LMFDB - Embedded newform 504.2.cx.a.425.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(185,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.185"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cx (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			425.22
Character	$\chi$	$=$	504.425
Dual form			504.2.cx.a.185.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.70521 + 0.303722i) q^{3} +2.22830 q^{5} +(2.51733 - 0.814280i) q^{7} +(2.81551 + 1.03582i) q^{9} +2.12135i q^{11} +(-5.10339 + 2.94644i) q^{13} +(3.79973 + 0.676785i) q^{15} +(-2.34020 - 4.05335i) q^{17} +(-4.54550 - 2.62435i) q^{19} +(4.53990 - 0.623952i) q^{21} -4.36380i q^{23} -0.0346748 q^{25} +(4.48644 + 2.62143i) q^{27} +(-2.25182 - 1.30009i) q^{29} +(6.59237 + 3.80611i) q^{31} +(-0.644302 + 3.61736i) q^{33} +(5.60937 - 1.81446i) q^{35} +(-1.80274 + 3.12244i) q^{37} +(-9.59726 + 3.47430i) q^{39} +(0.0395039 + 0.0684228i) q^{41} +(-1.24922 + 2.16371i) q^{43} +(6.27379 + 2.30813i) q^{45} +(1.89837 + 3.28807i) q^{47} +(5.67390 - 4.09962i) q^{49} +(-2.75945 - 7.62260i) q^{51} +(-4.08014 + 2.35567i) q^{53} +4.72701i q^{55} +(-6.95397 - 5.85564i) q^{57} +(6.59695 - 11.4262i) q^{59} +(-7.06624 + 4.07970i) q^{61} +(7.93100 + 0.314897i) q^{63} +(-11.3719 + 6.56556i) q^{65} +(2.37614 - 4.11559i) q^{67} +(1.32538 - 7.44121i) q^{69} -10.0325i q^{71} +(-12.6610 + 7.30986i) q^{73} +(-0.0591279 - 0.0105315i) q^{75} +(1.72737 + 5.34014i) q^{77} +(7.27414 + 12.5992i) q^{79} +(6.85414 + 5.83273i) q^{81} +(6.41294 - 11.1075i) q^{83} +(-5.21468 - 9.03209i) q^{85} +(-3.44497 - 2.90086i) q^{87} +(2.73464 - 4.73654i) q^{89} +(-10.4477 + 11.5728i) q^{91} +(10.0854 + 8.49248i) q^{93} +(-10.1287 - 5.84783i) q^{95} +(-12.9290 - 7.46454i) q^{97} +(-2.19734 + 5.97268i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{9} + 8 q^{15} - 10 q^{21} + 48 q^{25} + 18 q^{27} + 18 q^{29} + 18 q^{31} + 12 q^{33} - 4 q^{39} - 6 q^{41} - 6 q^{43} - 18 q^{45} + 18 q^{47} - 12 q^{49} + 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61}+ \cdots - 64 q^{99}+O(q^{100}) $ 48 * q + 2 * q^9 + 8 * q^15 - 10 * q^21 + 48 * q^25 + 18 * q^27 + 18 * q^29 + 18 * q^31 + 12 * q^33 - 4 * q^39 - 6 * q^41 - 6 * q^43 - 18 * q^45 + 18 * q^47 - 12 * q^49 + 6 * q^51 - 12 * q^53 + 4 * q^57 + 18 * q^61 - 32 * q^63 - 36 * q^65 - 12 * q^77 + 6 * q^79 + 6 * q^81 - 54 * q^87 - 18 * q^89 + 6 * q^91 + 4 * q^93 - 54 * q^95 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	1.70521	+	0.303722i	0.984505	+	0.175354i
$3$	1.70521	+	0.303722i	0.984505	+	0.175354i
$4$		0			0
$5$	2.22830			0.996526			0.498263	−	0.867026i	$-0.333971\pi$
$5$	2.22830			0.996526			0.498263	+	0.867026i	$0.333971\pi$
$6$		0			0
$7$	2.51733	−	0.814280i	0.951461	−	0.307769i
$7$	2.51733	−	0.814280i	0.951461	−	0.307769i
$8$		0			0
$9$	2.81551	+	1.03582i	0.938502	+	0.345274i
$10$		0			0
$11$			2.12135i			0.639612i	0.947483	+	0.319806i	$0.103618\pi$
$11$			2.12135i			0.639612i	−0.947483	+	0.319806i	$0.896382\pi$
$12$		0			0
$13$	−5.10339	+	2.94644i	−1.41542	+	0.817196i	−0.995892	−	0.0905443i	$-0.971139\pi$
$13$	−5.10339	+	2.94644i	−1.41542	+	0.817196i	−0.419533	+	0.907740i	$0.637806\pi$
$14$		0			0
$15$	3.79973	+	0.676785i	0.981086	+	0.174745i
$16$		0			0
$17$	−2.34020	−	4.05335i	−0.567583	−	0.983082i	−0.996804	−	0.0798828i	$-0.974545\pi$
$17$	−2.34020	−	4.05335i	−0.567583	−	0.983082i	0.429222	−	0.903199i	$-0.358788\pi$
$18$		0			0
$19$	−4.54550	−	2.62435i	−1.04281	−	0.602066i	−0.122181	−	0.992508i	$-0.538989\pi$
$19$	−4.54550	−	2.62435i	−1.04281	−	0.602066i	−0.920628	+	0.390442i	$0.872322\pi$
$20$		0			0
$21$	4.53990	−	0.623952i	0.990687	−	0.136158i
$22$		0			0
$23$		−	4.36380i		−	0.909915i	−0.890513	−	0.454958i	$-0.849654\pi$
$23$		−	4.36380i		−	0.909915i	0.890513	−	0.454958i	$-0.150346\pi$
$24$		0			0
$25$	−0.0346748			−0.00693496
$26$		0			0
$27$	4.48644	+	2.62143i	0.863415	+	0.504495i
$28$		0			0
$29$	−2.25182	−	1.30009i	−0.418152	−	0.241420i	0.276134	−	0.961119i	$-0.410947\pi$
$29$	−2.25182	−	1.30009i	−0.418152	−	0.241420i	−0.694286	+	0.719699i	$0.744280\pi$
$30$		0			0
$31$	6.59237	+	3.80611i	1.18402	+	0.683597i	0.956942	−	0.290278i	$-0.0937479\pi$
$31$	6.59237	+	3.80611i	1.18402	+	0.683597i	0.227083	+	0.973876i	$0.427081\pi$
$32$		0			0
$33$	−0.644302	+	3.61736i	−0.112159	+	0.629701i
$34$		0			0
$35$	5.60937	−	1.81446i	0.948156	−	0.306700i
$36$		0			0
$37$	−1.80274	+	3.12244i	−0.296369	+	0.513326i	−0.975302	−	0.220874i	$-0.929109\pi$
$37$	−1.80274	+	3.12244i	−0.296369	+	0.513326i	0.678934	+	0.734200i	$0.262442\pi$
$38$		0			0
$39$	−9.59726	+	3.47430i	−1.53679	+	0.556333i
$40$		0			0
$41$	0.0395039	+	0.0684228i	0.00616948	+	0.0106858i	0.869094	−	0.494648i	$-0.164703\pi$
$41$	0.0395039	+	0.0684228i	0.00616948	+	0.0106858i	−0.862924	+	0.505333i	$0.831370\pi$
$42$		0			0
$43$	−1.24922	+	2.16371i	−0.190504	+	0.329962i	−0.945417	−	0.325862i	$-0.894345\pi$
$43$	−1.24922	+	2.16371i	−0.190504	+	0.329962i	0.754914	+	0.655824i	$0.227679\pi$
$44$		0			0
$45$	6.27379	+	2.30813i	0.935242	+	0.344075i
$46$		0			0
$47$	1.89837	+	3.28807i	0.276905	+	0.479614i	0.970614	−	0.240642i	$-0.0773578\pi$
$47$	1.89837	+	3.28807i	0.276905	+	0.479614i	−0.693709	+	0.720256i	$0.744024\pi$
$48$		0			0
$49$	5.67390	−	4.09962i	0.810557	−	0.585660i
$50$		0			0
$51$	−2.75945	−	7.62260i	−0.386401	−	1.06738i
$52$		0			0
$53$	−4.08014	+	2.35567i	−0.560451	+	0.323576i	−0.753326	−	0.657647i	$-0.771552\pi$
$53$	−4.08014	+	2.35567i	−0.560451	+	0.323576i	0.192876	+	0.981223i	$0.438219\pi$
$54$		0			0
$55$			4.72701i			0.637390i
$56$		0			0
$57$	−6.95397	−	5.85564i	−0.921076	−	0.775598i
$58$		0			0
$59$	6.59695	−	11.4262i	0.858849	−	1.48757i	−0.0141784	−	0.999899i	$-0.504513\pi$
$59$	6.59695	−	11.4262i	0.858849	−	1.48757i	0.873028	−	0.487671i	$-0.162153\pi$
$60$		0			0
$61$	−7.06624	+	4.07970i	−0.904740	+	0.522352i	−0.878735	−	0.477310i	$-0.841612\pi$
$61$	−7.06624	+	4.07970i	−0.904740	+	0.522352i	−0.0260047	+	0.999662i	$0.508278\pi$
$62$		0			0
$63$	7.93100	+	0.314897i	0.999213	+	0.0396733i
$64$		0			0
$65$	−11.3719	+	6.56556i	−1.41051	+	0.814357i
$66$		0			0
$67$	2.37614	−	4.11559i	0.290292	−	0.502800i	−0.683587	−	0.729869i	$-0.739581\pi$
$67$	2.37614	−	4.11559i	0.290292	−	0.502800i	0.973879	+	0.227069i	$0.0729144\pi$
$68$		0			0
$69$	1.32538	−	7.44121i	0.159557	−	0.895816i
$70$		0			0
$71$		−	10.0325i		−	1.19064i	−0.803490	−	0.595318i	$-0.797026\pi$
$71$		−	10.0325i		−	1.19064i	0.803490	−	0.595318i	$-0.202974\pi$
$72$		0			0
$73$	−12.6610	+	7.30986i	−1.48186	+	0.855554i	−0.999788	−	0.0205755i	$-0.993450\pi$
$73$	−12.6610	+	7.30986i	−1.48186	+	0.855554i	−0.482075	+	0.876130i	$0.660117\pi$
$74$		0			0
