LMFDB - Embedded newform 441.2.w.a.188.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(62,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

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

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

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

chi := DirichletCharacter("441.62");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.w (of order $14$, degree $6$, 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:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			188.8
Character	$\chi$	$=$	441.188
Dual form			441.2.w.a.251.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.920203 + 0.733838i) q^{2} +(-0.136785 + 0.599296i) q^{4} +(1.46088 - 0.703524i) q^{5} +(-2.01956 + 1.70920i) q^{7} +(-1.33526 - 2.77270i) q^{8} +O(q^{10})$	\(q+(-0.920203 + 0.733838i) q^{2} +(-0.136785 + 0.599296i) q^{4} +(1.46088 - 0.703524i) q^{5} +(-2.01956 + 1.70920i) q^{7} +(-1.33526 - 2.77270i) q^{8} +(-0.828037 + 1.71944i) q^{10} +(-2.35512 + 1.87814i) q^{11} +(-2.44072 + 1.94641i) q^{13} +(0.604130 - 3.05484i) q^{14} +(2.15577 + 1.03816i) q^{16} +(-0.882993 - 3.86864i) q^{17} +6.34682i q^{19} +(0.221792 + 0.971733i) q^{20} +(0.788935 - 3.45655i) q^{22} +(1.23051 + 0.280855i) q^{23} +(-1.47822 + 1.85362i) q^{25} +(0.817612 - 3.58219i) q^{26} +(-0.748071 - 1.44411i) q^{28} +(-7.25165 + 1.65514i) q^{29} -1.49304i q^{31} +(3.25504 - 0.742941i) q^{32} +(3.65149 + 2.91197i) q^{34} +(-1.74788 + 3.91776i) q^{35} +(-1.72116 - 7.54089i) q^{37} +(-4.65754 - 5.84036i) q^{38} +(-3.90133 - 3.11121i) q^{40} +(-9.09214 + 4.37855i) q^{41} +(-0.978095 - 0.471026i) q^{43} +(-0.803418 - 1.66832i) q^{44} +(-1.33842 + 0.644549i) q^{46} +(5.44608 + 6.82916i) q^{47} +(1.15725 - 6.90368i) q^{49} -2.79048i q^{50} +(-0.832622 - 1.72896i) q^{52} +(-0.104261 - 0.0237970i) q^{53} +(-2.11923 + 4.40063i) q^{55} +(7.43576 + 3.31741i) q^{56} +(5.45839 - 6.84461i) q^{58} +(-1.54958 - 0.746240i) q^{59} +(-10.5852 + 2.41600i) q^{61} +(1.09565 + 1.37390i) q^{62} +(-5.43377 + 6.81373i) q^{64} +(-2.19626 + 4.56059i) q^{65} +11.0005 q^{67} +2.43924 q^{68} +(-1.26659 - 4.88779i) q^{70} +(-3.29503 - 0.752069i) q^{71} +(8.80135 + 7.01884i) q^{73} +(7.11761 + 5.67610i) q^{74} +(-3.80362 - 0.868152i) q^{76} +(1.54618 - 7.81840i) q^{77} +14.5682 q^{79} +3.87969 q^{80} +(5.15348 - 10.7013i) q^{82} +(-2.15744 + 2.70535i) q^{83} +(-4.01163 - 5.03043i) q^{85} +(1.24570 - 0.284324i) q^{86} +(8.35225 + 4.02223i) q^{88} +(7.65264 - 9.59610i) q^{89} +(1.60238 - 8.10259i) q^{91} +(-0.336631 + 0.699021i) q^{92} +(-10.0230 - 2.28768i) q^{94} +(4.46514 + 9.27196i) q^{95} +6.40900i q^{97} +(4.00127 + 7.20202i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 24 q^{4}+O(q^{10}) $ 120 * q + 24 * q^4	$ 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94}+O(q^{100}) $ 120 * q + 24 * q^4 - 32 * q^16 - 44 * q^22 - 4 * q^25 - 56 * q^28 + 112 * q^34 - 76 * q^37 + 28 * q^40 + 8 * q^43 - 40 * q^46 - 84 * q^49 - 140 * q^52 + 12 * q^58 - 84 * q^61 + 24 * q^64 + 16 * q^67 + 112 * q^70 - 84 * q^76 - 24 * q^79 + 140 * q^82 - 96 * q^85 - 24 * q^88 - 112 * q^91 - 112 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{14}\right)$	$-1$

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 $

$2$	−0.920203	+	0.733838i	−0.650682	+	0.518902i	−0.892284	−	0.451474i	$-0.850898\pi$
$2$	−0.920203	+	0.733838i	−0.650682	+	0.518902i	0.241602	+	0.970375i	$0.422327\pi$
$3$		0			0
$3$		0			0
$4$	−0.136785	+	0.599296i	−0.0683927	+	0.299648i
$5$	1.46088	−	0.703524i	0.653327	−	0.314626i	−0.0776976	−	0.996977i	$-0.524757\pi$
$5$	1.46088	−	0.703524i	0.653327	−	0.314626i	0.731024	+	0.682351i	$0.239043\pi$
$6$		0			0
$7$	−2.01956	+	1.70920i	−0.763322	+	0.646018i
$7$	−2.01956	+	1.70920i	−0.763322	+	0.646018i
$8$	−1.33526	−	2.77270i	−0.472087	−	0.980299i
$9$		0			0
$10$	−0.828037	+	1.71944i	−0.261848	+	0.543734i
$11$	−2.35512	+	1.87814i	−0.710095	+	0.566282i	−0.910539	−	0.413423i	$-0.864333\pi$
$11$	−2.35512	+	1.87814i	−0.710095	+	0.566282i	0.200444	+	0.979705i	$0.435762\pi$
$12$		0			0
$13$	−2.44072	+	1.94641i	−0.676935	+	0.539838i	−0.900503	−	0.434851i	$-0.856801\pi$
$13$	−2.44072	+	1.94641i	−0.676935	+	0.539838i	0.223567	+	0.974688i	$0.428230\pi$
$14$	0.604130	−	3.05484i	0.161460	−	0.816441i
$15$		0			0
$16$	2.15577	+	1.03816i	0.538941	+	0.259540i
$17$	−0.882993	−	3.86864i	−0.214157	−	0.938284i	−0.961707	−	0.274079i	$-0.911627\pi$
$17$	−0.882993	−	3.86864i	−0.214157	−	0.938284i	0.747550	−	0.664205i	$-0.231230\pi$
$18$		0			0
$19$			6.34682i			1.45606i	0.685545	+	0.728030i	$0.259564\pi$
$19$			6.34682i			1.45606i	−0.685545	+	0.728030i	$0.740436\pi$
$20$	0.221792	+	0.971733i	0.0495941	+	0.217286i
$21$		0			0
$22$	0.788935	−	3.45655i	0.168202	−	0.736939i
$23$	1.23051	+	0.280855i	0.256579	+	0.0585624i	0.348875	−	0.937169i	$-0.386564\pi$
$23$	1.23051	+	0.280855i	0.256579	+	0.0585624i	−0.0922967	+	0.995732i	$0.529421\pi$
$24$		0			0
$25$	−1.47822	+	1.85362i	−0.295643	+	0.370725i
$26$	0.817612	−	3.58219i	0.160347	−	0.702526i
$27$		0			0
$28$	−0.748071	−	1.44411i	−0.141372	−	0.272911i
$29$	−7.25165	+	1.65514i	−1.34660	+	0.307352i	−0.834232	−	0.551414i	$-0.814088\pi$
$29$	−7.25165	+	1.65514i	−1.34660	+	0.307352i	−0.512367	+	0.858767i	$0.671231\pi$
$30$		0			0
$31$		−	1.49304i		−	0.268158i	−0.990971	−	0.134079i	$-0.957192\pi$
$31$		−	1.49304i		−	0.268158i	0.990971	−	0.134079i	$-0.0428076\pi$
$32$	3.25504	−	0.742941i	0.575415	−	0.131335i
$33$		0			0
$34$	3.65149	+	2.91197i	0.626225	+	0.499398i
$35$	−1.74788	+	3.91776i	−0.295445	+	0.662221i
$36$		0			0
$37$	−1.72116	−	7.54089i	−0.282957	−	1.23971i	−0.893982	−	0.448103i	$-0.852100\pi$
$37$	−1.72116	−	7.54089i	−0.282957	−	1.23971i	0.611025	−	0.791611i	$-0.290757\pi$
$38$	−4.65754	−	5.84036i	−0.755552	−	0.947432i
$39$		0			0
$40$	−3.90133	−	3.11121i	−0.616854	−	0.491925i
$41$	−9.09214	+	4.37855i	−1.41995	+	0.683814i	−0.977100	−	0.212780i	$-0.931748\pi$
$41$	−9.09214	+	4.37855i	−1.41995	+	0.683814i	−0.442854	+	0.896594i	$0.646034\pi$
$42$		0			0
$43$	−0.978095	−	0.471026i	−0.149158	−	0.0718308i	0.357816	−	0.933792i	$-0.383522\pi$
$43$	−0.978095	−	0.471026i	−0.149158	−	0.0718308i	−0.506974	+	0.861961i	$0.669236\pi$
$44$	−0.803418	−	1.66832i	−0.121120	−	0.251508i
$45$		0			0
$46$	−1.33842	+	0.644549i	−0.197339	+	0.0950336i
$47$	5.44608	+	6.82916i	0.794392	+	0.996136i	0.999847	+	0.0174695i	$0.00556100\pi$
$47$	5.44608	+	6.82916i	0.794392	+	0.996136i	−0.205455	+	0.978666i	$0.565868\pi$
$48$		0			0
$49$	1.15725	−	6.90368i	0.165322	−	0.986240i
$50$		−	2.79048i		−	0.394634i
$51$		0			0
$52$	−0.832622	−	1.72896i	−0.115464	−	0.239763i
$53$	−0.104261	−	0.0237970i	−0.0143214	−	0.00326877i	0.215354	−	0.976536i	$-0.430909\pi$
$53$	−0.104261	−	0.0237970i	−0.0143214	−	0.00326877i	−0.229676	+	0.973267i	$0.573767\pi$
$54$		0			0
$55$	−2.11923	+	4.40063i	−0.285757	+	0.593381i
$56$	7.43576	+	3.31741i	0.993645	+	0.443308i
$57$		0			0
$58$	5.45839	−	6.84461i	0.716722	−	0.898741i
$59$	−1.54958	−	0.746240i	−0.201739	−	0.0971522i	0.330287	−	0.943881i	$-0.392855\pi$
$59$	−1.54958	−	0.746240i	−0.201739	−	0.0971522i	−0.532025	+	0.846728i	$0.678569\pi$
$60$		0			0
$61$	−10.5852	+	2.41600i	−1.35529	+	0.309337i	−0.837626	−	0.546244i	$-0.816057\pi$
$61$	−10.5852	+	2.41600i	−1.35529	+	0.309337i	−0.517668	+	0.855581i	$0.673200\pi$
$62$	1.09565	+	1.37390i	0.139148	+	0.174486i
$63$		0			0
$64$	−5.43377	+	6.81373i	−0.679221	+	0.851717i
$65$	−2.19626	+	4.56059i	−0.272413	+	0.565672i
$66$		0			0
$67$	11.0005			1.34392			0.671961	−	0.740587i	$-0.265452\pi$
$67$	11.0005			1.34392			0.671961	+	0.740587i	$0.265452\pi$
