LMFDB - Embedded newform 429.2.y.a.194.8

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			194.8
Character	$\chi$	$=$	429.194
Dual form			429.2.y.a.272.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.65880 - 2.28314i) q^{2} +(-0.535233 + 1.64728i) q^{3} +(-1.84308 - 5.67240i) q^{4} +(2.37713 - 1.72708i) q^{5} +(2.87312 + 3.95451i) q^{6} +(-10.6402 - 3.45720i) q^{8} +(-2.42705 - 1.76336i) q^{9} +O(q^{10})$	\(q+(1.65880 - 2.28314i) q^{2} +(-0.535233 + 1.64728i) q^{3} +(-1.84308 - 5.67240i) q^{4} +(2.37713 - 1.72708i) q^{5} +(2.87312 + 3.95451i) q^{6} +(-10.6402 - 3.45720i) q^{8} +(-2.42705 - 1.76336i) q^{9} -8.29218i q^{10} +(1.47640 + 2.96989i) q^{11} +10.3305 q^{12} +(2.11929 - 2.91695i) q^{13} +(1.57267 + 4.84018i) q^{15} +(-15.8927 + 11.5467i) q^{16} +(-8.05196 + 2.61624i) q^{18} +(-14.1779 - 10.3009i) q^{20} +(9.22971 + 1.55562i) q^{22} +(11.3900 - 15.6769i) q^{24} +(1.12283 - 3.45571i) q^{25} +(-3.14433 - 9.67726i) q^{26} +(4.20378 - 3.05422i) q^{27} +(13.6595 + 4.43825i) q^{30} +33.0633i q^{32} +(-5.68245 + 0.842460i) q^{33} +(-5.52923 + 17.0172i) q^{36} +(3.67072 + 5.05231i) q^{39} +(-31.2639 + 10.1583i) q^{40} +(7.44109 + 2.41776i) q^{41} +7.66385i q^{43} +(14.1253 - 13.8485i) q^{44} -8.81487 q^{45} +(-0.508040 + 1.56359i) q^{47} +(-10.5144 - 32.3598i) q^{48} +(5.66312 - 4.11450i) q^{49} +(-6.02731 - 8.29588i) q^{50} +(-20.4521 - 6.64530i) q^{52} -14.6641i q^{54} +(8.63884 + 4.50993i) q^{55} +(3.92408 + 12.0771i) q^{59} +(24.5569 - 17.8416i) q^{60} +(-1.35819 - 1.86938i) q^{61} +(43.7027 + 31.7519i) q^{64} -10.5942i q^{65} +(-7.50258 + 14.3713i) q^{66} +(-3.98153 + 2.89275i) q^{71} +(19.7280 + 27.1532i) q^{72} +(5.09154 + 3.69922i) q^{75} +17.6241 q^{78} +(10.4486 - 14.3813i) q^{79} +(-17.8368 + 54.8960i) q^{80} +(2.78115 + 8.55951i) q^{81} +(17.8633 - 12.9785i) q^{82} +(5.06034 + 6.96496i) q^{83} +(17.4976 + 12.7128i) q^{86} +(-5.44166 - 36.7044i) q^{88} -18.3671 q^{89} +(-14.6221 + 20.1255i) q^{90} +(2.72715 + 3.75360i) q^{94} +(-54.4645 - 17.6966i) q^{96} -19.7548i q^{98} +(1.65367 - 9.81149i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$-1$	$e\left(\frac{7}{10}\right)$	$-1$

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 $

$2$	1.65880	−	2.28314i	1.17295	−	1.61442i	0.532441	−	0.846467i	$-0.321275\pi$
$2$	1.65880	−	2.28314i	1.17295	−	1.61442i	0.640505	−	0.767954i	$-0.278725\pi$
$3$	−0.535233	+	1.64728i	−0.309017	+	0.951057i
$3$	−0.535233	+	1.64728i	−0.309017	+	0.951057i
$4$	−1.84308	−	5.67240i	−0.921538	−	2.83620i
$5$	2.37713	−	1.72708i	1.06308	−	0.772375i	0.0884268	−	0.996083i	$-0.471816\pi$
$5$	2.37713	−	1.72708i	1.06308	−	0.772375i	0.974656	+	0.223708i	$0.0718161\pi$
$6$	2.87312	+	3.95451i	1.17295	+	1.61442i
$7$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$7$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$8$	−10.6402	−	3.45720i	−3.76187	−	1.22231i
$9$	−2.42705	−	1.76336i	−0.809017	−	0.587785i
$10$		−	8.29218i		−	2.62222i
$11$	1.47640	+	2.96989i	0.445152	+	0.895455i
$11$	1.47640	+	2.96989i	0.445152	+	0.895455i
$12$	10.3305			2.98216
$13$	2.11929	−	2.91695i	0.587785	−	0.809017i
$13$	2.11929	−	2.91695i	0.587785	−	0.809017i
$14$		0			0
$15$	1.57267	+	4.84018i	0.406062	+	1.24973i
$16$	−15.8927	+	11.5467i	−3.97317	+	2.88668i
$17$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$17$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$18$	−8.05196	+	2.61624i	−1.89787	+	0.616654i
$19$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$19$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$20$	−14.1779	−	10.3009i	−3.17028	−	2.30334i
$21$		0			0
$22$	9.22971	+	1.55562i	1.96778	+	0.331658i
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$	11.3900	−	15.6769i	2.32496	−	3.20004i
$25$	1.12283	−	3.45571i	0.224565	−	0.691141i
$26$	−3.14433	−	9.67726i	−0.616654	−	1.89787i
$27$	4.20378	−	3.05422i	0.809017	−	0.587785i
$28$		0			0
$29$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$29$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$30$	13.6595	+	4.43825i	2.49388	+	0.810310i
$31$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$31$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$32$			33.0633i			5.84482i
$33$	−5.68245	+	0.842460i	−0.989188	+	0.146653i
$34$		0			0
$35$		0			0
$36$	−5.52923	+	17.0172i	−0.921538	+	2.83620i
$37$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$37$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$38$		0			0
$39$	3.67072	+	5.05231i	0.587785	+	0.809017i
$40$	−31.2639	+	10.1583i	−4.94326	+	1.60616i
$41$	7.44109	+	2.41776i	1.16210	+	0.377590i	0.825690	−	0.564124i	$-0.190786\pi$
$41$	7.44109	+	2.41776i	1.16210	+	0.377590i	0.336413	+	0.941714i	$0.390786\pi$
$42$		0			0
$43$			7.66385i			1.16873i	0.811492	+	0.584363i	$0.198656\pi$
$43$			7.66385i			1.16873i	−0.811492	+	0.584363i	$0.801344\pi$
$44$	14.1253	−	13.8485i	2.12947	−	2.08773i
$45$	−8.81487			−1.31404
$46$		0			0
$47$	−0.508040	+	1.56359i	−0.0741053	+	0.228073i	−0.981248	−	0.192751i	$-0.938259\pi$
$47$	−0.508040	+	1.56359i	−0.0741053	+	0.228073i	0.907142	+	0.420824i	$0.138259\pi$
$48$	−10.5144	−	32.3598i	−1.51762	−	4.67074i
$49$	5.66312	−	4.11450i	0.809017	−	0.587785i
$50$	−6.02731	−	8.29588i	−0.852390	−	1.17321i
$51$		0			0
$52$	−20.4521	−	6.64530i	−2.83620	−	0.921538i
$53$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$53$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$54$		−	14.6641i		−	1.99553i
$55$	8.63884	+	4.50993i	1.16486	+	0.608119i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.92408	+	12.0771i	0.510871	+	1.57230i	0.790670	+	0.612242i	$0.209732\pi$
$59$	3.92408	+	12.0771i	0.510871	+	1.57230i	−0.279799	+	0.960059i	$0.590268\pi$
$60$	24.5569	−	17.8416i	3.17028	−	2.30334i
$61$	−1.35819	−	1.86938i	−0.173898	−	0.239350i	0.713167	−	0.700994i	$-0.247260\pi$
$61$	−1.35819	−	1.86938i	−0.173898	−	0.239350i	−0.887066	+	0.461644i	$0.847260\pi$
$62$		0			0
$63$		0			0
$64$	43.7027	+	31.7519i	5.46284	+	3.96898i
