LMFDB - Embedded newform 1176.2.u.c.1097.21

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			1097.21
Character	$\chi$	$=$	1176.1097
Dual form			1176.2.u.c.521.21

$q$-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 $\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times$.

$n$	$295$	$589$	$785$	$1081$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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	−0.733526	−	0.679661i	$-0.762127\pi$
$5$	0.496051	−	0.859186i	0.221841	−	0.384240i	0.955367	+	0.295422i	$0.0954601\pi$
$6$		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	−0.790376	−	0.612622i	$-0.790115\pi$
$11$	−2.17245	+	1.25426i	−0.655018	+	0.378175i	0.135358	+	0.990797i	$0.456782\pi$
$12$		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	0.543162	−	0.839628i	$-0.317227\pi$
$17$	−1.87831	−	3.25333i	−0.455558	−	0.789049i	−0.998720	+	0.0505785i	$0.983893\pi$
$18$		0			0
$19$	2.31260	+	1.33518i	0.530547	+	0.306312i	0.741239	−	0.671241i	$-0.234238\pi$
$19$	2.31260	+	1.33518i	0.530547	+	0.306312i	−0.210692	+	0.977552i	$0.567572\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.51332	+	0.873715i	0.315549	+	0.182182i	0.649407	−	0.760441i	$-0.275017\pi$
$23$	1.51332	+	0.873715i	0.315549	+	0.182182i	−0.333858	+	0.942623i	$0.608351\pi$
$24$		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	$-0.584956\pi$
$31$	2.44846	−	1.41362i	0.439756	−	0.253893i	0.703494	+	0.710701i	$0.251622\pi$
$32$		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	−0.698863	−	0.715256i	$-0.746310\pi$
$37$	1.64234	−	2.84461i	0.269998	−	0.467651i	0.968861	+	0.247605i	$0.0796435\pi$
$38$		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	−0.169922	−	0.985457i	$-0.554352\pi$
$47$	5.26837	−	9.12508i	0.768470	−	1.33103i	0.938392	−	0.345572i	$-0.112315\pi$
$48$		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	0.258142	−	0.966107i	$-0.416890\pi$
$53$	8.91002	−	5.14420i	1.22389	−	0.706611i	0.965744	+	0.259496i	$0.0835565\pi$
$54$		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	0.976644	−	0.214862i	$-0.0689301\pi$
$59$	2.32160	+	4.02113i	0.302246	+	0.523506i	−0.674398	+	0.738368i	$0.735597\pi$
$60$		0			0
$61$	−6.97413	−	4.02651i	−0.892945	−	0.515542i	−0.0180407	−	0.999837i	$-0.505743\pi$
$61$	−6.97413	−	4.02651i	−0.892945	−	0.515542i	−0.874905	+	0.484295i	$0.839076\pi$
$62$		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	0.994792	−	0.101924i	$-0.0325000\pi$
$67$	3.34885	+	5.80038i	0.409127	+	0.708629i	−0.585665	+	0.810553i	$0.699167\pi$
$68$		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	$-0.727296\pi$
$73$	−2.80171	+	1.61757i	−0.327915	+	0.189322i	0.327000	+	0.945024i	$0.393962\pi$
$74$		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	−0.0963379	−	0.995349i	$-0.530713\pi$
$79$	7.23346	−	12.5287i	0.813828	−	1.40959i	0.910166	−	0.414243i	$-0.135954\pi$
$80$		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	−0.937739	−	0.347341i	$-0.887085\pi$
$89$	−1.58550	+	2.74617i	−0.168063	+	0.291094i	0.769676	+	0.638435i	$0.220418\pi$
$90$		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	$0.0159953\pi$
$97$			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	0.500414	−	0.865787i	$-0.333181\pi$
$101$	−5.02078	−	8.69625i	−0.499586	−	0.865309i	−1.00000		0.000477583i	$0.999848\pi$
$102$		0			0
$103$	−6.89056	−	3.97826i	−0.678947	−	0.391990i	0.120511	−	0.992712i	$-0.461547\pi$
$103$	−6.89056	−	3.97826i	−0.678947	−	0.391990i	−0.799458	+	0.600722i	$0.794880\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−14.1473	−	8.16794i	−1.36767	−	0.789624i	−0.377039	−	0.926197i	$-0.623058\pi$
$107$	−14.1473	−	8.16794i	−1.36767	−	0.789624i	−0.990630	+	0.136573i	$0.956391\pi$
$108$		0			0
