LMFDB - Embedded newform 429.2.p.a.263.2

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			263.2
Root			$1.88713 - 1.85439i$ of defining polynomial
Character	$\chi$	$=$	429.263
Dual form			429.2.p.a.230.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72474 - 0.158919i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.82843i q^{5} +(3.12250 + 1.80278i) q^{7} +(2.94949 + 0.548188i) q^{9} +O(q^{10})$	\(q+(-1.72474 - 0.158919i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.82843i q^{5} +(3.12250 + 1.80278i) q^{7} +(2.94949 + 0.548188i) q^{9} +(-3.11187 - 1.14728i) q^{11} +(-2.00000 + 2.82843i) q^{12} +(3.12250 + 1.80278i) q^{13} +(-0.449490 + 4.87832i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(2.54951 - 4.41588i) q^{17} +(-6.24500 - 3.60555i) q^{19} +(-4.89898 - 2.82843i) q^{20} +(-5.09902 - 3.60555i) q^{21} +(-1.22474 + 0.707107i) q^{23} -3.00000 q^{25} +(-5.00000 - 1.41421i) q^{27} +(6.24500 - 3.60555i) q^{28} +(2.54951 + 4.41588i) q^{29} +1.00000 q^{31} +(5.18486 + 2.47330i) q^{33} +(5.09902 - 8.83176i) q^{35} +(3.89898 - 4.56048i) q^{36} +(-4.00000 - 6.92820i) q^{37} +(-5.09902 - 3.60555i) q^{39} +(5.09902 + 8.83176i) q^{41} +(-3.12250 - 1.80278i) q^{43} +(-5.09902 + 4.24264i) q^{44} +(1.55051 - 8.34242i) q^{45} -9.89949i q^{47} +(2.89898 + 6.29253i) q^{48} +(3.00000 + 5.19615i) q^{49} +(-5.09902 + 7.21110i) q^{51} +(6.24500 - 3.60555i) q^{52} +4.24264i q^{53} +(-3.24500 + 8.80170i) q^{55} +(10.1980 + 7.21110i) q^{57} +(-3.67423 - 2.12132i) q^{59} +(8.00000 + 5.65685i) q^{60} +(3.12250 + 1.80278i) q^{61} +(8.22152 + 7.02899i) q^{63} -8.00000 q^{64} +(5.09902 - 8.83176i) q^{65} +(6.50000 + 11.2583i) q^{67} +(-5.09902 - 8.83176i) q^{68} +(2.22474 - 1.02494i) q^{69} +(2.44949 + 1.41421i) q^{71} +10.8167i q^{73} +(5.17423 + 0.476756i) q^{75} +(-12.4900 + 7.21110i) q^{76} +(-7.64853 - 9.19239i) q^{77} -3.60555i q^{79} +(-9.79796 + 5.65685i) q^{80} +(8.39898 + 3.23375i) q^{81} +5.09902 q^{83} +(-11.3440 + 5.22621i) q^{84} +(-12.4900 - 7.21110i) q^{85} +(-3.69549 - 8.02143i) q^{87} +(2.44949 - 1.41421i) q^{89} +(6.50000 + 11.2583i) q^{91} +2.82843i q^{92} +(-1.72474 - 0.158919i) q^{93} +(-10.1980 + 17.6635i) q^{95} +(5.50000 - 9.52628i) q^{97} +(-8.54951 - 5.08978i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

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

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	$-0.166667\pi$
$2$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$3$	−1.72474	−	0.158919i	−0.995782	−	0.0917517i
$3$	−1.72474	−	0.158919i	−0.995782	−	0.0917517i
$4$	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	0.956059	−	0.293173i	$-0.0947112\pi$
$7$	3.12250	+	1.80278i	1.18019	+	0.681385i	0.224134	+	0.974558i	$0.428045\pi$
$8$		0			0
$9$	2.94949	+	0.548188i	0.983163	+	0.182729i
$10$		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
$15$	−0.449490	+	4.87832i	−0.116058	+	1.25958i
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	2.54951	−	4.41588i	0.618347	−	1.07101i	−0.371440	−	0.928457i	$-0.621136\pi$
$17$	2.54951	−	4.41588i	0.618347	−	1.07101i	0.989787	−	0.142552i	$-0.0455307\pi$
$18$		0			0
$19$	−6.24500	−	3.60555i	−1.43270	−	0.827170i	−0.435375	−	0.900249i	$-0.643384\pi$
$19$	−6.24500	−	3.60555i	−1.43270	−	0.827170i	−0.997326	+	0.0730792i	$0.976717\pi$
$20$	−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	$-0.713771\pi$
$23$	−1.22474	+	0.707107i	−0.255377	+	0.147442i	0.366847	+	0.930281i	$0.380437\pi$
$24$		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	$-0.00968160\pi$
$29$	2.54951	+	4.41588i	0.473432	+	0.820008i	−0.526105	+	0.850419i	$0.676348\pi$
$30$		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
$33$	5.18486	+	2.47330i	0.902569	+	0.430546i
$34$		0			0
$35$	5.09902	−	8.83176i	0.861892	−	1.49284i
$36$	3.89898	−	4.56048i	0.649830	−	0.760080i
$37$	−4.00000	−	6.92820i	−0.657596	−	1.13899i	−0.981236	−	0.192809i	$-0.938240\pi$
$37$	−4.00000	−	6.92820i	−0.657596	−	1.13899i	0.323640	−	0.946180i	$-0.395093\pi$
$38$		0			0
$39$	−5.09902	−	3.60555i	−0.816497	−	0.577350i
$40$		0			0
$41$	5.09902	+	8.83176i	0.796333	+	1.37929i	0.921989	+	0.387215i	$0.126563\pi$
$41$	5.09902	+	8.83176i	0.796333	+	1.37929i	−0.125656	+	0.992074i	$0.540104\pi$
$42$		0			0
$43$	−3.12250	−	1.80278i	−0.476177	−	0.274921i	0.242645	−	0.970115i	$-0.421985\pi$
$43$	−3.12250	−	1.80278i	−0.476177	−	0.274921i	−0.718822	+	0.695194i	$0.755318\pi$
$44$	−5.09902	+	4.24264i	−0.768706	+	0.639602i
$45$	1.55051	−	8.34242i	0.231136	−	1.24361i
$46$		0			0
$47$		−	9.89949i		−	1.44399i	−0.691898	−	0.721995i	$-0.743225\pi$
$47$		−	9.89949i		−	1.44399i	0.691898	−	0.721995i	$-0.256775\pi$
$48$	2.89898	+	6.29253i	0.418432	+	0.908248i
$49$	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	$-0.422399\pi$
$59$	−3.67423	−	2.12132i	−0.478345	−	0.276172i	−0.719726	+	0.694258i	$0.755733\pi$
$60$	8.00000	+	5.65685i	1.03280	+	0.730297i
$61$	3.12250	+	1.80278i	0.399795	+	0.230822i	0.686396	−	0.727228i	$-0.259192\pi$
$61$	3.12250	+	1.80278i	0.399795	+	0.230822i	−0.286601	+	0.958050i	$0.592525\pi$
$62$		0			0
$63$	8.22152	+	7.02899i	1.03581	+	0.885569i
$64$	−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	0.923408	+	0.383819i	$0.125391\pi$
$67$	6.50000	+	11.2583i	0.794101	+	1.37542i	−0.129307	+	0.991605i	$0.541275\pi$
$68$	−5.09902	−	8.83176i	−0.618347	−	1.07101i
$69$	2.22474	−	1.02494i	0.267828	−	0.123389i
$70$		0			0
$71$	2.44949	+	1.41421i	0.290701	+	0.167836i	0.638258	−	0.769823i	$-0.279655\pi$
