LMFDB - Embedded newform 504.2.i.b.125.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(125,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))

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

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

chi := DirichletCharacter("504.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.i (of order $2$, degree $1$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			125.3
Character	$\chi$	$=$	504.125
Dual form			504.2.i.b.125.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39273 + 0.245576i) q^{2} +(1.87939 - 0.684040i) q^{4} -2.37285i q^{5} +(-1.53209 + 2.15701i) q^{7} +(-2.44949 + 1.41421i) q^{8} +O(q^{10})$	\(q+(-1.39273 + 0.245576i) q^{2} +(1.87939 - 0.684040i) q^{4} -2.37285i q^{5} +(-1.53209 + 2.15701i) q^{7} +(-2.44949 + 1.41421i) q^{8} +(0.582714 + 3.30474i) q^{10} -0.335967 q^{11} +6.30668 q^{13} +(1.60407 - 3.38038i) q^{14} +(3.06418 - 2.57115i) q^{16} +4.10990 q^{17} -2.19029 q^{19} +(-1.62312 - 4.45950i) q^{20} +(0.467911 - 0.0825054i) q^{22} -6.23877i q^{23} -0.630415 q^{25} +(-8.78350 + 1.54877i) q^{26} +(-1.40390 + 5.10187i) q^{28} -4.38425 q^{29} -8.10772i q^{31} +(-3.63616 + 4.33340i) q^{32} +(-5.72397 + 1.00929i) q^{34} +(5.11827 + 3.63542i) q^{35} -9.97448i q^{37} +(3.05048 - 0.537881i) q^{38} +(3.35572 + 5.81227i) q^{40} +7.35615 q^{41} -0.892951i q^{43} +(-0.631412 + 0.229815i) q^{44} +(1.53209 + 8.68891i) q^{46} +9.34720 q^{47} +(-2.30541 - 6.60947i) q^{49} +(0.877997 - 0.154815i) q^{50} +(11.8527 - 4.31403i) q^{52} +0.748092 q^{53} +0.797200i q^{55} +(0.702359 - 7.45028i) q^{56} +(6.10607 - 1.07666i) q^{58} +8.91900i q^{59} +7.33154 q^{61} +(1.99106 + 11.2918i) q^{62} +(4.00000 - 6.92820i) q^{64} -14.9648i q^{65} +5.56012i q^{67} +(7.72408 - 2.81133i) q^{68} +(-8.02113 - 3.80623i) q^{70} +2.08689i q^{71} +5.81227i q^{73} +(2.44949 + 13.8917i) q^{74} +(-4.11640 + 1.49825i) q^{76} +(0.514732 - 0.724686i) q^{77} -9.27631 q^{79} +(-6.10095 - 7.27083i) q^{80} +(-10.2451 + 1.80649i) q^{82} -1.64816i q^{83} -9.75216i q^{85} +(0.219287 + 1.24364i) q^{86} +(0.822948 - 0.475129i) q^{88} -11.3383 q^{89} +(-9.66240 + 13.6036i) q^{91} +(-4.26757 - 11.7250i) q^{92} +(-13.0181 + 2.29544i) q^{94} +5.19722i q^{95} -2.81578i q^{97} +(4.83393 + 8.63905i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 48 q^{22} - 72 q^{25} - 24 q^{28} - 72 q^{49} + 48 q^{58} + 96 q^{64} - 24 q^{70} + 48 q^{79} - 144 q^{88}+O(q^{100}) $ 24 * q + 48 * q^22 - 72 * q^25 - 24 * q^28 - 72 * q^49 + 48 * q^58 + 96 * q^64 - 24 * q^70 + 48 * q^79 - 144 * q^88

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.39273	+	0.245576i	−0.984808	+	0.173648i
$2$	−1.39273	+	0.245576i	−0.984808	+	0.173648i
$3$		0			0
$3$		0			0
$4$	1.87939	−	0.684040i	0.939693	−	0.342020i
$5$		−	2.37285i		−	1.06117i	−0.847632	−	0.530585i	$-0.821972\pi$
$5$		−	2.37285i		−	1.06117i	0.847632	−	0.530585i	$-0.178028\pi$
$6$		0			0
$7$	−1.53209	+	2.15701i	−0.579075	+	0.815274i
$7$	−1.53209	+	2.15701i	−0.579075	+	0.815274i
$8$	−2.44949	+	1.41421i	−0.866025	+	0.500000i
$9$		0			0
$10$	0.582714	+	3.30474i	0.184270	+	1.04505i
$11$	−0.335967			−0.101298			−0.0506490	−	0.998717i	$-0.516129\pi$
$11$	−0.335967			−0.101298			−0.0506490	+	0.998717i	$0.516129\pi$
$12$		0			0
$13$	6.30668			1.74916			0.874580	−	0.484882i	$-0.161137\pi$
$13$	6.30668			1.74916			0.874580	+	0.484882i	$0.161137\pi$
$14$	1.60407	−	3.38038i	0.428707	−	0.903444i
$15$		0			0
$16$	3.06418	−	2.57115i	0.766044	−	0.642788i
$17$	4.10990			0.996796			0.498398	−	0.866948i	$-0.333922\pi$
$17$	4.10990			0.996796			0.498398	+	0.866948i	$0.333922\pi$
$18$		0			0
$19$	−2.19029			−0.502487			−0.251243	−	0.967924i	$-0.580839\pi$
$19$	−2.19029			−0.502487			−0.251243	+	0.967924i	$0.580839\pi$
$20$	−1.62312	−	4.45950i	−0.362942	−	0.997174i
$21$		0			0
$22$	0.467911	−	0.0825054i	0.0997590	−	0.0175902i
$23$		−	6.23877i		−	1.30087i	−0.759561	−	0.650436i	$-0.774586\pi$
$23$		−	6.23877i		−	1.30087i	0.759561	−	0.650436i	$-0.225414\pi$
$24$		0			0
$25$	−0.630415			−0.126083
$26$	−8.78350	+	1.54877i	−1.72259	+	0.303738i
$27$		0			0
$28$	−1.40390	+	5.10187i	−0.265312	+	0.964162i
$29$	−4.38425			−0.814134			−0.407067	−	0.913398i	$-0.633449\pi$
$29$	−4.38425			−0.814134			−0.407067	+	0.913398i	$0.633449\pi$
$30$		0			0
$31$		−	8.10772i		−	1.45619i	−0.685477	−	0.728094i	$-0.740406\pi$
$31$		−	8.10772i		−	1.45619i	0.685477	−	0.728094i	$-0.259594\pi$
$32$	−3.63616	+	4.33340i	−0.642788	+	0.766044i
$33$		0			0
$34$	−5.72397	+	1.00929i	−0.981653	+	0.173092i
$35$	5.11827	+	3.63542i	0.865145	+	0.614498i
$36$		0			0
$37$		−	9.97448i		−	1.63979i	−0.572510	−	0.819897i	$-0.694030\pi$
$37$		−	9.97448i		−	1.63979i	0.572510	−	0.819897i	$-0.305970\pi$
$38$	3.05048	−	0.537881i	0.494853	−	0.0872559i
$39$		0			0
$40$	3.35572	+	5.81227i	0.530585	+	0.919001i
$41$	7.35615			1.14884			0.574418	−	0.818562i	$-0.305228\pi$
$41$	7.35615			1.14884			0.574418	+	0.818562i	$0.305228\pi$
$42$		0			0
$43$		−	0.892951i		−	0.136174i	−0.997679	−	0.0680869i	$-0.978310\pi$
$43$		−	0.892951i		−	0.136174i	0.997679	−	0.0680869i	$-0.0216895\pi$
$44$	−0.631412	+	0.229815i	−0.0951889	+	0.0346459i
$45$		0			0
$46$	1.53209	+	8.68891i	0.225894	+	1.28111i
$47$	9.34720			1.36343			0.681715	−	0.731618i	$-0.261235\pi$
$47$	9.34720			1.36343			0.681715	+	0.731618i	$0.261235\pi$
$48$		0			0
$49$	−2.30541	−	6.60947i	−0.329344	−	0.944210i
$50$	0.877997	−	0.154815i	0.124168	−	0.0218941i
$51$		0			0
$52$	11.8527	−	4.31403i	1.64367	−	0.598248i
$53$	0.748092			0.102758			0.0513792	−	0.998679i	$-0.483638\pi$
$53$	0.748092			0.102758			0.0513792	+	0.998679i	$0.483638\pi$
$54$		0			0
$55$			0.797200i			0.107494i
$56$	0.702359	−	7.45028i	0.0938567	−	0.995586i
$57$		0			0
$58$	6.10607	−	1.07666i	0.801766	−	0.141373i
$59$			8.91900i			1.16115i	0.814205	+	0.580577i	$0.197173\pi$
$59$			8.91900i			1.16115i	−0.814205	+	0.580577i	$0.802827\pi$
$60$		0			0
$61$	7.33154			0.938708			0.469354	−	0.883010i	$-0.344487\pi$
$61$	7.33154			0.938708			0.469354	+	0.883010i	$0.344487\pi$
$62$	1.99106	+	11.2918i	0.252865	+	1.43407i
$63$		0			0
$64$	4.00000	−	6.92820i	0.500000	−	0.866025i
$65$		−	14.9648i		−	1.85616i
$66$		0			0
$67$			5.56012i			0.679277i	0.940556	+	0.339639i	$0.110305\pi$
$67$			5.56012i			0.679277i	−0.940556	+	0.339639i	$0.889695\pi$
$68$	7.72408	−	2.81133i	0.936682	−	0.340924i
$69$		0			0
$70$	−8.02113	−	3.80623i	−0.958708	−	0.454931i
$71$			2.08689i			0.247668i	0.992303	+	0.123834i	$0.0395190\pi$
$71$			2.08689i			0.247668i	−0.992303	+	0.123834i	$0.960481\pi$
$72$		0			0
$73$			5.81227i			0.680275i	0.940376	+	0.340137i	$0.110474\pi$
$73$			5.81227i			0.680275i	−0.940376	+	0.340137i	$0.889526\pi$
