LMFDB - Embedded newform 1176.2.u.c.521.21

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1176,2,Mod(521,1176)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [48,0,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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			521.21
Character	$\chi$	$=$	1176.521
Dual form			1176.2.u.c.1097.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.51046 - 0.847647i) q^{3} +(0.496051 + 0.859186i) q^{5} +(1.56299 - 2.56068i) q^{9} +(-2.17245 - 1.25426i) q^{11} -6.74633i q^{13} +(1.47755 + 0.877291i) q^{15} +(-1.87831 + 3.25333i) q^{17} +(2.31260 - 1.33518i) q^{19} +(1.51332 - 0.873715i) q^{23} +(2.00787 - 3.47773i) q^{25} +(0.190283 - 5.19267i) q^{27} -6.69055i q^{29} +(2.44846 + 1.41362i) q^{31} +(-4.34458 - 0.0530474i) q^{33} +(1.64234 + 2.84461i) q^{37} +(-5.71851 - 10.1901i) q^{39} -9.02583 q^{41} +10.6558 q^{43} +(2.97542 + 0.0726708i) q^{45} +(5.26837 + 9.12508i) q^{47} +(-0.0794406 + 6.50618i) q^{51} +(8.91002 + 5.14420i) q^{53} -2.48872i q^{55} +(2.36133 - 3.97701i) q^{57} +(2.32160 - 4.02113i) q^{59} +(-6.97413 + 4.02651i) q^{61} +(5.79636 - 3.34653i) q^{65} +(3.34885 - 5.80038i) q^{67} +(1.54521 - 2.60247i) q^{69} +4.56245i q^{71} +(-2.80171 - 1.61757i) q^{73} +(0.0849199 - 6.95493i) q^{75} +(7.23346 + 12.5287i) q^{79} +(-4.11413 - 8.00462i) q^{81} -16.8613 q^{83} -3.72696 q^{85} +(-5.67122 - 10.1058i) q^{87} +(-1.58550 - 2.74617i) q^{89} +(4.89655 + 0.0597870i) q^{93} +(2.29434 + 1.32464i) q^{95} -0.989407i q^{97} +(-6.60728 + 3.60254i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.51046	−	0.847647i	0.872065	−	0.489389i
$3$	1.51046	−	0.847647i	0.872065	−	0.489389i
$4$		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
$9$	1.56299	−	2.56068i	0.520996	−	0.853559i
$10$		0			0
$11$	−2.17245	−	1.25426i	−0.655018	−	0.378175i	0.135358	−	0.990797i	$-0.456782\pi$
$11$	−2.17245	−	1.25426i	−0.655018	−	0.378175i	−0.790376	+	0.612622i	$0.790115\pi$
$12$		0			0
$13$		−	6.74633i		−	1.87110i	−0.353199	−	0.935548i	$-0.614906\pi$
$13$		−	6.74633i		−	1.87110i	0.353199	−	0.935548i	$-0.385094\pi$
$14$		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	−0.210692	−	0.977552i	$-0.567572\pi$
$19$	2.31260	−	1.33518i	0.530547	−	0.306312i	0.741239	+	0.671241i	$0.234238\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.51332	−	0.873715i	0.315549	−	0.182182i	−0.333858	−	0.942623i	$-0.608351\pi$
$23$	1.51332	−	0.873715i	0.315549	−	0.182182i	0.649407	+	0.760441i	$0.275017\pi$
$24$		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	$-0.786645\pi$
$29$		−	6.69055i		−	1.24240i	0.783651	−	0.621202i	$-0.213355\pi$
$30$		0			0
$31$	2.44846	+	1.41362i	0.439756	+	0.253893i	0.703494	−	0.710701i	$-0.251622\pi$
$31$	2.44846	+	1.41362i	0.439756	+	0.253893i	−0.263738	+	0.964594i	$0.584956\pi$
$32$		0			0
$33$	−4.34458	−	0.0530474i	−0.756294	−	0.00923437i
$34$		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
$39$	−5.71851	−	10.1901i	−0.915695	−	1.63172i
$40$		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
$45$	2.97542	+	0.0726708i	0.443550	+	0.0108331i
$46$		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
$51$	−0.0794406	+	6.50618i	−0.0111239	+	0.911048i
$52$		0			0
$53$	8.91002	+	5.14420i	1.22389	+	0.706611i	0.965744	−	0.259496i	$-0.0835565\pi$
$53$	8.91002	+	5.14420i	1.22389	+	0.706611i	0.258142	+	0.966107i	$0.416890\pi$
$54$		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	−0.874905	−	0.484295i	$-0.839076\pi$
$61$	−6.97413	+	4.02651i	−0.892945	+	0.515542i	−0.0180407	+	0.999837i	$0.505743\pi$
$62$		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	$0.0872656\pi$
