LMFDB - Embedded newform 429.2.y.a.116.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(116,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 9, 5]))

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

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

chi := DirichletCharacter("429.116");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.y (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{10}]$

Embedding invariants

Embedding label			116.5
Character	$\chi$	$=$	429.116
Dual form			429.2.y.a.233.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.658535 - 0.213971i) q^{2} +(1.40126 + 1.01807i) q^{3} +(-1.23015 + 0.893756i) q^{4} +(1.34694 - 4.14546i) q^{5} +(1.14062 + 0.370608i) q^{6} +(-1.43285 + 1.97215i) q^{8} +(0.927051 + 2.85317i) q^{9} +O(q^{10})$	\(q+(0.658535 - 0.213971i) q^{2} +(1.40126 + 1.01807i) q^{3} +(-1.23015 + 0.893756i) q^{4} +(1.34694 - 4.14546i) q^{5} +(1.14062 + 0.370608i) q^{6} +(-1.43285 + 1.97215i) q^{8} +(0.927051 + 2.85317i) q^{9} -3.01814i q^{10} +(3.28077 + 0.486394i) q^{11} -2.63367 q^{12} +(3.42908 - 1.11418i) q^{13} +(6.10780 - 4.43758i) q^{15} +(0.418151 - 1.28694i) q^{16} +(1.22099 + 1.68055i) q^{18} +(2.04809 + 6.30337i) q^{20} +(2.26457 - 0.381681i) q^{22} +(-4.01559 + 1.30475i) q^{24} +(-11.3255 - 8.22846i) q^{25} +(2.01977 - 1.46745i) q^{26} +(-1.60570 + 4.94183i) q^{27} +(3.07269 - 4.22919i) q^{30} -5.81239i q^{32} +(4.10201 + 4.02163i) q^{33} +(-3.69045 - 2.68127i) q^{36} +(5.93935 + 1.92981i) q^{39} +(6.24551 + 8.59621i) q^{40} +(-4.59885 + 6.32977i) q^{41} +12.4558i q^{43} +(-4.47055 + 2.33387i) q^{44} +13.0764 q^{45} +(-10.0626 - 7.31094i) q^{47} +(1.89613 - 1.37762i) q^{48} +(-2.16312 + 6.65740i) q^{49} +(-9.21889 - 2.99540i) q^{50} +(-3.22248 + 4.43537i) q^{52} +3.59794i q^{54} +(6.43533 - 12.9451i) q^{55} +(3.47744 - 2.52651i) q^{59} +(-3.54740 + 10.9178i) q^{60} +(-14.6525 - 4.76089i) q^{61} +(-0.407381 - 1.25379i) q^{64} -15.7159i q^{65} +(3.56183 + 1.77067i) q^{66} +(1.52081 - 4.68057i) q^{71} +(-6.95521 - 2.25988i) q^{72} +(-7.49278 - 23.0604i) q^{75} +4.32419 q^{78} +(5.16135 - 1.67702i) q^{79} +(-4.77172 - 3.46686i) q^{80} +(-7.28115 + 5.29007i) q^{81} +(-1.67411 + 5.15239i) q^{82} +(2.35302 + 0.764544i) q^{83} +(2.66517 + 8.20255i) q^{86} +(-5.66010 + 5.77324i) q^{88} -18.3671 q^{89} +(8.61126 - 2.79797i) q^{90} +(-8.19093 - 2.66139i) q^{94} +(5.91744 - 8.14466i) q^{96} +4.84697i q^{98} +(1.65367 + 9.81149i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} - 24 q^{9}+O(q^{10}) $ 32 * q + 16 * q^4 - 24 * q^9	$ 32 q + 16 q^{4} - 24 q^{9} - 24 q^{12} - 92 q^{16} + 28 q^{22} - 40 q^{25} + 180 q^{30} + 48 q^{36} - 72 q^{48} + 56 q^{49} - 260 q^{52} + 32 q^{55} + 184 q^{64} - 60 q^{66} - 144 q^{75} - 72 q^{81} + 204 q^{82} - 40 q^{88} + 60 q^{90}+O(q^{100}) $ 32 * q + 16 * q^4 - 24 * q^9 - 24 * q^12 - 92 * q^16 + 28 * q^22 - 40 * q^25 + 180 * q^30 + 48 * q^36 - 72 * q^48 + 56 * q^49 - 260 * q^52 + 32 * q^55 + 184 * q^64 - 60 * q^66 - 144 * q^75 - 72 * q^81 + 204 * q^82 - 40 * q^88 + 60 * q^90

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$-1$	$e\left(\frac{9}{10}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.658535	−	0.213971i	0.465654	−	0.151300i	−0.0667868	−	0.997767i	$-0.521275\pi$
$2$	0.658535	−	0.213971i	0.465654	−	0.151300i	0.532441	+	0.846467i	$0.321275\pi$
$3$	1.40126	+	1.01807i	0.809017	+	0.587785i
$3$	1.40126	+	1.01807i	0.809017	+	0.587785i
$4$	−1.23015	+	0.893756i	−0.615075	+	0.446878i
$5$	1.34694	−	4.14546i	0.602371	−	1.85391i	0.0884268	−	0.996083i	$-0.471816\pi$
$5$	1.34694	−	4.14546i	0.602371	−	1.85391i	0.513944	−	0.857824i	$-0.328184\pi$
$6$	1.14062	+	0.370608i	0.465654	+	0.151300i
$7$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$7$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$8$	−1.43285	+	1.97215i	−0.506590	+	0.697261i
$9$	0.927051	+	2.85317i	0.309017	+	0.951057i
$10$		−	3.01814i		−	0.954419i
$11$	3.28077	+	0.486394i	0.989188	+	0.146653i
$11$	3.28077	+	0.486394i	0.989188	+	0.146653i
$12$	−2.63367			−0.760274
$13$	3.42908	−	1.11418i	0.951057	−	0.309017i
$13$	3.42908	−	1.11418i	0.951057	−	0.309017i
$14$		0			0
$15$	6.10780	−	4.43758i	1.57703	−	1.14578i
$16$	0.418151	−	1.28694i	0.104538	−	0.321734i
$17$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$17$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$18$	1.22099	+	1.68055i	0.287790	+	0.396109i
$19$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$19$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$20$	2.04809	+	6.30337i	0.457967	+	1.40948i
$21$		0			0
$22$	2.26457	−	0.381681i	0.482808	−	0.0813746i
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$	−4.01559	+	1.30475i	−0.819679	+	0.266330i
$25$	−11.3255	−	8.22846i	−2.26510	−	1.64569i
$26$	2.01977	−	1.46745i	0.396109	−	0.287790i
$27$	−1.60570	+	4.94183i	−0.309017	+	0.951057i
$28$		0			0
$29$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$29$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$30$	3.07269	−	4.22919i	0.560993	−	0.772141i
$31$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$31$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$32$		−	5.81239i		−	1.02750i
$33$	4.10201	+	4.02163i	0.714069	+	0.700075i
$34$		0			0
$35$		0			0
$36$	−3.69045	−	2.68127i	−0.615075	−	0.446878i
$37$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$37$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$38$		0			0
$39$	5.93935	+	1.92981i	0.951057	+	0.309017i
$40$	6.24551	+	8.59621i	0.987502	+	1.35918i
$41$	−4.59885	+	6.32977i	−0.718219	+	0.988544i	0.281362	+	0.959602i	$0.409214\pi$
$41$	−4.59885	+	6.32977i	−0.718219	+	0.988544i	−0.999581	+	0.0289423i	$0.990786\pi$
$42$		0			0
$43$			12.4558i			1.89949i	0.313031	+	0.949743i	$0.398656\pi$
$43$			12.4558i			1.89949i	−0.313031	+	0.949743i	$0.601344\pi$
$44$	−4.47055	+	2.33387i	−0.673961	+	0.351843i
$45$	13.0764			1.94931
$46$		0			0
$47$	−10.0626	−	7.31094i	−1.46779	−	1.06641i	−0.981248	−	0.192751i	$-0.938259\pi$
$47$	−10.0626	−	7.31094i	−1.46779	−	1.06641i	−0.486540	−	0.873659i	$-0.661741\pi$
$48$	1.89613	−	1.37762i	0.273683	−	0.198842i
$49$	−2.16312	+	6.65740i	−0.309017	+	0.951057i
$50$	−9.21889	−	2.99540i	−1.30375	−	0.423614i
