LMFDB - Embedded newform 429.2.y.a.194.2

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			194.2
Character	$\chi$	$=$	429.194
Dual form			429.2.y.a.272.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.54330 + 2.12417i) q^{2} +(0.535233 - 1.64728i) q^{3} +(-1.51228 - 4.65433i) q^{4} +(3.60386 - 2.61836i) q^{5} +(2.67307 + 3.67916i) q^{6} +(7.22625 + 2.34795i) q^{8} +(-2.42705 - 1.76336i) q^{9} +O(q^{10})$	\(q+(-1.54330 + 2.12417i) q^{2} +(0.535233 - 1.64728i) q^{3} +(-1.51228 - 4.65433i) q^{4} +(3.60386 - 2.61836i) q^{5} +(2.67307 + 3.67916i) q^{6} +(7.22625 + 2.34795i) q^{8} +(-2.42705 - 1.76336i) q^{9} +11.6961i q^{10} +(-2.32189 + 2.36830i) q^{11} -8.47640 q^{12} +(2.11929 - 2.91695i) q^{13} +(-2.38426 - 7.33799i) q^{15} +(-8.22128 + 5.97311i) q^{16} +(7.49132 - 2.43408i) q^{18} +(-17.6368 - 12.8139i) q^{20} +(-1.44730 - 8.58706i) q^{22} +(7.73546 - 10.6469i) q^{24} +(4.58693 - 14.1171i) q^{25} +(2.92540 + 9.00345i) q^{26} +(-4.20378 + 3.05422i) q^{27} +(19.2667 + 6.26014i) q^{30} -11.4854i q^{32} +(2.65850 + 5.09239i) q^{33} +(-4.53685 + 13.9630i) q^{36} +(-3.67072 - 5.05231i) q^{39} +(32.1902 - 10.4592i) q^{40} +(-9.64207 - 3.13290i) q^{41} -0.0553950i q^{43} +(14.5342 + 7.22528i) q^{44} -13.3639 q^{45} +(-0.816692 + 2.51352i) q^{47} +(5.43908 + 16.7398i) q^{48} +(5.66312 - 4.11450i) q^{49} +(22.9081 + 31.5303i) q^{50} +(-16.7814 - 5.45261i) q^{52} -13.6431i q^{54} +(-2.16670 + 14.6146i) q^{55} +(2.90644 + 8.94511i) q^{59} +(-30.5478 + 22.1942i) q^{60} +(8.21635 + 11.3088i) q^{61} +(7.95433 + 5.77916i) q^{64} -16.0614i q^{65} +(-14.9199 - 2.21197i) q^{66} +(13.0395 - 9.47373i) q^{71} +(-13.3982 - 18.4411i) q^{72} +(-20.7997 - 15.1119i) q^{75} +16.3970 q^{78} +(3.26771 - 4.49762i) q^{79} +(-13.9886 + 43.0525i) q^{80} +(2.78115 + 8.55951i) q^{81} +(21.5354 - 15.6464i) q^{82} +(-4.66198 - 6.41666i) q^{83} +(0.117668 + 0.0854909i) q^{86} +(-22.3392 + 11.6623i) q^{88} +4.31872 q^{89} +(20.6244 - 28.3870i) q^{90} +(-4.07874 - 5.61390i) q^{94} +(-18.9197 - 6.14737i) q^{96} +18.3793i q^{98} +(9.81149 - 1.65367i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.54330	+	2.12417i	−1.09128	+	1.50201i	−0.244809	+	0.969571i	$0.578725\pi$
$2$	−1.54330	+	2.12417i	−1.09128	+	1.50201i	−0.846467	+	0.532441i	$0.821275\pi$
$3$	0.535233	−	1.64728i	0.309017	−	0.951057i
$3$	0.535233	−	1.64728i	0.309017	−	0.951057i
$4$	−1.51228	−	4.65433i	−0.756141	−	2.32716i
$5$	3.60386	−	2.61836i	1.61170	−	1.17097i	0.753872	−	0.657022i	$-0.228184\pi$
$5$	3.60386	−	2.61836i	1.61170	−	1.17097i	0.857824	−	0.513944i	$-0.171816\pi$
$6$	2.67307	+	3.67916i	1.09128	+	1.50201i
$7$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$7$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$8$	7.22625	+	2.34795i	2.55487	+	0.830127i
$9$	−2.42705	−	1.76336i	−0.809017	−	0.587785i
$10$			11.6961i			3.69863i
$11$	−2.32189	+	2.36830i	−0.700075	+	0.714069i
$11$	−2.32189	+	2.36830i	−0.700075	+	0.714069i
$12$	−8.47640			−2.44692
$13$	2.11929	−	2.91695i	0.587785	−	0.809017i
$13$	2.11929	−	2.91695i	0.587785	−	0.809017i
$14$		0			0
$15$	−2.38426	−	7.33799i	−0.615613	−	1.89466i
$16$	−8.22128	+	5.97311i	−2.05532	+	1.49328i
$17$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$17$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$18$	7.49132	−	2.43408i	1.76572	−	0.573718i
$19$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$19$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$20$	−17.6368	−	12.8139i	−3.94370	−	2.86526i
$21$		0			0
$22$	−1.44730	−	8.58706i	−0.308566	−	1.83077i
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$	7.73546	−	10.6469i	1.57899	−	2.17330i
$25$	4.58693	−	14.1171i	0.917386	−	2.82342i
$26$	2.92540	+	9.00345i	0.573718	+	1.76572i
$27$	−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	$0.900000\pi$
$30$	19.2667	+	6.26014i	3.51761	+	1.14294i
$31$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$31$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$32$		−	11.4854i		−	2.03035i
$33$	2.65850	+	5.09239i	0.462785	+	0.886471i
$34$		0			0
$35$		0			0
$36$	−4.53685	+	13.9630i	−0.756141	+	2.32716i
$37$		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
$40$	32.1902	−	10.4592i	5.08972	−	1.65375i
$41$	−9.64207	−	3.13290i	−1.50584	−	0.489277i	−0.564124	−	0.825690i	$-0.690786\pi$
$41$	−9.64207	−	3.13290i	−1.50584	−	0.489277i	−0.941714	+	0.336413i	$0.890786\pi$
$42$		0			0
$43$		−	0.0553950i		−	0.00844765i	−0.999991	−	0.00422383i	$-0.998656\pi$
$43$		−	0.0553950i		−	0.00844765i	0.999991	−	0.00422383i	$-0.00134449\pi$
$44$	14.5342	+	7.22528i	2.19111	+	1.08925i
$45$	−13.3639			−1.99217
$46$		0			0
$47$	−0.816692	+	2.51352i	−0.119127	+	0.366635i	−0.992785	−	0.119905i	$-0.961741\pi$
$47$	−0.816692	+	2.51352i	−0.119127	+	0.366635i	0.873659	+	0.486540i	$0.161741\pi$
$48$	5.43908	+	16.7398i	0.785063	+	2.41618i
$49$	5.66312	−	4.11450i	0.809017	−	0.587785i
$50$	22.9081	+	31.5303i	3.23970	+	4.45906i
$51$		0			0
$52$	−16.7814	−	5.45261i	−2.32716	−	0.756141i
$53$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$53$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$54$		−	13.6431i		−	1.85659i
$55$	−2.16670	+	14.6146i	−0.292158	+	1.97063i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.90644	+	8.94511i	0.378386	+	1.16455i	0.941165	+	0.337946i	$0.109732\pi$
$59$	2.90644	+	8.94511i	0.378386	+	1.16455i	−0.562779	+	0.826607i	$0.690268\pi$
$60$	−30.5478	+	22.1942i	−3.94370	+	2.86526i
$61$	8.21635	+	11.3088i	1.05200	+	1.44795i	0.887066	+	0.461644i	$0.152740\pi$
$61$	8.21635	+	11.3088i	1.05200	+	1.44795i	0.164931	+	0.986305i	$0.447260\pi$
