LMFDB - Embedded newform 468.2.bw.a.245.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [468,2,Mod(149,468)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("468.149"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(468, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 10, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 468 = 2^{2} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	468.bw (of order $12$, degree $4$, 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:	$3.73699881460$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			245.11
Character	$\chi$	$=$	468.245
Dual form			468.2.bw.a.149.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.06319 - 1.36734i) q^{3} +(-2.93450 - 0.786297i) q^{5} +(0.648304 + 0.173713i) q^{7} +(-0.739244 - 2.90749i) q^{9} +(-3.31036 - 3.31036i) q^{11} +(-1.91068 + 3.05766i) q^{13} +(-4.19507 + 3.17648i) q^{15} +(3.61521 - 6.26173i) q^{17} +(-4.17267 + 1.11806i) q^{19} +(0.926797 - 0.701763i) q^{21} +(-0.731021 + 1.26617i) q^{23} +(3.66289 + 2.11477i) q^{25} +(-4.76149 - 2.08043i) q^{27} -4.42172i q^{29} +(0.370153 - 1.38143i) q^{31} +(-8.04595 + 1.00684i) q^{33} +(-1.76586 - 1.01952i) q^{35} +(-1.14370 - 0.306454i) q^{37} +(2.14945 + 5.86344i) q^{39} +(2.03274 + 7.58629i) q^{41} +(8.20046 - 4.73454i) q^{43} +(-0.116843 + 9.11330i) q^{45} +(7.20323 - 1.93010i) q^{47} +(-5.67206 - 3.27476i) q^{49} +(-4.71825 - 11.6006i) q^{51} +7.46793i q^{53} +(7.11133 + 12.3172i) q^{55} +(-2.90758 + 6.89419i) q^{57} +(-2.92525 - 2.92525i) q^{59} +(2.80787 + 4.86337i) q^{61} +(0.0258135 - 2.01336i) q^{63} +(8.01112 - 7.47034i) q^{65} +(6.58970 - 1.76570i) q^{67} +(0.954064 + 2.34573i) q^{69} +(-2.32349 - 8.67138i) q^{71} +(8.37710 - 8.37710i) q^{73} +(6.78597 - 2.76001i) q^{75} +(-1.57107 - 2.72118i) q^{77} +(6.30240 - 10.9161i) q^{79} +(-7.90704 + 4.29869i) q^{81} +(-1.15005 - 4.29206i) q^{83} +(-15.5324 + 15.5324i) q^{85} +(-6.04600 - 4.70114i) q^{87} +(2.16797 - 8.09097i) q^{89} +(-1.76986 + 1.65039i) q^{91} +(-1.49534 - 1.97485i) q^{93} +13.1238 q^{95} +(-4.03682 + 15.0656i) q^{97} +(-7.17770 + 12.0720i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{7} + 4 q^{19} - 24 q^{21} + 8 q^{31} + 12 q^{33} - 66 q^{35} + 2 q^{37} + 24 q^{41} + 12 q^{43} - 30 q^{47} + 30 q^{57} + 84 q^{63} + 6 q^{65} + 28 q^{67} - 36 q^{69} + 24 q^{71} - 14 q^{73}+ \cdots - 42 q^{99}+O(q^{100}) $ 56 * q - 2 * q^7 + 4 * q^19 - 24 * q^21 + 8 * q^31 + 12 * q^33 - 66 * q^35 + 2 * q^37 + 24 * q^41 + 12 * q^43 - 30 * q^47 + 30 * q^57 + 84 * q^63 + 6 * q^65 + 28 * q^67 - 36 * q^69 + 24 * q^71 - 14 * q^73 - 24 * q^77 + 12 * q^79 - 12 * q^81 - 60 * q^83 + 36 * q^85 + 4 * q^91 - 54 * q^93 + 26 * q^97 - 42 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/468\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$235$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	1.06319	−	1.36734i	0.613834	−	0.789435i
$3$	1.06319	−	1.36734i	0.613834	−	0.789435i
$4$		0			0
$5$	−2.93450	−	0.786297i	−1.31235	−	0.351642i	−0.466242	−	0.884657i	$-0.654392\pi$
$5$	−2.93450	−	0.786297i	−1.31235	−	0.351642i	−0.846106	+	0.533015i	$0.821059\pi$
$6$		0			0
$7$	0.648304	+	0.173713i	0.245036	+	0.0656572i	0.379247	−	0.925296i	$-0.376183\pi$
$7$	0.648304	+	0.173713i	0.245036	+	0.0656572i	−0.134211	+	0.990953i	$0.542850\pi$
$8$		0			0
$9$	−0.739244	−	2.90749i	−0.246415	−	0.969165i
$10$		0			0
$11$	−3.31036	−	3.31036i	−0.998113	−	0.998113i	0.00188566	−	0.999998i	$-0.499400\pi$
$11$	−3.31036	−	3.31036i	−0.998113	−	0.998113i	−0.999998	+	0.00188566i	$0.999400\pi$
$12$		0			0
$13$	−1.91068	+	3.05766i	−0.529927	+	0.848043i
$13$	−1.91068	+	3.05766i	−0.529927	+	0.848043i
$14$		0			0
$15$	−4.19507	+	3.17648i	−1.08316	+	0.820163i
$16$		0			0
$17$	3.61521	−	6.26173i	0.876817	−	1.51869i	0.0220024	−	0.999758i	$-0.492996\pi$
$17$	3.61521	−	6.26173i	0.876817	−	1.51869i	0.854815	−	0.518934i	$-0.173671\pi$
$18$		0			0
$19$	−4.17267	+	1.11806i	−0.957277	+	0.256502i	−0.703447	−	0.710747i	$-0.748357\pi$
$19$	−4.17267	+	1.11806i	−0.957277	+	0.256502i	−0.253830	+	0.967249i	$0.581690\pi$
$20$		0			0
$21$	0.926797	−	0.701763i	0.202244	−	0.153137i
$22$		0			0
$23$	−0.731021	+	1.26617i	−0.152428	+	0.264014i	−0.932120	−	0.362150i	$-0.882043\pi$
$23$	−0.731021	+	1.26617i	−0.152428	+	0.264014i	0.779691	+	0.626164i	$0.215376\pi$
$24$		0			0
$25$	3.66289	+	2.11477i	0.732579	+	0.422954i
$26$		0			0
$27$	−4.76149	−	2.08043i	−0.916350	−	0.400378i
$28$		0			0
$29$		−	4.42172i		−	0.821093i	−0.911840	−	0.410546i	$-0.865338\pi$
$29$		−	4.42172i		−	0.821093i	0.911840	−	0.410546i	$-0.134662\pi$
$30$		0			0
$31$	0.370153	−	1.38143i	0.0664815	−	0.248112i	−0.924686	−	0.380732i	$-0.875672\pi$
$31$	0.370153	−	1.38143i	0.0664815	−	0.248112i	0.991167	+	0.132619i	$0.0423388\pi$
$32$		0			0
$33$	−8.04595	+	1.00684i	−1.40062	+	0.175269i
$34$		0			0
$35$	−1.76586	−	1.01952i	−0.298485	−	0.172330i
$36$		0			0
$37$	−1.14370	−	0.306454i	−0.188023	−	0.0503807i	0.163579	−	0.986530i	$-0.447696\pi$
$37$	−1.14370	−	0.306454i	−0.188023	−	0.0503807i	−0.351602	+	0.936150i	$0.614363\pi$
$38$		0			0
$39$	2.14945	+	5.86344i	0.344187	+	0.938901i
$40$		0			0
$41$	2.03274	+	7.58629i	0.317461	+	1.18478i	0.921676	+	0.387959i	$0.126820\pi$
$41$	2.03274	+	7.58629i	0.317461	+	1.18478i	−0.604216	+	0.796821i	$0.706513\pi$
$42$		0			0
$43$	8.20046	−	4.73454i	1.25056	−	0.722010i	0.279338	−	0.960193i	$-0.409885\pi$
$43$	8.20046	−	4.73454i	1.25056	−	0.722010i	0.971220	+	0.238183i	$0.0765517\pi$
$44$		0			0
$45$	−0.116843	+	9.11330i	−0.0174179	+	1.35853i
$46$		0			0
$47$	7.20323	−	1.93010i	1.05070	−	0.281534i	0.308159	−	0.951335i	$-0.400287\pi$
$47$	7.20323	−	1.93010i	1.05070	−	0.281534i	0.742541	+	0.669801i	$0.233621\pi$
$48$		0			0
$49$	−5.67206	−	3.27476i	−0.810294	−	0.467823i
$50$		0			0
$51$	−4.71825	−	11.6006i	−0.660687	−	1.62441i
$52$		0			0
$53$			7.46793i			1.02580i	0.858449	+	0.512900i	$0.171429\pi$
$53$			7.46793i			1.02580i	−0.858449	+	0.512900i	$0.828571\pi$
$54$		0			0
$55$	7.11133	+	12.3172i	0.958892	+	1.66085i
$56$		0			0
$57$	−2.90758	+	6.89419i	−0.385118	+	0.913157i
$58$		0			0
$59$	−2.92525	−	2.92525i	−0.380835	−	0.380835i	0.490568	−	0.871403i	$-0.336789\pi$
$59$	−2.92525	−	2.92525i	−0.380835	−	0.380835i	−0.871403	+	0.490568i	$0.836789\pi$
$60$		0			0
$61$	2.80787	+	4.86337i	0.359511	+	0.622691i	0.987879	−	0.155225i	$-0.0496102\pi$
$61$	2.80787	+	4.86337i	0.359511	+	0.622691i	−0.628368	+	0.777916i	$0.716277\pi$
$62$		0			0
$63$	0.0258135	−	2.01336i	0.00325219	−	0.253659i
$64$		0			0
$65$	8.01112	−	7.47034i	0.993657	−	0.926582i
$66$		0			0
$67$	6.58970	−	1.76570i	0.805060	−	0.215715i	0.167256	−	0.985914i	$-0.446510\pi$
$67$	6.58970	−	1.76570i	0.805060	−	0.215715i	0.637804	+	0.770198i	$0.279843\pi$
$68$		0			0
$69$	0.954064	+	2.34573i	0.114856	+	0.282393i
$70$		0			0
