LMFDB - Embedded newform 578.2.d.e.423.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [578,2,Mod(155,578)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(578, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("578.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 578 = 2 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	578.d (of order $8$, degree $4$, 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:	$4.61535323683$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{8})$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 34)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			423.1
Root			$0.923880 - 0.382683i$ of defining polynomial
Character	$\chi$	$=$	578.423
Dual form			578.2.d.e.399.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.765367 - 1.84776i) q^{3} +1.00000i q^{4} +(-0.765367 + 1.84776i) q^{6} +(-3.69552 - 1.53073i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.765367 - 1.84776i) q^{3} +1.00000i q^{4} +(-0.765367 + 1.84776i) q^{6} +(-3.69552 - 1.53073i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.707107 + 0.707107i) q^{9} +(-2.29610 + 5.54328i) q^{11} +(1.84776 - 0.765367i) q^{12} -2.00000i q^{13} +(1.53073 + 3.69552i) q^{14} -1.00000 q^{16} +1.00000 q^{18} +(2.82843 + 2.82843i) q^{19} +8.00000i q^{21} +(5.54328 - 2.29610i) q^{22} +(-1.84776 - 0.765367i) q^{24} +(-3.53553 + 3.53553i) q^{25} +(-1.41421 + 1.41421i) q^{26} +(-3.69552 - 1.53073i) q^{27} +(1.53073 - 3.69552i) q^{28} +(1.53073 + 3.69552i) q^{31} +(0.707107 + 0.707107i) q^{32} +12.0000 q^{33} +(-0.707107 - 0.707107i) q^{36} +(-1.53073 - 3.69552i) q^{37} -4.00000i q^{38} +(-3.69552 + 1.53073i) q^{39} +(5.54328 + 2.29610i) q^{41} +(5.65685 - 5.65685i) q^{42} +(-5.65685 + 5.65685i) q^{43} +(-5.54328 - 2.29610i) q^{44} +(0.765367 + 1.84776i) q^{48} +(6.36396 + 6.36396i) q^{49} +5.00000 q^{50} +2.00000 q^{52} +(4.24264 + 4.24264i) q^{53} +(1.53073 + 3.69552i) q^{54} +(-3.69552 + 1.53073i) q^{56} +(3.06147 - 7.39104i) q^{57} +(3.69552 + 1.53073i) q^{61} +(1.53073 - 3.69552i) q^{62} +(3.69552 - 1.53073i) q^{63} -1.00000i q^{64} +(-8.48528 - 8.48528i) q^{66} -8.00000 q^{67} +1.00000i q^{72} +(1.84776 - 0.765367i) q^{73} +(-1.53073 + 3.69552i) q^{74} +(9.23880 + 3.82683i) q^{75} +(-2.82843 + 2.82843i) q^{76} +(16.9706 - 16.9706i) q^{77} +(3.69552 + 1.53073i) q^{78} +(-3.06147 + 7.39104i) q^{79} +11.0000i q^{81} +(-2.29610 - 5.54328i) q^{82} -8.00000 q^{84} +8.00000 q^{86} +(2.29610 + 5.54328i) q^{88} -6.00000i q^{89} +(-3.06147 + 7.39104i) q^{91} +(5.65685 - 5.65685i) q^{93} +(0.765367 - 1.84776i) q^{96} +(-12.9343 + 5.35757i) q^{97} -9.00000i q^{98} +(-2.29610 - 5.54328i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 8 q^{16} + 8 q^{18} + 96 q^{33} + 40 q^{50} + 16 q^{52} - 64 q^{67} - 64 q^{84} + 64 q^{86}+O(q^{100}) $ 8 * q - 8 * q^16 + 8 * q^18 + 96 * q^33 + 40 * q^50 + 16 * q^52 - 64 * q^67 - 64 * q^84 + 64 * q^86

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/578\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{8}\right)$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−0.765367	−	1.84776i	−0.441885	−	1.06680i	−0.975287	−	0.220942i	$-0.929087\pi$
$3$	−0.765367	−	1.84776i	−0.441885	−	1.06680i	0.533402	−	0.845862i	$-0.320913\pi$
$4$			1.00000i			0.500000i
$5$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$5$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$6$	−0.765367	+	1.84776i	−0.312460	+	0.754344i
$7$	−3.69552	−	1.53073i	−1.39677	−	0.578563i	−0.447862	−	0.894103i	$-0.647814\pi$
$7$	−3.69552	−	1.53073i	−1.39677	−	0.578563i	−0.948912	+	0.315540i	$0.897814\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.707107	+	0.707107i	−0.235702	+	0.235702i
$10$		0			0
$11$	−2.29610	+	5.54328i	−0.692300	+	1.67136i	0.0477934	+	0.998857i	$0.484781\pi$
$11$	−2.29610	+	5.54328i	−0.692300	+	1.67136i	−0.740094	+	0.672504i	$0.765219\pi$
$12$	1.84776	−	0.765367i	0.533402	−	0.220942i
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$	1.53073	+	3.69552i	0.409106	+	0.987669i
$15$		0			0
$16$	−1.00000			−0.250000
$17$		0			0
$17$		0			0
$18$	1.00000			0.235702
$19$	2.82843	+	2.82843i	0.648886	+	0.648886i	0.952724	−	0.303838i	$-0.0982682\pi$
$19$	2.82843	+	2.82843i	0.648886	+	0.648886i	−0.303838	+	0.952724i	$0.598268\pi$
$20$		0			0
$21$			8.00000i			1.74574i
$22$	5.54328	−	2.29610i	1.18183	−	0.489530i
$23$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$23$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$24$	−1.84776	−	0.765367i	−0.377172	−	0.156230i
$25$	−3.53553	+	3.53553i	−0.707107	+	0.707107i
$26$	−1.41421	+	1.41421i	−0.277350	+	0.277350i
$27$	−3.69552	−	1.53073i	−0.711203	−	0.294590i
$28$	1.53073	−	3.69552i	0.289281	−	0.698387i
$29$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$29$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$30$		0			0
$31$	1.53073	+	3.69552i	0.274928	+	0.663735i	0.999681	−	0.0252745i	$-0.00804598\pi$
$31$	1.53073	+	3.69552i	0.274928	+	0.663735i	−0.724753	+	0.689009i	$0.758046\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	12.0000			2.08893
$34$		0			0
$35$		0			0
$36$	−0.707107	−	0.707107i	−0.117851	−	0.117851i
$37$	−1.53073	−	3.69552i	−0.251651	−	0.607539i	0.746687	−	0.665176i	$-0.231644\pi$
$37$	−1.53073	−	3.69552i	−0.251651	−	0.607539i	−0.998338	+	0.0576366i	$0.981644\pi$
$38$		−	4.00000i		−	0.648886i
$39$	−3.69552	+	1.53073i	−0.591756	+	0.245114i
$40$		0			0
$41$	5.54328	+	2.29610i	0.865714	+	0.358591i	0.770940	−	0.636908i	$-0.219787\pi$
$41$	5.54328	+	2.29610i	0.865714	+	0.358591i	0.0947747	+	0.995499i	$0.469787\pi$
$42$	5.65685	−	5.65685i	0.872872	−	0.872872i
$43$	−5.65685	+	5.65685i	−0.862662	+	0.862662i	−0.991647	−	0.128984i	$-0.958828\pi$
$43$	−5.65685	+	5.65685i	−0.862662	+	0.862662i	0.128984	+	0.991647i	$0.458828\pi$
$44$	−5.54328	−	2.29610i	−0.835680	−	0.346150i
$45$		0			0
$46$		0			0
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$	0.765367	+	1.84776i	0.110471	+	0.266701i
$49$	6.36396	+	6.36396i	0.909137	+	0.909137i
$50$	5.00000			0.707107
$51$		0			0
$52$	2.00000			0.277350
$53$	4.24264	+	4.24264i	0.582772	+	0.582772i	0.935664	−	0.352892i	$-0.114802\pi$
$53$	4.24264	+	4.24264i	0.582772	+	0.582772i	−0.352892	+	0.935664i	$0.614802\pi$
$54$	1.53073	+	3.69552i	0.208306	+	0.502896i
$55$		0			0
$56$	−3.69552	+	1.53073i	−0.493834	+	0.204553i
$57$	3.06147	−	7.39104i	0.405501	−	0.978967i
$58$		0			0
$59$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$59$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$60$		0			0
$61$	3.69552	+	1.53073i	0.473163	+	0.195990i	0.606505	−	0.795080i	$-0.292571\pi$
$61$	3.69552	+	1.53073i	0.473163	+	0.195990i	−0.133342	+	0.991070i	$0.542571\pi$
$62$	1.53073	−	3.69552i	0.194403	−	0.469331i
$63$	3.69552	−	1.53073i	0.465592	−	0.192854i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	−8.48528	−	8.48528i	−1.04447	−	1.04447i
$67$	−8.00000			−0.977356			−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000			−0.977356			−0.488678	+	0.872464i	$0.662521\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$71$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$72$			1.00000i			0.117851i
$73$	1.84776	−	0.765367i	0.216264	−	0.0895794i	−0.271921	−	0.962319i	$-0.587659\pi$
$73$	1.84776	−	0.765367i	0.216264	−	0.0895794i	0.488185	+	0.872740i	$0.337659\pi$
$74$	−1.53073	+	3.69552i	−0.177944	+	0.429595i
$75$	9.23880	+	3.82683i	1.06680	+	0.441885i
$76$	−2.82843	+	2.82843i	−0.324443	+	0.324443i