$109$	4.71712	+	8.17029i	0.451818	+	0.782572i	0.998499	−	0.0547692i	$-0.0174423\pi$
$109$	4.71712	+	8.17029i	0.451818	+	0.782572i	−0.546681	+	0.837341i	$0.684109\pi$
$110$		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
$117$	−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	−0.158419	−	0.987372i	$-0.550640\pi$
$131$	8.88035	−	15.3812i	0.775880	−	1.34386i	0.934299	−	0.356491i	$-0.116027\pi$
$132$		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	−0.478058	−	0.878328i	$-0.658659\pi$
$137$	0.509947	−	0.294418i	0.0435677	−	0.0251538i	0.521626	+	0.853174i	$0.325326\pi$
$138$		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	$-0.354089\pi$
$149$	−1.37760	−	0.795356i	−0.112857	−	0.0651581i	−0.555366	+	0.831606i	$0.687422\pi$
$150$		0			0
$151$	−7.60822	−	13.1778i	−0.619148	−	1.07240i	−0.989641	−	0.143561i	$-0.954145\pi$
$151$	−7.60822	−	13.1778i	−0.619148	−	1.07240i	0.370493	−	0.928835i	$-0.379189\pi$
$152$		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	$-0.692683\pi$
$157$	−1.77180	+	1.02295i	−0.141405	+	0.0816403i	0.427628	+	0.903955i	$0.359349\pi$
$158$		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	0.253090	+	0.967443i	$0.418553\pi$
$163$	−9.08108	+	15.7289i	−0.711285	+	1.23198i	−0.964375	+	0.264539i	$0.914780\pi$
$164$		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	−0.938706	−	0.344720i	$-0.887974\pi$
$173$	−2.24674	+	3.89147i	−0.170817	+	0.295863i	0.767889	+	0.640583i	$0.221307\pi$
$174$		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	0.313697	−	0.949523i	$-0.398432\pi$
$179$	17.2972	−	9.98657i	1.29286	−	0.746431i	0.979160	+	0.203092i	$0.0650991\pi$
$180$		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	$-0.295911\pi$
$191$	2.80773	+	1.62105i	0.203161	+	0.117295i	−0.394968	+	0.918695i	$0.629244\pi$
$192$		0			0
$193$	−6.63386	−	11.4902i	−0.477516	−	0.827082i	0.522152	−	0.852853i	$-0.325129\pi$
$193$	−6.63386	−	11.4902i	−0.477516	−	0.827082i	−0.999668	+	0.0257705i	$0.991796\pi$
$194$		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	$-0.652553\pi$
$199$	1.08304	−	0.625292i	0.0767745	−	0.0443258i	0.537896	+	0.843011i	$0.319219\pi$
$200$		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	$-0.748227\pi$
$223$		−	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	0.736548	−	0.676385i	$-0.236454\pi$
$227$	−3.27686	−	5.67568i	−0.217493	−	0.376708i	−0.954041	+	0.299677i	$0.903121\pi$
$228$		0			0
$229$	14.8892	+	8.59630i	0.983908	+	0.568059i	0.903448	−	0.428698i	$-0.141028\pi$
$229$	14.8892	+	8.59630i	0.983908	+	0.568059i	0.0804602	+	0.996758i	$0.474361\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	10.7831	+	6.22564i	0.706426	+	0.407855i	0.809736	−	0.586794i	$-0.199610\pi$
$233$	10.7831	+	6.22564i	0.706426	+	0.407855i	−0.103310	+	0.994649i	$0.532943\pi$
$234$		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	$-0.696439\pi$
$241$	−2.51127	+	1.44988i	−0.161765	+	0.0933951i	0.416932	+	0.908938i	$0.363105\pi$
$242$		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	−0.442997	−	0.896523i	$-0.646085\pi$
$257$	8.89593	−	15.4082i	0.554913	−	0.961137i	0.997910	−	0.0646145i	$-0.0205818\pi$
$258$		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	−0.0791363	−	0.996864i	$-0.525216\pi$
$263$	12.0755	−	6.97177i	0.744605	−	0.429898i	0.823741	+	0.566966i	$0.191883\pi$
$264$		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	0.886529	−	0.462674i	$-0.153110\pi$
$269$	0.698320	+	1.20953i	0.0425773	+	0.0737461i	−0.843951	+	0.536420i	$0.819776\pi$
$270$		0			0
$271$	−9.26119	−	5.34695i	−0.562577	−	0.324804i	0.191602	−	0.981473i	$-0.438632\pi$
$271$	−9.26119	−	5.34695i	−0.562577	−	0.324804i	−0.754179	+	0.656669i	$0.771965\pi$