$71$			4.56245i			0.541463i	−0.962655	+	0.270732i	$0.912734\pi$
$72$		0			0
$73$	−2.80171	−	1.61757i	−0.327915	−	0.189322i	0.327000	−	0.945024i	$-0.393962\pi$
$73$	−2.80171	−	1.61757i	−0.327915	−	0.189322i	−0.654915	+	0.755702i	$0.727296\pi$
$74$		0			0
$75$	0.0849199	−	6.95493i	0.00980571	−	0.803087i
$76$		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
$81$	−4.11413	−	8.00462i	−0.457126	−	0.889402i
$82$		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
$87$	−5.67122	−	10.1058i	−0.608019	−	1.08346i
$88$		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
$93$	4.89655	+	0.0597870i	0.507748	+	0.00619962i
$94$		0			0
$95$	2.29434	+	1.32464i	0.235394	+	0.135905i
$96$		0			0
$97$		−	0.989407i		−	0.100459i	−0.998738	−	0.0502295i	$-0.984005\pi$
$97$		−	0.989407i		−	0.100459i	0.998738	−	0.0502295i	$-0.0159953\pi$
$98$		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	−0.799458	−	0.600722i	$-0.794880\pi$
$103$	−6.89056	+	3.97826i	−0.678947	+	0.391990i	0.120511	+	0.992712i	$0.461547\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−14.1473	+	8.16794i	−1.36767	+	0.789624i	−0.990630	−	0.136573i	$-0.956391\pi$
$107$	−14.1473	+	8.16794i	−1.36767	+	0.789624i	−0.377039	+	0.926197i	$0.623058\pi$
$108$		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	$-0.662529\pi$
$113$		−	18.5486i		−	1.74490i	0.488702	−	0.872451i	$-0.337471\pi$
$114$		0			0
$115$	1.50137	+	0.866816i	0.140003	+	0.0808310i
$116$		0			0
$117$	−17.2752	−	10.5444i	−1.59709	−	0.974834i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−2.35364	−	4.07662i	−0.213967	−	0.370602i
$122$		0			0
$123$	−13.6332	+	7.65072i	−1.22926	+	0.689843i
$124$		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
$129$	16.0951	−	9.03233i	1.41710	−	0.795252i
$130$		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
$135$	4.55586	−	2.41234i	0.392106	−	0.207621i
$136$		0			0
$137$	0.509947	+	0.294418i	0.0435677	+	0.0251538i	0.521626	−	0.853174i	$-0.325326\pi$
$137$	0.509947	+	0.294418i	0.0435677	+	0.0251538i	−0.478058	+	0.878328i	$0.658659\pi$
$138$		0			0
$139$			2.88202i			0.244449i	0.992502	+	0.122225i	$0.0390029\pi$
$139$			2.88202i			0.244449i	−0.992502	+	0.122225i	$0.960997\pi$
$140$		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	−0.555366	−	0.831606i	$-0.687422\pi$
$149$	−1.37760	+	0.795356i	−0.112857	+	0.0651581i	0.442509	+	0.896764i	$0.354089\pi$
$150$		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	0.427628	−	0.903955i	$-0.359349\pi$
$157$	−1.77180	−	1.02295i	−0.141405	−	0.0816403i	−0.569033	+	0.822314i	$0.692683\pi$
$158$		0			0
$159$	17.8187	+	0.217567i	1.41312	+	0.0172542i
$160$		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
$165$	−2.10956	−	3.75912i	−0.164229	−	0.292647i
$166$		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
$171$	0.195602	−	8.00870i	0.0149581	−	0.612441i
$172$		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
$177$	0.0981888	−	8.04166i	0.00738032	−	0.604448i
$178$		0			0
$179$	17.2972	+	9.98657i	1.29286	+	0.746431i	0.979160	−	0.203092i	$-0.0650991\pi$
$179$	17.2972	+	9.98657i	1.29286	+	0.746431i	0.313697	+	0.949523i	$0.398432\pi$
$180$		0			0
$181$		−	4.43963i		−	0.329995i	−0.986294	−	0.164998i	$-0.947238\pi$
$181$		−	4.43963i		−	0.329995i	0.986294	−	0.164998i	$-0.0527616\pi$
$182$		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	−0.394968	−	0.918695i	$-0.629244\pi$
$191$	2.80773	−	1.62105i	0.203161	−	0.117295i	0.598129	+	0.801400i	$0.295911\pi$
$192$		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	$0.232315\pi$
