LMFDB - Embedded newform 1008.2.t.d.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(193,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))

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

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

chi := DirichletCharacter("1008.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.t (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:	$8.04892052375$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1008.193
Dual form			1008.2.t.d.961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50000 - 0.866025i) q^{3} -1.00000 q^{5} +(-0.500000 - 2.59808i) q^{7} +(1.50000 - 2.59808i) q^{9} -5.00000 q^{11} +(2.50000 - 4.33013i) q^{13} +(-1.50000 + 0.866025i) q^{15} +(-1.50000 + 2.59808i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-3.00000 - 3.46410i) q^{21} -3.00000 q^{23} -4.00000 q^{25} -5.19615i q^{27} +(0.500000 + 0.866025i) q^{29} +(-7.50000 + 4.33013i) q^{33} +(0.500000 + 2.59808i) q^{35} +(-1.50000 - 2.59808i) q^{37} -8.66025i q^{39} +(2.50000 - 4.33013i) q^{41} +(-0.500000 - 0.866025i) q^{43} +(-1.50000 + 2.59808i) q^{45} +(-6.50000 + 2.59808i) q^{49} +5.19615i q^{51} +(4.50000 - 7.79423i) q^{53} +5.00000 q^{55} +(1.50000 + 0.866025i) q^{57} +(7.00000 - 12.1244i) q^{61} +(-7.50000 - 2.59808i) q^{63} +(-2.50000 + 4.33013i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-4.50000 + 2.59808i) q^{69} +12.0000 q^{71} +(-1.50000 + 2.59808i) q^{73} +(-6.00000 + 3.46410i) q^{75} +(2.50000 + 12.9904i) q^{77} +(4.00000 - 6.92820i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-4.50000 - 7.79423i) q^{83} +(1.50000 - 2.59808i) q^{85} +(1.50000 + 0.866025i) q^{87} +(6.50000 + 11.2583i) q^{89} +(-12.5000 - 4.33013i) q^{91} +(-0.500000 - 0.866025i) q^{95} +(4.50000 + 7.79423i) q^{97} +(-7.50000 + 12.9904i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} - 2 q^{5} - q^{7} + 3 q^{9} - 10 q^{11} + 5 q^{13} - 3 q^{15} - 3 q^{17} + q^{19} - 6 q^{21} - 6 q^{23} - 8 q^{25} + q^{29} - 15 q^{33} + q^{35} - 3 q^{37} + 5 q^{41} - q^{43} - 3 q^{45}+ \cdots - 15 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 - 2 * q^5 - q^7 + 3 * q^9 - 10 * q^11 + 5 * q^13 - 3 * q^15 - 3 * q^17 + q^19 - 6 * q^21 - 6 * q^23 - 8 * q^25 + q^29 - 15 * q^33 + q^35 - 3 * q^37 + 5 * q^41 - q^43 - 3 * q^45 - 13 * q^49 + 9 * q^53 + 10 * q^55 + 3 * q^57 + 14 * q^61 - 15 * q^63 - 5 * q^65 + 4 * q^67 - 9 * q^69 + 24 * q^71 - 3 * q^73 - 12 * q^75 + 5 * q^77 + 8 * q^79 - 9 * q^81 - 9 * q^83 + 3 * q^85 + 3 * q^87 + 13 * q^89 - 25 * q^91 - q^95 + 9 * q^97 - 15 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$4$		0			0
$5$	−1.00000			−0.447214			−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000			−0.447214			−0.223607	+	0.974679i	$0.571783\pi$
$6$		0			0
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$8$		0			0
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$		0			0
$11$	−5.00000			−1.50756			−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000			−1.50756			−0.753778	+	0.657129i	$0.771771\pi$
$12$		0			0
$13$	2.50000	−	4.33013i	0.693375	−	1.20096i	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	2.50000	−	4.33013i	0.693375	−	1.20096i	0.970725	−	0.240192i	$-0.0772105\pi$
$14$		0			0
$15$	−1.50000	+	0.866025i	−0.387298	+	0.223607i
$16$		0			0
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$		0			0
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	−0.802955	+	0.596040i	$0.796740\pi$
$20$		0			0
$21$	−3.00000	−	3.46410i	−0.654654	−	0.755929i
$22$		0			0
$23$	−3.00000			−0.625543			−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000			−0.625543			−0.312772	+	0.949828i	$0.601257\pi$
$24$		0			0
$25$	−4.00000			−0.800000
$26$		0			0
$27$		−	5.19615i		−	1.00000i
$28$		0			0
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	0.908708	−	0.417432i	$-0.137070\pi$
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	−0.815861	+	0.578249i	$0.803736\pi$
$30$		0			0
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$		0			0
$33$	−7.50000	+	4.33013i	−1.30558	+	0.753778i
$34$		0			0
$35$	0.500000	+	2.59808i	0.0845154	+	0.439155i
$36$		0			0
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	0.715981	−	0.698119i	$-0.245980\pi$
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	−0.962580	+	0.270998i	$0.912646\pi$
$38$		0			0
$39$		−	8.66025i		−	1.38675i
$40$		0			0
$41$	2.50000	−	4.33013i	0.390434	−	0.676252i	−0.602072	−	0.798441i	$-0.705658\pi$
$41$	2.50000	−	4.33013i	0.390434	−	0.676252i	0.992507	+	0.122189i	$0.0389915\pi$
$42$		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
$45$	−1.50000	+	2.59808i	−0.223607	+	0.387298i
$46$		0			0
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$		0			0
$51$			5.19615i			0.727607i
$52$		0			0
$53$	4.50000	−	7.79423i	0.618123	−	1.07062i	−0.371706	−	0.928351i	$-0.621227\pi$
$53$	4.50000	−	7.79423i	0.618123	−	1.07062i	0.989828	−	0.142269i	$-0.0454398\pi$
$54$		0			0
$55$	5.00000			0.674200
$56$		0			0
$57$	1.50000	+	0.866025i	0.198680	+	0.114708i
$58$		0			0
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	7.00000	−	12.1244i	0.896258	−	1.55236i	0.0640184	−	0.997949i	$-0.479608\pi$
$61$	7.00000	−	12.1244i	0.896258	−	1.55236i	0.832240	−	0.554416i	$-0.187058\pi$
$62$		0			0
$63$	−7.50000	−	2.59808i	−0.944911	−	0.327327i
$64$		0			0
$65$	−2.50000	+	4.33013i	−0.310087	+	0.537086i
$66$		0			0
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$		0			0
$69$	−4.50000	+	2.59808i	−0.541736	+	0.312772i
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$		0			0
$73$	−1.50000	+	2.59808i	−0.175562	+	0.304082i	−0.940356	−	0.340193i	$-0.889507\pi$
$73$	−1.50000	+	2.59808i	−0.175562	+	0.304082i	0.764794	+	0.644275i	$0.222841\pi$
$74$		0			0
$75$	−6.00000	+	3.46410i	−0.692820	+	0.400000i
$76$		0			0
$77$	2.50000	+	12.9904i	0.284901	+	1.48039i
$78$		0			0
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	−0.548352	−	0.836247i	$-0.684745\pi$
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	0.998388	+	0.0567635i	$0.0180781\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		0			0
$83$	−4.50000	−	7.79423i	−0.493939	−	0.855528i	0.506036	−	0.862512i	$-0.331110\pi$
$83$	−4.50000	−	7.79423i	−0.493939	−	0.855528i	−0.999976	+	0.00698436i	$0.997777\pi$
$84$		0			0
$85$	1.50000	−	2.59808i	0.162698	−	0.281801i
$86$		0			0
