LMFDB - Embedded newform 468.2.bl.b.337.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [468,2,Mod(25,468)] 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("468.25"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(468, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 468 = 2^{2} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	468.bl (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.73699881460$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			337.11
Character	$\chi$	$=$	468.337
Dual form			468.2.bl.b.25.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.61974 - 0.613557i) q^{3} +(-2.41165 - 1.39237i) q^{5} +(1.00812 - 0.582041i) q^{7} +(2.24710 - 1.98760i) q^{9} +(-0.716675 + 0.413773i) q^{11} +(3.28700 - 1.48177i) q^{13} +(-4.76054 - 0.775584i) q^{15} +0.0570022 q^{17} -8.44213i q^{19} +(1.27578 - 1.56130i) q^{21} +(-1.18075 + 2.04511i) q^{23} +(1.37737 + 2.38568i) q^{25} +(2.42020 - 4.59811i) q^{27} +(-2.67021 - 4.62494i) q^{29} +(-0.351625 - 0.203011i) q^{31} +(-0.906952 + 1.10992i) q^{33} -3.24166 q^{35} +5.42478i q^{37} +(4.41492 - 4.41684i) q^{39} +(7.53743 + 4.35174i) q^{41} +(5.13879 + 8.90065i) q^{43} +(-8.18668 + 1.66462i) q^{45} +(-7.56840 + 4.36962i) q^{47} +(-2.82246 + 4.88864i) q^{49} +(0.0923285 - 0.0349741i) q^{51} -2.12542 q^{53} +2.30449 q^{55} +(-5.17973 - 13.6740i) q^{57} +(9.68012 + 5.58882i) q^{59} +(-0.225124 - 0.389927i) q^{61} +(1.10849 - 3.31165i) q^{63} +(-9.99026 - 1.00319i) q^{65} +(8.02892 + 4.63550i) q^{67} +(-0.657706 + 4.03700i) q^{69} +6.15280i q^{71} -8.45487i q^{73} +(3.69473 + 3.01907i) q^{75} +(-0.481665 + 0.834269i) q^{77} +(4.40104 + 7.62283i) q^{79} +(1.09888 - 8.93266i) q^{81} +(9.12486 - 5.26824i) q^{83} +(-0.137469 - 0.0793679i) q^{85} +(-7.16270 - 5.85286i) q^{87} -5.24698i q^{89} +(2.45125 - 3.40698i) q^{91} +(-0.694098 - 0.113082i) q^{93} +(-11.7545 + 20.3595i) q^{95} +(0.0761512 - 0.0439659i) q^{97} +(-0.788023 + 2.35425i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{3} + 2 q^{9} + 5 q^{13} - 4 q^{17} - 22 q^{23} + 16 q^{25} - 18 q^{27} + 22 q^{29} + 8 q^{35} + 37 q^{39} - 2 q^{43} + 22 q^{49} - 38 q^{51} - 12 q^{53} + 48 q^{55} + 8 q^{61} - q^{65} - 26 q^{69}+ \cdots - 48 q^{95}+O(q^{100}) $ 24 * q - 6 * q^3 + 2 * q^9 + 5 * q^13 - 4 * q^17 - 22 * q^23 + 16 * q^25 - 18 * q^27 + 22 * q^29 + 8 * q^35 + 37 * q^39 - 2 * q^43 + 22 * q^49 - 38 * q^51 - 12 * q^53 + 48 * q^55 + 8 * q^61 - q^65 - 26 * q^69 - 64 * q^75 - 24 * q^77 - 8 * q^79 + 2 * q^81 - 40 * q^87 + 22 * q^91 - 48 * q^95

Character values

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

$n$	$145$	$209$	$235$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	1.61974	−	0.613557i	0.935156	−	0.354237i
$3$	1.61974	−	0.613557i	0.935156	−	0.354237i
$4$		0			0
$5$	−2.41165	−	1.39237i	−1.07852	−	0.622685i	−0.148025	−	0.988984i	$-0.547292\pi$
$5$	−2.41165	−	1.39237i	−1.07852	−	0.622685i	−0.930498	+	0.366298i	$0.880625\pi$
$6$		0			0
$7$	1.00812	−	0.582041i	0.381035	−	0.219991i	−0.297233	−	0.954805i	$-0.596064\pi$
$7$	1.00812	−	0.582041i	0.381035	−	0.219991i	0.678269	+	0.734814i	$0.262731\pi$
$8$		0			0
$9$	2.24710	−	1.98760i	0.749032	−	0.662534i
$10$		0			0
$11$	−0.716675	+	0.413773i	−0.216086	+	0.124757i	−0.604136	−	0.796881i	$-0.706482\pi$
$11$	−0.716675	+	0.413773i	−0.216086	+	0.124757i	0.388051	+	0.921638i	$0.373148\pi$
$12$		0			0
$13$	3.28700	−	1.48177i	0.911649	−	0.410970i
$13$	3.28700	−	1.48177i	0.911649	−	0.410970i
$14$		0			0
$15$	−4.76054	−	0.775584i	−1.22916	−	0.200255i
$16$		0			0
$17$	0.0570022			0.0138251			0.00691253	−	0.999976i	$-0.497800\pi$
$17$	0.0570022			0.0138251			0.00691253	+	0.999976i	$0.497800\pi$
$18$		0			0
$19$		−	8.44213i		−	1.93676i	−0.249484	−	0.968379i	$-0.580261\pi$
$19$		−	8.44213i		−	1.93676i	0.249484	−	0.968379i	$-0.419739\pi$
$20$		0			0
$21$	1.27578	−	1.56130i	0.278398	−	0.340703i
$22$		0			0
$23$	−1.18075	+	2.04511i	−0.246203	+	0.426436i	−0.962469	−	0.271391i	$-0.912516\pi$
$23$	−1.18075	+	2.04511i	−0.246203	+	0.426436i	0.716266	+	0.697827i	$0.245850\pi$
$24$		0			0
$25$	1.37737	+	2.38568i	0.275474	+	0.477135i
$26$		0			0
$27$	2.42020	−	4.59811i	0.465767	−	0.884907i
$28$		0			0
$29$	−2.67021	−	4.62494i	−0.495846	−	0.858830i	0.504143	−	0.863620i	$-0.331808\pi$
$29$	−2.67021	−	4.62494i	−0.495846	−	0.858830i	−0.999989	+	0.00479056i	$0.998475\pi$
$30$		0			0
$31$	−0.351625	−	0.203011i	−0.0631536	−	0.0364618i	0.468091	−	0.883680i	$-0.344942\pi$
$31$	−0.351625	−	0.203011i	−0.0631536	−	0.0364618i	−0.531244	+	0.847219i	$0.678275\pi$
$32$		0			0
$33$	−0.906952	+	1.10992i	−0.157880	+	0.193213i
$34$		0			0
$35$	−3.24166			−0.547940
$36$		0			0
$37$			5.42478i			0.891829i	0.895076	+	0.445915i	$0.147121\pi$
$37$			5.42478i			0.891829i	−0.895076	+	0.445915i	$0.852879\pi$
$38$		0			0
$39$	4.41492	−	4.41684i	0.706953	−	0.707261i
$40$		0			0
$41$	7.53743	+	4.35174i	1.17715	+	0.679627i	0.955353	−	0.295466i	$-0.0954750\pi$
$41$	7.53743	+	4.35174i	1.17715	+	0.679627i	0.221795	+	0.975093i	$0.428808\pi$
$42$		0			0
$43$	5.13879	+	8.90065i	0.783659	+	1.35734i	0.929797	+	0.368072i	$0.119982\pi$
$43$	5.13879	+	8.90065i	0.783659	+	1.35734i	−0.146139	+	0.989264i	$0.546685\pi$
$44$		0			0
$45$	−8.18668	+	1.66462i	−1.22040	+	0.248146i
$46$		0			0
$47$	−7.56840	+	4.36962i	−1.10396	+	0.637374i	−0.937259	−	0.348633i	$-0.886646\pi$
$47$	−7.56840	+	4.36962i	−1.10396	+	0.637374i	−0.166705	+	0.986007i	$0.553313\pi$
$48$		0			0
$49$	−2.82246	+	4.88864i	−0.403208	+	0.698377i
$50$		0			0
$51$	0.0923285	−	0.0349741i	0.0129286	−	0.00489735i
$52$		0			0
$53$	−2.12542			−0.291949			−0.145975	−	0.989288i	$-0.546632\pi$
$53$	−2.12542			−0.291949			−0.145975	+	0.989288i	$0.546632\pi$
$54$		0			0
$55$	2.30449			0.310738
$56$		0			0
$57$	−5.17973	−	13.6740i	−0.686072	−	1.81117i
$58$		0			0
$59$	9.68012	+	5.58882i	1.26024	+	0.727602i	0.973122	−	0.230292i	$-0.0739680\pi$
$59$	9.68012	+	5.58882i	1.26024	+	0.727602i	0.287122	+	0.957894i	$0.407301\pi$
$60$		0			0
$61$	−0.225124	−	0.389927i	−0.0288242	−	0.0499250i	0.851253	−	0.524755i	$-0.175843\pi$
$61$	−0.225124	−	0.389927i	−0.0288242	−	0.0499250i	−0.880078	+	0.474830i	$0.842510\pi$
$62$		0			0
$63$	1.10849	−	3.31165i	0.139656	−	0.417229i
$64$		0			0
$65$	−9.99026	−	1.00319i	−1.23914	−	0.124431i
$66$		0			0
$67$	8.02892	+	4.63550i	0.980889	+	0.566316i	0.902538	−	0.430610i	$-0.141701\pi$
$67$	8.02892	+	4.63550i	0.980889	+	0.566316i	0.0783503	+	0.996926i	$0.475035\pi$
$68$		0			0
$69$	−0.657706	+	4.03700i	−0.0791785	+	0.485998i
$70$		0			0
$71$			6.15280i			0.730203i	0.930968	+	0.365102i	$0.118966\pi$
$71$			6.15280i			0.730203i	−0.930968	+	0.365102i	$0.881034\pi$
$72$		0			0
