LMFDB - Embedded newform 296.2.u.b.9.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [296,2,Mod(9,296)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(296, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("296.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 296 = 2^{3} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	296.u (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.36357189983$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			9.2
Character	$\chi$	$=$	296.9
Dual form			296.2.u.b.33.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.260200 + 1.47567i) q^{3} +(-1.75197 - 1.47008i) q^{5} +(-3.54112 - 2.97135i) q^{7} +(0.709192 + 0.258125i) q^{9} +(-2.89988 - 5.02274i) q^{11} +(1.41004 - 0.513213i) q^{13} +(2.62521 - 2.20281i) q^{15} +(-0.343576 - 0.125052i) q^{17} +(-0.769354 + 4.36322i) q^{19} +(5.30612 - 4.45236i) q^{21} +(1.15202 - 1.99536i) q^{23} +(0.0400348 + 0.227048i) q^{25} +(-2.81308 + 4.87240i) q^{27} +(-1.46198 - 2.53222i) q^{29} +0.428254 q^{31} +(8.16644 - 2.97234i) q^{33} +(1.83582 + 10.4115i) q^{35} +(-3.07776 - 5.24666i) q^{37} +(0.390438 + 2.21429i) q^{39} +(0.112369 - 0.0408990i) q^{41} -12.9003 q^{43} +(-0.863022 - 1.49480i) q^{45} +(3.30747 - 5.72870i) q^{47} +(2.49506 + 14.1502i) q^{49} +(0.273933 - 0.474465i) q^{51} +(-7.42052 + 6.22655i) q^{53} +(-2.30332 + 13.0628i) q^{55} +(-6.23847 - 2.27062i) q^{57} +(6.22119 - 5.22019i) q^{59} +(2.40272 - 0.874520i) q^{61} +(-1.74435 - 3.02131i) q^{63} +(-3.22482 - 1.17374i) q^{65} +(10.8202 + 9.07920i) q^{67} +(2.64473 + 2.21919i) q^{69} +(1.40794 - 7.98481i) q^{71} +13.2380 q^{73} -0.345465 q^{75} +(-4.65551 + 26.4027i) q^{77} +(8.48535 + 7.12005i) q^{79} +(-4.72366 - 3.96362i) q^{81} +(-6.92615 - 2.52091i) q^{83} +(0.418101 + 0.724172i) q^{85} +(4.11711 - 1.49851i) q^{87} +(10.7566 - 9.02586i) q^{89} +(-6.51806 - 2.37238i) q^{91} +(-0.111432 + 0.631960i) q^{93} +(7.76218 - 6.51324i) q^{95} +(-2.83368 + 4.90807i) q^{97} +(-0.760078 - 4.31062i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 6 q^{5} - 3 q^{7} - 3 q^{11} + 9 q^{13} + 3 q^{15} - 27 q^{17} + 9 q^{19} + 15 q^{21} - 3 q^{23} - 12 q^{25} - 3 q^{27} + 9 q^{29} - 6 q^{31} - 6 q^{33} + 9 q^{35} + 9 q^{37} - 12 q^{39} - 48 q^{43}+ \cdots - 6 q^{99}+O(q^{100}) $ 30 * q - 6 * q^5 - 3 * q^7 - 3 * q^11 + 9 * q^13 + 3 * q^15 - 27 * q^17 + 9 * q^19 + 15 * q^21 - 3 * q^23 - 12 * q^25 - 3 * q^27 + 9 * q^29 - 6 * q^31 - 6 * q^33 + 9 * q^35 + 9 * q^37 - 12 * q^39 - 48 * q^43 + 51 * q^45 + 6 * q^47 - 21 * q^49 + 12 * q^51 - 15 * q^53 + 21 * q^55 + 51 * q^57 + 36 * q^61 - 36 * q^63 - 6 * q^65 - 27 * q^67 - 15 * q^69 + 27 * q^71 - 114 * q^73 + 84 * q^75 - 105 * q^77 - 18 * q^79 - 12 * q^81 - 30 * q^83 + 21 * q^85 - 99 * q^87 + 39 * q^89 - 72 * q^91 - 3 * q^93 + 66 * q^95 - 12 * q^97 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/296\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.260200	+	1.47567i	−0.150226	+	0.851976i	0.812795	+	0.582550i	$0.197945\pi$
$3$	−0.260200	+	1.47567i	−0.150226	+	0.851976i	−0.963021	+	0.269426i	$0.913166\pi$
$4$		0			0
$5$	−1.75197	−	1.47008i	−0.783507	−	0.657440i	0.160622	−	0.987016i	$-0.448650\pi$
$5$	−1.75197	−	1.47008i	−0.783507	−	0.657440i	−0.944129	+	0.329576i	$0.893094\pi$
$6$		0			0
$7$	−3.54112	−	2.97135i	−1.33842	−	1.12307i	−0.982030	−	0.188727i	$-0.939564\pi$
$7$	−3.54112	−	2.97135i	−1.33842	−	1.12307i	−0.356388	−	0.934338i	$-0.615992\pi$
$8$		0			0
$9$	0.709192	+	0.258125i	0.236397	+	0.0860416i
$10$		0			0
$11$	−2.89988	−	5.02274i	−0.874347	−	1.51441i	−0.857457	−	0.514556i	$-0.827957\pi$
$11$	−2.89988	−	5.02274i	−0.874347	−	1.51441i	−0.0168905	−	0.999857i	$-0.505377\pi$
$12$		0			0
$13$	1.41004	−	0.513213i	0.391075	−	0.142340i	−0.138996	−	0.990293i	$-0.544388\pi$
$13$	1.41004	−	0.513213i	0.391075	−	0.142340i	0.530071	+	0.847953i	$0.322165\pi$
$14$		0			0
$15$	2.62521	−	2.20281i	0.677827	−	0.568764i
$16$		0			0
$17$	−0.343576	−	0.125052i	−0.0833295	−	0.0303294i	0.300019	−	0.953933i	$-0.403007\pi$
$17$	−0.343576	−	0.125052i	−0.0833295	−	0.0303294i	−0.383349	+	0.923604i	$0.625229\pi$
$18$		0			0
$19$	−0.769354	+	4.36322i	−0.176502	+	1.00099i	0.759894	+	0.650047i	$0.225251\pi$
$19$	−0.769354	+	4.36322i	−0.176502	+	1.00099i	−0.936396	+	0.350945i	$0.885860\pi$
$20$		0			0
$21$	5.30612	−	4.45236i	1.15789	−	0.971586i
$22$		0			0
$23$	1.15202	−	1.99536i	0.240213	−	0.416062i	−0.720562	−	0.693391i	$-0.756116\pi$
$23$	1.15202	−	1.99536i	0.240213	−	0.416062i	0.960775	+	0.277329i	$0.0894492\pi$
$24$		0			0
$25$	0.0400348	+	0.227048i	0.00800695	+	0.0454097i
$26$		0			0
$27$	−2.81308	+	4.87240i	−0.541378	+	0.937694i
$28$		0			0
$29$	−1.46198	−	2.53222i	−0.271482	−	0.470221i	0.697760	−	0.716332i	$-0.254180\pi$
$29$	−1.46198	−	2.53222i	−0.271482	−	0.470221i	−0.969242	+	0.246111i	$0.920847\pi$
$30$		0			0
$31$	0.428254			0.0769166			0.0384583	−	0.999260i	$-0.487755\pi$
$31$	0.428254			0.0769166			0.0384583	+	0.999260i	$0.487755\pi$
$32$		0			0
$33$	8.16644	−	2.97234i	1.42159	−	0.517418i
$34$		0			0
$35$	1.83582	+	10.4115i	0.310311	+	1.75986i
$36$		0			0
$37$	−3.07776	−	5.24666i	−0.505980	−	0.862545i
$37$	−3.07776	−	5.24666i	−0.505980	−	0.862545i
$38$		0			0
$39$	0.390438	+	2.21429i	0.0625202	+	0.354569i
$40$		0			0
$41$	0.112369	−	0.0408990i	0.0175491	−	0.00638734i	−0.333231	−	0.942845i	$-0.608139\pi$
$41$	0.112369	−	0.0408990i	0.0175491	−	0.00638734i	0.350780	+	0.936458i	$0.385917\pi$
$42$		0			0
$43$	−12.9003			−1.96728			−0.983640	−	0.180146i	$-0.942343\pi$
$43$	−12.9003			−1.96728			−0.983640	+	0.180146i	$0.942343\pi$
$44$		0			0
$45$	−0.863022	−	1.49480i	−0.128652	−	0.222831i
$46$		0			0
$47$	3.30747	−	5.72870i	0.482444	−	0.835617i	−0.517353	−	0.855772i	$-0.673083\pi$
$47$	3.30747	−	5.72870i	0.482444	−	0.835617i	0.999797	+	0.0201552i	$0.00641603\pi$
$48$		0			0
$49$	2.49506	+	14.1502i	0.356437	+	2.02145i
$50$		0			0
$51$	0.273933	−	0.474465i	0.0383582	−	0.0664384i
$52$		0			0
$53$	−7.42052	+	6.22655i	−1.01929	+	0.855283i	−0.989538	−	0.144274i	$-0.953915\pi$
$53$	−7.42052	+	6.22655i	−1.01929	+	0.855283i	−0.0297488	+	0.999557i	$0.509471\pi$
$54$		0			0
$55$	−2.30332	+	13.0628i	−0.310580	+	1.76138i
$56$		0			0
$57$	−6.23847	−	2.27062i	−0.826306	−	0.300751i
$58$		0			0
$59$	6.22119	−	5.22019i	0.809929	−	0.679611i	−0.140662	−	0.990058i	$-0.544923\pi$
$59$	6.22119	−	5.22019i	0.809929	−	0.679611i	0.950591	+	0.310446i	$0.100478\pi$
$60$		0			0
$61$	2.40272	−	0.874520i	0.307637	−	0.111971i	−0.183588	−	0.983003i	$-0.558771\pi$
$61$	2.40272	−	0.874520i	0.307637	−	0.111971i	0.491225	+	0.871032i	$0.336549\pi$
$62$		0			0
$63$	−1.74435	−	3.02131i	−0.219768	−	0.380649i
$64$		0			0
$65$	−3.22482	−	1.17374i	−0.399989	−	0.145584i
$66$		0			0
$67$	10.8202	+	9.07920i	1.32189	+	1.10920i	0.985900	+	0.167336i	$0.0535165\pi$
$67$	10.8202	+	9.07920i	1.32189	+	1.10920i	0.335994	+	0.941864i	$0.390928\pi$
