LMFDB - Embedded newform 456.2.bm.a.41.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [456,2,Mod(41,456)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(456, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 9, 13])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("456.41"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bm (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.9
Character	$\chi$	$=$	456.41
Dual form			456.2.bm.a.89.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.68394 - 0.405410i) q^{3} +(3.00241 + 0.529406i) q^{5} +(-0.251171 - 0.435040i) q^{7} +(2.67129 - 1.36537i) q^{9} +(-2.58513 - 1.49253i) q^{11} +(0.364767 - 1.00219i) q^{13} +(5.27050 - 0.325721i) q^{15} +(-0.866390 + 1.03252i) q^{17} +(1.71910 + 4.00558i) q^{19} +(-0.599325 - 0.630754i) q^{21} +(-8.83018 + 1.55700i) q^{23} +(4.03575 + 1.46889i) q^{25} +(3.94474 - 3.38216i) q^{27} +(-3.43732 + 2.88425i) q^{29} +(3.58316 - 2.06874i) q^{31} +(-4.95829 - 1.46528i) q^{33} +(-0.523805 - 1.43914i) q^{35} -1.40145i q^{37} +(0.207947 - 1.83550i) q^{39} +(4.19152 - 1.52559i) q^{41} +(-0.539473 + 3.05951i) q^{43} +(8.74314 - 2.68521i) q^{45} +(-1.56889 - 1.86974i) q^{47} +(3.37383 - 5.84364i) q^{49} +(-1.04035 + 2.08995i) q^{51} +(1.97942 + 11.2258i) q^{53} +(-6.97149 - 5.84977i) q^{55} +(4.51876 + 6.04821i) q^{57} +(-8.56486 - 7.18677i) q^{59} +(1.52156 + 8.62918i) q^{61} +(-1.26494 - 0.819177i) q^{63} +(1.62575 - 2.81587i) q^{65} +(-6.94344 - 8.27486i) q^{67} +(-14.2382 + 6.20173i) q^{69} +(-2.02777 + 11.5000i) q^{71} +(9.45460 - 3.44119i) q^{73} +(7.39144 + 0.837389i) q^{75} +1.49952i q^{77} +(0.310339 + 0.852649i) q^{79} +(5.27153 - 7.29458i) q^{81} +(6.19637 - 3.57748i) q^{83} +(-3.14788 + 2.64139i) q^{85} +(-4.61892 + 6.25042i) q^{87} +(-13.7483 - 5.00398i) q^{89} +(-0.527611 + 0.0930321i) q^{91} +(5.19513 - 4.93627i) q^{93} +(3.04087 + 12.9365i) q^{95} +(-9.45707 + 11.2705i) q^{97} +(-8.94348 - 0.457306i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 3 q^{3} - 3 q^{9} + 3 q^{13} - 9 q^{15} + 6 q^{17} + 3 q^{19} + 6 q^{25} + 6 q^{27} - 6 q^{29} + 45 q^{33} - 24 q^{35} + 18 q^{39} - 3 q^{41} - 21 q^{43} - 45 q^{45} + 18 q^{47} - 30 q^{49} - 6 q^{51}+ \cdots - 3 q^{99}+O(q^{100}) $ 60 * q - 3 * q^3 - 3 * q^9 + 3 * q^13 - 9 * q^15 + 6 * q^17 + 3 * q^19 + 6 * q^25 + 6 * q^27 - 6 * q^29 + 45 * q^33 - 24 * q^35 + 18 * q^39 - 3 * q^41 - 21 * q^43 - 45 * q^45 + 18 * q^47 - 30 * q^49 - 6 * q^51 + 36 * q^53 + 18 * q^55 + 48 * q^57 + 21 * q^59 - 6 * q^61 + 78 * q^63 - 24 * q^65 - 48 * q^67 + 21 * q^69 - 36 * q^71 - 57 * q^73 - 36 * q^79 - 39 * q^81 + 36 * q^83 + 6 * q^85 - 90 * q^87 + 24 * q^89 - 18 * q^91 - 54 * q^93 - 30 * q^95 + 15 * q^97 - 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.68394	−	0.405410i	0.972221	−	0.234064i
$3$	1.68394	−	0.405410i	0.972221	−	0.234064i
$4$		0			0
$5$	3.00241	+	0.529406i	1.34272	+	0.236758i	0.798404	−	0.602123i	$-0.205678\pi$
$5$	3.00241	+	0.529406i	1.34272	+	0.236758i	0.544316	+	0.838880i	$0.316789\pi$
$6$		0			0
$7$	−0.251171	−	0.435040i	−0.0949336	−	0.164430i	0.814647	−	0.579957i	$-0.196931\pi$
$7$	−0.251171	−	0.435040i	−0.0949336	−	0.164430i	−0.909581	+	0.415527i	$0.863597\pi$
$8$		0			0
$9$	2.67129	−	1.36537i	0.890429	−	0.455123i
$10$		0			0
$11$	−2.58513	−	1.49253i	−0.779447	−	0.450014i	0.0567871	−	0.998386i	$-0.481914\pi$
$11$	−2.58513	−	1.49253i	−0.779447	−	0.450014i	−0.836234	+	0.548372i	$0.815248\pi$
$12$		0			0
$13$	0.364767	−	1.00219i	0.101168	−	0.277957i	−0.878774	−	0.477237i	$-0.841638\pi$
$13$	0.364767	−	1.00219i	0.101168	−	0.277957i	0.979943	+	0.199280i	$0.0638604\pi$
$14$		0			0
$15$	5.27050	−	0.325721i	1.36084	−	0.0841008i
$16$		0			0
$17$	−0.866390	+	1.03252i	−0.210130	+	0.250424i	−0.860807	−	0.508931i	$-0.830041\pi$
$17$	−0.866390	+	1.03252i	−0.210130	+	0.250424i	0.650677	+	0.759355i	$0.274485\pi$
$18$		0			0
$19$	1.71910	+	4.00558i	0.394389	+	0.918944i
$19$	1.71910	+	4.00558i	0.394389	+	0.918944i
$20$		0			0
$21$	−0.599325	−	0.630754i	−0.130784	−	0.137642i
$22$		0			0
$23$	−8.83018	+	1.55700i	−1.84122	+	0.324657i	−0.982280	−	0.187419i	$-0.939988\pi$
$23$	−8.83018	+	1.55700i	−1.84122	+	0.324657i	−0.858940	+	0.512076i	$0.828877\pi$
$24$		0			0
$25$	4.03575	+	1.46889i	0.807149	+	0.293778i
$26$		0			0
$27$	3.94474	−	3.38216i	0.759166	−	0.650897i
$28$		0			0
$29$	−3.43732	+	2.88425i	−0.638294	+	0.535592i	−0.903494	−	0.428601i	$-0.859007\pi$
$29$	−3.43732	+	2.88425i	−0.638294	+	0.535592i	0.265200	+	0.964193i	$0.414562\pi$
$30$		0			0
$31$	3.58316	−	2.06874i	0.643555	−	0.371556i	−0.142428	−	0.989805i	$-0.545491\pi$
$31$	3.58316	−	2.06874i	0.643555	−	0.371556i	0.785983	+	0.618249i	$0.212158\pi$
$32$		0			0
$33$	−4.95829	−	1.46528i	−0.863127	−	0.255073i
$34$		0			0
$35$	−0.523805	−	1.43914i	−0.0885392	−	0.243259i
$36$		0			0
$37$		−	1.40145i		−	0.230397i	−0.993342	−	0.115199i	$-0.963250\pi$
$37$		−	1.40145i		−	0.230397i	0.993342	−	0.115199i	$-0.0367504\pi$
$38$		0			0
$39$	0.207947	−	1.83550i	0.0332982	−	0.293916i
$40$		0			0
$41$	4.19152	−	1.52559i	0.654605	−	0.238257i	0.00669960	−	0.999978i	$-0.497867\pi$
$41$	4.19152	−	1.52559i	0.654605	−	0.238257i	0.647905	+	0.761721i	$0.275645\pi$
$42$		0			0
$43$	−0.539473	+	3.05951i	−0.0822689	+	0.466570i	0.915644	+	0.401991i	$0.131682\pi$
$43$	−0.539473	+	3.05951i	−0.0822689	+	0.466570i	−0.997913	+	0.0645793i	$0.979429\pi$
$44$		0			0
$45$	8.74314	−	2.68521i	1.30335	−	0.400287i
$46$		0			0
$47$	−1.56889	−	1.86974i	−0.228847	−	0.272729i	0.639386	−	0.768886i	$-0.279189\pi$
$47$	−1.56889	−	1.86974i	−0.228847	−	0.272729i	−0.868233	+	0.496157i	$0.834744\pi$
$48$		0			0
$49$	3.37383	−	5.84364i	0.481975	−	0.834806i
$50$		0			0
$51$	−1.04035	+	2.08995i	−0.145678	+	0.292651i
$52$		0			0
$53$	1.97942	+	11.2258i	0.271894	+	1.54199i	0.748659	+	0.662956i	$0.230698\pi$
$53$	1.97942	+	11.2258i	0.271894	+	1.54199i	−0.476765	+	0.879031i	$0.658191\pi$
$54$		0			0
$55$	−6.97149	−	5.84977i	−0.940035	−	0.788783i
$56$		0			0
$57$	4.51876	+	6.04821i	0.598524	+	0.801105i
$58$		0			0
$59$	−8.56486	−	7.18677i	−1.11505	−	0.935638i	−0.116706	−	0.993166i	$-0.537234\pi$
$59$	−8.56486	−	7.18677i	−1.11505	−	0.935638i	−0.998344	+	0.0575285i	$0.981678\pi$
$60$		0			0
$61$	1.52156	+	8.62918i	0.194816	+	1.10485i	0.912681	+	0.408672i	$0.134008\pi$
$61$	1.52156	+	8.62918i	0.194816	+	1.10485i	−0.717866	+	0.696182i	$0.754881\pi$
$62$		0			0
$63$	−1.26494	−	0.819177i	−0.159367	−	0.103207i
$64$		0			0
$65$	1.62575	−	2.81587i	0.201649	−	0.349266i
$66$		0			0
$67$	−6.94344	−	8.27486i	−0.848276	−	1.01094i	−0.999747	−	0.0224739i	$-0.992846\pi$
$67$	−6.94344	−	8.27486i	−0.848276	−	1.01094i	0.151472	−	0.988462i	$-0.451599\pi$
$68$		0			0
$69$	−14.2382	+	6.20173i	−1.71408	+	0.746601i
$70$		0			0
$71$	−2.02777	+	11.5000i	−0.240652	+	1.36480i	0.589726	+	0.807604i	$0.299236\pi$
$71$	−2.02777	+	11.5000i	−0.240652	+	1.36480i	−0.830378	+	0.557201i	$0.811875\pi$
