LMFDB - Embedded newform 456.2.bm.b.89.1

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 = [60,0,0] 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			89.1
Character	$\chi$	$=$	456.89
Dual form			456.2.bm.b.41.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.55056 - 0.771852i) q^{3} +(-3.00241 + 0.529406i) q^{5} +(-0.251171 + 0.435040i) q^{7} +(1.80849 + 2.39361i) q^{9} +(2.58513 - 1.49253i) q^{11} +(0.364767 + 1.00219i) q^{13} +(5.06405 + 1.49654i) q^{15} +(0.866390 + 1.03252i) q^{17} +(1.71910 - 4.00558i) q^{19} +(0.725243 - 0.480691i) q^{21} +(8.83018 + 1.55700i) q^{23} +(4.03575 - 1.46889i) q^{25} +(-0.956666 - 5.10733i) q^{27} +(3.43732 + 2.88425i) q^{29} +(3.58316 + 2.06874i) q^{31} +(-5.16042 + 0.318918i) q^{33} +(0.523805 - 1.43914i) q^{35} +1.40145i q^{37} +(0.207947 - 1.83550i) q^{39} +(-4.19152 - 1.52559i) q^{41} +(-0.539473 - 3.05951i) q^{43} +(-6.69702 - 6.22917i) q^{45} +(1.56889 - 1.86974i) q^{47} +(3.37383 + 5.84364i) q^{49} +(-0.546437 - 2.26972i) q^{51} +(-1.97942 + 11.2258i) q^{53} +(-6.97149 + 5.84977i) q^{55} +(-5.75729 + 4.88402i) q^{57} +(8.56486 - 7.18677i) q^{59} +(1.52156 - 8.62918i) q^{61} +(-1.49556 + 0.185562i) q^{63} +(-1.62575 - 2.81587i) q^{65} +(-6.94344 + 8.27486i) q^{67} +(-12.4900 - 9.22982i) q^{69} +(2.02777 + 11.5000i) q^{71} +(9.45460 + 3.44119i) q^{73} +(-7.39144 - 0.837389i) q^{75} +1.49952i q^{77} +(0.310339 - 0.852649i) q^{79} +(-2.45873 + 8.65764i) q^{81} +(-6.19637 - 3.57748i) q^{83} +(-3.14788 - 2.64139i) q^{85} +(-3.10356 - 7.12531i) q^{87} +(13.7483 - 5.00398i) q^{89} +(-0.527611 - 0.0930321i) q^{91} +(-3.95916 - 5.97338i) q^{93} +(-3.04087 + 12.9365i) q^{95} +(-9.45707 - 11.2705i) q^{97} +(8.24772 + 3.48858i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 6 q^{9} + 3 q^{13} - 3 q^{15} - 6 q^{17} + 3 q^{19} + 6 q^{25} + 3 q^{27} + 6 q^{29} + 24 q^{35} + 18 q^{39} + 3 q^{41} - 21 q^{43} + 63 q^{45} - 18 q^{47} - 30 q^{49} + 33 q^{51} - 36 q^{53} + 18 q^{55}+ \cdots - 39 q^{99}+O(q^{100}) $ 60 * q - 6 * q^9 + 3 * q^13 - 3 * q^15 - 6 * q^17 + 3 * q^19 + 6 * q^25 + 3 * q^27 + 6 * q^29 + 24 * q^35 + 18 * q^39 + 3 * q^41 - 21 * q^43 + 63 * q^45 - 18 * q^47 - 30 * q^49 + 33 * q^51 - 36 * q^53 + 18 * q^55 - 24 * q^57 - 21 * q^59 - 6 * q^61 - 24 * q^63 + 24 * q^65 - 48 * q^67 - 21 * q^69 + 36 * q^71 - 57 * q^73 - 36 * q^79 + 6 * q^81 - 36 * q^83 + 6 * q^85 + 72 * q^87 - 24 * q^89 - 18 * q^91 + 108 * q^93 + 30 * q^95 + 15 * q^97 - 39 * q^99

Character values

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

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$	$-1$	$1$

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
$3$	−1.55056	−	0.771852i	−0.895218	−	0.445629i
$3$	−1.55056	−	0.771852i	−0.895218	−	0.445629i
$4$		0			0
$5$	−3.00241	+	0.529406i	−1.34272	+	0.236758i	−0.798404	−	0.602123i	$-0.794322\pi$
$5$	−3.00241	+	0.529406i	−1.34272	+	0.236758i	−0.544316	+	0.838880i	$0.683211\pi$
$6$		0			0
$7$	−0.251171	+	0.435040i	−0.0949336	+	0.164430i	−0.909581	−	0.415527i	$-0.863597\pi$
$7$	−0.251171	+	0.435040i	−0.0949336	+	0.164430i	0.814647	+	0.579957i	$0.196931\pi$
$8$		0			0
$9$	1.80849	+	2.39361i	0.602830	+	0.797870i
$10$		0			0
$11$	2.58513	−	1.49253i	0.779447	−	0.450014i	−0.0567871	−	0.998386i	$-0.518086\pi$
$11$	2.58513	−	1.49253i	0.779447	−	0.450014i	0.836234	+	0.548372i	$0.184752\pi$
$12$		0			0
$13$	0.364767	+	1.00219i	0.101168	+	0.277957i	0.979943	−	0.199280i	$-0.0638604\pi$
$13$	0.364767	+	1.00219i	0.101168	+	0.277957i	−0.878774	+	0.477237i	$0.841638\pi$
$14$		0			0
$15$	5.06405	+	1.49654i	1.30753	+	0.386405i
$16$		0			0
$17$	0.866390	+	1.03252i	0.210130	+	0.250424i	0.860807	−	0.508931i	$-0.169959\pi$
$17$	0.866390	+	1.03252i	0.210130	+	0.250424i	−0.650677	+	0.759355i	$0.725515\pi$
$18$		0			0
$19$	1.71910	−	4.00558i	0.394389	−	0.918944i
$19$	1.71910	−	4.00558i	0.394389	−	0.918944i
$20$		0			0
$21$	0.725243	−	0.480691i	0.158261	−	0.104895i
$22$		0			0
$23$	8.83018	+	1.55700i	1.84122	+	0.324657i	0.982280	−	0.187419i	$-0.0600123\pi$
$23$	8.83018	+	1.55700i	1.84122	+	0.324657i	0.858940	+	0.512076i	$0.171123\pi$
$24$		0			0
$25$	4.03575	−	1.46889i	0.807149	−	0.293778i
$26$		0			0
$27$	−0.956666	−	5.10733i	−0.184111	−	0.982906i
$28$		0			0
$29$	3.43732	+	2.88425i	0.638294	+	0.535592i	0.903494	−	0.428601i	$-0.140993\pi$
$29$	3.43732	+	2.88425i	0.638294	+	0.535592i	−0.265200	+	0.964193i	$0.585438\pi$
$30$		0			0
$31$	3.58316	+	2.06874i	0.643555	+	0.371556i	0.785983	−	0.618249i	$-0.212158\pi$
$31$	3.58316	+	2.06874i	0.643555	+	0.371556i	−0.142428	+	0.989805i	$0.545491\pi$
$32$		0			0
$33$	−5.16042	+	0.318918i	−0.898314	+	0.0555165i
$34$		0			0
$35$	0.523805	−	1.43914i	0.0885392	−	0.243259i
$36$		0			0
$37$			1.40145i			0.230397i	0.993342	+	0.115199i	$0.0367504\pi$
$37$			1.40145i			0.230397i	−0.993342	+	0.115199i	$0.963250\pi$
$38$		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	$-0.502133\pi$
$41$	−4.19152	−	1.52559i	−0.654605	−	0.238257i	−0.647905	+	0.761721i	$0.724355\pi$
$42$		0			0
$43$	−0.539473	−	3.05951i	−0.0822689	−	0.466570i	−0.997913	−	0.0645793i	$-0.979429\pi$
$43$	−0.539473	−	3.05951i	−0.0822689	−	0.466570i	0.915644	−	0.401991i	$-0.131682\pi$
$44$		0			0
$45$	−6.69702	−	6.22917i	−0.998333	−	0.928591i
$46$		0			0
$47$	1.56889	−	1.86974i	0.228847	−	0.272729i	−0.639386	−	0.768886i	$-0.720811\pi$
$47$	1.56889	−	1.86974i	0.228847	−	0.272729i	0.868233	+	0.496157i	$0.165256\pi$
$48$		0			0
$49$	3.37383	+	5.84364i	0.481975	+	0.834806i
$50$		0			0
$51$	−0.546437	−	2.26972i	−0.0765165	−	0.317824i
$52$		0			0
$53$	−1.97942	+	11.2258i	−0.271894	+	1.54199i	0.476765	+	0.879031i	$0.341809\pi$
$53$	−1.97942	+	11.2258i	−0.271894	+	1.54199i	−0.748659	+	0.662956i	$0.769302\pi$
$54$		0			0
$55$	−6.97149	+	5.84977i	−0.940035	+	0.788783i
$56$		0			0
$57$	−5.75729	+	4.88402i	−0.762571	+	0.646904i
$58$		0			0
$59$	8.56486	−	7.18677i	1.11505	−	0.935638i	0.116706	−	0.993166i	$-0.462766\pi$
$59$	8.56486	−	7.18677i	1.11505	−	0.935638i	0.998344	+	0.0575285i	$0.0183220\pi$
$60$		0			0
$61$	1.52156	−	8.62918i	0.194816	−	1.10485i	−0.717866	−	0.696182i	$-0.754881\pi$
$61$	1.52156	−	8.62918i	0.194816	−	1.10485i	0.912681	−	0.408672i	$-0.134008\pi$
