LMFDB - Embedded newform 312.2.bf.a.49.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [312,2,Mod(49,312)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(312, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("312.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	312.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.49133254306$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	312.49
Dual form			312.2.bf.a.121.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{3} +1.73205i q^{5} +(0.633975 + 0.366025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-0.633975 + 0.366025i) q^{11} +(2.59808 + 2.50000i) q^{13} +(-1.50000 + 0.866025i) q^{15} +(-1.86603 + 3.23205i) q^{17} +(-1.09808 - 0.633975i) q^{19} +0.732051i q^{21} +(-1.09808 - 1.90192i) q^{23} +2.00000 q^{25} -1.00000 q^{27} +(2.96410 + 5.13397i) q^{29} -5.46410i q^{31} +(-0.633975 - 0.366025i) q^{33} +(-0.633975 + 1.09808i) q^{35} +(7.33013 - 4.23205i) q^{37} +(-0.866025 + 3.50000i) q^{39} +(-4.33013 + 2.50000i) q^{41} +(0.901924 - 1.56218i) q^{43} +(-1.50000 - 0.866025i) q^{45} -6.73205i q^{47} +(-3.23205 - 5.59808i) q^{49} -3.73205 q^{51} +5.92820 q^{53} +(-0.633975 - 1.09808i) q^{55} -1.26795i q^{57} +(4.86603 - 8.42820i) q^{61} +(-0.633975 + 0.366025i) q^{63} +(-4.33013 + 4.50000i) q^{65} +(-4.56218 + 2.63397i) q^{67} +(1.09808 - 1.90192i) q^{69} +(-7.09808 - 4.09808i) q^{71} -1.19615i q^{73} +(1.00000 + 1.73205i) q^{75} -0.535898 q^{77} +12.3923 q^{79} +(-0.500000 - 0.866025i) q^{81} -15.6603i q^{83} +(-5.59808 - 3.23205i) q^{85} +(-2.96410 + 5.13397i) q^{87} +(-2.19615 + 1.26795i) q^{89} +(0.732051 + 2.53590i) q^{91} +(4.73205 - 2.73205i) q^{93} +(1.09808 - 1.90192i) q^{95} +(-8.66025 - 5.00000i) q^{97} -0.732051i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 6 q^{7} - 2 q^{9} - 6 q^{11} - 6 q^{15} - 4 q^{17} + 6 q^{19} + 6 q^{23} + 8 q^{25} - 4 q^{27} - 2 q^{29} - 6 q^{33} - 6 q^{35} + 12 q^{37} + 14 q^{43} - 6 q^{45} - 6 q^{49} - 8 q^{51} - 4 q^{53}+ \cdots - 6 q^{95}+O(q^{100}) $ 4 * q + 2 * q^3 + 6 * q^7 - 2 * q^9 - 6 * q^11 - 6 * q^15 - 4 * q^17 + 6 * q^19 + 6 * q^23 + 8 * q^25 - 4 * q^27 - 2 * q^29 - 6 * q^33 - 6 * q^35 + 12 * q^37 + 14 * q^43 - 6 * q^45 - 6 * q^49 - 8 * q^51 - 4 * q^53 - 6 * q^55 + 16 * q^61 - 6 * q^63 + 6 * q^67 - 6 * q^69 - 18 * q^71 + 4 * q^75 - 16 * q^77 + 8 * q^79 - 2 * q^81 - 12 * q^85 + 2 * q^87 + 12 * q^89 - 4 * q^91 + 12 * q^93 - 6 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$		0			0
$5$			1.73205i			0.774597i	0.921954	+	0.387298i	$0.126592\pi$
$5$			1.73205i			0.774597i	−0.921954	+	0.387298i	$0.873408\pi$
$6$		0			0
$7$	0.633975	+	0.366025i	0.239620	+	0.138345i	0.615002	−	0.788526i	$-0.289155\pi$
$7$	0.633975	+	0.366025i	0.239620	+	0.138345i	−0.375382	+	0.926870i	$0.622489\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−0.633975	+	0.366025i	−0.191151	+	0.110361i	−0.592521	−	0.805555i	$-0.701867\pi$
$11$	−0.633975	+	0.366025i	−0.191151	+	0.110361i	0.401371	+	0.915916i	$0.368534\pi$
$12$		0			0
$13$	2.59808	+	2.50000i	0.720577	+	0.693375i
$13$	2.59808	+	2.50000i	0.720577	+	0.693375i
$14$		0			0
$15$	−1.50000	+	0.866025i	−0.387298	+	0.223607i
$16$		0			0
$17$	−1.86603	+	3.23205i	−0.452578	+	0.783887i	−0.998545	−	0.0539188i	$-0.982829\pi$
$17$	−1.86603	+	3.23205i	−0.452578	+	0.783887i	0.545968	+	0.837806i	$0.316162\pi$
$18$		0			0
$19$	−1.09808	−	0.633975i	−0.251916	−	0.145444i	0.368725	−	0.929538i	$-0.379794\pi$
$19$	−1.09808	−	0.633975i	−0.251916	−	0.145444i	−0.620641	+	0.784095i	$0.713128\pi$
$20$		0			0
$21$			0.732051i			0.159747i
$22$		0			0
$23$	−1.09808	−	1.90192i	−0.228965	−	0.396579i	0.728537	−	0.685007i	$-0.240201\pi$
$23$	−1.09808	−	1.90192i	−0.228965	−	0.396579i	−0.957502	+	0.288428i	$0.906867\pi$
$24$		0			0
$25$	2.00000			0.400000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	2.96410	+	5.13397i	0.550420	+	0.953355i	0.998244	+	0.0592336i	$0.0188657\pi$
$29$	2.96410	+	5.13397i	0.550420	+	0.953355i	−0.447824	+	0.894122i	$0.647801\pi$
$30$		0			0
$31$		−	5.46410i		−	0.981382i	−0.871334	−	0.490691i	$-0.836744\pi$
$31$		−	5.46410i		−	0.981382i	0.871334	−	0.490691i	$-0.163256\pi$
$32$		0			0
$33$	−0.633975	−	0.366025i	−0.110361	−	0.0637168i
$34$		0			0
$35$	−0.633975	+	1.09808i	−0.107161	+	0.185609i
$36$		0			0
$37$	7.33013	−	4.23205i	1.20507	−	0.695745i	0.243388	−	0.969929i	$-0.421741\pi$
$37$	7.33013	−	4.23205i	1.20507	−	0.695745i	0.961677	+	0.274184i	$0.0884078\pi$
$38$		0			0
$39$	−0.866025	+	3.50000i	−0.138675	+	0.560449i
$40$		0			0
$41$	−4.33013	+	2.50000i	−0.676252	+	0.390434i	−0.798441	−	0.602072i	$-0.794342\pi$
$41$	−4.33013	+	2.50000i	−0.676252	+	0.390434i	0.122189	+	0.992507i	$0.461009\pi$
$42$		0			0
$43$	0.901924	−	1.56218i	0.137542	−	0.238230i	−0.789024	−	0.614363i	$-0.789413\pi$
$43$	0.901924	−	1.56218i	0.137542	−	0.238230i	0.926566	+	0.376133i	$0.122746\pi$
$44$		0			0
$45$	−1.50000	−	0.866025i	−0.223607	−	0.129099i
$46$		0			0
$47$		−	6.73205i		−	0.981971i	−0.871168	−	0.490985i	$-0.836637\pi$
$47$		−	6.73205i		−	0.981971i	0.871168	−	0.490985i	$-0.163363\pi$
$48$		0			0
$49$	−3.23205	−	5.59808i	−0.461722	−	0.799725i
$50$		0			0
$51$	−3.73205			−0.522592
$52$		0			0
$53$	5.92820			0.814301			0.407151	−	0.913361i	$-0.366522\pi$
$53$	5.92820			0.814301			0.407151	+	0.913361i	$0.366522\pi$
$54$		0			0
$55$	−0.633975	−	1.09808i	−0.0854851	−	0.148065i
$56$		0			0
$57$		−	1.26795i		−	0.167944i
$58$		0			0
$59$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$59$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$60$		0			0
$61$	4.86603	−	8.42820i	0.623031	−	1.07912i	−0.365887	−	0.930659i	$-0.619234\pi$
$61$	4.86603	−	8.42820i	0.623031	−	1.07912i	0.988918	−	0.148462i	$-0.0474322\pi$
$62$		0			0
$63$	−0.633975	+	0.366025i	−0.0798733	+	0.0461149i
$64$		0			0
$65$	−4.33013	+	4.50000i	−0.537086	+	0.558156i
$66$		0			0
$67$	−4.56218	+	2.63397i	−0.557359	+	0.321791i	−0.752085	−	0.659066i	$-0.770952\pi$
$67$	−4.56218	+	2.63397i	−0.557359	+	0.321791i	0.194726	+	0.980858i	$0.437618\pi$
$68$		0			0
$69$	1.09808	−	1.90192i	0.132193	−	0.228965i
$70$		0			0
$71$	−7.09808	−	4.09808i	−0.842387	−	0.486352i	0.0156881	−	0.999877i	$-0.495006\pi$
$71$	−7.09808	−	4.09808i	−0.842387	−	0.486352i	−0.858075	+	0.513525i	$0.828339\pi$
$72$		0			0
$73$		−	1.19615i		−	0.139999i	−0.997547	−	0.0699995i	$-0.977700\pi$
$73$		−	1.19615i		−	0.139999i	0.997547	−	0.0699995i	$-0.0222998\pi$
$74$		0			0
$75$	1.00000	+	1.73205i	0.115470	+	0.200000i