$62$		0			0
$63$		0			0
$64$	7.95433	+	5.77916i	0.994292	+	0.722395i
$65$		−	16.0614i		−	1.99217i
$66$	−14.9199	−	2.21197i	−1.83652	−	0.272275i
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	13.0395	−	9.47373i	1.54750	−	1.12433i	0.602097	−	0.798423i	$-0.294332\pi$
$71$	13.0395	−	9.47373i	1.54750	−	1.12433i	0.945403	−	0.325902i	$-0.105668\pi$
$72$	−13.3982	−	18.4411i	−1.57899	−	2.17330i
$73$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$73$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$74$		0			0
$75$	−20.7997	−	15.1119i	−2.40175	−	1.74497i
$76$		0			0
$77$		0			0
$78$	16.3970			1.85659
$79$	3.26771	−	4.49762i	0.367646	−	0.506022i	−0.584613	−	0.811312i	$-0.698754\pi$
$79$	3.26771	−	4.49762i	0.367646	−	0.506022i	0.952259	+	0.305291i	$0.0987536\pi$
$80$	−13.9886	+	43.0525i	−1.56398	+	4.81342i
$81$	2.78115	+	8.55951i	0.309017	+	0.951057i
$82$	21.5354	−	15.6464i	2.37819	−	1.72785i
$83$	−4.66198	−	6.41666i	−0.511719	−	0.704320i	0.472489	−	0.881336i	$-0.343356\pi$
$83$	−4.66198	−	6.41666i	−0.511719	−	0.704320i	−0.984208	+	0.177016i	$0.943356\pi$
$84$		0			0
$85$		0			0
$86$	0.117668	+	0.0854909i	0.0126885	+	0.00921872i
$87$		0			0
$88$	−22.3392	+	11.6623i	−2.38137	+	1.24320i
$89$	4.31872			0.457783			0.228892	−	0.973452i	$-0.426490\pi$
$89$	4.31872			0.457783			0.228892	+	0.973452i	$0.426490\pi$
$90$	20.6244	−	28.3870i	2.17400	−	2.99226i
$91$		0			0
$92$		0			0
$93$		0			0
$94$	−4.07874	−	5.61390i	−0.420690	−	0.579030i
$95$		0			0
$96$	−18.9197	−	6.14737i	−1.93098	−	0.627413i
$97$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$97$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$98$			18.3793i			1.85659i
$99$	9.81149	−	1.65367i	0.986092	−	0.166200i
$100$	−72.6424			−7.26424
$101$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$101$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$102$		0			0
$103$	5.19858	+	15.9996i	0.512231	+	1.57649i	0.788263	+	0.615338i	$0.210980\pi$
$103$	5.19858	+	15.9996i	0.512231	+	1.57649i	−0.276032	+	0.961148i	$0.589020\pi$
$104$	22.1634	−	16.1026i	2.17330	−	1.57899i
$105$		0			0
$106$		0			0
$107$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$107$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$108$	20.5726	+	14.9469i	1.97960	+	1.43827i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$	−27.6999	−	27.1570i	−2.64108	−	2.58932i
$111$		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
$118$	−23.4864	−	7.63119i	−2.16210	−	0.702508i
$119$		0			0
$120$		−	58.6243i		−	5.35165i
$121$	−0.217684	−	10.9978i	−0.0197895	−	0.999804i
$122$	−36.7021			−3.32286
$123$	−10.3215	+	14.2063i	−0.930659	+	1.28094i
$124$		0			0
$125$	−13.5503	−	41.7034i	−1.21197	−	3.73006i
$126$		0			0
$127$	7.06287	+	9.72121i	0.626729	+	0.862618i	0.997821	−	0.0659781i	$-0.0210167\pi$
$127$	7.06287	+	9.72121i	0.626729	+	0.862618i	−0.371093	+	0.928596i	$0.621017\pi$
$128$	−2.70527	+	0.878996i	−0.239115	+	0.0776930i
$129$	−0.0912509	−	0.0296492i	−0.00803419	−	0.00261047i
$130$	34.1170	+	24.7874i	2.99226	+	2.17400i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	19.6812	−	20.0746i	1.71303	−	1.74727i
$133$		0			0
$134$		0			0
$135$	−7.15278	+	22.0140i	−0.615613	+	1.89466i
$136$		0			0
$137$	−18.9217	+	13.7474i	−1.61659	+	1.17452i	−0.783444	+	0.621463i	$0.786539\pi$
$137$	−18.9217	+	13.7474i	−1.61659	+	1.17452i	−0.833143	+	0.553057i	$0.813461\pi$
$138$		0			0
$139$	−1.57028	+	0.510214i	−0.133189	+	0.0432758i	−0.374853	−	0.927084i	$-0.622307\pi$
$139$	−1.57028	+	0.510214i	−0.133189	+	0.0432758i	0.241664	+	0.970360i	$0.422307\pi$
$140$		0			0
$141$	3.70335	+	2.69064i	0.311878	+	0.226593i
$142$			42.3188i			3.55131i
$143$	1.98747	+	11.7919i	0.166200	+	0.986092i
$144$	30.4862			2.54052
$145$		0			0
$146$		0			0
$147$	−3.74663	−	11.5309i	−0.309017	−	0.951057i
$148$		0			0
$149$	13.5927	+	18.7087i	1.11356	+	1.53268i	0.816070	+	0.577953i	$0.196148\pi$
$149$	13.5927	+	18.7087i	1.11356	+	1.53268i	0.297487	+	0.954726i	$0.403852\pi$
$150$	64.2004	−	20.8600i	5.24194	−	1.70321i
$151$		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
$156$	−17.9639	+	24.7252i	−1.43827	+	1.97960i
$157$	−5.03726	+	15.5031i	−0.402017	+	1.23728i	0.521344	+	0.853347i	$0.325431\pi$
$157$	−5.03726	+	15.5031i	−0.402017	+	1.23728i	−0.923361	+	0.383934i	$0.874569\pi$
$158$	4.51064	+	13.8823i	0.358848	+	1.10442i
$159$		0			0
$160$	−30.0729	−	41.3918i	−2.37747	−	3.27231i
$161$		0			0
$162$	−22.4740	−	7.30223i	−1.76572	−	0.573718i
$163$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$163$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$164$			49.6152i			3.87430i
$165$	22.9145	+	11.3914i	1.78389	+	0.886816i
$166$	20.8249			1.61632
$167$	−10.8337	+	14.9114i	−0.838340	+	1.15388i	0.147973	+	0.988991i	$0.452725\pi$
$167$	−10.8337	+	14.9114i	−0.838340	+	1.15388i	−0.986313	+	0.164884i	$0.947275\pi$
$168$		0			0
$169$	−4.01722	−	12.3637i	−0.309017	−	0.951057i
$170$		0			0
$171$		0			0
$172$	−0.257826	+	0.0837728i	−0.0196591	+	0.00638762i
$173$		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
$176$	4.94277	−	33.3394i	0.372575	−	2.51305i
$177$	16.2907			1.22448
$178$	−6.66507	+	9.17368i	−0.499568	+	0.687596i
$179$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$179$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$180$	20.2099	+	62.1997i	1.50636	+	4.63610i
$181$	21.7201	−	15.7806i	1.61444	−	1.17296i	0.768091	−	0.640341i	$-0.221207\pi$
$181$	21.7201	−	15.7806i	1.61444	−	1.17296i	0.846353	−	0.532622i	$-0.178793\pi$
$182$		0			0
