LMFDB - Embedded newform 135.3.h.a.44.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [135,3,Mod(44,135)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(135, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("135.44"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	135.h (of order $6$, degree $2$, 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:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{18} - 19 x^{16} + 66 x^{14} + 109 x^{12} - 813 x^{10} + 981 x^{8} + 5346 x^{6} + \cdots + 59049 $ x^20 - 3x^18 - 19x^16 + 66x^14 + 109x^12 - 813x^10 + 981x^8 + 5346x^6 - 13851x^4 - 19683*x^2 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{12} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			44.5
Root			$-0.315300 + 1.70311i$ of defining polynomial
Character	$\chi$	$=$	135.44
Dual form			135.3.h.a.89.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.264396 - 0.457947i) q^{2} +(1.86019 - 3.22194i) q^{4} +(4.68146 - 1.75610i) q^{5} +(-2.39593 + 1.38329i) q^{7} -4.08247 q^{8} +(-2.04196 - 1.67955i) q^{10} +(7.99186 - 4.61410i) q^{11} +(-11.7678 - 6.79417i) q^{13} +(1.26695 + 0.731472i) q^{14} +(-6.36137 - 11.0182i) q^{16} +12.2161 q^{17} +20.2664 q^{19} +(3.05035 - 18.3501i) q^{20} +(-4.22603 - 2.43990i) q^{22} +(1.18564 - 2.05358i) q^{23} +(18.8322 - 16.4423i) q^{25} +7.18539i q^{26} +10.2927i q^{28} +(-30.2349 + 17.4561i) q^{29} +(-14.7233 + 25.5015i) q^{31} +(-11.5288 + 19.9684i) q^{32} +(-3.22989 - 5.59433i) q^{34} +(-8.78726 + 10.6833i) q^{35} +64.3630i q^{37} +(-5.35836 - 9.28095i) q^{38} +(-19.1119 + 7.16923i) q^{40} +(-34.5195 - 19.9299i) q^{41} +(58.5402 - 33.7982i) q^{43} -34.3324i q^{44} -1.25391 q^{46} +(46.6901 + 80.8696i) q^{47} +(-20.6730 + 35.8067i) q^{49} +(-12.5088 - 4.27688i) q^{50} +(-43.7808 + 25.2769i) q^{52} -9.82656 q^{53} +(29.3108 - 35.6353i) q^{55} +(9.78131 - 5.64724i) q^{56} +(15.9880 + 9.23066i) q^{58} +(50.6655 + 29.2517i) q^{59} +(7.75283 + 13.4283i) q^{61} +15.5711 q^{62} -38.6984 q^{64} +(-67.0220 - 11.1411i) q^{65} +(-13.4796 - 7.78243i) q^{67} +(22.7243 - 39.3596i) q^{68} +(7.21571 + 1.19947i) q^{70} +53.1970i q^{71} -23.6547i q^{73} +(29.4748 - 17.0173i) q^{74} +(37.6994 - 65.2973i) q^{76} +(-12.7653 + 22.1101i) q^{77} +(-17.2692 - 29.9112i) q^{79} +(-49.1297 - 40.4102i) q^{80} +21.0775i q^{82} +(-37.6730 - 65.2516i) q^{83} +(57.1893 - 21.4527i) q^{85} +(-30.9555 - 17.8722i) q^{86} +(-32.6265 + 18.8369i) q^{88} -29.1344i q^{89} +37.5932 q^{91} +(-4.41101 - 7.64010i) q^{92} +(24.6893 - 42.7631i) q^{94} +(94.8766 - 35.5899i) q^{95} +(-54.0151 + 31.1857i) q^{97} +21.8634 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 18 q^{4} + 12 q^{5} + 4 q^{10} + 24 q^{11} - 30 q^{14} - 26 q^{16} - 8 q^{19} - 144 q^{20} + 2 q^{25} + 114 q^{29} + 28 q^{31} - 4 q^{34} - 34 q^{40} - 102 q^{41} + 116 q^{46} - 40 q^{49} + 408 q^{50}+ \cdots + 762 q^{95}+O(q^{100}) $ 20 * q - 18 * q^4 + 12 * q^5 + 4 * q^10 + 24 * q^11 - 30 * q^14 - 26 * q^16 - 8 * q^19 - 144 * q^20 + 2 * q^25 + 114 * q^29 + 28 * q^31 - 4 * q^34 - 34 * q^40 - 102 * q^41 + 116 * q^46 - 40 * q^49 + 408 * q^50 + 36 * q^55 + 618 * q^56 - 120 * q^59 - 50 * q^61 + 140 * q^64 - 492 * q^65 - 54 * q^70 - 504 * q^74 - 96 * q^76 - 128 * q^79 - 74 * q^85 - 1488 * q^86 - 288 * q^91 + 218 * q^94 + 762 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.264396	−	0.457947i	−0.132198	−	0.228973i	0.792326	−	0.610098i	$-0.208870\pi$
$2$	−0.264396	−	0.457947i	−0.132198	−	0.228973i	−0.924524	+	0.381125i	$0.875537\pi$
$3$		0			0
$3$		0			0
$4$	1.86019	−	3.22194i	0.465047	−	0.805486i
$5$	4.68146	−	1.75610i	0.936293	−	0.351221i
$5$	4.68146	−	1.75610i	0.936293	−	0.351221i
$6$		0			0
$7$	−2.39593	+	1.38329i	−0.342276	+	0.197613i	−0.661278	−	0.750141i	$-0.729986\pi$
$7$	−2.39593	+	1.38329i	−0.342276	+	0.197613i	0.319002	+	0.947754i	$0.396652\pi$
$8$	−4.08247			−0.510309
$9$		0			0
$10$	−2.04196	−	1.67955i	−0.204196	−	0.167955i
$11$	7.99186	−	4.61410i	0.726533	−	0.419464i	−0.0906197	−	0.995886i	$-0.528885\pi$
$11$	7.99186	−	4.61410i	0.726533	−	0.419464i	0.817152	+	0.576422i	$0.195551\pi$
$12$		0			0
$13$	−11.7678	−	6.79417i	−0.905218	−	0.522628i	−0.0263288	−	0.999653i	$-0.508382\pi$
$13$	−11.7678	−	6.79417i	−0.905218	−	0.522628i	−0.878890	+	0.477025i	$0.841715\pi$
$14$	1.26695	+	0.731472i	0.0904962	+	0.0522480i
$15$		0			0
$16$	−6.36137	−	11.0182i	−0.397586	−	0.688639i
$17$	12.2161			0.718595			0.359297	−	0.933223i	$-0.383016\pi$
$17$	12.2161			0.718595			0.359297	+	0.933223i	$0.383016\pi$
$18$		0			0
$19$	20.2664			1.06665			0.533327	−	0.845909i	$-0.320941\pi$
$19$	20.2664			1.06665			0.533327	+	0.845909i	$0.320941\pi$
$20$	3.05035	−	18.3501i	0.152517	−	0.917505i
$21$		0			0
$22$	−4.22603	−	2.43990i	−0.192092	−	0.110904i
$23$	1.18564	−	2.05358i	0.0515494	−	0.0892861i	−0.839099	−	0.543978i	$-0.816917\pi$
$23$	1.18564	−	2.05358i	0.0515494	−	0.0892861i	0.890649	+	0.454692i	$0.150251\pi$
$24$		0			0
$25$	18.8322	−	16.4423i	0.753288	−	0.657690i
$26$			7.18539i			0.276361i
$27$		0			0
$28$			10.2927i			0.367598i
$29$	−30.2349	+	17.4561i	−1.04258	+	0.601936i	−0.920564	−	0.390592i	$-0.872270\pi$
$29$	−30.2349	+	17.4561i	−1.04258	+	0.601936i	−0.122020	+	0.992528i	$0.538937\pi$
$30$		0			0
$31$	−14.7233	+	25.5015i	−0.474945	+	0.822629i	−0.999588	−	0.0286933i	$-0.990865\pi$
$31$	−14.7233	+	25.5015i	−0.474945	+	0.822629i	0.524643	+	0.851322i	$0.324199\pi$
$32$	−11.5288	+	19.9684i	−0.360274	+	0.624013i
$33$		0			0
$34$	−3.22989	−	5.59433i	−0.0949967	−	0.164539i
$35$	−8.78726	+	10.6833i	−0.251065	+	0.305238i
$36$		0			0
$37$			64.3630i			1.73954i	0.493457	+	0.869770i	$0.335733\pi$
$37$			64.3630i			1.73954i	−0.493457	+	0.869770i	$0.664267\pi$
$38$	−5.35836	−	9.28095i	−0.141009	−	0.244235i
$39$		0			0
$40$	−19.1119	+	7.16923i	−0.477798	+	0.179231i
$41$	−34.5195	−	19.9299i	−0.841940	−	0.486094i	0.0159834	−	0.999872i	$-0.494912\pi$
$41$	−34.5195	−	19.9299i	−0.841940	−	0.486094i	−0.857923	+	0.513778i	$0.828245\pi$
$42$		0			0
$43$	58.5402	−	33.7982i	1.36140	−	0.786004i	0.371589	−	0.928397i	$-0.378813\pi$
$43$	58.5402	−	33.7982i	1.36140	−	0.786004i	0.989810	+	0.142393i	$0.0454796\pi$
$44$		−	34.3324i		−	0.780282i
$45$		0			0
$46$	−1.25391			−0.0272588
$47$	46.6901	+	80.8696i	0.993406	+	1.72063i	0.595992	+	0.802991i	$0.296759\pi$
$47$	46.6901	+	80.8696i	0.993406	+	1.72063i	0.397414	+	0.917639i	$0.369908\pi$
$48$		0			0
$49$	−20.6730	+	35.8067i	−0.421898	+	0.730749i
$50$	−12.5088	−	4.27688i	−0.250177	−	0.0855377i
$51$		0			0
$52$	−43.7808	+	25.2769i	−0.841939	+	0.486094i
$53$	−9.82656			−0.185407			−0.0927034	−	0.995694i	$-0.529551\pi$
$53$	−9.82656			−0.185407			−0.0927034	+	0.995694i	$0.529551\pi$
$54$		0			0
$55$	29.3108	−	35.6353i	0.532923	−	0.647914i
$56$	9.78131	−	5.64724i	0.174666	−	0.100844i
$57$		0			0
$58$	15.9880	+	9.23066i	0.275655	+	0.159149i
$59$	50.6655	+	29.2517i	0.858737	+	0.495792i	0.863589	−	0.504196i	$-0.168211\pi$
$59$	50.6655	+	29.2517i	0.858737	+	0.495792i	−0.00485217	+	0.999988i	$0.501544\pi$
$60$		0			0
$61$	7.75283	+	13.4283i	0.127096	+	0.220136i	0.922550	−	0.385877i	$-0.126101\pi$
$61$	7.75283	+	13.4283i	0.127096	+	0.220136i	−0.795455	+	0.606013i	$0.792768\pi$
$62$	15.5711			0.251147
$63$		0			0
$64$	−38.6984			−0.604662
$65$	−67.0220	−	11.1411i	−1.03111	−	0.171402i
$66$		0			0
$67$	−13.4796	−	7.78243i	−0.201188	−	0.116156i	0.396022	−	0.918241i	$-0.370390\pi$