$73$		−	8.45487i		−	0.989567i	−0.869016	−	0.494784i	$-0.835247\pi$
$73$		−	8.45487i		−	0.989567i	0.869016	−	0.494784i	$-0.164753\pi$
$74$		0			0
$75$	3.69473	+	3.01907i	0.426630	+	0.348612i
$76$		0			0
$77$	−0.481665	+	0.834269i	−0.0548909	+	0.0950738i
$78$		0			0
$79$	4.40104	+	7.62283i	0.495156	+	0.857635i	0.999984	−	0.00558427i	$-0.00177754\pi$
$79$	4.40104	+	7.62283i	0.495156	+	0.857635i	−0.504828	+	0.863220i	$0.668444\pi$
$80$		0			0
$81$	1.09888	−	8.93266i	0.122098	−	0.992518i
$82$		0			0
$83$	9.12486	−	5.26824i	1.00158	−	0.578264i	0.0928671	−	0.995679i	$-0.470397\pi$
$83$	9.12486	−	5.26824i	1.00158	−	0.578264i	0.908716	+	0.417414i	$0.137064\pi$
$84$		0			0
$85$	−0.137469	−	0.0793679i	−0.0149106	−	0.00860866i
$86$		0			0
$87$	−7.16270	−	5.85286i	−0.767922	−	0.627492i
$88$		0			0
$89$		−	5.24698i		−	0.556179i	−0.960555	−	0.278090i	$-0.910299\pi$
$89$		−	5.24698i		−	0.556179i	0.960555	−	0.278090i	$-0.0897012\pi$
$90$		0			0
$91$	2.45125	−	3.40698i	0.256961	−	0.357148i
$92$		0			0
$93$	−0.694098	−	0.113082i	−0.0719746	−	0.0117261i
$94$		0			0
$95$	−11.7545	+	20.3595i	−1.20599	+	2.08884i
$96$		0			0
$97$	0.0761512	−	0.0439659i	0.00773198	−	0.00446406i	−0.496129	−	0.868249i	$-0.665246\pi$
$97$	0.0761512	−	0.0439659i	0.00773198	−	0.00446406i	0.503861	+	0.863785i	$0.331912\pi$
$98$		0			0
$99$	−0.788023	+	2.35425i	−0.0791993	+	0.236611i
$100$		0			0
$101$	−7.39899	−	12.8154i	−0.736227	−	1.27518i	−0.954183	−	0.299225i	$-0.903272\pi$
$101$	−7.39899	−	12.8154i	−0.736227	−	1.27518i	0.217955	−	0.975959i	$-0.430061\pi$
$102$		0			0
$103$	−3.68863	+	6.38889i	−0.363452	+	0.629516i	−0.988526	−	0.151048i	$-0.951735\pi$
$103$	−3.68863	+	6.38889i	−0.363452	+	0.629516i	0.625075	+	0.780565i	$0.285068\pi$
$104$		0			0
$105$	−5.25064	+	1.98894i	−0.512410	+	0.194101i
$106$		0			0
$107$	2.04176			0.197384			0.0986921	−	0.995118i	$-0.468534\pi$
$107$	2.04176			0.197384			0.0986921	+	0.995118i	$0.468534\pi$
$108$		0			0
$109$			10.9783i			1.05153i	0.850631	+	0.525763i	$0.176220\pi$
$109$			10.9783i			1.05153i	−0.850631	+	0.525763i	$0.823780\pi$
$110$		0			0
$111$	3.32841	+	8.78672i	0.315919	+	0.833999i
$112$		0			0
$113$	0.921748	−	1.59651i	0.0867107	−	0.150187i	−0.819408	−	0.573210i	$-0.805698\pi$
$113$	0.921748	−	1.59651i	0.0867107	−	0.150187i	0.906119	+	0.423023i	$0.139031\pi$
$114$		0			0
$115$	5.69510	−	3.28807i	0.531071	−	0.306614i
$116$		0			0
$117$	4.44103	−	9.86292i	0.410573	−	0.911828i
$118$		0			0
$119$	0.0574653	−	0.0331776i	0.00526784	−	0.00304139i
$120$		0			0
$121$	−5.15758	+	8.93320i	−0.468871	+	0.812109i
$122$		0			0
$123$	14.8787	+	2.42403i	1.34157	+	0.218567i
$124$		0			0
$125$			6.25245i			0.559236i
$126$		0			0
$127$	−4.86492			−0.431692			−0.215846	−	0.976427i	$-0.569251\pi$
$127$	−4.86492			−0.431692			−0.215846	+	0.976427i	$0.569251\pi$
$128$		0			0
$129$	13.7845	+	11.2638i	1.21366	+	0.991720i
$130$		0			0
$131$	−9.48259	+	16.4243i	−0.828497	+	1.43500i	0.0707195	+	0.997496i	$0.477470\pi$
$131$	−9.48259	+	16.4243i	−0.828497	+	1.43500i	−0.899217	+	0.437503i	$0.855863\pi$
$132$		0			0
$133$	−4.91367	−	8.51072i	−0.426069	−	0.737973i
$134$		0			0
$135$	−12.2389	+	7.71924i	−1.05336	+	0.664366i
$136$		0			0
$137$	−11.2785	+	6.51163i	−0.963585	+	0.556326i	−0.897275	−	0.441473i	$-0.854456\pi$
$137$	−11.2785	+	6.51163i	−0.963585	+	0.556326i	−0.0663107	+	0.997799i	$0.521123\pi$
$138$		0			0
$139$	3.17067	−	5.49176i	0.268932	−	0.465805i	−0.699654	−	0.714482i	$-0.746663\pi$
$139$	3.17067	−	5.49176i	0.268932	−	0.465805i	0.968586	+	0.248677i	$0.0799958\pi$
$140$		0			0
$141$	−9.57780	+	11.7213i	−0.806597	+	0.987109i
$142$		0			0
$143$	−1.74259	+	2.42202i	−0.145723	+	0.202539i
$144$		0			0
$145$			14.8716i			1.23502i
$146$		0			0
$147$	−1.57218	+	9.65004i	−0.129671	+	0.795922i
$148$		0			0
$149$	−12.8659	−	7.42814i	−1.05402	−	0.608537i	−0.130245	−	0.991482i	$-0.541576\pi$
$149$	−12.8659	−	7.42814i	−1.05402	−	0.608537i	−0.923771	+	0.382945i	$0.874910\pi$
$150$		0			0
$151$	9.47215	−	5.46875i	0.770833	−	0.445041i	−0.0623387	−	0.998055i	$-0.519856\pi$
$151$	9.47215	−	5.46875i	0.770833	−	0.445041i	0.833172	+	0.553014i	$0.186523\pi$
$152$		0			0
$153$	0.128089	−	0.113298i	0.0103554	−	0.00915957i
$154$		0			0
$155$	0.565330	+	0.979181i	0.0454084	+	0.0786497i
$156$		0			0
$157$	1.54287	−	2.67234i	0.123135	−	0.213276i	−0.797868	−	0.602833i	$-0.794039\pi$
$157$	1.54287	−	2.67234i	0.123135	−	0.213276i	0.921002	+	0.389557i	$0.127372\pi$
$158$		0			0
$159$	−3.44263	+	1.30407i	−0.273018	+	0.103419i
$160$		0			0
$161$			2.74897i			0.216650i
$162$		0			0
$163$		−	7.89895i		−	0.618694i	−0.950949	−	0.309347i	$-0.899890\pi$
$163$		−	7.89895i		−	0.618694i	0.950949	−	0.309347i	$-0.100110\pi$
$164$		0			0
$165$	3.73267	−	1.41394i	0.290588	−	0.110075i
$166$		0			0
$167$	12.5292	+	7.23372i	0.969536	+	0.559762i	0.899095	−	0.437754i	$-0.144226\pi$
$167$	12.5292	+	7.23372i	0.969536	+	0.559762i	0.0704412	+	0.997516i	$0.477559\pi$
$168$		0			0
$169$	8.60870	−	9.74116i	0.662208	−	0.749320i
$170$		0			0
$171$	−16.7796	−	18.9703i	−1.28317	−	1.45069i
$172$		0			0
$173$	5.63954	+	9.76797i	0.428766	+	0.742645i	0.996764	−	0.0803854i	$-0.0256151\pi$
$173$	5.63954	+	9.76797i	0.428766	+	0.742645i	−0.567998	+	0.823030i	$0.692282\pi$
$174$		0			0
$175$	2.77712	+	1.60337i	0.209931	+	0.121204i
$176$		0			0
$177$	19.1083	+	3.11311i	1.43627	+	0.233996i
$178$		0			0
$179$	19.2349			1.43768			0.718840	−	0.695175i	$-0.244673\pi$
$179$	19.2349			1.43768			0.718840	+	0.695175i	$0.244673\pi$
$180$		0			0
$181$	−8.00126			−0.594729			−0.297365	−	0.954764i	$-0.596108\pi$
$181$	−8.00126			−0.594729			−0.297365	+	0.954764i	$0.596108\pi$
$182$		0			0
$183$	−0.603884	−	0.493452i	−0.0446404	−	0.0364770i
$184$		0			0
$185$	7.55329	−	13.0827i	0.555329	−	0.961858i
$186$		0			0
$187$	−0.0408520	+	0.0235859i	−0.00298740	+	0.00172477i
$188$		0			0
$189$	−0.236429	−	6.04413i	−0.0171977	−	0.439646i
$190$		0			0
$191$	−12.7333	−	22.0547i	−0.921349	−	1.59582i	−0.797330	−	0.603543i	$-0.793755\pi$
$191$	−12.7333	−	22.0547i	−0.921349	−	1.59582i	−0.124019	−	0.992280i	$-0.539578\pi$
$192$		0			0
$193$	−14.5610	−	8.40682i	−1.04813	−	0.605136i	−0.126002	−	0.992030i	$-0.540215\pi$
$193$	−14.5610	−	8.40682i	−1.04813	−	0.605136i	−0.922124	+	0.386894i	$0.873548\pi$
$194$		0			0
$195$	−16.7971	+	4.50469i	−1.20287	+	0.322587i
$196$		0			0
$197$		−	25.3622i		−	1.80698i	−0.428610	−	0.903489i	$-0.640997\pi$
$197$		−	25.3622i		−	1.80698i	0.428610	−	0.903489i	$-0.359003\pi$
$198$		0			0
$199$	9.28901			0.658480			0.329240	−	0.944246i	$-0.393207\pi$
$199$	9.28901			0.658480			0.329240	+	0.944246i	$0.393207\pi$
$200$		0			0
$201$	15.8489	+	2.58209i	1.11789	+	0.182127i