$77$	16.9706	−	16.9706i	1.93398	−	1.93398i
$78$	3.69552	+	1.53073i	0.418435	+	0.173321i
$79$	−3.06147	+	7.39104i	−0.344442	+	0.831557i	0.652813	+	0.757519i	$0.273589\pi$
$79$	−3.06147	+	7.39104i	−0.344442	+	0.831557i	−0.997255	+	0.0740378i	$0.976411\pi$
$80$		0			0
$81$			11.0000i			1.22222i
$82$	−2.29610	−	5.54328i	−0.253562	−	0.612153i
$83$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$83$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$84$	−8.00000			−0.872872
$85$		0			0
$86$	8.00000			0.862662
$87$		0			0
$88$	2.29610	+	5.54328i	0.244765	+	0.590915i
$89$		−	6.00000i		−	0.635999i	−0.948091	−	0.317999i	$-0.896989\pi$
$89$		−	6.00000i		−	0.635999i	0.948091	−	0.317999i	$-0.103011\pi$
$90$		0			0
$91$	−3.06147	+	7.39104i	−0.320929	+	0.774791i
$92$		0			0
$93$	5.65685	−	5.65685i	0.586588	−	0.586588i
$94$		0			0
$95$		0			0
$96$	0.765367	−	1.84776i	0.0781149	−	0.188586i
$97$	−12.9343	+	5.35757i	−1.31328	+	0.543979i	−0.925840	−	0.377916i	$-0.876641\pi$
$97$	−12.9343	+	5.35757i	−1.31328	+	0.543979i	−0.387441	+	0.921895i	$0.626641\pi$
$98$		−	9.00000i		−	0.909137i
$99$	−2.29610	−	5.54328i	−0.230767	−	0.557120i
$100$	−3.53553	−	3.53553i	−0.353553	−	0.353553i
$101$	−18.0000			−1.79107			−0.895533	−	0.444994i	$-0.853206\pi$
$101$	−18.0000			−1.79107			−0.895533	+	0.444994i	$0.853206\pi$
$102$		0			0
$103$	−16.0000			−1.57653			−0.788263	−	0.615338i	$-0.789020\pi$
$103$	−16.0000			−1.57653			−0.788263	+	0.615338i	$0.789020\pi$
$104$	−1.41421	−	1.41421i	−0.138675	−	0.138675i
$105$		0			0
$106$		−	6.00000i		−	0.582772i
$107$	−5.54328	+	2.29610i	−0.535889	+	0.221972i	−0.634180	−	0.773185i	$-0.718662\pi$
$107$	−5.54328	+	2.29610i	−0.535889	+	0.221972i	0.0982914	+	0.995158i	$0.468662\pi$
$108$	1.53073	−	3.69552i	0.147295	−	0.355601i
$109$	−14.7821	−	6.12293i	−1.41587	−	0.586471i	−0.462048	−	0.886855i	$-0.652885\pi$
$109$	−14.7821	−	6.12293i	−1.41587	−	0.586471i	−0.953818	+	0.300384i	$0.902885\pi$
$110$		0			0
$111$	−5.65685	+	5.65685i	−0.536925	+	0.536925i
$112$	3.69552	+	1.53073i	0.349194	+	0.144641i
$113$	2.29610	−	5.54328i	0.215999	−	0.521468i	−0.778325	−	0.627861i	$-0.783930\pi$
$113$	2.29610	−	5.54328i	0.215999	−	0.521468i	0.994324	+	0.106394i	$0.0339304\pi$
$114$	−7.39104	+	3.06147i	−0.692234	+	0.286733i
$115$		0			0
$116$		0			0
$117$	1.41421	+	1.41421i	0.130744	+	0.130744i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−17.6777	−	17.6777i	−1.60706	−	1.60706i
$122$	−1.53073	−	3.69552i	−0.138586	−	0.334576i
$123$		−	12.0000i		−	1.08200i
$124$	−3.69552	+	1.53073i	−0.331867	+	0.137464i
$125$		0			0
$126$	−3.69552	−	1.53073i	−0.329223	−	0.136369i
$127$	−11.3137	+	11.3137i	−1.00393	+	1.00393i	−0.00393704	+	0.999992i	$0.501253\pi$
$127$	−11.3137	+	11.3137i	−1.00393	+	1.00393i	−0.999992	+	0.00393704i	$0.998747\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	14.7821	+	6.12293i	1.30149	+	0.539094i
$130$		0			0
$131$	5.54328	−	2.29610i	0.484318	−	0.200611i	−0.127145	−	0.991884i	$-0.540581\pi$
$131$	5.54328	−	2.29610i	0.484318	−	0.200611i	0.611463	+	0.791273i	$0.290581\pi$
$132$			12.0000i			1.04447i
$133$	−6.12293	−	14.7821i	−0.530926	−	1.28177i
$134$	5.65685	+	5.65685i	0.488678	+	0.488678i
$135$		0			0
$136$		0			0
$137$	6.00000			0.512615			0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000			0.512615			0.256307	+	0.966595i	$0.417494\pi$
$138$		0			0
$139$	0.765367	+	1.84776i	0.0649176	+	0.156725i	0.953009	−	0.302942i	$-0.0979688\pi$
$139$	0.765367	+	1.84776i	0.0649176	+	0.156725i	−0.888091	+	0.459667i	$0.847969\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	11.0866	+	4.59220i	0.927104	+	0.384019i
$144$	0.707107	−	0.707107i	0.0589256	−	0.0589256i
$145$		0			0
$146$	−1.84776	−	0.765367i	−0.152922	−	0.0633422i
$147$	6.88830	−	16.6298i	0.568138	−	1.37161i
$148$	3.69552	−	1.53073i	0.303770	−	0.125826i
$149$		−	6.00000i		−	0.491539i	−0.969328	−	0.245770i	$-0.920959\pi$
$149$		−	6.00000i		−	0.491539i	0.969328	−	0.245770i	$-0.0790407\pi$
$150$	−3.82683	−	9.23880i	−0.312460	−	0.754344i
$151$	−11.3137	−	11.3137i	−0.920697	−	0.920697i	0.0763821	−	0.997079i	$-0.475663\pi$
$151$	−11.3137	−	11.3137i	−0.920697	−	0.920697i	−0.997079	+	0.0763821i	$0.975663\pi$
$152$	4.00000			0.324443
$153$		0			0
$154$	−24.0000			−1.93398
$155$		0			0
$156$	−1.53073	−	3.69552i	−0.122557	−	0.295878i
$157$			14.0000i			1.11732i	0.829396	+	0.558661i	$0.188685\pi$
$157$			14.0000i			1.11732i	−0.829396	+	0.558661i	$0.811315\pi$
$158$	7.39104	−	3.06147i	0.587999	−	0.243557i
$159$	4.59220	−	11.0866i	0.364185	−	0.879221i
$160$		0			0
$161$		0			0
$162$	7.77817	−	7.77817i	0.611111	−	0.611111i
$163$	−1.84776	−	0.765367i	−0.144728	−	0.0599482i	0.309144	−	0.951015i	$-0.399958\pi$
$163$	−1.84776	−	0.765367i	−0.144728	−	0.0599482i	−0.453872	+	0.891067i	$0.649958\pi$
$164$	−2.29610	+	5.54328i	−0.179295	+	0.432857i
$165$		0			0
$166$		0			0
$167$	−4.59220	−	11.0866i	−0.355355	−	0.857903i	−0.995940	−	0.0900162i	$-0.971308\pi$
$167$	−4.59220	−	11.0866i	−0.355355	−	0.857903i	0.640585	−	0.767887i	$-0.278692\pi$
$168$	5.65685	+	5.65685i	0.436436	+	0.436436i
$169$	9.00000			0.692308
$170$		0			0
$171$	−4.00000			−0.305888
$172$	−5.65685	−	5.65685i	−0.431331	−	0.431331i
$173$	9.18440	+	22.1731i	0.698277	+	1.68579i	0.727399	+	0.686214i	$0.240729\pi$
$173$	9.18440	+	22.1731i	0.698277	+	1.68579i	−0.0291222	+	0.999576i	$0.509271\pi$
$174$		0			0
$175$	18.4776	−	7.65367i	1.39677	−	0.578563i
$176$	2.29610	−	5.54328i	0.173075	−	0.417840i
$177$		0			0
$178$	−4.24264	+	4.24264i	−0.317999	+	0.317999i
$179$	−8.48528	+	8.48528i	−0.634220	+	0.634220i	−0.949124	−	0.314904i	$-0.898028\pi$
$179$	−8.48528	+	8.48528i	−0.634220	+	0.634220i	0.314904	+	0.949124i	$0.398028\pi$
$180$		0			0
$181$	1.53073	−	3.69552i	0.113779	−	0.274686i	−0.856725	−	0.515774i	$-0.827504\pi$
$181$	1.53073	−	3.69552i	0.113779	−	0.274686i	0.970503	+	0.241088i	$0.0775044\pi$
$182$	7.39104	−	3.06147i	0.547860	−	0.226931i
$183$		−	8.00000i		−	0.591377i
$184$		0			0
$185$		0			0
$186$	−8.00000			−0.586588
$187$		0			0
$188$		0			0
$189$	11.3137	+	11.3137i	0.822951	+	0.822951i
$190$		0			0
$191$		−	24.0000i		−	1.73658i	−0.496058	−	0.868290i	$-0.665220\pi$
$191$		−	24.0000i		−	1.73658i	0.496058	−	0.868290i	$-0.334780\pi$
$192$	−1.84776	+	0.765367i	−0.133351	+	0.0552356i
$193$	−3.82683	+	9.23880i	−0.275462	+	0.665023i	−0.999699	−	0.0245275i	$-0.992192\pi$
$193$	−3.82683	+	9.23880i	−0.275462	+	0.665023i	0.724238	+	0.689551i	$0.242192\pi$
$194$	12.9343	+	5.35757i	0.928630	+	0.384651i
$195$		0			0
$196$	−6.36396	+	6.36396i	−0.454569	+	0.454569i
$197$	11.0866	+	4.59220i	0.789884	+	0.327181i	0.740897	−	0.671619i	$-0.234401\pi$
$197$	11.0866	+	4.59220i	0.789884	+	0.327181i	0.0489872	+	0.998799i	$0.484401\pi$
$198$	−2.29610	+	5.54328i	−0.163177	+	0.393944i
$199$	14.7821	−	6.12293i	1.04787	−	0.434043i	0.208741	−	0.977971i	$-0.433063\pi$
$199$	14.7821	−	6.12293i	1.04787	−	0.434043i	0.839132	+	0.543928i	$0.183063\pi$
$200$			5.00000i			0.353553i
$201$	6.12293	+	14.7821i	0.431879	+	1.04265i
$202$	12.7279	+	12.7279i	0.895533	+	0.895533i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	11.3137	+	11.3137i	0.788263	+	0.788263i
$207$		0			0
$208$			2.00000i			0.138675i
$209$	−22.1731	+	9.18440i	−1.53375	+	0.635298i
$210$		0			0
$211$	−9.23880	−	3.82683i	−0.636025	−	0.263450i	0.0412856	−	0.999147i	$-0.486855\pi$
$211$	−9.23880	−	3.82683i	−0.636025	−	0.263450i	−0.677311	+	0.735697i	$0.736855\pi$
$212$	−4.24264	+	4.24264i	−0.291386	+	0.291386i