$68$		0			0
$69$	2.64473	+	2.21919i	0.318388	+	0.267160i
$70$		0			0
$71$	1.40794	−	7.98481i	0.167091	−	0.947623i	−0.779790	−	0.626041i	$-0.784674\pi$
$71$	1.40794	−	7.98481i	0.167091	−	0.947623i	0.946882	−	0.321582i	$-0.104215\pi$
$72$		0			0
$73$	13.2380			1.54939			0.774697	−	0.632332i	$-0.217902\pi$
$73$	13.2380			1.54939			0.774697	+	0.632332i	$0.217902\pi$
$74$		0			0
$75$	−0.345465			−0.0398908
$76$		0			0
$77$	−4.65551	+	26.4027i	−0.530544	+	3.00887i
$78$		0			0
$79$	8.48535	+	7.12005i	0.954676	+	0.801069i	0.980079	−	0.198609i	$-0.0636423\pi$
$79$	8.48535	+	7.12005i	0.954676	+	0.801069i	−0.0254025	+	0.999677i	$0.508087\pi$
$80$		0			0
$81$	−4.72366	−	3.96362i	−0.524851	−	0.440402i
$82$		0			0
$83$	−6.92615	−	2.52091i	−0.760243	−	0.276706i	−0.0673338	−	0.997731i	$-0.521449\pi$
$83$	−6.92615	−	2.52091i	−0.760243	−	0.276706i	−0.692910	+	0.721025i	$0.743671\pi$
$84$		0			0
$85$	0.418101	+	0.724172i	0.0453494	+	0.0785475i
$86$		0			0
$87$	4.11711	−	1.49851i	0.441400	−	0.160657i
$88$		0			0
$89$	10.7566	−	9.02586i	1.14020	−	0.956739i	0.140753	−	0.990045i	$-0.455048\pi$
$89$	10.7566	−	9.02586i	1.14020	−	0.956739i	0.999445	+	0.0333053i	$0.0106034\pi$
$90$		0			0
$91$	−6.51806	−	2.37238i	−0.683278	−	0.248693i
$92$		0			0
$93$	−0.111432	+	0.631960i	−0.0115549	+	0.0655311i
$94$		0			0
$95$	7.76218	−	6.51324i	0.796383	−	0.668245i
$96$		0			0
$97$	−2.83368	+	4.90807i	−0.287716	+	0.498339i	−0.973264	−	0.229688i	$-0.926229\pi$
$97$	−2.83368	+	4.90807i	−0.287716	+	0.498339i	0.685548	+	0.728027i	$0.259563\pi$
$98$		0			0
$99$	−0.760078	−	4.31062i	−0.0763908	−	0.433233i
$100$		0			0
$101$	5.70213	−	9.87638i	0.567383	−	0.982737i	−0.429440	−	0.903095i	$-0.641289\pi$
$101$	5.70213	−	9.87638i	0.567383	−	0.982737i	0.996824	−	0.0796415i	$-0.0253776\pi$
$102$		0			0
$103$	−2.91194	−	5.04362i	−0.286922	−	0.496963i	0.686152	−	0.727459i	$-0.259299\pi$
$103$	−2.91194	−	5.04362i	−0.286922	−	0.496963i	−0.973073	+	0.230495i	$0.925965\pi$
$104$		0			0
$105$	−15.8415			−1.54597
$106$		0			0
$107$	−0.627797	+	0.228499i	−0.0606914	+	0.0220899i	−0.372187	−	0.928158i	$-0.621392\pi$
$107$	−0.627797	+	0.228499i	−0.0606914	+	0.0220899i	0.311496	+	0.950247i	$0.399170\pi$
$108$		0			0
$109$	0.790209	+	4.48150i	0.0756883	+	0.429249i	0.998980	+	0.0451505i	$0.0143767\pi$
$109$	0.790209	+	4.48150i	0.0756883	+	0.429249i	−0.923292	+	0.384099i	$0.874512\pi$
$110$		0			0
$111$	8.54315	−	3.17656i	0.810879	−	0.301506i
$112$		0			0
$113$	−1.95736	−	11.1008i	−0.184133	−	1.04427i	−0.927064	−	0.374903i	$-0.877676\pi$
$113$	−1.95736	−	11.1008i	−0.184133	−	1.04427i	0.742931	−	0.669368i	$-0.233435\pi$
$114$		0			0
$115$	−4.95166	+	1.80226i	−0.461745	+	0.168061i
$116$		0			0
$117$	1.13246			0.104696
$118$		0			0
$119$	0.845072	+	1.46371i	0.0774677	+	0.134178i
$120$		0			0
$121$	−11.3186	+	19.6044i	−1.02897	+	1.78222i
$122$		0			0
$123$	0.0311148	+	0.176461i	0.00280553	+	0.0159109i
$124$		0			0
$125$	−5.45396	+	9.44654i	−0.487817	+	0.844924i
$126$		0			0
$127$	−4.43731	+	3.72334i	−0.393748	+	0.330393i	−0.818071	−	0.575117i	$-0.804956\pi$
$127$	−4.43731	+	3.72334i	−0.393748	+	0.330393i	0.424323	+	0.905511i	$0.360512\pi$
$128$		0			0
$129$	3.35666	−	19.0366i	0.295537	−	1.67608i
$130$		0			0
$131$	8.45349	+	3.07682i	0.738585	+	0.268823i	0.683794	−	0.729675i	$-0.260329\pi$
$131$	8.45349	+	3.07682i	0.738585	+	0.268823i	0.0547909	+	0.998498i	$0.482551\pi$
$132$		0			0
$133$	15.6890	−	13.1647i	1.36041	−	1.14152i
$134$		0			0
$135$	12.0913	−	4.40086i	1.04065	−	0.378766i
$136$		0			0
$137$	−8.39920	−	14.5478i	−0.717592	−	1.24291i	−0.961951	−	0.273221i	$-0.911911\pi$
$137$	−8.39920	−	14.5478i	−0.717592	−	1.24291i	0.244360	−	0.969685i	$-0.421422\pi$
$138$		0			0
$139$	−1.56922	−	0.571148i	−0.133099	−	0.0484442i	0.274612	−	0.961555i	$-0.411451\pi$
$139$	−1.56922	−	0.571148i	−0.133099	−	0.0484442i	−0.407711	+	0.913111i	$0.633673\pi$
$140$		0			0
$141$	7.59304	+	6.37132i	0.639450	+	0.536562i
$142$		0			0
$143$	−6.66668	−	5.59401i	−0.557496	−	0.467795i
$144$		0			0
$145$	−1.16122	+	6.58560i	−0.0964340	+	0.546904i
$146$		0			0
$147$	−21.5301			−1.77578
$148$		0			0
$149$	−8.20313			−0.672027			−0.336013	−	0.941857i	$-0.609079\pi$
$149$	−8.20313			−0.672027			−0.336013	+	0.941857i	$0.609079\pi$
$150$		0			0
$151$	0.827367	−	4.69223i	0.0673302	−	0.381849i	−0.932458	−	0.361278i	$-0.882341\pi$
$151$	0.827367	−	4.69223i	0.0673302	−	0.381849i	0.999788	−	0.0205707i	$-0.00654831\pi$
$152$		0			0
$153$	−0.211383	−	0.177371i	−0.0170893	−	0.0143396i
$154$		0			0
$155$	−0.750290	−	0.629568i	−0.0602647	−	0.0505681i
$156$		0			0
$157$	−16.4806	−	5.99844i	−1.31529	−	0.478728i	−0.413347	−	0.910574i	$-0.635640\pi$
$157$	−16.4806	−	5.99844i	−1.31529	−	0.478728i	−0.901947	+	0.431846i	$0.857862\pi$
$158$		0			0
$159$	−7.25750	−	12.5704i	−0.575557	−	0.996894i
$160$		0			0
$161$	−10.0084	+	3.64275i	−0.788770	+	0.287089i
$162$		0			0
$163$	12.6901	−	10.6482i	0.993962	−	0.834033i	0.00782579	−	0.999969i	$-0.497509\pi$
$163$	12.6901	−	10.6482i	0.993962	−	0.834033i	0.986137	+	0.165936i	$0.0530645\pi$
$164$		0			0
$165$	−18.6770	−	6.79786i	−1.45400	−	0.529213i
$166$		0			0
$167$	−0.109199	+	0.619296i	−0.00845005	+	0.0479226i	−0.988741	−	0.149635i	$-0.952190\pi$
$167$	−0.109199	+	0.619296i	−0.00845005	+	0.0479226i	0.980291	+	0.197558i	$0.0633011\pi$
$168$		0			0
$169$	−8.23375	+	6.90894i	−0.633366	+	0.531457i
$170$		0			0
$171$	−1.67188	+	2.89577i	−0.127852	+	0.221445i
$172$		0			0
$173$	−2.52976	−	14.3470i	−0.192334	−	1.09078i	−0.916164	−	0.400804i	$-0.868731\pi$
$173$	−2.52976	−	14.3470i	−0.192334	−	1.09078i	0.723829	−	0.689979i	$-0.242380\pi$
$174$		0			0
$175$	0.532873	−	0.922963i	0.0402814	−	0.0697694i
$176$		0			0
$177$	6.08451	+	10.5387i	0.457340	+	0.792136i
$178$		0			0
$179$	21.6343			1.61702			0.808512	−	0.588480i	$-0.200274\pi$
$179$	21.6343			1.61702			0.808512	+	0.588480i	$0.200274\pi$
$180$		0			0
$181$	1.10465	−	0.402060i	0.0821080	−	0.0298849i	−0.300640	−	0.953738i	$-0.597200\pi$
$181$	1.10465	−	0.402060i	0.0821080	−	0.0298849i	0.382748	+	0.923853i	$0.374978\pi$
$182$		0			0
$183$	0.665311	+	3.77317i	0.0491812	+	0.278920i
$184$		0			0
$185$	−2.32086	+	13.7166i	−0.170633	+	1.00846i
$186$		0			0
$187$	0.368229	+	2.08833i	0.0269276	+	0.152714i
$188$		0			0
$189$	24.4391	−	8.89510i	1.77768	−	0.647023i
$190$		0			0
$191$	10.6802			0.772790			0.386395	−	0.922333i	$-0.373720\pi$
$191$	10.6802			0.772790			0.386395	+	0.922333i	$0.373720\pi$
$192$		0			0
$193$	−0.500032	−	0.866081i	−0.0359931	−	0.0623418i	0.847468	−	0.530847i	$-0.178126\pi$
$193$	−0.500032	−	0.866081i	−0.0359931	−	0.0623418i	−0.883461	+	0.468505i	$0.844793\pi$
$194$		0			0
$195$	2.57114	−	4.45335i	0.184123	−	0.318911i
$196$		0			0
$197$	−0.587993	−	3.33467i	−0.0418928	−	0.237586i	0.956670	−	0.291173i	$-0.0940455\pi$
$197$	−0.587993	−	3.33467i	−0.0418928	−	0.237586i	−0.998563	+	0.0535874i	$0.982934\pi$