$68$	2.43924			0.295802
$69$		0			0
$70$	−1.26659	−	4.88779i	−0.151387	−	0.584203i
$71$	−3.29503	−	0.752069i	−0.391048	−	0.0892542i	0.0224758	−	0.999747i	$-0.492845\pi$
$71$	−3.29503	−	0.752069i	−0.391048	−	0.0892542i	−0.413524	+	0.910493i	$0.635702\pi$
$72$		0			0
$73$	8.80135	+	7.01884i	1.03012	+	0.821493i	0.984130	−	0.177449i	$-0.0567844\pi$
$73$	8.80135	+	7.01884i	1.03012	+	0.821493i	0.0459897	+	0.998942i	$0.485356\pi$
$74$	7.11761	+	5.67610i	0.827405	+	0.659833i
$75$		0			0
$76$	−3.80362	−	0.868152i	−0.436305	−	0.0995838i
$77$	1.54618	−	7.81840i	0.176203	−	0.890990i
$78$		0			0
$79$	14.5682			1.63905			0.819525	−	0.573044i	$-0.194238\pi$
$79$	14.5682			1.63905			0.819525	+	0.573044i	$0.194238\pi$
$80$	3.87969			0.433763
$81$		0			0
$82$	5.15348	−	10.7013i	0.569107	−	1.18176i
$83$	−2.15744	+	2.70535i	−0.236810	+	0.296950i	−0.886009	−	0.463668i	$-0.846533\pi$
$83$	−2.15744	+	2.70535i	−0.236810	+	0.296950i	0.649199	+	0.760619i	$0.275104\pi$
$84$		0			0
$85$	−4.01163	−	5.03043i	−0.435123	−	0.545627i
$86$	1.24570	−	0.284324i	0.134328	−	0.0306594i
$87$		0			0
$88$	8.35225	+	4.02223i	0.890352	+	0.428771i
$89$	7.65264	−	9.59610i	0.811178	−	1.01718i	−0.188207	−	0.982129i	$-0.560268\pi$
$89$	7.65264	−	9.59610i	0.811178	−	1.01718i	0.999385	−	0.0350556i	$-0.0111608\pi$
$90$		0			0
$91$	1.60238	−	8.10259i	0.167975	−	0.849382i
$92$	−0.336631	+	0.699021i	−0.0350962	+	0.0728780i
$93$		0			0
$94$	−10.0230	−	2.28768i	−1.03379	−	0.235957i
$95$	4.46514	+	9.27196i	0.458114	+	0.951283i
$96$		0			0
$97$			6.40900i			0.650736i	0.945587	+	0.325368i	$0.105488\pi$
$97$			6.40900i			0.650736i	−0.945587	+	0.325368i	$0.894512\pi$
$98$	4.00127	+	7.20202i	0.404189	+	0.727514i
$99$		0			0
$100$	−0.908671	−	1.13944i	−0.0908671	−	0.113944i
$101$	−0.402455	+	0.193812i	−0.0400458	+	0.0192850i	−0.453799	−	0.891104i	$-0.649932\pi$
$101$	−0.402455	+	0.193812i	−0.0400458	+	0.0192850i	0.413754	+	0.910389i	$0.364217\pi$
$102$		0			0
$103$	−1.04038	−	2.16038i	−0.102512	−	0.212869i	0.843404	−	0.537280i	$-0.180548\pi$
$103$	−1.04038	−	2.16038i	−0.102512	−	0.212869i	−0.945916	+	0.324411i	$0.894834\pi$
$104$	8.65584	+	4.16843i	0.848775	+	0.408749i
$105$		0			0
$106$	0.113405	−	0.0546129i	0.0110149	−	0.00530447i
$107$	12.7985	+	10.2065i	1.23728	+	0.986698i	0.999883	+	0.0152850i	$0.00486557\pi$
$107$	12.7985	+	10.2065i	1.23728	+	0.986698i	0.237397	+	0.971413i	$0.423706\pi$
$108$		0			0
$109$	12.8699	+	16.1383i	1.23271	+	1.54577i	0.734292	+	0.678834i	$0.237515\pi$
$109$	12.8699	+	16.1383i	1.23271	+	1.54577i	0.498419	+	0.866936i	$0.333914\pi$
$110$	−1.27923	−	5.60465i	−0.121969	−	0.534383i
$111$		0			0
$112$	−6.12813	+	1.58801i	−0.579054	+	0.150053i
$113$	−0.0806342	−	0.0643036i	−0.00758543	−	0.00604918i	0.619690	−	0.784847i	$-0.287258\pi$
$113$	−0.0806342	−	0.0643036i	−0.00758543	−	0.00604918i	−0.627275	+	0.778798i	$0.715830\pi$
$114$		0			0
$115$	1.99522	−	0.455395i	0.186055	−	0.0424658i
$116$		−	4.57228i		−	0.424526i
$117$		0			0
$118$	1.97355	−	0.450450i	0.181680	−	0.0414673i
$119$	8.39555	+	6.30375i	0.769619	+	0.577864i
$120$		0			0
$121$	−0.428573	+	1.87770i	−0.0389612	+	0.170700i
$122$	7.96757	−	9.99102i	0.721350	−	0.904544i
$123$		0			0
$124$	0.894772	+	0.204226i	0.0803529	+	0.0183400i
$125$	−2.65947	+	11.6519i	−0.237870	+	1.04218i
$126$		0			0
$127$	2.10534	+	9.22408i	0.186818	+	0.818504i	0.978280	+	0.207286i	$0.0664631\pi$
$127$	2.10534	+	9.22408i	0.186818	+	0.818504i	−0.791462	+	0.611218i	$0.790680\pi$
$128$		−	3.58003i		−	0.316433i
$129$		0			0
$130$	−1.32572	−	5.80837i	−0.116274	−	0.509428i
$131$	−9.38963	−	4.52181i	−0.820376	−	0.395072i	−0.0238790	−	0.999715i	$-0.507602\pi$
$131$	−9.38963	−	4.52181i	−0.820376	−	0.395072i	−0.796497	+	0.604643i	$0.793316\pi$
$132$		0			0
$133$	−10.8480	−	12.8178i	−0.940641	−	1.11144i
$134$	−10.1227	+	8.07256i	−0.874466	+	0.697363i
$135$		0			0
$136$	−9.54758	+	7.61394i	−0.818698	+	0.652890i
$137$	0.174028	−	0.361374i	0.0148682	−	0.0308742i	−0.893402	−	0.449257i	$-0.851689\pi$
$137$	0.174028	−	0.361374i	0.0148682	−	0.0308742i	0.908271	+	0.418383i	$0.137403\pi$
$138$		0			0
$139$	−0.906271	−	1.88189i	−0.0768689	−	0.159620i	0.858993	−	0.511988i	$-0.171091\pi$
$139$	−0.906271	−	1.88189i	−0.0768689	−	0.159620i	−0.935861	+	0.352368i	$0.885377\pi$
$140$	−2.10881	−	1.58339i	−0.178227	−	0.133821i
$141$		0			0
$142$	3.58400	−	1.72596i	0.300762	−	0.144839i
$143$	2.09255	−	9.16807i	0.174988	−	0.766672i
$144$		0			0
$145$	−9.42939	+	7.51968i	−0.783068	+	0.624476i
$146$	−13.2497			−1.09655
$147$		0			0
$148$	4.75465			0.390830
$149$	6.31126	−	5.03306i	0.517038	−	0.412324i	−0.329900	−	0.944016i	$-0.607015\pi$
$149$	6.31126	−	5.03306i	0.517038	−	0.412324i	0.846938	+	0.531692i	$0.178443\pi$
$150$		0			0
$151$	3.42041	−	14.9858i	0.278349	−	1.21953i	−0.621532	−	0.783389i	$-0.713489\pi$
$151$	3.42041	−	14.9858i	0.278349	−	1.21953i	0.899880	−	0.436137i	$-0.143654\pi$
$152$	17.5979	−	8.47468i	1.42737	−	0.687387i
$153$		0			0
$154$	4.31464	+	8.32916i	0.347684	+	0.671183i
$155$	−1.05039	−	2.18116i	−0.0843693	−	0.175195i
$156$		0			0
$157$	4.33471	−	9.00113i	0.345948	−	0.718368i	−0.653302	−	0.757097i	$-0.726617\pi$
$157$	4.33471	−	9.00113i	0.345948	−	0.718368i	0.999250	+	0.0387294i	$0.0123311\pi$
$158$	−13.4057	+	10.6907i	−1.06650	+	0.850505i
$159$		0			0
$160$	4.23255	−	3.37535i	0.334613	−	0.266845i
$161$	−2.96513	+	1.53598i	−0.233685	+	0.121052i
$162$		0			0
$163$	0.815328	+	0.392641i	0.0638614	+	0.0307540i	0.465542	−	0.885026i	$-0.345859\pi$
$163$	0.815328	+	0.392641i	0.0638614	+	0.0307540i	−0.401680	+	0.915780i	$0.631574\pi$
$164$	−1.38037	−	6.04780i	−0.107789	−	0.472254i
$165$		0			0
$166$		−	4.07268i		−	0.316101i
$167$	−0.422648	−	1.85174i	−0.0327055	−	0.143292i	0.955939	−	0.293565i	$-0.0948418\pi$
$167$	−0.422648	−	1.85174i	−0.0327055	−	0.143292i	−0.988644	+	0.150273i	$0.951985\pi$
$168$		0			0
$169$	−0.724159	+	3.17275i	−0.0557045	+	0.244057i
$170$	7.38304	+	1.68513i	0.566253	+	0.129244i
$171$		0			0
$172$	0.416073	−	0.521739i	0.0317253	−	0.0397822i
$173$	−1.64885	+	7.22409i	−0.125360	+	0.549237i	0.872771	+	0.488129i	$0.162321\pi$
$173$	−1.64885	+	7.22409i	−0.125360	+	0.549237i	−0.998131	+	0.0611080i	$0.980537\pi$
$174$		0			0
$175$	−0.182871	−	6.27008i	−0.0138238	−	0.473973i
$176$	−7.02690	+	1.60384i	−0.529673	+	0.120894i
$177$		0			0
$178$			14.4462i			1.08279i
$179$	−22.9124	+	5.22960i	−1.71255	+	0.390879i	−0.962667	−	0.270689i	$-0.912749\pi$
$179$	−22.9124	+	5.22960i	−1.71255	+	0.390879i	−0.749885	+	0.661568i	$0.769891\pi$
$180$		0			0
$181$	10.1147	+	8.06617i	0.751817	+	0.599554i	0.922601	−	0.385755i	$-0.126059\pi$
$181$	10.1147	+	8.06617i	0.751817	+	0.599554i	−0.170785	+	0.985308i	$0.554630\pi$
$182$	4.47147	+	8.63192i	0.331448	+	0.639840i
$183$		0			0
$184$	−0.864324	−	3.78685i	−0.0637188	−	0.279170i
$185$	−7.81961	−	9.80548i	−0.574909	−	0.720913i
$186$		0			0
$187$	9.34543	+	7.45273i	0.683405	+	0.544998i
$188$	−4.83763	+	2.32968i	−0.352821	+	0.169909i
$189$		0			0
$190$	−10.9130	−	5.25540i	−0.791709	−	0.381267i
$191$	8.84660	+	18.3702i	0.640118	+	1.32922i	0.928368	+	0.371663i	$0.121212\pi$
$191$	8.84660	+	18.3702i	0.640118	+	1.32922i	−0.288250	+	0.957555i	$0.593073\pi$
$192$		0			0
$193$	−3.34801	+	1.61232i	−0.240995	+	0.116057i	−0.550483	−	0.834846i	$-0.685557\pi$
$193$	−3.34801	+	1.61232i	−0.240995	+	0.116057i	0.309488	+	0.950903i	$0.399842\pi$
$194$	−4.70317	−	5.89759i	−0.337668	−	0.423422i
$195$		0			0
$196$	3.97905	+	1.63786i	0.284218	+	0.116990i
$197$		−	22.4887i		−	1.60225i	−0.598495	−	0.801127i	$-0.704234\pi$