$183$	23.0265	−	7.48175i	1.70217	−	0.553067i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	12.9338			0.943296
$189$		0			0
$190$		0			0
$191$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$191$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$192$	13.7773	−	10.0098i	0.994292	−	0.722395i
$193$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$193$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$194$		0			0
$195$	−26.4575	−	8.59657i	−1.89466	−	0.615613i
$196$	−27.7145	−	20.1357i	−1.97960	−	1.43827i
$197$		−	11.5652i		−	0.823984i	−0.911187	−	0.411992i	$-0.864833\pi$
$197$		−	11.5652i		−	0.823984i	0.911187	−	0.411992i	$-0.135167\pi$
$198$	−11.6294	+	23.3933i	−0.826464	+	1.66249i
$199$	11.1405			0.789726			0.394863	−	0.918740i	$-0.370792\pi$
$199$	11.1405			0.789726			0.394863	+	0.918740i	$0.370792\pi$
$200$	66.2926	−	91.2440i	4.68760	−	6.45192i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−42.9517	+	13.9559i	−2.99988	+	0.974720i
$206$	−42.0087	−	13.6495i	−2.92689	−	0.951004i
$207$		0			0
$208$			36.6399i			2.54052i
$209$		0			0
$210$		0			0
$211$	−7.17566	+	9.87645i	−0.493993	+	0.679923i	−0.981118	−	0.193409i	$-0.938046\pi$
$211$	−7.17566	+	9.87645i	−0.493993	+	0.679923i	0.487125	+	0.873332i	$0.338046\pi$
$212$		0			0
$213$	−8.62671	−	26.5503i	−0.591093	−	1.81920i
$214$		0			0
$215$	−0.145044	−	0.199636i	−0.00989191	−	0.0136150i
$216$	−37.5487	+	12.2003i	−2.55487	+	0.830127i
$217$		0			0
$218$		0			0
$219$		0			0
$220$	71.2976	−	12.0168i	4.80688	−	0.810173i
$221$		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
$225$	−36.0262	+	26.1746i	−2.40175	+	1.74497i
$226$		0			0
$227$	19.6494	−	6.38447i	1.30417	−	0.423752i	0.427143	−	0.904184i	$-0.359520\pi$
$227$	19.6494	−	6.38447i	1.30417	−	0.423752i	0.877032	+	0.480432i	$0.159520\pi$
$228$		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	$0.700000\pi$
$234$	8.77619	−	27.0103i	0.573718	−	1.76572i
$235$	3.63805	+	11.1968i	0.237320	+	0.730397i
$236$	37.2381	−	27.0551i	2.42399	−	1.76113i
$237$	−5.65985	−	7.79011i	−0.367646	−	0.506022i
$238$		0			0
$239$	23.0073	+	7.47551i	1.48822	+	0.483551i	0.936556	−	0.350518i	$-0.113995\pi$
$239$	23.0073	+	7.47551i	1.48822	+	0.483551i	0.551660	+	0.834069i	$0.313995\pi$
$240$	63.4323	+	46.0863i	4.09454	+	2.97486i
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$	23.6972	+	16.5105i	1.52331	+	1.06134i
$243$	15.5885			1.00000
$244$	40.2096	−	55.3438i	2.57416	−	3.54302i
$245$	9.63587	−	29.6561i	0.615613	−	1.89466i
$246$	−14.2475	−	43.8492i	−0.908386	−	2.79572i
$247$		0			0
$248$		0			0
$249$	−13.0653	+	4.24517i	−0.827978	+	0.269026i
$250$	109.497	+	35.5777i	6.92520	+	2.25013i
$251$		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
$254$	−31.5496			−1.97960
$255$		0			0
$256$	−3.76866	+	11.5988i	−0.235542	+	0.724922i
$257$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$257$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$258$	0.203807	−	0.148075i	0.0126885	−	0.00921872i
$259$		0			0
$260$	−74.7548	+	24.2893i	−4.63610	+	1.50636i
$261$		0			0
$262$		0			0
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$	7.25430	+	43.0409i	0.446471	+	2.64898i
$265$		0			0
$266$		0			0
$267$	2.31152	−	7.11413i	0.141463	−	0.435378i
$268$		0			0
$269$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$269$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$270$	−35.7225	−	49.1678i	−2.17400	−	2.99226i
$271$		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
$274$		−	61.4091i		−	3.70986i
$275$	22.7832	+	43.6416i	1.37388	+	2.63169i
$276$		0			0
$277$	−14.6829	+	20.2092i	−0.882208	+	1.21426i	0.0935962	+	0.995610i	$0.470164\pi$
$277$	−14.6829	+	20.2092i	−0.882208	+	1.21426i	−0.975804	+	0.218645i	$0.929836\pi$
$278$	1.33962	−	4.12294i	0.0803453	−	0.247277i
$279$		0			0
$280$		0			0
$281$	3.89444	+	5.36024i	0.232323	+	0.319765i	0.909223	−	0.416310i	$-0.136677\pi$
$281$	3.89444	+	5.36024i	0.232323	+	0.319765i	−0.676900	+	0.736075i	$0.736677\pi$
$282$	−11.4307	+	3.71407i	−0.680690	+	0.221170i
$283$	−31.8759	−	10.3571i	−1.89483	−	0.615667i	−0.974433	−	0.224679i	$-0.927867\pi$
$283$	−31.8759	−	10.3571i	−1.89483	−	0.615667i	−0.920396	−	0.390988i	$-0.872133\pi$
$284$	−63.8132	−	46.3630i	−3.78662	−	2.75114i
$285$		0			0
$286$	−28.1153	−	13.9768i	−1.66249	−	0.826464i
$287$		0			0
$288$	−20.2528	+	27.8757i	−1.19341	+	1.64259i
$289$	−5.25329	+	16.1680i	−0.309017	+	0.951057i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.188770	−	0.0613350i	0.0110280	−	0.00358323i	−0.303498	−	0.952832i	$-0.598154\pi$
$293$	0.188770	−	0.0613350i	0.0110280	−	0.00358323i	0.314526	+	0.949249i	$0.398154\pi$
$294$	30.2758	+	9.83721i	1.76572	+	0.573718i
$295$	33.8959	+	24.6268i	1.97350	+	1.43383i
$296$		0			0
$297$	2.52738	−	17.0474i	0.146653	−	0.989188i
$298$	−60.7180			−3.51730
$299$		0			0
$300$	−38.8806	+	119.662i	−2.24477	+	6.90870i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	59.2212	+	19.2421i	3.39100	+	1.10180i
$306$		0			0
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$		0			0
$309$	29.1382			1.65762
$310$		0			0
$311$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$311$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$312$	−14.6630	−	45.1279i	−0.830127	−	2.55487i
$313$	−14.2086	+	10.3232i	−0.803119	+	0.583500i	−0.911828	−	0.410574i	$-0.865329\pi$
$313$	−14.2086	+	10.3232i	−0.803119	+	0.583500i	0.108708	+	0.994074i	$0.465329\pi$
$314$	−25.1571	−	34.6258i	−1.41970	−	1.95405i
$315$		0			0
$316$	−25.8751	−	8.40733i	−1.45559	−	0.472949i
$317$	−5.03459	−	3.65784i	−0.282771	−	0.205445i	0.437354	−	0.899289i	$-0.355916\pi$