$87$	1.50000	+	0.866025i	0.160817	+	0.0928477i
$88$		0			0
$89$	6.50000	+	11.2583i	0.688999	+	1.19338i	0.972162	+	0.234309i	$0.0752827\pi$
$89$	6.50000	+	11.2583i	0.688999	+	1.19338i	−0.283164	+	0.959072i	$0.591384\pi$
$90$		0			0
$91$	−12.5000	−	4.33013i	−1.31036	−	0.453921i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.500000	−	0.866025i	−0.0512989	−	0.0888523i
$96$		0			0
$97$	4.50000	+	7.79423i	0.456906	+	0.791384i	0.998796	−	0.0490655i	$-0.0156243\pi$
$97$	4.50000	+	7.79423i	0.456906	+	0.791384i	−0.541890	+	0.840450i	$0.682291\pi$
$98$		0			0
$99$	−7.50000	+	12.9904i	−0.753778	+	1.30558i
$100$		0			0
$101$	−17.0000			−1.69156			−0.845782	−	0.533529i	$-0.820865\pi$
$101$	−17.0000			−1.69156			−0.845782	+	0.533529i	$0.820865\pi$
$102$		0			0
$103$	1.00000			0.0985329			0.0492665	−	0.998786i	$-0.484312\pi$
$103$	1.00000			0.0985329			0.0492665	+	0.998786i	$0.484312\pi$
$104$		0			0
$105$	3.00000	+	3.46410i	0.292770	+	0.338062i
$106$		0			0
$107$	8.50000	+	14.7224i	0.821726	+	1.42327i	0.904396	+	0.426694i	$0.140322\pi$
$107$	8.50000	+	14.7224i	0.821726	+	1.42327i	−0.0826699	+	0.996577i	$0.526345\pi$
$108$		0			0
$109$	4.50000	−	7.79423i	0.431022	−	0.746552i	−0.565940	−	0.824447i	$-0.691487\pi$
$109$	4.50000	−	7.79423i	0.431022	−	0.746552i	0.996962	+	0.0778949i	$0.0248199\pi$
$110$		0			0
$111$	−4.50000	−	2.59808i	−0.427121	−	0.246598i
$112$		0			0
$113$	0.500000	−	0.866025i	0.0470360	−	0.0814688i	−0.841549	−	0.540181i	$-0.818356\pi$
$113$	0.500000	−	0.866025i	0.0470360	−	0.0814688i	0.888585	+	0.458712i	$0.151689\pi$
$114$		0			0
$115$	3.00000			0.279751
$116$		0			0
$117$	−7.50000	−	12.9904i	−0.693375	−	1.20096i
$118$		0			0
$119$	7.50000	+	2.59808i	0.687524	+	0.238165i
$120$		0			0
$121$	14.0000			1.27273
$122$		0			0
$123$		−	8.66025i		−	0.780869i
$124$		0			0
$125$	9.00000			0.804984
$126$		0			0
$127$	12.0000			1.06483			0.532414	−	0.846484i	$-0.321285\pi$
$127$	12.0000			1.06483			0.532414	+	0.846484i	$0.321285\pi$
$128$		0			0
$129$	−1.50000	−	0.866025i	−0.132068	−	0.0762493i
$130$		0			0
$131$	1.00000			0.0873704			0.0436852	−	0.999045i	$-0.486090\pi$
$131$	1.00000			0.0873704			0.0436852	+	0.999045i	$0.486090\pi$
$132$		0			0
$133$	2.00000	−	1.73205i	0.173422	−	0.150188i
$134$		0			0
$135$			5.19615i			0.447214i
$136$		0			0
$137$	−9.00000			−0.768922			−0.384461	−	0.923141i	$-0.625613\pi$
$137$	−9.00000			−0.768922			−0.384461	+	0.923141i	$0.625613\pi$
$138$		0			0
$139$	4.50000	−	7.79423i	0.381685	−	0.661098i	−0.609618	−	0.792695i	$-0.708677\pi$
$139$	4.50000	−	7.79423i	0.381685	−	0.661098i	0.991303	+	0.131597i	$0.0420106\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−12.5000	+	21.6506i	−1.04530	+	1.81052i
$144$		0			0
$145$	−0.500000	−	0.866025i	−0.0415227	−	0.0719195i
$146$		0			0
$147$	−7.50000	+	9.52628i	−0.618590	+	0.785714i
$148$		0			0
$149$	3.00000			0.245770			0.122885	−	0.992421i	$-0.460785\pi$
$149$	3.00000			0.245770			0.122885	+	0.992421i	$0.460785\pi$
$150$		0			0
$151$	−5.00000			−0.406894			−0.203447	−	0.979086i	$-0.565214\pi$
$151$	−5.00000			−0.406894			−0.203447	+	0.979086i	$0.565214\pi$
$152$		0			0
$153$	4.50000	+	7.79423i	0.363803	+	0.630126i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	0.997609	+	0.0691164i	$0.0220180\pi$
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	−0.438948	+	0.898513i	$0.644649\pi$
$158$		0			0
$159$		−	15.5885i		−	1.23625i
$160$		0			0
$161$	1.50000	+	7.79423i	0.118217	+	0.614271i
$162$		0			0
$163$	−5.50000	−	9.52628i	−0.430793	−	0.746156i	0.566149	−	0.824303i	$-0.308433\pi$
$163$	−5.50000	−	9.52628i	−0.430793	−	0.746156i	−0.996942	+	0.0781474i	$0.975100\pi$
$164$		0			0
$165$	7.50000	−	4.33013i	0.583874	−	0.337100i
$166$		0			0
$167$	−9.50000	+	16.4545i	−0.735132	+	1.27329i	0.219533	+	0.975605i	$0.429547\pi$
$167$	−9.50000	+	16.4545i	−0.735132	+	1.27329i	−0.954665	+	0.297681i	$0.903787\pi$
$168$		0			0
$169$	−6.00000	−	10.3923i	−0.461538	−	0.799408i
$170$		0			0
$171$	3.00000			0.229416
$172$		0			0
$173$	7.00000	−	12.1244i	0.532200	−	0.921798i	−0.467093	−	0.884208i	$-0.654699\pi$
$173$	7.00000	−	12.1244i	0.532200	−	0.921798i	0.999293	−	0.0375896i	$-0.0119679\pi$
$174$		0			0
$175$	2.00000	+	10.3923i	0.151186	+	0.785584i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	9.50000	−	16.4545i	0.710063	−	1.22987i	−0.254770	−	0.967002i	$-0.582000\pi$
$179$	9.50000	−	16.4545i	0.710063	−	1.22987i	0.964833	−	0.262864i	$-0.0846670\pi$
$180$		0			0
$181$	−14.0000			−1.04061			−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000			−1.04061			−0.520306	+	0.853980i	$0.674182\pi$
$182$		0			0
$183$		−	24.2487i		−	1.79252i
$184$		0			0
$185$	1.50000	+	2.59808i	0.110282	+	0.191014i
$186$		0			0
$187$	7.50000	−	12.9904i	0.548454	−	0.949951i
$188$		0			0
$189$	−13.5000	+	2.59808i	−0.981981	+	0.188982i
$190$		0			0
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	−0.684244	−	0.729253i	$-0.739868\pi$
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	0.973674	+	0.227946i	$0.0732010\pi$
$192$		0			0
$193$	5.00000	+	8.66025i	0.359908	+	0.623379i	0.987945	−	0.154805i	$-0.0494748\pi$
$193$	5.00000	+	8.66025i	0.359908	+	0.623379i	−0.628037	+	0.778183i	$0.716141\pi$
$194$		0			0
$195$			8.66025i			0.620174i
$196$		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
$199$	1.50000	−	2.59808i	0.106332	−	0.184173i	−0.807950	−	0.589252i	$-0.799423\pi$
$199$	1.50000	−	2.59808i	0.106332	−	0.184173i	0.914282	+	0.405079i	$0.132756\pi$
$200$		0			0
$201$	6.00000	+	3.46410i	0.423207	+	0.244339i
$202$		0			0
$203$	2.00000	−	1.73205i	0.140372	−	0.121566i
$204$		0			0
$205$	−2.50000	+	4.33013i	−0.174608	+	0.302429i
$206$		0			0
$207$	−4.50000	+	7.79423i	−0.312772	+	0.541736i
$208$		0			0
$209$	−2.50000	−	4.33013i	−0.172929	−	0.299521i
$210$		0			0
$211$	6.50000	−	11.2583i	0.447478	−	0.775055i	−0.550743	−	0.834675i	$-0.685655\pi$
$211$	6.50000	−	11.2583i	0.447478	−	0.775055i	0.998221	+	0.0596196i	$0.0189888\pi$
$212$		0			0
$213$	18.0000	−	10.3923i	1.23334	−	0.712069i
$214$		0			0
$215$	0.500000	+	0.866025i	0.0340997	+	0.0590624i
$216$		0			0
$217$		0			0
$218$		0			0
$219$			5.19615i			0.351123i
$220$		0			0
$221$	7.50000	+	12.9904i	0.504505	+	0.873828i
$222$		0			0
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	0.986267	+	0.165161i	$0.0528144\pi$