$75$	−0.0591279	−	0.0105315i	−0.00682750	−	0.00121607i
$76$		0			0
$77$	1.72737	+	5.34014i	0.196853	+	0.608566i
$78$		0			0
$79$	7.27414	+	12.5992i	0.818405	+	1.41752i	0.906857	+	0.421439i	$0.138475\pi$
$79$	7.27414	+	12.5992i	0.818405	+	1.41752i	−0.0884516	+	0.996080i	$0.528192\pi$
$80$		0			0
$81$	6.85414	+	5.83273i	0.761571	+	0.648081i
$82$		0			0
$83$	6.41294	−	11.1075i	0.703911	−	1.21921i	−0.263172	−	0.964749i	$-0.584769\pi$
$83$	6.41294	−	11.1075i	0.703911	−	1.21921i	0.967083	−	0.254461i	$-0.0818982\pi$
$84$		0			0
$85$	−5.21468	−	9.03209i	−0.565611	−	0.979667i
$86$		0			0
$87$	−3.44497	−	2.90086i	−0.369339	−	0.311004i
$88$		0			0
$89$	2.73464	−	4.73654i	0.289871	−	0.502072i	−0.683907	−	0.729569i	$-0.739721\pi$
$89$	2.73464	−	4.73654i	0.289871	−	0.502072i	0.973779	+	0.227497i	$0.0730541\pi$
$90$		0			0
$91$	−10.4477	+	11.5728i	−1.09521	+	1.21315i
$92$		0			0
$93$	10.0854	+	8.49248i	1.04581	+	0.880629i
$94$		0			0
$95$	−10.1287	−	5.84783i	−1.03919	−	0.599975i
$96$		0			0
$97$	−12.9290	−	7.46454i	−1.31274	−	0.757909i	−0.330188	−	0.943915i	$-0.607112\pi$
$97$	−12.9290	−	7.46454i	−1.31274	−	0.757909i	−0.982549	+	0.186006i	$0.940446\pi$
$98$		0			0
$99$	−2.19734	+	5.97268i	−0.220841	+	0.600277i
$100$		0			0
$101$	−3.26604			−0.324983			−0.162492	−	0.986710i	$-0.551953\pi$
$101$	−3.26604			−0.324983			−0.162492	+	0.986710i	$0.551953\pi$
$102$		0			0
$103$			4.76828i			0.469833i	0.972016	+	0.234916i	$0.0754817\pi$
$103$			4.76828i			0.469833i	−0.972016	+	0.234916i	$0.924518\pi$
$104$		0			0
$105$	10.1163	−	1.39035i	0.987246	−	0.135685i
$106$		0			0
$107$	6.39655	+	3.69305i	0.618378	+	0.357021i	0.776237	−	0.630441i	$-0.217126\pi$
$107$	6.39655	+	3.69305i	0.618378	+	0.357021i	−0.157859	+	0.987462i	$0.550459\pi$
$108$		0			0
$109$	−1.17349	−	2.03254i	−0.112400	−	0.194682i	0.804338	−	0.594173i	$-0.202520\pi$
$109$	−1.17349	−	2.03254i	−0.112400	−	0.194682i	−0.916737	+	0.399490i	$0.869187\pi$
$110$		0			0
$111$	−4.02241	+	4.77689i	−0.381790	+	0.453402i
$112$		0			0
$113$	11.8961	−	6.86824i	1.11909	−	0.646109i	0.177925	−	0.984044i	$-0.443062\pi$
$113$	11.8961	−	6.86824i	1.11909	−	0.646109i	0.941170	+	0.337935i	$0.109728\pi$
$114$		0			0
$115$		−	9.72386i		−	0.906754i
$116$		0			0
$117$	−17.4206	+	3.00952i	−1.61054	+	0.278230i
$118$		0			0
$119$	−9.19163	−	8.29804i	−0.842595	−	0.760680i
$120$		0			0
$121$	6.49987			0.590897
$122$		0			0
$123$	0.0465811	+	0.128674i	0.00420008	+	0.0116021i
$124$		0			0
$125$	−11.2188			−1.00344
$126$		0			0
$127$	−5.97913			−0.530562			−0.265281	−	0.964171i	$-0.585465\pi$
$127$	−5.97913			−0.530562			−0.265281	+	0.964171i	$0.585465\pi$
$128$		0			0
$129$	−2.78735	+	3.31017i	−0.245412	+	0.291444i
$130$		0			0
$131$	−20.9585			−1.83115			−0.915576	−	0.402146i	$-0.868264\pi$
$131$	−20.9585			−1.83115			−0.915576	+	0.402146i	$0.868264\pi$
$132$		0			0
$133$	−13.5795	−	2.90503i	−1.17749	−	0.251898i
$134$		0			0
$135$	9.99713	+	5.84134i	0.860416	+	0.502742i
$136$		0			0
$137$		−	3.46483i		−	0.296021i	−0.988986	−	0.148010i	$-0.952713\pi$
$137$		−	3.46483i		−	0.296021i	0.988986	−	0.148010i	$-0.0472869\pi$
$138$		0			0
$139$	−0.379607	+	0.219166i	−0.0321979	+	0.0185895i	−0.516013	−	0.856581i	$-0.672584\pi$
$139$	−0.379607	+	0.219166i	−0.0321979	+	0.0185895i	0.483815	+	0.875170i	$0.339251\pi$
$140$		0			0
$141$	2.23846	+	6.18344i	0.188512	+	0.520739i
$142$		0			0
$143$	−6.25044	−	10.8261i	−0.522688	−	0.905322i
$144$		0			0
$145$	−5.01773	−	2.89699i	−0.416700	−	0.240582i
$146$		0			0
$147$	10.9204	−	5.26744i	0.900695	−	0.434451i
$148$		0			0
$149$			17.5006i			1.43370i	0.697225	+	0.716852i	$0.254418\pi$
$149$			17.5006i			1.43370i	−0.697225	+	0.716852i	$0.745582\pi$
$150$		0			0
$151$	−0.374840			−0.0305040			−0.0152520	−	0.999884i	$-0.504855\pi$
$151$	−0.374840			−0.0305040			−0.0152520	+	0.999884i	$0.504855\pi$
$152$		0			0
$153$	−2.39030	−	13.8363i	−0.193244	−	1.11860i
$154$		0			0
$155$	14.6898	+	8.48115i	1.17991	+	0.681223i
$156$		0			0
$157$	17.6279	+	10.1775i	1.40686	+	0.812249i	0.995084	−	0.0990372i	$-0.0315763\pi$
$157$	17.6279	+	10.1775i	1.40686	+	0.812249i	0.411773	+	0.911286i	$0.364910\pi$
$158$		0			0
$159$	−7.67299	+	2.77769i	−0.608507	+	0.220285i
$160$		0			0
$161$	−3.55336	−	10.9851i	−0.280044	−	0.865749i
$162$		0			0
$163$	−7.25400	+	12.5643i	−0.568177	+	0.984112i	0.428569	+	0.903509i	$0.359018\pi$
$163$	−7.25400	+	12.5643i	−0.568177	+	0.984112i	−0.996746	+	0.0806027i	$0.974316\pi$
$164$		0			0
$165$	−1.43570	+	8.06056i	−0.111769	+	0.627514i
$166$		0			0
$167$	7.62510	+	13.2071i	0.590048	+	1.02199i	0.994225	+	0.107313i	$0.0342246\pi$
$167$	7.62510	+	13.2071i	0.590048	+	1.02199i	−0.404177	+	0.914681i	$0.632442\pi$
$168$		0			0
$169$	10.8630	−	18.8153i	0.835619	−	1.44733i
$170$		0			0
$171$	−10.0795	−	12.0972i	−0.770800	−	0.925095i
$172$		0			0
$173$	0.940679	+	1.62930i	0.0715185	+	0.123874i	0.899567	−	0.436783i	$-0.143882\pi$
$173$	0.940679	+	1.62930i	0.0715185	+	0.123874i	−0.828048	+	0.560657i	$0.810549\pi$
$174$		0			0
$175$	−0.0872878	+	0.0282350i	−0.00659834	+	0.00213436i
$176$		0			0
$177$	14.7196	−	17.4805i	1.10639	−	1.31392i
$178$		0			0
$179$	−8.64064	+	4.98867i	−0.645831	+	0.372871i	−0.786857	−	0.617135i	$-0.788293\pi$
$179$	−8.64064	+	4.98867i	−0.645831	+	0.372871i	0.141026	+	0.990006i	$0.454960\pi$
$180$		0			0
$181$		−	11.2828i		−	0.838641i	−0.907838	−	0.419320i	$-0.862268\pi$
$181$		−	11.2828i		−	0.838641i	0.907838	−	0.419320i	$-0.137732\pi$
$182$		0			0
$183$	−13.2885	+	4.81058i	−0.982318	+	0.355608i
$184$		0			0
$185$	−4.01705	+	6.95773i	−0.295339	+	0.511543i
$186$		0			0
$187$	8.59858	−	4.96439i	0.628791	−	0.363032i
$188$		0			0
$189$	13.4284	+	2.94579i	0.976773	+	0.214275i
$190$		0			0
$191$	−11.1418	+	6.43270i	−0.806189	+	0.465454i	−0.845631	−	0.533768i	$-0.820775\pi$
$191$	−11.1418	+	6.43270i	−0.806189	+	0.465454i	0.0394414	+	0.999222i	$0.487442\pi$
$192$		0			0
$193$	6.01861	−	10.4245i	0.433229	−	0.750374i	−0.563920	−	0.825829i	$-0.690708\pi$
$193$	6.01861	−	10.4245i	0.433229	−	0.750374i	0.997149	+	0.0754547i	$0.0240408\pi$
$194$		0			0
$195$	−21.3856	+	7.74179i	−1.53145	+	0.554401i
$196$		0			0
$197$			27.7262i			1.97541i	0.156339	+	0.987703i	$0.450031\pi$
$197$			27.7262i			1.97541i	−0.156339	+	0.987703i	$0.549969\pi$
$198$		0			0
$199$	0.382862	−	0.221045i	0.0271404	−	0.0156695i	−0.486368	−	0.873754i	$-0.661679\pi$
$199$	0.382862	−	0.221045i	0.0271404	−	0.0156695i	0.513509	+	0.858084i	$0.328345\pi$
$200$		0			0
$201$	5.30182	−	6.29628i	0.373962	−	0.444105i
$202$		0			0
$203$	−6.72721	−	1.43914i	−0.472157	−	0.101008i
$204$		0			0
$205$	0.0880266	+	0.152467i	0.00614805	+	0.0106487i
$206$		0			0
$207$	4.52012	−	12.2863i	0.314170	−	0.853957i
$208$		0			0