$65$		−	10.5942i		−	1.31404i
$66$	−7.50258	+	14.3713i	−0.923503	+	1.76898i
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−3.98153	+	2.89275i	−0.472520	+	0.343306i	−0.798423	−	0.602097i	$-0.794332\pi$
$71$	−3.98153	+	2.89275i	−0.472520	+	0.343306i	0.325902	+	0.945403i	$0.394332\pi$
$72$	19.7280	+	27.1532i	2.32496	+	3.20004i
$73$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$73$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$74$		0			0
$75$	5.09154	+	3.69922i	0.587920	+	0.427149i
$76$		0			0
$77$		0			0
$78$	17.6241			1.99553
$79$	10.4486	−	14.3813i	1.17556	−	1.61802i	0.584613	−	0.811312i	$-0.301246\pi$
$79$	10.4486	−	14.3813i	1.17556	−	1.61802i	0.590949	−	0.806709i	$-0.298754\pi$
$80$	−17.8368	+	54.8960i	−1.99421	+	6.13756i
$81$	2.78115	+	8.55951i	0.309017	+	0.951057i
$82$	17.8633	−	12.9785i	1.97267	−	1.43323i
$83$	5.06034	+	6.96496i	0.555444	+	0.764504i	0.990738	−	0.135785i	$-0.0433556\pi$
$83$	5.06034	+	6.96496i	0.555444	+	0.764504i	−0.435294	+	0.900288i	$0.643356\pi$
$84$		0			0
$85$		0			0
$86$	17.4976	+	12.7128i	1.88682	+	1.37085i
$87$		0			0
$88$	−5.44166	−	36.7044i	−0.580082	−	3.91270i
$89$	−18.3671			−1.94690			−0.973452	−	0.228892i	$-0.926490\pi$
$89$	−18.3671			−1.94690			−0.973452	+	0.228892i	$0.926490\pi$
$90$	−14.6221	+	20.1255i	−1.54130	+	2.12142i
$91$		0			0
$92$		0			0
$93$		0			0
$94$	2.72715	+	3.75360i	0.281284	+	0.387154i
$95$		0			0
$96$	−54.4645	−	17.6966i	−5.55876	−	1.80615i
$97$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$97$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$98$		−	19.7548i		−	1.99553i
$99$	1.65367	−	9.81149i	0.166200	−	0.986092i
$100$	−21.6716			−2.16716
$101$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$101$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$102$		0			0
$103$	−2.14285	−	6.59503i	−0.211142	−	0.649827i	−0.999405	−	0.0344892i	$-0.989020\pi$
$103$	−2.14285	−	6.59503i	−0.211142	−	0.649827i	0.788263	−	0.615338i	$-0.210980\pi$
$104$	−32.6341	+	23.7101i	−3.20004	+	2.32496i
$105$		0			0
$106$		0			0
$107$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$107$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$108$	−25.0726	−	18.2163i	−2.41262	−	1.75287i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$	24.6269	−	12.2426i	2.34808	−	1.16728i
$111$		0			0
$112$		0			0
$113$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$113$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−10.2872	+	3.34253i	−0.951057	+	0.309017i
$118$	34.0828	+	11.0742i	3.13758	+	1.01946i
$119$		0			0
$120$		−	56.9374i		−	5.19765i
$121$	−6.64048	+	8.76949i	−0.603680	+	0.797227i
$122$	−6.52102			−0.590385
$123$	−7.96544	+	10.9635i	−0.718219	+	0.988544i
$124$		0			0
$125$	1.24072	+	3.81853i	0.110973	+	0.341540i
$126$		0			0
$127$	−12.3020	−	16.9323i	−1.09163	−	1.50250i	−0.846035	−	0.533127i	$-0.821017\pi$
$127$	−12.3020	−	16.9323i	−1.09163	−	1.50250i	−0.245595	−	0.969373i	$-0.578983\pi$
$128$	82.0975	−	26.6751i	7.25646	−	2.35777i
$129$	−12.6245	−	4.10194i	−1.11152	−	0.361156i
$130$	−24.1879	−	17.5735i	−2.12142	−	1.54130i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	15.2520	+	30.6804i	1.32751	+	2.67039i
$133$		0			0
$134$		0			0
$135$	4.71801	−	14.5205i	0.406062	−	1.24973i
$136$		0			0
$137$	−18.2430	+	13.2543i	−1.55860	+	1.13239i	−0.621463	+	0.783444i	$0.713461\pi$
$137$	−18.2430	+	13.2543i	−1.55860	+	1.13239i	−0.937142	+	0.348948i	$0.886539\pi$
$138$		0			0
$139$	−20.7904	+	6.75521i	−1.76342	+	0.572970i	−0.997545	−	0.0700216i	$-0.977693\pi$
$139$	−20.7904	+	6.75521i	−1.76342	+	0.572970i	−0.765874	+	0.642991i	$0.777693\pi$
$140$		0			0
$141$	−2.30374	−	1.67377i	−0.194010	−	0.140957i
$142$			13.8888i			1.16553i
$143$	11.7919	+	1.98747i	0.986092	+	0.166200i
$144$	58.9333			4.91111
$145$		0			0
$146$		0			0
$147$	3.74663	+	11.5309i	0.309017	+	0.951057i
$148$		0			0
$149$	−4.26883	−	5.87554i	−0.349716	−	0.481343i	0.597531	−	0.801846i	$-0.296148\pi$
$149$	−4.26883	−	5.87554i	−0.349716	−	0.481343i	−0.947248	+	0.320502i	$0.896148\pi$
$150$	16.8916	−	5.48843i	1.37920	−	0.448128i
$151$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$151$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	21.8933	−	30.1336i	1.75287	−	2.41262i
$157$	4.03726	−	12.4254i	0.322208	−	0.991655i	−0.650477	−	0.759526i	$-0.725431\pi$
$157$	4.03726	−	12.4254i	0.322208	−	0.991655i	0.972685	−	0.232129i	$-0.0745691\pi$
$158$	−15.5023	−	47.7112i	−1.23330	−	3.79570i
$159$		0			0
$160$	57.1031	+	78.5957i	4.51440	+	6.21353i
$161$		0			0
$162$	24.1559	+	7.84873i	1.89787	+	0.616654i
$163$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$163$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$164$		−	46.6650i		−	3.64392i
$165$	−12.0529	+	11.8167i	−0.938318	+	0.919929i
$166$	24.2960			1.88574
$167$	−2.24797	+	3.09406i	−0.173953	+	0.239426i	−0.887087	−	0.461602i	$-0.847275\pi$
$167$	−2.24797	+	3.09406i	−0.173953	+	0.239426i	0.713134	+	0.701027i	$0.247275\pi$
$168$		0			0
$169$	−4.01722	−	12.3637i	−0.309017	−	0.951057i
$170$		0			0
$171$		0			0
$172$	43.4724	−	14.1250i	3.31474	−	1.07702i
$173$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$173$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$174$		0			0
$175$		0			0
$176$	−57.7564	−	30.1519i	−4.35355	−	2.27279i
$177$	−21.9946			−1.65321
$178$	−30.4672	+	41.9345i	−2.28361	+	3.14312i
$179$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$179$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$180$	16.2465	+	50.0015i	1.21094	+	3.72689i
$181$	−16.7201	+	12.1479i	−1.24280	+	0.902945i	−0.997781	−	0.0665740i	$-0.978793\pi$
$181$	−16.7201	+	12.1479i	−1.24280	+	0.902945i	−0.245016	+	0.969519i	$0.578793\pi$
$182$		0			0
$183$	3.80634	−	1.23676i	0.281373	−	0.0914236i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	9.80565			0.715150
$189$		0			0
$190$		0			0
$191$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$191$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$192$	−75.6953	+	54.9958i	−5.46284	+	3.96898i
