LMFDB - Embedded newform 405.3.s.a.118.33

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,3,Mod(37,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.37"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([28, 9])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.s (of order $36$, degree $12$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$408$
Relative dimension:	$34$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			118.33
Character	$\chi$	$=$	405.118
Dual form			405.3.s.a.127.33

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.324599 - 3.71019i) q^{2} +(-9.72089 - 1.71405i) q^{4} +(4.74836 + 1.56622i) q^{5} +(7.47006 + 5.23059i) q^{7} +(-5.65912 + 21.1201i) q^{8} +(7.35227 - 17.1089i) q^{10} +(7.46500 + 2.71704i) q^{11} +(-0.449058 - 5.13275i) q^{13} +(21.8312 - 26.0175i) q^{14} +(39.4204 + 14.3478i) q^{16} +(-7.59419 - 28.3419i) q^{17} +(9.25934 - 5.34588i) q^{19} +(-43.4737 - 23.3640i) q^{20} +(12.5039 - 26.8146i) q^{22} +(23.0026 - 16.1066i) q^{23} +(20.0939 + 14.8739i) q^{25} -19.1892 q^{26} +(-63.6501 - 63.6501i) q^{28} +(19.8626 + 23.6713i) q^{29} +(-3.45942 + 19.6193i) q^{31} +(29.0665 - 62.3334i) q^{32} +(-107.619 + 18.9761i) q^{34} +(27.2783 + 36.5365i) q^{35} +(6.34170 + 23.6675i) q^{37} +(-16.8287 - 36.0892i) q^{38} +(-59.9502 + 91.4226i) q^{40} +(-33.8265 - 28.3838i) q^{41} +(-9.22262 - 19.7780i) q^{43} +(-67.9093 - 39.2075i) q^{44} +(-52.2918 - 90.5720i) q^{46} +(26.5416 + 18.5846i) q^{47} +(11.6837 + 32.1007i) q^{49} +(61.7075 - 69.7242i) q^{50} +(-4.43258 + 50.6646i) q^{52} +(-36.3531 - 36.3531i) q^{53} +(31.1911 + 24.5933i) q^{55} +(-152.745 + 128.168i) q^{56} +(94.2724 - 66.0103i) q^{58} +(-13.3870 - 36.7804i) q^{59} +(1.11435 + 6.31979i) q^{61} +(71.6685 + 19.2035i) q^{62} +(-76.5134 - 44.1751i) q^{64} +(5.90670 - 25.0755i) q^{65} +(53.2028 - 4.65465i) q^{67} +(25.2427 + 288.525i) q^{68} +(144.412 - 89.3480i) q^{70} +(20.4199 - 35.3683i) q^{71} +(-14.7960 + 55.2194i) q^{73} +(89.8695 - 15.8464i) q^{74} +(-99.1722 + 36.0957i) q^{76} +(41.5523 + 59.3428i) q^{77} +(32.7011 + 38.9717i) q^{79} +(164.710 + 129.870i) q^{80} +(-116.289 + 116.289i) q^{82} +(-121.744 - 10.6512i) q^{83} +(8.32953 - 146.472i) q^{85} +(-76.3736 + 27.7977i) q^{86} +(-99.6295 + 142.286i) q^{88} +(-77.2540 + 44.6026i) q^{89} +(23.4928 - 40.6908i) q^{91} +(-251.213 + 117.143i) q^{92} +(77.5677 - 92.4416i) q^{94} +(52.3395 - 10.8821i) q^{95} +(104.160 - 48.5706i) q^{97} +(122.892 - 32.9288i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 408 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 6 q^{8} - 6 q^{10} + 60 q^{11} - 12 q^{13} - 24 q^{16} + 6 q^{17} + 300 q^{20} - 12 q^{22} + 156 q^{23} + 6 q^{25} + 48 q^{26} - 24 q^{28} - 24 q^{31} - 72 q^{32}+ \cdots + 1032 q^{98}+O(q^{100}) $ 408 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 6 * q^8 - 6 * q^10 + 60 * q^11 - 12 * q^13 - 24 * q^16 + 6 * q^17 + 300 * q^20 - 12 * q^22 + 156 * q^23 + 6 * q^25 + 48 * q^26 - 24 * q^28 - 24 * q^31 - 72 * q^32 - 156 * q^35 - 6 * q^37 + 252 * q^38 - 108 * q^40 + 384 * q^41 - 12 * q^43 - 12 * q^46 + 210 * q^47 - 276 * q^50 - 60 * q^52 - 516 * q^53 - 24 * q^55 - 912 * q^56 - 12 * q^58 - 312 * q^61 + 6 * q^62 - 420 * q^65 - 480 * q^67 + 540 * q^68 - 12 * q^70 + 12 * q^71 - 6 * q^73 - 216 * q^76 + 876 * q^77 + 1644 * q^80 - 24 * q^82 + 372 * q^83 - 12 * q^85 - 516 * q^86 + 348 * q^88 - 12 * q^91 - 2082 * q^92 - 198 * q^95 + 600 * q^97 + 1032 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	0.324599	−	3.71019i	0.162300	−	1.85509i	−0.282252	−	0.959340i	$-0.591082\pi$
$2$	0.324599	−	3.71019i	0.162300	−	1.85509i	0.444552	−	0.895753i	$-0.353363\pi$
$3$		0			0
$3$		0			0
$4$	−9.72089	−	1.71405i	−2.43022	−	0.428514i
$5$	4.74836	+	1.56622i	0.949673	+	0.313243i
$5$	4.74836	+	1.56622i	0.949673	+	0.313243i
$6$		0			0
$7$	7.47006	+	5.23059i	1.06715	+	0.747227i	0.968780	−	0.247923i	$-0.0797478\pi$
$7$	7.47006	+	5.23059i	1.06715	+	0.747227i	0.0983713	+	0.995150i	$0.468637\pi$
$8$	−5.65912	+	21.1201i	−0.707390	+	2.64001i
$9$		0			0
$10$	7.35227	−	17.1089i	0.735227	−	1.71089i
$11$	7.46500	+	2.71704i	0.678637	+	0.247004i	0.658262	−	0.752789i	$-0.271292\pi$
$11$	7.46500	+	2.71704i	0.678637	+	0.247004i	0.0203746	+	0.999792i	$0.493514\pi$
$12$		0			0
$13$	−0.449058	−	5.13275i	−0.0345429	−	0.394827i	−0.993710	−	0.111986i	$-0.964279\pi$
$13$	−0.449058	−	5.13275i	−0.0345429	−	0.394827i	0.959167	−	0.282841i	$-0.0912768\pi$
$14$	21.8312	−	26.0175i	1.55937	−	1.85839i
$15$		0			0
$16$	39.4204	+	14.3478i	2.46377	+	0.896740i
$17$	−7.59419	−	28.3419i	−0.446717	−	1.66717i	−0.711363	−	0.702824i	$-0.751922\pi$
$17$	−7.59419	−	28.3419i	−0.446717	−	1.66717i	0.264646	−	0.964346i	$-0.414745\pi$
$18$		0			0
$19$	9.25934	−	5.34588i	0.487334	−	0.281362i	−0.236134	−	0.971721i	$-0.575880\pi$
$19$	9.25934	−	5.34588i	0.487334	−	0.281362i	0.723468	+	0.690358i	$0.242547\pi$
$20$	−43.4737	−	23.3640i	−2.17369	−	1.16820i
$21$		0			0
$22$	12.5039	−	26.8146i	0.568357	−	1.21885i
$23$	23.0026	−	16.1066i	1.00011	−	0.700286i	0.0457543	−	0.998953i	$-0.485431\pi$
$23$	23.0026	−	16.1066i	1.00011	−	0.700286i	0.954357	+	0.298667i	$0.0965420\pi$
$24$		0			0
$25$	20.0939	+	14.8739i	0.803758	+	0.594957i
$26$	−19.1892			−0.738047
$27$		0			0
$28$	−63.6501	−	63.6501i	−2.27322	−	2.27322i
$29$	19.8626	+	23.6713i	0.684917	+	0.816253i	0.990731	−	0.135839i	$-0.0433729\pi$
$29$	19.8626	+	23.6713i	0.684917	+	0.816253i	−0.305814	+	0.952091i	$0.598928\pi$
$30$		0			0
$31$	−3.45942	+	19.6193i	−0.111594	+	0.632882i	0.876786	+	0.480880i	$0.159683\pi$
$31$	−3.45942	+	19.6193i	−0.111594	+	0.632882i	−0.988380	+	0.152001i	$0.951428\pi$
$32$	29.0665	−	62.3334i	0.908329	−	1.94792i
$33$		0			0
$34$	−107.619	+	18.9761i	−3.16526	+	0.558120i
$35$	27.2783	+	36.5365i	0.779381	+	1.04390i
$36$		0			0
$37$	6.34170	+	23.6675i	0.171397	+	0.639663i	0.997137	+	0.0756123i	$0.0240911\pi$
$37$	6.34170	+	23.6675i	0.171397	+	0.639663i	−0.825740	+	0.564051i	$0.809242\pi$
$38$	−16.8287	−	36.0892i	−0.442859	−	0.949715i
$39$		0			0
$40$	−59.9502	+	91.4226i	−1.49875	+	2.28557i
$41$	−33.8265	−	28.3838i	−0.825035	−	0.692287i	0.129110	−	0.991630i	$-0.458788\pi$
$41$	−33.8265	−	28.3838i	−0.825035	−	0.692287i	−0.954145	+	0.299343i	$0.903232\pi$
$42$		0			0
$43$	−9.22262	−	19.7780i	−0.214480	−	0.459953i	0.769404	−	0.638762i	$-0.220553\pi$
$43$	−9.22262	−	19.7780i	−0.214480	−	0.459953i	−0.983884	+	0.178809i	$0.942775\pi$
$44$	−67.9093	−	39.2075i	−1.54339	−	0.891079i
$45$		0			0
$46$	−52.2918	−	90.5720i	−1.13678	−	1.96896i
$47$	26.5416	+	18.5846i	0.564714	+	0.395417i	0.820782	−	0.571242i	$-0.193538\pi$
$47$	26.5416	+	18.5846i	0.564714	+	0.395417i	−0.256068	+	0.966659i	$0.582427\pi$
$48$		0			0
$49$	11.6837	+	32.1007i	0.238443	+	0.655116i
$50$	61.7075	−	69.7242i	1.23415	−	1.39448i
$51$		0			0
$52$	−4.43258	+	50.6646i	−0.0852419	+	0.974320i
$53$	−36.3531	−	36.3531i	−0.685908	−	0.685908i	0.275417	−	0.961325i	$-0.411184\pi$
$53$	−36.3531	−	36.3531i	−0.685908	−	0.685908i	−0.961325	+	0.275417i	$0.911184\pi$
$54$		0			0
$55$	31.1911	+	24.5933i	0.567111	+	0.447151i
$56$	−152.745	+	128.168i	−2.72758	+	2.28871i
$57$		0			0
$58$	94.2724	−	66.0103i	1.62539	−	1.13811i
$59$	−13.3870	−	36.7804i	−0.226898	−	0.623396i	0.773042	−	0.634354i	$-0.218734\pi$
$59$	−13.3870	−	36.7804i	−0.226898	−	0.623396i	−0.999940	+	0.0109585i	$0.996512\pi$
$60$		0			0
$61$	1.11435	+	6.31979i	0.0182680	+	0.103603i	0.992578	−	0.121606i	$-0.0388045\pi$
$61$	1.11435	+	6.31979i	0.0182680	+	0.103603i	−0.974310	+	0.225209i	$0.927693\pi$
$62$	71.6685	+	19.2035i	1.15594	+	0.309734i
$63$		0			0
$64$	−76.5134	−	44.1751i	−1.19552	−	0.690235i
$65$	5.90670	−	25.0755i	0.0908724	−	0.385777i
$66$		0			0
$67$	53.2028	−	4.65465i	0.794072	−	0.0694723i	0.317102	−	0.948392i	$-0.397290\pi$