$51$		0			0
$52$	−3.22248	+	4.43537i	−0.446878	+	0.615075i
$53$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$53$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$54$			3.59794i			0.489618i
$55$	6.43533	−	12.9451i	0.867740	−	1.74552i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.47744	−	2.52651i	0.452724	−	0.328923i	−0.337946	−	0.941165i	$-0.609732\pi$
$59$	3.47744	−	2.52651i	0.452724	−	0.328923i	0.790670	+	0.612242i	$0.209732\pi$
$60$	−3.54740	+	10.9178i	−0.457967	+	1.40948i
$61$	−14.6525	−	4.76089i	−1.87606	−	0.609570i	−0.988998	−	0.147927i	$-0.952740\pi$
$61$	−14.6525	−	4.76089i	−1.87606	−	0.609570i	−0.887066	−	0.461644i	$-0.847260\pi$
$62$		0			0
$63$		0			0
$64$	−0.407381	−	1.25379i	−0.0509227	−	0.156724i
$65$		−	15.7159i		−	1.94931i
$66$	3.56183	+	1.77067i	0.438431	+	0.217954i
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.52081	−	4.68057i	0.180487	−	0.555481i	−0.819355	−	0.573287i	$-0.805668\pi$
$71$	1.52081	−	4.68057i	0.180487	−	0.555481i	0.999841	+	0.0178059i	$0.00566810\pi$
$72$	−6.95521	−	2.25988i	−0.819679	−	0.266330i
$73$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$73$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$74$		0			0
$75$	−7.49278	−	23.0604i	−0.865192	−	2.66279i
$76$		0			0
$77$		0			0
$78$	4.32419			0.489618
$79$	5.16135	−	1.67702i	0.580697	−	0.188680i	−0.00391577	−	0.999992i	$-0.501246\pi$
$79$	5.16135	−	1.67702i	0.580697	−	0.188680i	0.584613	+	0.811312i	$0.301246\pi$
$80$	−4.77172	−	3.46686i	−0.533494	−	0.387606i
$81$	−7.28115	+	5.29007i	−0.809017	+	0.587785i
$82$	−1.67411	+	5.15239i	−0.184875	+	0.568987i
$83$	2.35302	+	0.764544i	0.258278	+	0.0839196i	0.435294	−	0.900288i	$-0.356644\pi$
$83$	2.35302	+	0.764544i	0.258278	+	0.0839196i	−0.177016	+	0.984208i	$0.556644\pi$
$84$		0			0
$85$		0			0
$86$	2.66517	+	8.20255i	0.287393	+	0.884504i
$87$		0			0
$88$	−5.66010	+	5.77324i	−0.603368	+	0.615429i
$89$	−18.3671			−1.94690			−0.973452	−	0.228892i	$-0.926490\pi$
$89$	−18.3671			−1.94690			−0.973452	+	0.228892i	$0.926490\pi$
$90$	8.61126	−	2.79797i	0.907706	−	0.294932i
$91$		0			0
$92$		0			0
$93$		0			0
$94$	−8.19093	−	2.66139i	−0.844830	−	0.274502i
$95$		0			0
$96$	5.91744	−	8.14466i	0.603947	−	0.831261i
$97$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$97$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$98$			4.84697i			0.489618i
$99$	1.65367	+	9.81149i	0.166200	+	0.986092i
$100$	21.2863			2.12863
$101$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$101$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$102$		0			0
$103$	4.53279	−	3.29326i	0.446629	−	0.324495i	−0.341634	−	0.939833i	$-0.610980\pi$
$103$	4.53279	−	3.29326i	0.446629	−	0.324495i	0.788263	+	0.615338i	$0.210980\pi$
$104$	−2.71604	+	8.35912i	−0.266330	+	0.819679i
$105$		0			0
$106$		0			0
$107$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$107$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$108$	−2.44154	−	7.51430i	−0.234938	−	0.723064i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$	1.46800	−	9.90180i	0.139969	−	0.944099i
$111$		0			0
$112$		0			0
$113$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$113$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	6.35787	+	8.75086i	0.587785	+	0.809017i
$118$	1.74942	−	2.40786i	0.161047	−	0.221662i
$119$		0			0
$120$			18.4039i			1.68004i
$121$	10.5268	+	3.19149i	0.956986	+	0.290136i
$122$	−10.6679			−0.965826
$123$	−12.8883	+	4.18768i	−1.16210	+	0.377590i
$124$		0			0
$125$	−31.7339	+	23.0560i	−2.83836	+	2.06219i
$126$		0			0
$127$	20.7792	+	6.75157i	1.84386	+	0.599105i	0.997821	+	0.0659781i	$0.0210167\pi$
$127$	20.7792	+	6.75157i	1.84386	+	0.599105i	0.846035	+	0.533127i	$0.178983\pi$
$128$	6.29633	+	8.66615i	0.556522	+	0.765987i
$129$	−12.6809	+	17.4537i	−1.11649	+	1.53672i
$130$	−3.36274	−	10.3494i	−0.294932	−	0.907706i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	−8.64044	−	1.28100i	−0.752054	−	0.111497i
$133$		0			0
$134$		0			0
$135$	18.3234	+	13.3127i	1.57703	+	1.14578i
$136$		0			0
$137$	4.00076	−	12.3131i	0.341808	−	1.05198i	−0.621463	−	0.783444i	$-0.713461\pi$
$137$	4.00076	−	12.3131i	0.341808	−	1.05198i	0.963271	−	0.268533i	$-0.0865388\pi$
$138$		0			0
$139$	8.91171	+	12.2659i	0.755882	+	1.04038i	0.997545	+	0.0700216i	$0.0223068\pi$
$139$	8.91171	+	12.2659i	0.755882	+	1.04038i	−0.241664	+	0.970360i	$0.577693\pi$
$140$		0			0
$141$	−6.65729	−	20.4890i	−0.560645	−	1.72549i
$142$		−	3.40772i		−	0.285970i
$143$	11.7919	−	1.98747i	0.986092	−	0.166200i
$144$	4.05949			0.338291
$145$		0			0
$146$		0			0
$147$	−9.80881	+	7.12652i	−0.809017	+	0.587785i
$148$		0			0
$149$	18.6174	+	6.04918i	1.52520	+	0.495568i	0.947248	−	0.320502i	$-0.103852\pi$
$149$	18.6174	+	6.04918i	1.52520	+	0.495568i	0.577953	+	0.816070i	$0.303852\pi$
$150$	−9.86851	−	13.5828i	−0.805761	−	1.10903i
$151$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$151$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−9.03106	+	2.93437i	−0.723064	+	0.234938i
$157$	−19.7201	−	14.3275i	−1.57384	−	1.14346i	−0.923361	−	0.383934i	$-0.874569\pi$
$157$	−19.7201	−	14.3275i	−1.57384	−	1.14346i	−0.650477	−	0.759526i	$-0.725431\pi$
$158$	3.04009	−	2.20876i	0.241857	−	0.175719i
$159$		0			0
$160$	−24.0950	−	7.82895i	−1.90488	−	0.618933i
$161$		0			0
$162$	−3.66297	+	5.04165i	−0.287790	+	0.396109i
$163$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$163$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$164$		−	11.8968i		−	0.928985i
$165$	22.1967	−	11.5878i	1.72801	−	0.902113i
$166$	1.71314			0.132965
$167$	−11.3465	+	3.68670i	−0.878019	+	0.285286i	−0.713134	−	0.701027i	$-0.752725\pi$
$167$	−11.3465	+	3.68670i	−0.878019	+	0.285286i	−0.164884	+	0.986313i	$0.552725\pi$
$168$		0			0
$169$	10.5172	−	7.64121i	0.809017	−	0.587785i
$170$		0			0
$171$		0			0
$172$	−11.1324	−	15.3224i	−0.848838	−	1.16833i
$173$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$173$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$174$		0			0
$175$		0			0
$176$	1.99781	−	4.01875i	0.150591	−	0.302925i
$177$	7.44497			0.559598
$178$	−12.0953	+	3.93002i	−0.906584	+	0.294567i
