LMFDB - Embedded newform 420.2.bv.c.233.11

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			233.11
Character	$\chi$	$=$	420.233
Dual form			420.2.bv.c.137.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.62810 + 0.591022i) q^{3} +(1.94619 + 1.10107i) q^{5} +(-2.63610 + 0.225753i) q^{7} +(2.30139 + 1.92448i) q^{9} +O(q^{10})$	\(q+(1.62810 + 0.591022i) q^{3} +(1.94619 + 1.10107i) q^{5} +(-2.63610 + 0.225753i) q^{7} +(2.30139 + 1.92448i) q^{9} +(-1.86244 + 1.07528i) q^{11} +(3.89727 + 3.89727i) q^{13} +(2.51782 + 2.94289i) q^{15} +(1.09916 - 4.10211i) q^{17} +(0.631006 + 0.364311i) q^{19} +(-4.42525 - 1.19045i) q^{21} +(-1.48877 - 5.55616i) q^{23} +(2.57529 + 4.28578i) q^{25} +(2.60947 + 4.49340i) q^{27} -3.95947 q^{29} +(-2.33251 - 4.04003i) q^{31} +(-3.66775 + 0.649918i) q^{33} +(-5.37892 - 2.46318i) q^{35} +(-0.598238 - 2.23265i) q^{37} +(4.04175 + 8.64849i) q^{39} -4.95231i q^{41} +(3.57830 + 3.57830i) q^{43} +(2.35994 + 6.27938i) q^{45} +(9.34112 - 2.50295i) q^{47} +(6.89807 - 1.19022i) q^{49} +(4.21396 - 6.02899i) q^{51} +(-6.22687 - 1.66848i) q^{53} +(-4.80863 + 0.0420191i) q^{55} +(0.812022 + 0.966072i) q^{57} +(-4.01205 - 6.94907i) q^{59} +(-6.20108 + 10.7406i) q^{61} +(-6.50115 - 4.55358i) q^{63} +(3.29365 + 11.8760i) q^{65} +(-0.606066 - 0.162395i) q^{67} +(0.859954 - 9.92585i) q^{69} -4.00247i q^{71} +(2.79703 - 10.4387i) q^{73} +(1.65983 + 8.49970i) q^{75} +(4.66685 - 3.25501i) q^{77} +(-6.61039 - 3.81651i) q^{79} +(1.59276 + 8.85794i) q^{81} +(-6.56196 + 6.56196i) q^{83} +(6.65587 - 6.77322i) q^{85} +(-6.44640 - 2.34014i) q^{87} +(0.656714 - 1.13746i) q^{89} +(-11.1534 - 9.39378i) q^{91} +(-1.40981 - 7.95611i) q^{93} +(0.826923 + 1.40380i) q^{95} +(10.0207 - 10.0207i) q^{97} +(-6.35557 - 1.10959i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

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

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
$3$	1.62810	+	0.591022i	0.939981	+	0.341226i
$3$	1.62810	+	0.591022i	0.939981	+	0.341226i
$4$		0			0
$5$	1.94619	+	1.10107i	0.870361	+	0.492414i
$5$	1.94619	+	1.10107i	0.870361	+	0.492414i
$6$		0			0
$7$	−2.63610	+	0.225753i	−0.996353	+	0.0853265i
$7$	−2.63610	+	0.225753i	−0.996353	+	0.0853265i
$8$		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	0.996425	+	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
$17$	1.09916	−	4.10211i	0.266584	−	0.994907i	−0.694689	−	0.719310i	$-0.744458\pi$
$17$	1.09916	−	4.10211i	0.266584	−	0.994907i	0.961273	−	0.275596i	$-0.0888753\pi$
$18$		0			0
$19$	0.631006	+	0.364311i	0.144763	+	0.0835788i	0.570632	−	0.821206i	$-0.306698\pi$
$19$	0.631006	+	0.364311i	0.144763	+	0.0835788i	−0.425869	+	0.904785i	$0.640032\pi$
$20$		0			0
$21$	−4.42525	−	1.19045i	−0.965669	−	0.259777i
$22$		0			0
$23$	−1.48877	−	5.55616i	−0.310430	−	1.15854i	−0.928170	−	0.372157i	$-0.878618\pi$
$23$	−1.48877	−	5.55616i	−0.310430	−	1.15854i	0.617740	−	0.786382i	$-0.288048\pi$
$24$		0			0
$25$	2.57529	+	4.28578i	0.515058	+	0.857156i
$26$		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	0.576901	−	0.816814i	$-0.304262\pi$
$31$	−2.33251	−	4.04003i	−0.418931	−	0.725610i	−0.995832	+	0.0912037i	$0.970929\pi$
$32$		0			0
$33$	−3.66775	+	0.649918i	−0.638474	+	0.113136i
$34$		0			0
$35$	−5.37892	−	2.46318i	−0.909203	−	0.416353i
$36$		0			0
$37$	−0.598238	−	2.23265i	−0.0983497	−	0.367046i	0.899156	−	0.437628i	$-0.144181\pi$
$37$	−0.598238	−	2.23265i	−0.0983497	−	0.367046i	−0.997506	+	0.0705816i	$0.977514\pi$
$38$		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	0.925190	−	0.379504i	$-0.123905\pi$
$43$	3.57830	+	3.57830i	0.545686	+	0.545686i	−0.379504	+	0.925190i	$0.623905\pi$
$44$		0			0
$45$	2.35994	+	6.27938i	0.351800	+	0.936075i
$46$		0			0
$47$	9.34112	−	2.50295i	1.36254	−	0.365092i	0.497793	−	0.867296i	$-0.334144\pi$
$47$	9.34112	−	2.50295i	1.36254	−	0.365092i	0.864749	+	0.502204i	$0.167477\pi$
$48$		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
$53$	−6.22687	−	1.66848i	−0.855326	−	0.229184i	−0.195594	−	0.980685i	$-0.562663\pi$
$53$	−6.22687	−	1.66848i	−0.855326	−	0.229184i	−0.659732	+	0.751501i	$0.729330\pi$
$54$		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	−0.999663	−	0.0259723i	$-0.991732\pi$
$59$	−4.01205	−	6.94907i	−0.522324	−	0.904692i	0.477339	−	0.878719i	$-0.341601\pi$
$60$		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
$63$	−6.50115	−	4.55358i	−0.819068	−	0.573697i
$64$		0			0
$65$	3.29365	+	11.8760i	0.408526	+	1.47303i
$66$		0			0
$67$	−0.606066	−	0.162395i	−0.0740427	−	0.0198397i	0.221608	−	0.975136i	$-0.428870\pi$
$67$	−0.606066	−	0.162395i	−0.0740427	−	0.0198397i	−0.295650	+	0.955296i	$0.595536\pi$
