LMFDB - Embedded newform 704.2.w.c.225.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [704,2,Mod(97,704)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(704, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 6]))

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

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

chi := DirichletCharacter("704.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 704 = 2^{6} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	704.w (of order $10$, degree $4$, 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:	$5.62146830230$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			225.3
Character	$\chi$	$=$	704.225
Dual form			704.2.w.c.97.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14226 + 1.57219i) q^{3} +(-3.23842 - 1.05223i) q^{5} +(-2.10871 + 1.53207i) q^{7} +(-0.239964 - 0.738534i) q^{9} +O(q^{10})$	\(q+(-1.14226 + 1.57219i) q^{3} +(-3.23842 - 1.05223i) q^{5} +(-2.10871 + 1.53207i) q^{7} +(-0.239964 - 0.738534i) q^{9} +(0.494618 + 3.27954i) q^{11} +(-3.02091 + 0.981552i) q^{13} +(5.35342 - 3.88949i) q^{15} +(1.96895 - 6.05981i) q^{17} +(3.43992 - 4.73464i) q^{19} -5.06531i q^{21} +5.37633 q^{23} +(5.33508 + 3.87617i) q^{25} +(-4.10944 - 1.33524i) q^{27} +(-0.357100 - 0.491506i) q^{29} +(-0.484122 - 1.48997i) q^{31} +(-5.72103 - 2.96846i) q^{33} +(8.44096 - 2.74263i) q^{35} +(-5.63554 - 7.75665i) q^{37} +(1.90748 - 5.87063i) q^{39} +(-5.36172 - 3.89551i) q^{41} +3.95982i q^{43} +2.64418i q^{45} +(-1.16424 - 0.845869i) q^{47} +(-0.0636959 + 0.196036i) q^{49} +(7.27811 + 10.0175i) q^{51} +(12.8394 - 4.17177i) q^{53} +(1.84903 - 11.1410i) q^{55} +(3.51446 + 10.8164i) q^{57} +(2.04096 + 2.80914i) q^{59} +(5.17857 + 1.68262i) q^{61} +(1.63750 + 1.18971i) q^{63} +10.8158 q^{65} -2.03614i q^{67} +(-6.14118 + 8.45261i) q^{69} +(-0.962044 + 2.96087i) q^{71} +(-7.93606 + 5.76589i) q^{73} +(-12.1881 + 3.96016i) q^{75} +(-6.06747 - 6.15780i) q^{77} +(-1.82883 - 5.62855i) q^{79} +(8.67801 - 6.30494i) q^{81} +(-7.93803 - 2.57922i) q^{83} +(-12.7526 + 17.5524i) q^{85} +1.18064 q^{87} +9.86166 q^{89} +(4.86641 - 6.69804i) q^{91} +(2.89551 + 0.940809i) q^{93} +(-16.1218 + 11.7132i) q^{95} +(-4.24849 - 13.0755i) q^{97} +(2.30336 - 1.15226i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 12 q^{9}+O(q^{10}) $ 64 * q - 12 * q^9	$ 64 q - 12 q^{9} - 20 q^{17} + 12 q^{25} - 96 q^{33} - 36 q^{41} + 68 q^{49} + 96 q^{57} + 168 q^{65} + 4 q^{73} + 8 q^{81} - 24 q^{89} - 152 q^{97}+O(q^{100}) $ 64 * q - 12 * q^9 - 20 * q^17 + 12 * q^25 - 96 * q^33 - 36 * q^41 + 68 * q^49 + 96 * q^57 + 168 * q^65 + 4 * q^73 + 8 * q^81 - 24 * q^89 - 152 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/704\mathbb{Z}\right)^\times$.

$n$	$133$	$321$	$639$
$\chi(n)$	$-1$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.14226	+	1.57219i	−0.659485	+	0.907704i	−0.999464	−	0.0327294i	$-0.989580\pi$
$3$	−1.14226	+	1.57219i	−0.659485	+	0.907704i	0.339979	+	0.940433i	$0.389580\pi$
$4$		0			0
$5$	−3.23842	−	1.05223i	−1.44826	−	0.470570i	−0.523801	−	0.851841i	$-0.675486\pi$
$5$	−3.23842	−	1.05223i	−1.44826	−	0.470570i	−0.924463	+	0.381271i	$0.875486\pi$
$6$		0			0
$7$	−2.10871	+	1.53207i	−0.797017	+	0.579067i	−0.910037	−	0.414526i	$-0.863947\pi$
$7$	−2.10871	+	1.53207i	−0.797017	+	0.579067i	0.113021	+	0.993593i	$0.463947\pi$
$8$		0			0
$9$	−0.239964	−	0.738534i	−0.0799881	−	0.246178i
$10$		0			0
$11$	0.494618	+	3.27954i	0.149133	+	0.988817i
$11$	0.494618	+	3.27954i	0.149133	+	0.988817i
$12$		0			0
$13$	−3.02091	+	0.981552i	−0.837849	+	0.272234i	−0.696348	−	0.717704i	$-0.745193\pi$
$13$	−3.02091	+	0.981552i	−0.837849	+	0.272234i	−0.141501	+	0.989938i	$0.545193\pi$
$14$		0			0
$15$	5.35342	−	3.88949i	1.38225	−	1.00426i
$16$		0			0
$17$	1.96895	−	6.05981i	0.477541	−	1.46972i	−0.364959	−	0.931024i	$-0.618917\pi$
$17$	1.96895	−	6.05981i	0.477541	−	1.46972i	0.842500	−	0.538696i	$-0.181083\pi$
$18$		0			0
$19$	3.43992	−	4.73464i	0.789171	−	1.08620i	−0.205040	−	0.978754i	$-0.565732\pi$
$19$	3.43992	−	4.73464i	0.789171	−	1.08620i	0.994211	−	0.107447i	$-0.0342675\pi$
$20$		0			0
$21$		−	5.06531i		−	1.10534i
$22$		0			0
$23$	5.37633			1.12104			0.560521	−	0.828140i	$-0.310601\pi$
$23$	5.37633			1.12104			0.560521	+	0.828140i	$0.310601\pi$
$24$		0			0
$25$	5.33508	+	3.87617i	1.06702	+	0.775233i
$26$		0			0
$27$	−4.10944	−	1.33524i	−0.790862	−	0.256967i
$28$		0			0
$29$	−0.357100	−	0.491506i	−0.0663118	−	0.0912703i	0.774573	−	0.632485i	$-0.217965\pi$
$29$	−0.357100	−	0.491506i	−0.0663118	−	0.0912703i	−0.840885	+	0.541214i	$0.817965\pi$
$30$		0			0
$31$	−0.484122	−	1.48997i	−0.0869508	−	0.267607i	0.898122	−	0.439747i	$-0.144932\pi$
$31$	−0.484122	−	1.48997i	−0.0869508	−	0.267607i	−0.985073	+	0.172140i	$0.944932\pi$
$32$		0			0
$33$	−5.72103	−	2.96846i	−0.995904	−	0.516742i
$34$		0			0
$35$	8.44096	−	2.74263i	1.42678	−	0.463590i
$36$		0			0
$37$	−5.63554	−	7.75665i	−0.926477	−	1.27519i	−0.961218	−	0.275789i	$-0.911061\pi$
$37$	−5.63554	−	7.75665i	−0.926477	−	1.27519i	0.0347414	−	0.999396i	$-0.488939\pi$
$38$		0			0
$39$	1.90748	−	5.87063i	0.305442	−	0.940053i
$40$		0			0
$41$	−5.36172	−	3.89551i	−0.837359	−	0.608377i	0.0842724	−	0.996443i	$-0.473143\pi$
$41$	−5.36172	−	3.89551i	−0.837359	−	0.608377i	−0.921632	+	0.388066i	$0.873143\pi$
$42$		0			0
$43$			3.95982i			0.603866i	0.953329	+	0.301933i	$0.0976320\pi$
$43$			3.95982i			0.603866i	−0.953329	+	0.301933i	$0.902368\pi$
$44$		0			0
$45$			2.64418i			0.394171i
$46$		0			0
$47$	−1.16424	−	0.845869i	−0.169822	−	0.123383i	0.499628	−	0.866240i	$-0.333470\pi$
$47$	−1.16424	−	0.845869i	−0.169822	−	0.123383i	−0.669450	+	0.742857i	$0.733470\pi$
$48$		0			0
$49$	−0.0636959	+	0.196036i	−0.00909942	+	0.0280051i
$50$		0			0
$51$	7.27811	+	10.0175i	1.01914	+	1.40272i
$52$		0			0
$53$	12.8394	−	4.17177i	1.76363	−	0.573037i	0.766061	−	0.642768i	$-0.222214\pi$
$53$	12.8394	−	4.17177i	1.76363	−	0.573037i	0.997566	+	0.0697310i	$0.0222141\pi$
$54$		0			0
$55$	1.84903	−	11.1410i	0.249324	−	1.50225i
$56$		0			0
$57$	3.51446	+	10.8164i	0.465502	+	1.43267i
$58$		0			0
$59$	2.04096	+	2.80914i	0.265710	+	0.365719i	0.920936	−	0.389715i	$-0.127426\pi$
$59$	2.04096	+	2.80914i	0.265710	+	0.365719i	−0.655225	+	0.755433i	$0.727426\pi$
$60$		0			0
$61$	5.17857	+	1.68262i	0.663048	+	0.215437i	0.621159	−	0.783685i	$-0.286662\pi$
$61$	5.17857	+	1.68262i	0.663048	+	0.215437i	0.0418894	+	0.999122i	$0.486662\pi$
$62$		0			0
$63$	1.63750	+	1.18971i	0.206305	+	0.149890i
$64$		0			0
$65$	10.8158			1.34153
$66$		0			0
$67$		−	2.03614i		−	0.248754i	−0.992235	−	0.124377i	$-0.960307\pi$
$67$		−	2.03614i		−	0.248754i	0.992235	−	0.124377i	$-0.0396933\pi$
$68$		0			0
$69$	−6.14118	+	8.45261i	−0.739311	+	1.01757i