$209$	5.56716	−	9.64260i	0.385088	−	0.666993i
$210$		0			0
$211$	−0.219300	−	0.379839i	−0.0150972	−	0.0261492i	0.858378	−	0.513018i	$-0.171472\pi$
$211$	−0.219300	−	0.379839i	−0.0150972	−	0.0261492i	−0.873475	+	0.486868i	$0.838139\pi$
$212$		0			0
$213$	3.04709	−	17.1075i	0.208783	−	1.17219i
$214$		0			0
$215$	−2.78363	+	4.82139i	−0.189842	+	0.328816i
$216$		0			0
$217$	19.6944	+	4.21319i	1.33694	+	0.286010i
$218$		0			0
$219$	−23.8100	+	8.61943i	−1.60893	+	0.582447i
$220$		0			0
$221$	23.8859	+	13.7905i	1.60674	+	0.927653i
$222$		0			0
$223$	−17.6417	−	10.1854i	−1.18137	−	0.682066i	−0.225041	−	0.974349i	$-0.572252\pi$
$223$	−17.6417	−	10.1854i	−1.18137	−	0.682066i	−0.956332	+	0.292284i	$0.905585\pi$
$224$		0			0
$225$	−0.0976270	−	0.0359169i	−0.00650847	−	0.00239446i
$226$		0			0
$227$	1.50987			0.100214			0.0501068	−	0.998744i	$-0.484044\pi$
$227$	1.50987			0.100214			0.0501068	+	0.998744i	$0.484044\pi$
$228$		0			0
$229$			21.2348i			1.40323i	0.712554	+	0.701617i	$0.247538\pi$
$229$			21.2348i			1.40323i	−0.712554	+	0.701617i	$0.752462\pi$
$230$		0			0
$231$	1.32362	+	9.63072i	0.0870879	+	0.633655i
$232$		0			0
$233$	9.85938	+	5.69231i	0.645909	+	0.372916i	0.786887	−	0.617097i	$-0.211691\pi$
$233$	9.85938	+	5.69231i	0.645909	+	0.372916i	−0.140978	+	0.990013i	$0.545025\pi$
$234$		0			0
$235$	4.23013	+	7.32681i	0.275944	+	0.477948i
$236$		0			0
$237$	8.57731	+	23.6936i	0.557156	+	1.53907i
$238$		0			0
$239$	14.1401	−	8.16380i	0.914648	−	0.528072i	0.0327241	−	0.999464i	$-0.489582\pi$
$239$	14.1401	−	8.16380i	0.914648	−	0.528072i	0.881924	+	0.471392i	$0.156248\pi$
$240$		0			0
$241$		−	23.9706i		−	1.54408i	−0.635571	−	0.772042i	$-0.719235\pi$
$241$		−	23.9706i		−	1.54408i	0.635571	−	0.772042i	$-0.280765\pi$
$242$		0			0
$243$	9.91624	+	12.0278i	0.636127	+	0.771584i
$244$		0			0
$245$	12.6431	−	9.13519i	0.807741	−	0.583626i
$246$		0			0
$247$	30.9299			1.96802
$248$		0			0
$249$	14.3090	−	16.9930i	0.906798	−	1.07689i
$250$		0			0
$251$	25.9828			1.64002			0.820009	−	0.572351i	$-0.193969\pi$
$251$	25.9828			1.64002			0.820009	+	0.572351i	$0.193969\pi$
$252$		0			0
$253$	9.25715			0.581992
$254$		0			0
$255$	−6.14889	−	16.9854i	−0.385058	−	1.06367i
$256$		0			0
$257$	−1.95957			−0.122235			−0.0611173	−	0.998131i	$-0.519466\pi$
$257$	−1.95957			−0.122235			−0.0611173	+	0.998131i	$0.519466\pi$
$258$		0			0
$259$	−1.99555	+	9.32814i	−0.123998	+	0.579623i
$260$		0			0
$261$	−4.99335	−	5.99289i	−0.309080	−	0.370951i
$262$		0			0
$263$		−	3.59945i		−	0.221952i	−0.993823	−	0.110976i	$-0.964602\pi$
$263$		−	3.59945i		−	0.221952i	0.993823	−	0.110976i	$-0.0353976\pi$
$264$		0			0
$265$	−9.09179	+	5.24915i	−0.558504	+	0.322453i
$266$		0			0
$267$	6.10174	−	7.24623i	0.373420	−	0.443462i
$268$		0			0
$269$	−4.06967	−	7.04888i	−0.248132	−	0.429778i	0.714875	−	0.699252i	$-0.246483\pi$
$269$	−4.06967	−	7.04888i	−0.248132	−	0.429778i	−0.963008	+	0.269474i	$0.913150\pi$
$270$		0			0
$271$	16.3378	+	9.43265i	0.992452	+	0.572992i	0.906006	−	0.423264i	$-0.139116\pi$
$271$	16.3378	+	9.43265i	0.992452	+	0.572992i	0.0864458	+	0.996257i	$0.472449\pi$
$272$		0			0
$273$	−21.3304	+	16.5608i	−1.29098	+	1.00231i
$274$		0			0
$275$		−	0.0735574i		−	0.00443568i
$276$		0			0
$277$	21.6679			1.30190			0.650950	−	0.759120i	$-0.274371\pi$
$277$	21.6679			1.30190			0.650950	+	0.759120i	$0.274371\pi$
$278$		0			0
$279$	14.6184	+	17.5446i	0.875181	+	1.05037i
$280$		0			0
$281$	11.6851	+	6.74642i	0.697077	+	0.402457i	0.806258	−	0.591564i	$-0.201489\pi$
$281$	11.6851	+	6.74642i	0.697077	+	0.402457i	−0.109181	+	0.994022i	$0.534823\pi$
$282$		0			0
$283$	−1.76025	−	1.01628i	−0.104636	−	0.0604115i	0.446769	−	0.894649i	$-0.352575\pi$
$283$	−1.76025	−	1.01628i	−0.104636	−	0.0604115i	−0.551405	+	0.834238i	$0.685908\pi$
$284$		0			0
$285$	−15.4955	−	13.0481i	−0.917877	−	0.772904i
$286$		0			0
$287$	0.155160	+	0.140075i	0.00915879	+	0.00826839i
$288$		0			0
$289$	−2.45310	+	4.24890i	−0.144300	+	0.249935i
$290$		0			0
$291$	−19.7795	−	16.6554i	−1.15949	−	0.976359i
$292$		0			0
$293$	−15.8661	−	27.4809i	−0.926908	−	1.60545i	−0.788463	−	0.615083i	$-0.789123\pi$
$293$	−15.8661	−	27.4809i	−0.926908	−	1.60545i	−0.138446	−	0.990370i	$-0.544211\pi$
$294$		0			0
$295$	14.7000	−	25.4611i	0.855866	−	1.48240i
$296$		0			0
$297$	−5.56098	+	9.51731i	−0.322681	+	0.552250i
$298$		0			0
$299$	12.8577	+	22.2702i	0.743579	+	1.28792i
$300$		0			0
$301$	−1.38283	+	6.46397i	−0.0797048	+	0.372577i
$302$		0			0
$303$	−5.56930	−	0.991969i	−0.319948	−	0.0569872i
$304$		0			0
$305$	−15.7457	+	9.09079i	−0.901597	+	0.520537i
$306$		0			0
$307$			0.266045i			0.0151840i	0.999971	+	0.00759200i	$0.00241663\pi$
$307$			0.266045i			0.0151840i	−0.999971	+	0.00759200i	$0.997583\pi$
$308$		0			0
$309$	−1.44823	+	8.13094i	−0.0823872	+	0.462553i
$310$		0			0
$311$	2.18123	−	3.77799i	0.123686	−	0.214230i	−0.797533	−	0.603276i	$-0.793862\pi$
$311$	2.18123	−	3.77799i	0.123686	−	0.214230i	0.921219	+	0.389046i	$0.127195\pi$
$312$		0			0
$313$	−13.3702	+	7.71929i	−0.755728	+	0.436320i	−0.827760	−	0.561082i	$-0.810385\pi$
$313$	−13.3702	+	7.71929i	−0.755728	+	0.436320i	0.0720315	+	0.997402i	$0.477052\pi$
$314$		0			0
$315$	17.6727	+	0.701686i	0.995742	+	0.0395355i
$316$		0			0
$317$	18.8143	−	10.8624i	1.05671	−	0.610094i	0.132192	−	0.991224i	$-0.457798\pi$
$317$	18.8143	−	10.8624i	1.05671	−	0.610094i	0.924521	+	0.381130i	$0.124465\pi$
$318$		0			0
$319$	2.75794	−	4.77690i	0.154415	−	0.267455i
$320$		0			0
$321$	9.78582	+	8.24021i	0.546191	+	0.459924i
$322$		0			0
$323$			24.5660i			1.36689i
$324$		0			0
$325$	0.176959	−	0.102167i	0.00981591	−	0.00566722i
$326$		0			0
$327$	−1.38372	−	3.82233i	−0.0765199	−	0.211376i
$328$		0			0
$329$	7.45623	+	6.73135i	0.411075	+	0.371111i
$330$		0			0
$331$	7.57310	+	13.1170i	0.416255	+	0.720975i	0.995559	−	0.0941362i	$-0.0300089\pi$
$331$	7.57310	+	13.1170i	0.416255	+	0.720975i	−0.579304	+	0.815112i	$0.696676\pi$
$332$		0			0
$333$	−8.30992	+	6.92392i	−0.455381	+	0.379429i
$334$		0			0
$335$	5.29475	−	9.17078i	0.289283	−	0.501053i
$336$		0			0
$337$	3.75166	+	6.49807i	0.204366	+	0.353973i	0.949931	−	0.312461i	$-0.101153\pi$
$337$	3.75166	+	6.49807i	0.204366	+	0.353973i	−0.745564	+	0.666434i	$0.767820\pi$
$338$		0			0
$339$	22.3715	−	8.09869i	1.21505	−	0.439860i
$340$		0			0
$341$	−8.07409	+	13.9847i	−0.437237	+	0.757316i
$342$		0			0
$343$	10.9448	−	14.9402i	0.590965	−	0.806697i
$344$		0			0
$345$	2.95335	−	16.5813i	0.159003	−	0.892705i
$346$		0			0
$347$	4.23981	+	2.44786i	0.227605	+	0.131408i	0.609467	−	0.792812i	$-0.291384\pi$
$347$	4.23981	+	2.44786i	0.227605	+	0.131408i	−0.381862	+	0.924219i	$0.624717\pi$
$348$		0			0