$272$		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	0.914094	−	0.405503i	$-0.132904\pi$
$277$	1.76204	+	3.05194i	0.105871	+	0.183373i	−0.808223	+	0.588877i	$0.799570\pi$
$278$		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	$-0.438260\pi$
$283$	19.1594	−	11.0617i	1.13891	−	0.657550i	0.946160	+	0.323699i	$0.104926\pi$
$284$		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	$-0.682953\pi$
$307$		−	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	0.957512	−	0.288394i	$-0.0931213\pi$
$311$	4.03845	+	6.99480i	0.228999	+	0.396638i	−0.728512	+	0.685033i	$0.759788\pi$
$312$		0			0
$313$	1.04838	+	0.605284i	0.0592581	+	0.0342127i	0.529336	−	0.848412i	$-0.322441\pi$
$313$	1.04838	+	0.605284i	0.0592581	+	0.0342127i	−0.470078	+	0.882625i	$0.655774\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−25.7940	−	14.8922i	−1.44874	−	0.836429i	−0.450331	−	0.892862i	$-0.648694\pi$
$317$	−25.7940	−	14.8922i	−1.44874	−	0.836429i	−0.998406	+	0.0564326i	$0.982027\pi$
$318$		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	−0.643787	−	0.765204i	$-0.722638\pi$
$331$	6.20018	−	10.7390i	0.340793	−	0.590270i	0.984580	+	0.174934i	$0.0559712\pi$
$332$		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	−0.699843	−	0.714296i	$-0.746747\pi$
$347$	−8.03173	+	4.63712i	−0.431166	+	0.248934i	0.268677	+	0.963230i	$0.413414\pi$
$348$		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	0.909210	−	0.416337i	$-0.136686\pi$
$353$	1.76697	+	3.06049i	0.0940465	+	0.162893i	−0.815164	+	0.579231i	$0.803353\pi$
$354$		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	$-0.218139\pi$
$359$	11.6190	+	6.70821i	0.613225	+	0.354046i	−0.161001	+	0.986954i	$0.551472\pi$
$360$		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	$-0.743057\pi$
$367$	−7.88688	+	4.55350i	−0.411692	+	0.237691i	0.279824	+	0.960051i	$0.409724\pi$
$368$		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	−0.00646378	−	0.999979i	$-0.502058\pi$
$373$	16.6630	−	28.8611i	0.862775	−	1.49437i	0.869239	−	0.494392i	$-0.164609\pi$
$374$		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	0.253945	+	0.967219i	$0.418272\pi$
$383$	−13.9080	+	24.0893i	−0.710663	+	1.23091i	−0.964608	+	0.263687i	$0.915062\pi$
$384$		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	−0.0446107	−	0.999004i	$-0.514205\pi$
$389$	15.7439	−	9.08974i	0.798247	−	0.460868i	0.842858	+	0.538136i	$0.180871\pi$
$390$		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	$-0.350491\pi$
$397$	−1.85933	−	1.07349i	−0.0933172	−	0.0538767i	−0.545932	+	0.837829i	$0.683824\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−10.1853	−	5.88049i	−0.508630	−	0.293658i	0.223640	−	0.974672i	$-0.428206\pi$
$401$	−10.1853	−	5.88049i	−0.508630	−	0.293658i	−0.732270	+	0.681014i	$0.761539\pi$
$402$		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	$-0.822683\pi$
$409$	−16.4896	+	9.52030i	−0.815360	+	0.470748i	0.0334538	+	0.999440i	$0.489349\pi$
$410$		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	−0.918835	−	0.394641i	$-0.870869\pi$
$431$	−21.5180	+	12.4234i	−1.03648	+	0.598414i	−0.117649	+	0.993055i	$0.537536\pi$
$432$		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	$-0.456160\pi$
$439$	−13.6586	−	7.88578i	−0.651888	−	0.376368i	−0.789179	+	0.614163i	$0.789494\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	11.4712	+	6.62292i	0.545015	+	0.314665i	0.747109	−	0.664702i	$-0.231441\pi$
$443$	11.4712	+	6.62292i	0.545015	+	0.314665i	−0.202094	+	0.979366i	$0.564775\pi$
$444$		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
$453$	−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	−0.970630	−	0.240577i	$-0.922663\pi$
$457$	−5.92092	+	10.2553i	−0.276969	+	0.479725i	0.693661	+	0.720302i	$0.255997\pi$
