LMFDB - Embedded newform 578.2.d.e.155.2

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			155.2
Root			$0.382683 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	578.155
Dual form			578.2.d.e.179.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(1.84776 - 0.765367i) q^{3} +1.00000i q^{4} +(1.84776 + 0.765367i) q^{6} +(-1.53073 + 3.69552i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.707107 - 0.707107i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(1.84776 - 0.765367i) q^{3} +1.00000i q^{4} +(1.84776 + 0.765367i) q^{6} +(-1.53073 + 3.69552i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.707107 - 0.707107i) q^{9} +(5.54328 + 2.29610i) q^{11} +(0.765367 + 1.84776i) q^{12} -2.00000i q^{13} +(-3.69552 + 1.53073i) q^{14} -1.00000 q^{16} +1.00000 q^{18} +(-2.82843 - 2.82843i) q^{19} +8.00000i q^{21} +(2.29610 + 5.54328i) q^{22} +(-0.765367 + 1.84776i) q^{24} +(3.53553 - 3.53553i) q^{25} +(1.41421 - 1.41421i) q^{26} +(-1.53073 + 3.69552i) q^{27} +(-3.69552 - 1.53073i) q^{28} +(-3.69552 + 1.53073i) q^{31} +(-0.707107 - 0.707107i) q^{32} +12.0000 q^{33} +(0.707107 + 0.707107i) q^{36} +(3.69552 - 1.53073i) q^{37} -4.00000i q^{38} +(-1.53073 - 3.69552i) q^{39} +(2.29610 - 5.54328i) q^{41} +(-5.65685 + 5.65685i) q^{42} +(5.65685 - 5.65685i) q^{43} +(-2.29610 + 5.54328i) q^{44} +(-1.84776 + 0.765367i) q^{48} +(-6.36396 - 6.36396i) q^{49} +5.00000 q^{50} +2.00000 q^{52} +(-4.24264 - 4.24264i) q^{53} +(-3.69552 + 1.53073i) q^{54} +(-1.53073 - 3.69552i) q^{56} +(-7.39104 - 3.06147i) q^{57} +(1.53073 - 3.69552i) q^{61} +(-3.69552 - 1.53073i) q^{62} +(1.53073 + 3.69552i) q^{63} -1.00000i q^{64} +(8.48528 + 8.48528i) q^{66} -8.00000 q^{67} +1.00000i q^{72} +(0.765367 + 1.84776i) q^{73} +(3.69552 + 1.53073i) q^{74} +(3.82683 - 9.23880i) q^{75} +(2.82843 - 2.82843i) q^{76} +(-16.9706 + 16.9706i) q^{77} +(1.53073 - 3.69552i) q^{78} +(7.39104 + 3.06147i) q^{79} +11.0000i q^{81} +(5.54328 - 2.29610i) q^{82} -8.00000 q^{84} +8.00000 q^{86} +(-5.54328 + 2.29610i) q^{88} -6.00000i q^{89} +(7.39104 + 3.06147i) q^{91} +(-5.65685 + 5.65685i) q^{93} +(-1.84776 - 0.765367i) q^{96} +(-5.35757 - 12.9343i) q^{97} -9.00000i q^{98} +(5.54328 - 2.29610i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/578\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{8}\right)$

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
$3$	1.84776	−	0.765367i	1.06680	−	0.441885i	0.220942	−	0.975287i	$-0.429087\pi$
$3$	1.84776	−	0.765367i	1.06680	−	0.441885i	0.845862	+	0.533402i	$0.179087\pi$
$4$			1.00000i			0.500000i
$5$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$5$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$6$	1.84776	+	0.765367i	0.754344	+	0.312460i
$7$	−1.53073	+	3.69552i	−0.578563	+	1.39677i	0.315540	+	0.948912i	$0.397814\pi$
$7$	−1.53073	+	3.69552i	−0.578563	+	1.39677i	−0.894103	+	0.447862i	$0.852186\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	0.707107	−	0.707107i	0.235702	−	0.235702i
$10$		0			0
$11$	5.54328	+	2.29610i	1.67136	+	0.692300i	0.998857	−	0.0477934i	$-0.0152189\pi$
$11$	5.54328	+	2.29610i	1.67136	+	0.692300i	0.672504	+	0.740094i	$0.265219\pi$
$12$	0.765367	+	1.84776i	0.220942	+	0.533402i
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$	−3.69552	+	1.53073i	−0.987669	+	0.409106i
$15$		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	0.303838	−	0.952724i	$-0.401732\pi$
$19$	−2.82843	−	2.82843i	−0.648886	−	0.648886i	−0.952724	+	0.303838i	$0.901732\pi$
$20$		0			0
$21$			8.00000i			1.74574i
$22$	2.29610	+	5.54328i	0.489530	+	1.18183i
$23$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$23$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$24$	−0.765367	+	1.84776i	−0.156230	+	0.377172i
$25$	3.53553	−	3.53553i	0.707107	−	0.707107i
$26$	1.41421	−	1.41421i	0.277350	−	0.277350i
$27$	−1.53073	+	3.69552i	−0.294590	+	0.711203i
$28$	−3.69552	−	1.53073i	−0.698387	−	0.289281i
$29$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$29$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$30$		0			0
$31$	−3.69552	+	1.53073i	−0.663735	+	0.274928i	−0.689009	−	0.724753i	$-0.741954\pi$
$31$	−3.69552	+	1.53073i	−0.663735	+	0.274928i	0.0252745	+	0.999681i	$0.491954\pi$
$32$	−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
$37$	3.69552	−	1.53073i	0.607539	−	0.251651i	−0.0576366	−	0.998338i	$-0.518356\pi$
$37$	3.69552	−	1.53073i	0.607539	−	0.251651i	0.665176	+	0.746687i	$0.268356\pi$
$38$		−	4.00000i		−	0.648886i
$39$	−1.53073	−	3.69552i	−0.245114	−	0.591756i
$40$		0			0
$41$	2.29610	−	5.54328i	0.358591	−	0.865714i	−0.636908	−	0.770940i	$-0.719787\pi$
$41$	2.29610	−	5.54328i	0.358591	−	0.865714i	0.995499	−	0.0947747i	$-0.0302131\pi$
$42$	−5.65685	+	5.65685i	−0.872872	+	0.872872i
$43$	5.65685	−	5.65685i	0.862662	−	0.862662i	−0.128984	−	0.991647i	$-0.541172\pi$
$43$	5.65685	−	5.65685i	0.862662	−	0.862662i	0.991647	+	0.128984i	$0.0411717\pi$
$44$	−2.29610	+	5.54328i	−0.346150	+	0.835680i
$45$		0			0
$46$		0			0
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$	−1.84776	+	0.765367i	−0.266701	+	0.110471i
$49$	−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	0.352892	−	0.935664i	$-0.385198\pi$
$53$	−4.24264	−	4.24264i	−0.582772	−	0.582772i	−0.935664	+	0.352892i	$0.885198\pi$
$54$	−3.69552	+	1.53073i	−0.502896	+	0.208306i
$55$		0			0
$56$	−1.53073	−	3.69552i	−0.204553	−	0.493834i
$57$	−7.39104	−	3.06147i	−0.978967	−	0.405501i
$58$		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
$61$	1.53073	−	3.69552i	0.195990	−	0.473163i	−0.795080	−	0.606505i	$-0.792571\pi$
$61$	1.53073	−	3.69552i	0.195990	−	0.473163i	0.991070	+	0.133342i	$0.0425710\pi$
$62$	−3.69552	−	1.53073i	−0.469331	−	0.194403i
$63$	1.53073	+	3.69552i	0.192854	+	0.465592i
$64$		−	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		−0.382683	−	0.923880i	$-0.625000\pi$
$71$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$72$			1.00000i			0.117851i
$73$	0.765367	+	1.84776i	0.0895794	+	0.216264i	0.962319	−	0.271921i	$-0.0876591\pi$
$73$	0.765367	+	1.84776i	0.0895794	+	0.216264i	−0.872740	+	0.488185i	$0.837659\pi$
$74$	3.69552	+	1.53073i	0.429595	+	0.177944i
$75$	3.82683	−	9.23880i	0.441885	−	1.06680i
