LMFDB - Embedded newform 756.2.bx.a.41.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(41,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 17, 9]))

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

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

chi := DirichletCharacter("756.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bx (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.1
Character	$\chi$	$=$	756.41
Dual form			756.2.bx.a.461.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71962 + 0.207109i) q^{3} +(-1.79713 - 1.50797i) q^{5} +(1.89497 + 1.84637i) q^{7} +(2.91421 - 0.712300i) q^{9} +O(q^{10})$	\(q+(-1.71962 + 0.207109i) q^{3} +(-1.79713 - 1.50797i) q^{5} +(1.89497 + 1.84637i) q^{7} +(2.91421 - 0.712300i) q^{9} +(-3.19731 - 3.81041i) q^{11} +(-0.641096 - 0.113043i) q^{13} +(3.40271 + 2.22094i) q^{15} +(-3.77141 + 6.53228i) q^{17} +(5.92129 - 3.41866i) q^{19} +(-3.64104 - 2.78259i) q^{21} +(2.22669 + 6.11778i) q^{23} +(0.0874608 + 0.496015i) q^{25} +(-4.86382 + 1.82845i) q^{27} +(-7.72786 + 1.36263i) q^{29} +(-0.918136 - 2.52256i) q^{31} +(6.28735 + 5.89028i) q^{33} +(-0.621249 - 6.17574i) q^{35} +(-4.44203 + 7.69382i) q^{37} +(1.12586 + 0.0616138i) q^{39} +(-0.928485 + 5.26570i) q^{41} +(-6.45441 + 5.41589i) q^{43} +(-6.31135 - 3.11446i) q^{45} +(-6.07461 - 2.21098i) q^{47} +(0.181858 + 6.99764i) q^{49} +(5.13251 - 12.0142i) q^{51} +1.61492i q^{53} +11.6693i q^{55} +(-9.47436 + 7.10516i) q^{57} +(4.68332 + 3.92977i) q^{59} +(-2.19713 + 6.03656i) q^{61} +(6.83752 + 4.03091i) q^{63} +(0.981670 + 1.16991i) q^{65} +(-1.94386 + 11.0242i) q^{67} +(-5.09611 - 10.0591i) q^{69} +(-2.13151 - 1.23063i) q^{71} +(-1.21699 + 0.702630i) q^{73} +(-0.253129 - 0.834845i) q^{75} +(0.976587 - 13.1240i) q^{77} +(-1.34687 - 7.63850i) q^{79} +(7.98526 - 4.15158i) q^{81} +(-0.714931 - 4.05458i) q^{83} +(16.6282 - 6.05218i) q^{85} +(13.0068 - 3.94372i) q^{87} +(4.04962 + 7.01414i) q^{89} +(-1.00614 - 1.39791i) q^{91} +(2.10129 + 4.14770i) q^{93} +(-15.7966 - 2.78537i) q^{95} +(-8.91934 - 10.6296i) q^{97} +(-12.0318 - 8.82690i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} - 30 q^{21} + 48 q^{23} + 12 q^{29} - 27 q^{35} - 42 q^{39} + 18 q^{49} + 18 q^{51} + 30 q^{57} - 15 q^{63} + 42 q^{65} + 36 q^{71} - 51 q^{77} + 36 q^{79} + 18 q^{81} + 36 q^{85} + 9 q^{91} + 96 q^{93} - 48 q^{95} + 36 q^{99}+O(q^{100}) $ 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 - 30 * q^21 + 48 * q^23 + 12 * q^29 - 27 * q^35 - 42 * q^39 + 18 * q^49 + 18 * q^51 + 30 * q^57 - 15 * q^63 + 42 * q^65 + 36 * q^71 - 51 * q^77 + 36 * q^79 + 18 * q^81 + 36 * q^85 + 9 * q^91 + 96 * q^93 - 48 * q^95 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.71962	+	0.207109i	−0.992825	+	0.119575i
$3$	−1.71962	+	0.207109i	−0.992825	+	0.119575i
$4$		0			0
$5$	−1.79713	−	1.50797i	−0.803702	−	0.674386i	0.145394	−	0.989374i	$-0.453555\pi$
$5$	−1.79713	−	1.50797i	−0.803702	−	0.674386i	−0.949096	+	0.314988i	$0.898000\pi$
$6$		0			0
$7$	1.89497	+	1.84637i	0.716233	+	0.697861i
$7$	1.89497	+	1.84637i	0.716233	+	0.697861i
$8$		0			0
$9$	2.91421	−	0.712300i	0.971404	−	0.237433i
$10$		0			0
$11$	−3.19731	−	3.81041i	−0.964026	−	1.14888i	−0.988809	−	0.149189i	$-0.952334\pi$
$11$	−3.19731	−	3.81041i	−0.964026	−	1.14888i	0.0247822	−	0.999693i	$-0.492111\pi$
$12$		0			0
$13$	−0.641096	−	0.113043i	−0.177808	−	0.0313524i	0.0840351	−	0.996463i	$-0.473219\pi$
$13$	−0.641096	−	0.113043i	−0.177808	−	0.0313524i	−0.261843	+	0.965110i	$0.584330\pi$
$14$		0			0
$15$	3.40271	+	2.22094i	0.878575	+	0.573445i
$16$		0			0
$17$	−3.77141	+	6.53228i	−0.914702	+	1.58431i	−0.107364	+	0.994220i	$0.534241\pi$
$17$	−3.77141	+	6.53228i	−0.914702	+	1.58431i	−0.807338	+	0.590090i	$0.799092\pi$
$18$		0			0
$19$	5.92129	−	3.41866i	1.35844	−	0.784294i	0.369024	−	0.929420i	$-0.379692\pi$
$19$	5.92129	−	3.41866i	1.35844	−	0.784294i	0.989413	+	0.145125i	$0.0463585\pi$
$20$		0			0
$21$	−3.64104	−	2.78259i	−0.794541	−	0.607211i
$22$		0			0
$23$	2.22669	+	6.11778i	0.464297	+	1.27564i	0.922224	+	0.386655i	$0.126370\pi$
$23$	2.22669	+	6.11778i	0.464297	+	1.27564i	−0.457928	+	0.888989i	$0.651408\pi$
$24$		0			0
$25$	0.0874608	+	0.496015i	0.0174922	+	0.0992030i
$26$		0			0
$27$	−4.86382	+	1.82845i	−0.936043	+	0.351885i
$28$		0			0
$29$	−7.72786	+	1.36263i	−1.43503	+	0.253034i	−0.836455	−	0.548035i	$-0.815376\pi$
$29$	−7.72786	+	1.36263i	−1.43503	+	0.253034i	−0.598572	+	0.801069i	$0.704265\pi$
$30$		0			0
$31$	−0.918136	−	2.52256i	−0.164902	−	0.453065i	0.829528	−	0.558466i	$-0.188610\pi$
$31$	−0.918136	−	2.52256i	−0.164902	−	0.453065i	−0.994430	+	0.105401i	$0.966387\pi$
$32$		0			0
$33$	6.28735	+	5.89028i	1.09449	+	1.02537i
$34$		0			0
$35$	−0.621249	−	6.17574i	−0.105010	−	1.04389i
$36$		0			0
$37$	−4.44203	+	7.69382i	−0.730265	+	1.26486i	0.226505	+	0.974010i	$0.427270\pi$
$37$	−4.44203	+	7.69382i	−0.730265	+	1.26486i	−0.956770	+	0.290846i	$0.906063\pi$
$38$		0			0
$39$	1.12586	+	0.0616138i	0.180281	+	0.00986611i
$40$		0			0
$41$	−0.928485	+	5.26570i	−0.145005	+	0.822364i	0.822358	+	0.568970i	$0.192658\pi$
$41$	−0.928485	+	5.26570i	−0.145005	+	0.822364i	−0.967363	+	0.253394i	$0.918453\pi$
$42$		0			0
$43$	−6.45441	+	5.41589i	−0.984288	+	0.825916i	−0.984731	−	0.174084i	$-0.944304\pi$
$43$	−6.45441	+	5.41589i	−0.984288	+	0.825916i	0.000442447		1.00000i	$0.499859\pi$
$44$		0			0
$45$	−6.31135	−	3.11446i	−0.940841	−	0.464276i
$46$		0			0
$47$	−6.07461	−	2.21098i	−0.886072	−	0.322504i	−0.141415	−	0.989950i	$-0.545165\pi$
$47$	−6.07461	−	2.21098i	−0.886072	−	0.322504i	−0.744658	+	0.667446i	$0.767387\pi$
$48$		0			0
$49$	0.181858	+	6.99764i	0.0259798	+	0.999662i
$50$		0			0
$51$	5.13251	−	12.0142i	0.718696	−	1.68232i
$52$		0			0
$53$			1.61492i			0.221826i	0.993830	+	0.110913i	$0.0353775\pi$
$53$			1.61492i			0.221826i	−0.993830	+	0.110913i	$0.964623\pi$
$54$		0			0
$55$			11.6693i			1.57348i
$56$		0			0
$57$	−9.47436	+	7.10516i	−1.25491	+	0.941102i
$58$		0			0
$59$	4.68332	+	3.92977i	0.609717	+	0.511613i	0.894552	−	0.446963i	$-0.147495\pi$
$59$	4.68332	+	3.92977i	0.609717	+	0.511613i	−0.284836	+	0.958576i	$0.591939\pi$
$60$		0			0
$61$	−2.19713	+	6.03656i	−0.281314	+	0.772903i	0.715893	+	0.698210i	$0.246020\pi$
$61$	−2.19713	+	6.03656i	−0.281314	+	0.772903i	−0.997207	+	0.0746927i	$0.976202\pi$
$62$		0			0
$63$	6.83752	+	4.03091i	0.861447	+	0.507847i
$64$		0			0
$65$	0.981670	+	1.16991i	0.121761	+	0.145109i
$66$		0			0
$67$	−1.94386	+	11.0242i	−0.237480	+	1.34682i	0.599847	+	0.800115i	$0.295228\pi$
$67$	−1.94386	+	11.0242i	−0.237480	+	1.34682i	−0.837327	+	0.546702i	$0.815883\pi$
$68$		0			0
$69$	−5.09611	−	10.0591i	−0.613500	−	1.21097i
$70$		0			0
$71$	−2.13151	−	1.23063i	−0.252964	−	0.146049i	0.368157	−	0.929764i	$-0.379989\pi$
$71$	−2.13151	−	1.23063i	−0.252964	−	0.146049i	−0.621120	+	0.783715i	$0.713322\pi$
