LMFDB - Embedded newform 1176.2.u.c.521.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1176,2,Mod(521,1176)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1176, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("1176.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1176 = 2^{3} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1176.u (of order $6$, degree $2$, not 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:	$9.39040727770$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.12
Character	$\chi$	$=$	1176.521
Dual form			1176.2.u.c.1097.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0211468 - 1.73192i) q^{3} +(0.496051 + 0.859186i) q^{5} +(-2.99911 + 0.0732492i) q^{9} +(2.17245 + 1.25426i) q^{11} +6.74633i q^{13} +(1.47755 - 0.877291i) q^{15} +(-1.87831 + 3.25333i) q^{17} +(-2.31260 + 1.33518i) q^{19} +(-1.51332 + 0.873715i) q^{23} +(2.00787 - 3.47773i) q^{25} +(0.190283 + 5.19267i) q^{27} +6.69055i q^{29} +(-2.44846 - 1.41362i) q^{31} +(2.12635 - 3.78904i) q^{33} +(1.64234 + 2.84461i) q^{37} +(11.6841 - 0.142663i) q^{39} -9.02583 q^{41} +10.6558 q^{43} +(-1.55065 - 2.54046i) q^{45} +(5.26837 + 9.12508i) q^{47} +(5.67424 + 3.18429i) q^{51} +(-8.91002 - 5.14420i) q^{53} +2.48872i q^{55} +(2.36133 + 3.97701i) q^{57} +(2.32160 - 4.02113i) q^{59} +(6.97413 - 4.02651i) q^{61} +(-5.79636 + 3.34653i) q^{65} +(3.34885 - 5.80038i) q^{67} +(1.54521 + 2.60247i) q^{69} -4.56245i q^{71} +(2.80171 + 1.61757i) q^{73} +(-6.06561 - 3.40392i) q^{75} +(7.23346 + 12.5287i) q^{79} +(8.98927 - 0.439364i) q^{81} -16.8613 q^{83} -3.72696 q^{85} +(11.5875 - 0.141484i) q^{87} +(-1.58550 - 2.74617i) q^{89} +(-2.39650 + 4.27043i) q^{93} +(-2.29434 - 1.32464i) q^{95} +0.989407i q^{97} +(-6.60728 - 3.60254i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 32 q^{15} - 8 q^{25} - 16 q^{37} + 64 q^{39} + 32 q^{43} - 48 q^{51} + 96 q^{57} - 16 q^{67} - 80 q^{81} - 128 q^{85} + 32 q^{93} - 112 q^{99}+O(q^{100}) $ 48 * q - 32 * q^15 - 8 * q^25 - 16 * q^37 + 64 * q^39 + 32 * q^43 - 48 * q^51 + 96 * q^57 - 16 * q^67 - 80 * q^81 - 128 * q^85 + 32 * q^93 - 112 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times$.

$n$	$295$	$589$	$785$	$1081$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.0211468	−	1.73192i	−0.0122091	−	0.999925i
$3$	−0.0211468	−	1.73192i	−0.0122091	−	0.999925i
$4$		0			0
$5$	0.496051	+	0.859186i	0.221841	+	0.384240i	0.955367	−	0.295422i	$-0.0954601\pi$
$5$	0.496051	+	0.859186i	0.221841	+	0.384240i	−0.733526	+	0.679661i	$0.762127\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−2.99911	+	0.0732492i	−0.999702	+	0.0244164i
$10$		0			0
$11$	2.17245	+	1.25426i	0.655018	+	0.378175i	0.790376	−	0.612622i	$-0.209885\pi$
$11$	2.17245	+	1.25426i	0.655018	+	0.378175i	−0.135358	+	0.990797i	$0.543218\pi$
$12$		0			0
$13$			6.74633i			1.87110i	0.353199	+	0.935548i	$0.385094\pi$
$13$			6.74633i			1.87110i	−0.353199	+	0.935548i	$0.614906\pi$
$14$		0			0
$15$	1.47755	−	0.877291i	0.381503	−	0.226516i
$16$		0			0
$17$	−1.87831	+	3.25333i	−0.455558	+	0.789049i	−0.998720	−	0.0505785i	$-0.983893\pi$
$17$	−1.87831	+	3.25333i	−0.455558	+	0.789049i	0.543162	+	0.839628i	$0.317227\pi$
$18$		0			0
$19$	−2.31260	+	1.33518i	−0.530547	+	0.306312i	−0.741239	−	0.671241i	$-0.765762\pi$
$19$	−2.31260	+	1.33518i	−0.530547	+	0.306312i	0.210692	+	0.977552i	$0.432428\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.51332	+	0.873715i	−0.315549	+	0.182182i	−0.649407	−	0.760441i	$-0.724983\pi$
$23$	−1.51332	+	0.873715i	−0.315549	+	0.182182i	0.333858	+	0.942623i	$0.391649\pi$
$24$		0			0
$25$	2.00787	−	3.47773i	0.401573	−	0.695545i
$26$		0			0
$27$	0.190283	+	5.19267i	0.0366201	+	0.999329i
$28$		0			0
$29$			6.69055i			1.24240i	0.783651	+	0.621202i	$0.213355\pi$
$29$			6.69055i			1.24240i	−0.783651	+	0.621202i	$0.786645\pi$
$30$		0			0
$31$	−2.44846	−	1.41362i	−0.439756	−	0.253893i	0.263738	−	0.964594i	$-0.415044\pi$
$31$	−2.44846	−	1.41362i	−0.439756	−	0.253893i	−0.703494	+	0.710701i	$0.748378\pi$
$32$		0			0
$33$	2.12635	−	3.78904i	0.370150	−	0.659587i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.64234	+	2.84461i	0.269998	+	0.467651i	0.968861	−	0.247605i	$-0.0796435\pi$
$37$	1.64234	+	2.84461i	0.269998	+	0.467651i	−0.698863	+	0.715256i	$0.746310\pi$
$38$		0			0
$39$	11.6841	−	0.142663i	1.87096	−	0.0228444i
$40$		0			0
$41$	−9.02583			−1.40960			−0.704799	−	0.709407i	$-0.748963\pi$
$41$	−9.02583			−1.40960			−0.704799	+	0.709407i	$0.748963\pi$
$42$		0			0
$43$	10.6558			1.62499			0.812495	−	0.582969i	$-0.198109\pi$
$43$	10.6558			1.62499			0.812495	+	0.582969i	$0.198109\pi$
$44$		0			0
$45$	−1.55065	−	2.54046i	−0.231157	−	0.378709i
$46$		0			0
$47$	5.26837	+	9.12508i	0.768470	+	1.33103i	0.938392	+	0.345572i	$0.112315\pi$
$47$	5.26837	+	9.12508i	0.768470	+	1.33103i	−0.169922	+	0.985457i	$0.554352\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	5.67424	+	3.18429i	0.794552	+	0.445890i
$52$		0			0
$53$	−8.91002	−	5.14420i	−1.22389	−	0.706611i	−0.258142	−	0.966107i	$-0.583110\pi$
$53$	−8.91002	−	5.14420i	−1.22389	−	0.706611i	−0.965744	+	0.259496i	$0.916444\pi$
$54$		0			0
$55$			2.48872i			0.335579i
$56$		0			0
$57$	2.36133	+	3.97701i	0.312766	+	0.526768i
$58$		0			0
$59$	2.32160	−	4.02113i	0.302246	−	0.523506i	−0.674398	−	0.738368i	$-0.735597\pi$
$59$	2.32160	−	4.02113i	0.302246	−	0.523506i	0.976644	+	0.214862i	$0.0689301\pi$
$60$		0			0
$61$	6.97413	−	4.02651i	0.892945	−	0.515542i	0.0180407	−	0.999837i	$-0.494257\pi$
$61$	6.97413	−	4.02651i	0.892945	−	0.515542i	0.874905	+	0.484295i	$0.160924\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−5.79636	+	3.34653i	−0.718950	+	0.415086i
$66$		0			0
$67$	3.34885	−	5.80038i	0.409127	−	0.708629i	−0.585665	−	0.810553i	$-0.699167\pi$
$67$	3.34885	−	5.80038i	0.409127	−	0.708629i	0.994792	+	0.101924i	$0.0325000\pi$
$68$		0			0
$69$	1.54521	+	2.60247i	0.186021	+	0.313301i
$70$		0			0
$71$		−	4.56245i		−	0.541463i	−0.962655	−	0.270732i	$-0.912734\pi$
$71$		−	4.56245i		−	0.541463i	0.962655	−	0.270732i	$-0.0872656\pi$
$72$		0			0
$73$	2.80171	+	1.61757i	0.327915	+	0.189322i	0.654915	−	0.755702i	$-0.272704\pi$
$73$	2.80171	+	1.61757i	0.327915	+	0.189322i	−0.327000	+	0.945024i	$0.606038\pi$
$74$		0			0
$75$	−6.06561	−	3.40392i	−0.700396	−	0.393051i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	7.23346	+	12.5287i	0.813828	+	1.40959i	0.910166	+	0.414243i	$0.135954\pi$
