LMFDB - Embedded newform 429.2.y.a.116.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("429.116");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			116.1
Character	$\chi$	$=$	429.116
Dual form			429.2.y.a.233.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.60814 + 0.847436i) q^{2} +(-1.40126 - 1.01807i) q^{3} +(4.46622 - 3.24490i) q^{4} +(-0.309156 + 0.951485i) q^{5} +(4.51743 + 1.46780i) q^{6} +(-5.67484 + 7.81075i) q^{8} +(0.927051 + 2.85317i) q^{9} +O(q^{10})$	\(q+(-2.60814 + 0.847436i) q^{2} +(-1.40126 - 1.01807i) q^{3} +(4.46622 - 3.24490i) q^{4} +(-0.309156 + 0.951485i) q^{5} +(4.51743 + 1.46780i) q^{6} +(-5.67484 + 7.81075i) q^{8} +(0.927051 + 2.85317i) q^{9} -2.74360i q^{10} +(0.486394 - 3.28077i) q^{11} -9.56187 q^{12} +(-3.42908 + 1.11418i) q^{13} +(1.40189 - 1.01853i) q^{15} +(4.76979 - 14.6799i) q^{16} +(-4.83576 - 6.65585i) q^{18} +(1.70671 + 5.25272i) q^{20} +(1.51165 + 8.96889i) q^{22} +(15.9038 - 5.16747i) q^{24} +(3.23534 + 2.35061i) q^{25} +(7.99934 - 5.81186i) q^{26} +(1.60570 - 4.94183i) q^{27} +(-2.79319 + 3.84449i) q^{30} +23.0201i q^{32} +(-4.02163 + 4.10201i) q^{33} +(13.3987 + 9.73469i) q^{36} +(5.93935 + 1.92981i) q^{39} +(-5.67740 - 7.81427i) q^{40} +(-5.95913 + 8.20204i) q^{41} +12.4558i q^{43} +(-8.47340 - 16.2309i) q^{44} -3.00135 q^{45} +(4.66807 + 3.39155i) q^{47} +(-21.6289 + 15.7143i) q^{48} +(-2.16312 + 6.65740i) q^{49} +(-10.4302 - 3.38898i) q^{50} +(-11.6996 + 16.1032i) q^{52} +14.2497i q^{54} +(2.97123 + 1.47707i) q^{55} +(11.9319 - 8.66907i) q^{59} +(2.95611 - 9.09798i) q^{60} +(14.6525 + 4.76089i) q^{61} +(-9.96850 - 30.6799i) q^{64} -3.60718i q^{65} +(7.01277 - 14.1067i) q^{66} +(-4.98064 + 15.3288i) q^{71} +(-27.5463 - 8.95032i) q^{72} +(-2.14045 - 6.58763i) q^{75} -17.1260 q^{78} +(-5.16135 + 1.67702i) q^{79} +(12.4931 + 9.07676i) q^{80} +(-7.28115 + 5.29007i) q^{81} +(8.59154 - 26.4421i) q^{82} +(17.1686 + 5.57841i) q^{83} +(-10.5555 - 32.4864i) q^{86} +(22.8650 + 22.4169i) q^{88} +4.31872 q^{89} +(7.82795 - 2.54345i) q^{90} +(-15.0491 - 4.88975i) q^{94} +(23.4362 - 32.2571i) q^{96} -19.1965i q^{98} +(9.81149 - 1.65367i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−2.60814	+	0.847436i	−1.84423	+	0.599228i	−0.846467	+	0.532441i	$0.821275\pi$
$2$	−2.60814	+	0.847436i	−1.84423	+	0.599228i	−0.997767	+	0.0667868i	$0.978725\pi$
$3$	−1.40126	−	1.01807i	−0.809017	−	0.587785i
$3$	−1.40126	−	1.01807i	−0.809017	−	0.587785i
$4$	4.46622	−	3.24490i	2.23311	−	1.62245i
$5$	−0.309156	+	0.951485i	−0.138259	+	0.425517i	−0.996083	−	0.0884268i	$-0.971816\pi$
$5$	−0.309156	+	0.951485i	−0.138259	+	0.425517i	0.857824	+	0.513944i	$0.171816\pi$
$6$	4.51743	+	1.46780i	1.84423	+	0.599228i
$7$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$7$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$8$	−5.67484	+	7.81075i	−2.00636	+	2.76152i
$9$	0.927051	+	2.85317i	0.309017	+	0.951057i
$10$		−	2.74360i		−	0.867602i
$11$	0.486394	−	3.28077i	0.146653	−	0.989188i
$11$	0.486394	−	3.28077i	0.146653	−	0.989188i
$12$	−9.56187			−2.76027
$13$	−3.42908	+	1.11418i	−0.951057	+	0.309017i
$13$	−3.42908	+	1.11418i	−0.951057	+	0.309017i
$14$		0			0
$15$	1.40189	−	1.01853i	0.361966	−	0.262984i
$16$	4.76979	−	14.6799i	1.19245	−	3.66997i
$17$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$17$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$18$	−4.83576	−	6.65585i	−1.13980	−	1.56880i
$19$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$19$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$20$	1.70671	+	5.25272i	0.381632	+	1.17454i
$21$		0			0
$22$	1.51165	+	8.96889i	0.322286	+	1.91217i
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$	15.9038	−	5.16747i	3.24636	−	1.05481i
$25$	3.23534	+	2.35061i	0.647068	+	0.470122i
$26$	7.99934	−	5.81186i	1.56880	−	1.13980i
$27$	1.60570	−	4.94183i	0.309017	−	0.951057i
$28$		0			0
$29$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$29$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$30$	−2.79319	+	3.84449i	−0.509963	+	0.701905i
$31$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$31$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$32$			23.0201i			4.06942i
$33$	−4.02163	+	4.10201i	−0.700075	+	0.714069i
$34$		0			0
$35$		0			0
$36$	13.3987	+	9.73469i	2.23311	+	1.62245i
$37$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$37$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$38$		0			0
$39$	5.93935	+	1.92981i	0.951057	+	0.309017i
$40$	−5.67740	−	7.81427i	−0.897676	−	1.23554i
$41$	−5.95913	+	8.20204i	−0.930659	+	1.28094i	0.0289423	+	0.999581i	$0.490786\pi$
$41$	−5.95913	+	8.20204i	−0.930659	+	1.28094i	−0.959602	+	0.281362i	$0.909214\pi$
$42$		0			0
$43$			12.4558i			1.89949i	0.313031	+	0.949743i	$0.398656\pi$
$43$			12.4558i			1.89949i	−0.313031	+	0.949743i	$0.601344\pi$
$44$	−8.47340	−	16.2309i	−1.27741	−	2.44690i
$45$	−3.00135			−0.447415
$46$		0			0
$47$	4.66807	+	3.39155i	0.680907	+	0.494708i	0.873659	−	0.486540i	$-0.161741\pi$
$47$	4.66807	+	3.39155i	0.680907	+	0.494708i	−0.192751	+	0.981248i	$0.561741\pi$
$48$	−21.6289	+	15.7143i	−3.12187	+	2.26817i
$49$	−2.16312	+	6.65740i	−0.309017	+	0.951057i
$50$	−10.4302	−	3.38898i	−1.47505	−	0.479274i
$51$		0			0
$52$	−11.6996	+	16.1032i	−1.62245	+	2.23311i
$53$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$53$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$54$			14.2497i			1.93914i
$55$	2.97123	+	1.47707i	0.400640	+	0.199168i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	11.9319	−	8.66907i	1.55341	−	1.12862i	0.612242	−	0.790670i	$-0.290268\pi$
$59$	11.9319	−	8.66907i	1.55341	−	1.12862i	0.941165	−	0.337946i	$-0.109732\pi$
$60$	2.95611	−	9.09798i	0.381632	−	1.17454i
$61$	14.6525	+	4.76089i	1.87606	+	0.609570i	0.988998	+	0.147927i	$0.0472599\pi$
$61$	14.6525	+	4.76089i	1.87606	+	0.609570i	0.887066	+	0.461644i	$0.152740\pi$
$62$		0			0
$63$		0			0
$64$	−9.96850	−	30.6799i	−1.24606	−	3.83498i
$65$		−	3.60718i		−	0.447415i