$71$	2.44949	+	1.41421i	0.290701	+	0.167836i	−0.347557	+	0.937659i	$0.612989\pi$
$72$		0			0
$73$			10.8167i			1.26599i	0.774154	+	0.632997i	$0.218175\pi$
$73$			10.8167i			1.26599i	−0.774154	+	0.632997i	$0.781825\pi$
$74$		0			0
$75$	5.17423	+	0.476756i	0.597469	+	0.0550510i
$76$	−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	$-0.934987\pi$
$79$		−	3.60555i		−	0.405656i	0.979214	−	0.202828i	$-0.0650133\pi$
$80$	−9.79796	+	5.65685i	−1.09545	+	0.632456i
$81$	8.39898	+	3.23375i	0.933220	+	0.359306i
$82$		0			0
$83$	5.09902			0.559690			0.279845	−	0.960045i	$-0.409717\pi$
$83$	5.09902			0.559690			0.279845	+	0.960045i	$0.409717\pi$
$84$	−11.3440	+	5.22621i	−1.23773	+	0.570226i
$85$	−12.4900	−	7.21110i	−1.35473	−	0.782154i
$86$		0			0
$87$	−3.69549	−	8.02143i	−0.396198	−	0.859988i
$88$		0			0
$89$	2.44949	−	1.41421i	0.259645	−	0.149906i	−0.364527	−	0.931193i	$-0.618769\pi$
$89$	2.44949	−	1.41421i	0.259645	−	0.149906i	0.624173	+	0.781286i	$0.285436\pi$
$90$		0			0
$91$	6.50000	+	11.2583i	0.681385	+	1.18019i
$92$			2.82843i			0.294884i
$93$	−1.72474	−	0.158919i	−0.178848	−	0.0164791i
$94$		0			0
$95$	−10.1980	+	17.6635i	−1.04630	+	1.81224i
$96$		0			0
$97$	5.50000	−	9.52628i	0.558440	−	0.967247i	−0.439187	−	0.898396i	$-0.644733\pi$
$97$	5.50000	−	9.52628i	0.558440	−	0.967247i	0.997627	−	0.0688512i	$-0.0219334\pi$
$98$		0			0
$99$	−8.54951	−	5.08978i	−0.859258	−	0.511542i
$100$	−3.00000	+	5.19615i	−0.300000	+	0.519615i
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		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	$-0.0873958\pi$
$107$	2.54951	+	4.41588i	0.246470	+	0.426899i	−0.716074	+	0.698025i	$0.754063\pi$
$108$	−7.44949	+	7.24604i	−0.716827	+	0.697251i
$109$			3.60555i			0.345349i	0.984979	+	0.172675i	$0.0552409\pi$
$109$			3.60555i			0.345349i	−0.984979	+	0.172675i	$0.944759\pi$
$110$		0			0
$111$	5.79796	+	12.5851i	0.550318	+	1.19452i
$112$		−	14.4222i		−	1.36277i
$113$	11.0227	+	6.36396i	1.03693	+	0.598671i	0.918962	−	0.394346i	$-0.129029\pi$
$113$	11.0227	+	6.36396i	1.03693	+	0.598671i	0.117967	+	0.993018i	$0.462362\pi$
$114$		0			0
$115$	2.00000	+	3.46410i	0.186501	+	0.323029i
$116$	10.1980			0.946864
$117$	8.22152	+	7.02899i	0.760080	+	0.649830i
$118$		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
$123$	−7.39098	−	16.0429i	−0.666422	−	1.44654i
$124$	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	−0.632099	−	0.774887i	$-0.717807\pi$
$127$	−3.12250	+	1.80278i	−0.277077	+	0.159970i	0.355022	+	0.934858i	$0.384473\pi$
$128$		0			0
$129$	5.09902	+	3.60555i	0.448944	+	0.317451i
$130$		0			0
$131$	20.3961			1.78201			0.891007	−	0.453990i	$-0.150000\pi$
$131$	20.3961			1.78201			0.891007	+	0.453990i	$0.150000\pi$
$132$	9.46874	−	6.50714i	0.824148	−	0.566374i
$133$	−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	$-0.431008\pi$
$137$	−6.12372	−	3.53553i	−0.523185	−	0.302061i	−0.738237	+	0.674542i	$0.764341\pi$
$138$		0			0
$139$	9.36750	+	5.40833i	0.794541	+	0.458728i	0.841559	−	0.540166i	$-0.181638\pi$
$139$	9.36750	+	5.40833i	0.794541	+	0.458728i	−0.0470179	+	0.998894i	$0.514972\pi$
$140$	−10.1980	−	17.6635i	−0.861892	−	1.49284i
$141$	−1.57321	+	17.0741i	−0.132489	+	1.43790i
$142$		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
$147$	−4.34847	−	9.43879i	−0.358656	−	0.778499i
$148$	−16.0000			−1.31519
$149$	−7.64853	+	13.2476i	−0.626592	+	1.08529i	0.361639	+	0.932318i	$0.382217\pi$
$149$	−7.64853	+	13.2476i	−0.626592	+	1.08529i	−0.988231	+	0.152971i	$0.951116\pi$
$150$		0			0
$151$			7.21110i			0.586831i	0.955985	+	0.293416i	$0.0947920\pi$
$151$			7.21110i			0.586831i	−0.955985	+	0.293416i	$0.905208\pi$
$152$		0			0
$153$	9.94049	−	11.6270i	0.803641	−	0.939986i
$154$		0			0
$155$		−	2.82843i		−	0.227185i
$156$	−11.3440	+	5.22621i	−0.908248	+	0.418432i
$157$	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
$159$	0.674235	−	7.31747i	0.0534703	−	0.580313i
$160$		0			0
$161$	−5.09902			−0.401859
$162$		0			0
$163$	5.50000	−	9.52628i	0.430793	−	0.746156i	−0.566149	−	0.824303i	$-0.691567\pi$
$163$	5.50000	−	9.52628i	0.430793	−	0.746156i	0.996942	+	0.0781474i	$0.0249005\pi$
$164$	20.3961			1.59267
$165$	6.99555	−	14.6650i	0.544603	−	1.14167i
$166$		0			0
$167$	2.54951	+	4.41588i	0.197287	+	0.341711i	0.947648	−	0.319317i	$-0.103454\pi$
$167$	2.54951	+	4.41588i	0.197287	+	0.341711i	−0.750361	+	0.661028i	$0.770120\pi$
$168$		0			0
$169$	6.50000	+	11.2583i	0.500000	+	0.866025i
$170$		0			0
$171$	−16.4430	−	14.0580i	−1.25743	−	1.07504i
$172$	−6.24500	+	3.60555i	−0.476177	+	0.274921i
$173$	5.09902	−	8.83176i	0.387671	−	0.671466i	−0.604465	−	0.796632i	$-0.706613\pi$
$173$	5.09902	−	8.83176i	0.387671	−	0.671466i	0.992136	+	0.125166i	$0.0399462\pi$
$174$		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	$-0.843918\pi$
$179$	−12.2474	+	7.07107i	−0.915417	+	0.528516i	−0.0332471	+	0.999447i	$0.510585\pi$
$180$	−12.8990	−	11.0280i	−0.961433	−	0.821977i
$181$	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
$189$	−13.0630	−	13.4298i	−0.950192	−	0.976871i
$190$		0			0
$191$	8.57321	+	4.94975i	0.620336	+	0.358151i	0.777000	−	0.629501i	$-0.216741\pi$
$191$	8.57321	+	4.94975i	0.620336	+	0.358151i	−0.156664	+	0.987652i	$0.550074\pi$
$192$	13.7980	+	1.27135i	0.995782	+	0.0917517i
$193$	3.12250	−	1.80278i	0.224762	−	0.129767i	−0.383391	−	0.923586i	$-0.625244\pi$
$193$	3.12250	−	1.80278i	0.224762	−	0.129767i	0.608153	+	0.793819i	$0.291911\pi$