$67$	53.2028	−	4.65465i	0.794072	−	0.0694723i	0.476971	+	0.878919i	$0.341735\pi$
$68$	25.2427	+	288.525i	0.371216	+	4.24302i
$69$		0			0
$70$	144.412	−	89.3480i	2.06302	−	1.27640i
$71$	20.4199	−	35.3683i	0.287604	−	0.498145i	−0.685633	−	0.727947i	$-0.740475\pi$
$71$	20.4199	−	35.3683i	0.287604	−	0.498145i	0.973237	+	0.229802i	$0.0738079\pi$
$72$		0			0
$73$	−14.7960	+	55.2194i	−0.202685	+	0.756430i	0.787458	+	0.616368i	$0.211397\pi$
$73$	−14.7960	+	55.2194i	−0.202685	+	0.756430i	−0.990143	+	0.140062i	$0.955270\pi$
$74$	89.8695	−	15.8464i	1.21445	−	0.214141i
$75$		0			0
$76$	−99.1722	+	36.0957i	−1.30490	+	0.474944i
$77$	41.5523	+	59.3428i	0.539640	+	0.770686i
$78$		0			0
$79$	32.7011	+	38.9717i	0.413938	+	0.493312i	0.932217	−	0.361899i	$-0.117872\pi$
$79$	32.7011	+	38.9717i	0.413938	+	0.493312i	−0.518279	+	0.855212i	$0.673427\pi$
$80$	164.710	+	129.870i	2.05888	+	1.62337i
$81$		0			0
$82$	−116.289	+	116.289i	−1.41816	+	1.41816i
$83$	−121.744	−	10.6512i	−1.46679	−	0.128328i	−0.674412	−	0.738355i	$-0.735603\pi$
$83$	−121.744	−	10.6512i	−1.46679	−	0.128328i	−0.792380	+	0.610028i	$0.791158\pi$
$84$		0			0
$85$	8.32953	−	146.472i	0.0979945	−	1.72320i
$86$	−76.3736	+	27.7977i	−0.888065	+	0.323229i
$87$		0			0
$88$	−99.6295	+	142.286i	−1.13215	+	1.61688i
$89$	−77.2540	+	44.6026i	−0.868022	+	0.501153i	−0.866691	−	0.498846i	$-0.833757\pi$
$89$	−77.2540	+	44.6026i	−0.868022	+	0.501153i	−0.00133173	+	0.999999i	$0.500424\pi$
$90$		0			0
$91$	23.4928	−	40.6908i	0.258163	−	0.447152i
$92$	−251.213	+	117.143i	−2.73058	+	1.27329i
$93$		0			0
$94$	77.5677	−	92.4416i	0.825188	−	0.983421i
$95$	52.3395	−	10.8821i	0.550943	−	0.114548i
$96$		0			0
$97$	104.160	−	48.5706i	1.07381	−	0.500728i	0.196431	−	0.980518i	$-0.437065\pi$
$97$	104.160	−	48.5706i	1.07381	−	0.500728i	0.877383	+	0.479790i	$0.159287\pi$
$98$	122.892	−	32.9288i	1.25400	−	0.336009i
$99$		0			0
$100$	−169.836	−	179.030i	−1.69836	−	1.79030i
$101$	−9.98220	−	56.6119i	−0.0988336	−	0.560513i	−0.993505	−	0.113788i	$-0.963701\pi$
$101$	−9.98220	−	56.6119i	−0.0988336	−	0.560513i	0.894671	−	0.446725i	$-0.147410\pi$
$102$		0			0
$103$	79.5607	+	37.0998i	0.772434	+	0.360192i	0.768541	−	0.639801i	$-0.220983\pi$
$103$	79.5607	+	37.0998i	0.772434	+	0.360192i	0.00389284	+	0.999992i	$0.498761\pi$
$104$	110.946	+	19.5627i	1.06678	+	0.188103i
$105$		0			0
$106$	−146.677	+	123.077i	−1.38375	+	1.16110i
$107$	−66.6047	+	66.6047i	−0.622474	+	0.622474i	−0.946163	−	0.323690i	$-0.895077\pi$
$107$	−66.6047	+	66.6047i	−0.622474	+	0.622474i	0.323690	+	0.946163i	$0.395077\pi$
$108$		0			0
$109$			66.6182i			0.611176i	0.952164	+	0.305588i	$0.0988530\pi$
$109$			66.6182i			0.611176i	−0.952164	+	0.305588i	$0.901147\pi$
$110$	101.370	−	107.742i	0.921548	−	0.979471i
$111$		0			0
$112$	219.425	+	313.371i	1.95915	+	2.79795i
$113$	84.0689	+	39.2020i	0.743972	+	0.346920i	0.757366	−	0.652990i	$-0.226486\pi$
$113$	84.0689	+	39.2020i	0.743972	+	0.346920i	−0.0133940	+	0.999910i	$0.504264\pi$
$114$		0			0
$115$	134.451	−	40.4529i	1.16914	−	0.351764i
$116$	−152.508	−	264.152i	−1.31473	−	2.27717i
$117$		0			0
$118$	−140.807	+	37.7292i	−1.19328	+	0.319739i
$119$	91.5158	−	251.438i	0.769040	−	2.11292i
$120$		0			0
$121$	−44.3474	−	37.2119i	−0.366508	−	0.307536i
$122$	23.8093	−	2.08305i	0.195158	−	0.0170742i
$123$		0			0
$124$	67.2572	−	184.788i	0.542397	−	1.49022i
$125$	72.1176	+	102.098i	0.576941	+	0.816786i
$126$		0			0
$127$	−59.4764	−	15.9367i	−0.468318	−	0.125486i	0.0169396	−	0.999857i	$-0.494608\pi$
$127$	−59.4764	−	15.9367i	−0.468318	−	0.125486i	−0.485258	+	0.874371i	$0.661274\pi$
$128$	−30.9378	+	44.1838i	−0.241702	+	0.345186i
$129$		0			0
$130$	−91.1175	−	30.0545i	−0.700904	−	0.231188i
$131$	6.70011	−	37.9982i	0.0511459	−	0.290063i	−0.948497	−	0.316786i	$-0.897396\pi$
$131$	6.70011	−	37.9982i	0.0511459	−	0.290063i	0.999643	+	0.0267234i	$0.00850732\pi$
$132$		0			0
$133$	97.1300	+	8.49777i	0.730300	+	0.0638930i
$134$		−	198.903i		−	1.48435i
$135$		0			0
$136$	641.560			4.71736
$137$	2.62347	−	29.9863i	0.0191494	−	0.218878i	−0.980590	−	0.196067i	$-0.937183\pi$
$137$	2.62347	−	29.9863i	0.0191494	−	0.218878i	0.999740	−	0.0228110i	$-0.00726160\pi$
$138$		0			0
$139$	−255.255	−	45.0084i	−1.83637	−	0.323802i	−0.855401	−	0.517966i	$-0.826689\pi$
$139$	−255.255	−	45.0084i	−1.83637	−	0.323802i	−0.980969	+	0.194165i	$0.937800\pi$
$140$	−202.544	−	401.924i	−1.44674	−	2.87088i
$141$		0			0
$142$	−124.595	−	87.2421i	−0.877427	−	0.614381i
$143$	10.5937	−	39.5361i	0.0740816	−	0.276476i
$144$		0			0
$145$	57.2405	+	143.509i	0.394762	+	0.989719i
$146$	200.071	+	72.8200i	1.37035	+	0.498767i
$147$		0			0
$148$	−21.0795	−	240.939i	−0.142429	−	1.62797i
$149$	−168.712	+	201.064i	−1.13230	+	1.34942i	−0.203395	+	0.979097i	$0.565198\pi$
$149$	−168.712	+	201.064i	−1.13230	+	1.34942i	−0.928903	+	0.370324i	$0.879247\pi$
$150$		0			0
$151$	−5.52161	−	2.00970i	−0.0365669	−	0.0133093i	0.323672	−	0.946169i	$-0.395083\pi$
$151$	−5.52161	−	2.00970i	−0.0365669	−	0.0133093i	−0.360239	+	0.932860i	$0.617305\pi$
$152$	60.5060	+	225.811i	0.398066	+	1.48560i
$153$		0			0
$154$	233.661	−	134.904i	1.51728	−	0.876001i
$155$	−47.1547	+	87.7415i	−0.304224	+	0.566075i
$156$		0			0
$157$	21.3774	−	45.8440i	0.136162	−	0.292000i	−0.826390	−	0.563099i	$-0.809609\pi$
$157$	21.3774	−	45.8440i	0.136162	−	0.292000i	0.962552	+	0.271098i	$0.0873869\pi$
$158$	155.207	−	108.677i	0.982322	−	0.687830i
$159$		0			0
$160$	235.646	−	250.457i	1.47279	−	1.56536i
$161$	256.077			1.59054
$162$		0			0
$163$	19.6350	+	19.6350i	0.120460	+	0.120460i	0.764767	−	0.644307i	$-0.222854\pi$
$163$	19.6350	+	19.6350i	0.120460	+	0.120460i	−0.644307	+	0.764767i	$0.722854\pi$
$164$	280.172	+	333.896i	1.70837	+	2.03595i
$165$		0			0
$166$	−79.0359	+	448.235i	−0.476120	+	2.70021i
$167$	−102.754	+	220.357i	−0.615294	+	1.31950i	0.313740	+	0.949509i	$0.398418\pi$
$167$	−102.754	+	220.357i	−0.615294	+	1.31950i	−0.929034	+	0.369993i	$0.879360\pi$
$168$		0			0
$169$	140.289	−	24.7367i	0.830113	−	0.146371i
$170$	−540.734	−	78.4487i	−3.18079	−	0.461463i
$171$		0			0
$172$	55.7515	+	208.068i	0.324137	+	1.20970i
$173$	95.0822	+	203.904i	0.549608	+	1.17864i	0.963351	+	0.268244i	$0.0864435\pi$
$173$	95.0822	+	203.904i	0.549608	+	1.17864i	−0.413743	+	0.910394i	$0.635779\pi$
$174$		0			0
$175$	72.3035	+	216.212i	0.413163	+	1.23550i
$176$	255.289	+	214.213i	1.45051	+	1.21712i
$177$		0			0
$178$	140.407	+	301.105i	0.788806	+	1.69160i
$179$	−245.990	−	142.022i	−1.37424	−	0.793420i	−0.382785	−	0.923837i	$-0.625035\pi$
$179$	−245.990	−	142.022i	−1.37424	−	0.793420i	−0.991459	+	0.130417i	$0.958368\pi$
$180$		0			0
$181$	46.2375	+	80.0858i	0.255456	+	0.442463i	0.965019	−	0.262179i	$-0.0844411\pi$
$181$	46.2375	+	80.0858i	0.255456	+	0.442463i	−0.709563	+	0.704642i	$0.751108\pi$
$182$	−143.345	−	100.371i	−0.787608	−	0.551489i
$183$		0			0
$184$	209.998	+	576.966i	1.14130	+	3.13568i
$185$	−6.95576	+	122.315i	−0.0375987	+	0.661160i
$186$		0			0
$187$	20.3154	−	232.206i	0.108638	−	1.24174i
$188$	−226.152	−	226.152i	−1.20294	−	1.20294i
$189$		0			0
$190$	−23.3852	−	197.722i	−0.123080	−	1.04064i
$191$	−54.9994	+	46.1500i	−0.287955	+	0.241623i	−0.775310	−	0.631581i	$-0.782406\pi$
$191$	−54.9994	+	46.1500i	−0.287955	+	0.241623i	0.487355	+	0.873204i	$0.337962\pi$
$192$		0			0
$193$	−137.740	+	96.4463i	−0.713677	+	0.499722i	−0.873132	−	0.487483i	$-0.837915\pi$
$193$	−137.740	+	96.4463i	−0.713677	+	0.499722i	0.159455	+	0.987205i	$0.449026\pi$
$194$	−146.396	−	402.219i	−0.754617	−	2.07329i
$195$		0			0
$196$	−58.5536	−	332.074i	−0.298743	−	1.69425i
$197$	223.435	+	59.8693i	1.13419	+	0.303905i	0.776613	−	0.629979i	$-0.216936\pi$
$197$	223.435	+	59.8693i	1.13419	+	0.303905i	0.357577	+	0.933884i	$0.383603\pi$
$198$		0			0