$72$		0			0
$73$	9.45460	−	3.44119i	1.10658	−	0.402761i	0.276841	−	0.960916i	$-0.410713\pi$
$73$	9.45460	−	3.44119i	1.10658	−	0.402761i	0.829737	+	0.558155i	$0.188490\pi$
$74$		0			0
$75$	7.39144	+	0.837389i	0.853490	+	0.0966933i
$76$		0			0
$77$			1.49952i			0.170886i
$78$		0			0
$79$	0.310339	+	0.852649i	0.0349159	+	0.0959306i	0.955926	−	0.293609i	$-0.0948564\pi$
$79$	0.310339	+	0.852649i	0.0349159	+	0.0959306i	−0.921010	+	0.389540i	$0.872634\pi$
$80$		0			0
$81$	5.27153	−	7.29458i	0.585726	−	0.810509i
$82$		0			0
$83$	6.19637	−	3.57748i	0.680140	−	0.392679i	−0.119768	−	0.992802i	$-0.538215\pi$
$83$	6.19637	−	3.57748i	0.680140	−	0.392679i	0.799908	+	0.600123i	$0.204882\pi$
$84$		0			0
$85$	−3.14788	+	2.64139i	−0.341436	+	0.286499i
$86$		0			0
$87$	−4.61892	+	6.25042i	−0.495200	+	0.670116i
$88$		0			0
$89$	−13.7483	−	5.00398i	−1.45732	−	0.530421i	−0.512695	−	0.858571i	$-0.671353\pi$
$89$	−13.7483	−	5.00398i	−1.45732	−	0.530421i	−0.944626	+	0.328150i	$0.893575\pi$
$90$		0			0
$91$	−0.527611	+	0.0930321i	−0.0553087	+	0.00975242i
$92$		0			0
$93$	5.19513	−	4.93627i	0.538710	−	0.511868i
$94$		0			0
$95$	3.04087	+	12.9365i	0.311986	+	1.32726i
$96$		0			0
$97$	−9.45707	+	11.2705i	−0.960220	+	1.14435i	0.0292448	+	0.999572i	$0.490690\pi$
$97$	−9.45707	+	11.2705i	−0.960220	+	1.14435i	−0.989465	+	0.144773i	$0.953755\pi$
$98$		0			0
$99$	−8.94348	−	0.457306i	−0.898854	−	0.0459610i
$100$		0			0
$101$	−1.48369	+	4.07641i	−0.147633	+	0.405618i	−0.991362	−	0.131151i	$-0.958133\pi$
$101$	−1.48369	+	4.07641i	−0.147633	+	0.405618i	0.843730	+	0.536768i	$0.180355\pi$
$102$		0			0
$103$	−9.42665	−	5.44248i	−0.928836	−	0.536263i	−0.0423924	−	0.999101i	$-0.513498\pi$
$103$	−9.42665	−	5.44248i	−0.928836	−	0.536263i	−0.886443	+	0.462838i	$0.846831\pi$
$104$		0			0
$105$	−1.46550	−	2.21107i	−0.143018	−	0.215778i
$106$		0			0
$107$	−0.00726143	−	0.0125772i	−0.000701989	−	0.00121588i	0.865674	−	0.500608i	$-0.166890\pi$
$107$	−0.00726143	−	0.0125772i	−0.000701989	−	0.00121588i	−0.866376	+	0.499392i	$0.833557\pi$
$108$		0			0
$109$	2.18035	+	0.384455i	0.208840	+	0.0368241i	0.277089	−	0.960844i	$-0.410630\pi$
$109$	2.18035	+	0.384455i	0.208840	+	0.0368241i	−0.0682494	+	0.997668i	$0.521741\pi$
$110$		0			0
$111$	−0.568162	−	2.35995i	−0.0539276	−	0.223997i
$112$		0			0
$113$	2.29809			0.216186			0.108093	−	0.994141i	$-0.465526\pi$
$113$	2.29809			0.216186			0.108093	+	0.994141i	$0.465526\pi$
$114$		0			0
$115$	−27.3361			−2.54911
$116$		0			0
$117$	−0.393961	−	3.17517i	−0.0364217	−	0.293545i
$118$		0			0
$119$	0.666801	+	0.117575i	0.0611256	+	0.0107781i
$120$		0			0
$121$	−1.04472	−	1.80951i	−0.0949746	−	0.164501i
$122$		0			0
$123$	6.43976	−	4.26828i	0.580654	−	0.384857i
$124$		0			0
$125$	−1.86205	−	1.07506i	−0.166547	−	0.0961561i
$126$		0			0
$127$	−4.01211	+	11.0232i	−0.356018	+	0.978150i	0.624380	+	0.781121i	$0.285352\pi$
$127$	−4.01211	+	11.0232i	−0.356018	+	0.978150i	−0.980398	+	0.197029i	$0.936871\pi$
$128$		0			0
$129$	0.331915	+	5.37072i	0.0292235	+	0.472866i
$130$		0			0
$131$	6.67229	−	7.95173i	0.582961	−	0.694745i	−0.391276	−	0.920273i	$-0.627966\pi$
$131$	6.67229	−	7.95173i	0.582961	−	0.694745i	0.974237	+	0.225528i	$0.0724107\pi$
$132$		0			0
$133$	1.31080	−	1.75396i	0.113661	−	0.152088i
$134$		0			0
$135$	13.6343	−	8.06627i	1.17345	−	0.694234i
$136$		0			0
$137$	−12.8792	+	2.27095i	−1.10034	+	0.194020i	−0.694195	−	0.719787i	$-0.744240\pi$
$137$	−12.8792	+	2.27095i	−1.10034	+	0.194020i	−0.406148	+	0.913807i	$0.633128\pi$
$138$		0			0
$139$	12.6952	+	4.62068i	1.07679	+	0.391921i	0.818714	−	0.574202i	$-0.194688\pi$
$139$	12.6952	+	4.62068i	1.07679	+	0.391921i	0.258081	+	0.966123i	$0.416910\pi$
$140$		0			0
$141$	−3.39993	−	2.51247i	−0.286326	−	0.211588i
$142$		0			0
$143$	−2.43877	+	2.04637i	−0.203940	+	0.171126i
$144$		0			0
$145$	−11.8472	+	6.83998i	−0.983855	+	0.568029i
$146$		0			0
$147$	3.31224	−	11.2081i	0.273189	−	0.924429i
$148$		0			0
$149$	−6.94182	−	19.0725i	−0.568696	−	1.56248i	−0.806542	−	0.591176i	$-0.798664\pi$
$149$	−6.94182	−	19.0725i	−0.568696	−	1.56248i	0.237846	−	0.971303i	$-0.423559\pi$
$150$		0			0
$151$			23.4871i			1.91135i	0.294424	+	0.955675i	$0.404872\pi$
$151$			23.4871i			1.91135i	−0.294424	+	0.955675i	$0.595128\pi$
$152$		0			0
$153$	−0.904600	+	3.94111i	−0.0731325	+	0.318620i
$154$		0			0
$155$	11.8533	−	4.31426i	0.952082	−	0.346530i
$156$		0			0
$157$	3.34127	−	18.9493i	0.266662	−	1.51232i	−0.497597	−	0.867409i	$-0.665784\pi$
$157$	3.34127	−	18.9493i	0.266662	−	1.51232i	0.764259	−	0.644909i	$-0.223105\pi$
$158$		0			0
$159$	7.88428	+	18.1011i	0.625264	+	1.43551i
$160$		0			0
$161$	2.89524	+	3.45041i	0.228177	+	0.271931i
$162$		0			0
$163$	9.17668	−	15.8945i	0.718773	−	1.24495i	−0.242714	−	0.970098i	$-0.578038\pi$
$163$	9.17668	−	15.8945i	0.718773	−	1.24495i	0.961486	−	0.274853i	$-0.0886292\pi$
$164$		0			0
$165$	−14.1111	−	7.02433i	−1.09855	−	0.546844i
$166$		0			0
$167$	1.00462	+	5.69749i	0.0777399	+	0.440885i	0.998688	+	0.0512005i	$0.0163047\pi$
$167$	1.00462	+	5.69749i	0.0777399	+	0.440885i	−0.920949	+	0.389684i	$0.872584\pi$
$168$		0			0
$169$	9.08725	+	7.62511i	0.699019	+	0.586547i
$170$		0			0
$171$	10.0613	+	8.35285i	0.769407	+	0.638758i
$172$		0			0
$173$	6.03354	+	5.06274i	0.458722	+	0.384913i	0.842660	−	0.538445i	$-0.180988\pi$
$173$	6.03354	+	5.06274i	0.458722	+	0.384913i	−0.383939	+	0.923359i	$0.625433\pi$
$174$		0			0
$175$	−0.374634	−	2.12465i	−0.0283197	−	0.160609i
$176$		0			0
$177$	−17.3363	−	8.62979i	−1.30307	−	0.648655i
$178$		0			0
$179$	−1.55348	+	2.69071i	−0.116113	+	0.201113i	−0.918224	−	0.396062i	$-0.870377\pi$
$179$	−1.55348	+	2.69071i	−0.116113	+	0.201113i	0.802111	+	0.597174i	$0.203710\pi$
$180$		0			0
$181$	−13.0813	−	15.5897i	−0.972329	−	1.15878i	−0.987297	−	0.158888i	$-0.949209\pi$
$181$	−13.0813	−	15.5897i	−0.972329	−	1.15878i	0.0149680	−	0.999888i	$-0.495235\pi$
$182$		0			0
$183$	6.06056	+	13.9141i	0.448010	+	1.02856i
$184$		0			0
$185$	0.741937	−	4.20773i	0.0545483	−	0.309359i
$186$		0			0
$187$	3.78080	−	1.37610i	0.276480	−	0.100630i
$188$		0			0
$189$	−2.46218	−	0.866622i	−0.179097	−	0.0630375i
$190$		0			0
$191$		−	4.25429i		−	0.307829i	−0.988084	−	0.153915i	$-0.950812\pi$
$191$		−	4.25429i		−	0.307829i	0.988084	−	0.153915i	$-0.0491881\pi$
$192$		0			0
$193$	6.73569	+	18.5062i	0.484846	+	1.33210i	0.905294	+	0.424786i	$0.139651\pi$
$193$	6.73569	+	18.5062i	0.484846	+	1.33210i	−0.420448	+	0.907317i	$0.638127\pi$
$194$		0			0
$195$	1.59607	−	5.40085i	0.114297	−	0.386763i
$196$		0			0
$197$	−16.3958	+	9.46613i	−1.16815	+	0.674434i	−0.953245	−	0.302200i	$-0.902279\pi$
$197$	−16.3958	+	9.46613i	−1.16815	+	0.674434i	−0.214910	+	0.976634i	$0.568946\pi$
$198$		0			0
$199$	7.54426	−	6.33039i	0.534798	−	0.448749i	−0.334956	−	0.942234i	$-0.608722\pi$
$199$	7.54426	−	6.33039i	0.534798	−	0.448749i	0.869755	+	0.493485i	$0.164277\pi$
$200$		0			0
