LMFDB - Embedded newform 441.2.p.c.215.6

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			215.6
Root			$-0.793353 - 0.608761i$ of defining polynomial
Character	$\chi$	$=$	441.215
Dual form			441.2.p.c.80.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.358719 + 0.207107i) q^{2} +(-0.914214 - 1.58346i) q^{4} +(1.46508 - 2.53759i) q^{5} -1.58579i q^{8} +O(q^{10})$	\(q+(0.358719 + 0.207107i) q^{2} +(-0.914214 - 1.58346i) q^{4} +(1.46508 - 2.53759i) q^{5} -1.58579i q^{8} +(1.05110 - 0.606854i) q^{10} +(-4.18154 + 2.41421i) q^{11} -2.93015i q^{13} +(-1.50000 + 2.59808i) q^{16} +(-3.53701 - 6.12627i) q^{17} +(5.07517 + 2.93015i) q^{19} -5.35757 q^{20} -2.00000 q^{22} +(-1.73205 - 1.00000i) q^{23} +(-1.79289 - 3.10538i) q^{25} +(0.606854 - 1.05110i) q^{26} +0.828427i q^{29} +(5.07517 - 2.93015i) q^{31} +(-3.82282 + 2.20711i) q^{32} -2.93015i q^{34} +(2.70711 - 4.68885i) q^{37} +(1.21371 + 2.10220i) q^{38} +(-4.02407 - 2.32330i) q^{40} +1.21371 q^{41} +4.48528 q^{43} +(7.64564 + 4.41421i) q^{44} +(-0.414214 - 0.717439i) q^{46} +(2.93015 - 5.07517i) q^{47} -1.48528i q^{50} +(-4.63979 + 2.67878i) q^{52} +(6.12372 - 3.53553i) q^{53} +14.1480i q^{55} +(-0.171573 + 0.297173i) q^{58} +(2.93015 + 5.07517i) q^{59} +(1.05110 + 0.606854i) q^{61} +2.42742 q^{62} +4.17157 q^{64} +(-7.43551 - 4.29289i) q^{65} +(4.24264 + 7.34847i) q^{67} +(-6.46716 + 11.2014i) q^{68} -0.828427i q^{71} +(-6.12627 + 3.53701i) q^{73} +(1.94218 - 1.12132i) q^{74} -10.7151i q^{76} +(-0.828427 + 1.43488i) q^{79} +(4.39523 + 7.61276i) q^{80} +(0.435381 + 0.251367i) q^{82} +11.7206 q^{83} -20.7279 q^{85} +(1.60896 + 0.928932i) q^{86} +(3.82843 + 6.63103i) q^{88} +(-5.60894 + 9.71496i) q^{89} +3.65685i q^{92} +(2.10220 - 1.21371i) q^{94} +(14.8710 - 8.58579i) q^{95} +7.07401i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.358719	+	0.207107i	0.253653	+	0.146447i	0.621436	−	0.783465i	$-0.286550\pi$
$2$	0.358719	+	0.207107i	0.253653	+	0.146447i	−0.367783	+	0.929912i	$0.619883\pi$
$3$		0			0
$3$		0			0
$4$	−0.914214	−	1.58346i	−0.457107	−	0.791732i
$5$	1.46508	−	2.53759i	0.655202	−	1.13484i	−0.326641	−	0.945148i	$-0.605917\pi$
$5$	1.46508	−	2.53759i	0.655202	−	1.13484i	0.981843	−	0.189694i	$-0.0607497\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	1.58579i		−	0.560660i
$9$		0			0
$10$	1.05110	−	0.606854i	0.332388	−	0.191904i
$11$	−4.18154	+	2.41421i	−1.26078	+	0.727913i	−0.973226	−	0.229851i	$-0.926176\pi$
$11$	−4.18154	+	2.41421i	−1.26078	+	0.727913i	−0.287556	+	0.957764i	$0.592843\pi$
$12$		0			0
$13$		−	2.93015i		−	0.812678i	−0.913722	−	0.406339i	$-0.866805\pi$
$13$		−	2.93015i		−	0.812678i	0.913722	−	0.406339i	$-0.133195\pi$
$14$		0			0
$15$		0			0
$16$	−1.50000	+	2.59808i	−0.375000	+	0.649519i
$17$	−3.53701	−	6.12627i	−0.857850	−	1.48584i	−0.873976	−	0.485970i	$-0.838467\pi$
$17$	−3.53701	−	6.12627i	−0.857850	−	1.48584i	0.0161259	−	0.999870i	$-0.494867\pi$
$18$		0			0
$19$	5.07517	+	2.93015i	1.16432	+	0.672223i	0.952336	−	0.305050i	$-0.0986730\pi$
$19$	5.07517	+	2.93015i	1.16432	+	0.672223i	0.211988	+	0.977272i	$0.432006\pi$
$20$	−5.35757			−1.19799
$21$		0			0
$22$	−2.00000			−0.426401
$23$	−1.73205	−	1.00000i	−0.361158	−	0.208514i	0.308431	−	0.951247i	$-0.400196\pi$
$23$	−1.73205	−	1.00000i	−0.361158	−	0.208514i	−0.669588	+	0.742732i	$0.733529\pi$
$24$		0			0
$25$	−1.79289	−	3.10538i	−0.358579	−	0.621076i
$26$	0.606854	−	1.05110i	0.119014	−	0.206138i
$27$		0			0
$28$		0			0
$29$			0.828427i			0.153835i	0.997037	+	0.0769175i	$0.0245078\pi$
$29$			0.828427i			0.153835i	−0.997037	+	0.0769175i	$0.975492\pi$
$30$		0			0
$31$	5.07517	−	2.93015i	0.911528	−	0.526271i	0.0306053	−	0.999532i	$-0.490257\pi$
$31$	5.07517	−	2.93015i	0.911528	−	0.526271i	0.880922	+	0.473261i	$0.156923\pi$
$32$	−3.82282	+	2.20711i	−0.675786	+	0.390165i
$33$		0			0
$34$		−	2.93015i		−	0.502517i
$35$		0			0
$36$		0			0
$37$	2.70711	−	4.68885i	0.445046	−	0.770842i	−0.553010	−	0.833175i	$-0.686521\pi$
$37$	2.70711	−	4.68885i	0.445046	−	0.770842i	0.998055	+	0.0623331i	$0.0198541\pi$
$38$	1.21371	+	2.10220i	0.196890	+	0.341023i
$39$		0			0
$40$	−4.02407	−	2.32330i	−0.636261	−	0.367346i
$41$	1.21371			0.189549			0.0947747	−	0.995499i	$-0.469787\pi$
$41$	1.21371			0.189549			0.0947747	+	0.995499i	$0.469787\pi$
$42$		0			0
$43$	4.48528			0.683999			0.341999	−	0.939700i	$-0.388896\pi$
$43$	4.48528			0.683999			0.341999	+	0.939700i	$0.388896\pi$
$44$	7.64564	+	4.41421i	1.15262	+	0.665468i
$45$		0			0
$46$	−0.414214	−	0.717439i	−0.0610725	−	0.105781i
$47$	2.93015	−	5.07517i	0.427406	−	0.740290i	−0.569235	−	0.822175i	$-0.692761\pi$
$47$	2.93015	−	5.07517i	0.427406	−	0.740290i	0.996642	+	0.0818849i	$0.0260940\pi$
$48$		0			0
$49$		0			0
$50$		−	1.48528i		−	0.210051i
$51$		0			0
$52$	−4.63979	+	2.67878i	−0.643423	+	0.371481i
$53$	6.12372	−	3.53553i	0.841158	−	0.485643i	−0.0164995	−	0.999864i	$-0.505252\pi$
$53$	6.12372	−	3.53553i	0.841158	−	0.485643i	0.857658	+	0.514221i	$0.171919\pi$
$54$		0			0
$55$			14.1480i			1.90772i
$56$		0			0
$57$		0			0
$58$	−0.171573	+	0.297173i	−0.0225286	+	0.0390207i
$59$	2.93015	+	5.07517i	0.381473	+	0.660731i	0.991273	−	0.131824i	$-0.0420835\pi$
$59$	2.93015	+	5.07517i	0.381473	+	0.660731i	−0.609800	+	0.792555i	$0.708750\pi$
$60$		0			0
$61$	1.05110	+	0.606854i	0.134580	+	0.0776997i	0.565778	−	0.824557i	$-0.308576\pi$
$61$	1.05110	+	0.606854i	0.134580	+	0.0776997i	−0.431198	+	0.902257i	$0.641909\pi$
$62$	2.42742			0.308282
$63$		0			0
$64$	4.17157			0.521447
$65$	−7.43551	−	4.29289i	−0.922261	−	0.532468i
$66$		0			0
$67$	4.24264	+	7.34847i	0.518321	+	0.897758i	0.999773	+	0.0212861i	$0.00677610\pi$
$67$	4.24264	+	7.34847i	0.518321	+	0.897758i	−0.481452	+	0.876472i	$0.659891\pi$
$68$	−6.46716	+	11.2014i	−0.784258	+	1.35837i
$69$		0			0
$70$		0			0
$71$		−	0.828427i		−	0.0983162i	−0.998791	−	0.0491581i	$-0.984346\pi$
$71$		−	0.828427i		−	0.0983162i	0.998791	−	0.0491581i	$-0.0156538\pi$
$72$		0			0
$73$	−6.12627	+	3.53701i	−0.717026	+	0.413975i	−0.813657	−	0.581345i	$-0.802527\pi$
$73$	−6.12627	+	3.53701i	−0.717026	+	0.413975i	0.0966311	+	0.995320i	$0.469193\pi$
$74$	1.94218	−	1.12132i	0.225774	−	0.130351i
$75$		0			0
$76$		−	10.7151i		−	1.22911i
$77$		0			0
$78$		0			0
$79$	−0.828427	+	1.43488i	−0.0932053	+	0.161436i	−0.908858	−	0.417105i	$-0.863045\pi$
$79$	−0.828427	+	1.43488i	−0.0932053	+	0.161436i	0.815653	+	0.578542i	$0.196378\pi$
$80$	4.39523	+	7.61276i	0.491401	+	0.851132i
$81$		0			0
$82$	0.435381	+	0.251367i	0.0480798	+	0.0277589i
$83$	11.7206			1.28650			0.643252	−	0.765655i	$-0.277585\pi$
$83$	11.7206			1.28650			0.643252	+	0.765655i	$0.277585\pi$