$76$	2.82843	−	2.82843i	0.324443	−	0.324443i
$77$	−16.9706	+	16.9706i	−1.93398	+	1.93398i
$78$	1.53073	−	3.69552i	0.173321	−	0.418435i
$79$	7.39104	+	3.06147i	0.831557	+	0.344442i	0.757519	−	0.652813i	$-0.226411\pi$
$79$	7.39104	+	3.06147i	0.831557	+	0.344442i	0.0740378	+	0.997255i	$0.476411\pi$
$80$		0			0
$81$			11.0000i			1.22222i
$82$	5.54328	−	2.29610i	0.612153	−	0.253562i
$83$		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
$88$	−5.54328	+	2.29610i	−0.590915	+	0.244765i
$89$		−	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
$91$	7.39104	+	3.06147i	0.774791	+	0.320929i
$92$		0			0
$93$	−5.65685	+	5.65685i	−0.586588	+	0.586588i
$94$		0			0
$95$		0			0
$96$	−1.84776	−	0.765367i	−0.188586	−	0.0781149i
$97$	−5.35757	−	12.9343i	−0.543979	−	1.31328i	−0.921895	−	0.387441i	$-0.873359\pi$
$97$	−5.35757	−	12.9343i	−0.543979	−	1.31328i	0.377916	−	0.925840i	$-0.376641\pi$
$98$		−	9.00000i		−	0.909137i
$99$	5.54328	−	2.29610i	0.557120	−	0.230767i
$100$	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
$107$	−2.29610	−	5.54328i	−0.221972	−	0.535889i	0.773185	−	0.634180i	$-0.218662\pi$
$107$	−2.29610	−	5.54328i	−0.221972	−	0.535889i	−0.995158	+	0.0982914i	$0.968662\pi$
$108$	−3.69552	−	1.53073i	−0.355601	−	0.147295i
$109$	−6.12293	+	14.7821i	−0.586471	+	1.41587i	0.300384	+	0.953818i	$0.402885\pi$
$109$	−6.12293	+	14.7821i	−0.586471	+	1.41587i	−0.886855	+	0.462048i	$0.847115\pi$
$110$		0			0
$111$	5.65685	−	5.65685i	0.536925	−	0.536925i
$112$	1.53073	−	3.69552i	0.144641	−	0.349194i
$113$	−5.54328	−	2.29610i	−0.521468	−	0.215999i	0.106394	−	0.994324i	$-0.466070\pi$
$113$	−5.54328	−	2.29610i	−0.521468	−	0.215999i	−0.627861	+	0.778325i	$0.716070\pi$
$114$	−3.06147	−	7.39104i	−0.286733	−	0.692234i
$115$		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
$122$	3.69552	−	1.53073i	0.334576	−	0.138586i
$123$		−	12.0000i		−	1.08200i
$124$	−1.53073	−	3.69552i	−0.137464	−	0.331867i
$125$		0			0
$126$	−1.53073	+	3.69552i	−0.136369	+	0.329223i
$127$	11.3137	−	11.3137i	1.00393	−	1.00393i	0.00393704	−	0.999992i	$-0.498747\pi$
$127$	11.3137	−	11.3137i	1.00393	−	1.00393i	0.999992	−	0.00393704i	$-0.00125320\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	6.12293	−	14.7821i	0.539094	−	1.30149i
$130$		0			0
$131$	2.29610	+	5.54328i	0.200611	+	0.484318i	0.991884	−	0.127145i	$-0.0405813\pi$
$131$	2.29610	+	5.54328i	0.200611	+	0.484318i	−0.791273	+	0.611463i	$0.790581\pi$
$132$			12.0000i			1.04447i
$133$	14.7821	−	6.12293i	1.28177	−	0.530926i
$134$	−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
$139$	−1.84776	+	0.765367i	−0.156725	+	0.0649176i	−0.459667	−	0.888091i	$-0.652031\pi$
$139$	−1.84776	+	0.765367i	−0.156725	+	0.0649176i	0.302942	+	0.953009i	$0.402031\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	4.59220	−	11.0866i	0.384019	−	0.927104i
$144$	−0.707107	+	0.707107i	−0.0589256	+	0.0589256i
$145$		0			0
$146$	−0.765367	+	1.84776i	−0.0633422	+	0.152922i
$147$	−16.6298	−	6.88830i	−1.37161	−	0.568138i
$148$	1.53073	+	3.69552i	0.125826	+	0.303770i
$149$		−	6.00000i		−	0.491539i	−0.969328	−	0.245770i	$-0.920959\pi$
$149$		−	6.00000i		−	0.491539i	0.969328	−	0.245770i	$-0.0790407\pi$
$150$	9.23880	−	3.82683i	0.754344	−	0.312460i
$151$	11.3137	+	11.3137i	0.920697	+	0.920697i	0.997079	−	0.0763821i	$-0.0243369\pi$
$151$	11.3137	+	11.3137i	0.920697	+	0.920697i	−0.0763821	+	0.997079i	$0.524337\pi$
$152$	4.00000			0.324443
$153$		0			0
$154$	−24.0000			−1.93398
$155$		0			0
$156$	3.69552	−	1.53073i	0.295878	−	0.122557i
$157$			14.0000i			1.11732i	0.829396	+	0.558661i	$0.188685\pi$
$157$			14.0000i			1.11732i	−0.829396	+	0.558661i	$0.811315\pi$
$158$	3.06147	+	7.39104i	0.243557	+	0.587999i
$159$	−11.0866	−	4.59220i	−0.879221	−	0.364185i
$160$		0			0
$161$		0			0
$162$	−7.77817	+	7.77817i	−0.611111	+	0.611111i
$163$	−0.765367	+	1.84776i	−0.0599482	+	0.144728i	−0.951015	−	0.309144i	$-0.899958\pi$
$163$	−0.765367	+	1.84776i	−0.0599482	+	0.144728i	0.891067	+	0.453872i	$0.149958\pi$
$164$	5.54328	+	2.29610i	0.432857	+	0.179295i
$165$		0			0
$166$		0			0
$167$	11.0866	−	4.59220i	0.857903	−	0.355355i	0.0900162	−	0.995940i	$-0.471308\pi$
$167$	11.0866	−	4.59220i	0.857903	−	0.355355i	0.767887	+	0.640585i	$0.221308\pi$
$168$	−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
$173$	−22.1731	+	9.18440i	−1.68579	+	0.698277i	−0.999576	−	0.0291222i	$-0.990729\pi$
$173$	−22.1731	+	9.18440i	−1.68579	+	0.698277i	−0.686214	+	0.727399i	$0.740729\pi$
$174$		0			0
$175$	7.65367	+	18.4776i	0.578563	+	1.39677i
$176$	−5.54328	−	2.29610i	−0.417840	−	0.173075i
$177$		0			0
$178$	4.24264	−	4.24264i	0.317999	−	0.317999i
$179$	8.48528	−	8.48528i	0.634220	−	0.634220i	−0.314904	−	0.949124i	$-0.601972\pi$
$179$	8.48528	−	8.48528i	0.634220	−	0.634220i	0.949124	+	0.314904i	$0.101972\pi$
$180$		0			0
$181$	−3.69552	−	1.53073i	−0.274686	−	0.113779i	0.241088	−	0.970503i	$-0.422496\pi$
$181$	−3.69552	−	1.53073i	−0.274686	−	0.113779i	−0.515774	+	0.856725i	$0.672496\pi$
$182$	3.06147	+	7.39104i	0.226931	+	0.547860i
$183$		−	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	$-0.334780\pi$
$192$	−0.765367	−	1.84776i	−0.0552356	−	0.133351i
$193$	9.23880	+	3.82683i	0.665023	+	0.275462i	0.689551	−	0.724238i	$-0.257808\pi$
$193$	9.23880	+	3.82683i	0.665023	+	0.275462i	−0.0245275	+	0.999699i	$0.507808\pi$
$194$	5.35757	−	12.9343i	0.384651	−	0.928630i
$195$		0			0
$196$	6.36396	−	6.36396i	0.454569	−	0.454569i
$197$	4.59220	−	11.0866i	0.327181	−	0.789884i	−0.671619	−	0.740897i	$-0.734401\pi$
$197$	4.59220	−	11.0866i	0.327181	−	0.789884i	0.998799	−	0.0489872i	$-0.0155994\pi$
$198$	5.54328	+	2.29610i	0.393944	+	0.163177i
$199$	6.12293	+	14.7821i	0.434043	+	1.04787i	0.977971	+	0.208741i	$0.0669366\pi$
$199$	6.12293	+	14.7821i	0.434043	+	1.04787i	−0.543928	+	0.839132i	$0.683063\pi$
$200$			5.00000i			0.353553i
$201$	−14.7821	+	6.12293i	−1.04265	+	0.431879i
$202$	−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
$209$	−9.18440	−	22.1731i	−0.635298	−	1.53375i
$210$		0			0
$211$	−3.82683	+	9.23880i	−0.263450	+	0.636025i	−0.999147	−	0.0412856i	$-0.986855\pi$
$211$	−3.82683	+	9.23880i	−0.263450	+	0.636025i	0.735697	+	0.677311i	$0.236855\pi$
