LMFDB - Embedded newform 592.2.bc.g.33.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(33,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("592.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.bc (of order $9$, degree $6$, 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:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 296)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			33.4
Character	$\chi$	$=$	592.33
Dual form			592.2.bc.g.305.4

$q$-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 $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$1$	$1$

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	0.963021	+	0.269426i	$0.0868339\pi$
$3$	0.260200	+	1.47567i	0.150226	+	0.851976i	−0.812795	+	0.582550i	$0.802055\pi$
$4$		0			0
$5$	−1.75197	+	1.47008i	−0.783507	+	0.657440i	−0.944129	−	0.329576i	$-0.893094\pi$
$5$	−1.75197	+	1.47008i	−0.783507	+	0.657440i	0.160622	+	0.987016i	$0.448650\pi$
$6$		0			0
$7$	3.54112	−	2.97135i	1.33842	−	1.12307i	0.356388	−	0.934338i	$-0.384008\pi$
$7$	3.54112	−	2.97135i	1.33842	−	1.12307i	0.982030	−	0.188727i	$-0.0604362\pi$
$8$		0			0
$9$	0.709192	−	0.258125i	0.236397	−	0.0860416i
$10$		0			0
$11$	2.89988	−	5.02274i	0.874347	−	1.51441i	0.0168905	−	0.999857i	$-0.494623\pi$
$11$	2.89988	−	5.02274i	0.874347	−	1.51441i	0.857457	−	0.514556i	$-0.172043\pi$
$12$		0			0
$13$	1.41004	+	0.513213i	0.391075	+	0.142340i	0.530071	−	0.847953i	$-0.322165\pi$
$13$	1.41004	+	0.513213i	0.391075	+	0.142340i	−0.138996	+	0.990293i	$0.544388\pi$
$14$		0			0
$15$	−2.62521	−	2.20281i	−0.677827	−	0.568764i
$16$		0			0
$17$	−0.343576	+	0.125052i	−0.0833295	+	0.0303294i	−0.383349	−	0.923604i	$-0.625229\pi$
$17$	−0.343576	+	0.125052i	−0.0833295	+	0.0303294i	0.300019	+	0.953933i	$0.403007\pi$
$18$		0			0
$19$	0.769354	+	4.36322i	0.176502	+	1.00099i	0.936396	+	0.350945i	$0.114140\pi$
$19$	0.769354	+	4.36322i	0.176502	+	1.00099i	−0.759894	+	0.650047i	$0.774749\pi$
$20$		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	$-0.243884\pi$
$23$	−1.15202	−	1.99536i	−0.240213	−	0.416062i	−0.960775	+	0.277329i	$0.910551\pi$
$24$		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	−0.969242	−	0.246111i	$-0.920847\pi$
$29$	−1.46198	+	2.53222i	−0.271482	+	0.470221i	0.697760	+	0.716332i	$0.254180\pi$
$30$		0			0
$31$	−0.428254			−0.0769166			−0.0384583	−	0.999260i	$-0.512245\pi$
$31$	−0.428254			−0.0769166			−0.0384583	+	0.999260i	$0.512245\pi$
$32$		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	0.350780	−	0.936458i	$-0.385917\pi$
$41$	0.112369	+	0.0408990i	0.0175491	+	0.00638734i	−0.333231	+	0.942845i	$0.608139\pi$
$42$		0			0
$43$	12.9003			1.96728			0.983640	−	0.180146i	$-0.0576570\pi$
$43$	12.9003			1.96728			0.983640	+	0.180146i	$0.0576570\pi$
$44$		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	$-0.326917\pi$
$47$	−3.30747	−	5.72870i	−0.482444	−	0.835617i	−0.999797	+	0.0201552i	$0.993584\pi$
$48$		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	−0.0297488	−	0.999557i	$-0.509471\pi$
$53$	−7.42052	−	6.22655i	−1.01929	−	0.855283i	−0.989538	+	0.144274i	$0.953915\pi$
$54$		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	$-0.455077\pi$
$59$	−6.22119	−	5.22019i	−0.809929	−	0.679611i	−0.950591	+	0.310446i	$0.899522\pi$
$60$		0			0
$61$	2.40272	+	0.874520i	0.307637	+	0.111971i	0.491225	−	0.871032i	$-0.336549\pi$
$61$	2.40272	+	0.874520i	0.307637	+	0.111971i	−0.183588	+	0.983003i	$0.558771\pi$
$62$		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	−0.335994	+	0.941864i	$0.609072\pi$
$67$	−10.8202	+	9.07920i	−1.32189	+	1.10920i	−0.985900	+	0.167336i	$0.946484\pi$
$68$		0			0
$69$	2.64473	−	2.21919i	0.318388	−	0.267160i
$70$		0			0
$71$	−1.40794	−	7.98481i	−0.167091	−	0.947623i	−0.946882	−	0.321582i	$-0.895785\pi$