$317$	−5.03459	−	3.65784i	−0.282771	−	0.205445i	−0.720125	+	0.693844i	$0.755916\pi$
$318$		0			0
$319$		0			0
$320$	43.7982			2.44840
$321$		0			0
$322$		0			0
$323$		0			0
$324$	35.6329	−	25.8888i	1.97960	−	1.43827i
$325$	−31.4579	−	43.2981i	−1.74497	−	2.40175i
$326$		0			0
$327$		0			0
$328$	−62.3202	−	45.2783i	−3.44106	−	2.50007i
$329$		0			0
$330$	−59.5611	+	31.0941i	−3.27873	+	1.71167i
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$	−22.8150	+	31.4022i	−1.25214	+	1.72342i
$333$		0			0
$334$	−14.9545	−	46.0253i	−0.818276	−	2.51839i
$335$		0			0
$336$		0			0
$337$	23.8689	−	7.75547i	1.30022	−	0.422467i	0.424563	−	0.905399i	$-0.360428\pi$
$337$	23.8689	−	7.75547i	1.30022	−	0.422467i	0.875658	+	0.482931i	$0.160428\pi$
$338$	32.4624	+	10.5477i	1.76572	+	0.573718i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$	0.130065	−	0.400298i	0.00701262	−	0.0215826i
$345$		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
$352$	27.2009	+	26.6678i	1.44981	+	1.42140i
$353$	9.20815			0.490100			0.245050	−	0.969510i	$-0.421196\pi$
$353$	9.20815			0.490100			0.245050	+	0.969510i	$0.421196\pi$
$354$	−25.1414	+	34.6042i	−1.33625	+	1.83919i
$355$	22.1868	−	68.2840i	1.17755	−	3.62414i
$356$	−6.53112	−	20.1007i	−0.346149	−	1.06534i
$357$		0			0
$358$		0			0
$359$	−35.9847	+	11.6921i	−1.89920	+	0.617087i	−0.932504	+	0.361159i	$0.882381\pi$
$359$	−35.9847	+	11.6921i	−1.89920	+	0.617087i	−0.966696	+	0.255928i	$0.917619\pi$
$360$	−96.5706	−	31.3777i	−5.08972	−	1.65375i
$361$	15.3713	+	11.1679i	0.809017	+	0.587785i
$362$			70.4913i			3.70494i
$363$	−18.2330	−	5.52783i	−0.956986	−	0.290136i
$364$		0			0
$365$		0			0
$366$	−19.6442	+	60.4586i	−1.02682	+	3.16022i
$367$	4.80588	+	14.7910i	0.250865	+	0.772084i	0.994616	+	0.103627i	$0.0330448\pi$
$367$	4.80588	+	14.7910i	0.250865	+	0.772084i	−0.743751	+	0.668457i	$0.766955\pi$
$368$		0			0
$369$	17.8774	+	24.6061i	0.930659	+	1.28094i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		−	24.3200i		−	1.25924i	−0.776903	−	0.629621i	$-0.783210\pi$
$373$		−	24.3200i		−	1.25924i	0.776903	−	0.629621i	$-0.216790\pi$
$374$		0			0
$375$	−75.9496			−3.92202
$376$	−11.8033	+	16.2458i	−0.608706	+	0.837812i
$377$		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
$381$	19.7938	−	6.43140i	1.01407	−	0.329491i
$382$		0			0
$383$	−15.0159	−	10.9097i	−0.767274	−	0.557457i	0.133858	−	0.991000i	$-0.457263\pi$
$383$	−15.0159	−	10.9097i	−0.767274	−	0.557457i	−0.901133	+	0.433543i	$0.857263\pi$
$384$			4.92681i			0.251420i
$385$		0			0
$386$		0			0
$387$	−0.0976810	+	0.134446i	−0.00496541	+	0.00683429i
$388$		0			0
$389$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$389$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$390$	59.0923	−	42.9331i	2.99226	−	2.17400i
$391$		0			0
$392$	50.5838	−	16.4357i	2.55487	−	0.830127i
$393$		0			0
$394$	24.5664	+	17.8485i	1.23764	+	0.899194i
$395$		−	24.7648i		−	1.24605i
$396$	−22.5345	−	43.1651i	−1.13240	−	2.16913i
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$	−17.1930	+	23.6642i	−0.861809	+	1.18618i
$399$		0			0
$400$	46.6127	+	143.459i	2.33063	+	7.17295i
$401$	17.5187	−	12.7281i	0.874844	−	0.635611i	−0.0570386	−	0.998372i	$-0.518166\pi$
$401$	17.5187	−	12.7281i	0.874844	−	0.635611i	0.931882	+	0.362761i	$0.118166\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	32.4347	+	23.5652i	1.61170	+	1.17097i
$406$		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	$0.700000\pi$
$410$	36.6427	−	112.775i	1.80965	−	5.56955i
$411$	12.5183	+	38.5273i	0.617481	+	1.90041i
$412$	66.6056	−	48.3918i	3.28142	−	2.38409i
$413$		0			0
$414$		0			0
$415$	−33.6023	−	10.9180i	−1.64947	−	0.535945i
$416$	−33.5024	−	24.3409i	−1.64259	−	1.19341i
$417$			2.85976i			0.140043i
$418$		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	$0.600000\pi$
$422$	−9.90505	−	30.4846i	−0.482170	−	1.48397i
$423$	6.41439	−	4.66032i	0.311878	−	0.226593i
$424$		0			0
$425$		0			0
$426$	69.7108	+	22.6504i	3.37750	+	1.09742i
$427$		0			0
$428$		0			0
$429$	20.4884	+	3.03753i	0.989188	+	0.146653i
$430$	0.647905			0.0312448
$431$	−22.8363	+	31.4314i	−1.09998	+	1.51400i	−0.264578	+	0.964364i	$0.585233\pi$
$431$	−22.8363	+	31.4314i	−1.09998	+	1.51400i	−0.835406	+	0.549633i	$0.814767\pi$
$432$	16.3172	−	50.2193i	0.785063	−	2.41618i
$433$	12.5812	+	38.7210i	0.604614	+	1.86081i	0.499422	+	0.866359i	$0.333546\pi$
$433$	12.5812	+	38.7210i	0.604614	+	1.86081i	0.105192	+	0.994452i	$0.466454\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		−	41.9019i		−	1.99987i	−0.0115020	−	0.999934i	$-0.503661\pi$
$439$		−	41.9019i		−	1.99987i	0.0115020	−	0.999934i	$-0.496339\pi$
$440$	−49.9714	+	100.521i	−2.38229	+	4.79216i
$441$	−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
$445$	15.5641	−	11.3080i	0.737807	−	0.536048i
$446$		0			0
$447$	38.0937	−	12.3774i	1.80177	−	0.585431i
$448$		0			0
$449$	−21.7320	−	15.7892i	−1.02559	−	0.745138i	−0.0581727	−	0.998307i	$-0.518527\pi$
$449$	−21.7320	−	15.7892i	−1.02559	−	0.745138i	−0.967422	+	0.253168i	$0.918527\pi$
$450$		−	116.921i		−	5.51170i
$451$	29.8074	−	15.5611i	1.40358	−	0.732742i
$452$		0			0
$453$		0			0
$454$	−16.7631	+	51.5917i	−0.786733	+	2.42132i
$455$		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
$461$		−	24.9817i		−	1.16352i	−0.813362	−	0.581758i	$-0.802365\pi$
$461$		−	24.9817i		−	1.16352i	0.813362	−	0.581758i	$-0.197635\pi$
$462$		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	$0.800000\pi$
$468$	31.1145	+	42.8254i	1.43827	+	1.97960i
$469$		0			0
$470$	−29.3984	−	9.55212i	−1.35605	−	0.440606i
$471$	22.8418	+	16.5955i	1.05249	+	0.764681i