$79$	7.23346	+	12.5287i	0.813828	+	1.40959i	−0.0963379	+	0.995349i	$0.530713\pi$
$80$		0			0
$81$	8.98927	−	0.439364i	0.998808	−	0.0488183i
$82$		0			0
$83$	−16.8613			−1.85077			−0.925386	−	0.379025i	$-0.876259\pi$
$83$	−16.8613			−1.85077			−0.925386	+	0.379025i	$0.876259\pi$
$84$		0			0
$85$	−3.72696			−0.404245
$86$		0			0
$87$	11.5875	−	0.141484i	1.24231	−	0.0151686i
$88$		0			0
$89$	−1.58550	−	2.74617i	−0.168063	−	0.291094i	0.769676	−	0.638435i	$-0.220418\pi$
$89$	−1.58550	−	2.74617i	−0.168063	−	0.291094i	−0.937739	+	0.347341i	$0.887085\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−2.39650	+	4.27043i	−0.248505	+	0.442823i
$94$		0			0
$95$	−2.29434	−	1.32464i	−0.235394	−	0.135905i
$96$		0			0
$97$			0.989407i			0.100459i	0.998738	+	0.0502295i	$0.0159953\pi$
$97$			0.989407i			0.100459i	−0.998738	+	0.0502295i	$0.984005\pi$
$98$		0			0
$99$	−6.60728	−	3.60254i	−0.664057	−	0.362069i
$100$		0			0
$101$	−5.02078	+	8.69625i	−0.499586	+	0.865309i	−1.00000		0.000477583i	$-0.999848\pi$
$101$	−5.02078	+	8.69625i	−0.499586	+	0.865309i	0.500414	+	0.865787i	$0.333181\pi$
$102$		0			0
$103$	6.89056	−	3.97826i	0.678947	−	0.391990i	−0.120511	−	0.992712i	$-0.538453\pi$
$103$	6.89056	−	3.97826i	0.678947	−	0.391990i	0.799458	+	0.600722i	$0.205120\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	14.1473	−	8.16794i	1.36767	−	0.789624i	0.377039	−	0.926197i	$-0.376942\pi$
$107$	14.1473	−	8.16794i	1.36767	−	0.789624i	0.990630	+	0.136573i	$0.0436089\pi$
$108$		0			0
$109$	4.71712	−	8.17029i	0.451818	−	0.782572i	−0.546681	−	0.837341i	$-0.684109\pi$
$109$	4.71712	−	8.17029i	0.451818	−	0.782572i	0.998499	+	0.0547692i	$0.0174423\pi$
$110$		0			0
$111$	4.89191	−	2.90455i	0.464319	−	0.275688i
$112$		0			0
$113$			18.5486i			1.74490i	0.488702	+	0.872451i	$0.337471\pi$
$113$			18.5486i			1.74490i	−0.488702	+	0.872451i	$0.662529\pi$
$114$		0			0
$115$	−1.50137	−	0.866816i	−0.140003	−	0.0808310i
$116$		0			0
$117$	−0.494164	−	20.2330i	−0.0456855	−	1.87054i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−2.35364	−	4.07662i	−0.213967	−	0.370602i
$122$		0			0
$123$	0.190868	+	15.6320i	0.0172100	+	1.40949i
$124$		0			0
$125$	8.94453			0.800023
$126$		0			0
$127$	10.2002			0.905118			0.452559	−	0.891734i	$-0.350511\pi$
$127$	10.2002			0.905118			0.452559	+	0.891734i	$0.350511\pi$
$128$		0			0
$129$	−0.225335	−	18.4550i	−0.0198397	−	1.62487i
$130$		0			0
$131$	8.88035	+	15.3812i	0.775880	+	1.34386i	0.934299	+	0.356491i	$0.116027\pi$
$131$	8.88035	+	15.3812i	0.775880	+	1.34386i	−0.158419	+	0.987372i	$0.550640\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−4.36708	+	2.73932i	−0.375858	+	0.235763i
$136$		0			0
$137$	−0.509947	−	0.294418i	−0.0435677	−	0.0251538i	0.478058	−	0.878328i	$-0.341341\pi$
$137$	−0.509947	−	0.294418i	−0.0435677	−	0.0251538i	−0.521626	+	0.853174i	$0.674674\pi$
$138$		0			0
$139$		−	2.88202i		−	0.244449i	−0.992502	−	0.122225i	$-0.960997\pi$
$139$		−	2.88202i		−	0.244449i	0.992502	−	0.122225i	$-0.0390029\pi$
$140$		0			0
$141$	15.6925	−	9.31736i	1.32155	−	0.784663i
$142$		0			0
$143$	−8.46169	+	14.6561i	−0.707602	+	1.22560i
$144$		0			0
$145$	−5.74843	+	3.31886i	−0.477381	+	0.275616i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.37760	−	0.795356i	0.112857	−	0.0651581i	−0.442509	−	0.896764i	$-0.645911\pi$
$149$	1.37760	−	0.795356i	0.112857	−	0.0651581i	0.555366	+	0.831606i	$0.312578\pi$
$150$		0			0
$151$	−7.60822	+	13.1778i	−0.619148	+	1.07240i	0.370493	+	0.928835i	$0.379189\pi$
$151$	−7.60822	+	13.1778i	−0.619148	+	1.07240i	−0.989641	+	0.143561i	$0.954145\pi$
$152$		0			0
$153$	5.39495	−	9.89467i	0.436156	−	0.799937i
$154$		0			0
$155$		−	2.80491i		−	0.225295i
$156$		0			0
$157$	1.77180	+	1.02295i	0.141405	+	0.0816403i	0.569033	−	0.822314i	$-0.307317\pi$
$157$	1.77180	+	1.02295i	0.141405	+	0.0816403i	−0.427628	+	0.903955i	$0.640651\pi$
$158$		0			0
$159$	−8.72094	+	15.5402i	−0.691616	+	1.23242i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−9.08108	−	15.7289i	−0.711285	−	1.23198i	−0.964375	−	0.264539i	$-0.914780\pi$
$163$	−9.08108	−	15.7289i	−0.711285	−	1.23198i	0.253090	−	0.967443i	$-0.418553\pi$
$164$		0			0
$165$	4.31027	−	0.0526285i	0.335554	−	0.00409712i
$166$		0			0
$167$	5.59063			0.432616			0.216308	−	0.976325i	$-0.430598\pi$
$167$	5.59063			0.432616			0.216308	+	0.976325i	$0.430598\pi$
$168$		0			0
$169$	−32.5130			−2.50100
$170$		0			0
$171$	6.83794	−	4.17375i	0.522910	−	0.319174i
$172$		0			0
$173$	−2.24674	−	3.89147i	−0.170817	−	0.295863i	0.767889	−	0.640583i	$-0.221307\pi$
$173$	−2.24674	−	3.89147i	−0.170817	−	0.295863i	−0.938706	+	0.344720i	$0.887974\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−7.01337	−	3.93579i	−0.527157	−	0.295832i
$178$		0			0
$179$	−17.2972	−	9.98657i	−1.29286	−	0.746431i	−0.313697	−	0.949523i	$-0.601568\pi$
$179$	−17.2972	−	9.98657i	−1.29286	−	0.746431i	−0.979160	+	0.203092i	$0.934901\pi$
$180$		0			0
$181$			4.43963i			0.329995i	0.986294	+	0.164998i	$0.0527616\pi$
$181$			4.43963i			0.329995i	−0.986294	+	0.164998i	$0.947238\pi$
$182$		0			0
$183$	−7.12109	−	11.9935i	−0.526406	−	0.886585i
$184$		0			0
$185$	−1.62937	+	2.82214i	−0.119793	+	0.207488i
$186$		0			0
$187$	−8.16108	+	4.71180i	−0.596797	+	0.344561i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.80773	+	1.62105i	−0.203161	+	0.117295i	−0.598129	−	0.801400i	$-0.704089\pi$
$191$	−2.80773	+	1.62105i	−0.203161	+	0.117295i	0.394968	+	0.918695i	$0.370756\pi$
$192$		0			0
$193$	−6.63386	+	11.4902i	−0.477516	+	0.827082i	−0.999668	−	0.0257705i	$-0.991796\pi$
$193$	−6.63386	+	11.4902i	−0.477516	+	0.827082i	0.522152	+	0.852853i	$0.325129\pi$
$194$		0			0
$195$	5.91850	+	9.96807i	0.423833	+	0.713828i
$196$		0			0
$197$		−	18.7165i		−	1.33350i	−0.745282	−	0.666749i	$-0.767685\pi$
$197$		−	18.7165i		−	1.33350i	0.745282	−	0.666749i	$-0.232315\pi$
$198$		0			0
$199$	−1.08304	−	0.625292i	−0.0767745	−	0.0443258i	0.461121	−	0.887337i	$-0.347447\pi$
$199$	−1.08304	−	0.625292i	−0.0767745	−	0.0443258i	−0.537896	+	0.843011i	$0.680781\pi$
$200$		0			0
$201$	−10.1166	−	5.67728i	−0.713571	−	0.400445i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−4.47728	−	7.75487i	−0.312707	−	0.541624i
$206$		0			0
$207$	4.47461	−	2.73121i	0.311007	−	0.189833i
$208$		0			0
$209$	−6.69868			−0.463358
$210$		0			0