$71$	−1.40794	−	7.98481i	−0.167091	−	0.947623i	0.779790	−	0.626041i	$-0.215326\pi$
$72$		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	$-0.936358\pi$
$79$	−8.48535	+	7.12005i	−0.954676	+	0.801069i	0.0254025	+	0.999677i	$0.491913\pi$
$80$		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	$-0.478551\pi$
$83$	6.92615	−	2.52091i	0.760243	−	0.276706i	0.692910	+	0.721025i	$0.256329\pi$
$84$		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	0.999445	−	0.0333053i	$-0.0106034\pi$
$89$	10.7566	+	9.02586i	1.14020	+	0.956739i	0.140753	+	0.990045i	$0.455048\pi$
$90$		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	0.685548	−	0.728027i	$-0.259563\pi$
$97$	−2.83368	−	4.90807i	−0.287716	−	0.498339i	−0.973264	+	0.229688i	$0.926229\pi$
$98$		0			0
$99$	0.760078	−	4.31062i	0.0763908	−	0.433233i
$100$		0			0
$101$	5.70213	+	9.87638i	0.567383	+	0.982737i	0.996824	+	0.0796415i	$0.0253776\pi$
$101$	5.70213	+	9.87638i	0.567383	+	0.982737i	−0.429440	+	0.903095i	$0.641289\pi$
$102$		0			0
$103$	2.91194	−	5.04362i	0.286922	−	0.496963i	−0.686152	−	0.727459i	$-0.740701\pi$
$103$	2.91194	−	5.04362i	0.286922	−	0.496963i	0.973073	+	0.230495i	$0.0740347\pi$
$104$		0			0
$105$	−15.8415			−1.54597
$106$		0			0
$107$	0.627797	+	0.228499i	0.0606914	+	0.0220899i	0.372187	−	0.928158i	$-0.378608\pi$
$107$	0.627797	+	0.228499i	0.0606914	+	0.0220899i	−0.311496	+	0.950247i	$0.600830\pi$
$108$		0			0
$109$	0.790209	−	4.48150i	0.0756883	−	0.429249i	−0.923292	−	0.384099i	$-0.874512\pi$
$109$	0.790209	−	4.48150i	0.0756883	−	0.429249i	0.998980	−	0.0451505i	$-0.0143767\pi$
$110$		0			0
$111$	−8.54315	−	3.17656i	−0.810879	−	0.301506i
$112$		0			0
$113$	−1.95736	+	11.1008i	−0.184133	+	1.04427i	0.742931	+	0.669368i	$0.233435\pi$
$113$	−1.95736	+	11.1008i	−0.184133	+	1.04427i	−0.927064	+	0.374903i	$0.877676\pi$
$114$		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	$-0.195044\pi$
$127$	4.43731	+	3.72334i	0.393748	+	0.330393i	−0.424323	+	0.905511i	$0.639488\pi$
$128$		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	$-0.739671\pi$
$131$	−8.45349	+	3.07682i	−0.738585	+	0.268823i	−0.0547909	+	0.998498i	$0.517449\pi$
$132$		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	0.244360	+	0.969685i	$0.421422\pi$
$137$	−8.39920	+	14.5478i	−0.717592	+	1.24291i	−0.961951	+	0.273221i	$0.911911\pi$
$138$		0			0
$139$	1.56922	−	0.571148i	0.133099	−	0.0484442i	−0.274612	−	0.961555i	$-0.588549\pi$
$139$	1.56922	−	0.571148i	0.133099	−	0.0484442i	0.407711	+	0.913111i	$0.366327\pi$
$140$		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	−0.999788	−	0.0205707i	$-0.993452\pi$
$151$	−0.827367	−	4.69223i	−0.0673302	−	0.381849i	0.932458	−	0.361278i	$-0.117659\pi$
$152$		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	−0.901947	−	0.431846i	$-0.857862\pi$
$157$	−16.4806	+	5.99844i	−1.31529	+	0.478728i	−0.413347	+	0.910574i	$0.635640\pi$
$158$		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	$-0.502491\pi$
$163$	−12.6901	−	10.6482i	−0.993962	−	0.834033i	−0.986137	+	0.165936i	$0.946935\pi$
$164$		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	$-0.0478100\pi$
$167$	0.109199	+	0.619296i	0.00845005	+	0.0479226i	−0.980291	+	0.197558i	$0.936699\pi$
$168$		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	0.723829	+	0.689979i	$0.242380\pi$
$173$	−2.52976	+	14.3470i	−0.192334	+	1.09078i	−0.916164	+	0.400804i	$0.868731\pi$
$174$		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	$-0.799726\pi$
$179$	−21.6343			−1.61702			−0.808512	+	0.588480i	$0.799726\pi$
$180$		0			0
$181$	1.10465	+	0.402060i	0.0821080	+	0.0298849i	0.382748	−	0.923853i	$-0.374978\pi$
$181$	1.10465	+	0.402060i	0.0821080	+	0.0298849i	−0.300640	+	0.953738i	$0.597200\pi$
$182$		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	$-0.626280\pi$