$193$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$193$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$194$		0			0
$195$	17.4515	+	5.67034i	1.24973	+	0.406062i
$196$	−33.7766	−	24.5402i	−2.41262	−	1.75287i
$197$		−	3.09502i		−	0.220511i	−0.993903	−	0.110256i	$-0.964833\pi$
$197$		−	3.09502i		−	0.220511i	0.993903	−	0.110256i	$-0.0351669\pi$
$198$	−19.6579	−	20.0508i	−1.39702	−	1.42495i
$199$	−28.0948			−1.99159			−0.995793	−	0.0916309i	$-0.970792\pi$
$199$	−28.0948			−1.99159			−0.995793	+	0.0916309i	$0.970792\pi$
$200$	−23.8942	+	32.8875i	−1.68957	+	2.32550i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	21.8641	−	7.10407i	1.52705	−	0.496170i
$206$	−18.6119	−	6.04737i	−1.29675	−	0.421340i
$207$		0			0
$208$			70.8290i			4.91111i
$209$		0			0
$210$		0			0
$211$	−3.30268	+	4.54575i	−0.227366	+	0.312942i	−0.907424	−	0.420216i	$-0.861954\pi$
$211$	−3.30268	+	4.54575i	−0.227366	+	0.312942i	0.680058	+	0.733158i	$0.261954\pi$
$212$		0			0
$213$	−2.63412	−	8.10698i	−0.180487	−	0.555481i
$214$		0			0
$215$	13.2361	+	18.2179i	0.902695	+	1.24245i
$216$	−55.2880	+	17.9642i	−3.76187	+	1.22231i
$217$		0			0
$218$		0			0
$219$		0			0
$220$	9.66013	−	57.3151i	0.651286	−	3.86418i
$221$		0			0
$222$		0			0
$223$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$223$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$224$		0			0
$225$	−8.81880	+	6.40723i	−0.587920	+	0.427149i
$226$		0			0
$227$	12.2411	−	3.97739i	0.812473	−	0.263989i	0.126828	−	0.991925i	$-0.459520\pi$
$227$	12.2411	−	3.97739i	0.812473	−	0.263989i	0.685645	+	0.727936i	$0.259520\pi$
$228$		0			0
$229$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$229$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$233$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$234$	−9.43299	+	29.0318i	−0.616654	+	1.89787i
$235$	1.49277	+	4.59427i	0.0973775	+	0.299697i
$236$	61.2736	−	44.5179i	3.98857	−	2.89787i
$237$	18.0975	+	24.9091i	1.17556	+	1.61802i
$238$		0			0
$239$	28.3391	+	9.20792i	1.83310	+	0.595611i	0.999034	+	0.0439509i	$0.0139945\pi$
$239$	28.3391	+	9.20792i	1.83310	+	0.595611i	0.834069	+	0.551660i	$0.186005\pi$
$240$	−80.8821	−	58.7643i	−5.22092	−	3.79322i
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$	9.00675	+	29.7079i	0.578976	+	1.90970i
$243$	−15.5885			−1.00000
$244$	−8.10066	+	11.1496i	−0.518592	+	0.713780i
$245$	6.35587	−	19.5614i	0.406062	−	1.24973i
$246$	11.8181	+	36.3724i	0.753494	+	2.31902i
$247$		0			0
$248$		0			0
$249$	−14.1817	+	4.60791i	−0.898728	+	0.292014i
$250$	10.7763	+	3.50144i	0.681554	+	0.221450i
$251$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$251$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$252$		0			0
$253$		0			0
$254$	−59.0654			−3.70609
$255$		0			0
$256$	41.8942	−	128.937i	2.61839	−	8.05857i
$257$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$257$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$258$	−30.3067	+	22.0191i	−1.88682	+	1.37085i
$259$		0			0
$260$	−60.0943	+	19.5258i	−3.72689	+	1.21094i
$261$		0			0
$262$		0			0
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$	63.3749	+	10.6815i	3.90045	+	0.657399i
$265$		0			0
$266$		0			0
$267$	9.83066	−	30.2556i	0.601626	−	1.85162i
$268$		0			0
$269$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$269$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$270$	−25.3262	−	34.8585i	−1.54130	−	2.12142i
$271$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$271$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$272$		0			0
$273$		0			0
$274$			63.6375i			3.84448i
$275$	11.9208	−	1.76734i	0.718852	−	0.106574i
$276$		0			0
$277$	14.6829	−	20.2092i	0.882208	−	1.21426i	−0.0935962	−	0.995610i	$-0.529836\pi$
$277$	14.6829	−	20.2092i	0.882208	−	1.21426i	0.975804	−	0.218645i	$-0.0701637\pi$
$278$	−19.0640	+	58.6728i	−1.14338	+	3.51896i
$279$		0			0
$280$		0			0
$281$	9.67327	+	13.3141i	0.577059	+	0.794253i	0.993369	−	0.114969i	$-0.0366770\pi$
$281$	9.67327	+	13.3141i	0.577059	+	0.794253i	−0.416310	+	0.909223i	$0.636677\pi$
$282$	−7.64288	+	2.48332i	−0.455127	+	0.147880i
$283$	−12.5110	−	4.06508i	−0.743704	−	0.241644i	−0.0874340	−	0.996170i	$-0.527867\pi$
$283$	−12.5110	−	4.06508i	−0.743704	−	0.241644i	−0.656270	+	0.754526i	$0.727867\pi$
$284$	23.7471	+	17.2533i	1.40913	+	1.02379i
$285$		0			0
$286$	24.0981	−	23.6258i	1.42495	−	1.39702i
$287$		0			0
$288$	58.3024	−	80.2463i	3.43550	−	4.72856i
$289$	−5.25329	+	16.1680i	−0.309017	+	0.951057i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	26.4512	−	8.59453i	1.54530	−	0.502098i	0.592466	−	0.805596i	$-0.298154\pi$
$293$	26.4512	−	8.59453i	1.54530	−	0.502098i	0.952832	+	0.303498i	$0.0981545\pi$
$294$	32.5416	+	10.5734i	1.89787	+	0.616654i
$295$	30.1861	+	21.9315i	1.75750	+	1.27690i
$296$		0			0
$297$	15.2772	+	7.97549i	0.886471	+	0.462785i
$298$	−20.4958			−1.18729
$299$		0			0
$300$	11.5994	−	35.6992i	0.669690	−	2.06109i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−6.45717	−	2.09806i	−0.369736	−	0.120135i
$306$		0			0
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$		0			0
$309$	12.0108			0.683269
$310$		0			0
$311$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$311$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$312$	−21.5902	−	66.4479i	−1.22231	−	3.76187i
$313$	3.11188	−	2.26091i	0.175894	−	0.127794i	−0.496355	−	0.868120i	$-0.665329\pi$
$313$	3.11188	−	2.26091i	0.175894	−	0.127794i	0.672249	+	0.740325i	$0.265329\pi$
$314$	−21.6719	−	29.8288i	−1.22302	−	1.68334i
$315$		0			0
$316$	−100.834	−	32.7630i	−5.67236	−	1.84306i
$317$	−19.9885	−	14.5225i	−1.12266	−	0.815663i	−0.138053	−	0.990425i	$-0.544084\pi$
$317$	−19.9885	−	14.5225i	−1.12266	−	0.815663i	−0.984611	+	0.174762i	$0.944084\pi$
$318$		0			0
$319$		0			0
$320$	158.725			8.87299
$321$		0			0
$322$		0			0
$323$		0			0
$324$	43.4271	−	31.5516i	2.41262	−	1.75287i
$325$	−7.70054	−	10.5989i	−0.427149	−	0.587920i
$326$		0			0
$327$		0			0