$179$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$179$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$180$	−16.0859	+	11.6871i	−1.19897	+	0.871105i
$181$	−2.03726	+	6.27003i	−0.151428	+	0.466048i	−0.997781	−	0.0665740i	$-0.978793\pi$
$181$	−2.03726	+	6.27003i	−0.151428	+	0.466048i	0.846353	+	0.532622i	$0.178793\pi$
$182$		0			0
$183$	−15.6850	−	21.5886i	−1.15947	−	1.59588i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	18.9127			1.37935
$189$		0			0
$190$		0			0
$191$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$191$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$192$	0.705605	−	2.17163i	0.0509227	−	0.156724i
$193$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$193$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$194$		0			0
$195$	15.9999	−	22.0220i	1.14578	−	1.57703i
$196$	−3.28913	−	10.1229i	−0.234938	−	0.723064i
$197$			27.4911i			1.95866i	0.202274	+	0.979329i	$0.435167\pi$
$197$			27.4911i			1.95866i	−0.202274	+	0.979329i	$0.564833\pi$
$198$	3.18837	+	6.10737i	0.226588	+	0.434032i
$199$	−6.22307			−0.441142			−0.220571	−	0.975371i	$-0.570792\pi$
$199$	−6.22307			−0.441142			−0.220571	+	0.975371i	$0.570792\pi$
$200$	32.4556	−	10.5455i	2.29495	−	0.745676i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	20.0454	+	27.5902i	1.40003	+	1.92698i
$206$	2.28034	−	3.13861i	0.158879	−	0.218678i
$207$		0			0
$208$		−	4.87890i		−	0.338291i
$209$		0			0
$210$		0			0
$211$	20.2570	−	6.58190i	1.39455	−	0.453117i	0.487125	−	0.873332i	$-0.338046\pi$
$211$	20.2570	−	6.58190i	1.39455	−	0.453117i	0.907424	+	0.420216i	$0.138046\pi$
$212$		0			0
$213$	6.89621	−	5.01039i	0.472520	−	0.343306i
$214$		0			0
$215$	51.6349	+	16.7772i	3.52147	+	1.14419i
$216$	−7.44532	−	10.2476i	−0.506590	−	0.697261i
$217$		0			0
$218$		0			0
$219$		0			0
$220$	3.65338	+	21.6761i	0.246311	+	1.46140i
$221$		0			0
$222$		0			0
$223$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$223$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$224$		0			0
$225$	12.9779	−	39.9418i	0.865192	−	2.66279i
$226$		0			0
$227$	−17.5687	−	24.1813i	−1.16608	−	1.60497i	−0.685645	−	0.727936i	$-0.740480\pi$
$227$	−17.5687	−	24.1813i	−1.16608	−	1.60497i	−0.480432	−	0.877032i	$-0.659520\pi$
$228$		0			0
$229$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$229$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$233$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$234$	6.05931	+	4.40234i	0.396109	+	0.287790i
$235$	−43.8610	+	31.8669i	−2.86118	+	2.07877i
$236$	−2.01969	+	6.21597i	−0.131471	+	0.404625i
$237$	8.93972	+	2.90469i	0.580697	+	0.188680i
$238$		0			0
$239$	17.0209	−	23.4272i	1.10099	−	1.51538i	0.266919	−	0.963719i	$-0.413995\pi$
$239$	17.0209	−	23.4272i	1.10099	−	1.51538i	0.834069	−	0.551660i	$-0.186005\pi$
$240$	−3.15689	−	9.71592i	−0.203777	−	0.627160i
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$	7.61518	−	0.150730i	0.489522	−	0.00968928i
$243$	−15.5885			−1.00000
$244$	22.2799	−	7.23917i	1.42632	−	0.463440i
$245$	24.6844	+	17.9343i	1.57703	+	1.14578i
$246$	−7.59138	+	5.51546i	−0.484009	+	0.351653i
$247$		0			0
$248$		0			0
$249$	2.51883	+	3.46688i	0.159625	+	0.219704i
$250$	−15.9645	+	21.9733i	−1.00969	+	1.38971i
$251$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$251$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$252$		0			0
$253$		0			0
$254$	15.1285			0.949245
$255$		0			0
$256$	8.13373	+	5.90950i	0.508358	+	0.369344i
$257$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$257$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$258$	−4.61621	+	14.2072i	−0.287393	+	0.884504i
$259$		0			0
$260$	14.0461	+	19.3329i	0.871105	+	1.19897i
$261$		0			0
$262$		0			0
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$	−13.8088	+	2.32740i	−0.849875	+	0.143242i
$265$		0			0
$266$		0			0
$267$	−25.7370	−	18.6990i	−1.57508	−	1.14436i
$268$		0			0
$269$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$269$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$270$	14.9151	+	4.84622i	0.907706	+	0.294932i
$271$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$271$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$272$		0			0
$273$		0			0
$274$		−	8.96463i		−	0.541573i
$275$	−33.1541	−	32.5043i	−1.99926	−	1.96008i
$276$		0			0
$277$	23.7574	−	7.71924i	1.42744	−	0.463804i	0.509484	−	0.860480i	$-0.329836\pi$
$277$	23.7574	−	7.71924i	1.42744	−	0.463804i	0.917959	+	0.396676i	$0.129836\pi$
$278$	8.49322	+	6.17069i	0.509390	+	0.370093i
$279$		0			0
$280$		0			0
$281$	−21.5831	−	7.01278i	−1.28754	−	0.418347i	−0.416310	−	0.909223i	$-0.636677\pi$
$281$	−21.5831	−	7.01278i	−1.28754	−	0.418347i	−0.871230	+	0.490875i	$0.836677\pi$
$282$	−8.76811	−	12.0683i	−0.522133	−	0.718655i
$283$	−14.9216	+	20.5379i	−0.886999	+	1.22085i	0.0874340	+	0.996170i	$0.472133\pi$
$283$	−14.9216	+	20.5379i	−0.886999	+	1.22085i	−0.974433	+	0.224679i	$0.927867\pi$
$284$	2.31246	+	7.11703i	0.137219	+	0.422318i
$285$		0			0
$286$	7.34015	−	3.83195i	0.434032	−	0.226588i
$287$		0			0
$288$	16.5837	−	5.38838i	0.977206	−	0.317514i
$289$	13.7533	+	9.99235i	0.809017	+	0.587785i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	6.32905	+	8.71120i	0.369747	+	0.508913i	0.952832	−	0.303498i	$-0.0981545\pi$
$293$	6.32905	+	8.71120i	0.369747	+	0.508913i	−0.583085	+	0.812411i	$0.698154\pi$
$294$	−4.93457	+	6.79186i	−0.287790	+	0.396109i
$295$	−5.78963	−	17.8187i	−0.337085	−	1.03744i
$296$		0			0
$297$	−7.67160	+	15.4320i	−0.445152	+	0.895455i
$298$	13.5546			0.785196
$299$		0			0
$300$	29.8276	+	21.6710i	1.72210	+	1.25118i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−39.4722	+	54.3288i	−2.26017	+	3.11086i
$306$		0			0
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$		0			0
$309$	9.70440			0.552064
$310$		0			0
$311$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$311$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$312$	−12.3161	+	8.94816i	−0.697261	+	0.506590i
$313$	7.35046	−	22.6224i	0.415473	−	1.27869i	−0.496355	−	0.868120i	$-0.665329\pi$
$313$	7.35046	−	22.6224i	0.415473	−	1.27869i	0.911828	−	0.410574i	$-0.134671\pi$
$314$	−16.0521	−	5.21563i	−0.905870	−	0.294335i
$315$		0			0
$316$	−4.85038	+	6.67598i	−0.272855	+	0.375553i
