$164$		0			0
$165$	−2.91041	+	7.80407i	−0.226575	+	0.607546i
$166$		0			0
$167$	5.00089	−	5.00089i	0.386980	−	0.386980i	−0.486629	−	0.873609i	$-0.661774\pi$
$167$	5.00089	−	5.00089i	0.386980	−	0.386980i	0.873609	+	0.486629i	$0.161774\pi$
$168$		0			0
$169$		−	17.3774i		−	1.33672i
$170$		0			0
$171$	0.751079	+	2.05278i	0.0574365	+	0.156980i
$172$		0			0
$173$	−2.69465	+	0.722028i	−0.204870	+	0.0548948i	−0.359795	−	0.933032i	$-0.617153\pi$
$173$	−2.69465	+	0.722028i	−0.204870	+	0.0548948i	0.154925	+	0.987926i	$0.450487\pi$
$174$		0			0
$175$	10.9809	−	7.37703i	0.830076	−	0.557651i
$176$		0			0
$177$	13.6849	−	2.42494i	1.02862	−	0.182270i
$178$		0			0
$179$	−7.09783	−	12.2938i	−0.530517	−	0.918882i	−0.999366	−	0.0356039i	$-0.988665\pi$
$179$	−7.09783	−	12.2938i	−0.530517	−	0.918882i	0.468849	−	0.883278i	$-0.344669\pi$
$180$		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
$183$	13.8217	+	16.4439i	1.02173	+	1.21557i
$184$		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
$189$	7.89322	+	11.2560i	0.574148	+	0.818752i
$190$		0			0
$191$	−5.89882	−	3.40569i	−0.426824	−	0.246427i	0.271169	−	0.962532i	$-0.412590\pi$
$191$	−5.89882	−	3.40569i	−0.426824	−	0.246427i	−0.697993	+	0.716105i	$0.745923\pi$
$192$		0			0
$193$	8.23125	+	2.20556i	0.592498	+	0.158759i	0.542595	−	0.839995i	$-0.317442\pi$
$193$	8.23125	+	2.20556i	0.592498	+	0.158759i	0.0499036	+	0.998754i	$0.484109\pi$
$194$		0			0
$195$	2.02824	−	21.2496i	0.145245	−	1.52172i
$196$		0			0
$197$	−15.8809	+	15.8809i	−1.13147	+	1.13147i	−0.141537	+	0.989933i	$0.545204\pi$
$197$	−15.8809	+	15.8809i	−1.13147	+	1.13147i	−0.989933	+	0.141537i	$0.954796\pi$
$198$		0			0
$199$	7.68076	−	4.43449i	0.544475	−	0.314353i	−0.202416	−	0.979300i	$-0.564879\pi$
$199$	7.68076	−	4.43449i	0.544475	−	0.314353i	0.746891	+	0.664947i	$0.231546\pi$
$200$		0			0
$201$	−0.890753	−	0.622592i	−0.0628289	−	0.0439143i
$202$		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
$207$	15.6520	+	7.26648i	1.08789	+	0.505055i
$208$		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
$213$	−6.51640	−	2.36555i	−0.446497	−	0.162085i
$214$		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
$219$	−10.7233	+	15.3420i	−0.724615	+	1.03672i
$220$		0			0
$221$	20.2707	−	11.7033i	1.36355	−	0.787249i
$222$		0			0
$223$	17.3260	−	17.3260i	1.16023	−	1.16023i	0.175810	−	0.984424i	$-0.443746\pi$
$223$	17.3260	−	17.3260i	1.16023	−	1.16023i	0.984424	−	0.175810i	$-0.0562545\pi$
$224$		0			0
$225$	2.83760	−	14.7292i	0.189173	−	0.981944i
$226$		0			0
$227$	−21.6202	−	5.79310i	−1.43498	−	0.384502i	−0.544207	−	0.838951i	$-0.683170\pi$
$227$	−21.6202	−	5.79310i	−1.43498	−	0.384502i	−0.890773	+	0.454449i	$0.849836\pi$
$228$		0			0
$229$	−18.9575	−	10.9451i	−1.25274	−	0.723272i	−0.281091	−	0.959681i	$-0.590696\pi$
$229$	−18.9575	−	10.9451i	−1.25274	−	0.723272i	−0.971654	+	0.236409i	$0.924030\pi$
$230$		0			0
$231$	9.52185	−	2.54126i	0.626492	−	0.167202i
$232$		0			0
$233$	22.6220	−	6.06156i	1.48202	−	0.397106i	0.574986	−	0.818163i	$-0.305008\pi$
$233$	22.6220	−	6.06156i	1.48202	−	0.397106i	0.907034	+	0.421058i	$0.138341\pi$
$234$		0			0
$235$	−5.77905	+	20.8377i	−0.376984	+	1.35930i
$236$		0			0
$237$	10.1205	−	8.50670i	0.657398	−	0.552569i
$238$		0			0
$239$	−19.7365			−1.27665			−0.638323	−	0.769769i	$-0.720372\pi$
$239$	−19.7365			−1.27665			−0.638323	+	0.769769i	$0.720372\pi$
$240$		0			0
$241$	−6.49458	−	11.2489i	−0.418353	−	0.724608i	0.577421	−	0.816446i	$-0.304059\pi$
$241$	−6.49458	−	11.2489i	−0.418353	−	0.724608i	−0.995774	+	0.0918384i	$0.970726\pi$
$242$		0			0
$243$	15.3629	+	2.64206i	0.985532	+	0.169489i
$244$		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
$249$	14.5617	−	6.80523i	0.922813	−	0.431264i
$250$		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
$255$	14.9612	−	6.83327i	0.936907	−	0.427916i
$256$		0			0
$257$	−6.42263	−	23.9696i	−0.400633	−	1.49518i	−0.811970	−	0.583699i	$-0.801605\pi$
$257$	−6.42263	−	23.9696i	−0.400633	−	1.49518i	0.411337	−	0.911483i	$-0.365062\pi$
$258$		0			0
$259$	−2.08104	−	5.75045i	−0.129310	−	0.357316i
$260$		0			0
$261$	−9.11228	−	7.61993i	−0.564036	−	0.471662i
$262$		0			0
$263$	−3.10469	+	11.5869i	−0.191444	+	0.714477i	0.801715	+	0.597706i	$0.203921\pi$
$263$	−3.10469	+	11.5869i	−0.191444	+	0.714477i	−0.993159	+	0.116771i	$0.962746\pi$
$264$		0			0
$265$	−10.2815	+	10.1034i	−0.631589	+	0.620647i
$266$		0			0
$267$	1.46376	+	1.74146i	0.0895809	+	0.106575i
$268$		0			0
$269$	1.64773	+	2.85395i	0.100464	+	0.174008i	0.911876	−	0.410466i	$-0.134634\pi$
$269$	1.64773	+	2.85395i	0.100464	+	0.174008i	−0.811412	+	0.584474i	$0.801301\pi$
$270$		0			0
