LMFDB - Embedded newform 504.2.bu.a.41.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(41,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.41"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bu (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.7
Character	$\chi$	$=$	504.41
Dual form			504.2.bu.a.209.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.27553 + 1.17176i) q^{3} +(-0.00869840 + 0.0150661i) q^{5} +(2.50492 + 0.851694i) q^{7} +(0.253935 - 2.98923i) q^{9} +(4.13424 - 2.38691i) q^{11} +(-1.31594 - 0.759761i) q^{13} +(-0.00655885 - 0.0294097i) q^{15} -1.91072 q^{17} +6.45989i q^{19} +(-4.19307 + 1.84882i) q^{21} +(3.82432 + 2.20797i) q^{23} +(2.49985 + 4.32986i) q^{25} +(3.17878 + 4.11040i) q^{27} +(1.73895 - 1.00399i) q^{29} +(6.51946 + 3.76401i) q^{31} +(-2.47644 + 7.88892i) q^{33} +(-0.0346205 + 0.0303309i) q^{35} -6.10467 q^{37} +(2.56878 - 0.572882i) q^{39} +(4.67759 - 8.10182i) q^{41} +(-1.46638 - 2.53985i) q^{43} +(0.0428272 + 0.0298274i) q^{45} +(-1.45659 - 2.52289i) q^{47} +(5.54924 + 4.26685i) q^{49} +(2.43718 - 2.23892i) q^{51} +8.94416i q^{53} +0.0830491i q^{55} +(-7.56947 - 8.23976i) q^{57} +(-4.08337 + 7.07261i) q^{59} +(-0.484917 + 0.279967i) q^{61} +(3.18200 - 7.27151i) q^{63} +(0.0228932 - 0.0132174i) q^{65} +(-3.69036 + 6.39189i) q^{67} +(-7.46525 + 1.66488i) q^{69} -11.6825i q^{71} -12.8105i q^{73} +(-8.26221 - 2.59362i) q^{75} +(12.3889 - 2.45790i) q^{77} +(4.75827 + 8.24157i) q^{79} +(-8.87103 - 1.51814i) q^{81} +(-6.67701 - 11.5649i) q^{83} +(0.0166202 - 0.0287871i) q^{85} +(-1.04165 + 3.31825i) q^{87} +4.00356 q^{89} +(-2.64925 - 3.02392i) q^{91} +(-12.7263 + 2.83817i) q^{93} +(-0.0973252 - 0.0561907i) q^{95} +(4.09514 - 2.36433i) q^{97} +(-6.08519 - 12.9643i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{9} + 8 q^{15} - 4 q^{21} + 12 q^{23} - 24 q^{25} - 36 q^{29} + 32 q^{39} + 12 q^{43} + 6 q^{49} + 24 q^{51} + 28 q^{57} - 14 q^{63} + 36 q^{65} - 60 q^{77} - 12 q^{79} - 36 q^{81} - 12 q^{91}+ \cdots + 44 q^{99}+O(q^{100}) $ 48 * q - 4 * q^9 + 8 * q^15 - 4 * q^21 + 12 * q^23 - 24 * q^25 - 36 * q^29 + 32 * q^39 + 12 * q^43 + 6 * q^49 + 24 * q^51 + 28 * q^57 - 14 * q^63 + 36 * q^65 - 60 * q^77 - 12 * q^79 - 36 * q^81 - 12 * q^91 + 16 * q^93 - 108 * q^95 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.27553	+	1.17176i	−0.736426	+	0.676519i
$3$	−1.27553	+	1.17176i	−0.736426	+	0.676519i
$4$		0			0
$5$	−0.00869840	+	0.0150661i	−0.00389004	+	0.00673776i	−0.867964	−	0.496627i	$-0.834572\pi$
$5$	−0.00869840	+	0.0150661i	−0.00389004	+	0.00673776i	0.864074	+	0.503365i	$0.167905\pi$
$6$		0			0
$7$	2.50492	+	0.851694i	0.946770	+	0.321910i
$7$	2.50492	+	0.851694i	0.946770	+	0.321910i
$8$		0			0
$9$	0.253935	−	2.98923i	0.0846451	−	0.996411i
$10$		0			0
$11$	4.13424	−	2.38691i	1.24652	−	0.719679i	0.276107	−	0.961127i	$-0.410956\pi$
$11$	4.13424	−	2.38691i	1.24652	−	0.719679i	0.970414	+	0.241448i	$0.0776222\pi$
$12$		0			0
$13$	−1.31594	−	0.759761i	−0.364977	−	0.210720i	0.306285	−	0.951940i	$-0.400914\pi$
$13$	−1.31594	−	0.759761i	−0.364977	−	0.210720i	−0.671262	+	0.741220i	$0.734247\pi$
$14$		0			0
$15$	−0.00655885	−	0.0294097i	−0.00169349	−	0.00759354i
$16$		0			0
$17$	−1.91072			−0.463418			−0.231709	−	0.972785i	$-0.574432\pi$
$17$	−1.91072			−0.463418			−0.231709	+	0.972785i	$0.574432\pi$
$18$		0			0
$19$			6.45989i			1.48200i	0.671505	+	0.741000i	$0.265648\pi$
$19$			6.45989i			1.48200i	−0.671505	+	0.741000i	$0.734352\pi$
$20$		0			0
$21$	−4.19307	+	1.84882i	−0.915004	+	0.403445i
$22$		0			0
$23$	3.82432	+	2.20797i	0.797426	+	0.460394i	0.842570	−	0.538586i	$-0.181041\pi$
$23$	3.82432	+	2.20797i	0.797426	+	0.460394i	−0.0451444	+	0.998980i	$0.514375\pi$
$24$		0			0
$25$	2.49985	+	4.32986i	0.499970	+	0.865973i
$26$		0			0
$27$	3.17878	+	4.11040i	0.611756	+	0.791047i
$28$		0			0
$29$	1.73895	−	1.00399i	0.322916	−	0.186435i	−0.329776	−	0.944059i	$-0.606973\pi$
$29$	1.73895	−	1.00399i	0.322916	−	0.186435i	0.652691	+	0.757624i	$0.273640\pi$
$30$		0			0
$31$	6.51946	+	3.76401i	1.17093	+	0.676036i	0.953899	−	0.300129i	$-0.0970297\pi$
$31$	6.51946	+	3.76401i	1.17093	+	0.676036i	0.217030	+	0.976165i	$0.430363\pi$
$32$		0			0
$33$	−2.47644	+	7.88892i	−0.431093	+	1.37328i
$34$		0			0
$35$	−0.0346205	+	0.0303309i	−0.00585193	+	0.00512686i
$36$		0			0
$37$	−6.10467			−1.00360			−0.501801	−	0.864983i	$-0.667329\pi$
$37$	−6.10467			−1.00360			−0.501801	+	0.864983i	$0.667329\pi$
$38$		0			0
$39$	2.56878	−	0.572882i	0.411335	−	0.0917346i
$40$		0			0
$41$	4.67759	−	8.10182i	0.730516	−	1.26529i	−0.226146	−	0.974093i	$-0.572613\pi$
$41$	4.67759	−	8.10182i	0.730516	−	1.26529i	0.956663	−	0.291198i	$-0.0940539\pi$
$42$		0			0
$43$	−1.46638	−	2.53985i	−0.223621	−	0.387323i	0.732284	−	0.680999i	$-0.238454\pi$
$43$	−1.46638	−	2.53985i	−0.223621	−	0.387323i	−0.955905	+	0.293677i	$0.905121\pi$
$44$		0			0
$45$	0.0428272	+	0.0298274i	0.00638430	+	0.00444640i
$46$		0			0
$47$	−1.45659	−	2.52289i	−0.212466	−	0.368001i	0.740020	−	0.672585i	$-0.234816\pi$
$47$	−1.45659	−	2.52289i	−0.212466	−	0.368001i	−0.952486	+	0.304584i	$0.901483\pi$
$48$		0			0
$49$	5.54924	+	4.26685i	0.792748	+	0.609550i
$50$		0			0
$51$	2.43718	−	2.23892i	0.341273	−	0.313511i
$52$		0			0
$53$			8.94416i			1.22858i	0.789082	+	0.614288i	$0.210557\pi$
$53$			8.94416i			1.22858i	−0.789082	+	0.614288i	$0.789443\pi$
$54$		0			0
$55$			0.0830491i			0.0111983i
$56$		0			0
$57$	−7.56947	−	8.23976i	−1.00260	−	1.09138i
$58$		0			0
$59$	−4.08337	+	7.07261i	−0.531610	+	0.920776i	0.467709	+	0.883882i	$0.345079\pi$
$59$	−4.08337	+	7.07261i	−0.531610	+	0.920776i	−0.999319	+	0.0368933i	$0.988254\pi$
$60$		0			0
$61$	−0.484917	+	0.279967i	−0.0620873	+	0.0358461i	−0.530722	−	0.847546i	$-0.678079\pi$
$61$	−0.484917	+	0.279967i	−0.0620873	+	0.0358461i	0.468635	+	0.883392i	$0.344746\pi$
$62$		0			0
$63$	3.18200	−	7.27151i	0.400894	−	0.916124i
$64$		0			0
$65$	0.0228932	−	0.0132174i	0.00283956	−	0.00163942i
$66$		0			0
$67$	−3.69036	+	6.39189i	−0.450849	+	0.780893i	−0.998439	−	0.0558536i	$-0.982212\pi$
$67$	−3.69036	+	6.39189i	−0.450849	+	0.780893i	0.547590	+	0.836747i	$0.315545\pi$
$68$		0			0
$69$	−7.46525	+	1.66488i	−0.898710	+	0.200428i
$70$		0			0
$71$		−	11.6825i		−	1.38645i	−0.720719	−	0.693227i	$-0.756188\pi$
$71$		−	11.6825i		−	1.38645i	0.720719	−	0.693227i	$-0.243812\pi$
$72$		0			0
$73$		−	12.8105i		−	1.49936i	−0.661801	−	0.749680i	$-0.730208\pi$
$73$		−	12.8105i		−	1.49936i	0.661801	−	0.749680i	$-0.269792\pi$
$74$		0			0
$75$	−8.26221	−	2.59362i	−0.954037	−	0.299486i
$76$		0			0
$77$	12.3889	−	2.45790i	1.41184	−	0.280103i
$78$		0			0
$79$	4.75827	+	8.24157i	0.535348	+	0.927249i	0.999146	+	0.0413086i	$0.0131527\pi$
