LMFDB - Embedded newform 441.2.s.d.362.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(362,441)]

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([1, 5]))

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

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

chi := DirichletCharacter("441.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.s (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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			362.1
Character	$\chi$	$=$	441.362
Dual form			441.2.s.d.374.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.23278 + 1.28910i) q^{2} +(-0.625134 - 1.61530i) q^{3} +(2.32354 - 4.02449i) q^{4} +2.33189 q^{5} +(3.47807 + 2.80076i) q^{6} +6.82470i q^{8} +(-2.21841 + 2.01956i) q^{9} +O(q^{10})$	\(q+(-2.23278 + 1.28910i) q^{2} +(-0.625134 - 1.61530i) q^{3} +(2.32354 - 4.02449i) q^{4} +2.33189 q^{5} +(3.47807 + 2.80076i) q^{6} +6.82470i q^{8} +(-2.21841 + 2.01956i) q^{9} +(-5.20660 + 3.00603i) q^{10} +4.36608i q^{11} +(-7.95331 - 1.23738i) q^{12} +(1.14392 - 0.660445i) q^{13} +(-1.45774 - 3.76671i) q^{15} +(-4.15061 - 7.18908i) q^{16} +(2.89327 + 5.01130i) q^{17} +(2.34982 - 7.36900i) q^{18} +(0.584876 + 0.337678i) q^{19} +(5.41825 - 9.38468i) q^{20} +(-5.62830 - 9.74851i) q^{22} -5.56333i q^{23} +(11.0240 - 4.26635i) q^{24} +0.437717 q^{25} +(-1.70276 + 2.94926i) q^{26} +(4.64902 + 2.32092i) q^{27} +(3.86926 + 2.23392i) q^{29} +(8.11049 + 6.53107i) q^{30} +(3.47965 + 2.00898i) q^{31} +(6.71411 + 3.87639i) q^{32} +(7.05255 - 2.72939i) q^{33} +(-12.9201 - 7.45942i) q^{34} +(2.97314 + 13.6205i) q^{36} +(-1.50829 + 2.61243i) q^{37} -1.74120 q^{38} +(-1.78193 - 1.43492i) q^{39} +15.9145i q^{40} +(3.29501 + 5.70713i) q^{41} +(3.89217 - 6.74143i) q^{43} +(17.5713 + 10.1448i) q^{44} +(-5.17310 + 4.70940i) q^{45} +(7.17168 + 12.4217i) q^{46} +(-0.246705 - 0.427306i) q^{47} +(-9.01785 + 11.1986i) q^{48} +(-0.977326 + 0.564259i) q^{50} +(6.28609 - 7.80625i) q^{51} -6.13829i q^{52} +(-3.59025 + 2.07283i) q^{53} +(-13.3721 + 0.810934i) q^{54} +10.1812i q^{55} +(0.179827 - 1.15585i) q^{57} -11.5189 q^{58} +(-2.15699 + 3.73602i) q^{59} +(-18.5462 - 2.88543i) q^{60} +(1.77661 - 1.02572i) q^{61} -10.3591 q^{62} -3.38572 q^{64} +(2.66751 - 1.54009i) q^{65} +(-12.2284 + 15.1855i) q^{66} +(2.41218 - 4.17802i) q^{67} +26.8906 q^{68} +(-8.98648 + 3.47783i) q^{69} -1.17135i q^{71} +(-13.7829 - 15.1400i) q^{72} +(13.0902 - 7.55766i) q^{73} -7.77733i q^{74} +(-0.273632 - 0.707045i) q^{75} +(2.71797 - 1.56922i) q^{76} +(5.82840 + 0.906785i) q^{78} +(5.30428 + 9.18728i) q^{79} +(-9.67878 - 16.7641i) q^{80} +(0.842727 - 8.96046i) q^{81} +(-14.7141 - 8.49518i) q^{82} +(5.32432 - 9.22199i) q^{83} +(6.74680 + 11.6858i) q^{85} +20.0695i q^{86} +(1.18965 - 7.64653i) q^{87} -29.7972 q^{88} +(1.66268 - 2.87984i) q^{89} +(5.47953 - 17.1837i) q^{90} +(-22.3896 - 12.9266i) q^{92} +(1.06986 - 6.87658i) q^{93} +(1.10168 + 0.636053i) q^{94} +(1.36387 + 0.787429i) q^{95} +(2.06433 - 13.2686i) q^{96} +(12.7531 + 7.36299i) q^{97} +(-8.81758 - 9.68578i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4} - 8 q^{9}+O(q^{10}) $ 48 * q + 24 * q^4 - 8 * q^9	$ 48 q + 24 q^{4} - 8 q^{9} - 40 q^{15} - 24 q^{16} + 32 q^{18} + 48 q^{25} + 48 q^{30} - 120 q^{32} - 8 q^{36} - 32 q^{39} + 96 q^{44} + 48 q^{50} + 48 q^{53} + 80 q^{57} - 72 q^{60} - 48 q^{64} - 120 q^{65} + 32 q^{72} - 88 q^{78} - 24 q^{79} + 120 q^{81} - 24 q^{85} - 144 q^{92} + 16 q^{93} - 96 q^{95} - 72 q^{99}+O(q^{100}) $ 48 * q + 24 * q^4 - 8 * q^9 - 40 * q^15 - 24 * q^16 + 32 * q^18 + 48 * q^25 + 48 * q^30 - 120 * q^32 - 8 * q^36 - 32 * q^39 + 96 * q^44 + 48 * q^50 + 48 * q^53 + 80 * q^57 - 72 * q^60 - 48 * q^64 - 120 * q^65 + 32 * q^72 - 88 * q^78 - 24 * q^79 + 120 * q^81 - 24 * q^85 - 144 * q^92 + 16 * q^93 - 96 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−2.23278	+	1.28910i	−1.57882	+	0.911529i	−0.583790	+	0.811905i	$0.698431\pi$
$2$	−2.23278	+	1.28910i	−1.57882	+	0.911529i	−0.995025	+	0.0996245i	$0.968236\pi$
$3$	−0.625134	−	1.61530i	−0.360921	−	0.932596i
$3$	−0.625134	−	1.61530i	−0.360921	−	0.932596i
$4$	2.32354	−	4.02449i	1.16177	−	2.01225i
$5$	2.33189			1.04285			0.521427	−	0.853296i	$-0.325400\pi$
$5$	2.33189			1.04285			0.521427	+	0.853296i	$0.325400\pi$
$6$	3.47807	+	2.80076i	1.41992	+	1.14341i
$7$		0			0
$7$		0			0
$8$			6.82470i			2.41290i
$9$	−2.21841	+	2.01956i	−0.739472	+	0.673188i
$10$	−5.20660	+	3.00603i	−1.64647	+	0.950591i
$11$			4.36608i			1.31642i	0.752833	+	0.658212i	$0.228687\pi$
$11$			4.36608i			1.31642i	−0.752833	+	0.658212i	$0.771313\pi$
$12$	−7.95331	−	1.23738i	−2.29592	−	0.357201i
$13$	1.14392	−	0.660445i	0.317267	−	0.183174i	−0.332906	−	0.942960i	$-0.608029\pi$
$13$	1.14392	−	0.660445i	0.317267	−	0.183174i	0.650174	+	0.759785i	$0.274696\pi$
$14$		0			0
$15$	−1.45774	−	3.76671i	−0.376388	−	0.972561i
$16$	−4.15061	−	7.18908i	−1.03765	−	1.79727i
$17$	2.89327	+	5.01130i	0.701722	+	1.21542i	0.967862	+	0.251484i	$0.0809185\pi$
$17$	2.89327	+	5.01130i	0.701722	+	1.21542i	−0.266140	+	0.963935i	$0.585748\pi$
$18$	2.34982	−	7.36900i	0.553858	−	1.73689i
$19$	0.584876	+	0.337678i	0.134180	+	0.0774687i	0.565587	−	0.824688i	$-0.308650\pi$
$19$	0.584876	+	0.337678i	0.134180	+	0.0774687i	−0.431407	+	0.902157i	$0.641983\pi$
$20$	5.41825	−	9.38468i	1.21156	−	2.09848i
$21$		0			0
$22$	−5.62830	−	9.74851i	−1.19996	−	2.07839i
$23$		−	5.56333i		−	1.16004i	−0.814604	−	0.580018i	$-0.803046\pi$
$23$		−	5.56333i		−	1.16004i	0.814604	−	0.580018i	$-0.196954\pi$
$24$	11.0240	−	4.26635i	2.25026	−	0.870866i
$25$	0.437717			0.0875433
$26$	−1.70276	+	2.94926i	−0.333938	+	0.578397i
$27$	4.64902	+	2.32092i	0.894704	+	0.446661i
$28$		0			0
$29$	3.86926	+	2.23392i	0.718503	+	0.414828i	0.814202	−	0.580582i	$-0.197175\pi$
$29$	3.86926	+	2.23392i	0.718503	+	0.414828i	−0.0956983	+	0.995410i	$0.530508\pi$
$30$	8.11049	+	6.53107i	1.48077	+	1.19241i
$31$	3.47965	+	2.00898i	0.624964	+	0.360823i	0.778799	−	0.627273i	$-0.215829\pi$
$31$	3.47965	+	2.00898i	0.624964	+	0.360823i	−0.153835	+	0.988097i	$0.549162\pi$
$32$	6.71411	+	3.87639i	1.18690	+	0.685256i
$33$	7.05255	−	2.72939i	1.22769	−	0.475125i
$34$	−12.9201	−	7.45942i	−2.21578	−	1.27928i
$35$		0			0
$36$	2.97314	+	13.6205i	0.495523	+	2.27009i
$37$	−1.50829	+	2.61243i	−0.247961	+	0.429482i	−0.962960	−	0.269644i	$-0.913094\pi$
$37$	−1.50829	+	2.61243i	−0.247961	+	0.429482i	0.714999	+	0.699126i	$0.246427\pi$
$38$	−1.74120			−0.282460
$39$	−1.78193	−	1.43492i	−0.285336	−	0.229771i
$40$			15.9145i			2.51630i
$41$	3.29501	+	5.70713i	0.514594	+	0.891303i	0.999857	+	0.0169348i	$0.00539076\pi$
$41$	3.29501	+	5.70713i	0.514594	+	0.891303i	−0.485262	+	0.874369i	$0.661276\pi$
$42$		0			0
$43$	3.89217	−	6.74143i	0.593550	−	1.02806i	−0.400200	−	0.916428i	$-0.631059\pi$
$43$	3.89217	−	6.74143i	0.593550	−	1.02806i	0.993750	−	0.111631i	$-0.0356074\pi$
$44$	17.5713	+	10.1448i	2.64897	+	1.52938i
$45$	−5.17310	+	4.70940i	−0.771160	+	0.702036i
$46$	7.17168	+	12.4217i	1.05741	+	1.83148i
$47$	−0.246705	−	0.427306i	−0.0359856	−	0.0623289i	0.847472	−	0.530841i	$-0.178124\pi$
$47$	−0.246705	−	0.427306i	−0.0359856	−	0.0623289i	−0.883457	+	0.468512i	$0.844790\pi$
$48$	−9.01785	+	11.1986i	−1.30161	+	1.61638i
$49$		0			0
$50$	−0.977326	+	0.564259i	−0.138215	+	0.0797983i
$51$	6.28609	−	7.80625i	0.880228	−	1.09309i
$52$		−	6.13829i		−	0.851227i
$53$	−3.59025	+	2.07283i	−0.493159	+	0.284725i	−0.725884	−	0.687817i	$-0.758569\pi$
$53$	−3.59025	+	2.07283i	−0.493159	+	0.284725i	0.232725	+	0.972543i	$0.425236\pi$
$54$	−13.3721	+	0.810934i	−1.81972	+	0.110354i
$55$			10.1812i			1.37284i
$56$		0			0
$57$	0.179827	−	1.15585i	0.0238187	−	0.153096i
$58$	−11.5189			−1.51251
$59$	−2.15699	+	3.73602i	−0.280816	+	0.486388i	−0.971586	−	0.236687i	$-0.923939\pi$
$59$	−2.15699	+	3.73602i	−0.280816	+	0.486388i	0.690770	+	0.723075i	$0.257272\pi$
$60$	−18.5462	−	2.88543i	−2.39431	−	0.372508i
$61$	1.77661	−	1.02572i	0.227471	−	0.131330i	−0.381934	−	0.924190i	$-0.624742\pi$
$61$	1.77661	−	1.02572i	0.227471	−	0.131330i	0.609405	+	0.792859i	$0.291408\pi$
$62$	−10.3591			−1.31560
$63$		0			0
$64$	−3.38572			−0.423215
$65$	2.66751	−	1.54009i	0.330863	−	0.191024i
$66$	−12.2284	+	15.1855i	−1.50521	+	1.86921i
$67$	2.41218	−	4.17802i	0.294695	−	0.510427i	−0.680219	−	0.733009i	$-0.738115\pi$