$84$		0			0
$85$	−20.7279			−2.24826
$86$	1.60896	+	0.928932i	0.173498	+	0.100169i
$87$		0			0
$88$	3.82843	+	6.63103i	0.408112	+	0.706870i
$89$	−5.60894	+	9.71496i	−0.594546	+	1.02978i	0.399065	+	0.916923i	$0.369335\pi$
$89$	−5.60894	+	9.71496i	−0.594546	+	1.02978i	−0.993611	+	0.112861i	$0.963998\pi$
$90$		0			0
$91$		0			0
$92$			3.65685i			0.381253i
$93$		0			0
$94$	2.10220	−	1.21371i	0.216826	−	0.125184i
$95$	14.8710	−	8.58579i	1.52573	−	0.880883i
$96$		0			0
$97$			7.07401i			0.718257i	0.933288	+	0.359128i	$0.116926\pi$
$97$			7.07401i			0.718257i	−0.933288	+	0.359128i	$0.883074\pi$
$98$		0			0
$99$		0			0
$100$	−3.27817	+	5.67796i	−0.327817	+	0.567796i
$101$	−2.67878	−	4.63979i	−0.266549	−	0.461676i	0.701419	−	0.712749i	$-0.252550\pi$
$101$	−2.67878	−	4.63979i	−0.266549	−	0.461676i	−0.967968	+	0.251073i	$0.919217\pi$
$102$		0			0
$103$	−12.2525	−	7.07401i	−1.20728	−	0.697023i	−0.245115	−	0.969494i	$-0.578826\pi$
$103$	−12.2525	−	7.07401i	−1.20728	−	0.697023i	−0.962164	+	0.272471i	$0.912159\pi$
$104$	−4.64659			−0.455636
$105$		0			0
$106$	2.92893			0.284483
$107$	−11.5300	−	6.65685i	−1.11465	−	0.643542i	−0.174619	−	0.984636i	$-0.555869\pi$
$107$	−11.5300	−	6.65685i	−1.11465	−	0.643542i	−0.940029	+	0.341094i	$0.889203\pi$
$108$		0			0
$109$	2.70711	+	4.68885i	0.259294	+	0.449110i	0.966053	−	0.258344i	$-0.0831769\pi$
$109$	2.70711	+	4.68885i	0.259294	+	0.449110i	−0.706759	+	0.707454i	$0.749844\pi$
$110$	−2.93015	+	5.07517i	−0.279379	+	0.483899i
$111$		0			0
$112$		0			0
$113$			13.8995i			1.30755i	0.756687	+	0.653777i	$0.226817\pi$
$113$			13.8995i			1.30755i	−0.756687	+	0.653777i	$0.773183\pi$
$114$		0			0
$115$	−5.07517	+	2.93015i	−0.473262	+	0.273238i
$116$	1.31178	−	0.757359i	0.121796	−	0.0703190i
$117$		0			0
$118$			2.42742i			0.223462i
$119$		0			0
$120$		0			0
$121$	6.15685	−	10.6640i	0.559714	−	0.969453i
$122$	0.251367	+	0.435381i	0.0227577	+	0.0394175i
$123$		0			0
$124$	−9.27958	−	5.35757i	−0.833331	−	0.481124i
$125$	4.14386			0.370638
$126$		0			0
$127$	16.4853			1.46283			0.731416	−	0.681931i	$-0.238860\pi$
$127$	16.4853			1.46283			0.731416	+	0.681931i	$0.238860\pi$
$128$	9.14207	+	5.27817i	0.808052	+	0.466529i
$129$		0			0
$130$	−1.77817	−	3.07989i	−0.155956	−	0.270124i
$131$	4.14386	−	7.17738i	0.362051	−	0.627090i	−0.626248	−	0.779624i	$-0.715410\pi$
$131$	4.14386	−	7.17738i	0.362051	−	0.627090i	0.988298	+	0.152534i	$0.0487434\pi$
$132$		0			0
$133$		0			0
$134$			3.51472i			0.303625i
$135$		0			0
$136$	−9.71496	+	5.60894i	−0.833051	+	0.480962i
$137$	4.18154	−	2.41421i	0.357253	−	0.206260i	−0.310622	−	0.950534i	$-0.600537\pi$
$137$	4.18154	−	2.41421i	0.357253	−	0.206260i	0.667875	+	0.744273i	$0.267204\pi$
$138$		0			0
$139$		−	8.28772i		−	0.702955i	−0.936196	−	0.351478i	$-0.885679\pi$
$139$		−	8.28772i		−	0.702955i	0.936196	−	0.351478i	$-0.114321\pi$
$140$		0			0
$141$		0			0
$142$	0.171573	−	0.297173i	0.0143981	−	0.0249382i
$143$	7.07401	+	12.2525i	0.591559	+	1.02461i
$144$		0			0
$145$	2.10220	+	1.21371i	0.174579	+	0.100793i
$146$	−2.93015			−0.242501
$147$		0			0
$148$	−9.89949			−0.813733
$149$	3.67423	+	2.12132i	0.301005	+	0.173785i	0.642894	−	0.765955i	$-0.277733\pi$
$149$	3.67423	+	2.12132i	0.301005	+	0.173785i	−0.341889	+	0.939740i	$0.611067\pi$
$150$		0			0
$151$	−2.24264	−	3.88437i	−0.182504	−	0.316105i	0.760229	−	0.649655i	$-0.225087\pi$
$151$	−2.24264	−	3.88437i	−0.182504	−	0.316105i	−0.942732	+	0.333550i	$0.891753\pi$
$152$	4.64659	−	8.04814i	0.376889	−	0.652790i
$153$		0			0
$154$		0			0
$155$		−	17.1716i		−	1.37925i
$156$		0			0
$157$	19.8653	−	11.4692i	1.58542	−	0.915345i	0.591376	−	0.806396i	$-0.298585\pi$
$157$	19.8653	−	11.4692i	1.58542	−	0.915345i	0.994047	−	0.108949i	$-0.0347486\pi$
$158$	−0.594346	+	0.343146i	−0.0472836	+	0.0272992i
$159$		0			0
$160$			12.9343i			1.02255i
$161$		0			0
$162$		0			0
$163$	−4.58579	+	7.94282i	−0.359187	+	0.622129i	−0.987825	−	0.155568i	$-0.950279\pi$
$163$	−4.58579	+	7.94282i	−0.359187	+	0.622129i	0.628639	+	0.777698i	$0.283612\pi$
$164$	−1.10959	−	1.92186i	−0.0866443	−	0.150072i
$165$		0			0
$166$	4.20441	+	2.42742i	0.326325	+	0.188404i
$167$	14.1480			1.09481			0.547403	−	0.836869i	$-0.315616\pi$
$167$	14.1480			1.09481			0.547403	+	0.836869i	$0.315616\pi$
$168$		0			0
$169$	4.41421			0.339555
$170$	−7.43551	−	4.29289i	−0.570278	−	0.329250i
$171$		0			0
$172$	−4.10051	−	7.10228i	−0.312661	−	0.541544i
$173$	−0.606854	+	1.05110i	−0.0461383	+	0.0799138i	−0.888172	−	0.459511i	$-0.848025\pi$
$173$	−0.606854	+	1.05110i	−0.0461383	+	0.0799138i	0.842034	+	0.539424i	$0.181358\pi$
$174$		0			0
$175$		0			0
$176$		−	14.4853i		−	1.09187i
$177$		0			0
$178$	−4.02407	+	2.32330i	−0.301617	+	0.174138i
$179$	−22.9369	+	13.2426i	−1.71439	+	0.989801i	−0.785966	+	0.618269i	$0.787834\pi$
$179$	−22.9369	+	13.2426i	−1.71439	+	0.989801i	−0.928420	+	0.371532i	$0.878833\pi$
$180$		0			0
$181$		−	9.50143i		−	0.706236i	−0.935579	−	0.353118i	$-0.885121\pi$
$181$		−	9.50143i		−	0.706236i	0.935579	−	0.353118i	$-0.114879\pi$
$182$		0			0
$183$		0			0
$184$	−1.58579	+	2.74666i	−0.116906	+	0.202487i
$185$	−7.93223	−	13.7390i	−0.583189	−	1.01011i
$186$		0			0
$187$	29.5803	+	17.0782i	2.16312	+	1.24888i
$188$	−10.7151			−0.781482
$189$		0			0
$190$	7.11270			0.516009
$191$	13.1390	+	7.58579i	0.950702	+	0.548888i	0.893299	−	0.449463i	$-0.148385\pi$
$191$	13.1390	+	7.58579i	0.950702	+	0.548888i	0.0574033	+	0.998351i	$0.481718\pi$
$192$		0			0
$193$	3.17157	+	5.49333i	0.228295	+	0.395418i	0.957303	−	0.289087i	$-0.0933517\pi$
$193$	3.17157	+	5.49333i	0.228295	+	0.395418i	−0.729008	+	0.684505i	$0.760018\pi$
$194$	−1.46508	+	2.53759i	−0.105186	+	0.182188i
$195$		0			0
$196$		0			0
$197$			7.75736i			0.552689i	0.961059	+	0.276344i	$0.0891231\pi$
$197$			7.75736i			0.552689i	−0.961059	+	0.276344i	$0.910877\pi$
$198$		0			0
$199$	−14.3548	+	8.28772i	−1.01758	+	0.587501i	−0.913402	−	0.407058i	$-0.866555\pi$
$199$	−14.3548	+	8.28772i	−1.01758	+	0.587501i	−0.104179	+	0.994559i	$0.533221\pi$
$200$	−4.92447	+	2.84315i	−0.348213	+	0.201041i
$201$		0			0
$202$		−	2.21918i		−	0.156141i
$203$		0			0
$204$		0			0
$205$	1.77817	−	3.07989i	0.124193	−	0.215109i
$206$	−2.93015	−	5.07517i	−0.204153	−	0.353604i
$207$		0			0
$208$	7.61276	+	4.39523i	0.527850	+	0.304754i
$209$	−28.2960			−1.95728
$210$		0			0
$211$	−15.3137			−1.05424			−0.527120	−	0.849791i	$-0.676728\pi$
$211$	−15.3137			−1.05424			−0.527120	+	0.849791i	$0.676728\pi$
$212$	−11.1968	−	6.46447i	−0.768998	−	0.443981i
$213$		0			0
$214$	−2.75736	−	4.77589i	−0.188489	−	0.326473i
$215$	6.57128	−	11.3818i	0.448157	−	0.776231i