$211$	−1.04084			−0.0716546			−0.0358273	−	0.999358i	$-0.511407\pi$
$211$	−1.04084			−0.0716546			−0.0358273	+	0.999358i	$0.511407\pi$
$212$		0			0
$213$	−7.90181	+	0.0964813i	−0.541423	+	0.00661079i
$214$		0			0
$215$	5.28581	+	9.15529i	0.360489	+	0.624386i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	2.74225	−	4.88655i	0.185304	−	0.330202i
$220$		0			0
$221$	−21.9481	−	12.6717i	−1.47639	−	0.852392i
$222$		0			0
$223$		−	21.2360i		−	1.42207i	−0.703156	−	0.711035i	$-0.748227\pi$
$223$		−	21.2360i		−	1.42207i	0.703156	−	0.711035i	$-0.251773\pi$
$224$		0			0
$225$	−5.76706	+	10.5771i	−0.384471	+	0.705143i
$226$		0			0
$227$	−3.27686	+	5.67568i	−0.217493	+	0.376708i	−0.954041	−	0.299677i	$-0.903121\pi$
$227$	−3.27686	+	5.67568i	−0.217493	+	0.376708i	0.736548	+	0.676385i	$0.236454\pi$
$228$		0			0
$229$	−14.8892	+	8.59630i	−0.983908	+	0.568059i	−0.903448	−	0.428698i	$-0.858972\pi$
$229$	−14.8892	+	8.59630i	−0.983908	+	0.568059i	−0.0804602	+	0.996758i	$0.525639\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−10.7831	+	6.22564i	−0.706426	+	0.407855i	−0.809736	−	0.586794i	$-0.800390\pi$
$233$	−10.7831	+	6.22564i	−0.706426	+	0.407855i	0.103310	+	0.994649i	$0.467057\pi$
$234$		0			0
$235$	−5.22676	+	9.05302i	−0.340956	+	0.590554i
$236$		0			0
$237$	21.5458	−	12.7927i	1.39955	−	0.830978i
$238$		0			0
$239$			8.44730i			0.546410i	0.961956	+	0.273205i	$0.0880838\pi$
$239$			8.44730i			0.546410i	−0.961956	+	0.273205i	$0.911916\pi$
$240$		0			0
$241$	2.51127	+	1.44988i	0.161765	+	0.0933951i	0.578697	−	0.815543i	$-0.303561\pi$
$241$	2.51127	+	1.44988i	0.161765	+	0.0933951i	−0.416932	+	0.908938i	$0.636895\pi$
$242$		0			0
$243$	−0.951039	−	15.5594i	−0.0610092	−	0.998137i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−9.00758	−	15.6016i	−0.573139	−	0.992705i
$248$		0			0
$249$	0.356564	+	29.2025i	0.0225963	+	1.85063i
$250$		0			0
$251$	1.28400			0.0810455			0.0405227	−	0.999179i	$-0.487098\pi$
$251$	1.28400			0.0810455			0.0405227	+	0.999179i	$0.487098\pi$
$252$		0			0
$253$	−4.38348			−0.275587
$254$		0			0
$255$	0.0788133	+	6.45480i	0.00493548	+	0.404215i
$256$		0			0
$257$	8.89593	+	15.4082i	0.554913	+	0.961137i	0.997910	+	0.0646145i	$0.0205818\pi$
$257$	8.89593	+	15.4082i	0.554913	+	0.961137i	−0.442997	+	0.896523i	$0.646085\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.490077	−	20.0657i	−0.0303350	−	1.24203i
$262$		0			0
$263$	−12.0755	−	6.97177i	−0.744605	−	0.429898i	0.0791363	−	0.996864i	$-0.474784\pi$
$263$	−12.0755	−	6.97177i	−0.744605	−	0.429898i	−0.823741	+	0.566966i	$0.808117\pi$
$264$		0			0
$265$		−	10.2072i		−	0.627021i
$266$		0			0
$267$	−4.72263	+	2.80404i	−0.289020	+	0.171604i
$268$		0			0
$269$	0.698320	−	1.20953i	0.0425773	−	0.0737461i	−0.843951	−	0.536420i	$-0.819776\pi$
$269$	0.698320	−	1.20953i	0.0425773	−	0.0737461i	0.886529	+	0.462674i	$0.153110\pi$
$270$		0			0
$271$	9.26119	−	5.34695i	0.562577	−	0.324804i	−0.191602	−	0.981473i	$-0.561368\pi$
$271$	9.26119	−	5.34695i	0.562577	−	0.324804i	0.754179	+	0.656669i	$0.228035\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	8.72398	−	5.03679i	0.526076	−	0.303730i
$276$		0			0
$277$	1.76204	−	3.05194i	0.105871	−	0.183373i	−0.808223	−	0.588877i	$-0.799570\pi$
$277$	1.76204	−	3.05194i	0.105871	−	0.183373i	0.914094	+	0.405503i	$0.132904\pi$
$278$		0			0
$279$	7.44672	+	4.06024i	0.445824	+	0.243080i
$280$		0			0
$281$		−	7.84120i		−	0.467767i	−0.972265	−	0.233883i	$-0.924857\pi$
$281$		−	7.84120i		−	0.467767i	0.972265	−	0.233883i	$-0.0751434\pi$
$282$		0			0
$283$	−19.1594	−	11.0617i	−1.13891	−	0.657550i	−0.192749	−	0.981248i	$-0.561740\pi$
$283$	−19.1594	−	11.0617i	−1.13891	−	0.657550i	−0.946160	+	0.323699i	$0.895074\pi$
$284$		0			0
$285$	−2.24565	+	4.00163i	−0.133021	+	0.237036i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	1.44388	+	2.50088i	0.0849343	+	0.147110i
$290$		0			0
$291$	1.71357	−	0.0209228i	0.100452	−	0.00122652i
$292$		0			0
$293$	20.5775			1.20215			0.601074	−	0.799193i	$-0.294740\pi$
$293$	20.5775			1.20215			0.601074	+	0.799193i	$0.294740\pi$
$294$		0			0
$295$	4.60653			0.268203
$296$		0			0
$297$	−6.09960	+	11.5195i	−0.353935	+	0.668428i
$298$		0			0
$299$	−5.89438	−	10.2094i	−0.340881	−	0.590422i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	15.1674	+	8.51170i	0.871344	+	0.488984i
$304$		0			0
$305$	6.91905	+	3.99472i	0.396184	+	0.228737i
$306$		0			0
$307$		−	29.4122i		−	1.67864i	−0.543636	−	0.839321i	$-0.682953\pi$
$307$		−	29.4122i		−	1.67864i	0.543636	−	0.839321i	$-0.317047\pi$
$308$		0			0
$309$	−7.03576	−	11.8498i	−0.400250	−	0.674110i
$310$		0			0
$311$	4.03845	−	6.99480i	0.228999	−	0.396638i	−0.728512	−	0.685033i	$-0.759788\pi$
$311$	4.03845	−	6.99480i	0.228999	−	0.396638i	0.957512	+	0.288394i	$0.0931213\pi$
$312$		0			0
$313$	−1.04838	+	0.605284i	−0.0592581	+	0.0342127i	−0.529336	−	0.848412i	$-0.677559\pi$
$313$	−1.04838	+	0.605284i	−0.0592581	+	0.0342127i	0.470078	+	0.882625i	$0.344226\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	25.7940	−	14.8922i	1.44874	−	0.836429i	0.450331	−	0.892862i	$-0.351306\pi$
$317$	25.7940	−	14.8922i	1.44874	−	0.836429i	0.998406	+	0.0564326i	$0.0179726\pi$
$318$		0			0
$319$	−8.39172	+	14.5349i	−0.469846	+	0.813797i
$320$		0			0
$321$	−14.4454	−	24.3293i	−0.806263	−	1.35793i
$322$		0			0
$323$		−	10.0316i		−	0.558171i
$324$		0			0
$325$	23.4619	+	13.5457i	1.30143	+	0.751382i
$326$		0			0
$327$	−14.2501	−	7.99690i	−0.788030	−	0.442230i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	6.20018	+	10.7390i	0.340793	+	0.590270i	0.984580	−	0.174934i	$-0.0559712\pi$
$331$	6.20018	+	10.7390i	0.340793	+	0.590270i	−0.643787	+	0.765204i	$0.722638\pi$
$332$		0			0
$333$	−5.13390	−	8.41098i	−0.281336	−	0.460919i
$334$		0			0
$335$	6.64481			0.363044
$336$		0			0
$337$	1.60403			0.0873772			0.0436886	−	0.999045i	$-0.486089\pi$
$337$	1.60403			0.0873772			0.0436886	+	0.999045i	$0.486089\pi$
$338$		0			0
$339$	32.1247	−	0.392243i	1.74477	−	0.0213037i
$340$		0			0
$341$	−3.54610	−	6.14202i	−0.192032	−	0.332609i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−1.46951	+	2.61858i	−0.0791156	+	0.140980i
$346$		0			0
$347$	8.03173	+	4.63712i	0.431166	+	0.248934i	0.699843	−	0.714296i	$-0.253253\pi$
$347$	8.03173	+	4.63712i	0.431166	+	0.248934i	−0.268677	+	0.963230i	$0.586586\pi$
$348$		0			0