$68$		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
$73$	2.79703	−	10.4387i	0.327368	−	1.22175i	−0.584542	−	0.811364i	$-0.698726\pi$
$73$	2.79703	−	10.4387i	0.327368	−	1.22175i	0.911910	−	0.410391i	$-0.134608\pi$
$74$		0			0
$75$	1.65983	+	8.49970i	0.191660	+	0.981461i
$76$		0			0
$77$	4.66685	−	3.25501i	0.531837	−	0.370943i
$78$		0			0
$79$	−6.61039	−	3.81651i	−0.743727	−	0.429391i	0.0796961	−	0.996819i	$-0.474605\pi$
$79$	−6.61039	−	3.81651i	−0.743727	−	0.429391i	−0.823423	+	0.567428i	$0.807938\pi$
$80$		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	$-0.920098\pi$
$83$	−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
$87$	−6.44640	−	2.34014i	−0.691127	−	0.250889i
$88$		0			0
$89$	0.656714	−	1.13746i	0.0696116	−	0.120571i	−0.829119	−	0.559072i	$-0.811157\pi$
$89$	0.656714	−	1.13746i	0.0696116	−	0.120571i	0.898730	+	0.438502i	$0.144491\pi$
$90$		0			0
$91$	−11.1534	−	9.39378i	−1.16920	−	0.984735i
$92$		0			0
$93$	−1.40981	−	7.95611i	−0.146190	−	0.825011i
$94$		0			0
$95$	0.826923	+	1.40380i	0.0848405	+	0.144027i
$96$		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	$-0.793286\pi$
$101$	−6.74304	+	3.89310i	−0.670958	+	0.387378i	0.125482	+	0.992096i	$0.459952\pi$
$102$		0			0
$103$	−19.2527	+	5.15875i	−1.89703	+	0.508307i	−0.899592	+	0.436731i	$0.856136\pi$
$103$	−19.2527	+	5.15875i	−1.89703	+	0.508307i	−0.997435	+	0.0715756i	$0.977197\pi$
$104$		0			0
$105$	−7.30160	−	7.18934i	−0.712563	−	0.701608i
$106$		0			0
$107$	6.68059	−	1.79006i	0.645837	−	0.173052i	0.0789913	−	0.996875i	$-0.474830\pi$
$107$	6.68059	−	1.79006i	0.645837	−	0.173052i	0.566846	+	0.823824i	$0.308163\pi$
$108$		0			0
$109$	−5.29779	+	3.05868i	−0.507436	+	0.292968i	−0.731779	−	0.681542i	$-0.761310\pi$
$109$	−5.29779	+	3.05868i	−0.507436	+	0.292968i	0.224343	+	0.974510i	$0.427976\pi$
$110$		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
$115$	3.22030	−	12.4526i	0.300294	−	1.16121i
$116$		0			0
$117$	1.46891	+	16.4693i	0.135801	+	1.52259i
$118$		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
$123$	2.92692	−	8.06282i	0.263911	−	0.727000i
$124$		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
$129$	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
$133$	−1.74564	−	0.817911i	−0.151366	−	0.0709219i
$134$		0			0
$135$	0.130959	+	11.6182i	0.0112712	+	0.999936i
$136$		0			0
$137$	4.10332	−	15.3138i	0.350570	−	1.30835i	−0.535397	−	0.844600i	$-0.679838\pi$
$137$	4.10332	−	15.3138i	0.350570	−	1.30835i	0.885968	−	0.463747i	$-0.153495\pi$
$138$		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
$143$	−11.4491	−	3.06778i	−0.957423	−	0.256541i
$144$		0			0
$145$	−7.70588	−	4.35966i	−0.639938	−	0.362050i
$146$		0			0
$147$	11.9342	+	2.13913i	0.984313	+	0.176432i
$148$		0			0
$149$	−4.30668	+	7.45938i	−0.352817	+	0.611096i	−0.986742	−	0.162298i	$-0.948109\pi$
$149$	−4.30668	+	7.45938i	−0.352817	+	0.611096i	0.633925	+	0.773394i	$0.281443\pi$
$150$		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
$153$	10.4240	−	7.32523i	0.842730	−	0.592210i
$154$		0			0
$155$	−0.0911482	−	10.4309i	−0.00732120	−	0.837831i
$156$		0			0
$157$	1.27566	+	0.341811i	0.101808	+	0.0272795i	0.309364	−	0.950944i	$-0.399884\pi$
$157$	1.27566	+	0.341811i	0.101808	+	0.0272795i	−0.207555	+	0.978223i	$0.566551\pi$
$158$		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
$163$	21.5440	−	5.77269i	1.68745	−	0.452152i	0.717724	−	0.696328i	$-0.245184\pi$
$163$	21.5440	−	5.77269i	1.68745	−	0.452152i	0.969731	+	0.244176i	$0.0785175\pi$
$164$		0			0
$165$	−7.85374	−	2.77359i	−0.611413	−	0.215924i
$166$		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
$171$	0.751079	+	2.05278i	0.0574365	+	0.156980i
$172$		0			0
$173$	−0.722028	−	2.69465i	−0.0548948	−	0.204870i	0.933032	−	0.359795i	$-0.117153\pi$
$173$	−0.722028	−	2.69465i	−0.0548948	−	0.204870i	−0.987926	+	0.154925i	$0.950487\pi$
$174$		0			0
$175$	−7.75625	−	10.7164i	−0.586317	−	0.810081i
$176$		0			0
$177$	−2.42494	−	13.6849i	−0.182270	−	1.02862i
$178$		0			0
$179$	7.09783	+	12.2938i	0.530517	+	0.918882i	0.999366	+	0.0356039i	$0.0113355\pi$
$179$	7.09783	+	12.2938i	0.530517	+	0.918882i	−0.468849	+	0.883278i	$0.655331\pi$
$180$		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
$185$	1.29403	−	5.00386i	0.0951387	−	0.367891i
$186$		0			0
$187$	2.36381	+	8.82185i	0.172859	+	0.645117i
$188$		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
$193$	−2.20556	+	8.23125i	−0.158759	+	0.592498i	0.839995	+	0.542595i	$0.182558\pi$
$193$	−2.20556	+	8.23125i	−0.158759	+	0.592498i	−0.998754	+	0.0499036i	$0.984109\pi$
$194$		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	$-0.768454\pi$
$199$	−7.68076	+	4.43449i	−0.544475	+	0.314353i	0.202416	+	0.979300i	$0.435121\pi$