$216$		0			0
$217$		0			0
$218$			2.24264i			0.151891i
$219$		0			0
$220$	22.4029	−	12.9343i	1.51040	−	0.872031i
$221$	−17.9509	+	10.3640i	−1.20751	+	0.697155i
$222$		0			0
$223$		−	3.43289i		−	0.229883i	−0.993372	−	0.114942i	$-0.963332\pi$
$223$		−	3.43289i		−	0.229883i	0.993372	−	0.114942i	$-0.0366681\pi$
$224$		0			0
$225$		0			0
$226$	−2.87868	+	4.98602i	−0.191487	+	0.331665i
$227$	−7.07401	−	12.2525i	−0.469519	−	0.813230i	0.529874	−	0.848076i	$-0.322239\pi$
$227$	−7.07401	−	12.2525i	−0.469519	−	0.813230i	−0.999393	+	0.0348463i	$0.988906\pi$
$228$		0			0
$229$	−16.2766	−	9.39731i	−1.07559	−	0.620992i	−0.145886	−	0.989301i	$-0.546603\pi$
$229$	−16.2766	−	9.39731i	−1.07559	−	0.620992i	−0.929703	+	0.368310i	$0.879937\pi$
$230$	−2.42742			−0.160059
$231$		0			0
$232$	1.31371			0.0862492
$233$	4.47871	+	2.58579i	0.293410	+	0.169401i	0.639479	−	0.768809i	$-0.279150\pi$
$233$	4.47871	+	2.58579i	0.293410	+	0.169401i	−0.346069	+	0.938209i	$0.612484\pi$
$234$		0			0
$235$	−8.58579	−	14.8710i	−0.560075	−	0.970078i
$236$	5.35757	−	9.27958i	0.348748	−	0.604049i
$237$		0			0
$238$		0			0
$239$		−	11.6569i		−	0.754019i	−0.926209	−	0.377010i	$-0.876952\pi$
$239$		−	11.6569i		−	0.754019i	0.926209	−	0.377010i	$-0.123048\pi$
$240$		0			0
$241$	21.9675	−	12.6829i	1.41505	−	0.816980i	0.419193	−	0.907897i	$-0.362313\pi$
$241$	21.9675	−	12.6829i	1.41505	−	0.816980i	0.995858	+	0.0909167i	$0.0289797\pi$
$242$	4.41717	−	2.55025i	0.283946	−	0.163936i
$243$		0			0
$244$		−	2.21918i		−	0.142068i
$245$		0			0
$246$		0			0
$247$	8.58579	−	14.8710i	0.546301	−	0.946220i
$248$	−4.64659	−	8.04814i	−0.295059	−	0.511057i
$249$		0			0
$250$	1.48648	+	0.858221i	0.0940134	+	0.0542787i
$251$	−10.7151			−0.676333			−0.338167	−	0.941086i	$-0.609807\pi$
$251$	−10.7151			−0.676333			−0.338167	+	0.941086i	$0.609807\pi$
$252$		0			0
$253$	9.65685			0.607121
$254$	5.91359	+	3.41421i	0.371052	+	0.214227i
$255$		0			0
$256$	−1.98528	−	3.43861i	−0.124080	−	0.214913i
$257$	5.25345	−	9.09924i	0.327701	−	0.567595i	−0.654354	−	0.756188i	$-0.727059\pi$
$257$	5.25345	−	9.09924i	0.327701	−	0.567595i	0.982055	+	0.188593i	$0.0603928\pi$
$258$		0			0
$259$		0			0
$260$			15.6985i			0.973579i
$261$		0			0
$262$	2.97297	−	1.71644i	0.183670	−	0.106042i
$263$	−3.58719	+	2.07107i	−0.221196	+	0.127708i	−0.606504	−	0.795081i	$-0.707429\pi$
$263$	−3.58719	+	2.07107i	−0.221196	+	0.127708i	0.385308	+	0.922788i	$0.374095\pi$
$264$		0			0
$265$		−	20.7193i		−	1.27278i
$266$		0			0
$267$		0			0
$268$	7.75736	−	13.4361i	0.473856	−	0.820743i
$269$	−1.10959	−	1.92186i	−0.0676528	−	0.117178i	0.830215	−	0.557444i	$-0.188218\pi$
$269$	−1.10959	−	1.92186i	−0.0676528	−	0.117178i	−0.897868	+	0.440265i	$0.854884\pi$
$270$		0			0
$271$	−5.07517	−	2.93015i	−0.308295	−	0.177994i	0.337868	−	0.941193i	$-0.390294\pi$
$271$	−5.07517	−	2.93015i	−0.308295	−	0.177994i	−0.646163	+	0.763199i	$0.723627\pi$
$272$	21.2220			1.28677
$273$		0			0
$274$	2.00000			0.120824
$275$	14.9941	+	8.65685i	0.904179	+	0.522028i
$276$		0			0
$277$	−6.48528	−	11.2328i	−0.389663	−	0.674916i	0.602741	−	0.797937i	$-0.294075\pi$
$277$	−6.48528	−	11.2328i	−0.389663	−	0.674916i	−0.992404	+	0.123021i	$0.960742\pi$
$278$	1.71644	−	2.97297i	0.102945	−	0.178307i
$279$		0			0
$280$		0			0
$281$			13.1716i			0.785750i	0.919592	+	0.392875i	$0.128520\pi$
$281$			13.1716i			0.785750i	−0.919592	+	0.392875i	$0.871480\pi$
$282$		0			0
$283$	−8.04814	+	4.64659i	−0.478412	+	0.276211i	−0.719755	−	0.694229i	$-0.755746\pi$
$283$	−8.04814	+	4.64659i	−0.478412	+	0.276211i	0.241342	+	0.970440i	$0.422412\pi$
$284$	−1.31178	+	0.757359i	−0.0778401	+	0.0449410i
$285$		0			0
$286$			5.86030i			0.346527i
$287$		0			0
$288$		0			0
$289$	−16.5208	+	28.6149i	−0.971813	+	1.68323i
$290$	0.502734	+	0.870762i	0.0295216	+	0.0511329i
$291$		0			0
$292$	11.2014	+	6.46716i	0.655515	+	0.378462i
$293$	−22.9385			−1.34008			−0.670040	−	0.742325i	$-0.733723\pi$
$293$	−22.9385			−1.34008			−0.670040	+	0.742325i	$0.733723\pi$
$294$		0			0
$295$	17.1716			0.999768
$296$	−7.43551	−	4.29289i	−0.432180	−	0.249519i
$297$		0			0
$298$	0.878680	+	1.52192i	0.0509005	+	0.0881623i
$299$	−2.93015	+	5.07517i	−0.169455	+	0.293505i
$300$		0			0
$301$		0			0
$302$		−	1.85786i		−	0.106908i
$303$		0			0
$304$	−15.2255	+	8.79045i	−0.873243	+	0.504167i
$305$	3.07989	−	1.77817i	0.176354	−	0.101818i
$306$		0			0
$307$			22.4357i			1.28048i	0.768177	+	0.640238i	$0.221164\pi$
$307$			22.4357i			1.28048i	−0.768177	+	0.640238i	$0.778836\pi$
$308$		0			0
$309$		0			0
$310$	3.55635	−	6.15978i	0.201987	−	0.349852i
$311$	12.9343	+	22.4029i	0.733438	+	1.27035i	0.955405	+	0.295297i	$0.0954187\pi$
$311$	12.9343	+	22.4029i	0.733438	+	1.27035i	−0.221968	+	0.975054i	$0.571248\pi$
$312$		0			0
$313$	−4.63979	−	2.67878i	−0.262256	−	0.151414i	0.363107	−	0.931747i	$-0.381716\pi$
$313$	−4.63979	−	2.67878i	−0.262256	−	0.151414i	−0.625363	+	0.780334i	$0.715049\pi$
$314$	9.50143			0.536197
$315$		0			0
$316$	3.02944			0.170419
$317$	−27.9229	−	16.1213i	−1.56831	−	0.905464i	−0.996366	−	0.0851698i	$-0.972857\pi$
$317$	−27.9229	−	16.1213i	−1.56831	−	0.905464i	−0.571942	−	0.820294i	$-0.693810\pi$
$318$		0			0
$319$	−2.00000	−	3.46410i	−0.111979	−	0.193952i
$320$	6.11167	−	10.5857i	0.341653	−	0.591760i
$321$		0			0
$322$		0			0
$323$		−	41.4558i		−	2.30666i
$324$		0			0
$325$	−9.09924	+	5.25345i	−0.504735	+	0.291409i
$326$	−3.29002	+	1.89949i	−0.182217	+	0.105203i
$327$		0			0
$328$		−	1.92468i		−	0.106273i
$329$		0			0
$330$		0			0
$331$	−10.8284	+	18.7554i	−0.595184	+	1.03089i	0.398337	+	0.917239i	$0.369588\pi$
$331$	−10.8284	+	18.7554i	−0.595184	+	1.03089i	−0.993521	+	0.113650i	$0.963746\pi$
$332$	−10.7151	−	18.5592i	−0.588069	−	1.01857i
$333$		0			0
$334$	5.07517	+	2.93015i	0.277701	+	0.160331i
$335$	24.8632			1.35842
$336$		0			0
$337$	−27.0711			−1.47466			−0.737328	−	0.675535i	$-0.763913\pi$
$337$	−27.0711			−1.47466			−0.737328	+	0.675535i	$0.763913\pi$
$338$	1.58346	+	0.914214i	0.0861291	+	0.0497267i
$339$		0			0
$340$	18.9497	+	32.8219i	1.02769	+	1.78002i
$341$	−14.1480	+	24.5051i	−0.766158	+	1.32703i
$342$		0			0
$343$		0			0
$344$		−	7.11270i		−	0.383491i
$345$		0			0
$346$	−0.435381	+	0.251367i	−0.0234062	+	0.0135136i
$347$	12.9649	−	7.48528i	0.695992	−	0.401831i	−0.109861	−	0.993947i	$-0.535041\pi$
$347$	12.9649	−	7.48528i	0.695992	−	0.401831i	0.805853	+	0.592116i	$0.201707\pi$
$348$		0			0
$349$		−	11.2179i		−	0.600479i	−0.953864	−	0.300239i	$-0.902933\pi$
$349$		−	11.2179i		−	0.600479i	0.953864	−	0.300239i	$-0.0970666\pi$
$350$		0			0
$351$		0			0
$352$	10.6569	−	18.4582i	0.568012	−	0.983826i