$458$		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	−0.999903	−	0.0139024i	$-0.995575\pi$
$467$	−10.5439	+	18.2625i	−0.487912	+	0.845088i	0.511991	+	0.858991i	$0.328908\pi$
$468$		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	0.882518	−	0.470279i	$-0.155847\pi$
$479$	0.743810	+	1.28832i	0.0339855	+	0.0588647i	−0.848532	+	0.529143i	$0.822513\pi$
$480$		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	0.965598	+	0.260040i	$0.0837356\pi$
$487$	15.6242	+	27.0619i	0.708000	+	1.22629i	−0.257598	+	0.966252i	$0.582931\pi$
$488$		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
$495$	−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	−0.328039	−	0.944664i	$-0.606388\pi$
$499$	14.6111	−	25.3072i	0.654084	−	1.13291i	0.982123	−	0.188242i	$-0.0602789\pi$
$500$		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	−0.294828	−	0.955550i	$-0.595262\pi$
$509$	15.3441	−	26.5768i	0.680117	−	1.17800i	0.974945	−	0.222446i	$-0.0714042\pi$
$510$		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	0.882585	−	0.470152i	$-0.155801\pi$
$521$	0.779005	+	1.34928i	0.0341288	+	0.0591129i	−0.848456	+	0.529265i	$0.822468\pi$
$522$		0			0
$523$	2.12958	+	1.22951i	0.0931200	+	0.0537628i	0.545837	−	0.837891i	$-0.316212\pi$
$523$	2.12958	+	1.22951i	0.0931200	+	0.0537628i	−0.452717	+	0.891654i	$0.649545\pi$
$524$		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	−0.686792	−	0.726854i	$-0.740982\pi$
$541$	6.65399	−	11.5251i	0.286077	−	0.495501i	0.972870	+	0.231353i	$0.0743152\pi$
$542$		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	−0.993805	−	0.111139i	$-0.964550\pi$
$557$	−32.9104	+	19.0008i	−1.39446	+	0.805091i	−0.400653	+	0.916230i	$0.631217\pi$
$558$		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	0.910327	+	0.413890i	$0.135830\pi$
$563$	19.3049	+	33.4370i	0.813603	+	1.40920i	−0.0967240	+	0.995311i	$0.530836\pi$
$564$		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	$-0.163263\pi$
$569$	21.0393	+	12.1471i	0.882014	+	0.509231i	0.0106920	+	0.999943i	$0.496597\pi$
$570$		0			0
$571$	15.1612	+	26.2600i	0.634478	+	1.09895i	0.986625	+	0.163004i	$0.0521182\pi$
$571$	15.1612	+	26.2600i	0.634478	+	1.09895i	−0.352147	+	0.935945i	$0.614548\pi$
$572$		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	$-0.782405\pi$
$577$	−14.7967	+	8.54288i	−0.615995	+	0.355645i	0.159313	+	0.987228i	$0.449072\pi$
$578$		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	−0.728848	−	0.684675i	$-0.759944\pi$
$593$	5.56488	−	9.63866i	0.228522	−	0.395812i	0.957370	+	0.288863i	$0.0932773\pi$
$594$		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	0.205642	−	0.978627i	$-0.434072\pi$
$599$	28.2920	−	16.3344i	1.15598	−	0.667405i	0.950337	+	0.311222i	$0.100738\pi$
$600$		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	$-0.540498\pi$
$607$	−25.8534	−	14.9264i	−1.04936	−	0.605846i	−0.922469	+	0.386071i	$0.873832\pi$
$608$		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	0.999985	+	0.00541593i	$0.00172395\pi$
$613$	12.4954	+	21.6426i	0.504683	+	0.874137i	−0.495302	+	0.868721i	$0.664943\pi$
$614$		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	0.598391	−	0.801204i	$-0.295807\pi$
$619$	39.5948	−	22.8601i	1.59145	−	0.918824i	0.993059	−	0.117620i	$-0.0375265\pi$
$620$		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	−0.980134	−	0.198338i	$-0.936446\pi$
$641$	−32.8738	+	18.9797i	−1.29844	+	0.749652i	−0.318301	+	0.947990i	$0.603112\pi$
$642$		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	0.956385	−	0.292110i	$-0.0943575\pi$
$647$	5.72867	+	9.92235i	0.225217	+	0.390088i	−0.731167	+	0.682198i	$0.761024\pi$
$648$		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	$-0.332484\pi$
$653$	0.118160	+	0.0682197i	0.00462396	+	0.00266964i	−0.497686	+	0.867357i	$0.665817\pi$