$199$	−243.210	−	140.417i	−1.22216	−	0.705615i	−0.256783	−	0.966469i	$-0.582663\pi$
$199$	−243.210	−	140.417i	−1.22216	−	0.705615i	−0.965378	+	0.260854i	$0.915996\pi$
$200$	−427.853	+	340.213i	−2.13926	+	1.70106i
$201$		0			0
$202$	−213.281	+	18.6596i	−1.05585	+	0.0923745i
$203$	24.5598	+	280.719i	0.120984	+	1.38285i
$204$		0			0
$205$	−116.165	−	187.756i	−0.566660	−	0.915883i
$206$	163.472	−	283.142i	0.793555	−	1.37448i
$207$		0			0
$208$	55.9419	−	208.778i	0.268951	−	1.00374i
$209$	83.6460	−	14.7490i	0.400220	−	0.0705696i
$210$		0			0
$211$	−38.1041	+	13.8688i	−0.180588	+	0.0657287i	−0.430732	−	0.902480i	$-0.641744\pi$
$211$	−38.1041	+	13.8688i	−0.180588	+	0.0657287i	0.250143	+	0.968209i	$0.419522\pi$
$212$	291.073	+	415.696i	1.37299	+	1.96083i
$213$		0			0
$214$	225.496	+	268.736i	1.05372	+	1.25577i
$215$	−12.8158	−	108.358i	−0.0596084	−	0.503989i
$216$		0			0
$217$	−128.463	+	128.463i	−0.591994	+	0.591994i
$218$	247.166	+	21.6242i	1.13379	+	0.0991936i
$219$		0			0
$220$	−261.051	−	292.532i	−1.18659	−	1.32969i
$221$	−142.062	+	51.7062i	−0.642813	+	0.233965i
$222$		0			0
$223$	−74.9224	+	107.000i	−0.335975	+	0.479822i	−0.951220	−	0.308514i	$-0.900168\pi$
$223$	−74.9224	+	107.000i	−0.335975	+	0.479822i	0.615245	+	0.788336i	$0.289057\pi$
$224$	543.169	−	313.599i	2.42486	−	1.39999i
$225$		0			0
$226$	172.735	−	299.186i	0.764315	−	1.32383i
$227$	398.011	−	185.596i	1.75335	−	0.817602i	0.769496	−	0.638652i	$-0.220507\pi$
$227$	398.011	−	185.596i	1.75335	−	0.817602i	0.983858	−	0.178951i	$-0.0572703\pi$
$228$		0			0
$229$	27.3680	−	32.6159i	0.119511	−	0.142428i	−0.702972	−	0.711218i	$-0.748144\pi$
$229$	27.3680	−	32.6159i	0.119511	−	0.142428i	0.822483	+	0.568790i	$0.192588\pi$
$230$	−106.445	−	511.969i	−0.462805	−	2.22595i
$231$		0			0
$232$	−612.346	+	285.542i	−2.63942	+	1.23078i
$233$	−154.074	+	41.2840i	−0.661263	+	0.177185i	−0.573816	−	0.818984i	$-0.694537\pi$
$233$	−154.074	+	41.2840i	−0.661263	+	0.177185i	−0.0874468	+	0.996169i	$0.527871\pi$
$234$		0			0
$235$	96.9215	+	129.816i	0.412432	+	0.552409i
$236$	67.0895	+	380.484i	0.284278	+	1.61222i
$237$		0			0
$238$	−903.175	−	421.157i	−3.79485	−	1.76957i
$239$	186.365	+	32.8613i	0.779772	+	0.137495i	0.549346	−	0.835595i	$-0.314877\pi$
$239$	186.365	+	32.8613i	0.779772	+	0.137495i	0.230426	+	0.973090i	$0.425988\pi$
$240$		0			0
$241$	−78.8923	+	66.1985i	−0.327354	+	0.274683i	−0.791621	−	0.611013i	$-0.790762\pi$
$241$	−78.8923	+	66.1985i	−0.327354	+	0.274683i	0.464267	+	0.885695i	$0.346318\pi$
$242$	−152.458	+	152.458i	−0.629993	+	0.629993i
$243$		0			0
$244$		−	63.3441i		−	0.259607i
$245$	5.20186	+	170.725i	0.0212321	+	0.696837i
$246$		0			0
$247$	−31.5971	−	45.1253i	−0.127923	−	0.182694i
$248$	−394.785	−	184.091i	−1.59188	−	0.742304i
$249$		0			0
$250$	402.213	−	234.429i	1.60885	−	0.937715i
$251$	−239.077	−	414.094i	−0.952500	−	1.64978i	−0.739989	−	0.672619i	$-0.765169\pi$
$251$	−239.077	−	414.094i	−0.952500	−	1.64978i	−0.212510	−	0.977159i	$-0.568164\pi$
$252$		0			0
$253$	215.476	−	57.7367i	0.851685	−	0.228208i
$254$	−78.4340	+	215.496i	−0.308795	+	0.848408i
$255$		0			0
$256$	−116.833	−	98.0342i	−0.456377	−	0.382946i
$257$	−141.631	+	12.3911i	−0.551095	+	0.0482146i	−0.359303	−	0.933221i	$-0.616986\pi$
$257$	−141.631	+	12.3911i	−0.551095	+	0.0482146i	−0.191792	+	0.981436i	$0.561430\pi$
$258$		0			0
$259$	−76.4223	+	209.969i	−0.295067	+	0.810690i
$260$	−100.399	+	233.632i	−0.386151	+	0.898584i
$261$		0			0
$262$	−138.806	−	37.1929i	−0.529793	−	0.141958i
$263$	−149.199	+	213.078i	−0.567295	+	0.810181i	−0.995625	−	0.0934412i	$-0.970213\pi$
$263$	−149.199	+	213.078i	−0.567295	+	0.810181i	0.428330	+	0.903623i	$0.359102\pi$
$264$		0			0
$265$	−115.681	−	229.555i	−0.436532	−	0.866244i
$266$	63.0566	−	357.612i	0.237055	−	1.34441i
$267$		0			0
$268$	−525.157	−	45.9453i	−1.95954	−	0.171438i
$269$			487.371i			1.81179i	0.423503	+	0.905895i	$0.360800\pi$
$269$			487.371i			1.81179i	−0.423503	+	0.905895i	$0.639200\pi$
$270$		0			0
$271$	−283.160			−1.04487			−0.522435	−	0.852679i	$-0.674976\pi$
$271$	−283.160			−1.04487			−0.522435	+	0.852679i	$0.674976\pi$
$272$	107.279	−	1226.21i	0.394409	−	4.50812i
$273$		0			0
$274$	−110.403	−	19.4671i	−0.402932	−	0.0710478i
$275$	109.588	+	165.630i	0.398503	+	0.602290i
$276$		0			0
$277$	362.475	+	253.808i	1.30858	+	0.916274i	0.999397	−	0.0347295i	$-0.0110570\pi$
$277$	362.475	+	253.808i	1.30858	+	0.916274i	0.309179	+	0.951004i	$0.399946\pi$
$278$	−249.845	+	932.436i	−0.898724	+	3.35408i
$279$		0			0
$280$	−926.026	+	369.357i	−3.30723	+	1.31913i
$281$	−28.6840	−	10.4401i	−0.102078	−	0.0371534i	0.290476	−	0.956882i	$-0.406186\pi$
$281$	−28.6840	−	10.4401i	−0.102078	−	0.0371534i	−0.392554	+	0.919729i	$0.628409\pi$
$282$		0			0
$283$	21.1770	+	242.054i	0.0748304	+	0.855315i	0.937145	+	0.348941i	$0.113459\pi$
$283$	21.1770	+	242.054i	0.0748304	+	0.855315i	−0.862314	+	0.506374i	$0.830986\pi$
$284$	−259.123	+	308.810i	−0.912404	+	1.08736i
$285$		0			0
$286$	−143.248	−	52.1379i	−0.500866	−	0.182300i
$287$	−104.222	−	388.961i	−0.363142	−	1.35526i
$288$		0			0
$289$	−495.310	+	285.967i	−1.71387	+	0.989506i
$290$	551.026	−	165.790i	1.90009	−	0.571689i
$291$		0			0
$292$	238.479	−	511.420i	0.816710	−	1.75144i
$293$	−162.267	+	113.621i	−0.553812	+	0.387784i	−0.816717	−	0.577038i	$-0.804208\pi$
$293$	−162.267	+	113.621i	−0.553812	+	0.387784i	0.262905	+	0.964822i	$0.415320\pi$
$294$		0			0
$295$	−5.96019	−	195.613i	−0.0202040	−	0.663096i
$296$	−535.749			−1.80996
$297$		0			0
$298$	691.220	+	691.220i	2.31953	+	2.31953i
$299$	−93.0005	−	110.834i	−0.311039	−	0.370681i
$300$		0			0
$301$	34.5570	−	195.982i	0.114807	−	0.651104i
$302$	−9.24868	+	19.8338i	−0.0306248	+	0.0656750i
$303$		0			0
$304$	441.708	−	77.8851i	1.45299	−	0.256201i
$305$	−4.60682	+	31.7540i	−0.0151043	+	0.104111i
$306$		0			0
$307$	3.58859	+	13.3928i	0.0116892	+	0.0436247i	0.971524	−	0.236941i	$-0.0761447\pi$
$307$	3.58859	+	13.3928i	0.0116892	+	0.0436247i	−0.959835	+	0.280565i	$0.909478\pi$
$308$	−302.208	−	648.088i	−0.981196	−	2.10418i
$309$		0			0
$310$	310.231	+	203.433i	1.00075	+	0.656237i
$311$	191.095	+	160.348i	0.614455	+	0.515589i	0.896055	−	0.443943i	$-0.146421\pi$
$311$	191.095	+	160.348i	0.614455	+	0.515589i	−0.281600	+	0.959532i	$0.590865\pi$
$312$		0			0
$313$	−146.255	−	313.644i	−0.467267	−	1.00206i	−0.988858	−	0.148861i	$-0.952439\pi$
$313$	−146.255	−	313.644i	−0.467267	−	1.00206i	0.521591	−	0.853195i	$-0.325339\pi$
$314$	−163.151	−	94.1952i	−0.519589	−	0.299985i
$315$		0			0
$316$	−251.084	−	434.891i	−0.794571	−	1.37624i
$317$	−240.194	−	168.186i	−0.757710	−	0.530554i	0.129690	−	0.991555i	$-0.458602\pi$
$317$	−240.194	−	168.186i	−0.757710	−	0.530554i	−0.887400	+	0.461000i	$0.847491\pi$
$318$		0			0
$319$	83.9585	+	230.674i	0.263193	+	0.723116i
$320$	−294.126	−	329.596i	−0.919144	−	1.02999i
$321$		0			0
$322$	83.1225	−	950.095i	0.258145	−	2.95061i
$323$	−221.830	−	221.830i	−0.686779	−	0.686779i
$324$		0			0
$325$	67.3208	−	109.816i	0.207141	−	0.337897i
$326$	79.2232	−	66.4761i	0.243016	−	0.203915i
$327$		0			0
$328$	790.896	−	553.791i	2.41127	−	1.68839i
$329$	101.059	+	277.656i	0.307169	+	0.843939i
$330$		0			0
$331$	−17.8707	−	101.350i	−0.0539900	−	0.306193i	0.945840	−	0.324633i	$-0.105241\pi$
$331$	−17.8707	−	101.350i	−0.0539900	−	0.306193i	−0.999830	+	0.0184407i	$0.994130\pi$
$332$	1165.20	+	312.215i	3.50964	+	0.940405i
$333$		0			0
$334$	784.211	+	452.765i	2.34794	+	1.35558i
$335$	259.917	+	61.2251i	0.775871	+	0.182762i
$336$		0			0
$337$	545.773	−	47.7489i	1.61950	−	0.141688i	0.758986	−	0.651107i	$-0.225695\pi$
$337$	545.773	−	47.7489i	1.61950	−	0.141688i	0.860519	+	0.509419i	$0.170140\pi$
$338$	−46.2402	−	528.528i	−0.136805	−	1.56369i
$339$		0			0
$340$	−332.031	+	1409.56i	−0.976562	+	4.14576i
