LMFDB - Embedded newform 572.2.bq.a.69.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(49,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 12, 25]))

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

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

chi := DirichletCharacter("572.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bq (of order $30$, degree $8$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			69.3
Character	$\chi$	$=$	572.69
Dual form			572.2.bq.a.257.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.15084 - 0.457176i) q^{3} +(2.38726 - 3.28578i) q^{5} +(-1.00599 - 4.73282i) q^{7} +(1.67648 + 0.746415i) q^{9} +O(q^{10})$	\(q+(-2.15084 - 0.457176i) q^{3} +(2.38726 - 3.28578i) q^{5} +(-1.00599 - 4.73282i) q^{7} +(1.67648 + 0.746415i) q^{9} +(-3.11878 + 1.12837i) q^{11} +(3.21472 - 1.63265i) q^{13} +(-6.63680 + 5.97580i) q^{15} +(-0.649453 + 6.17913i) q^{17} +(0.0534385 + 0.0481162i) q^{19} +10.6395i q^{21} +(-0.386458 + 0.669366i) q^{23} +(-3.55226 - 10.9327i) q^{25} +(2.07224 + 1.50557i) q^{27} +(-1.36758 - 1.51885i) q^{29} +(-1.91694 - 2.63844i) q^{31} +(7.22386 - 1.00111i) q^{33} +(-17.9526 - 7.99300i) q^{35} +(-4.31262 + 3.88310i) q^{37} +(-7.66077 + 2.04188i) q^{39} +(1.33294 - 6.27097i) q^{41} +(1.76833 + 3.06283i) q^{43} +(6.45474 - 3.72664i) q^{45} +(9.73035 - 3.16158i) q^{47} +(-14.9927 + 6.67520i) q^{49} +(4.22182 - 12.9934i) q^{51} +(-4.72887 + 3.43572i) q^{53} +(-3.73777 + 12.9413i) q^{55} +(-0.0929402 - 0.127921i) q^{57} +(-1.06873 - 5.02799i) q^{59} +(0.533613 - 5.07699i) q^{61} +(1.84613 - 8.68534i) q^{63} +(2.30984 - 14.4604i) q^{65} +(-5.66461 - 3.27046i) q^{67} +(1.13723 - 1.26302i) q^{69} +(3.32268 + 0.349228i) q^{71} +(4.73006 + 1.53689i) q^{73} +(2.64217 + 25.1386i) q^{75} +(8.47782 + 13.6255i) q^{77} +(-0.812410 + 0.590250i) q^{79} +(-7.45257 - 8.27691i) q^{81} +(1.91470 - 2.63536i) q^{83} +(18.7529 + 16.8851i) q^{85} +(2.24706 + 3.89203i) q^{87} +(0.348441 + 0.201172i) q^{89} +(-10.9610 - 13.5723i) q^{91} +(2.91680 + 6.55125i) q^{93} +(0.285671 - 0.0607212i) q^{95} +(4.94920 - 11.1161i) q^{97} +(-6.07079 - 0.436226i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 20 q^{9}+O(q^{10}) $ 112 * q + 20 * q^9	$ 112 q + 20 q^{9} - 6 q^{11} + 11 q^{13} + 30 q^{15} + 16 q^{17} - 12 q^{19} + 6 q^{23} + 40 q^{25} - 12 q^{27} - 5 q^{29} + 9 q^{33} - 33 q^{35} - 45 q^{39} - 18 q^{41} + 30 q^{45} - 16 q^{49} + 48 q^{51} - 2 q^{53} - 20 q^{55} - 39 q^{59} + 4 q^{61} - 102 q^{63} - 6 q^{65} + 48 q^{67} + 34 q^{69} + 84 q^{71} - 56 q^{75} - 22 q^{77} - 24 q^{79} + 16 q^{81} + 60 q^{85} - 34 q^{87} - 66 q^{89} - 41 q^{91} + 123 q^{93} + 12 q^{95} - 15 q^{97}+O(q^{100}) $ 112 * q + 20 * q^9 - 6 * q^11 + 11 * q^13 + 30 * q^15 + 16 * q^17 - 12 * q^19 + 6 * q^23 + 40 * q^25 - 12 * q^27 - 5 * q^29 + 9 * q^33 - 33 * q^35 - 45 * q^39 - 18 * q^41 + 30 * q^45 - 16 * q^49 + 48 * q^51 - 2 * q^53 - 20 * q^55 - 39 * q^59 + 4 * q^61 - 102 * q^63 - 6 * q^65 + 48 * q^67 + 34 * q^69 + 84 * q^71 - 56 * q^75 - 22 * q^77 - 24 * q^79 + 16 * q^81 + 60 * q^85 - 34 * q^87 - 66 * q^89 - 41 * q^91 + 123 * q^93 + 12 * q^95 - 15 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{5}\right)$

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
$3$	−2.15084	−	0.457176i	−1.24179	−	0.263950i	−0.460240	−	0.887794i	$-0.652237\pi$
$3$	−2.15084	−	0.457176i	−1.24179	−	0.263950i	−0.781549	+	0.623844i	$0.785570\pi$
$4$		0			0
$5$	2.38726	−	3.28578i	1.06761	−	1.46945i	0.195147	−	0.980774i	$-0.437482\pi$
$5$	2.38726	−	3.28578i	1.06761	−	1.46945i	0.872468	−	0.488672i	$-0.162518\pi$
$6$		0			0
$7$	−1.00599	−	4.73282i	−0.380229	−	1.78884i	−0.586079	−	0.810254i	$-0.699329\pi$
$7$	−1.00599	−	4.73282i	−0.380229	−	1.78884i	0.205850	−	0.978584i	$-0.434004\pi$
$8$		0			0
$9$	1.67648	+	0.746415i	0.558825	+	0.248805i
$10$		0			0
$11$	−3.11878	+	1.12837i	−0.940348	+	0.340215i
$11$	−3.11878	+	1.12837i	−0.940348	+	0.340215i
$12$		0			0
$13$	3.21472	−	1.63265i	0.891604	−	0.452816i
$13$	3.21472	−	1.63265i	0.891604	−	0.452816i
$14$		0			0
$15$	−6.63680	+	5.97580i	−1.71361	+	1.54294i
$16$		0			0
$17$	−0.649453	+	6.17913i	−0.157515	+	1.49866i	0.575137	+	0.818057i	$0.304949\pi$
$17$	−0.649453	+	6.17913i	−0.157515	+	1.49866i	−0.732653	+	0.680603i	$0.761718\pi$
$18$		0			0
$19$	0.0534385	+	0.0481162i	0.0122596	+	0.0110386i	0.675238	−	0.737600i	$-0.264041\pi$
$19$	0.0534385	+	0.0481162i	0.0122596	+	0.0110386i	−0.662978	+	0.748639i	$0.730708\pi$
$20$		0			0
$21$			10.6395i			2.32172i
$22$		0			0
$23$	−0.386458	+	0.669366i	−0.0805821	+	0.139572i	−0.903500	−	0.428588i	$-0.859011\pi$
$23$	−0.386458	+	0.669366i	−0.0805821	+	0.139572i	0.822918	+	0.568160i	$0.192345\pi$
$24$		0			0
$25$	−3.55226	−	10.9327i	−0.710453	−	2.18655i
$26$		0			0
$27$	2.07224	+	1.50557i	0.398802	+	0.289746i
$28$		0			0
$29$	−1.36758	−	1.51885i	−0.253953	−	0.282043i	0.602665	−	0.797994i	$-0.294105\pi$
$29$	−1.36758	−	1.51885i	−0.253953	−	0.282043i	−0.856618	+	0.515951i	$0.827439\pi$
$30$		0			0
$31$	−1.91694	−	2.63844i	−0.344292	−	0.473878i	0.601397	−	0.798951i	$-0.294611\pi$
$31$	−1.91694	−	2.63844i	−0.344292	−	0.473878i	−0.945689	+	0.325073i	$0.894611\pi$
$32$		0			0
$33$	7.22386	−	1.00111i	1.25751	−	0.174270i
$34$		0			0
$35$	−17.9526	−	7.99300i	−3.03454	−	1.35106i
$36$		0			0
$37$	−4.31262	+	3.88310i	−0.708991	+	0.638378i	−0.942589	−	0.333955i	$-0.891617\pi$
$37$	−4.31262	+	3.88310i	−0.708991	+	0.638378i	0.233598	+	0.972333i	$0.424950\pi$
$38$		0			0
$39$	−7.66077	+	2.04188i	−1.22671	+	0.326963i
$40$		0			0
$41$	1.33294	−	6.27097i	0.208170	−	0.979362i	−0.742665	−	0.669663i	$-0.766439\pi$
$41$	1.33294	−	6.27097i	0.208170	−	0.979362i	0.950835	−	0.309699i	$-0.100228\pi$
$42$		0			0
$43$	1.76833	+	3.06283i	0.269667	+	0.467078i	0.968776	−	0.247938i	$-0.0797529\pi$
$43$	1.76833	+	3.06283i	0.269667	+	0.467078i	−0.699108	+	0.715016i	$0.746420\pi$
$44$		0			0
$45$	6.45474	−	3.72664i	0.962215	−	0.555535i
$46$		0			0
$47$	9.73035	−	3.16158i	1.41932	−	0.461164i	0.503932	−	0.863743i	$-0.331886\pi$
$47$	9.73035	−	3.16158i	1.41932	−	0.461164i	0.915385	+	0.402579i	$0.131886\pi$
$48$		0			0
$49$	−14.9927	+	6.67520i	−2.14182	+	0.953600i
$50$		0			0
$51$	4.22182	−	12.9934i	0.591173	−	1.81944i
$52$		0			0
$53$	−4.72887	+	3.43572i	−0.649560	+	0.471933i	−0.863121	−	0.504997i	$-0.831494\pi$
$53$	−4.72887	+	3.43572i	−0.649560	+	0.471933i	0.213561	+	0.976930i	$0.431494\pi$
$54$		0			0
$55$	−3.73777	+	12.9413i	−0.504001	+	1.74501i
$56$		0			0
$57$	−0.0929402	−	0.127921i	−0.0123102	−	0.0169436i
$58$		0			0
$59$	−1.06873	−	5.02799i	−0.139137	−	0.654588i	−0.991334	−	0.131367i	$-0.958063\pi$
$59$	−1.06873	−	5.02799i	−0.139137	−	0.654588i	0.852197	−	0.523221i	$-0.175270\pi$
$60$		0			0
$61$	0.533613	−	5.07699i	0.0683221	−	0.650042i	−0.905751	−	0.423810i	$-0.860693\pi$
$61$	0.533613	−	5.07699i	0.0683221	−	0.650042i	0.974073	−	0.226232i	$-0.0726408\pi$
$62$		0			0
$63$	1.84613	−	8.68534i	0.232590	−	1.09425i
$64$		0			0
$65$	2.30984	−	14.4604i	0.286501	−	1.79360i
$66$		0			0
