LMFDB - Embedded newform 441.2.i.d.68.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,2,Mod(68,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("441.68"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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			68.24
Character	$\chi$	$=$	441.68
Dual form			441.2.i.d.227.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.57819i q^{2} +(1.08633 + 1.34903i) q^{3} -4.64709 q^{4} +(1.16595 + 2.01948i) q^{5} +(-3.47807 + 2.80076i) q^{6} -6.82470i q^{8} +(-0.639786 + 2.93099i) q^{9} +(-5.20660 + 3.00603i) q^{10} +(3.78114 + 2.18304i) q^{11} +(-5.04826 - 6.26908i) q^{12} +(-1.14392 - 0.660445i) q^{13} +(-1.45774 + 3.76671i) q^{15} +8.30123 q^{16} +(-2.89327 - 5.01130i) q^{17} +(-7.55665 - 1.64949i) q^{18} +(0.584876 + 0.337678i) q^{19} +(-5.41825 - 9.38468i) q^{20} +(-5.62830 + 9.74851i) q^{22} +(4.81799 - 2.78167i) q^{23} +(9.20675 - 7.41386i) q^{24} +(-0.218858 + 0.379074i) q^{25} +(1.70276 - 2.94926i) q^{26} +(-4.64902 + 2.32092i) q^{27} +(3.86926 - 2.23392i) q^{29} +(-9.71132 - 3.75835i) q^{30} -4.01796i q^{31} +7.75278i q^{32} +(1.16256 + 7.47238i) q^{33} +(12.9201 - 7.45942i) q^{34} +(2.97314 - 13.6205i) q^{36} +(-1.50829 + 2.61243i) q^{37} +(-0.870601 + 1.50792i) q^{38} +(-0.351713 - 2.26065i) q^{39} +(13.7823 - 7.95723i) q^{40} +(-3.29501 + 5.70713i) q^{41} +(3.89217 + 6.74143i) q^{43} +(-17.5713 - 10.1448i) q^{44} +(-6.66501 + 2.12534i) q^{45} +(7.17168 + 12.4217i) q^{46} -0.493410 q^{47} +(9.01785 + 11.1986i) q^{48} +(-0.977326 - 0.564259i) q^{50} +(3.61737 - 9.34703i) q^{51} +(5.31591 + 3.06914i) q^{52} +(3.59025 - 2.07283i) q^{53} +(-5.98377 - 11.9861i) q^{54} +10.1812i q^{55} +(0.179827 + 1.15585i) q^{57} +(5.75947 + 9.97570i) q^{58} -4.31398 q^{59} +(6.77426 - 17.5042i) q^{60} +2.05145i q^{61} +10.3591 q^{62} -3.38572 q^{64} -3.08017i q^{65} +(-19.2652 + 2.99730i) q^{66} -4.82437 q^{67} +(13.4453 + 23.2879i) q^{68} +(8.98648 + 3.47783i) q^{69} +1.17135i q^{71} +(20.0031 + 4.36635i) q^{72} +(13.0902 - 7.55766i) q^{73} +(-6.73536 - 3.88866i) q^{74} +(-0.749135 + 0.116551i) q^{75} +(-2.71797 - 1.56922i) q^{76} +(5.82840 - 0.906785i) q^{78} -10.6086 q^{79} +(9.67878 + 16.7641i) q^{80} +(-8.18135 - 3.75041i) q^{81} +(-14.7141 - 8.49518i) q^{82} +(-5.32432 - 9.22199i) q^{83} +(6.74680 - 11.6858i) q^{85} +(-17.3807 + 10.0348i) q^{86} +(7.21691 + 2.79300i) q^{87} +(14.8986 - 25.8051i) q^{88} +(-1.66268 + 2.87984i) q^{89} +(-5.47953 - 17.1837i) q^{90} +(-22.3896 + 12.9266i) q^{92} +(5.42036 - 4.36482i) q^{93} -1.27211i q^{94} +1.57486i q^{95} +(-10.4588 + 8.42206i) q^{96} +(-12.7531 + 7.36299i) q^{97} +(-8.81758 + 9.68578i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4} - 8 q^{9} + 24 q^{11} - 40 q^{15} + 48 q^{16} - 16 q^{18} + 48 q^{23} - 24 q^{25} - 24 q^{30} - 8 q^{36} - 56 q^{39} - 96 q^{44} + 48 q^{50} - 24 q^{51} - 48 q^{53} + 80 q^{57} + 168 q^{60}+ \cdots - 72 q^{99}+O(q^{100}) $ 48 * q - 48 * q^4 - 8 * q^9 + 24 * q^11 - 40 * q^15 + 48 * q^16 - 16 * q^18 + 48 * q^23 - 24 * q^25 - 24 * q^30 - 8 * q^36 - 56 * q^39 - 96 * q^44 + 48 * q^50 - 24 * q^51 - 48 * q^53 + 80 * q^57 + 168 * q^60 - 48 * q^64 - 88 * q^72 + 168 * q^74 - 88 * q^78 + 48 * q^79 - 24 * q^81 - 24 * q^85 - 24 * q^86 - 144 * q^92 + 16 * q^93 - 72 * q^99

Character values

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

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

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 $

$2$			2.57819i			1.82306i	0.411235	+	0.911529i	$0.365098\pi$
$2$			2.57819i			1.82306i	−0.411235	+	0.911529i	$0.634902\pi$
$3$	1.08633	+	1.34903i	0.627191	+	0.778865i
$3$	1.08633	+	1.34903i	0.627191	+	0.778865i
$4$	−4.64709			−2.32354
$5$	1.16595	+	2.01948i	0.521427	+	0.903138i	0.999689	+	0.0249208i	$0.00793335\pi$
$5$	1.16595	+	2.01948i	0.521427	+	0.903138i	−0.478263	+	0.878217i	$0.658733\pi$
$6$	−3.47807	+	2.80076i	−1.41992	+	1.14341i
$7$		0			0
$7$		0			0
$8$		−	6.82470i		−	2.41290i
$9$	−0.639786	+	2.93099i	−0.213262	+	0.976995i
$10$	−5.20660	+	3.00603i	−1.64647	+	0.950591i
$11$	3.78114	+	2.18304i	1.14006	+	0.658212i	0.946444	−	0.322867i	$-0.104647\pi$
$11$	3.78114	+	2.18304i	1.14006	+	0.658212i	0.193612	+	0.981078i	$0.437980\pi$
$12$	−5.04826	−	6.26908i	−1.45731	−	1.80973i
$13$	−1.14392	−	0.660445i	−0.317267	−	0.183174i	0.332906	−	0.942960i	$-0.391971\pi$
$13$	−1.14392	−	0.660445i	−0.317267	−	0.183174i	−0.650174	+	0.759785i	$0.725304\pi$
$14$		0			0
$15$	−1.45774	+	3.76671i	−0.376388	+	0.972561i
$16$	8.30123			2.07531
$17$	−2.89327	−	5.01130i	−0.701722	−	1.21542i	−0.967862	−	0.251484i	$-0.919082\pi$
$17$	−2.89327	−	5.01130i	−0.701722	−	1.21542i	0.266140	−	0.963935i	$-0.414252\pi$
$18$	−7.55665	−	1.64949i	−1.78112	−	0.388789i
$19$	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
$23$	4.81799	−	2.78167i	1.00462	−	0.580018i	0.0950080	−	0.995477i	$-0.469712\pi$
$23$	4.81799	−	2.78167i	1.00462	−	0.580018i	0.909612	+	0.415459i	$0.136379\pi$
$24$	9.20675	−	7.41386i	1.87932	−	1.51335i
$25$	−0.218858	+	0.379074i	−0.0437717	+	0.0758147i
$26$	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	−0.0956983	−	0.995410i	$-0.530508\pi$
$29$	3.86926	−	2.23392i	0.718503	−	0.414828i	0.814202	+	0.580582i	$0.197175\pi$
$30$	−9.71132	−	3.75835i	−1.77304	−	0.686178i
$31$		−	4.01796i		−	0.721646i	−0.932634	−	0.360823i	$-0.882496\pi$
$31$		−	4.01796i		−	0.721646i	0.932634	−	0.360823i	$-0.117504\pi$
$32$			7.75278i			1.37051i
$33$	1.16256	+	7.47238i	0.202375	+	1.30077i
$34$	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	$0.246427\pi$
$38$	−0.870601	+	1.50792i	−0.141230	+	0.244618i
$39$	−0.351713	−	2.26065i	−0.0563192	−	0.361994i
$40$	13.7823	−	7.95723i	2.17918	−	1.25815i
$41$	−3.29501	+	5.70713i	−0.514594	+	0.891303i	0.485262	+	0.874369i	$0.338724\pi$
$41$	−3.29501	+	5.70713i	−0.514594	+	0.891303i	−0.999857	+	0.0169348i	$0.994609\pi$
$42$		0			0
$43$	3.89217	+	6.74143i	0.593550	+	1.02806i	0.993750	+	0.111631i	$0.0356074\pi$
$43$	3.89217	+	6.74143i	0.593550	+	1.02806i	−0.400200	+	0.916428i	$0.631059\pi$
$44$	−17.5713	−	10.1448i	−2.64897	−	1.52938i
$45$	−6.66501	+	2.12534i	−0.993561	+	0.316826i
$46$	7.17168	+	12.4217i	1.05741	+	1.83148i
$47$	−0.493410			−0.0719712			−0.0359856	−	0.999352i	$-0.511457\pi$
$47$	−0.493410			−0.0719712			−0.0359856	+	0.999352i	$0.511457\pi$
$48$	9.01785	+	11.1986i	1.30161	+	1.61638i
$49$		0			0
$50$	−0.977326	−	0.564259i	−0.138215	−	0.0797983i
$51$	3.61737	−	9.34703i	0.506533	−	1.30885i
$52$	5.31591	+	3.06914i	0.737184	+	0.425614i
$53$	3.59025	−	2.07283i	0.493159	−	0.284725i	−0.232725	−	0.972543i	$-0.574764\pi$
$53$	3.59025	−	2.07283i	0.493159	−	0.284725i	0.725884	+	0.687817i	$0.241431\pi$
$54$	−5.98377	−	11.9861i	−0.814288	−	1.63110i
$55$			10.1812i			1.37284i
$56$		0			0
$57$	0.179827	+	1.15585i	0.0238187	+	0.153096i
$58$	5.75947	+	9.97570i	0.756256	+	1.30987i
$59$	−4.31398			−0.561633			−0.280816	−	0.959762i	$-0.590605\pi$
$59$	−4.31398			−0.561633			−0.280816	+	0.959762i	$0.590605\pi$
$60$	6.77426	−	17.5042i	0.874554	−	2.25979i
$61$			2.05145i			0.262661i	0.991339	+	0.131330i	$0.0419249\pi$
$61$			2.05145i			0.262661i	−0.991339	+	0.131330i	$0.958075\pi$
$62$	10.3591			1.31560
$63$		0			0
$64$	−3.38572			−0.423215
$65$		−	3.08017i		−	0.382048i
$66$	−19.2652	+	2.99730i	−2.37139	+	0.368942i
$67$	−4.82437			−0.589390			−0.294695	−	0.955591i	$-0.595218\pi$
$67$	−4.82437			−0.589390			−0.294695	+	0.955591i	$0.595218\pi$
