LMFDB - Embedded newform 441.2.p.c.80.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(80,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("441.80");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{48})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{8} + 1 $ x^16 - x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			80.1
Root			$-0.608761 - 0.793353i$ of defining polynomial
Character	$\chi$	$=$	441.80
Dual form			441.2.p.c.215.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.09077 + 1.20711i) q^{2} +(1.91421 - 3.31552i) q^{4} +(-1.68925 - 2.92586i) q^{5} +4.41421i q^{8} +O(q^{10})$	\(q+(-2.09077 + 1.20711i) q^{2} +(1.91421 - 3.31552i) q^{4} +(-1.68925 - 2.92586i) q^{5} +4.41421i q^{8} +(7.06365 + 4.07820i) q^{10} +(0.717439 + 0.414214i) q^{11} -3.37849i q^{13} +(-1.50000 - 2.59808i) q^{16} +(-0.699709 + 1.21193i) q^{17} +(-5.85172 + 3.37849i) q^{19} -12.9343 q^{20} -2.00000 q^{22} +(-1.73205 + 1.00000i) q^{23} +(-3.20711 + 5.55487i) q^{25} +(4.07820 + 7.06365i) q^{26} +4.82843i q^{29} +(-5.85172 - 3.37849i) q^{31} +(-1.37333 - 0.792893i) q^{32} -3.37849i q^{34} +(1.29289 + 2.23936i) q^{37} +(8.15640 - 14.1273i) q^{38} +(12.9154 - 7.45669i) q^{40} +8.15640 q^{41} -12.4853 q^{43} +(2.74666 - 1.58579i) q^{44} +(2.41421 - 4.18154i) q^{46} +(-3.37849 - 5.85172i) q^{47} -15.4853i q^{50} +(-11.2014 - 6.46716i) q^{52} +(-6.12372 - 3.53553i) q^{53} -2.79884i q^{55} +(-5.82843 - 10.0951i) q^{58} +(-3.37849 + 5.85172i) q^{59} +(7.06365 - 4.07820i) q^{61} +16.3128 q^{62} +9.82843 q^{64} +(-9.88500 + 5.70711i) q^{65} +(-4.24264 + 7.34847i) q^{67} +(2.67878 + 4.63979i) q^{68} -4.82843i q^{71} +(-1.21193 - 0.699709i) q^{73} +(-5.40629 - 3.12132i) q^{74} +25.8686i q^{76} +(4.82843 + 8.36308i) q^{79} +(-5.06774 + 8.77758i) q^{80} +(-17.0532 + 9.84565i) q^{82} -13.5140 q^{83} +4.72792 q^{85} +(26.1039 - 15.0711i) q^{86} +(-1.82843 + 3.16693i) q^{88} +(-3.08866 - 5.34972i) q^{89} +7.65685i q^{92} +(14.1273 + 8.15640i) q^{94} +(19.7700 + 11.4142i) q^{95} -1.39942i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4}+O(q^{10}) $ 16 * q + 8 * q^4	$ 16 q + 8 q^{4} - 24 q^{16} - 32 q^{22} - 40 q^{25} + 32 q^{37} - 64 q^{43} + 16 q^{46} - 48 q^{58} + 112 q^{64} + 32 q^{79} - 128 q^{85} + 16 q^{88}+O(q^{100}) $ 16 * q + 8 * q^4 - 24 * q^16 - 32 * q^22 - 40 * q^25 + 32 * q^37 - 64 * q^43 + 16 * q^46 - 48 * q^58 + 112 * q^64 + 32 * q^79 - 128 * q^85 + 16 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−2.09077	+	1.20711i	−1.47840	+	0.853553i	−0.999702	−	0.0244272i	$-0.992224\pi$
$2$	−2.09077	+	1.20711i	−1.47840	+	0.853553i	−0.478696	+	0.877981i	$0.658890\pi$
$3$		0			0
$3$		0			0
$4$	1.91421	−	3.31552i	0.957107	−	1.65776i
$5$	−1.68925	−	2.92586i	−0.755454	−	1.30848i	−0.945148	−	0.326641i	$-0.894083\pi$
$5$	−1.68925	−	2.92586i	−0.755454	−	1.30848i	0.189694	−	0.981843i	$-0.439250\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			4.41421i			1.56066i
$9$		0			0
$10$	7.06365	+	4.07820i	2.23372	+	1.28964i
$11$	0.717439	+	0.414214i	0.216316	+	0.124890i	0.604243	−	0.796800i	$-0.293476\pi$
$11$	0.717439	+	0.414214i	0.216316	+	0.124890i	−0.387927	+	0.921690i	$0.626809\pi$
$12$		0			0
$13$		−	3.37849i		−	0.937025i	−0.883457	−	0.468513i	$-0.844790\pi$
$13$		−	3.37849i		−	0.937025i	0.883457	−	0.468513i	$-0.155210\pi$
$14$		0			0
$15$		0			0
$16$	−1.50000	−	2.59808i	−0.375000	−	0.649519i
$17$	−0.699709	+	1.21193i	−0.169704	+	0.293936i	−0.938316	−	0.345779i	$-0.887615\pi$
$17$	−0.699709	+	1.21193i	−0.169704	+	0.293936i	0.768612	+	0.639716i	$0.220948\pi$
$18$		0			0
$19$	−5.85172	+	3.37849i	−1.34248	+	0.775079i	−0.987170	−	0.159670i	$-0.948957\pi$
$19$	−5.85172	+	3.37849i	−1.34248	+	0.775079i	−0.355307	+	0.934750i	$0.615624\pi$
$20$	−12.9343			−2.89220
$21$		0			0
$22$	−2.00000			−0.426401
$23$	−1.73205	+	1.00000i	−0.361158	+	0.208514i	−0.669588	−	0.742732i	$-0.733529\pi$
$23$	−1.73205	+	1.00000i	−0.361158	+	0.208514i	0.308431	+	0.951247i	$0.400196\pi$
$24$		0			0
$25$	−3.20711	+	5.55487i	−0.641421	+	1.11097i
$26$	4.07820	+	7.06365i	0.799801	+	1.38530i
$27$		0			0
$28$		0			0
$29$			4.82843i			0.896616i	0.893879	+	0.448308i	$0.147973\pi$
$29$			4.82843i			0.896616i	−0.893879	+	0.448308i	$0.852027\pi$
$30$		0			0
$31$	−5.85172	−	3.37849i	−1.05100	−	0.606795i	−0.128071	−	0.991765i	$-0.540879\pi$
$31$	−5.85172	−	3.37849i	−1.05100	−	0.606795i	−0.922929	+	0.384970i	$0.874212\pi$
$32$	−1.37333	−	0.792893i	−0.242773	−	0.140165i
$33$		0			0
$34$		−	3.37849i		−	0.579407i
$35$		0			0
$36$		0			0
$37$	1.29289	+	2.23936i	0.212550	+	0.368148i	0.952512	−	0.304501i	$-0.0984897\pi$
$37$	1.29289	+	2.23936i	0.212550	+	0.368148i	−0.739962	+	0.672649i	$0.765156\pi$
$38$	8.15640	−	14.1273i	1.32314	−	2.29175i
$39$		0			0
$40$	12.9154	−	7.45669i	2.04210	−	1.17901i
$41$	8.15640			1.27382			0.636908	−	0.770940i	$-0.280213\pi$
$41$	8.15640			1.27382			0.636908	+	0.770940i	$0.280213\pi$
$42$		0			0
$43$	−12.4853			−1.90399			−0.951994	−	0.306117i	$-0.900970\pi$
$43$	−12.4853			−1.90399			−0.951994	+	0.306117i	$0.900970\pi$
$44$	2.74666	−	1.58579i	0.414075	−	0.239066i
$45$		0			0
$46$	2.41421	−	4.18154i	0.355956	−	0.616535i
$47$	−3.37849	−	5.85172i	−0.492804	−	0.853561i	0.507162	−	0.861851i	$-0.330695\pi$
$47$	−3.37849	−	5.85172i	−0.492804	−	0.853561i	−0.999966	+	0.00828959i	$0.997361\pi$
$48$		0			0
$49$		0			0
$50$		−	15.4853i		−	2.18995i
$51$		0			0
$52$	−11.2014	−	6.46716i	−1.55336	−	0.896833i
$53$	−6.12372	−	3.53553i	−0.841158	−	0.485643i	0.0164995	−	0.999864i	$-0.494748\pi$
$53$	−6.12372	−	3.53553i	−0.841158	−	0.485643i	−0.857658	+	0.514221i	$0.828081\pi$
$54$		0			0
$55$		−	2.79884i		−	0.377395i
$56$		0			0
$57$		0			0
$58$	−5.82843	−	10.0951i	−0.765310	−	1.32556i
$59$	−3.37849	+	5.85172i	−0.439842	+	0.761829i	−0.997677	−	0.0681229i	$-0.978299\pi$
$59$	−3.37849	+	5.85172i	−0.439842	+	0.761829i	0.557835	+	0.829952i	$0.311632\pi$
$60$		0			0
$61$	7.06365	−	4.07820i	0.904408	−	0.522160i	0.0257803	−	0.999668i	$-0.491793\pi$
$61$	7.06365	−	4.07820i	0.904408	−	0.522160i	0.878628	+	0.477507i	$0.158460\pi$
$62$	16.3128			2.07173
$63$		0			0
$64$	9.82843			1.22855
$65$	−9.88500	+	5.70711i	−1.22608	+	0.707879i
$66$		0			0
$67$	−4.24264	+	7.34847i	−0.518321	+	0.897758i	0.481452	+	0.876472i	$0.340109\pi$
$67$	−4.24264	+	7.34847i	−0.518321	+	0.897758i	−0.999773	+	0.0212861i	$0.993224\pi$
$68$	2.67878	+	4.63979i	0.324850	+	0.562657i
$69$		0			0
$70$		0			0
$71$		−	4.82843i		−	0.573029i	−0.958076	−	0.286514i	$-0.907503\pi$
$71$		−	4.82843i		−	0.573029i	0.958076	−	0.286514i	$-0.0924966\pi$
$72$		0			0
$73$	−1.21193	−	0.699709i	−0.141846	−	0.0818947i	0.427398	−	0.904064i	$-0.359430\pi$