$202$		0			0
$203$	−5.38381	−	3.10834i	−0.377869	−	0.218163i
$204$		0			0
$205$	−12.1184	−	20.9897i	−0.846387	−	1.46599i
$206$		0			0
$207$	1.41162	+	6.94242i	0.0981143	+	0.482532i
$208$		0			0
$209$	3.49312	+	6.05027i	0.241624	+	0.418506i
$210$		0			0
$211$	0.938966	−	1.62634i	0.0646411	−	0.111962i	−0.831894	−	0.554935i	$-0.812743\pi$
$211$	0.938966	−	1.62634i	0.0646411	−	0.111962i	0.896535	+	0.442973i	$0.146076\pi$
$212$		0			0
$213$	3.77509	+	9.96592i	0.258665	+	0.682854i
$214$		0			0
$215$		−	28.6203i		−	1.95189i
$216$		0			0
$217$	−0.472642			−0.0320850
$218$		0			0
$219$	−5.18754	−	13.6947i	−0.350542	−	0.925399i
$220$		0			0
$221$	0.187366	−	0.0844642i	0.0126036	−	0.00568168i
$222$		0			0
$223$	−18.3925	+	10.6189i	−1.23165	+	0.711094i	−0.967374	−	0.253353i	$-0.918466\pi$
$223$	−18.3925	+	10.6189i	−1.23165	+	0.711094i	−0.264276	+	0.964447i	$0.585133\pi$
$224$		0			0
$225$	7.83686	+	2.62318i	0.522457	+	0.174879i
$226$		0			0
$227$	−4.95045	+	2.85814i	−0.328573	+	0.189702i	−0.655207	−	0.755449i	$-0.727419\pi$
$227$	−4.95045	+	2.85814i	−0.328573	+	0.189702i	0.326635	+	0.945151i	$0.394085\pi$
$228$		0			0
$229$	−12.3566	−	7.13409i	−0.816548	−	0.471434i	0.0326767	−	0.999466i	$-0.489597\pi$
$229$	−12.3566	−	7.13409i	−0.816548	−	0.471434i	−0.849225	+	0.528032i	$0.822930\pi$
$230$		0			0
$231$	−0.268300	+	1.64683i	−0.0176528	+	0.108353i
$232$		0			0
$233$	21.4720			1.40668			0.703339	−	0.710855i	$-0.251692\pi$
$233$	21.4720			1.40668			0.703339	+	0.710855i	$0.251692\pi$
$234$		0			0
$235$	24.3364			1.58753
$236$		0			0
$237$	11.8056	+	9.64669i	0.766854	+	0.626620i
$238$		0			0
$239$	15.9300	+	9.19721i	1.03043	+	0.594918i	0.917107	−	0.398640i	$-0.130518\pi$
$239$	15.9300	+	9.19721i	1.03043	+	0.594918i	0.113321	+	0.993558i	$0.463851\pi$
$240$		0			0
$241$	−17.2448	+	9.95630i	−1.11084	+	0.641342i	−0.939046	−	0.343792i	$-0.888289\pi$
$241$	−17.2448	+	9.95630i	−1.11084	+	0.641342i	−0.171791	+	0.985133i	$0.554955\pi$
$242$		0			0
$243$	−3.70080	−	15.1428i	−0.237406	−	0.971410i
$244$		0			0
$245$	13.6136	−	7.85979i	0.869738	−	0.502143i
$246$		0			0
$247$	−12.5093	−	27.7493i	−0.795949	−	1.76564i
$248$		0			0
$249$	11.5475	−	14.1318i	0.731794	−	0.895565i
$250$		0			0
$251$	13.5673			0.856361			0.428180	−	0.903693i	$-0.359155\pi$
$251$	13.5673			0.856361			0.428180	+	0.903693i	$0.359155\pi$
$252$		0			0
$253$		−	1.95424i		−	0.122862i
$254$		0			0
$255$	−0.271361	−	0.0442100i	−0.0169933	−	0.00276854i
$256$		0			0
$257$	13.4387	−	23.2765i	0.838284	−	1.45195i	−0.0530440	−	0.998592i	$-0.516892\pi$
$257$	13.4387	−	23.2765i	0.838284	−	1.45195i	0.891328	−	0.453359i	$-0.149774\pi$
$258$		0			0
$259$	3.15745	+	5.46886i	0.196194	+	0.339818i
$260$		0			0
$261$	−15.1928	−	5.08537i	−0.940408	−	0.314776i
$262$		0			0
$263$	2.98437	+	5.16909i	0.184024	+	0.318740i	0.943247	−	0.332091i	$-0.107754\pi$
$263$	2.98437	+	5.16909i	0.184024	+	0.318740i	−0.759223	+	0.650831i	$0.774421\pi$
$264$		0			0
$265$	5.12578	+	2.95937i	0.314874	+	0.181793i
$266$		0			0
$267$	−3.21932	−	8.49873i	−0.197019	−	0.520114i
$268$		0			0
$269$	21.3267			1.30031			0.650155	−	0.759802i	$-0.274704\pi$
$269$	21.3267			1.30031			0.650155	+	0.759802i	$0.274704\pi$
$270$		0			0
$271$			8.47863i			0.515040i	0.966273	+	0.257520i	$0.0829053\pi$
$271$			8.47863i			0.515040i	−0.966273	+	0.257520i	$0.917095\pi$
$272$		0			0
$273$	1.88001	−	7.02239i	0.113783	−	0.425015i
$274$		0			0
$275$	−1.97425	−	1.13984i	−0.119052	−	0.0687347i
$276$		0			0
$277$	5.07822	+	8.79573i	0.305120	+	0.528484i	0.977288	−	0.211915i	$-0.0679699\pi$
$277$	5.07822	+	8.79573i	0.305120	+	0.528484i	−0.672168	+	0.740399i	$0.734637\pi$
$278$		0			0
$279$	−1.19364	+	0.242705i	−0.0714613	+	0.0145304i
$280$		0			0
$281$	−13.8777	+	8.01231i	−0.827876	+	0.477974i	−0.853125	−	0.521707i	$-0.825295\pi$
$281$	−13.8777	+	8.01231i	−0.827876	+	0.477974i	0.0252490	+	0.999681i	$0.491962\pi$
$282$		0			0
$283$	4.22246	−	7.31351i	0.250999	−	0.434743i	−0.712802	−	0.701365i	$-0.752574\pi$
$283$	4.22246	−	7.31351i	0.250999	−	0.434743i	0.963801	+	0.266622i	$0.0859076\pi$
$284$		0			0
$285$	−6.54758	+	40.1891i	−0.387845	+	2.38059i
$286$		0			0
$287$	10.1316			0.598047
$288$		0			0
$289$	−16.9968			−0.999809
$290$		0			0
$291$	0.0963693	−	0.117936i	0.00564927	−	0.00691355i
$292$		0			0
$293$	−5.90810	−	3.41104i	−0.345155	−	0.199275i	0.317394	−	0.948294i	$-0.397192\pi$
$293$	−5.90810	−	3.41104i	−0.345155	−	0.199275i	−0.662549	+	0.749018i	$0.730525\pi$
$294$		0			0
$295$	−15.5634	−	26.9566i	−0.906135	−	1.56947i
$296$		0			0
$297$	0.168077	+	4.29676i	0.00975282	+	0.249324i
$298$		0			0
$299$	−0.850720	+	8.47188i	−0.0491984	+	0.489942i
$300$		0			0
$301$	10.3611	+	5.98198i	0.597203	+	0.344796i
$302$		0			0
$303$	−19.8474	−	16.2179i	−1.14020	−	0.931696i
$304$		0			0
$305$			1.25382i			0.0717937i
$306$		0			0
$307$			7.51889i			0.429125i	0.976710	+	0.214563i	$0.0688326\pi$
$307$			7.51889i			0.429125i	−0.976710	+	0.214563i	$0.931167\pi$
$308$		0			0
$309$	−2.05466	+	12.6115i	−0.116886	+	0.717444i
$310$		0			0
$311$	−0.371290	+	0.643093i	−0.0210539	+	0.0364665i	−0.876360	−	0.481656i	$-0.840036\pi$
$311$	−0.371290	+	0.643093i	−0.0210539	+	0.0364665i	0.855306	+	0.518122i	$0.173369\pi$
$312$		0			0
$313$	−0.511692	−	0.886276i	−0.0289225	−	0.0500953i	0.851202	−	0.524838i	$-0.175874\pi$
$313$	−0.511692	−	0.886276i	−0.0289225	−	0.0500953i	−0.880124	+	0.474743i	$0.842541\pi$
$314$		0			0
$315$	−7.28432	+	6.44313i	−0.410425	+	0.363029i
$316$		0			0
$317$	2.44262	−	1.41025i	0.137191	−	0.0792073i	−0.429834	−	0.902908i	$-0.641428\pi$
$317$	2.44262	−	1.41025i	0.137191	−	0.0792073i	0.567025	+	0.823701i	$0.308094\pi$
$318$		0			0
$319$	3.82735	+	2.20972i	0.214290	+	0.123721i
$320$		0			0
$321$	3.30711	−	1.25273i	0.184585	−	0.0699208i
$322$		0			0
$323$		−	0.481220i		−	0.0267758i
$324$		0			0
$325$	8.06244	+	5.80076i	0.447224	+	0.321768i
$326$		0			0
$327$	6.73579	+	17.7819i	0.372490	+	0.983341i
$328$		0			0
$329$	−5.08659	+	8.81024i	−0.280433	+	0.485724i
$330$		0			0
$331$	−22.6827	+	13.0959i	−1.24676	+	0.719815i	−0.970461	−	0.241258i	$-0.922440\pi$
$331$	−22.6827	+	13.0959i	−1.24676	+	0.719815i	−0.276295	+	0.961073i	$0.589107\pi$
$332$		0			0
$333$	10.7823	+	12.1900i	0.590867	+	0.668009i
$334$		0			0
$335$	−12.9086	−	22.3584i	−0.705274	−	1.22157i
$336$		0			0
$337$	−14.5102	+	25.1323i	−0.790418	+	1.36904i	0.135290	+	0.990806i	$0.456803\pi$
$337$	−14.5102	+	25.1323i	−0.790418	+	1.36904i	−0.925708	+	0.378239i	$0.876530\pi$
$338$		0			0
$339$	0.513437	−	3.15148i	0.0278861	−	0.171165i
$340$		0			0
$341$	0.336001			0.0181955
$342$		0			0
$343$			14.7197i			0.794790i
$344$		0			0
$345$	7.20715	−	8.82007i	0.388020	−	0.474857i