$353$	10.2555	+	17.7631i	0.545847	+	0.945434i	0.998553	+	0.0537746i	$0.0171253\pi$
$353$	10.2555	+	17.7631i	0.545847	+	0.945434i	−0.452706	+	0.891660i	$0.649541\pi$
$354$		0			0
$355$	−2.10220	−	1.21371i	−0.111573	−	0.0644170i
$356$	20.5111			1.08708
$357$		0			0
$358$	−10.9706			−0.579812
$359$	30.2854	+	17.4853i	1.59840	+	0.922838i	0.991795	+	0.127836i	$0.0408030\pi$
$359$	30.2854	+	17.4853i	1.59840	+	0.922838i	0.606607	+	0.795002i	$0.292530\pi$
$360$		0			0
$361$	7.67157	+	13.2876i	0.403767	+	0.699345i
$362$	1.96781	−	3.40835i	0.103426	−	0.179139i
$363$		0			0
$364$		0			0
$365$			20.7279i			1.08495i
$366$		0			0
$367$	−17.3277	+	10.0042i	−0.904499	+	0.522213i	−0.878657	−	0.477453i	$-0.841560\pi$
$367$	−17.3277	+	10.0042i	−0.904499	+	0.522213i	−0.0258422	+	0.999666i	$0.508227\pi$
$368$	5.19615	−	3.00000i	0.270868	−	0.156386i
$369$		0			0
$370$		−	6.57128i		−	0.341624i
$371$		0			0
$372$		0			0
$373$	−11.3137	+	19.5959i	−0.585802	+	1.01464i	0.408973	+	0.912546i	$0.365887\pi$
$373$	−11.3137	+	19.5959i	−0.585802	+	1.01464i	−0.994775	+	0.102092i	$0.967446\pi$
$374$	7.07401	+	12.2525i	0.365788	+	0.633564i
$375$		0			0
$376$	−8.04814	−	4.64659i	−0.415051	−	0.239630i
$377$	2.42742			0.125018
$378$		0			0
$379$		0			0			−	1.00000i	$-0.5\pi$
$379$		0			0				1.00000i	$0.5\pi$
$380$	−27.1906	−	15.6985i	−1.39485	−	0.805315i
$381$		0			0
$382$	3.14214	+	5.44234i	0.160766	+	0.278454i
$383$	−11.7206	+	20.3007i	−0.598895	+	1.03732i	0.394090	+	0.919072i	$0.371060\pi$
$383$	−11.7206	+	20.3007i	−0.598895	+	1.03732i	−0.992985	+	0.118244i	$0.962273\pi$
$384$		0			0
$385$		0			0
$386$			2.62742i			0.133732i
$387$		0			0
$388$	11.2014	−	6.46716i	0.568667	−	0.328320i
$389$	22.3426	−	12.8995i	1.13281	−	0.654030i	0.188173	−	0.982136i	$-0.439744\pi$
$389$	22.3426	−	12.8995i	1.13281	−	0.654030i	0.944641	+	0.328106i	$0.106410\pi$
$390$		0			0
$391$			14.1480i			0.715496i
$392$		0			0
$393$		0			0
$394$	−1.60660	+	2.78272i	−0.0809394	+	0.140191i
$395$	2.42742	+	4.20441i	0.122137	+	0.211547i
$396$		0			0
$397$	−15.4059	−	8.89457i	−0.773198	−	0.446406i	0.0608165	−	0.998149i	$-0.480630\pi$
$397$	−15.4059	−	8.89457i	−0.773198	−	0.446406i	−0.834014	+	0.551743i	$0.813963\pi$
$398$	−6.86577			−0.344150
$399$		0			0
$400$	10.7574			0.537868
$401$	−4.47871	−	2.58579i	−0.223656	−	0.129128i	0.383986	−	0.923339i	$-0.374551\pi$
$401$	−4.47871	−	2.58579i	−0.223656	−	0.129128i	−0.607642	+	0.794211i	$0.707884\pi$
$402$		0			0
$403$	−8.58579	−	14.8710i	−0.427688	−	0.740778i
$404$	−4.89796	+	8.48352i	−0.243683	+	0.422071i
$405$		0			0
$406$		0			0
$407$			26.1421i			1.29582i
$408$		0			0
$409$	−8.22848	+	4.75071i	−0.406872	+	0.234908i	−0.689445	−	0.724338i	$-0.742145\pi$
$409$	−8.22848	+	4.75071i	−0.406872	+	0.234908i	0.282573	+	0.959246i	$0.408812\pi$
$410$	1.27573	−	0.736544i	0.0630039	−	0.0363753i
$411$		0			0
$412$			25.8686i			1.27446i
$413$		0			0
$414$		0			0
$415$	17.1716	−	29.7420i	0.842919	−	1.45998i
$416$	6.46716	+	11.2014i	0.317078	+	0.549196i
$417$		0			0
$418$	−10.1503	−	5.86030i	−0.496469	−	0.286637i
$419$	−19.0029			−0.928350			−0.464175	−	0.885743i	$-0.653649\pi$
$419$	−19.0029			−0.928350			−0.464175	+	0.885743i	$0.653649\pi$
$420$		0			0
$421$	−0.686292			−0.0334478			−0.0167239	−	0.999860i	$-0.505324\pi$
$421$	−0.686292			−0.0334478			−0.0167239	+	0.999860i	$0.505324\pi$
$422$	−5.49333	−	3.17157i	−0.267411	−	0.154390i
$423$		0			0
$424$	−5.60660	−	9.71092i	−0.272281	−	0.471604i
$425$	−12.6829	+	21.9675i	−0.615213	+	1.06558i
$426$		0			0
$427$		0			0
$428$			24.3431i			1.17667i
$429$		0			0
$430$	4.71449	−	2.72191i	0.227353	−	0.131262i
$431$	30.7057	−	17.7279i	1.47904	−	0.853924i	0.479321	−	0.877640i	$-0.340883\pi$
$431$	30.7057	−	17.7279i	1.47904	−	0.853924i	0.999719	+	0.0237157i	$0.00754966\pi$
$432$		0			0
$433$			1.21371i			0.0583271i	0.999575	+	0.0291636i	$0.00928436\pi$
$433$			1.21371i			0.0583271i	−0.999575	+	0.0291636i	$0.990716\pi$
$434$		0			0
$435$		0			0
$436$	4.94975	−	8.57321i	0.237050	−	0.410582i
$437$	−5.86030	−	10.1503i	−0.280336	−	0.485557i
$438$		0			0
$439$	−21.5321	−	12.4316i	−1.02767	−	0.593327i	−0.111355	−	0.993781i	$-0.535519\pi$
$439$	−21.5321	−	12.4316i	−1.02767	−	0.593327i	−0.916317	+	0.400454i	$0.868853\pi$
$440$	22.4357			1.06958
$441$		0			0
$442$	−8.58579			−0.408384
$443$	16.6031	+	9.58579i	0.788836	+	0.455434i	0.839552	−	0.543279i	$-0.182817\pi$
$443$	16.6031	+	9.58579i	0.788836	+	0.455434i	−0.0507168	+	0.998713i	$0.516151\pi$
$444$		0			0
$445$	16.4350	+	28.4663i	0.779095	+	1.34943i
$446$	0.710974	−	1.23144i	0.0336656	−	0.0583105i
$447$		0			0
$448$		0			0
$449$			15.7574i			0.743636i	0.928306	+	0.371818i	$0.121265\pi$
$449$			15.7574i			0.743636i	−0.928306	+	0.371818i	$0.878735\pi$
$450$		0			0
$451$	−5.07517	+	2.93015i	−0.238980	+	0.137975i
$452$	22.0094	−	12.7071i	1.03523	−	0.597692i
$453$		0			0
$454$		−	5.86030i		−	0.275038i
$455$		0			0
$456$		0			0
$457$	8.31371	−	14.3998i	0.388899	−	0.673593i	−0.603403	−	0.797437i	$-0.706189\pi$
$457$	8.31371	−	14.3998i	0.388899	−	0.673593i	0.992302	+	0.123844i	$0.0395222\pi$
$458$	−3.89249	−	6.74199i	−0.181884	−	0.315033i
$459$		0			0
$460$	9.27958	+	5.35757i	0.432663	+	0.249798i
$461$	−10.5069			−0.489355			−0.244677	−	0.969605i	$-0.578682\pi$
$461$	−10.5069			−0.489355			−0.244677	+	0.969605i	$0.578682\pi$
$462$		0			0
$463$	20.4853			0.952032			0.476016	−	0.879437i	$-0.342080\pi$
$463$	20.4853			0.952032			0.476016	+	0.879437i	$0.342080\pi$
$464$	−2.15232	−	1.24264i	−0.0999188	−	0.0576881i
$465$		0			0
$466$	1.07107	+	1.85514i	0.0496163	+	0.0859379i
$467$	7.07401	−	12.2525i	0.327346	−	0.566980i	−0.654638	−	0.755942i	$-0.727179\pi$
$467$	7.07401	−	12.2525i	0.327346	−	0.566980i	0.981984	+	0.188962i	$0.0605123\pi$
$468$		0			0
$469$		0			0
$470$		−	7.11270i		−	0.328084i
$471$		0			0
$472$	8.04814	−	4.64659i	0.370446	−	0.213877i
$473$	−18.7554	+	10.8284i	−0.862374	+	0.497892i
$474$		0			0
$475$		−	21.0138i		−	0.964179i
$476$		0			0
$477$		0			0
$478$	2.41421	−	4.18154i	0.110424	−	0.191259i
$479$	21.2220	+	36.7576i	0.969659	+	1.67950i	0.696538	+	0.717520i	$0.254723\pi$
$479$	21.2220	+	36.7576i	0.969659	+	1.67950i	0.273121	+	0.961980i	$0.411944\pi$
$480$		0			0
$481$	−13.7390	−	7.93223i	−0.626446	−	0.361679i
$482$	10.5069			0.478576
$483$		0			0
$484$	−22.5147			−1.02340
$485$	17.9509	+	10.3640i	0.815109	+	0.470603i
$486$		0			0
$487$	20.7279	+	35.9018i	0.939272	+	1.62687i	0.766833	+	0.641846i	$0.221831\pi$
$487$	20.7279	+	35.9018i	0.939272	+	1.62687i	0.172438	+	0.985020i	$0.444835\pi$
$488$	0.962341	−	1.66682i	0.0435631	−	0.0754536i
$489$		0			0
