LMFDB - Embedded newform 600.2.b.i.251.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(251,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("600.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.b (of order $2$, degree $1$, 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:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 24x^{14} + 192x^{12} + 672x^{10} + 1092x^{8} + 880x^{6} + 352x^{4} + 64x^{2} + 4 $ x^16 + 24x^14 + 192x^12 + 672x^10 + 1092x^8 + 880x^6 + 352x^4 + 64*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.7
Root			$1.05636i$ of defining polynomial
Character	$\chi$	$=$	600.251
Dual form			600.2.b.i.251.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.541196 + 1.30656i) q^{2} +(-1.64533 + 0.541196i) q^{3} +(-1.41421 - 1.41421i) q^{4} +(0.183339 - 2.44262i) q^{6} +3.29066i q^{7} +(2.61313 - 1.08239i) q^{8} +(2.41421 - 1.78089i) q^{9} +O(q^{10})$	\(q+(-0.541196 + 1.30656i) q^{2} +(-1.64533 + 0.541196i) q^{3} +(-1.41421 - 1.41421i) q^{4} +(0.183339 - 2.44262i) q^{6} +3.29066i q^{7} +(2.61313 - 1.08239i) q^{8} +(2.41421 - 1.78089i) q^{9} +2.51856i q^{11} +(3.09221 + 1.56148i) q^{12} +4.65369i q^{13} +(-4.29945 - 1.78089i) q^{14} +4.00000i q^{16} -3.69552i q^{17} +(1.02028 + 4.11813i) q^{18} -0.828427 q^{19} +(-1.78089 - 5.41421i) q^{21} +(-3.29066 - 1.36303i) q^{22} -2.61313 q^{23} +(-3.71366 + 3.19510i) q^{24} +(-6.08034 - 2.51856i) q^{26} +(-3.00836 + 4.23671i) q^{27} +(4.65369 - 4.65369i) q^{28} -6.08034 q^{29} +1.17157i q^{31} +(-5.22625 - 2.16478i) q^{32} +(-1.36303 - 4.14386i) q^{33} +(4.82843 + 2.00000i) q^{34} +(-5.93277 - 0.895653i) q^{36} -1.92762i q^{37} +(0.448342 - 1.08239i) q^{38} +(-2.51856 - 7.65685i) q^{39} -8.59890i q^{41} +(8.03782 + 0.603305i) q^{42} -6.01673 q^{43} +(3.56178 - 3.56178i) q^{44} +(1.41421 - 3.41421i) q^{46} -2.61313 q^{47} +(-2.16478 - 6.58132i) q^{48} -3.82843 q^{49} +(2.00000 + 6.08034i) q^{51} +(6.58132 - 6.58132i) q^{52} -4.59220 q^{53} +(-3.90742 - 6.22351i) q^{54} +(3.56178 + 8.59890i) q^{56} +(1.36303 - 0.448342i) q^{57} +(3.29066 - 7.94435i) q^{58} +2.51856i q^{59} +8.48528i q^{61} +(-1.53073 - 0.634051i) q^{62} +(5.86030 + 7.94435i) q^{63} +(5.65685 - 5.65685i) q^{64} +(6.15188 + 0.461750i) q^{66} -3.29066 q^{67} +(-5.22625 + 5.22625i) q^{68} +(4.29945 - 1.41421i) q^{69} +7.12356 q^{71} +(4.38102 - 7.26682i) q^{72} -6.58132 q^{73} +(2.51856 + 1.04322i) q^{74} +(1.17157 + 1.17157i) q^{76} -8.28772 q^{77} +(11.3672 + 0.853202i) q^{78} +16.4853i q^{79} +(2.65685 - 8.59890i) q^{81} +(11.2350 + 4.65369i) q^{82} -9.37011i q^{83} +(-5.13829 + 10.1754i) q^{84} +(3.25623 - 7.86123i) q^{86} +(10.0042 - 3.29066i) q^{87} +(2.72607 + 6.58132i) q^{88} -5.03712i q^{89} -15.3137 q^{91} +(3.69552 + 3.69552i) q^{92} +(-0.634051 - 1.92762i) q^{93} +(1.41421 - 3.41421i) q^{94} +(9.77048 + 0.733355i) q^{96} -2.72607 q^{97} +(2.07193 - 5.00208i) q^{98} +(4.48528 + 6.08034i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^9	$ 16 q + 16 q^{9} + 32 q^{19} + 32 q^{24} + 32 q^{34} - 32 q^{36} - 16 q^{49} + 32 q^{51} - 32 q^{54} + 64 q^{66} + 64 q^{76} - 48 q^{81} - 32 q^{84} - 64 q^{91} + 64 q^{96} - 64 q^{99}+O(q^{100}) $ 16 * q + 16 * q^9 + 32 * q^19 + 32 * q^24 + 32 * q^34 - 32 * q^36 - 16 * q^49 + 32 * q^51 - 32 * q^54 + 64 * q^66 + 64 * q^76 - 48 * q^81 - 32 * q^84 - 64 * q^91 + 64 * q^96 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	−0.541196	+	1.30656i	−0.382683	+	0.923880i
$2$	−0.541196	+	1.30656i	−0.382683	+	0.923880i
$3$	−1.64533	+	0.541196i	−0.949931	+	0.312460i
$3$	−1.64533	+	0.541196i	−0.949931	+	0.312460i
$4$	−1.41421	−	1.41421i	−0.707107	−	0.707107i
$5$		0			0
$5$		0			0
$6$	0.183339	−	2.44262i	0.0748477	−	0.997195i
$7$			3.29066i			1.24375i	0.783116	+	0.621876i	$0.213629\pi$
$7$			3.29066i			1.24375i	−0.783116	+	0.621876i	$0.786371\pi$
$8$	2.61313	−	1.08239i	0.923880	−	0.382683i
$9$	2.41421	−	1.78089i	0.804738	−	0.593630i
$10$		0			0
$11$			2.51856i			0.759374i	0.925115	+	0.379687i	$0.123968\pi$
$11$			2.51856i			0.759374i	−0.925115	+	0.379687i	$0.876032\pi$
$12$	3.09221	+	1.56148i	0.892645	+	0.450760i
$13$			4.65369i			1.29070i	0.763886	+	0.645351i	$0.223289\pi$
$13$			4.65369i			1.29070i	−0.763886	+	0.645351i	$0.776711\pi$
$14$	−4.29945	−	1.78089i	−1.14908	−	0.475963i
$15$		0			0
$16$			4.00000i			1.00000i
$17$		−	3.69552i		−	0.896295i	−0.893960	−	0.448147i	$-0.852084\pi$
$17$		−	3.69552i		−	0.896295i	0.893960	−	0.448147i	$-0.147916\pi$
$18$	1.02028	+	4.11813i	0.240483	+	0.970653i
$19$	−0.828427			−0.190054			−0.0950271	−	0.995475i	$-0.530294\pi$
$19$	−0.828427			−0.190054			−0.0950271	+	0.995475i	$0.530294\pi$
$20$		0			0
$21$	−1.78089	−	5.41421i	−0.388622	−	1.18148i
$22$	−3.29066	−	1.36303i	−0.701571	−	0.290600i
$23$	−2.61313			−0.544874			−0.272437	−	0.962174i	$-0.587830\pi$
$23$	−2.61313			−0.544874			−0.272437	+	0.962174i	$0.587830\pi$
$24$	−3.71366	+	3.19510i	−0.758049	+	0.652198i
$25$		0			0
$26$	−6.08034	−	2.51856i	−1.19245	−	0.493930i
$27$	−3.00836	+	4.23671i	−0.578960	+	0.815356i
$28$	4.65369	−	4.65369i	0.879465	−	0.879465i
$29$	−6.08034			−1.12909			−0.564546	−	0.825402i	$-0.690949\pi$
$29$	−6.08034			−1.12909			−0.564546	+	0.825402i	$0.690949\pi$
$30$		0			0
$31$			1.17157i			0.210421i	0.994450	+	0.105210i	$0.0335516\pi$
$31$			1.17157i			0.210421i	−0.994450	+	0.105210i	$0.966448\pi$
$32$	−5.22625	−	2.16478i	−0.923880	−	0.382683i
$33$	−1.36303	−	4.14386i	−0.237274	−	0.721353i
$34$	4.82843	+	2.00000i	0.828068	+	0.342997i
$35$		0			0
$36$	−5.93277	−	0.895653i	−0.988796	−	0.149276i
$37$		−	1.92762i		−	0.316899i	−0.987367	−	0.158450i	$-0.949350\pi$
$37$		−	1.92762i		−	0.316899i	0.987367	−	0.158450i	$-0.0506495\pi$
$38$	0.448342	−	1.08239i	0.0727306	−	0.175587i
$39$	−2.51856	−	7.65685i	−0.403292	−	1.22608i
$40$		0			0
$41$		−	8.59890i		−	1.34292i	−0.741039	−	0.671461i	$-0.765667\pi$
$41$		−	8.59890i		−	1.34292i	0.741039	−	0.671461i	$-0.234333\pi$
$42$	8.03782	+	0.603305i	1.24026	+	0.0930920i
$43$	−6.01673			−0.917542			−0.458771	−	0.888554i	$-0.651710\pi$
$43$	−6.01673			−0.917542			−0.458771	+	0.888554i	$0.651710\pi$
$44$	3.56178	−	3.56178i	0.536959	−	0.536959i
$45$		0			0
$46$	1.41421	−	3.41421i	0.208514	−	0.503398i
$47$	−2.61313			−0.381164			−0.190582	−	0.981671i	$-0.561037\pi$
$47$	−2.61313			−0.381164			−0.190582	+	0.981671i	$0.561037\pi$
$48$	−2.16478	−	6.58132i	−0.312460	−	0.949931i
$49$	−3.82843			−0.546918
$50$		0			0
$51$	2.00000	+	6.08034i	0.280056	+	0.851418i
$52$	6.58132	−	6.58132i	0.912664	−	0.912664i
$53$	−4.59220			−0.630787			−0.315394	−	0.948961i	$-0.602137\pi$
$53$	−4.59220			−0.630787			−0.315394	+	0.948961i	$0.602137\pi$
$54$	−3.90742	−	6.22351i	−0.531732	−	0.846912i
$55$		0			0
$56$	3.56178	+	8.59890i	0.475963	+	1.14908i
$57$	1.36303	−	0.448342i	0.180538	−	0.0593843i
$58$	3.29066	−	7.94435i	0.432085	−	1.04314i
$59$			2.51856i			0.327889i	0.986470	+	0.163944i	$0.0524217\pi$
$59$			2.51856i			0.327889i	−0.986470	+	0.163944i	$0.947578\pi$
$60$		0			0
$61$			8.48528i			1.08643i	0.839594	+	0.543214i	$0.182793\pi$
$61$			8.48528i			1.08643i	−0.839594	+	0.543214i	$0.817207\pi$
$62$	−1.53073	−	0.634051i	−0.194403	−	0.0805245i
$63$	5.86030	+	7.94435i	0.738329	+	1.00089i
$64$	5.65685	−	5.65685i	0.707107	−	0.707107i
$65$		0			0
$66$	6.15188	+	0.461750i	0.757244	+	0.0568375i
$67$	−3.29066			−0.402018			−0.201009	−	0.979589i	$-0.564422\pi$
$67$	−3.29066			−0.402018			−0.201009	+	0.979589i	$0.564422\pi$
$68$	−5.22625	+	5.22625i	−0.633776	+	0.633776i
$69$	4.29945	−	1.41421i	0.517593	−	0.170251i
$70$		0			0
$71$	7.12356			0.845412			0.422706	−	0.906267i	$-0.361080\pi$
