LMFDB - Embedded newform 324.3.j.a.307.31

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [324,3,Mod(19,324)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(324, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 16])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("324.19"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.j (of order $18$, degree $6$, 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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			307.31
Character	$\chi$	$=$	324.307
Dual form			324.3.j.a.19.31

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.90734 - 0.601703i) q^{2} +(3.27591 - 2.29531i) q^{4} +(0.755508 - 4.28470i) q^{5} +(-6.44162 - 7.67682i) q^{7} +(4.86718 - 6.34906i) q^{8} +(-1.13710 - 8.62697i) q^{10} +(-16.5915 + 2.92553i) q^{11} +(7.70282 - 2.80360i) q^{13} +(-16.9055 - 10.7664i) q^{14} +(5.46314 - 15.0384i) q^{16} +(-13.2638 + 22.9735i) q^{17} +(10.2637 - 5.92574i) q^{19} +(-7.35972 - 15.7704i) q^{20} +(-29.8854 + 15.5631i) q^{22} +(14.3578 - 17.1110i) q^{23} +(5.70448 + 2.07626i) q^{25} +(13.0050 - 9.98223i) q^{26} +(-38.7228 - 10.3631i) q^{28} +(29.1256 + 10.6009i) q^{29} +(12.9259 - 15.4045i) q^{31} +(1.37140 - 31.9706i) q^{32} +(-11.4753 + 51.7992i) q^{34} +(-37.7596 + 21.8005i) q^{35} +(20.1962 - 34.9808i) q^{37} +(16.0108 - 17.4781i) q^{38} +(-23.5266 - 25.6512i) q^{40} +(34.1160 - 12.4172i) q^{41} +(25.3466 - 4.46929i) q^{43} +(-47.6372 + 47.6664i) q^{44} +(17.0895 - 41.2756i) q^{46} +(12.9992 + 15.4919i) q^{47} +(-8.93040 + 50.6468i) q^{49} +(12.1297 + 0.527738i) q^{50} +(18.7986 - 26.8647i) q^{52} -46.7045 q^{53} +73.2998i q^{55} +(-80.0931 + 3.53372i) q^{56} +(61.9311 + 2.69449i) q^{58} +(-36.4280 - 6.42325i) q^{59} +(48.7491 - 40.9054i) q^{61} +(15.3852 - 37.1592i) q^{62} +(-16.6211 - 61.8040i) q^{64} +(-6.19303 - 35.1224i) q^{65} +(25.9527 + 71.3043i) q^{67} +(9.28040 + 105.704i) q^{68} +(-58.9030 + 64.3010i) q^{70} +(17.4692 + 10.0858i) q^{71} +(-50.2648 - 87.0613i) q^{73} +(17.4729 - 78.8724i) q^{74} +(20.0215 - 42.9705i) q^{76} +(129.335 + 108.525i) q^{77} +(-29.7876 + 81.8406i) q^{79} +(-60.3076 - 34.7695i) q^{80} +(57.5993 - 44.2115i) q^{82} +(-25.2237 + 69.3017i) q^{83} +(88.4137 + 74.1879i) q^{85} +(45.6555 - 23.7756i) q^{86} +(-62.1795 + 119.580i) q^{88} +(37.6081 + 65.1392i) q^{89} +(-71.1414 - 41.0735i) q^{91} +(7.75992 - 89.0095i) q^{92} +(34.1155 + 21.7266i) q^{94} +(-17.6357 - 48.4537i) q^{95} +(12.6145 + 71.5405i) q^{97} +(13.4410 + 101.974i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37}+ \cdots - 510 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	1.90734	−	0.601703i	0.953671	−	0.300851i
$2$	1.90734	−	0.601703i	0.953671	−	0.300851i
$3$		0			0
$3$		0			0
$4$	3.27591	−	2.29531i	0.818977	−	0.573827i
$5$	0.755508	−	4.28470i	0.151102	−	0.856939i	−0.811162	−	0.584821i	$-0.801165\pi$
$5$	0.755508	−	4.28470i	0.151102	−	0.856939i	0.962264	−	0.272118i	$-0.0877242\pi$
$6$		0			0
$7$	−6.44162	−	7.67682i	−0.920232	−	1.09669i	−0.995038	−	0.0994912i	$-0.968278\pi$
$7$	−6.44162	−	7.67682i	−0.920232	−	1.09669i	0.0748069	−	0.997198i	$-0.476166\pi$
$8$	4.86718	−	6.34906i	0.608398	−	0.793632i
$9$		0			0
$10$	−1.13710	−	8.62697i	−0.113710	−	0.862697i
$11$	−16.5915	+	2.92553i	−1.50832	+	0.265957i	−0.865830	−	0.500338i	$-0.833209\pi$
$11$	−16.5915	+	2.92553i	−1.50832	+	0.265957i	−0.642489	+	0.766295i	$0.722098\pi$
$12$		0			0
$13$	7.70282	−	2.80360i	0.592525	−	0.215661i	−0.0283148	−	0.999599i	$-0.509014\pi$
$13$	7.70282	−	2.80360i	0.592525	−	0.215661i	0.620840	+	0.783938i	$0.286792\pi$
$14$	−16.9055	−	10.7664i	−1.20754	−	0.769028i
$15$		0			0
$16$	5.46314	−	15.0384i	0.341446	−	0.939901i
$17$	−13.2638	+	22.9735i	−0.780222	+	1.35138i	0.151590	+	0.988443i	$0.451561\pi$
$17$	−13.2638	+	22.9735i	−0.780222	+	1.35138i	−0.931812	+	0.362941i	$0.881773\pi$
$18$		0			0
$19$	10.2637	−	5.92574i	0.540194	−	0.311881i	−0.204964	−	0.978770i	$-0.565708\pi$
$19$	10.2637	−	5.92574i	0.540194	−	0.311881i	0.745158	+	0.666888i	$0.232374\pi$
$20$	−7.35972	−	15.7704i	−0.367986	−	0.788519i
$21$		0			0
$22$	−29.8854	+	15.5631i	−1.35843	+	0.707416i
$23$	14.3578	−	17.1110i	0.624252	−	0.743955i	−0.357543	−	0.933897i	$-0.616385\pi$
$23$	14.3578	−	17.1110i	0.624252	−	0.743955i	0.981795	+	0.189942i	$0.0608299\pi$
$24$		0			0
$25$	5.70448	+	2.07626i	0.228179	+	0.0830505i
$26$	13.0050	−	9.98223i	0.500192	−	0.383932i
$27$		0			0
$28$	−38.7228	−	10.3631i	−1.38296	−	0.370110i
$29$	29.1256	+	10.6009i	1.00433	+	0.365547i	0.791254	−	0.611488i	$-0.209429\pi$
$29$	29.1256	+	10.6009i	1.00433	+	0.365547i	0.213078	+	0.977035i	$0.431651\pi$
$30$		0			0
$31$	12.9259	−	15.4045i	0.416965	−	0.496920i	−0.516150	−	0.856498i	$-0.672635\pi$
$31$	12.9259	−	15.4045i	0.416965	−	0.496920i	0.933115	+	0.359579i	$0.117080\pi$
$32$	1.37140	−	31.9706i	0.0428564	−	0.999081i
$33$		0			0
$34$	−11.4753	+	51.7992i	−0.337509	+	1.52351i
$35$	−37.7596	+	21.8005i	−1.07884	+	0.622871i
$36$		0			0
$37$	20.1962	−	34.9808i	0.545842	−	0.945426i	−0.452711	−	0.891657i	$-0.649543\pi$
$37$	20.1962	−	34.9808i	0.545842	−	0.945426i	0.998553	−	0.0537690i	$-0.0171235\pi$
$38$	16.0108	−	17.4781i	0.421338	−	0.459950i
$39$		0			0
$40$	−23.5266	−	25.6512i	−0.588165	−	0.641279i
$41$	34.1160	−	12.4172i	0.832096	−	0.302858i	0.109377	−	0.994000i	$-0.465114\pi$
$41$	34.1160	−	12.4172i	0.832096	−	0.302858i	0.722719	+	0.691142i	$0.242892\pi$
$42$		0			0
$43$	25.3466	−	4.46929i	0.589456	−	0.103937i	0.129039	−	0.991640i	$-0.458811\pi$
$43$	25.3466	−	4.46929i	0.589456	−	0.103937i	0.460417	+	0.887703i	$0.347700\pi$
$44$	−47.6372	+	47.6664i	−1.08266	+	1.08333i
$45$		0			0
$46$	17.0895	−	41.2756i	0.371511	−	0.897295i
$47$	12.9992	+	15.4919i	0.276579	+	0.329614i	0.886396	−	0.462928i	$-0.153201\pi$
$47$	12.9992	+	15.4919i	0.276579	+	0.329614i	−0.609817	+	0.792543i	$0.708757\pi$
$48$		0			0
$49$	−8.93040	+	50.6468i	−0.182253	+	1.03361i
$50$	12.1297	+	0.527738i	0.242594	+	0.0105548i
$51$		0			0
$52$	18.7986	−	26.8647i	0.361512	−	0.516628i
$53$	−46.7045			−0.881217			−0.440609	−	0.897699i	$-0.645237\pi$
$53$	−46.7045			−0.881217			−0.440609	+	0.897699i	$0.645237\pi$
$54$		0			0
$55$			73.2998i			1.33272i
$56$	−80.0931	+	3.53372i	−1.43023	+	0.0631021i
$57$		0			0
$58$	61.9311	+	2.69449i	1.06778	+	0.0464568i
$59$	−36.4280	−	6.42325i	−0.617424	−	0.108869i	−0.143817	−	0.989604i	$-0.545938\pi$
$59$	−36.4280	−	6.42325i	−0.617424	−	0.108869i	−0.473608	+	0.880736i	$0.657049\pi$
$60$		0			0
$61$	48.7491	−	40.9054i	0.799166	−	0.670580i	−0.148830	−	0.988863i	$-0.547551\pi$
$61$	48.7491	−	40.9054i	0.799166	−	0.670580i	0.947996	+	0.318283i	$0.103106\pi$
$62$	15.3852	−	37.1592i	0.248149	−	0.599342i
$63$		0			0
$64$	−16.6211	−	61.8040i	−0.259704	−	0.965688i
$65$	−6.19303	−	35.1224i	−0.0952773	−	0.540344i
$66$		0			0
$67$	25.9527	+	71.3043i	0.387353	+	1.06424i	0.968188	+	0.250223i	$0.0805038\pi$
$67$	25.9527	+	71.3043i	0.387353	+	1.06424i	−0.580835	+	0.814021i	$0.697274\pi$
$68$	9.28040	+	105.704i	0.136477	+	1.55446i
$69$		0			0
$70$	−58.9030	+	64.3010i	−0.841471	+	0.918586i
$71$	17.4692	+	10.0858i	0.246045	+	0.142054i	0.617952	−	0.786216i	$-0.287963\pi$
$71$	17.4692	+	10.0858i	0.246045	+	0.142054i	−0.371907	+	0.928270i	$0.621296\pi$
$72$		0			0
$73$	−50.2648	−	87.0613i	−0.688560	−	1.19262i	−0.972304	−	0.233720i	$-0.924910\pi$
$73$	−50.2648	−	87.0613i	−0.688560	−	1.19262i	0.283744	−	0.958900i	$-0.408423\pi$
$74$	17.4729	−	78.8724i	0.236121	−	1.06584i
$75$		0			0
$76$	20.0215	−	42.9705i	0.263441	−	0.565401i
$77$	129.335	+	108.525i	1.67967	+	1.40941i