$197$			18.7165i			1.33350i	−0.745282	+	0.666749i	$0.767685\pi$
$198$		0			0
$199$	1.08304	+	0.625292i	0.0767745	+	0.0443258i	0.537896	−	0.843011i	$-0.319219\pi$
$199$	1.08304	+	0.625292i	0.0767745	+	0.0443258i	−0.461121	+	0.887337i	$0.652553\pi$
$200$		0			0
$201$	0.141635	−	11.5999i	0.00999016	−	0.818193i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−4.47728	−	7.75487i	−0.312707	−	0.541624i
$206$		0			0
$207$	0.127998	−	5.24073i	0.00889647	−	0.364256i
$208$		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
$213$	3.86735	+	6.89141i	0.264986	+	0.472191i
$214$		0			0
$215$	5.28581	+	9.15529i	0.360489	+	0.624386i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−5.60300	−	0.0684128i	−0.378616	−	0.00462291i
$220$		0			0
$221$	21.9481	+	12.6717i	1.47639	+	0.852392i
$222$		0			0
$223$			21.2360i			1.42207i	0.703156	+	0.711035i	$0.251773\pi$
$223$			21.2360i			1.42207i	−0.703156	+	0.711035i	$0.748227\pi$
$224$		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	0.0804602	−	0.996758i	$-0.474361\pi$
$229$	14.8892	−	8.59630i	0.983908	−	0.568059i	0.903448	+	0.428698i	$0.141028\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	10.7831	−	6.22564i	0.706426	−	0.407855i	−0.103310	−	0.994649i	$-0.532943\pi$
$233$	10.7831	−	6.22564i	0.706426	−	0.407855i	0.809736	+	0.586794i	$0.199610\pi$
$234$		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	$-0.911916\pi$
$239$		−	8.44730i		−	0.546410i	0.961956	−	0.273205i	$-0.0880838\pi$
$240$		0			0
$241$	−2.51127	−	1.44988i	−0.161765	−	0.0933951i	0.416932	−	0.908938i	$-0.363105\pi$
$241$	−2.51127	−	1.44988i	−0.161765	−	0.0933951i	−0.578697	+	0.815543i	$0.696439\pi$
$242$		0			0
$243$	−12.9993	−	8.60333i	−0.833908	−	0.551904i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−9.00758	−	15.6016i	−0.573139	−	0.992705i
$248$		0			0
$249$	−25.4684	+	14.2925i	−1.61399	+	0.905748i
$250$		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
$255$	−5.62943	+	3.15915i	−0.352528	+	0.197833i
$256$		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
$261$	−17.1323	−	10.4572i	−1.06046	−	0.647287i
$262$		0			0
$263$	12.0755	+	6.97177i	0.744605	+	0.429898i	0.823741	−	0.566966i	$-0.191883\pi$
$263$	12.0755	+	6.97177i	0.744605	+	0.429898i	−0.0791363	+	0.996864i	$0.525216\pi$
$264$		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	−0.754179	−	0.656669i	$-0.771965\pi$
$271$	−9.26119	+	5.34695i	−0.562577	+	0.324804i	0.191602	+	0.981473i	$0.438632\pi$
$272$		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	$0.0751434\pi$
$281$			7.84120i			0.467767i	−0.972265	+	0.233883i	$0.924857\pi$
$282$		0			0
$283$	19.1594	+	11.0617i	1.13891	+	0.657550i	0.946160	−	0.323699i	$-0.104926\pi$
$283$	19.1594	+	11.0617i	1.13891	+	0.657550i	0.192749	+	0.981248i	$0.438260\pi$
$284$		0			0
$285$	4.58834	+	0.0560237i	0.271790	+	0.00331856i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	1.44388	+	2.50088i	0.0849343	+	0.147110i
$290$		0			0
$291$	−0.838668	−	1.49446i	−0.0491636	−	0.0876068i
$292$		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
$297$	−6.92636	+	11.0421i	−0.401908	+	0.640730i
$298$		0			0
$299$	−5.89438	−	10.2094i	−0.340881	−	0.590422i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−0.212347	+	17.3912i	−0.0121990	+	0.999098i
$304$		0			0
$305$	−6.91905	−	3.99472i	−0.396184	−	0.228737i
$306$		0			0
$307$			29.4122i			1.67864i	0.543636	+	0.839321i	$0.317047\pi$
$307$			29.4122i			1.67864i	−0.543636	+	0.839321i	$0.682953\pi$
$308$		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	−0.470078	−	0.882625i	$-0.655774\pi$