$79$	4.75827	+	8.24157i	0.535348	+	0.927249i	−0.463799	+	0.885940i	$0.653514\pi$
$80$		0			0
$81$	−8.87103	−	1.51814i	−0.985670	−	0.168683i
$82$		0			0
$83$	−6.67701	−	11.5649i	−0.732897	−	1.26942i	−0.955640	−	0.294538i	$-0.904834\pi$
$83$	−6.67701	−	11.5649i	−0.732897	−	1.26942i	0.222743	−	0.974877i	$-0.428499\pi$
$84$		0			0
$85$	0.0166202	−	0.0287871i	0.00180272	−	0.00312240i
$86$		0			0
$87$	−1.04165	+	3.31825i	−0.111676	+	0.355754i
$88$		0			0
$89$	4.00356			0.424376			0.212188	−	0.977229i	$-0.431941\pi$
$89$	4.00356			0.424376			0.212188	+	0.977229i	$0.431941\pi$
$90$		0			0
$91$	−2.64925	−	3.02392i	−0.277717	−	0.316993i
$92$		0			0
$93$	−12.7263	+	2.83817i	−1.31965	+	0.294305i
$94$		0			0
$95$	−0.0973252	−	0.0561907i	−0.00998536	−	0.00576505i
$96$		0			0
$97$	4.09514	−	2.36433i	0.415799	−	0.240062i	−0.277479	−	0.960732i	$-0.589499\pi$
$97$	4.09514	−	2.36433i	0.415799	−	0.240062i	0.693278	+	0.720670i	$0.256166\pi$
$98$		0			0
$99$	−6.08519	−	12.9643i	−0.611585	−	1.30296i
$100$		0			0
$101$	−2.98289	−	5.16652i	−0.296809	−	0.514088i	0.678595	−	0.734513i	$-0.262589\pi$
$101$	−2.98289	−	5.16652i	−0.296809	−	0.514088i	−0.975404	+	0.220424i	$0.929256\pi$
$102$		0			0
$103$	10.0607	+	5.80854i	0.991308	+	0.572332i	0.905665	−	0.423994i	$-0.139372\pi$
$103$	10.0607	+	5.80854i	0.991308	+	0.572332i	0.0856432	+	0.996326i	$0.472705\pi$
$104$		0			0
$105$	0.00861864	−	0.0792550i	0.000841093	−	0.00773449i
$106$		0			0
$107$		−	11.8633i		−	1.14687i	−0.819251	−	0.573434i	$-0.805611\pi$
$107$		−	11.8633i		−	1.14687i	0.819251	−	0.573434i	$-0.194389\pi$
$108$		0			0
$109$	−3.23313			−0.309677			−0.154839	−	0.987940i	$-0.549486\pi$
$109$	−3.23313			−0.309677			−0.154839	+	0.987940i	$0.549486\pi$
$110$		0			0
$111$	7.78667	−	7.15324i	0.739078	−	0.678955i
$112$		0			0
$113$	−3.33701	−	1.92662i	−0.313919	−	0.181241i	0.334760	−	0.942304i	$-0.391345\pi$
$113$	−3.33701	−	1.92662i	−0.313919	−	0.181241i	−0.648679	+	0.761062i	$0.724678\pi$
$114$		0			0
$115$	−0.0665310	+	0.0384117i	−0.00620404	+	0.00358191i
$116$		0			0
$117$	−2.60527	+	3.74074i	−0.240857	+	0.345831i
$118$		0			0
$119$	−4.78620	−	1.62735i	−0.438751	−	0.149179i
$120$		0			0
$121$	5.89464	−	10.2098i	0.535876	−	0.928165i
$122$		0			0
$123$	3.52704	+	15.8151i	0.318022	+	1.42600i
$124$		0			0
$125$	−0.173963			−0.0155597
$126$		0			0
$127$	−21.9600			−1.94864			−0.974318	−	0.225175i	$-0.927705\pi$
$127$	−21.9600			−1.94864			−0.974318	+	0.225175i	$0.927705\pi$
$128$		0			0
$129$	4.84651	+	1.52139i	0.426711	+	0.133951i
$130$		0			0
$131$	8.11460	−	14.0549i	0.708976	−	1.22798i	−0.256261	−	0.966608i	$-0.582491\pi$
$131$	8.11460	−	14.0549i	0.708976	−	1.22798i	0.965237	−	0.261375i	$-0.0841760\pi$
$132$		0			0
$133$	−5.50185	+	16.1815i	−0.477071	+	1.40311i
$134$		0			0
$135$	−0.0895779	+	0.0121378i	−0.00770964	+	0.00104465i
$136$		0			0
$137$	5.40456	−	3.12033i	0.461743	−	0.266587i	−0.251034	−	0.967978i	$-0.580771\pi$
$137$	5.40456	−	3.12033i	0.461743	−	0.266587i	0.712777	+	0.701391i	$0.247437\pi$
$138$		0			0
$139$	9.14307	+	5.27875i	0.775505	+	0.447738i	0.834835	−	0.550500i	$-0.185563\pi$
$139$	9.14307	+	5.27875i	0.775505	+	0.447738i	−0.0593300	+	0.998238i	$0.518896\pi$
$140$		0			0
$141$	4.81415	+	1.51123i	0.405425	+	0.127269i
$142$		0			0
$143$	−7.25391			−0.606603
$144$		0			0
$145$			0.0349323i			0.00290097i
$146$		0			0
$147$	−12.0779	+	1.05992i	−0.996171	+	0.0874208i
$148$		0			0
$149$	−7.13927	−	4.12186i	−0.584872	−	0.337676i	0.178195	−	0.983995i	$-0.442974\pi$
$149$	−7.13927	−	4.12186i	−0.584872	−	0.337676i	−0.763067	+	0.646319i	$0.776307\pi$
$150$		0			0
$151$	6.58096	+	11.3986i	0.535551	+	0.927602i	0.999136	+	0.0415494i	$0.0132294\pi$
$151$	6.58096	+	11.3986i	0.535551	+	0.927602i	−0.463585	+	0.886052i	$0.653437\pi$
$152$		0			0
$153$	−0.485200	+	5.71159i	−0.0392261	+	0.461755i
$154$		0			0
$155$	−0.113418	+	0.0654818i	−0.00910993	+	0.00525962i
$156$		0			0
$157$	−7.30128	−	4.21540i	−0.582705	−	0.336425i	0.179502	−	0.983758i	$-0.442551\pi$
$157$	−7.30128	−	4.21540i	−0.582705	−	0.336425i	−0.762208	+	0.647332i	$0.775885\pi$
$158$		0			0
$159$	−10.4805	−	11.4085i	−0.831154	−	0.904754i
$160$		0			0
$161$	7.69909	+	8.78794i	0.606774	+	0.692587i
$162$		0			0
$163$	−8.15879			−0.639046			−0.319523	−	0.947579i	$-0.603523\pi$
$163$	−8.15879			−0.639046			−0.319523	+	0.947579i	$0.603523\pi$
$164$		0			0
$165$	−0.0973140	−	0.105931i	−0.00757588	−	0.00824674i
$166$		0			0
$167$	−11.3487	+	19.6566i	−0.878191	+	1.52107i	−0.0248668	+	0.999691i	$0.507916\pi$
$167$	−11.3487	+	19.6566i	−0.878191	+	1.52107i	−0.853324	+	0.521381i	$0.825417\pi$
$168$		0			0
$169$	−5.34553	−	9.25872i	−0.411194	−	0.712210i
$170$		0			0
$171$	19.3101	+	1.64039i	1.47668	+	0.125444i
$172$		0			0
$173$	2.92866	+	5.07259i	0.222662	+	0.385662i	0.955615	−	0.294617i	$-0.0951921\pi$
$173$	2.92866	+	5.07259i	0.222662	+	0.385662i	−0.732953	+	0.680279i	$0.761859\pi$
$174$		0			0
$175$	2.57420	+	12.9751i	0.194591	+	0.980823i
$176$		0			0
$177$	−3.07898	−	13.8061i	−0.231431	−	1.03773i
$178$		0			0
$179$			13.8391i			1.03438i	0.855869	+	0.517192i	$0.173023\pi$
$179$			13.8391i			1.03438i	−0.855869	+	0.517192i	$0.826977\pi$
$180$		0			0
$181$		−	16.7885i		−	1.24788i	−0.781472	−	0.623940i	$-0.785531\pi$
$181$		−	16.7885i		−	1.24788i	0.781472	−	0.623940i	$-0.214469\pi$
$182$		0			0
$183$	0.290469	−	0.925314i	0.0214721	−	0.0684012i
$184$		0			0
$185$	0.0531009	−	0.0919735i	0.00390406	−	0.00676202i
$186$		0			0
$187$	−7.89939	+	4.56071i	−0.577660	+	0.333512i
$188$		0			0
$189$	4.46178	+	13.0036i	0.324546	+	0.945870i
$190$		0			0
$191$	−5.62396	+	3.24700i	−0.406935	+	0.234944i	−0.689472	−	0.724312i	$-0.742157\pi$
$191$	−5.62396	+	3.24700i	−0.406935	+	0.234944i	0.282537	+	0.959256i	$0.408824\pi$
$192$		0			0
$193$	8.37754	−	14.5103i	0.603028	−	1.04448i	−0.389331	−	0.921098i	$-0.627294\pi$
$193$	8.37754	−	14.5103i	0.603028	−	1.04448i	0.992360	−	0.123378i	$-0.0393728\pi$
$194$		0			0
$195$	−0.0137132	+	0.0436846i	−0.000982025	+	0.00312832i
$196$		0			0
$197$			5.89156i			0.419756i	0.977728	+	0.209878i	$0.0673067\pi$
$197$			5.89156i			0.419756i	−0.977728	+	0.209878i	$0.932693\pi$
$198$		0			0
$199$		−	18.7851i		−	1.33164i	−0.746113	−	0.665819i	$-0.768082\pi$
$199$		−	18.7851i		−	1.33164i	0.746113	−	0.665819i	$-0.231918\pi$
$200$		0			0
$201$	−2.78264	−	12.4772i	−0.196272	−	0.880077i
$202$		0			0
$203$	5.21103	−	1.03385i	0.365742	−	0.0725617i
$204$		0			0
$205$	0.0813751	+	0.140946i	0.00568348	+	0.00984408i
$206$		0			0
$207$	7.57127	−	10.8711i	0.526240	−	0.755594i
$208$		0			0
$209$	15.4191	+	26.7067i	1.06656	+	1.84734i
$210$		0			0
$211$	10.9508	−	18.9674i	0.753886	−	1.30577i	−0.192040	−	0.981387i	$-0.561510\pi$
$211$	10.9508	−	18.9674i	0.753886	−	1.30577i	0.945926	−	0.324382i	$-0.105156\pi$