$71$	−2.32349	−	8.67138i	−0.275747	−	1.02910i	−0.955339	−	0.295513i	$-0.904510\pi$
$71$	−2.32349	−	8.67138i	−0.275747	−	1.02910i	0.679591	−	0.733591i	$-0.262157\pi$
$72$		0			0
$73$	8.37710	−	8.37710i	0.980466	−	0.980466i	−0.0193471	−	0.999813i	$-0.506159\pi$
$73$	8.37710	−	8.37710i	0.980466	−	0.980466i	0.999813	+	0.0193471i	$0.00615876\pi$
$74$		0			0
$75$	6.78597	−	2.76001i	0.783577	−	0.318699i
$76$		0			0
$77$	−1.57107	−	2.72118i	−0.179040	−	0.310107i
$78$		0			0
$79$	6.30240	−	10.9161i	0.709076	−	1.22816i	−0.256125	−	0.966644i	$-0.582446\pi$
$79$	6.30240	−	10.9161i	0.709076	−	1.22816i	0.965200	−	0.261512i	$-0.0842210\pi$
$80$		0			0
$81$	−7.90704	+	4.29869i	−0.878560	+	0.477632i
$82$		0			0
$83$	−1.15005	−	4.29206i	−0.126235	−	0.471114i	0.873646	−	0.486562i	$-0.161749\pi$
$83$	−1.15005	−	4.29206i	−0.126235	−	0.471114i	−0.999881	+	0.0154478i	$0.995083\pi$
$84$		0			0
$85$	−15.5324	+	15.5324i	−1.68473	+	1.68473i
$86$		0			0
$87$	−6.04600	−	4.70114i	−0.648199	−	0.504015i
$88$		0			0
$89$	2.16797	−	8.09097i	0.229804	−	0.857641i	−0.750618	−	0.660736i	$-0.770244\pi$
$89$	2.16797	−	8.09097i	0.229804	−	0.857641i	0.980423	−	0.196905i	$-0.0630890\pi$
$90$		0			0
$91$	−1.76986	+	1.65039i	−0.185531	+	0.173008i
$92$		0			0
$93$	−1.49534	−	1.97485i	−0.155060	−	0.204783i
$94$		0			0
$95$	13.1238			1.34648
$96$		0			0
$97$	−4.03682	+	15.0656i	−0.409877	+	1.52968i	0.385004	+	0.922915i	$0.374200\pi$
$97$	−4.03682	+	15.0656i	−0.409877	+	1.52968i	−0.794881	+	0.606765i	$0.792467\pi$
$98$		0			0
$99$	−7.17770	+	12.0720i	−0.721386	+	1.21328i
$100$		0			0
$101$	9.77584			0.972732			0.486366	−	0.873755i	$-0.338322\pi$
$101$	9.77584			0.972732			0.486366	+	0.873755i	$0.338322\pi$
$102$		0			0
$103$	9.73205	−	5.61880i	0.958928	−	0.553637i	0.0630850	−	0.998008i	$-0.479906\pi$
$103$	9.73205	−	5.61880i	0.958928	−	0.553637i	0.895843	+	0.444371i	$0.146573\pi$
$104$		0			0
$105$	−3.27148	+	1.33059i	−0.319264	+	0.129852i
$106$		0			0
$107$	−14.6940	+	8.48360i	−1.42052	+	0.820140i	−0.996344	−	0.0854370i	$-0.972771\pi$
$107$	−14.6940	+	8.48360i	−1.42052	+	0.820140i	−0.424181	+	0.905577i	$0.639438\pi$
$108$		0			0
$109$	0.514307	+	0.514307i	0.0492617	+	0.0492617i	0.731309	−	0.682047i	$-0.238910\pi$
$109$	0.514307	+	0.514307i	0.0492617	+	0.0492617i	−0.682047	+	0.731309i	$0.738910\pi$
$110$		0			0
$111$	−1.63500	+	1.23801i	−0.155187	+	0.117507i
$112$		0			0
$113$			9.83918i			0.925592i	0.886465	+	0.462796i	$0.153154\pi$
$113$			9.83918i			0.925592i	−0.886465	+	0.462796i	$0.846846\pi$
$114$		0			0
$115$	3.14076	−	3.14076i	0.292878	−	0.292878i
$116$		0			0
$117$	10.3026	+	3.29493i	0.952475	+	0.304617i
$118$		0			0
$119$	3.43150	−	3.43150i	0.314565	−	0.314565i
$120$		0			0
$121$			10.9170i			0.992457i
$122$		0			0
$123$	12.5342	+	5.28624i	1.13018	+	0.476644i
$124$		0			0
$125$	1.65509	+	1.65509i	0.148036	+	0.148036i
$126$		0			0
$127$	12.2584	−	7.07742i	1.08776	−	0.628019i	0.154782	−	0.987949i	$-0.450533\pi$
$127$	12.2584	−	7.07742i	1.08776	−	0.628019i	0.932980	+	0.359929i	$0.117199\pi$
$128$		0			0
$129$	2.24494	−	16.2465i	0.197656	−	1.43043i
$130$		0			0
$131$	−2.29027	+	1.32229i	−0.200101	+	0.115529i	−0.596703	−	0.802462i	$-0.703523\pi$
$131$	−2.29027	+	1.32229i	−0.200101	+	0.115529i	0.396601	+	0.917991i	$0.370190\pi$
$132$		0			0
$133$	−2.89938			−0.251409
$134$		0			0
$135$	12.3368	+	9.84896i	1.06178	+	0.847663i
$136$		0			0
$137$	0.0251086	−	0.0937066i	0.00214517	−	0.00800590i	−0.964845	−	0.262820i	$-0.915348\pi$
$137$	0.0251086	−	0.0937066i	0.00214517	−	0.00800590i	0.966990	+	0.254814i	$0.0820142\pi$
$138$		0			0
$139$	12.0890			1.02538			0.512690	−	0.858574i	$-0.328649\pi$
$139$	12.0890			1.02538			0.512690	+	0.858574i	$0.328649\pi$
$140$		0			0
$141$	5.01932	−	11.9013i	0.422703	−	1.00227i
$142$		0			0
$143$	16.4470	−	3.79693i	1.37537	−	0.317515i
$144$		0			0
$145$	−3.47678	+	12.9755i	−0.288731	+	1.07756i
$146$		0			0
$147$	−10.5082	+	4.27393i	−0.866702	+	0.352508i
$148$		0			0
$149$	−8.93025	+	8.93025i	−0.731594	+	0.731594i	−0.970936	−	0.239341i	$-0.923069\pi$
$149$	−8.93025	+	8.93025i	−0.731594	+	0.731594i	0.239341	+	0.970936i	$0.423069\pi$
$150$		0			0
$151$	3.88081	+	14.4834i	0.315816	+	1.17864i	0.923228	+	0.384253i	$0.125541\pi$
$151$	3.88081	+	14.4834i	0.315816	+	1.17864i	−0.607412	+	0.794387i	$0.707792\pi$
$152$		0			0
$153$	−20.8784	−	5.88226i	−1.68792	−	0.475552i
$154$		0			0
$155$	−2.17243	+	3.76276i	−0.174494	+	0.302232i
$156$		0			0
$157$	−1.33213	−	2.30731i	−0.106315	−	0.184144i	0.807960	−	0.589238i	$-0.200572\pi$
$157$	−1.33213	−	2.30731i	−0.106315	−	0.184144i	−0.914275	+	0.405094i	$0.867239\pi$
$158$		0			0
$159$	10.2112	+	7.93985i	0.809802	+	0.629671i
$160$		0			0
$161$	−0.693873	+	0.693873i	−0.0546849	+	0.0546849i
$162$		0			0
$163$	−1.21282	−	4.52631i	−0.0949955	−	0.354528i	0.902023	−	0.431687i	$-0.142082\pi$
$163$	−1.21282	−	4.52631i	−0.0949955	−	0.354528i	−0.997019	+	0.0771594i	$0.975415\pi$
$164$		0			0
$165$	24.4025	+	3.37193i	1.89973	+	0.262504i
$166$		0			0
$167$	−15.0659	+	4.03690i	−1.16584	+	0.312385i	−0.789294	−	0.614015i	$-0.789553\pi$
$167$	−15.0659	+	4.03690i	−1.16584	+	0.312385i	−0.376541	+	0.926400i	$0.622887\pi$
$168$		0			0
$169$	−5.69860	−	11.6844i	−0.438354	−	0.898803i
$170$		0			0
$171$	6.33539	+	11.3055i	0.484479	+	0.864553i
$172$		0			0
$173$	−10.0055	−	17.3300i	−0.760702	−	1.31757i	−0.942489	−	0.334237i	$-0.891522\pi$
$173$	−10.0055	−	17.3300i	−0.760702	−	1.31757i	0.181787	−	0.983338i	$-0.441812\pi$
$174$		0			0
$175$	2.00731	+	2.00731i	0.151738	+	0.151738i
$176$		0			0
$177$	−7.10991	+	0.889710i	−0.534414	+	0.0668747i
$178$		0			0
$179$	−5.74519	−	9.95097i	−0.429416	−	0.743770i	0.567405	−	0.823439i	$-0.307947\pi$
$179$	−5.74519	−	9.95097i	−0.429416	−	0.743770i	−0.996821	+	0.0796682i	$0.974614\pi$
$180$		0			0
$181$			26.1318i			1.94236i	0.238350	+	0.971179i	$0.423394\pi$
$181$			26.1318i			1.94236i	−0.238350	+	0.971179i	$0.576606\pi$
$182$		0			0
$183$	9.63519	+	1.33139i	0.712254	+	0.0984188i
$184$		0			0
$185$	3.11522	+	1.79858i	0.229036	+	0.132234i
$186$		0			0
$187$	−32.6963	+	8.76094i	−2.39099	+	0.640663i
$188$		0			0
$189$	−2.72550	−	2.17588i	−0.198251	−	0.158272i
$190$		0			0
$191$	−2.06030	+	1.18952i	−0.149078	+	0.0860703i	−0.572684	−	0.819776i	$-0.694098\pi$
$191$	−2.06030	+	1.18952i	−0.149078	+	0.0860703i	0.423605	+	0.905847i	$0.360764\pi$
$192$		0			0
$193$	−4.29803	−	16.0404i	−0.309379	−	1.15462i	−0.929110	−	0.369803i	$-0.879425\pi$
$193$	−4.29803	−	16.0404i	−0.309379	−	1.15462i	0.619732	−	0.784814i	$-0.287241\pi$
$194$		0			0
$195$	−1.69715	−	18.8963i	−0.121535	−	1.35320i
$196$		0			0
$197$	−23.6064	−	6.32532i	−1.68189	−	0.450660i	−0.713611	−	0.700542i	$-0.752942\pi$
$197$	−23.6064	−	6.32532i	−1.68189	−	0.450660i	−0.968276	+	0.249882i	$0.919608\pi$
$198$		0			0
$199$	−11.8808	−	6.85940i	−0.842210	−	0.486250i	0.0158050	−	0.999875i	$-0.494969\pi$