$67$	−5.66461	−	3.27046i	−0.692042	−	0.399551i	0.112334	−	0.993670i	$-0.464167\pi$
$67$	−5.66461	−	3.27046i	−0.692042	−	0.399551i	−0.804377	+	0.594120i	$0.797501\pi$
$68$		0			0
$69$	1.13723	−	1.26302i	0.136906	−	0.152050i
$70$		0			0
$71$	3.32268	+	0.349228i	0.394330	+	0.0414457i	0.299619	−	0.954059i	$-0.403141\pi$
$71$	3.32268	+	0.349228i	0.394330	+	0.0414457i	0.0947113	+	0.995505i	$0.469807\pi$
$72$		0			0
$73$	4.73006	+	1.53689i	0.553612	+	0.179879i	0.572445	−	0.819943i	$-0.305995\pi$
$73$	4.73006	+	1.53689i	0.553612	+	0.179879i	−0.0188329	+	0.999823i	$0.505995\pi$
$74$		0			0
$75$	2.64217	+	25.1386i	0.305092	+	2.90276i
$76$		0			0
$77$	8.47782	+	13.6255i	0.966138	+	1.55277i
$78$		0			0
$79$	−0.812410	+	0.590250i	−0.0914032	+	0.0664083i	−0.632548	−	0.774521i	$-0.717991\pi$
$79$	−0.812410	+	0.590250i	−0.0914032	+	0.0664083i	0.541145	+	0.840929i	$0.317991\pi$
$80$		0			0
$81$	−7.45257	−	8.27691i	−0.828063	−	0.919657i
$82$		0			0
$83$	1.91470	−	2.63536i	0.210166	−	0.289268i	−0.690900	−	0.722950i	$-0.742786\pi$
$83$	1.91470	−	2.63536i	0.210166	−	0.289268i	0.901066	+	0.433681i	$0.142786\pi$
$84$		0			0
$85$	18.7529	+	16.8851i	2.03403	+	1.83145i
$86$		0			0
$87$	2.24706	+	3.89203i	0.240911	+	0.417269i
$88$		0			0
$89$	0.348441	+	0.201172i	0.0369347	+	0.0213242i	0.518354	−	0.855166i	$-0.326545\pi$
$89$	0.348441	+	0.201172i	0.0369347	+	0.0213242i	−0.481419	+	0.876491i	$0.659878\pi$
$90$		0			0
$91$	−10.9610	−	13.5723i	−1.14903	−	1.42276i
$92$		0			0
$93$	2.91680	+	6.55125i	0.302458	+	0.679332i
$94$		0			0
$95$	0.285671	−	0.0607212i	0.0293092	−	0.00622987i
$96$		0			0
$97$	4.94920	−	11.1161i	0.502515	−	1.12867i	−0.467138	−	0.884184i	$-0.654715\pi$
$97$	4.94920	−	11.1161i	0.502515	−	1.12867i	0.969653	−	0.244484i	$-0.0786184\pi$
$98$		0			0
$99$	−6.07079	−	0.436226i	−0.610137	−	0.0438423i
$100$		0			0
$101$	1.84107	+	17.5166i	0.183193	+	1.74297i	0.570753	+	0.821122i	$0.306651\pi$
$101$	1.84107	+	17.5166i	0.183193	+	1.74297i	−0.387560	+	0.921845i	$0.626682\pi$
$102$		0			0
$103$	−4.40213	+	13.5484i	−0.433755	+	1.33496i	0.460602	+	0.887607i	$0.347634\pi$
$103$	−4.40213	+	13.5484i	−0.433755	+	1.33496i	−0.894357	+	0.447354i	$0.852366\pi$
$104$		0			0
$105$	34.9589	+	25.3992i	3.41164	+	2.47870i
$106$		0			0
$107$	4.12595	+	0.876997i	0.398870	+	0.0847825i	0.402979	−	0.915209i	$-0.367975\pi$
$107$	4.12595	+	0.876997i	0.398870	+	0.0847825i	−0.00410913	+	0.999992i	$0.501308\pi$
$108$		0			0
$109$		−	14.1623i		−	1.35650i	−0.734830	−	0.678251i	$-0.762738\pi$
$109$		−	14.1623i		−	1.35650i	0.734830	−	0.678251i	$-0.237262\pi$
$110$		0			0
$111$	11.0510	−	6.38032i	1.04892	−	0.605593i
$112$		0			0
$113$	7.13201	−	7.92090i	0.670923	−	0.745135i	−0.307545	−	0.951534i	$-0.599507\pi$
$113$	7.13201	−	7.92090i	0.670923	−	0.745135i	0.978468	+	0.206398i	$0.0661742\pi$
$114$		0			0
$115$	1.27681	+	2.86777i	0.119063	+	0.267421i
$116$		0			0
$117$	6.60804	−	0.337583i	0.610913	−	0.0312096i
$118$		0			0
$119$	29.8981	−	3.14241i	2.74075	−	0.288064i
$120$		0			0
$121$	8.45358	−	7.03825i	0.768507	−	0.639841i
$122$		0			0
$123$	−5.73387	+	12.8785i	−0.517006	+	1.16121i
$124$		0			0
$125$	−25.0894	−	8.15205i	−2.24407	−	0.729141i
$126$		0			0
$127$	12.4070	−	5.52396i	1.10094	−	0.490172i	0.225868	−	0.974158i	$-0.427478\pi$
$127$	12.4070	−	5.52396i	1.10094	−	0.490172i	0.875076	+	0.483986i	$0.160811\pi$
$128$		0			0
$129$	−2.40314	−	7.39611i	−0.211585	−	0.651191i
$130$		0			0
$131$	−0.211595			−0.0184872			−0.00924359	−	0.999957i	$-0.502942\pi$
$131$	−0.211595			−0.0184872			−0.00924359	+	0.999957i	$0.502942\pi$
$132$		0			0
$133$	0.173967	−	0.301319i	0.0150848	−	0.0261277i
$134$		0			0
$135$	9.89393	−	3.21473i	0.851534	−	0.276680i
$136$		0			0
$137$	−8.82489	−	0.927533i	−0.753961	−	0.0792445i	−0.280253	−	0.959926i	$-0.590418\pi$
$137$	−8.82489	−	0.927533i	−0.753961	−	0.0792445i	−0.473708	+	0.880682i	$0.657085\pi$
$138$		0			0
$139$	−11.6536	+	2.47705i	−0.988444	+	0.210100i	−0.673643	−	0.739057i	$-0.735271\pi$
$139$	−11.6536	+	2.47705i	−0.988444	+	0.210100i	−0.314801	+	0.949158i	$0.601938\pi$
$140$		0			0
$141$	−22.3738	+	2.35159i	−1.88422	+	0.198039i
$142$		0			0
$143$	−8.18379	+	8.71927i	−0.684363	+	0.729142i
$144$		0			0
$145$	−8.25537	+	0.867675i	−0.685572	+	0.0720565i
$146$		0			0
$147$	35.2988	−	7.50298i	2.91139	−	0.618836i
$148$		0			0
$149$	6.97168	+	0.732753i	0.571142	+	0.0600294i	0.385698	−	0.922625i	$-0.373961\pi$
$149$	6.97168	+	0.732753i	0.571142	+	0.0600294i	0.185445	+	0.982655i	$0.440627\pi$
$150$		0			0
$151$	−0.381127	+	0.123836i	−0.0310157	+	0.0100776i	−0.324484	−	0.945891i	$-0.605191\pi$
$151$	−0.381127	+	0.123836i	−0.0310157	+	0.0100776i	0.293468	+	0.955969i	$0.405191\pi$
$152$		0			0
$153$	−5.70099	+	9.87440i	−0.460897	+	0.798298i
$154$		0			0
$155$	−13.2456			−1.06391
$156$		0			0
$157$	−4.41209	−	13.5790i	−0.352123	−	1.08372i	−0.957659	−	0.287905i	$-0.907041\pi$
$157$	−4.41209	−	13.5790i	−0.352123	−	1.08372i	0.605536	−	0.795818i	$-0.292959\pi$
$158$		0			0
$159$	11.7418	−	5.22778i	0.931183	−	0.414590i
$160$		0			0
$161$	3.55676	+	1.15566i	0.280312	+	0.0910789i
$162$		0			0
$163$	−4.28467	+	9.62352i	−0.335601	+	0.753772i	0.664379	+	0.747396i	$0.268696\pi$
$163$	−4.28467	+	9.62352i	−0.335601	+	0.753772i	−0.999980	+	0.00637608i	$0.997970\pi$
$164$		0			0
$165$	13.9558	−	26.1259i	1.08646	−	2.03390i
$166$		0			0
$167$	10.3656	−	1.08947i	0.802116	−	0.0843058i	0.305406	−	0.952222i	$-0.401208\pi$
$167$	10.3656	−	1.08947i	0.802116	−	0.0843058i	0.496710	+	0.867917i	$0.334541\pi$
$168$		0			0
$169$	7.66889	−	10.4971i	0.589915	−	0.807465i
$170$		0			0
$171$	0.0536736	+	0.120553i	0.00410452	+	0.00921891i
$172$		0			0
$173$	−4.04832	+	4.49611i	−0.307788	+	0.341833i	−0.877117	−	0.480277i	$-0.840536\pi$
$173$	−4.04832	+	4.49611i	−0.307788	+	0.341833i	0.569329	+	0.822110i	$0.307203\pi$
$174$		0			0
$175$	−48.1691	+	27.8105i	−3.64125	+	2.10227i
$176$		0			0
$177$			11.3030i			0.849586i
$178$		0			0
$179$	−9.75867	−	2.07427i	−0.729397	−	0.155038i	−0.171779	−	0.985136i	$-0.554951\pi$
$179$	−9.75867	−	2.07427i	−0.729397	−	0.155038i	−0.557619	+	0.830097i	$0.688285\pi$
$180$		0			0
$181$	−16.1696	−	11.7479i	−1.20188	−	0.873215i	−0.207409	−	0.978254i	$-0.566503\pi$
$181$	−16.1696	−	11.7479i	−1.20188	−	0.873215i	−0.994468	+	0.105039i	$0.966503\pi$
$182$		0			0
$183$	−3.46879	+	10.6758i	−0.256421	+	0.789181i
$184$		0			0
$185$	2.46368	+	23.4403i	0.181133	+	1.72337i
$186$		0			0
$187$	−4.94682	−	20.0042i	−0.361748	−	1.46285i
$188$		0			0
$189$	5.04093	−	11.3221i	0.366673	−	0.823562i
$190$		0			0
$191$	12.0397	−	2.55912i	0.871163	−	0.185171i	0.249422	−	0.968395i	$-0.419759\pi$
$191$	12.0397	−	2.55912i	0.871163	−	0.185171i	0.621740	+	0.783223i	$0.286426\pi$
$192$		0			0
$193$	−1.64285	−	3.68990i	−0.118255	−	0.265605i	0.844714	−	0.535218i	$-0.179771\pi$
$193$	−1.64285	−	3.68990i	−0.118255	−	0.265605i	−0.962969	+	0.269614i	$0.913104\pi$
$194$		0			0
$195$	−11.5791	+	30.0461i	−0.829194	+	2.15165i
$196$		0			0
$197$	0.351043	+	0.202675i	0.0250108	+	0.0144400i	0.512453	−	0.858715i	$-0.328737\pi$