$200$		0			0
$201$	−0.890753	−	0.622592i	−0.0628289	−	0.0439143i
$202$		0			0
$203$	10.4376	−	0.893863i	0.732575	−	0.0627369i
$204$		0			0
$205$	5.45284	−	9.63811i	0.380843	−	0.673155i
$206$		0			0
$207$	7.26648	−	15.6520i	0.505055	−	1.08789i
$208$		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
$213$	2.36555	−	6.51640i	0.162085	−	0.446497i
$214$		0			0
$215$	3.02408	+	10.9040i	0.206241	+	0.743647i
$216$		0			0
$217$	7.06079	+	10.1234i	0.479317	+	0.687218i
$218$		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	0.984424	+	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
$227$	−5.79310	+	21.6202i	−0.384502	+	1.43498i	0.454449	+	0.890773i	$0.349836\pi$
$227$	−5.79310	+	21.6202i	−0.384502	+	1.43498i	−0.838951	+	0.544207i	$0.816830\pi$
$228$		0			0
$229$	18.9575	+	10.9451i	1.25274	+	0.723272i	0.971654	−	0.236409i	$-0.0759704\pi$
$229$	18.9575	+	10.9451i	1.25274	+	0.723272i	0.281091	+	0.959681i	$0.409304\pi$
$230$		0			0
$231$	9.52185	−	2.54126i	0.626492	−	0.167202i
$232$		0			0
$233$	6.06156	+	22.6220i	0.397106	+	1.48202i	0.818163	+	0.574986i	$0.194992\pi$
$233$	6.06156	+	22.6220i	0.397106	+	1.48202i	−0.421058	+	0.907034i	$0.638341\pi$
$234$		0			0
$235$	20.9355	+	5.41403i	1.36568	+	0.353172i
$236$		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	0.577421	−	0.816446i	$-0.304059\pi$
$241$	−6.49458	−	11.2489i	−0.418353	−	0.724608i	−0.995774	+	0.0918384i	$0.970726\pi$
$242$		0			0
$243$	−2.64206	+	15.3629i	−0.169489	+	0.985532i
$244$		0			0
$245$	14.7354	+	5.27888i	0.941413	+	0.337255i
$246$		0			0
$247$	1.03938	+	3.87902i	0.0661341	+	0.246816i
$248$		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
$255$	14.8395	−	7.09368i	0.929286	−	0.444223i
$256$		0			0
$257$	−23.9696	+	6.42263i	−1.49518	+	0.400633i	−0.911483	−	0.411337i	$-0.865062\pi$
$257$	−23.9696	+	6.42263i	−1.49518	+	0.400633i	−0.583699	+	0.811970i	$0.698395\pi$
$258$		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
$263$	−11.5869	−	3.10469i	−0.714477	−	0.191444i	−0.116771	−	0.993159i	$-0.537254\pi$
$263$	−11.5869	−	3.10469i	−0.714477	−	0.191444i	−0.597706	+	0.801715i	$0.703921\pi$
$264$		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	0.811412	−	0.584474i	$-0.198699\pi$
$269$	−1.64773	−	2.85395i	−0.100464	−	0.174008i	−0.911876	+	0.410466i	$0.865366\pi$
$270$		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
$273$	−12.6069	−	21.8859i	−0.763004	−	1.32459i
$274$		0			0
$275$	−9.40476	−	5.21286i	−0.567128	−	0.314347i
$276$		0			0
$277$	−27.4065	−	7.34355i	−1.64670	−	0.441231i	−0.688012	−	0.725699i	$-0.741517\pi$
$277$	−27.4065	−	7.34355i	−1.64670	−	0.441231i	−0.958686	+	0.284467i	$0.908183\pi$
$278$		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
$283$	−0.753013	+	2.81028i	−0.0447620	+	0.167054i	−0.984689	−	0.174323i	$-0.944226\pi$
$283$	−0.753013	+	2.81028i	−0.0447620	+	0.167054i	0.939927	+	0.341376i	$0.110893\pi$
$284$		0			0
$285$	0.516633	+	2.77425i	0.0306027	+	0.164332i
$286$		0			0
$287$	1.11800	+	13.0548i	0.0659933	+	0.770600i
$288$		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	$-0.585336\pi$
$293$	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
$297$	−9.69167	−	5.56280i	−0.562368	−	0.322786i
$298$		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
$303$	−13.2792	+	2.35305i	−0.762871	+	0.135179i
$304$		0			0
$305$	−23.8946	+	14.0754i	−1.36820	+	0.805953i
$306$		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	$-0.674947\pi$
$311$	−0.794450	+	0.458676i	−0.0450491	+	0.0260091i	0.477306	+	0.878737i	$0.341613\pi$
$312$		0			0
$313$	−1.19570	+	0.320387i	−0.0675850	+	0.0181094i	−0.292453	−	0.956280i	$-0.594472\pi$
$313$	−1.19570	+	0.320387i	−0.0675850	+	0.0181094i	0.224868	+	0.974389i	$0.427805\pi$
$314$		0			0
$315$	−7.63864	−	16.0203i	−0.430389	−	0.902644i
$316$		0			0
$317$	−15.6963	+	4.20581i	−0.881591	+	0.236222i	−0.671093	−	0.741373i	$-0.734175\pi$
$317$	−15.6963	+	4.20581i	−0.881591	+	0.236222i	−0.210498	+	0.977594i	$0.567508\pi$
$318$		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
$325$	−6.66623	+	26.7394i	−0.369776	+	1.48324i
$326$		0			0
$327$	−10.4330	+	1.84871i	−0.576949	+	0.102234i
$328$		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
$333$	2.91992	−	6.28950i	0.160011	−	0.344662i
$334$		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
$339$	30.7507	−	14.3709i	1.67015	−	0.780520i
$340$		0			0
$341$	8.68835	+	5.01622i	0.470500	+	0.271643i
$342$		0			0
$343$	−17.9153	+	4.69479i	−0.967337	+	0.253495i
$344$		0			0
$345$	12.6027	−	18.3707i	0.678506	−	0.989044i
$346$		0			0
$347$	−0.290975	+	1.08593i	−0.0156204	+	0.0582960i	−0.973296	−	0.229553i	$-0.926274\pi$
