LMFDB - Embedded newform 600.2.bp.a.77.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [600,2,Mod(53,600)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("600.53"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(600, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 10, 10, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.bp (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	16.0.6879707136000000000000.9
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 9x^{12} + 81x^{8} - 729x^{4} + 6561 $ x^16 - 9x^12 + 81x^8 - 729*x^4 + 6561
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{20}]$

Embedding invariants

Embedding label			77.2
Root			$-0.270952 + 1.71073i$ of defining polynomial
Character	$\chi$	$=$	600.77
Dual form			600.2.bp.a.413.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39680 - 0.221232i) q^{2} +(0.786335 + 1.54327i) q^{3} +(1.90211 + 0.618034i) q^{4} +(1.93196 - 1.12585i) q^{5} +(-0.756934 - 2.32960i) q^{6} +(3.72858 + 3.72858i) q^{7} +(-2.52015 - 1.28408i) q^{8} +(-1.76336 + 2.42705i) q^{9} +(-2.94764 + 1.14518i) q^{10} +(3.48393 - 2.53123i) q^{11} +(0.541905 + 3.42145i) q^{12} +(-4.38320 - 6.03296i) q^{14} +(3.25665 + 2.09624i) q^{15} +(3.23607 + 2.35114i) q^{16} +(3.00000 - 3.00000i) q^{18} +(4.37062 - 0.947478i) q^{20} +(-2.82229 + 8.68610i) q^{21} +(-5.42636 + 2.76487i) q^{22} -4.89898i q^{24} +(2.46492 - 4.35019i) q^{25} +(-5.13218 - 0.812857i) q^{27} +(4.78779 + 9.39656i) q^{28} +(-8.89092 - 2.88884i) q^{29} +(-4.08515 - 3.64850i) q^{30} +(-3.40674 - 10.4849i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(6.64590 + 3.38626i) q^{33} +(11.4013 + 3.00564i) q^{35} +(-4.85410 + 3.52671i) q^{36} +(-6.31450 + 0.356520i) q^{40} +(5.86382 - 11.5084i) q^{42} +(8.19122 - 2.66149i) q^{44} +(-0.674235 + 6.67423i) q^{45} +(-1.08381 + 6.84291i) q^{48} +20.8046i q^{49} +(-4.40541 + 5.53103i) q^{50} +(2.50150 + 4.90947i) q^{53} +(6.98881 + 2.27080i) q^{54} +(3.88103 - 8.81261i) q^{55} +(-4.60877 - 14.1843i) q^{56} +(11.7798 + 6.00209i) q^{58} +(-5.61259 + 7.72506i) q^{59} +(4.89898 + 6.00000i) q^{60} +(2.43895 + 15.3990i) q^{62} +(-15.6243 + 2.47464i) q^{63} +(4.70228 + 6.47214i) q^{64} +(-8.53386 - 6.20021i) q^{66} +(-15.2604 - 6.72060i) q^{70} +(7.56044 - 3.85224i) q^{72} +(-0.464812 + 2.93471i) q^{73} +(8.65177 + 0.383336i) q^{75} +(22.4280 + 3.55224i) q^{77} +(-5.71796 - 1.85788i) q^{79} +(8.89898 + 0.898979i) q^{80} +(-2.78115 - 8.55951i) q^{81} +(13.1198 + 6.68488i) q^{83} +(-10.7366 + 14.7777i) q^{84} +(-2.53299 - 15.9927i) q^{87} +(-12.0303 + 1.90542i) q^{88} +(2.41832 - 9.17342i) q^{90} +(13.5021 - 13.5021i) q^{93} +(3.02774 - 9.31841i) q^{96} +(6.33893 - 3.22985i) q^{97} +(4.60263 - 29.0599i) q^{98} +12.9191i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 4 q^{5} + 4 q^{7} + 8 q^{8} + 8 q^{10} + 24 q^{11} - 12 q^{15} + 16 q^{16} + 48 q^{18} + 8 q^{20} - 36 q^{21} - 16 q^{22} + 32 q^{28} - 12 q^{30} - 64 q^{32} + 12 q^{33} - 8 q^{35} - 24 q^{36}+ \cdots - 72 q^{98}+O(q^{100}) $ 16 * q - 4 * q^2 + 4 * q^5 + 4 * q^7 + 8 * q^8 + 8 * q^10 + 24 * q^11 - 12 * q^15 + 16 * q^16 + 48 * q^18 + 8 * q^20 - 36 * q^21 - 16 * q^22 + 32 * q^28 - 12 * q^30 - 64 * q^32 + 12 * q^33 - 8 * q^35 - 24 * q^36 + 24 * q^42 + 48 * q^45 + 4 * q^50 + 28 * q^55 + 24 * q^56 - 8 * q^58 - 80 * q^59 + 12 * q^63 - 36 * q^66 - 32 * q^70 - 24 * q^72 - 28 * q^73 + 24 * q^75 + 12 * q^77 + 64 * q^80 + 36 * q^81 - 24 * q^83 - 36 * q^87 + 32 * q^88 - 24 * q^93 - 16 * q^97 - 72 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{20}\right)$

Coefficient data

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

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

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

$2$	−1.39680	−	0.221232i	−0.987688	−	0.156434i
$2$	−1.39680	−	0.221232i	−0.987688	−	0.156434i
$3$	0.786335	+	1.54327i	0.453990	+	0.891007i
$3$	0.786335	+	1.54327i	0.453990	+	0.891007i
$4$	1.90211	+	0.618034i	0.951057	+	0.309017i
$5$	1.93196	−	1.12585i	0.863998	−	0.503495i
$5$	1.93196	−	1.12585i	0.863998	−	0.503495i
$6$	−0.756934	−	2.32960i	−0.309017	−	0.951057i
$7$	3.72858	+	3.72858i	1.40927	+	1.40927i	0.763710	+	0.645560i	$0.223376\pi$
$7$	3.72858	+	3.72858i	1.40927	+	1.40927i	0.645560	+	0.763710i	$0.276624\pi$
$8$	−2.52015	−	1.28408i	−0.891007	−	0.453990i
$9$	−1.76336	+	2.42705i	−0.587785	+	0.809017i
$10$	−2.94764	+	1.14518i	−0.932125	+	0.362137i
$11$	3.48393	−	2.53123i	1.05045	−	0.763194i	0.0781486	−	0.996942i	$-0.475099\pi$
$11$	3.48393	−	2.53123i	1.05045	−	0.763194i	0.972297	+	0.233748i	$0.0750991\pi$
$12$	0.541905	+	3.42145i	0.156434	+	0.987688i
$13$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$13$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$14$	−4.38320	−	6.03296i	−1.17146	−	1.61238i
$15$	3.25665	+	2.09624i	0.840864	+	0.541246i
$16$	3.23607	+	2.35114i	0.809017	+	0.587785i
$17$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$17$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$18$	3.00000	−	3.00000i	0.707107	−	0.707107i
$19$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$19$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$20$	4.37062	−	0.947478i	0.977299	−	0.211862i
$21$	−2.82229	+	8.68610i	−0.615873	+	1.89546i
$22$	−5.42636	+	2.76487i	−1.15690	+	0.589471i
$23$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$23$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$24$		−	4.89898i		−	1.00000i
$25$	2.46492	−	4.35019i	0.492985	−	0.870038i
$26$		0			0
$27$	−5.13218	−	0.812857i	−0.987688	−	0.156434i
$28$	4.78779	+	9.39656i	0.904807	+	1.77578i
$29$	−8.89092	−	2.88884i	−1.65100	−	0.536443i	−0.672046	−	0.740510i	$-0.734584\pi$
$29$	−8.89092	−	2.88884i	−1.65100	−	0.536443i	−0.978957	+	0.204066i	$0.934584\pi$
$30$	−4.08515	−	3.64850i	−0.745843	−	0.666122i
$31$	−3.40674	−	10.4849i	−0.611868	−	1.88314i	−0.439941	−	0.898027i	$-0.645001\pi$
$31$	−3.40674	−	10.4849i	−0.611868	−	1.88314i	−0.171927	−	0.985110i	$-0.554999\pi$
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$	6.64590	+	3.38626i	1.15690	+	0.589471i
$34$		0			0
$35$	11.4013	+	3.00564i	1.92717	+	0.508045i
$36$	−4.85410	+	3.52671i	−0.809017	+	0.587785i
$37$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$37$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$38$		0			0
$39$		0			0
$40$	−6.31450	+	0.356520i	−0.998410	+	0.0563708i
$41$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$41$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$42$	5.86382	−	11.5084i	0.904807	−	1.77578i
$43$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$43$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$44$	8.19122	−	2.66149i	1.23487	−	0.401235i
$45$	−0.674235	+	6.67423i	−0.100509	+	0.994936i