$212$	4.24264	−	4.24264i	0.291386	−	0.291386i
$213$		0			0
$214$	2.29610	−	5.54328i	0.156958	−	0.378931i
$215$		0			0
$216$	−1.53073	−	3.69552i	−0.104153	−	0.251448i
$217$		−	16.0000i		−	1.08615i
$218$	−14.7821	+	6.12293i	−1.00117	+	0.414697i
$219$	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	0.870673	−	0.491862i	$-0.163684\pi$
$223$	5.65685	+	5.65685i	0.378811	+	0.378811i	−0.491862	+	0.870673i	$0.663684\pi$
$224$	3.69552	−	1.53073i	0.246917	−	0.102276i
$225$		−	5.00000i		−	0.333333i
$226$	−2.29610	−	5.54328i	−0.152734	−	0.368733i
$227$	5.54328	+	2.29610i	0.367920	+	0.152398i	0.558981	−	0.829181i	$-0.311193\pi$
$227$	5.54328	+	2.29610i	0.367920	+	0.152398i	−0.191060	+	0.981578i	$0.561193\pi$
$228$	3.06147	−	7.39104i	0.202751	−	0.489483i
$229$	−9.89949	+	9.89949i	−0.654177	+	0.654177i	−0.953996	−	0.299819i	$-0.903074\pi$
$229$	−9.89949	+	9.89949i	−0.654177	+	0.654177i	0.299819	+	0.953996i	$0.403074\pi$
$230$		0			0
$231$	−18.3688	+	44.3462i	−1.20858	+	2.91777i
$232$		0			0
$233$	−6.88830	−	16.6298i	−0.451268	−	1.08946i	−0.971841	−	0.235639i	$-0.924282\pi$
$233$	−6.88830	−	16.6298i	−0.451268	−	1.08946i	0.520573	−	0.853817i	$-0.325718\pi$
$234$		−	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
$241$	9.23880	−	3.82683i	0.595123	−	0.246508i	−0.0647298	−	0.997903i	$-0.520619\pi$
$241$	9.23880	−	3.82683i	0.595123	−	0.246508i	0.659853	+	0.751395i	$0.270619\pi$
$242$			25.0000i			1.60706i
$243$	3.82683	+	9.23880i	0.245492	+	0.592669i
$244$	3.69552	+	1.53073i	0.236581	+	0.0979952i
$245$		0			0
$246$	8.48528	−	8.48528i	0.541002	−	0.541002i
$247$	−5.65685	+	5.65685i	−0.359937	+	0.359937i
$248$	1.53073	−	3.69552i	0.0972017	−	0.234666i
$249$		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	$0.726453\pi$
$252$	−3.69552	+	1.53073i	−0.232796	+	0.0964272i
$253$		0			0
$254$	16.0000			1.00393
$255$		0			0
$256$	1.00000			0.0625000
$257$	4.24264	+	4.24264i	0.264649	+	0.264649i	0.826940	−	0.562291i	$-0.190080\pi$
$257$	4.24264	+	4.24264i	0.264649	+	0.264649i	−0.562291	+	0.826940i	$0.690080\pi$
$258$	14.7821	−	6.12293i	0.920292	−	0.381197i
$259$			16.0000i			0.994192i
$260$		0			0
$261$		0			0
$262$	−2.29610	+	5.54328i	−0.141854	+	0.342465i
$263$	−16.9706	+	16.9706i	−1.04645	+	1.04645i	−0.0475824	+	0.998867i	$0.515152\pi$
$263$	−16.9706	+	16.9706i	−1.04645	+	1.04645i	−0.998867	+	0.0475824i	$0.984848\pi$
$264$	−8.48528	+	8.48528i	−0.522233	+	0.522233i
$265$		0			0
$266$	14.7821	+	6.12293i	0.906347	+	0.375421i
$267$	−4.59220	−	11.0866i	−0.281038	−	0.678486i
$268$		−	8.00000i		−	0.488678i
$269$	−22.1731	+	9.18440i	−1.35192	+	0.559983i	−0.936826	−	0.349796i	$-0.886251\pi$
$269$	−22.1731	+	9.18440i	−1.35192	+	0.559983i	−0.415093	+	0.909779i	$0.636251\pi$
$270$		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
$275$	27.7164	−	11.4805i	1.67136	−	0.692300i
$276$		0			0
$277$	3.06147	+	7.39104i	0.183946	+	0.444084i	0.988773	−	0.149425i	$-0.0477421\pi$
$277$	3.06147	+	7.39104i	0.183946	+	0.444084i	−0.804827	+	0.593509i	$0.797742\pi$
$278$	−1.84776	−	0.765367i	−0.110821	−	0.0459037i
$279$	−1.53073	+	3.69552i	−0.0916426	+	0.221245i
$280$		0			0
$281$	4.24264	−	4.24264i	0.253095	−	0.253095i	−0.569143	−	0.822238i	$-0.692725\pi$
$281$	4.24264	−	4.24264i	0.253095	−	0.253095i	0.822238	+	0.569143i	$0.192725\pi$
$282$		0			0
$283$	12.9343	+	5.35757i	0.768865	+	0.318474i	0.732413	−	0.680861i	$-0.238394\pi$
$283$	12.9343	+	5.35757i	0.768865	+	0.318474i	0.0364525	+	0.999335i	$0.488394\pi$
$284$		0			0
$285$		0			0
$286$	11.0866	−	4.59220i	0.655562	−	0.271543i
$287$	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
$292$	−1.84776	+	0.765367i	−0.108132	+	0.0447897i
$293$			6.00000i			0.350524i	0.984522	+	0.175262i	$0.0560772\pi$
$293$			6.00000i			0.350524i	−0.984522	+	0.175262i	$0.943923\pi$
$294$	−6.88830	−	16.6298i	−0.401734	−	0.969871i
$295$		0			0
$296$	−1.53073	+	3.69552i	−0.0889721	+	0.214798i
$297$	−16.9706	+	16.9706i	−0.984732	+	0.984732i
$298$	4.24264	−	4.24264i	0.245770	−	0.245770i
$299$		0			0
$300$	9.23880	+	3.82683i	0.533402	+	0.220942i
$301$	12.2459	+	29.5641i	0.705840	+	1.70405i
$302$			16.0000i			0.920697i
$303$	−33.2597	+	13.7766i	−1.91072	+	0.791445i
$304$	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
$309$	−29.5641	+	12.2459i	−1.68185	+	0.696643i
$310$		0			0
$311$	4.59220	+	11.0866i	0.260400	+	0.628661i	0.998963	−	0.0455232i	$-0.0144955\pi$
$311$	4.59220	+	11.0866i	0.260400	+	0.628661i	−0.738563	+	0.674184i	$0.764495\pi$
$312$	3.69552	+	1.53073i	0.209218	+	0.0866607i
$313$	−13.0112	+	31.4119i	−0.735439	+	1.77551i	−0.111891	+	0.993721i	$0.535691\pi$
$313$	−13.0112	+	31.4119i	−0.735439	+	1.77551i	−0.623548	+	0.781785i	$0.714309\pi$
$314$	−9.89949	+	9.89949i	−0.558661	+	0.558661i
$315$		0			0
$316$	−3.06147	+	7.39104i	−0.172221	+	0.415778i
$317$	−11.0866	−	4.59220i	−0.622683	−	0.257924i	0.0489576	−	0.998801i	$-0.484410\pi$
$317$	−11.0866	−	4.59220i	−0.622683	−	0.257924i	−0.671641	+	0.740877i	$0.734410\pi$
$318$	−4.59220	−	11.0866i	−0.257518	−	0.621703i
$319$		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
$326$	−1.84776	+	0.765367i	−0.102338	+	0.0423898i
$327$			32.0000i			1.76960i
$328$	2.29610	+	5.54328i	0.126781	+	0.306076i
$329$		0			0
$330$		0			0
$331$	11.3137	−	11.3137i	0.621858	−	0.621858i	−0.324149	−	0.946006i	$-0.605078\pi$
$331$	11.3137	−	11.3137i	0.621858	−	0.621858i	0.946006	+	0.324149i	$0.105078\pi$
$332$		0			0
$333$	1.53073	−	3.69552i	0.0838837	−	0.202513i
$334$	11.0866	+	4.59220i	0.606629	+	0.251274i
$335$		0			0
$336$		−	8.00000i		−	0.436436i
$337$	−20.3253	+	8.41904i	−1.10719	+	0.458614i	−0.859970	−	0.510345i	$-0.829518\pi$
$337$	−20.3253	+	8.41904i	−1.10719	+	0.458614i	−0.247222	+	0.968959i	$0.579518\pi$
$338$	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
$343$	7.39104	−	3.06147i	0.399078	−	0.165304i
$344$			8.00000i			0.431331i
$345$		0			0
$346$	−22.1731	−	9.18440i	−1.19203	−	0.493757i
$347$	6.88830	−	16.6298i	0.369783	−	0.892736i	−0.624002	−	0.781423i	$-0.714494\pi$
$347$	6.88830	−	16.6298i	0.369783	−	0.892736i	0.993785	−	0.111313i	$-0.0355057\pi$
$348$		0			0
$349$	18.3848	−	18.3848i	0.984115	−	0.984115i	−0.0157613	−	0.999876i	$-0.505017\pi$