$67$	2.41218	−	4.17802i	0.294695	−	0.510427i	0.974914	+	0.222582i	$0.0714486\pi$
$68$	26.8906			3.26096
$69$	−8.98648	+	3.47783i	−1.08184	+	0.418681i
$70$		0			0
$71$		−	1.17135i		−	0.139014i	−0.997581	−	0.0695068i	$-0.977857\pi$
$71$		−	1.17135i		−	0.139014i	0.997581	−	0.0695068i	$-0.0221426\pi$
$72$	−13.7829	−	15.1400i	−1.62433	−	1.78427i
$73$	13.0902	−	7.55766i	1.53210	−	0.884557i	0.532833	−	0.846221i	$-0.321128\pi$
$73$	13.0902	−	7.55766i	1.53210	−	0.884557i	0.999265	−	0.0383363i	$-0.0122058\pi$
$74$		−	7.77733i		−	0.904096i
$75$	−0.273632	−	0.707045i	−0.0315963	−	0.0816426i
$76$	2.71797	−	1.56922i	0.311772	−	0.180002i
$77$		0			0
$78$	5.82840	+	0.906785i	0.659936	+	0.102673i
$79$	5.30428	+	9.18728i	0.596778	+	1.03365i	0.993293	+	0.115622i	$0.0368861\pi$
$79$	5.30428	+	9.18728i	0.596778	+	1.03365i	−0.396515	+	0.918028i	$0.629781\pi$
$80$	−9.67878	−	16.7641i	−1.08212	−	1.87429i
$81$	0.842727	−	8.96046i	0.0936363	−	0.995606i
$82$	−14.7141	−	8.49518i	−1.62490	−	0.938135i
$83$	5.32432	−	9.22199i	0.584420	−	1.01225i	−0.410527	−	0.911848i	$-0.634655\pi$
$83$	5.32432	−	9.22199i	0.584420	−	1.01225i	0.994947	−	0.100397i	$-0.0320113\pi$
$84$		0			0
$85$	6.74680	+	11.6858i	0.731793	+	1.26750i
$86$			20.0695i			2.16415i
$87$	1.18965	−	7.64653i	0.127544	−	0.819794i
$88$	−29.7972			−3.17639
$89$	1.66268	−	2.87984i	0.176243	−	0.305262i	−0.764348	−	0.644804i	$-0.776939\pi$
$89$	1.66268	−	2.87984i	0.176243	−	0.305262i	0.940591	+	0.339542i	$0.110272\pi$
$90$	5.47953	−	17.1837i	0.577593	−	1.81132i
$91$		0			0
$92$	−22.3896	−	12.9266i	−2.33428	−	1.34770i
$93$	1.06986	−	6.87658i	0.110939	−	0.713068i
$94$	1.10168	+	0.636053i	0.113629	+	0.0656039i
$95$	1.36387	+	0.787429i	0.139930	+	0.0807886i
$96$	2.06433	−	13.2686i	0.210690	−	1.35422i
$97$	12.7531	+	7.36299i	1.29488	+	0.747598i	0.979515	−	0.201373i	$-0.0645403\pi$
$97$	12.7531	+	7.36299i	1.29488	+	0.747598i	0.315363	+	0.948971i	$0.397874\pi$
$98$		0			0
$99$	−8.81758	−	9.68578i	−0.886200	−	0.973458i
$100$	1.01705	−	1.76159i	0.101705	−	0.176159i
$101$	−1.66418			−0.165593			−0.0827963	−	0.996566i	$-0.526385\pi$
$101$	−1.66418			−0.165593			−0.0827963	+	0.996566i	$0.526385\pi$
$102$	−3.97244	+	25.5330i	−0.393330	+	2.52815i
$103$		−	1.62562i		−	0.160177i	−0.996788	−	0.0800887i	$-0.974480\pi$
$103$		−	1.62562i		−	0.160177i	0.996788	−	0.0800887i	$-0.0255204\pi$
$104$	4.50734	+	7.80694i	0.441981	+	0.765533i
$105$		0			0
$106$	5.34416	−	9.25636i	0.519071	−	0.899057i
$107$	−15.8596	−	9.15652i	−1.53320	−	0.885194i	−0.999212	−	0.0397036i	$-0.987359\pi$
$107$	−15.8596	−	9.15652i	−1.53320	−	0.885194i	−0.533990	−	0.845491i	$-0.679308\pi$
$108$	20.1427	−	13.3172i	1.93823	−	1.28145i
$109$	7.98678	+	13.8335i	0.764995	+	1.32501i	0.940249	+	0.340487i	$0.110592\pi$
$109$	7.98678	+	13.8335i	0.764995	+	1.32501i	−0.175254	+	0.984523i	$0.556075\pi$
$110$	−13.1246	−	22.7325i	−1.25138	−	2.16746i
$111$	5.16276	+	0.803225i	0.490027	+	0.0762387i
$112$		0			0
$113$	−5.07612	+	2.93070i	−0.477521	+	0.275697i	−0.719383	−	0.694614i	$-0.755575\pi$
$113$	−5.07612	+	2.93070i	−0.477521	+	0.275697i	0.241862	+	0.970311i	$0.422242\pi$
$114$	1.08848	+	2.81257i	0.101946	+	0.263421i
$115$		−	12.9731i		−	1.20975i
$116$	17.9808	−	10.3812i	1.66947	−	0.963871i
$117$	−1.20389	+	3.77537i	−0.111299	+	0.349033i
$118$		−	11.1223i		−	1.02389i
$119$		0			0
$120$	25.7067	−	9.94867i	2.34669	−	0.908185i
$121$	−8.06267			−0.732970
$122$	−2.64451	+	4.58043i	−0.239423	+	0.414693i
$123$	7.15892	−	8.89016i	0.645498	−	0.801599i
$124$	16.1702	−	9.33589i	1.45213	−	0.838388i
$125$	−10.6387			−0.951559
$126$		0			0
$127$	−16.5710			−1.47044			−0.735218	−	0.677831i	$-0.762920\pi$
$127$	−16.5710			−1.47044			−0.735218	+	0.677831i	$0.762920\pi$
$128$	−5.86864	+	3.38826i	−0.518719	+	0.299483i
$129$	−13.3226	−	2.07273i	−1.17299	−	0.182494i
$130$	−3.97064	+	6.87735i	−0.348248	+	0.603183i
$131$	−7.11978			−0.622058			−0.311029	−	0.950400i	$-0.600674\pi$
$131$	−7.11978			−0.622058			−0.311029	+	0.950400i	$0.600674\pi$
$132$	5.40250	−	34.7248i	0.470227	−	3.02241i
$133$		0			0
$134$			12.4382i			1.07449i
$135$	10.8410	+	5.41212i	0.933045	+	0.465801i
$136$	−34.2006	+	19.7457i	−2.93268	+	1.69318i
$137$			0.827439i			0.0706929i	0.999375	+	0.0353465i	$0.0112535\pi$
$137$			0.827439i			0.0706929i	−0.999375	+	0.0353465i	$0.988747\pi$
$138$	15.5816	−	19.3497i	1.32639	−	1.64715i
$139$	12.0735	−	6.97062i	1.02406	−	0.591241i	0.108782	−	0.994066i	$-0.465305\pi$
$139$	12.0735	−	6.97062i	1.02406	−	0.591241i	0.915277	+	0.402825i	$0.131972\pi$
$140$		0			0
$141$	−0.536005	+	0.665627i	−0.0451397	+	0.0560559i
$142$	1.50998	+	2.61537i	0.126715	+	0.219477i
$143$	2.88356	+	4.99447i	0.241135	+	0.417658i
$144$	23.7266	+	7.56592i	1.97721	+	0.630493i
$145$	9.02269	+	5.20925i	0.749294	+	0.432605i
$146$	−19.4851	+	33.7492i	−1.61260	+	2.79310i
$147$		0			0
$148$	7.00915	+	12.1402i	0.576149	+	0.997919i
$149$		−	10.9340i		−	0.895752i	−0.894096	−	0.447876i	$-0.852181\pi$
$149$		−	10.9340i		−	0.895752i	0.894096	−	0.447876i	$-0.147819\pi$
$150$	1.52241	+	1.22594i	0.124304	+	0.100098i
$151$	−13.9455			−1.13487			−0.567436	−	0.823418i	$-0.692065\pi$
$151$	−13.9455			−1.13487			−0.567436	+	0.823418i	$0.692065\pi$
$152$	−2.30455	+	3.99160i	−0.186924	+	0.323762i
$153$	−16.5391	−	5.27399i	−1.33711	−	0.426376i
$154$		0			0
$155$	8.11417	+	4.68472i	0.651746	+	0.376286i
$156$	−9.91520	+	3.83725i	−0.793851	+	0.307226i
$157$	−13.6641	−	7.88894i	−1.09051	−	0.629606i	−0.156798	−	0.987631i	$-0.550117\pi$
$157$	−13.6641	−	7.88894i	−1.09051	−	0.629606i	−0.933712	+	0.358024i	$0.883450\pi$
$158$	−23.6866	−	13.6755i	−1.88440	−	1.08796i
$159$	5.59264	+	4.50355i	0.443525	+	0.357155i
$160$	15.6566	+	9.03932i	1.23776	+	0.714621i
$161$		0			0
$162$	9.66928	+	21.0931i	0.759690	+	1.65723i
$163$	3.38276	−	5.85911i	0.264958	−	0.458921i	−0.702594	−	0.711590i	$-0.747975\pi$
$163$	3.38276	−	5.85911i	0.264958	−	0.458921i	0.967553	+	0.252669i	$0.0813085\pi$
$164$	30.6244			2.39136
$165$	16.4458	−	6.36463i	1.28030	−	0.495486i
$166$			27.4543i			2.13086i
$167$	−9.54631	−	16.5347i	−0.738716	−	1.27949i	−0.953074	−	0.302738i	$-0.902099\pi$
$167$	−9.54631	−	16.5347i	−0.738716	−	1.27949i	0.214358	−	0.976755i	$-0.431234\pi$
$168$		0			0
$169$	−5.62763	+	9.74733i	−0.432894	+	0.749795i
$170$	−30.1283	−	17.3946i	−2.31073	−	1.33410i
$171$	−1.97946	+	0.432084i	−0.151373	+	0.0330423i
$172$	−18.0872	−	31.3280i	−1.37914	−	2.38874i
$173$	10.9246	+	18.9219i	0.830579	+	1.43860i	0.897580	+	0.440851i	$0.145323\pi$
$173$	10.9246	+	18.9219i	0.830579	+	1.43860i	−0.0670016	+	0.997753i	$0.521343\pi$
$174$	7.20089	+	18.6066i	0.545898	+	1.41056i
$175$		0			0
$176$	31.3881	−	18.1219i	2.36597	−	1.36599i
$177$	7.38322	+	1.14868i	0.554957	+	0.0863404i
$178$			8.57340i			0.642603i
$179$	−14.8866	+	8.59481i	−1.11268	+	0.642406i	−0.939522	−	0.342488i	$-0.888730\pi$
$179$	−14.8866	+	8.59481i	−1.11268	+	0.642406i	−0.173158	+	0.984894i	$0.555397\pi$
$180$	6.93304	+	31.7616i	0.516758	+	2.36737i
$181$			16.6462i			1.23730i	0.785666	+	0.618650i	$0.212320\pi$
$181$			16.6462i			1.23730i	−0.785666	+	0.618650i	$0.787680\pi$
$182$		0			0
$183$	−2.76747	−	2.22854i	−0.204577	−	0.164739i
$184$	37.9681			2.79904
$185$	−3.51717	+	6.09191i	−0.258587	+	0.447886i
$186$	6.47581	+	16.7331i	0.474829	+	1.22693i
$187$	−21.8797	+	12.6323i	−1.60000	+	0.923763i
$188$	−2.29292			−0.167228
$189$		0			0
$190$	−4.06029			−0.294565
$191$	−0.826254	+	0.477038i	−0.0597857	+	0.0345173i	−0.529595	−	0.848251i	$-0.677656\pi$
$191$	−0.826254	+	0.477038i	−0.0597857	+	0.0345173i	0.469809	+	0.882768i	$0.344323\pi$
$192$	2.11653	+	5.46897i	0.152747	+	0.394689i
$193$	0.847203	−	1.46740i	0.0609830	−	0.105626i	−0.833922	−	0.551882i	$-0.813910\pi$
$193$	0.847203	−	1.46740i	0.0609830	−	0.105626i	0.894905	+	0.446257i	$0.147243\pi$
$194$	−37.9664			−2.72583
$195$	−4.15526	−	3.34607i	−0.297564	−	0.239617i
$196$		0			0
$197$			12.7486i			0.908301i	0.890925	+	0.454150i	$0.150057\pi$
$197$			12.7486i			0.908301i	−0.890925	+	0.454150i	$0.849943\pi$
$198$	32.1736	+	10.2595i	2.28648	+	0.729112i
$199$	3.77420	−	2.17903i	0.267546	−	0.154468i	−0.360226	−	0.932865i	$-0.617300\pi$
$199$	3.77420	−	2.17903i	0.267546	−	0.154468i	0.627772	+	0.778397i	$0.283967\pi$
$200$			2.98728i			0.211233i
$201$	−8.25672	−	1.28458i	−0.582384	−	0.0906076i
$202$	3.71576	−	2.14530i	0.261440	−	0.150942i