$71$	7.12356			0.845412			0.422706	+	0.906267i	$0.361080\pi$
$72$	4.38102	−	7.26682i	0.516308	−	0.856403i
$73$	−6.58132			−0.770285			−0.385142	−	0.922857i	$-0.625848\pi$
$73$	−6.58132			−0.770285			−0.385142	+	0.922857i	$0.625848\pi$
$74$	2.51856	+	1.04322i	0.292777	+	0.121272i
$75$		0			0
$76$	1.17157	+	1.17157i	0.134389	+	0.134389i
$77$	−8.28772			−0.944473
$78$	11.3672	+	0.853202i	1.28708	+	0.0966061i
$79$			16.4853i			1.85474i	0.374147	+	0.927370i	$0.377936\pi$
$79$			16.4853i			1.85474i	−0.374147	+	0.927370i	$0.622064\pi$
$80$		0			0
$81$	2.65685	−	8.59890i	0.295206	−	0.955434i
$82$	11.2350	+	4.65369i	1.24070	+	0.513914i
$83$		−	9.37011i		−	1.02850i	−0.857639	−	0.514252i	$-0.828070\pi$
$83$		−	9.37011i		−	1.02850i	0.857639	−	0.514252i	$-0.171930\pi$
$84$	−5.13829	+	10.1754i	−0.560634	+	1.11023i
$85$		0			0
$86$	3.25623	−	7.86123i	0.351128	−	0.847699i
$87$	10.0042	−	3.29066i	1.07256	−	0.352796i
$88$	2.72607	+	6.58132i	0.290600	+	0.701571i
$89$		−	5.03712i		−	0.533934i	−0.963706	−	0.266967i	$-0.913979\pi$
$89$		−	5.03712i		−	0.533934i	0.963706	−	0.266967i	$-0.0860214\pi$
$90$		0			0
$91$	−15.3137			−1.60531
$92$	3.69552	+	3.69552i	0.385284	+	0.385284i
$93$	−0.634051	−	1.92762i	−0.0657480	−	0.199885i
$94$	1.41421	−	3.41421i	0.145865	−	0.352149i
$95$		0			0
$96$	9.77048	+	0.733355i	0.997195	+	0.0748477i
$97$	−2.72607			−0.276790			−0.138395	−	0.990377i	$-0.544194\pi$
$97$	−2.72607			−0.276790			−0.138395	+	0.990377i	$0.544194\pi$
$98$	2.07193	−	5.00208i	0.209297	−	0.505286i
$99$	4.48528	+	6.08034i	0.450788	+	0.611097i
$100$		0			0
$101$	−13.2039			−1.31384			−0.656919	−	0.753961i	$-0.728141\pi$
$101$	−13.2039			−1.31384			−0.656919	+	0.753961i	$0.728141\pi$
$102$	−9.02674	−	0.677532i	−0.893781	−	0.0670856i
$103$			6.01673i			0.592846i	0.955057	+	0.296423i	$0.0957938\pi$
$103$			6.01673i			0.592846i	−0.955057	+	0.296423i	$0.904206\pi$
$104$	5.03712	+	12.1607i	0.493930	+	1.19245i
$105$		0			0
$106$	2.48528	−	6.00000i	0.241392	−	0.582772i
$107$		−	8.47343i		−	0.819157i	−0.912275	−	0.409579i	$-0.865676\pi$
$107$		−	8.47343i		−	0.819157i	0.912275	−	0.409579i	$-0.134324\pi$
$108$	10.2461	−	1.73715i	0.985930	−	0.167157i
$109$			0.485281i			0.0464815i	0.999730	+	0.0232408i	$0.00739843\pi$
$109$			0.485281i			0.0464815i	−0.999730	+	0.0232408i	$0.992602\pi$
$110$		0			0
$111$	1.04322	+	3.17157i	0.0990182	+	0.301032i
$112$	−13.1626			−1.24375
$113$			8.92177i			0.839290i	0.907688	+	0.419645i	$0.137845\pi$
$113$			8.92177i			0.839290i	−0.907688	+	0.419645i	$0.862155\pi$
$114$	−0.151883	+	2.02353i	−0.0142251	+	0.189521i
$115$		0			0
$116$	8.59890	+	8.59890i	0.798388	+	0.798388i
$117$	8.28772	+	11.2350i	0.766200	+	1.03868i
$118$	−3.29066	−	1.36303i	−0.302930	−	0.125478i
$119$	12.1607			1.11477
$120$		0			0
$121$	4.65685			0.423350
$122$	−11.0866	−	4.59220i	−1.00373	−	0.415758i
$123$	4.65369	+	14.1480i	0.419609	+	1.27568i
$124$	1.65685	−	1.65685i	0.148790	−	0.148790i
$125$		0			0
$126$	−13.5514	+	3.35740i	−1.20725	+	0.299101i
$127$		−	3.29066i		−	0.291999i	−0.989285	−	0.145999i	$-0.953360\pi$
$127$		−	3.29066i		−	0.291999i	0.989285	−	0.145999i	$-0.0466397\pi$
$128$	4.32957	+	10.4525i	0.382683	+	0.923880i
$129$	9.89949	−	3.25623i	0.871602	−	0.286695i
$130$		0			0
$131$			21.8028i			1.90492i	0.304663	+	0.952460i	$0.401456\pi$
$131$			21.8028i			1.90492i	−0.304663	+	0.952460i	$0.598544\pi$
$132$	−3.93268	+	7.78793i	−0.342296	+	0.677852i
$133$		−	2.72607i		−	0.236380i
$134$	1.78089	−	4.29945i	0.153846	−	0.371416i
$135$		0			0
$136$	−4.00000	−	9.65685i	−0.342997	−	0.828068i
$137$			11.9832i			1.02380i	0.859046	+	0.511899i	$0.171058\pi$
$137$			11.9832i			1.02380i	−0.859046	+	0.511899i	$0.828942\pi$
$138$	−0.479087	+	6.38287i	−0.0407826	+	0.543346i
$139$	−14.4853			−1.22863			−0.614313	−	0.789063i	$-0.710567\pi$
$139$	−14.4853			−1.22863			−0.614313	+	0.789063i	$0.710567\pi$
$140$		0			0
$141$	4.29945	−	1.41421i	0.362079	−	0.119098i
$142$	−3.85525	+	9.30739i	−0.323525	+	0.781058i
$143$	−11.7206			−0.980126
$144$	7.12356	+	9.65685i	0.593630	+	0.804738i
$145$		0			0
$146$	3.56178	−	8.59890i	0.294775	−	0.711650i
$147$	6.29902	−	2.07193i	0.519535	−	0.170890i
$148$	−2.72607	+	2.72607i	−0.224082	+	0.224082i
$149$	14.6792			1.20257			0.601285	−	0.799034i	$-0.294656\pi$
$149$	14.6792			1.20257			0.601285	+	0.799034i	$0.294656\pi$
$150$		0			0
$151$		−	2.82843i		−	0.230174i	−0.993355	−	0.115087i	$-0.963285\pi$
$151$		−	2.82843i		−	0.230174i	0.993355	−	0.115087i	$-0.0367147\pi$
$152$	−2.16478	+	0.896683i	−0.175587	+	0.0727306i
$153$	−6.58132	−	8.92177i	−0.532068	−	0.721282i
$154$	4.48528	−	10.8284i	0.361434	−	0.872580i
$155$		0			0
$156$	−7.26665	+	14.3902i	−0.581797	+	1.15214i
$157$			5.78287i			0.461523i	0.973010	+	0.230762i	$0.0741217\pi$
$157$			5.78287i			0.461523i	−0.973010	+	0.230762i	$0.925878\pi$
$158$	−21.5391	−	8.92177i	−1.71356	−	0.709778i
$159$	7.55568	−	2.48528i	0.599204	−	0.197096i
$160$		0			0
$161$		−	8.59890i		−	0.677688i
$162$	9.79713	+	8.12504i	0.769735	+	0.638363i
$163$	6.01673			0.471266			0.235633	−	0.971842i	$-0.424284\pi$
$163$	6.01673			0.471266			0.235633	+	0.971842i	$0.424284\pi$
$164$	−12.1607	+	12.1607i	−0.949590	+	0.949590i
$165$		0			0
$166$	12.2426	+	5.07107i	0.950213	+	0.393591i
$167$	−17.3952			−1.34608			−0.673040	−	0.739606i	$-0.735012\pi$
$167$	−17.3952			−1.34608			−0.673040	+	0.739606i	$0.735012\pi$
$168$	−10.5140	−	12.2204i	−0.811172	−	0.942824i
$169$	−8.65685			−0.665912
$170$		0			0
$171$	−2.00000	+	1.47534i	−0.152944	+	0.112822i
$172$	8.50894	+	8.50894i	0.648800	+	0.648800i
$173$	21.5391			1.63758			0.818792	−	0.574090i	$-0.194644\pi$
$173$	21.5391			1.63758			0.818792	+	0.574090i	$0.194644\pi$
$174$	−1.11476	+	14.8520i	−0.0845099	+	1.12592i
$175$		0			0
$176$	−10.0742			−0.759374
$177$	−1.36303	−	4.14386i	−0.102452	−	0.311472i
$178$	6.58132	+	2.72607i	0.493290	+	0.204328i
$179$			9.64212i			0.720686i	0.932820	+	0.360343i	$0.117340\pi$
$179$			9.64212i			0.720686i	−0.932820	+	0.360343i	$0.882660\pi$
$180$		0			0
$181$		−	10.3431i		−	0.768800i	−0.923167	−	0.384400i	$-0.874408\pi$
$181$		−	10.3431i		−	0.768800i	0.923167	−	0.384400i	$-0.125592\pi$
$182$	8.28772	−	20.0083i	0.614327	−	1.48312i
$183$	−4.59220	−	13.9611i	−0.339465	−	1.03203i
$184$	−6.82843	+	2.82843i	−0.503398	+	0.208514i
$185$		0			0
$186$	2.86171	+	0.214795i	0.209830	+	0.0157495i
$187$	9.30739			0.680623
$188$	3.69552	+	3.69552i	0.269523	+	0.269523i
$189$	−13.9416	−	9.89949i	−1.01410	−	0.720082i
$190$		0			0
$191$	5.03712			0.364473			0.182237	−	0.983255i	$-0.441666\pi$
$191$	5.03712			0.364473			0.182237	+	0.983255i	$0.441666\pi$
$192$	−6.24592	+	12.3689i	−0.450760	+	0.892645i
$193$	19.7439			1.42120			0.710600	−	0.703596i	$-0.248424\pi$
$193$	19.7439			1.42120			0.710600	+	0.703596i	$0.248424\pi$
$194$	1.47534	−	3.56178i	0.105923	−	0.255721i
$195$		0			0
$196$	5.41421	+	5.41421i	0.386730	+	0.386730i
$197$	11.9832			0.853770			0.426885	−	0.904306i	$-0.359611\pi$
$197$	11.9832			0.853770			0.426885	+	0.904306i	$0.359611\pi$
$198$	−10.3718	+	2.56964i	−0.737089	+	0.182617i
$199$		−	9.17157i		−	0.650156i	−0.945687	−	0.325078i	$-0.894610\pi$
$199$		−	9.17157i		−	0.650156i	0.945687	−	0.325078i	$-0.105390\pi$
$200$		0			0
$201$	5.41421	−	1.78089i	0.381889	−	0.125614i
$202$	7.14590	−	17.2517i	0.502784	−	1.21383i
$203$		−	20.0083i		−	1.40431i
$204$	5.77048	−	11.4273i	0.404014	−	0.800073i
$205$		0			0
$206$	−7.86123	−	3.25623i	−0.547718	−	0.226872i
$207$	−6.30864	+	4.65369i	−0.438481	+	0.323454i
$208$	−18.6148			−1.29070
$209$		−	2.08644i		−	0.144322i
$210$		0			0