$46$		0			0
$47$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$47$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$48$	−1.08381	+	6.84291i	−0.156434	+	0.987688i
$49$			20.8046i			2.97208i
$50$	−4.40541	+	5.53103i	−0.623019	+	0.782206i
$51$		0			0
$52$		0			0
$53$	2.50150	+	4.90947i	0.343607	+	0.674367i	0.996546	−	0.0830438i	$-0.0264641\pi$
$53$	2.50150	+	4.90947i	0.343607	+	0.674367i	−0.652939	+	0.757411i	$0.726464\pi$
$54$	6.98881	+	2.27080i	0.951057	+	0.309017i
$55$	3.88103	−	8.81261i	0.523319	−	1.18829i
$56$	−4.60877	−	14.1843i	−0.615873	−	1.89546i
$57$		0			0
$58$	11.7798	+	6.00209i	1.54676	+	0.788113i
$59$	−5.61259	+	7.72506i	−0.730697	+	1.00572i	0.268404	+	0.963307i	$0.413504\pi$
$59$	−5.61259	+	7.72506i	−0.730697	+	1.00572i	−0.999100	+	0.0424110i	$0.986496\pi$
$60$	4.89898	+	6.00000i	0.632456	+	0.774597i
$61$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$61$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$62$	2.43895	+	15.3990i	0.309748	+	1.95567i
$63$	−15.6243	+	2.47464i	−1.96847	+	0.311775i
$64$	4.70228	+	6.47214i	0.587785	+	0.809017i
$65$		0			0
$66$	−8.53386	−	6.20021i	−1.05045	−	0.763194i
$67$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$67$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$68$		0			0
$69$		0			0
$70$	−15.2604	−	6.72060i	−1.82396	−	0.803266i
$71$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$71$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$72$	7.56044	−	3.85224i	0.891007	−	0.453990i
$73$	−0.464812	+	2.93471i	−0.0544022	+	0.343482i	0.945441	+	0.325792i	$0.105631\pi$
$73$	−0.464812	+	2.93471i	−0.0544022	+	0.343482i	−0.999844	+	0.0176895i	$0.994369\pi$
$74$		0			0
$75$	8.65177	+	0.383336i	0.999020	+	0.0442638i
$76$		0			0
$77$	22.4280	+	3.55224i	2.55591	+	0.404816i
$78$		0			0
$79$	−5.71796	−	1.85788i	−0.643321	−	0.209028i	−0.0308541	−	0.999524i	$-0.509823\pi$
$79$	−5.71796	−	1.85788i	−0.643321	−	0.209028i	−0.612467	+	0.790496i	$0.709823\pi$
$80$	8.89898	+	0.898979i	0.994936	+	0.100509i
$81$	−2.78115	−	8.55951i	−0.309017	−	0.951057i
$82$		0			0
$83$	13.1198	+	6.68488i	1.44009	+	0.733761i	0.987450	−	0.157933i	$-0.0504832\pi$
$83$	13.1198	+	6.68488i	1.44009	+	0.733761i	0.452638	+	0.891695i	$0.350483\pi$
$84$	−10.7366	+	14.7777i	−1.17146	+	1.61238i
$85$		0			0
$86$		0			0
$87$	−2.53299	−	15.9927i	−0.271565	−	1.71459i
$88$	−12.0303	+	1.90542i	−1.28244	+	0.203118i
$89$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$89$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$90$	2.41832	−	9.17342i	0.254914	−	0.966964i
$91$		0			0
$92$		0			0
$93$	13.5021	−	13.5021i	1.40010	−	1.40010i
$94$		0			0
$95$		0			0
$96$	3.02774	−	9.31841i	0.309017	−	0.951057i
$97$	6.33893	−	3.22985i	0.643621	−	0.327941i	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	6.33893	−	3.22985i	0.643621	−	0.327941i	0.745155	+	0.666891i	$0.232375\pi$
$98$	4.60263	−	29.0599i	0.464936	−	2.93549i
$99$			12.9191i			1.29842i
$100$	7.37713	−	6.75114i	0.737713	−	0.675114i
$101$	−20.0971			−1.99974			−0.999870	−	0.0161300i	$-0.994865\pi$
$101$	−20.0971			−1.99974			−0.999870	+	0.0161300i	$0.994865\pi$
$102$		0			0
$103$	−2.63397	−	5.16946i	−0.259533	−	0.509362i	0.724066	−	0.689730i	$-0.242271\pi$
$103$	−2.63397	−	5.16946i	−0.259533	−	0.509362i	−0.983599	+	0.180368i	$0.942271\pi$
$104$		0			0
$105$	4.32671	+	19.9587i	0.422244	+	1.94777i
$106$	−2.40797	−	7.41096i	−0.233883	−	0.719816i
$107$	−0.726734	−	0.726734i	−0.0702560	−	0.0702560i	0.671106	−	0.741362i	$-0.265820\pi$
$107$	−0.726734	−	0.726734i	−0.0702560	−	0.0702560i	−0.741362	+	0.671106i	$0.765820\pi$
$108$	−9.25961	−	4.71801i	−0.891007	−	0.453990i
$109$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$109$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$110$	−7.37067	+	11.4509i	−0.702766	+	1.09180i
$111$		0			0
$112$	3.29952	+	20.8323i	0.311775	+	1.96847i
$113$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$113$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$114$		0			0
$115$		0			0
$116$	−15.1261	−	10.9898i	−1.40443	−	1.02038i
$117$		0			0
$118$	9.54870	−	9.54870i	0.879029	−	0.879029i
$119$		0			0
$120$	−5.51552	−	9.46462i	−0.503495	−	0.863998i
$121$	2.33150	−	7.17563i	0.211955	−	0.652330i
$122$		0			0
$123$		0			0
$124$		−	22.0489i		−	1.98005i
$125$	−0.135529	−	11.1795i	−0.0121221	−	0.999927i
$126$	22.3715			1.99301
$127$	−20.7047	−	3.27930i	−1.83724	−	0.290991i	−0.861152	−	0.508348i	$-0.830256\pi$
$127$	−20.7047	−	3.27930i	−1.83724	−	0.290991i	−0.976092	+	0.217357i	$0.930256\pi$
$128$	−5.13632	−	10.0806i	−0.453990	−	0.891007i
$129$		0			0
$130$		0			0
$131$	−4.18734	−	12.8873i	−0.365849	−	1.12597i	−0.949447	−	0.313926i	$-0.898356\pi$
$131$	−4.18734	−	12.8873i	−0.365849	−	1.12597i	0.583598	−	0.812043i	$-0.301644\pi$
$132$	10.5484	+	10.5484i	0.918123	+	0.918123i
$133$		0			0
$134$		0			0
$135$	−10.8303	+	4.20766i	−0.932125	+	0.362137i
$136$		0			0
$137$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$137$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$138$		0			0
$139$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$139$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$140$	19.8289	+	12.7634i	1.67585	+	1.07871i
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−11.4127	+	3.70820i	−0.951057	+	0.309017i
$145$	−20.4293	+	4.42873i	−1.69656	+	0.367786i
$146$	1.29850	−	3.99638i	0.107465	−	0.330743i
$147$	−32.1070	+	16.3594i	−2.64814	+	1.34930i
$148$		0			0
$149$		−	0.999730i		−	0.0819010i	−0.999161	−	0.0409505i	$-0.986961\pi$
$149$		−	0.999730i		−	0.0819010i	0.999161	−	0.0409505i	$-0.0130386\pi$
$150$	−12.0000	−	2.44949i	−0.979796	−	0.200000i
$151$	23.9141			1.94610			0.973050	−	0.230596i	$-0.0740676\pi$
$151$	23.9141			1.94610			0.973050	+	0.230596i	$0.0740676\pi$
$152$		0			0
$153$		0			0
$154$	−30.5416	−	9.92357i	−2.46111	−	0.799664i
$155$	−18.3860	−	16.4208i	−1.47680	−	1.31895i
$156$		0			0
$157$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$157$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$158$	7.57584	+	3.86008i	0.602701	+	0.307092i
$159$	−5.60961	+	7.72096i	−0.444871	+	0.612312i
$160$	−12.2312	−	3.22443i	−0.966964	−	0.254914i
$161$		0			0
$162$	1.99109	+	12.5712i	0.156434	+	0.987688i
$163$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$163$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$164$		0			0
$165$	16.6520	−	0.940182i	1.29636	−	0.0731931i
$166$	−16.8469	−	12.2400i	−1.30757	−	0.950007i
$167$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$167$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$168$	18.2662	−	18.2662i	1.40927	−	1.40927i
$169$	12.3637	−	4.01722i	0.951057	−	0.309017i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.61981	+	10.2271i	−0.123152	+	0.777550i	0.846379	+	0.532581i	$0.178778\pi$