$203$		0			0
$204$	−16.8102	−	43.4365i	−1.17695	−	3.04116i
$205$	7.68361	+	13.3084i	0.536646	+	0.929499i
$206$	2.09559	+	3.62966i	0.146006	+	0.252891i
$207$	11.2355	+	12.3418i	0.780922	+	0.857813i
$208$	−9.49598	−	5.48250i	−0.658427	−	0.380143i
$209$	−1.47433	+	2.55362i	−0.101982	+	0.176637i
$210$		0			0
$211$	−2.24368	−	3.88617i	−0.154461	−	0.267535i	0.778401	−	0.627767i	$-0.216031\pi$
$211$	−2.24368	−	3.88617i	−0.154461	−	0.267535i	−0.932863	+	0.360232i	$0.882698\pi$
$212$			19.2653i			1.32314i
$213$	−1.89209	+	0.732251i	−0.129644	+	0.0501730i
$214$	47.2146			3.22752
$215$	9.07611	−	15.7203i	0.618986	−	1.07211i
$216$	−15.8396	+	31.7281i	−1.07775	+	2.15883i
$217$		0			0
$218$	−35.6655	−	20.5915i	−2.41557	−	1.39463i
$219$	−20.3911	−	16.4202i	−1.37790	−	1.10957i
$220$	40.9743	+	23.6565i	2.76249	+	1.59492i
$221$	6.61937	+	3.82170i	0.445267	+	0.257075i
$222$	−12.5627	+	4.86187i	−0.843156	+	0.326308i
$223$	−18.0005	−	10.3926i	−1.20540	−	0.695939i	−0.243650	−	0.969863i	$-0.578345\pi$
$223$	−18.0005	−	10.3926i	−1.20540	−	0.695939i	−0.961751	+	0.273924i	$0.911678\pi$
$224$		0			0
$225$	−0.971037	+	0.883997i	−0.0647358	+	0.0589331i
$226$	7.55591	−	13.0872i	0.502612	−	0.870549i
$227$	28.3159			1.87939			0.939696	−	0.342012i	$-0.111108\pi$
$227$	28.3159			1.87939			0.939696	+	0.342012i	$0.111108\pi$
$228$	−4.23386	−	3.40937i	−0.280394	−	0.225791i
$229$		−	21.7857i		−	1.43964i	−0.694160	−	0.719821i	$-0.744224\pi$
$229$		−	21.7857i		−	1.43964i	0.694160	−	0.719821i	$-0.255776\pi$
$230$	16.7236	+	28.9661i	1.10272	+	1.90997i
$231$		0			0
$232$	−15.2458	+	26.4065i	−1.00094	+	1.73367i
$233$	13.1926	+	7.61674i	0.864275	+	0.498989i	0.865441	−	0.501010i	$-0.167038\pi$
$233$	13.1926	+	7.61674i	0.864275	+	0.498989i	−0.00116682	+	0.999999i	$0.500371\pi$
$234$	−2.17880	−	9.98150i	−0.142432	−	0.652511i
$235$	−0.575289	−	0.996430i	−0.0375277	−	0.0649999i
$236$	10.0237	+	17.3616i	0.652489	+	1.13014i
$237$	11.5244	−	14.3113i	0.748588	−	0.929619i
$238$		0			0
$239$	−4.95125	+	2.85861i	−0.320270	+	0.184908i	−0.651513	−	0.758638i	$-0.725865\pi$
$239$	−4.95125	+	2.85861i	−0.320270	+	0.184908i	0.331243	+	0.943545i	$0.392532\pi$
$240$	−21.0287	+	26.1140i	−1.35739	+	1.68565i
$241$		−	4.47114i		−	0.288011i	−0.989577	−	0.144006i	$-0.954002\pi$
$241$		−	4.47114i		−	0.288011i	0.989577	−	0.144006i	$-0.0459984\pi$
$242$	18.0022	−	10.3936i	1.15722	−	0.668124i
$243$	−15.0007	+	4.24023i	−0.962294	+	0.272011i
$244$		−	9.53325i		−	0.610304i
$245$		0			0
$246$	−4.52402	+	29.0783i	−0.288441	+	1.85397i
$247$	0.892072			0.0567612
$248$	−13.7107	+	23.7476i	−0.870629	+	1.50797i
$249$	−18.2247	−	2.83541i	−1.15495	−	0.179687i
$250$	23.7540	−	13.7144i	1.50234	−	0.867374i
$251$	11.6265			0.733861			0.366931	−	0.930248i	$-0.380409\pi$
$251$	11.6265			0.733861			0.366931	+	0.930248i	$0.380409\pi$
$252$		0			0
$253$	24.2900			1.52710
$254$	36.9993	−	21.3616i	2.32155	−	1.34034i
$255$	14.6585	−	18.2033i	0.917949	−	1.13994i
$256$	12.1213	−	20.9947i	0.757582	−	1.31217i
$257$	2.10280			0.131169			0.0655846	−	0.997847i	$-0.479109\pi$
$257$	2.10280			0.131169			0.0655846	+	0.997847i	$0.479109\pi$
$258$	32.4184	−	12.5461i	2.01828	−	0.781089i
$259$		0			0
$260$		−	14.3138i		−	0.887705i
$261$	−13.0952	+	2.85846i	−0.810570	+	0.176934i
$262$	15.8969	−	9.17809i	0.982114	−	0.567024i
$263$			2.20286i			0.135834i	0.997691	+	0.0679170i	$0.0216353\pi$
$263$			2.20286i			0.135834i	−0.997691	+	0.0679170i	$0.978365\pi$
$264$	18.6272	+	48.1315i	1.14643	+	2.96229i
$265$	−8.37207	+	4.83362i	−0.514292	+	0.296927i
$266$		0			0
$267$	−5.69121	−	0.885441i	−0.348296	−	0.0541881i
$268$	−11.2096	−	19.4156i	−0.684737	−	1.18600i
$269$	−13.9312	−	24.1295i	−0.849398	−	1.47120i	−0.881746	−	0.471724i	$-0.843632\pi$
$269$	−13.9312	−	24.1295i	−0.849398	−	1.47120i	0.0323483	−	0.999477i	$-0.489701\pi$
$270$	−31.1823	+	1.89101i	−1.89770	+	0.115083i
$271$	−9.94228	−	5.74018i	−0.603950	−	0.348691i	0.166644	−	0.986017i	$-0.446707\pi$
$271$	−9.94228	−	5.74018i	−0.603950	−	0.348691i	−0.770594	+	0.637326i	$0.780040\pi$
$272$	24.0177	−	41.5999i	1.45629	−	2.52237i
$273$		0			0
$274$	−1.06665	−	1.84749i	−0.0644387	−	0.111611i
$275$			1.91111i			0.115244i
$276$	−6.88395	+	44.2469i	−0.414365	+	2.66335i
$277$	−10.2000			−0.612859			−0.306429	−	0.951893i	$-0.599134\pi$
$277$	−10.2000			−0.612859			−0.306429	+	0.951893i	$0.599134\pi$
$278$	−17.9716	+	31.1278i	−1.07787	+	1.86692i
$279$	−11.7766	+	2.57063i	−0.705045	+	0.153900i
$280$		0			0
$281$	9.45116	+	5.45663i	0.563809	+	0.325515i	0.754673	−	0.656101i	$-0.227796\pi$
$281$	9.45116	+	5.45663i	0.563809	+	0.325515i	−0.190864	+	0.981617i	$0.561129\pi$
$282$	0.338724	−	2.17716i	0.0201707	−	0.129648i
$283$	10.2766	+	5.93322i	0.610882	+	0.352693i	0.773311	−	0.634027i	$-0.218599\pi$
$283$	10.2766	+	5.93322i	0.610882	+	0.352693i	−0.162428	+	0.986720i	$0.551933\pi$
$284$	−4.71409	−	2.72168i	−0.279730	−	0.161502i
$285$	0.419338	−	2.69531i	0.0248394	−	0.159656i
$286$	−12.8767	−	7.43437i	−0.761415	−	0.439603i
$287$		0			0
$288$	−22.7233	+	4.96012i	−1.33898	+	0.292278i
$289$	−8.24207	+	14.2757i	−0.484828	+	0.839746i
$290$	−26.8609			−1.57733
$291$	3.92109	−	25.2029i	0.229858	−	1.47742i
$292$		−	70.2422i		−	4.11061i
$293$	−9.55012	−	16.5413i	−0.557924	−	0.966353i	−0.997670	−	0.0682302i	$-0.978265\pi$
$293$	−9.55012	−	16.5413i	−0.557924	−	0.966353i	0.439746	−	0.898122i	$-0.355069\pi$
$294$		0			0
$295$	−5.02987	+	8.71199i	−0.292850	+	0.507232i
$296$	−17.8291	−	10.2936i	−1.03629	−	0.598305i
$297$	−10.1333	+	20.2980i	−0.587994	+	1.17781i
$298$	14.0950	+	24.4133i	0.816504	+	1.41423i
$299$	−3.67427	−	6.36403i	−0.212489	−	0.368041i
$300$	−3.48129	−	0.541622i	−0.200993	−	0.0312705i
$301$		0			0
$302$	31.1373	−	17.9772i	1.79175	−	1.03447i
$303$	1.04034	+	2.68816i	0.0597659	+	0.154431i
$304$		−	5.60629i		−	0.321543i
$305$	4.14285	−	2.39188i	0.237219	−	0.136958i
$306$	43.7269	−	9.54487i	2.49970	−	0.545644i
$307$			2.35488i			0.134400i	0.997740	+	0.0672001i	$0.0214066\pi$
$307$			2.35488i			0.134400i	−0.997740	+	0.0672001i	$0.978593\pi$
$308$		0			0
$309$	−2.62588	+	1.01623i	−0.149381	+	0.0578114i
$310$	−24.1562			−1.37198
$311$	−3.92483	+	6.79801i	−0.222557	+	0.385480i	−0.955584	−	0.294720i	$-0.904774\pi$
$311$	−3.92483	+	6.79801i	−0.222557	+	0.385480i	0.733027	+	0.680200i	$0.238107\pi$
$312$	9.79289	−	12.1611i	0.554413	−	0.688487i
$313$	−26.0268	+	15.0266i	−1.47112	+	0.849352i	−0.999474	−	0.0324349i	$-0.989674\pi$
$313$	−26.0268	+	15.0266i	−1.47112	+	0.849352i	−0.471647	+	0.881787i	$0.656340\pi$
$314$	40.6785			2.29562
$315$		0			0
$316$	49.2989			2.77328
$317$	9.61906	−	5.55356i	0.540260	−	0.311919i	−0.204924	−	0.978778i	$-0.565695\pi$
$317$	9.61906	−	5.55356i	0.540260	−	0.311919i	0.745184	+	0.666859i	$0.232361\pi$
$318$	−18.2927	−	2.84598i	−1.02580	−	0.159595i
$319$	−9.75347	+	16.8935i	−0.546089	+	0.945854i
$320$	−7.89513			−0.441351
$321$	−4.87621	+	31.3421i	−0.272164	+	1.74934i
$322$		0			0
$323$			3.90798i			0.217446i
$324$	−34.1032	−	24.2116i	−1.89462	−	1.34509i
$325$	0.500715	−	0.289088i	0.0277746	−	0.0160357i
$326$			17.4428i			0.966069i
$327$	17.3525	−	21.5489i	0.959597	−	1.19166i
$328$	−38.9494	+	22.4875i	−2.15062	+	1.24166i
$329$		0			0
$330$	−28.5152	+	35.4110i	−1.56971	+	1.94931i
$331$	8.63362	+	14.9539i	0.474547	+	0.821939i	0.999575	−	0.0291457i	$-0.00927866\pi$
$331$	8.63362	+	14.9539i	0.474547	+	0.821939i	−0.525028	+	0.851085i	$0.675945\pi$
$332$	−24.7426	−	42.8554i	−1.35792	−	2.35199i
$333$	−1.92997	−	8.84155i	−0.105761	−	0.484514i
$334$	42.6297	+	24.6123i	2.33259	+	1.34672i
$335$	5.62495	−	9.74270i	0.307324	−	0.532300i
$336$		0			0
$337$	−3.82962	−	6.63309i	−0.208612	−	0.361327i	0.742665	−	0.669663i	$-0.233561\pi$
$337$	−3.82962	−	6.63309i	−0.208612	−	0.361327i	−0.951278	+	0.308336i	$0.900228\pi$
$338$		−	29.0182i		−	1.57838i
$339$	7.90723	+	6.36740i	0.429462	+	0.345830i
$340$	62.7059			3.40071
$341$	−8.77137	+	15.1925i	−0.474996	+	0.822717i
$342$	3.86271	−	3.51647i	0.208871	−	0.190149i
$343$		0			0
$344$	46.0082	+	26.5629i	2.48060	+	1.43217i
$345$	−20.9555	+	8.10992i	−1.12821	+	0.436623i
$346$	−48.7843	−	28.1656i	−2.62266	−	1.51419i
$347$	11.4014	+	6.58262i	0.612061	+	0.353374i	0.773772	−	0.633465i	$-0.218368\pi$
$347$	11.4014	+	6.58262i	0.612061	+	0.353374i	−0.161711	+	0.986838i	$0.551701\pi$
$348$	−28.0092	−	22.5548i	−1.50145	−	1.20906i