$211$	18.4853			1.27258			0.636290	−	0.771450i	$-0.280468\pi$
$211$	18.4853			1.27258			0.636290	+	0.771450i	$0.280468\pi$
$212$	6.49435	+	6.49435i	0.446034	+	0.446034i
$213$	−11.7206	+	3.85525i	−0.803083	+	0.264157i
$214$	11.0711	+	4.58579i	0.756803	+	0.313478i
$215$		0			0
$216$	−3.27545	+	14.3273i	−0.222866	+	0.974849i
$217$	−3.85525			−0.261711
$218$	−0.634051	−	0.262632i	−0.0429433	−	0.0177877i
$219$	10.8284	−	3.56178i	0.731717	−	0.240683i
$220$		0			0
$221$	17.1978			1.15685
$222$	−4.70845	−	0.353408i	−0.316010	−	0.0237192i
$223$		−	21.9054i		−	1.46690i	−0.679746	−	0.733448i	$-0.737910\pi$
$223$		−	21.9054i		−	1.46690i	0.679746	−	0.733448i	$-0.262090\pi$
$224$	7.12356	−	17.1978i	0.475963	−	1.14908i
$225$		0			0
$226$	−11.6569	−	4.82843i	−0.775402	−	0.321182i
$227$		−	4.14386i		−	0.275038i	−0.990499	−	0.137519i	$-0.956087\pi$
$227$		−	4.14386i		−	0.275038i	0.990499	−	0.137519i	$-0.0439128\pi$
$228$	−2.56167	−	1.29357i	−0.169651	−	0.0856689i
$229$			19.3137i			1.27629i	0.769918	+	0.638143i	$0.220297\pi$
$229$			19.3137i			1.27629i	−0.769918	+	0.638143i	$0.779703\pi$
$230$		0			0
$231$	13.6360	−	4.48528i	0.897184	−	0.295110i
$232$	−15.8887	+	6.58132i	−1.04314	+	0.432085i
$233$			15.9414i			1.04436i	0.852837	+	0.522178i	$0.174880\pi$
$233$			15.9414i			1.04436i	−0.852837	+	0.522178i	$0.825120\pi$
$234$	−19.1645	+	4.74808i	−1.25282	+	0.310392i
$235$		0			0
$236$	3.56178	−	3.56178i	0.231852	−	0.231852i
$237$	−8.92177	−	27.1237i	−0.579531	−	1.76187i
$238$	−6.58132	+	15.8887i	−0.426603	+	1.02991i
$239$	−22.2349			−1.43826			−0.719129	−	0.694877i	$-0.755459\pi$
$239$	−22.2349			−1.43826			−0.719129	+	0.694877i	$0.755459\pi$
$240$		0			0
$241$	−6.48528			−0.417754			−0.208877	−	0.977942i	$-0.566981\pi$
$241$	−6.48528			−0.417754			−0.208877	+	0.977942i	$0.566981\pi$
$242$	−2.52027	+	6.08447i	−0.162009	+	0.391125i
$243$	0.282294	+	15.5859i	0.0181092	+	0.999836i
$244$	12.0000	−	12.0000i	0.768221	−	0.768221i
$245$		0			0
$246$	−21.0038	−	1.57651i	−1.33916	−	0.100515i
$247$		−	3.85525i		−	0.245303i
$248$	1.26810	+	3.06147i	0.0805245	+	0.194403i
$249$	5.07107	+	15.4169i	0.321366	+	0.977007i
$250$		0			0
$251$		−	11.7286i		−	0.740301i	−0.928972	−	0.370150i	$-0.879306\pi$
$251$		−	11.7286i		−	0.740301i	0.928972	−	0.370150i	$-0.120694\pi$
$252$	2.94729	−	19.5227i	0.185662	−	1.22982i
$253$		−	6.58132i		−	0.413764i
$254$	4.29945	+	1.78089i	0.269772	+	0.111743i
$255$		0			0
$256$	−16.0000			−1.00000
$257$			16.3128i			1.01756i	0.860895	+	0.508782i	$0.169904\pi$
$257$			16.3128i			1.01756i	−0.860895	+	0.508782i	$0.830096\pi$
$258$	−1.10310	+	14.6966i	−0.0686760	+	0.914969i
$259$	6.34315			0.394144
$260$		0			0
$261$	−14.6792	+	10.8284i	−0.908622	+	0.670263i
$262$	−28.4867	−	11.7996i	−1.75992	−	0.728981i
$263$	22.2500			1.37200			0.685998	−	0.727604i	$-0.259366\pi$
$263$	22.2500			1.37200			0.685998	+	0.727604i	$0.259366\pi$
$264$	−8.04706	−	9.35309i	−0.495263	−	0.575643i
$265$		0			0
$266$	3.56178	+	1.47534i	0.218387	+	0.0904588i
$267$	2.72607	+	8.28772i	0.166833	+	0.507200i
$268$	4.65369	+	4.65369i	0.284270	+	0.284270i
$269$	−9.64212			−0.587891			−0.293945	−	0.955822i	$-0.594968\pi$
$269$	−9.64212			−0.587891			−0.293945	+	0.955822i	$0.594968\pi$
$270$		0			0
$271$			14.1421i			0.859074i	0.903049	+	0.429537i	$0.141323\pi$
$271$			14.1421i			0.859074i	−0.903049	+	0.429537i	$0.858677\pi$
$272$	14.7821			0.896295
$273$	25.1961	−	8.28772i	1.52494	−	0.501596i
$274$	−15.6569	−	6.48528i	−0.945865	−	0.391790i
$275$		0			0
$276$	−8.08034	−	4.08034i	−0.486379	−	0.245608i
$277$		−	15.0903i		−	0.906685i	−0.891336	−	0.453343i	$-0.850231\pi$
$277$		−	15.0903i		−	0.906685i	0.891336	−	0.453343i	$-0.149769\pi$
$278$	7.83938	−	18.9259i	0.470175	−	1.13510i
$279$	2.08644	+	2.82843i	0.124912	+	0.169334i
$280$		0			0
$281$			3.56178i			0.212478i	0.994341	+	0.106239i	$0.0338809\pi$
$281$			3.56178i			0.212478i	−0.994341	+	0.106239i	$0.966119\pi$
$282$	−0.479087	+	6.38287i	−0.0285292	+	0.380094i
$283$	18.0502			1.07297			0.536486	−	0.843909i	$-0.319751\pi$
$283$	18.0502			1.07297			0.536486	+	0.843909i	$0.319751\pi$
$284$	−10.0742	−	10.0742i	−0.597796	−	0.597796i
$285$		0			0
$286$	6.34315	−	15.3137i	0.375078	−	0.905519i
$287$	28.2960			1.67026
$288$	−16.4725	+	4.08113i	−0.970653	+	0.240483i
$289$	3.34315			0.196656
$290$		0			0
$291$	4.48528	−	1.47534i	0.262932	−	0.0864859i
$292$	9.30739	+	9.30739i	0.544674	+	0.544674i
$293$	−2.42742			−0.141811			−0.0709056	−	0.997483i	$-0.522589\pi$
$293$	−2.42742			−0.141811			−0.0709056	+	0.997483i	$0.522589\pi$
$294$	−0.701899	+	9.35139i	−0.0409356	+	0.545384i
$295$		0			0
$296$	−2.08644	−	5.03712i	−0.121272	−	0.292777i
$297$	−10.6704	−	7.57675i	−0.619161	−	0.439647i
$298$	−7.94435	+	19.1794i	−0.460204	+	1.11103i
$299$		−	12.1607i		−	0.703271i
$300$		0			0
$301$		−	19.7990i		−	1.14119i
$302$	3.69552	+	1.53073i	0.212653	+	0.0880838i
$303$	21.7248	−	7.14590i	1.24806	−	0.410521i
$304$		−	3.31371i		−	0.190054i
$305$		0			0
$306$	15.2186	−	3.77048i	0.869992	−	0.215544i
$307$	7.14590			0.407838			0.203919	−	0.978988i	$-0.434632\pi$
$307$	7.14590			0.407838			0.203919	+	0.978988i	$0.434632\pi$
$308$	11.7206	+	11.7206i	0.667843	+	0.667843i
$309$	−3.25623	−	9.89949i	−0.185240	−	0.563163i
$310$		0			0
$311$	−34.3956			−1.95040			−0.975198	−	0.221334i	$-0.928959\pi$
$311$	−34.3956			−1.95040			−0.975198	+	0.221334i	$0.928959\pi$
$312$	−14.8690	−	17.2823i	−0.841793	−	0.978415i
$313$	−17.0179			−0.961907			−0.480954	−	0.876746i	$-0.659709\pi$
$313$	−17.0179			−0.961907			−0.480954	+	0.876746i	$0.659709\pi$
$314$	−7.55568	−	3.12967i	−0.426392	−	0.176617i
$315$		0			0
$316$	23.3137	−	23.3137i	1.31150	−	1.31150i
$317$	13.2513			0.744269			0.372135	−	0.928179i	$-0.378626\pi$
$317$	13.2513			0.744269			0.372135	+	0.928179i	$0.378626\pi$
$318$	−0.841928	+	11.2170i	−0.0472130	+	0.629018i
$319$		−	15.3137i		−	0.857403i
$320$		0			0
$321$	4.58579	+	13.9416i	0.255954	+	0.778143i
$322$	11.2350	+	4.65369i	0.626102	+	0.259340i
$323$			3.06147i			0.170345i
$324$	−15.9180	+	8.40333i	−0.884336	+	0.466851i
$325$		0			0
$326$	−3.25623	+	7.86123i	−0.180346	+	0.435393i
$327$	−0.262632	−	0.798447i	−0.0145236	−	0.0441542i
$328$	−9.30739	−	22.4700i	−0.513914	−	1.24070i
$329$		−	8.59890i		−	0.474073i
$330$		0			0
$331$	−18.4853			−1.01604			−0.508021	−	0.861344i	$-0.669623\pi$
$331$	−18.4853			−1.01604			−0.508021	+	0.861344i	$0.669623\pi$
$332$	−13.2513	+	13.2513i	−0.727262	+	0.727262i
$333$	−3.43289	−	4.65369i	−0.188121	−	0.255021i
$334$	9.41421	−	22.7279i	0.515123	−	1.24362i
$335$		0			0
$336$	21.6569	−	7.12356i	1.18148	−	0.388622i
$337$	27.9222			1.52102			0.760508	−	0.649328i	$-0.224950\pi$
$337$	27.9222			1.52102			0.760508	+	0.649328i	$0.224950\pi$
$338$	4.68506	−	11.3107i	0.254833	−	0.615222i
$339$	−4.82843	−	14.6792i	−0.262244	−	0.797267i
$340$		0			0
$341$	−2.95068			−0.159788
$342$	−0.845230	−	3.41157i	−0.0457048	−	0.184477i
$343$			10.4366i			0.563521i
$344$	−15.7225	+	6.51246i	−0.847699	+	0.351128i
$345$		0			0
$346$	−11.6569	+	28.1421i	−0.626676	+	1.51293i
$347$			0.185709i			0.00996939i	0.999988	+	0.00498469i	$0.00158668\pi$
$347$			0.185709i			0.00996939i	−0.999988	+	0.00498469i	$0.998413\pi$
$348$	−18.8017	−	9.49433i	−1.00788	−	0.508949i
$349$			2.34315i			0.125426i	0.998032	+	0.0627129i	$0.0199752\pi$
$349$			2.34315i			0.125426i	−0.998032	+	0.0627129i	$0.980025\pi$
$350$		0			0
$351$	−19.7164	−	14.0000i	−1.05238	−	0.747265i
$352$	5.45214	−	13.1626i	0.290600	−	0.701571i
$353$			32.3630i			1.72251i	0.508175	+	0.861254i	$0.330320\pi$
$353$			32.3630i			1.72251i	−0.508175	+	0.861254i	$0.669680\pi$