$70$		0			0
$71$	−0.962044	+	2.96087i	−0.114174	+	0.351390i	−0.991774	−	0.128003i	$-0.959143\pi$
$71$	−0.962044	+	2.96087i	−0.114174	+	0.351390i	0.877600	+	0.479393i	$0.159143\pi$
$72$		0			0
$73$	−7.93606	+	5.76589i	−0.928846	+	0.674846i	−0.945710	−	0.325012i	$-0.894632\pi$
$73$	−7.93606	+	5.76589i	−0.928846	+	0.674846i	0.0168641	+	0.999858i	$0.494632\pi$
$74$		0			0
$75$	−12.1881	+	3.96016i	−1.40736	+	0.457280i
$76$		0			0
$77$	−6.06747	−	6.15780i	−0.691452	−	0.701746i
$78$		0			0
$79$	−1.82883	−	5.62855i	−0.205759	−	0.633262i	−0.999681	−	0.0252423i	$-0.991964\pi$
$79$	−1.82883	−	5.62855i	−0.205759	−	0.633262i	0.793922	−	0.608019i	$-0.208036\pi$
$80$		0			0
$81$	8.67801	−	6.30494i	0.964223	−	0.700549i
$82$		0			0
$83$	−7.93803	−	2.57922i	−0.871312	−	0.283107i	−0.160967	−	0.986960i	$-0.551461\pi$
$83$	−7.93803	−	2.57922i	−0.871312	−	0.283107i	−0.710345	+	0.703853i	$0.751461\pi$
$84$		0			0
$85$	−12.7526	+	17.5524i	−1.38321	+	1.90383i
$86$		0			0
$87$	1.18064			0.126578
$88$		0			0
$89$	9.86166			1.04533			0.522667	−	0.852537i	$-0.324937\pi$
$89$	9.86166			1.04533			0.522667	+	0.852537i	$0.324937\pi$
$90$		0			0
$91$	4.86641	−	6.69804i	0.510138	−	0.702145i
$92$		0			0
$93$	2.89551	+	0.940809i	0.300251	+	0.0975574i
$94$		0			0
$95$	−16.1218	+	11.7132i	−1.65406	+	1.20175i
$96$		0			0
$97$	−4.24849	−	13.0755i	−0.431369	−	1.32762i	−0.896762	−	0.442514i	$-0.854087\pi$
$97$	−4.24849	−	13.0755i	−0.431369	−	1.32762i	0.465393	−	0.885104i	$-0.345913\pi$
$98$		0			0
$99$	2.30336	−	1.15226i	0.231496	−	0.115807i
$100$		0			0
$101$	15.9103	−	5.16957i	1.58314	−	0.514392i	0.620273	−	0.784386i	$-0.287022\pi$
$101$	15.9103	−	5.16957i	1.58314	−	0.514392i	0.962862	+	0.269994i	$0.0870217\pi$
$102$		0			0
$103$	−14.0701	+	10.2225i	−1.38637	+	1.00726i	−0.390115	+	0.920766i	$0.627565\pi$
$103$	−14.0701	+	10.2225i	−1.38637	+	1.00726i	−0.996253	+	0.0864892i	$0.972435\pi$
$104$		0			0
$105$	−5.32985	+	16.4036i	−0.520140	+	1.60083i
$106$		0			0
$107$	−0.0957107	+	0.131734i	−0.00925270	+	0.0127353i	−0.813618	−	0.581399i	$-0.802505\pi$
$107$	−0.0957107	+	0.131734i	−0.00925270	+	0.0127353i	0.804366	+	0.594135i	$0.202505\pi$
$108$		0			0
$109$		−	8.78159i		−	0.841124i	−0.907264	−	0.420562i	$-0.861833\pi$
$109$		−	8.78159i		−	0.841124i	0.907264	−	0.420562i	$-0.138167\pi$
$110$		0			0
$111$	18.6322			1.76849
$112$		0			0
$113$	−9.12620	−	6.63057i	−0.858521	−	0.623752i	0.0689612	−	0.997619i	$-0.478032\pi$
$113$	−9.12620	−	6.63057i	−0.858521	−	0.623752i	−0.927482	+	0.373867i	$0.878032\pi$
$114$		0			0
$115$	−17.4108	−	5.65711i	−1.62357	−	0.527528i
$116$		0			0
$117$	1.44982	+	1.99550i	0.134036	+	0.184484i
$118$		0			0
$119$	5.13209	+	15.7949i	0.470458	+	1.44792i
$120$		0			0
$121$	−10.5107	+	3.24423i	−0.955519	+	0.294930i
$122$		0			0
$123$	12.2490	−	3.97993i	1.10445	−	0.358858i
$124$		0			0
$125$	−3.19137	−	4.39254i	−0.285445	−	0.392881i
$126$		0			0
$127$	−3.87870	+	11.9374i	−0.344179	+	1.05927i	0.617843	+	0.786302i	$0.288007\pi$
$127$	−3.87870	+	11.9374i	−0.344179	+	1.05927i	−0.962022	+	0.272972i	$0.911993\pi$
$128$		0			0
$129$	−6.22558	−	4.52315i	−0.548132	−	0.398241i
$130$		0			0
$131$		−	3.91564i		−	0.342111i	−0.985261	−	0.171056i	$-0.945282\pi$
$131$		−	3.91564i		−	0.342111i	0.985261	−	0.171056i	$-0.0547178\pi$
$132$		0			0
$133$			15.2541i			1.32270i
$134$		0			0
$135$	11.9031	+	8.64812i	1.02446	+	0.744311i
$136$		0			0
$137$	2.02994	−	6.24752i	0.173430	−	0.533762i	−0.826129	−	0.563482i	$-0.809462\pi$
$137$	2.02994	−	6.24752i	0.173430	−	0.533762i	0.999558	+	0.0297200i	$0.00946156\pi$
$138$		0			0
$139$	−10.3344	−	14.2240i	−0.876549	−	1.20647i	−0.977365	−	0.211561i	$-0.932145\pi$
$139$	−10.3344	−	14.2240i	−0.876549	−	1.20647i	0.100816	−	0.994905i	$-0.467855\pi$
$140$		0			0
$141$	2.65973	−	0.864199i	0.223990	−	0.0727787i
$142$		0			0
$143$	−4.71323	−	9.42168i	−0.394140	−	0.787881i
$144$		0			0
$145$	0.639264	+	1.96745i	0.0530879	+	0.163388i
$146$		0			0
$147$	−0.235448	−	0.324066i	−0.0194194	−	0.0267285i
$148$		0			0
$149$	0.0470625	+	0.0152915i	0.00385551	+	0.00125273i	0.310944	−	0.950428i	$-0.399355\pi$
$149$	0.0470625	+	0.0152915i	0.00385551	+	0.00125273i	−0.307089	+	0.951681i	$0.599355\pi$
$150$		0			0
$151$	−16.0167	−	11.6368i	−1.30342	−	0.946989i	−0.303436	−	0.952852i	$-0.598134\pi$
$151$	−16.0167	−	11.6368i	−1.30342	−	0.946989i	−0.999983	+	0.00586280i	$0.998134\pi$
$152$		0			0
$153$	−4.94785			−0.400010
$154$		0			0
$155$			5.33456i			0.428482i
$156$		0			0
$157$	2.19364	−	3.01928i	0.175071	−	0.240965i	−0.712460	−	0.701713i	$-0.752419\pi$
$157$	2.19364	−	3.01928i	0.175071	−	0.240965i	0.887531	+	0.460748i	$0.152419\pi$
$158$		0			0
$159$	−8.10714	+	24.9512i	−0.642938	+	1.97876i
$160$		0			0
$161$	−11.3371	+	8.23689i	−0.893490	+	0.649158i
$162$		0			0
$163$	−3.17740	+	1.03240i	−0.248874	+	0.0808639i	−0.430797	−	0.902449i	$-0.641768\pi$
$163$	−3.17740	+	1.03240i	−0.248874	+	0.0808639i	0.181924	+	0.983313i	$0.441768\pi$
$164$		0			0
$165$	15.4036	+	15.6329i	1.19917	+	1.21702i
$166$		0			0
$167$	−1.33788	−	4.11757i	−0.103528	−	0.318627i	0.885854	−	0.463964i	$-0.153573\pi$
$167$	−1.33788	−	4.11757i	−0.103528	−	0.318627i	−0.989382	+	0.145337i	$0.953573\pi$
$168$		0			0
$169$	−2.35478	+	1.71085i	−0.181137	+	0.131604i
$170$		0			0
$171$	−4.32215	−	1.40435i	−0.330523	−	0.107393i
$172$		0			0
$173$	−4.81702	+	6.63007i	−0.366232	+	0.504075i	−0.951872	−	0.306497i	$-0.900843\pi$
$173$	−4.81702	+	6.63007i	−0.366232	+	0.504075i	0.585640	+	0.810571i	$0.300843\pi$
$174$		0			0
$175$	−17.1887			−1.29934
$176$		0			0
$177$	−6.74781			−0.507196
$178$		0			0
$179$	−2.62766	+	3.61667i	−0.196401	+	0.270323i	−0.895847	−	0.444363i	$-0.853430\pi$
$179$	−2.62766	+	3.61667i	−0.196401	+	0.270323i	0.699446	+	0.714685i	$0.253430\pi$
$180$		0			0
$181$	−2.06936	−	0.672376i	−0.153814	−	0.0499773i	0.231098	−	0.972931i	$-0.425768\pi$
$181$	−2.06936	−	0.672376i	−0.153814	−	0.0499773i	−0.384912	+	0.922953i	$0.625768\pi$
$182$		0			0
$183$	−8.56068	+	6.21970i	−0.632824	+	0.459773i
$184$		0			0
$185$	10.0885	+	31.0491i	0.741720	+	2.28278i
$186$		0			0
$187$	20.8472	+	3.45996i	1.52450	+	0.253017i
$188$		0			0
$189$	10.7113	−	3.48031i	0.779131	−	0.253155i
$190$		0			0
$191$	16.3929	−	11.9101i	1.18615	−	0.861785i	0.193294	−	0.981141i	$-0.438083\pi$
$191$	16.3929	−	11.9101i	1.18615	−	0.861785i	0.992852	+	0.119355i	$0.0380828\pi$
$192$		0			0
$193$	5.89495	−	18.1428i	0.424328	−	1.30595i	−0.479309	−	0.877646i	$-0.659113\pi$
$193$	5.89495	−	18.1428i	0.424328	−	1.30595i	0.903636	−	0.428300i	$-0.140887\pi$
$194$		0			0
$195$	−12.3544	+	17.0044i	−0.884720	+	1.21771i
$196$		0			0
$197$		−	15.9802i		−	1.13854i	−0.822149	−	0.569272i	$-0.807225\pi$
$197$		−	15.9802i		−	1.13854i	0.822149	−	0.569272i	$-0.192775\pi$