$78$		0			0
$79$	−29.7876	+	81.8406i	−0.377058	+	1.03596i	0.595512	+	0.803346i	$0.296949\pi$
$79$	−29.7876	+	81.8406i	−0.377058	+	1.03596i	−0.972570	+	0.232611i	$0.925273\pi$
$80$	−60.3076	−	34.7695i	−0.753845	−	0.434619i
$81$		0			0
$82$	57.5993	−	44.2115i	0.702431	−	0.539165i
$83$	−25.2237	+	69.3017i	−0.303900	+	0.834960i	0.689912	+	0.723893i	$0.257649\pi$
$83$	−25.2237	+	69.3017i	−0.303900	+	0.834960i	−0.993813	+	0.111067i	$0.964573\pi$
$84$		0			0
$85$	88.4137	+	74.1879i	1.04016	+	0.872799i
$86$	45.6555	−	23.7756i	0.530878	−	0.276461i
$87$		0			0
$88$	−62.1795	+	119.580i	−0.706586	+	1.35886i
$89$	37.6081	+	65.1392i	0.422563	+	0.731901i	0.996189	−	0.0872163i	$-0.0277971\pi$
$89$	37.6081	+	65.1392i	0.422563	+	0.731901i	−0.573626	+	0.819117i	$0.694464\pi$
$90$		0			0
$91$	−71.1414	−	41.0735i	−0.781774	−	0.451357i
$92$	7.75992	−	89.0095i	0.0843470	−	0.967494i
$93$		0			0
$94$	34.1155	+	21.7266i	0.362930	+	0.231134i
$95$	−17.6357	−	48.4537i	−0.185639	−	0.510039i
$96$		0			0
$97$	12.6145	+	71.5405i	0.130047	+	0.737531i	0.978182	+	0.207751i	$0.0666144\pi$
$97$	12.6145	+	71.5405i	0.130047	+	0.737531i	−0.848135	+	0.529780i	$0.822274\pi$
$98$	13.4410	+	101.974i	0.137153	+	1.04055i
$99$		0			0
$100$	23.4530	−	6.29190i	0.234530	−	0.0629190i
$101$	−40.3702	+	33.8746i	−0.399705	+	0.335392i	−0.820379	−	0.571820i	$-0.806238\pi$
$101$	−40.3702	+	33.8746i	−0.399705	+	0.335392i	0.420675	+	0.907211i	$0.361793\pi$
$102$		0			0
$103$	42.8748	+	7.55998i	0.416260	+	0.0733979i	0.377856	−	0.925864i	$-0.376661\pi$
$103$	42.8748	+	7.55998i	0.416260	+	0.0733979i	0.0384042	+	0.999262i	$0.487773\pi$
$104$	19.6908	−	62.5513i	0.189335	−	0.601455i
$105$		0			0
$106$	−89.0815	+	28.1022i	−0.840391	+	0.265115i
$107$			70.5658i			0.659493i	0.944069	+	0.329747i	$0.106963\pi$
$107$			70.5658i			0.659493i	−0.944069	+	0.329747i	$0.893037\pi$
$108$		0			0
$109$	−89.3232			−0.819479			−0.409739	−	0.912203i	$-0.634380\pi$
$109$	−89.3232			−0.819479			−0.409739	+	0.912203i	$0.634380\pi$
$110$	44.1047	+	139.808i	0.400952	+	1.27098i
$111$		0			0
$112$	−150.639	+	54.9323i	−1.34499	+	0.490467i
$113$	13.7107	−	77.7573i	0.121334	−	0.688118i	−0.862084	−	0.506765i	$-0.830841\pi$
$113$	13.7107	−	77.7573i	0.121334	−	0.688118i	0.983418	−	0.181353i	$-0.0580476\pi$
$114$		0			0
$115$	−62.4678	−	74.4463i	−0.543199	−	0.647359i
$116$	119.745	−	32.1248i	1.03228	−	0.276938i
$117$		0			0
$118$	−73.3456	+	9.66753i	−0.621573	+	0.0819282i
$119$	261.804	−	46.1631i	2.20003	−	0.387925i
$120$		0			0
$121$	153.017	−	55.6935i	1.26460	−	0.460277i
$122$	68.3684	−	107.353i	0.560397	−	0.879943i
$123$		0			0
$124$	6.98604	−	80.1327i	0.0563390	−	0.646231i
$125$	67.5909	−	117.071i	0.540727	−	0.936567i
$126$		0			0
$127$	−82.1426	+	47.4250i	−0.646792	+	0.373425i	−0.787226	−	0.616665i	$-0.788483\pi$
$127$	−82.1426	+	47.4250i	−0.646792	+	0.373425i	0.140434	+	0.990090i	$0.455150\pi$
$128$	−68.8897	−	107.881i	−0.538201	−	0.842816i
$129$		0			0
$130$	−32.9455	−	63.2641i	−0.253427	−	0.486647i
$131$	7.26521	−	8.65835i	0.0554597	−	0.0660942i	−0.737601	−	0.675236i	$-0.764042\pi$
$131$	7.26521	−	8.65835i	0.0554597	−	0.0660942i	0.793061	+	0.609142i	$0.208486\pi$
$132$		0			0
$133$	−111.606	−	40.6211i	−0.839140	−	0.305422i
$134$	92.4046	+	120.386i	0.689587	+	0.898403i
$135$		0			0
$136$	81.3031	+	196.029i	0.597817	+	1.44139i
$137$	−147.499	−	53.6854i	−1.07664	−	0.391864i	−0.257982	−	0.966150i	$-0.583058\pi$
$137$	−147.499	−	53.6854i	−1.07664	−	0.391864i	−0.818655	+	0.574286i	$0.805280\pi$
$138$		0			0
$139$	113.198	−	134.904i	0.814376	−	0.970535i	−0.185551	−	0.982635i	$-0.559407\pi$
$139$	113.198	−	134.904i	0.814376	−	0.970535i	0.999927	+	0.0120996i	$0.00385153\pi$
$140$	−73.6580	+	158.086i	−0.526129	+	1.12919i
$141$		0			0
$142$	39.3884	+	8.72588i	0.277383	+	0.0614498i
$143$	−119.599	+	69.0507i	−0.836359	+	0.482872i
$144$		0			0
$145$	67.4261	−	116.785i	0.465008	−	0.805417i
$146$	−148.257	−	135.811i	−1.01546	−	0.930213i
$147$		0			0
$148$	−14.1309	−	160.950i	−0.0954788	−	1.08750i
$149$	92.5431	−	33.6829i	0.621094	−	0.226060i	−0.0122562	−	0.999925i	$-0.503901\pi$
$149$	92.5431	−	33.6829i	0.621094	−	0.226060i	0.633351	+	0.773865i	$0.281679\pi$
$150$		0			0
$151$	−0.769516	+	0.135686i	−0.00509613	+	0.000898586i	−0.176196	−	0.984355i	$-0.556379\pi$
$151$	−0.769516	+	0.135686i	−0.00509613	+	0.000898586i	0.171100	+	0.985254i	$0.445268\pi$
$152$	12.3324	−	94.0064i	0.0811339	−	0.618463i
$153$		0			0
$154$	311.986	+	129.173i	2.02588	+	0.838785i
$155$	−56.2380	−	67.0219i	−0.362826	−	0.432399i
$156$		0			0
$157$	−30.8928	+	175.202i	−0.196769	+	1.11593i	0.713107	+	0.701055i	$0.247287\pi$
$157$	−30.8928	+	175.202i	−0.196769	+	1.11593i	−0.909876	+	0.414879i	$0.863824\pi$
$158$	−7.57130	+	174.021i	−0.0479196	+	1.10140i
$159$		0			0
$160$	−135.948	−	30.0301i	−0.849676	−	0.187688i
$161$	−223.845			−1.39034
$162$		0			0
$163$			268.797i			1.64906i	0.565818	+	0.824530i	$0.308561\pi$
$163$			268.797i			1.64906i	−0.565818	+	0.824530i	$0.691439\pi$
$164$	83.2594	−	118.984i	0.507679	−	0.725513i
$165$		0			0
$166$	−6.41129	+	147.359i	−0.0386222	+	0.887706i
$167$	21.3074	+	3.75708i	0.127589	+	0.0224975i	0.237078	−	0.971491i	$-0.423810\pi$
$167$	21.3074	+	3.75708i	0.127589	+	0.0224975i	−0.109489	+	0.993988i	$0.534921\pi$
$168$		0			0
$169$	−77.9882	+	65.4399i	−0.461469	+	0.387218i
$170$	213.274	+	88.3029i	1.25455	+	0.519429i
$171$		0			0
$172$	72.7748	−	72.8192i	0.423109	−	0.423368i
$173$	20.3403	+	115.356i	0.117574	+	0.666796i	0.985443	+	0.170003i	$0.0543778\pi$
$173$	20.3403	+	115.356i	0.117574	+	0.666796i	−0.867869	+	0.496792i	$0.834511\pi$
$174$		0			0
$175$	−20.8070	−	57.1668i	−0.118897	−	0.326668i
$176$	−46.6463	+	265.493i	−0.265036	+	1.50848i
$177$		0			0
$178$	110.926	+	101.614i	0.623180	+	0.570864i
$179$	17.3998	+	10.0458i	0.0972054	+	0.0561216i	0.547815	−	0.836600i	$-0.315460\pi$
$179$	17.3998	+	10.0458i	0.0972054	+	0.0561216i	−0.450609	+	0.892721i	$0.648793\pi$
$180$		0			0
$181$	96.6241	+	167.358i	0.533835	+	0.924629i	0.999219	+	0.0395201i	$0.0125829\pi$
$181$	96.6241	+	167.358i	0.533835	+	0.924629i	−0.465384	+	0.885109i	$0.654084\pi$
$182$	−160.405	−	35.5352i	−0.881346	−	0.195249i
$183$		0			0
$184$	−38.7564	−	174.441i	−0.210633	−	0.948047i
$185$	−134.624	−	112.963i	−0.727695	−	0.610609i
$186$		0			0
$187$	152.856	−	419.969i	0.817413	−	2.24582i
$188$	78.1428	+	20.9127i	0.415653	+	0.111238i
$189$		0			0
$190$	−62.7921	−	81.8064i	−0.330485	−	0.430560i
$191$	−87.6196	+	240.733i	−0.458741	+	1.26038i	0.467682	+	0.883897i	$0.345089\pi$
$191$	−87.6196	+	240.733i	−0.458741	+	1.26038i	−0.926423	+	0.376484i	$0.877133\pi$
$192$		0			0
$193$	−217.111	−	182.178i	−1.12493	−	0.943928i	−0.126087	−	0.992019i	$-0.540242\pi$
$193$	−217.111	−	182.178i	−1.12493	−	0.943928i	−0.998843	+	0.0480909i	$0.984686\pi$
$194$	67.1064	+	128.862i	0.345909	+	0.664237i
$195$		0			0
$196$	86.9948	+	186.412i	0.443851	+	0.951083i
$197$	−142.022	−	245.990i	−0.720925	−	1.24868i	−0.960630	−	0.277832i	$-0.910384\pi$
$197$	−142.022	−	245.990i	−0.720925	−	1.24868i	0.239705	−	0.970846i	$-0.422949\pi$
$198$		0			0
$199$	−118.652	−	68.5039i	−0.596242	−	0.344241i	0.171320	−	0.985216i	$-0.445197\pi$
$199$	−118.652	−	68.5039i	−0.596242	−	0.344241i	−0.767562	+	0.640975i	$0.778530\pi$
$200$	40.9471	−	26.1126i	0.204735	−	0.130563i
$201$		0			0
$202$	−56.6173	+	88.9013i	−0.280283	+	0.440105i
$203$	−106.235	−	291.879i	−0.523326	−	1.43783i
$204$		0			0
$205$	−27.4290	−	155.558i	−0.133800	−	0.758818i
$206$	86.3258	−	11.3784i	0.419057	−	0.0552350i
$207$		0			0