$68$	13.4453	+	23.2879i	1.63048	+	2.82408i
$69$	8.98648	+	3.47783i	1.08184	+	0.418681i
$70$		0			0
$71$			1.17135i			0.139014i	0.997581	+	0.0695068i	$0.0221426\pi$
$71$			1.17135i			0.139014i	−0.997581	+	0.0695068i	$0.977857\pi$
$72$	20.0031	+	4.36635i	2.35739	+	0.514579i
$73$	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	$-0.0122058\pi$
$74$	−6.73536	−	3.88866i	−0.782970	−	0.452048i
$75$	−0.749135	+	0.116551i	−0.0865027	+	0.0134581i
$76$	−2.71797	−	1.56922i	−0.311772	−	0.180002i
$77$		0			0
$78$	5.82840	−	0.906785i	0.659936	−	0.102673i
$79$	−10.6086			−1.19356			−0.596778	−	0.802406i	$-0.703553\pi$
$79$	−10.6086			−1.19356			−0.596778	+	0.802406i	$0.703553\pi$
$80$	9.67878	+	16.7641i	1.08212	+	1.87429i
$81$	−8.18135	−	3.75041i	−0.909039	−	0.416712i
$82$	−14.7141	−	8.49518i	−1.62490	−	0.938135i
$83$	−5.32432	−	9.22199i	−0.584420	−	1.01225i	−0.994947	−	0.100397i	$-0.967989\pi$
$83$	−5.32432	−	9.22199i	−0.584420	−	1.01225i	0.410527	−	0.911848i	$-0.365345\pi$
$84$		0			0
$85$	6.74680	−	11.6858i	0.731793	−	1.26750i
$86$	−17.3807	+	10.0348i	−1.87421	+	1.08208i
$87$	7.21691	+	2.79300i	0.773734	+	0.299441i
$88$	14.8986	−	25.8051i	1.58820	−	2.75084i
$89$	−1.66268	+	2.87984i	−0.176243	+	0.305262i	−0.940591	−	0.339542i	$-0.889728\pi$
$89$	−1.66268	+	2.87984i	−0.176243	+	0.305262i	0.764348	+	0.644804i	$0.223061\pi$
$90$	−5.47953	−	17.1837i	−0.577593	−	1.81132i
$91$		0			0
$92$	−22.3896	+	12.9266i	−2.33428	+	1.34770i
$93$	5.42036	−	4.36482i	0.562065	−	0.452610i
$94$		−	1.27211i		−	0.131208i
$95$			1.57486i			0.161577i
$96$	−10.4588	+	8.42206i	−1.06744	+	0.859573i
$97$	−12.7531	+	7.36299i	−1.29488	+	0.747598i	−0.979515	−	0.201373i	$-0.935460\pi$
$97$	−12.7531	+	7.36299i	−1.29488	+	0.747598i	−0.315363	+	0.948971i	$0.602126\pi$
$98$		0			0
$99$	−8.81758	+	9.68578i	−0.886200	+	0.973458i
$100$	1.01705	−	1.76159i	0.101705	−	0.176159i
$101$	−0.832092	+	1.44123i	−0.0827963	+	0.143407i	−0.904450	−	0.426580i	$-0.859718\pi$
$101$	−0.832092	+	1.44123i	−0.0827963	+	0.143407i	0.821654	+	0.569987i	$0.193052\pi$
$102$	24.0985	+	9.32628i	2.38610	+	0.923439i
$103$	−1.40783	+	0.812812i	−0.138718	+	0.0800887i	−0.567753	−	0.823199i	$-0.692187\pi$
$103$	−1.40783	+	0.812812i	−0.138718	+	0.0800887i	0.429035	+	0.903288i	$0.358854\pi$
$104$	−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	$0.0126414\pi$
$107$	15.8596	+	9.15652i	1.53320	+	0.885194i	0.533990	+	0.845491i	$0.320692\pi$
$108$	21.6044	−	10.7855i	2.07888	−	1.03783i
$109$	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	$0.556075\pi$
$110$	−26.2492			−2.50276
$111$	−5.16276	+	0.803225i	−0.490027	+	0.0762387i
$112$		0			0
$113$	−5.07612	−	2.93070i	−0.477521	−	0.275697i	0.241862	−	0.970311i	$-0.422242\pi$
$113$	−5.07612	−	2.93070i	−0.477521	−	0.275697i	−0.719383	+	0.694614i	$0.755575\pi$
$114$	−2.98000	+	0.463630i	−0.279102	+	0.0434229i
$115$	11.2350	+	6.48654i	1.04767	+	0.604873i
$116$	−17.9808	+	10.3812i	−1.66947	+	0.963871i
$117$	2.66762	−	2.93028i	0.246622	−	0.270905i
$118$		−	11.1223i		−	1.02389i
$119$		0			0
$120$	25.7067	+	9.94867i	2.34669	+	0.908185i
$121$	4.03134	+	6.98248i	0.366485	+	0.634771i
$122$	−5.28903			−0.478846
$123$	−11.2786	+	1.75473i	−1.01695	+	0.158218i
$124$			18.6718i			1.67678i
$125$	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	$0.762920\pi$
$128$			6.77652i			0.598965i
$129$	−4.86625	+	12.5741i	−0.428450	+	1.10708i
$130$	7.94128			0.696496
$131$	−3.55989	−	6.16591i	−0.311029	−	0.538718i	0.667556	−	0.744559i	$-0.267340\pi$
$131$	−3.55989	−	6.16591i	−0.311029	−	0.538718i	−0.978585	+	0.205841i	$0.934007\pi$
$132$	−5.40250	−	34.7248i	−0.470227	−	3.02241i
$133$		0			0
$134$		−	12.4382i		−	1.07449i
$135$	−10.1075	−	6.68252i	−0.869918	−	0.575140i
$136$	−34.2006	+	19.7457i	−2.93268	+	1.69318i
$137$	0.716584	+	0.413720i	0.0612219	+	0.0353465i	0.530298	−	0.847811i	$-0.322080\pi$
$137$	0.716584	+	0.413720i	0.0612219	+	0.0353465i	−0.469077	+	0.883157i	$0.655413\pi$
$138$	−8.96652	+	23.1689i	−0.763281	+	1.97227i
$139$	−12.0735	−	6.97062i	−1.02406	−	0.591241i	−0.108782	−	0.994066i	$-0.534695\pi$
$139$	−12.0735	−	6.97062i	−1.02406	−	0.591241i	−0.915277	+	0.402825i	$0.868028\pi$
$140$		0			0
$141$	−0.536005	−	0.665627i	−0.0451397	−	0.0560559i
$142$	−3.01997			−0.253430
$143$	−2.88356	−	4.99447i	−0.241135	−	0.417658i
$144$	−5.31101	+	24.3308i	−0.442584	+	2.02757i
$145$	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
$149$	9.46916	−	5.46702i	0.775744	−	0.447876i	−0.0591761	−	0.998248i	$-0.518847\pi$
$149$	9.46916	−	5.46702i	0.775744	−	0.447876i	0.834920	+	0.550372i	$0.185514\pi$
$150$	−0.300491	−	1.93142i	−0.0245350	−	0.157699i
$151$	6.97277	−	12.0772i	0.567436	−	0.982828i	−0.429383	−	0.903123i	$-0.641269\pi$
$151$	6.97277	−	12.0772i	0.567436	−	0.982828i	0.996818	−	0.0797050i	$-0.0253978\pi$
$152$	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
$156$	1.63444	+	10.5054i	0.130860	+	0.841108i
$157$			15.7779i			1.25921i	0.776914	+	0.629606i	$0.216784\pi$
$157$			15.7779i			1.25921i	−0.776914	+	0.629606i	$0.783216\pi$
$158$		−	27.3509i		−	2.17592i
$159$	6.69651	+	2.59160i	0.531068	+	0.205527i
$160$	−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	$0.0813085\pi$
$164$	15.3122	−	26.5215i	1.19568	−	2.07098i
$165$	−13.7348	+	11.0601i	−1.06925	+	0.861031i
$166$	23.7761	−	13.7271i	1.84538	−	1.06543i
$167$	9.54631	−	16.5347i	0.738716	−	1.27949i	−0.214358	−	0.976755i	$-0.568766\pi$
$167$	9.54631	−	16.5347i	0.738716	−	1.27949i	0.953074	−	0.302738i	$-0.0979008\pi$
$168$		0			0
$169$	−5.62763	−	9.74733i	−0.432894	−	0.749795i
$170$	30.1283	+	17.3946i	2.31073	+	1.33410i
$171$	−1.36393	+	1.49822i	−0.104302	+	0.114572i
$172$	−18.0872	−	31.3280i	−1.37914	−	2.38874i
$173$	21.8491			1.66116			0.830579	−	0.556902i	$-0.188010\pi$
$173$	21.8491			1.66116			0.830579	+	0.556902i	$0.188010\pi$
$174$	−7.20089	+	18.6066i	−0.545898	+	1.41056i
$175$		0			0
$176$	31.3881	+	18.1219i	2.36597	+	1.36599i
$177$	−4.68640	−	5.81971i	−0.352251	−	0.437436i
$178$	−7.42478	−	4.28670i	−0.556511	−	0.321302i
$179$	14.8866	−	8.59481i	1.11268	−	0.642406i	0.173158	−	0.984894i	$-0.444603\pi$
$179$	14.8866	−	8.59481i	1.11268	−	0.642406i	0.939522	+	0.342488i	$0.111270\pi$
$180$	30.9729	−	9.87662i	2.30858	−	0.736160i
$181$			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
$184$	−18.9840	−	32.8813i	−1.39952	−	2.42404i
$185$	−7.03433			−0.517175
$186$	11.2533	+	13.9747i	0.825135	+	1.02468i
$187$		−	25.2645i		−	1.84753i
$188$	2.29292			0.167228
$189$		0			0
$190$	−4.06029			−0.294565
$191$			0.954076i			0.0690345i	0.999404	+	0.0345173i	$0.0109894\pi$
$191$			0.954076i			0.0690345i	−0.999404	+	0.0345173i	$0.989011\pi$
$192$	−3.67800	−	4.56745i	−0.265437	−	0.329628i
$193$	−1.69441			−0.121966			−0.0609830	−	0.998139i	$-0.519424\pi$
$193$	−1.69441			−0.121966			−0.0609830	+	0.998139i	$0.519424\pi$
$194$	−18.9832	−	32.8799i	−1.36292	−	2.36064i
$195$	4.15526	−	3.34607i	0.297564	−	0.239617i
$196$		0			0
$197$		−	12.7486i		−	0.908301i	−0.890925	−	0.454150i	$-0.849943\pi$
$197$		−	12.7486i		−	0.908301i	0.890925	−	0.454150i	$-0.150057\pi$
$198$	−24.9718	−	22.7334i	−1.77467	−	1.61559i
$199$	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	$0.283967\pi$
$200$	2.58706	+	1.49364i	0.182933	+	0.105616i
$201$	−5.24084	−	6.50824i	−0.369660	−	0.459056i
$202$	−3.71576	−	2.14530i	−0.261440	−	0.150942i
$203$		0			0
$204$	−16.8102	+	43.4365i	−1.17695	+	3.04116i
$205$	−15.3672			−1.07329