$191$	−10.6802			−0.772790			−0.386395	+	0.922333i	$0.626280\pi$
$192$		0			0
$193$	−0.500032	+	0.866081i	−0.0359931	+	0.0623418i	−0.883461	−	0.468505i	$-0.844793\pi$
$193$	−0.500032	+	0.866081i	−0.0359931	+	0.0623418i	0.847468	+	0.530847i	$0.178126\pi$
$194$		0			0
$195$	−2.57114	−	4.45335i	−0.184123	−	0.318911i
$196$		0			0
$197$	−0.587993	+	3.33467i	−0.0418928	+	0.237586i	−0.998563	−	0.0535874i	$-0.982934\pi$
$197$	−0.587993	+	3.33467i	−0.0418928	+	0.237586i	0.956670	+	0.291173i	$0.0940455\pi$
$198$		0			0
$199$	−13.8828	−	24.0457i	−0.984126	−	1.70456i	−0.645755	−	0.763544i	$-0.723457\pi$
$199$	−13.8828	−	24.0457i	−0.984126	−	1.70456i	−0.338371	−	0.941013i	$-0.609876\pi$
$200$		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	$-0.748448\pi$
$211$	3.82794	−	6.63019i	0.263526	−	0.456441i	0.967176	+	0.254106i	$0.0817811\pi$
$212$		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	$-0.510119\pi$
$223$	−0.949252			−0.0635666			−0.0317833	+	0.999495i	$0.510119\pi$
$224$		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	$-0.497403\pi$
$227$	14.9814	−	12.5709i	0.994349	−	0.834358i	0.986192	+	0.165609i	$0.0529589\pi$
$228$		0			0
$229$	3.75725	−	3.15271i	0.248286	−	0.208337i	−0.510148	−	0.860087i	$-0.670409\pi$
$229$	3.75725	−	3.15271i	0.248286	−	0.208337i	0.758434	+	0.651750i	$0.225965\pi$
$230$		0			0
$231$	37.7502	−	13.7399i	2.48378	−	0.904022i
$232$		0			0
$233$	7.80879	−	13.5252i	0.511571	−	0.886067i	−0.488339	−	0.872654i	$-0.662397\pi$
$233$	7.80879	−	13.5252i	0.511571	−	0.886067i	0.999910	−	0.0134130i	$-0.00426963\pi$
$234$		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	$-0.614559\pi$
$239$	−0.314666	+	0.114529i	−0.0203541	+	0.00740827i	0.331823	+	0.943342i	$0.392336\pi$
$240$		0			0
$241$	2.15209	+	12.2051i	0.138628	+	0.786201i	0.972264	+	0.233886i	$0.0751443\pi$
$241$	2.15209	+	12.2051i	0.138628	+	0.786201i	−0.833636	+	0.552315i	$0.813745\pi$
$242$		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	$-0.917249\pi$
$251$	−4.12847	+	7.15072i	−0.260587	+	0.451349i	0.705811	+	0.708400i	$0.250583\pi$
$252$		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	0.652846	+	0.757490i	$0.273575\pi$
$257$	−3.52215	+	19.9751i	−0.219705	+	1.24601i	−0.872552	+	0.488521i	$0.837536\pi$
$258$		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	$-0.134933\pi$
$263$	21.8177	+	7.94100i	1.34534	+	0.489663i	0.433849	+	0.900986i	$0.357155\pi$
$264$		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	0.830113	−	0.557595i	$-0.188276\pi$
$269$	−1.11257	−	1.92704i	−0.0678349	−	0.117493i	−0.897948	+	0.440102i	$0.854942\pi$
$270$		0			0
$271$	−5.00934	+	28.4094i	−0.304296	+	1.72575i	0.322505	+	0.946568i	$0.395475\pi$
$271$	−5.00934	+	28.4094i	−0.304296	+	1.72575i	−0.626801	+	0.779180i	$0.715636\pi$
$272$		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	−0.928515	−	0.371295i	$-0.878914\pi$
$277$	−3.04550	−	17.2719i	−0.182987	−	1.03777i	0.745529	−	0.666474i	$-0.232197\pi$
$278$		0			0
$279$	−0.303714	+	0.110543i	−0.0181829	+	0.00661803i
$280$		0			0
$281$	−13.4977	−	11.3259i	−0.805203	−	0.675645i	0.144255	−	0.989541i	$-0.453921\pi$
$281$	−13.4977	−	11.3259i	−0.805203	−	0.675645i	−0.949458	+	0.313895i	$0.898366\pi$
$282$		0			0
$283$	−21.2213	−	7.72390i	−1.26147	−	0.459138i	−0.377210	−	0.926128i	$-0.623116\pi$
$283$	−21.2213	−	7.72390i	−1.26147	−	0.459138i	−0.884263	+	0.466990i	$0.845339\pi$
$284$		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	−0.678059	−	0.735007i	$-0.737179\pi$
$293$	−5.00301	−	28.3735i	−0.292279	−	1.65760i	0.385780	−	0.922591i	$-0.373932\pi$
$294$		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	−0.0792721	−	0.996853i	$-0.525260\pi$
$307$	14.4318	−	24.9965i	0.823664	−	1.42663i	0.902936	−	0.429775i	$-0.141407\pi$
$308$		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	$-0.172939\pi$