$199$	−11.8808	−	6.85940i	−0.842210	−	0.486250i	−0.858015	+	0.513625i	$0.828302\pi$
$200$		0			0
$201$	4.59180	−	10.8877i	0.323880	−	0.767956i
$202$		0			0
$203$	0.768109	−	2.86662i	0.0539107	−	0.201197i
$204$		0			0
$205$		−	23.8603i		−	1.66648i
$206$		0			0
$207$	4.22177	+	1.18943i	0.293433	+	0.0826714i
$208$		0			0
$209$	17.5143	+	10.1119i	1.21149	+	0.699453i
$210$		0			0
$211$	7.36608	−	12.7584i	0.507102	−	0.878327i	−0.492864	−	0.870106i	$-0.664050\pi$
$211$	7.36608	−	12.7584i	0.507102	−	0.878327i	0.999966	−	0.00822025i	$-0.00261662\pi$
$212$		0			0
$213$	−14.3270	−	6.04234i	−0.981673	−	0.414014i
$214$		0			0
$215$	−27.7870	+	7.44550i	−1.89506	+	0.507779i
$216$		0			0
$217$	0.479944	−	0.831287i	0.0325807	−	0.0564314i
$218$		0			0
$219$	−2.54788	−	20.3608i	−0.172170	−	1.37586i
$220$		0			0
$221$	12.2387	+	23.0182i	0.823266	+	1.54837i
$222$		0			0
$223$	−18.7175	−	18.7175i	−1.25342	−	1.25342i	−0.954179	−	0.299237i	$-0.903268\pi$
$223$	−18.7175	−	18.7175i	−1.25342	−	1.25342i	−0.299237	−	0.954179i	$-0.596732\pi$
$224$		0			0
$225$	3.44092	−	12.2132i	0.229394	−	0.814211i
$226$		0			0
$227$	3.52179	+	0.943662i	0.233750	+	0.0626330i	0.373792	−	0.927512i	$-0.378057\pi$
$227$	3.52179	+	0.943662i	0.233750	+	0.0626330i	−0.140043	+	0.990145i	$0.544724\pi$
$228$		0			0
$229$	11.9036	+	3.18957i	0.786614	+	0.210773i	0.629699	−	0.776840i	$-0.283178\pi$
$229$	11.9036	+	3.18957i	0.786614	+	0.210773i	0.156915	+	0.987612i	$0.449845\pi$
$230$		0			0
$231$	−5.39113	−	0.744943i	−0.354710	−	0.0490136i
$232$		0			0
$233$	−1.46997			−0.0963010			−0.0481505	−	0.998840i	$-0.515333\pi$
$233$	−1.46997			−0.0963010			−0.0481505	+	0.998840i	$0.515333\pi$
$234$		0			0
$235$	−22.6555			−1.47788
$236$		0			0
$237$	−8.22534	−	20.2234i	−0.534293	−	1.31365i
$238$		0			0
$239$	4.01157	+	1.07490i	0.259487	+	0.0695293i	0.386217	−	0.922408i	$-0.373782\pi$
$239$	4.01157	+	1.07490i	0.259487	+	0.0695293i	−0.126730	+	0.991937i	$0.540448\pi$
$240$		0			0
$241$	8.46427	+	2.26800i	0.545232	+	0.146094i	0.520913	−	0.853610i	$-0.325592\pi$
$241$	8.46427	+	2.26800i	0.545232	+	0.146094i	0.0243189	+	0.999704i	$0.492258\pi$
$242$		0			0
$243$	−2.52892	+	15.3820i	−0.162231	+	0.986753i
$244$		0			0
$245$	14.0697	+	14.0697i	0.898880	+	0.898880i
$246$		0			0
$247$	4.55398	−	14.8949i	0.289763	−	0.947739i
$248$		0			0
$249$	−7.09143	−	2.99077i	−0.449401	−	0.189532i
$250$		0			0
$251$	8.12469	−	14.0724i	0.512826	−	0.888240i	−0.487064	−	0.873367i	$-0.661932\pi$
$251$	8.12469	−	14.0724i	0.512826	−	0.888240i	0.999889	−	0.0148739i	$-0.00473467\pi$
$252$		0			0
$253$	6.61142	−	1.77152i	0.415656	−	0.111375i
$254$		0			0
$255$	4.72416	+	37.7520i	0.295838	+	2.36412i
$256$		0			0
$257$	0.817029	−	1.41513i	0.0509648	−	0.0882737i	−0.839418	−	0.543487i	$-0.817104\pi$
$257$	0.817029	−	1.41513i	0.0509648	−	0.0882737i	0.890382	+	0.455213i	$0.150437\pi$
$258$		0			0
$259$	−0.688231	−	0.397350i	−0.0427646	−	0.0246902i
$260$		0			0
$261$	−12.8561	+	3.26873i	−0.795774	+	0.202329i
$262$		0			0
$263$			14.9031i			0.918964i	0.888187	+	0.459482i	$0.151965\pi$
$263$			14.9031i			0.918964i	−0.888187	+	0.459482i	$0.848035\pi$
$264$		0			0
$265$	5.87201	−	21.9146i	0.360715	−	1.34621i
$266$		0			0
$267$	−8.75814	−	11.5666i	−0.535990	−	0.707865i
$268$		0			0
$269$	2.95682	+	1.70712i	0.180280	+	0.104085i	0.587424	−	0.809279i	$-0.300142\pi$
$269$	2.95682	+	1.70712i	0.180280	+	0.104085i	−0.407144	+	0.913364i	$0.633475\pi$
$270$		0			0
$271$	−8.83826	−	2.36821i	−0.536886	−	0.143858i	−0.0198199	−	0.999804i	$-0.506309\pi$
$271$	−8.83826	−	2.36821i	−0.536886	−	0.143858i	−0.517066	+	0.855945i	$0.672976\pi$
$272$		0			0
$273$	0.374943	+	4.17468i	0.0226926	+	0.252663i
$274$		0			0
$275$	−5.12484	−	19.1262i	−0.309040	−	1.15335i
$276$		0			0
$277$	−7.46396	+	4.30932i	−0.448466	+	0.258922i	−0.707182	−	0.707031i	$-0.750034\pi$
$277$	−7.46396	+	4.30932i	−0.448466	+	0.258922i	0.258716	+	0.965953i	$0.416701\pi$
$278$		0			0
$279$	−4.29013	−	0.0550043i	−0.256844	−	0.00329302i
$280$		0			0
$281$	0.202633	−	0.0542955i	0.0120881	−	0.00323900i	−0.252770	−	0.967526i	$-0.581342\pi$
$281$	0.202633	−	0.0542955i	0.0120881	−	0.00323900i	0.264858	+	0.964287i	$0.414675\pi$
$282$		0			0
$283$	−19.9480	−	11.5170i	−1.18578	−	0.684612i	−0.228438	−	0.973558i	$-0.573362\pi$
$283$	−19.9480	−	11.5170i	−1.18578	−	0.684612i	−0.957345	+	0.288946i	$0.906695\pi$
$284$		0			0
$285$	13.9532	−	17.9448i	0.826514	−	1.06296i
$286$		0			0
$287$			5.27134i			0.311157i
$288$		0			0
$289$	−17.6395	−	30.5525i	−1.03762	−	1.79720i
$290$		0			0
$291$	16.3079	+	21.5373i	0.955986	+	1.26254i
$292$		0			0
$293$	18.2292	+	18.2292i	1.06496	+	1.06496i	0.997738	+	0.0672223i	$0.0214137\pi$
$293$	18.2292	+	18.2292i	1.06496	+	1.06496i	0.0672223	+	0.997738i	$0.478586\pi$
$294$		0			0
$295$	6.28402	+	10.8842i	0.365870	+	0.633705i
$296$		0			0
$297$	8.87531	+	22.6493i	0.514998	+	1.31424i
$298$		0			0
$299$	−2.47476	−	4.65445i	−0.143119	−	0.269174i
$300$		0			0
$301$	6.13884	−	1.64490i	0.353837	−	0.0948103i
$302$		0			0
$303$	10.3936	−	13.3669i	0.597097	−	0.767909i
$304$		0			0
$305$	−4.41564	−	16.4794i	−0.252839	−	0.943606i
$306$		0			0
$307$	23.1111	−	23.1111i	1.31902	−	1.31902i	0.404467	−	0.914553i	$-0.367457\pi$
$307$	23.1111	−	23.1111i	1.31902	−	1.31902i	0.914553	−	0.404467i	$-0.132543\pi$
$308$		0			0
$309$	2.66422	−	19.2809i	0.151562	−	1.09685i
$310$		0			0
$311$	8.87785	+	15.3769i	0.503417	+	0.871943i	0.999992	+	0.00394966i	$0.00125722\pi$
$311$	8.87785	+	15.3769i	0.503417	+	0.871943i	−0.496576	+	0.867993i	$0.665409\pi$
$312$		0			0
$313$	−4.89955	+	8.48627i	−0.276939	+	0.479672i	−0.970622	−	0.240608i	$-0.922653\pi$
$313$	−4.89955	+	8.48627i	−0.276939	+	0.479672i	0.693684	+	0.720280i	$0.255987\pi$
$314$		0			0
$315$	−1.65884	+	5.88789i	−0.0934653	+	0.331745i
$316$		0			0
$317$	2.71402	+	10.1289i	0.152435	+	0.568894i	0.999311	+	0.0371046i	$0.0118135\pi$
$317$	2.71402	+	10.1289i	0.152435	+	0.568894i	−0.846877	+	0.531789i	$0.821520\pi$
$318$		0			0
$319$	−14.6375	+	14.6375i	−0.819543	+	0.819543i
$320$		0			0
$321$	−4.02260	+	29.1114i	−0.224520	+	1.62484i
$322$		0			0
$323$	−8.08407	+	30.1702i	−0.449810	+	1.67871i
$324$		0			0
$325$	−13.4649	+	7.15924i	−0.746897	+	0.397123i
$326$		0			0
$327$	1.25004	−	0.156426i	0.0691274	−	0.00865037i
$328$		0			0
$329$	5.00517			0.275944
$330$		0			0
$331$	−4.02523	+	15.0224i	−0.221247	+	0.825705i	0.762627	+	0.646839i	$0.223909\pi$
$331$	−4.02523	+	15.0224i	−0.221247	+	0.825705i	−0.983873	+	0.178866i	$0.942757\pi$
$332$		0			0
$333$	−0.0455386	+	3.55185i	−0.00249550	+	0.194640i
$334$		0			0
$335$	−20.7258			−1.13237
$336$		0			0
$337$	−16.3011	+	9.41142i	−0.887975	+	0.512673i	−0.873280	−	0.487219i	$-0.838011\pi$
$337$	−16.3011	+	9.41142i	−0.887975	+	0.512673i	−0.0146957	+	0.999892i	$0.504678\pi$
$338$		0			0
$339$	13.4535	+	10.4609i	0.730695	+	0.568160i