$198$		0			0
$199$	13.8828	−	24.0457i	0.984126	−	1.70456i	0.338371	−	0.941013i	$-0.390124\pi$
$199$	13.8828	−	24.0457i	0.984126	−	1.70456i	0.645755	−	0.763544i	$-0.276543\pi$
$200$		0			0
$201$	−16.2133	+	13.6045i	−1.14360	+	0.959590i
$202$		0			0
$203$	−2.34707	+	13.3109i	−0.164732	+	0.934243i
$204$		0			0
$205$	−0.256992	−	0.0935375i	−0.0179491	−	0.00653294i
$206$		0			0
$207$	1.33206	−	1.11773i	0.0925844	−	0.0776875i
$208$		0			0
$209$	24.1464	−	8.78856i	1.67024	−	0.607918i
$210$		0			0
$211$	−3.82794	−	6.63019i	−0.263526	−	0.456441i	0.703650	−	0.710547i	$-0.251552\pi$
$211$	−3.82794	−	6.63019i	−0.263526	−	0.456441i	−0.967176	+	0.254106i	$0.918219\pi$
$212$		0			0
$213$	11.4166	+	4.15529i	0.782250	+	0.284716i
$214$		0			0
$215$	22.6010	+	18.9645i	1.54138	+	1.29337i
$216$		0			0
$217$	−1.51650	−	1.27249i	−0.102947	−	0.0863824i
$218$		0			0
$219$	−3.44453	+	19.5349i	−0.232760	+	1.32005i
$220$		0			0
$221$	−0.548634			−0.0369051
$222$		0			0
$223$	0.949252			0.0635666			0.0317833	−	0.999495i	$-0.489881\pi$
$223$	0.949252			0.0635666			0.0317833	+	0.999495i	$0.489881\pi$
$224$		0			0
$225$	−0.0302145	+	0.171355i	−0.00201430	+	0.0114237i
$226$		0			0
$227$	−14.9814	−	12.5709i	−0.994349	−	0.834358i	−0.00815758	−	0.999967i	$-0.502597\pi$
$227$	−14.9814	−	12.5709i	−0.994349	−	0.834358i	−0.986192	+	0.165609i	$0.947041\pi$
$228$		0			0
$229$	3.75725	+	3.15271i	0.248286	+	0.208337i	0.758434	−	0.651750i	$-0.225965\pi$
$229$	3.75725	+	3.15271i	0.248286	+	0.208337i	−0.510148	+	0.860087i	$0.670409\pi$
$230$		0			0
$231$	−37.7502	−	13.7399i	−2.48378	−	0.904022i
$232$		0			0
$233$	7.80879	+	13.5252i	0.511571	+	0.886067i	0.999910	+	0.0134130i	$0.00426963\pi$
$233$	7.80879	+	13.5252i	0.511571	+	0.886067i	−0.488339	+	0.872654i	$0.662397\pi$
$234$		0			0
$235$	−14.2162	+	5.17429i	−0.927366	+	0.337533i
$236$		0			0
$237$	−12.7147	+	10.6689i	−0.825909	+	0.693020i
$238$		0			0
$239$	0.314666	+	0.114529i	0.0203541	+	0.00740827i	0.352177	−	0.935933i	$-0.385441\pi$
$239$	0.314666	+	0.114529i	0.0203541	+	0.00740827i	−0.331823	+	0.943342i	$0.607664\pi$
$240$		0			0
$241$	2.15209	−	12.2051i	0.138628	−	0.786201i	−0.833636	−	0.552315i	$-0.813745\pi$
$241$	2.15209	−	12.2051i	0.138628	−	0.786201i	0.972264	−	0.233886i	$-0.0751443\pi$
$242$		0			0
$243$	−5.85160	+	4.91008i	−0.375381	+	0.314982i
$244$		0			0
$245$	16.4306	−	28.4587i	1.04971	−	1.81816i
$246$		0			0
$247$	1.15444	+	6.54716i	0.0734553	+	0.416586i
$248$		0			0
$249$	5.52220	−	9.56474i	0.349955	−	0.606141i
$250$		0			0
$251$	4.12847	+	7.15072i	0.260587	+	0.451349i	0.966398	−	0.257051i	$-0.0827507\pi$
$251$	4.12847	+	7.15072i	0.260587	+	0.451349i	−0.705811	+	0.708400i	$0.749417\pi$
$252$		0			0
$253$	−13.3629			−0.840120
$254$		0			0
$255$	−1.17743	+	0.428548i	−0.0737332	+	0.0268367i
$256$		0			0
$257$	−3.52215	−	19.9751i	−0.219705	−	1.24601i	−0.872552	−	0.488521i	$-0.837536\pi$
$257$	−3.52215	−	19.9751i	−0.219705	−	1.24601i	0.652846	−	0.757490i	$-0.273575\pi$
$258$		0			0
$259$	−4.69096	+	27.7241i	−0.291482	+	1.72269i
$260$		0			0
$261$	−0.383194	−	2.17320i	−0.0237191	−	0.134518i
$262$		0			0
$263$	−21.8177	+	7.94100i	−1.34534	+	0.489663i	−0.911490	−	0.411323i	$-0.865067\pi$
$263$	−21.8177	+	7.94100i	−1.34534	+	0.489663i	−0.433849	+	0.900986i	$0.642845\pi$
$264$		0			0
$265$	22.1541			1.36092
$266$		0			0
$267$	10.5203	+	18.2217i	0.643831	+	1.11515i
$268$		0			0
$269$	−1.11257	+	1.92704i	−0.0678349	+	0.117493i	−0.897948	−	0.440102i	$-0.854942\pi$
$269$	−1.11257	+	1.92704i	−0.0678349	+	0.117493i	0.830113	+	0.557595i	$0.188276\pi$
$270$		0			0
$271$	5.00934	+	28.4094i	0.304296	+	1.72575i	0.626801	+	0.779180i	$0.284364\pi$
$271$	5.00934	+	28.4094i	0.304296	+	1.72575i	−0.322505	+	0.946568i	$0.604525\pi$
$272$		0			0
$273$	5.19683	−	9.00118i	0.314527	−	0.544776i
$274$		0			0
$275$	1.02431	−	0.859498i	0.0617682	−	0.0518297i
$276$		0			0
$277$	−3.04550	+	17.2719i	−0.182987	+	1.03777i	0.745529	+	0.666474i	$0.232197\pi$
$277$	−3.04550	+	17.2719i	−0.182987	+	1.03777i	−0.928515	+	0.371295i	$0.878914\pi$
$278$		0			0
$279$	0.303714	+	0.110543i	0.0181829	+	0.00661803i
$280$		0			0
$281$	−13.4977	+	11.3259i	−0.805203	+	0.675645i	−0.949458	−	0.313895i	$-0.898366\pi$
$281$	−13.4977	+	11.3259i	−0.805203	+	0.675645i	0.144255	+	0.989541i	$0.453921\pi$
$282$		0			0
$283$	21.2213	−	7.72390i	1.26147	−	0.459138i	0.377210	−	0.926128i	$-0.376884\pi$
$283$	21.2213	−	7.72390i	1.26147	−	0.459138i	0.884263	+	0.466990i	$0.154661\pi$
$284$		0			0
$285$	7.59165	+	13.1491i	0.449691	+	0.778887i
$286$		0			0
$287$	−0.519437	−	0.189060i	−0.0306614	−	0.0111598i
$288$		0			0
$289$	−12.9203	−	10.8415i	−0.760021	−	0.637733i
$290$		0			0
$291$	−6.50535	−	5.45864i	−0.381350	−	0.319991i
$292$		0			0
$293$	−5.00301	+	28.3735i	−0.292279	+	1.65760i	0.385780	+	0.922591i	$0.373932\pi$
$293$	−5.00301	+	28.3735i	−0.292279	+	1.65760i	−0.678059	+	0.735007i	$0.737179\pi$
$294$		0			0
$295$	−18.5735			−1.08139
$296$		0			0
$297$	32.6304			1.89341
$298$		0			0
$299$	0.600353	−	3.40477i	0.0347193	−	0.196903i
$300$		0			0
$301$	45.6816	+	38.3314i	2.63304	+	2.20938i
$302$		0			0
$303$	13.0905	+	10.9843i	0.752032	+	0.631030i
$304$		0			0
$305$	−5.49512	−	2.00006i	−0.314650	−	0.114523i
$306$		0			0
$307$	−14.4318	−	24.9965i	−0.823664	−	1.42663i	−0.902936	−	0.429775i	$-0.858593\pi$
$307$	−14.4318	−	24.9965i	−0.823664	−	1.42663i	0.0792721	−	0.996853i	$-0.474740\pi$
$308$		0			0
$309$	8.20039	−	2.98470i	0.466504	−	0.169794i
$310$		0			0
$311$	−8.73891	+	7.33281i	−0.495538	+	0.415806i	−0.856006	−	0.516966i	$-0.827061\pi$
$311$	−8.73891	+	7.33281i	−0.495538	+	0.415806i	0.360468	+	0.932772i	$0.382617\pi$
$312$		0			0
$313$	11.0014	+	4.00419i	0.621837	+	0.226330i	0.633674	−	0.773600i	$-0.281546\pi$
$313$	11.0014	+	4.00419i	0.621837	+	0.226330i	−0.0118377	+	0.999930i	$0.503768\pi$
$314$		0			0
$315$	−1.38551	+	7.85760i	−0.0780644	+	0.442725i
$316$		0			0
$317$	−3.63509	+	3.05020i	−0.204167	+	0.171317i	−0.739138	−	0.673554i	$-0.764767\pi$
$317$	−3.63509	+	3.05020i	−0.204167	+	0.171317i	0.534971	+	0.844870i	$0.320323\pi$
$318$		0			0
$319$	−8.47911	+	14.6862i	−0.474739	+	0.822272i
$320$		0			0
$321$	−0.173836	−	0.985874i	−0.00970258	−	0.0550261i
$322$		0			0
$323$	0.809959	−	1.40289i	0.0450673	−	0.0780589i
$324$		0			0
$325$	0.172975	+	0.299601i	0.00959491	+	0.0166189i
$326$		0			0
$327$	−6.81880			−0.377081
$328$		0			0
$329$	−28.7341	+	10.4584i	−1.58416	+	0.576588i
$330$		0			0
$331$	−0.790965	−	4.48579i	−0.0434754	−	0.246561i	0.955323	−	0.295563i	$-0.0955072\pi$
$331$	−0.790965	−	4.48579i	−0.0434754	−	0.246561i	−0.998799	+	0.0490016i	$0.984396\pi$
$332$		0			0
$333$	−0.828428	−	4.51533i	−0.0453976	−	0.247439i
$334$		0			0
$335$	−5.60950	−	31.8130i	−0.306480	−	1.73813i
$336$		0			0
$337$	−11.1450	+	4.05646i	−0.607108	+	0.220969i	−0.627238	−	0.778828i	$-0.715814\pi$