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	−0.350100	+	0.936713i	$0.613852\pi$
$224$		0			0
$225$	−6.00000	+	10.3923i	−0.400000	+	0.692820i
$226$		0			0
$227$	3.00000			0.199117			0.0995585	−	0.995032i	$-0.468257\pi$
$227$	3.00000			0.199117			0.0995585	+	0.995032i	$0.468257\pi$
$228$		0			0
$229$	−1.00000			−0.0660819			−0.0330409	−	0.999454i	$-0.510519\pi$
$229$	−1.00000			−0.0660819			−0.0330409	+	0.999454i	$0.510519\pi$
$230$		0			0
$231$	15.0000	+	17.3205i	0.986928	+	1.13961i
$232$		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
$235$		0			0
$236$		0			0
$237$		−	13.8564i		−	0.900070i
$238$		0			0
$239$	−7.50000	+	12.9904i	−0.485135	+	0.840278i	−0.999854	−	0.0170808i	$-0.994563\pi$
$239$	−7.50000	+	12.9904i	−0.485135	+	0.840278i	0.514719	+	0.857359i	$0.327896\pi$
$240$		0			0
$241$	11.0000			0.708572			0.354286	−	0.935137i	$-0.384724\pi$
$241$	11.0000			0.708572			0.354286	+	0.935137i	$0.384724\pi$
$242$		0			0
$243$	−13.5000	−	7.79423i	−0.866025	−	0.500000i
$244$		0			0
$245$	6.50000	−	2.59808i	0.415270	−	0.165985i
$246$		0			0
$247$	5.00000			0.318142
$248$		0			0
$249$	−13.5000	−	7.79423i	−0.855528	−	0.493939i
$250$		0			0
$251$	28.0000			1.76734			0.883672	−	0.468106i	$-0.155064\pi$
$251$	28.0000			1.76734			0.883672	+	0.468106i	$0.155064\pi$
$252$		0			0
$253$	15.0000			0.943042
$254$		0			0
$255$		−	5.19615i		−	0.325396i
$256$		0			0
$257$	−29.0000			−1.80897			−0.904485	−	0.426505i	$-0.859745\pi$
$257$	−29.0000			−1.80897			−0.904485	+	0.426505i	$0.859745\pi$
$258$		0			0
$259$	−6.00000	+	5.19615i	−0.372822	+	0.322873i
$260$		0			0
$261$	3.00000			0.185695
$262$		0			0
$263$	−5.00000			−0.308313			−0.154157	−	0.988046i	$-0.549266\pi$
$263$	−5.00000			−0.308313			−0.154157	+	0.988046i	$0.549266\pi$
$264$		0			0
$265$	−4.50000	+	7.79423i	−0.276433	+	0.478796i
$266$		0			0
$267$	19.5000	+	11.2583i	1.19338	+	0.688999i
$268$		0			0
$269$	−1.50000	+	2.59808i	−0.0914566	+	0.158408i	−0.908124	−	0.418701i	$-0.862486\pi$
$269$	−1.50000	+	2.59808i	−0.0914566	+	0.158408i	0.816668	+	0.577108i	$0.195819\pi$
$270$		0			0
$271$	0.500000	+	0.866025i	0.0303728	+	0.0526073i	0.880812	−	0.473466i	$-0.156997\pi$
$271$	0.500000	+	0.866025i	0.0303728	+	0.0526073i	−0.850439	+	0.526073i	$0.823664\pi$
$272$		0			0
$273$	−22.5000	+	4.33013i	−1.36176	+	0.262071i
$274$		0			0
$275$	20.0000			1.20605
$276$		0			0
$277$	19.0000			1.14160			0.570800	−	0.821089i	$-0.306633\pi$
$277$	19.0000			1.14160			0.570800	+	0.821089i	$0.306633\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	14.5000	+	25.1147i	0.864997	+	1.49822i	0.867050	+	0.498222i	$0.166013\pi$
$281$	14.5000	+	25.1147i	0.864997	+	1.49822i	−0.00205220	+	0.999998i	$0.500653\pi$
$282$		0			0
$283$	14.0000	+	24.2487i	0.832214	+	1.44144i	0.896279	+	0.443491i	$0.146260\pi$
$283$	14.0000	+	24.2487i	0.832214	+	1.44144i	−0.0640654	+	0.997946i	$0.520407\pi$
$284$		0			0
$285$	−1.50000	−	0.866025i	−0.0888523	−	0.0512989i
$286$		0			0
$287$	−12.5000	−	4.33013i	−0.737852	−	0.255599i
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	13.5000	+	7.79423i	0.791384	+	0.456906i
$292$		0			0
$293$	2.50000	−	4.33013i	0.146052	−	0.252969i	−0.783713	−	0.621123i	$-0.786677\pi$
$293$	2.50000	−	4.33013i	0.146052	−	0.252969i	0.929765	+	0.368154i	$0.120010\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$			25.9808i			1.50756i
$298$		0			0
$299$	−7.50000	+	12.9904i	−0.433736	+	0.751253i
$300$		0			0
$301$	−2.00000	+	1.73205i	−0.115278	+	0.0998337i
$302$		0			0
$303$	−25.5000	+	14.7224i	−1.46494	+	0.845782i
$304$		0			0
$305$	−7.00000	+	12.1244i	−0.400819	+	0.694239i
$306$		0			0
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$		0			0
$309$	1.50000	−	0.866025i	0.0853320	−	0.0492665i
$310$		0			0
$311$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$311$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$312$		0			0
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	−0.993186	−	0.116543i	$-0.962819\pi$
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	0.597522	+	0.801852i	$0.296152\pi$
$314$		0			0
$315$	7.50000	+	2.59808i	0.422577	+	0.146385i
$316$		0			0
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	−0.769395	−	0.638774i	$-0.779442\pi$
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	0.937892	+	0.346929i	$0.112775\pi$
$318$		0			0
$319$	−2.50000	−	4.33013i	−0.139973	−	0.242441i
$320$		0			0
$321$	25.5000	+	14.7224i	1.42327	+	0.821726i
$322$		0			0
$323$	−3.00000			−0.166924
$324$		0			0
$325$	−10.0000	+	17.3205i	−0.554700	+	0.960769i
$326$		0			0
$327$		−	15.5885i		−	0.862044i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	−0.734905	−	0.678170i	$-0.762773\pi$
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	0.954765	+	0.297361i	$0.0961066\pi$
$332$		0			0
$333$	−9.00000			−0.493197
$334$		0			0
$335$	−2.00000	−	3.46410i	−0.109272	−	0.189264i
$336$		0			0
$337$	14.5000	−	25.1147i	0.789865	−	1.36809i	−0.136184	−	0.990684i	$-0.543484\pi$
$337$	14.5000	−	25.1147i	0.789865	−	1.36809i	0.926049	−	0.377403i	$-0.123183\pi$
$338$		0			0
$339$		−	1.73205i		−	0.0940721i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$		0			0
$345$	4.50000	−	2.59808i	0.242272	−	0.139876i
$346$		0			0
$347$	2.00000	+	3.46410i	0.107366	+	0.185963i	0.914702	−	0.404128i	$-0.132425\pi$
$347$	2.00000	+	3.46410i	0.107366	+	0.185963i	−0.807337	+	0.590091i	$0.799092\pi$
$348$		0			0
$349$	−9.50000	−	16.4545i	−0.508523	−	0.880788i	−0.999951	−	0.00987003i	$-0.996858\pi$
$349$	−9.50000	−	16.4545i	−0.508523	−	0.880788i	0.491428	−	0.870918i	$-0.336475\pi$
$350$		0			0
$351$	−22.5000	−	12.9904i	−1.20096	−	0.693375i
$352$		0			0
$353$	11.0000			0.585471			0.292735	−	0.956193i	$-0.405434\pi$
$353$	11.0000			0.585471			0.292735	+	0.956193i	$0.405434\pi$
$354$		0			0
$355$	−12.0000			−0.636894
$356$		0			0
$357$	13.5000	−	2.59808i	0.714496	−	0.137505i
$358$		0			0
$359$	−5.50000	−	9.52628i	−0.290279	−	0.502778i	0.683597	−	0.729860i	$-0.260415\pi$
$359$	−5.50000	−	9.52628i	−0.290279	−	0.502778i	−0.973876	+	0.227082i	$0.927081\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$		0			0
$363$	21.0000	−	12.1244i	1.10221	−	0.636364i
$364$		0			0
$365$	1.50000	−	2.59808i	0.0785136	−	0.135990i
$366$		0			0
$367$	3.00000			0.156599			0.0782994	−	0.996930i	$-0.475051\pi$
$367$	3.00000			0.156599			0.0782994	+	0.996930i	$0.475051\pi$
$368$		0			0