$349$			17.2999i			0.926043i	0.886347	+	0.463021i	$0.153235\pi$
$349$			17.2999i			0.926043i	−0.886347	+	0.463021i	$0.846765\pi$
$350$		0			0
$351$	−35.0315	+	1.28372i	−1.86984	+	0.0685197i
$352$		0			0
$353$	1.76697	−	3.06049i	0.0940465	−	0.162893i	−0.815164	−	0.579231i	$-0.803353\pi$
$353$	1.76697	−	3.06049i	0.0940465	−	0.162893i	0.909210	+	0.416337i	$0.136686\pi$
$354$		0			0
$355$	3.92000	−	2.26321i	0.208052	−	0.120119i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−11.6190	+	6.70821i	−0.613225	+	0.354046i	−0.774227	−	0.632908i	$-0.781861\pi$
$359$	−11.6190	+	6.70821i	−0.613225	+	0.354046i	0.161001	+	0.986954i	$0.448528\pi$
$360$		0			0
$361$	−5.93458	+	10.2790i	−0.312346	+	0.541000i
$362$		0			0
$363$	−7.01062	+	4.16253i	−0.367962	+	0.218476i
$364$		0			0
$365$			3.20959i			0.167998i
$366$		0			0
$367$	7.88688	+	4.55350i	0.411692	+	0.237691i	0.691516	−	0.722361i	$-0.256943\pi$
$367$	7.88688	+	4.55350i	0.411692	+	0.237691i	−0.279824	+	0.960051i	$0.590276\pi$
$368$		0			0
$369$	27.0694	−	0.661135i	1.40918	−	0.0344173i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	16.6630	+	28.8611i	0.862775	+	1.49437i	0.869239	+	0.494392i	$0.164609\pi$
$373$	16.6630	+	28.8611i	0.862775	+	1.49437i	−0.00646378	+	0.999979i	$0.502058\pi$
$374$		0			0
$375$	−0.189148	−	15.4912i	−0.00976758	−	0.799964i
$376$		0			0
$377$	−45.1367			−2.32466
$378$		0			0
$379$	−11.8875			−0.610620			−0.305310	−	0.952253i	$-0.598760\pi$
$379$	−11.8875			−0.610620			−0.305310	+	0.952253i	$0.598760\pi$
$380$		0			0
$381$	−0.215701	−	17.6659i	−0.0110507	−	0.905051i
$382$		0			0
$383$	−13.9080	−	24.0893i	−0.710663	−	1.23091i	−0.964608	−	0.263687i	$-0.915062\pi$
$383$	−13.9080	−	24.0893i	−0.710663	−	1.23091i	0.253945	−	0.967219i	$-0.418272\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−31.9578	+	0.780527i	−1.62451	+	0.0396764i
$388$		0			0
$389$	−15.7439	−	9.08974i	−0.798247	−	0.460868i	0.0446107	−	0.999004i	$-0.485795\pi$
$389$	−15.7439	−	9.08974i	−0.798247	−	0.460868i	−0.842858	+	0.538136i	$0.819129\pi$
$390$		0			0
$391$		−	6.56444i		−	0.331978i
$392$		0			0
$393$	26.4513	−	15.7053i	1.33429	−	0.792229i
$394$		0			0
$395$	−7.17634	+	12.4298i	−0.361081	+	0.625410i
$396$		0			0
$397$	1.85933	−	1.07349i	0.0933172	−	0.0538767i	−0.452615	−	0.891706i	$-0.649509\pi$
$397$	1.85933	−	1.07349i	0.0933172	−	0.0538767i	0.545932	+	0.837829i	$0.316176\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	10.1853	−	5.88049i	0.508630	−	0.293658i	−0.223640	−	0.974672i	$-0.571794\pi$
$401$	10.1853	−	5.88049i	0.508630	−	0.293658i	0.732270	+	0.681014i	$0.238461\pi$
$402$		0			0
$403$	9.53673	−	16.5181i	0.475058	−	0.822825i
$404$		0			0
$405$	4.83664	+	7.50551i	0.240334	+	0.372952i
$406$		0			0
$407$			8.23969i			0.408426i
$408$		0			0
$409$	16.4896	+	9.52030i	0.815360	+	0.470748i	0.848814	−	0.528692i	$-0.177317\pi$
$409$	16.4896	+	9.52030i	0.815360	+	0.470748i	−0.0334538	+	0.999440i	$0.510651\pi$
$410$		0			0
$411$	−0.499125	+	0.889414i	−0.0246200	+	0.0438715i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−8.36409	−	14.4870i	−0.410577	−	0.711141i
$416$		0			0
$417$	−4.99143	+	0.0609454i	−0.244431	+	0.00298451i
$418$		0			0
$419$	29.5570			1.44395			0.721976	−	0.691918i	$-0.243234\pi$
$419$	29.5570			1.44395			0.721976	+	0.691918i	$0.243234\pi$
$420$		0			0
$421$	8.76696			0.427275			0.213638	−	0.976913i	$-0.431469\pi$
$421$	8.76696			0.427275			0.213638	+	0.976913i	$0.431469\pi$
$422$		0			0
$423$	−16.4688	−	26.9812i	−0.800740	−	1.31187i
$424$		0			0
$425$	7.54280	+	13.0645i	0.365880	+	0.633722i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	25.5621	+	14.3451i	1.23415	+	0.692586i
$430$		0			0
$431$	21.5180	+	12.4234i	1.03648	+	0.598414i	0.918835	−	0.394641i	$-0.129131\pi$
$431$	21.5180	+	12.4234i	1.03648	+	0.598414i	0.117649	+	0.993055i	$0.462464\pi$
$432$		0			0
$433$		−	14.9303i		−	0.717502i	−0.933433	−	0.358751i	$-0.883203\pi$
$433$		−	14.9303i		−	0.717502i	0.933433	−	0.358751i	$-0.116797\pi$
$434$		0			0
$435$	5.86956	+	9.88564i	0.281424	+	0.473980i
$436$		0			0
$437$	2.33314	−	4.04111i	0.111609	−	0.193313i
$438$		0			0
$439$	13.6586	−	7.88578i	0.651888	−	0.376368i	−0.137291	−	0.990531i	$-0.543840\pi$
$439$	13.6586	−	7.88578i	0.651888	−	0.376368i	0.789179	+	0.614163i	$0.210506\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−11.4712	+	6.62292i	−0.545015	+	0.314665i	−0.747109	−	0.664702i	$-0.768559\pi$
$443$	−11.4712	+	6.62292i	−0.545015	+	0.314665i	0.202094	+	0.979366i	$0.435225\pi$
$444$		0			0
$445$	1.57298	−	2.72449i	0.0745665	−	0.129153i
$446$		0			0
$447$	−1.40663	−	2.36907i	−0.0665311	−	0.112053i
$448$		0			0
$449$			14.0532i			0.663212i	0.943418	+	0.331606i	$0.107591\pi$
$449$			14.0532i			0.663212i	−0.943418	+	0.331606i	$0.892409\pi$
$450$		0			0
$451$	−19.6082	−	11.3208i	−0.923313	−	0.533075i
$452$		0			0
$453$	22.9839	+	12.8982i	1.07988	+	0.606009i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−5.92092	−	10.2553i	−0.276969	−	0.479725i	0.693661	−	0.720302i	$-0.255997\pi$
$457$	−5.92092	−	10.2553i	−0.276969	−	0.479725i	−0.970630	+	0.240577i	$0.922663\pi$
$458$		0			0
$459$	−17.2509	−	9.13440i	−0.805202	−	0.426357i
$460$		0			0
$461$	18.8583			0.878318			0.439159	−	0.898409i	$-0.355276\pi$
$461$	18.8583			0.878318			0.439159	+	0.898409i	$0.355276\pi$
$462$		0			0
$463$	12.0554			0.560263			0.280131	−	0.959962i	$-0.409622\pi$
$463$	12.0554			0.560263			0.280131	+	0.959962i	$0.409622\pi$
$464$		0			0
$465$	−4.85788	+	0.0593148i	−0.225279	+	0.00275066i
$466$		0			0
$467$	−10.5439	−	18.2625i	−0.487912	−	0.845088i	0.511991	−	0.858991i	$-0.328908\pi$
$467$	−10.5439	−	18.2625i	−0.487912	−	0.845088i	−0.999903	+	0.0139024i	$0.995575\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	1.73420	−	3.09025i	0.0799077	−	0.142391i
$472$		0			0
$473$	23.1491	+	13.3652i	1.06440	+	0.614531i
$474$		0			0
$475$			10.7235i			0.492026i
$476$		0			0
$477$	27.0989	+	14.7754i	1.24077	+	0.676517i
$478$		0			0
$479$	0.743810	−	1.28832i	0.0339855	−	0.0588647i	−0.848532	−	0.529143i	$-0.822513\pi$
$479$	0.743810	−	1.28832i	0.0339855	−	0.0588647i	0.882518	+	0.470279i	$0.155847\pi$
$480$		0			0
$481$	−19.1907	+	11.0797i	−0.875019	+	0.505193i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.850085	+	0.490797i	−0.0386004	+	0.0222859i
$486$		0			0
$487$	15.6242	−	27.0619i	0.708000	−	1.22629i	−0.257598	−	0.966252i	$-0.582931\pi$