$66$	7.01277	−	14.1067i	0.863212	−	1.73642i
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−4.98064	+	15.3288i	−0.591093	+	1.81920i	−0.0178059	+	0.999841i	$0.505668\pi$
$71$	−4.98064	+	15.3288i	−0.591093	+	1.81920i	−0.573287	+	0.819355i	$0.694332\pi$
$72$	−27.5463	−	8.95032i	−3.24636	−	1.05481i
$73$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$73$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$74$		0			0
$75$	−2.14045	−	6.58763i	−0.247158	−	0.760674i
$76$		0			0
$77$		0			0
$78$	−17.1260			−1.93914
$79$	−5.16135	+	1.67702i	−0.580697	+	0.188680i	−0.584613	−	0.811312i	$-0.698754\pi$
$79$	−5.16135	+	1.67702i	−0.580697	+	0.188680i	0.00391577	+	0.999992i	$0.498754\pi$
$80$	12.4931	+	9.07676i	1.39677	+	1.01481i
$81$	−7.28115	+	5.29007i	−0.809017	+	0.587785i
$82$	8.59154	−	26.4421i	0.948777	−	2.92004i
$83$	17.1686	+	5.57841i	1.88450	+	0.612310i	0.984208	+	0.177016i	$0.0566444\pi$
$83$	17.1686	+	5.57841i	1.88450	+	0.612310i	0.900288	+	0.435294i	$0.143356\pi$
$84$		0			0
$85$		0			0
$86$	−10.5555	−	32.4864i	−1.13823	−	3.50310i
$87$		0			0
$88$	22.8650	+	22.4169i	2.43742	+	2.38965i
$89$	4.31872			0.457783			0.228892	−	0.973452i	$-0.426490\pi$
$89$	4.31872			0.457783			0.228892	+	0.973452i	$0.426490\pi$
$90$	7.82795	−	2.54345i	0.825138	−	0.268104i
$91$		0			0
$92$		0			0
$93$		0			0
$94$	−15.0491	−	4.88975i	−1.55220	−	0.504339i
$95$		0			0
$96$	23.4362	−	32.2571i	2.39194	−	3.29223i
$97$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$97$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$98$		−	19.1965i		−	1.93914i
$99$	9.81149	−	1.65367i	0.986092	−	0.166200i
$100$	22.0772			2.20772
$101$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$101$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$102$		0			0
$103$	4.53279	−	3.29326i	0.446629	−	0.324495i	−0.341634	−	0.939833i	$-0.610980\pi$
$103$	4.53279	−	3.29326i	0.446629	−	0.324495i	0.788263	+	0.615338i	$0.210980\pi$
$104$	10.7569	−	33.1065i	1.05481	−	3.24636i
$105$		0			0
$106$		0			0
$107$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$107$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$108$	−8.86434	−	27.2816i	−0.852972	−	2.62518i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$	−9.00110	−	1.33447i	−0.858221	−	0.127237i
$111$		0			0
$112$		0			0
$113$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$113$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−6.35787	−	8.75086i	−0.587785	−	0.809017i
$118$	−23.7737	+	32.7217i	−2.18855	+	3.01228i
$119$		0			0
$120$			16.7298i			1.52722i
$121$	−10.5268	−	3.19149i	−0.956986	−	0.290136i
$122$	−42.2504			−3.82517
$123$	16.7006	−	5.42634i	1.50584	−	0.489277i
$124$		0			0
$125$	−7.28370	+	5.29192i	−0.651474	+	0.473324i
$126$		0			0
$127$	−20.7792	−	6.75157i	−1.84386	−	0.599105i	−0.997821	−	0.0659781i	$-0.978983\pi$
$127$	−20.7792	−	6.75157i	−1.84386	−	0.599105i	−0.846035	−	0.533127i	$-0.821017\pi$
$128$	24.9367	+	34.3225i	2.20412	+	3.03371i
$129$	12.6809	−	17.4537i	1.11649	−	1.53672i
$130$	3.05685	+	9.40802i	0.268104	+	0.825138i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	−4.65084	+	31.3703i	−0.404804	+	2.73043i
$133$		0			0
$134$		0			0
$135$	4.20567	+	3.05560i	0.361966	+	0.262984i
$136$		0			0
$137$	−6.02688	+	18.5488i	−0.514911	+	1.58473i	0.268533	+	0.963271i	$0.413461\pi$
$137$	−6.02688	+	18.5488i	−0.514911	+	1.58473i	−0.783444	+	0.621463i	$0.786539\pi$
$138$		0			0
$139$	8.91171	+	12.2659i	0.755882	+	1.04038i	0.997545	+	0.0700216i	$0.0223068\pi$
$139$	8.91171	+	12.2659i	0.755882	+	1.04038i	−0.241664	+	0.970360i	$0.577693\pi$
$140$		0			0
$141$	−3.08832	−	9.50487i	−0.260083	−	0.800455i
$142$		−	44.2005i		−	3.70922i
$143$	1.98747	+	11.7919i	0.166200	+	0.986092i
$144$	46.3061			3.85884
$145$		0			0
$146$		0			0
$147$	9.80881	−	7.12652i	0.809017	−	0.587785i
$148$		0			0
$149$	−13.8736	−	4.50782i	−1.13657	−	0.369295i	−0.320502	−	0.947248i	$-0.603852\pi$
$149$	−13.8736	−	4.50782i	−1.13657	−	0.369295i	−0.816070	+	0.577953i	$0.803852\pi$
$150$	11.1652	+	15.3676i	0.911634	+	1.25476i
$151$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$151$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	32.7884	−	10.6536i	2.62518	−	0.852972i
$157$	−19.7201	−	14.3275i	−1.57384	−	1.14346i	−0.923361	−	0.383934i	$-0.874569\pi$
$157$	−19.7201	−	14.3275i	−1.57384	−	1.14346i	−0.650477	−	0.759526i	$-0.725431\pi$
$158$	12.0404	−	8.74783i	0.957879	−	0.695940i
$159$		0			0
$160$	−21.9033	−	7.11681i	−1.73161	−	0.562633i
$161$		0			0
$162$	14.5073	−	19.9676i	1.13980	−	1.56880i
$163$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$163$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$164$			55.9688i			4.37043i
$165$	−2.65970	−	5.09468i	−0.207057	−	0.396620i
$166$	−49.5054			−3.84237
$167$	21.8052	−	7.08495i	1.68734	−	0.548250i	0.701027	−	0.713134i	$-0.252725\pi$
$167$	21.8052	−	7.08495i	1.68734	−	0.548250i	0.986313	+	0.164884i	$0.0527251\pi$
$168$		0			0
$169$	10.5172	−	7.64121i	0.809017	−	0.587785i
$170$		0			0
$171$		0			0
$172$	40.4177	+	55.6301i	3.08182	+	4.24176i
$173$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$173$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$174$		0			0
$175$		0			0
$176$	−45.8413	−	22.7888i	−3.45542	−	1.71777i
$177$	−25.5455			−1.92012
$178$	−11.2638	+	3.65984i	−0.844259	+	0.274317i
$179$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$179$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$180$	−13.4047	+	9.73908i	−0.999127	+	0.725908i
$181$	−2.03726	+	6.27003i	−0.151428	+	0.466048i	−0.997781	−	0.0665740i	$-0.978793\pi$
$181$	−2.03726	+	6.27003i	−0.151428	+	0.466048i	0.846353	+	0.532622i	$0.178793\pi$
$182$		0			0
$183$	−15.6850	−	21.5886i	−1.15947	−	1.59588i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	31.8538			2.32318
$189$		0			0
$190$		0			0
$191$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$191$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$192$	−17.2659	+	53.1391i	−1.24606	+	3.83498i