$76$		0			0
$77$	−0.535898			−0.0610713
$78$		0			0
$79$	12.3923			1.39424			0.697122	−	0.716953i	$-0.254464\pi$
$79$	12.3923			1.39424			0.697122	+	0.716953i	$0.254464\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	15.6603i		−	1.71894i	−0.511189	−	0.859468i	$-0.670795\pi$
$83$		−	15.6603i		−	1.71894i	0.511189	−	0.859468i	$-0.329205\pi$
$84$		0			0
$85$	−5.59808	−	3.23205i	−0.607197	−	0.350565i
$86$		0			0
$87$	−2.96410	+	5.13397i	−0.317785	+	0.550420i
$88$		0			0
$89$	−2.19615	+	1.26795i	−0.232792	+	0.134402i	−0.611859	−	0.790967i	$-0.709578\pi$
$89$	−2.19615	+	1.26795i	−0.232792	+	0.134402i	0.379068	+	0.925369i	$0.376245\pi$
$90$		0			0
$91$	0.732051	+	2.53590i	0.0767398	+	0.265834i
$92$		0			0
$93$	4.73205	−	2.73205i	0.490691	−	0.283300i
$94$		0			0
$95$	1.09808	−	1.90192i	0.112660	−	0.195133i
$96$		0			0
$97$	−8.66025	−	5.00000i	−0.879316	−	0.507673i	−0.00888289	−	0.999961i	$-0.502828\pi$
$97$	−8.66025	−	5.00000i	−0.879316	−	0.507673i	−0.870433	+	0.492287i	$0.836161\pi$
$98$		0			0
$99$		−	0.732051i		−	0.0735739i
$100$		0			0
$101$	−7.23205	−	12.5263i	−0.719616	−	1.24641i	−0.961152	−	0.276020i	$-0.910985\pi$
$101$	−7.23205	−	12.5263i	−0.719616	−	1.24641i	0.241536	−	0.970392i	$-0.422349\pi$
$102$		0			0
$103$	2.73205			0.269197			0.134598	−	0.990900i	$-0.457026\pi$
$103$	2.73205			0.269197			0.134598	+	0.990900i	$0.457026\pi$
$104$		0			0
$105$	−1.26795			−0.123739
$106$		0			0
$107$	7.56218	+	13.0981i	0.731063	+	1.26624i	0.956429	+	0.291965i	$0.0943089\pi$
$107$	7.56218	+	13.0981i	0.731063	+	1.26624i	−0.225366	+	0.974274i	$0.572358\pi$
$108$		0			0
$109$			0.392305i			0.0375760i	0.999823	+	0.0187880i	$0.00598076\pi$
$109$			0.392305i			0.0375760i	−0.999823	+	0.0187880i	$0.994019\pi$
$110$		0			0
$111$	7.33013	+	4.23205i	0.695745	+	0.401688i
$112$		0			0
$113$	−2.33013	+	4.03590i	−0.219200	+	0.379665i	−0.954564	−	0.298007i	$-0.903678\pi$
$113$	−2.33013	+	4.03590i	−0.219200	+	0.379665i	0.735364	+	0.677673i	$0.237011\pi$
$114$		0			0
$115$	3.29423	−	1.90192i	0.307188	−	0.177355i
$116$		0			0
$117$	−3.46410	+	1.00000i	−0.320256	+	0.0924500i
$118$		0			0
$119$	−2.36603	+	1.36603i	−0.216893	+	0.125223i
$120$		0			0
$121$	−5.23205	+	9.06218i	−0.475641	+	0.823834i
$122$		0			0
$123$	−4.33013	−	2.50000i	−0.390434	−	0.225417i
$124$		0			0
$125$			12.1244i			1.08444i
$126$		0			0
$127$	2.00000	+	3.46410i	0.177471	+	0.307389i	0.941014	−	0.338368i	$-0.109875\pi$
$127$	2.00000	+	3.46410i	0.177471	+	0.307389i	−0.763542	+	0.645758i	$0.776542\pi$
$128$		0			0
$129$	1.80385			0.158820
$130$		0			0
$131$	19.3205			1.68804			0.844020	−	0.536311i	$-0.180183\pi$
$131$	19.3205			1.68804			0.844020	+	0.536311i	$0.180183\pi$
$132$		0			0
$133$	−0.464102	−	0.803848i	−0.0402427	−	0.0697024i
$134$		0			0
$135$		−	1.73205i		−	0.149071i
$136$		0			0
$137$	−10.7942	−	6.23205i	−0.922213	−	0.532440i	−0.0378727	−	0.999283i	$-0.512058\pi$
$137$	−10.7942	−	6.23205i	−0.922213	−	0.532440i	−0.884340	+	0.466843i	$0.845391\pi$
$138$		0			0
$139$	−10.0000	+	17.3205i	−0.848189	+	1.46911i	0.0346338	+	0.999400i	$0.488974\pi$
$139$	−10.0000	+	17.3205i	−0.848189	+	1.46911i	−0.882823	+	0.469706i	$0.844360\pi$
$140$		0			0
$141$	5.83013	−	3.36603i	0.490985	−	0.283470i
$142$		0			0
$143$	−2.56218	−	0.633975i	−0.214260	−	0.0530156i
$144$		0			0
$145$	−8.89230	+	5.13397i	−0.738466	+	0.426353i
$146$		0			0
$147$	3.23205	−	5.59808i	0.266575	−	0.461722i
$148$		0			0
$149$	8.30385	+	4.79423i	0.680278	+	0.392759i	0.799960	−	0.600054i	$-0.204854\pi$
$149$	8.30385	+	4.79423i	0.680278	+	0.392759i	−0.119682	+	0.992812i	$0.538187\pi$
$150$		0			0
$151$			20.7321i			1.68715i	0.537011	+	0.843575i	$0.319553\pi$
$151$			20.7321i			1.68715i	−0.537011	+	0.843575i	$0.680447\pi$
$152$		0			0
$153$	−1.86603	−	3.23205i	−0.150859	−	0.261296i
$154$		0			0
$155$	9.46410			0.760175
$156$		0			0
$157$	15.0526			1.20132			0.600662	−	0.799503i	$-0.294904\pi$
$157$	15.0526			1.20132			0.600662	+	0.799503i	$0.294904\pi$
$158$		0			0
$159$	2.96410	+	5.13397i	0.235069	+	0.407151i
$160$		0			0
$161$		−	1.60770i		−	0.126704i
$162$		0			0
$163$	−5.66025	−	3.26795i	−0.443345	−	0.255966i	0.261670	−	0.965157i	$-0.415727\pi$
$163$	−5.66025	−	3.26795i	−0.443345	−	0.255966i	−0.705016	+	0.709192i	$0.749060\pi$
$164$		0			0
$165$	0.633975	−	1.09808i	0.0493549	−	0.0854851i
$166$		0			0
$167$	−4.73205	+	2.73205i	−0.366177	+	0.211412i	−0.671787	−	0.740744i	$-0.734473\pi$
$167$	−4.73205	+	2.73205i	−0.366177	+	0.211412i	0.305610	+	0.952157i	$0.401140\pi$
$168$		0			0
$169$	0.500000	+	12.9904i	0.0384615	+	0.999260i
$170$		0			0
$171$	1.09808	−	0.633975i	0.0839720	−	0.0484812i
$172$		0			0
$173$	5.26795	−	9.12436i	0.400515	−	0.693712i	−0.593273	−	0.805001i	$-0.702165\pi$
$173$	5.26795	−	9.12436i	0.400515	−	0.693712i	0.993788	+	0.111289i	$0.0354980\pi$
$174$		0			0
$175$	1.26795	+	0.732051i	0.0958479	+	0.0553378i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	8.63397	+	14.9545i	0.645334	+	1.11775i	0.984224	+	0.176925i	$0.0566149\pi$
$179$	8.63397	+	14.9545i	0.645334	+	1.11775i	−0.338891	+	0.940826i	$0.610052\pi$
$180$		0			0
$181$	−8.80385			−0.654385			−0.327192	−	0.944958i	$-0.606103\pi$
$181$	−8.80385			−0.654385			−0.327192	+	0.944958i	$0.606103\pi$
$182$		0			0
$183$	9.73205			0.719414
$184$		0			0
$185$	7.33013	+	12.6962i	0.538922	+	0.933440i
$186$		0			0
$187$		−	2.73205i		−	0.199787i
$188$		0			0
$189$	−0.633975	−	0.366025i	−0.0461149	−	0.0266244i
$190$		0			0
$191$	0.535898	−	0.928203i	0.0387762	−	0.0671624i	−0.845986	−	0.533205i	$-0.820987\pi$
$191$	0.535898	−	0.928203i	0.0387762	−	0.0671624i	0.884762	+	0.466043i	$0.154321\pi$
$192$		0			0
$193$	7.16025	−	4.13397i	0.515406	−	0.297570i	−0.219647	−	0.975579i	$-0.570490\pi$
$193$	7.16025	−	4.13397i	0.515406	−	0.297570i	0.735053	+	0.678009i	$0.237157\pi$
$194$		0			0
$195$	−6.06218	−	1.50000i	−0.434122	−	0.107417i
$196$		0			0
$197$	12.9282	−	7.46410i	0.921096	−	0.531795i	0.0371117	−	0.999311i	$-0.488184\pi$
$197$	12.9282	−	7.46410i	0.921096	−	0.531795i	0.883985	+	0.467516i	$0.154851\pi$
$198$		0			0
$199$	−8.83013	+	15.2942i	−0.625951	+	1.08418i	0.362405	+	0.932021i	$0.381956\pi$
$199$	−8.83013	+	15.2942i	−0.625951	+	1.08418i	−0.988356	+	0.152158i	$0.951378\pi$
$200$		0			0
$201$	−4.56218	−	2.63397i	−0.321791	−	0.185786i
$202$		0			0
$203$			4.33975i			0.304590i
$204$		0			0
$205$	−4.33013	−	7.50000i	−0.302429	−	0.523823i
$206$		0			0
$207$	2.19615			0.152643
$208$		0			0
$209$	0.928203			0.0642052