$347$	−0.290975	+	1.08593i	−0.0156204	+	0.0582960i	0.957676	+	0.287849i	$0.0929402\pi$
$348$		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
$353$	6.63668	+	1.77829i	0.353235	+	0.0946489i	0.431073	−	0.902317i	$-0.358135\pi$
$353$	6.63668	+	1.77829i	0.353235	+	0.0946489i	−0.0778384	+	0.996966i	$0.524802\pi$
$354$		0			0
$355$	4.40700	−	7.78956i	0.233899	−	0.413427i
$356$		0			0
$357$	−9.74738	+	16.8444i	−0.515886	+	0.891498i
$358$		0			0
$359$	−1.02137	+	1.76907i	−0.0539060	+	0.0933680i	−0.891719	−	0.452589i	$-0.850500\pi$
$359$	−1.02137	+	1.76907i	−0.0539060	+	0.0933680i	0.837813	+	0.545957i	$0.183834\pi$
$360$		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
$367$	7.27299	+	1.94879i	0.379647	+	0.101726i	0.443596	−	0.896227i	$-0.353703\pi$
$367$	7.27299	+	1.94879i	0.379647	+	0.101726i	−0.0639485	+	0.997953i	$0.520369\pi$
$368$		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
$373$	1.39583	−	0.374011i	0.0722732	−	0.0193655i	−0.222501	−	0.974932i	$-0.571422\pi$
$373$	1.39583	−	0.374011i	0.0722732	−	0.0193655i	0.294774	+	0.955567i	$0.404755\pi$
$374$		0			0
$375$	−6.12844	+	18.3696i	−0.316471	+	0.948602i
$376$		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
$381$	9.63846	−	4.50440i	0.493793	−	0.230767i
$382$		0			0
$383$	4.52502	+	16.8876i	0.231218	+	0.862916i	0.979817	+	0.199894i	$0.0640598\pi$
$383$	4.52502	+	16.8876i	0.231218	+	0.862916i	−0.748600	+	0.663022i	$0.769274\pi$
$384$		0			0
$385$	12.6665	−	1.19633i	0.645547	−	0.0609705i
$386$		0			0
$387$	1.34869	+	15.1214i	0.0685578	+	0.768665i
$388$		0			0
$389$	11.9965	+	20.7786i	0.608249	+	1.05352i	0.991529	+	0.129886i	$0.0414610\pi$
$389$	11.9965	+	20.7786i	0.608249	+	1.05352i	−0.383280	+	0.923632i	$0.625206\pi$
$390$		0			0
$391$	−24.4283			−1.23539
$392$		0			0
$393$	−23.9879	−	28.5387i	−1.21003	−	1.43959i
$394$		0			0
$395$	−8.66280	−	14.7061i	−0.435873	−	0.739946i
$396$		0			0
$397$	−6.14509	−	22.9338i	−0.308413	−	1.15101i	−0.929967	−	0.367643i	$-0.880165\pi$
$397$	−6.14509	−	22.9338i	−0.308413	−	1.15101i	0.621554	−	0.783372i	$-0.286502\pi$
$398$		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
$403$	6.65465	−	24.8355i	0.331492	−	1.23714i
$404$		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	$-0.704463\pi$
$409$	−4.14956	+	2.39575i	−0.205183	+	0.118462i	0.393888	+	0.919158i	$0.371130\pi$
$410$		0			0
$411$	15.7314	−	22.5072i	0.775972	−	1.11020i
$412$		0			0
$413$	12.1449	+	17.4127i	0.597613	+	0.856824i
$414$		0			0
$415$	−19.9960	+	5.54562i	−0.981563	+	0.272224i
$416$		0			0
$417$	−6.75785	+	18.6159i	−0.330933	+	0.911627i
$418$		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
$423$	26.3144	+	12.2165i	1.27945	+	0.593988i
$424$		0			0
$425$	20.4114	−	5.85337i	0.990096	−	0.283930i
$426$		0			0
$427$	13.9220	−	29.7132i	0.673731	−	1.43792i
$428$		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	0.749409	−	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
$437$	1.08475	−	4.04834i	0.0518907	−	0.193659i
$438$		0			0
$439$	−8.95736	−	5.17153i	−0.427511	−	0.246824i	0.270775	−	0.962643i	$-0.412720\pi$
$439$	−8.95736	−	5.17153i	−0.427511	−	0.246824i	−0.698286	+	0.715819i	$0.746054\pi$
$440$		0			0
$441$	18.1657	+	10.5360i	0.865032	+	0.501716i
$442$		0			0
$443$	5.26730	+	19.6578i	0.250257	+	0.933971i	0.970668	+	0.240424i	$0.0772864\pi$
$443$	5.26730	+	19.6578i	0.250257	+	0.933971i	−0.720411	+	0.693547i	$0.756047\pi$
$444$		0			0
$445$	2.53051	−	1.49063i	0.119958	−	0.0706624i
$446$		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
$453$	3.01067	+	16.9905i	0.141454	+	0.798281i
$454$		0			0
$455$	−11.3634	−	30.5627i	−0.532725	−	1.43280i
$456$		0			0
$457$	−1.71551	−	6.40237i	−0.0802481	−	0.299490i	0.914124	−	0.405435i	$-0.132880\pi$
$457$	−1.71551	−	6.40237i	−0.0802481	−	0.299490i	−0.994372	+	0.105945i	$0.966213\pi$
$458$		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	0.631040	−	0.775750i	$-0.282628\pi$
$463$	−3.11379	−	3.11379i	−0.144710	−	0.144710i	−0.775750	+	0.631040i	$0.782628\pi$
$464$		0			0
$465$	6.01649	−	17.0364i	0.279008	−	0.790043i
$466$		0			0
$467$	−26.1138	+	6.99718i	−1.20840	+	0.323791i	−0.806135	−	0.591731i	$-0.798445\pi$
$467$	−26.1138	+	6.99718i	−1.20840	+	0.323791i	−0.402268	+	0.915522i	$0.631778\pi$
$468$		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
$473$	−10.5121	−	2.81670i	−0.483346	−	0.129512i
$474$		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	−0.869602	−	0.493753i	$-0.835625\pi$
$479$	−18.8746	−	32.6918i	−0.862404	−	1.49373i	0.00719862	−	0.999974i	$-0.497709\pi$
$480$		0			0
$481$	6.36975	−	11.0327i	0.290436	−	0.503050i
$482$		0			0
$483$	−0.0261378	+	26.3597i	−0.00118931	+	1.19941i
$484$		0			0
$485$	30.5356	−	8.46865i	1.38655	−	0.384542i