$472$			71.4638i			3.28939i
$473$	0.131192	+	0.128621i	0.00603221	+	0.00591399i
$474$	25.2823			1.16125
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−51.3863	+	37.3343i	−2.35035	+	1.70763i
$479$	−21.8695	−	30.1008i	−0.999245	−	1.37534i	−0.925787	−	0.378045i	$-0.876597\pi$
$479$	−21.8695	−	30.1008i	−0.999245	−	1.37534i	−0.0734577	−	0.997298i	$-0.523403\pi$
$480$	−84.2798	+	27.3842i	−3.84683	+	1.24991i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−50.8584	+	17.6450i	−2.31174	+	0.802047i
$485$		0			0
$486$	−24.0576	+	33.1125i	−1.09128	+	1.50201i
$487$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$487$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$488$	32.8208	+	101.012i	1.48573	+	4.57261i
$489$		0			0
$490$	48.1236	+	66.2364i	2.17400	+	2.99226i
$491$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$491$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$492$	81.7300	+	26.5557i	3.68467	+	1.19722i
$493$		0			0
$494$		0			0
$495$	31.0293	−	31.6496i	1.39467	−	1.42254i
$496$		0			0
$497$		0			0
$498$	11.1462	−	34.3044i	0.499472	−	1.53722i
$499$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$499$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$500$	−173.609	+	126.135i	−7.76405	+	5.64091i
$501$	18.7646	+	25.8272i	0.838340	+	1.15388i
$502$		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
$508$	34.5646	−	47.5741i	1.53356	−	2.11076i
$509$	7.61399	−	23.4335i	0.337484	−	1.03867i	−0.628001	−	0.778212i	$-0.716127\pi$
$509$	7.61399	−	23.4335i	0.337484	−	1.03867i	0.965485	−	0.260457i	$-0.0838733\pi$
$510$		0			0
$511$		0			0
$512$	−22.1654	−	30.5081i	−0.979583	−	1.34828i
$513$		0			0
$514$		0			0
$515$	60.6276	+	44.0485i	2.67157	+	1.94101i
$516$			0.469550i			0.0206708i
$517$	−4.05650	−	7.77028i	−0.178405	−	0.341737i
$518$		0			0
$519$		0			0
$520$	37.7113	−	116.063i	1.65375	−	5.08972i
$521$		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	0.617759	−	0.786367i	$-0.288041\pi$
$523$	−7.34144	−	10.1046i	−0.321019	−	0.441844i	−0.938778	+	0.344523i	$0.888041\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−52.2737	−	25.9864i	−2.27492	−	1.13092i
$529$	23.0000			1.00000
$530$		0			0
$531$	8.71932	−	26.8353i	0.378386	−	1.16455i
$532$		0			0
$533$	−29.5729	+	21.4859i	−1.28094	+	0.930659i
$534$	11.5442	+	15.8893i	0.499568	+	0.687596i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−3.40476	+	22.9654i	−0.146653	+	0.989188i
$540$	113.277			4.87468
$541$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$541$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$542$		0			0
$543$	−14.3697	−	44.2254i	−0.616663	−	1.89789i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−44.4827	−	14.4533i	−1.90194	−	0.617978i	−0.955121	−	0.296217i	$-0.904275\pi$
$547$	−44.4827	−	14.4533i	−1.90194	−	0.617978i	−0.946821	−	0.321761i	$-0.895725\pi$
$548$	92.5998	+	67.2777i	3.95567	+	2.87396i
$549$		−	41.9355i		−	1.78976i
$550$	−127.863	−	18.9565i	−5.45211	−	0.808310i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−20.2678	−	62.3777i	−0.861094	−	2.65018i
$555$		0			0
$556$	4.74940	+	6.53699i	0.201420	+	0.277230i
$557$	23.6018	−	7.66869i	1.00004	−	0.324933i	0.237159	−	0.971471i	$-0.423784\pi$
$557$	23.6018	−	7.66869i	1.00004	−	0.324933i	0.762882	+	0.646538i	$0.223784\pi$
$558$		0			0
$559$	−0.161584	−	0.117398i	−0.00683429	−	0.00496541i
$560$		0			0
$561$		0			0
$562$	−17.3963			−0.733819
$563$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$563$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$564$	6.92261	−	21.3056i	0.291494	−	0.897128i
$565$		0			0
$566$	71.1943	−	51.7257i	2.99252	−	2.17419i
$567$		0			0
$568$	116.470	−	37.8435i	4.88699	−	1.58788i
$569$		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	$0.793752\pi$
$572$	51.8780	−	27.0831i	2.16913	−	1.13240i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−9.11486	−	28.0526i	−0.379786	−	1.16886i
$577$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$577$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$578$	−26.2361	−	36.1108i	−1.09128	−	1.50201i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−28.3219	+	38.9817i	−1.17097	+	1.61170i
$586$	−0.161042	+	0.495636i	−0.00665258	+	0.0204745i
$587$	7.64975	+	23.5435i	0.315739	+	0.971745i	0.975449	+	0.220225i	$0.0706790\pi$
$587$	7.64975	+	23.5435i	0.315739	+	0.971745i	−0.659710	+	0.751520i	$0.729321\pi$
$588$	−48.0028	+	34.8761i	−1.97960	+	1.43827i
$589$		0			0
$590$	−104.623	+	33.9940i	−4.30726	+	1.39951i
$591$	−19.0511	−	6.19006i	−0.783656	−	0.254625i
$592$		0			0
$593$			14.7802i			0.606952i	0.952839	+	0.303476i	$0.0981472\pi$
$593$			14.7802i			0.606952i	−0.952839	+	0.303476i	$0.901853\pi$
$594$	32.3109	+	31.6777i	1.32573	+	1.29975i
$595$		0			0
$596$	66.5206	−	91.5577i	2.72479	−	3.75035i
$597$	5.96274	−	18.3514i	0.244039	−	0.751074i
$598$		0			0
$599$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$599$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$600$	−114.822	−	158.039i	−4.68760	−	6.45192i
$601$	45.9856	−	14.9416i	1.87579	−	0.609482i	0.886667	−	0.462408i	$-0.153015\pi$
$601$	45.9856	−	14.9416i	1.87579	−	0.609482i	0.989126	−	0.147074i	$-0.0469854\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−29.5808	−	39.0647i	−1.20263	−	1.58821i
$606$		0			0
$607$	−24.6944	+	33.9890i	−1.00232	+	1.37957i	−0.0784223	+	0.996920i	$0.524988\pi$
$607$	−24.6944	+	33.9890i	−1.00232	+	1.37957i	−0.923894	+	0.382649i	$0.875012\pi$
$608$		0			0
$609$		0			0
$610$	−132.269	+	96.0993i	−5.35543	+	3.89095i
$611$	5.60101	+	7.70913i	0.226593	+	0.311878i