$62$		0			0
$63$	−1.49556	+	0.185562i	−0.188422	+	0.0233786i
$64$		0			0
$65$	−1.62575	−	2.81587i	−0.201649	−	0.349266i
$66$		0			0
$67$	−6.94344	+	8.27486i	−0.848276	+	1.01094i	0.151472	+	0.988462i	$0.451599\pi$
$67$	−6.94344	+	8.27486i	−0.848276	+	1.01094i	−0.999747	+	0.0224739i	$0.992846\pi$
$68$		0			0
$69$	−12.4900	−	9.22982i	−1.50362	−	1.11114i
$70$		0			0
$71$	2.02777	+	11.5000i	0.240652	+	1.36480i	0.830378	+	0.557201i	$0.188125\pi$
$71$	2.02777	+	11.5000i	0.240652	+	1.36480i	−0.589726	+	0.807604i	$0.700764\pi$
$72$		0			0
$73$	9.45460	+	3.44119i	1.10658	+	0.402761i	0.829737	−	0.558155i	$-0.188490\pi$
$73$	9.45460	+	3.44119i	1.10658	+	0.402761i	0.276841	+	0.960916i	$0.410713\pi$
$74$		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	−0.921010	−	0.389540i	$-0.872634\pi$
$79$	0.310339	−	0.852649i	0.0349159	−	0.0959306i	0.955926	+	0.293609i	$0.0948564\pi$
$80$		0			0
$81$	−2.45873	+	8.65764i	−0.273192	+	0.961960i
$82$		0			0
$83$	−6.19637	−	3.57748i	−0.680140	−	0.392679i	0.119768	−	0.992802i	$-0.461785\pi$
$83$	−6.19637	−	3.57748i	−0.680140	−	0.392679i	−0.799908	+	0.600123i	$0.795118\pi$
$84$		0			0
$85$	−3.14788	−	2.64139i	−0.341436	−	0.286499i
$86$		0			0
$87$	−3.10356	−	7.12531i	−0.332737	−	0.763914i
$88$		0			0
$89$	13.7483	−	5.00398i	1.45732	−	0.530421i	0.512695	−	0.858571i	$-0.328647\pi$
$89$	13.7483	−	5.00398i	1.45732	−	0.530421i	0.944626	+	0.328150i	$0.106425\pi$
$90$		0			0
$91$	−0.527611	−	0.0930321i	−0.0553087	−	0.00975242i
$92$		0			0
$93$	−3.95916	−	5.97338i	−0.410545	−	0.619410i
$94$		0			0
$95$	−3.04087	+	12.9365i	−0.311986	+	1.32726i
$96$		0			0
$97$	−9.45707	−	11.2705i	−0.960220	−	1.14435i	−0.989465	−	0.144773i	$-0.953755\pi$
$97$	−9.45707	−	11.2705i	−0.960220	−	1.14435i	0.0292448	−	0.999572i	$-0.490690\pi$
$98$		0			0
$99$	8.24772	+	3.48858i	0.828927	+	0.350615i
$100$		0			0
$101$	1.48369	+	4.07641i	0.147633	+	0.405618i	0.991362	−	0.131151i	$-0.0418672\pi$
$101$	1.48369	+	4.07641i	0.147633	+	0.405618i	−0.843730	+	0.536768i	$0.819645\pi$
$102$		0			0
$103$	−9.42665	+	5.44248i	−0.928836	+	0.536263i	−0.886443	−	0.462838i	$-0.846831\pi$
$103$	−9.42665	+	5.44248i	−0.928836	+	0.536263i	−0.0423924	+	0.999101i	$0.513498\pi$
$104$		0			0
$105$	−1.92300	+	1.82718i	−0.187665	+	0.178315i
$106$		0			0
$107$	0.00726143	−	0.0125772i	0.000701989	−	0.00121588i	−0.865674	−	0.500608i	$-0.833110\pi$
$107$	0.00726143	−	0.0125772i	0.000701989	−	0.00121588i	0.866376	+	0.499392i	$0.166443\pi$
$108$		0			0
$109$	2.18035	−	0.384455i	0.208840	−	0.0368241i	−0.0682494	−	0.997668i	$-0.521741\pi$
$109$	2.18035	−	0.384455i	0.208840	−	0.0368241i	0.277089	+	0.960844i	$0.410630\pi$
$110$		0			0
$111$	1.08171	−	2.17304i	0.102672	−	0.206256i
$112$		0			0
$113$	−2.29809			−0.216186			−0.108093	−	0.994141i	$-0.534474\pi$
$113$	−2.29809			−0.216186			−0.108093	+	0.994141i	$0.534474\pi$
$114$		0			0
$115$	−27.3361			−2.54911
$116$		0			0
$117$	−1.73917	+	2.68556i	−0.160786	+	0.248280i
$118$		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
$123$	5.32168	+	5.60075i	0.479840	+	0.505002i
$124$		0			0
$125$	1.86205	−	1.07506i	0.166547	−	0.0961561i
$126$		0			0
$127$	−4.01211	−	11.0232i	−0.356018	−	0.978150i	−0.980398	−	0.197029i	$-0.936871\pi$
$127$	−4.01211	−	11.0232i	−0.356018	−	0.978150i	0.624380	−	0.781121i	$-0.285352\pi$
$128$		0			0
$129$	−1.52500	+	5.16035i	−0.134269	+	0.454343i
$130$		0			0
$131$	−6.67229	−	7.95173i	−0.582961	−	0.694745i	0.391276	−	0.920273i	$-0.372034\pi$
$131$	−6.67229	−	7.95173i	−0.582961	−	0.694745i	−0.974237	+	0.225528i	$0.927589\pi$
$132$		0			0
$133$	1.31080	+	1.75396i	0.113661	+	0.152088i
$134$		0			0
$135$	5.57616	+	14.8278i	0.479919	+	1.27618i
$136$		0			0
$137$	12.8792	+	2.27095i	1.10034	+	0.194020i	0.694195	−	0.719787i	$-0.255760\pi$
$137$	12.8792	+	2.27095i	1.10034	+	0.194020i	0.406148	+	0.913807i	$0.366872\pi$
$138$		0			0
$139$	12.6952	−	4.62068i	1.07679	−	0.391921i	0.258081	−	0.966123i	$-0.416910\pi$
$139$	12.6952	−	4.62068i	1.07679	−	0.391921i	0.818714	+	0.574202i	$0.194688\pi$
$140$		0			0
$141$	−3.87583	+	1.68819i	−0.326404	+	0.142171i
$142$		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
$147$	−0.720908	−	11.6650i	−0.0594595	−	0.962115i
$148$		0			0
$149$	6.94182	−	19.0725i	0.568696	−	1.56248i	−0.237846	−	0.971303i	$-0.576441\pi$
$149$	6.94182	−	19.0725i	0.568696	−	1.56248i	0.806542	−	0.591176i	$-0.201336\pi$
$150$		0			0
$151$		−	23.4871i		−	1.91135i	−0.294424	−	0.955675i	$-0.595128\pi$
$151$		−	23.4871i		−	1.91135i	0.294424	−	0.955675i	$-0.404872\pi$
$152$		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	0.764259	+	0.644909i	$0.223105\pi$
$157$	3.34127	+	18.9493i	0.266662	+	1.51232i	−0.497597	+	0.867409i	$0.665784\pi$
$158$		0			0
$159$	11.7339	−	15.8785i	0.930558	−	1.25925i
$160$		0			0
$161$	−2.89524	+	3.45041i	−0.228177	+	0.271931i
$162$		0			0
$163$	9.17668	+	15.8945i	0.718773	+	1.24495i	0.961486	+	0.274853i	$0.0886292\pi$
$163$	9.17668	+	15.8945i	0.718773	+	1.24495i	−0.242714	+	0.970098i	$0.578038\pi$
$164$		0			0
$165$	15.3249	−	3.68948i	1.19304	−	0.287226i
$166$		0			0
$167$	−1.00462	+	5.69749i	−0.0777399	+	0.440885i	0.920949	+	0.389684i	$0.127416\pi$
$167$	−1.00462	+	5.69749i	−0.0777399	+	0.440885i	−0.998688	+	0.0512005i	$0.983695\pi$
$168$		0			0
$169$	9.08725	−	7.62511i	0.699019	−	0.586547i
$170$		0			0
$171$	12.6968	−	3.12920i	0.970947	−	0.239296i
$172$		0			0
$173$	−6.03354	+	5.06274i	−0.458722	+	0.384913i	−0.842660	−	0.538445i	$-0.819012\pi$
$173$	−6.03354	+	5.06274i	−0.458722	+	0.384913i	0.383939	+	0.923359i	$0.374567\pi$
$174$		0			0
$175$	−0.374634	+	2.12465i	−0.0283197	+	0.160609i
$176$		0			0
$177$	−18.8275	+	4.53274i	−1.41516	+	0.340702i
$178$		0			0
$179$	1.55348	+	2.69071i	0.116113	+	0.201113i	0.918224	−	0.396062i	$-0.129623\pi$
$179$	1.55348	+	2.69071i	0.116113	+	0.201113i	−0.802111	+	0.597174i	$0.796290\pi$
$180$		0			0
$181$	−13.0813	+	15.5897i	−0.972329	+	1.15878i	0.0149680	+	0.999888i	$0.495235\pi$
$181$	−13.0813	+	15.5897i	−0.972329	+	1.15878i	−0.987297	+	0.158888i	$0.949209\pi$
$182$		0			0
$183$	−9.01972	+	12.2057i	−0.666757	+	0.902270i