$487$	15.6242	−	27.0619i	0.708000	−	1.22629i	0.965598	−	0.260040i	$-0.0837356\pi$
$488$		0			0
$489$	−27.0492	+	16.0603i	−1.22321	+	0.726273i
$490$		0			0
$491$			28.3082i			1.27753i	0.769401	+	0.638766i	$0.220555\pi$
$491$			28.3082i			1.27753i	−0.769401	+	0.638766i	$0.779445\pi$
$492$		0			0
$493$	−21.7666	−	12.5669i	−0.980317	−	0.565986i
$494$		0			0
$495$	−0.182297	−	7.46393i	−0.00819363	−	0.335479i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	14.6111	+	25.3072i	0.654084	+	1.13291i	0.982123	+	0.188242i	$0.0602789\pi$
$499$	14.6111	+	25.3072i	0.654084	+	1.13291i	−0.328039	+	0.944664i	$0.606388\pi$
$500$		0			0
$501$	−0.118224	−	9.68253i	−0.00528186	−	0.432584i
$502$		0			0
$503$	−37.0646			−1.65263			−0.826314	−	0.563210i	$-0.809566\pi$
$503$	−37.0646			−1.65263			−0.826314	+	0.563210i	$0.809566\pi$
$504$		0			0
$505$	−9.96226			−0.443315
$506$		0			0
$507$	0.687547	+	56.3100i	0.0305350	+	2.50082i
$508$		0			0
$509$	15.3441	+	26.5768i	0.680117	+	1.17800i	0.974945	+	0.222446i	$0.0714042\pi$
$509$	15.3441	+	26.5768i	0.680117	+	1.17800i	−0.294828	+	0.955550i	$0.595262\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−7.37320	−	11.7545i	−0.325535	−	0.518974i
$514$		0			0
$515$	6.83614	+	3.94685i	0.301236	+	0.173919i
$516$		0			0
$517$			26.4317i			1.16247i
$518$		0			0
$519$	−6.69221	+	3.97347i	−0.293755	+	0.174416i
$520$		0			0
$521$	0.779005	−	1.34928i	0.0341288	−	0.0591129i	−0.848456	−	0.529265i	$-0.822468\pi$
$521$	0.779005	−	1.34928i	0.0341288	−	0.0591129i	0.882585	+	0.470152i	$0.155801\pi$
$522$		0			0
$523$	−2.12958	+	1.22951i	−0.0931200	+	0.0537628i	−0.545837	−	0.837891i	$-0.683788\pi$
$523$	−2.12958	+	1.22951i	−0.0931200	+	0.0537628i	0.452717	+	0.891654i	$0.350455\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	9.19793	−	5.31043i	0.400668	−	0.231326i
$528$		0			0
$529$	−9.97324	+	17.2742i	−0.433619	+	0.751051i
$530$		0			0
$531$	−6.66818	+	12.2298i	−0.289374	+	0.530730i
$532$		0			0
$533$		−	60.8913i		−	2.63749i
$534$		0			0
$535$	14.0356	+	8.10343i	0.606810	+	0.350342i
$536$		0			0
$537$	−16.9302	+	30.1686i	−0.730591	+	1.30187i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	6.65399	+	11.5251i	0.286077	+	0.495501i	0.972870	−	0.231353i	$-0.0743152\pi$
$541$	6.65399	+	11.5251i	0.286077	+	0.495501i	−0.686792	+	0.726854i	$0.740982\pi$
$542$		0			0
$543$	7.68909	−	0.0938840i	0.329971	−	0.00402895i
$544$		0			0
$545$	9.35973			0.400927
$546$		0			0
$547$	15.1745			0.648815			0.324408	−	0.945917i	$-0.394835\pi$
$547$	15.1745			0.648815			0.324408	+	0.945917i	$0.394835\pi$
$548$		0			0
$549$	−20.6212	+	12.5868i	−0.880092	+	0.537191i
$550$		0			0
$551$	−8.93309	−	15.4726i	−0.380563	−	0.659154i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	4.92219	+	2.76225i	0.208935	+	0.117251i
$556$		0			0
$557$	32.9104	+	19.0008i	1.39446	+	0.805091i	0.993805	−	0.111139i	$-0.0354500\pi$
$557$	32.9104	+	19.0008i	1.39446	+	0.805091i	0.400653	+	0.916230i	$0.368783\pi$
$558$		0			0
$559$			71.8874i			3.04051i
$560$		0			0
$561$	8.33306	+	14.0347i	0.351822	+	0.592546i
$562$		0			0
$563$	19.3049	−	33.4370i	0.813603	−	1.40920i	−0.0967240	−	0.995311i	$-0.530836\pi$
$563$	19.3049	−	33.4370i	0.813603	−	1.40920i	0.910327	−	0.413890i	$-0.135830\pi$
$564$		0			0
$565$	−15.9367	+	9.20104i	−0.670461	+	0.387091i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−21.0393	+	12.1471i	−0.882014	+	0.509231i	−0.871322	−	0.490712i	$-0.836737\pi$
$569$	−21.0393	+	12.1471i	−0.882014	+	0.509231i	−0.0106920	+	0.999943i	$0.503403\pi$
$570$		0			0
$571$	15.1612	−	26.2600i	0.634478	−	1.09895i	−0.352147	−	0.935945i	$-0.614548\pi$
$571$	15.1612	−	26.2600i	0.634478	−	1.09895i	0.986625	−	0.163004i	$-0.0521182\pi$
$572$		0			0
$573$	2.86690	+	4.82850i	0.119766	+	0.201713i
$574$		0			0
$575$			7.01721i			0.292638i
$576$		0			0
$577$	14.7967	+	8.54288i	0.615995	+	0.355645i	0.775308	−	0.631583i	$-0.217595\pi$
$577$	14.7967	+	8.54288i	0.615995	+	0.355645i	−0.159313	+	0.987228i	$0.550928\pi$
$578$		0			0
$579$	20.0404	+	11.2464i	0.832850	+	0.467383i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−12.9044	−	22.3511i	−0.534445	−	0.925686i
$584$		0			0
$585$	17.1388	−	10.4612i	0.708601	−	0.432516i
$586$		0			0
$587$	3.21402			0.132657			0.0663284	−	0.997798i	$-0.478871\pi$
$587$	3.21402			0.132657			0.0663284	+	0.997798i	$0.478871\pi$
$588$		0			0
$589$	7.54974			0.311082
$590$		0			0
$591$	−32.4156	+	0.395795i	−1.33340	+	0.0162808i
$592$		0			0
$593$	5.56488	+	9.63866i	0.228522	+	0.395812i	0.957370	−	0.288863i	$-0.0932773\pi$
$593$	5.56488	+	9.63866i	0.228522	+	0.395812i	−0.728848	+	0.684675i	$0.759944\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.06005	+	1.88896i	−0.0433851	+	0.0773100i
$598$		0			0
$599$	−28.2920	−	16.3344i	−1.15598	−	0.667405i	−0.205642	−	0.978627i	$-0.565928\pi$
$599$	−28.2920	−	16.3344i	−1.15598	−	0.667405i	−0.950337	+	0.311222i	$0.899262\pi$
$600$		0			0
$601$			27.2379i			1.11106i	0.831497	+	0.555529i	$0.187484\pi$
$601$			27.2379i			1.11106i	−0.831497	+	0.555529i	$0.812516\pi$
$602$		0			0
$603$	−9.61868	+	17.6412i	−0.391703	+	0.718407i
$604$		0			0
$605$	2.33505	−	4.04443i	0.0949334	−	0.164429i
$606$		0			0
$607$	25.8534	−	14.9264i	1.04936	−	0.605846i	0.126887	−	0.991917i	$-0.459502\pi$
$607$	25.8534	−	14.9264i	1.04936	−	0.605846i	0.922469	+	0.386071i	$0.126168\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−61.5608	+	35.5422i	−2.49048	+	1.43788i
$612$		0			0
$613$	12.4954	−	21.6426i	0.504683	−	0.874137i	−0.495302	−	0.868721i	$-0.664943\pi$
$613$	12.4954	−	21.6426i	0.504683	−	0.874137i	0.999985	−	0.00541593i	$-0.00172395\pi$
$614$		0			0
$615$	−13.3362	+	7.91829i	−0.537766	+	0.319296i
$616$		0			0
$617$			28.4800i			1.14656i	0.819359	+	0.573281i	$0.194330\pi$
$617$			28.4800i			1.14656i	−0.819359	+	0.573281i	$0.805670\pi$
$618$		0			0
$619$	−39.5948	−	22.8601i	−1.59145	−	0.918824i	−0.993059	−	0.117620i	$-0.962473\pi$
$619$	−39.5948	−	22.8601i	−1.59145	−	0.918824i	−0.598391	−	0.801204i	$-0.704193\pi$
$620$		0			0
$621$	−4.82487	−	7.69191i	−0.193615	−	0.308666i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−5.60238	−	9.70361i	−0.224095	−	0.388144i
$626$		0			0
$627$	0.141656	+	11.6016i	0.00565719	+	0.463323i
$628$		0			0
$629$	−12.3393			−0.491999
$630$		0			0
$631$	37.3192			1.48565			0.742827	−	0.669483i	$-0.233484\pi$