$313$	1.04838	−	0.605284i	0.0592581	−	0.0342127i	0.529336	+	0.848412i	$0.322441\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−25.7940	+	14.8922i	−1.44874	+	0.836429i	−0.998406	−	0.0564326i	$-0.982027\pi$
$317$	−25.7940	+	14.8922i	−1.44874	+	0.836429i	−0.450331	+	0.892862i	$0.648694\pi$
$318$		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
$327$	0.199504	−	16.3394i	0.0110326	−	0.903569i
$328$		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
$333$	9.85107	+	0.240600i	0.539835	+	0.0131848i
$334$		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
$339$	−15.7226	−	28.0169i	−0.853936	−	1.52167i
$340$		0			0
$341$	−3.54610	−	6.14202i	−0.192032	−	0.332609i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	3.00251	+	0.0366608i	0.161650	+	0.00197375i
$346$		0			0
$347$	−8.03173	−	4.63712i	−0.431166	−	0.248934i	0.268677	−	0.963230i	$-0.413414\pi$
$347$	−8.03173	−	4.63712i	−0.431166	−	0.248934i	−0.699843	+	0.714296i	$0.746747\pi$
$348$		0			0
$349$		−	17.2999i		−	0.926043i	−0.886347	−	0.463021i	$-0.846765\pi$
$349$		−	17.2999i		−	0.926043i	0.886347	−	0.463021i	$-0.153235\pi$
$350$		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	−0.161001	−	0.986954i	$-0.551472\pi$
$359$	11.6190	−	6.70821i	0.613225	−	0.354046i	0.774227	+	0.632908i	$0.218139\pi$
$360$		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	0.279824	−	0.960051i	$-0.409724\pi$
$367$	−7.88688	−	4.55350i	−0.411692	−	0.237691i	−0.691516	+	0.722361i	$0.743057\pi$
$368$		0			0
$369$	−14.1073	+	23.1122i	−0.734395	+	1.20318i
$370$		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
$375$	13.5104	−	7.58181i	0.697673	−	0.391523i
$376$		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
$381$	15.4070	−	8.64614i	0.789322	−	0.442955i
$382$		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
$387$	16.6548	−	27.2860i	0.846613	−	1.38702i
$388$		0			0
$389$	15.7439	+	9.08974i	0.798247	+	0.460868i	0.842858	−	0.538136i	$-0.180871\pi$
$389$	15.7439	+	9.08974i	0.798247	+	0.460868i	−0.0446107	+	0.999004i	$0.514205\pi$
$390$		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	−0.545932	−	0.837829i	$-0.683824\pi$
$397$	−1.85933	+	1.07349i	−0.0933172	+	0.0538767i	0.452615	+	0.891706i	$0.350491\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−10.1853	+	5.88049i	−0.508630	+	0.293658i	−0.732270	−	0.681014i	$-0.761539\pi$
$401$	−10.1853	+	5.88049i	−0.508630	+	0.293658i	0.223640	+	0.974672i	$0.428206\pi$
$402$		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	0.0334538	−	0.999440i	$-0.489349\pi$
$409$	−16.4896	−	9.52030i	−0.815360	−	0.470748i	−0.848814	+	0.528692i	$0.822683\pi$
$410$		0			0
$411$	1.01982	+	0.0124520i	0.0503039	+	0.000614212i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−8.36409	−	14.4870i	−0.410577	−	0.711141i
$416$		0			0
$417$	2.44293	+	4.35317i	0.119631	+	0.213176i
$418$		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
$423$	31.6008	+	0.771807i	1.53648	+	0.0375266i
$424$		0			0
$425$	7.54280	+	13.0645i	0.365880	+	0.633722i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−0.357875	+	29.3100i	−0.0172784	+	1.41510i
$430$		0			0
$431$	−21.5180	−	12.4234i	−1.03648	−	0.598414i	−0.117649	−	0.993055i	$-0.537536\pi$
$431$	−21.5180	−	12.4234i	−1.03648	−	0.598414i	−0.918835	+	0.394641i	$0.870869\pi$
$432$		0			0
$433$			14.9303i			0.717502i	0.933433	+	0.358751i	$0.116797\pi$
$433$			14.9303i			0.717502i	−0.933433	+	0.358751i	$0.883203\pi$
$434$		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	−0.789179	−	0.614163i	$-0.789494\pi$
$439$	−13.6586	+	7.88578i	−0.651888	+	0.376368i	0.137291	+	0.990531i	$0.456160\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	11.4712	−	6.62292i	0.545015	−	0.314665i	−0.202094	−	0.979366i	$-0.564775\pi$