$173$	−1.61981	+	10.2271i	−0.123152	+	0.777550i	−0.969531	+	0.244969i	$0.921222\pi$
$174$			22.8990i			1.73597i
$175$	25.4107	−	7.02935i	1.92087	−	0.531369i
$176$	17.2255			1.29842
$177$	−16.3352	−	2.58724i	−1.22783	−	0.194469i
$178$		0			0
$179$	−0.882672	−	0.286798i	−0.0659740	−	0.0214363i	0.275844	−	0.961202i	$-0.411043\pi$
$179$	−0.882672	−	0.286798i	−0.0659740	−	0.0214363i	−0.341818	+	0.939766i	$0.611043\pi$
$180$	−5.40737	+	12.2784i	−0.403042	+	0.915182i
$181$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$181$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$	−21.8469	+	15.8727i	−1.60189	+	1.16384i
$187$		0			0
$188$		0			0
$189$	−16.1049	−	22.1665i	−1.17146	−	1.61238i
$190$		0			0
$191$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$191$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$192$	−6.29068	+	12.3461i	−0.453990	+	0.891007i
$193$	−13.2356	+	13.2356i	−0.952721	+	0.952721i	−0.998932	−	0.0462111i	$-0.985285\pi$
$193$	−13.2356	+	13.2356i	−0.952721	+	0.952721i	0.0462111	+	0.998932i	$0.485285\pi$
$194$	−9.56878	+	3.10908i	−0.686998	+	0.223219i
$195$		0			0
$196$	−12.8579	+	39.5726i	−0.918424	+	2.82662i
$197$	−18.6606	+	9.50803i	−1.32951	+	0.677419i	−0.967051	−	0.254581i	$-0.918062\pi$
$197$	−18.6606	+	9.50803i	−1.32951	+	0.677419i	−0.362458	+	0.932000i	$0.618062\pi$
$198$	2.85812	−	18.0455i	0.203118	−	1.28244i
$199$		−	25.7240i		−	1.82352i	−0.410718	−	0.911762i	$-0.634722\pi$
$199$		−	25.7240i		−	1.82352i	0.410718	−	0.911762i	$-0.365278\pi$
$200$	−11.7980	+	7.79796i	−0.834242	+	0.551399i
$201$		0			0
$202$	28.0717	+	4.44612i	1.97512	+	0.312828i
$203$	−22.3792	−	43.9217i	−1.57071	−	3.08270i
$204$		0			0
$205$		0			0
$206$	2.53549	+	7.80343i	0.176656	+	0.543691i
$207$		0			0
$208$		0			0
$209$		0			0
$210$	−1.62807	−	28.8355i	−0.112347	−	1.98984i
$211$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$211$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$212$	1.72391	+	10.8844i	0.118399	+	0.747541i
$213$		0			0
$214$	0.854327	+	1.17588i	0.0584006	+	0.0803815i
$215$		0			0
$216$	11.8901	+	8.63864i	0.809017	+	0.587785i
$217$	26.3913	−	51.7959i	1.79156	−	3.51613i
$218$		0			0
$219$	−4.89454	+	1.59033i	−0.330743	+	0.107465i
$220$	12.8287	−	14.3640i	0.864908	−	0.968419i
$221$		0			0
$222$		0			0
$223$	1.63454	−	10.3201i	0.109457	−	0.691082i	−0.870544	−	0.492090i	$-0.836233\pi$
$223$	1.63454	−	10.3201i	0.109457	−	0.691082i	0.980001	−	0.198992i	$-0.0637669\pi$
$224$		−	29.8286i		−	1.99301i
$225$	6.21159	+	13.6534i	0.414106	+	0.910229i
$226$		0			0
$227$	24.7244	+	3.91597i	1.64102	+	0.259912i	0.907591	−	0.419856i	$-0.137919\pi$
$227$	24.7244	+	3.91597i	1.64102	+	0.259912i	0.733428	+	0.679768i	$0.237919\pi$
$228$		0			0
$229$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$229$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$230$		0			0
$231$	12.1538	+	37.4057i	0.799664	+	2.46111i
$232$	18.6969	+	18.6969i	1.22751	+	1.22751i
$233$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$233$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$234$		0			0
$235$		0			0
$236$	−15.4501	+	11.2252i	−1.00572	+	0.730697i
$237$	−1.62903	−	10.2853i	−0.105817	−	0.668100i
$238$		0			0
$239$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$239$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$240$	5.61021	+	14.4404i	0.362137	+	0.932125i
$241$	15.0427	+	10.9291i	0.968984	+	0.704008i	0.955220	−	0.295897i	$-0.0956186\pi$
$241$	15.0427	+	10.9291i	0.968984	+	0.704008i	0.0137643	+	0.999905i	$0.495619\pi$
$242$	−4.84413	+	9.50714i	−0.311392	+	0.611142i
$243$	11.0227	−	11.0227i	0.707107	−	0.707107i
$244$		0			0
$245$	23.4228	+	40.1936i	1.49643	+	2.56787i
$246$		0			0
$247$		0			0
$248$	−4.87791	+	30.7979i	−0.309748	+	1.95567i
$249$			25.5040i			1.61625i
$250$	−2.28396	+	15.6456i	−0.144450	+	0.989512i
$251$	19.1943			1.21153			0.605767	−	0.795642i	$-0.292866\pi$
$251$	19.1943			1.21153			0.605767	+	0.795642i	$0.292866\pi$
$252$	−31.2485	−	4.94928i	−1.96847	−	0.311775i
$253$		0			0
$254$	28.1949	+	9.16107i	1.76910	+	0.574817i
$255$		0			0
$256$	4.94427	+	15.2169i	0.309017	+	0.951057i
$257$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$257$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	22.6892	−	16.4847i	1.40443	−	1.02038i
$262$	2.99780	+	18.9274i	0.185205	+	1.16934i
$263$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$263$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$264$	−12.4004	−	17.0677i	−0.763194	−	1.05045i
$265$	10.3601	+	6.66857i	0.636416	+	0.409647i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−4.62714	+	1.50345i	−0.282121	+	0.0916668i	−0.446660	−	0.894704i	$-0.647387\pi$
$269$	−4.62714	+	1.50345i	−0.282121	+	0.0916668i	0.164538	+	0.986371i	$0.447387\pi$
$270$	16.0587	−	3.48126i	0.977299	−	0.211862i
$271$	9.29968	−	28.6215i	0.564915	−	1.73863i	−0.103287	−	0.994652i	$-0.532936\pi$
$271$	9.29968	−	28.6215i	0.564915	−	1.73863i	0.668202	−	0.743980i	$-0.267064\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.42368	−	21.3951i	−0.146153	−	1.29017i
$276$		0			0
$277$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$277$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$278$		0			0
$279$	31.4546	+	10.2202i	1.88314	+	0.611868i
$280$	−24.8734	−	22.2148i	−1.48647	−	1.32759i
$281$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$281$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$282$		0			0
$283$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$283$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	16.7616	−	2.65478i	0.987688	−	0.156434i
$289$	−9.99235	−	13.7533i	−0.587785	−	0.809017i
$290$	29.5154	−	1.66646i	1.73321	−	0.0978578i
$291$	9.96904	+	7.24293i	0.584395	+	0.424588i
$292$	−2.69788	+	5.29488i	−0.157881	+	0.309859i
$293$	−23.7130	+	23.7130i	−1.38533	+	1.38533i	−0.550473	+	0.834853i	$0.685553\pi$
$293$	−23.7130	+	23.7130i	−1.38533	+	1.38533i	−0.834853	+	0.550473i	$0.814447\pi$
$294$	48.4664	−	15.7477i	2.82662	−	0.918424i
$295$	−2.14602	+	21.2434i	−0.124946	+	1.23684i
$296$		0			0
$297$	−19.9377	+	10.1588i	−1.15690	+	0.589471i
$298$	−0.221172	+	1.39642i	−0.0128121	+	0.0808927i
$299$		0			0
$300$	16.2197	+	6.07623i	0.936446	+	0.350812i
$301$		0			0
$302$	−33.4032	−	5.29055i	−1.92214	−	0.304437i
$303$	−15.8031	−	31.0153i	−0.907863	−	1.78178i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$307$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$308$	40.4652	+	20.6180i	2.30572	+	1.17482i
$309$	5.90668	−	8.12985i	0.336019	−	0.462491i
$310$	22.0489	+	27.0042i	1.25229	+	1.53374i
$311$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$311$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$312$		0			0