$631$	37.3192			1.48565			0.742827	+	0.669483i	$0.233484\pi$
$632$		0			0
$633$	0.0220105	+	1.80266i	0.000874839	+	0.0716493i
$634$		0			0
$635$	5.05980	+	8.76384i	0.200792	+	0.347782i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	0.334196	+	13.6833i	0.0132206	+	0.541302i
$640$		0			0
$641$	32.8738	+	18.9797i	1.29844	+	0.749652i	0.980134	−	0.198338i	$-0.0635543\pi$
$641$	32.8738	+	18.9797i	1.29844	+	0.749652i	0.318301	+	0.947990i	$0.396888\pi$
$642$		0			0
$643$		−	3.90637i		−	0.154052i	−0.997029	−	0.0770262i	$-0.975458\pi$
$643$		−	3.90637i		−	0.154052i	0.997029	−	0.0770262i	$-0.0245425\pi$
$644$		0			0
$645$	15.7445	−	9.34821i	0.619938	−	0.368086i
$646$		0			0
$647$	5.72867	−	9.92235i	0.225217	−	0.390088i	−0.731167	−	0.682198i	$-0.761024\pi$
$647$	5.72867	−	9.92235i	0.225217	−	0.390088i	0.956385	+	0.292110i	$0.0943575\pi$
$648$		0			0
$649$	10.0871	−	5.82380i	0.395954	−	0.228604i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−0.118160	+	0.0682197i	−0.00462396	+	0.00266964i	−0.502310	−	0.864687i	$-0.667516\pi$
$653$	−0.118160	+	0.0682197i	−0.00462396	+	0.00266964i	0.497686	+	0.867357i	$0.334183\pi$
$654$		0			0
$655$	−8.81022	+	15.2598i	−0.344244	+	0.596248i
$656$		0			0
$657$	−8.52111	−	4.64603i	−0.332440	−	0.181259i
$658$		0			0
$659$		−	10.0047i		−	0.389726i	−0.980830	−	0.194863i	$-0.937574\pi$
$659$		−	10.0047i		−	0.389726i	0.980830	−	0.194863i	$-0.0624263\pi$
$660$		0			0
$661$	−10.4004	−	6.00466i	−0.404528	−	0.233554i	0.283908	−	0.958852i	$-0.408369\pi$
$661$	−10.4004	−	6.00466i	−0.404528	−	0.233554i	−0.688436	+	0.725297i	$0.741702\pi$
$662$		0			0
$663$	−21.4823	+	38.2803i	−0.834304	+	1.48668i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−5.84563	−	10.1249i	−0.226344	−	0.392039i
$668$		0			0
$669$	−36.7792	+	0.449074i	−1.42196	+	0.0173622i
$670$		0			0
$671$	20.2013			0.779861
$672$		0			0
$673$	25.4740			0.981950			0.490975	−	0.871174i	$-0.336641\pi$
$673$	25.4740			0.981950			0.490975	+	0.871174i	$0.336641\pi$
$674$		0			0
$675$	18.4407	+	9.76443i	0.709784	+	0.375833i
$676$		0			0
$677$	−22.4573	−	38.8972i	−0.863105	−	1.49494i	−0.868917	−	0.494958i	$-0.835183\pi$
$677$	−22.4573	−	38.8972i	−0.863105	−	1.49494i	0.00581197	−	0.999983i	$-0.498150\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	9.89914	+	5.55524i	0.379336	+	0.212877i
$682$		0			0
$683$	20.3551	+	11.7520i	0.778866	+	0.449678i	0.836028	−	0.548687i	$-0.184872\pi$
$683$	20.3551	+	11.7520i	0.778866	+	0.449678i	−0.0571624	+	0.998365i	$0.518205\pi$
$684$		0			0
$685$		−	0.584186i		−	0.0223206i
$686$		0			0
$687$	15.2030	+	25.6052i	0.580030	+	0.976899i
$688$		0			0
$689$	34.7045	−	60.1100i	1.32214	−	2.29001i
$690$		0			0
$691$	17.7591	−	10.2532i	0.675587	−	0.390051i	−0.122603	−	0.992456i	$-0.539124\pi$
$691$	17.7591	−	10.2532i	0.675587	−	0.390051i	0.798190	+	0.602405i	$0.205791\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.47619	−	1.42963i	0.0939272	−	0.0542289i
$696$		0			0
$697$	16.9533	−	29.3640i	0.642154	−	1.11224i
$698$		0			0
$699$	11.0104	+	18.5439i	0.416450	+	0.701394i
$700$		0			0
$701$		−	20.4363i		−	0.771868i	−0.922526	−	0.385934i	$-0.873879\pi$
$701$		−	20.4363i		−	0.771868i	0.922526	−	0.385934i	$-0.126121\pi$
$702$		0			0
$703$	−7.59613	−	4.38563i	−0.286494	−	0.165407i
$704$		0			0
$705$	15.7896	+	8.86090i	0.594672	+	0.333721i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	8.93820	+	15.4814i	0.335681	+	0.581417i	0.983615	−	0.180279i	$-0.0577002\pi$
$709$	8.93820	+	15.4814i	0.335681	+	0.581417i	−0.647934	+	0.761696i	$0.724367\pi$
$710$		0			0
$711$	−22.6116	−	37.0451i	−0.848003	−	1.38930i
$712$		0			0
$713$	4.94039			0.185019
$714$		0			0
$715$	−16.7897			−0.627901
$716$		0			0
$717$	14.6301	−	0.178633i	0.546370	−	0.00667119i
$718$		0			0
$719$	−16.8707	−	29.2209i	−0.629170	−	1.08976i	−0.987719	−	0.156244i	$-0.950061\pi$
$719$	−16.8707	−	29.2209i	−0.629170	−	1.08976i	0.358548	−	0.933511i	$-0.383272\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	2.45798	−	4.37998i	0.0914131	−	0.162893i
$724$		0			0
$725$	23.2679	+	13.4337i	0.864148	+	0.498916i
$726$		0			0
$727$		−	11.5388i		−	0.427950i	−0.976839	−	0.213975i	$-0.931359\pi$
$727$		−	11.5388i		−	0.427950i	0.976839	−	0.213975i	$-0.0686411\pi$
$728$		0			0
$729$	−26.9276	+	1.97616i	−0.997318	+	0.0731910i
$730$		0			0
$731$	−20.0149	+	34.6668i	−0.740277	+	1.28220i
$732$		0			0
$733$	19.1264	−	11.0426i	0.706449	−	0.407869i	−0.103296	−	0.994651i	$-0.532939\pi$
$733$	19.1264	−	11.0426i	0.706449	−	0.407869i	0.809745	+	0.586782i	$0.199605\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	14.5504	−	8.40069i	0.535972	−	0.309443i
$738$		0			0
$739$	−0.524365	+	0.908228i	−0.0192891	+	0.0334097i	−0.875509	−	0.483202i	$-0.839474\pi$
$739$	−0.524365	+	0.908228i	−0.0192891	+	0.0334097i	0.856220	+	0.516612i	$0.172807\pi$
$740$		0			0
$741$	−26.8302	+	15.9303i	−0.985634	+	0.585216i
$742$		0			0
$743$			22.3254i			0.819040i	0.912301	+	0.409520i	$0.134304\pi$
$743$			22.3254i			0.819040i	−0.912301	+	0.409520i	$0.865696\pi$
$744$		0			0
$745$	1.36672	+	0.789075i	0.0500727	+	0.0289095i
$746$		0			0
$747$	50.5689	−	1.23508i	1.85022	−	0.0451892i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	4.54325	+	7.86913i	0.165785	+	0.287149i	0.936934	−	0.349507i	$-0.113651\pi$
$751$	4.54325	+	7.86913i	0.165785	+	0.287149i	−0.771149	+	0.636655i	$0.780317\pi$
$752$		0			0
$753$	−0.0271525	−	2.22379i	−0.000989494	−	0.0810395i
$754$		0			0
$755$	−15.0963			−0.549410
$756$		0			0
$757$	10.7231			0.389736			0.194868	−	0.980829i	$-0.437572\pi$
$757$	10.7231			0.389736			0.194868	+	0.980829i	$0.437572\pi$
$758$		0			0
$759$	0.0926967	+	7.59185i	0.00336468	+	0.275567i
$760$		0			0
$761$	−6.15464	−	10.6601i	−0.223105	−	0.386430i	0.732644	−	0.680612i	$-0.238286\pi$
$761$	−6.15464	−	10.6601i	−0.223105	−	0.386430i	−0.955749	+	0.294182i	$0.904953\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	11.1775	−	0.272997i	0.404125	−	0.00987022i
$766$		0			0
$767$	27.1279	+	15.6623i	0.979531	+	0.565532i
$768$		0			0
$769$			3.10213i			0.111866i	0.998435	+	0.0559328i	$0.0178133\pi$
$769$			3.10213i			0.111866i	−0.998435	+	0.0559328i	$0.982187\pi$
$770$		0			0
$771$	26.4977	−	15.7329i	0.954291	−	0.566606i
$772$		0			0
$773$	−14.9229	+	25.8472i	−0.536738	+	0.929658i	0.462339	+	0.886703i	$0.347010\pi$
$773$	−14.9229	+	25.8472i	−0.536738	+	0.929658i	−0.999077	+	0.0429546i	$0.986323\pi$