$349$	−2.64213	−	1.52543i	−0.141430	−	0.0816546i	0.427615	−	0.903961i	$-0.359354\pi$
$349$	−2.64213	−	1.52543i	−0.141430	−	0.0816546i	−0.569045	+	0.822306i	$0.692687\pi$
$350$		0			0
$351$	−30.6199	−	0.159157i	−1.63437	−	0.00849517i
$352$		0			0
$353$	−17.0378			−0.906830			−0.453415	−	0.891299i	$-0.649795\pi$
$353$	−17.0378			−0.906830			−0.453415	+	0.891299i	$0.649795\pi$
$354$		0			0
$355$		−	22.3554i		−	1.18650i
$356$		0			0
$357$	−13.1534	−	16.9416i	−0.696151	−	0.896646i
$358$		0			0
$359$	−2.27682	−	1.31452i	−0.120166	−	0.0693778i	0.438712	−	0.898628i	$-0.355435\pi$
$359$	−2.27682	−	1.31452i	−0.120166	−	0.0693778i	−0.558878	+	0.829250i	$0.688768\pi$
$360$		0			0
$361$	4.27438	+	7.40344i	0.224967	+	0.389655i
$362$		0			0
$363$	11.0837	+	1.97416i	0.581741	+	0.103616i
$364$		0			0
$365$	−28.2126	+	16.2886i	−1.47672	+	0.852583i
$366$		0			0
$367$		−	18.7565i		−	0.979080i	−0.871981	−	0.489540i	$-0.837165\pi$
$367$		−	18.7565i		−	0.979080i	0.871981	−	0.489540i	$-0.162835\pi$
$368$		0			0
$369$	0.0403496	+	0.233564i	0.00210052	+	0.0121588i
$370$		0			0
$371$	−8.35289	+	9.25238i	−0.433660	+	0.480360i
$372$		0			0
$373$	4.85959			0.251620			0.125810	−	0.992054i	$-0.459847\pi$
$373$	4.85959			0.251620			0.125810	+	0.992054i	$0.459847\pi$
$374$		0			0
$375$	−19.1304	−	3.40739i	−0.987890	−	0.175957i
$376$		0			0
$377$	15.3225			0.789151
$378$		0			0
$379$	−3.46902			−0.178192			−0.0890959	−	0.996023i	$-0.528398\pi$
$379$	−3.46902			−0.178192			−0.0890959	+	0.996023i	$0.528398\pi$
$380$		0			0
$381$	−10.1957	−	1.81600i	−0.522341	−	0.0930363i
$382$		0			0
$383$	−18.6060			−0.950720			−0.475360	−	0.879791i	$-0.657682\pi$
$383$	−18.6060			−0.950720			−0.475360	+	0.879791i	$0.657682\pi$
$384$		0			0
$385$	3.84911	+	11.8994i	0.196169	+	0.606452i
$386$		0			0
$387$	−5.75839	+	4.79796i	−0.292715	+	0.243894i
$388$		0			0
$389$			15.5437i			0.788098i	0.919090	+	0.394049i	$0.128926\pi$
$389$			15.5437i			0.788098i	−0.919090	+	0.394049i	$0.871074\pi$
$390$		0			0
$391$	−17.6880	+	10.2122i	−0.894521	+	0.516452i
$392$		0			0
$393$	−35.7387	−	6.36556i	−1.80278	−	0.321100i
$394$		0			0
$395$	16.2090	+	28.0748i	0.815562	+	1.41260i
$396$		0			0
$397$	−13.0507	−	7.53483i	−0.654996	−	0.378162i	0.135371	−	0.990795i	$-0.456777\pi$
$397$	−13.0507	−	7.53483i	−0.654996	−	0.378162i	−0.790368	+	0.612633i	$0.790111\pi$
$398$		0			0
$399$	−22.2736	−	9.07809i	−1.11507	−	0.454473i
$400$		0			0
$401$			7.78803i			0.388916i	0.980911	+	0.194458i	$0.0622947\pi$
$401$			7.78803i			0.388916i	−0.980911	+	0.194458i	$0.937705\pi$
$402$		0			0
$403$	−44.8579			−2.23453
$404$		0			0
$405$	15.2731	+	12.9971i	0.758926	+	0.645830i
$406$		0			0
$407$	−6.62379	−	3.82425i	−0.328329	−	0.189561i
$408$		0			0
$409$	−7.79314	−	4.49937i	−0.385346	−	0.222480i	0.294796	−	0.955560i	$-0.404748\pi$
$409$	−7.79314	−	4.49937i	−0.385346	−	0.222480i	−0.680142	+	0.733081i	$0.738082\pi$
$410$		0			0
$411$	1.05235	−	5.90828i	0.0519084	−	0.291434i
$412$		0			0
$413$	7.30252	−	34.1354i	0.359334	−	1.67969i
$414$		0			0
$415$	14.2900	−	24.7509i	0.701466	−	1.21498i
$416$		0			0
$417$	−0.713877	+	0.258430i	−0.0349587	+	0.0126554i
$418$		0			0
$419$	−6.70022	−	11.6051i	−0.327327	−	0.566947i	0.654653	−	0.755929i	$-0.272815\pi$
$419$	−6.70022	−	11.6051i	−0.327327	−	0.566947i	−0.981981	+	0.188982i	$0.939481\pi$
$420$		0			0
$421$	9.44700	−	16.3627i	0.460419	−	0.797469i	−0.538563	−	0.842585i	$-0.681033\pi$
$421$	9.44700	−	16.3627i	0.460419	−	0.797469i	0.998982	+	0.0451166i	$0.0143659\pi$
$422$		0			0
$423$	1.93901	+	11.2239i	0.0942778	+	0.545727i
$424$		0			0
$425$	0.0811460	+	0.140549i	0.00393616	+	0.00681763i
$426$		0			0
$427$	−14.4660	+	16.0238i	−0.700061	+	0.775448i
$428$		0			0
$429$	−7.37021	−	20.3592i	−0.355837	−	0.982950i
$430$		0			0
$431$	25.4056	−	14.6679i	1.22375	−	0.706530i	0.258031	−	0.966137i	$-0.416926\pi$
$431$	25.4056	−	14.6679i	1.22375	−	0.706530i	0.965714	+	0.259607i	$0.0835931\pi$
$432$		0			0
$433$		−	9.41744i		−	0.452573i	−0.974061	−	0.226287i	$-0.927341\pi$
$433$		−	9.41744i		−	0.452573i	0.974061	−	0.226287i	$-0.0726586\pi$
$434$		0			0
$435$	−7.67642	−	6.46398i	−0.368056	−	0.309924i
$436$		0			0
$437$	−11.4521	+	19.8356i	−0.547829	+	0.948868i
$438$		0			0
$439$	27.5379	−	15.8990i	1.31431	−	0.758819i	0.331505	−	0.943453i	$-0.392444\pi$
$439$	27.5379	−	15.8990i	1.31431	−	0.758819i	0.982807	+	0.184635i	$0.0591102\pi$
$440$		0			0
$441$	20.2214	−	5.66536i	0.962922	−	0.269779i
$442$		0			0
$443$	−32.0685	+	18.5147i	−1.52362	+	0.879662i	−0.524009	+	0.851713i	$0.675564\pi$
$443$	−32.0685	+	18.5147i	−1.52362	+	0.879662i	−0.999609	+	0.0279490i	$0.991102\pi$
$444$		0			0
$445$	6.09360	−	10.5544i	0.288864	−	0.500328i
$446$		0			0
$447$	−5.31532	+	29.8423i	−0.251406	+	1.41149i
$448$		0			0
$449$			19.3840i			0.914789i	0.889264	+	0.457394i	$0.151217\pi$
$449$			19.3840i			0.914789i	−0.889264	+	0.457394i	$0.848783\pi$
$450$		0			0
$451$	−0.145149	+	0.0838017i	−0.00683479	+	0.00394607i
$452$		0			0
$453$	−0.639181	−	0.113847i	−0.0300314	−	0.00534901i
$454$		0			0
$455$	−23.2806	+	25.7876i	−1.09141	+	1.20894i
$456$		0			0
$457$	−5.26746	−	9.12351i	−0.246401	−	0.426780i	0.716123	−	0.697974i	$-0.245915\pi$
$457$	−5.26746	−	9.12351i	−0.246401	−	0.426780i	−0.962525	+	0.271194i	$0.912581\pi$
$458$		0			0
$459$	0.126410	−	24.3198i	0.00590031	−	1.13515i
$460$		0			0
$461$	7.09138	−	12.2826i	0.330278	−	0.572059i	−0.652288	−	0.757971i	$-0.726191\pi$
$461$	7.09138	−	12.2826i	0.330278	−	0.572059i	0.982566	+	0.185912i	$0.0595240\pi$
$462$		0			0
$463$	5.05071	+	8.74808i	0.234726	+	0.406558i	0.959193	−	0.282752i	$-0.0912473\pi$
$463$	5.05071	+	8.74808i	0.234726	+	0.406558i	−0.724467	+	0.689310i	$0.757914\pi$
$464$		0			0
$465$	22.4733	+	18.9238i	1.04217	+	0.877570i
$466$		0			0
$467$	11.1047	−	19.2340i	0.513866	−	0.890042i	−0.486005	−	0.873956i	$-0.661546\pi$
$467$	11.1047	−	19.2340i	0.513866	−	0.890042i	0.999871	−	0.0160858i	$-0.00512048\pi$
$468$		0			0
$469$	2.63028	−	12.2951i	0.121455	−	0.567737i
$470$		0			0
$471$	26.9682	+	22.7087i	1.24263	+	1.04636i
$472$		0			0
$473$	−4.58998	−	2.65003i	−0.211048	−	0.121848i
$474$		0			0
$475$	0.157614	+	0.0909986i	0.00723184	+	0.00417530i
$476$		0			0
$477$	−13.9277	+	2.40610i	−0.637707	+	0.110168i
$478$		0			0
$479$	−9.42550			−0.430662			−0.215331	−	0.976541i	$-0.569083\pi$
$479$	−9.42550			−0.430662			−0.215331	+	0.976541i	$0.569083\pi$
$480$		0			0
$481$		−	21.2467i		−	0.968765i
$482$		0			0
$483$	−2.72280	−	19.8112i	−0.123892	−	0.901441i
$484$		0			0
$485$	−28.8096	−	16.6332i	−1.30818	−	0.755276i
$486$		0			0
$487$	14.6113	+	25.3076i	0.662103	+	1.14680i	0.980062	+	0.198692i	$0.0636692\pi$
$487$	14.6113	+	25.3076i	0.662103	+	1.14680i	−0.317959	+	0.948104i	$0.602997\pi$