$197$	0.351043	+	0.202675i	0.0250108	+	0.0144400i	−0.487442	+	0.873155i	$0.662070\pi$
$198$		0			0
$199$	−12.6094	−	21.8401i	−0.893857	−	1.54820i	−0.835213	−	0.549926i	$-0.814656\pi$
$199$	−12.6094	−	21.8401i	−0.893857	−	1.54820i	−0.0586430	−	0.998279i	$-0.518677\pi$
$200$		0			0
$201$	10.6885	+	9.62398i	0.753909	+	0.678823i
$202$		0			0
$203$	−5.81267	+	8.00046i	−0.407970	+	0.561522i
$204$		0			0
$205$	−17.4230	−	19.3502i	−1.21687	−	1.35148i
$206$		0			0
$207$	−1.14751	+	0.833716i	−0.0797576	+	0.0579473i
$208$		0			0
$209$	−0.220956	−	0.0897658i	−0.0152838	−	0.00620923i
$210$		0			0
$211$	1.18650	+	11.2888i	0.0816818	+	0.777151i	0.956310	+	0.292356i	$0.0944391\pi$
$211$	1.18650	+	11.2888i	0.0816818	+	0.777151i	−0.874628	+	0.484795i	$0.838894\pi$
$212$		0			0
$213$	−6.98691	−	2.27018i	−0.478735	−	0.155550i
$214$		0			0
$215$	14.2853	+	1.50144i	0.974246	+	0.102397i
$216$		0			0
$217$	−10.5588	+	11.7268i	−0.716781	+	0.796065i
$218$		0			0
$219$	−9.47099	−	5.46808i	−0.639990	−	0.369498i
$220$		0			0
$221$	8.00056	+	20.9245i	0.538176	+	1.40754i
$222$		0			0
$223$	−2.46784	+	11.6103i	−0.165258	+	0.777480i	0.814953	+	0.579527i	$0.196763\pi$
$223$	−2.46784	+	11.6103i	−0.165258	+	0.777480i	−0.980212	+	0.197953i	$0.936571\pi$
$224$		0			0
$225$	2.20508	−	20.9799i	0.147005	−	1.39866i
$226$		0			0
$227$	−4.39949	−	20.6980i	−0.292005	−	1.37377i	−0.842392	−	0.538865i	$-0.818853\pi$
$227$	−4.39949	−	20.6980i	−0.292005	−	1.37377i	0.550388	−	0.834909i	$-0.314480\pi$
$228$		0			0
$229$	−5.07806	−	6.98934i	−0.335567	−	0.461869i	0.607573	−	0.794264i	$-0.292143\pi$
$229$	−5.07806	−	6.98934i	−0.335567	−	0.461869i	−0.943140	+	0.332395i	$0.892143\pi$
$230$		0			0
$231$	−12.0052	−	33.1821i	−0.789885	−	2.18322i
$232$		0			0
$233$	17.5485	−	12.7498i	1.14964	−	0.835265i	0.161210	−	0.986920i	$-0.448460\pi$
$233$	17.5485	−	12.7498i	1.14964	−	0.835265i	0.988433	+	0.151655i	$0.0484604\pi$
$234$		0			0
$235$	12.8406	−	39.5193i	0.837628	−	2.57796i
$236$		0			0
$237$	2.01721	−	0.898121i	0.131032	−	0.0583392i
$238$		0			0
$239$	28.2864	−	9.19079i	1.82969	−	0.594503i	0.830389	−	0.557184i	$-0.188118\pi$
$239$	28.2864	−	9.19079i	1.82969	−	0.594503i	0.999303	−	0.0373186i	$-0.0118817\pi$
$240$		0			0
$241$	4.95911	−	2.86314i	0.319444	−	0.184431i	−0.331701	−	0.943385i	$-0.607622\pi$
$241$	4.95911	−	2.86314i	0.319444	−	0.184431i	0.651145	+	0.758953i	$0.274289\pi$
$242$		0			0
$243$	8.40316	+	14.5547i	0.539063	+	0.933684i
$244$		0			0
$245$	−13.8583	+	65.1983i	−0.885376	+	4.16537i
$246$		0			0
$247$	0.250347	+	0.0674339i	0.0159292	+	0.00429072i
$248$		0			0
$249$	−5.32304	+	4.79289i	−0.337334	+	0.303737i
$250$		0			0
$251$	9.48809	+	4.22437i	0.598883	+	0.266640i	0.683708	−	0.729756i	$-0.260366\pi$
$251$	9.48809	+	4.22437i	0.598883	+	0.266640i	−0.0848249	+	0.996396i	$0.527033\pi$
$252$		0			0
$253$	0.449989	−	2.52367i	0.0282906	−	0.158662i
$254$		0			0
$255$	−32.6150	−	44.8906i	−2.04243	−	2.81116i
$256$		0			0
$257$	7.59682	+	8.43713i	0.473877	+	0.526294i	0.931933	−	0.362629i	$-0.118121\pi$
$257$	7.59682	+	8.43713i	0.473877	+	0.526294i	−0.458057	+	0.888923i	$0.651454\pi$
$258$		0			0
$259$	22.7165	+	16.5045i	1.41153	+	1.02554i
$260$		0			0
$261$	−1.15902	−	3.56710i	−0.0717415	−	0.220798i
$262$		0			0
$263$	2.94930	−	5.10834i	0.181862	−	0.314994i	−0.760653	−	0.649159i	$-0.775121\pi$
$263$	2.94930	−	5.10834i	0.181862	−	0.314994i	0.942515	+	0.334165i	$0.108454\pi$
$264$		0			0
$265$			23.7400i			1.45834i
$266$		0			0
$267$	−0.657470	−	0.591989i	−0.0402365	−	0.0362291i
$268$		0			0
$269$	−1.89993	+	18.0766i	−0.115841	+	1.10215i	0.769962	+	0.638089i	$0.220275\pi$
$269$	−1.89993	+	18.0766i	−0.115841	+	1.10215i	−0.885803	+	0.464062i	$0.846392\pi$
$270$		0			0
$271$	14.8165	−	13.3409i	0.900040	−	0.810400i	−0.0824727	−	0.996593i	$-0.526282\pi$
$271$	14.8165	−	13.3409i	0.900040	−	0.810400i	0.982513	+	0.186193i	$0.0596151\pi$
$272$		0			0
$273$	17.3705	+	34.2029i	1.05131	+	2.07006i
$274$		0			0
$275$	23.4149	+	30.0886i	1.41197	+	1.81441i
$276$		0			0
$277$	12.6658	+	5.63918i	0.761014	+	0.338825i	0.750283	−	0.661117i	$-0.229917\pi$
$277$	12.6658	+	5.63918i	0.761014	+	0.338825i	0.0107314	+	0.999942i	$0.496584\pi$
$278$		0			0
$279$	−1.24433	−	5.85411i	−0.0744961	−	0.350476i
$280$		0			0
$281$	−0.353839	+	0.487018i	−0.0211083	+	0.0290531i	−0.819441	−	0.573164i	$-0.805716\pi$
$281$	−0.353839	+	0.487018i	−0.0211083	+	0.0290531i	0.798332	+	0.602217i	$0.205716\pi$
$282$		0			0
$283$	−3.64138	−	0.773998i	−0.216457	−	0.0460094i	0.0984064	−	0.995146i	$-0.468625\pi$
$283$	−3.64138	−	0.773998i	−0.216457	−	0.0460094i	−0.314864	+	0.949137i	$0.601959\pi$
$284$		0			0
$285$	−0.642193			−0.0380402
$286$		0			0
$287$	−31.0203			−1.83107
$288$		0			0
$289$	−21.1314	−	4.49161i	−1.24302	−	0.264212i
$290$		0			0
$291$	−15.7270	+	21.6463i	−0.921931	+	1.26893i
$292$		0			0
$293$	5.73949	+	27.0022i	0.335305	+	1.57748i	0.746149	+	0.665779i	$0.231901\pi$
$293$	5.73949	+	27.0022i	0.335305	+	1.57748i	−0.410844	+	0.911706i	$0.634766\pi$
$294$		0			0
$295$	−19.0722	−	8.49149i	−1.11043	−	0.494394i
$296$		0			0
$297$	−8.16168	−	2.35729i	−0.473589	−	0.136784i
$298$		0			0
$299$	−0.149516	+	2.78278i	−0.00864672	+	0.160932i
$300$		0			0
$301$	12.7169	−	11.4504i	0.732991	−	0.659988i
$302$		0			0
$303$	4.04831	−	38.5171i	0.232569	−	2.21275i
$304$		0			0
$305$	−15.4080	−	13.8734i	−0.882259	−	0.794390i
$306$		0			0
$307$			4.14067i			0.236321i	0.992995	+	0.118160i	$0.0376997\pi$
$307$			4.14067i			0.236321i	−0.992995	+	0.118160i	$0.962300\pi$
$308$		0			0
$309$	15.6623	−	27.1279i	0.890996	−	1.54325i
$310$		0			0
$311$	−5.44731	−	16.7651i	−0.308888	−	0.950661i	−0.978198	−	0.207677i	$-0.933410\pi$
$311$	−5.44731	−	16.7651i	−0.308888	−	0.950661i	0.669309	−	0.742984i	$-0.266590\pi$
$312$		0			0
$313$	23.0587	+	16.7531i	1.30335	+	0.946943i	0.999982	−	0.00592928i	$-0.00188736\pi$
$313$	23.0587	+	16.7531i	1.30335	+	0.946943i	0.303372	+	0.952872i	$0.401887\pi$
$314$		0			0
$315$	−24.1309	−	26.8001i	−1.35962	−	1.51002i
$316$		0			0
$317$	−14.2211	−	19.5737i	−0.798737	−	1.09937i	−0.992965	−	0.118411i	$-0.962220\pi$
$317$	−14.2211	−	19.5737i	−0.798737	−	1.09937i	0.194228	−	0.980956i	$-0.437780\pi$
$318$		0			0
$319$	5.97900	+	3.19383i	0.334760	+	0.178820i
$320$		0			0
$321$	−8.47332	−	3.77256i	−0.472934	−	0.210564i
$322$		0			0
$323$	−0.332022	+	0.298954i	−0.0184742	+	0.0166343i
$324$		0			0
$325$	−29.2689	−	29.3461i	−1.62355	−	1.62783i
$326$		0			0
$327$	−6.47466	+	30.4609i	−0.358050	+	1.68449i
$328$		0			0
$329$	−24.7518	−	42.8715i	−1.36461	−	2.36358i
$330$		0			0
$331$	2.91589	−	1.68349i	0.160272	−	0.0925330i	−0.417719	−	0.908576i	$-0.637170\pi$
$331$	2.91589	−	1.68349i	0.160272	−	0.0925330i	0.577991	+	0.816043i	$0.303837\pi$
$332$		0			0
$333$	−10.1284	+	3.29092i	−0.555034	+	0.180341i
$334$		0			0
$335$	−24.2689	+	10.8052i	−1.32595	+	0.590352i
$336$		0			0
$337$	2.70146	−	8.31423i	0.147158	−	0.452905i	−0.850124	−	0.526582i	$-0.823473\pi$