$340$		0			0
$341$	−5.79838	+	3.34770i	−0.314000	+	0.181288i
$342$		0			0
$343$	−6.43049	−	6.43049i	−0.347214	−	0.347214i
$344$		0			0
$345$	−0.955259	−	7.63373i	−0.0514294	−	0.410986i
$346$		0			0
$347$		−	13.0042i		−	0.698104i	−0.937103	−	0.349052i	$-0.886504\pi$
$347$		−	13.0042i		−	0.698104i	0.937103	−	0.349052i	$-0.113496\pi$
$348$		0			0
$349$	13.9143	−	13.9143i	0.744818	−	0.744818i	−0.228683	−	0.973501i	$-0.573442\pi$
$349$	13.9143	−	13.9143i	0.744818	−	0.744818i	0.973501	+	0.228683i	$0.0734420\pi$
$350$		0			0
$351$	15.4589	−	10.5840i	0.825137	−	0.564933i
$352$		0			0
$353$	1.42456	−	1.42456i	0.0758218	−	0.0758218i	−0.668179	−	0.744001i	$-0.732926\pi$
$353$	1.42456	−	1.42456i	0.0758218	−	0.0758218i	0.744001	+	0.668179i	$0.232926\pi$
$354$		0			0
$355$			27.2731i			1.44751i
$356$		0			0
$357$	−1.04369	−	8.34037i	−0.0552377	−	0.441419i
$358$		0			0
$359$	−12.9143	−	12.9143i	−0.681589	−	0.681589i	0.278769	−	0.960358i	$-0.410074\pi$
$359$	−12.9143	−	12.9143i	−0.681589	−	0.681589i	−0.960358	+	0.278769i	$0.910074\pi$
$360$		0			0
$361$	−0.293341	+	0.169361i	−0.0154390	+	0.00891372i
$362$		0			0
$363$	14.9273	+	11.6069i	0.783480	+	0.609205i
$364$		0			0
$365$	−31.1695	+	17.9957i	−1.63149	+	0.941938i
$366$		0			0
$367$	12.9286			0.674869			0.337435	−	0.941349i	$-0.390441\pi$
$367$	12.9286			0.674869			0.337435	+	0.941349i	$0.390441\pi$
$368$		0			0
$369$	20.5544	−	11.5183i	1.07002	−	0.599619i
$370$		0			0
$371$	−1.29727	+	4.84149i	−0.0673511	+	0.251358i
$372$		0			0
$373$	−22.2218			−1.15060			−0.575301	−	0.817942i	$-0.695115\pi$
$373$	−22.2218			−1.15060			−0.575301	+	0.817942i	$0.695115\pi$
$374$		0			0
$375$	4.02276	−	0.503395i	0.207735	−	0.0259952i
$376$		0			0
$377$	13.5201	+	8.44850i	0.696322	+	0.435120i
$378$		0			0
$379$	7.09076	−	26.4631i	0.364228	−	1.35932i	−0.504237	−	0.863565i	$-0.668226\pi$
$379$	7.09076	−	26.4631i	0.364228	−	1.35932i	0.868465	−	0.495751i	$-0.165107\pi$
$380$		0			0
$381$	3.35584	−	24.2861i	0.171925	−	1.24422i
$382$		0			0
$383$	−4.86478	+	4.86478i	−0.248578	+	0.248578i	−0.820387	−	0.571809i	$-0.806242\pi$
$383$	−4.86478	+	4.86478i	−0.248578	+	0.248578i	0.571809	+	0.820387i	$0.306242\pi$
$384$		0			0
$385$	2.47066	+	9.22062i	0.125916	+	0.469926i
$386$		0			0
$387$	−19.8278	−	20.3428i	−1.00790	−	1.03408i
$388$		0			0
$389$	−5.10145	+	8.83597i	−0.258654	+	0.448002i	−0.965882	−	0.258984i	$-0.916612\pi$
$389$	−5.10145	+	8.83597i	−0.258654	+	0.448002i	0.707228	+	0.706986i	$0.249946\pi$
$390$		0			0
$391$	5.28559	+	9.15491i	0.267304	+	0.462983i
$392$		0			0
$393$	−0.626978	+	4.53742i	−0.0316269	+	0.228883i
$394$		0			0
$395$	−27.0777	+	27.0777i	−1.36243	+	1.36243i
$396$		0			0
$397$	−5.15554	−	19.2407i	−0.258749	−	0.965665i	−0.965966	−	0.258669i	$-0.916716\pi$
$397$	−5.15554	−	19.2407i	−0.258749	−	0.965665i	0.707217	−	0.706997i	$-0.249950\pi$
$398$		0			0
$399$	−3.08260	+	3.96445i	−0.154323	+	0.198471i
$400$		0			0
$401$	25.2249	−	6.75899i	1.25967	−	0.337528i	0.433606	−	0.901102i	$-0.357241\pi$
$401$	25.2249	−	6.75899i	1.25967	−	0.337528i	0.826065	+	0.563574i	$0.190574\pi$
$402$		0			0
$403$	3.51670	+	3.77128i	0.175179	+	0.187861i
$404$		0			0
$405$	26.5832	−	6.39723i	1.32093	−	0.317881i
$406$		0			0
$407$	2.77159	+	4.80054i	0.137383	+	0.237954i
$408$		0			0
$409$	28.0046	+	28.0046i	1.38474	+	1.38474i	0.835987	+	0.548749i	$0.184896\pi$
$409$	28.0046	+	28.0046i	1.38474	+	1.38474i	0.548749	+	0.835987i	$0.315104\pi$
$410$		0			0
$411$	−0.101434	−	0.133960i	−0.00500335	−	0.00660777i
$412$		0			0
$413$	−1.38830	−	2.40460i	−0.0683137	−	0.118323i
$414$		0			0
$415$			13.4993i			0.662655i
$416$		0			0
$417$	12.8530	−	16.5298i	0.629413	−	0.809470i
$418$		0			0
$419$	−3.57956	−	2.06666i	−0.174873	−	0.100963i	0.410008	−	0.912082i	$-0.365526\pi$
$419$	−3.57956	−	2.06666i	−0.174873	−	0.100963i	−0.584882	+	0.811119i	$0.698859\pi$
$420$		0			0
$421$	0.651312	−	0.174519i	0.0317430	−	0.00850551i	−0.242913	−	0.970048i	$-0.578103\pi$
$421$	0.651312	−	0.174519i	0.0317430	−	0.00850551i	0.274656	+	0.961543i	$0.411436\pi$
$422$		0			0
$423$	−10.9367	−	19.5165i	−0.531761	−	0.948927i
$424$		0			0
$425$	26.4842	−	15.2907i	1.28467	−	0.741707i
$426$		0			0
$427$	0.975525	+	3.64071i	0.0472089	+	0.176186i
$428$		0			0
$429$	12.2947	−	26.5256i	0.593592	−	1.28067i
$430$		0			0
$431$	−15.1112	−	4.04903i	−0.727879	−	0.195035i	−0.124195	−	0.992258i	$-0.539635\pi$
$431$	−15.1112	−	4.04903i	−0.727879	−	0.195035i	−0.603685	+	0.797223i	$0.706301\pi$
$432$		0			0
$433$	32.7772	+	18.9239i	1.57517	+	0.909427i	0.995519	+	0.0945639i	$0.0301457\pi$
$433$	32.7772	+	18.9239i	1.57517	+	0.909427i	0.579654	+	0.814863i	$0.303188\pi$
$434$		0			0
$435$	14.0455	+	18.5494i	0.673430	+	0.889377i
$436$		0			0
$437$	1.63466	−	6.10062i	0.0781963	−	0.291832i
$438$		0			0
$439$			21.7452i			1.03784i	0.854822	+	0.518922i	$0.173667\pi$
$439$			21.7452i			1.03784i	−0.854822	+	0.518922i	$0.826333\pi$
$440$		0			0
$441$	−5.32832	+	18.9123i	−0.253730	+	0.900586i
$442$		0			0
$443$	1.49013	+	0.860330i	0.0707984	+	0.0408755i	0.534981	−	0.844864i	$-0.320319\pi$
$443$	1.49013	+	0.860330i	0.0707984	+	0.0408755i	−0.464183	+	0.885739i	$0.653652\pi$
$444$		0			0
$445$	−12.7238	+	22.0383i	−0.603166	+	1.04471i
$446$		0			0
$447$	2.71612	+	21.7053i	0.128468	+	1.02662i
$448$		0			0
$449$	7.08109	−	1.89737i	0.334177	−	0.0895425i	−0.0878286	−	0.996136i	$-0.527993\pi$
$449$	7.08109	−	1.89737i	0.334177	−	0.0895425i	0.422006	+	0.906593i	$0.361326\pi$
$450$		0			0
$451$	18.3843	−	31.8425i	0.865682	−	1.49941i
$452$		0			0
$453$	23.9298	+	10.0922i	1.12432	+	0.474174i
$454$		0			0
$455$	6.49134	−	3.45142i	0.304319	−	0.161805i
$456$		0			0
$457$	2.99233	+	2.99233i	0.139975	+	0.139975i	0.773622	−	0.633647i	$-0.218443\pi$
$457$	2.99233	+	2.99233i	0.139975	+	0.139975i	−0.633647	+	0.773622i	$0.718443\pi$
$458$		0			0
$459$	−30.2409	+	22.2940i	−1.41152	+	1.04059i
$460$		0			0
$461$	23.3999	+	6.26999i	1.08984	+	0.292023i	0.758623	−	0.651530i	$-0.225873\pi$
$461$	23.3999	+	6.26999i	1.08984	+	0.292023i	0.331221	+	0.943553i	$0.392539\pi$
$462$		0			0
$463$	6.77247	+	1.81468i	0.314744	+	0.0843353i	0.412733	−	0.910852i	$-0.364574\pi$
$463$	6.77247	+	1.81468i	0.314744	+	0.0843353i	−0.0979891	+	0.995187i	$0.531241\pi$
$464$		0			0
$465$	2.83526	+	6.97098i	0.131482	+	0.323272i
$466$		0			0
$467$	36.8585			1.70561			0.852804	−	0.522231i	$-0.174900\pi$
$467$	36.8585			1.70561			0.852804	+	0.522231i	$0.174900\pi$
$468$		0			0
$469$	4.57886			0.211432
$470$		0			0
$471$	−4.57119	−	0.631644i	−0.210629	−	0.0291046i
$472$		0			0
$473$	−42.8196	−	11.4735i	−1.96885	−	0.527550i
$474$		0			0
$475$	−17.6485	−	4.72890i	−0.809769	−	0.216977i
$476$		0			0
$477$	21.7130	−	5.52062i	0.994168	−	0.252772i
$478$		0			0
$479$	12.1081	+	12.1081i	0.553234	+	0.553234i	0.927373	−	0.374138i	$-0.122062\pi$