$73$	−1.21193	−	0.699709i	−0.141846	−	0.0818947i	−0.569243	+	0.822169i	$0.692764\pi$
$74$	−5.40629	−	3.12132i	−0.628468	−	0.362846i
$75$		0			0
$76$			25.8686i			2.96734i
$77$		0			0
$78$		0			0
$79$	4.82843	+	8.36308i	0.543240	+	0.940920i	0.998715	+	0.0506715i	$0.0161361\pi$
$79$	4.82843	+	8.36308i	0.543240	+	0.940920i	−0.455475	+	0.890249i	$0.650531\pi$
$80$	−5.06774	+	8.77758i	−0.566590	+	0.981363i
$81$		0			0
$82$	−17.0532	+	9.84565i	−1.88321	+	1.08727i
$83$	−13.5140			−1.48335			−0.741676	−	0.670759i	$-0.765969\pi$
$83$	−13.5140			−1.48335			−0.741676	+	0.670759i	$0.765969\pi$
$84$		0			0
$85$	4.72792			0.512815
$86$	26.1039	−	15.0711i	2.81485	−	1.62516i
$87$		0			0
$88$	−1.82843	+	3.16693i	−0.194911	+	0.337596i
$89$	−3.08866	−	5.34972i	−0.327398	−	0.567069i	0.654597	−	0.755978i	$-0.272838\pi$
$89$	−3.08866	−	5.34972i	−0.327398	−	0.567069i	−0.981995	+	0.188909i	$0.939505\pi$
$90$		0			0
$91$		0			0
$92$			7.65685i			0.798282i
$93$		0			0
$94$	14.1273	+	8.15640i	1.45712	+	0.841269i
$95$	19.7700	+	11.4142i	2.02836	+	1.17107i
$96$		0			0
$97$		−	1.39942i		−	0.142089i	−0.997473	−	0.0710447i	$-0.977367\pi$
$97$		−	1.39942i		−	0.142089i	0.997473	−	0.0710447i	$-0.0226333\pi$
$98$		0			0
$99$		0			0
$100$	12.2782	+	21.2664i	1.22782	+	2.12664i
$101$	−6.46716	+	11.2014i	−0.643506	+	1.11459i	0.341138	+	0.940013i	$0.389188\pi$
$101$	−6.46716	+	11.2014i	−0.643506	+	1.11459i	−0.984644	+	0.174572i	$0.944146\pi$
$102$		0			0
$103$	−2.42386	+	1.39942i	−0.238830	+	0.137889i	−0.614639	−	0.788809i	$-0.710698\pi$
$103$	−2.42386	+	1.39942i	−0.238830	+	0.137889i	0.375809	+	0.926697i	$0.377365\pi$
$104$	14.9134			1.46238
$105$		0			0
$106$	17.0711			1.65809
$107$	8.06591	−	4.65685i	0.779761	−	0.450195i	−0.0565847	−	0.998398i	$-0.518021\pi$
$107$	8.06591	−	4.65685i	0.779761	−	0.450195i	0.836345	+	0.548203i	$0.184688\pi$
$108$		0			0
$109$	1.29289	−	2.23936i	0.123837	−	0.214491i	−0.797441	−	0.603397i	$-0.793813\pi$
$109$	1.29289	−	2.23936i	0.123837	−	0.214491i	0.921278	+	0.388906i	$0.127147\pi$
$110$	3.37849	+	5.85172i	0.322127	+	0.557940i
$111$		0			0
$112$		0			0
$113$			5.89949i			0.554978i	0.960729	+	0.277489i	$0.0895022\pi$
$113$			5.89949i			0.554978i	−0.960729	+	0.277489i	$0.910498\pi$
$114$		0			0
$115$	5.85172	+	3.37849i	0.545676	+	0.315046i
$116$	16.0087	+	9.24264i	1.48637	+	0.858158i
$117$		0			0
$118$		−	16.3128i		−	1.50172i
$119$		0			0
$120$		0			0
$121$	−5.15685	−	8.93193i	−0.468805	−	0.811994i
$122$	−9.84565	+	17.0532i	−0.891383	+	1.54392i
$123$		0			0
$124$	−22.4029	+	12.9343i	−2.01184	+	1.16154i
$125$	4.77791			0.427349
$126$		0			0
$127$	−0.485281			−0.0430618			−0.0215309	−	0.999768i	$-0.506854\pi$
$127$	−0.485281			−0.0430618			−0.0215309	+	0.999768i	$0.506854\pi$
$128$	−17.8023	+	10.2782i	−1.57352	+	0.908471i
$129$		0			0
$130$	13.7782	−	23.8645i	1.20843	−	2.09305i
$131$	4.77791	+	8.27558i	0.417448	+	0.723041i	0.995682	−	0.0928299i	$-0.0295913\pi$
$131$	4.77791	+	8.27558i	0.417448	+	0.723041i	−0.578234	+	0.815871i	$0.696258\pi$
$132$		0			0
$133$		0			0
$134$		−	20.4853i		−	1.76966i
$135$		0			0
$136$	−5.34972	−	3.08866i	−0.458735	−	0.264851i
$137$	−0.717439	−	0.414214i	−0.0612949	−	0.0353887i	0.469039	−	0.883177i	$-0.344600\pi$
$137$	−0.717439	−	0.414214i	−0.0612949	−	0.0353887i	−0.530334	+	0.847789i	$0.677934\pi$
$138$		0			0
$139$			9.55582i			0.810514i	0.914203	+	0.405257i	$0.132818\pi$
$139$			9.55582i			0.810514i	−0.914203	+	0.405257i	$0.867182\pi$
$140$		0			0
$141$		0			0
$142$	5.82843	+	10.0951i	0.489111	+	0.847165i
$143$	1.39942	−	2.42386i	0.117025	−	0.202694i
$144$		0			0
$145$	14.1273	−	8.15640i	1.17321	−	0.677352i
$146$	3.37849			0.279606
$147$		0			0
$148$	9.89949			0.813733
$149$	−3.67423	+	2.12132i	−0.301005	+	0.173785i	−0.642894	−	0.765955i	$-0.722267\pi$
$149$	−3.67423	+	2.12132i	−0.301005	+	0.173785i	0.341889	+	0.939740i	$0.388933\pi$
$150$		0			0
$151$	6.24264	−	10.8126i	0.508019	−	0.879915i	−0.491938	−	0.870630i	$-0.663711\pi$
$151$	6.24264	−	10.8126i	0.508019	−	0.879915i	0.999957	−	0.00928431i	$-0.00295533\pi$
$152$	−14.9134	−	25.8307i	−1.20964	−	2.09515i
$153$		0			0
$154$		0			0
$155$			22.8284i			1.83362i
$156$		0			0
$157$	−6.35372	−	3.66832i	−0.507082	−	0.292764i	0.224551	−	0.974462i	$-0.427908\pi$
$157$	−6.35372	−	3.66832i	−0.507082	−	0.292764i	−0.731633	+	0.681698i	$0.761242\pi$
$158$	−20.1903	−	11.6569i	−1.60625	−	0.927370i
$159$		0			0
$160$			5.35757i			0.423553i
$161$		0			0
$162$		0			0
$163$	−7.41421	−	12.8418i	−0.580726	−	1.00585i	−0.995393	−	0.0958740i	$-0.969435\pi$
$163$	−7.41421	−	12.8418i	−0.580726	−	1.00585i	0.414667	−	0.909973i	$-0.363898\pi$
$164$	15.6131	−	27.0427i	1.21918	−	2.11168i
$165$		0			0
$166$	28.2546	−	16.3128i	2.19298	−	1.26612i
$167$	2.79884			0.216580			0.108290	−	0.994119i	$-0.465462\pi$
$167$	2.79884			0.216580			0.108290	+	0.994119i	$0.465462\pi$
$168$		0			0
$169$	1.58579			0.121984
$170$	−9.88500	+	5.70711i	−0.758145	+	0.437715i
$171$		0			0
$172$	−23.8995	+	41.3951i	−1.82232	+	3.15635i
$173$	−4.07820	−	7.06365i	−0.310060	−	0.537040i	0.668315	−	0.743878i	$-0.267016\pi$
$173$	−4.07820	−	7.06365i	−0.310060	−	0.537040i	−0.978375	+	0.206839i	$0.933682\pi$
$174$		0			0
$175$		0			0
$176$		−	2.48528i		−	0.187335i
$177$		0			0
$178$	12.9154	+	7.45669i	0.968048	+	0.558903i
$179$	−8.23999	−	4.75736i	−0.615886	−	0.355582i	0.159380	−	0.987217i	$-0.449051\pi$
$179$	−8.23999	−	4.75736i	−0.615886	−	0.355582i	−0.775265	+	0.631636i	$0.782384\pi$
$180$		0			0
$181$			17.7122i			1.31654i	0.752782	+	0.658270i	$0.228711\pi$
$181$			17.7122i			1.31654i	−0.752782	+	0.658270i	$0.771289\pi$
$182$		0			0
$183$		0			0
$184$	−4.41421	−	7.64564i	−0.325420	−	0.563644i
$185$	4.36803	−	7.56565i	0.321144	−	0.556238i
$186$		0			0
$187$	−1.00400	+	0.579658i	−0.0734195	+	0.0423888i
$188$	−25.8686			−1.88666
$189$		0			0
$190$	−55.1127			−3.99830
$191$	18.0379	−	10.4142i	1.30518	−	0.753546i	0.323892	−	0.946094i	$-0.395008\pi$
$191$	18.0379	−	10.4142i	1.30518	−	0.753546i	0.981288	+	0.192548i	$0.0616751\pi$
$192$		0			0
$193$	8.82843	−	15.2913i	0.635484	−	1.10069i	−0.350928	−	0.936402i	$-0.614134\pi$
$193$	8.82843	−	15.2913i	0.635484	−	1.10069i	0.986412	−	0.164288i	$-0.0525328\pi$
$194$	1.68925	+	2.92586i	0.121281	+	0.210065i
$195$		0			0
$196$		0			0
$197$		−	16.2426i		−	1.15724i	−0.815597	−	0.578620i	$-0.803591\pi$
$197$		−	16.2426i		−	1.15724i	0.815597	−	0.578620i	$-0.196409\pi$
$198$		0			0
$199$	−16.5512	−	9.55582i	−1.17328	−	0.677394i	−0.218830	−	0.975763i	$-0.570224\pi$
$199$	−16.5512	−	9.55582i	−1.17328	−	0.677394i	−0.954451	+	0.298369i	$0.903557\pi$
$200$	−24.5204	−	14.1569i	−1.73385	−	1.00104i
$201$		0			0
$202$		−	31.2262i		−	2.19707i
$203$		0			0
$204$		0			0
