LMFDB - Embedded newform 552.2.u.a.17.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(17,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 11, 7]))

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

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

chi := DirichletCharacter("552.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.u (of order $22$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			17.18
Character	$\chi$	$=$	552.17
Dual form			552.2.u.a.65.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00223 - 1.41263i) q^{3} +(0.260753 - 0.167576i) q^{5} +(0.155773 + 0.0223967i) q^{7} +(-0.991071 - 2.83157i) q^{9} +O(q^{10})$	\(q+(1.00223 - 1.41263i) q^{3} +(0.260753 - 0.167576i) q^{5} +(0.155773 + 0.0223967i) q^{7} +(-0.991071 - 2.83157i) q^{9} +(-1.68358 - 3.68652i) q^{11} +(0.0449179 + 0.312411i) q^{13} +(0.0246111 - 0.536298i) q^{15} +(3.04194 - 3.51059i) q^{17} +(0.271212 - 0.235007i) q^{19} +(0.187758 - 0.197603i) q^{21} +(0.421309 - 4.77729i) q^{23} +(-2.03716 + 4.46077i) q^{25} +(-4.99325 - 1.43786i) q^{27} +(4.94153 + 4.28186i) q^{29} +(4.74250 - 1.39252i) q^{31} +(-6.89504 - 1.31646i) q^{33} +(0.0443714 - 0.0202637i) q^{35} +(-0.645924 + 1.00508i) q^{37} +(0.486340 + 0.249655i) q^{39} +(-1.16093 - 1.80644i) q^{41} +(0.309700 - 1.05474i) q^{43} +(-0.732927 - 0.572260i) q^{45} -1.80784i q^{47} +(-6.69269 - 1.96515i) q^{49} +(-1.91045 - 7.81557i) q^{51} +(-0.929129 + 6.46224i) q^{53} +(-1.05677 - 0.679145i) q^{55} +(-0.0601617 - 0.618655i) q^{57} +(-1.56930 + 0.225631i) q^{59} +(2.11196 + 7.19268i) q^{61} +(-0.0909640 - 0.463278i) q^{63} +(0.0640649 + 0.0739349i) q^{65} +(5.86299 + 2.67754i) q^{67} +(-6.32632 - 5.38310i) q^{69} +(-7.58509 - 3.46399i) q^{71} +(8.26663 + 9.54020i) q^{73} +(4.25973 + 7.34848i) q^{75} +(-0.179689 - 0.611966i) q^{77} +(15.5052 - 2.22932i) q^{79} +(-7.03556 + 5.61257i) q^{81} +(7.55163 + 4.85314i) q^{83} +(0.204906 - 1.42515i) q^{85} +(11.0012 - 2.68916i) q^{87} +(-1.75886 - 0.516449i) q^{89} +0.0496711i q^{91} +(2.78595 - 8.09505i) q^{93} +(0.0313380 - 0.106727i) q^{95} +(-2.14806 - 3.34245i) q^{97} +(-8.77009 + 8.42077i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^9	$ 240 q - 4 q^{9} - 16 q^{25} + 12 q^{27} - 8 q^{31} + 44 q^{37} + 20 q^{39} + 44 q^{43} + 124 q^{49} + 12 q^{55} + 16 q^{69} - 74 q^{75} - 144 q^{81} + 24 q^{85} - 170 q^{87} + 12 q^{93} - 198 q^{99}+O(q^{100}) $ 240 * q - 4 * q^9 - 16 * q^25 + 12 * q^27 - 8 * q^31 + 44 * q^37 + 20 * q^39 + 44 * q^43 + 124 * q^49 + 12 * q^55 + 16 * q^69 - 74 * q^75 - 144 * q^81 + 24 * q^85 - 170 * q^87 + 12 * q^93 - 198 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{7}{22}\right)$	$-1$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	1.00223	−	1.41263i	0.578638	−	0.815585i
$3$	1.00223	−	1.41263i	0.578638	−	0.815585i
$4$		0			0
$5$	0.260753	−	0.167576i	0.116612	−	0.0749422i	−0.481035	−	0.876702i	$-0.659739\pi$
$5$	0.260753	−	0.167576i	0.116612	−	0.0749422i	0.597647	+	0.801759i	$0.296102\pi$
$6$		0			0
$7$	0.155773	+	0.0223967i	0.0588766	+	0.00846517i	0.171690	−	0.985151i	$-0.445077\pi$
$7$	0.155773	+	0.0223967i	0.0588766	+	0.00846517i	−0.112814	+	0.993616i	$0.535986\pi$
$8$		0			0
$9$	−0.991071	−	2.83157i	−0.330357	−	0.943856i
$10$		0			0
$11$	−1.68358	−	3.68652i	−0.507618	−	1.11153i	−0.973918	−	0.226901i	$-0.927141\pi$
$11$	−1.68358	−	3.68652i	−0.507618	−	1.11153i	0.466300	−	0.884627i	$-0.345587\pi$
$12$		0			0
$13$	0.0449179	+	0.312411i	0.0124580	+	0.0866471i	0.995102	−	0.0988549i	$-0.0315180\pi$
$13$	0.0449179	+	0.312411i	0.0124580	+	0.0866471i	−0.982644	+	0.185502i	$0.940609\pi$
$14$		0			0
$15$	0.0246111	−	0.536298i	0.00635456	−	0.138472i
$16$		0			0
$17$	3.04194	−	3.51059i	0.737780	−	0.851444i	−0.255544	−	0.966797i	$-0.582255\pi$
$17$	3.04194	−	3.51059i	0.737780	−	0.851444i	0.993324	+	0.115354i	$0.0368002\pi$
$18$		0			0
$19$	0.271212	−	0.235007i	0.0622204	−	0.0539143i	−0.623195	−	0.782066i	$-0.714166\pi$
$19$	0.271212	−	0.235007i	0.0622204	−	0.0539143i	0.685416	+	0.728152i	$0.259620\pi$
$20$		0			0
$21$	0.187758	−	0.197603i	0.0409723	−	0.0431206i
$22$		0			0
$23$	0.421309	−	4.77729i	0.0878490	−	0.996134i
$23$	0.421309	−	4.77729i	0.0878490	−	0.996134i
$24$		0			0
$25$	−2.03716	+	4.46077i	−0.407433	+	0.892154i
$26$		0			0
$27$	−4.99325	−	1.43786i	−0.960952	−	0.276716i
$28$		0			0
$29$	4.94153	+	4.28186i	0.917618	+	0.795121i	0.979182	−	0.202982i	$-0.0650634\pi$
$29$	4.94153	+	4.28186i	0.917618	+	0.795121i	−0.0615642	+	0.998103i	$0.519609\pi$
$30$		0			0
$31$	4.74250	−	1.39252i	0.851779	−	0.250105i	0.173431	−	0.984846i	$-0.444515\pi$
$31$	4.74250	−	1.39252i	0.851779	−	0.250105i	0.678348	+	0.734741i	$0.262696\pi$
$32$		0			0
$33$	−6.89504	−	1.31646i	−1.20027	−	0.229166i
$34$		0			0
$35$	0.0443714	−	0.0202637i	0.00750013	−	0.00342520i
$36$		0			0
$37$	−0.645924	+	1.00508i	−0.106189	+	0.165234i	−0.890282	−	0.455410i	$-0.849493\pi$
$37$	−0.645924	+	1.00508i	−0.106189	+	0.165234i	0.784092	+	0.620644i	$0.213129\pi$
$38$		0			0
$39$	0.486340	+	0.249655i	0.0778767	+	0.0399767i
$40$		0			0
$41$	−1.16093	−	1.80644i	−0.181307	−	0.282119i	0.738689	−	0.674046i	$-0.235445\pi$
$41$	−1.16093	−	1.80644i	−0.181307	−	0.282119i	−0.919996	+	0.391927i	$0.871809\pi$
$42$		0			0
$43$	0.309700	−	1.05474i	0.0472288	−	0.160847i	−0.932502	−	0.361164i	$-0.882379\pi$
$43$	0.309700	−	1.05474i	0.0472288	−	0.160847i	0.979731	+	0.200318i	$0.0641975\pi$
$44$		0			0
$45$	−0.732927	−	0.572260i	−0.109258	−	0.0853076i
$46$		0			0
$47$		−	1.80784i		−	0.263701i	−0.991270	−	0.131850i	$-0.957908\pi$
$47$		−	1.80784i		−	0.263701i	0.991270	−	0.131850i	$-0.0420919\pi$
$48$		0			0
$49$	−6.69269	−	1.96515i	−0.956098	−	0.280736i
$50$		0			0
$51$	−1.91045	−	7.81557i	−0.267517	−	1.09440i
$52$		0			0
$53$	−0.929129	+	6.46224i	−0.127626	+	0.887657i	0.820926	+	0.571035i	$0.193458\pi$
$53$	−0.929129	+	6.46224i	−0.127626	+	0.887657i	−0.948552	+	0.316622i	$0.897451\pi$
$54$		0			0
$55$	−1.05677	−	0.679145i	−0.142495	−	0.0915759i
$56$		0			0
$57$	−0.0601617	−	0.618655i	−0.00796861	−	0.0819428i
$58$		0			0
$59$	−1.56930	+	0.225631i	−0.204306	+	0.0293747i	−0.243708	−	0.969849i	$-0.578364\pi$
$59$	−1.56930	+	0.225631i	−0.204306	+	0.0293747i	0.0394021	+	0.999223i	$0.487455\pi$
$60$		0			0
$61$	2.11196	+	7.19268i	0.270409	+	0.920928i	0.976988	+	0.213294i	$0.0684192\pi$
$61$	2.11196	+	7.19268i	0.270409	+	0.920928i	−0.706579	+	0.707634i	$0.749763\pi$
$62$		0			0
$63$	−0.0909640	−	0.463278i	−0.0114604	−	0.0583675i
$64$		0			0
$65$	0.0640649	+	0.0739349i	0.00794628	+	0.00917049i
$66$		0			0
$67$	5.86299	+	2.67754i	0.716279	+	0.327114i	0.740002	−	0.672605i	$-0.234825\pi$
$67$	5.86299	+	2.67754i	0.716279	+	0.327114i	−0.0237230	+	0.999719i	$0.507552\pi$
$68$		0			0
$69$	−6.32632	−	5.38310i	−0.761599	−	0.648049i
$70$		0			0
$71$	−7.58509	−	3.46399i	−0.900185	−	0.411101i	−0.0890954	−	0.996023i	$-0.528398\pi$
$71$	−7.58509	−	3.46399i	−0.900185	−	0.411101i	−0.811089	+	0.584923i	$0.801125\pi$