$443$	11.4712	−	6.62292i	0.545015	−	0.314665i	0.747109	+	0.664702i	$0.231441\pi$
$444$		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	$-0.892409\pi$
$449$		−	14.0532i		−	0.663212i	0.943418	−	0.331606i	$-0.107591\pi$
$450$		0			0
$451$	19.6082	+	11.3208i	0.923313	+	0.533075i
$452$		0			0
$453$	−0.321779	+	26.3537i	−0.0151185	+	1.23820i
$454$		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
$459$	16.5361	+	10.3725i	0.771837	+	0.484147i
$460$		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
$465$	2.37757	+	4.23670i	0.110257	+	0.196472i
$466$		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
$471$	−3.54334	−	0.0432642i	−0.163268	−	0.00199351i
$472$		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	$-0.779445\pi$
$491$		−	28.3082i		−	1.27753i	0.769401	−	0.638766i	$-0.220555\pi$
$492$		0			0
$493$	21.7666	+	12.5669i	0.980317	+	0.565986i
$494$		0			0
$495$	−6.37281	−	3.88984i	−0.286436	−	0.174835i
$496$		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
$501$	8.44443	−	4.73888i	0.377269	−	0.211718i
$502$		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
$507$	−49.1097	+	27.5596i	−2.18104	+	1.22396i
$508$		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
$513$	−6.49310	−	12.2626i	−0.286677	−	0.541409i
$514$		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	−0.452717	−	0.891654i	$-0.649545\pi$
$523$	2.12958	−	1.22951i	0.0931200	−	0.0537628i	0.545837	+	0.837891i	$0.316212\pi$
$524$		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
$537$	34.5919	+	0.422368i	1.49275	+	0.0182265i
$538$		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
$543$	−3.76324	−	6.70589i	−0.161496	−	0.287777i
$544$		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
$549$	−0.589878	+	24.1519i	−0.0251754	+	1.03078i
$550$		0			0
$551$	−8.93309	−	15.4726i	−0.380563	−	0.659154i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−0.0689118	+	5.64387i	−0.00292514	+	0.239569i
$556$		0			0
$557$	−32.9104	−	19.0008i	−1.39446	−	0.805091i	−0.400653	−	0.916230i	$-0.631217\pi$
$557$	−32.9104	−	19.0008i	−1.39446	−	0.805091i	−0.993805	+	0.111139i	$0.964550\pi$
$558$		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	0.0106920	−	0.999943i	$-0.496597\pi$
$569$	21.0393	−	12.1471i	0.882014	−	0.509231i	0.871322	+	0.490712i	$0.163263\pi$
$570$		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	0.159313	−	0.987228i	$-0.449072\pi$
$577$	−14.7967	−	8.54288i	−0.615995	−	0.355645i	−0.775308	+	0.631583i	$0.782405\pi$
$578$		0			0
$579$	−0.280570	+	22.9787i	−0.0116601	+	0.954961i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−12.9044	−	22.3511i	−0.534445	−	0.925686i
$584$		0			0
$585$	0.490261	−	20.0732i	0.0202698	−	0.829924i
$586$		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
$591$	15.8650	+	28.2706i	0.652600	+	1.16290i
$592$		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
$597$	2.16591	+	0.0264459i	0.0886450	+	0.00108236i
$598$		0			0
$599$	28.2920	+	16.3344i	1.15598	+	0.667405i	0.950337	−	0.311222i	$-0.100738\pi$
$599$	28.2920	+	16.3344i	1.15598	+	0.667405i	0.205642	+	0.978627i	$0.434072\pi$
$600$		0			0
$601$		−	27.2379i		−	1.11106i	−0.831497	−	0.555529i	$-0.812516\pi$
$601$		−	27.2379i		−	1.11106i	0.831497	−	0.555529i	$-0.187484\pi$
$602$		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	−0.922469	−	0.386071i	$-0.873832\pi$
$607$	−25.8534	+	14.9264i	−1.04936	+	0.605846i	−0.126887	+	0.991917i	$0.540498\pi$
$608$		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	$-0.805670\pi$