$205$	−13.7782	−	23.8645i	−0.962309	−	1.66677i
$206$	3.37849	−	5.85172i	0.235391	−	0.407709i
$207$		0			0
$208$	−8.77758	+	5.06774i	−0.608616	+	0.351384i
$209$	−5.59767			−0.387199
$210$		0			0
$211$	7.31371			0.503496			0.251748	−	0.967793i	$-0.418995\pi$
$211$	7.31371			0.503496			0.251748	+	0.967793i	$0.418995\pi$
$212$	−23.4442	+	13.5355i	−1.61016	+	0.929624i
$213$		0			0
$214$	−11.2426	+	19.4728i	−0.768531	+	1.33113i
$215$	21.0907	+	36.5302i	1.43837	+	2.49134i
$216$		0			0
$217$		0			0
$218$			6.24264i			0.422805i
$219$		0			0
$220$	−9.27958	−	5.35757i	−0.625629	−	0.361207i
$221$	4.09450	+	2.36396i	0.275426	+	0.159017i
$222$		0			0
$223$		−	23.0698i		−	1.54487i	−0.635095	−	0.772434i	$-0.719039\pi$
$223$		−	23.0698i		−	1.54487i	0.635095	−	0.772434i	$-0.280961\pi$
$224$		0			0
$225$		0			0
$226$	−7.12132	−	12.3345i	−0.473703	−	0.820478i
$227$	−1.39942	+	2.42386i	−0.0928826	+	0.160877i	−0.908723	−	0.417400i	$-0.862941\pi$
$227$	−1.39942	+	2.42386i	−0.0928826	+	0.160877i	0.815840	+	0.578277i	$0.196275\pi$
$228$		0			0
$229$	10.4915	−	6.05728i	0.693299	−	0.400276i	−0.111548	−	0.993759i	$-0.535581\pi$
$229$	10.4915	−	6.05728i	0.693299	−	0.400276i	0.804847	+	0.593483i	$0.202248\pi$
$230$	−16.3128			−1.07563
$231$		0			0
$232$	−21.3137			−1.39931
$233$	9.37769	−	5.41421i	0.614353	−	0.354697i	−0.160314	−	0.987066i	$-0.551251\pi$
$233$	9.37769	−	5.41421i	0.614353	−	0.354697i	0.774667	+	0.632369i	$0.217917\pi$
$234$		0			0
$235$	−11.4142	+	19.7700i	−0.744581	+	1.28965i
$236$	12.9343	+	22.4029i	0.841952	+	1.45830i
$237$		0			0
$238$		0			0
$239$			0.343146i			0.0221963i	0.999938	+	0.0110981i	$0.00353272\pi$
$239$			0.343146i			0.0221963i	−0.999938	+	0.0110981i	$0.996467\pi$
$240$		0			0
$241$	7.77359	+	4.48808i	0.500741	+	0.289103i	0.729019	−	0.684493i	$-0.239976\pi$
$241$	7.77359	+	4.48808i	0.500741	+	0.289103i	−0.228279	+	0.973596i	$0.573310\pi$
$242$	21.5636	+	12.4497i	1.38616	+	0.800300i
$243$		0			0
$244$		−	31.2262i		−	1.99905i
$245$		0			0
$246$		0			0
$247$	11.4142	+	19.7700i	0.726269	+	1.25793i
$248$	14.9134	−	25.8307i	0.947001	−	1.64025i
$249$		0			0
$250$	−9.98951	+	5.76745i	−0.631792	+	0.364765i
$251$	−25.8686			−1.63281			−0.816407	−	0.577477i	$-0.804037\pi$
$251$	−25.8686			−1.63281			−0.816407	+	0.577477i	$0.804037\pi$
$252$		0			0
$253$	−1.65685			−0.104166
$254$	1.01461	−	0.585786i	0.0636624	−	0.0367555i
$255$		0			0
$256$	14.9853	−	25.9553i	0.936580	−	1.62220i
$257$	−10.8352	−	18.7671i	−0.675880	−	1.17066i	−0.976211	−	0.216824i	$-0.930430\pi$
$257$	−10.8352	−	18.7671i	−0.675880	−	1.17066i	0.300330	−	0.953835i	$-0.402903\pi$
$258$		0			0
$259$		0			0
$260$			43.6985i			2.71006i
$261$		0			0
$262$	−19.9790	−	11.5349i	−1.23431	−	0.712628i
$263$	20.9077	+	12.0711i	1.28922	+	0.744334i	0.978516	−	0.206171i	$-0.0661004\pi$
$263$	20.9077	+	12.0711i	1.28922	+	0.744334i	0.310708	+	0.950505i	$0.399434\pi$
$264$		0			0
$265$			23.8896i			1.46752i
$266$		0			0
$267$		0			0
$268$	16.2426	+	28.1331i	0.992177	+	1.71850i
$269$	15.6131	−	27.0427i	0.951947	−	1.64882i	0.210743	−	0.977541i	$-0.432412\pi$
$269$	15.6131	−	27.0427i	0.951947	−	1.64882i	0.741204	−	0.671280i	$-0.234255\pi$
$270$		0			0
$271$	5.85172	−	3.37849i	0.355467	−	0.205229i	−0.311624	−	0.950206i	$-0.600873\pi$
$271$	5.85172	−	3.37849i	0.355467	−	0.205229i	0.667090	+	0.744977i	$0.267539\pi$
$272$	4.19825			0.254556
$273$		0			0
$274$	2.00000			0.120824
$275$	−4.60181	+	2.65685i	−0.277499	+	0.160214i
$276$		0			0
$277$	10.4853	−	18.1610i	0.630000	−	1.09119i	−0.357552	−	0.933893i	$-0.616388\pi$
$277$	10.4853	−	18.1610i	0.630000	−	1.09119i	0.987551	−	0.157298i	$-0.0502783\pi$
$278$	−11.5349	−	19.9790i	−0.691817	−	1.19826i
$279$		0			0
$280$		0			0
$281$		−	18.8284i		−	1.12321i	−0.827406	−	0.561605i	$-0.810184\pi$
$281$		−	18.8284i		−	1.12321i	0.827406	−	0.561605i	$-0.189816\pi$
$282$		0			0
$283$	25.8307	+	14.9134i	1.53548	+	0.886509i	0.999095	+	0.0425346i	$0.0135433\pi$
$283$	25.8307	+	14.9134i	1.53548	+	0.886509i	0.536384	+	0.843974i	$0.319790\pi$
$284$	−16.0087	−	9.24264i	−0.949943	−	0.548450i
$285$		0			0
$286$			6.75699i			0.399549i
$287$		0			0
$288$		0			0
$289$	7.52082	+	13.0264i	0.442401	+	0.766261i
$290$	−19.6913	+	34.1063i	−1.15631	+	2.00279i
$291$		0			0
$292$	−4.63979	+	2.67878i	−0.271523	+	0.156764i
$293$	7.33664			0.428611			0.214306	−	0.976767i	$-0.431251\pi$
$293$	7.33664			0.428611			0.214306	+	0.976767i	$0.431251\pi$
$294$		0			0
$295$	22.8284			1.32912
$296$	−9.88500	+	5.70711i	−0.574554	+	0.331719i
$297$		0			0
$298$	5.12132	−	8.87039i	0.296670	−	0.513848i
$299$	3.37849	+	5.85172i	0.195383	+	0.338414i
$300$		0			0
$301$		0			0
$302$			30.1421i			1.73448i
$303$		0			0
$304$	17.5552	+	10.1355i	1.00686	+	0.581310i
$305$	−23.8645	−	13.7782i	−1.36648	−	0.788936i
$306$		0			0
$307$		−	12.3547i		−	0.705117i	−0.935790	−	0.352559i	$-0.885312\pi$
$307$		−	12.3547i		−	0.705117i	0.935790	−	0.352559i	$-0.114688\pi$
$308$		0			0
$309$		0			0
$310$	−27.5563	−	47.7290i	−1.56510	−	2.71082i
$311$	−5.35757	+	9.27958i	−0.303800	+	0.526197i	−0.976993	−	0.213270i	$-0.931589\pi$
$311$	−5.35757	+	9.27958i	−0.303800	+	0.526197i	0.673194	+	0.739466i	$0.264922\pi$
$312$		0			0
$313$	−11.2014	+	6.46716i	−0.633143	+	0.365545i	−0.781968	−	0.623318i	$-0.785784\pi$
$313$	−11.2014	+	6.46716i	−0.633143	+	0.365545i	0.148825	+	0.988864i	$0.452451\pi$
$314$	17.7122			0.999559
$315$		0			0
$316$	36.9706			2.07976
$317$	−20.5745	+	11.8787i	−1.15558	+	0.667173i	−0.950240	−	0.311518i	$-0.899163\pi$
$317$	−20.5745	+	11.8787i	−1.15558	+	0.667173i	−0.205338	+	0.978691i	$0.565829\pi$
$318$		0			0
$319$	−2.00000	+	3.46410i	−0.111979	+	0.193952i
$320$	−16.6026	−	28.7566i	−0.928116	−	1.60754i
$321$		0			0
$322$		0			0
$323$		−	9.45584i		−	0.526137i
$324$		0			0
$325$	18.7671	+	10.8352i	1.04101	+	0.601028i
$326$	31.0028	+	17.8995i	1.71709	+	0.991361i
$327$		0			0
$328$			36.0041i			1.98799i
$329$		0			0
$330$		0			0
$331$	−5.17157	−	8.95743i	−0.284255	−	0.492345i	0.688173	−	0.725547i	$-0.258413\pi$
$331$	−5.17157	−	8.95743i	−0.284255	−	0.492345i	−0.972428	+	0.233202i	$0.925080\pi$
$332$	−25.8686	+	44.8058i	−1.41973	+	2.45904i
$333$		0			0
$334$	−5.85172	+	3.37849i	−0.320192	+	0.184863i
$335$	28.6675			1.56627
$336$		0			0
$337$	−12.9289			−0.704284			−0.352142	−	0.935947i	$-0.614547\pi$
$337$	−12.9289			−0.704284			−0.352142	+	0.935947i	$0.614547\pi$
$338$	−3.31552	+	1.91421i	−0.180340	+	0.104119i
$339$		0			0
$340$	9.05025	−	15.6755i	0.490819	−	0.850123i
$341$	−2.79884	−	4.84772i	−0.151565	−	0.262519i
$342$		0			0
$343$		0			0
$344$		−	55.1127i		−	2.97148i
$345$		0			0
$346$	17.0532	+	9.84565i	0.916784	+	0.529305i
$347$	−16.4290	−	9.48528i	−0.881954	−	0.509197i	−0.0106521	−	0.999943i	$-0.503391\pi$