$479$	12.1081	+	12.1081i	0.553234	+	0.553234i	−0.374138	+	0.927373i	$0.622062\pi$
$480$		0			0
$481$	3.12228	−	2.91152i	0.142364	−	0.132754i
$482$		0			0
$483$	0.211041	+	1.68648i	0.00960268	+	0.0767376i
$484$		0			0
$485$	23.6921	−	41.0359i	1.07580	−	1.86334i
$486$		0			0
$487$	−11.2868	+	3.02430i	−0.511455	+	0.137044i	−0.505311	−	0.862937i	$-0.668622\pi$
$487$	−11.2868	+	3.02430i	−0.511455	+	0.137044i	−0.00614389	+	0.999981i	$0.501956\pi$
$488$		0			0
$489$	−7.47847	−	3.15400i	−0.338188	−	0.142629i
$490$		0			0
$491$	11.4891	−	19.8997i	0.518496	−	0.898062i	−0.481273	−	0.876571i	$-0.659825\pi$
$491$	11.4891	−	19.8997i	0.518496	−	0.898062i	0.999769	−	0.0214908i	$-0.00684124\pi$
$492$		0			0
$493$	−27.6876	−	15.9854i	−1.24699	−	0.719948i
$494$		0			0
$495$	30.5551	−	29.7816i	1.37335	−	1.33858i
$496$		0			0
$497$		−	6.02531i		−	0.270272i
$498$		0			0
$499$	3.31892	−	12.3864i	0.148575	−	0.554491i	−0.850995	−	0.525174i	$-0.824000\pi$
$499$	3.31892	−	12.3864i	0.148575	−	0.554491i	0.999570	−	0.0293168i	$-0.00933315\pi$
$500$		0			0
$501$	−10.4981	+	24.8922i	−0.469023	+	1.11210i
$502$		0			0
$503$	1.38363	+	0.798839i	0.0616930	+	0.0356184i	0.530529	−	0.847667i	$-0.321993\pi$
$503$	1.38363	+	0.798839i	0.0616930	+	0.0356184i	−0.468836	+	0.883285i	$0.655327\pi$
$504$		0			0
$505$	−28.6872	−	7.68671i	−1.27656	−	0.342054i
$506$		0			0
$507$	−22.0353	−	4.63087i	−0.978623	−	0.205664i
$508$		0			0
$509$	6.59314	+	24.6059i	0.292236	+	1.09064i	0.943388	+	0.331692i	$0.107619\pi$
$509$	6.59314	+	24.6059i	0.292236	+	1.09064i	−0.651152	+	0.758947i	$0.725714\pi$
$510$		0			0
$511$	6.88612	−	3.97570i	0.304624	−	0.175875i
$512$		0			0
$513$	22.1942	+	3.35729i	0.979899	+	0.148228i
$514$		0			0
$515$	−32.9767	+	8.83609i	−1.45313	+	0.389365i
$516$		0			0
$517$	−30.2347	−	17.4560i	−1.32972	−	0.767714i
$518$		0			0
$519$	−34.3337	−	4.74422i	−1.50708	−	0.208248i
$520$		0			0
$521$			24.5314i			1.07474i	0.843346	+	0.537370i	$0.180582\pi$
$521$			24.5314i			1.07474i	−0.843346	+	0.537370i	$0.819418\pi$
$522$		0			0
$523$	3.69447	+	6.39900i	0.161548	+	0.279809i	0.935424	−	0.353528i	$-0.115018\pi$
$523$	3.69447	+	6.39900i	0.161548	+	0.279809i	−0.773876	+	0.633337i	$0.781685\pi$
$524$		0			0
$525$	4.87883	−	0.610520i	0.212929	−	0.0266453i
$526$		0			0
$527$	−7.31196	−	7.31196i	−0.318514	−	0.318514i
$528$		0			0
$529$	10.4312	+	18.0674i	0.453531	+	0.785539i
$530$		0			0
$531$	−6.34267	+	10.6676i	−0.275248	+	0.462935i
$532$		0			0
$533$	−27.0802	−	8.27955i	−1.17298	−	0.358627i
$534$		0			0
$535$	49.7902	−	13.3412i	2.15262	−	0.576792i
$536$		0			0
$537$	−19.7146	−	2.72415i	−0.850748	−	0.117556i
$538$		0			0
$539$	7.93591	+	29.6172i	0.341824	+	1.27570i
$540$		0			0
$541$	−5.03374	+	5.03374i	−0.216418	+	0.216418i	−0.806987	−	0.590569i	$-0.798903\pi$
$541$	−5.03374	+	5.03374i	−0.216418	+	0.216418i	0.590569	+	0.806987i	$0.298903\pi$
$542$		0			0
$543$	35.7310	+	27.7831i	1.53337	+	1.19229i
$544$		0			0
$545$	−1.10484	−	1.91363i	−0.0473260	−	0.0819710i
$546$		0			0
$547$	9.69757	−	16.7967i	0.414638	−	0.718174i	−0.580752	−	0.814080i	$-0.697242\pi$
$547$	9.69757	−	16.7967i	0.414638	−	0.718174i	0.995390	+	0.0959061i	$0.0305748\pi$
$548$		0			0
$549$	12.0645	−	11.7591i	0.514901	−	0.501865i
$550$		0			0
$551$	4.94377	+	18.4504i	0.210612	+	0.786013i
$552$		0			0
$553$	5.98214	−	5.98214i	0.254386	−	0.254386i
$554$		0			0
$555$	5.77135	−	2.34734i	0.244980	−	0.0996391i
$556$		0			0
$557$	10.5583	−	39.4040i	0.447368	−	1.66960i	−0.262238	−	0.965003i	$-0.584460\pi$
$557$	10.5583	−	39.4040i	0.447368	−	1.66960i	0.709606	−	0.704598i	$-0.248873\pi$
$558$		0			0
$559$	−1.19184	+	34.1204i	−0.0504095	+	1.44314i
$560$		0			0
$561$	−22.7832	+	54.0215i	−0.961909	+	2.28079i
$562$		0			0
$563$	25.0022			1.05372			0.526858	−	0.849954i	$-0.323370\pi$
$563$	25.0022			1.05372			0.526858	+	0.849954i	$0.323370\pi$
$564$		0			0
$565$	7.73651	−	28.8731i	0.325478	−	1.21470i
$566$		0			0
$567$	−5.87290	+	1.41331i	−0.246639	+	0.0593534i
$568$		0			0
$569$	−10.6045			−0.444565			−0.222282	−	0.974982i	$-0.571351\pi$
$569$	−10.6045			−0.444565			−0.222282	+	0.974982i	$0.571351\pi$
$570$		0			0
$571$	−11.4489	+	6.61000i	−0.479120	+	0.276620i	−0.720050	−	0.693923i	$-0.755881\pi$
$571$	−11.4489	+	6.61000i	−0.479120	+	0.276620i	0.240930	+	0.970543i	$0.422548\pi$
$572$		0			0
$573$	−0.564023	+	4.08182i	−0.0235624	+	0.170520i
$574$		0			0
$575$	−5.35530	+	3.09189i	−0.223332	+	0.128941i
$576$		0			0
$577$	17.9959	+	17.9959i	0.749178	+	0.749178i	0.974325	−	0.225147i	$-0.0722861\pi$
$577$	17.9959	+	17.9959i	0.749178	+	0.749178i	−0.225147	+	0.974325i	$0.572286\pi$
$578$		0			0
$579$	−26.5024	−	11.1772i	−1.10140	−	0.464509i
$580$		0			0
$581$		−	2.98234i		−	0.123728i
$582$		0			0
$583$	24.7216	−	24.7216i	1.02386	−	1.02386i
$584$		0			0
$585$	−27.6421	−	17.7699i	−1.14286	−	0.734694i
$586$		0			0
$587$	15.1023	−	15.1023i	0.623338	−	0.623338i	−0.323045	−	0.946383i	$-0.604707\pi$
$587$	15.1023	−	15.1023i	0.623338	−	0.623338i	0.946383	+	0.323045i	$0.104707\pi$
$588$		0			0
$589$			6.17811i			0.254565i
$590$		0			0
$591$	−33.7470	+	25.5530i	−1.38817	+	1.05111i
$592$		0			0
$593$	−22.0256	−	22.0256i	−0.904484	−	0.904484i	0.0913365	−	0.995820i	$-0.470886\pi$
$593$	−22.0256	−	22.0256i	−0.904484	−	0.904484i	−0.995820	+	0.0913365i	$0.970886\pi$
$594$		0			0
$595$	−12.7679	+	7.37155i	−0.523433	+	0.302204i
$596$		0			0
$597$	−22.0107	+	8.95228i	−0.900840	+	0.366393i
$598$		0			0
$599$	14.0092	−	8.08823i	0.572401	−	0.330476i	−0.185707	−	0.982605i	$-0.559457\pi$
$599$	14.0092	−	8.08823i	0.572401	−	0.330476i	0.758108	+	0.652129i	$0.226124\pi$
$600$		0			0
$601$	−6.14761			−0.250766			−0.125383	−	0.992108i	$-0.540016\pi$
$601$	−6.14761			−0.250766			−0.125383	+	0.992108i	$0.540016\pi$
$602$		0			0
$603$	−10.0052	−	17.8542i	−0.407442	−	0.727080i
$604$		0			0
$605$	8.58402	−	32.0360i	0.348990	−	1.30245i
$606$		0			0
$607$	−0.0357598			−0.00145145			−0.000725723	−	1.00000i	$-0.500231\pi$
$607$	−0.0357598			−0.00145145			−0.000725723		1.00000i	$0.500231\pi$
$608$		0			0
$609$	−3.10300	−	4.09804i	−0.125740	−	0.166061i
$610$		0			0
$611$	−7.86148	+	25.7129i	−0.318042	+	1.04023i
$612$		0			0
$613$	−2.11344	+	7.88746i	−0.0853610	+	0.318572i	−0.995382	−	0.0959899i	$-0.969398\pi$
$613$	−2.11344	+	7.88746i	−0.0853610	+	0.318572i	0.910021	+	0.414561i	$0.136065\pi$
$614$		0			0
$615$	−32.6252	−	25.3681i	−1.31557	−	1.02294i
$616$		0			0
$617$	13.6052	−	13.6052i	0.547723	−	0.547723i	−0.378059	−	0.925782i	$-0.623408\pi$
$617$	13.6052	−	13.6052i	0.547723	−	0.547723i	0.925782	+	0.378059i	$0.123408\pi$
$618$		0			0
$619$	4.72181	+	17.6220i	0.189786	+	0.708290i	0.993555	+	0.113349i	$0.0361578\pi$
$619$	4.72181	+	17.6220i	0.189786	+	0.708290i	−0.803770	+	0.594941i	$0.797176\pi$
$620$		0			0
$621$	6.11492	−	4.50800i	0.245383	−	0.180900i
$622$		0			0