$369$	−7.50000	−	12.9904i	−0.390434	−	0.676252i
$370$		0			0
$371$	−22.5000	−	7.79423i	−1.16814	−	0.404656i
$372$		0			0
$373$	−25.0000			−1.29445			−0.647225	−	0.762299i	$-0.724071\pi$
$373$	−25.0000			−1.29445			−0.647225	+	0.762299i	$0.724071\pi$
$374$		0			0
$375$	13.5000	−	7.79423i	0.697137	−	0.402492i
$376$		0			0
$377$	5.00000			0.257513
$378$		0			0
$379$	12.0000			0.616399			0.308199	−	0.951322i	$-0.400274\pi$
$379$	12.0000			0.616399			0.308199	+	0.951322i	$0.400274\pi$
$380$		0			0
$381$	18.0000	−	10.3923i	0.922168	−	0.532414i
$382$		0			0
$383$	−27.0000			−1.37964			−0.689818	−	0.723983i	$-0.742309\pi$
$383$	−27.0000			−1.37964			−0.689818	+	0.723983i	$0.742309\pi$
$384$		0			0
$385$	−2.50000	−	12.9904i	−0.127412	−	0.662051i
$386$		0			0
$387$	−3.00000			−0.152499
$388$		0			0
$389$	−9.00000			−0.456318			−0.228159	−	0.973624i	$-0.573271\pi$
$389$	−9.00000			−0.456318			−0.228159	+	0.973624i	$0.573271\pi$
$390$		0			0
$391$	4.50000	−	7.79423i	0.227575	−	0.394171i
$392$		0			0
$393$	1.50000	−	0.866025i	0.0756650	−	0.0436852i
$394$		0			0
$395$	−4.00000	+	6.92820i	−0.201262	+	0.348596i
$396$		0			0
$397$	−7.50000	−	12.9904i	−0.376414	−	0.651969i	0.614123	−	0.789210i	$-0.289510\pi$
$397$	−7.50000	−	12.9904i	−0.376414	−	0.651969i	−0.990538	+	0.137241i	$0.956176\pi$
$398$		0			0
$399$	1.50000	−	4.33013i	0.0750939	−	0.216777i
$400$		0			0
$401$	3.00000			0.149813			0.0749064	−	0.997191i	$-0.476134\pi$
$401$	3.00000			0.149813			0.0749064	+	0.997191i	$0.476134\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	4.50000	+	7.79423i	0.223607	+	0.387298i
$406$		0			0
$407$	7.50000	+	12.9904i	0.371761	+	0.643909i
$408$		0			0
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	0.639430	−	0.768849i	$-0.279170\pi$
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	−0.985558	+	0.169338i	$0.945837\pi$
$410$		0			0
$411$	−13.5000	+	7.79423i	−0.665906	+	0.384461i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	4.50000	+	7.79423i	0.220896	+	0.382604i
$416$		0			0
$417$		−	15.5885i		−	0.763370i
$418$		0			0
$419$	4.50000	−	7.79423i	0.219839	−	0.380773i	−0.734919	−	0.678155i	$-0.762780\pi$
$419$	4.50000	−	7.79423i	0.219839	−	0.380773i	0.954759	+	0.297382i	$0.0961133\pi$
$420$		0			0
$421$	0.500000	+	0.866025i	0.0243685	+	0.0422075i	0.877952	−	0.478748i	$-0.158909\pi$
$421$	0.500000	+	0.866025i	0.0243685	+	0.0422075i	−0.853584	+	0.520955i	$0.825576\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$		0			0
$427$	−35.0000	−	12.1244i	−1.69377	−	0.586739i
$428$		0			0
$429$			43.3013i			2.09061i
$430$		0			0
$431$	−4.50000	+	7.79423i	−0.216757	+	0.375435i	−0.953815	−	0.300395i	$-0.902881\pi$
$431$	−4.50000	+	7.79423i	−0.216757	+	0.375435i	0.737057	+	0.675830i	$0.236215\pi$
$432$		0			0
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$		0			0
$435$	−1.50000	−	0.866025i	−0.0719195	−	0.0415227i
$436$		0			0
$437$	−1.50000	−	2.59808i	−0.0717547	−	0.124283i
$438$		0			0
$439$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$		0			0
$441$	−3.00000	+	20.7846i	−0.142857	+	0.989743i
$442$		0			0
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	−0.0212481	−	0.999774i	$-0.506764\pi$
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	0.876454	−	0.481486i	$-0.159903\pi$
$444$		0			0
$445$	−6.50000	−	11.2583i	−0.308130	−	0.533696i
$446$		0			0
$447$	4.50000	−	2.59808i	0.212843	−	0.122885i
$448$		0			0
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$		0			0
$451$	−12.5000	+	21.6506i	−0.588602	+	1.01949i
$452$		0			0
$453$	−7.50000	+	4.33013i	−0.352381	+	0.203447i
$454$		0			0
$455$	12.5000	+	4.33013i	0.586009	+	0.202999i
$456$		0			0
$457$	−11.0000	+	19.0526i	−0.514558	+	0.891241i	0.485299	+	0.874348i	$0.338711\pi$
$457$	−11.0000	+	19.0526i	−0.514558	+	0.891241i	−0.999857	+	0.0168929i	$0.994623\pi$
$458$		0			0
$459$	13.5000	+	7.79423i	0.630126	+	0.363803i
$460$		0			0
$461$	−9.50000	−	16.4545i	−0.442459	−	0.766362i	0.555412	−	0.831575i	$-0.312560\pi$
$461$	−9.50000	−	16.4545i	−0.442459	−	0.766362i	−0.997871	+	0.0652135i	$0.979227\pi$
$462$		0			0
$463$	6.50000	−	11.2583i	0.302081	−	0.523219i	−0.674526	−	0.738251i	$-0.735652\pi$
$463$	6.50000	−	11.2583i	0.302081	−	0.523219i	0.976607	+	0.215032i	$0.0689855\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−13.5000	−	23.3827i	−0.624705	−	1.08202i	−0.988598	−	0.150581i	$-0.951886\pi$
$467$	−13.5000	−	23.3827i	−0.624705	−	1.08202i	0.363892	−	0.931441i	$-0.381448\pi$
$468$		0			0
$469$	8.00000	−	6.92820i	0.369406	−	0.319915i
$470$		0			0
$471$	21.0000	+	12.1244i	0.967629	+	0.558661i
$472$		0			0
$473$	2.50000	+	4.33013i	0.114950	+	0.199099i
$474$		0			0
$475$	−2.00000	−	3.46410i	−0.0917663	−	0.158944i
$476$		0			0
$477$	−13.5000	−	23.3827i	−0.618123	−	1.07062i
$478$		0			0
$479$	−25.0000			−1.14228			−0.571140	−	0.820853i	$-0.693499\pi$
$479$	−25.0000			−1.14228			−0.571140	+	0.820853i	$0.693499\pi$
$480$		0			0
$481$	−15.0000			−0.683941
$482$		0			0
$483$	9.00000	+	10.3923i	0.409514	+	0.472866i
$484$		0			0
$485$	−4.50000	−	7.79423i	−0.204334	−	0.353918i
$486$		0			0
$487$	9.50000	−	16.4545i	0.430486	−	0.745624i	−0.566429	−	0.824110i	$-0.691675\pi$
$487$	9.50000	−	16.4545i	0.430486	−	0.745624i	0.996915	+	0.0784867i	$0.0250088\pi$
$488$		0			0
$489$	−16.5000	−	9.52628i	−0.746156	−	0.430793i
$490$		0			0
$491$	6.50000	−	11.2583i	0.293341	−	0.508081i	−0.681257	−	0.732045i	$-0.738566\pi$
$491$	6.50000	−	11.2583i	0.293341	−	0.508081i	0.974598	+	0.223963i	$0.0718996\pi$
$492$		0			0
$493$	−3.00000			−0.135113
$494$		0			0
$495$	7.50000	−	12.9904i	0.337100	−	0.583874i
$496$		0			0
$497$	−6.00000	−	31.1769i	−0.269137	−	1.39848i
$498$		0			0
$499$	−31.0000			−1.38775			−0.693875	−	0.720095i	$-0.744098\pi$
$499$	−31.0000			−1.38775			−0.693875	+	0.720095i	$0.744098\pi$
$500$		0			0
$501$			32.9090i			1.47026i
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	17.0000			0.756490
$506$		0			0
$507$	−18.0000	−	10.3923i	−0.799408	−	0.461538i
$508$		0			0
$509$	−29.0000			−1.28540			−0.642701	−	0.766117i	$-0.722186\pi$
$509$	−29.0000			−1.28540			−0.642701	+	0.766117i	$0.722186\pi$
$510$		0			0
$511$	7.50000	+	2.59808i	0.331780	+	0.114932i
$512$		0			0
$513$	4.50000	−	2.59808i	0.198680	−	0.114708i
$514$		0			0
$515$	−1.00000			−0.0440653
$516$		0			0
$517$		0			0
$518$		0			0
$519$		−	24.2487i		−	1.06440i
$520$		0			0