$486$		0			0
$487$	28.4795	+	7.63106i	1.29053	+	0.345796i	0.837861	−	0.545883i	$-0.183806\pi$
$487$	28.4795	+	7.63106i	1.29053	+	0.345796i	0.452668	+	0.891679i	$0.350472\pi$
$488$		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
$493$	−4.35208	+	16.2422i	−0.196008	+	0.731511i
$494$		0			0
$495$	−11.1474	−	9.15740i	−0.501037	−	0.411595i
$496$		0			0
$497$	0.903569	+	10.5509i	0.0405306	+	0.473274i
$498$		0			0
$499$	13.9880	+	8.07598i	0.626189	+	0.361531i	0.779275	−	0.626682i	$-0.215588\pi$
$499$	13.9880	+	8.07598i	0.626189	+	0.361531i	−0.153086	+	0.988213i	$0.548921\pi$
$500$		0			0
$501$	−5.18629	−	11.0976i	−0.231706	−	0.495802i
$502$		0			0
$503$	−25.0418	+	25.0418i	−1.11656	+	1.11656i	−0.124316	+	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
$507$	−10.2704	+	28.2920i	−0.456125	+	1.25649i
$508$		0			0
$509$	21.6658	−	37.5262i	0.960319	−	1.66332i	0.238621	−	0.971113i	$-0.423305\pi$
$509$	21.6658	−	37.5262i	0.960319	−	1.66332i	0.721698	−	0.692208i	$-0.243362\pi$
$510$		0			0
$511$	−5.01671	+	28.1488i	−0.221926	+	1.24523i
$512$		0			0
$513$	0.00959137	+	3.78602i	0.000423469	+	0.167157i
$514$		0			0
$515$	−43.1495	−	11.1587i	−1.90140	−	0.491711i
$516$		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
$523$	28.1932	−	7.55434i	1.23280	−	0.330328i	0.417132	−	0.908846i	$-0.363035\pi$
$523$	28.1932	−	7.55434i	1.23280	−	0.330328i	0.815670	+	0.578518i	$0.196369\pi$
$524$		0			0
$525$	−6.29430	−	22.0314i	−0.274706	−	0.961528i
$526$		0			0
$527$	−19.1364	+	5.12759i	−0.833595	+	0.223361i
$528$		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
$535$	14.9727	+	3.87201i	0.647325	+	0.167402i
$536$		0			0
$537$	4.29004	+	24.2105i	0.185129	+	1.04476i
$538$		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
$543$	−16.3265	−	5.92674i	−0.700636	−	0.254341i
$544$		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
$549$	−34.9411	+	12.7844i	−1.49125	+	0.545625i
$550$		0			0
$551$	−2.49845	−	1.44248i	−0.106438	−	0.0614518i
$552$		0			0
$553$	18.2872	+	8.56839i	0.777653	+	0.364365i
$554$		0			0
$555$	5.06419	−	7.38197i	0.214963	−	0.313347i
$556$		0			0
$557$	2.76552	−	10.3211i	0.117179	−	0.437318i	−0.882262	−	0.470759i	$-0.843980\pi$
$557$	2.76552	−	10.3211i	0.117179	−	0.437318i	0.999441	+	0.0334413i	$0.0106467\pi$
$558$		0			0
$559$			27.8912i			1.17967i
$560$		0			0
$561$	−1.36540	+	15.7599i	−0.0576473	+	0.665382i
$562$		0			0
$563$	−3.59434	−	0.963101i	−0.151483	−	0.0405898i	0.182280	−	0.983247i	$-0.441652\pi$
$563$	−3.59434	−	0.963101i	−0.151483	−	0.0405898i	−0.333764	+	0.942657i	$0.608319\pi$
$564$		0			0
$565$	42.2263	−	11.7109i	1.77648	−	0.492682i
$566$		0			0
$567$	−6.19839	−	22.9909i	−0.260308	−	0.965526i
$568$		0			0
$569$	1.12664	−	1.95139i	0.0472311	−	0.0818066i	−0.841443	−	0.540345i	$-0.818294\pi$
$569$	1.12664	−	1.95139i	0.0472311	−	0.0818066i	0.888674	+	0.458539i	$0.151627\pi$
$570$		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
$573$	−7.59101	−	9.03111i	−0.317119	−	0.377280i
$574$		0			0
$575$	19.9785	−	20.6892i	0.833159	−	0.862801i
$576$		0			0
$577$	16.1980	+	4.34025i	0.674332	+	0.180687i	0.579706	−	0.814826i	$-0.303168\pi$
$577$	16.1980	+	4.34025i	0.674332	+	0.180687i	0.0946268	+	0.995513i	$0.469834\pi$
$578$		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
$583$	13.3913	−	3.58818i	0.554610	−	0.148607i
$584$		0			0
$585$	−15.2751	+	33.6698i	−0.631548	+	1.39207i
$586$		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
$591$	16.4697	+	35.2417i	0.677473	+	1.44965i
$592$		0			0
$593$	−4.05578	−	15.1364i	−0.166551	−	0.621577i	−0.997837	−	0.0657322i	$-0.979062\pi$
$593$	−4.05578	−	15.1364i	−0.166551	−	0.621577i	0.831286	−	0.555844i	$-0.187605\pi$
$594$		0			0
$595$	−16.0165	+	19.3575i	−0.656612	+	0.793579i
$596$		0			0
$597$	−15.1259	+	2.68028i	−0.619062	+	0.109696i
$598$		0			0
$599$	16.5463	+	28.6589i	0.676062	+	1.17097i	0.976157	+	0.217064i	$0.0696480\pi$
$599$	16.5463	+	28.6589i	0.676062	+	1.17097i	−0.300096	+	0.953909i	$0.597019\pi$
$600$		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
$605$	−12.2825	+	7.23514i	−0.499355	+	0.294150i
$606$		0			0
$607$	−8.92202	−	33.2974i	−0.362134	−	1.35150i	−0.871265	−	0.490812i	$-0.836700\pi$
$607$	−8.92202	−	33.2974i	−0.362134	−	1.35150i	0.509132	−	0.860689i	$-0.329967\pi$
$608$		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
$613$	−5.15144	+	19.2254i	−0.208065	+	0.776509i	0.780429	+	0.625245i	$0.215001\pi$
$613$	−5.15144	+	19.2254i	−0.208065	+	0.776509i	−0.988493	+	0.151264i	$0.951666\pi$
$614$		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	$-0.845909\pi$
$619$	−23.0037	+	13.2812i	−0.924597	+	0.533816i	−0.0394980	+	0.999220i	$0.512576\pi$