$72$		0			0
$73$	8.26663	+	9.54020i	0.967536	+	1.11660i	0.993141	+	0.116923i	$0.0373032\pi$
$73$	8.26663	+	9.54020i	0.967536	+	1.11660i	−0.0256054	+	0.999672i	$0.508151\pi$
$74$		0			0
$75$	4.25973	+	7.34848i	0.491871	+	0.848530i
$76$		0			0
$77$	−0.179689	−	0.611966i	−0.0204775	−	0.0697400i
$78$		0			0
$79$	15.5052	−	2.22932i	1.74448	−	0.250818i	0.804962	−	0.593327i	$-0.202186\pi$
$79$	15.5052	−	2.22932i	1.74448	−	0.250818i	0.939515	+	0.342509i	$0.111277\pi$
$80$		0			0
$81$	−7.03556	+	5.61257i	−0.781728	+	0.623619i
$82$		0			0
$83$	7.55163	+	4.85314i	0.828899	+	0.532701i	0.884928	−	0.465728i	$-0.154208\pi$
$83$	7.55163	+	4.85314i	0.828899	+	0.532701i	−0.0560289	+	0.998429i	$0.517844\pi$
$84$		0			0
$85$	0.204906	−	1.42515i	0.0222252	−	0.154580i
$86$		0			0
$87$	11.0012	−	2.68916i	1.17946	−	0.288309i
$88$		0			0
$89$	−1.75886	−	0.516449i	−0.186439	−	0.0547435i	0.187180	−	0.982326i	$-0.440065\pi$
$89$	−1.75886	−	0.516449i	−0.186439	−	0.0547435i	−0.373619	+	0.927582i	$0.621883\pi$
$90$		0			0
$91$			0.0496711i			0.00520694i
$92$		0			0
$93$	2.78595	−	8.09505i	0.288890	−	0.839418i
$94$		0			0
$95$	0.0313380	−	0.106727i	0.00321521	−	0.0109500i
$96$		0			0
$97$	−2.14806	−	3.34245i	−0.218103	−	0.339374i	0.714911	−	0.699216i	$-0.246467\pi$
$97$	−2.14806	−	3.34245i	−0.218103	−	0.339374i	−0.933014	+	0.359841i	$0.882831\pi$
$98$		0			0
$99$	−8.77009	+	8.42077i	−0.881427	+	0.846319i
$100$		0			0
$101$	−4.03884	+	6.28455i	−0.401879	+	0.625336i	−0.981930	−	0.189244i	$-0.939396\pi$
$101$	−4.03884	+	6.28455i	−0.401879	+	0.625336i	0.580051	+	0.814580i	$0.303033\pi$
$102$		0			0
$103$	8.39204	−	3.83251i	0.826892	−	0.377629i	0.0434206	−	0.999057i	$-0.486174\pi$
$103$	8.39204	−	3.83251i	0.826892	−	0.377629i	0.783471	+	0.621428i	$0.213447\pi$
$104$		0			0
$105$	0.0158451	−	0.0829894i	0.00154632	−	0.00809894i
$106$		0			0
$107$	−4.99246	+	1.46592i	−0.482639	+	0.141716i	−0.513996	−	0.857793i	$-0.671835\pi$
$107$	−4.99246	+	1.46592i	−0.482639	+	0.141716i	0.0313569	+	0.999508i	$0.490017\pi$
$108$		0			0
$109$	8.87808	+	7.69290i	0.850366	+	0.736846i	0.966576	−	0.256379i	$-0.0825294\pi$
$109$	8.87808	+	7.69290i	0.850366	+	0.736846i	−0.116211	+	0.993225i	$0.537075\pi$
$110$		0			0
$111$	0.772443	+	1.91977i	0.0733170	+	0.182217i
$112$		0			0
$113$	−4.74989	+	10.4008i	−0.446832	+	0.978427i	0.543461	+	0.839434i	$0.317114\pi$
$113$	−4.74989	+	10.4008i	−0.446832	+	0.978427i	−0.990293	+	0.138992i	$0.955614\pi$
$114$		0			0
$115$	−0.690701	−	1.31629i	−0.0644082	−	0.122745i
$116$		0			0
$117$	0.840095	−	0.436809i	0.0776668	−	0.0403830i
$118$		0			0
$119$	0.552478	−	0.478725i	0.0506456	−	0.0438846i
$120$		0			0
$121$	−3.55254	+	4.09984i	−0.322958	+	0.372713i
$122$		0			0
$123$	−3.71537	−	0.170501i	−0.335003	−	0.0153735i
$124$		0			0
$125$	0.436878	+	3.03855i	0.0390756	+	0.271776i
$126$		0			0
$127$	1.91627	+	4.19605i	0.170042	+	0.372339i	0.975398	−	0.220452i	$-0.0707532\pi$
$127$	1.91627	+	4.19605i	0.170042	+	0.372339i	−0.805356	+	0.592791i	$0.798026\pi$
$128$		0			0
$129$	−1.17957	−	1.49459i	−0.103856	−	0.131591i
$130$		0			0
$131$	−11.8371	−	1.70192i	−1.03421	−	0.148698i	−0.395757	−	0.918355i	$-0.629518\pi$
$131$	−11.8371	−	1.70192i	−1.03421	−	0.148698i	−0.638457	+	0.769657i	$0.720427\pi$
$132$		0			0
$133$	0.0475109	−	0.0305334i	0.00411972	−	0.00264758i
$134$		0			0
$135$	−1.54296	+	0.461822i	−0.132797	+	0.0397473i
$136$		0			0
$137$	16.6151			1.41953			0.709763	−	0.704441i	$-0.248802\pi$
$137$	16.6151			1.41953			0.709763	+	0.704441i	$0.248802\pi$
$138$		0			0
$139$	−10.9470			−0.928514			−0.464257	−	0.885701i	$-0.653679\pi$
$139$	−10.9470			−0.928514			−0.464257	+	0.885701i	$0.653679\pi$
$140$		0			0
$141$	−2.55382	−	1.81187i	−0.215070	−	0.152587i
$142$		0			0
$143$	1.07609	−	0.691558i	0.0899868	−	0.0578310i
$144$		0			0
$145$	2.00605	+	0.288427i	0.166594	+	0.0239526i
$146$		0			0
$147$	−9.48365	+	7.48479i	−0.782198	+	0.617335i
$148$		0			0
$149$	7.50171	+	16.4265i	0.614564	+	1.34571i	0.919408	+	0.393305i	$0.128669\pi$
$149$	7.50171	+	16.4265i	0.614564	+	1.34571i	−0.304844	+	0.952402i	$0.598604\pi$
$150$		0			0
$151$	0.883993	+	6.14830i	0.0719383	+	0.500342i	0.993654	+	0.112477i	$0.0358783\pi$
$151$	0.883993	+	6.14830i	0.0719383	+	0.500342i	−0.921716	+	0.387865i	$0.873213\pi$
$152$		0			0
$153$	−12.9553	−	5.13423i	−1.04737	−	0.415078i
$154$		0			0
$155$	1.00327	−	1.15783i	0.0805845	−	0.0929995i
$156$		0			0
$157$	10.2651	−	8.89473i	0.819241	−	0.709877i	−0.140708	−	0.990051i	$-0.544938\pi$
$157$	10.2651	−	8.89473i	0.819241	−	0.709877i	0.959949	+	0.280174i	$0.0903923\pi$
$158$		0			0
$159$	8.19758	+	7.78917i	0.650110	+	0.617721i
$160$		0			0
$161$	0.172624	−	0.734736i	0.0136047	−	0.0579053i
$162$		0			0
$163$	−9.31819	+	20.4040i	−0.729857	+	1.59816i	0.0696955	+	0.997568i	$0.477797\pi$
$163$	−9.31819	+	20.4040i	−0.729857	+	1.59816i	−0.799553	+	0.600596i	$0.794930\pi$
$164$		0			0
$165$	−2.01851	+	0.812170i	−0.157141	+	0.0632274i
$166$		0			0
$167$	−3.14612	−	2.72613i	−0.243454	−	0.210954i	0.524583	−	0.851359i	$-0.324221\pi$
$167$	−3.14612	−	2.72613i	−0.243454	−	0.210954i	−0.768037	+	0.640405i	$0.778767\pi$
$168$		0			0
$169$	12.3778	−	3.63446i	0.952140	−	0.279574i
$170$		0			0
$171$	−0.934229	−	0.535048i	−0.0714423	−	0.0409161i
$172$		0			0
$173$	−7.48861	+	3.41993i	−0.569348	+	0.260013i	−0.679222	−	0.733933i	$-0.737683\pi$
$173$	−7.48861	+	3.41993i	−0.569348	+	0.260013i	0.109874	+	0.993946i	$0.464955\pi$
$174$		0			0
$175$	−0.417241	+	0.649240i	−0.0315405	+	0.0490780i
$176$		0			0
$177$	−1.25407	+	2.44298i	−0.0942613	+	0.183626i
$178$		0			0
$179$	7.19732	+	11.1992i	0.537953	+	0.837071i	0.998727	−	0.0504466i	$-0.0160645\pi$
$179$	7.19732	+	11.1992i	0.537953	+	0.837071i	−0.460774	+	0.887518i	$0.652428\pi$
$180$		0			0
$181$	4.89817	−	16.6816i	0.364078	−	1.23994i	−0.550262	−	0.834992i	$-0.685472\pi$
$181$	4.89817	−	16.6816i	0.364078	−	1.23994i	0.914341	−	0.404945i	$-0.132709\pi$
$182$		0			0
$183$	12.2773	+	4.22529i	0.907563	+	0.312342i
$184$		0			0
$185$			0.370318i			0.0272264i
$186$		0			0
$187$	−18.0632	−	5.30384i	−1.32091	−	0.387855i
$188$		0			0
$189$	−0.745609	−	0.335812i	−0.0542351	−	0.0244267i
$190$		0			0
$191$	0.323124	−	2.24738i	0.0233804	−	0.162614i	−0.974786	−	0.223141i	$-0.928369\pi$
$191$	0.323124	−	2.24738i	0.0233804	−	0.162614i	0.998167	+	0.0605267i	$0.0192780\pi$
$192$		0			0
$193$	−15.5850	−	10.0159i	−1.12183	−	0.720959i	−0.157995	−	0.987440i	$-0.550503\pi$
$193$	−15.5850	−	10.0159i	−1.12183	−	0.720959i	−0.963840	+	0.266481i	$0.914139\pi$
$194$		0			0
$195$	0.168651	−	0.0164006i	0.0120773	−	0.00117447i
$196$		0			0
$197$	−5.23856	+	0.753192i	−0.373232	+	0.0536627i	−0.326379	−	0.945239i	$-0.605828\pi$
$197$	−5.23856	+	0.753192i	−0.373232	+	0.0536627i	−0.0468534	+	0.998902i	$0.514919\pi$
$198$		0			0
$199$	0.0902579	+	0.307390i	0.00639821	+	0.0217903i	0.962630	−	0.270819i	$-0.0872946\pi$