$208$	−0.0801338	−	131.155i	−0.000385259	−	0.630552i
$209$	−152.954	+	128.344i	−0.731838	+	0.614085i
$210$		0			0
$211$	181.862	+	32.0671i	0.861903	+	0.151977i	0.587091	−	0.809521i	$-0.300273\pi$
$211$	181.862	+	32.0671i	0.861903	+	0.151977i	0.274813	+	0.961498i	$0.411384\pi$
$212$	−153.000	+	107.201i	−0.721696	+	0.505666i
$213$		0			0
$214$	42.4596	+	134.593i	0.198409	+	0.628940i
$215$		−	111.979i		−	0.520833i
$216$		0			0
$217$	−201.522			−0.928671
$218$	−170.370	+	53.7460i	−0.781513	+	0.246541i
$219$		0			0
$220$	168.246	+	240.123i	0.764753	+	1.09147i
$221$	−37.7599	+	214.147i	−0.170859	+	0.968992i
$222$		0			0
$223$	−140.359	−	167.273i	−0.629413	−	0.750105i	0.353245	−	0.935531i	$-0.385078\pi$
$223$	−140.359	−	167.273i	−0.629413	−	0.750105i	−0.982658	+	0.185426i	$0.940634\pi$
$224$	−254.267	+	195.414i	−1.13512	+	0.872386i
$225$		0			0
$226$	−20.6358	−	156.560i	−0.0913088	−	0.692741i
$227$	298.580	−	52.6476i	1.31533	−	0.231928i	0.528412	−	0.848988i	$-0.322788\pi$
$227$	298.580	−	52.6476i	1.31533	−	0.231928i	0.786916	+	0.617060i	$0.211676\pi$
$228$		0			0
$229$	−291.207	+	105.991i	−1.27164	+	0.462841i	−0.887660	−	0.460499i	$-0.847671\pi$
$229$	−291.207	+	105.991i	−1.27164	+	0.462841i	−0.383985	+	0.923340i	$0.625448\pi$
$230$	−163.942	−	104.407i	−0.712792	−	0.453945i
$231$		0			0
$232$	209.065	−	133.324i	0.901143	−	0.574672i
$233$	21.7586	−	37.6870i	0.0933845	−	0.161747i	−0.815549	−	0.578688i	$-0.803565\pi$
$233$	21.7586	−	37.6870i	0.0933845	−	0.161747i	0.908933	+	0.416942i	$0.136898\pi$
$234$		0			0
$235$	76.1989	−	43.9935i	0.324251	−	0.187206i
$236$	−134.078	+	62.5716i	−0.568128	+	0.265134i
$237$		0			0
$238$	471.573	−	245.577i	1.98140	−	1.03184i
$239$	214.161	−	255.227i	0.896069	−	1.06789i	−0.101260	−	0.994860i	$-0.532287\pi$
$239$	214.161	−	255.227i	0.896069	−	1.06789i	0.997329	−	0.0730337i	$-0.0232681\pi$
$240$		0			0
$241$	325.919	+	118.625i	1.35236	+	0.492219i	0.913684	−	0.406426i	$-0.133225\pi$
$241$	325.919	+	118.625i	1.35236	+	0.492219i	0.438677	+	0.898645i	$0.355447\pi$
$242$	258.344	−	198.297i	1.06754	−	0.819409i
$243$		0			0
$244$	65.8073	−	245.896i	0.269702	−	1.00777i
$245$	210.259	+	76.5281i	0.858201	+	0.312360i
$246$		0			0
$247$	62.4460	−	74.4202i	0.252818	−	0.301296i
$248$	−34.8913	−	157.044i	−0.140691	−	0.633242i
$249$		0			0
$250$	58.4770	−	263.964i	0.233908	−	1.05585i
$251$	12.1468	−	7.01295i	0.0483935	−	0.0279400i	−0.475608	−	0.879657i	$-0.657772\pi$
$251$	12.1468	−	7.01295i	0.0483935	−	0.0279400i	0.524002	+	0.851717i	$0.324439\pi$
$252$		0			0
$253$	−188.159	+	325.901i	−0.743711	+	1.28815i
$254$	−128.138	+	139.881i	−0.504481	+	0.550713i
$255$		0			0
$256$	−196.308	−	164.314i	−0.766829	−	0.641851i
$257$	159.478	−	58.0452i	0.620537	−	0.225857i	−0.0125705	−	0.999921i	$-0.504001\pi$
$257$	159.478	−	58.0452i	0.620537	−	0.225857i	0.633107	+	0.774064i	$0.281779\pi$
$258$		0			0
$259$	−398.637	+	70.2905i	−1.53914	+	0.271392i
$260$	−100.904	−	100.843i	−0.388094	−	0.387857i
$261$		0			0
$262$	8.64750	−	20.8859i	0.0330057	−	0.0797173i
$263$	−208.683	−	248.699i	−0.793473	−	0.945624i	0.205985	−	0.978555i	$-0.433960\pi$
$263$	−208.683	−	248.699i	−0.793473	−	0.945624i	−0.999458	+	0.0329313i	$0.989516\pi$
$264$		0			0
$265$	−35.2856	+	200.115i	−0.133153	+	0.755150i
$266$	−237.312	−	10.3250i	−0.892151	−	0.0388156i
$267$		0			0
$268$	248.684	+	174.017i	0.927924	+	0.649317i
$269$	281.085			1.04493			0.522463	−	0.852662i	$-0.325013\pi$
$269$	281.085			1.04493			0.522463	+	0.852662i	$0.325013\pi$
$270$		0			0
$271$		−	270.921i		−	0.999709i	−0.866109	−	0.499855i	$-0.833387\pi$
$271$		−	270.921i		−	0.999709i	0.866109	−	0.499855i	$-0.166613\pi$
$272$	273.024	+	324.974i	1.00376	+	1.19476i
$273$		0			0
$274$	−313.634	−	13.6456i	−1.14465	−	0.0498014i
$275$	−100.720	−	17.7597i	−0.366255	−	0.0645807i
$276$		0			0
$277$	80.9996	−	67.9667i	0.292417	−	0.245367i	−0.484763	−	0.874646i	$-0.661094\pi$
$277$	80.9996	−	67.9667i	0.292417	−	0.245367i	0.777180	+	0.629279i	$0.216650\pi$
$278$	134.735	−	325.420i	0.484659	−	1.17058i
$279$		0			0
$280$	−45.3701	+	345.845i	−0.162036	+	1.23516i
$281$	−14.7191	−	83.4761i	−0.0523811	−	0.297068i	0.947351	−	0.320196i	$-0.103749\pi$
$281$	−14.7191	−	83.4761i	−0.0523811	−	0.297068i	−0.999733	+	0.0231277i	$0.992638\pi$
$282$		0			0
$283$	110.305	+	303.060i	0.389770	+	1.07088i	0.967105	+	0.254376i	$0.0818702\pi$
$283$	110.305	+	303.060i	0.389770	+	1.07088i	−0.577336	+	0.816507i	$0.695908\pi$
$284$	80.3775	−	7.05686i	0.283019	−	0.0248481i
$285$		0			0
$286$	−186.569	+	203.667i	−0.652339	+	0.712121i
$287$	−315.087	−	181.915i	−1.09786	−	0.633851i
$288$		0			0
$289$	−207.355	−	359.150i	−0.717493	−	1.24273i
$290$	58.3345	−	263.320i	0.201153	−	0.908001i
$291$		0			0
$292$	−364.495	−	169.831i	−1.24827	−	0.581614i
$293$	−157.814	−	132.422i	−0.538615	−	0.451952i	0.332449	−	0.943121i	$-0.392125\pi$
$293$	−157.814	−	132.422i	−0.538615	−	0.451952i	−0.871064	+	0.491170i	$0.836570\pi$
$294$		0			0
$295$	−55.0433	+	151.230i	−0.186588	+	0.512645i
$296$	−123.797	−	298.484i	−0.418232	−	1.00839i
$297$		0			0
$298$	156.244	−	119.928i	0.524309	−	0.402444i
$299$	62.6233	−	172.056i	0.209443	−	0.575439i
$300$		0			0
$301$	−197.583	−	165.792i	−0.656423	−	0.550804i
$302$	−1.38609	+	0.721821i	−0.00458969	+	0.00239013i
$303$		0			0
$304$	−33.0419	−	186.723i	−0.108691	−	0.614220i
$305$	−138.437	−	239.780i	−0.453891	−	0.786163i
$306$		0			0
$307$	194.400	+	112.237i	0.633225	+	0.365593i	0.782000	−	0.623278i	$-0.214200\pi$
$307$	194.400	+	112.237i	0.633225	+	0.365593i	−0.148775	+	0.988871i	$0.547533\pi$
$308$	672.787	+	58.6542i	2.18437	+	0.190436i
$309$		0			0
$310$	−147.592	−	93.9950i	−0.476104	−	0.303210i
$311$	76.8272	+	211.081i	0.247033	+	0.678717i	0.999791	+	0.0204207i	$0.00650055\pi$
$311$	76.8272	+	211.081i	0.247033	+	0.678717i	−0.752759	+	0.658297i	$0.771277\pi$
$312$		0			0
$313$	−69.3890	−	393.525i	−0.221690	−	1.25727i	−0.868912	−	0.494966i	$-0.835181\pi$
$313$	−69.3890	−	393.525i	−0.221690	−	1.25727i	0.647222	−	0.762301i	$-0.275931\pi$
$314$	46.4963	+	352.758i	0.148077	+	1.12343i
$315$		0			0
$316$	90.2681	+	336.474i	0.285658	+	1.06479i
$317$	−11.8267	+	9.92380i	−0.0373083	+	0.0313054i	−0.661251	−	0.750165i	$-0.729974\pi$
$317$	−11.8267	+	9.92380i	−0.0373083	+	0.0313054i	0.623943	+	0.781470i	$0.285530\pi$
$318$		0			0
$319$	−514.251	−	90.6763i	−1.61207	−	0.284252i
$320$	−277.369	+	24.5228i	−0.866778	+	0.0766338i
$321$		0			0
$322$	−426.950	+	134.688i	−1.32593	+	0.418287i
$323$			314.391i			0.973346i
$324$		0			0
$325$	49.7616			0.153113
$326$	161.736	+	512.688i	0.496122	+	1.57266i
$327$		0			0
$328$	87.2111	−	277.041i	0.265887	−	0.844637i
$329$	35.1923	−	199.585i	0.106967	−	0.606643i
$330$		0			0
$331$	178.560	+	212.799i	0.539455	+	0.642898i	0.965065	−	0.262009i	$-0.0843850\pi$
$331$	178.560	+	212.799i	0.539455	+	0.642898i	−0.425610	+	0.904907i	$0.639941\pi$
$332$	76.4379	+	284.922i	0.230235	+	0.858199i
$333$		0			0
$334$	42.9012	−	5.65472i	0.128447	−	0.0169303i
$335$	325.125	−	57.3283i	0.970522	−	0.171129i
$336$		0			0
$337$	524.664	−	190.962i	1.55687	−	0.566653i	0.586850	−	0.809696i	$-0.300368\pi$
$337$	524.664	−	190.962i	1.55687	−	0.566653i	0.970015	+	0.243043i	$0.0781457\pi$
$338$	−109.375	+	171.742i	−0.323594	+	0.508112i
$339$		0			0
$340$	459.919	+	40.0961i	1.35270	+	0.117930i
$341$	−169.394	+	293.399i	−0.496757	+	0.860408i
$342$		0			0
$343$	21.0731	−	12.1666i	0.0614376	−	0.0354710i
$344$	94.9908	−	182.680i	0.276136	−	0.531046i
$345$		0			0
$346$	108.206	+	207.784i	0.312733	+	0.600531i