$313$	−4.30490	+	0.681829i	−0.243327	+	0.0385392i	−0.276907	−	0.960897i	$-0.589309\pi$
$313$	−4.30490	+	0.681829i	−0.243327	+	0.0385392i	0.0335795	+	0.999436i	$0.489309\pi$
$314$		0			0
$315$	−27.3993	+	22.3715i	−1.54378	+	1.26049i
$316$	−9.72798	−	7.06779i	−0.547241	−	0.397594i
$317$	16.0492	−	31.4984i	0.901414	−	1.76912i	0.343738	−	0.939066i	$-0.388307\pi$
$317$	16.0492	−	31.4984i	0.901414	−	1.76912i	0.557676	−	0.830059i	$-0.311693\pi$
$318$	9.54364	−	9.54364i	0.535181	−	0.535181i
$319$	−38.2877	+	12.4404i	−2.14370	+	0.696530i
$320$	16.3713	+	7.20983i	0.915182	+	0.403042i
$321$	0.550089	−	1.69300i	0.0307030	−	0.0944941i
$322$		0			0
$323$		0			0
$324$		−	18.0000i		−	1.00000i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$	−23.4676	−	2.37071i	−1.29185	−	0.130503i
$331$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$331$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$332$	20.8239	+	20.8239i	1.14286	+	1.14286i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	−29.5554	+	21.4732i	−1.61238	+	1.17146i
$337$	5.15400	+	32.5411i	0.280756	+	1.77262i	0.576244	+	0.817278i	$0.304518\pi$
$337$	5.15400	+	32.5411i	0.280756	+	1.77262i	−0.295488	+	0.955347i	$0.595482\pi$
$338$	−18.1584	+	2.87601i	−0.987688	+	0.156434i
$339$		0			0
$340$		0			0
$341$	−38.4084	−	27.9053i	−2.07993	−	1.51116i
$342$		0			0
$343$	−51.4714	+	51.4714i	−2.77919	+	2.77919i
$344$		0			0
$345$		0			0
$346$	4.52511	−	13.9268i	0.243271	−	0.748712i
$347$	2.66637	−	1.35859i	0.143138	−	0.0729327i	−0.380954	−	0.924594i	$-0.624404\pi$
$347$	2.66637	−	1.35859i	0.143138	−	0.0729327i	0.524093	+	0.851661i	$0.324404\pi$
$348$	5.06598	−	31.9853i	0.271565	−	1.71459i
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$	−37.0488	+	4.19697i	−1.98034	+	0.224338i
$351$		0			0
$352$	−24.0606	−	3.81083i	−1.28244	−	0.203118i
$353$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$353$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$354$	22.2447	+	7.22774i	1.18229	+	0.384150i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	1.16947	+	0.595875i	0.0618084	+	0.0314930i
$359$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$359$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$360$	10.2694	−	15.9543i	0.541246	−	0.840864i
$361$	15.3713	−	11.1679i	0.809017	−	0.587785i
$362$		0			0
$363$	12.9073	−	2.04431i	0.677456	−	0.107298i
$364$		0			0
$365$	2.40604	+	6.19305i	0.125938	+	0.324159i
$366$		0			0
$367$	−14.3616	+	28.1862i	−0.749670	+	1.47131i	0.127862	+	0.991792i	$0.459188\pi$
$367$	−14.3616	+	28.1862i	−0.749670	+	1.47131i	−0.877532	+	0.479518i	$0.840812\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−8.97829	+	27.6323i	−0.466130	+	1.43460i
$372$	34.0273	−	17.3378i	1.76423	−	0.898922i
$373$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$373$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$374$		0			0
$375$	17.1464	−	9.00000i	0.885438	−	0.464758i
$376$		0			0
$377$		0			0
$378$	17.5915	+	34.5252i	0.904807	+	1.77578i
$379$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$379$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$380$		0			0
$381$	−11.2200	−	34.5315i	−0.574817	−	1.76910i
$382$		0			0
$383$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$383$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$384$	11.5182	−	15.8534i	0.587785	−	0.809017i
$385$	47.3292	−	18.3878i	2.41212	−	0.937127i
$386$	21.4157	−	15.5594i	1.09003	−	0.791953i
$387$		0			0
$388$	14.0535	−	2.22586i	0.713459	−	0.113001i
$389$	11.2167	+	15.4385i	0.568712	+	0.782764i	0.992401	−	0.123043i	$-0.0392653\pi$
$389$	11.2167	+	15.4385i	0.568712	+	0.782764i	−0.423690	+	0.905807i	$0.639265\pi$
$390$		0			0
$391$		0			0
$392$	26.7147	−	52.4306i	1.34930	−	2.64814i
$393$	16.5959	−	16.5959i	0.837153	−	0.837153i
$394$	28.1686	−	9.15253i	1.41911	−	0.461098i
$395$	−13.1386	+	2.84822i	−0.661072	+	0.143310i
$396$	−7.98447	+	24.5737i	−0.401235	+	1.23487i
$397$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$397$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$398$	−5.69096	+	35.9313i	−0.285262	+	1.80107i
$399$		0			0
$400$	18.2046	−	8.28212i	0.910229	−	0.414106i
$401$		0			0		1.00000			$0$
$401$		0			0		−1.00000			$\pi$
$402$		0			0
$403$		0			0
$404$	−38.2270	−	12.4207i	−1.90187	−	0.617954i
$405$	−15.0098	−	13.4055i	−0.745843	−	0.666122i
$406$	21.5425	+	66.3010i	1.06914	+	3.29046i
$407$		0			0
$408$		0			0
$409$	−15.1819	+	20.8961i	−0.750697	+	1.03325i	0.247234	+	0.968956i	$0.420478\pi$
$409$	−15.1819	+	20.8961i	−0.750697	+	1.03325i	−0.997931	+	0.0642902i	$0.979522\pi$
$410$		0			0
$411$		0			0
$412$	−1.81521	−	11.4608i	−0.0894290	−	0.564632i
$413$	−49.7305	+	7.87653i	−2.44708	+	0.387579i
$414$		0			0
$415$	32.8731	−	1.85603i	1.61368	−	0.0911091i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	25.9037	−	8.41661i	1.26548	−	0.411178i	0.402034	−	0.915625i	$-0.368303\pi$
$419$	25.9037	−	8.41661i	1.26548	−	0.411178i	0.863443	+	0.504447i	$0.168303\pi$
$420$	−4.10524	+	40.6377i	−0.200315	+	1.98292i
$421$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$421$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$422$		0			0
$423$		0			0
$424$		−	15.5847i		−	0.756860i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.933184	−	1.83148i	−0.0451071	−	0.0885277i
$429$		0			0
$430$		0			0
$431$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$431$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$432$	−14.6969	−	14.6969i	−0.707107	−	0.707107i
$433$	−36.4416	−	18.5679i	−1.75127	−	0.892318i	−0.959597	−	0.281377i	$-0.909209\pi$
$433$	−36.4416	−	18.5679i	−1.75127	−	0.892318i	−0.791676	−	0.610941i	$-0.790791\pi$
$434$	−48.3223	+	66.5100i	−2.31955	+	3.19258i
$435$	−22.8990	−	28.0454i	−1.09792	−	1.34467i
$436$		0			0
$437$		0			0
$438$	7.18854	−	1.13855i	0.343482	−	0.0544022i
$439$	24.6307	+	33.9013i	1.17556	+	1.61802i	0.591022	+	0.806655i	$0.298725\pi$
$439$	24.6307	+	33.9013i	1.17556	+	1.61802i	0.584539	+	0.811366i	$0.301275\pi$
$440$	−21.0969	+	17.2255i	−1.00575	+	0.821194i
$441$	−50.4937	−	36.6859i	−2.40446	−	1.74695i
$442$		0			0
$443$	25.8335	−	25.8335i	1.22739	−	1.22739i	0.262440	−	0.964948i	$-0.415473\pi$
$443$	25.8335	−	25.8335i	1.22739	−	1.22739i	0.964948	−	0.262440i	$-0.0845272\pi$
$444$		0			0
$445$		0			0
$446$	−4.56625	+	14.0535i	−0.216218	+	0.665451i
$447$	1.54285	−	0.786122i	0.0729744	−	0.0371823i
$448$	−6.59904	+	41.6647i	−0.311775	+	1.96847i
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$	−5.65579	−	20.4453i	−0.266617	−	0.963803i
$451$		0			0
$452$		0			0
$453$	18.8045	+	36.9058i	0.883510	+	1.73399i
$454$	−33.6688	−	10.9397i	−1.58016	−	0.513424i
$455$		0			0
$456$		0			0