$271$	−4.06164	+	7.03497i	−0.246727	+	0.427344i	−0.962616	−	0.270870i	$-0.912689\pi$
$271$	−4.06164	+	7.03497i	−0.246727	+	0.427344i	0.715889	+	0.698215i	$0.246022\pi$
$272$		0			0
$273$	−21.8859	+	12.6069i	−1.32459	+	0.763004i
$274$		0			0
$275$	−9.21685	−	5.53833i	−0.555797	−	0.333974i
$276$		0			0
$277$	7.34355	−	27.4065i	0.441231	−	1.64670i	−0.284467	−	0.958686i	$-0.591817\pi$
$277$	7.34355	−	27.4065i	0.441231	−	1.64670i	0.725699	−	0.688012i	$-0.241517\pi$
$278$		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	0.341376	−	0.939927i	$-0.389107\pi$
$283$	2.81028	+	0.753013i	0.167054	+	0.0447620i	−0.174323	+	0.984689i	$0.555774\pi$
$284$		0			0
$285$	−2.78285	+	0.468074i	−0.164842	+	0.0277263i
$286$		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
$291$	22.2371	−	10.3922i	1.30356	−	0.609201i
$292$		0			0
$293$	−11.9716	−	11.9716i	−0.699387	−	0.699387i	0.264891	−	0.964278i	$-0.414664\pi$
$293$	−11.9716	−	11.9716i	−0.699387	−	0.699387i	−0.964278	+	0.264891i	$0.914664\pi$
$294$		0			0
$295$	−0.156780	+	17.9417i	−0.00912808	+	1.04461i
$296$		0			0
$297$	5.56280	−	9.69167i	0.322786	−	0.562368i
$298$		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
$303$	2.35305	+	13.2792i	0.135179	+	0.762871i
$304$		0			0
$305$	−24.1369	+	13.6556i	−1.38208	+	0.781920i
$306$		0			0
$307$	5.89474	+	5.89474i	0.336431	+	0.336431i	0.855022	−	0.518591i	$-0.173543\pi$
$307$	5.89474	+	5.89474i	0.336431	+	0.336431i	−0.518591	+	0.855022i	$0.673543\pi$
$308$		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	$-0.674947\pi$
$311$	−0.794450	+	0.458676i	−0.0450491	+	0.0260091i	0.477306	+	0.878737i	$0.341613\pi$
$312$		0			0
$313$	0.320387	+	1.19570i	0.0181094	+	0.0675850i	0.974389	−	0.224868i	$-0.0721951\pi$
$313$	0.320387	+	1.19570i	0.0181094	+	0.0675850i	−0.956280	+	0.292453i	$0.905528\pi$
$314$		0			0
$315$	−16.1514	+	7.35751i	−0.910027	+	0.414549i
$316$		0			0
$317$	−4.20581	−	15.6963i	−0.236222	−	0.881591i	−0.977594	−	0.210498i	$-0.932492\pi$
$317$	−4.20581	−	15.6963i	−0.236222	−	0.881591i	0.741373	−	0.671093i	$-0.234175\pi$
$318$		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
$327$	−1.84871	−	10.4330i	−0.102234	−	0.576949i
$328$		0			0
$329$	24.0591	−	8.70680i	1.32642	−	0.480022i
$330$		0			0
$331$	−5.43665	+	9.41656i	−0.298825	+	0.517581i	−0.975868	−	0.218364i	$-0.929928\pi$
$331$	−5.43665	+	9.41656i	−0.298825	+	0.517581i	0.677042	+	0.735944i	$0.263261\pi$
$332$		0			0
$333$	−6.28950	−	2.91992i	−0.344662	−	0.160011i
$334$		0			0
$335$	1.00071	−	0.983371i	0.0546746	−	0.0537273i
$336$		0			0
$337$	−2.89002	−	2.89002i	−0.157430	−	0.157430i	0.623997	−	0.781427i	$-0.285508\pi$
$337$	−2.89002	−	2.89002i	−0.157430	−	0.157430i	−0.781427	+	0.623997i	$0.785508\pi$
$338$		0			0
$339$	−30.7507	+	14.3709i	−1.67015	+	0.780520i
$340$		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
$345$	−12.9218	+	18.1476i	−0.695686	+	0.977036i
$346$		0			0
$347$	−1.08593	−	0.290975i	−0.0582960	−	0.0156204i	0.229553	−	0.973296i	$-0.426274\pi$
$347$	−1.08593	−	0.290975i	−0.0582960	−	0.0156204i	−0.287849	+	0.957676i	$0.592940\pi$
$348$		0			0
$349$			33.7351i			1.80580i	0.429852	+	0.902899i	$0.358566\pi$
$349$			33.7351i			1.80580i	−0.429852	+	0.902899i	$0.641434\pi$
$350$		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	$-0.858135\pi$
$353$	1.77829	−	6.63668i	0.0946489	−	0.353235i	0.996966	+	0.0778384i	$0.0248018\pi$
$354$		0			0
$355$	4.54245	−	7.71136i	0.241088	−	0.409276i
$356$		0			0
$357$	−16.8444	−	9.74738i	−0.891498	−	0.515886i
$358$		0			0
$359$	1.02137	−	1.76907i	0.0539060	−	0.0933680i	−0.837813	−	0.545957i	$-0.816166\pi$
$359$	1.02137	−	1.76907i	0.0539060	−	0.0933680i	0.891719	+	0.452589i	$0.149500\pi$
$360$		0			0
$361$	−9.23455	−	15.9947i	−0.486029	−	0.841827i
$362$		0			0
$363$	7.10476	+	8.45262i	0.372903	+	0.443647i
$364$		0			0
$365$	−16.9373	−	17.2359i	−0.886537	−	0.902167i
$366$		0			0
$367$	−1.94879	+	7.27299i	−0.101726	+	0.379647i	−0.997953	−	0.0639485i	$-0.979631\pi$
$367$	−1.94879	+	7.27299i	−0.101726	+	0.379647i	0.896227	+	0.443596i	$0.146297\pi$
$368$		0			0
$369$	−9.53061	+	11.3972i	−0.496144	+	0.593313i
$370$		0			0
$371$	16.7913	+	2.99256i	0.871762	+	0.155366i
$372$		0			0
$373$	−0.374011	−	1.39583i	−0.0193655	−	0.0722732i	0.955567	−	0.294774i	$-0.0952445\pi$
$373$	−0.374011	−	1.39583i	−0.0193655	−	0.0722732i	−0.974932	+	0.222501i	$0.928578\pi$
$374$		0			0
$375$	18.0232	+	7.08267i	0.930714	+	0.365747i
$376$		0			0
$377$	15.4311	−	15.4311i	0.794744	−	0.794744i
$378$		0			0
$379$			1.83298i			0.0941538i	0.998891	+	0.0470769i	$0.0149906\pi$
$379$			1.83298i			0.0941538i	−0.998891	+	0.0470769i	$0.985009\pi$