$212$		0			0
$213$	13.6891	+	14.9013i	0.937962	+	1.02102i
$214$		0			0
$215$	0.0510207			0.00347958
$216$		0			0
$217$	13.1249	+	14.9811i	0.890978	+	1.01698i
$218$		0			0
$219$	15.0109	+	16.3402i	1.01434	+	1.10417i
$220$		0			0
$221$	2.51440	+	1.45169i	0.169137	+	0.0976514i
$222$		0			0
$223$	−11.2455	+	6.49259i	−0.753054	+	0.434776i	−0.826796	−	0.562501i	$-0.809839\pi$
$223$	−11.2455	+	6.49259i	−0.753054	+	0.434776i	0.0737421	+	0.997277i	$0.476506\pi$
$224$		0			0
$225$	13.5778	−	6.37313i	0.905185	−	0.424875i
$226$		0			0
$227$	4.31567	+	7.47496i	0.286441	+	0.496131i	0.972958	−	0.230984i	$-0.0741944\pi$
$227$	4.31567	+	7.47496i	0.286441	+	0.496131i	−0.686516	+	0.727114i	$0.740861\pi$
$228$		0			0
$229$	7.37873	+	4.26011i	0.487600	+	0.281516i	0.723578	−	0.690242i	$-0.242496\pi$
$229$	7.37873	+	4.26011i	0.487600	+	0.281516i	−0.235978	+	0.971758i	$0.575829\pi$
$230$		0			0
$231$	−12.9222	+	17.6519i	−0.850221	+	1.16141i
$232$		0			0
$233$		−	0.246911i		−	0.0161757i	−0.999967	−	0.00808783i	$-0.997426\pi$
$233$		−	0.246911i		−	0.0161757i	0.999967	−	0.00808783i	$-0.00257447\pi$
$234$		0			0
$235$	0.0506801			0.00330600
$236$		0			0
$237$	−15.7265	−	4.93676i	−1.02154	−	0.320677i
$238$		0			0
$239$	−23.5814	−	13.6147i	−1.52535	−	0.880664i	−0.999548	−	0.0300592i	$-0.990430\pi$
$239$	−23.5814	−	13.6147i	−1.52535	−	0.880664i	−0.525806	−	0.850604i	$-0.676236\pi$
$240$		0			0
$241$	−5.71926	+	3.30201i	−0.368410	+	0.212701i	−0.672763	−	0.739858i	$-0.734893\pi$
$241$	−5.71926	+	3.30201i	−0.368410	+	0.212701i	0.304354	+	0.952559i	$0.401559\pi$
$242$		0			0
$243$	13.0941	−	8.45833i	0.839990	−	0.542602i
$244$		0			0
$245$	−0.112554	+	0.0464904i	−0.00719082	+	0.00297017i
$246$		0			0
$247$	4.90797	−	8.50086i	0.312287	−	0.540897i
$248$		0			0
$249$	22.0681	+	6.92748i	1.39851	+	0.439011i
$250$		0			0
$251$	−11.1930			−0.706496			−0.353248	−	0.935530i	$-0.614923\pi$
$251$	−11.1930			−0.706496			−0.353248	+	0.935530i	$0.614923\pi$
$252$		0			0
$253$	21.0809			1.32534
$254$		0			0
$255$	0.0125321	+	0.0561937i	0.000784793	+	0.00351899i
$256$		0			0
$257$	4.85692	−	8.41243i	0.302966	−	0.524753i	−0.673840	−	0.738877i	$-0.735356\pi$
$257$	4.85692	−	8.41243i	0.302966	−	0.524753i	0.976806	+	0.214124i	$0.0686898\pi$
$258$		0			0
$259$	−15.2917	−	5.19931i	−0.950180	−	0.323069i
$260$		0			0
$261$	−2.55956	−	5.45309i	−0.158433	−	0.337538i
$262$		0			0
$263$	−5.18772	+	2.99513i	−0.319888	+	0.184688i	−0.651343	−	0.758784i	$-0.725794\pi$
$263$	−5.18772	+	2.99513i	−0.319888	+	0.184688i	0.331454	+	0.943471i	$0.392461\pi$
$264$		0			0
$265$	−0.134753	−	0.0777999i	−0.00827784	−	0.00477921i
$266$		0			0
$267$	−5.10665	+	4.69123i	−0.312522	+	0.287099i
$268$		0			0
$269$	−22.7332			−1.38607			−0.693034	−	0.720905i	$-0.743727\pi$
$269$	−22.7332			−1.38607			−0.693034	+	0.720905i	$0.743727\pi$
$270$		0			0
$271$		−	1.03859i		−	0.0630896i	−0.999502	−	0.0315448i	$-0.989957\pi$
$271$		−	1.03859i		−	0.0630896i	0.999502	−	0.0315448i	$-0.0100427\pi$
$272$		0			0
$273$	6.92251	+	0.752794i	0.418970	+	0.0455611i
$274$		0			0
$275$	20.6700	+	11.9338i	1.24645	+	0.719636i
$276$		0			0
$277$	7.59222	+	13.1501i	0.456172	+	0.790113i	0.998755	−	0.0498891i	$-0.0158868\pi$
$277$	7.59222	+	13.1501i	0.456172	+	0.790113i	−0.542583	+	0.840002i	$0.682553\pi$
$278$		0			0
$279$	12.9070	−	18.5324i	0.772723	−	1.10950i
$280$		0			0
$281$	12.8641	−	7.42710i	0.767408	−	0.443063i	−0.0645409	−	0.997915i	$-0.520558\pi$
$281$	12.8641	−	7.42710i	0.767408	−	0.443063i	0.831949	+	0.554852i	$0.187225\pi$
$282$		0			0
$283$	−28.6064	−	16.5159i	−1.70048	−	0.981770i	−0.945274	−	0.326277i	$-0.894206\pi$
$283$	−28.6064	−	16.5159i	−1.70048	−	0.981770i	−0.755202	−	0.655493i	$-0.772461\pi$
$284$		0			0
$285$	0.189983	−	0.0423695i	0.0112536	−	0.00250975i
$286$		0			0
$287$	18.6172	−	16.3105i	1.09894	−	0.962780i
$288$		0			0
$289$	−13.3491			−0.785244
$290$		0			0
$291$	−2.45302	+	7.81432i	−0.143799	+	0.458083i
$292$		0			0
$293$	−12.7859	+	22.1459i	−0.746963	+	1.29378i	0.202309	+	0.979322i	$0.435155\pi$
$293$	−12.7859	+	22.1459i	−0.746963	+	1.29378i	−0.949272	+	0.314456i	$0.898178\pi$
$294$		0			0
$295$	−0.0710377	−	0.123041i	−0.00413597	−	0.00716372i
$296$		0			0
$297$	22.9530	+	9.40594i	1.33187	+	0.545788i
$298$		0			0
$299$	−3.35506	−	5.81114i	−0.194028	−	0.336067i
$300$		0			0
$301$	−1.50999	−	7.61101i	−0.0870345	−	0.438692i
$302$		0			0
$303$	9.85871	+	3.09479i	0.566368	+	0.177791i
$304$		0			0
$305$		−	0.00974107i		−	0.000557772i
$306$		0			0
$307$			6.04267i			0.344873i	0.985021	+	0.172437i	$0.0551640\pi$
$307$			6.04267i			0.344873i	−0.985021	+	0.172437i	$0.944836\pi$
$308$		0			0
$309$	−19.6389	+	4.37981i	−1.11722	+	0.249159i
$310$		0			0
$311$	−17.0708	+	29.5674i	−0.967994	+	1.67661i	−0.266648	+	0.963794i	$0.585916\pi$
$311$	−17.0708	+	29.5674i	−0.967994	+	1.67661i	−0.701346	+	0.712821i	$0.747417\pi$
$312$		0			0
$313$	−10.9506	+	6.32235i	−0.618966	+	0.357360i	−0.776466	−	0.630159i	$-0.782990\pi$
$313$	−10.9506	+	6.32235i	−0.618966	+	0.357360i	0.157500	+	0.987519i	$0.449657\pi$
$314$		0			0
$315$	0.0818749	+	0.111191i	0.00461313	+	0.00626489i
$316$		0			0
$317$	−4.95447	+	2.86047i	−0.278271	+	0.160660i	−0.632640	−	0.774446i	$-0.718029\pi$
$317$	−4.95447	+	2.86047i	−0.278271	+	0.160660i	0.354369	+	0.935105i	$0.384696\pi$
$318$		0			0
$319$	4.79284	−	8.30144i	0.268347	−	0.464791i
$320$		0			0
$321$	13.9010	+	15.1320i	0.775878	+	0.844583i
$322$		0			0
$323$		−	12.3431i		−	0.686786i
$324$		0			0
$325$		−	7.59715i		−	0.421414i
$326$		0			0
$327$	4.12394	−	3.78846i	0.228054	−	0.209502i
$328$		0			0
$329$	−1.49991	−	7.56021i	−0.0826929	−	0.416808i
$330$		0			0
$331$	7.18521	+	12.4452i	0.394935	+	0.684047i	0.993093	−	0.117331i	$-0.0374338\pi$
$331$	7.18521	+	12.4452i	0.394935	+	0.684047i	−0.598158	+	0.801378i	$0.704100\pi$
$332$		0			0
$333$	−1.55019	+	18.2483i	−0.0849500	+	1.00000i
$334$		0			0
$335$	−0.0642004	−	0.111198i	−0.00350764	−	0.00607542i
$336$		0			0
$337$	2.20813	−	3.82460i	0.120285	−	0.208339i	−0.799595	−	0.600539i	$-0.794953\pi$
$337$	2.20813	−	3.82460i	0.120285	−	0.208339i	0.919880	+	0.392200i	$0.128286\pi$
$338$		0			0
$339$	6.51399	−	1.45273i	0.353791	−	0.0789015i
$340$		0			0
$341$	35.9373			1.94612
$342$		0			0
$343$	10.2663	+	15.4144i	0.554330	+	0.832297i
$344$		0			0
$345$	0.0398526	−	0.126954i	0.00214559	−	0.00683496i
$346$		0			0
$347$	0.305641	+	0.176462i	0.0164077	+	0.00947298i	0.508181	−	0.861250i	$-0.330318\pi$
$347$	0.305641	+	0.176462i	0.0164077	+	0.00947298i	−0.491774	+	0.870723i	$0.663651\pi$
$348$		0			0
$349$	−1.16292	+	0.671412i	−0.0622497	+	0.0359399i	−0.530802	−	0.847496i	$-0.678109\pi$
$349$	−1.16292	+	0.671412i	−0.0622497	+	0.0359399i	0.468552	+	0.883436i	$0.344776\pi$
