LMFDB - Embedded newform 429.2.y.a.194.3

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			194.3
Character	$\chi$	$=$	429.194
Dual form			429.2.y.a.272.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.618195 + 0.850873i) q^{2} +(-0.535233 + 1.64728i) q^{3} +(0.276215 + 0.850102i) q^{4} +(-0.319931 + 0.232444i) q^{5} +(-1.07075 - 1.47376i) q^{6} +(-2.89461 - 0.940514i) q^{8} +(-2.42705 - 1.76336i) q^{9} +O(q^{10})$	\(q+(-0.618195 + 0.850873i) q^{2} +(-0.535233 + 1.64728i) q^{3} +(0.276215 + 0.850102i) q^{4} +(-0.319931 + 0.232444i) q^{5} +(-1.07075 - 1.47376i) q^{6} +(-2.89461 - 0.940514i) q^{8} +(-2.42705 - 1.76336i) q^{9} -0.415916i q^{10} +(-2.36830 - 2.32189i) q^{11} -1.54819 q^{12} +(-2.11929 + 2.91695i) q^{13} +(-0.211662 - 0.651427i) q^{15} +(1.14341 - 0.830736i) q^{16} +(3.00078 - 0.975014i) q^{18} +(-0.285971 - 0.207770i) q^{20} +(3.43970 - 0.579742i) q^{22} +(3.09858 - 4.26483i) q^{24} +(-1.49676 + 4.60655i) q^{25} +(-1.17182 - 3.60649i) q^{26} +(4.20378 - 3.05422i) q^{27} +(0.685130 + 0.222612i) q^{30} -4.60068i q^{32} +(5.09239 - 2.65850i) q^{33} +(0.828644 - 2.55031i) q^{36} +(-3.67072 - 5.05231i) q^{39} +(1.14469 - 0.371933i) q^{40} +(-7.44109 - 2.41776i) q^{41} -0.0553950i q^{43} +(1.31968 - 2.65464i) q^{44} +1.18637 q^{45} +(-4.15757 + 12.7957i) q^{47} +(0.756462 + 2.32815i) q^{48} +(5.66312 - 4.11450i) q^{49} +(-2.99430 - 4.12130i) q^{50} +(-3.06509 - 0.995907i) q^{52} +5.46498i q^{54} +(1.29740 + 0.192348i) q^{55} +(3.75348 + 11.5520i) q^{59} +(0.495316 - 0.359868i) q^{60} +(-8.21635 - 11.3088i) q^{61} +(6.20142 + 4.50559i) q^{64} -1.42584i q^{65} +(-0.886046 + 5.97644i) q^{66} +(-3.98153 + 2.89275i) q^{71} +(5.36689 + 7.38690i) q^{72} +(-6.78716 - 4.93116i) q^{75} +6.56809 q^{78} +(-3.26771 + 4.49762i) q^{79} +(-0.172713 + 0.531557i) q^{80} +(2.78115 + 8.55951i) q^{81} +(6.65725 - 4.83678i) q^{82} +(9.64205 + 13.2711i) q^{83} +(0.0471341 + 0.0342449i) q^{86} +(4.67152 + 8.94837i) q^{88} -18.3671 q^{89} +(-0.733409 + 1.00945i) q^{90} +(-8.31732 - 11.4478i) q^{94} +(7.57860 + 2.46244i) q^{96} +7.36216i q^{98} +(1.65367 + 9.81149i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} - 24 q^{9}+O(q^{10}) $ 32 * q + 16 * q^4 - 24 * q^9	$ 32 q + 16 q^{4} - 24 q^{9} - 24 q^{12} - 92 q^{16} + 28 q^{22} - 40 q^{25} + 180 q^{30} + 48 q^{36} - 72 q^{48} + 56 q^{49} - 260 q^{52} + 32 q^{55} + 184 q^{64} - 60 q^{66} - 144 q^{75} - 72 q^{81} + 204 q^{82} - 40 q^{88} + 60 q^{90}+O(q^{100}) $ 32 * q + 16 * q^4 - 24 * q^9 - 24 * q^12 - 92 * q^16 + 28 * q^22 - 40 * q^25 + 180 * q^30 + 48 * q^36 - 72 * q^48 + 56 * q^49 - 260 * q^52 + 32 * q^55 + 184 * q^64 - 60 * q^66 - 144 * q^75 - 72 * q^81 + 204 * q^82 - 40 * q^88 + 60 * q^90

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.618195	+	0.850873i	−0.437130	+	0.601658i	−0.969571	−	0.244809i	$-0.921275\pi$
$2$	−0.618195	+	0.850873i	−0.437130	+	0.601658i	0.532441	+	0.846467i	$0.321275\pi$
$3$	−0.535233	+	1.64728i	−0.309017	+	0.951057i
$3$	−0.535233	+	1.64728i	−0.309017	+	0.951057i
$4$	0.276215	+	0.850102i	0.138107	+	0.425051i
$5$	−0.319931	+	0.232444i	−0.143078	+	0.103952i	−0.657022	−	0.753872i	$-0.728184\pi$
$5$	−0.319931	+	0.232444i	−0.143078	+	0.103952i	0.513944	+	0.857824i	$0.328184\pi$
$6$	−1.07075	−	1.47376i	−0.437130	−	0.601658i
$7$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$7$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$8$	−2.89461	−	0.940514i	−1.02340	−	0.332522i
$9$	−2.42705	−	1.76336i	−0.809017	−	0.587785i
$10$		−	0.415916i		−	0.131524i
$11$	−2.36830	−	2.32189i	−0.714069	−	0.700075i
$11$	−2.36830	−	2.32189i	−0.714069	−	0.700075i
$12$	−1.54819			−0.446925
$13$	−2.11929	+	2.91695i	−0.587785	+	0.809017i
$13$	−2.11929	+	2.91695i	−0.587785	+	0.809017i
$14$		0			0
$15$	−0.211662	−	0.651427i	−0.0546508	−	0.168198i
$16$	1.14341	−	0.830736i	0.285853	−	0.207684i
$17$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$17$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$18$	3.00078	−	0.975014i	0.707291	−	0.229813i
$19$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$19$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$20$	−0.285971	−	0.207770i	−0.0639450	−	0.0464587i
$21$		0			0
$22$	3.43970	−	0.579742i	0.733347	−	0.123601i
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$	3.09858	−	4.26483i	0.632494	−	0.870554i
$25$	−1.49676	+	4.60655i	−0.299352	+	0.921310i
$26$	−1.17182	−	3.60649i	−0.229813	−	0.707291i
$27$	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	$0.900000\pi$
$30$	0.685130	+	0.222612i	0.125087	+	0.0406433i
$31$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$31$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$32$		−	4.60068i		−	0.813293i
$33$	5.09239	−	2.65850i	0.886471	−	0.462785i
$34$		0			0
$35$		0			0
$36$	0.828644	−	2.55031i	0.138107	−	0.425051i
$37$		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
$40$	1.14469	−	0.371933i	0.180992	−	0.0588077i
$41$	−7.44109	−	2.41776i	−1.16210	−	0.377590i	−0.336413	−	0.941714i	$-0.609214\pi$
$41$	−7.44109	−	2.41776i	−1.16210	−	0.377590i	−0.825690	+	0.564124i	$0.809214\pi$
$42$		0			0
$43$		−	0.0553950i		−	0.00844765i	−0.999991	−	0.00422383i	$-0.998656\pi$
$43$		−	0.0553950i		−	0.00844765i	0.999991	−	0.00422383i	$-0.00134449\pi$
$44$	1.31968	−	2.65464i	0.198949	−	0.400201i
$45$	1.18637			0.176854
$46$		0			0
$47$	−4.15757	+	12.7957i	−0.606444	+	1.86644i	−0.119905	+	0.992785i	$0.538259\pi$
$47$	−4.15757	+	12.7957i	−0.606444	+	1.86644i	−0.486540	+	0.873659i	$0.661741\pi$