$349$	1.05185	+	0.607283i	0.0563040	+	0.0325071i	0.527888	−	0.849314i	$-0.322984\pi$
$349$	1.05185	+	0.607283i	0.0563040	+	0.0325071i	−0.471584	+	0.881821i	$0.656318\pi$
$350$		0			0
$351$	6.85096	−	0.415467i	0.365677	−	0.0221760i
$352$	−16.9246	+	29.3143i	−0.902087	+	1.56246i
$353$	−26.8228			−1.42763			−0.713816	−	0.700333i	$-0.753035\pi$
$353$	−26.8228			−1.42763			−0.713816	+	0.700333i	$0.753035\pi$
$354$	−17.9659	+	6.95292i	−0.954876	+	0.369544i
$355$		−	2.73146i		−	0.144971i
$356$	−7.72659	−	13.3829i	−0.409509	−	0.709290i
$357$		0			0
$358$	22.1591	−	38.3807i	1.17114	−	2.02848i
$359$	6.45209	+	3.72512i	0.340529	+	0.196604i	0.660506	−	0.750821i	$-0.270342\pi$
$359$	6.45209	+	3.72512i	0.340529	+	0.196604i	−0.319977	+	0.947425i	$0.603675\pi$
$360$	−32.1403	−	35.3049i	−1.69394	−	1.86073i
$361$	−9.27195	−	16.0595i	−0.487997	−	0.845236i
$362$	−21.4585	−	37.1673i	−1.12784	−	1.95347i
$363$	5.04025	+	13.0237i	0.264545	+	0.683565i
$364$		0			0
$365$	30.5250	−	17.6236i	1.59775	−	0.922463i
$366$	9.05197	+	1.40831i	0.473154	+	0.0736135i
$367$			34.9875i			1.82633i	0.407588	+	0.913166i	$0.366370\pi$
$367$			34.9875i			1.82633i	−0.407588	+	0.913166i	$0.633630\pi$
$368$	−39.9952	+	23.0913i	−2.08490	+	1.20371i
$369$	−18.8356	−	6.00629i	−0.980542	−	0.312675i
$370$		−	18.1359i		−	0.942840i
$371$		0			0
$372$	−25.1889	−	20.2837i	−1.30598	−	1.05166i
$373$	−30.0990			−1.55847			−0.779233	−	0.626734i	$-0.784391\pi$
$373$	−30.0990			−1.55847			−0.779233	+	0.626734i	$0.784391\pi$
$374$	32.5684	−	56.4102i	1.68407	−	2.91690i
$375$	6.65064	+	17.1848i	0.343438	+	0.887420i
$376$	2.91623	−	1.68369i	0.150393	−	0.0868295i
$377$	5.90152			0.303944
$378$		0			0
$379$	−27.0996			−1.39201			−0.696006	−	0.718036i	$-0.745041\pi$
$379$	−27.0996			−1.39201			−0.696006	+	0.718036i	$0.745041\pi$
$380$	6.33801	−	3.65925i	0.325133	−	0.187716i
$381$	10.3591	+	26.7671i	0.530711	+	1.37132i
$382$	1.22990	−	2.13024i	0.0629270	−	0.108993i
$383$	3.66030			0.187033			0.0935164	−	0.995618i	$-0.470189\pi$
$383$	3.66030			0.187033			0.0935164	+	0.995618i	$0.470189\pi$
$384$	9.14176	+	7.36152i	0.466513	+	0.375666i
$385$		0			0
$386$			4.36851i			0.222351i
$387$	4.98031	+	22.8158i	0.253163	+	1.15979i
$388$	59.2646	−	34.2164i	3.00870	−	1.73708i
$389$		−	12.1690i		−	0.616992i	−0.951226	−	0.308496i	$-0.900174\pi$
$389$		−	12.1690i		−	0.616992i	0.951226	−	0.308496i	$-0.0998257\pi$
$390$	13.5912	+	2.11452i	0.688217	+	0.107073i
$391$	27.8795	−	16.0962i	1.40993	−	0.814022i
$392$		0			0
$393$	4.45082	+	11.5006i	0.224514	+	0.580129i
$394$	−16.4342	−	28.4649i	−0.827943	−	1.43404i
$395$	12.3690	+	21.4237i	0.622352	+	1.07795i
$396$	−59.4684	+	12.9810i	−2.98840	+	0.652318i
$397$	23.1870	+	13.3870i	1.16372	+	0.671876i	0.952194	−	0.305495i	$-0.0988220\pi$
$397$	23.1870	+	13.3870i	1.16372	+	0.671876i	0.211530	+	0.977371i	$0.432155\pi$
$398$	−5.61797	+	9.73061i	−0.281603	+	0.487752i
$399$		0			0
$400$	−1.81679	−	3.14678i	−0.0908397	−	0.157339i
$401$			7.72989i			0.386012i	0.981198	+	0.193006i	$0.0618237\pi$
$401$			7.72989i			0.386012i	−0.981198	+	0.193006i	$0.938176\pi$
$402$	20.0914	−	7.77552i	1.00207	−	0.387807i
$403$	5.30728			0.264374
$404$	−3.86680	+	6.69750i	−0.192381	+	0.333213i
$405$	1.96515	−	20.8948i	0.0976490	−	1.03827i
$406$		0			0
$407$	−11.4061	−	6.58532i	−0.565380	−	0.326422i
$408$	53.2753	+	42.9006i	2.63752	+	2.12390i
$409$	−7.84660	−	4.53024i	−0.387989	−	0.224006i	0.293299	−	0.956021i	$-0.405247\pi$
$409$	−7.84660	−	4.53024i	−0.387989	−	0.224006i	−0.681289	+	0.732015i	$0.738580\pi$
$410$	−34.3116	−	19.8098i	−1.69453	−	0.978338i
$411$	1.33657	−	0.517261i	0.0659280	−	0.0255146i
$412$	−6.54231	−	3.77720i	−0.322316	−	0.186090i
$413$		0			0
$414$	−40.9962	−	13.0728i	−2.01485	−	0.642495i
$415$	12.4157	−	21.5047i	0.609464	−	1.05562i
$416$	10.2406			0.502085
$417$	−18.8072	−	15.1448i	−0.920993	−	0.741642i
$418$		−	7.60223i		−	0.371837i
$419$	3.30466	+	5.72384i	0.161443	+	0.279628i	0.935386	−	0.353627i	$-0.115052\pi$
$419$	3.30466	+	5.72384i	0.161443	+	0.279628i	−0.773943	+	0.633255i	$0.781718\pi$
$420$		0			0
$421$	6.39209	−	11.0714i	0.311531	−	0.539588i	−0.667163	−	0.744912i	$-0.732491\pi$
$421$	6.39209	−	11.0714i	0.311531	−	0.539588i	0.978694	+	0.205324i	$0.0658248\pi$
$422$	10.0193	+	5.78464i	0.487732	+	0.281592i
$423$	1.41026	+	0.449704i	0.0685694	+	0.0218654i
$424$	−14.1465	−	24.5024i	−0.687013	−	1.18994i
$425$	1.26643	+	2.19353i	0.0614311	+	0.106402i
$426$	3.28067	−	4.07404i	0.158949	−	0.197388i
$427$		0			0
$428$	−73.7007	+	42.5511i	−3.56246	+	2.05679i
$429$	6.26497	−	7.78003i	0.302476	−	0.375623i
$430$			46.7999i			2.25689i
$431$	−18.9756	+	10.9556i	−0.914023	+	0.527712i	−0.881723	−	0.471767i	$-0.843616\pi$
$431$	−18.9756	+	10.9556i	−0.914023	+	0.527712i	−0.0322998	+	0.999478i	$0.510283\pi$
$432$	−2.61103	−	43.0554i	−0.125623	−	2.07150i
$433$			8.21181i			0.394635i	0.980340	+	0.197317i	$0.0632229\pi$
$433$			8.21181i			0.394635i	−0.980340	+	0.197317i	$0.936777\pi$
$434$		0			0
$435$	2.77414	−	17.8309i	0.133010	−	0.854925i
$436$	74.2305			3.55500
$437$	1.87862	−	3.25386i	0.0898665	−	0.155653i
$438$	66.6960	+	10.3766i	3.18686	+	0.495813i
$439$	32.7996	−	18.9368i	1.56544	−	0.903806i	0.568749	−	0.822511i	$-0.307428\pi$
$439$	32.7996	−	18.9368i	1.56544	−	0.903806i	0.996690	−	0.0812949i	$-0.0259056\pi$
$440$	−69.4838			−3.31251
$441$		0			0
$442$	−19.7061			−0.937326
$443$	−17.7210	+	10.2312i	−0.841950	+	0.486100i	−0.857926	−	0.513773i	$-0.828248\pi$
$443$	−17.7210	+	10.2312i	−0.841950	+	0.486100i	0.0159769	+	0.999872i	$0.494914\pi$
$444$	15.2285	−	18.9112i	0.722711	−	0.897484i
$445$	3.87718	−	6.71547i	0.183796	−	0.318344i
$446$	53.5882			2.53747
$447$	−17.6618	+	6.83524i	−0.835375	+	0.323296i
$448$		0			0
$449$		−	35.7054i		−	1.68504i	−0.538665	−	0.842520i	$-0.681071\pi$
$449$		−	35.7054i		−	1.68504i	0.538665	−	0.842520i	$-0.318929\pi$
$450$	1.02856	−	3.22553i	0.0484866	−	0.152053i
$451$	−24.9178	+	14.3863i	−1.17333	+	0.677424i
$452$			27.2384i			1.28119i
$453$	8.71783	+	22.5263i	0.409599	+	1.05838i
$454$	−63.2232	+	36.5019i	−2.96721	+	1.71312i
$455$		0			0
$456$	7.88831	+	1.22727i	0.369404	+	0.0574720i
$457$	0.127090	+	0.220126i	0.00594501	+	0.0102971i	0.868983	−	0.494843i	$-0.164774\pi$
$457$	0.127090	+	0.220126i	0.00594501	+	0.0102971i	−0.863038	+	0.505140i	$0.831441\pi$
$458$	28.0839	+	48.6428i	1.31228	+	2.27293i
$459$	1.82008	+	30.0126i	0.0849538	+	1.40087i
$460$	−52.2101	−	30.1435i	−2.43431	−	1.40545i
$461$	12.2175	−	21.1613i	0.569025	−	0.985581i	−0.427637	−	0.903950i	$-0.640654\pi$
$461$	12.2175	−	21.1613i	0.569025	−	0.985581i	0.996663	−	0.0816304i	$-0.0260127\pi$
$462$		0			0
$463$	0.409986	+	0.710116i	0.0190536	+	0.0330019i	0.875395	−	0.483408i	$-0.160601\pi$
$463$	0.409986	+	0.710116i	0.0190536	+	0.0330019i	−0.856341	+	0.516410i	$0.827268\pi$
$464$		−	37.0885i		−	1.72179i
$465$	2.49480	−	16.0354i	0.115694	−	0.743625i
$466$	−39.2749			−1.81937
$467$	−0.909625	+	1.57552i	−0.0420924	+	0.0729062i	−0.886304	−	0.463104i	$-0.846736\pi$
$467$	−0.909625	+	1.57552i	−0.0420924	+	0.0729062i	0.844212	+	0.536010i	$0.180069\pi$
$468$	12.3967	+	13.6173i	0.573036	+	0.629458i
$469$		0			0
$470$	2.56899	+	1.48321i	0.118499	+	0.0684152i
$471$	−4.20118	+	27.0033i	−0.193580	+	1.24424i
$472$	−25.4972	−	14.7208i	−1.17360	−	0.677581i
$473$	29.4336	+	16.9935i	1.35336	+	0.781363i
$474$	−7.28273	+	46.8101i	−0.334507	+	2.15006i
$475$	0.256010	+	0.147807i	0.0117465	+	0.00678187i
$476$		0			0
$477$	3.77845	−	11.8491i	0.173003	−	0.542535i
$478$	7.37004	−	12.7653i	0.337098	−	0.583871i
$479$	−1.36215			−0.0622381			−0.0311191	−	0.999516i	$-0.509907\pi$
$479$	−1.36215			−0.0622381			−0.0311191	+	0.999516i	$0.509907\pi$
$480$	4.81380	−	30.9409i	0.219719	−	1.41225i
$481$			3.98457i			0.181681i
$482$	5.76373	+	9.98308i	0.262531	+	0.454717i
$483$		0			0
$484$	−18.7340	+	32.4482i	−0.851544	+	1.47492i
$485$	29.7388	+	17.1697i	1.35037	+	0.779635i
$486$	28.0272	−	28.8048i	1.27134	−	1.30661i
$487$	−15.8061	−	27.3769i	−0.716241	−	1.24057i	−0.962479	−	0.271357i	$-0.912528\pi$
$487$	−15.8061	−	27.3769i	−0.716241	−	1.24057i	0.246238	−	0.969209i	$-0.420806\pi$
$488$	7.00026	+	12.1248i	0.316887	+	0.548864i
$489$	−11.5789	−	1.80145i	−0.523617	−	0.0814646i
$490$		0			0
$491$	−1.97415	+	1.13977i	−0.0890919	+	0.0514373i	−0.543884	−	0.839160i	$-0.683047\pi$