$317$	−1.51910	−	4.67532i	−0.0853214	−	0.262592i	0.899289	−	0.437354i	$-0.144084\pi$
$317$	−1.51910	−	4.67532i	−0.0853214	−	0.262592i	−0.984611	+	0.174762i	$0.944084\pi$
$318$		0			0
$319$		0			0
$320$	−5.74626			−0.321226
$321$		0			0
$322$		0			0
$323$		0			0
$324$	4.22888	−	13.0151i	0.234938	−	0.723064i
$325$	−48.0041	−	15.5975i	−2.66279	−	0.865192i
$326$		0			0
$327$		0			0
$328$	−5.89380	−	18.1393i	−0.325431	−	1.00157i
$329$		0			0
$330$	12.1378	−	12.3804i	0.668165	−	0.681521i
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$	−3.57789	+	1.16253i	−0.196362	+	0.0638019i
$333$		0			0
$334$	−6.68322	+	4.85564i	−0.365690	+	0.265689i
$335$		0			0
$336$		0			0
$337$	2.67598	+	3.68317i	0.145770	+	0.200635i	0.875658	−	0.482931i	$-0.160428\pi$
$337$	2.67598	+	3.68317i	0.145770	+	0.200635i	−0.729888	+	0.683567i	$0.760428\pi$
$338$	5.29096	−	7.28238i	0.287790	−	0.396109i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$	−24.5647	−	17.8473i	−1.32444	−	0.962260i
$345$		0			0
$346$		0			0
$347$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$347$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$348$		0			0
$349$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$349$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$350$		0			0
$351$			18.7350i			1.00000i
$352$	2.82711	−	19.0691i	0.150686	−	1.01639i
$353$	20.0152			1.06530			0.532652	−	0.846335i	$-0.321196\pi$
$353$	20.0152			1.06530			0.532652	+	0.846335i	$0.321196\pi$
$354$	4.90277	−	1.59301i	0.260579	−	0.0846673i
$355$	−17.3547	−	12.6089i	−0.921090	−	0.669211i
$356$	22.5942	−	16.4157i	1.19749	−	0.870028i
$357$		0			0
$358$		0			0
$359$	−1.23226	−	1.69606i	−0.0650361	−	0.0895145i	0.775260	−	0.631642i	$-0.217619\pi$
$359$	−1.23226	−	1.69606i	−0.0650361	−	0.0895145i	−0.840296	+	0.542128i	$0.817619\pi$
$360$	−18.7365	+	25.7886i	−0.987502	+	1.35918i
$361$	−5.87132	−	18.0701i	−0.309017	−	0.951057i
$362$			4.56495i			0.239928i
$363$	11.5017	+	15.1892i	0.603680	+	0.797227i
$364$		0			0
$365$		0			0
$366$	−14.9485	−	10.8607i	−0.781369	−	0.567698i
$367$	26.8302	−	19.4933i	1.40052	−	1.01754i	0.405908	−	0.913914i	$-0.366955\pi$
$367$	26.8302	−	19.4933i	1.40052	−	1.01754i	0.994616	−	0.103627i	$-0.0330448\pi$
$368$		0			0
$369$	−22.3233	−	7.25327i	−1.16210	−	0.377590i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		−	21.0249i		−	1.08863i	−0.838881	−	0.544315i	$-0.816790\pi$
$373$		−	21.0249i		−	1.08863i	0.838881	−	0.544315i	$-0.183210\pi$
$374$		0			0
$375$	−67.9401			−3.50841
$376$	28.8366	−	9.36957i	1.48713	−	0.483198i
$377$		0			0
$378$		0			0
$379$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$379$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$380$		0			0
$381$	22.2434	+	30.6155i	1.13957	+	1.56848i
$382$		0			0
$383$	11.9863	+	36.8901i	0.612472	+	1.88499i	0.433543	+	0.901133i	$0.357263\pi$
$383$	11.9863	+	36.8901i	0.612472	+	1.88499i	0.178929	+	0.983862i	$0.442737\pi$
$384$			18.5536i			0.946812i
$385$		0			0
$386$		0			0
$387$	−35.5384	+	11.5471i	−1.80652	+	0.586973i
$388$		0			0
$389$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$389$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$390$	5.82443	−	17.9258i	0.294932	−	0.907706i
$391$		0			0
$392$	−10.0300	−	13.8051i	−0.506590	−	0.697261i
$393$		0			0
$394$	5.88229	+	18.1038i	0.296346	+	0.912058i
$395$		−	23.6550i		−	1.19021i
$396$	−10.8033	−	10.5916i	−0.542888	−	0.532249i
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$	−4.09811	+	1.33156i	−0.205420	+	0.0667449i
$399$		0			0
$400$	−15.3253	+	11.1345i	−0.766264	+	0.556723i
$401$	−3.14684	+	9.68498i	−0.157146	+	0.483645i	−0.998372	−	0.0570386i	$-0.981834\pi$
$401$	−3.14684	+	9.68498i	−0.157146	+	0.483645i	0.841226	+	0.540683i	$0.181834\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	12.1225	+	37.3091i	0.602371	+	1.85391i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$409$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$410$	19.1041	+	13.8799i	0.943485	+	0.685482i
$411$	18.1417	−	13.1807i	0.894865	−	0.650157i
$412$	−2.63263	+	8.10242i	−0.129701	+	0.399177i
$413$		0			0
$414$		0			0
$415$	6.33877	−	8.72457i	0.311158	−	0.428272i
$416$	−6.47603	−	19.9312i	−0.317514	−	0.977206i
$417$			26.2605i			1.28598i
$418$		0			0
$419$		0			0		1.00000			$0$
$419$		0			0		−1.00000			$\pi$
$420$		0			0
$421$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$421$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$422$	11.9316	−	8.66882i	0.580821	−	0.421991i
$423$	11.5308	−	35.4880i	0.560645	−	1.72549i
$424$		0			0
$425$		0			0
$426$	3.46931	−	4.77510i	0.168089	−	0.231354i
$427$		0			0
$428$		0			0
$429$	18.5470	+	9.22012i	0.895455	+	0.445152i
$430$	37.5932			1.81290
$431$	−32.9893	+	10.7189i	−1.58904	+	0.516309i	−0.964364	−	0.264578i	$-0.914767\pi$
$431$	−32.9893	+	10.7189i	−1.58904	+	0.516309i	−0.624672	+	0.780887i	$0.714767\pi$
$432$	5.68840	+	4.13286i	0.273683	+	0.198842i
$433$	3.54171	−	2.57320i	0.170204	−	0.123660i	−0.499422	−	0.866359i	$-0.666454\pi$
$433$	3.54171	−	2.57320i	0.170204	−	0.123660i	0.669626	+	0.742698i	$0.266454\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		−	13.4068i		−	0.639871i	−0.947439	−	0.319936i	$-0.896339\pi$
$439$		−	13.4068i		−	0.639871i	0.947439	−	0.319936i	$-0.103661\pi$
$440$	16.3089	+	31.2399i	0.777497	+	1.48930i
$441$	−21.0000			−1.00000
$442$		0			0
$443$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$443$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$444$		0			0
$445$	−24.7394	+	76.1399i	−1.17276	+	3.60938i
$446$		0			0
$447$	19.9294	+	27.4304i	0.942626	+	1.29741i
$448$		0			0
$449$	−13.0737	−	40.2368i	−0.616987	−	1.89889i	−0.363819	−	0.931470i	$-0.618527\pi$
$449$	−13.0737	−	40.2368i	−0.616987	−	1.89889i	−0.253168	−	0.967422i	$-0.581473\pi$
$450$		−	29.0800i		−	1.37084i
$451$	−18.1665	+	18.5296i	−0.855427	+	0.872527i
$452$		0			0
$453$		0			0
$454$	−16.7437	−	12.1650i	−0.785821	−	0.570932i
$455$		0			0
$456$		0			0
$457$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$457$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			34.9272i			1.62672i	0.581758	+	0.813362i	$0.302365\pi$
$461$			34.9272i			1.62672i	−0.581758	+	0.813362i	$0.697635\pi$
$462$		0			0