$48$	0.756462	+	2.32815i	0.109186	+	0.336040i
$49$	5.66312	−	4.11450i	0.809017	−	0.587785i
$50$	−2.99430	−	4.12130i	−0.423458	−	0.582840i
$51$		0			0
$52$	−3.06509	−	0.995907i	−0.425051	−	0.138107i
$53$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$53$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$54$			5.46498i			0.743690i
$55$	1.29740	+	0.192348i	0.174942	+	0.0259362i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.75348	+	11.5520i	0.488661	+	1.50394i	0.826607	+	0.562779i	$0.190268\pi$
$59$	3.75348	+	11.5520i	0.488661	+	1.50394i	−0.337946	+	0.941165i	$0.609732\pi$
$60$	0.495316	−	0.359868i	0.0639450	−	0.0464587i
$61$	−8.21635	−	11.3088i	−1.05200	−	1.44795i	−0.887066	−	0.461644i	$-0.847260\pi$
$61$	−8.21635	−	11.3088i	−1.05200	−	1.44795i	−0.164931	−	0.986305i	$-0.552740\pi$
$62$		0			0
$63$		0			0
$64$	6.20142	+	4.50559i	0.775177	+	0.563199i
$65$		−	1.42584i		−	0.176854i
$66$	−0.886046	+	5.97644i	−0.109065	+	0.735649i
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−3.98153	+	2.89275i	−0.472520	+	0.343306i	−0.798423	−	0.602097i	$-0.794332\pi$
$71$	−3.98153	+	2.89275i	−0.472520	+	0.343306i	0.325902	+	0.945403i	$0.394332\pi$
$72$	5.36689	+	7.38690i	0.632494	+	0.870554i
$73$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$73$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$74$		0			0
$75$	−6.78716	−	4.93116i	−0.783713	−	0.569401i
$76$		0			0
$77$		0			0
$78$	6.56809			0.743690
$79$	−3.26771	+	4.49762i	−0.367646	+	0.506022i	−0.952259	−	0.305291i	$-0.901246\pi$
$79$	−3.26771	+	4.49762i	−0.367646	+	0.506022i	0.584613	+	0.811312i	$0.301246\pi$
$80$	−0.172713	+	0.531557i	−0.0193099	+	0.0594299i
$81$	2.78115	+	8.55951i	0.309017	+	0.951057i
$82$	6.65725	−	4.83678i	0.735170	−	0.534133i
$83$	9.64205	+	13.2711i	1.05835	+	1.45670i	0.881336	+	0.472489i	$0.156644\pi$
$83$	9.64205	+	13.2711i	1.05835	+	1.45670i	0.177016	+	0.984208i	$0.443356\pi$
$84$		0			0
$85$		0			0
$86$	0.0471341	+	0.0342449i	0.00508260	+	0.00369272i
$87$		0			0
$88$	4.67152	+	8.94837i	0.497986	+	0.953899i
$89$	−18.3671			−1.94690			−0.973452	−	0.228892i	$-0.926490\pi$
$89$	−18.3671			−1.94690			−0.973452	+	0.228892i	$0.926490\pi$
$90$	−0.733409	+	1.00945i	−0.0773081	+	0.106405i
$91$		0			0
$92$		0			0
$93$		0			0
$94$	−8.31732	−	11.4478i	−0.857866	−	1.18075i
$95$		0			0
$96$	7.57860	+	2.46244i	0.773488	+	0.251322i
$97$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$97$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$98$			7.36216i			0.743690i
$99$	1.65367	+	9.81149i	0.166200	+	0.986092i
$100$	−4.32946			−0.432946
$101$		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	$0.589020\pi$
$104$	8.87794	−	6.45020i	0.870554	−	0.632494i
$105$		0			0
$106$		0			0
$107$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$107$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$108$	3.75754	+	2.73002i	0.361570	+	0.262696i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$	−0.965711	+	0.985015i	−0.0920769	+	0.0939175i
$111$		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
$118$	−12.1497	−	3.94767i	−1.11847	−	0.363413i
$119$		0			0
$120$			2.08470i			0.190306i
$121$	0.217684	+	10.9978i	0.0197895	+	0.999804i
$122$	14.7017			1.33103
$123$	7.96544	−	10.9635i	0.718219	−	0.988544i
$124$		0			0
$125$	−1.20292	−	3.70220i	−0.107592	−	0.331135i
$126$		0			0
$127$	−7.06287	−	9.72121i	−0.626729	−	0.862618i	0.371093	−	0.928596i	$-0.378983\pi$
$127$	−7.06287	−	9.72121i	−0.626729	−	0.862618i	−0.997821	+	0.0659781i	$0.978983\pi$
$128$	1.08365	−	0.352098i	0.0957816	−	0.0311213i
$129$	0.0912509	+	0.0296492i	0.00803419	+	0.00261047i
$130$	1.21321	+	0.881448i	0.106405	+	0.0773081i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	3.66659	+	3.59473i	0.319135	+	0.312881i
$133$		0			0
$134$		0			0
$135$	−0.634985	+	1.95428i	−0.0546508	+	0.168198i
$136$		0			0
$137$	−0.800666	+	0.581718i	−0.0684055	+	0.0496995i	−0.621463	−	0.783444i	$-0.713461\pi$
$137$	−0.800666	+	0.581718i	−0.0684055	+	0.0496995i	0.553057	+	0.833143i	$0.313461\pi$
$138$		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
$141$	−18.8528	−	13.6974i	−1.58769	−	1.15353i
$142$		−	5.17606i		−	0.434365i
$143$	11.7919	−	1.98747i	0.986092	−	0.166200i
$144$	−4.24000			−0.353333
$145$		0			0
$146$		0			0
$147$	3.74663	+	11.5309i	0.309017	+	0.951057i
$148$		0			0
$149$	4.59910	+	6.33012i	0.376773	+	0.518583i	0.954726	−	0.297487i	$-0.0961483\pi$
$149$	4.59910	+	6.33012i	0.376773	+	0.518583i	−0.577953	+	0.816070i	$0.696148\pi$
$150$	8.39158	−	2.72659i	0.685169	−	0.222625i
$151$		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
$156$	3.28107	−	4.51601i	0.262696	−	0.361570i
$157$	−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	$0.874569\pi$
$158$	−1.80682	−	5.56082i	−0.143743	−	0.442395i
$159$		0			0
$160$	1.06940	+	1.47190i	0.0845435	+	0.116364i
$161$		0			0
$162$	−9.00235	−	2.92504i	−0.707291	−	0.229813i
$163$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$163$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$164$		−	6.99351i		−	0.546101i
$165$	−1.01126	+	2.03423i	−0.0787267	+	0.158365i
$166$	−17.2527			−1.33907
$167$	−10.6498	+	14.6582i	−0.824107	+	1.13429i	0.164884	+	0.986313i	$0.447275\pi$
$167$	−10.6498	+	14.6582i	−0.824107	+	1.13429i	−0.988991	+	0.147973i	$0.952725\pi$
$168$		0			0
$169$	−4.01722	−	12.3637i	−0.309017	−	0.951057i
$170$		0			0
$171$		0			0
$172$	0.0470914	−	0.0153009i	0.00359068	−	0.00116668i