$197$		−	22.4887i		−	1.60225i	0.598495	−	0.801127i	$-0.295766\pi$
$198$		0			0
$199$	−3.52589	−	7.32159i	−0.249944	−	0.519014i	0.737815	−	0.675003i	$-0.235858\pi$
$199$	−3.52589	−	7.32159i	−0.249944	−	0.519014i	−0.987759	+	0.155989i	$0.950143\pi$
$200$	7.11336	+	1.62358i	0.502991	+	0.114804i
$201$		0			0
$202$	0.228114	−	0.473683i	0.0160500	−	0.0333282i
$203$	11.8162	−	15.7372i	0.829334	−	1.10454i
$204$		0			0
$205$	−10.2021	+	12.7931i	−0.712549	+	0.893508i
$206$	2.54274	+	1.22452i	0.177161	+	0.0853161i
$207$		0			0
$208$	−7.28232	+	1.66214i	−0.504938	+	0.115249i
$209$	−11.9202	−	14.9475i	−0.824540	−	1.03394i
$210$		0			0
$211$	−7.04725	+	8.83697i	−0.485153	+	0.608362i	−0.962808	−	0.270185i	$-0.912915\pi$
$211$	−7.04725	+	8.83697i	−0.485153	+	0.608362i	0.477656	+	0.878547i	$0.341487\pi$
$212$	0.0285229	−	0.0592283i	0.00195896	−	0.00406782i
$213$		0			0
$214$	−19.2671			−1.31708
$215$	−1.76026			−0.120049
$216$		0			0
$217$	2.55191	+	3.01528i	0.173235	+	0.204691i
$218$	−23.6858	−	5.40613i	−1.60421	−	0.366149i
$219$		0			0
$220$	−2.34740	−	1.87199i	−0.158262	−	0.126209i
$221$	9.68512	+	7.72363i	0.651492	+	0.519547i
$222$		0			0
$223$	−14.7674	−	3.37056i	−0.988899	−	0.225710i	−0.302670	−	0.953095i	$-0.597878\pi$
$223$	−14.7674	−	3.37056i	−0.988899	−	0.225710i	−0.686229	+	0.727386i	$0.740735\pi$
$224$	−5.30391	+	7.06393i	−0.354382	+	0.471979i
$225$		0			0
$226$	0.121388			0.00807463
$227$	−10.2172			−0.678137			−0.339068	−	0.940762i	$-0.610112\pi$
$227$	−10.2172			−0.678137			−0.339068	+	0.940762i	$0.610112\pi$
$228$		0			0
$229$	8.72661	−	18.1210i	0.576670	−	1.19747i	−0.384912	−	0.922953i	$-0.625768\pi$
$229$	8.72661	−	18.1210i	0.576670	−	1.19747i	0.961583	−	0.274515i	$-0.0885173\pi$
$230$	−1.50182	+	1.88322i	−0.0990270	+	0.124176i
$231$		0			0
$232$	14.2721	+	17.8966i	0.937009	+	1.17497i
$233$	−13.2535	+	3.02504i	−0.868269	+	0.198177i	−0.633376	−	0.773845i	$-0.718331\pi$
$233$	−13.2535	+	3.02504i	−0.868269	+	0.198177i	−0.234893	+	0.972021i	$0.575474\pi$
$234$		0			0
$235$	12.7606	+	6.14516i	0.832407	+	0.400866i
$236$	0.659179	−	0.826584i	0.0429089	−	0.0538060i
$237$		0			0
$238$	−12.3515	+	0.360242i	−0.800632	+	0.0233510i
$239$	−4.93834	+	10.2546i	−0.319434	+	0.663312i	−0.997422	−	0.0717611i	$-0.977138\pi$
$239$	−4.93834	+	10.2546i	−0.319434	+	0.663312i	0.677987	+	0.735073i	$0.262852\pi$
$240$		0			0
$241$	−10.7608	−	2.45609i	−0.693166	−	0.158211i	−0.138598	−	0.990349i	$-0.544260\pi$
$241$	−10.7608	−	2.45609i	−0.693166	−	0.158211i	−0.554569	+	0.832138i	$0.687117\pi$
$242$	−0.983553	−	2.04237i	−0.0632252	−	0.131288i
$243$		0			0
$244$		−	6.67413i		−	0.427267i
$245$	−3.16629	−	10.8996i	−0.202287	−	0.696351i
$246$		0			0
$247$	−12.3535	−	15.4908i	−0.786036	−	0.985658i
$248$	−4.13976	+	1.99360i	−0.262875	+	0.126594i
$249$		0			0
$250$	−6.10336	−	12.6738i	−0.386010	−	0.801558i
$251$	−8.68576	−	4.18284i	−0.548240	−	0.264019i	0.139194	−	0.990265i	$-0.455549\pi$
$251$	−8.68576	−	4.18284i	−0.548240	−	0.264019i	−0.687434	+	0.726246i	$0.741263\pi$
$252$		0			0
$253$	−3.42548	+	1.64962i	−0.215358	+	0.103711i
$254$	−8.70631	−	6.94305i	−0.546283	−	0.435646i
$255$		0			0
$256$	−8.24038	−	10.3331i	−0.515024	−	0.645819i
$257$	−4.54669	−	19.9204i	−0.283615	−	1.24260i	−0.893121	−	0.449817i	$-0.851489\pi$
$257$	−4.54669	−	19.9204i	−0.283615	−	1.24260i	0.609506	−	0.792781i	$-0.291368\pi$
$258$		0			0
$259$	16.3649	+	12.2875i	1.01686	+	0.763507i
$260$	−2.43273	−	1.94003i	−0.150871	−	0.120316i
$261$		0			0
$262$	11.9586	−	2.72948i	0.738807	−	0.168628i
$263$		−	2.13098i		−	0.131402i	−0.997839	−	0.0657008i	$-0.979072\pi$
$263$		−	2.13098i		−	0.131402i	0.997839	−	0.0657008i	$-0.0209283\pi$
$264$		0			0
$265$	−0.169055	+	0.0385858i	−0.0103850	+	0.00237031i
$266$	19.3885	+	3.83430i	1.18879	+	0.235096i
$267$		0			0
$268$	−1.50470	+	6.59254i	−0.0919144	+	0.402703i
$269$	−12.2811	+	15.4000i	−0.748793	+	0.938957i	−0.999577	−	0.0290862i	$-0.990740\pi$
$269$	−12.2811	+	15.4000i	−0.748793	+	0.938957i	0.250784	+	0.968043i	$0.419312\pi$
$270$		0			0
$271$	−9.93868	−	2.26844i	−0.603732	−	0.137798i	−0.0902801	−	0.995916i	$-0.528776\pi$
$271$	−9.93868	−	2.26844i	−0.603732	−	0.137798i	−0.513452	+	0.858119i	$0.671633\pi$
$272$	2.11275	−	9.25658i	0.128105	−	0.561263i
$273$		0			0
$274$	0.105048	+	0.460246i	0.00634619	+	0.0278045i
$275$		−	7.14181i		−	0.430667i
$276$		0			0
$277$	1.55911	+	6.83089i	0.0936776	+	0.410428i	0.999924	−	0.0123214i	$-0.00392213\pi$
$277$	1.55911	+	6.83089i	0.0936776	+	0.410428i	−0.906247	+	0.422750i	$0.861065\pi$
$278$	2.21496	+	1.06667i	0.132844	+	0.0639744i
$279$		0			0
$280$	13.1967	−	0.384890i	0.788651	−	0.0230016i
$281$	19.0575	−	15.1979i	1.13688	−	0.906630i	0.140368	−	0.990099i	$-0.455172\pi$
$281$	19.0575	−	15.1979i	1.13688	−	0.906630i	0.996510	+	0.0834696i	$0.0266002\pi$
$282$		0			0
$283$	−11.2353	+	8.95982i	−0.667867	+	0.532606i	−0.897691	−	0.440626i	$-0.854756\pi$
$283$	−11.2353	+	8.95982i	−0.667867	+	0.532606i	0.229824	+	0.973232i	$0.426185\pi$
$284$	0.901424	−	1.87183i	0.0534897	−	0.111072i
$285$		0			0
$286$	4.80230	+	9.97208i	0.283966	+	0.589661i
$287$	10.8783	−	24.3831i	0.642127	−	1.43929i
$288$		0			0
$289$	1.12974	−	0.544053i	0.0664552	−	0.0320031i
$290$	3.15873	−	13.8393i	0.185487	−	0.812671i
$291$		0			0
$292$	−5.41026	+	4.31453i	−0.316611	+	0.252489i
$293$	−6.11482			−0.357232			−0.178616	−	0.983919i	$-0.557162\pi$
$293$	−6.11482			−0.357232			−0.178616	+	0.983919i	$0.557162\pi$
$294$		0			0
$295$	−2.78876			−0.162368
$296$	−18.6105	+	14.8413i	−1.08171	+	0.862636i
$297$		0			0
$298$	−2.11419	+	9.26288i	−0.122472	+	0.536584i
$299$	−3.54999	+	1.70959i	−0.205301	+	0.0988679i
$300$		0			0
$301$	2.78040	−	0.720497i	0.160260	−	0.0415288i
$302$	7.84966	+	16.3000i	0.451697	+	0.937959i
$303$		0			0
$304$	−6.58903	+	13.6823i	−0.377907	+	0.784731i
$305$	−13.7640	+	10.9764i	−0.788125	+	0.628508i
$306$		0			0
$307$	19.0106	−	15.1604i	1.08499	−	0.865253i	0.0935262	−	0.995617i	$-0.470186\pi$
$307$	19.0106	−	15.1604i	1.08499	−	0.865253i	0.991466	+	0.130364i	$0.0416147\pi$
$308$	4.47404	+	1.99606i	0.254932	+	0.113736i
$309$		0			0
$310$	2.56719	+	1.23629i	0.145806	+	0.0702167i
$311$	6.98480	+	30.6024i	0.396072	+	1.73530i	0.642632	+	0.766175i	$0.277843\pi$
$311$	6.98480	+	30.6024i	0.396072	+	1.73530i	−0.246560	+	0.969128i	$0.579300\pi$
$312$		0			0
$313$			23.8964i			1.35070i	0.737496	+	0.675351i	$0.236008\pi$
$313$			23.8964i			1.35070i	−0.737496	+	0.675351i	$0.763992\pi$
$314$	2.61655	+	11.4638i	0.147660	+	0.646942i
$315$		0			0
$316$	−1.99271	+	8.73065i	−0.112099	+	0.491138i
$317$	28.8101	+	6.57572i	1.61814	+	0.369329i	0.933224	−	0.359296i	$-0.116983\pi$
$317$	28.8101	+	6.57572i	1.61814	+	0.369329i	0.684913	+	0.728625i	$0.259840\pi$
$318$		0			0
$319$	13.9699	−	17.5177i	0.782165	−	0.980804i
$320$	−3.14448	+	13.7769i	−0.175782	+	0.770150i
$321$		0			0
$322$	1.60136	−	3.58934i	0.0892401	−	0.200026i
$323$	24.5536	−	5.60420i	1.36620	−	0.311826i
$324$		0			0
$325$		−	7.40140i		−	0.410556i
$326$	−1.03840	+	0.237009i	−0.0575118	+	0.0131267i
$327$		0			0
$328$	24.2808	+	19.3633i	1.34068	+	1.06916i
$329$	−22.6711	−	4.48347i	−1.24990	−	0.247182i
$330$		0			0
$331$	−2.23262	−	9.78176i	−0.122716	−	0.537654i	−0.998490	−	0.0549329i	$-0.982506\pi$
$331$	−2.23262	−	9.78176i	−0.122716	−	0.537654i	0.875774	−	0.482721i	$-0.160352\pi$
$332$	−1.32620	−	1.66300i	−0.0727845	−	0.0912688i
$333$		0			0
$334$	1.74780	+	1.39382i	0.0956353	+	0.0762666i
$335$	16.0704	−	7.73910i	0.878020	−	0.422832i
$336$		0			0
$337$	2.17525	+	1.04754i	0.118493	+	0.0570633i	0.492191	−	0.870487i	$-0.336196\pi$