$74$	2.44949	+	13.8917i	0.284747	+	1.61488i
$75$		0			0
$76$	−4.11640	+	1.49825i	−0.472183	+	0.171861i
$77$	0.514732	−	0.724686i	0.0586591	−	0.0825856i
$78$		0			0
$79$	−9.27631			−1.04367			−0.521833	−	0.853047i	$-0.674752\pi$
$79$	−9.27631			−1.04367			−0.521833	+	0.853047i	$0.674752\pi$
$80$	−6.10095	−	7.27083i	−0.682107	−	0.812904i
$81$		0			0
$82$	−10.2451	+	1.80649i	−1.13138	+	0.199493i
$83$		−	1.64816i		−	0.180910i	−0.995901	−	0.0904548i	$-0.971168\pi$
$83$		−	1.64816i		−	0.180910i	0.995901	−	0.0904548i	$-0.0288321\pi$
$84$		0			0
$85$		−	9.75216i		−	1.05777i
$86$	0.219287	+	1.24364i	0.0236463	+	0.134105i
$87$		0			0
$88$	0.822948	−	0.475129i	0.0877266	−	0.0506490i
$89$	−11.3383			−1.20185			−0.600927	−	0.799304i	$-0.705202\pi$
$89$	−11.3383			−1.20185			−0.600927	+	0.799304i	$0.705202\pi$
$90$		0			0
$91$	−9.66240	+	13.6036i	−1.01289	+	1.42604i
$92$	−4.26757	−	11.7250i	−0.444925	−	1.22242i
$93$		0			0
$94$	−13.0181	+	2.29544i	−1.34272	+	0.236757i
$95$			5.19722i			0.533224i
$96$		0			0
$97$		−	2.81578i		−	0.285899i	−0.989730	−	0.142950i	$-0.954341\pi$
$97$		−	2.81578i		−	0.285899i	0.989730	−	0.142950i	$-0.0456587\pi$
$98$	4.83393	+	8.63905i	0.488301	+	0.872675i
$99$		0			0
$100$	−1.18479	+	0.431229i	−0.118479	+	0.0431229i
$101$		−	2.37285i		−	0.236107i	−0.993007	−	0.118054i	$-0.962335\pi$
$101$		−	2.37285i		−	0.236107i	0.993007	−	0.118054i	$-0.0376655\pi$
$102$		0			0
$103$		−	8.10772i		−	0.798877i	−0.916760	−	0.399438i	$-0.869205\pi$
$103$		−	8.10772i		−	0.798877i	0.916760	−	0.399438i	$-0.130795\pi$
$104$	−15.4482	+	8.91900i	−1.51482	+	0.874580i
$105$		0			0
$106$	−1.04189	+	0.183713i	−0.101197	+	0.0178438i
$107$	18.3115			1.77024			0.885121	−	0.465360i	$-0.154075\pi$
$107$	18.3115			1.77024			0.885121	+	0.465360i	$0.154075\pi$
$108$		0			0
$109$			16.4849i			1.57896i	0.613774	+	0.789482i	$0.289651\pi$
$109$			16.4849i			1.57896i	−0.613774	+	0.789482i	$0.710349\pi$
$110$	−0.195773	−	1.11028i	−0.0186662	−	0.105861i
$111$		0			0
$112$	0.851411	+	10.5487i	0.0804508	+	0.996759i
$113$			4.88379i			0.459429i	0.973258	+	0.229714i	$0.0737792\pi$
$113$			4.88379i			0.459429i	−0.973258	+	0.229714i	$0.926221\pi$
$114$		0			0
$115$	−14.8037			−1.38045
$116$	−8.23969	+	2.99900i	−0.765036	+	0.278450i
$117$		0			0
$118$	−2.19029	−	12.4217i	−0.201632	−	1.14351i
$119$	−6.29673	+	8.86510i	−0.577220	+	0.812662i
$120$		0			0
$121$	−10.8871			−0.989739
$122$	−10.2108	+	1.80045i	−0.924447	+	0.163005i
$123$		0			0
$124$	−5.54600	−	15.2375i	−0.498046	−	1.36837i
$125$		−	10.3684i		−	0.927375i
$126$		0			0
$127$	15.1480			1.34416			0.672082	−	0.740477i	$-0.265400\pi$
$127$	15.1480			1.34416			0.672082	+	0.740477i	$0.265400\pi$
$128$	−3.86952	+	10.6314i	−0.342020	+	0.939693i
$129$		0			0
$130$	3.67499	+	20.8419i	0.322318	+	1.82796i
$131$			15.3129i			1.33789i	0.743312	+	0.668945i	$0.233254\pi$
$131$			15.3129i			1.33789i	−0.743312	+	0.668945i	$0.766746\pi$
$132$		0			0
$133$	3.35572	−	4.72448i	0.290977	−	0.409664i
$134$	−1.36543	−	7.74374i	−0.117955	−	0.668957i
$135$		0			0
$136$	−10.0671	+	5.81227i	−0.863251	+	0.498398i
$137$			9.55834i			0.816625i	0.912842	+	0.408312i	$0.133883\pi$
$137$			9.55834i			0.816625i	−0.912842	+	0.408312i	$0.866117\pi$
$138$		0			0
$139$	−6.71143			−0.569256			−0.284628	−	0.958638i	$-0.591870\pi$
$139$	−6.71143			−0.569256			−0.284628	+	0.958638i	$0.591870\pi$
$140$	12.1060	+	3.33125i	1.02314	+	0.281542i
$141$		0			0
$142$	−0.512489	−	2.90647i	−0.0430071	−	0.243905i
$143$	−2.11884			−0.177186
$144$		0			0
$145$			10.4032i			0.863935i
$146$	−1.42735	−	8.09491i	−0.118128	−	0.669940i
$147$		0			0
$148$	−6.82295	−	18.7459i	−0.560843	−	1.54090i
$149$	−7.11511			−0.582892			−0.291446	−	0.956587i	$-0.594136\pi$
$149$	−7.11511			−0.582892			−0.291446	+	0.956587i	$0.594136\pi$
$150$		0			0
$151$	−4.28581			−0.348774			−0.174387	−	0.984677i	$-0.555794\pi$
$151$	−4.28581			−0.348774			−0.174387	+	0.984677i	$0.555794\pi$
$152$	5.36509	−	3.09754i	0.435166	−	0.251243i
$153$		0			0
$154$	−0.538916	+	1.13570i	−0.0434271	+	0.0915170i
$155$	−19.2384			−1.54526
$156$		0			0
$157$	7.33154			0.585121			0.292560	−	0.956247i	$-0.405493\pi$
$157$	7.33154			0.585121			0.292560	+	0.956247i	$0.405493\pi$
$158$	12.9194	−	2.27804i	1.02781	−	0.181231i
$159$		0			0
$160$	10.2825	+	8.62805i	0.812904	+	0.682107i
$161$	13.4571	+	9.55834i	1.06057	+	0.753303i
$162$		0			0
$163$			8.91652i			0.698396i	0.937049	+	0.349198i	$0.113546\pi$
$163$			8.91652i			0.698396i	−0.937049	+	0.349198i	$0.886454\pi$
$164$	13.8250	−	5.03190i	1.07955	−	0.392925i
$165$		0			0
$166$	0.404749	+	2.29544i	0.0314146	+	0.178161i
$167$	−17.5670			−1.35937			−0.679687	−	0.733502i	$-0.737885\pi$
$167$	−17.5670			−1.35937			−0.679687	+	0.733502i	$0.737885\pi$
$168$		0			0
$169$	26.7743			2.05956
$170$	2.39489	+	13.5821i	0.183680	+	1.04170i
$171$		0			0
$172$	−0.610815	−	1.67820i	−0.0465742	−	0.127961i
$173$		−	5.09678i		−	0.387501i	−0.981051	−	0.193750i	$-0.937935\pi$
$173$		−	5.09678i		−	0.387501i	0.981051	−	0.193750i	$-0.0620652\pi$
$174$		0			0
$175$	0.965852	−	1.35981i	0.0730115	−	0.102792i
$176$	−1.02946	+	0.863822i	−0.0775987	+	0.0651131i
$177$		0			0
$178$	15.7911	−	2.78440i	1.18359	−	0.208700i
$179$	−2.70930			−0.202503			−0.101251	−	0.994861i	$-0.532285\pi$
$179$	−2.70930			−0.202503			−0.101251	+	0.994861i	$0.532285\pi$
$180$		0			0
$181$	0.404749			0.0300847			0.0150424	−	0.999887i	$-0.495212\pi$
$181$	0.404749			0.0300847			0.0150424	+	0.999887i	$0.495212\pi$
$182$	10.1164	−	21.3190i	0.749877	−	1.58027i
$183$		0			0
$184$	8.82295	+	15.2818i	0.650436	+	1.12659i
$185$	−23.6679			−1.74010
$186$		0			0
$187$	−1.38079			−0.100973
$188$	17.5670	−	6.39386i	1.28120	−	0.466320i
$189$		0			0
$190$	−1.27631	−	7.23832i	−0.0925934	−	0.525123i
$191$		−	15.8879i		−	1.14961i	−0.818292	−	0.574803i	$-0.805079\pi$
$191$		−	15.8879i		−	1.14961i	0.818292	−	0.574803i	$-0.194921\pi$
$192$		0			0
$193$	−10.5371			−0.758480			−0.379240	−	0.925298i	$-0.623815\pi$
$193$	−10.5371			−0.758480			−0.379240	+	0.925298i	$0.623815\pi$
$194$	0.691487	+	3.92162i	0.0496459	+	0.281556i
$195$		0			0
$196$	−8.85389	−	10.8447i	−0.632421	−	0.774625i
$197$	−17.1464			−1.22163			−0.610816	−	0.791772i	$-0.709159\pi$
$197$	−17.1464			−1.22163			−0.610816	+	0.791772i	$0.709159\pi$
$198$		0			0
$199$			20.5295i			1.45529i	0.685951	+	0.727647i	$0.259386\pi$
$199$			20.5295i			1.45529i	−0.685951	+	0.727647i	$0.740614\pi$
$200$	1.54419	−	0.891541i	0.109191	−	0.0630415i
$201$		0			0
$202$	0.582714	+	3.30474i	0.0409996	+	0.232520i
$203$	6.71706	−	9.45688i	0.471445	−	0.663743i
$204$		0			0
$205$		−	17.4550i		−	1.21911i
$206$	1.99106	+	11.2918i	0.138724	+	0.786740i
$207$		0			0
$208$	19.3248	−	16.2154i	1.33993	−	1.12434i