$347$	−288.093	+	343.336i	−0.830241	+	0.989442i	0.169752	+	0.985487i	$0.445703\pi$
$347$	−288.093	+	343.336i	−0.830241	+	0.989442i	−0.999992	+	0.00395526i	$0.998741\pi$
$348$		0			0
$349$	479.457	+	174.508i	1.37380	+	0.500023i	0.920294	−	0.391228i	$-0.127950\pi$
$349$	479.457	+	174.508i	1.37380	+	0.500023i	0.453509	+	0.891252i	$0.350172\pi$
$350$	−74.0836	−	96.5170i	−0.211667	−	0.275763i
$351$		0			0
$352$	70.7773	+	534.452i	0.201072	+	1.51833i
$353$	194.831	+	70.9126i	0.551928	+	0.200885i	0.602903	−	0.797814i	$-0.294011\pi$
$353$	194.831	+	70.9126i	0.551928	+	0.200885i	−0.0509748	+	0.998700i	$0.516233\pi$
$354$		0			0
$355$	56.4128	−	67.2302i	0.158909	−	0.189381i
$356$	272.715	+	127.068i	0.766054	+	0.356932i
$357$		0			0
$358$	39.2319	+	8.69121i	0.109586	+	0.0242771i
$359$	−52.8592	+	30.5183i	−0.147240	+	0.0850091i	−0.571810	−	0.820386i	$-0.693759\pi$
$359$	−52.8592	+	30.5183i	−0.147240	+	0.0850091i	0.424570	+	0.905395i	$0.360425\pi$
$360$		0			0
$361$	−110.271	+	190.995i	−0.305460	+	0.529073i
$362$	284.995	+	261.070i	0.787279	+	0.721187i
$363$		0			0
$364$	−327.329	+	28.7383i	−0.899255	+	0.0789515i
$365$	−411.007	+	149.594i	−1.12605	+	0.409847i
$366$		0			0
$367$	258.395	−	45.5620i	0.704073	−	0.124147i	0.189862	−	0.981811i	$-0.439196\pi$
$367$	258.395	−	45.5620i	0.704073	−	0.124147i	0.514211	+	0.857664i	$0.328085\pi$
$368$	−178.883	−	309.398i	−0.486096	−	0.840756i
$369$		0			0
$370$	−324.743	−	134.455i	−0.877684	−	0.363392i
$371$	300.853	+	358.542i	0.810924	+	0.966421i
$372$		0			0
$373$	−96.1685	+	545.399i	−0.257824	+	1.46219i	0.530893	+	0.847439i	$0.321857\pi$
$373$	−96.1685	+	545.399i	−0.257824	+	1.46219i	−0.788717	+	0.614756i	$0.789254\pi$
$374$	38.8525	−	892.999i	0.103884	−	2.38770i
$375$		0			0
$376$	161.628	−	7.13105i	0.429863	−	0.0189656i
$377$	254.070			0.673926
$378$		0			0
$379$			61.8712i			0.163249i	0.996663	+	0.0816243i	$0.0260107\pi$
$379$			61.8712i			0.163249i	−0.996663	+	0.0816243i	$0.973989\pi$
$380$	−168.989	−	118.251i	−0.444708	−	0.311186i
$381$		0			0
$382$	−22.2709	+	511.881i	−0.0583007	+	1.34000i
$383$	356.264	+	62.8189i	0.930193	+	0.164018i	0.618159	−	0.786053i	$-0.287879\pi$
$383$	356.264	+	62.8189i	0.930193	+	0.164018i	0.312034	+	0.950071i	$0.398990\pi$
$384$		0			0
$385$	562.710	−	472.170i	1.46158	−	1.22641i
$386$	−523.723	−	216.839i	−1.35680	−	0.561760i
$387$		0			0
$388$	205.531	+	205.406i	0.529720	+	0.529397i
$389$	51.9683	+	294.727i	0.133595	+	0.757653i	0.975828	+	0.218540i	$0.0701294\pi$
$389$	51.9683	+	294.727i	0.133595	+	0.757653i	−0.842233	+	0.539113i	$0.818759\pi$
$390$		0			0
$391$	202.661	+	556.805i	0.518313	+	1.42405i
$392$	278.094	+	303.207i	0.709423	+	0.773487i
$393$		0			0
$394$	−418.898	−	383.731i	−1.06319	−	0.973937i
$395$	328.158	+	189.462i	0.830778	+	0.479650i
$396$		0			0
$397$	197.081	+	341.354i	0.496425	+	0.859833i	0.999991	−	0.00412318i	$-0.00131245\pi$
$397$	197.081	+	341.354i	0.496425	+	0.859833i	−0.503567	+	0.863956i	$0.667979\pi$
$398$	−267.529	−	59.2670i	−0.672184	−	0.148912i
$399$		0			0
$400$	62.3881	−	74.4435i	0.155970	−	0.186109i
$401$	33.5438	+	28.1466i	0.0836503	+	0.0701909i	0.683654	−	0.729806i	$-0.260390\pi$
$401$	33.5438	+	28.1466i	0.0836503	+	0.0701909i	−0.600004	+	0.799997i	$0.704834\pi$
$402$		0			0
$403$	56.3780	−	154.897i	0.139896	−	0.384360i
$404$	−54.4963	+	203.632i	−0.134892	+	0.504039i
$405$		0			0
$406$	−378.251	−	492.791i	−0.931654	−	1.21377i
$407$	−232.747	+	639.468i	−0.571861	+	1.57117i
$408$		0			0
$409$	−318.044	−	266.870i	−0.777613	−	0.652495i	0.165033	−	0.986288i	$-0.447227\pi$
$409$	−318.044	−	266.870i	−0.777613	−	0.652495i	−0.942646	+	0.333793i	$0.891671\pi$
$410$	−145.916	−	280.198i	−0.355893	−	0.683409i
$411$		0			0
$412$	157.806	−	73.6450i	0.383025	−	0.178750i
$413$	185.346	+	321.028i	0.448778	+	0.777307i
$414$		0			0
$415$	277.880	+	160.434i	0.669590	+	0.386588i
$416$	−79.0690	−	250.109i	−0.190070	−	0.601223i
$417$		0			0
$418$	−214.511	+	336.828i	−0.513184	+	0.805809i
$419$	21.7249	+	59.6886i	0.0518493	+	0.142455i	0.962914	−	0.269809i	$-0.0869605\pi$
$419$	21.7249	+	59.6886i	0.0518493	+	0.142455i	−0.911065	+	0.412264i	$0.864738\pi$
$420$		0			0
$421$	108.764	+	616.830i	0.258346	+	1.46515i	0.787335	+	0.616525i	$0.211460\pi$
$421$	108.764	+	616.830i	0.258346	+	1.46515i	−0.528989	+	0.848629i	$0.677429\pi$
$422$	366.167	−	48.2637i	0.867695	−	0.114369i
$423$		0			0
$424$	−227.319	+	296.530i	−0.536131	+	0.699362i
$425$	−123.362	+	103.513i	−0.290264	+	0.243560i
$426$		0			0
$427$	−628.047	−	110.742i	−1.47084	−	0.259348i
$428$	161.970	+	231.167i	0.378435	+	0.540110i
$429$		0			0
$430$	−67.3782	−	213.583i	−0.156693	−	0.496704i
$431$			127.048i			0.294775i	0.989079	+	0.147388i	$0.0470865\pi$
$431$			127.048i			0.294775i	−0.989079	+	0.147388i	$0.952914\pi$
$432$		0			0
$433$	587.542			1.35691			0.678454	−	0.734642i	$-0.262650\pi$
$433$	587.542			1.35691			0.678454	+	0.734642i	$0.262650\pi$
$434$	−384.371	+	121.256i	−0.885647	+	0.279392i
$435$		0			0
$436$	−292.615	+	205.024i	−0.671134	+	0.470239i
$437$	45.9688	−	260.702i	0.105192	−	0.596573i
$438$		0			0
$439$	277.190	+	330.342i	0.631412	+	0.752488i	0.982988	−	0.183672i	$-0.0587984\pi$
$439$	277.190	+	330.342i	0.631412	+	0.752488i	−0.351576	+	0.936159i	$0.614354\pi$
$440$	465.385	+	356.764i	1.05769	+	0.810826i
$441$		0			0
$442$	56.8319	+	431.172i	0.128579	+	0.975503i
$443$	−774.476	+	136.561i	−1.74825	+	0.308264i	−0.954107	−	0.299465i	$-0.903192\pi$
$443$	−774.476	+	136.561i	−1.74825	+	0.308264i	−0.794145	+	0.607729i	$0.792081\pi$
$444$		0			0
$445$	307.515	−	111.926i	0.691045	−	0.251520i
$446$	−368.362	−	234.593i	−0.825923	−	0.525994i
$447$		0			0
$448$	−367.392	+	525.715i	−0.820072	+	1.17347i
$449$	242.525	−	420.066i	0.540145	−	0.935559i	−0.458750	−	0.888566i	$-0.651703\pi$
$449$	242.525	−	420.066i	0.540145	−	0.935559i	0.998895	−	0.0469939i	$-0.0149641\pi$
$450$		0			0
$451$	−529.708	+	305.827i	−1.17452	+	0.678109i
$452$	−133.562	−	286.196i	−0.295491	−	0.633177i
$453$		0			0
$454$	537.815	−	280.073i	1.18461	−	0.616901i
$455$	−229.735	+	273.788i	−0.504913	+	0.601732i
$456$		0			0
$457$	−813.496	−	296.088i	−1.78008	−	0.647896i	−0.999746	−	0.0225304i	$-0.992828\pi$
$457$	−813.496	−	296.088i	−1.78008	−	0.647896i	−0.780332	−	0.625365i	$-0.784950\pi$
$458$	−491.656	+	377.380i	−1.07348	+	0.823974i
$459$		0			0
$460$	−375.516	−	100.496i	−0.816339	−	0.218470i
$461$	652.111	+	237.349i	1.41456	+	0.514857i	0.932464	−	0.361263i	$-0.117654\pi$
$461$	652.111	+	237.349i	1.41456	+	0.514857i	0.482094	+	0.876120i	$0.339876\pi$
$462$		0			0
$463$	438.512	−	522.598i	0.947111	−	1.12872i	−0.0444414	−	0.999012i	$-0.514151\pi$
$463$	438.512	−	522.598i	0.947111	−	1.12872i	0.991552	−	0.129710i	$-0.0414048\pi$
$464$	318.537	−	380.089i	0.686503	−	0.819158i
$465$		0			0
$466$	18.8247	−	84.9742i	0.0403964	−	0.182348i
$467$	388.222	−	224.140i	0.831310	−	0.479957i	−0.0229910	−	0.999736i	$-0.507319\pi$
$467$	388.222	−	224.140i	0.831310	−	0.479957i	0.854301	+	0.519779i	$0.173986\pi$
$468$		0			0
$469$	380.214	−	658.549i	0.810690	−	1.40416i
$470$	118.866	−	129.760i	0.252907	−	0.276085i
$471$		0			0
$472$	−218.083	+	200.021i	−0.462041	+	0.423773i
$473$	−407.463	+	148.305i	−0.861445	+	0.313540i
$474$		0			0
$475$	70.8524	−	12.4932i	0.149163	−	0.0263015i
$476$	751.687	−	752.146i	1.57917	−	1.58014i
$477$		0			0
$478$	254.907	−	615.665i	0.533278	−	1.28800i
$479$	−370.059	−	441.020i	−0.772567	−	0.920709i	0.226006	−	0.974126i	$-0.427433\pi$
$479$	−370.059	−	441.020i	−0.772567	−	0.920709i	−0.998572	+	0.0534168i	$0.982989\pi$
$480$		0			0