$350$		0			0
$351$	−1.06017	−	7.82417i	−0.0565879	−	0.417623i
$352$		0			0
$353$	8.09184	+	14.0155i	0.430685	+	0.745968i	0.996932	−	0.0782669i	$-0.0249386\pi$
$353$	8.09184	+	14.0155i	0.430685	+	0.745968i	−0.566247	+	0.824235i	$0.691605\pi$
$354$		0			0
$355$	0.176009	+	0.101619i	0.00934159	+	0.00539337i
$356$		0			0
$357$	8.01180	−	3.53258i	0.424029	−	0.186964i
$358$		0			0
$359$			13.1262i			0.692777i	0.938091	+	0.346388i	$0.112592\pi$
$359$			13.1262i			0.692777i	−0.938091	+	0.346388i	$0.887408\pi$
$360$		0			0
$361$	−22.7302			−1.19632
$362$		0			0
$363$	4.44473	+	19.9300i	0.233288	+	1.04605i
$364$		0			0
$365$	0.193004	+	0.111431i	0.0101023	+	0.00583257i
$366$		0			0
$367$	27.4478	−	15.8470i	1.43276	−	0.827206i	0.435432	−	0.900222i	$-0.356596\pi$
$367$	27.4478	−	15.8470i	1.43276	−	0.827206i	0.997331	+	0.0730154i	$0.0232622\pi$
$368$		0			0
$369$	−23.0304	−	16.0397i	−1.19892	−	0.834995i
$370$		0			0
$371$	−7.61769	+	22.4044i	−0.395491	+	1.16318i
$372$		0			0
$373$	8.85016	−	15.3289i	0.458244	−	0.793702i	−0.540624	−	0.841264i	$-0.681812\pi$
$373$	8.85016	−	15.3289i	0.458244	−	0.793702i	0.998868	+	0.0475622i	$0.0151452\pi$
$374$		0			0
$375$	0.221894	−	0.203843i	0.0114586	−	0.0105264i
$376$		0			0
$377$	−3.05116			−0.157142
$378$		0			0
$379$	5.09384			0.261653			0.130827	−	0.991405i	$-0.458237\pi$
$379$	5.09384			0.261653			0.130827	+	0.991405i	$0.458237\pi$
$380$		0			0
$381$	28.0106	−	25.7320i	1.43503	−	1.31829i
$382$		0			0
$383$	−6.84567	+	11.8571i	−0.349798	+	0.605867i	−0.986213	−	0.165479i	$-0.947083\pi$
$383$	−6.84567	+	11.8571i	−0.349798	+	0.605867i	0.636416	+	0.771346i	$0.280416\pi$
$384$		0			0
$385$	−0.0707324	+	0.208031i	−0.00360486	+	0.0106023i
$386$		0			0
$387$	−7.96456	+	3.73840i	−0.404861	+	0.190033i
$388$		0			0
$389$	−15.9566	+	9.21256i	−0.809033	+	0.467095i	−0.846620	−	0.532198i	$-0.821366\pi$
$389$	−15.9566	+	9.21256i	−0.809033	+	0.467095i	0.0375873	+	0.999293i	$0.488033\pi$
$390$		0			0
$391$	−7.30721	−	4.21882i	−0.369542	−	0.213355i
$392$		0			0
$393$	6.11865	+	27.4358i	0.308645	+	1.38395i
$394$		0			0
$395$	−0.165558			−0.00833010
$396$		0			0
$397$			7.04050i			0.353352i	0.984269	+	0.176676i	$0.0565345\pi$
$397$			7.04050i			0.353352i	−0.984269	+	0.176676i	$0.943465\pi$
$398$		0			0
$399$	−11.9432	−	27.0868i	−0.597906	−	1.35604i
$400$		0			0
$401$	−31.0404	−	17.9212i	−1.55008	−	0.894940i	−0.998134	−	0.0610617i	$-0.980551\pi$
$401$	−31.0404	−	17.9212i	−1.55008	−	0.894940i	−0.551948	−	0.833879i	$-0.686115\pi$
$402$		0			0
$403$	−5.71949	−	9.90646i	−0.284908	−	0.493476i
$404$		0			0
$405$	0.100036	−	0.120446i	0.00497084	−	0.00598502i
$406$		0			0
$407$	−25.2382	+	14.5713i	−1.25101	+	0.722271i
$408$		0			0
$409$	−11.5808	−	6.68621i	−0.572636	−	0.330612i	0.185565	−	0.982632i	$-0.440588\pi$
$409$	−11.5808	−	6.68621i	−0.572636	−	0.330612i	−0.758202	+	0.652020i	$0.773922\pi$
$410$		0			0
$411$	−3.23738	+	10.3129i	−0.159688	+	0.508699i
$412$		0			0
$413$	−16.2522	+	14.2385i	−0.799720	+	0.700632i
$414$		0			0
$415$	0.232317			0.0114040
$416$		0			0
$417$	−17.8477	+	3.98034i	−0.874005	+	0.194918i
$418$		0			0
$419$	20.1508	−	34.9023i	0.984433	−	1.70509i	0.340001	−	0.940425i	$-0.389572\pi$
$419$	20.1508	−	34.9023i	0.984433	−	1.70509i	0.644431	−	0.764662i	$-0.277094\pi$
$420$		0			0
$421$	−6.04485	−	10.4700i	−0.294608	−	0.510276i	0.680286	−	0.732947i	$-0.261856\pi$
$421$	−6.04485	−	10.4700i	−0.294608	−	0.510276i	−0.974894	+	0.222671i	$0.928522\pi$
$422$		0			0
$423$	−7.91139	+	3.71344i	−0.384665	+	0.180554i
$424$		0			0
$425$	−4.77652	−	8.27317i	−0.231695	−	0.401308i
$426$		0			0
$427$	−1.45312	+	0.288294i	−0.0703216	+	0.0139515i
$428$		0			0
$429$	9.25256	−	8.49988i	0.446718	−	0.410378i
$430$		0			0
$431$		−	20.2652i		−	0.976140i	−0.872805	−	0.488070i	$-0.837701\pi$
$431$		−	20.2652i		−	0.976140i	0.872805	−	0.488070i	$-0.162299\pi$
$432$		0			0
$433$		−	33.6180i		−	1.61558i	−0.589472	−	0.807789i	$-0.700664\pi$
$433$		−	33.6180i		−	1.61558i	0.589472	−	0.807789i	$-0.299336\pi$
$434$		0			0
$435$	−0.0409324	−	0.0445570i	−0.00196256	−	0.00213635i
$436$		0			0
$437$	−14.2633	+	24.7047i	−0.682304	+	1.18179i
$438$		0			0
$439$	−10.2274	+	5.90480i	−0.488128	+	0.281821i	−0.723797	−	0.690013i	$-0.757605\pi$
$439$	−10.2274	+	5.90480i	−0.488128	+	0.281821i	0.235670	+	0.971833i	$0.424272\pi$
$440$		0			0
$441$	14.1638	−	15.5045i	0.674464	−	0.738307i
$442$		0			0
$443$	0.0807550	−	0.0466239i	0.00383678	−	0.00221517i	−0.498080	−	0.867131i	$-0.665962\pi$
$443$	0.0807550	−	0.0466239i	0.00383678	−	0.00221517i	0.501917	+	0.864916i	$0.332628\pi$
$444$		0			0
$445$	−0.0348246	+	0.0603179i	−0.00165084	+	0.00285934i
$446$		0			0
$447$	13.9362	−	3.10800i	0.659158	−	0.147003i
$448$		0			0
$449$			14.9759i			0.706755i	0.935481	+	0.353378i	$0.114967\pi$
$449$			14.9759i			0.706755i	−0.935481	+	0.353378i	$0.885033\pi$
$450$		0			0
$451$		−	44.6598i		−	2.10295i
$452$		0			0
$453$	−21.7506	−	6.82783i	−1.02193	−	0.320799i
$454$		0			0
$455$	0.0686029	−	0.0136105i	0.00321615	−	0.000638071i
$456$		0			0
$457$	−3.63391	−	6.29411i	−0.169987	−	0.294426i	0.768428	−	0.639936i	$-0.221039\pi$
$457$	−3.63391	−	6.29411i	−0.169987	−	0.294426i	−0.938415	+	0.345510i	$0.887706\pi$
$458$		0			0
$459$	−6.07376	−	7.85383i	−0.283499	−	0.366585i
$460$		0			0
$461$	−3.63421	−	6.29464i	−0.169262	−	0.293170i	0.768899	−	0.639371i	$-0.220805\pi$
$461$	−3.63421	−	6.29464i	−0.169262	−	0.293170i	−0.938161	+	0.346200i	$0.887472\pi$
$462$		0			0
$463$	−15.5092	+	26.8627i	−0.720774	+	1.24842i	0.239916	+	0.970794i	$0.422880\pi$
$463$	−15.5092	+	26.8627i	−0.720774	+	1.24842i	−0.960690	+	0.277624i	$0.910453\pi$
$464$		0			0
$465$	0.0679381	−	0.216423i	0.00315055	−	0.0100364i
$466$		0			0
$467$	22.6887			1.04991			0.524954	−	0.851130i	$-0.324082\pi$
$467$	22.6887			1.04991			0.524954	+	0.851130i	$0.324082\pi$
$468$		0			0
$469$	−14.6880	+	12.8681i	−0.678228	+	0.594194i
$470$		0			0
$471$	14.2524	−	3.17853i	0.656717	−	0.146459i
$472$		0			0
$473$	−12.1247	−	7.00022i	−0.557496	−	0.321871i
$474$		0			0
$475$	−27.9704	+	16.1487i	−1.28337	+	0.740955i
$476$		0			0
$477$	26.7362	+	2.27124i	1.22417	+	0.103993i
$478$		0			0
$479$	0.547354	+	0.948045i	0.0250092	+	0.0433173i	0.878259	−	0.478185i	$-0.158705\pi$
$479$	0.547354	+	0.948045i	0.0250092	+	0.0433173i	−0.853250	+	0.521502i	$0.825372\pi$
$480$		0			0
$481$	8.03341	+	4.63809i	0.366292	+	0.211479i
$482$		0			0
$483$	−20.1178	−	2.18772i	−0.915391	−	0.0995449i
$484$		0			0
$485$			0.0822637i			0.00373540i
$486$		0			0
$487$	12.3778			0.560892			0.280446	−	0.959870i	$-0.409518\pi$
$487$	12.3778			0.560892			0.280446	+	0.959870i	$0.409518\pi$
$488$		0			0
$489$	10.4067	−	9.56018i	0.470609	−	0.432326i
$490$		0			0
