LMFDB - Embedded newform 1470.2.d.g.1469.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(1469,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1470.1469");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.d (of order $2$, degree $1$, 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:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1469.20
Character	$\chi$	$=$	1470.1469
Dual form			1470.2.d.g.1469.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(1.29908 + 1.14560i) q^{3} +1.00000 q^{4} +(1.07275 + 1.96194i) q^{5} +(-1.29908 - 1.14560i) q^{6} -1.00000 q^{8} +(0.375199 + 2.97645i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(1.29908 + 1.14560i) q^{3} +1.00000 q^{4} +(1.07275 + 1.96194i) q^{5} +(-1.29908 - 1.14560i) q^{6} -1.00000 q^{8} +(0.375199 + 2.97645i) q^{9} +(-1.07275 - 1.96194i) q^{10} +0.115731i q^{11} +(1.29908 + 1.14560i) q^{12} -5.60599 q^{13} +(-0.854024 + 3.77765i) q^{15} +1.00000 q^{16} +1.39249i q^{17} +(-0.375199 - 2.97645i) q^{18} -1.52338i q^{19} +(1.07275 + 1.96194i) q^{20} -0.115731i q^{22} -6.58658 q^{23} +(-1.29908 - 1.14560i) q^{24} +(-2.69843 + 4.20933i) q^{25} +5.60599 q^{26} +(-2.92240 + 4.29646i) q^{27} +8.97567i q^{29} +(0.854024 - 3.77765i) q^{30} -7.15923i q^{31} -1.00000 q^{32} +(-0.132582 + 0.150344i) q^{33} -1.39249i q^{34} +(0.375199 + 2.97645i) q^{36} -1.70914i q^{37} +1.52338i q^{38} +(-7.28261 - 6.42223i) q^{39} +(-1.07275 - 1.96194i) q^{40} -3.82458 q^{41} +12.1163i q^{43} +0.115731i q^{44} +(-5.43712 + 3.92909i) q^{45} +6.58658 q^{46} -2.37293i q^{47} +(1.29908 + 1.14560i) q^{48} +(2.69843 - 4.20933i) q^{50} +(-1.59524 + 1.80895i) q^{51} -5.60599 q^{52} +10.2924 q^{53} +(2.92240 - 4.29646i) q^{54} +(-0.227058 + 0.124150i) q^{55} +(1.74518 - 1.97898i) q^{57} -8.97567i q^{58} -3.32689 q^{59} +(-0.854024 + 3.77765i) q^{60} +5.12186i q^{61} +7.15923i q^{62} +1.00000 q^{64} +(-6.01380 - 10.9986i) q^{65} +(0.132582 - 0.150344i) q^{66} +0.689946i q^{67} +1.39249i q^{68} +(-8.55647 - 7.54559i) q^{69} -6.77657i q^{71} +(-0.375199 - 2.97645i) q^{72} +11.1144 q^{73} +1.70914i q^{74} +(-8.32768 + 2.37691i) q^{75} -1.52338i q^{76} +(7.28261 + 6.42223i) q^{78} +14.3964 q^{79} +(1.07275 + 1.96194i) q^{80} +(-8.71845 + 2.23352i) q^{81} +3.82458 q^{82} +6.24996i q^{83} +(-2.73198 + 1.49379i) q^{85} -12.1163i q^{86} +(-10.2825 + 11.6601i) q^{87} -0.115731i q^{88} -6.83525 q^{89} +(5.43712 - 3.92909i) q^{90} -6.58658 q^{92} +(8.20162 - 9.30039i) q^{93} +2.37293i q^{94} +(2.98878 - 1.63420i) q^{95} +(-1.29908 - 1.14560i) q^{96} -16.3461 q^{97} +(-0.344467 + 0.0434222i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} + 24 q^{4} - 24 q^{8} + 8 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 + 24 * q^4 - 24 * q^8 + 8 * q^9	$ 24 q - 24 q^{2} + 24 q^{4} - 24 q^{8} + 8 q^{9} + 24 q^{16} - 8 q^{18} - 16 q^{23} + 8 q^{25} - 24 q^{32} + 8 q^{36} + 16 q^{39} + 16 q^{46} - 8 q^{50} + 16 q^{51} + 16 q^{53} + 16 q^{57} + 24 q^{64} - 48 q^{65} - 8 q^{72} - 16 q^{78} - 48 q^{79} - 24 q^{81} + 16 q^{85} - 16 q^{92} + 64 q^{93} - 112 q^{95} - 64 q^{99}+O(q^{100}) $ 24 * q - 24 * q^2 + 24 * q^4 - 24 * q^8 + 8 * q^9 + 24 * q^16 - 8 * q^18 - 16 * q^23 + 8 * q^25 - 24 * q^32 + 8 * q^36 + 16 * q^39 + 16 * q^46 - 8 * q^50 + 16 * q^51 + 16 * q^53 + 16 * q^57 + 24 * q^64 - 48 * q^65 - 8 * q^72 - 16 * q^78 - 48 * q^79 - 24 * q^81 + 16 * q^85 - 16 * q^92 + 64 * q^93 - 112 * q^95 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	1.29908	+	1.14560i	0.750022	+	0.661413i
$3$	1.29908	+	1.14560i	0.750022	+	0.661413i
$4$	1.00000			0.500000
$5$	1.07275	+	1.96194i	0.479746	+	0.877407i
$5$	1.07275	+	1.96194i	0.479746	+	0.877407i
$6$	−1.29908	−	1.14560i	−0.530346	−	0.467689i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	0.375199	+	2.97645i	0.125066	+	0.992148i
$10$	−1.07275	−	1.96194i	−0.339232	−	0.620421i
$11$			0.115731i			0.0348942i	0.999848	+	0.0174471i	$0.00555387\pi$
$11$			0.115731i			0.0348942i	−0.999848	+	0.0174471i	$0.994446\pi$
$12$	1.29908	+	1.14560i	0.375011	+	0.330706i
$13$	−5.60599			−1.55482			−0.777411	−	0.628993i	$-0.783467\pi$
$13$	−5.60599			−1.55482			−0.777411	+	0.628993i	$0.783467\pi$
$14$		0			0
$15$	−0.854024	+	3.77765i	−0.220508	+	0.975385i
$16$	1.00000			0.250000
$17$			1.39249i			0.337728i	0.985639	+	0.168864i	$0.0540099\pi$
$17$			1.39249i			0.337728i	−0.985639	+	0.168864i	$0.945990\pi$
$18$	−0.375199	−	2.97645i	−0.0884353	−	0.701555i
$19$		−	1.52338i		−	0.349487i	−0.984614	−	0.174743i	$-0.944090\pi$
$19$		−	1.52338i		−	0.349487i	0.984614	−	0.174743i	$-0.0559095\pi$
$20$	1.07275	+	1.96194i	0.239873	+	0.438704i
$21$		0			0
$22$		−	0.115731i		−	0.0246740i
$23$	−6.58658			−1.37340			−0.686698	−	0.726943i	$-0.740941\pi$
$23$	−6.58658			−1.37340			−0.686698	+	0.726943i	$0.740941\pi$
$24$	−1.29908	−	1.14560i	−0.265173	−	0.233845i
$25$	−2.69843	+	4.20933i	−0.539687	+	0.841866i
$26$	5.60599			1.09943
$27$	−2.92240	+	4.29646i	−0.562417	+	0.826854i
$28$		0			0
$29$			8.97567i			1.66674i	0.552716	+	0.833370i	$0.313592\pi$
$29$			8.97567i			1.66674i	−0.552716	+	0.833370i	$0.686408\pi$
$30$	0.854024	−	3.77765i	0.155923	−	0.689701i
$31$		−	7.15923i		−	1.28584i	−0.765935	−	0.642918i	$-0.777724\pi$
$31$		−	7.15923i		−	1.28584i	0.765935	−	0.642918i	$-0.222276\pi$
$32$	−1.00000			−0.176777
$33$	−0.132582	+	0.150344i	−0.0230795	+	0.0261715i
$34$		−	1.39249i		−	0.238810i
$35$		0			0
$36$	0.375199	+	2.97645i	0.0625332	+	0.496074i
$37$		−	1.70914i		−	0.280981i	−0.990082	−	0.140490i	$-0.955132\pi$
$37$		−	1.70914i		−	0.280981i	0.990082	−	0.140490i	$-0.0448679\pi$
$38$			1.52338i			0.247124i
$39$	−7.28261	−	6.42223i	−1.16615	−	1.02838i
$40$	−1.07275	−	1.96194i	−0.169616	−	0.310210i
$41$	−3.82458			−0.597300			−0.298650	−	0.954363i	$-0.596536\pi$
$41$	−3.82458			−0.597300			−0.298650	+	0.954363i	$0.596536\pi$
$42$		0			0
$43$			12.1163i			1.84772i	0.382725	+	0.923862i	$0.374986\pi$
$43$			12.1163i			1.84772i	−0.382725	+	0.923862i	$0.625014\pi$
$44$			0.115731i			0.0174471i
$45$	−5.43712	+	3.92909i	−0.810518	+	0.585714i
$46$	6.58658			0.971138
$47$		−	2.37293i		−	0.346128i	−0.984911	−	0.173064i	$-0.944633\pi$
$47$		−	2.37293i		−	0.346128i	0.984911	−	0.173064i	$-0.0553667\pi$
$48$	1.29908	+	1.14560i	0.187506	+	0.165353i
$49$		0			0
$50$	2.69843	−	4.20933i	0.381616	−	0.595289i
$51$	−1.59524	+	1.80895i	−0.223378	+	0.253304i
$52$	−5.60599			−0.777411
$53$	10.2924			1.41377			0.706884	−	0.707329i	$-0.250100\pi$
$53$	10.2924			1.41377			0.706884	+	0.707329i	$0.250100\pi$
$54$	2.92240	−	4.29646i	0.397689	−	0.584674i
$55$	−0.227058	+	0.124150i	−0.0306165	+	0.0167404i
$56$		0			0
$57$	1.74518	−	1.97898i	0.231155	−	0.262123i
$58$		−	8.97567i		−	1.17856i
$59$	−3.32689			−0.433124			−0.216562	−	0.976269i	$-0.569484\pi$
$59$	−3.32689			−0.433124			−0.216562	+	0.976269i	$0.569484\pi$
$60$	−0.854024	+	3.77765i	−0.110254	+	0.487693i
$61$			5.12186i			0.655787i	0.944715	+	0.327893i	$0.106339\pi$
$61$			5.12186i			0.655787i	−0.944715	+	0.327893i	$0.893661\pi$
$62$			7.15923i			0.909223i
$63$		0			0
$64$	1.00000			0.125000
$65$	−6.01380	−	10.9986i	−0.745920	−	1.36421i
$66$	0.132582	−	0.150344i	0.0163197	−	0.0185060i
$67$			0.689946i			0.0842903i	0.999111	+	0.0421452i	$0.0134192\pi$
$67$			0.689946i			0.0842903i	−0.999111	+	0.0421452i	$0.986581\pi$