$184$		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	−0.420448	−	0.907317i	$-0.638127\pi$
$193$	6.73569	−	18.5062i	0.484846	−	1.33210i	0.905294	−	0.424786i	$-0.139651\pi$
$194$		0			0
$195$	0.347384	+	5.62102i	0.0248767	+	0.402530i
$196$		0			0
$197$	16.3958	+	9.46613i	1.16815	+	0.674434i	0.953245	−	0.302200i	$-0.0977210\pi$
$197$	16.3958	+	9.46613i	1.16815	+	0.674434i	0.214910	+	0.976634i	$0.431054\pi$
$198$		0			0
$199$	7.54426	+	6.33039i	0.534798	+	0.448749i	0.869755	−	0.493485i	$-0.164277\pi$
$199$	7.54426	+	6.33039i	0.534798	+	0.448749i	−0.334956	+	0.942234i	$0.608722\pi$
$200$		0			0
$201$	17.1532	−	7.47139i	1.20989	−	0.526992i
$202$		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
$207$	12.2424	+	23.9518i	0.850909	+	1.66477i
$208$		0			0
$209$	−1.53434	−	12.9208i	−0.106133	−	0.893749i
$210$		0			0
$211$	4.12402	+	4.91482i	0.283909	+	0.338350i	0.889085	−	0.457742i	$-0.151342\pi$
$211$	4.12402	+	4.91482i	0.283909	+	0.338350i	−0.605176	+	0.796092i	$0.706897\pi$
$212$		0			0
$213$	5.73215	−	19.3967i	0.392760	−	1.32904i
$214$		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
$219$	−12.0039	−	12.6333i	−0.811146	−	0.853682i
$220$		0			0
$221$	−0.718753	+	1.24492i	−0.0483486	+	0.0837421i
$222$		0			0
$223$	12.6942	−	2.23832i	0.850064	−	0.149889i	0.268389	−	0.963311i	$-0.413509\pi$
$223$	12.6942	−	2.23832i	0.850064	−	0.149889i	0.581675	+	0.813421i	$0.302398\pi$
$224$		0			0
$225$	10.8146	+	7.00352i	0.720970	+	0.466901i
$226$		0			0
$227$	−21.6249			−1.43529			−0.717646	−	0.696408i	$-0.754780\pi$
$227$	−21.6249			−1.43529			−0.717646	+	0.696408i	$0.754780\pi$
$228$		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
$231$	1.15740	−	2.32510i	0.0761517	−	0.152980i
$232$		0			0
$233$	−13.5750	+	2.39364i	−0.889330	+	0.156813i	−0.599604	−	0.800297i	$-0.704675\pi$
$233$	−13.5750	+	2.39364i	−0.889330	+	0.156813i	−0.289726	+	0.957110i	$0.593564\pi$
$234$		0			0
$235$	−3.72062	+	6.44430i	−0.242706	+	0.420380i
$236$		0			0
$237$	−1.13932	+	1.08255i	−0.0740067	+	0.0703192i
$238$		0			0
$239$	−16.7801	+	9.68797i	−1.08541	+	0.626663i	−0.932351	−	0.361554i	$-0.882246\pi$
$239$	−16.7801	+	9.68797i	−1.08541	+	0.626663i	−0.153061	+	0.988217i	$0.548913\pi$
$240$		0			0
$241$	8.64165	+	23.7427i	0.556657	+	1.52940i	0.824454	+	0.565928i	$0.191482\pi$
$241$	8.64165	+	23.7427i	0.556657	+	1.52940i	−0.267797	+	0.963475i	$0.586296\pi$
$242$		0			0
$243$	10.4948	−	11.5264i	0.673243	−	0.739421i
$244$		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
$249$	6.84658	+	10.3298i	0.433885	+	0.654623i
$250$		0			0
$251$	−18.4169	−	3.24740i	−1.16247	−	0.204974i	−0.441054	−	0.897480i	$-0.645395\pi$
$251$	−18.4169	−	3.24740i	−1.16247	−	0.204974i	−0.721412	+	0.692506i	$0.756507\pi$
$252$		0			0
$253$	25.1511	−	9.15424i	1.58123	−	0.575522i
$254$		0			0
$255$	2.84223	+	6.52534i	0.177987	+	0.408633i
$256$		0			0
$257$	−6.22334	−	5.22200i	−0.388201	−	0.325739i	0.427711	−	0.903916i	$-0.359320\pi$
$257$	−6.22334	−	5.22200i	−0.388201	−	0.325739i	−0.815912	+	0.578176i	$0.803765\pi$
$258$		0			0
$259$	−0.609688	−	0.352003i	−0.0378842	−	0.0218724i
$260$		0			0
$261$	−0.687417	+	13.4437i	−0.0425500	+	0.832146i
$262$		0			0
$263$	3.43690	−	9.44282i	0.211929	−	0.582269i	−0.787491	−	0.616326i	$-0.788620\pi$
$263$	3.43690	−	9.44282i	0.211929	−	0.582269i	0.999420	+	0.0340568i	$0.0108427\pi$
$264$		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	$-0.428538\pi$
$269$	−3.82959	−	1.39386i	−0.233494	−	0.0849850i	−0.456117	+	0.889920i	$0.650760\pi$
$270$		0			0
$271$	0.785166	+	4.45290i	0.0476955	+	0.270494i	0.999324	−	0.0367557i	$-0.0117023\pi$
$271$	0.785166	+	4.45290i	0.0476955	+	0.270494i	−0.951629	+	0.307250i	$0.900591\pi$
$272$		0			0
$273$	0.746288	+	0.551490i	0.0451674	+	0.0333777i
$274$		0			0
$275$	8.24058	−	9.82074i	0.496926	−	0.592213i
$276$		0			0
$277$	11.8387	+	20.5052i	0.711317	+	1.23204i	0.964363	+	0.264583i	$0.0852344\pi$
$277$	11.8387	+	20.5052i	0.711317	+	1.23204i	−0.253046	+	0.967454i	$0.581432\pi$
$278$		0			0
$279$	1.52836	+	12.3180i	0.0915004	+	0.737458i
$280$		0			0
$281$	4.01031	−	22.7436i	0.239235	−	1.35677i	−0.594273	−	0.804264i	$-0.702560\pi$
$281$	4.01031	−	22.7436i	0.239235	−	1.35677i	0.833508	−	0.552507i	$-0.186329\pi$
$282$		0			0
$283$	−6.38454	+	5.35727i	−0.379522	+	0.318457i	−0.812515	−	0.582941i	$-0.801902\pi$
$283$	−6.38454	+	5.35727i	−0.379522	+	0.318457i	0.432993	+	0.901397i	$0.357457\pi$
$284$		0			0
$285$	14.7001	−	17.7118i	0.870760	−	1.04916i
$286$		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
$291$	5.96463	+	24.7751i	0.349653	+	1.45234i
$292$		0			0
$293$	−4.06803	−	7.04603i	−0.237657	−	0.411634i	0.722385	−	0.691491i	$-0.243046\pi$
$293$	−4.06803	−	7.04603i	−0.237657	−	0.411634i	−0.960041	+	0.279858i	$0.909713\pi$
$294$		0			0
$295$	−21.9105	+	26.1119i	−1.27568	+	1.52030i
$296$		0			0
$297$	−10.0959	−	11.7753i	−0.585826	−	0.683271i
$298$		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	−0.823672	−	0.567067i	$-0.808078\pi$
$307$	3.01020	−	8.27046i	0.171801	−	0.472020i	0.995473	+	0.0950472i	$0.0303002\pi$
$308$		0			0
$309$	18.8174	−	1.16293i	1.07048	−	0.0661568i
$310$		0			0
$311$	−2.88199	−	1.66392i	−0.163423	−	0.0943522i	0.416058	−	0.909338i	$-0.363411\pi$
$311$	−2.88199	−	1.66392i	−0.163423	−	0.0943522i	−0.579481	+	0.814986i	$0.696745\pi$
$312$		0			0
$313$	2.30378	+	1.93310i	0.130217	+	0.109265i	0.705570	−	0.708640i	$-0.250691\pi$
$313$	2.30378	+	1.93310i	0.130217	+	0.109265i	−0.575353	+	0.817905i	$0.695135\pi$
$314$		0			0
$315$	4.39204	−	1.34889i	0.247463	−	0.0760014i
$316$		0			0
$317$	−9.87705	+	3.59495i	−0.554750	+	0.201913i	−0.604156	−	0.796866i	$-0.706490\pi$
$317$	−9.87705	+	3.59495i	−0.554750	+	0.201913i	0.0494055	+	0.998779i	$0.484267\pi$
$318$		0			0
$319$	13.1908	+	2.32589i	0.738541	+	0.130225i
$320$		0			0
$321$	−0.0209670	+	0.0138969i	−0.00117026	+	0.000775651i
$322$		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
$327$	−3.67751	−	1.08679i	−0.203367	−	0.0600994i
$328$		0			0
$329$	0.419350	+	1.15216i	0.0231195	+	0.0635204i
$330$		0			0
$331$	12.2016	−	7.04460i	0.670660	−	0.387206i	−0.125666	−	0.992073i	$-0.540107\pi$