$490$		0			0
$491$		−	25.3137i		−	1.14239i	−0.820814	−	0.571196i	$-0.806480\pi$
$491$		−	25.3137i		−	1.14239i	0.820814	−	0.571196i	$-0.193520\pi$
$492$		0			0
$493$	5.07517	−	2.93015i	0.228574	−	0.131967i
$494$	6.15978	−	3.55635i	0.277141	−	0.160008i
$495$		0			0
$496$			17.5809i			0.789406i
$497$		0			0
$498$		0			0
$499$	−13.0711	+	22.6398i	−0.585141	+	1.01349i	0.409716	+	0.912213i	$0.365628\pi$
$499$	−13.0711	+	22.6398i	−0.585141	+	1.01349i	−0.994858	+	0.101282i	$0.967706\pi$
$500$	−3.78837	−	6.56165i	−0.169421	−	0.293446i
$501$		0			0
$502$	−3.84373	−	2.21918i	−0.171554	−	0.0990467i
$503$	4.85483			0.216466			0.108233	−	0.994126i	$-0.465481\pi$
$503$	4.85483			0.216466			0.108233	+	0.994126i	$0.465481\pi$
$504$		0			0
$505$	−15.6985			−0.698573
$506$	3.46410	+	2.00000i	0.153998	+	0.0889108i
$507$		0			0
$508$	−15.0711	−	26.1039i	−0.668671	−	1.15817i
$509$	−13.0384	+	22.5832i	−0.577918	+	1.00098i	0.417799	+	0.908539i	$0.362801\pi$
$509$	−13.0384	+	22.5832i	−0.577918	+	1.00098i	−0.995718	+	0.0924447i	$0.970532\pi$
$510$		0			0
$511$		0			0
$512$		−	22.7574i		−	1.00574i
$513$		0			0
$514$	3.76903	−	2.17605i	0.166245	−	0.0959814i
$515$	−35.9018	+	20.7279i	−1.58202	+	0.913381i
$516$		0			0
$517$			28.2960i			1.24446i
$518$		0			0
$519$		0			0
$520$	−6.80761	+	11.7911i	−0.298534	+	0.517075i
$521$	−1.96781	−	3.40835i	−0.0862113	−	0.149322i	0.819695	−	0.572800i	$-0.194143\pi$
$521$	−1.96781	−	3.40835i	−0.0862113	−	0.149322i	−0.905907	+	0.423477i	$0.860809\pi$
$522$		0			0
$523$	27.4781	+	15.8645i	1.20153	+	0.693705i	0.960896	−	0.276911i	$-0.0893107\pi$
$523$	27.4781	+	15.8645i	1.20153	+	0.693705i	0.240636	+	0.970615i	$0.422644\pi$
$524$	−15.1535			−0.661983
$525$		0			0
$526$	−1.71573			−0.0748093
$527$	−35.9018	−	20.7279i	−1.56391	−	0.902922i
$528$		0			0
$529$	−9.50000	−	16.4545i	−0.413043	−	0.715412i
$530$	4.29111	−	7.43242i	0.186394	−	0.322844i
$531$		0			0
$532$		0			0
$533$		−	3.55635i		−	0.154043i
$534$		0			0
$535$	−33.7847	+	19.5056i	−1.46064	+	0.843300i
$536$	11.6531	−	6.72792i	0.503337	−	0.290602i
$537$		0			0
$538$		−	0.919213i		−	0.0396301i
$539$		0			0
$540$		0			0
$541$	7.48528	−	12.9649i	0.321817	−	0.557404i	−0.659046	−	0.752103i	$-0.729040\pi$
$541$	7.48528	−	12.9649i	0.321817	−	0.557404i	0.980863	+	0.194699i	$0.0623730\pi$
$542$	−1.21371	−	2.10220i	−0.0521332	−	0.0902974i
$543$		0			0
$544$	27.0427	+	15.6131i	1.15945	+	0.669406i
$545$	15.8645			0.679559
$546$		0			0
$547$	18.6274			0.796451			0.398225	−	0.917288i	$-0.369626\pi$
$547$	18.6274			0.796451			0.398225	+	0.917288i	$0.369626\pi$
$548$	−7.64564	−	4.41421i	−0.326606	−	0.188566i
$549$		0			0
$550$	3.58579	+	6.21076i	0.152898	+	0.264828i
$551$	−2.42742	+	4.20441i	−0.103411	+	0.179114i
$552$		0			0
$553$		0			0
$554$		−	5.37258i		−	0.228259i
$555$		0			0
$556$	−13.1233	+	7.57675i	−0.556552	+	0.321326i
$557$	−11.6170	+	6.70711i	−0.492230	+	0.284189i	−0.725499	−	0.688223i	$-0.758391\pi$
$557$	−11.6170	+	6.70711i	−0.492230	+	0.284189i	0.233269	+	0.972412i	$0.425058\pi$
$558$		0			0
$559$		−	13.1426i		−	0.555871i
$560$		0			0
$561$		0			0
$562$	−2.72792	+	4.72490i	−0.115070	+	0.199308i
$563$	−7.07401	−	12.2525i	−0.298134	−	0.516383i	0.677575	−	0.735454i	$-0.263031\pi$
$563$	−7.07401	−	12.2525i	−0.298134	−	0.516383i	−0.975709	+	0.219070i	$0.929698\pi$
$564$		0			0
$565$	35.2712	+	20.3638i	1.48387	+	0.856712i
$566$	−3.84936			−0.161801
$567$		0			0
$568$	−1.31371			−0.0551220
$569$	32.1405	+	18.5563i	1.34740	+	0.777923i	0.987881	−	0.155214i	$-0.0496069\pi$
$569$	32.1405	+	18.5563i	1.34740	+	0.777923i	0.359521	+	0.933137i	$0.382940\pi$
$570$		0			0
$571$	−5.65685	−	9.79796i	−0.236732	−	0.410032i	0.723043	−	0.690803i	$-0.242743\pi$
$571$	−5.65685	−	9.79796i	−0.236732	−	0.410032i	−0.959775	+	0.280772i	$0.909410\pi$
$572$	12.9343	−	22.4029i	0.540811	−	0.936712i
$573$		0			0
$574$		0			0
$575$			7.17157i			0.299075i
$576$		0			0
$577$	25.5562	−	14.7549i	1.06392	−	0.614254i	0.137405	−	0.990515i	$-0.456124\pi$
$577$	25.5562	−	14.7549i	1.06392	−	0.614254i	0.926514	+	0.376261i	$0.122791\pi$
$578$	−11.8527	+	6.84315i	−0.493006	+	0.284637i
$579$		0			0
$580$		−	4.43835i		−	0.184293i
$581$		0			0
$582$		0			0
$583$	−17.0711	+	29.5680i	−0.707011	+	1.22458i
$584$	5.60894	+	9.71496i	0.232099	+	0.402008i
$585$		0			0
$586$	−8.22848	−	4.75071i	−0.339915	−	0.196250i
$587$	17.5809			0.725642			0.362821	−	0.931859i	$-0.381814\pi$
$587$	17.5809			0.725642			0.362821	+	0.931859i	$0.381814\pi$
$588$		0			0
$589$	34.3431			1.41508
$590$	6.15978	+	3.55635i	0.253594	+	0.146413i
$591$		0			0
$592$	8.12132	+	14.0665i	0.333784	+	0.578131i
$593$	11.8247	−	20.4810i	0.485583	−	0.841055i	−0.514279	−	0.857623i	$-0.671941\pi$
$593$	11.8247	−	20.4810i	0.485583	−	0.841055i	0.999863	+	0.0165678i	$0.00527393\pi$
$594$		0			0
$595$		0			0
$596$		−	7.75736i		−	0.317754i
$597$		0			0
$598$	−2.10220	+	1.21371i	−0.0859655	+	0.0496322i
$599$	−9.08052	+	5.24264i	−0.371020	+	0.214208i	−0.673904	−	0.738819i	$-0.735384\pi$
$599$	−9.08052	+	5.24264i	−0.371020	+	0.214208i	0.302884	+	0.953027i	$0.402051\pi$
$600$		0			0
$601$		−	40.5194i		−	1.65282i	−0.563069	−	0.826410i	$-0.690379\pi$
$601$		−	40.5194i		−	1.65282i	0.563069	−	0.826410i	$-0.309621\pi$
$602$		0			0
$603$		0			0
$604$	−4.10051	+	7.10228i	−0.166847	+	0.288988i
$605$	−18.0405	−	31.2471i	−0.733451	−	1.27037i
$606$		0			0
$607$	2.97297	+	1.71644i	0.120669	+	0.0696683i	0.559120	−	0.829087i	$-0.311139\pi$
$607$	2.97297	+	1.71644i	0.120669	+	0.0696683i	−0.438451	+	0.898755i	$0.644473\pi$
$608$	−25.8686			−1.04911
$609$		0			0
$610$	1.47309			0.0596436
$611$	−14.8710	−	8.58579i	−0.601617	−	0.347344i
$612$		0			0
$613$	−21.4350	−	37.1266i	−0.865753	−	1.49953i	−0.866298	−	0.499528i	$-0.833507\pi$
$613$	−21.4350	−	37.1266i	−0.865753	−	1.49953i	0.000545229	−	1.00000i	$-0.499826\pi$
$614$	−4.64659	+	8.04814i	−0.187521	+	0.324796i
$615$		0			0
$616$		0			0
$617$		−	13.5147i		−	0.544082i	−0.962286	−	0.272041i	$-0.912301\pi$
$617$		−	13.5147i		−	0.544082i	0.962286	−	0.272041i	$-0.0876986\pi$
$618$		0			0
$619$	38.8598	−	22.4357i	1.56191	−	0.901769i	0.564845	−	0.825197i	$-0.308936\pi$
$619$	38.8598	−	22.4357i	1.56191	−	0.901769i	0.997064	−	0.0765715i	$-0.0243973\pi$
$620$	−27.1906	+	15.6985i	−1.09200	+	0.630466i
$621$		0			0
$622$			10.7151i			0.429638i
$623$		0			0
$624$		0			0
$625$	15.0355	−	26.0423i	0.601421	−	1.04169i
$626$	−1.10959	−	1.92186i	−0.0443481	−	0.0768131i
$627$		0			0
$628$	−36.3223	−	20.9707i	−1.44942	−	0.836821i
$629$	−38.3002			−1.52713
$630$		0			0
$631$	−26.8284			−1.06802			−0.534011	−	0.845477i	$-0.679316\pi$