$347$	−16.4290	−	9.48528i	−0.881954	−	0.509197i	−0.871302	+	0.490747i	$0.836724\pi$
$348$		0			0
$349$			6.17733i			0.330665i	0.986238	+	0.165332i	$0.0528697\pi$
$349$			6.17733i			0.330665i	−0.986238	+	0.165332i	$0.947130\pi$
$350$		0			0
$351$		0			0
$352$	−0.656854	−	1.13770i	−0.0350104	−	0.0606399i
$353$	−11.8247	+	20.4810i	−0.629367	+	1.09009i	0.358312	+	0.933602i	$0.383352\pi$
$353$	−11.8247	+	20.4810i	−0.629367	+	1.09009i	−0.987679	+	0.156493i	$0.949981\pi$
$354$		0			0
$355$	−14.1273	+	8.15640i	−0.749799	+	0.432897i
$356$	−23.6494			−1.25342
$357$		0			0
$358$	22.9706			1.21403
$359$	0.891519	−	0.514719i	0.0470526	−	0.0271658i	−0.476289	−	0.879289i	$-0.658018\pi$
$359$	0.891519	−	0.514719i	0.0470526	−	0.0271658i	0.523342	+	0.852123i	$0.324685\pi$
$360$		0			0
$361$	13.3284	−	23.0855i	0.701496	−	1.21503i
$362$	−21.3805	−	37.0322i	−1.12374	−	1.94637i
$363$		0			0
$364$		0			0
$365$			4.72792i			0.247471i
$366$		0			0
$367$	3.42786	+	1.97908i	0.178933	+	0.103307i	0.586791	−	0.809738i	$-0.300391\pi$
$367$	3.42786	+	1.97908i	0.178933	+	0.103307i	−0.407858	+	0.913045i	$0.633724\pi$
$368$	5.19615	+	3.00000i	0.270868	+	0.156386i
$369$		0			0
$370$			21.0907i			1.09645i
$371$		0			0
$372$		0			0
$373$	11.3137	+	19.5959i	0.585802	+	1.01464i	0.994775	+	0.102092i	$0.0325536\pi$
$373$	11.3137	+	19.5959i	0.585802	+	1.01464i	−0.408973	+	0.912546i	$0.634113\pi$
$374$	1.39942	−	2.42386i	0.0723622	−	0.125335i
$375$		0			0
$376$	25.8307	−	14.9134i	1.33212	−	0.769099i
$377$	16.3128			0.840152
$378$		0			0
$379$		0			0			−	1.00000i	$-0.5\pi$
$379$		0			0				1.00000i	$0.5\pi$
$380$	75.6880	−	43.6985i	3.88271	−	2.24168i
$381$		0			0
$382$	−25.1421	+	43.5475i	−1.28638	+	2.22808i
$383$	13.5140	+	23.4069i	0.690532	+	1.19604i	0.971664	+	0.236367i	$0.0759567\pi$
$383$	13.5140	+	23.4069i	0.690532	+	1.19604i	−0.281132	+	0.959669i	$0.590710\pi$
$384$		0			0
$385$		0			0
$386$			42.6274i			2.16968i
$387$		0			0
$388$	−4.63979	−	2.67878i	−0.235550	−	0.135995i
$389$	−11.9503	−	6.89949i	−0.605903	−	0.349818i	0.165457	−	0.986217i	$-0.447090\pi$
$389$	−11.9503	−	6.89949i	−0.605903	−	0.349818i	−0.771360	+	0.636399i	$0.780423\pi$
$390$		0			0
$391$		−	2.79884i		−	0.141543i
$392$		0			0
$393$		0			0
$394$	19.6066	+	33.9596i	0.987766	+	1.71086i
$395$	16.3128	−	28.2546i	0.820786	−	1.42164i
$396$		0			0
$397$	−23.6148	+	13.6340i	−1.18519	+	0.684272i	−0.957210	−	0.289393i	$-0.906547\pi$
$397$	−23.6148	+	13.6340i	−1.18519	+	0.684272i	−0.227983	+	0.973665i	$0.573213\pi$
$398$	46.1396			2.31277
$399$		0			0
$400$	19.2426			0.962132
$401$	−9.37769	+	5.41421i	−0.468300	+	0.270373i	−0.715528	−	0.698584i	$-0.753814\pi$
$401$	−9.37769	+	5.41421i	−0.468300	+	0.270373i	0.247228	+	0.968957i	$0.420480\pi$
$402$		0			0
$403$	−11.4142	+	19.7700i	−0.568582	+	0.984814i
$404$	24.7590	+	42.8839i	1.23181	+	2.13355i
$405$		0			0
$406$		0			0
$407$			2.14214i			0.106182i
$408$		0			0
$409$	−15.3392	−	8.85611i	−0.758476	−	0.437907i	0.0702721	−	0.997528i	$-0.477613\pi$
$409$	−15.3392	−	8.85611i	−0.758476	−	0.437907i	−0.828748	+	0.559621i	$0.810947\pi$
$410$	57.6140	+	33.2635i	2.84535	+	1.64276i
$411$		0			0
$412$			10.7151i			0.527897i
$413$		0			0
$414$		0			0
$415$	22.8284	+	39.5400i	1.12060	+	1.94094i
$416$	−2.67878	+	4.63979i	−0.131338	+	0.227484i
$417$		0			0
$418$	11.7034	−	6.75699i	0.572434	−	0.330495i
$419$	−35.4244			−1.73060			−0.865299	−	0.501256i	$-0.832871\pi$
$419$	−35.4244			−1.73060			−0.865299	+	0.501256i	$0.832871\pi$
$420$		0			0
$421$	−23.3137			−1.13624			−0.568120	−	0.822946i	$-0.692329\pi$
$421$	−23.3137			−1.13624			−0.568120	+	0.822946i	$0.692329\pi$
$422$	−15.2913	+	8.82843i	−0.744368	+	0.429761i
$423$		0			0
$424$	15.6066	−	27.0314i	0.757924	−	1.31276i
$425$	−4.48808	−	7.77359i	−0.217704	−	0.377074i
$426$		0			0
$427$		0			0
$428$		−	35.6569i		−	1.72354i
$429$		0			0
$430$	−88.1917	−	50.9175i	−4.25298	−	2.45546i
$431$	−13.3852	−	7.72792i	−0.644740	−	0.372241i	0.141698	−	0.989910i	$-0.454744\pi$
$431$	−13.3852	−	7.72792i	−0.644740	−	0.372241i	−0.786438	+	0.617669i	$0.788077\pi$
$432$		0			0
$433$		−	8.15640i		−	0.391972i	−0.980607	−	0.195986i	$-0.937209\pi$
$433$		−	8.15640i		−	0.391972i	0.980607	−	0.195986i	$-0.0627907\pi$
$434$		0			0
$435$		0			0
$436$	−4.94975	−	8.57321i	−0.237050	−	0.410582i
$437$	6.75699	−	11.7034i	0.323230	−	0.559852i
$438$		0			0
$439$	−24.8268	+	14.3337i	−1.18492	+	0.684112i	−0.957147	−	0.289603i	$-0.906477\pi$
$439$	−24.8268	+	14.3337i	−1.18492	+	0.684112i	−0.227769	+	0.973715i	$0.573143\pi$
$440$	12.3547			0.588985
$441$		0			0
$442$	−11.4142			−0.542919
$443$	21.5020	−	12.4142i	1.02159	−	0.589817i	0.107028	−	0.994256i	$-0.465867\pi$
$443$	21.5020	−	12.4142i	1.02159	−	0.589817i	0.914565	+	0.404439i	$0.132533\pi$
$444$		0			0
$445$	−10.4350	+	18.0740i	−0.494668	+	0.856790i
$446$	27.8477	+	48.2336i	1.31863	+	2.28393i
$447$		0			0
$448$		0			0
$449$		−	24.2426i		−	1.14408i	−0.820225	−	0.572040i	$-0.806152\pi$
$449$		−	24.2426i		−	1.14408i	0.820225	−	0.572040i	$-0.193848\pi$
$450$		0			0
$451$	5.85172	+	3.37849i	0.275547	+	0.159087i
$452$	19.5599	+	11.2929i	0.920019	+	0.531173i
$453$		0			0
$454$		−	6.75699i		−	0.317121i
$455$		0			0
$456$		0			0
$457$	−14.3137	−	24.7921i	−0.669567	−	1.15972i	−0.978025	−	0.208486i	$-0.933146\pi$
$457$	−14.3137	−	24.7921i	−0.669567	−	1.15972i	0.308458	−	0.951238i	$-0.400187\pi$
$458$	−14.6236	+	25.3287i	−0.683314	+	1.18353i
$459$		0			0
$460$	22.4029	−	12.9343i	1.04454	−	0.603065i
$461$	21.6704			1.00929			0.504645	−	0.863327i	$-0.331623\pi$
$461$	21.6704			1.00929			0.504645	+	0.863327i	$0.331623\pi$
$462$		0			0
$463$	3.51472			0.163343			0.0816714	−	0.996659i	$-0.473974\pi$
$463$	3.51472			0.163343			0.0816714	+	0.996659i	$0.473974\pi$
$464$	12.5446	−	7.24264i	0.582369	−	0.336231i
$465$		0			0
$466$	−13.0711	+	22.6398i	−0.605506	+	1.04877i
$467$	1.39942	+	2.42386i	0.0647573	+	0.112163i	0.896586	−	0.442869i	$-0.146039\pi$
$467$	1.39942	+	2.42386i	0.0647573	+	0.112163i	−0.831829	+	0.555032i	$0.812706\pi$
$468$		0			0
$469$		0			0
$470$		−	55.1127i		−	2.54216i
$471$		0			0
$472$	−25.8307	−	14.9134i	−1.18896	−	0.686444i
$473$	−8.95743	−	5.17157i	−0.411863	−	0.237789i
$474$		0			0
$475$		−	43.3407i		−	1.98861i
$476$		0			0
$477$		0			0
$478$	−0.414214	−	0.717439i	−0.0189457	−	0.0328149i
$479$	4.19825	−	7.27159i	0.191823	−	0.332247i	−0.754031	−	0.656838i	$-0.771893\pi$
$479$	4.19825	−	7.27159i	0.191823	−	0.332247i	0.945854	+	0.324591i	$0.105227\pi$
$480$		0			0
$481$	7.56565	−	4.36803i	0.344964	−	0.199165i
$482$	−21.6704			−0.987059
$483$		0			0
$484$	−39.4853			−1.79479
$485$	−4.09450	+	2.36396i	−0.185922	+	0.107342i
$486$		0			0