$206$	−2.09559	−	3.62966i	−0.146006	−	0.252891i
$207$	5.07054	+	15.9011i	0.352427	+	1.10520i
$208$	−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	−0.932863	−	0.360232i	$-0.882698\pi$
$211$	−2.24368	+	3.88617i	−0.154461	+	0.267535i	0.778401	+	0.627767i	$0.216031\pi$
$212$	−16.6842	+	9.63263i	−1.14588	+	0.661571i
$213$	−1.58019	+	1.27247i	−0.108273	+	0.0871882i
$214$	−23.6073	+	40.8890i	−1.61376	+	2.79512i
$215$	−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
$219$	24.4158	+	9.44910i	1.64987	+	0.638511i
$220$		−	47.3130i		−	3.18984i
$221$			7.64339i			0.514150i
$222$	−2.07087	−	13.3106i	−0.138988	−	0.893349i
$223$	18.0005	−	10.3926i	1.20540	−	0.695939i	0.243650	−	0.969863i	$-0.421655\pi$
$223$	18.0005	−	10.3926i	1.20540	−	0.695939i	0.961751	+	0.273924i	$0.0883218\pi$
$224$		0			0
$225$	−0.971037	−	0.883997i	−0.0647358	−	0.0589331i
$226$	7.55591	−	13.0872i	0.502612	−	0.870549i
$227$	14.1579	−	24.5223i	0.939696	−	1.62760i	0.173657	−	0.984806i	$-0.444442\pi$
$227$	14.1579	−	24.5223i	0.939696	−	1.62760i	0.766039	−	0.642795i	$-0.222225\pi$
$228$	−0.835673	−	5.37132i	−0.0553438	−	0.355724i
$229$	−18.8670	+	10.8929i	−1.24677	+	0.719821i	−0.970463	−	0.241250i	$-0.922443\pi$
$229$	−18.8670	+	10.8929i	−1.24677	+	0.719821i	−0.276303	+	0.961071i	$0.589109\pi$
$230$	−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	0.00116682	−	0.999999i	$-0.499629\pi$
$233$	−13.1926	−	7.61674i	−0.864275	−	0.498989i	−0.865441	+	0.501010i	$0.832962\pi$
$234$	7.55483	+	6.87764i	0.493875	+	0.449606i
$235$	−0.575289	−	0.996430i	−0.0375277	−	0.0649999i
$236$	20.0474			1.30498
$237$	−11.5244	−	14.3113i	−0.748588	−	0.929619i
$238$		0			0
$239$	−4.95125	−	2.85861i	−0.320270	−	0.184908i	0.331243	−	0.943545i	$-0.392532\pi$
$239$	−4.95125	−	2.85861i	−0.320270	−	0.184908i	−0.651513	+	0.758638i	$0.725865\pi$
$240$	−12.1011	+	31.2684i	−0.781121	+	2.01836i
$241$	3.87212	+	2.23557i	0.249425	+	0.144006i	0.619501	−	0.784996i	$-0.287335\pi$
$241$	3.87212	+	2.23557i	0.249425	+	0.144006i	−0.370076	+	0.929002i	$0.620668\pi$
$242$	−18.0022	+	10.3936i	−1.15722	+	0.668124i
$243$	−3.82820	−	15.1111i	−0.245579	−	0.969377i
$244$		−	9.53325i		−	0.610304i
$245$		0			0
$246$	−4.52402	−	29.0783i	−0.288441	−	1.85397i
$247$	−0.446036	−	0.772557i	−0.0283806	−	0.0491566i
$248$	−27.4214			−1.74126
$249$	6.65683	−	17.2008i	0.421859	−	1.09006i
$250$			27.4288i			1.73475i
$251$	−11.6265			−0.733861			−0.366931	−	0.930248i	$-0.619591\pi$
$251$	−11.6265			−0.733861			−0.366931	+	0.930248i	$0.619591\pi$
$252$		0			0
$253$	24.2900			1.52710
$254$		−	42.7232i		−	2.68069i
$255$	23.0938	−	3.59294i	1.44619	−	0.224999i
$256$	−24.2426			−1.51516
$257$	1.05140	+	1.82108i	0.0655846	+	0.113596i	0.896953	−	0.442126i	$-0.145775\pi$
$257$	1.05140	+	1.82108i	0.0655846	+	0.113596i	−0.831369	+	0.555721i	$0.812442\pi$
$258$	−32.4184	−	12.5461i	−2.01828	−	0.781089i
$259$		0			0
$260$			14.3138i			0.887705i
$261$	4.07208	+	12.7700i	0.252056	+	0.790441i
$262$	15.8969	−	9.17809i	0.982114	−	0.567024i
$263$	1.90773	+	1.10143i	0.117636	+	0.0679170i	0.557663	−	0.830067i	$-0.311698\pi$
$263$	1.90773	+	1.10143i	0.117636	+	0.0679170i	−0.440028	+	0.897984i	$0.645031\pi$
$264$	50.9968	−	7.93410i	3.13863	−	0.488310i
$265$	8.37207	+	4.83362i	0.514292	+	0.296927i
$266$		0			0
$267$	−5.69121	+	0.885441i	−0.348296	+	0.0541881i
$268$	22.4192			1.36947
$269$	13.9312	+	24.1295i	0.849398	+	1.47120i	0.881746	+	0.471724i	$0.156368\pi$
$269$	13.9312	+	24.1295i	0.849398	+	1.47120i	−0.0323483	+	0.999477i	$0.510299\pi$
$270$	17.2288	−	26.0592i	1.04851	−	1.58591i
$271$	−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
$275$	−1.65507	+	0.955553i	−0.0998043	+	0.0576220i
$276$	−41.7609	−	16.1618i	−2.51371	−	0.972824i
$277$	5.10000	−	8.83346i	0.306429	−	0.530751i	−0.671149	−	0.741322i	$-0.734199\pi$
$277$	5.10000	−	8.83346i	0.306429	−	0.530751i	0.977579	+	0.210571i	$0.0675323\pi$
$278$	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	−0.190864	−	0.981617i	$-0.561129\pi$
$281$	9.45116	−	5.45663i	0.563809	−	0.325515i	0.754673	+	0.656101i	$0.227796\pi$
$282$	1.71612	−	1.38192i	0.102193	−	0.0822924i
$283$		−	11.8664i		−	0.705386i	−0.935739	−	0.352693i	$-0.885266\pi$
$283$		−	11.8664i		−	0.705386i	0.935739	−	0.352693i	$-0.114734\pi$
$284$		−	5.44336i		−	0.323004i
$285$	−2.12454	+	1.71081i	−0.125847	+	0.101340i
$286$	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
$290$	−13.4305	+	23.2622i	−0.788664	+	1.36601i
$291$	−23.7869	−	9.20571i	−1.39441	−	0.539648i
$292$	−60.8315	+	35.1211i	−3.55989	+	2.05531i
$293$	9.55012	−	16.5413i	0.557924	−	0.966353i	−0.439746	−	0.898122i	$-0.644931\pi$
$293$	9.55012	−	16.5413i	0.557924	−	0.966353i	0.997670	−	0.0682302i	$-0.0217352\pi$
$294$		0			0
$295$	−5.02987	−	8.71199i	−0.292850	−	0.507232i
$296$	17.8291	+	10.2936i	1.03629	+	0.598305i
$297$	−22.6452	−	1.37329i	−1.31401	−	0.0796863i
$298$	14.0950	+	24.4133i	0.816504	+	1.41423i
$299$	−7.34855			−0.424978
$300$	3.48129	−	0.541622i	0.200993	−	0.0312705i
$301$		0			0
$302$	31.1373	+	17.9772i	1.79175	+	1.03447i
$303$	−2.84819	+	0.443123i	−0.163624	+	0.0254567i
$304$	4.85519	+	2.80315i	0.278464	+	0.160771i
$305$	−4.14285	+	2.39188i	−0.237219	+	0.136958i
$306$	13.5974	+	42.6410i	0.777309	+	2.43763i
$307$			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
$310$	12.0781	+	20.9199i	0.685991	+	1.18817i
$311$	−7.84967			−0.445114			−0.222557	−	0.974920i	$-0.571440\pi$
$311$	−7.84967			−0.445114			−0.222557	+	0.974920i	$0.571440\pi$
$312$	−15.4283	+	2.40034i	−0.873454	+	0.135892i
$313$		−	30.0532i		−	1.69870i	−0.527826	−	0.849352i	$-0.676993\pi$
$313$		−	30.0532i		−	1.69870i	0.527826	−	0.849352i	$-0.323007\pi$
$314$	−40.6785			−2.29562
$315$		0			0
$316$	49.2989			2.77328
$317$		−	11.1071i		−	0.623838i	−0.950109	−	0.311919i	$-0.899028\pi$
$317$		−	11.1071i		−	0.623838i	0.950109	−	0.311919i	$-0.100972\pi$
$318$	−6.68164	+	17.2649i	−0.374688	+	0.968167i
$319$	19.5069			1.09218
$320$	−3.94757	−	6.83739i	−0.220676	−	0.382222i
$321$	4.87621	+	31.3421i	0.272164	+	1.74934i
$322$		0			0
$323$		−	3.90798i		−	0.217446i
$324$	38.0194	+	17.4285i	2.11219	+	0.968248i
$325$	0.500715	−	0.289088i	0.0277746	−	0.0160357i
$326$	15.1059	+	8.72141i	0.836640	+	0.483034i
$327$	−9.98562	+	25.8022i	−0.552206	+	1.42686i
$328$	38.9494	+	22.4875i	2.15062	+	1.24166i
$329$		0			0
$330$	−28.5152	−	35.4110i	−1.56971	−	1.94931i
$331$	−17.2672			−0.949093			−0.474547	−	0.880230i	$-0.657388\pi$
$331$	−17.2672			−0.949093			−0.474547	+	0.880230i	$0.657388\pi$
$332$	24.7426	+	42.8554i	1.35792	+	2.35199i
$333$	−6.69202	−	6.09217i	−0.366721	−	0.333849i
$334$	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	−0.951278	−	0.308336i	$-0.900228\pi$
$337$	−3.82962	+	6.63309i	−0.208612	+	0.361327i	0.742665	+	0.669663i	$0.233561\pi$
$338$	25.1305	−	14.5091i	1.36692	−	0.789192i
$339$	−1.56071	−	10.0316i	−0.0847664	−	0.544840i
$340$	−31.3530	+	54.3049i	−1.70035	+	2.94510i
$341$	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
$345$	3.45434	+	22.2029i	0.185976	+	1.19537i
$346$			56.3312i			3.02839i
$347$			13.1652i			0.706747i	0.935482	+	0.353374i	$0.114966\pi$
$347$			13.1652i			0.706747i	−0.935482	+	0.353374i	$0.885034\pi$
$348$	−33.5376	−	12.9793i	−1.79780	−	0.695763i
$349$	−1.05185	+	0.607283i	−0.0563040	+	0.0325071i	−0.527888	−	0.849314i	$-0.677016\pi$
$349$	−1.05185	+	0.607283i	−0.0563040	+	0.0325071i	0.471584	+	0.881821i	$0.343682\pi$