$328$	−70.8159	−	51.4507i	−3.91015	−	2.84089i
$329$		0			0
$330$	6.98583	+	47.1199i	0.384557	+	2.59387i
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$	30.1815	−	41.5412i	1.65642	−	2.27987i
$333$		0			0
$334$	3.33524	+	10.2648i	0.182496	+	0.561666i
$335$		0			0
$336$		0			0
$337$	31.6148	−	10.2723i	1.72217	−	0.559567i	0.729888	−	0.683567i	$-0.239572\pi$
$337$	31.6148	−	10.2723i	1.72217	−	0.559567i	0.992282	+	0.123999i	$0.0395721\pi$
$338$	−34.8918	−	11.3370i	−1.89787	−	0.616654i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$	26.4955	−	81.5447i	1.42854	−	4.39660i
$345$		0			0
$346$		0			0
$347$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$347$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$348$		0			0
$349$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$349$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$350$		0			0
$351$		−	18.7350i		−	1.00000i
$352$	−98.1944	+	48.8147i	−5.23378	+	2.60183i
$353$	−34.8856			−1.85677			−0.928387	−	0.371614i	$-0.878804\pi$
$353$	−34.8856			−1.85677			−0.928387	+	0.371614i	$0.878804\pi$
$354$	−36.4845	+	50.2167i	−1.93913	+	2.66899i
$355$	−4.46857	+	13.7529i	−0.237167	+	0.729926i
$356$	33.8519	+	104.185i	1.79414	+	5.52181i
$357$		0			0
$358$		0			0
$359$	1.99383	−	0.647836i	0.105231	−	0.0341915i	−0.255928	−	0.966696i	$-0.582381\pi$
$359$	1.99383	−	0.647836i	0.105231	−	0.0341915i	0.361159	+	0.932504i	$0.382381\pi$
$360$	93.7918	+	30.4748i	4.94326	+	1.60616i
$361$	15.3713	+	11.1679i	0.809017	+	0.587785i
$362$			58.3252i			3.06550i
$363$	−10.8916	−	15.6324i	−0.571660	−	0.820491i
$364$		0			0
$365$		0			0
$366$	3.49026	−	10.7419i	0.182439	−	0.561490i
$367$	−8.80588	−	27.1017i	−0.459663	−	1.41470i	−0.865572	−	0.500785i	$-0.833045\pi$
$367$	−8.80588	−	27.1017i	−0.459663	−	1.41470i	0.405908	−	0.913914i	$-0.366955\pi$
$368$		0			0
$369$	−13.7965	−	18.9893i	−0.718219	−	0.988544i
$370$		0			0
$371$		0			0
$372$		0			0
$373$			2.03646i			0.105444i	0.998609	+	0.0527219i	$0.0167897\pi$
$373$			2.03646i			0.105444i	−0.998609	+	0.0527219i	$0.983210\pi$
$374$		0			0
$375$	−6.95425			−0.359116
$376$	10.8113	−	14.8804i	0.557549	−	0.767400i
$377$		0			0
$378$		0			0
$379$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$379$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$380$		0			0
$381$	34.4767	−	11.2022i	1.76629	−	0.573904i
$382$		0			0
$383$	−5.66588	−	4.11651i	−0.289513	−	0.210344i	0.433543	−	0.901133i	$-0.357263\pi$
$383$	−5.66588	−	4.11651i	−0.289513	−	0.210344i	−0.723056	+	0.690789i	$0.757263\pi$
$384$			149.515i			7.62990i
$385$		0			0
$386$		0			0
$387$	13.5141	−	18.6005i	0.686960	−	0.945519i
$388$		0			0
$389$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$389$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$390$	41.8947	−	30.4383i	2.12142	−	1.54130i
$391$		0			0
$392$	−74.4812	+	24.2004i	−3.76187	+	1.22231i
$393$		0			0
$394$	−7.06635	−	5.13401i	−0.355998	−	0.258648i
$395$		−	52.2318i		−	2.62807i
$396$	−58.7026	+	8.70303i	−2.94991	+	0.437344i
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$	−46.6035	+	64.1442i	−2.33602	+	3.21526i
$399$		0			0
$400$	22.0573	+	67.8854i	1.10287	+	3.39427i
$401$	11.7539	−	8.53967i	0.586959	−	0.426451i	−0.254267	−	0.967134i	$-0.581834\pi$
$401$	11.7539	−	8.53967i	0.586959	−	0.426451i	0.841226	+	0.540683i	$0.181834\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	21.3941	+	15.5437i	1.06308	+	0.772375i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$409$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$410$	20.0485	−	61.7029i	0.990124	−	3.04729i
$411$	−12.0693	−	37.1454i	−0.595334	−	1.83225i
$412$	−33.4602	+	24.3103i	−1.64847	+	1.19768i
$413$		0			0
$414$		0			0
$415$	24.0581	+	7.81696i	1.18097	+	0.383720i
$416$	96.4441	+	70.0707i	4.72856	+	3.43550i
$417$		−	37.8632i		−	1.85417i
$418$		0			0
$419$		0			0		1.00000			$0$
$419$		0			0		−1.00000			$\pi$
$420$		0			0
$421$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$421$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$422$	4.90010	+	15.0809i	0.238533	+	0.734129i
$423$	3.99020	−	2.89905i	0.194010	−	0.140957i
$424$		0			0
$425$		0			0
$426$	−22.8788	−	7.43377i	−1.10848	−	0.360167i
$427$		0			0
$428$		0			0
$429$	−9.58535	+	18.3609i	−0.462785	+	0.886471i
$430$	63.5500			3.06465
$431$	−19.0579	+	26.2310i	−0.917988	+	1.26350i	0.0463767	+	0.998924i	$0.485233\pi$
$431$	−19.0579	+	26.2310i	−0.917988	+	1.26350i	−0.964364	+	0.264578i	$0.914767\pi$
$432$	−31.5431	+	97.0795i	−1.51762	+	4.67074i
$433$	8.61170	+	26.5041i	0.413852	+	1.27370i	0.913274	+	0.407346i	$0.133546\pi$
$433$	8.61170	+	26.5041i	0.413852	+	1.27370i	−0.499422	+	0.866359i	$0.666454\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		−	34.1826i		−	1.63145i	−0.578441	−	0.815724i	$-0.696339\pi$
$439$		−	34.1826i		−	1.63145i	0.578441	−	0.815724i	$-0.303661\pi$
$440$	−76.3270	−	77.8527i	−3.63875	−	3.71148i
$441$	−21.0000			−1.00000
$442$		0			0
$443$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$443$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$444$		0			0
$445$	−43.6608	+	31.7214i	−2.06972	+	1.50374i
$446$		0			0
$447$	11.9635	−	3.88717i	0.565853	−	0.183857i
$448$		0			0
$449$	12.4737	+	9.06270i	0.588672	+	0.427695i	0.841840	−	0.539727i	$-0.181473\pi$
$449$	12.4737	+	9.06270i	0.588672	+	0.427695i	−0.253168	+	0.967422i	$0.581473\pi$
$450$			30.7628i			1.45017i
$451$	3.80556	+	25.6688i	0.179197	+	1.20870i
$452$		0			0
$453$		0			0
$454$	11.2246	−	34.5459i	0.526798	−	1.62132i
$455$		0			0
$456$		0			0
$457$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$457$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		−	34.9272i		−	1.62672i	−0.581758	−	0.813362i	$-0.697635\pi$
$461$		−	34.9272i		−	1.62672i	0.581758	−	0.813362i	$-0.302365\pi$
$462$		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		0.809017	−	0.587785i	$-0.200000\pi$
$467$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$468$	37.9203	+	52.1929i	1.75287	+	2.41262i
