LMFDB - Embedded newform 429.2.p.a.230.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(230,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("429.230");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.p (of order $6$, degree $2$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.151613669376.7
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 12x^{6} + 95x^{4} + 588x^{2} + 2401 $ x^8 + 12x^6 + 95x^4 + 588*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			230.4
Root			$-1.88713 - 1.85439i$ of defining polynomial
Character	$\chi$	$=$	429.230
Dual form			429.2.p.a.263.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.724745 + 1.57313i) q^{3} +(1.00000 + 1.73205i) q^{4} -2.82843i q^{5} +(3.12250 - 1.80278i) q^{7} +(-1.94949 + 2.28024i) q^{9} +O(q^{10})$	\(q+(0.724745 + 1.57313i) q^{3} +(1.00000 + 1.73205i) q^{4} -2.82843i q^{5} +(3.12250 - 1.80278i) q^{7} +(-1.94949 + 2.28024i) q^{9} +(3.11187 - 1.14728i) q^{11} +(-2.00000 + 2.82843i) q^{12} +(3.12250 - 1.80278i) q^{13} +(4.44949 - 2.04989i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(-2.54951 - 4.41588i) q^{17} +(-6.24500 + 3.60555i) q^{19} +(4.89898 - 2.82843i) q^{20} +(5.09902 + 3.60555i) q^{21} +(1.22474 + 0.707107i) q^{23} -3.00000 q^{25} +(-5.00000 - 1.41421i) q^{27} +(6.24500 + 3.60555i) q^{28} +(-2.54951 + 4.41588i) q^{29} +1.00000 q^{31} +(4.06014 + 4.06390i) q^{33} +(-5.09902 - 8.83176i) q^{35} +(-5.89898 - 1.09638i) q^{36} +(-4.00000 + 6.92820i) q^{37} +(5.09902 + 3.60555i) q^{39} +(-5.09902 + 8.83176i) q^{41} +(-3.12250 + 1.80278i) q^{43} +(5.09902 + 4.24264i) q^{44} +(6.44949 + 5.51399i) q^{45} -9.89949i q^{47} +(-6.89898 - 0.635674i) q^{48} +(3.00000 - 5.19615i) q^{49} +(5.09902 - 7.21110i) q^{51} +(6.24500 + 3.60555i) q^{52} +4.24264i q^{53} +(-3.24500 - 8.80170i) q^{55} +(-10.1980 - 7.21110i) q^{57} +(3.67423 - 2.12132i) q^{59} +(8.00000 + 5.65685i) q^{60} +(3.12250 - 1.80278i) q^{61} +(-1.97652 + 10.6345i) q^{63} -8.00000 q^{64} +(-5.09902 - 8.83176i) q^{65} +(6.50000 - 11.2583i) q^{67} +(5.09902 - 8.83176i) q^{68} +(-0.224745 + 2.43916i) q^{69} +(-2.44949 + 1.41421i) q^{71} -10.8167i q^{73} +(-2.17423 - 4.71940i) q^{75} +(-12.4900 - 7.21110i) q^{76} +(7.64853 - 9.19239i) q^{77} +3.60555i q^{79} +(9.79796 + 5.65685i) q^{80} +(-1.39898 - 8.89060i) q^{81} -5.09902 q^{83} +(-1.14598 + 12.4373i) q^{84} +(-12.4900 + 7.21110i) q^{85} +(-8.79451 - 0.810329i) q^{87} +(-2.44949 - 1.41421i) q^{89} +(6.50000 - 11.2583i) q^{91} +2.82843i q^{92} +(0.724745 + 1.57313i) q^{93} +(10.1980 + 17.6635i) q^{95} +(5.50000 + 9.52628i) q^{97} +(-3.45049 + 9.33242i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 8 q^{4} + 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 + 8 * q^4 + 4 * q^9	$ 8 q - 4 q^{3} + 8 q^{4} + 4 q^{9} - 16 q^{12} + 16 q^{15} - 16 q^{16} - 24 q^{25} - 40 q^{27} + 8 q^{31} + 12 q^{33} - 8 q^{36} - 32 q^{37} + 32 q^{45} - 16 q^{48} + 24 q^{49} + 24 q^{55} + 64 q^{60} - 64 q^{64} + 52 q^{67} + 8 q^{69} + 12 q^{75} + 28 q^{81} + 52 q^{91} - 4 q^{93} + 44 q^{97} - 48 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 + 8 * q^4 + 4 * q^9 - 16 * q^12 + 16 * q^15 - 16 * q^16 - 24 * q^25 - 40 * q^27 + 8 * q^31 + 12 * q^33 - 8 * q^36 - 32 * q^37 + 32 * q^45 - 16 * q^48 + 24 * q^49 + 24 * q^55 + 64 * q^60 - 64 * q^64 + 52 * q^67 + 8 * q^69 + 12 * q^75 + 28 * q^81 + 52 * q^91 - 4 * q^93 + 44 * q^97 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$

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			0		−0.866025	−	0.500000i	$-0.833333\pi$
$2$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$3$	0.724745	+	1.57313i	0.418432	+	0.908248i
$3$	0.724745	+	1.57313i	0.418432	+	0.908248i
$4$	1.00000	+	1.73205i	0.500000	+	0.866025i
$5$		−	2.82843i		−	1.26491i	−0.774597	−	0.632456i	$-0.782047\pi$
$5$		−	2.82843i		−	1.26491i	0.774597	−	0.632456i	$-0.217953\pi$
$6$		0			0
$7$	3.12250	−	1.80278i	1.18019	−	0.681385i	0.224134	−	0.974558i	$-0.428045\pi$
$7$	3.12250	−	1.80278i	1.18019	−	0.681385i	0.956059	+	0.293173i	$0.0947112\pi$
$8$		0			0
$9$	−1.94949	+	2.28024i	−0.649830	+	0.760080i
$10$		0			0
$11$	3.11187	−	1.14728i	0.938265	−	0.345918i
$11$	3.11187	−	1.14728i	0.938265	−	0.345918i
$12$	−2.00000	+	2.82843i	−0.577350	+	0.816497i
$13$	3.12250	−	1.80278i	0.866025	−	0.500000i
$13$	3.12250	−	1.80278i	0.866025	−	0.500000i
$14$		0			0
$15$	4.44949	−	2.04989i	1.14885	−	0.529279i
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$	−2.54951	−	4.41588i	−0.618347	−	1.07101i	−0.989787	−	0.142552i	$-0.954469\pi$
$17$	−2.54951	−	4.41588i	−0.618347	−	1.07101i	0.371440	−	0.928457i	$-0.378864\pi$
$18$		0			0
$19$	−6.24500	+	3.60555i	−1.43270	+	0.827170i	−0.997326	−	0.0730792i	$-0.976717\pi$
$19$	−6.24500	+	3.60555i	−1.43270	+	0.827170i	−0.435375	+	0.900249i	$0.643384\pi$
$20$	4.89898	−	2.82843i	1.09545	−	0.632456i
$21$	5.09902	+	3.60555i	1.11270	+	0.786796i
$22$		0			0
$23$	1.22474	+	0.707107i	0.255377	+	0.147442i	0.622224	−	0.782839i	$-0.286229\pi$
$23$	1.22474	+	0.707107i	0.255377	+	0.147442i	−0.366847	+	0.930281i	$0.619563\pi$
$24$		0			0
$25$	−3.00000			−0.600000
$26$		0			0
$27$	−5.00000	−	1.41421i	−0.962250	−	0.272166i
$28$	6.24500	+	3.60555i	1.18019	+	0.681385i
$29$	−2.54951	+	4.41588i	−0.473432	+	0.820008i	−0.999537	−	0.0304110i	$-0.990318\pi$
$29$	−2.54951	+	4.41588i	−0.473432	+	0.820008i	0.526105	+	0.850419i	$0.323652\pi$
$30$		0			0
$31$	1.00000			0.179605			0.0898027	−	0.995960i	$-0.471376\pi$
$31$	1.00000			0.179605			0.0898027	+	0.995960i	$0.471376\pi$
$32$		0			0
$33$	4.06014	+	4.06390i	0.706779	+	0.707434i
$34$		0			0
$35$	−5.09902	−	8.83176i	−0.861892	−	1.49284i
$36$	−5.89898	−	1.09638i	−0.983163	−	0.182729i
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	0.323640	+	0.946180i	$0.395093\pi$
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	−0.981236	+	0.192809i	$0.938240\pi$
$38$		0			0
$39$	5.09902	+	3.60555i	0.816497	+	0.577350i
$40$		0			0
$41$	−5.09902	+	8.83176i	−0.796333	+	1.37929i	0.125656	+	0.992074i	$0.459896\pi$
$41$	−5.09902	+	8.83176i	−0.796333	+	1.37929i	−0.921989	+	0.387215i	$0.873437\pi$
$42$		0			0
$43$	−3.12250	+	1.80278i	−0.476177	+	0.274921i	−0.718822	−	0.695194i	$-0.755318\pi$
$43$	−3.12250	+	1.80278i	−0.476177	+	0.274921i	0.242645	+	0.970115i	$0.421985\pi$
$44$	5.09902	+	4.24264i	0.768706	+	0.639602i
$45$	6.44949	+	5.51399i	0.961433	+	0.821977i
$46$		0			0
$47$		−	9.89949i		−	1.44399i	−0.691898	−	0.721995i	$-0.743225\pi$
$47$		−	9.89949i		−	1.44399i	0.691898	−	0.721995i	$-0.256775\pi$
$48$	−6.89898	−	0.635674i	−0.995782	−	0.0917517i
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$		0			0
$51$	5.09902	−	7.21110i	0.714006	−	1.00976i
$52$	6.24500	+	3.60555i	0.866025	+	0.500000i
$53$			4.24264i			0.582772i	0.956606	+	0.291386i	$0.0941163\pi$
$53$			4.24264i			0.582772i	−0.956606	+	0.291386i	$0.905884\pi$
$54$		0			0
$55$	−3.24500	−	8.80170i	−0.437555	−	1.18682i
$56$		0			0
$57$	−10.1980	−	7.21110i	−1.35076	−	0.955134i
$58$		0			0
$59$	3.67423	−	2.12132i	0.478345	−	0.276172i	−0.241382	−	0.970430i	$-0.577601\pi$
$59$	3.67423	−	2.12132i	0.478345	−	0.276172i	0.719726	+	0.694258i	$0.244267\pi$
$60$	8.00000	+	5.65685i	1.03280	+	0.730297i
$61$	3.12250	−	1.80278i	0.399795	−	0.230822i	−0.286601	−	0.958050i	$-0.592525\pi$
$61$	3.12250	−	1.80278i	0.399795	−	0.230822i	0.686396	+	0.727228i	$0.259192\pi$
$62$		0			0