$331$	12.2016	−	7.04460i	0.670660	−	0.387206i	0.796327	+	0.604867i	$0.206774\pi$
$332$		0			0
$333$	−3.35453	+	2.53451i	−0.183827	+	0.138890i
$334$		0			0
$335$	16.4663	−	28.5204i	0.899649	−	1.55824i
$336$		0			0
$337$	−23.2737	+	4.10377i	−1.26780	+	0.223547i	−0.766791	−	0.641897i	$-0.778148\pi$
$337$	−23.2737	+	4.10377i	−1.26780	+	0.223547i	−0.501006	+	0.865444i	$0.667037\pi$
$338$		0			0
$339$	3.56333	+	1.77379i	0.193534	+	0.0963388i
$340$		0			0
$341$	12.3506			0.668823
$342$		0			0
$343$	−6.90602			−0.372890
$344$		0			0
$345$	42.3864	+	21.0994i	2.28201	+	1.13596i
$346$		0			0
$347$	27.6393	−	4.87356i	1.48376	−	0.261626i	0.627679	−	0.778472i	$-0.284005\pi$
$347$	27.6393	−	4.87356i	1.48376	−	0.261626i	0.856078	+	0.516846i	$0.172894\pi$
$348$		0			0
$349$	−6.13085	+	10.6190i	−0.328177	+	0.568419i	−0.982150	−	0.188098i	$-0.939768\pi$
$349$	−6.13085	+	10.6190i	−0.328177	+	0.568419i	0.653973	+	0.756518i	$0.273101\pi$
$350$		0			0
$351$	4.76955	−	2.82174i	0.254579	−	0.150614i
$352$		0			0
$353$	−8.24176	+	4.75838i	−0.438665	+	0.253263i	−0.703031	−	0.711159i	$-0.748171\pi$
$353$	−8.24176	+	4.75838i	−0.438665	+	0.253263i	0.264366	+	0.964422i	$0.414837\pi$
$354$		0			0
$355$	−12.1764	−	33.4544i	−0.646256	−	1.77557i
$356$		0			0
$357$	1.12467	+	0.332364i	0.0595237	+	0.0175906i
$358$		0			0
$359$	13.5098	+	16.1003i	0.713018	+	0.849741i	0.993933	−	0.109991i	$-0.0350823\pi$
$359$	13.5098	+	16.1003i	0.713018	+	0.849741i	−0.280915	+	0.959733i	$0.590638\pi$
$360$		0			0
$361$	−13.0894	−	13.7720i	−0.688915	−	0.724842i
$362$		0			0
$363$	3.01658	−	1.99939i	0.158329	−	0.104941i
$364$		0			0
$365$	−30.2084	−	5.32656i	−1.58118	−	0.278805i
$366$		0			0
$367$	−8.76232	+	3.18922i	−0.457389	+	0.166476i	−0.560431	−	0.828201i	$-0.689365\pi$
$367$	−8.76232	+	3.18922i	−0.457389	+	0.166476i	0.103042	+	0.994677i	$0.467142\pi$
$368$		0			0
$369$	−3.92866	−	12.7919i	−0.204518	−	0.665918i
$370$		0			0
$371$	−4.38652	−	3.68073i	−0.227737	−	0.191094i
$372$		0			0
$373$	−23.1689	−	13.3766i	−1.19964	−	0.692612i	−0.239164	−	0.970979i	$-0.576873\pi$
$373$	−23.1689	−	13.3766i	−1.19964	−	0.692612i	−0.960475	+	0.278367i	$0.910207\pi$
$374$		0			0
$375$	−3.71702	+	0.229715i	−0.191946	+	0.0118624i
$376$		0			0
$377$	−1.63675	+	4.49692i	−0.0842967	+	0.231603i
$378$		0			0
$379$		−	14.5951i		−	0.749702i	−0.927085	−	0.374851i	$-0.877694\pi$
$379$		−	14.5951i		−	0.749702i	0.927085	−	0.374851i	$-0.122306\pi$
$380$		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	$-0.459486\pi$
$383$	−8.09064	−	2.94475i	−0.413412	−	0.150470i	−0.540349	+	0.841441i	$0.681708\pi$
$384$		0			0
$385$	−0.793854	−	4.50217i	−0.0404585	−	0.229452i
$386$		0			0
$387$	6.34763	−	6.82437i	0.322668	−	0.346902i
$388$		0			0
$389$	6.90987	−	8.23486i	0.350344	−	0.417524i	−0.561878	−	0.827220i	$-0.689921\pi$
$389$	6.90987	−	8.23486i	0.350344	−	0.417524i	0.912222	+	0.409696i	$0.134365\pi$
$390$		0			0
$391$	6.04274	+	10.4663i	0.305595	+	0.529305i
$392$		0			0
$393$	4.20825	+	17.4797i	0.212278	+	0.881733i
$394$		0			0
$395$	−0.480368	+	2.72430i	−0.0241699	+	0.137074i
$396$		0			0
$397$	−25.1589	+	21.1108i	−1.26269	+	1.05952i	−0.267300	+	0.963613i	$0.586131\pi$
$397$	−25.1589	+	21.1108i	−1.26269	+	1.05952i	−0.995390	+	0.0959094i	$0.969424\pi$
$398$		0			0
$399$	−0.678683	−	3.73138i	−0.0339767	−	0.186802i
$400$		0			0
$401$	−28.2343	+	23.6914i	−1.40995	+	1.18309i	−0.453479	+	0.891267i	$0.649817\pi$
$401$	−28.2343	+	23.6914i	−1.40995	+	1.18309i	−0.956472	+	0.291823i	$0.905738\pi$
$402$		0			0
$403$	−0.766248	+	4.34561i	−0.0381695	+	0.216470i
$404$		0			0
$405$	2.79871	−	27.2955i	0.139069	−	1.35632i
$406$		0			0
$407$	2.09170	+	3.62294i	0.103682	+	0.179582i
$408$		0			0
$409$	−4.93171	+	5.87739i	−0.243858	+	0.290618i	−0.874065	−	0.485808i	$-0.838525\pi$
$409$	−4.93171	+	5.87739i	−0.243858	+	0.290618i	0.630208	+	0.776427i	$0.282970\pi$
$410$		0			0
$411$	−18.2172	−	13.4621i	−0.898586	−	0.664035i
$412$		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	−0.877705	−	0.479202i	$-0.840926\pi$
$421$	2.10684	−	5.78848i	0.102681	−	0.282113i	0.980386	+	0.197088i	$0.0631485\pi$
$422$		0			0
$423$	7.31275	+	0.373922i	0.355558	+	0.0181807i
$424$		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
$429$	−2.20197	−	5.05539i	−0.106312	−	0.244076i
$430$		0			0
$431$	−27.3336	+	9.94860i	−1.31661	+	0.479207i	−0.902371	−	0.430960i	$-0.858175\pi$
$431$	−27.3336	+	9.94860i	−1.31661	+	0.479207i	−0.414240	+	0.910168i	$0.635953\pi$
$432$		0			0
$433$	1.86446	+	0.328754i	0.0896001	+	0.0157989i	0.218268	−	0.975889i	$-0.429959\pi$
$433$	1.86446	+	0.328754i	0.0896001	+	0.0157989i	−0.128668	+	0.991688i	$0.541070\pi$
$434$		0			0
$435$	13.0904	+	19.7501i	0.627635	+	0.946944i
$436$		0			0
$437$	21.4167	−	32.6934i	1.02450	−	1.56394i
$438$		0			0
$439$	−16.4094	−	19.5560i	−0.783179	−	0.933357i	0.215893	−	0.976417i	$-0.430734\pi$
$439$	−16.4094	−	19.5560i	−0.783179	−	0.933357i	−0.999072	+	0.0430602i	$0.986289\pi$
$440$		0			0
$441$	−7.88585	+	18.6438i	−0.375517	+	0.887799i
$442$		0			0
$443$	−3.36718	−	9.25126i	−0.159980	−	0.439541i	0.833642	−	0.552305i	$-0.186252\pi$
$443$	−3.36718	−	9.25126i	−0.159980	−	0.439541i	−0.993622	+	0.112764i	$0.964029\pi$
$444$		0			0
$445$	−38.6290	+	22.3025i	−1.83119	+	1.05724i
$446$		0			0
$447$	−25.4849	+	24.2150i	−1.20539	+	1.14533i
$448$		0			0
$449$	−4.70447	+	8.14838i	−0.222018	+	0.384546i	−0.955420	−	0.295249i	$-0.904598\pi$
$449$	−4.70447	+	8.14838i	−0.222018	+	0.384546i	0.733403	+	0.679794i	$0.237931\pi$
$450$		0			0
$451$	−13.1126	+	2.31211i	−0.617449	+	0.108873i
$452$		0			0
$453$	−18.1285	+	36.4182i	−0.851752	+	1.71107i
$454$		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
$459$	4.44459	−	5.41272i	0.207456	−	0.252644i
$460$		0			0
$461$	−39.2642	+	6.92335i	−1.82872	+	0.322452i	−0.978856	−	0.204552i	$-0.934426\pi$
$461$	−39.2642	+	6.92335i	−1.82872	+	0.322452i	−0.849862	+	0.527004i	$0.823315\pi$
$462$		0			0
$463$	16.8000	−	29.0985i	0.780763	−	1.35232i	−0.150735	−	0.988574i	$-0.548164\pi$
$463$	16.8000	−	29.0985i	0.780763	−	1.35232i	0.931498	−	0.363747i	$-0.118503\pi$
$464$		0			0
$465$	15.0494	+	15.8385i	0.697898	+	0.734495i
$466$		0			0