$774$		0			0
$775$	−9.83234	+	5.67670i	−0.353188	+	0.203913i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	20.8732	−	12.0511i	0.747859	−	0.431776i
$780$		0			0
$781$	5.72252	−	9.91170i	0.204768	−	0.354668i
$782$		0			0
$783$	−34.7418	+	1.27310i	−1.24157	+	0.0454969i
$784$		0			0
$785$			2.02974i			0.0724446i
$786$		0			0
$787$	35.2831	+	20.3707i	1.25771	+	0.726137i	0.972628	−	0.232367i	$-0.0746471\pi$
$787$	35.2831	+	20.3707i	1.25771	+	0.726137i	0.285078	+	0.958504i	$0.407980\pi$
$788$		0			0
$789$	−11.8192	+	21.0612i	−0.420775	+	0.749798i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	27.1642	+	47.0498i	0.964629	+	1.67079i
$794$		0			0
$795$	−17.6780	+	0.215849i	−0.626974	+	0.00765537i
$796$		0			0
$797$	34.2662			1.21377			0.606885	−	0.794789i	$-0.292419\pi$
$797$	34.2662			1.21377			0.606885	+	0.794789i	$0.292419\pi$
$798$		0			0
$799$	−39.5826			−1.40033
$800$		0			0
$801$	4.95625	+	8.11992i	0.175120	+	0.286903i
$802$		0			0
$803$	4.05772	+	7.02817i	0.143194	+	0.248019i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−2.10957	−	1.18386i	−0.0742604	−	0.0416738i
$808$		0			0
$809$	32.6805	+	18.8681i	1.14898	+	0.663367i	0.948640	−	0.316359i	$-0.102460\pi$
$809$	32.6805	+	18.8681i	1.14898	+	0.663367i	0.200345	+	0.979725i	$0.435794\pi$
$810$		0			0
$811$		−	33.3795i		−	1.17211i	−0.810270	−	0.586057i	$-0.800680\pi$
$811$		−	33.3795i		−	1.17211i	0.810270	−	0.586057i	$-0.199320\pi$
$812$		0			0
$813$	−9.45634	−	15.9266i	−0.331648	−	0.558570i
$814$		0			0
$815$	9.00937	−	15.6047i	0.315584	−	0.546608i
$816$		0			0
$817$	−24.6426	+	14.2274i	−0.862134	+	0.497753i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	7.03122	−	4.05948i	0.245391	−	0.141677i	−0.372261	−	0.928128i	$-0.621417\pi$
$821$	7.03122	−	4.05948i	0.245391	−	0.141677i	0.617652	+	0.786451i	$0.288084\pi$
$822$		0			0
$823$	−23.8466	+	41.3035i	−0.831241	+	1.43975i	0.0658143	+	0.997832i	$0.479036\pi$
$823$	−23.8466	+	41.3035i	−0.831241	+	1.43975i	−0.897055	+	0.441919i	$0.854298\pi$
$824$		0			0
$825$	−8.90781	−	15.0027i	−0.310130	−	0.522328i
$826$		0			0
$827$		−	11.7724i		−	0.409367i	−0.978828	−	0.204684i	$-0.934383\pi$
$827$		−	11.7724i		−	0.409367i	0.978828	−	0.204684i	$-0.0656166\pi$
$828$		0			0
$829$	−2.23286	−	1.28914i	−0.0775504	−	0.0447738i	0.460723	−	0.887544i	$-0.347590\pi$
$829$	−2.23286	−	1.28914i	−0.0775504	−	0.0447738i	−0.538274	+	0.842770i	$0.680923\pi$
$830$		0			0
$831$	−5.32298	−	2.98717i	−0.184652	−	0.103624i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	2.77324	+	4.80339i	0.0959719	+	0.166228i
$836$		0			0
$837$	6.87454	−	12.9830i	0.237619	−	0.448758i
$838$		0			0
$839$	−15.1790			−0.524036			−0.262018	−	0.965063i	$-0.584388\pi$
$839$	−15.1790			−0.524036			−0.262018	+	0.965063i	$0.584388\pi$
$840$		0			0
$841$	−15.7634			−0.543566
$842$		0			0
$843$	−13.5803	+	0.165816i	−0.467732	+	0.00571102i
$844$		0			0
$845$	−16.1281	−	27.9347i	−0.554825	−	0.960985i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−18.7528	+	33.4165i	−0.643595	+	1.14685i
$850$		0			0
$851$	−4.97076	−	2.86987i	−0.170395	−	0.0983778i
$852$		0			0
$853$			5.00496i			0.171367i	0.996322	+	0.0856833i	$0.0273073\pi$
$853$			5.00496i			0.171367i	−0.996322	+	0.0856833i	$0.972693\pi$
$854$		0			0
$855$	6.97799	+	3.80467i	0.238642	+	0.130117i
$856$		0			0
$857$	−10.8110	+	18.7251i	−0.369296	+	0.639639i	−0.989456	−	0.144837i	$-0.953734\pi$
$857$	−10.8110	+	18.7251i	−0.369296	+	0.639639i	0.620160	+	0.784475i	$0.287068\pi$
$858$		0			0
$859$	−8.35591	+	4.82429i	−0.285100	+	0.164603i	−0.635730	−	0.771912i	$-0.719301\pi$
$859$	−8.35591	+	4.82429i	−0.285100	+	0.164603i	0.350630	+	0.936514i	$0.385967\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	39.4774	−	22.7923i	1.34383	−	0.775858i	0.356459	−	0.934311i	$-0.383984\pi$
$863$	39.4774	−	22.7923i	1.34383	−	0.775858i	0.987367	+	0.158453i	$0.0506505\pi$
$864$		0			0
$865$	2.22900	−	3.86074i	0.0757882	−	0.131269i
$866$		0			0
$867$	4.30079	−	2.55358i	0.146063	−	0.0867240i
$868$		0			0
$869$			36.2907i			1.23108i
$870$		0			0
$871$	39.1313	+	22.5925i	1.32591	+	0.765516i
$872$		0			0
$873$	−0.0724733	−	2.96733i	−0.00245285	−	0.100429i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−25.7585	−	44.6150i	−0.869802	−	1.50654i	−0.862199	−	0.506570i	$-0.830913\pi$
$877$	−25.7585	−	44.6150i	−0.869802	−	1.50654i	−0.00760306	−	0.999971i	$-0.502420\pi$
$878$		0			0
$879$	−0.435148	−	35.6385i	−0.0146772	−	1.20206i
$880$		0			0
$881$	10.4316			0.351448			0.175724	−	0.984439i	$-0.443773\pi$
$881$	10.4316			0.351448			0.175724	+	0.984439i	$0.443773\pi$
$882$		0			0
$883$	−10.6345			−0.357880			−0.178940	−	0.983860i	$-0.557267\pi$
$883$	−10.6345			−0.357880			−0.178940	+	0.983860i	$0.557267\pi$
$884$		0			0
$885$	−0.0974134	−	7.97815i	−0.00327452	−	0.268183i
$886$		0			0
$887$	9.85887	+	17.0761i	0.331028	+	0.573358i	0.982714	−	0.185131i	$-0.0592711\pi$
$887$	9.85887	+	17.0761i	0.331028	+	0.573358i	−0.651685	+	0.758489i	$0.725938\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	20.0798	+	10.3204i	0.672699	+	0.345747i
$892$		0			0
$893$	−24.3673	−	14.0684i	−0.815419	−	0.470783i
$894$		0			0
$895$		−	19.8154i		−	0.662356i
$896$		0			0
$897$	−17.5572	+	10.4245i	−0.586217	+	0.348064i
$898$		0			0
$899$	9.45787	−	16.3815i	0.315437	−	0.546354i
$900$		0			0
$901$	33.4716	−	19.3249i	1.11510	−	0.643804i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−3.81447	+	2.20229i	−0.126797	+	0.0732064i
$906$		0			0
$907$	20.4758	−	35.4651i	0.679888	−	1.17760i	−0.295126	−	0.955458i	$-0.595362\pi$
$907$	20.4758	−	35.4651i	0.679888	−	1.17760i	0.975014	−	0.222142i	$-0.0713049\pi$
$908$		0			0
$909$	14.4209	−	26.4487i	0.478310	−	0.877249i
$910$		0			0
$911$		−	27.0641i		−	0.896672i	−0.893865	−	0.448336i	$-0.852017\pi$
$911$		−	27.0641i		−	0.896672i	0.893865	−	0.448336i	$-0.147983\pi$
$912$		0			0
$913$	−36.6304	−	21.1486i	−1.21229	−	0.699916i
$914$		0			0
$915$	6.77222	−	12.0677i	0.223883	−	0.398947i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	9.40788	+	16.2949i	0.310337	+	0.537520i	0.978435	−	0.206553i	$-0.0662247\pi$
$919$	9.40788	+	16.2949i	0.310337	+	0.537520i	−0.668098	+	0.744073i	$0.732891\pi$
$920$		0			0
$921$	−50.9396	+	0.621974i	−1.67852	+	0.0204947i
$922$		0			0
$923$	30.7798			1.01313
$924$		0			0
$925$	13.1904			0.433696