$380$		0			0
$381$	9.63846	−	4.50440i	0.493793	−	0.230767i
$382$		0			0
$383$	16.8876	−	4.52502i	0.862916	−	0.231218i	0.199894	−	0.979817i	$-0.435940\pi$
$383$	16.8876	−	4.52502i	0.862916	−	0.231218i	0.663022	+	0.748600i	$0.269274\pi$
$384$		0			0
$385$	0.974795	+	12.6855i	0.0496801	+	0.646514i
$386$		0			0
$387$	−15.1214	+	1.34869i	−0.768665	+	0.0685578i
$388$		0			0
$389$	−11.9965	−	20.7786i	−0.608249	−	1.05352i	−0.991529	−	0.129886i	$-0.958539\pi$
$389$	−11.9965	−	20.7786i	−0.608249	−	1.05352i	0.383280	−	0.923632i	$-0.374794\pi$
$390$		0			0
$391$	−24.4283			−1.23539
$392$		0			0
$393$	−28.5387	+	23.9879i	−1.43959	+	1.21003i
$394$		0			0
$395$	8.40449	+	14.8553i	0.422876	+	0.747450i
$396$		0			0
$397$	22.9338	−	6.14509i	1.15101	−	0.308413i	0.367643	−	0.929967i	$-0.380165\pi$
$397$	22.9338	−	6.14509i	1.15101	−	0.308413i	0.783372	+	0.621554i	$0.213498\pi$
$398$		0			0
$399$	2.35867	+	2.36335i	0.118081	+	0.118315i
$400$		0			0
$401$	2.79781	+	1.61532i	0.139716	+	0.0806650i	0.568229	−	0.822871i	$-0.307629\pi$
$401$	2.79781	+	1.61532i	0.139716	+	0.0806650i	−0.428513	+	0.903536i	$0.640962\pi$
$402$		0			0
$403$	−24.8355	−	6.65465i	−1.23714	−	0.331492i
$404$		0			0
$405$	−6.98429	+	18.8738i	−0.347052	+	0.937846i
$406$		0			0
$407$	−3.51492	+	3.51492i	−0.174228	+	0.174228i
$408$		0			0
$409$	4.14956	−	2.39575i	0.205183	−	0.118462i	−0.393888	−	0.919158i	$-0.628870\pi$
$409$	4.14956	−	2.39575i	0.205183	−	0.118462i	0.599071	+	0.800696i	$0.295537\pi$
$410$		0			0
$411$	15.7314	−	22.5072i	0.775972	−	1.11020i
$412$		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
$417$	−18.6159	−	6.75785i	−0.911627	−	0.330933i
$418$		0			0
$419$	−20.3805			−0.995651			−0.497826	−	0.867277i	$-0.665868\pi$
$419$	−20.3805			−0.995651			−0.497826	+	0.867277i	$0.665868\pi$
$420$		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
$423$	12.2165	−	26.3144i	0.593988	−	1.27945i
$424$		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
$429$	16.8271	+	11.7613i	0.812421	+	0.567841i
$430$		0			0
$431$	−1.88165	+	1.08637i	−0.0906357	+	0.0523285i	−0.544633	−	0.838675i	$-0.683331\pi$
$431$	−1.88165	+	1.08637i	−0.0906357	+	0.0523285i	0.453997	+	0.891003i	$0.349998\pi$
$432$		0			0
$433$	1.81661	−	1.81661i	0.0873009	−	0.0873009i	−0.662108	−	0.749409i	$-0.730338\pi$
$433$	1.81661	−	1.81661i	0.0873009	−	0.0873009i	0.749409	+	0.662108i	$0.230338\pi$
$434$		0			0
$435$	11.8247	−	9.76410i	0.566952	−	0.468153i
$436$		0			0
$437$	4.04834	+	1.08475i	0.193659	+	0.0518907i
$438$		0			0
$439$	8.95736	+	5.17153i	0.427511	+	0.246824i	0.698286	−	0.715819i	$-0.253946\pi$
$439$	8.95736	+	5.17153i	0.427511	+	0.246824i	−0.270775	+	0.962643i	$0.587280\pi$
$440$		0			0
$441$	18.1657	+	10.5360i	0.865032	+	0.501716i
$442$		0			0
$443$	19.6578	−	5.26730i	0.933971	−	0.250257i	0.240424	−	0.970668i	$-0.422714\pi$
$443$	19.6578	−	5.26730i	0.933971	−	0.250257i	0.693547	+	0.720411i	$0.256047\pi$
$444$		0			0
$445$	−2.55618	+	1.44618i	−0.121174	+	0.0685554i
$446$		0			0
$447$	−9.59925	−	11.4203i	−0.454029	−	0.540163i
$448$		0			0
$449$	14.6156			0.689754			0.344877	−	0.938648i	$-0.387921\pi$
$449$	14.6156			0.689754			0.344877	+	0.938648i	$0.387921\pi$
$450$		0			0
$451$	5.32513	+	9.22340i	0.250751	+	0.434313i
$452$		0			0
$453$	16.9905	−	3.01067i	0.798281	−	0.141454i
$454$		0			0
$455$	−10.8276	−	30.7566i	−0.507605	−	1.44189i
$456$		0			0
$457$	6.40237	−	1.71551i	0.299490	−	0.0802481i	−0.105945	−	0.994372i	$-0.533787\pi$
$457$	6.40237	−	1.71551i	0.299490	−	0.0802481i	0.405435	+	0.914124i	$0.367120\pi$
$458$		0			0
$459$	−21.3006	+	5.76536i	−0.994228	+	0.269104i
$460$		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	−0.775750	−	0.631040i	$-0.782628\pi$
$463$	−3.11379	+	3.11379i	−0.144710	+	0.144710i	0.631040	+	0.775750i	$0.282628\pi$
$464$		0			0
$465$	−16.9286	−	6.31329i	−0.785047	−	0.292772i
$466$		0			0
$467$	−6.99718	−	26.1138i	−0.323791	−	1.20840i	−0.915522	−	0.402268i	$-0.868222\pi$
$467$	−6.99718	−	26.1138i	−0.323791	−	1.20840i	0.591731	−	0.806135i	$-0.298445\pi$
$468$		0			0
$469$	−1.63431	−	0.291268i	−0.0754655	−	0.0134495i
$470$		0			0
$471$	1.87487	+	1.31044i	0.0863895	+	0.0603820i
$472$		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
$477$	15.8233	−	11.1195i	0.724499	−	0.509125i
$478$		0			0
$479$	18.8746	+	32.6918i	0.862404	+	1.49373i	0.869602	+	0.493753i	$0.164375\pi$
$479$	18.8746	+	32.6918i	0.862404	+	1.49373i	−0.00719862	+	0.999974i	$0.502291\pi$
$480$		0			0
$481$	6.36975	−	11.0327i	0.290436	−	0.503050i
$482$		0			0
$483$	26.3597	+	0.0261378i	1.19941	+	0.00118931i
$484$		0			0
$485$	7.93374	+	30.6790i	0.360253	+	1.39306i
$486$		0			0