$198$		0			0
$199$	−4.57913			−0.324606			−0.162303	−	0.986741i	$-0.551892\pi$
$199$	−4.57913			−0.324606			−0.162303	+	0.986741i	$0.551892\pi$
$200$		0			0
$201$	3.20120	+	2.32581i	0.225795	+	0.164050i
$202$		0			0
$203$	1.50604	+	0.489342i	0.105703	+	0.0343451i
$204$		0			0
$205$	13.2645	+	18.2570i	0.926434	+	1.27513i
$206$		0			0
$207$	−1.29013	−	3.97060i	−0.0896700	−	0.275976i
$208$		0			0
$209$	17.2289	+	8.93949i	1.19174	+	0.618358i
$210$		0			0
$211$	−3.82824	+	1.24387i	−0.263547	+	0.0856317i	−0.437810	−	0.899068i	$-0.644246\pi$
$211$	−3.82824	+	1.24387i	−0.263547	+	0.0856317i	0.174263	+	0.984699i	$0.444246\pi$
$212$		0			0
$213$	−3.55613	−	4.89460i	−0.243662	−	0.335372i
$214$		0			0
$215$	4.16662	−	12.8235i	0.284161	−	0.874558i
$216$		0			0
$217$	3.30361	+	2.40021i	0.224264	+	0.162937i
$218$		0			0
$219$		−	19.0631i		−	1.28817i
$220$		0			0
$221$			20.2388i			1.36141i
$222$		0			0
$223$	−8.39332	−	6.09811i	−0.562058	−	0.408359i	0.270153	−	0.962817i	$-0.412926\pi$
$223$	−8.39332	−	6.09811i	−0.562058	−	0.408359i	−0.832212	+	0.554458i	$0.812926\pi$
$224$		0			0
$225$	1.58245	−	4.87028i	0.105497	−	0.324685i
$226$		0			0
$227$	−11.0524	−	15.2123i	−0.733574	−	1.00968i	−0.998963	−	0.0455360i	$-0.985500\pi$
$227$	−11.0524	−	15.2123i	−0.733574	−	1.00968i	0.265389	−	0.964141i	$-0.414500\pi$
$228$		0			0
$229$	8.16399	−	2.65264i	0.539491	−	0.175291i	−0.0265814	−	0.999647i	$-0.508462\pi$
$229$	8.16399	−	2.65264i	0.539491	−	0.175291i	0.566073	+	0.824355i	$0.308462\pi$
$230$		0			0
$231$	16.6119	−	2.50539i	1.09298	−	0.164843i
$232$		0			0
$233$	2.04170	+	6.28371i	0.133756	+	0.411660i	0.995394	−	0.0958634i	$-0.0305612\pi$
$233$	2.04170	+	6.28371i	0.133756	+	0.411660i	−0.861638	+	0.507523i	$0.830561\pi$
$234$		0			0
$235$	2.88025	+	3.96432i	0.187887	+	0.258604i
$236$		0			0
$237$	10.9382	+	3.55402i	0.710509	+	0.230858i
$238$		0			0
$239$	17.7945	+	12.9284i	1.15103	+	0.836270i	0.988617	−	0.150453i	$-0.0480732\pi$
$239$	17.7945	+	12.9284i	1.15103	+	0.836270i	0.162410	+	0.986723i	$0.448073\pi$
$240$		0			0
$241$	15.7042			1.01160			0.505798	−	0.862652i	$-0.331198\pi$
$241$	15.7042			1.01160			0.505798	+	0.862652i	$0.331198\pi$
$242$		0			0
$243$			7.88260i			0.505669i
$244$		0			0
$245$	0.412548	−	0.567824i	0.0263567	−	0.0362769i
$246$		0			0
$247$	−5.74437	+	17.6794i	−0.365506	+	1.12491i
$248$		0			0
$249$	13.1223	−	9.53394i	0.831595	−	0.604189i
$250$		0			0
$251$	10.9788	−	3.56722i	0.692974	−	0.225161i	0.0587073	−	0.998275i	$-0.481302\pi$
$251$	10.9788	−	3.56722i	0.692974	−	0.225161i	0.634267	+	0.773114i	$0.281302\pi$
$252$		0			0
$253$	2.65923	+	17.6319i	0.167184	+	1.10851i
$254$		0			0
$255$	−13.0289	−	40.0989i	−0.815903	−	2.51109i
$256$		0			0
$257$	−2.73277	+	1.98547i	−0.170465	+	0.123850i	−0.669747	−	0.742590i	$-0.733597\pi$
$257$	−2.73277	+	1.98547i	−0.170465	+	0.123850i	0.499282	+	0.866440i	$0.333597\pi$
$258$		0			0
$259$	23.7674	+	7.72250i	1.47683	+	0.479853i
$260$		0			0
$261$	−0.277303	+	0.381674i	−0.0171646	+	0.0236250i
$262$		0			0
$263$	−20.7613			−1.28020			−0.640099	−	0.768292i	$-0.721107\pi$
$263$	−20.7613			−1.28020			−0.640099	+	0.768292i	$0.721107\pi$
$264$		0			0
$265$	−45.9690			−2.82385
$266$		0			0
$267$	−11.2646	+	15.5044i	−0.689382	+	0.948854i
$268$		0			0
$269$	−18.4782	−	6.00392i	−1.12663	−	0.366065i	−0.314338	−	0.949311i	$-0.601782\pi$
$269$	−18.4782	−	6.00392i	−1.12663	−	0.366065i	−0.812296	+	0.583246i	$0.801782\pi$
$270$		0			0
$271$	24.2915	−	17.6488i	1.47560	−	1.07209i	0.496665	−	0.867943i	$-0.334558\pi$
$271$	24.2915	−	17.6488i	1.47560	−	1.07209i	0.978940	−	0.204147i	$-0.0654421\pi$
$272$		0			0
$273$	4.97187	+	15.3018i	0.300911	+	0.926109i
$274$		0			0
$275$	−10.0732	+	19.4138i	−0.607437	+	1.17070i
$276$		0			0
$277$	0.204141	−	0.0663295i	0.0122657	−	0.00398536i	−0.302878	−	0.953029i	$-0.597947\pi$
$277$	0.204141	−	0.0663295i	0.0122657	−	0.00398536i	0.315143	+	0.949044i	$0.397947\pi$
$278$		0			0
$279$	−0.984224	+	0.715080i	−0.0589239	+	0.0428107i
$280$		0			0
$281$	−3.63731	+	11.1945i	−0.216984	+	0.667807i	0.782023	+	0.623249i	$0.214188\pi$
$281$	−3.63731	+	11.1945i	−0.216984	+	0.667807i	−0.999007	+	0.0445575i	$0.985812\pi$
$282$		0			0
$283$	15.9613	−	21.9688i	0.948800	−	1.30591i	−0.00325806	−	0.999995i	$-0.501037\pi$
$283$	15.9613	−	21.9688i	0.948800	−	1.30591i	0.952058	−	0.305917i	$-0.0989629\pi$
$284$		0			0
$285$		−	38.7260i		−	2.29393i
$286$		0			0
$287$	17.2745			1.01968
$288$		0			0
$289$	−19.0913	−	13.8706i	−1.12301	−	0.815918i
$290$		0			0
$291$	25.4101	+	8.25624i	1.48957	+	0.483989i
$292$		0			0
$293$	−11.6321	−	16.0102i	−0.679556	−	0.935328i	0.320373	−	0.947292i	$-0.396192\pi$
$293$	−11.6321	−	16.0102i	−0.679556	−	0.935328i	−0.999928	+	0.0119634i	$0.996192\pi$
$294$		0			0
$295$	−3.65363	−	11.2447i	−0.212723	−	0.654693i
$296$		0			0
$297$	2.34636	−	14.1375i	0.136150	−	0.820340i
$298$		0			0
$299$	−16.2414	+	5.27715i	−0.939264	+	0.305185i
$300$		0			0
$301$	−6.06670	−	8.35010i	−0.349679	−	0.481292i
$302$		0			0
$303$	−10.0462	+	30.9190i	−0.577139	+	1.77625i
$304$		0			0
$305$	−14.9999	−	10.8980i	−0.858890	−	0.624020i
$306$		0			0
$307$		−	15.6760i		−	0.894676i	−0.894365	−	0.447338i	$-0.852372\pi$
$307$		−	15.6760i		−	0.894676i	0.894365	−	0.447338i	$-0.147628\pi$
$308$		0			0
$309$		−	33.7977i		−	1.92268i
$310$		0			0
$311$	20.1723	+	14.6560i	1.14386	+	0.831065i	0.987653	−	0.156658i	$-0.0500721\pi$
$311$	20.1723	+	14.6560i	1.14386	+	0.831065i	0.156211	+	0.987724i	$0.450072\pi$
$312$		0			0
$313$	7.29337	−	22.4467i	0.412245	−	1.26876i	−0.502446	−	0.864609i	$-0.667566\pi$
$313$	7.29337	−	22.4467i	0.412245	−	1.26876i	0.914692	−	0.404153i	$-0.132434\pi$
$314$		0			0
$315$	−4.05105	−	5.57580i	−0.228251	−	0.314161i
$316$		0			0
$317$	−18.6596	+	6.06287i	−1.04803	+	0.340525i	−0.781894	−	0.623411i	$-0.785746\pi$
$317$	−18.6596	+	6.06287i	−1.04803	+	0.340525i	−0.266134	+	0.963936i	$0.585746\pi$
$318$		0			0
$319$	1.43528	−	1.41423i	0.0803604	−	0.0791816i
$320$		0			0
$321$	−0.0977848	−	0.300951i	−0.00545781	−	0.0167974i
$322$		0			0
$323$	−21.9180	−	30.1675i	−1.21955	−	1.67857i
$324$		0			0
$325$	−19.9215	−	6.47287i	−1.10504	−	0.359050i
$326$		0			0
$327$	13.8063	+	10.0309i	0.763491	+	0.554709i
$328$		0			0
$329$	3.75097			0.206798
$330$		0			0
$331$			35.1699i			1.93311i	0.256452	+	0.966557i	$0.417446\pi$
$331$			35.1699i			1.93311i	−0.256452	+	0.966557i	$0.582554\pi$
$332$		0			0
$333$	−4.37622	+	6.02335i	−0.239816	+	0.330078i
$334$		0			0
$335$	−2.14248	+	6.59388i	−0.117056	+	0.360262i
$336$		0			0
$337$	19.6313	−	14.2630i	1.06939	−	0.776954i	0.0935839	−	0.995611i	$-0.470168\pi$
$337$	19.6313	−	14.2630i	1.06939	−	0.776954i	0.975802	+	0.218657i	$0.0701677\pi$