$491$	27.1411	+	15.6700i	1.22486	+	0.707175i	0.965951	−	0.258726i	$-0.0833026\pi$
$491$	27.1411	+	15.6700i	1.22486	+	0.707175i	0.258912	+	0.965901i	$0.416636\pi$
$492$		0			0
$493$	−3.32266	+	1.91834i	−0.149645	+	0.0863975i
$494$		0			0
$495$	0.248253	+	0.0210891i	0.0111581	+	0.000947884i
$496$		0			0
$497$	9.94989	−	29.2636i	0.446314	−	1.31265i
$498$		0			0
$499$	16.9940	−	29.4345i	0.760756	−	1.31767i	−0.181706	−	0.983353i	$-0.558162\pi$
$499$	16.9940	−	29.4345i	0.760756	−	1.31767i	0.942462	−	0.334315i	$-0.108505\pi$
$500$		0			0
$501$	−8.55728	−	38.3705i	−0.382311	−	1.71427i
$502$		0			0
$503$	−1.16212			−0.0518163			−0.0259082	−	0.999664i	$-0.508248\pi$
$503$	−1.16212			−0.0518163			−0.0259082	+	0.999664i	$0.508248\pi$
$504$		0			0
$505$	0.103786			0.00461840
$506$		0			0
$507$	17.6674	+	5.54605i	0.784637	+	0.246309i
$508$		0			0
$509$	18.3129	−	31.7189i	0.811705	−	1.40591i	−0.0999657	−	0.994991i	$-0.531873\pi$
$509$	18.3129	−	31.7189i	0.811705	−	1.40591i	0.911670	−	0.410923i	$-0.134793\pi$
$510$		0			0
$511$	10.9107	−	32.0893i	0.482659	−	1.41955i
$512$		0			0
$513$	−26.5527	+	20.5345i	−1.17233	+	0.906622i
$514$		0			0
$515$	−0.175024	+	0.101050i	−0.00771247	+	0.00445280i
$516$		0			0
$517$	−12.0438	−	6.95349i	−0.529686	−	0.305814i
$518$		0			0
$519$	−9.67946	−	3.03852i	−0.424881	−	0.133376i
$520$		0			0
$521$	−42.9713			−1.88261			−0.941303	−	0.337563i	$-0.890397\pi$
$521$	−42.9713			−1.88261			−0.941303	+	0.337563i	$0.890397\pi$
$522$		0			0
$523$			21.1229i			0.923639i	0.886974	+	0.461820i	$0.152803\pi$
$523$			21.1229i			0.923639i	−0.886974	+	0.461820i	$0.847197\pi$
$524$		0			0
$525$	−18.4872	−	13.5337i	−0.806847	−	0.590658i
$526$		0			0
$527$	−12.4569	−	7.19197i	−0.542630	−	0.313287i
$528$		0			0
$529$	−1.74972	−	3.03060i	−0.0760746	−	0.131765i
$530$		0			0
$531$	20.1048	+	14.0021i	0.872473	+	0.607641i
$532$		0			0
$533$	−12.3109	+	7.10770i	−0.533244	+	0.307868i
$534$		0			0
$535$	0.178733	+	0.103192i	0.00772732	+	0.00446137i
$536$		0			0
$537$	−16.2162	−	17.6522i	−0.699780	−	0.761747i
$538$		0			0
$539$	33.1264	+	4.39468i	1.42686	+	0.189292i
$540$		0			0
$541$	−32.2695			−1.38737			−0.693687	−	0.720277i	$-0.744015\pi$
$541$	−32.2695			−1.38737			−0.693687	+	0.720277i	$0.744015\pi$
$542$		0			0
$543$	19.6722	+	21.4142i	0.844214	+	0.918971i
$544$		0			0
$545$	0.0281230	−	0.0487105i	0.00120466	−	0.00208653i
$546$		0			0
$547$	−11.9637	−	20.7218i	−0.511532	−	0.886000i	−0.999911	−	0.0133677i	$-0.995745\pi$
$547$	−11.9637	−	20.7218i	−0.511532	−	0.886000i	0.488379	−	0.872632i	$-0.337589\pi$
$548$		0			0
$549$	0.713749	+	1.52062i	0.0304621	+	0.0648987i
$550$		0			0
$551$	6.48563	+	11.2334i	0.276297	+	0.478561i
$552$		0			0
$553$	4.89979	+	24.6971i	0.208360	+	1.05023i
$554$		0			0
$555$	0.0400396	+	0.179536i	0.00169959	+	0.00762089i
$556$		0			0
$557$		−	34.1881i		−	1.44860i	−0.689486	−	0.724299i	$-0.742164\pi$
$557$		−	34.1881i		−	1.44860i	0.689486	−	0.724299i	$-0.257836\pi$
$558$		0			0
$559$			4.45639i			0.188485i
$560$		0			0
$561$	4.73179	−	15.0735i	0.199777	−	0.636405i
$562$		0			0
$563$	−9.79724	+	16.9693i	−0.412904	+	0.715171i	−0.995206	−	0.0978016i	$-0.968819\pi$
$563$	−9.79724	+	16.9693i	−0.412904	+	0.715171i	0.582302	+	0.812973i	$0.302152\pi$
$564$		0			0
$565$	0.0580533	−	0.0335171i	0.00244232	−	0.00141007i
$566$		0			0
$567$	−20.9282	−	11.3582i	−0.878903	−	0.477001i
$568$		0			0
$569$	21.5347	−	12.4330i	0.902780	−	0.521220i	0.0246790	−	0.999695i	$-0.492144\pi$
$569$	21.5347	−	12.4330i	0.902780	−	0.521220i	0.878101	+	0.478475i	$0.158810\pi$
$570$		0			0
$571$	7.82182	−	13.5478i	0.327333	−	0.566957i	−0.654649	−	0.755933i	$-0.727183\pi$
$571$	7.82182	−	13.5478i	0.327333	−	0.566957i	0.981982	+	0.188976i	$0.0605168\pi$
$572$		0			0
$573$	3.36880	−	10.7316i	0.140733	−	0.448318i
$574$		0			0
$575$			22.0784i			0.920732i
$576$		0			0
$577$		−	0.540475i		−	0.0225003i	−0.999937	−	0.0112501i	$-0.996419\pi$
$577$		−	0.540475i		−	0.0225003i	0.999937	−	0.0112501i	$-0.00358110\pi$
$578$		0			0
$579$	6.31691	+	28.3248i	0.262522	+	1.17714i
$580$		0			0
$581$	−6.87560	−	34.6560i	−0.285248	−	1.43777i
$582$		0			0
$583$	21.3489	+	36.9773i	0.884180	+	1.53144i
$584$		0			0
$585$	−0.0336965	−	0.0717896i	−0.00139318	−	0.00296813i
$586$		0			0
$587$	−18.2822	−	31.6656i	−0.754586	−	1.30698i	−0.945580	−	0.325390i	$-0.894504\pi$
$587$	−18.2822	−	31.6656i	−0.754586	−	1.30698i	0.190994	−	0.981591i	$-0.438829\pi$
$588$		0			0
$589$	−24.3151	+	42.1150i	−1.00189	+	1.73532i
$590$		0			0
$591$	−6.90352	−	7.51484i	−0.283973	−	0.309119i
$592$		0			0
$593$	−42.9714			−1.76462			−0.882312	−	0.470665i	$-0.844014\pi$
$593$	−42.9714			−1.76462			−0.882312	+	0.470665i	$0.844014\pi$
$594$		0			0
$595$	0.0661501	−	0.0579540i	0.00271189	−	0.00237588i
$596$		0			0
$597$	22.0117	+	23.9608i	0.900878	+	0.980652i
$598$		0			0
$599$	22.7897	+	13.1576i	0.931161	+	0.537606i	0.887178	−	0.461426i	$-0.152662\pi$
$599$	22.7897	+	13.1576i	0.931161	+	0.537606i	0.0439823	+	0.999032i	$0.485995\pi$
$600$		0			0
$601$	27.3703	−	15.8022i	1.11646	−	0.644587i	0.175963	−	0.984397i	$-0.443696\pi$
$601$	27.3703	−	15.8022i	1.11646	−	0.644587i	0.940494	+	0.339810i	$0.110363\pi$
$602$		0			0
$603$	18.1697	+	12.6545i	0.739929	+	0.515330i
$604$		0			0
$605$	0.102548	+	0.177618i	0.00416917	+	0.00722121i
$606$		0			0
$607$	7.85286	+	4.53385i	0.318738	+	0.184023i	0.650830	−	0.759224i	$-0.274421\pi$
$607$	7.85286	+	4.53385i	0.318738	+	0.184023i	−0.332092	+	0.943247i	$0.607754\pi$
$608$		0			0
$609$	−5.43538	+	7.42479i	−0.220253	+	0.300868i
$610$		0			0
$611$			4.42665i			0.179083i
$612$		0			0
$613$	15.2630			0.616465			0.308233	−	0.951311i	$-0.400262\pi$
$613$	15.2630			0.616465			0.308233	+	0.951311i	$0.400262\pi$
$614$		0			0
$615$	−0.268951	−	0.0844276i	−0.0108452	−	0.00340445i
$616$		0			0
$617$	12.1768	+	7.03028i	0.490219	+	0.283028i	0.724665	−	0.689101i	$-0.241994\pi$
$617$	12.1768	+	7.03028i	0.490219	+	0.283028i	−0.234446	+	0.972129i	$0.575328\pi$
$618$		0			0
$619$	4.52202	−	2.61079i	0.181755	−	0.104936i	−0.406362	−	0.913712i	$-0.633203\pi$
$619$	4.52202	−	2.61079i	0.181755	−	0.104936i	0.588117	+	0.808776i	$0.299869\pi$
$620$		0			0
$621$	3.08101	+	22.7381i	0.123637	+	0.912450i
$622$		0			0
$623$	10.0286	+	3.40981i	0.401787	+	0.136611i
$624$		0			0
$625$	−12.4977	+	21.6467i	−0.499909	+	0.865868i
$626$		0			0
$627$	−50.9616	−	15.9976i	−2.03521	−	0.638881i
$628$		0			0
$629$	11.6643			0.465087
$630$		0			0
$631$	34.8593			1.38773			0.693863	−	0.720107i	$-0.255907\pi$
$631$	34.8593			1.38773			0.693863	+	0.720107i	$0.255907\pi$
$632$		0			0
$633$	8.25725	+	37.0252i	0.328196	+	1.47162i
$634$		0			0
$635$	0.191017	−	0.330851i	0.00758028	−	0.0131294i
$636$		0			0