$487$	−4.72792	+	8.18900i	−0.214243	+	0.371079i	−0.953038	−	0.302851i	$-0.902062\pi$
$487$	−4.72792	+	8.18900i	−0.214243	+	0.371079i	0.738795	+	0.673930i	$0.235395\pi$
$488$	18.0021	+	31.1805i	0.814915	+	1.41147i
$489$		0			0
$490$		0			0
$491$			2.68629i			0.121231i	0.998161	+	0.0606153i	$0.0193063\pi$
$491$			2.68629i			0.121231i	−0.998161	+	0.0606153i	$0.980694\pi$
$492$		0			0
$493$	−5.85172	−	3.37849i	−0.263548	−	0.152160i
$494$	−47.7290	−	27.5563i	−2.14743	−	1.23982i
$495$		0			0
$496$			20.2710i			0.910193i
$497$		0			0
$498$		0			0
$499$	1.07107	+	1.85514i	0.0479476	+	0.0830476i	0.889003	−	0.457901i	$-0.151399\pi$
$499$	1.07107	+	1.85514i	0.0479476	+	0.0830476i	−0.841056	+	0.540949i	$0.818065\pi$
$500$	9.14594	−	15.8412i	0.409019	−	0.708442i
$501$		0			0
$502$	54.0854	−	31.2262i	2.41395	−	1.39369i
$503$	32.6256			1.45470			0.727352	−	0.686264i	$-0.240751\pi$
$503$	32.6256			1.45470			0.727352	+	0.686264i	$0.240751\pi$
$504$		0			0
$505$	43.6985			1.94456
$506$	3.46410	−	2.00000i	0.153998	−	0.0889108i
$507$		0			0
$508$	−0.928932	+	1.60896i	−0.0412147	+	0.0713860i
$509$	−18.4119	−	31.8904i	−0.816095	−	1.41352i	−0.908539	−	0.417799i	$-0.862801\pi$
$509$	−18.4119	−	31.8904i	−0.816095	−	1.41352i	0.0924447	−	0.995718i	$-0.470532\pi$
$510$		0			0
$511$		0			0
$512$			31.2426i			1.38074i
$513$		0			0
$514$	45.3078	+	26.1585i	1.99844	+	1.15380i
$515$	8.18900	+	4.72792i	0.360851	+	0.208337i
$516$		0			0
$517$		−	5.59767i		−	0.246185i
$518$		0			0
$519$		0			0
$520$	−25.1924	−	43.6345i	−1.10476	−	1.91350i
$521$	21.3805	−	37.0322i	0.936699	−	1.62241i	0.165122	−	0.986273i	$-0.447198\pi$
$521$	21.3805	−	37.0322i	0.936699	−	1.62241i	0.771576	−	0.636137i	$-0.219469\pi$
$522$		0			0
$523$	−15.1313	+	8.73606i	−0.661646	+	0.382001i	−0.792904	−	0.609347i	$-0.791432\pi$
$523$	−15.1313	+	8.73606i	−0.661646	+	0.382001i	0.131258	+	0.991348i	$0.458098\pi$
$524$	36.5838			1.59817
$525$		0			0
$526$	−58.2843			−2.54131
$527$	8.18900	−	4.72792i	0.356718	−	0.205952i
$528$		0			0
$529$	−9.50000	+	16.4545i	−0.413043	+	0.715412i
$530$	−28.8372	−	49.9476i	−1.25261	−	2.16958i
$531$		0			0
$532$		0			0
$533$		−	27.5563i		−	1.19360i
$534$		0			0
$535$	−27.2506	−	15.7331i	−1.17815	−	0.680203i
$536$	−32.4377	−	18.7279i	−1.40110	−	0.808923i
$537$		0			0
$538$			75.3867i			3.25015i
$539$		0			0
$540$		0			0
$541$	−9.48528	−	16.4290i	−0.407804	−	0.706337i	0.586839	−	0.809703i	$-0.300372\pi$
$541$	−9.48528	−	16.4290i	−0.407804	−	0.706337i	−0.994643	+	0.103366i	$0.967039\pi$
$542$	−8.15640	+	14.1273i	−0.350348	+	0.606820i
$543$		0			0
$544$	1.92186	−	1.10959i	0.0823992	−	0.0475732i
$545$	−8.73606			−0.374212
$546$		0			0
$547$	−26.6274			−1.13851			−0.569253	−	0.822162i	$-0.692768\pi$
$547$	−26.6274			−1.13851			−0.569253	+	0.822162i	$0.692768\pi$
$548$	−2.74666	+	1.58579i	−0.117332	+	0.0677414i
$549$		0			0
$550$	6.41421	−	11.1097i	0.273503	−	0.473721i
$551$	−16.3128	−	28.2546i	−0.694949	−	1.20369i
$552$		0			0
$553$		0			0
$554$			50.6274i			2.15095i
$555$		0			0
$556$	31.6825	+	18.2919i	1.34364	+	0.775749i
$557$	−9.16756	−	5.29289i	−0.388442	−	0.224267i	0.293043	−	0.956099i	$-0.405332\pi$
$557$	−9.16756	−	5.29289i	−0.388442	−	0.224267i	−0.681485	+	0.731832i	$0.738665\pi$
$558$		0			0
$559$			42.1814i			1.78408i
$560$		0			0
$561$		0			0
$562$	22.7279	+	39.3659i	0.958720	+	1.66055i
$563$	−1.39942	+	2.42386i	−0.0589784	+	0.102154i	−0.894007	−	0.448053i	$-0.852118\pi$
$563$	−1.39942	+	2.42386i	−0.0589784	+	0.102154i	0.835029	+	0.550206i	$0.185451\pi$
$564$		0			0
$565$	17.2611	−	9.96570i	0.726180	−	0.419260i
$566$	−72.0082			−3.02673
$567$		0			0
$568$	21.3137			0.894303
$569$	−21.7482	+	12.5563i	−0.911733	+	0.526390i	−0.880988	−	0.473138i	$-0.843121\pi$
$569$	−21.7482	+	12.5563i	−0.911733	+	0.526390i	−0.0307450	+	0.999527i	$0.509788\pi$
$570$		0			0
$571$	5.65685	−	9.79796i	0.236732	−	0.410032i	−0.723043	−	0.690803i	$-0.757257\pi$
$571$	5.65685	−	9.79796i	0.236732	−	0.410032i	0.959775	+	0.280772i	$0.0905903\pi$
$572$	−5.35757	−	9.27958i	−0.224011	−	0.387999i
$573$		0			0
$574$		0			0
$575$		−	12.8284i		−	0.534982i
$576$		0			0
$577$	11.9114	+	6.87704i	0.495877	+	0.286295i	0.727009	−	0.686628i	$-0.240910\pi$
$577$	11.9114	+	6.87704i	0.495877	+	0.286295i	−0.231132	+	0.972922i	$0.574243\pi$
$578$	−31.4486	−	18.1569i	−1.30809	−	0.755226i
$579$		0			0
$580$		−	62.4524i		−	2.59319i
$581$		0			0
$582$		0			0
$583$	−2.92893	−	5.07306i	−0.121304	−	0.210105i
$584$	3.08866	−	5.34972i	0.127810	−	0.221373i
$585$		0			0
$586$	−15.3392	+	8.85611i	−0.633658	+	0.365843i
$587$	−20.2710			−0.836672			−0.418336	−	0.908292i	$-0.637387\pi$
$587$	−20.2710			−0.836672			−0.418336	+	0.908292i	$0.637387\pi$
$588$		0			0
$589$	45.6569			1.88126
$590$	−47.7290	+	27.5563i	−1.96497	+	1.13448i
$591$		0			0
$592$	3.87868	−	6.71807i	0.159413	−	0.276111i
$593$	10.2555	+	17.7631i	0.421144	+	0.729443i	0.996052	−	0.0887754i	$-0.0282953\pi$
$593$	10.2555	+	17.7631i	0.421144	+	0.729443i	−0.574908	+	0.818218i	$0.694962\pi$
$594$		0			0
$595$		0			0
$596$			16.2426i			0.665324i
$597$		0			0
$598$	−14.1273	−	8.15640i	−0.577708	−	0.333540i
$599$	5.61642	+	3.24264i	0.229481	+	0.132491i	0.610332	−	0.792145i	$-0.291036\pi$
$599$	5.61642	+	3.24264i	0.229481	+	0.132491i	−0.380852	+	0.924636i	$0.624369\pi$
$600$		0			0
$601$		−	27.6076i		−	1.12614i	−0.826410	−	0.563069i	$-0.809621\pi$
$601$		−	27.6076i		−	1.12614i	0.826410	−	0.563069i	$-0.190379\pi$
$602$		0			0
$603$		0			0
$604$	−23.8995	−	41.3951i	−0.972457	−	1.68434i
$605$	−17.4224	+	30.1765i	−0.708321	+	1.22685i
$606$		0			0
$607$	−19.9790	+	11.5349i	−0.810924	+	0.468187i	−0.847277	−	0.531152i	$-0.821759\pi$
$607$	−19.9790	+	11.5349i	−0.810924	+	0.468187i	0.0363529	+	0.999339i	$0.488426\pi$
$608$	10.7151			0.434556
$609$		0			0
$610$	66.5269			2.69360
$611$	−19.7700	+	11.4142i	−0.799809	+	0.461770i
$612$		0			0
$613$	5.43503	−	9.41375i	0.219519	−	0.380218i	−0.735142	−	0.677913i	$-0.762885\pi$
$613$	5.43503	−	9.41375i	0.219519	−	0.380218i	0.954661	+	0.297695i	$0.0962180\pi$
$614$	14.9134	+	25.8307i	0.601855	+	1.04244i
$615$		0			0
$616$		0			0
$617$			30.4853i			1.22729i	0.789582	+	0.613646i	$0.210298\pi$
$617$			30.4853i			1.22729i	−0.789582	+	0.613646i	$0.789702\pi$
$618$		0			0
$619$	21.3989	+	12.3547i	0.860094	+	0.496576i	0.864044	−	0.503417i	$-0.167924\pi$
$619$	21.3989	+	12.3547i	0.860094	+	0.496576i	−0.00394972	+	0.999992i	$0.501257\pi$
$620$	75.6880	+	43.6985i	3.03970	+	1.75497i
$621$		0			0
$622$		−	25.8686i		−	1.03724i
$623$		0			0
$624$		0			0
$625$	7.96447	+	13.7949i	0.318579	+	0.551794i
$626$	15.6131	−	27.0427i	0.624025	−	1.08084i
$627$		0			0
$628$	−24.3248	+	14.0439i	−0.970663	+	0.560413i