$467$	−19.8364	+	11.4526i	−0.917920	+	0.529961i	−0.882971	−	0.469428i	$-0.844460\pi$
$467$	−19.8364	+	11.4526i	−0.917920	+	0.529961i	−0.0349490	+	0.999389i	$0.511127\pi$
$468$		0			0
$469$	−1.85591	−	5.09908i	−0.0856981	−	0.235454i
$470$		0			0
$471$	9.44519	−	31.9610i	0.435211	−	1.47269i
$472$		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
$477$	−30.4500	+	15.5639i	−1.39421	+	0.712620i
$478$		0			0
$479$	−26.6499	−	4.69910i	−1.21767	−	0.214707i	−0.472345	−	0.881414i	$-0.656592\pi$
$479$	−26.6499	−	4.69910i	−1.21767	−	0.214707i	−0.745320	+	0.666706i	$0.767703\pi$
$480$		0			0
$481$	−1.40452	+	0.511203i	−0.0640405	+	0.0233088i
$482$		0			0
$483$	7.15246	−	3.11539i	0.325448	−	0.141755i
$484$		0			0
$485$	34.3607	+	28.8320i	1.56024	+	1.30920i
$486$		0			0
$487$	−7.28099	−	4.20368i	−0.329933	−	0.190487i	0.325878	−	0.945412i	$-0.394340\pi$
$487$	−7.28099	−	4.20368i	−0.329933	−	0.190487i	−0.655811	+	0.754925i	$0.727673\pi$
$488$		0			0
$489$	−1.96084	−	31.7284i	−0.0886723	−	1.43481i
$490$		0			0
$491$	6.36016	−	17.4744i	0.287030	−	0.788608i	−0.709449	−	0.704757i	$-0.751056\pi$
$491$	6.36016	−	17.4744i	0.287030	−	0.788608i	0.996478	−	0.0838507i	$-0.0267219\pi$
$492$		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	0.844406	+	0.535704i	$0.179954\pi$
$499$	5.23041	+	29.6631i	0.234145	+	1.32790i	−0.610261	+	0.792201i	$0.708935\pi$
$500$		0			0
$501$	5.95534	−	8.05889i	0.266065	−	0.360045i
$502$		0			0
$503$	6.47202	−	7.71305i	0.288573	−	0.343908i	−0.602209	−	0.798338i	$-0.705713\pi$
$503$	6.47202	−	7.71305i	0.288573	−	0.343908i	0.890782	+	0.454430i	$0.150157\pi$
$504$		0			0
$505$	−6.61273	−	11.4536i	−0.294262	−	0.509677i
$506$		0			0
$507$	−19.9758	+	4.80920i	−0.887157	+	0.213584i
$508$		0			0
$509$	0.370885	−	2.10339i	0.0164392	−	0.0932312i	−0.975484	−	0.220069i	$-0.929372\pi$
$509$	0.370885	−	2.10339i	0.0164392	−	0.0932312i	0.991923	+	0.126838i	$0.0404828\pi$
$510$		0			0
$511$	−3.87178	+	3.24881i	−0.171277	+	0.143719i
$512$		0			0
$513$	−22.1024	−	4.94800i	−0.975846	−	0.218459i
$514$		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
$519$	13.2631	−	3.19310i	0.582184	−	0.140162i
$520$		0			0
$521$	16.6879	+	28.9043i	0.731109	+	1.26632i	0.956409	+	0.292029i	$0.0943304\pi$
$521$	16.6879	+	28.9043i	0.731109	+	1.26632i	−0.225300	+	0.974289i	$0.572336\pi$
$522$		0			0
$523$	4.68360	−	5.58170i	0.204800	−	0.244071i	−0.653862	−	0.756614i	$-0.726852\pi$
$523$	4.68360	−	5.58170i	0.204800	−	0.244071i	0.858661	+	0.512543i	$0.171297\pi$
$524$		0			0
$525$	2.22081	−	3.00525i	0.0969242	−	0.131160i
$526$		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
$537$	−0.331942	−	5.37116i	−0.0143244	−	0.231783i
$538$		0			0
$539$	17.4436	+	10.0711i	0.751349	+	0.433791i
$540$		0			0
$541$	1.84017	+	1.54409i	0.0791152	+	0.0663855i	0.681488	−	0.731830i	$-0.261333\pi$
$541$	1.84017	+	1.54409i	0.0791152	+	0.0663855i	−0.602372	+	0.798215i	$0.705778\pi$
$542$		0			0
$543$	32.3164	−	14.0760i	1.38683	−	0.604059i
$544$		0			0
$545$	−6.34278	+	2.30858i	−0.271695	+	0.0988889i
$546$		0			0
$547$	−33.0653	−	5.83030i	−1.41377	−	0.249286i	−0.585980	−	0.810325i	$-0.699290\pi$
$547$	−33.0653	−	5.83030i	−1.41377	−	0.249286i	−0.827789	+	0.561040i	$0.810402\pi$
$548$		0			0
$549$	23.4066	−	11.9638i	0.998970	−	0.510602i
$550$		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
$555$	−2.09733	+	7.09702i	−0.0890265	+	0.301252i
$556$		0			0
$557$	3.34296	+	9.18470i	0.141646	+	0.389168i	0.990148	−	0.140023i	$-0.0447176\pi$
$557$	3.34296	+	9.18470i	0.141646	+	0.389168i	−0.848503	+	0.529191i	$0.822495\pi$
$558$		0			0
$559$	2.86942	−	1.65666i	0.121364	−	0.0700693i
$560$		0			0
$561$	−4.80023	−	5.05195i	−0.202666	−	0.213294i
$562$		0			0
$563$	−9.04768	+	15.6710i	−0.381314	+	0.660455i	−0.991250	−	0.131995i	$-0.957862\pi$
$563$	−9.04768	+	15.6710i	−0.381314	+	0.660455i	0.609936	+	0.792450i	$0.291195\pi$
$564$		0			0
$565$	6.89982	−	1.21662i	0.290277	−	0.0511837i
$566$		0			0
$567$	−3.14886	−	3.24419i	−0.132240	−	0.136243i
$568$		0			0
$569$	35.0017			1.46735			0.733674	−	0.679501i	$-0.237804\pi$
$569$	35.0017			1.46735			0.733674	+	0.679501i	$0.237804\pi$
$570$		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
$573$	−3.28368	+	6.59654i	−0.137178	+	0.275574i
$574$		0			0
$575$	37.9234	−	6.68692i	1.58152	−	0.278864i
$576$		0			0
$577$	8.22977	−	14.2544i	0.342610	−	0.593418i	−0.642307	−	0.766448i	$-0.722022\pi$
$577$	8.22977	−	14.2544i	0.342610	−	0.593418i	0.984917	+	0.173030i	$0.0553558\pi$
$578$		0			0
$579$	−24.7281	+	23.4960i	−1.02767	+	0.976461i
$580$		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
$585$	3.79996	−	8.98388i	0.157109	−	0.371438i
$586$		0			0
$587$	12.4840	+	14.8778i	0.515269	+	0.614073i	0.959455	−	0.281861i	$-0.0909517\pi$
$587$	12.4840	+	14.8778i	0.515269	+	0.614073i	−0.444186	+	0.895934i	$0.646507\pi$
$588$		0			0
$589$	14.4463	−	10.7963i	0.595250	−	0.444853i
$590$		0			0
$591$	−18.1163	−	27.3330i	−0.745205	−	1.12433i
$592$		0			0
$593$	21.9176	+	3.86466i	0.900046	+	0.158702i	0.604481	−	0.796620i	$-0.293381\pi$
$593$	21.9176	+	3.86466i	0.900046	+	0.158702i	0.295566	+	0.955322i	$0.404492\pi$
$594$		0			0
$595$	1.93977	−	0.706018i	0.0795227	−	0.0289439i
$596$		0			0
$597$	−6.81173	−	15.6387i	−0.278786	−	0.640050i
$598$		0			0
$599$	−0.151035	−	0.126734i	−0.00617113	−	0.00517819i	0.639697	−	0.768627i	$-0.279060\pi$
$599$	−0.151035	−	0.126734i	−0.00617113	−	0.00517819i	−0.645868	+	0.763449i	$0.723504\pi$
$600$		0			0
$601$	3.50826	+	2.02550i	0.143105	+	0.0826217i	0.569843	−	0.821754i	$-0.307004\pi$
$601$	3.50826	+	2.02550i	0.143105	+	0.0826217i	−0.426738	+	0.904375i	$0.640337\pi$
$602$		0			0
$603$	−32.3639	−	1.65486i	−1.31796	−	0.0673911i
$604$		0			0
$605$	2.17872	−	5.98597i	0.0885774	−	0.243364i
$606$		0			0
$607$		−	5.76518i		−	0.234001i	−0.993132	−	0.117001i	$-0.962672\pi$
$607$		−	5.76518i		−	0.234001i	0.993132	−	0.117001i	$-0.0373280\pi$
$608$		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	0.755433	+	0.655226i	$0.227427\pi$
$613$	6.67643	+	37.8639i	0.269659	+	1.52931i	−0.485774	+	0.874084i	$0.661462\pi$
$614$		0			0
$615$	−18.9430	−	13.9984i	−0.763854	−	0.564471i
$616$		0			0