$521$	−1.50000	+	2.59808i	−0.0657162	+	0.113824i	−0.897011	−	0.442007i	$-0.854267\pi$
$521$	−1.50000	+	2.59808i	−0.0657162	+	0.113824i	0.831295	+	0.555831i	$0.187600\pi$
$522$		0			0
$523$	0.500000	+	0.866025i	0.0218635	+	0.0378686i	0.876750	−	0.480946i	$-0.159707\pi$
$523$	0.500000	+	0.866025i	0.0218635	+	0.0378686i	−0.854887	+	0.518815i	$0.826373\pi$
$524$		0			0
$525$	12.0000	+	13.8564i	0.523723	+	0.604743i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−14.0000			−0.608696
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−12.5000	−	21.6506i	−0.541435	−	0.937793i
$534$		0			0
$535$	−8.50000	−	14.7224i	−0.367487	−	0.636506i
$536$		0			0
$537$		−	32.9090i		−	1.42013i
$538$		0			0
$539$	32.5000	−	12.9904i	1.39987	−	0.559535i
$540$		0			0
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	0.999042	+	0.0437584i	$0.0139332\pi$
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	−0.461625	+	0.887075i	$0.652733\pi$
$542$		0			0
$543$	−21.0000	+	12.1244i	−0.901196	+	0.520306i
$544$		0			0
$545$	−4.50000	+	7.79423i	−0.192759	+	0.333868i
$546$		0			0
$547$	−14.5000	−	25.1147i	−0.619975	−	1.07383i	−0.989490	−	0.144604i	$-0.953809\pi$
$547$	−14.5000	−	25.1147i	−0.619975	−	1.07383i	0.369514	−	0.929225i	$-0.379524\pi$
$548$		0			0
$549$	−21.0000	−	36.3731i	−0.896258	−	1.55236i
$550$		0			0
$551$	−0.500000	+	0.866025i	−0.0213007	+	0.0368939i
$552$		0			0
$553$	−20.0000	−	6.92820i	−0.850487	−	0.294617i
$554$		0			0
$555$	4.50000	+	2.59808i	0.191014	+	0.110282i
$556$		0			0
$557$	18.5000	−	32.0429i	0.783870	−	1.35770i	−0.145802	−	0.989314i	$-0.546576\pi$
$557$	18.5000	−	32.0429i	0.783870	−	1.35770i	0.929672	−	0.368389i	$-0.120091\pi$
$558$		0			0
$559$	−5.00000			−0.211477
$560$		0			0
$561$		−	25.9808i		−	1.09691i
$562$		0			0
$563$	−14.0000	−	24.2487i	−0.590030	−	1.02196i	−0.994228	−	0.107290i	$-0.965783\pi$
$563$	−14.0000	−	24.2487i	−0.590030	−	1.02196i	0.404198	−	0.914671i	$-0.367551\pi$
$564$		0			0
$565$	−0.500000	+	0.866025i	−0.0210352	+	0.0364340i
$566$		0			0
$567$	−18.0000	+	15.5885i	−0.755929	+	0.654654i
$568$		0			0
$569$	17.0000	−	29.4449i	0.712677	−	1.23439i	−0.251172	−	0.967943i	$-0.580816\pi$
$569$	17.0000	−	29.4449i	0.712677	−	1.23439i	0.963849	−	0.266450i	$-0.0858508\pi$
$570$		0			0
$571$	16.0000	+	27.7128i	0.669579	+	1.15975i	0.978022	+	0.208502i	$0.0668588\pi$
$571$	16.0000	+	27.7128i	0.669579	+	1.15975i	−0.308443	+	0.951243i	$0.599808\pi$
$572$		0			0
$573$		−	13.8564i		−	0.578860i
$574$		0			0
$575$	12.0000			0.500435
$576$		0			0
$577$	−15.5000	+	26.8468i	−0.645273	+	1.11765i	0.338965	+	0.940799i	$0.389923\pi$
$577$	−15.5000	+	26.8468i	−0.645273	+	1.11765i	−0.984238	+	0.176847i	$0.943410\pi$
$578$		0			0
$579$	15.0000	+	8.66025i	0.623379	+	0.359908i
$580$		0			0
$581$	−18.0000	+	15.5885i	−0.746766	+	0.646718i
$582$		0			0
$583$	−22.5000	+	38.9711i	−0.931855	+	1.61402i
$584$		0			0
$585$	7.50000	+	12.9904i	0.310087	+	0.537086i
$586$		0			0
$587$	−18.5000	−	32.0429i	−0.763577	−	1.32255i	−0.940996	−	0.338418i	$-0.890108\pi$
$587$	−18.5000	−	32.0429i	−0.763577	−	1.32255i	0.177419	−	0.984135i	$-0.443225\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	3.00000	−	1.73205i	0.123404	−	0.0712470i
$592$		0			0
$593$	−7.50000	−	12.9904i	−0.307988	−	0.533451i	0.669934	−	0.742421i	$-0.266322\pi$
$593$	−7.50000	−	12.9904i	−0.307988	−	0.533451i	−0.977922	+	0.208970i	$0.932989\pi$
$594$		0			0
$595$	−7.50000	−	2.59808i	−0.307470	−	0.106511i
$596$		0			0
$597$		−	5.19615i		−	0.212664i
$598$		0			0
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	0.509631	−	0.860393i	$-0.329782\pi$
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	−0.999938	+	0.0111569i	$0.996449\pi$
$600$		0			0
$601$	4.50000	+	7.79423i	0.183559	+	0.317933i	0.943090	−	0.332538i	$-0.107905\pi$
$601$	4.50000	+	7.79423i	0.183559	+	0.317933i	−0.759531	+	0.650471i	$0.774572\pi$
$602$		0			0
$603$	12.0000			0.488678
$604$		0			0
$605$	−14.0000			−0.569181
$606$		0			0
$607$	1.00000			0.0405887			0.0202944	−	0.999794i	$-0.493540\pi$
$607$	1.00000			0.0405887			0.0202944	+	0.999794i	$0.493540\pi$
$608$		0			0
$609$	1.50000	−	4.33013i	0.0607831	−	0.175466i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−9.50000	+	16.4545i	−0.383701	+	0.664590i	−0.991588	−	0.129433i	$-0.958684\pi$
$613$	−9.50000	+	16.4545i	−0.383701	+	0.664590i	0.607887	+	0.794024i	$0.292017\pi$
$614$		0			0
$615$			8.66025i			0.349215i
$616$		0			0
$617$	−13.5000	+	23.3827i	−0.543490	+	0.941351i	0.455211	+	0.890384i	$0.349564\pi$
$617$	−13.5000	+	23.3827i	−0.543490	+	0.941351i	−0.998700	+	0.0509678i	$0.983769\pi$
$618$		0			0
$619$	−25.0000			−1.00483			−0.502417	−	0.864625i	$-0.667556\pi$
$619$	−25.0000			−1.00483			−0.502417	+	0.864625i	$0.667556\pi$
$620$		0			0
$621$			15.5885i			0.625543i
$622$		0			0
$623$	26.0000	−	22.5167i	1.04167	−	0.902111i
$624$		0			0
$625$	11.0000			0.440000
$626$		0			0
$627$	−7.50000	−	4.33013i	−0.299521	−	0.172929i
$628$		0			0
$629$	9.00000			0.358854
$630$		0			0
$631$	40.0000			1.59237			0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000			1.59237			0.796187	+	0.605050i	$0.206847\pi$
$632$		0			0
$633$		−	22.5167i		−	0.894957i
$634$		0			0
$635$	−12.0000			−0.476205
$636$		0			0
$637$	−5.00000	+	34.6410i	−0.198107	+	1.37253i
$638$		0			0
$639$	18.0000	−	31.1769i	0.712069	−	1.23334i
$640$		0			0
$641$	−9.00000			−0.355479			−0.177739	−	0.984078i	$-0.556878\pi$
$641$	−9.00000			−0.355479			−0.177739	+	0.984078i	$0.556878\pi$
$642$		0			0
$643$	−9.50000	+	16.4545i	−0.374643	+	0.648901i	−0.990274	−	0.139134i	$-0.955568\pi$
$643$	−9.50000	+	16.4545i	−0.374643	+	0.648901i	0.615630	+	0.788035i	$0.288902\pi$
$644$		0			0
$645$	1.50000	+	0.866025i	0.0590624	+	0.0340997i
$646$		0			0
$647$	15.5000	−	26.8468i	0.609368	−	1.05546i	−0.381977	−	0.924172i	$-0.624757\pi$
$647$	15.5000	−	26.8468i	0.609368	−	1.05546i	0.991345	−	0.131284i	$-0.0419101\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3.00000			0.117399			0.0586995	−	0.998276i	$-0.481305\pi$
$653$	3.00000			0.117399			0.0586995	+	0.998276i	$0.481305\pi$
$654$		0			0
$655$	−1.00000			−0.0390732
$656$		0			0
$657$	4.50000	+	7.79423i	0.175562	+	0.304082i
$658$		0			0
$659$	13.5000	+	23.3827i	0.525885	+	0.910860i	0.999545	+	0.0301523i	$0.00959924\pi$
$659$	13.5000	+	23.3827i	0.525885	+	0.910860i	−0.473660	+	0.880708i	$0.657067\pi$