$209$	0.735865			0.0509008
$210$		0			0
$211$		−	15.3696i		−	1.05809i	−0.848595	−	0.529043i	$-0.822551\pi$
$211$		−	15.3696i		−	1.05809i	0.848595	−	0.529043i	$-0.177449\pi$
$212$	1.40595	−	0.511725i	0.0965613	−	0.0351454i
$213$		0			0
$214$	−25.5030	+	4.49687i	−1.74335	+	0.307399i
$215$	−2.11884			−0.144504
$216$		0			0
$217$	17.4884	+	12.4217i	1.18719	+	0.843243i
$218$	−4.04828	−	22.9589i	−0.274184	−	1.55498i
$219$		0			0
$220$	0.545317	+	1.49825i	0.0367652	+	0.101012i
$221$	25.9198			1.74356
$222$		0			0
$223$			15.9386i			1.06733i	0.845697	+	0.533663i	$0.179185\pi$
$223$			15.9386i			1.06733i	−0.845697	+	0.533663i	$0.820815\pi$
$224$	−3.77629	−	14.4824i	−0.252314	−	0.967645i
$225$		0			0
$226$	−1.19934	−	6.80180i	−0.0797789	−	0.452449i
$227$		−	22.0113i		−	1.46094i	−0.682944	−	0.730470i	$-0.739301\pi$
$227$		−	22.0113i		−	1.46094i	0.682944	−	0.730470i	$-0.260699\pi$
$228$		0			0
$229$	−10.6873			−0.706234			−0.353117	−	0.935579i	$-0.614878\pi$
$229$	−10.6873			−0.706234			−0.353117	+	0.935579i	$0.614878\pi$
$230$	20.6175	−	3.63542i	1.35948	−	0.239712i
$231$		0			0
$232$	10.7392	−	6.20026i	0.705061	−	0.407067i
$233$		−	3.49730i		−	0.229116i	−0.993417	−	0.114558i	$-0.963455\pi$
$233$		−	3.49730i		−	0.229116i	0.993417	−	0.114558i	$-0.0365451\pi$
$234$		0			0
$235$		−	22.1795i		−	1.44683i
$236$	6.10095	+	16.7622i	0.397138	+	1.09113i
$237$		0			0
$238$	6.59258	−	13.8930i	0.427333	−	0.900549i
$239$			14.8425i			0.960083i	0.877246	+	0.480042i	$0.159378\pi$
$239$			14.8425i			0.960083i	−0.877246	+	0.480042i	$0.840622\pi$
$240$		0			0
$241$		−	14.4403i		−	0.930183i	−0.885263	−	0.465091i	$-0.846021\pi$
$241$		−	14.4403i		−	0.930183i	0.885263	−	0.465091i	$-0.153979\pi$
$242$	15.1628	−	2.67361i	0.974702	−	0.171866i
$243$		0			0
$244$	13.7788	−	5.01507i	0.882097	−	0.321057i
$245$	−15.6833	+	5.47038i	−1.00197	+	0.349490i
$246$		0			0
$247$	−13.8135			−0.878929
$248$	11.4660	+	19.8598i	0.728094	+	1.26110i
$249$		0			0
$250$	2.54622	+	14.4403i	0.161037	+	0.913286i
$251$			16.7622i			1.05802i	0.848615	+	0.529011i	$0.177437\pi$
$251$			16.7622i			1.05802i	−0.848615	+	0.529011i	$0.822563\pi$
$252$		0			0
$253$			2.09602i			0.131776i
$254$	−21.0970	+	3.71997i	−1.32374	+	0.233412i
$255$		0			0
$256$	2.77837	−	15.7569i	0.173648	−	0.984808i
$257$	4.84576			0.302270			0.151135	−	0.988513i	$-0.451707\pi$
$257$	4.84576			0.302270			0.151135	+	0.988513i	$0.451707\pi$
$258$		0			0
$259$	21.5151	+	15.2818i	1.33688	+	0.949565i
$260$	−10.2365	−	28.1246i	−0.634843	−	1.74422i
$261$		0			0
$262$	−3.76046	−	21.3267i	−0.232322	−	1.31757i
$263$		−	12.5368i		−	0.773051i	−0.922279	−	0.386525i	$-0.873675\pi$
$263$		−	12.5368i		−	0.773051i	0.922279	−	0.386525i	$-0.126325\pi$
$264$		0			0
$265$		−	1.77511i		−	0.109044i
$266$	−3.51338	+	7.40400i	−0.215419	+	0.453968i
$267$		0			0
$268$	3.80335	+	10.4496i	0.232326	+	0.638312i
$269$		−	6.54615i		−	0.399126i	−0.979885	−	0.199563i	$-0.936048\pi$
$269$		−	6.54615i		−	0.399126i	0.979885	−	0.199563i	$-0.0639522\pi$
$270$		0			0
$271$		−	5.11122i		−	0.310485i	−0.987876	−	0.155242i	$-0.950384\pi$
$271$		−	5.11122i		−	0.310485i	0.987876	−	0.155242i	$-0.0496159\pi$
$272$	12.5935	−	10.5672i	0.763590	−	0.640728i
$273$		0			0
$274$	−2.34730	−	13.3122i	−0.141805	−	0.804218i
$275$	0.211799			0.0127719
$276$		0			0
$277$			25.8391i			1.55252i	0.630412	+	0.776261i	$0.282886\pi$
$277$			25.8391i			1.55252i	−0.630412	+	0.776261i	$0.717114\pi$
$278$	9.34720	−	1.64816i	0.560608	−	0.0988503i
$279$		0			0
$280$	−17.6784	−	1.66659i	−1.05649	−	0.0995980i
$281$			15.6967i			0.936388i	0.883626	+	0.468194i	$0.155095\pi$
$281$			15.6967i			0.936388i	−0.883626	+	0.468194i	$0.844905\pi$
$282$		0			0
$283$	29.7479			1.76833			0.884164	−	0.467177i	$-0.154729\pi$
$283$	29.7479			1.76833			0.884164	+	0.467177i	$0.154729\pi$
$284$	1.42751	+	3.92206i	0.0847074	+	0.232732i
$285$		0			0
$286$	2.95097	−	0.520335i	0.174494	−	0.0307681i
$287$	−11.2703	+	15.8673i	−0.665263	+	0.936617i
$288$		0			0
$289$	−0.108755			−0.00639736
$290$	−2.55476	−	14.4888i	−0.150021	−	0.850810i
$291$		0			0
$292$	3.97583	+	10.9235i	0.232668	+	0.639249i
$293$			17.4869i			1.02160i	0.859701	+	0.510798i	$0.170650\pi$
$293$			17.4869i			1.02160i	−0.859701	+	0.510798i	$0.829350\pi$
$294$		0			0
$295$	21.1634			1.23218
$296$	14.1060	+	24.4324i	0.819897	+	1.42010i
$297$		0			0
$298$	9.90941	−	1.74730i	0.574037	−	0.101218i
$299$		−	39.3459i		−	2.27543i
$300$		0			0
$301$	1.92611	+	1.36808i	0.111019	+	0.0788549i
$302$	5.96897	−	1.05249i	0.343475	−	0.0605640i
$303$		0			0
$304$	−6.71143	+	5.63156i	−0.384927	+	0.322992i
$305$		−	17.3966i		−	0.996129i
$306$		0			0
$307$	2.99979			0.171207			0.0856034	−	0.996329i	$-0.472718\pi$
$307$	2.99979			0.171207			0.0856034	+	0.996329i	$0.472718\pi$
$308$	0.471665	−	1.71406i	0.0268756	−	0.0976677i
$309$		0			0
$310$	26.7939	−	4.72448i	1.52179	−	0.268332i
$311$	19.6858			1.11628			0.558141	−	0.829746i	$-0.311515\pi$
$311$	19.6858			1.11628			0.558141	+	0.829746i	$0.311515\pi$
$312$		0			0
$313$			17.2561i			0.975373i	0.873019	+	0.487686i	$0.162159\pi$
$313$			17.2561i			0.975373i	−0.873019	+	0.487686i	$0.837841\pi$
$314$	−10.2108	+	1.80045i	−0.576232	+	0.101605i
$315$		0			0
$316$	−17.4338	+	6.34537i	−0.980726	+	0.356955i
$317$	0.309518			0.0173843			0.00869213	−	0.999962i	$-0.497233\pi$
$317$	0.309518			0.0173843			0.00869213	+	0.999962i	$0.497233\pi$
$318$		0			0
$319$	1.47296			0.0824701
$320$	−16.4396	−	9.49140i	−0.919001	−	0.530585i
$321$		0			0
$322$	−21.0894	−	10.0074i	−1.17527	−	0.557693i
$323$	−9.00186			−0.500877
$324$		0			0
$325$	−3.97583			−0.220539
$326$	−2.18968	−	12.4183i	−0.121275	−	0.687786i
$327$		0			0
$328$	−18.0188	+	10.4032i	−0.994922	+	0.574418i
$329$	−14.3207	+	20.1620i	−0.789528	+	1.11157i
$330$		0			0
$331$			12.1278i			0.666605i	0.942820	+	0.333302i	$0.108163\pi$
$331$			12.1278i			0.666605i	−0.942820	+	0.333302i	$0.891837\pi$
$332$	−1.12741	−	3.09754i	−0.0618747	−	0.169999i
$333$		0			0
$334$	24.4661	−	4.31403i	1.33872	−	0.236053i
$335$	13.1933			0.720829
$336$		0			0
$337$	−12.2567			−0.667666			−0.333833	−	0.942632i	$-0.608342\pi$
$337$	−12.2567			−0.667666			−0.333833	+	0.942632i	$0.608342\pi$
$338$	−37.2893	+	6.57510i	−2.02827	+	0.357638i
$339$		0			0
$340$	−6.67087	−	18.3281i	−0.361779	−	0.993979i
$341$			2.72393i			0.147509i
$342$		0			0
$343$	17.7888	+	5.15350i	0.960505	+	0.278263i
$344$	1.26282	+	2.18727i	0.0680869	+	0.117930i
$345$		0			0
$346$	1.25164	+	7.09843i	0.0672888	+	0.381614i
$347$	−21.2758			−1.14214			−0.571071	−	0.820901i	$-0.693472\pi$
$347$	−21.2758			−1.14214			−0.571071	+	0.820901i	$0.693472\pi$
$348$		0			0
$349$	−26.6563			−1.42688			−0.713441	−	0.700716i	$-0.752864\pi$