$349$	18.3848	−	18.3848i	0.984115	−	0.984115i	0.999876	+	0.0157613i	$0.00501718\pi$
$350$	−7.65367	+	18.4776i	−0.409106	+	0.987669i
$351$	7.39104	+	3.06147i	0.394504	+	0.163409i
$352$	−2.29610	−	5.54328i	−0.122383	−	0.295458i
$353$		−	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	0.995050	−	0.0993777i	$-0.0316852\pi$
$359$	16.9706	+	16.9706i	0.895672	+	0.895672i	−0.0993777	+	0.995050i	$0.531685\pi$
$360$		0			0
$361$		−	3.00000i		−	0.157895i
$362$	−1.53073	−	3.69552i	−0.0804536	−	0.194232i
$363$	46.1940	+	19.1342i	2.42455	+	1.00428i
$364$	−3.06147	+	7.39104i	−0.160464	+	0.387396i
$365$		0			0
$366$	5.65685	−	5.65685i	0.295689	−	0.295689i
$367$	6.12293	−	14.7821i	0.319615	−	0.771618i	−0.679660	−	0.733528i	$-0.737873\pi$
$367$	6.12293	−	14.7821i	0.319615	−	0.771618i	0.999274	−	0.0380903i	$-0.0121275\pi$
$368$		0			0
$369$	−2.29610	−	5.54328i	−0.119530	−	0.288571i
$370$		0			0
$371$	22.1731	−	9.18440i	1.15117	−	0.476830i
$372$	−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
$379$	5.35757	+	12.9343i	0.275200	+	0.664391i	0.999690	−	0.0248939i	$-0.00792480\pi$
$379$	5.35757	+	12.9343i	0.275200	+	0.664391i	−0.724490	+	0.689285i	$0.757925\pi$
$380$		0			0
$381$	12.2459	−	29.5641i	0.627375	−	1.51462i
$382$	16.9706	−	16.9706i	0.868290	−	0.868290i
$383$	−16.9706	+	16.9706i	−0.867155	+	0.867155i	−0.992157	−	0.125001i	$-0.960106\pi$
$383$	−16.9706	+	16.9706i	−0.867155	+	0.867155i	0.125001	+	0.992157i	$0.460106\pi$
$384$	0.765367	−	1.84776i	0.0390575	−	0.0942931i
$385$		0			0
$386$	3.82683	+	9.23880i	0.194781	+	0.470242i
$387$		−	8.00000i		−	0.406663i
$388$	12.9343	−	5.35757i	0.656640	−	0.271989i
$389$	−21.2132	−	21.2132i	−1.07555	−	1.07555i	−0.996902	−	0.0786498i	$-0.974939\pi$
$389$	−21.2132	−	21.2132i	−1.07555	−	1.07555i	−0.0786498	−	0.996902i	$-0.525061\pi$
$390$		0			0
$391$		0			0
$392$	9.00000			0.454569
$393$	8.48528	+	8.48528i	0.428026	+	0.428026i
$394$	11.0866	−	4.59220i	0.558533	−	0.231352i
$395$		0			0
$396$	2.29610	+	5.54328i	0.115383	+	0.278560i
$397$	−18.4776	−	7.65367i	−0.927364	−	0.384127i	−0.132686	−	0.991158i	$-0.542360\pi$
$397$	−18.4776	−	7.65367i	−0.927364	−	0.384127i	−0.794678	+	0.607032i	$0.792360\pi$
$398$	−6.12293	+	14.7821i	−0.306915	+	0.740958i
$399$	22.6274	−	22.6274i	1.13279	−	1.13279i
$400$	−3.53553	+	3.53553i	−0.176777	+	0.176777i
$401$	−11.4805	+	27.7164i	−0.573309	+	1.38409i	0.325413	+	0.945572i	$0.394497\pi$
$401$	−11.4805	+	27.7164i	−0.573309	+	1.38409i	−0.898722	+	0.438518i	$0.855503\pi$
$402$	−14.7821	−	6.12293i	−0.737263	−	0.305384i
$403$	3.06147	+	7.39104i	0.152503	+	0.368174i
$404$		−	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
$411$	11.0866	−	4.59220i	0.546859	−	0.226517i
$412$		−	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
$418$	9.18440	−	22.1731i	0.449224	−	1.08452i
$419$	−27.7164	−	11.4805i	−1.35403	−	0.560859i	−0.416622	−	0.909080i	$-0.636786\pi$
$419$	−27.7164	−	11.4805i	−1.35403	−	0.560859i	−0.937413	+	0.348221i	$0.886786\pi$
$420$		0			0
$421$		−	2.00000i		−	0.0974740i	−0.998812	−	0.0487370i	$-0.984480\pi$
$421$		−	2.00000i		−	0.0974740i	0.998812	−	0.0487370i	$-0.0155196\pi$
$422$	−9.23880	+	3.82683i	−0.449738	+	0.186287i
$423$		0			0
$424$	6.00000			0.291386
$425$		0			0
$426$		0			0
$427$	11.3137	+	11.3137i	0.547509	+	0.547509i
$428$	5.54328	−	2.29610i	0.267944	−	0.110986i
$429$		−	24.0000i		−	1.15873i
$430$		0			0
$431$	−22.1731	−	9.18440i	−1.06804	−	0.442397i	−0.221742	−	0.975105i	$-0.571174\pi$
$431$	−22.1731	−	9.18440i	−1.06804	−	0.442397i	−0.846299	+	0.532708i	$0.821174\pi$
$432$	1.53073	−	3.69552i	0.0736475	−	0.177801i
$433$	−1.41421	+	1.41421i	−0.0679628	+	0.0679628i	−0.740271	−	0.672308i	$-0.765303\pi$
$433$	−1.41421	+	1.41421i	−0.0679628	+	0.0679628i	0.672308	+	0.740271i	$0.265303\pi$
$434$	11.3137	−	11.3137i	0.543075	−	0.543075i
$435$		0			0
$436$	−14.7821	−	6.12293i	−0.707933	−	0.293235i
$437$		0			0
$438$			4.00000i			0.191127i
$439$	7.39104	−	3.06147i	0.352755	−	0.146116i	−0.199268	−	0.979945i	$-0.563856\pi$
$439$	7.39104	−	3.06147i	0.352755	−	0.146116i	0.552022	+	0.833829i	$0.313856\pi$
$440$		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
$447$	−4.59220	−	11.0866i	−0.217204	−	0.524376i
$448$	3.69552	+	1.53073i	0.174597	+	0.0723204i
$449$	−6.88830	+	16.6298i	−0.325079	+	0.784810i	0.673864	+	0.738855i	$0.264633\pi$
$449$	−6.88830	+	16.6298i	−0.325079	+	0.784810i	−0.998943	+	0.0459553i	$0.985367\pi$
$450$	3.53553	−	3.53553i	0.166667	−	0.166667i
$451$	25.4558	−	25.4558i	1.19867	−	1.19867i
$452$	2.29610	−	5.54328i	0.107999	−	0.260734i
$453$	29.5641	+	12.2459i	1.38904	+	0.575361i
$454$	2.29610	+	5.54328i	0.107761	+	0.260159i
$455$		0			0
$456$	7.39104	−	3.06147i	0.346117	−	0.143366i
$457$	−18.3848	−	18.3848i	−0.860004	−	0.860004i	0.131335	−	0.991338i	$-0.458074\pi$
$457$	−18.3848	−	18.3848i	−0.860004	−	0.860004i	−0.991338	+	0.131335i	$0.958074\pi$
$458$	−14.0000			−0.654177
$459$		0			0
$460$		0			0
$461$	−4.24264	−	4.24264i	−0.197599	−	0.197599i	0.601371	−	0.798970i	$-0.294622\pi$
$461$	−4.24264	−	4.24264i	−0.197599	−	0.197599i	−0.798970	+	0.601371i	$0.794622\pi$
$462$	−44.3462	+	18.3688i	−2.06317	+	0.854594i
$463$		−	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
$466$	6.88830	−	16.6298i	0.319094	−	0.770362i
$467$	−8.48528	+	8.48528i	−0.392652	+	0.392652i	−0.875632	−	0.482980i	$-0.839555\pi$
$467$	−8.48528	+	8.48528i	−0.392652	+	0.392652i	0.482980	+	0.875632i	$0.339555\pi$
$468$	1.41421	−	1.41421i	0.0653720	−	0.0653720i
$469$	12.2459	−	29.5641i	0.565462	−	1.36515i
$470$		0			0
$471$	10.7151	+	25.8686i	0.493727	+	1.19196i
$472$		0			0
$473$	44.3462	−	18.3688i	2.03904	−	0.844599i
$474$	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
$479$	−22.1731	+	9.18440i	−1.01312	+	0.419646i	−0.826590	−	0.562804i	$-0.809723\pi$
$479$	−22.1731	+	9.18440i	−1.01312	+	0.419646i	−0.186525	+	0.982450i	$0.559723\pi$
$480$		0			0
$481$	−3.06147	−	7.39104i	−0.139591	−	0.337002i
$482$	9.23880	+	3.82683i	0.420816	+	0.174308i
$483$		0			0
$484$	−17.6777	+	17.6777i	−0.803530	+	0.803530i
$485$		0			0
$486$	−3.82683	+	9.23880i	−0.173589	+	0.419080i
$487$	7.39104	+	3.06147i	0.334920	+	0.138728i	0.543804	−	0.839212i	$-0.316983\pi$