$68$			1.39249i			0.168864i
$69$	−8.55647	−	7.54559i	−1.03008	−	0.908382i
$70$		0			0
$71$		−	6.77657i		−	0.804231i	−0.915589	−	0.402115i	$-0.868275\pi$
$71$		−	6.77657i		−	0.804231i	0.915589	−	0.402115i	$-0.131725\pi$
$72$	−0.375199	−	2.97645i	−0.0442176	−	0.350777i
$73$	11.1144			1.30085			0.650423	−	0.759572i	$-0.274592\pi$
$73$	11.1144			1.30085			0.650423	+	0.759572i	$0.274592\pi$
$74$			1.70914i			0.198684i
$75$	−8.32768	+	2.37691i	−0.961598	+	0.274462i
$76$		−	1.52338i		−	0.174743i
$77$		0			0
$78$	7.28261	+	6.42223i	0.824593	+	0.727174i
$79$	14.3964			1.61972			0.809858	−	0.586625i	$-0.199544\pi$
$79$	14.3964			1.61972			0.809858	+	0.586625i	$0.199544\pi$
$80$	1.07275	+	1.96194i	0.119937	+	0.219352i
$81$	−8.71845	+	2.23352i	−0.968717	+	0.248169i
$82$	3.82458			0.422355
$83$			6.24996i			0.686022i	0.939331	+	0.343011i	$0.111447\pi$
$83$			6.24996i			0.686022i	−0.939331	+	0.343011i	$0.888553\pi$
$84$		0			0
$85$	−2.73198	+	1.49379i	−0.296325	+	0.162024i
$86$		−	12.1163i		−	1.30654i
$87$	−10.2825	+	11.6601i	−1.10240	+	1.25009i
$88$		−	0.115731i		−	0.0123370i
$89$	−6.83525			−0.724535			−0.362267	−	0.932074i	$-0.617997\pi$
$89$	−6.83525			−0.724535			−0.362267	+	0.932074i	$0.617997\pi$
$90$	5.43712	−	3.92909i	0.573123	−	0.414162i
$91$		0			0
$92$	−6.58658			−0.686698
$93$	8.20162	−	9.30039i	0.850468	−	0.964405i
$94$			2.37293i			0.244749i
$95$	2.98878	−	1.63420i	0.306642	−	0.167665i
$96$	−1.29908	−	1.14560i	−0.132586	−	0.116922i
$97$	−16.3461			−1.65969			−0.829845	−	0.557994i	$-0.811571\pi$
$97$	−16.3461			−1.65969			−0.829845	+	0.557994i	$0.811571\pi$
$98$		0			0
$99$	−0.344467	+	0.0434222i	−0.0346203	+	0.00436410i
$100$	−2.69843	+	4.20933i	−0.269843	+	0.420933i
$101$	9.06786			0.902286			0.451143	−	0.892452i	$-0.351016\pi$
$101$	9.06786			0.902286			0.451143	+	0.892452i	$0.351016\pi$
$102$	1.59524	−	1.80895i	0.157952	−	0.179113i
$103$	12.5117			1.23282			0.616409	−	0.787427i	$-0.288587\pi$
$103$	12.5117			1.23282			0.616409	+	0.787427i	$0.288587\pi$
$104$	5.60599			0.549713
$105$		0			0
$106$	−10.2924			−0.999685
$107$	−3.99362			−0.386078			−0.193039	−	0.981191i	$-0.561834\pi$
$107$	−3.99362			−0.386078			−0.193039	+	0.981191i	$0.561834\pi$
$108$	−2.92240	+	4.29646i	−0.281209	+	0.413427i
$109$	5.70919			0.546841			0.273421	−	0.961895i	$-0.411845\pi$
$109$	5.70919			0.546841			0.273421	+	0.961895i	$0.411845\pi$
$110$	0.227058	−	0.124150i	0.0216491	−	0.0118372i
$111$	1.95799	−	2.22030i	0.185844	−	0.210742i
$112$		0			0
$113$	7.34715			0.691162			0.345581	−	0.938389i	$-0.387682\pi$
$113$	7.34715			0.691162			0.345581	+	0.938389i	$0.387682\pi$
$114$	−1.74518	+	1.97898i	−0.163451	+	0.185349i
$115$	−7.06572	−	12.9225i	−0.658882	−	1.20503i
$116$			8.97567i			0.833370i
$117$	−2.10336	−	16.6859i	−0.194456	−	1.54261i
$118$	3.32689			0.306265
$119$		0			0
$120$	0.854024	−	3.77765i	0.0779613	−	0.344851i
$121$	10.9866			0.998782
$122$		−	5.12186i		−	0.463711i
$123$	−4.96843	−	4.38145i	−0.447988	−	0.395062i
$124$		−	7.15923i		−	0.642918i
$125$	−11.1532	−	0.778634i	−0.997572	−	0.0696431i
$126$		0			0
$127$		−	11.4466i		−	1.01572i	−0.861440	−	0.507859i	$-0.830437\pi$
$127$		−	11.4466i		−	1.01572i	0.861440	−	0.507859i	$-0.169563\pi$
$128$	−1.00000			−0.0883883
$129$	−13.8805	+	15.7400i	−1.22211	+	1.38583i
$130$	6.01380	+	10.9986i	0.527445	+	0.964644i
$131$	−16.7557			−1.46396			−0.731978	−	0.681328i	$-0.761403\pi$
$131$	−16.7557			−1.46396			−0.731978	+	0.681328i	$0.761403\pi$
$132$	−0.132582	+	0.150344i	−0.0115397	+	0.0130857i
$133$		0			0
$134$		−	0.689946i		−	0.0596023i
$135$	−11.5644	−	1.12458i	−0.995305	−	0.0967887i
$136$		−	1.39249i		−	0.119405i
$137$	−8.35228			−0.713584			−0.356792	−	0.934184i	$-0.616129\pi$
$137$	−8.35228			−0.713584			−0.356792	+	0.934184i	$0.616129\pi$
$138$	8.55647	+	7.54559i	0.728375	+	0.642323i
$139$			5.96744i			0.506151i	0.967446	+	0.253076i	$0.0814422\pi$
$139$			5.96744i			0.506151i	−0.967446	+	0.253076i	$0.918558\pi$
$140$		0			0
$141$	2.71843	−	3.08262i	0.228933	−	0.259603i
$142$			6.77657i			0.568677i
$143$		−	0.648788i		−	0.0542543i
$144$	0.375199	+	2.97645i	0.0312666	+	0.248037i
$145$	−17.6097	+	9.62861i	−1.46241	+	0.799612i
$146$	−11.1144			−0.919837
$147$		0			0
$148$		−	1.70914i		−	0.140490i
$149$			15.9414i			1.30597i	0.757372	+	0.652984i	$0.226483\pi$
$149$			15.9414i			1.30597i	−0.757372	+	0.652984i	$0.773517\pi$
$150$	8.32768	−	2.37691i	0.679952	−	0.194074i
$151$	15.9786			1.30032			0.650162	−	0.759796i	$-0.274701\pi$
$151$	15.9786			1.30032			0.650162	+	0.759796i	$0.274701\pi$
$152$			1.52338i			0.123562i
$153$	−4.14467	+	0.522460i	−0.335076	+	0.0422384i
$154$		0			0
$155$	14.0460	−	7.68003i	1.12820	−	0.616875i
$156$	−7.28261	−	6.42223i	−0.583075	−	0.514190i
$157$	−5.20320			−0.415260			−0.207630	−	0.978207i	$-0.566575\pi$
$157$	−5.20320			−0.415260			−0.207630	+	0.978207i	$0.566575\pi$
$158$	−14.3964			−1.14531
$159$	13.3706	+	11.7910i	1.06036	+	0.935085i
$160$	−1.07275	−	1.96194i	−0.0848080	−	0.155105i
$161$		0			0
$162$	8.71845	−	2.23352i	0.684986	−	0.175482i
$163$			15.4578i			1.21075i	0.795941	+	0.605374i	$0.206976\pi$
$163$			15.4578i			1.21075i	−0.795941	+	0.605374i	$0.793024\pi$
$164$	−3.82458			−0.298650
$165$	−0.437192	−	0.0988371i	−0.0340353	−	0.00769446i
$166$		−	6.24996i		−	0.485091i
$167$		−	6.80860i		−	0.526865i	−0.964678	−	0.263433i	$-0.915145\pi$
$167$		−	6.80860i		−	0.526865i	0.964678	−	0.263433i	$-0.0848547\pi$
$168$		0			0
$169$	18.4271			1.41747
$170$	2.73198	−	1.49379i	0.209533	−	0.114568i
$171$	4.53425	−	0.571569i	0.346742	−	0.0437090i
$172$			12.1163i			0.923862i
$173$			1.30728i			0.0993909i	0.998764	+	0.0496954i	$0.0158251\pi$
$173$			1.30728i			0.0993909i	−0.998764	+	0.0496954i	$0.984175\pi$
$174$	10.2825	−	11.6601i	0.779517	−	0.883948i
$175$		0			0
$176$			0.115731i			0.00872356i
$177$	−4.32188	−	3.81129i	−0.324853	−	0.286474i
$178$	6.83525			0.512323
$179$		−	1.03424i		−	0.0773026i	−0.999253	−	0.0386513i	$-0.987694\pi$
$179$		−	1.03424i		−	0.0773026i	0.999253	−	0.0386513i	$-0.0123062\pi$
$180$	−5.43712	+	3.92909i	−0.405259	+	0.292857i
$181$			22.8296i			1.69691i	0.529265	+	0.848457i	$0.322468\pi$
$181$			22.8296i			1.69691i	−0.529265	+	0.848457i	$0.677532\pi$
$182$		0			0
$183$	−5.86761	+	6.65369i	−0.433746	+	0.491855i
$184$	6.58658			0.485569
$185$	3.35323	−	1.83347i	0.246535	−	0.134800i
$186$	−8.20162	+	9.30039i	−0.601372	+	0.681938i
$187$	−0.161154			−0.0117848
$188$		−	2.37293i		−	0.173064i
$189$		0			0
$190$	−2.98878	+	1.63420i	−0.216829	+	0.118557i
$191$			11.8242i			0.855570i	0.903881	+	0.427785i	$0.140706\pi$
$191$			11.8242i			0.855570i	−0.903881	+	0.427785i	$0.859294\pi$
$192$	1.29908	+	1.14560i	0.0937528	+	0.0826766i
$193$			4.35205i			0.313267i	0.987657	+	0.156634i	$0.0500642\pi$
$193$			4.35205i			0.313267i	−0.987657	+	0.156634i	$0.949936\pi$
$194$	16.3461			1.17358
$195$	4.78765	−	21.1775i	0.342851	−	1.51655i
$196$		0			0
$197$	−17.2157			−1.22657			−0.613284	−	0.789862i	$-0.710152\pi$
$197$	−17.2157			−1.22657			−0.613284	+	0.789862i	$0.710152\pi$
$198$	0.344467	−	0.0434222i	0.0244802	−	0.00308588i
$199$		−	2.62215i		−	0.185880i	−0.995672	−	0.0929398i	$-0.970374\pi$
$199$		−	2.62215i		−	0.185880i	0.995672	−	0.0929398i	$-0.0296264\pi$
$200$	2.69843	−	4.20933i	0.190808	−	0.297645i