$350$		0			0
$351$	6.85096	+	0.415467i	0.365677	+	0.0221760i
$352$	−16.9246	+	29.3143i	−0.902087	+	1.56246i
$353$	−13.4114	+	23.2292i	−0.713816	+	1.23637i	0.249598	+	0.968349i	$0.419701\pi$
$353$	−13.4114	+	23.2292i	−0.713816	+	1.23637i	−0.963414	+	0.268016i	$0.913632\pi$
$354$	15.0043	−	12.0824i	0.797472	−	0.642175i
$355$	−2.36551	+	1.36573i	−0.125548	+	0.0724854i
$356$	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	0.319977	−	0.947425i	$-0.396325\pi$
$359$	−6.45209	−	3.72512i	−0.340529	−	0.196604i	−0.660506	+	0.750821i	$0.729658\pi$
$360$	14.5048	+	45.4867i	0.764469	+	2.39736i
$361$	−9.27195	−	16.0595i	−0.487997	−	0.845236i
$362$	−42.9171			−2.25567
$363$	−5.04025	+	13.0237i	−0.264545	+	0.683565i
$364$		0			0
$365$	30.5250	+	17.6236i	1.59775	+	0.922463i
$366$	−5.74562	−	7.13508i	−0.300328	−	0.372957i
$367$	−30.3000	−	17.4937i	−1.58165	−	0.913166i	−0.994619	−	0.103601i	$-0.966963\pi$
$367$	−30.3000	−	17.4937i	−1.58165	−	0.913166i	−0.587031	−	0.809565i	$-0.699703\pi$
$368$	39.9952	−	23.0913i	2.08490	−	1.20371i
$369$	−14.6194	−	13.3090i	−0.761056	−	0.692837i
$370$		−	18.1359i		−	0.942840i
$371$		0			0
$372$	−25.1889	+	20.2837i	−1.30598	+	1.05166i
$373$	15.0495	+	26.0665i	0.779233	+	1.34967i	0.932384	+	0.361469i	$0.117725\pi$
$373$	15.0495	+	26.0665i	0.779233	+	1.34967i	−0.153151	+	0.988203i	$0.548942\pi$
$374$	65.1369			3.36815
$375$	11.5572	+	14.3520i	0.596809	+	0.741136i
$376$			3.36737i			0.173659i
$377$	−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	$0.745041\pi$
$380$		−	7.31850i		−	0.375431i
$381$	−18.0015	−	22.3548i	−0.922244	−	1.14527i
$382$	−2.45979			−0.125854
$383$	1.83015	+	3.16992i	0.0935164	+	0.161975i	0.908988	−	0.416821i	$-0.136856\pi$
$383$	1.83015	+	3.16992i	0.0935164	+	0.161975i	−0.815472	+	0.578796i	$0.803523\pi$
$384$	−9.14176	+	7.36152i	−0.466513	+	0.375666i
$385$		0			0
$386$		−	4.36851i		−	0.222351i
$387$	−22.2492	+	7.09481i	−1.13099	+	0.360650i
$388$	59.2646	−	34.2164i	3.00870	−	1.73708i
$389$	−10.5387	−	6.08449i	−0.534331	−	0.308496i	0.208447	−	0.978034i	$-0.433159\pi$
$389$	−10.5387	−	6.08449i	−0.534331	−	0.308496i	−0.742778	+	0.669537i	$0.766492\pi$
$390$	8.62683	+	10.7131i	0.436836	+	0.542477i
$391$	−27.8795	−	16.0962i	−1.40993	−	0.814022i
$392$		0			0
$393$	4.45082	−	11.5006i	0.224514	−	0.580129i
$394$	32.8684			1.65589
$395$	−12.3690	−	21.4237i	−0.622352	−	1.07795i
$396$	40.9760	−	45.0106i	2.05912	−	2.26187i
$397$	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
$401$	−6.69428	+	3.86494i	−0.334296	+	0.193006i	−0.657747	−	0.753239i	$-0.728490\pi$
$401$	−6.69428	+	3.86494i	−0.334296	+	0.193006i	0.323451	+	0.946245i	$0.395157\pi$
$402$	16.7795	−	13.5119i	0.836885	−	0.673913i
$403$	−2.65364	+	4.59624i	−0.132187	+	0.228955i
$404$	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
$408$	−63.7907	−	24.6875i	−3.15811	−	1.22221i
$409$			9.06047i			0.448012i	0.974588	+	0.224006i	$0.0719135\pi$
$409$			9.06047i			0.448012i	−0.974588	+	0.224006i	$0.928087\pi$
$410$		−	39.6197i		−	1.95668i
$411$	0.220322	+	1.41613i	0.0108677	+	0.0698526i
$412$	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
$416$	5.12029	−	8.86860i	0.251043	−	0.434819i
$417$	−3.71214	−	23.8599i	−0.181784	−	1.16842i
$418$	−6.58372	+	3.80111i	−0.322020	+	0.185919i
$419$	−3.30466	+	5.72384i	−0.161443	+	0.279628i	−0.935386	−	0.353627i	$-0.884948\pi$
$419$	−3.30466	+	5.72384i	−0.161443	+	0.279628i	0.773943	+	0.633255i	$0.218282\pi$
$420$		0			0
$421$	6.39209	+	11.0714i	0.311531	+	0.539588i	0.978694	−	0.205324i	$-0.0658248\pi$
$421$	6.39209	+	11.0714i	0.311531	+	0.539588i	−0.667163	+	0.744912i	$0.732491\pi$
$422$	−10.0193	−	5.78464i	−0.487732	−	0.281592i
$423$	0.315677	−	1.44618i	0.0153487	−	0.0703155i
$424$	−14.1465	−	24.5024i	−0.687013	−	1.18994i
$425$	2.53287			0.122862
$426$	−3.28067	−	4.07404i	−0.158949	−	0.197388i
$427$		0			0
$428$	−73.7007	−	42.5511i	−3.56246	−	2.05679i
$429$	3.60522	−	9.31564i	0.174062	−	0.449763i
$430$	−40.5299	−	23.4000i	−1.95453	−	1.12845i
$431$	18.9756	−	10.9556i	0.914023	−	0.527712i	0.0322998	−	0.999478i	$-0.489717\pi$
$431$	18.9756	−	10.9556i	0.914023	−	0.527712i	0.881723	+	0.471767i	$0.156384\pi$
$432$	−38.5925	+	19.2665i	−1.85678	+	0.926958i
$433$			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
$436$	−37.1153	−	64.2855i	−1.77750	−	3.07872i
$437$	3.75724			0.179733
$438$	−24.3616	+	62.9488i	−1.16404	+	3.00781i
$439$			37.8737i			1.80761i	0.427942	+	0.903806i	$0.359239\pi$
$439$			37.8737i			1.80761i	−0.427942	+	0.903806i	$0.640761\pi$
$440$	69.4838			3.31251
$441$		0			0
$442$	−19.7061			−0.937326
$443$			20.4624i			0.972200i	0.873903	+	0.486100i	$0.161581\pi$
$443$			20.4624i			0.972200i	−0.873903	+	0.486100i	$0.838419\pi$
$444$	23.9918	−	3.73265i	1.13860	−	0.177144i
$445$	−7.75436			−0.367592
$446$	26.7941	+	46.4087i	1.26874	+	2.19752i
$447$	17.6618	+	6.83524i	0.835375	+	0.323296i
$448$		0			0
$449$			35.7054i			1.68504i	0.538665	+	0.842520i	$0.318929\pi$
$449$			35.7054i			1.68504i	−0.538665	+	0.842520i	$0.681071\pi$
$450$	2.27911	−	2.50352i	0.107438	−	0.118017i
$451$	−24.9178	+	14.3863i	−1.17333	+	0.677424i
$452$	23.5892	+	13.6192i	1.10954	+	0.640594i
$453$	23.8672	−	3.71328i	1.12138	−	0.174465i
$454$	63.2232	+	36.5019i	2.96721	+	1.71312i
$455$		0			0
$456$	7.88831	−	1.22727i	0.369404	−	0.0574720i
$457$	−0.254179			−0.0118900			−0.00594501	−	0.999982i	$-0.501892\pi$
$457$	−0.254179			−0.0118900			−0.00594501	+	0.999982i	$0.501892\pi$
$458$	−28.0839	−	48.6428i	−1.31228	−	2.27293i
$459$	25.0817	+	16.5826i	1.17071	+	0.774007i
$460$	−52.2101	−	30.1435i	−2.43431	−	1.40545i
$461$	−12.2175	−	21.1613i	−0.569025	−	0.985581i	−0.996663	−	0.0816304i	$-0.973987\pi$
$461$	−12.2175	−	21.1613i	−0.569025	−	0.985581i	0.427637	−	0.903950i	$-0.359346\pi$
$462$		0			0
$463$	0.409986	−	0.710116i	0.0190536	−	0.0330019i	−0.856341	−	0.516410i	$-0.827268\pi$
$463$	0.409986	−	0.710116i	0.0190536	−	0.0330019i	0.875395	+	0.483408i	$0.160601\pi$
$464$	32.1196	−	18.5443i	1.49112	−	0.860896i
$465$	15.1345	+	5.85716i	0.701845	+	0.271619i
$466$	19.6374	−	34.0130i	0.909686	−	1.57562i
$467$	0.909625	−	1.57552i	0.0420924	−	0.0729062i	−0.844212	−	0.536010i	$-0.819931\pi$
$467$	0.909625	−	1.57552i	0.0420924	−	0.0729062i	0.886304	+	0.463104i	$0.153264\pi$
$468$	−12.3967	+	13.6173i	−0.573036	+	0.629458i
$469$		0			0
$470$	2.56899	−	1.48321i	0.118499	−	0.0684152i
$471$	−21.2849	+	17.1400i	−0.980757	+	0.789767i
$472$			29.4416i			1.35516i
$473$			33.9870i			1.56273i
$474$	36.8973	−	29.7121i	1.69475	−	1.36472i
$475$	−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
$479$	−0.681074	+	1.17965i	−0.0311191	+	0.0538998i	−0.881166	−	0.472808i	$-0.843240\pi$
$479$	−0.681074	+	1.17965i	−0.0311191	+	0.0538998i	0.850046	+	0.526708i	$0.176574\pi$
$480$	−29.2025	−	11.3016i	−1.33291	−	0.515844i
$481$	3.45074	−	1.99228i	0.157340	−	0.0908403i
$482$	−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
$486$	38.9593	−	9.86983i	1.76723	−	0.447705i
$487$	−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	$-0.420806\pi$
$488$	14.0005			0.633773
$489$	11.5789	−	1.80145i	0.523617	−	0.0814646i
$490$		0			0
$491$	−1.97415	−	1.13977i	−0.0890919	−	0.0514373i	0.454792	−	0.890598i	$-0.349714\pi$
$491$	−1.97415	−	1.13977i	−0.0890919	−	0.0514373i	−0.543884	+	0.839160i	$0.683047\pi$
$492$	52.4125	−	8.15436i	2.36294	−	0.367627i
$493$	−22.3897	−	12.9267i	−1.00838	−	0.582188i
$494$	1.99180	−	1.14997i	0.0896154	−	0.0517395i