$173$		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
$176$	−4.63681	−	0.687437i	−0.349513	−	0.0518175i
$177$	−21.0384			−1.58134
$178$	11.3544	−	15.6280i	0.851050	−	1.17137i
$179$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$179$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$180$	0.327693	+	1.00854i	0.0244248	+	0.0751718i
$181$	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
$188$	−12.0260			−0.877088
$189$		0			0
$190$		0			0
$191$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$191$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$192$	−10.7412	+	7.80392i	−0.775177	+	0.563199i
$193$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$193$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$194$		0			0
$195$	2.34876	+	0.763157i	0.168198	+	0.0546508i
$196$	5.06198	+	3.67774i	0.361570	+	0.262696i
$197$		−	25.5782i		−	1.82237i	−0.411992	−	0.911187i	$-0.635167\pi$
$197$		−	25.5782i		−	1.82237i	0.411992	−	0.911187i	$-0.364833\pi$
$198$	−9.37062	−	4.65835i	−0.665941	−	0.331055i
$199$	−11.1405			−0.789726			−0.394863	−	0.918740i	$-0.629208\pi$
$199$	−11.1405			−0.789726			−0.394863	+	0.918740i	$0.629208\pi$
$200$	8.66505	−	11.9264i	0.612712	−	0.843325i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	2.94263	−	0.956119i	0.205522	−	0.0667782i
$206$	−16.8274	−	5.46754i	−1.17242	−	0.380942i
$207$		0			0
$208$			5.09584i			0.353333i
$209$		0			0
$210$		0			0
$211$	7.17566	−	9.87645i	0.493993	−	0.679923i	−0.487125	−	0.873332i	$-0.661954\pi$
$211$	7.17566	−	9.87645i	0.493993	−	0.679923i	0.981118	+	0.193409i	$0.0619544\pi$
$212$		0			0
$213$	−2.63412	−	8.10698i	−0.180487	−	0.555481i
$214$		0			0
$215$	0.0128762	+	0.0177226i	0.000878150	+	0.00120867i
$216$	−15.0408	+	4.88706i	−1.02340	+	0.332522i
$217$		0			0
$218$		0			0
$219$		0			0
$220$	0.194846	+	1.15605i	0.0131365	+	0.0779410i
$221$		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
$225$	11.7557	−	8.54101i	0.783713	−	0.569401i
$226$		0			0
$227$	20.8614	−	6.77826i	1.38462	−	0.449889i	0.480432	−	0.877032i	$-0.340480\pi$
$227$	20.8614	−	6.77826i	1.38462	−	0.449889i	0.904184	+	0.427143i	$0.140480\pi$
$228$		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	$0.700000\pi$
$234$	−3.51546	+	10.8195i	−0.229813	+	0.707291i
$235$	−1.64414	−	5.06015i	−0.107252	−	0.330087i
$236$	−8.78362	+	6.38168i	−0.571765	+	0.415412i
$237$	−5.65985	−	7.79011i	−0.367646	−	0.506022i
$238$		0			0
$239$	18.3133	+	5.95034i	1.18459	+	0.384896i	0.834069	−	0.551660i	$-0.186005\pi$
$239$	18.3133	+	5.95034i	1.18459	+	0.384896i	0.350518	+	0.936556i	$0.386005\pi$
$240$	−0.783180	−	0.569014i	−0.0505541	−	0.0367297i
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$	−9.49234	−	6.61360i	−0.610191	−	0.425138i
$243$	−15.5885			−1.00000
$244$	7.34419	−	10.1084i	0.470163	−	0.647124i
$245$	−0.855420	+	2.63271i	−0.0546508	+	0.168198i
$246$	4.40433	+	13.5551i	0.280810	+	0.864245i
$247$		0			0
$248$		0			0
$249$	−27.0220	+	8.77998i	−1.71245	+	0.556409i
$250$	3.89374	+	1.26515i	0.246262	+	0.0800153i
$251$		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
$254$	12.6377			0.792963
$255$		0			0
$256$	−5.10777	+	15.7201i	−0.319236	+	0.982507i
$257$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$257$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$258$	−0.0816386	+	0.0593139i	−0.00508260	+	0.00369272i
$259$		0			0
$260$	1.21211	−	0.393838i	0.0751718	−	0.0244248i
$261$		0			0
$262$		0			0
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$	−17.2408	+	2.90584i	−1.06110	+	0.178842i
$265$		0			0
$266$		0			0
$267$	9.83066	−	30.2556i	0.601626	−	1.85162i
$268$		0			0
$269$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$269$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$270$	−1.27030	−	1.74842i	−0.0773081	−	0.106405i
$271$		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
$274$		−	1.04088i		−	0.0628819i
$275$	14.2407	−	7.43439i	0.858744	−	0.448310i
$276$		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	$0.929836\pi$
$278$	0.536610	−	1.65152i	0.0321838	−	0.0990514i
$279$		0			0
$280$		0			0
$281$	−19.3175	−	26.5883i	−1.15239	−	1.58612i	−0.736075	−	0.676900i	$-0.763323\pi$
$281$	−19.3175	−	26.5883i	−1.15239	−	1.58612i	−0.416310	−	0.909223i	$-0.636677\pi$
$282$	23.3094	−	7.57369i	1.38806	−	0.451007i
$283$	31.8759	+	10.3571i	1.89483	+	0.615667i	0.974433	+	0.224679i	$0.0721333\pi$
$283$	31.8759	+	10.3571i	1.89483	+	0.615667i	0.920396	+	0.390988i	$0.127867\pi$
$284$	−3.55889	−	2.58568i	−0.211181	−	0.153432i
$285$		0			0
$286$	−5.59865	+	11.2621i	−0.331055	+	0.665941i
$287$		0			0
$288$	−8.11264	+	11.1661i	−0.478042	+	0.657968i
$289$	−5.25329	+	16.1680i	−0.309017	+	0.951057i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	32.5584	−	10.5789i	1.90208	−	0.618024i	0.949249	−	0.314526i	$-0.101846\pi$
$293$	32.5584	−	10.5789i	1.90208	−	0.618024i	0.952832	−	0.303498i	$-0.0981545\pi$
$294$	−12.1275	−	3.94047i	−0.707291	−	0.229813i
$295$	−3.88605	−	2.82338i	−0.226254	−	0.164384i
$296$		0			0
$297$	−17.0474	−	2.52738i	−0.989188	−	0.146653i
$298$	−8.22927			−0.476709
$299$		0			0
$300$	2.31727	−	7.13183i	0.133788	−	0.411756i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	5.25734	+	1.70821i	0.301034	+	0.0978120i
$306$		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	$0.600000\pi$
$312$	5.87351	+	18.0768i	0.332522	+	1.02340i
$313$	14.2086	−	10.3232i	0.803119	−	0.583500i	−0.108708	−	0.994074i	$-0.534671\pi$
$313$	14.2086	−	10.3232i	0.803119	−	0.583500i	0.911828	+	0.410574i	$0.134671\pi$