$337$	−11.1450	+	4.05646i	−0.607108	+	0.220969i	0.0201292	+	0.999797i	$0.493592\pi$
$338$		0			0
$339$	16.8903			0.917356
$340$		0			0
$341$	−1.24189	−	2.15101i	−0.0672518	−	0.116484i
$342$		0			0
$343$	17.0307	−	29.4981i	0.919573	−	1.59275i
$344$		0			0
$345$	−1.37111	−	7.77594i	−0.0738180	−	0.418643i
$346$		0			0
$347$	3.27651	−	5.67508i	0.175892	−	0.304654i	−0.764578	−	0.644532i	$-0.777052\pi$
$347$	3.27651	−	5.67508i	0.175892	−	0.304654i	0.940470	+	0.339878i	$0.110386\pi$
$348$		0			0
$349$	−14.0683	+	11.8047i	−0.753060	+	0.631892i	−0.936310	−	0.351174i	$-0.885783\pi$
$349$	−14.0683	+	11.8047i	−0.753060	+	0.631892i	0.183250	+	0.983066i	$0.441338\pi$
$350$		0			0
$351$	−1.46598	+	8.31399i	−0.0782483	+	0.443768i
$352$		0			0
$353$	29.3818	+	10.6941i	1.56383	+	0.569189i	0.971611	−	0.236586i	$-0.0760285\pi$
$353$	29.3818	+	10.6941i	1.56383	+	0.569189i	0.592222	+	0.805775i	$0.298251\pi$
$354$		0			0
$355$	−14.2050	+	11.9194i	−0.753923	+	0.632616i
$356$		0			0
$357$	−2.37983	+	0.866188i	−0.125954	+	0.0458435i
$358$		0			0
$359$	−5.01282	−	8.68245i	−0.264566	−	0.458242i	0.702884	−	0.711305i	$-0.251895\pi$
$359$	−5.01282	−	8.68245i	−0.264566	−	0.458242i	−0.967450	+	0.253063i	$0.918562\pi$
$360$		0			0
$361$	−0.591652	−	0.215344i	−0.0311396	−	0.0113339i
$362$		0			0
$363$	−25.9845	−	21.8036i	−1.36383	−	1.14439i
$364$		0			0
$365$	−23.1927	−	19.4610i	−1.21396	−	1.01863i
$366$		0			0
$367$	−3.60310	+	20.4342i	−0.188080	+	1.06666i	0.733853	+	0.679308i	$0.237720\pi$
$367$	−3.60310	+	20.4342i	−0.188080	+	1.06666i	−0.921934	+	0.387348i	$0.873391\pi$
$368$		0			0
$369$	0.0902482			0.00469813
$370$		0			0
$371$	44.7782			2.32477
$372$		0			0
$373$	1.73428	−	9.83558i	0.0897975	−	0.509267i	−0.906420	−	0.422377i	$-0.861196\pi$
$373$	1.73428	−	9.83558i	0.0897975	−	0.509267i	0.996218	−	0.0868903i	$-0.0276930\pi$
$374$		0			0
$375$	−12.5208	−	10.5062i	−0.646572	−	0.542538i
$376$		0			0
$377$	−3.36101	−	2.82022i	−0.173101	−	0.145249i
$378$		0			0
$379$	2.34138	+	0.852192i	0.120269	+	0.0437742i	0.401453	−	0.915879i	$-0.368505\pi$
$379$	2.34138	+	0.852192i	0.120269	+	0.0437742i	−0.281185	+	0.959654i	$0.590727\pi$
$380$		0			0
$381$	−4.33983	−	7.51680i	−0.222336	−	0.385097i
$382$		0			0
$383$	−9.17264	+	3.33857i	−0.468700	+	0.170593i	−0.565563	−	0.824705i	$-0.691341\pi$
$383$	−9.17264	+	3.33857i	−0.468700	+	0.170593i	0.0968634	+	0.995298i	$0.469119\pi$
$384$		0			0
$385$	46.9704	−	39.4129i	2.39383	−	2.00867i
$386$		0			0
$387$	−9.14880	−	3.32989i	−0.465060	−	0.169268i
$388$		0			0
$389$	4.81811	−	27.3249i	0.244288	−	1.38543i	−0.577853	−	0.816141i	$-0.696109\pi$
$389$	4.81811	−	27.3249i	0.244288	−	1.38543i	0.822141	−	0.569285i	$-0.192780\pi$
$390$		0			0
$391$	−0.645331	+	0.541497i	−0.0326358	+	0.0273847i
$392$		0			0
$393$	−6.73996	+	11.6739i	−0.339986	+	0.588873i
$394$		0			0
$395$	−4.39906	−	24.9483i	−0.221341	−	1.25529i
$396$		0			0
$397$	7.60298	−	13.1688i	0.381583	−	0.660921i	−0.609706	−	0.792628i	$-0.708712\pi$
$397$	7.60298	−	13.1688i	0.381583	−	0.660921i	0.991289	+	0.131707i	$0.0420458\pi$
$398$		0			0
$399$	15.3444	+	26.5772i	0.768180	+	1.33053i
$400$		0			0
$401$	−16.4705			−0.822499			−0.411250	−	0.911523i	$-0.634908\pi$
$401$	−16.4705			−0.822499			−0.411250	+	0.911523i	$0.634908\pi$
$402$		0			0
$403$	0.603855	−	0.219785i	0.0300802	−	0.0109483i
$404$		0			0
$405$	2.44889	+	13.8883i	0.121686	+	0.690116i
$406$		0			0
$407$	−17.4275	+	30.6735i	−0.863848	+	1.52043i
$408$		0			0
$409$	−4.03616	−	22.8902i	−0.199575	−	1.13185i	−0.905751	−	0.423811i	$-0.860692\pi$
$409$	−4.03616	−	22.8902i	−0.199575	−	1.13185i	0.706175	−	0.708037i	$-0.250419\pi$
$410$		0			0
$411$	23.6532	−	8.60907i	1.16673	−	0.424654i
$412$		0			0
$413$	−37.5410			−1.84727
$414$		0			0
$415$	8.42849	+	14.5986i	0.413738	+	0.716615i
$416$		0			0
$417$	1.25113	−	2.16703i	0.0612683	−	0.106120i
$418$		0			0
$419$	1.07471	+	6.09498i	0.0525030	+	0.297759i	0.999741	−	0.0227727i	$-0.00724941\pi$
$419$	1.07471	+	6.09498i	0.0525030	+	0.297759i	−0.947238	+	0.320532i	$0.896138\pi$
$420$		0			0
$421$	14.6700	−	25.4092i	0.714973	−	1.23837i	−0.247998	−	0.968761i	$-0.579773\pi$
$421$	14.6700	−	25.4092i	0.714973	−	1.23837i	0.962970	−	0.269608i	$-0.0868941\pi$
$422$		0			0
$423$	3.82435	−	3.20901i	0.185946	−	0.156027i
$424$		0			0
$425$	0.0146378	−	0.0830148i	0.000710036	−	0.00402681i
$426$		0			0
$427$	−11.1068	−	4.04256i	−0.537497	−	0.195633i
$428$		0			0
$429$	9.98956	−	8.38224i	0.482301	−	0.404698i
$430$		0			0
$431$	−5.61297	+	2.04295i	−0.270367	+	0.0984056i	−0.473646	−	0.880715i	$-0.657062\pi$
$431$	−5.61297	+	2.04295i	−0.270367	+	0.0984056i	0.203279	+	0.979121i	$0.434840\pi$
$432$		0			0
$433$	1.15529	+	2.00102i	0.0555198	+	0.0961631i	0.892450	−	0.451147i	$-0.148985\pi$
$433$	1.15529	+	2.00102i	0.0555198	+	0.0961631i	−0.836930	+	0.547310i	$0.815652\pi$
$434$		0			0
$435$	−9.41599	−	3.42714i	−0.451462	−	0.164319i
$436$		0			0
$437$	7.81990	+	6.56167i	0.374076	+	0.313887i
$438$		0			0
$439$	12.9591	+	10.8739i	0.618502	+	0.518985i	0.897332	−	0.441355i	$-0.145502\pi$
$439$	12.9591	+	10.8739i	0.618502	+	0.518985i	−0.278830	+	0.960340i	$0.589947\pi$
$440$		0			0
$441$	−1.88303	+	10.6792i	−0.0896683	+	0.508534i
$442$		0			0
$443$	16.5099			0.784409			0.392205	−	0.919878i	$-0.371713\pi$
$443$	16.5099			0.784409			0.392205	+	0.919878i	$0.371713\pi$
$444$		0			0
$445$	−32.1140			−1.52235
$446$		0			0
$447$	2.13445	−	12.1051i	0.100956	−	0.572551i
$448$		0			0
$449$	−9.09088	−	7.62815i	−0.429025	−	0.359995i	0.402559	−	0.915394i	$-0.368121\pi$
$449$	−9.09088	−	7.62815i	−0.429025	−	0.359995i	−0.831584	+	0.555399i	$0.812565\pi$
$450$		0			0
$451$	−0.531281	−	0.445798i	−0.0250171	−	0.0209918i
$452$		0			0
$453$	6.70889	+	2.44184i	0.315211	+	0.114727i
$454$		0			0
$455$	7.93188	+	13.7384i	0.371852	+	0.644067i
$456$		0			0
$457$	4.43033	−	1.61251i	0.207242	−	0.0754299i	−0.236313	−	0.971677i	$-0.575939\pi$
$457$	4.43033	−	1.61251i	0.207242	−	0.0754299i	0.443555	+	0.896247i	$0.353717\pi$
$458$		0			0
$459$	1.57581	−	1.32226i	0.0735525	−	0.0617179i
$460$		0			0
$461$	−4.56103	−	1.66008i	−0.212428	−	0.0773175i	0.233614	−	0.972329i	$-0.424945\pi$
$461$	−4.56103	−	1.66008i	−0.212428	−	0.0773175i	−0.446042	+	0.895012i	$0.647167\pi$
$462$		0			0
$463$	0.387848	−	2.19960i	0.0180248	−	0.102224i	−0.974468	−	0.224526i	$-0.927917\pi$
$463$	0.387848	−	2.19960i	0.0180248	−	0.102224i	0.992493	+	0.122302i	$0.0390277\pi$
$464$		0			0
$465$	1.12426	−	0.943363i	0.0521362	−	0.0437474i
$466$		0			0
$467$	12.3177	−	21.3349i	0.569996	−	0.987261i	−0.426570	−	0.904455i	$-0.640278\pi$
$467$	12.3177	−	21.3349i	0.569996	−	0.987261i	0.996566	−	0.0828068i	$-0.0263885\pi$
$468$		0			0
$469$	−11.3380	−	64.3010i	−0.523541	−	2.96915i
$470$		0			0
$471$	13.1399	−	22.7591i	0.605457	−	1.04868i
$472$		0			0
$473$	37.4094	+	64.7950i	1.72009	+	2.97928i
$474$		0			0
$475$	−1.02146			−0.0468680