$617$	5.06906	−	6.04107i	0.204073	−	0.243204i	−0.654295	−	0.756239i	$-0.727035\pi$
$617$	5.06906	−	6.04107i	0.204073	−	0.243204i	0.858368	+	0.513035i	$0.171479\pi$
$618$		0			0
$619$	18.8705	+	32.6847i	0.758469	+	1.31371i	0.943631	+	0.330999i	$0.107386\pi$
$619$	18.8705	+	32.6847i	0.758469	+	1.31371i	−0.185162	+	0.982708i	$0.559281\pi$
$620$		0			0
$621$	−0.495434	−	46.5882i	−0.0198811	−	1.86952i
$622$		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
$627$	−7.59383	+	21.2188i	−0.303268	+	0.847396i
$628$		0			0
$629$	−1.44703	+	1.21420i	−0.0576969	+	0.0484134i
$630$		0			0
$631$	7.84793	−	44.5078i	0.312421	−	1.77183i	−0.273909	−	0.961755i	$-0.588317\pi$
$631$	7.84793	−	44.5078i	0.312421	−	1.77183i	0.586330	−	0.810072i	$-0.300572\pi$
$632$		0			0
$633$	−2.60104	−	10.8039i	−0.103382	−	0.429415i
$634$		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
$639$	−23.8594	+	25.6514i	−0.943864	+	1.01475i
$640$		0			0
$641$	−5.87061	−	33.2939i	−0.231875	−	1.31503i	−0.849096	−	0.528239i	$-0.822852\pi$
$641$	−5.87061	−	33.2939i	−0.231875	−	1.31503i	0.617221	−	0.786790i	$-0.288259\pi$
$642$		0			0
$643$	24.7485	+	9.00773i	0.975987	+	0.355230i	0.780279	−	0.625432i	$-0.215077\pi$
$643$	24.7485	+	9.00773i	0.975987	+	0.355230i	0.195708	+	0.980662i	$0.437299\pi$
$644$		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
$651$	3.59309	−	0.222055i	0.140824	−	0.00870304i
$652$		0			0
$653$	−1.61603	−	0.933017i	−0.0632403	−	0.0365118i	0.468046	−	0.883704i	$-0.344958\pi$
$653$	−1.61603	−	0.933017i	−0.0632403	−	0.0365118i	−0.531287	+	0.847192i	$0.678291\pi$
$654$		0			0
$655$	24.2427	+	20.3420i	0.947239	+	0.794828i
$656$		0			0
$657$	8.86168	+	28.8540i	0.345727	+	1.12570i
$658$		0			0
$659$	−21.7551	+	7.91819i	−0.847457	+	0.308449i	−0.729003	−	0.684511i	$-0.760016\pi$
$659$	−21.7551	+	7.91819i	−0.847457	+	0.308449i	−0.118454	+	0.992960i	$0.537794\pi$
$660$		0			0
$661$	31.4688	+	5.54881i	1.22400	+	0.215824i	0.748045	−	0.663648i	$-0.230993\pi$
$661$	31.4688	+	5.54881i	1.22400	+	0.215824i	0.475951	+	0.879472i	$0.342104\pi$
$662$		0			0
$663$	2.07536	−	1.37555i	0.0806004	−	0.0534220i
$664$		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
$669$	−21.4107	−	6.32735i	−0.827787	−	0.244629i
$670$		0			0
$671$	−8.94587	−	24.5786i	−0.345351	−	0.948845i
$672$		0			0
$673$	23.8610	−	13.7761i	0.919773	−	0.531031i	0.0362101	−	0.999344i	$-0.488471\pi$
$673$	23.8610	−	13.7761i	0.919773	−	0.531031i	0.883563	+	0.468313i	$0.155138\pi$
$674$		0			0
$675$	−11.3630	−	19.2066i	−0.437361	−	0.739264i
$676$		0			0
$677$	−7.78920	+	13.4913i	−0.299363	+	0.518512i	−0.975990	−	0.217814i	$-0.930108\pi$
$677$	−7.78920	+	13.4913i	−0.299363	+	0.518512i	0.676627	+	0.736326i	$0.263441\pi$
$678$		0			0
$679$	7.27846	−	1.28339i	0.279322	−	0.0492520i
$680$		0			0
$681$	33.5307	+	16.6912i	1.28490	+	0.639607i
$682$		0			0
$683$	8.29883			0.317546			0.158773	−	0.987315i	$-0.449246\pi$
$683$	8.29883			0.317546			0.158773	+	0.987315i	$0.449246\pi$
$684$		0			0
$685$	−39.8709			−1.52339
$686$		0			0
$687$	−16.1973	−	8.06280i	−0.617964	−	0.307615i
$688$		0			0
$689$	−11.9724	+	2.11106i	−0.456113	+	0.0804251i
$690$		0			0
$691$	1.43902	−	2.49245i	0.0547428	−	0.0948173i	−0.837355	−	0.546659i	$-0.815899\pi$
$691$	1.43902	−	2.49245i	0.0547428	−	0.0948173i	0.892098	+	0.451842i	$0.149233\pi$
$692$		0			0
$693$	−3.58926	+	2.71186i	−0.136345	+	0.103015i
$694$		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
$699$	22.8965	+	6.76642i	0.866024	+	0.255929i
$700$		0			0
$701$	−27.5980	−	32.8900i	−1.04236	−	1.24224i	−0.969550	−	0.244892i	$-0.921248\pi$
$701$	−27.5980	−	32.8900i	−1.04236	−	1.24224i	−0.0728104	−	0.997346i	$-0.523197\pi$
$702$		0			0
$703$	5.61363	+	2.40923i	0.211722	+	0.0908660i
$704$		0			0
$705$	10.7431	−	7.12053i	0.404608	−	0.268175i
$706$		0			0
$707$	−2.14606	−	0.378408i	−0.0807109	−	0.0142315i
$708$		0			0
$709$	5.43501	−	1.97818i	0.204116	−	0.0742922i	−0.237939	−	0.971280i	$-0.576472\pi$
$709$	5.43501	−	1.97818i	0.204116	−	0.0742922i	0.442055	+	0.896988i	$0.354250\pi$
$710$		0			0
$711$	2.60215	−	0.799178i	0.0975884	−	0.0299715i
$712$		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
$717$	33.4962	−	2.07009i	1.25094	−	0.0773090i
$718$		0			0
$719$	−6.82611	+	18.7546i	−0.254571	+	0.699428i	0.744908	+	0.667167i	$0.232493\pi$
$719$	−6.82611	+	18.7546i	−0.254571	+	0.699428i	−0.999479	+	0.0322615i	$0.989729\pi$
$720$		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	−0.700619	−	0.713536i	$-0.747093\pi$
$727$	−7.71938	−	43.7788i	−0.286296	−	1.62367i	0.414323	−	0.910130i	$-0.364018\pi$
$728$		0			0
$729$	−25.1696	+	9.77202i	−0.932207	+	0.361927i
$730$		0			0
$731$	2.69162	−	3.20774i	0.0995530	−	0.118643i
$732$		0			0
$733$	−20.5246	−	35.5497i	−0.758094	−	1.31306i	−0.943822	−	0.330455i	$-0.892798\pi$
$733$	−20.5246	−	35.5497i	−0.758094	−	1.31306i	0.185728	−	0.982601i	$-0.440536\pi$
$734$		0			0
$735$	8.34000	+	34.6416i	0.307625	+	1.27777i
$736$		0			0
$737$	−5.59925	+	31.7549i	−0.206251	+	1.16971i
$738$		0			0
$739$	16.8328	−	14.1244i	0.619203	−	0.519573i	−0.278350	−	0.960480i	$-0.589787\pi$
$739$	16.8328	−	14.1244i	0.619203	−	0.519573i	0.897553	+	0.440907i	$0.145343\pi$
$740$		0			0
$741$	−6.99478	−	3.98836i	−0.256959	−	0.146516i
$742$		0			0
$743$	37.9084	−	31.8089i	1.39072	−	1.16696i	0.425678	−	0.904875i	$-0.360036\pi$
$743$	37.9084	−	31.8089i	1.39072	−	1.16696i	0.965046	−	0.262081i	$-0.0844088\pi$
$744$		0			0
$745$	−10.7451	+	60.9385i	−0.393670	+	2.23261i
$746$		0			0
$747$	−2.64300	−	21.3015i	−0.0967022	−	0.779382i
$748$		0			0
$749$	0.00364772	+	0.00631803i	0.000133285	+	0.000230856i
$750$		0			0
$751$	−13.7962	+	16.4416i	−0.503429	+	0.599964i	−0.956580	−	0.291470i	$-0.905856\pi$
$751$	−13.7962	+	16.4416i	−0.503429	+	0.599964i	0.453151	+	0.891434i	$0.350300\pi$
$752$		0			0
$753$	26.0501	+	19.2504i	0.949318	+	0.701525i
$754$		0			0
$755$	12.4342	+	70.5178i	0.452527	+	2.56641i
$756$		0			0
$757$	−42.8982	−	15.6137i	−1.55916	−	0.567489i	−0.588618	−	0.808411i	$-0.700328\pi$
$757$	−42.8982	−	15.6137i	−1.55916	−	0.567489i	−0.970544	+	0.240922i	$0.922550\pi$
$758$		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