$311$	8.73891	+	7.33281i	0.495538	+	0.415806i	−0.360468	+	0.932772i	$0.617383\pi$
$312$		0			0
$313$	11.0014	−	4.00419i	0.621837	−	0.226330i	−0.0118377	−	0.999930i	$-0.503768\pi$
$313$	11.0014	−	4.00419i	0.621837	−	0.226330i	0.633674	+	0.773600i	$0.281546\pi$
$314$		0			0
$315$	1.38551	+	7.85760i	0.0780644	+	0.442725i
$316$		0			0
$317$	−3.63509	−	3.05020i	−0.204167	−	0.171317i	0.534971	−	0.844870i	$-0.320323\pi$
$317$	−3.63509	−	3.05020i	−0.204167	−	0.171317i	−0.739138	+	0.673554i	$0.764767\pi$
$318$		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	$-0.904493\pi$
$331$	0.790965	−	4.48579i	0.0434754	−	0.246561i	0.998799	+	0.0490016i	$0.0156040\pi$
$332$		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	0.0201292	−	0.999797i	$-0.493592\pi$
$337$	−11.1450	−	4.05646i	−0.607108	−	0.220969i	−0.627238	+	0.778828i	$0.715814\pi$
$338$		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	$-0.222948\pi$
$347$	−3.27651	−	5.67508i	−0.175892	−	0.304654i	−0.940470	+	0.339878i	$0.889614\pi$
$348$		0			0
$349$	−14.0683	−	11.8047i	−0.753060	−	0.631892i	0.183250	−	0.983066i	$-0.441338\pi$
$349$	−14.0683	−	11.8047i	−0.753060	−	0.631892i	−0.936310	+	0.351174i	$0.885783\pi$
$350$		0			0
$351$	1.46598	+	8.31399i	0.0782483	+	0.443768i
$352$		0			0
$353$	29.3818	−	10.6941i	1.56383	−	0.569189i	0.592222	−	0.805775i	$-0.298251\pi$
$353$	29.3818	−	10.6941i	1.56383	−	0.569189i	0.971611	+	0.236586i	$0.0760285\pi$
$354$		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	$-0.748105\pi$
$359$	5.01282	−	8.68245i	0.264566	−	0.458242i	0.967450	+	0.253063i	$0.0814379\pi$
$360$		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	0.921934	+	0.387348i	$0.126609\pi$
$367$	3.60310	+	20.4342i	0.188080	+	1.06666i	−0.733853	+	0.679308i	$0.762280\pi$
$368$		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	0.996218	+	0.0868903i	$0.0276930\pi$
$373$	1.73428	+	9.83558i	0.0897975	+	0.509267i	−0.906420	+	0.422377i	$0.861196\pi$
$374$		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	$-0.631495\pi$
$379$	−2.34138	+	0.852192i	−0.120269	+	0.0437742i	0.281185	+	0.959654i	$0.409273\pi$
$380$		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	$-0.308659\pi$
$383$	9.17264	+	3.33857i	0.468700	+	0.170593i	−0.0968634	+	0.995298i	$0.530881\pi$
$384$		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	0.822141	+	0.569285i	$0.192780\pi$
$389$	4.81811	+	27.3249i	0.244288	+	1.38543i	−0.577853	+	0.816141i	$0.696109\pi$
$390$		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	0.991289	−	0.131707i	$-0.0420458\pi$
$397$	7.60298	+	13.1688i	0.381583	+	0.660921i	−0.609706	+	0.792628i	$0.708712\pi$
$398$		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	0.706175	+	0.708037i	$0.250419\pi$
$409$	−4.03616	+	22.8902i	−0.199575	+	1.13185i	−0.905751	+	0.423811i	$0.860692\pi$
$410$		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	$-0.992751\pi$
$419$	−1.07471	+	6.09498i	−0.0525030	+	0.297759i	0.947238	+	0.320532i	$0.103862\pi$
$420$		0			0
$421$	14.6700	+	25.4092i	0.714973	+	1.23837i	0.962970	+	0.269608i	$0.0868941\pi$
$421$	14.6700	+	25.4092i	0.714973	+	1.23837i	−0.247998	+	0.968761i	$0.579773\pi$
$422$		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	$-0.342938\pi$
$431$	5.61297	+	2.04295i	0.270367	+	0.0984056i	−0.203279	+	0.979121i	$0.565160\pi$
$432$		0			0
$433$	1.15529	−	2.00102i	0.0555198	−	0.0961631i	−0.836930	−	0.547310i	$-0.815652\pi$
$433$	1.15529	−	2.00102i	0.0555198	−	0.0961631i	0.892450	+	0.451147i	$0.148985\pi$
$434$		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	$-0.854498\pi$
$439$	−12.9591	+	10.8739i	−0.618502	+	0.518985i	0.278830	+	0.960340i	$0.410053\pi$
$440$		0			0
$441$	−1.88303	−	10.6792i	−0.0896683	−	0.508534i
$442$		0			0
$443$	−16.5099			−0.784409			−0.392205	−	0.919878i	$-0.628287\pi$