$620$		0			0
$621$	21.0812	−	21.1883i	0.845958	−	0.850255i
$622$		0			0
$623$	−1.47438	+	3.14672i	−0.0590698	+	0.126071i
$624$		0			0
$625$	−11.7358	+	22.0742i	−0.469431	+	0.882969i
$626$		0			0
$627$	−2.55115	−	0.926102i	−0.101883	−	0.0369850i
$628$		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
$633$	23.5369	+	8.54424i	0.935509	+	0.339603i
$634$		0			0
$635$	13.2354	−	3.67066i	0.525230	−	0.145666i
$636$		0			0
$637$	31.5222	+	22.2450i	1.24896	+	0.881381i
$638$		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	0.565117	−	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
$647$	6.54113	−	24.4118i	0.257159	−	0.959729i	−0.709718	−	0.704485i	$-0.751178\pi$
$647$	6.54113	−	24.4118i	0.257159	−	0.959729i	0.966877	−	0.255243i	$-0.0821555\pi$
$648$		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
$653$	−3.41075	−	12.7291i	−0.133473	−	0.498129i	0.866526	−	0.499131i	$-0.166347\pi$
$653$	−3.41075	−	12.7291i	−0.133473	−	0.498129i	−0.999999	+	0.00100275i	$0.999681\pi$
$654$		0			0
$655$	−24.4281	−	41.4696i	−0.954484	−	1.62035i
$656$		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	0.955932	−	0.293587i	$-0.0948491\pi$
$661$	5.75162	+	9.96211i	0.223712	+	0.387481i	−0.732220	+	0.681068i	$0.761516\pi$
$662$		0			0
$663$	39.9195	−	7.07365i	1.55035	−	0.274718i
$664$		0			0
$665$	−2.49677	−	3.51388i	−0.0968204	−	0.136262i
$666$		0			0
$667$	5.89474	+	21.9995i	0.228245	+	0.851823i
$668$		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	0.746030	−	0.665912i	$-0.231957\pi$
$673$	2.07846	+	2.07846i	0.0801187	+	0.0801187i	−0.665912	+	0.746030i	$0.731957\pi$
$674$		0			0
$675$	−12.5376	+	22.7554i	−0.482572	+	0.875856i
$676$		0			0
$677$	−17.1414	+	4.59302i	−0.658797	+	0.176524i	−0.572703	−	0.819763i	$-0.694105\pi$
$677$	−17.1414	+	4.59302i	−0.658797	+	0.176524i	−0.0860941	+	0.996287i	$0.527439\pi$
$678$		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
$683$	−11.1202	−	2.97965i	−0.425503	−	0.114013i	0.0397112	−	0.999211i	$-0.487356\pi$
$683$	−11.1202	−	2.97965i	−0.425503	−	0.114013i	−0.465215	+	0.885198i	$0.654023\pi$
$684$		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	−0.907657	−	0.419712i	$-0.862131\pi$
$691$	−2.37495	+	4.11354i	−0.0903475	+	0.156486i	0.817310	+	0.576198i	$0.195464\pi$
$692$		0			0
$693$	17.0044	+	1.49021i	0.645944	+	0.0566086i
$694$		0			0
$695$	−12.5898	+	22.2531i	−0.477560	+	0.844107i
$696$		0			0
$697$	−20.3149	−	5.44336i	−0.769481	−	0.206182i
$698$		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
$703$	0.435890	−	1.62676i	0.0164399	−	0.0613545i
$704$		0			0
$705$	30.8851	+	21.1879i	1.16320	+	0.797982i
$706$		0			0
$707$	16.8965	−	11.7849i	0.635457	−	0.443215i
$708$		0			0
$709$	−4.99216	−	2.88222i	−0.187484	−	0.108244i	0.403320	−	0.915059i	$-0.367856\pi$
$709$	−4.99216	−	2.88222i	−0.187484	−	0.108244i	−0.590804	+	0.806815i	$0.701189\pi$
$710$		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
$717$	32.1328	+	11.6647i	1.20002	+	0.435625i
$718$		0			0
$719$	18.4248	−	31.9127i	0.687129	−	1.19014i	−0.285633	−	0.958339i	$-0.592204\pi$
$719$	18.4248	−	31.9127i	0.687129	−	1.19014i	0.972763	−	0.231804i	$-0.0744627\pi$
$720$		0			0
$721$	49.5875	−	17.9454i	1.84674	−	0.668320i
$722$		0			0
$723$	−3.92542	−	22.1528i	−0.145988	−	0.823871i
$724$		0			0
$725$	−10.1968	−	16.9694i	−0.378699	−	0.630229i
$726$		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
$733$	17.9065	−	4.79803i	0.661391	−	0.177219i	0.0875174	−	0.996163i	$-0.472107\pi$
$733$	17.9065	−	4.79803i	0.661391	−	0.177219i	0.573874	+	0.818944i	$0.305440\pi$
$734$		0			0
$735$	20.8708	+	17.3035i	0.769830	+	0.638249i
$736$		0			0
$737$	1.30338	−	0.349241i	0.0480108	−	0.0128644i
$738$		0			0
$739$	−6.24688	+	3.60664i	−0.229795	+	0.132672i	−0.610478	−	0.792034i	$-0.709022\pi$
$739$	−6.24688	+	3.60664i	−0.229795	+	0.132672i	0.380682	+	0.924706i	$0.375689\pi$
$740$		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
$745$	−16.5949	+	9.77540i	−0.607990	+	0.358143i
$746$		0			0
$747$	−27.7299	+	2.47325i	−1.01459	+	0.0904916i
$748$		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
$753$	−1.09183	+	3.00768i	−0.0397885	+	0.109606i
$754$		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
$759$	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
$763$	13.2750	−	9.25898i	0.480587	−	0.335198i
$764$		0			0
$765$	28.3526	−	2.77871i	1.02509	−	0.100465i
$766$		0			0
$767$	11.4464	−	42.7184i	0.413304	−	1.54247i
$768$		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
$773$	−5.86442	−	1.57137i	−0.210929	−	0.0565182i	0.151807	−	0.988410i	$-0.451491\pi$
$773$	−5.86442	−	1.57137i	−0.210929	−	0.0565182i	−0.362736	+	0.931892i	$0.618157\pi$
$774$		0			0