$354$	6.15188	+	0.461750i	0.326969	+	0.0245417i
$355$		0			0
$356$	−7.12356	+	7.12356i	−0.377548	+	0.377548i
$357$	−20.0083	+	6.58132i	−1.05895	+	0.348320i
$358$	−12.5980	−	5.21828i	−0.665827	−	0.275795i
$359$	−9.21001			−0.486086			−0.243043	−	0.970016i	$-0.578146\pi$
$359$	−9.21001			−0.486086			−0.243043	+	0.970016i	$0.578146\pi$
$360$		0			0
$361$	−18.3137			−0.963879
$362$	13.5140	+	5.59767i	0.710279	+	0.294207i
$363$	−7.66206	+	2.52027i	−0.402154	+	0.132280i
$364$	21.6569	+	21.6569i	1.13513	+	1.13513i
$365$		0			0
$366$	20.7263	+	1.55568i	1.08338	+	0.0813167i
$367$		−	2.16148i		−	0.112828i	−0.998407	−	0.0564142i	$-0.982033\pi$
$367$		−	2.16148i		−	0.112828i	0.998407	−	0.0564142i	$-0.0179667\pi$
$368$		−	10.4525i		−	0.544874i
$369$	−15.3137	−	20.7596i	−0.797200	−	1.08070i
$370$		0			0
$371$		−	15.1114i		−	0.784543i
$372$	−1.82939	+	3.62275i	−0.0948493	+	0.187831i
$373$		−	24.3976i		−	1.26326i	−0.775269	−	0.631631i	$-0.782386\pi$
$373$		−	24.3976i		−	1.26326i	0.775269	−	0.631631i	$-0.217614\pi$
$374$	−5.03712	+	12.1607i	−0.260463	+	0.628814i
$375$		0			0
$376$	−6.82843	+	2.82843i	−0.352149	+	0.145865i
$377$		−	28.2960i		−	1.45732i
$378$	20.4794	−	12.8580i	1.05335	−	0.661343i
$379$	−20.8284			−1.06988			−0.534942	−	0.844889i	$-0.679667\pi$
$379$	−20.8284			−1.06988			−0.534942	+	0.844889i	$0.679667\pi$
$380$		0			0
$381$	1.78089	+	5.41421i	0.0912378	+	0.277379i
$382$	−2.72607	+	6.58132i	−0.139478	+	0.336729i
$383$	−29.1158			−1.48775			−0.743874	−	0.668320i	$-0.767014\pi$
$383$	−29.1158			−1.48775			−0.743874	+	0.668320i	$0.767014\pi$
$384$	−12.7804	−	14.8547i	−0.652198	−	0.758049i
$385$		0			0
$386$	−10.6853	+	25.7967i	−0.543870	+	1.31302i
$387$	−14.5257	+	10.7151i	−0.738381	+	0.544681i
$388$	3.85525	+	3.85525i	0.195720	+	0.195720i
$389$	−7.55568			−0.383088			−0.191544	−	0.981484i	$-0.561350\pi$
$389$	−7.55568			−0.383088			−0.191544	+	0.981484i	$0.561350\pi$
$390$		0			0
$391$			9.65685i			0.488368i
$392$	−10.0042	+	4.14386i	−0.505286	+	0.209297i
$393$	−11.7996	−	35.8728i	−0.595211	−	1.80954i
$394$	−6.48528	+	15.6569i	−0.326724	+	0.788781i
$395$		0			0
$396$	2.25576	−	14.9420i	0.113356	−	0.750866i
$397$			27.1237i			1.36130i	0.732609	+	0.680650i	$0.238303\pi$
$397$			27.1237i			1.36130i	−0.732609	+	0.680650i	$0.761697\pi$
$398$	11.9832	+	4.96362i	0.600665	+	0.248804i
$399$	1.47534	+	4.48528i	0.0738593	+	0.224545i
$400$		0			0
$401$			15.1114i			0.754625i	0.926086	+	0.377313i	$0.123152\pi$
$401$			15.1114i			0.754625i	−0.926086	+	0.377313i	$0.876848\pi$
$402$	−0.603305	+	8.03782i	−0.0300901	+	0.400890i
$403$	−5.45214			−0.271590
$404$	18.6731	+	18.6731i	0.929024	+	0.929024i
$405$		0			0
$406$	26.1421	+	10.8284i	1.29741	+	0.537406i
$407$	4.85483			0.240645
$408$	11.8076	+	13.7239i	0.584562	+	0.679435i
$409$	12.8284			0.634325			0.317162	−	0.948371i	$-0.397270\pi$
$409$	12.8284			0.634325			0.317162	+	0.948371i	$0.397270\pi$
$410$		0			0
$411$	−6.48528	−	19.7164i	−0.319895	−	0.972537i
$412$	8.50894	−	8.50894i	0.419205	−	0.419205i
$413$	−8.28772			−0.407812
$414$	−2.66613	−	10.7612i	−0.131033	−	0.528884i
$415$		0			0
$416$	10.0742	−	24.3214i	0.493930	−	1.19245i
$417$	23.8331	−	7.83938i	1.16711	−	0.383896i
$418$	2.72607	+	1.12918i	0.133336	+	0.0552298i
$419$		−	2.51856i		−	0.123040i	−0.998106	−	0.0615199i	$-0.980405\pi$
$419$		−	2.51856i		−	0.123040i	0.998106	−	0.0615199i	$-0.0195948\pi$
$420$		0			0
$421$			34.8284i			1.69743i	0.528848	+	0.848717i	$0.322624\pi$
$421$			34.8284i			1.69743i	−0.528848	+	0.848717i	$0.677376\pi$
$422$	−10.0042	+	24.1522i	−0.486995	+	1.17571i
$423$	−6.30864	+	4.65369i	−0.306737	+	0.226270i
$424$	−12.0000	+	4.97056i	−0.582772	+	0.241392i
$425$		0			0
$426$	1.30603	−	17.4002i	0.0632771	−	0.843040i
$427$	−27.9222			−1.35125
$428$	−11.9832	+	11.9832i	−0.579232	+	0.579232i
$429$	19.2842	−	6.34315i	0.931052	−	0.306250i
$430$		0			0
$431$	27.2720			1.31365			0.656824	−	0.754044i	$-0.271899\pi$
$431$	27.2720			1.31365			0.656824	+	0.754044i	$0.271899\pi$
$432$	−16.9469	−	12.0335i	−0.815356	−	0.578960i
$433$	23.5992			1.13410			0.567052	−	0.823682i	$-0.308084\pi$
$433$	23.5992			1.13410			0.567052	+	0.823682i	$0.308084\pi$
$434$	2.08644	−	5.03712i	0.100152	−	0.241790i
$435$		0			0
$436$	0.686292	−	0.686292i	0.0328674	−	0.0328674i
$437$	2.16478			0.103556
$438$	−1.20661	+	16.0756i	−0.0576541	+	0.768124i
$439$			28.4853i			1.35953i	0.733431	+	0.679764i	$0.237918\pi$
$439$			28.4853i			1.35953i	−0.733431	+	0.679764i	$0.762082\pi$
$440$		0			0
$441$	−9.24264	+	6.81801i	−0.440126	+	0.324667i
$442$	−9.30739	+	22.4700i	−0.442707	+	1.06879i
$443$		−	1.60766i		−	0.0763821i	−0.999270	−	0.0381910i	$-0.987840\pi$
$443$		−	1.60766i		−	0.0763821i	0.999270	−	0.0381910i	$-0.0121595\pi$
$444$	3.00994	−	5.96062i	0.142846	−	0.282878i
$445$		0			0
$446$	28.6208	+	11.8551i	1.35524	+	0.561357i
$447$	−24.1522	+	7.94435i	−1.14236	+	0.375755i
$448$	18.6148	+	18.6148i	0.879465	+	0.879465i
$449$			35.0067i			1.65207i	0.563620	+	0.826035i	$0.309408\pi$
$449$			35.0067i			1.65207i	−0.563620	+	0.826035i	$0.690592\pi$
$450$		0			0
$451$	21.6569			1.01978
$452$	12.6173	−	12.6173i	0.593467	−	0.593467i
$453$	1.53073	+	4.65369i	0.0719201	+	0.218650i
$454$	5.41421	+	2.24264i	0.254102	+	0.105252i
$455$		0			0
$456$	3.07650	−	2.64691i	0.144070	−	0.123953i
$457$	−18.6148			−0.870762			−0.435381	−	0.900246i	$-0.643386\pi$
$457$	−18.6148			−0.870762			−0.435381	+	0.900246i	$0.643386\pi$
$458$	−25.2346	−	10.4525i	−1.17913	−	0.488413i
$459$	15.6569	+	11.1175i	0.730799	+	0.518919i
$460$		0			0
$461$	−3.99390			−0.186014			−0.0930072	−	0.995665i	$-0.529648\pi$
$461$	−3.99390			−0.186014			−0.0930072	+	0.995665i	$0.529648\pi$
$462$	−1.51946	+	20.2437i	−0.0706917	+	0.941824i
$463$			25.7607i			1.19720i	0.801048	+	0.598600i	$0.204276\pi$
$463$			25.7607i			1.19720i	−0.801048	+	0.598600i	$0.795724\pi$
$464$		−	24.3214i		−	1.12909i
$465$		0			0
$466$	−20.8284	−	8.62742i	−0.964858	−	0.399657i
$467$			15.8645i			0.734120i	0.930197	+	0.367060i	$0.119636\pi$
$467$			15.8645i			0.734120i	−0.930197	+	0.367060i	$0.880364\pi$
$468$	4.16810	−	27.6093i	0.192670	−	1.27624i
$469$		−	10.8284i		−	0.500010i
$470$		0			0
$471$	−3.12967	−	9.51472i	−0.144207	−	0.438415i
$472$	2.72607	+	6.58132i	0.125478	+	0.302930i
$473$		−	15.1535i		−	0.696758i
$474$	40.2673	+	3.02239i	1.84954	+	0.138823i
$475$		0			0
$476$	−17.1978	−	17.1978i	−0.788260	−	0.788260i
$477$	−11.0866	+	8.17821i	−0.507618	+	0.374455i
$478$	12.0335	−	29.0513i	0.550397	−	1.32878i
$479$	19.2842			0.881120			0.440560	−	0.897723i	$-0.354780\pi$
$479$	19.2842			0.881120			0.440560	+	0.897723i	$0.354780\pi$
$480$		0			0
$481$	8.97056			0.409022
$482$	3.50981	−	8.47343i	0.159867	−	0.385954i
$483$	4.65369	+	14.1480i	0.211750	+	0.643757i
$484$	−6.58579	−	6.58579i	−0.299354	−	0.299354i
$485$		0			0
$486$	−20.5167	−	8.06619i	−0.930658	−	0.365890i
$487$		−	8.74280i		−	0.396174i	−0.980184	−	0.198087i	$-0.936527\pi$
$487$		−	8.74280i		−	0.396174i	0.980184	−	0.198087i	$-0.0634729\pi$
$488$	9.18440	+	22.1731i	0.415758	+	1.00373i
$489$	−9.89949	+	3.25623i	−0.447671	+	0.147252i
$490$		0			0
$491$		−	36.9142i		−	1.66591i	−0.553338	−	0.832957i	$-0.686646\pi$
$491$		−	36.9142i		−	1.66591i	0.553338	−	0.832957i	$-0.313354\pi$
$492$	13.4270	−	26.5896i	0.605336	−	1.19875i
$493$			22.4700i			1.01200i
$494$	5.03712	+	2.08644i	0.226631	+	0.0938735i
$495$		0			0
$496$	−4.68629			−0.210421
$497$			23.4412i			1.05148i
$498$	−22.8876	−	1.71790i	−1.02562	−	0.0769811i
$499$	37.1127			1.66139			0.830696	−	0.556726i	$-0.187943\pi$
$499$	37.1127			1.66139			0.830696	+	0.556726i	$0.187943\pi$