$337$	2.17525	+	1.04754i	0.118493	+	0.0570633i	−0.373698	+	0.927550i	$0.621910\pi$
$338$	−1.66191	−	3.45099i	−0.0903959	−	0.187709i
$339$		0			0
$340$	3.56345	−	1.71607i	0.193255	−	0.0930668i
$341$	2.80414	+	3.51629i	0.151853	+	0.190418i
$342$		0			0
$343$	9.46264	+	15.9204i	0.510934	+	0.859620i
$344$			3.34091i			0.180130i
$345$		0			0
$346$	−3.78403	−	7.85762i	−0.203431	−	0.422428i
$347$	21.6209	+	4.93483i	1.16067	+	0.264916i	0.759139	−	0.650929i	$-0.225620\pi$
$347$	21.6209	+	4.93483i	1.16067	+	0.264916i	0.401533	+	0.915845i	$0.368478\pi$
$348$		0			0
$349$	−12.3332	+	25.6101i	−0.660180	+	1.37088i	0.254648	+	0.967034i	$0.418040\pi$
$349$	−12.3332	+	25.6101i	−0.660180	+	1.37088i	−0.914828	+	0.403844i	$0.867674\pi$
$350$	4.76950	+	5.63555i	0.254940	+	0.301233i
$351$		0			0
$352$	−6.27065	+	7.86315i	−0.334227	+	0.419107i
$353$	8.75844	+	4.21784i	0.466165	+	0.224493i	0.652195	−	0.758051i	$-0.273848\pi$
$353$	8.75844	+	4.21784i	0.466165	+	0.224493i	−0.186031	+	0.982544i	$0.559562\pi$
$354$		0			0
$355$	−5.34276	+	1.21945i	−0.283564	+	0.0647216i
$356$	4.70413	+	5.89880i	0.249319	+	0.312636i
$357$		0			0
$358$	17.2464	−	21.6263i	0.911500	−	1.14298i
$359$	5.14678	−	10.6874i	0.271637	−	0.564059i	−0.719871	−	0.694108i	$-0.755799\pi$
$359$	5.14678	−	10.6874i	0.271637	−	0.564059i	0.991508	+	0.130049i	$0.0415134\pi$
$360$		0			0
$361$	−21.2821			−1.12011
$362$	−15.2268			−0.800303
$363$		0			0
$364$	4.63667	+	2.06861i	0.243027	+	0.108425i
$365$	17.7957	+	4.06174i	0.931468	+	0.212601i
$366$		0			0
$367$	−24.7126	−	19.7076i	−1.28999	−	1.02873i	−0.997368	−	0.0725000i	$-0.976902\pi$
$367$	−24.7126	−	19.7076i	−1.28999	−	1.02873i	−0.292618	−	0.956230i	$-0.594526\pi$
$368$	2.36111	+	1.88292i	0.123082	+	0.0981543i
$369$		0			0
$370$	14.3913	+	3.28471i	0.748166	+	0.170764i
$371$	0.251236	−	0.130144i	0.0130435	−	0.00675676i
$372$		0			0
$373$	21.5782			1.11728			0.558638	−	0.829411i	$-0.311324\pi$
$373$	21.5782			1.11728			0.558638	+	0.829411i	$0.311324\pi$
$374$	−14.0688			−0.727480
$375$		0			0
$376$	11.6633	−	24.2191i	0.601489	−	1.24900i
$377$	14.4777	−	18.1545i	0.745639	−	0.935002i
$378$		0			0
$379$	5.85961	+	7.34772i	0.300988	+	0.377427i	0.909208	−	0.416341i	$-0.136688\pi$
$379$	5.85961	+	7.34772i	0.300988	+	0.377427i	−0.608221	+	0.793768i	$0.708116\pi$
$380$	−6.16741	+	1.40767i	−0.316382	+	0.0722120i
$381$		0			0
$382$	−21.6214	−	10.4123i	−1.10625	−	0.532740i
$383$	−0.146422	+	0.183607i	−0.00748181	+	0.00938190i	−0.785558	−	0.618788i	$-0.787624\pi$
$383$	−0.146422	+	0.183607i	−0.00748181	+	0.00938190i	0.778077	+	0.628170i	$0.216196\pi$
$384$		0			0
$385$	−3.24165	−	12.5095i	−0.165210	−	0.637545i
$386$	1.89767	−	3.94056i	0.0965890	−	0.200569i
$387$		0			0
$388$	−3.84089	−	0.876658i	−0.194992	−	0.0445056i
$389$	−10.9367	−	22.7103i	−0.554513	−	1.15146i	−0.970279	−	0.241987i	$-0.922201\pi$
$389$	−10.9367	−	22.7103i	−0.554513	−	1.15146i	0.415766	−	0.909472i	$-0.363514\pi$
$390$		0			0
$391$		−	5.00839i		−	0.253285i
$392$	−20.6871	+	6.00951i	−1.04486	+	0.303526i
$393$		0			0
$394$	16.5031	+	20.6942i	0.831412	+	1.04256i
$395$	21.2824	−	10.2491i	1.07083	−	0.515687i
$396$		0			0
$397$	−10.6086	−	22.0291i	−0.532432	−	1.10561i	−0.977661	−	0.210190i	$-0.932592\pi$
$397$	−10.6086	−	22.0291i	−0.532432	−	1.10561i	0.445229	−	0.895417i	$-0.353122\pi$
$398$	8.61740	+	4.14992i	0.431951	+	0.208017i
$399$		0			0
$400$	−5.11105	+	2.46135i	−0.255552	+	0.123068i
$401$	13.1606	+	10.4952i	0.657209	+	0.524107i	0.894350	−	0.447369i	$-0.147639\pi$
$401$	13.1606	+	10.4952i	0.657209	+	0.524107i	−0.237141	+	0.971475i	$0.576210\pi$
$402$		0			0
$403$	2.90607	+	3.64410i	0.144762	+	0.181525i
$404$	−0.0611008	−	0.267700i	−0.00303988	−	0.0133186i
$405$		0			0
$406$	0.675262	+	23.1526i	0.0335127	+	1.14904i
$407$	18.2164	+	14.5271i	0.902954	+	0.720082i
$408$		0			0
$409$	−8.16130	+	1.86276i	−0.403550	+	0.0921077i	−0.419478	−	0.907765i	$-0.637787\pi$
$409$	−8.16130	+	1.86276i	−0.403550	+	0.0921077i	0.0159278	+	0.999873i	$0.494930\pi$
$410$		−	19.2590i		−	0.951132i
$411$		0			0
$412$	1.43702	−	0.327990i	0.0707967	−	0.0161589i
$413$	4.40495	−	1.14147i	0.216754	−	0.0561683i
$414$		0			0
$415$	−1.24849	+	5.47001i	−0.0612861	+	0.268512i
$416$	−6.49858	+	8.14896i	−0.318619	+	0.399536i
$417$		0			0
$418$	21.9381	+	5.00723i	1.07303	+	0.244912i
$419$	−5.69223	+	24.9393i	−0.278084	+	1.21836i	0.622129	+	0.782915i	$0.286268\pi$
$419$	−5.69223	+	24.9393i	−0.278084	+	1.21836i	−0.900213	+	0.435450i	$0.856589\pi$
$420$		0			0
$421$	0.390341	+	1.71019i	0.0190240	+	0.0833497i	0.983549	−	0.180643i	$-0.0578178\pi$
$421$	0.390341	+	1.71019i	0.0190240	+	0.0833497i	−0.964525	+	0.263992i	$0.914961\pi$
$422$		−	13.3034i		−	0.647597i
$423$		0			0
$424$	0.0732345	+	0.320861i	0.00355658	+	0.0155824i
$425$	8.47627	+	4.08195i	0.411159	+	0.198004i
$426$		0			0
$427$	17.2480	−	22.9715i	0.834689	−	1.11167i
$428$	−7.86735	+	6.27400i	−0.380283	+	0.303265i
$429$		0			0
$430$	1.61980	−	1.29175i	0.0781136	−	0.0622935i
$431$	−11.7556	+	24.4108i	−0.566248	+	1.17583i	0.399593	+	0.916693i	$0.369151\pi$
$431$	−11.7556	+	24.4108i	−0.566248	+	1.17583i	−0.965841	+	0.259134i	$0.916563\pi$
$432$		0			0
$433$	−13.8451	−	28.7496i	−0.665351	−	1.38162i	−0.911061	−	0.412273i	$-0.864735\pi$
$433$	−13.8451	−	28.7496i	−0.665351	−	1.38162i	0.245709	−	0.969344i	$-0.420979\pi$
$434$	−4.56100	−	0.901990i	−0.218935	−	0.0432969i
$435$		0			0
$436$	−11.4320	+	5.50538i	−0.547495	+	0.263660i
$437$	−1.78254	+	7.80981i	−0.0852704	+	0.373594i
$438$		0			0
$439$	23.1323	−	18.4474i	1.10405	−	0.880448i	0.110500	−	0.993876i	$-0.464755\pi$
$439$	23.1323	−	18.4474i	1.10405	−	0.880448i	0.993546	+	0.113429i	$0.0361833\pi$
$440$	15.0314			0.716594
$441$		0			0
$442$	−14.5802			−0.693508
$443$	−2.08603	+	1.66356i	−0.0991105	+	0.0790380i	−0.671791	−	0.740740i	$-0.734475\pi$
$443$	−2.08603	+	1.66356i	−0.0991105	+	0.0790380i	0.572681	+	0.819778i	$0.305903\pi$
$444$		0			0
$445$	4.42852	−	19.4026i	0.209932	−	0.919771i
$446$	16.0625	−	7.73528i	0.760580	−	0.366276i
$447$		0			0
$448$	−0.672217	−	23.0482i	−0.0317593	−	1.08892i
$449$	−7.81973	−	16.2378i	−0.369036	−	0.766310i	0.630919	−	0.775849i	$-0.282678\pi$
$449$	−7.81973	−	16.2378i	−0.369036	−	0.766310i	−0.999955	+	0.00953840i	$0.996964\pi$
$450$		0			0
$451$	13.1895	−	27.3884i	0.621071	−	1.28967i
$452$	0.0495665	−	0.0395279i	0.00233141	−	0.00185924i
$453$		0			0
$454$	9.40186	−	7.49774i	0.441251	−	0.351886i
$455$	−3.35948	−	12.9643i	−0.157495	−	0.607774i
$456$		0			0
$457$	−17.2758	−	8.31958i	−0.808127	−	0.389173i	−0.0162604	−	0.999868i	$-0.505176\pi$
$457$	−17.2758	−	8.31958i	−0.808127	−	0.389173i	−0.791866	+	0.610694i	$0.790890\pi$
$458$	5.26761	+	23.0789i	0.246139	+	1.07841i
$459$		0			0
$460$			1.25802i			0.0586553i
$461$	−3.12162	−	13.6767i	−0.145389	−	0.636989i	−0.994131	−	0.108182i	$-0.965497\pi$
$461$	−3.12162	−	13.6767i	−0.145389	−	0.636989i	0.848743	−	0.528806i	$-0.177360\pi$
$462$		0			0
$463$	4.48852	−	19.6655i	0.208599	−	0.913932i	−0.756901	−	0.653529i	$-0.773288\pi$
$463$	4.48852	−	19.6655i	0.208599	−	0.913932i	0.965500	−	0.260403i	$-0.0838553\pi$
$464$	−17.3512	−	3.96029i	−0.805508	−	0.183852i
$465$		0			0
$466$	9.97607	−	12.5096i	0.462133	−	0.579496i
$467$	−8.78197	+	38.4763i	−0.406381	+	1.78047i	0.194257	+	0.980951i	$0.437771\pi$
$467$	−8.78197	+	38.4763i	−0.406381	+	1.78047i	−0.600638	+	0.799521i	$0.705087\pi$
$468$		0			0
$469$	−22.2161	+	18.8020i	−1.02585	+	0.868197i
$470$	−16.2519	+	3.70938i	−0.749643	+	0.171101i
$471$		0			0
$472$			5.29296i			0.243628i
$473$	3.18819	−	0.727683i	0.146593	−	0.0334589i
$474$		0			0
$475$	−11.7646	−	9.38197i	−0.539798	−	0.430474i