$617$		−	28.4800i		−	1.14656i	0.819359	−	0.573281i	$-0.194330\pi$
$618$		0			0
$619$	39.5948	+	22.8601i	1.59145	+	0.918824i	0.993059	+	0.117620i	$0.0375265\pi$
$619$	39.5948	+	22.8601i	1.59145	+	0.918824i	0.598391	+	0.801204i	$0.295807\pi$
$620$		0			0
$621$	−4.24895	−	8.02442i	−0.170505	−	0.322009i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−5.60238	−	9.70361i	−0.224095	−	0.388144i
$626$		0			0
$627$	−10.1181	+	5.67812i	−0.404078	+	0.226762i
$628$		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
$633$	−1.57215	+	0.882268i	−0.0624875	+	0.0350670i
$634$		0			0
$635$	5.05980	+	8.76384i	0.200792	+	0.347782i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	11.6830	+	7.13106i	0.462171	+	0.282100i
$640$		0			0
$641$	−32.8738	−	18.9797i	−1.29844	−	0.749652i	−0.318301	−	0.947990i	$-0.603112\pi$
$641$	−32.8738	−	18.9797i	−1.29844	−	0.749652i	−0.980134	+	0.198338i	$0.936446\pi$
$642$		0			0
$643$			3.90637i			0.154052i	0.997029	+	0.0770262i	$0.0245425\pi$
$643$			3.90637i			0.154052i	−0.997029	+	0.0770262i	$0.975458\pi$
$644$		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	−0.497686	−	0.867357i	$-0.665817\pi$
$653$	0.118160	−	0.0682197i	0.00462396	−	0.00266964i	0.502310	+	0.864687i	$0.332484\pi$
$654$		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	$0.0624263\pi$
$659$			10.0047i			0.389726i	−0.980830	+	0.194863i	$0.937574\pi$
$660$		0			0
$661$	10.4004	+	6.00466i	0.404528	+	0.233554i	0.688436	−	0.725297i	$-0.258298\pi$
$661$	10.4004	+	6.00466i	0.404528	+	0.233554i	−0.283908	+	0.958852i	$0.591631\pi$
$662$		0			0
$663$	43.8929	+	0.535933i	1.70466	+	0.0208139i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−5.84563	−	10.1249i	−0.226344	−	0.392039i
$668$		0			0
$669$	18.0007	+	32.0762i	0.695946	+	1.24014i
$670$		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
$675$	−17.6766	−	11.0879i	−0.680373	−	0.426775i
$676$		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
$681$	−0.138590	+	11.3505i	−0.00531079	+	0.434953i
$682$		0			0
$683$	−20.3551	−	11.7520i	−0.778866	−	0.449678i	0.0571624	−	0.998365i	$-0.481795\pi$
$683$	−20.3551	−	11.7520i	−0.778866	−	0.449678i	−0.836028	+	0.548687i	$0.815128\pi$
$684$		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	−0.798190	−	0.602405i	$-0.794209\pi$
$691$	−17.7591	+	10.2532i	−0.675587	+	0.390051i	0.122603	+	0.992456i	$0.460876\pi$
$692$		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	$0.126121\pi$
$701$			20.4363i			0.771868i	−0.922526	+	0.385934i	$0.873879\pi$
$702$		0			0
$703$	7.59613	+	4.38563i	0.286494	+	0.165407i
$704$		0			0
$705$	−0.221059	+	18.1047i	−0.00832555	+	0.681862i
$706$		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
$711$	43.3878	+	1.05969i	1.62717	+	0.0397415i
$712$		0			0
$713$	4.94039			0.185019
$714$		0			0
$715$	−16.7897			−0.627901
$716$		0			0
$717$	−7.16033	−	12.7593i	−0.267407	−	0.476506i
$718$		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
$723$	−5.02216	−	0.0613207i	−0.186776	−	0.00228054i
$724$		0			0
$725$	−23.2679	−	13.4337i	−0.864148	−	0.498916i
$726$		0			0
$727$			11.5388i			0.427950i	0.976839	+	0.213975i	$0.0686411\pi$
$727$			11.5388i			0.427950i	−0.976839	+	0.213975i	$0.931359\pi$
$728$		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	−0.809745	−	0.586782i	$-0.800395\pi$
$733$	−19.1264	+	11.0426i	−0.706449	+	0.407869i	0.103296	+	0.994651i	$0.467061\pi$
$734$		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	$-0.865696\pi$
$743$		−	22.3254i		−	0.819040i	0.912301	−	0.409520i	$-0.134304\pi$
$744$		0			0
$745$	−1.36672	−	0.789075i	−0.0500727	−	0.0289095i