$487$	7.39104	+	3.06147i	0.334920	+	0.138728i	−0.208885	+	0.977940i	$0.566983\pi$
$488$	1.53073	+	3.69552i	0.0692931	+	0.167288i
$489$			4.00000i			0.180886i
$490$		0			0
$491$	8.48528	+	8.48528i	0.382935	+	0.382935i	0.872159	−	0.489223i	$-0.162720\pi$
$491$	8.48528	+	8.48528i	0.382935	+	0.382935i	−0.489223	+	0.872159i	$0.662720\pi$
$492$	12.0000			0.541002
$493$		0			0
$494$	−8.00000			−0.359937
$495$		0			0
$496$	3.69552	−	1.53073i	0.165934	−	0.0687320i
$497$		0			0
$498$		0			0
$499$	−12.9343	−	5.35757i	−0.579019	−	0.239838i	0.0738993	−	0.997266i	$-0.476456\pi$
$499$	−12.9343	−	5.35757i	−0.579019	−	0.239838i	−0.652919	+	0.757428i	$0.726456\pi$
$500$		0			0
$501$	16.9706	−	16.9706i	0.758189	−	0.758189i
$502$	−16.9706	+	16.9706i	−0.757433	+	0.757433i
$503$	9.18440	−	22.1731i	0.409512	−	0.988650i	−0.575754	−	0.817623i	$-0.695291\pi$
$503$	9.18440	−	22.1731i	0.409512	−	0.988650i	0.985266	−	0.171027i	$-0.0547086\pi$
$504$	−3.69552	−	1.53073i	−0.164611	−	0.0681843i
$505$		0			0
$506$		0			0
$507$	16.6298	−	6.88830i	0.738557	−	0.305920i
$508$	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
$513$	14.7821	−	6.12293i	0.652644	−	0.270334i
$514$			6.00000i			0.264649i
$515$		0			0
$516$	14.7821	+	6.12293i	0.650744	+	0.269547i
$517$		0			0
$518$	−11.3137	+	11.3137i	−0.497096	+	0.497096i
$519$	−33.9411	+	33.9411i	−1.48985	+	1.48985i
$520$		0			0
$521$	−16.6298	−	6.88830i	−0.728566	−	0.301782i	−0.0126035	−	0.999921i	$-0.504012\pi$
$521$	−16.6298	−	6.88830i	−0.728566	−	0.301782i	−0.715963	+	0.698139i	$0.754012\pi$
$522$		0			0
$523$			16.0000i			0.699631i	0.936819	+	0.349816i	$0.113756\pi$
$523$			16.0000i			0.699631i	−0.936819	+	0.349816i	$0.886244\pi$
$524$	−5.54328	+	2.29610i	−0.242159	+	0.100306i
$525$	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
$532$	6.12293	+	14.7821i	0.265463	+	0.640884i
$533$	−11.0866	−	4.59220i	−0.480212	−	0.198910i
$534$	4.59220	−	11.0866i	0.198724	−	0.479762i
$535$		0			0
$536$	5.65685	−	5.65685i	0.244339	−	0.244339i
$537$	9.18440	−	22.1731i	0.396336	−	0.956840i
$538$	−22.1731	−	9.18440i	−0.955951	−	0.395968i
$539$	−20.6649	−	49.8895i	−0.890100	−	2.14889i
$540$		0			0
$541$	18.4776	−	7.65367i	0.794414	−	0.329057i	0.0516971	−	0.998663i	$-0.483537\pi$
$541$	18.4776	−	7.65367i	0.794414	−	0.329057i	0.742717	+	0.669606i	$0.233537\pi$
$542$	−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
$547$	−1.84776	+	0.765367i	−0.0790045	+	0.0327247i	−0.421836	−	0.906672i	$-0.638614\pi$
$547$	−1.84776	+	0.765367i	−0.0790045	+	0.0327247i	0.342831	+	0.939397i	$0.388614\pi$
$548$			6.00000i			0.256307i
$549$	−1.53073	−	3.69552i	−0.0653301	−	0.157721i
$550$	27.7164	+	11.4805i	1.18183	+	0.489530i
$551$		0			0
$552$		0			0
$553$	−22.6274	+	22.6274i	−0.962216	+	0.962216i
$554$	−3.06147	+	7.39104i	−0.130069	+	0.314015i
$555$		0			0
$556$	−0.765367	−	1.84776i	−0.0324588	−	0.0783624i
$557$			30.0000i			1.27114i	0.772043	+	0.635570i	$0.219235\pi$
$557$			30.0000i			1.27114i	−0.772043	+	0.635570i	$0.780765\pi$
$558$	−3.69552	+	1.53073i	−0.156444	+	0.0648011i
$559$	−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	0.252399	−	0.967623i	$-0.418780\pi$
$563$	−16.9706	−	16.9706i	−0.715224	−	0.715224i	−0.967623	+	0.252399i	$0.918780\pi$
$564$		0			0
$565$		0			0
$566$	5.35757	+	12.9343i	0.225195	+	0.543670i
$567$	−40.6507	−	16.8381i	−1.70717	−	0.707133i
$568$		0			0
$569$	21.2132	−	21.2132i	0.889304	−	0.889304i	−0.105152	−	0.994456i	$-0.533533\pi$
$569$	21.2132	−	21.2132i	0.889304	−	0.889304i	0.994456	+	0.105152i	$0.0335330\pi$
$570$		0			0
$571$	−9.94977	+	24.0209i	−0.416385	+	1.00524i	0.567001	+	0.823717i	$0.308103\pi$
$571$	−9.94977	+	24.0209i	−0.416385	+	1.00524i	−0.983386	+	0.181525i	$0.941897\pi$
$572$	11.0866	+	4.59220i	0.463552	+	0.192010i
$573$	−18.3688	−	44.3462i	−0.767368	−	1.85259i
$574$			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
$583$	−13.7766	−	33.2597i	−0.570569	−	1.37747i
$584$	−1.84776	−	0.765367i	−0.0764608	−	0.0316711i
$585$		0			0
$586$	−4.24264	+	4.24264i	−0.175262	+	0.175262i
$587$	8.48528	−	8.48528i	0.350225	−	0.350225i	−0.509968	−	0.860193i	$-0.670343\pi$
$587$	8.48528	−	8.48528i	0.350225	−	0.350225i	0.860193	+	0.509968i	$0.170343\pi$
$588$	6.88830	−	16.6298i	0.284069	−	0.685803i
$589$	14.7821	+	6.12293i	0.609085	+	0.252291i
$590$		0			0
$591$		−	24.0000i		−	0.987228i
$592$	−3.69552	+	1.53073i	−0.151885	+	0.0629128i
$593$	21.2132	+	21.2132i	0.871122	+	0.871122i	0.992595	−	0.121473i	$-0.0387618\pi$
$593$	21.2132	+	21.2132i	0.871122	+	0.871122i	−0.121473	+	0.992595i	$0.538762\pi$
$594$	−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	$-0.163115\pi$
$600$	3.82683	+	9.23880i	0.156230	+	0.377172i
$601$	42.4985	+	17.6034i	1.73355	+	0.718059i	0.999229	+	0.0392547i	$0.0124984\pi$
$601$	42.4985	+	17.6034i	1.73355	+	0.718059i	0.734319	+	0.678804i	$0.237502\pi$
$602$	−12.2459	+	29.5641i	−0.499104	+	1.20494i
$603$	−5.65685	+	5.65685i	−0.230365	+	0.230365i
$604$	−11.3137	+	11.3137i	−0.460348	+	0.460348i
$605$		0			0
$606$	−33.2597	−	13.7766i	−1.35108	−	0.559636i
$607$	−7.65367	−	18.4776i	−0.310653	−	0.749982i	−0.999681	−	0.0252479i	$-0.991962\pi$
$607$	−7.65367	−	18.4776i	−0.310653	−	0.749982i	0.689028	−	0.724734i	$-0.258038\pi$
$608$			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
$617$	−11.4805	−	27.7164i	−0.462188	−	1.11582i	−0.967497	−	0.252882i	$-0.918622\pi$
$617$	−11.4805	−	27.7164i	−0.462188	−	1.11582i	0.505310	−	0.862938i	$-0.331378\pi$
$618$	−29.5641	−	12.2459i	−1.18924	−	0.492601i
$619$	9.94977	−	24.0209i	0.399915	−	0.965480i	−0.587770	−	0.809028i	$-0.699994\pi$
$619$	9.94977	−	24.0209i	0.399915	−	0.965480i	0.987685	−	0.156452i	$-0.0500058\pi$
$620$		0			0
$621$		0			0
$622$	−4.59220	+	11.0866i	−0.184130	+	0.444530i
$623$	22.1731	+	9.18440i	0.888347	+	0.367965i
$624$	1.53073	+	3.69552i	0.0612784	+	0.147939i
$625$		−	25.0000i		−	1.00000i
$626$	−31.4119	+	13.0112i	−1.25547	+	0.520034i
$627$	−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	0.810682	−	0.585486i	$-0.199096\pi$
$631$	5.65685	+	5.65685i	0.225196	+	0.225196i	−0.585486	+	0.810682i	$0.699096\pi$
$632$	−7.39104	+	3.06147i	−0.294000	+	0.121779i