$72$		0			0
$73$	−1.21699	+	0.702630i	−0.142438	+	0.0822366i	−0.569525	−	0.821974i	$-0.692873\pi$
$73$	−1.21699	+	0.702630i	−0.142438	+	0.0822366i	0.427087	+	0.904210i	$0.359540\pi$
$74$		0			0
$75$	−0.253129	−	0.834845i	−0.0292288	−	0.0963996i
$76$		0			0
$77$	0.976587	−	13.1240i	0.111292	−	1.49562i
$78$		0			0
$79$	−1.34687	−	7.63850i	−0.151535	−	0.859398i	−0.961886	−	0.273452i	$-0.911834\pi$
$79$	−1.34687	−	7.63850i	−0.151535	−	0.859398i	0.810350	−	0.585945i	$-0.199277\pi$
$80$		0			0
$81$	7.98526	−	4.15158i	0.887251	−	0.461287i
$82$		0			0
$83$	−0.714931	−	4.05458i	−0.0784739	−	0.445047i	−0.998575	−	0.0533665i	$-0.983005\pi$
$83$	−0.714931	−	4.05458i	−0.0784739	−	0.445047i	0.920101	−	0.391681i	$-0.128106\pi$
$84$		0			0
$85$	16.6282	−	6.05218i	1.80358	−	0.656451i
$86$		0			0
$87$	13.0068	−	3.94372i	1.39447	−	0.422811i
$88$		0			0
$89$	4.04962	+	7.01414i	0.429258	+	0.743497i	0.996808	−	0.0798422i	$-0.0254416\pi$
$89$	4.04962	+	7.01414i	0.429258	+	0.743497i	−0.567549	+	0.823340i	$0.692108\pi$
$90$		0			0
$91$	−1.00614	−	1.39791i	−0.105472	−	0.146541i
$92$		0			0
$93$	2.10129	+	4.14770i	0.217894	+	0.430096i
$94$		0			0
$95$	−15.7966	−	2.78537i	−1.62070	−	0.285772i
$96$		0			0
$97$	−8.91934	−	10.6296i	−0.905621	−	1.07928i	−0.996515	−	0.0834168i	$-0.973417\pi$
$97$	−8.91934	−	10.6296i	−0.905621	−	1.07928i	0.0908935	−	0.995861i	$-0.471028\pi$
$98$		0			0
$99$	−12.0318	−	8.82690i	−1.20924	−	0.887137i
$100$		0			0
$101$	6.09800	+	2.21949i	0.606773	+	0.220847i	0.627091	−	0.778946i	$-0.284245\pi$
$101$	6.09800	+	2.21949i	0.606773	+	0.220847i	−0.0203174	+	0.999794i	$0.506468\pi$
$102$		0			0
$103$	7.24622	−	8.63571i	0.713992	−	0.850902i	−0.280041	−	0.959988i	$-0.590348\pi$
$103$	7.24622	−	8.63571i	0.713992	−	0.850902i	0.994032	+	0.109086i	$0.0347924\pi$
$104$		0			0
$105$	2.34737	+	10.4913i	0.229079	+	1.02384i
$106$		0			0
$107$		−	10.2696i		−	0.992801i	−0.868094	−	0.496401i	$-0.834655\pi$
$107$		−	10.2696i		−	0.992801i	0.868094	−	0.496401i	$-0.165345\pi$
$108$		0			0
$109$	−7.99620			−0.765897			−0.382949	−	0.923770i	$-0.625091\pi$
$109$	−7.99620			−0.765897			−0.382949	+	0.923770i	$0.625091\pi$
$110$		0			0
$111$	6.04516	−	14.1505i	0.573781	−	1.34310i
$112$		0			0
$113$	3.99442	−	4.76037i	0.375764	−	0.447818i	−0.544709	−	0.838625i	$-0.683360\pi$
$113$	3.99442	−	4.76037i	0.375764	−	0.447818i	0.920472	+	0.390808i	$0.127804\pi$
$114$		0			0
$115$	5.22379	−	14.3522i	0.487121	−	1.33835i
$116$		0			0
$117$	−1.94881	+	0.127223i	−0.180168	+	0.0117617i
$118$		0			0
$119$	−19.2077	+	5.41509i	−1.76077	+	0.496400i
$120$		0			0
$121$	−2.38628	+	13.5333i	−0.216935	+	1.23030i
$122$		0			0
$123$	0.506070	−	9.24732i	0.0456308	−	0.833803i
$124$		0			0
$125$	−5.27418	+	9.13514i	−0.471737	+	0.817072i
$126$		0			0
$127$	6.39794	+	11.0815i	0.567725	+	0.983328i	0.996790	+	0.0800551i	$0.0255096\pi$
$127$	6.39794	+	11.0815i	0.567725	+	0.983328i	−0.429066	+	0.903273i	$0.641157\pi$
$128$		0			0
$129$	9.97748	−	10.6501i	0.878468	−	0.937686i
$130$		0			0
$131$	13.0357	−	4.74461i	1.13894	−	0.414539i	0.297407	−	0.954751i	$-0.403878\pi$
$131$	13.0357	−	4.74461i	1.13894	−	0.414539i	0.841529	+	0.540212i	$0.181656\pi$
$132$		0			0
$133$	17.5328	+	4.45461i	1.52029	+	0.386263i
$134$		0			0
$135$	11.4982	+	4.04855i	0.989606	+	0.348444i
$136$		0			0
$137$	0.719233	−	0.126820i	0.0614482	−	0.0108350i	−0.142840	−	0.989746i	$-0.545623\pi$
$137$	0.719233	−	0.126820i	0.0614482	−	0.0108350i	0.204288	+	0.978911i	$0.434512\pi$
$138$		0			0
$139$	−2.12581	−	5.84060i	−0.180308	−	0.495393i	0.816305	−	0.577621i	$-0.196019\pi$
$139$	−2.12581	−	5.84060i	−0.180308	−	0.495393i	−0.996614	+	0.0822275i	$0.973797\pi$
$140$		0			0
$141$	10.9040	+	2.54394i	0.918278	+	0.214238i
$142$		0			0
$143$	1.61905	+	2.80427i	0.135392	+	0.234505i
$144$		0			0
$145$	15.9428	+	9.20457i	1.32398	+	0.764398i
$146$		0			0
$147$	−1.76200	−	11.9956i	−0.145328	−	0.989384i
$148$		0			0
$149$	5.74715	+	1.01338i	0.470825	+	0.0830191i	0.404026	−	0.914747i	$-0.367610\pi$
$149$	5.74715	+	1.01338i	0.470825	+	0.0830191i	0.0667984	+	0.997766i	$0.478722\pi$
$150$		0			0
$151$	−1.98738	+	1.66761i	−0.161731	+	0.135708i	−0.720062	−	0.693910i	$-0.755886\pi$
$151$	−1.98738	+	1.66761i	−0.161731	+	0.135708i	0.558331	+	0.829618i	$0.311442\pi$
$152$		0			0
$153$	−6.33775	+	21.7228i	−0.512377	+	1.75618i
$154$		0			0
$155$	−2.15394	+	5.91790i	−0.173008	+	0.475337i
$156$		0			0
$157$	−15.6783	+	18.6847i	−1.25127	+	1.49120i	−0.449838	+	0.893110i	$0.648518\pi$
$157$	−15.6783	+	18.6847i	−1.25127	+	1.49120i	−0.801428	+	0.598091i	$0.795926\pi$
$158$		0			0
$159$	−0.334464	−	2.77705i	−0.0265247	−	0.220234i
$160$		0			0
$161$	−7.07614	+	15.7043i	−0.557678	+	1.23767i
$162$		0			0
$163$	18.5915			1.45620			0.728101	−	0.685470i	$-0.240403\pi$
$163$	18.5915			1.45620			0.728101	+	0.685470i	$0.240403\pi$
$164$		0			0
$165$	−2.41681	−	20.0668i	−0.188149	−	1.56220i
$166$		0			0
$167$	−0.975351	−	0.818417i	−0.0754749	−	0.0633310i	0.604270	−	0.796780i	$-0.293465\pi$
$167$	−0.975351	−	0.818417i	−0.0754749	−	0.0633310i	−0.679745	+	0.733449i	$0.737909\pi$
$168$		0			0
$169$	−11.8178	−	4.30132i	−0.909060	−	0.330871i
$170$		0			0
$171$	14.8208	−	14.1804i	1.13337	−	1.08440i
$172$		0			0
$173$	12.3352	−	10.3504i	0.937826	−	0.786930i	−0.0393795	−	0.999224i	$-0.512538\pi$
$173$	12.3352	−	10.3504i	0.937826	−	0.786930i	0.977206	+	0.212295i	$0.0680937\pi$
$174$		0			0
$175$	−0.750089	+	1.10142i	−0.0567014	+	0.0832596i
$176$		0			0
$177$	−8.86744	−	5.78777i	−0.666518	−	0.435036i
$178$		0			0
$179$	−12.0315	−	6.94641i	−0.899279	−	0.519199i	−0.0223130	−	0.999751i	$-0.507103\pi$
$179$	−12.0315	−	6.94641i	−0.899279	−	0.519199i	−0.876966	+	0.480552i	$0.840436\pi$
$180$		0			0
$181$	−4.17915	+	2.41283i	−0.310633	+	0.179344i	−0.647210	−	0.762312i	$-0.724064\pi$
$181$	−4.17915	+	2.41283i	−0.310633	+	0.179344i	0.336576	+	0.941656i	$0.390731\pi$
$182$		0			0
$183$	2.52801	−	10.8357i	0.186876	−	0.800995i
$184$		0			0
$185$	19.5850	−	7.12835i	1.43992	−	0.524087i
$186$		0			0
$187$	36.9490	−	6.51511i	2.70198	−	0.476432i
$188$		0			0
$189$	−12.5928	−	5.51554i	−0.915992	−	0.401197i
$190$		0			0
$191$	−17.7036	+	3.12162i	−1.28099	+	0.225873i	−0.772399	−	0.635137i	$-0.780944\pi$
$191$	−17.7036	+	3.12162i	−1.28099	+	0.225873i	−0.508588	+	0.861010i	$0.669832\pi$
$192$		0			0
$193$	−20.6777	+	7.52607i	−1.48841	+	0.541738i	−0.953031	−	0.302872i	$-0.902055\pi$
$193$	−20.6777	+	7.52607i	−1.48841	+	0.541738i	−0.535382	+	0.844610i	$0.679832\pi$
$194$		0			0
$195$	−1.93040	−	1.80849i	−0.138239	−	0.129509i
$196$		0			0
$197$	15.8130	−	9.12962i	1.12663	−	0.650458i	0.183542	−	0.983012i	$-0.441244\pi$
$197$	15.8130	−	9.12962i	1.12663	−	0.650458i	0.943084	+	0.332553i	$0.107910\pi$
$198$		0			0
$199$	9.72801	+	5.61647i	0.689600	+	0.398141i	0.803462	−	0.595356i	$-0.202989\pi$