$495$	−29.8410	−	6.51381i	−1.34125	−	0.292774i
$496$		−	33.3540i		−	1.49764i
$497$		0			0
$498$	44.3470	+	17.1626i	1.98724	+	0.769074i
$499$	−13.5195	−	23.4164i	−0.605215	−	1.04826i	−0.992017	−	0.126101i	$-0.959754\pi$
$499$	−13.5195	−	23.4164i	−0.605215	−	1.04826i	0.386802	−	0.922163i	$-0.373580\pi$
$500$	−49.4392			−2.21099
$501$	32.6763	−	5.08379i	1.45987	−	0.227127i
$502$		−	29.9755i		−	1.33787i
$503$	−0.276948			−0.0123485			−0.00617426	−	0.999981i	$-0.501965\pi$
$503$	−0.276948			−0.0123485			−0.00617426	+	0.999981i	$0.501965\pi$
$504$		0			0
$505$	−3.88070			−0.172689
$506$			62.6243i			2.78399i
$507$	7.03604	−	18.1807i	0.312482	−	0.807431i
$508$	77.0067			3.41662
$509$	−9.21476	−	15.9604i	−0.408437	−	0.707434i	0.586278	−	0.810110i	$-0.300593\pi$
$509$	−9.21476	−	15.9604i	−0.408437	−	0.707434i	−0.994715	+	0.102676i	$0.967259\pi$
$510$	9.26330	+	59.5402i	0.410186	+	2.63649i
$511$		0			0
$512$		−	48.9492i		−	2.16327i
$513$	−3.50282	−	0.212424i	−0.154653	−	0.00937874i
$514$	−4.69510	+	2.71072i	−0.207092	+	0.119565i
$515$	−3.28291	−	1.89539i	−0.144662	−	0.0835208i
$516$	22.6139	−	58.4328i	0.995521	−	2.57236i
$517$	−1.86565	−	1.07713i	−0.0820512	−	0.0473723i
$518$		0			0
$519$	23.7353	+	29.4752i	1.04186	+	1.29382i
$520$	−21.0212			−0.921842
$521$	11.6264	+	20.1374i	0.509360	+	0.882237i	0.999941	+	0.0108420i	$0.00345117\pi$
$521$	11.6264	+	20.1374i	0.509360	+	0.882237i	−0.490581	+	0.871395i	$0.663215\pi$
$522$	−32.9235	+	10.4986i	−1.44102	+	0.459512i
$523$	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
$527$	−20.1352	+	11.6251i	−0.877102	+	0.506395i
$528$	9.65065	+	62.0300i	0.419991	+	2.69951i
$529$	3.97534	−	6.88549i	0.172841	−	0.299369i
$530$	−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
$534$	−2.28284	−	14.6730i	−0.0987881	−	0.634965i
$535$			42.7040i			1.84626i
$536$			32.9249i			1.42214i
$537$	27.7665	+	10.7458i	1.19821	+	0.463716i
$538$	−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	$-0.0579524\pi$
$542$	14.7993	−	25.6331i	0.635684	−	1.10104i
$543$	−22.4563	+	18.0832i	−0.963690	+	0.776024i
$544$	38.8515	−	22.4309i	1.66574	−	0.961718i
$545$	−18.6243	+	32.2582i	−0.797778	+	1.38179i
$546$		0			0
$547$	−0.572061	−	0.990840i	−0.0244596	−	0.0423652i	0.853537	−	0.521033i	$-0.174453\pi$
$547$	−0.572061	−	0.990840i	−0.0244596	−	0.0423652i	−0.877996	+	0.478668i	$0.841120\pi$
$548$	−3.33002	−	1.92259i	−0.142252	−	0.0821290i
$549$	−6.01276	−	1.31249i	−0.256618	−	0.0560156i
$550$	−2.46360	−	4.26708i	−0.105048	−	0.181949i
$551$	3.01738			0.128545
$552$	23.7351	−	61.3300i	1.01023	−	2.61038i
$553$		0			0
$554$	22.7744	+	13.1488i	0.967591	+	0.558639i
$555$	−7.64159	−	9.48956i	−0.324367	−	0.402809i
$556$	56.1065	+	32.3931i	2.37944	+	1.37377i
$557$	−8.35388	+	4.82312i	−0.353965	+	0.204362i	−0.666430	−	0.745567i	$-0.732179\pi$
$557$	−8.35388	+	4.82312i	−0.353965	+	0.204362i	0.312465	+	0.949929i	$0.398845\pi$
$558$	−6.62759	+	30.3623i	−0.280568	+	1.28534i
$559$		−	10.2822i		−	0.434893i
$560$		0			0
$561$	34.0827	−	27.4456i	1.43897	−	1.15875i
$562$	14.0683	+	24.3669i	0.593434	+	1.02786i
$563$	−3.08791			−0.130140			−0.0650698	−	0.997881i	$-0.520727\pi$
$563$	−3.08791			−0.130140			−0.0650698	+	0.997881i	$0.520727\pi$
$564$	2.49086	+	3.09322i	0.104884	+	0.130248i
$565$		−	13.6681i		−	0.575023i
$566$	30.5940			1.28596
$567$		0			0
$568$	7.99411			0.335425
$569$			8.43610i			0.353660i	0.984241	+	0.176830i	$0.0565842\pi$
$569$			8.43610i			0.353660i	−0.984241	+	0.176830i	$0.943416\pi$
$570$	−4.41081	−	5.47747i	−0.184748	−	0.229426i
$571$	−34.0415			−1.42459			−0.712297	−	0.701879i	$-0.752345\pi$
$571$	−34.0415			−1.42459			−0.712297	+	0.701879i	$0.752345\pi$
$572$	13.4001	+	23.2097i	0.560288	+	0.970447i
$573$	−1.28708	+	1.03644i	−0.0537686	+	0.0432979i
$574$		0			0
$575$			2.43516i			0.101553i
$576$	2.16614	−	9.92350i	0.0902557	−	0.413479i
$577$	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	$0.210335\pi$
$578$	−36.8055	−	21.2497i	−1.53091	−	0.883869i
$579$	−1.84068	−	2.28581i	−0.0764960	−	0.0949951i
$580$	−41.9292	−	24.2078i	−1.74102	−	1.00518i
$581$		0			0
$582$	23.7341	−	61.3273i	0.983810	−	2.54210i
$583$	18.1003			0.749638
$584$	−51.5787	−	89.3370i	−2.13434	−	3.69679i
$585$	9.02794	+	1.97065i	0.373259	+	0.0814764i
$586$	42.6467	+	24.6221i	1.76172	+	1.01713i
$587$	4.04900	+	7.01308i	0.167120	+	0.289461i	0.937406	−	0.348238i	$-0.113220\pi$
$587$	4.04900	+	7.01308i	0.167120	+	0.289461i	−0.770286	+	0.637699i	$0.779887\pi$
$588$		0			0
$589$	1.35678	−	2.35001i	0.0559050	−	0.0968304i
$590$	22.4612	−	12.9680i	0.924713	−	0.533883i
$591$	17.1983	−	13.8492i	0.707444	−	0.569678i
$592$	−12.5207	+	21.6864i	−0.514596	+	0.891306i
$593$	−3.33216	+	5.77148i	−0.136836	+	0.237006i	−0.926297	−	0.376794i	$-0.877027\pi$
$593$	−3.33216	+	5.77148i	−0.136836	+	0.237006i	0.789462	+	0.613800i	$0.210360\pi$
$594$	3.54060	−	58.3838i	0.145273	−	2.39552i
$595$		0			0
$596$	−44.0040	+	25.4057i	−1.80247	+	1.04066i
$597$	7.03960	+	2.72438i	0.288112	+	0.111501i
$598$		−	18.9460i		−	0.774759i
$599$			3.58607i			0.146523i	0.997313	+	0.0732614i	$0.0233407\pi$
$599$			3.58607i			0.146523i	−0.997313	+	0.0732614i	$0.976659\pi$
$600$	0.795424	+	5.11262i	0.0324731	+	0.208722i
$601$	4.86949	−	2.81140i	0.198631	−	0.114679i	−0.397386	−	0.917652i	$-0.630083\pi$
$601$	4.86949	−	2.81140i	0.198631	−	0.114679i	0.596017	+	0.802972i	$0.296749\pi$
$602$		0			0
$603$	3.08656	−	14.1401i	0.125695	−	0.575831i
$604$	−32.4030	+	56.1237i	−1.31846	+	2.28364i
$605$	−9.40064	+	16.2824i	−0.382190	+	0.661973i
$606$	−1.14246	−	7.34318i	−0.0464091	−	0.298296i
$607$	1.93239	−	1.11566i	0.0784332	−	0.0452834i	−0.460270	−	0.887779i	$-0.652248\pi$
$607$	1.93239	−	1.11566i	0.0784332	−	0.0452834i	0.538704	+	0.842495i	$0.318914\pi$
$608$	−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
$612$	−76.8587	+	24.5087i	−3.10683	+	0.990704i
$613$	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	$0.789351\pi$
$614$	−6.07134			−0.245019
$615$	−16.6938	−	20.7309i	−0.673160	−	0.835950i
$616$		0			0
$617$	−2.35139	−	1.35757i	−0.0946632	−	0.0546538i	0.451921	−	0.892058i	$-0.350739\pi$
$617$	−2.35139	−	1.35757i	−0.0946632	−	0.0546538i	−0.546584	+	0.837404i	$0.684072\pi$
$618$	2.62004	−	6.77002i	0.105394	−	0.272330i
$619$	−23.1886	−	13.3880i	−0.932029	−	0.538107i	−0.0445762	−	0.999006i	$-0.514194\pi$
$619$	−23.1886	−	13.3880i	−0.932029	−	0.538107i	−0.887453	+	0.460899i	$0.847527\pi$
$620$	−37.7072	+	21.7703i	−1.51436	+	0.874316i
$621$	−15.9429	+	24.1142i	−0.639766	+	0.967668i
$622$		−	20.2380i		−	0.811469i
$623$		0			0
$624$	−2.91965	−	18.7662i	−0.116880	−	0.751249i
$625$	13.4985	+	23.3801i	0.539940	+	0.935203i
$626$	77.4829			3.09684
$627$	−1.84331	+	4.76299i	−0.0736147	+	0.190215i
$628$		−	73.3212i		−	2.92583i
$629$	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	$0.571316\pi$
$632$			72.4002i			2.87993i
$633$	−7.67994	+	1.19485i	−0.305250	+	0.0474910i
$634$	28.6363			1.13729
$635$	−19.3208	−	33.4647i	−0.766724	−	1.32801i
$636$	−31.1192	−	12.0434i	−1.23396	−	0.477551i
$637$		0			0
$638$			50.2927i			1.99111i
$639$	−3.43321	−	0.749413i	−0.135816	−	0.0296463i
$640$	−13.6850	+	7.90105i	−0.540948	+	0.312317i
$641$	−38.6251	−	22.3002i	−1.52560	−	0.880805i	−0.999539	−	0.0303565i	$-0.990336\pi$
$641$	−38.6251	−	22.3002i	−1.52560	−	0.880805i	−0.526059	−	0.850448i	$-0.676331\pi$
$642$	−80.8059	+	12.5718i	−3.18916	+	0.496170i