$199$	0.0902579	+	0.307390i	0.00639821	+	0.0217903i	−0.956232	+	0.292610i	$0.905476\pi$
$200$		0			0
$201$	9.65845	−	5.59876i	0.681255	−	0.394906i
$202$		0			0
$203$	0.673855	+	0.777671i	0.0472954	+	0.0545818i
$204$		0			0
$205$	−0.605433	−	0.276492i	−0.0422853	−	0.0193110i
$206$		0			0
$207$	−13.9448	+	3.54167i	−0.969228	+	0.246163i
$208$		0			0
$209$	−1.32296	−	0.604178i	−0.0915114	−	0.0417918i
$210$		0			0
$211$	−10.4708	−	12.0840i	−0.720841	−	0.831895i	0.270567	−	0.962701i	$-0.412789\pi$
$211$	−10.4708	−	12.0840i	−0.720841	−	0.831895i	−0.991408	+	0.130806i	$0.958243\pi$
$212$		0			0
$213$	−12.4954	+	7.24324i	−0.856168	+	0.496299i
$214$		0			0
$215$	−0.0959940	−	0.326925i	−0.00654673	−	0.0222961i
$216$		0			0
$217$	0.769941	−	0.110701i	0.0522670	−	0.00751486i
$218$		0			0
$219$	21.7619	−	2.11625i	1.47053	−	0.143003i
$220$		0			0
$221$	1.23338	+	0.792647i	0.0829664	+	0.0533192i
$222$		0			0
$223$	−3.81205	+	26.5134i	−0.255274	+	1.77547i	0.310168	+	0.950682i	$0.399615\pi$
$223$	−3.81205	+	26.5134i	−0.255274	+	1.77547i	−0.565442	+	0.824788i	$0.691294\pi$
$224$		0			0
$225$	14.6499	+	1.34743i	0.976663	+	0.0898287i
$226$		0			0
$227$	−24.7212	−	7.25881i	−1.64081	−	0.481784i	−0.674307	−	0.738452i	$-0.735557\pi$
$227$	−24.7212	−	7.25881i	−1.64081	−	0.481784i	−0.966500	+	0.256667i	$0.917376\pi$
$228$		0			0
$229$		−	7.09896i		−	0.469112i	−0.972103	−	0.234556i	$-0.924636\pi$
$229$		−	7.09896i		−	0.469112i	0.972103	−	0.234556i	$-0.0753637\pi$
$230$		0			0
$231$	−1.04457	−	0.359495i	−0.0687280	−	0.0236530i
$232$		0			0
$233$	7.81322	−	26.6094i	0.511861	−	1.74324i	−0.145202	−	0.989402i	$-0.546383\pi$
$233$	7.81322	−	26.6094i	0.511861	−	1.74324i	0.657063	−	0.753836i	$-0.271799\pi$
$234$		0			0
$235$	−0.302951	−	0.471401i	−0.0197623	−	0.0307508i
$236$		0			0
$237$	12.3906	−	24.1375i	0.804856	−	1.56790i
$238$		0			0
$239$	2.14427	−	3.33656i	0.138702	−	0.215824i	−0.764953	−	0.644086i	$-0.777238\pi$
$239$	2.14427	−	3.33656i	0.138702	−	0.215824i	0.903654	+	0.428262i	$0.140874\pi$
$240$		0			0
$241$	15.2011	−	6.94211i	0.979188	−	0.447180i	0.139484	−	0.990224i	$-0.455456\pi$
$241$	15.2011	−	6.94211i	0.979188	−	0.447180i	0.839704	+	0.543044i	$0.182728\pi$
$242$		0			0
$243$	0.877269	+	15.5638i	0.0562768	+	0.998415i
$244$		0			0
$245$	−2.07445	+	0.609114i	−0.132532	+	0.0389148i
$246$		0			0
$247$	0.0856009	+	0.0741736i	0.00544665	+	0.00471955i
$248$		0			0
$249$	14.4242	−	5.80373i	0.914095	−	0.367797i
$250$		0			0
$251$	6.02759	−	13.1986i	0.380458	−	0.833086i	−0.618426	−	0.785843i	$-0.712229\pi$
$251$	6.02759	−	13.1986i	0.380458	−	0.833086i	0.998883	−	0.0472431i	$-0.0150435\pi$
$252$		0			0
$253$	−18.3209	+	6.48977i	−1.15182	+	0.408009i
$254$		0			0
$255$	−1.80786	−	1.71779i	−0.113212	−	0.107572i
$256$		0			0
$257$	7.08093	−	6.13566i	0.441696	−	0.382732i	−0.405428	−	0.914127i	$-0.632878\pi$
$257$	7.08093	−	6.13566i	0.441696	−	0.382732i	0.847124	+	0.531395i	$0.178332\pi$
$258$		0			0
$259$	−0.123128	+	0.142097i	−0.00765079	+	0.00882949i
$260$		0			0
$261$	7.22696	−	18.2359i	0.447338	−	1.12877i
$262$		0			0
$263$	−2.84708	−	19.8019i	−0.175559	−	1.22104i	−0.866890	−	0.498500i	$-0.833884\pi$
$263$	−2.84708	−	19.8019i	−0.175559	−	1.22104i	0.691331	−	0.722538i	$-0.257025\pi$
$264$		0			0
$265$	0.840641	+	1.84075i	0.0516402	+	0.113076i
$266$		0			0
$267$	−2.49234	+	1.96703i	−0.152529	+	0.120380i
$268$		0			0
$269$	14.8902	+	2.14089i	0.907872	+	0.130532i	0.580403	−	0.814330i	$-0.302895\pi$
$269$	14.8902	+	2.14089i	0.907872	+	0.130532i	0.327469	+	0.944862i	$0.393804\pi$
$270$		0			0
$271$	14.9274	−	9.59326i	0.906775	−	0.582749i	−0.00201693	−	0.999998i	$-0.500642\pi$
$271$	14.9274	−	9.59326i	0.906775	−	0.582749i	0.908792	+	0.417249i	$0.137006\pi$
$272$		0			0
$273$	0.0701671	+	0.0497818i	0.00424670	+	0.00301293i
$274$		0			0
$275$	19.8744			1.19847
$276$		0			0
$277$	−11.0401			−0.663333			−0.331666	−	0.943397i	$-0.607611\pi$
$277$	−11.0401			−0.663333			−0.331666	+	0.943397i	$0.607611\pi$
$278$		0			0
$279$	−8.64319	−	12.0486i	−0.517454	−	0.721333i
$280$		0			0
$281$	−11.9326	+	7.66860i	−0.711838	+	0.457470i	−0.845789	−	0.533517i	$-0.820870\pi$
$281$	−11.9326	+	7.66860i	−0.711838	+	0.457470i	0.133951	+	0.990988i	$0.457233\pi$
$282$		0			0
$283$	−14.8781	−	2.13915i	−0.884412	−	0.127159i	−0.314883	−	0.949130i	$-0.601965\pi$
$283$	−14.8781	−	2.13915i	−0.884412	−	0.127159i	−0.569529	+	0.821971i	$0.692874\pi$
$284$		0			0
$285$	−0.119359	−	0.151234i	−0.00707021	−	0.00895836i
$286$		0			0
$287$	−0.140383	−	0.307396i	−0.00828655	−	0.0181450i
$288$		0			0
$289$	−0.651472	−	4.53109i	−0.0383219	−	0.266535i
$290$		0			0
$291$	−6.87451	−	0.315476i	−0.402991	−	0.0184935i
$292$		0			0
$293$	5.36457	−	6.19104i	0.313401	−	0.361684i	−0.577093	−	0.816678i	$-0.695813\pi$
$293$	5.36457	−	6.19104i	0.313401	−	0.361684i	0.890495	+	0.454994i	$0.150359\pi$
$294$		0			0
$295$	−0.371390	+	0.321811i	−0.0216231	+	0.0187366i
$296$		0			0
$297$	3.10582	+	20.8285i	0.180218	+	1.20859i
$298$		0			0
$299$	1.51140	−	0.0829643i	0.0874065	−	0.00479795i
$300$		0			0
$301$	0.0718656	−	0.157364i	0.00414227	−	0.00907030i
$302$		0			0
$303$	4.82993	+	12.0040i	0.277472	+	0.689610i
$304$		0			0
$305$	1.75602	+	1.52160i	0.100549	+	0.0871265i
$306$		0			0
$307$	3.98193	−	1.16920i	0.227261	−	0.0667298i	−0.166120	−	0.986106i	$-0.553124\pi$
$307$	3.98193	−	1.16920i	0.227261	−	0.0667298i	0.393380	+	0.919376i	$0.371306\pi$
$308$		0			0
$309$	2.99681	−	15.6959i	0.170482	−	0.892911i
$310$		0			0
$311$	15.2640	−	6.97083i	0.865541	−	0.395279i	0.0673828	−	0.997727i	$-0.478535\pi$
$311$	15.2640	−	6.97083i	0.865541	−	0.395279i	0.798158	+	0.602448i	$0.205808\pi$
$312$		0			0
$313$	−2.20930	+	3.43774i	−0.124877	+	0.194313i	−0.898063	−	0.439867i	$-0.855026\pi$
$313$	−2.20930	+	3.43774i	−0.124877	+	0.194313i	0.773186	+	0.634179i	$0.218662\pi$
$314$		0			0
$315$	−0.101353	−	0.105558i	−0.00571061	−	0.00594751i
$316$		0			0
$317$	−14.4018	−	22.4097i	−0.808887	−	1.25865i	−0.962705	−	0.270554i	$-0.912793\pi$
$317$	−14.4018	−	22.4097i	−0.808887	−	1.25865i	0.153817	−	0.988099i	$-0.450843\pi$
$318$		0			0
$319$	7.46571	−	25.4259i	0.418000	−	1.42358i
$320$		0			0
$321$	−2.93278	+	8.52170i	−0.163692	+	0.475635i
$322$		0			0
$323$		−	1.66699i		−	0.0927540i
$324$		0			0
$325$	−1.48510	−	0.436064i	−0.0823783	−	0.0241885i
$326$		0			0
$327$	19.7651	−	4.83143i	1.09301	−	0.267178i
$328$		0			0
$329$	0.0404898	−	0.281613i	0.00223227	−	0.0155258i
$330$		0			0
$331$	−29.2045	−	18.7686i	−1.60522	−	1.03161i	−0.964585	−	0.263772i	$-0.915033\pi$
$331$	−29.2045	−	18.7686i	−1.60522	−	1.03161i	−0.640638	−	0.767843i	$-0.721330\pi$
$332$		0			0
$333$	3.48610	+	0.832875i	0.191037	+	0.0456413i
$334$		0			0
$335$	1.97748	−	0.284319i	0.108042	−	0.0155340i
$336$		0			0
$337$	−6.40047	−	21.7980i	−0.348656	−	1.18741i	−0.928078	−	0.372385i	$-0.878540\pi$
$337$	−6.40047	−	21.7980i	−0.348656	−	1.18741i	0.579423	−	0.815027i	$-0.303278\pi$
$338$		0			0
$339$	9.93207	+	17.1339i	0.539436	+	0.930584i