$341$	−79.1310	+	137.059i	−0.232056	+	0.401932i
$342$		0			0
$343$	35.0239	−	130.711i	0.102111	−	0.381082i
$344$	469.905	−	82.8569i	1.36600	−	0.240863i
$345$		0			0
$346$	787.387	−	286.585i	2.27568	−	0.828282i
$347$	−146.016	−	208.532i	−0.420795	−	0.600957i	0.551654	−	0.834073i	$-0.313997\pi$
$347$	−146.016	−	208.532i	−0.420795	−	0.600957i	−0.972449	+	0.233116i	$0.925108\pi$
$348$		0			0
$349$	−247.270	−	294.685i	−0.708511	−	0.844371i	0.284950	−	0.958542i	$-0.408023\pi$
$349$	−247.270	−	294.685i	−0.708511	−	0.844371i	−0.993461	+	0.114172i	$0.963579\pi$
$350$	825.657	−	198.077i	2.35902	−	0.565935i
$351$		0			0
$352$	386.344	−	386.344i	1.09757	−	1.09757i
$353$	−444.615	−	38.8987i	−1.25953	−	0.110195i	−0.562235	−	0.826977i	$-0.690058\pi$
$353$	−444.615	−	38.8987i	−1.25953	−	0.110195i	−0.697297	+	0.716783i	$0.745614\pi$
$354$		0			0
$355$	152.355	−	135.960i	0.429170	−	0.382985i
$356$	827.429	−	301.159i	2.32424	−	0.845953i
$357$		0			0
$358$	−606.777	+	866.568i	−1.69491	+	2.42058i
$359$	142.071	−	82.0247i	0.395741	−	0.228481i	−0.288904	−	0.957358i	$-0.593291\pi$
$359$	142.071	−	82.0247i	0.395741	−	0.228481i	0.684645	+	0.728877i	$0.259957\pi$
$360$		0			0
$361$	−123.343	+	213.636i	−0.341671	+	0.591791i
$362$	312.142	−	145.554i	0.862270	−	0.402083i
$363$		0			0
$364$	−298.118	+	355.283i	−0.819004	+	0.976051i
$365$	−156.742	+	239.028i	−0.429431	+	0.654871i
$366$		0			0
$367$	167.015	−	77.8802i	0.455081	−	0.212208i	−0.181542	−	0.983383i	$-0.558109\pi$
$367$	167.015	−	77.8802i	0.455081	−	0.212208i	0.636622	+	0.771176i	$0.280331\pi$
$368$	1137.86	−	304.890i	3.09202	−	0.828505i
$369$		0			0
$370$	451.552	+	65.5104i	1.22041	+	0.177055i
$371$	−81.4116	−	461.708i	−0.219438	−	1.24450i
$372$		0			0
$373$	498.225	+	232.326i	1.33572	+	0.622859i	0.953551	−	0.301232i	$-0.0973977\pi$
$373$	498.225	+	232.326i	1.33572	+	0.622859i	0.382174	+	0.924090i	$0.375176\pi$
$374$	−854.933	−	150.748i	−2.28592	−	0.403069i
$375$		0			0
$376$	−542.710	+	455.388i	−1.44338	+	1.21114i
$377$	112.580	−	112.580i	0.298620	−	0.298620i
$378$		0			0
$379$			205.714i			0.542780i	0.962469	+	0.271390i	$0.0874833\pi$
$379$			205.714i			0.542780i	−0.962469	+	0.271390i	$0.912517\pi$
$380$	−527.439	+	16.0707i	−1.38800	+	0.0422913i
$381$		0			0
$382$	153.372	+	219.038i	0.401498	+	0.573399i
$383$	149.033	+	69.4952i	0.389120	+	0.181450i	0.607325	−	0.794453i	$-0.292243\pi$
$383$	149.033	+	69.4952i	0.389120	+	0.181450i	−0.218205	+	0.975903i	$0.570020\pi$
$384$		0			0
$385$	104.362	+	346.861i	0.271070	+	0.900938i
$386$	313.124	+	542.346i	0.811201	+	1.40504i
$387$		0			0
$388$	−1095.78	+	293.613i	−2.82417	+	0.756735i
$389$	−86.4883	+	237.625i	−0.222335	+	0.610860i	−0.999838	−	0.0180194i	$-0.994264\pi$
$389$	−86.4883	+	237.625i	−0.222335	+	0.610860i	0.777503	+	0.628880i	$0.216486\pi$
$390$		0			0
$391$	−631.177	−	529.620i	−1.61426	−	1.35453i
$392$	−744.090	+	65.0994i	−1.89819	+	0.166070i
$393$		0			0
$394$	294.653	−	809.553i	0.747851	−	2.05470i
$395$	94.2388	+	236.269i	0.238579	+	0.598149i
$396$		0			0
$397$	92.8533	+	24.8800i	0.233887	+	0.0626699i	0.373859	−	0.927486i	$-0.378034\pi$
$397$	92.8533	+	24.8800i	0.233887	+	0.0626699i	−0.139972	+	0.990156i	$0.544701\pi$
$398$	−599.921	+	856.776i	−1.50734	+	2.15270i
$399$		0			0
$400$	578.702	+	874.640i	1.44675	+	2.18660i
$401$	12.1246	−	68.7622i	0.0302360	−	0.171477i	−0.965950	−	0.258727i	$-0.916697\pi$
$401$	12.1246	−	68.7622i	0.0302360	−	0.171477i	0.996186	+	0.0872504i	$0.0278080\pi$
$402$		0			0
$403$	102.255	+	8.94612i	0.253734	+	0.0221988i
$404$			567.428i			1.40452i
$405$		0			0
$406$	1049.49			2.58496
$407$	−16.9648	+	193.909i	−0.0416826	+	0.476434i
$408$		0			0
$409$	160.227	+	28.2524i	0.391754	+	0.0690767i	0.366056	−	0.930593i	$-0.380708\pi$
$409$	160.227	+	28.2524i	0.391754	+	0.0690767i	0.0256981	+	0.999670i	$0.491819\pi$
$410$	−734.317	+	370.049i	−1.79102	+	0.902559i
$411$		0			0
$412$	−709.809	−	497.014i	−1.72284	−	1.20634i
$413$	92.3817	−	344.773i	0.223684	−	0.834802i
$414$		0			0
$415$	−561.402	−	241.253i	−1.35278	−	0.581332i
$416$	−332.994	−	121.200i	−0.800467	−	0.291346i
$417$		0			0
$418$	−27.5703	−	315.130i	−0.0659576	−	0.753899i
$419$	211.108	−	251.589i	0.503839	−	0.600451i	−0.452842	−	0.891591i	$-0.649590\pi$
$419$	211.108	−	251.589i	0.503839	−	0.600451i	0.956681	+	0.291139i	$0.0940343\pi$
$420$		0			0
$421$	152.668	+	55.5665i	0.362631	+	0.131987i	0.516909	−	0.856041i	$-0.327083\pi$
$421$	152.668	+	55.5665i	0.362631	+	0.131987i	−0.154277	+	0.988028i	$0.549305\pi$
$422$	39.0871	+	145.875i	0.0926235	+	0.345675i
$423$		0			0
$424$	973.508	−	562.055i	2.29601	−	1.32560i
$425$	268.958	−	682.456i	0.632842	−	1.60578i
$426$		0			0
$427$	−24.7320	+	53.0379i	−0.0579204	+	0.124211i
$428$	761.621	−	533.293i	1.77949	−	1.24601i
$429$		0			0
$430$	−406.187	+	12.3762i	−0.944621	+	0.0287819i
$431$	−94.7520			−0.219842			−0.109921	−	0.993940i	$-0.535060\pi$
$431$	−94.7520			−0.219842			−0.109921	+	0.993940i	$0.535060\pi$
$432$		0			0
$433$	−341.222	−	341.222i	−0.788042	−	0.788042i	0.193131	−	0.981173i	$-0.438136\pi$
$433$	−341.222	−	341.222i	−0.788042	−	0.788042i	−0.981173	+	0.193131i	$0.938136\pi$
$434$	434.922	+	518.320i	1.00212	+	1.19428i
$435$		0			0
$436$	114.187	−	647.588i	0.261897	−	1.48529i
$437$	126.885	−	272.105i	0.290354	−	0.622667i
$438$		0			0
$439$	256.791	−	45.2792i	0.584946	−	0.103142i	0.126659	−	0.991946i	$-0.459574\pi$
$439$	256.791	−	45.2792i	0.584946	−	0.103142i	0.458287	+	0.888804i	$0.348463\pi$
$440$	−695.927	+	519.583i	−1.58165	+	1.18087i
$441$		0			0
$442$	145.727	+	543.859i	0.329698	+	1.23045i
$443$	−267.576	−	573.819i	−0.604009	−	1.29530i	−0.935994	−	0.352017i	$-0.885496\pi$
$443$	−267.576	−	573.819i	−0.604009	−	1.29530i	0.331984	−	0.943285i	$-0.392282\pi$
$444$		0			0
$445$	−436.687	+	90.7931i	−0.981320	+	0.204029i
$446$	372.671	+	312.708i	0.835585	+	0.701139i
$447$		0			0
$448$	−340.498	−	730.201i	−0.760041	−	1.62991i
$449$	−75.4227	−	43.5453i	−0.167979	−	0.0969828i	0.413653	−	0.910434i	$-0.364253\pi$
$449$	−75.4227	−	43.5453i	−0.167979	−	0.0969828i	−0.581633	+	0.813452i	$0.697586\pi$
$450$		0			0
$451$	−175.395	−	303.793i	−0.388902	−	0.673598i
$452$	−750.030	−	525.177i	−1.65936	−	1.16189i
$453$		0			0
$454$	−559.401	−	1536.94i	−1.23216	−	3.38533i
$455$	175.283	−	156.420i	0.385238	−	0.343780i
$456$		0			0
$457$	−61.4885	+	702.817i	−0.134548	+	1.53789i	0.566071	+	0.824357i	$0.308463\pi$
$457$	−61.4885	+	702.817i	−0.134548	+	1.53789i	−0.700619	+	0.713536i	$0.747093\pi$
$458$	−112.128	−	112.128i	−0.244820	−	0.244820i
$459$		0			0
$460$	−1376.32	+	162.782i	−2.99200	+	0.353874i
$461$	−290.221	+	243.525i	−0.629547	+	0.528253i	−0.900788	−	0.434258i	$-0.857010\pi$
$461$	−290.221	+	243.525i	−0.629547	+	0.528253i	0.271241	+	0.962512i	$0.412566\pi$
$462$		0			0
$463$	−472.637	+	330.944i	−1.02081	+	0.714782i	−0.959029	−	0.283307i	$-0.908568\pi$
$463$	−472.637	+	330.944i	−1.02081	+	0.714782i	−0.0617857	+	0.998089i	$0.519680\pi$
$464$	443.359	+	1218.12i	0.955514	+	2.62525i
$465$		0			0
$466$	103.159	+	585.045i	0.221372	+	1.25546i
$467$	−476.253	−	127.612i	−1.01981	−	0.273258i	−0.290089	−	0.957000i	$-0.593685\pi$
$467$	−476.253	−	127.612i	−1.01981	−	0.273258i	−0.729724	+	0.683741i	$0.760352\pi$
$468$		0			0
$469$	421.775	+	243.512i	0.899307	+	0.519215i
$470$	513.103	−	317.459i	1.09171	−	0.675444i
$471$		0			0
$472$	852.564	−	74.5897i	1.80628	−	0.158029i
$473$	−15.1094	−	172.701i	−0.0319437	−	0.365118i
$474$		0			0
$475$	265.571	+	30.3029i	0.559097	+	0.0637955i
$476$	−1320.59	+	2287.33i	−2.77436	+	4.80532i
$477$		0			0
$478$	182.415	−	680.784i	0.381622	−	1.42423i
$479$	−306.170	+	53.9861i	−0.639186	+	0.112706i	−0.483843	−	0.875155i	$-0.660759\pi$
$479$	−306.170	+	53.9861i	−0.639186	+	0.112706i	−0.155343	+	0.987861i	$0.549648\pi$
$480$		0			0