$654$		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	$-0.591631\pi$
$661$	10.4004	−	6.00466i	0.404528	−	0.233554i	0.688436	+	0.725297i	$0.258298\pi$
$662$		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	0.00581197	+	0.999983i	$0.498150\pi$
$677$	−22.4573	+	38.8972i	−0.863105	+	1.49494i	−0.868917	+	0.494958i	$0.835183\pi$
$678$		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	−0.836028	−	0.548687i	$-0.815128\pi$
$683$	−20.3551	+	11.7520i	−0.778866	+	0.449678i	0.0571624	+	0.998365i	$0.481795\pi$
$684$		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	$-0.460876\pi$
$691$	−17.7591	−	10.2532i	−0.675587	−	0.390051i	−0.798190	+	0.602405i	$0.794209\pi$
$692$		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
$705$	−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	−0.647934	−	0.761696i	$-0.724367\pi$
$709$	8.93820	−	15.4814i	0.335681	−	0.581417i	0.983615	+	0.180279i	$0.0577002\pi$
$710$		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	0.358548	+	0.933511i	$0.383272\pi$
$719$	−16.8707	+	29.2209i	−0.629170	+	1.08976i	−0.987719	+	0.156244i	$0.950061\pi$
$720$		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	$-0.931359\pi$
$727$		−	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	$-0.467061\pi$
$733$	−19.1264	−	11.0426i	−0.706449	−	0.407869i	−0.809745	+	0.586782i	$0.800395\pi$
$734$		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	0.856220	−	0.516612i	$-0.172807\pi$
$739$	−0.524365	−	0.908228i	−0.0192891	−	0.0334097i	−0.875509	+	0.483202i	$0.839474\pi$
$740$		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
$747$	−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	−0.771149	−	0.636655i	$-0.780317\pi$
$751$	4.54325	−	7.86913i	0.165785	−	0.287149i	0.936934	+	0.349507i	$0.113651\pi$
$752$		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	−0.955749	−	0.294182i	$-0.904953\pi$
$761$	−6.15464	+	10.6601i	−0.223105	+	0.386430i	0.732644	+	0.680612i	$0.238286\pi$
$762$		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	$0.0178133\pi$
$769$			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	−0.999077	−	0.0429546i	$-0.986323\pi$
$773$	−14.9229	−	25.8472i	−0.536738	−	0.929658i	0.462339	−	0.886703i	$-0.347010\pi$
$774$		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	$-0.925353\pi$
$787$	−35.2831	+	20.3707i	−1.25771	+	0.726137i	−0.285078	+	0.958504i	$0.592020\pi$
$788$		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	−0.948640	−	0.316359i	$-0.897540\pi$
$809$	−32.6805	+	18.8681i	−1.14898	+	0.663367i	−0.200345	+	0.979725i	$0.564206\pi$
$810$		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	$-0.378583\pi$
$821$	−7.03122	−	4.05948i	−0.245391	−	0.141677i	−0.617652	+	0.786451i	$0.711916\pi$
$822$		0			0
$823$	−23.8466	−	41.3035i	−0.831241	−	1.43975i	−0.897055	−	0.441919i	$-0.854298\pi$
$823$	−23.8466	−	41.3035i	−0.831241	−	1.43975i	0.0658143	−	0.997832i	$-0.479036\pi$
$824$		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	$-0.652410\pi$
$829$	2.23286	−	1.28914i	0.0775504	−	0.0447738i	0.538274	+	0.842770i	$0.319077\pi$
$830$		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	$0.0273073\pi$
$853$			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	0.620160	−	0.784475i	$-0.287068\pi$
$857$	−10.8110	−	18.7251i	−0.369296	−	0.639639i	−0.989456	+	0.144837i	$0.953734\pi$
$858$		0			0
$859$	8.35591	+	4.82429i	0.285100	+	0.164603i	0.635730	−	0.771912i	$-0.280699\pi$
$859$	8.35591	+	4.82429i	0.285100	+	0.164603i	−0.350630	+	0.936514i	$0.614033\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−39.4774	−	22.7923i	−1.34383	−	0.775858i	−0.356459	−	0.934311i	$-0.616016\pi$