$340$		0			0
$341$	−13.1179	−	15.1389i	−0.710377	−	0.819818i
$342$		0			0
$343$	−2.00060	−	0.913642i	−0.108022	−	0.0493320i
$344$		0			0
$345$	−2.55168	−	0.343522i	−0.137378	−	0.0184946i
$346$		0			0
$347$	1.02145	+	0.466482i	0.0548345	+	0.0250421i	0.442644	−	0.896698i	$-0.354041\pi$
$347$	1.02145	+	0.466482i	0.0548345	+	0.0250421i	−0.387809	+	0.921740i	$0.626768\pi$
$348$		0			0
$349$	6.04588	+	6.97731i	0.323628	+	0.373487i	0.894128	−	0.447811i	$-0.147796\pi$
$349$	6.04588	+	6.97731i	0.323628	+	0.373487i	−0.570500	+	0.821297i	$0.693251\pi$
$350$		0			0
$351$	0.224917	−	1.62453i	0.0120052	−	0.0867110i
$352$		0			0
$353$	0.206404	+	0.702949i	0.0109858	+	0.0374142i	0.964803	−	0.262972i	$-0.0847027\pi$
$353$	0.206404	+	0.702949i	0.0109858	+	0.0374142i	−0.953818	+	0.300386i	$0.902884\pi$
$354$		0			0
$355$	−2.55832	+	0.367831i	−0.135781	+	0.0195224i
$356$		0			0
$357$	−0.122553	−	1.26024i	−0.00648621	−	0.0666991i
$358$		0			0
$359$	24.3927	+	15.6763i	1.28740	+	0.827361i	0.991781	−	0.127946i	$-0.0408383\pi$
$359$	24.3927	+	15.6763i	1.28740	+	0.827361i	0.295617	+	0.955306i	$0.404475\pi$
$360$		0			0
$361$	−2.68565	+	18.6791i	−0.141350	+	0.983112i
$362$		0			0
$363$	2.23112	+	9.12742i	0.117104	+	0.479065i
$364$		0			0
$365$	3.75425	+	1.10235i	0.196507	+	0.0576996i
$366$		0			0
$367$			33.1295i			1.72935i	0.502335	+	0.864673i	$0.332474\pi$
$367$			33.1295i			1.72935i	−0.502335	+	0.864673i	$0.667526\pi$
$368$		0			0
$369$	−3.96450	+	5.07757i	−0.206384	+	0.264328i
$370$		0			0
$371$	−0.289466	+	0.985831i	−0.0150283	+	0.0511818i
$372$		0			0
$373$	−16.8596	−	26.2341i	−0.872957	−	1.35835i	−0.932896	−	0.360146i	$-0.882727\pi$
$373$	−16.8596	−	26.2341i	−0.872957	−	1.35835i	0.0599384	−	0.998202i	$-0.480910\pi$
$374$		0			0
$375$	4.73022	+	2.42818i	0.244267	+	0.125391i
$376$		0			0
$377$	−1.11573	+	1.73612i	−0.0574632	+	0.0894145i
$378$		0			0
$379$	−2.81576	+	1.28591i	−0.144636	+	0.0660530i	−0.486418	−	0.873726i	$-0.661697\pi$
$379$	−2.81576	+	1.28591i	−0.144636	+	0.0660530i	0.341782	+	0.939779i	$0.388970\pi$
$380$		0			0
$381$	7.84803	+	1.49842i	0.402067	+	0.0767662i
$382$		0			0
$383$	−24.5525	+	7.20926i	−1.25457	+	0.368376i	−0.840472	−	0.541855i	$-0.817722\pi$
$383$	−24.5525	+	7.20926i	−1.25457	+	0.368376i	−0.414101	+	0.910231i	$0.635904\pi$
$384$		0			0
$385$	−0.149405	−	0.129460i	−0.00761440	−	0.00659792i
$386$		0			0
$387$	−3.29351	+	0.168387i	−0.167418	+	0.00855961i
$388$		0			0
$389$	−6.20907	+	13.5960i	−0.314812	+	0.689343i	−0.999209	−	0.0397671i	$-0.987338\pi$
$389$	−6.20907	+	13.5960i	−0.314812	+	0.689343i	0.684397	+	0.729110i	$0.260066\pi$
$390$		0			0
$391$	−15.4895	−	16.0113i	−0.783338	−	0.809726i
$392$		0			0
$393$	−14.2677	+	15.0158i	−0.719711	+	0.757448i
$394$		0			0
$395$	3.66946	−	3.17961i	0.184631	−	0.159983i
$396$		0			0
$397$	−23.7599	+	27.4204i	−1.19247	+	1.37619i	−0.283693	+	0.958915i	$0.591560\pi$
$397$	−23.7599	+	27.4204i	−1.19247	+	1.37619i	−0.908781	+	0.417274i	$0.862986\pi$
$398$		0			0
$399$	0.00448430	−	0.0977170i	0.000224496	−	0.00489197i
$400$		0			0
$401$	−2.63757	−	18.3447i	−0.131714	−	0.916089i	−0.943320	−	0.331884i	$-0.892316\pi$
$401$	−2.63757	−	18.3447i	−0.131714	−	0.916089i	0.811606	−	0.584205i	$-0.198593\pi$
$402$		0			0
$403$	0.648063	+	1.41906i	0.0322823	+	0.0706884i
$404$		0			0
$405$	−0.894011	+	2.64248i	−0.0444238	+	0.131306i
$406$		0			0
$407$	4.79270	+	0.689087i	0.237566	+	0.0341568i
$408$		0			0
$409$	5.89739	−	3.79002i	0.291607	−	0.187405i	−0.386655	−	0.922224i	$-0.626370\pi$
$409$	5.89739	−	3.79002i	0.291607	−	0.187405i	0.678262	+	0.734820i	$0.262733\pi$
$410$		0			0
$411$	16.6522	−	23.4711i	0.821391	−	1.15774i
$412$		0			0
$413$	−0.249508			−0.0122775
$414$		0			0
$415$	2.78238			0.136582
$416$		0			0
$417$	−10.9714	+	15.4641i	−0.537273	+	0.757282i
$418$		0			0
$419$	−4.51850	+	2.90386i	−0.220743	+	0.141863i	−0.646339	−	0.763050i	$-0.723701\pi$
$419$	−4.51850	+	2.90386i	−0.220743	+	0.141863i	0.425596	+	0.904913i	$0.360065\pi$
$420$		0			0
$421$	−17.3878	−	2.49999i	−0.847429	−	0.121842i	−0.295098	−	0.955467i	$-0.595352\pi$
$421$	−17.3878	−	2.49999i	−0.847429	−	0.121842i	−0.552331	+	0.833625i	$0.686261\pi$
$422$		0			0
$423$	−5.11903	+	1.79170i	−0.248896	+	0.0871155i
$424$		0			0
$425$	9.46299	+	20.7211i	0.459023	+	1.00512i
$426$		0			0
$427$	0.167893	+	1.16772i	0.00812493	+	0.0565101i
$428$		0			0
$429$	0.101566	−	2.21322i	0.00490366	−	0.106855i
$430$		0			0
$431$	−16.8030	+	19.3917i	−0.809371	+	0.934064i	−0.998856	−	0.0478200i	$-0.984773\pi$
$431$	−16.8030	+	19.3917i	−0.809371	+	0.934064i	0.189485	+	0.981884i	$0.439318\pi$
$432$		0			0
$433$	18.6151	−	16.1301i	0.894585	−	0.775162i	−0.0805553	−	0.996750i	$-0.525669\pi$
$433$	18.6151	−	16.1301i	0.894585	−	0.775162i	0.975140	+	0.221588i	$0.0711239\pi$
$434$		0			0
$435$	2.41797	−	2.54475i	0.115933	−	0.122011i
$436$		0			0
$437$	−1.00843	−	1.39467i	−0.0482398	−	0.0667161i
$438$		0			0
$439$	9.50009	−	20.8023i	0.453415	−	0.992840i	−0.535525	−	0.844520i	$-0.679886\pi$
$439$	9.50009	−	20.8023i	0.453415	−	0.992840i	0.988939	−	0.148320i	$-0.0473866\pi$
$440$		0			0
$441$	1.06847	+	20.8984i	0.0508797	+	0.995162i
$442$		0			0
$443$	6.30982	+	5.46749i	0.299789	+	0.259768i	0.791745	−	0.610851i	$-0.209173\pi$
$443$	6.30982	+	5.46749i	0.299789	+	0.259768i	−0.491957	+	0.870620i	$0.663718\pi$
$444$		0			0
$445$	−0.545173	+	0.160077i	−0.0258437	+	0.00758839i
$446$		0			0
$447$	30.7230	+	5.86591i	1.45315	+	0.277448i
$448$		0			0
$449$	0.838548	−	0.382952i	0.0395735	−	0.0180726i	−0.395530	−	0.918453i	$-0.629439\pi$
$449$	0.838548	−	0.382952i	0.0395735	−	0.0180726i	0.435103	+	0.900380i	$0.356712\pi$
$450$		0			0
$451$	−4.70498	+	7.32109i	−0.221549	+	0.344737i
$452$		0			0
$453$	9.57127	+	4.91325i	0.449697	+	0.230845i
$454$		0			0
$455$	0.00832367	+	0.0129519i	0.000390220	+	0.000607194i
$456$		0			0
$457$	−0.912896	+	3.10904i	−0.0427035	+	0.145435i	−0.978085	−	0.208205i	$-0.933238\pi$
$457$	−0.912896	+	3.10904i	−0.0427035	+	0.145435i	0.935382	+	0.353640i	$0.115056\pi$
$458$		0			0
$459$	−20.2369	+	13.1554i	−0.944579	+	0.614040i
$460$		0			0
$461$			31.3905i			1.46200i	0.682376	+	0.731002i	$0.260947\pi$
$461$			31.3905i			1.46200i	−0.682376	+	0.731002i	$0.739053\pi$
$462$		0			0
$463$	−13.4991	−	3.96369i	−0.627356	−	0.184208i	−0.0474261	−	0.998875i	$-0.515102\pi$
$463$	−13.4991	−	3.96369i	−0.627356	−	0.184208i	−0.579930	+	0.814666i	$0.696920\pi$
$464$		0			0
$465$	−0.630090	−	2.57767i	−0.0292197	−	0.119537i
$466$		0			0
$467$	−4.64524	+	32.3083i	−0.214956	+	1.49505i	0.541330	+	0.840810i	$0.317921\pi$
$467$	−4.64524	+	32.3083i	−0.214956	+	1.49505i	−0.756286	+	0.654241i	$0.772988\pi$
$468$		0			0
$469$	0.853326	+	0.548400i	0.0394030	+	0.0253227i
$470$		0			0
$471$	−2.27705	−	23.4153i	−0.104921	−	1.07892i
$472$		0			0
$473$	−4.40973	+	0.634024i	−0.202760	+	0.0291524i
$474$		0			0
$475$	0.495807	+	1.68856i	0.0227492	+	0.0774766i
$476$		0			0