$213$		0			0
$214$	5.54328	+	2.29610i	0.378931	+	0.156958i
$215$		0			0
$216$	−3.69552	+	1.53073i	−0.251448	+	0.104153i
$217$		−	16.0000i		−	1.08615i
$218$	6.12293	+	14.7821i	0.414697	+	1.00117i
$219$	−2.82843	−	2.82843i	−0.191127	−	0.191127i
$220$		0			0
$221$		0			0
$222$	8.00000			0.536925
$223$	−5.65685	−	5.65685i	−0.378811	−	0.378811i	0.491862	−	0.870673i	$-0.336316\pi$
$223$	−5.65685	−	5.65685i	−0.378811	−	0.378811i	−0.870673	+	0.491862i	$0.836316\pi$
$224$	−1.53073	−	3.69552i	−0.102276	−	0.246917i
$225$		−	5.00000i		−	0.333333i
$226$	−5.54328	+	2.29610i	−0.368733	+	0.152734i
$227$	−2.29610	+	5.54328i	−0.152398	+	0.367920i	−0.981578	−	0.191060i	$-0.938807\pi$
$227$	−2.29610	+	5.54328i	−0.152398	+	0.367920i	0.829181	+	0.558981i	$0.188807\pi$
$228$	7.39104	+	3.06147i	0.489483	+	0.202751i
$229$	9.89949	−	9.89949i	0.654177	−	0.654177i	−0.299819	−	0.953996i	$-0.596926\pi$
$229$	9.89949	−	9.89949i	0.654177	−	0.654177i	0.953996	+	0.299819i	$0.0969263\pi$
$230$		0			0
$231$	−44.3462	−	18.3688i	−2.91777	−	1.20858i
$232$		0			0
$233$	−16.6298	+	6.88830i	−1.08946	+	0.451268i	−0.853817	−	0.520573i	$-0.825718\pi$
$233$	−16.6298	+	6.88830i	−1.08946	+	0.451268i	−0.235639	+	0.971841i	$0.575718\pi$
$234$		−	2.00000i		−	0.130744i
$235$		0			0
$236$		0			0
$237$	16.0000			1.03931
$238$		0			0
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$		0			0
$241$	−3.82683	−	9.23880i	−0.246508	−	0.595123i	0.751395	−	0.659853i	$-0.229381\pi$
$241$	−3.82683	−	9.23880i	−0.246508	−	0.595123i	−0.997903	+	0.0647298i	$0.979381\pi$
$242$			25.0000i			1.60706i
$243$	9.23880	−	3.82683i	0.592669	−	0.245492i
$244$	−1.53073	+	3.69552i	−0.0979952	+	0.236581i
$245$		0			0
$246$	−8.48528	+	8.48528i	−0.541002	+	0.541002i
$247$	5.65685	−	5.65685i	0.359937	−	0.359937i
$248$	3.69552	+	1.53073i	0.234666	+	0.0972017i
$249$		0			0
$250$		0			0
$251$			24.0000i			1.51487i	0.652913	+	0.757433i	$0.273547\pi$
$251$			24.0000i			1.51487i	−0.652913	+	0.757433i	$0.726453\pi$
$252$	1.53073	+	3.69552i	0.0964272	+	0.232796i
$253$		0			0
$254$	16.0000			1.00393
$255$		0			0
$256$	1.00000			0.0625000
$257$	−4.24264	−	4.24264i	−0.264649	−	0.264649i	0.562291	−	0.826940i	$-0.309920\pi$
$257$	−4.24264	−	4.24264i	−0.264649	−	0.264649i	−0.826940	+	0.562291i	$0.809920\pi$
$258$	−6.12293	−	14.7821i	−0.381197	−	0.920292i
$259$			16.0000i			0.994192i
$260$		0			0
$261$		0			0
$262$	−5.54328	−	2.29610i	−0.342465	−	0.141854i
$263$	16.9706	−	16.9706i	1.04645	−	1.04645i	0.0475824	−	0.998867i	$-0.484848\pi$
$263$	16.9706	−	16.9706i	1.04645	−	1.04645i	0.998867	−	0.0475824i	$-0.0151517\pi$
$264$	8.48528	−	8.48528i	0.522233	−	0.522233i
$265$		0			0
$266$	−6.12293	+	14.7821i	−0.375421	+	0.906347i
$267$	−11.0866	+	4.59220i	−0.678486	+	0.281038i
$268$		−	8.00000i		−	0.488678i
$269$	9.18440	+	22.1731i	0.559983	+	1.35192i	0.909779	+	0.415093i	$0.136251\pi$
$269$	9.18440	+	22.1731i	0.559983	+	1.35192i	−0.349796	+	0.936826i	$0.613749\pi$
$270$		0			0
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$		0			0
$273$	16.0000			0.968364
$274$	−4.24264	−	4.24264i	−0.256307	−	0.256307i
$275$	−11.4805	−	27.7164i	−0.692300	−	1.67136i
$276$		0			0
$277$	7.39104	−	3.06147i	0.444084	−	0.183946i	−0.149425	−	0.988773i	$-0.547742\pi$
$277$	7.39104	−	3.06147i	0.444084	−	0.183946i	0.593509	+	0.804827i	$0.297742\pi$
$278$	0.765367	−	1.84776i	0.0459037	−	0.110821i
$279$	−3.69552	−	1.53073i	−0.221245	−	0.0916426i
$280$		0			0
$281$	−4.24264	+	4.24264i	−0.253095	+	0.253095i	−0.822238	−	0.569143i	$-0.807275\pi$
$281$	−4.24264	+	4.24264i	−0.253095	+	0.253095i	0.569143	+	0.822238i	$0.307275\pi$
$282$		0			0
$283$	−5.35757	+	12.9343i	−0.318474	+	0.768865i	0.680861	+	0.732413i	$0.261606\pi$
$283$	−5.35757	+	12.9343i	−0.318474	+	0.768865i	−0.999335	+	0.0364525i	$0.988394\pi$
$284$		0			0
$285$		0			0
$286$	−4.59220	−	11.0866i	−0.271543	−	0.655562i
$287$	−16.9706	−	16.9706i	−1.00174	−	1.00174i
$288$	−1.00000			−0.0589256
$289$		0			0
$290$		0			0
$291$	19.7990	+	19.7990i	1.16064	+	1.16064i
$292$	0.765367	+	1.84776i	0.0447897	+	0.108132i
$293$			6.00000i			0.350524i	0.984522	+	0.175262i	$0.0560772\pi$
$293$			6.00000i			0.350524i	−0.984522	+	0.175262i	$0.943923\pi$
$294$	−16.6298	+	6.88830i	−0.969871	+	0.401734i
$295$		0			0
$296$	−3.69552	−	1.53073i	−0.214798	−	0.0889721i
$297$	16.9706	−	16.9706i	0.984732	−	0.984732i
$298$	−4.24264	+	4.24264i	−0.245770	+	0.245770i
$299$		0			0
$300$	−3.82683	+	9.23880i	−0.220942	+	0.533402i
$301$	29.5641	−	12.2459i	1.70405	−	0.705840i
$302$			16.0000i			0.920697i
$303$	13.7766	+	33.2597i	0.791445	+	1.91072i
$304$	−2.82843	−	2.82843i	−0.162221	−	0.162221i
$305$		0			0
$306$		0			0
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$	16.9706	+	16.9706i	0.966988	+	0.966988i
$309$	12.2459	+	29.5641i	0.696643	+	1.68185i
$310$		0			0
$311$	11.0866	−	4.59220i	0.628661	−	0.260400i	−0.0455232	−	0.998963i	$-0.514495\pi$
$311$	11.0866	−	4.59220i	0.628661	−	0.260400i	0.674184	+	0.738563i	$0.264495\pi$
$312$	−1.53073	+	3.69552i	−0.0866607	+	0.209218i
$313$	−31.4119	−	13.0112i	−1.77551	−	0.735439i	−0.993721	−	0.111891i	$-0.964309\pi$
$313$	−31.4119	−	13.0112i	−1.77551	−	0.735439i	−0.781785	−	0.623548i	$-0.785691\pi$
$314$	9.89949	−	9.89949i	0.558661	−	0.558661i
$315$		0			0
$316$	−7.39104	−	3.06147i	−0.415778	−	0.172221i
$317$	4.59220	−	11.0866i	0.257924	−	0.622683i	−0.740877	−	0.671641i	$-0.765590\pi$
$317$	4.59220	−	11.0866i	0.257924	−	0.622683i	0.998801	+	0.0489576i	$0.0155899\pi$
$318$	−11.0866	+	4.59220i	−0.621703	+	0.257518i
$319$		0			0
$320$		0			0
$321$	8.48528	+	8.48528i	0.473602	+	0.473602i
$322$		0			0
$323$		0			0
$324$	−11.0000			−0.611111
$325$	7.07107	+	7.07107i	0.392232	+	0.392232i
$326$	0.765367	+	1.84776i	0.0423898	+	0.102338i
$327$			32.0000i			1.76960i
$328$	5.54328	−	2.29610i	0.306076	−	0.126781i
$329$		0			0
$330$		0			0
$331$	−11.3137	+	11.3137i	−0.621858	+	0.621858i	−0.946006	−	0.324149i	$-0.894922\pi$
$331$	−11.3137	+	11.3137i	−0.621858	+	0.621858i	0.324149	+	0.946006i	$0.394922\pi$
$332$		0			0
$333$	3.69552	+	1.53073i	0.202513	+	0.0838837i
$334$	−4.59220	+	11.0866i	−0.251274	+	0.606629i
$335$		0			0
$336$		−	8.00000i		−	0.436436i
$337$	8.41904	+	20.3253i	0.458614	+	1.10719i	0.968959	+	0.247222i	$0.0795178\pi$
$337$	8.41904	+	20.3253i	0.458614	+	1.10719i	−0.510345	+	0.859970i	$0.670482\pi$
$338$	−6.36396	−	6.36396i	−0.346154	−	0.346154i
$339$	−12.0000			−0.651751
$340$		0			0
$341$	−24.0000			−1.29967
$342$	2.82843	+	2.82843i	0.152944	+	0.152944i
$343$	−3.06147	−	7.39104i	−0.165304	−	0.399078i
$344$			8.00000i			0.431331i
$345$		0			0
$346$	9.18440	−	22.1731i	0.493757	−	1.19203i
$347$	16.6298	+	6.88830i	0.892736	+	0.369783i	0.781423	−	0.624002i	$-0.214494\pi$
$347$	16.6298	+	6.88830i	0.892736	+	0.369783i	0.111313	+	0.993785i	$0.464494\pi$
$348$		0			0
$349$	−18.3848	+	18.3848i	−0.984115	+	0.984115i	−0.999876	−	0.0157613i	$-0.994983\pi$
$349$	−18.3848	+	18.3848i	−0.984115	+	0.984115i	0.0157613	+	0.999876i	$0.494983\pi$
$350$	−18.4776	−	7.65367i	−0.987669	−	0.409106i
$351$	−3.06147	+	7.39104i	−0.163409	+	0.394504i
$352$	−5.54328	+	2.29610i	−0.295458	+	0.122383i
$353$		−	6.00000i		−	0.319348i	−0.987170	−	0.159674i	$-0.948956\pi$
$353$		−	6.00000i		−	0.319348i	0.987170	−	0.159674i	$-0.0510443\pi$
$354$		0			0
$355$		0			0
$356$	6.00000			0.317999
$357$		0			0
$358$	12.0000			0.634220
$359$	−16.9706	−	16.9706i	−0.895672	−	0.895672i	0.0993777	−	0.995050i	$-0.468315\pi$