$349$	−26.6563			−1.42688			−0.713441	+	0.700716i	$0.752864\pi$
$350$	−1.01123	+	2.13104i	−0.0540526	+	0.113909i
$351$		0			0
$352$	1.22163	−	1.45588i	0.0651131	−	0.0775987i
$353$	23.5402			1.25292			0.626458	−	0.779455i	$-0.284504\pi$
$353$	23.5402			1.25292			0.626458	+	0.779455i	$0.284504\pi$
$354$		0			0
$355$	4.95187			0.262818
$356$	−21.3090	+	7.75583i	−1.12937	+	0.411058i
$357$		0			0
$358$	3.77332	−	0.665338i	0.199426	−	0.0351642i
$359$		−	0.240762i		−	0.0127069i	−0.999980	−	0.00635347i	$-0.997978\pi$
$359$		−	0.240762i		−	0.0127069i	0.999980	−	0.00635347i	$-0.00202239\pi$
$360$		0			0
$361$	−14.2026			−0.747507
$362$	−0.563705	+	0.0993965i	−0.0296277	+	0.00522416i
$363$		0			0
$364$	−8.85396	+	32.1759i	−0.464074	+	1.68647i
$365$	13.7916			0.721888
$366$		0			0
$367$			0.276865i			0.0144522i	0.999974	+	0.00722611i	$0.00230016\pi$
$367$			0.276865i			0.0144522i	−0.999974	+	0.00722611i	$0.997700\pi$
$368$	−16.0408	−	19.1167i	−0.836185	−	0.996526i
$369$		0			0
$370$	32.9630	−	5.81227i	1.71367	−	0.302166i
$371$	−1.14614	+	1.61364i	−0.0595048	+	0.0837762i
$372$		0			0
$373$		−	16.0869i		−	0.832950i	−0.909147	−	0.416475i	$-0.863265\pi$
$373$		−	16.0869i		−	0.832950i	0.909147	−	0.416475i	$-0.136735\pi$
$374$	1.92307	−	0.339088i	0.0994394	−	0.0175338i
$375$		0			0
$376$	−22.8959	+	13.2189i	−1.18076	+	0.681715i
$377$	−27.6501			−1.42405
$378$		0			0
$379$		−	13.5837i		−	0.697747i	−0.937170	−	0.348874i	$-0.886564\pi$
$379$		−	13.5837i		−	0.697747i	0.937170	−	0.348874i	$-0.113436\pi$
$380$	3.55511	+	9.76759i	0.182373	+	0.501067i
$381$		0			0
$382$	3.90167	+	22.1275i	0.199627	+	1.13214i
$383$	−16.5756			−0.846972			−0.423486	−	0.905903i	$-0.639194\pi$
$383$	−16.5756			−0.846972			−0.423486	+	0.905903i	$0.639194\pi$
$384$		0			0
$385$	−1.71957	−	1.22138i	−0.0876374	−	0.0622473i
$386$	14.6754	−	2.58766i	0.746957	−	0.131709i
$387$		0			0
$388$	−1.92611	−	5.29194i	−0.0977833	−	0.268657i
$389$	37.9339			1.92333			0.961663	−	0.274236i	$-0.0884248\pi$
$389$	37.9339			1.92333			0.961663	+	0.274236i	$0.0884248\pi$
$390$		0			0
$391$		−	25.6407i		−	1.29670i
$392$	14.9943	+	12.9295i	0.757325	+	0.653038i
$393$		0			0
$394$	23.8803	−	4.21074i	1.20307	−	0.212134i
$395$			22.0113i			1.10751i
$396$		0			0
$397$	−15.5643			−0.781152			−0.390576	−	0.920571i	$-0.627724\pi$
$397$	−15.5643			−0.781152			−0.390576	+	0.920571i	$0.627724\pi$
$398$	−5.04153	−	28.5920i	−0.252709	−	1.43319i
$399$		0			0
$400$	−1.93170	+	1.62089i	−0.0965852	+	0.0810446i
$401$		−	38.4426i		−	1.91973i	−0.280458	−	0.959866i	$-0.590486\pi$
$401$		−	38.4426i		−	1.91973i	0.280458	−	0.959866i	$-0.409514\pi$
$402$		0			0
$403$		−	51.1328i		−	2.54711i
$404$	−1.62312	−	4.45950i	−0.0807535	−	0.221868i
$405$		0			0
$406$	−7.03266	+	14.8204i	−0.349025	+	0.735525i
$407$			3.35110i			0.166108i
$408$		0			0
$409$			13.0382i			0.644699i	0.946621	+	0.322349i	$0.104473\pi$
$409$			13.0382i			0.644699i	−0.946621	+	0.322349i	$0.895527\pi$
$410$	4.28653	+	24.3101i	0.211697	+	1.20059i
$411$		0			0
$412$	−5.54600	−	15.2375i	−0.273232	−	0.750699i
$413$	−19.2384	−	13.6647i	−0.946659	−	0.672396i
$414$		0			0
$415$	−3.91085			−0.191976
$416$	−22.9321	+	27.3294i	−1.12434	+	1.33993i
$417$		0			0
$418$	−1.02486	+	0.180710i	−0.0501275	+	0.00883884i
$419$		−	34.9738i		−	1.70858i	−0.519794	−	0.854292i	$-0.673991\pi$
$419$		−	34.9738i		−	1.70858i	0.519794	−	0.854292i	$-0.326009\pi$
$420$		0			0
$421$			38.0242i			1.85319i	0.376064	+	0.926594i	$0.377277\pi$
$421$			38.0242i			1.85319i	−0.376064	+	0.926594i	$0.622723\pi$
$422$	3.77440	+	21.4057i	0.183735	+	1.04201i
$423$		0			0
$424$	−1.83244	+	1.05796i	−0.0889913	+	0.0513792i
$425$	−2.59094			−0.125679
$426$		0			0
$427$	−11.2326	+	15.8142i	−0.543582	+	0.765304i
$428$	34.4144	−	12.5258i	1.66348	−	0.605459i
$429$		0			0
$430$	2.95097	−	0.520335i	0.142308	−	0.0250928i
$431$		−	19.9986i		−	0.963299i	−0.876364	−	0.481649i	$-0.840038\pi$
$431$		−	19.9986i		−	0.963299i	0.876364	−	0.481649i	$-0.159962\pi$
$432$		0			0
$433$		−	11.6245i		−	0.558640i	−0.960198	−	0.279320i	$-0.909891\pi$
$433$		−	11.6245i		−	0.558640i	0.960198	−	0.279320i	$-0.0901090\pi$
$434$	−27.4071	−	13.0054i	−1.31558	−	0.624278i
$435$		0			0
$436$	11.2763	+	30.9814i	0.540037	+	1.48374i
$437$			13.6647i			0.653671i
$438$		0			0
$439$			11.9014i			0.568023i	0.958821	+	0.284012i	$0.0916654\pi$
$439$			11.9014i			0.568023i	−0.958821	+	0.284012i	$0.908335\pi$
$440$	−1.12741	−	1.95273i	−0.0537472	−	0.0930929i
$441$		0			0
$442$	−36.0993	+	6.36527i	−1.71707	+	0.302765i
$443$	2.06551			0.0981354			0.0490677	−	0.998795i	$-0.484375\pi$
$443$	2.06551			0.0981354			0.0490677	+	0.998795i	$0.484375\pi$
$444$		0			0
$445$			26.9040i			1.27537i
$446$	−3.91412	−	22.1981i	−0.185339	−	1.05111i
$447$		0			0
$448$	8.81587	+	19.2427i	0.416511	+	0.909131i
$449$		−	0.954583i		−	0.0450496i	−0.999746	−	0.0225248i	$-0.992830\pi$
$449$		−	0.954583i		−	0.0450496i	0.999746	−	0.0225248i	$-0.00717047\pi$
$450$		0			0
$451$	−2.47142			−0.116375
$452$	3.34071	+	9.17853i	0.157134	+	0.431722i
$453$		0			0
$454$	5.40544	+	30.6558i	0.253690	+	1.43875i
$455$	32.2793	+	22.9274i	1.51328	+	1.07485i
$456$		0			0
$457$	−4.00000			−0.187112			−0.0935561	−	0.995614i	$-0.529823\pi$
$457$	−4.00000			−0.187112			−0.0935561	+	0.995614i	$0.529823\pi$
$458$	14.8845	−	2.62453i	0.695505	−	0.122636i
$459$		0			0
$460$	−27.8218	+	10.1263i	−1.29720	+	0.472141i
$461$			30.0068i			1.39756i	0.715338	+	0.698778i	$0.246273\pi$
$461$			30.0068i			1.39756i	−0.715338	+	0.698778i	$0.753727\pi$
$462$		0			0
$463$	−17.1088			−0.795111			−0.397556	−	0.917578i	$-0.630141\pi$
$463$	−17.1088			−0.795111			−0.397556	+	0.917578i	$0.630141\pi$
$464$	−13.4341	+	11.2726i	−0.623663	+	0.523315i
$465$		0			0
$466$	0.858851	+	4.87079i	0.0397855	+	0.225635i
$467$			40.7953i			1.88778i	0.330258	+	0.943891i	$0.392864\pi$
$467$			40.7953i			1.88778i	−0.330258	+	0.943891i	$0.607136\pi$
$468$		0			0
$469$	−11.9933	−	8.51860i	−0.553797	−	0.393352i
$470$	5.44675	+	30.8900i	0.251240	+	1.42485i
$471$		0			0
$472$	−12.6134	−	21.8470i	−0.580577	−	1.00559i
$473$			0.300002i			0.0137941i
$474$		0			0
$475$	1.38079			0.0633550
$476$	−5.76989	+	20.9681i	−0.264462	+	0.961073i
$477$		0			0
$478$	−3.64496	−	20.6716i	−0.166717	−	0.945498i
$479$	−16.1840			−0.739467			−0.369733	−	0.929138i	$-0.620551\pi$
$479$	−16.1840			−0.739467			−0.369733	+	0.929138i	$0.620551\pi$
$480$		0			0
$481$		−	62.9059i		−	2.86826i
$482$	3.54619	+	20.1114i	0.161525	+	0.916051i
$483$		0			0
$484$	−20.4611	+	7.44723i	−0.930050	+	0.338511i
$485$	−6.68142			−0.303388
$486$		0			0
$487$	−14.4142			−0.653168			−0.326584	−	0.945168i	$-0.605898\pi$
$487$	−14.4142			−0.653168			−0.326584	+	0.945168i	$0.605898\pi$