$746$		0			0
$747$	−26.3541	+	43.1765i	−0.964246	+	1.57974i
$748$		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
$753$	1.93944	−	1.08838i	0.0706770	−	0.0396628i
$754$		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
$759$	−6.62108	+	3.71565i	−0.240330	+	0.134869i
$760$		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
$765$	−5.82519	+	9.54354i	−0.210610	+	0.345047i
$766$		0			0
$767$	−27.1279	−	15.6623i	−0.979531	−	0.565532i
$768$		0			0
$769$		−	3.10213i		−	0.111866i	−0.998435	−	0.0559328i	$-0.982187\pi$
$769$		−	3.10213i		−	0.111866i	0.998435	−	0.0559328i	$-0.0178133\pi$
$770$		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	−0.285078	−	0.958504i	$-0.592020\pi$
$787$	−35.2831	−	20.3707i	−1.25771	−	0.726137i	−0.972628	+	0.232367i	$0.925353\pi$
$788$		0			0
$789$	24.1491	+	0.294861i	0.859732	+	0.0104973i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	27.1642	+	47.0498i	0.964629	+	1.67079i
$794$		0			0
$795$	8.65207	+	15.4175i	0.306857	+	0.546803i
$796$		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
$801$	−9.51018	−	0.232274i	−0.336026	−	0.00820699i
$802$		0			0
$803$	4.05772	+	7.02817i	0.143194	+	0.248019i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	0.0295345	−	2.41887i	0.00103966	−	0.0851483i
$808$		0			0
$809$	−32.6805	−	18.8681i	−1.14898	−	0.663367i	−0.200345	−	0.979725i	$-0.564206\pi$
$809$	−32.6805	−	18.8681i	−1.14898	−	0.663367i	−0.948640	+	0.316359i	$0.897540\pi$
$810$		0			0
$811$			33.3795i			1.17211i	0.810270	+	0.586057i	$0.199320\pi$
$811$			33.3795i			1.17211i	−0.810270	+	0.586057i	$0.800680\pi$
$812$		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	−0.617652	−	0.786451i	$-0.711916\pi$
$821$	−7.03122	+	4.05948i	−0.245391	+	0.141677i	0.372261	+	0.928128i	$0.378583\pi$
$822$		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	$0.0656166\pi$
$827$			11.7724i			0.409367i	−0.978828	+	0.204684i	$0.934383\pi$
$828$		0			0
$829$	2.23286	+	1.28914i	0.0775504	+	0.0447738i	0.538274	−	0.842770i	$-0.319077\pi$
$829$	2.23286	+	1.28914i	0.0775504	+	0.0447738i	−0.460723	+	0.887544i	$0.652410\pi$
$830$		0			0
$831$	0.0745230	−	6.10342i	0.00258517	−	0.211725i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	2.77324	+	4.80339i	0.0959719	+	0.166228i
$836$		0			0
$837$	7.80634	−	12.4450i	0.269827	−	0.430163i
$838$		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
$843$	6.64657	+	11.8438i	0.228920	+	0.407923i
$844$		0			0
$845$	−16.1281	−	27.9347i	−0.554825	−	0.960985i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	38.3160	+	0.467839i	1.31500	+	0.0160562i
$850$		0			0
$851$	4.97076	+	2.86987i	0.170395	+	0.0983778i
$852$		0			0
$853$		−	5.00496i		−	0.171367i	−0.996322	−	0.0856833i	$-0.972693\pi$
$853$		−	5.00496i		−	0.171367i	0.996322	−	0.0856833i	$-0.0273073\pi$
$854$		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	−0.350630	−	0.936514i	$-0.614033\pi$
$859$	8.35591	−	4.82429i	0.285100	−	0.164603i	0.635730	+	0.771912i	$0.280699\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−39.4774	+	22.7923i	−1.34383	+	0.775858i	−0.987367	−	0.158453i	$-0.949349\pi$
$863$	−39.4774	+	22.7923i	−1.34383	+	0.775858i	−0.356459	+	0.934311i	$0.616016\pi$
$864$		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
$873$	−2.53355	−	1.54643i	−0.0857477	−	0.0523388i
$874$		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
$879$	31.0815	−	17.4424i	1.04835	−	0.588318i
$880$		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
$885$	6.95799	−	3.90471i	0.233890	−	0.131255i
$886$		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