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$467$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$468$	−15.6423	−	5.08248i	−0.723064	−	0.234938i
$469$		0			0
$470$	−22.0654	+	30.3704i	−1.01780	+	1.40088i
$471$	−13.0465	−	40.1531i	−0.601152	−	1.85016i
$472$			10.4782i			0.482296i
$473$	−6.05841	+	40.8644i	−0.278566	+	1.87895i
$474$	6.50863			0.298951
$475$		0			0
$476$		0			0
$477$		0			0
$478$	6.19609	−	19.0696i	0.283402	−	0.872223i
$479$	−40.4303	−	13.1366i	−1.84731	−	0.600226i	−0.997298	−	0.0734577i	$-0.976597\pi$
$479$	−40.4303	−	13.1366i	−1.84731	−	0.600226i	−0.850009	−	0.526769i	$-0.823403\pi$
$480$	−25.7929	−	35.5009i	−1.17728	−	1.62039i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−15.8020	+	5.48242i	−0.718273	+	0.249201i
$485$		0			0
$486$	−10.2655	+	3.33548i	−0.465654	+	0.151300i
$487$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$487$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$488$	30.3841	−	22.0754i	1.37542	−	0.999304i
$489$		0			0
$490$	20.0929	+	6.52859i	0.907706	+	0.294932i
$491$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$491$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$492$	12.1118	−	16.6705i	0.546044	−	0.751565i
$493$		0			0
$494$		0			0
$495$	42.9006	+	6.36028i	1.92824	+	0.285873i
$496$		0			0
$497$		0			0
$498$	2.40055	+	1.74410i	0.107571	+	0.0781550i
$499$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$499$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$500$	18.4310	−	56.7247i	0.824258	−	2.53680i
$501$	−19.6527	−	6.38556i	−0.878019	−	0.285286i
$502$		0			0
$503$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$503$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	22.5167			1.00000
$508$	−31.5958	+	10.2661i	−1.40184	+	0.455484i
$509$	−28.4083	−	20.6398i	−1.25917	−	0.914844i	−0.260457	−	0.965485i	$-0.583873\pi$
$509$	−28.4083	−	20.6398i	−1.25917	−	0.914844i	−0.998717	+	0.0506418i	$0.983873\pi$
$510$		0			0
$511$		0			0
$512$	−13.7545	−	4.46912i	−0.607870	−	0.197509i
$513$		0			0
$514$		0			0
$515$	−7.54670	−	23.2263i	−0.332547	−	1.02347i
$516$		−	32.8043i		−	1.44413i
$517$	−29.4572	−	28.8799i	−1.29552	−	1.27014i
$518$		0			0
$519$		0			0
$520$	30.9941	+	22.5185i	1.35918	+	0.987502i
$521$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$521$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$522$		0			0
$523$	11.8787	+	3.85962i	0.519419	+	0.168769i	0.556982	−	0.830525i	$-0.311959\pi$
$523$	11.8787	+	3.85962i	0.519419	+	0.168769i	−0.0375627	+	0.999294i	$0.511959\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$	6.89083	−	3.59738i	0.299885	−	0.156556i
$529$	23.0000			1.00000
$530$		0			0
$531$	10.4323	+	7.57953i	0.452724	+	0.328923i
$532$		0			0
$533$	−8.71735	+	26.8292i	−0.377590	+	1.16210i
$534$	−20.9497	−	6.80699i	−0.906584	−	0.294567i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−10.3348	+	20.7892i	−0.445152	+	0.895455i
$540$	−34.4388			−1.48201
$541$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$541$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$542$		0			0
$543$	−9.23808	+	6.71186i	−0.396444	+	0.288033i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	22.4584	−	30.9113i	0.960250	−	1.32167i	0.0134293	−	0.999910i	$-0.495725\pi$
$547$	22.4584	−	30.9113i	0.960250	−	1.32167i	0.946821	−	0.321761i	$-0.104275\pi$
$548$	6.08335	+	18.7226i	0.259868	+	0.799791i
$549$		−	46.2197i		−	1.97261i
$550$	−28.7881	−	14.3112i	−1.22753	−	0.610233i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	13.9934	−	10.1668i	0.594521	−	0.431945i
$555$		0			0
$556$	−21.9255	−	7.12402i	−0.929847	−	0.302126i
$557$	10.5193	+	14.4786i	0.445719	+	0.613479i	0.971471	−	0.237159i	$-0.0762162\pi$
$557$	10.5193	+	14.4786i	0.445719	+	0.613479i	−0.525752	+	0.850638i	$0.676216\pi$
$558$		0			0
$559$	13.8779	+	42.7118i	0.586973	+	1.80652i
$560$		0			0
$561$		0			0
$562$	−15.7138			−0.662845
$563$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$563$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$564$	26.5016	+	19.2546i	1.11592	+	0.810764i
$565$		0			0
$566$	−5.43191	+	16.7177i	−0.228320	+	0.702697i
$567$		0			0
$568$	7.05169	+	9.70582i	0.295882	+	0.407247i
$569$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$569$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$570$		0			0
$571$		−	28.8444i		−	1.20710i	−0.797325	−	0.603550i	$-0.793752\pi$
$571$		−	28.8444i		−	1.20710i	0.797325	−	0.603550i	$-0.206248\pi$
$572$	−12.7295	+	12.9840i	−0.532249	+	0.542888i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	3.19961	−	2.32466i	0.133317	−	0.0968606i
$577$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$577$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$578$	11.1951	+	3.63751i	0.465654	+	0.151300i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	44.8400	−	14.5694i	1.85391	−	0.602371i
$586$	6.03184	+	4.38239i	0.249173	+	0.181035i
$587$	33.7000	−	24.4845i	1.39095	−	1.01058i	0.395189	−	0.918600i	$-0.370679\pi$
$587$	33.7000	−	24.4845i	1.39095	−	1.01058i	0.995760	−	0.0919844i	$-0.0293210\pi$
$588$	5.69694	−	17.5334i	0.234938	−	0.723064i
$589$		0			0
$590$	−7.62535	−	10.4954i	−0.313931	−	0.432088i
$591$	−27.9879	+	38.5221i	−1.15127	+	1.58459i
$592$		0			0
$593$			46.2311i			1.89848i	0.314548	+	0.949242i	$0.398147\pi$
$593$			46.2311i			1.89848i	−0.314548	+	0.949242i	$0.601853\pi$
$594$	−1.75002	+	11.8040i	−0.0718042	+	0.484324i
$595$		0			0
$596$	−28.3087	+	9.19806i	−1.15957	+	0.376767i
$597$	−8.72013	−	6.33554i	−0.356891	−	0.259297i
$598$		0			0
$599$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$599$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$600$	56.2147	+	18.2653i	2.29495	+	0.745676i
$601$	−13.3264	−	18.3422i	−0.543594	−	0.748193i	0.445532	−	0.895266i	$-0.353015\pi$
$601$	−13.3264	−	18.3422i	−0.543594	−	0.748193i	−0.989126	+	0.147074i	$0.953015\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	27.4092	−	39.3399i	1.11434	−	1.59939i
$606$		0			0
$607$	−10.9416	+	3.55516i	−0.444108	+	0.144299i	−0.522530	−	0.852621i	$-0.675012\pi$
$607$	−10.9416	+	3.55516i	−0.444108	+	0.144299i	0.0784223	+	0.996920i	$0.475012\pi$
$608$		0			0
$609$		0			0
$610$	−14.3690	+	44.2233i	−0.581785	+	1.79055i