$926$		0			0
$927$	−20.3741	+	12.4360i	−0.669173	+	0.408451i
$928$		0			0
$929$	−13.6737	−	23.6836i	−0.448620	−	0.777033i	0.549676	−	0.835378i	$-0.314751\pi$
$929$	−13.6737	−	23.6836i	−0.448620	−	0.777033i	−0.998296	+	0.0583449i	$0.981418\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−12.1998	−	6.84636i	−0.399405	−	0.224140i
$934$		0			0
$935$	−8.09663	−	4.67459i	−0.264788	−	0.152876i
$936$		0			0
$937$		−	49.4739i		−	1.61624i	−0.589018	−	0.808120i	$-0.700485\pi$
$937$		−	49.4739i		−	1.61624i	0.589018	−	0.808120i	$-0.299515\pi$
$938$		0			0
$939$	1.07047	+	1.80292i	0.0349336	+	0.0588360i
$940$		0			0
$941$	24.2430	−	41.9900i	0.790298	−	1.36884i	−0.135485	−	0.990779i	$-0.543259\pi$
$941$	24.2430	−	41.9900i	0.790298	−	1.36884i	0.925782	−	0.378057i	$-0.123408\pi$
$942$		0			0
$943$	13.6590	−	7.88601i	0.444797	−	0.256804i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−7.42426	+	4.28640i	−0.241256	+	0.139289i	−0.615754	−	0.787939i	$-0.711148\pi$
$947$	−7.42426	+	4.28640i	−0.241256	+	0.139289i	0.374498	+	0.927228i	$0.377815\pi$
$948$		0			0
$949$	−10.9127	+	18.9013i	−0.354240	+	0.613561i
$950$		0			0
$951$	−26.3376	−	44.3583i	−0.854054	−	1.43842i
$952$		0			0
$953$		−	44.7977i		−	1.45114i	−0.688149	−	0.725570i	$-0.741576\pi$
$953$		−	44.7977i		−	1.45114i	0.688149	−	0.725570i	$-0.258424\pi$
$954$		0			0
$955$	−2.78556	−	1.60824i	−0.0901386	−	0.0520416i
$956$		0			0
$957$	25.3507	+	14.2264i	0.819473	+	0.459875i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−11.5034	−	19.9244i	−0.371077	−	0.642724i
$962$		0			0
$963$	−41.8309	+	25.5328i	−1.34798	+	0.822782i
$964$		0			0
$965$	−13.1630			−0.423730
$966$		0			0
$967$	14.4085			0.463346			0.231673	−	0.972794i	$-0.425580\pi$
$967$	14.4085			0.463346			0.231673	+	0.972794i	$0.425580\pi$
$968$		0			0
$969$	−17.3739	+	0.212135i	−0.558129	+	0.00681477i
$970$		0			0
$971$	−1.91524	−	3.31730i	−0.0614630	−	0.106457i	0.833657	−	0.552283i	$-0.186243\pi$
$971$	−1.91524	−	3.31730i	−0.0614630	−	0.106457i	−0.895120	+	0.445826i	$0.852910\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	22.9640	−	40.9206i	0.735437	−	1.31051i
$976$		0			0
$977$	−31.0908	−	17.9503i	−0.994683	−	0.574281i	−0.0880123	−	0.996119i	$-0.528051\pi$
$977$	−31.0908	−	17.9503i	−0.994683	−	0.574281i	−0.906671	+	0.421839i	$0.861385\pi$
$978$		0			0
$979$		−	7.95456i		−	0.254229i
$980$		0			0
$981$	−13.5487	+	24.8491i	−0.432576	+	0.793370i
$982$		0			0
$983$	23.7286	−	41.0991i	0.756824	−	1.31086i	−0.187638	−	0.982238i	$-0.560083\pi$
$983$	23.7286	−	41.0991i	0.756824	−	1.31086i	0.944462	−	0.328620i	$-0.106583\pi$
$984$		0			0
$985$	16.0810	−	9.28436i	0.512383	−	0.295824i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−16.1256	+	9.31011i	−0.512764	+	0.296044i
$990$		0			0
$991$	−28.0314	+	48.5518i	−0.890446	+	1.54230i	−0.0511039	+	0.998693i	$0.516274\pi$
$991$	−28.0314	+	48.5518i	−0.890446	+	1.54230i	−0.839342	+	0.543604i	$0.817059\pi$
$992$		0			0
$993$	18.4680	−	10.9653i	0.586066	−	0.347974i
$994$		0			0
$995$		−	1.24071i		−	0.0393331i
$996$		0			0
$997$	45.6872	+	26.3775i	1.44693	+	0.835385i	0.998297	−	0.0583312i	$-0.0185779\pi$
$997$	45.6872	+	26.3775i	1.44693	+	0.835385i	0.448632	+	0.893716i	$0.351911\pi$
$998$		0			0
$999$	−14.4586	+	9.06938i	−0.457450	+	0.286943i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1176.2.u.c.521.12		48
3.2	odd	2	inner	1176.2.u.c.521.4		48
7.2	even	3	inner	1176.2.u.c.1097.21		48
7.3	odd	6		1176.2.k.b.881.19	yes	24
7.4	even	3		1176.2.k.b.881.6	yes	24
7.5	odd	6	inner	1176.2.u.c.1097.4		48
7.6	odd	2	inner	1176.2.u.c.521.13		48
21.2	odd	6	inner	1176.2.u.c.1097.13		48
21.5	even	6	inner	1176.2.u.c.1097.12		48
21.11	odd	6		1176.2.k.b.881.20	yes	24
21.17	even	6		1176.2.k.b.881.5	✓	24
21.20	even	2	inner	1176.2.u.c.521.21		48
28.3	even	6		2352.2.k.j.881.6		24
28.11	odd	6		2352.2.k.j.881.19		24
84.11	even	6		2352.2.k.j.881.5		24
84.59	odd	6		2352.2.k.j.881.20		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1176.2.k.b.881.5	✓	24	21.17	even	6
1176.2.k.b.881.6	yes	24	7.4	even	3
1176.2.k.b.881.19	yes	24	7.3	odd	6
1176.2.k.b.881.20	yes	24	21.11	odd	6
1176.2.u.c.521.4		48	3.2	odd	2	inner
1176.2.u.c.521.12		48	1.1	even	1	trivial
1176.2.u.c.521.13		48	7.6	odd	2	inner
1176.2.u.c.521.21		48	21.20	even	2	inner
1176.2.u.c.1097.4		48	7.5	odd	6	inner
1176.2.u.c.1097.12		48	21.5	even	6	inner
1176.2.u.c.1097.13		48	21.2	odd	6	inner
1176.2.u.c.1097.21		48	7.2	even	3	inner
2352.2.k.j.881.5		24	84.11	even	6
2352.2.k.j.881.6		24	28.3	even	6
2352.2.k.j.881.19		24	28.11	odd	6
2352.2.k.j.881.20		24	84.59	odd	6

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:	\( N \)	\(=\)	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1176.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0211468 - 1.73192i) q^{3} +(0.496051 + 0.859186i) q^{5} +(-2.99911 + 0.0732492i) q^{9} +(2.17245 + 1.25426i) q^{11} +6.74633i q^{13} +(1.47755 - 0.877291i) q^{15} +(-1.87831 + 3.25333i) q^{17} +(-2.31260 + 1.33518i) q^{19} +(-1.51332 + 0.873715i) q^{23} +(2.00787 - 3.47773i) q^{25} +(0.190283 + 5.19267i) q^{27} +6.69055i q^{29} +(-2.44846 - 1.41362i) q^{31} +(2.12635 - 3.78904i) q^{33} +(1.64234 + 2.84461i) q^{37} +(11.6841 - 0.142663i) q^{39} -9.02583 q^{41} +10.6558 q^{43} +(-1.55065 - 2.54046i) q^{45} +(5.26837 + 9.12508i) q^{47} +(5.67424 + 3.18429i) q^{51} +(-8.91002 - 5.14420i) q^{53} +2.48872i q^{55} +(2.36133 + 3.97701i) q^{57} +(2.32160 - 4.02113i) q^{59} +(6.97413 - 4.02651i) q^{61} +(-5.79636 + 3.34653i) q^{65} +(3.34885 - 5.80038i) q^{67} +(1.54521 + 2.60247i) q^{69} -4.56245i q^{71} +(2.80171 + 1.61757i) q^{73} +(-6.06561 - 3.40392i) q^{75} +(7.23346 + 12.5287i) q^{79} +(8.98927 - 0.439364i) q^{81} -16.8613 q^{83} -3.72696 q^{85} +(11.5875 - 0.141484i) q^{87} +(-1.58550 - 2.74617i) q^{89} +(-2.39650 + 4.27043i) q^{93} +(-2.29434 - 1.32464i) q^{95} +0.989407i q^{97} +(-6.60728 - 3.60254i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 32 q^{15} - 8 q^{25} - 16 q^{37} + 64 q^{39} + 32 q^{43} - 48 q^{51} + 96 q^{57} - 16 q^{67} - 80 q^{81} - 128 q^{85} + 32 q^{93} - 112 q^{99}+O(q^{100}) \) 48 * q - 32 * q^15 - 8 * q^25 - 16 * q^37 + 64 * q^39 + 32 * q^43 - 48 * q^51 + 96 * q^57 - 16 * q^67 - 80 * q^81 - 128 * q^85 + 32 * q^93 - 112 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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