$210$		0			0
$211$	−11.6603	−	20.1962i	−0.802725	−	1.39036i	−0.917816	−	0.397006i	$-0.870049\pi$
$211$	−11.6603	−	20.1962i	−0.802725	−	1.39036i	0.115091	−	0.993355i	$-0.463284\pi$
$212$		0			0
$213$		−	8.19615i		−	0.561591i
$214$		0			0
$215$	2.70577	+	1.56218i	0.184532	+	0.106540i
$216$		0			0
$217$	2.00000	−	3.46410i	0.135769	−	0.235159i
$218$		0			0
$219$	1.03590	−	0.598076i	0.0699995	−	0.0404142i
$220$		0			0
$221$	−12.9282	+	3.73205i	−0.869645	+	0.251045i
$222$		0			0
$223$	−21.4641	+	12.3923i	−1.43734	+	0.829850i	−0.997664	−	0.0683053i	$-0.978241\pi$
$223$	−21.4641	+	12.3923i	−1.43734	+	0.829850i	−0.439678	+	0.898155i	$0.644907\pi$
$224$		0			0
$225$	−1.00000	+	1.73205i	−0.0666667	+	0.115470i
$226$		0			0
$227$	−13.9019	−	8.02628i	−0.922703	−	0.532723i	−0.0382067	−	0.999270i	$-0.512165\pi$
$227$	−13.9019	−	8.02628i	−0.922703	−	0.532723i	−0.884496	+	0.466547i	$0.845498\pi$
$228$		0			0
$229$			27.8564i			1.84080i	0.390974	+	0.920402i	$0.372138\pi$
$229$			27.8564i			1.84080i	−0.390974	+	0.920402i	$0.627862\pi$
$230$		0			0
$231$	−0.267949	−	0.464102i	−0.0176298	−	0.0305356i
$232$		0			0
$233$	2.00000			0.131024			0.0655122	−	0.997852i	$-0.479132\pi$
$233$	2.00000			0.131024			0.0655122	+	0.997852i	$0.479132\pi$
$234$		0			0
$235$	11.6603			0.760631
$236$		0			0
$237$	6.19615	+	10.7321i	0.402483	+	0.697122i
$238$		0			0
$239$		−	26.7321i		−	1.72915i	−0.502502	−	0.864576i	$-0.667587\pi$
$239$		−	26.7321i		−	1.72915i	0.502502	−	0.864576i	$-0.332413\pi$
$240$		0			0
$241$	−19.6244	−	11.3301i	−1.26412	−	0.729838i	−0.290248	−	0.956952i	$-0.593738\pi$
$241$	−19.6244	−	11.3301i	−1.26412	−	0.729838i	−0.973868	+	0.227114i	$0.927071\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$	9.69615	−	5.59808i	0.619464	−	0.357648i
$246$		0			0
$247$	−1.26795	−	4.39230i	−0.0806777	−	0.279476i
$248$		0			0
$249$	13.5622	−	7.83013i	0.859468	−	0.496214i
$250$		0			0
$251$	−4.73205	+	8.19615i	−0.298684	+	0.517337i	−0.975835	−	0.218508i	$-0.929881\pi$
$251$	−4.73205	+	8.19615i	−0.298684	+	0.517337i	0.677151	+	0.735844i	$0.263214\pi$
$252$		0			0
$253$	1.39230	+	0.803848i	0.0875335	+	0.0505375i
$254$		0			0
$255$		−	6.46410i		−	0.404798i
$256$		0			0
$257$	−8.86603	−	15.3564i	−0.553047	−	0.957906i	−0.998053	−	0.0623783i	$-0.980131\pi$
$257$	−8.86603	−	15.3564i	−0.553047	−	0.957906i	0.445005	−	0.895528i	$-0.353202\pi$
$258$		0			0
$259$	6.19615			0.385010
$260$		0			0
$261$	−5.92820			−0.366947
$262$		0			0
$263$	−6.16987	−	10.6865i	−0.380451	−	0.658960i	0.610676	−	0.791881i	$-0.290898\pi$
$263$	−6.16987	−	10.6865i	−0.380451	−	0.658960i	−0.991127	+	0.132921i	$0.957564\pi$
$264$		0			0
$265$			10.2679i			0.630755i
$266$		0			0
$267$	−2.19615	−	1.26795i	−0.134402	−	0.0775972i
$268$		0			0
$269$	−4.73205	+	8.19615i	−0.288518	+	0.499728i	−0.973456	−	0.228873i	$-0.926496\pi$
$269$	−4.73205	+	8.19615i	−0.288518	+	0.499728i	0.684938	+	0.728601i	$0.259829\pi$
$270$		0			0
$271$	13.8564	−	8.00000i	0.841717	−	0.485965i	−0.0161307	−	0.999870i	$-0.505135\pi$
$271$	13.8564	−	8.00000i	0.841717	−	0.485965i	0.857847	+	0.513905i	$0.171801\pi$
$272$		0			0
$273$	−1.83013	+	1.90192i	−0.110764	+	0.115110i
$274$		0			0
$275$	−1.26795	+	0.732051i	−0.0764602	+	0.0441443i
$276$		0			0
$277$	−4.06218	+	7.03590i	−0.244073	+	0.422746i	−0.961870	−	0.273505i	$-0.911817\pi$
$277$	−4.06218	+	7.03590i	−0.244073	+	0.422746i	0.717798	+	0.696252i	$0.245150\pi$
$278$		0			0
$279$	4.73205	+	2.73205i	0.283300	+	0.163564i
$280$		0			0
$281$		−	24.7128i		−	1.47424i	−0.675760	−	0.737121i	$-0.736185\pi$
$281$		−	24.7128i		−	1.47424i	0.675760	−	0.737121i	$-0.263815\pi$
$282$		0			0
$283$	−10.7583	−	18.6340i	−0.639516	−	1.10767i	−0.985539	−	0.169449i	$-0.945801\pi$
$283$	−10.7583	−	18.6340i	−0.639516	−	1.10767i	0.346023	−	0.938226i	$-0.387532\pi$
$284$		0			0
$285$	2.19615			0.130089
$286$		0			0
$287$	−3.66025			−0.216058
$288$		0			0
$289$	1.53590	+	2.66025i	0.0903470	+	0.156486i
$290$		0			0
$291$		−	10.0000i		−	0.586210i
$292$		0			0
$293$	−1.83975	−	1.06218i	−0.107479	−	0.0620531i	0.445297	−	0.895383i	$-0.353098\pi$
$293$	−1.83975	−	1.06218i	−0.107479	−	0.0620531i	−0.552776	+	0.833330i	$0.686431\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	0.633975	−	0.366025i	0.0367869	−	0.0212389i
$298$		0			0
$299$	1.90192	−	7.68653i	0.109991	−	0.444524i
$300$		0			0
$301$	1.14359	−	0.660254i	0.0659156	−	0.0380564i
$302$		0			0
$303$	7.23205	−	12.5263i	0.415470	−	0.719616i
$304$		0			0
$305$	14.5981	+	8.42820i	0.835883	+	0.482598i
$306$		0			0
$307$		−	10.7321i		−	0.612510i	−0.951949	−	0.306255i	$-0.900924\pi$
$307$		−	10.7321i		−	0.612510i	0.951949	−	0.306255i	$-0.0990761\pi$
$308$		0			0
$309$	1.36603	+	2.36603i	0.0777105	+	0.134598i
$310$		0			0
$311$	4.33975			0.246084			0.123042	−	0.992401i	$-0.460735\pi$
$311$	4.33975			0.246084			0.123042	+	0.992401i	$0.460735\pi$
$312$		0			0
$313$	3.32051			0.187686			0.0938431	−	0.995587i	$-0.470085\pi$
$313$	3.32051			0.187686			0.0938431	+	0.995587i	$0.470085\pi$
$314$		0			0
$315$	−0.633975	−	1.09808i	−0.0357204	−	0.0618696i
$316$		0			0
$317$		−	11.1962i		−	0.628839i	−0.949284	−	0.314419i	$-0.898190\pi$
$317$		−	11.1962i		−	0.628839i	0.949284	−	0.314419i	$-0.101810\pi$
$318$		0			0
$319$	−3.75833	−	2.16987i	−0.210426	−	0.121490i
$320$		0			0
$321$	−7.56218	+	13.0981i	−0.422080	+	0.731063i
$322$		0			0
$323$	4.09808	−	2.36603i	0.228023	−	0.131649i
$324$		0			0
$325$	5.19615	+	5.00000i	0.288231	+	0.277350i
$326$		0			0
$327$	−0.339746	+	0.196152i	−0.0187880	+	0.0108473i
$328$		0			0
$329$	2.46410	−	4.26795i	0.135850	−	0.235300i
$330$		0			0
$331$	10.3923	+	6.00000i	0.571213	+	0.329790i	0.757634	−	0.652680i	$-0.226355\pi$
$331$	10.3923	+	6.00000i	0.571213	+	0.329790i	−0.186421	+	0.982470i	$0.559689\pi$
$332$		0			0
$333$			8.46410i			0.463830i
$334$		0			0
$335$	−4.56218	−	7.90192i	−0.249258	−	0.431728i
$336$		0			0
$337$	17.9282			0.976611			0.488306	−	0.872673i	$-0.337615\pi$
$337$	17.9282			0.976611			0.488306	+	0.872673i	$0.337615\pi$
$338$		0			0
$339$	−4.66025			−0.253110
$340$		0			0
$341$	2.00000	+	3.46410i	0.108306	+	0.187592i
$342$		0			0
$343$		−	9.85641i		−	0.532196i
$344$		0			0
$345$	3.29423	+	1.90192i	0.177355	+	0.102396i
$346$		0			0
$347$	−13.7583	+	23.8301i	−0.738586	+	1.27927i	0.214546	+	0.976714i	$0.431173\pi$
$347$	−13.7583	+	23.8301i	−0.738586	+	1.27927i	−0.953132	+	0.302554i	$0.902161\pi$
$348$		0			0
$349$	−7.26795	+	4.19615i	−0.389044	+	0.224615i	−0.681746	−	0.731589i	$-0.738779\pi$