$193$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$193$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$194$		0			0
$195$	−3.67237	+	5.05459i	−0.262984	+	0.361966i
$196$	11.9416	+	36.7525i	0.852972	+	2.62518i
$197$		−	5.67809i		−	0.404548i	−0.979329	−	0.202274i	$-0.935167\pi$
$197$		−	5.67809i		−	0.404548i	0.979329	−	0.202274i	$-0.0648331\pi$
$198$	−24.1884	+	12.6276i	−1.71899	+	0.897406i
$199$	6.22307			0.441142			0.220571	−	0.975371i	$-0.429208\pi$
$199$	6.22307			0.441142			0.220571	+	0.975371i	$0.429208\pi$
$200$	−36.7201	+	11.9311i	−2.59650	+	0.843654i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−5.96181	−	8.20573i	−0.416391	−	0.573113i
$206$	−9.03132	+	12.4306i	−0.629242	+	0.866077i
$207$		0			0
$208$			55.6530i			3.85884i
$209$		0			0
$210$		0			0
$211$	−20.2570	+	6.58190i	−1.39455	+	0.453117i	−0.907424	−	0.420216i	$-0.861954\pi$
$211$	−20.2570	+	6.58190i	−1.39455	+	0.453117i	−0.487125	+	0.873332i	$0.661954\pi$
$212$		0			0
$213$	22.5850	−	16.4090i	1.54750	−	1.12433i
$214$		0			0
$215$	−11.8515	−	3.85078i	−0.808264	−	0.262621i
$216$	29.4873	+	40.5858i	2.00636	+	2.76152i
$217$		0			0
$218$		0			0
$219$		0			0
$220$	18.0631	−	3.04443i	1.21781	−	0.205255i
$221$		0			0
$222$		0			0
$223$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$223$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$224$		0			0
$225$	−3.70737	+	11.4101i	−0.247158	+	0.760674i
$226$		0			0
$227$	−2.24635	−	3.09184i	−0.149096	−	0.205213i	0.727936	−	0.685645i	$-0.240480\pi$
$227$	−2.24635	−	3.09184i	−0.149096	−	0.205213i	−0.877032	+	0.480432i	$0.840480\pi$
$228$		0			0
$229$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$229$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$233$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$234$	23.9980	+	17.4356i	1.56880	+	1.13980i
$235$	−4.67017	+	3.39308i	−0.304648	+	0.221340i
$236$	25.1604	−	77.4359i	1.63781	−	5.04065i
$237$	8.93972	+	2.90469i	0.580697	+	0.188680i
$238$		0			0
$239$	−6.37028	+	8.76793i	−0.412059	+	0.567150i	−0.963719	−	0.266919i	$-0.913995\pi$
$239$	−6.37028	+	8.76793i	−0.412059	+	0.567150i	0.551660	+	0.834069i	$0.313995\pi$
$240$	−8.26524	−	25.4378i	−0.533519	−	1.64200i
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$	30.1601	−	0.596969i	1.93876	−	0.0383746i
$243$	15.5885			1.00000
$244$	80.8900	−	26.2827i	5.17845	−	1.68258i
$245$	−5.66567	−	4.11635i	−0.361966	−	0.262984i
$246$	−38.9589	+	28.3053i	−2.48393	+	1.80468i
$247$		0			0
$248$		0			0
$249$	−18.3784	−	25.2957i	−1.16468	−	1.60305i
$250$	14.5124	−	19.9746i	0.917842	−	1.26330i
$251$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$251$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$252$		0			0
$253$		0			0
$254$	59.9166			3.75950
$255$		0			0
$256$	−41.9289	−	30.4631i	−2.62056	−	1.90395i
$257$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$257$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$258$	−18.2826	+	56.2681i	−1.13823	+	3.50310i
$259$		0			0
$260$	−11.7049	−	16.1104i	−0.725908	−	0.999127i
$261$		0			0
$262$		0			0
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$	−9.21772	−	54.6902i	−0.567312	−	3.36595i
$265$		0			0
$266$		0			0
$267$	−6.05164	−	4.39677i	−0.370354	−	0.269078i
$268$		0			0
$269$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$269$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$270$	−13.5584	−	4.40539i	−0.825138	−	0.268104i
$271$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$271$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$272$		0			0
$273$		0			0
$274$		−	53.4853i		−	3.23117i
$275$	9.28545	−	9.47106i	0.559934	−	0.571127i
$276$		0			0
$277$	23.7574	−	7.71924i	1.42744	−	0.463804i	0.509484	−	0.860480i	$-0.329836\pi$
$277$	23.7574	−	7.71924i	1.42744	−	0.463804i	0.917959	+	0.396676i	$0.129836\pi$
$278$	−33.6376	−	24.4391i	−2.01745	−	1.46576i
$279$		0			0
$280$		0			0
$281$	23.4699	+	7.62584i	1.40010	+	0.454919i	0.909223	−	0.416310i	$-0.136677\pi$
$281$	23.4699	+	7.62584i	1.40010	+	0.454919i	0.490875	+	0.871230i	$0.336677\pi$
$282$	16.1095	+	22.1729i	0.959310	+	1.32038i
$283$	14.9216	−	20.5379i	0.886999	−	1.22085i	−0.0874340	−	0.996170i	$-0.527867\pi$
$283$	14.9216	−	20.5379i	0.886999	−	1.22085i	0.974433	−	0.224679i	$-0.0721333\pi$
$284$	27.4958	+	84.6235i	1.63158	+	5.02148i
$285$		0			0
$286$	−15.1765	−	29.0708i	−0.897406	−	1.71899i
$287$		0			0
$288$	−65.6803	+	21.3408i	−3.87025	+	1.25752i
$289$	13.7533	+	9.99235i	0.809017	+	0.587785i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−19.1013	−	26.2907i	−1.11591	−	1.53592i	−0.812411	−	0.583085i	$-0.801846\pi$
$293$	−19.1013	−	26.2907i	−1.11591	−	1.53592i	−0.303498	−	0.952832i	$-0.598154\pi$
$294$	−19.5435	+	26.8993i	−1.13980	+	1.56880i
$295$	4.55965	+	14.0332i	0.265473	+	0.817043i
$296$		0			0
$297$	−15.4320	−	7.67160i	−0.895455	−	0.445152i
$298$	40.0045			2.31740
$299$		0			0
$300$	−30.9359	−	22.4762i	−1.78608	−	1.29767i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−9.05984	+	12.4698i	−0.518765	+	0.714019i
$306$		0			0
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$		0			0
$309$	−9.70440			−0.552064
$310$		0			0
$311$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$311$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$312$	−48.7781	+	35.4394i	−2.76152	+	2.00636i
$313$	−7.35046	+	22.6224i	−0.415473	+	1.27869i	0.496355	+	0.868120i	$0.334671\pi$
$313$	−7.35046	+	22.6224i	−0.415473	+	1.27869i	−0.911828	+	0.410574i	$0.865329\pi$
$314$	63.5745	+	20.6566i	3.58772	+	1.16572i
$315$		0			0
$316$	−17.6099	+	24.2380i	−0.990636	+	1.36349i
$317$	10.8984	+	33.5419i	0.612116	+	1.88390i	0.437354	+	0.899289i	$0.355916\pi$
$317$	10.8984	+	33.5419i	0.612116	+	1.88390i	0.174762	+	0.984611i	$0.444084\pi$
$318$		0			0
$319$		0			0
$320$	32.2733			1.80413
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−15.3535	+	47.2532i	−0.852972	+	2.62518i
$325$	−13.7132	−	4.45570i	−0.760674	−	0.247158i
$326$		0			0
$327$		0			0
$328$	−30.2469	−	93.0905i	−1.67011	−	5.14006i
