LMFDB - Embedded newform 1444.2.e.a.653.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1444,2,Mod(429,1444)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1444, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("1444.429");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1444 = 2^{2} \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1444.e (of order $3$, degree $2$, not 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:	$11.5303980519$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 76)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			653.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1444.653
Dual form			1444.2.e.a.429.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{3} +(0.500000 + 0.866025i) q^{5} -3.00000 q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{3} +(0.500000 + 0.866025i) q^{5} -3.00000 q^{7} +(-0.500000 + 0.866025i) q^{9} +5.00000 q^{11} +(2.00000 - 3.46410i) q^{13} +(1.00000 - 1.73205i) q^{15} +(1.50000 + 2.59808i) q^{17} +(3.00000 + 5.19615i) q^{21} +(-4.00000 + 6.92820i) q^{23} +(2.00000 - 3.46410i) q^{25} -4.00000 q^{27} +(1.00000 - 1.73205i) q^{29} +4.00000 q^{31} +(-5.00000 - 8.66025i) q^{33} +(-1.50000 - 2.59808i) q^{35} +10.0000 q^{37} -8.00000 q^{39} +(-5.00000 - 8.66025i) q^{41} +(-0.500000 - 0.866025i) q^{43} -1.00000 q^{45} +(0.500000 - 0.866025i) q^{47} +2.00000 q^{49} +(3.00000 - 5.19615i) q^{51} +(2.00000 - 3.46410i) q^{53} +(2.50000 + 4.33013i) q^{55} +(-3.00000 - 5.19615i) q^{59} +(6.50000 - 11.2583i) q^{61} +(1.50000 - 2.59808i) q^{63} +4.00000 q^{65} +(6.00000 - 10.3923i) q^{67} +16.0000 q^{69} +(-1.00000 - 1.73205i) q^{71} +(-4.50000 - 7.79423i) q^{73} -8.00000 q^{75} -15.0000 q^{77} +(-4.00000 - 6.92820i) q^{79} +(5.50000 + 9.52628i) q^{81} -12.0000 q^{83} +(-1.50000 + 2.59808i) q^{85} -4.00000 q^{87} +(-6.00000 + 10.3923i) q^{89} +(-6.00000 + 10.3923i) q^{91} +(-4.00000 - 6.92820i) q^{93} +(4.00000 + 6.92820i) q^{97} +(-2.50000 + 4.33013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} + q^{5} - 6 q^{7} - q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 + q^5 - 6 * q^7 - q^9	$ 2 q - 2 q^{3} + q^{5} - 6 q^{7} - q^{9} + 10 q^{11} + 4 q^{13} + 2 q^{15} + 3 q^{17} + 6 q^{21} - 8 q^{23} + 4 q^{25} - 8 q^{27} + 2 q^{29} + 8 q^{31} - 10 q^{33} - 3 q^{35} + 20 q^{37} - 16 q^{39} - 10 q^{41} - q^{43} - 2 q^{45} + q^{47} + 4 q^{49} + 6 q^{51} + 4 q^{53} + 5 q^{55} - 6 q^{59} + 13 q^{61} + 3 q^{63} + 8 q^{65} + 12 q^{67} + 32 q^{69} - 2 q^{71} - 9 q^{73} - 16 q^{75} - 30 q^{77} - 8 q^{79} + 11 q^{81} - 24 q^{83} - 3 q^{85} - 8 q^{87} - 12 q^{89} - 12 q^{91} - 8 q^{93} + 8 q^{97} - 5 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 + q^5 - 6 * q^7 - q^9 + 10 * q^11 + 4 * q^13 + 2 * q^15 + 3 * q^17 + 6 * q^21 - 8 * q^23 + 4 * q^25 - 8 * q^27 + 2 * q^29 + 8 * q^31 - 10 * q^33 - 3 * q^35 + 20 * q^37 - 16 * q^39 - 10 * q^41 - q^43 - 2 * q^45 + q^47 + 4 * q^49 + 6 * q^51 + 4 * q^53 + 5 * q^55 - 6 * q^59 + 13 * q^61 + 3 * q^63 + 8 * q^65 + 12 * q^67 + 32 * q^69 - 2 * q^71 - 9 * q^73 - 16 * q^75 - 30 * q^77 - 8 * q^79 + 11 * q^81 - 24 * q^83 - 3 * q^85 - 8 * q^87 - 12 * q^89 - 12 * q^91 - 8 * q^93 + 8 * q^97 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1444\mathbb{Z}\right)^\times$.

$n$	$723$	$1085$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	−0.995782	−	0.0917517i	$-0.970753\pi$
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	0.418432	−	0.908248i	$-0.362580\pi$
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	0.955901	−	0.293691i	$-0.0948835\pi$
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	−0.732294	+	0.680989i	$0.761550\pi$
$6$		0			0
$7$	−3.00000			−1.13389			−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000			−1.13389			−0.566947	+	0.823754i	$0.691875\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	5.00000			1.50756			0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000			1.50756			0.753778	+	0.657129i	$0.228229\pi$
$12$		0			0
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	−0.443227	−	0.896410i	$-0.646166\pi$
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	0.997927	−	0.0643593i	$-0.0205004\pi$
$14$		0			0
$15$	1.00000	−	1.73205i	0.258199	−	0.447214i
$16$		0			0
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		0			0
$19$		0			0
$19$		0			0
$20$		0			0
$21$	3.00000	+	5.19615i	0.654654	+	1.13389i
$22$		0			0
$23$	−4.00000	+	6.92820i	−0.834058	+	1.44463i	0.0607377	+	0.998154i	$0.480655\pi$
$23$	−4.00000	+	6.92820i	−0.834058	+	1.44463i	−0.894795	+	0.446476i	$0.852679\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$		0			0
$27$	−4.00000			−0.769800
$28$		0			0
$29$	1.00000	−	1.73205i	0.185695	−	0.321634i	−0.758115	−	0.652121i	$-0.773880\pi$
$29$	1.00000	−	1.73205i	0.185695	−	0.321634i	0.943811	+	0.330487i	$0.107213\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$		0			0
$33$	−5.00000	−	8.66025i	−0.870388	−	1.50756i
$34$		0			0
$35$	−1.50000	−	2.59808i	−0.253546	−	0.439155i
$36$		0			0
$37$	10.0000			1.64399			0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000			1.64399			0.821995	+	0.569495i	$0.192861\pi$
$38$		0			0
$39$	−8.00000			−1.28103
$40$		0			0
$41$	−5.00000	−	8.66025i	−0.780869	−	1.35250i	−0.931436	−	0.363905i	$-0.881443\pi$
$41$	−5.00000	−	8.66025i	−0.780869	−	1.35250i	0.150567	−	0.988600i	$-0.451890\pi$
$42$		0			0
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	0.825380	−	0.564578i	$-0.190961\pi$
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	−0.901629	+	0.432511i	$0.857628\pi$
$44$		0			0
$45$	−1.00000			−0.149071
$46$		0			0
$47$	0.500000	−	0.866025i	0.0729325	−	0.126323i	−0.827253	−	0.561830i	$-0.810098\pi$
$47$	0.500000	−	0.866025i	0.0729325	−	0.126323i	0.900185	+	0.435507i	$0.143431\pi$
$48$		0			0
$49$	2.00000			0.285714
$50$		0			0
$51$	3.00000	−	5.19615i	0.420084	−	0.727607i
$52$		0			0
$53$	2.00000	−	3.46410i	0.274721	−	0.475831i	−0.695344	−	0.718677i	$-0.744748\pi$
$53$	2.00000	−	3.46410i	0.274721	−	0.475831i	0.970065	+	0.242846i	$0.0780811\pi$
$54$		0			0
$55$	2.50000	+	4.33013i	0.337100	+	0.583874i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$		0			0
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	0.896258	−	0.443533i	$-0.146275\pi$
$62$		0			0
$63$	1.50000	−	2.59808i	0.188982	−	0.327327i
$64$		0			0
$65$	4.00000			0.496139
$66$		0			0