$611$	−42.6513	−	13.8583i	−1.72549	−	0.560645i
$612$		0			0
$613$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$613$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$614$		0			0
$615$			59.0687i			2.38188i
$616$		0			0
$617$	30.1401			1.21340			0.606698	−	0.794932i	$-0.292494\pi$
$617$	30.1401			1.21340			0.606698	+	0.794932i	$0.292494\pi$
$618$	6.39068	−	2.07646i	0.257071	−	0.0835274i
$619$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$619$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$	4.96708	−	6.83660i	0.198842	−	0.273683i
$625$	31.2043	+	96.0370i	1.24817	+	3.84148i
$626$		−	16.4704i		−	0.658290i
$627$		0			0
$628$	37.0640			1.47901
$629$		0			0
$630$		0			0
$631$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$631$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$632$	−4.08810	+	12.5819i	−0.162616	+	0.500481i
$633$	35.0862	+	11.4002i	1.39455	+	0.453117i
$634$	−2.00077	−	2.75382i	−0.0794606	−	0.109368i
$635$	55.9768	−	77.0454i	2.22137	−	3.05745i
$636$		0			0
$637$			25.2389i			1.00000i
$638$		0			0
$639$	14.7643			0.584067
$640$	44.4060	−	14.4284i	1.75530	−	0.570332i
$641$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$641$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$642$		0			0
$643$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$643$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$644$		0			0
$645$	55.2734	+	76.0773i	2.17639	+	2.99554i
$646$		0			0
$647$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$647$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$648$		−	21.9394i		−	0.861862i
$649$	12.6375	−	6.59747i	0.496067	−	0.258974i
$650$	−34.9498			−1.37084
$651$		0			0
$652$		0			0
$653$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$653$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$654$		0			0
$655$		0			0
$656$	6.22300	+	8.56522i	0.242967	+	0.334416i
$657$		0			0
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$	−16.9485	+	34.0932i	−0.659720	+	1.32708i
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$		0			0
$663$		0			0
$664$	−4.87933	+	3.54504i	−0.189355	+	0.137574i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	10.6629	−	14.6762i	0.412559	−	0.567839i
$669$		0			0
$670$		0			0
$671$	−45.7558	−	22.7463i	−1.76638	−	0.878111i
$672$		0			0
$673$	−2.01975	+	0.656257i	−0.0778557	+	0.0252969i	−0.347686	−	0.937611i	$-0.613032\pi$
$673$	−2.01975	+	0.656257i	−0.0778557	+	0.0252969i	0.269830	+	0.962908i	$0.413032\pi$
$674$	2.55032	+	1.85292i	0.0982346	+	0.0713716i
$675$	58.8491	−	42.7564i	2.26510	−	1.64569i
$676$	−6.10838	+	18.7997i	−0.234938	+	0.723064i
$677$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$677$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		−	51.7705i		−	1.98385i
$682$		0			0
$683$	47.3006			1.80991			0.904954	−	0.425510i	$-0.139905\pi$
$683$	47.3006			1.80991			0.904954	+	0.425510i	$0.139905\pi$
$684$		0			0
$685$	−45.6546	−	33.1700i	−1.74437	−	1.26736i
$686$		0			0
$687$		0			0
$688$	16.0298	+	5.20839i	0.611129	+	0.198568i
$689$		0			0
$690$		0			0
$691$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$691$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	62.8514	−	20.4217i	2.38409	−	0.774638i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$701$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$702$	4.00874	+	12.3376i	0.151300	+	0.465654i
$703$		0			0
$704$	−0.726686	−	4.31154i	−0.0273880	−	0.162497i
$705$	−93.9034			−3.53661
$706$	13.1807	−	4.28268i	0.496063	−	0.161181i
$707$		0			0
$708$	−9.15842	+	6.65398i	−0.344195	+	0.250072i
$709$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$709$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$710$	−14.1266	−	4.59001i	−0.530161	−	0.172260i
$711$	9.56967	+	13.1715i	0.358891	+	0.493970i
$712$	26.3173	−	36.2226i	0.986282	−	1.35750i
$713$		0			0
$714$		0			0
$715$	7.64411	−	51.5600i	0.285873	−	1.92824i
$716$		0			0
$717$	47.7012	−	15.4991i	1.78144	−	0.578823i
$718$	−1.17439	−	0.853245i	−0.0438279	−	0.0318428i
$719$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$719$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$720$	5.46790	−	16.8285i	0.203777	−	0.627160i
$721$		0			0
$722$	−7.73294	−	10.6435i	−0.287790	−	0.396109i
$723$		0			0
$724$	−3.09775	−	9.53389i	−0.115127	−	0.354324i
$725$		0			0
$726$	10.8243	+	7.54160i	0.401727	+	0.279895i
$727$	−29.7733			−1.10423			−0.552116	−	0.833767i	$-0.686179\pi$
$727$	−29.7733			−1.10423			−0.552116	+	0.833767i	$0.686179\pi$
$728$		0			0
$729$	−21.8435	−	15.8702i	−0.809017	−	0.587785i
$730$		0			0
$731$		0			0
$732$	38.5899	+	12.5386i	1.42632	+	0.463440i
$733$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$733$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$734$	13.4976	−	18.5779i	0.498206	−	0.685722i
$735$	16.3308	+	50.2610i	0.602371	+	1.85391i
$736$		0			0
$737$		0			0
$738$	−16.2526			−0.598268
$739$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$739$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	50.5537	+	16.4259i	1.85464	+	0.602608i	0.995929	+	0.0901418i	$0.0287320\pi$
$743$	50.5537	+	16.4259i	1.85464	+	0.602608i	0.858707	+	0.512466i	$0.171268\pi$
$744$		0			0
$745$	50.1532	−	69.0300i	1.83747	−	2.52906i
$746$	−4.49872	−	13.8456i	−0.164710	−	0.506925i
$747$			7.42235i			0.271569i
$748$		0			0
$749$		0			0
$750$	−44.7409	+	14.5372i	−1.63371	+	0.530824i
$751$	−43.9984	−	31.9667i	−1.60552	−	1.16648i	−0.875713	−	0.482832i	$-0.839608\pi$
$751$	−43.9984	−	31.9667i	−1.60552	−	1.16648i	−0.729810	−	0.683650i	$-0.760392\pi$
$752$	−13.6164	+	9.89290i	−0.496539	+	0.360757i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	6.62694	+	20.3956i	0.240860	+	0.741292i	0.996290	+	0.0860619i	$0.0274283\pi$
$757$	6.62694	+	20.3956i	0.240860	+	0.741292i	−0.755429	+	0.655230i	$0.772572\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−38.7001	+	12.5744i	−1.40288	+	0.455823i	−0.910120	−	0.414344i	$-0.864011\pi$
$761$	−38.7001	+	12.5744i	−1.40288	+	0.455823i	−0.492757	+	0.870167i	$0.664011\pi$
$762$	21.1989	+	15.4019i	0.767955	+	0.557952i
$763$		0			0
$764$		0			0
$765$		0			0
$766$	15.7868	+	21.7287i	0.570401	+	0.785089i
$767$	9.10946	−	12.5381i	0.328923	−	0.452724i