$337$	2.70146	−	8.31423i	0.147158	−	0.452905i	0.997282	+	0.0736770i	$0.0234734\pi$
$338$		0			0
$339$	−18.9611	+	13.7760i	−1.02982	+	0.748211i
$340$		0			0
$341$	8.95564	+	6.06570i	0.484975	+	0.328476i
$342$		0			0
$343$	26.7669	+	36.8415i	1.44528	+	1.98925i
$344$		0			0
$345$	−1.43515	−	6.75184i	−0.0772658	−	0.363507i
$346$		0			0
$347$	0.396381	−	3.77132i	0.0212789	−	0.202455i	−0.978717	−	0.205213i	$-0.934211\pi$
$347$	0.396381	−	3.77132i	0.0212789	−	0.202455i	0.999996	+	0.00275811i	$0.000877934\pi$
$348$		0			0
$349$	2.57907	−	12.1336i	0.138055	−	0.649496i	−0.853638	−	0.520866i	$-0.825609\pi$
$349$	2.57907	−	12.1336i	0.138055	−	0.649496i	0.991693	−	0.128629i	$-0.0410577\pi$
$350$		0			0
$351$	9.11973	+	1.45674i	0.486775	+	0.0777552i
$352$		0			0
$353$	10.0120	+	5.78042i	0.532884	+	0.307661i	0.742190	−	0.670189i	$-0.233787\pi$
$353$	10.0120	+	5.78042i	0.532884	+	0.307661i	−0.209306	+	0.977850i	$0.567120\pi$
$354$		0			0
$355$	9.07959	−	10.0839i	0.481895	−	0.535198i
$356$		0			0
$357$	−65.7426	−	6.90983i	−3.47947	−	0.365707i
$358$		0			0
$359$	−18.0942	−	5.87916i	−0.954975	−	0.310290i	−0.210239	−	0.977650i	$-0.567424\pi$
$359$	−18.0942	−	5.87916i	−0.954975	−	0.310290i	−0.744736	+	0.667360i	$0.767424\pi$
$360$		0			0
$361$	−1.98550	−	18.8908i	−0.104500	−	0.994251i
$362$		0			0
$363$	−21.4000	+	11.2734i	−1.12321	+	0.591700i
$364$		0			0
$365$	16.3418	−	11.8730i	0.855367	−	0.621461i
$366$		0			0
$367$	−6.06903	−	6.74034i	−0.316801	−	0.351843i	0.563622	−	0.826033i	$-0.309408\pi$
$367$	−6.06903	−	6.74034i	−0.316801	−	0.351843i	−0.880422	+	0.474190i	$0.842741\pi$
$368$		0			0
$369$	6.91538	−	9.51821i	0.360000	−	0.495498i
$370$		0			0
$371$	21.0179	+	18.9246i	1.09119	+	0.982515i
$372$		0			0
$373$	12.0103	+	20.8024i	0.621868	+	1.07711i	0.989138	+	0.146993i	$0.0469595\pi$
$373$	12.0103	+	20.8024i	0.621868	+	1.07711i	−0.367269	+	0.930115i	$0.619707\pi$
$374$		0			0
$375$	50.2365	+	29.0040i	2.59420	+	1.49776i
$376$		0			0
$377$	−6.87614	−	2.64990i	−0.354139	−	0.136477i
$378$		0			0
$379$	−8.04074	−	18.0598i	−0.413025	−	0.927670i	−0.993547	−	0.113425i	$-0.963818\pi$
$379$	−8.04074	−	18.0598i	−0.413025	−	0.927670i	0.580522	−	0.814245i	$-0.302849\pi$
$380$		0			0
$381$	−29.2109	+	6.20897i	−1.49652	+	0.318095i
$382$		0			0
$383$	−5.35638	+	12.0306i	−0.273698	+	0.614736i	−0.997134	−	0.0756554i	$-0.975895\pi$
$383$	−5.35638	+	12.0306i	−0.273698	+	0.614736i	0.723436	+	0.690392i	$0.242562\pi$
$384$		0			0
$385$	65.0092	+	4.67133i	3.31317	+	0.238073i
$386$		0			0
$387$	0.678413	+	6.45467i	0.0344857	+	0.328109i
$388$		0			0
$389$	0.0973756	−	0.299691i	0.00493714	−	0.0151950i	−0.948558	−	0.316605i	$-0.897457\pi$
$389$	0.0973756	−	0.299691i	0.00493714	−	0.0151950i	0.953495	+	0.301410i	$0.0974572\pi$
$390$		0			0
$391$	−3.88511	−	2.82270i	−0.196478	−	0.142750i
$392$		0			0
$393$	0.455108	+	0.0967362i	0.0229572	+	0.00487970i
$394$		0			0
$395$			4.07848i			0.205211i
$396$		0			0
$397$	1.12971	−	0.652237i	0.0566984	−	0.0327348i	−0.471383	−	0.881929i	$-0.656245\pi$
$397$	1.12971	−	0.652237i	0.0566984	−	0.0327348i	0.528081	+	0.849194i	$0.322912\pi$
$398$		0			0
$399$	−0.511931	+	0.568557i	−0.0256286	+	0.0284634i
$400$		0			0
$401$	−4.25371	−	9.55398i	−0.212420	−	0.477103i	0.775640	−	0.631176i	$-0.217428\pi$
$401$	−4.25371	−	9.55398i	−0.212420	−	0.477103i	−0.988059	+	0.154073i	$0.950761\pi$
$402$		0			0
$403$	−10.4701	−	5.35216i	−0.521552	−	0.266610i
$404$		0			0
$405$	−44.9873	+	4.72836i	−2.23544	+	0.234954i
$406$		0			0
$407$	9.06856	−	16.9768i	0.449512	−	0.841507i
$408$		0			0
$409$	−4.06235	+	9.12419i	−0.200870	+	0.451162i	−0.985691	−	0.168560i	$-0.946088\pi$
$409$	−4.06235	+	9.12419i	−0.200870	+	0.451162i	0.784821	+	0.619723i	$0.212755\pi$
$410$		0			0
$411$	18.5569	+	6.02950i	0.915344	+	0.297413i
$412$		0			0
$413$	−22.7214	+	10.1162i	−1.11805	+	0.497787i
$414$		0			0
$415$	−4.08833	−	12.5826i	−0.200688	−	0.617655i
$416$		0			0
$417$	26.1975			1.28290
$418$		0			0
$419$	19.4834	−	33.7462i	0.951825	−	1.64861i	0.210353	−	0.977626i	$-0.432539\pi$
$419$	19.4834	−	33.7462i	0.951825	−	1.64861i	0.741472	−	0.670983i	$-0.234128\pi$
$420$		0			0
$421$	−36.6721	+	11.9155i	−1.78729	+	0.580725i	−0.999385	−	0.0350763i	$-0.988833\pi$
$421$	−36.6721	+	11.9155i	−1.78729	+	0.580725i	−0.787902	+	0.615801i	$0.788833\pi$
$422$		0			0
$423$	18.6725	+	1.96256i	0.907890	+	0.0954231i
$424$		0			0
$425$	69.8619	−	14.8496i	3.38880	−	0.720311i
$426$		0			0
$427$	−24.5653	+	2.58192i	−1.18880	+	0.124948i
$428$		0			0
$429$	21.5883	−	15.0123i	1.04229	−	0.724803i
$430$		0			0
$431$	38.6349	−	4.06069i	1.86098	−	0.195597i	0.893588	−	0.448889i	$-0.148180\pi$
$431$	38.6349	−	4.06069i	1.86098	−	0.195597i	0.967390	+	0.253292i	$0.0815134\pi$
$432$		0			0
$433$	−17.2868	+	3.67442i	−0.830750	+	0.176581i	−0.603609	−	0.797280i	$-0.706271\pi$
$433$	−17.2868	+	3.67442i	−0.830750	+	0.176581i	−0.227141	+	0.973862i	$0.572938\pi$
$434$		0			0
$435$	18.1527	+	1.90792i	0.870355	+	0.0914780i
$436$		0			0
$437$	−0.0528591	+	0.0171750i	−0.00252859	+	0.000821590i
$438$		0			0
$439$	8.63641	−	14.9587i	0.412193	−	0.713940i	−0.582936	−	0.812518i	$-0.698096\pi$
$439$	8.63641	−	14.9587i	0.412193	−	0.713940i	0.995129	+	0.0985783i	$0.0314295\pi$
$440$		0			0
$441$	−30.1174			−1.43416
$442$		0			0
$443$	4.70946	+	14.4942i	0.223753	+	0.688641i	0.998416	+	0.0562667i	$0.0179197\pi$
$443$	4.70946	+	14.4942i	0.223753	+	0.688641i	−0.774663	+	0.632375i	$0.782080\pi$
$444$		0			0
$445$	1.49283	−	0.664649i	0.0707668	−	0.0315074i
$446$		0			0
$447$	−14.6600	−	4.76332i	−0.693393	−	0.225297i
$448$		0			0
$449$	−13.1905	+	29.6263i	−0.622498	+	1.39815i	0.276847	+	0.960914i	$0.410711\pi$
$449$	−13.1905	+	29.6263i	−0.622498	+	1.39815i	−0.899345	+	0.437240i	$0.855956\pi$
$450$		0			0
$451$	2.91882	+	21.0618i	0.137442	+	0.991763i
$452$		0			0
$453$	0.876360	−	0.0921091i	0.0411750	−	0.00432766i
$454$		0			0
$455$	−70.7623	+	3.61502i	−3.31739	+	0.169475i
$456$		0			0
$457$	−12.5648	−	28.2211i	−0.587759	−	1.32013i	−0.925450	−	0.378871i	$-0.876313\pi$
$457$	−12.5648	−	28.2211i	−0.587759	−	1.32013i	0.337691	−	0.941257i	$-0.390354\pi$
$458$		0			0
$459$	−10.6489	+	11.8268i	−0.497049	+	0.552029i
$460$		0			0
$461$	−3.09081	+	1.78448i	−0.143953	+	0.0831115i	−0.570247	−	0.821473i	$-0.693152\pi$
$461$	−3.09081	+	1.78448i	−0.143953	+	0.0831115i	0.426293	+	0.904585i	$0.359819\pi$
$462$		0			0
$463$			20.2661i			0.941844i	0.882175	+	0.470922i	$0.156079\pi$
$463$			20.2661i			0.941844i	−0.882175	+	0.470922i	$0.843921\pi$
$464$		0			0
$465$	28.4891	+	6.05555i	1.32115	+	0.280819i
$466$		0			0
$467$	−0.143215	−	0.104052i	−0.00662722	−	0.00481496i	0.584467	−	0.811418i	$-0.301304\pi$
$467$	−0.143215	−	0.104052i	−0.00662722	−	0.00481496i	−0.591094	+	0.806603i	$0.701304\pi$
$468$		0			0
$469$	−9.77997	+	30.0996i	−0.451597	+	1.38987i
$470$		0			0
$471$	3.28171	+	31.2234i	0.151213	+	1.43870i
$472$		0			0
$473$	−8.97102	−	7.55698i	−0.412488	−	0.347470i
$474$		0			0
$475$	0.336215	−	0.755151i	0.0154266	−	0.0346487i
$476$		0			0
$477$	−10.4923	+	2.23021i	−0.480410	+	0.102114i