$612$		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
$615$			78.2231i			3.15426i
$616$		0			0
$617$	−14.2333			−0.573011			−0.286505	−	0.958079i	$-0.592494\pi$
$617$	−14.2333			−0.573011			−0.286505	+	0.958079i	$0.592494\pi$
$618$	−44.9689	+	61.8944i	−1.80892	+	2.48976i
$619$		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
$624$	60.3560	+	19.6109i	2.41618	+	0.785063i
$625$	−97.9839	−	71.1895i	−3.91936	−	2.84758i
$626$		−	46.1132i		−	1.84305i
$627$		0			0
$628$	79.7742			3.18334
$629$		0			0
$630$		0			0
$631$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$631$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$632$	34.1735	−	24.8285i	1.35935	−	0.987625i
$633$	12.4286	+	17.1065i	0.493993	+	0.679923i
$634$	15.5397	−	5.04917i	0.617162	−	0.200528i
$635$	50.9072	+	16.5408i	2.02019	+	0.656400i
$636$		0			0
$637$		−	25.2389i		−	1.00000i
$638$		0			0
$639$	−48.3530			−1.91282
$640$	−7.44790	+	10.2512i	−0.294404	+	0.405212i
$641$		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
$645$	−0.406488	+	0.132076i	−0.0160054	+	0.00520048i
$646$		0			0
$647$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$647$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$648$			68.3832i			2.68635i
$649$	−27.9331	−	13.8862i	−1.09647	−	0.545081i
$650$	140.521			5.51170
$651$		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
$656$	97.9834	−	31.8367i	3.82561	−	1.24302i
$657$		0			0
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$	18.3658	−	123.879i	0.714888	−	4.82197i
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$		0			0
$663$		0			0
$664$	−18.6226	−	57.3146i	−0.722698	−	2.22424i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	85.7860	+	27.8736i	3.31916	+	1.07846i
$669$		0			0
$670$		0			0
$671$	−45.8602	−	6.79906i	−1.77041	−	0.262475i
$672$		0			0
$673$	−18.9205	+	26.0418i	−0.729332	+	1.00384i	0.269830	+	0.962908i	$0.413032\pi$
$673$	−18.9205	+	26.0418i	−0.729332	+	1.00384i	−0.999162	+	0.0409312i	$0.986968\pi$
$674$	−20.3629	+	62.6705i	−0.784348	+	2.41398i
$675$	23.8344	+	73.3547i	0.917386	+	2.82342i
$676$	−51.4697	+	37.3949i	−1.97960	+	1.43827i
$677$		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
$681$		−	35.7852i		−	1.37129i
$682$		0			0
$683$	−45.7958			−1.75233			−0.876163	−	0.482015i	$-0.839905\pi$
$683$	−45.7958			−1.75233			−0.876163	+	0.482015i	$0.839905\pi$
$684$		0			0
$685$	−32.1955	+	99.0874i	−1.23013	+	3.78594i
$686$		0			0
$687$		0			0
$688$	0.330880	+	0.455418i	0.0126147	+	0.0173626i
$689$		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
$695$	−4.32313	+	5.95028i	−0.163986	+	0.225707i
$696$		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	$0.100000\pi$
$702$	−39.7962	−	28.9137i	−1.50201	−	1.09128i
$703$		0			0
$704$	−32.1558	+	5.41969i	−1.21192	+	0.204262i
$705$	20.3914			0.767985
$706$	−14.2109	+	19.5596i	−0.534835	+	0.736137i
$707$		0			0
$708$	−24.6361	−	75.8223i	−0.925883	−	2.84958i
$709$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$709$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$710$	110.806	+	152.511i	4.15847	+	5.72364i
$711$	−15.8618	+	5.15382i	−0.594864	+	0.193283i
$712$	31.2082	+	10.1401i	1.16958	+	0.380018i
$713$		0			0
$714$		0			0
$715$	38.0381	+	37.2926i	1.42254	+	1.39467i
$716$		0			0
$717$	24.6285	−	33.8982i	0.919768	−	1.26595i
$718$	30.6990	−	94.4819i	1.14568	−	3.52603i
$719$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$719$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$720$	109.868	−	79.8238i	4.09454	−	2.97486i
$721$		0			0
$722$	−47.4450	+	15.4158i	−1.76572	+	0.573718i
$723$		0			0
$724$	−106.295	−	77.2279i	−3.95042	−	2.87015i
$725$		0			0
$726$	39.8810	−	30.1989i	1.48012	−	1.12079i
$727$	−50.5149			−1.87349			−0.936747	−	0.350007i	$-0.886179\pi$
$727$	−50.5149			−1.87349			−0.936747	+	0.350007i	$0.886179\pi$
$728$		0			0
$729$	8.34346	−	25.6785i	0.309017	−	0.951057i
$730$		0			0
$731$		0			0
$732$	−69.6451	−	95.8582i	−2.57416	−	3.54302i
$733$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$733$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$734$	−38.8354	−	12.6184i	−1.43344	−	0.465754i
$735$	−43.6945	−	31.7459i	−1.61170	−	1.17097i
$736$		0			0
$737$		0			0
$738$	−79.8576			−2.93960
$739$		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
$743$	−24.1206	−	33.1991i	−0.884898	−	1.21796i	−0.975040	−	0.222029i	$-0.928732\pi$
$743$	−24.1206	−	33.1991i	−0.884898	−	1.21796i	0.0901418	−	0.995929i	$-0.471268\pi$
$744$		0			0
$745$	97.9723	+	31.8331i	3.58943	+	1.16628i
$746$	51.6597	+	37.5330i	1.89140	+	1.37418i
$747$			23.7943i			0.870588i
$748$		0			0
$749$		0			0
$750$	117.213	−	161.330i	4.28001	−	5.89093i
$751$	7.19249	−	22.1362i	0.262458	−	0.807762i	−0.729810	−	0.683650i	$-0.760392\pi$
$751$	7.19249	−	22.1362i	0.262458	−	0.807762i	0.992268	−	0.124112i	$-0.0396083\pi$
$752$	−8.29928	−	25.5426i	−0.302644	−	0.931442i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	10.0620	+	7.31047i	0.365709	+	0.265703i	0.755429	−	0.655230i	$-0.227428\pi$
$757$	10.0620	+	7.31047i	0.365709	+	0.265703i	−0.389720	+	0.920933i	$0.627428\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−3.65877	+	5.03587i	−0.132630	+	0.182550i	−0.870167	−	0.492757i	$-0.835989\pi$
$761$	−3.65877	+	5.03587i	−0.132630	+	0.182550i	0.737536	+	0.675307i	$0.235989\pi$
$762$	−16.8864	+	51.9709i	−0.611729	+	1.88271i
$763$		0			0
$764$		0			0
$765$		0			0
$766$	46.3479	−	15.0593i	1.67462	−	0.544116i
$767$	32.2520	+	10.4793i	1.16455	+	0.378386i
$768$	17.0893	+	12.4161i	0.616656	+	0.448027i
$769$		0			0			−	1.00000i	$-0.5\pi$