$481$	57.4954	−	326.073i	0.119533	−	0.677905i
$482$	693.015	+	30.1517i	1.43779	+	0.0625553i
$483$		0			0
$484$	373.434	−	533.666i	0.771559	−	1.10262i
$485$	316.060			0.651670
$486$		0			0
$487$		−	109.976i		−	0.225824i	−0.993605	−	0.112912i	$-0.963982\pi$
$487$		−	109.976i		−	0.225824i	0.993605	−	0.112912i	$-0.0360178\pi$
$488$	−22.4397	−	508.605i	−0.0459830	−	1.04222i
$489$		0			0
$490$	447.083	+	19.4517i	0.912415	+	0.0396973i
$491$	−382.906	−	67.5166i	−0.779849	−	0.137508i	−0.230467	−	0.973080i	$-0.574025\pi$
$491$	−382.906	−	67.5166i	−0.779849	−	0.137508i	−0.549381	+	0.835572i	$0.685137\pi$
$492$		0			0
$493$	−629.855	+	528.511i	−1.27760	+	1.07203i
$494$	74.3269	−	179.519i	0.150459	−	0.363398i
$495$		0			0
$496$	−161.043	−	278.542i	−0.324684	−	0.561577i
$497$	−35.1026	−	199.077i	−0.0706290	−	0.400557i
$498$		0			0
$499$	−36.1272	−	99.2586i	−0.0723992	−	0.198915i	0.898215	−	0.439557i	$-0.144864\pi$
$499$	−36.1272	−	99.2586i	−0.0723992	−	0.198915i	−0.970614	+	0.240642i	$0.922642\pi$
$500$	−47.2920	−	538.655i	−0.0945840	−	1.07731i
$501$		0			0
$502$	18.9484	−	20.6848i	0.0377457	−	0.0412049i
$503$	−417.548	−	241.072i	−0.830116	−	0.479268i	0.0237762	−	0.999717i	$-0.492431\pi$
$503$	−417.548	−	241.072i	−0.830116	−	0.479268i	−0.853892	+	0.520449i	$0.825764\pi$
$504$		0			0
$505$	114.642	+	198.566i	0.227015	+	0.393201i
$506$	−162.788	+	734.820i	−0.321715	+	1.45221i
$507$		0			0
$508$	−160.236	+	343.902i	−0.315426	+	0.676973i
$509$	466.979	+	391.842i	0.917443	+	0.769826i	0.973520	−	0.228600i	$-0.0734148\pi$
$509$	466.979	+	391.842i	0.917443	+	0.769826i	−0.0560770	+	0.998426i	$0.517859\pi$
$510$		0			0
$511$	−344.567	+	946.690i	−0.674299	+	1.85262i
$512$	−473.295	−	195.283i	−0.924405	−	0.381413i
$513$		0			0
$514$	269.253	−	206.670i	0.523839	−	0.402083i
$515$	64.7845	−	177.994i	0.125795	−	0.345619i
$516$		0			0
$517$	−260.999	−	219.004i	−0.504833	−	0.423605i
$518$	−718.043	+	373.929i	−1.38618	+	0.721871i
$519$		0			0
$520$	−253.137	−	131.627i	−0.486801	−	0.253129i
$521$	96.1278	+	166.498i	0.184506	+	0.319575i	0.943410	−	0.331628i	$-0.107598\pi$
$521$	96.1278	+	166.498i	0.184506	+	0.319575i	−0.758904	+	0.651203i	$0.774265\pi$
$522$		0			0
$523$	261.108	+	150.751i	0.499250	+	0.288242i	0.728404	−	0.685148i	$-0.240262\pi$
$523$	261.108	+	150.751i	0.499250	+	0.288242i	−0.229154	+	0.973390i	$0.573596\pi$
$524$	3.92661	−	45.0398i	0.00749353	−	0.0859539i
$525$		0			0
$526$	−547.673	−	348.789i	−1.04120	−	0.663097i
$527$	182.449	+	501.276i	0.346204	+	0.951188i
$528$		0			0
$529$	5.22135	+	29.6117i	0.00987022	+	0.0559768i
$530$	53.1078	+	402.919i	0.100203	+	0.760224i
$531$		0			0
$532$	−458.848	+	123.098i	−0.862496	+	0.231387i
$533$	227.976	−	191.295i	0.427723	−	0.358902i
$534$		0			0
$535$	302.353	+	53.3130i	0.565146	+	0.0996504i
$536$	579.032	+	182.276i	1.08028	+	0.340068i
$537$		0			0
$538$	536.126	−	169.130i	0.996517	−	0.314368i
$539$		−	866.433i		−	1.60748i
$540$		0			0
$541$	−53.7516			−0.0993561			−0.0496780	−	0.998765i	$-0.515820\pi$
$541$	−53.7516			−0.0993561			−0.0496780	+	0.998765i	$0.515820\pi$
$542$	−163.014	−	516.739i	−0.300764	−	0.953394i
$543$		0			0
$544$	716.287	+	455.557i	1.31670	+	0.837421i
$545$	−67.4844	+	382.723i	−0.123825	+	0.702244i
$546$		0			0
$547$	−309.469	−	368.810i	−0.565756	−	0.674242i	0.404998	−	0.914318i	$-0.367272\pi$
$547$	−309.469	−	368.810i	−0.565756	−	0.674242i	−0.970754	+	0.240076i	$0.922828\pi$
$548$	−606.418	+	162.688i	−1.10660	+	0.296876i
$549$		0			0
$550$	−202.794	+	26.7298i	−0.368716	+	0.0485997i
$551$	361.754	−	63.7870i	0.656541	−	0.115766i
$552$		0			0
$553$	820.156	−	298.512i	1.48310	−	0.539806i
$554$	113.598	−	178.373i	0.205051	−	0.321974i
$555$		0			0
$556$	61.1799	−	701.759i	0.110036	−	1.26216i
$557$	−220.981	+	382.751i	−0.396735	+	0.687165i	−0.993321	−	0.115384i	$-0.963190\pi$
$557$	−220.981	+	382.751i	−0.396735	+	0.687165i	0.596586	+	0.802549i	$0.296523\pi$
$558$		0			0
$559$	182.710	−	105.488i	0.326852	−	0.188708i
$560$	121.559	+	686.943i	0.217070	+	1.22668i
$561$		0			0
$562$	−78.3021	−	150.361i	−0.139328	−	0.267546i
$563$	539.434	−	642.872i	0.958142	−	1.14187i	−0.0316719	−	0.999498i	$-0.510083\pi$
$563$	539.434	−	642.872i	0.958142	−	1.14187i	0.989813	−	0.142370i	$-0.0454724\pi$
$564$		0			0
$565$	−322.808	−	117.492i	−0.571341	−	0.207951i
$566$	392.741	+	511.668i	0.693889	+	0.904008i
$567$		0			0
$568$	149.061	−	61.8232i	0.262432	−	0.108844i
$569$	−1001.95	−	364.680i	−1.76090	−	0.640914i	−0.760927	−	0.648838i	$-0.775255\pi$
$569$	−1001.95	−	364.680i	−1.76090	−	0.640914i	−0.999969	+	0.00792419i	$0.997478\pi$
$570$		0			0
$571$	−421.903	+	502.804i	−0.738884	+	0.880567i	−0.996319	−	0.0857285i	$-0.972678\pi$
$571$	−421.903	+	502.804i	−0.738884	+	0.880567i	0.257435	+	0.966296i	$0.417123\pi$
$572$	−233.304	+	500.721i	−0.407874	+	0.875387i
$573$		0			0
$574$	−710.437	−	157.386i	−1.23770	−	0.274192i
$575$	117.431	−	67.7987i	0.204227	−	0.117911i
$576$		0			0
$577$	−117.795	+	204.027i	−0.204151	+	0.353600i	−0.949862	−	0.312670i	$-0.898777\pi$
$577$	−117.795	+	204.027i	−0.204151	+	0.353600i	0.745711	+	0.666270i	$0.232110\pi$
$578$	−611.599	−	560.256i	−1.05813	−	0.969300i
$579$		0			0
$580$	−47.1767	−	537.342i	−0.0813392	−	0.926451i
$581$	694.498	−	252.777i	1.19535	−	0.435072i
$582$		0			0
$583$	774.898	−	136.635i	1.32916	−	0.234366i
$584$	−797.405	−	104.609i	−1.36542	−	0.179124i
$585$		0			0
$586$	−380.684	−	157.616i	−0.649632	−	0.268970i
$587$	−294.660	−	351.162i	−0.501976	−	0.598232i	0.454245	−	0.890877i	$-0.349909\pi$
$587$	−294.660	−	351.162i	−0.501976	−	0.598232i	−0.956221	+	0.292645i	$0.905465\pi$
$588$		0			0
$589$	41.3844	−	234.703i	0.0702622	−	0.398477i
$590$	−13.9907	+	321.568i	−0.0237131	+	0.545030i
$591$		0			0
$592$	−415.721	−	494.823i	−0.702232	−	0.835850i
$593$	−530.547			−0.894683			−0.447342	−	0.894363i	$-0.647629\pi$
$593$	−530.547			−0.894683			−0.447342	+	0.894363i	$0.647629\pi$
$594$		0			0
$595$		−	1156.63i		−	1.94391i
$596$	225.850	−	322.757i	0.378943	−	0.541538i
$597$		0			0
$598$	15.9174	−	365.851i	0.0266177	−	0.611790i
$599$	−367.257	−	64.7574i	−0.613118	−	0.108109i	−0.141538	−	0.989933i	$-0.545205\pi$
$599$	−367.257	−	64.7574i	−0.613118	−	0.108109i	−0.471579	+	0.881824i	$0.656316\pi$
$600$		0			0
$601$	−335.573	+	281.579i	−0.558358	+	0.468518i	−0.877759	−	0.479102i	$-0.840962\pi$
$601$	−335.573	+	281.579i	−0.558358	+	0.468518i	0.319402	+	0.947619i	$0.396518\pi$
$602$	−476.616	−	197.336i	−0.791722	−	0.327800i
$603$		0			0
$604$	−2.20942	+	2.21077i	−0.00365798	+	0.00366022i
$605$	−123.024	−	697.706i	−0.203346	−	1.15323i
$606$		0			0
$607$	−56.8614	−	156.226i	−0.0936762	−	0.257373i	0.884001	−	0.467484i	$-0.154840\pi$
$607$	−56.8614	−	156.226i	−0.0936762	−	0.257373i	−0.977677	+	0.210111i	$0.932617\pi$
$608$	−175.374	−	336.263i	−0.288444	−	0.553064i
$609$		0			0
$610$	−408.322	−	374.044i	−0.669381	−	0.613187i
$611$	143.564	+	82.8865i	0.234965	+	0.135657i
$612$		0			0
$613$	−95.7272	−	165.804i	−0.156162	−	0.270480i	0.777320	−	0.629106i	$-0.216579\pi$
$613$	−95.7272	−	165.804i	−0.156162	−	0.270480i	−0.933481	+	0.358626i	$0.883245\pi$
$614$	438.321	+	97.1032i	0.713878	+	0.158149i
$615$		0			0
$616$	1318.53	−	292.945i	2.14047	−	0.475559i
$617$	−216.274	−	181.476i	−0.350526	−	0.294126i	0.450475	−	0.892789i	$-0.351255\pi$
$617$	−216.274	−	181.476i	−0.350526	−	0.294126i	−0.801001	+	0.598663i	$0.795699\pi$
$618$		0			0
$619$	22.1636	−	60.8940i	0.0358055	−	0.0983748i	−0.920502	−	0.390739i	$-0.872220\pi$
$619$	22.1636	−	60.8940i	0.0358055	−	0.0983748i	0.956307	+	0.292364i	$0.0944418\pi$