$500$		0			0
$501$	28.6208	−	9.41421i	1.27868	−	0.420596i
$502$	15.3241	+	6.34746i	0.683949	+	0.283301i
$503$	−9.63274			−0.429503			−0.214751	−	0.976669i	$-0.568894\pi$
$503$	−9.63274			−0.429503			−0.214751	+	0.976669i	$0.568894\pi$
$504$	23.9126	+	14.4164i	1.06515	+	0.642159i
$505$		0			0
$506$	8.59890	+	3.56178i	0.382268	+	0.158341i
$507$	14.2434	−	4.68506i	0.632570	−	0.208071i
$508$	−4.65369	+	4.65369i	−0.206474	+	0.206474i
$509$	13.2039			0.585253			0.292626	−	0.956227i	$-0.405471\pi$
$509$	13.2039			0.585253			0.292626	+	0.956227i	$0.405471\pi$
$510$		0			0
$511$		−	21.6569i		−	0.958043i
$512$	8.65914	−	20.9050i	0.382683	−	0.923880i
$513$	2.49221	−	3.50981i	0.110034	−	0.154962i
$514$	−21.3137	−	8.82843i	−0.940107	−	0.389405i
$515$		0			0
$516$	−18.6050	−	9.39500i	−0.819040	−	0.413592i
$517$		−	6.58132i		−	0.289446i
$518$	−3.43289	+	8.28772i	−0.150832	+	0.364141i
$519$	−35.4388	+	11.6569i	−1.55559	+	0.511679i
$520$		0			0
$521$			34.3956i			1.50690i	0.657506	+	0.753450i	$0.271612\pi$
$521$			34.3956i			1.50690i	−0.657506	+	0.753450i	$0.728388\pi$
$522$	−6.20367	−	25.0397i	−0.271527	−	1.09596i
$523$	−12.5980			−0.550874			−0.275437	−	0.961319i	$-0.588823\pi$
$523$	−12.5980			−0.550874			−0.275437	+	0.961319i	$0.588823\pi$
$524$	30.8338	−	30.8338i	1.34698	−	1.34698i
$525$		0			0
$526$	−12.0416	+	29.0711i	−0.525040	+	1.26756i
$527$	4.32957			0.188599
$528$	16.5754	−	5.45214i	0.721353	−	0.237274i
$529$	−16.1716			−0.703112
$530$		0			0
$531$	4.48528	+	6.08034i	0.194645	+	0.263864i
$532$	−3.85525	+	3.85525i	−0.167146	+	0.167146i
$533$	40.0166			1.73331
$534$	−12.3038	−	0.923499i	−0.532436	−	0.0399637i
$535$		0			0
$536$	−8.59890	+	3.56178i	−0.371416	+	0.153846i
$537$	−5.21828	−	15.8645i	−0.225185	−	0.684602i
$538$	5.21828	−	12.5980i	0.224976	−	0.543140i
$539$		−	9.64212i		−	0.415316i
$540$		0			0
$541$			16.0000i			0.687894i	0.938989	+	0.343947i	$0.111764\pi$
$541$			16.0000i			0.687894i	−0.938989	+	0.343947i	$0.888236\pi$
$542$	−18.4776	−	7.65367i	−0.793680	−	0.328753i
$543$	5.59767	+	17.0179i	0.240219	+	0.730307i
$544$	−8.00000	+	19.3137i	−0.342997	+	0.828068i
$545$		0			0
$546$	−2.80760	+	37.4056i	−0.120154	+	1.60081i
$547$	−11.0011			−0.470375			−0.235188	−	0.971950i	$-0.575570\pi$
$547$	−11.0011			−0.470375			−0.235188	+	0.971950i	$0.575570\pi$
$548$	16.9469	−	16.9469i	0.723934	−	0.723934i
$549$	15.1114	+	20.4853i	0.644937	+	0.874291i
$550$		0			0
$551$	5.03712			0.214589
$552$	9.70427	−	8.34921i	0.413041	−	0.355366i
$553$	−54.2474			−2.30683
$554$	19.7164	+	8.16679i	0.837668	+	0.346973i
$555$		0			0
$556$	20.4853	+	20.4853i	0.868769	+	0.868769i
$557$	−4.96362			−0.210315			−0.105158	−	0.994456i	$-0.533535\pi$
$557$	−4.96362			−0.210315			−0.105158	+	0.994456i	$0.533535\pi$
$558$	−4.82469	+	1.19534i	−0.204246	+	0.0506026i
$559$		−	28.0000i		−	1.18427i
$560$		0			0
$561$	−15.3137	+	5.03712i	−0.646545	+	0.212667i
$562$	−4.65369	−	1.92762i	−0.196304	−	0.0813119i
$563$		−	21.9874i		−	0.926658i	−0.886186	−	0.463329i	$-0.846655\pi$
$563$		−	21.9874i		−	0.926658i	0.886186	−	0.463329i	$-0.153345\pi$
$564$	−8.08034	−	4.08034i	−0.340244	−	0.171813i
$565$		0			0
$566$	−9.76869	+	23.5837i	−0.410609	+	0.991297i
$567$	28.2960	+	8.74280i	1.18832	+	0.367163i
$568$	18.6148	−	7.71049i	0.781058	−	0.323525i
$569$			15.7225i			0.659120i	0.944135	+	0.329560i	$0.106900\pi$
$569$			15.7225i			0.659120i	−0.944135	+	0.329560i	$0.893100\pi$
$570$		0			0
$571$	21.1127			0.883539			0.441769	−	0.897129i	$-0.354351\pi$
$571$	21.1127			0.883539			0.441769	+	0.897129i	$0.354351\pi$
$572$	16.5754	+	16.5754i	0.693054	+	0.693054i
$573$	−8.28772	+	2.72607i	−0.346224	+	0.113883i
$574$	−15.3137	+	36.9706i	−0.639182	+	1.54312i
$575$		0			0
$576$	3.58261	−	23.7311i	0.149276	−	0.988796i
$577$	3.85525			0.160496			0.0802480	−	0.996775i	$-0.474429\pi$
$577$	3.85525			0.160496			0.0802480	+	0.996775i	$0.474429\pi$
$578$	−1.80930	+	4.36803i	−0.0752569	+	0.181686i
$579$	−32.4853	+	10.6853i	−1.35004	+	0.444068i
$580$		0			0
$581$	30.8338			1.27920
$582$	−0.499794	+	6.65875i	−0.0207171	+	0.276014i
$583$		−	11.5657i		−	0.479004i
$584$	−17.1978	+	7.12356i	−0.711650	+	0.294775i
$585$		0			0
$586$	1.31371	−	3.17157i	0.0542688	−	0.131016i
$587$		−	7.20533i		−	0.297396i	−0.988883	−	0.148698i	$-0.952492\pi$
$587$		−	7.20533i		−	0.297396i	0.988883	−	0.148698i	$-0.0475082\pi$
$588$	−11.8383	−	5.97801i	−0.488204	−	0.246529i
$589$		−	0.970563i		−	0.0399913i
$590$		0			0
$591$	−19.7164	+	6.48528i	−0.811023	+	0.266769i
$592$	7.71049			0.316899
$593$			1.00547i			0.0412897i	0.999787	+	0.0206448i	$0.00657192\pi$
$593$			1.00547i			0.0412897i	−0.999787	+	0.0206448i	$0.993428\pi$
$594$	15.6743	−	9.84107i	0.643124	−	0.403784i
$595$		0			0
$596$	−20.7596	−	20.7596i	−0.850346	−	0.850346i
$597$	4.96362	+	15.0903i	0.203147	+	0.617603i
$598$	15.8887	+	6.58132i	0.649737	+	0.269130i
$599$	32.3092			1.32012			0.660058	−	0.751214i	$-0.270532\pi$
$599$	32.3092			1.32012			0.660058	+	0.751214i	$0.270532\pi$
$600$		0			0
$601$	13.5147			0.551277			0.275638	−	0.961261i	$-0.411111\pi$
$601$	13.5147			0.551277			0.275638	+	0.961261i	$0.411111\pi$
$602$	25.8686	+	10.7151i	1.05433	+	0.436716i
$603$	−7.94435	+	5.86030i	−0.323519	+	0.238650i
$604$	−4.00000	+	4.00000i	−0.162758	+	0.162758i
$605$		0			0
$606$	−2.42079	+	32.2521i	−0.0983378	+	1.31015i
$607$			4.88755i			0.198380i	0.995069	+	0.0991898i	$0.0316251\pi$
$607$			4.88755i			0.198380i	−0.995069	+	0.0991898i	$0.968375\pi$
$608$	4.32957	+	1.79337i	0.175587	+	0.0727306i
$609$	10.8284	+	32.9203i	0.438790	+	1.33400i
$610$		0			0
$611$		−	12.1607i		−	0.491969i
$612$	−3.30990	+	21.9247i	−0.133795	+	0.886252i
$613$			23.2685i			0.939804i	0.882718	+	0.469902i	$0.155711\pi$
$613$			23.2685i			0.939804i	−0.882718	+	0.469902i	$0.844289\pi$
$614$	−3.86733	+	9.33657i	−0.156073	+	0.376793i
$615$		0			0
$616$	−21.6569	+	8.97056i	−0.872580	+	0.361434i
$617$			8.55035i			0.344224i	0.985077	+	0.172112i	$0.0550591\pi$
$617$			8.55035i			0.344224i	−0.985077	+	0.172112i	$0.944941\pi$
$618$	14.6966	+	1.10310i	0.591183	+	0.0443732i
$619$	2.48528			0.0998919			0.0499459	−	0.998752i	$-0.484095\pi$
$619$	2.48528			0.0998919			0.0499459	+	0.998752i	$0.484095\pi$
$620$		0			0
$621$	7.86123	−	11.0711i	0.315460	−	0.444267i
$622$	18.6148	−	44.9400i	0.746384	−	1.80193i
$623$	16.5754			0.664081
$624$	30.6274	−	10.0742i	1.22608	−	0.403292i
$625$		0			0
$626$	9.21001	−	22.2349i	0.368106	−	0.888686i
$627$	1.12918	+	3.43289i	0.0450949	+	0.137096i
$628$	8.17821	−	8.17821i	0.326346	−	0.326346i
$629$	−7.12356			−0.284035
$630$		0			0
$631$			2.14214i			0.0852771i	0.999091	+	0.0426385i	$0.0135764\pi$
$631$			2.14214i			0.0852771i	−0.999091	+	0.0426385i	$0.986424\pi$
$632$	17.8435	+	43.0781i	0.709778	+	1.71356i
$633$	−30.4144	+	10.0042i	−1.20886	+	0.397630i
$634$	−7.17157	+	17.3137i	−0.284820	+	0.687615i
$635$		0			0
$636$	−14.2001	−	7.17063i	−0.563069	−	0.284334i
$637$		−	17.8163i		−	0.705908i
$638$	20.0083	+	8.28772i	0.792137	+	0.328114i
$639$	17.1978	−	12.6863i	0.680335	−	0.501862i
$640$		0			0
$641$			35.0067i			1.38268i	0.722529	+	0.691341i	$0.242980\pi$
$641$			35.0067i			1.38268i	−0.722529	+	0.691341i	$0.757020\pi$
$642$	−20.6974	−	1.55351i	−0.816859	−	0.0613121i
$643$	−35.0681			−1.38295			−0.691475	−	0.722401i	$-0.743039\pi$
$643$	−35.0681			−1.38295			−0.691475	+	0.722401i	$0.743039\pi$
$644$	−12.1607	+	12.1607i	−0.479198	+	0.479198i
$645$		0			0
$646$	−4.00000	−	1.65685i	−0.157378	−	0.0651881i
$647$	−28.3730			−1.11546			−0.557728	−	0.830024i	$-0.688327\pi$
$647$	−28.3730			−1.11546			−0.557728	+	0.830024i	$0.688327\pi$