$488$	−17.9585	+	10.3684i	−0.812945	+	0.469354i
$489$		0			0
$490$	20.4992	−	11.4702i	0.926057	−	0.518170i
$491$	12.4262			0.560787			0.280394	−	0.959885i	$-0.409535\pi$
$491$	12.4262			0.560787			0.280394	+	0.959885i	$0.409535\pi$
$492$		0			0
$493$	−18.0188			−0.811526
$494$	19.2384	−	3.39225i	0.865576	−	0.152624i
$495$		0			0
$496$	−20.8462	−	24.8435i	−0.936020	−	1.11551i
$497$	−4.50144	−	3.19730i	−0.201917	−	0.143418i
$498$		0			0
$499$		−	2.34883i		−	0.105148i	−0.998617	−	0.0525741i	$-0.983257\pi$
$499$		−	2.34883i		−	0.105148i	0.998617	−	0.0525741i	$-0.0167426\pi$
$500$	−7.09238	−	19.4862i	−0.317181	−	0.871447i
$501$		0			0
$502$	−4.11640	−	23.3452i	−0.183724	−	1.04195i
$503$	28.0416			1.25031			0.625157	−	0.780499i	$-0.285035\pi$
$503$	28.0416			1.25031			0.625157	+	0.780499i	$0.285035\pi$
$504$		0			0
$505$	−5.63041			−0.250550
$506$	−0.514732	−	2.91919i	−0.0228826	−	0.129774i
$507$		0			0
$508$	28.4688	−	10.3618i	1.26310	−	0.459731i
$509$			42.7945i			1.89683i	0.317025	+	0.948417i	$0.397316\pi$
$509$			42.7945i			1.89683i	−0.317025	+	0.948417i	$0.602684\pi$
$510$		0			0
$511$	−12.5371	−	8.90492i	−0.554610	−	0.393930i
$512$			22.6274i			1.00000i
$513$		0			0
$514$	−6.74883	+	1.19000i	−0.297678	+	0.0524887i
$515$	−19.2384			−0.847745
$516$		0			0
$517$	−3.14035			−0.138113
$518$	−33.7175	−	15.9998i	−1.48146	−	0.702991i
$519$		0			0
$520$	21.1634	+	36.6561i	0.928078	+	1.60748i
$521$	14.8401			0.650155			0.325078	−	0.945687i	$-0.394610\pi$
$521$	14.8401			0.650155			0.325078	+	0.945687i	$0.394610\pi$
$522$		0			0
$523$	24.5149			1.07196			0.535980	−	0.844231i	$-0.319942\pi$
$523$	24.5149			1.07196			0.535980	+	0.844231i	$0.319942\pi$
$524$	10.4746	+	28.7788i	0.457586	+	1.25721i
$525$		0			0
$526$	3.07873	+	17.4603i	0.134239	+	0.761306i
$527$		−	33.3219i		−	1.45152i
$528$		0			0
$529$	−15.9222			−0.692270
$530$	0.435924	+	2.47225i	0.0189353	+	0.107388i
$531$		0			0
$532$	3.07495	−	11.1746i	0.133316	−	0.484479i
$533$	46.3929			2.00950
$534$		0			0
$535$		−	43.4505i		−	1.87853i
$536$	−7.86320	−	13.6195i	−0.339639	−	0.588271i
$537$		0			0
$538$	1.60757	+	9.11701i	0.0693074	+	0.393062i
$539$	0.774541	+	2.22057i	0.0333619	+	0.0956465i
$540$		0			0
$541$		−	8.08088i		−	0.347424i	−0.984796	−	0.173712i	$-0.944424\pi$
$541$		−	8.08088i		−	0.347424i	0.984796	−	0.173712i	$-0.0555762\pi$
$542$	1.25519	+	7.11855i	0.0539151	+	0.305768i
$543$		0			0
$544$	−14.9442	+	17.8098i	−0.640728	+	0.763590i
$545$	39.1161			1.67555
$546$		0			0
$547$			20.0368i			0.856710i	0.903610	+	0.428355i	$0.140907\pi$
$547$			20.0368i			0.856710i	−0.903610	+	0.428355i	$0.859093\pi$
$548$	6.53829	+	17.9638i	0.279302	+	0.767376i
$549$		0			0
$550$	−0.294978	+	0.0520126i	−0.0125779	+	0.00221783i
$551$	9.60277			0.409092
$552$		0			0
$553$	14.2121	−	20.0091i	0.604361	−	0.850874i
$554$	−6.34546	−	35.9869i	−0.269593	−	1.52894i
$555$		0			0
$556$	−12.6134	+	4.59089i	−0.534926	+	0.194697i
$557$	10.2696			0.435136			0.217568	−	0.976045i	$-0.430188\pi$
$557$	10.2696			0.435136			0.217568	+	0.976045i	$0.430188\pi$
$558$		0			0
$559$		−	5.63156i		−	0.238190i
$560$	25.0305	−	2.02027i	1.05773	−	0.0853720i
$561$		0			0
$562$	−3.85473	−	21.8613i	−0.162602	−	0.922162i
$563$		−	25.6812i		−	1.08233i	−0.840915	−	0.541167i	$-0.817983\pi$
$563$		−	25.6812i		−	1.08233i	0.840915	−	0.541167i	$-0.182017\pi$
$564$		0			0
$565$	11.5885			0.487532
$566$	−41.4307	+	7.30535i	−1.74146	+	0.307067i
$567$		0			0
$568$	−2.95130	−	5.11181i	−0.123834	−	0.214487i
$569$			9.96254i			0.417651i	0.977953	+	0.208826i	$0.0669641\pi$
$569$			9.96254i			0.417651i	−0.977953	+	0.208826i	$0.933036\pi$
$570$		0			0
$571$		−	44.5078i		−	1.86259i	−0.364262	−	0.931297i	$-0.618679\pi$
$571$		−	44.5078i		−	1.86259i	0.364262	−	0.931297i	$-0.381321\pi$
$572$	−3.98211	+	1.44937i	−0.166501	+	0.0606012i
$573$		0			0
$574$	11.7998	−	24.8665i	0.492514	−	1.03791i
$575$			3.93301i			0.164018i
$576$		0			0
$577$		−	10.2224i		−	0.425566i	−0.977099	−	0.212783i	$-0.931747\pi$
$577$		−	10.2224i		−	0.425566i	0.977099	−	0.212783i	$-0.0682528\pi$
$578$	0.151466	−	0.0267076i	0.00630017	−	0.00111089i
$579$		0			0
$580$	7.11618	+	19.5515i	0.295483	+	0.811834i
$581$	3.55511	+	2.52513i	0.147491	+	0.104760i
$582$		0			0
$583$	−0.251334			−0.0104092
$584$	−8.21979	−	14.2371i	−0.340137	−	0.589135i
$585$		0			0
$586$	−4.29436	−	24.3545i	−0.177398	−	1.00608i
$587$			9.69019i			0.399957i	0.979800	+	0.199978i	$0.0640872\pi$
$587$			9.69019i			0.399957i	−0.979800	+	0.199978i	$0.935913\pi$
$588$		0			0
$589$			17.7582i			0.731715i
$590$	−29.4749	+	5.19722i	−1.21346	+	0.213966i
$591$		0			0
$592$	−25.6459	−	30.5636i	−1.05404	−	1.25616i
$593$	43.2260			1.77508			0.887540	−	0.460732i	$-0.152413\pi$
$593$	43.2260			1.77508			0.887540	+	0.460732i	$0.152413\pi$
$594$		0			0
$595$	21.0355	+	14.9412i	0.862373	+	0.612529i
$596$	−13.3720	+	4.86702i	−0.547740	+	0.199361i
$597$		0			0
$598$	9.66240	+	54.7982i	0.395125	+	2.24086i
$599$		−	36.2650i		−	1.48175i	−0.671645	−	0.740873i	$-0.734412\pi$
$599$		−	36.2650i		−	1.48175i	0.671645	−	0.740873i	$-0.265588\pi$
$600$		0			0
$601$			35.0659i			1.43037i	0.698936	+	0.715185i	$0.253657\pi$
$601$			35.0659i			1.43037i	−0.698936	+	0.715185i	$0.746343\pi$
$602$	−3.01851	−	1.43236i	−0.123025	−	0.0583786i
$603$		0			0
$604$	−8.05468	+	2.93166i	−0.327740	+	0.119288i
$605$			25.8335i			1.05028i
$606$		0			0
$607$			39.3800i			1.59838i	0.601076	+	0.799192i	$0.294739\pi$
$607$			39.3800i			1.59838i	−0.601076	+	0.799192i	$0.705261\pi$
$608$	7.96423	−	9.49140i	0.322992	−	0.384927i
$609$		0			0
$610$	4.27219	+	24.2288i	0.172976	+	0.980996i
$611$	58.9498			2.38486
$612$		0			0
$613$			17.8330i			0.720270i	0.932900	+	0.360135i	$0.117269\pi$
$613$			17.8330i			0.720270i	−0.932900	+	0.360135i	$0.882731\pi$
$614$	−4.17789	+	0.736674i	−0.168606	+	0.0297298i
$615$		0			0
$616$	−0.235970	+	2.50305i	−0.00950749	+	0.100851i
$617$			33.2311i			1.33783i	0.743337	+	0.668917i	$0.233242\pi$
$617$			33.2311i			1.33783i	−0.743337	+	0.668917i	$0.766758\pi$
$618$		0			0
$619$	21.3745			0.859114			0.429557	−	0.903040i	$-0.358670\pi$
$619$	21.3745			0.859114			0.429557	+	0.903040i	$0.358670\pi$
$620$	−36.1563	+	13.1598i	−1.45207	+	0.528512i
$621$		0			0
$622$	−27.4170	+	4.83436i	−1.09932	+	0.193840i
$623$	17.3712	−	24.4568i	0.695963	−	0.979840i
$624$		0			0
$625$	−27.7547			−1.11019
$626$	−4.23768	−	24.0331i	−0.169372	−	0.960554i
$627$		0			0
$628$	13.7788	−	5.01507i	0.549834	−	0.200123i
$629$		−	40.9941i		−	1.63454i
$630$		0			0
$631$	−22.4979			−0.895629			−0.447814	−	0.894127i	$-0.647797\pi$
$631$	−22.4979			−0.895629			−0.447814	+	0.894127i	$0.647797\pi$
$632$	22.7222	−	13.1187i	0.903842	−	0.521833i
$633$		0			0