$338$		0			0
$339$	20.8490	−	6.77426i	1.13236	−	0.367927i
$340$		0			0
$341$	4.64696	−	2.32466i	0.251647	−	0.125887i
$342$		0			0
$343$	−5.80421	−	17.8635i	−0.313398	−	0.964539i
$344$		0			0
$345$	28.7817	−	20.9112i	1.54956	−	1.12582i
$346$		0			0
$347$	13.8108	+	4.48740i	0.741403	+	0.240896i	0.655278	−	0.755388i	$-0.272552\pi$
$347$	13.8108	+	4.48740i	0.741403	+	0.240896i	0.0861251	+	0.996284i	$0.472552\pi$
$348$		0			0
$349$	−16.9994	+	23.3977i	−0.909957	+	1.25245i	0.0572248	+	0.998361i	$0.481775\pi$
$349$	−16.9994	+	23.3977i	−0.909957	+	1.25245i	−0.967181	+	0.254087i	$0.918225\pi$
$350$		0			0
$351$	13.7248			0.732578
$352$		0			0
$353$	−9.27236			−0.493518			−0.246759	−	0.969077i	$-0.579366\pi$
$353$	−9.27236			−0.493518			−0.246759	+	0.969077i	$0.579366\pi$
$354$		0			0
$355$	6.23100	−	8.57623i	0.330707	−	0.455179i
$356$		0			0
$357$	−30.6948	−	9.97335i	−1.62454	−	0.527846i
$358$		0			0
$359$	18.1803	−	13.2088i	0.959521	−	0.697133i	0.00648164	−	0.999979i	$-0.497937\pi$
$359$	18.1803	−	13.2088i	0.959521	−	0.697133i	0.953039	+	0.302846i	$0.0979368\pi$
$360$		0			0
$361$	−4.71245	−	14.5034i	−0.248024	−	0.763339i
$362$		0			0
$363$	6.90544	−	20.2306i	0.362441	−	1.06183i
$364$		0			0
$365$	31.7673	−	10.3218i	1.66278	−	0.540269i
$366$		0			0
$367$	−24.0875	+	17.5006i	−1.25735	+	0.913522i	−0.998625	−	0.0524280i	$-0.983304\pi$
$367$	−24.0875	+	17.5006i	−1.25735	+	0.913522i	−0.258730	+	0.965950i	$0.583304\pi$
$368$		0			0
$369$	−1.59035	+	4.89459i	−0.0827903	+	0.254802i
$370$		0			0
$371$	−20.6831	+	28.4679i	−1.07381	+	1.47798i
$372$		0			0
$373$			25.7294i			1.33222i	0.745855	+	0.666108i	$0.232041\pi$
$373$			25.7294i			1.33222i	−0.745855	+	0.666108i	$0.767959\pi$
$374$		0			0
$375$	10.5513			0.544866
$376$		0			0
$377$	1.56120	+	1.13428i	0.0804061	+	0.0584185i
$378$		0			0
$379$	−16.7821	−	5.45284i	−0.862040	−	0.280094i	−0.155560	−	0.987827i	$-0.549718\pi$
$379$	−16.7821	−	5.45284i	−0.862040	−	0.280094i	−0.706480	+	0.707733i	$0.749718\pi$
$380$		0			0
$381$	−14.3374	−	19.7337i	−0.734526	−	1.01099i
$382$		0			0
$383$	−0.434764	−	1.33807i	−0.0222154	−	0.0683720i	0.939334	−	0.343003i	$-0.111444\pi$
$383$	−0.434764	−	1.33807i	−0.0222154	−	0.0683720i	−0.961550	+	0.274631i	$0.911444\pi$
$384$		0			0
$385$	13.1696	+	26.3259i	0.671185	+	1.34169i
$386$		0			0
$387$	2.92446	−	0.950214i	0.148659	−	0.0483021i
$388$		0			0
$389$	0.293178	+	0.403525i	0.0148647	+	0.0204595i	0.816385	−	0.577509i	$-0.195975\pi$
$389$	0.293178	+	0.403525i	0.0148647	+	0.0204595i	−0.801520	+	0.597968i	$0.795975\pi$
$390$		0			0
$391$	10.5857	−	32.5795i	0.535344	−	1.64762i
$392$		0			0
$393$	6.15613	+	4.47269i	0.310536	+	0.225617i
$394$		0			0
$395$			20.1519i			1.01395i
$396$		0			0
$397$			6.66352i			0.334432i	0.985920	+	0.167216i	$0.0534778\pi$
$397$			6.66352i			0.334432i	−0.985920	+	0.167216i	$0.946522\pi$
$398$		0			0
$399$	−23.9824	−	17.4242i	−1.20062	−	0.872303i
$400$		0			0
$401$	−2.47090	+	7.60464i	−0.123391	+	0.379758i	−0.993604	−	0.112917i	$-0.963981\pi$
$401$	−2.47090	+	7.60464i	−0.123391	+	0.379758i	0.870214	+	0.492674i	$0.163981\pi$
$402$		0			0
$403$	2.92497	+	4.02588i	0.145703	+	0.200543i
$404$		0			0
$405$	−34.7372	+	11.2868i	−1.72611	+	0.560846i
$406$		0			0
$407$	22.6508	−	22.3185i	1.12276	−	1.10629i
$408$		0			0
$409$	1.46068	+	4.49552i	0.0722261	+	0.222289i	0.980653	−	0.195755i	$-0.0627158\pi$
$409$	1.46068	+	4.49552i	0.0722261	+	0.222289i	−0.908427	+	0.418044i	$0.862716\pi$
$410$		0			0
$411$	7.50355	+	10.3278i	0.370123	+	0.509431i
$412$		0			0
$413$	−8.60758	−	2.79677i	−0.423551	−	0.137620i
$414$		0			0
$415$	22.9927	+	16.7052i	1.12867	+	0.820026i
$416$		0			0
$417$	34.1674			1.67318
$418$		0			0
$419$			28.2116i			1.37823i	0.724653	+	0.689114i	$0.242000\pi$
$419$			28.2116i			1.37823i	−0.724653	+	0.689114i	$0.758000\pi$
$420$		0			0
$421$	−2.59708	+	3.57457i	−0.126574	+	0.174214i	−0.867601	−	0.497261i	$-0.834339\pi$
$421$	−2.59708	+	3.57457i	−0.126574	+	0.174214i	0.741027	+	0.671475i	$0.234339\pi$
$422$		0			0
$423$	−0.345327	+	1.06281i	−0.0167904	+	0.0516755i
$424$		0			0
$425$	33.9934	−	24.6976i	1.64892	−	1.19801i
$426$		0			0
$427$	−13.4980	+	4.38576i	−0.653213	+	0.212242i
$428$		0			0
$429$	20.1964	+	3.35194i	0.975092	+	0.161833i
$430$		0			0
$431$	−0.338821	−	1.04278i	−0.0163204	−	0.0502292i	0.942565	−	0.334024i	$-0.108407\pi$
$431$	−0.338821	−	1.04278i	−0.0163204	−	0.0502292i	−0.958885	+	0.283795i	$0.908407\pi$
$432$		0			0
$433$	−23.0637	+	16.7567i	−1.10837	+	0.805277i	−0.982406	−	0.186758i	$-0.940202\pi$
$433$	−23.0637	+	16.7567i	−1.10837	+	0.805277i	−0.125963	+	0.992035i	$0.540202\pi$
$434$		0			0
$435$	−3.82341	−	1.24230i	−0.183319	−	0.0595638i
$436$		0			0
$437$	18.4941	−	25.4550i	0.884694	−	1.21768i
$438$		0			0
$439$	−21.0156			−1.00302			−0.501511	−	0.865151i	$-0.667222\pi$
$439$	−21.0156			−1.00302			−0.501511	+	0.865151i	$0.667222\pi$
$440$		0			0
$441$	0.160064			0.00762209
$442$		0			0
$443$	−6.63350	+	9.13022i	−0.315167	+	0.433790i	−0.936984	−	0.349373i	$-0.886395\pi$
$443$	−6.63350	+	9.13022i	−0.315167	+	0.433790i	0.621817	+	0.783163i	$0.286395\pi$
$444$		0			0
$445$	−31.9362	−	10.3767i	−1.51392	−	0.491902i
$446$		0			0
$447$	−0.0777990	+	0.0565243i	−0.00367976	+	0.00267351i
$448$		0			0
$449$	−2.92199	−	8.99296i	−0.137897	−	0.424404i	0.858132	−	0.513429i	$-0.171625\pi$
$449$	−2.92199	−	8.99296i	−0.137897	−	0.424404i	−0.996029	+	0.0890247i	$0.971625\pi$
$450$		0			0
$451$	10.1235	−	19.5107i	0.476696	−	0.918724i
$452$		0			0
$453$	36.5905	−	11.8890i	1.71917	−	0.558592i
$454$		0			0
$455$	−22.8073	+	16.5705i	−1.06922	+	0.776836i
$456$		0			0
$457$	−0.834701	+	2.56895i	−0.0390457	+	0.120170i	−0.968679	−	0.248315i	$-0.920123\pi$
$457$	−0.834701	+	2.56895i	−0.0390457	+	0.120170i	0.929634	+	0.368485i	$0.120123\pi$
$458$		0			0
$459$	−16.1826	+	22.2734i	−0.755338	+	1.03963i
$460$		0			0
$461$			2.50763i			0.116792i	0.998293	+	0.0583960i	$0.0185986\pi$
$461$			2.50763i			0.116792i	−0.998293	+	0.0583960i	$0.981401\pi$
$462$		0			0
$463$	−1.57854			−0.0733612			−0.0366806	−	0.999327i	$-0.511678\pi$
$463$	−1.57854			−0.0733612			−0.0366806	+	0.999327i	$0.511678\pi$
$464$		0			0
$465$	−8.38694	−	6.09347i	−0.388935	−	0.282578i
$466$		0			0
$467$	11.0204	+	3.58075i	0.509964	+	0.165697i	0.552686	−	0.833390i	$-0.313603\pi$
$467$	11.0204	+	3.58075i	0.509964	+	0.165697i	−0.0427217	+	0.999087i	$0.513603\pi$
$468$		0			0
$469$	3.11950	+	4.29363i	0.144045	+	0.198261i
$470$		0			0
$471$	2.24118	+	6.89763i	0.103268	+	0.317826i
$472$		0			0
$473$	−12.9864	+	1.95859i	−0.597114	+	0.0900563i
$474$		0			0
$475$	36.7045	−	11.9260i	1.68412	−	0.547203i
$476$		0			0
$477$	−6.16199	−	8.48125i	−0.282138	−	0.388330i
$478$		0			0