$481$	118.632	−	43.1784i	0.246636	−	0.0897681i
$482$	220.000	+	314.193i	0.456432	+	0.651853i
$483$		0			0
$484$	367.313	+	437.747i	0.758911	+	0.904435i
$485$	570.661	−	67.4939i	1.17662	−	0.139163i
$486$		0			0
$487$	72.4558	−	72.4558i	0.148780	−	0.148780i	−0.628793	−	0.777573i	$-0.716451\pi$
$487$	72.4558	−	72.4558i	0.148780	−	0.148780i	0.777573	+	0.628793i	$0.216451\pi$
$488$	−139.781	−	12.2293i	−0.286436	−	0.0250599i
$489$		0			0
$490$	635.110	+	36.1173i	1.29614	+	0.0737088i
$491$	401.682	−	146.200i	0.818089	−	0.297760i	0.101128	−	0.994873i	$-0.467755\pi$
$491$	401.682	−	146.200i	0.818089	−	0.297760i	0.716961	+	0.697113i	$0.245533\pi$
$492$		0			0
$493$	520.050	−	742.708i	1.05487	−	1.50651i
$494$	−177.680	+	102.583i	−0.359675	+	0.207659i
$495$		0			0
$496$	−417.866	+	723.766i	−0.842473	+	1.45921i
$497$	337.535	−	157.395i	0.679145	−	0.316690i
$498$		0			0
$499$	−322.082	+	383.842i	−0.645454	+	0.769223i	−0.985221	−	0.171287i	$-0.945207\pi$
$499$	−322.082	+	383.842i	−0.645454	+	0.769223i	0.339767	+	0.940510i	$0.389652\pi$
$500$	−526.045	−	1116.10i	−1.05209	−	2.23220i
$501$		0			0
$502$	−1613.97	+	752.607i	−3.21508	+	1.49922i
$503$	776.540	−	208.073i	1.54382	−	0.413664i	0.616320	−	0.787496i	$-0.288623\pi$
$503$	776.540	−	208.073i	1.54382	−	0.413664i	0.927497	+	0.373831i	$0.121956\pi$
$504$		0			0
$505$	41.2672	−	284.448i	0.0817173	−	0.563263i
$506$	−144.271	−	818.199i	−0.285120	−	1.61699i
$507$		0			0
$508$	550.848	+	256.864i	1.08435	+	0.505639i
$509$	133.375	+	23.5177i	0.262034	+	0.0462037i	0.303122	−	0.952952i	$-0.401971\pi$
$509$	133.375	+	23.5177i	0.262034	+	0.0462037i	−0.0410875	+	0.999156i	$0.513082\pi$
$510$		0			0
$511$	−399.357	+	335.100i	−0.781520	+	0.655773i
$512$	−554.210	+	554.210i	−1.08244	+	1.08244i
$513$		0			0
$514$			529.501i			1.03016i
$515$	319.677	+	300.772i	0.620732	+	0.584024i
$516$		0			0
$517$	147.638	+	210.848i	0.285566	+	0.407831i
$518$	754.216	+	351.697i	1.45602	+	0.678951i
$519$		0			0
$520$	496.171	+	266.655i	0.954174	+	0.512799i
$521$	−175.694	−	304.312i	−0.337225	−	0.584091i	0.646684	−	0.762758i	$-0.276155\pi$
$521$	−175.694	−	304.312i	−0.337225	−	0.584091i	−0.983910	+	0.178666i	$0.942822\pi$
$522$		0			0
$523$	−208.565	+	55.8848i	−0.398785	+	0.106854i	−0.452637	−	0.891695i	$-0.649517\pi$
$523$	−208.565	+	55.8848i	−0.398785	+	0.106854i	0.0538519	+	0.998549i	$0.482850\pi$
$524$	−130.262	+	357.892i	−0.248592	+	0.683001i
$525$		0			0
$526$	742.128	+	622.720i	1.41089	+	1.18388i
$527$	582.320	−	50.9464i	1.10497	−	0.0966725i
$528$		0			0
$529$	88.7679	−	243.888i	0.167803	−	0.461035i
$530$	−889.240	+	354.685i	−1.67781	+	0.669217i
$531$		0			0
$532$	−929.624	−	249.092i	−1.74741	−	0.468218i
$533$	−130.497	+	186.369i	−0.244835	+	0.349660i
$534$		0			0
$535$	−420.581	+	211.946i	−0.786132	+	0.396161i
$536$	−202.774	+	1149.99i	−0.378311	+	2.14551i
$537$		0			0
$538$	1808.24	+	158.200i	3.36104	+	0.294053i
$539$			271.377i			0.503482i
$540$		0			0
$541$	−441.887			−0.816797			−0.408399	−	0.912804i	$-0.633913\pi$
$541$	−441.887			−0.816797			−0.408399	+	0.912804i	$0.633913\pi$
$542$	−91.9135	+	1050.58i	−0.169582	+	1.93833i
$543$		0			0
$544$	−1987.38	−	350.429i	−3.65328	−	0.644171i
$545$	−104.338	+	316.327i	−0.191447	+	0.580417i
$546$		0			0
$547$	−586.171	−	410.442i	−1.07161	−	0.750350i	−0.101947	−	0.994790i	$-0.532507\pi$
$547$	−586.171	−	410.442i	−1.07161	−	0.750350i	−0.969665	+	0.244439i	$0.921396\pi$
$548$	−76.9007	+	286.997i	−0.140330	+	0.523718i
$549$		0			0
$550$	650.090	−	352.830i	1.18198	−	0.641508i
$551$	310.459	+	112.998i	0.563446	+	0.205078i
$552$		0			0
$553$	40.4344	+	462.167i	0.0731182	+	0.835745i
$554$	1059.33	−	1262.47i	1.91216	−	2.27882i
$555$		0			0
$556$	2404.16	+	875.044i	4.32403	+	1.57382i
$557$	91.3239	+	340.825i	0.163957	+	0.611895i	0.998171	+	0.0604543i	$0.0192549\pi$
$557$	91.3239	+	340.825i	0.163957	+	0.611895i	−0.834214	+	0.551440i	$0.814078\pi$
$558$		0			0
$559$	−97.3739	+	56.2189i	−0.174193	+	0.100570i
$560$	551.102	+	1831.67i	0.984111	+	3.27083i
$561$		0			0
$562$	−48.0455	+	103.034i	−0.0854903	+	0.183334i
$563$	−255.686	+	179.033i	−0.454150	+	0.317999i	−0.778173	−	0.628050i	$-0.783853\pi$
$563$	−255.686	+	179.033i	−0.454150	+	0.317999i	0.324023	+	0.946049i	$0.394964\pi$
$564$		0			0
$565$	337.791	+	317.815i	0.597860	+	0.562505i
$566$	904.940			1.59883
$567$		0			0
$568$	631.424	+	631.424i	1.11166	+	1.11166i
$569$	−27.0610	−	32.2501i	−0.0475589	−	0.0566785i	0.741741	−	0.670687i	$-0.234001\pi$
$569$	−27.0610	−	32.2501i	−0.0475589	−	0.0566785i	−0.789300	+	0.614008i	$0.789556\pi$
$570$		0			0
$571$	117.215	−	664.762i	0.205281	−	1.16421i	−0.691716	−	0.722170i	$-0.743145\pi$
$571$	117.215	−	664.762i	0.205281	−	1.16421i	0.896997	−	0.442037i	$-0.145744\pi$
$572$	−170.747	+	366.168i	−0.298509	+	0.640154i
$573$		0			0
$574$	−1476.95	+	260.426i	−2.57308	+	0.453703i
$575$	701.780	+	18.4939i	1.22049	+	0.0321634i
$576$		0			0
$577$	−47.2820	−	176.459i	−0.0819446	−	0.305821i	0.912773	−	0.408466i	$-0.133936\pi$
$577$	−47.2820	−	176.459i	−0.0819446	−	0.305821i	−0.994718	+	0.102645i	$0.967270\pi$
$578$	900.214	+	1930.52i	1.55746	+	3.33999i
$579$		0			0
$580$	−310.446	−	1493.15i	−0.535251	−	2.57440i
$581$	−853.721	−	716.357i	−1.46940	−	1.23297i
$582$		0			0
$583$	−172.603	−	370.149i	−0.296060	−	0.634904i
$584$	−1082.51	−	624.986i	−1.85361	−	1.07018i
$585$		0			0
$586$	368.882	+	638.922i	0.629491	+	1.09031i
$587$	620.546	+	434.511i	1.05715	+	0.740224i	0.966761	−	0.255683i	$-0.0823003\pi$
$587$	620.546	+	434.511i	1.05715	+	0.740224i	0.0903883	+	0.995907i	$0.471189\pi$
$588$		0			0
$589$	72.8507	+	200.156i	0.123685	+	0.339823i
$590$	−727.697	−	41.3825i	−1.23338	−	0.0701399i
$591$		0			0
$592$	−89.5860	+	1023.97i	−0.151328	+	1.72968i
$593$	−388.235	−	388.235i	−0.654697	−	0.654697i	0.299423	−	0.954120i	$-0.403206\pi$
$593$	−388.235	−	388.235i	−0.654697	−	0.654697i	−0.954120	+	0.299423i	$0.903206\pi$
$594$		0			0
$595$	828.356	−	1050.58i	1.39219	−	1.76569i
$596$	1984.67	−	1665.33i	3.32998	−	2.79419i
$597$		0			0
$598$	−441.402	+	309.073i	−0.738130	+	0.516844i
$599$	−231.477	−	635.977i	−0.386439	−	1.06173i	−0.968593	−	0.248653i	$-0.920012\pi$
$599$	−231.477	−	635.977i	−0.386439	−	1.06173i	0.582154	−	0.813079i	$-0.302210\pi$
$600$		0			0
$601$	−167.114	−	947.753i	−0.278061	−	1.57696i	−0.729069	−	0.684440i	$-0.760047\pi$
$601$	−167.114	−	947.753i	−0.278061	−	1.57696i	0.451008	−	0.892520i	$-0.351065\pi$
$602$	−715.914	−	191.829i	−1.18923	−	0.318652i
$603$		0			0
$604$	50.2302	+	29.0004i	0.0831626	+	0.0480139i
$605$	−152.296	−	246.153i	−0.251729	−	0.406865i
$606$		0			0
$607$	803.166	−	70.2679i	1.32317	−	0.115763i	0.596426	−	0.802668i	$-0.296587\pi$
$607$	803.166	−	70.2679i	1.32317	−	0.115763i	0.726747	+	0.686905i	$0.241031\pi$
$608$	−64.0900	−	732.552i	−0.105411	−	1.20486i
$609$		0			0
$610$	116.318	+	27.3995i	0.190685	+	0.0449172i
$611$	83.4714	−	144.577i	0.136614	−	0.236623i
$612$		0			0
$613$	3.29244	−	12.2875i	0.00537102	−	0.0200449i	−0.963188	−	0.268828i	$-0.913364\pi$
$613$	3.29244	−	12.2875i	0.00537102	−	0.0200449i	0.968559	+	0.248783i	$0.0800305\pi$
$614$	50.8546	−	8.96703i	0.0828250	−	0.0146043i
$615$		0			0
$616$	−1488.48	+	541.761i	−2.41636	+	0.879482i
$617$	−194.394	−	277.624i	−0.315063	−	0.449957i	0.630120	−	0.776498i	$-0.283006\pi$
$617$	−194.394	−	277.624i	−0.315063	−	0.449957i	−0.945183	+	0.326541i	$0.894117\pi$
$618$		0			0
$619$	105.967	+	126.287i	0.171191	+	0.204017i	0.844818	−	0.535055i	$-0.179709\pi$
$619$	105.967	+	126.287i	0.171191	+	0.204017i	−0.673627	+	0.739072i	$0.735264\pi$
$620$	608.779	−	772.100i	0.981902	−	1.24532i
$621$		0			0
$622$	656.951	−	656.951i	1.05619	−	1.05619i
$623$	−810.390	−	70.8999i	−1.30079	−	0.113804i
$624$		0			0
$625$	182.533	+	597.751i	0.292053	+	0.956402i