$443$	−16.5099			−0.784409			−0.392205	+	0.919878i	$0.628287\pi$
$444$		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	−0.831584	−	0.555399i	$-0.812565\pi$
$449$	−9.09088	+	7.62815i	−0.429025	+	0.359995i	0.402559	+	0.915394i	$0.368121\pi$
$450$		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	0.443555	−	0.896247i	$-0.353717\pi$
$457$	4.43033	+	1.61251i	0.207242	+	0.0754299i	−0.236313	+	0.971677i	$0.575939\pi$
$458$		0			0
$459$	−1.57581	−	1.32226i	−0.0735525	−	0.0617179i
$460$		0			0
$461$	−4.56103	+	1.66008i	−0.212428	+	0.0773175i	−0.446042	−	0.895012i	$-0.647167\pi$
$461$	−4.56103	+	1.66008i	−0.212428	+	0.0773175i	0.233614	+	0.972329i	$0.424945\pi$
$462$		0			0
$463$	−0.387848	−	2.19960i	−0.0180248	−	0.102224i	0.974468	−	0.224526i	$-0.0720834\pi$
$463$	−0.387848	−	2.19960i	−0.0180248	−	0.102224i	−0.992493	+	0.122302i	$0.960972\pi$
$464$		0			0
$465$	1.12426	+	0.943363i	0.0521362	+	0.0437474i
$466$		0			0
$467$	−12.3177	−	21.3349i	−0.569996	−	0.987261i	−0.996566	−	0.0828068i	$-0.973612\pi$
$467$	−12.3177	−	21.3349i	−0.569996	−	0.987261i	0.426570	−	0.904455i	$-0.359722\pi$
$468$		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	0.814487	+	0.580182i	$0.197019\pi$
$479$	−3.26791	+	18.5332i	−0.149314	+	0.846804i	−0.963801	+	0.266622i	$0.914092\pi$
$480$		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	$-0.143530\pi$
$487$	39.7247			1.80010			0.900050	+	0.435787i	$0.143530\pi$
$488$		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	$-0.114378\pi$
$491$	3.62359	+	6.27624i	0.163530	+	0.283243i	−0.772602	+	0.634891i	$0.781045\pi$
$492$		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	−0.867193	−	0.497972i	$-0.834078\pi$
$499$	−4.97283	−	28.2023i	−0.222615	−	1.26251i	0.644578	−	0.764538i	$-0.277033\pi$
$500$		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	$-0.150160\pi$
$503$	13.4101	+	11.2524i	0.597928	+	0.501721i	−0.292851	+	0.956158i	$0.594604\pi$
$504$		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	−0.970060	−	0.242864i	$-0.921913\pi$
$509$	−35.1289	+	12.7859i	−1.55706	+	0.566723i	−0.586999	+	0.809588i	$0.699691\pi$
$510$		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	0.970931	−	0.239360i	$-0.0769377\pi$
$521$	−0.532100	−	3.01769i	−0.0233117	−	0.132207i	−0.994243	+	0.107153i	$0.965827\pi$
$522$		0			0
$523$	−16.2249	+	13.6143i	−0.709466	+	0.595313i	−0.924449	−	0.381305i	$-0.875475\pi$
$523$	−16.2249	+	13.6143i	−0.709466	+	0.595313i	0.214983	+	0.976618i	$0.431030\pi$
$524$		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	0.995582	+	0.0938928i	$0.0299311\pi$
$541$	13.4696	+	23.3301i	0.579105	+	1.00304i	−0.416478	+	0.909146i	$0.636736\pi$
$542$		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	−0.382195	−	0.924082i	$-0.624832\pi$
$547$	14.2475	−	24.6775i	0.609181	−	1.05513i	0.991376	−	0.131050i	$-0.0418349\pi$
$548$		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	−0.193387	−	0.981123i	$-0.561947\pi$
$557$	7.64434	−	43.3532i	0.323901	−	1.83693i	0.517288	−	0.855811i	$-0.326942\pi$
$558$		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	0.287530	+	0.957772i	$0.407166\pi$
$563$	−16.2698	+	28.1801i	−0.685689	+	1.18765i	−0.973220	+	0.229877i	$0.926167\pi$
$564$		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	−0.997117	−	0.0758857i	$-0.975822\pi$
$569$	−13.4601	−	23.3136i	−0.564277	−	0.977357i	0.432839	−	0.901471i	$-0.357512\pi$
$570$		0			0
$571$	−8.98942	−	7.54302i	−0.376195	−	0.315665i	0.435011	−	0.900425i	$-0.356744\pi$
$571$	−8.98942	−	7.54302i	−0.376195	−	0.315665i	−0.811207	+	0.584760i	$0.801189\pi$
$572$		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	0.529836	−	0.848100i	$-0.322253\pi$
$577$	−5.12542	−	4.30074i	−0.213374	−	0.179042i	−0.743210	+	0.669058i	$0.766698\pi$