$488$		0			0
$489$	−16.1857	+	19.2216i	−0.731942	+	0.869231i
$490$		0			0
$491$	6.31308	−	3.64486i	0.284905	−	0.164490i	−0.350737	−	0.936474i	$-0.614069\pi$
$491$	6.31308	−	3.64486i	0.284905	−	0.164490i	0.635642	+	0.771984i	$0.280735\pi$
$492$		0			0
$493$			12.1699i			0.548104i
$494$		0			0
$495$	−4.89634	+	13.3089i	−0.220074	+	0.598192i
$496$		0			0
$497$	−8.16925	−	25.2550i	−0.366441	−	1.13284i
$498$		0			0
$499$	15.6199			0.699243			0.349622	−	0.936891i	$-0.386310\pi$
$499$	15.6199			0.699243			0.349622	+	0.936891i	$0.386310\pi$
$500$		0			0
$501$	8.99114	+	24.8368i	0.401695	+	1.10963i
$502$		0			0
$503$	−6.09425			−0.271729			−0.135865	−	0.990727i	$-0.543381\pi$
$503$	−6.09425			−0.271729			−0.135865	+	0.990727i	$0.543381\pi$
$504$		0			0
$505$	−7.27772			−0.323854
$506$		0			0
$507$	24.2384	−	28.7848i	1.07647	−	1.27838i
$508$		0			0
$509$	28.3599			1.25703			0.628515	−	0.777798i	$-0.283663\pi$
$509$	28.3599			1.25703			0.628515	+	0.777798i	$0.283663\pi$
$510$		0			0
$511$	−25.9198	+	28.7110i	−1.14662	+	1.27010i
$512$		0			0
$513$	−13.5135	−	23.6897i	−0.596638	−	1.04592i
$514$		0			0
$515$			10.6252i			0.468201i
$516$		0			0
$517$	−6.97515	+	4.02710i	−0.306767	+	0.177112i
$518$		0			0
$519$	1.10920	+	3.06402i	0.0486886	+	0.134495i
$520$		0			0
$521$	19.2896	+	33.4105i	0.845091	+	1.46374i	0.885542	+	0.464559i	$0.153787\pi$
$521$	19.2896	+	33.4105i	0.845091	+	1.46374i	−0.0404517	+	0.999181i	$0.512880\pi$
$522$		0			0
$523$	−24.1399	−	13.9372i	−1.05556	−	0.609429i	−0.131361	−	0.991335i	$-0.541935\pi$
$523$	−24.1399	−	13.9372i	−1.05556	−	0.609429i	−0.924201	+	0.381905i	$0.875268\pi$
$524$		0			0
$525$	−0.157420	+	0.0216354i	−0.00687037	+	0.000944246i
$526$		0			0
$527$		−	35.6283i		−	1.55199i
$528$		0			0
$529$	3.95726			0.172055
$530$		0			0
$531$	30.4093	−	25.3374i	1.31965	−	1.09955i
$532$		0			0
$533$	−0.403208	−	0.232792i	−0.0174649	−	0.0100833i
$534$		0			0
$535$	14.2534	+	8.22923i	0.616230	+	0.355781i
$536$		0			0
$537$	−16.2493	+	5.88240i	−0.701209	+	0.253844i
$538$		0			0
$539$	8.69674	+	12.0363i	0.374595	+	0.518441i
$540$		0			0
$541$	−10.9182	+	18.9109i	−0.469410	+	0.813041i	−0.999388	−	0.0349697i	$-0.988867\pi$
$541$	−10.9182	+	18.9109i	−0.469410	+	0.813041i	0.529979	+	0.848011i	$0.322200\pi$
$542$		0			0
$543$	3.42683	−	19.2395i	0.147059	−	0.825646i
$544$		0			0
$545$	−2.61489	−	4.52912i	−0.112009	−	0.194006i
$546$		0			0
$547$	12.5173	−	21.6806i	0.535201	−	0.926995i	−0.463953	−	0.885860i	$-0.653569\pi$
$547$	12.5173	−	21.6806i	0.535201	−	0.926995i	0.999154	−	0.0411350i	$-0.0130974\pi$
$548$		0			0
$549$	−24.1209	+	4.16703i	−1.02945	+	0.177845i
$550$		0			0
$551$	6.82376	+	11.8191i	0.290702	+	0.503511i
$552$		0			0
$553$	28.5707	+	25.7931i	1.21495	+	1.09683i
$554$		0			0
$555$	−8.96314	+	10.6444i	−0.380464	+	0.451828i
$556$		0			0
$557$	−11.1937	+	6.46267i	−0.474291	+	0.273832i	−0.718034	−	0.696008i	$-0.754958\pi$
$557$	−11.1937	+	6.46267i	−0.474291	+	0.273832i	0.243743	+	0.969840i	$0.421625\pi$
$558$		0			0
$559$		−	14.7230i		−	0.622715i
$560$		0			0
$561$	16.1702	−	5.85377i	0.682707	−	0.247146i
$562$		0			0
$563$	−7.81056	+	13.5283i	−0.329176	+	0.570150i	−0.982349	−	0.187060i	$-0.940104\pi$
$563$	−7.81056	+	13.5283i	−0.329176	+	0.570150i	0.653173	+	0.757209i	$0.273438\pi$
$564$		0			0
$565$	26.5082	−	15.3045i	1.11521	−	0.643865i
$566$		0			0
$567$	22.0036	+	9.10171i	0.924065	+	0.382236i
$568$		0			0
$569$	−36.8986	+	21.3034i	−1.54687	+	0.893087i	−0.548494	+	0.836155i	$0.684799\pi$
$569$	−36.8986	+	21.3034i	−1.54687	+	0.893087i	−0.998378	+	0.0569323i	$0.981868\pi$
$570$		0			0
$571$	9.89848	−	17.1447i	0.414239	−	0.717482i	−0.581110	−	0.813825i	$-0.697381\pi$
$571$	9.89848	−	17.1447i	0.414239	−	0.717482i	0.995348	+	0.0963431i	$0.0307146\pi$
$572$		0			0
$573$	−20.9528	+	7.58512i	−0.875317	+	0.316873i
$574$		0			0
$575$			0.151314i			0.00631022i
$576$		0			0
$577$	−40.6443	+	23.4660i	−1.69204	+	0.976902i	−0.739178	+	0.673511i	$0.764786\pi$
$577$	−40.6443	+	23.4660i	−1.69204	+	0.976902i	−0.952866	+	0.303391i	$0.901881\pi$
$578$		0			0
$579$	13.4292	−	15.9481i	0.558097	−	0.662779i
$580$		0			0
$581$	7.09883	−	33.1833i	0.294509	−	1.37667i
$582$		0			0
$583$	−4.99721	−	8.65542i	−0.206963	−	0.358471i
$584$		0			0
$585$	−38.8184	+	6.70611i	−1.60494	+	0.277264i
$586$		0			0
$587$	2.18063	−	3.77696i	0.0900041	−	0.155892i	−0.817509	−	0.575917i	$-0.804645\pi$
$587$	2.18063	−	3.77696i	0.0900041	−	0.155892i	0.907513	+	0.420025i	$0.137979\pi$
$588$		0			0
$589$	−19.9771	−	34.6013i	−0.823141	−	1.42572i
$590$		0			0
$591$	−8.42105	+	47.2790i	−0.346396	+	1.94480i
$592$		0			0
$593$	−2.31077	+	4.00236i	−0.0948918	+	0.164357i	−0.909563	−	0.415565i	$-0.863584\pi$
$593$	−2.31077	+	4.00236i	−0.0948918	+	0.164357i	0.814672	+	0.579922i	$0.196917\pi$
$594$		0			0
$595$	−20.4817	−	18.4905i	−0.839668	−	0.758038i
$596$		0			0
$597$	0.719998	−	0.260646i	0.0294675	−	0.0106675i
$598$		0			0
$599$	22.0986	+	12.7586i	0.902924	+	0.521304i	0.878148	−	0.478389i	$-0.158779\pi$
$599$	22.0986	+	12.7586i	0.902924	+	0.521304i	0.0247764	+	0.999693i	$0.492113\pi$
$600$		0			0
$601$	22.6824	+	13.0957i	0.925235	+	0.534185i	0.885301	−	0.465018i	$-0.153952\pi$
$601$	22.6824	+	13.0957i	0.925235	+	0.534185i	0.0399336	+	0.999202i	$0.487285\pi$
$602$		0			0
$603$	10.9531	−	9.12622i	0.446043	−	0.371648i
$604$		0			0
$605$	14.4837			0.588845
$606$		0			0
$607$		−	5.87462i		−	0.238443i	−0.992868	−	0.119222i	$-0.961960\pi$
$607$		−	5.87462i		−	0.238443i	0.992868	−	0.119222i	$-0.0380399\pi$
$608$		0			0
$609$	−11.0342	−	4.49724i	−0.447129	−	0.182237i
$610$		0			0
$611$	−19.3762	−	11.1869i	−0.783878	−	0.452572i
$612$		0			0
$613$	12.4511	+	21.5660i	0.502896	+	0.871041i	0.999994	+	0.00334675i	$0.00106531\pi$
$613$	12.4511	+	21.5660i	0.502896	+	0.871041i	−0.497099	+	0.867694i	$0.665601\pi$
$614$		0			0
$615$	0.103797	+	0.286724i	0.00418549	+	0.0115618i
$616$		0			0
$617$	26.1105	−	15.0749i	1.05117	−	0.606894i	0.128194	−	0.991749i	$-0.459082\pi$
$617$	26.1105	−	15.0749i	1.05117	−	0.606894i	0.922977	+	0.384855i	$0.125749\pi$
$618$		0			0
$619$			34.1737i			1.37356i	0.726867	+	0.686779i	$0.240976\pi$
$619$			34.1737i			1.37356i	−0.726867	+	0.686779i	$0.759024\pi$
$620$		0			0
$621$	11.4394	−	19.5779i	0.459047	−	0.785634i
$622$		0			0
$623$	3.02712	−	14.1502i	0.121279	−	0.566915i
$624$		0			0
$625$	−24.8254			−0.993017
$626$		0			0
$627$	12.4219	−	14.7518i	0.496082	−	0.589131i
$628$		0			0
$629$	16.8751			0.672855
$630$		0			0
$631$	8.55990			0.340764			0.170382	−	0.985378i	$-0.445500\pi$
$631$	8.55990			0.340764			0.170382	+	0.985378i	$0.445500\pi$
$632$		0			0
$633$	−0.258588	−	0.714313i	−0.0102779	−	0.0283914i