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	−0.222571	−	0.974916i	$-0.571445\pi$
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	0.955588	−	0.294706i	$-0.0952216\pi$
$68$		0			0
$69$	16.0000			1.92617
$70$		0			0
$71$	−1.00000	−	1.73205i	−0.118678	−	0.205557i	0.800566	−	0.599245i	$-0.204532\pi$
$71$	−1.00000	−	1.73205i	−0.118678	−	0.205557i	−0.919244	+	0.393688i	$0.871199\pi$
$72$		0			0
$73$	−4.50000	−	7.79423i	−0.526685	−	0.912245i	−0.999517	−	0.0310925i	$-0.990101\pi$
$73$	−4.50000	−	7.79423i	−0.526685	−	0.912245i	0.472831	−	0.881153i	$-0.343232\pi$
$74$		0			0
$75$	−8.00000			−0.923760
$76$		0			0
$77$	−15.0000			−1.70941
$78$		0			0
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$		0			0
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$		0			0
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$		0			0
$85$	−1.50000	+	2.59808i	−0.162698	+	0.281801i
$86$		0			0
$87$	−4.00000			−0.428845
$88$		0			0
$89$	−6.00000	+	10.3923i	−0.635999	+	1.10158i	0.350304	+	0.936636i	$0.386078\pi$
$89$	−6.00000	+	10.3923i	−0.635999	+	1.10158i	−0.986303	+	0.164946i	$0.947255\pi$
$90$		0			0
$91$	−6.00000	+	10.3923i	−0.628971	+	1.08941i
$92$		0			0
$93$	−4.00000	−	6.92820i	−0.414781	−	0.718421i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	4.00000	+	6.92820i	0.406138	+	0.703452i	0.994453	−	0.105180i	$-0.0335417\pi$
$97$	4.00000	+	6.92820i	0.406138	+	0.703452i	−0.588315	+	0.808632i	$0.700208\pi$
$98$		0			0
$99$	−2.50000	+	4.33013i	−0.251259	+	0.435194i
$100$		0			0
$101$	5.00000	−	8.66025i	0.497519	−	0.861727i	−0.502477	−	0.864590i	$-0.667578\pi$
$101$	5.00000	−	8.66025i	0.497519	−	0.861727i	0.999996	+	0.00286291i	$0.000911295\pi$
$102$		0			0
$103$	−6.00000			−0.591198			−0.295599	−	0.955312i	$-0.595519\pi$
$103$	−6.00000			−0.591198			−0.295599	+	0.955312i	$0.595519\pi$
$104$		0			0
$105$	−3.00000	+	5.19615i	−0.292770	+	0.507093i
$106$		0			0
$107$	2.00000			0.193347			0.0966736	−	0.995316i	$-0.469180\pi$
$107$	2.00000			0.193347			0.0966736	+	0.995316i	$0.469180\pi$
$108$		0			0
$109$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$109$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$110$		0			0
$111$	−10.0000	−	17.3205i	−0.949158	−	1.64399i
$112$		0			0
$113$	−10.0000			−0.940721			−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−10.0000			−0.940721			−0.470360	+	0.882474i	$0.655876\pi$
$114$		0			0
$115$	−8.00000			−0.746004
$116$		0			0
$117$	2.00000	+	3.46410i	0.184900	+	0.320256i
$118$		0			0
$119$	−4.50000	−	7.79423i	−0.412514	−	0.714496i
$120$		0			0
$121$	14.0000			1.27273
$122$		0			0
$123$	−10.0000	+	17.3205i	−0.901670	+	1.56174i
$124$		0			0
$125$	9.00000			0.804984
$126$		0			0
$127$	−3.00000	+	5.19615i	−0.266207	+	0.461084i	−0.967879	−	0.251416i	$-0.919104\pi$
$127$	−3.00000	+	5.19615i	−0.266207	+	0.461084i	0.701672	+	0.712500i	$0.252437\pi$
$128$		0			0
$129$	−1.00000	+	1.73205i	−0.0880451	+	0.152499i
$130$		0			0
$131$	4.50000	+	7.79423i	0.393167	+	0.680985i	0.992865	−	0.119241i	$-0.0380462\pi$
$131$	4.50000	+	7.79423i	0.393167	+	0.680985i	−0.599699	+	0.800226i	$0.704713\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−2.00000	−	3.46410i	−0.172133	−	0.298142i
$136$		0			0
$137$	5.50000	−	9.52628i	0.469897	−	0.813885i	−0.529511	−	0.848303i	$-0.677624\pi$
$137$	5.50000	−	9.52628i	0.469897	−	0.813885i	0.999408	+	0.0344182i	$0.0109578\pi$
$138$		0			0
$139$	1.50000	−	2.59808i	0.127228	−	0.220366i	−0.795373	−	0.606120i	$-0.792725\pi$
$139$	1.50000	−	2.59808i	0.127228	−	0.220366i	0.922602	+	0.385754i	$0.126059\pi$
$140$		0			0
$141$	−2.00000			−0.168430
$142$		0			0
$143$	10.0000	−	17.3205i	0.836242	−	1.44841i
$144$		0			0
$145$	2.00000			0.166091
$146$		0			0
$147$	−2.00000	−	3.46410i	−0.164957	−	0.285714i
$148$		0			0
$149$	7.50000	+	12.9904i	0.614424	+	1.06421i	0.990485	+	0.137619i	$0.0439449\pi$
$149$	7.50000	+	12.9904i	0.614424	+	1.06421i	−0.376061	+	0.926595i	$0.622722\pi$
$150$		0			0
$151$	2.00000			0.162758			0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000			0.162758			0.0813788	+	0.996683i	$0.474068\pi$
$152$		0			0
$153$	−3.00000			−0.242536
$154$		0			0
$155$	2.00000	+	3.46410i	0.160644	+	0.278243i
$156$		0			0
$157$	1.00000	+	1.73205i	0.0798087	+	0.138233i	0.903167	−	0.429289i	$-0.141236\pi$
$157$	1.00000	+	1.73205i	0.0798087	+	0.138233i	−0.823359	+	0.567521i	$0.807902\pi$
$158$		0			0
$159$	−8.00000			−0.634441
$160$		0			0
$161$	12.0000	−	20.7846i	0.945732	−	1.63806i
$162$		0			0
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$		0			0
$165$	5.00000	−	8.66025i	0.389249	−	0.674200i
$166$		0			0
$167$	3.00000	−	5.19615i	0.232147	−	0.402090i	−0.726293	−	0.687386i	$-0.758758\pi$
$167$	3.00000	−	5.19615i	0.232147	−	0.402090i	0.958440	+	0.285295i	$0.0920916\pi$
$168$		0			0
$169$	−1.50000	−	2.59808i	−0.115385	−	0.199852i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$		0			0
$175$	−6.00000	+	10.3923i	−0.453557	+	0.785584i
$176$		0			0
$177$	−6.00000	+	10.3923i	−0.450988	+	0.781133i
$178$		0			0
$179$	18.0000			1.34538			0.672692	−	0.739923i	$-0.265138\pi$
$179$	18.0000			1.34538			0.672692	+	0.739923i	$0.265138\pi$
$180$		0			0
$181$	−5.00000	+	8.66025i	−0.371647	+	0.643712i	−0.989819	−	0.142331i	$-0.954540\pi$
$181$	−5.00000	+	8.66025i	−0.371647	+	0.643712i	0.618172	+	0.786043i	$0.287874\pi$
$182$		0			0
$183$	−26.0000			−1.92198
$184$		0			0
$185$	5.00000	+	8.66025i	0.367607	+	0.636715i
$186$		0			0
$187$	7.50000	+	12.9904i	0.548454	+	0.949951i
$188$		0			0
$189$	12.0000			0.872872
$190$		0			0
$191$	25.0000			1.80894			0.904468	−	0.426541i	$-0.140268\pi$
$191$	25.0000			1.80894			0.904468	+	0.426541i	$0.140268\pi$
$192$		0			0
$193$	−6.00000	−	10.3923i	−0.431889	−	0.748054i	0.565147	−	0.824991i	$-0.308820\pi$
$193$	−6.00000	−	10.3923i	−0.431889	−	0.748054i	−0.997036	+	0.0769360i	$0.975486\pi$
$194$		0			0
$195$	−4.00000	−	6.92820i	−0.286446	−	0.496139i
$196$		0			0
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$		0			0
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	−0.714893	−	0.699234i	$-0.753524\pi$
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	0.963001	+	0.269498i	$0.0868577\pi$
$200$		0			0
$201$	−24.0000			−1.69283
$202$		0			0
$203$	−3.00000	+	5.19615i	−0.210559	+	0.364698i
$204$		0			0
$205$	5.00000	−	8.66025i	0.349215	−	0.604858i
$206$		0			0
$207$	−4.00000	−	6.92820i	−0.278019	−	0.481543i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−9.00000	−	15.5885i	−0.619586	−	1.07315i	−0.989561	−	0.144112i	$-0.953967\pi$