$623$	2.81101	−	4.86881i	0.112621	−	0.195065i
$624$		0			0
$625$	−14.1293	−	24.4727i	−0.565174	−	0.978909i
$626$		0			0
$627$	32.4474	−	13.1971i	1.29583	−	0.527042i
$628$		0			0
$629$	−6.05365	+	6.05365i	−0.241375	+	0.241375i
$630$		0			0
$631$	8.96498	+	33.4578i	0.356890	+	1.33193i	0.878089	+	0.478497i	$0.158818\pi$
$631$	8.96498	+	33.4578i	0.356890	+	1.33193i	−0.521199	+	0.853435i	$0.674515\pi$
$632$		0			0
$633$	−9.61356	−	23.6366i	−0.382105	−	0.939471i
$634$		0			0
$635$	−41.5373	+	11.1299i	−1.64836	+	0.441677i
$636$		0			0
$637$	20.8506	−	11.0862i	0.826131	−	0.439251i
$638$		0			0
$639$	−23.4944	+	13.1658i	−0.929422	+	0.520831i
$640$		0			0
$641$	−1.80368	−	3.12406i	−0.0712409	−	0.123393i	0.828205	−	0.560426i	$-0.189363\pi$
$641$	−1.80368	−	3.12406i	−0.0712409	−	0.123393i	−0.899445	+	0.437033i	$0.856029\pi$
$642$		0			0
$643$	−10.7220	−	10.7220i	−0.422834	−	0.422834i	0.463345	−	0.886178i	$-0.346649\pi$
$643$	−10.7220	−	10.7220i	−0.422834	−	0.422834i	−0.886178	+	0.463345i	$0.846649\pi$
$644$		0			0
$645$	−19.3624	+	45.9103i	−0.762393	+	1.80772i
$646$		0			0
$647$	23.1852	+	40.1580i	0.911505	+	1.57877i	0.811939	+	0.583743i	$0.198412\pi$
$647$	23.1852	+	40.1580i	0.911505	+	1.57877i	0.0995668	+	0.995031i	$0.468254\pi$
$648$		0			0
$649$			19.3673i			0.760232i
$650$		0			0
$651$	−0.626380	−	1.54006i	−0.0245498	−	0.0603599i
$652$		0			0
$653$	9.39828	+	5.42610i	0.367783	+	0.212340i	0.672490	−	0.740107i	$-0.265225\pi$
$653$	9.39828	+	5.42610i	0.367783	+	0.212340i	−0.304706	+	0.952446i	$0.598558\pi$
$654$		0			0
$655$	7.76049	−	2.07942i	0.303228	−	0.0812496i
$656$		0			0
$657$	−30.5491	−	18.1637i	−1.19183	−	0.708632i
$658$		0			0
$659$	−18.9112	+	10.9184i	−0.736674	+	0.425319i	−0.820859	−	0.571131i	$-0.806505\pi$
$659$	−18.9112	+	10.9184i	−0.736674	+	0.425319i	0.0841846	+	0.996450i	$0.473171\pi$
$660$		0			0
$661$	−2.47944	−	9.25341i	−0.0964392	−	0.359916i	0.900795	−	0.434245i	$-0.142985\pi$
$661$	−2.47944	−	9.25341i	−0.0964392	−	0.359916i	−0.997234	+	0.0743297i	$0.976318\pi$
$662$		0			0
$663$	44.4859	+	7.73830i	1.72769	+	0.300531i
$664$		0			0
$665$	8.50824	+	2.27978i	0.329935	+	0.0884059i
$666$		0			0
$667$	5.59863	+	3.23237i	0.216780	+	0.125158i
$668$		0			0
$669$	−45.4935	+	5.69290i	−1.75888	+	0.220100i
$670$		0			0
$671$	6.80446	−	25.3946i	0.262683	−	0.980348i
$672$		0			0
$673$			37.6574i			1.45159i	0.687913	+	0.725793i	$0.258527\pi$
$673$			37.6574i			1.45159i	−0.687913	+	0.725793i	$0.741473\pi$
$674$		0			0
$675$	−13.0412	−	17.6899i	−0.501956	−	0.680883i
$676$		0			0
$677$	−20.6548	−	11.9251i	−0.793829	−	0.458317i	0.0474798	−	0.998872i	$-0.484881\pi$
$677$	−20.6548	−	11.9251i	−0.793829	−	0.458317i	−0.841309	+	0.540555i	$0.818214\pi$
$678$		0			0
$679$	−5.23417	+	9.06585i	−0.200869	+	0.347915i
$680$		0			0
$681$	5.03465	−	3.81220i	0.192928	−	0.146084i
$682$		0			0
$683$	37.2984	−	9.99406i	1.42718	−	0.382412i	0.539156	−	0.842206i	$-0.318743\pi$
$683$	37.2984	−	9.99406i	1.42718	−	0.382412i	0.888026	+	0.459794i	$0.152077\pi$
$684$		0			0
$685$	−0.147362	+	0.255239i	−0.00563043	+	0.00975219i
$686$		0			0
$687$	17.0171	−	12.8852i	0.649242	−	0.491601i
$688$		0			0
$689$	−22.8344	−	14.2688i	−0.869922	−	0.543599i
$690$		0			0
$691$	26.6903	+	26.6903i	1.01535	+	1.01535i	0.999880	+	0.0154675i	$0.00492364\pi$
$691$	26.6903	+	26.6903i	1.01535	+	1.01535i	0.0154675	+	0.999880i	$0.495076\pi$
$692$		0			0
$693$	−6.75040	+	6.57949i	−0.256426	+	0.249934i
$694$		0			0
$695$	−35.4753	−	9.50557i	−1.34565	−	0.360567i
$696$		0			0
$697$	54.8521	+	14.6976i	2.07767	+	0.556710i
$698$		0			0
$699$	−1.56286	+	2.00995i	−0.0591129	+	0.0760234i
$700$		0			0
$701$	47.2060			1.78295			0.891473	−	0.453073i	$-0.149672\pi$
$701$	47.2060			1.78295			0.891473	+	0.453073i	$0.149672\pi$
$702$		0			0
$703$	5.11493			0.192913
$704$		0			0
$705$	−24.0872	+	30.9778i	−0.907175	+	1.16669i
$706$		0			0
$707$	6.33772	+	1.69819i	0.238354	+	0.0638669i
$708$		0			0
$709$	−28.2711	−	7.57523i	−1.06174	−	0.284494i	−0.314647	−	0.949209i	$-0.601886\pi$
$709$	−28.2711	−	7.57523i	−1.06174	−	0.284494i	−0.747097	+	0.664715i	$0.768553\pi$
$710$		0			0
$711$	−36.3975	−	10.2546i	−1.36501	−	0.384576i
$712$		0			0
$713$	1.47853	+	1.47853i	0.0553714	+	0.0553714i
$714$		0			0
$715$	−51.2493	−	1.79016i	−1.91661	−	0.0669482i
$716$		0			0
$717$	5.73482	−	4.34236i	0.214171	−	0.162169i
$718$		0			0
$719$	14.4340	−	25.0004i	0.538297	−	0.932357i	−0.460699	−	0.887556i	$-0.652401\pi$
$719$	14.4340	−	25.0004i	0.538297	−	0.932357i	0.998996	−	0.0448010i	$-0.0142654\pi$
$720$		0			0
$721$	7.28539	−	1.95211i	0.271322	−	0.0727005i
$722$		0			0
$723$	12.1003	−	9.16223i	0.450014	−	0.340747i
$724$		0			0
$725$	9.35093	−	16.1963i	0.347285	−	0.601515i
$726$		0			0
$727$	−33.1912	−	19.1629i	−1.23099	−	0.710714i	−0.263755	−	0.964590i	$-0.584961\pi$
$727$	−33.1912	−	19.1629i	−1.23099	−	0.710714i	−0.967237	+	0.253876i	$0.918294\pi$
$728$		0			0
$729$	18.3436	+	19.8119i	0.679394	+	0.733773i
$730$		0			0
$731$		−	68.4654i		−	2.53228i
$732$		0			0
$733$	10.4482	−	38.9931i	0.385911	−	1.44024i	−0.450814	−	0.892618i	$-0.648866\pi$
$733$	10.4482	−	38.9931i	0.385911	−	1.44024i	0.836725	−	0.547623i	$-0.184467\pi$
$734$		0			0
$735$	34.1969	−	4.27928i	1.26137	−	0.157844i
$736$		0			0
$737$	−27.6594	−	15.9692i	−1.01885	−	0.588232i
$738$		0			0
$739$	−6.38584	−	1.71108i	−0.234907	−	0.0629431i	0.139445	−	0.990230i	$-0.455468\pi$
$739$	−6.38584	−	1.71108i	−0.234907	−	0.0629431i	−0.374352	+	0.927287i	$0.622135\pi$
$740$		0			0
$741$	−15.5246	−	22.0630i	−0.570312	−	0.810504i
$742$		0			0
$743$	−4.40470	−	16.4386i	−0.161593	−	0.603072i	−0.998450	−	0.0556514i	$-0.982276\pi$
$743$	−4.40470	−	16.4386i	−0.161593	−	0.603072i	0.836858	−	0.547421i	$-0.184390\pi$
$744$		0			0
$745$	33.2276	−	19.1840i	1.21737	−	0.702847i
$746$		0			0
$747$	−11.6290	+	6.51665i	−0.425481	+	0.238432i
$748$		0			0
$749$	−10.9999	+	2.94742i	−0.401928	+	0.107696i
$750$		0			0
$751$	0.0835960	+	0.0482642i	0.00305046	+	0.00176119i	0.501524	−	0.865143i	$-0.332773\pi$
$751$	0.0835960	+	0.0482642i	0.00305046	+	0.00176119i	−0.498474	+	0.866905i	$0.666106\pi$
$752$		0			0
$753$	−10.6036	−	26.0709i	−0.386418	−	0.950075i
$754$		0			0
$755$		−	45.5529i		−	1.65784i
$756$		0			0
$757$	−14.1700	−	24.5432i	−0.515019	−	0.892039i	−0.999848	−	0.0174302i	$-0.994452\pi$
$757$	−14.1700	−	24.5432i	−0.515019	−	0.892039i	0.484829	−	0.874609i	$-0.338882\pi$
$758$		0			0
$759$	4.60693	−	10.9235i	0.167221	−	0.396499i
$760$		0			0
$761$	10.0002	+	10.0002i	0.362505	+	0.362505i	0.864735	−	0.502229i	$-0.167487\pi$
$761$	10.0002	+	10.0002i	0.362505	+	0.362505i	−0.502229	+	0.864735i	$0.667487\pi$
$762$		0			0
$763$	0.244086	+	0.422769i	0.00883651	+	0.0153053i
$764$		0			0
$765$	56.6426	+	33.6781i	2.04792	+	1.21764i
$766$		0			0
$767$	14.5336	−	3.35521i	0.524779	−	0.121149i
$768$		0			0