$477$	19.2191	−	3.77364i	0.879982	−	0.172783i
$478$		0			0
$479$	−0.624672	−	0.720910i	−0.0285420	−	0.0329392i	0.741299	−	0.671175i	$-0.234210\pi$
$479$	−0.624672	−	0.720910i	−0.0285420	−	0.0329392i	−0.769841	+	0.638236i	$0.779665\pi$
$480$		0			0
$481$	−0.343010	−	0.156648i	−0.0156399	−	0.00714252i
$482$		0			0
$483$	−0.864904	−	0.980229i	−0.0393545	−	0.0446020i
$484$		0			0
$485$	−1.12023	−	0.511591i	−0.0508669	−	0.0232301i
$486$		0			0
$487$	1.19179	+	1.37540i	0.0540051	+	0.0623252i	0.782109	−	0.623141i	$-0.214144\pi$
$487$	1.19179	+	1.37540i	0.0540051	+	0.0623252i	−0.728104	+	0.685466i	$0.759598\pi$
$488$		0			0
$489$	19.4844	+	33.6127i	0.881116	+	1.52002i
$490$		0			0
$491$	−0.748763	−	2.55005i	−0.0337912	−	0.115082i	0.940870	−	0.338767i	$-0.110010\pi$
$491$	−0.748763	−	2.55005i	−0.0337912	−	0.115082i	−0.974662	+	0.223684i	$0.928192\pi$
$492$		0			0
$493$	30.0637	−	4.32251i	1.35400	−	0.194676i
$494$		0			0
$495$	−0.875710	+	3.66540i	−0.0393603	+	0.164747i
$496$		0			0
$497$	−1.10397	−	0.709477i	−0.0495197	−	0.0318244i
$498$		0			0
$499$	3.73026	−	25.9445i	0.166989	−	1.16144i	−0.718074	−	0.695967i	$-0.754976\pi$
$499$	3.73026	−	25.9445i	0.166989	−	1.16144i	0.885063	−	0.465470i	$-0.154115\pi$
$500$		0			0
$501$	−7.00415	+	1.71211i	−0.312922	+	0.0764914i
$502$		0			0
$503$	−38.9323	−	11.4316i	−1.73591	−	0.509708i	−0.747860	−	0.663857i	$-0.768919\pi$
$503$	−38.9323	−	11.4316i	−1.73591	−	0.509708i	−0.988048	+	0.154148i	$0.950737\pi$
$504$		0			0
$505$			2.31553i			0.103040i
$506$		0			0
$507$	7.27127	−	21.1279i	0.322928	−	0.938323i
$508$		0			0
$509$	−10.2293	+	34.8378i	−0.453406	+	1.54416i	0.342964	+	0.939348i	$0.388569\pi$
$509$	−10.2293	+	34.8378i	−0.453406	+	1.54416i	−0.796370	+	0.604810i	$0.793249\pi$
$510$		0			0
$511$	1.07405	+	1.67125i	0.0475130	+	0.0739317i
$512$		0			0
$513$	−1.69214	+	0.783483i	−0.0747097	+	0.0345916i
$514$		0			0
$515$	1.54601	−	2.40564i	0.0681254	−	0.106005i
$516$		0			0
$517$	−6.66465	+	3.04364i	−0.293111	+	0.133859i
$518$		0			0
$519$	−2.67419	+	14.0062i	−0.117384	+	0.614805i
$520$		0			0
$521$	12.3970	−	3.64009i	0.543123	−	0.159475i	0.00134818	−	0.999999i	$-0.499571\pi$
$521$	12.3970	−	3.64009i	0.543123	−	0.159475i	0.541774	+	0.840524i	$0.317753\pi$
$522$		0			0
$523$	34.0614	+	29.5144i	1.48940	+	1.29058i	0.856266	+	0.516536i	$0.172779\pi$
$523$	34.0614	+	29.5144i	1.48940	+	1.29058i	0.633137	+	0.774039i	$0.281767\pi$
$524$		0			0
$525$	0.498967	+	1.24010i	0.0217767	+	0.0541223i
$526$		0			0
$527$	9.53785	−	20.8850i	0.415475	−	0.909764i
$528$		0			0
$529$	−22.6450	−	4.02543i	−0.984565	−	0.175019i
$530$		0			0
$531$	2.19418	+	4.21997i	0.0952193	+	0.183131i
$532$		0			0
$533$	0.512206	−	0.443829i	0.0221861	−	0.0192244i
$534$		0			0
$535$	−1.05615	+	1.21886i	−0.0456612	+	0.0526958i
$536$		0			0
$537$	23.0338	+	1.05704i	0.993982	+	0.0456146i
$538$		0			0
$539$	4.02309	+	27.9812i	0.173287	+	1.20524i
$540$		0			0
$541$	14.7369	+	32.2692i	0.633587	+	1.38736i	0.905212	+	0.424960i	$0.139712\pi$
$541$	14.7369	+	32.2692i	0.633587	+	1.38736i	−0.271625	+	0.962403i	$0.587561\pi$
$542$		0			0
$543$	−18.6560	−	23.6382i	−0.800605	−	1.01441i
$544$		0			0
$545$	3.60413	+	0.518196i	0.154384	+	0.0221971i
$546$		0			0
$547$	17.2692	−	11.0982i	0.738378	−	0.474527i	−0.116608	−	0.993178i	$-0.537202\pi$
$547$	17.2692	−	11.0982i	0.738378	−	0.474527i	0.854986	+	0.518651i	$0.173566\pi$
$548$		0			0
$549$	18.2734	−	13.1086i	0.779892	−	0.559462i
$550$		0			0
$551$	2.34647			0.0999629
$552$		0			0
$553$	2.46522			0.104832
$554$		0			0
$555$	0.523125	+	0.371144i	0.0222054	+	0.0157542i
$556$		0			0
$557$	−11.1072	+	7.13814i	−0.470626	+	0.302453i	−0.754373	−	0.656446i	$-0.772059\pi$
$557$	−11.1072	+	7.13814i	−0.470626	+	0.302453i	0.283747	+	0.958899i	$0.408422\pi$
$558$		0			0
$559$	0.343424	+	0.0493768i	0.0145253	+	0.00208842i
$560$		0			0
$561$	−25.5959	+	20.2011i	−1.08066	+	0.852889i
$562$		0			0
$563$	−8.37062	−	18.3291i	−0.352780	−	0.772480i	−0.999949	−	0.0101331i	$-0.996774\pi$
$563$	−8.37062	−	18.3291i	−0.352780	−	0.772480i	0.647169	−	0.762347i	$-0.275953\pi$
$564$		0			0
$565$	0.504376	+	3.50801i	0.0212193	+	0.147583i
$566$		0			0
$567$	−1.22165	+	0.716712i	−0.0513045	+	0.0300991i
$568$		0			0
$569$	29.5546	−	34.1079i	1.23899	−	1.42988i	0.374506	−	0.927225i	$-0.377812\pi$
$569$	29.5546	−	34.1079i	1.23899	−	1.42988i	0.864489	−	0.502652i	$-0.167642\pi$
$570$		0			0
$571$	12.8753	−	11.1565i	0.538815	−	0.466886i	−0.342432	−	0.939543i	$-0.611251\pi$
$571$	12.8753	−	11.1565i	0.538815	−	0.466886i	0.881246	+	0.472657i	$0.156705\pi$
$572$		0			0
$573$	−2.85088	−	2.70884i	−0.119097	−	0.113164i
$574$		0			0
$575$	20.4521	+	11.6115i	0.852912	+	0.484232i
$576$		0			0
$577$	−14.9331	+	32.6990i	−0.621674	+	1.36128i	0.292622	+	0.956228i	$0.405472\pi$
$577$	−14.9331	+	32.6990i	−0.621674	+	1.36128i	−0.914296	+	0.405047i	$0.867255\pi$
$578$		0			0
$579$	−29.7686	+	11.9777i	−1.23714	+	0.497777i
$580$		0			0
$581$	1.06764	+	0.925118i	0.0442933	+	0.0383804i
$582$		0			0
$583$	25.3874	−	7.45442i	1.05144	−	0.308731i
$584$		0			0
$585$	0.145859	−	0.254679i	0.00603052	−	0.0105297i
$586$		0			0
$587$	−7.70400	+	3.51830i	−0.317978	+	0.145216i	−0.568009	−	0.823022i	$-0.692286\pi$
$587$	−7.70400	+	3.51830i	−0.317978	+	0.145216i	0.250031	+	0.968238i	$0.419559\pi$
$588$		0			0
$589$	0.958973	−	1.49219i	0.0395138	−	0.0614847i
$590$		0			0
$591$	−4.18626	+	8.15504i	−0.172200	+	0.335454i
$592$		0			0
$593$	−19.8656	−	30.9116i	−0.815784	−	1.26939i	−0.960045	−	0.279846i	$-0.909717\pi$
$593$	−19.8656	−	30.9116i	−0.815784	−	1.26939i	0.144261	−	0.989540i	$-0.453920\pi$
$594$		0			0
$595$	0.0638376	−	0.217411i	0.00261709	−	0.00891298i
$596$		0			0
$597$	0.524689	+	0.180574i	0.0214741	+	0.00739041i
$598$		0			0
$599$			21.3331i			0.871648i	0.900032	+	0.435824i	$0.143543\pi$
$599$			21.3331i			0.871648i	−0.900032	+	0.435824i	$0.856457\pi$
$600$		0			0
$601$	13.7998	+	4.05199i	0.562906	+	0.165284i	0.550792	−	0.834643i	$-0.314326\pi$
$601$	13.7998	+	4.05199i	0.562906	+	0.165284i	0.0121139	+	0.999927i	$0.496144\pi$
$602$		0			0
$603$	1.77099	−	19.2551i	0.0721203	−	0.784128i
$604$		0			0
$605$	−0.239300	+	1.66437i	−0.00972892	+	0.0676661i
$606$		0			0
$607$	−35.5052	−	22.8178i	−1.44111	−	0.926147i	−0.999582	−	0.0289015i	$-0.990799\pi$
$607$	−35.5052	−	22.8178i	−1.44111	−	0.926147i	−0.441531	−	0.897246i	$-0.645565\pi$
$608$		0			0
$609$	1.77392	−	0.172507i	0.0718829	−	0.00699032i
$610$		0			0
$611$	0.564789	−	0.0812044i	0.0228489	−	0.00328518i
$612$		0			0
$613$	−9.13740	−	31.1191i	−0.369056	−	1.25689i	−0.909569	−	0.415553i	$-0.863588\pi$
$613$	−9.13740	−	31.1191i	−0.369056	−	1.25689i	0.540513	−	0.841336i	$-0.318230\pi$
$614$		0			0
$615$	−0.997365	+	0.578147i	−0.0402176	+	0.0233131i
$616$		0			0
$617$	−4.98590	−	5.75404i	−0.200725	−	0.231649i	0.646459	−	0.762949i	$-0.276249\pi$
$617$	−4.98590	−	5.75404i	−0.200725	−	0.231649i	−0.847184	+	0.531300i	$0.821704\pi$
$618$		0			0