$634$	−0.431074	+	0.0760101i	−0.0171202	+	0.00301875i
$635$		−	35.9438i		−	1.42639i
$636$		0			0
$637$	−14.5395	−	41.6838i	−0.576075	−	1.65157i
$638$	−2.05144	+	0.361724i	−0.0812172	+	0.0143208i
$639$		0			0
$640$	25.2267	+	9.18178i	0.997174	+	0.362942i
$641$		−	18.3848i		−	0.726155i	−0.931759	−	0.363078i	$-0.881726\pi$
$641$		−	18.3848i		−	0.726155i	0.931759	−	0.363078i	$-0.118274\pi$
$642$		0			0
$643$	38.7902			1.52973			0.764867	−	0.644188i	$-0.222804\pi$
$643$	38.7902			1.52973			0.764867	+	0.644188i	$0.222804\pi$
$644$	31.8294	+	8.75861i	1.25425	+	0.345138i
$645$		0			0
$646$	12.5371	−	2.21064i	0.493267	−	0.0869763i
$647$	−34.3981			−1.35233			−0.676165	−	0.736750i	$-0.736359\pi$
$647$	−34.3981			−1.35233			−0.676165	+	0.736750i	$0.736359\pi$
$648$		0			0
$649$		−	2.99649i		−	0.117623i
$650$	5.53725	−	0.976366i	0.217189	−	0.0382962i
$651$		0			0
$652$	6.09926	+	16.7576i	0.238865	+	0.656277i
$653$	−32.8297			−1.28473			−0.642363	−	0.766401i	$-0.722046\pi$
$653$	−32.8297			−1.28473			−0.642363	+	0.766401i	$0.722046\pi$
$654$		0			0
$655$	36.3351			1.41973
$656$	22.5405	−	18.9138i	0.880060	−	0.738458i
$657$		0			0
$658$	14.9936	−	31.5971i	0.584512	−	1.23178i
$659$	−29.6586			−1.15533			−0.577667	−	0.816273i	$-0.696037\pi$
$659$	−29.6586			−1.15533			−0.577667	+	0.816273i	$0.696037\pi$
$660$		0			0
$661$	−12.8028			−0.497969			−0.248985	−	0.968507i	$-0.580097\pi$
$661$	−12.8028			−0.497969			−0.248985	+	0.968507i	$0.580097\pi$
$662$	−2.97829	−	16.8907i	−0.115755	−	0.656478i
$663$		0			0
$664$	2.33086	+	4.03716i	0.0904548	+	0.156672i
$665$	−11.2105	−	7.96261i	−0.434724	−	0.308777i
$666$		0			0
$667$			27.3523i			1.05909i
$668$	−33.0152	+	12.0165i	−1.27739	+	0.464934i
$669$		0			0
$670$	−18.3747	+	3.23996i	−0.709878	+	0.125171i
$671$	−2.46316			−0.0950892
$672$		0			0
$673$	−1.63041			−0.0628479			−0.0314239	−	0.999506i	$-0.510004\pi$
$673$	−1.63041			−0.0628479			−0.0314239	+	0.999506i	$0.510004\pi$
$674$	17.0703	−	3.00995i	0.657522	−	0.115939i
$675$		0			0
$676$	50.3191	−	18.3147i	1.93535	−	0.704410i
$677$		−	16.3421i		−	0.628078i	−0.949410	−	0.314039i	$-0.898318\pi$
$677$		−	16.3421i		−	0.628078i	0.949410	−	0.314039i	$-0.101682\pi$
$678$		0			0
$679$	6.07367	+	4.31403i	0.233086	+	0.165557i
$680$	13.7916	+	23.8878i	0.528885	+	0.916056i
$681$		0			0
$682$	−0.668930	−	3.79369i	−0.0256147	−	0.145268i
$683$	−25.2263			−0.965258			−0.482629	−	0.875825i	$-0.660318\pi$
$683$	−25.2263			−0.965258			−0.482629	+	0.875825i	$0.660318\pi$
$684$		0			0
$685$	22.6805			0.866578
$686$	−26.0405	−	2.80894i	−0.994233	−	0.107246i
$687$		0			0
$688$	−2.29591	−	2.73616i	−0.0875308	−	0.104315i
$689$	4.71798			0.179741
$690$		0			0
$691$	−26.8457			−1.02126			−0.510630	−	0.859801i	$-0.670588\pi$
$691$	−26.8457			−1.02126			−0.510630	+	0.859801i	$0.670588\pi$
$692$	−3.48640	−	9.57881i	−0.132533	−	0.364132i
$693$		0			0
$694$	29.6313	−	5.22481i	1.12479	−	0.198331i
$695$			15.9252i			0.604078i
$696$		0			0
$697$	30.2330			1.14516
$698$	37.1250	−	6.54615i	1.40520	−	0.247775i
$699$		0			0
$700$	0.885041	−	3.21629i	0.0334514	−	0.121564i
$701$	−23.4703			−0.886462			−0.443231	−	0.896407i	$-0.646168\pi$
$701$	−23.4703			−0.886462			−0.443231	+	0.896407i	$0.646168\pi$
$702$		0			0
$703$			21.8470i			0.823975i
$704$	−1.34387	+	2.32765i	−0.0506490	+	0.0877266i
$705$		0			0
$706$	−32.7851	+	5.78089i	−1.23388	+	0.217567i
$707$	5.11827	+	3.63542i	0.192492	+	0.136724i
$708$		0			0
$709$		−	7.48054i		−	0.280938i	−0.990085	−	0.140469i	$-0.955139\pi$
$709$		−	7.48054i		−	0.280938i	0.990085	−	0.140469i	$-0.0448610\pi$
$710$	−6.89661	+	1.21606i	−0.258825	+	0.0456378i
$711$		0			0
$712$	27.7730	−	16.0347i	1.04084	−	0.600927i
$713$	−50.5821			−1.89432
$714$		0			0
$715$			5.02769i			0.188025i
$716$	−5.09182	+	1.85327i	−0.190290	+	0.0692599i
$717$		0			0
$718$	0.0591253	+	0.335316i	0.00220654	+	0.0125139i
$719$	−2.51038			−0.0936215			−0.0468108	−	0.998904i	$-0.514906\pi$
$719$	−2.51038			−0.0936215			−0.0468108	+	0.998904i	$0.514906\pi$
$720$		0			0
$721$	17.4884	+	12.4217i	0.651304	+	0.462610i
$722$	19.7804	−	3.48782i	0.736151	−	0.129803i
$723$		0			0
$724$	0.760679	−	0.276865i	0.0282704	−	0.0102896i
$725$	2.76390			0.102648
$726$		0			0
$727$		−	3.51683i		−	0.130432i	−0.997871	−	0.0652159i	$-0.979226\pi$
$727$		−	3.51683i		−	0.130432i	0.997871	−	0.0652159i	$-0.0207736\pi$
$728$	4.42956	−	46.9866i	0.164170	−	1.74144i
$729$		0			0
$730$	−19.2080	+	3.38689i	−0.710921	+	0.125354i
$731$		−	3.66994i		−	0.135738i
$732$		0			0
$733$	19.2012			0.709212			0.354606	−	0.935016i	$-0.384615\pi$
$733$	19.2012			0.709212			0.354606	+	0.935016i	$0.384615\pi$
$734$	−0.0679912	−	0.385597i	−0.00250960	−	0.0142326i
$735$		0			0
$736$	27.0351	+	22.6851i	0.996526	+	0.836185i
$737$		−	1.86802i		−	0.0688094i
$738$		0			0
$739$		−	34.3776i		−	1.26460i	−0.774723	−	0.632301i	$-0.782111\pi$
$739$		−	34.3776i		−	1.26460i	0.774723	−	0.632301i	$-0.217889\pi$
$740$	−44.4812	+	16.1898i	−1.63516	+	0.595150i
$741$		0			0
$742$	1.20000	−	2.52883i	0.0440532	−	0.0928364i
$743$			9.86797i			0.362021i	0.983481	+	0.181010i	$0.0579368\pi$
$743$			9.86797i			0.362021i	−0.983481	+	0.181010i	$0.942063\pi$
$744$		0			0
$745$			16.8831i			0.618548i
$746$	3.95056	+	22.4047i	0.144640	+	0.820296i
$747$		0			0
$748$	−2.59504	+	0.944516i	−0.0948839	+	0.0345349i
$749$	−28.0549	+	39.4982i	−1.02510	+	1.44323i
$750$		0			0
$751$	−47.7452			−1.74225			−0.871123	−	0.491065i	$-0.836608\pi$
$751$	−47.7452			−1.74225			−0.871123	+	0.491065i	$0.836608\pi$
$752$	28.6415	−	24.0331i	1.04445	−	0.876396i
$753$		0			0
$754$	38.5090	−	6.79018i	1.40242	−	0.247284i
$755$			10.1696i			0.370109i
$756$		0			0
$757$			12.7984i			0.465167i	0.972576	+	0.232584i	$0.0747180\pi$
$757$			12.7984i			0.465167i	−0.972576	+	0.232584i	$0.925282\pi$
$758$	3.33582	+	18.9184i	0.121163	+	0.687147i
$759$		0			0
$760$	−7.34998	−	12.7305i	−0.266612	−	0.461785i
$761$	−8.09201			−0.293335			−0.146668	−	0.989186i	$-0.546855\pi$
$761$	−8.09201			−0.293335			−0.146668	+	0.989186i	$0.546855\pi$
$762$		0			0
$763$	−35.5581	−	25.2563i	−1.28729	−	0.914339i
$764$	−10.8679	−	29.8594i	−0.393188	−	1.08028i
$765$		0			0
$766$	23.0853	−	4.07055i	0.834104	−	0.147075i
$767$			56.2493i			2.03104i
$768$		0			0
$769$			0.553729i			0.0199680i	0.999950	+	0.00998399i	$0.00317806\pi$
$769$			0.553729i			0.0199680i	−0.999950	+	0.00998399i	$0.996822\pi$
$770$	2.69484	+	1.27877i	0.0971151	+	0.0460836i
$771$		0			0
$772$	−19.8033	+	7.20783i	−0.712738	+	0.259415i
$773$		−	26.4059i		−	0.949755i	−0.880052	−	0.474877i	$-0.842492\pi$
$773$		−	26.4059i		−	0.949755i	0.880052	−	0.474877i	$-0.157508\pi$
$774$		0			0
$775$			5.11122i			0.183601i
$776$	3.98211	+	6.89722i	0.142950	+	0.247596i