$487$	−7.63106	+	28.4795i	−0.345796	+	1.29053i	0.545883	+	0.837861i	$0.316194\pi$
$487$	−7.63106	+	28.4795i	−0.345796	+	1.29053i	−0.891679	+	0.452668i	$0.850472\pi$
$488$		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
$495$	10.9856	+	9.35080i	0.493768	+	0.420287i
$496$		0			0
$497$	−10.5509	+	0.903569i	−0.473274	+	0.0405306i
$498$		0			0
$499$	−13.9880	−	8.07598i	−0.626189	−	0.361531i	0.153086	−	0.988213i	$-0.451079\pi$
$499$	−13.9880	−	8.07598i	−0.626189	−	0.361531i	−0.779275	+	0.626682i	$0.784412\pi$
$500$		0			0
$501$	−5.18629	−	11.0976i	−0.231706	−	0.495802i
$502$		0			0
$503$	25.0418	+	25.0418i	1.11656	+	1.11656i	0.992243	+	0.124316i	$0.0396736\pi$
$503$	25.0418	+	25.0418i	1.11656	+	1.11656i	0.124316	+	0.992243i	$0.460326\pi$
$504$		0			0
$505$	−17.4098	−	0.152132i	−0.774726	−	0.00676977i
$506$		0			0
$507$	−28.2920	−	10.2704i	−1.25649	−	0.456125i
$508$		0			0
$509$	−21.6658	+	37.5262i	−0.960319	+	1.66332i	−0.238621	+	0.971113i	$0.576695\pi$
$509$	−21.6658	+	37.5262i	−0.960319	+	1.66332i	−0.721698	+	0.692208i	$0.756638\pi$
$510$		0			0
$511$	−5.01671	+	28.1488i	−0.221926	+	1.24523i
$512$		0			0
$513$	3.78602	−	0.00959137i	0.167157	−	0.000423469i
$514$		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	$-0.846653\pi$
$521$	−21.1824	+	12.2297i	−0.928018	+	0.535791i	−0.0418336	+	0.999125i	$0.513320\pi$
$522$		0			0
$523$	−7.55434	−	28.1932i	−0.330328	−	1.23280i	−0.908846	−	0.417132i	$-0.863035\pi$
$523$	−7.55434	−	28.1932i	−0.330328	−	1.23280i	0.578518	−	0.815670i	$-0.303631\pi$
$524$		0			0
$525$	−5.52057	−	22.2379i	−0.240937	−	0.970541i
$526$		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
$537$	−24.2105	+	4.29004i	−1.04476	+	0.185129i
$538$		0			0
$539$	11.5675	−	9.63409i	0.498246	−	0.414970i
$540$		0			0
$541$	4.55156	−	7.88354i	0.195687	−	0.338940i	−0.751439	−	0.659803i	$-0.770640\pi$
$541$	4.55156	−	7.88354i	0.195687	−	0.338940i	0.947125	+	0.320863i	$0.103973\pi$
$542$		0			0
$543$	−5.92674	+	16.3265i	−0.254341	+	0.700636i
$544$		0			0
$545$	13.6783	+	0.119525i	0.585914	+	0.00511988i
$546$		0			0
$547$	−17.5854	−	17.5854i	−0.751900	−	0.751900i	0.222934	−	0.974834i	$-0.428437\pi$
$547$	−17.5854	−	17.5854i	−0.751900	−	0.751900i	−0.974834	+	0.222934i	$0.928437\pi$
$548$		0			0
$549$	34.9411	−	12.7844i	1.49125	−	0.545625i
$550$		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
$555$	5.19242	−	7.29234i	0.220406	−	0.309543i
$556$		0			0
$557$	10.3211	+	2.76552i	0.437318	+	0.117179i	0.470759	−	0.882262i	$-0.343980\pi$
$557$	10.3211	+	2.76552i	0.437318	+	0.117179i	−0.0334413	+	0.999441i	$0.510647\pi$
$558$		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	$-0.941652\pi$
$563$	−0.963101	+	3.59434i	−0.0405898	+	0.151483i	0.942657	+	0.333764i	$0.108319\pi$
$564$		0			0
$565$	−10.9712	−	42.4245i	−0.461562	−	1.78481i
$566$		0			0
$567$	22.9909	−	6.19839i	0.965526	−	0.260308i
$568$		0			0
$569$	−1.12664	+	1.95139i	−0.0472311	+	0.0818066i	−0.888674	−	0.458539i	$-0.848373\pi$
$569$	−1.12664	+	1.95139i	−0.0472311	+	0.0818066i	0.841443	+	0.540345i	$0.181706\pi$
$570$		0			0
$571$	2.03062	+	3.51713i	0.0849787	+	0.147187i	0.905382	−	0.424598i	$-0.139584\pi$
$571$	2.03062	+	3.51713i	0.0849787	+	0.147187i	−0.820403	+	0.571785i	$0.806251\pi$
$572$		0			0
$573$	−9.03111	+	7.59101i	−0.377280	+	0.317119i
$574$		0			0
$575$	−19.9785	−	20.6892i	−0.833159	−	0.862801i
$576$		0			0
$577$	−4.34025	+	16.1980i	−0.180687	+	0.674332i	0.814826	+	0.579706i	$0.196832\pi$
$577$	−4.34025	+	16.1980i	−0.180687	+	0.674332i	−0.995513	+	0.0946268i	$0.969834\pi$
$578$		0			0
$579$	8.45570	−	12.0977i	0.351407	−	0.502764i
$580$		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
$585$	−33.3977	−	15.8612i	−1.38082	−	0.655778i
$586$		0			0
$587$	−11.2728	+	11.2728i	−0.465279	+	0.465279i	−0.900381	−	0.435102i	$-0.856712\pi$
$587$	−11.2728	+	11.2728i	−0.465279	+	0.465279i	0.435102	+	0.900381i	$0.356712\pi$
$588$		0			0
$589$			3.39904i			0.140055i
$590$		0			0
$591$	16.4697	+	35.2417i	0.677473	+	1.44965i
$592$		0			0
$593$	−15.1364	+	4.05578i	−0.621577	+	0.166551i	−0.555844	−	0.831286i	$-0.687605\pi$
$593$	−15.1364	+	4.05578i	−0.621577	+	0.166551i	−0.0657322	+	0.997837i	$0.520938\pi$
$594$		0			0
$595$	16.3523	−	19.0746i	0.670379	−	0.781983i
$596$		0			0
$597$	−2.68028	−	15.1259i	−0.109696	−	0.619062i
$598$		0			0
$599$	−16.5463	−	28.6589i	−0.676062	−	1.17097i	−0.976157	−	0.217064i	$-0.930352\pi$
$599$	−16.5463	−	28.6589i	−0.676062	−	1.17097i	0.300096	−	0.953909i	$-0.402981\pi$
$600$		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
$603$	−1.54009	+	1.08227i	−0.0627175	+	0.0440733i
$604$		0			0