$199$	9.72801	+	5.61647i	0.689600	+	0.398141i	−0.113862	+	0.993497i	$0.536322\pi$
$200$		0			0
$201$	1.05950	−	19.3600i	0.0747314	−	1.36555i
$202$		0			0
$203$	−17.1600	−	11.6863i	−1.20440	−	0.820218i
$204$		0			0
$205$	9.60915	−	8.06303i	0.671132	−	0.563147i
$206$		0			0
$207$	10.8467	+	16.2424i	0.753900	+	1.12893i
$208$		0			0
$209$	−31.9587	−	11.6320i	−2.21063	−	0.804604i
$210$		0			0
$211$	−14.9968	−	12.5838i	−1.03242	−	0.866307i	−0.0412868	−	0.999147i	$-0.513146\pi$
$211$	−14.9968	−	12.5838i	−1.03242	−	0.866307i	−0.991137	+	0.132841i	$0.957590\pi$
$212$		0			0
$213$	3.92027	+	1.67476i	0.268612	+	0.114753i
$214$		0			0
$215$	19.7665			1.34806
$216$		0			0
$217$	2.91772	−	6.47540i	0.198068	−	0.439579i
$218$		0			0
$219$	1.94724	−	1.46031i	0.131583	−	0.0986785i
$220$		0			0
$221$	3.15626	−	3.76149i	0.212313	−	0.253025i
$222$		0			0
$223$	2.55113	−	7.00918i	0.170837	−	0.469370i	−0.824497	−	0.565867i	$-0.808542\pi$
$223$	2.55113	−	7.00918i	0.170837	−	0.469370i	0.995333	+	0.0964972i	$0.0307639\pi$
$224$		0			0
$225$	0.608190	+	1.38319i	0.0405460	+	0.0922129i
$226$		0			0
$227$	−9.58425	+	8.04214i	−0.636129	+	0.533776i	−0.902827	−	0.430005i	$-0.858512\pi$
$227$	−9.58425	+	8.04214i	−0.636129	+	0.533776i	0.266698	+	0.963780i	$0.414067\pi$
$228$		0			0
$229$	−2.96475	−	0.522766i	−0.195916	−	0.0345453i	0.0748288	−	0.997196i	$-0.476159\pi$
$229$	−2.96475	−	0.522766i	−0.195916	−	0.0345453i	−0.270745	+	0.962651i	$0.587270\pi$
$230$		0			0
$231$	1.03875	+	22.7707i	0.0683446	+	1.49820i
$232$		0			0
$233$	−7.54280	−	4.35484i	−0.494145	−	0.285295i	0.232147	−	0.972681i	$-0.425425\pi$
$233$	−7.54280	−	4.35484i	−0.494145	−	0.285295i	−0.726293	+	0.687386i	$0.758758\pi$
$234$		0			0
$235$	7.58278	+	13.1338i	0.494646	+	0.856752i
$236$		0			0
$237$	3.89812	+	12.8564i	0.253210	+	0.835112i
$238$		0			0
$239$	0.0251934	+	0.0692183i	0.00162963	+	0.00447736i	0.940505	−	0.339780i	$-0.110353\pi$
$239$	0.0251934	+	0.0692183i	0.00162963	+	0.00447736i	−0.938875	+	0.344258i	$0.888131\pi$
$240$		0			0
$241$	2.62249	−	0.462416i	0.168930	−	0.0297869i	−0.0885435	−	0.996072i	$-0.528221\pi$
$241$	2.62249	−	0.462416i	0.168930	−	0.0297869i	0.257473	+	0.966285i	$0.417110\pi$
$242$		0			0
$243$	−12.8718	+	8.79298i	−0.825727	+	0.564070i
$244$		0			0
$245$	10.2254	−	12.8499i	0.653278	−	0.820951i
$246$		0			0
$247$	−4.18257	+	1.52233i	−0.266131	+	0.0968637i
$248$		0			0
$249$	2.06915	+	6.82427i	0.131127	+	0.432471i
$250$		0			0
$251$	11.2610	+	19.5046i	0.710789	+	1.23112i	0.964561	+	0.263858i	$0.0849951\pi$
$251$	11.2610	+	19.5046i	0.710789	+	1.23112i	−0.253773	+	0.967264i	$0.581672\pi$
$252$		0			0
$253$	16.1918	−	28.0451i	1.01797	−	1.76318i
$254$		0			0
$255$	−27.3408	+	13.8513i	−1.71215	+	0.867404i
$256$		0			0
$257$	0.971963	−	5.51228i	0.0606294	−	0.343847i	−0.939370	−	0.342905i	$-0.888589\pi$
$257$	0.971963	−	5.51228i	0.0606294	−	0.343847i	1.00000		0.000941653i	$-0.000299738\pi$
$258$		0			0
$259$	−22.6231	+	6.37798i	−1.40573	+	0.396308i
$260$		0			0
$261$	−21.5500	+	9.47554i	−1.33391	+	0.586521i
$262$		0			0
$263$	−1.10523	+	3.03659i	−0.0681513	+	0.187244i	−0.969093	−	0.246696i	$-0.920655\pi$
$263$	−1.10523	+	3.03659i	−0.0681513	+	0.187244i	0.900942	+	0.433940i	$0.142877\pi$
$264$		0			0
$265$	2.43525	−	2.90222i	0.149596	−	0.178282i
$266$		0			0
$267$	−8.41651	−	11.2230i	−0.515082	−	0.686835i
$268$		0			0
$269$	−11.5439			−0.703846			−0.351923	−	0.936029i	$-0.614472\pi$
$269$	−11.5439			−0.703846			−0.351923	+	0.936029i	$0.614472\pi$
$270$		0			0
$271$			17.2984i			1.05080i	0.850854	+	0.525402i	$0.176085\pi$
$271$			17.2984i			1.05080i	−0.850854	+	0.525402i	$0.823915\pi$
$272$		0			0
$273$	2.01971	+	2.19550i	0.122238	+	0.132878i
$274$		0			0
$275$	1.61038	−	1.91918i	0.0971096	−	0.115731i
$276$		0			0
$277$	6.69177	+	2.43561i	0.402069	+	0.146341i	0.535136	−	0.844766i	$-0.320260\pi$
$277$	6.69177	+	2.43561i	0.402069	+	0.146341i	−0.133067	+	0.991107i	$0.542482\pi$
$278$		0			0
$279$	−4.47246	−	6.69728i	−0.267759	−	0.400956i
$280$		0			0
$281$	19.7632	+	23.5528i	1.17897	+	1.40504i	0.894916	+	0.446235i	$0.147235\pi$
$281$	19.7632	+	23.5528i	1.17897	+	1.40504i	0.284055	+	0.958808i	$0.408320\pi$
$282$		0			0
$283$	−26.3090	−	4.63898i	−1.56391	−	0.275759i	−0.676393	−	0.736541i	$-0.736458\pi$
$283$	−26.3090	−	4.63898i	−1.56391	−	0.275759i	−0.887513	+	0.460782i	$0.847569\pi$
$284$		0			0
$285$	27.7411	+	1.51816i	1.64324	+	0.0899282i
$286$		0			0
$287$	−11.4819	+	8.26405i	−0.677754	+	0.487811i
$288$		0			0
$289$	−19.9471	−	34.5494i	−1.17336	−	2.03232i
$290$		0			0
$291$	17.5394	+	16.4317i	1.02818	+	0.963245i
$292$		0			0
$293$	−10.5965	+	3.85682i	−0.619055	+	0.225318i	−0.632461	−	0.774592i	$-0.717955\pi$
$293$	−10.5965	+	3.85682i	−0.619055	+	0.225318i	0.0134053	+	0.999910i	$0.495733\pi$
$294$		0			0
$295$	−2.49056	−	14.1246i	−0.145006	−	0.822369i
$296$		0			0
$297$	22.5183	+	12.6870i	1.30664	+	0.736177i
$298$		0			0
$299$	−0.735953	−	4.17379i	−0.0425612	−	0.241377i
$300$		0			0
$301$	−22.2307	−	1.65423i	−1.28135	−	0.0953482i
$302$		0			0
$303$	−10.9459	−	2.55374i	−0.628828	−	0.146708i
$304$		0			0
$305$	13.0515	−	7.53529i	0.747327	−	0.431469i
$306$		0			0
$307$	16.6590	+	9.61809i	0.950780	+	0.548933i	0.893323	−	0.449415i	$-0.148367\pi$
$307$	16.6590	+	9.61809i	0.950780	+	0.548933i	0.0574569	+	0.998348i	$0.481701\pi$
$308$		0			0
$309$	−10.6722	+	16.3509i	−0.607123	+	0.930172i
$310$		0			0
$311$	−0.213637	+	1.21160i	−0.0121143	+	0.0687033i	−0.990266	−	0.139191i	$-0.955550\pi$
$311$	−0.213637	+	1.21160i	−0.0121143	+	0.0687033i	0.978151	+	0.207894i	$0.0666610\pi$
$312$		0			0
$313$	−13.8556	−	16.5124i	−0.783164	−	0.933339i	0.215908	−	0.976414i	$-0.430729\pi$
$313$	−13.8556	−	16.5124i	−0.783164	−	0.933339i	−0.999072	+	0.0430752i	$0.986285\pi$
$314$		0			0
$315$	−6.20942	−	17.5549i	−0.349861	−	0.989106i
$316$		0			0
$317$	−3.17832	+	8.73237i	−0.178512	+	0.490459i	−0.996386	−	0.0849388i	$-0.972931\pi$
$317$	−3.17832	+	8.73237i	−0.178512	+	0.490459i	0.817874	+	0.575398i	$0.195153\pi$
$318$		0			0
$319$	29.9006	+	25.0896i	1.67411	+	1.40475i
$320$		0			0
$321$	2.12693	+	17.6599i	0.118714	+	0.985678i
$322$		0			0
$323$			51.5727i			2.86958i
$324$		0			0
$325$		−	0.327880i		−	0.0181875i
$326$		0			0
$327$	13.7505	−	1.65609i	0.760402	−	0.0915818i
$328$		0			0
$329$	−7.42895	−	15.4057i	−0.409571	−	0.849344i
$330$		0			0
$331$	11.4048	+	4.15102i	0.626867	+	0.228161i	0.635867	−	0.771799i	$-0.280643\pi$
$331$	11.4048	+	4.15102i	0.626867	+	0.228161i	−0.00900029	+	0.999959i	$0.502865\pi$
$332$		0			0
$333$	−7.46471	+	25.5855i	−0.409063	+	1.40207i
$334$		0			0
$335$	20.1175	−	16.8806i	1.09914	−	0.922286i
$336$		0			0
$337$	2.74014	−	15.5401i	0.149265	−	0.846525i	−0.814578	−	0.580054i	$-0.803031\pi$
$337$	2.74014	−	15.5401i	0.149265	−	0.846525i	0.963843	−	0.266471i	$-0.0858576\pi$
$338$		0			0
$339$	−5.88299	+	9.01332i	−0.319520	+	0.489537i
$340$		0			0