$629$	−3.61859			−0.144283
$630$		0			0
$631$	−21.1716			−0.842827			−0.421414	−	0.906869i	$-0.638466\pi$
$631$	−21.1716			−0.842827			−0.421414	+	0.906869i	$0.638466\pi$
$632$	−36.9164	+	21.3137i	−1.46846	+	0.847814i
$633$		0			0
$634$	28.6777	−	49.6712i	1.13894	−	1.97269i
$635$	0.819760	+	1.41987i	0.0325312	+	0.0563456i
$636$		0			0
$637$		0			0
$638$		−	9.65685i		−	0.382319i
$639$		0			0
$640$	60.1450	+	34.7247i	2.37744	+	1.37262i
$641$	6.50794	+	3.75736i	0.257048	+	0.148407i	0.622987	−	0.782232i	$-0.285919\pi$
$641$	6.50794	+	3.75736i	0.257048	+	0.148407i	−0.365939	+	0.930639i	$0.619252\pi$
$642$		0			0
$643$		−	6.75699i		−	0.266469i	−0.991085	−	0.133235i	$-0.957464\pi$
$643$		−	6.75699i		−	0.266469i	0.991085	−	0.133235i	$-0.0425364\pi$
$644$		0			0
$645$		0			0
$646$	11.4142	+	19.7700i	0.449086	+	0.777840i
$647$	−12.9343	+	22.4029i	−0.508500	+	0.880748i	0.491451	+	0.870905i	$0.336467\pi$
$647$	−12.9343	+	22.4029i	−0.508500	+	0.880748i	−0.999952	+	0.00984331i	$0.996867\pi$
$648$		0			0
$649$	−4.84772	+	2.79884i	−0.190290	+	0.109864i
$650$	−52.3169			−2.05204
$651$		0			0
$652$	−56.7696			−2.22327
$653$	33.3292	−	19.2426i	1.30427	−	0.753023i	0.323140	−	0.946351i	$-0.395262\pi$
$653$	33.3292	−	19.2426i	1.30427	−	0.753023i	0.981134	+	0.193329i	$0.0619283\pi$
$654$		0			0
$655$	16.1421	−	27.9590i	0.630725	−	1.09245i
$656$	−12.2346	−	21.1910i	−0.477681	−	0.827368i
$657$		0			0
$658$		0			0
$659$			47.4558i			1.84862i	0.381646	+	0.924309i	$0.375357\pi$
$659$			47.4558i			1.84862i	−0.381646	+	0.924309i	$0.624643\pi$
$660$		0			0
$661$	6.35372	+	3.66832i	0.247131	+	0.142681i	0.618450	−	0.785824i	$-0.287761\pi$
$661$	6.35372	+	3.66832i	0.247131	+	0.142681i	−0.371319	+	0.928505i	$0.621094\pi$
$662$	21.6251	+	12.4853i	0.840485	+	0.485254i
$663$		0			0
$664$		−	59.6536i		−	2.31501i
$665$		0			0
$666$		0			0
$667$	−4.82843	−	8.36308i	−0.186957	−	0.323820i
$668$	5.35757	−	9.27958i	0.207291	−	0.359038i
$669$		0			0
$670$	−59.9371	+	34.6047i	−2.31557	+	1.33690i
$671$	6.75699			0.260851
$672$		0			0
$673$	−37.8995			−1.46092			−0.730459	−	0.682956i	$-0.760694\pi$
$673$	−37.8995			−1.46092			−0.730459	+	0.682956i	$0.760694\pi$
$674$	27.0314	−	15.6066i	1.04121	−	0.601144i
$675$		0			0
$676$	3.03553	−	5.25770i	0.116751	−	0.202219i
$677$	16.4329	+	28.4625i	0.631566	+	1.09390i	0.987232	+	0.159291i	$0.0509209\pi$
$677$	16.4329	+	28.4625i	0.631566	+	1.09390i	−0.355666	+	0.934613i	$0.615746\pi$
$678$		0			0
$679$		0			0
$680$			20.8701i			0.800330i
$681$		0			0
$682$	11.7034	+	6.75699i	0.448148	+	0.258738i
$683$	33.5754	+	19.3848i	1.28473	+	0.741738i	0.977709	−	0.209966i	$-0.0673352\pi$
$683$	33.5754	+	19.3848i	1.28473	+	0.741738i	0.307019	+	0.951703i	$0.400669\pi$
$684$		0			0
$685$			2.79884i			0.106938i
$686$		0			0
$687$		0			0
$688$	18.7279	+	32.4377i	0.713995	+	1.23668i
$689$	−11.9448	+	20.6890i	−0.455060	+	0.788187i
$690$		0			0
$691$	8.27558	−	4.77791i	0.314818	−	0.181760i	−0.334262	−	0.942480i	$-0.608487\pi$
$691$	8.27558	−	4.77791i	0.314818	−	0.181760i	0.649080	+	0.760720i	$0.275154\pi$
$692$	−31.2262			−1.18704
$693$		0			0
$694$	45.7990			1.73851
$695$	27.9590	−	16.1421i	1.06055	−	0.612306i
$696$		0			0
$697$	−5.70711	+	9.88500i	−0.216172	+	0.374421i
$698$	−7.45669	−	12.9154i	−0.282240	−	0.488854i
$699$		0			0
$700$		0			0
$701$			40.7696i			1.53984i	0.638138	+	0.769922i	$0.279705\pi$
$701$			40.7696i			1.53984i	−0.638138	+	0.769922i	$0.720295\pi$
$702$		0			0
$703$	−15.1313	−	8.73606i	−0.570688	−	0.329487i
$704$	7.05130	+	4.07107i	0.265756	+	0.153434i
$705$		0			0
$706$		−	57.0948i		−	2.14879i
$707$		0			0
$708$		0			0
$709$	16.3640	+	28.3432i	0.614561	+	1.06445i	0.990461	+	0.137791i	$0.0440003\pi$
$709$	16.3640	+	28.3432i	0.614561	+	1.06445i	−0.375900	+	0.926660i	$0.622666\pi$
$710$	19.6913	−	34.1063i	0.739001	−	1.27999i
$711$		0			0
$712$	23.6148	−	13.6340i	0.885003	−	0.510957i
$713$	13.5140			0.506102
$714$		0			0
$715$	−9.45584			−0.353629
$716$	−31.5462	+	18.2132i	−1.17894	+	0.680659i
$717$		0			0
$718$	−1.24264	+	2.15232i	−0.0463749	+	0.0803237i
$719$	6.75699	+	11.7034i	0.251993	+	0.436465i	0.964074	−	0.265632i	$-0.0855807\pi$
$719$	6.75699	+	11.7034i	0.251993	+	0.436465i	−0.712081	+	0.702097i	$0.752247\pi$
$720$		0			0
$721$		0			0
$722$			64.3553i			2.39506i
$723$		0			0
$724$	58.7251	+	33.9050i	2.18250	+	1.26007i
$725$	−26.8213	−	15.4853i	−0.996118	−	0.575109i
$726$		0			0
$727$			43.3407i			1.60742i	0.595022	+	0.803710i	$0.297143\pi$
$727$			43.3407i			1.60742i	−0.595022	+	0.803710i	$0.702857\pi$
$728$		0			0
$729$		0			0
$730$	−5.70711	−	9.88500i	−0.211229	−	0.365860i
$731$	8.73606	−	15.1313i	0.323115	−	0.559651i
$732$		0			0
$733$	20.1870	−	11.6549i	0.745622	−	0.430485i	−0.0784876	−	0.996915i	$-0.525009\pi$
$733$	20.1870	−	11.6549i	0.745622	−	0.430485i	0.824110	+	0.566430i	$0.191676\pi$
$734$	−9.55582			−0.352712
$735$		0			0
$736$	3.17157			0.116906
$737$	−6.08767	+	3.51472i	−0.224242	+	0.129466i
$738$		0			0
$739$	9.41421	−	16.3059i	0.346307	−	0.599822i	−0.639283	−	0.768972i	$-0.720769\pi$
$739$	9.41421	−	16.3059i	0.346307	−	0.599822i	0.985590	+	0.169149i	$0.0541021\pi$
$740$	−16.7227	−	28.9645i	−0.614738	−	1.06476i
$741$		0			0
$742$		0			0
$743$		−	52.4264i		−	1.92334i	−0.274212	−	0.961669i	$-0.588417\pi$
$743$		−	52.4264i		−	1.92334i	0.274212	−	0.961669i	$-0.411583\pi$
$744$		0			0
$745$	12.4134	+	7.16687i	0.454791	+	0.262574i
$746$	−47.3087	−	27.3137i	−1.73210	−	1.00003i
$747$		0			0
$748$			4.43835i			0.162282i
$749$		0			0
$750$		0			0
$751$	−10.3431	−	17.9149i	−0.377427	−	0.653722i	0.613260	−	0.789881i	$-0.289858\pi$
$751$	−10.3431	−	17.9149i	−0.377427	−	0.653722i	−0.990687	+	0.136159i	$0.956524\pi$
$752$	−10.1355	+	17.5552i	−0.369603	+	0.640171i
$753$		0			0
$754$	−34.1063	+	19.6913i	−1.24208	+	0.717115i
$755$	−42.1814			−1.53514
$756$		0			0
$757$	6.87006			0.249696			0.124848	−	0.992176i	$-0.460156\pi$
$757$	6.87006			0.249696			0.124848	+	0.992176i	$0.460156\pi$
$758$		0			0
$759$		0			0
$760$	−50.3848	+	87.2690i	−1.82765	+	3.16558i
$761$	0.289829	+	0.501998i	0.0105063	+	0.0181974i	0.871231	−	0.490874i	$-0.163322\pi$
$761$	0.289829	+	0.501998i	0.0105063	+	0.0181974i	−0.860724	+	0.509071i	$0.829989\pi$
$762$		0			0
$763$		0			0
$764$		−	79.7401i		−	2.88490i
$765$		0			0
$766$	−56.5092	−	32.6256i	−2.04176	−	1.17881i
$767$	19.7700	+	11.4142i	0.713853	+	0.412143i
$768$		0			0
$769$			45.8995i			1.65518i	0.561335	+	0.827589i	$0.310288\pi$
$769$			45.8995i			1.65518i	−0.561335	+	0.827589i	$0.689712\pi$
$770$		0			0
$771$		0			0
$772$	−33.7990	−	58.5416i	−1.21645	−	2.10696i
$773$	−9.43577	+	16.3432i	−0.339381	+	0.587825i	−0.984316	−	0.176412i	$-0.943551\pi$