$211$	−9.00000	−	15.5885i	−0.619586	−	1.07315i	0.369976	−	0.929041i	$-0.379366\pi$
$212$		0			0
$213$	−2.00000	+	3.46410i	−0.137038	+	0.237356i
$214$		0			0
$215$	0.500000	−	0.866025i	0.0340997	−	0.0590624i
$216$		0			0
$217$	−12.0000			−0.814613
$218$		0			0
$219$	−9.00000	+	15.5885i	−0.608164	+	1.05337i
$220$		0			0
$221$	12.0000			0.807207
$222$		0			0
$223$	−1.00000	−	1.73205i	−0.0669650	−	0.115987i	0.830599	−	0.556871i	$-0.187998\pi$
$223$	−1.00000	−	1.73205i	−0.0669650	−	0.115987i	−0.897564	+	0.440884i	$0.854665\pi$
$224$		0			0
$225$	2.00000	+	3.46410i	0.133333	+	0.230940i
$226$		0			0
$227$	4.00000			0.265489			0.132745	−	0.991150i	$-0.457621\pi$
$227$	4.00000			0.265489			0.132745	+	0.991150i	$0.457621\pi$
$228$		0			0
$229$	17.0000			1.12339			0.561696	−	0.827344i	$-0.310149\pi$
$229$	17.0000			1.12339			0.561696	+	0.827344i	$0.310149\pi$
$230$		0			0
$231$	15.0000	+	25.9808i	0.986928	+	1.70941i
$232$		0			0
$233$	−1.50000	−	2.59808i	−0.0982683	−	0.170206i	0.812700	−	0.582683i	$-0.197997\pi$
$233$	−1.50000	−	2.59808i	−0.0982683	−	0.170206i	−0.910968	+	0.412477i	$0.864664\pi$
$234$		0			0
$235$	1.00000			0.0652328
$236$		0			0
$237$	−8.00000	+	13.8564i	−0.519656	+	0.900070i
$238$		0			0
$239$	21.0000			1.35838			0.679189	−	0.733964i	$-0.262332\pi$
$239$	21.0000			1.35838			0.679189	+	0.733964i	$0.262332\pi$
$240$		0			0
$241$	13.0000	−	22.5167i	0.837404	−	1.45043i	−0.0546547	−	0.998505i	$-0.517406\pi$
$241$	13.0000	−	22.5167i	0.837404	−	1.45043i	0.892058	−	0.451920i	$-0.149261\pi$
$242$		0			0
$243$	5.00000	−	8.66025i	0.320750	−	0.555556i
$244$		0			0
$245$	1.00000	+	1.73205i	0.0638877	+	0.110657i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	12.0000	+	20.7846i	0.760469	+	1.31717i
$250$		0			0
$251$	−5.50000	+	9.52628i	−0.347157	+	0.601293i	−0.985743	−	0.168257i	$-0.946186\pi$
$251$	−5.50000	+	9.52628i	−0.347157	+	0.601293i	0.638586	+	0.769550i	$0.279520\pi$
$252$		0			0
$253$	−20.0000	+	34.6410i	−1.25739	+	2.17786i
$254$		0			0
$255$	6.00000			0.375735
$256$		0			0
$257$	−16.0000	+	27.7128i	−0.998053	+	1.72868i	−0.445005	+	0.895528i	$0.646798\pi$
$257$	−16.0000	+	27.7128i	−0.998053	+	1.72868i	−0.553047	+	0.833150i	$0.686535\pi$
$258$		0			0
$259$	−30.0000			−1.86411
$260$		0			0
$261$	1.00000	+	1.73205i	0.0618984	+	0.107211i
$262$		0			0
$263$	10.5000	+	18.1865i	0.647458	+	1.12143i	0.983728	+	0.179664i	$0.0575011\pi$
$263$	10.5000	+	18.1865i	0.647458	+	1.12143i	−0.336270	+	0.941766i	$0.609166\pi$
$264$		0			0
$265$	4.00000			0.245718
$266$		0			0
$267$	24.0000			1.46878
$268$		0			0
$269$	12.0000	+	20.7846i	0.731653	+	1.26726i	0.956176	+	0.292791i	$0.0945841\pi$
$269$	12.0000	+	20.7846i	0.731653	+	1.26726i	−0.224523	+	0.974469i	$0.572083\pi$
$270$		0			0
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	0.961563	−	0.274586i	$-0.0885408\pi$
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	−0.718580	+	0.695444i	$0.755208\pi$
$272$		0			0
$273$	24.0000			1.45255
$274$		0			0
$275$	10.0000	−	17.3205i	0.603023	−	1.04447i
$276$		0			0
$277$	1.00000			0.0600842			0.0300421	−	0.999549i	$-0.490436\pi$
$277$	1.00000			0.0600842			0.0300421	+	0.999549i	$0.490436\pi$
$278$		0			0
$279$	−2.00000	+	3.46410i	−0.119737	+	0.207390i
$280$		0			0
$281$	−11.0000	+	19.0526i	−0.656205	+	1.13658i	0.325385	+	0.945582i	$0.394506\pi$
$281$	−11.0000	+	19.0526i	−0.656205	+	1.13658i	−0.981590	+	0.190999i	$0.938827\pi$
$282$		0			0
$283$	1.50000	+	2.59808i	0.0891657	+	0.154440i	0.907159	−	0.420789i	$-0.138247\pi$
$283$	1.50000	+	2.59808i	0.0891657	+	0.154440i	−0.817993	+	0.575228i	$0.804913\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	15.0000	+	25.9808i	0.885422	+	1.53360i
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$		0			0
$291$	8.00000	−	13.8564i	0.468968	−	0.812277i
$292$		0			0
$293$	−12.0000			−0.701047			−0.350524	−	0.936554i	$-0.613996\pi$
$293$	−12.0000			−0.701047			−0.350524	+	0.936554i	$0.613996\pi$
$294$		0			0
$295$	3.00000	−	5.19615i	0.174667	−	0.302532i
$296$		0			0
$297$	−20.0000			−1.16052
$298$		0			0
$299$	16.0000	+	27.7128i	0.925304	+	1.60267i
$300$		0			0
$301$	1.50000	+	2.59808i	0.0864586	+	0.149751i
$302$		0			0
$303$	−20.0000			−1.14897
$304$		0			0
$305$	13.0000			0.744378
$306$		0			0
$307$	−6.00000	−	10.3923i	−0.342438	−	0.593120i	0.642447	−	0.766330i	$-0.277919\pi$
$307$	−6.00000	−	10.3923i	−0.342438	−	0.593120i	−0.984885	+	0.173210i	$0.944586\pi$
$308$		0			0
$309$	6.00000	+	10.3923i	0.341328	+	0.591198i
$310$		0			0
$311$	7.00000			0.396934			0.198467	−	0.980108i	$-0.436404\pi$
$311$	7.00000			0.396934			0.198467	+	0.980108i	$0.436404\pi$
$312$		0			0
$313$	5.00000	−	8.66025i	0.282617	−	0.489506i	−0.689412	−	0.724370i	$-0.742131\pi$
$313$	5.00000	−	8.66025i	0.282617	−	0.489506i	0.972028	+	0.234863i	$0.0754642\pi$
$314$		0			0
$315$	3.00000			0.169031
$316$		0			0
$317$	−15.0000	+	25.9808i	−0.842484	+	1.45922i	0.0453045	+	0.998973i	$0.485574\pi$
$317$	−15.0000	+	25.9808i	−0.842484	+	1.45922i	−0.887788	+	0.460252i	$0.847759\pi$
$318$		0			0
$319$	5.00000	−	8.66025i	0.279946	−	0.484881i
$320$		0			0
$321$	−2.00000	−	3.46410i	−0.111629	−	0.193347i
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−8.00000	−	13.8564i	−0.443760	−	0.768615i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.50000	+	2.59808i	−0.0826977	+	0.143237i
$330$		0			0
$331$	−4.00000			−0.219860			−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000			−0.219860			−0.109930	+	0.993939i	$0.535063\pi$
$332$		0			0
$333$	−5.00000	+	8.66025i	−0.273998	+	0.474579i
$334$		0			0
$335$	12.0000			0.655630
$336$		0			0
$337$	16.0000	+	27.7128i	0.871576	+	1.50961i	0.860366	+	0.509676i	$0.170235\pi$
$337$	16.0000	+	27.7128i	0.871576	+	1.50961i	0.0112091	+	0.999937i	$0.496432\pi$
$338$		0			0
$339$	10.0000	+	17.3205i	0.543125	+	0.940721i
$340$		0			0
$341$	20.0000			1.08306
$342$		0			0
$343$	15.0000			0.809924
$344$		0			0
$345$	8.00000	+	13.8564i	0.430706	+	0.746004i
$346$		0			0
$347$	−9.50000	−	16.4545i	−0.509987	−	0.883323i	−0.999933	−	0.0115703i	$-0.996317\pi$
$347$	−9.50000	−	16.4545i	−0.509987	−	0.883323i	0.489946	−	0.871753i	$-0.337016\pi$
$348$		0			0
$349$	−11.0000			−0.588817			−0.294408	−	0.955680i	$-0.595123\pi$
$349$	−11.0000			−0.588817			−0.294408	+	0.955680i	$0.595123\pi$
$350$		0			0