$341$	−6.67641	+	11.5639i	−0.361548	+	0.626220i
$342$		0			0
$343$	−12.5756	+	13.5961i	−0.679018	+	0.734122i
$344$		0			0
$345$	−6.01047	+	25.7623i	−0.323593	+	1.38700i
$346$		0			0
$347$	−6.56058	−	18.0250i	−0.352190	−	0.967635i	−0.981665	−	0.190614i	$-0.938952\pi$
$347$	−6.56058	−	18.0250i	−0.352190	−	0.967635i	0.629475	−	0.777021i	$-0.283270\pi$
$348$		0			0
$349$	−20.5974	+	3.63188i	−1.10255	+	0.194410i	−0.695168	−	0.718847i	$-0.744670\pi$
$349$	−20.5974	+	3.63188i	−1.10255	+	0.194410i	−0.407385	+	0.913257i	$0.633559\pi$
$350$		0			0
$351$	3.32487	−	0.622391i	0.177469	−	0.0332208i
$352$		0			0
$353$	−4.40450	−	24.9791i	−0.234428	−	1.32951i	−0.843816	−	0.536633i	$-0.819696\pi$
$353$	−4.40450	−	24.9791i	−0.234428	−	1.32951i	0.609388	−	0.792872i	$-0.291415\pi$
$354$		0			0
$355$	1.97485	+	5.42586i	0.104814	+	0.287975i
$356$		0			0
$357$	31.9085	−	13.2900i	1.68878	−	0.703382i
$358$		0			0
$359$	28.3176	−	16.3492i	1.49455	−	0.862876i	0.494565	−	0.869141i	$-0.335327\pi$
$359$	28.3176	−	16.3492i	1.49455	−	0.862876i	0.999980	+	0.00626441i	$0.00199404\pi$
$360$		0			0
$361$	13.8745	−	24.0313i	0.730235	−	1.26480i
$362$		0			0
$363$	1.30064	−	23.7664i	0.0682660	−	1.24741i
$364$		0			0
$365$	3.24664	+	0.572470i	0.169937	+	0.0299645i
$366$		0			0
$367$	8.14912	+	9.71174i	0.425381	+	0.506949i	0.935584	−	0.353105i	$-0.114874\pi$
$367$	8.14912	+	9.71174i	0.425381	+	0.506949i	−0.510203	+	0.860054i	$0.670430\pi$
$368$		0			0
$369$	1.04495	+	16.0067i	0.0543981	+	0.833277i
$370$		0			0
$371$	−2.98173	+	3.06023i	−0.154804	+	0.158879i
$372$		0			0
$373$	10.9860	+	9.21837i	0.568835	+	0.477309i	0.881259	−	0.472633i	$-0.156697\pi$
$373$	10.9860	+	9.21837i	0.568835	+	0.477309i	−0.312424	+	0.949943i	$0.601141\pi$
$374$		0			0
$375$	7.17763	−	16.8013i	0.370651	−	0.867617i
$376$		0			0
$377$	5.10834			0.263093
$378$		0			0
$379$	11.1394			0.572195			0.286097	−	0.958201i	$-0.407642\pi$
$379$	11.1394			0.572195			0.286097	+	0.958201i	$0.407642\pi$
$380$		0			0
$381$	−13.2971	−	17.7310i	−0.681233	−	0.908388i
$382$		0			0
$383$	−1.50269	−	1.26091i	−0.0767840	−	0.0644295i	0.603588	−	0.797297i	$-0.293737\pi$
$383$	−1.50269	−	1.26091i	−0.0767840	−	0.0644295i	−0.680372	+	0.732867i	$0.738182\pi$
$384$		0			0
$385$	−21.5458	+	22.1130i	−1.09807	+	1.12698i
$386$		0			0
$387$	−14.9518	+	20.3805i	−0.760042	+	1.03600i
$388$		0			0
$389$	−4.87061	−	5.80457i	−0.246950	−	0.294303i	0.628303	−	0.777969i	$-0.283750\pi$
$389$	−4.87061	−	5.80457i	−0.246950	−	0.294303i	−0.875253	+	0.483665i	$0.839305\pi$
$390$		0			0
$391$	−48.3608	−	8.52731i	−2.44571	−	0.431244i
$392$		0			0
$393$	−21.4339	+	10.8588i	−1.08120	+	0.547752i
$394$		0			0
$395$	−9.09814	+	15.7584i	−0.457777	+	0.792893i
$396$		0			0
$397$	−16.0855	+	9.28697i	−0.807308	+	0.466100i	−0.846020	−	0.533151i	$-0.821008\pi$
$397$	−16.0855	+	9.28697i	−0.807308	+	0.466100i	0.0387120	+	0.999250i	$0.487674\pi$
$398$		0			0
$399$	−31.0724	−	4.02904i	−1.55557	−	0.201704i
$400$		0			0
$401$	−1.44255	−	3.96337i	−0.0720374	−	0.197921i	0.898449	−	0.439079i	$-0.144695\pi$
$401$	−1.44255	−	3.96337i	−0.0720374	−	0.197921i	−0.970486	+	0.241158i	$0.922473\pi$
$402$		0			0
$403$	0.303457	+	1.72099i	0.0151163	+	0.0857287i
$404$		0			0
$405$	−20.6110	−	4.58061i	−1.02417	−	0.227612i
$406$		0			0
$407$	43.5192	−	7.67360i	2.15716	−	0.380366i
$408$		0			0
$409$	0.0910480	+	0.250152i	0.00450203	+	0.0123692i	0.941923	−	0.335828i	$-0.109016\pi$
$409$	0.0910480	+	0.250152i	0.00450203	+	0.0123692i	−0.937421	+	0.348197i	$0.886794\pi$
$410$		0			0
$411$	−1.21054	+	0.367043i	−0.0597117	+	0.0181049i
$412$		0			0
$413$	1.61897	+	16.0940i	0.0796644	+	0.791932i
$414$		0			0
$415$	−4.82936	+	8.36470i	−0.237064	+	0.410607i
$416$		0			0
$417$	4.86523	+	9.60337i	0.238251	+	0.470279i
$418$		0			0
$419$	1.95852	−	11.1073i	0.0956802	−	0.542629i	−0.898857	−	0.438243i	$-0.855601\pi$
$419$	1.95852	−	11.1073i	0.0956802	−	0.542629i	0.994537	−	0.104386i	$-0.0332879\pi$
$420$		0			0
$421$	12.5380	−	10.5206i	0.611063	−	0.512743i	−0.283917	−	0.958849i	$-0.591634\pi$
$421$	12.5380	−	10.5206i	0.611063	−	0.512743i	0.894980	+	0.446106i	$0.147189\pi$
$422$		0			0
$423$	−19.2776	−	2.11631i	−0.937307	−	0.102899i
$424$		0			0
$425$	−3.56996	−	1.29936i	−0.173168	−	0.0630281i
$426$		0			0
$427$	−15.3092	+	7.38243i	−0.740865	+	0.357261i
$428$		0			0
$429$	−3.36494	−	4.48697i	−0.162461	−	0.216633i
$430$		0			0
$431$			2.90056i			0.139715i	0.997557	+	0.0698576i	$0.0222545\pi$
$431$			2.90056i			0.139715i	−0.997557	+	0.0698576i	$0.977746\pi$
$432$		0			0
$433$			11.9635i			0.574927i	0.957792	+	0.287464i	$0.0928121\pi$
$433$			11.9635i			0.574927i	−0.957792	+	0.287464i	$0.907188\pi$
$434$		0			0
$435$	−29.3220	−	12.5265i	−1.40588	−	0.600600i
$436$		0			0
$437$	34.0995	+	28.6129i	1.63120	+	1.36874i
$438$		0			0
$439$	1.77751	−	4.88367i	0.0848359	−	0.233085i	−0.890020	−	0.455922i	$-0.849310\pi$
$439$	1.77751	−	4.88367i	0.0848359	−	0.233085i	0.974856	+	0.222837i	$0.0715319\pi$
$440$		0			0
$441$	5.51439	+	20.2631i	0.262590	+	0.964908i
$442$		0			0
$443$	6.69996	+	7.98470i	0.318325	+	0.379365i	0.901351	−	0.433088i	$-0.142576\pi$
$443$	6.69996	+	7.98470i	0.318325	+	0.379365i	−0.583027	+	0.812453i	$0.698132\pi$
$444$		0			0
$445$	3.29944	−	18.7120i	0.156408	−	0.887036i
$446$		0			0
$447$	−10.0928	−	0.552341i	−0.477373	−	0.0261248i
$448$		0			0
$449$	23.0621	+	13.3149i	1.08837	+	0.628369i	0.933141	−	0.359510i	$-0.117056\pi$
$449$	23.0621	+	13.3149i	1.08837	+	0.628369i	0.155225	+	0.987879i	$0.450390\pi$
$450$		0			0
$451$	23.0331	−	13.2982i	1.08459	−	0.626187i
$452$		0			0
$453$	3.07217	−	3.27927i	0.144343	−	0.154074i
$454$		0			0
$455$	−0.299841	+	4.02947i	−0.0140568	+	0.188904i
$456$		0			0
$457$	−2.68295	−	15.2158i	−0.125503	−	0.711763i	−0.981008	−	0.193968i	$-0.937864\pi$
$457$	−2.68295	−	15.2158i	−0.125503	−	0.711763i	0.855505	−	0.517795i	$-0.173247\pi$
$458$		0			0
$459$	6.39956	−	38.6677i	0.298706	−	1.80485i
$460$		0			0
$461$	0.115338	+	0.654115i	0.00537183	+	0.0304652i	0.987376	−	0.158395i	$-0.0506319\pi$
$461$	0.115338	+	0.654115i	0.00537183	+	0.0304652i	−0.982004	+	0.188860i	$0.939521\pi$
$462$		0			0
$463$	−10.1113	+	3.68020i	−0.469910	+	0.171033i	−0.566112	−	0.824329i	$-0.691553\pi$
$463$	−10.1113	+	3.68020i	−0.469910	+	0.171033i	0.0962015	+	0.995362i	$0.469331\pi$
$464$		0			0
$465$	2.47831	−	10.6227i	0.114929	−	0.492614i
$466$		0			0
$467$	−3.73386	−	6.46723i	−0.172782	−	0.299268i	0.766609	−	0.642114i	$-0.221942\pi$
$467$	−3.73386	−	6.46723i	−0.172782	−	0.299268i	−0.939392	+	0.342846i	$0.888609\pi$
$468$		0			0
$469$	−24.0382	+	17.3015i	−1.10998	+	0.798907i
$470$		0			0
$471$	23.0910	−	35.3778i	1.06398	−	1.63012i
$472$		0			0
$473$	41.2736	+	7.27764i	1.89776	+	0.334626i
$474$		0			0
$475$	2.21359	+	2.63805i	0.101566	+	0.121042i
$476$		0			0
$477$	1.15030	+	4.70621i	0.0526688	+	0.215482i