$768$	5.38115	+	16.5615i	0.194176	+	0.597611i
$769$		0			0			−	1.00000i	$-0.5\pi$
$769$		0			0				1.00000i	$0.5\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−38.3773	−	27.8827i	−1.38033	−	1.00287i	−0.996849	−	0.0793244i	$-0.974724\pi$
$773$	−38.3773	−	27.8827i	−1.38033	−	1.00287i	−0.383485	−	0.923547i	$-0.625276\pi$
$774$	−20.9325	+	15.2084i	−0.752404	+	0.546653i
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$			41.3903i			1.48201i
$781$	7.26601	−	14.6161i	0.259998	−	0.523006i
$782$		0			0
$783$		0			0
$784$	7.66313	+	5.56759i	0.273683	+	0.198842i
$785$	−85.9560	+	62.4507i	−3.06790	+	2.22896i
$786$		0			0
$787$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$787$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$788$	−24.5703	−	33.8181i	−0.875281	−	1.20472i
$789$		0			0
$790$	−5.06149	−	15.5777i	−0.180080	−	0.554228i
$791$		0			0
$792$	−21.7192	−	10.7971i	−0.771759	−	0.383659i
$793$	−55.5492			−1.97261
$794$		0			0
$795$		0			0
$796$	7.65530	−	5.56190i	0.271335	−	0.197136i
$797$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$797$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$798$		0			0
$799$		0			0
$800$	−47.8271	+	65.8283i	−1.69094	+	2.32738i
$801$	−17.0272	−	52.4043i	−0.601626	−	1.85162i
$802$			7.05123i			0.248987i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$809$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$810$	15.9661	+	21.9755i	0.560993	+	0.772141i
$811$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$811$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$	−49.3178	−	16.0243i	−1.72225	−	0.559593i
$821$	−32.0579	−	44.1239i	−1.11883	−	1.53994i	−0.807724	−	0.589560i	$-0.799301\pi$
$821$	−32.0579	−	44.1239i	−1.11883	−	1.53994i	−0.311105	−	0.950376i	$-0.600699\pi$
$822$	9.12666	−	12.5618i	0.318329	−	0.438142i
$823$	−9.01824	−	27.7553i	−0.314356	−	0.967489i	−0.976019	−	0.217687i	$-0.930149\pi$
$823$	−9.01824	−	27.7553i	−0.314356	−	0.967489i	0.661662	−	0.749802i	$-0.269851\pi$
$824$			13.6581i			0.475803i
$825$	−13.3656	−	79.3002i	−0.465331	−	2.76088i
$826$		0			0
$827$	37.5517	−	12.2013i	1.30580	−	0.424281i	0.428205	−	0.903681i	$-0.359146\pi$
$827$	37.5517	−	12.2013i	1.30580	−	0.424281i	0.877596	+	0.479401i	$0.159146\pi$
$828$		0			0
$829$	31.9104	−	23.1843i	1.10829	−	0.805223i	0.125900	−	0.992043i	$-0.459818\pi$
$829$	31.9104	−	23.1843i	1.10829	−	0.805223i	0.982394	+	0.186820i	$0.0598181\pi$
$830$	2.30750	−	7.10175i	0.0800944	−	0.246505i
$831$	41.1490	+	13.3701i	1.42744	+	0.463804i
$832$	−2.79389	−	3.84546i	−0.0968606	−	0.133317i
$833$		0			0
$834$	5.61898	+	17.2935i	0.194570	+	0.598823i
$835$			52.0023i			1.79961i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	17.4708	+	12.6933i	0.603159	+	0.438221i	0.846999	−	0.531595i	$-0.178407\pi$
$839$	17.4708	+	12.6933i	0.603159	+	0.438221i	−0.243840	+	0.969816i	$0.578407\pi$
$840$		0			0
$841$	−8.96149	+	27.5806i	−0.309017	+	0.951057i
$842$		0			0
$843$	−23.1040	−	31.7999i	−0.795744	−	1.09525i
$844$	−19.0365	+	26.2015i	−0.655264	+	0.901894i
$845$	−17.5102	−	53.8910i	−0.602371	−	1.85391i
$846$		−	25.8374i		−	0.888306i
$847$		0			0
$848$		0			0
$849$	−41.8181	+	13.5875i	−1.43519	+	0.466323i
$850$		0			0
$851$		0			0
$852$	−4.00530	+	12.3271i	−0.137219	+	0.422318i
$853$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$853$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$	14.1866	+	2.10326i	0.484324	+	0.0718042i
$859$	25.5011			0.870086			0.435043	−	0.900410i	$-0.356733\pi$
$859$	25.5011			0.870086			0.435043	+	0.900410i	$0.356733\pi$
$860$	−78.5133	+	25.5105i	−2.67728	+	0.869902i
$861$		0			0
$862$	−19.4311	+	14.1175i	−0.661824	+	0.480843i
$863$	−14.6428	+	45.0660i	−0.498448	+	1.53407i	0.313065	+	0.949732i	$0.398644\pi$
$863$	−14.6428	+	45.0660i	−0.498448	+	1.53407i	−0.811513	+	0.584334i	$0.801356\pi$
$864$	28.7239	+	9.33295i	0.977206	+	0.317514i
$865$		0			0
$866$	1.78175	−	2.45237i	0.0605463	−	0.0833348i
$867$	9.09896	+	28.0037i	0.309017	+	0.951057i
$868$		0			0
$869$	17.7489	−	2.99147i	0.602089	−	0.101479i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$877$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$878$	−2.86866	−	8.82884i	−0.0968127	−	0.297959i
$879$			18.6501i			0.629052i
$880$	−13.9686	−	13.6949i	−0.470882	−	0.461654i
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−13.8292	+	4.49339i	−0.465654	+	0.151300i
$883$	47.7256	+	34.6747i	1.60609	+	1.16690i	0.874322	+	0.485346i	$0.161306\pi$
$883$	47.7256	+	34.6747i	1.60609	+	1.16690i	0.731772	+	0.681550i	$0.238694\pi$
$884$		0			0
$885$	10.0279	−	30.8628i	0.337085	−	1.03744i
$886$		0			0
$887$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$887$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$888$		0			0
$889$		0			0
$890$			55.4343i			1.85816i
$891$	−26.4608	+	13.8140i	−0.886471	+	0.462785i
$892$		0			0
$893$		0			0
$894$	18.9935	+	13.7996i	0.635237	+	0.461527i
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−17.2190	−	23.6999i	−0.574606	−	0.790877i
$899$		0			0
$900$	19.7335	+	60.7334i	0.657783	+	2.02445i
$901$		0			0
$902$	−7.99847	+	16.0895i	−0.266320	+	0.535722i
$903$		0			0
$904$		0			0
$905$	23.2481	+	16.8907i	0.772793	+	0.561467i
$906$		0			0
$907$	−18.6083	+	57.2704i	−0.617878	+	1.90163i	−0.287559	+	0.957763i	$0.592844\pi$
$907$	−18.6083	+	57.2704i	−0.617878	+	1.90163i	−0.330319	+	0.943869i	$0.607156\pi$
$908$	43.2243	+	14.0444i	1.43445	+	0.466081i
$909$		0			0
$910$		0			0
$911$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$911$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$912$		0			0
$913$	7.34785	+	3.65279i	0.243178	+	0.120890i
$914$		0			0
$915$	−110.622	+	35.9431i	−3.65703	+	1.18824i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−21.8236	−	7.09092i	−0.719895	−	0.233908i	−0.0739171	−	0.997264i	$-0.523550\pi$
$919$	−21.8236	−	7.09092i	−0.719895	−	0.233908i	−0.645977	+	0.763356i	$0.723550\pi$
$920$		0			0
$921$		0			0
$922$	7.47342	+	23.0008i	0.246124	+	0.757491i
$923$		−	17.7445i		−	0.584067i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	13.5984	+	9.87979i	0.446629	+	0.324495i
$928$		0			0
$929$	12.4787	−	38.4056i	0.409414	−	1.26005i	−0.507739	−	0.861511i	$-0.669519\pi$