$457$	−24.3716	−	24.3716i	−1.14006	−	1.14006i	−0.988439	−	0.151617i	$-0.951552\pi$
$457$	−24.3716	−	24.3716i	−1.14006	−	1.14006i	−0.151617	−	0.988439i	$-0.548448\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−20.1958	+	14.6731i	−0.940611	+	0.683394i	−0.948568	−	0.316574i	$-0.897467\pi$
$461$	−20.1958	+	14.6731i	−0.940611	+	0.683394i	0.00795653	+	0.999968i	$0.497467\pi$
$462$	−8.70119	−	54.9371i	−0.404816	−	2.55591i
$463$	42.1086	−	6.66935i	1.95695	−	0.309951i	0.957160	−	0.289558i	$-0.0935083\pi$
$463$	42.1086	−	6.66935i	1.95695	−	0.309951i	0.999792	−	0.0203929i	$-0.00649172\pi$
$464$	−21.9796	−	30.2523i	−1.02038	−	1.40443i
$465$	10.8842	−	41.2869i	0.504741	−	1.91463i
$466$		0			0
$467$	−9.92183	+	19.4727i	−0.459127	+	0.901088i	0.539138	+	0.842217i	$0.318750\pi$
$467$	−9.92183	+	19.4727i	−0.459127	+	0.901088i	−0.998266	+	0.0588709i	$0.981250\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	24.0641	−	12.2613i	1.10764	−	0.564372i
$473$		0			0
$474$			14.7269i			0.676428i
$475$		0			0
$476$		0			0
$477$	−16.3266	−	2.58587i	−0.747541	−	0.118399i
$478$		0			0
$479$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$479$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$480$	−4.64167	−	21.4116i	−0.211862	−	0.977299i
$481$		0			0
$482$	−18.5938	−	18.5938i	−0.846923	−	0.846923i
$483$		0			0
$484$	8.86957	−	12.2079i	0.403162	−	0.554905i
$485$	8.61023	−	13.3766i	0.390970	−	0.607401i
$486$	−17.8351	+	12.9580i	−0.809017	+	0.587785i
$487$	−1.38800	−	8.76346i	−0.0628961	−	0.397110i	−0.998973	−	0.0453143i	$-0.985571\pi$
$487$	−1.38800	−	8.76346i	−0.0628961	−	0.397110i	0.936077	−	0.351796i	$-0.114429\pi$
$488$		0			0
$489$		0			0
$490$	−23.8250	−	61.3243i	−1.07630	−	2.77035i
$491$	30.3062	+	22.0188i	1.36770	+	0.993692i	0.997913	+	0.0645759i	$0.0205695\pi$
$491$	30.3062	+	22.0188i	1.36770	+	0.993692i	0.369787	+	0.929116i	$0.379431\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	14.5450	+	24.9592i	0.653750	+	1.12183i
$496$	13.6269	−	41.9394i	0.611868	−	1.88314i
$497$		0			0
$498$	5.64229	−	35.6240i	0.252837	−	1.59635i
$499$		0			0			−	1.00000i	$-0.5\pi$
$499$		0			0				1.00000i	$0.5\pi$
$500$	6.65153	−	21.3485i	0.297465	−	0.954733i
$501$		0			0
$502$	−26.8107	−	4.24639i	−1.19662	−	0.189526i
$503$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$503$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$504$	42.5530	+	13.8263i	1.89546	+	0.615873i
$505$	−38.8268	+	22.6264i	−1.72777	+	1.00686i
$506$		0			0
$507$	15.9217	+	15.9217i	0.707107	+	0.707107i
$508$	−37.3559	−	19.0338i	−1.65740	−	0.844488i
$509$	26.4041	−	36.3421i	1.17034	−	1.61084i	0.508949	−	0.860796i	$-0.330034\pi$
$509$	26.4041	−	36.3421i	1.17034	−	1.61084i	0.661392	−	0.750040i	$-0.269966\pi$
$510$		0			0
$511$	−12.6754	+	9.20920i	−0.560726	+	0.407391i
$512$	−3.53971	−	22.3488i	−0.156434	−	0.987688i
$513$		0			0
$514$		0			0
$515$	−10.9088	−	7.02172i	−0.480697	−	0.309414i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−17.0568	+	5.54210i	−0.748712	+	0.243271i
$520$		0			0
$521$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$521$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$522$	−35.3393	+	18.0063i	−1.54676	+	0.788113i
$523$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$523$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$524$		−	27.1010i		−	1.18391i
$525$	30.8295	+	33.6881i	1.34551	+	1.47027i
$526$		0			0
$527$		0			0
$528$	13.5450	+	26.5836i	0.589471	+	1.15690i
$529$	−21.8743	−	7.10739i	−0.951057	−	0.309017i
$530$	−12.9957	−	11.6067i	−0.564498	−	0.504161i
$531$	−8.85213	−	27.2441i	−0.384150	−	1.18229i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−2.22221	−	0.585826i	−0.0960746	−	0.0253275i
$536$		0			0
$537$	−0.251470	−	1.58772i	−0.0108517	−	0.0685151i
$538$	6.79580	−	1.07635i	0.292988	−	0.0464047i
$539$	52.6611	+	72.4817i	2.26827	+	3.12201i
$540$	−23.2009	+	1.30994i	−0.998410	+	0.0563708i
$541$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$541$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$542$	−19.3218	+	37.9212i	−0.829942	+	1.62885i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$547$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$548$		0			0
$549$		0			0
$550$	−1.34786	+	30.4209i	−0.0574731	+	1.29715i
$551$		0			0
$552$		0			0
$553$	−14.3926	−	28.2471i	−0.612036	−	1.20119i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	0.329576	+	0.329576i	0.0139646	+	0.0139646i	0.714055	−	0.700090i	$-0.246857\pi$
$557$	0.329576	+	0.329576i	0.0139646	+	0.0139646i	−0.700090	+	0.714055i	$0.746857\pi$
$558$	−41.6748	−	21.2344i	−1.76423	−	0.898922i
$559$		0			0
$560$	29.8286	+	36.5324i	1.26049	+	1.54378i
$561$		0			0
$562$		0			0
$563$	−14.9386	+	2.36604i	−0.629587	+	0.0997168i	−0.463070	−	0.886322i	$-0.653252\pi$
$563$	−14.9386	+	2.36604i	−0.629587	+	0.0997168i	−0.166517	+	0.986039i	$0.553252\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	21.5450	−	42.2845i	0.904807	−	1.77578i
$568$		0			0
$569$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$569$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$570$		0			0
$571$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$571$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−24.0000			−1.00000
$577$	−8.82845	−	1.39829i	−0.367533	−	0.0582115i	−0.0300636	−	0.999548i	$-0.509571\pi$
$577$	−8.82845	−	1.39829i	−0.367533	−	0.0582115i	−0.337470	+	0.941336i	$0.609571\pi$
$578$	10.9147	+	21.4212i	0.453990	+	0.891007i
$579$	−30.8337	−	10.0185i	−1.28141	−	0.416354i
$580$	−41.5959	−	4.20204i	−1.72718	−	0.174480i
$581$	23.9932	+	73.8433i	0.995404	+	3.06354i
$582$	−12.3224	−	12.3224i	−0.510780	−	0.510780i
$583$	21.1420	+	10.7724i	0.875613	+	0.446147i
$584$	4.93980	−	6.79905i	0.204410	−	0.281346i
$585$		0			0
$586$	38.3684	−	27.8763i	1.58498	−	1.15156i
$587$	7.31999	+	46.2166i	0.302128	+	1.90756i	0.407638	+	0.913144i	$0.366353\pi$
$587$	7.31999	+	46.2166i	0.302128	+	1.90756i	−0.105509	+	0.994418i	$0.533647\pi$
$588$	−71.1818	+	11.2741i	−2.93549	+	0.464936i
$589$		0			0
$590$	7.69729	−	29.1981i	0.316892	−	1.20207i
$591$	−29.3469	−	21.3218i	−1.20717	−	0.877060i
$592$		0			0
$593$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$593$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$594$	30.0965	−	9.77894i	1.23487	−	0.401235i
$595$		0			0
$596$	0.617867	−	1.90160i	0.0253088	−	0.0778925i
$597$	39.6990	−	20.2277i	1.62477	−	0.827863i
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$	−21.3115	−	12.0756i	−0.870038	−	0.492985i
$601$	27.1774			1.10859			0.554296	−	0.832320i	$-0.312988\pi$
$601$	27.1774			1.10859			0.554296	+	0.832320i	$0.312988\pi$
$602$		0			0
$603$		0			0
$604$	45.4873	+	14.7797i	1.85085	+	0.601378i
$605$	−3.57432	−	16.4879i	−0.145317	−	0.670330i