$478$		0			0
$479$	16.1266	+	36.2209i	0.736843	+	1.65498i	0.755498	+	0.655151i	$0.227395\pi$
$479$	16.1266	+	36.2209i	0.736843	+	1.65498i	−0.0186542	+	0.999826i	$0.505938\pi$
$480$		0			0
$481$	−7.52413	+	19.5241i	−0.343071	+	0.890223i
$482$		0			0
$483$	−7.12169	−	4.11171i	−0.324048	−	0.187089i
$484$		0			0
$485$	−24.7100	−	42.7990i	−1.12202	−	1.94340i
$486$		0			0
$487$	7.29038	+	6.56428i	0.330358	+	0.297456i	0.817572	−	0.575827i	$-0.195320\pi$
$487$	7.29038	+	6.56428i	0.330358	+	0.297456i	−0.487213	+	0.873283i	$0.661987\pi$
$488$		0			0
$489$	13.6153	−	18.7398i	0.615704	−	0.847444i
$490$		0			0
$491$	10.1304	+	11.2510i	0.457179	+	0.507749i	0.927025	−	0.375000i	$-0.122357\pi$
$491$	10.1304	+	11.2510i	0.457179	+	0.507749i	−0.469846	+	0.882748i	$0.655691\pi$
$492$		0			0
$493$	10.2734	−	7.46403i	0.462688	−	0.336163i
$494$		0			0
$495$	−15.9259	+	18.9059i	−0.715815	+	0.849757i
$496$		0			0
$497$	−1.68976	−	16.0770i	−0.0757960	−	0.721151i
$498$		0			0
$499$	17.7181	+	5.75696i	0.793172	+	0.257717i	0.677454	−	0.735565i	$-0.263083\pi$
$499$	17.7181	+	5.75696i	0.793172	+	0.257717i	0.115718	+	0.993282i	$0.463083\pi$
$500$		0			0
$501$	−22.7929	−	2.39563i	−1.01831	−	0.107029i
$502$		0			0
$503$	−1.33963	+	1.48781i	−0.0597311	+	0.0663381i	−0.772270	−	0.635295i	$-0.780879\pi$
$503$	−1.33963	+	1.48781i	−0.0597311	+	0.0663381i	0.712539	+	0.701633i	$0.247545\pi$
$504$		0			0
$505$	61.9508	+	35.7673i	2.75677	+	1.59162i
$506$		0			0
$507$	−21.2936	+	19.0715i	−0.945681	+	0.846993i
$508$		0			0
$509$	3.59604	−	16.9181i	0.159392	−	0.749880i	−0.823738	−	0.566971i	$-0.808115\pi$
$509$	3.59604	−	16.9181i	0.159392	−	0.749880i	0.983130	−	0.182909i	$-0.0585514\pi$
$510$		0			0
$511$	2.51542	−	23.9326i	0.111276	−	1.05872i
$512$		0			0
$513$	0.0382949	+	0.180163i	0.00169076	+	0.00795441i
$514$		0			0
$515$	34.0080	+	46.8079i	1.49857	+	2.06260i
$516$		0			0
$517$	−26.7794	+	20.8397i	−1.17776	+	0.916528i
$518$		0			0
$519$	10.7628	−	7.81964i	0.472435	−	0.343244i
$520$		0			0
$521$	−10.9558	+	33.7185i	−0.479982	+	1.47723i	0.359137	+	0.933285i	$0.383071\pi$
$521$	−10.9558	+	33.7185i	−0.479982	+	1.47723i	−0.839119	+	0.543948i	$0.816929\pi$
$522$		0			0
$523$	25.0652	−	11.1598i	1.09603	−	0.487982i	0.222585	−	0.974913i	$-0.428550\pi$
$523$	25.0652	−	11.1598i	1.09603	−	0.487982i	0.873440	+	0.486931i	$0.161884\pi$
$524$		0			0
$525$	116.318	−	37.7942i	5.07655	−	1.64947i
$526$		0			0
$527$	17.5482	−	10.1315i	0.764413	−	0.441334i
$528$		0			0
$529$	11.2013	+	19.4012i	0.487013	+	0.843531i
$530$		0			0
$531$	1.96126	−	9.22701i	0.0851115	−	0.400418i
$532$		0			0
$533$	−5.95330	−	22.3357i	−0.257866	−	0.967465i
$534$		0			0
$535$	12.7313	−	11.4633i	0.550423	−	0.495603i
$536$		0			0
$537$	20.0411	+	8.92285i	0.864835	+	0.385050i
$538$		0			0
$539$	39.2270	−	37.7358i	1.68963	−	1.62540i
$540$		0			0
$541$	18.3279	+	25.2262i	0.787979	+	1.08456i	0.994357	+	0.106088i	$0.0338326\pi$
$541$	18.3279	+	25.2262i	0.787979	+	1.08456i	−0.206377	+	0.978472i	$0.566167\pi$
$542$		0			0
$543$	29.4074	+	32.6602i	1.26199	+	1.40159i
$544$		0			0
$545$	−46.5342	−	33.8091i	−1.99331	−	1.44822i
$546$		0			0
$547$	−3.26275	−	10.0417i	−0.139505	−	0.429353i	0.856758	−	0.515718i	$-0.172475\pi$
$547$	−3.26275	−	10.0417i	−0.139505	−	0.429353i	−0.996264	+	0.0863653i	$0.972475\pi$
$548$		0			0
$549$	4.68413	−	8.11315i	0.199914	−	0.346261i
$550$		0			0
$551$		−	0.146968i		−	0.00626104i
$552$		0			0
$553$	3.61083	+	3.25120i	0.153548	+	0.138255i
$554$		0			0
$555$	5.41736	−	51.5427i	0.229954	−	2.18787i
$556$		0			0
$557$	24.1000	−	21.6997i	1.02115	−	0.919447i	0.0243749	−	0.999703i	$-0.492240\pi$
$557$	24.1000	−	21.6997i	1.02115	−	0.919447i	0.996774	+	0.0802560i	$0.0255738\pi$
$558$		0			0
$559$	10.6852	+	6.95910i	0.451937	+	0.294339i
$560$		0			0
$561$	1.49442	+	45.2874i	0.0630943	+	1.91203i
$562$		0			0
$563$	−9.12317	−	4.06190i	−0.384496	−	0.171189i	0.205380	−	0.978682i	$-0.434157\pi$
$563$	−9.12317	−	4.06190i	−0.384496	−	0.171189i	−0.589876	+	0.807494i	$0.700824\pi$
$564$		0			0
$565$	−9.00038	−	42.3435i	−0.378649	−	1.78140i
$566$		0			0
$567$	−31.6759	+	43.5982i	−1.33026	+	1.83095i
$568$		0			0
$569$	−11.9900	−	2.54855i	−0.502646	−	0.106841i	−0.0503915	−	0.998730i	$-0.516047\pi$
$569$	−11.9900	−	2.54855i	−0.502646	−	0.106841i	−0.452255	+	0.891889i	$0.649380\pi$
$570$		0			0
$571$	−14.0331			−0.587267			−0.293633	−	0.955918i	$-0.594864\pi$
$571$	−14.0331			−0.587267			−0.293633	+	0.955918i	$0.594864\pi$
$572$		0			0
$573$	−27.0655			−1.13068
$574$		0			0
$575$	8.69080	+	1.84729i	0.362431	+	0.0770372i
$576$		0			0
$577$	−16.5965	+	22.8432i	−0.690923	+	0.950974i	−1.00000		6.30452e-5i	$-0.999980\pi$
$577$	−16.5965	+	22.8432i	−0.690923	+	0.950974i	0.309077	+	0.951037i	$0.399980\pi$
$578$		0			0
$579$	1.84658	+	8.68746i	0.0767411	+	0.361039i
$580$		0			0
$581$	−14.3989	−	6.41079i	−0.597366	−	0.265964i
$582$		0			0
$583$	10.8715	−	16.0512i	0.450253	−	0.664771i
$584$		0			0
$585$	14.6659	−	22.5185i	0.606360	−	0.931024i
$586$		0			0
$587$	−28.1053	+	25.3061i	−1.16003	+	1.04450i	−0.161694	+	0.986841i	$0.551696\pi$
$587$	−28.1053	+	25.3061i	−1.16003	+	1.04450i	−0.998337	+	0.0576551i	$0.981638\pi$
$588$		0			0
$589$	0.0245135	−	0.233230i	0.00101006	−	0.00961008i
$590$		0			0
$591$	−0.662381	−	0.596410i	−0.0272467	−	0.0245330i
$592$		0			0
$593$		−	20.0291i		−	0.822498i	−0.911523	−	0.411249i	$-0.865093\pi$
$593$		−	20.0291i		−	0.822498i	0.911523	−	0.411249i	$-0.134907\pi$
$594$		0			0
$595$	61.0491	−	105.740i	2.50277	−	4.33493i
$596$		0			0
$597$	17.1361	+	52.7393i	0.701332	+	2.15848i
$598$		0			0
$599$	27.8739	+	20.2516i	1.13890	+	0.827458i	0.986965	−	0.160933i	$-0.0514504\pi$
$599$	27.8739	+	20.2516i	1.13890	+	0.827458i	0.151932	+	0.988391i	$0.451450\pi$
$600$		0			0
$601$	−6.24722	−	6.93824i	−0.254829	−	0.283017i	0.602133	−	0.798396i	$-0.294318\pi$
$601$	−6.24722	−	6.93824i	−0.254829	−	0.283017i	−0.856962	+	0.515379i	$0.827651\pi$
$602$		0			0
$603$	−7.05546	−	9.71100i	−0.287320	−	0.395463i
$604$		0			0
$605$	−2.94527	−	44.5787i	−0.119742	−	1.81238i
$606$		0			0
$607$	−29.5192	−	13.1428i	−1.19815	−	0.533449i	−0.292002	−	0.956418i	$-0.594321\pi$
$607$	−29.5192	−	13.1428i	−1.19815	−	0.533449i	−0.906144	+	0.422968i	$0.860988\pi$
$608$		0			0
$609$	16.1597	−	14.5503i	0.654826	−	0.589608i
$610$		0			0
$611$	26.1186	−	26.0499i	1.05665	−	1.05387i
$612$		0			0
$613$	−5.21891	+	24.5530i	−0.210790	+	0.991688i	0.737761	+	0.675062i	$0.235883\pi$
$613$	−5.21891	+	24.5530i	−0.210790	+	0.991688i	−0.948551	+	0.316626i	$0.897450\pi$
$614$		0			0
$615$	28.6276	+	49.5845i	1.15438	+	1.99944i
$616$		0			0
$617$	20.4703	−	11.8185i	0.824104	−	0.475796i	−0.0277259	−	0.999616i	$-0.508827\pi$
$617$	20.4703	−	11.8185i	0.824104	−	0.475796i	0.851830	+	0.523819i	$0.175493\pi$
$618$		0			0
$619$	−10.1030	+	3.28267i	−0.406075	+	0.131942i	−0.504930	−	0.863160i	$-0.668482\pi$
$619$	−10.1030	+	3.28267i	−0.406075	+	0.131942i	0.0988557	+	0.995102i	$0.468482\pi$
$620$		0			0
$621$	−1.80861	+	0.805244i	−0.0725769	+	0.0323133i