$351$	−8.00000	+	13.8564i	−0.427008	+	0.739600i
$352$		0			0
$353$	−6.00000			−0.319348			−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000			−0.319348			−0.159674	+	0.987170i	$0.551044\pi$
$354$		0			0
$355$	1.00000	−	1.73205i	0.0530745	−	0.0919277i
$356$		0			0
$357$	−9.00000	+	15.5885i	−0.476331	+	0.825029i
$358$		0			0
$359$	−10.5000	−	18.1865i	−0.554169	−	0.959849i	−0.997968	−	0.0637221i	$-0.979703\pi$
$359$	−10.5000	−	18.1865i	−0.554169	−	0.959849i	0.443799	−	0.896126i	$-0.353630\pi$
$360$		0			0
$361$		0			0
$362$		0			0
$363$	−14.0000	−	24.2487i	−0.734809	−	1.27273i
$364$		0			0
$365$	4.50000	−	7.79423i	0.235541	−	0.407969i
$366$		0			0
$367$	−8.00000	+	13.8564i	−0.417597	+	0.723299i	−0.995697	−	0.0926670i	$-0.970461\pi$
$367$	−8.00000	+	13.8564i	−0.417597	+	0.723299i	0.578101	+	0.815966i	$0.303794\pi$
$368$		0			0
$369$	10.0000			0.520579
$370$		0			0
$371$	−6.00000	+	10.3923i	−0.311504	+	0.539542i
$372$		0			0
$373$	−4.00000			−0.207112			−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000			−0.207112			−0.103556	+	0.994624i	$0.533022\pi$
$374$		0			0
$375$	−9.00000	−	15.5885i	−0.464758	−	0.804984i
$376$		0			0
$377$	−4.00000	−	6.92820i	−0.206010	−	0.356821i
$378$		0			0
$379$	−30.0000			−1.54100			−0.770498	−	0.637442i	$-0.779993\pi$
$379$	−30.0000			−1.54100			−0.770498	+	0.637442i	$0.779993\pi$
$380$		0			0
$381$	12.0000			0.614779
$382$		0			0
$383$	−2.00000	−	3.46410i	−0.102195	−	0.177007i	0.810394	−	0.585886i	$-0.199253\pi$
$383$	−2.00000	−	3.46410i	−0.102195	−	0.177007i	−0.912589	+	0.408879i	$0.865920\pi$
$384$		0			0
$385$	−7.50000	−	12.9904i	−0.382235	−	0.662051i
$386$		0			0
$387$	1.00000			0.0508329
$388$		0			0
$389$	10.5000	−	18.1865i	0.532371	−	0.922094i	−0.466915	−	0.884302i	$-0.654634\pi$
$389$	10.5000	−	18.1865i	0.532371	−	0.922094i	0.999286	−	0.0377914i	$-0.0120322\pi$
$390$		0			0
$391$	−24.0000			−1.21373
$392$		0			0
$393$	9.00000	−	15.5885i	0.453990	−	0.786334i
$394$		0			0
$395$	4.00000	−	6.92820i	0.201262	−	0.348596i
$396$		0			0
$397$	−2.50000	−	4.33013i	−0.125471	−	0.217323i	0.796446	−	0.604710i	$-0.206711\pi$
$397$	−2.50000	−	4.33013i	−0.125471	−	0.217323i	−0.921917	+	0.387387i	$0.873378\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−14.0000	−	24.2487i	−0.699127	−	1.21092i	−0.968770	−	0.247962i	$-0.920239\pi$
$401$	−14.0000	−	24.2487i	−0.699127	−	1.21092i	0.269643	−	0.962960i	$-0.413094\pi$
$402$		0			0
$403$	8.00000	−	13.8564i	0.398508	−	0.690237i
$404$		0			0
$405$	−5.50000	+	9.52628i	−0.273297	+	0.473365i
$406$		0			0
$407$	50.0000			2.47841
$408$		0			0
$409$	10.0000	−	17.3205i	0.494468	−	0.856444i	−0.505511	−	0.862820i	$-0.668696\pi$
$409$	10.0000	−	17.3205i	0.494468	−	0.856444i	0.999980	+	0.00637586i	$0.00202951\pi$
$410$		0			0
$411$	−22.0000			−1.08518
$412$		0			0
$413$	9.00000	+	15.5885i	0.442861	+	0.767058i
$414$		0			0
$415$	−6.00000	−	10.3923i	−0.294528	−	0.510138i
$416$		0			0
$417$	−6.00000			−0.293821
$418$		0			0
$419$	−36.0000			−1.75872			−0.879358	−	0.476162i	$-0.842028\pi$
$419$	−36.0000			−1.75872			−0.879358	+	0.476162i	$0.842028\pi$
$420$		0			0
$421$	20.0000	+	34.6410i	0.974740	+	1.68830i	0.680789	+	0.732479i	$0.261637\pi$
$421$	20.0000	+	34.6410i	0.974740	+	1.68830i	0.293951	+	0.955820i	$0.405030\pi$
$422$		0			0
$423$	0.500000	+	0.866025i	0.0243108	+	0.0421076i
$424$		0			0
$425$	12.0000			0.582086
$426$		0			0
$427$	−19.5000	+	33.7750i	−0.943671	+	1.63449i
$428$		0			0
$429$	−40.0000			−1.93122
$430$		0			0
$431$	−12.0000	+	20.7846i	−0.578020	+	1.00116i	0.417687	+	0.908591i	$0.362841\pi$
$431$	−12.0000	+	20.7846i	−0.578020	+	1.00116i	−0.995706	+	0.0925683i	$0.970492\pi$
$432$		0			0
$433$	−1.00000	+	1.73205i	−0.0480569	+	0.0832370i	−0.889053	−	0.457804i	$-0.848636\pi$
$433$	−1.00000	+	1.73205i	−0.0480569	+	0.0832370i	0.840996	+	0.541041i	$0.181970\pi$
$434$		0			0
$435$	−2.00000	−	3.46410i	−0.0958927	−	0.166091i
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−1.00000	−	1.73205i	−0.0477274	−	0.0826663i	0.841175	−	0.540763i	$-0.181865\pi$
$439$	−1.00000	−	1.73205i	−0.0477274	−	0.0826663i	−0.888902	+	0.458097i	$0.848531\pi$
$440$		0			0
$441$	−1.00000	+	1.73205i	−0.0476190	+	0.0824786i
$442$		0			0
$443$	2.50000	−	4.33013i	0.118779	−	0.205731i	−0.800505	−	0.599326i	$-0.795435\pi$
$443$	2.50000	−	4.33013i	0.118779	−	0.205731i	0.919284	+	0.393595i	$0.128769\pi$
$444$		0			0
$445$	−12.0000			−0.568855
$446$		0			0
$447$	15.0000	−	25.9808i	0.709476	−	1.22885i
$448$		0			0
$449$	16.0000			0.755087			0.377543	−	0.925992i	$-0.376769\pi$
$449$	16.0000			0.755087			0.377543	+	0.925992i	$0.376769\pi$
$450$		0			0
$451$	−25.0000	−	43.3013i	−1.17720	−	2.03898i
$452$		0			0
$453$	−2.00000	−	3.46410i	−0.0939682	−	0.162758i
$454$		0			0
$455$	−12.0000			−0.562569
$456$		0			0
$457$	−13.0000			−0.608114			−0.304057	−	0.952654i	$-0.598341\pi$
$457$	−13.0000			−0.608114			−0.304057	+	0.952654i	$0.598341\pi$
$458$		0			0
$459$	−6.00000	−	10.3923i	−0.280056	−	0.485071i
$460$		0			0
$461$	9.50000	+	16.4545i	0.442459	+	0.766362i	0.997871	−	0.0652135i	$-0.0207728\pi$
$461$	9.50000	+	16.4545i	0.442459	+	0.766362i	−0.555412	+	0.831575i	$0.687440\pi$
$462$		0			0
$463$	19.0000			0.883005			0.441502	−	0.897260i	$-0.354446\pi$
$463$	19.0000			0.883005			0.441502	+	0.897260i	$0.354446\pi$
$464$		0			0
$465$	4.00000	−	6.92820i	0.185496	−	0.321288i
$466$		0			0
$467$	−5.00000			−0.231372			−0.115686	−	0.993286i	$-0.536907\pi$
$467$	−5.00000			−0.231372			−0.115686	+	0.993286i	$0.536907\pi$
$468$		0			0
$469$	−18.0000	+	31.1769i	−0.831163	+	1.43962i
$470$		0			0
$471$	2.00000	−	3.46410i	0.0921551	−	0.159617i
$472$		0			0
$473$	−2.50000	−	4.33013i	−0.114950	−	0.199099i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	2.00000	+	3.46410i	0.0915737	+	0.158610i
$478$		0			0
$479$	−2.00000	+	3.46410i	−0.0913823	+	0.158279i	−0.908093	−	0.418769i	$-0.862462\pi$
$479$	−2.00000	+	3.46410i	−0.0913823	+	0.158279i	0.816711	+	0.577047i	$0.195795\pi$
$480$		0			0
$481$	20.0000	−	34.6410i	0.911922	−	1.57949i
$482$		0			0
$483$	−48.0000			−2.18408
$484$		0			0
$485$	−4.00000	+	6.92820i	−0.181631	+	0.314594i
$486$		0			0
$487$	−26.0000			−1.17817			−0.589086	−	0.808070i	$-0.700512\pi$
$487$	−26.0000			−1.17817			−0.589086	+	0.808070i	$0.700512\pi$
$488$		0			0
$489$	4.00000	+	6.92820i	0.180886	+	0.313304i
$490$		0			0
$491$	14.0000	+	24.2487i	0.631811	+	1.09433i	0.987181	+	0.159603i	$0.0510215\pi$