$648$	−2.36469	−	25.3458i	−0.0928938	−	0.995676i
$649$	−6.34315			−0.248990
$650$		0			0
$651$	6.34315	−	2.08644i	0.248607	−	0.0817742i
$652$	−8.50894	−	8.50894i	−0.333236	−	0.333236i
$653$	−24.2291			−0.948158			−0.474079	−	0.880482i	$-0.657219\pi$
$653$	−24.2291			−0.948158			−0.474079	+	0.880482i	$0.657219\pi$
$654$	1.18536	+	0.0889709i	0.0463511	+	0.00347904i
$655$		0			0
$656$	34.3956			1.34292
$657$	−15.8887	+	11.7206i	−0.619877	+	0.457264i
$658$	11.2350	+	4.65369i	0.437986	+	0.181420i
$659$		−	14.6792i		−	0.571822i	−0.958256	−	0.285911i	$-0.907704\pi$
$659$		−	14.6792i		−	0.571822i	0.958256	−	0.285911i	$-0.0922962\pi$
$660$		0			0
$661$		−	44.7696i		−	1.74133i	−0.491873	−	0.870667i	$-0.663688\pi$
$661$		−	44.7696i		−	1.74133i	0.491873	−	0.870667i	$-0.336312\pi$
$662$	10.0042	−	24.1522i	0.388823	−	0.938701i
$663$	−28.2960	+	9.30739i	−1.09893	+	0.361469i
$664$	−10.1421	−	24.4853i	−0.393591	−	0.950213i
$665$		0			0
$666$	7.93821	−	1.96672i	0.307599	−	0.0762089i
$667$	15.8887			0.615213
$668$	24.6005	+	24.6005i	0.951823	+	0.951823i
$669$	11.8551	+	36.0416i	0.458346	+	1.39345i
$670$		0			0
$671$	−21.3707			−0.825006
$672$	−2.41322	+	32.1513i	−0.0930920	+	1.24026i
$673$	47.6661			1.83739			0.918697	−	0.394964i	$-0.129243\pi$
$673$	47.6661			1.83739			0.918697	+	0.394964i	$0.129243\pi$
$674$	−15.1114	+	36.4821i	−0.582068	+	1.40524i
$675$		0			0
$676$	12.2426	+	12.2426i	0.470871	+	0.470871i
$677$	1.00547			0.0386433			0.0193217	−	0.999813i	$-0.493849\pi$
$677$	1.00547			0.0386433			0.0193217	+	0.999813i	$0.493849\pi$
$678$	21.7925	+	1.63571i	0.836935	+	0.0628189i
$679$		−	8.97056i		−	0.344259i
$680$		0			0
$681$	2.24264	+	6.81801i	0.0859382	+	0.261267i
$682$	1.59689	−	3.85525i	0.0611483	−	0.147625i
$683$		−	14.9678i		−	0.572726i	−0.958121	−	0.286363i	$-0.907554\pi$
$683$		−	14.9678i		−	0.572726i	0.958121	−	0.286363i	$-0.0924464\pi$
$684$	4.91487	+	0.741983i	0.187925	+	0.0283704i
$685$		0			0
$686$	−13.6360	−	5.64823i	−0.520626	−	0.215650i
$687$	−10.4525	−	31.7774i	−0.398788	−	1.21238i
$688$		−	24.0669i		−	0.917542i
$689$		−	21.3707i		−	0.814159i
$690$		0			0
$691$	−7.17157			−0.272819			−0.136410	−	0.990653i	$-0.543556\pi$
$691$	−7.17157			−0.272819			−0.136410	+	0.990653i	$0.543556\pi$
$692$	−30.4608	−	30.4608i	−1.15795	−	1.15795i
$693$	−20.0083	+	14.7595i	−0.760053	+	0.560668i
$694$	−0.242641	−	0.100505i	−0.00921051	−	0.00381512i
$695$		0			0
$696$	22.5804	−	19.4273i	0.855906	−	0.736391i
$697$	−31.7774			−1.20365
$698$	−3.06147	−	1.26810i	−0.115878	−	0.0479983i
$699$	−8.62742	−	26.2288i	−0.326319	−	0.992065i
$700$		0			0
$701$	−26.8399			−1.01373			−0.506865	−	0.862025i	$-0.669196\pi$
$701$	−26.8399			−1.01373			−0.506865	+	0.862025i	$0.669196\pi$
$702$	28.9623	−	18.1839i	1.09311	−	0.686308i
$703$			1.59689i			0.0602280i
$704$	14.2471	+	14.2471i	0.536959	+	0.536959i
$705$		0			0
$706$	−42.2843	−	17.5147i	−1.59139	−	0.659175i
$707$		−	43.4495i		−	1.63409i
$708$	−3.93268	+	7.78793i	−0.147799	+	0.292688i
$709$		−	36.2843i		−	1.36268i	−0.731965	−	0.681342i	$-0.761397\pi$
$709$		−	36.2843i		−	1.36268i	0.731965	−	0.681342i	$-0.238603\pi$
$710$		0			0
$711$	29.3585	+	39.7990i	1.10103	+	1.49258i
$712$	−5.45214	−	13.1626i	−0.204328	−	0.493290i
$713$		−	3.06147i		−	0.114653i
$714$	2.22952	−	29.7039i	0.0834379	−	1.11164i
$715$		0			0
$716$	13.6360	−	13.6360i	0.509602	−	0.509602i
$717$	36.5838	−	12.0335i	1.36625	−	0.449398i
$718$	4.98442	−	12.0335i	0.186017	−	0.449085i
$719$	−2.95068			−0.110042			−0.0550208	−	0.998485i	$-0.517523\pi$
$719$	−2.95068			−0.110042			−0.0550208	+	0.998485i	$0.517523\pi$
$720$		0			0
$721$	−19.7990			−0.737353
$722$	9.91131	−	23.9280i	0.368861	−	0.890508i
$723$	10.6704	−	3.50981i	0.396837	−	0.130531i
$724$	−14.6274	+	14.6274i	−0.543624	+	0.543624i
$725$		0			0
$726$	0.853782	−	11.3749i	0.0316868	−	0.422163i
$727$			47.1015i			1.74690i	0.486915	+	0.873449i	$0.338122\pi$
$727$			47.1015i			1.74690i	−0.486915	+	0.873449i	$0.661878\pi$
$728$	−40.0166	+	16.5754i	−1.48312	+	0.614327i
$729$	−8.89949	−	25.4912i	−0.329611	−	0.944117i
$730$		0			0
$731$			22.2349i			0.822388i
$732$	−13.2496	+	26.2383i	−0.489719	+	0.969795i
$733$			9.63811i			0.355992i	0.984031	+	0.177996i	$0.0569614\pi$
$733$			9.63811i			0.355992i	−0.984031	+	0.177996i	$0.943039\pi$
$734$	2.82411	+	1.16979i	0.104240	+	0.0431776i
$735$		0			0
$736$	13.6569	+	5.65685i	0.503398	+	0.208514i
$737$		−	8.28772i		−	0.305282i
$738$	35.4114	−	8.77332i	1.30351	−	0.322950i
$739$	27.1716			0.999522			0.499761	−	0.866163i	$-0.333421\pi$
$739$	27.1716			0.999522			0.499761	+	0.866163i	$0.333421\pi$
$740$		0			0
$741$	2.08644	+	6.34315i	0.0766474	+	0.233021i
$742$	19.7439	+	8.17821i	0.724823	+	0.300232i
$743$	15.2304			0.558750			0.279375	−	0.960182i	$-0.409873\pi$
$743$	15.2304			0.558750			0.279375	+	0.960182i	$0.409873\pi$
$744$	−3.74330	−	4.35083i	−0.137236	−	0.159509i
$745$		0			0
$746$	31.8771	+	13.2039i	1.16710	+	0.483429i
$747$	−16.6871	−	22.6215i	−0.610551	−	0.827676i
$748$	−13.1626	−	13.1626i	−0.481273	−	0.481273i
$749$	27.8832			1.01883
$750$		0			0
$751$		−	35.1127i		−	1.28128i	−0.767841	−	0.640640i	$-0.778669\pi$
$751$		−	35.1127i		−	1.28128i	0.767841	−	0.640640i	$-0.221331\pi$
$752$		−	10.4525i		−	0.381164i
$753$	6.34746	+	19.2974i	0.231314	+	0.703235i
$754$	36.9706	+	15.3137i	1.34639	+	0.557692i
$755$		0			0
$756$	5.71637	+	33.7164i	0.207902	+	1.22625i
$757$		−	12.8319i		−	0.466383i	−0.972431	−	0.233192i	$-0.925083\pi$
$757$		−	12.8319i		−	0.466383i	0.972431	−	0.233192i	$-0.0749170\pi$
$758$	11.2723	−	27.2137i	0.409427	−	0.988444i
$759$	3.56178	+	10.8284i	0.129284	+	0.393047i
$760$		0			0
$761$		−	17.1978i		−	0.623420i	−0.950177	−	0.311710i	$-0.899098\pi$
$761$		−	17.1978i		−	0.623420i	0.950177	−	0.311710i	$-0.100902\pi$
$762$	−8.03782	−	0.603305i	−0.291180	−	0.0218554i
$763$	−1.59689			−0.0578115
$764$	−7.12356	−	7.12356i	−0.257722	−	0.257722i
$765$		0			0
$766$	15.7574	−	38.0416i	0.569337	−	1.37450i
$767$	−11.7206			−0.423207
$768$	26.3253	−	8.65914i	0.949931	−	0.312460i
$769$	49.5980			1.78855			0.894274	−	0.447519i	$-0.147692\pi$
$769$	49.5980			1.78855			0.894274	+	0.447519i	$0.147692\pi$
$770$		0			0
$771$	−8.82843	−	26.8399i	−0.317948	−	0.966616i
$772$	−27.9222	−	27.9222i	−1.00494	−	1.00494i
$773$	−18.8490			−0.677952			−0.338976	−	0.940795i	$-0.610081\pi$
$773$	−18.8490			−0.677952			−0.338976	+	0.940795i	$0.610081\pi$
$774$	−6.13877	−	24.7777i	−0.220653	−	0.890616i
$775$		0			0
$776$	−7.12356	+	2.95068i	−0.255721	+	0.105923i
$777$	−10.4366	+	3.43289i	−0.374410	+	0.123154i
$778$	4.08910	−	9.87197i	0.146602	−	0.353927i
$779$			7.12356i			0.255228i
$780$		0			0
$781$			17.9411i			0.641984i
$782$	−12.6173	−	5.22625i	−0.451193	−	0.186890i
$783$	18.2919	−	25.7607i	0.653699	−	0.920611i
$784$		−	15.3137i		−	0.546918i
$785$		0			0
$786$	53.2560	+	3.99730i	1.89958	+	0.142579i
$787$	48.2307			1.71924			0.859619	−	0.510935i	$-0.170701\pi$
$787$	48.2307			1.71924			0.859619	+	0.510935i	$0.170701\pi$
$788$	−16.9469	−	16.9469i	−0.603707	−	0.603707i
$789$	−36.6086	+	12.0416i	−1.30330	+	0.428693i
$790$		0			0
$791$	−29.3585			−1.04387
$792$	18.3019	+	11.0339i	0.650330	+	0.392071i
$793$	−39.4879			−1.40226
$794$	−35.4388	−	14.6792i	−1.25768	−	0.520947i
$795$		0			0
$796$	−12.9706	+	12.9706i	−0.459729	+	0.459729i
$797$	8.92177			0.316025			0.158013	−	0.987437i	$-0.449491\pi$
$797$	8.92177			0.316025			0.158013	+	0.987437i	$0.449491\pi$
$798$	−6.65875	−	0.499794i	−0.235717	−	0.0176925i
$799$			9.65685i			0.341635i
$800$		0			0
$801$	−8.97056	−	12.1607i	−0.316959	−	0.429677i