$201$	−15.0470	−	11.1194i	−1.06133	−	0.784303i
$202$		0			0
$203$	2.11812	+	0.770933i	0.148663	+	0.0541089i
$204$		0			0
$205$	13.3923	−	2.36143i	0.935360	−	0.164929i
$206$		0			0
$207$	−21.4621	+	16.2156i	−1.49172	+	1.12707i
$208$		0			0
$209$	1.53434	−	12.9208i	0.106133	−	0.893749i
$210$		0			0
$211$	4.12402	−	4.91482i	0.283909	−	0.338350i	−0.605176	−	0.796092i	$-0.706897\pi$
$211$	4.12402	−	4.91482i	0.283909	−	0.338350i	0.889085	+	0.457742i	$0.151342\pi$
$212$		0			0
$213$	1.24760	+	20.1874i	0.0854841	+	1.38322i
$214$		0			0
$215$	−3.23944	+	8.90030i	−0.220928	+	0.606995i
$216$		0			0
$217$	−1.79997	−	1.03921i	−0.122190	−	0.0705464i
$218$		0			0
$219$	14.5259	−	9.62774i	0.981567	−	0.650583i
$220$		0			0
$221$	0.718753	+	1.24492i	0.0483486	+	0.0837421i
$222$		0			0
$223$	12.6942	+	2.23832i	0.850064	+	0.149889i	0.581675	−	0.813421i	$-0.302398\pi$
$223$	12.6942	+	2.23832i	0.850064	+	0.149889i	0.268389	+	0.963311i	$0.413509\pi$
$224$		0			0
$225$	12.7862	−	1.58645i	0.852414	−	0.105764i
$226$		0			0
$227$	21.6249			1.43529			0.717646	−	0.696408i	$-0.245220\pi$
$227$	21.6249			1.43529			0.717646	+	0.696408i	$0.245220\pi$
$228$		0			0
$229$	10.4460			0.690294			0.345147	−	0.938549i	$-0.387829\pi$
$229$	10.4460			0.690294			0.345147	+	0.938549i	$0.387829\pi$
$230$		0			0
$231$	0.607919	+	2.52509i	0.0399981	+	0.166139i
$232$		0			0
$233$	13.5750	+	2.39364i	0.889330	+	0.156813i	0.599604	−	0.800297i	$-0.295325\pi$
$233$	13.5750	+	2.39364i	0.889330	+	0.156813i	0.289726	+	0.957110i	$0.406436\pi$
$234$		0			0
$235$	−3.72062	−	6.44430i	−0.242706	−	0.420380i
$236$		0			0
$237$	0.868264	+	1.30999i	0.0563998	+	0.0850932i
$238$		0			0
$239$	16.7801	+	9.68797i	1.08541	+	0.626663i	0.932351	−	0.361554i	$-0.117754\pi$
$239$	16.7801	+	9.68797i	1.08541	+	0.626663i	0.153061	+	0.988217i	$0.451087\pi$
$240$		0			0
$241$	8.64165	−	23.7427i	0.556657	−	1.52940i	−0.267797	−	0.963475i	$-0.586296\pi$
$241$	8.64165	−	23.7427i	0.556657	−	1.52940i	0.824454	−	0.565928i	$-0.191482\pi$
$242$		0			0
$243$	5.91963	−	14.4207i	0.379745	−	0.925091i
$244$		0			0
$245$	13.2233	−	15.7589i	0.844804	−	1.00680i
$246$		0			0
$247$	4.64142	−	0.261758i	0.295327	−	0.0166553i
$248$		0			0
$249$	8.98395	−	8.53632i	0.569335	−	0.540967i
$250$		0			0
$251$	18.4169	−	3.24740i	1.16247	−	0.204974i	0.441054	−	0.897480i	$-0.354605\pi$
$251$	18.4169	−	3.24740i	1.16247	−	0.204974i	0.721412	+	0.692506i	$0.243493\pi$
$252$		0			0
$253$	25.1511	+	9.15424i	1.58123	+	0.575522i
$254$		0			0
$255$	−4.22999	+	5.72411i	−0.264892	+	0.358458i
$256$		0			0
$257$	6.22334	−	5.22200i	0.388201	−	0.325739i	−0.427711	−	0.903916i	$-0.640680\pi$
$257$	6.22334	−	5.22200i	0.388201	−	0.325739i	0.815912	+	0.578176i	$0.196235\pi$
$258$		0			0
$259$	−0.609688	+	0.352003i	−0.0378842	+	0.0218724i
$260$		0			0
$261$	−5.24399	+	12.3979i	−0.324595	+	0.767409i
$262$		0			0
$263$	−3.43690	−	9.44282i	−0.211929	−	0.582269i	0.787491	−	0.616326i	$-0.211380\pi$
$263$	−3.43690	−	9.44282i	−0.211929	−	0.582269i	−0.999420	+	0.0340568i	$0.989157\pi$
$264$		0			0
$265$			34.7525i			2.13483i
$266$		0			0
$267$	−25.1800	−	2.85268i	−1.54099	−	0.174581i
$268$		0			0
$269$	3.82959	−	1.39386i	0.233494	−	0.0849850i	−0.222623	−	0.974905i	$-0.571462\pi$
$269$	3.82959	−	1.39386i	0.233494	−	0.0849850i	0.456117	+	0.889920i	$0.349240\pi$
$270$		0			0
$271$	0.785166	−	4.45290i	0.0476955	−	0.270494i	−0.951629	−	0.307250i	$-0.900591\pi$
$271$	0.785166	−	4.45290i	0.0476955	−	0.270494i	0.999324	+	0.0367557i	$0.0117023\pi$
$272$		0			0
$273$	−0.850748	+	0.370559i	−0.0514896	+	0.0224273i
$274$		0			0
$275$	−8.24058	−	9.82074i	−0.496926	−	0.592213i
$276$		0			0
$277$	11.8387	−	20.5052i	0.711317	−	1.23204i	−0.253046	−	0.967454i	$-0.581432\pi$
$277$	11.8387	−	20.5052i	0.711317	−	1.23204i	0.964363	−	0.264583i	$-0.0852344\pi$
$278$		0			0
$279$	6.74705	−	10.4185i	0.403936	−	0.623741i
$280$		0			0
$281$	−4.01031	−	22.7436i	−0.239235	−	1.35677i	−0.833508	−	0.552507i	$-0.813671\pi$
$281$	−4.01031	−	22.7436i	−0.239235	−	1.35677i	0.594273	−	0.804264i	$-0.297440\pi$
$282$		0			0
$283$	−6.38454	−	5.35727i	−0.379522	−	0.318457i	0.432993	−	0.901397i	$-0.357457\pi$
$283$	−6.38454	−	5.35727i	−0.379522	−	0.318457i	−0.812515	+	0.582941i	$0.801902\pi$
$284$		0			0
$285$	10.3652	+	20.5515i	0.613982	+	1.21736i
$286$		0			0
$287$	−1.71648	−	1.44030i	−0.101321	−	0.0850180i
$288$		0			0
$289$	2.63655	+	14.9526i	0.155091	+	0.879564i
$290$		0			0
$291$	−11.3559	+	22.8128i	−0.665697	+	1.33731i
$292$		0			0
$293$	4.06803	−	7.04603i	0.237657	−	0.411634i	−0.722385	−	0.691491i	$-0.756954\pi$
$293$	4.06803	−	7.04603i	0.237657	−	0.411634i	0.960041	+	0.279858i	$0.0902873\pi$
$294$		0			0
$295$	−21.9105	−	26.1119i	−1.27568	−	1.52030i
$296$		0			0
$297$	−15.2457	+	2.85570i	−0.884643	+	0.165705i
$298$		0			0
$299$	−1.66055	+	9.41745i	−0.0960321	+	0.544625i
$300$		0			0
$301$	1.46651	−	0.533766i	0.0845282	−	0.0307657i
$302$		0			0
$303$	−0.845826	+	7.46591i	−0.0485914	+	0.428905i
$304$		0			0
$305$			26.7139i			1.52963i
$306$		0			0
$307$	3.01020	+	8.27046i	0.171801	+	0.472020i	0.995473	−	0.0950472i	$-0.0303002\pi$
$307$	3.01020	+	8.27046i	0.171801	+	0.472020i	−0.823672	+	0.567067i	$0.808078\pi$
$308$		0			0
$309$	−18.0803	−	5.34313i	−1.02855	−	0.303960i
$310$		0			0
$311$	2.88199	−	1.66392i	0.163423	−	0.0943522i	−0.416058	−	0.909338i	$-0.636589\pi$
$311$	2.88199	−	1.66392i	0.163423	−	0.0943522i	0.579481	+	0.814986i	$0.303255\pi$
$312$		0			0
$313$	2.30378	−	1.93310i	0.130217	−	0.109265i	−0.575353	−	0.817905i	$-0.695135\pi$
$313$	2.30378	−	1.93310i	0.130217	−	0.109265i	0.705570	+	0.708640i	$0.250691\pi$
$314$		0			0
$315$	−3.36419	−	3.12917i	−0.189551	−	0.176309i
$316$		0			0
$317$	9.87705	+	3.59495i	0.554750	+	0.201913i	0.604156	−	0.796866i	$-0.293510\pi$
$317$	9.87705	+	3.59495i	0.554750	+	0.201913i	−0.0494055	+	0.998779i	$0.515733\pi$
$318$		0			0
$319$	13.1908	−	2.32589i	0.738541	−	0.130225i
$320$		0			0
$321$	−0.0173267	−	0.0182353i	−0.000967082	−	0.00101779i
$322$		0			0
$323$	−5.62527	−	1.69539i	−0.312998	−	0.0943338i
$324$		0			0
$325$	2.94421	−	3.50878i	0.163315	−	0.194632i
$326$		0			0
$327$	3.82744	−	0.236539i	0.211658	−	0.0130806i
$328$		0			0
$329$	−0.419350	+	1.15216i	−0.0231195	+	0.0635204i
$330$		0			0
$331$	12.2016	+	7.04460i	0.670660	+	0.387206i	0.796327	−	0.604867i	$-0.206774\pi$
$331$	12.2016	+	7.04460i	0.670660	+	0.387206i	−0.125666	+	0.992073i	$0.540107\pi$
$332$		0			0
$333$	−1.91350	−	3.74368i	−0.104859	−	0.205152i
$334$		0			0
$335$	−16.4663	−	28.5204i	−0.899649	−	1.55824i
$336$		0			0
$337$	−23.2737	−	4.10377i	−1.26780	−	0.223547i	−0.501006	−	0.865444i	$-0.667037\pi$
$337$	−23.2737	−	4.10377i	−1.26780	−	0.223547i	−0.766791	+	0.641897i	$0.778148\pi$
$338$		0			0
$339$	3.86984	−	0.931669i	0.210181	−	0.0506013i
$340$		0			0
$341$	−12.3506			−0.668823
$342$		0			0
$343$	−6.90602			−0.372890
$344$		0			0
$345$	−46.0323	+	11.0823i	−2.47830	+	0.596653i