$478$		0			0
$479$	−2.61641	−	0.952296i	−0.119547	−	0.0435115i	0.281554	−	0.959545i	$-0.409150\pi$
$479$	−2.61641	−	0.952296i	−0.119547	−	0.0435115i	−0.401101	+	0.916034i	$0.631372\pi$
$480$		0			0
$481$	3.71750	−	4.43034i	0.169503	−	0.202006i
$482$		0			0
$483$	8.91579	−	28.4710i	0.405683	−	1.29548i
$484$		0			0
$485$			32.5530i			1.47816i
$486$		0			0
$487$	−21.8409			−0.989705			−0.494853	−	0.868977i	$-0.664778\pi$
$487$	−21.8409			−0.989705			−0.494853	+	0.868977i	$0.664778\pi$
$488$		0			0
$489$	−31.9704	+	3.85048i	−1.44575	+	0.174125i
$490$		0			0
$491$	−6.35572	+	7.57445i	−0.286830	+	0.341830i	−0.890149	−	0.455669i	$-0.849400\pi$
$491$	−6.35572	+	7.57445i	−0.286830	+	0.341830i	0.603320	+	0.797500i	$0.293844\pi$
$492$		0			0
$493$	20.2439	−	55.6195i	0.911737	−	2.50498i
$494$		0			0
$495$	8.31202	+	34.0067i	0.373597	+	1.52849i
$496$		0			0
$497$	−1.76697	−	6.26756i	−0.0792593	−	0.281138i
$498$		0			0
$499$	0.896248	−	5.08287i	0.0401216	−	0.227541i	−0.958153	−	0.286256i	$-0.907589\pi$
$499$	0.896248	−	5.08287i	0.0401216	−	0.227541i	0.998275	+	0.0587152i	$0.0187004\pi$
$500$		0			0
$501$	1.84674	+	1.20536i	0.0825062	+	0.0538517i
$502$		0			0
$503$	−14.3052	+	24.7774i	−0.637839	+	1.10477i	0.348067	+	0.937470i	$0.386838\pi$
$503$	−14.3052	+	24.7774i	−0.637839	+	1.10477i	−0.985906	+	0.167300i	$0.946495\pi$
$504$		0			0
$505$	−7.61198	−	13.1843i	−0.338729	−	0.586695i
$506$		0			0
$507$	21.2130	+	4.94908i	0.942101	+	0.219796i
$508$		0			0
$509$	15.1000	−	5.49596i	0.669296	−	0.243604i	0.0150515	−	0.999887i	$-0.495209\pi$
$509$	15.1000	−	5.49596i	0.669296	−	0.243604i	0.654245	+	0.756283i	$0.272987\pi$
$510$		0			0
$511$	−3.60348	−	0.915545i	−0.159408	−	0.0405013i
$512$		0			0
$513$	−22.5493	+	27.4545i	−0.995575	+	1.21215i
$514$		0			0
$515$	−26.0448	+	4.59241i	−1.14767	+	0.202366i
$516$		0			0
$517$	10.9977	+	30.2159i	0.483678	+	1.32890i
$518$		0			0
$519$	−19.0682	+	20.3536i	−0.837001	+	0.893424i
$520$		0			0
$521$	−19.5136	−	33.7986i	−0.854907	−	1.48074i	−0.876731	−	0.480981i	$-0.840281\pi$
$521$	−19.5136	−	33.7986i	−0.854907	−	1.48074i	0.0218243	−	0.999762i	$-0.493053\pi$
$522$		0			0
$523$	−33.6169	−	19.4087i	−1.46997	−	0.848685i	−0.470533	−	0.882382i	$-0.655938\pi$
$523$	−33.6169	−	19.4087i	−1.46997	−	0.848685i	−0.999432	+	0.0336976i	$0.989272\pi$
$524$		0			0
$525$	1.06176	−	2.04938i	0.0463389	−	0.0894422i
$526$		0			0
$527$	19.9407	+	3.51609i	0.868631	+	0.153163i
$528$		0			0
$529$	−14.8500	+	12.4607i	−0.645653	+	0.541767i
$530$		0			0
$531$	16.4474	+	8.11626i	0.713755	+	0.352216i
$532$		0			0
$533$	1.19050	−	3.27086i	0.0515661	−	0.141677i
$534$		0			0
$535$	−15.4863	+	18.4559i	−0.669531	+	0.797916i
$536$		0			0
$537$	22.1284	+	9.45337i	0.954910	+	0.407943i
$538$		0			0
$539$	26.0824	−	23.0666i	1.12345	−	0.993549i
$540$		0			0
$541$	−20.1205			−0.865048			−0.432524	−	0.901622i	$-0.642377\pi$
$541$	−20.1205			−0.865048			−0.432524	+	0.901622i	$0.642377\pi$
$542$		0			0
$543$	6.68684	−	5.01470i	0.286960	−	0.215201i
$544$		0			0
$545$	14.3702	+	12.0581i	0.615553	+	0.516510i
$546$		0			0
$547$	9.79544	+	3.56525i	0.418823	+	0.152439i	0.542831	−	0.839842i	$-0.317353\pi$
$547$	9.79544	+	3.56525i	0.418823	+	0.152439i	−0.124008	+	0.992281i	$0.539575\pi$
$548$		0			0
$549$	−2.10306	+	19.1568i	−0.0897564	+	0.817594i
$550$		0			0
$551$	−41.1005	+	34.4874i	−1.75094	+	1.46921i
$552$		0			0
$553$	11.5512	−	16.9616i	0.491206	−	0.721280i
$554$		0			0
$555$	−32.2024	+	16.3143i	−1.36692	+	0.692504i
$556$		0			0
$557$	−10.3651	−	5.98428i	−0.439182	−	0.253562i	0.264069	−	0.964504i	$-0.414935\pi$
$557$	−10.3651	−	5.98428i	−0.439182	−	0.253562i	−0.703251	+	0.710942i	$0.748269\pi$
$558$		0			0
$559$	4.75013	−	2.74249i	0.200909	−	0.115995i
$560$		0			0
$561$	−62.1891	+	18.8560i	−2.62563	+	0.796102i
$562$		0			0
$563$	0.0519426	−	0.0189055i	0.00218912	−	0.000796774i	−0.340925	−	0.940090i	$-0.610740\pi$
$563$	0.0519426	−	0.0189055i	0.00218912	−	0.000796774i	0.343114	+	0.939294i	$0.388518\pi$
$564$		0			0
$565$	−14.3570	+	2.53153i	−0.604004	+	0.106502i
$566$		0			0
$567$	22.7972	+	6.87657i	0.957393	+	0.288789i
$568$		0			0
$569$	−30.7812	+	5.42756i	−1.29042	+	0.227535i	−0.776397	−	0.630244i	$-0.782955\pi$
$569$	−30.7812	+	5.42756i	−1.29042	+	0.227535i	−0.514018	+	0.857779i	$0.671844\pi$
$570$		0			0
$571$	12.9262	−	4.70474i	0.540943	−	0.196887i	−0.0570749	−	0.998370i	$-0.518177\pi$
$571$	12.9262	−	4.70474i	0.540943	−	0.196887i	0.598018	+	0.801483i	$0.295955\pi$
$572$		0			0
$573$	29.7970	−	9.03459i	1.24479	−	0.377426i
$574$		0			0
$575$	−2.83976	+	1.63954i	−0.118426	+	0.0683734i
$576$		0			0
$577$	23.7601	+	13.7179i	0.989145	+	0.571083i	0.905019	−	0.425372i	$-0.139857\pi$
$577$	23.7601	+	13.7179i	0.989145	+	0.571083i	0.0841264	+	0.996455i	$0.473190\pi$
$578$		0			0
$579$	33.9991	−	17.2245i	1.41296	−	0.715828i
$580$		0			0
$581$	6.13146	−	9.00334i	0.254376	−	0.373522i
$582$		0			0
$583$	6.15349	−	5.16339i	0.254852	−	0.213846i
$584$		0			0
$585$	3.69412	+	2.71012i	0.152733	+	0.112050i
$586$		0			0
$587$	−9.31421	−	3.39009i	−0.384439	−	0.139924i	0.142569	−	0.989785i	$-0.454464\pi$
$587$	−9.31421	−	3.39009i	−0.384439	−	0.139924i	−0.527007	+	0.849861i	$0.676686\pi$
$588$		0			0
$589$	−14.0603	−	11.7980i	−0.579346	−	0.486129i
$590$		0			0
$591$	−25.3015	+	18.9745i	−1.04077	+	0.780507i
$592$		0			0
$593$	18.3392			0.753100			0.376550	−	0.926396i	$-0.377110\pi$
$593$	18.3392			0.753100			0.376550	+	0.926396i	$0.377110\pi$
$594$		0			0
$595$	42.6846	+	19.2331i	1.74990	+	0.788479i
$596$		0			0
$597$	−17.8917	−	7.64345i	−0.732260	−	0.312826i
$598$		0			0
$599$	−2.40384	+	2.86479i	−0.0982183	+	0.117052i	−0.812915	−	0.582383i	$-0.802120\pi$
$599$	−2.40384	+	2.86479i	−0.0982183	+	0.117052i	0.714696	+	0.699435i	$0.246565\pi$
$600$		0			0
$601$	4.15045	−	11.4033i	0.169301	−	0.465149i	−0.825806	−	0.563954i	$-0.809280\pi$
$601$	4.15045	−	11.4033i	0.169301	−	0.465149i	0.995107	+	0.0988043i	$0.0315018\pi$
$602$		0			0
$603$	2.18770	+	33.5114i	0.0890899	+	1.36469i
$604$		0			0
$605$	24.6963	−	20.7226i	1.00405	−	0.842495i
$606$		0			0
$607$	17.2145	+	3.03538i	0.698716	+	0.123202i	0.511712	−	0.859157i	$-0.329011\pi$
$607$	17.2145	+	3.03538i	0.698716	+	0.123202i	0.187003	+	0.982359i	$0.440122\pi$
$608$		0			0
$609$	31.9291	+	16.5421i	1.29383	+	0.670318i
$610$		0			0
$611$	3.64447	+	2.10414i	0.147440	+	0.0851243i
$612$		0			0
$613$	17.3531	+	30.0565i	0.700887	+	1.21397i	0.968155	+	0.250350i	$0.0805456\pi$
$613$	17.3531	+	30.0565i	0.700887	+	1.21397i	−0.267269	+	0.963622i	$0.586121\pi$
$614$		0			0
$615$	−14.8542	+	15.8555i	−0.598979	+	0.639356i
$616$		0			0
$617$	6.29094	+	17.2842i	0.253264	+	0.695836i	0.999544	+	0.0302040i	$0.00961571\pi$
$617$	6.29094	+	17.2842i	0.253264	+	0.695836i	−0.746280	+	0.665632i	$0.768162\pi$
$618$		0			0
$619$	−23.9520	+	4.22339i	−0.962714	+	0.169752i	−0.632848	−	0.774276i	$-0.718114\pi$