$67$	−13.4796	−	7.78243i	−0.201188	−	0.116156i	−0.597209	+	0.802085i	$0.703724\pi$
$68$	22.7243	−	39.3596i	0.334181	−	0.578818i
$69$		0			0
$70$	7.21571	+	1.19947i	0.103082	+	0.0171353i
$71$			53.1970i			0.749254i	0.927176	+	0.374627i	$0.122229\pi$
$71$			53.1970i			0.749254i	−0.927176	+	0.374627i	$0.877771\pi$
$72$		0			0
$73$		−	23.6547i		−	0.324037i	−0.986788	−	0.162019i	$-0.948200\pi$
$73$		−	23.6547i		−	0.324037i	0.986788	−	0.162019i	$-0.0518005\pi$
$74$	29.4748	−	17.0173i	0.398308	−	0.229963i
$75$		0			0
$76$	37.6994	−	65.2973i	0.496045	−	0.859175i
$77$	−12.7653	+	22.1101i	−0.165783	+	0.287145i
$78$		0			0
$79$	−17.2692	−	29.9112i	−0.218598	−	0.378623i	0.735782	−	0.677219i	$-0.236815\pi$
$79$	−17.2692	−	29.9112i	−0.218598	−	0.378623i	−0.954380	+	0.298596i	$0.903482\pi$
$80$	−49.1297	−	40.4102i	−0.614121	−	0.505127i
$81$		0			0
$82$			21.0775i			0.257042i
$83$	−37.6730	−	65.2516i	−0.453892	−	0.786163i	0.544732	−	0.838610i	$-0.316631\pi$
$83$	−37.6730	−	65.2516i	−0.453892	−	0.786163i	−0.998624	+	0.0524468i	$0.983298\pi$
$84$		0			0
$85$	57.1893	−	21.4527i	0.672815	−	0.252385i
$86$	−30.9555	−	17.8722i	−0.359948	−	0.207816i
$87$		0			0
$88$	−32.6265	+	18.8369i	−0.370756	+	0.214056i
$89$		−	29.1344i		−	0.327352i	−0.986514	−	0.163676i	$-0.947665\pi$
$89$		−	29.1344i		−	0.327352i	0.986514	−	0.163676i	$-0.0523352\pi$
$90$		0			0
$91$	37.5932			0.413112
$92$	−4.41101	−	7.64010i	−0.0479458	−	0.0830445i
$93$		0			0
$94$	24.6893	−	42.7631i	0.262652	−	0.454927i
$95$	94.8766	−	35.5899i	0.998701	−	0.374631i
$96$		0			0
$97$	−54.0151	+	31.1857i	−0.556857	+	0.321502i	−0.751883	−	0.659296i	$-0.770854\pi$
$97$	−54.0151	+	31.1857i	−0.556857	+	0.321502i	0.195026	+	0.980798i	$0.437521\pi$
$98$	21.8634			0.223096
$99$		0			0
$100$	−17.9446	−	91.2620i	−0.179446	−	0.912620i
$101$	118.734	−	68.5511i	1.17558	−	0.678723i	0.220595	−	0.975366i	$-0.429200\pi$
$101$	118.734	−	68.5511i	1.17558	−	0.678723i	0.954989	+	0.296642i	$0.0958669\pi$
$102$		0			0
$103$	−94.2266	−	54.4017i	−0.914821	−	0.528172i	−0.0328419	−	0.999461i	$-0.510456\pi$
$103$	−94.2266	−	54.4017i	−0.914821	−	0.528172i	−0.881979	+	0.471288i	$0.843789\pi$
$104$	48.0418	+	27.7370i	0.461941	+	0.266702i
$105$		0			0
$106$	2.59810	+	4.50004i	0.0245104	+	0.0424532i
$107$	64.0002			0.598133			0.299067	−	0.954232i	$-0.403325\pi$
$107$	64.0002			0.598133			0.299067	+	0.954232i	$0.403325\pi$
$108$		0			0
$109$	−14.8135			−0.135904			−0.0679520	−	0.997689i	$-0.521646\pi$
$109$	−14.8135			−0.135904			−0.0679520	+	0.997689i	$0.521646\pi$
$110$	−24.0687	−	4.00095i	−0.218806	−	0.0363723i
$111$		0			0
$112$	30.4828	+	17.5993i	0.272168	+	0.157136i
$113$	−41.4033	+	71.7126i	−0.366401	+	0.634625i	−0.989000	−	0.147916i	$-0.952743\pi$
$113$	−41.4033	+	71.7126i	−0.366401	+	0.634625i	0.622599	+	0.782541i	$0.286077\pi$
$114$		0			0
$115$	1.94421	−	11.6959i	0.0169062	−	0.101703i
$116$			129.887i			1.11972i
$117$		0			0
$118$		−	30.9361i		−	0.262170i
$119$	−29.2690	+	16.8984i	−0.245958	+	0.142004i
$120$		0			0
$121$	−17.9201	+	31.0386i	−0.148100	+	0.256517i
$122$	4.09963	−	7.10077i	0.0336035	−	0.0582030i
$123$		0			0
$124$	54.7763	+	94.8753i	0.441744	+	0.765123i
$125$	59.2880	−	110.045i	0.474304	−	0.880361i
$126$		0			0
$127$		−	36.7291i		−	0.289206i	−0.989490	−	0.144603i	$-0.953810\pi$
$127$		−	36.7291i		−	0.289206i	0.989490	−	0.144603i	$-0.0461904\pi$
$128$	56.3468	+	97.5955i	0.440209	+	0.762465i
$129$		0			0
$130$	12.6183	+	33.6381i	0.0970637	+	0.258755i
$131$	−50.1743	−	28.9682i	−0.383010	−	0.221131i	0.296117	−	0.955152i	$-0.404308\pi$
$131$	−50.1743	−	28.9682i	−0.383010	−	0.221131i	−0.679127	+	0.734021i	$0.737641\pi$
$132$		0			0
$133$	−48.5570	+	28.0344i	−0.365090	+	0.210785i
$134$			8.23056i			0.0614221i
$135$		0			0
$136$	−49.8719			−0.366705
$137$	−28.7895	−	49.8649i	−0.210143	−	0.363978i	0.741616	−	0.670824i	$-0.234059\pi$
$137$	−28.7895	−	49.8649i	−0.210143	−	0.363978i	−0.951759	+	0.306847i	$0.900726\pi$
$138$		0			0
$139$	30.3246	−	52.5237i	0.218162	−	0.377868i	−0.736084	−	0.676890i	$-0.763327\pi$
$139$	30.3246	−	52.5237i	0.218162	−	0.377868i	0.954246	+	0.299022i	$0.0966605\pi$
$140$	18.0751	+	48.1851i	0.129108	+	0.344179i
$141$		0			0
$142$	24.3614	−	14.0651i	0.171559	−	0.0990497i
$143$	−125.396			−0.876894
$144$		0			0
$145$	−110.889	+	134.816i	−0.764751	+	0.929765i
$146$	−10.8326	+	6.25420i	−0.0741959	+	0.0428370i
$147$		0			0
$148$	207.374	+	119.727i	1.40118	+	0.808969i
$149$	−204.106	−	117.841i	−1.36984	−	0.790879i	−0.378934	−	0.925424i	$-0.623709\pi$
$149$	−204.106	−	117.841i	−1.36984	−	0.790879i	−0.990907	+	0.134545i	$0.957043\pi$
$150$		0			0
$151$	7.41840	+	12.8490i	0.0491285	+	0.0850930i	0.889544	−	0.456850i	$-0.151022\pi$
$151$	7.41840	+	12.8490i	0.0491285	+	0.0850930i	−0.840415	+	0.541943i	$0.817689\pi$
$152$	−82.7371			−0.544323
$153$		0			0
$154$	13.5003			0.0876646
$155$	−24.1433	+	145.240i	−0.155763	+	0.937032i
$156$		0			0
$157$	127.486	+	73.6041i	0.812013	+	0.468816i	0.847654	−	0.530549i	$-0.178014\pi$
$157$	127.486	+	73.6041i	0.812013	+	0.468816i	−0.0356413	+	0.999365i	$0.511347\pi$
$158$	−9.13182	+	15.8168i	−0.0577963	+	0.100106i
$159$		0			0
$160$	−18.9049	+	113.727i	−0.118156	+	0.710795i
$161$			6.56031i			0.0407473i
$162$		0			0
$163$			9.62130i			0.0590264i	0.999564	+	0.0295132i	$0.00939571\pi$
$163$			9.62130i			0.0590264i	−0.999564	+	0.0295132i	$0.990604\pi$
$164$	−128.426	+	74.1466i	−0.783084	+	0.452114i
$165$		0			0
$166$	−19.9212	+	34.5045i	−0.120007	+	0.207858i
$167$	41.5393	−	71.9482i	0.248738	−	0.430828i	−0.714438	−	0.699699i	$-0.753317\pi$
$167$	41.5393	−	71.9482i	0.248738	−	0.430828i	0.963176	+	0.268872i	$0.0866507\pi$
$168$		0			0
$169$	7.82136	+	13.5470i	0.0462803	+	0.0801598i
$170$	−24.9448	−	20.5176i	−0.146734	−	0.120692i
$171$		0			0
$172$		−	251.484i		−	1.46212i
$173$	−0.219578	−	0.380321i	−0.00126924	−	0.00219839i	0.865390	−	0.501099i	$-0.167071\pi$
$173$	−0.219578	−	0.380321i	−0.00126924	−	0.00219839i	−0.866659	+	0.498900i	$0.833737\pi$
$174$		0			0
$175$	−22.3762	+	65.4449i	−0.127864	+	0.373971i
$176$	−101.678	−	58.7040i	−0.577718	−	0.333546i
$177$		0			0
$178$	−13.3420	+	7.70300i	−0.0749550	+	0.0432753i
$179$			102.699i			0.573740i	0.957970	+	0.286870i	$0.0926148\pi$
$179$			102.699i			0.573740i	−0.957970	+	0.286870i	$0.907385\pi$
$180$		0			0
$181$	−120.426			−0.665337			−0.332669	−	0.943044i	$-0.607949\pi$
$181$	−120.426			−0.665337			−0.332669	+	0.943044i	$0.607949\pi$
$182$	−9.93949	−	17.2157i	−0.0546126	−	0.0945917i
$183$		0			0
$184$	−4.84032	+	8.38368i	−0.0263061	+	0.0455635i
$185$	113.028	+	301.313i	0.610962	+	1.62872i
$186$		0			0
$187$	97.6295	−	56.3664i	0.522083	−	0.301425i
$188$	347.410			1.84792
$189$		0			0
$190$	−41.3833	−	34.0386i	−0.217807	−	0.179150i
$191$	126.755	−	73.1823i	0.663641	−	0.383153i	−0.130022	−	0.991511i	$-0.541505\pi$
$191$	126.755	−	73.1823i	0.663641	−	0.383153i	0.793663	+	0.608358i	$0.208171\pi$
$192$		0			0
$193$	−112.932	−	65.2014i	−0.585141	−	0.337831i	0.178033	−	0.984025i	$-0.443027\pi$
$193$	−112.932	−	65.2014i	−0.585141	−	0.337831i	−0.763174	+	0.646193i	$0.776360\pi$
$194$	28.5627	+	16.4907i	0.147231	+	0.0850036i
$195$		0			0
$196$	76.9115	+	133.215i	0.392405	+	0.679666i
$197$	−186.652			−0.947470			−0.473735	−	0.880668i	$-0.657094\pi$
$197$	−186.652			−0.947470			−0.473735	+	0.880668i	$0.657094\pi$
$198$		0			0
$199$	45.1917			0.227094			0.113547	−	0.993533i	$-0.463779\pi$