$619$	35.0286	+	15.9970i	1.40792	+	0.642974i	0.967047	−	0.254596i	$-0.0819426\pi$
$619$	35.0286	+	15.9970i	1.40792	+	0.642974i	0.440870	+	0.897571i	$0.354670\pi$
$620$		0			0
$621$	−8.97278	+	23.2484i	−0.360065	+	0.932927i
$622$		0			0
$623$	−0.262416	−	0.119841i	−0.0105135	−	0.00480135i
$624$		0			0
$625$	−15.4338	−	17.8116i	−0.617354	−	0.712464i
$626$		0			0
$627$	−2.17940	+	1.26334i	−0.0870367	+	0.0504530i
$628$		0			0
$629$	1.56355	+	5.32497i	0.0623429	+	0.212320i
$630$		0			0
$631$	−7.65631	+	1.10081i	−0.304793	+	0.0438226i	−0.293014	−	0.956108i	$-0.594658\pi$
$631$	−7.65631	+	1.10081i	−0.304793	+	0.0438226i	−0.0117786	+	0.999931i	$0.503749\pi$
$632$		0			0
$633$	−27.5644	+	2.68053i	−1.09559	+	0.106541i
$634$		0			0
$635$	1.20283	+	0.773013i	0.0477329	+	0.0306761i
$636$		0			0
$637$	0.313313	−	2.17914i	0.0124139	−	0.0863405i
$638$		0			0
$639$	−2.29117	+	24.9108i	−0.0906373	+	0.985455i
$640$		0			0
$641$	4.47471	+	1.31389i	0.176741	+	0.0518957i	0.368905	−	0.929467i	$-0.379733\pi$
$641$	4.47471	+	1.31389i	0.176741	+	0.0518957i	−0.192165	+	0.981363i	$0.561551\pi$
$642$		0			0
$643$			23.0934i			0.910713i	0.890309	+	0.455356i	$0.150488\pi$
$643$			23.0934i			0.910713i	−0.890309	+	0.455356i	$0.849512\pi$
$644$		0			0
$645$	−0.558034	−	0.192050i	−0.0219726	−	0.00756196i
$646$		0			0
$647$	−7.11714	+	24.2387i	−0.279804	+	0.952923i	0.692931	+	0.721004i	$0.256319\pi$
$647$	−7.11714	+	24.2387i	−0.279804	+	0.952923i	−0.972735	+	0.231920i	$0.925499\pi$
$648$		0			0
$649$	3.47384	+	5.40539i	0.136360	+	0.212180i
$650$		0			0
$651$	0.615278	−	1.19859i	0.0241146	−	0.0469766i
$652$		0			0
$653$	0.293139	−	0.456133i	0.0114714	−	0.0178499i	−0.835470	−	0.549535i	$-0.814805\pi$
$653$	0.293139	−	0.456133i	0.0114714	−	0.0178499i	0.846942	+	0.531685i	$0.178441\pi$
$654$		0			0
$655$	−3.37177	+	1.53983i	−0.131746	+	0.0601663i
$656$		0			0
$657$	18.8209	−	32.8625i	0.734273	−	1.28209i
$658$		0			0
$659$	31.8395	−	9.34891i	1.24029	−	0.364182i	0.405166	−	0.914243i	$-0.367214\pi$
$659$	31.8395	−	9.34891i	1.24029	−	0.364182i	0.835124	+	0.550061i	$0.185396\pi$
$660$		0			0
$661$	20.7641	+	17.9922i	0.807631	+	0.699816i	0.957356	−	0.288911i	$-0.0932933\pi$
$661$	20.7641	+	17.9922i	0.807631	+	0.699816i	−0.149725	+	0.988728i	$0.547839\pi$
$662$		0			0
$663$	2.35585	−	0.947905i	0.0914938	−	0.0368136i
$664$		0			0
$665$	0.00727195	−	0.0159234i	0.000281994	−	0.000617481i
$666$		0			0
$667$	22.5376	−	21.8031i	0.872658	−	0.844220i
$668$		0			0
$669$	33.6332	+	31.9576i	1.30033	+	1.23555i
$670$		0			0
$671$	22.9603	−	19.8952i	0.886373	−	0.768046i
$672$		0			0
$673$	−29.1298	+	33.6176i	−1.12287	+	1.29586i	−0.172408	+	0.985026i	$0.555155\pi$
$673$	−29.1298	+	33.6176i	−1.12287	+	1.29586i	−0.950463	+	0.310837i	$0.899391\pi$
$674$		0			0
$675$	16.5860	−	19.3446i	0.638397	−	0.744573i
$676$		0			0
$677$	5.77634	+	40.1753i	0.222003	+	1.54406i	0.730448	+	0.682969i	$0.239311\pi$
$677$	5.77634	+	40.1753i	0.222003	+	1.54406i	−0.508445	+	0.861094i	$0.669779\pi$
$678$		0			0
$679$	−0.259750	−	0.568772i	−0.00996827	−	0.0218275i
$680$		0			0
$681$	−35.0304	+	27.6471i	−1.34237	+	1.05944i
$682$		0			0
$683$	−33.3132	−	4.78971i	−1.27469	−	0.183273i	−0.528460	−	0.848958i	$-0.677230\pi$
$683$	−33.3132	−	4.78971i	−1.27469	−	0.183273i	−0.746233	+	0.665685i	$0.768140\pi$
$684$		0			0
$685$	4.33244	−	2.78429i	0.165534	−	0.106382i
$686$		0			0
$687$	−10.0282	−	7.11479i	−0.382601	−	0.271446i
$688$		0			0
$689$	−2.06061			−0.0785028
$690$		0			0
$691$	18.0276			0.685800			0.342900	−	0.939372i	$-0.388591\pi$
$691$	18.0276			0.685800			0.342900	+	0.939372i	$0.388591\pi$
$692$		0			0
$693$	−1.55474	+	1.11531i	−0.0590596	+	0.0423669i
$694$		0			0
$695$	−2.85447	+	1.83446i	−0.108276	+	0.0695849i
$696$		0			0
$697$	−9.87318	−	1.41955i	−0.373973	−	0.0537692i
$698$		0			0
$699$	−29.7587	−	37.7059i	−1.12558	−	1.42617i
$700$		0			0
$701$	−11.5649	−	25.3237i	−0.436802	−	0.956462i	−0.992174	−	0.124861i	$-0.960152\pi$
$701$	−11.5649	−	25.3237i	−0.436802	−	0.956462i	0.555372	−	0.831602i	$-0.312576\pi$
$702$		0			0
$703$	0.0610175	+	0.424386i	0.00230132	+	0.0160060i
$704$		0			0
$705$	−0.969543	−	0.0444930i	−0.0365151	−	0.00167570i
$706$		0			0
$707$	−0.769894	+	0.888505i	−0.0289548	+	0.0334157i
$708$		0			0
$709$	−13.6923	+	11.8645i	−0.514226	+	0.445579i	−0.872911	−	0.487879i	$-0.837771\pi$
$709$	−13.6923	+	11.8645i	−0.514226	+	0.445579i	0.358685	+	0.933459i	$0.383225\pi$
$710$		0			0
$711$	−21.6793	−	41.6947i	−0.813036	−	1.56367i
$712$		0			0
$713$	−4.65444	−	23.2430i	−0.174310	−	0.870457i
$714$		0			0
$715$	0.164704	−	0.360652i	0.00615959	−	0.0134876i
$716$		0			0
$717$	−2.56428	−	6.37307i	−0.0957647	−	0.238007i
$718$		0			0
$719$	18.5472	+	16.0712i	0.691694	+	0.599356i	0.928115	−	0.372295i	$-0.121429\pi$
$719$	18.5472	+	16.0712i	0.691694	+	0.599356i	−0.236421	+	0.971651i	$0.575974\pi$
$720$		0			0
$721$	1.39309	−	0.409047i	0.0518812	−	0.0152337i
$722$		0			0
$723$	5.42833	−	28.4312i	0.201882	−	1.05737i
$724$		0			0
$725$	−29.1671	+	13.3202i	−1.08324	+	0.494698i
$726$		0			0
$727$	−21.2267	+	33.0294i	−0.787254	+	1.22499i	0.183050	+	0.983104i	$0.441403\pi$
$727$	−21.2267	+	33.0294i	−0.787254	+	1.22499i	−0.970304	+	0.241888i	$0.922233\pi$
$728$		0			0
$729$	22.8651	+	14.3592i	0.846856	+	0.531822i
$730$		0			0
$731$	−2.76068	−	4.29570i	−0.102107	−	0.158882i
$732$		0			0
$733$	6.50117	−	22.1410i	0.240126	−	0.817795i	−0.747940	−	0.663766i	$-0.768957\pi$
$733$	6.50117	−	22.1410i	0.240126	−	0.817795i	0.988066	−	0.154029i	$-0.0492248\pi$
$734$		0			0
$735$	−1.21862	+	3.54091i	−0.0449495	+	0.130608i
$736$		0			0
$737$		−	26.1219i		−	0.962212i
$738$		0			0
$739$	9.29196	+	2.72837i	0.341810	+	0.100365i	0.448132	−	0.893967i	$-0.352089\pi$
$739$	9.29196	+	2.72837i	0.341810	+	0.100365i	−0.106322	+	0.994332i	$0.533907\pi$
$740$		0			0
$741$	0.190572	−	0.0465838i	0.00700084	−	0.00171130i
$742$		0			0
$743$	−5.23102	+	36.3825i	−0.191907	+	1.33475i	0.635046	+	0.772475i	$0.280981\pi$
$743$	−5.23102	+	36.3825i	−0.191907	+	1.33475i	−0.826953	+	0.562271i	$0.809928\pi$
$744$		0			0
$745$	4.70877	+	3.02614i	0.172516	+	0.110869i
$746$		0			0
$747$	6.25779	−	26.1928i	0.228960	−	0.958343i
$748$		0			0
$749$	−0.810520	+	0.116535i	−0.0296158	+	0.00425811i
$750$		0			0
$751$	−9.24251	−	31.4771i	−0.337264	−	1.14862i	−0.937265	−	0.348617i	$-0.886651\pi$
$751$	−9.24251	−	31.4771i	−0.337264	−	1.14862i	0.600001	−	0.799999i	$-0.295167\pi$
$752$		0			0
$753$	−12.6037	−	21.7428i	−0.459305	−	0.792351i
$754$		0			0
$755$	1.26081	+	1.45505i	0.0458856	+	0.0529548i
$756$		0			0
$757$	−17.5501	−	8.01488i	−0.637871	−	0.291306i	0.0701082	−	0.997539i	$-0.477666\pi$
$757$	−17.5501	−	8.01488i	−0.637871	−	0.291306i	−0.707979	+	0.706234i	$0.750393\pi$
$758$		0			0
$759$	−9.19406	+	32.3850i	−0.333723	+	1.17550i
$760$		0			0
$761$	−22.2948	−	10.1817i	−0.808188	−	0.369087i	−0.0319200	−	0.999490i	$-0.510162\pi$
$761$	−22.2948	−	10.1817i	−0.808188	−	0.369087i	−0.776268	+	0.630404i	$0.782889\pi$