$619$	−23.9520	+	4.22339i	−0.962714	+	0.169752i	−0.329865	+	0.944028i	$0.607003\pi$
$620$		0			0
$621$	−22.0163	−	25.6844i	−0.883482	−	1.03068i
$622$		0			0
$623$	−5.27676	+	20.7687i	−0.211409	+	0.832080i
$624$		0			0
$625$	25.6204	−	9.32506i	1.02482	−	0.373002i
$626$		0			0
$627$	57.3661	+	13.3838i	2.29098	+	0.534496i
$628$		0			0
$629$	−33.5054	−	58.0331i	−1.33595	−	2.31393i
$630$		0			0
$631$	16.4195	−	28.4393i	0.653648	−	1.13215i	−0.328582	−	0.944475i	$-0.606571\pi$
$631$	16.4195	−	28.4393i	0.653648	−	1.13215i	0.982231	−	0.187677i	$-0.0600958\pi$
$632$		0			0
$633$	28.3951	+	18.5335i	1.12861	+	0.736640i
$634$		0			0
$635$	5.21274	−	29.5629i	0.206861	−	1.17317i
$636$		0			0
$637$	0.674442	−	4.50672i	0.0267224	−	0.178563i
$638$		0			0
$639$	−7.08824	−	2.06804i	−0.280407	−	0.0818102i
$640$		0			0
$641$	0.532432	−	1.46284i	0.0210298	−	0.0577789i	−0.928734	−	0.370748i	$-0.879101\pi$
$641$	0.532432	−	1.46284i	0.0210298	−	0.0577789i	0.949763	+	0.312969i	$0.101324\pi$
$642$		0			0
$643$	10.9968	−	13.1055i	0.433672	−	0.516830i	−0.504306	−	0.863525i	$-0.668252\pi$
$643$	10.9968	−	13.1055i	0.433672	−	0.516830i	0.937978	+	0.346695i	$0.112696\pi$
$644$		0			0
$645$	−33.9909	+	4.09381i	−1.33839	+	0.161194i
$646$		0			0
$647$	−12.0608			−0.474160			−0.237080	−	0.971490i	$-0.576190\pi$
$647$	−12.0608			−0.474160			−0.237080	+	0.971490i	$0.576190\pi$
$648$		0			0
$649$		−	30.4101i		−	1.19370i
$650$		0			0
$651$	−3.67627	+	11.7395i	−0.144084	+	0.460109i
$652$		0			0
$653$	2.81471	−	3.35445i	0.110148	−	0.131270i	−0.708153	−	0.706059i	$-0.750471\pi$
$653$	2.81471	−	3.35445i	0.110148	−	0.131270i	0.818302	+	0.574789i	$0.194916\pi$
$654$		0			0
$655$	−30.5816	−	11.1308i	−1.19492	−	0.434917i
$656$		0			0
$657$	−3.04608	+	2.91447i	−0.118839	+	0.113704i
$658$		0			0
$659$	−5.53473	−	6.59604i	−0.215603	−	0.256945i	0.647393	−	0.762156i	$-0.275859\pi$
$659$	−5.53473	−	6.59604i	−0.215603	−	0.256945i	−0.862996	+	0.505211i	$0.831415\pi$
$660$		0			0
$661$	33.7360	+	5.94857i	1.31218	+	0.231373i	0.785590	−	0.618747i	$-0.212359\pi$
$661$	33.7360	+	5.94857i	1.31218	+	0.231373i	0.526589	+	0.850120i	$0.323471\pi$
$662$		0			0
$663$	−4.64855	+	7.12203i	−0.180535	+	0.276597i
$664$		0			0
$665$	−24.7913	−	34.4445i	−0.961367	−	1.33570i
$666$		0			0
$667$	−25.5438	−	44.2432i	−0.989060	−	1.71310i
$668$		0			0
$669$	−2.93532	+	12.5815i	−0.113486	+	0.486430i
$670$		0			0
$671$	30.0267	−	10.9288i	1.15917	−	0.421903i
$672$		0			0
$673$	−5.11516	−	29.0095i	−0.197175	−	1.11823i	−0.909287	−	0.416169i	$-0.863373\pi$
$673$	−5.11516	−	29.0095i	−0.197175	−	1.11823i	0.712113	−	0.702065i	$-0.247739\pi$
$674$		0			0
$675$	−1.33233	−	2.25261i	−0.0512814	−	0.0867031i
$676$		0			0
$677$	3.24773	+	18.4188i	0.124820	+	0.707892i	0.981414	+	0.191901i	$0.0614651\pi$
$677$	3.24773	+	18.4188i	0.124820	+	0.707892i	−0.856594	+	0.515991i	$0.827424\pi$
$678$		0			0
$679$	2.72432	−	36.6113i	0.104550	−	1.40501i
$680$		0			0
$681$	14.8157	−	15.8144i	0.567739	−	0.606011i
$682$		0			0
$683$	42.6384	−	24.6173i	1.63151	−	0.941956i	0.647889	−	0.761735i	$-0.275652\pi$
$683$	42.6384	−	24.6173i	1.63151	−	0.941956i	0.983626	−	0.180220i	$-0.0576811\pi$
$684$		0			0
$685$	−1.48380	−	0.856671i	−0.0566930	−	0.0327317i
$686$		0			0
$687$	5.20653	+	0.284933i	0.198641	+	0.0108709i
$688$		0			0
$689$	0.182554	−	1.03532i	0.00695476	−	0.0394424i
$690$		0			0
$691$	12.7384	+	15.1810i	0.484590	+	0.577512i	0.951833	−	0.306617i	$-0.0991971\pi$
$691$	12.7384	+	15.1810i	0.484590	+	0.577512i	−0.467243	+	0.884129i	$0.654753\pi$
$692$		0			0
$693$	−6.50227	−	38.9419i	−0.247001	−	1.47928i
$694$		0			0
$695$	−4.98712	+	13.7020i	−0.189172	+	0.519746i
$696$		0			0
$697$	−30.8953	−	25.9242i	−1.17024	−	0.981951i
$698$		0			0
$699$	13.8727	+	5.92650i	0.524714	+	0.224161i
$700$		0			0
$701$			30.7104i			1.15991i	0.814647	+	0.579957i	$0.196931\pi$
$701$			30.7104i			1.15991i	−0.814647	+	0.579957i	$0.803069\pi$
$702$		0			0
$703$			60.7431i			2.29097i
$704$		0			0
$705$	−15.7596	−	21.0147i	−0.593543	−	0.791458i
$706$		0			0
$707$	7.45756	+	15.4650i	0.280470	+	0.581622i
$708$		0			0
$709$	−25.5869	−	9.31285i	−0.960935	−	0.349752i	−0.186535	−	0.982448i	$-0.559726\pi$
$709$	−25.5869	−	9.31285i	−0.960935	−	0.349752i	−0.774400	+	0.632697i	$0.781948\pi$
$710$		0			0
$711$	−9.36597	−	21.3008i	−0.351251	−	0.798843i
$712$		0			0
$713$	13.3880	−	11.2339i	0.501386	−	0.420713i
$714$		0			0
$715$	1.31912	−	7.48113i	0.0493325	−	0.279778i
$716$		0			0
$717$	−0.0576589	−	0.113812i	−0.00215331	−	0.00425037i
$718$		0			0
$719$	5.40428	−	9.36049i	0.201546	−	0.349088i	−0.747481	−	0.664283i	$-0.768737\pi$
$719$	5.40428	−	9.36049i	0.201546	−	0.349088i	0.949027	+	0.315196i	$0.102070\pi$
$720$		0			0
$721$	29.6761	−	2.98527i	1.10520	−	0.111177i
$722$		0			0
$723$	−4.41393	+	1.33832i	−0.164156	+	0.0497728i
$724$		0			0
$725$	−1.35177	−	3.71396i	−0.0502034	−	0.137933i
$726$		0			0
$727$	40.6981	−	7.17617i	1.50941	−	0.266150i	0.643148	−	0.765742i	$-0.277628\pi$
$727$	40.6981	−	7.17617i	1.50941	−	0.266150i	0.866261	+	0.499592i	$0.166517\pi$
$728$		0			0
$729$	20.3136	−	17.7865i	0.752354	−	0.658759i
$730$		0			0
$731$	−11.0359	−	62.5876i	−0.408177	−	2.31488i
$732$		0			0
$733$	−6.10683	−	16.7784i	−0.225561	−	0.619724i	0.774354	−	0.632752i	$-0.218075\pi$
$733$	−6.10683	−	16.7784i	−0.225561	−	0.619724i	−0.999915	+	0.0130288i	$0.995853\pi$
$734$		0			0
$735$	−14.9225	+	24.2148i	−0.550426	+	0.893176i
$736$		0			0
$737$	48.2218	−	27.8408i	1.77627	−	1.02553i
$738$		0			0
$739$	−14.9900	+	25.9634i	−0.551416	+	0.955081i	0.446757	+	0.894656i	$0.352579\pi$
$739$	−14.9900	+	25.9634i	−0.551416	+	0.955081i	−0.998173	+	0.0604252i	$0.980754\pi$
$740$		0			0
$741$	6.87716	−	3.48409i	0.252639	−	0.127991i
$742$		0			0
$743$	0.406433	+	0.0716651i	0.0149106	+	0.00262914i	0.181098	−	0.983465i	$-0.442035\pi$
$743$	0.406433	+	0.0716651i	0.0149106	+	0.00262914i	−0.166188	+	0.986094i	$0.553146\pi$
$744$		0			0
$745$	−8.80024	−	10.4877i	−0.322416	−	0.384240i
$746$		0			0
$747$	−4.97153	−	11.3066i	−0.181899	−	0.413689i
$748$		0			0
$749$	18.9615	−	19.4607i	0.692837	−	0.711077i
$750$		0			0
$751$	14.2296	+	11.9401i	0.519246	+	0.435699i	0.864369	−	0.502858i	$-0.167718\pi$
$751$	14.2296	+	11.9401i	0.519246	+	0.435699i	−0.345123	+	0.938558i	$0.612163\pi$
$752$		0			0
$753$	−23.4043	−	31.2084i	−0.852900	−	1.13730i
$754$		0			0
$755$	6.08630			0.221503
$756$		0			0
$757$	2.11746			0.0769605			0.0384803	−	0.999259i	$-0.487748\pi$
$757$	2.11746			0.0769605			0.0384803	+	0.999259i	$0.487748\pi$
$758$		0			0
$759$	−22.0354	+	51.5804i	−0.799836	+	1.87225i
$760$		0			0
$761$	7.56248	+	6.34567i	0.274140	+	0.230031i	0.769484	−	0.638666i	$-0.220514\pi$
$761$	7.56248	+	6.34567i	0.274140	+	0.230031i	−0.495344	+	0.868697i	$0.664958\pi$
$762$		0			0
$763$	−15.1526	−	14.7639i	−0.548561	−	0.534490i