$476$	−4.92620	+	4.16916i	−0.225792	+	0.191093i
$477$		0			0
$478$	−2.98091	−	13.0602i	−0.136344	−	0.597360i
$479$	15.8455	+	19.8697i	0.724001	+	0.907869i	0.998557	−	0.0537025i	$-0.0171023\pi$
$479$	15.8455	+	19.8697i	0.724001	+	0.907869i	−0.274556	+	0.961571i	$0.588531\pi$
$480$		0			0
$481$	18.8786	+	15.0551i	0.860788	+	0.686456i
$482$	11.7045	−	5.63660i	0.533127	−	0.256740i
$483$		0			0
$484$	−1.06667	−	0.513684i	−0.0484852	−	0.0233493i
$485$	4.50889	+	9.36281i	0.204738	+	0.425143i
$486$		0			0
$487$	−4.73926	+	2.28231i	−0.214757	+	0.103421i	−0.538170	−	0.842837i	$-0.680884\pi$
$487$	−4.73926	+	2.28231i	−0.214757	+	0.103421i	0.323413	+	0.946258i	$0.395170\pi$
$488$	20.8329	+	26.1236i	0.943060	+	1.18256i
$489$		0			0
$490$	10.9122	+	7.70633i	0.492962	+	0.348136i
$491$			32.1882i			1.45263i	0.687361	+	0.726316i	$0.258769\pi$
$491$			32.1882i			1.45263i	−0.687361	+	0.726316i	$0.741231\pi$
$492$		0			0
$493$	12.8063	+	26.5926i	0.576768	+	1.19767i
$494$	22.7355	+	5.18923i	1.02292	+	0.233475i
$495$		0			0
$496$	1.55002	−	3.21864i	0.0695978	−	0.144521i
$497$	7.93996	−	4.11303i	0.356156	−	0.184494i
$498$		0			0
$499$	−16.9252	+	21.2236i	−0.757677	+	0.950097i	−0.999797	−	0.0201497i	$-0.993586\pi$
$499$	−16.9252	+	21.2236i	−0.757677	+	0.950097i	0.242120	+	0.970246i	$0.422157\pi$
$500$	−6.61916	−	3.18762i	−0.296018	−	0.142555i
$501$		0			0
$502$	11.0622	−	2.52487i	0.493730	−	0.112691i
$503$	−24.4642	−	30.6772i	−1.09081	−	1.36783i	−0.924247	−	0.381796i	$-0.875306\pi$
$503$	−24.4642	−	30.6772i	−1.09081	−	1.36783i	−0.166559	−	0.986031i	$-0.553266\pi$
$504$		0			0
$505$	−0.451588	+	0.566274i	−0.0200954	+	0.0251988i
$506$	1.94158	−	4.03174i	0.0863138	−	0.179233i
$507$		0			0
$508$	−5.81593			−0.258040
$509$	−43.5926			−1.93221			−0.966104	−	0.258153i	$-0.916886\pi$
$509$	−43.5926			−1.93221			−0.966104	+	0.258153i	$0.916886\pi$
$510$		0			0
$511$	−29.7715	+	0.868307i	−1.31701	+	0.0384116i
$512$	22.1462	+	5.05472i	0.978733	+	0.223389i
$513$		0			0
$514$	18.8022	+	14.9943i	0.829329	+	0.661368i
$515$	−3.03976	−	2.42413i	−0.133948	−	0.106820i
$516$		0			0
$517$	−25.6523	−	5.85497i	−1.12819	−	0.257501i
$518$	−24.0760	+	0.702196i	−1.05784	+	0.0308527i
$519$		0			0
$520$	15.5778			0.683130
$521$	−8.32018			−0.364514			−0.182257	−	0.983251i	$-0.558340\pi$
$521$	−8.32018			−0.364514			−0.182257	+	0.983251i	$0.558340\pi$
$522$		0			0
$523$	−12.8076	+	26.5953i	−0.560039	+	1.16293i	0.408197	+	0.912894i	$0.366158\pi$
$523$	−12.8076	+	26.5953i	−0.560039	+	1.16293i	−0.968236	+	0.250039i	$0.919557\pi$
$524$	3.99426	−	5.00865i	0.174490	−	0.218804i
$525$		0			0
$526$	1.56379	+	1.96093i	0.0681845	+	0.0855007i
$527$	−5.77604	+	1.31834i	−0.251608	+	0.0574279i
$528$		0			0
$529$	−19.2870	−	9.28814i	−0.838566	−	0.403832i
$530$	0.127250	−	0.159566i	0.00552737	−	0.00693111i
$531$		0			0
$532$	9.16549	−	4.74787i	0.397375	−	0.205846i
$533$	13.6690	−	28.3839i	0.592068	−	1.22944i
$534$		0			0
$535$	25.8777	+	5.90641i	1.11879	+	0.255356i
$536$	−14.6885	−	30.5011i	−0.634448	−	1.31745i
$537$		0			0
$538$		−	23.1835i		−	0.999513i
$539$	10.2406	+	18.4325i	0.441095	+	0.793943i
$540$		0			0
$541$	−26.2932	−	32.9706i	−1.13043	−	1.41752i	−0.895250	−	0.445565i	$-0.853003\pi$
$541$	−26.2932	−	32.9706i	−1.13043	−	1.41752i	−0.235182	−	0.971951i	$-0.575569\pi$
$542$	10.8103	−	5.20595i	0.464341	−	0.223615i
$543$		0			0
$544$	−5.74835	−	11.9366i	−0.246458	−	0.511776i
$545$	30.1551	+	14.5219i	1.29170	+	0.622051i
$546$		0			0
$547$	22.5823	−	10.8751i	0.965549	−	0.464984i	0.116438	−	0.993198i	$-0.462852\pi$
$547$	22.5823	−	10.8751i	0.965549	−	0.464984i	0.849111	+	0.528214i	$0.177138\pi$
$548$	0.192765	+	0.153725i	0.00823452	+	0.00656681i
$549$		0			0
$550$	5.24093	+	6.57192i	0.223474	+	0.280227i
$551$	−10.5049	−	46.0249i	−0.447523	−	1.96073i
$552$		0			0
$553$	−29.4213	+	24.9000i	−1.25112	+	1.05885i
$554$	−6.44746	−	5.14168i	−0.273926	−	0.218449i
$555$		0			0
$556$	1.25177	−	0.285709i	0.0530870	−	0.0121168i
$557$		−	38.6766i		−	1.63878i	−0.573237	−	0.819389i	$-0.694313\pi$
$557$		−	38.6766i		−	1.63878i	0.573237	−	0.819389i	$-0.305687\pi$
$558$		0			0
$559$	3.30407	−	0.754133i	0.139747	−	0.0318964i
$560$	−7.83528	+	6.63118i	−0.331101	+	0.280219i
$561$		0			0
$562$	−6.38404	+	27.9703i	−0.269294	+	1.17986i
$563$	−16.3519	+	20.5046i	−0.689150	+	0.864167i	−0.996161	−	0.0875387i	$-0.972100\pi$
$563$	−16.3519	+	20.5046i	−0.689150	+	0.864167i	0.307011	+	0.951706i	$0.400671\pi$
$564$		0			0
$565$	−0.163036	−	0.0372120i	−0.00685899	−	0.00156552i
$566$	3.76367	−	16.4897i	0.158199	−	0.693114i
$567$		0			0
$568$	2.31447	+	10.1404i	0.0971131	+	0.425480i
$569$		−	0.617863i		−	0.0259022i	−0.999916	−	0.0129511i	$-0.995877\pi$
$569$		−	0.617863i		−	0.0259022i	0.999916	−	0.0129511i	$-0.00412257\pi$
$570$		0			0
$571$	7.72061	+	33.8262i	0.323098	+	1.41558i	0.832008	+	0.554763i	$0.187191\pi$
$571$	7.72061	+	33.8262i	0.323098	+	1.41558i	−0.508911	+	0.860819i	$0.669952\pi$
$572$	5.20815	+	2.50811i	0.217764	+	0.104870i
$573$		0			0
$574$	7.88294	+	30.4203i	0.329028	+	1.26972i
$575$	−2.33956	+	1.86573i	−0.0975663	+	0.0778065i
$576$		0			0
$577$	20.0054	−	15.9538i	0.832837	−	0.664165i	−0.111275	−	0.993790i	$-0.535494\pi$
$577$	20.0054	−	15.9538i	0.832837	−	0.664165i	0.944112	+	0.329624i	$0.106922\pi$
$578$	−0.640342	+	1.32968i	−0.0266347	+	0.0553076i
$579$		0			0
$580$	−3.21671	−	6.67957i	−0.133567	−	0.277354i
$581$	−0.266899	−	9.15112i	−0.0110728	−	0.379652i
$582$		0			0
$583$	0.290242	−	0.139773i	0.0120206	−	0.00578882i
$584$	7.70905	−	33.7755i	0.319003	−	1.39764i
$585$		0			0
$586$	5.62688	−	4.48729i	0.232444	−	0.185368i
$587$	−28.4634			−1.17481			−0.587405	−	0.809293i	$-0.699850\pi$
$587$	−28.4634			−1.17481			−0.587405	+	0.809293i	$0.699850\pi$
$588$		0			0
$589$	9.47605			0.390454
$590$	2.56622	−	2.04650i	0.105650	−	0.0842529i
$591$		0			0
$592$	4.11825	−	18.0432i	0.169259	−	0.741572i
$593$	−19.9794	+	9.62156i	−0.820455	+	0.395110i	−0.796527	−	0.604604i	$-0.793332\pi$
$593$	−19.9794	+	9.62156i	−0.820455	+	0.395110i	−0.0239281	+	0.999714i	$0.507617\pi$
$594$		0			0
$595$	16.6998	+	3.30257i	0.684624	+	0.135392i
$596$	2.15300	+	4.47076i	0.0881905	+	0.183129i
$597$		0			0
$598$	2.01216	−	4.17829i	0.0822832	−	0.170863i
$599$	11.2925	−	9.00546i	0.461398	−	0.367953i	−0.365029	−	0.930996i	$-0.618941\pi$
$599$	11.2925	−	9.00546i	0.461398	−	0.367953i	0.826427	+	0.563043i	$0.190370\pi$
$600$		0			0
$601$	3.05140	−	2.43341i	0.124469	−	0.0992610i	−0.559277	−	0.828981i	$-0.688921\pi$
$601$	3.05140	−	2.43341i	0.124469	−	0.0992610i	0.683746	+	0.729720i	$0.260350\pi$
$602$	−2.02981	+	2.70337i	−0.0827288	+	0.110181i
$603$		0			0
$604$	8.51305	+	4.09967i	0.346391	+	0.166813i
$605$	0.694913	+	3.04461i	0.0282522	+	0.123781i
$606$		0			0
$607$			40.6191i			1.64868i	0.566097	+	0.824338i	$0.308453\pi$
$607$			40.6191i			1.64868i	−0.566097	+	0.824338i	$0.691547\pi$
$608$	4.71531	+	20.6591i	0.191231	+	0.837839i
$609$		0			0
$610$	4.61077	−	20.2011i	0.186685	−	0.817918i
$611$	−26.5847	−	6.06779i	−1.07550	−	0.245477i
$612$		0			0
$613$	−6.96530	+	8.73421i	−0.281326	+	0.352771i	−0.902338	−	0.431030i	$-0.858150\pi$
$613$	−6.96530	+	8.73421i	−0.281326	+	0.352771i	0.621012	+	0.783801i	$0.286722\pi$
$614$	−6.36831	+	27.9014i	−0.257004	+	1.12601i
$615$		0			0
$616$	−23.7427	+	6.15254i	−0.956620	+	0.247893i
$617$	26.4798	−	6.04385i	1.06604	−	0.243316i	0.346699	−	0.937976i	$-0.387302\pi$
$617$	26.4798	−	6.04385i	1.06604	−	0.243316i	0.719338	+	0.694660i	$0.244445\pi$
$618$		0			0
$619$			13.0186i			0.523262i	0.965168	+	0.261631i	$0.0842603\pi$