$469$		0			0
$470$	12.9655	+	4.21276i	0.598056	+	0.194320i
$471$	18.3072	+	13.3010i	0.843552	+	0.612876i
$472$		−	142.069i		−	6.53923i
$473$	−22.7608	+	11.3149i	−1.04654	+	0.520260i
$474$	86.8911			3.99104
$475$		0			0
$476$		0			0
$477$		0			0
$478$	68.0317	−	49.4279i	3.11170	−	2.26078i
$479$	23.8192	+	32.7844i	1.08833	+	1.49796i	0.850009	+	0.526769i	$0.176597\pi$
$479$	23.8192	+	32.7844i	1.08833	+	1.49796i	0.238320	+	0.971187i	$0.423403\pi$
$480$	−160.032	+	51.9977i	−7.30444	+	2.37336i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	61.9830	+	21.5046i	2.81741	+	0.977484i
$485$		0			0
$486$	−25.8581	+	35.5906i	−1.17295	+	1.61442i
$487$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$487$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$488$	7.98851	+	24.5861i	0.361623	+	1.11296i
$489$		0			0
$490$	−34.1182	−	46.9596i	−1.54130	−	2.12142i
$491$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$491$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$492$	76.8702	+	24.9766i	3.46558	+	1.12603i
$493$		0			0
$494$		0			0
$495$	−13.0143	−	26.1792i	−0.584948	−	1.17667i
$496$		0			0
$497$		0			0
$498$	−13.0040	+	40.0223i	−0.582725	+	1.79344i
$499$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$499$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$500$	19.3735	−	14.0757i	0.866409	−	0.629483i
$501$	−3.89359	−	5.35907i	−0.173953	−	0.239426i
$502$		0			0
$503$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$503$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	22.5167			1.00000
$508$	−73.3733	+	100.990i	−3.25541	+	4.48069i
$509$	−13.9256	+	42.8586i	−0.617241	+	1.89967i	−0.260457	+	0.965485i	$0.583873\pi$
$509$	−13.9256	+	42.8586i	−0.617241	+	1.89967i	−0.356784	+	0.934187i	$0.616127\pi$
$510$		0			0
$511$		0			0
$512$	−123.409	−	169.858i	−5.45396	−	7.50674i
$513$		0			0
$514$		0			0
$515$	−16.4840	−	11.9763i	−0.726371	−	0.527740i
$516$			79.1714i			3.48532i
$517$	−5.39375	+	0.799658i	−0.237217	+	0.0351689i
$518$		0			0
$519$		0			0
$520$	−36.6261	+	112.724i	−1.60616	+	4.94326i
$521$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$521$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$522$		0			0
$523$	7.34144	+	10.1046i	0.321019	+	0.441844i	0.938778	−	0.344523i	$-0.111959\pi$
$523$	7.34144	+	10.1046i	0.321019	+	0.441844i	−0.617759	+	0.786367i	$0.711959\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$	80.5818	−	79.0026i	3.50687	−	3.43815i
$529$	23.0000			1.00000
$530$		0			0
$531$	11.7722	−	36.2312i	0.510871	−	1.57230i
$532$		0			0
$533$	22.8223	−	16.5814i	0.988544	−	0.718219i
$534$	−52.7707	−	72.6327i	−2.28361	−	3.14312i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	20.5806	+	10.7442i	0.886471	+	0.462785i
$540$	−91.0620			−3.91868
$541$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$541$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$542$		0			0
$543$	−11.0618	−	34.0447i	−0.474706	−	1.46100i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	13.1777	+	4.28170i	0.563438	+	0.183072i	0.576868	−	0.816838i	$-0.304275\pi$
$547$	13.1777	+	4.28170i	0.563438	+	0.183072i	−0.0134293	+	0.999910i	$0.504275\pi$
$548$	108.807	+	79.0529i	4.64800	+	3.37697i
$549$			6.93206i			0.295853i
$550$	15.7391	−	30.1485i	0.671118	−	1.28554i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−21.7846	−	67.0460i	−0.925538	−	2.84851i
$555$		0			0
$556$	76.6365	+	105.481i	3.25011	+	4.47340i
$557$	34.2469	−	11.1275i	1.45109	−	0.471487i	0.525752	−	0.850638i	$-0.323784\pi$
$557$	34.2469	−	11.1275i	1.45109	−	0.471487i	0.925335	+	0.379151i	$0.123784\pi$
$558$		0			0
$559$	22.3551	+	16.2419i	0.945519	+	0.686960i
$560$		0			0
$561$		0			0
$562$	46.4439			1.95912
$563$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$563$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$564$	−5.24831	+	16.1526i	−0.220994	+	0.680148i
$565$		0			0
$566$	−30.0344	+	21.8213i	−1.26244	+	0.917216i
$567$		0			0
$568$	52.3650	−	17.0144i	2.19719	−	0.713909i
$569$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$569$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$570$		0			0
$571$			28.8444i			1.20710i	0.797325	+	0.603550i	$0.206248\pi$
$571$			28.8444i			1.20710i	−0.797325	+	0.603550i	$0.793752\pi$
$572$	−10.4597	−	70.5517i	−0.437344	−	2.94991i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−50.0788	−	154.127i	−2.08662	−	6.42195i
$577$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$577$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$578$	28.1995	+	38.8133i	1.17295	+	1.61442i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−18.6813	+	25.7126i	−0.772375	+	1.06308i
$586$	24.2547	−	74.6484i	1.00195	−	3.08370i
$587$	−12.8723	−	39.6168i	−0.531296	−	1.63516i	−0.751520	−	0.659710i	$-0.770679\pi$
$587$	−12.8723	−	39.6168i	−0.531296	−	1.63516i	0.220225	−	0.975449i	$-0.429321\pi$
$588$	58.5028	−	42.5048i	2.41262	−	1.75287i
$589$		0			0
$590$	100.145	−	32.5392i	4.12292	−	1.33962i
$591$	5.09836	+	1.65656i	0.209718	+	0.0681417i
$592$		0			0
$593$			0.283491i			0.0116416i	0.999983	+	0.00582080i	$0.00185283\pi$
$593$			0.283491i			0.0116416i	−0.999983	+	0.00582080i	$0.998147\pi$
$594$	43.5508	−	21.6501i	1.78691	−	0.888315i
$595$		0			0
$596$	−25.4607	+	35.0436i	−1.04291	+	1.43544i
$597$	15.0373	−	46.2799i	0.615434	−	1.89411i
$598$		0			0
$599$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$599$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$600$	−41.3859	−	56.9628i	−1.68957	−	2.32550i
$601$	−41.7470	+	13.5644i	−1.70290	+	0.553305i	−0.989126	−	0.147074i	$-0.953015\pi$
$601$	−41.7470	+	13.5644i	−1.70290	+	0.553305i	−0.713772	+	0.700378i	$0.753015\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.639619	+	32.3149i	−0.0260042	+	1.31379i
$606$		0			0
$607$	−11.0827	+	15.2540i	−0.449831	+	0.619140i	−0.972361	−	0.233481i	$-0.924988\pi$
$607$	−11.0827	+	15.2540i	−0.449831	+	0.619140i	0.522530	+	0.852621i	$0.324988\pi$
$608$		0			0
$609$		0			0