$359$	−16.9706	−	16.9706i	−0.895672	−	0.895672i	−0.995050	+	0.0993777i	$0.968315\pi$
$360$		0			0
$361$		−	3.00000i		−	0.157895i
$362$	−3.69552	+	1.53073i	−0.194232	+	0.0804536i
$363$	−19.1342	+	46.1940i	−1.00428	+	2.42455i
$364$	−7.39104	−	3.06147i	−0.387396	−	0.160464i
$365$		0			0
$366$	−5.65685	+	5.65685i	−0.295689	+	0.295689i
$367$	14.7821	+	6.12293i	0.771618	+	0.319615i	0.733528	−	0.679660i	$-0.237873\pi$
$367$	14.7821	+	6.12293i	0.771618	+	0.319615i	0.0380903	+	0.999274i	$0.487873\pi$
$368$		0			0
$369$	−5.54328	+	2.29610i	−0.288571	+	0.119530i
$370$		0			0
$371$	−9.18440	−	22.1731i	−0.476830	−	1.15117i
$372$	5.65685	+	5.65685i	0.293294	+	0.293294i
$373$	22.0000			1.13912			0.569558	−	0.821951i	$-0.307114\pi$
$373$	22.0000			1.13912			0.569558	+	0.821951i	$0.307114\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		−	16.0000i		−	0.822951i
$379$	12.9343	−	5.35757i	0.664391	−	0.275200i	−0.0248939	−	0.999690i	$-0.507925\pi$
$379$	12.9343	−	5.35757i	0.664391	−	0.275200i	0.689285	+	0.724490i	$0.257925\pi$
$380$		0			0
$381$	29.5641	+	12.2459i	1.51462	+	0.627375i
$382$	−16.9706	+	16.9706i	−0.868290	+	0.868290i
$383$	16.9706	−	16.9706i	0.867155	−	0.867155i	−0.125001	−	0.992157i	$-0.539894\pi$
$383$	16.9706	−	16.9706i	0.867155	−	0.867155i	0.992157	+	0.125001i	$0.0398935\pi$
$384$	1.84776	+	0.765367i	0.0942931	+	0.0390575i
$385$		0			0
$386$	9.23880	−	3.82683i	0.470242	−	0.194781i
$387$		−	8.00000i		−	0.406663i
$388$	−5.35757	−	12.9343i	−0.271989	−	0.656640i
$389$	21.2132	+	21.2132i	1.07555	+	1.07555i	0.996902	+	0.0786498i	$0.0250609\pi$
$389$	21.2132	+	21.2132i	1.07555	+	1.07555i	0.0786498	+	0.996902i	$0.474939\pi$
$390$		0			0
$391$		0			0
$392$	9.00000			0.454569
$393$	−8.48528	−	8.48528i	−0.428026	−	0.428026i
$394$	−4.59220	−	11.0866i	−0.231352	−	0.558533i
$395$		0			0
$396$	5.54328	−	2.29610i	0.278560	−	0.115383i
$397$	7.65367	−	18.4776i	0.384127	−	0.927364i	−0.607032	−	0.794678i	$-0.707640\pi$
$397$	7.65367	−	18.4776i	0.384127	−	0.927364i	0.991158	−	0.132686i	$-0.0423602\pi$
$398$	−14.7821	−	6.12293i	−0.740958	−	0.306915i
$399$	−22.6274	+	22.6274i	−1.13279	+	1.13279i
$400$	3.53553	−	3.53553i	0.176777	−	0.176777i
$401$	−27.7164	−	11.4805i	−1.38409	−	0.573309i	−0.438518	−	0.898722i	$-0.644497\pi$
$401$	−27.7164	−	11.4805i	−1.38409	−	0.573309i	−0.945572	+	0.325413i	$0.894497\pi$
$402$	6.12293	−	14.7821i	0.305384	−	0.737263i
$403$	7.39104	−	3.06147i	0.368174	−	0.152503i
$404$		−	18.0000i		−	0.895533i
$405$		0			0
$406$		0			0
$407$	24.0000			1.18964
$408$		0			0
$409$	−10.0000			−0.494468			−0.247234	−	0.968956i	$-0.579522\pi$
$409$	−10.0000			−0.494468			−0.247234	+	0.968956i	$0.579522\pi$
$410$		0			0
$411$	−4.59220	−	11.0866i	−0.226517	−	0.546859i
$412$		−	16.0000i		−	0.788263i
$413$		0			0
$414$		0			0
$415$		0			0
$416$	1.41421	−	1.41421i	0.0693375	−	0.0693375i
$417$	2.82843	−	2.82843i	0.138509	−	0.138509i
$418$	22.1731	+	9.18440i	1.08452	+	0.449224i
$419$	11.4805	−	27.7164i	0.560859	−	1.35403i	−0.348221	−	0.937413i	$-0.613214\pi$
$419$	11.4805	−	27.7164i	0.560859	−	1.35403i	0.909080	−	0.416622i	$-0.136786\pi$
$420$		0			0
$421$		−	2.00000i		−	0.0974740i	−0.998812	−	0.0487370i	$-0.984480\pi$
$421$		−	2.00000i		−	0.0974740i	0.998812	−	0.0487370i	$-0.0155196\pi$
$422$	3.82683	+	9.23880i	0.186287	+	0.449738i
$423$		0			0
$424$	6.00000			0.291386
$425$		0			0
$426$		0			0
$427$	−11.3137	−	11.3137i	−0.547509	−	0.547509i
$428$	−2.29610	−	5.54328i	−0.110986	−	0.267944i
$429$		−	24.0000i		−	1.15873i
$430$		0			0
$431$	9.18440	−	22.1731i	0.442397	−	1.06804i	−0.532708	−	0.846299i	$-0.678826\pi$
$431$	9.18440	−	22.1731i	0.442397	−	1.06804i	0.975105	−	0.221742i	$-0.0711743\pi$
$432$	3.69552	+	1.53073i	0.177801	+	0.0736475i
$433$	1.41421	−	1.41421i	0.0679628	−	0.0679628i	−0.672308	−	0.740271i	$-0.734697\pi$
$433$	1.41421	−	1.41421i	0.0679628	−	0.0679628i	0.740271	+	0.672308i	$0.234697\pi$
$434$	−11.3137	+	11.3137i	−0.543075	+	0.543075i
$435$		0			0
$436$	6.12293	−	14.7821i	0.293235	−	0.707933i
$437$		0			0
$438$			4.00000i			0.191127i
$439$	−3.06147	−	7.39104i	−0.146116	−	0.352755i	0.833829	−	0.552022i	$-0.186144\pi$
$439$	−3.06147	−	7.39104i	−0.146116	−	0.352755i	−0.979945	+	0.199268i	$0.936144\pi$
$440$		0			0
$441$	−9.00000			−0.428571
$442$		0			0
$443$	−24.0000			−1.14027			−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000			−1.14027			−0.570137	+	0.821549i	$0.693110\pi$
$444$	−5.65685	−	5.65685i	−0.268462	−	0.268462i
$445$		0			0
$446$			8.00000i			0.378811i
$447$	−11.0866	+	4.59220i	−0.524376	+	0.217204i
$448$	−1.53073	+	3.69552i	−0.0723204	+	0.174597i
$449$	−16.6298	−	6.88830i	−0.784810	−	0.325079i	−0.0459553	−	0.998943i	$-0.514633\pi$
$449$	−16.6298	−	6.88830i	−0.784810	−	0.325079i	−0.738855	+	0.673864i	$0.764633\pi$
$450$	−3.53553	+	3.53553i	−0.166667	+	0.166667i
$451$	−25.4558	+	25.4558i	−1.19867	+	1.19867i
$452$	5.54328	+	2.29610i	0.260734	+	0.107999i
$453$	−12.2459	+	29.5641i	−0.575361	+	1.38904i
$454$	5.54328	−	2.29610i	0.260159	−	0.107761i
$455$		0			0
$456$	−3.06147	−	7.39104i	−0.143366	−	0.346117i
$457$	18.3848	+	18.3848i	0.860004	+	0.860004i	0.991338	−	0.131335i	$-0.0419262\pi$
$457$	18.3848	+	18.3848i	0.860004	+	0.860004i	−0.131335	+	0.991338i	$0.541926\pi$
$458$	−14.0000			−0.654177
$459$		0			0
$460$		0			0
$461$	4.24264	+	4.24264i	0.197599	+	0.197599i	0.798970	−	0.601371i	$-0.205378\pi$
$461$	4.24264	+	4.24264i	0.197599	+	0.197599i	−0.601371	+	0.798970i	$0.705378\pi$
$462$	18.3688	+	44.3462i	0.854594	+	2.06317i
$463$		−	16.0000i		−	0.743583i	−0.928316	−	0.371792i	$-0.878744\pi$
$463$		−	16.0000i		−	0.743583i	0.928316	−	0.371792i	$-0.121256\pi$
$464$		0			0
$465$		0			0
$466$	16.6298	+	6.88830i	0.770362	+	0.319094i
$467$	8.48528	−	8.48528i	0.392652	−	0.392652i	−0.482980	−	0.875632i	$-0.660445\pi$
$467$	8.48528	−	8.48528i	0.392652	−	0.392652i	0.875632	+	0.482980i	$0.160445\pi$
$468$	−1.41421	+	1.41421i	−0.0653720	+	0.0653720i
$469$	29.5641	+	12.2459i	1.36515	+	0.565462i
$470$		0			0
$471$	25.8686	−	10.7151i	1.19196	−	0.493727i
$472$		0			0
$473$	−18.3688	−	44.3462i	−0.844599	−	2.03904i
$474$	−11.3137	−	11.3137i	−0.519656	−	0.519656i
$475$	−20.0000			−0.917663
$476$		0			0
$477$	−6.00000			−0.274721
$478$	−16.9706	−	16.9706i	−0.776215	−	0.776215i
$479$	9.18440	+	22.1731i	0.419646	+	1.01312i	0.982450	+	0.186525i	$0.0597225\pi$
$479$	9.18440	+	22.1731i	0.419646	+	1.01312i	−0.562804	+	0.826590i	$0.690277\pi$
$480$		0			0
$481$	−7.39104	+	3.06147i	−0.337002	+	0.139591i
$482$	−3.82683	+	9.23880i	−0.174308	+	0.420816i
$483$		0			0
$484$	17.6777	−	17.6777i	0.803530	−	0.803530i
$485$		0			0
$486$	−9.23880	−	3.82683i	−0.419080	−	0.173589i
$487$	−3.06147	+	7.39104i	−0.138728	+	0.334920i	−0.977940	−	0.208885i	$-0.933017\pi$
$487$	−3.06147	+	7.39104i	−0.138728	+	0.334920i	0.839212	+	0.543804i	$0.183017\pi$
$488$	3.69552	−	1.53073i	0.167288	−	0.0692931i
$489$			4.00000i			0.180886i
$490$		0			0
$491$	−8.48528	−	8.48528i	−0.382935	−	0.382935i	0.489223	−	0.872159i	$-0.337280\pi$
$491$	−8.48528	−	8.48528i	−0.382935	−	0.382935i	−0.872159	+	0.489223i	$0.837280\pi$
$492$	12.0000			0.541002
$493$		0			0
$494$	−8.00000			−0.359937
$495$		0			0
$496$	−1.53073	−	3.69552i	−0.0687320	−	0.165934i
$497$		0			0
$498$		0			0
$499$	5.35757	−	12.9343i	0.239838	−	0.579019i	−0.757428	−	0.652919i	$-0.773544\pi$
$499$	5.35757	−	12.9343i	0.239838	−	0.579019i	0.997266	+	0.0738993i	$0.0235443\pi$
$500$		0			0
$501$	−16.9706	+	16.9706i	−0.758189	+	0.758189i