$769$	−4.48940	+	1.20293i	−0.161892	+	0.0433788i	−0.338855	−	0.940839i	$-0.610039\pi$
$769$	−4.48940	+	1.20293i	−0.161892	+	0.0433788i	0.176963	+	0.984218i	$0.443373\pi$
$770$		0			0
$771$	−1.06631	−	2.62172i	−0.0384023	−	0.0944189i
$772$		0			0
$773$	8.37392	+	31.2519i	0.301189	+	1.12405i	0.936177	+	0.351530i	$0.114338\pi$
$773$	8.37392	+	31.2519i	0.301189	+	1.12405i	−0.634988	+	0.772522i	$0.718995\pi$
$774$		0			0
$775$	4.27724	−	4.27724i	0.153643	−	0.153643i
$776$		0			0
$777$	−1.27504	+	0.518587i	−0.0457417	+	0.0186042i
$778$		0			0
$779$	−16.9639	−	29.3824i	−0.607796	−	1.05273i
$780$		0			0
$781$	−21.0138	+	36.3970i	−0.751934	+	1.30239i
$782$		0			0
$783$	−9.19907	+	21.0540i	−0.328748	+	0.752408i
$784$		0			0
$785$	2.09489	+	7.81825i	0.0747700	+	0.279045i
$786$		0			0
$787$	−15.9398	+	15.9398i	−0.568194	+	0.568194i	−0.931622	−	0.363428i	$-0.881606\pi$
$787$	−15.9398	+	15.9398i	−0.568194	+	0.568194i	0.363428	+	0.931622i	$0.381606\pi$
$788$		0			0
$789$	20.3776	+	15.8449i	0.725462	+	0.564092i
$790$		0			0
$791$	−1.70919	+	6.37878i	−0.0607718	+	0.226803i
$792$		0			0
$793$	−20.2355	−	0.706835i	−0.718583	−	0.0251004i
$794$		0			0
$795$	−23.7217	−	31.3285i	−0.841322	−	1.11111i
$796$		0			0
$797$	7.91200			0.280257			0.140129	−	0.990133i	$-0.455248\pi$
$797$	7.91200			0.280257			0.140129	+	0.990133i	$0.455248\pi$
$798$		0			0
$799$	13.9554	−	52.0824i	0.493708	−	1.84254i
$800$		0			0
$801$	−25.1271	−	0.322157i	−0.887822	−	0.0113829i
$802$		0			0
$803$	−55.4625			−1.95723
$804$		0			0
$805$	2.58176	−	1.49058i	0.0909951	−	0.0525360i
$806$		0			0
$807$	5.47788	−	2.22798i	0.192830	−	0.0784286i
$808$		0			0
$809$	18.5652	−	10.7186i	0.652716	−	0.376846i	−0.136780	−	0.990601i	$-0.543675\pi$
$809$	18.5652	−	10.7186i	0.652716	−	0.376846i	0.789496	+	0.613756i	$0.210342\pi$
$810$		0			0
$811$	22.3538	+	22.3538i	0.784949	+	0.784949i	0.980661	−	0.195712i	$-0.0627019\pi$
$811$	22.3538	+	22.3538i	0.784949	+	0.784949i	−0.195712	+	0.980661i	$0.562702\pi$
$812$		0			0
$813$	−12.6349	+	9.56706i	−0.443126	+	0.335532i
$814$		0			0
$815$			14.2361i			0.498668i
$816$		0			0
$817$	−28.9243	+	28.9243i	−1.01193	+	1.01193i
$818$		0			0
$819$	6.10684	+	3.92581i	0.213390	+	0.137179i
$820$		0			0
$821$	−25.1202	+	25.1202i	−0.876702	+	0.876702i	−0.993192	−	0.116490i	$-0.962836\pi$
$821$	−25.1202	+	25.1202i	−0.876702	+	0.876702i	0.116490	+	0.993192i	$0.462836\pi$
$822$		0			0
$823$			33.6922i			1.17444i	0.809429	+	0.587218i	$0.199777\pi$
$823$			33.6922i			1.17444i	−0.809429	+	0.587218i	$0.800223\pi$
$824$		0			0
$825$	−31.6007	−	13.3274i	−1.10020	−	0.464000i
$826$		0			0
$827$	−3.95015	−	3.95015i	−0.137360	−	0.137360i	0.635083	−	0.772444i	$-0.280966\pi$
$827$	−3.95015	−	3.95015i	−0.137360	−	0.137360i	−0.772444	+	0.635083i	$0.780966\pi$
$828$		0			0
$829$	24.2862	−	14.0217i	0.843495	−	0.486992i	−0.0149557	−	0.999888i	$-0.504761\pi$
$829$	24.2862	−	14.0217i	0.843495	−	0.486992i	0.858451	+	0.512896i	$0.171427\pi$
$830$		0			0
$831$	−2.04332	+	14.7874i	−0.0708819	+	0.512970i
$832$		0			0
$833$	−41.0113	+	23.6779i	−1.42096	+	0.820391i
$834$		0			0
$835$	47.3851			1.63983
$836$		0			0
$837$	−4.63645	+	5.80760i	−0.160259	+	0.200740i
$838$		0			0
$839$	9.23741	−	34.4745i	0.318911	−	1.19019i	−0.601382	−	0.798962i	$-0.705383\pi$
$839$	9.23741	−	34.4745i	0.318911	−	1.19019i	0.920293	−	0.391230i	$-0.127950\pi$
$840$		0			0
$841$	9.44839			0.325807
$842$		0			0
$843$	0.141198	−	0.334796i	0.00486311	−	0.0115310i
$844$		0			0
$845$	7.53510	+	38.7687i	0.259215	+	1.33369i
$846$		0			0
$847$	−1.89643	+	7.07756i	−0.0651620	+	0.243188i
$848$		0			0
$849$	−36.9561	+	15.0309i	−1.26833	+	0.515860i
$850$		0			0
$851$	1.22409	−	1.22409i	0.0419613	−	0.0419613i
$852$		0			0
$853$	−5.74656	−	21.4464i	−0.196758	−	0.734312i	−0.991805	−	0.127763i	$-0.959220\pi$
$853$	−5.74656	−	21.4464i	−0.196758	−	0.734312i	0.795046	−	0.606549i	$-0.207447\pi$
$854$		0			0
$855$	−9.70171	−	38.1575i	−0.331792	−	1.30496i
$856$		0			0
$857$	9.54760	−	16.5369i	0.326140	−	0.564891i	−0.655603	−	0.755106i	$-0.727585\pi$
$857$	9.54760	−	16.5369i	0.326140	−	0.564891i	0.981742	+	0.190215i	$0.0609186\pi$
$858$		0			0
$859$	−27.1199	−	46.9730i	−0.925319	−	1.60270i	−0.791047	−	0.611755i	$-0.790464\pi$
$859$	−27.1199	−	46.9730i	−0.925319	−	1.60270i	−0.134272	−	0.990945i	$-0.542870\pi$
$860$		0			0
$861$	7.20772	+	5.60445i	0.245638	+	0.190999i
$862$		0			0
$863$	10.0822	−	10.0822i	0.343201	−	0.343201i	−0.514368	−	0.857569i	$-0.671974\pi$
$863$	10.0822	−	10.0822i	0.343201	−	0.343201i	0.857569	+	0.514368i	$0.171974\pi$
$864$		0			0
$865$	15.7345	+	58.7221i	0.534990	+	1.99661i
$866$		0			0
$867$	−60.5298	−	8.36397i	−2.05570	−	0.284055i
$868$		0			0
$869$	−56.9995	+	15.2730i	−1.93357	+	0.518100i
$870$		0			0
$871$	−7.19188	+	23.5228i	−0.243688	+	0.797039i
$872$		0			0
$873$	46.7873	+	0.599866i	1.58351	+	0.0203024i
$874$		0			0
$875$	0.785494	+	1.36052i	0.0265546	+	0.0459938i
$876$		0			0
$877$	2.48569	+	2.48569i	0.0839358	+	0.0839358i	0.747828	−	0.663892i	$-0.231097\pi$
$877$	2.48569	+	2.48569i	0.0839358	+	0.0839358i	−0.663892	+	0.747828i	$0.731097\pi$
$878$		0			0
$879$	44.3066	−	5.54438i	1.49443	−	0.187007i
$880$		0			0
$881$	−14.0958	−	24.4146i	−0.474899	−	0.822549i	0.524688	−	0.851295i	$-0.324182\pi$
$881$	−14.0958	−	24.4146i	−0.474899	−	0.822549i	−0.999587	+	0.0287456i	$0.990849\pi$
$882$		0			0
$883$		−	8.66822i		−	0.291709i	−0.989306	−	0.145854i	$-0.953407\pi$
$883$		−	8.66822i		−	0.291709i	0.989306	−	0.145854i	$-0.0465931\pi$
$884$		0			0
$885$	21.5636	+	2.97965i	0.724853	+	0.100160i
$886$		0			0
$887$	−8.68587	−	5.01479i	−0.291643	−	0.168380i	0.347040	−	0.937851i	$-0.387187\pi$
$887$	−8.68587	−	5.01479i	−0.291643	−	0.168380i	−0.638683	+	0.769470i	$0.720520\pi$
$888$		0			0
$889$	9.17664	−	2.45887i	0.307775	−	0.0824680i
$890$		0			0
$891$	40.4054	+	11.9449i	1.35363	+	0.400171i
$892$		0			0
$893$	−27.8988	+	16.1074i	−0.933597	+	0.539012i
$894$		0			0
$895$	9.03485	+	33.7185i	0.302002	+	1.12709i
$896$		0			0
$897$	−8.99537	−	1.56474i	−0.300347	−	0.0522451i
$898$		0			0
$899$	−6.10830	−	1.63671i	−0.203723	−	0.0545875i
$900$		0			0
$901$	46.7621	+	26.9981i	1.55787	+	0.899438i
$902$		0			0
$903$	4.27763	−	10.1427i	0.142351	−	0.337529i
$904$		0			0
$905$	20.5473	−	76.6836i	0.683016	−	2.54905i
$906$		0			0
$907$			26.8808i			0.892564i	0.894892	+	0.446282i	$0.147252\pi$
$907$			26.8808i			0.892564i	−0.894892	+	0.446282i	$0.852748\pi$
$908$		0			0
$909$	−7.22673	−	28.4232i	−0.239695	−	0.942738i
$910$		0			0
$911$	37.9403	+	21.9048i	1.25702	+	0.725740i	0.972494	−	0.232929i	$-0.0748309\pi$
$911$	37.9403	+	21.9048i	1.25702	+	0.725740i	0.284525	+	0.958669i	$0.408164\pi$
$912$		0			0
$913$	−10.4012	+	18.0154i	−0.344229	+	0.596222i
$914$		0			0
$915$	−27.2276	−	11.4831i	−0.900117	−	0.379619i
$916$		0			0
$917$	−1.71449	+	0.459395i	−0.0566174	+	0.0151706i