$622$		0			0
$623$	0.601584	−	1.85149i	0.0241020	−	0.0741782i
$624$		0			0
$625$	−40.1811	+	29.1933i	−1.60724	+	1.16773i
$626$		0			0
$627$	0.434202	+	0.294087i	0.0173404	+	0.0117447i
$628$		0			0
$629$	−21.1934	−	29.1702i	−0.845035	−	1.16309i
$630$		0			0
$631$	5.64427	+	26.5542i	0.224695	+	1.05711i	0.935393	+	0.353609i	$0.115046\pi$
$631$	5.64427	+	26.5542i	0.224695	+	1.05711i	−0.710698	+	0.703497i	$0.751621\pi$
$632$		0			0
$633$	2.60898	−	24.8228i	0.103698	−	0.986617i
$634$		0			0
$635$	11.4682	−	53.9538i	0.455103	−	2.14109i
$636$		0			0
$637$	−37.2993	+	45.9369i	−1.47785	+	1.82008i
$638$		0			0
$639$	5.30973	+	3.06557i	0.210050	+	0.121272i
$640$		0			0
$641$	3.66734	−	4.07299i	0.144851	−	0.160873i	−0.666353	−	0.745636i	$-0.732146\pi$
$641$	3.66734	−	4.07299i	0.144851	−	0.160873i	0.811204	+	0.584763i	$0.198812\pi$
$642$		0			0
$643$	40.9445	+	4.30344i	1.61469	+	0.169711i	0.868385	−	0.495891i	$-0.165158\pi$
$643$	40.9445	+	4.30344i	1.61469	+	0.169711i	0.746307	+	0.665602i	$0.231825\pi$
$644$		0			0
$645$	−30.0389	−	9.76023i	−1.18278	−	0.384309i
$646$		0			0
$647$	0.603505	+	5.74196i	0.0237262	+	0.225740i	0.999959	+	0.00901683i	$0.00287019\pi$
$647$	0.603505	+	5.74196i	0.0237262	+	0.225740i	−0.976233	+	0.216723i	$0.930463\pi$
$648$		0			0
$649$	9.00655	+	14.4753i	0.353538	+	0.568204i
$650$		0			0
$651$	28.0716	−	20.3952i	1.10021	−	0.799351i
$652$		0			0
$653$	19.0057	+	21.1079i	0.743750	+	0.826018i	0.989684	−	0.143269i	$-0.0457614\pi$
$653$	19.0057	+	21.1079i	0.743750	+	0.826018i	−0.245934	+	0.969287i	$0.579095\pi$
$654$		0			0
$655$	−0.505133	+	0.695256i	−0.0197372	+	0.0271659i
$656$		0			0
$657$	6.78267	+	6.10715i	0.264617	+	0.238262i
$658$		0			0
$659$	7.38570	+	12.7924i	0.287706	+	0.498321i	0.973262	−	0.229699i	$-0.0737741\pi$
$659$	7.38570	+	12.7924i	0.287706	+	0.498321i	−0.685556	+	0.728020i	$0.740441\pi$
$660$		0			0
$661$	−35.5781	−	20.5411i	−1.38383	−	0.798954i	−0.391219	−	0.920298i	$-0.627946\pi$
$661$	−35.5781	−	20.5411i	−1.38383	−	0.798954i	−0.992611	+	0.121343i	$0.961280\pi$
$662$		0			0
$663$	−7.64176	−	48.6630i	−0.296781	−	1.88991i
$664$		0			0
$665$	−0.574765	−	1.29094i	−0.0222884	−	0.0500607i
$666$		0			0
$667$	1.54518	−	0.328438i	0.0598295	−	0.0127172i
$668$		0			0
$669$	10.6158	−	23.8436i	0.410432	−	0.921846i
$670$		0			0
$671$	4.06448	+	16.4361i	0.156908	+	0.634509i
$672$		0			0
$673$	−0.0838285	−	0.797575i	−0.00323135	−	0.0307442i	0.992787	−	0.119888i	$-0.0382536\pi$
$673$	−0.0838285	−	0.797575i	−0.00323135	−	0.0307442i	−0.996019	+	0.0891439i	$0.971587\pi$
$674$		0			0
$675$	9.09885	−	28.0034i	0.350215	−	1.07785i
$676$		0			0
$677$	28.2633	+	20.5345i	1.08625	+	0.789205i	0.978762	−	0.205002i	$-0.0657201\pi$
$677$	28.2633	+	20.5345i	1.08625	+	0.789205i	0.107485	+	0.994207i	$0.465720\pi$
$678$		0			0
$679$	−57.5893	−	12.2410i	−2.21007	−	0.469766i
$680$		0			0
$681$			46.5294i			1.78301i
$682$		0			0
$683$	−38.9355	+	22.4794i	−1.48982	+	0.860151i	−0.999932	−	0.0116322i	$-0.996297\pi$
$683$	−38.9355	+	22.4794i	−1.48982	+	0.860151i	−0.489892	+	0.871783i	$0.662964\pi$
$684$		0			0
$685$	−24.1150	+	26.7824i	−0.921386	+	1.02330i
$686$		0			0
$687$	7.72674	+	17.3545i	0.294793	+	0.662117i
$688$		0			0
$689$	−9.59266	+	18.7655i	−0.365451	+	0.714908i
$690$		0			0
$691$	−23.4511	+	2.46481i	−0.892122	+	0.0937658i	−0.539486	−	0.841995i	$-0.681381\pi$
$691$	−23.4511	+	2.46481i	−0.892122	+	0.0937658i	−0.352636	+	0.935761i	$0.614715\pi$
$692$		0			0
$693$	4.04259	+	29.1708i	0.153565	+	1.10811i
$694$		0			0
$695$	−19.6811	+	44.2045i	−0.746547	+	1.67677i
$696$		0			0
$697$	37.8835	+	12.3091i	1.43494	+	0.466240i
$698$		0			0
$699$	−43.5730	+	19.4000i	−1.64808	+	0.733774i
$700$		0			0
$701$	9.92155	+	30.5354i	0.374732	+	1.15331i	0.943659	+	0.330918i	$0.107358\pi$
$701$	9.92155	+	30.5354i	0.374732	+	1.15331i	−0.568928	+	0.822388i	$0.692642\pi$
$702$		0			0
$703$	−0.417300			−0.0157388
$704$		0			0
$705$	−45.6854	+	79.1294i	−1.72061	+	2.98018i
$706$		0			0
$707$	81.0508	−	26.3350i	3.04823	−	0.990430i
$708$		0			0
$709$	0.0928561	+	0.00975957i	0.00348729	+	0.000366528i	0.106272	−	0.994337i	$-0.466109\pi$
$709$	0.0928561	+	0.00975957i	0.00348729	+	0.000366528i	−0.102785	+	0.994704i	$0.532775\pi$
$710$		0			0
$711$	−1.80256	+	0.383145i	−0.0676011	+	0.0143691i
$712$		0			0
$713$	2.50690	−	0.263486i	0.0938841	−	0.00986761i
$714$		0			0
$715$	9.11278	+	47.7053i	0.340799	+	1.78408i
$716$		0			0
$717$	−65.0413	+	6.83611i	−2.42901	+	0.255299i
$718$		0			0
$719$	−12.9942	+	2.76200i	−0.484602	+	0.103005i	−0.443733	−	0.896159i	$-0.646346\pi$
$719$	−12.9942	+	2.76200i	−0.484602	+	0.103005i	−0.0408690	+	0.999165i	$0.513013\pi$
$720$		0			0
$721$	68.5505	+	7.20495i	2.55296	+	0.268326i
$722$		0			0
$723$	−11.9752	+	3.89098i	−0.445363	+	0.144707i
$724$		0			0
$725$	−11.7472	+	20.3467i	−0.436280	+	0.755659i
$726$		0			0
$727$	−30.0180			−1.11331			−0.556653	−	0.830745i	$-0.687915\pi$
$727$	−30.0180			−1.11331			−0.556653	+	0.830745i	$0.687915\pi$
$728$		0			0
$729$	−1.09461	−	3.36885i	−0.0405410	−	0.124772i
$730$		0			0
$731$	−20.0741	+	8.93756i	−0.742467	+	0.330568i
$732$		0			0
$733$	−4.95698	−	1.61062i	−0.183090	−	0.0594896i	0.216037	−	0.976385i	$-0.430687\pi$
$733$	−4.95698	−	1.61062i	−0.183090	−	0.0594896i	−0.399127	+	0.916896i	$0.630687\pi$
$734$		0			0
$735$	59.6141	−	133.896i	2.19890	−	4.93881i
$736$		0			0
$737$	21.3570	+	3.80810i	0.786694	+	0.140273i
$738$		0			0
$739$	−13.7053	+	1.44049i	−0.504159	+	0.0529892i	−0.353194	−	0.935550i	$-0.614905\pi$
$739$	−13.7053	+	1.44049i	−0.504159	+	0.0529892i	−0.150965	+	0.988539i	$0.548238\pi$
$740$		0			0
$741$	−0.507628	−	0.259492i	−0.0186482	−	0.00953269i
$742$		0			0
$743$	−5.96351	−	13.3943i	−0.218780	−	0.491388i	0.770496	−	0.637444i	$-0.220008\pi$
$743$	−5.96351	−	13.3943i	−0.218780	−	0.491388i	−0.989276	+	0.146057i	$0.953342\pi$
$744$		0			0
$745$	19.0509	−	21.1581i	0.697970	−	0.775174i
$746$		0			0
$747$	5.17702	−	2.98896i	0.189417	−	0.109360i
$748$		0			0
$749$		−	20.4096i		−	0.745751i
$750$		0			0
$751$	−36.4372	−	7.74497i	−1.32961	−	0.282618i	−0.512297	−	0.858808i	$-0.671205\pi$
$751$	−36.4372	−	7.74497i	−1.32961	−	0.282618i	−0.817316	+	0.576190i	$0.804539\pi$
$752$		0			0
$753$	−18.4761	−	13.4237i	−0.673306	−	0.489186i
$754$		0			0
$755$	−0.502953	+	1.54793i	−0.0183043	+	0.0563349i
$756$		0			0
$757$	1.10773	+	10.5393i	0.0402611	+	0.383059i	0.996035	+	0.0889576i	$0.0283536\pi$
$757$	1.10773	+	10.5393i	0.0402611	+	0.383059i	−0.955774	+	0.294101i	$0.904980\pi$
$758$		0			0
$759$	−2.12162	+	5.22229i	−0.0770098	+	0.189557i
$760$		0			0
$761$	−10.2080	+	22.9276i	−0.370041	+	0.831126i	0.628535	+	0.777781i	$0.283655\pi$
$761$	−10.2080	+	22.9276i	−0.370041	+	0.831126i	−0.998576	+	0.0533447i	$0.983012\pi$
$762$		0			0
$763$	−67.0276	+	14.2472i	−2.42656	+	0.515782i
$764$		0			0
$765$	18.8354	+	42.3049i	0.680994	+	1.52954i
$766$		0			0
$767$	−11.6446	−	14.4187i	−0.420463	−	0.520630i
$768$		0			0
$769$	−14.1129	−	8.14809i	−0.508924	−	0.293828i	0.223467	−	0.974711i	$-0.428262\pi$