$491$	14.0000	+	24.2487i	0.631811	+	1.09433i	−0.355370	+	0.934726i	$0.615645\pi$
$492$		0			0
$493$	6.00000			0.270226
$494$		0			0
$495$	−5.00000			−0.224733
$496$		0			0
$497$	3.00000	+	5.19615i	0.134568	+	0.233079i
$498$		0			0
$499$	−9.50000	−	16.4545i	−0.425278	−	0.736604i	0.571168	−	0.820833i	$-0.306490\pi$
$499$	−9.50000	−	16.4545i	−0.425278	−	0.736604i	−0.996446	+	0.0842294i	$0.973157\pi$
$500$		0			0
$501$	−12.0000			−0.536120
$502$		0			0
$503$	18.0000	−	31.1769i	0.802580	−	1.39011i	−0.115332	−	0.993327i	$-0.536793\pi$
$503$	18.0000	−	31.1769i	0.802580	−	1.39011i	0.917912	−	0.396783i	$-0.129873\pi$
$504$		0			0
$505$	10.0000			0.444994
$506$		0			0
$507$	−3.00000	+	5.19615i	−0.133235	+	0.230769i
$508$		0			0
$509$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$509$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$510$		0			0
$511$	13.5000	+	23.3827i	0.597205	+	1.03439i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−3.00000	−	5.19615i	−0.132196	−	0.228970i
$516$		0			0
$517$	2.50000	−	4.33013i	0.109950	−	0.190439i
$518$		0			0
$519$	−6.00000	+	10.3923i	−0.263371	+	0.456172i
$520$		0			0
$521$	32.0000			1.40195			0.700973	−	0.713188i	$-0.252749\pi$
$521$	32.0000			1.40195			0.700973	+	0.713188i	$0.252749\pi$
$522$		0			0
$523$	−13.0000	+	22.5167i	−0.568450	+	0.984585i	0.428269	+	0.903651i	$0.359124\pi$
$523$	−13.0000	+	22.5167i	−0.568450	+	0.984585i	−0.996719	+	0.0809336i	$0.974210\pi$
$524$		0			0
$525$	24.0000			1.04745
$526$		0			0
$527$	6.00000	+	10.3923i	0.261364	+	0.452696i
$528$		0			0
$529$	−20.5000	−	35.5070i	−0.891304	−	1.54378i
$530$		0			0
$531$	6.00000			0.260378
$532$		0			0
$533$	−40.0000			−1.73259
$534$		0			0
$535$	1.00000	+	1.73205i	0.0432338	+	0.0748831i
$536$		0			0
$537$	−18.0000	−	31.1769i	−0.776757	−	1.34538i
$538$		0			0
$539$	10.0000			0.430730
$540$		0			0
$541$	−5.50000	+	9.52628i	−0.236463	+	0.409567i	−0.959697	−	0.281037i	$-0.909322\pi$
$541$	−5.50000	+	9.52628i	−0.236463	+	0.409567i	0.723234	+	0.690604i	$0.242655\pi$
$542$		0			0
$543$	20.0000			0.858282
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−14.0000	+	24.2487i	−0.598597	+	1.03680i	0.394432	+	0.918925i	$0.370941\pi$
$547$	−14.0000	+	24.2487i	−0.598597	+	1.03680i	−0.993028	+	0.117875i	$0.962392\pi$
$548$		0			0
$549$	6.50000	+	11.2583i	0.277413	+	0.480494i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	12.0000	+	20.7846i	0.510292	+	0.883852i
$554$		0			0
$555$	10.0000	−	17.3205i	0.424476	−	0.735215i
$556$		0			0
$557$	−0.500000	+	0.866025i	−0.0211857	+	0.0366947i	−0.876424	−	0.481540i	$-0.840077\pi$
$557$	−0.500000	+	0.866025i	−0.0211857	+	0.0366947i	0.855238	+	0.518235i	$0.173411\pi$
$558$		0			0
$559$	−4.00000			−0.169182
$560$		0			0
$561$	15.0000	−	25.9808i	0.633300	−	1.09691i
$562$		0			0
$563$	42.0000			1.77009			0.885044	−	0.465506i	$-0.154128\pi$
$563$	42.0000			1.77009			0.885044	+	0.465506i	$0.154128\pi$
$564$		0			0
$565$	−5.00000	−	8.66025i	−0.210352	−	0.364340i
$566$		0			0
$567$	−16.5000	−	28.5788i	−0.692935	−	1.20020i
$568$		0			0
$569$	−8.00000			−0.335377			−0.167689	−	0.985840i	$-0.553630\pi$
$569$	−8.00000			−0.335377			−0.167689	+	0.985840i	$0.553630\pi$
$570$		0			0
$571$	20.0000			0.836974			0.418487	−	0.908223i	$-0.362561\pi$
$571$	20.0000			0.836974			0.418487	+	0.908223i	$0.362561\pi$
$572$		0			0
$573$	−25.0000	−	43.3013i	−1.04439	−	1.80894i
$574$		0			0
$575$	16.0000	+	27.7128i	0.667246	+	1.15570i
$576$		0			0
$577$	−13.0000			−0.541197			−0.270599	−	0.962692i	$-0.587222\pi$
$577$	−13.0000			−0.541197			−0.270599	+	0.962692i	$0.587222\pi$
$578$		0			0
$579$	−12.0000	+	20.7846i	−0.498703	+	0.863779i
$580$		0			0
$581$	36.0000			1.49353
$582$		0			0
$583$	10.0000	−	17.3205i	0.414158	−	0.717342i
$584$		0			0
$585$	−2.00000	+	3.46410i	−0.0826898	+	0.143223i
$586$		0			0
$587$	−1.50000	−	2.59808i	−0.0619116	−	0.107234i	0.833408	−	0.552658i	$-0.186386\pi$
$587$	−1.50000	−	2.59808i	−0.0619116	−	0.107234i	−0.895320	+	0.445424i	$0.853053\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	−2.00000	−	3.46410i	−0.0822690	−	0.142494i
$592$		0			0
$593$	−11.0000	+	19.0526i	−0.451716	+	0.782395i	−0.998493	−	0.0548835i	$-0.982521\pi$
$593$	−11.0000	+	19.0526i	−0.451716	+	0.782395i	0.546777	+	0.837278i	$0.315855\pi$
$594$		0			0
$595$	4.50000	−	7.79423i	0.184482	−	0.319532i
$596$		0			0
$597$	−14.0000			−0.572982
$598$		0			0
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	−0.717021	−	0.697051i	$-0.754495\pi$
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	0.962175	+	0.272433i	$0.0878284\pi$
$600$		0			0
$601$	10.0000			0.407909			0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000			0.407909			0.203954	+	0.978980i	$0.434621\pi$
$602$		0			0
$603$	6.00000	+	10.3923i	0.244339	+	0.423207i
$604$		0			0
$605$	7.00000	+	12.1244i	0.284590	+	0.492925i
$606$		0			0
$607$	32.0000			1.29884			0.649420	−	0.760430i	$-0.275012\pi$
$607$	32.0000			1.29884			0.649420	+	0.760430i	$0.275012\pi$
$608$		0			0
$609$	12.0000			0.486265
$610$		0			0
$611$	−2.00000	−	3.46410i	−0.0809113	−	0.140143i
$612$		0			0
$613$	23.5000	+	40.7032i	0.949156	+	1.64399i	0.747208	+	0.664590i	$0.231394\pi$
$613$	23.5000	+	40.7032i	0.949156	+	1.64399i	0.201948	+	0.979396i	$0.435273\pi$
$614$		0			0
$615$	−20.0000			−0.806478
$616$		0			0
$617$	−4.50000	+	7.79423i	−0.181163	+	0.313784i	−0.942277	−	0.334835i	$-0.891320\pi$
$617$	−4.50000	+	7.79423i	−0.181163	+	0.313784i	0.761114	+	0.648618i	$0.224653\pi$
$618$		0			0
$619$	4.00000			0.160774			0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000			0.160774			0.0803868	+	0.996764i	$0.474384\pi$
$620$		0			0
$621$	16.0000	−	27.7128i	0.642058	−	1.11208i
$622$		0			0
$623$	18.0000	−	31.1769i	0.721155	−	1.24908i
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	15.0000	+	25.9808i	0.598089	+	1.03592i
$630$		0			0
$631$	3.50000	−	6.06218i	0.139333	−	0.241331i	−0.787911	−	0.615789i	$-0.788838\pi$
$631$	3.50000	−	6.06218i	0.139333	−	0.241331i	0.927244	+	0.374457i	$0.122171\pi$
$632$		0			0
$633$	−18.0000	+	31.1769i	−0.715436	+	1.23917i
$634$		0			0
$635$	−6.00000			−0.238103
$636$		0			0
$637$	4.00000	−	6.92820i	0.158486	−	0.274505i
$638$		0			0
$639$	2.00000			0.0791188
$640$		0			0
$641$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$641$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$642$		0			0