$349$	−7.26795	+	4.19615i	−0.389044	+	0.224615i	0.292702	+	0.956204i	$0.405446\pi$
$350$		0			0
$351$	−2.59808	−	2.50000i	−0.138675	−	0.133440i
$352$		0			0
$353$	21.1865	−	12.2321i	1.12765	−	0.651046i	0.184304	−	0.982869i	$-0.440997\pi$
$353$	21.1865	−	12.2321i	1.12765	−	0.651046i	0.943342	+	0.331823i	$0.107664\pi$
$354$		0			0
$355$	7.09808	−	12.2942i	0.376727	−	0.652510i
$356$		0			0
$357$	−2.36603	−	1.36603i	−0.125223	−	0.0722977i
$358$		0			0
$359$			19.5167i			1.03005i	0.857175	+	0.515025i	$0.172217\pi$
$359$			19.5167i			1.03005i	−0.857175	+	0.515025i	$0.827783\pi$
$360$		0			0
$361$	−8.69615	−	15.0622i	−0.457692	−	0.792746i
$362$		0			0
$363$	−10.4641			−0.549223
$364$		0			0
$365$	2.07180			0.108443
$366$		0			0
$367$	−11.5622	−	20.0263i	−0.603541	−	1.04536i	−0.992280	−	0.124016i	$-0.960423\pi$
$367$	−11.5622	−	20.0263i	−0.603541	−	1.04536i	0.388740	−	0.921348i	$-0.372911\pi$
$368$		0			0
$369$		−	5.00000i		−	0.260290i
$370$		0			0
$371$	3.75833	+	2.16987i	0.195123	+	0.112654i
$372$		0			0
$373$	7.66987	−	13.2846i	0.397131	−	0.687851i	−0.596240	−	0.802806i	$-0.703339\pi$
$373$	7.66987	−	13.2846i	0.397131	−	0.687851i	0.993371	+	0.114955i	$0.0366725\pi$
$374$		0			0
$375$	−10.5000	+	6.06218i	−0.542218	+	0.313050i
$376$		0			0
$377$	−5.13397	+	20.7487i	−0.264413	+	1.06861i
$378$		0			0
$379$	−31.5167	+	18.1962i	−1.61890	+	0.934674i	−0.631697	+	0.775215i	$0.717642\pi$
$379$	−31.5167	+	18.1962i	−1.61890	+	0.934674i	−0.987205	+	0.159459i	$0.949025\pi$
$380$		0			0
$381$	−2.00000	+	3.46410i	−0.102463	+	0.177471i
$382$		0			0
$383$	−30.5885	−	17.6603i	−1.56300	−	0.902397i	−0.996952	−	0.0780229i	$-0.975139\pi$
$383$	−30.5885	−	17.6603i	−1.56300	−	0.902397i	−0.566046	−	0.824374i	$-0.691527\pi$
$384$		0			0
$385$		−	0.928203i		−	0.0473056i
$386$		0			0
$387$	0.901924	+	1.56218i	0.0458474	+	0.0794100i
$388$		0			0
$389$	−24.4641			−1.24038			−0.620190	−	0.784452i	$-0.712944\pi$
$389$	−24.4641			−1.24038			−0.620190	+	0.784452i	$0.712944\pi$
$390$		0			0
$391$	8.19615			0.414497
$392$		0			0
$393$	9.66025	+	16.7321i	0.487295	+	0.844020i
$394$		0			0
$395$			21.4641i			1.07998i
$396$		0			0
$397$	−9.12436	−	5.26795i	−0.457938	−	0.264391i	0.253239	−	0.967404i	$-0.418504\pi$
$397$	−9.12436	−	5.26795i	−0.457938	−	0.264391i	−0.711177	+	0.703013i	$0.751838\pi$
$398$		0			0
$399$	0.464102	−	0.803848i	0.0232341	−	0.0402427i
$400$		0			0
$401$	13.4545	−	7.76795i	0.671885	−	0.387913i	−0.124906	−	0.992169i	$-0.539863\pi$
$401$	13.4545	−	7.76795i	0.671885	−	0.387913i	0.796790	+	0.604256i	$0.206529\pi$
$402$		0			0
$403$	13.6603	−	14.1962i	0.680466	−	0.707161i
$404$		0			0
$405$	1.50000	−	0.866025i	0.0745356	−	0.0430331i
$406$		0			0
$407$	−3.09808	+	5.36603i	−0.153566	+	0.265984i
$408$		0			0
$409$	19.7487	+	11.4019i	0.976511	+	0.563789i	0.901215	−	0.433372i	$-0.142677\pi$
$409$	19.7487	+	11.4019i	0.976511	+	0.563789i	0.0752960	+	0.997161i	$0.476010\pi$
$410$		0			0
$411$		−	12.4641i		−	0.614809i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	27.1244			1.33148
$416$		0			0
$417$	−20.0000			−0.979404
$418$		0			0
$419$	16.1962	+	28.0526i	0.791234	+	1.37046i	0.925203	+	0.379472i	$0.123894\pi$
$419$	16.1962	+	28.0526i	0.791234	+	1.37046i	−0.133970	+	0.990985i	$0.542772\pi$
$420$		0			0
$421$			5.00000i			0.243685i	0.992549	+	0.121843i	$0.0388803\pi$
$421$			5.00000i			0.243685i	−0.992549	+	0.121843i	$0.961120\pi$
$422$		0			0
$423$	5.83013	+	3.36603i	0.283470	+	0.163662i
$424$		0			0
$425$	−3.73205	+	6.46410i	−0.181031	+	0.313555i
$426$		0			0
$427$	6.16987	−	3.56218i	0.298581	−	0.172386i
$428$		0			0
$429$	−0.732051	−	2.53590i	−0.0353437	−	0.122434i
$430$		0			0
$431$	−8.70577	+	5.02628i	−0.419342	+	0.242107i	−0.694796	−	0.719207i	$-0.744505\pi$
$431$	−8.70577	+	5.02628i	−0.419342	+	0.242107i	0.275454	+	0.961314i	$0.411172\pi$
$432$		0			0
$433$	−15.4282	+	26.7224i	−0.741432	+	1.28420i	0.210411	+	0.977613i	$0.432520\pi$
$433$	−15.4282	+	26.7224i	−0.741432	+	1.28420i	−0.951843	+	0.306585i	$0.900814\pi$
$434$		0			0
$435$	−8.89230	−	5.13397i	−0.426353	−	0.246155i
$436$		0			0
$437$			2.78461i			0.133206i
$438$		0			0
$439$	10.0981	+	17.4904i	0.481955	+	0.834770i	0.999785	−	0.0207128i	$-0.00659358\pi$
$439$	10.0981	+	17.4904i	0.481955	+	0.834770i	−0.517831	+	0.855483i	$0.673260\pi$
$440$		0			0
$441$	6.46410			0.307814
$442$		0			0
$443$	−15.3205			−0.727899			−0.363950	−	0.931419i	$-0.618572\pi$
$443$	−15.3205			−0.727899			−0.363950	+	0.931419i	$0.618572\pi$
$444$		0			0
$445$	−2.19615	−	3.80385i	−0.104108	−	0.180320i
$446$		0			0
$447$			9.58846i			0.453518i
$448$		0			0
$449$	27.1244	+	15.6603i	1.28008	+	0.739053i	0.976862	−	0.213869i	$-0.0686066\pi$
$449$	27.1244	+	15.6603i	1.28008	+	0.739053i	0.303215	+	0.952922i	$0.401940\pi$
$450$		0			0
$451$	1.83013	−	3.16987i	0.0861773	−	0.149263i
$452$		0			0
$453$	−17.9545	+	10.3660i	−0.843575	+	0.487038i
$454$		0			0
$455$	−4.39230	+	1.26795i	−0.205914	+	0.0594424i
$456$		0			0
$457$	16.8397	−	9.72243i	0.787730	−	0.454796i	−0.0514327	−	0.998676i	$-0.516379\pi$
$457$	16.8397	−	9.72243i	0.787730	−	0.454796i	0.839163	+	0.543880i	$0.183045\pi$
$458$		0			0
$459$	1.86603	−	3.23205i	0.0870986	−	0.150859i
$460$		0			0
$461$	−2.08846	−	1.20577i	−0.0972692	−	0.0561584i	0.450576	−	0.892738i	$-0.351219\pi$
$461$	−2.08846	−	1.20577i	−0.0972692	−	0.0561584i	−0.547846	+	0.836580i	$0.684552\pi$
$462$		0			0
$463$		−	23.6603i		−	1.09959i	−0.835301	−	0.549793i	$-0.814707\pi$
$463$		−	23.6603i		−	1.09959i	0.835301	−	0.549793i	$-0.185293\pi$
$464$		0			0
$465$	4.73205	+	8.19615i	0.219444	+	0.380087i
$466$		0			0
$467$	5.66025			0.261925			0.130963	−	0.991387i	$-0.458193\pi$
$467$	5.66025			0.261925			0.130963	+	0.991387i	$0.458193\pi$
$468$		0			0
$469$	−3.85641			−0.178072
$470$		0			0
$471$	7.52628	+	13.0359i	0.346793	+	0.600662i
$472$		0			0
$473$			1.32051i			0.0607170i
$474$		0			0
$475$	−2.19615	−	1.26795i	−0.100766	−	0.0581775i
$476$		0			0
$477$	−2.96410	+	5.13397i	−0.135717	+	0.235069i
$478$		0			0
$479$	4.73205	−	2.73205i	0.216213	−	0.124831i	−0.387983	−	0.921667i	$-0.626828\pi$
$479$	4.73205	−	2.73205i	0.216213	−	0.124831i	0.604195	+	0.796836i	$0.293495\pi$
$480$		0			0
$481$	29.6244	+	7.33013i	1.35075	+	0.334225i
$482$		0			0
$483$	1.39230	−	0.803848i	0.0633521	−	0.0365763i
$484$		0			0
$485$	8.66025	−	15.0000i	0.393242	−	0.681115i
$486$		0			0
$487$	26.4904	+	15.2942i	1.20039	+	0.693048i	0.960643	−	0.277787i	$-0.0896009\pi$