$194$		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	−0.958320	−	0.285696i	$-0.907775\pi$
$197$	−10.1980	−	17.6635i	−0.726580	−	1.25847i	0.231740	−	0.972778i	$-0.425558\pi$
$198$		0			0
$199$	−0.500000	+	0.866025i	−0.0354441	+	0.0613909i	−0.883203	−	0.468990i	$-0.844618\pi$
$199$	−0.500000	+	0.866025i	−0.0354441	+	0.0613909i	0.847759	+	0.530381i	$0.177951\pi$
$200$		0			0
$201$	−9.42168	−	20.4507i	−0.664554	−	1.44248i
$202$		0			0
$203$			18.3848i			1.29036i
$204$	7.39098	+	16.0429i	0.517472	+	1.12323i
$205$	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	−0.929491	−	0.368844i	$-0.879754\pi$
$211$	−15.6125	+	9.01388i	−1.07481	+	0.620541i	−0.145317	+	0.989385i	$0.546420\pi$
$212$	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
$219$	1.71897	−	18.6560i	0.116157	−	1.26065i
$220$	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	0.747922	−	0.663786i	$-0.231052\pi$
$223$	−3.00000	−	5.19615i	−0.200895	−	0.347960i	−0.948817	+	0.315826i	$0.897718\pi$
$224$		0			0
$225$	−8.84847	−	1.64456i	−0.589898	−	0.109638i
$226$		0			0
$227$	−5.09902	+	8.83176i	−0.338434	+	0.586185i	−0.984138	−	0.177403i	$-0.943230\pi$
$227$	−5.09902	+	8.83176i	−0.338434	+	0.586185i	0.645705	+	0.763587i	$0.276564\pi$
$228$	22.6880	−	10.4524i	1.50255	−	0.692228i
$229$	−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
$231$	11.7309	+	17.0700i	0.771838	+	1.12312i
$232$		0			0
$233$	−15.2971			−1.00214			−0.501072	−	0.865406i	$-0.667061\pi$
$233$	−15.2971			−1.00214			−0.501072	+	0.865406i	$0.667061\pi$
$234$		0			0
$235$	−28.0000			−1.82652
$236$	−7.34847	+	4.24264i	−0.478345	+	0.276172i
$237$	−0.572989	+	6.21866i	−0.0372197	+	0.403945i
$238$		0			0
$239$	−5.09902			−0.329828			−0.164914	−	0.986308i	$-0.552735\pi$
$239$	−5.09902			−0.329828			−0.164914	+	0.986308i	$0.552735\pi$
$240$	17.7980	−	8.19955i	1.14885	−	0.529279i
$241$	−6.24500	−	3.60555i	−0.402276	−	0.232254i	0.285190	−	0.958471i	$-0.407943\pi$
$241$	−6.24500	−	3.60555i	−0.402276	−	0.232254i	−0.687465	+	0.726217i	$0.741277\pi$
$242$		0			0
$243$	−13.9722	−	6.91215i	−0.896317	−	0.443415i
$244$	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
$249$	−8.79451	−	0.810329i	−0.557329	−	0.0513525i
$250$		0			0
$251$	8.57321	+	4.94975i	0.541136	+	0.312425i	0.745539	−	0.666462i	$-0.232192\pi$
$251$	8.57321	+	4.94975i	0.541136	+	0.312425i	−0.204403	+	0.978887i	$0.565525\pi$
$252$	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	$-0.521262\pi$
$257$	12.2474	−	7.07107i	0.763975	−	0.441081i	0.830721	+	0.556689i	$0.187928\pi$
$258$		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	$-0.0103330\pi$
$263$	7.64853	+	13.2476i	0.471629	+	0.816885i	−0.527845	+	0.849341i	$0.677000\pi$
$264$		0			0
$265$	12.0000			0.737154
$266$		0			0
$267$	−4.44949	+	2.04989i	−0.272304	+	0.125451i
$268$	26.0000			1.58820
$269$	−9.79796	−	5.65685i	−0.597392	−	0.344904i	0.170623	−	0.985336i	$-0.445422\pi$
$269$	−9.79796	−	5.65685i	−0.597392	−	0.344904i	−0.768015	+	0.640432i	$0.778755\pi$
$270$		0			0
$271$	−3.12250	+	1.80278i	−0.189678	+	0.109511i	−0.591832	−	0.806061i	$-0.701595\pi$
$271$	−3.12250	+	1.80278i	−0.189678	+	0.109511i	0.402154	+	0.915572i	$0.368262\pi$
$272$	−20.3961			−1.23669
$273$	−9.42168	−	20.4507i	−0.570226	−	1.23773i
$274$		0			0
$275$	9.33562	+	3.44184i	0.562959	+	0.207551i
$276$	0.449490	−	4.87832i	0.0270561	−	0.293640i
$277$	−12.4900	−	7.21110i	−0.750451	−	0.433273i	0.0754058	−	0.997153i	$-0.475975\pi$
$277$	−12.4900	−	7.21110i	−0.750451	−	0.433273i	−0.825857	+	0.563880i	$0.809308\pi$
$278$		0			0
$279$	2.94949	+	0.548188i	0.176581	+	0.0328192i
$280$		0			0
$281$	−25.4951			−1.52091			−0.760455	−	0.649391i	$-0.775024\pi$
$281$	−25.4951			−1.52091			−0.760455	+	0.649391i	$0.775024\pi$
$282$		0			0
$283$	15.6125	−	9.01388i	0.928066	−	0.535819i	0.0418670	−	0.999123i	$-0.486669\pi$
$283$	15.6125	−	9.01388i	0.928066	−	0.535819i	0.886200	+	0.463304i	$0.153336\pi$
$284$	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	$-0.980781\pi$
$293$	−7.64853	+	13.2476i	−0.446832	+	0.773935i	0.551346	+	0.834277i	$0.314114\pi$
$294$		0			0
$295$	−6.00000	+	10.3923i	−0.349334	+	0.605063i
$296$		0			0
$297$	13.9369	+	10.1373i	0.808699	+	0.588223i
$298$		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	$0.0998837\pi$
$307$			10.8167i			0.617339i	−0.951169	+	0.308670i	$0.900116\pi$
$308$	−23.5702	+	4.05525i	−1.34304	+	0.231069i
$309$	−1.72474	−	0.158919i	−0.0981173	−	0.00904056i
$310$		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
$315$	19.8810	−	23.2540i	1.12017	−	1.31021i
$316$	−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
$321$	−3.69549	−	8.02143i	−0.206262	−	0.447713i
$322$		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
$327$	0.572989	−	6.21866i	0.0316864	−	0.343892i
$328$		0			0
$329$	17.8466	−	30.9112i	0.983913	−	1.70419i
$330$		0			0
$331$	−5.50000	+	9.52628i	−0.302307	+	0.523612i	−0.976658	−	0.214799i	$-0.931090\pi$
$331$	−5.50000	+	9.52628i	−0.302307	+	0.523612i	0.674351	+	0.738411i	$0.264424\pi$
$332$	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
$336$	−2.29196	+	24.8746i	−0.125037	+	1.35702i
$337$		−	18.0278i		−	0.982034i	−0.871150	−	0.491017i	$-0.836625\pi$
$337$		−	18.0278i		−	0.982034i	0.871150	−	0.491017i	$-0.163375\pi$
$338$		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
$345$	−2.89898	−	6.29253i	−0.156076	−	0.338778i
$346$		0			0
$347$	−7.64853	+	13.2476i	−0.410595	+	0.711171i	−0.994955	−	0.100324i	$-0.968012\pi$
$347$	−7.64853	+	13.2476i	−0.410595	+	0.711171i	0.584360	+	0.811494i	$0.301345\pi$