$777$		0			0
$778$	−52.8316	+	9.31564i	−1.89411	+	0.333982i
$779$	−16.1121			−0.577275
$780$		0			0
$781$		−	0.701126i		−	0.0250882i
$782$	6.29673	+	35.7105i	0.225170	+	1.27701i
$783$		0			0
$784$	−24.0581	−	14.3250i	−0.859219	−	0.511609i
$785$		−	17.3966i		−	0.620913i
$786$		0			0
$787$	−48.6510			−1.73422			−0.867110	−	0.498117i	$-0.834025\pi$
$787$	−48.6510			−1.73422			−0.867110	+	0.498117i	$0.834025\pi$
$788$	−32.2247	+	11.7288i	−1.14796	+	0.417823i
$789$		0			0
$790$	−5.40544	−	30.6558i	−0.192317	−	1.09068i
$791$	−10.5344	−	7.48241i	−0.374560	−	0.266044i
$792$		0			0
$793$	46.2377			1.64195
$794$	21.6769	−	3.82222i	0.769284	−	0.135646i
$795$		0			0
$796$	14.0430	+	38.5828i	0.497740	+	1.36753i
$797$		−	36.0271i		−	1.27614i	−0.769977	−	0.638072i	$-0.779732\pi$
$797$		−	36.0271i		−	1.27614i	0.769977	−	0.638072i	$-0.220268\pi$
$798$		0			0
$799$	38.4160			1.35906
$800$	2.29229	−	2.73184i	0.0810446	−	0.0965852i
$801$		0			0
$802$	9.44057	+	53.5401i	0.333358	+	1.89057i
$803$		−	1.95273i		−	0.0689104i
$804$		0			0
$805$	22.6805	−	31.9317i	0.799383	−	1.12544i
$806$	12.5570	+	71.2141i	0.442300	+	2.50841i
$807$		0			0
$808$	3.35572	+	5.81227i	0.118054	+	0.204475i
$809$			29.3162i			1.03070i	0.856979	+	0.515351i	$0.172338\pi$
$809$			29.3162i			1.03070i	−0.856979	+	0.515351i	$0.827662\pi$
$810$		0			0
$811$	−11.9015			−0.417918			−0.208959	−	0.977924i	$-0.567008\pi$
$811$	−11.9015			−0.417918			−0.208959	+	0.977924i	$0.567008\pi$
$812$	6.15505	−	22.3679i	0.216000	−	0.784958i
$813$		0			0
$814$	−0.822948	−	4.66717i	−0.0288443	−	0.163584i
$815$	21.1576			0.741117
$816$		0			0
$817$			1.95582i			0.0684255i
$818$	−3.20187	−	18.1587i	−0.111951	−	0.634905i
$819$		0			0
$820$	−11.9399	−	32.8047i	−0.416961	−	1.14559i
$821$	29.5229			1.03036			0.515179	−	0.857083i	$-0.327726\pi$
$821$	29.5229			1.03036			0.515179	+	0.857083i	$0.327726\pi$
$822$		0			0
$823$	20.3114			0.708011			0.354005	−	0.935243i	$-0.384819\pi$
$823$	20.3114			0.708011			0.354005	+	0.935243i	$0.384819\pi$
$824$	11.4660	+	19.8598i	0.399438	+	0.691848i
$825$		0			0
$826$	30.1496	+	14.3067i	1.04904	+	0.497795i
$827$	33.9138			1.17930			0.589649	−	0.807660i	$-0.299266\pi$
$827$	33.9138			1.17930			0.589649	+	0.807660i	$0.299266\pi$
$828$		0			0
$829$	9.44704			0.328109			0.164055	−	0.986451i	$-0.447543\pi$
$829$	9.44704			0.328109			0.164055	+	0.986451i	$0.447543\pi$
$830$	5.44675	−	0.960408i	0.189059	−	0.0333363i
$831$		0			0
$832$	25.2267	−	43.6940i	0.874580	−	1.51482i
$833$	−9.47498	−	27.1642i	−0.328289	−	0.941185i
$834$		0			0
$835$			41.6838i			1.44253i
$836$	1.38297	−	0.503361i	0.0478311	−	0.0174091i
$837$		0			0
$838$	8.58872	+	48.7091i	0.296692	+	1.68263i
$839$	−6.10095			−0.210628			−0.105314	−	0.994439i	$-0.533585\pi$
$839$	−6.10095			−0.210628			−0.105314	+	0.994439i	$0.533585\pi$
$840$		0			0
$841$	−9.77837			−0.337185
$842$	−9.33782	−	52.9574i	−0.321803	−	1.82503i
$843$		0			0
$844$	−10.5134	−	28.8854i	−0.361887	−	0.994276i
$845$		−	63.5313i		−	2.18554i
$846$		0			0
$847$	16.6800	−	23.4837i	0.573133	−	0.806908i
$848$	2.29229	−	1.92346i	0.0787175	−	0.0660518i
$849$		0			0
$850$	3.60848	−	0.636272i	0.123770	−	0.0218239i
$851$	−62.2285			−2.13316
$852$		0			0
$853$	27.4658			0.940412			0.470206	−	0.882557i	$-0.344180\pi$
$853$	27.4658			0.940412			0.470206	+	0.882557i	$0.344180\pi$
$854$	11.7603	−	24.7834i	0.402431	−	0.848070i
$855$		0			0
$856$	−44.8539	+	25.8964i	−1.53308	+	0.885121i
$857$	−36.7335			−1.25479			−0.627396	−	0.778700i	$-0.715879\pi$
$857$	−36.7335			−1.25479			−0.627396	+	0.778700i	$0.715879\pi$
$858$		0			0
$859$	14.0918			0.480806			0.240403	−	0.970673i	$-0.422720\pi$
$859$	14.0918			0.480806			0.240403	+	0.970673i	$0.422720\pi$
$860$	−3.98211	+	1.44937i	−0.135789	+	0.0494231i
$861$		0			0
$862$	4.91117	+	27.8526i	0.167275	+	0.948664i
$863$			28.8469i			0.981961i	0.871171	+	0.490980i	$0.163361\pi$
$863$			28.8469i			0.981961i	−0.871171	+	0.490980i	$0.836639\pi$
$864$		0			0
$865$	−12.0939			−0.411204
$866$	2.85470	+	16.1898i	0.0970068	+	0.550153i
$867$		0			0
$868$	41.3645	+	11.3824i	1.40400	+	0.386345i
$869$	3.11654			0.105721
$870$		0			0
$871$			35.0659i			1.18816i
$872$	−23.3131	−	40.3795i	−0.789482	−	1.36742i
$873$		0			0
$874$	−3.35572	−	19.0312i	−0.113509	−	0.643740i
$875$	22.3647	+	15.8853i	0.756065	+	0.537020i
$876$		0			0
$877$		−	47.7764i		−	1.61329i	−0.591033	−	0.806647i	$-0.701280\pi$
$877$		−	47.7764i		−	1.61329i	0.591033	−	0.806647i	$-0.298720\pi$
$878$	−2.92269	−	16.5754i	−0.0986362	−	0.559394i
$879$		0			0
$880$	2.04972	+	2.44276i	0.0690961	+	0.0823455i
$881$	20.5495			0.692330			0.346165	−	0.938174i	$-0.387484\pi$
$881$	20.5495			0.692330			0.346165	+	0.938174i	$0.387484\pi$
$882$		0			0
$883$			5.92064i			0.199245i	0.995025	+	0.0996226i	$0.0317636\pi$
$883$			5.92064i			0.199245i	−0.995025	+	0.0996226i	$0.968236\pi$
$884$	48.7133	−	17.7302i	1.63841	−	0.596331i
$885$		0			0
$886$	−2.87670	+	0.507239i	−0.0966445	+	0.0170410i
$887$	−28.2972			−0.950126			−0.475063	−	0.879952i	$-0.657575\pi$
$887$	−28.2972			−0.950126			−0.475063	+	0.879952i	$0.657575\pi$
$888$		0			0
$889$	−23.2080	+	32.6743i	−0.778372	+	1.09586i
$890$	−6.60696	−	37.4699i	−0.221466	−	1.25600i
$891$		0			0
$892$	10.9026	+	29.9547i	0.365047	+	1.00296i
$893$	−20.4731			−0.685105
$894$		0			0
$895$			6.42876i			0.214890i
$896$	−17.0036	−	24.6349i	−0.568052	−	0.822993i
$897$		0			0
$898$	0.234422	+	1.32948i	0.00782278	+	0.0443652i
$899$			35.5462i			1.18553i
$900$		0			0
$901$	3.07458			0.102429
$902$	3.44202	−	0.606921i	0.114607	−	0.0202083i
$903$		0			0
$904$	−6.90673	−	11.9628i	−0.229714	−	0.397877i
$905$		−	0.960408i		−	0.0319250i
$906$		0			0
$907$			18.3212i			0.608344i	0.952617	+	0.304172i	$0.0983798\pi$
$907$			18.3212i			0.608344i	−0.952617	+	0.304172i	$0.901620\pi$
$908$	−15.0566	−	41.3677i	−0.499671	−	1.37284i
$909$		0			0
$910$	−50.5867	−	24.0047i	−1.67693	−	0.795747i
$911$		−	0.296200i		−	0.00981356i	−0.999988	−	0.00490678i	$-0.998438\pi$
$911$		−	0.296200i		−	0.00981356i	0.999988	−	0.00490678i	$-0.00156188\pi$
$912$		0			0
$913$			0.553729i			0.0183258i
$914$	5.57091	−	0.982302i	0.184269	−	0.0324917i
$915$		0			0
$916$	−20.0855	+	7.31052i	−0.663643	+	0.241546i
$917$	−33.0300	−	23.4607i	−1.09075	−	0.774739i
$918$		0			0
$919$	32.1385			1.06015			0.530075	−	0.847951i	$-0.322164\pi$
$919$	32.1385			1.06015			0.530075	+	0.847951i	$0.322164\pi$
$920$	36.2614	−	20.9355i	1.19550	−	0.690224i
$921$		0			0
$922$	−7.36894	−	41.7913i	−0.242683	−	1.37632i
$923$			13.1613i			0.433211i
$924$		0			0
$925$			6.28806i			0.206750i
$926$	23.8279	−	4.20149i	0.783032	−	0.138070i
$927$		0			0
$928$	15.9418	−	18.9987i	0.523315	−	0.623663i