$63$	−1.97652	+	10.6345i	−0.249018	+	1.33983i
$64$	−8.00000			−1.00000
$65$	−5.09902	−	8.83176i	−0.632456	−	1.09545i
$66$		0			0
$67$	6.50000	−	11.2583i	0.794101	−	1.37542i	−0.129307	−	0.991605i	$-0.541275\pi$
$67$	6.50000	−	11.2583i	0.794101	−	1.37542i	0.923408	−	0.383819i	$-0.125391\pi$
$68$	5.09902	−	8.83176i	0.618347	−	1.07101i
$69$	−0.224745	+	2.43916i	−0.0270561	+	0.293640i
$70$		0			0
$71$	−2.44949	+	1.41421i	−0.290701	+	0.167836i	−0.638258	−	0.769823i	$-0.720345\pi$
$71$	−2.44949	+	1.41421i	−0.290701	+	0.167836i	0.347557	+	0.937659i	$0.387011\pi$
$72$		0			0
$73$		−	10.8167i		−	1.26599i	−0.774154	−	0.632997i	$-0.781825\pi$
$73$		−	10.8167i		−	1.26599i	0.774154	−	0.632997i	$-0.218175\pi$
$74$		0			0
$75$	−2.17423	−	4.71940i	−0.251059	−	0.544949i
$76$	−12.4900	−	7.21110i	−1.43270	−	0.827170i
$77$	7.64853	−	9.19239i	0.871631	−	1.04757i
$78$		0			0
$79$			3.60555i			0.405656i	0.979214	+	0.202828i	$0.0650133\pi$
$79$			3.60555i			0.405656i	−0.979214	+	0.202828i	$0.934987\pi$
$80$	9.79796	+	5.65685i	1.09545	+	0.632456i
$81$	−1.39898	−	8.89060i	−0.155442	−	0.987845i
$82$		0			0
$83$	−5.09902			−0.559690			−0.279845	−	0.960045i	$-0.590283\pi$
$83$	−5.09902			−0.559690			−0.279845	+	0.960045i	$0.590283\pi$
$84$	−1.14598	+	12.4373i	−0.125037	+	1.35702i
$85$	−12.4900	+	7.21110i	−1.35473	+	0.782154i
$86$		0			0
$87$	−8.79451	−	0.810329i	−0.942870	−	0.0868764i
$88$		0			0
$89$	−2.44949	−	1.41421i	−0.259645	−	0.149906i	0.364527	−	0.931193i	$-0.381231\pi$
$89$	−2.44949	−	1.41421i	−0.259645	−	0.149906i	−0.624173	+	0.781286i	$0.714564\pi$
$90$		0			0
$91$	6.50000	−	11.2583i	0.681385	−	1.18019i
$92$			2.82843i			0.294884i
$93$	0.724745	+	1.57313i	0.0751525	+	0.163126i
$94$		0			0
$95$	10.1980	+	17.6635i	1.04630	+	1.81224i
$96$		0			0
$97$	5.50000	+	9.52628i	0.558440	+	0.967247i	0.997627	+	0.0688512i	$0.0219334\pi$
$97$	5.50000	+	9.52628i	0.558440	+	0.967247i	−0.439187	+	0.898396i	$0.644733\pi$
$98$		0			0
$99$	−3.45049	+	9.33242i	−0.346787	+	0.937944i
$100$	−3.00000	−	5.19615i	−0.300000	−	0.519615i
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$		0			0
$103$	1.00000			0.0985329			0.0492665	−	0.998786i	$-0.484312\pi$
$103$	1.00000			0.0985329			0.0492665	+	0.998786i	$0.484312\pi$
$104$		0			0
$105$	10.1980	−	14.4222i	0.995227	−	1.40746i
$106$		0			0
$107$	−2.54951	+	4.41588i	−0.246470	+	0.426899i	−0.962544	−	0.271126i	$-0.912604\pi$
$107$	−2.54951	+	4.41588i	−0.246470	+	0.426899i	0.716074	+	0.698025i	$0.245937\pi$
$108$	−2.55051	−	10.0745i	−0.245423	−	0.969416i
$109$		−	3.60555i		−	0.345349i	−0.984979	−	0.172675i	$-0.944759\pi$
$109$		−	3.60555i		−	0.345349i	0.984979	−	0.172675i	$-0.0552409\pi$
$110$		0			0
$111$	−13.7980	−	1.27135i	−1.30964	−	0.120671i
$112$			14.4222i			1.36277i
$113$	−11.0227	+	6.36396i	−1.03693	+	0.598671i	−0.918962	−	0.394346i	$-0.870971\pi$
$113$	−11.0227	+	6.36396i	−1.03693	+	0.598671i	−0.117967	+	0.993018i	$0.537638\pi$
$114$		0			0
$115$	2.00000	−	3.46410i	0.186501	−	0.323029i
$116$	−10.1980			−0.946864
$117$	−1.97652	+	10.6345i	−0.182729	+	0.983163i
$118$		0			0
$119$	−15.9217	−	9.19239i	−1.45954	−	0.842665i
$120$		0			0
$121$	8.36750	−	7.14038i	0.760682	−	0.649125i
$122$		0			0
$123$	−17.5890	−	1.62066i	−1.58595	−	0.146130i
$124$	1.00000	+	1.73205i	0.0898027	+	0.155543i
$125$		−	5.65685i		−	0.505964i
$126$		0			0
$127$	−3.12250	−	1.80278i	−0.277077	−	0.159970i	0.355022	−	0.934858i	$-0.384473\pi$
$127$	−3.12250	−	1.80278i	−0.277077	−	0.159970i	−0.632099	+	0.774887i	$0.717807\pi$
$128$		0			0
$129$	−5.09902	−	3.60555i	−0.448944	−	0.317451i
$130$		0			0
$131$	−20.3961			−1.78201			−0.891007	−	0.453990i	$-0.850000\pi$
$131$	−20.3961			−1.78201			−0.891007	+	0.453990i	$0.850000\pi$
$132$	−2.97875	+	11.0963i	−0.259267	+	0.965806i
$133$	−13.0000	+	22.5167i	−1.12724	+	1.95244i
$134$		0			0
$135$	−4.00000	+	14.1421i	−0.344265	+	1.21716i
$136$		0			0
$137$	6.12372	−	3.53553i	0.523185	−	0.302061i	−0.215052	−	0.976603i	$-0.568992\pi$
$137$	6.12372	−	3.53553i	0.523185	−	0.302061i	0.738237	+	0.674542i	$0.235659\pi$
$138$		0			0
$139$	9.36750	−	5.40833i	0.794541	−	0.458728i	−0.0470179	−	0.998894i	$-0.514972\pi$
$139$	9.36750	−	5.40833i	0.794541	−	0.458728i	0.841559	+	0.540166i	$0.181638\pi$
$140$	10.1980	−	17.6635i	0.861892	−	1.49284i
$141$	15.5732	−	7.17461i	1.31150	−	0.604211i
$142$		0			0
$143$	7.64853	−	9.19239i	0.639602	−	0.768706i
$144$	−4.00000	−	11.3137i	−0.333333	−	0.942809i
$145$	12.4900	+	7.21110i	1.03724	+	0.598849i
$146$		0			0
$147$	10.3485	+	0.953512i	0.853527	+	0.0786443i
$148$	−16.0000			−1.31519
$149$	7.64853	+	13.2476i	0.626592	+	1.08529i	0.988231	+	0.152971i	$0.0488840\pi$
$149$	7.64853	+	13.2476i	0.626592	+	1.08529i	−0.361639	+	0.932318i	$0.617783\pi$
$150$		0			0
$151$		−	7.21110i		−	0.586831i	−0.955985	−	0.293416i	$-0.905208\pi$
$151$		−	7.21110i		−	0.586831i	0.955985	−	0.293416i	$-0.0947920\pi$
$152$		0			0
$153$	15.0395	+	2.79522i	1.21587	+	0.225980i
$154$		0			0
$155$		−	2.82843i		−	0.227185i
$156$	−1.14598	+	12.4373i	−0.0917517	+	0.995782i
$157$	7.00000			0.558661			0.279330	−	0.960195i	$-0.409888\pi$
$157$	7.00000			0.558661			0.279330	+	0.960195i	$0.409888\pi$
$158$		0			0
$159$	−6.67423	+	3.07483i	−0.529301	+	0.243850i
$160$		0			0
$161$	5.09902			0.401859
$162$		0			0
$163$	5.50000	+	9.52628i	0.430793	+	0.746156i	0.996942	−	0.0781474i	$-0.0249005\pi$
$163$	5.50000	+	9.52628i	0.430793	+	0.746156i	−0.566149	+	0.824303i	$0.691567\pi$
$164$	−20.3961			−1.59267
$165$	11.4944	−	11.4838i	0.894842	−	0.894013i
$166$		0			0
$167$	−2.54951	+	4.41588i	−0.197287	+	0.341711i	−0.947648	−	0.319317i	$-0.896546\pi$
$167$	−2.54951	+	4.41588i	−0.197287	+	0.341711i	0.750361	+	0.661028i	$0.229880\pi$
$168$		0			0
$169$	6.50000	−	11.2583i	0.500000	−	0.866025i
$170$		0			0
$171$	3.95304	−	21.2691i	0.302297	−	1.62649i
$172$	−6.24500	−	3.60555i	−0.476177	−	0.274921i
$173$	−5.09902	−	8.83176i	−0.387671	−	0.671466i	0.604465	−	0.796632i	$-0.293387\pi$
$173$	−5.09902	−	8.83176i	−0.387671	−	0.671466i	−0.992136	+	0.125166i	$0.960054\pi$
$174$		0			0
$175$	−9.36750	+	5.40833i	−0.708116	+	0.408831i
$176$	−2.24945	+	13.0744i	−0.169559	+	0.985520i
$177$	6.00000	+	4.24264i	0.450988	+	0.318896i
$178$		0			0
$179$	12.2474	+	7.07107i	0.915417	+	0.528516i	0.882170	−	0.470931i	$-0.156082\pi$
$179$	12.2474	+	7.07107i	0.915417	+	0.528516i	0.0332471	+	0.999447i	$0.489415\pi$
$180$	−3.10102	+	16.6848i	−0.231136	+	1.24361i
$181$	24.0000			1.78391			0.891953	−	0.452128i	$-0.149335\pi$
$181$	24.0000			1.78391			0.891953	+	0.452128i	$0.149335\pi$
$182$		0			0
$183$	5.09902	+	3.60555i	0.376930	+	0.266530i
$184$		0			0
$185$	19.5959	+	11.3137i	1.44072	+	0.831800i
$186$		0			0
$187$	−13.0000	−	10.8167i	−0.950654	−	0.790992i
$188$	17.1464	−	9.89949i	1.25053	−	0.721995i
$189$	−18.1620	+	4.59800i	−1.32109	+	0.334455i
$190$		0			0
$191$	−8.57321	+	4.94975i	−0.620336	+	0.358151i	−0.777000	−	0.629501i	$-0.783259\pi$
$191$	−8.57321	+	4.94975i	−0.620336	+	0.358151i	0.156664	+	0.987652i	$0.449926\pi$
$192$	−5.79796	−	12.5851i	−0.418432	−	0.908248i
$193$	3.12250	+	1.80278i	0.224762	+	0.129767i	0.608153	−	0.793819i	$-0.291911\pi$
$193$	3.12250	+	1.80278i	0.224762	+	0.129767i	−0.383391	+	0.923586i	$0.625244\pi$
$194$		0			0
$195$	10.1980	−	14.4222i	0.730297	−	1.03280i
$196$	12.0000			0.857143
$197$	10.1980	−	17.6635i	0.726580	−	1.25847i	−0.231740	−	0.972778i	$-0.574442\pi$