$634$		0			0
$635$	−13.3233			−0.528719
$636$		0			0
$637$	−16.8768	+	37.6398i	−0.668683	+	1.49134i
$638$		0			0
$639$	10.3919	−	28.2465i	0.411096	−	1.11741i
$640$		0			0
$641$		−	40.4996i		−	1.59964i	−0.600242	−	0.799818i	$-0.704929\pi$
$641$		−	40.4996i		−	1.59964i	0.600242	−	0.799818i	$-0.295071\pi$
$642$		0			0
$643$	−31.8435	+	18.3849i	−1.25579	+	0.725028i	−0.972252	−	0.233935i	$-0.924840\pi$
$643$	−31.8435	+	18.3849i	−1.25579	+	0.725028i	−0.283533	+	0.958963i	$0.591507\pi$
$644$		0			0
$645$	−6.21105	+	7.37604i	−0.244560	+	0.290431i
$646$		0			0
$647$	−23.5492	−	40.7884i	−0.925815	−	1.60356i	−0.790246	−	0.612790i	$-0.790047\pi$
$647$	−23.5492	−	40.7884i	−0.925815	−	1.60356i	−0.135569	−	0.990768i	$-0.543286\pi$
$648$		0			0
$649$	24.2391	+	13.9944i	0.951467	+	0.549330i
$650$		0			0
$651$	32.3035	+	13.1660i	1.26608	+	0.516017i
$652$		0			0
$653$			2.50279i			0.0979416i	0.998800	+	0.0489708i	$0.0155941\pi$
$653$			2.50279i			0.0979416i	−0.998800	+	0.0489708i	$0.984406\pi$
$654$		0			0
$655$	−46.7018			−1.82479
$656$		0			0
$657$	−43.2190	+	7.46635i	−1.68613	+	0.291290i
$658$		0			0
$659$	36.2490	+	20.9284i	1.41206	+	0.815254i	0.995582	−	0.0938917i	$-0.0299307\pi$
$659$	36.2490	+	20.9284i	1.41206	+	0.815254i	0.416479	+	0.909146i	$0.363264\pi$
$660$		0			0
$661$	7.35519	+	4.24652i	0.286084	+	0.165170i	0.636174	−	0.771545i	$-0.280516\pi$
$661$	7.35519	+	4.24652i	0.286084	+	0.165170i	−0.350091	+	0.936716i	$0.613849\pi$
$662$		0			0
$663$	36.5421	+	30.7705i	1.41918	+	1.19503i
$664$		0			0
$665$	−30.2592	−	6.47329i	−1.17340	−	0.251023i
$666$		0			0
$667$	−5.67333	+	9.82649i	−0.219672	+	0.380483i
$668$		0			0
$669$	−26.9892	−	22.7265i	−1.04346	−	0.878656i
$670$		0			0
$671$	−8.65447	−	14.9900i	−0.334102	−	0.578682i
$672$		0			0
$673$	−16.9974	+	29.4403i	−0.655201	+	1.13484i	0.326642	+	0.945148i	$0.394083\pi$
$673$	−16.9974	+	29.4403i	−0.655201	+	1.13484i	−0.981843	+	0.189694i	$0.939251\pi$
$674$		0			0
$675$	−0.155566	−	0.0908975i	−0.00598774	−	0.00349865i
$676$		0			0
$677$	−19.5176	−	33.8054i	−0.750121	−	1.29925i	−0.947764	−	0.318973i	$-0.896662\pi$
$677$	−19.5176	−	33.8054i	−0.750121	−	1.29925i	0.197643	−	0.980274i	$-0.436671\pi$
$678$		0			0
$679$	−38.6247	−	8.26291i	−1.48228	−	0.317101i
$680$		0			0
$681$	2.57465	+	0.458581i	0.0986609	+	0.0175729i
$682$		0			0
$683$	1.91400	−	1.10505i	0.0732373	−	0.0422836i	−0.462934	−	0.886393i	$-0.653203\pi$
$683$	1.91400	−	1.10505i	0.0732373	−	0.0422836i	0.536171	+	0.844109i	$0.319870\pi$
$684$		0			0
$685$		−	7.72069i		−	0.294992i
$686$		0			0
$687$	−6.44948	+	36.2099i	−0.246063	+	1.38149i
$688$		0			0
$689$	13.8817	−	24.0438i	0.528851	−	0.915997i
$690$		0			0
$691$	2.96039	−	1.70918i	0.112619	−	0.0650203i	−0.442633	−	0.896703i	$-0.645955\pi$
$691$	2.96039	−	1.70918i	0.112619	−	0.0650203i	0.555251	+	0.831683i	$0.312622\pi$
$692$		0			0
$693$	−0.668008	+	16.8244i	−0.0253755	+	0.639108i
$694$		0			0
$695$	−0.845879	+	0.488369i	−0.0320860	+	0.0185249i
$696$		0			0
$697$	0.184894	−	0.320247i	0.00700338	−	0.0121302i
$698$		0			0
$699$	15.0835	+	12.7011i	0.570509	+	0.480401i
$700$		0			0
$701$		−	37.5732i		−	1.41912i	−0.704645	−	0.709560i	$-0.748894\pi$
$701$		−	37.5732i		−	1.41912i	0.704645	−	0.709560i	$-0.251106\pi$
$702$		0			0
$703$	16.3887	−	9.46203i	0.618112	−	0.356867i
$704$		0			0
$705$	4.98797	+	13.7786i	0.187858	+	0.518930i
$706$		0			0
$707$	−8.22170	+	2.65947i	−0.309209	+	0.100020i
$708$		0			0
$709$	13.4390	+	23.2770i	0.504712	+	0.874187i	0.999985	+	0.00544993i	$0.00173477\pi$
$709$	13.4390	+	23.2770i	0.504712	+	0.874187i	−0.495273	+	0.868738i	$0.664932\pi$
$710$		0			0
$711$	7.42987	+	43.0078i	0.278642	+	1.61292i
$712$		0			0
$713$	16.6091	−	28.7678i	0.622015	−	1.07736i
$714$		0			0
$715$	−13.9279	−	24.1238i	−0.520872	−	0.902177i
$716$		0			0
$717$	26.5914	−	9.62635i	0.993075	−	0.359503i
$718$		0			0
$719$	−1.41278	+	2.44701i	−0.0526879	+	0.0912580i	−0.891166	−	0.453676i	$-0.850112\pi$
$719$	−1.41278	+	2.44701i	−0.0526879	+	0.0912580i	0.838479	+	0.544935i	$0.183446\pi$
$720$		0			0
$721$	3.88272	+	12.0033i	0.144600	+	0.447028i
$722$		0			0
$723$	7.28042	−	40.8750i	0.270762	−	1.52016i
$724$		0			0
$725$	0.0780813	+	0.0450803i	0.00289987	+	0.00167424i
$726$		0			0
$727$	0.622076	+	0.359156i	0.0230715	+	0.0133203i	0.511491	−	0.859288i	$-0.329093\pi$
$727$	0.622076	+	0.359156i	0.0230715	+	0.0133203i	−0.488420	+	0.872609i	$0.662427\pi$
$728$		0			0
$729$	13.2562	+	23.5218i	0.490970	+	0.871176i
$730$		0			0
$731$	11.6937			0.432506
$732$		0			0
$733$			38.6236i			1.42659i	0.700862	+	0.713297i	$0.252799\pi$
$733$			38.6236i			1.42659i	−0.700862	+	0.713297i	$0.747201\pi$
$734$		0			0
$735$	24.3338	−	11.7374i	0.897567	−	0.432942i
$736$		0			0
$737$	8.73062	+	5.04063i	0.321596	+	0.185674i
$738$		0			0
$739$	11.9491	+	20.6965i	0.439556	+	0.761334i	0.997655	−	0.0684405i	$-0.0218023\pi$
$739$	11.9491	+	20.6965i	0.439556	+	0.761334i	−0.558099	+	0.829775i	$0.688469\pi$
$740$		0			0
$741$	52.7421	+	9.39411i	1.93753	+	0.345101i
$742$		0			0
$743$	20.5325	−	11.8544i	0.753264	−	0.434897i	−0.0736078	−	0.997287i	$-0.523451\pi$
$743$	20.5325	−	11.8544i	0.753264	−	0.434897i	0.826872	+	0.562390i	$0.190118\pi$
$744$		0			0
$745$			38.9966i			1.42872i
$746$		0			0
$747$	29.5611	−	24.6307i	1.08158	−	0.901189i
$748$		0			0
$749$	19.1094	+	4.08804i	0.698242	+	0.149374i
$750$		0			0
$751$	13.7869			0.503090			0.251545	−	0.967846i	$-0.419061\pi$
$751$	13.7869			0.503090			0.251545	+	0.967846i	$0.419061\pi$
$752$		0			0
$753$	44.3062	+	7.89155i	1.61461	+	0.287584i
$754$		0			0
$755$	−0.835255			−0.0303981
$756$		0			0
$757$	−19.6447			−0.714000			−0.357000	−	0.934104i	$-0.616200\pi$
$757$	−19.6447			−0.714000			−0.357000	+	0.934104i	$0.616200\pi$
$758$		0			0
$759$	15.7854	+	2.81160i	0.572974	+	0.102055i
$760$		0			0
$761$	52.9464			1.91931			0.959653	−	0.281187i	$-0.0907280\pi$
$761$	52.9464			1.91931			0.959653	+	0.281187i	$0.0907280\pi$
$762$		0			0
$763$	−4.60912	−	4.16103i	−0.166861	−	0.150639i
$764$		0			0
$765$	−5.32631	−	30.8314i	−0.192573	−	1.11471i
$766$		0			0
$767$			77.7501i			2.80739i
$768$		0			0
$769$	17.6774	−	10.2060i	0.637462	−	0.368039i	−0.146174	−	0.989259i	$-0.546696\pi$
$769$	17.6774	−	10.2060i	0.637462	−	0.368039i	0.783636	+	0.621220i	$0.213363\pi$
$770$		0			0
$771$	−3.34149	−	0.595165i	−0.120341	−	0.0214344i
$772$		0			0
$773$	1.07789	+	1.86697i	0.0387692	+	0.0671501i	0.884759	−	0.466049i	$-0.154323\pi$
$773$	1.07789	+	1.86697i	0.0387692	+	0.0671501i	−0.845990	+	0.533199i	$0.820990\pi$
$774$		0			0
$775$	−0.228589	−	0.131976i	−0.00821116	−	0.00474072i
$776$		0			0
$777$	−6.23601	+	15.3004i	−0.223716	+	0.548898i