$314$	−10.0771	−	13.8700i	−0.568686	−	0.782729i
$315$		0			0
$316$	−4.72603	−	1.53558i	−0.265860	−	0.0863831i
$317$	28.3649	+	20.6083i	1.59313	+	1.15748i	0.899289	+	0.437354i	$0.144084\pi$
$317$	28.3649	+	20.6083i	1.59313	+	1.15748i	0.693844	+	0.720125i	$0.255916\pi$
$318$		0			0
$319$		0			0
$320$	−3.03132			−0.169456
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−6.50826	+	4.72853i	−0.361570	+	0.262696i
$325$	−10.2650	−	14.1286i	−0.569401	−	0.783713i
$326$		0			0
$327$		0			0
$328$	19.2651	+	13.9969i	1.06374	+	0.772850i
$329$		0			0
$330$	−1.10571	−	2.11801i	−0.0608675	−	0.116592i
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$	−8.61855	+	11.8624i	−0.473004	+	0.651034i
$333$		0			0
$334$	−5.88861	−	18.1233i	−0.322210	−	0.991661i
$335$		0			0
$336$		0			0
$337$	−23.8689	+	7.75547i	−1.30022	+	0.422467i	−0.875658	−	0.482931i	$-0.839572\pi$
$337$	−23.8689	+	7.75547i	−1.30022	+	0.422467i	−0.424563	+	0.905399i	$0.639572\pi$
$338$	13.0034	+	4.22506i	0.707291	+	0.229813i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$	−0.0520997	+	0.160347i	−0.00280903	+	0.00864531i
$345$		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
$352$	−10.6823	+	10.8958i	−0.569367	+	0.580748i
$353$	36.4309			1.93902			0.969510	−	0.245050i	$-0.0788044\pi$
$353$	36.4309			1.93902			0.969510	+	0.245050i	$0.0788044\pi$
$354$	13.0058	−	17.9010i	0.691252	−	0.951426i
$355$	0.601414	−	1.85096i	0.0319197	−	0.0982388i
$356$	−5.07325	−	15.6139i	−0.268882	−	0.827533i
$357$		0			0
$358$		0			0
$359$	−1.99383	+	0.647836i	−0.105231	+	0.0341915i	−0.361159	−	0.932504i	$-0.617619\pi$
$359$	−1.99383	+	0.647836i	−0.105231	+	0.0341915i	0.255928	+	0.966696i	$0.417619\pi$
$360$	−3.43407	−	1.11580i	−0.180992	−	0.0588077i
$361$	15.3713	+	11.1679i	0.809017	+	0.587785i
$362$			28.2366i			1.48408i
$363$	−18.2330	−	5.52783i	−0.956986	−	0.290136i
$364$		0			0
$365$		0			0
$366$	−7.86884	+	24.2178i	−0.411311	+	1.26588i
$367$	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
$369$	13.7965	+	18.9893i	0.718219	+	0.988544i
$370$		0			0
$371$		0			0
$372$		0			0
$373$			24.3200i			1.25924i	0.776903	+	0.629621i	$0.216790\pi$
$373$			24.3200i			1.25924i	−0.776903	+	0.629621i	$0.783210\pi$
$374$		0			0
$375$	6.74240			0.348176
$376$	24.0691	−	33.1282i	1.24127	−	1.70846i
$377$		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
$383$	27.8789	+	20.2552i	1.42454	+	1.03499i	0.991000	+	0.133858i	$0.0427368\pi$
$383$	27.8789	+	20.2552i	1.42454	+	1.03499i	0.433543	+	0.901133i	$0.357263\pi$
$384$			1.97352i			0.100711i
$385$		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	$0.400000\pi$
$390$	−2.10134	+	1.52671i	−0.106405	+	0.0773081i
$391$		0			0
$392$	−20.2622	+	6.58360i	−1.02340	+	0.332522i
$393$		0			0
$394$	21.7638	+	15.8124i	1.09645	+	0.796615i
$395$		−	2.19849i		−	0.110618i
$396$	−7.88400	+	4.11587i	−0.396186	+	0.206830i
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$	6.88698	−	9.47912i	0.345213	−	0.475145i
$399$		0			0
$400$	2.11542	+	6.51059i	0.105771	+	0.325529i
$401$	−27.2567	+	19.8031i	−1.36113	+	0.988921i	−0.362761	+	0.931882i	$0.618166\pi$
$401$	−27.2567	+	19.8031i	−1.36113	+	0.988921i	−0.998372	+	0.0570386i	$0.981834\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−2.87938	−	2.09199i	−0.143078	−	0.103952i
$406$		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	$0.700000\pi$
$410$	−1.00559	+	3.09487i	−0.0496623	+	0.152845i
$411$	−0.529708	−	1.63027i	−0.0261286	−	0.0804155i
$412$	−12.1654	+	8.83865i	−0.599344	+	0.435449i
$413$		0			0
$414$		0			0
$415$	−6.16959	−	2.00462i	−0.302853	−	0.0984029i
$416$	13.4200	+	9.75018i	0.657968	+	0.478042i
$417$		−	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	$0.600000\pi$
$422$	3.96765	+	12.2112i	0.193142	+	0.594430i
$423$	32.6540	−	23.7245i	1.58769	−	1.15353i
$424$		0			0
$425$		0			0
$426$	8.52640	+	2.77040i	0.413106	+	0.134226i
$427$		0			0
$428$		0			0
$429$	−3.03753	+	20.4884i	−0.146653	+	0.989188i
$430$	−0.0230397			−0.00111107
$431$	−8.61004	+	11.8507i	−0.414731	+	0.570828i	−0.964364	−	0.264578i	$-0.914767\pi$
$431$	−8.61004	+	11.8507i	−0.414731	+	0.570828i	0.549633	+	0.835406i	$0.314767\pi$
$432$	2.26939	−	6.98446i	0.109186	−	0.336040i
$433$	−12.5812	−	38.7210i	−0.604614	−	1.86081i	−0.499422	−	0.866359i	$-0.666454\pi$
$433$	−12.5812	−	38.7210i	−0.604614	−	1.86081i	−0.105192	−	0.994452i	$-0.533546\pi$
$434$		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	$-0.496339\pi$
$440$	−3.57456	−	1.77700i	−0.170410	−	0.0847149i
$441$	−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
$445$	5.87620	−	4.26931i	0.278558	−	0.202385i
$446$		0			0
$447$	−12.8891	+	4.18791i	−0.609631	+	0.198081i
$448$		0			0
$449$	−26.5183	−	19.2667i	−1.25147	−	0.909250i	−0.253168	−	0.967422i	$-0.581473\pi$
$449$	−26.5183	−	19.2667i	−1.25147	−	0.909250i	−0.998307	+	0.0581727i	$0.981473\pi$
$450$			15.2826i			0.720430i
$451$	12.0090	+	23.0033i	0.565481	+	1.08319i
$452$		0			0
$453$		0			0
$454$	−7.12895	+	21.9407i	−0.334578	+	1.02973i
$455$		0			0
$456$		0			0
$457$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$457$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			34.9272i			1.62672i	0.581758	+	0.813362i	$0.302365\pi$
$461$			34.9272i			1.62672i	−0.581758	+	0.813362i	$0.697635\pi$
$462$		0			0
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$467$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$468$	5.68298	+	7.82195i	0.262696	+	0.361570i
$469$		0			0