$197$	10.1980	−	17.6635i	0.726580	−	1.25847i	0.958320	−	0.285696i	$-0.0922248\pi$
$198$		0			0
$199$	−0.500000	−	0.866025i	−0.0354441	−	0.0613909i	0.847759	−	0.530381i	$-0.177951\pi$
$199$	−0.500000	−	0.866025i	−0.0354441	−	0.0613909i	−0.883203	+	0.468990i	$0.844618\pi$
$200$		0			0
$201$	22.4217	+	2.06594i	1.58150	+	0.145720i
$202$		0			0
$203$			18.3848i			1.29036i
$204$	17.5890	+	1.62066i	1.23148	+	0.113469i
$205$	24.9800	+	14.4222i	1.74468	+	1.00729i
$206$		0			0
$207$	−4.00000	+	1.41421i	−0.278019	+	0.0982946i
$208$			14.4222i			1.00000i
$209$	−15.2971	+	18.3848i	−1.05812	+	1.27170i
$210$		0			0
$211$	−15.6125	−	9.01388i	−1.07481	−	0.620541i	−0.145317	−	0.989385i	$-0.546420\pi$
$211$	−15.6125	−	9.01388i	−1.07481	−	0.620541i	−0.929491	+	0.368844i	$0.879754\pi$
$212$	−7.34847	+	4.24264i	−0.504695	+	0.291386i
$213$	−4.00000	−	2.82843i	−0.274075	−	0.193801i
$214$		0			0
$215$	5.09902	+	8.83176i	0.347750	+	0.602321i
$216$		0			0
$217$	3.12250	−	1.80278i	0.211969	−	0.122380i
$218$		0			0
$219$	17.0160	−	7.83931i	1.14984	−	0.529732i
$220$	12.0000	−	14.4222i	0.809040	−	0.972345i
$221$	−15.9217	−	9.19239i	−1.07101	−	0.618347i
$222$		0			0
$223$	−3.00000	+	5.19615i	−0.200895	+	0.347960i	−0.948817	−	0.315826i	$-0.897718\pi$
$223$	−3.00000	+	5.19615i	−0.200895	+	0.347960i	0.747922	+	0.663786i	$0.231052\pi$
$224$		0			0
$225$	5.84847	−	6.84072i	0.389898	−	0.456048i
$226$		0			0
$227$	5.09902	+	8.83176i	0.338434	+	0.586185i	0.984138	−	0.177403i	$-0.0567695\pi$
$227$	5.09902	+	8.83176i	0.338434	+	0.586185i	−0.645705	+	0.763587i	$0.723436\pi$
$228$	2.29196	−	24.8746i	0.151789	−	1.64736i
$229$	−28.0000			−1.85029			−0.925146	−	0.379611i	$-0.876058\pi$
$229$	−28.0000			−1.85029			−0.925146	+	0.379611i	$0.876058\pi$
$230$		0			0
$231$	20.0041	+	5.37001i	1.31617	+	0.353321i
$232$		0			0
$233$	15.2971			1.00214			0.501072	−	0.865406i	$-0.332939\pi$
$233$	15.2971			1.00214			0.501072	+	0.865406i	$0.332939\pi$
$234$		0			0
$235$	−28.0000			−1.82652
$236$	7.34847	+	4.24264i	0.478345	+	0.276172i
$237$	−5.67201	+	2.61310i	−0.368437	+	0.169739i
$238$		0			0
$239$	5.09902			0.329828			0.164914	−	0.986308i	$-0.447265\pi$
$239$	5.09902			0.329828			0.164914	+	0.986308i	$0.447265\pi$
$240$	−1.79796	+	19.5133i	−0.116058	+	1.25958i
$241$	−6.24500	+	3.60555i	−0.402276	+	0.232254i	−0.687465	−	0.726217i	$-0.741277\pi$
$241$	−6.24500	+	3.60555i	−0.402276	+	0.232254i	0.285190	+	0.958471i	$0.407943\pi$
$242$		0			0
$243$	12.9722	−	8.64420i	0.832167	−	0.554526i
$244$	6.24500	+	3.60555i	0.399795	+	0.230822i
$245$	−14.6969	−	8.48528i	−0.938953	−	0.542105i
$246$		0			0
$247$	−13.0000	+	22.5167i	−0.827170	+	1.43270i
$248$		0			0
$249$	−3.69549	−	8.02143i	−0.234192	−	0.508338i
$250$		0			0
$251$	−8.57321	+	4.94975i	−0.541136	+	0.312425i	−0.745539	−	0.666462i	$-0.767808\pi$
$251$	−8.57321	+	4.94975i	−0.541136	+	0.312425i	0.204403	+	0.978887i	$0.434475\pi$
$252$	−20.3961	+	7.21110i	−1.28483	+	0.454257i
$253$	4.62250	+	0.795301i	0.290614	+	0.0500001i
$254$		0			0
$255$	−20.3961	−	14.4222i	−1.27725	−	0.903154i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−12.2474	−	7.07107i	−0.763975	−	0.441081i	0.0667462	−	0.997770i	$-0.478738\pi$
$257$	−12.2474	−	7.07107i	−0.763975	−	0.441081i	−0.830721	+	0.556689i	$0.812072\pi$
$258$		0			0
$259$			28.8444i			1.79230i
$260$	10.1980	−	17.6635i	0.632456	−	1.09545i
$261$	−5.09902	−	14.4222i	−0.315621	−	0.892712i
$262$		0			0
$263$	−7.64853	+	13.2476i	−0.471629	+	0.816885i	−0.999473	−	0.0324564i	$-0.989667\pi$
$263$	−7.64853	+	13.2476i	−0.471629	+	0.816885i	0.527845	+	0.849341i	$0.323000\pi$
$264$		0			0
$265$	12.0000			0.737154
$266$		0			0
$267$	0.449490	−	4.87832i	0.0275083	−	0.298548i
$268$	26.0000			1.58820
$269$	9.79796	−	5.65685i	0.597392	−	0.344904i	−0.170623	−	0.985336i	$-0.554578\pi$
$269$	9.79796	−	5.65685i	0.597392	−	0.344904i	0.768015	+	0.640432i	$0.221245\pi$
$270$		0			0
$271$	−3.12250	−	1.80278i	−0.189678	−	0.109511i	0.402154	−	0.915572i	$-0.368262\pi$
$271$	−3.12250	−	1.80278i	−0.189678	−	0.109511i	−0.591832	+	0.806061i	$0.701595\pi$
$272$	20.3961			1.23669
$273$	22.4217	+	2.06594i	1.35702	+	0.125037i
$274$		0			0
$275$	−9.33562	+	3.44184i	−0.562959	+	0.207551i
$276$	−4.44949	+	2.04989i	−0.267828	+	0.123389i
$277$	−12.4900	+	7.21110i	−0.750451	+	0.433273i	−0.825857	−	0.563880i	$-0.809308\pi$
$277$	−12.4900	+	7.21110i	−0.750451	+	0.433273i	0.0754058	+	0.997153i	$0.475975\pi$
$278$		0			0
$279$	−1.94949	+	2.28024i	−0.116713	+	0.136514i
$280$		0			0
$281$	25.4951			1.52091			0.760455	−	0.649391i	$-0.224976\pi$
$281$	25.4951			1.52091			0.760455	+	0.649391i	$0.224976\pi$
$282$		0			0
$283$	15.6125	+	9.01388i	0.928066	+	0.535819i	0.886200	−	0.463304i	$-0.153336\pi$
$283$	15.6125	+	9.01388i	0.928066	+	0.535819i	0.0418670	+	0.999123i	$0.486669\pi$
$284$	−4.89898	−	2.82843i	−0.290701	−	0.167836i
$285$	−20.3961	+	28.8444i	−1.20816	+	1.70860i
$286$		0			0
$287$			36.7696i			2.17044i
$288$		0			0
$289$	−4.50000	+	7.79423i	−0.264706	+	0.458484i
$290$		0			0
$291$	−11.0000	+	15.5563i	−0.644831	+	0.911929i
$292$	18.7350	−	10.8167i	1.09638	−	0.632997i
$293$	7.64853	+	13.2476i	0.446832	+	0.773935i	0.998178	−	0.0603412i	$-0.0192189\pi$
$293$	7.64853	+	13.2476i	0.446832	+	0.773935i	−0.551346	+	0.834277i	$0.685886\pi$
$294$		0			0
$295$	−6.00000	−	10.3923i	−0.349334	−	0.605063i
$296$		0			0
$297$	−17.1819	+	1.33555i	−0.996993	+	0.0774964i
$298$		0			0
$299$	5.09902			0.294884
$300$	6.00000	−	8.48528i	0.346410	−	0.489898i
$301$	−6.50000	+	11.2583i	−0.374654	+	0.648919i
$302$		0			0
$303$		0			0
$304$		−	28.8444i		−	1.65434i
$305$	−5.09902	−	8.83176i	−0.291969	−	0.505705i
$306$		0			0
$307$		−	10.8167i		−	0.617339i	−0.951169	−	0.308670i	$-0.900116\pi$
$307$		−	10.8167i		−	0.617339i	0.951169	−	0.308670i	$-0.0998837\pi$
$308$	23.5702	+	4.05525i	1.34304	+	0.231069i
$309$	0.724745	+	1.57313i	0.0412293	+	0.0894924i
$310$		0			0
$311$		−	14.1421i		−	0.801927i	−0.916094	−	0.400963i	$-0.868675\pi$
$311$		−	14.1421i		−	0.801927i	0.916094	−	0.400963i	$-0.131325\pi$
$312$		0			0
$313$	−5.00000			−0.282617			−0.141308	−	0.989966i	$-0.545131\pi$
$313$	−5.00000			−0.282617			−0.141308	+	0.989966i	$0.545131\pi$
$314$		0			0
$315$	30.0790	+	5.59044i	1.69476	+	0.314986i
$316$	−6.24500	+	3.60555i	−0.351309	+	0.202828i
$317$		−	7.07107i		−	0.397151i	−0.980086	−	0.198575i	$-0.936369\pi$
$317$		−	7.07107i		−	0.397151i	0.980086	−	0.198575i	$-0.0636315\pi$
$318$		0			0
$319$	−2.86750	+	16.6667i	−0.160549	+	0.933154i
$320$			22.6274i			1.26491i
$321$	−8.79451	−	0.810329i	−0.490862	−	0.0452282i
$322$		0			0
$323$	31.8434	+	18.3848i	1.77181	+	1.02296i
$324$	14.0000	−	11.3137i	0.777778	−	0.628539i
$325$	−9.36750	+	5.40833i	−0.519615	+	0.300000i
$326$		0			0
$327$	5.67201	−	2.61310i	0.313663	−	0.144505i
$328$		0			0
$329$	−17.8466	−	30.9112i	−0.983913	−	1.70419i
$330$		0			0
$331$	−5.50000	−	9.52628i	−0.302307	−	0.523612i	0.674351	−	0.738411i	$-0.264424\pi$
$331$	−5.50000	−	9.52628i	−0.302307	−	0.523612i	−0.976658	+	0.214799i	$0.931090\pi$
$332$	−5.09902	−	8.83176i	−0.279845	−	0.484706i
$333$	−8.00000	−	22.6274i	−0.438397	−	1.23997i
$334$		0			0
$335$	−31.8434	−	18.3848i	−1.73979	−	1.00447i
$336$	−22.6880	+	10.4524i	−1.23773	+	0.570226i
$337$			18.0278i			0.982034i	0.871150	+	0.491017i	$0.163375\pi$
$337$			18.0278i			0.982034i	−0.871150	+	0.491017i	$0.836625\pi$