$329$		0			0
$330$	11.2543	+	11.0337i	0.619528	+	0.607386i
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$	94.7800	−	30.7959i	5.20173	−	1.69014i
$333$		0			0
$334$	−50.8671	+	36.9571i	−2.78332	+	2.02220i
$335$		0			0
$336$		0			0
$337$	−2.67598	−	3.68317i	−0.145770	−	0.200635i	0.729888	−	0.683567i	$-0.239572\pi$
$337$	−2.67598	−	3.68317i	−0.145770	−	0.200635i	−0.875658	+	0.482931i	$0.839572\pi$
$338$	−20.9550	+	28.8420i	−1.13980	+	1.56880i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$	−97.2888	−	70.6845i	−5.24546	−	3.81105i
$345$		0			0
$346$		0			0
$347$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$347$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$348$		0			0
$349$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$349$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$350$		0			0
$351$			18.7350i			1.00000i
$352$	75.5235	+	11.1968i	4.02542	+	0.596794i
$353$	−31.8024			−1.69267			−0.846335	−	0.532652i	$-0.821196\pi$
$353$	−31.8024			−1.69267			−0.846335	+	0.532652i	$0.821196\pi$
$354$	66.6263	−	21.6482i	3.54115	−	1.15059i
$355$	−13.0453	−	9.47800i	−0.692375	−	0.503040i
$356$	19.2883	−	14.0138i	1.02228	−	0.742730i
$357$		0			0
$358$		0			0
$359$	−22.2398	−	30.6104i	−1.17377	−	1.61556i	−0.631642	−	0.775260i	$-0.717619\pi$
$359$	−22.2398	−	30.6104i	−1.17377	−	1.61556i	−0.542128	−	0.840296i	$-0.682381\pi$
$360$	17.0322	−	23.4428i	0.897676	−	1.23554i
$361$	−5.87132	−	18.0701i	−0.309017	−	0.951057i
$362$		−	18.0796i		−	0.950241i
$363$	11.5017	+	15.1892i	0.603680	+	0.797227i
$364$		0			0
$365$		0			0
$366$	59.2038	+	43.0140i	3.09463	+	2.24838i
$367$	26.8302	−	19.4933i	1.40052	−	1.01754i	0.405908	−	0.913914i	$-0.366955\pi$
$367$	26.8302	−	19.4933i	1.40052	−	1.01754i	0.994616	−	0.103627i	$-0.0330448\pi$
$368$		0			0
$369$	−28.9262	−	9.39870i	−1.50584	−	0.489277i
$370$		0			0
$371$		0			0
$372$		0			0
$373$			21.0249i			1.08863i	0.838881	+	0.544315i	$0.183210\pi$
$373$			21.0249i			1.08863i	−0.838881	+	0.544315i	$0.816790\pi$
$374$		0			0
$375$	15.5939			0.805267
$376$	−52.9811	+	17.2146i	−2.73229	+	0.887775i
$377$		0			0
$378$		0			0
$379$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$379$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$380$		0			0
$381$	22.2434	+	30.6155i	1.13957	+	1.56848i
$382$		0			0
$383$	1.61904	+	4.98289i	0.0827291	+	0.254614i	0.983862	−	0.178929i	$-0.0572632\pi$
$383$	1.61904	+	4.98289i	0.0827291	+	0.254614i	−0.901133	+	0.433543i	$0.857263\pi$
$384$		−	73.4821i		−	3.74987i
$385$		0			0
$386$		0			0
$387$	−35.5384	+	11.5471i	−1.80652	+	0.586973i
$388$		0			0
$389$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$389$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$390$	5.29462	−	16.2952i	0.268104	−	0.825138i
$391$		0			0
$392$	−39.7239	−	54.6752i	−2.00636	−	2.76152i
$393$		0			0
$394$	4.81182	+	14.8093i	0.242416	+	0.746080i
$395$		−	5.42941i		−	0.273183i
$396$	38.4543	−	39.2229i	1.93240	−	1.97103i
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$	−16.2306	+	5.27365i	−0.813568	+	0.264344i
$399$		0			0
$400$	49.9386	−	36.2825i	2.49693	−	1.81413i
$401$	−11.9694	+	36.8379i	−0.597722	+	1.83960i	−0.0570386	+	0.998372i	$0.518166\pi$
$401$	−11.9694	+	36.8379i	−0.597722	+	1.83960i	−0.540683	+	0.841226i	$0.681834\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−2.78241	−	8.56337i	−0.138259	−	0.425517i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$409$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$410$	22.5031	+	16.3494i	1.11135	+	0.807442i
$411$	27.3293	−	19.8559i	1.34805	−	0.979419i
$412$	9.55812	−	29.4169i	0.470895	−	1.44927i
$413$		0			0
$414$		0			0
$415$	−10.6155	+	14.6110i	−0.521097	+	0.717228i
$416$	−25.6485	−	78.9378i	−1.25752	−	3.87025i
$417$		−	26.2605i		−	1.28598i
$418$		0			0
$419$		0			0		1.00000			$0$
$419$		0			0		−1.00000			$\pi$
$420$		0			0
$421$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$421$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$422$	47.2554	−	34.3330i	2.30036	−	1.67131i
$423$	−5.34913	+	16.4629i	−0.260083	+	0.800455i
$424$		0			0
$425$		0			0
$426$	−44.9994	+	61.9363i	−2.18023	+	3.00082i
$427$		0			0
$428$		0			0
$429$	9.22012	−	18.5470i	0.445152	−	0.895455i
$430$	34.1736			1.64800
$431$	−21.7044	+	7.05219i	−1.04546	+	0.339692i	−0.780887	−	0.624672i	$-0.785233\pi$
$431$	−21.7044	+	7.05219i	−1.04546	+	0.339692i	−0.264578	+	0.964364i	$0.585233\pi$
$432$	−64.8868	−	47.1430i	−3.12187	−	2.26817i
$433$	−3.54171	+	2.57320i	−0.170204	+	0.123660i	−0.669626	−	0.742698i	$-0.733546\pi$
$433$	−3.54171	+	2.57320i	−0.170204	+	0.123660i	0.499422	+	0.866359i	$0.333546\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		−	13.4068i		−	0.639871i	−0.947439	−	0.319936i	$-0.896339\pi$
$439$		−	13.4068i		−	0.639871i	0.947439	−	0.319936i	$-0.103661\pi$
$440$	−28.3982	+	14.8254i	−1.35383	+	0.706773i
$441$	−21.0000			−1.00000
$442$		0			0
$443$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$443$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$444$		0			0
$445$	−1.33516	+	4.10920i	−0.0632926	+	0.194795i
$446$		0			0
$447$	14.8513	+	20.4410i	0.702440	+	0.966826i
$448$		0			0
$449$	−0.761824	−	2.34465i	−0.0359527	−	0.110651i	0.931470	−	0.363819i	$-0.118527\pi$
$449$	−0.761824	−	2.34465i	−0.0359527	−	0.110651i	−0.967422	+	0.253168i	$0.918527\pi$
$450$		−	32.9009i		−	1.55096i
$451$	24.0105	+	23.5399i	1.13061	+	1.10845i
$452$		0			0
$453$		0			0
$454$	8.47895	+	6.16031i	0.397937	+	0.289118i
$455$		0			0
$456$		0			0
$457$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$457$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		−	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		0.309017	−	0.951057i	$-0.400000\pi$
$467$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$468$	−56.7913	−	18.4526i	−2.62518	−	0.852972i
$469$		0			0
$470$	9.30504	−	12.8073i	0.429210	−	0.590756i
$471$	13.0465	+	40.1531i	0.601152	+	1.85016i
$472$			142.393i			6.55417i
$473$	40.8644	+	6.05841i	1.87895	+	0.278566i