$643$	−23.6268	−	13.6410i	−0.931751	−	0.537947i	−0.0443860	−	0.999014i	$-0.514133\pi$
$643$	−23.6268	−	13.6410i	−0.931751	−	0.537947i	−0.887365	+	0.461068i	$0.847466\pi$
$644$		0			0
$645$	−31.0668	+	4.83339i	−1.22326	+	0.190315i
$646$	10.0755			0.396417
$647$	22.4675	+	38.9148i	0.883288	+	1.52990i	0.847663	+	0.530534i	$0.178009\pi$
$647$	22.4675	+	38.9148i	0.883288	+	1.52990i	0.0356246	+	0.999365i	$0.488658\pi$
$648$	−25.5954	+	55.8352i	−1.00548	+	2.19342i
$649$	−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
$653$	24.0549	−	13.8881i	0.941343	−	0.543484i	0.0509617	−	0.998701i	$-0.483771\pi$
$653$	24.0549	−	13.8881i	0.941343	−	0.543484i	0.890381	+	0.455216i	$0.150438\pi$
$654$	−66.5230	−	25.7449i	−2.60125	−	1.00670i
$655$	8.30128	−	14.3782i	0.324358	−	0.561804i
$656$	−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	−0.484298	−	0.874903i	$-0.660925\pi$
$659$	0.801975	−	0.463021i	0.0312405	−	0.0180367i	0.515539	+	0.856866i	$0.327592\pi$
$660$	63.8269	−	51.3974i	2.48446	−	2.00064i
$661$		−	32.6813i		−	1.27115i	−0.772037	−	0.635577i	$-0.780762\pi$
$661$		−	32.6813i		−	1.27115i	0.772037	−	0.635577i	$-0.219238\pi$
$662$		−	44.5183i		−	1.73025i
$663$	−10.3112	+	8.30322i	−0.400454	+	0.322471i
$664$	−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
$668$	−44.3625	+	76.8382i	−1.71644	+	2.97296i
$669$	33.5744	+	12.9935i	1.29806	+	0.502358i
$670$	25.1186	−	14.5022i	0.970415	−	0.560269i
$671$	−4.47839	+	7.75681i	−0.172886	+	0.299448i
$672$		0			0
$673$	−15.6947	−	27.1840i	−0.604987	−	1.04787i	−0.992054	−	0.125816i	$-0.959845\pi$
$673$	−15.6947	−	27.1840i	−0.604987	−	1.04787i	0.387067	−	0.922052i	$-0.373488\pi$
$674$	−17.1014	−	9.87349i	−0.658721	−	0.380313i
$675$	0.137677	−	2.27027i	0.00529921	−	0.0873828i
$676$	26.1521	+	45.2967i	1.00585	+	1.74218i
$677$	−21.5765			−0.829252			−0.414626	−	0.909992i	$-0.636088\pi$
$677$	−21.5765			−0.829252			−0.414626	+	0.909992i	$0.636088\pi$
$678$	25.8633	−	4.02383i	0.993274	−	0.154534i
$679$		0			0
$680$	−79.7521	−	46.0449i	−3.05835	−	1.76574i
$681$	48.4615	−	7.53967i	1.85705	−	0.288921i
$682$	39.1691	+	22.6143i	1.49986	+	0.865946i
$683$	−31.4015	+	18.1296i	−1.20154	+	0.693711i	−0.960898	−	0.276902i	$-0.910692\pi$
$683$	−31.4015	+	18.1296i	−1.20154	+	0.693711i	−0.240645	+	0.970613i	$0.577359\pi$
$684$	6.33828	−	6.96236i	0.242350	−	0.266213i
$685$			1.92950i			0.0737224i
$686$		0			0
$687$	−35.1906	−	13.6190i	−1.34260	−	0.519597i
$688$	32.3098	+	55.9622i	1.23180	+	2.13354i
$689$	−5.47596			−0.208618
$690$	−57.2435	+	8.90597i	−2.17922	+	0.339044i
$691$		−	7.11745i		−	0.270761i	−0.990794	−	0.135380i	$-0.956774\pi$
$691$		−	7.11745i		−	0.270761i	0.990794	−	0.135380i	$-0.0432256\pi$
$692$	−101.535			−3.85977
$693$		0			0
$694$	−33.9426			−1.28844
$695$		−	32.5095i		−	1.23315i
$696$	19.0614	−	49.2533i	0.722519	−	1.86694i
$697$	38.1335			1.44441
$698$	−1.56569	−	2.71186i	−0.0592624	−	0.102645i
$699$	−4.05622	−	26.0715i	−0.153420	−	0.986115i
$700$		0			0
$701$			29.4609i			1.11272i	0.830940	+	0.556362i	$0.187803\pi$
$701$			29.4609i			1.11272i	−0.830940	+	0.556362i	$0.812197\pi$
$702$	−1.07115	+	17.6631i	−0.0404281	+	0.666651i
$703$	−1.76433	+	1.01863i	−0.0665428	+	0.0384185i
$704$	−12.8019	−	7.39117i	−0.482489	−	0.278565i
$705$	0.719266	−	1.85853i	0.0270891	−	0.0699964i
$706$	−59.8894	−	34.5772i	−2.25397	−	1.30133i
$707$		0			0
$708$	21.7781	+	27.0447i	0.818471	+	1.01640i
$709$	−38.0722			−1.42983			−0.714916	−	0.699211i	$-0.753535\pi$
$709$	−38.0722			−1.42983			−0.714916	+	0.699211i	$0.753535\pi$
$710$	−3.52112	−	6.09875i	−0.132145	−	0.228882i
$711$	6.78721	−	31.0935i	0.254540	−	1.16610i
$712$	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
$716$	−69.1795	+	39.9408i	−2.58536	+	1.49266i
$717$	−1.52232	−	9.78479i	−0.0568522	−	0.365420i
$718$	9.60408	−	16.6348i	0.358421	−	0.620803i
$719$	−19.1057	+	33.0921i	−0.712523	+	1.23413i	0.251385	+	0.967887i	$0.419114\pi$
$719$	−19.1057	+	33.0921i	−0.712523	+	1.23413i	−0.963907	+	0.266238i	$0.914219\pi$
$720$	−55.3278	+	17.6429i	−2.06195	+	0.657512i
$721$		0			0
$722$	41.4045	−	23.9049i	1.54091	−	0.889647i
$723$	1.19053	+	7.65218i	0.0442763	+	0.284588i
$724$		−	77.3562i		−	2.87492i
$725$			1.95565i			0.0726309i
$726$	−33.5775	−	12.9947i	−1.24618	−	0.482280i
$727$	17.7563	−	10.2516i	0.658546	−	0.380212i	−0.133177	−	0.991092i	$-0.542518\pi$
$727$	17.7563	−	10.2516i	0.658546	−	0.380212i	0.791723	+	0.610881i	$0.209184\pi$
$728$		0			0
$729$	16.2267	−	21.5800i	0.600989	−	0.799257i
$730$	−45.4372	+	78.6995i	−1.68170	+	2.91280i
$731$	22.5222	−	39.0096i	0.833014	−	1.44282i
$732$	12.8607	−	10.3562i	0.475344	−	0.382777i
$733$	−0.900627	+	0.519977i	−0.0332654	+	0.0192058i	−0.516540	−	0.856263i	$-0.672780\pi$
$733$	−0.900627	+	0.519977i	−0.0332654	+	0.0192058i	0.483275	+	0.875469i	$0.339447\pi$
$734$	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
$738$	34.3131	−	37.6917i	1.26308	−	1.38745i
$739$	−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	$0.979912\pi$
$740$	32.6892			1.20168
$741$	0.557665	−	1.44097i	0.0204863	−	0.0529353i
$742$		0			0
$743$	−13.1637	−	7.60008i	−0.482930	−	0.278820i	0.238707	−	0.971092i	$-0.423277\pi$
$743$	−13.1637	−	7.60008i	−0.482930	−	0.278820i	−0.721637	+	0.692272i	$0.756610\pi$
$744$	−29.7886	−	36.9923i	−1.09210	−	1.35620i
$745$	22.0810	+	12.7485i	0.808987	+	0.467069i
$746$	−67.2045	+	38.8005i	−2.46053	+	1.42059i
$747$	30.4359	−	9.70540i	1.11359	−	0.355102i
$748$			117.406i			4.29281i
$749$		0			0
$750$	−37.0023	+	29.7966i	−1.35113	+	1.08802i
$751$	−1.52037	−	2.63336i	−0.0554791	−	0.0960926i	0.836952	−	0.547276i	$-0.184335\pi$
$751$	−1.52037	−	2.63336i	−0.0554791	−	0.0960926i	−0.892431	+	0.451184i	$0.851002\pi$
$752$	−4.09591			−0.149362
$753$	−12.6302	−	15.6846i	−0.460271	−	0.571579i
$754$		−	15.2153i		−	0.554107i
$755$	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	$0.211036\pi$
$758$		−	69.8680i		−	2.53772i
$759$	26.3869	+	32.7680i	0.957782	+	1.18940i
$760$	10.7479			0.389869
$761$	14.6319	+	25.3432i	0.530406	+	0.918690i	0.999371	+	0.0354731i	$0.0112938\pi$
$761$	14.6319	+	25.3432i	0.530406	+	0.918690i	−0.468965	+	0.883217i	$0.655373\pi$
$762$	57.6350	−	46.4113i	2.08790	−	1.68131i
$763$		0			0
$764$		−	4.43367i		−	0.160405i
$765$	29.9344	+	27.2512i	1.08228	+	0.985269i
$766$	−8.17266	+	4.71849i	−0.295290	+	0.170486i
$767$	4.93487	+	2.84915i	0.178188	+	0.102877i
$768$	−26.3354	−	32.7041i	−0.950298	−	1.18011i
$769$	29.6496	+	17.1182i	1.06919	+	0.617299i	0.927961	−	0.372678i	$-0.121560\pi$
$769$	29.6496	+	17.1182i	1.06919	+	0.617299i	0.141232	+	0.989977i	$0.454894\pi$
$770$		0			0
$771$	−1.31453	+	3.39666i	−0.0473418	+	0.122328i
$772$	7.87405			0.283393
$773$	16.9927	+	29.4322i	0.611185	+	1.05860i	0.991041	+	0.133558i	$0.0426403\pi$
$773$	16.9927	+	29.4322i	0.611185	+	1.05860i	−0.379856	+	0.925046i	$0.624026\pi$
$774$	−18.2918	−	57.3627i	−0.657485	−	2.06186i
$775$	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
$779$	−3.85435	+	2.22531i	−0.138096	+	0.0797299i
$780$	−19.3098	+	15.5495i	−0.691403	+	0.556761i
$781$	−2.55710	+	4.42904i	−0.0915004	+	0.158483i
$782$	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
$786$	29.6508	+	11.4751i	1.05761	+	0.409302i
$787$			27.5078i			0.980549i	0.871568	+	0.490274i	$0.163103\pi$
$787$			27.5078i			0.980549i	−0.871568	+	0.490274i	$0.836897\pi$
$788$			59.2439i			2.11048i
$789$	0.586555	+	3.77011i	0.0208819	+	0.134219i
$790$	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