$802$	−19.7439	−	8.17821i	−0.697183	−	0.288783i
$803$		−	16.5754i		−	0.584935i
$804$	−10.1754	−	5.13829i	−0.358859	−	0.181214i
$805$		0			0
$806$	2.95068	−	7.12356i	0.103933	−	0.250917i
$807$	15.8645	−	5.21828i	0.558456	−	0.183692i
$808$	−34.5035	+	14.2918i	−1.21383	+	0.502784i
$809$		−	4.17289i		−	0.146711i	−0.997306	−	0.0733555i	$-0.976629\pi$
$809$		−	4.17289i		−	0.146711i	0.997306	−	0.0733555i	$-0.0233708\pi$
$810$		0			0
$811$	−14.4853			−0.508647			−0.254324	−	0.967119i	$-0.581853\pi$
$811$	−14.4853			−0.508647			−0.254324	+	0.967119i	$0.581853\pi$
$812$	−28.2960	+	28.2960i	−0.992996	+	0.992996i
$813$	−7.65367	−	23.2685i	−0.268426	−	0.816061i
$814$	−2.62742	+	6.34315i	−0.0920909	+	0.222327i
$815$		0			0
$816$	−24.3214	+	8.00000i	−0.851418	+	0.280056i
$817$	4.98442			0.174383
$818$	−6.94269	+	16.7611i	−0.242746	+	0.586040i
$819$	−36.9706	+	27.2720i	−1.29186	+	0.952962i
$820$		0			0
$821$	23.8893			0.833741			0.416870	−	0.908966i	$-0.363127\pi$
$821$	23.8893			0.833741			0.416870	+	0.908966i	$0.363127\pi$
$822$	29.2705	+	2.19699i	1.02093	+	0.0766289i
$823$		−	23.5023i		−	0.819239i	−0.912256	−	0.409620i	$-0.865661\pi$
$823$		−	23.5023i		−	0.819239i	0.912256	−	0.409620i	$-0.134339\pi$
$824$	6.51246	+	15.7225i	0.226872	+	0.547718i
$825$		0			0
$826$	4.48528	−	10.8284i	0.156063	−	0.376769i
$827$			35.5014i			1.23450i	0.786766	+	0.617252i	$0.211754\pi$
$827$			35.5014i			1.23450i	−0.786766	+	0.617252i	$0.788246\pi$
$828$	15.5031	+	2.34045i	0.538769	+	0.0813364i
$829$		−	5.17157i		−	0.179616i	−0.995959	−	0.0898081i	$-0.971375\pi$
$829$		−	5.17157i		−	0.179616i	0.995959	−	0.0898081i	$-0.0286254\pi$
$830$		0			0
$831$	8.16679	+	24.8284i	0.283303	+	0.861289i
$832$	26.3253	+	26.3253i	0.912664	+	0.912664i
$833$			14.1480i			0.490200i
$834$	−2.65571	+	35.3820i	−0.0919598	+	1.22518i
$835$		0			0
$836$	−2.95068	+	2.95068i	−0.102051	+	0.102051i
$837$	−4.96362	−	3.52452i	−0.171568	−	0.121825i
$838$	3.29066	+	1.36303i	0.113674	+	0.0470853i
$839$	−53.6799			−1.85323			−0.926617	−	0.376006i	$-0.877297\pi$
$839$	−53.6799			−1.85323			−0.926617	+	0.376006i	$0.877297\pi$
$840$		0			0
$841$	7.97056			0.274847
$842$	−45.5055	−	18.8490i	−1.56822	−	0.649580i
$843$	−1.92762	−	5.86030i	−0.0663908	−	0.201840i
$844$	−26.1421	−	26.1421i	−0.899849	−	0.899849i
$845$		0			0
$846$	−2.66613	−	10.7612i	−0.0916634	−	0.369978i
$847$			15.3241i			0.526543i
$848$		−	18.3688i		−	0.630787i
$849$	−29.6985	+	9.76869i	−1.01925	+	0.335261i
$850$		0			0
$851$			5.03712i			0.172670i
$852$	22.0276	+	11.1233i	0.754652	+	0.381078i
$853$			36.4311i			1.24738i	0.781673	+	0.623688i	$0.214367\pi$
$853$			36.4311i			1.24738i	−0.781673	+	0.623688i	$0.785633\pi$
$854$	15.1114	−	36.4821i	0.517100	−	1.24839i
$855$		0			0
$856$	−9.17157	−	22.1421i	−0.313478	−	0.756803i
$857$			28.5587i			0.975546i	0.872971	+	0.487773i	$0.162191\pi$
$857$			28.5587i			0.975546i	−0.872971	+	0.487773i	$0.837809\pi$
$858$	−2.14884	+	28.6290i	−0.0733602	+	0.977377i
$859$	−3.85786			−0.131629			−0.0658143	−	0.997832i	$-0.520965\pi$
$859$	−3.85786			−0.131629			−0.0658143	+	0.997832i	$0.520965\pi$
$860$		0			0
$861$	−46.5563	+	15.3137i	−1.58663	+	0.521890i
$862$	−14.7595	+	35.6326i	−0.502711	+	1.21365i
$863$	−20.0852			−0.683710			−0.341855	−	0.939753i	$-0.611055\pi$
$863$	−20.0852			−0.683710			−0.341855	+	0.939753i	$0.611055\pi$
$864$	24.8940	−	15.6297i	0.846912	−	0.531732i
$865$		0			0
$866$	−12.7718	+	30.8338i	−0.434003	+	1.04778i
$867$	−5.50057	+	1.80930i	−0.186809	+	0.0614470i
$868$	5.45214	+	5.45214i	0.185058	+	0.185058i
$869$	−41.5192			−1.40844
$870$		0			0
$871$		−	15.3137i		−	0.518885i
$872$	0.525265	+	1.26810i	0.0177877	+	0.0429433i
$873$	−6.58132	+	4.85483i	−0.222744	+	0.164311i
$874$	−1.17157	+	2.82843i	−0.0396290	+	0.0956730i
$875$		0			0
$876$	−20.3508	−	10.2766i	−0.687591	−	0.347214i
$877$			35.3019i			1.19206i	0.802962	+	0.596031i	$0.203256\pi$
$877$			35.3019i			1.19206i	−0.802962	+	0.596031i	$0.796744\pi$
$878$	−37.2178	−	15.4161i	−1.25604	−	0.520269i
$879$	3.99390	−	1.31371i	0.134711	−	0.0443103i
$880$		0			0
$881$		−	42.9945i		−	1.44852i	−0.689526	−	0.724261i	$-0.742181\pi$
$881$		−	42.9945i		−	1.44852i	0.689526	−	0.724261i	$-0.257819\pi$
$882$	−3.90608	−	15.7660i	−0.131525	−	0.530868i
$883$	37.7941			1.27187			0.635937	−	0.771741i	$-0.280614\pi$
$883$	37.7941			1.27187			0.635937	+	0.771741i	$0.280614\pi$
$884$	−24.3214	−	24.3214i	−0.818016	−	0.818016i
$885$		0			0
$886$	2.10051	+	0.870058i	0.0705678	+	0.0292302i
$887$	−12.5404			−0.421064			−0.210532	−	0.977587i	$-0.567520\pi$
$887$	−12.5404			−0.421064			−0.210532	+	0.977587i	$0.567520\pi$
$888$	6.15896	+	7.15854i	0.206681	+	0.240225i
$889$	10.8284			0.363174
$890$		0			0
$891$	21.6569	+	6.69145i	0.725532	+	0.224172i
$892$	−30.9790	+	30.9790i	−1.03725	+	1.03725i
$893$	2.16478			0.0724417
$894$	2.69127	−	35.8558i	0.0900097	−	1.19920i
$895$		0			0
$896$	−34.3956	+	14.2471i	−1.14908	+	0.475963i
$897$	6.58132	+	20.0083i	0.219744	+	0.668059i
$898$	−45.7385	−	18.9455i	−1.52631	−	0.632219i
$899$		−	7.12356i		−	0.237584i
$900$		0			0
$901$			16.9706i			0.565371i
$902$	−11.7206	+	28.2960i	−0.390253	+	0.942155i
$903$	10.7151	+	32.5758i	0.356577	+	1.08406i
$904$	9.65685	+	23.3137i	0.321182	+	0.775402i
$905$		0			0
$906$	−6.90877	−	0.518560i	−0.229528	−	0.0172280i
$907$	7.61362			0.252806			0.126403	−	0.991979i	$-0.459657\pi$
$907$	7.61362			0.252806			0.126403	+	0.991979i	$0.459657\pi$
$908$	−5.86030	+	5.86030i	−0.194481	+	0.194481i
$909$	−31.8771	+	23.5147i	−1.05730	+	0.779934i
$910$		0			0
$911$	−2.95068			−0.0977603			−0.0488801	−	0.998805i	$-0.515565\pi$
$911$	−2.95068			−0.0977603			−0.0488801	+	0.998805i	$0.515565\pi$
$912$	1.79337	+	5.45214i	0.0593843	+	0.180538i
$913$	23.5992			0.781019
$914$	10.0742	−	24.3214i	0.333226	−	0.804479i
$915$		0			0
$916$	27.3137	−	27.3137i	0.902470	−	0.902470i
$917$	−71.7456			−2.36925
$918$	−22.9991	+	14.4399i	−0.759083	+	0.476589i
$919$		−	6.14214i		−	0.202610i	−0.994855	−	0.101305i	$-0.967698\pi$
$919$		−	6.14214i		−	0.202610i	0.994855	−	0.101305i	$-0.0323019\pi$
$920$		0			0
$921$	−11.7574	+	3.86733i	−0.387418	+	0.127433i
$922$	2.16148	−	5.21828i	0.0711846	−	0.171855i
$923$			33.1509i			1.09117i
$924$	−25.6274	−	12.9411i	−0.843079	−	0.425731i
$925$		0			0
$926$	−33.6579	−	13.9416i	−1.10607	−	0.458149i
$927$	10.7151	+	14.5257i	0.351931	+	0.477085i
$928$	31.7774	+	13.1626i	1.04314	+	0.432085i
$929$		−	26.6609i		−	0.874717i	−0.899287	−	0.437359i	$-0.855914\pi$
$929$		−	26.6609i		−	0.874717i	0.899287	−	0.437359i	$-0.144086\pi$
$930$		0			0
$931$	3.17157			0.103944
$932$	22.5445	−	22.5445i	0.738471	−	0.738471i
$933$	56.5921	−	18.6148i	1.85274	−	0.609420i
$934$	−20.7279	−	8.58579i	−0.678238	−	0.280936i
$935$		0			0
$936$	33.8175	+	20.3879i	1.10536	+	0.666400i
$937$	8.17821			0.267170			0.133585	−	0.991037i	$-0.457351\pi$
$937$	8.17821			0.267170			0.133585	+	0.991037i	$0.457351\pi$
$938$	14.1480	+	5.86030i	0.461949	+	0.191346i
$939$	28.0000	−	9.21001i	0.913745	−	0.300557i
$940$		0			0
$941$	−23.2781			−0.758846			−0.379423	−	0.925223i	$-0.623877\pi$
$941$	−23.2781			−0.758846			−0.379423	+	0.925223i	$0.623877\pi$
$942$	14.1253	+	1.06022i	0.460229	+	0.0345440i
$943$			22.4700i			0.731724i
$944$	−10.0742			−0.327889
$945$		0			0
$946$	19.7990	+	8.20101i	0.643721	+	0.266638i
$947$		−	21.6160i		−	0.702425i	−0.936296	−	0.351213i	$-0.885769\pi$
$947$		−	21.6160i		−	0.702425i	0.936296	−	0.351213i	$-0.114231\pi$
$948$	−25.7414	+	50.9760i	−0.836043	+	1.65562i
$949$		−	30.6274i		−	0.994208i
$950$		0			0
$951$	−21.8028	+	7.17157i	−0.707005	+	0.232554i
$952$	31.7774	−	13.1626i	1.02991	−	0.426603i