$346$		0			0
$347$	−1.34270	+	2.32563i	−0.0720801	+	0.124846i	−0.899813	−	0.436276i	$-0.856297\pi$
$347$	−1.34270	+	2.32563i	−0.0720801	+	0.124846i	0.827733	+	0.561123i	$0.189630\pi$
$348$		0			0
$349$	6.19331	−	3.57571i	0.331520	−	0.191403i	−0.324996	−	0.945715i	$-0.605363\pi$
$349$	6.19331	−	3.57571i	0.331520	−	0.191403i	0.656516	+	0.754312i	$0.272030\pi$
$350$		0			0
$351$	1.14183	−	18.7002i	0.0609464	−	0.998141i
$352$		0			0
$353$	9.09836	−	5.25294i	0.484257	−	0.279586i	−0.237932	−	0.971282i	$-0.576469\pi$
$353$	9.09836	−	5.25294i	0.484257	−	0.279586i	0.722189	+	0.691696i	$0.243136\pi$
$354$		0			0
$355$	8.56696	−	14.8384i	0.454687	−	0.787541i
$356$		0			0
$357$	0.0727223	−	0.0889973i	0.00384887	−	0.00471023i
$358$		0			0
$359$		−	18.6468i		−	0.984141i	−0.870555	−	0.492070i	$-0.836240\pi$
$359$		−	18.6468i		−	0.984141i	0.870555	−	0.492070i	$-0.163760\pi$
$360$		0			0
$361$	−52.2696			−2.75103
$362$		0			0
$363$	−2.87291	+	17.6339i	−0.150788	+	0.925540i
$364$		0			0
$365$	−11.7723	+	20.3902i	−0.616189	+	1.06727i
$366$		0			0
$367$	1.69546	+	2.93662i	0.0885023	+	0.153290i	0.906878	−	0.421393i	$-0.138459\pi$
$367$	1.69546	+	2.93662i	0.0885023	+	0.153290i	−0.818376	+	0.574683i	$0.805125\pi$
$368$		0			0
$369$	25.5868	−	5.20263i	1.33200	−	0.270838i
$370$		0			0
$371$	−2.14269	+	1.23708i	−0.111243	+	0.0642262i
$372$		0			0
$373$	15.7393	−	27.2613i	0.814950	−	1.41153i	−0.0944144	−	0.995533i	$-0.530098\pi$
$373$	15.7393	−	27.2613i	0.814950	−	1.41153i	0.909364	−	0.416001i	$-0.136569\pi$
$374$		0			0
$375$	3.83623	+	10.1273i	0.198102	+	0.522973i
$376$		0			0
$377$	−15.6301	−	11.2455i	−0.804990	−	0.579174i
$378$		0			0
$379$		−	28.3567i		−	1.45658i	−0.685267	−	0.728292i	$-0.740314\pi$
$379$		−	28.3567i		−	1.45658i	0.685267	−	0.728292i	$-0.259686\pi$
$380$		0			0
$381$	−7.87989	+	2.98491i	−0.403699	+	0.152921i
$382$		0			0
$383$	18.0655	+	10.4301i	0.923106	+	0.532956i	0.884625	−	0.466304i	$-0.154415\pi$
$383$	18.0655	+	10.4301i	0.923106	+	0.532956i	0.0384816	+	0.999259i	$0.487748\pi$
$384$		0			0
$385$	2.32322	−	1.34131i	0.118402	−	0.0683595i
$386$		0			0
$387$	29.2383	+	9.78674i	1.48627	+	0.497488i
$388$		0			0
$389$	11.4705	+	19.8676i	0.581580	+	1.00733i	0.995292	+	0.0969184i	$0.0308986\pi$
$389$	11.4705	+	19.8676i	0.581580	+	1.00733i	−0.413712	+	0.910408i	$0.635768\pi$
$390$		0			0
$391$	−0.0673052	+	0.116576i	−0.00340377	+	0.00589550i
$392$		0			0
$393$	−5.28204	+	32.4212i	−0.266444	+	1.63543i
$394$		0			0
$395$		−	24.5115i		−	1.23331i
$396$		0			0
$397$		−	14.4766i		−	0.726562i	−0.931680	−	0.363281i	$-0.881657\pi$
$397$		−	14.4766i		−	0.726562i	0.931680	−	0.363281i	$-0.118343\pi$
$398$		0			0
$399$	−13.1807	−	10.7703i	−0.659859	−	0.539190i
$400$		0			0
$401$	−28.4504	−	16.4259i	−1.42075	−	0.820268i	−0.424383	−	0.905483i	$-0.639509\pi$
$401$	−28.4504	−	16.4259i	−1.42075	−	0.820268i	−0.996363	+	0.0852145i	$0.972842\pi$
$402$		0			0
$403$	−1.45660	−	0.146268i	−0.0725586	−	0.00728611i
$404$		0			0
$405$	−15.0877	+	20.0124i	−0.749712	+	0.994425i
$406$		0			0
$407$	−2.24463	−	3.88781i	−0.111262	−	0.192711i
$408$		0			0
$409$	26.2128	+	15.1340i	1.29614	+	0.748327i	0.979735	−	0.200297i	$-0.0641909\pi$
$409$	26.2128	+	15.1340i	1.29614	+	0.748327i	0.316405	+	0.948624i	$0.397524\pi$
$410$		0			0
$411$	−14.2729	+	17.4671i	−0.704031	+	0.861589i
$412$		0			0
$413$	13.0117			0.640264
$414$		0			0
$415$	−29.3413			−1.44031
$416$		0			0
$417$	1.76614	−	10.8406i	0.0864883	−	0.530866i
$418$		0			0
$419$	−0.634571	+	1.09911i	−0.0310008	+	0.0536950i	−0.881110	−	0.472912i	$-0.843203\pi$
$419$	−0.634571	+	1.09911i	−0.0310008	+	0.0536950i	0.850109	+	0.526607i	$0.176536\pi$
$420$		0			0
$421$	−4.45783	+	2.57373i	−0.217261	+	0.125436i	−0.604681	−	0.796467i	$-0.706700\pi$
$421$	−4.45783	+	2.57373i	−0.217261	+	0.125436i	0.387420	+	0.921903i	$0.373366\pi$
$422$		0			0
$423$	−8.32186	+	24.8619i	−0.404623	+	1.20883i
$424$		0			0
$425$	0.0785131	+	0.135989i	0.00380845	+	0.00659642i
$426$		0			0
$427$	−0.453907	−	0.262063i	−0.0219661	−	0.0126821i
$428$		0			0
$429$	−1.33650	+	4.99221i	−0.0645266	+	0.241026i
$430$		0			0
$431$			27.6418i			1.33146i	0.746193	+	0.665730i	$0.231880\pi$
$431$			27.6418i			1.33146i	−0.746193	+	0.665730i	$0.768120\pi$
$432$		0			0
$433$	28.6165			1.37522			0.687610	−	0.726080i	$-0.258660\pi$
$433$	28.6165			1.37522			0.687610	+	0.726080i	$0.258660\pi$
$434$		0			0
$435$	9.12460	+	24.0882i	0.437491	+	1.15494i
$436$		0			0
$437$	17.2651	+	9.96803i	0.825903	+	0.476835i
$438$		0			0
$439$	−5.14544	−	8.91216i	−0.245578	−	0.425354i	0.716716	−	0.697365i	$-0.245644\pi$
$439$	−5.14544	−	8.91216i	−0.245578	−	0.425354i	−0.962294	+	0.272011i	$0.912311\pi$
$440$		0			0
$441$	3.37433	+	16.5952i	0.160683	+	0.790246i
$442$		0			0
$443$	10.5570	+	18.2852i	0.501578	+	0.868758i	0.999998	+	0.00182269i	$0.000580182\pi$
$443$	10.5570	+	18.2852i	0.501578	+	0.868758i	−0.498421	+	0.866935i	$0.666086\pi$
$444$		0			0
$445$	−7.30573	+	12.6539i	−0.346325	+	0.599852i
$446$		0			0
$447$	−25.3970	−	4.13766i	−1.20124	−	0.195705i
$448$		0			0
$449$			30.5172i			1.44020i	0.693872	+	0.720099i	$0.255904\pi$
$449$			30.5172i			1.44020i	−0.693872	+	0.720099i	$0.744096\pi$
$450$		0			0
$451$	−7.20251			−0.339153
$452$		0			0
$453$	11.9870	−	14.6696i	0.563199	−	0.689240i
$454$		0			0
$455$	−10.6553	+	4.80340i	−0.499529	+	0.225187i
$456$		0			0
$457$	−10.8631	+	6.27183i	−0.508156	+	0.293384i	−0.732075	−	0.681224i	$-0.761448\pi$
$457$	−10.8631	+	6.27183i	−0.508156	+	0.293384i	0.223919	+	0.974608i	$0.428115\pi$
$458$		0			0
$459$	0.137957	−	0.262102i	0.00643926	−	0.0122339i
$460$		0			0
$461$	12.4016	−	7.16006i	0.577599	−	0.333477i	−0.182580	−	0.983191i	$-0.558445\pi$
$461$	12.4016	−	7.16006i	0.577599	−	0.333477i	0.760179	+	0.649714i	$0.225111\pi$
$462$		0			0
$463$	7.05577	+	4.07365i	0.327909	+	0.189319i	0.654913	−	0.755705i	$-0.272705\pi$
$463$	7.05577	+	4.07365i	0.327909	+	0.189319i	−0.327003	+	0.945023i	$0.606039\pi$
$464$		0			0
$465$	1.51647	+	1.23915i	0.0703246	+	0.0574644i
$466$		0			0
$467$	−2.80280			−0.129698			−0.0648491	−	0.997895i	$-0.520657\pi$
$467$	−2.80280			−0.129698			−0.0648491	+	0.997895i	$0.520657\pi$
$468$		0			0
$469$	10.7922			0.498338
$470$		0			0
$471$	0.859420	−	5.27512i	0.0396000	−	0.243065i
$472$		0			0
$473$	−7.36569	−	4.25258i	−0.338675	−	0.195534i
$474$		0			0
$475$	20.1402	−	11.6279i	0.924095	−	0.533527i
$476$		0			0
$477$	−4.77603	+	4.22449i	−0.218679	+	0.193426i
$478$		0			0
$479$	−19.3809	+	11.1896i	−0.885535	+	0.511264i	−0.872479	−	0.488651i	$-0.837489\pi$
$479$	−19.3809	+	11.1896i	−0.885535	+	0.511264i	−0.0130558	+	0.999915i	$0.504156\pi$
$480$		0			0