$633$			20.0000i			0.794929i
$634$	−4.59220	−	11.0866i	−0.182380	−	0.440303i
$635$		0			0
$636$	4.59220	−	11.0866i	0.182093	−	0.439610i
$637$	−12.7279	+	12.7279i	−0.504299	+	0.504299i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	6.88830	+	16.6298i	0.272072	+	0.656839i	0.999572	−	0.0292688i	$-0.00931788\pi$
$641$	6.88830	+	16.6298i	0.272072	+	0.656839i	−0.727500	+	0.686108i	$0.759318\pi$
$642$		−	12.0000i		−	0.473602i
$643$	12.9343	−	5.35757i	0.510080	−	0.211282i	−0.112774	−	0.993621i	$-0.535973\pi$
$643$	12.9343	−	5.35757i	0.510080	−	0.211282i	0.622853	+	0.782339i	$0.285973\pi$
$644$		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
$651$	−12.2459	−	29.5641i	−0.479953	−	1.15871i
$652$	−1.84776	−	0.765367i	−0.0723638	−	0.0299741i
$653$	9.18440	−	22.1731i	0.359413	−	0.867701i	−0.635969	−	0.771714i	$-0.719399\pi$
$653$	9.18440	−	22.1731i	0.359413	−	0.867701i	0.995383	−	0.0959864i	$-0.0306005\pi$
$654$	−22.6274	+	22.6274i	−0.884802	+	0.884802i
$655$		0			0
$656$	−2.29610	+	5.54328i	−0.0896477	+	0.216429i
$657$	1.84776	+	0.765367i	0.0720879	+	0.0298598i
$658$		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	$0.102537\pi$
$661$	32.5269	+	32.5269i	1.26515	+	1.26515i	0.316587	+	0.948564i	$0.397463\pi$
$662$	16.0000			0.621858
$663$		0			0
$664$		0			0
$665$		0			0
$666$	3.69552	−	1.53073i	0.143198	−	0.0593147i
$667$		0			0
$668$	4.59220	+	11.0866i	0.177678	+	0.428952i
$669$	14.7821	+	6.12293i	0.571508	+	0.236726i
$670$		0			0
$671$	16.9706	−	16.9706i	0.655141	−	0.655141i
$672$	5.65685	−	5.65685i	0.218218	−	0.218218i
$673$	−14.5420	+	35.1074i	−0.560552	+	1.35329i	0.348774	+	0.937207i	$0.386598\pi$
$673$	−14.5420	+	35.1074i	−0.560552	+	1.35329i	−0.909326	+	0.416085i	$0.863402\pi$
$674$	−20.3253	−	8.41904i	−0.782903	−	0.324289i
$675$	7.65367	+	18.4776i	0.294590	+	0.711203i
$676$			9.00000i			0.346154i
$677$	−11.0866	+	4.59220i	−0.426091	+	0.176493i	−0.585415	−	0.810734i	$-0.699068\pi$
$677$	−11.0866	+	4.59220i	−0.426091	+	0.176493i	0.159324	+	0.987226i	$0.449068\pi$
$678$	−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
$683$	−27.7164	+	11.4805i	−1.06054	+	0.439289i	−0.843642	−	0.536906i	$-0.819593\pi$
$683$	−27.7164	+	11.4805i	−1.06054	+	0.439289i	−0.216896	+	0.976195i	$0.569593\pi$
$684$		−	4.00000i		−	0.152944i
$685$		0			0
$686$	7.39104	+	3.06147i	0.282191	+	0.116887i
$687$	−10.7151	+	25.8686i	−0.408808	+	0.986950i
$688$	−5.65685	+	5.65685i	−0.215666	+	0.215666i
$689$	−8.48528	+	8.48528i	−0.323263	+	0.323263i
$690$		0			0
$691$	−9.23880	−	3.82683i	−0.351460	−	0.145580i	0.199967	−	0.979803i	$-0.435917\pi$
$691$	−9.23880	−	3.82683i	−0.351460	−	0.145580i	−0.551427	+	0.834223i	$0.685917\pi$
$692$	−9.18440	−	22.1731i	−0.349139	−	0.842895i
$693$			24.0000i			0.911685i
$694$	16.6298	−	6.88830i	0.631260	−	0.261476i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	26.0000			0.984115
$699$	−25.4558	−	25.4558i	−0.962828	−	0.962828i
$700$	−18.4776	+	7.65367i	−0.698387	+	0.289281i
$701$			18.0000i			0.679851i	0.940452	+	0.339925i	$0.110402\pi$
$701$			18.0000i			0.679851i	−0.940452	+	0.339925i	$0.889598\pi$
$702$	3.06147	+	7.39104i	0.115548	+	0.278957i
$703$	−14.7821	−	6.12293i	−0.557516	−	0.230931i
$704$	2.29610	−	5.54328i	0.0865375	−	0.208920i
$705$		0			0
$706$	4.24264	−	4.24264i	0.159674	−	0.159674i
$707$	27.5532	−	66.5193i	1.03625	−	2.50172i
$708$		0			0
$709$	6.12293	+	14.7821i	0.229952	+	0.555152i	0.996171	−	0.0874268i	$-0.0278644\pi$
$709$	6.12293	+	14.7821i	0.229952	+	0.555152i	−0.766219	+	0.642579i	$0.777864\pi$
$710$		0			0
$711$	7.39104	−	3.06147i	0.277186	−	0.114814i
$712$	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
$717$	44.3462	−	18.3688i	1.65614	−	0.685996i
$718$			24.0000i			0.895672i
$719$	18.3688	+	44.3462i	0.685041	+	1.65383i	0.754541	+	0.656253i	$0.227860\pi$
$719$	18.3688	+	44.3462i	0.685041	+	1.65383i	−0.0695002	+	0.997582i	$0.522140\pi$
$720$		0			0
$721$	24.4917	−	59.1283i	0.912120	−	2.20205i
$722$	2.12132	−	2.12132i	0.0789474	−	0.0789474i
$723$	14.1421	−	14.1421i	0.525952	−	0.525952i
$724$	1.53073	−	3.69552i	0.0568893	−	0.137343i
$725$		0			0
$726$	19.1342	+	46.1940i	0.710136	+	1.71442i
$727$		−	8.00000i		−	0.296704i	−0.988935	−	0.148352i	$-0.952603\pi$
$727$		−	8.00000i		−	0.296704i	0.988935	−	0.148352i	$-0.0473968\pi$
$728$	−7.39104	+	3.06147i	−0.273930	+	0.113466i
$729$	−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	0.358820	−	0.933407i	$-0.383179\pi$
$733$	−15.5563	−	15.5563i	−0.574587	−	0.574587i	−0.933407	+	0.358820i	$0.883179\pi$
$734$	14.7821	−	6.12293i	0.545616	−	0.226002i
$735$		0			0
$736$		0			0
$737$	−44.3462	−	18.3688i	−1.63351	−	0.676624i
$738$	2.29610	−	5.54328i	0.0845206	−	0.204051i
$739$	−14.1421	+	14.1421i	−0.520227	+	0.520227i	−0.917640	−	0.397413i	$-0.869908\pi$
$739$	−14.1421	+	14.1421i	−0.520227	+	0.520227i	0.397413	+	0.917640i	$0.369908\pi$
$740$		0			0
$741$	−6.12293	+	14.7821i	−0.224932	+	0.543033i
$742$	22.1731	+	9.18440i	0.814000	+	0.337170i
$743$	13.7766	+	33.2597i	0.505415	+	1.22018i	0.946497	+	0.322712i	$0.104595\pi$
$743$	13.7766	+	33.2597i	0.505415	+	1.22018i	−0.441083	+	0.897467i	$0.645405\pi$
$744$		−	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
$751$	−7.39104	+	3.06147i	−0.269703	+	0.111715i	−0.513436	−	0.858128i	$-0.671628\pi$
$751$	−7.39104	+	3.06147i	−0.269703	+	0.111715i	0.243734	+	0.969842i	$0.421628\pi$
$752$		0			0
$753$	18.3688	+	44.3462i	0.669396	+	1.61607i
$754$		0			0
$755$		0			0
$756$	11.3137	−	11.3137i	0.411476	−	0.411476i
$757$	−7.07107	+	7.07107i	−0.257002	+	0.257002i	−0.823834	−	0.566831i	$-0.808169\pi$
$757$	−7.07107	+	7.07107i	−0.257002	+	0.257002i	0.566831	+	0.823834i	$0.308169\pi$
$758$	−5.35757	+	12.9343i	−0.194596	+	0.469795i
$759$		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	$-0.0346848\pi$
$762$	29.5641	−	12.2459i	1.07100	−	0.443621i
$763$	−45.2548	−	45.2548i	−1.63833	−	1.63833i
$764$	24.0000			0.868290
$765$		0			0
$766$	−24.0000			−0.867155
$767$		0			0
$768$	1.84776	−	0.765367i	0.0666753	−	0.0276178i
$769$			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
$771$	11.0866	+	4.59220i	0.399273	+	0.165384i
$772$	−3.82683	+	9.23880i	−0.137731	+	0.332512i