$626$	−1211.15	+	440.823i	−1.93475	+	0.704190i
$627$		0			0
$628$	−286.387	+	409.003i	−0.456030	+	0.651278i
$629$	622.623	−	359.471i	0.989861	−	0.571497i
$630$		0			0
$631$	183.527	−	317.879i	0.290852	−	0.503770i	−0.683160	−	0.730269i	$-0.739395\pi$
$631$	183.527	−	317.879i	0.290852	−	0.503770i	0.974011	+	0.226499i	$0.0727280\pi$
$632$	−1008.15	+	470.106i	−1.59517	+	0.743839i
$633$		0			0
$634$	−701.967	+	836.572i	−1.10720	+	1.31951i
$635$	−257.456	−	168.826i	−0.405442	−	0.265868i
$636$		0			0
$637$	159.518	−	74.3846i	0.250421	−	0.116773i
$638$	883.096	−	236.625i	1.38416	−	0.370886i
$639$		0			0
$640$	−216.106	+	161.346i	−0.337665	+	0.252102i
$641$	−123.893	−	702.630i	−0.193280	−	1.09615i	−0.914847	−	0.403801i	$-0.867689\pi$
$641$	−123.893	−	702.630i	−0.193280	−	1.09615i	0.721567	−	0.692345i	$-0.243422\pi$
$642$		0			0
$643$	141.102	+	65.7967i	0.219443	+	0.102328i	0.529231	−	0.848478i	$-0.322480\pi$
$643$	141.102	+	65.7967i	0.219443	+	0.102328i	−0.309789	+	0.950805i	$0.600258\pi$
$644$	−2489.30	−	438.931i	−3.86537	−	0.681570i
$645$		0			0
$646$	−895.035	+	751.024i	−1.38550	+	1.16258i
$647$	273.393	−	273.393i	0.422555	−	0.422555i	−0.463527	−	0.886083i	$-0.653416\pi$
$647$	273.393	−	273.393i	0.422555	−	0.422555i	0.886083	+	0.463527i	$0.153416\pi$
$648$		0			0
$649$		−	310.938i		−	0.479104i
$650$	−385.587	−	285.419i	−0.593211	−	0.439106i
$651$		0			0
$652$	−157.215	−	224.526i	−0.241127	−	0.344364i
$653$	259.196	+	120.865i	0.396932	+	0.185092i	0.610827	−	0.791764i	$-0.290837\pi$
$653$	259.196	+	120.865i	0.396932	+	0.185092i	−0.213895	+	0.976857i	$0.568615\pi$
$654$		0			0
$655$	91.3280	−	169.936i	0.139432	−	0.259444i
$656$	−926.205	−	1604.23i	−1.41190	−	2.44548i
$657$		0			0
$658$	1062.96	−	284.819i	1.61544	−	0.432856i
$659$	173.443	−	476.530i	0.263191	−	0.723110i	−0.735757	−	0.677246i	$-0.763173\pi$
$659$	173.443	−	476.530i	0.263191	−	0.723110i	0.998948	−	0.0458648i	$-0.0146043\pi$
$660$		0			0
$661$	−191.112	−	160.362i	−0.289126	−	0.242605i	0.486675	−	0.873583i	$-0.338210\pi$
$661$	−191.112	−	160.362i	−0.289126	−	0.242605i	−0.775801	+	0.630978i	$0.782654\pi$
$662$	−381.827	+	33.4056i	−0.576779	+	0.0504616i
$663$		0			0
$664$	913.917	−	2510.97i	1.37638	−	3.78157i
$665$	447.899	+	192.477i	0.673533	+	0.289439i
$666$		0			0
$667$	838.155	+	224.583i	1.25660	+	0.336706i
$668$	1376.57	−	1965.94i	2.06073	−	2.94302i
$669$		0			0
$670$	311.525	−	944.466i	0.464963	−	1.40965i
$671$	−8.85250	+	50.2050i	−0.0131930	+	0.0748212i
$672$		0			0
$673$	1017.54	+	89.0230i	1.51194	+	0.132278i	0.812732	−	0.582638i	$-0.197979\pi$
$673$	1017.54	+	89.0230i	1.51194	+	0.132278i	0.699210	+	0.714916i	$0.253535\pi$
$674$		−	2040.42i		−	3.02733i
$675$		0			0
$676$	−1406.13			−2.08008
$677$	−66.1686	+	756.311i	−0.0977380	+	1.11715i	0.775993	+	0.630741i	$0.217249\pi$
$677$	−66.1686	+	756.311i	−0.0977380	+	1.11715i	−0.873731	+	0.486409i	$0.838307\pi$
$678$		0			0
$679$	1032.13	+	181.993i	1.52008	+	0.268031i
$680$	3046.36	+	1004.82i	4.47994	+	1.47768i
$681$		0			0
$682$	482.829	+	338.080i	0.707960	+	0.495719i
$683$	−112.220	+	418.812i	−0.164305	+	0.613195i	0.833823	+	0.552032i	$0.186147\pi$
$683$	−112.220	+	418.812i	−0.164305	+	0.613195i	−0.998128	+	0.0611626i	$0.980519\pi$
$684$		0			0
$685$	59.4222	−	138.277i	0.0867478	−	0.201865i
$686$	−473.594	−	172.374i	−0.690370	−	0.251274i
$687$		0			0
$688$	−79.7879	−	911.979i	−0.115971	−	1.32555i
$689$	−170.267	+	202.916i	−0.247122	+	0.294508i
$690$		0			0
$691$	−328.942	−	119.725i	−0.476038	−	0.173264i	0.0928477	−	0.995680i	$-0.470403\pi$
$691$	−328.942	−	119.725i	−0.476038	−	0.173264i	−0.568885	+	0.822417i	$0.692625\pi$
$692$	−574.780	−	2145.11i	−0.830607	−	3.09987i
$693$		0			0
$694$	−821.090	+	474.057i	−1.18313	+	0.683079i
$695$	−1141.55	−	613.501i	−1.64252	−	0.882736i
$696$		0			0
$697$	−547.565	+	1174.26i	−0.785603	+	1.68473i
$698$	−1173.60	+	821.765i	−1.68138	+	1.17731i
$699$		0			0
$700$	−332.255	−	2225.71i	−0.474649	−	3.17958i
$701$	−1152.89			−1.64463			−0.822317	−	0.569030i	$-0.807319\pi$
$701$	−1152.89			−1.64463			−0.822317	+	0.569030i	$0.807319\pi$
$702$		0			0
$703$	185.244	+	185.244i	0.263505	+	0.263505i
$704$	−451.148	−	537.657i	−0.640835	−	0.763717i
$705$		0			0
$706$	−288.643	+	1636.98i	−0.408843	+	2.31866i
$707$	221.546	−	475.107i	0.313360	−	0.672004i
$708$		0			0
$709$	−1315.07	+	231.883i	−1.85483	+	0.327056i	−0.985829	−	0.167755i	$-0.946348\pi$
$709$	−1315.07	+	231.883i	−1.85483	+	0.327056i	−0.869000	+	0.494812i	$0.835237\pi$
$710$	−454.981	−	609.400i	−0.640818	−	0.858309i
$711$		0			0
$712$	−504.823	−	1884.02i	−0.709021	−	2.64610i
$713$	236.425	+	507.014i	0.331591	+	0.711100i
$714$		0			0
$715$	112.225	−	171.140i	0.156958	−	0.239357i
$716$	2147.81	+	1802.22i	2.99973	+	2.51707i
$717$		0			0
$718$	−258.211	−	553.735i	−0.359625	−	0.771218i
$719$	149.862	+	86.5229i	0.208431	+	0.120338i	0.600582	−	0.799563i	$-0.294936\pi$
$719$	149.862	+	86.5229i	0.208431	+	0.120338i	−0.392151	+	0.919901i	$0.628269\pi$
$720$		0			0
$721$	400.269	+	693.287i	0.555158	+	0.961563i
$722$	752.594	+	526.972i	1.04237	+	0.729878i
$723$		0			0
$724$	−312.199	−	857.758i	−0.431213	−	1.18475i
$725$	47.0324	+	771.085i	0.0648723	+	1.06357i
$726$		0			0
$727$	48.1402	−	550.246i	0.0662177	−	0.756871i	−0.888406	−	0.459058i	$-0.848187\pi$
$727$	48.1402	−	550.246i	0.0662177	−	0.756871i	0.954624	−	0.297814i	$-0.0962574\pi$
$728$	726.445	+	726.445i	0.997864	+	0.997864i
$729$		0			0
$730$	835.960	+	659.131i	1.14515	+	0.902919i
$731$	−490.507	+	411.584i	−0.671008	+	0.563043i
$732$		0			0
$733$	−373.397	+	261.455i	−0.509409	+	0.356692i	−0.799849	−	0.600201i	$-0.795087\pi$
$733$	−373.397	+	261.455i	−0.509409	+	0.356692i	0.290440	+	0.956893i	$0.406198\pi$
$734$	−234.737	−	644.935i	−0.319805	−	0.878658i
$735$		0			0
$736$	−335.372	−	1901.99i	−0.455669	−	2.58422i
$737$	409.806	+	109.807i	0.556046	+	0.148992i
$738$		0			0
$739$	−799.156	−	461.393i	−1.08140	−	0.624348i	−0.150128	−	0.988667i	$-0.547968\pi$
$739$	−799.156	−	461.393i	−1.08140	−	0.624348i	−0.931274	+	0.364319i	$0.881302\pi$
$740$	277.270	−	1177.08i	0.374689	−	1.59065i
$741$		0			0
$742$	−1739.45	+	152.182i	−2.34427	+	0.205097i
$743$	7.19167	+	82.2012i	0.00967923	+	0.110634i	0.999497	−	0.0317042i	$-0.0100935\pi$
$743$	7.19167	+	82.2012i	0.00967923	+	0.110634i	−0.989818	+	0.142338i	$0.954538\pi$
$744$		0			0
$745$	−1116.02	+	690.484i	−1.49801	+	0.926824i
$746$	1023.70	−	1773.10i	1.37225	−	2.37680i
$747$		0			0
$748$	−595.497	+	2222.43i	−0.796120	+	2.97116i
$749$	−845.923	+	149.159i	−1.12940	+	0.199144i
$750$		0			0
$751$	−123.653	+	45.0058i	−0.164651	+	0.0599279i	−0.423030	−	0.906116i	$-0.639034\pi$
$751$	−123.653	+	45.0058i	−0.164651	+	0.0599279i	0.258380	+	0.966043i	$0.416811\pi$
$752$	779.629	+	1113.43i	1.03674	+	1.48062i
$753$		0			0
$754$	−381.148	−	454.235i	−0.505501	−	0.602433i
$755$	−23.0710	−	18.1908i	−0.0305576	−	0.0240938i
$756$		0			0
$757$	−361.781	+	361.781i	−0.477914	+	0.477914i	−0.904464	−	0.426550i	$-0.859729\pi$
$757$	−361.781	+	361.781i	−0.477914	+	0.477914i	0.426550	+	0.904464i	$0.359729\pi$
$758$	763.236	+	66.7745i	1.00691	+	0.0880930i
$759$		0			0
$760$	−66.3647	+	1167.00i	−0.0873220	+	1.53553i
$761$	−251.832	+	91.6592i	−0.330922	+	0.120446i	−0.502137	−	0.864788i	$-0.667453\pi$
$761$	−251.832	+	91.6592i	−0.330922	+	0.120446i	0.171215	+	0.985234i	$0.445231\pi$
$762$		0			0
$763$	−348.452	+	497.642i	−0.456687	+	0.652217i
$764$	613.747	−	354.347i	0.803334	−	0.463805i
$765$		0			0
$766$	306.216	−	530.382i	0.399760	−	0.692404i
$767$	−182.773	+	85.2284i	−0.238296	+	0.111119i
$768$		0			0
$769$	709.441	−	845.479i	0.922550	−	1.09945i	−0.0722280	−	0.997388i	$-0.523011\pi$
$769$	709.441	−	845.479i	0.922550	−	1.09945i	0.994778	−	0.102064i	$-0.0325446\pi$
$770$	1320.80	−	274.611i	1.71532	−	0.356637i