$481$	8.03829	+	17.8313i	0.366515	+	0.813035i
$482$		0			0
$483$	1.68665	+	4.45262i	0.0767453	+	0.202601i
$484$		0			0
$485$	−0.244867			−0.0111188
$486$		0			0
$487$		−	39.3335i		−	1.78237i	−0.453640	−	0.891185i	$-0.649875\pi$
$487$		−	39.3335i		−	1.78237i	0.453640	−	0.891185i	$-0.350125\pi$
$488$		0			0
$489$	−4.84646	−	12.7942i	−0.219164	−	0.578575i
$490$		0			0
$491$	16.5130	−	28.6014i	0.745221	−	1.29076i	−0.204870	−	0.978789i	$-0.565677\pi$
$491$	16.5130	−	28.6014i	0.745221	−	1.29076i	0.950091	−	0.311972i	$-0.100989\pi$
$492$		0			0
$493$	−0.152208	−	0.263632i	−0.00685509	−	0.0118734i
$494$		0			0
$495$	5.17842	−	4.58041i	0.232753	−	0.205874i
$496$		0			0
$497$	3.58118	+	6.20279i	0.160638	+	0.278233i
$498$		0			0
$499$	−13.7223	−	7.92255i	−0.614293	−	0.354662i	0.160351	−	0.987060i	$-0.448737\pi$
$499$	−13.7223	−	7.92255i	−0.614293	−	0.354662i	−0.774644	+	0.632398i	$0.782071\pi$
$500$		0			0
$501$	24.7322	+	4.02936i	1.10496	+	0.180019i
$502$		0			0
$503$	−15.5341			−0.692631			−0.346316	−	0.938118i	$-0.612567\pi$
$503$	−15.5341			−0.692631			−0.346316	+	0.938118i	$0.612567\pi$
$504$		0			0
$505$			41.2085i			1.83375i
$506$		0			0
$507$	7.96708	−	21.0600i	0.353830	−	0.935310i
$508$		0			0
$509$	−0.292155	−	0.168676i	−0.0129496	−	0.00747643i	0.493511	−	0.869739i	$-0.335713\pi$
$509$	−0.292155	−	0.168676i	−0.0129496	−	0.00747643i	−0.506461	+	0.862263i	$0.669047\pi$
$510$		0			0
$511$	−4.92108	−	8.52356i	−0.217696	−	0.377060i
$512$		0			0
$513$	−38.8179	−	20.4316i	−1.71385	−	0.902079i
$514$		0			0
$515$	17.7914	−	10.2719i	0.783981	−	0.452632i
$516$		0			0
$517$	3.61605	−	6.26319i	0.159034	−	0.275455i
$518$		0			0
$519$	15.1278	+	12.3614i	0.664035	+	0.542603i
$520$		0			0
$521$	−42.3817			−1.85678			−0.928388	−	0.371613i	$-0.878805\pi$
$521$	−42.3817			−1.85678			−0.928388	+	0.371613i	$0.878805\pi$
$522$		0			0
$523$	−20.4121			−0.892557			−0.446279	−	0.894894i	$-0.647251\pi$
$523$	−20.4121			−0.892557			−0.446279	+	0.894894i	$0.647251\pi$
$524$		0			0
$525$	5.48197	+	0.893119i	0.239253	+	0.0389789i
$526$		0			0
$527$	−0.0200434	−	0.0115720i	−0.000873103	−	0.000504086i
$528$		0			0
$529$	8.71167	+	15.0891i	0.378768	+	0.656046i
$530$		0			0
$531$	32.8605	−	6.68160i	1.42602	−	0.289957i
$532$		0			0
$533$	31.2238	+	3.13540i	1.35245	+	0.135809i
$534$		0			0
$535$	−4.92401	−	2.84288i	−0.212883	−	0.122908i
$536$		0			0
$537$	31.1554	−	11.8017i	1.34446	−	0.509280i
$538$		0			0
$539$		−	4.67142i		−	0.201212i
$540$		0			0
$541$			7.27818i			0.312913i	0.987685	+	0.156457i	$0.0500072\pi$
$541$			7.27818i			0.312913i	−0.987685	+	0.156457i	$0.949993\pi$
$542$		0			0
$543$	−12.9599	+	4.90923i	−0.556164	+	0.210675i
$544$		0			0
$545$	15.2858	−	26.4757i	0.654770	−	1.13410i
$546$		0			0
$547$	21.3676	+	37.0098i	0.913614	+	1.58243i	0.808918	+	0.587921i	$0.200054\pi$
$547$	21.3676	+	37.0098i	0.913614	+	1.58243i	0.104696	+	0.994504i	$0.466613\pi$
$548$		0			0
$549$	−1.28089	−	0.428745i	−0.0546673	−	0.0182984i
$550$		0			0
$551$	−39.0443	+	22.5423i	−1.66335	+	0.960333i
$552$		0			0
$553$	8.87360	+	5.12318i	0.377344	+	0.217860i
$554$		0			0
$555$	4.20737	−	25.8249i	0.178593	−	1.09620i
$556$		0			0
$557$			19.6148i			0.831105i	0.909569	+	0.415552i	$0.136412\pi$
$557$			19.6148i			0.831105i	−0.909569	+	0.415552i	$0.863588\pi$
$558$		0			0
$559$	30.0799	+	21.6419i	1.27225	+	0.915355i
$560$		0			0
$561$	−0.0516983	+	0.0632681i	−0.00218270	+	0.00267118i
$562$		0			0
$563$	−21.9568	+	38.0302i	−0.925367	+	1.60278i	−0.134397	+	0.990928i	$0.542910\pi$
$563$	−21.9568	+	38.0302i	−0.925367	+	1.60278i	−0.790970	+	0.611855i	$0.790424\pi$
$564$		0			0
$565$	−4.44587	+	2.56682i	−0.187039	+	0.107987i
$566$		0			0
$567$	−4.09137	−	9.64483i	−0.171821	−	0.405045i
$568$		0			0
$569$	−20.0889	−	34.7950i	−0.842171	−	1.45868i	−0.888055	−	0.459736i	$-0.847944\pi$
$569$	−20.0889	−	34.7950i	−0.842171	−	1.45868i	0.0458843	−	0.998947i	$-0.485389\pi$
$570$		0			0
$571$	−6.40209	+	11.0887i	−0.267919	+	0.464049i	−0.968324	−	0.249696i	$-0.919669\pi$
$571$	−6.40209	+	11.0887i	−0.267919	+	0.464049i	0.700405	+	0.713745i	$0.253003\pi$
$572$		0			0
$573$	−34.1564	−	27.9102i	−1.42690	−	1.16597i
$574$		0			0
$575$	−6.50531			−0.271290
$576$		0			0
$577$		−	21.6624i		−	0.901816i	−0.892570	−	0.450908i	$-0.851100\pi$
$577$		−	21.6624i		−	0.901816i	0.892570	−	0.450908i	$-0.148900\pi$
$578$		0			0
$579$	−28.7431	−	4.68281i	−1.19452	−	0.194611i
$580$		0			0
$581$	6.13267	−	10.6221i	0.254426	−	0.440678i
$582$		0			0
$583$	1.52324	−	0.879442i	0.0630861	−	0.0364228i
$584$		0			0
$585$	−24.4430	+	17.6024i	−1.01059	+	0.727769i
$586$		0			0
$587$	9.45422	−	5.45839i	0.390217	−	0.225292i	−0.292037	−	0.956407i	$-0.594333\pi$
$587$	9.45422	−	5.45839i	0.390217	−	0.225292i	0.682254	+	0.731115i	$0.261000\pi$
$588$		0			0
$589$	−1.71384	+	2.96846i	−0.0706176	+	0.122313i
$590$		0			0
$591$	−15.5611	−	41.0800i	−0.640099	−	1.68981i
$592$		0			0
$593$		−	1.28924i		−	0.0529429i	−0.999650	−	0.0264715i	$-0.991573\pi$
$593$		−	1.28924i		−	0.0529429i	0.999650	−	0.0264715i	$-0.00842711\pi$
$594$		0			0
$595$	−0.184782			−0.00757531
$596$		0			0
$597$	15.0457	−	5.69933i	0.615781	−	0.233258i
$598$		0			0
$599$	−12.7091	+	22.0128i	−0.519281	+	0.899420i	0.480468	+	0.877012i	$0.340467\pi$
$599$	−12.7091	+	22.0128i	−0.519281	+	0.899420i	−0.999749	+	0.0224084i	$0.992867\pi$
$600$		0			0
$601$	8.30319	+	14.3815i	0.338694	+	0.586635i	0.984187	−	0.177131i	$-0.0566815\pi$
$601$	8.30319	+	14.3815i	0.338694	+	0.586635i	−0.645493	+	0.763766i	$0.723348\pi$
$602$		0			0
$603$	27.2553	−	5.54188i	1.10992	−	0.225683i
$604$		0			0
$605$	24.8766	−	14.3625i	1.01138	−	0.583919i
$606$		0			0
$607$	−14.9774	+	25.9416i	−0.607914	+	1.05294i	0.383669	+	0.923471i	$0.374660\pi$
$607$	−14.9774	+	25.9416i	−0.607914	+	1.05294i	−0.991584	+	0.129468i	$0.958673\pi$
$608$		0			0
$609$	−10.6275	−	1.73143i	−0.430648	−	0.0701610i
$610$		0			0
$611$	−18.4025	+	25.5775i	−0.744486	+	1.03476i
$612$		0			0
$613$		−	40.3638i		−	1.63028i	−0.579264	−	0.815140i	$-0.696660\pi$
$613$		−	40.3638i		−	1.63028i	0.579264	−	0.815140i	$-0.303340\pi$
$614$		0			0
$615$	−32.5071	−	26.5625i	−1.31081	−	1.07110i
$616$		0			0
$617$	1.30727	+	0.754755i	0.0526289	+	0.0303853i	0.526084	−	0.850433i	$-0.323660\pi$
$617$	1.30727	+	0.754755i	0.0526289	+	0.0303853i	−0.473455	+	0.880818i	$0.656993\pi$
$618$		0			0
$619$	−22.1343	+	12.7792i	−0.889651	+	0.513640i	−0.873828	−	0.486235i	$-0.838370\pi$
$619$	−22.1343	+	12.7792i	−0.889651	+	0.513640i	−0.0158227	+	0.999875i	$0.505037\pi$
$620$		0			0
$621$	6.54602	+	10.3788i	0.262683	+	0.416487i
$622$		0			0
$623$	−3.05396	−	5.28961i	−0.122354	−	0.211924i
$624$		0			0
$625$	15.5926	−	27.0071i	0.623702	−	1.08028i