$199$	45.1917			0.227094			0.113547	+	0.993533i	$0.463779\pi$
$200$	−76.8819	+	67.1250i	−0.384410	+	0.335625i
$201$		0			0
$202$	−62.7855	−	36.2492i	−0.310819	−	0.179451i
$203$	48.2939	−	83.6474i	0.237901	−	0.412056i
$204$		0			0
$205$	−196.601	−	32.6811i	−0.959028	−	0.159420i
$206$			57.5343i			0.279293i
$207$		0			0
$208$			172.881i			0.831158i
$209$	161.967	−	93.5114i	0.774959	−	0.447423i
$210$		0			0
$211$	69.1054	−	119.694i	0.327514	−	0.567270i	−0.654504	−	0.756058i	$-0.727123\pi$
$211$	69.1054	−	119.694i	0.327514	−	0.567270i	0.982018	+	0.188788i	$0.0604559\pi$
$212$	−18.2793	+	31.6606i	−0.0862229	+	0.149343i
$213$		0			0
$214$	−16.9214	−	29.3087i	−0.0790719	−	0.136957i
$215$	214.701	−	261.028i	0.998608	−	1.21408i
$216$		0			0
$217$		−	81.4664i		−	0.375421i
$218$	3.91664	+	6.78381i	0.0179662	+	0.0311184i
$219$		0			0
$220$	−60.2913	−	160.726i	−0.274051	−	0.730573i
$221$	−143.757	−	82.9983i	−0.650485	−	0.375558i
$222$		0			0
$223$	50.4072	−	29.1026i	0.226041	−	0.130505i	−0.382703	−	0.923871i	$-0.625007\pi$
$223$	50.4072	−	29.1026i	0.226041	−	0.130505i	0.608744	+	0.793366i	$0.291673\pi$
$224$		−	63.7906i		−	0.284780i
$225$		0			0
$226$	43.7874			0.193750
$227$	−187.291	−	324.397i	−0.825069	−	1.42906i	−0.901866	−	0.432015i	$-0.857803\pi$
$227$	−187.291	−	324.397i	−0.825069	−	1.42906i	0.0767971	−	0.997047i	$-0.475531\pi$
$228$		0			0
$229$	−33.8418	+	58.6157i	−0.147781	+	0.255964i	−0.930407	−	0.366528i	$-0.880546\pi$
$229$	−33.8418	+	58.6157i	−0.147781	+	0.255964i	0.782626	+	0.622492i	$0.213880\pi$
$230$	−5.87012	+	2.20199i	−0.0255223	+	0.00957387i
$231$		0			0
$232$	123.433	−	71.2642i	0.532040	−	0.307173i
$233$	−282.378			−1.21192			−0.605961	−	0.795495i	$-0.707211\pi$
$233$	−282.378			−1.21192			−0.605961	+	0.795495i	$0.707211\pi$
$234$		0			0
$235$	360.593	+	296.596i	1.53444	+	1.26211i
$236$	188.495	−	108.828i	0.798707	−	0.461134i
$237$		0			0
$238$	15.4772	+	8.93575i	0.0650301	+	0.0375452i
$239$	319.035	+	184.195i	1.33488	+	0.770691i	0.986042	−	0.166494i	$-0.0532447\pi$
$239$	319.035	+	184.195i	1.33488	+	0.770691i	0.348833	+	0.937185i	$0.386578\pi$
$240$		0			0
$241$	−185.554	−	321.389i	−0.769934	−	1.33357i	−0.937598	−	0.347721i	$-0.886956\pi$
$241$	−185.554	−	321.389i	−0.769934	−	1.33357i	0.167664	−	0.985844i	$-0.446378\pi$
$242$	18.9520			0.0783141
$243$		0			0
$244$	57.6870			0.236422
$245$	−33.8997	+	203.932i	−0.138366	+	0.832374i
$246$		0			0
$247$	−238.492	−	137.694i	−0.965555	−	0.557464i
$248$	60.1074	−	104.109i	0.242369	−	0.419795i
$249$		0			0
$250$	−66.0703	+	1.94471i	−0.264281	+	0.00777886i
$251$			306.449i			1.22091i	0.792049	+	0.610457i	$0.209014\pi$
$251$			306.449i			1.22091i	−0.792049	+	0.610457i	$0.790986\pi$
$252$		0			0
$253$		−	21.8826i		−	0.0864924i
$254$	−16.8200	+	9.71102i	−0.0662204	+	0.0382323i
$255$		0			0
$256$	−47.6010	+	82.4474i	−0.185941	+	0.322060i
$257$	152.974	−	264.959i	0.595230	−	1.03097i	−0.398284	−	0.917262i	$-0.630394\pi$
$257$	152.974	−	264.959i	0.595230	−	1.03097i	0.993514	−	0.113707i	$-0.0362724\pi$
$258$		0			0
$259$	−89.0328	−	154.209i	−0.343756	−	0.595403i
$260$	−160.570	+	195.216i	−0.617575	+	0.750832i
$261$		0			0
$262$			30.6362i			0.116932i
$263$	73.3426	+	127.033i	0.278869	+	0.483016i	0.971104	−	0.238657i	$-0.0767070\pi$
$263$	73.3426	+	127.033i	0.278869	+	0.483016i	−0.692235	+	0.721672i	$0.743374\pi$
$264$		0			0
$265$	−46.0027	+	17.2564i	−0.173595	+	0.0651187i
$266$	25.6765	+	14.8243i	0.0965282	+	0.0557306i
$267$		0			0
$268$	−50.1491	+	28.9536i	−0.187124	+	0.108036i
$269$		−	276.133i		−	1.02652i	−0.858234	−	0.513258i	$-0.828438\pi$
$269$		−	276.133i		−	1.02652i	0.858234	−	0.513258i	$-0.171562\pi$
$270$		0			0
$271$	304.822			1.12480			0.562402	−	0.826864i	$-0.309877\pi$
$271$	304.822			1.12480			0.562402	+	0.826864i	$0.309877\pi$
$272$	−77.7112	−	134.600i	−0.285703	−	0.494852i
$273$		0			0
$274$	−15.2237	+	26.3681i	−0.0555608	+	0.0962341i
$275$	74.6381	−	218.298i	0.271411	−	0.793811i
$276$		0			0
$277$	355.555	−	205.280i	1.28359	−	0.741083i	0.306090	−	0.952003i	$-0.400979\pi$
$277$	355.555	−	205.280i	1.28359	−	0.741083i	0.977503	+	0.210920i	$0.0676460\pi$
$278$	−32.0707			−0.115362
$279$		0			0
$280$	35.8737	−	43.6144i	0.128120	−	0.155766i
$281$	−89.9230	+	51.9171i	−0.320011	+	0.184758i	−0.651397	−	0.758737i	$-0.725817\pi$
$281$	−89.9230	+	51.9171i	−0.320011	+	0.184758i	0.331387	+	0.943495i	$0.392484\pi$
$282$		0			0
$283$	−243.762	−	140.736i	−0.861351	−	0.497301i	0.00311372	−	0.999995i	$-0.499009\pi$
$283$	−243.762	−	140.736i	−0.861351	−	0.497301i	−0.864464	+	0.502694i	$0.832342\pi$
$284$	171.398	+	98.9566i	0.603513	+	0.348439i
$285$		0			0
$286$	33.1541	+	57.4246i	0.115924	+	0.200785i
$287$	110.275			0.384234
$288$		0			0
$289$	−139.767			−0.483621
$290$	91.0571	+	15.1365i	0.313990	+	0.0521947i
$291$		0			0
$292$	−76.2142	−	44.0023i	−0.261007	−	0.150693i
$293$	−204.334	+	353.917i	−0.697387	+	1.20791i	0.271983	+	0.962302i	$0.412321\pi$
$293$	−204.334	+	353.917i	−0.697387	+	1.20791i	−0.969369	+	0.245607i	$0.921013\pi$
$294$		0			0
$295$	288.558	+	47.9671i	0.978162	+	0.162600i
$296$		−	262.760i		−	0.887703i
$297$		0			0
$298$			124.626i			0.418210i
$299$	−27.9047	+	16.1108i	−0.0933268	+	0.0538823i
$300$		0			0
$301$	−93.5055	+	161.956i	−0.310649	+	0.538060i
$302$	3.92278	−	6.79446i	0.0129893	−	0.0224982i
$303$		0			0
$304$	−128.922	−	223.300i	−0.424087	−	0.734540i
$305$	59.8761	+	49.2493i	0.196315	+	0.161473i
$306$		0			0
$307$			174.133i			0.567208i	0.958941	+	0.283604i	$0.0915301\pi$
$307$			174.133i			0.567208i	−0.958941	+	0.283604i	$0.908470\pi$
$308$	47.4917	+	82.2581i	0.154194	+	0.267072i
$309$		0			0
$310$	72.8955	−	27.3444i	0.235147	−	0.0882079i
$311$	−237.573	−	137.163i	−0.763900	−	0.441038i	0.0667941	−	0.997767i	$-0.478723\pi$
$311$	−237.573	−	137.163i	−0.763900	−	0.441038i	−0.830694	+	0.556729i	$0.812056\pi$
$312$		0			0
$313$	−184.560	+	106.555i	−0.589647	+	0.340433i	−0.764958	−	0.644080i	$-0.777240\pi$
$313$	−184.560	+	106.555i	−0.589647	+	0.340433i	0.175311	+	0.984513i	$0.443907\pi$
$314$		−	77.8424i		−	0.247906i
$315$		0			0
$316$	−128.496			−0.406634
$317$	121.062	+	209.686i	0.381899	+	0.661469i	0.991334	−	0.131368i	$-0.0419368\pi$
$317$	121.062	+	209.686i	0.381899	+	0.661469i	−0.609435	+	0.792836i	$0.708604\pi$
$318$		0			0
$319$	−161.089	+	279.014i	−0.504981	+	0.874653i
$320$	−181.165	+	67.9583i	−0.566140	+	0.212370i
$321$		0			0
$322$	3.00427	−	1.73452i	0.00933004	−	0.00538670i
$323$	247.577			0.766493
$324$		0			0
$325$	−333.326	+	65.5408i	−1.02562	+	0.201664i
$326$	4.40604	−	2.54383i	0.0135155	−	0.00780316i
$327$		0			0
$328$	140.925	+	81.3630i	0.429649	+	0.248058i
$329$	−223.732	−	129.172i	−0.680038	−	0.392620i
$330$		0			0
$331$	99.4647	+	172.278i	0.300498	+	0.520477i	0.976249	−	0.216653i	$-0.0695139\pi$
$331$	99.4647	+	172.278i	0.300498	+	0.520477i	−0.675751	+	0.737130i	$0.736181\pi$
$332$	−280.316			−0.844325
$333$		0			0
$334$	−43.9313			−0.131531
$335$	−76.7709	−	12.7617i	−0.229167	−	0.0380945i
$336$		0			0
$337$	273.013	+	157.624i	0.810128	+	0.467728i	0.847000	−	0.531592i	$-0.178406\pi$
$337$	273.013	+	157.624i	0.810128	+	0.467728i	−0.0368724	+	0.999320i	$0.511740\pi$
$338$	4.13587	−	7.16353i	0.0122363	−	0.0211939i
$339$		0			0
$340$	37.2634	−	224.167i	0.109598	−	0.659314i
$341$			271.739i			0.796889i
$342$		0			0
$343$		−	249.950i		−	0.728716i