$606$	15.2122	+	46.8184i	0.617954	+	1.90187i
$607$	33.2266	+	33.2266i	1.34863	+	1.34863i	0.887154	+	0.461473i	$0.152679\pi$
$607$	33.2266	+	33.2266i	1.34863	+	1.34863i	0.461473	+	0.887154i	$0.347321\pi$
$608$		0			0
$609$	50.1855	−	69.0744i	2.03362	−	2.79903i
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$613$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$614$		0			0
$615$		0			0
$616$	−51.9605	−	37.7515i	−2.09355	−	1.52105i
$617$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$617$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$618$	−10.0490	+	10.0490i	−0.404232	+	0.404232i
$619$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$619$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$620$	−24.8237	−	42.5975i	−0.996944	−	1.71076i
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−12.8483	−	21.4458i	−0.513932	−	0.857831i
$626$	6.16393			0.246360
$627$		0			0
$628$		0			0
$629$		0			0
$630$	43.2207	−	25.1869i	1.72195	−	1.00347i
$631$	−1.51387	−	4.65921i	−0.0602661	−	0.185480i	0.916391	−	0.400284i	$-0.131089\pi$
$631$	−1.51387	−	4.65921i	−0.0602661	−	0.185480i	−0.976657	+	0.214804i	$0.931089\pi$
$632$	12.0244	+	12.0244i	0.478307	+	0.478307i
$633$		0			0
$634$	−29.3860	+	40.4464i	−1.16707	+	1.60633i
$635$	−43.6926	+	16.9749i	−1.73389	+	0.673628i
$636$	−15.4419	+	11.2192i	−0.612312	+	0.444871i
$637$		0			0
$638$	56.2325	−	8.90636i	2.22627	−	0.352606i
$639$		0			0
$640$	−21.2724	−	13.6926i	−0.840864	−	0.541246i
$641$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$641$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$642$	−1.14291	+	2.24309i	−0.0451071	+	0.0885277i
$643$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$643$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$647$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$648$	−3.98217	+	25.1424i	−0.156434	+	0.987688i
$649$			41.1203i			1.61411i
$650$		0			0
$651$	100.687			3.94625
$652$		0			0
$653$	−0.732848	−	1.43830i	−0.0286786	−	0.0562849i	0.876223	−	0.481906i	$-0.160055\pi$
$653$	−0.732848	−	1.43830i	−0.0286786	−	0.0562849i	−0.904901	+	0.425622i	$0.860055\pi$
$654$		0			0
$655$	−22.5989	−	20.1834i	−0.883013	−	0.788631i
$656$		0			0
$657$	−6.30306	−	6.30306i	−0.245906	−	0.245906i
$658$		0			0
$659$	24.7758	−	34.1009i	0.965126	−	1.32838i	0.0206555	−	0.999787i	$-0.493425\pi$
$659$	24.7758	−	34.1009i	0.965126	−	1.32838i	0.944471	−	0.328596i	$-0.106575\pi$
$660$	32.2551	+	8.50318i	1.25553	+	0.330986i
$661$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$661$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$662$		0			0
$663$		0			0
$664$	−24.4800	−	33.6938i	−0.950007	−	1.30757i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	17.2119	−	5.59249i	0.665451	−	0.216218i
$670$		0			0
$671$		0			0
$672$	46.0336	−	23.4553i	1.77578	−	0.904807i
$673$	−3.04805	+	19.2446i	−0.117494	+	0.741826i	0.856650	+	0.515897i	$0.172541\pi$
$673$	−3.04805	+	19.2446i	−0.117494	+	0.741826i	−0.974144	+	0.225928i	$0.927459\pi$
$674$		−	46.5936i		−	1.79472i
$675$	−16.1865	+	20.3223i	−0.623019	+	0.782206i
$676$	26.0000			1.00000
$677$	47.9467	+	7.59400i	1.84274	+	0.291861i	0.977726	−	0.209887i	$-0.0673095\pi$
$677$	47.9467	+	7.59400i	1.84274	+	0.291861i	0.865014	+	0.501748i	$0.167310\pi$
$678$		0			0
$679$	35.6779	+	11.5925i	1.36919	+	0.444878i
$680$		0			0
$681$	13.3983	+	41.2357i	0.513424	+	1.58016i
$682$	47.4754	+	47.4754i	1.81793	+	1.81793i
$683$	−23.1356	−	11.7882i	−0.885260	−	0.451063i	−0.0486213	−	0.998817i	$-0.515483\pi$
$683$	−23.1356	−	11.7882i	−0.885260	−	0.451063i	−0.836639	+	0.547755i	$0.815483\pi$
$684$		0			0
$685$		0			0
$686$	83.2825	−	60.5082i	3.17974	−	2.31022i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$691$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$692$	−9.40174	+	18.4520i	−0.357401	+	0.701438i
$693$	−48.1700	+	48.1700i	−1.82983	+	1.82983i
$694$	−4.02496	+	1.30779i	−0.152785	+	0.0496430i
$695$		0			0
$696$	−14.1523	+	43.5564i	−0.536443	+	1.65100i
$697$		0			0
$698$		0			0
$699$		0			0
$700$	52.6784	+	2.33403i	1.99105	+	0.0882182i
$701$	0.944387			0.0356690			0.0178345	−	0.999841i	$-0.494323\pi$
$701$	0.944387			0.0356690			0.0178345	+	0.999841i	$0.494323\pi$
$702$		0			0
$703$		0			0
$704$	32.7649	+	10.6460i	1.23487	+	0.401235i
$705$		0			0
$706$		0			0
$707$	−74.9337	−	74.9337i	−2.81817	−	2.81817i
$708$	−29.4724	−	15.0170i	−1.10764	−	0.564372i
$709$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$709$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$710$		0			0
$711$	14.5920	−	10.6017i	0.547241	−	0.397594i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.50169	−	1.09104i	−0.0561209	−	0.0407742i
$717$		0			0
$718$		0			0
$719$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$719$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$720$	−17.8739	+	20.0131i	−0.666122	+	0.745843i
$721$	9.45376	−	29.0957i	0.352077	−	1.08358i
$722$	−23.9414	+	12.1988i	−0.891007	+	0.453990i
$723$	−5.03803	+	31.8089i	−0.187366	+	1.18298i
$724$		0			0
$725$	−34.4824	+	31.5564i	−1.28065	+	1.17198i
$726$	−18.4812			−0.685901
$727$	−36.2392	−	5.73972i	−1.34404	−	0.212875i	−0.557376	−	0.830260i	$-0.688192\pi$
$727$	−36.2392	−	5.73972i	−1.34404	−	0.212875i	−0.786661	+	0.617386i	$0.788192\pi$
$728$		0			0
$729$	25.6785	+	8.34346i	0.951057	+	0.309017i
$730$	−1.99067	−	9.18275i	−0.0736780	−	0.339869i
$731$		0			0
$732$		0			0
$733$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$733$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$734$	26.2960	−	36.1934i	0.970604	−	1.33592i
$735$	−43.6113	+	67.7533i	−1.60863	+	2.49912i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$739$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$740$		0			0
$741$		0			0
$742$	18.6541	−	36.6106i	0.684812	−	1.34402i
$743$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$743$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$744$	−51.3651	+	16.6895i	−1.88314	+	0.611868i
$745$	−1.12555	−	1.93144i	−0.0412368	−	0.0707623i
$746$		0			0
$747$	−39.3595	+	20.0546i	−1.44009	+	0.733761i
$748$		0			0
$749$		−	5.41937i		−	0.198019i
$750$	−25.9413	+	8.77789i	−0.947241	+	0.320523i
$751$	−26.1631			−0.954706			−0.477353	−	0.878712i	$-0.658404\pi$
$751$	−26.1631			−0.954706			−0.477353	+	0.878712i	$0.658404\pi$
$752$		0			0
$753$	15.0932	+	29.6220i	0.550025	+	1.07949i
$754$		0			0
$755$	46.2010	−	26.9236i	1.68143	−	0.979852i
$756$	−16.9337	−	52.1166i	−0.615873	−	1.89546i
$757$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$757$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$761$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$762$	8.03261	+	50.7159i	0.290991	+	1.83724i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−19.5959	+	19.5959i	−0.707107	+	0.707107i