$201$	−0.790403	+	0.896293i	−0.0557507	+	0.0632196i
$202$	−9.06786			−0.638012
$203$		0			0
$204$	−1.59524	+	1.80895i	−0.111689	+	0.126652i
$205$	−4.10281	−	7.50361i	−0.286552	−	0.524075i
$206$	−12.5117			−0.871733
$207$	−2.47128	−	19.6046i	−0.171766	−	1.36261i
$208$	−5.60599			−0.388706
$209$	0.176302			0.0121951
$210$		0			0
$211$	−24.9808			−1.71975			−0.859873	−	0.510507i	$-0.829458\pi$
$211$	−24.9808			−1.71975			−0.859873	+	0.510507i	$0.829458\pi$
$212$	10.2924			0.706884
$213$	7.76324	−	8.80328i	0.531929	−	0.603191i
$214$	3.99362			0.272998
$215$	−23.7716	+	12.9977i	−1.62121	+	0.886439i
$216$	2.92240	−	4.29646i	0.198844	−	0.292337i
$217$		0			0
$218$	−5.70919			−0.386675
$219$	14.4385	+	12.7327i	0.975663	+	0.860396i
$220$	−0.227058	+	0.124150i	−0.0153082	+	0.00837019i
$221$		−	7.80628i		−	0.525107i
$222$	−1.95799	+	2.22030i	−0.131412	+	0.149017i
$223$	3.33467			0.223306			0.111653	−	0.993747i	$-0.464386\pi$
$223$	3.33467			0.223306			0.111653	+	0.993747i	$0.464386\pi$
$224$		0			0
$225$	−13.5413	−	6.45241i	−0.902752	−	0.430160i
$226$	−7.34715			−0.488725
$227$		−	19.5117i		−	1.29504i	−0.762050	−	0.647519i	$-0.775807\pi$
$227$		−	19.5117i		−	1.29504i	0.762050	−	0.647519i	$-0.224193\pi$
$228$	1.74518	−	1.97898i	0.115577	−	0.131061i
$229$		−	28.1753i		−	1.86188i	−0.365175	−	0.930939i	$-0.618991\pi$
$229$		−	28.1753i		−	1.86188i	0.365175	−	0.930939i	$-0.381009\pi$
$230$	7.06572	+	12.9225i	0.465900	+	0.852083i
$231$		0			0
$232$		−	8.97567i		−	0.589282i
$233$	−1.61616			−0.105878			−0.0529390	−	0.998598i	$-0.516859\pi$
$233$	−1.61616			−0.105878			−0.0529390	+	0.998598i	$0.516859\pi$
$234$	2.10336	+	16.6859i	0.137501	+	1.09079i
$235$	4.65555	−	2.54555i	0.303695	−	0.166053i
$236$	−3.32689			−0.216562
$237$	18.7020	+	16.4925i	1.21482	+	1.07130i
$238$		0			0
$239$			17.8576i			1.15511i	0.816352	+	0.577555i	$0.195993\pi$
$239$			17.8576i			1.15511i	−0.816352	+	0.577555i	$0.804007\pi$
$240$	−0.854024	+	3.77765i	−0.0551270	+	0.243846i
$241$			13.8552i			0.892491i	0.894910	+	0.446246i	$0.147239\pi$
$241$			13.8552i			0.892491i	−0.894910	+	0.446246i	$0.852761\pi$
$242$	−10.9866			−0.706246
$243$	−13.8847	−	7.08635i	−0.890701	−	0.454590i
$244$			5.12186i			0.327893i
$245$		0			0
$246$	4.96843	+	4.38145i	0.316775	+	0.279351i
$247$			8.54003i			0.543389i
$248$			7.15923i			0.454612i
$249$	−7.15995	+	8.11917i	−0.453744	+	0.514532i
$250$	11.1532	+	0.778634i	0.705390	+	0.0492451i
$251$	23.0104			1.45241			0.726203	−	0.687480i	$-0.241283\pi$
$251$	23.0104			1.45241			0.726203	+	0.687480i	$0.241283\pi$
$252$		0			0
$253$		−	0.762272i		−	0.0479236i
$254$			11.4466i			0.718221i
$255$	−5.26033	−	1.18922i	−0.329415	−	0.0744717i
$256$	1.00000			0.0625000
$257$			10.3913i			0.648192i	0.946024	+	0.324096i	$0.105060\pi$
$257$			10.3913i			0.648192i	−0.946024	+	0.324096i	$0.894940\pi$
$258$	13.8805	−	15.7400i	0.864161	−	0.979933i
$259$		0			0
$260$	−6.01380	−	10.9986i	−0.372960	−	0.682106i
$261$	−26.7156	+	3.36766i	−1.65365	+	0.208453i
$262$	16.7557			1.03517
$263$	25.2467			1.55678			0.778389	−	0.627783i	$-0.216037\pi$
$263$	25.2467			1.55678			0.778389	+	0.627783i	$0.216037\pi$
$264$	0.132582	−	0.150344i	0.00815983	−	0.00925301i
$265$	11.0411	+	20.1931i	0.678250	+	1.24045i
$266$		0			0
$267$	−8.87951	−	7.83046i	−0.543417	−	0.479216i
$268$			0.689946i			0.0421452i
$269$	−30.3714			−1.85178			−0.925888	−	0.377797i	$-0.876682\pi$
$269$	−30.3714			−1.85178			−0.925888	+	0.377797i	$0.876682\pi$
$270$	11.5644	+	1.12458i	0.703787	+	0.0684400i
$271$			17.3027i			1.05106i	0.850775	+	0.525531i	$0.176133\pi$
$271$			17.3027i			1.05106i	−0.850775	+	0.525531i	$0.823867\pi$
$272$			1.39249i			0.0844320i
$273$		0			0
$274$	8.35228			0.504580
$275$	−0.487150	−	0.312293i	−0.0293763	−	0.0188320i
$276$	−8.55647	−	7.54559i	−0.515039	−	0.454191i
$277$		−	12.4130i		−	0.745825i	−0.927867	−	0.372912i	$-0.878359\pi$
$277$		−	12.4130i		−	0.745825i	0.927867	−	0.372912i	$-0.121641\pi$
$278$		−	5.96744i		−	0.357903i
$279$	21.3091	−	2.68614i	1.27574	−	0.160815i
$280$		0			0
$281$			4.53857i			0.270748i	0.990795	+	0.135374i	$0.0432236\pi$
$281$			4.53857i			0.270748i	−0.990795	+	0.135374i	$0.956776\pi$
$282$	−2.71843	+	3.08262i	−0.161880	+	0.183567i
$283$	9.80557			0.582881			0.291440	−	0.956589i	$-0.405865\pi$
$283$	9.80557			0.582881			0.291440	+	0.956589i	$0.405865\pi$
$284$		−	6.77657i		−	0.402115i
$285$	5.75478	+	1.30100i	0.340884	+	0.0770646i
$286$			0.648788i			0.0383636i
$287$		0			0
$288$	−0.375199	−	2.97645i	−0.0221088	−	0.175389i
$289$	15.0610			0.885940
$290$	17.6097	−	9.62861i	1.03408	−	0.565411i
$291$	−21.2348	−	18.7260i	−1.24480	−	1.09774i
$292$	11.1144			0.650423
$293$		−	26.6749i		−	1.55836i	−0.626799	−	0.779181i	$-0.715635\pi$
$293$		−	26.6749i		−	1.55836i	0.626799	−	0.779181i	$-0.284365\pi$
$294$		0			0
$295$	−3.56891	−	6.52717i	−0.207790	−	0.380026i
$296$			1.70914i			0.0993418i
$297$	−0.497234	−	0.338213i	−0.0288524	−	0.0196251i
$298$		−	15.9414i		−	0.923459i
$299$	36.9243			2.13539
$300$	−8.32768	+	2.37691i	−0.480799	+	0.137231i
$301$		0			0
$302$	−15.9786			−0.919468
$303$	11.7798	+	10.3881i	0.676734	+	0.596783i
$304$		−	1.52338i		−	0.0873716i
$305$	−10.0488	+	5.49445i	−0.575392	+	0.314611i
$306$	4.14467	−	0.522460i	0.236935	−	0.0298671i
$307$	23.3482			1.33255			0.666275	−	0.745706i	$-0.267888\pi$
$307$	23.3482			1.33255			0.666275	+	0.745706i	$0.267888\pi$
$308$		0			0
$309$	16.2537	+	14.3334i	0.924640	+	0.815401i
$310$	−14.0460	+	7.68003i	−0.797759	+	0.436197i
$311$	26.3635			1.49494			0.747468	−	0.664298i	$-0.231270\pi$
$311$	26.3635			1.49494			0.747468	+	0.664298i	$0.231270\pi$
$312$	7.28261	+	6.42223i	0.412297	+	0.363587i
$313$	−9.15989			−0.517748			−0.258874	−	0.965911i	$-0.583351\pi$
$313$	−9.15989			−0.517748			−0.258874	+	0.965911i	$0.583351\pi$
$314$	5.20320			0.293633
$315$		0			0
$316$	14.3964			0.809858
$317$	28.5498			1.60351			0.801757	−	0.597650i	$-0.203899\pi$
$317$	28.5498			1.60351			0.801757	+	0.597650i	$0.203899\pi$
$318$	−13.3706	−	11.7910i	−0.749786	−	0.661205i
$319$	−1.03876			−0.0581596
$320$	1.07275	+	1.96194i	0.0599683	+	0.109676i
$321$	−5.18802	−	4.57509i	−0.289567	−	0.255357i
$322$		0			0
$323$	2.12128			0.118031
$324$	−8.71845	+	2.23352i	−0.484358	+	0.124084i
$325$	15.1274	−	23.5975i	0.839117	−	1.30895i
$326$		−	15.4578i		−	0.856128i
$327$	7.41668	+	6.54045i	0.410143	+	0.361688i
$328$	3.82458			0.211177
$329$		0			0
$330$	0.437192	+	0.0988371i	0.0240666	+	0.00544080i
$331$	−4.29752			−0.236213			−0.118107	−	0.993001i	$-0.537682\pi$
$331$	−4.29752			−0.236213			−0.118107	+	0.993001i	$0.537682\pi$
$332$			6.24996i			0.343011i
$333$	5.08716	−	0.641268i	0.278775	−	0.0351413i
$334$			6.80860i			0.372550i
$335$	−1.35363	+	0.740137i	−0.0739570	+	0.0404380i
$336$		0			0
$337$		−	10.9814i		−	0.598196i	−0.954222	−	0.299098i	$-0.903314\pi$
$337$		−	10.9814i		−	0.598196i	0.954222	−	0.299098i	$-0.0966857\pi$
$338$	−18.4271			−1.00230
$339$	9.54451	+	8.41690i	0.518386	+	0.457143i
$340$	−2.73198	+	1.49379i	−0.148163	+	0.0810119i
$341$	0.828546			0.0448683
$342$	−4.53425	+	0.571569i	−0.245184	+	0.0309069i
$343$		0			0
$344$		−	12.1163i		−	0.653269i
$345$	5.62509	−	24.8818i	0.302845	−	1.33959i
$346$		−	1.30728i		−	0.0702800i
$347$	−1.76157			−0.0945662			−0.0472831	−	0.998882i	$-0.515056\pi$