$610$	−15.5013	+	11.2623i	−0.627629	+	0.455999i
$611$	3.48422	+	4.79562i	0.140957	+	0.194010i
$612$		0			0
$613$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$613$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$614$		0			0
$615$			39.8186i			1.60564i
$616$		0			0
$617$	−28.2447			−1.13709			−0.568545	−	0.822652i	$-0.692494\pi$
$617$	−28.2447			−1.13709			−0.568545	+	0.822652i	$0.692494\pi$
$618$	19.9234	−	27.4222i	0.801437	−	1.10308i
$619$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$619$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$	−116.675	−	37.9100i	−4.67074	−	1.51762i
$625$	24.2423	+	17.6130i	0.969690	+	0.704521i
$626$		−	10.8552i		−	0.433863i
$627$		0			0
$628$	−77.9228			−3.10946
$629$		0			0
$630$		0			0
$631$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$631$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$632$	−160.894	+	116.896i	−6.40003	+	4.64989i
$633$	−5.72041	−	7.87347i	−0.227366	−	0.312942i
$634$	−66.3135	+	21.5466i	−2.63365	+	0.855724i
$635$	−58.4870	−	19.0036i	−2.32099	−	0.754134i
$636$		0			0
$637$		−	25.2389i		−	1.00000i
$638$		0			0
$639$	14.7643			0.584067
$640$	149.086	−	205.199i	5.89314	−	8.11121i
$641$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$641$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$642$		0			0
$643$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$643$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$644$		0			0
$645$	−37.0944	+	12.0527i	−1.46059	+	0.474575i
$646$		0			0
$647$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$647$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$648$		−	100.690i		−	3.95546i
$649$	−30.0740	+	29.4847i	−1.18051	+	1.15737i
$650$	−36.9723			−1.45017
$651$		0			0
$652$		0			0
$653$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$653$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$654$		0			0
$655$		0			0
$656$	−146.176	+	47.4955i	−5.70722	+	1.85439i
$657$		0			0
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$	89.2435	+	46.5899i	3.47380	+	1.81351i
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$		0			0
$663$		0			0
$664$	−29.7636	−	91.6030i	−1.15505	−	3.55489i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	21.6939	+	7.04878i	0.839363	+	0.272726i
$669$		0			0
$670$		0			0
$671$	3.54664	−	6.79363i	0.136916	−	0.262265i
$672$		0			0
$673$	28.5943	−	39.3566i	1.10223	−	1.51709i	0.269830	−	0.962908i	$-0.413032\pi$
$673$	28.5943	−	39.3566i	1.10223	−	1.51709i	0.832398	−	0.554179i	$-0.186968\pi$
$674$	28.9895	−	89.2206i	1.11664	−	3.43665i
$675$	−5.83438	−	17.9564i	−0.224565	−	0.691141i
$676$	−62.7280	+	45.5746i	−2.41262	+	1.75287i
$677$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$677$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$			22.2934i			0.854285i
$682$		0			0
$683$	35.7689			1.36866			0.684330	−	0.729173i	$-0.260095\pi$
$683$	35.7689			1.36866			0.684330	+	0.729173i	$0.260095\pi$
$684$		0			0
$685$	−20.4746	+	63.0143i	−0.782294	+	2.40765i
$686$		0			0
$687$		0			0
$688$	−88.4922	−	121.799i	−3.37373	−	4.64355i
$689$		0			0
$690$		0			0
$691$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$691$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−37.7546	+	51.9647i	−1.43211	+	1.97114i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$701$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$702$	−42.7745	−	31.0775i	−1.61442	−	1.17295i
$703$		0			0
$704$	−29.7768	+	176.671i	−1.12226	+	6.65852i
$705$	−8.36702			−0.315120
$706$	−57.8681	+	79.6486i	−2.17790	+	2.99762i
$707$		0			0
$708$	40.5377	+	124.762i	1.52350	+	4.68885i
$709$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$709$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$710$	23.9872	+	33.0155i	0.900223	+	1.23905i
$711$	−50.7187	+	16.4795i	−1.90210	+	0.618029i
$712$	195.429	+	63.4986i	7.32400	+	2.37971i
$713$		0			0
$714$		0			0
$715$	31.4635	−	15.6412i	1.17667	−	0.584948i
$716$		0			0
$717$	−30.3360	+	41.7540i	−1.13292	+	1.55933i
$718$	1.82827	−	5.62682i	0.0682303	−	0.209991i
$719$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$719$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$720$	140.092	−	101.783i	5.22092	−	3.79322i
$721$		0			0
$722$	50.9958	−	16.5695i	1.89787	−	0.616654i
$723$		0			0
$724$	99.7241	+	72.4538i	3.70622	+	2.69272i
$725$		0			0
$726$	−53.7579	−	1.06405i	−1.99514	−	0.0394906i
$727$	33.5606			1.24469			0.622347	−	0.782742i	$-0.286179\pi$
$727$	33.5606			1.24469			0.622347	+	0.782742i	$0.286179\pi$
$728$		0			0
$729$	8.34346	−	25.6785i	0.309017	−	0.951057i
$730$		0			0
$731$		0			0
$732$	−14.0308	−	19.3117i	−0.518592	−	0.713780i
$733$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$733$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$734$	−76.4841	−	24.8512i	−2.82308	−	0.917274i
$735$	28.8211	+	20.9398i	1.06308	+	0.772375i
$736$		0			0
$737$		0			0
$738$	−66.2408			−2.43836
$739$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$739$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	16.4213	+	22.6020i	0.602440	+	0.829188i	0.995929	−	0.0901418i	$-0.0287320\pi$
$743$	16.4213	+	22.6020i	0.602440	+	0.829188i	−0.393489	+	0.919329i	$0.628732\pi$
$744$		0			0
$745$	−20.2951	−	6.59428i	−0.743555	−	0.241596i
$746$	4.64952	+	3.37807i	0.170231	+	0.123680i
$747$		−	25.8275i		−	0.944978i
$748$		0			0
$749$		0			0
$750$	−11.5357	+	15.8775i	−0.421224	+	0.579765i
$751$	−14.8318	+	45.6476i	−0.541221	+	1.66571i	0.188590	+	0.982056i	$0.439608\pi$
$751$	−14.8318	+	45.6476i	−0.541221	+	1.66571i	−0.729810	+	0.683650i	$0.760392\pi$
$752$	−9.98016	−	30.7158i	−0.363939	−	1.12009i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−44.3528	−	32.2242i	−1.61203	−	1.17121i	−0.856601	−	0.515979i	$-0.827428\pi$
$757$	−44.3528	−	32.2242i	−1.61203	−	1.17121i	−0.755429	−	0.655230i	$-0.772572\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	13.4370	−	18.4944i	0.487091	−	0.670423i	−0.492757	−	0.870167i	$-0.664011\pi$