$491$	−1.97415	+	1.13977i	−0.0890919	+	0.0514373i	0.454792	+	0.890598i	$0.349714\pi$
$492$	−19.1444	−	49.4677i	−0.863094	−	2.23018i
$493$			25.8533i			1.16438i
$494$	−1.99180	+	1.14997i	−0.0896154	+	0.0517395i
$495$	−20.5616	−	22.5862i	−0.924177	−	1.01517i
$496$		−	33.3540i		−	1.49764i
$497$		0			0
$498$	44.3470	−	17.1626i	1.98724	−	0.769074i
$499$	27.0390			1.21043			0.605215	−	0.796062i	$-0.293087\pi$
$499$	27.0390			1.21043			0.605215	+	0.796062i	$0.293087\pi$
$500$	−24.7196	+	42.8156i	−1.10549	+	1.91477i
$501$	−20.7408	+	25.7566i	−0.926633	+	1.15072i
$502$	−25.9595	+	14.9877i	−1.15863	+	0.668936i
$503$	0.276948			0.0123485			0.00617426	−	0.999981i	$-0.498035\pi$
$503$	0.276948			0.0123485			0.00617426	+	0.999981i	$0.498035\pi$
$504$		0			0
$505$	−3.88070			−0.172689
$506$	−54.2342	+	31.3121i	−2.41100	+	1.39199i
$507$	19.2629	+	2.99694i	0.855497	+	0.133099i
$508$	−38.5033	+	66.6897i	−1.70831	+	2.95888i
$509$	−18.4295			−0.816874			−0.408437	−	0.912786i	$-0.633926\pi$
$509$	−18.4295			−0.816874			−0.408437	+	0.912786i	$0.633926\pi$
$510$	−9.26330	+	59.5402i	−0.410186	+	2.63649i
$511$		0			0
$512$			48.9492i			2.16327i
$513$	1.93538	+	2.92732i	0.0854489	+	0.129244i
$514$	−4.69510	+	2.71072i	−0.207092	+	0.119565i
$515$		−	3.79078i		−	0.167042i
$516$	−39.2973	+	48.8006i	−1.72997	+	2.14833i
$517$	1.86565	−	1.07713i	0.0820512	−	0.0473723i
$518$		0			0
$519$	23.7353	−	29.4752i	1.04186	−	1.29382i
$520$	10.5106	+	18.2049i	0.460921	+	0.798339i
$521$	−11.6264	−	20.1374i	−0.509360	−	0.882237i	−0.999941	−	0.0108420i	$-0.996549\pi$
$521$	−11.6264	−	20.1374i	−0.509360	−	0.882237i	0.490581	−	0.871395i	$-0.336785\pi$
$522$	25.5538	−	23.2632i	1.11846	−	1.01820i
$523$	11.5227	+	6.65262i	0.503852	+	0.290899i	0.730303	−	0.683124i	$-0.239379\pi$
$523$	11.5227	+	6.65262i	0.503852	+	0.290899i	−0.226451	+	0.974023i	$0.572712\pi$
$524$	−16.5431	+	28.6535i	−0.722689	+	1.25173i
$525$		0			0
$526$	−2.83970	−	4.91850i	−0.123817	−	0.214457i
$527$			23.2501i			1.01279i
$528$	−48.8942	−	39.3727i	−2.12785	−	1.71348i
$529$	−7.95068			−0.345682
$530$	12.4620	−	21.5848i	0.541315	−	0.937585i
$531$	−2.76003	−	12.6442i	−0.119775	−	0.548712i
$532$		0			0
$533$	7.53848	+	4.35235i	0.326528	+	0.188521i
$534$	13.8486	−	5.35952i	0.599290	−	0.231929i
$535$	−36.9828	−	21.3520i	−1.59890	−	0.923128i
$536$	28.5138	+	16.4624i	1.23161	+	0.711069i
$537$	23.1894	+	18.6736i	1.00070	+	0.805823i
$538$	62.2105	+	35.9172i	2.68208	+	1.54850i
$539$		0			0
$540$	46.9706	−	31.0542i	2.02129	−	1.33636i
$541$	15.0846	−	26.1273i	0.648537	−	1.12330i	−0.334935	−	0.942241i	$-0.608714\pi$
$541$	15.0846	−	26.1273i	0.648537	−	1.12330i	0.983472	−	0.181059i	$-0.0579524\pi$
$542$	29.5986			1.27137
$543$	26.8886	−	10.4061i	1.15390	−	0.446568i
$544$			44.8619i			1.92344i
$545$	18.6243	+	32.2582i	0.797778	+	1.38179i
$546$		0			0
$547$	−0.572061	+	0.990840i	−0.0244596	+	0.0423652i	−0.877996	−	0.478668i	$-0.841120\pi$
$547$	−0.572061	+	0.990840i	−0.0244596	+	0.0423652i	0.853537	+	0.521033i	$0.174453\pi$
$548$	3.33002	+	1.92259i	0.142252	+	0.0821290i
$549$	−1.86973	+	5.86345i	−0.0797983	+	0.250246i
$550$	−2.46360	−	4.26708i	−0.105048	−	0.181949i
$551$	1.50869	+	2.61313i	0.0642724	+	0.111323i
$552$	−23.7351	−	61.3300i	−1.01023	−	2.61038i
$553$		0			0
$554$	22.7744	−	13.1488i	0.967591	−	0.558639i
$555$	12.0390	+	1.87303i	0.511027	+	0.0795058i
$556$		−	64.7862i		−	2.74755i
$557$	8.35388	−	4.82312i	0.353965	−	0.204362i	−0.312465	−	0.949929i	$-0.601155\pi$
$557$	8.35388	−	4.82312i	0.353965	−	0.204362i	0.666430	+	0.745567i	$0.267821\pi$
$558$	22.9807	−	20.9208i	0.972851	−	0.885648i
$559$		−	10.2822i		−	0.434893i
$560$		0			0
$561$	34.0827	+	27.4456i	1.43897	+	1.15875i
$562$	−28.1365			−1.18687
$563$	−1.54395	+	2.67420i	−0.0650698	+	0.112704i	−0.896725	−	0.442588i	$-0.854060\pi$
$563$	−1.54395	+	2.67420i	−0.0650698	+	0.112704i	0.831655	+	0.555292i	$0.187394\pi$
$564$	1.43338	+	3.70376i	0.0603562	+	0.155956i
$565$	−11.8370	+	6.83407i	−0.497985	+	0.287512i
$566$	−30.5940			−1.28596
$567$		0			0
$568$	7.99411			0.335425
$569$	−7.30588	+	4.21805i	−0.306278	+	0.176830i	−0.645260	−	0.763963i	$-0.723251\pi$
$569$	−7.30588	+	4.21805i	−0.306278	+	0.176830i	0.338982	+	0.940793i	$0.389918\pi$
$570$	2.53823	+	6.55861i	0.106315	+	0.274710i
$571$	17.0208	−	29.4808i	0.712297	−	1.23373i	−0.251696	−	0.967806i	$-0.580988\pi$
$571$	17.0208	−	29.4808i	0.712297	−	1.23373i	0.963993	−	0.265928i	$-0.0856782\pi$
$572$	26.8003			1.12058
$573$	1.28708	+	1.03644i	0.0537686	+	0.0432979i
$574$		0			0
$575$		−	2.43516i		−	0.101553i
$576$	7.51093	−	6.83768i	0.312956	−	0.284903i
$577$	15.6796	−	9.05260i	0.652749	−	0.376865i	−0.136760	−	0.990604i	$-0.543669\pi$
$577$	15.6796	−	9.05260i	0.652749	−	0.376865i	0.789509	+	0.613739i	$0.210335\pi$
$578$		−	42.4993i		−	1.76774i
$579$	−2.89991	−	0.451169i	−0.120516	−	0.0187500i
$580$	41.9292	−	24.2078i	1.74102	−	1.00518i
$581$		0			0
$582$	23.7341	+	61.3273i	0.983810	+	2.54210i
$583$	−9.05015	−	15.6753i	−0.374819	−	0.649206i
$584$	51.5787	+	89.3370i	2.13434	+	3.69679i
$585$	−2.80733	+	8.80375i	−0.116069	+	0.363990i
$586$	42.6467	+	24.6221i	1.76172	+	1.01713i
$587$	−4.04900	+	7.01308i	−0.167120	+	0.289461i	−0.937406	−	0.348238i	$-0.886780\pi$
$587$	−4.04900	+	7.01308i	−0.167120	+	0.289461i	0.770286	+	0.637699i	$0.220113\pi$
$588$		0			0
$589$	1.35678	+	2.35001i	0.0559050	+	0.0968304i
$590$		−	25.9360i		−	1.06777i
$591$	20.5929	−	7.96959i	0.847078	−	0.327825i
$592$	25.0413			1.02919
$593$	3.33216	−	5.77148i	0.136836	−	0.237006i	−0.789462	−	0.613800i	$-0.789640\pi$
$593$	3.33216	−	5.77148i	0.136836	−	0.237006i	0.926297	+	0.376794i	$0.122973\pi$
$594$	−3.54060	−	58.3838i	−0.145273	−	2.39552i
$595$		0			0
$596$	−44.0040	−	25.4057i	−1.80247	−	1.04066i
$597$	−5.87918	−	4.73429i	−0.240619	−	0.193761i
$598$	16.4077	+	9.47299i	0.670961	+	0.387380i
$599$	3.10562	+	1.79303i	0.126892	+	0.0732614i	0.562103	−	0.827068i	$-0.309993\pi$
$599$	3.10562	+	1.79303i	0.126892	+	0.0732614i	−0.435210	+	0.900329i	$0.643326\pi$
$600$	4.82537	−	1.86745i	0.196995	−	0.0762385i
$601$	−4.86949	−	2.81140i	−0.198631	−	0.114679i	0.397386	−	0.917652i	$-0.369917\pi$
$601$	−4.86949	−	2.81140i	−0.198631	−	0.114679i	−0.596017	+	0.802972i	$0.703251\pi$
$602$		0			0
$603$	3.08656	+	14.1401i	0.125695	+	0.575831i
$604$	−32.4030	+	56.1237i	−1.31846	+	2.28364i
$605$	−18.8013			−0.764381
$606$	−5.78815	−	4.66099i	−0.235128	−	0.189340i
$607$			2.23133i			0.0905669i	0.998974	+	0.0452834i	$0.0144191\pi$
$607$			2.23133i			0.0905669i	−0.998974	+	0.0452834i	$0.985581\pi$
$608$	2.61795	+	4.53442i	0.106172	+	0.183895i
$609$		0			0
$610$	−6.16672	+	10.6811i	−0.249683	+	0.432464i
$611$	−0.564423	−	0.325870i	−0.0228341	−	0.0131833i
$612$	−59.6545	+	54.3072i	−2.41139	+	2.19524i
$613$	3.41019	+	5.90662i	0.137736	+	0.238566i	0.926639	−	0.375951i	$-0.122684\pi$
$613$	3.41019	+	5.90662i	0.137736	+	0.238566i	−0.788903	+	0.614518i	$0.789351\pi$
$614$	−3.03567	−	5.25793i	−0.122510	−	0.212193i
$615$	16.6938	−	20.7309i	0.673160	−	0.835950i
$616$		0			0
$617$	−2.35139	+	1.35757i	−0.0946632	+	0.0546538i	−0.546584	−	0.837404i	$-0.684072\pi$
$617$	−2.35139	+	1.35757i	−0.0946632	+	0.0546538i	0.451921	+	0.892058i	$0.350739\pi$
$618$	4.55298	−	5.65403i	0.183148	−	0.227439i
$619$			26.7759i			1.07621i	0.842876	+	0.538107i	$0.180860\pi$
$619$			26.7759i			1.07621i	−0.842876	+	0.538107i	$0.819140\pi$
$620$	37.7072	−	21.7703i	1.51436	−	0.874316i
$621$	12.9120	−	25.8640i	0.518142	−	1.03789i
$622$		−	20.2380i		−	0.811469i
$623$		0			0
$624$	−2.91965	+	18.7662i	−0.116880	+	0.751249i
$625$	−26.9970			−1.07988
$626$	38.7414	−	67.1021i	1.54842	−	2.68194i
$627$	5.04652	+	0.785141i	0.201539	+	0.0313555i
$628$	−63.4980	+	36.6606i	−2.53385	+	1.46292i
$629$	−17.4556			−0.696000
$630$		0			0
$631$	−11.1620			−0.444354			−0.222177	−	0.975006i	$-0.571316\pi$
$631$	−11.1620			−0.444354			−0.222177	+	0.975006i	$0.571316\pi$
$632$	−62.7004	+	36.2001i	−2.49409	+	1.43996i
$633$	−4.87474	+	6.05360i	−0.193754	+	0.240609i
$634$	−14.3182	+	24.7998i	−0.568647	+	0.984926i
$635$	−38.6417			−1.53345
$636$	31.1192	−	12.0434i	1.23396	−	0.477551i
$637$		0			0
$638$		−	50.2927i		−	1.99111i
$639$	2.36562	+	2.59854i	0.0935823	+	0.102797i
$640$	−13.6850	+	7.90105i	−0.540948	+	0.312317i
$641$		−	44.6004i		−	1.76161i	−0.473480	−	0.880805i	$-0.657002\pi$