$347$	−1.76157			−0.0945662			−0.0472831	+	0.998882i	$0.515056\pi$
$348$	−10.2825	+	11.6601i	−0.551201	+	0.625046i
$349$			8.42636i			0.451053i	0.974237	+	0.225526i	$0.0724102\pi$
$349$			8.42636i			0.451053i	−0.974237	+	0.225526i	$0.927590\pi$
$350$		0			0
$351$	16.3830	−	24.0859i	0.874458	−	1.28561i
$352$		−	0.115731i		−	0.00616849i
$353$		−	19.0584i		−	1.01438i	−0.861835	−	0.507188i	$-0.830685\pi$
$353$		−	19.0584i		−	1.01438i	0.861835	−	0.507188i	$-0.169315\pi$
$354$	4.32188	+	3.81129i	0.229706	+	0.202568i
$355$	13.2952	−	7.26954i	0.705638	−	0.385827i
$356$	−6.83525			−0.362267
$357$		0			0
$358$			1.03424i			0.0546612i
$359$			21.9942i			1.16081i	0.814328	+	0.580405i	$0.197106\pi$
$359$			21.9942i			1.16081i	−0.814328	+	0.580405i	$0.802894\pi$
$360$	5.43712	−	3.92909i	0.286561	−	0.207081i
$361$	16.6793			0.877859
$362$		−	22.8296i		−	1.19990i
$363$	14.2724	+	12.5863i	0.749109	+	0.660607i
$364$		0			0
$365$	11.9230	+	21.8059i	0.624076	+	1.14137i
$366$	5.86761	−	6.65369i	0.306705	−	0.347794i
$367$	16.0333			0.836931			0.418465	−	0.908233i	$-0.362568\pi$
$367$	16.0333			0.836931			0.418465	+	0.908233i	$0.362568\pi$
$368$	−6.58658			−0.343349
$369$	−1.43498	−	11.3837i	−0.0747021	−	0.592610i
$370$	−3.35323	+	1.83347i	−0.174326	+	0.0953177i
$371$		0			0
$372$	8.20162	−	9.30039i	0.425234	−	0.482203i
$373$			15.5769i			0.806541i	0.915081	+	0.403270i	$0.132127\pi$
$373$			15.5769i			0.806541i	−0.915081	+	0.403270i	$0.867873\pi$
$374$	0.161154			0.00833309
$375$	−13.5968	−	13.7886i	−0.702138	−	0.712041i
$376$			2.37293i			0.122375i
$377$		−	50.3175i		−	2.59148i
$378$		0			0
$379$	7.30235			0.375097			0.187548	−	0.982255i	$-0.439946\pi$
$379$	7.30235			0.375097			0.187548	+	0.982255i	$0.439946\pi$
$380$	2.98878	−	1.63420i	0.153321	−	0.0838324i
$381$	13.1132	−	14.8700i	0.671809	−	0.761811i
$382$		−	11.8242i		−	0.604979i
$383$		−	15.8538i		−	0.810090i	−0.914297	−	0.405045i	$-0.867256\pi$
$383$		−	15.8538i		−	0.810090i	0.914297	−	0.405045i	$-0.132744\pi$
$384$	−1.29908	−	1.14560i	−0.0662932	−	0.0584612i
$385$		0			0
$386$		−	4.35205i		−	0.221513i
$387$	−36.0636	+	4.54604i	−1.83322	+	0.231088i
$388$	−16.3461			−0.829845
$389$			2.89083i			0.146571i	0.997311	+	0.0732855i	$0.0233484\pi$
$389$			2.89083i			0.146571i	−0.997311	+	0.0732855i	$0.976652\pi$
$390$	−4.78765	+	21.1775i	−0.242432	+	1.07236i
$391$		−	9.17173i		−	0.463834i
$392$		0			0
$393$	−21.7670	−	19.1954i	−1.09800	−	0.968279i
$394$	17.2157			0.867315
$395$	15.4436	+	28.2448i	0.777053	+	1.42115i
$396$	−0.344467	+	0.0434222i	−0.0173101	+	0.00218205i
$397$	10.5240			0.528183			0.264091	−	0.964498i	$-0.414928\pi$
$397$	10.5240			0.528183			0.264091	+	0.964498i	$0.414928\pi$
$398$			2.62215i			0.131437i
$399$		0			0
$400$	−2.69843	+	4.20933i	−0.134922	+	0.210466i
$401$		−	35.1257i		−	1.75409i	−0.480404	−	0.877047i	$-0.659510\pi$
$401$		−	35.1257i		−	1.75409i	0.480404	−	0.877047i	$-0.340490\pi$
$402$	0.790403	−	0.896293i	0.0394217	−	0.0447030i
$403$			40.1346i			1.99925i
$404$	9.06786			0.451143
$405$	−13.7347	−	14.7091i	−0.682483	−	0.730901i
$406$		0			0
$407$	0.197801			0.00980462
$408$	1.59524	−	1.80895i	0.0789759	−	0.0895563i
$409$			19.8638i			0.982202i	0.871103	+	0.491101i	$0.163405\pi$
$409$			19.8638i			0.982202i	−0.871103	+	0.491101i	$0.836595\pi$
$410$	4.10281	+	7.50361i	0.202623	+	0.370577i
$411$	−10.8503	−	9.56838i	−0.535204	−	0.471973i
$412$	12.5117			0.616409
$413$		0			0
$414$	2.47128	+	19.6046i	0.121457	+	0.963513i
$415$	−12.2621	+	6.70461i	−0.601921	+	0.329116i
$416$	5.60599			0.274856
$417$	−6.83630	+	7.75216i	−0.334775	+	0.379625i
$418$	−0.176302			−0.00862322
$419$	14.0283			0.685327			0.342664	−	0.939458i	$-0.388671\pi$
$419$	14.0283			0.685327			0.342664	+	0.939458i	$0.388671\pi$
$420$		0			0
$421$	15.8988			0.774859			0.387429	−	0.921899i	$-0.373363\pi$
$421$	15.8988			0.774859			0.387429	+	0.921899i	$0.373363\pi$
$422$	24.9808			1.21604
$423$	7.06290	−	0.890321i	0.343410	−	0.0432889i
$424$	−10.2924			−0.499843
$425$	−5.86144	−	3.75754i	−0.284322	−	0.182267i
$426$	−7.76324	+	8.80328i	−0.376130	+	0.426520i
$427$		0			0
$428$	−3.99362			−0.193039
$429$	0.743251	−	0.842825i	0.0358845	−	0.0406920i
$430$	23.7716	−	12.9977i	1.14637	−	0.626807i
$431$			9.78952i			0.471545i	0.971808	+	0.235772i	$0.0757620\pi$
$431$			9.78952i			0.471545i	−0.971808	+	0.235772i	$0.924238\pi$
$432$	−2.92240	+	4.29646i	−0.140604	+	0.206713i
$433$	−18.4072			−0.884595			−0.442298	−	0.896868i	$-0.645837\pi$
$433$	−18.4072			−0.884595			−0.442298	+	0.896868i	$0.645837\pi$
$434$		0			0
$435$	−33.9069	−	7.66543i	−1.62571	−	0.367529i
$436$	5.70919			0.273421
$437$			10.0338i			0.479984i
$438$	−14.4385	−	12.7327i	−0.689898	−	0.608392i
$439$		−	22.4392i		−	1.07096i	−0.844547	−	0.535482i	$-0.820130\pi$
$439$		−	22.4392i		−	1.07096i	0.844547	−	0.535482i	$-0.179870\pi$
$440$	0.227058	−	0.124150i	0.0108246	−	0.00591862i
$441$		0			0
$442$			7.80628i			0.371307i
$443$	31.3372			1.48888			0.744438	−	0.667692i	$-0.232717\pi$
$443$	31.3372			1.48888			0.744438	+	0.667692i	$0.232717\pi$
$444$	1.95799	−	2.22030i	0.0929222	−	0.105371i
$445$	−7.33248	−	13.4104i	−0.347593	−	0.635712i
$446$	−3.33467			−0.157901
$447$	−18.2624	+	20.7091i	−0.863784	+	0.979505i
$448$		0			0
$449$		−	6.53984i		−	0.308634i	−0.988021	−	0.154317i	$-0.950682\pi$
$449$		−	6.53984i		−	0.308634i	0.988021	−	0.154317i	$-0.0493177\pi$
$450$	13.5413	+	6.45241i	0.638342	+	0.304169i
$451$		−	0.442623i		−	0.0208423i
$452$	7.34715			0.345581
$453$	20.7575	+	18.3051i	0.975271	+	0.860051i
$454$			19.5117i			0.915729i
$455$		0			0
$456$	−1.74518	+	1.97898i	−0.0817256	+	0.0926743i
$457$			10.5360i			0.492855i	0.969161	+	0.246427i	$0.0792567\pi$
$457$			10.5360i			0.492855i	−0.969161	+	0.246427i	$0.920743\pi$
$458$			28.1753i			1.31655i
$459$	−5.98277	−	4.06941i	−0.279252	−	0.189944i
$460$	−7.06572	−	12.9225i	−0.329441	−	0.602514i
$461$	10.3034			0.479877			0.239939	−	0.970788i	$-0.422873\pi$
$461$	10.3034			0.479877			0.239939	+	0.970788i	$0.422873\pi$
$462$		0			0
$463$		−	41.3015i		−	1.91944i	−0.280956	−	0.959721i	$-0.590651\pi$
$463$		−	41.3015i		−	1.91944i	0.280956	−	0.959721i	$-0.409349\pi$
$464$			8.97567i			0.416685i
$465$	27.0451	+	6.11415i	1.25419	+	0.283537i
$466$	1.61616			0.0748671
$467$			14.3402i			0.663585i	0.943352	+	0.331792i	$0.107653\pi$
$467$			14.3402i			0.663585i	−0.943352	+	0.331792i	$0.892347\pi$
$468$	−2.10336	−	16.6859i	−0.0972280	−	0.771307i
$469$		0			0
$470$	−4.65555	+	2.54555i	−0.214745	+	0.117417i
$471$	−6.75935	−	5.96078i	−0.311454	−	0.274658i
$472$	3.32689			0.153133
$473$	−1.40224			−0.0644749
$474$	−18.7020	−	16.4925i	−0.859010	−	0.757525i
$475$	6.41239	+	4.11073i	0.294221	+	0.188613i
$476$		0			0
$477$	3.86170	+	30.6347i	0.176815	+	1.40267i
$478$		−	17.8576i		−	0.816786i
$479$	22.4434			1.02546			0.512732	−	0.858549i	$-0.328633\pi$
$479$	22.4434			1.02546			0.512732	+	0.858549i	$0.328633\pi$
$480$	0.854024	−	3.77765i	0.0389807	−	0.172425i
$481$			9.58143i			0.436875i
$482$		−	13.8552i		−	0.631087i
$483$		0			0
$484$	10.9866			0.499391
$485$	−17.5352	−	32.0700i	−0.796230	−	1.45622i
$486$	13.8847	+	7.08635i	0.629821	+	0.321443i
$487$			6.14199i			0.278320i	0.990270	+	0.139160i	$0.0444403\pi$
$487$			6.14199i			0.278320i	−0.990270	+	0.139160i	$0.955560\pi$