$660$		0			0
$661$	7.00000	+	12.1244i	0.272268	+	0.471583i	0.969442	−	0.245319i	$-0.0788928\pi$
$661$	7.00000	+	12.1244i	0.272268	+	0.471583i	−0.697174	+	0.716902i	$0.745559\pi$
$662$		0			0
$663$	22.5000	+	12.9904i	0.873828	+	0.504505i
$664$		0			0
$665$	−2.00000	+	1.73205i	−0.0775567	+	0.0671660i
$666$		0			0
$667$	−1.50000	−	2.59808i	−0.0580802	−	0.100598i
$668$		0			0
$669$	28.5000	+	16.4545i	1.10187	+	0.636167i
$670$		0			0
$671$	−35.0000	+	60.6218i	−1.35116	+	2.34028i
$672$		0			0
$673$	14.5000	+	25.1147i	0.558934	+	0.968102i	0.997586	+	0.0694449i	$0.0221228\pi$
$673$	14.5000	+	25.1147i	0.558934	+	0.968102i	−0.438652	+	0.898657i	$0.644544\pi$
$674$		0			0
$675$			20.7846i			0.800000i
$676$		0			0
$677$	−21.0000	+	36.3731i	−0.807096	+	1.39793i	0.107772	+	0.994176i	$0.465628\pi$
$677$	−21.0000	+	36.3731i	−0.807096	+	1.39793i	−0.914867	+	0.403755i	$0.867705\pi$
$678$		0			0
$679$	18.0000	−	15.5885i	0.690777	−	0.598230i
$680$		0			0
$681$	4.50000	−	2.59808i	0.172440	−	0.0995585i
$682$		0			0
$683$	−4.50000	+	7.79423i	−0.172188	+	0.298238i	−0.939184	−	0.343413i	$-0.888417\pi$
$683$	−4.50000	+	7.79423i	−0.172188	+	0.298238i	0.766997	+	0.641651i	$0.221750\pi$
$684$		0			0
$685$	9.00000			0.343872
$686$		0			0
$687$	−1.50000	+	0.866025i	−0.0572286	+	0.0330409i
$688$		0			0
$689$	−22.5000	−	38.9711i	−0.857182	−	1.48468i
$690$		0			0
$691$	−14.0000	+	24.2487i	−0.532585	+	0.922464i	0.466691	+	0.884420i	$0.345446\pi$
$691$	−14.0000	+	24.2487i	−0.532585	+	0.922464i	−0.999276	+	0.0380440i	$0.987887\pi$
$692$		0			0
$693$	37.5000	+	12.9904i	1.42451	+	0.493464i
$694$		0			0
$695$	−4.50000	+	7.79423i	−0.170695	+	0.295652i
$696$		0			0
$697$	7.50000	+	12.9904i	0.284083	+	0.492046i
$698$		0			0
$699$	−4.50000	−	2.59808i	−0.170206	−	0.0982683i
$700$		0			0
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$		0			0
$703$	1.50000	−	2.59808i	0.0565736	−	0.0979883i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	8.50000	+	44.1673i	0.319675	+	1.66108i
$708$		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
$711$	−12.0000	−	20.7846i	−0.450035	−	0.779484i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	12.5000	−	21.6506i	0.467473	−	0.809688i
$716$		0			0
$717$			25.9808i			0.970269i
$718$		0			0
$719$	−13.5000	−	23.3827i	−0.503465	−	0.872027i	−0.999992	−	0.00400572i	$-0.998725\pi$
$719$	−13.5000	−	23.3827i	−0.503465	−	0.872027i	0.496527	−	0.868021i	$-0.334608\pi$
$720$		0			0
$721$	−0.500000	−	2.59808i	−0.0186210	−	0.0967574i
$722$		0			0
$723$	16.5000	−	9.52628i	0.613642	−	0.354286i
$724$		0			0
$725$	−2.00000	−	3.46410i	−0.0742781	−	0.128654i
$726$		0			0
$727$	23.5000	+	40.7032i	0.871567	+	1.50960i	0.860376	+	0.509661i	$0.170229\pi$
$727$	23.5000	+	40.7032i	0.871567	+	1.50960i	0.0111912	+	0.999937i	$0.496438\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	3.00000			0.110959
$732$		0			0
$733$	27.0000			0.997268			0.498634	−	0.866813i	$-0.333835\pi$
$733$	27.0000			0.997268			0.498634	+	0.866813i	$0.333835\pi$
$734$		0			0
$735$	7.50000	−	9.52628i	0.276642	−	0.351382i
$736$		0			0
$737$	−10.0000	−	17.3205i	−0.368355	−	0.638009i
$738$		0			0
$739$	−4.50000	+	7.79423i	−0.165535	+	0.286715i	−0.936845	−	0.349744i	$-0.886268\pi$
$739$	−4.50000	+	7.79423i	−0.165535	+	0.286715i	0.771310	+	0.636460i	$0.219602\pi$
$740$		0			0
$741$	7.50000	−	4.33013i	0.275519	−	0.159071i
$742$		0			0
$743$	−7.50000	+	12.9904i	−0.275148	+	0.476571i	−0.970173	−	0.242415i	$-0.922060\pi$
$743$	−7.50000	+	12.9904i	−0.275148	+	0.476571i	0.695024	+	0.718986i	$0.255394\pi$
$744$		0			0
$745$	−3.00000			−0.109911
$746$		0			0
$747$	−27.0000			−0.987878
$748$		0			0
$749$	34.0000	−	29.4449i	1.24233	−	1.07589i
$750$		0			0
$751$	−31.0000			−1.13121			−0.565603	−	0.824678i	$-0.691357\pi$
$751$	−31.0000			−1.13121			−0.565603	+	0.824678i	$0.691357\pi$
$752$		0			0
$753$	42.0000	−	24.2487i	1.53057	−	0.883672i
$754$		0			0
$755$	5.00000			0.181969
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$		0			0
$759$	22.5000	−	12.9904i	0.816698	−	0.471521i
$760$		0			0
$761$	27.0000			0.978749			0.489375	−	0.872074i	$-0.337225\pi$
$761$	27.0000			0.978749			0.489375	+	0.872074i	$0.337225\pi$
$762$		0			0
$763$	−22.5000	−	7.79423i	−0.814555	−	0.282170i
$764$		0			0
$765$	−4.50000	−	7.79423i	−0.162698	−	0.281801i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−11.5000	+	19.9186i	−0.414701	+	0.718283i	−0.995397	−	0.0958377i	$-0.969447\pi$
$769$	−11.5000	+	19.9186i	−0.414701	+	0.718283i	0.580696	+	0.814120i	$0.302780\pi$
$770$		0			0
$771$	−43.5000	+	25.1147i	−1.56661	+	0.904485i
$772$		0			0
$773$	−15.5000	+	26.8468i	−0.557496	+	0.965612i	0.440208	+	0.897896i	$0.354905\pi$
$773$	−15.5000	+	26.8468i	−0.557496	+	0.965612i	−0.997705	+	0.0677162i	$0.978429\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−4.50000	+	12.9904i	−0.161437	+	0.466027i
$778$		0			0
$779$	5.00000			0.179144
$780$		0			0
$781$	−60.0000			−2.14697
$782$		0			0
$783$	4.50000	−	2.59808i	0.160817	−	0.0928477i
$784$		0			0
$785$	−7.00000	−	12.1244i	−0.249841	−	0.432737i
$786$		0			0
$787$	14.0000	+	24.2487i	0.499046	+	0.864373i	0.999999	−	0.00110111i	$-0.000350496\pi$
$787$	14.0000	+	24.2487i	0.499046	+	0.864373i	−0.500953	+	0.865474i	$0.667017\pi$
$788$		0			0
$789$	−7.50000	+	4.33013i	−0.267007	+	0.154157i
$790$		0			0
$791$	−2.50000	−	0.866025i	−0.0888898	−	0.0307923i
$792$		0			0
$793$	−35.0000	−	60.6218i	−1.24289	−	2.15274i
$794$		0			0
$795$			15.5885i			0.552866i
$796$		0			0
$797$	−11.5000	+	19.9186i	−0.407351	+	0.705552i	−0.994592	−	0.103860i	$-0.966881\pi$
$797$	−11.5000	+	19.9186i	−0.407351	+	0.705552i	0.587241	+	0.809412i	$0.300214\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	39.0000			1.37800
$802$		0			0
$803$	7.50000	−	12.9904i	0.264669	−	0.458421i
$804$		0			0
$805$	−1.50000	−	7.79423i	−0.0528681	−	0.274710i
$806$		0			0
$807$			5.19615i			0.182913i
$808$		0			0
$809$	4.50000	−	7.79423i	0.158212	−	0.274030i	−0.776012	−	0.630718i	$-0.782761\pi$
$809$	4.50000	−	7.79423i	0.158212	−	0.274030i	0.934224	+	0.356687i	$0.116094\pi$
$810$		0			0
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$		0			0
$813$	1.50000	+	0.866025i	0.0526073	+	0.0303728i
$814$		0			0
$815$	5.50000	+	9.52628i	0.192657	+	0.333691i
$816$		0			0
$817$	0.500000	−	0.866025i	0.0174928	−	0.0302984i
$818$		0			0