$502$	16.9706	−	16.9706i	0.757433	−	0.757433i
$503$	22.1731	+	9.18440i	0.988650	+	0.409512i	0.817623	−	0.575754i	$-0.195291\pi$
$503$	22.1731	+	9.18440i	0.988650	+	0.409512i	0.171027	+	0.985266i	$0.445291\pi$
$504$	1.53073	−	3.69552i	0.0681843	−	0.164611i
$505$		0			0
$506$		0			0
$507$	−6.88830	−	16.6298i	−0.305920	−	0.738557i
$508$	−11.3137	−	11.3137i	−0.501965	−	0.501965i
$509$	−30.0000			−1.32973			−0.664863	−	0.746965i	$-0.731510\pi$
$509$	−30.0000			−1.32973			−0.664863	+	0.746965i	$0.731510\pi$
$510$		0			0
$511$	−8.00000			−0.353899
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−6.12293	−	14.7821i	−0.270334	−	0.652644i
$514$			6.00000i			0.264649i
$515$		0			0
$516$	−6.12293	+	14.7821i	−0.269547	+	0.650744i
$517$		0			0
$518$	11.3137	−	11.3137i	0.497096	−	0.497096i
$519$	33.9411	−	33.9411i	1.48985	−	1.48985i
$520$		0			0
$521$	6.88830	−	16.6298i	0.301782	−	0.728566i	−0.698139	−	0.715963i	$-0.745988\pi$
$521$	6.88830	−	16.6298i	0.301782	−	0.728566i	0.999921	−	0.0126035i	$-0.00401193\pi$
$522$		0			0
$523$			16.0000i			0.699631i	0.936819	+	0.349816i	$0.113756\pi$
$523$			16.0000i			0.699631i	−0.936819	+	0.349816i	$0.886244\pi$
$524$	2.29610	+	5.54328i	0.100306	+	0.242159i
$525$	−28.2843	−	28.2843i	−1.23443	−	1.23443i
$526$	−24.0000			−1.04645
$527$		0			0
$528$	−12.0000			−0.522233
$529$	16.2635	+	16.2635i	0.707107	+	0.707107i
$530$		0			0
$531$		0			0
$532$	14.7821	−	6.12293i	0.640884	−	0.265463i
$533$	4.59220	−	11.0866i	0.198910	−	0.480212i
$534$	11.0866	+	4.59220i	0.479762	+	0.198724i
$535$		0			0
$536$	−5.65685	+	5.65685i	−0.244339	+	0.244339i
$537$	22.1731	+	9.18440i	0.956840	+	0.396336i
$538$	9.18440	−	22.1731i	0.395968	−	0.955951i
$539$	−49.8895	+	20.6649i	−2.14889	+	0.890100i
$540$		0			0
$541$	−7.65367	−	18.4776i	−0.329057	−	0.794414i	−0.998663	−	0.0516971i	$-0.983537\pi$
$541$	−7.65367	−	18.4776i	−0.329057	−	0.794414i	0.669606	−	0.742717i	$-0.266463\pi$
$542$	5.65685	+	5.65685i	0.242983	+	0.242983i
$543$	−8.00000			−0.343313
$544$		0			0
$545$		0			0
$546$	−11.3137	−	11.3137i	−0.484182	−	0.484182i
$547$	0.765367	+	1.84776i	0.0327247	+	0.0790045i	0.939397	−	0.342831i	$-0.111386\pi$
$547$	0.765367	+	1.84776i	0.0327247	+	0.0790045i	−0.906672	+	0.421836i	$0.861386\pi$
$548$			6.00000i			0.256307i
$549$	−3.69552	+	1.53073i	−0.157721	+	0.0653301i
$550$	−11.4805	+	27.7164i	−0.489530	+	1.18183i
$551$		0			0
$552$		0			0
$553$	22.6274	−	22.6274i	0.962216	−	0.962216i
$554$	−7.39104	−	3.06147i	−0.314015	−	0.130069i
$555$		0			0
$556$	−1.84776	+	0.765367i	−0.0783624	+	0.0324588i
$557$			30.0000i			1.27114i	0.772043	+	0.635570i	$0.219235\pi$
$557$			30.0000i			1.27114i	−0.772043	+	0.635570i	$0.780765\pi$
$558$	1.53073	+	3.69552i	0.0648011	+	0.156444i
$559$	11.3137	+	11.3137i	0.478519	+	0.478519i
$560$		0			0
$561$		0			0
$562$	6.00000			0.253095
$563$	16.9706	+	16.9706i	0.715224	+	0.715224i	0.967623	−	0.252399i	$-0.0812196\pi$
$563$	16.9706	+	16.9706i	0.715224	+	0.715224i	−0.252399	+	0.967623i	$0.581220\pi$
$564$		0			0
$565$		0			0
$566$	12.9343	−	5.35757i	0.543670	−	0.225195i
$567$	16.8381	−	40.6507i	0.707133	−	1.70717i
$568$		0			0
$569$	−21.2132	+	21.2132i	−0.889304	+	0.889304i	−0.994456	−	0.105152i	$-0.966467\pi$
$569$	−21.2132	+	21.2132i	−0.889304	+	0.889304i	0.105152	+	0.994456i	$0.466467\pi$
$570$		0			0
$571$	−24.0209	−	9.94977i	−1.00524	−	0.416385i	−0.181525	−	0.983386i	$-0.558103\pi$
$571$	−24.0209	−	9.94977i	−1.00524	−	0.416385i	−0.823717	+	0.567001i	$0.808103\pi$
$572$	−4.59220	+	11.0866i	−0.192010	+	0.463552i
$573$	−44.3462	+	18.3688i	−1.85259	+	0.767368i
$574$			24.0000i			1.00174i
$575$		0			0
$576$	0.707107	+	0.707107i	0.0294628	+	0.0294628i
$577$	−14.0000			−0.582828			−0.291414	−	0.956597i	$-0.594126\pi$
$577$	−14.0000			−0.582828			−0.291414	+	0.956597i	$0.594126\pi$
$578$		0			0
$579$	20.0000			0.831172
$580$		0			0
$581$		0			0
$582$		−	28.0000i		−	1.16064i
$583$	−33.2597	+	13.7766i	−1.37747	+	0.570569i
$584$	0.765367	−	1.84776i	0.0316711	−	0.0764608i
$585$		0			0
$586$	4.24264	−	4.24264i	0.175262	−	0.175262i
$587$	−8.48528	+	8.48528i	−0.350225	+	0.350225i	−0.860193	−	0.509968i	$-0.829657\pi$
$587$	−8.48528	+	8.48528i	−0.350225	+	0.350225i	0.509968	+	0.860193i	$0.329657\pi$
$588$	16.6298	+	6.88830i	0.685803	+	0.284069i
$589$	−6.12293	+	14.7821i	−0.252291	+	0.609085i
$590$		0			0
$591$		−	24.0000i		−	0.987228i
$592$	1.53073	+	3.69552i	0.0629128	+	0.151885i
$593$	−21.2132	−	21.2132i	−0.871122	−	0.871122i	0.121473	−	0.992595i	$-0.461238\pi$
$593$	−21.2132	−	21.2132i	−0.871122	−	0.871122i	−0.992595	+	0.121473i	$0.961238\pi$
$594$	−24.0000			−0.984732
$595$		0			0
$596$	6.00000			0.245770
$597$	−22.6274	−	22.6274i	−0.926079	−	0.926079i
$598$		0			0
$599$		−	24.0000i		−	0.980613i	−0.871550	−	0.490307i	$-0.836885\pi$
$599$		−	24.0000i		−	0.980613i	0.871550	−	0.490307i	$-0.163115\pi$
$600$	9.23880	−	3.82683i	0.377172	−	0.156230i
$601$	−17.6034	+	42.4985i	−0.718059	+	1.73355i	−0.0392547	+	0.999229i	$0.512498\pi$
$601$	−17.6034	+	42.4985i	−0.718059	+	1.73355i	−0.678804	+	0.734319i	$0.737502\pi$
$602$	−29.5641	−	12.2459i	−1.20494	−	0.499104i
$603$	5.65685	−	5.65685i	0.230365	−	0.230365i
$604$	11.3137	−	11.3137i	0.460348	−	0.460348i
$605$		0			0
$606$	13.7766	−	33.2597i	0.559636	−	1.35108i
$607$	−18.4776	+	7.65367i	−0.749982	+	0.310653i	−0.724734	−	0.689028i	$-0.758038\pi$
$607$	−18.4776	+	7.65367i	−0.749982	+	0.310653i	−0.0252479	+	0.999681i	$0.508038\pi$
$608$			4.00000i			0.162221i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	14.0000			0.565455			0.282727	−	0.959200i	$-0.408761\pi$
$613$	14.0000			0.565455			0.282727	+	0.959200i	$0.408761\pi$
$614$	−14.1421	−	14.1421i	−0.570730	−	0.570730i
$615$		0			0
$616$		−	24.0000i		−	0.966988i
$617$	−27.7164	+	11.4805i	−1.11582	+	0.462188i	−0.862938	−	0.505310i	$-0.831378\pi$
$617$	−27.7164	+	11.4805i	−1.11582	+	0.462188i	−0.252882	+	0.967497i	$0.581378\pi$
$618$	12.2459	−	29.5641i	0.492601	−	1.18924i
$619$	24.0209	+	9.94977i	0.965480	+	0.399915i	0.809028	−	0.587770i	$-0.199994\pi$
$619$	24.0209	+	9.94977i	0.965480	+	0.399915i	0.156452	+	0.987685i	$0.449994\pi$
$620$		0			0
$621$		0			0
$622$	−11.0866	−	4.59220i	−0.444530	−	0.184130i
$623$	−9.18440	+	22.1731i	−0.367965	+	0.888347i
$624$	3.69552	−	1.53073i	0.147939	−	0.0612784i
$625$		−	25.0000i		−	1.00000i
$626$	13.0112	+	31.4119i	0.520034	+	1.25547i
$627$	33.9411	+	33.9411i	1.35548	+	1.35548i
$628$	−14.0000			−0.558661
$629$		0			0
$630$		0			0
$631$	−5.65685	−	5.65685i	−0.225196	−	0.225196i	0.585486	−	0.810682i	$-0.300904\pi$
$631$	−5.65685	−	5.65685i	−0.225196	−	0.225196i	−0.810682	+	0.585486i	$0.800904\pi$
$632$	3.06147	+	7.39104i	0.121779	+	0.294000i
$633$			20.0000i			0.794929i
$634$	−11.0866	+	4.59220i	−0.440303	+	0.182380i
$635$		0			0
$636$	11.0866	+	4.59220i	0.439610	+	0.182093i
$637$	12.7279	−	12.7279i	0.504299	−	0.504299i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	16.6298	−	6.88830i	0.656839	−	0.272072i	−0.0292688	−	0.999572i	$-0.509318\pi$
$641$	16.6298	−	6.88830i	0.656839	−	0.272072i	0.686108	+	0.727500i	$0.259318\pi$
$642$		−	12.0000i		−	0.473602i
$643$	−5.35757	−	12.9343i	−0.211282	−	0.510080i	0.782339	−	0.622853i	$-0.214027\pi$
$643$	−5.35757	−	12.9343i	−0.211282	−	0.510080i	−0.993621	+	0.112774i	$0.964027\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−48.0000			−1.88707			−0.943537	−	0.331266i	$-0.892524\pi$
$647$	−48.0000			−1.88707			−0.943537	+	0.331266i	$0.892524\pi$