$338$		0			0
$339$	−18.0000	−	12.7279i	−0.977626	−	0.691286i
$340$	−24.9800	−	14.4222i	−1.35473	−	0.782154i
$341$	3.11187	−	1.14728i	0.168517	−	0.0621287i
$342$		0			0
$343$			3.60555i			0.194681i
$344$		0			0
$345$	6.89898	+	0.635674i	0.371429	+	0.0342236i
$346$		0			0
$347$	7.64853	+	13.2476i	0.410595	+	0.711171i	0.994955	−	0.100324i	$-0.0319878\pi$
$347$	7.64853	+	13.2476i	0.410595	+	0.711171i	−0.584360	+	0.811494i	$0.698655\pi$
$348$	−7.39098	−	16.0429i	−0.396198	−	0.859988i
$349$	9.36750	+	5.40833i	0.501431	+	0.289501i	0.729304	−	0.684190i	$-0.239844\pi$
$349$	9.36750	+	5.40833i	0.501431	+	0.289501i	−0.227874	+	0.973691i	$0.573177\pi$
$350$		0			0
$351$	−18.1620	+	4.59800i	−0.969416	+	0.245423i
$352$		0			0
$353$	−7.34847	−	4.24264i	−0.391120	−	0.225813i	0.291526	−	0.956563i	$-0.405837\pi$
$353$	−7.34847	−	4.24264i	−0.391120	−	0.225813i	−0.682645	+	0.730750i	$0.739170\pi$
$354$		0			0
$355$	4.00000	+	6.92820i	0.212298	+	0.367711i
$356$		−	5.65685i		−	0.299813i
$357$	2.92168	−	31.7090i	0.154632	−	1.67822i
$358$		0			0
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	16.5000	−	28.5788i	0.868421	−	1.50415i
$362$		0			0
$363$	17.2971	+	7.98823i	0.907860	+	0.419273i
$364$	26.0000			1.36277
$365$	−30.5941			−1.60137
$366$		0			0
$367$	16.5000	−	28.5788i	0.861293	−	1.49180i	−0.00938849	−	0.999956i	$-0.502988\pi$
$367$	16.5000	−	28.5788i	0.861293	−	1.49180i	0.870681	−	0.491847i	$-0.163678\pi$
$368$	−4.89898	+	2.82843i	−0.255377	+	0.147442i
$369$	−10.1980	−	28.8444i	−0.530889	−	1.50158i
$370$		0			0
$371$	7.64853	+	13.2476i	0.397092	+	0.687783i
$372$	−2.00000	+	2.82843i	−0.103695	+	0.146647i
$373$	21.8575	−	12.6194i	1.13174	−	0.653409i	0.187367	−	0.982290i	$-0.440005\pi$
$373$	21.8575	−	12.6194i	1.13174	−	0.653409i	0.944371	+	0.328881i	$0.106671\pi$
$374$		0			0
$375$	8.89898	−	4.09978i	0.459541	−	0.211712i
$376$		0			0
$377$			18.3848i			0.946864i
$378$		0			0
$379$	9.50000	−	16.4545i	0.487982	−	0.845210i	−0.511922	−	0.859032i	$-0.671066\pi$
$379$	9.50000	−	16.4545i	0.487982	−	0.845210i	0.999904	+	0.0138218i	$0.00439975\pi$
$380$	−20.3961	+	35.3270i	−1.04630	+	1.81224i
$381$	0.572989	−	6.21866i	0.0293551	−	0.318591i
$382$		0			0
$383$	−22.0454	+	12.7279i	−1.12647	+	0.650366i	−0.943044	−	0.332668i	$-0.892051\pi$
$383$	−22.0454	+	12.7279i	−1.12647	+	0.650366i	−0.183424	+	0.983034i	$0.558718\pi$
$384$		0			0
$385$	−26.0000	−	21.6333i	−1.32508	−	1.10254i
$386$		0			0
$387$	1.97652	−	10.6345i	0.100472	−	0.540584i
$388$	−11.0000	+	19.0526i	−0.558440	+	0.967247i
$389$			24.0416i			1.21896i	0.792802	+	0.609480i	$0.208622\pi$
$389$			24.0416i			1.21896i	−0.792802	+	0.609480i	$0.791378\pi$
$390$		0			0
$391$		−	7.21110i		−	0.364681i
$392$		0			0
$393$	−14.7820	−	32.0857i	−0.745651	−	1.61851i
$394$		0			0
$395$	10.1980			0.513119
$396$	−19.6147	+	3.35600i	−0.985677	+	0.168645i
$397$	−3.50000	−	6.06218i	−0.175660	−	0.304252i	0.764730	−	0.644351i	$-0.222873\pi$
$397$	−3.50000	−	6.06218i	−0.175660	−	0.304252i	−0.940389	+	0.340099i	$0.889539\pi$
$398$		0			0
$399$	−44.8434	−	4.13188i	−2.24498	−	0.206853i
$400$	6.00000	−	10.3923i	0.300000	−	0.519615i
$401$	−13.4722	−	7.77817i	−0.672769	−	0.388424i	0.124356	−	0.992238i	$-0.460314\pi$
$401$	−13.4722	−	7.77817i	−0.672769	−	0.388424i	−0.797125	+	0.603814i	$0.793647\pi$
$402$		0			0
$403$	3.12250	−	1.80278i	0.155543	−	0.0898027i
$404$		0			0
$405$	−25.1464	+	3.95691i	−1.24954	+	0.196621i
$406$		0			0
$407$	−4.49890	+	26.1488i	−0.223002	+	1.29615i
$408$		0			0
$409$	−9.36750	+	5.40833i	−0.463193	+	0.267425i	−0.713386	−	0.700771i	$-0.752839\pi$
$409$	−9.36750	+	5.40833i	−0.463193	+	0.267425i	0.250193	+	0.968196i	$0.419506\pi$
$410$		0			0
$411$	10.0000	+	7.07107i	0.493264	+	0.348790i
$412$	1.00000	+	1.73205i	0.0492665	+	0.0853320i
$413$	7.64853	−	13.2476i	0.376360	−	0.651874i
$414$		0			0
$415$			14.4222i			0.707958i
$416$		0			0
$417$	15.2971	+	10.8167i	0.749100	+	0.529694i
$418$		0			0
$419$	−1.22474	−	0.707107i	−0.0598327	−	0.0345444i	0.469785	−	0.882781i	$-0.344331\pi$
$419$	−1.22474	−	0.707107i	−0.0598327	−	0.0345444i	−0.529618	+	0.848236i	$0.677665\pi$
$420$	35.1780	+	3.24132i	1.71651	+	0.158160i
$421$	−5.00000			−0.243685			−0.121843	−	0.992549i	$-0.538880\pi$
$421$	−5.00000			−0.243685			−0.121843	+	0.992549i	$0.538880\pi$
$422$		0			0
$423$	22.5732	+	19.2990i	1.09755	+	0.938348i
$424$		0			0
$425$	7.64853	+	13.2476i	0.371008	+	0.642605i
$426$		0			0
$427$	6.50000	−	11.2583i	0.314557	−	0.544829i
$428$	−10.1980			−0.492941
$429$	20.0041	+	5.37001i	0.965806	+	0.259267i
$430$		0			0
$431$	−12.7475	+	22.0794i	−0.614028	+	1.06353i	0.376526	+	0.926406i	$0.377118\pi$
$431$	−12.7475	+	22.0794i	−0.614028	+	1.06353i	−0.990554	+	0.137121i	$0.956215\pi$
$432$	14.8990	−	14.4921i	0.716827	−	0.697251i
$433$	9.50000	+	16.4545i	0.456541	+	0.790752i	0.998775	−	0.0494752i	$-0.0157549\pi$
$433$	9.50000	+	16.4545i	0.456541	+	0.790752i	−0.542234	+	0.840227i	$0.682422\pi$
$434$		0			0
$435$	−2.29196	+	24.8746i	−0.109891	+	1.19265i
$436$	6.24500	−	3.60555i	0.299081	−	0.172675i
$437$	−10.1980			−0.487838
$438$		0			0
$439$	−15.6125	−	9.01388i	−0.745144	−	0.430209i	0.0787928	−	0.996891i	$-0.474893\pi$
$439$	−15.6125	−	9.01388i	−0.745144	−	0.430209i	−0.823937	+	0.566682i	$0.808227\pi$
$440$		0			0
$441$	6.00000	+	16.9706i	0.285714	+	0.808122i
$442$		0			0
$443$		−	2.82843i		−	0.134383i	−0.997740	−	0.0671913i	$-0.978596\pi$
$443$		−	2.82843i		−	0.134383i	0.997740	−	0.0671913i	$-0.0214038\pi$
$444$	−11.5959	−	25.1701i	−0.550318	−	1.19452i
$445$	−4.00000	+	6.92820i	−0.189618	+	0.328428i
$446$		0			0
$447$	−15.2971	+	21.6333i	−0.723526	+	1.02322i
$448$	−24.9800	+	14.4222i	−1.18019	+	0.681385i
$449$	30.6186	−	17.6777i	1.44498	−	0.834261i	0.446806	−	0.894631i	$-0.352561\pi$
$449$	30.6186	−	17.6777i	1.44498	−	0.834261i	0.998176	+	0.0603700i	$0.0192281\pi$
$450$		0			0
$451$	−5.73499	+	33.3333i	−0.270050	+	1.56960i
$452$	−22.0454	−	12.7279i	−1.03693	−	0.598671i
$453$	11.3440	−	5.22621i	0.532988	−	0.245549i
$454$		0			0
$455$	−31.8434	−	18.3848i	−1.49284	−	0.861892i
$456$		0			0
$457$	−28.1025	−	16.2250i	−1.31458	−	0.758973i	−0.331728	−	0.943375i	$-0.607632\pi$
$457$	−28.1025	−	16.2250i	−1.31458	−	0.758973i	−0.982851	+	0.184402i	$0.940965\pi$
$458$		0			0
$459$	6.50255	+	25.6850i	0.303513	+	1.19887i
$460$	8.00000			0.373002
$461$	12.7475	+	22.0794i	0.593713	+	1.02834i	0.993727	+	0.111832i	$0.0356717\pi$
$461$	12.7475	+	22.0794i	0.593713	+	1.02834i	−0.400015	+	0.916509i	$0.630995\pi$
$462$		0			0
$463$	−11.0000			−0.511213			−0.255607	−	0.966781i	$-0.582275\pi$
$463$	−11.0000			−0.511213			−0.255607	+	0.966781i	$0.582275\pi$
$464$	−10.1980	−	17.6635i	−0.473432	−	0.820008i
$465$	4.44949	−	2.04989i	0.206340	−	0.0950613i
$466$		0			0
$467$		0			0		1.00000			$0$
$467$		0			0		−1.00000			$\pi$
$468$	−20.3961	+	7.21110i	−0.942809	+	0.333333i
$469$		−	46.8722i		−	2.16436i
$470$		0			0
$471$	5.07321	+	11.0119i	0.233761	+	0.507403i
$472$		0			0
$473$	−7.64853	+	9.19239i	−0.351680	+	0.422666i
$474$		0			0
$475$	18.7350	−	10.8167i	0.859620	−	0.496302i
$476$		−	36.7696i		−	1.68533i
$477$	−9.67423	−	8.27098i	−0.442953	−	0.378702i
$478$		0			0
$479$	15.2971	−	26.4953i	0.698940	−	1.21060i	−0.269894	−	0.962890i	$-0.586989\pi$
$479$	15.2971	−	26.4953i	0.698940	−	1.21060i	0.968834	−	0.247710i	$-0.0796781\pi$
$480$		0			0
$481$			28.8444i			1.31519i
$482$		0			0