$641$		−	44.6004i		−	1.76161i	0.473480	−	0.880805i	$-0.342998\pi$
$642$	−29.5154	−	76.2659i	−1.16488	−	3.00998i
$643$	23.6268	−	13.6410i	0.931751	−	0.537947i	0.0443860	−	0.999014i	$-0.485867\pi$
$643$	23.6268	−	13.6410i	0.931751	−	0.537947i	0.887365	+	0.461068i	$0.152534\pi$
$644$		0			0
$645$	−31.0668	−	4.83339i	−1.22326	−	0.190315i
$646$	−5.03777	−	8.72568i	−0.198208	−	0.343307i
$647$	−22.4675	−	38.9148i	−0.883288	−	1.52990i	−0.847663	−	0.530534i	$-0.821991\pi$
$647$	−22.4675	−	38.9148i	−0.883288	−	1.52990i	−0.0356246	−	0.999365i	$-0.511342\pi$
$648$	61.1524	+	5.75136i	2.40229	+	0.225935i
$649$	−16.3118	−	9.41760i	−0.640293	−	0.369673i
$650$	−0.745324	+	1.29094i	−0.0292340	+	0.0506348i
$651$		0			0
$652$	−15.7200	−	27.2278i	−0.615642	−	1.06632i
$653$		−	27.7763i		−	1.08697i	−0.839419	−	0.543484i	$-0.817105\pi$
$653$		−	27.7763i		−	1.08697i	0.839419	−	0.543484i	$-0.182895\pi$
$654$	−10.9658	+	70.4830i	−0.428796	+	2.75610i
$655$	−16.6026			−0.648715
$656$	27.3526	−	47.3762i	1.06794	−	1.84973i
$657$	−13.7764	+	43.2026i	−0.537470	+	1.68549i
$658$		0			0
$659$	0.801975	+	0.463021i	0.0312405	+	0.0180367i	0.515539	−	0.856866i	$-0.327592\pi$
$659$	0.801975	+	0.463021i	0.0312405	+	0.0180367i	−0.484298	+	0.874903i	$0.660925\pi$
$660$	12.5980	−	80.9744i	0.490378	−	3.15193i
$661$	28.3028	+	16.3406i	1.10085	+	0.635577i	0.936445	−	0.350815i	$-0.114095\pi$
$661$	28.3028	+	16.3406i	1.10085	+	0.635577i	0.164408	+	0.986392i	$0.447429\pi$
$662$	−38.5540	−	22.2592i	−1.49844	−	0.865126i
$663$	2.03521	−	13.0814i	0.0790408	−	0.508038i
$664$	62.9373	+	36.3369i	2.44244	+	1.41014i
$665$		0			0
$666$	15.7068	+	17.2533i	0.608626	+	0.668553i
$667$	12.4280	−	21.5260i	0.481215	−	0.833489i
$668$	−88.7251			−3.43288
$669$	−5.53447	+	35.5730i	−0.213975	+	1.37533i
$670$			29.0044i			1.12054i
$671$	4.47839	+	7.75681i	0.172886	+	0.299448i
$672$		0			0
$673$	−15.6947	+	27.1840i	−0.604987	+	1.04787i	0.387067	+	0.922052i	$0.373488\pi$
$673$	−15.6947	+	27.1840i	−0.604987	+	1.04787i	−0.992054	+	0.125816i	$0.959845\pi$
$674$	17.1014	+	9.87349i	0.658721	+	0.380313i
$675$	2.03495	+	1.01590i	0.0783253	+	0.0391021i
$676$	26.1521	+	45.2967i	1.00585	+	1.74218i
$677$	−10.7882	−	18.6858i	−0.414626	−	0.718153i	0.580763	−	0.814072i	$-0.302754\pi$
$677$	−10.7882	−	18.6858i	−0.414626	−	0.718153i	−0.995389	+	0.0959196i	$0.969421\pi$
$678$	−25.8633	−	4.02383i	−0.993274	−	0.154534i
$679$		0			0
$680$	−79.7521	+	46.0449i	−3.05835	+	1.76574i
$681$	−17.7012	−	45.7388i	−0.678313	−	1.75271i
$682$		−	45.2286i		−	1.73189i
$683$	31.4015	−	18.1296i	1.20154	−	0.693711i	0.240645	−	0.970613i	$-0.422641\pi$
$683$	31.4015	−	18.1296i	1.20154	−	0.693711i	0.960898	+	0.276902i	$0.0893077\pi$
$684$	−2.86044	+	8.97029i	−0.109372	+	0.342988i
$685$			1.92950i			0.0737224i
$686$		0			0
$687$	−35.1906	+	13.6190i	−1.34260	+	0.519597i
$688$	−64.6195			−2.46360
$689$	−2.73798	+	4.74232i	−0.104309	+	0.180668i
$690$	36.3345	−	45.1213i	1.38323	−	1.71774i
$691$	−6.16389	+	3.55872i	−0.234485	+	0.135380i	−0.612640	−	0.790362i	$-0.709892\pi$
$691$	−6.16389	+	3.55872i	−0.234485	+	0.135380i	0.378154	+	0.925743i	$0.376559\pi$
$692$	101.535			3.85977
$693$		0			0
$694$	−33.9426			−1.28844
$695$	28.1540	−	16.2547i	1.06794	−	0.616577i
$696$	52.1853	+	8.11901i	1.97808	+	0.307750i
$697$	−19.0667	+	33.0246i	−0.722204	+	1.25089i
$698$	−3.13139			−0.118525
$699$	4.05622	−	26.0715i	0.153420	−	0.986115i
$700$		0			0
$701$		−	29.4609i		−	1.11272i	−0.830940	−	0.556362i	$-0.812197\pi$
$701$		−	29.4609i		−	1.11272i	0.830940	−	0.556362i	$-0.187803\pi$
$702$	−14.7611	+	9.75920i	−0.557122	+	0.368337i
$703$	−1.76433	+	1.01863i	−0.0665428	+	0.0384185i
$704$		−	14.7823i		−	0.557130i
$705$	−1.24990	+	1.55217i	−0.0470741	+	0.0584581i
$706$	59.8894	−	34.5772i	2.25397	−	1.30133i
$707$		0			0
$708$	21.7781	−	27.0447i	0.818471	−	1.01640i
$709$	19.0361	+	32.9715i	0.714916	+	1.23827i	0.962992	+	0.269530i	$0.0868683\pi$
$709$	19.0361	+	32.9715i	0.714916	+	1.23827i	−0.248076	+	0.968740i	$0.579798\pi$
$710$	3.52112	+	6.09875i	0.132145	+	0.228882i
$711$	−30.3214	−	9.66887i	−1.13714	−	0.362611i
$712$	19.6540	+	11.3473i	0.736566	+	0.425257i
$713$	11.1766	−	19.3585i	0.418568	−	0.724980i
$714$		0			0
$715$	6.72414	+	11.6466i	0.251469	+	0.435556i
$716$			79.8816i			2.98532i
$717$	7.71272	+	6.21077i	0.288037	+	0.231945i
$718$	−19.2082			−0.716842
$719$	19.1057	−	33.0921i	0.712523	−	1.23413i	−0.251385	−	0.967887i	$-0.580886\pi$
$719$	19.1057	−	33.0921i	0.712523	−	1.23413i	0.963907	−	0.266238i	$-0.0857807\pi$
$720$	55.3278	+	17.6429i	2.06195	+	0.657512i
$721$		0			0
$722$	41.4045	+	23.9049i	1.54091	+	0.889647i
$723$	−7.22225	+	2.79506i	−0.268598	+	0.103949i
$724$	66.9924	+	38.6781i	2.48975	+	1.43746i
$725$	1.69364	+	0.977823i	0.0629002	+	0.0363154i
$726$	−28.0426	−	22.5816i	−1.04076	−	0.838083i
$727$	−17.7563	−	10.2516i	−0.658546	−	0.380212i	0.133177	−	0.991092i	$-0.457482\pi$
$727$	−17.7563	−	10.2516i	−0.658546	−	0.380212i	−0.791723	+	0.610881i	$0.790816\pi$
$728$		0			0
$729$	16.2267	+	21.5800i	0.600989	+	0.799257i
$730$	−45.4372	+	78.6995i	−1.68170	+	2.91280i
$731$	45.0444			1.66603
$732$	−15.3991	+	5.95956i	−0.569167	+	0.220272i
$733$		−	1.03995i		−	0.0384116i	−0.999816	−	0.0192058i	$-0.993886\pi$
$733$		−	1.03995i		−	0.0384116i	0.999816	−	0.0192058i	$-0.00611377\pi$
$734$	−45.1023	−	78.1194i	−1.66475	−	2.88344i
$735$		0			0
$736$	21.5657	−	37.3528i	0.794921	−	1.37684i
$737$	18.2416	+	10.5318i	0.671938	+	0.387944i
$738$	49.7985	−	10.8702i	1.83311	−	0.400137i
$739$	−12.0805	−	20.9240i	−0.444387	−	0.769701i	0.553622	−	0.832768i	$-0.313245\pi$
$739$	−12.0805	−	20.9240i	−0.444387	−	0.769701i	−0.998009	+	0.0630670i	$0.979912\pi$
$740$	16.3446	+	28.3096i	0.600839	+	1.04068i
$741$	−0.557665	−	1.44097i	−0.0204863	−	0.0529353i
$742$		0			0
$743$	−13.1637	+	7.60008i	−0.482930	+	0.278820i	−0.721637	−	0.692272i	$-0.756610\pi$
$743$	−13.1637	+	7.60008i	−0.482930	+	0.278820i	0.238707	+	0.971092i	$0.423277\pi$
$744$	46.9306	+	7.30148i	1.72056	+	0.267685i
$745$		−	25.4970i		−	0.934138i
$746$	67.2045	−	38.8005i	2.46053	−	1.42059i
$747$	6.81285	+	31.2110i	0.249269	+	1.14195i
$748$			117.406i			4.29281i
$749$		0			0
$750$	−37.0023	−	29.7966i	−1.35113	−	1.08802i
$751$	3.04074			0.110958			0.0554791	−	0.998460i	$-0.482331\pi$
$751$	3.04074			0.110958			0.0554791	+	0.998460i	$0.482331\pi$
$752$	−2.04795	+	3.54716i	−0.0746812	+	0.129352i
$753$	−7.26815	−	18.7804i	−0.264866	−	0.684396i
$754$	−13.1768	+	7.60763i	−0.479871	+	0.277053i
$755$	−32.5195			−1.18350
$756$		0			0
$757$	43.3700			1.57631			0.788155	−	0.615477i	$-0.211036\pi$
$757$	43.3700			1.57631			0.788155	+	0.615477i	$0.211036\pi$
$758$	60.5075	−	34.9340i	2.19773	−	1.26886i
$759$	−15.1845	−	39.2357i	−0.551162	−	1.42417i
$760$	−5.37397	+	9.30799i	−0.194934	+	0.337636i
$761$	29.2638			1.06081			0.530406	−	0.847744i	$-0.322040\pi$
$761$	29.2638			1.06081			0.530406	+	0.847744i	$0.322040\pi$
$762$	−57.6350	−	46.4113i	−2.08790	−	1.68131i
$763$		0			0
$764$			4.43367i			0.160405i
$765$	−38.5674	−	12.2984i	−1.39441	−	0.444648i
$766$	−8.17266	+	4.71849i	−0.295290	+	0.170486i
$767$			5.69830i			0.205754i
$768$	−41.4903	−	6.45508i	−1.49715	−	0.232928i
$769$	−29.6496	+	17.1182i	−1.06919	+	0.617299i	−0.927961	−	0.372678i	$-0.878440\pi$
$769$	−29.6496	+	17.1182i	−1.06919	+	0.617299i	−0.141232	+	0.989977i	$0.545106\pi$
$770$		0			0
$771$	−1.31453	−	3.39666i	−0.0473418	−	0.122328i
$772$	−3.93702	−	6.81912i	−0.141697	−	0.245426i
$773$	−16.9927	−	29.4322i	−0.611185	−	1.05860i	−0.991041	−	0.133558i	$-0.957360\pi$
$773$	−16.9927	−	29.4322i	−0.611185	−	1.05860i	0.379856	−	0.925046i	$-0.375974\pi$
$774$	−40.5317	−	44.5225i	−1.45688	−	1.60033i
$775$	1.52310	+	0.879363i	0.0547114	+	0.0315877i
$776$	−50.2502	+	87.0359i	−1.80388	+	3.12441i
$777$		0			0
$778$	15.6870	+	27.1707i	0.562406	+	0.974117i
$779$			4.45062i			0.159460i
$780$	−23.1212	+	8.94806i	−0.827871	+	0.320392i
$781$	5.11421			0.183001
$782$	−41.4993	+	71.8788i	−1.48401	+	2.57038i
$783$	12.8035	+	19.3657i	0.457560	+	0.692075i
$784$		0			0
$785$	−31.8631	−	18.3962i	−1.13724	−	0.656587i
$786$	−24.7631	−	19.9408i	−0.883271	−	0.711265i
$787$	−23.8225	−	13.7539i	−0.849180	−	0.490274i	0.0111939	−	0.999937i	$-0.496437\pi$
$787$	−23.8225	−	13.7539i	−0.849180	−	0.490274i	−0.860374	+	0.509663i	$0.829770\pi$
$788$	51.3067	+	29.6219i	1.82773	+	1.05524i