$819$	−30.0000	+	25.9808i	−1.04828	+	0.907841i
$820$		0			0
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	−0.991616	−	0.129217i	$-0.958754\pi$
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	0.607714	+	0.794156i	$0.292087\pi$
$822$		0			0
$823$	−12.0000	−	20.7846i	−0.418294	−	0.724506i	0.577474	−	0.816409i	$-0.304038\pi$
$823$	−12.0000	−	20.7846i	−0.418294	−	0.724506i	−0.995768	+	0.0919029i	$0.970705\pi$
$824$		0			0
$825$	30.0000	−	17.3205i	1.04447	−	0.603023i
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	12.5000	−	21.6506i	0.434143	−	0.751958i	−0.563082	−	0.826401i	$-0.690385\pi$
$829$	12.5000	−	21.6506i	0.434143	−	0.751958i	0.997225	+	0.0744432i	$0.0237179\pi$
$830$		0			0
$831$	28.5000	−	16.4545i	0.988654	−	0.570800i
$832$		0			0
$833$	3.00000	−	20.7846i	0.103944	−	0.720144i
$834$		0			0
$835$	9.50000	−	16.4545i	0.328761	−	0.569431i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−18.5000	−	32.0429i	−0.638691	−	1.10625i	−0.985720	−	0.168391i	$-0.946143\pi$
$839$	−18.5000	−	32.0429i	−0.638691	−	1.10625i	0.347029	−	0.937854i	$-0.387190\pi$
$840$		0			0
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$		0			0
$843$	43.5000	+	25.1147i	1.49822	+	0.864997i
$844$		0			0
$845$	6.00000	+	10.3923i	0.206406	+	0.357506i
$846$		0			0
$847$	−7.00000	−	36.3731i	−0.240523	−	1.24979i
$848$		0			0
$849$	42.0000	+	24.2487i	1.44144	+	0.832214i
$850$		0			0
$851$	4.50000	+	7.79423i	0.154258	+	0.267183i
$852$		0			0
$853$	18.5000	+	32.0429i	0.633428	+	1.09713i	0.986846	+	0.161664i	$0.0516860\pi$
$853$	18.5000	+	32.0429i	0.633428	+	1.09713i	−0.353418	+	0.935466i	$0.614981\pi$
$854$		0			0
$855$	−3.00000			−0.102598
$856$		0			0
$857$	11.0000			0.375753			0.187876	−	0.982193i	$-0.439840\pi$
$857$	11.0000			0.375753			0.187876	+	0.982193i	$0.439840\pi$
$858$		0			0
$859$	1.00000			0.0341196			0.0170598	−	0.999854i	$-0.494569\pi$
$859$	1.00000			0.0341196			0.0170598	+	0.999854i	$0.494569\pi$
$860$		0			0
$861$	−22.5000	+	4.33013i	−0.766798	+	0.147570i
$862$		0			0
$863$	−19.5000	−	33.7750i	−0.663788	−	1.14971i	−0.979612	−	0.200897i	$-0.935615\pi$
$863$	−19.5000	−	33.7750i	−0.663788	−	1.14971i	0.315825	−	0.948818i	$-0.397719\pi$
$864$		0			0
$865$	−7.00000	+	12.1244i	−0.238007	+	0.412240i
$866$		0			0
$867$	12.0000	+	6.92820i	0.407541	+	0.235294i
$868$		0			0
$869$	−20.0000	+	34.6410i	−0.678454	+	1.17512i
$870$		0			0
$871$	20.0000			0.677674
$872$		0			0
$873$	27.0000			0.913812
$874$		0			0
$875$	−4.50000	−	23.3827i	−0.152128	−	0.790479i
$876$		0			0
$877$	−53.0000			−1.78968			−0.894841	−	0.446384i	$-0.852711\pi$
$877$	−53.0000			−1.78968			−0.894841	+	0.446384i	$0.852711\pi$
$878$		0			0
$879$		−	8.66025i		−	0.292103i
$880$		0			0
$881$	−42.0000			−1.41502			−0.707508	−	0.706705i	$-0.750181\pi$
$881$	−42.0000			−1.41502			−0.707508	+	0.706705i	$0.750181\pi$
$882$		0			0
$883$	−44.0000			−1.48072			−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000			−1.48072			−0.740359	+	0.672212i	$0.765344\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	29.0000			0.973725			0.486862	−	0.873479i	$-0.338141\pi$
$887$	29.0000			0.973725			0.486862	+	0.873479i	$0.338141\pi$
$888$		0			0
$889$	−6.00000	−	31.1769i	−0.201234	−	1.04564i
$890$		0			0
$891$	22.5000	+	38.9711i	0.753778	+	1.30558i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−9.50000	+	16.4545i	−0.317550	+	0.550013i
$896$		0			0
$897$			25.9808i			0.867472i
$898$		0			0
$899$		0			0
$900$		0			0
$901$	13.5000	+	23.3827i	0.449750	+	0.778990i
$902$		0			0
$903$	−1.50000	+	4.33013i	−0.0499169	+	0.144098i
$904$		0			0
$905$	14.0000			0.465376
$906$		0			0
$907$	−5.00000			−0.166022			−0.0830111	−	0.996549i	$-0.526454\pi$
$907$	−5.00000			−0.166022			−0.0830111	+	0.996549i	$0.526454\pi$
$908$		0			0
$909$	−25.5000	+	44.1673i	−0.845782	+	1.46494i
$910$		0			0
$911$	13.5000	+	23.3827i	0.447275	+	0.774703i	0.998208	−	0.0598468i	$-0.0190612\pi$
$911$	13.5000	+	23.3827i	0.447275	+	0.774703i	−0.550933	+	0.834550i	$0.685728\pi$
$912$		0			0
$913$	22.5000	+	38.9711i	0.744641	+	1.28976i
$914$		0			0
$915$			24.2487i			0.801638i
$916$		0			0
$917$	−0.500000	−	2.59808i	−0.0165115	−	0.0857960i
$918$		0			0
$919$	8.50000	+	14.7224i	0.280389	+	0.485648i	0.971481	−	0.237119i	$-0.0762032\pi$
$919$	8.50000	+	14.7224i	0.280389	+	0.485648i	−0.691091	+	0.722767i	$0.742870\pi$
$920$		0			0
$921$	−42.0000	+	24.2487i	−1.38395	+	0.799022i
$922$		0			0
$923$	30.0000	−	51.9615i	0.987462	−	1.71033i
$924$		0			0
$925$	6.00000	+	10.3923i	0.197279	+	0.341697i
$926$		0			0
$927$	1.50000	−	2.59808i	0.0492665	−	0.0853320i
$928$		0			0
$929$	7.00000	−	12.1244i	0.229663	−	0.397787i	−0.728046	−	0.685529i	$-0.759571\pi$
$929$	7.00000	−	12.1244i	0.229663	−	0.397787i	0.957708	+	0.287742i	$0.0929044\pi$
$930$		0			0
$931$	−5.50000	−	4.33013i	−0.180255	−	0.141914i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−7.50000	+	12.9904i	−0.245276	+	0.424831i
$936$		0			0
$937$	42.0000			1.37208			0.686040	−	0.727564i	$-0.259347\pi$
$937$	42.0000			1.37208			0.686040	+	0.727564i	$0.259347\pi$
$938$		0			0
$939$			24.2487i			0.791327i
$940$		0			0
$941$	7.00000	+	12.1244i	0.228193	+	0.395243i	0.957273	−	0.289187i	$-0.0933848\pi$
$941$	7.00000	+	12.1244i	0.228193	+	0.395243i	−0.729079	+	0.684429i	$0.760051\pi$
$942$		0			0
$943$	−7.50000	+	12.9904i	−0.244234	+	0.423025i
$944$		0			0
$945$	13.5000	−	2.59808i	0.439155	−	0.0845154i
$946$		0			0
$947$	−10.0000	+	17.3205i	−0.324956	+	0.562841i	−0.981504	−	0.191444i	$-0.938683\pi$
$947$	−10.0000	+	17.3205i	−0.324956	+	0.562841i	0.656547	+	0.754285i	$0.272016\pi$
$948$		0			0
$949$	7.50000	+	12.9904i	0.243460	+	0.421686i
$950$		0			0
$951$		−	10.3923i		−	0.336994i
$952$		0			0
$953$	−26.0000			−0.842223			−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000			−0.842223			−0.421111	+	0.907009i	$0.638360\pi$
$954$		0			0
$955$	−4.00000	+	6.92820i	−0.129437	+	0.224191i
$956$		0			0
$957$	−7.50000	−	4.33013i	−0.242441	−	0.139973i
$958$		0			0
$959$	4.50000	+	23.3827i	0.145313	+	0.755066i
$960$		0			0
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$		0			0
$963$	51.0000			1.64345
$964$		0			0
$965$	−5.00000	−	8.66025i	−0.160956	−	0.278783i
$966$		0			0
$967$	6.50000	−	11.2583i	0.209026	−	0.362043i	−0.742382	−	0.669977i	$-0.766304\pi$