$771$		0			0
$772$	1504.27	−	701.451i	1.94853	−	0.908615i
$773$	1314.48	−	352.215i	1.70050	−	0.455646i	0.727431	−	0.686180i	$-0.240714\pi$
$773$	1314.48	−	352.215i	1.70050	−	0.455646i	0.973064	+	0.230534i	$0.0740473\pi$
$774$		0			0
$775$	−361.330	+	342.775i	−0.466232	+	0.442290i
$776$	436.363	+	2474.74i	0.562323	+	3.18909i
$777$		0			0
$778$	853.558	+	398.020i	1.09712	+	0.511594i
$779$	−464.947	−	81.9827i	−0.596851	−	0.105241i
$780$		0			0
$781$	248.532	−	208.543i	0.318222	−	0.267020i
$782$	−2169.87	+	2169.87i	−2.77477	+	2.77477i
$783$		0			0
$784$			1433.06i			1.82788i
$785$	173.309	−	184.203i	0.220776	−	0.234653i
$786$		0			0
$787$	−547.559	−	781.995i	−0.695754	−	0.993640i	−0.999168	−	0.0407813i	$-0.987015\pi$
$787$	−547.559	−	781.995i	−0.695754	−	0.993640i	0.303414	−	0.952859i	$-0.401874\pi$
$788$	−2069.37	−	964.963i	−2.62611	−	1.22457i
$789$		0			0
$790$	907.191	−	272.951i	1.14834	−	0.345508i
$791$	422.950	+	732.571i	0.534703	+	0.926132i
$792$		0			0
$793$	31.9375	−	8.55763i	0.0402743	−	0.0107915i
$794$	122.449	−	336.427i	0.154218	−	0.423712i
$795$		0			0
$796$	2123.54	+	1781.86i	2.66776	+	2.23852i
$797$	191.664	−	16.7684i	0.240482	−	0.0210394i	0.0337223	−	0.999431i	$-0.489264\pi$
$797$	191.664	−	16.7684i	0.240482	−	0.0210394i	0.206759	+	0.978392i	$0.433708\pi$
$798$		0			0
$799$	325.161	−	893.373i	0.406960	−	1.11811i
$800$	1511.20	−	820.190i	1.88900	−	1.02524i
$801$		0			0
$802$	−251.185	−	67.3048i	−0.313198	−	0.0839212i
$803$	−260.485	+	372.012i	−0.324390	+	0.463277i
$804$		0			0
$805$	1215.95	+	401.072i	1.51050	+	0.498227i
$806$	66.3836	−	376.480i	0.0823617	−	0.467097i
$807$		0			0
$808$	1252.14	+	109.548i	1.54968	+	0.135579i
$809$			1045.60i			1.29246i	0.763141	+	0.646232i	$0.223656\pi$
$809$			1045.60i			1.29246i	−0.763141	+	0.646232i	$0.776344\pi$
$810$		0			0
$811$	729.313			0.899276			0.449638	−	0.893211i	$-0.351553\pi$
$811$	729.313			0.899276			0.449638	+	0.893211i	$0.351553\pi$
$812$	242.426	−	2770.94i	0.298554	−	3.41249i
$813$		0			0
$814$	713.931	+	125.885i	0.877065	+	0.154650i
$815$	62.4816	+	123.987i	0.0766646	+	0.152131i
$816$		0			0
$817$	−191.126	−	133.828i	−0.233937	−	0.163804i
$818$	156.831	−	585.302i	0.191725	−	0.715528i
$819$		0			0
$820$	807.406	+	2024.27i	0.984641	+	2.46862i
$821$	915.354	+	333.161i	1.11493	+	0.405800i	0.832798	−	0.553577i	$-0.186738\pi$
$821$	915.354	+	333.161i	1.11493	+	0.405800i	0.282127	+	0.959377i	$0.408960\pi$
$822$		0			0
$823$	−101.760	−	1163.13i	−0.123646	−	1.41328i	−0.764010	−	0.645205i	$-0.776772\pi$
$823$	−101.760	−	1163.13i	−0.123646	−	1.41328i	0.640364	−	0.768071i	$-0.278783\pi$
$824$	−1233.79	+	1470.38i	−1.49732	+	1.78444i
$825$		0			0
$826$	−1249.19	−	454.666i	−1.51233	−	0.550443i
$827$	225.109	+	840.119i	0.272200	+	1.01586i	0.957695	+	0.287786i	$0.0929192\pi$
$827$	225.109	+	840.119i	0.272200	+	1.01586i	−0.685495	+	0.728077i	$0.740414\pi$
$828$		0			0
$829$	−480.585	+	277.466i	−0.579716	+	0.334699i	−0.761021	−	0.648728i	$-0.775301\pi$
$829$	−480.585	+	277.466i	−0.579716	+	0.334699i	0.181304	+	0.983427i	$0.441968\pi$
$830$	−1077.32	+	2004.59i	−1.29798	+	2.41517i
$831$		0			0
$832$	−192.381	+	412.562i	−0.231227	+	0.495867i
$833$	821.066	−	574.917i	0.985674	−	0.690176i
$834$		0			0
$835$	−833.040	+	885.400i	−0.997653	+	1.06036i
$836$	−838.394			−1.00286
$837$		0			0
$838$	−864.917	−	864.917i	−1.03212	−	1.03212i
$839$	75.9873	+	90.5581i	0.0905689	+	0.107936i	0.809426	−	0.587223i	$-0.199779\pi$
$839$	75.9873	+	90.5581i	0.0905689	+	0.107936i	−0.718857	+	0.695158i	$0.755334\pi$
$840$		0			0
$841$	−19.7707	+	112.125i	−0.0235085	+	0.133324i
$842$	255.718	−	548.389i	0.303703	−	0.651293i
$843$		0			0
$844$	394.177	−	69.5041i	0.467035	−	0.0823508i
$845$	704.887	+	102.264i	0.834185	+	0.121022i
$846$		0			0
$847$	−136.638	−	509.938i	−0.161319	−	0.602052i
$848$	−911.464	−	1954.64i	−1.07484	−	2.30500i
$849$		0			0
$850$	−2444.73	−	1219.41i	−2.87616	−	1.43460i
$851$	527.078	+	442.271i	0.619363	+	0.519707i
$852$		0			0
$853$	276.438	+	592.824i	0.324078	+	0.694987i	0.999083	−	0.0428264i	$-0.0136363\pi$
$853$	276.438	+	592.824i	0.324078	+	0.694987i	−0.675005	+	0.737813i	$0.735858\pi$
$854$	188.753	+	108.976i	0.221022	+	0.127607i
$855$		0			0
$856$	−1029.77	−	1783.62i	−1.20301	−	2.08367i
$857$	−1161.75	−	813.469i	−1.35560	−	0.949205i	−0.999893	−	0.0146091i	$-0.995350\pi$
$857$	−1161.75	−	813.469i	−1.35560	−	0.949205i	−0.355712	−	0.934596i	$-0.615761\pi$
$858$		0			0
$859$	85.7399	+	235.568i	0.0998136	+	0.274236i	0.979542	−	0.201242i	$-0.0644976\pi$
$859$	85.7399	+	235.568i	0.0998136	+	0.274236i	−0.879728	+	0.475477i	$0.842275\pi$
$860$	−61.1499	+	1075.30i	−0.0711046	+	1.25035i
$861$		0			0
$862$	−30.7564	+	351.548i	−0.0356803	+	0.407828i
$863$	−885.467	−	885.467i	−1.02603	−	1.02603i	−0.999652	−	0.0263813i	$-0.991602\pi$
$863$	−885.467	−	885.467i	−1.02603	−	1.02603i	−0.0263813	−	0.999652i	$-0.508398\pi$
$864$		0			0
$865$	132.127	+	1117.13i	0.152748	+	1.29148i
$866$	−1376.76	+	1155.24i	−1.58979	+	1.33399i
$867$		0			0
$868$	1468.96	−	1028.58i	1.69236	−	1.18500i
$869$	138.226	+	379.774i	0.159064	+	0.437024i
$870$		0			0
$871$	−47.7823	−	270.987i	−0.0548591	−	0.311121i
$872$	−1406.98	−	377.000i	−1.61351	−	0.432340i
$873$		0			0
$874$	−968.375	−	559.091i	−1.10798	−	0.639693i
$875$	4.68846	+	1139.90i	0.00535824	+	1.30274i
$876$		0			0
$877$	1345.05	−	117.676i	1.53369	−	0.134181i	0.711212	−	0.702977i	$-0.248146\pi$
$877$	1345.05	−	117.676i	1.53369	−	0.134181i	0.822478	+	0.568797i	$0.192591\pi$
$878$	−84.6401	−	967.441i	−0.0964011	−	1.10187i
$879$		0			0
$880$	876.703	+	1417.00i	0.996254	+	1.61023i
$881$	−305.858	+	529.761i	−0.347171	+	0.601318i	−0.985746	−	0.168242i	$-0.946191\pi$
$881$	−305.858	+	529.761i	−0.347171	+	0.601318i	0.638575	+	0.769560i	$0.279524\pi$
$882$		0			0
$883$	346.237	−	1292.17i	0.392114	−	1.46339i	−0.434526	−	0.900659i	$-0.643084\pi$
$883$	346.237	−	1292.17i	0.392114	−	1.46339i	0.826640	−	0.562731i	$-0.190249\pi$
$884$	1469.59	−	259.129i	1.66244	−	0.293132i
$885$		0			0
$886$	−2215.83	+	806.496i	−2.50094	+	0.910266i
$887$	−600.168	−	857.129i	−0.676627	−	0.966324i	−0.999800	−	0.0199838i	$-0.993639\pi$
$887$	−600.168	−	857.129i	−0.676627	−	0.966324i	0.323173	−	0.946340i	$-0.395250\pi$
$888$		0			0
$889$	−360.934	−	430.145i	−0.406000	−	0.483852i
$890$	195.111	+	1649.66i	0.219226	+	1.85355i
$891$		0			0
$892$	911.716	−	911.716i	1.02210	−	1.02210i
$893$	345.108	+	30.1931i	0.386460	+	0.0338108i
$894$		0			0
$895$	−945.612	−	1059.65i	−1.05655	−	1.18396i
$896$	−462.215	+	168.232i	−0.515865	+	0.187759i
$897$		0			0
$898$	−186.043	+	265.697i	−0.207175	+	0.295877i
$899$	−533.129	+	307.802i	−0.593024	+	0.342383i
$900$		0			0
$901$	−754.243	+	1306.39i	−0.837118	+	1.44993i
$902$	−1184.06	+	552.136i	−1.31271	+	0.612125i
$903$		0			0
$904$	−1303.71	+	1553.70i	−1.44215	+	1.71869i
$905$	94.1211	+	452.694i	0.104001	+	0.500215i
$906$		0			0
$907$	197.246	−	91.9774i	0.217471	−	0.101408i	−0.310830	−	0.950466i	$-0.600607\pi$
$907$	197.246	−	91.9774i	0.217471	−	0.101408i	0.528301	+	0.849057i	$0.322829\pi$
$908$	−4187.15	+	1121.94i	−4.61139	+	1.23562i
$909$		0			0
$910$	−523.450	−	701.107i	−0.575220	−	0.770447i
$911$	−230.151	−	1305.25i	−0.252635	−	1.43277i	−0.802070	−	0.597230i	$-0.796268\pi$
$911$	−230.151	−	1305.25i	−0.252635	−	1.43277i	0.549435	−	0.835537i	$-0.314843\pi$
$912$		0			0
$913$	−879.878	−	410.294i	−0.963721	−	0.449391i
$914$	2587.62	+	456.268i	2.83110	+	0.499199i
$915$		0			0
$916$	−321.947	+	270.146i	−0.351470	+	0.294919i
$917$	248.803	−	248.803i	0.271323	−	0.271323i
$918$		0			0
$919$			388.093i			0.422299i	0.977454	+	0.211149i	$0.0677207\pi$
$919$			388.093i			0.422299i	−0.977454	+	0.211149i	$0.932279\pi$
$920$	93.4963	+	3068.55i	0.101626	+	3.33538i
$921$		0			0