$929$	15.3204			0.502645			0.251323	−	0.967903i	$-0.419135\pi$
$929$	15.3204			0.502645			0.251323	+	0.967903i	$0.419135\pi$
$930$		0			0
$931$	5.04951	+	14.4766i	0.165491	+	0.474453i
$932$	−2.39229	−	6.57277i	−0.0783622	−	0.215298i
$933$		0			0
$934$	−10.0183	−	56.8168i	−0.327810	−	1.85910i
$935$			3.27641i			0.107150i
$936$		0			0
$937$			30.8365i			1.00738i	0.863884	+	0.503692i	$0.168025\pi$
$937$			30.8365i			1.00738i	−0.863884	+	0.503692i	$0.831975\pi$
$938$	18.7953	+	8.91885i	0.613689	+	0.291211i
$939$		0			0
$940$	−15.1717	−	41.6838i	−0.494845	−	1.35958i
$941$		−	7.99552i		−	0.260646i	−0.991472	−	0.130323i	$-0.958398\pi$
$941$		−	7.99552i		−	0.260646i	0.991472	−	0.130323i	$-0.0416015\pi$
$942$		0			0
$943$		−	45.8933i		−	1.49449i
$944$	22.9321	+	27.3294i	0.746376	+	0.889496i
$945$		0			0
$946$	−0.0736733	−	0.417822i	−0.00239532	−	0.0135846i
$947$	19.7796			0.642750			0.321375	−	0.946952i	$-0.395855\pi$
$947$	19.7796			0.642750			0.321375	+	0.946952i	$0.395855\pi$
$948$		0			0
$949$			36.6561i			1.18991i
$950$	−1.92307	+	0.339088i	−0.0623925	+	0.0110015i
$951$		0			0
$952$	2.88662	−	30.6199i	0.0935560	−	0.992396i
$953$			1.93689i			0.0627419i	0.999508	+	0.0313709i	$0.00998732\pi$
$953$			1.93689i			0.0627419i	−0.999508	+	0.0313709i	$0.990013\pi$
$954$		0			0
$955$	−37.6995			−1.21993
$956$	10.1529	+	27.8948i	0.328368	+	0.902183i
$957$		0			0
$958$	22.5399	−	3.97440i	0.728233	−	0.128407i
$959$	−20.6175	−	14.6442i	−0.665773	−	0.472887i
$960$		0			0
$961$	−34.7351			−1.12049
$962$	15.4482	+	87.6108i	0.498069	+	2.82469i
$963$		0			0
$964$	−9.87776	−	27.1389i	−0.318141	−	0.874086i
$965$			25.0031i			0.804877i
$966$		0			0
$967$	−18.7547			−0.603109			−0.301554	−	0.953449i	$-0.597506\pi$
$967$	−18.7547			−0.603109			−0.301554	+	0.953449i	$0.597506\pi$
$968$	26.6679	−	15.3967i	0.857139	−	0.494869i
$969$		0			0
$970$	9.30541	−	1.64079i	0.298779	−	0.0526827i
$971$			18.7150i			0.600592i	0.953846	+	0.300296i	$0.0970854\pi$
$971$			18.7150i			0.600592i	−0.953846	+	0.300296i	$0.902915\pi$
$972$		0			0
$973$	10.2825	−	14.4766i	0.329642	−	0.464100i
$974$	20.0750	−	3.53977i	0.643245	−	0.113421i
$975$		0			0
$976$	22.4652	−	18.8505i	0.719092	−	0.603390i
$977$			26.8843i			0.860106i	0.902804	+	0.430053i	$0.141505\pi$
$977$			26.8843i			0.860106i	−0.902804	+	0.430053i	$0.858495\pi$
$978$		0			0
$979$	3.80928			0.121745
$980$	−25.7330	+	21.0090i	−0.822009	+	0.671106i
$981$		0			0
$982$	−17.3063	+	3.05157i	−0.552268	+	0.0973797i
$983$	17.5670			0.560300			0.280150	−	0.959956i	$-0.409616\pi$
$983$	17.5670			0.560300			0.280150	+	0.959956i	$0.409616\pi$
$984$		0			0
$985$			40.6859i			1.29636i
$986$	25.0953	−	4.42498i	0.799197	−	0.140920i
$987$		0			0
$988$	−25.9608	+	9.44896i	−0.825923	+	0.300611i
$989$	−5.57091			−0.177145
$990$		0			0
$991$	13.9007			0.441572			0.220786	−	0.975322i	$-0.429138\pi$
$991$	13.9007			0.441572			0.220786	+	0.975322i	$0.429138\pi$
$992$	35.1340	+	29.4809i	1.11551	+	0.936020i
$993$		0			0
$994$	7.05446	+	3.34752i	0.223754	+	0.106177i
$995$	48.7133			1.54432
$996$		0			0
$997$	55.5518			1.75934			0.879671	−	0.475582i	$-0.157762\pi$
$997$	55.5518			1.75934			0.879671	+	0.475582i	$0.157762\pi$
$998$	0.576816	+	3.27129i	0.0182588	+	0.103551i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.i.b.125.3	yes	24
3.2	odd	2	inner	504.2.i.b.125.22	yes	24
4.3	odd	2		2016.2.i.b.881.17		24
7.6	odd	2	inner	504.2.i.b.125.4	yes	24
8.3	odd	2		2016.2.i.b.881.8		24
8.5	even	2	inner	504.2.i.b.125.24	yes	24
12.11	even	2		2016.2.i.b.881.22		24
21.20	even	2	inner	504.2.i.b.125.21	yes	24
24.5	odd	2	inner	504.2.i.b.125.1	✓	24
24.11	even	2		2016.2.i.b.881.3		24
28.27	even	2		2016.2.i.b.881.4		24
56.13	odd	2	inner	504.2.i.b.125.23	yes	24
56.27	even	2		2016.2.i.b.881.21		24
84.83	odd	2		2016.2.i.b.881.7		24
168.83	odd	2		2016.2.i.b.881.18		24
168.125	even	2	inner	504.2.i.b.125.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.i.b.125.1	✓	24	24.5	odd	2	inner
504.2.i.b.125.2	yes	24	168.125	even	2	inner
504.2.i.b.125.3	yes	24	1.1	even	1	trivial
504.2.i.b.125.4	yes	24	7.6	odd	2	inner
504.2.i.b.125.21	yes	24	21.20	even	2	inner
504.2.i.b.125.22	yes	24	3.2	odd	2	inner
504.2.i.b.125.23	yes	24	56.13	odd	2	inner
504.2.i.b.125.24	yes	24	8.5	even	2	inner
2016.2.i.b.881.3		24	24.11	even	2
2016.2.i.b.881.4		24	28.27	even	2
2016.2.i.b.881.7		24	84.83	odd	2
2016.2.i.b.881.8		24	8.3	odd	2
2016.2.i.b.881.17		24	4.3	odd	2
2016.2.i.b.881.18		24	168.83	odd	2
2016.2.i.b.881.21		24	56.27	even	2
2016.2.i.b.881.22		24	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39273 + 0.245576i) q^{2} +(1.87939 - 0.684040i) q^{4} -2.37285i q^{5} +(-1.53209 + 2.15701i) q^{7} +(-2.44949 + 1.41421i) q^{8} +O(q^{10})\)	\(q+(-1.39273 + 0.245576i) q^{2} +(1.87939 - 0.684040i) q^{4} -2.37285i q^{5} +(-1.53209 + 2.15701i) q^{7} +(-2.44949 + 1.41421i) q^{8} +(0.582714 + 3.30474i) q^{10} -0.335967 q^{11} +6.30668 q^{13} +(1.60407 - 3.38038i) q^{14} +(3.06418 - 2.57115i) q^{16} +4.10990 q^{17} -2.19029 q^{19} +(-1.62312 - 4.45950i) q^{20} +(0.467911 - 0.0825054i) q^{22} -6.23877i q^{23} -0.630415 q^{25} +(-8.78350 + 1.54877i) q^{26} +(-1.40390 + 5.10187i) q^{28} -4.38425 q^{29} -8.10772i q^{31} +(-3.63616 + 4.33340i) q^{32} +(-5.72397 + 1.00929i) q^{34} +(5.11827 + 3.63542i) q^{35} -9.97448i q^{37} +(3.05048 - 0.537881i) q^{38} +(3.35572 + 5.81227i) q^{40} +7.35615 q^{41} -0.892951i q^{43} +(-0.631412 + 0.229815i) q^{44} +(1.53209 + 8.68891i) q^{46} +9.34720 q^{47} +(-2.30541 - 6.60947i) q^{49} +(0.877997 - 0.154815i) q^{50} +(11.8527 - 4.31403i) q^{52} +0.748092 q^{53} +0.797200i q^{55} +(0.702359 - 7.45028i) q^{56} +(6.10607 - 1.07666i) q^{58} +8.91900i q^{59} +7.33154 q^{61} +(1.99106 + 11.2918i) q^{62} +(4.00000 - 6.92820i) q^{64} -14.9648i q^{65} +5.56012i q^{67} +(7.72408 - 2.81133i) q^{68} +(-8.02113 - 3.80623i) q^{70} +2.08689i q^{71} +5.81227i q^{73} +(2.44949 + 13.8917i) q^{74} +(-4.11640 + 1.49825i) q^{76} +(0.514732 - 0.724686i) q^{77} -9.27631 q^{79} +(-6.10095 - 7.27083i) q^{80} +(-10.2451 + 1.80649i) q^{82} -1.64816i q^{83} -9.75216i q^{85} +(0.219287 + 1.24364i) q^{86} +(0.822948 - 0.475129i) q^{88} -11.3383 q^{89} +(-9.66240 + 13.6036i) q^{91} +(-4.26757 - 11.7250i) q^{92} +(-13.0181 + 2.29544i) q^{94} +5.19722i q^{95} -2.81578i q^{97} +(4.83393 + 8.63905i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 48 q^{22} - 72 q^{25} - 24 q^{28} - 72 q^{49} + 48 q^{58} + 96 q^{64} - 24 q^{70} + 48 q^{79} - 144 q^{88}+O(q^{100}) \) 24 * q + 48 * q^22 - 72 * q^25 - 24 * q^28 - 72 * q^49 + 48 * q^58 + 96 * q^64 - 24 * q^70 + 48 * q^79 - 144 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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