$929$	12.4787	−	38.4056i	0.409414	−	1.26005i	0.917153	−	0.398535i	$-0.130481\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−26.3679			−0.861862
$937$	−19.4737	+	6.32739i	−0.636178	+	0.206707i	−0.609310	−	0.792932i	$-0.708553\pi$
$937$	−19.4737	+	6.32739i	−0.636178	+	0.206707i	−0.0268681	+	0.999639i	$0.508553\pi$
$938$		0			0
$939$	33.3312	−	24.2165i	1.08772	−	0.790276i
$940$	25.4744	−	78.4021i	0.830882	−	2.55719i
$941$	36.0660	+	11.7185i	1.17572	+	0.382014i	0.830774	−	0.556610i	$-0.187898\pi$
$941$	36.0660	+	11.7185i	1.17572	+	0.382014i	0.344943	+	0.938624i	$0.387898\pi$
$942$	−17.1832	−	23.6506i	−0.559859	−	0.770579i
$943$		0			0
$944$	−1.79736	−	5.53170i	−0.0584991	−	0.180042i
$945$		0			0
$946$	4.75412	+	28.2070i	0.154570	+	0.917088i
$947$	17.2322			0.559972			0.279986	−	0.960004i	$-0.409670\pi$
$947$	17.2322			0.559972			0.279986	+	0.960004i	$0.409670\pi$
$948$	−13.5933	+	4.41672i	−0.441489	+	0.143448i
$949$		0			0
$950$		0			0
$951$	2.63117	−	8.09790i	0.0853214	−	0.262592i
$952$		0			0
$953$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$953$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$954$		0			0
$955$		0			0
$956$			44.0314i			1.42408i
$957$		0			0
$958$	−29.4356			−0.951021
$959$		0			0
$960$	−8.05199	−	5.85012i	−0.259877	−	0.188812i
$961$	−25.0795	+	18.2213i	−0.809017	+	0.587785i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0			−	1.00000i	$-0.5\pi$
$967$		0			0				1.00000i	$0.5\pi$
$968$	−21.3775	+	16.1876i	−0.687099	+	0.520289i
$969$		0			0
$970$		0			0
$971$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$971$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$972$	19.1761	−	13.9323i	0.615075	−	0.446878i
$973$		0			0
$974$		0			0
$975$	−51.3867	−	70.7278i	−1.64569	−	2.26510i
$976$	−12.2539	+	16.8661i	−0.392239	+	0.539870i
$977$	10.9440	+	33.6821i	0.350128	+	1.07758i	0.958781	+	0.284147i	$0.0917105\pi$
$977$	10.9440	+	33.6821i	0.350128	+	1.07758i	−0.608652	+	0.793437i	$0.708289\pi$
$978$		0			0
$979$	−60.2580	−	8.93363i	−1.92585	−	0.285520i
$980$	−46.3943			−1.48201
$981$		0			0
$982$		0			0
$983$	−20.9938	+	15.2529i	−0.669600	+	0.486493i	−0.869891	−	0.493244i	$-0.835811\pi$
$983$	−20.9938	+	15.2529i	−0.669600	+	0.486493i	0.200292	+	0.979736i	$0.435811\pi$
$984$	10.2084	−	31.4181i	0.325431	−	1.00157i
$985$	113.963	+	37.0289i	3.63117	+	1.17984i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	29.6124	−	4.99101i	0.941145	−	0.158625i
$991$	43.1793			1.37164			0.685818	−	0.727773i	$-0.259445\pi$
$991$	43.1793			1.37164			0.685818	+	0.727773i	$0.259445\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−8.38211	+	25.7975i	−0.265731	+	0.817835i
$996$	−6.19708	−	2.01355i	−0.196362	−	0.0638019i
$997$	−8.15982	−	11.2310i	−0.258424	−	0.355690i	0.660015	−	0.751252i	$-0.270550\pi$
$997$	−8.15982	−	11.2310i	−0.258424	−	0.355690i	−0.918439	+	0.395562i	$0.870550\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.y.a.116.5	yes	32
3.2	odd	2	inner	429.2.y.a.116.4	✓	32
11.2	odd	10	inner	429.2.y.a.233.5	yes	32
13.12	even	2	inner	429.2.y.a.116.4	✓	32
33.2	even	10	inner	429.2.y.a.233.4	yes	32
39.38	odd	2	CM	429.2.y.a.116.5	yes	32
143.90	odd	10	inner	429.2.y.a.233.4	yes	32
429.233	even	10	inner	429.2.y.a.233.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.y.a.116.4	✓	32	3.2	odd	2	inner
429.2.y.a.116.4	✓	32	13.12	even	2	inner
429.2.y.a.116.5	yes	32	1.1	even	1	trivial
429.2.y.a.116.5	yes	32	39.38	odd	2	CM
429.2.y.a.233.4	yes	32	33.2	even	10	inner
429.2.y.a.233.4	yes	32	143.90	odd	10	inner
429.2.y.a.233.5	yes	32	11.2	odd	10	inner
429.2.y.a.233.5	yes	32	429.233	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.658535 - 0.213971i) q^{2} +(1.40126 + 1.01807i) q^{3} +(-1.23015 + 0.893756i) q^{4} +(1.34694 - 4.14546i) q^{5} +(1.14062 + 0.370608i) q^{6} +(-1.43285 + 1.97215i) q^{8} +(0.927051 + 2.85317i) q^{9} +O(q^{10})\)	\(q+(0.658535 - 0.213971i) q^{2} +(1.40126 + 1.01807i) q^{3} +(-1.23015 + 0.893756i) q^{4} +(1.34694 - 4.14546i) q^{5} +(1.14062 + 0.370608i) q^{6} +(-1.43285 + 1.97215i) q^{8} +(0.927051 + 2.85317i) q^{9} -3.01814i q^{10} +(3.28077 + 0.486394i) q^{11} -2.63367 q^{12} +(3.42908 - 1.11418i) q^{13} +(6.10780 - 4.43758i) q^{15} +(0.418151 - 1.28694i) q^{16} +(1.22099 + 1.68055i) q^{18} +(2.04809 + 6.30337i) q^{20} +(2.26457 - 0.381681i) q^{22} +(-4.01559 + 1.30475i) q^{24} +(-11.3255 - 8.22846i) q^{25} +(2.01977 - 1.46745i) q^{26} +(-1.60570 + 4.94183i) q^{27} +(3.07269 - 4.22919i) q^{30} -5.81239i q^{32} +(4.10201 + 4.02163i) q^{33} +(-3.69045 - 2.68127i) q^{36} +(5.93935 + 1.92981i) q^{39} +(6.24551 + 8.59621i) q^{40} +(-4.59885 + 6.32977i) q^{41} +12.4558i q^{43} +(-4.47055 + 2.33387i) q^{44} +13.0764 q^{45} +(-10.0626 - 7.31094i) q^{47} +(1.89613 - 1.37762i) q^{48} +(-2.16312 + 6.65740i) q^{49} +(-9.21889 - 2.99540i) q^{50} +(-3.22248 + 4.43537i) q^{52} +3.59794i q^{54} +(6.43533 - 12.9451i) q^{55} +(3.47744 - 2.52651i) q^{59} +(-3.54740 + 10.9178i) q^{60} +(-14.6525 - 4.76089i) q^{61} +(-0.407381 - 1.25379i) q^{64} -15.7159i q^{65} +(3.56183 + 1.77067i) q^{66} +(1.52081 - 4.68057i) q^{71} +(-6.95521 - 2.25988i) q^{72} +(-7.49278 - 23.0604i) q^{75} +4.32419 q^{78} +(5.16135 - 1.67702i) q^{79} +(-4.77172 - 3.46686i) q^{80} +(-7.28115 + 5.29007i) q^{81} +(-1.67411 + 5.15239i) q^{82} +(2.35302 + 0.764544i) q^{83} +(2.66517 + 8.20255i) q^{86} +(-5.66010 + 5.77324i) q^{88} -18.3671 q^{89} +(8.61126 - 2.79797i) q^{90} +(-8.19093 - 2.66139i) q^{94} +(5.91744 - 8.14466i) q^{96} +4.84697i q^{98} +(1.65367 + 9.81149i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) 32 * q + 16 * q^4 - 24 * q^9	\( 32 q + 16 q^{4} - 24 q^{9} - 24 q^{12} - 92 q^{16} + 28 q^{22} - 40 q^{25} + 180 q^{30} + 48 q^{36} - 72 q^{48} + 56 q^{49} - 260 q^{52} + 32 q^{55} + 184 q^{64} - 60 q^{66} - 144 q^{75} - 72 q^{81} + 204 q^{82} - 40 q^{88} + 60 q^{90}+O(q^{100}) \) 32 * q + 16 * q^4 - 24 * q^9 - 24 * q^12 - 92 * q^16 + 28 * q^22 - 40 * q^25 + 180 * q^30 + 48 * q^36 - 72 * q^48 + 56 * q^49 - 260 * q^52 + 32 * q^55 + 184 * q^64 - 60 * q^66 - 144 * q^75 - 72 * q^81 + 204 * q^82 - 40 * q^88 + 60 * q^90

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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