$476$		0			0
$477$	−6.86980	+	2.50040i	−0.314546	+	0.114486i
$478$		0			0
$479$	3.26791	+	18.5332i	0.149314	+	0.846804i	0.963801	+	0.266622i	$0.0859076\pi$
$479$	3.26791	+	18.5332i	0.149314	+	0.846804i	−0.814487	+	0.580182i	$0.802981\pi$
$480$		0			0
$481$	−7.03241	−	5.81845i	−0.320650	−	0.265299i
$482$		0			0
$483$	−2.77131	−	15.7169i	−0.126099	−	0.715142i
$484$		0			0
$485$	12.1798	−	4.43308i	0.553056	−	0.201296i
$486$		0			0
$487$	−39.7247			−1.80010			−0.900050	−	0.435787i	$-0.856470\pi$
$487$	−39.7247			−1.80010			−0.900050	+	0.435787i	$0.856470\pi$
$488$		0			0
$489$	12.4113	+	21.4970i	0.561257	+	0.972126i
$490$		0			0
$491$	−3.62359	+	6.27624i	−0.163530	+	0.283243i	−0.936132	−	0.351648i	$-0.885622\pi$
$491$	−3.62359	+	6.27624i	−0.163530	+	0.283243i	0.772602	+	0.634891i	$0.218955\pi$
$492$		0			0
$493$	0.185643	+	1.05283i	0.00836092	+	0.0474171i
$494$		0			0
$495$	−5.00532	+	8.66947i	−0.224972	+	0.389664i
$496$		0			0
$497$	−28.7114	+	24.0917i	−1.28788	+	1.08066i
$498$		0			0
$499$	4.97283	−	28.2023i	0.222615	−	1.26251i	−0.644578	−	0.764538i	$-0.722967\pi$
$499$	4.97283	−	28.2023i	0.222615	−	1.26251i	0.867193	−	0.497972i	$-0.165922\pi$
$500$		0			0
$501$	−0.885461	−	0.322281i	−0.0395595	−	0.0143985i
$502$		0			0
$503$	−13.4101	+	11.2524i	−0.597928	+	0.501721i	−0.890779	−	0.454437i	$-0.849840\pi$
$503$	−13.4101	+	11.2524i	−0.597928	+	0.501721i	0.292851	+	0.956158i	$0.405396\pi$
$504$		0			0
$505$	−24.5091	+	8.92057i	−1.09064	+	0.396960i
$506$		0			0
$507$	−8.05286	−	13.9480i	−0.357640	−	0.619451i
$508$		0			0
$509$	−35.1289	−	12.7859i	−1.55706	−	0.566723i	−0.586999	−	0.809588i	$-0.699691\pi$
$509$	−35.1289	−	12.7859i	−1.55706	−	0.566723i	−0.970060	+	0.242864i	$0.921913\pi$
$510$		0			0
$511$	−46.8775	−	39.3349i	−2.07374	−	1.74007i
$512$		0			0
$513$	−19.0951	−	16.0227i	−0.843070	−	0.707420i
$514$		0			0
$515$	−2.31290	+	13.1171i	−0.101918	+	0.578008i
$516$		0			0
$517$	−38.3650			−1.68729
$518$		0			0
$519$	21.8296			0.958215
$520$		0			0
$521$	−0.532100	+	3.01769i	−0.0233117	+	0.132207i	−0.994243	−	0.107153i	$-0.965827\pi$
$521$	−0.532100	+	3.01769i	−0.0233117	+	0.132207i	0.970931	+	0.239360i	$0.0769377\pi$
$522$		0			0
$523$	16.2249	+	13.6143i	0.709466	+	0.595313i	0.924449	−	0.381305i	$-0.124525\pi$
$523$	16.2249	+	13.6143i	0.709466	+	0.595313i	−0.214983	+	0.976618i	$0.568970\pi$
$524$		0			0
$525$	1.22333	+	1.02650i	0.0533906	+	0.0448000i
$526$		0			0
$527$	−0.147138	−	0.0535538i	−0.00640942	−	0.00233284i
$528$		0			0
$529$	8.84569	+	15.3212i	0.384595	+	0.666138i
$530$		0			0
$531$	5.75948	−	2.09628i	0.249940	−	0.0909707i
$532$		0			0
$533$	0.137455	−	0.115338i	0.00595383	−	0.00499586i
$534$		0			0
$535$	1.43580	+	0.522587i	0.0620749	+	0.0225934i
$536$		0			0
$537$	−5.62924	+	31.9250i	−0.242920	+	1.37767i
$538$		0			0
$539$	63.8373	−	53.5658i	2.74967	−	2.30724i
$540$		0			0
$541$	13.4696	−	23.3301i	0.579105	−	1.00304i	−0.416478	−	0.909146i	$-0.636736\pi$
$541$	13.4696	−	23.3301i	0.579105	−	1.00304i	0.995582	−	0.0938928i	$-0.0299311\pi$
$542$		0			0
$543$	0.305876	+	1.73471i	0.0131264	+	0.0744436i
$544$		0			0
$545$	5.20374	−	9.01313i	0.222904	−	0.386080i
$546$		0			0
$547$	−14.2475	−	24.6775i	−0.609181	−	1.05513i	−0.991376	−	0.131050i	$-0.958165\pi$
$547$	−14.2475	−	24.6775i	−0.609181	−	1.05513i	0.382195	−	0.924082i	$-0.375168\pi$
$548$		0			0
$549$	1.92973			0.0823587
$550$		0			0
$551$	12.1734	−	4.43075i	0.518604	−	0.188756i
$552$		0			0
$553$	−8.89145	−	50.4259i	−0.378103	−	2.14433i
$554$		0			0
$555$	−19.6372	−	6.99386i	−0.833551	−	0.296873i
$556$		0			0
$557$	7.64434	+	43.3532i	0.323901	+	1.83693i	0.517288	+	0.855811i	$0.326942\pi$
$557$	7.64434	+	43.3532i	0.323901	+	1.83693i	−0.193387	+	0.981123i	$0.561947\pi$
$558$		0			0
$559$	−18.1900	+	6.62060i	−0.769353	+	0.280022i
$560$		0			0
$561$	−3.17749			−0.134154
$562$		0			0
$563$	16.2698	+	28.1801i	0.685689	+	1.18765i	0.973220	+	0.229877i	$0.0738325\pi$
$563$	16.2698	+	28.1801i	0.685689	+	1.18765i	−0.287530	+	0.957772i	$0.592834\pi$
$564$		0			0
$565$	−12.8898	+	22.3257i	−0.542277	+	0.939251i
$566$		0			0
$567$	4.94973	+	28.0713i	0.207869	+	1.17888i
$568$		0			0
$569$	−13.4601	+	23.3136i	−0.564277	+	0.977357i	0.432839	+	0.901471i	$0.357512\pi$
$569$	−13.4601	+	23.3136i	−0.564277	+	0.977357i	−0.997117	+	0.0758857i	$0.975822\pi$
$570$		0			0
$571$	8.98942	−	7.54302i	0.376195	−	0.315665i	−0.435011	−	0.900425i	$-0.643256\pi$
$571$	8.98942	−	7.54302i	0.376195	−	0.315665i	0.811207	+	0.584760i	$0.198811\pi$
$572$		0			0
$573$	−2.77898	+	15.7604i	−0.116093	+	0.658399i
$574$		0			0
$575$	0.499165	+	0.181681i	0.0208166	+	0.00757663i
$576$		0			0
$577$	−5.12542	+	4.30074i	−0.213374	+	0.179042i	−0.743210	−	0.669058i	$-0.766698\pi$
$577$	−5.12542	+	4.30074i	−0.213374	+	0.179042i	0.529836	+	0.848100i	$0.322253\pi$
$578$		0			0
$579$	1.40815	−	0.512526i	0.0585209	−	0.0212999i
$580$		0			0
$581$	17.0358	+	29.5069i	0.706764	+	1.22415i
$582$		0			0
$583$	52.7930	+	19.2151i	2.18646	+	0.795807i
$584$		0			0
$585$	−1.98404	−	1.66481i	−0.0820301	−	0.0688314i
$586$		0			0
$587$	18.5228	+	15.5425i	0.764520	+	0.641508i	0.939299	−	0.343099i	$-0.111477\pi$
$587$	18.5228	+	15.5425i	0.764520	+	0.641508i	−0.174779	+	0.984608i	$0.555921\pi$
$588$		0			0
$589$	−0.329479	+	1.86857i	−0.0135759	+	0.0769930i
$590$		0			0
$591$	5.07386			0.208711
$592$		0			0
$593$	21.5119			0.883388			0.441694	−	0.897166i	$-0.354378\pi$
$593$	21.5119			0.883388			0.441694	+	0.897166i	$0.354378\pi$
$594$		0			0
$595$	0.671225	−	3.80670i	0.0275175	−	0.156060i
$596$		0			0
$597$	31.8712	+	26.7431i	1.30440	+	1.09452i
$598$		0			0
$599$	14.7915	+	12.4116i	0.604366	+	0.507123i	0.892846	−	0.450363i	$-0.148705\pi$
$599$	14.7915	+	12.4116i	0.604366	+	0.507123i	−0.288480	+	0.957486i	$0.593150\pi$
$600$		0			0
$601$	15.2325	+	5.54418i	0.621347	+	0.226152i	0.633461	−	0.773775i	$-0.281634\pi$
$601$	15.2325	+	5.54418i	0.621347	+	0.226152i	−0.0121137	+	0.999927i	$0.503856\pi$
$602$		0			0
$603$	5.33001	+	9.23184i	0.217055	+	0.375950i
$604$		0			0
$605$	48.6500	−	17.7072i	1.97790	−	0.719899i
$606$		0			0
$607$	12.4121	−	10.4150i	0.503793	−	0.422733i	−0.355145	−	0.934811i	$-0.615569\pi$
$607$	12.4121	−	10.4150i	0.503793	−	0.422733i	0.858939	+	0.512078i	$0.171124\pi$
$608$		0			0
$609$	−19.0318	−	6.92700i	−0.771206	−	0.280696i
$610$		0			0
$611$	1.72362	−	9.77513i	0.0697302	−	0.395459i
$612$		0			0
$613$	8.94765	−	7.50797i	0.361392	−	0.303244i	−0.443953	−	0.896050i	$-0.646424\pi$
$613$	8.94765	−	7.50797i	0.361392	−	0.303244i	0.805345	+	0.592806i	$0.201980\pi$
$614$		0			0
$615$	0.204899	−	0.354896i	0.00826234	−	0.0143108i
$616$		0			0
$617$	3.01838	+	17.1181i	0.121515	+	0.689147i	0.983317	+	0.181901i	$0.0582252\pi$
$617$	3.01838	+	17.1181i	0.121515	+	0.689147i	−0.861802	+	0.507246i	$0.830664\pi$
$618$		0			0
$619$	3.05948	−	5.29917i	0.122971	−	0.212991i	−0.797967	−	0.602701i	$-0.794091\pi$