$470$	5.32194	+	1.72920i	0.245483	+	0.0797622i
$471$	−22.8418	−	16.5955i	−1.05249	−	0.764681i
$472$		−	36.9687i		−	1.70162i
$473$	−0.128621	+	0.131192i	−0.00591399	+	0.00603221i
$474$	10.1273			0.465161
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−16.3842	+	11.9038i	−0.749394	+	0.544467i
$479$	13.5530	+	18.6541i	0.619254	+	0.852330i	0.997298	−	0.0734577i	$-0.0234034\pi$
$479$	13.5530	+	18.6541i	0.619254	+	0.852330i	−0.378045	+	0.925787i	$0.623403\pi$
$480$	−2.99701	+	0.973788i	−0.136794	+	0.0444471i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−9.28916	+	3.22282i	−0.422235	+	0.146492i
$485$		0			0
$486$	9.63671	−	13.2638i	0.437130	−	0.601658i
$487$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$487$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$488$	13.1470	+	40.4622i	0.595136	+	1.83164i
$489$		0			0
$490$	−1.71129	−	2.35538i	−0.0773081	−	0.106405i
$491$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$491$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$492$	11.5202	+	3.74316i	0.519373	+	0.168754i
$493$		0			0
$494$		0			0
$495$	−2.80968	−	2.75462i	−0.126286	−	0.123811i
$496$		0			0
$497$		0			0
$498$	9.23423	−	28.4200i	0.413796	−	1.27353i
$499$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$499$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$500$	2.81498	−	2.04521i	0.125890	−	0.0914644i
$501$	−18.4460	−	25.3888i	−0.824107	−	1.13429i
$502$		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
$508$	6.31315	−	8.68930i	0.280101	−	0.385525i
$509$	11.6811	−	35.9507i	0.517755	−	1.59349i	−0.260457	−	0.965485i	$-0.583873\pi$
$509$	11.6811	−	35.9507i	0.517755	−	1.59349i	0.778212	−	0.628001i	$-0.216127\pi$
$510$		0			0
$511$		0			0
$512$	−8.87876	−	12.2206i	−0.392389	−	0.540078i
$513$		0			0
$514$		0			0
$515$	−5.38219	−	3.91039i	−0.237168	−	0.172312i
$516$			0.0857621i			0.00377547i
$517$	39.5565	−	20.6506i	1.73969	−	0.908213i
$518$		0			0
$519$		0			0
$520$	−1.34102	+	4.12724i	−0.0588077	+	0.180992i
$521$		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
$528$	3.61418	−	7.27018i	0.157287	−	0.316394i
$529$	23.0000			1.00000
$530$		0			0
$531$	11.2604	−	34.6561i	0.488661	−	1.50394i
$532$		0			0
$533$	22.8223	−	16.5814i	0.988544	−	0.718219i
$534$	19.6664	+	27.0685i	0.851050	+	1.17137i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−22.9654	−	3.40476i	−0.989188	−	0.146653i
$540$	−1.83673			−0.0790403
$541$		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	$-0.895725\pi$
$548$	−0.715676	−	0.519969i	−0.0305721	−	0.0222120i
$549$			41.9355i			1.78976i
$550$	−2.47779	+	16.7129i	−0.105653	+	0.712640i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−8.11861	−	24.9865i	−0.344927	−	1.06158i
$555$		0			0
$556$	−0.867467	−	1.19397i	−0.0367888	−	0.0506354i
$557$	−38.1864	+	12.4075i	−1.61801	+	0.525723i	−0.971471	−	0.237159i	$-0.923784\pi$
$557$	−38.1864	+	12.4075i	−1.61801	+	0.525723i	−0.646538	+	0.762882i	$0.723784\pi$
$558$		0			0
$559$	0.161584	+	0.117398i	0.00683429	+	0.00496541i
$560$		0			0
$561$		0			0
$562$	34.5652			1.45805
$563$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$563$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$564$	6.43673	−	19.8102i	0.271035	−	0.834160i
$565$		0			0
$566$	−28.5182	+	20.7197i	−1.19871	+	0.870912i
$567$		0			0
$568$	14.2456	−	4.62868i	0.597733	−	0.194215i
$569$		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	$-0.793752\pi$
$571$		−	28.8444i		−	1.20710i	0.797325	−	0.603550i	$-0.206248\pi$
$572$	4.94666	+	9.47539i	0.206830	+	0.396186i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−7.10619	−	21.8706i	−0.296091	−	0.911275i
$577$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$577$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$578$	−10.5093	−	14.4648i	−0.437130	−	0.601658i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−2.51426	+	3.46059i	−0.103952	+	0.143078i
$586$	−11.1262	+	34.2428i	−0.459618	+	1.41456i
$587$	−12.8723	−	39.6168i	−0.531296	−	1.63516i	−0.751520	−	0.659710i	$-0.770679\pi$
$587$	−12.8723	−	39.6168i	−0.531296	−	1.63516i	0.220225	−	0.975449i	$-0.429321\pi$
$588$	−8.76760	+	6.37004i	−0.361570	+	0.262696i
$589$		0			0
$590$	4.80467	−	1.56113i	0.197805	−	0.0642708i
$591$	42.1345	+	13.6903i	1.73318	+	0.563145i
$592$		0			0
$593$		−	46.4063i		−	1.90568i	−0.303476	−	0.952839i	$-0.598147\pi$
$593$		−	46.4063i		−	1.90568i	0.303476	−	0.952839i	$-0.401853\pi$
$594$	12.6891	−	12.9427i	0.520639	−	0.531046i
$595$		0			0
$596$	−4.11090	+	5.65818i	−0.168389	+	0.231768i
$597$	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	$0.800000\pi$
$600$	15.0083	+	20.6572i	0.612712	+	0.843325i
$601$	−45.9856	+	14.9416i	−1.87579	+	0.609482i	−0.886667	+	0.462408i	$0.846985\pi$
$601$	−45.9856	+	14.9416i	−1.87579	+	0.609482i	−0.989126	+	0.147074i	$0.953015\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−2.62602	−	3.46796i	−0.106763	−	0.140992i
$606$		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
$610$	−4.70353	+	3.41732i	−0.190440	+	0.138363i
$611$	−28.5133	−	39.2452i	−1.15353	−	1.58769i
$612$		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
$615$			5.35908i			0.216099i
$616$		0			0
$617$	−47.5964			−1.91616			−0.958079	−	0.286505i	$-0.907506\pi$
$617$	−47.5964			−1.91616			−0.958079	+	0.286505i	$0.907506\pi$
$618$	18.0131	−	24.7929i	0.724594	−	0.997318i
$619$		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
$624$	−8.39427	−	2.72746i	−0.336040	−	0.109186i