$648$	7.77817	+	7.77817i	0.305556	+	0.305556i
$649$		0			0
$650$		−	10.0000i		−	0.392232i
$651$	−29.5641	+	12.2459i	−1.15871	+	0.479953i
$652$	0.765367	−	1.84776i	0.0299741	−	0.0723638i
$653$	22.1731	+	9.18440i	0.867701	+	0.359413i	0.771714	−	0.635969i	$-0.219399\pi$
$653$	22.1731	+	9.18440i	0.867701	+	0.359413i	0.0959864	+	0.995383i	$0.469399\pi$
$654$	22.6274	−	22.6274i	0.884802	−	0.884802i
$655$		0			0
$656$	−5.54328	−	2.29610i	−0.216429	−	0.0896477i
$657$	−0.765367	+	1.84776i	−0.0298598	+	0.0720879i
$658$		0			0
$659$			12.0000i			0.467454i	0.972302	+	0.233727i	$0.0750921\pi$
$659$			12.0000i			0.467454i	−0.972302	+	0.233727i	$0.924908\pi$
$660$		0			0
$661$	−32.5269	−	32.5269i	−1.26515	−	1.26515i	−0.948564	−	0.316587i	$-0.897463\pi$
$661$	−32.5269	−	32.5269i	−1.26515	−	1.26515i	−0.316587	−	0.948564i	$-0.602537\pi$
$662$	16.0000			0.621858
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−1.53073	−	3.69552i	−0.0593147	−	0.143198i
$667$		0			0
$668$	11.0866	−	4.59220i	0.428952	−	0.177678i
$669$	−6.12293	+	14.7821i	−0.236726	+	0.571508i
$670$		0			0
$671$	−16.9706	+	16.9706i	−0.655141	+	0.655141i
$672$	−5.65685	+	5.65685i	−0.218218	+	0.218218i
$673$	−35.1074	−	14.5420i	−1.35329	−	0.560552i	−0.416085	−	0.909326i	$-0.636598\pi$
$673$	−35.1074	−	14.5420i	−1.35329	−	0.560552i	−0.937207	+	0.348774i	$0.886598\pi$
$674$	8.41904	−	20.3253i	0.324289	−	0.782903i
$675$	18.4776	−	7.65367i	0.711203	−	0.294590i
$676$			9.00000i			0.346154i
$677$	4.59220	+	11.0866i	0.176493	+	0.426091i	0.987226	−	0.159324i	$-0.0509315\pi$
$677$	4.59220	+	11.0866i	0.176493	+	0.426091i	−0.810734	+	0.585415i	$0.800932\pi$
$678$	8.48528	+	8.48528i	0.325875	+	0.325875i
$679$	56.0000			2.14908
$680$		0			0
$681$	12.0000			0.459841
$682$	16.9706	+	16.9706i	0.649836	+	0.649836i
$683$	11.4805	+	27.7164i	0.439289	+	1.06054i	0.976195	+	0.216896i	$0.0695931\pi$
$683$	11.4805	+	27.7164i	0.439289	+	1.06054i	−0.536906	+	0.843642i	$0.680407\pi$
$684$		−	4.00000i		−	0.152944i
$685$		0			0
$686$	−3.06147	+	7.39104i	−0.116887	+	0.282191i
$687$	−25.8686	−	10.7151i	−0.986950	−	0.408808i
$688$	5.65685	−	5.65685i	0.215666	−	0.215666i
$689$	8.48528	−	8.48528i	0.323263	−	0.323263i
$690$		0			0
$691$	3.82683	−	9.23880i	0.145580	−	0.351460i	−0.834223	−	0.551427i	$-0.814083\pi$
$691$	3.82683	−	9.23880i	0.145580	−	0.351460i	0.979803	+	0.199967i	$0.0640834\pi$
$692$	−22.1731	+	9.18440i	−0.842895	+	0.349139i
$693$			24.0000i			0.911685i
$694$	−6.88830	−	16.6298i	−0.261476	−	0.631260i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	26.0000			0.984115
$699$	25.4558	+	25.4558i	0.962828	+	0.962828i
$700$	7.65367	+	18.4776i	0.289281	+	0.698387i
$701$			18.0000i			0.679851i	0.940452	+	0.339925i	$0.110402\pi$
$701$			18.0000i			0.679851i	−0.940452	+	0.339925i	$0.889598\pi$
$702$	7.39104	−	3.06147i	0.278957	−	0.115548i
$703$	6.12293	−	14.7821i	0.230931	−	0.557516i
$704$	5.54328	+	2.29610i	0.208920	+	0.0865375i
$705$		0			0
$706$	−4.24264	+	4.24264i	−0.159674	+	0.159674i
$707$	66.5193	+	27.5532i	2.50172	+	1.03625i
$708$		0			0
$709$	14.7821	−	6.12293i	0.555152	−	0.229952i	−0.0874268	−	0.996171i	$-0.527864\pi$
$709$	14.7821	−	6.12293i	0.555152	−	0.229952i	0.642579	+	0.766219i	$0.277864\pi$
$710$		0			0
$711$	−3.06147	−	7.39104i	−0.114814	−	0.277186i
$712$	−4.24264	−	4.24264i	−0.159000	−	0.159000i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−8.48528	−	8.48528i	−0.317110	−	0.317110i
$717$	−18.3688	−	44.3462i	−0.685996	−	1.65614i
$718$			24.0000i			0.895672i
$719$	44.3462	−	18.3688i	1.65383	−	0.685041i	0.656253	−	0.754541i	$-0.272140\pi$
$719$	44.3462	−	18.3688i	1.65383	−	0.685041i	0.997582	+	0.0695002i	$0.0221404\pi$
$720$		0			0
$721$	59.1283	+	24.4917i	2.20205	+	0.912120i
$722$	−2.12132	+	2.12132i	−0.0789474	+	0.0789474i
$723$	−14.1421	+	14.1421i	−0.525952	+	0.525952i
$724$	3.69552	+	1.53073i	0.137343	+	0.0568893i
$725$		0			0
$726$	46.1940	−	19.1342i	1.71442	−	0.710136i
$727$		−	8.00000i		−	0.296704i	−0.988935	−	0.148352i	$-0.952603\pi$
$727$		−	8.00000i		−	0.296704i	0.988935	−	0.148352i	$-0.0473968\pi$
$728$	3.06147	+	7.39104i	0.113466	+	0.273930i
$729$	9.19239	+	9.19239i	0.340459	+	0.340459i
$730$		0			0
$731$		0			0
$732$	8.00000			0.295689
$733$	15.5563	+	15.5563i	0.574587	+	0.574587i	0.933407	−	0.358820i	$-0.116821\pi$
$733$	15.5563	+	15.5563i	0.574587	+	0.574587i	−0.358820	+	0.933407i	$0.616821\pi$
$734$	−6.12293	−	14.7821i	−0.226002	−	0.545616i
$735$		0			0
$736$		0			0
$737$	18.3688	−	44.3462i	0.676624	−	1.63351i
$738$	5.54328	+	2.29610i	0.204051	+	0.0845206i
$739$	14.1421	−	14.1421i	0.520227	−	0.520227i	−0.397413	−	0.917640i	$-0.630092\pi$
$739$	14.1421	−	14.1421i	0.520227	−	0.520227i	0.917640	+	0.397413i	$0.130092\pi$
$740$		0			0
$741$	−14.7821	−	6.12293i	−0.543033	−	0.224932i
$742$	−9.18440	+	22.1731i	−0.337170	+	0.814000i
$743$	33.2597	−	13.7766i	1.22018	−	0.505415i	0.322712	−	0.946497i	$-0.395405\pi$
$743$	33.2597	−	13.7766i	1.22018	−	0.505415i	0.897467	+	0.441083i	$0.145405\pi$
$744$		−	8.00000i		−	0.293294i
$745$		0			0
$746$	−15.5563	−	15.5563i	−0.569558	−	0.569558i
$747$		0			0
$748$		0			0
$749$	24.0000			0.876941
$750$		0			0
$751$	3.06147	+	7.39104i	0.111715	+	0.269703i	0.969842	−	0.243734i	$-0.0783723\pi$
$751$	3.06147	+	7.39104i	0.111715	+	0.269703i	−0.858128	+	0.513436i	$0.828372\pi$
$752$		0			0
$753$	44.3462	−	18.3688i	1.61607	−	0.669396i
$754$		0			0
$755$		0			0
$756$	−11.3137	+	11.3137i	−0.411476	+	0.411476i
$757$	7.07107	−	7.07107i	0.257002	−	0.257002i	−0.566831	−	0.823834i	$-0.691831\pi$
$757$	7.07107	−	7.07107i	0.257002	−	0.257002i	0.823834	+	0.566831i	$0.191831\pi$
$758$	−12.9343	−	5.35757i	−0.469795	−	0.194596i
$759$		0			0
$760$		0			0
$761$		−	6.00000i		−	0.217500i	−0.994069	−	0.108750i	$-0.965315\pi$
$761$		−	6.00000i		−	0.217500i	0.994069	−	0.108750i	$-0.0346848\pi$
$762$	−12.2459	−	29.5641i	−0.443621	−	1.07100i
$763$	45.2548	+	45.2548i	1.63833	+	1.63833i
$764$	24.0000			0.868290
$765$		0			0
$766$	−24.0000			−0.867155
$767$		0			0
$768$	−0.765367	−	1.84776i	−0.0276178	−	0.0666753i
$769$			14.0000i			0.504853i	0.967616	+	0.252426i	$0.0812286\pi$
$769$			14.0000i			0.504853i	−0.967616	+	0.252426i	$0.918771\pi$
$770$		0			0
$771$	−4.59220	+	11.0866i	−0.165384	+	0.399273i
$772$	−9.23880	−	3.82683i	−0.332512	−	0.137731i
$773$	−29.6985	+	29.6985i	−1.06818	+	1.06818i	−0.0706813	+	0.997499i	$0.522517\pi$
$773$	−29.6985	+	29.6985i	−1.06818	+	1.06818i	−0.997499	+	0.0706813i	$0.977483\pi$
$774$	−5.65685	+	5.65685i	−0.203331	+	0.203331i
$775$	−18.4776	−	7.65367i	−0.663735	−	0.274928i
$776$	−5.35757	+	12.9343i	−0.192325	+	0.464315i
$777$	29.5641	−	12.2459i	1.06061	−	0.439318i
$778$		−	30.0000i		−	1.07555i
$779$	9.18440	+	22.1731i	0.329065	+	0.794434i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−6.36396	−	6.36396i	−0.227284	−	0.227284i
$785$		0			0
$786$			12.0000i			0.428026i
$787$	−42.4985	+	17.6034i	−1.51491	+	0.627495i	−0.976563	−	0.215231i	$-0.930950\pi$
$787$	−42.4985	+	17.6034i	−1.51491	+	0.627495i	−0.538343	+	0.842726i	$0.680950\pi$
$788$	−4.59220	+	11.0866i	−0.163590	+	0.394942i
$789$	−44.3462	−	18.3688i	−1.57877	−	0.653947i
$790$		0			0
$791$	−16.9706	+	16.9706i	−0.603404	+	0.603404i
$792$	−5.54328	−	2.29610i	−0.196972	−	0.0815884i
$793$	3.06147	−	7.39104i	0.108716	−	0.262463i
$794$	−18.4776	+	7.65367i	−0.655745	+	0.271619i
$795$		0			0
$796$	6.12293	+	14.7821i	0.217022	+	0.523937i
$797$	29.6985	+	29.6985i	1.05197	+	1.05197i	0.998573	+	0.0534012i	$0.0170062\pi$