$578$		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	$-0.888523\pi$
$587$	−18.5228	+	15.5425i	−0.764520	+	0.641508i	0.174779	+	0.984608i	$0.444079\pi$
$588$		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	$-0.851295\pi$
$599$	−14.7915	+	12.4116i	−0.604366	+	0.507123i	0.288480	+	0.957486i	$0.406850\pi$
$600$		0			0
$601$	15.2325	−	5.54418i	0.621347	−	0.226152i	−0.0121137	−	0.999927i	$-0.503856\pi$
$601$	15.2325	−	5.54418i	0.621347	−	0.226152i	0.633461	+	0.773775i	$0.281634\pi$
$602$		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	$-0.384431\pi$
$607$	−12.4121	−	10.4150i	−0.503793	−	0.422733i	−0.858939	+	0.512078i	$0.828876\pi$
$608$		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	0.805345	−	0.592806i	$-0.201980\pi$
$613$	8.94765	+	7.50797i	0.361392	+	0.303244i	−0.443953	+	0.896050i	$0.646424\pi$
$614$		0			0
$615$	−0.204899	−	0.354896i	−0.00826234	−	0.0143108i
$616$		0			0
$617$	3.01838	−	17.1181i	0.121515	−	0.689147i	−0.861802	−	0.507246i	$-0.830664\pi$
$617$	3.01838	−	17.1181i	0.121515	−	0.689147i	0.983317	−	0.181901i	$-0.0582252\pi$
$618$		0			0
$619$	−3.05948	−	5.29917i	−0.122971	−	0.212991i	0.797967	−	0.602701i	$-0.205909\pi$
$619$	−3.05948	−	5.29917i	−0.122971	−	0.212991i	−0.920938	+	0.389709i	$0.872575\pi$
$620$		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	−0.731669	−	0.681661i	$-0.761258\pi$
$631$	4.74804	−	26.9275i	0.189017	−	1.07197i	0.920685	−	0.390306i	$-0.127631\pi$
$632$		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	0.889890	+	0.456175i	$0.150781\pi$
$641$	−2.59140	+	14.6966i	−0.102354	+	0.580479i	−0.992244	+	0.124304i	$0.960330\pi$
$642$		0			0
$643$	−7.91287	−	13.7055i	−0.312053	−	0.540492i	0.666754	−	0.745278i	$-0.267683\pi$
$643$	−7.91287	−	13.7055i	−0.312053	−	0.540492i	−0.978807	+	0.204786i	$0.934350\pi$
$644$		0			0
$645$	−33.8661	−	28.4170i	−1.33347	−	1.11892i
$646$		0			0
$647$	6.66717	+	37.8114i	0.262113	+	1.48652i	0.777131	+	0.629339i	$0.216674\pi$
$647$	6.66717	+	37.8114i	0.262113	+	1.48652i	−0.515017	+	0.857180i	$0.672215\pi$
$648$		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	0.533953	−	0.845514i	$-0.320706\pi$
$653$	10.2087	+	3.71567i	0.399498	+	0.145405i	−0.134455	+	0.990920i	$0.542928\pi$
$654$		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	$-0.837263\pi$
$659$	−13.9069	+	11.6693i	−0.541737	+	0.454571i	0.330394	+	0.943843i	$0.392818\pi$
$660$		0			0
$661$	5.39465	−	4.52664i	0.209827	−	0.176066i	−0.531817	−	0.846859i	$-0.678491\pi$
$661$	5.39465	−	4.52664i	0.209827	−	0.176066i	0.741644	+	0.670793i	$0.234046\pi$
$662$		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	−0.458551	−	0.888668i	$-0.651631\pi$
$673$	8.74225	−	7.33562i	0.336989	−	0.282767i	0.795540	+	0.605900i	$0.207187\pi$
$674$		0			0
$675$	1.21889	−	0.443641i	0.0469152	−	0.0170757i
$676$		0			0
$677$	−14.9313	+	25.8619i	−0.573858	+	0.993952i	0.422306	+	0.906453i	$0.361221\pi$
$677$	−14.9313	+	25.8619i	−0.573858	+	0.993952i	−0.996165	+	0.0874985i	$0.972113\pi$
$678$		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	$-0.308033\pi$
$683$	40.0133	−	14.5637i	1.53107	−	0.557263i	0.963882	+	0.266328i	$0.0858105\pi$
$684$		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	0.531703	+	0.846931i	$0.321552\pi$
$691$	−6.77155	+	38.4034i	−0.257602	+	1.46093i	−0.789305	+	0.614002i	$0.789559\pi$
$692$		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	0.813153	+	0.582049i	$0.197749\pi$
$701$	−3.97235	+	22.5283i	−0.150033	+	0.850882i	−0.963187	+	0.268833i	$0.913362\pi$
$702$		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	$-0.145857\pi$
$719$	16.5427	+	13.8810i	0.616939	+	0.517673i	−0.279901	+	0.960029i	$0.590302\pi$
$720$		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	$-0.403989\pi$