$619$	3.05948	−	5.29917i	0.122971	−	0.212991i	0.920938	+	0.389709i	$0.127425\pi$
$620$		0			0
$621$	6.48147	+	11.2262i	0.260093	+	0.450494i
$622$		0			0
$623$	−64.9094			−2.60054
$624$		0			0
$625$	24.5256	−	8.92659i	0.981024	−	0.357064i
$626$		0			0
$627$	6.68610	+	37.9188i	0.267017	+	1.51433i
$628$		0			0
$629$	0.401341	+	2.18750i	0.0160025	+	0.0872215i
$630$		0			0
$631$	−4.74804	−	26.9275i	−0.189017	−	1.07197i	−0.920685	−	0.390306i	$-0.872369\pi$
$631$	−4.74804	−	26.9275i	−0.189017	−	1.07197i	0.731669	−	0.681661i	$-0.238742\pi$
$632$		0			0
$633$	10.7800	−	3.92359i	0.428465	−	0.155949i
$634$		0			0
$635$	13.2477			0.525718
$636$		0			0
$637$	10.7802	+	18.6718i	0.427126	+	0.739804i
$638$		0			0
$639$	3.05958	−	5.29934i	0.121035	−	0.209639i
$640$		0			0
$641$	−2.59140	−	14.6966i	−0.102354	−	0.580479i	−0.992244	−	0.124304i	$-0.960330\pi$
$641$	−2.59140	−	14.6966i	−0.102354	−	0.580479i	0.889890	−	0.456175i	$-0.150781\pi$
$642$		0			0
$643$	7.91287	−	13.7055i	0.312053	−	0.540492i	−0.666754	−	0.745278i	$-0.732317\pi$
$643$	7.91287	−	13.7055i	0.312053	−	0.540492i	0.978807	+	0.204786i	$0.0656499\pi$
$644$		0			0
$645$	−33.8661	+	28.4170i	−1.33347	+	1.11892i
$646$		0			0
$647$	−6.66717	+	37.8114i	−0.262113	+	1.48652i	0.515017	+	0.857180i	$0.327785\pi$
$647$	−6.66717	+	37.8114i	−0.262113	+	1.48652i	−0.777131	+	0.629339i	$0.783326\pi$
$648$		0			0
$649$	−44.2604	−	16.1095i	−1.73737	−	0.632352i
$650$		0			0
$651$	2.27237	−	1.90674i	0.0890611	−	0.0747311i
$652$		0			0
$653$	10.2087	−	3.71567i	0.399498	−	0.145405i	−0.134455	−	0.990920i	$-0.542928\pi$
$653$	10.2087	−	3.71567i	0.399498	−	0.145405i	0.533953	+	0.845514i	$0.320706\pi$
$654$		0			0
$655$	−10.2871	−	17.8178i	−0.401951	−	0.696200i
$656$		0			0
$657$	9.38830	+	3.41706i	0.366273	+	0.133312i
$658$		0			0
$659$	13.9069	+	11.6693i	0.541737	+	0.454571i	0.872132	−	0.489272i	$-0.162737\pi$
$659$	13.9069	+	11.6693i	0.541737	+	0.454571i	−0.330394	+	0.943843i	$0.607182\pi$
$660$		0			0
$661$	5.39465	+	4.52664i	0.209827	+	0.176066i	0.741644	−	0.670793i	$-0.234046\pi$
$661$	5.39465	+	4.52664i	0.209827	+	0.176066i	−0.531817	+	0.846859i	$0.678491\pi$
$662$		0			0
$663$	0.142754	−	0.809601i	0.00554412	−	0.0314423i
$664$		0			0
$665$	−46.8399			−1.81637
$666$		0			0
$667$	−6.73692			−0.260854
$668$		0			0
$669$	−0.246995	+	1.40078i	−0.00954939	+	0.0541573i
$670$		0			0
$671$	−11.3601	−	9.53225i	−0.438552	−	0.367989i
$672$		0			0
$673$	8.74225	+	7.33562i	0.336989	+	0.282767i	0.795540	−	0.605900i	$-0.207187\pi$
$673$	8.74225	+	7.33562i	0.336989	+	0.282767i	−0.458551	+	0.888668i	$0.651631\pi$
$674$		0			0
$675$	−1.21889	−	0.443641i	−0.0469152	−	0.0170757i
$676$		0			0
$677$	−14.9313	−	25.8619i	−0.573858	−	0.993952i	−0.996165	−	0.0874985i	$-0.972113\pi$
$677$	−14.9313	−	25.8619i	−0.573858	−	0.993952i	0.422306	−	0.906453i	$-0.361221\pi$
$678$		0			0
$679$	24.6180	−	8.96022i	0.944752	−	0.343862i
$680$		0			0
$681$	22.4486	−	18.8366i	0.860231	−	0.721819i
$682$		0			0
$683$	−40.0133	−	14.5637i	−1.53107	−	0.557263i	−0.567184	−	0.823591i	$-0.691967\pi$
$683$	−40.0133	−	14.5637i	−1.53107	−	0.557263i	−0.963882	+	0.266328i	$0.914189\pi$
$684$		0			0
$685$	−6.67132	+	37.8349i	−0.254898	+	1.44560i
$686$		0			0
$687$	−5.62998	+	4.72412i	−0.214797	+	0.180236i
$688$		0			0
$689$	−7.26768	+	12.5880i	−0.276877	+	0.479564i
$690$		0			0
$691$	6.77155	+	38.4034i	0.257602	+	1.46093i	0.789305	+	0.614002i	$0.210441\pi$
$691$	6.77155	+	38.4034i	0.257602	+	1.46093i	−0.531703	+	0.846931i	$0.678448\pi$
$692$		0			0
$693$	−10.1168	+	17.5229i	−0.384307	+	0.665639i
$694$		0			0
$695$	1.90959	+	3.30751i	0.0724350	+	0.125461i
$696$		0			0
$697$	−0.0437218			−0.00165608
$698$		0			0
$699$	−21.9906	+	8.00391i	−0.831759	+	0.302736i
$700$		0			0
$701$	−3.97235	−	22.5283i	−0.150033	−	0.850882i	−0.963187	−	0.268833i	$-0.913362\pi$
$701$	−3.97235	−	22.5283i	−0.150033	−	0.850882i	0.813153	−	0.582049i	$-0.197749\pi$
$702$		0			0
$703$	25.2602	−	9.39240i	0.952707	−	0.354241i
$704$		0			0
$705$	−3.93646	−	22.3248i	−0.148256	−	0.840800i
$706$		0			0
$707$	−49.5381	+	18.0304i	−1.86307	+	0.678103i
$708$		0			0
$709$	−24.7872			−0.930902			−0.465451	−	0.885074i	$-0.654108\pi$
$709$	−24.7872			−0.930902			−0.465451	+	0.885074i	$0.654108\pi$
$710$		0			0
$711$	4.17988	+	7.23976i	0.156758	+	0.271512i
$712$		0			0
$713$	0.493358	−	0.854521i	0.0184764	−	0.0320021i
$714$		0			0
$715$	3.45621	+	19.6011i	0.129255	+	0.733041i
$716$		0			0
$717$	−0.250883	+	0.434542i	−0.00936939	+	0.0162283i
$718$		0			0
$719$	−16.5427	+	13.8810i	−0.616939	+	0.517673i	−0.896840	−	0.442356i	$-0.854143\pi$
$719$	−16.5427	+	13.8810i	−0.616939	+	0.517673i	0.279901	+	0.960029i	$0.409698\pi$
$720$		0			0
$721$	−4.67486	+	26.5125i	−0.174101	+	0.987376i
$722$		0			0
$723$	17.4507	+	6.35154i	0.648999	+	0.236216i
$724$		0			0
$725$	0.516406	−	0.433316i	0.0191788	−	0.0160929i
$726$		0			0
$727$	2.40292	−	0.874590i	0.0891193	−	0.0324368i	−0.297076	−	0.954854i	$-0.596011\pi$
$727$	2.40292	−	0.874590i	0.0891193	−	0.0324368i	0.386195	+	0.922417i	$0.373789\pi$
$728$		0			0
$729$	−14.9725	−	25.9331i	−0.554537	−	0.960486i
$730$		0			0
$731$	4.43224	+	1.61320i	0.163932	+	0.0596665i
$732$		0			0
$733$	27.5944	+	23.1545i	1.01922	+	0.855230i	0.989530	−	0.144329i	$-0.0461024\pi$
$733$	27.5944	+	23.1545i	1.01922	+	0.855230i	0.0296935	+	0.999559i	$0.490547\pi$
$734$		0			0
$735$	37.7202	+	31.6510i	1.39133	+	1.16747i
$736$		0			0
$737$	14.2253	−	80.6755i	0.523994	−	2.97172i
$738$		0			0
$739$	9.09681			0.334632			0.167316	−	0.985903i	$-0.446490\pi$
$739$	9.09681			0.334632			0.167316	+	0.985903i	$0.446490\pi$
$740$		0			0
$741$	−9.96181			−0.365956
$742$		0			0
$743$	−1.55697	+	8.83000i	−0.0571196	+	0.323941i	−0.999957	−	0.00931280i	$-0.997036\pi$
$743$	−1.55697	+	8.83000i	−0.0571196	+	0.323941i	0.942837	+	0.333254i	$0.108147\pi$
$744$		0			0
$745$	14.3717	+	12.0593i	0.526537	+	0.441817i
$746$		0			0
$747$	−4.26126	−	3.57562i	−0.155911	−	0.130825i
$748$		0			0
$749$	2.90205	+	1.05626i	0.106039	+	0.0385950i
$750$		0			0
$751$	−17.8566	−	30.9286i	−0.651597	−	1.12860i	−0.982735	−	0.185017i	$-0.940766\pi$
$751$	−17.8566	−	30.9286i	−0.651597	−	1.12860i	0.331138	−	0.943582i	$-0.392567\pi$
$752$		0			0
$753$	−11.6263	+	4.23163i	−0.423686	+	0.154209i
$754$		0			0
$755$	−8.34749	+	7.00437i	−0.303796	+	0.254915i
$756$		0			0
$757$	39.0582	+	14.2160i	1.41960	+	0.516691i	0.933931	−	0.357454i	$-0.116355\pi$
$757$	39.0582	+	14.2160i	1.41960	+	0.516691i	0.485665	+	0.874145i	$0.338577\pi$
$758$		0			0
$759$	3.47703	−	19.7192i	0.126208	−	0.715762i
$760$		0			0
$761$	5.27255	−	4.42419i	0.191130	−	0.160377i	−0.542201	−	0.840249i	$-0.682409\pi$
$761$	5.27255	−	4.42419i	0.191130	−	0.160377i	0.733331	+	0.679872i	$0.237965\pi$
$762$		0			0
$763$	10.5179	−	18.2175i	0.380773	−	0.659518i
$764$		0			0