$626$		0			0
$627$	9.37012	+	7.65661i	0.374207	+	0.305776i
$628$		0			0
$629$			0.309225i			0.0123296i
$630$		0			0
$631$			40.1082i			1.59668i	0.602204	+	0.798342i	$0.294289\pi$
$631$			40.1082i			1.59668i	−0.602204	+	0.798342i	$0.705711\pi$
$632$		0			0
$633$	0.523028	−	3.21035i	0.0207885	−	0.127600i
$634$		0			0
$635$	11.7325	+	6.77375i	0.465589	+	0.268808i
$636$		0			0
$637$	−2.03356	+	20.2512i	−0.0805726	+	0.802381i
$638$		0			0
$639$	12.2293	+	13.8259i	0.483784	+	0.546946i
$640$		0			0
$641$	−10.4289	−	18.0634i	−0.411918	−	0.713463i	0.583182	−	0.812342i	$-0.301808\pi$
$641$	−10.4289	−	18.0634i	−0.411918	−	0.713463i	−0.995099	+	0.0988791i	$0.968474\pi$
$642$		0			0
$643$	−13.8468	−	7.99443i	−0.546063	−	0.315270i	0.201470	−	0.979495i	$-0.435428\pi$
$643$	−13.8468	−	7.99443i	−0.546063	−	0.315270i	−0.747533	+	0.664225i	$0.768762\pi$
$644$		0			0
$645$	−17.5602	−	46.3574i	−0.691432	−	1.82532i
$646$		0			0
$647$	41.0986			1.61575			0.807877	−	0.589351i	$-0.200617\pi$
$647$	41.0986			1.61575			0.807877	+	0.589351i	$0.200617\pi$
$648$		0			0
$649$	−9.25000			−0.363094
$650$		0			0
$651$	−0.765556	+	0.289993i	−0.0300045	+	0.0113657i
$652$		0			0
$653$	17.0312	−	29.4989i	0.666483	−	1.15438i	−0.312398	−	0.949951i	$-0.601132\pi$
$653$	17.0312	−	29.4989i	0.666483	−	1.15438i	0.978881	−	0.204431i	$-0.0655345\pi$
$654$		0			0
$655$	45.7374	−	26.4065i	1.78711	−	1.03179i
$656$		0			0
$657$	−16.8049	−	18.9989i	−0.655622	−	0.741217i
$658$		0			0
$659$	−11.9493	−	20.6967i	−0.465477	−	0.806230i	0.533746	−	0.845645i	$-0.320784\pi$
$659$	−11.9493	−	20.6967i	−0.465477	−	0.806230i	−0.999223	+	0.0394152i	$0.987451\pi$
$660$		0			0
$661$	−1.54967	−	0.894700i	−0.0602750	−	0.0347998i	0.469560	−	0.882901i	$-0.344413\pi$
$661$	−1.54967	−	0.894700i	−0.0602750	−	0.0347998i	−0.529835	+	0.848101i	$0.677746\pi$
$662$		0			0
$663$	0.251660	−	0.251770i	0.00977367	−	0.00977792i
$664$		0			0
$665$			27.3665i			1.06123i
$666$		0			0
$667$	12.6114			0.488314
$668$		0			0
$669$	−23.2757	+	28.4846i	−0.899889	+	1.10128i
$670$		0			0
$671$	0.322682	+	0.186301i	0.0124570	+	0.00719205i
$672$		0			0
$673$	−8.93185	−	15.4704i	−0.344298	−	0.596341i	0.640928	−	0.767601i	$-0.278550\pi$
$673$	−8.93185	−	15.4704i	−0.344298	−	0.596341i	−0.985226	+	0.171260i	$0.945216\pi$
$674$		0			0
$675$	14.3031	−	0.559497i	0.550527	−	0.0215350i
$676$		0			0
$677$	19.3289	+	33.4786i	0.742869	+	1.28669i	0.951184	+	0.308625i	$0.0998688\pi$
$677$	19.3289	+	33.4786i	0.742869	+	1.28669i	−0.208315	+	0.978062i	$0.566798\pi$
$678$		0			0
$679$	0.0511799	−	0.0886462i	0.00196411	−	0.00340193i
$680$		0			0
$681$	−6.26479	+	7.66682i	−0.240067	+	0.293793i
$682$		0			0
$683$			22.6437i			0.866438i	0.901289	+	0.433219i	$0.142622\pi$
$683$			22.6437i			0.866438i	−0.901289	+	0.433219i	$0.857378\pi$
$684$		0			0
$685$	36.2663			1.38566
$686$		0			0
$687$	−24.3916	−	3.97387i	−0.930599	−	0.151613i
$688$		0			0
$689$	−6.98626	+	3.14939i	−0.266155	+	0.119982i
$690$		0			0
$691$	29.5626	−	17.0680i	1.12462	−	0.649297i	0.182041	−	0.983291i	$-0.441730\pi$
$691$	29.5626	−	17.0680i	1.12462	−	0.649297i	0.942575	+	0.333994i	$0.108396\pi$
$692$		0			0
$693$	0.575846	+	2.83204i	0.0218746	+	0.107580i
$694$		0			0
$695$	−15.2931	+	8.82946i	−0.580099	+	0.334921i
$696$		0			0
$697$	0.429650	+	0.248058i	0.0162741	+	0.00939588i
$698$		0			0
$699$	34.7790	−	13.1743i	1.31546	−	0.498298i
$700$		0			0
$701$	−30.5519			−1.15393			−0.576965	−	0.816769i	$-0.695763\pi$
$701$	−30.5519			−1.15393			−0.576965	+	0.816769i	$0.695763\pi$
$702$		0			0
$703$	45.7968			1.72726
$704$		0			0
$705$	39.4186	−	14.9318i	1.48459	−	0.562363i
$706$		0			0
$707$	−14.9182	−	8.61304i	−0.561057	−	0.323927i
$708$		0			0
$709$	−6.97406	+	4.02648i	−0.261916	+	0.151218i	−0.625208	−	0.780458i	$-0.714986\pi$
$709$	−6.97406	+	4.02648i	−0.261916	+	0.151218i	0.363292	+	0.931675i	$0.381653\pi$
$710$		0			0
$711$	25.0407	+	8.38171i	0.939100	+	0.314339i
$712$		0			0
$713$	0.830360	−	0.479408i	0.0310972	−	0.0179540i
$714$		0			0
$715$	7.57486	−	3.41473i	0.283284	−	0.127704i
$716$		0			0
$717$	31.4455	+	5.12308i	1.17435	+	0.191325i
$718$		0			0
$719$	1.13026			0.0421515			0.0210757	−	0.999778i	$-0.493291\pi$
$719$	1.13026			0.0421515			0.0210757	+	0.999778i	$0.493291\pi$
$720$		0			0
$721$			8.58774i			0.319824i
$722$		0			0
$723$	−21.8233	+	26.7073i	−0.811618	+	0.993254i
$724$		0			0
$725$	7.35574	−	12.7405i	0.273185	−	0.473171i
$726$		0			0
$727$	−9.66960	−	16.7482i	−0.358626	−	0.621158i	0.629106	−	0.777320i	$-0.283421\pi$
$727$	−9.66960	−	16.7482i	−0.358626	−	0.621158i	−0.987732	+	0.156162i	$0.950088\pi$
$728$		0			0
$729$	−15.2853	−	22.2567i	−0.566122	−	0.824322i
$730$		0			0
$731$	0.292922	+	0.507357i	0.0108341	+	0.0187653i
$732$		0			0
$733$	−45.2652	−	26.1339i	−1.67191	−	0.965276i	−0.966570	−	0.256404i	$-0.917462\pi$
$733$	−45.2652	−	26.1339i	−1.67191	−	0.965276i	−0.705337	−	0.708872i	$-0.749204\pi$
$734$		0			0
$735$	17.2279	−	21.0835i	0.635462	−	0.777676i
$736$		0			0
$737$	−7.67217			−0.282608
$738$		0			0
$739$		−	37.8316i		−	1.39166i	−0.718207	−	0.695829i	$-0.755037\pi$
$739$		−	37.8316i		−	1.39166i	0.718207	−	0.695829i	$-0.244963\pi$
$740$		0			0
$741$	−37.2876	−	37.2713i	−1.36979	−	1.36920i
$742$		0			0
$743$	−14.6017	−	8.43032i	−0.535686	−	0.309278i	0.207643	−	0.978205i	$-0.433421\pi$
$743$	−14.6017	−	8.43032i	−0.535686	−	0.309278i	−0.743329	+	0.668926i	$0.766754\pi$
$744$		0			0
$745$	20.6854	+	35.8281i	0.757854	+	1.31264i
$746$		0			0
$747$	10.0333	−	29.9748i	0.367098	−	1.09672i
$748$		0			0
$749$	2.05835	−	1.18839i	0.0752104	−	0.0434227i
$750$		0			0
$751$	−22.2277	+	38.4996i	−0.811102	+	1.40487i	0.100991	+	0.994887i	$0.467799\pi$
$751$	−22.2277	+	38.4996i	−0.811102	+	1.40487i	−0.912093	+	0.409983i	$0.865535\pi$
$752$		0			0
$753$	21.9755	−	8.32431i	0.800830	−	0.303355i
$754$		0			0
$755$	−30.4580			−1.10848
$756$		0			0
$757$	18.6044			0.676187			0.338094	−	0.941112i	$-0.390218\pi$
$757$	18.6044			0.676187			0.338094	+	0.941112i	$0.390218\pi$
$758$		0			0
$759$	−1.19904	−	3.16536i	−0.0435224	−	0.114895i
$760$		0			0
$761$	−10.1160	−	5.84048i	−0.366705	−	0.211717i	0.305313	−	0.952252i	$-0.401239\pi$
$761$	−10.1160	−	5.84048i	−0.366705	−	0.211717i	−0.672018	+	0.740535i	$0.734572\pi$
$762$		0			0
$763$	6.38980	+	11.0675i	0.231326	+	0.400669i
$764$		0			0
$765$	−0.466659	+	0.0948868i	−0.0168721	+	0.00343064i
$766$		0			0
$767$	40.0999	+	4.02671i	1.44792	+	0.145396i
$768$		0			0
$769$	−0.140759	−	0.0812671i	−0.00507589	−	0.00293057i	0.497460	−	0.867487i	$-0.334266\pi$
$769$	−0.140759	−	0.0812671i	−0.00507589	−	0.00293057i	−0.502536	+	0.864556i	$0.667599\pi$
$770$		0			0