$474$	−25.7776			−1.18400
$475$		0			0
$476$		0			0
$477$		0			0
$478$	9.18431	−	28.2664i	0.420081	−	1.29288i
$479$	−9.92120	−	3.22359i	−0.453311	−	0.147290i	0.0734577	−	0.997298i	$-0.476597\pi$
$479$	−9.92120	−	3.22359i	−0.453311	−	0.147290i	−0.526769	+	0.850009i	$0.676597\pi$
$480$	23.4467	+	32.2716i	1.07019	+	1.47299i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−57.3712	+	19.9046i	−2.60778	+	0.904755i
$485$		0			0
$486$	−40.6569	+	13.2102i	−1.84423	+	0.599228i
$487$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$487$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$488$	−120.337	+	87.4299i	−5.44740	+	3.95777i
$489$		0			0
$490$	18.2652	+	5.93473i	0.825138	+	0.268104i
$491$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$491$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$492$	56.9804	−	78.4268i	2.56888	−	3.53575i
$493$		0			0
$494$		0			0
$495$	−1.45984	+	9.84673i	−0.0656150	+	0.442578i
$496$		0			0
$497$		0			0
$498$	69.3699	+	50.4002i	3.10854	+	2.25849i
$499$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$499$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$500$	−15.3589	+	47.2697i	−0.686870	+	2.11397i
$501$	−37.7678	−	12.2715i	−1.68734	−	0.548250i
$502$		0			0
$503$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$503$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−22.5167			−1.00000
$508$	−114.713	+	37.2724i	−5.08955	+	1.65369i
$509$	22.9249	+	16.6559i	1.01613	+	0.738260i	0.965485	−	0.260457i	$-0.0838733\pi$
$509$	22.9249	+	16.6559i	1.01613	+	0.738260i	0.0506418	+	0.998717i	$0.483873\pi$
$510$		0			0
$511$		0			0
$512$	54.4751	+	17.7000i	2.40748	+	0.782239i
$513$		0			0
$514$		0			0
$515$	1.73215	+	5.33102i	0.0763277	+	0.234913i
$516$		−	119.100i		−	5.24310i
$517$	13.3974	−	13.6652i	0.589217	−	0.600995i
$518$		0			0
$519$		0			0
$520$	28.1747	+	20.4702i	1.23554	+	0.897676i
$521$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$521$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$522$		0			0
$523$	11.8787	+	3.85962i	0.519419	+	0.168769i	0.556982	−	0.830525i	$-0.311959\pi$
$523$	11.8787	+	3.85962i	0.519419	+	0.168769i	−0.0375627	+	0.999294i	$0.511959\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$	41.0349	+	78.6028i	1.78581	+	3.42075i
$529$	23.0000			1.00000
$530$		0			0
$531$	35.7958	+	26.0072i	1.55341	+	1.12862i
$532$		0			0
$533$	11.2958	−	34.7650i	0.489277	−	1.50584i
$534$	19.5095	+	6.33903i	0.844259	+	0.274317i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	20.7892	+	10.3348i	0.895455	+	0.445152i
$540$	28.6985			1.23499
$541$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$541$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$542$		0			0
$543$	9.23808	−	6.71186i	0.396444	−	0.288033i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	22.4584	−	30.9113i	0.960250	−	1.32167i	0.0134293	−	0.999910i	$-0.495725\pi$
$547$	22.4584	−	30.9113i	0.960250	−	1.32167i	0.946821	−	0.321761i	$-0.104275\pi$
$548$	33.2717	+	102.400i	1.42130	+	4.37430i
$549$			46.2197i			1.97261i
$550$	−16.1917	+	32.5707i	−0.690414	+	1.38882i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−55.4210	+	40.2657i	−2.35461	+	1.71073i
$555$		0			0
$556$	79.6033	+	25.8647i	3.37593	+	1.09691i
$557$	−25.6729	−	35.3357i	−1.08780	−	1.49722i	−0.850638	−	0.525752i	$-0.823784\pi$
$557$	−25.6729	−	35.3357i	−1.08780	−	1.49722i	−0.237159	−	0.971471i	$-0.576216\pi$
$558$		0			0
$559$	−13.8779	−	42.7118i	−0.586973	−	1.80652i
$560$		0			0
$561$		0			0
$562$	−67.6753			−2.85471
$563$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$563$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$564$	−44.6354	−	32.4295i	−1.87949	−	1.36553i
$565$		0			0
$566$	−21.5132	+	66.2108i	−0.904267	+	2.78305i
$567$		0			0
$568$	−91.4653	−	125.891i	−3.83780	−	5.28227i
$569$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$569$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$570$		0			0
$571$			28.8444i			1.20710i	0.797325	+	0.603550i	$0.206248\pi$
$571$			28.8444i			1.20710i	−0.797325	+	0.603550i	$0.793752\pi$
$572$	47.1401	+	46.2163i	1.97103	+	1.93240i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	78.2936	−	56.8836i	3.26223	−	2.37015i
$577$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$577$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$578$	−44.3384	−	14.4064i	−1.84423	−	0.599228i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	10.2919	−	3.34404i	0.425517	−	0.138259i
$586$	72.0985	+	52.3826i	2.97836	+	2.16391i
$587$	−20.0273	+	14.5507i	−0.826615	+	0.600571i	−0.918600	−	0.395189i	$-0.870679\pi$
$587$	−20.0273	+	14.5507i	−0.826615	+	0.600571i	0.0919844	+	0.995760i	$0.470679\pi$
$588$	20.6835	−	63.6572i	0.852972	−	2.62518i
$589$		0			0
$590$	−23.7844	−	32.7365i	−0.979190	−	1.34774i
$591$	−5.78072	+	7.95648i	−0.237787	+	0.327286i
$592$		0			0
$593$			15.3195i			0.629095i	0.949242	+	0.314548i	$0.101853\pi$
$593$			15.3195i			0.629095i	−0.949242	+	0.314548i	$0.898147\pi$
$594$	46.7500	+	6.93099i	1.91818	+	0.284382i
$595$		0			0
$596$	−76.5901	+	24.8856i	−3.13725	+	1.01935i
$597$	−8.72013	−	6.33554i	−0.356891	−	0.259297i
$598$		0			0
$599$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$599$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$600$	63.6010	+	20.6652i	2.59650	+	0.843654i
$601$	13.3264	+	18.3422i	0.543594	+	0.748193i	0.989126	−	0.147074i	$-0.0469854\pi$
$601$	13.3264	+	18.3422i	0.543594	+	0.748193i	−0.445532	+	0.895266i	$0.646985\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	6.29109	−	9.02946i	0.255769	−	0.367100i
$606$		0			0
$607$	−10.9416	+	3.55516i	−0.444108	+	0.144299i	−0.522530	−	0.852621i	$-0.675012\pi$
$607$	−10.9416	+	3.55516i	−0.444108	+	0.144299i	0.0784223	+	0.996920i	$0.475012\pi$
$608$		0			0
$609$		0			0
$610$	13.0620	−	40.2006i	0.528864	−	1.62768i
$611$	−19.7860	−	6.42885i	−0.800455	−	0.260083i
$612$		0			0
$613$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$613$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$614$		0			0