$773$	−9.43577	+	16.3432i	−0.339381	+	0.587825i	0.644935	+	0.764237i	$0.276884\pi$
$774$		0			0
$775$	37.5342	−	21.6704i	1.34827	−	0.778423i
$776$	6.17733			0.221753
$777$		0			0
$778$	33.3137			1.19435
$779$	−47.7290	+	27.5563i	−1.71007	+	0.987309i
$780$		0			0
$781$	2.00000	−	3.46410i	0.0715656	−	0.123955i
$782$	3.37849	+	5.85172i	0.120815	+	0.209257i
$783$		0			0
$784$		0			0
$785$			24.7868i			0.884679i
$786$		0			0
$787$	−11.7034	−	6.75699i	−0.417183	−	0.240861i	0.276689	−	0.960960i	$-0.410763\pi$
$787$	−11.7034	−	6.75699i	−0.417183	−	0.240861i	−0.693871	+	0.720099i	$0.744096\pi$
$788$	−53.8527	−	31.0919i	−1.91842	−	1.10760i
$789$		0			0
$790$			78.7652i			2.80234i
$791$		0			0
$792$		0			0
$793$	−13.7782	−	23.8645i	−0.489277	−	0.847453i
$794$	32.9154	−	57.0112i	1.16813	−	2.02325i
$795$		0			0
$796$	−63.3649	+	36.5838i	−2.24591	+	1.29668i
$797$	−1.73897			−0.0615976			−0.0307988	−	0.999526i	$-0.509805\pi$
$797$	−1.73897			−0.0615976			−0.0307988	+	0.999526i	$0.509805\pi$
$798$		0			0
$799$	9.45584			0.334524
$800$	8.80884	−	5.08579i	0.311440	−	0.179810i
$801$		0			0
$802$	13.0711	−	22.6398i	0.461555	−	0.799437i
$803$	−0.579658	−	1.00400i	−0.0204557	−	0.0354303i
$804$		0			0
$805$		0			0
$806$		−	55.1127i		−	1.94126i
$807$		0			0
$808$	−49.4456	−	28.5474i	−1.73949	−	1.00429i
$809$	27.7489	+	16.0208i	0.975598	+	0.563262i	0.900938	−	0.433947i	$-0.142880\pi$
$809$	27.7489	+	16.0208i	0.975598	+	0.563262i	0.0746599	+	0.997209i	$0.476213\pi$
$810$		0			0
$811$		−	9.55582i		−	0.335550i	−0.985825	−	0.167775i	$-0.946342\pi$
$811$		−	9.55582i		−	0.335550i	0.985825	−	0.167775i	$-0.0536583\pi$
$812$		0			0
$813$		0			0
$814$	−2.58579	−	4.47871i	−0.0906318	−	0.156979i
$815$	−25.0489	+	43.3859i	−0.877424	+	1.51974i
$816$		0			0
$817$	73.0604	−	42.1814i	2.55606	−	1.47574i
$818$	42.7611			1.49511
$819$		0			0
$820$	−105.497			−3.68413
$821$	−27.9229	+	16.1213i	−0.974518	+	0.562638i	−0.900610	−	0.434627i	$-0.856880\pi$
$821$	−27.9229	+	16.1213i	−0.974518	+	0.562638i	−0.0739071	+	0.997265i	$0.523547\pi$
$822$		0			0
$823$	−12.9706	+	22.4657i	−0.452125	+	0.783104i	−0.998518	−	0.0544251i	$-0.982667\pi$
$823$	−12.9706	+	22.4657i	−0.452125	+	0.783104i	0.546392	+	0.837529i	$0.316001\pi$
$824$	−6.17733	−	10.6994i	−0.215197	−	0.372733i
$825$		0			0
$826$		0			0
$827$		−	28.3431i		−	0.985588i	−0.870146	−	0.492794i	$-0.835976\pi$
$827$		−	28.3431i		−	0.985588i	0.870146	−	0.492794i	$-0.164024\pi$
$828$		0			0
$829$	−30.1765	−	17.4224i	−1.04807	−	0.605105i	−0.125963	−	0.992035i	$-0.540202\pi$
$829$	−30.1765	−	17.4224i	−1.04807	−	0.605105i	−0.922109	+	0.386930i	$0.873535\pi$
$830$	−95.4580	−	55.1127i	−3.31340	−	1.91299i
$831$		0			0
$832$		−	33.2053i		−	1.15119i
$833$		0			0
$834$		0			0
$835$	−4.72792	−	8.18900i	−0.163616	−	0.283392i
$836$	−10.7151	+	18.5592i	−0.370591	+	0.641882i
$837$		0			0
$838$	74.0644	−	42.7611i	2.55851	−	1.47716i
$839$	−20.2710			−0.699831			−0.349916	−	0.936781i	$-0.613790\pi$
$839$	−20.2710			−0.699831			−0.349916	+	0.936781i	$0.613790\pi$
$840$		0			0
$841$	5.68629			0.196079
$842$	48.7436	−	28.1421i	1.67982	−	0.969842i
$843$		0			0
$844$	14.0000	−	24.2487i	0.481900	−	0.834675i
$845$	−2.67878	−	4.63979i	−0.0921530	−	0.159614i
$846$		0			0
$847$		0			0
$848$			21.2132i			0.728464i
$849$		0			0
$850$	18.7671	+	10.8352i	0.643706	+	0.371644i
$851$	−4.47871	−	2.58579i	−0.153528	−	0.0886396i
$852$		0			0
$853$		−	38.8029i		−	1.32859i	−0.747472	−	0.664294i	$-0.768732\pi$
$853$		−	38.8029i		−	1.32859i	0.747472	−	0.664294i	$-0.231268\pi$
$854$		0			0
$855$		0			0
$856$	20.5563	+	35.6046i	0.702602	+	1.21694i
$857$	9.84565	−	17.0532i	0.336321	−	0.582525i	−0.647417	−	0.762136i	$-0.724151\pi$
$857$	9.84565	−	17.0532i	0.336321	−	0.582525i	0.983738	+	0.179611i	$0.0574840\pi$
$858$		0			0
$859$	25.8307	−	14.9134i	0.881334	−	0.508838i	0.0102358	−	0.999948i	$-0.496742\pi$
$859$	25.8307	−	14.9134i	0.881334	−	0.508838i	0.871098	+	0.491109i	$0.163408\pi$
$860$	161.489			5.50671
$861$		0			0
$862$	37.3137			1.27091
$863$	28.8505	−	16.6569i	0.982083	−	0.567006i	0.0791847	−	0.996860i	$-0.474768\pi$
$863$	28.8505	−	16.6569i	0.982083	−	0.567006i	0.902898	+	0.429854i	$0.141435\pi$
$864$		0			0
$865$	−13.7782	+	23.8645i	−0.468472	+	0.811417i
$866$	9.84565	+	17.0532i	0.334569	+	0.579490i
$867$		0			0
$868$		0			0
$869$			8.00000i			0.271381i
$870$		0			0
$871$	24.8268	+	14.3337i	0.841222	+	0.485680i
$872$	9.88500	+	5.70711i	0.334748	+	0.193267i
$873$		0			0
$874$			32.6256i			1.10358i
$875$		0			0
$876$		0			0
$877$	−16.2635	−	28.1691i	−0.549178	−	0.951204i	−0.998331	−	0.0577493i	$-0.981608\pi$
$877$	−16.2635	−	28.1691i	−0.549178	−	0.951204i	0.449153	−	0.893455i	$-0.351726\pi$
$878$	34.6047	−	59.9371i	1.16785	−	2.02278i
$879$		0			0
$880$	−7.27159	+	4.19825i	−0.245125	+	0.141523i
$881$	20.5111			0.691035			0.345518	−	0.938412i	$-0.387703\pi$
$881$	20.5111			0.691035			0.345518	+	0.938412i	$0.387703\pi$
$882$		0			0
$883$	−37.4558			−1.26049			−0.630245	−	0.776397i	$-0.717045\pi$
$883$	−37.4558			−1.26049			−0.630245	+	0.776397i	$0.717045\pi$
$884$	15.6755	−	9.05025i	0.527224	−	0.304393i
$885$		0			0
$886$	−29.9706	+	51.9105i	−1.00688	+	1.74397i
$887$	−8.97616	−	15.5472i	−0.301390	−	0.522023i	0.675061	−	0.737762i	$-0.264117\pi$
$887$	−8.97616	−	15.5472i	−0.301390	−	0.522023i	−0.976451	+	0.215739i	$0.930784\pi$
$888$		0			0
$889$		0			0
$890$		−	50.3848i		−	1.68890i
$891$		0			0
$892$	−76.4882	−	44.1605i	−2.56102	−	1.47860i
$893$	39.5400	+	22.8284i	1.32316	+	0.763924i
$894$		0			0
$895$			32.1454i			1.07450i
$896$		0			0
$897$		0			0
$898$	29.2635	+	50.6858i	0.976534	+	1.69141i
$899$	16.3128	−	28.2546i	0.544063	−	0.942344i
$900$		0			0
$901$	8.56965	−	4.94769i	0.285496	−	0.164831i
$902$	−16.3128			−0.543157
$903$		0			0
$904$	−26.0416			−0.866132
$905$	51.8235	−	29.9203i	1.72267	−	0.994585i
$906$		0			0
$907$	22.3848	−	38.7716i	0.743274	−	1.28739i	−0.207722	−	0.978188i	$-0.566605\pi$
$907$	22.3848	−	38.7716i	0.743274	−	1.28739i	0.950997	−	0.309201i	$-0.100062\pi$
$908$	5.35757	+	9.27958i	0.177797	+	0.307954i
$909$		0			0
$910$		0			0
$911$		−	25.5147i		−	0.845340i	−0.906284	−	0.422670i	$-0.861093\pi$
$911$		−	25.5147i		−	0.845340i	0.906284	−	0.422670i	$-0.138907\pi$
$912$		0			0
$913$	−9.69545	−	5.59767i	−0.320873	−	0.185256i
$914$	59.8534	+	34.5563i	1.97977	+	1.14302i
$915$		0			0
$916$		−	46.3797i		−	1.53243i
$917$		0			0
$918$		0			0
$919$	−4.72792	−	8.18900i	−0.155960	−	0.270130i	0.777448	−	0.628947i	$-0.216514\pi$
$919$	−4.72792	−	8.18900i	−0.155960	−	0.270130i	−0.933408	+	0.358817i	$0.883180\pi$
$920$	−14.9134	+	25.8307i	−0.491680	+	0.851615i
$921$		0			0
$922$	−45.3078	+	26.1585i	−1.49213	+	0.861483i
$923$	−16.3128			−0.536943