$620$	−338.066	−	90.4739i	−0.545268	−	0.145926i
$621$		0			0
$622$	273.544	+	356.377i	0.439781	+	0.572953i
$623$	257.805	−	708.313i	0.413812	−	1.13694i
$624$		0			0
$625$	−334.289	−	280.502i	−0.534862	−	0.448803i
$626$	−369.133	−	708.834i	−0.589670	−	1.13232i
$627$		0			0
$628$	300.940	+	644.853i	0.479203	+	1.02684i
$629$	535.754	+	927.954i	0.851756	+	1.47528i
$630$		0			0
$631$	−310.209	−	179.099i	−0.491615	−	0.283834i	0.233629	−	0.972326i	$-0.424940\pi$
$631$	−310.209	−	179.099i	−0.491615	−	0.283834i	−0.725244	+	0.688492i	$0.758273\pi$
$632$	374.629	+	587.456i	0.592768	+	0.929519i
$633$		0			0
$634$	−16.5864	+	26.0443i	−0.0261616	+	0.0410793i
$635$	141.143	+	387.786i	0.222272	+	0.610686i
$636$		0			0
$637$	73.2040	+	415.161i	0.114920	+	0.651744i
$638$	−1035.41	+	136.476i	−1.62290	+	0.213912i
$639$		0			0
$640$	−514.282	+	213.667i	−0.803566	+	0.333855i
$641$	575.070	−	482.541i	0.897146	−	0.752795i	−0.0724847	−	0.997370i	$-0.523093\pi$
$641$	575.070	−	482.541i	0.897146	−	0.752795i	0.969630	+	0.244575i	$0.0786484\pi$
$642$		0			0
$643$	−899.318	−	158.574i	−1.39863	−	0.246616i	−0.577049	−	0.816709i	$-0.695796\pi$
$643$	−899.318	−	158.574i	−1.39863	−	0.246616i	−0.821580	+	0.570093i	$0.806907\pi$
$644$	−733.297	+	513.794i	−1.13866	+	0.797816i
$645$		0			0
$646$	189.170	+	599.651i	0.292833	+	0.928252i
$647$			457.889i			0.707710i	0.935300	+	0.353855i	$0.115129\pi$
$647$			457.889i			0.707710i	−0.935300	+	0.353855i	$0.884871\pi$
$648$		0			0
$649$	623.187			0.960227
$650$	94.9125	−	29.9417i	0.146019	−	0.0460642i
$651$		0			0
$652$	616.971	+	880.554i	0.946275	+	1.35054i
$653$	−44.8800	+	254.527i	−0.0687289	+	0.389781i	0.930967	+	0.365104i	$0.118967\pi$
$653$	−44.8800	+	254.527i	−0.0687289	+	0.389781i	−0.999695	+	0.0246765i	$0.992144\pi$
$654$		0			0
$655$	−31.6095	−	37.6707i	−0.0482587	−	0.0575125i
$656$	−0.354914	−	580.887i	−0.000541028	−	0.885498i
$657$		0			0
$658$	−52.9674	−	401.853i	−0.0804976	−	0.610719i
$659$	−773.092	+	136.317i	−1.17313	+	0.206854i	−0.726051	−	0.687640i	$-0.758647\pi$
$659$	−773.092	+	136.317i	−1.17313	+	0.206854i	−0.447078	+	0.894495i	$0.647535\pi$
$660$		0			0
$661$	871.348	−	317.145i	1.31823	−	0.479795i	0.415337	−	0.909668i	$-0.363664\pi$
$661$	871.348	−	317.145i	1.31823	−	0.479795i	0.902890	+	0.429872i	$0.141441\pi$
$662$	468.616	+	298.441i	0.707880	+	0.450817i
$663$		0			0
$664$	317.232	+	497.451i	0.477758	+	0.749173i
$665$	−258.368	+	447.507i	−0.388524	+	0.672943i
$666$		0			0
$667$	599.571	−	346.162i	0.898907	−	0.518984i
$668$	78.4248	−	36.5993i	0.117402	−	0.0547893i
$669$		0			0
$670$	585.630	−	304.973i	0.874074	−	0.455184i
$671$	−689.152	+	821.299i	−1.02705	+	1.22399i
$672$		0			0
$673$	−435.450	−	158.491i	−0.647029	−	0.235499i	−0.00240244	−	0.999997i	$-0.500765\pi$
$673$	−435.450	−	158.491i	−0.647029	−	0.235499i	−0.644626	+	0.764498i	$0.722987\pi$
$674$	885.811	−	679.921i	1.31426	−	1.00879i
$675$		0			0
$676$	−105.278	+	393.382i	−0.155736	+	0.581926i
$677$	−1255.40	−	456.930i	−1.85436	−	0.674933i	−0.982806	−	0.184642i	$-0.940887\pi$
$677$	−1255.40	−	456.930i	−1.85436	−	0.674933i	−0.871559	−	0.490291i	$-0.836890\pi$
$678$		0			0
$679$	467.946	−	557.676i	0.689169	−	0.821320i
$680$	901.349	−	200.258i	1.32551	−	0.294497i
$681$		0			0
$682$	−146.553	+	661.537i	−0.214888	+	0.969996i
$683$	608.347	−	351.229i	0.890698	−	0.514245i	0.0165271	−	0.999863i	$-0.494739\pi$
$683$	608.347	−	351.229i	0.890698	−	0.514245i	0.874171	+	0.485619i	$0.161406\pi$
$684$		0			0
$685$	−341.462	+	591.430i	−0.498485	+	0.863402i
$686$	32.8730	−	35.8855i	0.0479198	−	0.0523113i
$687$		0			0
$688$	71.2609	−	405.589i	0.103577	−	0.589520i
$689$	−359.757	+	130.941i	−0.522143	+	0.190045i
$690$		0			0
$691$	−57.8084	+	10.1932i	−0.0836590	+	0.0147513i	−0.215321	−	0.976543i	$-0.569080\pi$
$691$	−57.8084	+	10.1932i	−0.0836590	+	0.0147513i	0.131662	+	0.991295i	$0.457969\pi$
$692$	331.410	+	331.207i	0.478916	+	0.478623i
$693$		0			0
$694$	−342.906	+	828.207i	−0.494101	+	1.19338i
$695$	−492.502	−	586.941i	−0.708636	−	0.844520i
$696$		0			0
$697$	−167.240	+	948.463i	−0.239942	+	1.36078i
$698$	1019.49	+	44.3559i	1.46059	+	0.0635472i
$699$		0			0
$700$	−199.377	−	139.515i	−0.284825	−	0.199307i
$701$	50.6411			0.0722413			0.0361206	−	0.999347i	$-0.488500\pi$
$701$	50.6411			0.0722413			0.0361206	+	0.999347i	$0.488500\pi$
$702$		0			0
$703$		−	478.709i		−	0.680951i
$704$	456.578	+	976.797i	0.648548	+	1.38750i
$705$		0			0
$706$	414.277	+	18.0243i	0.586795	+	0.0255302i
$707$	520.099	+	91.7074i	0.735641	+	0.129713i
$708$		0			0
$709$	−541.957	+	454.756i	−0.764397	+	0.641405i	−0.939267	−	0.343186i	$-0.888494\pi$
$709$	−541.957	+	454.756i	−0.764397	+	0.641405i	0.174870	+	0.984591i	$0.444049\pi$
$710$	67.1459	−	162.175i	0.0945718	−	0.228415i
$711$		0			0
$712$	596.618	+	78.2681i	0.837947	+	0.109927i
$713$	−77.9982	−	442.350i	−0.109394	−	0.620406i
$714$		0			0
$715$	205.503	+	564.615i	0.287417	+	0.789672i
$716$	80.0581	−	7.02882i	0.111813	−	0.00981679i
$717$		0			0
$718$	−82.4576	+	90.0143i	−0.114843	+	0.125368i
$719$	1042.00	+	601.598i	1.44923	+	0.836715i	0.998436	−	0.0559107i	$-0.0178062\pi$
$719$	1042.00	+	601.598i	1.44923	+	0.836715i	0.450798	+	0.892626i	$0.351140\pi$
$720$		0			0
$721$	−218.147	−	377.841i	−0.302561	−	0.524051i
$722$	−95.4024	+	430.644i	−0.132136	+	0.596459i
$723$		0			0
$724$	700.669	+	326.467i	0.967775	+	0.450921i
$725$	144.136	+	120.945i	0.198809	+	0.166821i
$726$		0			0
$727$	−74.9737	+	205.989i	−0.103128	+	0.283341i	−0.980516	−	0.196441i	$-0.937062\pi$
$727$	−74.9737	+	205.989i	−0.103128	+	0.283341i	0.877388	+	0.479781i	$0.159284\pi$
$728$	−607.036	+	251.769i	−0.833841	+	0.345836i
$729$		0			0
$730$	−693.919	+	532.631i	−0.950574	+	0.729632i
$731$	−233.516	+	641.581i	−0.319448	+	0.877676i
$732$		0			0
$733$	18.6768	+	15.6717i	0.0254799	+	0.0213802i	0.655439	−	0.755248i	$-0.272484\pi$
$733$	18.6768	+	15.6717i	0.0254799	+	0.0213802i	−0.629959	+	0.776629i	$0.716928\pi$
$734$	465.433	−	242.379i	0.634104	−	0.330217i
$735$		0			0
$736$	−527.357	−	482.494i	−0.716518	−	0.655562i
$737$	−639.196	−	1107.12i	−0.867295	−	1.50220i
$738$		0			0
$739$	223.668	+	129.135i	0.302664	+	0.174743i	0.643639	−	0.765329i	$-0.277424\pi$
$739$	223.668	+	129.135i	0.302664	+	0.174743i	−0.340975	+	0.940072i	$0.610757\pi$
$740$	−700.298	−	61.0526i	−0.946349	−	0.0825035i
$741$		0			0
$742$	789.565	+	502.839i	1.06410	+	0.677680i
$743$	−118.080	−	324.422i	−0.158923	−	0.436638i	0.834518	−	0.550980i	$-0.185746\pi$
$743$	−118.080	−	324.422i	−0.158923	−	0.436638i	−0.993441	+	0.114342i	$0.963524\pi$
$744$		0			0
$745$	−74.4041	−	421.967i	−0.0998713	−	0.566398i
$746$	144.742	+	1098.13i	0.194024	+	1.47202i
$747$		0			0
$748$	−463.215	−	1726.63i	−0.619271	−	2.30833i
$749$	541.721	−	454.558i	0.723259	−	0.606886i
$750$		0			0
$751$	−461.870	−	81.4402i	−0.615007	−	0.108442i	−0.142538	−	0.989789i	$-0.545526\pi$
$751$	−461.870	−	81.4402i	−0.615007	−	0.108442i	−0.472470	+	0.881347i	$0.656637\pi$
$752$	303.990	−	110.854i	0.404242	−	0.147412i
$753$		0			0
$754$	484.598	−	152.875i	0.642703	−	0.202752i
$755$			3.39966i			0.00450285i
$756$		0			0
$757$	−653.653			−0.863479			−0.431739	−	0.901998i	$-0.642100\pi$
$757$	−653.653			−0.863479			−0.431739	+	0.901998i	$0.642100\pi$
$758$	37.2281	+	118.010i	0.0491136	+	0.155685i
$759$		0			0
$760$	−393.472	−	123.863i	−0.517726	−	0.162978i
$761$	−114.654	+	650.234i	−0.150662	+	0.854446i	0.811983	+	0.583681i	$0.198388\pi$
$761$	−114.654	+	650.234i	−0.150662	+	0.854446i	−0.962645	+	0.270766i	$0.912723\pi$
$762$		0			0