$615$			17.5679i			0.708407i
$616$		0			0
$617$	39.4914			1.58986			0.794932	−	0.606698i	$-0.207506\pi$
$617$	39.4914			1.58986			0.794932	+	0.606698i	$0.207506\pi$
$618$	25.3104	−	8.22386i	1.01814	−	0.330812i
$619$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$619$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$	56.6588	−	77.9842i	2.26817	−	3.12187i
$625$	3.39557	+	10.4505i	0.135823	+	0.418019i
$626$		−	65.2314i		−	2.60717i
$627$		0			0
$628$	−134.566			−5.36976
$629$		0			0
$630$		0			0
$631$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$631$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$632$	16.1910	−	49.8308i	0.644044	−	1.98216i
$633$	35.0862	+	11.4002i	1.39455	+	0.453117i
$634$	−56.8492	−	78.2463i	−2.25777	−	3.10756i
$635$	12.8480	−	17.6838i	0.509859	−	0.701761i
$636$		0			0
$637$		−	25.2389i		−	1.00000i
$638$		0			0
$639$	−48.3530			−1.91282
$640$	−40.3667	+	13.1159i	−1.59563	+	0.518452i
$641$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$641$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$642$		0			0
$643$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$643$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$644$		0			0
$645$	12.6866	+	17.4616i	0.499534	+	0.687550i
$646$		0			0
$647$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$647$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$648$		−	86.8916i		−	3.41342i
$649$	−22.6375	−	43.3625i	−0.888601	−	1.70213i
$650$	39.5420			1.55096
$651$		0			0
$652$		0			0
$653$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$653$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$654$		0			0
$655$		0			0
$656$	91.9813	+	126.601i	3.59127	+	4.94295i
$657$		0			0
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$	−28.4105	−	14.1235i	−1.10588	−	0.549757i
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$		0			0
$663$		0			0
$664$	−141.001	+	102.443i	−5.47188	+	3.97555i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	74.3970	−	102.399i	2.87851	−	3.96192i
$669$		0			0
$670$		0			0
$671$	22.7463	−	45.7558i	0.878111	−	1.76638i
$672$		0			0
$673$	−2.01975	+	0.656257i	−0.0778557	+	0.0252969i	−0.347686	−	0.937611i	$-0.613032\pi$
$673$	−2.01975	+	0.656257i	−0.0778557	+	0.0252969i	0.269830	+	0.962908i	$0.413032\pi$
$674$	10.1006	+	7.33851i	0.389060	+	0.282669i
$675$	16.8113	−	12.2141i	0.647068	−	0.470122i
$676$	22.1773	−	68.2546i	0.852972	−	2.62518i
$677$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$677$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$			6.61942i			0.253657i
$682$		0			0
$683$	22.2408			0.851019			0.425510	−	0.904954i	$-0.360095\pi$
$683$	22.2408			0.851019			0.425510	+	0.904954i	$0.360095\pi$
$684$		0			0
$685$	−15.7857	−	11.4690i	−0.603140	−	0.438207i
$686$		0			0
$687$		0			0
$688$	182.849	+	59.4113i	6.97106	+	2.26504i
$689$		0			0
$690$		0			0
$691$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$691$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−14.4259	+	4.68728i	−0.547207	+	0.177798i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$701$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$702$	−15.8767	−	48.8635i	−0.599228	−	1.84423i
$703$		0			0
$704$	−105.502	+	17.7818i	−3.97626	+	0.670176i
$705$	9.99852			0.376566
$706$	82.9451	−	26.9505i	3.12168	−	1.01429i
$707$		0			0
$708$	−114.092	+	82.8925i	−4.28783	+	3.11529i
$709$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$709$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$710$	42.0561	+	13.6649i	1.57834	+	0.512833i
$711$	−9.56967	−	13.1715i	−0.358891	−	0.493970i
$712$	−24.5080	+	33.7324i	−0.918478	+	1.26418i
$713$		0			0
$714$		0			0
$715$	−11.8343	−	1.75451i	−0.442578	−	0.0656150i
$716$		0			0
$717$	17.8528	−	5.80073i	0.666725	−	0.216632i
$718$	83.9448	+	60.9895i	3.13279	+	2.27611i
$719$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$719$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$720$	−14.3158	+	44.0595i	−0.533519	+	1.64200i
$721$		0			0
$722$	30.6265	+	42.1537i	1.13980	+	1.56880i
$723$		0			0
$724$	11.2468	+	34.6140i	0.417983	+	1.28642i
$725$		0			0
$726$	−42.8698	−	29.8687i	−1.59105	−	1.10853i
$727$	29.7733			1.10423			0.552116	−	0.833767i	$-0.313821\pi$
$727$	29.7733			1.10423			0.552116	+	0.833767i	$0.313821\pi$
$728$		0			0
$729$	−21.8435	−	15.8702i	−0.809017	−	0.587785i
$730$		0			0
$731$		0			0
$732$	−140.106	−	45.5231i	−5.17845	−	1.68258i
$733$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$733$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$734$	−53.4576	+	73.5781i	−1.97316	+	2.71582i
$735$	3.74832	+	11.5361i	0.138259	+	0.425517i
$736$		0			0
$737$		0			0
$738$	83.4085			3.07031
$739$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$739$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−11.5117	−	3.74039i	−0.422324	−	0.137221i	0.0901418	−	0.995929i	$-0.471268\pi$
$743$	−11.5117	−	3.74039i	−0.422324	−	0.137221i	−0.512466	+	0.858707i	$0.671268\pi$
$744$		0			0
$745$	8.57824	−	11.8069i	0.314282	−	0.432573i
$746$	−17.8173	−	54.8360i	−0.652337	−	2.00769i
$747$			54.1563i			1.98148i
$748$		0			0
$749$		0			0
$750$	−40.6711	+	13.2149i	−1.48510	+	0.482538i
$751$	−43.9984	−	31.9667i	−1.60552	−	1.16648i	−0.875713	−	0.482832i	$-0.839608\pi$
$751$	−43.9984	−	31.9667i	−1.60552	−	1.16648i	−0.729810	−	0.683650i	$-0.760392\pi$
$752$	72.0533	−	52.3498i	2.62751	−	1.90900i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−6.62694	−	20.3956i	−0.240860	−	0.741292i	−0.996290	−	0.0860619i	$-0.972572\pi$
$757$	−6.62694	−	20.3956i	−0.240860	−	0.741292i	0.755429	−	0.655230i	$-0.227428\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−35.4348	+	11.5135i	−1.28451	+	0.417363i	−0.870167	−	0.492757i	$-0.835989\pi$
$761$	−35.4348	+	11.5135i	−1.28451	+	0.417363i	−0.414344	+	0.910120i	$0.635989\pi$
$762$	−83.9587	−	60.9996i	−3.04150	−	2.20978i
$763$		0			0
$764$		0			0
$765$		0			0
$766$	−8.44537	−	11.6241i	−0.305144	−	0.419994i