$619$			13.0186i			0.523262i	−0.965168	+	0.261631i	$0.915740\pi$
$620$	1.45084	−	0.331144i	0.0582670	−	0.0132991i
$621$		0			0
$622$	−28.8846	−	23.0347i	−1.15817	−	0.923608i
$623$	0.946715	+	32.4598i	0.0379293	+	1.30048i
$624$		0			0
$625$	1.67438	+	7.33593i	0.0669751	+	0.293437i
$626$	−17.5361	−	21.9895i	−0.700882	−	0.878878i
$627$		0			0
$628$	4.80141	+	3.82900i	0.191597	+	0.152794i
$629$	−27.6532	+	13.3171i	−1.10261	+	0.530988i
$630$		0			0
$631$	−13.3941	−	6.45024i	−0.533209	−	0.256780i	0.147848	−	0.989010i	$-0.452765\pi$
$631$	−13.3941	−	6.45024i	−0.533209	−	0.256780i	−0.681057	+	0.732230i	$0.738480\pi$
$632$	−19.4524	−	40.3933i	−0.773774	−	1.60676i
$633$		0			0
$634$	−31.3367	+	15.0909i	−1.24454	+	0.599338i
$635$	9.56501	+	11.9941i	0.379576	+	0.475973i
$636$		0			0
$637$	10.6129	+	19.1025i	0.420497	+	0.756867i
$638$			26.3715i			1.04406i
$639$		0			0
$640$	−2.51864	−	5.23001i	−0.0995580	−	0.206734i
$641$	−3.54318	−	0.808708i	−0.139947	−	0.0319420i	0.151973	−	0.988385i	$-0.451437\pi$
$641$	−3.54318	−	0.808708i	−0.139947	−	0.0319420i	−0.291921	+	0.956443i	$0.594294\pi$
$642$		0			0
$643$	−9.21696	+	19.1392i	−0.363482	+	0.754777i	−0.999862	−	0.0165979i	$-0.994716\pi$
$643$	−9.21696	+	19.1392i	−0.363482	+	0.754777i	0.636381	+	0.771375i	$0.280431\pi$
$644$	−0.514922	−	1.98709i	−0.0202908	−	0.0783022i
$645$		0			0
$646$	−18.4817	+	23.1753i	−0.727154	+	0.911822i
$647$	39.8148	+	19.1738i	1.56528	+	0.753799i	0.997586	−	0.0694398i	$-0.0221212\pi$
$647$	39.8148	+	19.1738i	1.56528	+	0.753799i	0.567695	+	0.823239i	$0.307835\pi$
$648$		0			0
$649$	5.05100	−	1.15286i	0.198269	−	0.0452536i
$650$	5.43143	+	6.81080i	0.213038	+	0.267141i
$651$		0			0
$652$	−0.346833	+	0.434915i	−0.0135830	+	0.0170326i
$653$	10.1195	−	21.0133i	0.396006	−	0.822314i	−0.603679	−	0.797227i	$-0.706299\pi$
$653$	10.1195	−	21.0133i	0.396006	−	0.822314i	0.999685	−	0.0250873i	$-0.00798639\pi$
$654$		0			0
$655$	−16.8984			−0.660273
$656$	−24.1462			−0.942750
$657$		0			0
$658$	24.1522	−	12.5112i	0.941550	−	0.487738i
$659$	−1.63674	−	0.373574i	−0.0637582	−	0.0145524i	0.190523	−	0.981683i	$-0.438982\pi$
$659$	−1.63674	−	0.373574i	−0.0637582	−	0.0145524i	−0.254281	+	0.967130i	$0.581839\pi$
$660$		0			0
$661$	19.4053	+	15.4752i	0.754778	+	0.601915i	0.923433	−	0.383760i	$-0.125371\pi$
$661$	19.4053	+	15.4752i	0.754778	+	0.601915i	−0.168655	+	0.985675i	$0.553942\pi$
$662$	9.23270	+	7.36283i	0.358839	+	0.286164i
$663$		0			0
$664$	10.3819	+	2.36960i	0.402895	+	0.0919582i
$665$	−24.8653	−	11.0935i	−0.964234	−	0.430186i
$666$		0			0
$667$	−9.38807			−0.363508
$668$	1.16755			0.0451739
$669$		0			0
$670$	−9.10880	+	18.9146i	−0.351904	+	0.730736i
$671$	20.3918	−	25.5705i	0.787216	−	0.987137i
$672$		0			0
$673$	−28.7486	−	36.0496i	−1.10818	−	1.38961i	−0.912566	−	0.408930i	$-0.865902\pi$
$673$	−28.7486	−	36.0496i	−1.10818	−	1.38961i	−0.195612	−	0.980681i	$-0.562669\pi$
$674$	−2.77040	+	0.632325i	−0.106712	+	0.0243562i
$675$		0			0
$676$	−1.80236	−	0.867971i	−0.0693215	−	0.0333835i
$677$	13.8596	−	17.3794i	0.532669	−	0.667945i	−0.440576	−	0.897715i	$-0.645226\pi$
$677$	13.8596	−	17.3794i	0.532669	−	0.667945i	0.973245	+	0.229770i	$0.0737973\pi$
$678$		0			0
$679$	−10.9543	−	12.9434i	−0.420387	−	0.496721i
$680$	−8.59131	+	17.8400i	−0.329462	+	0.684134i
$681$		0			0
$682$	−5.16077	−	1.17791i	−0.197616	−	0.0451046i
$683$	−6.17866	−	12.8301i	−0.236420	−	0.490931i	0.748676	−	0.662936i	$-0.230690\pi$
$683$	−6.17866	−	12.8301i	−0.236420	−	0.490931i	−0.985096	+	0.172005i	$0.944976\pi$
$684$		0			0
$685$		−	0.650358i		−	0.0248489i
$686$	−20.3905	−	7.70595i	−0.778514	−	0.294215i
$687$		0			0
$688$	−1.61954	−	2.03084i	−0.0617445	−	0.0774252i
$689$	0.300792	−	0.144854i	0.0114593	−	0.00551849i
$690$		0			0
$691$	11.3856	+	23.6425i	0.433130	+	0.899404i	0.997278	+	0.0737304i	$0.0234904\pi$
$691$	11.3856	+	23.6425i	0.433130	+	0.899404i	−0.564148	+	0.825674i	$0.690795\pi$
$692$	−4.10383	−	1.97630i	−0.156004	−	0.0751276i
$693$		0			0
$694$	−23.5170	+	11.3252i	−0.892693	+	0.429898i
$695$	−2.64791	−	2.11164i	−0.100441	−	0.0800990i
$696$		0			0
$697$	24.9673	+	31.3080i	0.945705	+	1.18588i
$698$	−7.44463	−	32.6171i	−0.281784	−	1.23457i
$699$		0			0
$700$	3.78264	+	0.748061i	0.142971	+	0.0282740i
$701$	6.68543	+	5.33145i	0.252505	+	0.201366i	0.741559	−	0.670887i	$-0.234087\pi$
$701$	6.68543	+	5.33145i	0.252505	+	0.201366i	−0.489054	+	0.872253i	$0.662658\pi$
$702$		0			0
$703$	47.8607	−	10.9239i	1.80510	−	0.412002i
$704$		−	26.2526i		−	0.989431i
$705$		0			0
$706$	−11.1548	+	2.54600i	−0.419815	+	0.0958200i
$707$	0.481518	−	1.07929i	0.0181094	−	0.0405910i
$708$		0			0
$709$	−2.32873	+	10.2028i	−0.0874573	+	0.383176i	−0.999646	−	0.0265942i	$-0.991534\pi$
$709$	−2.32873	+	10.2028i	−0.0874573	+	0.383176i	0.912189	+	0.409770i	$0.134391\pi$
$710$	4.02154	−	5.04286i	0.150926	−	0.189255i
$711$		0			0
$712$	−36.8255	−	8.40517i	−1.38009	−	0.314997i
$713$	0.419328	−	1.83720i	0.0157040	−	0.0688036i
$714$		0			0
$715$	−3.39298	−	14.8656i	−0.126890	−	0.555943i
$716$		−	14.4466i		−	0.539896i
$717$		0			0
$718$	3.10673	+	13.6115i	0.115942	+	0.507976i
$719$	24.6264	+	11.8595i	0.918411	+	0.442283i	0.832503	−	0.554020i	$-0.186907\pi$
$719$	24.6264	+	11.8595i	0.918411	+	0.442283i	0.0859072	+	0.996303i	$0.472621\pi$
$720$		0			0
$721$	5.79365	+	2.58479i	0.215767	+	0.0962628i
$722$	19.5839	−	15.6176i	0.728836	−	0.581228i
$723$		0			0
$724$	−6.21756	+	4.95834i	−0.231074	+	0.184275i
$725$	7.65150	−	15.8885i	0.284169	−	0.590084i
$726$		0			0
$727$	−8.59104	−	17.8395i	−0.318624	−	0.661629i	0.678725	−	0.734392i	$-0.262533\pi$
$727$	−8.59104	−	17.8395i	−0.318624	−	0.661629i	−0.997349	+	0.0727629i	$0.976818\pi$
$728$	−24.6057	+	6.37618i	−0.911948	+	0.236317i
$729$		0			0
$730$	−19.3563	+	9.32150i	−0.716408	+	0.345004i
$731$	−0.958581	+	4.19982i	−0.0354544	+	0.155336i
$732$		0			0
$733$	4.46629	−	3.56175i	0.164966	−	0.131556i	−0.537527	−	0.843246i	$-0.680641\pi$
$733$	4.46629	−	3.56175i	0.164966	−	0.131556i	0.702493	+	0.711690i	$0.252070\pi$
$734$	37.2028			1.37318
$735$		0			0
$736$	4.21401			0.155330
$737$	−25.9074	+	20.6605i	−0.954312	+	0.761039i
$738$		0			0
$739$	1.07259	−	4.69931i	0.0394558	−	0.172867i	−0.951361	−	0.308078i	$-0.900314\pi$
$739$	1.07259	−	4.69931i	0.0394558	−	0.172867i	0.990817	+	0.135211i	$0.0431713\pi$
$740$	6.94599	−	3.34501i	0.255340	−	0.122965i
$741$		0			0
$742$	−0.135684	+	0.304126i	−0.00498110	+	0.0111648i
$743$	−4.67324	−	9.70408i	−0.171444	−	0.356008i	0.797488	−	0.603335i	$-0.206162\pi$
$743$	−4.67324	−	9.70408i	−0.171444	−	0.356008i	−0.968932	+	0.247327i	$0.920448\pi$
$744$		0			0
$745$	5.67913	−	11.7928i	0.208067	−	0.432056i
$746$	−19.8563	+	15.8349i	−0.726992	+	0.579757i
$747$		0			0
$748$	−5.74471	+	4.58125i	−0.210047	+	0.167507i
$749$	−43.2923	+	1.26265i	−1.58187	+	0.0461363i
$750$		0			0
$751$	41.2195	+	19.8503i	1.50412	+	0.724346i	0.990986	−	0.133962i	$-0.0427700\pi$
$751$	41.2195	+	19.8503i	1.50412	+	0.724346i	0.513134	+	0.858308i	$0.328484\pi$
$752$	4.65069	+	20.3760i	0.169593	+	0.743036i
$753$		0			0
$754$			27.3301i			0.995303i
$755$	−5.54605	−	24.2988i	−0.201841	−	0.884324i
$756$		0			0
$757$	−4.65249	+	20.3839i	−0.169098	+	0.740866i	0.817263	+	0.576265i	$0.195491\pi$
$757$	−4.65249	+	20.3839i	−0.169098	+	0.740866i	−0.986360	+	0.164600i	$0.947367\pi$
$758$	−10.7841	−	2.46139i	−0.391695	−	0.0894018i
$759$		0			0
$760$	19.7463	−	24.7610i	0.716272	−	0.898177i
$761$	−10.3439	+	45.3197i	−0.374967	+	1.64284i	0.337641	+	0.941275i	$0.390371\pi$
$761$	−10.3439	+	45.3197i	−0.374967	+	1.64284i	−0.712608	+	0.701562i	$0.752486\pi$
$762$		0			0