$727$	−2.40292	−	0.874590i	−0.0891193	−	0.0324368i	−0.386195	+	0.922417i	$0.626211\pi$
$728$		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	0.0296935	−	0.999559i	$-0.490547\pi$
$733$	27.5944	−	23.1545i	1.01922	−	0.855230i	0.989530	+	0.144329i	$0.0461024\pi$
$734$		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	$-0.553510\pi$
$739$	−9.09681			−0.334632			−0.167316	+	0.985903i	$0.553510\pi$
$740$		0			0
$741$	−9.96181			−0.365956
$742$		0			0
$743$	1.55697	+	8.83000i	0.0571196	+	0.323941i	0.999957	−	0.00931280i	$-0.00296440\pi$
$743$	1.55697	+	8.83000i	0.0571196	+	0.323941i	−0.942837	+	0.333254i	$0.891853\pi$
$744$		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	−0.331138	−	0.943582i	$-0.607433\pi$
$751$	17.8566	−	30.9286i	0.651597	−	1.12860i	0.982735	−	0.185017i	$-0.0592340\pi$
$752$		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	0.485665	−	0.874145i	$-0.338577\pi$
$757$	39.0582	−	14.2160i	1.41960	−	0.516691i	0.933931	+	0.357454i	$0.116355\pi$
$758$		0			0
$759$	−3.47703	−	19.7192i	−0.126208	−	0.715762i
$760$		0			0
$761$	5.27255	+	4.42419i	0.191130	+	0.160377i	0.733331	−	0.679872i	$-0.237965\pi$
$761$	5.27255	+	4.42419i	0.191130	+	0.160377i	−0.542201	+	0.840249i	$0.682409\pi$
$762$		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	−0.910021	−	0.414563i	$-0.863934\pi$
$769$	−2.66183	+	4.61043i	−0.0959881	+	0.166256i	0.814032	+	0.580819i	$0.197268\pi$
$770$		0			0
$771$	−30.3930			−1.09458
$772$		0			0
$773$	31.5436	+	11.4809i	1.13454	+	0.412940i	0.839940	−	0.542679i	$-0.182590\pi$
$773$	31.5436	+	11.4809i	1.13454	+	0.412940i	0.294604	+	0.955619i	$0.404812\pi$
$774$		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	$-0.0609756\pi$
$787$	9.14463	+	15.8390i	0.325971	+	0.564598i	−0.655738	+	0.754989i	$0.727642\pi$
$788$		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	0.276560	−	0.960997i	$-0.410806\pi$
$797$	31.2275	−	11.3659i	1.10613	−	0.402600i	0.829574	+	0.558397i	$0.188583\pi$
$798$		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	−0.797043	−	0.603923i	$-0.793603\pi$
$809$	−9.69050	+	8.13129i	−0.340700	+	0.285881i	0.456343	+	0.889804i	$0.349159\pi$
$810$		0			0
$811$	6.32995	+	35.8989i	0.222275	+	1.26058i	0.867827	+	0.496866i	$0.165516\pi$
$811$	6.32995	+	35.8989i	0.222275	+	1.26058i	−0.645553	+	0.763716i	$0.723373\pi$
$812$		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	−0.537146	−	0.843489i	$-0.680497\pi$
$821$	5.73792	−	4.81469i	0.200255	−	0.168034i	0.737401	+	0.675456i	$0.236053\pi$
$822$		0			0
$823$	36.0723	−	13.1292i	1.25740	−	0.457657i	0.374505	−	0.927225i	$-0.377813\pi$
$823$	36.0723	−	13.1292i	1.25740	−	0.457657i	0.882896	+	0.469568i	$0.155590\pi$
$824$		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	$-0.437560\pi$
$827$	−8.23186	−	2.99615i	−0.286250	−	0.104186i	−0.481155	+	0.876636i	$0.659782\pi$
$828$		0			0
$829$	3.09992	+	2.60114i	0.107665	+	0.0903414i	0.695031	−	0.718980i	$-0.255391\pi$
$829$	3.09992	+	2.60114i	0.107665	+	0.0903414i	−0.587366	+	0.809321i	$0.699835\pi$
$830$		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	$-0.993639\pi$
$839$	−1.54853	+	8.78212i	−0.0534610	+	0.303193i	0.946339	+	0.323175i	$0.104750\pi$
$840$		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	0.788656	+	0.614835i	$0.210777\pi$
$853$	−4.75255	+	26.9530i	−0.162724	+	0.922854i	−0.951380	+	0.308020i	$0.900334\pi$
$854$		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	$-0.839852\pi$
$859$	−0.600179	+	1.03954i	−0.0204778	+	0.0354687i	0.855605	+	0.517629i	$0.173185\pi$
$860$		0			0
$861$	0.414146	+	0.717322i	0.0141141	+	0.0244463i
$862$		0			0
$863$	8.28755	−	47.0010i	0.282112	−	1.59993i	−0.433312	−	0.901244i	$-0.642655\pi$
$863$	8.28755	−	47.0010i	0.282112	−	1.59993i	0.715424	−	0.698691i	$-0.246234\pi$
$864$		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	0.359939	+	0.932976i	$0.382798\pi$