$767$	−31.2568	+	43.0213i	−1.12862	+	1.55341i
$768$	27.7395	+	85.3735i	1.00096	+	3.08065i
$769$		0			0			−	1.00000i	$-0.5\pi$
$769$		0			0				1.00000i	$0.5\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	23.4718	+	17.0533i	0.844223	+	0.613364i	0.923547	−	0.383485i	$-0.125276\pi$
$773$	23.4718	+	17.0533i	0.844223	+	0.613364i	−0.0793244	+	0.996849i	$0.525276\pi$
$774$	82.9037	−	60.2331i	2.97991	−	2.16503i
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$			34.4913i			1.23499i
$781$	47.8677	+	23.7961i	1.71284	+	0.851493i
$782$		0			0
$783$		0			0
$784$	87.4123	+	63.5087i	3.12187	+	2.26817i
$785$	19.7290	−	14.3340i	0.704159	−	0.511601i
$786$		0			0
$787$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$787$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$788$	−18.4248	−	25.3596i	−0.656357	−	0.903399i
$789$		0			0
$790$	4.60108	+	14.1607i	0.163699	+	0.503814i
$791$		0			0
$792$	−42.7623	+	86.0194i	−1.51949	+	3.05657i
$793$	−55.5492			−1.97261
$794$		0			0
$795$		0			0
$796$	27.7936	−	20.1932i	0.985117	−	0.715730i
$797$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$797$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$798$		0			0
$799$		0			0
$800$	−54.1113	+	74.4778i	−1.91312	+	2.63319i
$801$	4.00367	+	12.3220i	0.141463	+	0.435378i
$802$		−	106.222i		−	3.75082i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$809$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$810$	14.5138	+	19.9766i	0.509963	+	0.701905i
$811$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$811$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$	−53.2535	−	17.3031i	−1.85969	−	0.604251i
$821$	10.3385	+	14.2297i	0.360815	+	0.496620i	0.950376	−	0.311105i	$-0.100699\pi$
$821$	10.3385	+	14.2297i	0.360815	+	0.496620i	−0.589560	+	0.807724i	$0.700699\pi$
$822$	−54.4520	+	74.9468i	−1.89923	+	2.61407i
$823$	−9.01824	−	27.7553i	−0.314356	−	0.967489i	−0.976019	−	0.217687i	$-0.930149\pi$
$823$	−9.01824	−	27.7553i	−0.314356	−	0.967489i	0.661662	−	0.749802i	$-0.269851\pi$
$824$			54.0932i			1.88443i
$825$	−22.6536	+	3.81813i	−0.788696	+	0.132930i
$826$		0			0
$827$	39.7741	−	12.9234i	1.38308	−	0.449391i	0.479401	−	0.877596i	$-0.340854\pi$
$827$	39.7741	−	12.9234i	1.38308	−	0.449391i	0.903681	+	0.428205i	$0.140854\pi$
$828$		0			0
$829$	−31.9104	+	23.1843i	−1.10829	+	0.805223i	−0.982394	−	0.186820i	$-0.940182\pi$
$829$	−31.9104	+	23.1843i	−1.10829	+	0.805223i	−0.125900	+	0.992043i	$0.540182\pi$
$830$	15.3049	−	47.1037i	0.531241	−	1.63499i
$831$	−41.1490	−	13.3701i	−1.42744	−	0.463804i
$832$	68.3656	+	94.0972i	2.37015	+	3.26223i
$833$		0			0
$834$	22.2541	+	68.4911i	0.770597	+	2.37165i
$835$			22.9377i			0.793792i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−43.4891	−	31.5967i	−1.50141	−	1.09084i	−0.969816	−	0.243840i	$-0.921593\pi$
$839$	−43.4891	−	31.5967i	−1.50141	−	1.09084i	−0.531595	−	0.846999i	$-0.678407\pi$
$840$		0			0
$841$	−8.96149	+	27.5806i	−0.309017	+	0.951057i
$842$		0			0
$843$	−25.1238	−	34.5799i	−0.865308	−	1.19099i
$844$	−69.1146	+	95.1281i	−2.37902	+	3.27444i
$845$	4.01903	+	12.3693i	0.138259	+	0.425517i
$846$		−	47.4707i		−	1.63207i
$847$		0			0
$848$		0			0
$849$	−41.8181	+	13.5875i	−1.43519	+	0.466323i
$850$		0			0
$851$		0			0
$852$	47.6242	−	146.572i	1.63158	−	5.02148i
$853$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$853$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$	−8.33001	+	56.1865i	−0.284382	+	1.91818i
$859$	−25.5011			−0.870086			−0.435043	−	0.900410i	$-0.643267\pi$
$859$	−25.5011			−0.870086			−0.435043	+	0.900410i	$0.643267\pi$
$860$	−65.4266	+	21.2584i	−2.23103	+	0.724905i
$861$		0			0
$862$	50.6319	−	36.7862i	1.72453	−	1.25294i
$863$	−10.7342	+	33.0366i	−0.365398	+	1.12458i	0.584334	+	0.811513i	$0.301356\pi$
$863$	−10.7342	+	33.0366i	−0.365398	+	1.12458i	−0.949732	+	0.313065i	$0.898644\pi$
$864$	113.762	+	36.9634i	3.87025	+	1.25752i
$865$		0			0
$866$	7.05666	−	9.71265i	0.239795	−	0.330049i
$867$	−9.09896	−	28.0037i	−0.309017	−	0.951057i
$868$		0			0
$869$	2.99147	+	17.7489i	0.101479	+	0.602089i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$877$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$878$	11.3614	+	34.9668i	0.383429	+	1.18007i
$879$			56.2865i			1.89850i
$880$	35.8553	−	36.5720i	1.20868	−	1.23284i
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	54.7710	−	17.7962i	1.84423	−	0.599228i
$883$	−47.7256	−	34.6747i	−1.60609	−	1.16690i	−0.874322	−	0.485346i	$-0.838694\pi$
$883$	−47.7256	−	34.6747i	−1.60609	−	1.16690i	−0.731772	−	0.681550i	$-0.761306\pi$
$884$		0			0
$885$	7.89755	−	24.3062i	0.265473	−	0.817043i
$886$		0			0
$887$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$887$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$888$		0			0
$889$		0			0
$890$		−	11.8488i		−	0.397173i
$891$	13.8140	+	26.4608i	0.462785	+	0.886471i
$892$		0			0
$893$		0			0
$894$	−56.0566	−	40.7275i	−1.87481	−	1.36213i
$895$		0			0
$896$		0			0
$897$		0			0
$898$	3.97389	+	5.46959i	0.132610	+	0.182523i
$899$		0			0
$900$	20.4667	+	62.9900i	0.682224	+	2.09967i
$901$		0			0
$902$	−82.5713	−	41.0481i	−2.74932	−	1.36675i
$903$		0			0
$904$		0			0
$905$	−5.33601	−	3.87684i	−0.177375	−	0.128870i
$906$		0			0
$907$	18.6083	−	57.2704i	0.617878	−	1.90163i	0.287559	−	0.957763i	$-0.407156\pi$
$907$	18.6083	−	57.2704i	0.617878	−	1.90163i	0.330319	−	0.943869i	$-0.392844\pi$
$908$	−20.0654	−	6.51965i	−0.665894	−	0.216362i
$909$		0			0
$910$		0			0
$911$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$911$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$912$		0			0
$913$	26.6522	−	53.6128i	0.882057	−	1.77432i
$914$		0			0
$915$	25.3904	−	8.24983i	0.839379	−	0.272731i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	21.8236	+	7.09092i	0.719895	+	0.233908i	0.645977	−	0.763356i	$-0.276450\pi$
$919$	21.8236	+	7.09092i	0.719895	+	0.233908i	0.0739171	+	0.997264i	$0.476450\pi$
$920$		0			0
$921$		0			0
$922$	21.1704	+	65.1559i	0.697211	+	2.14580i