$348$	−17.5890	−	1.62066i	−0.942870	−	0.0868764i
$349$	9.36750	−	5.40833i	0.501431	−	0.289501i	−0.227874	−	0.973691i	$-0.573177\pi$
$349$	9.36750	−	5.40833i	0.501431	−	0.289501i	0.729304	+	0.684190i	$0.239844\pi$
$350$		0			0
$351$	−13.0630	−	13.4298i	−0.697251	−	0.716827i
$352$		0			0
$353$	7.34847	−	4.24264i	0.391120	−	0.225813i	−0.291526	−	0.956563i	$-0.594163\pi$
$353$	7.34847	−	4.24264i	0.391120	−	0.225813i	0.682645	+	0.730750i	$0.260830\pi$
$354$		0			0
$355$	4.00000	−	6.92820i	0.212298	−	0.367711i
$356$		−	5.65685i		−	0.299813i
$357$	−28.9217	+	13.3243i	−1.53070	+	0.705195i
$358$		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
$363$	−13.2971	−	13.6451i	−0.697915	−	0.716181i
$364$	26.0000			1.36277
$365$	30.5941			1.60137
$366$		0			0
$367$	16.5000	+	28.5788i	0.861293	+	1.49180i	0.870681	+	0.491847i	$0.163678\pi$
$367$	16.5000	+	28.5788i	0.861293	+	1.49180i	−0.00938849	+	0.999956i	$0.502988\pi$
$368$	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	0.944371	−	0.328881i	$-0.106671\pi$
$373$	21.8575	+	12.6194i	1.13174	+	0.653409i	0.187367	+	0.982290i	$0.440005\pi$
$374$		0			0
$375$	−0.898979	+	9.75663i	−0.0464231	+	0.503830i
$376$		0			0
$377$			18.3848i			0.946864i
$378$		0			0
$379$	9.50000	+	16.4545i	0.487982	+	0.845210i	0.999904	−	0.0138218i	$-0.00439975\pi$
$379$	9.50000	+	16.4545i	0.487982	+	0.845210i	−0.511922	+	0.859032i	$0.671066\pi$
$380$	20.3961	+	35.3270i	1.04630	+	1.81224i
$381$	5.67201	−	2.61310i	0.290586	−	0.133873i
$382$		0			0
$383$	22.0454	+	12.7279i	1.12647	+	0.650366i	0.943044	−	0.332668i	$-0.107949\pi$
$383$	22.0454	+	12.7279i	1.12647	+	0.650366i	0.183424	+	0.983034i	$0.441282\pi$
$384$		0			0
$385$	−26.0000	+	21.6333i	−1.32508	+	1.10254i
$386$		0			0
$387$	−8.22152	−	7.02899i	−0.417923	−	0.357303i
$388$	−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
$393$	−35.1780	−	3.24132i	−1.77450	−	0.163503i
$394$		0			0
$395$	−10.1980			−0.513119
$396$	−17.3653	+	9.71840i	−0.872638	+	0.488368i
$397$	−3.50000	+	6.06218i	−0.175660	+	0.304252i	−0.940389	−	0.340099i	$-0.889539\pi$
$397$	−3.50000	+	6.06218i	−0.175660	+	0.304252i	0.764730	+	0.644351i	$0.222873\pi$
$398$		0			0
$399$	18.8434	+	40.9014i	0.943348	+	2.04763i
$400$	6.00000	+	10.3923i	0.300000	+	0.519615i
$401$	13.4722	−	7.77817i	0.672769	−	0.388424i	−0.124356	−	0.992238i	$-0.539686\pi$
$401$	13.4722	−	7.77817i	0.672769	−	0.388424i	0.797125	+	0.603814i	$0.206353\pi$
$402$		0			0
$403$	3.12250	+	1.80278i	0.155543	+	0.0898027i
$404$		0			0
$405$	9.14643	−	23.7559i	0.454490	−	1.18044i
$406$		0			0
$407$	4.49890	+	26.1488i	0.223002	+	1.29615i
$408$		0			0
$409$	−9.36750	−	5.40833i	−0.463193	−	0.267425i	0.250193	−	0.968196i	$-0.419506\pi$
$409$	−9.36750	−	5.40833i	−0.463193	−	0.267425i	−0.713386	+	0.700771i	$0.752839\pi$
$410$		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	$-0.655669\pi$
$419$	1.22474	−	0.707107i	0.0598327	−	0.0345444i	0.529618	+	0.848236i	$0.322335\pi$
$420$	14.7820	+	32.0857i	0.721285	+	1.56562i
$421$	−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
$423$	5.42679	−	29.1985i	0.263859	−	1.41968i
$424$		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
$429$	11.7309	+	17.0700i	0.566374	+	0.824148i
$430$		0			0
$431$	12.7475	+	22.0794i	0.614028	+	1.06353i	0.990554	+	0.137121i	$0.0437851\pi$
$431$	12.7475	+	22.0794i	0.614028	+	1.06353i	−0.376526	+	0.926406i	$0.622882\pi$
$432$	5.10102	+	20.1489i	0.245423	+	0.969416i
$433$	9.50000	−	16.4545i	0.456541	−	0.790752i	−0.542234	−	0.840227i	$-0.682422\pi$
$433$	9.50000	−	16.4545i	0.456541	−	0.790752i	0.998775	+	0.0494752i	$0.0157549\pi$
$434$		0			0
$435$	−22.6880	+	10.4524i	−1.08781	+	0.501155i
$436$	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	−0.823937	−	0.566682i	$-0.808227\pi$
$439$	−15.6125	+	9.01388i	−0.745144	+	0.430209i	0.0787928	+	0.996891i	$0.474893\pi$
$440$		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	$-0.0214038\pi$
$444$	27.5959	+	2.54270i	1.30964	+	0.120671i
$445$	−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	$-0.647439\pi$
$449$	−30.6186	−	17.6777i	−1.44498	−	0.834261i	−0.998176	+	0.0603700i	$0.980772\pi$
$450$		0			0
$451$	−5.73499	−	33.3333i	−0.270050	−	1.56960i
$452$	22.0454	−	12.7279i	1.03693	−	0.598671i
$453$	1.14598	−	12.4373i	0.0538428	−	0.584356i
$454$		0			0
$455$	31.8434	−	18.3848i	1.49284	−	0.861892i
$456$		0			0
$457$	−28.1025	+	16.2250i	−1.31458	+	0.758973i	−0.982851	−	0.184402i	$-0.940965\pi$
$457$	−28.1025	+	16.2250i	−1.31458	+	0.758973i	−0.331728	+	0.943375i	$0.607632\pi$
$458$		0			0
$459$	−18.9925	+	18.4739i	−0.886496	+	0.862286i
$460$	8.00000			0.373002
$461$	−12.7475	+	22.0794i	−0.593713	+	1.02834i	0.400015	+	0.916509i	$0.369005\pi$
$461$	−12.7475	+	22.0794i	−0.593713	+	1.02834i	−0.993727	+	0.111832i	$0.964328\pi$
$462$		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
$465$	−0.449490	+	4.87832i	−0.0208446	+	0.226226i
$466$		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
$471$	−12.0732	−	1.11243i	−0.556304	−	0.0512581i
$472$		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
$477$	−2.32577	+	12.5136i	−0.106489	+	0.572960i
$478$		0			0
$479$	−15.2971	−	26.4953i	−0.698940	−	1.21060i	−0.968834	−	0.247710i	$-0.920322\pi$
$479$	−15.2971	−	26.4953i	−0.698940	−	1.21060i	0.269894	−	0.962890i	$-0.413011\pi$
$480$		0			0
$481$		−	28.8444i		−	1.31519i
$482$		0			0
$483$	8.79451	+	0.810329i	0.400164	+	0.0368713i
$484$	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	−0.842479	−	0.538730i	$-0.818904\pi$