$631$	−26.8284			−1.06802			−0.534011	+	0.845477i	$0.679316\pi$
$632$	2.27541	+	1.31371i	0.0905109	+	0.0522565i
$633$		0			0
$634$	−6.67767	−	11.5661i	−0.265204	−	0.459347i
$635$	24.1522	−	41.8328i	0.958450	−	1.66008i
$636$		0			0
$637$		0			0
$638$		−	1.65685i		−	0.0655955i
$639$		0			0
$640$	26.7876	−	15.4658i	1.05887	−	0.611341i
$641$	21.2049	−	12.2426i	0.837542	−	0.483555i	−0.0188858	−	0.999822i	$-0.506012\pi$
$641$	21.2049	−	12.2426i	0.837542	−	0.483555i	0.856428	+	0.516266i	$0.172679\pi$
$642$		0			0
$643$		−	5.86030i		−	0.231108i	−0.993301	−	0.115554i	$-0.963136\pi$
$643$		−	5.86030i		−	0.231108i	0.993301	−	0.115554i	$-0.0368643\pi$
$644$		0			0
$645$		0			0
$646$	8.58579	−	14.8710i	0.337803	−	0.585092i
$647$	−5.35757	−	9.27958i	−0.210628	−	0.364818i	0.741283	−	0.671192i	$-0.234217\pi$
$647$	−5.35757	−	9.27958i	−0.210628	−	0.364818i	−0.951911	+	0.306374i	$0.900884\pi$
$648$		0			0
$649$	−24.5051	−	14.1480i	−0.961909	−	0.555358i
$650$	−4.35210			−0.170703
$651$		0			0
$652$	16.7696			0.656746
$653$	18.6323	+	10.7574i	0.729138	+	0.420968i	0.818107	−	0.575066i	$-0.195024\pi$
$653$	18.6323	+	10.7574i	0.729138	+	0.420968i	−0.0889688	+	0.996034i	$0.528357\pi$
$654$		0			0
$655$	−12.1421	−	21.0308i	−0.474432	−	0.821741i
$656$	−1.82056	+	3.15331i	−0.0710810	+	0.123116i
$657$		0			0
$658$		0			0
$659$			3.45584i			0.134621i	0.997732	+	0.0673103i	$0.0214417\pi$
$659$			3.45584i			0.134621i	−0.997732	+	0.0673103i	$0.978558\pi$
$660$		0			0
$661$	−19.8653	+	11.4692i	−0.772671	+	0.446102i	−0.833827	−	0.552027i	$-0.813855\pi$
$661$	−19.8653	+	11.4692i	−0.772671	+	0.446102i	0.0611558	+	0.998128i	$0.480521\pi$
$662$	−7.76874	+	4.48528i	−0.301940	+	0.174325i
$663$		0			0
$664$		−	18.5864i		−	0.721291i
$665$		0			0
$666$		0			0
$667$	0.828427	−	1.43488i	0.0320768	−	0.0555587i
$668$	−12.9343	−	22.4029i	−0.500444	−	0.866794i
$669$		0			0
$670$	8.91890	+	5.14933i	0.344567	+	0.198936i
$671$	−5.86030			−0.226234
$672$		0			0
$673$	−18.1005			−0.697723			−0.348862	−	0.937174i	$-0.613432\pi$
$673$	−18.1005			−0.697723			−0.348862	+	0.937174i	$0.613432\pi$
$674$	−9.71092	−	5.60660i	−0.374051	−	0.215958i
$675$		0			0
$676$	−4.03553	−	6.98975i	−0.155213	−	0.268837i
$677$	23.0426	−	39.9109i	0.885599	−	1.53390i	0.0405732	−	0.999177i	$-0.487082\pi$
$677$	23.0426	−	39.9109i	0.885599	−	1.53390i	0.845026	−	0.534726i	$-0.179585\pi$
$678$		0			0
$679$		0			0
$680$			32.8701i			1.26051i
$681$		0			0
$682$	−10.1503	+	5.86030i	−0.388677	+	0.224403i
$683$	−30.1113	+	17.3848i	−1.15218	+	0.665210i	−0.949417	−	0.314018i	$-0.898325\pi$
$683$	−30.1113	+	17.3848i	−1.15218	+	0.665210i	−0.202761	+	0.979228i	$0.564991\pi$
$684$		0			0
$685$		−	14.1480i		−	0.540568i
$686$		0			0
$687$		0			0
$688$	−6.72792	+	11.6531i	−0.256500	+	0.444270i
$689$	−10.3596	−	17.9434i	−0.394671	−	0.683591i
$690$		0			0
$691$	7.17738	+	4.14386i	0.273040	+	0.157640i	0.630268	−	0.776377i	$-0.282945\pi$
$691$	7.17738	+	4.14386i	0.273040	+	0.157640i	−0.357228	+	0.934017i	$0.616278\pi$
$692$	2.21918			0.0843605
$693$		0			0
$694$	6.20101			0.235387
$695$	−21.0308	−	12.1421i	−0.797744	−	0.460577i
$696$		0			0
$697$	−4.29289	−	7.43551i	−0.162605	−	0.281640i
$698$	2.32330	−	4.02407i	0.0879381	−	0.152313i
$699$		0			0
$700$		0			0
$701$			32.7696i			1.23769i	0.785514	+	0.618844i	$0.212399\pi$
$701$			32.7696i			1.23769i	−0.785514	+	0.618844i	$0.787601\pi$
$702$		0			0
$703$	27.4781	−	15.8645i	1.03635	−	0.598340i
$704$	−17.4436	+	10.0711i	−0.657430	+	0.379568i
$705$		0			0
$706$			8.49596i			0.319750i
$707$		0			0
$708$		0			0
$709$	3.63604	−	6.29780i	0.136554	−	0.236519i	−0.789636	−	0.613576i	$-0.789731\pi$
$709$	3.63604	−	6.29780i	0.136554	−	0.236519i	0.926190	+	0.377057i	$0.123064\pi$
$710$	−0.502734	−	0.870762i	−0.0188673	−	0.0326791i
$711$		0			0
$712$	15.4059	+	8.89457i	0.577359	+	0.333338i
$713$	−11.7206			−0.438940
$714$		0			0
$715$	41.4558			1.55036
$716$	41.9385	+	24.2132i	1.56732	+	0.904890i
$717$		0			0
$718$	7.24264	+	12.5446i	0.270293	+	0.468161i
$719$	−5.86030	+	10.1503i	−0.218552	+	0.378544i	−0.954366	−	0.298641i	$-0.903467\pi$
$719$	−5.86030	+	10.1503i	−0.218552	+	0.378544i	0.735813	+	0.677185i	$0.236800\pi$
$720$		0			0
$721$		0			0
$722$			6.35534i			0.236521i
$723$		0			0
$724$	−15.0452	+	8.68633i	−0.559149	+	0.322825i
$725$	2.57258	−	1.48528i	0.0955433	−	0.0551620i
$726$		0			0
$727$			21.0138i			0.779358i	0.920951	+	0.389679i	$0.127414\pi$
$727$			21.0138i			0.779358i	−0.920951	+	0.389679i	$0.872586\pi$
$728$		0			0
$729$		0			0
$730$	−4.29289	+	7.43551i	−0.158887	+	0.275201i
$731$	−15.8645	−	27.4781i	−0.586768	−	1.01631i
$732$		0			0
$733$	32.7336	+	18.8987i	1.20904	+	0.698041i	0.962550	−	0.271104i	$-0.0873888\pi$
$733$	32.7336	+	18.8987i	1.20904	+	0.698041i	0.246492	+	0.969145i	$0.420722\pi$
$734$	−8.28772			−0.305905
$735$		0			0
$736$	8.82843			0.325420
$737$	−35.4815	−	20.4853i	−1.30698	−	0.754585i
$738$		0			0
$739$	6.58579	+	11.4069i	0.242262	+	0.419610i	0.961358	−	0.275300i	$-0.0887773\pi$
$739$	6.58579	+	11.4069i	0.242262	+	0.419610i	−0.719096	+	0.694911i	$0.755444\pi$
$740$	−14.5035	+	25.1208i	−0.533160	+	0.923459i
$741$		0			0
$742$		0			0
$743$		−	32.4264i		−	1.18961i	−0.803870	−	0.594805i	$-0.797229\pi$
$743$		−	32.4264i		−	1.18961i	0.803870	−	0.594805i	$-0.202771\pi$
$744$		0			0
$745$	10.7661	−	6.21579i	0.394438	−	0.227729i
$746$	−8.11689	+	4.68629i	−0.297181	+	0.171577i
$747$		0			0
$748$		−	62.4524i		−	2.28349i
$749$		0			0
$750$		0			0
$751$	−21.6569	+	37.5108i	−0.790270	+	1.36879i	0.135530	+	0.990773i	$0.456726\pi$
$751$	−21.6569	+	37.5108i	−0.790270	+	1.36879i	−0.925800	+	0.378014i	$0.876607\pi$
$752$	8.79045	+	15.2255i	0.320555	+	0.555217i
$753$		0			0
$754$	0.870762	+	0.502734i	0.0317113	+	0.0183085i
$755$	−13.1426			−0.478306
$756$		0			0
$757$	−46.8701			−1.70352			−0.851761	−	0.523931i	$-0.824465\pi$
$757$	−46.8701			−1.70352			−0.851761	+	0.523931i	$0.824465\pi$
$758$		0			0
$759$		0			0
$760$	−13.6152	−	23.5823i	−0.493876	−	0.855418i
$761$	−8.53909	+	14.7901i	−0.309542	+	0.536142i	−0.978262	−	0.207372i	$-0.933509\pi$
$761$	−8.53909	+	14.7901i	−0.309542	+	0.536142i	0.668721	+	0.743514i	$0.266842\pi$
$762$		0			0
$763$		0			0
$764$		−	27.7401i		−	1.00360i
$765$		0			0
$766$	−8.40882	+	4.85483i	−0.303823	+	0.175412i
$767$	14.8710	−	8.58579i	0.536961	−	0.310015i
$768$		0			0
$769$			48.0961i			1.73439i	0.497968	+	0.867195i	$0.334080\pi$
$769$			48.0961i			1.73439i	−0.497968	+	0.867195i	$0.665920\pi$
$770$		0			0
$771$		0			0
$772$	5.79899	−	10.0441i	0.208710	−	0.361497i
$773$	12.3275	+	21.3518i	0.443388	+	0.767970i	0.997938	−	0.0641797i	$-0.0204431\pi$