$765$	0.109587	+	0.621499i	0.00396213	+	0.0224703i
$766$		0			0
$767$	6.09305	−	10.5535i	0.220007	−	0.381064i
$768$		0			0
$769$	−2.66183	−	4.61043i	−0.0959881	−	0.166256i	0.814032	−	0.580819i	$-0.197268\pi$
$769$	−2.66183	−	4.61043i	−0.0959881	−	0.166256i	−0.910021	+	0.414563i	$0.863934\pi$
$770$		0			0
$771$	30.3930			1.09458
$772$		0			0
$773$	31.5436	−	11.4809i	1.13454	−	0.412940i	0.294604	−	0.955619i	$-0.404812\pi$
$773$	31.5436	−	11.4809i	1.13454	−	0.412940i	0.839940	+	0.542679i	$0.182590\pi$
$774$		0			0
$775$	0.0171450	+	0.0972344i	0.000615868	+	0.00349276i
$776$		0			0
$777$	−39.6910	−	14.1361i	−1.42391	−	0.507130i
$778$		0			0
$779$	0.0919998	+	0.521757i	0.00329623	+	0.0186939i
$780$		0			0
$781$	−44.1885	+	16.0833i	−1.58119	+	0.575506i
$782$		0			0
$783$	16.4506			0.587898
$784$		0			0
$785$	20.0554	+	34.7369i	0.715807	+	1.23981i
$786$		0			0
$787$	−9.14463	+	15.8390i	−0.325971	+	0.564598i	−0.981708	−	0.190391i	$-0.939024\pi$
$787$	−9.14463	+	15.8390i	−0.325971	+	0.564598i	0.655738	+	0.754989i	$0.272358\pi$
$788$		0			0
$789$	−6.04130	−	34.2619i	−0.215076	−	1.21976i
$790$		0			0
$791$	−26.0530	+	45.1251i	−0.926339	+	1.60447i
$792$		0			0
$793$	2.93912	−	2.46622i	0.104371	−	0.0875779i
$794$		0			0
$795$	−5.76449	+	32.6920i	−0.204445	+	1.15947i
$796$		0			0
$797$	31.2275	+	11.3659i	1.10613	+	0.402600i	0.829574	−	0.558397i	$-0.188583\pi$
$797$	31.2275	+	11.3659i	1.10613	+	0.402600i	0.276560	+	0.960997i	$0.410806\pi$
$798$		0			0
$799$	−1.85275	+	1.55464i	−0.0655456	+	0.0549993i
$800$		0			0
$801$	9.95829	−	3.62452i	0.351859	−	0.128066i
$802$		0			0
$803$	−38.3887	−	66.4912i	−1.35471	−	2.34642i
$804$		0			0
$805$	22.8896	+	8.33112i	0.806751	+	0.293633i
$806$		0			0
$807$	−2.55417	−	2.14320i	−0.0899110	−	0.0754443i
$808$		0			0
$809$	−9.69050	−	8.13129i	−0.340700	−	0.285881i	0.456343	−	0.889804i	$-0.349159\pi$
$809$	−9.69050	−	8.13129i	−0.340700	−	0.285881i	−0.797043	+	0.603923i	$0.793603\pi$
$810$		0			0
$811$	−6.32995	+	35.8989i	−0.222275	+	1.26058i	0.645553	+	0.763716i	$0.276627\pi$
$811$	−6.32995	+	35.8989i	−0.222275	+	1.26058i	−0.867827	+	0.496866i	$0.834484\pi$
$812$		0			0
$813$	−43.2262			−1.51601
$814$		0			0
$815$	−37.8864			−1.32710
$816$		0			0
$817$	9.92491	−	56.2870i	0.347229	−	1.96923i
$818$		0			0
$819$	−4.01018	−	3.36494i	−0.140127	−	0.117581i
$820$		0			0
$821$	5.73792	+	4.81469i	0.200255	+	0.168034i	0.737401	−	0.675456i	$-0.236053\pi$
$821$	5.73792	+	4.81469i	0.200255	+	0.168034i	−0.537146	+	0.843489i	$0.680497\pi$
$822$		0			0
$823$	−36.0723	−	13.1292i	−1.25740	−	0.457657i	−0.374505	−	0.927225i	$-0.622187\pi$
$823$	−36.0723	−	13.1292i	−1.25740	−	0.457657i	−0.882896	+	0.469568i	$0.844410\pi$
$824$		0			0
$825$	1.00181	+	1.73518i	0.0348784	+	0.0604112i
$826$		0			0
$827$	8.23186	−	2.99615i	0.286250	−	0.104186i	−0.194905	−	0.980822i	$-0.562440\pi$
$827$	8.23186	−	2.99615i	0.286250	−	0.104186i	0.481155	+	0.876636i	$0.340218\pi$
$828$		0			0
$829$	3.09992	−	2.60114i	0.107665	−	0.0903414i	−0.587366	−	0.809321i	$-0.699835\pi$
$829$	3.09992	−	2.60114i	0.107665	−	0.0903414i	0.695031	+	0.718980i	$0.255391\pi$
$830$		0			0
$831$	−24.6951	−	8.98829i	−0.856664	−	0.311800i
$832$		0			0
$833$	0.912258	−	5.17367i	0.0316079	−	0.179257i
$834$		0			0
$835$	1.10173	−	0.924460i	0.0381269	−	0.0319923i
$836$		0			0
$837$	−1.20471	+	2.08662i	−0.0416410	+	0.0721243i
$838$		0			0
$839$	1.54853	+	8.78212i	0.0534610	+	0.303193i	0.999800	−	0.0199822i	$-0.00636094\pi$
$839$	1.54853	+	8.78212i	0.0534610	+	0.303193i	−0.946339	+	0.323175i	$0.895250\pi$
$840$		0			0
$841$	10.2253	−	17.7107i	0.352595	−	0.610713i
$842$		0			0
$843$	−13.2011	−	22.8650i	−0.454671	−	0.787513i
$844$		0			0
$845$	24.5820			0.845647
$846$		0			0
$847$	98.3323	−	35.7900i	3.37874	−	1.22976i
$848$		0			0
$849$	5.87614	+	33.3252i	0.201669	+	1.14372i
$850$		0			0
$851$	−14.0146	+	0.0969685i	−0.480415	+	0.00332404i
$852$		0			0
$853$	−4.75255	−	26.9530i	−0.162724	−	0.922854i	−0.951380	−	0.308020i	$-0.900334\pi$
$853$	−4.75255	−	26.9530i	−0.162724	−	0.922854i	0.788656	−	0.614835i	$-0.210777\pi$
$854$		0			0
$855$	7.18610	−	2.61553i	0.245760	−	0.0894492i
$856$		0			0
$857$	−3.62035			−0.123669			−0.0618344	−	0.998086i	$-0.519695\pi$
$857$	−3.62035			−0.123669			−0.0618344	+	0.998086i	$0.519695\pi$
$858$		0			0
$859$	0.600179	+	1.03954i	0.0204778	+	0.0354687i	0.876083	−	0.482161i	$-0.160148\pi$
$859$	0.600179	+	1.03954i	0.0204778	+	0.0354687i	−0.855605	+	0.517629i	$0.826815\pi$
$860$		0			0
$861$	0.414146	−	0.717322i	0.0141141	−	0.0244463i
$862$		0			0
$863$	−8.28755	−	47.0010i	−0.282112	−	1.59993i	−0.715424	−	0.698691i	$-0.753766\pi$
$863$	−8.28755	−	47.0010i	−0.282112	−	1.59993i	0.433312	−	0.901244i	$-0.357345\pi$
$864$		0			0
$865$	−16.6592	+	28.8545i	−0.566429	+	0.981084i
$866$		0			0
$867$	19.3602	−	16.2452i	0.657508	−	0.551715i
$868$		0			0
$869$	11.1557	−	63.2670i	0.378431	−	2.14619i
$870$		0			0
$871$	19.9164	+	7.24898i	0.674842	+	0.245622i
$872$		0			0
$873$	−3.27651	+	2.74932i	−0.110893	+	0.0930505i
$874$		0			0
$875$	47.3821	−	17.2457i	1.60181	−	0.583010i
$876$		0			0
$877$	−18.5981	−	32.2128i	−0.628012	−	1.08775i	−0.987950	−	0.154772i	$-0.950536\pi$
$877$	−18.5981	−	32.2128i	−0.628012	−	1.08775i	0.359939	−	0.932976i	$-0.382798\pi$
$878$		0			0
$879$	−40.5680	−	14.7656i	−1.36833	−	0.498030i
$880$		0			0
$881$	0.922572	+	0.774130i	0.0310822	+	0.0260811i	0.658196	−	0.752846i	$-0.271320\pi$
$881$	0.922572	+	0.774130i	0.0310822	+	0.0260811i	−0.627114	+	0.778927i	$0.715764\pi$
$882$		0			0
$883$	16.3100	+	13.6857i	0.548875	+	0.460561i	0.874560	−	0.484918i	$-0.161150\pi$
$883$	16.3100	+	13.6857i	0.548875	+	0.460561i	−0.325685	+	0.945478i	$0.605595\pi$
$884$		0			0
$885$	4.83281	−	27.4082i	0.162453	−	0.921318i
$886$		0			0
$887$	−24.9441			−0.837542			−0.418771	−	0.908092i	$-0.637539\pi$
$887$	−24.9441			−0.837542			−0.418771	+	0.908092i	$0.637539\pi$
$888$		0			0
$889$	26.7764			0.898052
$890$		0			0
$891$	−6.21019	+	35.2198i	−0.208049	+	1.17991i
$892$		0			0
$893$	22.4510	+	18.8386i	0.751293	+	0.630410i
$894$		0			0
$895$	−37.9027	−	31.8042i	−1.26695	−	1.06310i
$896$		0			0
$897$	4.86810	+	1.77184i	0.162541	+	0.0591601i
$898$		0			0
$899$	−0.626096	−	1.08443i	−0.0208815	−	0.0361678i
$900$		0			0
$901$	3.32815	−	1.21135i	0.110877	−	0.0403559i
$902$		0			0
$903$	−68.4506	+	57.4369i	−2.27789	+	1.91138i
$904$		0			0
$905$	−2.52638	−	0.919527i	−0.0839797	−	0.0305661i
$906$		0			0
$907$	1.33823	−	7.58946i	0.0444351	−	0.252004i	−0.954496	−	0.298223i	$-0.903606\pi$
$907$	1.33823	−	7.58946i	0.0444351	−	0.252004i	0.998931	+	0.0462190i	$0.0147172\pi$
$908$		0			0
$909$	6.59324	−	5.53239i	0.218684	−	0.183498i
$910$		0			0
$911$	11.9052	−	20.6205i	0.394438	−	0.683186i	−0.598592	−	0.801054i	$-0.704273\pi$
$911$	11.9052	−	20.6205i	0.394438	−	0.683186i	0.993029	+	0.117868i	$0.0376061\pi$
$912$		0			0
$913$	7.42312	+	42.0986i	0.245669	+	1.39326i