$762$		0			0
$763$	1.21067	+	1.39718i	0.0438291	+	0.0505815i
$764$		0			0
$765$	−4.23850	+	0.832223i	−0.153243	+	0.0300891i
$766$		0			0
$767$	−0.140979	−	0.480131i	−0.00509047	−	0.0173365i
$768$		0			0
$769$	12.9741	−	1.86540i	0.467859	−	0.0672679i	0.0956461	−	0.995415i	$-0.469508\pi$
$769$	12.9741	−	1.86540i	0.467859	−	0.0672679i	0.372213	+	0.928147i	$0.378599\pi$
$770$		0			0
$771$	−1.57073	−	16.1521i	−0.0565683	−	0.581704i
$772$		0			0
$773$	4.48880	+	2.88478i	0.161451	+	0.103758i	0.618871	−	0.785492i	$-0.287590\pi$
$773$	4.48880	+	2.88478i	0.161451	+	0.103758i	−0.457420	+	0.889251i	$0.651227\pi$
$774$		0			0
$775$	−3.44953	+	23.9920i	−0.123911	+	0.861819i
$776$		0			0
$777$	0.0773289	+	0.316349i	0.00277416	+	0.0113489i
$778$		0			0
$779$	−0.739386	−	0.217103i	−0.0264912	−	0.00777853i
$780$		0			0
$781$			33.7945i			1.20926i
$782$		0			0
$783$	−18.5176	−	28.4856i	−0.661764	−	1.01799i
$784$		0			0
$785$	1.18611	−	4.03951i	0.0423339	−	0.144176i
$786$		0			0
$787$	−9.37291	−	14.5845i	−0.334108	−	0.519882i	0.633032	−	0.774125i	$-0.281810\pi$
$787$	−9.37291	−	14.5845i	−0.334108	−	0.519882i	−0.967140	+	0.254243i	$0.918174\pi$
$788$		0			0
$789$	−30.8263	−	15.8242i	−1.09745	−	0.563355i
$790$		0			0
$791$	−0.972848	+	1.51378i	−0.0345905	+	0.0538239i
$792$		0			0
$793$	−2.15220	+	0.982878i	−0.0764270	+	0.0349030i
$794$		0			0
$795$	3.44282	+	0.657333i	0.122104	+	0.0233132i
$796$		0			0
$797$	43.6251	−	12.8095i	1.54528	−	0.453735i	0.605593	−	0.795774i	$-0.292936\pi$
$797$	43.6251	−	12.8095i	1.54528	−	0.453735i	0.939686	+	0.342039i	$0.111118\pi$
$798$		0			0
$799$	−6.34660	−	5.49936i	−0.224526	−	0.194553i
$800$		0			0
$801$	0.280799	+	5.49218i	0.00992154	+	0.194057i
$802$		0			0
$803$	21.2526	−	46.5368i	0.749989	−	1.64225i
$804$		0			0
$805$	−0.0781117	−	0.220512i	−0.00275307	−	0.00777203i
$806$		0			0
$807$	17.9477	−	18.8888i	0.631789	−	0.664916i
$808$		0			0
$809$	23.0820	−	20.0006i	0.811519	−	0.703185i	−0.146712	−	0.989179i	$-0.546869\pi$
$809$	23.0820	−	20.0006i	0.811519	−	0.703185i	0.958231	+	0.285994i	$0.0923237\pi$
$810$		0			0
$811$	−23.5073	+	27.1289i	−0.825453	+	0.952624i	−0.999484	−	0.0321161i	$-0.989775\pi$
$811$	−23.5073	+	27.1289i	−0.825453	+	0.952624i	0.174031	+	0.984740i	$0.444321\pi$
$812$		0			0
$813$	1.40892	−	30.7016i	0.0494130	−	1.07675i
$814$		0			0
$815$	0.989469	+	6.88191i	0.0346596	+	0.241063i
$816$		0			0
$817$	−0.163877	−	0.358841i	−0.00573333	−	0.0125542i
$818$		0			0
$819$	0.140647	−	0.0492276i	0.00491460	−	0.00172015i
$820$		0			0
$821$	15.2955	+	2.19916i	0.533817	+	0.0767512i	0.403951	−	0.914780i	$-0.367636\pi$
$821$	15.2955	+	2.19916i	0.533817	+	0.0767512i	0.129865	+	0.991532i	$0.458546\pi$
$822$		0			0
$823$	13.8311	−	8.88871i	0.482122	−	0.309841i	−0.276908	−	0.960896i	$-0.589310\pi$
$823$	13.8311	−	8.88871i	0.482122	−	0.309841i	0.759030	+	0.651055i	$0.225673\pi$
$824$		0			0
$825$	19.9188	−	28.0753i	0.693482	−	0.977457i
$826$		0			0
$827$	−2.80525			−0.0975481			−0.0487740	−	0.998810i	$-0.515531\pi$
$827$	−2.80525			−0.0975481			−0.0487740	+	0.998810i	$0.515531\pi$
$828$		0			0
$829$	48.0278			1.66808			0.834038	−	0.551708i	$-0.186024\pi$
$829$	48.0278			1.66808			0.834038	+	0.551708i	$0.186024\pi$
$830$		0			0
$831$	−11.0647	+	15.5956i	−0.383829	+	0.541004i
$832$		0			0
$833$	−27.2576	+	17.5174i	−0.944421	+	0.606942i
$834$		0			0
$835$	−1.27719	−	0.183633i	−0.0441991	−	0.00635487i
$836$		0			0
$837$	−25.6828	+	0.134168i	−0.887726	+	0.00463754i
$838$		0			0
$839$	−8.10078	−	17.7382i	−0.279670	−	0.612392i	0.716713	−	0.697368i	$-0.245646\pi$
$839$	−8.10078	−	17.7382i	−0.279670	−	0.612392i	−0.996383	+	0.0849766i	$0.972918\pi$
$840$		0			0
$841$	1.95725	+	13.6130i	0.0674914	+	0.469413i
$842$		0			0
$843$	−1.12625	+	24.5421i	−0.0387902	+	0.845274i
$844$		0			0
$845$	2.61851	−	3.02192i	0.0900794	−	0.103957i
$846$		0			0
$847$	−0.645211	+	0.559079i	−0.0221697	+	0.0192102i
$848$		0			0
$849$	−17.9331	+	18.8734i	−0.615463	+	0.647734i
$850$		0			0
$851$	4.52941	+	3.50922i	0.155266	+	0.120294i
$852$		0			0
$853$	15.1552	−	33.1853i	0.518905	−	1.13624i	−0.450948	−	0.892550i	$-0.648914\pi$
$853$	15.1552	−	33.1853i	0.518905	−	1.13624i	0.969853	−	0.243692i	$-0.0783587\pi$
$854$		0			0
$855$	−0.333264	+	0.0170388i	−0.0113974	+	0.000582715i
$856$		0			0
$857$	−33.3215	−	28.8732i	−1.13824	−	0.986290i	−0.138248	−	0.990398i	$-0.544147\pi$
$857$	−33.3215	−	28.8732i	−1.13824	−	0.986290i	−0.999992	+	0.00410720i	$0.998693\pi$
$858$		0			0
$859$	23.9611	−	7.03561i	0.817542	−	0.240052i	0.153885	−	0.988089i	$-0.450821\pi$
$859$	23.9611	−	7.03561i	0.817542	−	0.240052i	0.663657	+	0.748037i	$0.269003\pi$
$860$		0			0
$861$	−0.574934	−	0.109771i	−0.0195937	−	0.00374100i
$862$		0			0
$863$	50.9993	−	23.2906i	1.73604	−	0.792821i	0.743807	−	0.668394i	$-0.233018\pi$
$863$	50.9993	−	23.2906i	1.73604	−	0.792821i	0.992229	−	0.124427i	$-0.0397092\pi$
$864$		0			0
$865$	−1.37958	+	2.14667i	−0.0469071	+	0.0729889i
$866$		0			0
$867$	−7.05369	−	3.62090i	−0.239556	−	0.122972i
$868$		0			0
$869$	−34.3227	−	53.4072i	−1.16432	−	1.81171i
$870$		0			0
$871$	−0.573139	+	1.95193i	−0.0194201	+	0.0661386i
$872$		0			0
$873$	−7.33549	+	9.39499i	−0.248269	+	0.317972i
$874$		0			0
$875$			0.483108i			0.0163320i
$876$		0			0
$877$	14.6067	+	4.28891i	0.493233	+	0.144826i	0.518884	−	0.854845i	$-0.326348\pi$
$877$	14.6067	+	4.28891i	0.493233	+	0.144826i	−0.0256509	+	0.999671i	$0.508166\pi$
$878$		0			0
$879$	−3.36915	−	13.7830i	−0.113639	−	0.464890i
$880$		0			0
$881$	4.70903	−	32.7520i	0.158651	−	1.10344i	−0.742471	−	0.669878i	$-0.766346\pi$
$881$	4.70903	−	32.7520i	0.158651	−	1.10344i	0.901122	−	0.433565i	$-0.142745\pi$
$882$		0			0
$883$	22.1674	+	14.2461i	0.745991	+	0.479419i	0.857590	−	0.514334i	$-0.171961\pi$
$883$	22.1674	+	14.2461i	0.745991	+	0.479419i	−0.111599	+	0.993753i	$0.535597\pi$
$884$		0			0
$885$	0.0823835	+	0.847167i	0.00276929	+	0.0284772i
$886$		0			0
$887$	2.96428	−	0.426199i	0.0995307	−	0.0143104i	−0.0923695	−	0.995725i	$-0.529444\pi$
$887$	2.96428	−	0.426199i	0.0995307	−	0.0143104i	0.191900	+	0.981414i	$0.438535\pi$
$888$		0			0
$889$	0.204525	+	0.696549i	0.00685956	+	0.0233615i
$890$		0			0
$891$	32.5358	+	16.4875i	1.08999	+	0.552353i
$892$		0			0
$893$	−0.424855	−	0.490309i	−0.0142172	−	0.0164076i
$894$		0			0
$895$	3.75345	+	1.71414i	0.125464	+	0.0572974i
$896$		0			0
$897$	1.39757	−	2.21821i	0.0466636	−	0.0740637i
$898$		0			0
$899$	29.3978	+	13.4255i	0.980471	+	0.447766i
$900$		0			0
$901$	19.8599	+	22.9196i	0.661630	+	0.763561i
$902$		0			0
$903$	−0.150272	−	0.259234i	−0.00500072	−	0.00862678i
$904$		0			0
$905$	−1.51823	−	5.17061i	−0.0504676	−	0.171877i
$906$		0			0
$907$	22.4730	−	3.23113i	0.746204	−	0.107288i	0.241284	−	0.970454i	$-0.422431\pi$
$907$	22.4730	−	3.23113i	0.746204	−	0.107288i	0.504919	+	0.863167i	$0.331522\pi$
$908$		0			0
$909$	21.7979	+	5.20780i	0.722991	+	0.172732i
$910$		0			0