$487$	26.4904	+	15.2942i	1.20039	+	0.693048i	0.239751	+	0.970834i	$0.422934\pi$
$488$		0			0
$489$		−	6.53590i		−	0.295564i
$490$		0			0
$491$	19.9545	+	34.5622i	0.900533	+	1.55977i	0.826803	+	0.562491i	$0.190157\pi$
$491$	19.9545	+	34.5622i	0.900533	+	1.55977i	0.0737298	+	0.997278i	$0.476510\pi$
$492$		0			0
$493$	−22.1244			−0.996431
$494$		0			0
$495$	1.26795			0.0569901
$496$		0			0
$497$	−3.00000	−	5.19615i	−0.134568	−	0.233079i
$498$		0			0
$499$			13.8564i			0.620298i	0.950688	+	0.310149i	$0.100379\pi$
$499$			13.8564i			0.620298i	−0.950688	+	0.310149i	$0.899621\pi$
$500$		0			0
$501$	−4.73205	−	2.73205i	−0.211412	−	0.122059i
$502$		0			0
$503$	−6.36603	+	11.0263i	−0.283847	+	0.491638i	−0.972329	−	0.233616i	$-0.924944\pi$
$503$	−6.36603	+	11.0263i	−0.283847	+	0.491638i	0.688482	+	0.725254i	$0.258277\pi$
$504$		0			0
$505$	21.6962	−	12.5263i	0.965466	−	0.557412i
$506$		0			0
$507$	−11.0000	+	6.92820i	−0.488527	+	0.307692i
$508$		0			0
$509$	1.37564	−	0.794229i	0.0609744	−	0.0352036i	−0.469203	−	0.883090i	$-0.655459\pi$
$509$	1.37564	−	0.794229i	0.0609744	−	0.0352036i	0.530177	+	0.847887i	$0.322125\pi$
$510$		0			0
$511$	0.437822	−	0.758330i	0.0193681	−	0.0335466i
$512$		0			0
$513$	1.09808	+	0.633975i	0.0484812	+	0.0279907i
$514$		0			0
$515$			4.73205i			0.208519i
$516$		0			0
$517$	2.46410	+	4.26795i	0.108371	+	0.187704i
$518$		0			0
$519$	10.5359			0.462475
$520$		0			0
$521$	−31.9808			−1.40110			−0.700551	−	0.713602i	$-0.747063\pi$
$521$	−31.9808			−1.40110			−0.700551	+	0.713602i	$0.747063\pi$
$522$		0			0
$523$	−11.2942	−	19.5622i	−0.493862	−	0.855394i	0.506113	−	0.862467i	$-0.331082\pi$
$523$	−11.2942	−	19.5622i	−0.493862	−	0.855394i	−0.999975	+	0.00707295i	$0.997749\pi$
$524$		0			0
$525$			1.46410i			0.0638986i
$526$		0			0
$527$	17.6603	+	10.1962i	0.769293	+	0.444151i
$528$		0			0
$529$	9.08846	−	15.7417i	0.395150	−	0.684420i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−17.5000	−	4.33013i	−0.758009	−	0.187559i
$534$		0			0
$535$	−22.6865	+	13.0981i	−0.980824	+	0.566279i
$536$		0			0
$537$	−8.63397	+	14.9545i	−0.372584	+	0.645334i
$538$		0			0
$539$	4.09808	+	2.36603i	0.176517	+	0.101912i
$540$		0			0
$541$			3.39230i			0.145847i	0.997338	+	0.0729233i	$0.0232328\pi$
$541$			3.39230i			0.145847i	−0.997338	+	0.0729233i	$0.976767\pi$
$542$		0			0
$543$	−4.40192	−	7.62436i	−0.188905	−	0.327192i
$544$		0			0
$545$	−0.679492			−0.0291062
$546$		0			0
$547$	36.0526			1.54150			0.770748	−	0.637140i	$-0.219883\pi$
$547$	36.0526			1.54150			0.770748	+	0.637140i	$0.219883\pi$
$548$		0			0
$549$	4.86603	+	8.42820i	0.207677	+	0.359707i
$550$		0			0
$551$		−	7.51666i		−	0.320221i
$552$		0			0
$553$	7.85641	+	4.53590i	0.334088	+	0.192886i
$554$		0			0
$555$	−7.33013	+	12.6962i	−0.311147	+	0.538922i
$556$		0			0
$557$	−27.3564	+	15.7942i	−1.15913	+	0.669223i	−0.951095	−	0.308899i	$-0.900040\pi$
$557$	−27.3564	+	15.7942i	−1.15913	+	0.669223i	−0.208033	+	0.978122i	$0.566706\pi$
$558$		0			0
$559$	6.24871	−	1.80385i	0.264292	−	0.0762946i
$560$		0			0
$561$	2.36603	−	1.36603i	0.0998937	−	0.0576736i
$562$		0			0
$563$	−2.53590	+	4.39230i	−0.106875	+	0.185114i	−0.914503	−	0.404579i	$-0.867418\pi$
$563$	−2.53590	+	4.39230i	−0.106875	+	0.185114i	0.807627	+	0.589693i	$0.200751\pi$
$564$		0			0
$565$	−6.99038	−	4.03590i	−0.294088	−	0.169792i
$566$		0			0
$567$		−	0.732051i		−	0.0307432i
$568$		0			0
$569$	−8.00000	−	13.8564i	−0.335377	−	0.580891i	0.648180	−	0.761487i	$-0.275531\pi$
$569$	−8.00000	−	13.8564i	−0.335377	−	0.580891i	−0.983557	+	0.180597i	$0.942197\pi$
$570$		0			0
$571$	−3.66025			−0.153177			−0.0765884	−	0.997063i	$-0.524403\pi$
$571$	−3.66025			−0.153177			−0.0765884	+	0.997063i	$0.524403\pi$
$572$		0			0
$573$	1.07180			0.0447750
$574$		0			0
$575$	−2.19615	−	3.80385i	−0.0915859	−	0.158631i
$576$		0			0
$577$		−	5.58846i		−	0.232651i	−0.993211	−	0.116325i	$-0.962889\pi$
$577$		−	5.58846i		−	0.232651i	0.993211	−	0.116325i	$-0.0371115\pi$
$578$		0			0
$579$	7.16025	+	4.13397i	0.297570	+	0.171802i
$580$		0			0
$581$	5.73205	−	9.92820i	0.237806	−	0.411891i
$582$		0			0
$583$	−3.75833	+	2.16987i	−0.155654	+	0.0898670i
$584$		0			0
$585$	−1.73205	−	6.00000i	−0.0716115	−	0.248069i
$586$		0			0
$587$	1.85641	−	1.07180i	0.0766221	−	0.0442378i	−0.461199	−	0.887296i	$-0.652581\pi$
$587$	1.85641	−	1.07180i	0.0766221	−	0.0442378i	0.537822	+	0.843059i	$0.319247\pi$
$588$		0			0
$589$	−3.46410	+	6.00000i	−0.142736	+	0.247226i
$590$		0			0
$591$	12.9282	+	7.46410i	0.531795	+	0.307032i
$592$		0			0
$593$		−	34.1769i		−	1.40348i	−0.712434	−	0.701739i	$-0.752407\pi$
$593$		−	34.1769i		−	1.40348i	0.712434	−	0.701739i	$-0.247593\pi$
$594$		0			0
$595$	−2.36603	−	4.09808i	−0.0969976	−	0.168005i
$596$		0			0
$597$	−17.6603			−0.722786
$598$		0			0
$599$	−33.4641			−1.36731			−0.683653	−	0.729807i	$-0.739610\pi$
$599$	−33.4641			−1.36731			−0.683653	+	0.729807i	$0.739610\pi$
$600$		0			0
$601$	−13.8205	−	23.9378i	−0.563750	−	0.976444i	−0.997165	−	0.0752494i	$-0.976025\pi$
$601$	−13.8205	−	23.9378i	−0.563750	−	0.976444i	0.433414	−	0.901195i	$-0.357309\pi$
$602$		0			0
$603$		−	5.26795i		−	0.214527i
$604$		0			0
$605$	−15.6962	−	9.06218i	−0.638139	−	0.368430i
$606$		0			0
$607$	20.3923	−	35.3205i	0.827698	−	1.43362i	−0.0721415	−	0.997394i	$-0.522983\pi$
$607$	20.3923	−	35.3205i	0.827698	−	1.43362i	0.899840	−	0.436221i	$-0.143683\pi$
$608$		0			0
$609$	−3.75833	+	2.16987i	−0.152295	+	0.0879277i
$610$		0			0
$611$	16.8301	−	17.4904i	0.680874	−	0.707585i
$612$		0			0
$613$	−1.45448	+	0.839746i	−0.0587460	+	0.0339170i	−0.529085	−	0.848569i	$-0.677465\pi$
$613$	−1.45448	+	0.839746i	−0.0587460	+	0.0339170i	0.470339	+	0.882486i	$0.344132\pi$
$614$		0			0
$615$	4.33013	−	7.50000i	0.174608	−	0.302429i
$616$		0			0
$617$	3.27757	+	1.89230i	0.131950	+	0.0761813i	0.564522	−	0.825418i	$-0.309061\pi$
$617$	3.27757	+	1.89230i	0.131950	+	0.0761813i	−0.432572	+	0.901599i	$0.642394\pi$
$618$		0			0
$619$			23.6077i			0.948873i	0.880290	+	0.474437i	$0.157348\pi$
$619$			23.6077i			0.948873i	−0.880290	+	0.474437i	$0.842652\pi$
$620$		0			0
$621$	1.09808	+	1.90192i	0.0440643	+	0.0763216i
$622$		0			0
$623$	−1.85641			−0.0743754
$624$		0			0
$625$	−11.0000			−0.440000
$626$		0			0
$627$	0.464102	+	0.803848i	0.0185344	+	0.0321026i
$628$		0			0
$629$			31.5885i			1.25951i
$630$		0			0
$631$	5.32051	+	3.07180i	0.211806	+	0.122286i	0.602150	−	0.798383i	$-0.294311\pi$
$631$	5.32051	+	3.07180i	0.211806	+	0.122286i	−0.390344	+	0.920669i	$0.627644\pi$