$764$		0			0
$765$	44.1472	−	29.4816i	1.59614	−	1.06591i
$766$		0			0
$767$	−2.55823	−	3.04878i	−0.0923723	−	0.110085i
$768$		0			0
$769$	−19.7536	−	3.48309i	−0.712332	−	0.125603i	−0.194272	−	0.980948i	$-0.562235\pi$
$769$	−19.7536	−	3.48309i	−0.712332	−	0.125603i	−0.518060	+	0.855344i	$0.673346\pi$
$770$		0			0
$771$	−0.529768	+	9.68035i	−0.0190791	+	0.348629i
$772$		0			0
$773$	−7.89854	+	13.6807i	−0.284091	+	0.492060i	−0.972388	−	0.233369i	$-0.925025\pi$
$773$	−7.89854	+	13.6807i	−0.284091	+	0.492060i	0.688297	+	0.725429i	$0.258358\pi$
$774$		0			0
$775$	1.17093	−	0.676034i	0.0420609	−	0.0242839i
$776$		0			0
$777$	37.5823	−	15.6532i	1.34826	−	0.561555i
$778$		0			0
$779$	12.5038	+	34.3539i	0.447995	+	1.23086i
$780$		0			0
$781$	2.12591	+	12.0566i	0.0760710	+	0.431420i
$782$		0			0
$783$	35.0954	−	20.7576i	1.25421	−	0.741815i
$784$		0			0
$785$	56.3520	−	9.93639i	2.01129	−	0.354645i
$786$		0			0
$787$	−8.55976	−	23.5178i	−0.305123	−	0.838317i	−0.993589	−	0.113050i	$-0.963938\pi$
$787$	−8.55976	−	23.5178i	−0.305123	−	0.838317i	0.688467	−	0.725268i	$-0.258284\pi$
$788$		0			0
$789$	1.27167	−	5.45069i	0.0452727	−	0.194050i
$790$		0			0
$791$	16.3587	−	1.64561i	0.581649	−	0.0585110i
$792$		0			0
$793$	2.09096	−	3.62165i	0.0742522	−	0.128609i
$794$		0			0
$795$	−3.58664	+	5.49508i	−0.127205	+	0.194891i
$796$		0			0
$797$	0.894200	−	5.07126i	0.0316742	−	0.179633i	−0.964866	−	0.262741i	$-0.915373\pi$
$797$	0.894200	−	5.07126i	0.0316742	−	0.179633i	0.996541	+	0.0831078i	$0.0264846\pi$
$798$		0			0
$799$	37.3525	−	31.3425i	1.32144	−	1.10882i
$800$		0			0
$801$	16.7976	+	17.5561i	0.593514	+	0.620316i
$802$		0			0
$803$	6.56841	+	2.39071i	0.231794	+	0.0843661i
$804$		0			0
$805$	36.3984	−	17.5521i	1.28288	−	0.618630i
$806$		0			0
$807$	19.8512	−	2.39085i	0.698796	−	0.0841620i
$808$		0			0
$809$			2.38375i			0.0838082i	0.999122	+	0.0419041i	$0.0133424\pi$
$809$			2.38375i			0.0838082i	−0.999122	+	0.0419041i	$0.986658\pi$
$810$		0			0
$811$		−	32.6746i		−	1.14736i	−0.819079	−	0.573681i	$-0.805515\pi$
$811$		−	32.6746i		−	1.14736i	0.819079	−	0.573681i	$-0.194485\pi$
$812$		0			0
$813$	−3.58266	−	29.7467i	−0.125649	−	1.04326i
$814$		0			0
$815$	−33.4114	−	28.0355i	−1.17035	−	0.982042i
$816$		0			0
$817$	−19.7034	+	54.1345i	−0.689333	+	1.89393i
$818$		0			0
$819$	−3.92785	−	3.35714i	−0.137250	−	0.117308i
$820$		0			0
$821$	12.3296	+	14.6939i	0.430307	+	0.512820i	0.937011	−	0.349300i	$-0.113581\pi$
$821$	12.3296	+	14.6939i	0.430307	+	0.512820i	−0.506704	+	0.862120i	$0.669136\pi$
$822$		0			0
$823$	−8.95480	+	50.7852i	−0.312145	+	1.77026i	0.275658	+	0.961256i	$0.411104\pi$
$823$	−8.95480	+	50.7852i	−0.312145	+	1.77026i	−0.587803	+	0.809004i	$0.700007\pi$
$824$		0			0
$825$	−2.37177	+	3.63379i	−0.0825744	+	0.126512i
$826$		0			0
$827$	−10.0018	−	5.77453i	−0.347796	−	0.200800i	0.315918	−	0.948786i	$-0.397687\pi$
$827$	−10.0018	−	5.77453i	−0.347796	−	0.200800i	−0.663714	+	0.747986i	$0.731021\pi$
$828$		0			0
$829$	4.45189	−	2.57030i	0.154620	−	0.0892702i	−0.420694	−	0.907203i	$-0.638213\pi$
$829$	4.45189	−	2.57030i	0.154620	−	0.0892702i	0.575314	+	0.817933i	$0.304880\pi$
$830$		0			0
$831$	−12.0118	−	2.80240i	−0.416683	−	0.0972141i
$832$		0			0
$833$	−46.3964	−	25.2030i	−1.60754	−	0.873233i
$834$		0			0
$835$	0.518684	+	2.94161i	0.0179498	+	0.101798i
$836$		0			0
$837$	9.07802	+	10.5905i	0.313782	+	0.366062i
$838$		0			0
$839$	5.60616	+	31.7941i	0.193546	+	1.09766i	0.914474	+	0.404645i	$0.132605\pi$
$839$	5.60616	+	31.7941i	0.193546	+	1.09766i	−0.720928	+	0.693010i	$0.756284\pi$
$840$		0			0
$841$	30.6119	−	11.1418i	1.05558	−	0.384201i
$842$		0			0
$843$	−38.8632	−	36.4088i	−1.33852	−	1.25399i
$844$		0			0
$845$	14.7518	+	25.5509i	0.507479	+	0.878979i
$846$		0			0
$847$	−29.5093	+	21.2393i	−1.01395	+	0.729790i
$848$		0			0
$849$	46.2023	+	2.52847i	1.58566	+	0.0867770i
$850$		0			0
$851$	−56.9601	−	10.0436i	−1.95257	−	0.344290i
$852$		0			0
$853$	22.1942	+	26.4501i	0.759916	+	0.905632i	0.997843	−	0.0656506i	$-0.0209123\pi$
$853$	22.1942	+	26.4501i	0.759916	+	0.905632i	−0.237927	+	0.971283i	$0.576468\pi$
$854$		0			0
$855$	−48.0186	+	3.13476i	−1.64220	+	0.107207i
$856$		0			0
$857$	3.57977	+	1.30293i	0.122282	+	0.0445072i	0.402437	−	0.915448i	$-0.368163\pi$
$857$	3.57977	+	1.30293i	0.122282	+	0.0445072i	−0.280154	+	0.959955i	$0.590386\pi$
$858$		0			0
$859$	−4.54150	+	5.41235i	−0.154954	+	0.184667i	−0.837936	−	0.545768i	$-0.816238\pi$
$859$	−4.54150	+	5.41235i	−0.154954	+	0.184667i	0.682982	+	0.730435i	$0.260683\pi$
$860$		0			0
$861$	18.0329	−	16.5891i	0.614561	−	0.565353i
$862$		0			0
$863$			28.6402i			0.974922i	0.873145	+	0.487461i	$0.162077\pi$
$863$			28.6402i			0.974922i	−0.873145	+	0.487461i	$0.837923\pi$
$864$		0			0
$865$	−37.7761			−1.28443
$866$		0			0
$867$	41.4570	+	55.2807i	1.40795	+	1.87743i
$868$		0			0
$869$	−24.7994	+	29.5548i	−0.841263	+	1.00258i
$870$		0			0
$871$	2.49240	−	6.84782i	0.0844518	−	0.232030i
$872$		0			0
$873$	−33.5643	−	24.6238i	−1.13598	−	0.833390i
$874$		0			0
$875$	−26.8612	+	7.57280i	−0.908076	+	0.256007i
$876$		0			0
$877$	−4.90931	+	27.8421i	−0.165776	+	0.940160i	0.782485	+	0.622669i	$0.213952\pi$
$877$	−4.90931	+	27.8421i	−0.165776	+	0.940160i	−0.948261	+	0.317491i	$0.897160\pi$
$878$		0			0
$879$	17.4232	−	8.82691i	0.587672	−	0.297724i
$880$		0			0
$881$	2.34121	−	4.05509i	0.0788774	−	0.136620i	−0.823888	−	0.566752i	$-0.808200\pi$
$881$	2.34121	−	4.05509i	0.0788774	−	0.136620i	0.902766	+	0.430132i	$0.141533\pi$
$882$		0			0
$883$	−12.6699	−	21.9449i	−0.426375	−	0.738503i	0.570173	−	0.821525i	$-0.306876\pi$
$883$	−12.6699	−	21.9449i	−0.426375	−	0.738503i	−0.996548	+	0.0830217i	$0.973543\pi$
$884$		0			0
$885$	7.20816	+	23.7733i	0.242300	+	0.799129i
$886$		0			0
$887$	−30.1398	+	10.9700i	−1.01199	+	0.368336i	−0.794198	−	0.607659i	$-0.792109\pi$
$887$	−30.1398	+	10.9700i	−1.01199	+	0.368336i	−0.217796	+	0.975994i	$0.569887\pi$
$888$		0			0
$889$	−8.33668	+	32.8122i	−0.279603	+	1.10049i
$890$		0			0
$891$	−41.3506	−	17.1532i	−1.38530	−	0.574654i
$892$		0			0
$893$	−43.5281	+	7.67518i	−1.45661	+	0.256840i
$894$		0			0
$895$	11.1473	+	30.6269i	0.372612	+	1.02374i
$896$		0			0
$897$	2.12999	+	7.02493i	0.0711184	+	0.234556i
$898$		0			0
$899$	10.5325	+	18.2429i	0.351280	+	0.608435i
$900$		0			0
$901$	−10.5491	−	6.09051i	−0.351441	−	0.202904i
$902$		0			0
$903$	38.5710	−	1.75952i	1.28356	−	0.0585533i
$904$		0			0
$905$	11.1490	+	1.96586i	0.370604	+	0.0653475i
$906$		0			0
$907$	4.98161	−	4.18007i	0.165412	−	0.138797i	−0.556325	−	0.830965i	$-0.687789\pi$
$907$	4.98161	−	4.18007i	0.165412	−	0.138797i	0.721736	+	0.692168i	$0.243344\pi$
$908$		0			0
$909$	19.3518	+	2.12446i	0.641859	+	0.0704639i
$910$		0			0
$911$	−11.6346	+	31.9657i	−0.385470	+	1.05907i	0.583547	+	0.812079i	$0.301664\pi$
$911$	−11.6346	+	31.9657i	−0.385470	+	1.05907i	−0.969018	+	0.246992i	$0.920558\pi$