$771$	7.48571	−	45.9473i	0.269591	−	1.65475i
$772$		0			0
$773$		−	22.5752i		−	0.811974i	−0.913879	−	0.405987i	$-0.866928\pi$
$773$		−	22.5752i		−	0.811974i	0.913879	−	0.405987i	$-0.133072\pi$
$774$		0			0
$775$		−	1.11848i		−	0.0401771i
$776$		0			0
$777$	8.46969	+	6.92084i	0.303849	+	0.248284i
$778$		0			0
$779$	36.7379	−	63.6320i	1.31627	−	2.27985i
$780$		0			0
$781$	−2.54586	−	4.40956i	−0.0910980	−	0.157786i
$782$		0			0
$783$	−27.7284	+	1.08466i	−0.990933	+	0.0387625i
$784$		0			0
$785$	−7.44174	+	4.29649i	−0.265607	+	0.153348i
$786$		0			0
$787$	26.0884	+	15.0621i	0.929951	+	0.536907i	0.886796	−	0.462161i	$-0.152926\pi$
$787$	26.0884	+	15.0621i	0.929951	+	0.536907i	0.0431548	+	0.999068i	$0.486259\pi$
$788$		0			0
$789$	8.00543	+	6.54148i	0.285001	+	0.232883i
$790$		0			0
$791$		−	2.14598i		−	0.0763023i
$792$		0			0
$793$	−1.31777	−	0.948105i	−0.0467952	−	0.0336682i
$794$		0			0
$795$	10.1182	+	1.64844i	0.358854	+	0.0584643i
$796$		0			0
$797$	−16.8338	+	29.1570i	−0.596285	+	1.03280i	0.397079	+	0.917784i	$0.370024\pi$
$797$	−16.8338	+	29.1570i	−0.596285	+	1.03280i	−0.993364	+	0.115011i	$0.963310\pi$
$798$		0			0
$799$	−0.431415	+	0.249078i	−0.0152624	+	0.00881173i
$800$		0			0
$801$	−10.4289	−	11.7905i	−0.368487	−	0.416596i
$802$		0			0
$803$	3.49839	+	6.05939i	0.123456	+	0.213831i
$804$		0			0
$805$	3.82758	−	6.62956i	0.134904	−	0.233661i
$806$		0			0
$807$	34.5436	−	13.0851i	1.21599	−	0.460618i
$808$		0			0
$809$	−35.7648			−1.25742			−0.628712	−	0.777638i	$-0.716418\pi$
$809$	−35.7648			−1.25742			−0.628712	+	0.777638i	$0.716418\pi$
$810$		0			0
$811$		−	0.328149i		−	0.0115229i	−0.999983	−	0.00576144i	$-0.998166\pi$
$811$		−	0.328149i		−	0.0115229i	0.999983	−	0.00576144i	$-0.00183393\pi$
$812$		0			0
$813$	5.20212	+	13.7331i	0.182446	+	0.481642i
$814$		0			0
$815$	−10.9982	+	19.0495i	−0.385252	+	0.667275i
$816$		0			0
$817$	75.1405	−	43.3824i	2.62883	−	1.51776i
$818$		0			0
$819$	−1.26352	−	12.5279i	−0.0441509	−	0.437761i
$820$		0			0
$821$	−43.7841	+	25.2787i	−1.52807	+	0.882234i	−0.528631	+	0.848852i	$0.677295\pi$
$821$	−43.7841	+	25.2787i	−1.52807	+	0.882234i	−0.999443	+	0.0333824i	$0.989372\pi$
$822$		0			0
$823$	8.63338	−	14.9534i	0.300941	−	0.521244i	−0.675409	−	0.737444i	$-0.736033\pi$
$823$	8.63338	−	14.9534i	0.300941	−	0.521244i	0.976349	+	0.216199i	$0.0693661\pi$
$824$		0			0
$825$	−3.89713	−	0.634918i	−0.135681	−	0.0221050i
$826$		0			0
$827$		−	25.4686i		−	0.885630i	−0.896613	−	0.442815i	$-0.853980\pi$
$827$		−	25.4686i		−	0.885630i	0.896613	−	0.442815i	$-0.146020\pi$
$828$		0			0
$829$	−28.6937			−0.996573			−0.498287	−	0.867012i	$-0.666037\pi$
$829$	−28.6937			−0.996573			−0.498287	+	0.867012i	$0.666037\pi$
$830$		0			0
$831$	13.6221	+	11.1310i	0.472544	+	0.386130i
$832$		0			0
$833$	−0.160886	+	0.278663i	−0.00557437	+	0.00965510i
$834$		0			0
$835$	−20.1440	−	34.8904i	−0.697111	−	1.20743i
$836$		0			0
$837$	−1.78447	+	1.12548i	−0.0616802	+	0.0389024i
$838$		0			0
$839$	−9.92991	+	5.73304i	−0.342819	+	0.197926i	−0.661518	−	0.749929i	$-0.730087\pi$
$839$	−9.92991	+	5.73304i	−0.342819	+	0.197926i	0.318699	+	0.947856i	$0.396754\pi$
$840$		0			0
$841$	0.239959	−	0.415621i	0.00827445	−	0.0143318i
$842$		0			0
$843$	−17.5623	+	21.4926i	−0.604876	+	0.740245i
$844$		0			0
$845$	−34.3245	+	11.5058i	−1.18080	+	0.395811i
$846$		0			0
$847$			12.0077i			0.412590i
$848$		0			0
$849$	2.35202	−	14.4367i	0.0807210	−	0.495466i
$850$		0			0
$851$	−11.0943	−	6.40530i	−0.380308	−	0.219571i
$852$		0			0
$853$	1.06793	−	0.616572i	0.0365654	−	0.0211110i	−0.481606	−	0.876388i	$-0.659946\pi$
$853$	1.06793	−	0.616572i	0.0365654	−	0.0211110i	0.518171	+	0.855277i	$0.326613\pi$
$854$		0			0
$855$	14.0529	+	69.1130i	0.480600	+	2.36362i
$856$		0			0
$857$	−9.29462	−	16.0987i	−0.317498	−	0.549923i	0.662467	−	0.749091i	$-0.269509\pi$
$857$	−9.29462	−	16.0987i	−0.317498	−	0.549923i	−0.979965	+	0.199168i	$0.936176\pi$
$858$		0			0
$859$	−6.59651	+	11.4255i	−0.225070	+	0.389833i	−0.956340	−	0.292255i	$-0.905594\pi$
$859$	−6.59651	+	11.4255i	−0.225070	+	0.389833i	0.731270	+	0.682088i	$0.238928\pi$
$860$		0			0
$861$	16.4105	−	6.21629i	0.559267	−	0.211850i
$862$		0			0
$863$			33.4436i			1.13843i	0.822188	+	0.569217i	$0.192753\pi$
$863$			33.4436i			1.13843i	−0.822188	+	0.569217i	$0.807247\pi$
$864$		0			0
$865$		−	31.4092i		−	1.06795i
$866$		0			0
$867$	−27.5303	+	10.4285i	−0.934977	+	0.354169i
$868$		0			0
$869$	−6.30824	−	3.64206i	−0.213992	−	0.123548i
$870$		0			0
$871$	33.2598	+	3.33985i	1.12697	+	0.113166i
$872$		0			0
$873$	0.0837323	−	0.250154i	0.00283391	−	0.00846642i
$874$		0			0
$875$	3.63918	+	6.30325i	0.123027	+	0.213089i
$876$		0			0
$877$	43.5316	+	25.1330i	1.46996	+	0.848681i	0.999432	−	0.0337054i	$-0.0107308\pi$
$877$	43.5316	+	25.1330i	1.46996	+	0.848681i	0.470526	+	0.882386i	$0.344064\pi$
$878$		0			0
$879$	−11.6624	−	1.90004i	−0.393364	−	0.0640867i
$880$		0			0
$881$	−29.3997			−0.990501			−0.495251	−	0.868750i	$-0.664924\pi$
$881$	−29.3997			−0.990501			−0.495251	+	0.868750i	$0.664924\pi$
$882$		0			0
$883$	−18.4705			−0.621582			−0.310791	−	0.950478i	$-0.600594\pi$
$883$	−18.4705			−0.621582			−0.310791	+	0.950478i	$0.600594\pi$
$884$		0			0
$885$	−41.7479	−	34.1135i	−1.40334	−	1.14671i
$886$		0			0
$887$	14.0631	−	24.3580i	0.472192	−	0.817860i	−0.527302	−	0.849678i	$-0.676796\pi$
$887$	14.0631	−	24.3580i	0.472192	−	0.817860i	0.999494	+	0.0318180i	$0.0101297\pi$
$888$		0			0
$889$	−4.90445	+	2.83158i	−0.164490	+	0.0949683i
$890$		0			0
$891$	2.90855	+	6.85650i	0.0974401	+	0.229702i
$892$		0			0
$893$	36.8889	+	63.8934i	1.23444	+	2.13811i
$894$		0			0
$895$	−46.3878	−	26.7820i	−1.55057	−	0.895223i
$896$		0			0
$897$	3.82004	+	14.2442i	0.127547	+	0.475600i
$898$		0			0
$899$			2.16832i			0.0723176i
$900$		0			0
$901$	−0.121154			−0.00403622
$902$		0			0
$903$	20.4525	+	3.33211i	0.680617	+	0.110886i
$904$		0			0
$905$	19.2962	+	11.1407i	0.641429	+	0.370329i
$906$		0			0
$907$	4.81770	+	8.34450i	0.159969	+	0.277075i	0.934857	−	0.355024i	$-0.115527\pi$
$907$	4.81770	+	8.34450i	0.159969	+	0.277075i	−0.774888	+	0.632098i	$0.782194\pi$
$908$		0			0
$909$	−42.0982	−	14.0913i	−1.39631	−	0.467378i
$910$		0			0
$911$	−13.3962	−	23.2030i	−0.443837	−	0.768749i	0.554133	−	0.832428i	$-0.313050\pi$
$911$	−13.3962	−	23.2030i	−0.443837	−	0.768749i	−0.997970	+	0.0636793i	$0.979717\pi$
$912$		0			0
$913$	−4.35971	+	7.55123i	−0.144285	+	0.249909i
$914$		0			0
$915$	0.769291	+	2.03086i	0.0254320	+	0.0671383i
$916$		0			0
$917$			22.0770i			0.729047i
$918$		0			0
$919$	−18.0185			−0.594375			−0.297188	−	0.954819i	$-0.596049\pi$
$919$	−18.0185			−0.594375			−0.297188	+	0.954819i	$0.596049\pi$