$637$	−4.06070	−	9.83103i	−0.160891	−	0.389519i
$638$		0			0
$639$	−34.9216	−	2.96659i	−1.38148	−	0.117357i
$640$		0			0
$641$	−5.33065	+	3.07765i	−0.210548	+	0.121560i	−0.601566	−	0.798823i	$-0.705456\pi$
$641$	−5.33065	+	3.07765i	−0.210548	+	0.121560i	0.391018	+	0.920383i	$0.372123\pi$
$642$		0			0
$643$	−9.75081	−	5.62963i	−0.384534	−	0.222011i	0.295255	−	0.955419i	$-0.404595\pi$
$643$	−9.75081	−	5.62963i	−0.384534	−	0.222011i	−0.679789	+	0.733407i	$0.737929\pi$
$644$		0			0
$645$	−0.0650782	+	0.0597842i	−0.00256245	+	0.00235400i
$646$		0			0
$647$	7.33809			0.288490			0.144245	−	0.989542i	$-0.453925\pi$
$647$	7.33809			0.288490			0.144245	+	0.989542i	$0.453925\pi$
$648$		0			0
$649$			38.9865i			1.53035i
$650$		0			0
$651$	−34.2955	−	3.72949i	−1.34415	−	0.146170i
$652$		0			0
$653$	1.18110	+	0.681911i	0.0462202	+	0.0266852i	0.522932	−	0.852374i	$-0.324838\pi$
$653$	1.18110	+	0.681911i	0.0462202	+	0.0266852i	−0.476712	+	0.879060i	$0.658171\pi$
$654$		0			0
$655$	0.141168	+	0.244511i	0.00551590	+	0.00955382i
$656$		0			0
$657$	−38.2937	−	3.25305i	−1.49398	−	0.126913i
$658$		0			0
$659$	35.8162	−	20.6785i	1.39520	−	0.805519i	0.401314	−	0.915940i	$-0.368553\pi$
$659$	35.8162	−	20.6785i	1.39520	−	0.805519i	0.993885	+	0.110422i	$0.0352202\pi$
$660$		0			0
$661$	36.0595	+	20.8190i	1.40255	+	0.809763i	0.994654	−	0.103264i	$-0.0329288\pi$
$661$	36.0595	+	20.8190i	1.40255	+	0.809763i	0.407897	+	0.913028i	$0.366262\pi$
$662$		0			0
$663$	−4.90823	+	1.09462i	−0.190620	+	0.0425115i
$664$		0			0
$665$	−0.195934	−	0.223644i	−0.00759801	−	0.00867256i
$666$		0			0
$667$	8.86709			0.343335
$668$		0			0
$669$	6.73614	−	21.4586i	0.260434	−	0.829636i
$670$		0			0
$671$	−1.33651	+	2.31490i	−0.0515954	+	0.0893658i
$672$		0			0
$673$	25.4080	+	44.0079i	0.979406	+	1.69638i	0.664555	+	0.747239i	$0.268621\pi$
$673$	25.4080	+	44.0079i	0.979406	+	1.69638i	0.314851	+	0.949141i	$0.398046\pi$
$674$		0			0
$675$	−9.85101	+	24.0390i	−0.379166	+	0.925263i
$676$		0			0
$677$	10.7278	+	18.5810i	0.412302	+	0.714128i	0.995141	−	0.0984599i	$-0.0313916\pi$
$677$	10.7278	+	18.5810i	0.412302	+	0.714128i	−0.582839	+	0.812587i	$0.698058\pi$
$678$		0			0
$679$	12.2717	−	2.43465i	0.470944	−	0.0934334i
$680$		0			0
$681$	−14.2637	−	4.47756i	−0.546584	−	0.171581i
$682$		0			0
$683$			5.66012i			0.216578i	0.994119	+	0.108289i	$0.0345373\pi$
$683$			5.66012i			0.216578i	−0.994119	+	0.108289i	$0.965463\pi$
$684$		0			0
$685$			0.108567i			0.00414815i
$686$		0			0
$687$	−14.4036	+	3.21225i	−0.549532	+	0.122555i
$688$		0			0
$689$	6.79543	−	11.7700i	0.258885	−	0.448402i
$690$		0			0
$691$	−15.6444	+	9.03228i	−0.595140	+	0.343604i	−0.767127	−	0.641495i	$-0.778314\pi$
$691$	−15.6444	+	9.03228i	−0.595140	+	0.343604i	0.171988	+	0.985099i	$0.444981\pi$
$692$		0			0
$693$	−4.20126	−	37.6573i	−0.159593	−	1.43048i
$694$		0			0
$695$	−0.159060	+	0.0918335i	−0.00603350	+	0.00348344i
$696$		0			0
$697$	−8.93757	+	15.4803i	−0.338535	+	0.586359i
$698$		0			0
$699$	0.289321	+	0.314941i	0.0109431	+	0.0119122i
$700$		0			0
$701$		−	28.7091i		−	1.08433i	−0.840273	−	0.542163i	$-0.817605\pi$
$701$		−	28.7091i		−	1.08433i	0.840273	−	0.542163i	$-0.182395\pi$
$702$		0			0
$703$		−	39.4355i		−	1.48734i
$704$		0			0
$705$	−0.0646438	+	0.0593851i	−0.00243463	+	0.00223657i
$706$		0			0
$707$	−3.07161	−	15.4822i	−0.115520	−	0.582269i
$708$		0			0
$709$	13.3468	+	23.1174i	0.501251	+	0.868193i	0.999999	+	0.00144551i	$0.000460119\pi$
$709$	13.3468	+	23.1174i	0.501251	+	0.868193i	−0.498748	+	0.866747i	$0.666207\pi$
$710$		0			0
$711$	25.8443	−	12.1308i	0.969236	−	0.454939i
$712$		0			0
$713$	16.6217	+	28.7896i	0.622486	+	1.07818i
$714$		0			0
$715$	0.0630975	−	0.109288i	0.00235971	−	0.00408714i
$716$		0			0
$717$	46.0320	−	10.2659i	1.71910	−	0.383387i
$718$		0			0
$719$	25.2381			0.941224			0.470612	−	0.882340i	$-0.344033\pi$
$719$	25.2381			0.941224			0.470612	+	0.882340i	$0.344033\pi$
$720$		0			0
$721$	20.2541	+	23.1185i	0.754302	+	0.860979i
$722$		0			0
$723$	3.42588	−	10.9134i	0.127410	−	0.405875i
$724$		0			0
$725$	8.69424	+	5.01962i	0.322896	+	0.186424i
$726$		0			0
$727$	24.5712	−	14.1862i	0.911294	−	0.526136i	0.0304464	−	0.999536i	$-0.490307\pi$
$727$	24.5712	−	14.1862i	0.911294	−	0.526136i	0.880847	+	0.473401i	$0.156974\pi$
$728$		0			0
$729$	−6.79075	+	26.1321i	−0.251509	+	0.967855i
$730$		0			0
$731$	2.80185	+	4.85294i	0.103630	+	0.179492i
$732$		0			0
$733$	16.2190	+	9.36404i	0.599062	+	0.345869i	0.768673	−	0.639642i	$-0.220918\pi$
$733$	16.2190	+	9.36404i	0.599062	+	0.345869i	−0.169610	+	0.985511i	$0.554251\pi$
$734$		0			0
$735$	0.0890899	−	0.191187i	0.00328613	−	0.00705203i
$736$		0			0
$737$			35.2341i			1.29787i
$738$		0			0
$739$	−31.3341			−1.15265			−0.576323	−	0.817222i	$-0.695513\pi$
$739$	−31.3341			−1.15265			−0.576323	+	0.817222i	$0.695513\pi$
$740$		0			0
$741$	3.70076	+	16.5941i	0.135951	+	0.609598i
$742$		0			0
$743$	16.2784	+	9.39834i	0.597197	+	0.344792i	0.767938	−	0.640524i	$-0.221283\pi$
$743$	16.2784	+	9.39834i	0.597197	+	0.344792i	−0.170741	+	0.985316i	$0.554616\pi$
$744$		0			0
$745$	0.124200	−	0.0717072i	0.00455035	−	0.00262715i
$746$		0			0
$747$	−36.2658	+	17.0224i	−1.32690	+	0.622817i
$748$		0			0
$749$	10.1039	−	29.7166i	0.369189	−	1.08582i
$750$		0			0
$751$	−7.34792	+	12.7270i	−0.268129	+	0.464414i	−0.968379	−	0.249485i	$-0.919739\pi$
$751$	−7.34792	+	12.7270i	−0.268129	+	0.464414i	0.700249	+	0.713898i	$0.253072\pi$
$752$		0			0
$753$	14.2770	−	13.1156i	0.520282	−	0.477958i
$754$		0			0
$755$	−0.228975			−0.00833327
$756$		0			0
$757$	15.4439			0.561318			0.280659	−	0.959808i	$-0.409447\pi$
$757$	15.4439			0.561318			0.280659	+	0.959808i	$0.409447\pi$
$758$		0			0
$759$	−26.8892	+	24.7018i	−0.976017	+	0.896620i
$760$		0			0
$761$	0.201785	−	0.349502i	0.00731470	−	0.0126694i	−0.862345	−	0.506321i	$-0.831005\pi$
$761$	0.201785	−	0.349502i	0.00731470	−	0.0126694i	0.869660	+	0.493652i	$0.164338\pi$
$762$		0			0
$763$	−8.09872	−	2.75363i	−0.293193	−	0.0996882i
$764$		0			0
$765$	−0.0818309	−	0.0569918i	−0.00295860	−	0.00206054i
$766$		0			0
$767$	10.7470	−	6.20478i	0.388051	−	0.224042i
$768$		0			0
$769$	10.4462	+	6.03109i	0.376698	+	0.217487i	0.676381	−	0.736552i	$-0.263547\pi$
$769$	10.4462	+	6.03109i	0.376698	+	0.217487i	−0.299682	+	0.954039i	$0.596881\pi$
$770$		0			0
$771$	3.66226	+	16.4214i	0.131893	+	0.591404i
$772$		0			0
$773$	−35.6215			−1.28122			−0.640608	−	0.767868i	$-0.721318\pi$
$773$	−35.6215			−1.28122			−0.640608	+	0.767868i	$0.721318\pi$
$774$		0			0
$775$			37.6378i			1.35199i
$776$		0			0
$777$	25.5973	−	11.2864i	0.918300	−	0.404898i
$778$		0			0
$779$	52.3369	+	30.2167i	1.87516	+	1.08263i
$780$		0			0
$781$	−27.8850	−	48.2982i	−0.997802	−	1.72824i
$782$		0			0