$346$		0			0
$347$	−27.6393	−	4.87356i	−1.48376	−	0.261626i	−0.627679	−	0.778472i	$-0.715995\pi$
$347$	−27.6393	−	4.87356i	−1.48376	−	0.261626i	−0.856078	+	0.516846i	$0.827106\pi$
$348$		0			0
$349$	−6.13085	−	10.6190i	−0.328177	−	0.568419i	0.653973	−	0.756518i	$-0.273101\pi$
$349$	−6.13085	−	10.6190i	−0.328177	−	0.568419i	−0.982150	+	0.188098i	$0.939768\pi$
$350$		0			0
$351$	−1.95065	−	5.18708i	−0.104118	−	0.276866i
$352$		0			0
$353$	8.24176	+	4.75838i	0.438665	+	0.253263i	0.703031	−	0.711159i	$-0.251829\pi$
$353$	8.24176	+	4.75838i	0.438665	+	0.253263i	−0.264366	+	0.964422i	$0.585163\pi$
$354$		0			0
$355$	−12.1764	+	33.4544i	−0.646256	+	1.77557i
$356$		0			0
$357$	1.17052	−	0.0723389i	0.0619503	−	0.00382858i
$358$		0			0
$359$	−13.5098	+	16.1003i	−0.713018	+	0.849741i	−0.993933	−	0.109991i	$-0.964918\pi$
$359$	−13.5098	+	16.1003i	−0.713018	+	0.849741i	0.280915	+	0.959733i	$0.409362\pi$
$360$		0			0
$361$	−13.0894	+	13.7720i	−0.688915	+	0.724842i
$362$		0			0
$363$	−2.49284	−	2.62356i	−0.130840	−	0.137701i
$364$		0			0
$365$	30.2084	−	5.32656i	1.58118	−	0.278805i
$366$		0			0
$367$	−8.76232	−	3.18922i	−0.457389	−	0.166476i	0.103042	−	0.994677i	$-0.467142\pi$
$367$	−8.76232	−	3.18922i	−0.457389	−	0.166476i	−0.560431	+	0.828201i	$0.689365\pi$
$368$		0			0
$369$	9.11375	−	9.79825i	0.474443	−	0.510076i
$370$		0			0
$371$	4.38652	−	3.68073i	0.227737	−	0.191094i
$372$		0			0
$373$	−23.1689	+	13.3766i	−1.19964	+	0.692612i	−0.960475	−	0.278367i	$-0.910207\pi$
$373$	−23.1689	+	13.3766i	−1.19964	+	0.692612i	−0.239164	+	0.970979i	$0.576873\pi$
$374$		0			0
$375$	−3.57142	−	1.05543i	−0.184427	−	0.0545024i
$376$		0			0
$377$	1.63675	+	4.49692i	0.0842967	+	0.231603i
$378$		0			0
$379$			14.5951i			0.749702i	0.927085	+	0.374851i	$0.122306\pi$
$379$			14.5951i			0.749702i	−0.927085	+	0.374851i	$0.877694\pi$
$380$		0			0
$381$	−2.28723	+	20.1889i	−0.117179	+	1.03431i
$382$		0			0
$383$	8.09064	−	2.94475i	0.413412	−	0.150470i	−0.126937	−	0.991911i	$-0.540514\pi$
$383$	8.09064	−	2.94475i	0.413412	−	0.150470i	0.540349	+	0.841441i	$0.318292\pi$
$384$		0			0
$385$	−0.793854	+	4.50217i	−0.0404585	+	0.229452i
$386$		0			0
$387$	2.73627	+	8.90939i	0.139092	+	0.452890i
$388$		0			0
$389$	−6.90987	−	8.23486i	−0.350344	−	0.417524i	0.561878	−	0.827220i	$-0.310079\pi$
$389$	−6.90987	−	8.23486i	−0.350344	−	0.417524i	−0.912222	+	0.409696i	$0.865635\pi$
$390$		0			0
$391$	6.04274	−	10.4663i	0.305595	−	0.529305i
$392$		0			0
$393$	8.01201	−	16.0952i	0.404152	−	0.811896i
$394$		0			0
$395$	0.480368	+	2.72430i	0.0241699	+	0.137074i
$396$		0			0
$397$	−25.1589	−	21.1108i	−1.26269	−	1.05952i	−0.995390	−	0.0959094i	$-0.969424\pi$
$397$	−25.1589	−	21.1108i	−1.26269	−	1.05952i	−0.267300	−	0.963613i	$-0.586131\pi$
$398$		0			0
$399$	1.49624	−	3.48498i	0.0749055	−	0.174467i
$400$		0			0
$401$	28.2343	+	23.6914i	1.40995	+	1.18309i	0.956472	+	0.291823i	$0.0942618\pi$
$401$	28.2343	+	23.6914i	1.40995	+	1.18309i	0.453479	+	0.891267i	$0.350183\pi$
$402$		0			0
$403$	−0.766248	−	4.34561i	−0.0381695	−	0.216470i
$404$		0			0
$405$	19.6891	−	19.1106i	0.978360	−	0.949611i
$406$		0			0
$407$	−2.09170	+	3.62294i	−0.103682	+	0.179582i
$408$		0			0
$409$	−4.93171	−	5.87739i	−0.243858	−	0.290618i	0.630208	−	0.776427i	$-0.282970\pi$
$409$	−4.93171	−	5.87739i	−0.243858	−	0.290618i	−0.874065	+	0.485808i	$0.838525\pi$
$410$		0			0
$411$	−20.7671	+	9.04549i	−1.02436	+	0.446181i
$412$		0			0
$413$	−0.975294	+	5.53117i	−0.0479911	+	0.272171i
$414$		0			0
$415$	20.4980	−	7.46066i	1.00621	−	0.366230i
$416$		0			0
$417$	23.2512	+	2.63417i	1.13862	+	0.128996i
$418$		0			0
$419$		−	3.25003i		−	0.158774i	−0.996844	−	0.0793872i	$-0.974704\pi$
$419$		−	3.25003i		−	0.158774i	0.996844	−	0.0793872i	$-0.0252963\pi$
$420$		0			0
$421$	2.10684	+	5.78848i	0.102681	+	0.282113i	0.980386	−	0.197088i	$-0.0631485\pi$
$421$	2.10684	+	5.78848i	0.102681	+	0.282113i	−0.877705	+	0.479202i	$0.840926\pi$
$422$		0			0
$423$	−6.74385	−	2.85248i	−0.327897	−	0.138692i
$424$		0			0
$425$	−5.01319	+	2.89437i	−0.243176	+	0.140397i
$426$		0			0
$427$	3.37187	−	2.82934i	0.163176	−	0.136921i
$428$		0			0
$429$	−3.27711	+	4.43465i	−0.158220	+	0.214107i
$430$		0			0
$431$	27.3336	+	9.94860i	1.31661	+	0.479207i	0.902371	−	0.430960i	$-0.141825\pi$
$431$	27.3336	+	9.94860i	1.31661	+	0.479207i	0.414240	+	0.910168i	$0.364047\pi$
$432$		0			0
$433$	1.86446	−	0.328754i	0.0896001	−	0.0157989i	−0.128668	−	0.991688i	$-0.541070\pi$
$433$	1.86446	−	0.328754i	0.0896001	−	0.0157989i	0.218268	+	0.975889i	$0.429959\pi$
$434$		0			0
$435$	−17.1769	+	16.3211i	−0.823570	+	0.782535i
$436$		0			0
$437$	−21.4167	−	32.6934i	−1.02450	−	1.56394i
$438$		0			0
$439$	−16.4094	+	19.5560i	−0.783179	+	0.933357i	−0.999072	−	0.0430602i	$-0.986289\pi$
$439$	−16.4094	+	19.5560i	−0.783179	+	0.933357i	0.215893	+	0.976417i	$0.430734\pi$
$440$		0			0
$441$	1.03373	−	20.2165i	0.0492252	−	0.962693i
$442$		0			0
$443$	3.36718	−	9.25126i	0.159980	−	0.439541i	−0.833642	−	0.552305i	$-0.813748\pi$
$443$	3.36718	−	9.25126i	0.159980	−	0.439541i	0.993622	+	0.112764i	$0.0359705\pi$
$444$		0			0
$445$	−38.6290	−	22.3025i	−1.83119	−	1.05724i
$446$		0			0
$447$	−19.4218	−	29.3026i	−0.918618	−	1.38596i
$448$		0			0
$449$	4.70447	+	8.14838i	0.222018	+	0.384546i	0.955420	−	0.295249i	$-0.0954024\pi$
$449$	4.70447	+	8.14838i	0.222018	+	0.384546i	−0.733403	+	0.679794i	$0.762069\pi$
$450$		0			0
$451$	−13.1126	−	2.31211i	−0.617449	−	0.108873i
$452$		0			0
$453$	9.52189	+	39.5507i	0.447377	+	1.85825i
$454$		0			0
$455$	−1.63336			−0.0765730
$456$		0			0
$457$	−36.9364			−1.72781			−0.863906	−	0.503653i	$-0.831989\pi$
$457$	−36.9364			−1.72781			−0.863906	+	0.503653i	$0.831989\pi$
$458$		0			0
$459$	0.0744755	+	7.00331i	0.00347622	+	0.326886i
$460$		0			0
$461$	39.2642	+	6.92335i	1.82872	+	0.322452i	0.978856	−	0.204552i	$-0.0655738\pi$
$461$	39.2642	+	6.92335i	1.82872	+	0.322452i	0.849862	+	0.527004i	$0.176685\pi$
$462$		0			0
$463$	16.8000	+	29.0985i	0.780763	+	1.35232i	0.931498	+	0.363747i	$0.118503\pi$
$463$	16.8000	+	29.0985i	0.780763	+	1.35232i	−0.150735	+	0.988574i	$0.548164\pi$
$464$		0			0
$465$	18.2112	−	12.0704i	0.844525	−	0.559751i
$466$		0			0
$467$	19.8364	+	11.4526i	0.917920	+	0.529961i	0.882971	−	0.469428i	$-0.155540\pi$
$467$	19.8364	+	11.4526i	0.917920	+	0.529961i	0.0349490	+	0.999389i	$0.488873\pi$
$468$		0			0
$469$	−1.85591	+	5.09908i	−0.0856981	+	0.235454i
$470$		0			0
$471$	−2.05574	−	33.2640i	−0.0947235	−	1.53272i
$472$		0			0
$473$	5.96101	−	7.10405i	0.274087	−	0.326645i
$474$		0			0
$475$	1.05408	+	18.6907i	0.0483646	+	0.857587i
$476$		0			0
$477$	20.6150	+	27.2848i	0.943896	+	1.24928i
$478$		0			0
$479$	26.6499	−	4.69910i	1.21767	−	0.214707i	0.472345	−	0.881414i	$-0.343408\pi$
$479$	26.6499	−	4.69910i	1.21767	−	0.214707i	0.745320	+	0.666706i	$0.232297\pi$
$480$		0			0
$481$	−1.40452	−	0.511203i	−0.0640405	−	0.0233088i