$625$	−18.3474	−	13.3302i	−0.733897	−	0.533207i
$626$			18.4715i			0.738268i
$627$		0			0
$628$	−14.5706			−0.581429
$629$		0			0
$630$		0			0
$631$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$631$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$632$	13.6888	−	9.94551i	0.544512	−	0.395611i
$633$	12.4286	+	17.1065i	0.493993	+	0.679923i
$634$	−35.0701	+	11.3950i	−1.39281	+	0.452552i
$635$	4.51927	+	1.46840i	0.179342	+	0.0582716i
$636$		0			0
$637$			25.2389i			1.00000i
$638$		0			0
$639$	14.7643			0.584067
$640$	−0.264849	+	0.364534i	−0.0104691	+	0.0144095i
$641$		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
$645$	−0.0360858	+	0.0117250i	−0.00142088	+	0.000461671i
$646$		0			0
$647$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$647$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$648$		−	27.3921i		−	1.07606i
$649$	17.9331	−	36.0738i	0.703936	−	1.41602i
$650$	18.3674			0.720430
$651$		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
$656$	−10.5167	+	3.41709i	−0.410610	+	0.133415i
$657$		0			0
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$	−2.00863	−	0.297792i	−0.0781857	−	0.0115915i
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$		0			0
$663$		0			0
$664$	−15.4282	−	47.4832i	−0.598731	−	1.84271i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−15.4026	−	5.00461i	−0.595945	−	0.193634i
$669$		0			0
$670$		0			0
$671$	−6.79906	+	45.8602i	−0.262475	+	1.77041i
$672$		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	$0.986968\pi$
$674$	8.15671	−	25.1038i	0.314185	−	0.966961i
$675$	7.77739	+	23.9363i	0.299352	+	0.921310i
$676$	9.40082	−	6.83009i	0.361570	−	0.262696i
$677$		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
$681$			37.9924i			1.45587i
$682$		0			0
$683$	−25.1942			−0.964030			−0.482015	−	0.876163i	$-0.660095\pi$
$683$	−25.1942			−0.964030			−0.482015	+	0.876163i	$0.660095\pi$
$684$		0			0
$685$	0.120942	−	0.372220i	0.00462094	−	0.0142218i
$686$		0			0
$687$		0			0
$688$	−0.0460186	−	0.0633392i	−0.00175444	−	0.00241478i
$689$		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
$695$	0.383785	−	0.528234i	0.0145578	−	0.0200371i
$696$		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	$0.100000\pi$
$702$	−15.9411	−	11.5819i	−0.601658	−	0.437130i
$703$		0			0
$704$	−4.22533	−	25.0696i	−0.159248	−	0.944845i
$705$	9.21547			0.347075
$706$	−22.5214	+	30.9981i	−0.847604	+	1.16663i
$707$		0			0
$708$	−5.81111	−	17.8848i	−0.218395	−	0.672150i
$709$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$709$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$710$	1.20314	+	1.65598i	0.0451531	+	0.0621479i
$711$	15.8618	−	5.15382i	0.594864	−	0.193283i
$712$	53.1654	+	17.2745i	1.99246	+	0.647388i
$713$		0			0
$714$		0			0
$715$	−3.31064	+	3.37682i	−0.123811	+	0.126286i
$716$		0			0
$717$	−19.6037	+	26.9822i	−0.732115	+	1.00767i
$718$	0.681353	−	2.09699i	0.0254279	−	0.0782589i
$719$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$719$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$720$	1.35651	−	0.985561i	0.0505541	−	0.0367297i
$721$		0			0
$722$	−19.0050	+	6.17509i	−0.707291	+	0.229813i
$723$		0			0
$724$	19.4145	+	14.1055i	0.721535	+	0.524226i
$725$		0			0
$726$	15.9750	−	12.0967i	0.592890	−	0.448951i
$727$	50.5149			1.87349			0.936747	−	0.350007i	$-0.113821\pi$
$727$	50.5149			1.87349			0.936747	+	0.350007i	$0.113821\pi$
$728$		0			0
$729$	8.34346	−	25.6785i	0.309017	−	0.951057i
$730$		0			0
$731$		0			0
$732$	12.7205	+	17.5083i	0.470163	+	0.647124i
$733$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$733$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$734$	−15.5562	−	5.05453i	−0.574191	−	0.186566i
$735$	−3.87896	−	2.81823i	−0.143078	−	0.103952i
$736$		0			0
$737$		0			0
$738$	−24.6864			−0.908721
$739$		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
$743$	21.0950	+	29.0348i	0.773900	+	1.06518i	0.995929	+	0.0901418i	$0.0287320\pi$
$743$	21.0950	+	29.0348i	0.773900	+	1.06518i	−0.222029	+	0.975040i	$0.571268\pi$
$744$		0			0
$745$	−2.94279	−	0.956171i	−0.107816	−	0.0350314i
$746$	−20.6932	−	15.0345i	−0.757633	−	0.550452i
$747$		−	49.2121i		−	1.80058i
$748$		0			0
$749$		0			0
$750$	−4.16812	+	5.73692i	−0.152198	+	0.209483i
$751$	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	$-0.0396083\pi$
$752$	5.87603	+	18.0846i	0.214277	+	0.659476i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−10.0620	−	7.31047i	−0.365709	−	0.265703i	0.389720	−	0.920933i	$-0.372572\pi$
$757$	−10.0620	−	7.31047i	−0.365709	−	0.265703i	−0.755429	+	0.655230i	$0.772572\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−32.2225	+	44.3505i	−1.16806	+	1.60770i	−0.492757	+	0.870167i	$0.664011\pi$
$761$	−32.2225	+	44.3505i	−1.16806	+	1.60770i	−0.675307	+	0.737536i	$0.735989\pi$
$762$	−6.76414	+	20.8179i	−0.245039	+	0.754152i
$763$		0			0
$764$		0			0
$765$		0			0
$766$	−34.4692	+	11.1997i	−1.24542	+	0.404662i
$767$	−41.6514	−	13.5334i	−1.50394	−	0.488661i
$768$	−23.1616	−	16.8279i	−0.835770	−	0.607223i
$769$		0			0			−	1.00000i	$-0.5\pi$
$769$		0			0				1.00000i	$0.5\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−6.58947	+	20.2803i	−0.237007	+	0.729432i	0.759842	+	0.650108i	$0.225276\pi$
$773$	−6.58947	+	20.2803i	−0.237007	+	0.729432i	−0.996849	+	0.0793244i	$0.974724\pi$
$774$	−0.0540108	−	0.166228i	−0.00194138	−	0.00597495i
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$			2.20748i			0.0790403i
$781$	16.1461	+	2.39376i	0.577752	+	0.0856554i
$782$		0			0