$922$	809.316	+	1155.82i	0.877783	+	1.25360i
$923$	−190.706	−	88.9278i	−0.206616	−	0.0963465i
$924$		0			0
$925$	−224.599	+	569.900i	−0.242810	+	0.616108i
$926$	1074.45	+	1861.00i	1.16031	+	2.00972i
$927$		0			0
$928$	2052.85	−	550.060i	2.21212	−	0.592737i
$929$	23.1011	−	63.4697i	0.0248666	−	0.0683204i	−0.926638	−	0.375954i	$-0.877315\pi$
$929$	23.1011	−	63.4697i	0.0248666	−	0.0683204i	0.951505	+	0.307634i	$0.0995372\pi$
$930$		0			0
$931$	279.790	+	234.772i	0.300526	+	0.252171i
$932$	1568.50	−	137.226i	1.68294	−	0.147238i
$933$		0			0
$934$	−628.054	+	1725.57i	−0.672435	+	1.84750i
$935$	460.149	−	1070.78i	0.492138	−	1.14522i
$936$		0			0
$937$	58.4636	+	15.6653i	0.0623945	+	0.0167185i	0.289881	−	0.957063i	$-0.406384\pi$
$937$	58.4636	+	15.6653i	0.0623945	+	0.0167185i	−0.227487	+	0.973781i	$0.573051\pi$
$938$	1040.38	−	1485.82i	1.10915	−	1.58403i
$939$		0			0
$940$	−719.651	−	1428.06i	−0.765586	−	1.51921i
$941$	−200.718	+	1138.33i	−0.213302	+	1.20970i	0.670526	+	0.741886i	$0.266069\pi$
$941$	−200.718	+	1138.33i	−0.213302	+	1.20970i	−0.883828	+	0.467812i	$0.845042\pi$
$942$		0			0
$943$	−1235.26	−	108.071i	−1.30993	−	0.114604i
$944$		−	1641.97i		−	1.73937i
$945$		0			0
$946$	−645.657			−0.682512
$947$	−86.4965	+	988.660i	−0.0913374	+	1.04399i	0.802815	+	0.596228i	$0.203335\pi$
$947$	−86.4965	+	988.660i	−0.0913374	+	1.04399i	−0.894152	+	0.447763i	$0.852221\pi$
$948$		0			0
$949$	290.072	+	51.1475i	0.305660	+	0.0538962i
$950$	198.633	−	975.481i	0.209088	−	1.02682i
$951$		0			0
$952$	4792.49	+	3355.74i	5.03413	+	3.52494i
$953$	−122.213	+	456.106i	−0.128240	+	0.478600i	−0.999934	−	0.0114507i	$-0.996355\pi$
$953$	−122.213	+	456.106i	−0.128240	+	0.478600i	0.871694	+	0.490051i	$0.163022\pi$
$954$		0			0
$955$	−333.438	+	132.996i	−0.349150	+	0.139263i
$956$	−1755.31	−	638.881i	−1.83610	−	0.668286i
$957$		0			0
$958$	100.916	+	1153.47i	0.105340	+	1.20404i
$959$	176.444	−	210.277i	0.183987	−	0.219267i
$960$		0			0
$961$	530.094	+	192.938i	0.551607	+	0.200768i
$962$	−121.692	−	454.162i	−0.126499	−	0.472102i
$963$		0			0
$964$	880.371	−	508.283i	0.913248	−	0.527264i
$965$	−805.094	+	242.232i	−0.834294	+	0.251018i
$966$		0			0
$967$	−731.432	+	1568.56i	−0.756393	+	1.62209i	0.0262778	+	0.999655i	$0.491635\pi$
$967$	−731.432	+	1568.56i	−0.756393	+	1.62209i	−0.782671	+	0.622436i	$0.786143\pi$
$968$	1036.89	−	726.036i	1.07116	−	0.750037i
$969$		0			0
$970$	−65.1789	−	2139.17i	−0.0671947	−	2.20533i
$971$	1317.64			1.35699			0.678495	−	0.734605i	$-0.262633\pi$
$971$	1317.64			1.35699			0.678495	+	0.734605i	$0.262633\pi$
$972$		0			0
$973$	−1671.35	−	1671.35i	−1.71773	−	1.71773i
$974$	−245.306	−	292.344i	−0.251854	−	0.300148i
$975$		0			0
$976$	−46.7473	+	265.117i	−0.0478968	+	0.271636i
$977$	478.479	−	1026.10i	0.489743	−	1.05026i	−0.493799	−	0.869576i	$-0.664392\pi$
$977$	478.479	−	1026.10i	0.489743	−	1.05026i	0.983542	−	0.180681i	$-0.0578302\pi$
$978$		0			0
$979$	−697.888	+	123.057i	−0.712858	+	0.125696i
$980$	242.065	−	1668.51i	0.247005	−	1.70257i
$981$		0			0
$982$	−412.044	−	1537.77i	−0.419597	−	1.56596i
$983$	305.033	+	654.146i	0.310309	+	0.665459i	0.998176	−	0.0603779i	$-0.0192306\pi$
$983$	305.033	+	654.146i	0.310309	+	0.665459i	−0.687867	+	0.725837i	$0.741453\pi$
$984$		0			0
$985$	967.184	+	634.229i	0.981913	+	0.643888i
$986$	−2586.78	−	2170.56i	−2.62351	−	2.20138i
$987$		0			0
$988$	229.804	+	492.817i	0.232596	+	0.498803i
$989$	−530.699	−	306.399i	−0.536602	−	0.309807i
$990$		0			0
$991$	135.118	+	234.031i	0.136345	+	0.236157i	0.926111	−	0.377252i	$-0.123131\pi$
$991$	135.118	+	234.031i	0.136345	+	0.236157i	−0.789765	+	0.613409i	$0.789798\pi$
$992$	1122.39	+	785.903i	1.13144	+	0.792241i
$993$		0			0
$994$	−474.402	−	1303.41i	−0.477265	−	1.31128i
$995$	−934.927	−	1047.67i	−0.939625	−	1.05294i
$996$		0			0
$997$	151.510	−	1731.77i	0.151966	−	1.73698i	−0.412000	−	0.911184i	$-0.635170\pi$
$997$	151.510	−	1731.77i	0.151966	−	1.73698i	0.563967	−	0.825798i	$-0.309275\pi$
$998$	1319.58	+	1319.58i	1.32222	+	1.32222i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.s.a.118.33		408
3.2	odd	2		135.3.r.a.103.2	yes	408
5.2	odd	4	inner	405.3.s.a.37.33		408
15.2	even	4		135.3.r.a.22.2	✓	408
27.11	odd	18		135.3.r.a.43.2	yes	408
27.16	even	9	inner	405.3.s.a.208.33		408
135.92	even	36		135.3.r.a.97.2	yes	408
135.97	odd	36	inner	405.3.s.a.127.33		408

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.r.a.22.2	✓	408	15.2	even	4
135.3.r.a.43.2	yes	408	27.11	odd	18
135.3.r.a.97.2	yes	408	135.92	even	36
135.3.r.a.103.2	yes	408	3.2	odd	2
405.3.s.a.37.33		408	5.2	odd	4	inner
405.3.s.a.118.33		408	1.1	even	1	trivial
405.3.s.a.127.33		408	135.97	odd	36	inner
405.3.s.a.208.33		408	27.16	even	9	inner

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.s (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.324599 - 3.71019i) q^{2} +(-9.72089 - 1.71405i) q^{4} +(4.74836 + 1.56622i) q^{5} +(7.47006 + 5.23059i) q^{7} +(-5.65912 + 21.1201i) q^{8} +(7.35227 - 17.1089i) q^{10} +(7.46500 + 2.71704i) q^{11} +(-0.449058 - 5.13275i) q^{13} +(21.8312 - 26.0175i) q^{14} +(39.4204 + 14.3478i) q^{16} +(-7.59419 - 28.3419i) q^{17} +(9.25934 - 5.34588i) q^{19} +(-43.4737 - 23.3640i) q^{20} +(12.5039 - 26.8146i) q^{22} +(23.0026 - 16.1066i) q^{23} +(20.0939 + 14.8739i) q^{25} -19.1892 q^{26} +(-63.6501 - 63.6501i) q^{28} +(19.8626 + 23.6713i) q^{29} +(-3.45942 + 19.6193i) q^{31} +(29.0665 - 62.3334i) q^{32} +(-107.619 + 18.9761i) q^{34} +(27.2783 + 36.5365i) q^{35} +(6.34170 + 23.6675i) q^{37} +(-16.8287 - 36.0892i) q^{38} +(-59.9502 + 91.4226i) q^{40} +(-33.8265 - 28.3838i) q^{41} +(-9.22262 - 19.7780i) q^{43} +(-67.9093 - 39.2075i) q^{44} +(-52.2918 - 90.5720i) q^{46} +(26.5416 + 18.5846i) q^{47} +(11.6837 + 32.1007i) q^{49} +(61.7075 - 69.7242i) q^{50} +(-4.43258 + 50.6646i) q^{52} +(-36.3531 - 36.3531i) q^{53} +(31.1911 + 24.5933i) q^{55} +(-152.745 + 128.168i) q^{56} +(94.2724 - 66.0103i) q^{58} +(-13.3870 - 36.7804i) q^{59} +(1.11435 + 6.31979i) q^{61} +(71.6685 + 19.2035i) q^{62} +(-76.5134 - 44.1751i) q^{64} +(5.90670 - 25.0755i) q^{65} +(53.2028 - 4.65465i) q^{67} +(25.2427 + 288.525i) q^{68} +(144.412 - 89.3480i) q^{70} +(20.4199 - 35.3683i) q^{71} +(-14.7960 + 55.2194i) q^{73} +(89.8695 - 15.8464i) q^{74} +(-99.1722 + 36.0957i) q^{76} +(41.5523 + 59.3428i) q^{77} +(32.7011 + 38.9717i) q^{79} +(164.710 + 129.870i) q^{80} +(-116.289 + 116.289i) q^{82} +(-121.744 - 10.6512i) q^{83} +(8.32953 - 146.472i) q^{85} +(-76.3736 + 27.7977i) q^{86} +(-99.6295 + 142.286i) q^{88} +(-77.2540 + 44.6026i) q^{89} +(23.4928 - 40.6908i) q^{91} +(-251.213 + 117.143i) q^{92} +(77.5677 - 92.4416i) q^{94} +(52.3395 - 10.8821i) q^{95} +(104.160 - 48.5706i) q^{97} +(122.892 - 32.9288i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 408 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 6 q^{8} - 6 q^{10} + 60 q^{11} - 12 q^{13} - 24 q^{16} + 6 q^{17} + 300 q^{20} - 12 q^{22} + 156 q^{23} + 6 q^{25} + 48 q^{26} - 24 q^{28} - 24 q^{31} - 72 q^{32}+ \cdots + 1032 q^{98}+O(q^{100}) \) 408 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 6 * q^8 - 6 * q^10 + 60 * q^11 - 12 * q^13 - 24 * q^16 + 6 * q^17 + 300 * q^20 - 12 * q^22 + 156 * q^23 + 6 * q^25 + 48 * q^26 - 24 * q^28 - 24 * q^31 - 72 * q^32 - 156 * q^35 - 6 * q^37 + 252 * q^38 - 108 * q^40 + 384 * q^41 - 12 * q^43 - 12 * q^46 + 210 * q^47 - 276 * q^50 - 60 * q^52 - 516 * q^53 - 24 * q^55 - 912 * q^56 - 12 * q^58 - 312 * q^61 + 6 * q^62 - 420 * q^65 - 480 * q^67 + 540 * q^68 - 12 * q^70 + 12 * q^71 - 6 * q^73 - 216 * q^76 + 876 * q^77 + 1644 * q^80 - 24 * q^82 + 372 * q^83 - 12 * q^85 - 516 * q^86 + 348 * q^88 - 12 * q^91 - 2082 * q^92 - 198 * q^95 + 600 * q^97 + 1032 * q^98

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