$605$	−12.4071	+	7.01940i	−0.504419	+	0.285379i
$606$		0			0
$607$	33.2974	−	8.92202i	1.35150	−	0.362134i	0.490812	−	0.871265i	$-0.336700\pi$
$607$	33.2974	−	8.92202i	1.35150	−	0.362134i	0.860689	+	0.509132i	$0.170033\pi$
$608$		0			0
$609$	−17.5217	−	4.71354i	−0.710014	−	0.191002i
$610$		0			0
$611$	46.1595	+	26.6502i	1.86741	+	1.07815i
$612$		0			0
$613$	19.2254	+	5.15144i	0.776509	+	0.208065i	0.625245	−	0.780429i	$-0.284999\pi$
$613$	19.2254	+	5.15144i	0.776509	+	0.208065i	0.151264	+	0.988493i	$0.451666\pi$
$614$		0			0
$615$	−12.2124	−	14.7897i	−0.492453	−	0.596380i
$616$		0			0
$617$	12.3161	−	12.3161i	0.495829	−	0.495829i	−0.414308	−	0.910137i	$-0.635976\pi$
$617$	12.3161	−	12.3161i	0.495829	−	0.495829i	0.910137	+	0.414308i	$0.135976\pi$
$618$		0			0
$619$	23.0037	−	13.2812i	0.924597	−	0.533816i	0.0394980	−	0.999220i	$-0.487424\pi$
$619$	23.0037	−	13.2812i	0.924597	−	0.533816i	0.885099	+	0.465404i	$0.154091\pi$
$620$		0			0
$621$	21.0812	−	21.1883i	0.845958	−	0.850255i
$622$		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
$627$	0.926102	−	2.55115i	0.0369850	−	0.101883i
$628$		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
$633$	8.54424	−	23.5369i	0.339603	−	0.935509i
$634$		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
$639$	−7.70267	+	9.21124i	−0.304713	+	0.364391i
$640$		0			0
$641$	28.8842	−	16.6763i	1.14086	−	0.658674i	0.194214	−	0.980959i	$-0.437784\pi$
$641$	28.8842	−	16.6763i	1.14086	−	0.658674i	0.946643	+	0.322286i	$0.104451\pi$
$642$		0			0
$643$	−6.59026	+	6.59026i	−0.259895	+	0.259895i	−0.825011	−	0.565117i	$-0.808831\pi$
$643$	−6.59026	+	6.59026i	−0.259895	+	0.259895i	0.565117	+	0.825011i	$0.308831\pi$
$644$		0			0
$645$	1.86224	−	19.5105i	0.0733258	−	0.768225i
$646$		0			0
$647$	24.4118	+	6.54113i	0.959729	+	0.257159i	0.704485	−	0.709718i	$-0.251178\pi$
$647$	24.4118	+	6.54113i	0.959729	+	0.257159i	0.255243	+	0.966877i	$0.417844\pi$
$648$		0			0
$649$	−14.9444	−	8.62817i	−0.586620	−	0.338685i
$650$		0			0
$651$	5.51251	+	20.6549i	0.216052	+	0.809528i
$652$		0			0
$653$	−12.7291	+	3.41075i	−0.498129	+	0.133473i	−0.499131	−	0.866526i	$-0.666347\pi$
$653$	−12.7291	+	3.41075i	−0.498129	+	0.133473i	0.00100275	+	0.999999i	$0.499681\pi$
$654$		0			0
$655$	−23.6997	−	41.8901i	−0.926022	−	1.63678i
$656$		0			0
$657$	18.6406	+	26.5261i	0.727239	+	1.03488i
$658$		0			0
$659$	34.5112			1.34437			0.672183	−	0.740385i	$-0.265357\pi$
$659$	34.5112			1.34437			0.672183	+	0.740385i	$0.265357\pi$
$660$		0			0
$661$	5.75162	+	9.96211i	0.223712	+	0.387481i	0.955932	−	0.293587i	$-0.0948491\pi$
$661$	5.75162	+	9.96211i	0.223712	+	0.387481i	−0.732220	+	0.681068i	$0.761516\pi$
$662$		0			0
$663$	−7.07365	−	39.9195i	−0.274718	−	1.55035i
$664$		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
$669$	−17.9683	−	38.4484i	−0.694696	−	1.48650i
$670$		0			0
$671$		−	26.6717i		−	1.02965i
$672$		0			0
$673$	2.07846	−	2.07846i	0.0801187	−	0.0801187i	−0.665912	−	0.746030i	$-0.731957\pi$
$673$	2.07846	−	2.07846i	0.0801187	−	0.0801187i	0.746030	+	0.665912i	$0.231957\pi$
$674$		0			0
$675$	−22.3034	−	13.3251i	−0.858458	−	0.512885i
$676$		0			0
$677$	−4.59302	−	17.1414i	−0.176524	−	0.658797i	−0.996287	−	0.0860941i	$-0.972561\pi$
$677$	−4.59302	−	17.1414i	−0.176524	−	0.658797i	0.819763	−	0.572703i	$-0.194105\pi$
$678$		0			0
$679$	24.1534	−	28.6778i	0.926921	−	1.10055i
$680$		0			0
$681$	−22.2097	+	31.7758i	−0.851078	+	1.21765i
$682$		0			0
$683$	−2.97965	+	11.1202i	−0.114013	+	0.425503i	−0.999211	−	0.0397112i	$-0.987356\pi$
$683$	−2.97965	+	11.1202i	−0.114013	+	0.425503i	0.885198	+	0.465215i	$0.154023\pi$
$684$		0			0
$685$	24.8474	+	25.2855i	0.949371	+	0.966109i
$686$		0			0
$687$	−29.0239	+	24.3958i	−1.10733	+	0.930757i
$688$		0			0
$689$	17.7652	+	30.7703i	0.676801	+	1.17225i
$690$		0			0
$691$	−2.37495	+	4.11354i	−0.0903475	+	0.156486i	−0.907657	−	0.419712i	$-0.862131\pi$
$691$	−2.37495	+	4.11354i	−0.0903475	+	0.156486i	0.817310	+	0.576198i	$0.195464\pi$
$692$		0			0
$693$	1.49021	−	17.0044i	0.0566086	−	0.645944i
$694$		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
$705$	30.5102	+	21.7244i	1.14908	+	0.818187i
$706$		0			0
$707$	11.7849	+	16.8965i	0.443215	+	0.635457i
$708$		0			0
$709$	4.99216	+	2.88222i	0.187484	+	0.108244i	0.590804	−	0.806815i	$-0.298811\pi$
$709$	4.99216	+	2.88222i	0.187484	+	0.108244i	−0.403320	+	0.915059i	$0.632144\pi$
$710$		0			0
$711$	−7.86827	−	21.5048i	−0.295083	−	0.806493i
$712$		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
$717$	−11.6647	+	32.1328i	−0.435625	+	1.20002i
$718$		0			0
$719$	−18.4248	+	31.9127i	−0.687129	+	1.19014i	0.285633	+	0.958339i	$0.407796\pi$