$344$	−238.988	+	137.980i	−0.694734	+	0.401105i
$345$		0			0
$346$	−0.116111	+	0.201110i	−0.000335581	+	0.000581244i
$347$	−253.003	+	438.213i	−0.729114	+	1.26286i	0.228144	+	0.973627i	$0.426734\pi$
$347$	−253.003	+	438.213i	−0.729114	+	1.26286i	−0.957258	+	0.289235i	$0.906599\pi$
$348$		0			0
$349$	280.837	+	486.423i	0.804689	+	1.39376i	0.916501	+	0.400033i	$0.131001\pi$
$349$	280.837	+	486.423i	0.804689	+	1.39376i	−0.111811	+	0.993729i	$0.535665\pi$
$350$	35.8865	−	7.05624i	0.102533	−	0.0201607i
$351$		0			0
$352$			212.780i			0.604488i
$353$	−120.900	−	209.404i	−0.342492	−	0.593213i	0.642403	−	0.766367i	$-0.277938\pi$
$353$	−120.900	−	209.404i	−0.342492	−	0.593213i	−0.984895	+	0.173154i	$0.944604\pi$
$354$		0			0
$355$	93.4194	+	249.040i	0.263153	+	0.701521i
$356$	−93.8693	−	54.1955i	−0.263678	−	0.152234i
$357$		0			0
$358$	47.0309	−	27.1533i	0.131371	−	0.0758472i
$359$			361.904i			1.00809i	0.863678	+	0.504044i	$0.168155\pi$
$359$			361.904i			1.00809i	−0.863678	+	0.504044i	$0.831845\pi$
$360$		0			0
$361$	49.7285			0.137752
$362$	31.8401	+	55.1487i	0.0879561	+	0.152344i
$363$		0			0
$364$	69.9305	−	121.123i	0.192117	−	0.332756i
$365$	−41.5401	−	110.739i	−0.113809	−	0.303394i
$366$		0			0
$367$	−227.601	+	131.406i	−0.620168	+	0.358054i	−0.776934	−	0.629582i	$-0.783226\pi$
$367$	−227.601	+	131.406i	−0.620168	+	0.358054i	0.156767	+	0.987636i	$0.449893\pi$
$368$	−30.1691			−0.0819812
$369$		0			0
$370$	108.101	−	131.427i	0.292165	−	0.355207i
$371$	23.5437	−	13.5930i	0.0634602	−	0.0366388i
$372$		0			0
$373$	270.755	+	156.320i	0.725883	+	0.419089i	0.816914	−	0.576759i	$-0.195683\pi$
$373$	270.755	+	156.320i	0.725883	+	0.419089i	−0.0910309	+	0.995848i	$0.529016\pi$
$374$	−51.6256	−	29.8061i	−0.138036	−	0.0796953i
$375$		0			0
$376$	−190.611	−	330.148i	−0.506944	−	0.878052i
$377$	474.400			1.25835
$378$		0			0
$379$	256.518			0.676830			0.338415	−	0.940997i	$-0.390109\pi$
$379$	256.518			0.676830			0.338415	+	0.940997i	$0.390109\pi$
$380$	61.8197	−	371.891i	0.162683	−	0.978661i
$381$		0			0
$382$	−67.0272	−	38.6982i	−0.175464	−	0.101304i
$383$	19.4145	−	33.6269i	0.0506906	−	0.0877986i	−0.839567	−	0.543257i	$-0.817191\pi$
$383$	19.4145	−	33.6269i	0.0506906	−	0.0877986i	0.890257	+	0.455458i	$0.150524\pi$
$384$		0			0
$385$	−20.9326	+	125.925i	−0.0543704	+	0.327078i
$386$			68.9559i			0.178642i
$387$		0			0
$388$			232.045i			0.598054i
$389$	−265.870	+	153.500i	−0.683469	+	0.394601i	−0.801161	−	0.598449i	$-0.795784\pi$
$389$	−265.870	+	153.500i	−0.683469	+	0.394601i	0.117691	+	0.993050i	$0.462451\pi$
$390$		0			0
$391$	14.4839	−	25.0868i	0.0370431	−	0.0641605i
$392$	84.3969	−	146.180i	0.215298	−	0.372908i
$393$		0			0
$394$	49.3498	+	85.4764i	0.125253	+	0.216945i
$395$	−133.372	−	109.702i	−0.337652	−	0.277726i
$396$		0			0
$397$		−	47.0129i		−	0.118420i	−0.998246	−	0.0592102i	$-0.981142\pi$
$397$		−	47.0129i		−	0.118420i	0.998246	−	0.0592102i	$-0.0188582\pi$
$398$	−11.9485	−	20.6954i	−0.0300213	−	0.0519985i
$399$		0			0
$400$	−300.963	−	102.902i	−0.752408	−	0.257255i
$401$	492.460	+	284.322i	1.22808	+	0.709032i	0.966628	−	0.256184i	$-0.0824654\pi$
$401$	492.460	+	284.322i	1.22808	+	0.709032i	0.261452	+	0.965216i	$0.415799\pi$
$402$		0			0
$403$	346.523	−	200.065i	0.859858	−	0.496439i
$404$		−	510.072i		−	1.26255i
$405$		0			0
$406$	−51.0747			−0.125800
$407$	296.977	+	514.380i	0.729674	+	1.26383i
$408$		0			0
$409$	281.070	−	486.828i	0.687213	−	1.19029i	−0.285523	−	0.958372i	$-0.592167\pi$
$409$	281.070	−	486.828i	0.687213	−	1.19029i	0.972736	−	0.231916i	$-0.0744994\pi$
$410$	37.0142	+	98.6734i	0.0902785	+	0.240667i
$411$		0			0
$412$	−350.559	+	202.395i	−0.850870	+	0.491250i
$413$	−161.855			−0.391900
$414$		0			0
$415$	−290.953	−	239.315i	−0.701092	−	0.576663i
$416$	271.338	−	156.657i	0.652254	−	0.376579i
$417$		0			0
$418$	−85.6465	−	49.4480i	−0.204896	−	0.118297i
$419$	−180.183	−	104.029i	−0.430031	−	0.248279i	0.269329	−	0.963048i	$-0.413198\pi$
$419$	−180.183	−	104.029i	−0.430031	−	0.248279i	−0.699360	+	0.714770i	$0.746531\pi$
$420$		0			0
$421$	197.236	+	341.622i	0.468493	+	0.811454i	0.999352	−	0.0360063i	$-0.0114636\pi$
$421$	197.236	+	341.622i	0.468493	+	0.811454i	−0.530858	+	0.847461i	$0.678130\pi$
$422$	−73.0846			−0.173186
$423$		0			0
$424$	40.1166			0.0946147
$425$	230.056	−	200.861i	0.541309	−	0.472613i
$426$		0			0
$427$	−37.1505	−	21.4488i	−0.0870035	−	0.0502315i
$428$	119.053	−	206.205i	0.278160	−	0.481788i
$429$		0			0
$430$	−176.303	−	29.3069i	−0.410006	−	0.0681556i
$431$		−	216.515i		−	0.502355i	−0.967941	−	0.251177i	$-0.919182\pi$
$431$		−	216.515i		−	0.502355i	0.967941	−	0.251177i	$-0.0808177\pi$
$432$		0			0
$433$		−	614.024i		−	1.41807i	−0.705173	−	0.709035i	$-0.749131\pi$
$433$		−	614.024i		−	1.41807i	0.705173	−	0.709035i	$-0.250869\pi$
$434$	−37.3073	+	21.5394i	−0.0859614	+	0.0496299i
$435$		0			0
$436$	−27.5560	+	47.7284i	−0.0632018	+	0.109469i
$437$	24.0286	−	41.6188i	0.0549854	−	0.0952374i
$438$		0			0
$439$	−259.851	−	450.074i	−0.591915	−	1.02523i	−0.993974	−	0.109613i	$-0.965039\pi$
$439$	−259.851	−	450.074i	−0.591915	−	1.02523i	0.402059	−	0.915614i	$-0.368295\pi$
$440$	−119.660	+	145.480i	−0.271955	+	0.330636i
$441$		0			0
$442$			87.7775i			0.198592i
$443$	−250.825	−	434.441i	−0.566196	−	0.980680i	−0.996937	−	0.0782045i	$-0.975081\pi$
$443$	−250.825	−	434.441i	−0.566196	−	0.980680i	0.430742	−	0.902475i	$-0.358252\pi$
$444$		0			0
$445$	−51.1629	−	136.391i	−0.114973	−	0.306498i
$446$	−26.6549	−	15.3892i	−0.0597643	−	0.0345049i
$447$		0			0
$448$	92.7186	−	53.5311i	0.206961	−	0.119489i
$449$			166.389i			0.370576i	0.982684	+	0.185288i	$0.0593218\pi$
$449$			166.389i			0.370576i	−0.982684	+	0.185288i	$0.940678\pi$
$450$		0			0
$451$	−367.834			−0.815596
$452$	154.036	+	266.798i	0.340788	+	0.590261i
$453$		0			0
$454$	−99.0377	+	171.538i	−0.218145	+	0.377838i
$455$	175.991	−	66.0176i	0.386794	−	0.145094i
$456$		0			0
$457$	−720.569	+	416.021i	−1.57674	+	0.910330i	−0.581428	+	0.813598i	$0.697506\pi$
$457$	−720.569	+	416.021i	−1.57674	+	0.910330i	−0.995310	+	0.0967320i	$0.969161\pi$
$458$	35.7905			0.0781452
$459$		0			0
$460$	−34.0668	−	28.0207i	−0.0740582	−	0.0609145i
$461$	−376.087	+	217.134i	−0.815806	+	0.471006i	−0.848968	−	0.528444i	$-0.822776\pi$
$461$	−376.087	+	217.134i	−0.815806	+	0.471006i	0.0331619	+	0.999450i	$0.489442\pi$
$462$		0			0
$463$	150.734	+	87.0264i	0.325560	+	0.187962i	0.653868	−	0.756609i	$-0.273145\pi$
$463$	150.734	+	87.0264i	0.325560	+	0.187962i	−0.328308	+	0.944571i	$0.606478\pi$
$464$	384.671	+	222.090i	0.829033	+	0.478643i
$465$		0			0
$466$	74.6594	+	129.314i	0.160213	+	0.277498i
$467$	−134.443			−0.287886			−0.143943	−	0.989586i	$-0.545978\pi$
$467$	−134.443			−0.287886			−0.143943	+	0.989586i	$0.545978\pi$
$468$		0			0
$469$	43.0615			0.0918155
$470$	40.4856	−	243.551i	0.0861397	−	0.518194i
$471$		0			0
$472$	−206.840	−	119.419i	−0.438221	−	0.253007i
$473$	311.897	−	540.221i	0.659401	−	1.14212i
$474$		0			0
$475$	381.662	−	333.226i	0.803498	−	0.701529i
$476$			125.737i			0.264154i
$477$		0			0
$478$		−	194.802i		−	0.407535i
$479$	617.101	−	356.283i	1.28831	−	0.743806i	0.309958	−	0.950750i	$-0.399685\pi$
$479$	617.101	−	356.283i	1.28831	−	0.743806i	0.978353	+	0.206944i	$0.0663518\pi$
$480$		0			0
$481$	437.293	−	757.413i	0.909133	−	1.57466i
$482$	−98.1194	+	169.948i	−0.203567	+	0.352589i
$483$		0			0