$488$		−	5.12186i		−	0.231856i
$489$	−17.7085	+	20.0809i	−0.800804	+	0.908088i
$490$		0			0
$491$		−	23.7049i		−	1.06979i	−0.844919	−	0.534894i	$-0.820352\pi$
$491$		−	23.7049i		−	1.06979i	0.844919	−	0.534894i	$-0.179648\pi$
$492$	−4.96843	−	4.38145i	−0.223994	−	0.197531i
$493$	−12.4985			−0.562905
$494$		−	8.54003i		−	0.384234i
$495$	−0.454718	−	0.629244i	−0.0204380	−	0.0282824i
$496$		−	7.15923i		−	0.321459i
$497$		0			0
$498$	7.15995	−	8.11917i	0.320845	−	0.363829i
$499$	4.46829			0.200028			0.100014	−	0.994986i	$-0.468111\pi$
$499$	4.46829			0.200028			0.100014	+	0.994986i	$0.468111\pi$
$500$	−11.1532	−	0.778634i	−0.498786	−	0.0348216i
$501$	7.79994	−	8.84489i	0.348475	−	0.395161i
$502$	−23.0104			−1.02701
$503$			31.7055i			1.41368i	0.707374	+	0.706839i	$0.249879\pi$
$503$			31.7055i			1.41368i	−0.707374	+	0.706839i	$0.750121\pi$
$504$		0			0
$505$	9.72750	+	17.7906i	0.432868	+	0.791672i
$506$			0.762272i			0.0338871i
$507$	23.9383	+	21.1101i	1.06314	+	0.937534i
$508$		−	11.4466i		−	0.507859i
$509$	11.4778			0.508744			0.254372	−	0.967107i	$-0.418131\pi$
$509$	11.4778			0.508744			0.254372	+	0.967107i	$0.418131\pi$
$510$	5.26033	+	1.18922i	0.232932	+	0.0526595i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	6.54512	+	4.45192i	0.288974	+	0.196557i
$514$		−	10.3913i		−	0.458341i
$515$	13.4219	+	24.5473i	0.591439	+	1.08168i
$516$	−13.8805	+	15.7400i	−0.611054	+	0.692917i
$517$	0.274622			0.0120779
$518$		0			0
$519$	−1.49762	+	1.69826i	−0.0657384	+	0.0745454i
$520$	6.01380	+	10.9986i	0.263723	+	0.482322i
$521$	−29.8994			−1.30992			−0.654958	−	0.755666i	$-0.727314\pi$
$521$	−29.8994			−1.30992			−0.654958	+	0.755666i	$0.727314\pi$
$522$	26.7156	−	3.36766i	1.16931	−	0.147399i
$523$	−12.5069			−0.546887			−0.273443	−	0.961888i	$-0.588163\pi$
$523$	−12.5069			−0.546887			−0.273443	+	0.961888i	$0.588163\pi$
$524$	−16.7557			−0.731978
$525$		0			0
$526$	−25.2467			−1.10081
$527$	9.96915			0.434263
$528$	−0.132582	+	0.150344i	−0.00576987	+	0.00654286i
$529$	20.3830			0.886218
$530$	−11.0411	−	20.1931i	−0.479595	−	0.877131i
$531$	−1.24825	−	9.90231i	−0.0541693	−	0.429723i
$532$		0			0
$533$	21.4406			0.928695
$534$	8.87951	+	7.83046i	0.384254	+	0.338857i
$535$	−4.28414	−	7.83525i	−0.185219	−	0.338747i
$536$		−	0.689946i		−	0.0298011i
$537$	1.18482	−	1.34355i	0.0511289	−	0.0579787i
$538$	30.3714			1.30940
$539$		0			0
$540$	−11.5644	−	1.12458i	−0.497652	−	0.0483944i
$541$	−32.4843			−1.39661			−0.698304	−	0.715802i	$-0.746062\pi$
$541$	−32.4843			−1.39661			−0.698304	+	0.715802i	$0.746062\pi$
$542$		−	17.3027i		−	0.743213i
$543$	−26.1536	+	29.6574i	−1.12236	+	1.27272i
$544$		−	1.39249i		−	0.0597024i
$545$	6.12451	+	11.2011i	0.262345	+	0.479803i
$546$		0			0
$547$			31.9508i			1.36612i	0.730363	+	0.683059i	$0.239351\pi$
$547$			31.9508i			1.36612i	−0.730363	+	0.683059i	$0.760649\pi$
$548$	−8.35228			−0.356792
$549$	−15.2449	+	1.92172i	−0.650638	+	0.0820169i
$550$	0.487150	+	0.312293i	0.0207722	+	0.0133162i
$551$	13.6733			0.582503
$552$	8.55647	+	7.54559i	0.364187	+	0.321161i
$553$		0			0
$554$			12.4130i			0.527378i
$555$	6.45654	+	1.45965i	0.274065	+	0.0619585i
$556$			5.96744i			0.253076i
$557$	−9.16988			−0.388540			−0.194270	−	0.980948i	$-0.562234\pi$
$557$	−9.16988			−0.388540			−0.194270	+	0.980948i	$0.562234\pi$
$558$	−21.3091	+	2.68614i	−0.902085	+	0.113713i
$559$		−	67.9241i		−	2.87288i
$560$		0			0
$561$	−0.209352	−	0.184618i	−0.00883883	−	0.00779459i
$562$		−	4.53857i		−	0.191448i
$563$			4.43363i			0.186855i	0.995626	+	0.0934277i	$0.0297824\pi$
$563$			4.43363i			0.186855i	−0.995626	+	0.0934277i	$0.970218\pi$
$564$	2.71843	−	3.08262i	0.114467	−	0.129802i
$565$	7.88162	+	14.4147i	0.331582	+	0.606430i
$566$	−9.80557			−0.412159
$567$		0			0
$568$			6.77657i			0.284339i
$569$			9.00597i			0.377550i	0.982020	+	0.188775i	$0.0604517\pi$
$569$			9.00597i			0.377550i	−0.982020	+	0.188775i	$0.939548\pi$
$570$	−5.75478	−	1.30100i	−0.241041	−	0.0544929i
$571$	−19.9709			−0.835755			−0.417878	−	0.908503i	$-0.637226\pi$
$571$	−19.9709			−0.835755			−0.417878	+	0.908503i	$0.637226\pi$
$572$		−	0.648788i		−	0.0271272i
$573$	−13.5458	+	15.3606i	−0.565885	+	0.641696i
$574$		0			0
$575$	17.7734	−	27.7251i	0.741204	−	1.15622i
$576$	0.375199	+	2.97645i	0.0156333	+	0.124019i
$577$	−25.4389			−1.05904			−0.529518	−	0.848299i	$-0.677627\pi$
$577$	−25.4389			−1.05904			−0.529518	+	0.848299i	$0.677627\pi$
$578$	−15.0610			−0.626454
$579$	−4.98571	+	5.65364i	−0.207199	+	0.234957i
$580$	−17.6097	+	9.62861i	−0.731205	+	0.399806i
$581$		0			0
$582$	21.2348	+	18.7260i	0.880210	+	0.776220i
$583$			1.19115i			0.0493324i
$584$	−11.1144			−0.459918
$585$	30.4804	−	22.0264i	1.26021	−	0.910681i
$586$			26.6749i			1.10193i
$587$		−	4.54732i		−	0.187688i	−0.995587	−	0.0938440i	$-0.970085\pi$
$587$		−	4.54732i		−	0.187688i	0.995587	−	0.0938440i	$-0.0299155\pi$
$588$		0			0
$589$	−10.9062			−0.449382
$590$	3.56891	+	6.52717i	0.146930	+	0.268719i
$591$	−22.3645	−	19.7223i	−0.919953	−	0.811268i
$592$		−	1.70914i		−	0.0702452i
$593$			10.0606i			0.413138i	0.978432	+	0.206569i	$0.0662297\pi$
$593$			10.0606i			0.413138i	−0.978432	+	0.206569i	$0.933770\pi$
$594$	0.497234	+	0.338213i	0.0204018	+	0.0138771i
$595$		0			0
$596$			15.9414i			0.652984i
$597$	3.00394	−	3.40638i	0.122943	−	0.139414i
$598$	−36.9243			−1.50995
$599$		−	9.29206i		−	0.379663i	−0.981817	−	0.189832i	$-0.939206\pi$
$599$		−	9.29206i		−	0.379663i	0.981817	−	0.189832i	$-0.0607942\pi$
$600$	8.32768	−	2.37691i	0.339976	−	0.0970370i
$601$		−	8.86899i		−	0.361774i	−0.983504	−	0.180887i	$-0.942103\pi$
$601$		−	8.86899i		−	0.361774i	0.983504	−	0.180887i	$-0.0578968\pi$
$602$		0			0
$603$	−2.05359	+	0.258867i	−0.0836285	+	0.0105419i
$604$	15.9786			0.650162
$605$	11.7858	+	21.5551i	0.479162	+	0.876339i
$606$	−11.7798	−	10.3881i	−0.478523	−	0.421990i
$607$	−12.3180			−0.499971			−0.249986	−	0.968250i	$-0.580426\pi$
$607$	−12.3180			−0.499971			−0.249986	+	0.968250i	$0.580426\pi$
$608$			1.52338i			0.0617811i
$609$		0			0
$610$	10.0488	−	5.49445i	0.406864	−	0.222464i
$611$			13.3026i			0.538167i
$612$	−4.14467	+	0.522460i	−0.167538	+	0.0211192i
$613$			37.2300i			1.50370i	0.659332	+	0.751852i	$0.270839\pi$
$613$			37.2300i			1.50370i	−0.659332	+	0.751852i	$0.729161\pi$
$614$	−23.3482			−0.942256
$615$	3.26629	−	14.4479i	0.131709	−	0.582597i
$616$		0			0
$617$	16.0744			0.647132			0.323566	−	0.946206i	$-0.395118\pi$
$617$	16.0744			0.647132			0.323566	+	0.946206i	$0.395118\pi$
$618$	−16.2537	−	14.3334i	−0.653819	−	0.576576i
$619$			14.7594i			0.593230i	0.954997	+	0.296615i	$0.0958578\pi$
$619$			14.7594i			0.593230i	−0.954997	+	0.296615i	$0.904142\pi$
$620$	14.0460	−	7.68003i	0.564101	−	0.308438i
$621$	19.2486	−	28.2990i	0.772422	−	1.13560i
$622$	−26.3635			−1.05708
$623$		0			0
$624$	−7.28261	−	6.42223i	−0.291538	−	0.257095i
$625$	−10.4369	−	22.7172i	−0.417476	−	0.908688i
$626$	9.15989			0.366103
$627$	0.229030	+	0.201972i	0.00914657	+	0.00806597i
$628$	−5.20320			−0.207630
$629$	2.37996			0.0948952
$630$		0			0
$631$	−16.1597			−0.643307			−0.321653	−	0.946857i	$-0.604239\pi$
$631$	−16.1597			−0.643307			−0.321653	+	0.946857i	$0.604239\pi$
$632$	−14.3964			−0.572656
$633$	−32.4519	−	28.6180i	−1.28985	−	1.13746i
$634$	−28.5498			−1.13386