$797$	29.6985	+	29.6985i	1.05197	+	1.05197i	0.0534012	+	0.998573i	$0.482994\pi$
$798$	32.0000			1.13279
$799$		0			0
$800$	−5.00000			−0.176777
$801$	4.24264	+	4.24264i	0.149906	+	0.149906i
$802$	11.4805	+	27.7164i	0.405391	+	0.978700i
$803$			12.0000i			0.423471i
$804$	−14.7821	+	6.12293i	−0.521324	+	0.215939i
$805$		0			0
$806$	−7.39104	−	3.06147i	−0.260338	−	0.107836i
$807$	33.9411	−	33.9411i	1.19478	−	1.19478i
$808$	−12.7279	+	12.7279i	−0.447767	+	0.447767i
$809$	−27.7164	−	11.4805i	−0.974456	−	0.403633i	−0.162087	−	0.986776i	$-0.551823\pi$
$809$	−27.7164	−	11.4805i	−0.974456	−	0.403633i	−0.812369	+	0.583143i	$0.801823\pi$
$810$		0			0
$811$	−35.1074	+	14.5420i	−1.23279	+	0.510638i	−0.901454	−	0.432876i	$-0.857499\pi$
$811$	−35.1074	+	14.5420i	−1.23279	+	0.510638i	−0.331335	+	0.943513i	$0.607499\pi$
$812$		0			0
$813$	6.12293	+	14.7821i	0.214741	+	0.518430i
$814$	−16.9706	−	16.9706i	−0.594818	−	0.594818i
$815$		0			0
$816$		0			0
$817$	−32.0000			−1.11954
$818$	7.07107	+	7.07107i	0.247234	+	0.247234i
$819$	−3.06147	−	7.39104i	−0.106976	−	0.258264i
$820$		0			0
$821$	33.2597	−	13.7766i	1.16077	−	0.480807i	0.282639	−	0.959226i	$-0.408790\pi$
$821$	33.2597	−	13.7766i	1.16077	−	0.480807i	0.878131	+	0.478420i	$0.158790\pi$
$822$	−4.59220	+	11.0866i	−0.160171	+	0.386688i
$823$	−14.7821	−	6.12293i	−0.515271	−	0.213432i	0.109867	−	0.993946i	$-0.464957\pi$
$823$	−14.7821	−	6.12293i	−0.515271	−	0.213432i	−0.625138	+	0.780514i	$0.714957\pi$
$824$	−11.3137	+	11.3137i	−0.394132	+	0.394132i
$825$	−42.4264	+	42.4264i	−1.47710	+	1.47710i
$826$		0			0
$827$	−2.29610	+	5.54328i	−0.0798432	+	0.192759i	−0.958760	−	0.284216i	$-0.908267\pi$
$827$	−2.29610	+	5.54328i	−0.0798432	+	0.192759i	0.878917	+	0.476975i	$0.158267\pi$
$828$		0			0
$829$			10.0000i			0.347314i	0.984806	+	0.173657i	$0.0555585\pi$
$829$			10.0000i			0.347314i	−0.984806	+	0.173657i	$0.944442\pi$
$830$		0			0
$831$	−11.3137	−	11.3137i	−0.392468	−	0.392468i
$832$	−2.00000			−0.0693375
$833$		0			0
$834$	−4.00000			−0.138509
$835$		0			0
$836$	−9.18440	−	22.1731i	−0.317649	−	0.766873i
$837$		−	16.0000i		−	0.553041i
$838$	−27.7164	+	11.4805i	−0.957447	+	0.396587i
$839$	−13.7766	+	33.2597i	−0.475621	+	1.14825i	0.486022	+	0.873947i	$0.338448\pi$
$839$	−13.7766	+	33.2597i	−0.475621	+	1.14825i	−0.961643	+	0.274304i	$0.911552\pi$
$840$		0			0
$841$	−20.5061	+	20.5061i	−0.707107	+	0.707107i
$842$	−1.41421	+	1.41421i	−0.0487370	+	0.0487370i
$843$	11.0866	+	4.59220i	0.381841	+	0.158164i
$844$	3.82683	−	9.23880i	0.131725	−	0.318012i
$845$		0			0
$846$		0			0
$847$	38.2683	+	92.3880i	1.31492	+	3.17449i
$848$	−4.24264	−	4.24264i	−0.145693	−	0.145693i
$849$	28.0000			0.960958
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−15.3073	−	36.9552i	−0.524113	−	1.26532i	−0.935328	−	0.353783i	$-0.884895\pi$
$853$	−15.3073	−	36.9552i	−0.524113	−	1.26532i	0.411214	−	0.911539i	$-0.365105\pi$
$854$			16.0000i			0.547509i
$855$		0			0
$856$	−2.29610	+	5.54328i	−0.0784791	+	0.189465i
$857$	−16.6298	−	6.88830i	−0.568064	−	0.235300i	0.0801177	−	0.996785i	$-0.474470\pi$
$857$	−16.6298	−	6.88830i	−0.568064	−	0.235300i	−0.648182	+	0.761486i	$0.724470\pi$
$858$	−16.9706	+	16.9706i	−0.579365	+	0.579365i
$859$	11.3137	−	11.3137i	0.386019	−	0.386019i	−0.487246	−	0.873265i	$-0.661998\pi$
$859$	11.3137	−	11.3137i	0.386019	−	0.386019i	0.873265	+	0.487246i	$0.161998\pi$
$860$		0			0
$861$	−18.3688	+	44.3462i	−0.626007	+	1.51132i
$862$	−22.1731	+	9.18440i	−0.755219	+	0.312822i
$863$		−	48.0000i		−	1.63394i	−0.576681	−	0.816970i	$-0.695652\pi$
$863$		−	48.0000i		−	1.63394i	0.576681	−	0.816970i	$-0.304348\pi$
$864$	−1.53073	−	3.69552i	−0.0520766	−	0.125724i
$865$		0			0
$866$	−2.00000			−0.0679628
$867$		0			0
$868$	16.0000			0.543075
$869$	−33.9411	−	33.9411i	−1.15137	−	1.15137i
$870$		0			0
$871$			16.0000i			0.542139i
$872$	−14.7821	+	6.12293i	−0.500584	+	0.207349i
$873$	5.35757	−	12.9343i	0.181326	−	0.437760i
$874$		0			0
$875$		0			0
$876$	2.82843	−	2.82843i	0.0955637	−	0.0955637i
$877$	−29.5641	−	12.2459i	−0.998310	−	0.413514i	−0.177133	−	0.984187i	$-0.556682\pi$
$877$	−29.5641	−	12.2459i	−0.998310	−	0.413514i	−0.821177	+	0.570673i	$0.806682\pi$
$878$	−3.06147	+	7.39104i	−0.103320	+	0.249435i
$879$	11.0866	−	4.59220i	0.373940	−	0.154891i
$880$		0			0
$881$	−6.88830	−	16.6298i	−0.232073	−	0.560273i	0.764348	−	0.644804i	$-0.223061\pi$
$881$	−6.88830	−	16.6298i	−0.232073	−	0.560273i	−0.996421	+	0.0845306i	$0.973061\pi$
$882$	6.36396	+	6.36396i	0.214286	+	0.214286i
$883$	16.0000			0.538443			0.269221	−	0.963078i	$-0.413234\pi$
$883$	16.0000			0.538443			0.269221	+	0.963078i	$0.413234\pi$
$884$		0			0
$885$		0			0
$886$	16.9706	+	16.9706i	0.570137	+	0.570137i
$887$	9.18440	+	22.1731i	0.308382	+	0.744500i	0.999758	+	0.0220048i	$0.00700491\pi$
$887$	9.18440	+	22.1731i	0.308382	+	0.744500i	−0.691376	+	0.722495i	$0.742995\pi$
$888$			8.00000i			0.268462i
$889$	59.1283	−	24.4917i	1.98310	−	0.821427i
$890$		0			0
$891$	−60.9760	−	25.2571i	−2.04277	−	0.846145i
$892$	5.65685	−	5.65685i	0.189405	−	0.189405i
$893$		0			0
$894$	11.0866	+	4.59220i	0.370790	+	0.153586i
$895$		0			0
$896$	3.69552	−	1.53073i	0.123459	−	0.0511382i
$897$		0			0
$898$	6.88830	+	16.6298i	0.229866	+	0.554945i
$899$		0			0
$900$	5.00000			0.166667
$901$		0			0
$902$	36.0000			1.19867
$903$	−45.2548	−	45.2548i	−1.50599	−	1.50599i
$904$	−2.29610	−	5.54328i	−0.0763672	−	0.184367i
$905$		0			0
$906$	29.5641	−	12.2459i	0.982203	−	0.406842i
$907$	−22.1956	+	53.5850i	−0.736994	+	1.77926i	−0.119277	+	0.992861i	$0.538058\pi$
$907$	−22.1956	+	53.5850i	−0.736994	+	1.77926i	−0.617717	+	0.786400i	$0.711942\pi$
$908$	−5.54328	−	2.29610i	−0.183960	−	0.0761988i
$909$	12.7279	−	12.7279i	0.422159	−	0.422159i
$910$		0			0
$911$	−11.0866	−	4.59220i	−0.367314	−	0.152146i	0.191389	−	0.981514i	$-0.438701\pi$
$911$	−11.0866	−	4.59220i	−0.367314	−	0.152146i	−0.558703	+	0.829368i	$0.688701\pi$
$912$	−3.06147	+	7.39104i	−0.101375	+	0.244742i
$913$		0			0
$914$		−	26.0000i		−	0.860004i
$915$		0			0
$916$	9.89949	+	9.89949i	0.327089	+	0.327089i
$917$	−24.0000			−0.792550
$918$		0			0
$919$	56.0000			1.84727			0.923635	−	0.383274i	$-0.125203\pi$
$919$	56.0000			1.84727			0.923635	+	0.383274i	$0.125203\pi$
$920$		0			0
$921$	−15.3073	−	36.9552i	−0.504394	−	1.21771i
$922$		−	6.00000i		−	0.197599i
$923$		0			0
$924$	18.3688	−	44.3462i	0.604289	−	1.45888i
$925$	18.4776	+	7.65367i	0.607539	+	0.251651i
$926$	−11.3137	+	11.3137i	−0.371792	+	0.371792i
$927$	11.3137	−	11.3137i	0.371591	−	0.371591i
$928$		0			0
$929$	6.88830	−	16.6298i	0.225998	−	0.545607i	−0.769685	−	0.638423i	$-0.779587\pi$
$929$	6.88830	−	16.6298i	0.225998	−	0.545607i	0.995683	+	0.0928163i	$0.0295869\pi$
$930$		0			0
$931$			36.0000i			1.17985i
$932$	−6.88830	−	16.6298i	−0.225634	−	0.544728i
$933$	−16.9706	−	16.9706i	−0.555591	−	0.555591i
$934$	−12.0000			−0.392652
$935$		0			0
$936$	2.00000			0.0653720
$937$	41.0122	+	41.0122i	1.33981	+	1.33981i	0.896240	+	0.443570i	$0.146288\pi$
$937$	41.0122	+	41.0122i	1.33981	+	1.33981i	0.443570	+	0.896240i	$0.353712\pi$
$938$	−12.2459	−	29.5641i	−0.399842	−	0.965304i
$939$			68.0000i			2.21910i
$940$		0			0
$941$	−13.7766	+	33.2597i	−0.449104	+	1.08423i	0.523554	+	0.851993i	$0.324606\pi$
$941$	−13.7766	+	33.2597i	−0.449104	+	1.08423i	−0.972658	+	0.232241i	$0.925394\pi$
$942$	−25.8686	−	10.7151i	−0.842845	−	0.349118i
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−18.3688	+	44.3462i	−0.597221	+	1.44182i