$773$	29.6985	−	29.6985i	1.06818	−	1.06818i	0.0706813	−	0.997499i	$-0.477483\pi$
$773$	29.6985	−	29.6985i	1.06818	−	1.06818i	0.997499	−	0.0706813i	$-0.0225173\pi$
$774$	5.65685	−	5.65685i	0.203331	−	0.203331i
$775$	−7.65367	+	18.4776i	−0.274928	+	0.663735i
$776$	12.9343	+	5.35757i	0.464315	+	0.192325i
$777$	12.2459	+	29.5641i	0.439318	+	1.06061i
$778$		−	30.0000i		−	1.07555i
$779$	−22.1731	+	9.18440i	−0.794434	+	0.329065i
$780$		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
$787$	−17.6034	−	42.4985i	−0.627495	−	1.51491i	−0.842726	−	0.538343i	$-0.819050\pi$
$787$	−17.6034	−	42.4985i	−0.627495	−	1.51491i	0.215231	−	0.976563i	$-0.430950\pi$
$788$	11.0866	+	4.59220i	0.394942	+	0.163590i
$789$	−18.3688	+	44.3462i	−0.653947	+	1.57877i
$790$		0			0
$791$	16.9706	−	16.9706i	0.603404	−	0.603404i
$792$	−2.29610	+	5.54328i	−0.0815884	+	0.196972i
$793$	−7.39104	−	3.06147i	−0.262463	−	0.108716i
$794$	−7.65367	−	18.4776i	−0.271619	−	0.655745i
$795$		0			0
$796$	−14.7821	+	6.12293i	−0.523937	+	0.217022i
$797$	−29.6985	−	29.6985i	−1.05197	−	1.05197i	−0.998573	−	0.0534012i	$-0.982994\pi$
$797$	−29.6985	−	29.6985i	−1.05197	−	1.05197i	−0.0534012	−	0.998573i	$-0.517006\pi$
$798$	32.0000			1.13279
$799$		0			0
$800$	−5.00000			−0.176777
$801$	−4.24264	−	4.24264i	−0.149906	−	0.149906i
$802$	−27.7164	+	11.4805i	−0.978700	+	0.405391i
$803$			12.0000i			0.423471i
$804$	−6.12293	−	14.7821i	−0.215939	−	0.521324i
$805$		0			0
$806$	−3.06147	+	7.39104i	−0.107836	+	0.260338i
$807$	−33.9411	+	33.9411i	−1.19478	+	1.19478i
$808$	12.7279	−	12.7279i	0.447767	−	0.447767i
$809$	−11.4805	+	27.7164i	−0.403633	+	0.974456i	0.583143	+	0.812369i	$0.301823\pi$
$809$	−11.4805	+	27.7164i	−0.403633	+	0.974456i	−0.986776	+	0.162087i	$0.948177\pi$
$810$		0			0
$811$	−14.5420	−	35.1074i	−0.510638	−	1.23279i	−0.943513	−	0.331335i	$-0.892501\pi$
$811$	−14.5420	−	35.1074i	−0.510638	−	1.23279i	0.432876	−	0.901454i	$-0.357499\pi$
$812$		0			0
$813$	−14.7821	+	6.12293i	−0.518430	+	0.214741i
$814$	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
$819$	7.39104	−	3.06147i	0.258264	−	0.106976i
$820$		0			0
$821$	13.7766	+	33.2597i	0.480807	+	1.16077i	0.959226	+	0.282639i	$0.0912098\pi$
$821$	13.7766	+	33.2597i	0.480807	+	1.16077i	−0.478420	+	0.878131i	$0.658790\pi$
$822$	11.0866	+	4.59220i	0.386688	+	0.160171i
$823$	−6.12293	+	14.7821i	−0.213432	+	0.515271i	−0.993946	−	0.109867i	$-0.964957\pi$
$823$	−6.12293	+	14.7821i	−0.213432	+	0.515271i	0.780514	+	0.625138i	$0.214957\pi$
$824$	11.3137	−	11.3137i	0.394132	−	0.394132i
$825$	42.4264	−	42.4264i	1.47710	−	1.47710i
$826$		0			0
$827$	5.54328	+	2.29610i	0.192759	+	0.0798432i	0.476975	−	0.878917i	$-0.341733\pi$
$827$	5.54328	+	2.29610i	0.192759	+	0.0798432i	−0.284216	+	0.958760i	$0.591733\pi$
$828$		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
$836$	22.1731	−	9.18440i	0.766873	−	0.317649i
$837$		−	16.0000i		−	0.553041i
$838$	−11.4805	−	27.7164i	−0.396587	−	0.957447i
$839$	33.2597	+	13.7766i	1.14825	+	0.475621i	0.873947	−	0.486022i	$-0.161552\pi$
$839$	33.2597	+	13.7766i	1.14825	+	0.475621i	0.274304	+	0.961643i	$0.411552\pi$
$840$		0			0
$841$	20.5061	−	20.5061i	0.707107	−	0.707107i
$842$	1.41421	−	1.41421i	0.0487370	−	0.0487370i
$843$	4.59220	−	11.0866i	0.158164	−	0.381841i
$844$	−9.23880	−	3.82683i	−0.318012	−	0.131725i
$845$		0			0
$846$		0			0
$847$	−92.3880	+	38.2683i	−3.17449	+	1.31492i
$848$	4.24264	+	4.24264i	0.145693	+	0.145693i
$849$	28.0000			0.960958
$850$		0			0
$851$		0			0
$852$		0			0
$853$	36.9552	−	15.3073i	1.26532	−	0.524113i	0.353783	−	0.935328i	$-0.384895\pi$
$853$	36.9552	−	15.3073i	1.26532	−	0.524113i	0.911539	+	0.411214i	$0.134895\pi$
$854$			16.0000i			0.547509i
$855$		0			0
$856$	5.54328	+	2.29610i	0.189465	+	0.0784791i
$857$	−6.88830	+	16.6298i	−0.235300	+	0.568064i	−0.996785	−	0.0801177i	$-0.974470\pi$
$857$	−6.88830	+	16.6298i	−0.235300	+	0.568064i	0.761486	+	0.648182i	$0.224470\pi$
$858$	16.9706	−	16.9706i	0.579365	−	0.579365i
$859$	−11.3137	+	11.3137i	−0.386019	+	0.386019i	−0.873265	−	0.487246i	$-0.838002\pi$
$859$	−11.3137	+	11.3137i	−0.386019	+	0.386019i	0.487246	+	0.873265i	$0.338002\pi$
$860$		0			0
$861$	44.3462	+	18.3688i	1.51132	+	0.626007i
$862$	−9.18440	−	22.1731i	−0.312822	−	0.755219i
$863$		−	48.0000i		−	1.63394i	−0.576681	−	0.816970i	$-0.695652\pi$
$863$		−	48.0000i		−	1.63394i	0.576681	−	0.816970i	$-0.304348\pi$
$864$	3.69552	−	1.53073i	0.125724	−	0.0520766i
$865$		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
$872$	−6.12293	−	14.7821i	−0.207349	−	0.500584i
$873$	−12.9343	−	5.35757i	−0.437760	−	0.181326i
$874$		0			0
$875$		0			0
$876$	−2.82843	+	2.82843i	−0.0955637	+	0.0955637i
$877$	−12.2459	+	29.5641i	−0.413514	+	0.998310i	0.570673	+	0.821177i	$0.306682\pi$
$877$	−12.2459	+	29.5641i	−0.413514	+	0.998310i	−0.984187	+	0.177133i	$0.943318\pi$
$878$	7.39104	+	3.06147i	0.249435	+	0.103320i
$879$	4.59220	+	11.0866i	0.154891	+	0.373940i
$880$		0			0
$881$	16.6298	−	6.88830i	0.560273	−	0.232073i	−0.0845306	−	0.996421i	$-0.526939\pi$
$881$	16.6298	−	6.88830i	0.560273	−	0.232073i	0.644804	+	0.764348i	$0.276939\pi$
$882$	−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
$887$	−22.1731	+	9.18440i	−0.744500	+	0.308382i	−0.722495	−	0.691376i	$-0.757005\pi$
$887$	−22.1731	+	9.18440i	−0.744500	+	0.308382i	−0.0220048	+	0.999758i	$0.507005\pi$
$888$			8.00000i			0.268462i
$889$	24.4917	+	59.1283i	0.821427	+	1.98310i
$890$		0			0
$891$	−25.2571	+	60.9760i	−0.846145	+	2.04277i
$892$	−5.65685	+	5.65685i	−0.189405	+	0.189405i
$893$		0			0
$894$	4.59220	−	11.0866i	0.153586	−	0.370790i
$895$		0			0
$896$	1.53073	+	3.69552i	0.0511382	+	0.123459i
$897$		0			0
$898$	−16.6298	+	6.88830i	−0.554945	+	0.229866i
$899$		0			0
$900$	5.00000			0.166667
$901$		0			0
$902$	36.0000			1.19867
$903$	45.2548	+	45.2548i	1.50599	+	1.50599i
$904$	5.54328	−	2.29610i	0.184367	−	0.0763672i
$905$		0			0
$906$	12.2459	+	29.5641i	0.406842	+	0.982203i
$907$	53.5850	+	22.1956i	1.77926	+	0.736994i	0.992861	+	0.119277i	$0.0380575\pi$
$907$	53.5850	+	22.1956i	1.77926	+	0.736994i	0.786400	+	0.617717i	$0.211942\pi$
$908$	−2.29610	+	5.54328i	−0.0761988	+	0.183960i