$783$		0			0
$784$	3.05721	−	9.40911i	0.109186	−	0.336040i
$785$	−1.99202	−	6.13080i	−0.0710982	−	0.218818i
$786$		0			0
$787$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$787$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$788$	21.7441	−	7.06509i	0.774602	−	0.251683i
$789$		0			0
$790$	1.87063	+	1.35910i	0.0665542	+	0.0483545i
$791$		0			0
$792$	4.44112	−	29.9557i	0.157808	−	1.06443i
$793$	50.4002			1.78976
$794$		0			0
$795$		0			0
$796$	−3.07716	−	9.47052i	−0.109067	−	0.335674i
$797$		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
$800$	21.1933	+	6.88611i	0.749295	+	0.243461i
$801$	44.5778	+	32.3877i	1.57508	+	1.14436i
$802$		−	35.4342i		−	1.25122i
$803$		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	$0.300000\pi$
$810$	3.56004	−	1.15673i	0.125087	−	0.0406433i
$811$		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
$820$	1.62560	+	2.23744i	0.0567683	+	0.0781348i
$821$	32.1319	−	10.4403i	1.12141	−	0.364368i	0.311105	−	0.950376i	$-0.399301\pi$
$821$	32.1319	−	10.4403i	1.12141	−	0.364368i	0.810306	+	0.586007i	$0.199301\pi$
$822$	1.71462	+	0.557114i	0.0598042	+	0.0194316i
$823$	−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	$-0.669851\pi$
$824$		−	51.2018i		−	1.78370i
$825$	4.62443	+	27.4375i	0.161002	+	0.955250i
$826$		0			0
$827$	4.32706	−	5.95569i	0.150467	−	0.207100i	−0.727129	−	0.686500i	$-0.759146\pi$
$827$	4.32706	−	5.95569i	0.150467	−	0.207100i	0.877596	+	0.479401i	$0.159146\pi$
$828$		0			0
$829$	2.24035	+	6.89509i	0.0778105	+	0.239476i	0.982394	−	0.186820i	$-0.0598181\pi$
$829$	2.24035	+	6.89509i	0.0778105	+	0.239476i	−0.904584	+	0.426296i	$0.859818\pi$
$830$	5.51969	−	4.01029i	0.191591	−	0.139199i
$831$	−25.4315	−	35.0034i	−0.882208	−	1.21426i
$832$	−26.2852	+	8.54058i	−0.911275	+	0.296091i
$833$		0			0
$834$	2.43330	+	1.76789i	0.0842582	+	0.0612171i
$835$		−	7.16510i		−	0.247959i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−4.36513	+	13.4345i	−0.150701	+	0.463810i	−0.997700	−	0.0677843i	$-0.978407\pi$
$839$	−4.36513	+	13.4345i	−0.150701	+	0.463810i	0.846999	+	0.531595i	$0.178407\pi$
$840$		0			0
$841$	23.4615	−	17.0458i	0.809017	−	0.587785i
$842$		0			0
$843$	54.1376	−	17.5904i	1.86460	−	0.605845i
$844$	10.3780	+	3.37202i	0.357226	+	0.116070i
$845$	4.15911	+	3.02177i	0.143078	+	0.103952i
$846$			42.4508i			1.45949i
$847$		0			0
$848$		0			0
$849$	−34.1221	+	46.9651i	−1.17107	+	1.61184i
$850$		0			0
$851$		0			0
$852$	6.16417	−	4.47853i	0.211181	−	0.153432i
$853$		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	$0.5\pi$
$858$	−15.5552	−	15.2504i	−0.531046	−	0.520639i
$859$	58.0767			1.98155			0.990776	−	0.135509i	$-0.0432668\pi$
$859$	58.0767			1.98155			0.990776	+	0.135509i	$0.0432668\pi$
$860$	−0.0115094	+	0.0158413i	−0.000392467	+	0.000540185i
$861$		0			0
$862$	−4.76076	−	14.6521i	−0.162152	−	0.499053i
$863$	−47.5323	+	34.5343i	−1.61802	+	1.17556i	−0.806506	+	0.591226i	$0.798644\pi$
$863$	−47.5323	+	34.5343i	−1.61802	+	1.17556i	−0.811513	+	0.584334i	$0.801356\pi$
$864$	−14.0515	−	19.3402i	−0.478042	−	0.657968i
$865$		0			0
$866$	40.7243	+	13.2321i	1.38387	+	0.449646i
$867$	−23.8214	−	17.3073i	−0.809017	−	0.587785i
$868$		0			0
$869$	18.1819	−	3.06445i	0.616778	−	0.103954i
$870$		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	$0.100000\pi$
$878$	35.6532	+	25.9035i	1.20324	+	0.874202i
$879$			59.2949i			1.99997i
$880$	1.64325	−	0.857865i	0.0553940	−	0.0289186i
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	12.9821	−	17.8683i	0.437130	−	0.601658i
$883$	−3.51528	+	10.8189i	−0.118298	+	0.364085i	−0.992621	−	0.121261i	$-0.961306\pi$
$883$	−3.51528	+	10.8189i	−0.118298	+	0.364085i	0.874322	+	0.485346i	$0.161306\pi$
$884$		0			0
$885$	6.73083	−	4.89024i	0.226254	−	0.164384i
$886$		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
$890$			7.63916i			0.256065i
$891$	13.2876	−	26.7290i	0.445152	−	0.895455i
$892$		0			0
$893$		0			0
$894$	4.40458	−	13.5559i	0.147311	−	0.453377i
$895$		0			0
$896$		0			0
$897$		0			0
$898$	32.7869	−	10.6531i	1.09411	−	0.355499i
$899$		0			0
$900$	10.5078	+	7.63438i	0.350261	+	0.254479i
$901$		0			0
$902$	−26.9968	−	4.00245i	−0.898896	−	0.133267i
$903$		0			0
$904$		0			0
$905$	−3.28085	+	10.0974i	−0.109059	+	0.335649i
$906$		0			0
$907$	−38.7691	+	28.1674i	−1.28731	+	0.935283i	−0.999747	−	0.0224801i	$-0.992844\pi$
$907$	−38.7691	+	28.1674i	−1.28731	+	0.935283i	−0.287559	+	0.957763i	$0.592844\pi$
$908$	11.5244	+	15.8620i	0.382452	+	0.526400i
$909$		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
$913$	7.97883	−	53.8178i	0.264061	−	1.78111i
$914$		0			0
$915$	−5.62780	+	7.74601i	−0.186049	+	0.256075i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	35.5399	+	48.9165i	1.17235	+	1.61361i	0.645977	+	0.763356i	$0.276450\pi$
$919$	35.5399	+	48.9165i	1.17235	+	1.61361i	0.526377	+	0.850251i	$0.323550\pi$
$920$		0			0
$921$		0			0
$922$	−29.7186	−	21.5919i	−0.978732	−	0.711090i
$923$		−	17.7445i		−	0.584067i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	15.5957	−	47.9988i	0.512231	−	1.57649i
$928$		0			0
$929$	25.0401	−	18.1927i	0.821539	−	0.596883i	−0.0956136	−	0.995419i	$-0.530481\pi$
$929$	25.0401	−	18.1927i	0.821539	−	0.596883i	0.917153	+	0.398535i	$0.130481\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−32.9212			−1.07606
$937$	−28.5335	+	39.2730i	−0.932148	+	1.28299i	0.0268681	+	0.999639i	$0.491447\pi$
$937$	−28.5335	+	39.2730i	−0.932148	+	1.28299i	−0.959016	+	0.283352i	$0.908553\pi$
$938$		0			0