$920$		0			0
$921$	4.61326	+	12.1786i	0.152012	+	0.401299i
$922$		0			0
$923$	9.11705	+	20.2242i	0.300091	+	0.665689i
$924$		0			0
$925$	−12.9418	+	7.47194i	−0.425523	+	0.245676i
$926$		0			0
$927$	4.40987	+	21.6880i	0.144839	+	0.712327i
$928$		0			0
$929$	21.6927	−	12.5243i	0.711716	−	0.410909i	−0.0999803	−	0.994989i	$-0.531878\pi$
$929$	21.6927	−	12.5243i	0.711716	−	0.410909i	0.811696	+	0.584080i	$0.198545\pi$
$930$		0			0
$931$	41.2705	+	23.8275i	1.35259	+	0.780916i
$932$		0			0
$933$	−0.206818	+	1.26945i	−0.00677092	+	0.0415599i
$934$		0			0
$935$	0.131361			0.00429597
$936$		0			0
$937$	31.9869			1.04497			0.522483	−	0.852650i	$-0.325006\pi$
$937$	31.9869			1.04497			0.522483	+	0.852650i	$0.325006\pi$
$938$		0			0
$939$	−1.37259	−	1.12158i	−0.0447927	−	0.0366015i
$940$		0			0
$941$	28.3105	+	16.3451i	0.922897	+	0.532835i	0.884558	−	0.466430i	$-0.154460\pi$
$941$	28.3105	+	16.3451i	0.922897	+	0.532835i	0.0383385	+	0.999265i	$0.487793\pi$
$942$		0			0
$943$	−17.7996	+	10.2766i	−0.579635	+	0.334652i
$944$		0			0
$945$	−7.84546	+	14.9055i	−0.255213	+	0.484876i
$946$		0			0
$947$	−5.96037	+	3.44122i	−0.193686	+	0.111825i	−0.593707	−	0.804681i	$-0.702336\pi$
$947$	−5.96037	+	3.44122i	−0.193686	+	0.111825i	0.400021	+	0.916506i	$0.369003\pi$
$948$		0			0
$949$	−12.5282	−	27.7911i	−0.406682	−	0.902138i
$950$		0			0
$951$	3.09113	−	3.78291i	0.100237	−	0.122669i
$952$		0			0
$953$	−9.64310			−0.312371			−0.156185	−	0.987728i	$-0.549920\pi$
$953$	−9.64310			−0.312371			−0.156185	+	0.987728i	$0.549920\pi$
$954$		0			0
$955$			70.9177i			2.29484i
$956$		0			0
$957$	7.55508	+	1.23087i	0.244221	+	0.0397884i
$958$		0			0
$959$	−7.58008	+	13.1291i	−0.244773	+	0.423960i
$960$		0			0
$961$	−15.4176	−	26.7040i	−0.497341	−	0.861420i
$962$		0			0
$963$	4.58803	−	4.05820i	0.147847	−	0.130774i
$964$		0			0
$965$	23.4108	+	40.5486i	0.753619	+	1.30531i
$966$		0			0
$967$	16.7187	+	9.65256i	0.537638	+	0.310405i	0.744121	−	0.668045i	$-0.232869\pi$
$967$	16.7187	+	9.65256i	0.537638	+	0.310405i	−0.206483	+	0.978450i	$0.566202\pi$
$968$		0			0
$969$	−0.295256	−	0.779450i	−0.00948498	−	0.0250395i
$970$		0			0
$971$	−19.4628			−0.624592			−0.312296	−	0.949985i	$-0.601098\pi$
$971$	−19.4628			−0.624592			−0.312296	+	0.949985i	$0.601098\pi$
$972$		0			0
$973$		−	7.38183i		−	0.236651i
$974$		0			0
$975$	16.6181	+	4.44894i	0.532206	+	0.142480i
$976$		0			0
$977$	−41.4347	−	23.9223i	−1.32561	−	0.765343i	−0.340996	−	0.940065i	$-0.610764\pi$
$977$	−41.4347	−	23.9223i	−1.32561	−	0.765343i	−0.984618	+	0.174722i	$0.944097\pi$
$978$		0			0
$979$	2.17106	+	3.76038i	0.0693873	+	0.120182i
$980$		0			0
$981$	21.8204	+	24.6692i	0.696672	+	0.787627i
$982$		0			0
$983$	54.1819	−	31.2819i	1.72813	−	0.997739i	0.830460	−	0.557079i	$-0.188078\pi$
$983$	54.1819	−	31.2819i	1.72813	−	0.997739i	0.897674	−	0.440660i	$-0.145256\pi$
$984$		0			0
$985$	−35.3134	+	61.1646i	−1.12518	+	1.94887i
$986$		0			0
$987$	−2.83336	+	17.3912i	−0.0901869	+	0.553567i
$988$		0			0
$989$	−24.2705			−0.771756
$990$		0			0
$991$	−20.8223			−0.661441			−0.330720	−	0.943729i	$-0.607292\pi$
$991$	−20.8223			−0.661441			−0.330720	+	0.943729i	$0.607292\pi$
$992$		0			0
$993$	−28.7050	+	35.1290i	−0.910925	+	1.11479i
$994$		0			0
$995$	−22.4018	−	12.9337i	−0.710186	−	0.410026i
$996$		0			0
$997$	4.26438	+	7.38612i	0.135054	+	0.233921i	0.925618	−	0.378459i	$-0.123546\pi$
$997$	4.26438	+	7.38612i	0.135054	+	0.233921i	−0.790564	+	0.612379i	$0.790212\pi$
$998$		0			0
$999$	24.9438	+	13.1291i	0.789186	+	0.415385i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	468.2.bl.b.337.11	yes	24
3.2	odd	2		1404.2.bl.b.1117.11		24
9.2	odd	6		1404.2.bl.b.181.2		24
9.4	even	3		4212.2.b.g.649.11		12
9.5	odd	6		4212.2.b.h.649.2		12
9.7	even	3	inner	468.2.bl.b.25.12	yes	24
13.12	even	2	inner	468.2.bl.b.337.12	yes	24
39.38	odd	2		1404.2.bl.b.1117.2		24
117.25	even	6	inner	468.2.bl.b.25.11	✓	24
117.38	odd	6		1404.2.bl.b.181.11		24
117.77	odd	6		4212.2.b.h.649.11		12
117.103	even	6		4212.2.b.g.649.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
468.2.bl.b.25.11	✓	24	117.25	even	6	inner
468.2.bl.b.25.12	yes	24	9.7	even	3	inner
468.2.bl.b.337.11	yes	24	1.1	even	1	trivial
468.2.bl.b.337.12	yes	24	13.12	even	2	inner
1404.2.bl.b.181.2		24	9.2	odd	6
1404.2.bl.b.181.11		24	117.38	odd	6
1404.2.bl.b.1117.2		24	39.38	odd	2
1404.2.bl.b.1117.11		24	3.2	odd	2
4212.2.b.g.649.2		12	117.103	even	6
4212.2.b.g.649.11		12	9.4	even	3
4212.2.b.h.649.2		12	9.5	odd	6
4212.2.b.h.649.11		12	117.77	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	468.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.61974 - 0.613557i) q^{3} +(-2.41165 - 1.39237i) q^{5} +(1.00812 - 0.582041i) q^{7} +(2.24710 - 1.98760i) q^{9} +(-0.716675 + 0.413773i) q^{11} +(3.28700 - 1.48177i) q^{13} +(-4.76054 - 0.775584i) q^{15} +0.0570022 q^{17} -8.44213i q^{19} +(1.27578 - 1.56130i) q^{21} +(-1.18075 + 2.04511i) q^{23} +(1.37737 + 2.38568i) q^{25} +(2.42020 - 4.59811i) q^{27} +(-2.67021 - 4.62494i) q^{29} +(-0.351625 - 0.203011i) q^{31} +(-0.906952 + 1.10992i) q^{33} -3.24166 q^{35} +5.42478i q^{37} +(4.41492 - 4.41684i) q^{39} +(7.53743 + 4.35174i) q^{41} +(5.13879 + 8.90065i) q^{43} +(-8.18668 + 1.66462i) q^{45} +(-7.56840 + 4.36962i) q^{47} +(-2.82246 + 4.88864i) q^{49} +(0.0923285 - 0.0349741i) q^{51} -2.12542 q^{53} +2.30449 q^{55} +(-5.17973 - 13.6740i) q^{57} +(9.68012 + 5.58882i) q^{59} +(-0.225124 - 0.389927i) q^{61} +(1.10849 - 3.31165i) q^{63} +(-9.99026 - 1.00319i) q^{65} +(8.02892 + 4.63550i) q^{67} +(-0.657706 + 4.03700i) q^{69} +6.15280i q^{71} -8.45487i q^{73} +(3.69473 + 3.01907i) q^{75} +(-0.481665 + 0.834269i) q^{77} +(4.40104 + 7.62283i) q^{79} +(1.09888 - 8.93266i) q^{81} +(9.12486 - 5.26824i) q^{83} +(-0.137469 - 0.0793679i) q^{85} +(-7.16270 - 5.85286i) q^{87} -5.24698i q^{89} +(2.45125 - 3.40698i) q^{91} +(-0.694098 - 0.113082i) q^{93} +(-11.7545 + 20.3595i) q^{95} +(0.0761512 - 0.0439659i) q^{97} +(-0.788023 + 2.35425i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{3} + 2 q^{9} + 5 q^{13} - 4 q^{17} - 22 q^{23} + 16 q^{25} - 18 q^{27} + 22 q^{29} + 8 q^{35} + 37 q^{39} - 2 q^{43} + 22 q^{49} - 38 q^{51} - 12 q^{53} + 48 q^{55} + 8 q^{61} - q^{65} - 26 q^{69}+ \cdots - 48 q^{95}+O(q^{100}) \) 24 * q - 6 * q^3 + 2 * q^9 + 5 * q^13 - 4 * q^17 - 22 * q^23 + 16 * q^25 - 18 * q^27 + 22 * q^29 + 8 * q^35 + 37 * q^39 - 2 * q^43 + 22 * q^49 - 38 * q^51 - 12 * q^53 + 48 * q^55 + 8 * q^61 - q^65 - 26 * q^69 - 64 * q^75 - 24 * q^77 - 8 * q^79 + 2 * q^81 - 40 * q^87 + 22 * q^91 - 48 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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