$643$	5.50000	+	9.52628i	0.216899	+	0.375680i	0.953858	−	0.300257i	$-0.0970725\pi$
$643$	5.50000	+	9.52628i	0.216899	+	0.375680i	−0.736959	+	0.675937i	$0.763739\pi$
$644$		0			0
$645$	−2.00000			−0.0787499
$646$		0			0
$647$	−7.00000			−0.275198			−0.137599	−	0.990488i	$-0.543939\pi$
$647$	−7.00000			−0.275198			−0.137599	+	0.990488i	$0.543939\pi$
$648$		0			0
$649$	−15.0000	−	25.9808i	−0.588802	−	1.01983i
$650$		0			0
$651$	12.0000	+	20.7846i	0.470317	+	0.814613i
$652$		0			0
$653$	−27.0000			−1.05659			−0.528296	−	0.849060i	$-0.677169\pi$
$653$	−27.0000			−1.05659			−0.528296	+	0.849060i	$0.677169\pi$
$654$		0			0
$655$	−4.50000	+	7.79423i	−0.175830	+	0.304546i
$656$		0			0
$657$	9.00000			0.351123
$658$		0			0
$659$	17.0000	−	29.4449i	0.662226	−	1.14701i	−0.317803	−	0.948157i	$-0.602945\pi$
$659$	17.0000	−	29.4449i	0.662226	−	1.14701i	0.980029	−	0.198852i	$-0.0637214\pi$
$660$		0			0
$661$	−8.00000	+	13.8564i	−0.311164	+	0.538952i	−0.978615	−	0.205702i	$-0.934052\pi$
$661$	−8.00000	+	13.8564i	−0.311164	+	0.538952i	0.667451	+	0.744654i	$0.267385\pi$
$662$		0			0
$663$	−12.0000	−	20.7846i	−0.466041	−	0.807207i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	8.00000	+	13.8564i	0.309761	+	0.536522i
$668$		0			0
$669$	−2.00000	+	3.46410i	−0.0773245	+	0.133930i
$670$		0			0
$671$	32.5000	−	56.2917i	1.25465	−	2.17312i
$672$		0			0
$673$	−10.0000			−0.385472			−0.192736	−	0.981251i	$-0.561736\pi$
$673$	−10.0000			−0.385472			−0.192736	+	0.981251i	$0.561736\pi$
$674$		0			0
$675$	−8.00000	+	13.8564i	−0.307920	+	0.533333i
$676$		0			0
$677$	−2.00000			−0.0768662			−0.0384331	−	0.999261i	$-0.512237\pi$
$677$	−2.00000			−0.0768662			−0.0384331	+	0.999261i	$0.512237\pi$
$678$		0			0
$679$	−12.0000	−	20.7846i	−0.460518	−	0.797640i
$680$		0			0
$681$	−4.00000	−	6.92820i	−0.153280	−	0.265489i
$682$		0			0
$683$	−20.0000			−0.765279			−0.382639	−	0.923898i	$-0.624985\pi$
$683$	−20.0000			−0.765279			−0.382639	+	0.923898i	$0.624985\pi$
$684$		0			0
$685$	11.0000			0.420288
$686$		0			0
$687$	−17.0000	−	29.4449i	−0.648590	−	1.12339i
$688$		0			0
$689$	−8.00000	−	13.8564i	−0.304776	−	0.527887i
$690$		0			0
$691$	−33.0000			−1.25538			−0.627690	−	0.778464i	$-0.715999\pi$
$691$	−33.0000			−1.25538			−0.627690	+	0.778464i	$0.715999\pi$
$692$		0			0
$693$	7.50000	−	12.9904i	0.284901	−	0.493464i
$694$		0			0
$695$	3.00000			0.113796
$696$		0			0
$697$	15.0000	−	25.9808i	0.568166	−	0.984092i
$698$		0			0
$699$	−3.00000	+	5.19615i	−0.113470	+	0.196537i
$700$		0			0
$701$	5.00000	+	8.66025i	0.188847	+	0.327093i	0.944866	−	0.327457i	$-0.106192\pi$
$701$	5.00000	+	8.66025i	0.188847	+	0.327093i	−0.756019	+	0.654550i	$0.772858\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−1.00000	−	1.73205i	−0.0376622	−	0.0652328i
$706$		0			0
$707$	−15.0000	+	25.9808i	−0.564133	+	0.977107i
$708$		0			0
$709$	3.00000	−	5.19615i	0.112667	−	0.195146i	−0.804178	−	0.594389i	$-0.797394\pi$
$709$	3.00000	−	5.19615i	0.112667	−	0.195146i	0.916845	+	0.399244i	$0.130727\pi$
$710$		0			0
$711$	8.00000			0.300023
$712$		0			0
$713$	−16.0000	+	27.7128i	−0.599205	+	1.03785i
$714$		0			0
$715$	20.0000			0.747958
$716$		0			0
$717$	−21.0000	−	36.3731i	−0.784259	−	1.35838i
$718$		0			0
$719$	−6.50000	−	11.2583i	−0.242409	−	0.419865i	0.718991	−	0.695019i	$-0.244604\pi$
$719$	−6.50000	−	11.2583i	−0.242409	−	0.419865i	−0.961400	+	0.275155i	$0.911271\pi$
$720$		0			0
$721$	18.0000			0.670355
$722$		0			0
$723$	−52.0000			−1.93390
$724$		0			0
$725$	−4.00000	−	6.92820i	−0.148556	−	0.257307i
$726$		0			0
$727$	−3.50000	−	6.06218i	−0.129808	−	0.224834i	0.793794	−	0.608186i	$-0.208103\pi$
$727$	−3.50000	−	6.06218i	−0.129808	−	0.224834i	−0.923602	+	0.383353i	$0.874769\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	1.50000	−	2.59808i	0.0554795	−	0.0960933i
$732$		0			0
$733$	−6.00000			−0.221615			−0.110808	−	0.993842i	$-0.535344\pi$
$733$	−6.00000			−0.221615			−0.110808	+	0.993842i	$0.535344\pi$
$734$		0			0
$735$	2.00000	−	3.46410i	0.0737711	−	0.127775i
$736$		0			0
$737$	30.0000	−	51.9615i	1.10506	−	1.91403i
$738$		0			0
$739$	21.5000	+	37.2391i	0.790890	+	1.36986i	0.925416	+	0.378952i	$0.123715\pi$
$739$	21.5000	+	37.2391i	0.790890	+	1.36986i	−0.134526	+	0.990910i	$0.542951\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	20.0000	+	34.6410i	0.733729	+	1.27086i	0.955279	+	0.295707i	$0.0955551\pi$
$743$	20.0000	+	34.6410i	0.733729	+	1.27086i	−0.221550	+	0.975149i	$0.571112\pi$
$744$		0			0
$745$	−7.50000	+	12.9904i	−0.274779	+	0.475931i
$746$		0			0
$747$	6.00000	−	10.3923i	0.219529	−	0.380235i
$748$		0			0
$749$	−6.00000			−0.219235
$750$		0			0
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	−0.682341	−	0.731034i	$-0.739038\pi$
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	0.974265	+	0.225407i	$0.0723712\pi$
$752$		0			0
$753$	22.0000			0.801725
$754$		0			0
$755$	1.00000	+	1.73205i	0.0363937	+	0.0630358i
$756$		0			0
$757$	2.50000	+	4.33013i	0.0908640	+	0.157381i	0.907875	−	0.419241i	$-0.137704\pi$
$757$	2.50000	+	4.33013i	0.0908640	+	0.157381i	−0.817011	+	0.576622i	$0.804370\pi$
$758$		0			0
$759$	80.0000			2.90382
$760$		0			0
$761$	9.00000			0.326250			0.163125	−	0.986605i	$-0.447843\pi$
$761$	9.00000			0.326250			0.163125	+	0.986605i	$0.447843\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−1.50000	−	2.59808i	−0.0542326	−	0.0939336i
$766$		0			0
$767$	−24.0000			−0.866590
$768$		0			0
$769$	−15.5000	+	26.8468i	−0.558944	+	0.968120i	0.438641	+	0.898663i	$0.355460\pi$
$769$	−15.5000	+	26.8468i	−0.558944	+	0.968120i	−0.997585	+	0.0694574i	$0.977873\pi$
$770$		0			0
$771$	64.0000			2.30490
$772$		0			0
$773$	−9.00000	+	15.5885i	−0.323708	+	0.560678i	−0.981250	−	0.192740i	$-0.938263\pi$
$773$	−9.00000	+	15.5885i	−0.323708	+	0.560678i	0.657542	+	0.753418i	$0.271596\pi$
$774$		0			0
$775$	8.00000	−	13.8564i	0.287368	−	0.497737i
$776$		0			0
$777$	30.0000	+	51.9615i	1.07624	+	1.86411i
$778$		0			0
$779$		0			0
$780$		0			0
$781$	−5.00000	−	8.66025i	−0.178914	−	0.309888i
$782$		0			0
$783$	−4.00000	+	6.92820i	−0.142948	+	0.247594i
$784$		0			0
$785$	−1.00000	+	1.73205i	−0.0356915	+	0.0618195i
$786$		0			0
$787$	4.00000			0.142585			0.0712923	−	0.997455i	$-0.477288\pi$
$787$	4.00000			0.142585			0.0712923	+	0.997455i	$0.477288\pi$
$788$		0			0
$789$	21.0000	−	36.3731i	0.747620	−	1.29492i
$790$		0			0
$791$	30.0000			1.06668
$792$		0			0