$765$	0.629534	−	12.3117i	0.0227608	−	0.445131i
$766$		0			0
$767$	10.3267	+	5.96211i	0.372875	+	0.215279i
$768$		0			0
$769$	−12.0324	−	10.0964i	−0.433900	−	0.364085i	0.399521	−	0.916724i	$-0.369176\pi$
$769$	−12.0324	−	10.0964i	−0.433900	−	0.364085i	−0.833421	+	0.552639i	$0.813621\pi$
$770$		0			0
$771$	5.61907	+	12.9005i	0.202366	+	0.464601i
$772$		0			0
$773$	30.7512	−	11.1925i	1.10604	−	0.402566i	0.276502	−	0.961013i	$-0.410825\pi$
$773$	30.7512	−	11.1925i	1.10604	−	0.402566i	0.829540	+	0.558447i	$0.188603\pi$
$774$		0			0
$775$	17.4995	+	3.08563i	0.628600	+	0.110839i
$776$		0			0
$777$	0.673665	+	1.01639i	0.0241676	+	0.0364629i
$778$		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
$783$	11.4425	−	20.3148i	0.408920	−	0.725991i
$784$		0			0
$785$	−20.0637	−	55.1247i	−0.716106	−	1.96748i
$786$		0			0
$787$	−0.916770	+	0.529298i	−0.0326793	+	0.0188674i	−0.516251	−	0.856438i	$-0.672673\pi$
$787$	−0.916770	+	0.529298i	−0.0326793	+	0.0188674i	0.483571	+	0.875305i	$0.339339\pi$
$788$		0			0
$789$	−12.6176	+	11.9889i	−0.449198	+	0.426816i
$790$		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
$795$	−26.8238	+	53.8859i	−0.951341	+	1.91114i
$796$		0			0
$797$	35.5116			1.25789			0.628944	−	0.777451i	$-0.283488\pi$
$797$	35.5116			1.25789			0.628944	+	0.777451i	$0.283488\pi$
$798$		0			0
$799$	3.28982			0.116385
$800$		0			0
$801$	36.8413	+	23.8585i	1.30172	+	0.842998i
$802$		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
$807$	4.86217	+	5.11714i	0.171157	+	0.180132i
$808$		0			0
$809$	7.36932	−	4.25468i	0.259091	−	0.149587i	−0.364829	−	0.931075i	$-0.618872\pi$
$809$	7.36932	−	4.25468i	0.259091	−	0.149587i	0.623920	+	0.781488i	$0.285539\pi$
$810$		0			0
$811$	2.74045	+	7.52932i	0.0962302	+	0.264390i	0.978463	−	0.206424i	$-0.0661825\pi$
$811$	2.74045	+	7.52932i	0.0962302	+	0.264390i	−0.882232	+	0.470814i	$0.843960\pi$
$812$		0			0
$813$	2.21953	−	7.51053i	0.0778422	−	0.263406i
$814$		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
$819$	−0.731497	−	1.43114i	−0.0255606	−	0.0500082i
$820$		0			0
$821$	−3.69233	−	0.651058i	−0.128863	−	0.0227221i	0.108844	−	0.994059i	$-0.465285\pi$
$821$	−3.69233	−	0.651058i	−0.128863	−	0.0227221i	−0.237708	+	0.971337i	$0.576396\pi$
$822$		0			0
$823$	−24.8907	+	9.05947i	−0.867634	+	0.315793i	−0.737209	−	0.675665i	$-0.763857\pi$
$823$	−24.8907	+	9.05947i	−0.867634	+	0.315793i	−0.130426	+	0.991458i	$0.541634\pi$
$824$		0			0
$825$	−20.3577	+	8.86717i	−0.708764	+	0.308715i
$826$		0			0
$827$	35.2983	+	29.6188i	1.22744	+	1.02995i	0.998401	+	0.0565290i	$0.0180033\pi$
$827$	35.2983	+	29.6188i	1.22744	+	1.02995i	0.229041	+	0.973417i	$0.426441\pi$
$828$		0			0
$829$	0.547722	+	0.316227i	0.0190232	+	0.0109830i	0.509481	−	0.860482i	$-0.329837\pi$
$829$	0.547722	+	0.316227i	0.0190232	+	0.0109830i	−0.490458	+	0.871465i	$0.663171\pi$
$830$		0			0
$831$	−2.52965	−	40.9323i	−0.0877525	−	1.41993i
$832$		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	$-0.559362\pi$
$839$	−27.7805	−	10.1113i	−0.959090	−	0.349080i	−0.773677	+	0.633580i	$0.781585\pi$
$840$		0			0
$841$	−1.53955	−	8.73124i	−0.0530880	−	0.301077i
$842$		0			0
$843$	−23.7729	+	32.1700i	−0.818784	+	1.10800i
$844$		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
$849$	14.0347	−	3.37886i	0.481668	−	0.115962i
$850$		0			0
$851$	−2.18206	+	12.3751i	−0.0748000	+	0.424212i
$852$		0			0
$853$	17.3096	−	14.5245i	0.592669	−	0.497308i	−0.296411	−	0.955060i	$-0.595790\pi$
$853$	17.3096	−	14.5245i	0.592669	−	0.497308i	0.889080	+	0.457752i	$0.151345\pi$
$854$		0			0
$855$	−36.4643	+	16.1169i	−1.24705	+	0.551187i
$856$		0			0
$857$	29.5954	−	24.8335i	1.01096	−	0.848297i	0.0224963	−	0.999747i	$-0.492839\pi$
$857$	29.5954	−	24.8335i	1.01096	−	0.848297i	0.988465	+	0.151450i	$0.0483941\pi$
$858$		0			0
$859$	4.80636	−	27.2582i	0.163991	−	0.930039i	−0.786108	−	0.618090i	$-0.787907\pi$
$859$	4.80636	−	27.2582i	0.163991	−	0.930039i	0.950099	−	0.311950i	$-0.100982\pi$
$860$		0			0
$861$	−3.77320	+	0.908403i	−0.128590	+	0.0309583i
$862$		0			0
$863$	5.59402	+	9.68913i	0.190423	+	0.329822i	0.945390	−	0.325940i	$-0.105681\pi$
$863$	5.59402	+	9.68913i	0.190423	+	0.329822i	−0.754968	+	0.655762i	$0.772347\pi$
$864$		0			0
$865$	15.4349	−	18.3946i	0.524803	−	0.625436i
$866$		0			0
$867$	−15.6293	+	21.1499i	−0.530799	+	0.718289i
$868$		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	0.655897	+	0.754851i	$0.272291\pi$
$877$	−9.82475	+	26.9933i	−0.331758	+	0.911498i	−0.987655	+	0.156647i	$0.949931\pi$
$878$		0			0
$879$	0.869242	+	14.0652i	0.0293188	+	0.474408i
$880$		0			0
$881$	9.40019	+	5.42720i	0.316700	+	0.182847i	0.649921	−	0.760002i	$-0.274802\pi$
$881$	9.40019	+	5.42720i	0.316700	+	0.182847i	−0.333220	+	0.942849i	$0.608135\pi$
$882$		0			0
$883$	−14.2903	−	11.9910i	−0.480906	−	0.403528i	0.369848	−	0.929092i	$-0.379410\pi$
$883$	−14.2903	−	11.9910i	−0.480906	−	0.403528i	−0.850754	+	0.525564i	$0.823854\pi$
$884$		0			0
$885$	54.1282	−	23.5765i	1.81950	−	0.792517i
$886$		0			0
$887$	−4.51160	+	1.64209i	−0.151485	+	0.0551359i	−0.416650	−	0.909067i	$-0.636796\pi$
$887$	−4.51160	+	1.64209i	−0.151485	+	0.0551359i	0.265165	+	0.964203i	$0.414574\pi$
$888$		0			0
$889$	5.80326	+	1.02327i	0.194635	+	0.0343194i
$890$		0			0
$891$	6.56562	+	26.0509i	0.219957	+	0.872737i
$892$		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
$897$	4.69409	−	15.8840i	0.156731	−	0.530353i
$898$		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
$903$	−1.86193	−	1.95956i	−0.0619610	−	0.0652102i
$904$		0			0
$905$	31.0223	−	53.7322i	1.03122	−	1.78612i
$906$		0			0
$907$	−51.8502	+	9.14259i	−1.72166	+	0.303575i	−0.945175	−	0.326563i	$-0.894109\pi$
$907$	−51.8502	+	9.14259i	−1.72166	+	0.303575i	−0.776483	+	0.630138i	$0.782998\pi$
$908$		0			0
$909$	−7.07408	+	10.9235i	−0.234633	+	0.362310i
$910$		0			0
$911$	−1.55433			−0.0514972			−0.0257486	−	0.999668i	$-0.508197\pi$
$911$	−1.55433			−0.0514972			−0.0257486	+	0.999668i	$0.508197\pi$
$912$		0			0
$913$	−21.3579			−0.706845
$914$		0			0
$915$	20.6192	−	41.4216i	0.681648	−	1.36935i
$916$		0			0
$917$	5.13521	−	0.905475i	0.169579	−	0.0299014i