$909$	−12.7279	+	12.7279i	−0.422159	+	0.422159i
$910$		0			0
$911$	−4.59220	+	11.0866i	−0.152146	+	0.367314i	−0.981514	−	0.191389i	$-0.938701\pi$
$911$	−4.59220	+	11.0866i	−0.152146	+	0.367314i	0.829368	+	0.558703i	$0.188701\pi$
$912$	7.39104	+	3.06147i	0.244742	+	0.101375i
$913$		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
$921$	36.9552	−	15.3073i	1.21771	−	0.504394i
$922$		−	6.00000i		−	0.197599i
$923$		0			0
$924$	−44.3462	−	18.3688i	−1.45888	−	0.604289i
$925$	7.65367	−	18.4776i	0.251651	−	0.607539i
$926$	11.3137	−	11.3137i	0.371792	−	0.371792i
$927$	−11.3137	+	11.3137i	−0.371591	+	0.371591i
$928$		0			0
$929$	−16.6298	−	6.88830i	−0.545607	−	0.225998i	0.0928163	−	0.995683i	$-0.470413\pi$
$929$	−16.6298	−	6.88830i	−0.545607	−	0.225998i	−0.638423	+	0.769685i	$0.720413\pi$
$930$		0			0
$931$			36.0000i			1.17985i
$932$	16.6298	−	6.88830i	0.544728	−	0.225634i
$933$	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	$-0.853712\pi$
$937$	−41.0122	−	41.0122i	−1.33981	−	1.33981i	−0.443570	−	0.896240i	$-0.646288\pi$
$938$	29.5641	−	12.2459i	0.965304	−	0.399842i
$939$			68.0000i			2.21910i
$940$		0			0
$941$	33.2597	+	13.7766i	1.08423	+	0.449104i	0.851993	−	0.523554i	$-0.175394\pi$
$941$	33.2597	+	13.7766i	1.08423	+	0.449104i	0.232241	+	0.972658i	$0.425394\pi$
$942$	−10.7151	+	25.8686i	−0.349118	+	0.842845i
$943$		0			0
$944$		0			0
$945$		0			0
$946$	44.3462	+	18.3688i	1.44182	+	0.597221i
$947$	−6.88830	−	16.6298i	−0.223840	−	0.540397i	0.771565	−	0.636150i	$-0.219474\pi$
$947$	−6.88830	−	16.6298i	−0.223840	−	0.540397i	−0.995405	+	0.0957531i	$0.969474\pi$
$948$			16.0000i			0.519656i
$949$	3.69552	−	1.53073i	0.119962	−	0.0496897i
$950$	−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
$958$	−22.1731	−	9.18440i	−0.716381	−	0.296735i
$959$	−9.18440	+	22.1731i	−0.296580	+	0.716007i
$960$		0			0
$961$	−10.6066	+	10.6066i	−0.342148	+	0.342148i
$962$	3.06147	−	7.39104i	0.0987057	−	0.238297i
$963$	−5.54328	−	2.29610i	−0.178630	−	0.0739908i
$964$	3.82683	+	9.23880i	0.123254	+	0.297562i
$965$		0			0
$966$		0			0
$967$	28.2843	+	28.2843i	0.909561	+	0.909561i	0.996237	−	0.0866757i	$-0.0276244\pi$
$967$	28.2843	+	28.2843i	0.909561	+	0.909561i	−0.0866757	+	0.996237i	$0.527624\pi$
$968$	−25.0000			−0.803530
$969$		0			0
$970$		0			0
$971$	−16.9706	−	16.9706i	−0.544611	−	0.544611i	0.380266	−	0.924877i	$-0.375832\pi$
$971$	−16.9706	−	16.9706i	−0.544611	−	0.544611i	−0.924877	+	0.380266i	$0.875832\pi$
$972$	−9.23880	+	3.82683i	−0.296334	+	0.122746i
$973$		−	8.00000i		−	0.256468i
$974$	3.06147	+	7.39104i	0.0980957	+	0.236824i
$975$	−18.4776	−	7.65367i	−0.591756	−	0.245114i
$976$	−1.53073	+	3.69552i	−0.0489976	+	0.118291i
$977$	−29.6985	+	29.6985i	−0.950139	+	0.950139i	−0.998815	−	0.0486759i	$-0.984500\pi$
$977$	−29.6985	+	29.6985i	−0.950139	+	0.950139i	0.0486759	+	0.998815i	$0.484500\pi$
$978$	−2.82843	+	2.82843i	−0.0904431	+	0.0904431i
$979$	13.7766	−	33.2597i	0.440302	−	1.06298i
$980$		0			0
$981$	6.12293	+	14.7821i	0.195490	+	0.471955i
$982$			12.0000i			0.382935i
$983$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$983$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$984$	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
$991$	−6.12293	−	14.7821i	−0.194501	−	0.469568i	0.796298	−	0.604904i	$-0.206789\pi$
$991$	−6.12293	−	14.7821i	−0.194501	−	0.469568i	−0.990800	+	0.135336i	$0.956789\pi$
$992$	3.69552	+	1.53073i	0.117333	+	0.0486008i
$993$	12.2459	−	29.5641i	0.388611	−	0.938190i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−25.8686	−	10.7151i	−0.819268	−	0.339352i	−0.0666226	−	0.997778i	$-0.521222\pi$
$997$	−25.8686	−	10.7151i	−0.819268	−	0.339352i	−0.752645	+	0.658426i	$0.771222\pi$
$998$	−5.35757	−	12.9343i	−0.169591	−	0.409429i
$999$			16.0000i			0.506218i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	578.2.d.e.155.2		8
17.2	even	8	inner	578.2.d.e.399.2		8
17.3	odd	16		578.2.a.a.1.1		1
17.4	even	4	inner	578.2.d.e.423.1		8
17.5	odd	16		578.2.b.a.577.2		2
17.6	odd	16		578.2.c.e.327.2		4
17.7	odd	16		578.2.c.e.251.1		4
17.8	even	8	inner	578.2.d.e.179.1		8
17.9	even	8	inner	578.2.d.e.179.2		8
17.10	odd	16		578.2.c.e.251.2		4
17.11	odd	16		578.2.c.e.327.1		4
17.12	odd	16		578.2.b.a.577.1		2
17.13	even	4	inner	578.2.d.e.423.2		8
17.14	odd	16		34.2.a.a.1.1	✓	1
17.15	even	8	inner	578.2.d.e.399.1		8
17.16	even	2	inner	578.2.d.e.155.1		8
51.14	even	16		306.2.a.a.1.1		1
51.20	even	16		5202.2.a.d.1.1		1
68.3	even	16		4624.2.a.a.1.1		1
68.31	even	16		272.2.a.d.1.1		1
85.14	odd	16		850.2.a.e.1.1		1
85.48	even	16		850.2.c.b.749.1		2
85.82	even	16		850.2.c.b.749.2		2
119.48	even	16		1666.2.a.m.1.1		1
136.99	even	16		1088.2.a.d.1.1		1
136.133	odd	16		1088.2.a.l.1.1		1
187.65	even	16		4114.2.a.a.1.1		1
204.167	odd	16		2448.2.a.k.1.1		1
221.116	odd	16		5746.2.a.b.1.1		1
255.14	even	16		7650.2.a.ci.1.1		1
340.99	even	16		6800.2.a.b.1.1		1
408.269	even	16		9792.2.a.y.1.1		1
408.371	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	17.14	odd	16
272.2.a.d.1.1		1	68.31	even	16
306.2.a.a.1.1		1	51.14	even	16
578.2.a.a.1.1		1	17.3	odd	16
578.2.b.a.577.1		2	17.12	odd	16
578.2.b.a.577.2		2	17.5	odd	16
578.2.c.e.251.1		4	17.7	odd	16
578.2.c.e.251.2		4	17.10	odd	16
578.2.c.e.327.1		4	17.11	odd	16
578.2.c.e.327.2		4	17.6	odd	16
578.2.d.e.155.1		8	17.16	even	2	inner
578.2.d.e.155.2		8	1.1	even	1	trivial
578.2.d.e.179.1		8	17.8	even	8	inner
578.2.d.e.179.2		8	17.9	even	8	inner
578.2.d.e.399.1		8	17.15	even	8	inner
578.2.d.e.399.2		8	17.2	even	8	inner
578.2.d.e.423.1		8	17.4	even	4	inner
578.2.d.e.423.2		8	17.13	even	4	inner
850.2.a.e.1.1		1	85.14	odd	16
850.2.c.b.749.1		2	85.48	even	16
850.2.c.b.749.2		2	85.82	even	16
1088.2.a.d.1.1		1	136.99	even	16
1088.2.a.l.1.1		1	136.133	odd	16
1666.2.a.m.1.1		1	119.48	even	16
2448.2.a.k.1.1		1	204.167	odd	16
4114.2.a.a.1.1		1	187.65	even	16
4624.2.a.a.1.1		1	68.3	even	16
5202.2.a.d.1.1		1	51.20	even	16
5746.2.a.b.1.1		1	221.116	odd	16
6800.2.a.b.1.1		1	340.99	even	16
7650.2.a.ci.1.1		1	255.14	even	16
9792.2.a.y.1.1		1	408.269	even	16
9792.2.a.bj.1.1		1	408.371	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)

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