$719$	−18.4248	+	31.9127i	−0.687129	+	1.19014i	−0.972763	+	0.231804i	$0.925537\pi$
$720$		0			0
$721$	49.5875	−	17.9454i	1.84674	−	0.668320i
$722$		0			0
$723$	−22.1528	+	3.92542i	−0.823871	+	0.145988i
$724$		0			0
$725$	9.59756	+	17.3154i	0.356445	+	0.643078i
$726$		0			0
$727$	−5.34727	−	5.34727i	−0.198319	−	0.198319i	0.600960	−	0.799279i	$-0.294785\pi$
$727$	−5.34727	−	5.34727i	−0.198319	−	0.198319i	−0.799279	+	0.600960i	$0.794785\pi$
$728$		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	−0.996163	−	0.0875174i	$-0.972107\pi$
$733$	−4.79803	−	17.9065i	−0.177219	−	0.661391i	0.818944	−	0.573874i	$-0.194560\pi$
$734$		0			0
$735$	−17.6656	+	20.5652i	−0.651604	+	0.758559i
$736$		0			0
$737$	0.349241	+	1.30338i	0.0128644	+	0.0480108i
$738$		0			0
$739$	6.24688	−	3.60664i	0.229795	−	0.132672i	−0.380682	−	0.924706i	$-0.624311\pi$
$739$	6.24688	−	3.60664i	0.229795	−	0.132672i	0.610478	+	0.792034i	$0.290978\pi$
$740$		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	$-0.330212\pi$
$743$	−9.61154	−	9.61154i	−0.352613	−	0.352613i	−0.861081	+	0.508468i	$0.830212\pi$
$744$		0			0
$745$	16.7632	−	9.48391i	0.614156	−	0.347464i
$746$		0			0
$747$	−2.47325	−	27.7299i	−0.0904916	−	1.01459i
$748$		0			0
$749$	17.2066	−	6.22694i	0.628716	−	0.227528i
$750$		0			0
$751$	8.51460	−	14.7477i	0.310702	−	0.538152i	−0.667812	−	0.744330i	$-0.732769\pi$
$751$	8.51460	−	14.7477i	0.310702	−	0.538152i	0.978515	+	0.206178i	$0.0661025\pi$
$752$		0			0
$753$	3.00768	+	1.09183i	0.109606	+	0.0397885i
$754$		0			0
$755$	−0.194649	+	22.2754i	−0.00708400	+	0.810686i
$756$		0			0
$757$	−18.5494	−	18.5494i	−0.674191	−	0.674191i	0.284488	−	0.958679i	$-0.408176\pi$
$757$	−18.5494	−	18.5494i	−0.674191	−	0.674191i	−0.958679	+	0.284488i	$0.908176\pi$
$758$		0			0
$759$	−9.07148	−	19.4110i	−0.329274	−	0.704576i
$760$		0			0
$761$	−33.0626	−	19.0887i	−1.19852	−	0.691965i	−0.238294	−	0.971193i	$-0.576588\pi$
$761$	−33.0626	−	19.0887i	−1.19852	−	0.691965i	−0.960225	+	0.279228i	$0.909922\pi$
$762$		0			0
$763$	−9.25898	−	13.2750i	−0.335198	−	0.480587i
$764$		0			0
$765$	−2.28282	−	28.3969i	−0.0825355	−	1.02669i
$766$		0			0
$767$	42.7184	+	11.4464i	1.54247	+	0.413304i
$768$		0			0
$769$			16.7248i			0.603110i	0.953449	+	0.301555i	$0.0975057\pi$
$769$			16.7248i			0.603110i	−0.953449	+	0.301555i	$0.902494\pi$
$770$		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	$-0.951491\pi$
$773$	−1.57137	+	5.86442i	−0.0565182	+	0.210929i	0.931892	+	0.362736i	$0.118157\pi$
$774$		0			0
$775$	12.0138	−	19.9932i	0.431548	−	0.718179i
$776$		0			0
$777$	−10.5922	−	0.0105031i	−0.379994	−	0.000376796i
$778$		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
$783$	−17.7915	+	10.3321i	−0.635817	+	0.369240i
$784$		0			0
$785$	−2.10631	+	2.06982i	−0.0751774	+	0.0738749i
$786$		0			0
$787$	−3.20956	+	11.9782i	−0.114409	+	0.426978i	−0.999242	−	0.0389290i	$-0.987605\pi$
$787$	−3.20956	+	11.9782i	−0.114409	+	0.426978i	0.884833	+	0.465907i	$0.154272\pi$
$788$		0			0
$789$	17.0296	+	11.9028i	0.606269	+	0.423752i
$790$		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
$795$	10.3727	+	22.7106i	0.367881	+	0.805463i
$796$		0			0
$797$	17.2195	−	17.2195i	0.609945	−	0.609945i	−0.332986	−	0.942932i	$-0.608056\pi$
$797$	17.2195	−	17.2195i	0.609945	−	0.609945i	0.942932	+	0.332986i	$0.108056\pi$
$798$		0			0
$799$			41.0694i			1.45293i
$800$		0			0
$801$	3.70038	−	1.35391i	0.130746	−	0.0478380i
$802$		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
$807$	5.62034	−	0.995912i	0.197845	−	0.0350578i
$808$		0			0
$809$	0.599532	+	1.03842i	0.0210784	+	0.0365089i	0.876372	−	0.481634i	$-0.159957\pi$
$809$	0.599532	+	1.03842i	0.0210784	+	0.0365089i	−0.855294	+	0.518143i	$0.826623\pi$
$810$		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
$813$	9.05309	+	10.7706i	0.317506	+	0.377740i
$814$		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
$819$	7.59020	+	43.0832i	0.265223	+	1.50545i
$820$		0			0
$821$	−33.8794	−	19.5603i	−1.18240	−	0.682659i	−0.225831	−	0.974166i	$-0.572510\pi$
$821$	−33.8794	−	19.5603i	−1.18240	−	0.682659i	−0.956568	+	0.291508i	$0.905843\pi$
$822$		0			0
$823$	1.79793	+	0.481753i	0.0626718	+	0.0167929i	0.290019	−	0.957021i	$-0.406338\pi$
$823$	1.79793	+	0.481753i	0.0626718	+	0.0167929i	−0.227347	+	0.973814i	$0.573005\pi$
$824$		0			0
$825$	−14.4643	+	11.7326i	−0.503582	+	0.408478i
$826$		0			0
$827$	−23.1571	+	23.1571i	−0.805251	+	0.805251i	−0.983911	−	0.178660i	$-0.942824\pi$
$827$	−23.1571	+	23.1571i	−0.805251	+	0.805251i	0.178660	+	0.983911i	$0.442824\pi$
$828$		0			0
$829$	−27.5833	+	15.9252i	−0.958008	+	0.553106i	−0.895559	−	0.444942i	$-0.853224\pi$