$763$	575.386	+	685.719i	0.754110	+	0.898714i
$764$	265.522	+	989.732i	0.347542	+	1.29546i
$765$		0			0
$766$	717.316	−	94.5479i	0.936443	−	0.123431i
$767$	−298.607	+	52.6525i	−0.389318	+	0.0686473i
$768$		0			0
$769$	−1263.92	+	460.030i	−1.64359	+	0.598219i	−0.987662	−	0.156602i	$-0.949946\pi$
$769$	−1263.92	+	460.030i	−1.64359	+	0.598219i	−0.655931	+	0.754821i	$0.727724\pi$
$770$	789.174	−	1239.17i	1.02490	−	1.60932i
$771$		0			0
$772$	−1129.39	−	98.4613i	−1.46294	−	0.127541i
$773$	116.766	−	202.245i	0.151056	−	0.261637i	−0.780560	−	0.625081i	$-0.785066\pi$
$773$	116.766	−	202.245i	0.151056	−	0.261637i	0.931616	+	0.363444i	$0.118399\pi$
$774$		0			0
$775$	105.720	−	61.0372i	0.136412	−	0.0787577i
$776$	515.612	+	268.110i	0.664449	+	0.345503i
$777$		0			0
$778$	276.460	+	530.876i	0.355346	+	0.682360i
$779$	276.574	−	329.609i	0.355038	−	0.423117i
$780$		0			0
$781$	−319.346	−	116.233i	−0.408894	−	0.148825i
$782$	721.574	+	940.077i	0.922729	+	1.20214i
$783$		0			0
$784$	712.860	+	410.989i	0.909260	+	0.524221i
$785$	727.346	+	264.732i	0.926556	+	0.337239i
$786$		0			0
$787$	−393.189	+	468.584i	−0.499604	+	0.595405i	−0.955633	−	0.294560i	$-0.904827\pi$
$787$	−393.189	+	468.584i	−0.499604	+	0.595405i	0.456029	+	0.889965i	$0.349271\pi$
$788$	−1029.87	−	479.855i	−1.30695	−	0.608953i
$789$		0			0
$790$	739.908	+	163.915i	0.936593	+	0.207488i
$791$	−685.248	+	395.628i	−0.866306	+	0.500162i
$792$		0			0
$793$	260.824	−	451.760i	0.328908	−	0.569685i
$794$	581.294	+	532.494i	0.732108	+	0.670648i
$795$		0			0
$796$	−545.931	+	47.9308i	−0.685843	+	0.0602146i
$797$	−494.327	+	179.920i	−0.620234	+	0.225747i	−0.632975	−	0.774172i	$-0.718167\pi$
$797$	−494.327	+	179.920i	−0.620234	+	0.225747i	0.0127409	+	0.999919i	$0.495944\pi$
$798$		0			0
$799$	−528.321	+	93.1573i	−0.661228	+	0.116592i
$800$	74.2025	−	179.528i	0.0927531	−	0.224411i
$801$		0			0
$802$	80.9153	+	33.5017i	0.100892	+	0.0417727i
$803$	1088.67	+	1297.43i	1.35575	+	1.61572i
$804$		0			0
$805$	−169.117	+	959.109i	−0.210083	+	1.19144i
$806$	14.3300	−	329.365i	0.0177791	−	0.408641i
$807$		0			0
$808$	18.5828	+	421.186i	0.0229985	+	0.521270i
$809$	−544.887			−0.673531			−0.336766	−	0.941588i	$-0.609333\pi$
$809$	−544.887			−0.673531			−0.336766	+	0.941588i	$0.609333\pi$
$810$		0			0
$811$			770.624i			0.950214i	0.879928	+	0.475107i	$0.157591\pi$
$811$			770.624i			0.950214i	−0.879928	+	0.475107i	$0.842409\pi$
$812$	−1017.97	−	712.326i	−1.25366	−	0.877249i
$813$		0			0
$814$	−59.1590	+	1359.73i	−0.0726769	+	1.67043i
$815$	1151.71	+	203.078i	1.41315	+	0.249176i
$816$		0			0
$817$	233.666	−	196.069i	0.286005	−	0.239986i
$818$	−767.195	−	317.645i	−0.937891	−	0.388319i
$819$		0			0
$820$	−446.908	−	446.635i	−0.545009	−	0.544677i
$821$	−11.4448	−	64.9068i	−0.0139401	−	0.0790582i	0.977044	−	0.213037i	$-0.0683356\pi$
$821$	−11.4448	−	64.9068i	−0.0139401	−	0.0790582i	−0.990984	+	0.133979i	$0.957224\pi$
$822$		0			0
$823$	−408.452	−	1122.21i	−0.496297	−	1.36356i	−0.894828	−	0.446410i	$-0.852702\pi$
$823$	−408.452	−	1122.21i	−0.496297	−	1.36356i	0.398531	−	0.917155i	$-0.369520\pi$
$824$	256.678	−	235.419i	0.311503	−	0.285702i
$825$		0			0
$826$	546.681	+	500.787i	0.661841	+	0.606280i
$827$	956.879	+	552.455i	1.15705	+	0.668022i	0.950595	−	0.310434i	$-0.100474\pi$
$827$	956.879	+	552.455i	1.15705	+	0.668022i	0.206454	+	0.978456i	$0.433808\pi$
$828$		0			0
$829$	281.510	+	487.590i	0.339578	+	0.588167i	0.984353	−	0.176205i	$-0.0563823\pi$
$829$	281.510	+	487.590i	0.339578	+	0.588167i	−0.644775	+	0.764372i	$0.723049\pi$
$830$	626.545	+	138.801i	0.754874	+	0.167231i
$831$		0			0
$832$	−301.303	−	429.467i	−0.362143	−	0.516186i
$833$	−1045.09	−	876.931i	−1.25460	−	1.05274i
$834$		0			0
$835$	32.1959	−	88.4574i	0.0385579	−	0.105937i
$836$	−206.475	+	771.519i	−0.246980	+	0.922869i
$837$		0			0
$838$	77.3515	+	100.775i	0.0923049	+	0.120256i
$839$	341.688	−	938.779i	0.407256	−	1.11893i	−0.551371	−	0.834260i	$-0.685895\pi$
$839$	341.688	−	938.779i	0.407256	−	1.11893i	0.958627	−	0.284666i	$-0.0918828\pi$
$840$		0			0
$841$	91.6803	+	76.9289i	0.109013	+	0.0914731i
$842$	578.598	+	1111.06i	0.687171	+	1.31955i
$843$		0			0
$844$	669.366	−	312.379i	0.793087	−	0.370118i
$845$	221.469	+	383.596i	0.262094	+	0.453960i
$846$		0			0
$847$	−1413.22	−	815.925i	−1.66850	−	0.963312i
$848$	−255.153	+	702.362i	−0.300888	+	0.828257i
$849$		0			0
$850$	−173.010	+	271.662i	−0.203541	+	0.319603i
$851$	−308.582	−	847.823i	−0.362611	−	0.996266i
$852$		0			0
$853$	23.3839	+	132.617i	0.0274137	+	0.155471i	0.995442	−	0.0953710i	$-0.0304037\pi$
$853$	23.3839	+	132.617i	0.0274137	+	0.155471i	−0.968028	+	0.250842i	$0.919293\pi$
$854$	−1264.53	+	166.676i	−1.48072	+	0.195170i
$855$		0			0
$856$	448.026	+	343.456i	0.523395	+	0.401234i
$857$	−219.310	+	184.023i	−0.255904	+	0.214729i	−0.761710	−	0.647918i	$-0.775640\pi$
$857$	−219.310	+	184.023i	−0.255904	+	0.214729i	0.505806	+	0.862647i	$0.331195\pi$
$858$		0			0
$859$	−1032.05	−	181.978i	−1.20145	−	0.211848i	−0.463126	−	0.886292i	$-0.653272\pi$
$859$	−1032.05	−	181.978i	−1.20145	−	0.211848i	−0.738326	+	0.674444i	$0.764383\pi$
$860$	−257.026	−	366.833i	−0.298868	−	0.426550i
$861$		0			0
$862$	76.4452	+	242.324i	0.0886836	+	0.281119i
$863$		−	1607.61i		−	1.86282i	−0.363973	−	0.931409i	$-0.618580\pi$
$863$		−	1607.61i		−	1.86282i	0.363973	−	0.931409i	$-0.381420\pi$
$864$		0			0
$865$	509.631			0.589169
$866$	1120.64	−	353.525i	1.29404	−	0.408228i
$867$		0			0
$868$	−660.166	+	462.554i	−0.760560	+	0.532896i
$869$	254.793	−	1445.00i	0.293203	−	1.66283i
$870$		0			0
$871$	399.817	+	476.484i	0.459032	+	0.547054i
$872$	−434.752	+	567.118i	−0.498569	+	0.650365i
$873$		0			0
$874$	−69.1870	−	524.908i	−0.0791613	−	0.600581i
$875$	−1334.13	+	235.243i	−1.52472	+	0.268849i
$876$		0			0
$877$	1014.63	−	369.294i	1.15693	−	0.421087i	0.308929	−	0.951085i	$-0.400030\pi$
$877$	1014.63	−	369.294i	1.15693	−	0.421087i	0.847999	+	0.529998i	$0.177807\pi$
$878$	727.464	+	463.289i	0.828546	+	0.527664i
$879$		0			0
$880$	1102.31	+	400.447i	1.25263	+	0.455053i
$881$	−152.141	+	263.516i	−0.172691	+	0.299110i	−0.939360	−	0.342933i	$-0.888580\pi$
$881$	−152.141	+	263.516i	−0.172691	+	0.299110i	0.766668	+	0.642043i	$0.221913\pi$
$882$		0			0
$883$	960.150	−	554.343i	1.08737	−	0.627795i	0.154497	−	0.987993i	$-0.450624\pi$
$883$	960.150	−	554.343i	1.08737	−	0.627795i	0.932876	+	0.360198i	$0.117291\pi$
$884$	367.836	+	788.197i	0.416104	+	0.891626i
$885$		0			0
$886$	−1395.02	+	726.473i	−1.57452	+	0.819947i
$887$	215.519	−	256.845i	0.242975	−	0.289566i	−0.630750	−	0.775986i	$-0.717253\pi$
$887$	215.519	−	256.845i	0.242975	−	0.289566i	0.873725	+	0.486419i	$0.161697\pi$
$888$		0			0
$889$	893.205	+	325.100i	1.00473	+	0.365692i
$890$	519.190	−	398.514i	0.583359	−	0.447769i
$891$		0			0
$892$	−843.747	−	225.805i	−0.945905	−	0.253145i
$893$	225.221	+	81.9736i	0.252207	+	0.0917958i
$894$		0			0
$895$	56.1887	−	66.9631i	0.0627807	−	0.0748191i
$896$	−384.418	+	1223.78i	−0.429038	+	1.36583i
$897$		0			0
$898$	209.824	−	947.138i	0.233657	−	1.05472i
$899$	539.776	−	311.640i	0.600419	−	0.346652i
$900$		0			0
$901$	619.478	−	1072.97i	0.687545	−	1.19086i
$902$	−826.317	+	902.044i	−0.916095	+	1.00005i
$903$		0			0
$904$	−426.953	−	465.509i	−0.472293	−	0.514944i
$905$	790.078	−	287.565i	0.873014	−	0.317751i
$906$		0			0
$907$	187.688	−	33.0945i	0.206933	−	0.0364878i	−0.0692208	−	0.997601i	$-0.522051\pi$
$907$	187.688	−	33.0945i	0.206933	−	0.0364878i	0.276154	+	0.961114i	$0.410940\pi$
$908$	857.276	−	857.800i	0.944137	−	0.944714i