$479$	9.96662	−	30.6741i	0.455387	−	1.40154i	−0.415294	−	0.909687i	$-0.636321\pi$
$479$	9.96662	−	30.6741i	0.455387	−	1.40154i	0.870681	−	0.491849i	$-0.163679\pi$
$480$		0			0
$481$	24.6380	+	17.9006i	1.12340	+	0.816195i
$482$		0			0
$483$		−	27.2328i		−	1.23913i
$484$		0			0
$485$			46.8144i			2.12573i
$486$		0			0
$487$	11.1936	+	8.13261i	0.507229	+	0.368524i	0.811771	−	0.583975i	$-0.198503\pi$
$487$	11.1936	+	8.13261i	0.507229	+	0.368524i	−0.304542	+	0.952499i	$0.598503\pi$
$488$		0			0
$489$	2.00630	−	6.17475i	0.0907280	−	0.279232i
$490$		0			0
$491$	−1.81614	−	2.49970i	−0.0819613	−	0.112810i	0.766068	−	0.642760i	$-0.222211\pi$
$491$	−1.81614	−	2.49970i	−0.0819613	−	0.112810i	−0.848029	+	0.529950i	$0.822211\pi$
$492$		0			0
$493$	−3.68155	+	1.19621i	−0.165808	+	0.0538744i
$494$		0			0
$495$	−8.67167	+	1.30786i	−0.389763	+	0.0587838i
$496$		0			0
$497$	−2.50757	−	7.71752i	−0.112480	−	0.346178i
$498$		0			0
$499$	2.94801	+	4.05758i	0.131971	+	0.181642i	0.869888	−	0.493248i	$-0.164191\pi$
$499$	2.94801	+	4.05758i	0.131971	+	0.181642i	−0.737918	+	0.674891i	$0.764191\pi$
$500$		0			0
$501$	8.00181	+	2.59994i	0.357494	+	0.116157i
$502$		0			0
$503$	−6.47445	−	4.70396i	−0.288681	−	0.209739i	0.434014	−	0.900906i	$-0.357097\pi$
$503$	−6.47445	−	4.70396i	−0.288681	−	0.209739i	−0.722695	+	0.691167i	$0.757097\pi$
$504$		0			0
$505$	−56.9638			−2.53486
$506$		0			0
$507$		−	5.65640i		−	0.251210i
$508$		0			0
$509$	3.18604	−	4.38521i	0.141219	−	0.194371i	−0.732549	−	0.680714i	$-0.761670\pi$
$509$	3.18604	−	4.38521i	0.141219	−	0.194371i	0.873768	+	0.486343i	$0.161670\pi$
$510$		0			0
$511$	7.90112	−	24.3171i	0.349525	−	1.07573i
$512$		0			0
$513$	−20.4580	+	14.8636i	−0.903243	+	0.656244i
$514$		0			0
$515$	56.3213	−	18.2999i	2.48181	−	0.806389i
$516$		0			0
$517$	2.19820	−	4.23654i	0.0966769	−	0.186323i
$518$		0			0
$519$	−4.92141	−	15.1465i	−0.216026	−	0.664860i
$520$		0			0
$521$	9.78363	−	7.10822i	0.428629	−	0.311417i	−0.352472	−	0.935822i	$-0.614659\pi$
$521$	9.78363	−	7.10822i	0.428629	−	0.311417i	0.781100	+	0.624406i	$0.214659\pi$
$522$		0			0
$523$	−14.7046	−	4.77781i	−0.642987	−	0.208919i	−0.0306676	−	0.999530i	$-0.509763\pi$
$523$	−14.7046	−	4.77781i	−0.642987	−	0.208919i	−0.612319	+	0.790611i	$0.709763\pi$
$524$		0			0
$525$	19.6340	−	27.0238i	0.856897	−	1.17942i
$526$		0			0
$527$	−9.98217			−0.434830
$528$		0			0
$529$	5.90493			0.256736
$530$		0			0
$531$	1.58489	−	2.18141i	0.0687783	−	0.0946652i
$532$		0			0
$533$	20.0209	+	6.50518i	0.867201	+	0.281771i
$534$		0			0
$535$	0.448566	−	0.325902i	0.0193932	−	0.0140900i
$536$		0			0
$537$	−2.68461	−	8.26237i	−0.115849	−	0.356548i
$538$		0			0
$539$	−0.674412	−	0.111930i	−0.0290490	−	0.00482118i
$540$		0			0
$541$	36.4922	−	11.8570i	1.56892	−	0.509773i	0.609748	−	0.792595i	$-0.291271\pi$
$541$	36.4922	−	11.8570i	1.56892	−	0.509773i	0.959172	+	0.282822i	$0.0912707\pi$
$542$		0			0
$543$	3.42085	−	2.48540i	0.146803	−	0.106659i
$544$		0			0
$545$	−9.24022	+	28.4385i	−0.395807	+	1.21817i
$546$		0			0
$547$	−8.88056	+	12.2230i	−0.379705	+	0.522620i	−0.955506	−	0.294970i	$-0.904690\pi$
$547$	−8.88056	+	12.2230i	−0.379705	+	0.522620i	0.575801	+	0.817590i	$0.304690\pi$
$548$		0			0
$549$		−	4.22832i		−	0.180460i
$550$		0			0
$551$	−3.55550			−0.151469
$552$		0			0
$553$	12.4798	+	9.06709i	0.530694	+	0.385572i
$554$		0			0
$555$	−60.3388	−	19.6053i	−2.56124	−	0.832197i
$556$		0			0
$557$	−14.9174	−	20.5320i	−0.632070	−	0.869969i	0.366092	−	0.930579i	$-0.380696\pi$
$557$	−14.9174	−	20.5320i	−0.632070	−	0.869969i	−0.998162	+	0.0606095i	$0.980696\pi$
$558$		0			0
$559$	−3.88677	−	11.9622i	−0.164393	−	0.505949i
$560$		0			0
$561$	−29.2527	+	28.8236i	−1.23505	+	1.21693i
$562$		0			0
$563$	11.7867	−	3.82974i	0.496751	−	0.161404i	−0.0499175	−	0.998753i	$-0.515896\pi$
$563$	11.7867	−	3.82974i	0.496751	−	0.161404i	0.546668	+	0.837349i	$0.315896\pi$
$564$		0			0
$565$	22.5776	+	31.0754i	0.949847	+	1.30735i
$566$		0			0
$567$	−8.63980	+	26.5906i	−0.362837	+	1.11670i
$568$		0			0
$569$	−34.1584	−	24.8175i	−1.43199	−	1.04040i	−0.989641	−	0.143562i	$-0.954144\pi$
$569$	−34.1584	−	24.8175i	−1.43199	−	1.04040i	−0.442352	−	0.896842i	$-0.645856\pi$
$570$		0			0
$571$			17.3652i			0.726710i	0.931651	+	0.363355i	$0.118369\pi$
$571$			17.3652i			0.726710i	−0.931651	+	0.363355i	$0.881631\pi$
$572$		0			0
$573$			39.3771i			1.64500i
$574$		0			0
$575$	28.6832	+	20.8395i	1.19617	+	0.869069i
$576$		0			0
$577$	−8.25385	+	25.4027i	−0.343612	+	1.05753i	0.618710	+	0.785619i	$0.287656\pi$
$577$	−8.25385	+	25.4027i	−0.343612	+	1.05753i	−0.962322	+	0.271911i	$0.912344\pi$
$578$		0			0
$579$	21.7903	+	29.9918i	0.905575	+	1.24642i
$580$		0			0
$581$	20.6905	−	6.72276i	0.858388	−	0.278907i
$582$		0			0
$583$	20.0321	+	40.0438i	0.829643	+	1.65845i
$584$		0			0
$585$	−2.59540	−	7.98782i	−0.107307	−	0.330256i
$586$		0			0
$587$	−7.76527	−	10.6880i	−0.320507	−	0.441140i	0.618115	−	0.786088i	$-0.287897\pi$
$587$	−7.76527	−	10.6880i	−0.320507	−	0.441140i	−0.938622	+	0.344948i	$0.887897\pi$
$588$		0			0
$589$	−8.71982	−	2.83324i	−0.359294	−	0.116742i
$590$		0			0
$591$	25.1239	+	18.2536i	1.03346	+	0.750853i
$592$		0			0
$593$	13.6144			0.559075			0.279537	−	0.960135i	$-0.409819\pi$
$593$	13.6144			0.559075			0.279537	+	0.960135i	$0.409819\pi$
$594$		0			0
$595$		−	56.5507i		−	2.31835i
$596$		0			0
$597$	5.23057	−	7.19926i	0.214073	−	0.294646i
$598$		0			0
$599$	−5.03988	+	15.5112i	−0.205924	+	0.633769i	0.793750	+	0.608244i	$0.208126\pi$
$599$	−5.03988	+	15.5112i	−0.205924	+	0.633769i	−0.999674	+	0.0255249i	$0.991874\pi$
$600$		0			0
$601$	24.0783	−	17.4939i	0.982173	−	0.713590i	0.0239795	−	0.999712i	$-0.492366\pi$
$601$	24.0783	−	17.4939i	0.982173	−	0.713590i	0.958193	+	0.286122i	$0.0923664\pi$
$602$		0			0
$603$	−1.50376	+	0.488601i	−0.0612378	+	0.0198974i
$604$		0			0
$605$	37.4517	+	0.553459i	1.52263	+	0.0225013i
$606$		0			0
$607$	−5.37499	−	16.5425i	−0.218164	−	0.671440i	−0.998914	−	0.0465960i	$-0.985163\pi$
$607$	−5.37499	−	16.5425i	−0.218164	−	0.671440i	0.780750	−	0.624844i	$-0.214837\pi$
$608$		0			0
$609$	−2.48963	+	1.80882i	−0.100885	+	0.0732971i
$610$		0			0
$611$	4.34732	+	1.41253i	0.175874	+	0.0571449i
$612$		0			0
$613$	−14.9698	+	20.6042i	−0.604625	+	0.832195i	−0.996122	−	0.0879848i	$-0.971957\pi$
$613$	−14.9698	+	20.6042i	−0.604625	+	0.832195i	0.391497	+	0.920179i	$0.371957\pi$
$614$		0			0
$615$	−43.8551			−1.76841
$616$		0			0
$617$	21.7924			0.877328			0.438664	−	0.898651i	$-0.355452\pi$
$617$	21.7924			0.877328			0.438664	+	0.898651i	$0.355452\pi$
$618$		0			0
$619$	−9.19511	+	12.6560i	−0.369583	+	0.508687i	−0.952787	−	0.303638i	$-0.901799\pi$
$619$	−9.19511	+	12.6560i	−0.369583	+	0.508687i	0.583205	+	0.812325i	$0.301799\pi$