$484$	66.6697	+	115.475i	0.137747	+	0.238585i
$485$	−198.105	+	240.851i	−0.408463	+	0.496599i
$486$		0			0
$487$			208.661i			0.428462i	0.976783	+	0.214231i	$0.0687246\pi$
$487$			208.661i			0.428462i	−0.976783	+	0.214231i	$0.931275\pi$
$488$	−31.6507	−	54.8206i	−0.0648580	−	0.112337i
$489$		0			0
$490$	102.353	−	38.3944i	0.208883	−	0.0783559i
$491$	356.432	+	205.786i	0.725931	+	0.419117i	0.816932	−	0.576734i	$-0.195673\pi$
$491$	356.432	+	205.786i	0.725931	+	0.419117i	−0.0910005	+	0.995851i	$0.529006\pi$
$492$		0			0
$493$	−369.353	+	213.246i	−0.749195	+	0.432548i
$494$			145.622i			0.294782i
$495$		0			0
$496$	374.641			0.755326
$497$	−73.5870	−	127.456i	−0.148062	−	0.256451i
$498$		0			0
$499$	167.299	−	289.770i	0.335269	−	0.580702i	−0.648268	−	0.761412i	$-0.724506\pi$
$499$	167.299	−	289.770i	0.335269	−	0.580702i	0.983536	+	0.180710i	$0.0578396\pi$
$500$	−244.272	−	395.727i	−0.488545	−	0.791455i
$501$		0			0
$502$	140.337	−	81.0239i	0.279557	−	0.161402i
$503$	−85.4624			−0.169905			−0.0849527	−	0.996385i	$-0.527074\pi$
$503$	−85.4624			−0.169905			−0.0849527	+	0.996385i	$0.527074\pi$
$504$		0			0
$505$	435.466	−	529.428i	0.862309	−	1.04837i
$506$	−10.0210	+	5.78565i	−0.0198044	+	0.0114341i
$507$		0			0
$508$	−118.339	−	68.3231i	−0.232951	−	0.134494i
$509$	−142.153	−	82.0719i	−0.279278	−	0.161241i	0.353818	−	0.935314i	$-0.384883\pi$
$509$	−142.153	−	82.0719i	−0.279278	−	0.161241i	−0.633097	+	0.774073i	$0.718216\pi$
$510$		0			0
$511$	32.7214	+	56.6750i	0.0640340	+	0.110910i
$512$	501.116			0.978743
$513$		0			0
$514$	−161.783			−0.314752
$515$	−536.653	−	89.2082i	−1.04205	−	0.173220i
$516$		0			0
$517$	746.281	+	430.866i	1.44348	+	0.833396i
$518$	−47.0797	+	81.5445i	−0.0908875	+	0.157422i
$519$		0			0
$520$	273.615	+	45.4832i	0.526183	+	0.0874677i
$521$		−	954.386i		−	1.83184i	−0.401366	−	0.915918i	$-0.631464\pi$
$521$		−	954.386i		−	1.83184i	0.401366	−	0.915918i	$-0.368536\pi$
$522$		0			0
$523$			53.5836i			0.102454i	0.998687	+	0.0512271i	$0.0163132\pi$
$523$			53.5836i			0.102454i	−0.998687	+	0.0512271i	$0.983687\pi$
$524$	−186.668	+	107.773i	−0.356236	+	0.205673i
$525$		0			0
$526$	38.7829	−	67.1740i	0.0737318	−	0.127707i
$527$	−179.861	+	311.529i	−0.341293	+	0.591137i
$528$		0			0
$529$	261.689	+	453.258i	0.494685	+	0.856820i
$530$	20.0654	+	16.5042i	0.0378593	+	0.0311401i
$531$		0			0
$532$			208.597i			0.392100i
$533$	270.814	+	469.063i	0.508093	+	0.880043i
$534$		0			0
$535$	299.615	−	112.391i	0.560028	−	0.210077i
$536$	55.0299	+	31.7715i	0.102668	+	0.0592753i
$537$		0			0
$538$	−126.454	+	73.0083i	−0.235045	+	0.135703i
$539$			381.550i			0.707884i
$540$		0			0
$541$	−502.886			−0.929549			−0.464774	−	0.885429i	$-0.653865\pi$
$541$	−502.886			−0.929549			−0.464774	+	0.885429i	$0.653865\pi$
$542$	−80.5935	−	139.592i	−0.148697	−	0.257550i
$543$		0			0
$544$	−140.837	+	243.937i	−0.258891	+	0.448413i
$545$	−69.3491	+	26.0141i	−0.127246	+	0.0477323i
$546$		0			0
$547$	−632.220	+	365.012i	−1.15579	+	0.667298i	−0.950293	−	0.311359i	$-0.899216\pi$
$547$	−632.220	+	365.012i	−1.15579	+	0.667298i	−0.205502	+	0.978657i	$0.565883\pi$
$548$	−214.216			−0.390905
$549$		0			0
$550$	−119.703	+	23.5368i	−0.217641	+	0.0427941i
$551$	−612.754	+	353.774i	−1.11208	+	0.642058i
$552$		0			0
$553$	82.7518	+	47.7768i	0.149642	+	0.0863956i
$554$	−188.014	−	108.550i	−0.339376	−	0.195939i
$555$		0			0
$556$	−112.819	−	195.408i	−0.202912	−	0.351453i
$557$	419.491			0.753125			0.376562	−	0.926391i	$-0.377106\pi$
$557$	419.491			0.753125			0.376562	+	0.926391i	$0.377106\pi$
$558$		0			0
$559$	−918.522			−1.64315
$560$	173.610	+	28.8594i	0.310018	+	0.0515346i
$561$		0			0
$562$	47.5505	+	27.4533i	0.0846094	+	0.0488493i
$563$	−317.922	+	550.657i	−0.564693	+	0.978077i	0.432385	+	0.901689i	$0.357672\pi$
$563$	−317.922	+	550.657i	−0.564693	+	0.978077i	−0.997078	+	0.0763882i	$0.975661\pi$
$564$		0			0
$565$	−67.8933	+	408.428i	−0.120165	+	0.722882i
$566$			148.840i			0.262968i
$567$		0			0
$568$		−	217.175i		−	0.382351i
$569$	767.241	−	442.967i	1.34840	−	0.778501i	0.360380	−	0.932806i	$-0.382647\pi$
$569$	767.241	−	442.967i	1.34840	−	0.778501i	0.988023	+	0.154305i	$0.0493138\pi$
$570$		0			0
$571$	−463.096	+	802.105i	−0.811026	+	1.40474i	0.101121	+	0.994874i	$0.467757\pi$
$571$	−463.096	+	802.105i	−0.811026	+	1.40474i	−0.912147	+	0.409864i	$0.865576\pi$
$572$	−233.260	+	404.018i	−0.407798	+	0.706326i
$573$		0			0
$574$	−29.1563	−	50.5001i	−0.0507949	−	0.0879794i
$575$	−11.4374	−	58.1680i	−0.0198911	−	0.101162i
$576$		0			0
$577$		−	261.287i		−	0.452837i	−0.974030	−	0.226418i	$-0.927298\pi$
$577$		−	261.287i		−	0.452837i	0.974030	−	0.226418i	$-0.0727016\pi$
$578$	36.9537	+	64.0056i	0.0639337	+	0.110736i
$579$		0			0
$580$	228.095	+	608.061i	0.393267	+	1.04838i
$581$	180.524	+	104.225i	0.310712	+	0.179390i
$582$		0			0
$583$	−78.5325	+	45.3407i	−0.134704	+	0.0777714i
$584$			96.5696i			0.165359i
$585$		0			0
$586$	216.100			0.368772
$587$	301.693	+	522.548i	0.513958	+	0.890201i	0.999869	+	0.0161926i	$0.00515450\pi$
$587$	301.693	+	522.548i	0.513958	+	0.890201i	−0.485911	+	0.874008i	$0.661512\pi$
$588$		0			0
$589$	−298.389	+	516.825i	−0.506602	+	0.877461i
$590$	−54.3270	−	144.826i	−0.0920797	−	0.245468i
$591$		0			0
$592$	709.166	−	409.437i	1.19792	−	0.691617i
$593$	−314.000			−0.529511			−0.264756	−	0.964316i	$-0.585291\pi$
$593$	−314.000			−0.529511			−0.264756	+	0.964316i	$0.585291\pi$
$594$		0			0
$595$	−107.346	+	130.509i	−0.180414	+	0.219342i
$596$	−759.354	+	438.413i	−1.27408	+	0.735592i
$597$		0			0
$598$	14.7558	+	8.51925i	0.0246752	+	0.0142462i
$599$	−652.734	−	376.856i	−1.08971	−	0.629142i	−0.156208	−	0.987724i	$-0.549927\pi$
$599$	−652.734	−	376.856i	−1.08971	−	0.629142i	−0.933498	+	0.358582i	$0.883260\pi$
$600$		0			0
$601$	168.976	+	292.675i	0.281158	+	0.486979i	0.971670	−	0.236341i	$-0.0759483\pi$
$601$	168.976	+	292.675i	0.281158	+	0.486979i	−0.690512	+	0.723320i	$0.742615\pi$
$602$	98.8897			0.164269
$603$		0			0
$604$	55.1985			0.0913883
$605$	−29.3855	+	176.775i	−0.0485711	+	0.292191i
$606$		0			0
$607$	−382.344	−	220.747i	−0.629892	−	0.363668i	0.150818	−	0.988562i	$-0.451809\pi$
$607$	−382.344	−	220.747i	−0.629892	−	0.363668i	−0.780710	+	0.624893i	$0.785143\pi$
$608$	−233.647	+	404.689i	−0.384288	+	0.665607i
$609$		0			0
$610$	6.72259	−	40.4414i	0.0110206	−	0.0662973i
$611$		−	1268.88i		−	2.07673i
$612$		0			0
$613$			406.010i			0.662332i	0.943572	+	0.331166i	$0.107442\pi$
$613$			406.010i			0.662332i	−0.943572	+	0.331166i	$0.892558\pi$
$614$	79.7436	−	46.0400i	0.129876	−	0.0749837i
$615$		0			0
$616$	52.1139	−	90.2639i	0.0846005	−	0.146532i
$617$	447.854	−	775.706i	0.725858	−	1.25722i	−0.232762	−	0.972534i	$-0.574776\pi$
$617$	447.854	−	775.706i	0.725858	−	1.25722i	0.958620	−	0.284689i	$-0.0918903\pi$
$618$		0			0
$619$	−185.811	−	321.834i	−0.300179	−	0.519925i	0.675997	−	0.736904i	$-0.263713\pi$
$619$	−185.811	−	321.834i	−0.300179	−	0.519925i	−0.976176	+	0.216979i	$0.930380\pi$
$620$	423.044	+	347.962i	0.682329	+	0.561230i
$621$		0			0
$622$			145.061i			0.233217i
$623$	40.3013	+	69.8039i	0.0646891	+	0.112045i
$624$		0			0
$625$	84.3040	−	619.288i	0.134886	−	0.990861i
$626$	97.5935	+	56.3456i	0.155900	+	0.0900090i
$627$		0			0
$628$	474.297	−	273.835i	0.755249	−	0.436043i
$629$			786.266i			1.25002i
$630$		0			0
$631$	150.820			0.239017			0.119508	−	0.992833i	$-0.461868\pi$