$487$	1.00000	−	1.73205i	0.0453143	−	0.0784867i	0.887793	+	0.460243i	$0.152238\pi$
$488$		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	$-0.240577\pi$
$491$	−5.09902	−	8.83176i	−0.230116	−	0.398572i	−0.957842	+	0.287296i	$0.907244\pi$
$492$	−35.1780	−	3.24132i	−1.58595	−	0.146130i
$493$	26.0000			1.17098
$494$		0			0
$495$	−14.3961	+	24.1817i	−0.647056	+	1.08689i
$496$	−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
$501$	−3.69549	−	8.02143i	−0.165102	−	0.358371i
$502$		0			0
$503$	12.7475	−	22.0794i	0.568385	−	0.984472i	−0.428341	−	0.903617i	$-0.640902\pi$
$503$	12.7475	−	22.0794i	0.568385	−	0.984472i	0.996726	−	0.0808546i	$-0.0257649\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−9.42168	−	20.4507i	−0.418432	−	0.908248i
$508$			7.21110i			0.319941i
$509$	−35.5176	+	20.5061i	−1.57429	+	0.908917i	−0.578656	+	0.815572i	$0.696423\pi$
$509$	−35.5176	+	20.5061i	−1.57429	+	0.908917i	−0.995634	+	0.0933452i	$0.970244\pi$
$510$		0			0
$511$	−19.5000	+	33.7750i	−0.862629	+	1.49412i
$512$		0			0
$513$	26.1260	+	26.8595i	1.15349	+	1.18588i
$514$		0			0
$515$		−	2.82843i		−	0.124635i
$516$	11.3440	−	5.22621i	0.499393	−	0.230071i
$517$	−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	0.375040	−	0.927008i	$-0.377629\pi$
$523$	31.2250	−	18.0278i	1.36537	−	0.788299i	0.990333	+	0.138710i	$0.0442955\pi$
$524$	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
$528$	−1.80196	−	22.9075i	−0.0784203	−	0.996920i
$529$	−10.5000	+	18.1865i	−0.456522	+	0.790719i
$530$		0			0
$531$	−9.67423	−	8.27098i	−0.419826	−	0.358930i
$532$	−52.0000			−2.25449
$533$			36.7696i			1.59267i
$534$		0			0
$535$	12.4900	−	7.21110i	0.539990	−	0.311763i
$536$		0			0
$537$	22.2474	−	10.2494i	0.960048	−	0.442296i
$538$		0			0
$539$	−3.37417	−	19.6116i	−0.145336	−	0.844732i
$540$	20.4949	+	21.0703i	0.881960	+	0.906723i
$541$		−	10.8167i		−	0.465044i	−0.972591	−	0.232522i	$-0.925302\pi$
$541$		−	10.8167i		−	0.465044i	0.972591	−	0.232522i	$-0.0746978\pi$
$542$		0			0
$543$	−41.3939	−	3.81405i	−1.77638	−	0.163676i
$544$		0			0
$545$	10.1980			0.436836
$546$		0			0
$547$		−	25.2389i		−	1.07914i	−0.841942	−	0.539568i	$-0.818588\pi$
$547$		−	25.2389i		−	1.07914i	0.841942	−	0.539568i	$-0.181412\pi$
$548$	−12.2474	+	7.07107i	−0.523185	+	0.302061i
$549$	8.22152	+	7.02899i	0.350886	+	0.299990i
$550$		0			0
$551$		−	36.7696i		−	1.56644i
$552$		0			0
$553$	6.50000	−	11.2583i	0.276408	−	0.478753i
$554$		0			0
$555$	35.5959	−	16.3991i	1.51096	−	0.696103i
$556$	18.7350	−	10.8167i	0.794541	−	0.458728i
$557$	−2.54951	−	4.41588i	−0.108026	−	0.187107i	0.806944	−	0.590627i	$-0.201120\pi$
$557$	−2.54951	−	4.41588i	−0.108026	−	0.187107i	−0.914971	+	0.403521i	$0.867786\pi$
$558$		0			0
$559$	−6.50000	−	11.2583i	−0.274921	−	0.476177i
$560$	−40.7922			−1.72378
$561$	24.1407	−	16.5900i	1.01922	−	0.700431i
$562$		0			0
$563$	15.2971	−	26.4953i	0.644694	−	1.11664i	−0.339678	−	0.940542i	$-0.610318\pi$
$563$	15.2971	−	26.4953i	0.644694	−	1.11664i	0.984372	−	0.176101i	$-0.0563486\pi$
$564$	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	0.876600	+	0.481219i	$0.159806\pi$
$569$	20.3961	+	35.3270i	0.855048	+	1.48099i	−0.0215523	+	0.999768i	$0.506861\pi$
$570$		0			0
$571$			14.4222i			0.603550i	0.953379	+	0.301775i	$0.0975792\pi$
$571$			14.4222i			0.603550i	−0.953379	+	0.301775i	$0.902421\pi$
$572$	−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
$576$	−23.5959	−	4.38551i	−0.983163	−	0.182729i
$577$	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
$579$	−5.67201	+	2.61310i	−0.235721	+	0.108597i
$580$		−	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
$585$	19.8810	−	23.2540i	0.821977	−	0.961433i
$586$		0			0
$587$	8.57321	−	4.94975i	0.353854	−	0.204298i	−0.312527	−	0.949909i	$-0.601176\pi$
$587$	8.57321	−	4.94975i	0.353854	−	0.204298i	0.666382	+	0.745611i	$0.267842\pi$
$588$	−20.6969	−	1.90702i	−0.853527	−	0.0786443i
$589$	−6.24500	−	3.60555i	−0.257321	−	0.148564i
$590$		0			0
$591$	14.7820	+	32.0857i	0.608048	+	1.31983i
$592$	−16.0000	+	27.7128i	−0.657596	+	1.13899i
$593$	−45.8912			−1.88452			−0.942262	−	0.334876i	$-0.891306\pi$
$593$	−45.8912			−1.88452			−0.942262	+	0.334876i	$0.891306\pi$
$594$		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	−0.529005	+	0.848619i	$0.677435\pi$
$601$	−37.4700	+	21.6333i	−1.52843	+	0.882441i	−0.999428	+	0.0338222i	$0.989232\pi$
$602$		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	$-0.333333\pi$
$607$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$608$		0			0
$609$	2.92168	−	31.7090i	0.118393	−	1.28492i
$610$		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	0.394274	−	0.918993i	$-0.370996\pi$
$613$	34.3475	−	19.8305i	1.38728	−	0.800948i	0.993008	+	0.118045i	$0.0376628\pi$
$614$		0			0
$615$	−45.3761	+	20.9048i	−1.82974	+	0.842964i
$616$		0			0
$617$	−18.3712	−	10.6066i	−0.739596	−	0.427006i	0.0823267	−	0.996605i	$-0.473765\pi$
$617$	−18.3712	−	10.6066i	−0.739596	−	0.427006i	−0.821922	+	0.569600i	$0.807098\pi$
$618$		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
$621$	7.12372	−	1.80348i	0.285865	−	0.0723713i
$622$		0			0
$623$	10.1980			0.408576
$624$	−2.29196	+	24.8746i	−0.0917517	+	0.995782i
$625$	−31.0000			−1.24000
$626$		0			0
$627$	−23.4618	−	34.1400i	−0.936976	−	1.36342i
$628$	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	0.418559	+	0.908190i	$0.362535\pi$
$631$	−14.5000	+	25.1147i	−0.577236	+	0.999802i	−0.995795	+	0.0916122i	$0.970798\pi$