$773$	12.3275	+	21.3518i	0.443388	+	0.767970i	−0.554550	+	0.832150i	$0.687110\pi$
$774$		0			0
$775$	−18.1985	−	10.5069i	−0.653709	−	0.377419i
$776$	11.2179			0.402698
$777$		0			0
$778$	10.6863			0.383122
$779$	6.15978	+	3.55635i	0.220697	+	0.127419i
$780$		0			0
$781$	2.00000	+	3.46410i	0.0715656	+	0.123955i
$782$	−2.93015	+	5.07517i	−0.104782	+	0.181488i
$783$		0			0
$784$		0			0
$785$		−	67.2132i		−	2.39894i
$786$		0			0
$787$	10.1503	−	5.86030i	0.361821	−	0.208897i	−0.308058	−	0.951367i	$-0.599679\pi$
$787$	10.1503	−	5.86030i	0.361821	−	0.208897i	0.669879	+	0.742470i	$0.266346\pi$
$788$	12.2835	−	7.09188i	0.437582	−	0.252638i
$789$		0			0
$790$			2.01094i			0.0715460i
$791$		0			0
$792$		0			0
$793$	1.77817	−	3.07989i	0.0631448	−	0.109370i
$794$	−3.68425	−	6.38131i	−0.130749	−	0.226464i
$795$		0			0
$796$	26.2466	+	15.1535i	0.930287	+	0.537101i
$797$	51.2345			1.81482			0.907410	−	0.420247i	$-0.138056\pi$
$797$	51.2345			1.81482			0.907410	+	0.420247i	$0.138056\pi$
$798$		0			0
$799$	−41.4558			−1.46660
$800$	13.7078	+	7.91421i	0.484645	+	0.279810i
$801$		0			0
$802$	−1.07107	−	1.85514i	−0.0378207	−	0.0655074i
$803$	17.0782	−	29.5803i	0.602676	−	1.04386i
$804$		0			0
$805$		0			0
$806$		−	7.11270i		−	0.250534i
$807$		0			0
$808$	−7.35772	+	4.24798i	−0.258844	+	0.149443i
$809$	−13.8925	+	8.02082i	−0.488433	+	0.281997i	−0.723924	−	0.689880i	$-0.757663\pi$
$809$	−13.8925	+	8.02082i	−0.488433	+	0.281997i	0.235491	+	0.971876i	$0.424330\pi$
$810$		0			0
$811$			8.28772i			0.291021i	0.989357	+	0.145511i	$0.0464825\pi$
$811$			8.28772i			0.291021i	−0.989357	+	0.145511i	$0.953518\pi$
$812$		0			0
$813$		0			0
$814$	−5.41421	+	9.37769i	−0.189768	+	0.328688i
$815$	13.4370	+	23.2736i	0.470679	+	0.815240i
$816$		0			0
$817$	22.7636	+	13.1426i	0.796396	+	0.459800i
$818$	−3.93562			−0.137606
$819$		0			0
$820$	−6.50253			−0.227078
$821$	−20.5745	−	11.8787i	−0.718054	−	0.414569i	0.0959819	−	0.995383i	$-0.469401\pi$
$821$	−20.5745	−	11.8787i	−0.718054	−	0.414569i	−0.814036	+	0.580814i	$0.802734\pi$
$822$		0			0
$823$	20.9706	+	36.3221i	0.730988	+	1.26611i	0.956461	+	0.291859i	$0.0942737\pi$
$823$	20.9706	+	36.3221i	0.730988	+	1.26611i	−0.225474	+	0.974249i	$0.572393\pi$
$824$	−11.2179	+	19.4299i	−0.390793	+	0.676873i
$825$		0			0
$826$		0			0
$827$			39.6569i			1.37900i	0.724284	+	0.689502i	$0.242171\pi$
$827$			39.6569i			1.37900i	−0.724284	+	0.689502i	$0.757829\pi$
$828$		0			0
$829$	−31.2471	+	18.0405i	−1.08526	+	0.626573i	−0.932309	−	0.361661i	$-0.882210\pi$
$829$	−31.2471	+	18.0405i	−1.08526	+	0.626573i	−0.152947	+	0.988234i	$0.548876\pi$
$830$	12.3196	−	7.11270i	0.427618	−	0.246885i
$831$		0			0
$832$		−	12.2233i		−	0.423768i
$833$		0			0
$834$		0			0
$835$	20.7279	−	35.9018i	0.717319	−	1.24243i
$836$	25.8686	+	44.8058i	0.894685	+	1.54964i
$837$		0			0
$838$	−6.81669	−	3.93562i	−0.235479	−	0.135954i
$839$	17.5809			0.606960			0.303480	−	0.952838i	$-0.401851\pi$
$839$	17.5809			0.606960			0.303480	+	0.952838i	$0.401851\pi$
$840$		0			0
$841$	28.3137			0.976335
$842$	−0.246186	−	0.142136i	−0.00848413	−	0.00489832i
$843$		0			0
$844$	14.0000	+	24.2487i	0.481900	+	0.834675i
$845$	6.46716	−	11.2014i	0.222477	−	0.385341i
$846$		0			0
$847$		0			0
$848$			21.2132i			0.728464i
$849$		0			0
$850$	−9.09924	+	5.25345i	−0.312101	+	0.180192i
$851$	−9.37769	+	5.41421i	−0.321463	+	0.185597i
$852$		0			0
$853$			16.0727i			0.550319i	0.961399	+	0.275159i	$0.0887306\pi$
$853$			16.0727i			0.550319i	−0.961399	+	0.275159i	$0.911269\pi$
$854$		0			0
$855$		0			0
$856$	−10.5563	+	18.2841i	−0.360809	+	0.624939i
$857$	−0.251367	−	0.435381i	−0.00858654	−	0.0148723i	0.861700	−	0.507418i	$-0.169400\pi$
$857$	−0.251367	−	0.435381i	−0.00858654	−	0.0148723i	−0.870287	+	0.492545i	$0.836067\pi$
$858$		0			0
$859$	−8.04814	−	4.64659i	−0.274599	−	0.158540i	0.356377	−	0.934342i	$-0.384012\pi$
$859$	−8.04814	−	4.64659i	−0.274599	−	0.158540i	−0.630976	+	0.775803i	$0.717345\pi$
$860$	−24.0302			−0.819423
$861$		0			0
$862$	14.6863			0.500217
$863$	9.25460	+	5.34315i	0.315030	+	0.181883i	0.649175	−	0.760639i	$-0.275114\pi$
$863$	9.25460	+	5.34315i	0.315030	+	0.181883i	−0.334145	+	0.942522i	$0.608448\pi$
$864$		0			0
$865$	1.77817	+	3.07989i	0.0604597	+	0.104719i
$866$	−0.251367	+	0.435381i	−0.00854181	+	0.0147948i
$867$		0			0
$868$		0			0
$869$		−	8.00000i		−	0.271381i
$870$		0			0
$871$	21.5321	−	12.4316i	0.729588	−	0.421228i
$872$	7.43551	−	4.29289i	0.251798	−	0.145376i
$873$		0			0
$874$		−	4.85483i		−	0.164217i
$875$		0			0
$876$		0			0
$877$	16.2635	−	28.1691i	0.549178	−	0.951204i	−0.449153	−	0.893455i	$-0.648274\pi$
$877$	16.2635	−	28.1691i	0.549178	−	0.951204i	0.998331	−	0.0577493i	$-0.0183924\pi$
$878$	−5.14933	−	8.91890i	−0.173781	−	0.300998i
$879$		0			0
$880$	−36.7576	−	21.2220i	−1.23910	−	0.715395i
$881$	23.6494			0.796770			0.398385	−	0.917218i	$-0.369571\pi$
$881$	23.6494			0.796770			0.398385	+	0.917218i	$0.369571\pi$
$882$		0			0
$883$	13.4558			0.452825			0.226413	−	0.974031i	$-0.427300\pi$
$883$	13.4558			0.452825			0.226413	+	0.974031i	$0.427300\pi$
$884$	32.8219	+	18.9497i	1.10392	+	0.637349i
$885$		0			0
$886$	3.97056	+	6.87722i	0.133394	+	0.231045i
$887$	−25.3659	+	43.9350i	−0.851703	+	1.47519i	0.0279667	+	0.999609i	$0.491097\pi$
$887$	−25.3659	+	43.9350i	−0.851703	+	1.47519i	−0.879670	+	0.475585i	$0.842237\pi$
$888$		0			0
$889$		0			0
$890$			13.6152i			0.456383i
$891$		0			0
$892$	−5.43585	+	3.13839i	−0.182006	+	0.105081i
$893$	29.7420	−	17.1716i	0.995279	−	0.574625i
$894$		0			0
$895$			77.6059i			2.59408i
$896$		0			0
$897$		0			0
$898$	−3.26346	+	5.65247i	−0.108903	+	0.188625i
$899$	2.42742	+	4.20441i	0.0809589	+	0.140225i
$900$		0			0
$901$	−43.3193	−	25.0104i	−1.44317	−	0.833217i
$902$	−2.42742			−0.0808241
$903$		0			0
$904$	22.0416			0.733094
$905$	−24.1107	−	13.9203i	−0.801466	−	0.462727i
$906$		0			0
$907$	−14.3848	−	24.9152i	−0.477639	−	0.827294i	0.522033	−	0.852925i	$-0.325174\pi$
$907$	−14.3848	−	24.9152i	−0.477639	−	0.827294i	−0.999671	+	0.0256310i	$0.991841\pi$
$908$	−12.9343	+	22.4029i	−0.429240	+	0.743466i
$909$		0			0
$910$		0			0
$911$			42.4853i			1.40760i	0.710398	+	0.703800i	$0.248515\pi$
$911$			42.4853i			1.40760i	−0.710398	+	0.703800i	$0.751485\pi$
$912$		0			0
$913$	−49.0102	+	28.2960i	−1.62200	+	0.936462i
$914$	5.96458	−	3.44365i	0.197291	−	0.113906i
$915$		0			0
$916$			34.3646i			1.13544i
$917$		0			0
$918$		0			0
$919$	20.7279	−	35.9018i	0.683751	−	1.18429i	−0.290077	−	0.957003i	$-0.593681\pi$
$919$	20.7279	−	35.9018i	0.683751	−	1.18429i	0.973828	−	0.227288i	$-0.0729859\pi$