$947$	−16.6298	+	6.88830i	−0.540397	+	0.223840i	−0.636150	−	0.771565i	$-0.719474\pi$
$947$	−16.6298	+	6.88830i	−0.540397	+	0.223840i	0.0957531	+	0.995405i	$0.469474\pi$
$948$			16.0000i			0.519656i
$949$	−1.53073	−	3.69552i	−0.0496897	−	0.119962i
$950$	14.1421	+	14.1421i	0.458831	+	0.458831i
$951$	−24.0000			−0.778253
$952$		0			0
$953$	−30.0000			−0.971795			−0.485898	−	0.874016i	$-0.661507\pi$
$953$	−30.0000			−0.971795			−0.485898	+	0.874016i	$0.661507\pi$
$954$	4.24264	+	4.24264i	0.137361	+	0.137361i
$955$		0			0
$956$			24.0000i			0.776215i
$957$		0			0
$958$	9.18440	−	22.1731i	0.296735	−	0.716381i
$959$	−22.1731	−	9.18440i	−0.716007	−	0.296580i
$960$		0			0
$961$	10.6066	−	10.6066i	0.342148	−	0.342148i
$962$	7.39104	+	3.06147i	0.238297	+	0.0987057i
$963$	2.29610	−	5.54328i	0.0739908	−	0.178630i
$964$	9.23880	−	3.82683i	0.297562	−	0.123254i
$965$		0			0
$966$		0			0
$967$	−28.2843	−	28.2843i	−0.909561	−	0.909561i	0.0866757	−	0.996237i	$-0.472376\pi$
$967$	−28.2843	−	28.2843i	−0.909561	−	0.909561i	−0.996237	+	0.0866757i	$0.972376\pi$
$968$	−25.0000			−0.803530
$969$		0			0
$970$		0			0
$971$	16.9706	+	16.9706i	0.544611	+	0.544611i	0.924877	−	0.380266i	$-0.124168\pi$
$971$	16.9706	+	16.9706i	0.544611	+	0.544611i	−0.380266	+	0.924877i	$0.624168\pi$
$972$	3.82683	+	9.23880i	0.122746	+	0.296334i
$973$		−	8.00000i		−	0.256468i
$974$	7.39104	−	3.06147i	0.236824	−	0.0980957i
$975$	7.65367	−	18.4776i	0.245114	−	0.591756i
$976$	−3.69552	−	1.53073i	−0.118291	−	0.0489976i
$977$	29.6985	−	29.6985i	0.950139	−	0.950139i	−0.0486759	−	0.998815i	$-0.515500\pi$
$977$	29.6985	−	29.6985i	0.950139	−	0.950139i	0.998815	+	0.0486759i	$0.0155002\pi$
$978$	2.82843	−	2.82843i	0.0904431	−	0.0904431i
$979$	33.2597	+	13.7766i	1.06298	+	0.440302i
$980$		0			0
$981$	14.7821	−	6.12293i	0.471955	−	0.195490i
$982$			12.0000i			0.382935i
$983$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$983$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$984$	−8.48528	−	8.48528i	−0.270501	−	0.270501i
$985$		0			0
$986$		0			0
$987$		0			0
$988$	5.65685	+	5.65685i	0.179969	+	0.179969i
$989$		0			0
$990$		0			0
$991$	−14.7821	+	6.12293i	−0.469568	+	0.194501i	−0.604904	−	0.796298i	$-0.706789\pi$
$991$	−14.7821	+	6.12293i	−0.469568	+	0.194501i	0.135336	+	0.990800i	$0.456789\pi$
$992$	−1.53073	+	3.69552i	−0.0486008	+	0.117333i
$993$	29.5641	+	12.2459i	0.938190	+	0.388611i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	10.7151	−	25.8686i	0.339352	−	0.819268i	−0.658426	−	0.752645i	$-0.728778\pi$
$997$	10.7151	−	25.8686i	0.339352	−	0.819268i	0.997778	−	0.0666226i	$-0.0212223\pi$
$998$	−12.9343	+	5.35757i	−0.409429	+	0.169591i
$999$			16.0000i			0.506218i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	578.2.d.e.423.1		8
17.2	even	8	inner	578.2.d.e.179.1		8
17.3	odd	16		578.2.b.a.577.1		2
17.4	even	4	inner	578.2.d.e.155.1		8
17.5	odd	16		578.2.a.a.1.1		1
17.6	odd	16		578.2.c.e.251.1		4
17.7	odd	16		578.2.c.e.327.1		4
17.8	even	8	inner	578.2.d.e.399.1		8
17.9	even	8	inner	578.2.d.e.399.2		8
17.10	odd	16		578.2.c.e.327.2		4
17.11	odd	16		578.2.c.e.251.2		4
17.12	odd	16		34.2.a.a.1.1	✓	1
17.13	even	4	inner	578.2.d.e.155.2		8
17.14	odd	16		578.2.b.a.577.2		2
17.15	even	8	inner	578.2.d.e.179.2		8
17.16	even	2	inner	578.2.d.e.423.2		8
51.5	even	16		5202.2.a.d.1.1		1
51.29	even	16		306.2.a.a.1.1		1
68.39	even	16		4624.2.a.a.1.1		1
68.63	even	16		272.2.a.d.1.1		1
85.12	even	16		850.2.c.b.749.2		2
85.29	odd	16		850.2.a.e.1.1		1
85.63	even	16		850.2.c.b.749.1		2
119.97	even	16		1666.2.a.m.1.1		1
136.29	odd	16		1088.2.a.l.1.1		1
136.131	even	16		1088.2.a.d.1.1		1
187.131	even	16		4114.2.a.a.1.1		1
204.131	odd	16		2448.2.a.k.1.1		1
221.12	odd	16		5746.2.a.b.1.1		1
255.29	even	16		7650.2.a.ci.1.1		1
340.199	even	16		6800.2.a.b.1.1		1
408.29	even	16		9792.2.a.y.1.1		1
408.131	odd	16		9792.2.a.bj.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
34.2.a.a.1.1	✓	1	17.12	odd	16
272.2.a.d.1.1		1	68.63	even	16
306.2.a.a.1.1		1	51.29	even	16
578.2.a.a.1.1		1	17.5	odd	16
578.2.b.a.577.1		2	17.3	odd	16
578.2.b.a.577.2		2	17.14	odd	16
578.2.c.e.251.1		4	17.6	odd	16
578.2.c.e.251.2		4	17.11	odd	16
578.2.c.e.327.1		4	17.7	odd	16
578.2.c.e.327.2		4	17.10	odd	16
578.2.d.e.155.1		8	17.4	even	4	inner
578.2.d.e.155.2		8	17.13	even	4	inner
578.2.d.e.179.1		8	17.2	even	8	inner
578.2.d.e.179.2		8	17.15	even	8	inner
578.2.d.e.399.1		8	17.8	even	8	inner
578.2.d.e.399.2		8	17.9	even	8	inner
578.2.d.e.423.1		8	1.1	even	1	trivial
578.2.d.e.423.2		8	17.16	even	2	inner
850.2.a.e.1.1		1	85.29	odd	16
850.2.c.b.749.1		2	85.63	even	16
850.2.c.b.749.2		2	85.12	even	16
1088.2.a.d.1.1		1	136.131	even	16
1088.2.a.l.1.1		1	136.29	odd	16
1666.2.a.m.1.1		1	119.97	even	16
2448.2.a.k.1.1		1	204.131	odd	16
4114.2.a.a.1.1		1	187.131	even	16
4624.2.a.a.1.1		1	68.39	even	16
5202.2.a.d.1.1		1	51.5	even	16
5746.2.a.b.1.1		1	221.12	odd	16
6800.2.a.b.1.1		1	340.199	even	16
7650.2.a.ci.1.1		1	255.29	even	16
9792.2.a.y.1.1		1	408.29	even	16
9792.2.a.bj.1.1		1	408.131	odd	16

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:	\( N \)	\(=\)	\( 578 = 2 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	578.d (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.765367 - 1.84776i) q^{3} +1.00000i q^{4} +(-0.765367 + 1.84776i) q^{6} +(-3.69552 - 1.53073i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.765367 - 1.84776i) q^{3} +1.00000i q^{4} +(-0.765367 + 1.84776i) q^{6} +(-3.69552 - 1.53073i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.707107 + 0.707107i) q^{9} +(-2.29610 + 5.54328i) q^{11} +(1.84776 - 0.765367i) q^{12} -2.00000i q^{13} +(1.53073 + 3.69552i) q^{14} -1.00000 q^{16} +1.00000 q^{18} +(2.82843 + 2.82843i) q^{19} +8.00000i q^{21} +(5.54328 - 2.29610i) q^{22} +(-1.84776 - 0.765367i) q^{24} +(-3.53553 + 3.53553i) q^{25} +(-1.41421 + 1.41421i) q^{26} +(-3.69552 - 1.53073i) q^{27} +(1.53073 - 3.69552i) q^{28} +(1.53073 + 3.69552i) q^{31} +(0.707107 + 0.707107i) q^{32} +12.0000 q^{33} +(-0.707107 - 0.707107i) q^{36} +(-1.53073 - 3.69552i) q^{37} -4.00000i q^{38} +(-3.69552 + 1.53073i) q^{39} +(5.54328 + 2.29610i) q^{41} +(5.65685 - 5.65685i) q^{42} +(-5.65685 + 5.65685i) q^{43} +(-5.54328 - 2.29610i) q^{44} +(0.765367 + 1.84776i) q^{48} +(6.36396 + 6.36396i) q^{49} +5.00000 q^{50} +2.00000 q^{52} +(4.24264 + 4.24264i) q^{53} +(1.53073 + 3.69552i) q^{54} +(-3.69552 + 1.53073i) q^{56} +(3.06147 - 7.39104i) q^{57} +(3.69552 + 1.53073i) q^{61} +(1.53073 - 3.69552i) q^{62} +(3.69552 - 1.53073i) q^{63} -1.00000i q^{64} +(-8.48528 - 8.48528i) q^{66} -8.00000 q^{67} +1.00000i q^{72} +(1.84776 - 0.765367i) q^{73} +(-1.53073 + 3.69552i) q^{74} +(9.23880 + 3.82683i) q^{75} +(-2.82843 + 2.82843i) q^{76} +(16.9706 - 16.9706i) q^{77} +(3.69552 + 1.53073i) q^{78} +(-3.06147 + 7.39104i) q^{79} +11.0000i q^{81} +(-2.29610 - 5.54328i) q^{82} -8.00000 q^{84} +8.00000 q^{86} +(2.29610 + 5.54328i) q^{88} -6.00000i q^{89} +(-3.06147 + 7.39104i) q^{91} +(5.65685 - 5.65685i) q^{93} +(0.765367 - 1.84776i) q^{96} +(-12.9343 + 5.35757i) q^{97} -9.00000i q^{98} +(-2.29610 - 5.54328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 8 q^{16} + 8 q^{18} + 96 q^{33} + 40 q^{50} + 16 q^{52} - 64 q^{67} - 64 q^{84} + 64 q^{86}+O(q^{100}) \) 8 * q - 8 * q^16 + 8 * q^18 + 96 * q^33 + 40 * q^50 + 16 * q^52 - 64 * q^67 - 64 * q^84 + 64 * q^86

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