$789$	3.55829	−	1.37708i	0.126678	−	0.0490254i
$790$	−55.2346	−	31.8897i	−1.96516	−	1.13458i
$791$		0			0
$792$	66.1025	−	60.1773i	2.34885	−	2.13831i
$793$	1.35487	−	2.34670i	0.0481128	−	0.0833338i
$794$	−69.0288			−2.44974
$795$	13.0414	+	10.5018i	0.462532	+	0.372460i
$796$		−	20.2523i		−	0.717824i
$797$	21.0873	+	36.5243i	0.746952	+	1.29376i	0.949277	+	0.314440i	$0.101817\pi$
$797$	21.0873	+	36.5243i	0.746952	+	1.29376i	−0.202326	+	0.979318i	$0.564850\pi$
$798$		0			0
$799$	1.42757	−	2.47262i	0.0505038	−	0.0874751i
$800$	2.93888	+	1.69676i	0.103905	+	0.0599896i
$801$	2.12751	+	9.74655i	0.0751720	+	0.344378i
$802$	−9.96458	−	17.2592i	−0.351861	−	0.609442i
$803$	32.9974	+	57.1531i	1.16445	+	2.01689i
$804$	−24.3546	+	30.2443i	−0.858922	+	1.06664i
$805$		0			0
$806$	−11.8500	+	6.84160i	−0.417398	+	0.240985i
$807$	−30.2676	+	37.5872i	−1.06547	+	1.32313i
$808$		−	11.3576i		−	0.399558i
$809$	−4.18377	+	2.41550i	−0.147094	+	0.0849245i	−0.571740	−	0.820435i	$-0.693732\pi$
$809$	−4.18377	+	2.41550i	−0.147094	+	0.0849245i	0.424647	+	0.905359i	$0.360398\pi$
$810$	22.5477	+	49.1868i	0.792245	+	1.72825i
$811$			6.46035i			0.226853i	0.993546	+	0.113427i	$0.0361827\pi$
$811$			6.46035i			0.226853i	−0.993546	+	0.113427i	$0.963817\pi$
$812$		0			0
$813$	−3.05687	+	19.6482i	−0.107209	+	0.689092i
$814$	33.9565			1.19017
$815$	7.88823	−	13.6628i	0.276313	−	0.478587i
$816$	−82.2108	−	12.7904i	−2.87796	−	0.447754i
$817$	4.55287	−	2.62860i	0.159285	−	0.0919631i
$818$	23.3597			0.816751
$819$		0			0
$820$	71.4128			2.49384
$821$	−14.5455	+	8.39783i	−0.507640	+	0.293086i	−0.731863	−	0.681452i	$-0.761349\pi$
$821$	−14.5455	+	8.39783i	−0.507640	+	0.293086i	0.224223	+	0.974538i	$0.428016\pi$
$822$	−2.31746	+	2.87789i	−0.0808307	+	0.100378i
$823$	7.51749	−	13.0207i	0.262043	−	0.453872i	−0.704741	−	0.709464i	$-0.748937\pi$
$823$	7.51749	−	13.0207i	0.262043	−	0.453872i	0.966785	+	0.255592i	$0.0822703\pi$
$824$	11.0944			0.386491
$825$	3.08702	−	1.19470i	0.107476	−	0.0415940i
$826$		0			0
$827$			29.2462i			1.01699i	0.861065	+	0.508495i	$0.169798\pi$
$827$			29.2462i			1.01699i	−0.861065	+	0.508495i	$0.830202\pi$
$828$	75.7756	−	16.5406i	2.63338	−	0.574824i
$829$	−1.30270	+	0.752115i	−0.0452447	+	0.0261220i	−0.522452	−	0.852669i	$-0.674983\pi$
$829$	−1.30270	+	0.752115i	−0.0452447	+	0.0261220i	0.477207	+	0.878791i	$0.341649\pi$
$830$			64.0204i			2.22218i
$831$	6.37637	+	16.4761i	0.221194	+	0.571550i
$832$	−3.87301	+	2.23608i	−0.134272	+	0.0775222i
$833$		0			0
$834$	61.5155	+	9.57061i	2.13011	+	0.331403i
$835$	−22.2610	−	38.5571i	−0.770373	−	1.33432i
$836$	6.85135	+	11.8669i	0.236959	+	0.410425i
$837$	11.5143	+	17.4158i	0.397992	+	0.601977i
$838$	−14.7572	−	8.52005i	−0.509778	−	0.294320i
$839$	−22.9477	+	39.7466i	−0.792243	+	1.37221i	0.132331	+	0.991206i	$0.457754\pi$
$839$	−22.9477	+	39.7466i	−0.792243	+	1.37221i	−0.924575	+	0.381000i	$0.875580\pi$
$840$		0			0
$841$	−4.51923	−	7.82753i	−0.155835	−	0.269915i
$842$			32.9601i			1.13588i
$843$	2.90588	−	18.6776i	0.100084	−	0.643292i
$844$	−20.8531			−0.717795
$845$	−13.1230	+	22.7297i	−0.451445	+	0.781926i
$846$	−3.72853	+	0.813876i	−0.128189	+	0.0279816i
$847$		0			0
$848$	29.8035	+	17.2071i	1.02346	+	0.590893i
$849$	3.15967	−	20.3089i	0.108440	−	0.697001i
$850$	−5.65534	−	3.26511i	−0.193977	−	0.111992i
$851$	14.5338	+	8.39112i	0.498214	+	0.287644i
$852$	−1.44940	+	9.31610i	−0.0496558	+	0.319164i
$853$	−24.3086	−	14.0346i	−0.832310	−	0.480534i	0.0223330	−	0.999751i	$-0.492891\pi$
$853$	−24.3086	−	14.0346i	−0.832310	−	0.480534i	−0.854643	+	0.519216i	$0.826224\pi$
$854$		0			0
$855$	−4.61589	+	1.00757i	−0.157860	+	0.0344583i
$856$	62.4905	−	108.237i	2.13588	−	3.69946i
$857$	17.1085			0.584416			0.292208	−	0.956355i	$-0.405610\pi$
$857$	17.1085			0.584416			0.292208	+	0.956355i	$0.405610\pi$
$858$	−3.95910	+	25.4473i	−0.135161	+	0.868755i
$859$			5.20765i			0.177683i	0.996046	+	0.0888414i	$0.0283164\pi$
$859$			5.20765i			0.177683i	−0.996046	+	0.0888414i	$0.971684\pi$
$860$	−42.1775	−	73.0535i	−1.43824	−	2.49110i
$861$		0			0
$862$	28.2456	−	48.9228i	0.962049	−	1.66632i
$863$	−38.7134	−	22.3512i	−1.31782	−	0.760844i	−0.334442	−	0.942416i	$-0.608548\pi$
$863$	−38.7134	−	22.3512i	−1.31782	−	0.760844i	−0.983378	+	0.181573i	$0.941881\pi$
$864$	22.2172	+	33.6043i	0.755845	+	1.14324i
$865$	25.4749	+	44.1238i	0.866172	+	1.50025i
$866$	−10.5858	−	18.3352i	−0.359721	−	0.623055i
$867$	28.2120	+	4.38923i	0.958129	+	0.149066i
$868$		0			0
$869$	−40.1124	+	23.1589i	−1.36072	+	0.785613i
$870$	16.7917	+	43.3886i	0.569291	+	1.47101i
$871$		−	6.37246i		−	0.215922i
$872$	−94.4096	+	54.5074i	−3.19711	+	1.84585i
$873$	−43.1616	+	9.42147i	−1.46080	+	0.318869i
$874$			9.68688i			0.327664i
$875$		0			0
$876$	−113.462	+	43.9108i	−3.83354	+	1.48361i
$877$	−5.74863			−0.194117			−0.0970587	−	0.995279i	$-0.530943\pi$
$877$	−5.74863			−0.194117			−0.0970587	+	0.995279i	$0.530943\pi$
$878$	−48.8229	+	84.5637i	−1.64769	+	2.85389i
$879$	−20.7491	+	25.7669i	−0.699850	+	0.869095i
$880$	73.1936	−	42.2584i	2.46736	−	1.42453i
$881$	9.98120			0.336275			0.168138	−	0.985764i	$-0.446225\pi$
$881$	9.98120			0.336275			0.168138	+	0.985764i	$0.446225\pi$
$882$		0			0
$883$	−32.0942			−1.08006			−0.540028	−	0.841647i	$-0.681586\pi$
$883$	−32.0942			−1.08006			−0.540028	+	0.841647i	$0.681586\pi$
$884$	30.7608	−	17.7597i	1.03460	−	0.597325i
$885$	17.2169	+	2.67861i	0.578738	+	0.0900404i
$886$	26.3781	−	45.6881i	0.886188	−	1.53492i
$887$	−8.53623			−0.286619			−0.143309	−	0.989678i	$-0.545774\pi$
$887$	−8.53623			−0.286619			−0.143309	+	0.989678i	$0.545774\pi$
$888$	−5.48177	+	35.2343i	−0.183956	+	1.18239i
$889$		0			0
$890$			19.9922i			0.670141i
$891$	39.1221	+	3.67941i	1.31064	+	0.123265i
$892$	−83.6498	+	48.2952i	−2.80080	+	1.61704i
$893$		−	0.333228i		−	0.0111510i
$894$	30.6237	−	38.0294i	1.02421	−	1.27189i
$895$	−34.7140	+	20.0422i	−1.16036	+	0.669935i
$896$		0			0
$897$	−7.98293	+	9.91344i	−0.266542	+	0.331000i
$898$	46.0277	+	79.7223i	1.53596	+	2.66037i
$899$	8.97579	+	15.5465i	0.299359	+	0.518505i
$900$	1.30139	+	5.96194i	0.0433798	+	0.198731i
$901$	−20.7752	−	11.9945i	−0.692121	−	0.399596i
$902$	37.0906	−	64.2429i	1.23498	−	2.13905i
$903$		0			0
$904$	−20.0011	−	34.6430i	−0.665228	−	1.15221i
$905$			38.8171i			1.29032i
$906$	−48.5036	−	39.0581i	−1.61142	−	1.29762i
$907$	32.0544			1.06435			0.532175	−	0.846634i	$-0.321375\pi$
$907$	32.0544			1.06435			0.532175	+	0.846634i	$0.321375\pi$
$908$	65.7932	−	113.957i	2.18342	−	3.78180i
$909$	3.69185	−	3.36093i	0.122451	−	0.111475i
$910$		0			0
$911$	26.3261	+	15.1994i	0.872221	+	0.503577i	0.868086	−	0.496414i	$-0.165350\pi$
$911$	26.3261	+	15.1994i	0.872221	+	0.503577i	0.00413539	+	0.999991i	$0.498684\pi$
$912$	−9.05587	+	3.50468i	−0.299870	+	0.116052i
$913$	40.2640	+	23.2464i	1.33254	+	0.769344i
$914$	−0.567527	−	0.327662i	−0.0187721	−	0.0108381i
$915$	−6.45344	−	5.19672i	−0.213344	−	0.171798i
$916$	−87.6765	−	50.6201i	−2.89691	−	1.67253i
$917$		0			0
$918$	−42.7530	−	64.6654i	−1.41106	−	2.13428i
$919$	8.72153	−	15.1061i	0.287697	−	0.498305i	−0.685563	−	0.728013i	$-0.740444\pi$
$919$	8.72153	−	15.1061i	0.287697	−	0.498305i	0.973260	+	0.229708i	$0.0737772\pi$
$920$	88.5374			2.91899
$921$	3.80385	−	1.47212i	0.125341	−	0.0485079i
$922$			62.9981i			2.07473i
$923$	−0.773612	−	1.33994i	−0.0254637	−	0.0441045i
$924$		0			0
$925$	−0.660203	+	1.14351i	−0.0217074	+	0.0375982i
$926$	−1.83082	−	1.05702i	−0.0601644	−	0.0347359i
$927$	3.28305	+	3.60631i	0.107829	+	0.118447i
$928$	17.3191	+	29.9975i	0.568527	+	0.984717i
$929$	5.21392	+	9.03077i	0.171063	+	0.296290i	0.938792	−	0.344485i	$-0.111946\pi$
$929$	5.21392	+	9.03077i	0.171063	+	0.296290i	−0.767729	+	0.640775i	$0.778613\pi$
$930$	15.1009	+	39.0197i	0.495178	+	1.27951i
$931$		0			0
$932$	61.3070	−	35.3956i	2.00818	−	1.15942i
$933$	13.4344	+	2.09013i	0.439823	+	0.0684278i
$934$		−	4.69038i		−	0.153474i
$935$	−51.0212	+	29.4571i	−1.66857	+	0.963350i
$936$	−25.7657	−	8.21617i	−0.842180	−	0.268554i
$937$		−	51.3201i		−	1.67655i	−0.545245	−	0.838277i	$-0.683563\pi$
$937$		−	51.3201i		−	1.67655i	0.545245	−	0.838277i	$-0.316437\pi$
$938$		0			0
$939$	40.5427	+	32.6476i	1.32306	+	1.06541i
$940$	−5.34683			−0.174395
$941$	24.6673	−	42.7251i	0.804133	−	1.39280i	−0.112742	−	0.993624i	$-0.535963\pi$