$783$	9.65452	+	3.95635i	0.345025	+	0.141388i
$784$		0			0
$785$	0.127019	−	0.0733344i	0.00453350	−	0.00261742i
$786$		0			0
$787$	−16.7626	−	9.67792i	−0.597524	−	0.344981i	0.170543	−	0.985350i	$-0.445448\pi$
$787$	−16.7626	−	9.67792i	−0.597524	−	0.344981i	−0.768067	+	0.640370i	$0.778781\pi$
$788$		0			0
$789$	3.10748	−	9.89915i	0.110629	−	0.352419i
$790$		0			0
$791$	−6.71804	−	7.66814i	−0.238866	−	0.272648i
$792$		0			0
$793$	0.850832			0.0302139
$794$		0			0
$795$	0.263045	−	0.0586634i	0.00932924	−	0.00208058i
$796$		0			0
$797$	−9.71888	+	16.8336i	−0.344261	+	0.596277i	−0.985219	−	0.171299i	$-0.945204\pi$
$797$	−9.71888	+	16.8336i	−0.344261	+	0.596277i	0.640959	+	0.767575i	$0.278537\pi$
$798$		0			0
$799$	2.78314	+	4.82054i	0.0984605	+	0.170539i
$800$		0			0
$801$	1.01664	−	11.9676i	0.0359214	−	0.422853i
$802$		0			0
$803$	−30.5775	−	52.9618i	−1.07906	−	1.86898i
$804$		0			0
$805$	−0.199370	+	0.0395541i	−0.00702686	+	0.00139410i
$806$		0			0
$807$	28.9968	−	26.6380i	1.02074	−	0.937701i
$808$		0			0
$809$		−	4.83109i		−	0.169852i	−0.996387	−	0.0849261i	$-0.972935\pi$
$809$		−	4.83109i		−	0.169852i	0.996387	−	0.0849261i	$-0.0270654\pi$
$810$		0			0
$811$			36.9933i			1.29901i	0.760358	+	0.649505i	$0.225024\pi$
$811$			36.9933i			1.29901i	−0.760358	+	0.649505i	$0.774976\pi$
$812$		0			0
$813$	1.21698	+	1.32474i	0.0426813	+	0.0464608i
$814$		0			0
$815$	0.0709684	−	0.122921i	0.00248592	−	0.00430573i
$816$		0			0
$817$	16.4071	−	9.47266i	0.574012	−	0.331406i
$818$		0			0
$819$	−9.71195	+	7.15135i	−0.339363	+	0.249888i
$820$		0			0
$821$	32.3478	−	18.6760i	1.12895	−	0.651798i	0.185277	−	0.982686i	$-0.440682\pi$
$821$	32.3478	−	18.6760i	1.12895	−	0.651798i	0.943670	+	0.330888i	$0.107348\pi$
$822$		0			0
$823$	−8.13705	+	14.0938i	−0.283640	+	0.491279i	−0.972278	−	0.233826i	$-0.924875\pi$
$823$	−8.13705	+	14.0938i	−0.283640	+	0.491279i	0.688639	+	0.725105i	$0.258209\pi$
$824$		0			0
$825$	−40.3487	+	8.99844i	−1.40476	+	0.313286i
$826$		0			0
$827$			19.0164i			0.661265i	0.943760	+	0.330633i	$0.107262\pi$
$827$			19.0164i			0.661265i	−0.943760	+	0.330633i	$0.892738\pi$
$828$		0			0
$829$			54.5471i			1.89450i	0.320497	+	0.947250i	$0.396150\pi$
$829$			54.5471i			1.89450i	−0.320497	+	0.947250i	$0.603850\pi$
$830$		0			0
$831$	−25.0929	−	7.87702i	−0.870463	−	0.273251i
$832$		0			0
$833$	−10.6030	−	8.15276i	−0.367374	−	0.282476i
$834$		0			0
$835$	−0.197432	−	0.341962i	−0.00683240	−	0.0118341i
$836$		0			0
$837$	5.25232	+	38.7625i	0.181547	+	1.33983i
$838$		0			0
$839$	−11.7950	−	20.4295i	−0.407208	−	0.705305i	0.587368	−	0.809320i	$-0.300164\pi$
$839$	−11.7950	−	20.4295i	−0.407208	−	0.705305i	−0.994576	+	0.104015i	$0.966831\pi$
$840$		0			0
$841$	−12.4840	+	21.6230i	−0.430484	+	0.745620i
$842$		0			0
$843$	−7.70570	+	24.5472i	−0.265398	+	0.845449i
$844$		0			0
$845$	0.185990			0.00639826
$846$		0			0
$847$	23.4612	−	20.5543i	0.806137	−	0.706255i
$848$		0			0
$849$	55.8410	−	12.4535i	1.91646	−	0.427403i
$850$		0			0
$851$	−23.3462	−	13.4789i	−0.800298	−	0.462052i
$852$		0			0
$853$	44.4097	−	25.6400i	1.52056	−	0.877895i	0.520853	−	0.853646i	$-0.325614\pi$
$853$	44.4097	−	25.6400i	1.52056	−	0.877895i	0.999706	−	0.0242489i	$-0.00771943\pi$
$854$		0			0
$855$	−0.192682	+	0.276659i	−0.00658957	+	0.00946154i
$856$		0			0
$857$	−25.4437	−	44.0698i	−0.869141	−	1.50540i	−0.862875	−	0.505417i	$-0.831339\pi$
$857$	−25.4437	−	44.0698i	−0.869141	−	1.50540i	−0.00626618	−	0.999980i	$-0.501995\pi$
$858$		0			0
$859$	3.87842	+	2.23921i	0.132330	+	0.0764007i	0.564704	−	0.825294i	$-0.308991\pi$
$859$	3.87842	+	2.23921i	0.132330	+	0.0764007i	−0.432374	+	0.901695i	$0.642324\pi$
$860$		0			0
$861$	−4.63469	+	42.6195i	−0.157950	+	1.45247i
$862$		0			0
$863$		−	19.5957i		−	0.667046i	−0.942742	−	0.333523i	$-0.891763\pi$
$863$		−	19.5957i		−	0.667046i	0.942742	−	0.333523i	$-0.108237\pi$
$864$		0			0
$865$	−0.101899			−0.00346466
$866$		0			0
$867$	17.0272	−	15.6421i	0.578273	−	0.531232i
$868$		0			0
$869$	39.3437	+	22.7151i	1.33464	+	0.770557i
$870$		0			0
$871$	9.71261	−	5.60758i	0.329099	−	0.190006i
$872$		0			0
$873$	−6.02764	−	12.8417i	−0.204005	−	0.434627i
$874$		0			0
$875$	−0.435763	−	0.148163i	−0.0147315	−	0.00500883i
$876$		0			0
$877$	10.7024	−	18.5371i	0.361395	−	0.625954i	−0.626796	−	0.779183i	$-0.715634\pi$
$877$	10.7024	−	18.5371i	0.361395	−	0.625954i	0.988191	+	0.153230i	$0.0489674\pi$
$878$		0			0
$879$	−9.64098	−	43.2298i	−0.325182	−	1.45811i
$880$		0			0
$881$	−9.43135			−0.317750			−0.158875	−	0.987299i	$-0.550787\pi$
$881$	−9.43135			−0.317750			−0.158875	+	0.987299i	$0.550787\pi$
$882$		0			0
$883$	39.5587			1.33126			0.665628	−	0.746284i	$-0.268164\pi$
$883$	39.5587			1.33126			0.665628	+	0.746284i	$0.268164\pi$
$884$		0			0
$885$	0.234785	+	0.0737025i	0.00789223	+	0.00247748i
$886$		0			0
$887$	20.1249	−	34.8573i	0.675727	−	1.17039i	−0.300529	−	0.953773i	$-0.597163\pi$
$887$	20.1249	−	34.8573i	0.675727	−	1.17039i	0.976256	−	0.216620i	$-0.0695034\pi$
$888$		0			0
$889$	−55.0081	−	18.7032i	−1.84491	−	0.627286i
$890$		0			0
$891$	−40.2987	+	14.8979i	−1.35006	+	0.499100i
$892$		0			0
$893$	16.2976	−	9.40942i	0.545378	−	0.314874i
$894$		0			0
$895$	−0.208501	−	0.120378i	−0.00696943	−	0.00402380i
$896$		0			0
$897$	11.0888	+	3.48092i	0.370243	+	0.116224i
$898$		0			0
$899$	15.1160			0.504148
$900$		0			0
$901$		−	17.0898i		−	0.569344i
$902$		0			0
$903$	10.8444	+	7.93869i	0.360877	+	0.264183i
$904$		0			0
$905$	0.252937	+	0.146033i	0.00840791	+	0.00485431i
$906$		0			0
$907$	−2.84241	−	4.92321i	−0.0943808	−	0.163472i	0.814969	−	0.579504i	$-0.196754\pi$
$907$	−2.84241	−	4.92321i	−0.0943808	−	0.163472i	−0.909350	+	0.416032i	$0.863420\pi$
$908$		0			0
$909$	−16.2014	+	7.60460i	−0.537367	+	0.252229i
$910$		0			0
$911$	−40.0431	+	23.1189i	−1.32669	+	0.765963i	−0.984786	−	0.173773i	$-0.944404\pi$
$911$	−40.0431	+	23.1189i	−1.32669	+	0.765963i	−0.341901	+	0.939736i	$0.611071\pi$
$912$		0			0
$913$	−55.2088	−	31.8748i	−1.82714	−	1.05490i
$914$		0			0
$915$	0.0114142	+	0.0124250i	0.000377343	+	0.000410757i
$916$		0			0
$917$	32.2969	−	28.2952i	1.06654	−	0.934391i
$918$		0			0
$919$	−50.9663			−1.68122			−0.840612	−	0.541637i	$-0.817805\pi$
$919$	−50.9663			−1.68122			−0.840612	+	0.541637i	$0.817805\pi$
$920$		0			0
$921$	−7.08058	−	7.70758i	−0.233313	−	0.253973i
$922$		0			0
$923$	−8.87589	+	15.3735i	−0.292153	+	0.506024i
$924$		0			0
$925$	−15.2608	−	26.4324i	−0.501770	−	0.869092i
$926$		0			0
$927$	19.9178	−	28.5987i	0.654188	−	0.939306i
$928$		0			0
$929$	14.4161	+	24.9694i	0.472977	+	0.819221i	0.999522	−	0.0309269i	$-0.00984590\pi$
$929$	14.4161	+	24.9694i	0.472977	+	0.819221i	−0.526544	+	0.850148i	$0.676513\pi$
$930$		0			0
$931$	−27.5634	+	35.8474i	−0.903353	+	1.17485i