$632$		0			0
$633$	11.6603	−	20.1962i	0.463453	−	0.802725i
$634$		0			0
$635$	−6.00000	+	3.46410i	−0.238103	+	0.137469i
$636$		0			0
$637$	5.59808	−	22.6244i	0.221804	−	0.896410i
$638$		0			0
$639$	7.09808	−	4.09808i	0.280796	−	0.162117i
$640$		0			0
$641$	16.2583	−	28.1603i	0.642165	−	1.11226i	−0.342783	−	0.939415i	$-0.611370\pi$
$641$	16.2583	−	28.1603i	0.642165	−	1.11226i	0.984948	−	0.172849i	$-0.0552971\pi$
$642$		0			0
$643$	−24.0000	−	13.8564i	−0.946468	−	0.546443i	−0.0544858	−	0.998515i	$-0.517352\pi$
$643$	−24.0000	−	13.8564i	−0.946468	−	0.546443i	−0.891982	+	0.452071i	$0.850685\pi$
$644$		0			0
$645$			3.12436i			0.123021i
$646$		0			0
$647$	17.1244	+	29.6603i	0.673228	+	1.16606i	0.976983	+	0.213315i	$0.0684260\pi$
$647$	17.1244	+	29.6603i	0.673228	+	1.16606i	−0.303756	+	0.952750i	$0.598241\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	4.00000			0.156772
$652$		0			0
$653$	−13.2679	−	22.9808i	−0.519215	−	0.899307i	−0.999751	−	0.0223315i	$-0.992891\pi$
$653$	−13.2679	−	22.9808i	−0.519215	−	0.899307i	0.480536	−	0.876975i	$-0.340442\pi$
$654$		0			0
$655$			33.4641i			1.30755i
$656$		0			0
$657$	1.03590	+	0.598076i	0.0404142	+	0.0233332i
$658$		0			0
$659$	21.6603	−	37.5167i	0.843764	−	1.46144i	−0.0429268	−	0.999078i	$-0.513668\pi$
$659$	21.6603	−	37.5167i	0.843764	−	1.46144i	0.886691	−	0.462363i	$-0.152998\pi$
$660$		0			0
$661$	−13.3301	+	7.69615i	−0.518482	+	0.299346i	−0.736313	−	0.676641i	$-0.763435\pi$
$661$	−13.3301	+	7.69615i	−0.518482	+	0.299346i	0.217831	+	0.975986i	$0.430102\pi$
$662$		0			0
$663$	−9.69615	−	9.33013i	−0.376567	−	0.362352i
$664$		0			0
$665$	1.39230	−	0.803848i	0.0539913	−	0.0311719i
$666$		0			0
$667$	6.50962	−	11.2750i	0.252053	−	0.436569i
$668$		0			0
$669$	−21.4641	−	12.3923i	−0.829850	−	0.479114i
$670$		0			0
$671$			7.12436i			0.275033i
$672$		0			0
$673$	−3.10770	−	5.38269i	−0.119793	−	0.207487i	0.799893	−	0.600143i	$-0.204890\pi$
$673$	−3.10770	−	5.38269i	−0.119793	−	0.207487i	−0.919685	+	0.392656i	$0.871556\pi$
$674$		0			0
$675$	−2.00000			−0.0769800
$676$		0			0
$677$	14.5359			0.558660			0.279330	−	0.960195i	$-0.409888\pi$
$677$	14.5359			0.558660			0.279330	+	0.960195i	$0.409888\pi$
$678$		0			0
$679$	−3.66025	−	6.33975i	−0.140468	−	0.243297i
$680$		0			0
$681$		−	16.0526i		−	0.615135i
$682$		0			0
$683$	8.78461	+	5.07180i	0.336134	+	0.194067i	0.658561	−	0.752527i	$-0.271165\pi$
$683$	8.78461	+	5.07180i	0.336134	+	0.194067i	−0.322427	+	0.946594i	$0.604499\pi$
$684$		0			0
$685$	10.7942	−	18.6962i	0.412426	−	0.714343i
$686$		0			0
$687$	−24.1244	+	13.9282i	−0.920402	+	0.531394i
$688$		0			0
$689$	15.4019	+	14.8205i	0.586767	+	0.564616i
$690$		0			0
$691$	8.95448	−	5.16987i	0.340645	−	0.196671i	−0.319912	−	0.947447i	$-0.603654\pi$
$691$	8.95448	−	5.16987i	0.340645	−	0.196671i	0.660557	+	0.750776i	$0.270320\pi$
$692$		0			0
$693$	0.267949	−	0.464102i	0.0101785	−	0.0176298i
$694$		0			0
$695$	−30.0000	−	17.3205i	−1.13796	−	0.657004i
$696$		0			0
$697$		−	18.6603i		−	0.706808i
$698$		0			0
$699$	1.00000	+	1.73205i	0.0378235	+	0.0655122i
$700$		0			0
$701$	−32.1051			−1.21259			−0.606297	−	0.795238i	$-0.707346\pi$
$701$	−32.1051			−1.21259			−0.606297	+	0.795238i	$0.707346\pi$
$702$		0			0
$703$	−10.7321			−0.404767
$704$		0			0
$705$	5.83013	+	10.0981i	0.219575	+	0.380316i
$706$		0			0
$707$		−	10.5885i		−	0.398220i
$708$		0			0
$709$	−30.1865	−	17.4282i	−1.13368	−	0.654530i	−0.188821	−	0.982011i	$-0.560467\pi$
$709$	−30.1865	−	17.4282i	−1.13368	−	0.654530i	−0.944858	+	0.327482i	$0.893800\pi$
$710$		0			0
$711$	−6.19615	+	10.7321i	−0.232374	+	0.402483i
$712$		0			0
$713$	−10.3923	+	6.00000i	−0.389195	+	0.224702i
$714$		0			0
$715$	1.09808	−	4.43782i	0.0410657	−	0.165965i
$716$		0			0
$717$	23.1506	−	13.3660i	0.864576	−	0.499163i
$718$		0			0
$719$	18.5885	−	32.1962i	0.693232	−	1.20071i	−0.277540	−	0.960714i	$-0.589519\pi$
$719$	18.5885	−	32.1962i	0.693232	−	1.20071i	0.970773	−	0.240000i	$-0.0771474\pi$
$720$		0			0
$721$	1.73205	+	1.00000i	0.0645049	+	0.0372419i
$722$		0			0
$723$		−	22.6603i		−	0.842744i
$724$		0			0
$725$	5.92820	+	10.2679i	0.220168	+	0.381342i
$726$		0			0
$727$	−1.26795			−0.0470256			−0.0235128	−	0.999724i	$-0.507485\pi$
$727$	−1.26795			−0.0470256			−0.0235128	+	0.999724i	$0.507485\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	3.36603	+	5.83013i	0.124497	+	0.215635i
$732$		0			0
$733$			35.0000i			1.29275i	0.763018	+	0.646377i	$0.223717\pi$
$733$			35.0000i			1.29275i	−0.763018	+	0.646377i	$0.776283\pi$
$734$		0			0
$735$	9.69615	+	5.59808i	0.357648	+	0.206488i
$736$		0			0
$737$	1.92820	−	3.33975i	0.0710263	−	0.123021i
$738$		0			0
$739$	−21.4641	+	12.3923i	−0.789570	+	0.455858i	−0.839811	−	0.542879i	$-0.817334\pi$
$739$	−21.4641	+	12.3923i	−0.789570	+	0.455858i	0.0502413	+	0.998737i	$0.484001\pi$
$740$		0			0
$741$	3.16987	−	3.29423i	0.116448	−	0.121017i
$742$		0			0
$743$	27.8038	−	16.0526i	1.02002	−	0.588911i	0.105913	−	0.994375i	$-0.466223\pi$
$743$	27.8038	−	16.0526i	1.02002	−	0.588911i	0.914111	+	0.405464i	$0.132890\pi$
$744$		0			0
$745$	−8.30385	+	14.3827i	−0.304229	+	0.526941i
$746$		0			0
$747$	13.5622	+	7.83013i	0.496214	+	0.286489i
$748$		0			0
$749$			11.0718i			0.404555i
$750$		0			0
$751$	−0.830127	−	1.43782i	−0.0302918	−	0.0524669i	0.850482	−	0.526004i	$-0.176310\pi$
$751$	−0.830127	−	1.43782i	−0.0302918	−	0.0524669i	−0.880774	+	0.473537i	$0.842977\pi$
$752$		0			0
$753$	−9.46410			−0.344891
$754$		0			0
$755$	−35.9090			−1.30686
$756$		0			0
$757$	−17.3923	−	30.1244i	−0.632134	−	1.09489i	−0.987115	−	0.160015i	$-0.948846\pi$
$757$	−17.3923	−	30.1244i	−0.632134	−	1.09489i	0.354981	−	0.934874i	$-0.384487\pi$
$758$		0			0
$759$			1.60770i			0.0583556i
$760$		0			0
$761$	8.19615	+	4.73205i	0.297110	+	0.171537i	0.641144	−	0.767421i	$-0.278460\pi$
$761$	8.19615	+	4.73205i	0.297110	+	0.171537i	−0.344034	+	0.938957i	$0.611793\pi$
$762$		0			0
$763$	−0.143594	+	0.248711i	−0.00519844	+	0.00900395i
$764$		0			0
$765$	5.59808	−	3.23205i	0.202399	−	0.116855i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−34.2679	+	19.7846i	−1.23573	+	0.713451i	−0.968219	−	0.250103i	$-0.919536\pi$
$769$	−34.2679	+	19.7846i	−1.23573	+	0.713451i	−0.267515	+	0.963554i	$0.586202\pi$
$770$		0			0
$771$	8.86603	−	15.3564i	0.319302	−	0.553047i
$772$		0			0
$773$	40.5167	+	23.3923i	1.45728	+	0.841363i	0.998877	−	0.0473801i	$-0.0150872\pi$
$773$	40.5167	+	23.3923i	1.45728	+	0.841363i	0.458406	+	0.888743i	$0.348421\pi$