$775$	11.3078	−	20.4009i	0.406187	−	0.732821i
$776$		0			0
$777$	−0.0105031	+	10.5922i	−0.000376796	+	0.379994i
$778$		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
$787$	11.9782	+	3.20956i	0.426978	+	0.114409i	0.465907	−	0.884833i	$-0.345728\pi$
$787$	11.9782	+	3.20956i	0.426978	+	0.114409i	−0.0389290	+	0.999242i	$0.512395\pi$
$788$		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
$793$	−66.0262	+	17.6917i	−2.34466	+	0.628249i
$794$		0			0
$795$	−10.7680	−	22.5259i	−0.381901	−	0.798911i
$796$		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
$801$	3.70038	−	1.35391i	0.130746	−	0.0478380i
$802$		0			0
$803$	6.01521	+	22.4491i	0.212272	+	0.792210i
$804$		0			0
$805$	−5.67784	+	33.5532i	−0.200118	+	1.18260i
$806$		0			0
$807$	−0.995912	−	5.62034i	−0.0350578	−	0.197845i
$808$		0			0
$809$	−0.599532	−	1.03842i	−0.0210784	−	0.0365089i	0.855294	−	0.518143i	$-0.173377\pi$
$809$	−0.599532	−	1.03842i	−0.0210784	−	0.0365089i	−0.876372	+	0.481634i	$0.840043\pi$
$810$		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
$815$	48.2847	+	12.4867i	1.69134	+	0.437390i
$816$		0			0
$817$	0.954314	+	3.56155i	0.0333872	+	0.124603i
$818$		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
$823$	−0.481753	+	1.79793i	−0.0167929	+	0.0626718i	−0.973814	−	0.227347i	$-0.926995\pi$
$823$	−0.481753	+	1.79793i	−0.0167929	+	0.0626718i	0.957021	+	0.290019i	$0.0936615\pi$
$824$		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	$-0.480109\pi$
$829$	27.5833	−	15.9252i	0.958008	−	0.553106i	0.895559	+	0.444942i	$0.146776\pi$
$830$		0			0
$831$	−40.2802	−	28.1538i	−1.39731	−	0.976646i
$832$		0			0
$833$	2.69967	−	29.6048i	0.0935379	−	1.02575i
$834$		0			0
$835$	−4.22633	−	15.2390i	−0.146258	−	0.527367i
$836$		0			0
$837$	12.0669	−	21.0232i	0.417092	−	0.726669i
$838$		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
$843$	−8.59007	+	23.6632i	−0.295858	+	0.815003i
$844$		0			0
$845$	−19.1337	+	33.8196i	−0.658220	+	1.16343i
$846$		0			0
$847$	7.15629	−	15.2734i	0.245893	−	0.524801i
$848$		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	0.105157	−	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
$857$	−4.57762	+	17.0839i	−0.156368	+	0.583575i	0.842616	+	0.538515i	$0.181015\pi$
$857$	−4.57762	+	17.0839i	−0.156368	+	0.583575i	−0.998984	+	0.0450600i	$0.985652\pi$
$858$		0			0
$859$	−14.7883	−	8.53804i	−0.504571	−	0.291314i	0.226028	−	0.974121i	$-0.427426\pi$
$859$	−14.7883	−	8.53804i	−0.504571	−	0.291314i	−0.730599	+	0.682806i	$0.760759\pi$
$860$		0			0
$861$	−5.89545	+	21.9152i	−0.200917	+	0.746868i
$862$		0			0
$863$	−1.21811	−	4.54605i	−0.0414650	−	0.154749i	0.942089	−	0.335362i	$-0.108859\pi$
$863$	−1.21811	−	4.54605i	−0.0414650	−	0.154749i	−0.983554	+	0.180613i	$0.942192\pi$
$864$		0			0
$865$	1.56179	−	6.03929i	0.0531025	−	0.205342i
$866$		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
$873$	42.3461	−	3.77688i	1.43320	−	0.127828i
$874$		0			0
$875$	−3.29564	−	29.3962i	−0.111413	−	0.993774i
$876$		0			0
$877$	−5.72343	−	21.3601i	−0.193267	−	0.721281i	−0.992709	−	0.120538i	$-0.961538\pi$
$877$	−5.72343	−	21.3601i	−0.193267	−	0.721281i	0.799442	−	0.600743i	$-0.205128\pi$
$878$		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	0.342287	−	0.939595i	$-0.388798\pi$
$883$	−17.7492	−	17.7492i	−0.597308	−	0.597308i	−0.939595	+	0.342287i	$0.888798\pi$
$884$		0			0
$885$	10.3487	−	29.3035i	0.347868	−	0.985027i
$886$		0			0
$887$	24.7885	−	6.64206i	0.832316	−	0.223019i	0.182592	−	0.983189i	$-0.441551\pi$
$887$	24.7885	−	6.64206i	0.832316	−	0.223019i	0.649724	+	0.760170i	$0.274884\pi$
$888$		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
$893$	6.80615	+	1.82370i	0.227759	+	0.0610279i
$894$		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
$903$	−11.5751	−	20.0947i	−0.385195	−	0.668708i
$904$		0			0
$905$	−19.5163	−	11.0415i	−0.648743	−	0.367031i
$906$		0			0
$907$	−1.61412	−	0.432502i	−0.0535960	−	0.0143610i	0.231921	−	0.972735i	$-0.425499\pi$
$907$	−1.61412	−	0.432502i	−0.0535960	−	0.0143610i	−0.285517	+	0.958374i	$0.592165\pi$
$908$		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
$913$	5.16532	−	19.2772i	0.170947	−	0.637983i
$914$		0			0
$915$	−47.2215	+	8.79380i	−1.56110	+	0.290714i
$916$		0			0
$917$	51.5679	+	24.1619i	1.70292	+	0.797895i
$918$		0			0
$919$	17.0980	+	9.87155i	0.564012	+	0.325632i	0.754754	−	0.656008i	$-0.227756\pi$
$919$	17.0980	+	9.87155i	0.564012	+	0.325632i	−0.190742	+	0.981640i	$0.561089\pi$
$920$		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
$927$	−54.2359	−	25.1792i	−1.78134	−	0.826993i
$928$		0			0
$929$	−25.3654	+	43.9342i	−0.832212	+	1.44143i	0.0640690	+	0.997945i	$0.479592\pi$