$620$		0			0
$621$	−22.0937	−	7.17868i	−0.886590	−	0.288071i
$622$		0			0
$623$	−20.7954	+	15.1087i	−0.833149	+	0.605318i
$624$		0			0
$625$	−4.47606	−	13.7759i	−0.179043	−	0.551036i
$626$		0			0
$627$	−33.7344	+	16.8758i	−1.34722	+	0.673953i
$628$		0			0
$629$	−58.1000	+	18.8778i	−2.31660	+	0.752708i
$630$		0			0
$631$	−16.2897	+	11.8352i	−0.648483	+	0.471150i	−0.862754	−	0.505624i	$-0.831262\pi$
$631$	−16.2897	+	11.8352i	−0.648483	+	0.471150i	0.214271	+	0.976774i	$0.431262\pi$
$632$		0			0
$633$	2.41726	−	7.43955i	0.0960773	−	0.295696i
$634$		0			0
$635$	25.1217	−	34.5771i	0.996924	−	1.37215i
$636$		0			0
$637$		−	0.654727i		−	0.0259412i
$638$		0			0
$639$	2.41756			0.0956370
$640$		0			0
$641$	10.6009	+	7.70197i	0.418709	+	0.304210i	0.777118	−	0.629355i	$-0.216681\pi$
$641$	10.6009	+	7.70197i	0.418709	+	0.304210i	−0.358409	+	0.933565i	$0.616681\pi$
$642$		0			0
$643$	−8.17659	−	2.65674i	−0.322453	−	0.104771i	0.143318	−	0.989677i	$-0.454223\pi$
$643$	−8.17659	−	2.65674i	−0.322453	−	0.104771i	−0.465771	+	0.884905i	$0.654223\pi$
$644$		0			0
$645$	15.4017	+	21.1986i	0.606440	+	0.834692i
$646$		0			0
$647$	−10.9146	−	33.5917i	−0.429097	−	1.32062i	−0.899016	−	0.437915i	$-0.855717\pi$
$647$	−10.9146	−	33.5917i	−0.429097	−	1.32062i	0.469919	−	0.882709i	$-0.344283\pi$
$648$		0			0
$649$	−8.20318	+	8.08285i	−0.322003	+	0.317280i
$650$		0			0
$651$	−7.54717	+	2.45222i	−0.295797	+	0.0961103i
$652$		0			0
$653$	16.8538	+	23.1973i	0.659542	+	0.907782i	0.999466	−	0.0326711i	$-0.0104014\pi$
$653$	16.8538	+	23.1973i	0.659542	+	0.907782i	−0.339924	+	0.940453i	$0.610401\pi$
$654$		0			0
$655$	−4.12014	+	12.6805i	−0.160987	+	0.495468i
$656$		0			0
$657$	6.16267	+	4.47744i	0.240429	+	0.174682i
$658$		0			0
$659$		−	44.1553i		−	1.72005i	−0.510253	−	0.860024i	$-0.670448\pi$
$659$		−	44.1553i		−	1.72005i	0.510253	−	0.860024i	$-0.329552\pi$
$660$		0			0
$661$			0.114617i			0.00445807i	0.999998	+	0.00222904i	$0.000709525\pi$
$661$			0.114617i			0.00445807i	−0.999998	+	0.00222904i	$0.999290\pi$
$662$		0			0
$663$	−31.8192	−	23.1180i	−1.23575	−	0.897827i
$664$		0			0
$665$	16.0508	−	49.3993i	0.622423	−	1.91562i
$666$		0			0
$667$	−1.91989	−	2.64250i	−0.0743383	−	0.102318i
$668$		0			0
$669$	19.1747	−	6.23025i	0.741339	−	0.240876i
$670$		0			0
$671$	−2.95680	+	17.8156i	−0.114146	+	0.687762i
$672$		0			0
$673$	11.9716	+	36.8449i	0.461473	+	1.42027i	0.863365	+	0.504580i	$0.168353\pi$
$673$	11.9716	+	36.8449i	0.461473	+	1.42027i	−0.401892	+	0.915687i	$0.631647\pi$
$674$		0			0
$675$	−16.7486	−	23.0525i	−0.644654	−	0.887290i
$676$		0			0
$677$	21.9132	+	7.12003i	0.842192	+	0.273645i	0.698172	−	0.715930i	$-0.253997\pi$
$677$	21.9132	+	7.12003i	0.842192	+	0.273645i	0.144020	+	0.989575i	$0.453997\pi$
$678$		0			0
$679$	28.9914	+	21.0635i	1.11259	+	0.808342i
$680$		0			0
$681$	36.5414			1.40027
$682$		0			0
$683$		−	0.882081i		−	0.0337519i	−0.999858	−	0.0168759i	$-0.994628\pi$
$683$		−	0.882081i		−	0.0337519i	0.999858	−	0.0168759i	$-0.00537203\pi$
$684$		0			0
$685$	−13.1476	+	18.0961i	−0.502344	+	0.691417i
$686$		0			0
$687$	−5.15496	+	15.8653i	−0.196674	+	0.605300i
$688$		0			0
$689$	−34.6918	+	25.2051i	−1.32165	+	0.960237i
$690$		0			0
$691$	−44.5746	+	14.4832i	−1.69570	+	0.550966i	−0.987852	−	0.155400i	$-0.950333\pi$
$691$	−44.5746	+	14.4832i	−1.69570	+	0.550966i	−0.707847	+	0.706366i	$0.750333\pi$
$692$		0			0
$693$	−3.09177	+	5.95868i	−0.117446	+	0.226352i
$694$		0			0
$695$	18.5001	+	56.9374i	0.701748	+	2.15976i
$696$		0			0
$697$	−34.1630	+	24.8209i	−1.29402	+	0.940159i
$698$		0			0
$699$	−12.2113	−	3.96771i	−0.461875	−	0.150072i
$700$		0			0
$701$	2.35424	−	3.24033i	0.0889184	−	0.122386i	−0.762240	−	0.647294i	$-0.775901\pi$
$701$	2.35424	−	3.24033i	0.0889184	−	0.122386i	0.851159	+	0.524909i	$0.175901\pi$
$702$		0			0
$703$	−56.1107			−2.11626
$704$		0			0
$705$	−9.52266			−0.358644
$706$		0			0
$707$	−25.6301	+	35.2768i	−0.963918	+	1.32672i
$708$		0			0
$709$	−14.0995	−	4.58121i	−0.529518	−	0.172051i	0.0320423	−	0.999487i	$-0.489799\pi$
$709$	−14.0995	−	4.58121i	−0.529518	−	0.172051i	−0.561561	+	0.827436i	$0.689799\pi$
$710$		0			0
$711$	−3.71802	+	2.70130i	−0.139437	+	0.101307i
$712$		0			0
$713$	−2.60280	−	8.01059i	−0.0974755	−	0.299999i
$714$		0			0
$715$	5.34967	+	35.4707i	0.200066	+	1.32653i
$716$		0			0
$717$	−40.6519	+	13.2086i	−1.51817	+	0.493284i
$718$		0			0
$719$	−28.6129	+	20.7885i	−1.06708	+	0.775279i	−0.975385	−	0.220508i	$-0.929229\pi$
$719$	−28.6129	+	20.7885i	−1.06708	+	0.775279i	−0.0916953	+	0.995787i	$0.529229\pi$
$720$		0			0
$721$	14.0081	−	43.1126i	0.521691	−	1.60560i
$722$		0			0
$723$	−17.9383	+	24.6900i	−0.667133	+	0.918229i
$724$		0			0
$725$		−	4.00640i		−	0.148794i
$726$		0			0
$727$	4.71792			0.174978			0.0874891	−	0.996165i	$-0.472116\pi$
$727$	4.71792			0.174978			0.0874891	+	0.996165i	$0.472116\pi$
$728$		0			0
$729$	13.6411	+	9.91083i	0.505225	+	0.367068i
$730$		0			0
$731$	23.9957	+	7.79669i	0.887515	+	0.288371i
$732$		0			0
$733$	3.37900	+	4.65080i	0.124806	+	0.171781i	0.866848	−	0.498573i	$-0.166142\pi$
$733$	3.37900	+	4.65080i	0.124806	+	0.171781i	−0.742042	+	0.670354i	$0.766142\pi$
$734$		0			0
$735$	0.421488	+	1.29721i	0.0155468	+	0.0478482i
$736$		0			0
$737$	6.67760	−	1.00711i	0.245973	−	0.0370974i
$738$		0			0
$739$	−17.1781	+	5.58152i	−0.631908	+	0.205319i	−0.607420	−	0.794381i	$-0.707796\pi$
$739$	−17.1781	+	5.58152i	−0.631908	+	0.205319i	−0.0244879	+	0.999700i	$0.507796\pi$
$740$		0			0
$741$	−21.2337	−	29.2257i	−0.780040	−	1.07363i
$742$		0			0
$743$	−3.27472	+	10.0786i	−0.120138	+	0.369747i	−0.992984	−	0.118249i	$-0.962272\pi$
$743$	−3.27472	+	10.0786i	−0.120138	+	0.369747i	0.872846	+	0.487996i	$0.162272\pi$
$744$		0			0
$745$	−0.136318	−	0.0990408i	−0.00499431	−	0.00362858i
$746$		0			0
$747$			6.48143i			0.237143i
$748$		0			0
$749$		−	0.424425i		−	0.0155081i
$750$		0			0
$751$	14.4122	+	10.4711i	0.525909	+	0.382096i	0.818825	−	0.574043i	$-0.194626\pi$
$751$	14.4122	+	10.4711i	0.525909	+	0.382096i	−0.292916	+	0.956138i	$0.594626\pi$
$752$		0			0
$753$	−6.93229	+	21.3354i	−0.252627	+	0.777505i
$754$		0			0
$755$	39.6242	+	54.5380i	1.44207	+	1.98484i
$756$		0			0
$757$	−1.14730	+	0.372782i	−0.0416995	+	0.0135490i	−0.329792	−	0.944053i	$-0.606979\pi$
$757$	−1.14730	+	0.372782i	−0.0416995	+	0.0135490i	0.288093	+	0.957602i	$0.406979\pi$
$758$		0			0
$759$	−30.7582	−	15.9594i	−1.11645	−	0.579290i
$760$		0			0
$761$	2.72591	+	8.38949i	0.0988141	+	0.304119i	0.988229	−	0.152982i	$-0.0488878\pi$
$761$	2.72591	+	8.38949i	0.0988141	+	0.304119i	−0.889415	+	0.457101i	$0.848888\pi$
$762$		0			0
$763$	13.4540	+	18.5178i	0.487067	+	0.670390i
$764$		0			0
$765$	16.0232	+	5.20626i	0.579321	+	0.188233i
$766$		0			0