$482$		0			0
$483$	6.27423	+	4.63652i	0.285488	+	0.210969i
$484$		0			0
$485$	−34.3607	+	28.8320i	−1.56024	+	1.30920i
$486$		0			0
$487$	−7.28099	+	4.20368i	−0.329933	+	0.190487i	−0.655811	−	0.754925i	$-0.727673\pi$
$487$	−7.28099	+	4.20368i	−0.329933	+	0.190487i	0.325878	+	0.945412i	$0.394340\pi$
$488$		0			0
$489$	9.00917	−	30.4856i	0.407409	−	1.37861i
$490$		0			0
$491$	−6.36016	−	17.4744i	−0.287030	−	0.788608i	−0.996478	−	0.0838507i	$-0.973278\pi$
$491$	−6.36016	−	17.4744i	−0.287030	−	0.788608i	0.709449	−	0.704757i	$-0.248944\pi$
$492$		0			0
$493$		−	6.04800i		−	0.272388i
$494$		0			0
$495$	−26.6099	−	6.10776i	−1.19603	−	0.274523i
$496$		0			0
$497$	5.51230	−	2.00631i	0.247261	−	0.0899955i
$498$		0			0
$499$	5.23041	−	29.6631i	0.234145	−	1.32790i	−0.610261	−	0.792201i	$-0.708935\pi$
$499$	5.23041	−	29.6631i	0.234145	−	1.32790i	0.844406	−	0.535704i	$-0.179954\pi$
$500$		0			0
$501$	4.00153	+	9.18692i	0.178775	+	0.410441i
$502$		0			0
$503$	−6.47202	−	7.71305i	−0.288573	−	0.343908i	0.602209	−	0.798338i	$-0.294287\pi$
$503$	−6.47202	−	7.71305i	−0.288573	−	0.343908i	−0.890782	+	0.454430i	$0.849843\pi$
$504$		0			0
$505$	−6.61273	+	11.4536i	−0.294262	+	0.509677i
$506$		0			0
$507$	18.3936	+	9.15614i	0.816891	+	0.406638i
$508$		0			0
$509$	−0.370885	−	2.10339i	−0.0164392	−	0.0932312i	0.975484	−	0.220069i	$-0.0706283\pi$
$509$	−0.370885	−	2.10339i	−0.0164392	−	0.0932312i	−0.991923	+	0.126838i	$0.959517\pi$
$510$		0			0
$511$	−3.87178	−	3.24881i	−0.171277	−	0.143719i
$512$		0			0
$513$	20.3289	+	9.98672i	0.897544	+	0.440924i
$514$		0			0
$515$	−25.4214	−	21.3311i	−1.12020	−	0.939960i
$516$		0			0
$517$	1.26517	+	7.17514i	0.0556421	+	0.315562i
$518$		0			0
$519$	12.2126	+	6.07928i	0.536073	+	0.266851i
$520$		0			0
$521$	−16.6879	+	28.9043i	−0.731109	+	1.26632i	0.225300	+	0.974289i	$0.427664\pi$
$521$	−16.6879	+	28.9043i	−0.731109	+	1.26632i	−0.956409	+	0.292029i	$0.905670\pi$
$522$		0			0
$523$	4.68360	+	5.58170i	0.204800	+	0.244071i	0.858661	−	0.512543i	$-0.171297\pi$
$523$	4.68360	+	5.58170i	0.204800	+	0.244071i	−0.653862	+	0.756614i	$0.726852\pi$
$524$		0			0
$525$	−1.49222	−	3.42590i	−0.0651256	−	0.149519i
$526$		0			0
$527$	−0.968393	+	5.49203i	−0.0421839	+	0.239237i
$528$		0			0
$529$	53.9349	−	19.6307i	2.34500	−	0.853509i
$530$		0			0
$531$	−32.6918	−	7.50372i	−1.41870	−	0.325634i
$532$		0			0
$533$		−	4.75717i		−	0.206056i
$534$		0			0
$535$	−0.0151434	−	0.0416061i	−0.000654705	−	0.00179879i
$536$		0			0
$537$	−1.52512	+	5.16077i	−0.0658139	+	0.222704i
$538$		0			0
$539$	−17.4436	+	10.0711i	−0.751349	+	0.433791i
$540$		0			0
$541$	1.84017	−	1.54409i	0.0791152	−	0.0663855i	−0.602372	−	0.798215i	$-0.705778\pi$
$541$	1.84017	−	1.54409i	0.0791152	−	0.0663855i	0.681488	+	0.731830i	$0.261333\pi$
$542$		0			0
$543$	−28.3484	−	20.9488i	−1.21655	−	0.899000i
$544$		0			0
$545$	6.34278	+	2.30858i	0.271695	+	0.0988889i
$546$		0			0
$547$	−33.0653	+	5.83030i	−1.41377	+	0.249286i	−0.827789	−	0.561040i	$-0.810402\pi$
$547$	−33.0653	+	5.83030i	−1.41377	+	0.249286i	−0.585980	+	0.810325i	$0.699290\pi$
$548$		0			0
$549$	15.8465	+	20.9735i	0.676314	+	0.895128i
$550$		0			0
$551$	−17.4622	−	8.81015i	−0.743915	−	0.375325i
$552$		0			0
$553$	0.292989	−	0.349171i	0.0124592	−	0.0148482i
$554$		0			0
$555$	−0.456482	−	7.38635i	−0.0193766	−	0.313533i
$556$		0			0
$557$	−3.34296	+	9.18470i	−0.141646	+	0.389168i	−0.990148	−	0.140023i	$-0.955282\pi$
$557$	−3.34296	+	9.18470i	−0.141646	+	0.389168i	0.848503	+	0.529191i	$0.177505\pi$
$558$		0			0
$559$	2.86942	+	1.65666i	0.121364	+	0.0700693i
$560$		0			0
$561$	5.80875	−	3.85004i	0.245246	−	0.162549i
$562$		0			0
$563$	9.04768	+	15.6710i	0.381314	+	0.660455i	0.991250	−	0.131995i	$-0.0421383\pi$
$563$	9.04768	+	15.6710i	0.381314	+	0.660455i	−0.609936	+	0.792450i	$0.708805\pi$
$564$		0			0
$565$	6.89982	+	1.21662i	0.290277	+	0.0511837i
$566$		0			0
$567$	−4.49749	−	0.461145i	−0.188877	−	0.0193663i
$568$		0			0
$569$	−35.0017			−1.46735			−0.733674	−	0.679501i	$-0.762196\pi$
$569$	−35.0017			−1.46735			−0.733674	+	0.679501i	$0.762196\pi$
$570$		0			0
$571$	31.7338			1.32802			0.664009	−	0.747725i	$-0.268854\pi$
$571$	31.7338			1.32802			0.664009	+	0.747725i	$0.268854\pi$
$572$		0			0
$573$	−1.72473	−	7.16395i	−0.0720516	−	0.299278i
$574$		0			0
$575$	−37.9234	−	6.68692i	−1.58152	−	0.278864i
$576$		0			0
$577$	8.22977	+	14.2544i	0.342610	+	0.593418i	0.984917	−	0.173030i	$-0.0553558\pi$
$577$	8.22977	+	14.2544i	0.342610	+	0.593418i	−0.642307	+	0.766448i	$0.722022\pi$
$578$		0			0
$579$	18.8451	+	28.4325i	0.783174	+	1.18161i
$580$		0			0
$581$	−3.11269	−	1.79712i	−0.129136	−	0.0745569i
$582$		0			0
$583$	11.6378	−	31.9746i	0.481989	−	1.32425i
$584$		0			0
$585$	0.498123	−	9.74175i	0.0205949	−	0.402772i
$586$		0			0
$587$	−12.4840	+	14.8778i	−0.515269	+	0.614073i	−0.959455	−	0.281861i	$-0.909048\pi$
$587$	−12.4840	+	14.8778i	−0.515269	+	0.614073i	0.444186	+	0.895934i	$0.353493\pi$
$588$		0			0
$589$	14.4463	+	10.7963i	0.595250	+	0.444853i
$590$		0			0
$591$	−23.7719	+	22.5874i	−0.977844	+	0.929122i
$592$		0			0
$593$	−21.9176	+	3.86466i	−0.900046	+	0.158702i	−0.604481	−	0.796620i	$-0.706619\pi$
$593$	−21.9176	+	3.86466i	−0.900046	+	0.158702i	−0.295566	+	0.955322i	$0.595508\pi$
$594$		0			0
$595$	1.93977	+	0.706018i	0.0795227	+	0.0289439i
$596$		0			0
$597$	10.1377	−	13.7185i	0.414907	−	0.561460i
$598$		0			0
$599$	0.151035	−	0.126734i	0.00617113	−	0.00517819i	−0.639697	−	0.768627i	$-0.720940\pi$
$599$	0.151035	−	0.126734i	0.00617113	−	0.00517819i	0.645868	+	0.763449i	$0.276496\pi$
$600$		0			0
$601$	3.50826	−	2.02550i	0.143105	−	0.0826217i	−0.426738	−	0.904375i	$-0.640337\pi$
$601$	3.50826	−	2.02550i	0.143105	−	0.0826217i	0.569843	+	0.821754i	$0.307004\pi$
$602$		0			0
$603$	−29.8461	−	12.6242i	−1.21543	−	0.514096i
$604$		0			0
$605$	−2.17872	−	5.98597i	−0.0885774	−	0.243364i
$606$		0			0
$607$			5.76518i			0.234001i	0.993132	+	0.117001i	$0.0373280\pi$
$607$			5.76518i			0.234001i	−0.993132	+	0.117001i	$0.962672\pi$
$608$		0			0
$609$	3.87932	+	0.439495i	0.157198	+	0.0178092i
$610$		0			0
$611$	−2.44611	+	0.890311i	−0.0989590	+	0.0360181i
$612$		0			0
$613$	6.67643	−	37.8639i	0.269659	−	1.52931i	−0.485774	−	0.874084i	$-0.661462\pi$
$613$	6.67643	−	37.8639i	0.269659	−	1.52931i	0.755433	−	0.655226i	$-0.227427\pi$
$614$		0			0
$615$	21.5945	−	9.40587i	0.870773	−	0.379281i
$616$		0			0
$617$	−5.06906	−	6.04107i	−0.204073	−	0.243204i	0.654295	−	0.756239i	$-0.272965\pi$
$617$	−5.06906	−	6.04107i	−0.204073	−	0.243204i	−0.858368	+	0.513035i	$0.828521\pi$
$618$		0			0
$619$	18.8705	−	32.6847i	0.758469	−	1.31371i	−0.185162	−	0.982708i	$-0.559281\pi$
$619$	18.8705	−	32.6847i	0.758469	−	1.31371i	0.943631	−	0.330999i	$-0.107386\pi$
$620$		0			0
$621$	−29.5668	+	36.0071i	−1.18647	+	1.44491i
$622$		0			0
$623$	1.27624	+	7.23794i	0.0511316	+	0.289982i
$624$		0			0
$625$	−21.4714	−	18.0166i	−0.858854	−	0.720664i