$939$	9.40021	+	28.9309i	0.306764	+	0.944123i
$940$	3.84750	−	2.79537i	0.125492	−	0.0911750i
$941$	34.6953	+	47.7540i	1.13103	+	1.55673i	0.786091	+	0.618111i	$0.212102\pi$
$941$	34.6953	+	47.7540i	1.13103	+	1.55673i	0.344943	+	0.938624i	$0.387898\pi$
$942$	28.2414	−	9.17618i	0.920153	−	0.298976i
$943$		0			0
$944$	13.8884	+	10.0905i	0.452030	+	0.328419i
$945$		0			0
$946$	−0.0321148	−	0.190542i	−0.00104414	−	0.00619506i
$947$	61.5183			1.99908			0.999539	−	0.0303751i	$-0.00967017\pi$
$947$	61.5183			1.99908			0.999539	+	0.0303751i	$0.00967017\pi$
$948$	5.05905	−	6.96319i	0.164310	−	0.226154i
$949$		0			0
$950$		0			0
$951$	−49.1295	+	35.6947i	−1.59313	+	1.15748i
$952$		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
$956$			17.2117i			0.556667i
$957$		0			0
$958$	−24.2507			−0.783505
$959$		0			0
$960$	1.62246	−	4.99343i	0.0523648	−	0.161162i
$961$	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	$0.5\pi$
$968$	9.71352	−	32.0392i	0.312204	−	1.02978i
$969$		0			0
$970$		0			0
$971$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$971$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$972$	−4.30576	−	13.2518i	−0.138107	−	0.425051i
$973$		0			0
$974$		0			0
$975$	28.7679	−	9.34726i	0.921310	−	0.299352i
$976$	−18.7893	−	6.10502i	−0.601432	−	0.195417i
$977$	−28.6517	−	20.8167i	−0.916648	−	0.665984i	0.0260393	−	0.999661i	$-0.491711\pi$
$977$	−28.6517	−	20.8167i	−0.916648	−	0.665984i	−0.942687	+	0.333677i	$0.891711\pi$
$978$		0			0
$979$	43.4987	+	42.6462i	1.39022	+	1.36298i
$980$	−2.47435			−0.0790403
$981$		0			0
$982$		0			0
$983$	19.2546	+	59.2596i	0.614127	+	1.89009i	0.413835	+	0.910352i	$0.364189\pi$
$983$	19.2546	+	59.2596i	0.614127	+	1.89009i	0.200292	+	0.979736i	$0.435811\pi$
$984$	−33.3681	+	24.2434i	−1.06374	+	0.772850i
$985$	5.94550	+	8.18328i	0.189439	+	0.260741i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	4.08076	−	0.687789i	0.129695	−	0.0218594i
$991$	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
$995$	3.56418	−	2.58953i	0.112992	−	0.0820936i
$996$	−14.9278	−	20.5463i	−0.473004	−	0.651034i
$997$	−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.194.3	✓	32
3.2	odd	2	inner	429.2.y.a.194.6	yes	32
11.8	odd	10	inner	429.2.y.a.272.3	yes	32
13.12	even	2	inner	429.2.y.a.194.6	yes	32
33.8	even	10	inner	429.2.y.a.272.6	yes	32
39.38	odd	2	CM	429.2.y.a.194.3	✓	32
143.129	odd	10	inner	429.2.y.a.272.6	yes	32
429.272	even	10	inner	429.2.y.a.272.3	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.y.a.194.3	✓	32	1.1	even	1	trivial
429.2.y.a.194.3	✓	32	39.38	odd	2	CM
429.2.y.a.194.6	yes	32	3.2	odd	2	inner
429.2.y.a.194.6	yes	32	13.12	even	2	inner
429.2.y.a.272.3	yes	32	11.8	odd	10	inner
429.2.y.a.272.3	yes	32	429.272	even	10	inner
429.2.y.a.272.6	yes	32	33.8	even	10	inner
429.2.y.a.272.6	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)

\(f(q)\)	\(=\)	\(q+(-0.618195 + 0.850873i) q^{2} +(-0.535233 + 1.64728i) q^{3} +(0.276215 + 0.850102i) q^{4} +(-0.319931 + 0.232444i) q^{5} +(-1.07075 - 1.47376i) q^{6} +(-2.89461 - 0.940514i) q^{8} +(-2.42705 - 1.76336i) q^{9} +O(q^{10})\)	\(q+(-0.618195 + 0.850873i) q^{2} +(-0.535233 + 1.64728i) q^{3} +(0.276215 + 0.850102i) q^{4} +(-0.319931 + 0.232444i) q^{5} +(-1.07075 - 1.47376i) q^{6} +(-2.89461 - 0.940514i) q^{8} +(-2.42705 - 1.76336i) q^{9} -0.415916i q^{10} +(-2.36830 - 2.32189i) q^{11} -1.54819 q^{12} +(-2.11929 + 2.91695i) q^{13} +(-0.211662 - 0.651427i) q^{15} +(1.14341 - 0.830736i) q^{16} +(3.00078 - 0.975014i) q^{18} +(-0.285971 - 0.207770i) q^{20} +(3.43970 - 0.579742i) q^{22} +(3.09858 - 4.26483i) q^{24} +(-1.49676 + 4.60655i) q^{25} +(-1.17182 - 3.60649i) q^{26} +(4.20378 - 3.05422i) q^{27} +(0.685130 + 0.222612i) q^{30} -4.60068i q^{32} +(5.09239 - 2.65850i) q^{33} +(0.828644 - 2.55031i) q^{36} +(-3.67072 - 5.05231i) q^{39} +(1.14469 - 0.371933i) q^{40} +(-7.44109 - 2.41776i) q^{41} -0.0553950i q^{43} +(1.31968 - 2.65464i) q^{44} +1.18637 q^{45} +(-4.15757 + 12.7957i) q^{47} +(0.756462 + 2.32815i) q^{48} +(5.66312 - 4.11450i) q^{49} +(-2.99430 - 4.12130i) q^{50} +(-3.06509 - 0.995907i) q^{52} +5.46498i q^{54} +(1.29740 + 0.192348i) q^{55} +(3.75348 + 11.5520i) q^{59} +(0.495316 - 0.359868i) q^{60} +(-8.21635 - 11.3088i) q^{61} +(6.20142 + 4.50559i) q^{64} -1.42584i q^{65} +(-0.886046 + 5.97644i) q^{66} +(-3.98153 + 2.89275i) q^{71} +(5.36689 + 7.38690i) q^{72} +(-6.78716 - 4.93116i) q^{75} +6.56809 q^{78} +(-3.26771 + 4.49762i) q^{79} +(-0.172713 + 0.531557i) q^{80} +(2.78115 + 8.55951i) q^{81} +(6.65725 - 4.83678i) q^{82} +(9.64205 + 13.2711i) q^{83} +(0.0471341 + 0.0342449i) q^{86} +(4.67152 + 8.94837i) q^{88} -18.3671 q^{89} +(-0.733409 + 1.00945i) q^{90} +(-8.31732 - 11.4478i) q^{94} +(7.57860 + 2.46244i) q^{96} +7.36216i q^{98} +(1.65367 + 9.81149i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) 32 * q + 16 * q^4 - 24 * q^9	\( 32 q + 16 q^{4} - 24 q^{9} - 24 q^{12} - 92 q^{16} + 28 q^{22} - 40 q^{25} + 180 q^{30} + 48 q^{36} - 72 q^{48} + 56 q^{49} - 260 q^{52} + 32 q^{55} + 184 q^{64} - 60 q^{66} - 144 q^{75} - 72 q^{81} + 204 q^{82} - 40 q^{88} + 60 q^{90}+O(q^{100}) \) 32 * q + 16 * q^4 - 24 * q^9 - 24 * q^12 - 92 * q^16 + 28 * q^22 - 40 * q^25 + 180 * q^30 + 48 * q^36 - 72 * q^48 + 56 * q^49 - 260 * q^52 + 32 * q^55 + 184 * q^64 - 60 * q^66 - 144 * q^75 - 72 * q^81 + 204 * q^82 - 40 * q^88 + 60 * q^90

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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