$774$		0			0
$775$		−	10.9282i		−	0.392553i
$776$		0			0
$777$	3.09808	+	5.36603i	0.111143	+	0.192505i
$778$		0			0
$779$	6.33975			0.227145
$780$		0			0
$781$	6.00000			0.214697
$782$		0			0
$783$	−2.96410	−	5.13397i	−0.105928	−	0.183473i
$784$		0			0
$785$			26.0718i			0.930542i
$786$		0			0
$787$	−7.51666	−	4.33975i	−0.267940	−	0.154695i	0.360011	−	0.932948i	$-0.382773\pi$
$787$	−7.51666	−	4.33975i	−0.267940	−	0.154695i	−0.627951	+	0.778253i	$0.716106\pi$
$788$		0			0
$789$	6.16987	−	10.6865i	0.219653	−	0.380451i
$790$		0			0
$791$	−2.95448	+	1.70577i	−0.105049	+	0.0606502i
$792$		0			0
$793$	33.7128	−	9.73205i	1.19718	−	0.345595i
$794$		0			0
$795$	−8.89230	+	5.13397i	−0.315378	+	0.182083i
$796$		0			0
$797$	3.00000	−	5.19615i	0.106265	−	0.184057i	−0.807989	−	0.589197i	$-0.799444\pi$
$797$	3.00000	−	5.19615i	0.106265	−	0.184057i	0.914255	+	0.405140i	$0.132777\pi$
$798$		0			0
$799$	21.7583	+	12.5622i	0.769754	+	0.444418i
$800$		0			0
$801$		−	2.53590i		−	0.0896016i
$802$		0			0
$803$	0.437822	+	0.758330i	0.0154504	+	0.0267609i
$804$		0			0
$805$	2.78461			0.0981446
$806$		0			0
$807$	−9.46410			−0.333152
$808$		0			0
$809$	−1.13397	−	1.96410i	−0.0398684	−	0.0690541i	0.845403	−	0.534130i	$-0.179361\pi$
$809$	−1.13397	−	1.96410i	−0.0398684	−	0.0690541i	−0.885271	+	0.465075i	$0.846027\pi$
$810$		0			0
$811$			50.2487i			1.76447i	0.470808	+	0.882235i	$0.343962\pi$
$811$			50.2487i			1.76447i	−0.470808	+	0.882235i	$0.656038\pi$
$812$		0			0
$813$	13.8564	+	8.00000i	0.485965	+	0.280572i
$814$		0			0
$815$	5.66025	−	9.80385i	0.198270	−	0.343414i
$816$		0			0
$817$	−1.98076	+	1.14359i	−0.0692981	+	0.0400093i
$818$		0			0
$819$	−2.56218	−	0.633975i	−0.0895297	−	0.0221529i
$820$		0			0
$821$	25.0526	−	14.4641i	0.874340	−	0.504801i	0.00555219	−	0.999985i	$-0.498233\pi$
$821$	25.0526	−	14.4641i	0.874340	−	0.504801i	0.868788	+	0.495184i	$0.164899\pi$
$822$		0			0
$823$	−12.0000	+	20.7846i	−0.418294	+	0.724506i	−0.995768	−	0.0919029i	$-0.970705\pi$
$823$	−12.0000	+	20.7846i	−0.418294	+	0.724506i	0.577474	+	0.816409i	$0.304038\pi$
$824$		0			0
$825$	−1.26795	−	0.732051i	−0.0441443	−	0.0254867i
$826$		0			0
$827$		−	35.6077i		−	1.23820i	−0.785312	−	0.619100i	$-0.787497\pi$
$827$		−	35.6077i		−	1.23820i	0.785312	−	0.619100i	$-0.212503\pi$
$828$		0			0
$829$	11.1340	+	19.2846i	0.386699	+	0.669782i	0.992003	−	0.126212i	$-0.0402819\pi$
$829$	11.1340	+	19.2846i	0.386699	+	0.669782i	−0.605304	+	0.795994i	$0.706949\pi$
$830$		0			0
$831$	−8.12436			−0.281831
$832$		0			0
$833$	24.1244			0.835859
$834$		0			0
$835$	−4.73205	−	8.19615i	−0.163759	−	0.283640i
$836$		0			0
$837$			5.46410i			0.188867i
$838$		0			0
$839$	8.53590	+	4.92820i	0.294692	+	0.170140i	0.640056	−	0.768328i	$-0.278911\pi$
$839$	8.53590	+	4.92820i	0.294692	+	0.170140i	−0.345364	+	0.938469i	$0.612245\pi$
$840$		0			0
$841$	−3.07180	+	5.32051i	−0.105924	+	0.183466i
$842$		0			0
$843$	21.4019	−	12.3564i	0.737121	−	0.425577i
$844$		0			0
$845$	−22.5000	+	0.866025i	−0.774024	+	0.0297922i
$846$		0			0
$847$	−6.63397	+	3.83013i	−0.227946	+	0.131605i
$848$		0			0
$849$	10.7583	−	18.6340i	0.369225	−	0.639516i
$850$		0			0
$851$	−16.0981	−	9.29423i	−0.551835	−	0.318602i
$852$		0			0
$853$			56.0333i			1.91854i	0.282483	+	0.959272i	$0.408842\pi$
$853$			56.0333i			1.91854i	−0.282483	+	0.959272i	$0.591158\pi$
$854$		0			0
$855$	1.09808	+	1.90192i	0.0375534	+	0.0650444i
$856$		0			0
$857$	−10.5167			−0.359242			−0.179621	−	0.983736i	$-0.557487\pi$
$857$	−10.5167			−0.359242			−0.179621	+	0.983736i	$0.557487\pi$
$858$		0			0
$859$	−24.4449			−0.834048			−0.417024	−	0.908895i	$-0.636927\pi$
$859$	−24.4449			−0.834048			−0.417024	+	0.908895i	$0.636927\pi$
$860$		0			0
$861$	−1.83013	−	3.16987i	−0.0623706	−	0.108029i
$862$		0			0
$863$			10.3397i			0.351969i	0.984393	+	0.175985i	$0.0563109\pi$
$863$			10.3397i			0.351969i	−0.984393	+	0.175985i	$0.943689\pi$
$864$		0			0
$865$	15.8038	+	9.12436i	0.537347	+	0.310237i
$866$		0			0
$867$	−1.53590	+	2.66025i	−0.0521618	+	0.0903470i
$868$		0			0
$869$	−7.85641	+	4.53590i	−0.266510	+	0.153870i
$870$		0			0
$871$	−18.4378	−	4.56218i	−0.624742	−	0.154583i
$872$		0			0
$873$	8.66025	−	5.00000i	0.293105	−	0.169224i
$874$		0			0
$875$	−4.43782	+	7.68653i	−0.150026	+	0.259852i
$876$		0			0
$877$	16.4545	+	9.50000i	0.555628	+	0.320792i	0.751389	−	0.659860i	$-0.229384\pi$
$877$	16.4545	+	9.50000i	0.555628	+	0.320792i	−0.195761	+	0.980652i	$0.562718\pi$
$878$		0			0
$879$		−	2.12436i		−	0.0716527i
$880$		0			0
$881$	10.2583	+	17.7679i	0.345612	+	0.598617i	0.985465	−	0.169880i	$-0.0543380\pi$
$881$	10.2583	+	17.7679i	0.345612	+	0.598617i	−0.639853	+	0.768497i	$0.721005\pi$
$882$		0			0
$883$	−32.7846			−1.10329			−0.551645	−	0.834079i	$-0.686000\pi$
$883$	−32.7846			−1.10329			−0.551645	+	0.834079i	$0.686000\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.07180	+	1.85641i	0.0359874	+	0.0623320i	0.883458	−	0.468510i	$-0.155209\pi$
$887$	1.07180	+	1.85641i	0.0359874	+	0.0623320i	−0.847471	+	0.530842i	$0.821876\pi$
$888$		0			0
$889$			2.92820i			0.0982088i
$890$		0			0
$891$	0.633975	+	0.366025i	0.0212389	+	0.0122623i
$892$		0			0
$893$	−4.26795	+	7.39230i	−0.142821	+	0.247374i
$894$		0			0
$895$	−25.9019	+	14.9545i	−0.865806	+	0.499873i
$896$		0			0
$897$	7.60770	−	2.19615i	0.254014	−	0.0733274i
$898$		0			0
$899$	28.0526	−	16.1962i	0.935605	−	0.540172i
$900$		0			0
$901$	−11.0622	+	19.1603i	−0.368535	+	0.638321i
$902$		0			0
$903$	1.14359	+	0.660254i	0.0380564	+	0.0219719i
$904$		0			0
$905$		−	15.2487i		−	0.506884i
$906$		0			0
$907$	19.5167	+	33.8038i	0.648040	+	1.12244i	0.983590	+	0.180416i	$0.0577444\pi$
$907$	19.5167	+	33.8038i	0.648040	+	1.12244i	−0.335550	+	0.942022i	$0.608922\pi$
$908$		0			0
$909$	14.4641			0.479744
$910$		0			0
$911$	−9.46410			−0.313560			−0.156780	−	0.987634i	$-0.550111\pi$
$911$	−9.46410			−0.313560			−0.156780	+	0.987634i	$0.550111\pi$
$912$		0			0
$913$	5.73205	+	9.92820i	0.189703	+	0.328576i
$914$		0			0
$915$			16.8564i			0.557256i
$916$		0			0
$917$	12.2487	+	7.07180i	0.404488	+	0.233531i
$918$		0			0
$919$	4.19615	−	7.26795i	0.138418	−	0.239748i	−0.788480	−	0.615061i	$-0.789131\pi$
$919$	4.19615	−	7.26795i	0.138418	−	0.239748i	0.926898	+	0.375313i	$0.122465\pi$
$920$		0			0
$921$	9.29423	−	5.36603i	0.306255	−	0.176817i
$922$		0			0
$923$	−8.19615	−	28.3923i	−0.269780	−	0.934544i
$924$		0			0
$925$	14.6603	−	8.46410i	0.482026	−	0.278298i