$794$	−34.5144	+	59.7807i	−1.22487	+	2.12154i
$795$	2.57410	+	16.5451i	0.0912937	+	0.586794i
$796$	−17.5390	+	10.1262i	−0.621654	+	0.358912i
$797$	−21.0873	+	36.5243i	−0.746952	+	1.29376i	0.202326	+	0.979318i	$0.435150\pi$
$797$	−21.0873	+	36.5243i	−0.746952	+	1.29376i	−0.949277	+	0.314440i	$0.898183\pi$
$798$		0			0
$799$	1.42757	+	2.47262i	0.0505038	+	0.0874751i
$800$	−2.93888	−	1.69676i	−0.103905	−	0.0599896i
$801$	−7.37701	−	6.71576i	−0.260654	−	0.237290i
$802$	−9.96458	−	17.2592i	−0.351861	−	0.609442i
$803$	65.9947			2.32890
$804$	24.3546	+	30.2443i	0.858922	+	1.06664i
$805$		0			0
$806$	−11.8500	−	6.84160i	−0.417398	−	0.240985i
$807$	−17.4177	+	45.0061i	−0.613132	+	1.58429i
$808$	9.83594	+	5.67878i	0.346027	+	0.199779i
$809$	4.18377	−	2.41550i	0.147094	−	0.0849245i	−0.424647	−	0.905359i	$-0.639602\pi$
$809$	4.18377	−	2.41550i	0.147094	−	0.0849245i	0.571740	+	0.820435i	$0.306268\pi$
$810$	53.8709	−	5.06653i	1.89283	−	0.178020i
$811$			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
$814$	−16.9782	−	29.4071i	−0.595086	−	1.03072i
$815$	15.7765			0.552625
$816$	30.0286	−	77.5919i	1.05121	−	2.71626i
$817$			5.25720i			0.183926i
$818$	−23.3597			−0.816751
$819$		0			0
$820$	71.4128			2.49384
$821$			16.7957i			0.586172i	0.956086	+	0.293086i	$0.0946823\pi$
$821$			16.7957i			0.586172i	−0.956086	+	0.293086i	$0.905318\pi$
$822$	−3.65106	+	0.568034i	−0.127345	+	0.0198124i
$823$	−15.0350			−0.524087			−0.262043	−	0.965056i	$-0.584396\pi$
$823$	−15.0350			−0.524087			−0.262043	+	0.965056i	$0.584396\pi$
$824$	5.54719	+	9.60802i	0.193246	+	0.334711i
$825$	−3.08702	−	1.19470i	−0.107476	−	0.0415940i
$826$		0			0
$827$		−	29.2462i		−	1.01699i	−0.861065	−	0.508495i	$-0.830202\pi$
$827$		−	29.2462i		−	1.01699i	0.861065	−	0.508495i	$-0.169798\pi$
$828$	−23.5632	−	73.8939i	−0.818879	−	2.56799i
$829$	−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	$0.341649\pi$
$830$	55.4433	+	32.0102i	1.92446	+	1.11109i
$831$	17.4569	−	2.71596i	0.605574	−	0.0942155i
$832$	3.87301	+	2.23608i	0.134272	+	0.0775222i
$833$		0			0
$834$	61.5155	−	9.57061i	2.13011	−	0.331403i
$835$	44.5219			1.54075
$836$	−6.85135	−	11.8669i	−0.236959	−	0.410425i
$837$	9.32534	+	18.6795i	0.322331	+	0.645660i
$838$	−14.7572	−	8.52005i	−0.509778	−	0.294320i
$839$	22.9477	+	39.7466i	0.792243	+	1.37221i	0.924575	+	0.381000i	$0.124420\pi$
$839$	22.9477	+	39.7466i	0.792243	+	1.37221i	−0.132331	+	0.991206i	$0.542246\pi$
$840$		0			0
$841$	−4.51923	+	7.82753i	−0.155835	+	0.269915i
$842$	−28.5443	+	16.4800i	−0.983701	+	0.567940i
$843$	17.6282	+	6.82225i	0.607149	+	0.234971i
$844$	10.4266	−	18.0593i	0.358897	−	0.621628i
$845$	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
$849$	16.0082	−	12.8908i	0.549401	−	0.442412i
$850$			6.53023i			0.223985i
$851$			16.7822i			0.575288i
$852$	7.34328	−	5.91327i	0.251577	−	0.202585i
$853$	24.3086	−	14.0346i	0.832310	−	0.480534i	−0.0223330	−	0.999751i	$-0.507109\pi$
$853$	24.3086	−	14.0346i	0.832310	−	0.480534i	0.854643	+	0.519216i	$0.173776\pi$
$854$		0			0
$855$	−4.61589	−	1.00757i	−0.157860	−	0.0344583i
$856$	62.4905	−	108.237i	2.13588	−	3.69946i
$857$	8.55426	−	14.8164i	0.292208	−	0.506119i	−0.682123	−	0.731237i	$-0.738943\pi$
$857$	8.55426	−	14.8164i	0.292208	−	0.506119i	0.974332	+	0.225118i	$0.0722767\pi$
$858$	24.0175	+	9.29495i	0.819945	+	0.317325i
$859$	4.50996	−	2.60383i	0.153878	−	0.0888414i	−0.421084	−	0.907022i	$-0.638350\pi$
$859$	4.50996	−	2.60383i	0.153878	−	0.0888414i	0.574962	+	0.818180i	$0.305017\pi$
$860$	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	0.983378	−	0.181573i	$-0.0581187\pi$
$863$	38.7134	+	22.3512i	1.31782	+	0.760844i	0.334442	+	0.942416i	$0.391452\pi$
$864$	−17.9936	−	36.0428i	−0.612153	−	1.22620i
$865$	25.4749	+	44.1238i	0.866172	+	1.50025i
$866$	−21.1716			−0.719442
$867$	−28.2120	+	4.38923i	−0.958129	+	0.149066i
$868$		0			0
$869$	−40.1124	−	23.1589i	−1.36072	−	0.785613i
$870$	−45.9714	+	7.15226i	−1.55858	+	0.242484i
$871$	5.51871	+	3.18623i	0.186994	+	0.107961i
$872$	94.4096	−	54.5074i	3.19711	−	1.84585i
$873$	−13.4216	−	42.0898i	−0.454251	−	1.42452i
$874$			9.68688i			0.327664i
$875$		0			0
$876$	−113.462	−	43.9108i	−3.83354	−	1.48361i
$877$	2.87432	+	4.97846i	0.0970587	+	0.168111i	0.910466	−	0.413584i	$-0.135723\pi$
$877$	2.87432	+	4.97846i	0.0970587	+	0.168111i	−0.813407	+	0.581695i	$0.802390\pi$
$878$	−97.6457			−3.29538
$879$	32.6893	−	5.08582i	1.10258	−	0.171540i
$880$			84.5167i			2.84906i
$881$	−9.98120			−0.336275			−0.168138	−	0.985764i	$-0.553775\pi$
$881$	−9.98120			−0.336275			−0.168138	+	0.985764i	$0.553775\pi$
$882$		0			0
$883$	−32.0942			−1.08006			−0.540028	−	0.841647i	$-0.681586\pi$
$883$	−32.0942			−1.08006			−0.540028	+	0.841647i	$0.681586\pi$
$884$		−	35.5195i		−	1.19465i
$885$	6.28869	−	16.2495i	0.211392	−	0.546222i
$886$	−52.7561			−1.77238
$887$	−4.26812	−	7.39260i	−0.143309	−	0.248219i	0.785432	−	0.618949i	$-0.212441\pi$
$887$	−4.26812	−	7.39260i	−0.143309	−	0.248219i	−0.928741	+	0.370729i	$0.879108\pi$
$888$	5.48177	+	35.2343i	0.183956	+	1.18239i
$889$		0			0
$890$		−	19.9922i		−	0.670141i
$891$	−22.7475	−	32.0410i	−0.762070	−	1.07341i
$892$	−83.6498	+	48.2952i	−2.80080	+	1.61704i
$893$	−0.288584	−	0.166614i	−0.00965709	−	0.00557552i
$894$	−17.6226	+	45.5356i	−0.589387	+	1.52294i
$895$	34.7140	+	20.0422i	1.16036	+	0.669935i
$896$		0			0
$897$	−7.98293	−	9.91344i	−0.266542	−	0.331000i
$898$	−92.0554			−3.07193
$899$	−8.97579	−	15.5465i	−0.299359	−	0.518505i
$900$	4.51249	+	4.10801i	0.150416	+	0.136934i
$901$	−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
$905$	−33.6166	+	19.4085i	−1.11745	+	0.645162i
$906$	9.57355	+	61.5344i	0.318060	+	2.04434i
$907$	−16.0272	+	27.7599i	−0.532175	+	0.921754i	0.467120	+	0.884194i	$0.345292\pi$
$907$	−16.0272	+	27.7599i	−0.532175	+	0.921754i	−0.999294	+	0.0375597i	$0.988042\pi$
$908$	−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	0.00413539	−	0.999991i	$-0.498684\pi$
$911$	26.3261	−	15.1994i	0.872221	−	0.503577i	0.868086	+	0.496414i	$0.165350\pi$
$912$	1.49279	+	9.59495i	0.0494311	+	0.317721i
$913$		−	46.4928i		−	1.53869i
$914$		−	0.655324i		−	0.0216762i
$915$	−7.72721	−	2.99049i	−0.255454	−	0.0988624i
$916$	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	$0.0737772\pi$
$920$	44.2687	−	76.6757i	1.45950	−	2.52792i
$921$	−3.17681	+	2.55817i	−0.104680	+	0.0842946i
$922$	54.5580	−	31.4991i	1.79677	−	1.03737i
$923$	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
$927$	−1.48163	−	4.64636i	−0.0486631	−	0.152606i
$928$	17.3191	+	29.9975i	0.568527	+	0.984717i
$929$	10.4278			0.342126			0.171063	−	0.985260i	$-0.445280\pi$
$929$	10.4278			0.342126			0.171063	+	0.985260i	$0.445280\pi$
$930$	−15.1009	+	39.0197i	−0.495178	+	1.27951i
$931$		0			0
$932$	61.3070	+	35.3956i	2.00818	+	1.15942i
$933$	−8.52731	−	10.5895i	−0.279172	−	0.346684i
$934$	4.06199	+	2.34519i	0.132912	+	0.0767369i
$935$	51.0212	−	29.4571i	1.66857	−	0.963350i
$936$	−19.9983	−	18.2057i	−0.653664	−	0.595072i
$937$		−	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
$940$	2.67342	+	4.63049i	0.0871973	+	0.151030i
$941$	49.3347			1.60827			0.804133	−	0.594450i	$-0.202630\pi$
$941$	49.3347			1.60827			0.804133	+	0.594450i	$0.202630\pi$
$942$	−44.1901	−	54.8766i	−1.43979	−	1.78798i
$943$			36.6625i			1.19389i
$944$	−35.8114			−1.16556
$945$		0			0
$946$	−87.6252			−2.84894