$626$		0			0
$627$	−2.65448	−	22.3798i	−0.106010	−	0.893763i
$628$		0			0
$629$	1.44703	+	1.21420i	0.0576969	+	0.0484134i
$630$		0			0
$631$	7.84793	+	44.5078i	0.312421	+	1.77183i	0.586330	+	0.810072i	$0.300572\pi$
$631$	7.84793	+	44.5078i	0.312421	+	1.77183i	−0.273909	+	0.961755i	$0.588317\pi$
$632$		0			0
$633$	4.95207	−	9.94816i	0.196827	−	0.395404i
$634$		0			0
$635$	−17.8818	+	30.9721i	−0.709616	+	1.22909i
$636$		0			0
$637$	−4.62577	−	5.51278i	−0.183280	−	0.218424i
$638$		0			0
$639$	10.2851	+	33.4886i	0.406871	+	1.32479i
$640$		0			0
$641$	5.87061	−	33.2939i	0.231875	−	1.31503i	−0.617221	−	0.786790i	$-0.711741\pi$
$641$	5.87061	−	33.2939i	0.231875	−	1.31503i	0.849096	−	0.528239i	$-0.177148\pi$
$642$		0			0
$643$	24.7485	−	9.00773i	0.975987	−	0.355230i	0.195708	−	0.980662i	$-0.437299\pi$
$643$	24.7485	−	9.00773i	0.975987	−	0.355230i	0.780279	+	0.625432i	$0.215077\pi$
$644$		0			0
$645$	−1.84675	+	16.3008i	−0.0727157	+	0.641845i
$646$		0			0
$647$		−	35.2829i		−	1.38711i	−0.720402	−	0.693557i	$-0.756043\pi$
$647$		−	35.2829i		−	1.38711i	0.720402	−	0.693557i	$-0.243957\pi$
$648$		0			0
$649$	11.4149	+	31.3621i	0.448072	+	1.23107i
$650$		0			0
$651$	−3.45234	−	1.02024i	−0.135308	−	0.0399865i
$652$		0			0
$653$	1.61603	−	0.933017i	0.0632403	−	0.0365118i	−0.468046	−	0.883704i	$-0.655042\pi$
$653$	1.61603	−	0.933017i	0.0632403	−	0.0365118i	0.531287	+	0.847192i	$0.321709\pi$
$654$		0			0
$655$	24.2427	−	20.3420i	0.947239	−	0.794828i
$656$		0			0
$657$	20.5574	−	22.1014i	0.802022	−	0.862259i
$658$		0			0
$659$	21.7551	+	7.91819i	0.847457	+	0.308449i	0.729003	−	0.684511i	$-0.239984\pi$
$659$	21.7551	+	7.91819i	0.847457	+	0.308449i	0.118454	+	0.992960i	$0.462206\pi$
$660$		0			0
$661$	31.4688	−	5.54881i	1.22400	−	0.215824i	0.475951	−	0.879472i	$-0.342104\pi$
$661$	31.4688	−	5.54881i	1.22400	−	0.215824i	0.748045	+	0.663648i	$0.230993\pi$
$662$		0			0
$663$	1.71504	+	1.80497i	0.0666065	+	0.0700993i
$664$		0			0
$665$	4.86413	−	4.57217i	0.188623	−	0.177301i
$666$		0			0
$667$	25.8614	−	30.8204i	1.00136	−	1.19337i
$668$		0			0
$669$	22.2836	−	1.37714i	0.861534	−	0.0532435i
$670$		0			0
$671$	8.94587	−	24.5786i	0.345351	−	0.948845i
$672$		0			0
$673$	23.8610	+	13.7761i	0.919773	+	0.531031i	0.883563	−	0.468313i	$-0.155138\pi$
$673$	23.8610	+	13.7761i	0.919773	+	0.531031i	0.0362101	+	0.999344i	$0.488471\pi$
$674$		0			0
$675$	20.8880	−	7.85514i	0.803979	−	0.302345i
$676$		0			0
$677$	7.78920	+	13.4913i	0.299363	+	0.518512i	0.975990	−	0.217814i	$-0.0698925\pi$
$677$	7.78920	+	13.4913i	0.299363	+	0.518512i	−0.676627	+	0.736326i	$0.736559\pi$
$678$		0			0
$679$	7.27846	+	1.28339i	0.279322	+	0.0492520i
$680$		0			0
$681$	36.4149	−	8.76693i	1.39542	−	0.335949i
$682$		0			0
$683$	−8.29883			−0.317546			−0.158773	−	0.987315i	$-0.550754\pi$
$683$	−8.29883			−0.317546			−0.158773	+	0.987315i	$0.550754\pi$
$684$		0			0
$685$	−39.8709			−1.52339
$686$		0			0
$687$	17.5905	−	4.23493i	0.671119	−	0.161573i
$688$		0			0
$689$	11.9724	+	2.11106i	0.456113	+	0.0804251i
$690$		0			0
$691$	1.43902	+	2.49245i	0.0547428	+	0.0948173i	0.892098	−	0.451842i	$-0.149233\pi$
$691$	1.43902	+	2.49245i	0.0547428	+	0.0948173i	−0.837355	+	0.546659i	$0.815899\pi$
$692$		0			0
$693$	2.04739	+	4.00564i	0.0777741	+	0.152162i
$694$		0			0
$695$	35.6701	+	20.5941i	1.35304	+	0.781180i
$696$		0			0
$697$	−2.05628	+	5.64959i	−0.0778873	+	0.213994i
$698$		0			0
$699$	23.8299	−	1.47271i	0.901330	−	0.0557029i
$700$		0			0
$701$	27.5980	−	32.8900i	1.04236	−	1.24224i	0.0728104	−	0.997346i	$-0.476803\pi$
$701$	27.5980	−	32.8900i	1.04236	−	1.24224i	0.969550	−	0.244892i	$-0.0787524\pi$
$702$		0			0
$703$	5.61363	−	2.40923i	0.211722	−	0.0908660i
$704$		0			0
$705$	−8.87787	−	9.34342i	−0.334360	−	0.351894i
$706$		0			0
$707$	2.14606	−	0.378408i	0.0807109	−	0.0142315i
$708$		0			0
$709$	5.43501	+	1.97818i	0.204116	+	0.0742922i	0.442055	−	0.896988i	$-0.354250\pi$
$709$	5.43501	+	1.97818i	0.204116	+	0.0742922i	−0.237939	+	0.971280i	$0.576472\pi$
$710$		0			0
$711$	1.99319	+	1.85394i	0.0747503	+	0.0695283i
$712$		0			0
$713$	−28.4189	+	23.8463i	−1.06430	+	0.893052i
$714$		0			0
$715$	−8.40554	+	4.85294i	−0.314349	+	0.181490i
$716$		0			0
$717$	32.1842	+	9.51113i	1.20194	+	0.355200i
$718$		0			0
$719$	6.82611	+	18.7546i	0.254571	+	0.699428i	0.999479	+	0.0322615i	$0.0102709\pi$
$719$	6.82611	+	18.7546i	0.254571	+	0.699428i	−0.744908	+	0.667167i	$0.767507\pi$
$720$		0			0
$721$			5.46797i			0.203638i
$722$		0			0
$723$	4.92645	−	43.4847i	0.183217	−	1.61721i
$724$		0			0
$725$	−18.1088	+	6.59106i	−0.672544	+	0.244786i
$726$		0			0
$727$	−7.71938	+	43.7788i	−0.286296	+	1.62367i	0.414323	+	0.910130i	$0.364018\pi$
$727$	−7.71938	+	43.7788i	−0.286296	+	1.62367i	−0.700619	+	0.713536i	$0.747093\pi$
$728$		0			0
$729$	4.12198	−	26.6835i	0.152666	−	0.988278i
$730$		0			0
$731$	−2.69162	−	3.20774i	−0.0995530	−	0.118643i
$732$		0			0
$733$	−20.5246	+	35.5497i	−0.758094	+	1.31306i	0.185728	+	0.982601i	$0.440536\pi$
$733$	−20.5246	+	35.5497i	−0.758094	+	1.31306i	−0.943822	+	0.330455i	$0.892798\pi$
$734$		0			0
$735$	15.8784	−	31.8978i	0.585682	−	1.17657i
$736$		0			0
$737$	5.59925	+	31.7549i	0.206251	+	1.16971i
$738$		0			0
$739$	16.8328	+	14.1244i	0.619203	+	0.519573i	0.897553	−	0.440907i	$-0.145343\pi$
$739$	16.8328	+	14.1244i	0.619203	+	0.519573i	−0.278350	+	0.960480i	$0.589787\pi$
$740$		0			0
$741$	7.70974	−	2.32246i	0.283224	−	0.0853178i
$742$		0			0
$743$	−37.9084	−	31.8089i	−1.39072	−	1.16696i	−0.965046	−	0.262081i	$-0.915591\pi$
$743$	−37.9084	−	31.8089i	−1.39072	−	1.16696i	−0.425678	−	0.904875i	$-0.639964\pi$
$744$		0			0
$745$	−10.7451	−	60.9385i	−0.393670	−	2.23261i
$746$		0			0
$747$	11.6677	−	18.0168i	0.426899	−	0.659200i
$748$		0			0
$749$	−0.00364772	+	0.00631803i	−0.000133285	+	0.000230856i
$750$		0			0
$751$	−13.7962	−	16.4416i	−0.503429	−	0.599964i	0.453151	−	0.891434i	$-0.350300\pi$
$751$	−13.7962	−	16.4416i	−0.503429	−	0.599964i	−0.956580	+	0.291470i	$0.905856\pi$
$752$		0			0
$753$	29.6964	−	12.9348i	1.08220	−	0.471371i
$754$		0			0
$755$	−12.4342	+	70.5178i	−0.452527	+	2.56641i
$756$		0			0
$757$	−42.8982	+	15.6137i	−1.55916	+	0.567489i	−0.970544	−	0.240922i	$-0.922550\pi$
$757$	−42.8982	+	15.6137i	−1.55916	+	0.567489i	−0.588618	+	0.808411i	$0.700328\pi$
$758$		0			0
$759$	46.0640	+	5.21867i	1.67202	+	0.189426i
$760$		0			0
$761$			39.4370i			1.42959i	0.699334	+	0.714795i	$0.253480\pi$
$761$			39.4370i			1.42959i	−0.699334	+	0.714795i	$0.746520\pi$
$762$		0			0
$763$	−0.380387	−	1.04510i	−0.0137709	−	0.0378353i
$764$		0			0
$765$	−4.80243	+	11.3539i	−0.173632	+	0.410502i
$766$		0			0
$767$	−10.3267	+	5.96211i	−0.372875	+	0.215279i
$768$		0			0
$769$	−12.0324	+	10.0964i	−0.433900	+	0.364085i	−0.833421	−	0.552639i	$-0.813621\pi$
$769$	−12.0324	+	10.0964i	−0.433900	+	0.364085i	0.399521	+	0.916724i	$0.369176\pi$
$770$		0			0