$767$	−8.92287	−	6.48284i	−0.322186	−	0.234082i
$768$		0			0
$769$	−7.65112			−0.275906			−0.137953	−	0.990439i	$-0.544052\pi$
$769$	−7.65112			−0.275906			−0.137953	+	0.990439i	$0.544052\pi$
$770$		0			0
$771$		−	6.56435i		−	0.236409i
$772$		0			0
$773$	−8.65795	+	11.9166i	−0.311405	+	0.428612i	−0.935819	−	0.352482i	$-0.885338\pi$
$773$	−8.65795	+	11.9166i	−0.311405	+	0.428612i	0.624414	+	0.781094i	$0.285338\pi$
$774$		0			0
$775$	3.19255	−	9.82567i	0.114680	−	0.352948i
$776$		0			0
$777$	−39.2898	+	28.5457i	−1.40951	+	1.02407i
$778$		0			0
$779$	−36.8877	+	11.9855i	−1.32164	+	0.429427i
$780$		0			0
$781$	−10.1861	−	1.69056i	−0.364488	−	0.0604930i
$782$		0			0
$783$	0.811203	+	2.49663i	0.0289900	+	0.0892222i
$784$		0			0
$785$	−10.2809	+	7.46950i	−0.366941	+	0.266598i
$786$		0			0
$787$	−12.9556	−	4.20954i	−0.461818	−	0.150054i	0.0688616	−	0.997626i	$-0.478063\pi$
$787$	−12.9556	−	4.20954i	−0.461818	−	0.150054i	−0.530680	+	0.847572i	$0.678063\pi$
$788$		0			0
$789$	23.7149	−	32.6407i	0.844272	−	1.16204i
$790$		0			0
$791$	29.4030			1.04545
$792$		0			0
$793$	−17.2956			−0.614183
$794$		0			0
$795$	52.5086	−	72.2719i	1.86229	−	2.56322i
$796$		0			0
$797$	29.7328	+	9.66078i	1.05319	+	0.342202i	0.783920	−	0.620862i	$-0.213217\pi$
$797$	29.7328	+	9.66078i	1.05319	+	0.342202i	0.269271	+	0.963065i	$0.413217\pi$
$798$		0			0
$799$	−7.41814	+	5.38959i	−0.262435	+	0.190670i
$800$		0			0
$801$	−2.36645	−	7.28317i	−0.0836142	−	0.257338i
$802$		0			0
$803$	−22.8347	−	23.1747i	−0.805821	−	0.817817i
$804$		0			0
$805$	45.3814	−	14.7453i	1.59948	−	0.519704i
$806$		0			0
$807$	30.5462	−	22.1931i	1.07528	−	0.781234i
$808$		0			0
$809$	7.69285	−	23.6762i	0.270466	−	0.832409i	−0.719917	−	0.694060i	$-0.755820\pi$
$809$	7.69285	−	23.6762i	0.270466	−	0.832409i	0.990383	−	0.138349i	$-0.0441797\pi$
$810$		0			0
$811$	29.5148	−	40.6237i	1.03641	−	1.42649i	0.136379	−	0.990657i	$-0.456454\pi$
$811$	29.5148	−	40.6237i	1.03641	−	1.42649i	0.900027	−	0.435834i	$-0.143546\pi$
$812$		0			0
$813$			58.3504i			2.04644i
$814$		0			0
$815$	11.3761			0.398487
$816$		0			0
$817$	18.7483	+	13.6214i	0.655920	+	0.476554i
$818$		0			0
$819$	−6.11449	−	1.98672i	−0.213658	−	0.0694216i
$820$		0			0
$821$	−30.4059	−	41.8501i	−1.06117	−	1.46058i	−0.878704	−	0.477366i	$-0.841592\pi$
$821$	−30.4059	−	41.8501i	−1.06117	−	1.46058i	−0.182468	−	0.983212i	$-0.558408\pi$
$822$		0			0
$823$	−7.40139	−	22.7792i	−0.257996	−	0.794031i	−0.993224	−	0.116211i	$-0.962925\pi$
$823$	−7.40139	−	22.7792i	−0.257996	−	0.794031i	0.735228	−	0.677820i	$-0.237075\pi$
$824$		0			0
$825$	−19.0160	−	38.0126i	−0.662051	−	1.32343i
$826$		0			0
$827$	13.0270	−	4.23272i	0.452992	−	0.147186i	−0.0736298	−	0.997286i	$-0.523458\pi$
$827$	13.0270	−	4.23272i	0.452992	−	0.147186i	0.526622	+	0.850100i	$0.323458\pi$
$828$		0			0
$829$	11.6339	+	16.0126i	0.404061	+	0.556142i	0.961757	−	0.273903i	$-0.0883147\pi$
$829$	11.6339	+	16.0126i	0.404061	+	0.556142i	−0.557697	+	0.830045i	$0.688315\pi$
$830$		0			0
$831$	−0.128900	+	0.396714i	−0.00447150	+	0.0137619i
$832$		0			0
$833$	1.06253	+	0.771970i	0.0368144	+	0.0267472i
$834$		0			0
$835$			14.7422i			0.510174i
$836$		0			0
$837$			6.76937i			0.233984i
$838$		0			0
$839$	−1.11385	−	0.809262i	−0.0384545	−	0.0279388i	0.568392	−	0.822758i	$-0.307566\pi$
$839$	−1.11385	−	0.809262i	−0.0384545	−	0.0279388i	−0.606846	+	0.794819i	$0.707566\pi$
$840$		0			0
$841$	8.84744	−	27.2296i	0.305084	−	0.938952i
$842$		0			0
$843$	−13.4451	−	18.5056i	−0.463073	−	0.637366i
$844$		0			0
$845$	9.42597	−	3.06268i	0.324263	−	0.105360i
$846$		0			0
$847$	17.1936	−	22.9442i	0.590780	−	0.788373i
$848$		0			0
$849$	16.3072	+	50.1883i	0.559661	+	1.72246i
$850$		0			0
$851$	−30.2985	−	41.7023i	−1.03862	−	1.42954i
$852$		0			0
$853$	7.27263	+	2.36302i	0.249010	+	0.0809083i	0.430863	−	0.902418i	$-0.358209\pi$
$853$	7.27263	+	2.36302i	0.249010	+	0.0809083i	−0.181852	+	0.983326i	$0.558209\pi$
$854$		0			0
$855$	12.5192	+	9.09575i	0.428148	+	0.311068i
$856$		0			0
$857$	−15.6967			−0.536189			−0.268094	−	0.963393i	$-0.586394\pi$
$857$	−15.6967			−0.536189			−0.268094	+	0.963393i	$0.586394\pi$
$858$		0			0
$859$		−	23.1057i		−	0.788356i	−0.919034	−	0.394178i	$-0.871029\pi$
$859$		−	23.1057i		−	0.788356i	0.919034	−	0.394178i	$-0.128971\pi$
$860$		0			0
$861$	−19.7320	+	27.1587i	−0.672464	+	0.925567i
$862$		0			0
$863$	−2.73159	+	8.40697i	−0.0929845	+	0.286177i	−0.986723	−	0.162411i	$-0.948073\pi$
$863$	−2.73159	+	8.40697i	−0.0929845	+	0.286177i	0.893739	+	0.448588i	$0.148073\pi$
$864$		0			0
$865$	22.5759	−	16.4023i	0.767602	−	0.557696i
$866$		0			0
$867$	43.6144	−	14.1712i	1.48122	−	0.481279i
$868$		0			0
$869$	17.5545	−	8.78169i	0.595495	−	0.297898i
$870$		0			0
$871$	1.99858	+	6.15100i	0.0677193	+	0.208419i
$872$		0			0
$873$	−8.63723	+	6.27531i	−0.292326	+	0.212387i
$874$		0			0
$875$	13.4593	+	4.37320i	0.455009	+	0.147841i
$876$		0			0
$877$	8.53243	−	11.7439i	0.288120	−	0.396563i	−0.640282	−	0.768140i	$-0.721183\pi$
$877$	8.53243	−	11.7439i	0.288120	−	0.396563i	0.928402	+	0.371577i	$0.121183\pi$
$878$		0			0
$879$	38.4580			1.29716
$880$		0			0
$881$	−12.0963			−0.407536			−0.203768	−	0.979019i	$-0.565319\pi$
$881$	−12.0963			−0.407536			−0.203768	+	0.979019i	$0.565319\pi$
$882$		0			0
$883$	−4.57811	+	6.30122i	−0.154066	+	0.212053i	−0.879072	−	0.476689i	$-0.841837\pi$
$883$	−4.57811	+	6.30122i	−0.154066	+	0.212053i	0.725006	+	0.688742i	$0.241837\pi$
$884$		0			0
$885$	21.8522	+	7.10022i	0.734554	+	0.238671i
$886$		0			0
$887$	−0.895795	+	0.650834i	−0.0300779	+	0.0218529i	−0.602723	−	0.797951i	$-0.705917\pi$
$887$	−0.895795	+	0.650834i	−0.0300779	+	0.0218529i	0.572645	+	0.819804i	$0.305917\pi$
$888$		0			0
$889$	−10.1099	−	31.1149i	−0.339074	−	1.04356i
$890$		0			0
$891$	24.9696	+	25.3413i	0.836512	+	0.848965i
$892$		0			0
$893$	−8.00977	+	2.60253i	−0.268037	+	0.0870904i
$894$		0			0
$895$	12.3150	−	8.94739i	0.411646	−	0.299078i
$896$		0			0
$897$	10.2553	−	31.5624i	0.342413	−	1.05384i
$898$		0			0
$899$	−0.559451	+	0.770018i	−0.0186587	+	0.0256815i
$900$		0			0
$901$		−	86.0183i		−	2.86569i
$902$		0			0
$903$	20.0577			0.667478
$904$		0			0
$905$	5.99396	+	4.35487i	0.199246	+	0.144761i
$906$		0			0
$907$	22.9755	+	7.46519i	0.762888	+	0.247877i	0.664518	−	0.747272i	$-0.268637\pi$
$907$	22.9755	+	7.46519i	0.762888	+	0.247877i	0.0983706	+	0.995150i	$0.468637\pi$
$908$		0			0
$909$	−7.63581	−	10.5098i	−0.253264	−	0.348588i
$910$		0			0
$911$	−5.10130	−	15.7002i	−0.169014	−	0.520171i	0.830296	−	0.557323i	$-0.188171\pi$
$911$	−5.10130	−	15.7002i	−0.169014	−	0.520171i	−0.999310	+	0.0371522i	$0.988171\pi$
$912$		0			0
$913$	4.53236	−	27.3088i	0.149999	−	0.903789i
$914$		0			0
$915$	34.2676	−	11.1342i	1.13285	−	0.368086i