$778$		0			0
$779$		−	0.414688i		−	0.0148577i
$780$		0			0
$781$	21.2824			0.761544
$782$		0			0
$783$	−6.69455	−	11.7358i	−0.239244	−	0.419402i
$784$		0			0
$785$	39.2802	+	22.6784i	1.40197	+	0.809428i
$786$		0			0
$787$	18.0946	+	10.4469i	0.645004	+	0.372393i	0.786539	−	0.617540i	$-0.211871\pi$
$787$	18.0946	+	10.4469i	0.645004	+	0.372393i	−0.141536	+	0.989933i	$0.545204\pi$
$788$		0			0
$789$	1.09323	−	6.13783i	0.0389202	−	0.218513i
$790$		0			0
$791$	24.3538	−	26.9764i	0.865922	−	0.959170i
$792$		0			0
$793$	24.0412	−	41.6405i	0.853727	−	1.47870i
$794$		0			0
$795$	−17.0977	+	6.18954i	−0.606394	+	0.219520i
$796$		0			0
$797$	13.9964	+	24.2424i	0.495777	+	0.858710i	0.999988	−	0.00486976i	$-0.00155010\pi$
$797$	13.9964	+	24.2424i	0.495777	+	0.858710i	−0.504211	+	0.863580i	$0.668217\pi$
$798$		0			0
$799$	8.88513	−	15.3895i	0.314333	−	0.544441i
$800$		0			0
$801$	12.6056	−	10.5031i	0.445397	−	0.371110i
$802$		0			0
$803$	−15.5068	−	26.8585i	−0.547222	−	0.947817i
$804$		0			0
$805$	−7.91794	−	24.4782i	−0.279071	−	0.862742i
$806$		0			0
$807$	−4.79876	−	13.2559i	−0.168924	−	0.466630i
$808$		0			0
$809$	−37.1345	+	21.4396i	−1.30558	+	0.753777i	−0.981355	−	0.192203i	$-0.938437\pi$
$809$	−37.1345	+	21.4396i	−1.30558	+	0.753777i	−0.324225	+	0.945980i	$0.605103\pi$
$810$		0			0
$811$		−	23.7421i		−	0.833699i	−0.908976	−	0.416849i	$-0.863134\pi$
$811$		−	23.7421i		−	0.833699i	0.908976	−	0.416849i	$-0.136866\pi$
$812$		0			0
$813$	24.9946	+	21.0468i	0.876598	+	0.738145i
$814$		0			0
$815$	−16.1641	+	27.9970i	−0.566204	+	0.980693i
$816$		0			0
$817$	11.3566	−	6.55675i	0.397318	−	0.229392i
$818$		0			0
$819$	−41.4028	+	21.7612i	−1.44673	+	0.760398i
$820$		0			0
$821$	1.37437	−	0.793495i	0.0479660	−	0.0276932i	−0.475825	−	0.879540i	$-0.657851\pi$
$821$	1.37437	−	0.793495i	0.0479660	−	0.0276932i	0.523791	+	0.851847i	$0.324517\pi$
$822$		0			0
$823$	−1.54101	+	2.66911i	−0.0537164	+	0.0930395i	−0.891633	−	0.452758i	$-0.850440\pi$
$823$	−1.54101	+	2.66911i	−0.0537164	+	0.0930395i	0.837917	+	0.545798i	$0.183773\pi$
$824$		0			0
$825$	0.0223410	−	0.125431i	0.000777815	−	0.00436695i
$826$		0			0
$827$		−	20.7448i		−	0.721369i	−0.932688	−	0.360685i	$-0.882543\pi$
$827$		−	20.7448i		−	0.721369i	0.932688	−	0.360685i	$-0.117457\pi$
$828$		0			0
$829$	−0.917576	+	0.529763i	−0.0318687	+	0.0183994i	−0.515850	−	0.856679i	$-0.672524\pi$
$829$	−0.917576	+	0.529763i	−0.0318687	+	0.0183994i	0.483981	+	0.875079i	$0.339190\pi$
$830$		0			0
$831$	36.9485	+	6.58104i	1.28173	+	0.228294i
$832$		0			0
$833$	−29.8953	−	13.4043i	−1.03581	−	0.464433i
$834$		0			0
$835$	16.9910	+	29.4293i	0.587999	+	1.01844i
$836$		0			0
$837$	19.5988	+	34.3573i	0.677434	+	1.18756i
$838$		0			0
$839$	−19.2137	+	33.2792i	−0.663332	+	1.14892i	0.316403	+	0.948625i	$0.397525\pi$
$839$	−19.2137	+	33.2792i	−0.663332	+	1.14892i	−0.979735	+	0.200299i	$0.935809\pi$
$840$		0			0
$841$	−11.1195	−	19.2596i	−0.383432	−	0.664124i
$842$		0			0
$843$	17.8766	+	15.0531i	0.615703	+	0.518457i
$844$		0			0
$845$	24.2061	−	41.9262i	0.832716	−	1.44231i
$846$		0			0
$847$	16.3623	−	5.29271i	0.562216	−	0.181860i
$848$		0			0
$849$	−2.69293	−	2.26760i	−0.0924211	−	0.0778237i
$850$		0			0
$851$	13.6257	+	7.86680i	0.467083	+	0.269670i
$852$		0			0
$853$	−12.0659	−	6.96626i	−0.413129	−	0.238520i	0.279004	−	0.960290i	$-0.409996\pi$
$853$	−12.0659	−	6.96626i	−0.413129	−	0.238520i	−0.692133	+	0.721770i	$0.743329\pi$
$854$		0			0
$855$	−22.4602	−	26.9562i	−0.768123	−	0.921882i
$856$		0			0
$857$	−26.9264			−0.919788			−0.459894	−	0.887974i	$-0.652113\pi$
$857$	−26.9264			−0.919788			−0.459894	+	0.887974i	$0.652113\pi$
$858$		0			0
$859$		−	20.2001i		−	0.689217i	−0.938746	−	0.344609i	$-0.888012\pi$
$859$		−	20.2001i		−	0.689217i	0.938746	−	0.344609i	$-0.111988\pi$
$860$		0			0
$861$	0.222036	+	0.285984i	0.00756698	+	0.00974631i
$862$		0			0
$863$	−38.1427	−	22.0217i	−1.29839	−	0.749627i	−0.318266	−	0.948001i	$-0.603101\pi$
$863$	−38.1427	−	22.0217i	−1.29839	−	0.749627i	−0.980126	+	0.198374i	$0.936434\pi$
$864$		0			0
$865$	2.09612	+	3.63058i	0.0712701	+	0.123443i
$866$		0			0
$867$	−5.47355	+	6.50022i	−0.185891	+	0.220759i
$868$		0			0
$869$	−26.7273	+	15.4310i	−0.906662	+	0.523461i
$870$		0			0
$871$			28.0046i			0.948900i
$872$		0			0
$873$	−28.6696	−	34.4086i	−0.970319	−	1.16455i
$874$		0			0
$875$	−28.2413	+	9.13522i	−0.954732	+	0.308827i
$876$		0			0
$877$	−54.0872			−1.82640			−0.913198	−	0.407517i	$-0.866395\pi$
$877$	−54.0872			−1.82640			−0.913198	+	0.407517i	$0.866395\pi$
$878$		0			0
$879$	−18.7085	−	51.6797i	−0.631024	−	1.74311i
$880$		0			0
$881$	6.82593			0.229972			0.114986	−	0.993367i	$-0.463318\pi$
$881$	6.82593			0.229972			0.114986	+	0.993367i	$0.463318\pi$
$882$		0			0
$883$	−9.87685			−0.332382			−0.166191	−	0.986094i	$-0.553147\pi$
$883$	−9.87685			−0.332382			−0.166191	+	0.986094i	$0.553147\pi$
$884$		0			0
$885$	32.7997	−	38.9519i	1.10255	−	1.30935i
$886$		0			0
$887$	35.0825			1.17795			0.588977	−	0.808150i	$-0.299531\pi$
$887$	35.0825			1.17795			0.588977	+	0.808150i	$0.299531\pi$
$888$		0			0
$889$	−15.0514	+	4.86869i	−0.504809	+	0.163291i
$890$		0			0
$891$	−12.3733	+	14.5400i	−0.414520	+	0.487110i
$892$		0			0
$893$		−	19.9279i		−	0.666861i
$894$		0			0
$895$	−19.2539	+	11.1163i	−0.643588	+	0.371576i
$896$		0			0
$897$	15.1611	+	41.8805i	0.506216	+	1.39835i
$898$		0			0
$899$	−9.89655	−	17.1413i	−0.330069	−	0.571695i
$900$		0			0
$901$	19.0967	+	11.0255i	0.636204	+	0.367313i
$902$		0			0
$903$	−4.32127	+	10.6025i	−0.143803	+	0.352828i
$904$		0			0
$905$		−	25.1414i		−	0.835728i
$906$		0			0
$907$	34.4463			1.14377			0.571885	−	0.820334i	$-0.306213\pi$
$907$	34.4463			1.14377			0.571885	+	0.820334i	$0.306213\pi$
$908$		0			0
$909$	−9.19555	−	3.38304i	−0.304997	−	0.112208i
$910$		0			0
$911$	−45.9046	−	26.5030i	−1.52089	−	0.878084i	−0.999696	−	0.0246430i	$-0.992155\pi$
$911$	−45.9046	−	26.5030i	−1.52089	−	0.878084i	−0.521190	−	0.853441i	$-0.674512\pi$
$912$		0			0
$913$	23.5630	+	13.6041i	0.779821	+	0.450230i
$914$		0			0
$915$	−29.6109	+	10.7194i	−0.978906	+	0.354373i
$916$		0			0
$917$	−52.7594	+	17.0661i	−1.74227	+	0.563571i
$918$		0			0
$919$	5.73193	−	9.92799i	0.189079	−	0.327494i	−0.755865	−	0.654728i	$-0.772783\pi$
$919$	5.73193	−	9.92799i	0.189079	−	0.327494i	0.944943	+	0.327234i	$0.106116\pi$
$920$		0			0
$921$	−0.0808038	+	0.453664i	−0.00266258	+	0.0149487i
$922$		0			0
$923$	29.5601	+	51.1996i	0.972983	+	1.68526i
$924$		0			0
$925$	0.0625096	−	0.108270i	0.00205530	−	0.00355989i
$926$		0			0
$927$	−4.93910	+	13.4251i	−0.162221	+	0.440939i
$928$		0			0
$929$	17.3933	+	30.1261i	0.570656	+	0.988405i	0.996499	+	0.0836078i	$0.0266443\pi$