$920$	4.64659	+	8.04814i	0.153194	+	0.265339i
$921$		0			0
$922$	−3.76903	−	2.17605i	−0.124126	−	0.0716644i
$923$	−2.42742			−0.0798994
$924$		0			0
$925$	−19.4142			−0.638335
$926$	7.34847	+	4.24264i	0.241486	+	0.139422i
$927$		0			0
$928$	−1.82843	−	3.16693i	−0.0600211	−	0.103960i
$929$	−0.251367	+	0.435381i	−0.00824709	+	0.0142844i	−0.870119	−	0.492841i	$-0.835958\pi$
$929$	−0.251367	+	0.435381i	−0.00824709	+	0.0142844i	0.861872	+	0.507125i	$0.169292\pi$
$930$		0			0
$931$		0			0
$932$		−	9.45584i		−	0.309736i
$933$		0			0
$934$	5.07517	−	2.93015i	0.166065	−	0.0958775i
$935$	86.6746	−	50.0416i	2.83456	−	1.63654i
$936$		0			0
$937$		−	51.2345i		−	1.67376i	−0.547387	−	0.836879i	$-0.684378\pi$
$937$		−	51.2345i		−	1.67376i	0.547387	−	0.836879i	$-0.315622\pi$
$938$		0			0
$939$		0			0
$940$	−15.6985	+	27.1906i	−0.512028	+	0.886859i
$941$	2.32330	+	4.02407i	0.0757373	+	0.131181i	0.901407	−	0.432973i	$-0.142536\pi$
$941$	2.32330	+	4.02407i	0.0757373	+	0.131181i	−0.825669	+	0.564154i	$0.809202\pi$
$942$		0			0
$943$	−2.10220	−	1.21371i	−0.0684572	−	0.0395238i
$944$	−17.5809			−0.572210
$945$		0			0
$946$	−8.97056			−0.291658
$947$	9.50079	+	5.48528i	0.308734	+	0.178248i	0.646360	−	0.763033i	$-0.276291\pi$
$947$	9.50079	+	5.48528i	0.308734	+	0.178248i	−0.337626	+	0.941280i	$0.609624\pi$
$948$		0			0
$949$	10.3640	+	17.9509i	0.336428	+	0.582711i
$950$	4.35210	−	7.53806i	0.141201	−	0.244567i
$951$		0			0
$952$		0			0
$953$			10.3848i			0.336396i	0.985753	+	0.168198i	$0.0537948\pi$
$953$			10.3848i			0.336396i	−0.985753	+	0.168198i	$0.946205\pi$
$954$		0			0
$955$	38.4992	−	22.2275i	1.24580	−	0.719265i
$956$	−18.4582	+	10.6569i	−0.596981	+	0.344667i
$957$		0			0
$958$			17.5809i			0.568013i
$959$		0			0
$960$		0			0
$961$	1.67157	−	2.89525i	0.0539217	−	0.0933951i
$962$	−3.28564	−	5.69089i	−0.105933	−	0.183482i
$963$		0			0
$964$	−40.1660	−	23.1898i	−1.29366	−	0.746895i
$965$	18.5864			0.598317
$966$		0			0
$967$	−19.1127			−0.614623			−0.307311	−	0.951609i	$-0.599429\pi$
$967$	−19.1127			−0.614623			−0.307311	+	0.951609i	$0.599429\pi$
$968$	−16.9108	−	9.76346i	−0.543534	−	0.313809i
$969$		0			0
$970$	4.29289	+	7.43551i	0.137836	+	0.238740i
$971$	−2.42742	+	4.20441i	−0.0778995	+	0.134926i	−0.902343	−	0.431018i	$-0.858155\pi$
$971$	−2.42742	+	4.20441i	−0.0778995	+	0.134926i	0.824444	+	0.565944i	$0.191488\pi$
$972$		0			0
$973$		0			0
$974$			17.1716i			0.550213i
$975$		0			0
$976$	−3.15331	+	1.82056i	−0.100935	+	0.0582748i
$977$	38.8226	−	22.4142i	1.24204	−	0.717094i	0.272534	−	0.962146i	$-0.412138\pi$
$977$	38.8226	−	22.4142i	1.24204	−	0.717094i	0.969510	+	0.245052i	$0.0788050\pi$
$978$		0			0
$979$		−	54.1647i		−	1.73111i
$980$		0			0
$981$		0			0
$982$	5.24264	−	9.08052i	0.167299	−	0.289771i
$983$	15.8645	+	27.4781i	0.505998	+	0.876414i	0.999976	+	0.00693961i	$0.00220897\pi$
$983$	15.8645	+	27.4781i	0.505998	+	0.876414i	−0.493978	+	0.869474i	$0.664458\pi$
$984$		0			0
$985$	19.6850	+	11.3651i	0.627215	+	0.362123i
$986$	2.42742			0.0773047
$987$		0			0
$988$	−31.3970			−0.998871
$989$	−7.76874	−	4.48528i	−0.247031	−	0.142624i
$990$		0			0
$991$	29.6985	+	51.4393i	0.943403	+	1.63402i	0.758917	+	0.651188i	$0.225729\pi$
$991$	29.6985	+	51.4393i	0.943403	+	1.63402i	0.184487	+	0.982835i	$0.440938\pi$
$992$	−12.9343	+	22.4029i	−0.410665	+	0.711292i
$993$		0			0
$994$		0			0
$995$			48.5685i			1.53973i
$996$		0			0
$997$	34.2201	−	19.7570i	1.08376	−	0.625709i	0.151852	−	0.988403i	$-0.451476\pi$
$997$	34.2201	−	19.7570i	1.08376	−	0.625709i	0.931908	+	0.362694i	$0.118143\pi$
$998$	−9.37769	+	5.41421i	−0.296846	+	0.171384i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.p.c.215.6		16
3.2	odd	2	inner	441.2.p.c.215.3		16
7.2	even	3		441.2.c.b.440.3	✓	8
7.3	odd	6	inner	441.2.p.c.80.3		16
7.4	even	3	inner	441.2.p.c.80.4		16
7.5	odd	6		441.2.c.b.440.4	yes	8
7.6	odd	2	inner	441.2.p.c.215.5		16
21.2	odd	6		441.2.c.b.440.6	yes	8
21.5	even	6		441.2.c.b.440.5	yes	8
21.11	odd	6	inner	441.2.p.c.80.5		16
21.17	even	6	inner	441.2.p.c.80.6		16
21.20	even	2	inner	441.2.p.c.215.4		16
28.19	even	6		7056.2.k.g.881.6		8
28.23	odd	6		7056.2.k.g.881.4		8
84.23	even	6		7056.2.k.g.881.5		8
84.47	odd	6		7056.2.k.g.881.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.c.b.440.3	✓	8	7.2	even	3
441.2.c.b.440.4	yes	8	7.5	odd	6
441.2.c.b.440.5	yes	8	21.5	even	6
441.2.c.b.440.6	yes	8	21.2	odd	6
441.2.p.c.80.3		16	7.3	odd	6	inner
441.2.p.c.80.4		16	7.4	even	3	inner
441.2.p.c.80.5		16	21.11	odd	6	inner
441.2.p.c.80.6		16	21.17	even	6	inner
441.2.p.c.215.3		16	3.2	odd	2	inner
441.2.p.c.215.4		16	21.20	even	2	inner
441.2.p.c.215.5		16	7.6	odd	2	inner
441.2.p.c.215.6		16	1.1	even	1	trivial
7056.2.k.g.881.3		8	84.47	odd	6
7056.2.k.g.881.4		8	28.23	odd	6
7056.2.k.g.881.5		8	84.23	even	6
7056.2.k.g.881.6		8	28.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.358719 + 0.207107i) q^{2} +(-0.914214 - 1.58346i) q^{4} +(1.46508 - 2.53759i) q^{5} -1.58579i q^{8} +O(q^{10})\)	\(q+(0.358719 + 0.207107i) q^{2} +(-0.914214 - 1.58346i) q^{4} +(1.46508 - 2.53759i) q^{5} -1.58579i q^{8} +(1.05110 - 0.606854i) q^{10} +(-4.18154 + 2.41421i) q^{11} -2.93015i q^{13} +(-1.50000 + 2.59808i) q^{16} +(-3.53701 - 6.12627i) q^{17} +(5.07517 + 2.93015i) q^{19} -5.35757 q^{20} -2.00000 q^{22} +(-1.73205 - 1.00000i) q^{23} +(-1.79289 - 3.10538i) q^{25} +(0.606854 - 1.05110i) q^{26} +0.828427i q^{29} +(5.07517 - 2.93015i) q^{31} +(-3.82282 + 2.20711i) q^{32} -2.93015i q^{34} +(2.70711 - 4.68885i) q^{37} +(1.21371 + 2.10220i) q^{38} +(-4.02407 - 2.32330i) q^{40} +1.21371 q^{41} +4.48528 q^{43} +(7.64564 + 4.41421i) q^{44} +(-0.414214 - 0.717439i) q^{46} +(2.93015 - 5.07517i) q^{47} -1.48528i q^{50} +(-4.63979 + 2.67878i) q^{52} +(6.12372 - 3.53553i) q^{53} +14.1480i q^{55} +(-0.171573 + 0.297173i) q^{58} +(2.93015 + 5.07517i) q^{59} +(1.05110 + 0.606854i) q^{61} +2.42742 q^{62} +4.17157 q^{64} +(-7.43551 - 4.29289i) q^{65} +(4.24264 + 7.34847i) q^{67} +(-6.46716 + 11.2014i) q^{68} -0.828427i q^{71} +(-6.12627 + 3.53701i) q^{73} +(1.94218 - 1.12132i) q^{74} -10.7151i q^{76} +(-0.828427 + 1.43488i) q^{79} +(4.39523 + 7.61276i) q^{80} +(0.435381 + 0.251367i) q^{82} +11.7206 q^{83} -20.7279 q^{85} +(1.60896 + 0.928932i) q^{86} +(3.82843 + 6.63103i) q^{88} +(-5.60894 + 9.71496i) q^{89} +3.65685i q^{92} +(2.10220 - 1.21371i) q^{94} +(14.8710 - 8.58579i) q^{95} +7.07401i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 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

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Database

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