$483$	3.69549	+	8.02143i	0.168151	+	0.364988i
$484$	20.7350	+	7.35255i	0.942500	+	0.334207i
$485$	26.9444	−	15.5563i	1.22348	−	0.706377i
$486$		0			0
$487$	1.00000	+	1.73205i	0.0453143	+	0.0784867i	0.887793	−	0.460243i	$-0.152238\pi$
$487$	1.00000	+	1.73205i	0.0453143	+	0.0784867i	−0.842479	+	0.538730i	$0.818904\pi$
$488$		0			0
$489$	−11.0000	+	15.5563i	−0.497437	+	0.703482i
$490$		0			0
$491$	5.09902	−	8.83176i	0.230116	−	0.398572i	−0.727726	−	0.685868i	$-0.759423\pi$
$491$	5.09902	−	8.83176i	0.230116	−	0.398572i	0.957842	+	0.287296i	$0.0927563\pi$
$492$	−14.7820	−	32.0857i	−0.666422	−	1.44654i
$493$	26.0000			1.17098
$494$		0			0
$495$	26.3961	+	9.75946i	1.18642	+	0.438655i
$496$	−2.00000	+	3.46410i	−0.0898027	+	0.155543i
$497$	−5.09902	+	8.83176i	−0.228722	+	0.396159i
$498$		0			0
$499$	−10.0000			−0.447661			−0.223831	−	0.974628i	$-0.571856\pi$
$499$	−10.0000			−0.447661			−0.223831	+	0.974628i	$0.571856\pi$
$500$	9.79796	−	5.65685i	0.438178	−	0.252982i
$501$	−8.79451	−	0.810329i	−0.392910	−	0.0362028i
$502$		0			0
$503$	−12.7475	−	22.0794i	−0.568385	−	0.984472i	−0.996726	−	0.0808546i	$-0.974235\pi$
$503$	−12.7475	−	22.0794i	−0.568385	−	0.984472i	0.428341	−	0.903617i	$-0.359098\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	22.4217	+	2.06594i	0.995782	+	0.0917517i
$508$		−	7.21110i		−	0.319941i
$509$	35.5176	+	20.5061i	1.57429	+	0.908917i	0.995634	+	0.0933452i	$0.0297560\pi$
$509$	35.5176	+	20.5061i	1.57429	+	0.908917i	0.578656	+	0.815572i	$0.303577\pi$
$510$		0			0
$511$	−19.5000	−	33.7750i	−0.862629	−	1.49412i
$512$		0			0
$513$	36.3240	−	9.19600i	1.60374	−	0.406013i
$514$		0			0
$515$		−	2.82843i		−	0.124635i
$516$	1.14598	−	12.4373i	0.0504489	−	0.547522i
$517$	−11.3575	−	30.8060i	−0.499502	−	1.35484i
$518$		0			0
$519$	10.1980	−	14.4222i	0.447644	−	0.633065i
$520$		0			0
$521$		−	18.3848i		−	0.805452i	−0.915321	−	0.402726i	$-0.868063\pi$
$521$		−	18.3848i		−	0.805452i	0.915321	−	0.402726i	$-0.131937\pi$
$522$		0			0
$523$	31.2250	+	18.0278i	1.36537	+	0.788299i	0.990333	−	0.138710i	$-0.0442955\pi$
$523$	31.2250	+	18.0278i	1.36537	+	0.788299i	0.375040	+	0.927008i	$0.377629\pi$
$524$	−20.3961	−	35.3270i	−0.891007	−	1.54327i
$525$	−15.2971	−	10.8167i	−0.667618	−	0.472077i
$526$		0			0
$527$	−2.54951	−	4.41588i	−0.111058	−	0.192359i
$528$	−22.1980	+	5.93692i	−0.966046	+	0.258371i
$529$	−10.5000	−	18.1865i	−0.456522	−	0.790719i
$530$		0			0
$531$	−2.32577	+	12.5136i	−0.100930	+	0.543045i
$532$	−52.0000			−2.25449
$533$			36.7696i			1.59267i
$534$		0			0
$535$	12.4900	+	7.21110i	0.539990	+	0.311763i
$536$		0			0
$537$	−2.24745	+	24.3916i	−0.0969846	+	1.05257i
$538$		0			0
$539$	3.37417	−	19.6116i	0.145336	−	0.844732i
$540$	−28.4949	+	7.21393i	−1.22623	+	0.310438i
$541$			10.8167i			0.465044i	0.972591	+	0.232522i	$0.0746978\pi$
$541$			10.8167i			0.465044i	−0.972591	+	0.232522i	$0.925302\pi$
$542$		0			0
$543$	17.3939	+	37.7552i	0.746443	+	1.62023i
$544$		0			0
$545$	−10.1980			−0.436836
$546$		0			0
$547$			25.2389i			1.07914i	0.841942	+	0.539568i	$0.181412\pi$
$547$			25.2389i			1.07914i	−0.841942	+	0.539568i	$0.818588\pi$
$548$	12.2474	+	7.07107i	0.523185	+	0.302061i
$549$	−1.97652	+	10.6345i	−0.0843558	+	0.453871i
$550$		0			0
$551$		−	36.7696i		−	1.56644i
$552$		0			0
$553$	6.50000	+	11.2583i	0.276408	+	0.478753i
$554$		0			0
$555$	−3.59592	+	39.0265i	−0.152638	+	1.65658i
$556$	18.7350	+	10.8167i	0.794541	+	0.458728i
$557$	2.54951	−	4.41588i	0.108026	−	0.187107i	−0.806944	−	0.590627i	$-0.798880\pi$
$557$	2.54951	−	4.41588i	0.108026	−	0.187107i	0.914971	+	0.403521i	$0.132214\pi$
$558$		0			0
$559$	−6.50000	+	11.2583i	−0.274921	+	0.476177i
$560$	40.7922			1.72378
$561$	7.59434	−	28.2900i	0.320633	−	1.19441i
$562$		0			0
$563$	−15.2971	−	26.4953i	−0.644694	−	1.11664i	−0.984372	−	0.176101i	$-0.943651\pi$
$563$	−15.2971	−	26.4953i	−0.644694	−	1.11664i	0.339678	−	0.940542i	$-0.389682\pi$
$564$	28.0000	+	19.7990i	1.17901	+	0.833688i
$565$	18.0000	+	31.1769i	0.757266	+	1.31162i
$566$		0			0
$567$	−20.3961	−	25.2389i	−0.856555	−	1.05993i
$568$		0			0
$569$	−20.3961	+	35.3270i	−0.855048	+	1.48099i	0.0215523	+	0.999768i	$0.493139\pi$
$569$	−20.3961	+	35.3270i	−0.855048	+	1.48099i	−0.876600	+	0.481219i	$0.840194\pi$
$570$		0			0
$571$		−	14.4222i		−	0.603550i	−0.953379	−	0.301775i	$-0.902421\pi$
$571$		−	14.4222i		−	0.603550i	0.953379	−	0.301775i	$-0.0975792\pi$
$572$	23.5702	+	4.05525i	0.985520	+	0.169559i
$573$	−14.0000	−	9.89949i	−0.584858	−	0.413557i
$574$		0			0
$575$	−3.67423	−	2.12132i	−0.153226	−	0.0884652i
$576$	15.5959	−	18.2419i	0.649830	−	0.760080i
$577$	12.0000			0.499567			0.249783	−	0.968302i	$-0.419641\pi$
$577$	12.0000			0.499567			0.249783	+	0.968302i	$0.419641\pi$
$578$		0			0
$579$	−0.572989	+	6.21866i	−0.0238126	+	0.258439i
$580$			28.8444i			1.19770i
$581$	−15.9217	+	9.19239i	−0.660543	+	0.381365i
$582$		0			0
$583$	4.86750	+	13.2026i	0.201591	+	0.546794i
$584$		0			0
$585$	30.0790	+	5.59044i	1.24361	+	0.231136i
$586$		0			0
$587$	−8.57321	−	4.94975i	−0.353854	−	0.204298i	0.312527	−	0.949909i	$-0.398824\pi$
$587$	−8.57321	−	4.94975i	−0.353854	−	0.204298i	−0.666382	+	0.745611i	$0.732158\pi$
$588$	8.69694	+	18.8776i	0.358656	+	0.778499i
$589$	−6.24500	+	3.60555i	−0.257321	+	0.148564i
$590$		0			0
$591$	35.1780	+	3.24132i	1.44703	+	0.133330i
$592$	−16.0000	−	27.7128i	−0.657596	−	1.13899i
$593$	45.8912			1.88452			0.942262	−	0.334876i	$-0.108694\pi$
$593$	45.8912			1.88452			0.942262	+	0.334876i	$0.108694\pi$
$594$		0			0
$595$	−26.0000	+	45.0333i	−1.06590	+	1.84619i
$596$	−15.2971	+	26.4953i	−0.626592	+	1.08529i
$597$	1.00000	−	1.41421i	0.0409273	−	0.0578799i
$598$		0			0
$599$		−	45.2548i		−	1.84906i	−0.381106	−	0.924531i	$-0.624457\pi$
$599$		−	45.2548i		−	1.84906i	0.381106	−	0.924531i	$-0.375543\pi$
$600$		0			0
$601$	−37.4700	−	21.6333i	−1.52843	−	0.882441i	−0.999428	−	0.0338222i	$-0.989232\pi$
$601$	−37.4700	−	21.6333i	−1.52843	−	0.882441i	−0.529005	−	0.848619i	$-0.677435\pi$
$602$		0			0
$603$	13.0000	+	36.7696i	0.529401	+	1.49737i
$604$	12.4900	−	7.21110i	0.508211	−	0.293416i
$605$	−20.1960	−	23.6669i	−0.821086	−	0.962195i
$606$		0			0
$607$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$607$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$608$		0			0
$609$	−28.9217	+	13.3243i	−1.17197	+	0.539927i
$610$		0			0
$611$	−17.8466	−	30.9112i	−0.721995	−	1.25053i
$612$	10.1980	+	28.8444i	0.412231	+	1.16597i
$613$	34.3475	+	19.8305i	1.38728	+	0.800948i	0.993008	−	0.118045i	$-0.0376628\pi$
$613$	34.3475	+	19.8305i	1.38728	+	0.800948i	0.394274	+	0.918993i	$0.370996\pi$
$614$		0			0
$615$	−4.58391	+	49.7492i	−0.184841	+	2.00608i
$616$		0			0
$617$	18.3712	−	10.6066i	0.739596	−	0.427006i	−0.0823267	−	0.996605i	$-0.526235\pi$
$617$	18.3712	−	10.6066i	0.739596	−	0.427006i	0.821922	+	0.569600i	$0.192902\pi$
$618$		0			0
$619$	31.0000			1.24600			0.622998	−	0.782224i	$-0.285915\pi$
$619$	31.0000			1.24600			0.622998	+	0.782224i	$0.285915\pi$
$620$	4.89898	−	2.82843i	0.196748	−	0.113592i
$621$	−5.12372	−	5.26758i	−0.205608	−	0.211381i
$622$		0			0
$623$	−10.1980			−0.408576
$624$	−22.6880	+	10.4524i	−0.908248	+	0.418432i
$625$	−31.0000			−1.24000
$626$		0			0
$627$	−40.0081	−	10.7400i	−1.59777	−	0.428915i
$628$	7.00000	+	12.1244i	0.279330	+	0.483814i
$629$	40.7922			1.62649
$630$		0			0