$631$	150.820			0.239017			0.119508	+	0.992833i	$0.461868\pi$
$632$	70.5011	+	122.112i	0.111552	+	0.193214i
$633$		0			0
$634$	64.0165	−	110.880i	0.100972	−	0.174889i
$635$	−64.5001	−	171.946i	−0.101575	−	0.270781i
$636$		0			0
$637$	486.553	−	280.912i	0.763820	−	0.440992i
$638$	170.365			0.267029
$639$		0			0
$640$	435.173	+	357.939i	0.679958	+	0.559280i
$641$	−175.963	+	101.592i	−0.274513	+	0.158490i	−0.630937	−	0.775834i	$-0.717329\pi$
$641$	−175.963	+	101.592i	−0.274513	+	0.158490i	0.356424	+	0.934324i	$0.383996\pi$
$642$		0			0
$643$	42.7186	+	24.6636i	0.0664365	+	0.0383571i	0.532850	−	0.846210i	$-0.321121\pi$
$643$	42.7186	+	24.6636i	0.0664365	+	0.0383571i	−0.466414	+	0.884567i	$0.654454\pi$
$644$	21.1370	+	12.2034i	0.0328214	+	0.0189494i
$645$		0			0
$646$	−65.4583	−	113.377i	−0.101329	−	0.175506i
$647$	−1189.39			−1.83832			−0.919159	−	0.393887i	$-0.871130\pi$
$647$	−1189.39			−1.83832			−0.919159	+	0.393887i	$0.871130\pi$
$648$		0			0
$649$	539.882			0.831867
$650$	118.144	+	135.317i	0.181760	+	0.208180i
$651$		0			0
$652$	30.9993	+	17.8975i	0.0475449	+	0.0274501i
$653$	170.606	−	295.498i	0.261265	−	0.452524i	−0.705313	−	0.708896i	$-0.749194\pi$
$653$	170.606	−	295.498i	0.261265	−	0.452524i	0.966578	+	0.256371i	$0.0825270\pi$
$654$		0			0
$655$	−285.760	−	47.5021i	−0.436275	−	0.0725223i
$656$			507.125i			0.773056i
$657$		0			0
$658$			136.610i			0.207614i
$659$	322.418	−	186.148i	0.489254	−	0.282471i	−0.235011	−	0.971993i	$-0.575513\pi$
$659$	322.418	−	186.148i	0.489254	−	0.282471i	0.724265	+	0.689522i	$0.242179\pi$
$660$		0			0
$661$	−166.221	+	287.904i	−0.251469	+	0.435557i	−0.963931	−	0.266154i	$-0.914247\pi$
$661$	−166.221	+	287.904i	−0.251469	+	0.435557i	0.712461	+	0.701711i	$0.247580\pi$
$662$	52.5961	−	91.0991i	0.0794502	−	0.137612i
$663$		0			0
$664$	153.799	+	266.387i	0.231625	+	0.401186i
$665$	−178.086	+	216.513i	−0.267799	+	0.325583i
$666$		0			0
$667$			82.7865i			0.124118i
$668$	−154.542	−	267.675i	−0.231350	−	0.400711i
$669$		0			0
$670$	14.4537	+	38.5311i	0.0215727	+	0.0575091i
$671$	123.919	+	71.5447i	0.184678	+	0.106624i
$672$		0			0
$673$	196.887	−	113.673i	0.292551	−	0.168905i	−0.346541	−	0.938035i	$-0.612644\pi$
$673$	196.887	−	113.673i	0.292551	−	0.168905i	0.639092	+	0.769130i	$0.279310\pi$
$674$		−	166.701i		−	0.247330i
$675$		0			0
$676$	58.1969			0.0860901
$677$	−530.736	−	919.261i	−0.783952	−	1.35785i	−0.929623	−	0.368512i	$-0.879867\pi$
$677$	−530.736	−	919.261i	−0.783952	−	1.35785i	0.145671	−	0.989333i	$-0.453466\pi$
$678$		0			0
$679$	86.2777	−	149.437i	0.127066	−	0.220084i
$680$	−233.474	+	87.5802i	−0.343343	+	0.128794i
$681$		0			0
$682$	124.442	−	71.8466i	0.182466	−	0.105347i
$683$	633.553			0.927604			0.463802	−	0.885939i	$-0.346485\pi$
$683$	633.553			0.927604			0.463802	+	0.885939i	$0.346485\pi$
$684$		0			0
$685$	−222.345	−	182.884i	−0.324591	−	0.266983i
$686$	−114.464	+	66.0856i	−0.166857	+	0.0963347i
$687$		0			0
$688$	−744.792	−	430.006i	−1.08255	−	0.625008i
$689$	115.637	+	66.7633i	0.167834	+	0.0968988i
$690$		0			0
$691$	−540.899	−	936.864i	−0.782777	−	1.35581i	−0.930318	−	0.366753i	$-0.880469\pi$
$691$	−540.899	−	936.864i	−0.782777	−	1.35581i	0.147542	−	0.989056i	$-0.452864\pi$
$692$	−1.63383			−0.00236103
$693$		0			0
$694$	267.571			0.385549
$695$	49.7264	−	299.141i	0.0715487	−	0.430418i
$696$		0			0
$697$	−421.694	−	243.465i	−0.605014	−	0.349305i
$698$	148.504	−	257.216i	0.212756	−	0.368505i
$699$		0			0
$700$	169.236	+	193.835i	0.241766	+	0.276907i
$701$		−	143.009i		−	0.204007i	−0.994784	−	0.102003i	$-0.967475\pi$
$701$		−	143.009i		−	0.204007i	0.994784	−	0.102003i	$-0.0325253\pi$
$702$		0			0
$703$			1304.41i			1.85549i
$704$	−309.272	+	178.558i	−0.439306	+	0.253634i
$705$		0			0
$706$	−63.9307	+	110.731i	−0.0905534	+	0.156843i
$707$	−189.652	+	328.487i	−0.268249	+	0.464621i
$708$		0			0
$709$	−424.541	−	735.327i	−0.598789	−	1.03713i	−0.993000	−	0.118113i	$-0.962315\pi$
$709$	−424.541	−	735.327i	−0.598789	−	1.03713i	0.394211	−	0.919020i	$-0.371018\pi$
$710$	89.3473	−	108.626i	0.125841	−	0.152995i
$711$		0			0
$712$			118.940i			0.167051i
$713$	34.9129	+	60.4709i	0.0489662	+	0.0848120i
$714$		0			0
$715$	−587.036	+	220.208i	−0.821030	+	0.307983i
$716$	330.892	+	191.040i	0.462139	+	0.266816i
$717$		0			0
$718$	165.733	−	95.6858i	0.230825	−	0.133267i
$719$		−	155.493i		−	0.216263i	−0.994137	−	0.108131i	$-0.965513\pi$
$719$		−	155.493i		−	0.216263i	0.994137	−	0.108131i	$-0.0344867\pi$
$720$		0			0
$721$	301.014			0.417495
$722$	−13.1480	−	22.7730i	−0.0182105	−	0.0315416i
$723$		0			0
$724$	−224.015	+	388.006i	−0.309413	+	0.535920i
$725$	−282.372	+	825.869i	−0.389479	+	1.13913i
$726$		0			0
$727$	540.769	−	312.213i	0.743837	−	0.429454i	−0.0796259	−	0.996825i	$-0.525373\pi$
$727$	540.769	−	312.213i	0.743837	−	0.429454i	0.823463	+	0.567370i	$0.192039\pi$
$728$	−153.473			−0.210815
$729$		0			0
$730$	−39.7294	+	48.3020i	−0.0544238	+	0.0661671i
$731$	715.133	−	412.882i	0.978295	−	0.564819i
$732$		0			0
$733$	−392.871	−	226.824i	−0.535977	−	0.309447i	0.207470	−	0.978241i	$-0.433477\pi$
$733$	−392.871	−	226.824i	−0.535977	−	0.309447i	−0.743447	+	0.668795i	$0.766810\pi$
$734$	120.354	+	69.4862i	0.163970	+	0.0946679i
$735$		0			0
$736$	27.3378	+	47.3505i	0.0371438	+	0.0643350i
$737$	−143.636			−0.194892
$738$		0			0
$739$	827.126			1.11925			0.559625	−	0.828746i	$-0.310945\pi$
$739$	827.126			1.11925			0.559625	+	0.828746i	$0.310945\pi$
$740$	1181.07	+	196.330i	1.59604	+	0.265310i
$741$		0			0
$742$	−12.4497	−	7.18785i	−0.0167786	−	0.00968713i
$743$	301.483	−	522.184i	0.405765	−	0.702805i	−0.588645	−	0.808391i	$-0.700339\pi$
$743$	301.483	−	522.184i	0.405765	−	0.702805i	0.994410	+	0.105586i	$0.0336719\pi$
$744$		0			0
$745$	−1162.46	−	193.236i	−1.56035	−	0.259377i
$746$		−	165.321i		−	0.221611i
$747$		0			0
$748$		−	419.409i		−	0.560707i
$749$	−153.340	+	88.5309i	−0.204726	+	0.118199i
$750$		0			0
$751$	172.482	−	298.747i	0.229669	−	0.397799i	−0.728041	−	0.685534i	$-0.759569\pi$
$751$	172.482	−	298.747i	0.229669	−	0.397799i	0.957710	+	0.287735i	$0.0929023\pi$
$752$	594.026	−	1028.88i	0.789928	−	1.36820i
$753$		0			0
$754$	−125.429	−	217.250i	−0.166352	−	0.288130i
$755$	57.2932	+	47.1248i	0.0758850	+	0.0624170i
$756$		0			0
$757$		−	1248.67i		−	1.64950i	−0.565501	−	0.824748i	$-0.691317\pi$
$757$		−	1248.67i		−	1.64950i	0.565501	−	0.824748i	$-0.308683\pi$
$758$	−67.8223	−	117.472i	−0.0894754	−	0.154976i
$759$		0			0
$760$	−387.331	+	145.295i	−0.509646	+	0.191177i
$761$	960.298	+	554.428i	1.26189	+	0.728552i	0.973440	−	0.228942i	$-0.0735268\pi$
$761$	960.298	+	554.428i	1.26189	+	0.728552i	0.288450	+	0.957495i	$0.406860\pi$
$762$		0			0
$763$	35.4922	−	20.4914i	0.0465167	−	0.0268564i
$764$		−	544.532i		−	0.712738i
$765$		0			0
$766$	−20.5324			−0.0268047
$767$	−397.482	−	688.459i	−0.518230	−	0.897600i
$768$		0			0
$769$	576.165	−	997.947i	0.749239	−	1.29772i	−0.198949	−	0.980010i	$-0.563753\pi$
$769$	576.165	−	997.947i	0.749239	−	1.29772i	0.948188	−	0.317710i	$-0.102914\pi$
$770$	63.2014	−	23.7080i	0.0820797	−	0.0307896i
$771$		0			0
$772$	−420.151	+	242.574i	−0.544237	+	0.314215i
$773$	1116.83			1.44480			0.722399	−	0.691476i	$-0.243039\pi$
$773$	1116.83			1.44480			0.722399	+	0.691476i	$0.243039\pi$
$774$		0			0
$775$	142.030	+	722.334i	0.183265	+	0.932044i
$776$	220.515	−	127.314i	0.284169	−	0.164065i