$635$	22.4575	−	12.2792i	0.891198	−	0.487287i
$636$	13.3706	+	11.7910i	0.530179	+	0.467542i
$637$		0			0
$638$	1.03876			0.0411251
$639$	20.1701	−	2.54256i	0.797916	−	0.100582i
$640$	−1.07275	−	1.96194i	−0.0424040	−	0.0775526i
$641$			20.3494i			0.803752i	0.915694	+	0.401876i	$0.131642\pi$
$641$			20.3494i			0.803752i	−0.915694	+	0.401876i	$0.868358\pi$
$642$	5.18802	+	4.57509i	0.204755	+	0.180564i
$643$	−14.4935			−0.571569			−0.285784	−	0.958294i	$-0.592254\pi$
$643$	−14.4935			−0.571569			−0.285784	+	0.958294i	$0.592254\pi$
$644$		0			0
$645$	−45.7713	−	10.3476i	−1.80224	−	0.407438i
$646$	−2.12128			−0.0834608
$647$		−	37.3791i		−	1.46952i	−0.678325	−	0.734762i	$-0.737294\pi$
$647$		−	37.3791i		−	1.46952i	0.678325	−	0.734762i	$-0.262706\pi$
$648$	8.71845	−	2.23352i	0.342493	−	0.0877409i
$649$		−	0.385025i		−	0.0151135i
$650$	−15.1274	+	23.5975i	−0.593345	+	0.925569i
$651$		0			0
$652$			15.4578i			0.605374i
$653$	−13.7997			−0.540024			−0.270012	−	0.962857i	$-0.587028\pi$
$653$	−13.7997			−0.540024			−0.270012	+	0.962857i	$0.587028\pi$
$654$	−7.41668	−	6.54045i	−0.290015	−	0.255752i
$655$	−17.9746	−	32.8738i	−0.702327	−	1.28449i
$656$	−3.82458			−0.149325
$657$	4.17012	+	33.0815i	0.162692	+	1.29063i
$658$		0			0
$659$			34.0473i			1.32629i	0.748489	+	0.663147i	$0.230780\pi$
$659$			34.0473i			1.32629i	−0.748489	+	0.663147i	$0.769220\pi$
$660$	−0.437192	−	0.0988371i	−0.0170177	−	0.00384723i
$661$			26.9652i			1.04882i	0.851465	+	0.524412i	$0.175715\pi$
$661$			26.9652i			1.04882i	−0.851465	+	0.524412i	$0.824285\pi$
$662$	4.29752			0.167028
$663$	8.94287	−	10.1410i	0.347312	−	0.393842i
$664$		−	6.24996i		−	0.242545i
$665$		0			0
$666$	−5.08716	+	0.641268i	−0.197124	+	0.0248486i
$667$		−	59.1189i		−	2.28909i
$668$		−	6.80860i		−	0.263433i
$669$	4.33199	+	3.82020i	0.167484	+	0.147697i
$670$	1.35363	−	0.740137i	0.0522955	−	0.0285940i
$671$	−0.592759			−0.0228832
$672$		0			0
$673$		−	2.80953i		−	0.108300i	−0.998533	−	0.0541498i	$-0.982755\pi$
$673$		−	2.80953i		−	0.108300i	0.998533	−	0.0541498i	$-0.0172449\pi$
$674$			10.9814i			0.422988i
$675$	−10.1993	−	23.8951i	−0.392571	−	0.919722i
$676$	18.4271			0.708736
$677$			1.35867i			0.0522178i	0.999659	+	0.0261089i	$0.00831166\pi$
$677$			1.35867i			0.0522178i	−0.999659	+	0.0261089i	$0.991688\pi$
$678$	−9.54451	−	8.41690i	−0.366555	−	0.323249i
$679$		0			0
$680$	2.73198	−	1.49379i	0.104767	−	0.0572841i
$681$	22.3526	−	25.3472i	0.856554	−	0.971306i
$682$	−0.828546			−0.0317267
$683$	25.6509			0.981506			0.490753	−	0.871299i	$-0.336722\pi$
$683$	25.6509			0.981506			0.490753	+	0.871299i	$0.336722\pi$
$684$	4.53425	−	0.571569i	0.173371	−	0.0218545i
$685$	−8.95987	−	16.3867i	−0.342339	−	0.626104i
$686$		0			0
$687$	32.2777	−	36.6019i	1.23147	−	1.39645i
$688$			12.1163i			0.461931i
$689$	−57.6990			−2.19816
$690$	−5.62509	+	24.8818i	−0.214144	+	0.947234i
$691$		−	2.21555i		−	0.0842837i	−0.999112	−	0.0421418i	$-0.986582\pi$
$691$		−	2.21555i		−	0.0842837i	0.999112	−	0.0421418i	$-0.0134181\pi$
$692$			1.30728i			0.0496954i
$693$		0			0
$694$	1.76157			0.0668684
$695$	−11.7078	+	6.40154i	−0.444101	+	0.242824i
$696$	10.2825	−	11.6601i	0.389758	−	0.441974i
$697$		−	5.32569i		−	0.201725i
$698$		−	8.42636i		−	0.318942i
$699$	−2.09951	−	1.85147i	−0.0794108	−	0.0700291i
$700$		0			0
$701$			33.8049i			1.27680i	0.769707	+	0.638398i	$0.220402\pi$
$701$			33.8049i			1.27680i	−0.769707	+	0.638398i	$0.779598\pi$
$702$	−16.3830	+	24.0859i	−0.618335	+	0.909064i
$703$	−2.60366			−0.0981991
$704$			0.115731i			0.00436178i
$705$	8.96410	+	2.02654i	0.337608	+	0.0763239i
$706$			19.0584i			0.717272i
$707$		0			0
$708$	−4.32188	−	3.81129i	−0.162426	−	0.143237i
$709$	−25.5761			−0.960532			−0.480266	−	0.877123i	$-0.659460\pi$
$709$	−25.5761			−0.960532			−0.480266	+	0.877123i	$0.659460\pi$
$710$	−13.2952	+	7.26954i	−0.498961	+	0.272821i
$711$	5.40150	+	42.8500i	0.202572	+	1.60700i
$712$	6.83525			0.256162
$713$			47.1548i			1.76596i
$714$		0			0
$715$	1.27288	−	0.695984i	0.0476032	−	0.0260283i
$716$		−	1.03424i		−	0.0386513i
$717$	−20.4576	+	23.1983i	−0.764004	+	0.866358i
$718$		−	21.9942i		−	0.820816i
$719$	−11.9693			−0.446380			−0.223190	−	0.974775i	$-0.571647\pi$
$719$	−11.9693			−0.446380			−0.223190	+	0.974775i	$0.571647\pi$
$720$	−5.43712	+	3.92909i	−0.202630	+	0.146428i
$721$		0			0
$722$	−16.6793			−0.620740
$723$	−15.8725	+	17.9990i	−0.590305	+	0.669388i
$724$			22.8296i			0.848457i
$725$	−37.7815	−	24.2203i	−1.40317	−	0.899518i
$726$	−14.2724	−	12.5863i	−0.529700	−	0.467120i
$727$	4.55409			0.168902			0.0844509	−	0.996428i	$-0.473086\pi$
$727$	4.55409			0.168902			0.0844509	+	0.996428i	$0.473086\pi$
$728$		0			0
$729$	−9.91910	−	25.1120i	−0.367374	−	0.930073i
$730$	−11.9230	−	21.8059i	−0.441288	−	0.807071i
$731$	−16.8719			−0.624028
$732$	−5.86761	+	6.65369i	−0.216873	+	0.245927i
$733$	−1.52076			−0.0561706			−0.0280853	−	0.999606i	$-0.508941\pi$
$733$	−1.52076			−0.0561706			−0.0280853	+	0.999606i	$0.508941\pi$
$734$	−16.0333			−0.591800
$735$		0			0
$736$	6.58658			0.242784
$737$	−0.0798482			−0.00294125
$738$	1.43498	+	11.3837i	0.0528224	+	0.419039i
$739$	7.98264			0.293646			0.146823	−	0.989163i	$-0.453095\pi$
$739$	7.98264			0.293646			0.146823	+	0.989163i	$0.453095\pi$
$740$	3.35323	−	1.83347i	0.123267	−	0.0673998i
$741$	−9.78347	+	11.0942i	−0.359405	+	0.407554i
$742$		0			0
$743$	23.8272			0.874136			0.437068	−	0.899429i	$-0.356017\pi$
$743$	23.8272			0.874136			0.437068	+	0.899429i	$0.356017\pi$
$744$	−8.20162	+	9.30039i	−0.300686	+	0.340969i
$745$	−31.2760	+	17.1010i	−1.14587	+	0.626533i
$746$		−	15.5769i		−	0.570310i
$747$	−18.6027	+	2.34498i	−0.680636	+	0.0857983i
$748$	−0.161154			−0.00589238
$749$		0			0
$750$	13.5968	+	13.7886i	0.496487	+	0.503489i
$751$	35.3284			1.28915			0.644577	−	0.764540i	$-0.277034\pi$
$751$	35.3284			1.28915			0.644577	+	0.764540i	$0.277034\pi$
$752$		−	2.37293i		−	0.0865319i
$753$	29.8923	+	26.3608i	1.08934	+	0.960640i
$754$			50.3175i			1.83246i
$755$	17.1410	+	31.3492i	0.623825	+	1.14091i
$756$		0			0
$757$			44.6062i			1.62124i	0.585574	+	0.810619i	$0.300869\pi$
$757$			44.6062i			1.62124i	−0.585574	+	0.810619i	$0.699131\pi$
$758$	−7.30235			−0.265233
$759$	0.873259	−	0.990250i	0.0316973	−	0.0359438i
$760$	−2.98878	+	1.63420i	−0.108414	+	0.0592785i
$761$	−14.9794			−0.543004			−0.271502	−	0.962438i	$-0.587520\pi$
$761$	−14.9794			−0.543004			−0.271502	+	0.962438i	$0.587520\pi$
$762$	−13.1132	+	14.8700i	−0.475040	+	0.538681i
$763$		0			0
$764$			11.8242i			0.427785i
$765$	−5.47121	−	7.57113i	−0.197812	−	0.273735i
$766$			15.8538i			0.572820i
$767$	18.6505			0.673431
$768$	1.29908	+	1.14560i	0.0468764	+	0.0413383i
$769$		−	0.368578i		−	0.0132913i	−0.999978	−	0.00664564i	$-0.997885\pi$
$769$		−	0.368578i		−	0.0132913i	0.999978	−	0.00664564i	$-0.00211539\pi$
$770$		0			0
$771$	−11.9043	+	13.4991i	−0.428723	+	0.486159i
$772$			4.35205i			0.156634i
$773$			19.7918i			0.711862i	0.934512	+	0.355931i	$0.115836\pi$
$773$			19.7918i			0.711862i	−0.934512	+	0.355931i	$0.884164\pi$
$774$	36.0636	−	4.54604i	1.29628	−	0.163404i
$775$	30.1356	+	19.3187i	1.08250	+	0.693949i
$776$	16.3461			0.586789
$777$		0			0
$778$		−	2.89083i		−	0.103641i
$779$			5.82628i			0.208748i
$780$	4.78765	−	21.1775i	0.171425	−	0.758275i