$631$	−14.5000	−	25.1147i	−0.577236	−	0.999802i	−0.995795	−	0.0916122i	$-0.970798\pi$
$631$	−14.5000	−	25.1147i	−0.577236	−	0.999802i	0.418559	−	0.908190i	$-0.362535\pi$
$632$		0			0
$633$	2.86495	−	31.0933i	0.113871	−	1.23585i
$634$		0			0
$635$	−5.09902	+	8.83176i	−0.202348	+	0.350478i
$636$	−12.0000	−	8.48528i	−0.475831	−	0.336463i
$637$		−	21.6333i		−	0.857143i
$638$		0			0
$639$	1.55051	−	8.34242i	0.0613372	−	0.330021i
$640$		0			0
$641$	−30.6186	+	17.6777i	−1.20936	+	0.698226i	−0.962620	−	0.270855i	$-0.912694\pi$
$641$	−30.6186	+	17.6777i	−1.20936	+	0.698226i	−0.246743	+	0.969081i	$0.579360\pi$
$642$		0			0
$643$	−1.50000	−	2.59808i	−0.0591542	−	0.102458i	0.834932	−	0.550353i	$-0.185507\pi$
$643$	−1.50000	−	2.59808i	−0.0591542	−	0.102458i	−0.894086	+	0.447895i	$0.852174\pi$
$644$	5.09902	+	8.83176i	0.200930	+	0.348020i
$645$	−10.1980	+	14.4222i	−0.401547	+	0.567874i
$646$		0			0
$647$	31.8434	+	18.3848i	1.25189	+	0.722780i	0.971485	−	0.237101i	$-0.0761973\pi$
$647$	31.8434	+	18.3848i	1.25189	+	0.722780i	0.280407	+	0.959881i	$0.409531\pi$
$648$		0			0
$649$	9.00000	−	10.8167i	0.353281	−	0.424591i
$650$		0			0
$651$	5.09902	+	3.60555i	0.199846	+	0.141313i
$652$	−11.0000	+	19.0526i	−0.430793	+	0.746156i
$653$	13.4722	+	7.77817i	0.527208	+	0.304383i	0.739879	−	0.672740i	$-0.234883\pi$
$653$	13.4722	+	7.77817i	0.527208	+	0.304383i	−0.212671	+	0.977124i	$0.568216\pi$
$654$		0			0
$655$			57.6888i			2.25409i
$656$	−20.3961	−	35.3270i	−0.796333	−	1.37929i
$657$	24.6646	+	21.0870i	0.962256	+	0.822680i
$658$		0			0
$659$	5.09902	+	8.83176i	0.198630	+	0.344037i	0.948084	−	0.318019i	$-0.103018\pi$
$659$	5.09902	+	8.83176i	0.198630	+	0.344037i	−0.749455	+	0.662056i	$0.769684\pi$
$660$	31.3850	+	8.42517i	1.22166	+	0.327949i
$661$	−6.50000	+	11.2583i	−0.252821	+	0.437898i	−0.964301	−	0.264807i	$-0.914692\pi$
$661$	−6.50000	+	11.2583i	−0.252821	+	0.437898i	0.711481	+	0.702706i	$0.248025\pi$
$662$		0			0
$663$	2.92168	−	31.7090i	0.113469	−	1.23148i
$664$		0			0
$665$	63.6867	+	36.7696i	2.46967	+	1.42586i
$666$		0			0
$667$	−6.24500	+	3.60555i	−0.241807	+	0.139608i
$668$	−10.1980			−0.394574
$669$	−10.3485	−	0.953512i	−0.400095	−	0.0368649i
$670$		0			0
$671$	7.64853	−	9.19239i	0.295268	−	0.354868i
$672$		0			0
$673$	−9.36750	−	5.40833i	−0.361090	−	0.208476i	0.308469	−	0.951235i	$-0.400184\pi$
$673$	−9.36750	−	5.40833i	−0.361090	−	0.208476i	−0.669559	+	0.742759i	$0.733517\pi$
$674$		0			0
$675$	15.0000	+	4.24264i	0.577350	+	0.163299i
$676$	26.0000			1.00000
$677$	−5.09902			−0.195971			−0.0979856	−	0.995188i	$-0.531240\pi$
$677$	−5.09902			−0.195971			−0.0979856	+	0.995188i	$0.531240\pi$
$678$		0			0
$679$	34.3475	+	19.8305i	1.31814	+	0.761026i
$680$		0			0
$681$	−10.1980	+	14.4222i	−0.390790	+	0.552660i
$682$		0			0
$683$	−19.5959	+	11.3137i	−0.749817	+	0.432907i	−0.825628	−	0.564215i	$-0.809179\pi$
$683$	−19.5959	+	11.3137i	−0.749817	+	0.432907i	0.0758108	+	0.997122i	$0.475845\pi$
$684$	40.7922	−	14.4222i	1.55973	−	0.551447i
$685$	−10.0000	−	17.3205i	−0.382080	−	0.661783i
$686$		0			0
$687$	−20.2929	−	44.0477i	−0.774221	−	1.68052i
$688$		−	14.4222i		−	0.549841i
$689$	7.64853	+	13.2476i	0.291386	+	0.504695i
$690$		0			0
$691$	−13.5000	+	23.3827i	−0.513564	+	0.889519i	0.486312	+	0.873785i	$0.338342\pi$
$691$	−13.5000	+	23.3827i	−0.513564	+	0.889519i	−0.999876	+	0.0157341i	$0.994991\pi$
$692$	10.1980	−	17.6635i	0.387671	−	0.671466i
$693$	6.05011	+	35.3609i	0.229825	+	1.34325i
$694$		0			0
$695$	−15.2971	−	26.4953i	−0.580251	−	1.00502i
$696$		0			0
$697$	52.0000			1.96964
$698$		0			0
$699$	11.0865	+	24.0643i	0.419329	+	0.910195i
$700$	−18.7350	−	10.8167i	−0.708116	−	0.408831i
$701$	−15.2971			−0.577762			−0.288881	−	0.957365i	$-0.593283\pi$
$701$	−15.2971			−0.577762			−0.288881	+	0.957365i	$0.593283\pi$
$702$		0			0
$703$		−	57.6888i		−	2.17578i
$704$	−24.8950	+	9.17824i	−0.938265	+	0.345918i
$705$	−20.2929	−	44.0477i	−0.764273	−	1.65893i
$706$		0			0
$707$		0			0
$708$	−1.34847	+	14.6349i	−0.0506786	+	0.550015i
$709$	14.5000	+	25.1147i	0.544559	+	0.943204i	0.998635	+	0.0522406i	$0.0166363\pi$
$709$	14.5000	+	25.1147i	0.544559	+	0.943204i	−0.454076	+	0.890963i	$0.650030\pi$
$710$		0			0
$711$	−8.22152	−	7.02899i	−0.308331	−	0.263608i
$712$		0			0
$713$	1.22474	+	0.707107i	0.0458671	+	0.0264814i
$714$		0			0
$715$	−26.0000	−	21.6333i	−0.972345	−	0.809040i
$716$			28.2843i			1.05703i
$717$	3.69549	+	8.02143i	0.138011	+	0.299566i
$718$		0			0
$719$	23.2702	−	13.4350i	0.867830	−	0.501042i	0.00120365	−	0.999999i	$-0.499617\pi$
$719$	23.2702	−	13.4350i	0.867830	−	0.501042i	0.866627	+	0.498957i	$0.166284\pi$
$720$	−32.0000	+	11.3137i	−1.19257	+	0.421637i
$721$	3.12250	−	1.80278i	0.116288	−	0.0671389i
$722$		0			0
$723$	−10.1980	−	7.21110i	−0.379269	−	0.268184i
$724$	24.0000	+	41.5692i	0.891953	+	1.54491i
$725$	7.64853	−	13.2476i	0.284059	−	0.492005i
$726$		0			0
$727$	11.0000			0.407967			0.203984	−	0.978974i	$-0.434611\pi$
$727$	11.0000			0.407967			0.203984	+	0.978974i	$0.434611\pi$
$728$		0			0
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$		0			0
$731$	15.9217	+	9.19239i	0.588885	+	0.339993i
$732$	−1.14598	+	12.4373i	−0.0423566	+	0.459696i
$733$			3.60555i			0.133174i	0.997781	+	0.0665870i	$0.0212110\pi$
$733$			3.60555i			0.133174i	−0.997781	+	0.0665870i	$0.978789\pi$
$734$		0			0
$735$	2.69694	−	29.2699i	0.0994781	−	1.07964i
$736$		0			0
$737$	7.31071	−	42.4918i	0.269294	−	1.56521i
$738$		0			0
$739$	−12.4900	−	7.21110i	−0.459452	−	0.265265i	0.252362	−	0.967633i	$-0.418793\pi$
$739$	−12.4900	−	7.21110i	−0.459452	−	0.265265i	−0.711814	+	0.702368i	$0.752126\pi$
$740$			45.2548i			1.66360i
$741$	−44.8434	−	4.13188i	−1.64736	−	0.151789i
$742$		0			0
$743$	10.1980	−	17.6635i	0.374130	−	0.648012i	−0.616067	−	0.787694i	$-0.711275\pi$
$743$	10.1980	−	17.6635i	0.374130	−	0.648012i	0.990196	+	0.139682i	$0.0446081\pi$
$744$		0			0
$745$	37.4700	−	21.6333i	1.37279	−	0.792583i
$746$		0			0
$747$	9.94049	−	11.6270i	0.363703	−	0.425409i
$748$	5.73499	−	33.3333i	0.209692	−	1.21879i
$749$			18.3848i			0.671765i
$750$		0			0
$751$	−2.00000	+	3.46410i	−0.0729810	+	0.126407i	−0.900207	−	0.435463i	$-0.856585\pi$
$751$	−2.00000	+	3.46410i	−0.0729810	+	0.126407i	0.827225	+	0.561870i	$0.189918\pi$
$752$	34.2929	+	19.7990i	1.25053	+	0.721995i
$753$	−14.0000	−	9.89949i	−0.510188	−	0.360758i
$754$		0			0
$755$	−20.3961			−0.742289
$756$	−26.1260	−	26.8595i	−0.950192	−	0.976871i
$757$	14.0000	−	24.2487i	0.508839	−	0.881334i	−0.491109	−	0.871098i	$-0.663408\pi$
$757$	14.0000	−	24.2487i	0.508839	−	0.881334i	0.999948	−	0.0102362i	$-0.00325836\pi$
$758$		0			0
$759$	2.09902	+	7.84819i	0.0761896	+	0.284871i
$760$		0			0
$761$	12.7475	+	22.0794i	0.462098	+	0.800378i	0.999065	−	0.0432255i	$-0.0137634\pi$
$761$	12.7475	+	22.0794i	0.462098	+	0.800378i	−0.536967	+	0.843603i	$0.680430\pi$
$762$		0			0
$763$	−6.50000	−	11.2583i	−0.235316	−	0.407579i
$764$	−17.1464	−	9.89949i	−0.620336	−	0.358151i
$765$	7.90608	−	42.5381i	0.285845	−	1.53797i
$766$		0			0
$767$	7.64853	−	13.2476i	0.276172	−	0.478345i
$768$	16.0000	−	22.6274i	0.577350	−	0.816497i
$769$	12.4900	+	7.21110i	0.450401	+	0.260039i	0.707999	−	0.706213i	$-0.249598\pi$
$769$	12.4900	+	7.21110i	0.450401	+	0.260039i	−0.257599	+	0.966252i	$0.582931\pi$
$770$		0			0
$771$	2.24745	−	24.3916i	0.0809399	−	0.878441i
$772$			7.21110i			0.259533i