$769$	−14.1129	−	8.14809i	−0.508924	−	0.293828i	−0.732391	+	0.680884i	$0.761596\pi$
$770$		0			0
$771$	−12.4823	−	21.6200i	−0.449540	−	0.778626i
$772$		0			0
$773$	0.935947	+	0.842730i	0.0336637	+	0.0303109i	0.685791	−	0.727799i	$-0.259457\pi$
$773$	0.935947	+	0.842730i	0.0336637	+	0.0303109i	−0.652127	+	0.758110i	$0.726123\pi$
$774$		0			0
$775$	−22.0359	+	30.3298i	−0.791553	+	1.08948i
$776$		0			0
$777$	−41.3141	−	45.8840i	−1.48214	−	1.64608i
$778$		0			0
$779$	0.372966	−	0.270976i	0.0133629	−	0.00970870i
$780$		0			0
$781$	−10.7568	+	2.66004i	−0.384908	+	0.0951837i
$782$		0			0
$783$	−0.547214	−	5.20640i	−0.0195558	−	0.186061i
$784$		0			0
$785$	−55.1505	−	17.9195i	−1.96840	−	0.639573i
$786$		0			0
$787$	45.3089	+	4.76216i	1.61509	+	0.169753i	0.868555	−	0.495593i	$-0.165049\pi$
$787$	45.3089	+	4.76216i	1.61509	+	0.169753i	0.746535	+	0.665346i	$0.231716\pi$
$788$		0			0
$789$	−8.67889	+	9.63888i	−0.308977	+	0.343153i
$790$		0			0
$791$	−44.6629	−	25.7862i	−1.58803	−	0.916850i
$792$		0			0
$793$	−6.57354	−	17.1923i	−0.233433	−	0.610517i
$794$		0			0
$795$	10.8533	−	51.0610i	0.384928	−	1.81095i
$796$		0			0
$797$	1.20280	−	11.4439i	0.0426055	−	0.405364i	−0.952347	−	0.305017i	$-0.901338\pi$
$797$	1.20280	−	11.4439i	0.0426055	−	0.405364i	0.994952	−	0.100348i	$-0.0319955\pi$
$798$		0			0
$799$	13.2164	+	62.1784i	0.467563	+	2.19971i
$800$		0			0
$801$	0.433994	+	0.597342i	0.0153344	+	0.0211060i
$802$		0			0
$803$	−16.4862	+	0.544020i	−0.581785	+	0.0191980i
$804$		0			0
$805$	12.2882	−	8.92787i	0.433101	−	0.314666i
$806$		0			0
$807$	12.3506	−	38.0114i	0.434763	−	1.33806i
$808$		0			0
$809$	−3.46656	+	1.54341i	−0.121878	+	0.0542635i	−0.466770	−	0.884379i	$-0.654582\pi$
$809$	−3.46656	+	1.54341i	−0.121878	+	0.0542635i	0.344892	+	0.938642i	$0.387916\pi$
$810$		0			0
$811$	−15.9265	+	5.17482i	−0.559253	+	0.181712i	−0.574985	−	0.818164i	$-0.694992\pi$
$811$	−15.9265	+	5.17482i	−0.559253	+	0.181712i	0.0157318	+	0.999876i	$0.494992\pi$
$812$		0			0
$813$	−37.9671	+	21.9203i	−1.33157	+	0.768780i
$814$		0			0
$815$	21.3922	+	37.0523i	0.749335	+	1.29789i
$816$		0			0
$817$	−0.0528752	+	0.248758i	−0.00184987	+	0.00870296i
$818$		0			0
$819$	−8.24536	−	30.9351i	−0.288116	−	1.08096i
$820$		0			0
$821$	3.44251	−	3.09965i	0.120144	−	0.108179i	−0.606869	−	0.794802i	$-0.707575\pi$
$821$	3.44251	−	3.09965i	0.120144	−	0.108179i	0.727013	+	0.686624i	$0.240908\pi$
$822$		0			0
$823$	46.5294	+	20.7162i	1.62191	+	0.722121i	0.998225	−	0.0595535i	$-0.0189677\pi$
$823$	46.5294	+	20.7162i	1.62191	+	0.722121i	0.623686	+	0.781675i	$0.285634\pi$
$824$		0			0
$825$	−36.6059	−	75.4204i	−1.27445	−	2.62580i
$826$		0			0
$827$	8.91158	+	12.2657i	0.309886	+	0.426522i	0.935346	−	0.353735i	$-0.115088\pi$
$827$	8.91158	+	12.2657i	0.309886	+	0.426522i	−0.625460	+	0.780257i	$0.715088\pi$
$828$		0			0
$829$	−5.64330	−	6.26752i	−0.196000	−	0.217680i	0.637131	−	0.770755i	$-0.280121\pi$
$829$	−5.64330	−	6.26752i	−0.196000	−	0.217680i	−0.833131	+	0.553075i	$0.813454\pi$
$830$		0			0
$831$	−24.6640	−	17.9195i	−0.855586	−	0.621620i
$832$		0			0
$833$	−31.5099	−	96.9774i	−1.09175	−	3.36007i
$834$		0			0
$835$	21.1657	−	36.6600i	0.732468	−	1.26867i
$836$		0			0
$837$		−	8.35355i		−	0.288741i
$838$		0			0
$839$	−9.95343	−	8.96211i	−0.343631	−	0.309406i	0.479186	−	0.877713i	$-0.340932\pi$
$839$	−9.95343	−	8.96211i	−0.343631	−	0.309406i	−0.822817	+	0.568307i	$0.807599\pi$
$840$		0			0
$841$	2.59469	−	24.6868i	0.0894721	−	0.851270i
$842$		0			0
$843$	0.983706	−	0.885733i	0.0338806	−	0.0305063i
$844$		0			0
$845$	−16.1834	−	50.2575i	−0.556725	−	1.72891i
$846$		0			0
$847$	−41.8150	−	32.9288i	−1.43678	−	1.13145i
$848$		0			0
$849$	7.47817	+	3.32950i	0.256650	+	0.114268i
$850$		0			0
$851$	−0.932566	−	4.38738i	−0.0319680	−	0.150397i
$852$		0			0
$853$	−6.61382	+	9.10315i	−0.226453	+	0.311686i	−0.907091	−	0.420934i	$-0.861702\pi$
$853$	−6.61382	+	9.10315i	−0.226453	+	0.311686i	0.680638	+	0.732620i	$0.261702\pi$
$854$		0			0
$855$	0.524243	+	0.111431i	0.0179287	+	0.00381087i
$856$		0			0
$857$	45.4664			1.55310			0.776552	−	0.630053i	$-0.216967\pi$
$857$	45.4664			1.55310			0.776552	+	0.630053i	$0.216967\pi$
$858$		0			0
$859$	38.8275			1.32478			0.662388	−	0.749161i	$-0.269543\pi$
$859$	38.8275			1.32478			0.662388	+	0.749161i	$0.269543\pi$
$860$		0			0
$861$	66.7198	+	14.1817i	2.27380	+	0.483312i
$862$		0			0
$863$	−13.1956	+	18.1622i	−0.449184	+	0.618248i	−0.972222	−	0.234061i	$-0.924798\pi$
$863$	−13.1956	+	18.1622i	−0.449184	+	0.618248i	0.523038	+	0.852309i	$0.324798\pi$
$864$		0			0
$865$	5.10886	+	24.0353i	0.173706	+	0.817224i
$866$		0			0
$867$	43.3968	+	19.3215i	1.47383	+	0.656192i
$868$		0			0
$869$	1.86771	−	2.75756i	0.0633577	−	0.0935437i
$870$		0			0
$871$	−23.5497	−	1.26530i	−0.797951	−	0.0428731i
$872$		0			0
$873$	16.5944	−	14.9417i	0.561636	−	0.505700i
$874$		0			0
$875$	−13.3424	+	126.945i	−0.451056	+	4.29151i
$876$		0			0
$877$	27.3727	+	24.6465i	0.924312	+	0.832254i	0.986154	−	0.165832i	$-0.0530308\pi$
$877$	27.3727	+	24.6465i	0.924312	+	0.832254i	−0.0618421	+	0.998086i	$0.519698\pi$
$878$		0			0
$879$		−	60.7014i		−	2.04741i
$880$		0			0
$881$	5.11752	−	8.86380i	0.172414	−	0.298629i	−0.766850	−	0.641827i	$-0.778177\pi$
$881$	5.11752	−	8.86380i	0.172414	−	0.298629i	0.939263	+	0.343198i	$0.111510\pi$
$882$		0			0
$883$	−4.84048	−	14.8975i	−0.162895	−	0.501339i	0.835980	−	0.548760i	$-0.184900\pi$
$883$	−4.84048	−	14.8975i	−0.162895	−	0.501339i	−0.998875	+	0.0474207i	$0.984900\pi$
$884$		0			0
$885$	37.1392	+	26.9832i	1.24842	+	0.907031i
$886$		0			0
$887$	−7.86879	−	8.73917i	−0.264208	−	0.293433i	0.596414	−	0.802677i	$-0.296592\pi$
$887$	−7.86879	−	8.73917i	−0.264208	−	0.293433i	−0.860622	+	0.509244i	$0.829925\pi$
$888$		0			0
$889$	−38.6252	−	53.1631i	−1.29545	−	1.78303i
$890$		0			0
$891$	32.5823	+	17.4047i	1.09155	+	0.583078i
$892$		0			0
$893$	0.672098	+	0.299238i	0.0224909	+	0.0100136i
$894$		0			0
$895$	−30.1121	+	27.1130i	−1.00654	+	0.906289i
$896$		0			0
$897$	1.59380	−	5.91696i	0.0532155	−	0.197562i
$898$		0			0
$899$	−1.38583	+	6.51982i	−0.0462200	+	0.217448i
$900$		0			0
$901$	−18.1586	−	31.4516i	−0.604951	−	1.04781i
$902$		0			0
$903$	−32.5869	+	18.8141i	−1.08442	+	0.626093i
$904$		0			0
$905$	−77.2021	+	25.0845i	−2.56628	+	0.833836i
$906$		0			0
$907$	13.2666	−	5.90668i	0.440511	−	0.196128i	−0.174483	−	0.984660i	$-0.555825\pi$
$907$	13.2666	−	5.90668i	0.440511	−	0.196128i	0.614994	+	0.788532i	$0.289159\pi$
$908$		0			0
$909$	−9.98814	+	30.7403i	−0.331286	+	1.01959i
$910$		0			0
$911$	17.1221	−	12.4400i	0.567282	−	0.412154i	−0.266835	−	0.963742i	$-0.585978\pi$
$911$	17.1221	−	12.4400i	0.567282	−	0.412154i	0.834117	+	0.551588i	$0.185978\pi$
$912$		0			0
$913$	−2.99788	+	10.3796i	−0.0992154	+	0.343515i
$914$		0			0
$915$	26.7976	+	36.8837i	0.885901	+	1.21934i
$916$		0			0
$917$	0.212863	+	1.00144i	0.00702936	+	0.0330706i
$918$		0			0
$919$	2.44429	−	23.2559i	0.0806297	−	0.767140i	−0.877262	−	0.480011i	$-0.840632\pi$