$781$	0.784260			0.0280630
$782$			9.17173i			0.327981i
$783$	−38.5636	−	26.2305i	−1.37815	−	0.937403i
$784$		0			0
$785$	−5.58170	−	10.2084i	−0.199220	−	0.364352i
$786$	21.7670	+	19.1954i	0.776403	+	0.684677i
$787$	12.0023			0.427837			0.213918	−	0.976852i	$-0.431377\pi$
$787$	12.0023			0.427837			0.213918	+	0.976852i	$0.431377\pi$
$788$	−17.2157			−0.613284
$789$	32.7974	+	28.9226i	1.16762	+	1.02967i
$790$	−15.4436	−	28.2448i	−0.549460	−	1.00491i
$791$		0			0
$792$	0.344467	−	0.0434222i	0.0122401	−	0.00154294i
$793$		−	28.7131i		−	1.01963i
$794$	−10.5240			−0.373482
$795$	−8.78995	+	38.8811i	−0.311747	+	1.37897i
$796$		−	2.62215i		−	0.0929398i
$797$		−	45.5838i		−	1.61466i	−0.590099	−	0.807331i	$-0.700911\pi$
$797$		−	45.5838i		−	1.61466i	0.590099	−	0.807331i	$-0.299089\pi$
$798$		0			0
$799$	3.30428			0.116897
$800$	2.69843	−	4.20933i	0.0954041	−	0.148822i
$801$	−2.56458	−	20.3447i	−0.0906149	−	0.718846i
$802$			35.1257i			1.24033i
$803$			1.28629i			0.0453920i
$804$	−0.790403	+	0.896293i	−0.0278754	+	0.0316098i
$805$		0			0
$806$		−	40.1346i		−	1.41368i
$807$	−39.4548	−	34.7935i	−1.38887	−	1.22479i
$808$	−9.06786			−0.319006
$809$			37.7256i			1.32636i	0.748460	+	0.663180i	$0.230794\pi$
$809$			37.7256i			1.32636i	−0.748460	+	0.663180i	$0.769206\pi$
$810$	13.7347	+	14.7091i	0.482589	+	0.516825i
$811$		−	30.8984i		−	1.08499i	−0.840059	−	0.542495i	$-0.817480\pi$
$811$		−	30.8984i		−	1.08499i	0.840059	−	0.542495i	$-0.182520\pi$
$812$		0			0
$813$	−19.8219	+	22.4775i	−0.695186	+	0.788319i
$814$	−0.197801			−0.00693291
$815$	−30.3273	+	16.5823i	−1.06232	+	0.580852i
$816$	−1.59524	+	1.80895i	−0.0558444	+	0.0633259i
$817$	18.4577			0.645755
$818$		−	19.8638i		−	0.694522i
$819$		0			0
$820$	−4.10281	−	7.50361i	−0.143276	−	0.262038i
$821$		−	2.54824i		−	0.0889341i	−0.999011	−	0.0444670i	$-0.985841\pi$
$821$		−	2.54824i		−	0.0889341i	0.999011	−	0.0444670i	$-0.0141590\pi$
$822$	10.8503	+	9.56838i	0.378446	+	0.333736i
$823$		−	39.9687i		−	1.39322i	−0.717449	−	0.696611i	$-0.754690\pi$
$823$		−	39.9687i		−	1.39322i	0.717449	−	0.696611i	$-0.245310\pi$
$824$	−12.5117			−0.435867
$825$	−0.275083	−	0.963772i	−0.00957715	−	0.0335542i
$826$		0			0
$827$	4.82747			0.167868			0.0839338	−	0.996471i	$-0.473252\pi$
$827$	4.82747			0.167868			0.0839338	+	0.996471i	$0.473252\pi$
$828$	−2.47128	−	19.6046i	−0.0858828	−	0.681306i
$829$		−	38.5397i		−	1.33854i	−0.743019	−	0.669270i	$-0.766607\pi$
$829$		−	38.5397i		−	1.33854i	0.743019	−	0.669270i	$-0.233393\pi$
$830$	12.2621	−	6.70461i	0.425622	−	0.232721i
$831$	14.2203	−	16.1254i	0.493298	−	0.559385i
$832$	−5.60599			−0.194353
$833$		0			0
$834$	6.83630	−	7.75216i	0.236722	−	0.268435i
$835$	13.3581	−	7.30390i	0.462276	−	0.252762i
$836$	0.176302			0.00609753
$837$	30.7593	+	20.9222i	1.06320	+	0.723176i
$838$	−14.0283			−0.484599
$839$	2.66619			0.0920471			0.0460236	−	0.998940i	$-0.485345\pi$
$839$	2.66619			0.0920471			0.0460236	+	0.998940i	$0.485345\pi$
$840$		0			0
$841$	−51.5626			−1.77802
$842$	−15.8988			−0.547908
$843$	−5.19938	+	5.89594i	−0.179076	+	0.203067i
$844$	−24.9808			−0.859873
$845$	19.7676	+	36.1530i	0.680027	+	1.24370i
$846$	−7.06290	+	0.890321i	−0.242827	+	0.0306099i
$847$		0			0
$848$	10.2924			0.353442
$849$	12.7382	+	11.2333i	0.437174	+	0.385525i
$850$	5.86144	+	3.75754i	0.201046	+	0.128883i
$851$			11.2574i			0.385898i
$852$	7.76324	−	8.80328i	0.265964	−	0.301596i
$853$	−12.9140			−0.442167			−0.221083	−	0.975255i	$-0.570959\pi$
$853$	−12.9140			−0.442167			−0.221083	+	0.975255i	$0.570959\pi$
$854$		0			0
$855$	5.98548	+	8.28278i	0.204699	+	0.283265i
$856$	3.99362			0.136499
$857$		−	3.50975i		−	0.119891i	−0.998202	−	0.0599453i	$-0.980907\pi$
$857$		−	3.50975i		−	0.119891i	0.998202	−	0.0599453i	$-0.0190926\pi$
$858$	−0.743251	+	0.842825i	−0.0253742	+	0.0287736i
$859$		−	42.6001i		−	1.45350i	−0.686905	−	0.726748i	$-0.741031\pi$
$859$		−	42.6001i		−	1.45350i	0.686905	−	0.726748i	$-0.258969\pi$
$860$	−23.7716	+	12.9977i	−0.810603	+	0.443219i
$861$		0			0
$862$		−	9.78952i		−	0.333432i
$863$	−22.1376			−0.753572			−0.376786	−	0.926300i	$-0.622971\pi$
$863$	−22.1376			−0.753572			−0.376786	+	0.926300i	$0.622971\pi$
$864$	2.92240	−	4.29646i	0.0994222	−	0.146168i
$865$	−2.56481	+	1.40238i	−0.0872063	+	0.0476824i
$866$	18.4072			0.625503
$867$	19.5654	+	17.2539i	0.664474	+	0.585972i
$868$		0			0
$869$			1.66611i			0.0565188i
$870$	33.9069	+	7.66543i	1.14955	+	0.259883i
$871$		−	3.86783i		−	0.131056i
$872$	−5.70919			−0.193338
$873$	−6.13302	−	48.6531i	−0.207571	−	1.64666i
$874$		−	10.0338i		−	0.339400i
$875$		0			0
$876$	14.4385	+	12.7327i	0.487831	+	0.430198i
$877$			12.4506i			0.420426i	0.977656	+	0.210213i	$0.0674158\pi$
$877$			12.4506i			0.420426i	−0.977656	+	0.210213i	$0.932584\pi$
$878$			22.4392i			0.757286i
$879$	30.5587	−	34.6527i	1.03072	−	1.16881i
$880$	−0.227058	+	0.124150i	−0.00765412	+	0.00418510i
$881$	−50.0756			−1.68709			−0.843545	−	0.537059i	$-0.819535\pi$
$881$	−50.0756			−1.68709			−0.843545	+	0.537059i	$0.819535\pi$
$882$		0			0
$883$			11.7597i			0.395745i	0.980228	+	0.197872i	$0.0634032\pi$
$883$			11.7597i			0.395745i	−0.980228	+	0.197872i	$0.936597\pi$
$884$		−	7.80628i		−	0.262554i
$885$	2.84124	−	12.5678i	0.0955073	−	0.422463i
$886$	−31.3372			−1.05279
$887$			38.3417i			1.28739i	0.765282	+	0.643695i	$0.222599\pi$
$887$			38.3417i			1.28739i	−0.765282	+	0.643695i	$0.777401\pi$
$888$	−1.95799	+	2.22030i	−0.0657059	+	0.0745085i
$889$		0			0
$890$	7.33248	+	13.4104i	0.245785	+	0.449516i
$891$	−0.258488	−	1.00900i	−0.00865966	−	0.0338026i
$892$	3.33467			0.111653
$893$	−3.61487			−0.120967
$894$	18.2624	−	20.7091i	0.610787	−	0.692614i
$895$	2.02912	−	1.10947i	0.0678259	−	0.0370856i
$896$		0			0
$897$	47.9675	+	42.3005i	1.60159	+	1.41237i
$898$			6.53984i			0.218237i
$899$	64.2589			2.14315
$900$	−13.5413	−	6.45241i	−0.451376	−	0.215080i
$901$			14.3320i			0.477469i
$902$			0.442623i			0.0147378i
$903$		0			0
$904$	−7.34715			−0.244363
$905$	−44.7904	+	24.4904i	−1.48888	+	0.814088i
$906$	−20.7575	−	18.3051i	−0.689621	−	0.608148i
$907$			20.5081i			0.680961i	0.940252	+	0.340480i	$0.110590\pi$
$907$			20.5081i			0.680961i	−0.940252	+	0.340480i	$0.889410\pi$
$908$		−	19.5117i		−	0.647519i
$909$	3.40225	+	26.9900i	0.112846	+	0.895201i
$910$		0			0
$911$			9.28164i			0.307514i	0.988109	+	0.153757i	$0.0491374\pi$
$911$			9.28164i			0.307514i	−0.988109	+	0.153757i	$0.950863\pi$
$912$	1.74518	−	1.97898i	0.0577887	−	0.0655307i
$913$	−0.723315			−0.0239382
$914$		−	10.5360i		−	0.348501i
$915$	−19.3486	−	4.37419i	−0.639645	−	0.144606i
$916$		−	28.1753i		−	0.930939i
$917$		0			0
$918$	5.98277	+	4.06941i	0.197461	+	0.134311i
$919$	−28.5962			−0.943300			−0.471650	−	0.881786i	$-0.656341\pi$
$919$	−28.5962			−0.943300			−0.471650	+	0.881786i	$0.656341\pi$
$920$	7.06572	+	12.9225i	0.232950	+	0.426042i
$921$	30.3311	+	26.7477i	0.999443	+	0.881366i
$922$	−10.3034			−0.339324
$923$			37.9894i			1.25044i
$924$		0			0
$925$	7.19433	+	4.61200i	0.236548	+	0.151642i
$926$			41.3015i			1.35725i
$927$	4.69439	+	37.2405i	0.154184	+	1.22314i
$928$		−	8.97567i		−	0.294641i
$929$	−35.0068			−1.14854			−0.574268	−	0.818667i	$-0.694713\pi$
$929$	−35.0068			−1.14854			−0.574268	+	0.818667i	$0.694713\pi$
$930$	−27.0451	−	6.11415i	−0.886843	−	0.200491i