$829$	−27.5833	+	15.9252i	−0.958008	+	0.553106i	−0.0624485	+	0.998048i	$0.519891\pi$
$830$		0			0
$831$	−40.2802	−	28.1538i	−1.39731	−	0.976646i
$832$		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
$837$	21.0232	+	12.0669i	0.726669	+	0.417092i
$838$		0			0
$839$	−25.9027			−0.894262			−0.447131	−	0.894469i	$-0.647554\pi$
$839$	−25.9027			−0.894262			−0.447131	+	0.894469i	$0.647554\pi$
$840$		0			0
$841$	−13.3226			−0.459399
$842$		0			0
$843$	23.6632	+	8.59007i	0.815003	+	0.295858i
$844$		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
$849$	2.88691	−	4.13036i	0.0990786	−	0.141754i
$850$		0			0
$851$	−11.5143	+	6.64781i	−0.394706	+	0.227884i
$852$		0			0
$853$	−25.9730	+	25.9730i	−0.889299	+	0.889299i	−0.994456	−	0.105157i	$-0.966465\pi$
$853$	−25.9730	+	25.9730i	−0.889299	+	0.889299i	0.105157	+	0.994456i	$0.466465\pi$
$854$		0			0
$855$	−0.882659	+	4.80739i	−0.0301863	+	0.164409i
$856$		0			0
$857$	−17.0839	−	4.57762i	−0.583575	−	0.156368i	−0.0450600	−	0.998984i	$-0.514348\pi$
$857$	−17.0839	−	4.57762i	−0.583575	−	0.156368i	−0.538515	+	0.842616i	$0.681015\pi$
$858$		0			0
$859$	14.7883	+	8.53804i	0.504571	+	0.291314i	0.730599	−	0.682806i	$-0.239241\pi$
$859$	14.7883	+	8.53804i	0.504571	+	0.291314i	−0.226028	+	0.974121i	$0.572574\pi$
$860$		0			0
$861$	−5.89545	+	21.9152i	−0.200917	+	0.746868i
$862$		0			0
$863$	−4.54605	+	1.21811i	−0.154749	+	0.0414650i	−0.335362	−	0.942089i	$-0.608859\pi$
$863$	−4.54605	+	1.21811i	−0.154749	+	0.0414650i	0.180613	+	0.983554i	$0.442192\pi$
$864$		0			0
$865$	−6.01107	−	1.66709i	−0.204383	−	0.0566828i
$866$		0			0
$867$	1.37284	−	1.15393i	0.0466241	−	0.0391894i
$868$		0			0
$869$	−16.4153			−0.556851
$870$		0			0
$871$	−1.72910	−	2.99489i	−0.0585884	−	0.101478i
$872$		0			0
$873$	−3.77688	−	42.3461i	−0.127828	−	1.43320i
$874$		0			0
$875$	29.5286	−	1.75062i	0.998247	−	0.0591817i
$876$		0			0
$877$	21.3601	−	5.72343i	0.721281	−	0.193267i	0.120538	−	0.992709i	$-0.461538\pi$
$877$	21.3601	−	5.72343i	0.721281	−	0.193267i	0.600743	+	0.799442i	$0.294872\pi$
$878$		0			0
$879$	−26.5663	+	12.4154i	−0.896060	+	0.418761i
$880$		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	−0.939595	−	0.342287i	$-0.888798\pi$
$883$	−17.7492	+	17.7492i	−0.597308	+	0.597308i	0.342287	+	0.939595i	$0.388798\pi$
$884$		0			0
$885$	29.1182	+	10.8592i	0.978797	+	0.365028i
$886$		0			0
$887$	6.64206	+	24.7885i	0.223019	+	0.832316i	0.983189	+	0.182592i	$0.0584489\pi$
$887$	6.64206	+	24.7885i	0.223019	+	0.832316i	−0.760170	+	0.649724i	$0.774884\pi$
$888$		0			0
$889$	10.4691	−	12.4301i	0.351121	−	0.416893i
$890$		0			0
$891$	−12.4912	−	14.7848i	−0.418472	−	0.495308i
$892$		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
$897$	35.3322	+	42.0351i	1.17971	+	1.40351i
$898$		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
$903$	−20.0947	+	11.5751i	−0.668708	+	0.385195i
$904$		0			0
$905$	−19.3203	−	11.3808i	−0.642230	−	0.378312i
$906$		0			0
$907$	0.432502	−	1.61412i	0.0143610	−	0.0535960i	−0.958374	−	0.285517i	$-0.907835\pi$
$907$	0.432502	−	1.61412i	0.0143610	−	0.0535960i	0.972735	+	0.231921i	$0.0745012\pi$
$908$		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
$915$	7.96725	+	47.3680i	0.263389	+	1.56594i
$916$		0			0
$917$	−24.1619	+	51.5679i	−0.797895	+	1.70292i
$918$		0			0
$919$	−17.0980	−	9.87155i	−0.564012	−	0.325632i	0.190742	−	0.981640i	$-0.438911\pi$
$919$	−17.0980	−	9.87155i	−0.564012	−	0.325632i	−0.754754	+	0.656008i	$0.772244\pi$
$920$		0			0
$921$	13.0811	−	6.11328i	0.431038	−	0.201439i
$922$		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
$927$	25.1792	−	54.2359i	0.826993	−	1.78134i
$928$		0			0
$929$	25.3654	−	43.9342i	0.832212	−	1.44143i	−0.0640690	−	0.997945i	$-0.520408\pi$
$929$	25.3654	−	43.9342i	0.832212	−	1.44143i	0.896281	−	0.443487i	$-0.146259\pi$
$930$		0			0
$931$	4.78633	+	1.76201i	0.156866	+	0.0577477i
$932$		0			0
$933$	0.277231	+	1.56453i	0.00907613	+	0.0512203i
$934$		0			0
$935$	−19.6793	−	5.45780i	−0.643582	−	0.178489i
$936$		0			0
$937$	−26.5787	−	26.5787i	−0.868287	−	0.868287i	0.123995	−	0.992283i	$-0.460429\pi$
$937$	−26.5787	−	26.5787i	−0.868287	−	0.868287i	−0.992283	+	0.123995i	$0.960429\pi$
$938$		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	$-0.813313\pi$
$941$	−23.6212	+	13.6377i	−0.770030	+	0.444577i	0.0628556	+	0.998023i	$0.479979\pi$
$942$		0			0
$943$	7.37283	+	27.5158i	0.240093	+	0.896037i
$944$		0			0
$945$	2.43292	+	30.6444i	0.0791429	+	0.996863i
$946$		0			0
$947$	−0.412833	−	1.54071i	−0.0134153	−	0.0500664i	0.958894	−	0.283765i	$-0.0915837\pi$
$947$	−0.412833	−	1.54071i	−0.0134153	−	0.0500664i	−0.972309	+	0.233699i	$0.924917\pi$