$771$	8.36266	−	11.3165i	0.301174	−	0.407555i
$772$		0			0
$773$	−30.7512	−	11.1925i	−1.10604	−	0.402566i	−0.276502	−	0.961013i	$-0.589175\pi$
$773$	−30.7512	−	11.1925i	−1.10604	−	0.402566i	−0.829540	+	0.558447i	$0.811397\pi$
$774$		0			0
$775$	17.4995	−	3.08563i	0.628600	−	0.110839i
$776$		0			0
$777$	−0.883970	+	0.839925i	−0.0317123	+	0.0301321i
$778$		0			0
$779$	13.3165	+	14.1668i	0.477113	+	0.507579i
$780$		0			0
$781$	22.4062	−	26.7027i	0.801757	−	0.955497i
$782$		0			0
$783$	−3.80433	+	23.0032i	−0.135956	+	0.822067i
$784$		0			0
$785$	20.0637	−	55.1247i	0.716106	−	1.96748i
$786$		0			0
$787$	−0.916770	−	0.529298i	−0.0326793	−	0.0188674i	0.483571	−	0.875305i	$-0.339339\pi$
$787$	−0.916770	−	0.529298i	−0.0326793	−	0.0188674i	−0.516251	+	0.856438i	$0.672673\pi$
$788$		0			0
$789$	−9.61574	−	14.5077i	−0.342329	−	0.516490i
$790$		0			0
$791$	−0.577213	−	0.999762i	−0.0205233	−	0.0355475i
$792$		0			0
$793$	9.20308	+	1.62275i	0.326811	+	0.0576256i
$794$		0			0
$795$	14.0890	+	58.5210i	0.499686	+	2.07553i
$796$		0			0
$797$	−35.5116			−1.25789			−0.628944	−	0.777451i	$-0.716512\pi$
$797$	−35.5116			−1.25789			−0.628944	+	0.777451i	$0.716512\pi$
$798$		0			0
$799$	3.28982			0.116385
$800$		0			0
$801$	−43.5580	+	5.40448i	−1.53905	+	0.190958i
$802$		0			0
$803$	−29.5775	−	5.21531i	−1.04377	−	0.184044i
$804$		0			0
$805$	6.86604	+	11.8923i	0.241996	+	0.419149i
$806$		0			0
$807$	5.88371	−	3.89972i	0.207116	−	0.137277i
$808$		0			0
$809$	−7.36932	−	4.25468i	−0.259091	−	0.149587i	0.364829	−	0.931075i	$-0.381128\pi$
$809$	−7.36932	−	4.25468i	−0.259091	−	0.149587i	−0.623920	+	0.781488i	$0.714461\pi$
$810$		0			0
$811$	2.74045	−	7.52932i	0.0962302	−	0.264390i	−0.882232	−	0.470814i	$-0.843960\pi$
$811$	2.74045	−	7.52932i	0.0962302	−	0.264390i	0.978463	+	0.206424i	$0.0661825\pi$
$812$		0			0
$813$	−0.483079	−	7.81671i	−0.0169423	−	0.274144i
$814$		0			0
$815$	35.9668	−	42.8636i	1.25986	−	1.50144i
$816$		0			0
$817$	−13.1825	+	3.09869i	−0.461198	+	0.108409i
$818$		0			0
$819$	−1.28238	+	0.968900i	−0.0448099	+	0.0338561i
$820$		0			0
$821$	3.69233	−	0.651058i	0.128863	−	0.0227221i	−0.108844	−	0.994059i	$-0.534715\pi$
$821$	3.69233	−	0.651058i	0.128863	−	0.0227221i	0.237708	+	0.971337i	$0.423604\pi$
$822$		0			0
$823$	−24.8907	−	9.05947i	−0.867634	−	0.315793i	−0.130426	−	0.991458i	$-0.541634\pi$
$823$	−24.8907	−	9.05947i	−0.867634	−	0.315793i	−0.737209	+	0.675665i	$0.763857\pi$
$824$		0			0
$825$	−17.8580	−	13.1967i	−0.621737	−	0.459450i
$826$		0			0
$827$	−35.2983	+	29.6188i	−1.22744	+	1.02995i	−0.229041	+	0.973417i	$0.573559\pi$
$827$	−35.2983	+	29.6188i	−1.22744	+	1.02995i	−0.998401	+	0.0565290i	$0.981997\pi$
$828$		0			0
$829$	0.547722	−	0.316227i	0.0190232	−	0.0109830i	−0.490458	−	0.871465i	$-0.663171\pi$
$829$	0.547722	−	0.316227i	0.0190232	−	0.0109830i	0.509481	+	0.860482i	$0.329837\pi$
$830$		0			0
$831$	11.6226	−	39.3290i	0.403183	−	1.36431i
$832$		0			0
$833$	3.11064	+	8.54643i	0.107777	+	0.296116i
$834$		0			0
$835$			17.6381i			0.610390i
$836$		0			0
$837$	7.13784	−	20.2795i	0.246720	−	0.700961i
$838$		0			0
$839$	27.7805	−	10.1113i	0.959090	−	0.349080i	0.185413	−	0.982661i	$-0.440638\pi$
$839$	27.7805	−	10.1113i	0.959090	−	0.349080i	0.773677	+	0.633580i	$0.218415\pi$
$840$		0			0
$841$	−1.53955	+	8.73124i	−0.0530880	+	0.301077i
$842$		0			0
$843$	−15.9736	−	36.6730i	−0.550160	−	1.26309i
$844$		0			0
$845$	23.2469	+	27.7046i	0.799717	+	0.953066i
$846$		0			0
$847$	−0.524806	+	0.908991i	−0.0180326	+	0.0312333i
$848$		0			0
$849$	−12.9231	−	6.43294i	−0.443518	−	0.220778i
$850$		0			0
$851$	2.18206	+	12.3751i	0.0748000	+	0.424212i
$852$		0			0
$853$	17.3096	+	14.5245i	0.592669	+	0.497308i	0.889080	−	0.457752i	$-0.151345\pi$
$853$	17.3096	+	14.5245i	0.592669	+	0.497308i	−0.296411	+	0.955060i	$0.595790\pi$
$854$		0			0
$855$	25.7861	+	30.4052i	0.881867	+	1.03984i
$856$		0			0
$857$	−29.5954	−	24.8335i	−1.01096	−	0.848297i	−0.0224963	−	0.999747i	$-0.507161\pi$
$857$	−29.5954	−	24.8335i	−1.01096	−	0.848297i	−0.988465	+	0.151450i	$0.951606\pi$
$858$		0			0
$859$	4.80636	+	27.2582i	0.163991	+	0.930039i	0.950099	+	0.311950i	$0.100982\pi$
$859$	4.80636	+	27.2582i	0.163991	+	0.930039i	−0.786108	+	0.618090i	$0.787907\pi$
$860$		0			0
$861$	−3.47435	−	1.72949i	−0.118406	−	0.0589409i
$862$		0			0
$863$	−5.59402	+	9.68913i	−0.190423	+	0.329822i	−0.945390	−	0.325940i	$-0.894319\pi$
$863$	−5.59402	+	9.68913i	−0.190423	+	0.329822i	0.754968	+	0.655762i	$0.227653\pi$
$864$		0			0
$865$	15.4349	+	18.3946i	0.524803	+	0.625436i
$866$		0			0
$867$	10.5017	+	24.1103i	0.356657	+	0.818830i
$868$		0			0
$869$	0.470335	−	2.66740i	0.0159550	−	0.0904854i
$870$		0			0
$871$	−10.8257	+	3.94024i	−0.366815	+	0.133510i
$872$		0			0
$873$	−9.87415	+	43.0191i	−0.334189	+	1.45598i
$874$		0			0
$875$			1.08009i			0.0365138i
$876$		0			0
$877$	−9.82475	−	26.9933i	−0.331758	−	0.911498i	−0.987655	−	0.156647i	$-0.949931\pi$
$877$	−9.82475	−	26.9933i	−0.331758	−	0.911498i	0.655897	−	0.754851i	$-0.272291\pi$
$878$		0			0
$879$	3.99377	−	13.5143i	0.134707	−	0.455826i
$880$		0			0
$881$	−9.40019	+	5.42720i	−0.316700	+	0.182847i	−0.649921	−	0.760002i	$-0.725198\pi$
$881$	−9.40019	+	5.42720i	−0.316700	+	0.182847i	0.333220	+	0.942849i	$0.391865\pi$
$882$		0			0
$883$	−14.2903	+	11.9910i	−0.480906	+	0.403528i	−0.850754	−	0.525564i	$-0.823854\pi$
$883$	−14.2903	+	11.9910i	−0.480906	+	0.403528i	0.369848	+	0.929092i	$0.379410\pi$
$884$		0			0
$885$	−47.4820	−	35.0881i	−1.59609	−	1.17947i
$886$		0			0
$887$	4.51160	+	1.64209i	0.151485	+	0.0551359i	0.416650	−	0.909067i	$-0.363204\pi$
$887$	4.51160	+	1.64209i	0.151485	+	0.0551359i	−0.265165	+	0.964203i	$0.585426\pi$
$888$		0			0
$889$	5.80326	−	1.02327i	0.194635	−	0.0343194i
$890$		0			0
$891$	−24.5150	+	10.9896i	−0.821283	+	0.368164i
$892$		0			0
$893$	4.79230	−	9.49860i	0.160368	−	0.317859i
$894$		0			0
$895$	−6.08866	+	7.25619i	−0.203522	+	0.242548i
$896$		0			0
$897$	1.02167	+	16.5316i	0.0341124	+	0.551974i
$898$		0			0
$899$	−6.34970	+	17.4457i	−0.211774	+	0.581845i
$900$		0			0
$901$	−13.3059	−	7.68216i	−0.443283	−	0.255930i
$902$		0			0
$903$	2.25311	−	1.49336i	0.0749789	−	0.0496961i
$904$		0			0
$905$	−31.0223	−	53.7322i	−1.03122	−	1.78612i
$906$		0			0
$907$	−51.8502	−	9.14259i	−1.72166	−	0.303575i	−0.776483	−	0.630138i	$-0.782998\pi$
$907$	−51.8502	−	9.14259i	−1.72166	−	0.303575i	−0.945175	+	0.326563i	$0.894109\pi$
$908$		0			0
$909$	1.60244	+	12.9150i	0.0531495	+	0.428365i
$910$		0			0
$911$	1.55433			0.0514972			0.0257486	−	0.999668i	$-0.491803\pi$
$911$	1.55433			0.0514972			0.0257486	+	0.999668i	$0.491803\pi$
$912$		0			0
$913$	−21.3579			−0.706845
$914$		0			0
$915$	10.8301	+	44.9845i	0.358031	+	1.48714i
$916$		0			0
$917$	−5.13521	−	0.905475i	−0.169579	−	0.0299014i
$918$		0			0
$919$	−18.3505	−	31.7840i	−0.605327	−	1.04846i	−0.992000	−	0.126241i	$-0.959709\pi$