$919$	2.44429	−	23.2559i	0.0806297	−	0.767140i	0.957892	−	0.287129i	$-0.0927008\pi$
$920$		0			0
$921$	1.89301	−	8.90593i	0.0623769	−	0.293460i
$922$		0			0
$923$	11.2517	−	4.30211i	0.370353	−	0.141606i
$924$		0			0
$925$	57.7725	+	33.3550i	1.89955	+	1.09671i
$926$		0			0
$927$	−17.4928	+	19.4277i	−0.574538	+	0.638089i
$928$		0			0
$929$	−18.4915	−	1.94354i	−0.606687	−	0.0637654i	−0.203796	−	0.979013i	$-0.565328\pi$
$929$	−18.4915	−	1.94354i	−0.606687	−	0.0637654i	−0.402891	+	0.915248i	$0.631995\pi$
$930$		0			0
$931$	−1.12238	−	0.364682i	−0.0367844	−	0.0119520i
$932$		0			0
$933$	4.05171	+	38.5494i	0.132647	+	1.26205i
$934$		0			0
$935$	−77.5387	−	31.5010i	−2.53579	−	1.03019i
$936$		0			0
$937$	41.8649	−	30.4167i	1.36767	−	0.993669i	0.369753	−	0.929130i	$-0.379442\pi$
$937$	41.8649	−	30.4167i	1.36767	−	0.993669i	0.997915	−	0.0645389i	$-0.0205577\pi$
$938$		0			0
$939$	−41.9365	−	46.5752i	−1.36855	−	1.51992i
$940$		0			0
$941$	−23.2125	+	31.9493i	−0.756707	+	1.04152i	0.240774	+	0.970581i	$0.422599\pi$
$941$	−23.2125	+	31.9493i	−0.756707	+	1.04152i	−0.997481	+	0.0709362i	$0.977401\pi$
$942$		0			0
$943$	3.68245	+	3.31569i	0.119917	+	0.107974i
$944$		0			0
$945$	−25.1680	−	43.5922i	−0.818714	−	1.41805i
$946$		0			0
$947$	−29.3350	−	16.9366i	−0.953259	−	0.550364i	−0.0591672	−	0.998248i	$-0.518845\pi$
$947$	−29.3350	−	16.9366i	−0.953259	−	0.550364i	−0.894092	+	0.447884i	$0.852178\pi$
$948$		0			0
$949$	17.7150	−	2.78187i	0.575055	−	0.0903033i
$950$		0			0
$951$	21.6387	+	48.6014i	0.701684	+	1.57601i
$952$		0			0
$953$	2.21669	−	0.471171i	0.0718055	−	0.0152627i	−0.171869	−	0.985120i	$-0.554981\pi$
$953$	2.21669	−	0.471171i	0.0718055	−	0.0152627i	0.243674	+	0.969857i	$0.421647\pi$
$954$		0			0
$955$	20.3332	−	45.6691i	0.657967	−	1.47782i
$956$		0			0
$957$	−11.3997	−	9.60287i	−0.368501	−	0.310417i
$958$		0			0
$959$	4.48792	+	42.6997i	0.144922	+	1.37885i
$960$		0			0
$961$	6.29282	−	19.3673i	0.202994	−	0.624751i
$962$		0			0
$963$	6.26244	+	4.54993i	0.201804	+	0.146619i
$964$		0			0
$965$	−16.0461	−	3.41071i	−0.516543	−	0.109795i
$966$		0			0
$967$		−	55.2810i		−	1.77772i	−0.458181	−	0.888859i	$-0.651499\pi$
$967$		−	55.2810i		−	1.77772i	0.458181	−	0.888859i	$-0.348501\pi$
$968$		0			0
$969$	0.850802	−	0.491211i	0.0273317	−	0.0157800i
$970$		0			0
$971$	10.5554	−	11.7230i	0.338740	−	0.376208i	−0.549575	−	0.835445i	$-0.685210\pi$
$971$	10.5554	−	11.7230i	0.338740	−	0.376208i	0.888314	+	0.459236i	$0.151877\pi$
$972$		0			0
$973$	23.4468	+	52.6624i	0.751671	+	1.68828i
$974$		0			0
$975$	49.5365	+	76.4999i	1.58644	+	2.44996i
$976$		0			0
$977$	31.9738	−	3.36058i	1.02293	−	0.107515i	0.421821	−	0.906679i	$-0.361391\pi$
$977$	31.9738	−	3.36058i	1.02293	−	0.107515i	0.601112	+	0.799165i	$0.294724\pi$
$978$		0			0
$979$	−1.31371	−	0.234244i	−0.0419862	−	0.00748646i
$980$		0			0
$981$	10.5710	−	23.7428i	0.337505	−	0.758048i
$982$		0			0
$983$	32.9726	+	10.7135i	1.05166	+	0.341706i	0.783321	−	0.621617i	$-0.213524\pi$
$983$	32.9726	+	10.7135i	1.05166	+	0.341706i	0.268342	+	0.963324i	$0.413524\pi$
$984$		0			0
$985$	1.50398	−	0.669614i	0.0479207	−	0.0213357i
$986$		0			0
$987$	33.6375	+	103.526i	1.07069	+	3.29526i
$988$		0			0
$989$	−2.73354			−0.0869215
$990$		0			0
$991$	−1.30957	+	2.26825i	−0.0416000	+	0.0720533i	−0.886076	−	0.463541i	$-0.846579\pi$
$991$	−1.30957	+	2.26825i	−0.0416000	+	0.0720533i	0.844476	+	0.535594i	$0.179912\pi$
$992$		0			0
$993$	−7.04127	+	2.28785i	−0.223448	+	0.0726027i
$994$		0			0
$995$	−101.864	−	10.7063i	−3.22930	−	0.339413i
$996$		0			0
$997$	56.2813	−	11.9630i	1.78245	−	0.378871i	0.805540	−	0.592541i	$-0.201875\pi$
$997$	56.2813	−	11.9630i	1.78245	−	0.378871i	0.976906	+	0.213670i	$0.0685418\pi$
$998$		0			0
$999$	−14.7830	+	1.55376i	−0.467715	+	0.0491588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bq.a.69.3	✓	112
11.4	even	5	inner	572.2.bq.a.433.12	yes	112
13.10	even	6	inner	572.2.bq.a.465.12	yes	112
143.114	even	30	inner	572.2.bq.a.257.3	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bq.a.69.3	✓	112	1.1	even	1	trivial
572.2.bq.a.257.3	yes	112	143.114	even	30	inner
572.2.bq.a.433.12	yes	112	11.4	even	5	inner
572.2.bq.a.465.12	yes	112	13.10	even	6	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bq (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.15084 - 0.457176i) q^{3} +(2.38726 - 3.28578i) q^{5} +(-1.00599 - 4.73282i) q^{7} +(1.67648 + 0.746415i) q^{9} +O(q^{10})\)	\(q+(-2.15084 - 0.457176i) q^{3} +(2.38726 - 3.28578i) q^{5} +(-1.00599 - 4.73282i) q^{7} +(1.67648 + 0.746415i) q^{9} +(-3.11878 + 1.12837i) q^{11} +(3.21472 - 1.63265i) q^{13} +(-6.63680 + 5.97580i) q^{15} +(-0.649453 + 6.17913i) q^{17} +(0.0534385 + 0.0481162i) q^{19} +10.6395i q^{21} +(-0.386458 + 0.669366i) q^{23} +(-3.55226 - 10.9327i) q^{25} +(2.07224 + 1.50557i) q^{27} +(-1.36758 - 1.51885i) q^{29} +(-1.91694 - 2.63844i) q^{31} +(7.22386 - 1.00111i) q^{33} +(-17.9526 - 7.99300i) q^{35} +(-4.31262 + 3.88310i) q^{37} +(-7.66077 + 2.04188i) q^{39} +(1.33294 - 6.27097i) q^{41} +(1.76833 + 3.06283i) q^{43} +(6.45474 - 3.72664i) q^{45} +(9.73035 - 3.16158i) q^{47} +(-14.9927 + 6.67520i) q^{49} +(4.22182 - 12.9934i) q^{51} +(-4.72887 + 3.43572i) q^{53} +(-3.73777 + 12.9413i) q^{55} +(-0.0929402 - 0.127921i) q^{57} +(-1.06873 - 5.02799i) q^{59} +(0.533613 - 5.07699i) q^{61} +(1.84613 - 8.68534i) q^{63} +(2.30984 - 14.4604i) q^{65} +(-5.66461 - 3.27046i) q^{67} +(1.13723 - 1.26302i) q^{69} +(3.32268 + 0.349228i) q^{71} +(4.73006 + 1.53689i) q^{73} +(2.64217 + 25.1386i) q^{75} +(8.47782 + 13.6255i) q^{77} +(-0.812410 + 0.590250i) q^{79} +(-7.45257 - 8.27691i) q^{81} +(1.91470 - 2.63536i) q^{83} +(18.7529 + 16.8851i) q^{85} +(2.24706 + 3.89203i) q^{87} +(0.348441 + 0.201172i) q^{89} +(-10.9610 - 13.5723i) q^{91} +(2.91680 + 6.55125i) q^{93} +(0.285671 - 0.0607212i) q^{95} +(4.94920 - 11.1161i) q^{97} +(-6.07079 - 0.436226i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 20 q^{9}+O(q^{10}) \) 112 * q + 20 * q^9	\( 112 q + 20 q^{9} - 6 q^{11} + 11 q^{13} + 30 q^{15} + 16 q^{17} - 12 q^{19} + 6 q^{23} + 40 q^{25} - 12 q^{27} - 5 q^{29} + 9 q^{33} - 33 q^{35} - 45 q^{39} - 18 q^{41} + 30 q^{45} - 16 q^{49} + 48 q^{51} - 2 q^{53} - 20 q^{55} - 39 q^{59} + 4 q^{61} - 102 q^{63} - 6 q^{65} + 48 q^{67} + 34 q^{69} + 84 q^{71} - 56 q^{75} - 22 q^{77} - 24 q^{79} + 16 q^{81} + 60 q^{85} - 34 q^{87} - 66 q^{89} - 41 q^{91} + 123 q^{93} + 12 q^{95} - 15 q^{97}+O(q^{100}) \) 112 * q + 20 * q^9 - 6 * q^11 + 11 * q^13 + 30 * q^15 + 16 * q^17 - 12 * q^19 + 6 * q^23 + 40 * q^25 - 12 * q^27 - 5 * q^29 + 9 * q^33 - 33 * q^35 - 45 * q^39 - 18 * q^41 + 30 * q^45 - 16 * q^49 + 48 * q^51 - 2 * q^53 - 20 * q^55 - 39 * q^59 + 4 * q^61 - 102 * q^63 - 6 * q^65 + 48 * q^67 + 34 * q^69 + 84 * q^71 - 56 * q^75 - 22 * q^77 - 24 * q^79 + 16 * q^81 + 60 * q^85 - 34 * q^87 - 66 * q^89 - 41 * q^91 + 123 * q^93 + 12 * q^95 - 15 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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