$763$	−53.5752	−	10.5951i	−1.93955	−	0.383568i
$764$	−12.2192	+	2.78896i	−0.442077	+	0.100901i
$765$		0			0
$766$		−	0.276406i		−	0.00998696i
$767$	5.23460	−	1.19476i	0.189010	−	0.0431404i
$768$		0			0
$769$	33.0698	+	26.3723i	1.19253	+	0.951009i	0.999544	−	0.0301926i	$-0.00961206\pi$
$769$	33.0698	+	26.3723i	1.19253	+	0.951009i	0.192984	+	0.981202i	$0.438183\pi$
$770$	12.1630	+	9.13248i	0.438323	+	0.329112i
$771$		0			0
$772$	−0.508296	−	2.22699i	−0.0182940	−	0.0801511i
$773$	−11.8115	−	14.8111i	−0.424829	−	0.532719i	0.522645	−	0.852550i	$-0.324945\pi$
$773$	−11.8115	−	14.8111i	−0.424829	−	0.532719i	−0.947475	+	0.319831i	$0.896374\pi$
$774$		0			0
$775$	2.76753	+	2.20703i	0.0994128	+	0.0792790i
$776$	17.7703	−	8.55772i	0.637916	−	0.307204i
$777$		0			0
$778$	26.7297	+	12.8723i	0.958306	+	0.461496i
$779$	−27.7898	−	57.7062i	−0.995674	−	2.06754i
$780$		0			0
$781$	9.17269	−	4.41733i	0.328225	−	0.158065i
$782$	3.67535	+	4.60874i	0.131430	+	0.164808i
$783$		0			0
$784$	9.66190	−	13.6813i	0.345068	−	0.488618i
$785$		−	16.1992i		−	0.578173i
$786$		0			0
$787$	−8.74293	−	18.1549i	−0.311652	−	0.647152i	0.685033	−	0.728512i	$-0.259788\pi$
$787$	−8.74293	−	18.1549i	−0.311652	−	0.647152i	−0.996685	+	0.0813603i	$0.974074\pi$
$788$	13.4774	+	3.07612i	0.480112	+	0.109582i
$789$		0			0
$790$	−12.0630	+	25.0491i	−0.429182	+	0.891206i
$791$	0.272754	−	0.00795506i	0.00969800	−	0.000282849i
$792$		0			0
$793$	21.1330	−	26.4999i	0.750454	−	0.941040i
$794$	25.9279	+	12.4862i	0.920145	+	0.443119i
$795$		0			0
$796$	4.87009	−	1.11157i	0.172616	−	0.0393984i
$797$	19.9227	+	24.9823i	0.705700	+	0.884919i	0.997435	−	0.0715797i	$-0.0228040\pi$
$797$	19.9227	+	24.9823i	0.705700	+	0.884919i	−0.291735	+	0.956499i	$0.594233\pi$
$798$		0			0
$799$	21.6108	−	27.0990i	0.764534	−	0.958695i
$800$	−3.43452	+	7.13184i	−0.121428	+	0.252149i
$801$		0			0
$802$	−19.8122			−0.699594
$803$	−33.9106			−1.19668
$804$		0			0
$805$	−3.25110	+	4.32993i	−0.114586	+	0.152610i
$806$	−5.34835	−	1.22073i	−0.188388	−	0.0429983i
$807$		0			0
$808$	1.07477	+	0.857098i	0.0378102	+	0.0301526i
$809$	28.6281	+	22.8302i	1.00651	+	0.802666i	0.980405	−	0.196993i	$-0.0631178\pi$
$809$	28.6281	+	22.8302i	1.00651	+	0.802666i	0.0261062	+	0.999659i	$0.491689\pi$
$810$		0			0
$811$	−31.4471	−	7.17759i	−1.10426	−	0.252039i	−0.368731	−	0.929536i	$-0.620207\pi$
$811$	−31.4471	−	7.17759i	−1.10426	−	0.252039i	−0.735525	+	0.677497i	$0.763065\pi$
$812$	7.81496	+	9.23401i	0.274251	+	0.324050i
$813$		0			0
$814$	−27.4233			−0.961188
$815$	1.46733			0.0513984
$816$		0			0
$817$	2.98952	−	6.20779i	0.104590	−	0.217183i
$818$	6.14309	−	7.70319i	0.214788	−	0.269336i
$819$		0			0
$820$	−6.27134	−	7.86401i	−0.219005	−	0.274623i
$821$	−1.83900	+	0.419740i	−0.0641816	+	0.0146490i	−0.254491	−	0.967075i	$-0.581908\pi$
$821$	−1.83900	+	0.419740i	−0.0641816	+	0.0146490i	0.190310	+	0.981724i	$0.439051\pi$
$822$		0			0
$823$	8.90635	+	4.28907i	0.310456	+	0.149508i	0.582623	−	0.812742i	$-0.302026\pi$
$823$	8.90635	+	4.28907i	0.310456	+	0.149508i	−0.272168	+	0.962250i	$0.587741\pi$
$824$	−4.60091	+	5.76936i	−0.160280	+	0.200985i
$825$		0			0
$826$	−3.21580	+	4.28291i	−0.111892	+	0.149021i
$827$	0.402679	−	0.836172i	0.0140025	−	0.0290765i	−0.893850	−	0.448366i	$-0.852006\pi$
$827$	0.402679	−	0.836172i	0.0140025	−	0.0290765i	0.907853	+	0.419289i	$0.137721\pi$
$828$		0			0
$829$	13.6428	+	3.11387i	0.473833	+	0.108149i	0.452767	−	0.891629i	$-0.350437\pi$
$829$	13.6428	+	3.11387i	0.473833	+	0.108149i	0.0210656	+	0.999778i	$0.493294\pi$
$830$	−2.86523	−	5.94971i	−0.0994536	−	0.206518i
$831$		0			0
$832$		−	27.2068i		−	0.943226i
$833$	−27.7297	+	1.61889i	−0.960778	+	0.0560913i
$834$		0			0
$835$	−1.92018	−	2.40783i	−0.0664507	−	0.0833265i
$836$	10.5885	−	5.09915i	0.366211	−	0.176358i
$837$		0			0
$838$	−13.0634	−	27.1264i	−0.451267	−	0.937066i
$839$	35.6979	+	17.1912i	1.23243	+	0.593507i	0.932747	−	0.360532i	$-0.117405\pi$
$839$	35.6979	+	17.1912i	1.23243	+	0.593507i	0.299683	+	0.954039i	$0.403119\pi$
$840$		0			0
$841$	23.7189	−	11.4224i	0.817893	−	0.393876i
$842$	−1.61420	−	1.28728i	−0.0556289	−	0.0443626i
$843$		0			0
$844$	−4.33200	−	5.43216i	−0.149114	−	0.186983i
$845$	1.17419	+	5.14448i	0.0403935	+	0.176975i
$846$		0			0
$847$	−2.34384	−	4.52465i	−0.0805353	−	0.155469i
$848$	−0.200058	−	0.159541i	−0.00687002	−	0.00547866i
$849$		0			0
$850$	−10.7954	+	2.46398i	−0.370279	+	0.0845137i
$851$		−	9.76252i		−	0.334655i
$852$		0			0
$853$	−17.8729	+	4.07937i	−0.611955	+	0.139675i	−0.517255	−	0.855831i	$-0.673046\pi$
$853$	−17.8729	+	4.07937i	−0.611955	+	0.139675i	−0.0946999	+	0.995506i	$0.530189\pi$
$854$	0.985675	+	33.7957i	0.0337291	+	1.15646i
$855$		0			0
$856$	11.2102	−	49.1149i	0.383155	−	1.67871i
$857$	−34.8821	+	43.7407i	−1.19155	+	1.49416i	−0.365263	+	0.930904i	$0.619021\pi$
$857$	−34.8821	+	43.7407i	−1.19155	+	1.49416i	−0.826286	+	0.563251i	$0.809551\pi$
$858$		0			0
$859$	41.0178	+	9.36205i	1.39951	+	0.319429i	0.854696	−	0.519128i	$-0.173743\pi$
$859$	41.0178	+	9.36205i	1.39951	+	0.319429i	0.544814	+	0.838557i	$0.316600\pi$
$860$	0.240778	−	1.05492i	0.00821046	−	0.0359724i
$861$		0			0
$862$	−7.09600	−	31.0896i	−0.241691	−	1.05892i
$863$		−	32.2608i		−	1.09817i	−0.835766	−	0.549085i	$-0.814976\pi$
$863$		−	32.2608i		−	1.09817i	0.835766	−	0.549085i	$-0.185024\pi$
$864$		0			0
$865$	2.67354	+	11.7136i	0.0909032	+	0.398273i
$866$	33.8378	+	16.2954i	1.14986	+	0.553741i
$867$		0			0
$868$	−2.15611	+	1.11690i	−0.0731832	+	0.0379101i
$869$	−34.3098	+	27.3612i	−1.16388	+	0.928164i
$870$		0			0
$871$	−26.8491	+	21.4115i	−0.909748	+	0.725500i
$872$	27.5621	−	57.2333i	0.933370	−	1.93816i
$873$		0			0
$874$	−4.09084	−	8.49471i	−0.138375	−	0.287338i
$875$	−14.5445	−	28.0773i	−0.491694	−	0.949187i
$876$		0			0
$877$	36.2669	−	17.4652i	1.22465	−	0.589758i	0.294044	−	0.955792i	$-0.404999\pi$
$877$	36.2669	−	17.4652i	1.22465	−	0.589758i	0.930602	+	0.366034i	$0.119285\pi$
$878$	−7.74904	+	33.9508i	−0.261517	+	1.14578i
$879$		0			0
$880$	−9.13714	+	7.28663i	−0.308013	+	0.245632i
$881$	13.8361			0.466150			0.233075	−	0.972459i	$-0.425121\pi$
$881$	13.8361			0.466150			0.233075	+	0.972459i	$0.425121\pi$
$882$		0			0
$883$	8.08344			0.272029			0.136015	−	0.990707i	$-0.456571\pi$
$883$	8.08344			0.272029			0.136015	+	0.990707i	$0.456571\pi$
$884$	−5.95352	+	4.74777i	−0.200239	+	0.159685i
$885$		0			0
$886$	0.698795	−	3.06162i	0.0234765	−	0.102857i
$887$	−3.19597	+	1.53910i	−0.107310	+	0.0516778i	−0.486769	−	0.873531i	$-0.661825\pi$
$887$	−3.19597	+	1.53910i	−0.107310	+	0.0516778i	0.379459	+	0.925209i	$0.376110\pi$
$888$		0			0
$889$	−20.0177	−	15.0301i	−0.671371	−	0.504095i
$890$	10.1632	+	21.1042i	0.340672	+	0.707413i
$891$		0			0
$892$	4.03993	−	8.38900i	0.135267	−	0.280885i
$893$	−43.3435	+	34.5653i	−1.45043	+	1.15668i
$894$		0			0
$895$	−29.7932	+	23.7593i	−0.995876	+	0.794185i
$896$	6.11900	+	7.23009i	0.204421	+	0.241540i
$897$		0			0
$898$	19.1117	+	9.20369i	0.637765	+	0.307131i
$899$	2.47119	+	10.8270i	0.0824189	+	0.361101i
$900$		0			0
$901$			0.424363i			0.0141376i
$902$	7.96155	+	34.8818i	0.265091	+	1.16144i
$903$		0			0
$904$	−0.0706270	+	0.309437i	−0.00234902	+	0.0102917i
$905$	20.4511	+	4.66782i	0.679817	+	0.155164i
$906$		0			0
$907$	7.87768	−	9.87830i	0.261574	−	0.328003i	−0.633650	−	0.773620i	$-0.718444\pi$
$907$	7.87768	−	9.87830i	0.261574	−	0.328003i	0.895224	+	0.445616i	$0.147015\pi$
$908$	1.39756	−	6.12310i	0.0463796	−	0.203202i
$909$		0			0
$910$	12.6051	+	9.46444i	0.417854	+	0.313743i
$911$	−14.2777	+	3.25879i	−0.473041	+	0.107969i	−0.452394	−	0.891818i	$-0.649430\pi$