$919$	−18.3505	−	31.7840i	−0.605327	−	1.04846i	0.386672	−	0.922217i	$-0.373624\pi$
$920$		0			0
$921$	8.42191	+	12.7066i	0.277512	+	0.418696i
$922$		0			0
$923$	10.7856	+	6.22704i	0.355011	+	0.204966i
$924$		0			0
$925$	2.05858	−	5.65590i	0.0676857	−	0.185965i
$926$		0			0
$927$	−32.6123	−	1.66756i	−1.07113	−	0.0547698i
$928$		0			0
$929$	15.9003	−	18.9493i	0.521673	−	0.621706i	−0.439302	−	0.898339i	$-0.644774\pi$
$929$	15.9003	−	18.9493i	0.521673	−	0.621706i	0.960976	+	0.276633i	$0.0892188\pi$
$930$		0			0
$931$	29.2071	+	3.46834i	0.957225	+	0.113670i
$932$		0			0
$933$	4.17852	−	3.97032i	0.136799	−	0.129983i
$934$		0			0
$935$	12.0800	−	2.13004i	0.395060	−	0.0696597i
$936$		0			0
$937$	−30.2959	−	11.0268i	−0.989724	−	0.360230i	−0.204110	−	0.978948i	$-0.565430\pi$
$937$	−30.2959	−	11.0268i	−0.989724	−	0.360230i	−0.785613	+	0.618718i	$0.787652\pi$
$938$		0			0
$939$	3.09572	−	4.18919i	0.101025	−	0.136709i
$940$		0			0
$941$	−36.5786	+	30.6931i	−1.19243	+	1.00057i	−0.192614	+	0.981275i	$0.561697\pi$
$941$	−36.5786	+	30.6931i	−1.19243	+	1.00057i	−0.999814	+	0.0192917i	$0.993859\pi$
$942$		0			0
$943$	−34.6365	+	19.9974i	−1.12792	+	0.651205i
$944$		0			0
$945$	−6.93369	−	3.90545i	−0.225553	−	0.127044i
$946$		0			0
$947$	−12.4715	−	34.2652i	−0.405270	−	1.11347i	−0.959648	−	0.281205i	$-0.909266\pi$
$947$	−12.4715	−	34.2652i	−0.405270	−	1.11347i	0.554378	−	0.832265i	$-0.312956\pi$
$948$		0			0
$949$		−	10.7305i		−	0.348328i
$950$		0			0
$951$	18.0898	+	2.04942i	0.586601	+	0.0664569i
$952$		0			0
$953$	35.9606	−	13.0886i	1.16488	−	0.423981i	0.314041	−	0.949409i	$-0.398317\pi$
$953$	35.9606	−	13.0886i	1.16488	−	0.423981i	0.850838	+	0.525428i	$0.176095\pi$
$954$		0			0
$955$	2.25225	−	12.7731i	0.0728810	−	0.413329i
$956$		0			0
$957$	21.2695	−	9.26431i	0.687544	−	0.299473i
$958$		0			0
$959$	4.22283	+	5.03257i	0.136362	+	0.162510i
$960$		0			0
$961$	−6.94064	+	12.0215i	−0.223892	+	0.387792i
$962$		0			0
$963$	−0.0365698	−	0.0236827i	−0.00117845	−	0.000763163i
$964$		0			0
$965$	10.4260	+	59.1291i	0.335626	+	1.90343i
$966$		0			0
$967$	8.52174	+	7.15059i	0.274041	+	0.229947i	0.769442	−	0.638717i	$-0.220534\pi$
$967$	8.52174	+	7.15059i	0.274041	+	0.229947i	−0.495401	+	0.868664i	$0.664979\pi$
$968$		0			0
$969$	−10.1599	−	0.574384i	−0.326384	−	0.0184519i
$970$		0			0
$971$	12.1336	+	10.1813i	0.389386	+	0.326734i	0.816374	−	0.577524i	$-0.195981\pi$
$971$	12.1336	+	10.1813i	0.389386	+	0.326734i	−0.426988	+	0.904257i	$0.640425\pi$
$972$		0			0
$973$	−1.17848	−	6.68352i	−0.0377805	−	0.214264i
$974$		0			0
$975$	3.53537	−	7.10217i	0.113223	−	0.227451i
$976$		0			0
$977$	−4.12154	+	7.13872i	−0.131860	+	0.228388i	−0.924393	−	0.381440i	$-0.875428\pi$
$977$	−4.12154	+	7.13872i	−0.131860	+	0.228388i	0.792534	+	0.609828i	$0.208762\pi$
$978$		0			0
$979$	28.0727	+	33.4557i	0.897207	+	1.06925i
$980$		0			0
$981$	6.34926	−	1.95000i	0.202716	−	0.0622586i
$982$		0			0
$983$	3.81477	−	21.6346i	0.121672	−	0.690037i	−0.861557	−	0.507661i	$-0.830510\pi$
$983$	3.81477	−	21.6346i	0.121672	−	0.690037i	0.983229	−	0.182376i	$-0.0583787\pi$
$984$		0			0
$985$	−54.2385	+	19.7412i	−1.72818	+	0.629006i
$986$		0			0
$987$	−0.239064	+	2.11017i	−0.00760950	+	0.0671673i
$988$		0			0
$989$		−	27.8560i		−	0.885768i
$990$		0			0
$991$	−8.41455	−	23.1188i	−0.267297	−	0.734393i	−0.998628	−	0.0523696i	$-0.983323\pi$
$991$	−8.41455	−	23.1188i	−0.267297	−	0.734393i	0.731331	−	0.682023i	$-0.238900\pi$
$992$		0			0
$993$	23.4027	+	6.91600i	0.742661	+	0.219473i
$994$		0			0
$995$	26.0023	−	15.0124i	0.824329	−	0.475927i
$996$		0			0
$997$	13.6792	−	11.4782i	0.433225	−	0.363519i	−0.399942	−	0.916540i	$-0.630970\pi$
$997$	13.6792	−	11.4782i	0.433225	−	0.363519i	0.833167	+	0.553022i	$0.186525\pi$
$998$		0			0
$999$	−4.73993	−	5.52836i	−0.149965	−	0.174910i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.bm.a.41.9	✓	60
3.2	odd	2		456.2.bm.b.41.1	yes	60
4.3	odd	2		912.2.cc.h.497.2		60
12.11	even	2		912.2.cc.g.497.10		60
19.13	odd	18		456.2.bm.b.89.1	yes	60
57.32	even	18	inner	456.2.bm.a.89.9	yes	60
76.51	even	18		912.2.cc.g.545.10		60
228.203	odd	18		912.2.cc.h.545.2		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bm.a.41.9	✓	60	1.1	even	1	trivial
456.2.bm.a.89.9	yes	60	57.32	even	18	inner
456.2.bm.b.41.1	yes	60	3.2	odd	2
456.2.bm.b.89.1	yes	60	19.13	odd	18
912.2.cc.g.497.10		60	12.11	even	2
912.2.cc.g.545.10		60	76.51	even	18
912.2.cc.h.497.2		60	4.3	odd	2
912.2.cc.h.545.2		60	228.203	odd	18

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:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bm (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.68394 - 0.405410i) q^{3} +(3.00241 + 0.529406i) q^{5} +(-0.251171 - 0.435040i) q^{7} +(2.67129 - 1.36537i) q^{9} +(-2.58513 - 1.49253i) q^{11} +(0.364767 - 1.00219i) q^{13} +(5.27050 - 0.325721i) q^{15} +(-0.866390 + 1.03252i) q^{17} +(1.71910 + 4.00558i) q^{19} +(-0.599325 - 0.630754i) q^{21} +(-8.83018 + 1.55700i) q^{23} +(4.03575 + 1.46889i) q^{25} +(3.94474 - 3.38216i) q^{27} +(-3.43732 + 2.88425i) q^{29} +(3.58316 - 2.06874i) q^{31} +(-4.95829 - 1.46528i) q^{33} +(-0.523805 - 1.43914i) q^{35} -1.40145i q^{37} +(0.207947 - 1.83550i) q^{39} +(4.19152 - 1.52559i) q^{41} +(-0.539473 + 3.05951i) q^{43} +(8.74314 - 2.68521i) q^{45} +(-1.56889 - 1.86974i) q^{47} +(3.37383 - 5.84364i) q^{49} +(-1.04035 + 2.08995i) q^{51} +(1.97942 + 11.2258i) q^{53} +(-6.97149 - 5.84977i) q^{55} +(4.51876 + 6.04821i) q^{57} +(-8.56486 - 7.18677i) q^{59} +(1.52156 + 8.62918i) q^{61} +(-1.26494 - 0.819177i) q^{63} +(1.62575 - 2.81587i) q^{65} +(-6.94344 - 8.27486i) q^{67} +(-14.2382 + 6.20173i) q^{69} +(-2.02777 + 11.5000i) q^{71} +(9.45460 - 3.44119i) q^{73} +(7.39144 + 0.837389i) q^{75} +1.49952i q^{77} +(0.310339 + 0.852649i) q^{79} +(5.27153 - 7.29458i) q^{81} +(6.19637 - 3.57748i) q^{83} +(-3.14788 + 2.64139i) q^{85} +(-4.61892 + 6.25042i) q^{87} +(-13.7483 - 5.00398i) q^{89} +(-0.527611 + 0.0930321i) q^{91} +(5.19513 - 4.93627i) q^{93} +(3.04087 + 12.9365i) q^{95} +(-9.45707 + 11.2705i) q^{97} +(-8.94348 - 0.457306i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 3 q^{3} - 3 q^{9} + 3 q^{13} - 9 q^{15} + 6 q^{17} + 3 q^{19} + 6 q^{25} + 6 q^{27} - 6 q^{29} + 45 q^{33} - 24 q^{35} + 18 q^{39} - 3 q^{41} - 21 q^{43} - 45 q^{45} + 18 q^{47} - 30 q^{49} - 6 q^{51}+ \cdots - 3 q^{99}+O(q^{100}) \) 60 * q - 3 * q^3 - 3 * q^9 + 3 * q^13 - 9 * q^15 + 6 * q^17 + 3 * q^19 + 6 * q^25 + 6 * q^27 - 6 * q^29 + 45 * q^33 - 24 * q^35 + 18 * q^39 - 3 * q^41 - 21 * q^43 - 45 * q^45 + 18 * q^47 - 30 * q^49 - 6 * q^51 + 36 * q^53 + 18 * q^55 + 48 * q^57 + 21 * q^59 - 6 * q^61 + 78 * q^63 - 24 * q^65 - 48 * q^67 + 21 * q^69 - 36 * q^71 - 57 * q^73 - 36 * q^79 - 39 * q^81 + 36 * q^83 + 6 * q^85 - 90 * q^87 + 24 * q^89 - 18 * q^91 - 54 * q^93 - 30 * q^95 + 15 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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