$891$	−1.10216	+	22.5498i	−0.0369237	+	0.755448i
$892$		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	$0.147983\pi$
$911$			27.0641i			0.896672i	−0.893865	+	0.448336i	$0.852017\pi$
$912$		0			0
$913$	36.6304	+	21.1486i	1.21229	+	0.699916i
$914$		0			0
$915$	−13.8371	−	0.168951i	−0.457439	−	0.00558535i
$916$		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
$921$	24.9312	+	44.4260i	0.821509	+	1.46389i
$922$		0			0
$923$	30.7798			1.01313
$924$		0			0
$925$	13.1904			0.433696
$926$		0			0
$927$	−0.582810	+	23.8625i	−0.0191420	+	0.783746i
$928$		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
$933$	0.170801	−	13.9885i	0.00559176	−	0.457965i
$934$		0			0
$935$	8.09663	+	4.67459i	0.264788	+	0.152876i
$936$		0			0
$937$			49.4739i			1.61624i	0.589018	+	0.808120i	$0.299515\pi$
$937$			49.4739i			1.61624i	−0.589018	+	0.808120i	$0.700485\pi$
$938$		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	−0.374498	−	0.927228i	$-0.622185\pi$
$947$	7.42426	−	4.28640i	0.241256	−	0.139289i	0.615754	+	0.787939i	$0.288852\pi$
$948$		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	$0.258424\pi$
$953$			44.7977i			1.45114i	−0.688149	+	0.725570i	$0.741576\pi$
$954$		0			0
$955$	2.78556	+	1.60824i	0.0901386	+	0.0520416i
$956$		0			0
$957$	−0.354916	+	29.0676i	−0.0114728	+	0.939622i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−11.5034	−	19.9244i	−0.371077	−	0.642724i
$962$		0			0
$963$	−1.19659	+	48.9930i	−0.0385596	+	1.57878i
$964$		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
$969$	8.50322	+	15.1523i	0.273163	+	0.486761i
$970$		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
$975$	−46.9203	−	0.572898i	−1.50265	−	0.0183474i
$976$		0			0
$977$	31.0908	+	17.9503i	0.994683	+	0.574281i	0.906671	−	0.421839i	$-0.138615\pi$
$977$	31.0908	+	17.9503i	0.994683	+	0.574281i	0.0880123	+	0.996119i	$0.471949\pi$
$978$		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	−0.448632	−	0.893716i	$-0.648089\pi$
$997$	−45.6872	−	26.3775i	−1.44693	−	0.835385i	−0.998297	+	0.0583312i	$0.981422\pi$
$998$		0			0
$999$	15.0836	−	7.98682i	0.477224	−	0.252692i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(1.51046 - 0.847647i) q^{3} +(0.496051 + 0.859186i) q^{5} +(1.56299 - 2.56068i) q^{9} +(-2.17245 - 1.25426i) q^{11} -6.74633i q^{13} +(1.47755 + 0.877291i) q^{15} +(-1.87831 + 3.25333i) q^{17} +(2.31260 - 1.33518i) q^{19} +(1.51332 - 0.873715i) q^{23} +(2.00787 - 3.47773i) q^{25} +(0.190283 - 5.19267i) q^{27} -6.69055i q^{29} +(2.44846 + 1.41362i) q^{31} +(-4.34458 - 0.0530474i) q^{33} +(1.64234 + 2.84461i) q^{37} +(-5.71851 - 10.1901i) q^{39} -9.02583 q^{41} +10.6558 q^{43} +(2.97542 + 0.0726708i) q^{45} +(5.26837 + 9.12508i) q^{47} +(-0.0794406 + 6.50618i) q^{51} +(8.91002 + 5.14420i) q^{53} -2.48872i q^{55} +(2.36133 - 3.97701i) q^{57} +(2.32160 - 4.02113i) q^{59} +(-6.97413 + 4.02651i) q^{61} +(5.79636 - 3.34653i) q^{65} +(3.34885 - 5.80038i) q^{67} +(1.54521 - 2.60247i) q^{69} +4.56245i q^{71} +(-2.80171 - 1.61757i) q^{73} +(0.0849199 - 6.95493i) q^{75} +(7.23346 + 12.5287i) q^{79} +(-4.11413 - 8.00462i) q^{81} -16.8613 q^{83} -3.72696 q^{85} +(-5.67122 - 10.1058i) q^{87} +(-1.58550 - 2.74617i) q^{89} +(4.89655 + 0.0597870i) q^{93} +(2.29434 + 1.32464i) q^{95} -0.989407i q^{97} +(-6.60728 + 3.60254i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 32 q^{15} - 8 q^{25} - 16 q^{37} + 64 q^{39} + 32 q^{43} - 48 q^{51} + 96 q^{57} - 16 q^{67} - 80 q^{81} - 128 q^{85} + 32 q^{93} - 112 q^{99}+O(q^{100}) \) 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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