$918$		0			0
$919$	−18.3505	+	31.7840i	−0.605327	+	1.04846i	0.386672	+	0.922217i	$0.373624\pi$
$919$	−18.3505	+	31.7840i	−0.605327	+	1.04846i	−0.992000	+	0.126241i	$0.959709\pi$
$920$		0			0
$921$	−11.0511	+	10.5004i	−0.364145	+	0.346001i
$922$		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
$927$	−30.0752	−	12.7210i	−0.987798	−	0.417814i
$928$		0			0
$929$	−15.9003	−	18.9493i	−0.521673	−	0.621706i	0.439302	−	0.898339i	$-0.355226\pi$
$929$	−15.9003	−	18.9493i	−0.521673	−	0.621706i	−0.960976	+	0.276633i	$0.910781\pi$
$930$		0			0
$931$	29.2071	−	3.46834i	0.957225	−	0.113670i
$932$		0			0
$933$	3.18441	+	4.80448i	0.104253	+	0.157292i
$934$		0			0
$935$	−12.0800	−	2.13004i	−0.395060	−	0.0696597i
$936$		0			0
$937$	−30.2959	+	11.0268i	−0.989724	+	0.360230i	−0.785613	−	0.618718i	$-0.787652\pi$
$937$	−30.2959	+	11.0268i	−0.989724	+	0.360230i	−0.204110	+	0.978948i	$0.565430\pi$
$938$		0			0
$939$	−2.08009	−	4.77557i	−0.0678811	−	0.155845i
$940$		0			0
$941$	36.5786	+	30.6931i	1.19243	+	1.00057i	0.999814	+	0.0192917i	$0.00614113\pi$
$941$	36.5786	+	30.6931i	1.19243	+	1.00057i	0.192614	+	0.981275i	$0.438303\pi$
$942$		0			0
$943$	−34.6365	−	19.9974i	−1.12792	−	0.651205i
$944$		0			0
$945$	−7.85128	−	1.29846i	−0.255402	−	0.0422390i
$946$		0			0
$947$	12.4715	−	34.2652i	0.405270	−	1.11347i	−0.554378	−	0.832265i	$-0.687044\pi$
$947$	12.4715	−	34.2652i	0.405270	−	1.11347i	0.959648	−	0.281205i	$-0.0907340\pi$
$948$		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	$-0.601683\pi$
$953$	−35.9606	−	13.0886i	−1.16488	−	0.423981i	−0.850838	+	0.525428i	$0.823905\pi$
$954$		0			0
$955$	2.25225	+	12.7731i	0.0728810	+	0.413329i
$956$		0			0
$957$	−18.6579	−	13.7877i	−0.603123	−	0.445694i
$958$		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
$963$	0.0432370	−	0.00536465i	0.00139329	−	0.000172874i
$964$		0			0
$965$	−10.4260	+	59.1291i	−0.335626	+	1.90343i
$966$		0			0
$967$	8.52174	−	7.15059i	0.274041	−	0.229947i	−0.495401	−	0.868664i	$-0.664979\pi$
$967$	8.52174	−	7.15059i	0.274041	−	0.229947i	0.769442	+	0.638717i	$0.220534\pi$
$968$		0			0
$969$	−10.0309	−	1.71307i	−0.322240	−	0.0550317i
$970$		0			0
$971$	−12.1336	+	10.1813i	−0.389386	+	0.326734i	−0.816374	−	0.577524i	$-0.804019\pi$
$971$	−12.1336	+	10.1813i	−0.389386	+	0.326734i	0.426988	+	0.904257i	$0.359575\pi$
$972$		0			0
$973$	−1.17848	+	6.68352i	−0.0377805	+	0.214264i
$974$		0			0
$975$	−1.85693	−	7.71307i	−0.0594694	−	0.247016i
$976$		0			0
$977$	4.12154	+	7.13872i	0.131860	+	0.228388i	0.924393	−	0.381440i	$-0.124572\pi$
$977$	4.12154	+	7.13872i	0.131860	+	0.228388i	−0.792534	+	0.609828i	$0.791238\pi$
$978$		0			0
$979$	28.0727	−	33.4557i	0.897207	−	1.06925i
$980$		0			0
$981$	4.86338	+	4.52363i	0.155276	+	0.144428i
$982$		0			0
$983$	−3.81477	−	21.6346i	−0.121672	−	0.690037i	−0.983229	−	0.182376i	$-0.941621\pi$
$983$	−3.81477	−	21.6346i	−0.121672	−	0.690037i	0.861557	−	0.507661i	$-0.169490\pi$
$984$		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	0.731331	+	0.682023i	$0.238900\pi$
$991$	−8.41455	+	23.1188i	−0.267297	+	0.734393i	−0.998628	+	0.0523696i	$0.983323\pi$
$992$		0			0
$993$	−24.3567	+	1.50526i	−0.772937	+	0.0477681i
$994$		0			0
$995$	−26.0023	−	15.0124i	−0.824329	−	0.475927i
$996$		0			0
$997$	13.6792	+	11.4782i	0.433225	+	0.363519i	0.833167	−	0.553022i	$-0.186525\pi$
$997$	13.6792	+	11.4782i	0.433225	+	0.363519i	−0.399942	+	0.916540i	$0.630970\pi$
$998$		0			0
$999$	7.15767	−	1.34072i	0.226459	−	0.0424185i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bm.a.41.9	✓	60	19.3	odd	18
456.2.bm.a.89.9	yes	60	3.2	odd	2
456.2.bm.b.41.1	yes	60	57.41	even	18	inner
456.2.bm.b.89.1	yes	60	1.1	even	1	trivial
912.2.cc.g.497.10		60	228.155	odd	18
912.2.cc.g.545.10		60	4.3	odd	2
912.2.cc.h.497.2		60	76.3	even	18
912.2.cc.h.545.2		60	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.55056 - 0.771852i) q^{3} +(-3.00241 + 0.529406i) q^{5} +(-0.251171 + 0.435040i) q^{7} +(1.80849 + 2.39361i) q^{9} +(2.58513 - 1.49253i) q^{11} +(0.364767 + 1.00219i) q^{13} +(5.06405 + 1.49654i) q^{15} +(0.866390 + 1.03252i) q^{17} +(1.71910 - 4.00558i) q^{19} +(0.725243 - 0.480691i) q^{21} +(8.83018 + 1.55700i) q^{23} +(4.03575 - 1.46889i) q^{25} +(-0.956666 - 5.10733i) q^{27} +(3.43732 + 2.88425i) q^{29} +(3.58316 + 2.06874i) q^{31} +(-5.16042 + 0.318918i) q^{33} +(0.523805 - 1.43914i) q^{35} +1.40145i q^{37} +(0.207947 - 1.83550i) q^{39} +(-4.19152 - 1.52559i) q^{41} +(-0.539473 - 3.05951i) q^{43} +(-6.69702 - 6.22917i) q^{45} +(1.56889 - 1.86974i) q^{47} +(3.37383 + 5.84364i) q^{49} +(-0.546437 - 2.26972i) q^{51} +(-1.97942 + 11.2258i) q^{53} +(-6.97149 + 5.84977i) q^{55} +(-5.75729 + 4.88402i) q^{57} +(8.56486 - 7.18677i) q^{59} +(1.52156 - 8.62918i) q^{61} +(-1.49556 + 0.185562i) q^{63} +(-1.62575 - 2.81587i) q^{65} +(-6.94344 + 8.27486i) q^{67} +(-12.4900 - 9.22982i) q^{69} +(2.02777 + 11.5000i) q^{71} +(9.45460 + 3.44119i) q^{73} +(-7.39144 - 0.837389i) q^{75} +1.49952i q^{77} +(0.310339 - 0.852649i) q^{79} +(-2.45873 + 8.65764i) q^{81} +(-6.19637 - 3.57748i) q^{83} +(-3.14788 - 2.64139i) q^{85} +(-3.10356 - 7.12531i) q^{87} +(13.7483 - 5.00398i) q^{89} +(-0.527611 - 0.0930321i) q^{91} +(-3.95916 - 5.97338i) q^{93} +(-3.04087 + 12.9365i) q^{95} +(-9.45707 - 11.2705i) q^{97} +(8.24772 + 3.48858i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 6 q^{9} + 3 q^{13} - 3 q^{15} - 6 q^{17} + 3 q^{19} + 6 q^{25} + 3 q^{27} + 6 q^{29} + 24 q^{35} + 18 q^{39} + 3 q^{41} - 21 q^{43} + 63 q^{45} - 18 q^{47} - 30 q^{49} + 33 q^{51} - 36 q^{53} + 18 q^{55}+ \cdots - 39 q^{99}+O(q^{100}) \) 60 * q - 6 * q^9 + 3 * q^13 - 3 * q^15 - 6 * q^17 + 3 * q^19 + 6 * q^25 + 3 * q^27 + 6 * q^29 + 24 * q^35 + 18 * q^39 + 3 * q^41 - 21 * q^43 + 63 * q^45 - 18 * q^47 - 30 * q^49 + 33 * q^51 - 36 * q^53 + 18 * q^55 - 24 * q^57 - 21 * q^59 - 6 * q^61 - 24 * q^63 + 24 * q^65 - 48 * q^67 - 21 * q^69 + 36 * q^71 - 57 * q^73 - 36 * q^79 + 6 * q^81 - 36 * q^83 + 6 * q^85 + 72 * q^87 - 24 * q^89 - 18 * q^91 + 108 * q^93 + 30 * q^95 + 15 * q^97 - 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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