$773$	17.1464	−	9.89949i	0.616714	−	0.356060i	−0.158874	−	0.987299i	$-0.550787\pi$
$773$	17.1464	−	9.89949i	0.616714	−	0.356060i	0.775589	+	0.631239i	$0.217453\pi$
$774$		0			0
$775$	−3.00000			−0.107763
$776$		0			0
$777$	−45.3761	+	20.9048i	−1.62786	+	0.749957i
$778$		0			0
$779$		−	73.5391i		−	2.63481i
$780$	35.1780	+	3.24132i	1.25958	+	0.116058i
$781$	−6.00000	+	7.21110i	−0.214697	+	0.258034i
$782$		0			0
$783$	18.9925	−	18.4739i	0.678738	−	0.660202i
$784$	12.0000	+	20.7846i	0.428571	+	0.742307i
$785$		−	19.7990i		−	0.706656i
$786$		0			0
$787$	9.36750	−	5.40833i	0.333915	−	0.192786i	−0.323663	−	0.946172i	$-0.604914\pi$
$787$	9.36750	−	5.40833i	0.333915	−	0.192786i	0.657578	+	0.753386i	$0.271581\pi$
$788$	40.7922			1.45316
$789$	−26.3835	−	2.43099i	−0.939278	−	0.0865454i
$790$		0			0
$791$	−22.9456	+	39.7429i	−0.815851	+	1.41310i
$792$		0			0
$793$	6.50000	−	11.2583i	0.230822	−	0.399795i
$794$		0			0
$795$	8.69694	+	18.8776i	0.308449	+	0.669519i
$796$	1.00000	−	1.73205i	0.0354441	−	0.0613909i
$797$	−11.0227	+	6.36396i	−0.390444	+	0.225423i	−0.682353	−	0.731023i	$-0.739043\pi$
$797$	−11.0227	+	6.36396i	−0.390444	+	0.225423i	0.291908	+	0.956446i	$0.405710\pi$
$798$		0			0
$799$	−43.7150	+	25.2389i	−1.54653	+	0.892887i
$800$		0			0
$801$	8.00000	−	2.82843i	0.282666	−	0.0999376i
$802$		0			0
$803$	−12.4097	−	33.6600i	−0.437930	−	1.18784i
$804$	18.8434	+	40.9014i	0.664554	+	1.44248i
$805$		−	14.4222i		−	0.508316i
$806$		0			0
$807$	16.0000	+	11.3137i	0.563227	+	0.398261i
$808$		0			0
$809$	20.3961	−	35.3270i	0.717088	−	1.24203i	−0.245061	−	0.969508i	$-0.578808\pi$
$809$	20.3961	−	35.3270i	0.717088	−	1.24203i	0.962149	−	0.272525i	$-0.0878587\pi$
$810$		0			0
$811$		−	10.8167i		−	0.379824i	−0.981801	−	0.189912i	$-0.939180\pi$
$811$		−	10.8167i		−	0.379824i	0.981801	−	0.189912i	$-0.0608203\pi$
$812$	−31.8434	+	18.3848i	−1.11748	+	0.645179i
$813$	0.572989	−	6.21866i	0.0200956	−	0.218098i
$814$		0			0
$815$	26.9444	−	15.5563i	0.943821	−	0.544915i
$816$	14.7820	+	32.0857i	0.517472	+	1.12323i
$817$	13.0000	−	22.5167i	0.454812	−	0.787758i
$818$		0			0
$819$	13.0000	+	36.7696i	0.454257	+	1.28483i
$820$			57.6888i			2.01458i
$821$	−15.2971	+	26.4953i	−0.533871	+	0.924692i	0.465346	+	0.885129i	$0.345930\pi$
$821$	−15.2971	+	26.4953i	−0.533871	+	0.924692i	−0.999217	+	0.0395629i	$0.987403\pi$
$822$		0			0
$823$	3.00000	+	5.19615i	0.104573	+	0.181126i	0.913564	−	0.406695i	$-0.133319\pi$
$823$	3.00000	+	5.19615i	0.104573	+	0.181126i	−0.808990	+	0.587822i	$0.799986\pi$
$824$		0			0
$825$	−12.1804	−	12.1917i	−0.424067	−	0.424461i
$826$		0			0
$827$	−15.2971			−0.531931			−0.265965	−	0.963983i	$-0.585691\pi$
$827$	−15.2971			−0.531931			−0.265965	+	0.963983i	$0.585691\pi$
$828$	−6.44949	−	5.51399i	−0.224135	−	0.191624i
$829$	−17.5000	+	30.3109i	−0.607800	+	1.05274i	0.383802	+	0.923415i	$0.374614\pi$
$829$	−17.5000	+	30.3109i	−0.607800	+	1.05274i	−0.991602	+	0.129325i	$0.958719\pi$
$830$		0			0
$831$	−20.3961	−	14.4222i	−0.707532	−	0.500301i
$832$	−24.9800	+	14.4222i	−0.866025	+	0.500000i
$833$	−30.5941			−1.06002
$834$		0			0
$835$	12.4900	+	7.21110i	0.432234	+	0.249550i
$836$	−47.1404	−	8.11051i	−1.63039	−	0.280508i
$837$	−5.00000	−	1.41421i	−0.172825	−	0.0488824i
$838$		0			0
$839$	26.9444	−	15.5563i	0.930224	−	0.537065i	0.0433413	−	0.999060i	$-0.486200\pi$
$839$	26.9444	−	15.5563i	0.930224	−	0.537065i	0.886882	+	0.461996i	$0.152866\pi$
$840$		0			0
$841$	1.50000	+	2.59808i	0.0517241	+	0.0895888i
$842$		0			0
$843$	18.4774	+	40.1072i	0.636397	+	1.38136i
$844$		−	36.0555i		−	1.24108i
$845$	−31.8434	−	18.3848i	−1.09545	−	0.632456i
$846$		0			0
$847$	13.2550	−	37.3805i	0.455447	−	1.28441i
$848$	−14.6969	−	8.48528i	−0.504695	−	0.291386i
$849$	−2.86495	+	31.0933i	−0.0983247	+	1.06712i
$850$		0			0
$851$	−9.79796	+	5.65685i	−0.335870	+	0.193914i
$852$	0.898979	−	9.75663i	0.0307985	−	0.334257i
$853$			25.2389i			0.864162i	0.901835	+	0.432081i	$0.142221\pi$
$853$			25.2389i			0.864162i	−0.901835	+	0.432081i	$0.857779\pi$
$854$		0			0
$855$	−60.1580	−	11.1809i	−2.05736	−	0.382378i
$856$		0			0
$857$	20.3961			0.696717			0.348358	−	0.937361i	$-0.386739\pi$
$857$	20.3961			0.696717			0.348358	+	0.937361i	$0.386739\pi$
$858$		0			0
$859$	23.0000			0.784750			0.392375	−	0.919805i	$-0.371654\pi$
$859$	23.0000			0.784750			0.392375	+	0.919805i	$0.371654\pi$
$860$	−10.1980	+	17.6635i	−0.347750	+	0.602321i
$861$	−57.8434	+	26.6485i	−1.97130	+	0.908180i
$862$		0			0
$863$		−	33.9411i		−	1.15537i	−0.816260	−	0.577685i	$-0.803956\pi$
$863$		−	33.9411i		−	1.15537i	0.816260	−	0.577685i	$-0.196044\pi$
$864$		0			0
$865$	−24.9800	+	14.4222i	−0.849345	+	0.490370i
$866$		0			0
$867$	−15.5227	−	1.43027i	−0.527179	−	0.0485744i
$868$	6.24500	+	3.60555i	0.211969	+	0.122380i
$869$	4.13658	+	11.2200i	0.140324	+	0.380613i
$870$		0			0
$871$		−	46.8722i		−	1.58820i
$872$		0			0
$873$	−32.4444	−	6.03007i	−1.09808	−	0.204087i
$874$		0			0
$875$	−10.1980	−	17.6635i	−0.344757	−	0.597136i
$876$	30.5941	+	21.6333i	1.03368	+	0.730922i
$877$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$877$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$878$		0			0
$879$	−15.2971	+	21.6333i	−0.515957	+	0.729673i
$880$	36.9800	+	6.36240i	1.24660	+	0.214477i
$881$	28.1691	+	16.2635i	0.949042	+	0.547930i	0.892783	−	0.450486i	$-0.148749\pi$
$881$	28.1691	+	16.2635i	0.949042	+	0.547930i	0.0562589	+	0.998416i	$0.482083\pi$
$882$		0			0
$883$	−27.0000			−0.908622			−0.454311	−	0.890843i	$-0.650115\pi$
$883$	−27.0000			−0.908622			−0.454311	+	0.890843i	$0.650115\pi$
$884$		−	36.7696i		−	1.23669i
$885$	12.0000	−	16.9706i	0.403376	−	0.570459i
$886$		0			0
$887$	−28.0446	+	48.5747i	−0.941646	+	1.63098i	−0.179314	+	0.983792i	$0.557388\pi$
$887$	−28.0446	+	48.5747i	−0.941646	+	1.63098i	−0.762332	+	0.647186i	$0.775946\pi$
$888$		0			0
$889$	−13.0000			−0.436006
$890$		0			0
$891$	−14.5535	−	26.0614i	−0.487559	−	0.873090i
$892$	−12.0000			−0.401790
$893$	35.6931	+	61.8223i	1.19443	+	2.06881i
$894$		0			0
$895$	20.0000	−	34.6410i	0.668526	−	1.15792i
$896$		0			0
$897$	3.69549	+	8.02143i	0.123389	+	0.267828i
$898$		0			0
$899$	−2.54951	+	4.41588i	−0.0850309	+	0.147278i
$900$	17.6969	+	3.28913i	0.589898	+	0.109638i
$901$	18.7350	−	10.8167i	0.624153	−	0.360355i
$902$		0			0
$903$	−22.4217	−	2.06594i	−0.746147	−	0.0687502i
$904$		0			0
$905$		−	67.8823i		−	2.25648i
$906$		0			0
$907$	−21.0000	+	36.3731i	−0.697294	+	1.20775i	0.272108	+	0.962267i	$0.412279\pi$
$907$	−21.0000	+	36.3731i	−0.697294	+	1.20775i	−0.969401	+	0.245481i	$0.921054\pi$
$908$	−10.1980	+	17.6635i	−0.338434	+	0.586185i
$909$		0			0
$910$		0			0
$911$			2.82843i			0.0937100i	0.998902	+	0.0468550i	$0.0149199\pi$
$911$			2.82843i			0.0937100i	−0.998902	+	0.0468550i	$0.985080\pi$
$912$	45.3761	−	20.9048i	1.50255	−	0.692228i
$913$	−15.8675	+	5.85000i	−0.525138	+	0.193607i
$914$		0			0
$915$	10.1980	−	14.4222i	0.337137	−	0.476783i
$916$	−28.0000	−	48.4974i	−0.925146	−	1.60240i
$917$	−63.6867	+	36.7696i	−2.10312	+	1.21424i
$918$		0			0
$919$	−43.7150	+	25.2389i	−1.44202	+	0.832553i	−0.997985	−	0.0634540i	$-0.979788\pi$
$919$	−43.7150	+	25.2389i	−1.44202	+	0.832553i	−0.444040	+	0.896007i	$0.646455\pi$
$920$		0			0
$921$	17.0160	−	7.83931i	0.560697	−	0.258314i
$922$		0			0
$923$	−5.09902	+	8.83176i	−0.167836	+	0.290701i
$924$	10.7029	+	40.0181i	0.352101	+	1.31650i