$947$		−	43.9327i		−	1.42762i	−0.700339	−	0.713810i	$-0.746968\pi$
$947$		−	43.9327i		−	1.42762i	0.700339	−	0.713810i	$-0.253032\pi$
$948$	53.5547	+	66.5059i	1.73938	+	2.16001i
$949$	−19.9657			−0.648113
$950$	−0.381076	−	0.660044i	−0.0123637	−	0.0214146i
$951$	14.9839	−	12.0660i	0.485886	−	0.391266i
$952$		0			0
$953$		−	21.0833i		−	0.682956i	−0.939890	−	0.341478i	$-0.889072\pi$
$953$		−	21.0833i		−	0.682956i	0.939890	−	0.341478i	$-0.110928\pi$
$954$	−30.5494	+	9.74157i	−0.989073	+	0.315395i
$955$	−1.92673	+	1.11240i	−0.0623477	+	0.0359964i
$956$	23.0089	+	13.2842i	0.744161	+	0.429641i
$957$	21.1909	+	26.3155i	0.685005	+	0.850660i
$958$	−3.04138	−	1.75594i	−0.0982625	−	0.0567319i
$959$		0			0
$960$	4.93552	−	12.7530i	0.159293	−	0.411603i
$961$	14.8560			0.479226
$962$	5.13650	+	8.89667i	0.165607	+	0.286840i
$963$	−36.9844	+	40.6259i	−1.19180	+	1.30915i
$964$	−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	−0.0495039	+	0.998774i	$0.515764\pi$
$967$	−27.6671	+	47.9209i	−0.889716	+	1.54103i	−0.840212	+	0.542259i	$0.817569\pi$
$968$	47.6533	−	27.5127i	1.53164	−	0.884290i
$969$	5.27200	−	4.24535i	0.169361	−	0.136380i
$970$	44.2668	−	76.6723i	1.42132	−	2.46180i
$971$	−3.41733	+	5.91898i	−0.109667	+	0.189949i	−0.915635	−	0.402010i	$-0.868312\pi$
$971$	−3.41733	+	5.91898i	−0.109667	+	0.189949i	0.805968	+	0.591959i	$0.201645\pi$
$972$	17.7900	+	70.2225i	0.570613	+	2.25239i
$973$		0			0
$974$	70.5830	−	40.7511i	2.26162	−	1.30575i
$975$	0.933929	+	0.361437i	0.0299097	+	0.0115753i
$976$			17.0295i			0.545102i
$977$		−	36.0246i		−	1.15253i	−0.817264	−	0.576264i	$-0.804510\pi$
$977$		−	36.0246i		−	1.15253i	0.817264	−	0.576264i	$-0.195490\pi$
$978$	4.64450	+	29.8527i	0.148515	+	0.954585i
$979$	−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
$983$	20.6863	−	35.8298i	0.659791	−	1.14279i	−0.320878	−	0.947120i	$-0.603978\pi$
$983$	20.6863	−	35.8298i	0.659791	−	1.14279i	0.980670	−	0.195671i	$-0.0626886\pi$
$984$	11.9755	+	76.9728i	0.381764	+	2.45380i
$985$	25.7455	−	14.8642i	0.820321	−	0.473612i
$986$	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
$990$	16.7939	−	76.9360i	0.533744	−	2.44519i
$991$	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	$0.721470\pi$
$992$	31.1504			0.989025
$993$	−18.7579	−	23.2941i	−0.595263	−	0.739216i
$994$		0			0
$995$	8.80102	+	5.08127i	0.279011	+	0.161087i
$996$	−30.9348	+	79.9335i	−0.980208	+	2.53279i
$997$	11.8699	+	6.85308i	0.375923	+	0.217039i	0.676043	−	0.736862i	$-0.263693\pi$
$997$	11.8699	+	6.85308i	0.375923	+	0.217039i	−0.300120	+	0.953901i	$0.597027\pi$
$998$	60.3721	−	34.8559i	1.91105	−	1.10334i
$999$	0.948821	−	15.6459i	0.0300194	−	0.495013i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.i.d.68.24		48
3.2	odd	2		1323.2.i.d.1097.2		48
7.2	even	3		441.2.o.e.293.23	yes	48
7.3	odd	6		441.2.s.d.374.1		48
7.4	even	3		441.2.s.d.374.2		48
7.5	odd	6		441.2.o.e.293.24	yes	48
7.6	odd	2	inner	441.2.i.d.68.23		48
9.2	odd	6		441.2.s.d.362.1		48
9.7	even	3		1323.2.s.d.656.24		48
21.2	odd	6		1323.2.o.e.881.2		48
21.5	even	6		1323.2.o.e.881.1		48
21.11	odd	6		1323.2.s.d.962.23		48
21.17	even	6		1323.2.s.d.962.24		48
21.20	even	2		1323.2.i.d.1097.14		48
63.2	odd	6		441.2.o.e.146.24	yes	48
63.11	odd	6	inner	441.2.i.d.227.1		48
63.16	even	3		1323.2.o.e.440.1		48
63.20	even	6		441.2.s.d.362.2		48
63.25	even	3		1323.2.i.d.521.14		48
63.34	odd	6		1323.2.s.d.656.23		48
63.38	even	6	inner	441.2.i.d.227.2		48
63.47	even	6		441.2.o.e.146.23	✓	48
63.52	odd	6		1323.2.i.d.521.2		48
63.61	odd	6		1323.2.o.e.440.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.23		48	7.6	odd	2	inner
441.2.i.d.68.24		48	1.1	even	1	trivial
441.2.i.d.227.1		48	63.11	odd	6	inner
441.2.i.d.227.2		48	63.38	even	6	inner
441.2.o.e.146.23	✓	48	63.47	even	6
441.2.o.e.146.24	yes	48	63.2	odd	6
441.2.o.e.293.23	yes	48	7.2	even	3
441.2.o.e.293.24	yes	48	7.5	odd	6
441.2.s.d.362.1		48	9.2	odd	6
441.2.s.d.362.2		48	63.20	even	6
441.2.s.d.374.1		48	7.3	odd	6
441.2.s.d.374.2		48	7.4	even	3
1323.2.i.d.521.2		48	63.52	odd	6
1323.2.i.d.521.14		48	63.25	even	3
1323.2.i.d.1097.2		48	3.2	odd	2
1323.2.i.d.1097.14		48	21.20	even	2
1323.2.o.e.440.1		48	63.16	even	3
1323.2.o.e.440.2		48	63.61	odd	6
1323.2.o.e.881.1		48	21.5	even	6
1323.2.o.e.881.2		48	21.2	odd	6
1323.2.s.d.656.23		48	63.34	odd	6
1323.2.s.d.656.24		48	9.7	even	3
1323.2.s.d.962.23		48	21.11	odd	6
1323.2.s.d.962.24		48	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.57819i q^{2} +(1.08633 + 1.34903i) q^{3} -4.64709 q^{4} +(1.16595 + 2.01948i) q^{5} +(-3.47807 + 2.80076i) q^{6} -6.82470i q^{8} +(-0.639786 + 2.93099i) q^{9} +(-5.20660 + 3.00603i) q^{10} +(3.78114 + 2.18304i) q^{11} +(-5.04826 - 6.26908i) q^{12} +(-1.14392 - 0.660445i) q^{13} +(-1.45774 + 3.76671i) q^{15} +8.30123 q^{16} +(-2.89327 - 5.01130i) q^{17} +(-7.55665 - 1.64949i) q^{18} +(0.584876 + 0.337678i) q^{19} +(-5.41825 - 9.38468i) q^{20} +(-5.62830 + 9.74851i) q^{22} +(4.81799 - 2.78167i) q^{23} +(9.20675 - 7.41386i) q^{24} +(-0.218858 + 0.379074i) q^{25} +(1.70276 - 2.94926i) q^{26} +(-4.64902 + 2.32092i) q^{27} +(3.86926 - 2.23392i) q^{29} +(-9.71132 - 3.75835i) q^{30} -4.01796i q^{31} +7.75278i q^{32} +(1.16256 + 7.47238i) q^{33} +(12.9201 - 7.45942i) q^{34} +(2.97314 - 13.6205i) q^{36} +(-1.50829 + 2.61243i) q^{37} +(-0.870601 + 1.50792i) q^{38} +(-0.351713 - 2.26065i) q^{39} +(13.7823 - 7.95723i) q^{40} +(-3.29501 + 5.70713i) q^{41} +(3.89217 + 6.74143i) q^{43} +(-17.5713 - 10.1448i) q^{44} +(-6.66501 + 2.12534i) q^{45} +(7.17168 + 12.4217i) q^{46} -0.493410 q^{47} +(9.01785 + 11.1986i) q^{48} +(-0.977326 - 0.564259i) q^{50} +(3.61737 - 9.34703i) q^{51} +(5.31591 + 3.06914i) q^{52} +(3.59025 - 2.07283i) q^{53} +(-5.98377 - 11.9861i) q^{54} +10.1812i q^{55} +(0.179827 + 1.15585i) q^{57} +(5.75947 + 9.97570i) q^{58} -4.31398 q^{59} +(6.77426 - 17.5042i) q^{60} +2.05145i q^{61} +10.3591 q^{62} -3.38572 q^{64} -3.08017i q^{65} +(-19.2652 + 2.99730i) q^{66} -4.82437 q^{67} +(13.4453 + 23.2879i) q^{68} +(8.98648 + 3.47783i) q^{69} +1.17135i q^{71} +(20.0031 + 4.36635i) q^{72} +(13.0902 - 7.55766i) q^{73} +(-6.73536 - 3.88866i) q^{74} +(-0.749135 + 0.116551i) q^{75} +(-2.71797 - 1.56922i) q^{76} +(5.82840 - 0.906785i) q^{78} -10.6086 q^{79} +(9.67878 + 16.7641i) q^{80} +(-8.18135 - 3.75041i) q^{81} +(-14.7141 - 8.49518i) q^{82} +(-5.32432 - 9.22199i) q^{83} +(6.74680 - 11.6858i) q^{85} +(-17.3807 + 10.0348i) q^{86} +(7.21691 + 2.79300i) q^{87} +(14.8986 - 25.8051i) q^{88} +(-1.66268 + 2.87984i) q^{89} +(-5.47953 - 17.1837i) q^{90} +(-22.3896 + 12.9266i) q^{92} +(5.42036 - 4.36482i) q^{93} -1.27211i q^{94} +1.57486i q^{95} +(-10.4588 + 8.42206i) q^{96} +(-12.7531 + 7.36299i) q^{97} +(-8.81758 + 9.68578i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} - 8 q^{9} + 24 q^{11} - 40 q^{15} + 48 q^{16} - 16 q^{18} + 48 q^{23} - 24 q^{25} - 24 q^{30} - 8 q^{36} - 56 q^{39} - 96 q^{44} + 48 q^{50} - 24 q^{51} - 48 q^{53} + 80 q^{57} + 168 q^{60}+ \cdots - 72 q^{99}+O(q^{100}) \) 48 * q - 48 * q^4 - 8 * q^9 + 24 * q^11 - 40 * q^15 + 48 * q^16 - 16 * q^18 + 48 * q^23 - 24 * q^25 - 24 * q^30 - 8 * q^36 - 56 * q^39 - 96 * q^44 + 48 * q^50 - 24 * q^51 - 48 * q^53 + 80 * q^57 + 168 * q^60 - 48 * q^64 - 88 * q^72 + 168 * q^74 - 88 * q^78 + 48 * q^79 - 24 * q^81 - 24 * q^85 - 24 * q^86 - 144 * q^92 + 16 * q^93 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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