$967$	6.50000	−	11.2583i	0.209026	−	0.362043i	0.951408	+	0.307933i	$0.0996374\pi$
$968$		0			0
$969$	−4.50000	+	2.59808i	−0.144561	+	0.0834622i
$970$		0			0
$971$	28.5000	+	49.3634i	0.914609	+	1.58415i	0.807473	+	0.589904i	$0.200834\pi$
$971$	28.5000	+	49.3634i	0.914609	+	1.58415i	0.107135	+	0.994244i	$0.465832\pi$
$972$		0			0
$973$	−22.5000	−	7.79423i	−0.721317	−	0.249871i
$974$		0			0
$975$			34.6410i			1.10940i
$976$		0			0
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	0.685381	−	0.728184i	$-0.259636\pi$
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	−0.973317	+	0.229465i	$0.926302\pi$
$978$		0			0
$979$	−32.5000	−	56.2917i	−1.03870	−	1.79909i
$980$		0			0
$981$	−13.5000	−	23.3827i	−0.431022	−	0.746552i
$982$		0			0
$983$	3.00000			0.0956851			0.0478426	−	0.998855i	$-0.484765\pi$
$983$	3.00000			0.0956851			0.0478426	+	0.998855i	$0.484765\pi$
$984$		0			0
$985$	−2.00000			−0.0637253
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.50000	+	2.59808i	0.0476972	+	0.0826140i
$990$		0			0
$991$	−18.5000	+	32.0429i	−0.587672	+	1.01788i	0.406865	+	0.913488i	$0.366622\pi$
$991$	−18.5000	+	32.0429i	−0.587672	+	1.01788i	−0.994537	+	0.104389i	$0.966711\pi$
$992$		0			0
$993$		−	13.8564i		−	0.439720i
$994$		0			0
$995$	−1.50000	+	2.59808i	−0.0475532	+	0.0823646i
$996$		0			0
$997$	−17.0000			−0.538395			−0.269198	−	0.963085i	$-0.586759\pi$
$997$	−17.0000			−0.538395			−0.269198	+	0.963085i	$0.586759\pi$
$998$		0			0
$999$	−13.5000	+	7.79423i	−0.427121	+	0.246598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.t.d.193.1		2
3.2	odd	2		3024.2.t.d.1873.1		2
4.3	odd	2		63.2.g.a.4.1	✓	2
7.2	even	3		1008.2.q.c.625.1		2
9.2	odd	6		3024.2.q.b.2881.1		2
9.7	even	3		1008.2.q.c.529.1		2
12.11	even	2		189.2.g.a.172.1		2
21.2	odd	6		3024.2.q.b.2305.1		2
28.3	even	6		441.2.f.a.148.1		2
28.11	odd	6		441.2.f.b.148.1		2
28.19	even	6		441.2.h.a.373.1		2
28.23	odd	6		63.2.h.a.58.1	yes	2
28.27	even	2		441.2.g.a.67.1		2
36.7	odd	6		63.2.h.a.25.1	yes	2
36.11	even	6		189.2.h.a.46.1		2
36.23	even	6		567.2.e.b.487.1		2
36.31	odd	6		567.2.e.a.487.1		2
63.2	odd	6		3024.2.t.d.289.1		2
63.16	even	3	inner	1008.2.t.d.961.1		2
84.11	even	6		1323.2.f.a.442.1		2
84.23	even	6		189.2.h.a.37.1		2
84.47	odd	6		1323.2.h.a.226.1		2
84.59	odd	6		1323.2.f.b.442.1		2
84.83	odd	2		1323.2.g.a.361.1		2
252.11	even	6		1323.2.f.a.883.1		2
252.23	even	6		567.2.e.b.163.1		2
252.31	even	6		3969.2.a.f.1.1		1
252.47	odd	6		1323.2.g.a.667.1		2
252.59	odd	6		3969.2.a.a.1.1		1
252.67	odd	6		3969.2.a.d.1.1		1
252.79	odd	6		63.2.g.a.16.1	yes	2
252.83	odd	6		1323.2.h.a.802.1		2
252.95	even	6		3969.2.a.c.1.1		1
252.115	even	6		441.2.f.a.295.1		2
252.151	odd	6		441.2.f.b.295.1		2
252.187	even	6		441.2.g.a.79.1		2
252.191	even	6		189.2.g.a.100.1		2
252.223	even	6		441.2.h.a.214.1		2
252.227	odd	6		1323.2.f.b.883.1		2
252.247	odd	6		567.2.e.a.163.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.a.4.1	✓	2	4.3	odd	2
63.2.g.a.16.1	yes	2	252.79	odd	6
63.2.h.a.25.1	yes	2	36.7	odd	6
63.2.h.a.58.1	yes	2	28.23	odd	6
189.2.g.a.100.1		2	252.191	even	6
189.2.g.a.172.1		2	12.11	even	2
189.2.h.a.37.1		2	84.23	even	6
189.2.h.a.46.1		2	36.11	even	6
441.2.f.a.148.1		2	28.3	even	6
441.2.f.a.295.1		2	252.115	even	6
441.2.f.b.148.1		2	28.11	odd	6
441.2.f.b.295.1		2	252.151	odd	6
441.2.g.a.67.1		2	28.27	even	2
441.2.g.a.79.1		2	252.187	even	6
441.2.h.a.214.1		2	252.223	even	6
441.2.h.a.373.1		2	28.19	even	6
567.2.e.a.163.1		2	252.247	odd	6
567.2.e.a.487.1		2	36.31	odd	6
567.2.e.b.163.1		2	252.23	even	6
567.2.e.b.487.1		2	36.23	even	6
1008.2.q.c.529.1		2	9.7	even	3
1008.2.q.c.625.1		2	7.2	even	3
1008.2.t.d.193.1		2	1.1	even	1	trivial
1008.2.t.d.961.1		2	63.16	even	3	inner
1323.2.f.a.442.1		2	84.11	even	6
1323.2.f.a.883.1		2	252.11	even	6
1323.2.f.b.442.1		2	84.59	odd	6
1323.2.f.b.883.1		2	252.227	odd	6
1323.2.g.a.361.1		2	84.83	odd	2
1323.2.g.a.667.1		2	252.47	odd	6
1323.2.h.a.226.1		2	84.47	odd	6
1323.2.h.a.802.1		2	252.83	odd	6
3024.2.q.b.2305.1		2	21.2	odd	6
3024.2.q.b.2881.1		2	9.2	odd	6
3024.2.t.d.289.1		2	63.2	odd	6
3024.2.t.d.1873.1		2	3.2	odd	2
3969.2.a.a.1.1		1	252.59	odd	6
3969.2.a.c.1.1		1	252.95	even	6
3969.2.a.d.1.1		1	252.67	odd	6
3969.2.a.f.1.1		1	252.31	even	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{3} -1.00000 q^{5} +(-0.500000 - 2.59808i) q^{7} +(1.50000 - 2.59808i) q^{9} -5.00000 q^{11} +(2.50000 - 4.33013i) q^{13} +(-1.50000 + 0.866025i) q^{15} +(-1.50000 + 2.59808i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-3.00000 - 3.46410i) q^{21} -3.00000 q^{23} -4.00000 q^{25} -5.19615i q^{27} +(0.500000 + 0.866025i) q^{29} +(-7.50000 + 4.33013i) q^{33} +(0.500000 + 2.59808i) q^{35} +(-1.50000 - 2.59808i) q^{37} -8.66025i q^{39} +(2.50000 - 4.33013i) q^{41} +(-0.500000 - 0.866025i) q^{43} +(-1.50000 + 2.59808i) q^{45} +(-6.50000 + 2.59808i) q^{49} +5.19615i q^{51} +(4.50000 - 7.79423i) q^{53} +5.00000 q^{55} +(1.50000 + 0.866025i) q^{57} +(7.00000 - 12.1244i) q^{61} +(-7.50000 - 2.59808i) q^{63} +(-2.50000 + 4.33013i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-4.50000 + 2.59808i) q^{69} +12.0000 q^{71} +(-1.50000 + 2.59808i) q^{73} +(-6.00000 + 3.46410i) q^{75} +(2.50000 + 12.9904i) q^{77} +(4.00000 - 6.92820i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-4.50000 - 7.79423i) q^{83} +(1.50000 - 2.59808i) q^{85} +(1.50000 + 0.866025i) q^{87} +(6.50000 + 11.2583i) q^{89} +(-12.5000 - 4.33013i) q^{91} +(-0.500000 - 0.866025i) q^{95} +(4.50000 + 7.79423i) q^{97} +(-7.50000 + 12.9904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} - 2 q^{5} - q^{7} + 3 q^{9} - 10 q^{11} + 5 q^{13} - 3 q^{15} - 3 q^{17} + q^{19} - 6 q^{21} - 6 q^{23} - 8 q^{25} + q^{29} - 15 q^{33} + q^{35} - 3 q^{37} + 5 q^{41} - q^{43} - 3 q^{45}+ \cdots - 15 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 - 2 * q^5 - q^7 + 3 * q^9 - 10 * q^11 + 5 * q^13 - 3 * q^15 - 3 * q^17 + q^19 - 6 * q^21 - 6 * q^23 - 8 * q^25 + q^29 - 15 * q^33 + q^35 - 3 * q^37 + 5 * q^41 - q^43 - 3 * q^45 - 13 * q^49 + 9 * q^53 + 10 * q^55 + 3 * q^57 + 14 * q^61 - 15 * q^63 - 5 * q^65 + 4 * q^67 - 9 * q^69 + 24 * q^71 - 3 * q^73 - 12 * q^75 + 5 * q^77 + 8 * q^79 - 9 * q^81 - 9 * q^83 + 3 * q^85 + 3 * q^87 + 13 * q^89 - 25 * q^91 - q^95 + 9 * q^97 - 15 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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