$925$	12.0000	−	20.7846i	0.394558	−	0.683394i
$926$		0			0
$927$	−1.94949	+	2.28024i	−0.0640296	+	0.0748929i
$928$		0			0
$929$	−39.1918	+	22.6274i	−1.28584	+	0.742381i	−0.977910	−	0.209027i	$-0.932970\pi$
$929$	−39.1918	+	22.6274i	−1.28584	+	0.742381i	−0.307932	+	0.951408i	$0.599637\pi$
$930$		0			0
$931$			43.2666i			1.41801i
$932$	15.2971	+	26.4953i	0.501072	+	0.867882i
$933$	22.2474	−	10.2494i	0.728349	−	0.335552i
$934$		0			0
$935$	−30.5941	+	36.7696i	−1.00053	+	1.20249i
$936$		0			0
$937$			21.6333i			0.706729i	0.935486	+	0.353365i	$0.114963\pi$
$937$			21.6333i			0.706729i	−0.935486	+	0.353365i	$0.885037\pi$
$938$		0			0
$939$	−3.62372	−	7.86566i	−0.118256	−	0.256686i
$940$	−28.0000	−	48.4974i	−0.913259	−	1.58181i
$941$	40.7922			1.32979			0.664893	−	0.746938i	$-0.268477\pi$
$941$	40.7922			1.32979			0.664893	+	0.746938i	$0.268477\pi$
$942$		0			0
$943$	−12.4900	+	7.21110i	−0.406730	+	0.234826i
$944$			16.9706i			0.552345i
$945$	13.0051	+	51.3699i	0.423056	+	1.67106i
$946$		0			0
$947$	−14.6969	−	8.48528i	−0.477586	−	0.275735i	0.241824	−	0.970320i	$-0.422254\pi$
$947$	−14.6969	−	8.48528i	−0.477586	−	0.275735i	−0.719410	+	0.694586i	$0.755588\pi$
$948$	−10.1980	−	7.21110i	−0.331217	−	0.234206i
$949$	−19.5000	−	33.7750i	−0.632997	−	1.09638i
$950$		0			0
$951$	11.1237	−	5.12472i	0.360711	−	0.166180i
$952$		0			0
$953$	−2.54951	−	4.41588i	−0.0825867	−	0.143044i	0.821774	−	0.569814i	$-0.192985\pi$
$953$	−2.54951	−	4.41588i	−0.0825867	−	0.143044i	−0.904360	+	0.426770i	$0.859651\pi$
$954$		0			0
$955$	14.0000	+	24.2487i	0.453029	+	0.784670i
$956$	5.09902	+	8.83176i	0.164914	+	0.285640i
$957$	−28.2971	+	7.56812i	−0.914714	+	0.244643i
$958$		0			0
$959$	12.7475	−	22.0794i	0.411640	−	0.712981i
$960$	−35.5959	+	16.3991i	−1.14885	+	0.529279i
$961$	−30.0000			−0.967742
$962$		0			0
$963$	−5.09902	−	14.4222i	−0.164314	−	0.464749i
$964$	−12.4900	−	7.21110i	−0.402276	−	0.232254i
$965$	5.09902	−	8.83176i	0.164143	−	0.284304i
$966$		0			0
$967$		−	50.4777i		−	1.62325i	−0.584176	−	0.811627i	$-0.698582\pi$
$967$		−	50.4777i		−	1.62325i	0.584176	−	0.811627i	$-0.301418\pi$
$968$		0			0
$969$	−5.84337	+	63.4181i	−0.187716	+	2.03728i
$970$		0			0
$971$	−31.8434	+	18.3848i	−1.02190	+	0.589996i	−0.914654	−	0.404237i	$-0.867537\pi$
$971$	−31.8434	+	18.3848i	−1.02190	+	0.589996i	−0.107248	+	0.994232i	$0.534204\pi$
$972$	27.9444	+	13.8243i	0.896317	+	0.443415i
$973$	19.5000	−	33.7750i	0.625141	−	1.08278i
$974$		0			0
$975$	−15.2971	−	10.8167i	−0.489898	−	0.346410i
$976$			14.4222i			0.461644i
$977$	−9.79796	−	5.65685i	−0.313464	−	0.180979i	0.335011	−	0.942214i	$-0.391260\pi$
$977$	−9.79796	−	5.65685i	−0.313464	−	0.180979i	−0.648476	+	0.761235i	$0.724593\pi$
$978$		0			0
$979$	−9.24500	−	1.59060i	−0.295471	−	0.0508358i
$980$		−	33.9411i		−	1.08421i
$981$	8.22152	+	7.02899i	0.262493	+	0.224418i
$982$		0			0
$983$			28.2843i			0.902128i	0.892492	+	0.451064i	$0.148955\pi$
$983$			28.2843i			0.902128i	−0.892492	+	0.451064i	$0.851045\pi$
$984$		0			0
$985$	−49.9600	−	28.8444i	−1.59186	−	0.919059i
$986$		0			0
$987$	35.6931	−	50.4777i	1.13613	−	1.60672i
$988$	−52.0000			−1.65434
$989$	−5.09902			−0.162139
$990$		0			0
$991$	7.00000	−	12.1244i	0.222362	−	0.385143i	−0.733163	−	0.680053i	$-0.761957\pi$
$991$	7.00000	−	12.1244i	0.222362	−	0.385143i	0.955525	+	0.294911i	$0.0952899\pi$
$992$		0			0
$993$	11.0000	−	15.5563i	0.349074	−	0.493666i
$994$		0			0
$995$	−2.44949	+	1.41421i	−0.0776540	+	0.0448336i
$996$	10.1980	−	14.4222i	0.323137	−	0.456985i
$997$	15.6125	−	9.01388i	0.494453	−	0.285472i	−0.231967	−	0.972724i	$-0.574516\pi$
$997$	15.6125	−	9.01388i	0.494453	−	0.285472i	0.726420	+	0.687251i	$0.241183\pi$
$998$		0			0
$999$	29.7980	−	28.9842i	0.942766	−	0.917018i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.p.a.230.4	yes	8
3.2	odd	2	inner	429.2.p.a.230.2	yes	8
11.10	odd	2	inner	429.2.p.a.230.3	yes	8
13.3	even	3	inner	429.2.p.a.263.1	yes	8
33.32	even	2	inner	429.2.p.a.230.1	✓	8
39.29	odd	6	inner	429.2.p.a.263.3	yes	8
143.120	odd	6	inner	429.2.p.a.263.2	yes	8
429.263	even	6	inner	429.2.p.a.263.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.p.a.230.1	✓	8	33.32	even	2	inner
429.2.p.a.230.2	yes	8	3.2	odd	2	inner
429.2.p.a.230.3	yes	8	11.10	odd	2	inner
429.2.p.a.230.4	yes	8	1.1	even	1	trivial
429.2.p.a.263.1	yes	8	13.3	even	3	inner
429.2.p.a.263.2	yes	8	143.120	odd	6	inner
429.2.p.a.263.3	yes	8	39.29	odd	6	inner
429.2.p.a.263.4	yes	8	429.263	even	6	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.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.724745 + 1.57313i) q^{3} +(1.00000 + 1.73205i) q^{4} -2.82843i q^{5} +(3.12250 - 1.80278i) q^{7} +(-1.94949 + 2.28024i) q^{9} +O(q^{10})\)	\(q+(0.724745 + 1.57313i) q^{3} +(1.00000 + 1.73205i) q^{4} -2.82843i q^{5} +(3.12250 - 1.80278i) q^{7} +(-1.94949 + 2.28024i) q^{9} +(3.11187 - 1.14728i) q^{11} +(-2.00000 + 2.82843i) q^{12} +(3.12250 - 1.80278i) q^{13} +(4.44949 - 2.04989i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(-2.54951 - 4.41588i) q^{17} +(-6.24500 + 3.60555i) q^{19} +(4.89898 - 2.82843i) q^{20} +(5.09902 + 3.60555i) q^{21} +(1.22474 + 0.707107i) q^{23} -3.00000 q^{25} +(-5.00000 - 1.41421i) q^{27} +(6.24500 + 3.60555i) q^{28} +(-2.54951 + 4.41588i) q^{29} +1.00000 q^{31} +(4.06014 + 4.06390i) q^{33} +(-5.09902 - 8.83176i) q^{35} +(-5.89898 - 1.09638i) q^{36} +(-4.00000 + 6.92820i) q^{37} +(5.09902 + 3.60555i) q^{39} +(-5.09902 + 8.83176i) q^{41} +(-3.12250 + 1.80278i) q^{43} +(5.09902 + 4.24264i) q^{44} +(6.44949 + 5.51399i) q^{45} -9.89949i q^{47} +(-6.89898 - 0.635674i) q^{48} +(3.00000 - 5.19615i) q^{49} +(5.09902 - 7.21110i) q^{51} +(6.24500 + 3.60555i) q^{52} +4.24264i q^{53} +(-3.24500 - 8.80170i) q^{55} +(-10.1980 - 7.21110i) q^{57} +(3.67423 - 2.12132i) q^{59} +(8.00000 + 5.65685i) q^{60} +(3.12250 - 1.80278i) q^{61} +(-1.97652 + 10.6345i) q^{63} -8.00000 q^{64} +(-5.09902 - 8.83176i) q^{65} +(6.50000 - 11.2583i) q^{67} +(5.09902 - 8.83176i) q^{68} +(-0.224745 + 2.43916i) q^{69} +(-2.44949 + 1.41421i) q^{71} -10.8167i q^{73} +(-2.17423 - 4.71940i) q^{75} +(-12.4900 - 7.21110i) q^{76} +(7.64853 - 9.19239i) q^{77} +3.60555i q^{79} +(9.79796 + 5.65685i) q^{80} +(-1.39898 - 8.89060i) q^{81} -5.09902 q^{83} +(-1.14598 + 12.4373i) q^{84} +(-12.4900 + 7.21110i) q^{85} +(-8.79451 - 0.810329i) q^{87} +(-2.44949 - 1.41421i) q^{89} +(6.50000 - 11.2583i) q^{91} +2.82843i q^{92} +(0.724745 + 1.57313i) q^{93} +(10.1980 + 17.6635i) q^{95} +(5.50000 + 9.52628i) q^{97} +(-3.45049 + 9.33242i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 8 q^{4} + 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 + 8 * q^4 + 4 * q^9	\( 8 q - 4 q^{3} + 8 q^{4} + 4 q^{9} - 16 q^{12} + 16 q^{15} - 16 q^{16} - 24 q^{25} - 40 q^{27} + 8 q^{31} + 12 q^{33} - 8 q^{36} - 32 q^{37} + 32 q^{45} - 16 q^{48} + 24 q^{49} + 24 q^{55} + 64 q^{60} - 64 q^{64} + 52 q^{67} + 8 q^{69} + 12 q^{75} + 28 q^{81} + 52 q^{91} - 4 q^{93} + 44 q^{97} - 48 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 + 8 * q^4 + 4 * q^9 - 16 * q^12 + 16 * q^15 - 16 * q^16 - 24 * q^25 - 40 * q^27 + 8 * q^31 + 12 * q^33 - 8 * q^36 - 32 * q^37 + 32 * q^45 - 16 * q^48 + 24 * q^49 + 24 * q^55 + 64 * q^60 - 64 * q^64 + 52 * q^67 + 8 * q^69 + 12 * q^75 + 28 * q^81 + 52 * q^91 - 4 * q^93 + 44 * q^97 - 48 * q^99

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