$911$	18.5698	+	11.9341i	0.615246	+	0.395395i	0.810821	−	0.585294i	$-0.199021\pi$
$911$	18.5698	+	11.9341i	0.615246	+	0.395395i	−0.195575	+	0.980689i	$0.562657\pi$
$912$		0			0
$913$	5.17744	−	36.0099i	0.171348	−	1.19175i
$914$		0			0
$915$	3.90940	−	0.955621i	0.129241	−	0.0315918i
$916$		0			0
$917$	−1.80578	−	0.530226i	−0.0596322	−	0.0175096i
$918$		0			0
$919$			23.6712i			0.780842i	0.920636	+	0.390421i	$0.127671\pi$
$919$			23.6712i			0.780842i	−0.920636	+	0.390421i	$0.872329\pi$
$920$		0			0
$921$	2.33916	−	6.79682i	0.0770778	−	0.223963i
$922$		0			0
$923$	0.741483	−	2.52526i	0.0244062	−	0.0831199i
$924$		0			0
$925$	−3.16757	−	4.92883i	−0.104149	−	0.162059i
$926$		0			0
$927$	−19.1691	−	19.9643i	−0.629597	−	0.655714i
$928$		0			0
$929$	−2.09597	+	3.26139i	−0.0687666	+	0.107003i	−0.873934	−	0.486045i	$-0.838439\pi$
$929$	−2.09597	+	3.26139i	−0.0687666	+	0.107003i	0.805167	+	0.593048i	$0.202075\pi$
$930$		0			0
$931$	−2.27696	+	1.03985i	−0.0746245	+	0.0340798i
$932$		0			0
$933$	5.45079	−	28.5488i	0.178451	−	0.934646i
$934$		0			0
$935$	−5.59884	+	1.64397i	−0.183102	+	0.0537635i
$936$		0			0
$937$	34.2478	+	29.6759i	1.11883	+	0.969470i	0.999726	−	0.0234119i	$-0.00745291\pi$
$937$	34.2478	+	29.6759i	1.11883	+	0.969470i	0.119102	+	0.992882i	$0.461998\pi$
$938$		0			0
$939$	2.64204	+	6.56634i	0.0862198	+	0.214284i
$940$		0			0
$941$	7.60584	−	16.6545i	0.247943	−	0.542920i	−0.744210	−	0.667945i	$-0.767174\pi$
$941$	7.60584	−	16.6545i	0.247943	−	0.542920i	0.992154	+	0.125025i	$0.0399012\pi$
$942$		0			0
$943$	−9.11902	+	4.78503i	−0.296956	+	0.155822i
$944$		0			0
$945$	−0.250694	+	0.0373821i	−0.00815507	+	0.00121604i
$946$		0			0
$947$	32.0304	−	27.7545i	1.04085	−	0.901900i	0.0455695	−	0.998961i	$-0.485490\pi$
$947$	32.0304	−	27.7545i	1.04085	−	0.901900i	0.995278	+	0.0970613i	$0.0309443\pi$
$948$		0			0
$949$	−2.60914	+	3.01111i	−0.0846962	+	0.0977447i
$950$		0			0
$951$	−46.0906	−	2.11513i	−1.49459	−	0.0685879i
$952$		0			0
$953$	−6.40218	−	44.5281i	−0.207387	−	1.44241i	−0.781640	−	0.623730i	$-0.785617\pi$
$953$	−6.40218	−	44.5281i	−0.207387	−	1.44241i	0.574253	−	0.818678i	$-0.305292\pi$
$954$		0			0
$955$	−0.292350	−	0.640158i	−0.00946024	−	0.0207150i
$956$		0			0
$957$	−28.4351	−	36.0289i	−0.919176	−	1.16465i
$958$		0			0
$959$	2.58818	+	0.372125i	0.0835768	+	0.0120165i
$960$		0			0
$961$	−5.52664	+	3.55175i	−0.178279	+	0.114573i
$962$		0			0
$963$	9.09873	+	12.6837i	0.293202	+	0.408725i
$964$		0			0
$965$	−5.74227			−0.184850
$966$		0			0
$967$	−48.0215			−1.54427			−0.772134	−	0.635460i	$-0.780810\pi$
$967$	−48.0215			−1.54427			−0.772134	+	0.635460i	$0.780810\pi$
$968$		0			0
$969$	−2.35485	−	1.67071i	−0.0756488	−	0.0536710i
$970$		0			0
$971$	−31.2007	+	20.0515i	−1.00128	+	0.643483i	−0.935122	−	0.354326i	$-0.884710\pi$
$971$	−31.2007	+	20.0515i	−1.00128	+	0.643483i	−0.0661571	+	0.997809i	$0.521074\pi$
$972$		0			0
$973$	−1.70525	−	0.245178i	−0.0546677	−	0.00786003i
$974$		0			0
$975$	−2.10441	+	1.66086i	−0.0673949	+	0.0531902i
$976$		0			0
$977$	23.6534	+	51.7937i	0.756739	+	1.65703i	0.753862	+	0.657032i	$0.228189\pi$
$977$	23.6534	+	51.7937i	0.756739	+	1.65703i	0.00287703	+	0.999996i	$0.499084\pi$
$978$		0			0
$979$	1.05728	+	7.35357i	0.0337909	+	0.235021i
$980$		0			0
$981$	12.9842	−	32.7631i	0.414552	−	1.04605i
$982$		0			0
$983$	−34.7861	+	40.1453i	−1.10950	+	1.28044i	−0.153156	+	0.988202i	$0.548944\pi$
$983$	−34.7861	+	40.1453i	−1.10950	+	1.28044i	−0.956347	+	0.292233i	$0.905602\pi$
$984$		0			0
$985$	−1.23975	+	1.07425i	−0.0395019	+	0.0342286i
$986$		0			0
$987$	−0.357236	−	0.339438i	−0.0113709	−	0.0108044i
$988$		0			0
$989$	−4.90833	−	1.92390i	−0.156076	−	0.0611764i
$990$		0			0
$991$	−8.35226	+	18.2889i	−0.265318	+	0.580966i	−0.994663	−	0.103181i	$-0.967098\pi$
$991$	−8.35226	+	18.2889i	−0.265318	+	0.580966i	0.729344	+	0.684147i	$0.239825\pi$
$992$		0			0
$993$	−55.7827	+	22.4448i	−1.77021	+	0.712265i
$994$		0			0
$995$	0.0750462	+	0.0650279i	0.00237912	+	0.00206152i
$996$		0			0
$997$	−0.206849	+	0.0607362i	−0.00655096	+	0.00192354i	−0.285006	−	0.958526i	$-0.591996\pi$
$997$	−0.206849	+	0.0607362i	−0.00655096	+	0.00192354i	0.278455	+	0.960449i	$0.410178\pi$
$998$		0			0
$999$	4.67042	−	4.08986i	0.147766	−	0.129397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.u.a.17.18	yes	240
3.2	odd	2	inner	552.2.u.a.17.13	✓	240
23.19	odd	22	inner	552.2.u.a.65.13	yes	240
69.65	even	22	inner	552.2.u.a.65.18	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.u.a.17.13	✓	240	3.2	odd	2	inner
552.2.u.a.17.18	yes	240	1.1	even	1	trivial
552.2.u.a.65.13	yes	240	23.19	odd	22	inner
552.2.u.a.65.18	yes	240	69.65	even	22	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.u (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00223 - 1.41263i) q^{3} +(0.260753 - 0.167576i) q^{5} +(0.155773 + 0.0223967i) q^{7} +(-0.991071 - 2.83157i) q^{9} +O(q^{10})\)	\(q+(1.00223 - 1.41263i) q^{3} +(0.260753 - 0.167576i) q^{5} +(0.155773 + 0.0223967i) q^{7} +(-0.991071 - 2.83157i) q^{9} +(-1.68358 - 3.68652i) q^{11} +(0.0449179 + 0.312411i) q^{13} +(0.0246111 - 0.536298i) q^{15} +(3.04194 - 3.51059i) q^{17} +(0.271212 - 0.235007i) q^{19} +(0.187758 - 0.197603i) q^{21} +(0.421309 - 4.77729i) q^{23} +(-2.03716 + 4.46077i) q^{25} +(-4.99325 - 1.43786i) q^{27} +(4.94153 + 4.28186i) q^{29} +(4.74250 - 1.39252i) q^{31} +(-6.89504 - 1.31646i) q^{33} +(0.0443714 - 0.0202637i) q^{35} +(-0.645924 + 1.00508i) q^{37} +(0.486340 + 0.249655i) q^{39} +(-1.16093 - 1.80644i) q^{41} +(0.309700 - 1.05474i) q^{43} +(-0.732927 - 0.572260i) q^{45} -1.80784i q^{47} +(-6.69269 - 1.96515i) q^{49} +(-1.91045 - 7.81557i) q^{51} +(-0.929129 + 6.46224i) q^{53} +(-1.05677 - 0.679145i) q^{55} +(-0.0601617 - 0.618655i) q^{57} +(-1.56930 + 0.225631i) q^{59} +(2.11196 + 7.19268i) q^{61} +(-0.0909640 - 0.463278i) q^{63} +(0.0640649 + 0.0739349i) q^{65} +(5.86299 + 2.67754i) q^{67} +(-6.32632 - 5.38310i) q^{69} +(-7.58509 - 3.46399i) q^{71} +(8.26663 + 9.54020i) q^{73} +(4.25973 + 7.34848i) q^{75} +(-0.179689 - 0.611966i) q^{77} +(15.5052 - 2.22932i) q^{79} +(-7.03556 + 5.61257i) q^{81} +(7.55163 + 4.85314i) q^{83} +(0.204906 - 1.42515i) q^{85} +(11.0012 - 2.68916i) q^{87} +(-1.75886 - 0.516449i) q^{89} +0.0496711i q^{91} +(2.78595 - 8.09505i) q^{93} +(0.0313380 - 0.106727i) q^{95} +(-2.14806 - 3.34245i) q^{97} +(-8.77009 + 8.42077i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^9	\( 240 q - 4 q^{9} - 16 q^{25} + 12 q^{27} - 8 q^{31} + 44 q^{37} + 20 q^{39} + 44 q^{43} + 124 q^{49} + 12 q^{55} + 16 q^{69} - 74 q^{75} - 144 q^{81} + 24 q^{85} - 170 q^{87} + 12 q^{93} - 198 q^{99}+O(q^{100}) \) 240 * q - 4 * q^9 - 16 * q^25 + 12 * q^27 - 8 * q^31 + 44 * q^37 + 20 * q^39 + 44 * q^43 + 124 * q^49 + 12 * q^55 + 16 * q^69 - 74 * q^75 - 144 * q^81 + 24 * q^85 - 170 * q^87 + 12 * q^93 - 198 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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