$911$	−14.2777	+	3.25879i	−0.473041	+	0.107969i	−0.0206474	+	0.999787i	$0.506573\pi$
$912$		0			0
$913$		−	10.4234i		−	0.344964i
$914$	22.0024	−	5.02192i	0.727776	−	0.166110i
$915$		0			0
$916$	9.66616	+	7.70850i	0.319379	+	0.254696i
$917$	26.6916	−	6.91671i	0.881435	−	0.228410i
$918$		0			0
$919$	−5.83118	−	25.5481i	−0.192353	−	0.842753i	−0.975339	−	0.220714i	$-0.929161\pi$
$919$	−5.83118	−	25.5481i	−0.192353	−	0.842753i	0.782986	−	0.622040i	$-0.213696\pi$
$920$	−3.92682	−	4.92408i	−0.129463	−	0.162342i
$921$		0			0
$922$	12.9090	+	10.2946i	0.425136	+	0.339035i
$923$	9.50610	−	4.57790i	0.312897	−	0.150683i
$924$		0			0
$925$	16.5222	+	7.95668i	0.543247	+	0.261614i
$926$	10.3009	+	21.3901i	0.338509	+	0.702922i
$927$		0			0
$928$	−22.3747	+	10.7751i	−0.734487	+	0.353710i
$929$	19.2409	+	24.1274i	0.631274	+	0.791593i	0.989882	−	0.141895i	$-0.0453197\pi$
$929$	19.2409	+	24.1274i	0.631274	+	0.791593i	−0.358607	+	0.933489i	$0.616748\pi$
$930$		0			0
$931$	43.8164	+	7.34488i	1.43602	+	0.240719i
$932$		−	8.35657i		−	0.273729i
$933$		0			0
$934$	−20.1542	−	41.8506i	−0.659465	−	1.36939i
$935$	18.8958	+	4.31283i	0.617957	+	0.141045i
$936$		0			0
$937$	17.1374	−	35.5862i	0.559855	−	1.16255i	−0.408451	−	0.912780i	$-0.633931\pi$
$937$	17.1374	−	35.5862i	0.559855	−	1.16255i	0.968305	−	0.249770i	$-0.0803550\pi$
$938$	6.64572	−	33.6047i	0.216990	−	1.09723i
$939$		0			0
$940$	−5.42823	+	6.80678i	−0.177049	+	0.222013i
$941$	8.05728	+	3.88018i	0.262660	+	0.126490i	0.560579	−	0.828101i	$-0.310578\pi$
$941$	8.05728	+	3.88018i	0.262660	+	0.126490i	−0.297920	+	0.954591i	$0.596293\pi$
$942$		0			0
$943$	−12.4177	+	2.83426i	−0.404376	+	0.0922961i
$944$	−2.56582	−	3.21744i	−0.0835103	−	0.104719i
$945$		0			0
$946$	−2.39978	+	3.00923i	−0.0780235	+	0.0978384i
$947$	−6.37741	+	13.2428i	−0.207238	+	0.430334i	−0.978518	−	0.206162i	$-0.933903\pi$
$947$	−6.37741	+	13.2428i	−0.207238	+	0.430334i	0.771280	+	0.636496i	$0.219617\pi$
$948$		0			0
$949$	−35.1432			−1.14080
$950$	17.7107			0.574610
$951$		0			0
$952$	6.26816	−	31.6956i	0.203152	−	1.02726i
$953$	26.9110	+	6.14226i	0.871733	+	0.198967i	0.634911	−	0.772585i	$-0.281037\pi$
$953$	26.9110	+	6.14226i	0.871733	+	0.198967i	0.236823	+	0.971553i	$0.423894\pi$
$954$		0			0
$955$	25.8477	+	20.6129i	0.836412	+	0.667016i
$956$	−5.47002	−	4.36220i	−0.176913	−	0.141084i
$957$		0			0
$958$	−29.1622	−	6.65609i	−0.942189	−	0.215049i
$959$	0.266200	+	1.02727i	0.00859604	+	0.0331721i
$960$		0			0
$961$	28.7708			0.928091
$962$	−28.4202			−0.916302
$963$		0			0
$964$	2.94385	−	6.11296i	0.0948150	−	0.196885i
$965$	−3.75675	+	4.71081i	−0.120934	+	0.151646i
$966$		0			0
$967$	−20.2313	−	25.3692i	−0.650594	−	0.815819i	0.341689	−	0.939813i	$-0.389001\pi$
$967$	−20.2313	−	25.3692i	−0.650594	−	0.815819i	−0.992283	+	0.123994i	$0.960430\pi$
$968$	5.77857	−	1.31892i	0.185730	−	0.0423917i
$969$		0			0
$970$	−11.0199	−	5.30689i	−0.353827	−	0.170394i
$971$	−27.1145	+	34.0005i	−0.870146	+	1.09113i	0.124945	+	0.992164i	$0.460125\pi$
$971$	−27.1145	+	34.0005i	−0.870146	+	1.09113i	−0.995091	+	0.0989652i	$0.968447\pi$
$972$		0			0
$973$	5.04680	+	2.25159i	0.161793	+	0.0721828i
$974$	2.68624	−	5.57804i	0.0860727	−	0.178732i
$975$		0			0
$976$	−25.3274	−	5.78081i	−0.810709	−	0.185039i
$977$	−9.09110	−	18.8779i	−0.290850	−	0.603957i	0.703429	−	0.710765i	$-0.251651\pi$
$977$	−9.09110	−	18.8779i	−0.290850	−	0.603957i	−0.994280	+	0.106808i	$0.965937\pi$
$978$		0			0
$979$			36.9727i			1.18165i
$980$	6.96520	−	0.406636i	0.222495	−	0.0129895i
$981$		0			0
$982$	−23.6209	−	29.6197i	−0.753774	−	0.945202i
$983$	40.4338	−	19.4719i	1.28964	−	0.621057i	0.341789	−	0.939777i	$-0.388967\pi$
$983$	40.4338	−	19.4719i	1.28964	−	0.621057i	0.947849	+	0.318720i	$0.103253\pi$
$984$		0			0
$985$	−15.8213	−	32.8534i	−0.504110	−	1.04680i
$986$	−31.2991	−	15.0728i	−0.996765	−	0.480017i
$987$		0			0
$988$	10.9734	−	5.28450i	0.349110	−	0.168122i
$989$	−1.07126	−	0.854305i	−0.0340642	−	0.0271653i
$990$		0			0
$991$	33.7996	+	42.3833i	1.07368	+	1.34635i	0.934452	+	0.356090i	$0.115890\pi$
$991$	33.7996	+	42.3833i	1.07368	+	1.34635i	0.139227	+	0.990261i	$0.455538\pi$
$992$	−1.10924	−	4.85990i	−0.0352184	−	0.154302i
$993$		0			0
$994$	−4.28808	+	9.61146i	−0.136010	+	0.304857i
$995$	−10.3018	−	8.21544i	−0.326590	−	0.260447i
$996$		0			0
$997$	22.8150	−	5.20738i	0.722559	−	0.164919i	0.154601	−	0.987977i	$-0.450591\pi$
$997$	22.8150	−	5.20738i	0.722559	−	0.164919i	0.567958	+	0.823058i	$0.307734\pi$
$998$		−	31.9503i		−	1.01137i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.w.a.188.8	✓	120
3.2	odd	2	inner	441.2.w.a.188.13	yes	120
49.6	odd	14	inner	441.2.w.a.251.13	yes	120
147.104	even	14	inner	441.2.w.a.251.8	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.w.a.188.8	✓	120	1.1	even	1	trivial
441.2.w.a.188.13	yes	120	3.2	odd	2	inner
441.2.w.a.251.8	yes	120	147.104	even	14	inner
441.2.w.a.251.13	yes	120	49.6	odd	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.w (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.920203 + 0.733838i) q^{2} +(-0.136785 + 0.599296i) q^{4} +(1.46088 - 0.703524i) q^{5} +(-2.01956 + 1.70920i) q^{7} +(-1.33526 - 2.77270i) q^{8} +O(q^{10})\)	\(q+(-0.920203 + 0.733838i) q^{2} +(-0.136785 + 0.599296i) q^{4} +(1.46088 - 0.703524i) q^{5} +(-2.01956 + 1.70920i) q^{7} +(-1.33526 - 2.77270i) q^{8} +(-0.828037 + 1.71944i) q^{10} +(-2.35512 + 1.87814i) q^{11} +(-2.44072 + 1.94641i) q^{13} +(0.604130 - 3.05484i) q^{14} +(2.15577 + 1.03816i) q^{16} +(-0.882993 - 3.86864i) q^{17} +6.34682i q^{19} +(0.221792 + 0.971733i) q^{20} +(0.788935 - 3.45655i) q^{22} +(1.23051 + 0.280855i) q^{23} +(-1.47822 + 1.85362i) q^{25} +(0.817612 - 3.58219i) q^{26} +(-0.748071 - 1.44411i) q^{28} +(-7.25165 + 1.65514i) q^{29} -1.49304i q^{31} +(3.25504 - 0.742941i) q^{32} +(3.65149 + 2.91197i) q^{34} +(-1.74788 + 3.91776i) q^{35} +(-1.72116 - 7.54089i) q^{37} +(-4.65754 - 5.84036i) q^{38} +(-3.90133 - 3.11121i) q^{40} +(-9.09214 + 4.37855i) q^{41} +(-0.978095 - 0.471026i) q^{43} +(-0.803418 - 1.66832i) q^{44} +(-1.33842 + 0.644549i) q^{46} +(5.44608 + 6.82916i) q^{47} +(1.15725 - 6.90368i) q^{49} -2.79048i q^{50} +(-0.832622 - 1.72896i) q^{52} +(-0.104261 - 0.0237970i) q^{53} +(-2.11923 + 4.40063i) q^{55} +(7.43576 + 3.31741i) q^{56} +(5.45839 - 6.84461i) q^{58} +(-1.54958 - 0.746240i) q^{59} +(-10.5852 + 2.41600i) q^{61} +(1.09565 + 1.37390i) q^{62} +(-5.43377 + 6.81373i) q^{64} +(-2.19626 + 4.56059i) q^{65} +11.0005 q^{67} +2.43924 q^{68} +(-1.26659 - 4.88779i) q^{70} +(-3.29503 - 0.752069i) q^{71} +(8.80135 + 7.01884i) q^{73} +(7.11761 + 5.67610i) q^{74} +(-3.80362 - 0.868152i) q^{76} +(1.54618 - 7.81840i) q^{77} +14.5682 q^{79} +3.87969 q^{80} +(5.15348 - 10.7013i) q^{82} +(-2.15744 + 2.70535i) q^{83} +(-4.01163 - 5.03043i) q^{85} +(1.24570 - 0.284324i) q^{86} +(8.35225 + 4.02223i) q^{88} +(7.65264 - 9.59610i) q^{89} +(1.60238 - 8.10259i) q^{91} +(-0.336631 + 0.699021i) q^{92} +(-10.0230 - 2.28768i) q^{94} +(4.46514 + 9.27196i) q^{95} +6.40900i q^{97} +(4.00127 + 7.20202i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 24 q^{4}+O(q^{10}) \) 120 * q + 24 * q^4	\( 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94}+O(q^{100}) \) 120 * q + 24 * q^4 - 32 * q^16 - 44 * q^22 - 4 * q^25 - 56 * q^28 + 112 * q^34 - 76 * q^37 + 28 * q^40 + 8 * q^43 - 40 * q^46 - 84 * q^49 - 140 * q^52 + 12 * q^58 - 84 * q^61 + 24 * q^64 + 16 * q^67 + 112 * q^70 - 84 * q^76 - 24 * q^79 + 140 * q^82 - 96 * q^85 - 24 * q^88 - 112 * q^91 - 112 * q^94

Introduction

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