$632$		0			0
$633$	28.3600	−	13.0655i	1.12721	−	0.519308i
$634$		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
$639$	6.44949	+	5.51399i	0.255138	+	0.218130i
$640$		0			0
$641$	30.6186	+	17.6777i	1.20936	+	0.698226i	0.962620	−	0.270855i	$-0.0873064\pi$
$641$	30.6186	+	17.6777i	1.20936	+	0.698226i	0.246743	+	0.969081i	$0.420640\pi$
$642$		0			0
$643$	−1.50000	+	2.59808i	−0.0591542	+	0.102458i	−0.894086	−	0.447895i	$-0.852174\pi$
$643$	−1.50000	+	2.59808i	−0.0591542	+	0.102458i	0.834932	+	0.550353i	$0.185507\pi$
$644$	−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	$-0.923803\pi$
$647$	−31.8434	+	18.3848i	−1.25189	+	0.722780i	−0.280407	+	0.959881i	$0.590469\pi$
$648$		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	$-0.765117\pi$
$653$	−13.4722	+	7.77817i	−0.527208	+	0.304383i	0.212671	+	0.977124i	$0.431784\pi$
$654$		0			0
$655$		−	57.6888i		−	2.25409i
$656$	20.3961	−	35.3270i	0.796333	−	1.37929i
$657$	−5.92956	+	31.9036i	−0.231334	+	1.24468i
$658$		0			0
$659$	−5.09902	+	8.83176i	−0.198630	+	0.344037i	−0.948084	−	0.318019i	$-0.896982\pi$
$659$	−5.09902	+	8.83176i	−0.198630	+	0.344037i	0.749455	+	0.662056i	$0.230316\pi$
$660$	−18.4050	−	26.7816i	−0.716413	−	1.04247i
$661$	−6.50000	−	11.2583i	−0.252821	−	0.437898i	0.711481	−	0.702706i	$-0.248025\pi$
$661$	−6.50000	−	11.2583i	−0.252821	−	0.437898i	−0.964301	+	0.264807i	$0.914692\pi$
$662$		0			0
$663$	−28.9217	+	13.3243i	−1.12323	+	0.517472i
$664$		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
$669$	4.34847	+	9.43879i	0.168122	+	0.364925i
$670$		0			0
$671$	−7.64853	−	9.19239i	−0.295268	−	0.354868i
$672$		0			0
$673$	−9.36750	+	5.40833i	−0.361090	+	0.208476i	−0.669559	−	0.742759i	$-0.733517\pi$
$673$	−9.36750	+	5.40833i	−0.361090	+	0.208476i	0.308469	+	0.951235i	$0.400184\pi$
$674$		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	$-0.468760\pi$
$677$	5.09902			0.195971			0.0979856	+	0.995188i	$0.468760\pi$
$678$		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	$-0.190821\pi$
$683$	19.5959	+	11.3137i	0.749817	+	0.432907i	−0.0758108	+	0.997122i	$0.524155\pi$
$684$	−40.7922	+	14.4222i	−1.55973	+	0.551447i
$685$	−10.0000	+	17.3205i	−0.382080	+	0.661783i
$686$		0			0
$687$	48.2929	+	4.44972i	1.84249	+	0.169767i
$688$			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	−0.999876	−	0.0157341i	$-0.994991\pi$
$691$	−13.5000	−	23.3827i	−0.513564	−	0.889519i	0.486312	−	0.873785i	$-0.338342\pi$
$692$	−10.1980	−	17.6635i	−0.387671	−	0.671466i
$693$	−17.5201	−	31.3057i	−0.665534	−	1.18920i
$694$		0			0
$695$	15.2971	−	26.4953i	0.580251	−	1.00502i
$696$		0			0
$697$	52.0000			1.96964
$698$		0			0
$699$	26.3835	+	2.43099i	0.997916	+	0.0919484i
$700$	−18.7350	+	10.8167i	−0.708116	+	0.408831i
$701$	15.2971			0.577762			0.288881	−	0.957365i	$-0.406717\pi$
$701$	15.2971			0.577762			0.288881	+	0.957365i	$0.406717\pi$
$702$		0			0
$703$			57.6888i			2.17578i
$704$	24.8950	+	9.17824i	0.938265	+	0.345918i
$705$	48.2929	+	4.44972i	1.81881	+	0.167586i
$706$		0			0
$707$		0			0
$708$	13.3485	−	6.14966i	0.501666	−	0.231119i
$709$	14.5000	−	25.1147i	0.544559	−	0.943204i	−0.454076	−	0.890963i	$-0.650030\pi$
$709$	14.5000	−	25.1147i	0.544559	−	0.943204i	0.998635	−	0.0522406i	$-0.0166363\pi$
$710$		0			0
$711$	1.97652	−	10.6345i	0.0741253	−	0.398826i
$712$		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
$717$	8.79451	+	0.810329i	0.328437	+	0.0302623i
$718$		0			0
$719$	−23.2702	−	13.4350i	−0.867830	−	0.501042i	−0.00120365	−	0.999999i	$-0.500383\pi$
$719$	−23.2702	−	13.4350i	−0.867830	−	0.501042i	−0.866627	+	0.498957i	$0.833716\pi$
$720$	−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
$732$	−11.3440	+	5.22621i	−0.419287	+	0.193166i
$733$		−	3.60555i		−	0.133174i	−0.997781	−	0.0665870i	$-0.978789\pi$
$733$		−	3.60555i		−	0.133174i	0.997781	−	0.0665870i	$-0.0212110\pi$
$734$		0			0
$735$	−26.6969	+	12.2993i	−0.984731	+	0.453668i
$736$		0			0
$737$	−7.31071	−	42.4918i	−0.269294	−	1.56521i
$738$		0			0
$739$	−12.4900	+	7.21110i	−0.459452	+	0.265265i	−0.711814	−	0.702368i	$-0.752126\pi$
$739$	−12.4900	+	7.21110i	−0.459452	+	0.265265i	0.252362	+	0.967633i	$0.418793\pi$
$740$			45.2548i			1.66360i
$741$	18.8434	+	40.9014i	0.692228	+	1.50255i
$742$		0			0
$743$	−10.1980	−	17.6635i	−0.374130	−	0.648012i	0.616067	−	0.787694i	$-0.288725\pi$
$743$	−10.1980	−	17.6635i	−0.374130	−	0.648012i	−0.990196	+	0.139682i	$0.955392\pi$
$744$		0			0
$745$	37.4700	+	21.6333i	1.37279	+	0.792583i
$746$		0			0
$747$	15.0395	+	2.79522i	0.550267	+	0.102272i
$748$	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	0.827225	−	0.561870i	$-0.189918\pi$
$751$	−2.00000	−	3.46410i	−0.0729810	−	0.126407i	−0.900207	+	0.435463i	$0.856585\pi$
$752$	−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
$756$	−36.3240	+	9.19600i	−1.32109	+	0.334455i
$757$	14.0000	+	24.2487i	0.508839	+	0.881334i	0.999948	+	0.0102362i	$0.00325836\pi$
$757$	14.0000	+	24.2487i	0.508839	+	0.881334i	−0.491109	+	0.871098i	$0.663408\pi$
$758$		0			0
$759$	−8.09902	+	0.637089i	−0.293976	+	0.0231249i
$760$		0			0
$761$	−12.7475	+	22.0794i	−0.462098	+	0.800378i	−0.999065	−	0.0432255i	$-0.986237\pi$
$761$	−12.7475	+	22.0794i	−0.462098	+	0.800378i	0.536967	+	0.843603i	$0.319570\pi$
$762$		0			0
$763$	−6.50000	+	11.2583i	−0.235316	+	0.407579i
$764$	17.1464	−	9.89949i	0.620336	−	0.358151i
$765$	−32.8861	−	28.1159i	−1.18900	−	1.01653i
$766$		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	−0.257599	−	0.966252i	$-0.582931\pi$