$924$		0			0
$925$	−16.5858			−0.545337
$926$	−7.34847	+	4.24264i	−0.241486	+	0.139422i
$927$		0			0
$928$	3.82843	−	6.63103i	0.125674	−	0.217674i
$929$	9.84565	+	17.0532i	0.323025	+	0.559496i	0.981111	−	0.193447i	$-0.0619668\pi$
$929$	9.84565	+	17.0532i	0.323025	+	0.559496i	−0.658085	+	0.752943i	$0.728633\pi$
$930$		0			0
$931$		0			0
$932$		−	41.4558i		−	1.35793i
$933$		0			0
$934$	−5.85172	−	3.37849i	−0.191474	−	0.110548i
$935$	3.39200	+	1.95837i	0.110930	+	0.0640455i
$936$		0			0
$937$		−	1.73897i		−	0.0568098i	−0.999596	−	0.0284049i	$-0.990957\pi$
$937$		−	1.73897i		−	0.0568098i	0.999596	−	0.0284049i	$-0.00904277\pi$
$938$		0			0
$939$		0			0
$940$	43.6985	+	75.6880i	1.42529	+	2.46867i
$941$	−7.45669	+	12.9154i	−0.243081	+	0.421029i	−0.961590	−	0.274488i	$-0.911492\pi$
$941$	−7.45669	+	12.9154i	−0.243081	+	0.421029i	0.718509	+	0.695518i	$0.244825\pi$
$942$		0			0
$943$	−14.1273	+	8.15640i	−0.460048	+	0.265609i
$944$	20.2710			0.659763
$945$		0			0
$946$	24.9706			0.811863
$947$	−19.8931	+	11.4853i	−0.646439	+	0.373221i	−0.787090	−	0.616838i	$-0.788414\pi$
$947$	−19.8931	+	11.4853i	−0.646439	+	0.373221i	0.140652	+	0.990059i	$0.455080\pi$
$948$		0			0
$949$	−2.36396	+	4.09450i	−0.0767374	+	0.132913i
$950$	52.3169	+	90.6155i	1.69738	+	2.93996i
$951$		0			0
$952$		0			0
$953$			26.3848i			0.854687i	0.904089	+	0.427343i	$0.140550\pi$
$953$			26.3848i			0.854687i	−0.904089	+	0.427343i	$0.859450\pi$
$954$		0			0
$955$	−60.9411	−	35.1843i	−1.97201	−	1.13854i
$956$	1.13770	+	0.656854i	0.0367960	+	0.0212442i
$957$		0			0
$958$			20.2710i			0.654925i
$959$		0			0
$960$		0			0
$961$	7.32843	+	12.6932i	0.236401	+	0.409458i
$962$	−10.5454	+	18.2651i	−0.339996	+	0.588890i
$963$		0			0
$964$	29.7606	−	17.1823i	0.958525	−	0.553404i
$965$	−59.6536			−1.92032
$966$		0			0
$967$	43.1127			1.38641			0.693205	−	0.720740i	$-0.256198\pi$
$967$	43.1127			1.38641			0.693205	+	0.720740i	$0.256198\pi$
$968$	39.4275	−	22.7635i	1.26725	−	0.731645i
$969$		0			0
$970$	5.70711	−	9.88500i	0.183244	−	0.317388i
$971$	−16.3128	−	28.2546i	−0.523503	−	0.906734i	−0.999626	−	0.0273548i	$-0.991292\pi$
$971$	−16.3128	−	28.2546i	−0.523503	−	0.906734i	0.476123	−	0.879379i	$-0.342042\pi$
$972$		0			0
$973$		0			0
$974$		−	22.8284i		−	0.731470i
$975$		0			0
$976$	−21.1910	−	12.2346i	−0.678306	−	0.391620i
$977$	33.9236	+	19.5858i	1.08531	+	0.626605i	0.932324	−	0.361623i	$-0.117777\pi$
$977$	33.9236	+	19.5858i	1.08531	+	0.626605i	0.152987	+	0.988228i	$0.451111\pi$
$978$		0			0
$979$		−	5.11747i		−	0.163555i
$980$		0			0
$981$		0			0
$982$	−3.24264	−	5.61642i	−0.103477	−	0.179227i
$983$	−8.73606	+	15.1313i	−0.278637	+	0.482614i	−0.971046	−	0.238891i	$-0.923216\pi$
$983$	−8.73606	+	15.1313i	−0.278637	+	0.482614i	0.692409	+	0.721505i	$0.256549\pi$
$984$		0			0
$985$	−47.5237	+	27.4378i	−1.51423	+	0.874242i
$986$	16.3128			0.519506
$987$		0			0
$988$	87.3970			2.78047
$989$	21.6251	−	12.4853i	0.687639	−	0.397009i
$990$		0			0
$991$	−29.6985	+	51.4393i	−0.943403	+	1.63402i	−0.184487	+	0.982835i	$0.559062\pi$
$991$	−29.6985	+	51.4393i	−0.943403	+	1.63402i	−0.758917	+	0.651188i	$0.774271\pi$
$992$	5.35757	+	9.27958i	0.170103	+	0.294627i
$993$		0			0
$994$		0			0
$995$			64.5685i			2.04696i
$996$		0			0
$997$	10.1974	+	5.88750i	0.322956	+	0.186459i	0.652710	−	0.757608i	$-0.273632\pi$
$997$	10.1974	+	5.88750i	0.322956	+	0.186459i	−0.329753	+	0.944067i	$0.606966\pi$
$998$	−4.47871	−	2.58579i	−0.141771	−	0.0818516i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.p.c.80.1		16
3.2	odd	2	inner	441.2.p.c.80.8		16
7.2	even	3	inner	441.2.p.c.215.7		16
7.3	odd	6		441.2.c.b.440.1	✓	8
7.4	even	3		441.2.c.b.440.2	yes	8
7.5	odd	6	inner	441.2.p.c.215.8		16
7.6	odd	2	inner	441.2.p.c.80.2		16
21.2	odd	6	inner	441.2.p.c.215.2		16
21.5	even	6	inner	441.2.p.c.215.1		16
21.11	odd	6		441.2.c.b.440.7	yes	8
21.17	even	6		441.2.c.b.440.8	yes	8
21.20	even	2	inner	441.2.p.c.80.7		16
28.3	even	6		7056.2.k.g.881.2		8
28.11	odd	6		7056.2.k.g.881.8		8
84.11	even	6		7056.2.k.g.881.1		8
84.59	odd	6		7056.2.k.g.881.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.c.b.440.1	✓	8	7.3	odd	6
441.2.c.b.440.2	yes	8	7.4	even	3
441.2.c.b.440.7	yes	8	21.11	odd	6
441.2.c.b.440.8	yes	8	21.17	even	6
441.2.p.c.80.1		16	1.1	even	1	trivial
441.2.p.c.80.2		16	7.6	odd	2	inner
441.2.p.c.80.7		16	21.20	even	2	inner
441.2.p.c.80.8		16	3.2	odd	2	inner
441.2.p.c.215.1		16	21.5	even	6	inner
441.2.p.c.215.2		16	21.2	odd	6	inner
441.2.p.c.215.7		16	7.2	even	3	inner
441.2.p.c.215.8		16	7.5	odd	6	inner
7056.2.k.g.881.1		8	84.11	even	6
7056.2.k.g.881.2		8	28.3	even	6
7056.2.k.g.881.7		8	84.59	odd	6
7056.2.k.g.881.8		8	28.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.09077 + 1.20711i) q^{2} +(1.91421 - 3.31552i) q^{4} +(-1.68925 - 2.92586i) q^{5} +4.41421i q^{8} +O(q^{10})\)	\(q+(-2.09077 + 1.20711i) q^{2} +(1.91421 - 3.31552i) q^{4} +(-1.68925 - 2.92586i) q^{5} +4.41421i q^{8} +(7.06365 + 4.07820i) q^{10} +(0.717439 + 0.414214i) q^{11} -3.37849i q^{13} +(-1.50000 - 2.59808i) q^{16} +(-0.699709 + 1.21193i) q^{17} +(-5.85172 + 3.37849i) q^{19} -12.9343 q^{20} -2.00000 q^{22} +(-1.73205 + 1.00000i) q^{23} +(-3.20711 + 5.55487i) q^{25} +(4.07820 + 7.06365i) q^{26} +4.82843i q^{29} +(-5.85172 - 3.37849i) q^{31} +(-1.37333 - 0.792893i) q^{32} -3.37849i q^{34} +(1.29289 + 2.23936i) q^{37} +(8.15640 - 14.1273i) q^{38} +(12.9154 - 7.45669i) q^{40} +8.15640 q^{41} -12.4853 q^{43} +(2.74666 - 1.58579i) q^{44} +(2.41421 - 4.18154i) q^{46} +(-3.37849 - 5.85172i) q^{47} -15.4853i q^{50} +(-11.2014 - 6.46716i) q^{52} +(-6.12372 - 3.53553i) q^{53} -2.79884i q^{55} +(-5.82843 - 10.0951i) q^{58} +(-3.37849 + 5.85172i) q^{59} +(7.06365 - 4.07820i) q^{61} +16.3128 q^{62} +9.82843 q^{64} +(-9.88500 + 5.70711i) q^{65} +(-4.24264 + 7.34847i) q^{67} +(2.67878 + 4.63979i) q^{68} -4.82843i q^{71} +(-1.21193 - 0.699709i) q^{73} +(-5.40629 - 3.12132i) q^{74} +25.8686i q^{76} +(4.82843 + 8.36308i) q^{79} +(-5.06774 + 8.77758i) q^{80} +(-17.0532 + 9.84565i) q^{82} -13.5140 q^{83} +4.72792 q^{85} +(26.1039 - 15.0711i) q^{86} +(-1.82843 + 3.16693i) q^{88} +(-3.08866 - 5.34972i) q^{89} +7.65685i q^{92} +(14.1273 + 8.15640i) q^{94} +(19.7700 + 11.4142i) q^{95} -1.39942i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 16 * q + 8 * q^4	\( 16 q + 8 q^{4} - 24 q^{16} - 32 q^{22} - 40 q^{25} + 32 q^{37} - 64 q^{43} + 16 q^{46} - 48 q^{58} + 112 q^{64} + 32 q^{79} - 128 q^{85} + 16 q^{88}+O(q^{100}) \) 16 * q + 8 * q^4 - 24 * q^16 - 32 * q^22 - 40 * q^25 + 32 * q^37 - 64 * q^43 + 16 * q^46 - 48 * q^58 + 112 * q^64 + 32 * q^79 - 128 * q^85 + 16 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more