$793$	−26.0000	−	45.0333i	−0.923287	−	1.59918i
$794$		0			0
$795$	−4.00000	−	6.92820i	−0.141865	−	0.245718i
$796$		0			0
$797$	−12.0000			−0.425062			−0.212531	−	0.977154i	$-0.568171\pi$
$797$	−12.0000			−0.425062			−0.212531	+	0.977154i	$0.568171\pi$
$798$		0			0
$799$	3.00000			0.106132
$800$		0			0
$801$	−6.00000	−	10.3923i	−0.212000	−	0.367194i
$802$		0			0
$803$	−22.5000	−	38.9711i	−0.794008	−	1.37526i
$804$		0			0
$805$	24.0000			0.845889
$806$		0			0
$807$	24.0000	−	41.5692i	0.844840	−	1.46331i
$808$		0			0
$809$	39.0000			1.37117			0.685583	−	0.727994i	$-0.259547\pi$
$809$	39.0000			1.37117			0.685583	+	0.727994i	$0.259547\pi$
$810$		0			0
$811$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$811$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$812$		0			0
$813$	8.00000	−	13.8564i	0.280572	−	0.485965i
$814$		0			0
$815$	−2.00000	−	3.46410i	−0.0700569	−	0.121342i
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−6.00000	−	10.3923i	−0.209657	−	0.363137i
$820$		0			0
$821$	−22.5000	+	38.9711i	−0.785255	+	1.36010i	0.143591	+	0.989637i	$0.454135\pi$
$821$	−22.5000	+	38.9711i	−0.785255	+	1.36010i	−0.928846	+	0.370465i	$0.879198\pi$
$822$		0			0
$823$	−26.5000	+	45.8993i	−0.923732	+	1.59995i	−0.130144	+	0.991495i	$0.541544\pi$
$823$	−26.5000	+	45.8993i	−0.923732	+	1.59995i	−0.793588	+	0.608456i	$0.791789\pi$
$824$		0			0
$825$	−40.0000			−1.39262
$826$		0			0
$827$	14.0000	−	24.2487i	0.486828	−	0.843210i	−0.513058	−	0.858354i	$-0.671487\pi$
$827$	14.0000	−	24.2487i	0.486828	−	0.843210i	0.999885	+	0.0151439i	$0.00482062\pi$
$828$		0			0
$829$	−48.0000			−1.66711			−0.833554	−	0.552437i	$-0.813698\pi$
$829$	−48.0000			−1.66711			−0.833554	+	0.552437i	$0.813698\pi$
$830$		0			0
$831$	−1.00000	−	1.73205i	−0.0346896	−	0.0600842i
$832$		0			0
$833$	3.00000	+	5.19615i	0.103944	+	0.180036i
$834$		0			0
$835$	6.00000			0.207639
$836$		0			0
$837$	−16.0000			−0.553041
$838$		0			0
$839$	5.00000	+	8.66025i	0.172619	+	0.298985i	0.939335	−	0.343002i	$-0.111444\pi$
$839$	5.00000	+	8.66025i	0.172619	+	0.298985i	−0.766716	+	0.641987i	$0.778110\pi$
$840$		0			0
$841$	12.5000	+	21.6506i	0.431034	+	0.746574i
$842$		0			0
$843$	44.0000			1.51544
$844$		0			0
$845$	1.50000	−	2.59808i	0.0516016	−	0.0893765i
$846$		0			0
$847$	−42.0000			−1.44314
$848$		0			0
$849$	3.00000	−	5.19615i	0.102960	−	0.178331i
$850$		0			0
$851$	−40.0000	+	69.2820i	−1.37118	+	2.37496i
$852$		0			0
$853$	−21.0000	−	36.3731i	−0.719026	−	1.24539i	−0.961386	−	0.275204i	$-0.911255\pi$
$853$	−21.0000	−	36.3731i	−0.719026	−	1.24539i	0.242360	−	0.970186i	$-0.422079\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	0.670366	−	0.742030i	$-0.266137\pi$
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	−0.977800	+	0.209539i	$0.932804\pi$
$858$		0			0
$859$	−0.500000	+	0.866025i	−0.0170598	+	0.0295484i	−0.874429	−	0.485153i	$-0.838764\pi$
$859$	−0.500000	+	0.866025i	−0.0170598	+	0.0295484i	0.857369	+	0.514701i	$0.172097\pi$
$860$		0			0
$861$	30.0000	−	51.9615i	1.02240	−	1.77084i
$862$		0			0
$863$	6.00000			0.204242			0.102121	−	0.994772i	$-0.467437\pi$
$863$	6.00000			0.204242			0.102121	+	0.994772i	$0.467437\pi$
$864$		0			0
$865$	3.00000	−	5.19615i	0.102003	−	0.176674i
$866$		0			0
$867$	−16.0000			−0.543388
$868$		0			0
$869$	−20.0000	−	34.6410i	−0.678454	−	1.17512i
$870$		0			0
$871$	−24.0000	−	41.5692i	−0.813209	−	1.40852i
$872$		0			0
$873$	−8.00000			−0.270759
$874$		0			0
$875$	−27.0000			−0.912767
$876$		0			0
$877$	−17.0000	−	29.4449i	−0.574049	−	0.994282i	−0.996144	−	0.0877308i	$-0.972038\pi$
$877$	−17.0000	−	29.4449i	−0.574049	−	0.994282i	0.422095	−	0.906552i	$-0.361295\pi$
$878$		0			0
$879$	12.0000	+	20.7846i	0.404750	+	0.701047i
$880$		0			0
$881$	−51.0000			−1.71823			−0.859117	−	0.511780i	$-0.828986\pi$
$881$	−51.0000			−1.71823			−0.859117	+	0.511780i	$0.828986\pi$
$882$		0			0
$883$	−0.500000	+	0.866025i	−0.0168263	+	0.0291441i	−0.874316	−	0.485357i	$-0.838690\pi$
$883$	−0.500000	+	0.866025i	−0.0168263	+	0.0291441i	0.857490	+	0.514501i	$0.172023\pi$
$884$		0			0
$885$	−12.0000			−0.403376
$886$		0			0
$887$	−11.0000	+	19.0526i	−0.369344	+	0.639722i	−0.989463	−	0.144785i	$-0.953751\pi$
$887$	−11.0000	+	19.0526i	−0.369344	+	0.639722i	0.620119	+	0.784508i	$0.287084\pi$
$888$		0			0
$889$	9.00000	−	15.5885i	0.301850	−	0.522820i
$890$		0			0
$891$	27.5000	+	47.6314i	0.921285	+	1.59571i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	9.00000	+	15.5885i	0.300837	+	0.521065i
$896$		0			0
$897$	32.0000	−	55.4256i	1.06845	−	1.85061i
$898$		0			0
$899$	4.00000	−	6.92820i	0.133407	−	0.231069i
$900$		0			0
$901$	12.0000			0.399778
$902$		0			0
$903$	3.00000	−	5.19615i	0.0998337	−	0.172917i
$904$		0			0
$905$	−10.0000			−0.332411
$906$		0			0
$907$	20.0000	+	34.6410i	0.664089	+	1.15024i	0.979531	+	0.201291i	$0.0645138\pi$
$907$	20.0000	+	34.6410i	0.664089	+	1.15024i	−0.315442	+	0.948945i	$0.602153\pi$
$908$		0			0
$909$	5.00000	+	8.66025i	0.165840	+	0.287242i
$910$		0			0
$911$	−18.0000			−0.596367			−0.298183	−	0.954509i	$-0.596381\pi$
$911$	−18.0000			−0.596367			−0.298183	+	0.954509i	$0.596381\pi$
$912$		0			0
$913$	−60.0000			−1.98571
$914$		0			0
$915$	−13.0000	−	22.5167i	−0.429767	−	0.744378i
$916$		0			0
$917$	−13.5000	−	23.3827i	−0.445809	−	0.772164i
$918$		0			0
$919$	−28.0000			−0.923635			−0.461817	−	0.886975i	$-0.652802\pi$
$919$	−28.0000			−0.923635			−0.461817	+	0.886975i	$0.652802\pi$
$920$		0			0
$921$	−12.0000	+	20.7846i	−0.395413	+	0.684876i
$922$		0			0
$923$	−8.00000			−0.263323
$924$		0			0
$925$	20.0000	−	34.6410i	0.657596	−	1.13899i
$926$		0			0
$927$	3.00000	−	5.19615i	0.0985329	−	0.170664i
$928$		0			0
$929$	−7.00000	−	12.1244i	−0.229663	−	0.397787i	0.728046	−	0.685529i	$-0.240429\pi$
$929$	−7.00000	−	12.1244i	−0.229663	−	0.397787i	−0.957708	+	0.287742i	$0.907096\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−7.00000	−	12.1244i	−0.229170	−	0.396934i
$934$		0			0
$935$	−7.50000	+	12.9904i	−0.245276	+	0.424831i
$936$		0			0
$937$	15.5000	−	26.8468i	0.506363	−	0.877046i	−0.493610	−	0.869683i	$-0.664323\pi$
$937$	15.5000	−	26.8468i	0.506363	−	0.877046i	0.999973	−	0.00736293i	$-0.00234371\pi$
$938$		0			0
$939$	−20.0000			−0.652675
$940$		0			0
$941$	13.0000	−	22.5167i	0.423788	−	0.734022i	−0.572518	−	0.819892i	$-0.694034\pi$
$941$	13.0000	−	22.5167i	0.423788	−	0.734022i	0.996306	+	0.0858697i	$0.0273669\pi$
$942$		0			0