$769$	12.4900	−	7.21110i	0.450401	−	0.260039i	0.707999	+	0.706213i	$0.249598\pi$
$770$		0			0
$771$	−22.2474	+	10.2494i	−0.801222	+	0.369125i
$772$		−	7.21110i		−	0.259533i
$773$	−17.1464	−	9.89949i	−0.616714	−	0.356060i	0.158874	−	0.987299i	$-0.449213\pi$
$773$	−17.1464	−	9.89949i	−0.616714	−	0.356060i	−0.775589	+	0.631239i	$0.782547\pi$
$774$		0			0
$775$	−3.00000			−0.107763
$776$		0			0
$777$	−4.58391	+	49.7492i	−0.164447	+	1.78474i
$778$		0			0
$779$		−	73.5391i		−	2.63481i
$780$	14.7820	+	32.0857i	0.529279	+	1.14885i
$781$	−6.00000	−	7.21110i	−0.214697	−	0.258034i
$782$		0			0
$783$	−6.50255	−	25.6850i	−0.232382	−	0.917905i
$784$	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	0.657578	−	0.753386i	$-0.271581\pi$
$787$	9.36750	+	5.40833i	0.333915	+	0.192786i	−0.323663	+	0.946172i	$0.604914\pi$
$788$	−40.7922			−1.45316
$789$	−11.0865	−	24.0643i	−0.394689	−	0.856712i
$790$		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
$795$	−20.6969	−	1.90702i	−0.734045	−	0.0676352i
$796$	1.00000	+	1.73205i	0.0354441	+	0.0613909i
$797$	11.0227	+	6.36396i	0.390444	+	0.225423i	0.682353	−	0.731023i	$-0.260957\pi$
$797$	11.0227	+	6.36396i	0.390444	+	0.225423i	−0.291908	+	0.956446i	$0.594290\pi$
$798$		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
$804$	−44.8434	−	4.13188i	−1.58150	−	0.145720i
$805$			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	−0.962149	−	0.272525i	$-0.912141\pi$
$809$	−20.3961	−	35.3270i	−0.717088	−	1.24203i	0.245061	−	0.969508i	$-0.421192\pi$
$810$		0			0
$811$			10.8167i			0.379824i	0.981801	+	0.189912i	$0.0608203\pi$
$811$			10.8167i			0.379824i	−0.981801	+	0.189912i	$0.939180\pi$
$812$	31.8434	+	18.3848i	1.11748	+	0.645179i
$813$	5.67201	−	2.61310i	0.198926	−	0.0916456i
$814$		0			0
$815$	−26.9444	−	15.5563i	−0.943821	−	0.544915i
$816$	35.1780	+	3.24132i	1.23148	+	0.113469i
$817$	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	0.999217	+	0.0395629i	$0.0125966\pi$
$821$	15.2971	+	26.4953i	0.533871	+	0.924692i	−0.465346	+	0.885129i	$0.654070\pi$
$822$		0			0
$823$	3.00000	−	5.19615i	0.104573	−	0.181126i	−0.808990	−	0.587822i	$-0.799986\pi$
$823$	3.00000	−	5.19615i	0.104573	−	0.181126i	0.913564	+	0.406695i	$0.133319\pi$
$824$		0			0
$825$	−15.5546	−	7.41990i	−0.541541	−	0.258328i
$826$		0			0
$827$	15.2971			0.531931			0.265965	−	0.963983i	$-0.414309\pi$
$827$	15.2971			0.531931			0.265965	+	0.963983i	$0.414309\pi$
$828$	−1.55051	+	8.34242i	−0.0538840	+	0.289919i
$829$	−17.5000	−	30.3109i	−0.607800	−	1.05274i	−0.991602	−	0.129325i	$-0.958719\pi$
$829$	−17.5000	−	30.3109i	−0.607800	−	1.05274i	0.383802	−	0.923415i	$-0.374614\pi$
$830$		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	$-0.513800\pi$
$839$	−26.9444	−	15.5563i	−0.930224	−	0.537065i	−0.886882	+	0.461996i	$0.847134\pi$
$840$		0			0
$841$	1.50000	−	2.59808i	0.0517241	−	0.0895888i
$842$		0			0
$843$	43.9725	+	4.05165i	1.51449	+	0.139546i
$844$			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
$849$	−28.3600	+	13.0655i	−0.973314	+	0.448408i
$850$		0			0
$851$	9.79796	+	5.65685i	0.335870	+	0.193914i
$852$	−8.89898	+	4.09978i	−0.304874	+	0.140456i
$853$		−	25.2389i		−	0.864162i	−0.901835	−	0.432081i	$-0.857779\pi$
$853$		−	25.2389i		−	0.864162i	0.901835	−	0.432081i	$-0.142221\pi$
$854$		0			0
$855$	−39.7619	+	46.5079i	−1.35983	+	1.59054i
$856$		0			0
$857$	−20.3961			−0.696717			−0.348358	−	0.937361i	$-0.613261\pi$
$857$	−20.3961			−0.696717			−0.348358	+	0.937361i	$0.613261\pi$
$858$		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
$861$	5.84337	−	63.4181i	0.199141	−	2.16128i
$862$		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
$867$	6.52270	+	14.1582i	0.221523	+	0.480837i
$868$	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
$873$	21.4444	−	25.0826i	0.725783	−	0.848918i
$874$		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	$-0.333333\pi$
$877$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$878$		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	$-0.851251\pi$
$881$	−28.1691	+	16.2635i	−0.949042	+	0.547930i	−0.0562589	+	0.998416i	$0.517917\pi$
$882$		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	0.762332	+	0.647186i	$0.224054\pi$
$887$	28.0446	+	48.5747i	0.941646	+	1.63098i	0.179314	+	0.983792i	$0.442612\pi$
$888$		0			0
$889$	−13.0000			−0.436006
$890$		0			0
$891$	−22.4265	−	19.6990i	−0.751317	−	0.659941i
$892$	−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
$897$	8.79451	+	0.810329i	0.293640	+	0.0270561i
$898$		0			0
$899$	2.54951	+	4.41588i	0.0850309	+	0.147278i
$900$	−11.6969	+	13.6814i	−0.389898	+	0.456048i
$901$	18.7350	+	10.8167i	0.624153	+	0.360355i
$902$		0			0
$903$	9.42168	+	20.4507i	0.313534	+	0.680557i
$904$		0			0
$905$		−	67.8823i		−	2.25648i
$906$		0			0
$907$	−21.0000	−	36.3731i	−0.697294	−	1.20775i	−0.969401	−	0.245481i	$-0.921054\pi$
$907$	−21.0000	−	36.3731i	−0.697294	−	1.20775i	0.272108	−	0.962267i	$-0.412279\pi$
$908$	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	$0.985080\pi$
$912$	4.58391	−	49.7492i	0.151789	−	1.64736i
$913$	−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	−0.444040	−	0.896007i	$-0.646455\pi$
$919$	−43.7150	−	25.2389i	−1.44202	−	0.832553i	−0.997985	+	0.0634540i	$0.979788\pi$
$920$		0			0
$921$	1.71897	−	18.6560i	0.0566419	−	0.614735i
$922$		0			0
$923$	5.09902	+	8.83176i	0.167836	+	0.290701i
$924$	41.2971	−	3.24853i	1.35857	−	0.106869i
$925$	12.0000	+	20.7846i	0.394558	+	0.683394i