$931$		0			0
$932$	−1.61616			−0.0529390
$933$	34.2482	+	30.2020i	1.12123	+	0.988769i
$934$		−	14.3402i		−	0.469225i
$935$	−0.172877	−	0.316175i	−0.00565370	−	0.0103400i
$936$	2.10336	+	16.6859i	0.0687506	+	0.545396i
$937$	37.0650			1.21086			0.605431	−	0.795898i	$-0.293001\pi$
$937$	37.0650			1.21086			0.605431	+	0.795898i	$0.293001\pi$
$938$		0			0
$939$	−11.8994	−	10.4936i	−0.388322	−	0.342445i
$940$	4.65555	−	2.54555i	0.151847	−	0.0830267i
$941$	24.9310			0.812727			0.406364	−	0.913711i	$-0.366797\pi$
$941$	24.9310			0.812727			0.406364	+	0.913711i	$0.366797\pi$
$942$	6.75935	+	5.96078i	0.220231	+	0.194213i
$943$	25.1909			0.820329
$944$	−3.32689			−0.108281
$945$		0			0
$946$	1.40224			0.0455907
$947$	28.1276			0.914026			0.457013	−	0.889460i	$-0.348919\pi$
$947$	28.1276			0.914026			0.457013	+	0.889460i	$0.348919\pi$
$948$	18.7020	+	16.4925i	0.607412	+	0.535651i
$949$	−62.3074			−2.02258
$950$	−6.41239	−	4.11073i	−0.208045	−	0.133370i
$951$	37.0883	+	32.7066i	1.20267	+	1.06058i
$952$		0			0
$953$	−21.7868			−0.705745			−0.352872	−	0.935671i	$-0.614795\pi$
$953$	−21.7868			−0.705745			−0.352872	+	0.935671i	$0.614795\pi$
$954$	−3.86170	−	30.6347i	−0.125027	−	0.991836i
$955$	−23.1984	+	12.6844i	−0.750683	+	0.410456i
$956$			17.8576i			0.577555i
$957$	−1.34943	−	1.19001i	−0.0436210	−	0.0384675i
$958$	−22.4434			−0.725113
$959$		0			0
$960$	−0.854024	+	3.77765i	−0.0275635	+	0.121923i
$961$	−20.2546			−0.653374
$962$		−	9.58143i		−	0.308918i
$963$	−1.49840	−	11.8868i	−0.0482853	−	0.383046i
$964$			13.8552i			0.446246i
$965$	−8.53847	+	4.66864i	−0.274863	+	0.150289i
$966$		0			0
$967$		−	24.7893i		−	0.797169i	−0.917132	−	0.398584i	$-0.869502\pi$
$967$		−	24.7893i		−	0.797169i	0.917132	−	0.398584i	$-0.130498\pi$
$968$	−10.9866			−0.353123
$969$	2.75571	+	2.43014i	0.0885262	+	0.0780675i
$970$	17.5352	+	32.0700i	0.563020	+	1.02971i
$971$	0.430384			0.0138117			0.00690585	−	0.999976i	$-0.497802\pi$
$971$	0.430384			0.0138117			0.00690585	+	0.999976i	$0.497802\pi$
$972$	−13.8847	−	7.08635i	−0.445351	−	0.227295i
$973$		0			0
$974$		−	6.14199i		−	0.196802i
$975$	46.6849	−	13.3249i	1.49511	−	0.426740i
$976$			5.12186i			0.163947i
$977$	−39.7977			−1.27324			−0.636621	−	0.771177i	$-0.719668\pi$
$977$	−39.7977			−1.27324			−0.636621	+	0.771177i	$0.719668\pi$
$978$	17.7085	−	20.0809i	0.566254	−	0.642115i
$979$		−	0.791051i		−	0.0252821i
$980$		0			0
$981$	2.14208	+	16.9931i	0.0683915	+	0.542548i
$982$			23.7049i			0.756454i
$983$		−	12.9667i		−	0.413572i	−0.978386	−	0.206786i	$-0.933700\pi$
$983$		−	12.9667i		−	0.413572i	0.978386	−	0.206786i	$-0.0663004\pi$
$984$	4.96843	+	4.38145i	0.158388	+	0.139675i
$985$	−18.4681	−	33.7762i	−0.588442	−	1.07620i
$986$	12.4985			0.398034
$987$		0			0
$988$			8.54003i			0.271695i
$989$		−	79.8052i		−	2.53766i
$990$	0.454718	+	0.629244i	0.0144519	+	0.0199987i
$991$	−13.9146			−0.442011			−0.221006	−	0.975273i	$-0.570934\pi$
$991$	−13.9146			−0.442011			−0.221006	+	0.975273i	$0.570934\pi$
$992$			7.15923i			0.227306i
$993$	−5.58281	−	4.92324i	−0.177165	−	0.156234i
$994$		0			0
$995$	5.14451	−	2.81290i	0.163092	−	0.0891750i
$996$	−7.15995	+	8.11917i	−0.226872	+	0.257266i
$997$	−25.8161			−0.817604			−0.408802	−	0.912623i	$-0.634053\pi$
$997$	−25.8161			−0.817604			−0.408802	+	0.912623i	$0.634053\pi$
$998$	−4.46829			−0.141441
$999$	7.34325	+	4.99480i	0.232330	+	0.158028i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.d.g.1469.20	yes	24
3.2	odd	2		1470.2.d.h.1469.19	yes	24
5.4	even	2		1470.2.d.h.1469.5	yes	24
7.6	odd	2	inner	1470.2.d.g.1469.5	✓	24
15.14	odd	2	inner	1470.2.d.g.1469.6	yes	24
21.20	even	2		1470.2.d.h.1469.6	yes	24
35.34	odd	2		1470.2.d.h.1469.20	yes	24
105.104	even	2	inner	1470.2.d.g.1469.19	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.d.g.1469.5	✓	24	7.6	odd	2	inner
1470.2.d.g.1469.6	yes	24	15.14	odd	2	inner
1470.2.d.g.1469.19	yes	24	105.104	even	2	inner
1470.2.d.g.1469.20	yes	24	1.1	even	1	trivial
1470.2.d.h.1469.5	yes	24	5.4	even	2
1470.2.d.h.1469.6	yes	24	21.20	even	2
1470.2.d.h.1469.19	yes	24	3.2	odd	2
1470.2.d.h.1469.20	yes	24	35.34	odd	2

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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(1.29908 + 1.14560i) q^{3} +1.00000 q^{4} +(1.07275 + 1.96194i) q^{5} +(-1.29908 - 1.14560i) q^{6} -1.00000 q^{8} +(0.375199 + 2.97645i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(1.29908 + 1.14560i) q^{3} +1.00000 q^{4} +(1.07275 + 1.96194i) q^{5} +(-1.29908 - 1.14560i) q^{6} -1.00000 q^{8} +(0.375199 + 2.97645i) q^{9} +(-1.07275 - 1.96194i) q^{10} +0.115731i q^{11} +(1.29908 + 1.14560i) q^{12} -5.60599 q^{13} +(-0.854024 + 3.77765i) q^{15} +1.00000 q^{16} +1.39249i q^{17} +(-0.375199 - 2.97645i) q^{18} -1.52338i q^{19} +(1.07275 + 1.96194i) q^{20} -0.115731i q^{22} -6.58658 q^{23} +(-1.29908 - 1.14560i) q^{24} +(-2.69843 + 4.20933i) q^{25} +5.60599 q^{26} +(-2.92240 + 4.29646i) q^{27} +8.97567i q^{29} +(0.854024 - 3.77765i) q^{30} -7.15923i q^{31} -1.00000 q^{32} +(-0.132582 + 0.150344i) q^{33} -1.39249i q^{34} +(0.375199 + 2.97645i) q^{36} -1.70914i q^{37} +1.52338i q^{38} +(-7.28261 - 6.42223i) q^{39} +(-1.07275 - 1.96194i) q^{40} -3.82458 q^{41} +12.1163i q^{43} +0.115731i q^{44} +(-5.43712 + 3.92909i) q^{45} +6.58658 q^{46} -2.37293i q^{47} +(1.29908 + 1.14560i) q^{48} +(2.69843 - 4.20933i) q^{50} +(-1.59524 + 1.80895i) q^{51} -5.60599 q^{52} +10.2924 q^{53} +(2.92240 - 4.29646i) q^{54} +(-0.227058 + 0.124150i) q^{55} +(1.74518 - 1.97898i) q^{57} -8.97567i q^{58} -3.32689 q^{59} +(-0.854024 + 3.77765i) q^{60} +5.12186i q^{61} +7.15923i q^{62} +1.00000 q^{64} +(-6.01380 - 10.9986i) q^{65} +(0.132582 - 0.150344i) q^{66} +0.689946i q^{67} +1.39249i q^{68} +(-8.55647 - 7.54559i) q^{69} -6.77657i q^{71} +(-0.375199 - 2.97645i) q^{72} +11.1144 q^{73} +1.70914i q^{74} +(-8.32768 + 2.37691i) q^{75} -1.52338i q^{76} +(7.28261 + 6.42223i) q^{78} +14.3964 q^{79} +(1.07275 + 1.96194i) q^{80} +(-8.71845 + 2.23352i) q^{81} +3.82458 q^{82} +6.24996i q^{83} +(-2.73198 + 1.49379i) q^{85} -12.1163i q^{86} +(-10.2825 + 11.6601i) q^{87} -0.115731i q^{88} -6.83525 q^{89} +(5.43712 - 3.92909i) q^{90} -6.58658 q^{92} +(8.20162 - 9.30039i) q^{93} +2.37293i q^{94} +(2.98878 - 1.63420i) q^{95} +(-1.29908 - 1.14560i) q^{96} -16.3461 q^{97} +(-0.344467 + 0.0434222i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} + 24 q^{4} - 24 q^{8} + 8 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 + 24 * q^4 - 24 * q^8 + 8 * q^9	\( 24 q - 24 q^{2} + 24 q^{4} - 24 q^{8} + 8 q^{9} + 24 q^{16} - 8 q^{18} - 16 q^{23} + 8 q^{25} - 24 q^{32} + 8 q^{36} + 16 q^{39} + 16 q^{46} - 8 q^{50} + 16 q^{51} + 16 q^{53} + 16 q^{57} + 24 q^{64} - 48 q^{65} - 8 q^{72} - 16 q^{78} - 48 q^{79} - 24 q^{81} + 16 q^{85} - 16 q^{92} + 64 q^{93} - 112 q^{95} - 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 24 * q^4 - 24 * q^8 + 8 * q^9 + 24 * q^16 - 8 * q^18 - 16 * q^23 + 8 * q^25 - 24 * q^32 + 8 * q^36 + 16 * q^39 + 16 * q^46 - 8 * q^50 + 16 * q^51 + 16 * q^53 + 16 * q^57 + 24 * q^64 - 48 * q^65 - 8 * q^72 - 16 * q^78 - 48 * q^79 - 24 * q^81 + 16 * q^85 - 16 * q^92 + 64 * q^93 - 112 * q^95 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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