$909$		0			0
$910$	−273.445	+	660.440i	−0.300489	+	0.725758i
$911$	358.732	+	427.520i	0.393778	+	0.469287i	0.926112	−	0.377248i	$-0.123129\pi$
$911$	358.732	+	427.520i	0.393778	+	0.469287i	−0.532334	+	0.846534i	$0.678685\pi$
$912$		0			0
$913$	215.756	−	1223.61i	0.236315	−	1.34021i
$914$	−1729.77	−	75.2588i	−1.89253	−	0.0823400i
$915$		0			0
$916$	−710.685	+	1015.62i	−0.775857	+	1.10876i
$917$	−113.268			−0.123521
$918$		0			0
$919$			1133.08i			1.23295i	0.787376	+	0.616473i	$0.211439\pi$
$919$			1133.08i			1.23295i	−0.787376	+	0.616473i	$0.788561\pi$
$920$	−776.706	+	34.2683i	−0.844246	+	0.0372482i
$921$		0			0
$922$	1386.61	+	60.3286i	1.50392	+	0.0654323i
$923$	162.839	+	28.7128i	0.176423	+	0.0311082i
$924$		0			0
$925$	187.838	−	157.615i	0.203068	−	0.170394i
$926$	521.944	−	1260.63i	0.563654	−	1.36137i
$927$		0			0
$928$	378.859	−	916.626i	0.408253	−	0.987743i
$929$	2.83827	+	16.0966i	0.00305519	+	0.0173269i	0.986297	−	0.164978i	$-0.0527553\pi$
$929$	2.83827	+	16.0966i	0.00305519	+	0.0173269i	−0.983242	+	0.182305i	$0.941644\pi$
$930$		0			0
$931$	208.461	+	572.742i	0.223911	+	0.615190i
$932$	−15.2241	−	173.402i	−0.0163348	−	0.186053i
$933$		0			0
$934$	605.606	−	661.106i	0.648400	−	0.707822i
$935$	−1683.96	−	972.232i	−1.80102	−	1.03982i
$936$		0			0
$937$	−208.069	−	360.386i	−0.222059	−	0.384617i	0.733374	−	0.679825i	$-0.237944\pi$
$937$	−208.069	−	360.386i	−0.222059	−	0.384617i	−0.955433	+	0.295208i	$0.904611\pi$
$938$	328.946	−	1484.85i	0.350689	−	1.58300i
$939$		0			0
$940$	148.642	−	319.018i	0.158130	−	0.339381i
$941$	248.379	+	208.415i	0.263952	+	0.221482i	0.765153	−	0.643849i	$-0.222664\pi$
$941$	248.379	+	208.415i	0.263952	+	0.221482i	−0.501200	+	0.865331i	$0.667108\pi$
$942$		0			0
$943$	277.360	−	762.040i	0.294125	−	0.808102i
$944$	−295.607	+	512.729i	−0.313143	+	0.543145i
$945$		0			0
$946$	−687.937	+	528.040i	−0.727206	+	0.558181i
$947$	505.822	−	1389.74i	0.534131	−	1.46751i	−0.319980	−	0.947424i	$-0.603676\pi$
$947$	505.822	−	1389.74i	0.534131	−	1.46751i	0.854112	−	0.520090i	$-0.174101\pi$
$948$		0			0
$949$	−631.266	−	529.695i	−0.665191	−	0.558161i
$950$	127.623	−	66.4609i	0.134340	−	0.0699589i
$951$		0			0
$952$	981.155	−	1886.89i	1.03063	−	1.98203i
$953$	711.138	+	1231.73i	0.746210	+	1.29247i	0.949627	+	0.313382i	$0.101462\pi$
$953$	711.138	+	1231.73i	0.746210	+	1.29247i	−0.203417	+	0.979092i	$0.565205\pi$
$954$		0			0
$955$	965.270	+	557.299i	1.01075	+	0.583559i
$956$	115.747	−	1327.66i	0.121074	−	1.38877i
$957$		0			0
$958$	−971.193	−	618.510i	−1.01377	−	0.645626i
$959$	538.002	+	1478.15i	0.561003	+	1.54134i
$960$		0			0
$961$	96.6563	+	548.165i	0.100579	+	0.570411i
$962$	−86.5354	−	656.527i	−0.0899537	−	0.682460i
$963$		0			0
$964$	1339.96	−	359.480i	1.39000	−	0.372904i
$965$	−944.607	+	792.620i	−0.978868	+	0.821368i
$966$		0			0
$967$	1199.62	+	211.526i	1.24056	+	0.218745i	0.755156	−	0.655545i	$-0.227561\pi$
$967$	1199.62	+	211.526i	1.24056	+	0.218745i	0.485405	+	0.874289i	$0.338672\pi$
$968$	391.158	−	1242.58i	0.404089	−	1.28366i
$969$		0			0
$970$	602.834	−	190.174i	0.621478	−	0.196056i
$971$			203.866i			0.209955i	0.994475	+	0.104977i	$0.0334770\pi$
$971$			203.866i			0.209955i	−0.994475	+	0.104977i	$0.966523\pi$
$972$		0			0
$973$	−1764.82			−1.81379
$974$	−66.1730	−	209.762i	−0.0679394	−	0.215362i
$975$		0			0
$976$	−348.829	−	956.582i	−0.357407	−	0.980104i
$977$	65.5958	−	372.012i	0.0671400	−	0.380770i	−0.932660	−	0.360757i	$-0.882518\pi$
$977$	65.5958	−	372.012i	0.0671400	−	0.380770i	0.999800	−	0.0200126i	$-0.00637062\pi$
$978$		0			0
$979$	−814.542	−	970.733i	−0.832014	−	0.991556i
$980$	864.445	−	231.910i	0.882087	−	0.236643i
$981$		0			0
$982$	−770.957	+	101.618i	−0.785089	+	0.103481i
$983$	215.781	−	38.0481i	0.219513	−	0.0387061i	−0.0628098	−	0.998026i	$-0.520006\pi$
$983$	215.781	−	38.0481i	0.219513	−	0.0387061i	0.282323	+	0.959319i	$0.408895\pi$
$984$		0			0
$985$	−1161.29	+	422.675i	−1.17897	+	0.429112i
$986$	−883.342	+	1387.04i	−0.895884	+	1.40673i
$987$		0			0
$988$	33.7500	−	387.126i	0.0341599	−	0.391828i
$989$	287.448	−	497.874i	0.290645	−	0.503412i
$990$		0			0
$991$	−1357.24	+	783.603i	−1.36957	+	0.790720i	−0.990873	−	0.134802i	$-0.956960\pi$
$991$	−1357.24	+	783.603i	−1.36957	+	0.790720i	−0.378694	+	0.925522i	$0.623627\pi$
$992$	−474.765	−	434.375i	−0.478594	−	0.437878i
$993$		0			0
$994$	−186.738	−	358.586i	−0.187865	−	0.360751i
$995$	−383.161	+	456.633i	−0.385086	+	0.458928i
$996$		0			0
$997$	136.762	+	49.7773i	0.137174	+	0.0499271i	0.409695	−	0.912223i	$-0.365635\pi$
$997$	136.762	+	49.7773i	0.137174	+	0.0499271i	−0.272521	+	0.962150i	$0.587857\pi$
$998$	−128.631	−	167.582i	−0.128889	−	0.167918i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.j.a.307.31		204
3.2	odd	2		108.3.j.a.31.4	yes	204
4.3	odd	2	inner	324.3.j.a.307.23		204
12.11	even	2		108.3.j.a.31.12	yes	204
27.7	even	9	inner	324.3.j.a.19.23		204
27.20	odd	18		108.3.j.a.7.12	yes	204
108.7	odd	18	inner	324.3.j.a.19.31		204
108.47	even	18		108.3.j.a.7.4	✓	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.7.4	✓	204	108.47	even	18
108.3.j.a.7.12	yes	204	27.20	odd	18
108.3.j.a.31.4	yes	204	3.2	odd	2
108.3.j.a.31.12	yes	204	12.11	even	2
324.3.j.a.19.23		204	27.7	even	9	inner
324.3.j.a.19.31		204	108.7	odd	18	inner
324.3.j.a.307.23		204	4.3	odd	2	inner
324.3.j.a.307.31		204	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.j (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.90734 - 0.601703i) q^{2} +(3.27591 - 2.29531i) q^{4} +(0.755508 - 4.28470i) q^{5} +(-6.44162 - 7.67682i) q^{7} +(4.86718 - 6.34906i) q^{8} +(-1.13710 - 8.62697i) q^{10} +(-16.5915 + 2.92553i) q^{11} +(7.70282 - 2.80360i) q^{13} +(-16.9055 - 10.7664i) q^{14} +(5.46314 - 15.0384i) q^{16} +(-13.2638 + 22.9735i) q^{17} +(10.2637 - 5.92574i) q^{19} +(-7.35972 - 15.7704i) q^{20} +(-29.8854 + 15.5631i) q^{22} +(14.3578 - 17.1110i) q^{23} +(5.70448 + 2.07626i) q^{25} +(13.0050 - 9.98223i) q^{26} +(-38.7228 - 10.3631i) q^{28} +(29.1256 + 10.6009i) q^{29} +(12.9259 - 15.4045i) q^{31} +(1.37140 - 31.9706i) q^{32} +(-11.4753 + 51.7992i) q^{34} +(-37.7596 + 21.8005i) q^{35} +(20.1962 - 34.9808i) q^{37} +(16.0108 - 17.4781i) q^{38} +(-23.5266 - 25.6512i) q^{40} +(34.1160 - 12.4172i) q^{41} +(25.3466 - 4.46929i) q^{43} +(-47.6372 + 47.6664i) q^{44} +(17.0895 - 41.2756i) q^{46} +(12.9992 + 15.4919i) q^{47} +(-8.93040 + 50.6468i) q^{49} +(12.1297 + 0.527738i) q^{50} +(18.7986 - 26.8647i) q^{52} -46.7045 q^{53} +73.2998i q^{55} +(-80.0931 + 3.53372i) q^{56} +(61.9311 + 2.69449i) q^{58} +(-36.4280 - 6.42325i) q^{59} +(48.7491 - 40.9054i) q^{61} +(15.3852 - 37.1592i) q^{62} +(-16.6211 - 61.8040i) q^{64} +(-6.19303 - 35.1224i) q^{65} +(25.9527 + 71.3043i) q^{67} +(9.28040 + 105.704i) q^{68} +(-58.9030 + 64.3010i) q^{70} +(17.4692 + 10.0858i) q^{71} +(-50.2648 - 87.0613i) q^{73} +(17.4729 - 78.8724i) q^{74} +(20.0215 - 42.9705i) q^{76} +(129.335 + 108.525i) q^{77} +(-29.7876 + 81.8406i) q^{79} +(-60.3076 - 34.7695i) q^{80} +(57.5993 - 44.2115i) q^{82} +(-25.2237 + 69.3017i) q^{83} +(88.4137 + 74.1879i) q^{85} +(45.6555 - 23.7756i) q^{86} +(-62.1795 + 119.580i) q^{88} +(37.6081 + 65.1392i) q^{89} +(-71.1414 - 41.0735i) q^{91} +(7.75992 - 89.0095i) q^{92} +(34.1155 + 21.7266i) q^{94} +(-17.6357 - 48.4537i) q^{95} +(12.6145 + 71.5405i) q^{97} +(13.4410 + 101.974i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37}+ \cdots - 510 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

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