$943$	80.0000			2.60516
$944$		0			0
$945$	6.00000	+	10.3923i	0.195180	+	0.338062i
$946$		0			0
$947$	6.00000	+	10.3923i	0.194974	+	0.337705i	0.946892	−	0.321552i	$-0.104204\pi$
$947$	6.00000	+	10.3923i	0.194974	+	0.337705i	−0.751918	+	0.659256i	$0.770871\pi$
$948$		0			0
$949$	−36.0000			−1.16861
$950$		0			0
$951$	60.0000			1.94563
$952$		0			0
$953$	8.00000	+	13.8564i	0.259145	+	0.448853i	0.966013	−	0.258493i	$-0.0832258\pi$
$953$	8.00000	+	13.8564i	0.259145	+	0.448853i	−0.706868	+	0.707346i	$0.749892\pi$
$954$		0			0
$955$	12.5000	+	21.6506i	0.404491	+	0.700598i
$956$		0			0
$957$	−20.0000			−0.646508
$958$		0			0
$959$	−16.5000	+	28.5788i	−0.532813	+	0.922859i
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$	−1.00000	+	1.73205i	−0.0322245	+	0.0558146i
$964$		0			0
$965$	6.00000	−	10.3923i	0.193147	−	0.334540i
$966$		0			0
$967$	−24.0000	−	41.5692i	−0.771788	−	1.33678i	−0.936582	−	0.350448i	$-0.886029\pi$
$967$	−24.0000	−	41.5692i	−0.771788	−	1.33678i	0.164794	−	0.986328i	$-0.447304\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−10.0000	−	17.3205i	−0.320915	−	0.555842i	0.659762	−	0.751475i	$-0.270657\pi$
$971$	−10.0000	−	17.3205i	−0.320915	−	0.555842i	−0.980677	+	0.195633i	$0.937324\pi$
$972$		0			0
$973$	−4.50000	+	7.79423i	−0.144263	+	0.249871i
$974$		0			0
$975$	−16.0000	+	27.7128i	−0.512410	+	0.887520i
$976$		0			0
$977$	56.0000			1.79160			0.895799	−	0.444459i	$-0.146604\pi$
$977$	56.0000			1.79160			0.895799	+	0.444459i	$0.146604\pi$
$978$		0			0
$979$	−30.0000	+	51.9615i	−0.958804	+	1.66070i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	6.00000	+	10.3923i	0.191370	+	0.331463i	0.945705	−	0.325027i	$-0.105374\pi$
$983$	6.00000	+	10.3923i	0.191370	+	0.331463i	−0.754334	+	0.656490i	$0.772040\pi$
$984$		0			0
$985$	1.00000	+	1.73205i	0.0318626	+	0.0551877i
$986$		0			0
$987$	6.00000			0.190982
$988$		0			0
$989$	8.00000			0.254385
$990$		0			0
$991$	19.0000	+	32.9090i	0.603555	+	1.04539i	0.992278	+	0.124033i	$0.0395829\pi$
$991$	19.0000	+	32.9090i	0.603555	+	1.04539i	−0.388723	+	0.921355i	$0.627084\pi$
$992$		0			0
$993$	4.00000	+	6.92820i	0.126936	+	0.219860i
$994$		0			0
$995$	7.00000			0.221915
$996$		0			0
$997$	−18.5000	+	32.0429i	−0.585901	+	1.01481i	0.408862	+	0.912596i	$0.365926\pi$
$997$	−18.5000	+	32.0429i	−0.585901	+	1.01481i	−0.994762	+	0.102214i	$0.967407\pi$
$998$		0			0
$999$	−40.0000			−1.26554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1444.2.e.a.653.1		2
19.7	even	3		76.2.a.a.1.1	✓	1
19.8	odd	6		1444.2.e.c.429.1		2
19.11	even	3	inner	1444.2.e.a.429.1		2
19.12	odd	6		1444.2.a.a.1.1		1
19.18	odd	2		1444.2.e.c.653.1		2
57.26	odd	6		684.2.a.b.1.1		1
76.7	odd	6		304.2.a.a.1.1		1
76.31	even	6		5776.2.a.p.1.1		1
95.7	odd	12		1900.2.c.b.1749.1		2
95.64	even	6		1900.2.a.b.1.1		1
95.83	odd	12		1900.2.c.b.1749.2		2
133.83	odd	6		3724.2.a.a.1.1		1
152.45	even	6		1216.2.a.c.1.1		1
152.83	odd	6		1216.2.a.q.1.1		1
209.197	odd	6		9196.2.a.f.1.1		1
228.83	even	6		2736.2.a.q.1.1		1
380.159	odd	6		7600.2.a.p.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.a.a.1.1	✓	1	19.7	even	3
304.2.a.a.1.1		1	76.7	odd	6
684.2.a.b.1.1		1	57.26	odd	6
1216.2.a.c.1.1		1	152.45	even	6
1216.2.a.q.1.1		1	152.83	odd	6
1444.2.a.a.1.1		1	19.12	odd	6
1444.2.e.a.429.1		2	19.11	even	3	inner
1444.2.e.a.653.1		2	1.1	even	1	trivial
1444.2.e.c.429.1		2	19.8	odd	6
1444.2.e.c.653.1		2	19.18	odd	2
1900.2.a.b.1.1		1	95.64	even	6
1900.2.c.b.1749.1		2	95.7	odd	12
1900.2.c.b.1749.2		2	95.83	odd	12
2736.2.a.q.1.1		1	228.83	even	6
3724.2.a.a.1.1		1	133.83	odd	6
5776.2.a.p.1.1		1	76.31	even	6
7600.2.a.p.1.1		1	380.159	odd	6
9196.2.a.f.1.1		1	209.197	odd	6

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:	\( N \)	\(=\)	\( 1444 = 2^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1444.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{3} +(0.500000 + 0.866025i) q^{5} -3.00000 q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{3} +(0.500000 + 0.866025i) q^{5} -3.00000 q^{7} +(-0.500000 + 0.866025i) q^{9} +5.00000 q^{11} +(2.00000 - 3.46410i) q^{13} +(1.00000 - 1.73205i) q^{15} +(1.50000 + 2.59808i) q^{17} +(3.00000 + 5.19615i) q^{21} +(-4.00000 + 6.92820i) q^{23} +(2.00000 - 3.46410i) q^{25} -4.00000 q^{27} +(1.00000 - 1.73205i) q^{29} +4.00000 q^{31} +(-5.00000 - 8.66025i) q^{33} +(-1.50000 - 2.59808i) q^{35} +10.0000 q^{37} -8.00000 q^{39} +(-5.00000 - 8.66025i) q^{41} +(-0.500000 - 0.866025i) q^{43} -1.00000 q^{45} +(0.500000 - 0.866025i) q^{47} +2.00000 q^{49} +(3.00000 - 5.19615i) q^{51} +(2.00000 - 3.46410i) q^{53} +(2.50000 + 4.33013i) q^{55} +(-3.00000 - 5.19615i) q^{59} +(6.50000 - 11.2583i) q^{61} +(1.50000 - 2.59808i) q^{63} +4.00000 q^{65} +(6.00000 - 10.3923i) q^{67} +16.0000 q^{69} +(-1.00000 - 1.73205i) q^{71} +(-4.50000 - 7.79423i) q^{73} -8.00000 q^{75} -15.0000 q^{77} +(-4.00000 - 6.92820i) q^{79} +(5.50000 + 9.52628i) q^{81} -12.0000 q^{83} +(-1.50000 + 2.59808i) q^{85} -4.00000 q^{87} +(-6.00000 + 10.3923i) q^{89} +(-6.00000 + 10.3923i) q^{91} +(-4.00000 - 6.92820i) q^{93} +(4.00000 + 6.92820i) q^{97} +(-2.50000 + 4.33013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} + q^{5} - 6 q^{7} - q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 + q^5 - 6 * q^7 - q^9	\( 2 q - 2 q^{3} + q^{5} - 6 q^{7} - q^{9} + 10 q^{11} + 4 q^{13} + 2 q^{15} + 3 q^{17} + 6 q^{21} - 8 q^{23} + 4 q^{25} - 8 q^{27} + 2 q^{29} + 8 q^{31} - 10 q^{33} - 3 q^{35} + 20 q^{37} - 16 q^{39} - 10 q^{41} - q^{43} - 2 q^{45} + q^{47} + 4 q^{49} + 6 q^{51} + 4 q^{53} + 5 q^{55} - 6 q^{59} + 13 q^{61} + 3 q^{63} + 8 q^{65} + 12 q^{67} + 32 q^{69} - 2 q^{71} - 9 q^{73} - 16 q^{75} - 30 q^{77} - 8 q^{79} + 11 q^{81} - 24 q^{83} - 3 q^{85} - 8 q^{87} - 12 q^{89} - 12 q^{91} - 8 q^{93} + 8 q^{97} - 5 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 + q^5 - 6 * q^7 - q^9 + 10 * q^11 + 4 * q^13 + 2 * q^15 + 3 * q^17 + 6 * q^21 - 8 * q^23 + 4 * q^25 - 8 * q^27 + 2 * q^29 + 8 * q^31 - 10 * q^33 - 3 * q^35 + 20 * q^37 - 16 * q^39 - 10 * q^41 - q^43 - 2 * q^45 + q^47 + 4 * q^49 + 6 * q^51 + 4 * q^53 + 5 * q^55 - 6 * q^59 + 13 * q^61 + 3 * q^63 + 8 * q^65 + 12 * q^67 + 32 * q^69 - 2 * q^71 - 9 * q^73 - 16 * q^75 - 30 * q^77 - 8 * q^79 + 11 * q^81 - 24 * q^83 - 3 * q^85 - 8 * q^87 - 12 * q^89 - 12 * q^91 - 8 * q^93 + 8 * q^97 - 5 * q^99

Introduction

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