$769$		0			0				1.00000i	$0.5\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	15.8694	−	48.8411i	0.570783	−	1.75669i	−0.0793244	−	0.996849i	$-0.525276\pi$
$773$	15.8694	−	48.8411i	0.570783	−	1.75669i	0.650108	−	0.759842i	$-0.274724\pi$
$774$	−0.134836	−	0.414981i	−0.00484657	−	0.0149162i
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$			136.142i			4.87468i
$781$	−7.83955	+	52.8783i	−0.280521	+	1.89213i
$782$		0			0
$783$		0			0
$784$	−21.9818	+	67.6529i	−0.785063	+	2.41618i
$785$	22.4390	+	69.0603i	0.800884	+	2.46487i
$786$		0			0
$787$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$787$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$788$	−53.8281	+	17.4898i	−1.91755	+	0.623049i
$789$		0			0
$790$	52.6047	+	38.2195i	1.87159	+	1.35979i
$791$		0			0
$792$	74.7831	+	11.0871i	2.65730	+	0.393962i
$793$	50.4002			1.78976
$794$		0			0
$795$		0			0
$796$	−16.8475	−	51.8514i	−0.597145	−	1.83782i
$797$		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
$800$	−162.141	−	52.6827i	−5.73254	−	1.86262i
$801$	−10.4817	−	7.61544i	−0.370354	−	0.269078i
$802$			56.8560i			2.00765i
$803$		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	$0.300000\pi$
$810$	−100.113	+	32.5287i	−3.51761	+	1.14294i
$811$		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
$820$	129.910	+	178.806i	4.53667	+	6.24419i
$821$	−44.0221	+	14.3037i	−1.53638	+	0.499201i	−0.950376	−	0.311105i	$-0.899301\pi$
$821$	−44.0221	+	14.3037i	−1.53638	+	0.499201i	−0.586007	+	0.810306i	$0.699301\pi$
$822$	−101.158	−	32.8682i	−3.52829	−	1.14641i
$823$	−42.5918	−	30.9448i	−1.48466	−	1.07867i	−0.976019	−	0.217687i	$-0.930149\pi$
$823$	−42.5918	−	30.9448i	−1.48466	−	1.07867i	−0.508639	−	0.860980i	$-0.669851\pi$
$824$			127.823i			4.45293i
$825$	84.0841	−	14.1719i	2.92743	−	0.493402i
$826$		0			0
$827$	33.5285	−	46.1481i	1.16590	−	1.60473i	0.479401	−	0.877596i	$-0.340854\pi$
$827$	33.5285	−	46.1481i	1.16590	−	1.60473i	0.686500	−	0.727129i	$-0.259146\pi$
$828$		0			0
$829$	−2.24035	−	6.89509i	−0.0778105	−	0.239476i	0.904584	−	0.426296i	$-0.140182\pi$
$829$	−2.24035	−	6.89509i	−0.0778105	−	0.239476i	−0.982394	+	0.186820i	$0.940182\pi$
$830$	75.0500	−	54.5270i	2.60502	−	1.89266i
$831$	25.4315	+	35.0034i	0.882208	+	1.21426i
$832$	33.7151	−	10.9547i	1.16886	−	0.379786i
$833$		0			0
$834$	−6.07462	−	4.41347i	−0.210347	−	0.152826i
$835$			82.1051i			2.84136i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−17.3613	+	53.4326i	−0.599379	+	1.84470i	−0.0677843	+	0.997700i	$0.521593\pi$
$839$	−17.3613	+	53.4326i	−0.599379	+	1.84470i	−0.531595	+	0.846999i	$0.678407\pi$
$840$		0			0
$841$	23.4615	−	17.0458i	0.809017	−	0.587785i
$842$		0			0
$843$	10.9142	−	3.54625i	0.375906	−	0.122139i
$844$	56.8199	+	18.4619i	1.95582	+	0.635485i
$845$	−46.8502	−	34.0387i	−1.61170	−	1.17097i
$846$			20.8175i			0.715720i
$847$		0			0
$848$		0			0
$849$	−34.1221	+	46.9651i	−1.17107	+	1.61184i
$850$		0			0
$851$		0			0
$852$	−110.528	+	80.3031i	−3.78662	+	2.75114i
$853$		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	$0.5\pi$
$858$	−38.0719	+	38.8329i	−1.29975	+	1.32573i
$859$	−58.0767			−1.98155			−0.990776	−	0.135509i	$-0.956733\pi$
$859$	−58.0767			−1.98155			−0.990776	+	0.135509i	$0.956733\pi$
$860$	−0.709823	+	0.976987i	−0.0242048	+	0.0333150i
$861$		0			0
$862$	−31.5224	−	97.0160i	−1.07366	−	3.30438i
$863$	−0.202467	+	0.147101i	−0.00689205	+	0.00500737i	−0.591226	−	0.806506i	$-0.701356\pi$
$863$	−0.202467	+	0.147101i	−0.00689205	+	0.00500737i	0.584334	+	0.811513i	$0.301356\pi$
$864$	35.0790	+	48.2820i	1.19341	+	1.64259i
$865$		0			0
$866$	−101.666	−	33.0334i	−3.45476	−	1.12252i
$867$	23.8214	+	17.3073i	0.809017	+	0.587785i
$868$		0			0
$869$	3.06445	+	18.1819i	0.103954	+	0.616778i
$870$		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	$0.100000\pi$
$878$	89.0066	+	64.6671i	3.00383	+	2.18241i
$879$		−	0.343785i		−	0.0115956i
$880$	−69.4813	−	133.092i	−2.34221	−	4.48654i
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	32.4092	−	44.6075i	1.09128	−	1.50201i
$883$	3.51528	−	10.8189i	0.118298	−	0.364085i	−0.874322	−	0.485346i	$-0.838694\pi$
$883$	3.51528	−	10.8189i	0.118298	−	0.364085i	0.992621	+	0.121261i	$0.0386937\pi$
$884$		0			0
$885$	58.7094	−	42.6549i	1.97350	−	1.43383i
$886$		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
$890$			50.5122i			1.69317i
$891$	−26.7290	−	13.2876i	−0.895455	−	0.445152i
$892$		0			0
$893$		0			0
$894$	−32.4983	+	100.019i	−1.08691	+	3.34515i
$895$		0			0
$896$		0			0
$897$		0			0
$898$	67.0778	−	21.7949i	2.23841	−	0.727305i
$899$		0			0
$900$	176.307	+	128.094i	5.87690	+	4.26981i
$901$		0			0
$902$	−12.9474	+	87.3313i	−0.431102	+	2.90782i
$903$		0			0
$904$		0			0
$905$	36.9571	−	113.742i	1.22849	−	3.78092i
$906$		0			0
$907$	38.7691	−	28.1674i	1.28731	−	0.935283i	0.287559	−	0.957763i	$-0.407156\pi$
$907$	38.7691	−	28.1674i	1.28731	−	0.935283i	0.999747	+	0.0224801i	$0.00715625\pi$
$908$	−59.4308	−	81.7995i	−1.97228	−	2.71461i
$909$		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
$913$	26.0212	+	3.85780i	0.861175	+	0.127675i
$914$		0			0
$915$	63.3943	−	87.2548i	2.09575	−	2.88455i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−35.5399	−	48.9165i	−1.17235	−	1.61361i	−0.645977	−	0.763356i	$-0.723550\pi$
$919$	−35.5399	−	48.9165i	−1.17235	−	1.61361i	−0.526377	−	0.850251i	$-0.676450\pi$
$920$		0			0
$921$		0			0
$922$	53.0654	+	38.5542i	1.74761	+	1.26972i
$923$		−	58.1131i		−	1.91282i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	15.5957	−	47.9988i	0.512231	−	1.57649i
$928$		0			0
$929$	−42.4870	+	30.8686i	−1.39395	+	1.01277i	−0.398535	+	0.917153i	$0.630481\pi$