$914$		0			0
$915$	4.38125	−	7.58855i	0.144840	−	0.250870i
$916$		0			0
$917$	−20.7925	−	36.0137i	−0.686629	−	1.18928i
$918$		0			0
$919$	42.8179			1.41243			0.706216	−	0.707997i	$-0.250401\pi$
$919$	42.8179			1.41243			0.706216	+	0.707997i	$0.250401\pi$
$920$		0			0
$921$	40.6417	−	14.7924i	1.33919	−	0.487425i
$922$		0			0
$923$	−2.11266	−	11.9815i	−0.0695390	−	0.394375i
$924$		0			0
$925$	1.06803	−	0.908848i	0.0351165	−	0.0298828i
$926$		0			0
$927$	−0.763239	−	4.32854i	−0.0250680	−	0.142168i
$928$		0			0
$929$	51.9266	−	18.8997i	1.70366	−	0.620080i	0.707422	−	0.706792i	$-0.249858\pi$
$929$	51.9266	−	18.8997i	1.70366	−	0.620080i	0.996233	+	0.0867117i	$0.0276359\pi$
$930$		0			0
$931$	−63.6599			−2.08637
$932$		0			0
$933$	−8.54692	−	14.8037i	−0.279814	−	0.484651i
$934$		0			0
$935$	2.42489	−	4.20002i	0.0793022	−	0.137355i
$936$		0			0
$937$	4.88641	+	27.7122i	0.159632	+	0.905318i	0.954428	+	0.298442i	$0.0964668\pi$
$937$	4.88641	+	27.7122i	0.159632	+	0.905318i	−0.794796	+	0.606877i	$0.792422\pi$
$938$		0			0
$939$	−8.77141	+	15.1925i	−0.286244	+	0.495789i
$940$		0			0
$941$	−2.90978	+	2.44159i	−0.0948561	+	0.0795937i	−0.688982	−	0.724778i	$-0.741942\pi$
$941$	−2.90978	+	2.44159i	−0.0948561	+	0.0795937i	0.594126	+	0.804372i	$0.297498\pi$
$942$		0			0
$943$	0.0478434	−	0.271333i	0.00155799	−	0.00883583i
$944$		0			0
$945$	−55.8932	−	20.3434i	−1.81820	−	0.661772i
$946$		0			0
$947$	−5.71306	+	4.79383i	−0.185650	+	0.155779i	−0.730876	−	0.682510i	$-0.760888\pi$
$947$	−5.71306	+	4.79383i	−0.185650	+	0.155779i	0.545226	+	0.838289i	$0.316444\pi$
$948$		0			0
$949$	18.6662	−	6.79392i	0.605929	−	0.220540i
$950$		0			0
$951$	−3.55523	−	6.15784i	−0.115286	−	0.199682i
$952$		0			0
$953$	4.88614	+	1.77841i	0.158278	+	0.0576083i	0.419944	−	0.907550i	$-0.362050\pi$
$953$	4.88614	+	1.77841i	0.158278	+	0.0576083i	−0.261666	+	0.965158i	$0.584272\pi$
$954$		0			0
$955$	−18.7114	−	15.7007i	−0.605486	−	0.508063i
$956$		0			0
$957$	−19.4657	−	16.3337i	−0.629238	−	0.527993i
$958$		0			0
$959$	−13.4842	+	76.4726i	−0.435427	+	2.46943i
$960$		0			0
$961$	−30.8166			−0.994084
$962$		0			0
$963$	−0.504210			−0.0162479
$964$		0			0
$965$	−0.397166	+	2.25244i	−0.0127852	+	0.0725085i
$966$		0			0
$967$	22.0122	+	18.4704i	0.707865	+	0.593969i	0.923999	−	0.382394i	$-0.124900\pi$
$967$	22.0122	+	18.4704i	0.707865	+	0.593969i	−0.216134	+	0.976364i	$0.569345\pi$
$968$		0			0
$969$	1.85945	+	1.56026i	0.0597340	+	0.0501228i
$970$		0			0
$971$	35.4110	+	12.8886i	1.13639	+	0.413613i	0.840610	−	0.541641i	$-0.182197\pi$
$971$	35.4110	+	12.8886i	1.13639	+	0.413613i	0.295784	+	0.955255i	$0.404419\pi$
$972$		0			0
$973$	3.85970	+	6.68520i	0.123736	+	0.214318i
$974$		0			0
$975$	−0.487119	+	0.177297i	−0.0156003	+	0.00567804i
$976$		0			0
$977$	18.6843	−	15.6780i	0.597764	−	0.501583i	−0.292962	−	0.956124i	$-0.594641\pi$
$977$	18.6843	−	15.6780i	0.597764	−	0.501583i	0.890726	+	0.454541i	$0.150197\pi$
$978$		0			0
$979$	−76.5274	−	27.8537i	−2.44583	−	0.890209i
$980$		0			0
$981$	−0.596375	+	3.38221i	−0.0190408	+	0.107986i
$982$		0			0
$983$	42.3410	−	35.5283i	1.35047	−	1.13318i	0.371666	−	0.928367i	$-0.378787\pi$
$983$	42.3410	−	35.5283i	1.35047	−	1.13318i	0.978802	−	0.204810i	$-0.0656577\pi$
$984$		0			0
$985$	−3.87209	+	6.70666i	−0.123375	+	0.213692i
$986$		0			0
$987$	−7.95644	−	45.1232i	−0.253256	−	1.43629i
$988$		0			0
$989$	−14.8615	+	25.7408i	−0.472567	+	0.818510i
$990$		0			0
$991$	20.1746	+	34.9435i	0.640869	+	1.11002i	0.985239	+	0.171183i	$0.0547591\pi$
$991$	20.1746	+	34.9435i	0.640869	+	1.11002i	−0.344370	+	0.938834i	$0.611908\pi$
$992$		0			0
$993$	6.82533			0.216595
$994$		0			0
$995$	−59.6715	+	21.7187i	−1.89171	+	0.688528i
$996$		0			0
$997$	−2.34851	−	13.3191i	−0.0743781	−	0.421819i	−0.999147	−	0.0412903i	$-0.986853\pi$
$997$	−2.34851	−	13.3191i	−0.0743781	−	0.421819i	0.924769	−	0.380529i	$-0.124258\pi$
$998$		0			0
$999$	34.2218	−	0.236784i	1.08273	−	0.00749151i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	296.2.u.b.9.2	✓	30
4.3	odd	2		592.2.bc.g.305.4		30
37.33	even	9	inner	296.2.u.b.33.2	yes	30
148.107	odd	18		592.2.bc.g.33.4		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
296.2.u.b.9.2	✓	30	1.1	even	1	trivial
296.2.u.b.33.2	yes	30	37.33	even	9	inner
592.2.bc.g.33.4		30	148.107	odd	18
592.2.bc.g.305.4		30	4.3	odd	2

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:	\( N \)	\(=\)	\( 296 = 2^{3} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	296.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.260200 + 1.47567i) q^{3} +(-1.75197 - 1.47008i) q^{5} +(-3.54112 - 2.97135i) q^{7} +(0.709192 + 0.258125i) q^{9} +(-2.89988 - 5.02274i) q^{11} +(1.41004 - 0.513213i) q^{13} +(2.62521 - 2.20281i) q^{15} +(-0.343576 - 0.125052i) q^{17} +(-0.769354 + 4.36322i) q^{19} +(5.30612 - 4.45236i) q^{21} +(1.15202 - 1.99536i) q^{23} +(0.0400348 + 0.227048i) q^{25} +(-2.81308 + 4.87240i) q^{27} +(-1.46198 - 2.53222i) q^{29} +0.428254 q^{31} +(8.16644 - 2.97234i) q^{33} +(1.83582 + 10.4115i) q^{35} +(-3.07776 - 5.24666i) q^{37} +(0.390438 + 2.21429i) q^{39} +(0.112369 - 0.0408990i) q^{41} -12.9003 q^{43} +(-0.863022 - 1.49480i) q^{45} +(3.30747 - 5.72870i) q^{47} +(2.49506 + 14.1502i) q^{49} +(0.273933 - 0.474465i) q^{51} +(-7.42052 + 6.22655i) q^{53} +(-2.30332 + 13.0628i) q^{55} +(-6.23847 - 2.27062i) q^{57} +(6.22119 - 5.22019i) q^{59} +(2.40272 - 0.874520i) q^{61} +(-1.74435 - 3.02131i) q^{63} +(-3.22482 - 1.17374i) q^{65} +(10.8202 + 9.07920i) q^{67} +(2.64473 + 2.21919i) q^{69} +(1.40794 - 7.98481i) q^{71} +13.2380 q^{73} -0.345465 q^{75} +(-4.65551 + 26.4027i) q^{77} +(8.48535 + 7.12005i) q^{79} +(-4.72366 - 3.96362i) q^{81} +(-6.92615 - 2.52091i) q^{83} +(0.418101 + 0.724172i) q^{85} +(4.11711 - 1.49851i) q^{87} +(10.7566 - 9.02586i) q^{89} +(-6.51806 - 2.37238i) q^{91} +(-0.111432 + 0.631960i) q^{93} +(7.76218 - 6.51324i) q^{95} +(-2.83368 + 4.90807i) q^{97} +(-0.760078 - 4.31062i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{5} - 3 q^{7} - 3 q^{11} + 9 q^{13} + 3 q^{15} - 27 q^{17} + 9 q^{19} + 15 q^{21} - 3 q^{23} - 12 q^{25} - 3 q^{27} + 9 q^{29} - 6 q^{31} - 6 q^{33} + 9 q^{35} + 9 q^{37} - 12 q^{39} - 48 q^{43}+ \cdots - 6 q^{99}+O(q^{100}) \) 30 * q - 6 * q^5 - 3 * q^7 - 3 * q^11 + 9 * q^13 + 3 * q^15 - 27 * q^17 + 9 * q^19 + 15 * q^21 - 3 * q^23 - 12 * q^25 - 3 * q^27 + 9 * q^29 - 6 * q^31 - 6 * q^33 + 9 * q^35 + 9 * q^37 - 12 * q^39 - 48 * q^43 + 51 * q^45 + 6 * q^47 - 21 * q^49 + 12 * q^51 - 15 * q^53 + 21 * q^55 + 51 * q^57 + 36 * q^61 - 36 * q^63 - 6 * q^65 - 27 * q^67 - 15 * q^69 + 27 * q^71 - 114 * q^73 + 84 * q^75 - 105 * q^77 - 18 * q^79 - 12 * q^81 - 30 * q^83 + 21 * q^85 - 99 * q^87 + 39 * q^89 - 72 * q^91 - 3 * q^93 + 66 * q^95 - 12 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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