$932$		0			0
$933$	−12.8719	−	57.7169i	−0.421406	−	1.88957i
$934$		0			0
$935$		−	0.158684i		−	0.00518951i
$936$		0			0
$937$			21.8146i			0.712652i	0.934362	+	0.356326i	$0.115971\pi$
$937$			21.8146i			0.712652i	−0.934362	+	0.356326i	$0.884029\pi$
$938$		0			0
$939$	6.55951	−	20.8959i	0.214062	−	0.681911i
$940$		0			0
$941$	−5.21225	+	9.02789i	−0.169915	+	0.294301i	−0.938390	−	0.345579i	$-0.887683\pi$
$941$	−5.21225	+	9.02789i	−0.169915	+	0.294301i	0.768475	+	0.639880i	$0.221016\pi$
$942$		0			0
$943$	35.7772	−	20.6560i	1.16507	−	0.672651i
$944$		0			0
$945$	−0.234723	−	0.0458887i	−0.00763554	−	0.00149276i
$946$		0			0
$947$	−18.8197	+	10.8655i	−0.611557	+	0.353083i	−0.773575	−	0.633705i	$-0.781533\pi$
$947$	−18.8197	+	10.8655i	−0.611557	+	0.353083i	0.162018	+	0.986788i	$0.448200\pi$
$948$		0			0
$949$	−9.73294	+	16.8580i	−0.315945	+	0.547232i
$950$		0			0
$951$	2.96777	−	9.45407i	0.0962364	−	0.306569i
$952$		0			0
$953$			22.2100i			0.719453i	0.933058	+	0.359726i	$0.117130\pi$
$953$			22.2100i			0.719453i	−0.933058	+	0.359726i	$0.882870\pi$
$954$		0			0
$955$		−	0.112975i		−	0.00365578i
$956$		0			0
$957$	3.61394	+	16.2048i	0.116822	+	0.523826i
$958$		0			0
$959$	16.1956	−	3.21313i	0.522982	−	0.103757i
$960$		0			0
$961$	12.8355	+	22.2318i	0.414049	+	0.717155i
$962$		0			0
$963$	−35.4622	−	3.01251i	−1.14275	−	0.0970768i
$964$		0			0
$965$	0.145742	+	0.252433i	0.00469162	+	0.00812612i
$966$		0			0
$967$	−30.2262	+	52.3534i	−0.972010	+	1.68357i	−0.282541	+	0.959255i	$0.591177\pi$
$967$	−30.2262	+	52.3534i	−0.972010	+	1.68357i	−0.689469	+	0.724315i	$0.742156\pi$
$968$		0			0
$969$	14.4632	+	15.7439i	0.464623	+	0.505767i
$970$		0			0
$971$	24.7707			0.794931			0.397466	−	0.917617i	$-0.369890\pi$
$971$	24.7707			0.794931			0.397466	+	0.917617i	$0.369890\pi$
$972$		0			0
$973$	18.4068	+	21.0099i	0.590094	+	0.673548i
$974$		0			0
$975$	8.90207	+	9.69037i	0.285094	+	0.310340i
$976$		0			0
$977$	18.1210	+	10.4621i	0.579741	+	0.334714i	0.761030	−	0.648716i	$-0.224694\pi$
$977$	18.1210	+	10.4621i	0.579741	+	0.334714i	−0.181290	+	0.983430i	$0.558027\pi$
$978$		0			0
$979$	16.5517	−	9.55612i	0.528994	−	0.305415i
$980$		0			0
$981$	−0.821005	+	9.66457i	−0.0262127	+	0.308566i
$982$		0			0
$983$	19.1275	+	33.1297i	0.610071	+	1.05667i	0.991228	+	0.132164i	$0.0421924\pi$
$983$	19.1275	+	33.1297i	0.610071	+	1.05667i	−0.381157	+	0.924510i	$0.624474\pi$
$984$		0			0
$985$	−0.0887627	−	0.0512472i	−0.00282821	−	0.00163287i
$986$		0			0
$987$	10.7720	+	7.88570i	0.342875	+	0.251004i
$988$		0			0
$989$		−	12.9509i		−	0.411815i
$990$		0			0
$991$	21.5607			0.684898			0.342449	−	0.939536i	$-0.388744\pi$
$991$	21.5607			0.684898			0.342449	+	0.939536i	$0.388744\pi$
$992$		0			0
$993$	−23.7477	−	7.45474i	−0.753611	−	0.236569i
$994$		0			0
$995$	0.283017	+	0.163400i	0.00897225	+	0.00518013i
$996$		0			0
$997$	23.2029	−	13.3962i	0.734845	−	0.424263i	−0.0853473	−	0.996351i	$-0.527200\pi$
$997$	23.2029	−	13.3962i	0.734845	−	0.424263i	0.820192	+	0.572089i	$0.193867\pi$
$998$		0			0
$999$	−19.4054	−	25.0926i	−0.613959	−	0.793896i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bu.a.41.7	✓	48
3.2	odd	2		1512.2.bu.a.881.13		48
4.3	odd	2		1008.2.cc.d.545.18		48
7.6	odd	2	inner	504.2.bu.a.41.18	yes	48
9.2	odd	6	inner	504.2.bu.a.209.18	yes	48
9.4	even	3		4536.2.k.a.3401.25		48
9.5	odd	6		4536.2.k.a.3401.24		48
9.7	even	3		1512.2.bu.a.1385.12		48
12.11	even	2		3024.2.cc.d.881.13		48
21.20	even	2		1512.2.bu.a.881.12		48
28.27	even	2		1008.2.cc.d.545.7		48
36.7	odd	6		3024.2.cc.d.2897.12		48
36.11	even	6		1008.2.cc.d.209.7		48
63.13	odd	6		4536.2.k.a.3401.23		48
63.20	even	6	inner	504.2.bu.a.209.7	yes	48
63.34	odd	6		1512.2.bu.a.1385.13		48
63.41	even	6		4536.2.k.a.3401.26		48
84.83	odd	2		3024.2.cc.d.881.12		48
252.83	odd	6		1008.2.cc.d.209.18		48
252.223	even	6		3024.2.cc.d.2897.13		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bu.a.41.7	✓	48	1.1	even	1	trivial
504.2.bu.a.41.18	yes	48	7.6	odd	2	inner
504.2.bu.a.209.7	yes	48	63.20	even	6	inner
504.2.bu.a.209.18	yes	48	9.2	odd	6	inner
1008.2.cc.d.209.7		48	36.11	even	6
1008.2.cc.d.209.18		48	252.83	odd	6
1008.2.cc.d.545.7		48	28.27	even	2
1008.2.cc.d.545.18		48	4.3	odd	2
1512.2.bu.a.881.12		48	21.20	even	2
1512.2.bu.a.881.13		48	3.2	odd	2
1512.2.bu.a.1385.12		48	9.7	even	3
1512.2.bu.a.1385.13		48	63.34	odd	6
3024.2.cc.d.881.12		48	84.83	odd	2
3024.2.cc.d.881.13		48	12.11	even	2
3024.2.cc.d.2897.12		48	36.7	odd	6
3024.2.cc.d.2897.13		48	252.223	even	6
4536.2.k.a.3401.23		48	63.13	odd	6
4536.2.k.a.3401.24		48	9.5	odd	6
4536.2.k.a.3401.25		48	9.4	even	3
4536.2.k.a.3401.26		48	63.41	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bu (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27553 + 1.17176i) q^{3} +(-0.00869840 + 0.0150661i) q^{5} +(2.50492 + 0.851694i) q^{7} +(0.253935 - 2.98923i) q^{9} +(4.13424 - 2.38691i) q^{11} +(-1.31594 - 0.759761i) q^{13} +(-0.00655885 - 0.0294097i) q^{15} -1.91072 q^{17} +6.45989i q^{19} +(-4.19307 + 1.84882i) q^{21} +(3.82432 + 2.20797i) q^{23} +(2.49985 + 4.32986i) q^{25} +(3.17878 + 4.11040i) q^{27} +(1.73895 - 1.00399i) q^{29} +(6.51946 + 3.76401i) q^{31} +(-2.47644 + 7.88892i) q^{33} +(-0.0346205 + 0.0303309i) q^{35} -6.10467 q^{37} +(2.56878 - 0.572882i) q^{39} +(4.67759 - 8.10182i) q^{41} +(-1.46638 - 2.53985i) q^{43} +(0.0428272 + 0.0298274i) q^{45} +(-1.45659 - 2.52289i) q^{47} +(5.54924 + 4.26685i) q^{49} +(2.43718 - 2.23892i) q^{51} +8.94416i q^{53} +0.0830491i q^{55} +(-7.56947 - 8.23976i) q^{57} +(-4.08337 + 7.07261i) q^{59} +(-0.484917 + 0.279967i) q^{61} +(3.18200 - 7.27151i) q^{63} +(0.0228932 - 0.0132174i) q^{65} +(-3.69036 + 6.39189i) q^{67} +(-7.46525 + 1.66488i) q^{69} -11.6825i q^{71} -12.8105i q^{73} +(-8.26221 - 2.59362i) q^{75} +(12.3889 - 2.45790i) q^{77} +(4.75827 + 8.24157i) q^{79} +(-8.87103 - 1.51814i) q^{81} +(-6.67701 - 11.5649i) q^{83} +(0.0166202 - 0.0287871i) q^{85} +(-1.04165 + 3.31825i) q^{87} +4.00356 q^{89} +(-2.64925 - 3.02392i) q^{91} +(-12.7263 + 2.83817i) q^{93} +(-0.0973252 - 0.0561907i) q^{95} +(4.09514 - 2.36433i) q^{97} +(-6.08519 - 12.9643i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{9} + 8 q^{15} - 4 q^{21} + 12 q^{23} - 24 q^{25} - 36 q^{29} + 32 q^{39} + 12 q^{43} + 6 q^{49} + 24 q^{51} + 28 q^{57} - 14 q^{63} + 36 q^{65} - 60 q^{77} - 12 q^{79} - 36 q^{81} - 12 q^{91}+ \cdots + 44 q^{99}+O(q^{100}) \) 48 * q - 4 * q^9 + 8 * q^15 - 4 * q^21 + 12 * q^23 - 24 * q^25 - 36 * q^29 + 32 * q^39 + 12 * q^43 + 6 * q^49 + 24 * q^51 + 28 * q^57 - 14 * q^63 + 36 * q^65 - 60 * q^77 - 12 * q^79 - 36 * q^81 - 12 * q^91 + 16 * q^93 - 108 * q^95 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more