$877$	−18.5981	+	32.2128i	−0.628012	+	1.08775i	−0.987950	+	0.154772i	$0.950536\pi$
$878$		0			0
$879$	40.5680	−	14.7656i	1.36833	−	0.498030i
$880$		0			0
$881$	0.922572	−	0.774130i	0.0310822	−	0.0260811i	−0.627114	−	0.778927i	$-0.715764\pi$
$881$	0.922572	−	0.774130i	0.0310822	−	0.0260811i	0.658196	+	0.752846i	$0.271320\pi$
$882$		0			0
$883$	−16.3100	+	13.6857i	−0.548875	+	0.460561i	−0.874560	−	0.484918i	$-0.838850\pi$
$883$	−16.3100	+	13.6857i	−0.548875	+	0.460561i	0.325685	+	0.945478i	$0.394405\pi$
$884$		0			0
$885$	4.83281	+	27.4082i	0.162453	+	0.921318i
$886$		0			0
$887$	24.9441			0.837542			0.418771	−	0.908092i	$-0.362461\pi$
$887$	24.9441			0.837542			0.418771	+	0.908092i	$0.362461\pi$
$888$		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	$-0.0963939\pi$
$907$	−1.33823	−	7.58946i	−0.0444351	−	0.252004i	−0.998931	+	0.0462190i	$0.985283\pi$
$908$		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	$-0.295727\pi$
$911$	−11.9052	−	20.6205i	−0.394438	−	0.683186i	−0.993029	+	0.117868i	$0.962394\pi$
$912$		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	$-0.749599\pi$
$919$	−42.8179			−1.41243			−0.706216	+	0.707997i	$0.749599\pi$
$920$		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	0.996233	−	0.0867117i	$-0.0276359\pi$
$929$	51.9266	+	18.8997i	1.70366	+	0.620080i	0.707422	+	0.706792i	$0.249858\pi$
$930$		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	−0.794796	−	0.606877i	$-0.792422\pi$
$937$	4.88641	−	27.7122i	0.159632	−	0.905318i	0.954428	−	0.298442i	$-0.0964668\pi$
$938$		0			0
$939$	8.77141	+	15.1925i	0.286244	+	0.495789i
$940$		0			0
$941$	−2.90978	−	2.44159i	−0.0948561	−	0.0795937i	0.594126	−	0.804372i	$-0.297498\pi$
$941$	−2.90978	−	2.44159i	−0.0948561	−	0.0795937i	−0.688982	+	0.724778i	$0.741942\pi$
$942$		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	$-0.239112\pi$
$947$	5.71306	+	4.79383i	0.185650	+	0.155779i	−0.545226	+	0.838289i	$0.683556\pi$
$948$		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	−0.261666	−	0.965158i	$-0.584272\pi$
$953$	4.88614	−	1.77841i	0.158278	−	0.0576083i	0.419944	+	0.907550i	$0.362050\pi$
$954$		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	$-0.875100\pi$
$967$	−22.0122	+	18.4704i	−0.707865	+	0.593969i	0.216134	+	0.976364i	$0.430655\pi$
$968$		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	$-0.817803\pi$
$971$	−35.4110	+	12.8886i	−1.13639	+	0.413613i	−0.295784	+	0.955255i	$0.595581\pi$
$972$		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	0.890726	−	0.454541i	$-0.150197\pi$
$977$	18.6843	+	15.6780i	0.597764	+	0.501583i	−0.292962	+	0.956124i	$0.594641\pi$
$978$		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	−0.978802	−	0.204810i	$-0.934342\pi$
$983$	−42.3410	−	35.5283i	−1.35047	−	1.13318i	−0.371666	−	0.928367i	$-0.621213\pi$
$984$		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	0.344370	+	0.938834i	$0.388092\pi$
$991$	−20.1746	+	34.9435i	−0.640869	+	1.11002i	−0.985239	+	0.171183i	$0.945241\pi$
$992$		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	0.924769	+	0.380529i	$0.124258\pi$
$997$	−2.34851	+	13.3191i	−0.0743781	+	0.421819i	−0.999147	+	0.0412903i	$0.986853\pi$
$998$		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	592.2.bc.g.33.4		30
4.3	odd	2		296.2.u.b.33.2	yes	30
37.9	even	9	inner	592.2.bc.g.305.4		30
148.83	odd	18		296.2.u.b.9.2	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
296.2.u.b.9.2	✓	30	148.83	odd	18
296.2.u.b.33.2	yes	30	4.3	odd	2
592.2.bc.g.33.4		30	1.1	even	1	trivial
592.2.bc.g.305.4		30	37.9	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.bc (of order \(9\), degree \(6\), not 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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