$761$	13.4370	−	18.4944i	0.487091	−	0.670423i	0.979848	+	0.199744i	$0.0640110\pi$
$762$	31.6137	−	97.2971i	1.14524	−	3.52470i
$763$		0			0
$764$		0			0
$765$		0			0
$766$	−18.7971	+	6.10755i	−0.679167	+	0.220675i
$767$	43.5445	+	14.1485i	1.57230	+	0.510871i
$768$	189.972	+	138.023i	6.85503	+	4.98047i
$769$		0			0			−	1.00000i	$-0.5\pi$
$769$		0			0				1.00000i	$0.5\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	13.0565	−	40.1836i	0.469608	−	1.44531i	−0.383485	−	0.923547i	$-0.625276\pi$
$773$	13.0565	−	40.1836i	0.469608	−	1.44531i	0.853093	−	0.521758i	$-0.174724\pi$
$774$	−20.0505	−	61.7090i	−0.720699	−	2.21808i
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		−	109.443i		−	3.91868i
$781$	−14.4695	−	7.55384i	−0.517758	−	0.270298i
$782$		0			0
$783$		0			0
$784$	−42.4932	+	130.781i	−1.51762	+	4.67074i
$785$	−11.8626	−	36.5094i	−0.423395	−	1.30308i
$786$		0			0
$787$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$787$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$788$	−17.5562	+	5.70435i	−0.625414	+	0.203209i
$789$		0			0
$790$	−119.252	−	86.6419i	−4.24281	−	3.08258i
$791$		0			0
$792$	−51.5157	+	98.6789i	−1.83053	+	3.50640i
$793$	−8.33130			−0.295853
$794$		0			0
$795$		0			0
$796$	51.7808	+	159.365i	1.83532	+	5.64854i
$797$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$797$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$798$		0			0
$799$		0			0
$800$	114.257	+	37.1244i	4.03960	+	1.31255i
$801$	44.5778	+	32.3877i	1.57508	+	1.14436i
$802$		−	41.0012i		−	1.44780i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$809$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$810$	70.9770	−	23.0618i	2.49388	−	0.810310i
$811$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$811$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$	−80.5943	−	110.929i	−2.81447	−	3.87379i
$821$	31.9382	−	10.3774i	1.11465	−	0.362172i	0.306928	−	0.951733i	$-0.400699\pi$
$821$	31.9382	−	10.3774i	1.11465	−	0.362172i	0.807724	+	0.589560i	$0.200699\pi$
$822$	−104.829	−	34.0609i	−3.65632	−	1.18801i
$823$	−30.7131	−	22.3144i	−1.07059	−	0.777831i	−0.0945738	−	0.995518i	$-0.530149\pi$
$823$	−30.7131	−	22.3144i	−1.07059	−	0.777831i	−0.976019	+	0.217687i	$0.930149\pi$
$824$			77.5805i			2.70265i
$825$	−3.46912	+	20.5828i	−0.120779	+	0.716602i
$826$		0			0
$827$	30.5504	−	42.0490i	1.06234	−	1.46219i	0.184745	−	0.982786i	$-0.440854\pi$
$827$	30.5504	−	42.0490i	1.06234	−	1.46219i	0.877596	−	0.479401i	$-0.159146\pi$
$828$		0			0
$829$	−16.0968	−	49.5407i	−0.559063	−	1.72062i	−0.684964	−	0.728577i	$-0.740182\pi$
$829$	−16.0968	−	49.5407i	−0.559063	−	1.72062i	0.125900	−	0.992043i	$-0.459818\pi$
$830$	57.7547	−	41.9613i	2.00470	−	1.45650i
$831$	25.4315	+	35.0034i	0.882208	+	1.21426i
$832$	185.237	−	60.1872i	6.42195	−	2.08662i
$833$		0			0
$834$	−86.4468	−	62.8073i	−2.99341	−	2.17484i
$835$			11.2374i			0.388886i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−17.8605	+	54.9689i	−0.616613	+	1.89774i	−0.243840	+	0.969816i	$0.578407\pi$
$839$	−17.8605	+	54.9689i	−0.616613	+	1.89774i	−0.372773	+	0.927923i	$0.621593\pi$
$840$		0			0
$841$	23.4615	−	17.0458i	0.809017	−	0.587785i
$842$		0			0
$843$	−27.1095	+	8.80841i	−0.933701	+	0.303378i
$844$	31.8724	+	10.3560i	1.09709	+	0.356467i
$845$	−30.9026	−	22.4521i	−1.06308	−	0.772375i
$846$		−	13.9191i		−	0.478549i
$847$		0			0
$848$		0			0
$849$	13.3926	−	18.4334i	0.459634	−	0.632632i
$850$		0			0
$851$		0			0
$852$	−41.1312	+	29.8835i	−1.40913	+	1.02379i
$853$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$853$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$	26.0202	+	52.3416i	0.888315	+	1.78691i
$859$	−51.6539			−1.76241			−0.881205	−	0.472735i	$-0.843267\pi$
$859$	−51.6539			−1.76241			−0.881205	+	0.472735i	$0.843267\pi$
$860$	78.9443	−	108.658i	2.69198	−	3.70519i
$861$		0			0
$862$	28.2757	+	87.0237i	0.963074	+	2.96404i
$863$	−14.8809	+	10.8116i	−0.506550	+	0.368030i	−0.811513	−	0.584334i	$-0.801356\pi$
$863$	−14.8809	+	10.8116i	−0.506550	+	0.368030i	0.304963	+	0.952364i	$0.401356\pi$
$864$	100.983	+	138.991i	3.43550	+	4.72856i
$865$		0			0
$866$	74.7975	+	24.3032i	2.54172	+	0.825855i
$867$	−23.8214	−	17.3073i	−0.809017	−	0.587785i
$868$		0			0
$869$	58.1372	+	9.79869i	1.97217	+	0.332398i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$877$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$878$	−78.0436	−	56.7020i	−2.63385	−	1.91360i
$879$			48.1726i			1.62482i
$880$	−189.369	+	28.0752i	−6.38363	+	0.946414i
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−34.8347	+	47.9459i	−1.17295	+	1.61442i
$883$	13.4390	−	41.3611i	0.452260	−	1.39191i	−0.422062	−	0.906567i	$-0.638694\pi$
$883$	13.4390	−	41.3611i	0.452260	−	1.39191i	0.874322	−	0.485346i	$-0.161306\pi$
$884$		0			0
$885$	−52.2839	+	37.9865i	−1.75750	+	1.27690i
$886$		0			0
$887$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$887$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$888$		0			0
$889$		0			0
$890$			152.303i			5.10521i
$891$	−21.3147	+	20.8970i	−0.714069	+	0.700075i
$892$		0			0
$893$		0			0
$894$	10.9700	−	33.7623i	0.366893	−	1.12918i
$895$		0			0
$896$		0			0
$897$		0			0
$898$	41.3828	−	13.4461i	1.38096	−	0.448701i
$899$		0			0
$900$	52.5981	+	38.2148i	1.75327	+	1.27383i
$901$		0			0
$902$	64.9180	+	33.8907i	2.16153	+	1.12844i
$903$		0			0
$904$		0			0
$905$	−18.7654	+	57.7541i	−0.623785	+	1.91981i
$906$		0			0
$907$	16.0962	−	11.6946i	0.534467	−	0.388313i	−0.287559	−	0.957763i	$-0.592844\pi$
$907$	16.0962	−	11.6946i	0.534467	−	0.388313i	0.822026	+	0.569450i	$0.192844\pi$
$908$	−45.1227	−	62.1061i	−1.49745	−	2.06106i
$909$		0			0
$910$		0			0
$911$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$911$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$912$		0			0
$913$	−13.2141	+	25.3117i	−0.437322	+	0.837696i
$914$		0			0
$915$	6.91218	−	9.51380i	0.228510	−	0.314516i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	30.3008	+	41.7054i	0.999530	+	1.37574i	0.925613	+	0.378471i	$0.123550\pi$