$941$	24.6673	−	42.7251i	0.804133	−	1.39280i	0.916875	−	0.399174i	$-0.130703\pi$
$942$	−25.4295	−	65.7081i	−0.828538	−	2.14089i
$943$	31.7506	−	18.3312i	1.03394	−	0.596947i
$944$	35.8114			1.16556
$945$		0			0
$946$	−87.6252			−2.84894
$947$	38.0468	−	21.9663i	1.23636	−	0.713810i	0.268008	−	0.963417i	$-0.413635\pi$
$947$	38.0468	−	21.9663i	1.23636	−	0.713810i	0.968347	+	0.249607i	$0.0803013\pi$
$948$	−30.8184	−	79.6327i	−1.00094	−	2.58635i
$949$	9.98283	−	17.2908i	0.324056	−	0.561282i
$950$	−0.762153			−0.0247275
$951$	−14.9839	−	12.0660i	−0.485886	−	0.391266i
$952$		0			0
$953$			21.0833i			0.682956i	0.939890	+	0.341478i	$0.110928\pi$
$953$			21.0833i			0.682956i	−0.939890	+	0.341478i	$0.889072\pi$
$954$	6.83824	+	31.3273i	0.221396	+	1.01426i
$955$	−1.92673	+	1.11240i	−0.0623477	+	0.0359964i
$956$			26.5684i			0.859283i
$957$	33.3854	+	5.19411i	1.07920	+	0.167902i
$958$	3.04138	−	1.75594i	0.0982625	−	0.0567319i
$959$		0			0
$960$	4.93552	+	12.7530i	0.159293	+	0.411603i
$961$	−7.42801	−	12.8657i	−0.239613	−	0.415022i
$962$	−5.13650	−	8.89667i	−0.165607	−	0.286840i
$963$	53.6753	−	11.7164i	1.72966	−	0.377557i
$964$	−17.9941	−	10.3889i	−0.579550	−	0.334603i
$965$	1.97558	−	3.42181i	0.0635963	−	0.110152i
$966$		0			0
$967$	−27.6671	−	47.9209i	−0.889716	−	1.54103i	−0.840212	−	0.542259i	$-0.817569\pi$
$967$	−27.6671	−	47.9209i	−0.889716	−	1.54103i	−0.0495039	−	0.998774i	$-0.515764\pi$
$968$		−	55.0253i		−	1.76858i
$969$	6.31258	−	2.44301i	0.202789	−	0.0784809i
$970$	−88.5336			−2.84264
$971$	3.41733	−	5.91898i	0.109667	−	0.189949i	−0.805968	−	0.591959i	$-0.798355\pi$
$971$	3.41733	−	5.91898i	0.109667	−	0.189949i	0.915635	+	0.402010i	$0.131688\pi$
$972$	−17.7900	+	70.2225i	−0.570613	+	2.25239i
$973$		0			0
$974$	70.5830	+	40.7511i	2.26162	+	1.30575i
$975$	−0.779978	−	0.628088i	−0.0249793	−	0.0201149i
$976$	−14.7480	−	8.51477i	−0.472072	−	0.272551i
$977$	−31.1982	−	18.0123i	−0.998118	−	0.576264i	−0.0904272	−	0.995903i	$-0.528823\pi$
$977$	−31.1982	−	18.0123i	−0.998118	−	0.576264i	−0.907691	+	0.419639i	$0.862157\pi$
$978$	28.1755	−	10.9041i	0.900952	−	0.348675i
$979$	12.5736	+	7.25938i	0.401854	+	0.232011i
$980$		0			0
$981$	−45.6557	−	14.5587i	−1.45767	−	0.464822i
$982$	2.93856	−	5.08973i	0.0937731	−	0.162420i
$983$	41.3726			1.31958			0.659791	−	0.751449i	$-0.270645\pi$
$983$	41.3726			1.31958			0.659791	+	0.751449i	$0.270645\pi$
$984$	60.6727	+	48.8575i	1.93417	+	1.55752i
$985$			29.7284i			0.947225i
$986$	−33.3275	−	57.7249i	−1.06136	−	1.83833i
$987$		0			0
$988$	2.07277	−	3.59014i	0.0659435	−	0.114218i
$989$	−37.5048	−	21.6534i	−1.19258	−	0.688539i
$990$	75.0254	+	23.9241i	2.38446	+	0.760357i
$991$	10.8367	+	18.7697i	0.344239	+	0.596240i	0.985215	−	0.171321i	$-0.0548036\pi$
$991$	10.8367	+	18.7697i	0.344239	+	0.596240i	−0.640976	+	0.767561i	$0.721470\pi$
$992$	15.5752	+	26.9770i	0.494512	+	0.856520i
$993$	18.7579	−	23.2941i	0.595263	−	0.739216i
$994$		0			0
$995$	8.80102	−	5.08127i	0.279011	−	0.161087i
$996$	−53.7571	+	66.7571i	−1.70336	+	2.11528i
$997$		−	13.7062i		−	0.434078i	−0.976163	−	0.217039i	$-0.930360\pi$
$997$		−	13.7062i		−	0.434078i	0.976163	−	0.217039i	$-0.0696399\pi$
$998$	−60.3721	+	34.8559i	−1.91105	+	1.10334i
$999$	−13.0753	+	8.64463i	−0.413684	+	0.273504i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.s.d.362.1		48
3.2	odd	2		1323.2.s.d.656.24		48
7.2	even	3		441.2.o.e.146.24	yes	48
7.3	odd	6		441.2.i.d.227.2		48
7.4	even	3		441.2.i.d.227.1		48
7.5	odd	6		441.2.o.e.146.23	✓	48
7.6	odd	2	inner	441.2.s.d.362.2		48
9.4	even	3		1323.2.i.d.1097.2		48
9.5	odd	6		441.2.i.d.68.24		48
21.2	odd	6		1323.2.o.e.440.1		48
21.5	even	6		1323.2.o.e.440.2		48
21.11	odd	6		1323.2.i.d.521.14		48
21.17	even	6		1323.2.i.d.521.2		48
21.20	even	2		1323.2.s.d.656.23		48
63.4	even	3		1323.2.s.d.962.23		48
63.5	even	6		441.2.o.e.293.24	yes	48
63.13	odd	6		1323.2.i.d.1097.14		48
63.23	odd	6		441.2.o.e.293.23	yes	48
63.31	odd	6		1323.2.s.d.962.24		48
63.32	odd	6	inner	441.2.s.d.374.2		48
63.40	odd	6		1323.2.o.e.881.1		48
63.41	even	6		441.2.i.d.68.23		48
63.58	even	3		1323.2.o.e.881.2		48
63.59	even	6	inner	441.2.s.d.374.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.23		48	63.41	even	6
441.2.i.d.68.24		48	9.5	odd	6
441.2.i.d.227.1		48	7.4	even	3
441.2.i.d.227.2		48	7.3	odd	6
441.2.o.e.146.23	✓	48	7.5	odd	6
441.2.o.e.146.24	yes	48	7.2	even	3
441.2.o.e.293.23	yes	48	63.23	odd	6
441.2.o.e.293.24	yes	48	63.5	even	6
441.2.s.d.362.1		48	1.1	even	1	trivial
441.2.s.d.362.2		48	7.6	odd	2	inner
441.2.s.d.374.1		48	63.59	even	6	inner
441.2.s.d.374.2		48	63.32	odd	6	inner
1323.2.i.d.521.2		48	21.17	even	6
1323.2.i.d.521.14		48	21.11	odd	6
1323.2.i.d.1097.2		48	9.4	even	3
1323.2.i.d.1097.14		48	63.13	odd	6
1323.2.o.e.440.1		48	21.2	odd	6
1323.2.o.e.440.2		48	21.5	even	6
1323.2.o.e.881.1		48	63.40	odd	6
1323.2.o.e.881.2		48	63.58	even	3
1323.2.s.d.656.23		48	21.20	even	2
1323.2.s.d.656.24		48	3.2	odd	2
1323.2.s.d.962.23		48	63.4	even	3
1323.2.s.d.962.24		48	63.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.23278 + 1.28910i) q^{2} +(-0.625134 - 1.61530i) q^{3} +(2.32354 - 4.02449i) q^{4} +2.33189 q^{5} +(3.47807 + 2.80076i) q^{6} +6.82470i q^{8} +(-2.21841 + 2.01956i) q^{9} +O(q^{10})\)	\(q+(-2.23278 + 1.28910i) q^{2} +(-0.625134 - 1.61530i) q^{3} +(2.32354 - 4.02449i) q^{4} +2.33189 q^{5} +(3.47807 + 2.80076i) q^{6} +6.82470i q^{8} +(-2.21841 + 2.01956i) q^{9} +(-5.20660 + 3.00603i) q^{10} +4.36608i q^{11} +(-7.95331 - 1.23738i) q^{12} +(1.14392 - 0.660445i) q^{13} +(-1.45774 - 3.76671i) q^{15} +(-4.15061 - 7.18908i) q^{16} +(2.89327 + 5.01130i) q^{17} +(2.34982 - 7.36900i) q^{18} +(0.584876 + 0.337678i) q^{19} +(5.41825 - 9.38468i) q^{20} +(-5.62830 - 9.74851i) q^{22} -5.56333i q^{23} +(11.0240 - 4.26635i) q^{24} +0.437717 q^{25} +(-1.70276 + 2.94926i) q^{26} +(4.64902 + 2.32092i) q^{27} +(3.86926 + 2.23392i) q^{29} +(8.11049 + 6.53107i) q^{30} +(3.47965 + 2.00898i) q^{31} +(6.71411 + 3.87639i) q^{32} +(7.05255 - 2.72939i) q^{33} +(-12.9201 - 7.45942i) q^{34} +(2.97314 + 13.6205i) q^{36} +(-1.50829 + 2.61243i) q^{37} -1.74120 q^{38} +(-1.78193 - 1.43492i) q^{39} +15.9145i q^{40} +(3.29501 + 5.70713i) q^{41} +(3.89217 - 6.74143i) q^{43} +(17.5713 + 10.1448i) q^{44} +(-5.17310 + 4.70940i) q^{45} +(7.17168 + 12.4217i) q^{46} +(-0.246705 - 0.427306i) q^{47} +(-9.01785 + 11.1986i) q^{48} +(-0.977326 + 0.564259i) q^{50} +(6.28609 - 7.80625i) q^{51} -6.13829i q^{52} +(-3.59025 + 2.07283i) q^{53} +(-13.3721 + 0.810934i) q^{54} +10.1812i q^{55} +(0.179827 - 1.15585i) q^{57} -11.5189 q^{58} +(-2.15699 + 3.73602i) q^{59} +(-18.5462 - 2.88543i) q^{60} +(1.77661 - 1.02572i) q^{61} -10.3591 q^{62} -3.38572 q^{64} +(2.66751 - 1.54009i) q^{65} +(-12.2284 + 15.1855i) q^{66} +(2.41218 - 4.17802i) q^{67} +26.8906 q^{68} +(-8.98648 + 3.47783i) q^{69} -1.17135i q^{71} +(-13.7829 - 15.1400i) q^{72} +(13.0902 - 7.55766i) q^{73} -7.77733i q^{74} +(-0.273632 - 0.707045i) q^{75} +(2.71797 - 1.56922i) q^{76} +(5.82840 + 0.906785i) q^{78} +(5.30428 + 9.18728i) q^{79} +(-9.67878 - 16.7641i) q^{80} +(0.842727 - 8.96046i) q^{81} +(-14.7141 - 8.49518i) q^{82} +(5.32432 - 9.22199i) q^{83} +(6.74680 + 11.6858i) q^{85} +20.0695i q^{86} +(1.18965 - 7.64653i) q^{87} -29.7972 q^{88} +(1.66268 - 2.87984i) q^{89} +(5.47953 - 17.1837i) q^{90} +(-22.3896 - 12.9266i) q^{92} +(1.06986 - 6.87658i) q^{93} +(1.10168 + 0.636053i) q^{94} +(1.36387 + 0.787429i) q^{95} +(2.06433 - 13.2686i) q^{96} +(12.7531 + 7.36299i) q^{97} +(-8.81758 - 9.68578i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} - 8 q^{9}+O(q^{10}) \) 48 * q + 24 * q^4 - 8 * q^9	\( 48 q + 24 q^{4} - 8 q^{9} - 40 q^{15} - 24 q^{16} + 32 q^{18} + 48 q^{25} + 48 q^{30} - 120 q^{32} - 8 q^{36} - 32 q^{39} + 96 q^{44} + 48 q^{50} + 48 q^{53} + 80 q^{57} - 72 q^{60} - 48 q^{64} - 120 q^{65} + 32 q^{72} - 88 q^{78} - 24 q^{79} + 120 q^{81} - 24 q^{85} - 144 q^{92} + 16 q^{93} - 96 q^{95} - 72 q^{99}+O(q^{100}) \) 48 * q + 24 * q^4 - 8 * q^9 - 40 * q^15 - 24 * q^16 + 32 * q^18 + 48 * q^25 + 48 * q^30 - 120 * q^32 - 8 * q^36 - 32 * q^39 + 96 * q^44 + 48 * q^50 + 48 * q^53 + 80 * q^57 - 72 * q^60 - 48 * q^64 - 120 * q^65 + 32 * q^72 - 88 * q^78 - 24 * q^79 + 120 * q^81 - 24 * q^85 - 144 * q^92 + 16 * q^93 - 96 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more