$918$		0			0
$919$	−0.847859	+	1.46853i	−0.0279683	+	0.0484425i	−0.879671	−	0.475583i	$-0.842237\pi$
$919$	−0.847859	+	1.46853i	−0.0279683	+	0.0484425i	0.851702	+	0.524026i	$0.175570\pi$
$920$		0			0
$921$	−7.02921	−	56.1723i	−0.231620	−	1.85094i
$922$		0			0
$923$	30.9536	+	9.46379i	1.01885	+	0.311504i
$924$		0			0
$925$	−3.54117	−	3.54117i	−0.116433	−	0.116433i
$926$		0			0
$927$	−23.5310	−	24.1422i	−0.772859	−	0.792935i
$928$		0			0
$929$	49.3522	+	13.2239i	1.61919	+	0.433861i	0.950764	−	0.309916i	$-0.100301\pi$
$929$	49.3522	+	13.2239i	1.61919	+	0.433861i	0.668428	+	0.743777i	$0.266968\pi$
$930$		0			0
$931$	27.3290	+	7.32279i	0.895673	+	0.239995i
$932$		0			0
$933$	30.4643	+	4.20954i	0.997357	+	0.137814i
$934$		0			0
$935$	102.836			3.36309
$936$		0			0
$937$	−7.45635			−0.243588			−0.121794	−	0.992555i	$-0.538865\pi$
$937$	−7.45635			−0.243588			−0.121794	+	0.992555i	$0.538865\pi$
$938$		0			0
$939$	6.39446	+	15.7219i	0.208675	+	0.513065i
$940$		0			0
$941$	−26.5673	−	7.11870i	−0.866070	−	0.232063i	−0.201683	−	0.979451i	$-0.564641\pi$
$941$	−26.5673	−	7.11870i	−0.866070	−	0.232063i	−0.664388	+	0.747388i	$0.731308\pi$
$942$		0			0
$943$	−11.0915	−	2.97195i	−0.361188	−	0.0967801i
$944$		0			0
$945$	6.28709	+	8.52817i	0.204519	+	0.277421i
$946$		0			0
$947$	−18.2887	−	18.2887i	−0.594304	−	0.594304i	0.344487	−	0.938791i	$-0.388053\pi$
$947$	−18.2887	−	18.2887i	−0.594304	−	0.594304i	−0.938791	+	0.344487i	$0.888053\pi$
$948$		0			0
$949$	9.60838	+	41.6203i	0.311901	+	1.35105i
$950$		0			0
$951$	16.7351	+	7.05794i	0.542674	+	0.228869i
$952$		0			0
$953$	−23.8503	+	41.3099i	−0.772586	+	1.33816i	0.163555	+	0.986534i	$0.447704\pi$
$953$	−23.8503	+	41.3099i	−0.772586	+	1.33816i	−0.936141	+	0.351624i	$0.885629\pi$
$954$		0			0
$955$	6.98126	−	1.87062i	0.225908	−	0.0605319i
$956$		0			0
$957$	4.45198	+	35.5770i	0.143912	+	1.15004i
$958$		0			0
$959$	0.0325560	−	0.0563887i	0.00105129	−	0.00182089i
$960$		0			0
$961$	25.0755	+	14.4773i	0.808886	+	0.467010i
$962$		0			0
$963$	35.5285	+	36.4513i	1.14489	+	1.17463i
$964$		0			0
$965$			50.4502i			1.62405i
$966$		0			0
$967$	14.2436	−	53.1577i	0.458042	−	1.70944i	−0.220944	−	0.975286i	$-0.570914\pi$
$967$	14.2436	−	53.1577i	0.458042	−	1.70944i	0.678986	−	0.734151i	$-0.262419\pi$
$968$		0			0
$969$	32.6580	+	43.1304i	1.04913	+	1.38555i
$970$		0			0
$971$	22.0094	+	12.7071i	0.706316	+	0.407792i	0.809696	−	0.586850i	$-0.199632\pi$
$971$	22.0094	+	12.7071i	0.706316	+	0.407792i	−0.103379	+	0.994642i	$0.532966\pi$
$972$		0			0
$973$	7.83738	+	2.10002i	0.251255	+	0.0673235i
$974$		0			0
$975$	−4.52664	+	26.0227i	−0.144968	+	0.833394i
$976$		0			0
$977$	−11.3845	−	42.4875i	−0.364222	−	1.35930i	−0.868472	−	0.495738i	$-0.834898\pi$
$977$	−11.3845	−	42.4875i	−0.364222	−	1.35930i	0.504250	−	0.863558i	$-0.331769\pi$
$978$		0			0
$979$	−33.9608	+	19.6073i	−1.08539	+	0.626652i
$980$		0			0
$981$	1.11515	−	1.87554i	0.0356039	−	0.0598815i
$982$		0			0
$983$	−44.4766	+	11.9175i	−1.41858	+	0.380108i	−0.884981	−	0.465627i	$-0.845829\pi$
$983$	−44.4766	+	11.9175i	−1.41858	+	0.380108i	−0.533603	+	0.845735i	$0.679162\pi$
$984$		0			0
$985$	64.2994	+	37.1233i	2.04875	+	1.18285i
$986$		0			0
$987$	5.32146	−	6.84378i	0.169384	−	0.217840i
$988$		0			0
$989$			13.8442i			0.440219i
$990$		0			0
$991$	−16.6829	−	28.8957i	−0.529951	−	0.917901i	−0.999390	−	0.0349364i	$-0.988877\pi$
$991$	−16.6829	−	28.8957i	−0.529951	−	0.917901i	0.469439	−	0.882965i	$-0.344456\pi$
$992$		0			0
$993$	16.2611	+	21.4756i	0.516031	+	0.681506i
$994$		0			0
$995$	29.4708	+	29.4708i	0.934286	+	0.934286i
$996$		0			0
$997$	−8.75444	−	15.1631i	−0.277256	−	0.480222i	0.693446	−	0.720509i	$-0.256092\pi$
$997$	−8.75444	−	15.1631i	−0.277256	−	0.480222i	−0.970702	+	0.240287i	$0.922758\pi$
$998$		0			0
$999$	4.80817	+	3.83856i	0.152124	+	0.121447i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	468.2.bw.a.245.11	yes	56
3.2	odd	2		1404.2.bz.a.89.13		56
9.4	even	3		1404.2.cc.a.557.13		56
9.5	odd	6		468.2.bz.a.401.1	yes	56
13.6	odd	12		468.2.bz.a.461.1	yes	56
39.32	even	12		1404.2.cc.a.305.13		56
117.32	even	12	inner	468.2.bw.a.149.11	✓	56
117.58	odd	12		1404.2.bz.a.773.13		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
468.2.bw.a.149.11	✓	56	117.32	even	12	inner
468.2.bw.a.245.11	yes	56	1.1	even	1	trivial
468.2.bz.a.401.1	yes	56	9.5	odd	6
468.2.bz.a.461.1	yes	56	13.6	odd	12
1404.2.bz.a.89.13		56	3.2	odd	2
1404.2.bz.a.773.13		56	117.58	odd	12
1404.2.cc.a.305.13		56	39.32	even	12
1404.2.cc.a.557.13		56	9.4	even	3

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:	\( N \)	\(=\)	\( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	468.bw (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.06319 - 1.36734i) q^{3} +(-2.93450 - 0.786297i) q^{5} +(0.648304 + 0.173713i) q^{7} +(-0.739244 - 2.90749i) q^{9} +(-3.31036 - 3.31036i) q^{11} +(-1.91068 + 3.05766i) q^{13} +(-4.19507 + 3.17648i) q^{15} +(3.61521 - 6.26173i) q^{17} +(-4.17267 + 1.11806i) q^{19} +(0.926797 - 0.701763i) q^{21} +(-0.731021 + 1.26617i) q^{23} +(3.66289 + 2.11477i) q^{25} +(-4.76149 - 2.08043i) q^{27} -4.42172i q^{29} +(0.370153 - 1.38143i) q^{31} +(-8.04595 + 1.00684i) q^{33} +(-1.76586 - 1.01952i) q^{35} +(-1.14370 - 0.306454i) q^{37} +(2.14945 + 5.86344i) q^{39} +(2.03274 + 7.58629i) q^{41} +(8.20046 - 4.73454i) q^{43} +(-0.116843 + 9.11330i) q^{45} +(7.20323 - 1.93010i) q^{47} +(-5.67206 - 3.27476i) q^{49} +(-4.71825 - 11.6006i) q^{51} +7.46793i q^{53} +(7.11133 + 12.3172i) q^{55} +(-2.90758 + 6.89419i) q^{57} +(-2.92525 - 2.92525i) q^{59} +(2.80787 + 4.86337i) q^{61} +(0.0258135 - 2.01336i) q^{63} +(8.01112 - 7.47034i) q^{65} +(6.58970 - 1.76570i) q^{67} +(0.954064 + 2.34573i) q^{69} +(-2.32349 - 8.67138i) q^{71} +(8.37710 - 8.37710i) q^{73} +(6.78597 - 2.76001i) q^{75} +(-1.57107 - 2.72118i) q^{77} +(6.30240 - 10.9161i) q^{79} +(-7.90704 + 4.29869i) q^{81} +(-1.15005 - 4.29206i) q^{83} +(-15.5324 + 15.5324i) q^{85} +(-6.04600 - 4.70114i) q^{87} +(2.16797 - 8.09097i) q^{89} +(-1.76986 + 1.65039i) q^{91} +(-1.49534 - 1.97485i) q^{93} +13.1238 q^{95} +(-4.03682 + 15.0656i) q^{97} +(-7.17770 + 12.0720i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{7} + 4 q^{19} - 24 q^{21} + 8 q^{31} + 12 q^{33} - 66 q^{35} + 2 q^{37} + 24 q^{41} + 12 q^{43} - 30 q^{47} + 30 q^{57} + 84 q^{63} + 6 q^{65} + 28 q^{67} - 36 q^{69} + 24 q^{71} - 14 q^{73}+ \cdots - 42 q^{99}+O(q^{100}) \) 56 * q - 2 * q^7 + 4 * q^19 - 24 * q^21 + 8 * q^31 + 12 * q^33 - 66 * q^35 + 2 * q^37 + 24 * q^41 + 12 * q^43 - 30 * q^47 + 30 * q^57 + 84 * q^63 + 6 * q^65 + 28 * q^67 - 36 * q^69 + 24 * q^71 - 14 * q^73 - 24 * q^77 + 12 * q^79 - 12 * q^81 - 60 * q^83 + 36 * q^85 + 4 * q^91 - 54 * q^93 + 26 * q^97 - 42 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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