$919$	30.3008	+	41.7054i	0.999530	+	1.37574i	0.0739171	+	0.997264i	$0.476450\pi$
$920$		0			0
$921$		0			0
$922$	−79.7437	−	57.9372i	−2.62622	−	1.90806i
$923$			17.7445i			0.584067i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−6.42856	+	19.7851i	−0.211142	+	0.649827i
$928$		0			0
$929$	4.71536	−	3.42591i	0.154706	−	0.112401i	−0.507739	−	0.861511i	$-0.669519\pi$
$929$	4.71536	−	3.42591i	0.154706	−	0.112401i	0.662445	+	0.749110i	$0.269519\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$	121.014			3.95546
$937$	−10.1964	+	14.0341i	−0.333101	+	0.458474i	−0.942410	−	0.334458i	$-0.891447\pi$
$937$	−10.1964	+	14.0341i	−0.333101	+	0.458474i	0.609310	+	0.792932i	$0.291447\pi$
$938$		0			0
$939$	2.05877	+	6.33625i	0.0671855	+	0.206776i
$940$	23.3093	−	16.9352i	0.760264	−	0.552364i
$941$	−20.0722	−	27.6270i	−0.654334	−	0.900614i	0.344943	−	0.938624i	$-0.387898\pi$
$941$	−20.0722	−	27.6270i	−0.654334	−	0.900614i	−0.999277	+	0.0380096i	$0.987898\pi$
$942$	60.7359	−	19.7343i	1.97888	−	0.642978i
$943$		0			0
$944$	−201.815	−	146.627i	−6.56850	−	4.77230i
$945$		0			0
$946$	−11.9220	+	70.7351i	−0.387618	+	2.29980i
$947$	−48.6705			−1.58158			−0.790790	−	0.612088i	$-0.790330\pi$
$947$	−48.6705			−1.58158			−0.790790	+	0.612088i	$0.790330\pi$
$948$	107.939	−	148.566i	3.50571	−	4.82520i
$949$		0			0
$950$		0			0
$951$	34.6210	−	25.1536i	1.12266	−	0.815663i
$952$		0			0
$953$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$953$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$954$		0			0
$955$		0			0
$956$		−	177.722i		−	5.74793i
$957$		0			0
$958$	114.362			3.69488
$959$		0			0
$960$	−84.9548	+	261.464i	−2.74191	+	8.43872i
$961$	9.57953	+	29.4828i	0.309017	+	0.951057i
$962$		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	$0.5\pi$
$968$	100.974	−	70.3515i	3.24542	−	2.26118i
$969$		0			0
$970$		0			0
$971$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$971$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$972$	28.7307	+	88.4240i	0.921538	+	2.83620i
$973$		0			0
$974$		0			0
$975$	21.5809	−	7.01205i	0.691141	−	0.224565i
$976$	43.1705	+	14.0269i	1.38185	+	0.448991i
$977$	−28.6517	−	20.8167i	−0.916648	−	0.665984i	0.0260393	−	0.999661i	$-0.491711\pi$
$977$	−28.6517	−	20.8167i	−0.916648	−	0.665984i	−0.942687	+	0.333677i	$0.891711\pi$
$978$		0			0
$979$	−27.1171	−	54.5481i	−0.866667	−	1.74337i
$980$	−122.674			−3.91868
$981$		0			0
$982$		0			0
$983$	−16.8560	−	51.8774i	−0.537622	−	1.65463i	−0.737914	−	0.674895i	$-0.764189\pi$
$983$	−16.8560	−	51.8774i	−0.537622	−	1.65463i	0.200292	−	0.979736i	$-0.435811\pi$
$984$	122.657	−	89.1153i	3.91015	−	2.84089i
$985$	−5.34536	−	7.35725i	−0.170317	−	0.234422i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−81.3587	−	13.7125i	−2.58575	−	0.435813i
$991$	−61.8656			−1.96523			−0.982613	−	0.185667i	$-0.940555\pi$
$991$	−61.8656			−1.96523			−0.982613	+	0.185667i	$0.940555\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−66.7848	+	48.5220i	−2.11722	+	1.53825i
$996$	52.2758	+	71.9515i	1.65642	+	2.27987i
$997$	−45.1201	+	14.6604i	−1.42897	+	0.464299i	−0.918439	−	0.395562i	$-0.870550\pi$
$997$	−45.1201	+	14.6604i	−1.42897	+	0.464299i	−0.510527	+	0.859862i	$0.670550\pi$
$998$		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.194.8	yes	32
3.2	odd	2	inner	429.2.y.a.194.1	✓	32
11.8	odd	10	inner	429.2.y.a.272.8	yes	32
13.12	even	2	inner	429.2.y.a.194.1	✓	32
33.8	even	10	inner	429.2.y.a.272.1	yes	32
39.38	odd	2	CM	429.2.y.a.194.8	yes	32
143.129	odd	10	inner	429.2.y.a.272.1	yes	32
429.272	even	10	inner	429.2.y.a.272.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.y.a.194.1	✓	32	3.2	odd	2	inner
429.2.y.a.194.1	✓	32	13.12	even	2	inner
429.2.y.a.194.8	yes	32	1.1	even	1	trivial
429.2.y.a.194.8	yes	32	39.38	odd	2	CM
429.2.y.a.272.1	yes	32	33.8	even	10	inner
429.2.y.a.272.1	yes	32	143.129	odd	10	inner
429.2.y.a.272.8	yes	32	11.8	odd	10	inner
429.2.y.a.272.8	yes	32	429.272	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)

\(f(q)\)	\(=\)	\(q+(1.65880 - 2.28314i) q^{2} +(-0.535233 + 1.64728i) q^{3} +(-1.84308 - 5.67240i) q^{4} +(2.37713 - 1.72708i) q^{5} +(2.87312 + 3.95451i) q^{6} +(-10.6402 - 3.45720i) q^{8} +(-2.42705 - 1.76336i) q^{9} +O(q^{10})\)	\(q+(1.65880 - 2.28314i) q^{2} +(-0.535233 + 1.64728i) q^{3} +(-1.84308 - 5.67240i) q^{4} +(2.37713 - 1.72708i) q^{5} +(2.87312 + 3.95451i) q^{6} +(-10.6402 - 3.45720i) q^{8} +(-2.42705 - 1.76336i) q^{9} -8.29218i q^{10} +(1.47640 + 2.96989i) q^{11} +10.3305 q^{12} +(2.11929 - 2.91695i) q^{13} +(1.57267 + 4.84018i) q^{15} +(-15.8927 + 11.5467i) q^{16} +(-8.05196 + 2.61624i) q^{18} +(-14.1779 - 10.3009i) q^{20} +(9.22971 + 1.55562i) q^{22} +(11.3900 - 15.6769i) q^{24} +(1.12283 - 3.45571i) q^{25} +(-3.14433 - 9.67726i) q^{26} +(4.20378 - 3.05422i) q^{27} +(13.6595 + 4.43825i) q^{30} +33.0633i q^{32} +(-5.68245 + 0.842460i) q^{33} +(-5.52923 + 17.0172i) q^{36} +(3.67072 + 5.05231i) q^{39} +(-31.2639 + 10.1583i) q^{40} +(7.44109 + 2.41776i) q^{41} +7.66385i q^{43} +(14.1253 - 13.8485i) q^{44} -8.81487 q^{45} +(-0.508040 + 1.56359i) q^{47} +(-10.5144 - 32.3598i) q^{48} +(5.66312 - 4.11450i) q^{49} +(-6.02731 - 8.29588i) q^{50} +(-20.4521 - 6.64530i) q^{52} -14.6641i q^{54} +(8.63884 + 4.50993i) q^{55} +(3.92408 + 12.0771i) q^{59} +(24.5569 - 17.8416i) q^{60} +(-1.35819 - 1.86938i) q^{61} +(43.7027 + 31.7519i) q^{64} -10.5942i q^{65} +(-7.50258 + 14.3713i) q^{66} +(-3.98153 + 2.89275i) q^{71} +(19.7280 + 27.1532i) q^{72} +(5.09154 + 3.69922i) q^{75} +17.6241 q^{78} +(10.4486 - 14.3813i) q^{79} +(-17.8368 + 54.8960i) q^{80} +(2.78115 + 8.55951i) q^{81} +(17.8633 - 12.9785i) q^{82} +(5.06034 + 6.96496i) q^{83} +(17.4976 + 12.7128i) q^{86} +(-5.44166 - 36.7044i) q^{88} -18.3671 q^{89} +(-14.6221 + 20.1255i) q^{90} +(2.72715 + 3.75360i) q^{94} +(-54.4645 - 17.6966i) q^{96} -19.7548i q^{98} +(1.65367 - 9.81149i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more