$929$	−42.4870	+	30.8686i	−1.39395	+	1.01277i	−0.995419	+	0.0956136i	$0.969519\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−82.1864			−2.68635
$937$	28.5335	−	39.2730i	0.932148	−	1.28299i	−0.0268681	−	0.999639i	$-0.508553\pi$
$937$	28.5335	−	39.2730i	0.932148	−	1.28299i	0.959016	−	0.283352i	$-0.0914466\pi$
$938$		0			0
$939$	9.40021	+	28.9309i	0.306764	+	0.944123i
$940$	46.6117	−	33.8654i	1.52031	−	1.10457i
$941$	9.83196	+	13.5325i	0.320513	+	0.441148i	0.938624	−	0.344943i	$-0.112102\pi$
$941$	9.83196	+	13.5325i	0.320513	+	0.441148i	−0.618111	+	0.786091i	$0.712102\pi$
$942$	−70.5033	+	22.9079i	−2.29712	+	0.746380i
$943$		0			0
$944$	−77.3248	−	56.1798i	−2.51671	−	1.82850i
$945$		0			0
$946$	−0.475680	+	0.0801732i	−0.0154657	+	0.00260665i
$947$	1.86949			0.0607501			0.0303751	−	0.999539i	$-0.490330\pi$
$947$	1.86949			0.0607501			0.0303751	+	0.999539i	$0.490330\pi$
$948$	−27.6984	+	38.1236i	−0.899603	+	1.23820i
$949$		0			0
$950$		0			0
$951$	−8.72017	+	6.33557i	−0.282771	+	0.205445i
$952$		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
$956$		−	118.388i		−	3.82896i
$957$		0			0
$958$	97.6904			3.15623
$959$		0			0
$960$	23.4423	−	72.1479i	0.756596	−	2.32856i
$961$	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	$0.5\pi$
$968$	24.2494	−	79.9843i	0.779404	−	2.57079i
$969$		0			0
$970$		0			0
$971$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$971$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$972$	−23.5742	−	72.5538i	−0.756141	−	2.32716i
$973$		0			0
$974$		0			0
$975$	−88.1614	+	28.6454i	−2.82342	+	0.917386i
$976$	−135.098	−	43.8960i	−4.32438	−	1.40508i
$977$	−41.6761	−	30.2795i	−1.33334	−	0.968727i	−0.999661	−	0.0260393i	$-0.991711\pi$
$977$	−41.6761	−	30.2795i	−1.33334	−	0.968727i	−0.333677	−	0.942687i	$-0.608289\pi$
$978$		0			0
$979$	−10.0276	+	10.2280i	−0.320483	+	0.326889i
$980$	−152.602			−4.87468
$981$		0			0
$982$		0			0
$983$	−2.17540	−	6.69520i	−0.0693845	−	0.213544i	0.910352	−	0.413835i	$-0.135811\pi$
$983$	−2.17540	−	6.69520i	−0.0693845	−	0.213544i	−0.979736	+	0.200292i	$0.935811\pi$
$984$	−107.942	+	78.4242i	−3.44106	+	2.50007i
$985$	−30.2818	−	41.6793i	−0.964857	−	1.32801i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	19.3415	+	114.756i	0.614714	+	3.64719i
$991$	56.9213			1.80817			0.904083	−	0.427357i	$-0.140555\pi$
$991$	56.9213			1.80817			0.904083	+	0.427357i	$0.140555\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	40.1487	−	29.1697i	1.27280	−	0.924742i
$996$	39.5168	+	54.3902i	1.25214	+	1.72342i
$997$	−59.8029	+	19.4311i	−1.89398	+	0.615391i	−0.918439	+	0.395562i	$0.870550\pi$
$997$	−59.8029	+	19.4311i	−1.89398	+	0.615391i	−0.975539	+	0.219829i	$0.929450\pi$
$998$		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.194.2	✓	32
3.2	odd	2	inner	429.2.y.a.194.7	yes	32
11.8	odd	10	inner	429.2.y.a.272.2	yes	32
13.12	even	2	inner	429.2.y.a.194.7	yes	32
33.8	even	10	inner	429.2.y.a.272.7	yes	32
39.38	odd	2	CM	429.2.y.a.194.2	✓	32
143.129	odd	10	inner	429.2.y.a.272.7	yes	32
429.272	even	10	inner	429.2.y.a.272.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.y.a.194.2	✓	32	1.1	even	1	trivial
429.2.y.a.194.2	✓	32	39.38	odd	2	CM
429.2.y.a.194.7	yes	32	3.2	odd	2	inner
429.2.y.a.194.7	yes	32	13.12	even	2	inner
429.2.y.a.272.2	yes	32	11.8	odd	10	inner
429.2.y.a.272.2	yes	32	429.272	even	10	inner
429.2.y.a.272.7	yes	32	33.8	even	10	inner
429.2.y.a.272.7	yes	32	143.129	odd	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)

\(f(q)\)	\(=\)	\(q+(-1.54330 + 2.12417i) q^{2} +(0.535233 - 1.64728i) q^{3} +(-1.51228 - 4.65433i) q^{4} +(3.60386 - 2.61836i) q^{5} +(2.67307 + 3.67916i) q^{6} +(7.22625 + 2.34795i) q^{8} +(-2.42705 - 1.76336i) q^{9} +O(q^{10})\)	\(q+(-1.54330 + 2.12417i) q^{2} +(0.535233 - 1.64728i) q^{3} +(-1.51228 - 4.65433i) q^{4} +(3.60386 - 2.61836i) q^{5} +(2.67307 + 3.67916i) q^{6} +(7.22625 + 2.34795i) q^{8} +(-2.42705 - 1.76336i) q^{9} +11.6961i q^{10} +(-2.32189 + 2.36830i) q^{11} -8.47640 q^{12} +(2.11929 - 2.91695i) q^{13} +(-2.38426 - 7.33799i) q^{15} +(-8.22128 + 5.97311i) q^{16} +(7.49132 - 2.43408i) q^{18} +(-17.6368 - 12.8139i) q^{20} +(-1.44730 - 8.58706i) q^{22} +(7.73546 - 10.6469i) q^{24} +(4.58693 - 14.1171i) q^{25} +(2.92540 + 9.00345i) q^{26} +(-4.20378 + 3.05422i) q^{27} +(19.2667 + 6.26014i) q^{30} -11.4854i q^{32} +(2.65850 + 5.09239i) q^{33} +(-4.53685 + 13.9630i) q^{36} +(-3.67072 - 5.05231i) q^{39} +(32.1902 - 10.4592i) q^{40} +(-9.64207 - 3.13290i) q^{41} -0.0553950i q^{43} +(14.5342 + 7.22528i) q^{44} -13.3639 q^{45} +(-0.816692 + 2.51352i) q^{47} +(5.43908 + 16.7398i) q^{48} +(5.66312 - 4.11450i) q^{49} +(22.9081 + 31.5303i) q^{50} +(-16.7814 - 5.45261i) q^{52} -13.6431i q^{54} +(-2.16670 + 14.6146i) q^{55} +(2.90644 + 8.94511i) q^{59} +(-30.5478 + 22.1942i) q^{60} +(8.21635 + 11.3088i) q^{61} +(7.95433 + 5.77916i) q^{64} -16.0614i q^{65} +(-14.9199 - 2.21197i) q^{66} +(13.0395 - 9.47373i) q^{71} +(-13.3982 - 18.4411i) q^{72} +(-20.7997 - 15.1119i) q^{75} +16.3970 q^{78} +(3.26771 - 4.49762i) q^{79} +(-13.9886 + 43.0525i) q^{80} +(2.78115 + 8.55951i) q^{81} +(21.5354 - 15.6464i) q^{82} +(-4.66198 - 6.41666i) q^{83} +(0.117668 + 0.0854909i) q^{86} +(-22.3392 + 11.6623i) q^{88} +4.31872 q^{89} +(20.6244 - 28.3870i) q^{90} +(-4.07874 - 5.61390i) q^{94} +(-18.9197 - 6.14737i) q^{96} +18.3793i q^{98} +(9.81149 - 1.65367i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) 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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