$769$	−36.6705	+	11.9150i	−1.32237	+	0.429664i	−0.883309	−	0.468792i	$-0.844689\pi$
$769$	−36.6705	+	11.9150i	−1.32237	+	0.429664i	−0.439063	+	0.898456i	$0.644689\pi$
$770$	−70.1775	+	15.2133i	−2.52902	+	0.548251i
$771$		0			0
$772$	−33.3557	+	16.9956i	−1.20050	+	0.611684i
$773$	2.27213	−	14.3457i	0.0817229	−	0.515978i	−0.912538	−	0.408993i	$-0.865880\pi$
$773$	2.27213	−	14.3457i	0.0817229	−	0.515978i	0.994261	−	0.106985i	$-0.0341198\pi$
$774$		0			0
$775$	−54.0085	−	11.0244i	−1.94004	−	0.396009i
$776$	−20.1224			−0.722353
$777$		0			0
$778$	−12.2521	−	24.0461i	−0.439259	−	0.862093i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	43.2816	+	22.0531i	1.54676	+	0.788113i
$784$	−48.9145	+	67.3250i	−1.74695	+	2.40446i
$785$		0			0
$786$	−26.8528	+	19.5097i	−0.957806	+	0.695887i
$787$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$787$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$788$	−41.3708	+	6.55249i	−1.47377	+	0.233423i
$789$		0			0
$790$	18.9821	−	1.07174i	0.675352	−	0.0381308i
$791$		0			0
$792$	16.5892	−	32.5581i	0.589471	−	1.15690i
$793$		0			0
$794$		0			0
$795$	−2.14488	+	21.2322i	−0.0760712	+	0.753027i
$796$	15.8983	−	48.9299i	0.563500	−	1.73427i
$797$	29.6669	−	15.1160i	1.05086	−	0.535437i	0.158775	−	0.987315i	$-0.449246\pi$
$797$	29.6669	−	15.1160i	1.05086	−	0.535437i	0.892080	+	0.451877i	$0.149246\pi$
$798$		0			0
$799$		0			0
$800$	−27.2605	+	7.54106i	−0.963803	+	0.266617i
$801$		0			0
$802$		0			0
$803$	5.80904	+	11.4009i	0.204997	+	0.402328i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−5.95870	−	5.95870i	−0.209756	−	0.209756i
$808$	50.6477	+	25.8063i	1.78178	+	0.907863i
$809$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$809$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$810$	18.0000	+	22.0454i	0.632456	+	0.774597i
$811$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$811$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$812$	−15.4227	−	97.3752i	−0.541231	−	3.41720i
$813$	51.4833	−	8.15415i	1.80560	−	0.285979i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	25.8290	−	25.8290i	0.903090	−	0.903090i
$819$		0			0
$820$		0			0
$821$	−15.3298	+	47.1802i	−0.535013	+	1.64660i	0.208609	+	0.977999i	$0.433106\pi$
$821$	−15.3298	+	47.1802i	−0.535013	+	1.64660i	−0.743622	+	0.668601i	$0.766894\pi$
$822$		0			0
$823$	−7.94660	+	50.1728i	−0.277001	+	1.74892i	0.320686	+	0.947186i	$0.396087\pi$
$823$	−7.94660	+	50.1728i	−0.277001	+	1.74892i	−0.597687	+	0.801730i	$0.703913\pi$
$824$			16.4100i			0.571670i
$825$	31.1125	−	20.5641i	1.08320	−	0.715949i
$826$	71.2061			2.47758
$827$	−56.3094	−	8.91853i	−1.95807	−	0.310128i	−0.999697	−	0.0246037i	$-0.992168\pi$
$827$	−56.3094	−	8.91853i	−1.95807	−	0.310128i	−0.958372	−	0.285524i	$-0.907832\pi$
$828$		0			0
$829$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$829$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$830$	−46.3279	−	4.68006i	−1.60806	−	0.162447i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	8.96129	+	56.5794i	0.309748	+	1.95567i
$838$	−38.0443	+	6.02563i	−1.31422	+	0.208152i
$839$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$839$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$840$	14.7246	−	55.8546i	0.508045	−	1.92717i
$841$	47.2416	+	34.3231i	1.62902	+	1.18355i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	19.3634	−	21.6808i	0.666122	−	0.745843i
$846$		0			0
$847$	35.4481	−	18.0617i	1.21801	−	0.620607i
$848$	−3.44783	+	21.7687i	−0.118399	+	0.747541i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$853$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$854$		0			0
$855$		0			0
$856$	0.898292	+	2.76466i	0.0307030	+	0.0944941i
$857$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$857$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$858$		0			0
$859$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$859$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$863$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$864$	17.2773	+	23.7801i	0.587785	+	0.809017i
$865$	8.38475	+	21.5819i	0.285090	+	0.733808i
$866$	46.7939	+	33.9978i	1.59012	+	1.15529i
$867$	13.3677	−	26.2356i	0.453990	−	0.891007i
$868$	82.2109	−	82.2109i	2.79042	−	2.79042i
$869$	−24.6237	+	8.00073i	−0.835302	+	0.271406i
$870$	25.7808	+	44.2399i	0.874051	+	1.49987i
$871$		0			0
$872$		0			0
$873$	−3.33879	+	21.0803i	−0.113001	+	0.713459i
$874$		0			0
$875$	41.1784	−	42.1890i	1.39208	−	1.42625i
$876$	−10.2929			−0.347763
$877$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$877$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$878$	−26.9042	−	52.8025i	−0.907974	−	1.78200i
$879$	−55.2418	−	17.9491i	−1.86326	−	0.605410i
$880$	33.2790	−	19.3933i	1.12183	−	0.653750i
$881$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$881$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$882$	62.4137	+	62.4137i	2.10158	+	2.10158i
$883$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$883$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$884$		0			0
$885$	−34.4718	+	13.3926i	−1.15876	+	0.450186i
$886$	−41.7995	+	30.3691i	−1.40428	+	1.02027i
$887$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$887$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$888$		0			0
$889$	−64.9719	−	89.4261i	−2.17909	−	2.99926i
$890$		0			0
$891$	−31.3554	−	22.7810i	−1.05045	−	0.763194i
$892$	9.48722	−	18.6197i	0.317656	−	0.623434i
$893$		0			0
$894$	−2.32897	+	0.756729i	−0.0778925	+	0.0253088i
$895$	−2.02818	+	0.439675i	−0.0677945	+	0.0146967i
$896$	18.4351	−	56.7374i	0.615873	−	1.89546i
$897$		0			0
$898$		0			0
$899$			103.062i			3.43730i
$900$	3.37687	+	29.8093i	0.112562	+	0.993645i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−18.1014	−	55.7103i	−0.601378	−	1.85085i
$907$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$907$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$908$	44.6085	+	22.7292i	1.48038	+	0.754293i
$909$	35.4384	−	48.7768i	1.17542	−	1.61782i
$910$		0			0
$911$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$911$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$912$		0			0
$913$	62.6295	−	9.91954i	2.07274	−	0.328289i
$914$	28.6506	+	39.4341i	0.947676	+	1.30436i
$915$		0			0
$916$		0			0
$917$	32.4385	−	63.6641i	1.07121	−	2.10237i
$918$		0			0
$919$	32.6144	−	10.5971i	1.07585	−	0.349565i	0.283087	−	0.959094i	$-0.408641\pi$
$919$	32.6144	−	10.5971i	1.07585	−	0.349565i	0.792764	+	0.609529i	$0.208641\pi$
$920$		0			0
$921$		0			0
$922$	31.4557	−	16.0275i	1.03594	−	0.527836i
$923$		0			0
$924$			78.6613i			2.58777i
$925$		0			0
$926$	−60.2929			−1.98135
$927$	17.1912	+	2.72281i	0.564632	+	0.0894290i