$912$		0			0
$913$	−13.1637	+	15.6879i	−0.435656	+	0.519195i
$914$		0			0
$915$	−20.8831	+	15.6610i	−0.690372	+	0.517735i
$916$		0			0
$917$	33.4626	+	15.0778i	1.10503	+	0.497912i
$918$		0			0
$919$	4.33395			0.142964			0.0714819	−	0.997442i	$-0.477227\pi$
$919$	4.33395			0.142964			0.0714819	+	0.997442i	$0.477227\pi$
$920$		0			0
$921$	−30.6392	−	13.0893i	−1.00960	−	0.431306i
$922$		0			0
$923$	1.22739	+	1.02990i	0.0404000	+	0.0338996i
$924$		0			0
$925$	−4.20475	−	1.53040i	−0.138251	−	0.0503194i
$926$		0			0
$927$	14.9658	−	30.3278i	0.491542	−	0.996095i
$928$		0			0
$929$	−6.01924	+	5.05074i	−0.197485	+	0.165709i	−0.736168	−	0.676799i	$-0.763367\pi$
$929$	−6.01924	+	5.05074i	−0.197485	+	0.165709i	0.538683	+	0.842509i	$0.318922\pi$
$930$		0			0
$931$	24.9994	+	40.8133i	0.819322	+	1.33760i
$932$		0			0
$933$	0.116443	−	2.12774i	0.00381217	−	0.0696590i
$934$		0			0
$935$	−76.2269	−	44.0096i	−2.49289	−	1.43927i
$936$		0			0
$937$	8.77806	−	5.06801i	0.286767	−	0.165565i	−0.349716	−	0.936856i	$-0.613722\pi$
$937$	8.77806	−	5.06801i	0.286767	−	0.165565i	0.636483	+	0.771291i	$0.280389\pi$
$938$		0			0
$939$	27.2463	+	25.5256i	0.889149	+	0.832996i
$940$		0			0
$941$	−30.4573	+	11.0856i	−0.992880	+	0.361379i	−0.786835	−	0.617164i	$-0.788282\pi$
$941$	−30.4573	+	11.0856i	−0.992880	+	0.361379i	−0.206045	+	0.978542i	$0.566059\pi$
$942$		0			0
$943$	−34.2818	+	6.04481i	−1.11637	+	0.196846i
$944$		0			0
$945$	14.3136	+	28.9018i	0.465623	+	0.940175i
$946$		0			0
$947$	9.72702	−	1.71514i	0.316086	−	0.0557344i	−0.0133547	−	0.999911i	$-0.504251\pi$
$947$	9.72702	−	1.71514i	0.316086	−	0.0557344i	0.329440	+	0.944176i	$0.393140\pi$
$948$		0			0
$949$	0.859635	−	0.312882i	0.0279049	−	0.0101566i
$950$		0			0
$951$	3.65697	−	15.6747i	0.118585	−	0.508286i
$952$		0			0
$953$	22.3537	−	12.9059i	0.724108	−	0.418064i	−0.0921551	−	0.995745i	$-0.529376\pi$
$953$	22.3537	−	12.9059i	0.724108	−	0.418064i	0.816263	+	0.577681i	$0.196042\pi$
$954$		0			0
$955$	36.5230	+	21.0866i	1.18186	+	0.682346i
$956$		0			0
$957$	−56.6140	−	36.9519i	−1.83007	−	1.19449i
$958$		0			0
$959$	1.59708	+	1.08765i	0.0515726	+	0.0351219i
$960$		0			0
$961$	18.2270	−	15.2943i	0.587969	−	0.493365i
$962$		0			0
$963$	−7.31504	−	29.9278i	−0.235724	−	0.964411i
$964$		0			0
$965$	48.5097	+	17.6561i	1.56158	+	0.568369i
$966$		0			0
$967$	10.3171	+	8.65703i	0.331774	+	0.278391i	0.793422	−	0.608672i	$-0.208297\pi$
$967$	10.3171	+	8.65703i	0.331774	+	0.278391i	−0.461648	+	0.887063i	$0.652742\pi$
$968$		0			0
$969$	−10.6812	−	88.6856i	−0.343129	−	2.84899i
$970$		0			0
$971$	15.5953			0.500477			0.250238	−	0.968184i	$-0.419491\pi$
$971$	15.5953			0.500477			0.250238	+	0.968184i	$0.419491\pi$
$972$		0			0
$973$	6.75555	−	14.9928i	0.216573	−	0.480647i
$974$		0			0
$975$	0.0679070	+	0.563830i	0.00217476	+	0.0180570i
$976$		0			0
$977$	−2.80160	+	3.33881i	−0.0896310	+	0.106818i	−0.808996	−	0.587814i	$-0.799989\pi$
$977$	−2.80160	+	3.33881i	−0.0896310	+	0.106818i	0.719365	+	0.694632i	$0.244433\pi$
$978$		0			0
$979$	13.7789	−	37.8571i	0.440374	−	1.20992i
$980$		0			0
$981$	−23.3026	+	5.69569i	−0.743996	+	0.181849i
$982$		0			0
$983$	34.5288	−	28.9731i	1.10130	−	0.924098i	0.103785	−	0.994600i	$-0.466905\pi$
$983$	34.5288	−	28.9731i	1.10130	−	0.924098i	0.997512	+	0.0705019i	$0.0224601\pi$
$984$		0			0
$985$	−42.1852	−	7.43839i	−1.34413	−	0.237007i
$986$		0			0
$987$	15.9657	+	24.9534i	0.508193	+	0.794275i
$988$		0			0
$989$	−47.5052	−	27.4271i	−1.51058	−	0.872132i
$990$		0			0
$991$	24.4112	+	42.2815i	0.775448	+	1.34312i	0.934542	+	0.355852i	$0.115809\pi$
$991$	24.4112	+	42.2815i	0.775448	+	1.34312i	−0.159094	+	0.987263i	$0.550857\pi$
$992$		0			0
$993$	−20.4717	−	4.77615i	−0.649651	−	0.151567i
$994$		0			0
$995$	−9.01304	−	24.7631i	−0.285732	−	0.785044i
$996$		0			0
$997$	−40.8214	+	7.19792i	−1.29283	+	0.227960i	−0.777418	−	0.628984i	$-0.783471\pi$
$997$	−40.8214	+	7.19792i	−1.29283	+	0.227960i	−0.515409	+	0.856944i	$0.672360\pi$
$998$		0			0
$999$	7.53750	−	45.5434i	0.238476	−	1.44093i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bx.a.41.1	✓	144
7.6	odd	2	inner	756.2.bx.a.41.24	yes	144
27.2	odd	18	inner	756.2.bx.a.461.24	yes	144
189.83	even	18	inner	756.2.bx.a.461.1	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bx.a.41.1	✓	144	1.1	even	1	trivial
756.2.bx.a.41.24	yes	144	7.6	odd	2	inner
756.2.bx.a.461.1	yes	144	189.83	even	18	inner
756.2.bx.a.461.24	yes	144	27.2	odd	18	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bx (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.71962 + 0.207109i) q^{3} +(-1.79713 - 1.50797i) q^{5} +(1.89497 + 1.84637i) q^{7} +(2.91421 - 0.712300i) q^{9} +O(q^{10})\)	\(q+(-1.71962 + 0.207109i) q^{3} +(-1.79713 - 1.50797i) q^{5} +(1.89497 + 1.84637i) q^{7} +(2.91421 - 0.712300i) q^{9} +(-3.19731 - 3.81041i) q^{11} +(-0.641096 - 0.113043i) q^{13} +(3.40271 + 2.22094i) q^{15} +(-3.77141 + 6.53228i) q^{17} +(5.92129 - 3.41866i) q^{19} +(-3.64104 - 2.78259i) q^{21} +(2.22669 + 6.11778i) q^{23} +(0.0874608 + 0.496015i) q^{25} +(-4.86382 + 1.82845i) q^{27} +(-7.72786 + 1.36263i) q^{29} +(-0.918136 - 2.52256i) q^{31} +(6.28735 + 5.89028i) q^{33} +(-0.621249 - 6.17574i) q^{35} +(-4.44203 + 7.69382i) q^{37} +(1.12586 + 0.0616138i) q^{39} +(-0.928485 + 5.26570i) q^{41} +(-6.45441 + 5.41589i) q^{43} +(-6.31135 - 3.11446i) q^{45} +(-6.07461 - 2.21098i) q^{47} +(0.181858 + 6.99764i) q^{49} +(5.13251 - 12.0142i) q^{51} +1.61492i q^{53} +11.6693i q^{55} +(-9.47436 + 7.10516i) q^{57} +(4.68332 + 3.92977i) q^{59} +(-2.19713 + 6.03656i) q^{61} +(6.83752 + 4.03091i) q^{63} +(0.981670 + 1.16991i) q^{65} +(-1.94386 + 11.0242i) q^{67} +(-5.09611 - 10.0591i) q^{69} +(-2.13151 - 1.23063i) q^{71} +(-1.21699 + 0.702630i) q^{73} +(-0.253129 - 0.834845i) q^{75} +(0.976587 - 13.1240i) q^{77} +(-1.34687 - 7.63850i) q^{79} +(7.98526 - 4.15158i) q^{81} +(-0.714931 - 4.05458i) q^{83} +(16.6282 - 6.05218i) q^{85} +(13.0068 - 3.94372i) q^{87} +(4.04962 + 7.01414i) q^{89} +(-1.00614 - 1.39791i) q^{91} +(2.10129 + 4.14770i) q^{93} +(-15.7966 - 2.78537i) q^{95} +(-8.91934 - 10.6296i) q^{97} +(-12.0318 - 8.82690i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} - 30 q^{21} + 48 q^{23} + 12 q^{29} - 27 q^{35} - 42 q^{39} + 18 q^{49} + 18 q^{51} + 30 q^{57} - 15 q^{63} + 42 q^{65} + 36 q^{71} - 51 q^{77} + 36 q^{79} + 18 q^{81} + 36 q^{85} + 9 q^{91} + 96 q^{93} - 48 q^{95} + 36 q^{99}+O(q^{100}) \) 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 - 30 * q^21 + 48 * q^23 + 12 * q^29 - 27 * q^35 - 42 * q^39 + 18 * q^49 + 18 * q^51 + 30 * q^57 - 15 * q^63 + 42 * q^65 + 36 * q^71 - 51 * q^77 + 36 * q^79 + 18 * q^81 + 36 * q^85 + 9 * q^91 + 96 * q^93 - 48 * q^95 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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