$916$		0			0
$917$	5.99903	+	8.25695i	0.198105	+	0.272669i
$918$		0			0
$919$	6.64175	−	20.4412i	0.219091	−	0.674293i	−0.779747	−	0.626095i	$-0.784652\pi$
$919$	6.64175	−	20.4412i	0.219091	−	0.674293i	0.998838	−	0.0481978i	$-0.0153478\pi$
$920$		0			0
$921$	24.6456	+	17.9061i	0.812100	+	0.590025i
$922$		0			0
$923$		−	9.88880i		−	0.325494i
$924$		0			0
$925$		−	63.2267i		−	2.07888i
$926$		0			0
$927$	10.9260	+	7.93820i	0.358857	+	0.260725i
$928$		0			0
$929$	−12.3525	+	38.0170i	−0.405271	+	1.24730i	0.515397	+	0.856951i	$0.327644\pi$
$929$	−12.3525	+	38.0170i	−0.405271	+	1.24730i	−0.920669	+	0.390345i	$0.872356\pi$
$930$		0			0
$931$	0.709050	+	0.975924i	0.0232382	+	0.0319846i
$932$		0			0
$933$	−46.0840	+	14.9736i	−1.50872	+	0.490214i
$934$		0			0
$935$	−63.8714	−	33.1408i	−2.08882	−	1.08382i
$936$		0			0
$937$	6.66937	+	20.5262i	0.217879	+	0.670562i	0.998937	+	0.0461036i	$0.0146804\pi$
$937$	6.66937	+	20.5262i	0.217879	+	0.670562i	−0.781058	+	0.624459i	$0.785320\pi$
$938$		0			0
$939$	26.9595	+	37.1065i	0.879789	+	1.21093i
$940$		0			0
$941$	−23.8739	−	7.75711i	−0.778268	−	0.252875i	−0.107168	−	0.994241i	$-0.534178\pi$
$941$	−23.8739	−	7.75711i	−0.778268	−	0.252875i	−0.671101	+	0.741366i	$0.734178\pi$
$942$		0			0
$943$	−28.8264	−	20.9436i	−0.938715	−	0.682017i
$944$		0			0
$945$	−38.3497			−1.24751
$946$		0			0
$947$			15.9378i			0.517908i	0.965890	+	0.258954i	$0.0833778\pi$
$947$			15.9378i			0.517908i	−0.965890	+	0.258954i	$0.916622\pi$
$948$		0			0
$949$	18.3146	−	25.2079i	0.594517	−	0.818282i
$950$		0			0
$951$	11.7822	−	36.2618i	0.382063	−	1.17587i
$952$		0			0
$953$	−5.10343	+	3.70786i	−0.165316	+	0.120109i	−0.667367	−	0.744729i	$-0.732579\pi$
$953$	−5.10343	+	3.70786i	−0.165316	+	0.120109i	0.502051	+	0.864838i	$0.332579\pi$
$954$		0			0
$955$	−65.6191	+	21.3209i	−2.12338	+	0.689929i
$956$		0			0
$957$	0.583966	+	3.87196i	0.0188769	+	0.125163i
$958$		0			0
$959$	5.29106	+	16.2842i	0.170857	+	0.525844i
$960$		0			0
$961$	23.0939	−	16.7787i	0.744964	−	0.541248i
$962$		0			0
$963$	0.120257	+	0.0390740i	0.00387524	+	0.00125914i
$964$		0			0
$965$	−38.1806	+	52.5511i	−1.22908	+	1.69168i
$966$		0			0
$967$	61.0241			1.96240			0.981201	−	0.192987i	$-0.0618175\pi$
$967$	61.0241			1.96240			0.981201	+	0.192987i	$0.0618175\pi$
$968$		0			0
$969$	72.4651			2.32791
$970$		0			0
$971$	−3.22693	+	4.44148i	−0.103557	+	0.142534i	−0.857650	−	0.514233i	$-0.828077\pi$
$971$	−3.22693	+	4.44148i	−0.103557	+	0.142534i	0.754093	+	0.656767i	$0.228077\pi$
$972$		0			0
$973$	43.5843	+	14.1614i	1.39725	+	0.453993i
$974$		0			0
$975$	32.9321	−	23.9266i	1.05467	−	0.766264i
$976$		0			0
$977$	−0.851388	−	2.62030i	−0.0272383	−	0.0838310i	0.936513	−	0.350632i	$-0.114033\pi$
$977$	−0.851388	−	2.62030i	−0.0272383	−	0.0838310i	−0.963752	+	0.266801i	$0.914033\pi$
$978$		0			0
$979$	4.87775	+	32.3417i	0.155894	+	1.03364i
$980$		0			0
$981$	−6.48550	+	2.10727i	−0.207066	+	0.0672799i
$982$		0			0
$983$	2.87292	−	2.08730i	0.0916319	−	0.0665744i	−0.541026	−	0.841006i	$-0.681964\pi$
$983$	2.87292	−	2.08730i	0.0916319	−	0.0665744i	0.632658	+	0.774431i	$0.281964\pi$
$984$		0			0
$985$	−16.8148	+	51.7506i	−0.535764	+	1.64891i
$986$		0			0
$987$	−4.28459	+	5.89723i	−0.136380	+	0.187711i
$988$		0			0
$989$			21.2893i			0.676960i
$990$		0			0
$991$	−42.0870			−1.33694			−0.668469	−	0.743740i	$-0.733050\pi$
$991$	−42.0870			−1.33694			−0.668469	+	0.743740i	$0.733050\pi$
$992$		0			0
$993$	−55.2938	−	40.1733i	−1.75469	−	1.27486i
$994$		0			0
$995$	14.8291	+	4.81828i	0.470115	+	0.152750i
$996$		0			0
$997$	−4.80105	−	6.60808i	−0.152051	−	0.209280i	0.726196	−	0.687488i	$-0.241287\pi$
$997$	−4.80105	−	6.60808i	−0.152051	−	0.209280i	−0.878247	+	0.478208i	$0.841287\pi$
$998$		0			0
$999$	12.8019	+	39.4003i	0.405035	+	1.24657i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	704.2.w.c.225.3	yes	64
4.3	odd	2	inner	704.2.w.c.225.13	yes	64
8.3	odd	2	inner	704.2.w.c.225.4	yes	64
8.5	even	2	inner	704.2.w.c.225.14	yes	64
11.9	even	5	inner	704.2.w.c.97.14	yes	64
44.31	odd	10	inner	704.2.w.c.97.4	yes	64
88.53	even	10	inner	704.2.w.c.97.3	✓	64
88.75	odd	10	inner	704.2.w.c.97.13	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
704.2.w.c.97.3	✓	64	88.53	even	10	inner
704.2.w.c.97.4	yes	64	44.31	odd	10	inner
704.2.w.c.97.13	yes	64	88.75	odd	10	inner
704.2.w.c.97.14	yes	64	11.9	even	5	inner
704.2.w.c.225.3	yes	64	1.1	even	1	trivial
704.2.w.c.225.4	yes	64	8.3	odd	2	inner
704.2.w.c.225.13	yes	64	4.3	odd	2	inner
704.2.w.c.225.14	yes	64	8.5	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 704 = 2^{6} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	704.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14226 + 1.57219i) q^{3} +(-3.23842 - 1.05223i) q^{5} +(-2.10871 + 1.53207i) q^{7} +(-0.239964 - 0.738534i) q^{9} +O(q^{10})\)	\(q+(-1.14226 + 1.57219i) q^{3} +(-3.23842 - 1.05223i) q^{5} +(-2.10871 + 1.53207i) q^{7} +(-0.239964 - 0.738534i) q^{9} +(0.494618 + 3.27954i) q^{11} +(-3.02091 + 0.981552i) q^{13} +(5.35342 - 3.88949i) q^{15} +(1.96895 - 6.05981i) q^{17} +(3.43992 - 4.73464i) q^{19} -5.06531i q^{21} +5.37633 q^{23} +(5.33508 + 3.87617i) q^{25} +(-4.10944 - 1.33524i) q^{27} +(-0.357100 - 0.491506i) q^{29} +(-0.484122 - 1.48997i) q^{31} +(-5.72103 - 2.96846i) q^{33} +(8.44096 - 2.74263i) q^{35} +(-5.63554 - 7.75665i) q^{37} +(1.90748 - 5.87063i) q^{39} +(-5.36172 - 3.89551i) q^{41} +3.95982i q^{43} +2.64418i q^{45} +(-1.16424 - 0.845869i) q^{47} +(-0.0636959 + 0.196036i) q^{49} +(7.27811 + 10.0175i) q^{51} +(12.8394 - 4.17177i) q^{53} +(1.84903 - 11.1410i) q^{55} +(3.51446 + 10.8164i) q^{57} +(2.04096 + 2.80914i) q^{59} +(5.17857 + 1.68262i) q^{61} +(1.63750 + 1.18971i) q^{63} +10.8158 q^{65} -2.03614i q^{67} +(-6.14118 + 8.45261i) q^{69} +(-0.962044 + 2.96087i) q^{71} +(-7.93606 + 5.76589i) q^{73} +(-12.1881 + 3.96016i) q^{75} +(-6.06747 - 6.15780i) q^{77} +(-1.82883 - 5.62855i) q^{79} +(8.67801 - 6.30494i) q^{81} +(-7.93803 - 2.57922i) q^{83} +(-12.7526 + 17.5524i) q^{85} +1.18064 q^{87} +9.86166 q^{89} +(4.86641 - 6.69804i) q^{91} +(2.89551 + 0.940809i) q^{93} +(-16.1218 + 11.7132i) q^{95} +(-4.24849 - 13.0755i) q^{97} +(2.30336 - 1.15226i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 12 q^{9}+O(q^{10}) \) 64 * q - 12 * q^9	\( 64 q - 12 q^{9} - 20 q^{17} + 12 q^{25} - 96 q^{33} - 36 q^{41} + 68 q^{49} + 96 q^{57} + 168 q^{65} + 4 q^{73} + 8 q^{81} - 24 q^{89} - 152 q^{97}+O(q^{100}) \) 64 * q - 12 * q^9 - 20 * q^17 + 12 * q^25 - 96 * q^33 - 36 * q^41 + 68 * q^49 + 96 * q^57 + 168 * q^65 + 4 * q^73 + 8 * q^81 - 24 * q^89 - 152 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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