$923$		−	58.1131i		−	1.91282i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	13.5984	+	9.87979i	0.446629	+	0.324495i
$928$		0			0
$929$	14.1113	−	43.4300i	0.462976	−	1.42489i	−0.398535	−	0.917153i	$-0.630481\pi$
$929$	14.1113	−	43.4300i	0.462976	−	1.42489i	0.861511	−	0.507739i	$-0.169519\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$	104.431			3.41342
$937$	19.4737	−	6.32739i	0.636178	−	0.206707i	0.0268681	−	0.999639i	$-0.491447\pi$
$937$	19.4737	−	6.32739i	0.636178	−	0.206707i	0.609310	+	0.792932i	$0.291447\pi$
$938$		0			0
$939$	33.3312	−	24.2165i	1.08772	−	0.790276i
$940$	−9.84781	+	30.3084i	−0.321200	+	0.988552i
$941$	45.8674	+	14.9032i	1.49523	+	0.485831i	0.938624	−	0.344943i	$-0.112102\pi$
$941$	45.8674	+	14.9032i	1.49523	+	0.485831i	0.556610	+	0.830774i	$0.312102\pi$
$942$	−68.0544	−	93.6688i	−2.21733	−	3.05190i
$943$		0			0
$944$	−70.3482	−	216.509i	−2.28964	−	7.04678i
$945$		0			0
$946$	−111.714	+	18.8288i	−3.63215	+	0.612177i
$947$	59.0851			1.92001			0.960004	−	0.279986i	$-0.0903298\pi$
$947$	59.0851			1.92001			0.960004	+	0.279986i	$0.0903298\pi$
$948$	49.3521	−	16.0355i	1.60288	−	0.520808i
$949$		0			0
$950$		0			0
$951$	18.8766	−	58.0963i	0.612116	−	1.88390i
$952$		0			0
$953$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$953$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$954$		0			0
$955$		0			0
$956$			59.8304i			1.93505i
$957$		0			0
$958$	28.6077			0.924272
$959$		0			0
$960$	−45.2232	−	32.8566i	−1.45957	−	1.06044i
$961$	−25.0795	+	18.2213i	−0.809017	+	0.587785i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0			−	1.00000i	$-0.5\pi$
$967$		0			0				1.00000i	$0.5\pi$
$968$	84.6661	−	64.1113i	2.72127	−	2.06062i
$969$		0			0
$970$		0			0
$971$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$971$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$972$	69.6214	−	50.5829i	2.23311	−	1.62245i
$973$		0			0
$974$		0			0
$975$	14.6796	+	20.2047i	0.470122	+	0.647068i
$976$	139.779	−	192.389i	4.47421	−	6.15823i
$977$	15.9189	+	48.9932i	0.509290	+	1.56743i	0.793437	+	0.608652i	$0.208289\pi$
$977$	15.9189	+	48.9932i	0.509290	+	1.56743i	−0.284147	+	0.958781i	$0.591711\pi$
$978$		0			0
$979$	2.10060	−	14.1687i	0.0671355	−	0.452834i
$980$	−38.6613			−1.23499
$981$		0			0
$982$		0			0
$983$	−46.1821	+	33.5533i	−1.47298	+	1.07018i	−0.493244	+	0.869891i	$0.664189\pi$
$983$	−46.1821	+	33.5533i	−1.47298	+	1.07018i	−0.979736	+	0.200292i	$0.935811\pi$
$984$	−52.3892	+	161.238i	−1.67011	+	5.14006i
$985$	5.40262	+	1.75542i	0.172142	+	0.0559323i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−4.53701	−	26.9188i	−0.144196	−	0.855535i
$991$	43.1793			1.37164			0.685818	−	0.727773i	$-0.259445\pi$
$991$	43.1793			1.37164			0.685818	+	0.727773i	$0.259445\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.92390	+	5.92116i	−0.0609917	+	0.187713i
$996$	−164.164	−	53.3400i	−5.20173	−	1.69014i
$997$	−8.15982	−	11.2310i	−0.258424	−	0.355690i	0.660015	−	0.751252i	$-0.270550\pi$
$997$	−8.15982	−	11.2310i	−0.258424	−	0.355690i	−0.918439	+	0.395562i	$0.870550\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.y.a.116.1	✓	32
3.2	odd	2	inner	429.2.y.a.116.8	yes	32
11.2	odd	10	inner	429.2.y.a.233.1	yes	32
13.12	even	2	inner	429.2.y.a.116.8	yes	32
33.2	even	10	inner	429.2.y.a.233.8	yes	32
39.38	odd	2	CM	429.2.y.a.116.1	✓	32
143.90	odd	10	inner	429.2.y.a.233.8	yes	32
429.233	even	10	inner	429.2.y.a.233.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.y.a.116.1	✓	32	1.1	even	1	trivial
429.2.y.a.116.1	✓	32	39.38	odd	2	CM
429.2.y.a.116.8	yes	32	3.2	odd	2	inner
429.2.y.a.116.8	yes	32	13.12	even	2	inner
429.2.y.a.233.1	yes	32	11.2	odd	10	inner
429.2.y.a.233.1	yes	32	429.233	even	10	inner
429.2.y.a.233.8	yes	32	33.2	even	10	inner
429.2.y.a.233.8	yes	32	143.90	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)

\(f(q)\)	\(=\)	\(q+(-2.60814 + 0.847436i) q^{2} +(-1.40126 - 1.01807i) q^{3} +(4.46622 - 3.24490i) q^{4} +(-0.309156 + 0.951485i) q^{5} +(4.51743 + 1.46780i) q^{6} +(-5.67484 + 7.81075i) q^{8} +(0.927051 + 2.85317i) q^{9} +O(q^{10})\)	\(q+(-2.60814 + 0.847436i) q^{2} +(-1.40126 - 1.01807i) q^{3} +(4.46622 - 3.24490i) q^{4} +(-0.309156 + 0.951485i) q^{5} +(4.51743 + 1.46780i) q^{6} +(-5.67484 + 7.81075i) q^{8} +(0.927051 + 2.85317i) q^{9} -2.74360i q^{10} +(0.486394 - 3.28077i) q^{11} -9.56187 q^{12} +(-3.42908 + 1.11418i) q^{13} +(1.40189 - 1.01853i) q^{15} +(4.76979 - 14.6799i) q^{16} +(-4.83576 - 6.65585i) q^{18} +(1.70671 + 5.25272i) q^{20} +(1.51165 + 8.96889i) q^{22} +(15.9038 - 5.16747i) q^{24} +(3.23534 + 2.35061i) q^{25} +(7.99934 - 5.81186i) q^{26} +(1.60570 - 4.94183i) q^{27} +(-2.79319 + 3.84449i) q^{30} +23.0201i q^{32} +(-4.02163 + 4.10201i) q^{33} +(13.3987 + 9.73469i) q^{36} +(5.93935 + 1.92981i) q^{39} +(-5.67740 - 7.81427i) q^{40} +(-5.95913 + 8.20204i) q^{41} +12.4558i q^{43} +(-8.47340 - 16.2309i) q^{44} -3.00135 q^{45} +(4.66807 + 3.39155i) q^{47} +(-21.6289 + 15.7143i) q^{48} +(-2.16312 + 6.65740i) q^{49} +(-10.4302 - 3.38898i) q^{50} +(-11.6996 + 16.1032i) q^{52} +14.2497i q^{54} +(2.97123 + 1.47707i) q^{55} +(11.9319 - 8.66907i) q^{59} +(2.95611 - 9.09798i) q^{60} +(14.6525 + 4.76089i) q^{61} +(-9.96850 - 30.6799i) q^{64} -3.60718i q^{65} +(7.01277 - 14.1067i) q^{66} +(-4.98064 + 15.3288i) q^{71} +(-27.5463 - 8.95032i) q^{72} +(-2.14045 - 6.58763i) q^{75} -17.1260 q^{78} +(-5.16135 + 1.67702i) q^{79} +(12.4931 + 9.07676i) q^{80} +(-7.28115 + 5.29007i) q^{81} +(8.59154 - 26.4421i) q^{82} +(17.1686 + 5.57841i) q^{83} +(-10.5555 - 32.4864i) q^{86} +(22.8650 + 22.4169i) q^{88} +4.31872 q^{89} +(7.82795 - 2.54345i) q^{90} +(-15.0491 - 4.88975i) q^{94} +(23.4362 - 32.2571i) q^{96} -19.1965i q^{98} +(9.81149 - 1.65367i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) 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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Database

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