$929$	17.3933	+	30.1261i	0.570656	+	0.988405i	−0.425843	+	0.904797i	$0.640022\pi$
$930$		0			0
$931$	−36.5495	+	3.74457i	−1.19786	+	0.122723i
$932$		0			0
$933$	4.86692	−	5.77980i	0.159336	−	0.189222i
$934$		0			0
$935$	19.1602	−	11.0622i	0.626606	−	0.361771i
$936$		0			0
$937$		−	18.5180i		−	0.604956i	−0.953156	−	0.302478i	$-0.902186\pi$
$937$		−	18.5180i		−	0.604956i	0.953156	−	0.302478i	$-0.0978139\pi$
$938$		0			0
$939$	−25.1436	+	9.10221i	−0.820529	+	0.297039i
$940$		0			0
$941$	−4.89224	+	8.47360i	−0.159482	+	0.276232i	−0.934682	−	0.355485i	$-0.884316\pi$
$941$	−4.89224	+	8.47360i	−0.159482	+	0.276232i	0.775200	+	0.631716i	$0.217649\pi$
$942$		0			0
$943$	0.298583	−	0.172387i	0.00972321	−	0.00561370i
$944$		0			0
$945$	29.9225	+	6.56411i	0.973381	+	0.213530i
$946$		0			0
$947$	29.0554	−	16.7752i	0.944174	−	0.545119i	0.0529077	−	0.998599i	$-0.483151\pi$
$947$	29.0554	−	16.7752i	0.944174	−	0.545119i	0.891266	+	0.453480i	$0.149818\pi$
$948$		0			0
$949$	43.0762	−	74.6101i	1.39831	−	2.42195i
$950$		0			0
$951$	35.3815	−	12.8084i	1.14732	−	0.415342i
$952$		0			0
$953$		−	10.8871i		−	0.352668i	−0.984330	−	0.176334i	$-0.943576\pi$
$953$		−	10.8871i		−	0.352668i	0.984330	−	0.176334i	$-0.0564239\pi$
$954$		0			0
$955$	−24.8272	+	14.3340i	−0.803389	+	0.463837i
$956$		0			0
$957$	6.15374	−	7.30798i	0.198922	−	0.236234i
$958$		0			0
$959$	−2.82134	−	8.72212i	−0.0911059	−	0.281652i
$960$		0			0
$961$	13.4729	+	23.3358i	0.434610	+	0.752766i
$962$		0			0
$963$	14.1842	+	17.0235i	0.457079	+	0.548575i
$964$		0			0
$965$	13.4113	−	23.2290i	0.431724	−	0.747768i
$966$		0			0
$967$	26.3931	+	45.7142i	0.848746	+	1.47007i	0.882328	+	0.470635i	$0.155975\pi$
$967$	26.3931	+	45.7142i	0.848746	+	1.47007i	−0.0335826	+	0.999436i	$0.510692\pi$
$968$		0			0
$969$	−7.46125	+	41.8903i	−0.239690	+	1.34571i
$970$		0			0
$971$	−15.7931	+	27.3544i	−0.506824	+	0.877844i	0.493145	+	0.869947i	$0.335847\pi$
$971$	−15.7931	+	27.3544i	−0.506824	+	0.877844i	−0.999969	+	0.00789735i	$0.997486\pi$
$972$		0			0
$973$	−0.777134	+	0.860821i	−0.0249138	+	0.0275966i
$974$		0			0
$975$	0.332783	−	0.120471i	0.0106576	−	0.00385815i
$976$		0			0
$977$	−34.0048	−	19.6327i	−1.08791	−	0.628106i	−0.154891	−	0.987932i	$-0.549503\pi$
$977$	−34.0048	−	19.6327i	−1.08791	−	0.628106i	−0.933019	+	0.359826i	$0.882836\pi$
$978$		0			0
$979$	10.0479	+	5.80113i	0.321131	+	0.185405i
$980$		0			0
$981$	−1.19861	−	6.93816i	−0.0382687	−	0.221519i
$982$		0			0
$983$	−39.8341			−1.27051			−0.635255	−	0.772302i	$-0.719105\pi$
$983$	−39.8341			−1.27051			−0.635255	+	0.772302i	$0.719105\pi$
$984$		0			0
$985$			61.7822i			1.96855i
$986$		0			0
$987$	10.6700	+	13.7430i	0.339630	+	0.437445i
$988$		0			0
$989$	9.44198	+	5.45133i	0.300237	+	0.173342i
$990$		0			0
$991$	−19.9472	−	34.5496i	−0.633645	−	1.09750i	−0.986801	−	0.161940i	$-0.948225\pi$
$991$	−19.9472	−	34.5496i	−0.633645	−	1.09750i	0.353156	−	0.935565i	$-0.385109\pi$
$992$		0			0
$993$	8.92983	+	24.6674i	0.283380	+	0.782796i
$994$		0			0
$995$	0.853132	−	0.492556i	0.0270461	−	0.0156151i
$996$		0			0
$997$		−	29.5700i		−	0.936492i	−0.883598	−	0.468246i	$-0.844886\pi$
$997$		−	29.5700i		−	0.936492i	0.883598	−	0.468246i	$-0.155114\pi$
$998$		0			0
$999$	−16.2731	+	9.28286i	−0.514859	+	0.293697i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cx.a.425.22	yes	48
3.2	odd	2		1512.2.cx.a.89.6		48
4.3	odd	2		1008.2.df.e.929.3		48
7.3	odd	6		504.2.bs.a.353.14	yes	48
9.4	even	3		1512.2.bs.a.1097.6		48
9.5	odd	6		504.2.bs.a.257.14	✓	48
12.11	even	2		3024.2.df.e.1601.6		48
21.17	even	6		1512.2.bs.a.521.6		48
28.3	even	6		1008.2.ca.e.353.11		48
36.23	even	6		1008.2.ca.e.257.11		48
36.31	odd	6		3024.2.ca.e.2609.6		48
63.31	odd	6		1512.2.cx.a.17.6		48
63.59	even	6	inner	504.2.cx.a.185.22	yes	48
84.59	odd	6		3024.2.ca.e.2033.6		48
252.31	even	6		3024.2.df.e.17.6		48
252.59	odd	6		1008.2.df.e.689.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.14	✓	48	9.5	odd	6
504.2.bs.a.353.14	yes	48	7.3	odd	6
504.2.cx.a.185.22	yes	48	63.59	even	6	inner
504.2.cx.a.425.22	yes	48	1.1	even	1	trivial
1008.2.ca.e.257.11		48	36.23	even	6
1008.2.ca.e.353.11		48	28.3	even	6
1008.2.df.e.689.3		48	252.59	odd	6
1008.2.df.e.929.3		48	4.3	odd	2
1512.2.bs.a.521.6		48	21.17	even	6
1512.2.bs.a.1097.6		48	9.4	even	3
1512.2.cx.a.17.6		48	63.31	odd	6
1512.2.cx.a.89.6		48	3.2	odd	2
3024.2.ca.e.2033.6		48	84.59	odd	6
3024.2.ca.e.2609.6		48	36.31	odd	6
3024.2.df.e.17.6		48	252.31	even	6
3024.2.df.e.1601.6		48	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cx (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.70521 + 0.303722i) q^{3} +2.22830 q^{5} +(2.51733 - 0.814280i) q^{7} +(2.81551 + 1.03582i) q^{9} +2.12135i q^{11} +(-5.10339 + 2.94644i) q^{13} +(3.79973 + 0.676785i) q^{15} +(-2.34020 - 4.05335i) q^{17} +(-4.54550 - 2.62435i) q^{19} +(4.53990 - 0.623952i) q^{21} -4.36380i q^{23} -0.0346748 q^{25} +(4.48644 + 2.62143i) q^{27} +(-2.25182 - 1.30009i) q^{29} +(6.59237 + 3.80611i) q^{31} +(-0.644302 + 3.61736i) q^{33} +(5.60937 - 1.81446i) q^{35} +(-1.80274 + 3.12244i) q^{37} +(-9.59726 + 3.47430i) q^{39} +(0.0395039 + 0.0684228i) q^{41} +(-1.24922 + 2.16371i) q^{43} +(6.27379 + 2.30813i) q^{45} +(1.89837 + 3.28807i) q^{47} +(5.67390 - 4.09962i) q^{49} +(-2.75945 - 7.62260i) q^{51} +(-4.08014 + 2.35567i) q^{53} +4.72701i q^{55} +(-6.95397 - 5.85564i) q^{57} +(6.59695 - 11.4262i) q^{59} +(-7.06624 + 4.07970i) q^{61} +(7.93100 + 0.314897i) q^{63} +(-11.3719 + 6.56556i) q^{65} +(2.37614 - 4.11559i) q^{67} +(1.32538 - 7.44121i) q^{69} -10.0325i q^{71} +(-12.6610 + 7.30986i) q^{73} +(-0.0591279 - 0.0105315i) q^{75} +(1.72737 + 5.34014i) q^{77} +(7.27414 + 12.5992i) q^{79} +(6.85414 + 5.83273i) q^{81} +(6.41294 - 11.1075i) q^{83} +(-5.21468 - 9.03209i) q^{85} +(-3.44497 - 2.90086i) q^{87} +(2.73464 - 4.73654i) q^{89} +(-10.4477 + 11.5728i) q^{91} +(10.0854 + 8.49248i) q^{93} +(-10.1287 - 5.84783i) q^{95} +(-12.9290 - 7.46454i) q^{97} +(-2.19734 + 5.97268i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{9} + 8 q^{15} - 10 q^{21} + 48 q^{25} + 18 q^{27} + 18 q^{29} + 18 q^{31} + 12 q^{33} - 4 q^{39} - 6 q^{41} - 6 q^{43} - 18 q^{45} + 18 q^{47} - 12 q^{49} + 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61}+ \cdots - 64 q^{99}+O(q^{100}) \) 48 * q + 2 * q^9 + 8 * q^15 - 10 * q^21 + 48 * q^25 + 18 * q^27 + 18 * q^29 + 18 * q^31 + 12 * q^33 - 4 * q^39 - 6 * q^41 - 6 * q^43 - 18 * q^45 + 18 * q^47 - 12 * q^49 + 6 * q^51 - 12 * q^53 + 4 * q^57 + 18 * q^61 - 32 * q^63 - 36 * q^65 - 12 * q^77 + 6 * q^79 + 6 * q^81 - 54 * q^87 - 18 * q^89 + 6 * q^91 + 4 * q^93 - 54 * q^95 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more