$953$		−	44.0836i		−	1.42801i	−0.700142	−	0.714004i	$-0.746880\pi$
$953$		−	44.0836i		−	1.42801i	0.700142	−	0.714004i	$-0.253120\pi$
$954$	−4.68535	−	18.9113i	−0.151694	−	0.612276i
$955$		0			0
$956$	31.4449	+	31.4449i	1.01700	+	1.01700i
$957$	8.28772	+	25.1961i	0.267904	+	0.814474i
$958$	−10.4366	+	25.1961i	−0.337190	+	0.814049i
$959$	−39.4327			−1.27335
$960$		0			0
$961$	29.6274			0.955723
$962$	−4.85483	+	11.7206i	−0.156526	+	0.377887i
$963$	−15.0903	−	20.4567i	−0.486277	−	0.659207i
$964$	9.17157	+	9.17157i	0.295396	+	0.295396i
$965$		0			0
$966$	−21.0038	−	1.57651i	−0.675788	−	0.0507234i
$967$		−	55.2797i		−	1.77768i	−0.458222	−	0.888838i	$-0.651513\pi$
$967$		−	55.2797i		−	1.77768i	0.458222	−	0.888838i	$-0.348487\pi$
$968$	12.1689	−	5.04054i	0.391125	−	0.162009i
$969$	−1.65685	−	5.03712i	−0.0532258	−	0.161816i
$970$		0			0
$971$			13.8150i			0.443345i	0.975121	+	0.221672i	$0.0711516\pi$
$971$			13.8150i			0.443345i	−0.975121	+	0.221672i	$0.928848\pi$
$972$	21.6426	−	22.4410i	0.694186	−	0.719796i
$973$		−	47.6661i		−	1.52811i
$974$	11.4230	+	4.73157i	0.366017	+	0.151609i
$975$		0			0
$976$	−33.9411			−1.08643
$977$		−	33.2597i		−	1.06407i	−0.846722	−	0.532035i	$-0.821427\pi$
$977$		−	33.2597i		−	1.06407i	0.846722	−	0.532035i	$-0.178573\pi$
$978$	1.10310	−	14.6966i	0.0352732	−	0.469945i
$979$	12.6863			0.405456
$980$		0			0
$981$	0.864233	+	1.17157i	0.0275928	+	0.0374054i
$982$	48.2307	+	19.9778i	1.53910	+	0.637517i
$983$	−10.0042			−0.319083			−0.159542	−	0.987191i	$-0.551002\pi$
$983$	−10.0042			−0.319083			−0.159542	+	0.987191i	$0.551002\pi$
$984$	27.4744	+	31.9334i	0.875852	+	1.01800i
$985$		0			0
$986$	−29.3585	−	12.1607i	−0.934965	−	0.387275i
$987$	4.65369	+	14.1480i	0.148129	+	0.450336i
$988$	−5.45214	+	5.45214i	−0.173456	+	0.173456i
$989$	15.7225			0.499945
$990$		0			0
$991$			19.7990i			0.628936i	0.949268	+	0.314468i	$0.101826\pi$
$991$			19.7990i			0.628936i	−0.949268	+	0.314468i	$0.898174\pi$
$992$	2.53620	−	6.12293i	0.0805245	−	0.194403i
$993$	30.4144	−	10.0042i	0.965171	−	0.317472i
$994$	−30.6274	−	12.6863i	−0.971443	−	0.402385i
$995$		0			0
$996$	14.6312	−	28.9744i	0.463608	−	0.918088i
$997$			8.50894i			0.269481i	0.990881	+	0.134740i	$0.0430200\pi$
$997$			8.50894i			0.269481i	−0.990881	+	0.134740i	$0.956980\pi$
$998$	−20.0852	+	48.4901i	−0.635787	+	1.53493i
$999$	8.16679	+	5.79899i	0.258386	+	0.183472i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.b.i.251.7		16
3.2	odd	2	inner	600.2.b.i.251.9		16
4.3	odd	2		2400.2.b.i.2351.13		16
5.2	odd	4		120.2.m.b.59.2	yes	16
5.3	odd	4		120.2.m.b.59.15	yes	16
5.4	even	2	inner	600.2.b.i.251.10		16
8.3	odd	2	inner	600.2.b.i.251.11		16
8.5	even	2		2400.2.b.i.2351.14		16
12.11	even	2		2400.2.b.i.2351.15		16
15.2	even	4		120.2.m.b.59.16	yes	16
15.8	even	4		120.2.m.b.59.1	✓	16
15.14	odd	2	inner	600.2.b.i.251.8		16
20.3	even	4		480.2.m.b.239.11		16
20.7	even	4		480.2.m.b.239.5		16
20.19	odd	2		2400.2.b.i.2351.4		16
24.5	odd	2		2400.2.b.i.2351.16		16
24.11	even	2	inner	600.2.b.i.251.5		16
40.3	even	4		120.2.m.b.59.13	yes	16
40.13	odd	4		480.2.m.b.239.12		16
40.19	odd	2	inner	600.2.b.i.251.6		16
40.27	even	4		120.2.m.b.59.4	yes	16
40.29	even	2		2400.2.b.i.2351.3		16
40.37	odd	4		480.2.m.b.239.6		16
60.23	odd	4		480.2.m.b.239.8		16
60.47	odd	4		480.2.m.b.239.10		16
60.59	even	2		2400.2.b.i.2351.2		16
120.29	odd	2		2400.2.b.i.2351.1		16
120.53	even	4		480.2.m.b.239.7		16
120.59	even	2	inner	600.2.b.i.251.12		16
120.77	even	4		480.2.m.b.239.9		16
120.83	odd	4		120.2.m.b.59.3	yes	16
120.107	odd	4		120.2.m.b.59.14	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.m.b.59.1	✓	16	15.8	even	4
120.2.m.b.59.2	yes	16	5.2	odd	4
120.2.m.b.59.3	yes	16	120.83	odd	4
120.2.m.b.59.4	yes	16	40.27	even	4
120.2.m.b.59.13	yes	16	40.3	even	4
120.2.m.b.59.14	yes	16	120.107	odd	4
120.2.m.b.59.15	yes	16	5.3	odd	4
120.2.m.b.59.16	yes	16	15.2	even	4
480.2.m.b.239.5		16	20.7	even	4
480.2.m.b.239.6		16	40.37	odd	4
480.2.m.b.239.7		16	120.53	even	4
480.2.m.b.239.8		16	60.23	odd	4
480.2.m.b.239.9		16	120.77	even	4
480.2.m.b.239.10		16	60.47	odd	4
480.2.m.b.239.11		16	20.3	even	4
480.2.m.b.239.12		16	40.13	odd	4
600.2.b.i.251.5		16	24.11	even	2	inner
600.2.b.i.251.6		16	40.19	odd	2	inner
600.2.b.i.251.7		16	1.1	even	1	trivial
600.2.b.i.251.8		16	15.14	odd	2	inner
600.2.b.i.251.9		16	3.2	odd	2	inner
600.2.b.i.251.10		16	5.4	even	2	inner
600.2.b.i.251.11		16	8.3	odd	2	inner
600.2.b.i.251.12		16	120.59	even	2	inner
2400.2.b.i.2351.1		16	120.29	odd	2
2400.2.b.i.2351.2		16	60.59	even	2
2400.2.b.i.2351.3		16	40.29	even	2
2400.2.b.i.2351.4		16	20.19	odd	2
2400.2.b.i.2351.13		16	4.3	odd	2
2400.2.b.i.2351.14		16	8.5	even	2
2400.2.b.i.2351.15		16	12.11	even	2
2400.2.b.i.2351.16		16	24.5	odd	2

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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.541196 + 1.30656i) q^{2} +(-1.64533 + 0.541196i) q^{3} +(-1.41421 - 1.41421i) q^{4} +(0.183339 - 2.44262i) q^{6} +3.29066i q^{7} +(2.61313 - 1.08239i) q^{8} +(2.41421 - 1.78089i) q^{9} +O(q^{10})\)	\(q+(-0.541196 + 1.30656i) q^{2} +(-1.64533 + 0.541196i) q^{3} +(-1.41421 - 1.41421i) q^{4} +(0.183339 - 2.44262i) q^{6} +3.29066i q^{7} +(2.61313 - 1.08239i) q^{8} +(2.41421 - 1.78089i) q^{9} +2.51856i q^{11} +(3.09221 + 1.56148i) q^{12} +4.65369i q^{13} +(-4.29945 - 1.78089i) q^{14} +4.00000i q^{16} -3.69552i q^{17} +(1.02028 + 4.11813i) q^{18} -0.828427 q^{19} +(-1.78089 - 5.41421i) q^{21} +(-3.29066 - 1.36303i) q^{22} -2.61313 q^{23} +(-3.71366 + 3.19510i) q^{24} +(-6.08034 - 2.51856i) q^{26} +(-3.00836 + 4.23671i) q^{27} +(4.65369 - 4.65369i) q^{28} -6.08034 q^{29} +1.17157i q^{31} +(-5.22625 - 2.16478i) q^{32} +(-1.36303 - 4.14386i) q^{33} +(4.82843 + 2.00000i) q^{34} +(-5.93277 - 0.895653i) q^{36} -1.92762i q^{37} +(0.448342 - 1.08239i) q^{38} +(-2.51856 - 7.65685i) q^{39} -8.59890i q^{41} +(8.03782 + 0.603305i) q^{42} -6.01673 q^{43} +(3.56178 - 3.56178i) q^{44} +(1.41421 - 3.41421i) q^{46} -2.61313 q^{47} +(-2.16478 - 6.58132i) q^{48} -3.82843 q^{49} +(2.00000 + 6.08034i) q^{51} +(6.58132 - 6.58132i) q^{52} -4.59220 q^{53} +(-3.90742 - 6.22351i) q^{54} +(3.56178 + 8.59890i) q^{56} +(1.36303 - 0.448342i) q^{57} +(3.29066 - 7.94435i) q^{58} +2.51856i q^{59} +8.48528i q^{61} +(-1.53073 - 0.634051i) q^{62} +(5.86030 + 7.94435i) q^{63} +(5.65685 - 5.65685i) q^{64} +(6.15188 + 0.461750i) q^{66} -3.29066 q^{67} +(-5.22625 + 5.22625i) q^{68} +(4.29945 - 1.41421i) q^{69} +7.12356 q^{71} +(4.38102 - 7.26682i) q^{72} -6.58132 q^{73} +(2.51856 + 1.04322i) q^{74} +(1.17157 + 1.17157i) q^{76} -8.28772 q^{77} +(11.3672 + 0.853202i) q^{78} +16.4853i q^{79} +(2.65685 - 8.59890i) q^{81} +(11.2350 + 4.65369i) q^{82} -9.37011i q^{83} +(-5.13829 + 10.1754i) q^{84} +(3.25623 - 7.86123i) q^{86} +(10.0042 - 3.29066i) q^{87} +(2.72607 + 6.58132i) q^{88} -5.03712i q^{89} -15.3137 q^{91} +(3.69552 + 3.69552i) q^{92} +(-0.634051 - 1.92762i) q^{93} +(1.41421 - 3.41421i) q^{94} +(9.77048 + 0.733355i) q^{96} -2.72607 q^{97} +(2.07193 - 5.00208i) q^{98} +(4.48528 + 6.08034i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^9	\( 16 q + 16 q^{9} + 32 q^{19} + 32 q^{24} + 32 q^{34} - 32 q^{36} - 16 q^{49} + 32 q^{51} - 32 q^{54} + 64 q^{66} + 64 q^{76} - 48 q^{81} - 32 q^{84} - 64 q^{91} + 64 q^{96} - 64 q^{99}+O(q^{100}) \) 16 * q + 16 * q^9 + 32 * q^19 + 32 * q^24 + 32 * q^34 - 32 * q^36 - 16 * q^49 + 32 * q^51 - 32 * q^54 + 64 * q^66 + 64 * q^76 - 48 * q^81 - 32 * q^84 - 64 * q^91 + 64 * q^96 - 64 * q^99

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