$929$	−25.3654	+	43.9342i	−0.832212	+	1.44143i	−0.896281	+	0.443487i	$0.853741\pi$
$930$		0			0
$931$	4.78633	+	1.76201i	0.156866	+	0.0577477i
$932$		0			0
$933$	−1.56453	+	0.277231i	−0.0512203	+	0.00907613i
$934$		0			0
$935$	−5.11306	+	19.7717i	−0.167215	+	0.646603i
$936$		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	$-0.813313\pi$
$941$	−23.6212	+	13.6377i	−0.770030	+	0.444577i	0.0628556	+	0.998023i	$0.479979\pi$
$942$		0			0
$943$	−27.5158	+	7.37283i	−0.896037	+	0.240093i
$944$		0			0
$945$	−2.96807	−	30.5972i	−0.0965512	−	0.995328i
$946$		0			0
$947$	−1.54071	+	0.412833i	−0.0500664	+	0.0134153i	−0.283765	−	0.958894i	$-0.591584\pi$
$947$	−1.54071	+	0.412833i	−0.0500664	+	0.0134153i	0.233699	+	0.972309i	$0.424917\pi$
$948$		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
$955$	−7.73031	−	13.1231i	−0.250147	−	0.424654i
$956$		0			0
$957$	14.5224	−	2.57333i	0.469442	−	0.0831840i
$958$		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
$963$	18.8196	+	8.73704i	0.606452	+	0.281547i
$964$		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
$969$	4.85547	−	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
$973$	−2.58130	−	30.1417i	−0.0827527	−	0.966298i
$974$		0			0
$975$	−26.6568	+	39.5944i	−0.853702	+	1.26804i
$976$		0			0
$977$	12.2030	−	45.5422i	0.390408	−	1.45702i	−0.439054	−	0.898461i	$-0.644686\pi$
$977$	12.2030	−	45.5422i	0.390408	−	1.45702i	0.829462	−	0.558563i	$-0.188647\pi$
$978$		0			0
$979$			2.82461i			0.0902751i
$980$		0			0
$981$	−18.0786	−	3.15627i	−0.577206	−	0.100772i
$982$		0			0
$983$	−35.1504	−	9.41853i	−1.12112	−	0.300404i	−0.349786	−	0.936830i	$-0.613746\pi$
$983$	−35.1504	−	9.41853i	−1.12112	−	0.300404i	−0.771338	+	0.636425i	$0.780412\pi$
$984$		0			0
$985$	13.4212	+	48.3933i	0.427636	+	1.54194i
$986$		0			0
$987$	−44.3164	−	0.0439434i	−1.41061	−	0.00139874i
$988$		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
$993$	−14.4168	+	12.1179i	−0.457503	+	0.384549i
$994$		0			0
$995$	−19.8309	+	0.173288i	−0.628681	+	0.00549359i
$996$		0			0
$997$	34.1721	+	9.15638i	1.08224	+	0.289985i	0.755513	−	0.655133i	$-0.227388\pi$
$997$	34.1721	+	9.15638i	1.08224	+	0.289985i	0.326727	+	0.945119i	$0.394054\pi$
$998$		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.233.11	yes	48
3.2	odd	2	inner	420.2.bv.c.233.1	yes	48
5.2	odd	4	inner	420.2.bv.c.317.8	yes	48
7.4	even	3	inner	420.2.bv.c.53.6	✓	48
15.2	even	4	inner	420.2.bv.c.317.6	yes	48
21.11	odd	6	inner	420.2.bv.c.53.8	yes	48
35.32	odd	12	inner	420.2.bv.c.137.1	yes	48
105.32	even	12	inner	420.2.bv.c.137.11	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bv.c.53.6	✓	48	7.4	even	3	inner
420.2.bv.c.53.8	yes	48	21.11	odd	6	inner
420.2.bv.c.137.1	yes	48	35.32	odd	12	inner
420.2.bv.c.137.11	yes	48	105.32	even	12	inner
420.2.bv.c.233.1	yes	48	3.2	odd	2	inner
420.2.bv.c.233.11	yes	48	1.1	even	1	trivial
420.2.bv.c.317.6	yes	48	15.2	even	4	inner
420.2.bv.c.317.8	yes	48	5.2	odd	4	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)

\(f(q)\)	\(=\)	\(q+(1.62810 + 0.591022i) q^{3} +(1.94619 + 1.10107i) q^{5} +(-2.63610 + 0.225753i) q^{7} +(2.30139 + 1.92448i) q^{9} +O(q^{10})\)	\(q+(1.62810 + 0.591022i) q^{3} +(1.94619 + 1.10107i) q^{5} +(-2.63610 + 0.225753i) q^{7} +(2.30139 + 1.92448i) q^{9} +(-1.86244 + 1.07528i) q^{11} +(3.89727 + 3.89727i) q^{13} +(2.51782 + 2.94289i) q^{15} +(1.09916 - 4.10211i) q^{17} +(0.631006 + 0.364311i) q^{19} +(-4.42525 - 1.19045i) q^{21} +(-1.48877 - 5.55616i) q^{23} +(2.57529 + 4.28578i) q^{25} +(2.60947 + 4.49340i) q^{27} -3.95947 q^{29} +(-2.33251 - 4.04003i) q^{31} +(-3.66775 + 0.649918i) q^{33} +(-5.37892 - 2.46318i) q^{35} +(-0.598238 - 2.23265i) q^{37} +(4.04175 + 8.64849i) q^{39} -4.95231i q^{41} +(3.57830 + 3.57830i) q^{43} +(2.35994 + 6.27938i) q^{45} +(9.34112 - 2.50295i) q^{47} +(6.89807 - 1.19022i) q^{49} +(4.21396 - 6.02899i) q^{51} +(-6.22687 - 1.66848i) q^{53} +(-4.80863 + 0.0420191i) q^{55} +(0.812022 + 0.966072i) q^{57} +(-4.01205 - 6.94907i) q^{59} +(-6.20108 + 10.7406i) q^{61} +(-6.50115 - 4.55358i) q^{63} +(3.29365 + 11.8760i) q^{65} +(-0.606066 - 0.162395i) q^{67} +(0.859954 - 9.92585i) q^{69} -4.00247i q^{71} +(2.79703 - 10.4387i) q^{73} +(1.65983 + 8.49970i) q^{75} +(4.66685 - 3.25501i) q^{77} +(-6.61039 - 3.81651i) q^{79} +(1.59276 + 8.85794i) q^{81} +(-6.56196 + 6.56196i) q^{83} +(6.65587 - 6.77322i) q^{85} +(-6.44640 - 2.34014i) q^{87} +(0.656714 - 1.13746i) q^{89} +(-11.1534 - 9.39378i) q^{91} +(-1.40981 - 7.95611i) q^{93} +(0.826923 + 1.40380i) q^{95} +(10.0207 - 10.0207i) q^{97} +(-6.35557 - 1.10959i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{3} - 8 q^{7}+O(q^{10}) \) 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