$926$		0			0
$927$	−1.36603	+	2.36603i	−0.0448662	+	0.0777105i
$928$		0			0
$929$	22.5788	+	13.0359i	0.740788	+	0.427694i	0.822356	−	0.568974i	$-0.192659\pi$
$929$	22.5788	+	13.0359i	0.740788	+	0.427694i	−0.0815680	+	0.996668i	$0.525993\pi$
$930$		0			0
$931$			8.19615i			0.268618i
$932$		0			0
$933$	2.16987	+	3.75833i	0.0710385	+	0.123042i
$934$		0			0
$935$	4.73205			0.154755
$936$		0			0
$937$	−54.3205			−1.77457			−0.887287	−	0.461218i	$-0.847413\pi$
$937$	−54.3205			−1.77457			−0.887287	+	0.461218i	$0.847413\pi$
$938$		0			0
$939$	1.66025	+	2.87564i	0.0541803	+	0.0938431i
$940$		0			0
$941$			14.7846i			0.481965i	0.970530	+	0.240982i	$0.0774696\pi$
$941$			14.7846i			0.481965i	−0.970530	+	0.240982i	$0.922530\pi$
$942$		0			0
$943$	9.50962	+	5.49038i	0.309676	+	0.178791i
$944$		0			0
$945$	0.633975	−	1.09808i	0.0206232	−	0.0357204i
$946$		0			0
$947$	−11.3205	+	6.53590i	−0.367867	+	0.212388i	−0.672526	−	0.740073i	$-0.734791\pi$
$947$	−11.3205	+	6.53590i	−0.367867	+	0.212388i	0.304659	+	0.952461i	$0.401457\pi$
$948$		0			0
$949$	2.99038	−	3.10770i	0.0970719	−	0.100880i
$950$		0			0
$951$	9.69615	−	5.59808i	0.314419	−	0.181530i
$952$		0			0
$953$	−4.39230	+	7.60770i	−0.142281	+	0.246437i	−0.928355	−	0.371694i	$-0.878777\pi$
$953$	−4.39230	+	7.60770i	−0.142281	+	0.246437i	0.786074	+	0.618132i	$0.212110\pi$
$954$		0			0
$955$	1.60770	+	0.928203i	0.0520238	+	0.0300360i
$956$		0			0
$957$		−	4.33975i		−	0.140284i
$958$		0			0
$959$	−4.56218	−	7.90192i	−0.147320	−	0.255166i
$960$		0			0
$961$	1.14359			0.0368901
$962$		0			0
$963$	−15.1244			−0.487376
$964$		0			0
$965$	7.16025	+	12.4019i	0.230497	+	0.399232i
$966$		0			0
$967$		−	0.732051i		−	0.0235412i	−0.999931	−	0.0117706i	$-0.996253\pi$
$967$		−	0.732051i		−	0.0235412i	0.999931	−	0.0117706i	$-0.00374678\pi$
$968$		0			0
$969$	4.09808	+	2.36603i	0.131649	+	0.0760077i
$970$		0			0
$971$	10.1962	−	17.6603i	0.327210	−	0.566745i	−0.654747	−	0.755848i	$-0.727225\pi$
$971$	10.1962	−	17.6603i	0.327210	−	0.566745i	0.981957	+	0.189104i	$0.0605582\pi$
$972$		0			0
$973$	−12.6795	+	7.32051i	−0.406486	+	0.234685i
$974$		0			0
$975$	−1.73205	+	7.00000i	−0.0554700	+	0.224179i
$976$		0			0
$977$	−47.5981	+	27.4808i	−1.52280	+	0.879187i	−0.523161	+	0.852234i	$0.675247\pi$
$977$	−47.5981	+	27.4808i	−1.52280	+	0.879187i	−0.999637	+	0.0269534i	$0.991419\pi$
$978$		0			0
$979$	0.928203	−	1.60770i	0.0296655	−	0.0513822i
$980$		0			0
$981$	−0.339746	−	0.196152i	−0.0108473	−	0.00626266i
$982$		0			0
$983$			26.6410i			0.849716i	0.905260	+	0.424858i	$0.139676\pi$
$983$			26.6410i			0.849716i	−0.905260	+	0.424858i	$0.860324\pi$
$984$		0			0
$985$	12.9282	+	22.3923i	0.411927	+	0.713478i
$986$		0			0
$987$	4.92820			0.156866
$988$		0			0
$989$	−3.96152			−0.125969
$990$		0			0
$991$	6.43782	+	11.1506i	0.204504	+	0.354212i	0.949975	−	0.312327i	$-0.101108\pi$
$991$	6.43782	+	11.1506i	0.204504	+	0.354212i	−0.745470	+	0.666539i	$0.767775\pi$
$992$		0			0
$993$			12.0000i			0.380808i
$994$		0			0
$995$	−26.4904	−	15.2942i	−0.839802	−	0.484860i
$996$		0			0
$997$	15.9904	−	27.6962i	0.506420	−	0.877146i	−0.493552	−	0.869716i	$-0.664302\pi$
$997$	15.9904	−	27.6962i	0.506420	−	0.877146i	0.999972	−	0.00742963i	$-0.00236495\pi$
$998$		0			0
$999$	−7.33013	+	4.23205i	−0.231915	+	0.133896i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.2.bf.a.49.1	✓	4
3.2	odd	2		936.2.bi.a.361.1		4
4.3	odd	2		624.2.bv.c.49.2		4
12.11	even	2		1872.2.by.g.1297.2		4
13.2	odd	12		4056.2.a.t.1.2		2
13.3	even	3		4056.2.c.k.337.4		4
13.4	even	6	inner	312.2.bf.a.121.1	yes	4
13.10	even	6		4056.2.c.k.337.1		4
13.11	odd	12		4056.2.a.u.1.1		2
39.17	odd	6		936.2.bi.a.433.1		4
52.11	even	12		8112.2.a.br.1.1		2
52.15	even	12		8112.2.a.bw.1.2		2
52.43	odd	6		624.2.bv.c.433.2		4
156.95	even	6		1872.2.by.g.433.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bf.a.49.1	✓	4	1.1	even	1	trivial
312.2.bf.a.121.1	yes	4	13.4	even	6	inner
624.2.bv.c.49.2		4	4.3	odd	2
624.2.bv.c.433.2		4	52.43	odd	6
936.2.bi.a.361.1		4	3.2	odd	2
936.2.bi.a.433.1		4	39.17	odd	6
1872.2.by.g.433.2		4	156.95	even	6
1872.2.by.g.1297.2		4	12.11	even	2
4056.2.a.t.1.2		2	13.2	odd	12
4056.2.a.u.1.1		2	13.11	odd	12
4056.2.c.k.337.1		4	13.10	even	6
4056.2.c.k.337.4		4	13.3	even	3
8112.2.a.br.1.1		2	52.11	even	12
8112.2.a.bw.1.2		2	52.15	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	312.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +1.73205i q^{5} +(0.633975 + 0.366025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-0.633975 + 0.366025i) q^{11} +(2.59808 + 2.50000i) q^{13} +(-1.50000 + 0.866025i) q^{15} +(-1.86603 + 3.23205i) q^{17} +(-1.09808 - 0.633975i) q^{19} +0.732051i q^{21} +(-1.09808 - 1.90192i) q^{23} +2.00000 q^{25} -1.00000 q^{27} +(2.96410 + 5.13397i) q^{29} -5.46410i q^{31} +(-0.633975 - 0.366025i) q^{33} +(-0.633975 + 1.09808i) q^{35} +(7.33013 - 4.23205i) q^{37} +(-0.866025 + 3.50000i) q^{39} +(-4.33013 + 2.50000i) q^{41} +(0.901924 - 1.56218i) q^{43} +(-1.50000 - 0.866025i) q^{45} -6.73205i q^{47} +(-3.23205 - 5.59808i) q^{49} -3.73205 q^{51} +5.92820 q^{53} +(-0.633975 - 1.09808i) q^{55} -1.26795i q^{57} +(4.86603 - 8.42820i) q^{61} +(-0.633975 + 0.366025i) q^{63} +(-4.33013 + 4.50000i) q^{65} +(-4.56218 + 2.63397i) q^{67} +(1.09808 - 1.90192i) q^{69} +(-7.09808 - 4.09808i) q^{71} -1.19615i q^{73} +(1.00000 + 1.73205i) q^{75} -0.535898 q^{77} +12.3923 q^{79} +(-0.500000 - 0.866025i) q^{81} -15.6603i q^{83} +(-5.59808 - 3.23205i) q^{85} +(-2.96410 + 5.13397i) q^{87} +(-2.19615 + 1.26795i) q^{89} +(0.732051 + 2.53590i) q^{91} +(4.73205 - 2.73205i) q^{93} +(1.09808 - 1.90192i) q^{95} +(-8.66025 - 5.00000i) q^{97} -0.732051i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 6 q^{7} - 2 q^{9} - 6 q^{11} - 6 q^{15} - 4 q^{17} + 6 q^{19} + 6 q^{23} + 8 q^{25} - 4 q^{27} - 2 q^{29} - 6 q^{33} - 6 q^{35} + 12 q^{37} + 14 q^{43} - 6 q^{45} - 6 q^{49} - 8 q^{51} - 4 q^{53}+ \cdots - 6 q^{95}+O(q^{100}) \) 4 * q + 2 * q^3 + 6 * q^7 - 2 * q^9 - 6 * q^11 - 6 * q^15 - 4 * q^17 + 6 * q^19 + 6 * q^23 + 8 * q^25 - 4 * q^27 - 2 * q^29 - 6 * q^33 - 6 * q^35 + 12 * q^37 + 14 * q^43 - 6 * q^45 - 6 * q^49 - 8 * q^51 - 4 * q^53 - 6 * q^55 + 16 * q^61 - 6 * q^63 + 6 * q^67 - 6 * q^69 - 18 * q^71 + 4 * q^75 - 16 * q^77 + 8 * q^79 - 2 * q^81 - 12 * q^85 + 2 * q^87 + 12 * q^89 - 4 * q^91 + 12 * q^93 - 6 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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