$863$	−39.4774	−	22.7923i	−1.34383	−	0.775858i	−0.987367	+	0.158453i	$0.949349\pi$
$864$		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	−0.00760306	+	0.999971i	$0.502420\pi$
$877$	−25.7585	+	44.6150i	−0.869802	+	1.50654i	−0.862199	+	0.506570i	$0.830913\pi$
$878$		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	−0.651685	−	0.758489i	$-0.725938\pi$
$887$	9.85887	−	17.0761i	0.331028	−	0.573358i	0.982714	+	0.185131i	$0.0592711\pi$
$888$		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	0.975014	+	0.222142i	$0.0713049\pi$
$907$	20.4758	+	35.4651i	0.679888	+	1.17760i	−0.295126	+	0.955458i	$0.595362\pi$
$908$		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
$915$	−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	−0.668098	−	0.744073i	$-0.732891\pi$
$919$	9.40788	−	16.2949i	0.310337	−	0.537520i	0.978435	+	0.206553i	$0.0662247\pi$
$920$		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	−0.998296	−	0.0583449i	$-0.981418\pi$
$929$	−13.6737	+	23.6836i	−0.448620	+	0.777033i	0.549676	+	0.835378i	$0.314751\pi$
$930$		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	$-0.700485\pi$
$937$		−	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	0.925782	+	0.378057i	$0.123408\pi$
$941$	24.2430	+	41.9900i	0.790298	+	1.36884i	−0.135485	+	0.990779i	$0.543259\pi$
$942$		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	$-0.288852\pi$
$947$	7.42426	+	4.28640i	0.241256	+	0.139289i	−0.374498	+	0.927228i	$0.622185\pi$
$948$		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
$957$	−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	−0.895120	−	0.445826i	$-0.852910\pi$
$971$	−1.91524	+	3.31730i	−0.0614630	+	0.106457i	0.833657	+	0.552283i	$0.186243\pi$
$972$		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	0.0880123	−	0.996119i	$-0.471949\pi$
$977$	31.0908	−	17.9503i	0.994683	−	0.574281i	0.906671	+	0.421839i	$0.138615\pi$
$978$		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	0.944462	+	0.328620i	$0.106583\pi$
$983$	23.7286	+	41.0991i	0.756824	+	1.31086i	−0.187638	+	0.982238i	$0.560083\pi$
$984$		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	−0.839342	−	0.543604i	$-0.817059\pi$
$991$	−28.0314	−	48.5518i	−0.890446	−	1.54230i	−0.0511039	−	0.998693i	$-0.516274\pi$
$992$		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	$-0.981422\pi$
$997$	−45.6872	+	26.3775i	−1.44693	+	0.835385i	−0.448632	+	0.893716i	$0.648089\pi$
$998$		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.1097.21		48
3.2	odd	2	inner	1176.2.u.c.1097.13		48
7.2	even	3		1176.2.k.b.881.6	yes	24
7.3	odd	6	inner	1176.2.u.c.521.13		48
7.4	even	3	inner	1176.2.u.c.521.12		48
7.5	odd	6		1176.2.k.b.881.19	yes	24
7.6	odd	2	inner	1176.2.u.c.1097.4		48
21.2	odd	6		1176.2.k.b.881.20	yes	24
21.5	even	6		1176.2.k.b.881.5	✓	24
21.11	odd	6	inner	1176.2.u.c.521.4		48
21.17	even	6	inner	1176.2.u.c.521.21		48
21.20	even	2	inner	1176.2.u.c.1097.12		48
28.19	even	6		2352.2.k.j.881.6		24
28.23	odd	6		2352.2.k.j.881.19		24
84.23	even	6		2352.2.k.j.881.5		24
84.47	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	21.5	even	6
1176.2.k.b.881.6	yes	24	7.2	even	3
1176.2.k.b.881.19	yes	24	7.5	odd	6
1176.2.k.b.881.20	yes	24	21.2	odd	6
1176.2.u.c.521.4		48	21.11	odd	6	inner
1176.2.u.c.521.12		48	7.4	even	3	inner
1176.2.u.c.521.13		48	7.3	odd	6	inner
1176.2.u.c.521.21		48	21.17	even	6	inner
1176.2.u.c.1097.4		48	7.6	odd	2	inner
1176.2.u.c.1097.12		48	21.20	even	2	inner
1176.2.u.c.1097.13		48	3.2	odd	2	inner
1176.2.u.c.1097.21		48	1.1	even	1	trivial
2352.2.k.j.881.5		24	84.23	even	6
2352.2.k.j.881.6		24	28.19	even	6
2352.2.k.j.881.19		24	28.23	odd	6
2352.2.k.j.881.20		24	84.47	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)

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