$777$		0			0
$778$	140.590	+	81.1694i	0.180706	+	0.104331i
$779$	−699.588	−	403.907i	−0.898059	−	0.518495i
$780$		0			0
$781$	245.456	+	425.143i	0.314285	+	0.544357i
$782$	−15.3179			−0.0195881
$783$		0			0
$784$	526.035			0.670963
$785$	726.078	+	120.696i	0.924940	+	0.153753i
$786$		0			0
$787$	−922.485	−	532.597i	−1.17215	−	0.676743i	−0.217967	−	0.975956i	$-0.569943\pi$
$787$	−922.485	−	532.597i	−1.17215	−	0.676743i	−0.954186	+	0.299213i	$0.903276\pi$
$788$	−347.207	+	601.381i	−0.440618	+	0.763173i
$789$		0			0
$790$	−14.9744	+	90.0821i	−0.0189549	+	0.114028i
$791$		−	229.091i		−	0.289622i
$792$		0			0
$793$		−	210.696i		−	0.265695i
$794$	−21.5294	+	12.4300i	−0.0271151	+	0.0156549i
$795$		0			0
$796$	84.0651	−	145.605i	0.105609	−	0.182921i
$797$	−94.4897	+	163.661i	−0.118557	+	0.205346i	−0.919196	−	0.393801i	$-0.871160\pi$
$797$	−94.4897	+	163.661i	−0.118557	+	0.205346i	0.800639	+	0.599147i	$0.204493\pi$
$798$		0			0
$799$	570.371	+	987.912i	0.713857	+	1.23644i
$800$	111.214	+	565.609i	0.139017	+	0.707011i
$801$		0			0
$802$		−	300.694i		−	0.374930i
$803$	−109.145	−	189.045i	−0.135922	−	0.235424i
$804$		0			0
$805$	11.5206	+	30.7119i	0.0143113	+	0.0381514i
$806$	−183.238	−	105.793i	−0.227343	−	0.131256i
$807$		0			0
$808$	−484.728	+	279.858i	−0.599910	+	0.346358i
$809$			1105.36i			1.36633i	0.730266	+	0.683163i	$0.239396\pi$
$809$			1105.36i			1.36633i	−0.730266	+	0.683163i	$0.760604\pi$
$810$		0			0
$811$	4.70248			0.00579838			0.00289919	−	0.999996i	$-0.499077\pi$
$811$	4.70248			0.00579838			0.00289919	+	0.999996i	$0.499077\pi$
$812$	−179.672	−	311.200i	−0.221270	−	0.383251i
$813$		0			0
$814$	157.039	−	272.000i	0.192923	−	0.334152i
$815$	16.8960	+	45.0418i	0.0207313	+	0.0552660i
$816$		0			0
$817$	1186.40	−	684.969i	1.45214	−	0.838395i
$818$	−297.255			−0.363392
$819$		0			0
$820$	−471.011	+	572.644i	−0.574404	+	0.698346i
$821$	−759.412	+	438.447i	−0.924984	+	0.534040i	−0.885222	−	0.465169i	$-0.845993\pi$
$821$	−759.412	+	438.447i	−0.924984	+	0.534040i	−0.0397625	+	0.999209i	$0.512660\pi$
$822$		0			0
$823$	992.214	+	572.855i	1.20561	+	0.696057i	0.961796	−	0.273766i	$-0.0882693\pi$
$823$	992.214	+	572.855i	1.20561	+	0.696057i	0.243810	+	0.969823i	$0.421603\pi$
$824$	384.677	+	222.093i	0.466841	+	0.269531i
$825$		0			0
$826$	42.7937	+	74.1208i	0.0518083	+	0.0897346i
$827$	−255.412			−0.308841			−0.154421	−	0.988005i	$-0.549351\pi$
$827$	−255.412			−0.308841			−0.154421	+	0.988005i	$0.549351\pi$
$828$		0			0
$829$	−829.155			−1.00019			−0.500093	−	0.865971i	$-0.666701\pi$
$829$	−829.155			−1.00019			−0.500093	+	0.865971i	$0.666701\pi$
$830$	−32.6668	+	196.515i	−0.0393576	+	0.236765i
$831$		0			0
$832$	455.396	+	262.923i	0.547351	+	0.316013i
$833$	−252.544	+	437.419i	−0.303174	+	0.525113i
$834$		0			0
$835$	68.1164	−	409.770i	0.0815765	−	0.490743i
$836$		−	695.796i		−	0.832292i
$837$		0			0
$838$			110.019i			0.131288i
$839$	−393.010	+	226.904i	−0.468427	+	0.270446i	−0.715581	−	0.698530i	$-0.753838\pi$
$839$	−393.010	+	226.904i	−0.468427	+	0.270446i	0.247154	+	0.968976i	$0.420505\pi$
$840$		0			0
$841$	188.934	−	327.244i	0.224654	−	0.389113i
$842$	104.297	−	180.647i	0.123868	−	0.214545i
$843$		0			0
$844$	−257.098	−	445.307i	−0.304619	−	0.527615i
$845$	60.4054	+	49.6847i	0.0714856	+	0.0587984i
$846$		0			0
$847$		−	99.1550i		−	0.117066i
$848$	62.5104	+	108.271i	0.0737151	+	0.127678i
$849$		0			0
$850$	−152.809	−	52.2469i	−0.179776	−	0.0614669i
$851$	132.175	+	76.3110i	0.155317	+	0.0896722i
$852$		0			0
$853$	14.0948	−	8.13764i	0.0165238	−	0.00954002i	−0.491715	−	0.870756i	$-0.663630\pi$
$853$	14.0948	−	8.13764i	0.0165238	−	0.00954002i	0.508239	+	0.861216i	$0.330297\pi$
$854$			22.6839i			0.0265620i
$855$		0			0
$856$	−261.279			−0.305232
$857$	−530.849	−	919.457i	−0.619427	−	1.07288i	−0.989590	−	0.143912i	$-0.954032\pi$
$857$	−530.849	−	919.457i	−0.619427	−	1.07288i	0.370164	−	0.928967i	$-0.379302\pi$
$858$		0			0
$859$	−811.869	+	1406.20i	−0.945133	+	1.63702i	−0.189648	+	0.981852i	$0.560735\pi$
$859$	−811.869	+	1406.20i	−0.945133	+	1.63702i	−0.755485	+	0.655166i	$0.772599\pi$
$860$	−441.632	−	1177.31i	−0.513526	−	1.36897i
$861$		0			0
$862$	−99.1522	+	57.2456i	−0.115026	+	0.0664102i
$863$	−687.358			−0.796475			−0.398238	−	0.917282i	$-0.630378\pi$
$863$	−687.358			−0.796475			−0.398238	+	0.917282i	$0.630378\pi$
$864$		0			0
$865$	−1.69583	−	1.39486i	−0.00196050	−	0.00161255i
$866$	−281.190	+	162.345i	−0.324700	+	0.187466i
$867$		0			0
$868$	−262.480	−	151.543i	−0.302397	−	0.174589i
$869$	−276.027	−	159.364i	−0.317637	−	0.183388i
$870$		0			0
$871$	105.750	+	183.165i	0.121412	+	0.210293i
$872$	60.4758			0.0693530
$873$		0			0
$874$	−25.4122			−0.0290758
$875$	10.1745	+	345.673i	0.0116281	+	0.395055i
$876$		0			0
$877$	1345.72	+	776.955i	1.53446	+	0.885923i	0.999148	+	0.0412710i	$0.0131407\pi$
$877$	1345.72	+	776.955i	1.53446	+	0.885923i	0.535316	+	0.844652i	$0.320193\pi$
$878$	−137.407	+	237.995i	−0.156500	+	0.271065i
$879$		0			0
$880$	−579.094	−	96.2632i	−0.658061	−	0.109390i
$881$			452.136i			0.513208i	0.966517	+	0.256604i	$0.0826036\pi$
$881$			452.136i			0.513208i	−0.966517	+	0.256604i	$0.917396\pi$
$882$		0			0
$883$			1014.46i			1.14888i	0.818546	+	0.574441i	$0.194781\pi$
$883$			1014.46i			1.14888i	−0.818546	+	0.574441i	$0.805219\pi$
$884$	−534.832	+	308.785i	−0.605013	+	0.349304i
$885$		0			0
$886$	−132.634	+	229.729i	−0.149700	+	0.259287i
$887$	−104.060	+	180.237i	−0.117317	+	0.203199i	−0.918704	−	0.394948i	$-0.870763\pi$
$887$	−104.060	+	180.237i	−0.117317	+	0.203199i	0.801387	+	0.598147i	$0.204096\pi$
$888$		0			0
$889$	50.8071	+	88.0004i	0.0571508	+	0.0989881i
$890$	−48.9328	+	59.4912i	−0.0549806	+	0.0668441i
$891$		0			0
$892$		−	216.545i		−	0.242764i
$893$	946.242	+	1638.94i	1.05962	+	1.83532i
$894$		0			0
$895$	180.351	+	480.784i	0.201509	+	0.537189i
$896$	−270.006	−	155.888i	−0.301346	−	0.173982i
$897$		0			0
$898$	76.1971	−	43.9924i	0.0848521	−	0.0489894i
$899$		−	1028.05i		−	1.14355i
$900$		0			0
$901$	−120.042			−0.133232
$902$	97.2536	+	168.448i	0.107820	+	0.186750i
$903$		0			0
$904$	169.028	−	292.765i	0.186978	−	0.323855i
$905$	−563.770	+	211.480i	−0.622950	+	0.233680i
$906$		0			0
$907$	−205.665	+	118.741i	−0.226753	+	0.130916i	−0.609073	−	0.793114i	$-0.708458\pi$
$907$	−205.665	+	118.741i	−0.226753	+	0.130916i	0.382320	+	0.924030i	$0.375125\pi$
$908$	−1393.59			−1.53479
$909$		0			0
$910$	−76.7639	−	63.1399i	−0.0843559	−	0.0693845i
$911$	−1167.48	+	674.042i	−1.28153	+	0.739893i	−0.977128	−	0.212650i	$-0.931791\pi$
$911$	−1167.48	+	674.042i	−1.28153	+	0.739893i	−0.304404	+	0.952543i	$0.598457\pi$
$912$		0			0
$913$	−602.155	−	347.654i	−0.659534	−	0.380782i
$914$	381.031	+	219.988i	0.416883	+	0.240687i
$915$		0			0
$916$	125.904	+	218.073i	0.137450	+	0.238071i
$917$	160.286			0.174793
$918$		0			0
$919$	−153.887			−0.167450			−0.0837250	−	0.996489i	$-0.526682\pi$
$919$	−153.887			−0.167450			−0.0837250	+	0.996489i	$0.526682\pi$
$920$	−7.93718	+	47.7480i	−0.00862737	+	0.0519000i
$921$		0			0
$922$	198.871	+	114.818i	0.215696	+	0.124532i
$923$	361.429	−	626.014i	0.391581	−	0.678238i
$924$		0			0
$925$	1058.27	+	1212.10i	1.14408	+	1.31038i
$926$		−	92.0376i		−	0.0993926i
$927$		0			0
$928$		−	804.992i		−	0.867448i
$929$	665.491	−	384.221i	0.716352	−	0.413586i	−0.0970567	−	0.995279i	$-0.530943\pi$