$948$		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	$-0.117767\pi$
$953$	17.6192	+	17.6192i	0.570741	+	0.570741i	−0.361594	+	0.932336i	$0.617767\pi$
$954$		0			0
$955$	−7.49980	−	13.2562i	−0.242688	−	0.428961i
$956$		0			0
$957$	2.57333	+	14.5224i	0.0831840	+	0.469442i
$958$		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
$963$	8.73704	−	18.8196i	0.281547	−	0.606452i
$964$		0			0
$965$	13.3556	+	13.5911i	0.429932	+	0.437512i
$966$		0			0
$967$	−8.13992	−	8.13992i	−0.261762	−	0.261762i	0.564007	−	0.825770i	$-0.309259\pi$
$967$	−8.13992	−	8.13992i	−0.261762	−	0.261762i	−0.825770	+	0.564007i	$0.809259\pi$
$968$		0			0
$969$	−4.85547	+	2.26914i	−0.155980	+	0.0728951i
$970$		0			0
$971$	−3.45490	−	1.99469i	−0.110873	−	0.0640125i	0.443538	−	0.896256i	$-0.353723\pi$
$971$	−3.45490	−	1.99469i	−0.110873	−	0.0640125i	−0.554411	+	0.832243i	$0.687056\pi$
$972$		0			0
$973$	−30.1417	+	2.58130i	−0.966298	+	0.0827527i
$974$		0			0
$975$	28.0242	−	38.6387i	0.897492	−	1.23743i
$976$		0			0
$977$	45.5422	+	12.2030i	1.45702	+	0.390408i	0.898461	−	0.439054i	$-0.144686\pi$
$977$	45.5422	+	12.2030i	1.45702	+	0.390408i	0.558563	+	0.829462i	$0.311353\pi$
$978$		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	0.636425	+	0.771338i	$0.280412\pi$
$983$	−9.41853	+	35.1504i	−0.300404	+	1.12112i	−0.936830	+	0.349786i	$0.886254\pi$
$984$		0			0
$985$	−48.6205	+	12.5735i	−1.54918	+	0.400625i
$986$		0			0
$987$	0.0439434	−	44.3164i	0.00139874	−	1.41061i
$988$		0			0
$989$	−14.5543	+	25.2089i	−0.462801	+	0.801596i
$990$		0			0
$991$	−7.14153	−	12.3695i	−0.226858	−	0.392930i	0.730017	−	0.683429i	$-0.239512\pi$
$991$	−7.14153	−	12.3695i	−0.226858	−	0.392930i	−0.956875	+	0.290499i	$0.906179\pi$
$992$		0			0
$993$	12.1179	+	14.4168i	0.384549	+	0.457503i
$994$		0			0
$995$	19.8309	+	0.173288i	0.628681	+	0.00549359i
$996$		0			0
$997$	−9.15638	+	34.1721i	−0.289985	+	1.08224i	0.655133	+	0.755513i	$0.272612\pi$
$997$	−9.15638	+	34.1721i	−0.289985	+	1.08224i	−0.945119	+	0.326727i	$0.894054\pi$
$998$		0			0
$999$	−8.47113	+	8.51416i	−0.268015	+	0.269376i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.bv.c.317.8	yes	48
3.2	odd	2	inner	420.2.bv.c.317.6	yes	48
5.3	odd	4	inner	420.2.bv.c.233.11	yes	48
7.4	even	3	inner	420.2.bv.c.137.1	yes	48
15.8	even	4	inner	420.2.bv.c.233.1	yes	48
21.11	odd	6	inner	420.2.bv.c.137.11	yes	48
35.18	odd	12	inner	420.2.bv.c.53.6	✓	48
105.53	even	12	inner	420.2.bv.c.53.8	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bv.c.53.6	✓	48	35.18	odd	12	inner
420.2.bv.c.53.8	yes	48	105.53	even	12	inner
420.2.bv.c.137.1	yes	48	7.4	even	3	inner
420.2.bv.c.137.11	yes	48	21.11	odd	6	inner
420.2.bv.c.233.1	yes	48	15.8	even	4	inner
420.2.bv.c.233.11	yes	48	5.3	odd	4	inner
420.2.bv.c.317.6	yes	48	3.2	odd	2	inner
420.2.bv.c.317.8	yes	48	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.591022 - 1.62810i) q^{3} +(1.92665 + 1.13491i) q^{5} +(-0.225753 - 2.63610i) q^{7} +(-2.30139 - 1.92448i) q^{9} +O(q^{10})\)	\(q+(0.591022 - 1.62810i) q^{3} +(1.92665 + 1.13491i) q^{5} +(-0.225753 - 2.63610i) q^{7} +(-2.30139 - 1.92448i) q^{9} +(-1.86244 + 1.07528i) q^{11} +(3.89727 - 3.89727i) q^{13} +(2.98644 - 2.46601i) q^{15} +(4.10211 + 1.09916i) q^{17} +(-0.631006 - 0.364311i) q^{19} +(-4.42525 - 1.19045i) q^{21} +(-5.55616 + 1.48877i) q^{23} +(2.42395 + 4.37315i) q^{25} +(-4.49340 + 2.60947i) q^{27} +3.95947 q^{29} +(-2.33251 - 4.04003i) q^{31} +(0.649918 + 3.66775i) q^{33} +(2.55680 - 5.33505i) q^{35} +(2.23265 - 0.598238i) q^{37} +(-4.04175 - 8.64849i) q^{39} -4.95231i q^{41} +(3.57830 - 3.57830i) q^{43} +(-2.24985 - 6.31967i) q^{45} +(2.50295 + 9.34112i) q^{47} +(-6.89807 + 1.19022i) q^{49} +(4.21396 - 6.02899i) q^{51} +(-1.66848 + 6.22687i) q^{53} +(-4.80863 - 0.0420191i) q^{55} +(-0.966072 + 0.812022i) q^{57} +(4.01205 + 6.94907i) q^{59} +(-6.20108 + 10.7406i) q^{61} +(-4.55358 + 6.50115i) q^{63} +(11.9317 - 3.08561i) q^{65} +(0.162395 - 0.606066i) q^{67} +(-0.859954 + 9.92585i) q^{69} -4.00247i q^{71} +(-10.4387 - 2.79703i) q^{73} +(8.55252 - 1.36179i) q^{75} +(3.25501 + 4.66685i) q^{77} +(6.61039 + 3.81651i) q^{79} +(1.59276 + 8.85794i) q^{81} +(6.56196 + 6.56196i) q^{83} +(6.65587 + 6.77322i) q^{85} +(2.34014 - 6.44640i) q^{87} +(-0.656714 + 1.13746i) q^{89} +(-11.1534 - 9.39378i) q^{91} +(-7.95611 + 1.40981i) q^{93} +(-0.802265 - 1.41804i) q^{95} +(10.0207 + 10.0207i) q^{97} +(6.35557 + 1.10959i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{3} - 8 q^{7}+O(q^{10}) \) 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

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