$926$		0			0
$927$	2.94949	+	0.548188i	0.0968740	+	0.0180049i
$928$		0			0
$929$	39.1918	+	22.6274i	1.28584	+	0.742381i	0.977910	−	0.209027i	$-0.0670296\pi$
$929$	39.1918	+	22.6274i	1.28584	+	0.742381i	0.307932	+	0.951408i	$0.400363\pi$
$930$		0			0
$931$		−	43.2666i		−	1.41801i
$932$	−15.2971	+	26.4953i	−0.501072	+	0.867882i
$933$	−2.24745	+	24.3916i	−0.0735782	+	0.798544i
$934$		0			0
$935$	30.5941	+	36.7696i	1.00053	+	1.20249i
$936$		0			0
$937$		−	21.6333i		−	0.706729i	−0.935486	−	0.353365i	$-0.885037\pi$
$937$		−	21.6333i		−	0.706729i	0.935486	−	0.353365i	$-0.114963\pi$
$938$		0			0
$939$	8.62372	+	0.794593i	0.281425	+	0.0259306i
$940$	−28.0000	+	48.4974i	−0.913259	+	1.58181i
$941$	−40.7922			−1.32979			−0.664893	−	0.746938i	$-0.731523\pi$
$941$	−40.7922			−1.32979			−0.664893	+	0.746938i	$0.731523\pi$
$942$		0			0
$943$	−12.4900	−	7.21110i	−0.406730	−	0.234826i
$944$			16.9706i			0.552345i
$945$	−37.9851	+	36.9477i	−1.23566	+	1.20191i
$946$		0			0
$947$	14.6969	−	8.48528i	0.477586	−	0.275735i	−0.241824	−	0.970320i	$-0.577746\pi$
$947$	14.6969	−	8.48528i	0.477586	−	0.275735i	0.719410	+	0.694586i	$0.244412\pi$
$948$	10.1980	+	7.21110i	0.331217	+	0.234206i
$949$	−19.5000	+	33.7750i	−0.632997	+	1.09638i
$950$		0			0
$951$	−1.12372	+	12.1958i	−0.0364393	+	0.395476i
$952$		0			0
$953$	2.54951	−	4.41588i	0.0825867	−	0.143044i	−0.821774	−	0.569814i	$-0.807015\pi$
$953$	2.54951	−	4.41588i	0.0825867	−	0.143044i	0.904360	+	0.426770i	$0.140349\pi$
$954$		0			0
$955$	14.0000	−	24.2487i	0.453029	−	0.784670i
$956$	−5.09902	+	8.83176i	−0.164914	+	0.285640i
$957$	2.29706	+	29.2014i	0.0742534	+	0.943948i
$958$		0			0
$959$	−12.7475	−	22.0794i	−0.411640	−	0.712981i
$960$	3.59592	−	39.0265i	0.116058	−	1.25958i
$961$	−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	$0.301418\pi$
$967$			50.4777i			1.62325i	−0.584176	+	0.811627i	$0.698582\pi$
$968$		0			0
$969$	57.8434	−	26.6485i	1.85820	−	0.856075i
$970$		0			0
$971$	31.8434	+	18.3848i	1.02190	+	0.589996i	0.914654	−	0.404237i	$-0.132463\pi$
$971$	31.8434	+	18.3848i	1.02190	+	0.589996i	0.107248	+	0.994232i	$0.465796\pi$
$972$	−25.9444	+	17.2884i	−0.832167	+	0.554526i
$973$	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	$-0.608740\pi$
$977$	9.79796	−	5.65685i	0.313464	−	0.180979i	0.648476	+	0.761235i	$0.275407\pi$
$978$		0			0
$979$	−9.24500	+	1.59060i	−0.295471	+	0.0508358i
$980$		−	33.9411i		−	1.08421i
$981$	−1.97652	+	10.6345i	−0.0631054	+	0.339535i
$982$		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	0.955525	−	0.294911i	$-0.0952899\pi$
$991$	7.00000	+	12.1244i	0.222362	+	0.385143i	−0.733163	+	0.680053i	$0.761957\pi$
$992$		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	0.726420	−	0.687251i	$-0.241183\pi$
$997$	15.6125	+	9.01388i	0.494453	+	0.285472i	−0.231967	+	0.972724i	$0.574516\pi$
$998$		0			0
$999$	10.2020	+	40.2979i	0.322778	+	1.27497i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.p.a.230.1	✓	8	39.35	odd	6	inner
429.2.p.a.230.2	yes	8	429.230	even	6	inner
429.2.p.a.230.3	yes	8	13.9	even	3	inner
429.2.p.a.230.4	yes	8	143.87	odd	6	inner
429.2.p.a.263.1	yes	8	11.10	odd	2	inner
429.2.p.a.263.2	yes	8	1.1	even	1	trivial
429.2.p.a.263.3	yes	8	33.32	even	2	inner
429.2.p.a.263.4	yes	8	3.2	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-1.72474 - 0.158919i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.82843i q^{5} +(3.12250 + 1.80278i) q^{7} +(2.94949 + 0.548188i) q^{9} +O(q^{10})\)	\(q+(-1.72474 - 0.158919i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.82843i q^{5} +(3.12250 + 1.80278i) q^{7} +(2.94949 + 0.548188i) q^{9} +(-3.11187 - 1.14728i) q^{11} +(-2.00000 + 2.82843i) q^{12} +(3.12250 + 1.80278i) q^{13} +(-0.449490 + 4.87832i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(2.54951 - 4.41588i) q^{17} +(-6.24500 - 3.60555i) q^{19} +(-4.89898 - 2.82843i) q^{20} +(-5.09902 - 3.60555i) q^{21} +(-1.22474 + 0.707107i) q^{23} -3.00000 q^{25} +(-5.00000 - 1.41421i) q^{27} +(6.24500 - 3.60555i) q^{28} +(2.54951 + 4.41588i) q^{29} +1.00000 q^{31} +(5.18486 + 2.47330i) q^{33} +(5.09902 - 8.83176i) q^{35} +(3.89898 - 4.56048i) q^{36} +(-4.00000 - 6.92820i) q^{37} +(-5.09902 - 3.60555i) q^{39} +(5.09902 + 8.83176i) q^{41} +(-3.12250 - 1.80278i) q^{43} +(-5.09902 + 4.24264i) q^{44} +(1.55051 - 8.34242i) q^{45} -9.89949i q^{47} +(2.89898 + 6.29253i) q^{48} +(3.00000 + 5.19615i) q^{49} +(-5.09902 + 7.21110i) q^{51} +(6.24500 - 3.60555i) q^{52} +4.24264i q^{53} +(-3.24500 + 8.80170i) q^{55} +(10.1980 + 7.21110i) q^{57} +(-3.67423 - 2.12132i) q^{59} +(8.00000 + 5.65685i) q^{60} +(3.12250 + 1.80278i) q^{61} +(8.22152 + 7.02899i) q^{63} -8.00000 q^{64} +(5.09902 - 8.83176i) q^{65} +(6.50000 + 11.2583i) q^{67} +(-5.09902 - 8.83176i) q^{68} +(2.22474 - 1.02494i) q^{69} +(2.44949 + 1.41421i) q^{71} +10.8167i q^{73} +(5.17423 + 0.476756i) q^{75} +(-12.4900 + 7.21110i) q^{76} +(-7.64853 - 9.19239i) q^{77} -3.60555i q^{79} +(-9.79796 + 5.65685i) q^{80} +(8.39898 + 3.23375i) q^{81} +5.09902 q^{83} +(-11.3440 + 5.22621i) q^{84} +(-12.4900 - 7.21110i) q^{85} +(-3.69549 - 8.02143i) q^{87} +(2.44949 - 1.41421i) q^{89} +(6.50000 + 11.2583i) q^{91} +2.82843i q^{92} +(-1.72474 - 0.158919i) q^{93} +(-10.1980 + 17.6635i) q^{95} +(5.50000 - 9.52628i) q^{97} +(-8.54951 - 5.08978i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 8 q^{4} + 4 q^{9}+O(q^{10}) \) 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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