$928$	24.0083	+	47.1190i	0.788113	+	1.54676i
$929$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$929$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$930$	−24.3370	+	55.2617i	−0.798042	+	1.81210i
$931$		0			0
$932$		0			0
$933$		0			0
$934$	18.1668	−	25.0045i	0.594436	−	0.818171i
$935$		0			0
$936$		0			0
$937$	6.85051	+	43.2524i	0.223796	+	1.41299i	0.802108	+	0.597178i	$0.203712\pi$
$937$	6.85051	+	43.2524i	0.223796	+	1.41299i	−0.578312	+	0.815816i	$0.696288\pi$
$938$		0			0
$939$	−4.43733	−	6.10747i	−0.144807	−	0.199310i
$940$		0			0
$941$	−20.6648	−	15.0139i	−0.673654	−	0.489438i	0.197592	−	0.980284i	$-0.436688\pi$
$941$	−20.6648	−	15.0139i	−0.673654	−	0.489438i	−0.871246	+	0.490846i	$0.836688\pi$
$942$		0			0
$943$		0			0
$944$	−36.3254	+	11.8028i	−1.18229	+	0.384150i
$945$	−56.0702	−	24.6931i	−1.82396	−	0.803266i
$946$		0			0
$947$	41.2595	−	21.0228i	1.34075	−	0.683148i	0.371321	−	0.928505i	$-0.378905\pi$
$947$	41.2595	−	21.0228i	1.34075	−	0.683148i	0.969433	+	0.245357i	$0.0789051\pi$
$948$	3.25805	−	20.5705i	0.105817	−	0.668100i
$949$		0			0
$950$		0			0
$951$	61.2305			1.98553
$952$		0			0
$953$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$953$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$954$	22.2329	+	7.22390i	0.719816	+	0.233883i
$955$		0			0
$956$		0			0
$957$	−49.3059	−	49.3059i	−1.59383	−	1.59383i
$958$		0			0
$959$		0			0
$960$	1.74658	+	30.9346i	0.0563708	+	0.998410i
$961$	−73.2469	+	53.2170i	−2.36280	+	1.71668i
$962$		0			0
$963$	3.04531	−	0.482330i	0.0981337	−	0.0155429i
$964$	21.8583	+	30.0854i	0.704008	+	0.968984i
$965$	−10.6693	+	40.4720i	−0.343458	+	1.30284i
$966$		0			0
$967$	26.0892	−	51.2030i	0.838973	−	1.64658i	0.0787703	−	0.996893i	$-0.474901\pi$
$967$	26.0892	−	51.2030i	0.838973	−	1.64658i	0.760203	−	0.649685i	$-0.225099\pi$
$968$	−15.0898	+	15.0898i	−0.485005	+	0.485005i
$969$		0			0
$970$	−14.9861	+	16.7796i	−0.481175	+	0.538761i
$971$	16.6469	−	51.2340i	0.534225	−	1.64418i	−0.211092	−	0.977466i	$-0.567702\pi$
$971$	16.6469	−	51.2340i	0.534225	−	1.64418i	0.745318	−	0.666710i	$-0.232298\pi$
$972$	27.7788	−	14.1540i	0.891007	−	0.453990i
$973$		0			0
$974$			12.5479i			0.402060i
$975$		0			0
$976$		0			0
$977$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$977$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$978$		0			0
$979$		0			0
$980$	19.7119	+	90.9288i	0.629672	+	2.90461i
$981$		0			0
$982$	−37.4605	−	37.4605i	−1.19541	−	1.19541i
$983$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$983$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$984$		0			0
$985$	−25.3468	+	39.3781i	−0.807616	+	1.25469i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−14.7947	−	38.0809i	−0.470207	−	1.21029i
$991$	−4.34689	−	3.15820i	−0.138083	−	0.100323i	0.516599	−	0.856227i	$-0.327198\pi$
$991$	−4.34689	−	3.15820i	−0.138083	−	0.100323i	−0.654683	+	0.755904i	$0.727198\pi$
$992$	−28.3125	+	55.5664i	−0.898922	+	1.76423i
$993$		0			0
$994$		0			0
$995$	−28.9613	−	49.6976i	−0.918136	−	1.57552i
$996$	−15.7623	+	48.5114i	−0.499448	+	1.53714i
$997$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$997$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.bp.a.77.2	✓	16
3.2	odd	2		600.2.bp.b.77.1	yes	16
8.5	even	2		600.2.bp.b.77.1	yes	16
24.5	odd	2	CM	600.2.bp.a.77.2	✓	16
25.13	odd	20	inner	600.2.bp.a.413.2	yes	16
75.38	even	20		600.2.bp.b.413.1	yes	16
200.13	odd	20		600.2.bp.b.413.1	yes	16
600.413	even	20	inner	600.2.bp.a.413.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.bp.a.77.2	✓	16	1.1	even	1	trivial
600.2.bp.a.77.2	✓	16	24.5	odd	2	CM
600.2.bp.a.413.2	yes	16	25.13	odd	20	inner
600.2.bp.a.413.2	yes	16	600.413	even	20	inner
600.2.bp.b.77.1	yes	16	3.2	odd	2
600.2.bp.b.77.1	yes	16	8.5	even	2
600.2.bp.b.413.1	yes	16	75.38	even	20
600.2.bp.b.413.1	yes	16	200.13	odd	20

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.bp (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39680 - 0.221232i) q^{2} +(0.786335 + 1.54327i) q^{3} +(1.90211 + 0.618034i) q^{4} +(1.93196 - 1.12585i) q^{5} +(-0.756934 - 2.32960i) q^{6} +(3.72858 + 3.72858i) q^{7} +(-2.52015 - 1.28408i) q^{8} +(-1.76336 + 2.42705i) q^{9} +(-2.94764 + 1.14518i) q^{10} +(3.48393 - 2.53123i) q^{11} +(0.541905 + 3.42145i) q^{12} +(-4.38320 - 6.03296i) q^{14} +(3.25665 + 2.09624i) q^{15} +(3.23607 + 2.35114i) q^{16} +(3.00000 - 3.00000i) q^{18} +(4.37062 - 0.947478i) q^{20} +(-2.82229 + 8.68610i) q^{21} +(-5.42636 + 2.76487i) q^{22} -4.89898i q^{24} +(2.46492 - 4.35019i) q^{25} +(-5.13218 - 0.812857i) q^{27} +(4.78779 + 9.39656i) q^{28} +(-8.89092 - 2.88884i) q^{29} +(-4.08515 - 3.64850i) q^{30} +(-3.40674 - 10.4849i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(6.64590 + 3.38626i) q^{33} +(11.4013 + 3.00564i) q^{35} +(-4.85410 + 3.52671i) q^{36} +(-6.31450 + 0.356520i) q^{40} +(5.86382 - 11.5084i) q^{42} +(8.19122 - 2.66149i) q^{44} +(-0.674235 + 6.67423i) q^{45} +(-1.08381 + 6.84291i) q^{48} +20.8046i q^{49} +(-4.40541 + 5.53103i) q^{50} +(2.50150 + 4.90947i) q^{53} +(6.98881 + 2.27080i) q^{54} +(3.88103 - 8.81261i) q^{55} +(-4.60877 - 14.1843i) q^{56} +(11.7798 + 6.00209i) q^{58} +(-5.61259 + 7.72506i) q^{59} +(4.89898 + 6.00000i) q^{60} +(2.43895 + 15.3990i) q^{62} +(-15.6243 + 2.47464i) q^{63} +(4.70228 + 6.47214i) q^{64} +(-8.53386 - 6.20021i) q^{66} +(-15.2604 - 6.72060i) q^{70} +(7.56044 - 3.85224i) q^{72} +(-0.464812 + 2.93471i) q^{73} +(8.65177 + 0.383336i) q^{75} +(22.4280 + 3.55224i) q^{77} +(-5.71796 - 1.85788i) q^{79} +(8.89898 + 0.898979i) q^{80} +(-2.78115 - 8.55951i) q^{81} +(13.1198 + 6.68488i) q^{83} +(-10.7366 + 14.7777i) q^{84} +(-2.53299 - 15.9927i) q^{87} +(-12.0303 + 1.90542i) q^{88} +(2.41832 - 9.17342i) q^{90} +(13.5021 - 13.5021i) q^{93} +(3.02774 - 9.31841i) q^{96} +(6.33893 - 3.22985i) q^{97} +(4.60263 - 29.0599i) q^{98} +12.9191i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 4 q^{5} + 4 q^{7} + 8 q^{8} + 8 q^{10} + 24 q^{11} - 12 q^{15} + 16 q^{16} + 48 q^{18} + 8 q^{20} - 36 q^{21} - 16 q^{22} + 32 q^{28} - 12 q^{30} - 64 q^{32} + 12 q^{33} - 8 q^{35} - 24 q^{36}+ \cdots - 72 q^{98}+O(q^{100}) \) 16 * q - 4 * q^2 + 4 * q^5 + 4 * q^7 + 8 * q^8 + 8 * q^10 + 24 * q^11 - 12 * q^15 + 16 * q^16 + 48 * q^18 + 8 * q^20 - 36 * q^21 - 16 * q^22 + 32 * q^28 - 12 * q^30 - 64 * q^32 + 12 * q^33 - 8 * q^35 - 24 * q^36 + 24 * q^42 + 48 * q^45 + 4 * q^50 + 28 * q^55 + 24 * q^56 - 8 * q^58 - 80 * q^59 + 12 * q^63 - 36 * q^66 - 32 * q^70 - 24 * q^72 - 28 * q^73 + 24 * q^75 + 12 * q^77 + 64 * q^80 + 36 * q^81 - 24 * q^83 - 36 * q^87 + 32 * q^88 - 24 * q^93 - 16 * q^97 - 72 * q^98

Introduction

L-functions

Modular forms

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