$929$	665.491	−	384.221i	0.716352	−	0.413586i	0.813408	+	0.581693i	$0.197609\pi$
$930$		0			0
$931$	−418.968	+	725.674i	−0.450020	+	0.779457i
$932$	−525.276	+	909.805i	−0.563601	+	0.976186i
$933$		0			0
$934$	35.5461	+	61.5677i	0.0380579	+	0.0659183i
$935$	358.064	−	435.325i	0.382956	−	0.465588i
$936$		0			0
$937$		−	359.563i		−	0.383738i	−0.981421	−	0.191869i	$-0.938545\pi$
$937$		−	359.563i		−	0.383738i	0.981421	−	0.191869i	$-0.0614549\pi$
$938$	−11.3853	−	19.7199i	−0.0121378	−	0.0210233i
$939$		0			0
$940$	1626.39	−	610.087i	1.73020	−	0.649029i
$941$	−183.507	−	105.948i	−0.195013	−	0.112591i	0.399314	−	0.916814i	$-0.369248\pi$
$941$	−183.507	−	105.948i	−0.195013	−	0.112591i	−0.594327	+	0.804223i	$0.702582\pi$
$942$		0			0
$943$	−81.8551	+	47.2591i	−0.0868029	+	0.0501157i
$944$		−	744.325i		−	0.788479i
$945$		0			0
$946$	−329.856			−0.348685
$947$	773.466	+	1339.68i	0.816754	+	1.41466i	0.908062	+	0.418837i	$0.137562\pi$
$947$	773.466	+	1339.68i	0.816754	+	1.41466i	−0.0913074	+	0.995823i	$0.529105\pi$
$948$		0			0
$949$	−160.714	+	278.365i	−0.169351	+	0.293324i
$950$	−253.509	−	86.6772i	−0.266852	−	0.0912392i
$951$		0			0
$952$	119.490	−	68.9874i	0.125514	−	0.0724657i
$953$	1453.97			1.52568			0.762838	−	0.646589i	$-0.223805\pi$
$953$	1453.97			1.52568			0.762838	+	0.646589i	$0.223805\pi$
$954$		0			0
$955$	464.885	−	565.196i	0.486791	−	0.591828i
$956$	1186.93	−	685.276i	1.24156	−	0.716816i
$957$		0			0
$958$	−326.317	−	188.399i	−0.340624	−	0.196659i
$959$	137.955	+	79.6486i	0.143853	+	0.0830538i
$960$		0			0
$961$	46.9491	+	81.3183i	0.0488544	+	0.0846184i
$962$	−462.473			−0.480741
$963$		0			0
$964$	−1380.66			−1.43222
$965$	−643.188	−	106.918i	−0.666517	−	0.110795i
$966$		0			0
$967$	−331.339	−	191.299i	−0.342646	−	0.197827i	0.318795	−	0.947824i	$-0.396722\pi$
$967$	−331.339	−	191.299i	−0.342646	−	0.197827i	−0.661442	+	0.749997i	$0.730055\pi$
$968$	73.1583	−	126.714i	0.0755768	−	0.130903i
$969$		0			0
$970$	162.675	+	27.0415i	0.167706	+	0.0278779i
$971$			1474.96i			1.51901i	0.650503	+	0.759504i	$0.274558\pi$
$971$			1474.96i			1.51901i	−0.650503	+	0.759504i	$0.725442\pi$
$972$		0			0
$973$			167.791i			0.172447i
$974$	95.5557	−	55.1691i	0.0981064	−	0.0566418i
$975$		0			0
$976$	98.6373	−	170.845i	0.101063	−	0.175046i
$977$	708.905	−	1227.86i	0.725593	−	1.25676i	−0.233136	−	0.972444i	$-0.574899\pi$
$977$	708.905	−	1227.86i	0.725593	−	1.25676i	0.958729	−	0.284320i	$-0.0917680\pi$
$978$		0			0
$979$	−134.429	−	232.838i	−0.137313	−	0.237832i
$980$	593.997	+	488.575i	0.606119	+	0.498546i
$981$		0			0
$982$		−	217.636i		−	0.221625i
$983$	222.160	+	384.792i	0.226002	+	0.391447i	0.956620	−	0.291340i	$-0.0941011\pi$
$983$	222.160	+	384.792i	0.226002	+	0.391447i	−0.730618	+	0.682787i	$0.760768\pi$
$984$		0			0
$985$	−873.802	+	327.779i	−0.887109	+	0.332771i
$986$	195.311	+	112.763i	0.198084	+	0.114364i
$987$		0			0
$988$	−887.282	+	512.272i	−0.898058	+	0.518494i
$989$		−	160.289i		−	0.162072i
$990$		0			0
$991$	1177.77			1.18847			0.594235	−	0.804291i	$-0.297455\pi$
$991$	1177.77			1.18847			0.594235	+	0.804291i	$0.297455\pi$
$992$	−339.483	−	588.002i	−0.342221	−	0.592744i
$993$		0			0
$994$	−38.9121	+	67.3978i	−0.0391470	+	0.0678046i
$995$	211.563	−	79.3613i	0.212626	−	0.0797601i
$996$		0			0
$997$	87.6487	−	50.6040i	0.0879125	−	0.0507563i	−0.455399	−	0.890287i	$-0.650503\pi$
$997$	87.6487	−	50.6040i	0.0879125	−	0.0507563i	0.543312	+	0.839531i	$0.317170\pi$
$998$	−176.933			−0.177287
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.h.a.44.5		20
3.2	odd	2		45.3.h.a.14.6	yes	20
5.2	odd	4		675.3.j.e.476.6		20
5.3	odd	4		675.3.j.e.476.5		20
5.4	even	2	inner	135.3.h.a.44.6		20
9.2	odd	6	inner	135.3.h.a.89.6		20
9.4	even	3		405.3.d.a.404.11		20
9.5	odd	6		405.3.d.a.404.10		20
9.7	even	3		45.3.h.a.29.5	yes	20
15.2	even	4		225.3.j.e.176.5		20
15.8	even	4		225.3.j.e.176.6		20
15.14	odd	2		45.3.h.a.14.5	✓	20
45.2	even	12		675.3.j.e.251.6		20
45.4	even	6		405.3.d.a.404.9		20
45.7	odd	12		225.3.j.e.101.5		20
45.14	odd	6		405.3.d.a.404.12		20
45.29	odd	6	inner	135.3.h.a.89.5		20
45.34	even	6		45.3.h.a.29.6	yes	20
45.38	even	12		675.3.j.e.251.5		20
45.43	odd	12		225.3.j.e.101.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.h.a.14.5	✓	20	15.14	odd	2
45.3.h.a.14.6	yes	20	3.2	odd	2
45.3.h.a.29.5	yes	20	9.7	even	3
45.3.h.a.29.6	yes	20	45.34	even	6
135.3.h.a.44.5		20	1.1	even	1	trivial
135.3.h.a.44.6		20	5.4	even	2	inner
135.3.h.a.89.5		20	45.29	odd	6	inner
135.3.h.a.89.6		20	9.2	odd	6	inner
225.3.j.e.101.5		20	45.7	odd	12
225.3.j.e.101.6		20	45.43	odd	12
225.3.j.e.176.5		20	15.2	even	4
225.3.j.e.176.6		20	15.8	even	4
405.3.d.a.404.9		20	45.4	even	6
405.3.d.a.404.10		20	9.5	odd	6
405.3.d.a.404.11		20	9.4	even	3
405.3.d.a.404.12		20	45.14	odd	6
675.3.j.e.251.5		20	45.38	even	12
675.3.j.e.251.6		20	45.2	even	12
675.3.j.e.476.5		20	5.3	odd	4
675.3.j.e.476.6		20	5.2	odd	4

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.264396 - 0.457947i) q^{2} +(1.86019 - 3.22194i) q^{4} +(4.68146 - 1.75610i) q^{5} +(-2.39593 + 1.38329i) q^{7} -4.08247 q^{8} +(-2.04196 - 1.67955i) q^{10} +(7.99186 - 4.61410i) q^{11} +(-11.7678 - 6.79417i) q^{13} +(1.26695 + 0.731472i) q^{14} +(-6.36137 - 11.0182i) q^{16} +12.2161 q^{17} +20.2664 q^{19} +(3.05035 - 18.3501i) q^{20} +(-4.22603 - 2.43990i) q^{22} +(1.18564 - 2.05358i) q^{23} +(18.8322 - 16.4423i) q^{25} +7.18539i q^{26} +10.2927i q^{28} +(-30.2349 + 17.4561i) q^{29} +(-14.7233 + 25.5015i) q^{31} +(-11.5288 + 19.9684i) q^{32} +(-3.22989 - 5.59433i) q^{34} +(-8.78726 + 10.6833i) q^{35} +64.3630i q^{37} +(-5.35836 - 9.28095i) q^{38} +(-19.1119 + 7.16923i) q^{40} +(-34.5195 - 19.9299i) q^{41} +(58.5402 - 33.7982i) q^{43} -34.3324i q^{44} -1.25391 q^{46} +(46.6901 + 80.8696i) q^{47} +(-20.6730 + 35.8067i) q^{49} +(-12.5088 - 4.27688i) q^{50} +(-43.7808 + 25.2769i) q^{52} -9.82656 q^{53} +(29.3108 - 35.6353i) q^{55} +(9.78131 - 5.64724i) q^{56} +(15.9880 + 9.23066i) q^{58} +(50.6655 + 29.2517i) q^{59} +(7.75283 + 13.4283i) q^{61} +15.5711 q^{62} -38.6984 q^{64} +(-67.0220 - 11.1411i) q^{65} +(-13.4796 - 7.78243i) q^{67} +(22.7243 - 39.3596i) q^{68} +(7.21571 + 1.19947i) q^{70} +53.1970i q^{71} -23.6547i q^{73} +(29.4748 - 17.0173i) q^{74} +(37.6994 - 65.2973i) q^{76} +(-12.7653 + 22.1101i) q^{77} +(-17.2692 - 29.9112i) q^{79} +(-49.1297 - 40.4102i) q^{80} +21.0775i q^{82} +(-37.6730 - 65.2516i) q^{83} +(57.1893 - 21.4527i) q^{85} +(-30.9555 - 17.8722i) q^{86} +(-32.6265 + 18.8369i) q^{88} -29.1344i q^{89} +37.5932 q^{91} +(-4.41101 - 7.64010i) q^{92} +(24.6893 - 42.7631i) q^{94} +(94.8766 - 35.5899i) q^{95} +(-54.0151 + 31.1857i) q^{97} +21.8634 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 18 q^{4} + 12 q^{5} + 4 q^{10} + 24 q^{11} - 30 q^{14} - 26 q^{16} - 8 q^{19} - 144 q^{20} + 2 q^{25} + 114 q^{29} + 28 q^{31} - 4 q^{34} - 34 q^{40} - 102 q^{41} + 116 q^{46} - 40 q^{49} + 408 q^{50}+ \cdots + 762 q^{95}+O(q^{100}) \) 20 * q - 18 * q^4 + 12 * q^5 + 4 * q^10 + 24 * q^11 - 30 * q^14 - 26 * q^16 - 8 * q^19 - 144 * q^20 + 2 * q^25 + 114 * q^29 + 28 * q^31 - 4 * q^34 - 34 * q^40 - 102 * q^41 + 116 * q^46 - 40 * q^49 + 408 * q^50 + 36 * q^55 + 618 * q^56 - 120 * q^59 - 50 * q^61 + 140 * q^64 - 492 * q^65 - 54 * q^70 - 504 * q^74 - 96 * q^76 - 128 * q^79 - 74 * q^85 - 1488 * q^86 - 288 * q^91 + 218 * q^94 + 762 * q^95

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