LMFDB - Embedded newform 198.3.j.c.145.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [198,3,Mod(19,198)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("198.19"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(198, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	198.j (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.39510923433$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 889x^{12} - 18240x^{10} + 235606x^{8} - 2565840x^{6} + 30314764x^{4} - 184688100x^{2} + 519885601 $ x^16 + 889x^12 - 18240x^10 + 235606x^8 - 2565840x^6 + 30314764x^4 - 184688100x^2 + 519885601
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			145.1
Root			$3.12252 + 1.01457i$ of defining polynomial
Character	$\chi$	$=$	198.145
Dual form			198.3.j.c.127.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34500 - 0.437016i) q^{2} +(1.61803 + 1.17557i) q^{4} +(-1.75757 - 5.40926i) q^{5} +(-6.36870 + 8.76576i) q^{7} +(-1.66251 - 2.28825i) q^{8} +8.04353i q^{10} +(7.37659 + 8.16002i) q^{11} +(-4.28248 - 1.39146i) q^{13} +(12.3967 - 9.00670i) q^{14} +(1.23607 + 3.80423i) q^{16} +(-16.5995 + 5.39350i) q^{17} +(19.7800 + 27.2249i) q^{19} +(3.51515 - 10.8185i) q^{20} +(-6.35542 - 14.1989i) q^{22} -7.03543 q^{23} +(-5.94559 + 4.31973i) q^{25} +(5.15183 + 3.74302i) q^{26} +(-20.6095 + 6.69644i) q^{28} +(-31.8760 + 43.8736i) q^{29} +(-11.8915 + 36.5982i) q^{31} -5.65685i q^{32} +24.6833 q^{34} +(58.6097 + 19.0435i) q^{35} +(16.2382 + 11.7977i) q^{37} +(-14.7064 - 45.2616i) q^{38} +(-9.45573 + 13.0147i) q^{40} +(8.83200 + 12.1562i) q^{41} -67.5682i q^{43} +(2.34288 + 21.8749i) q^{44} +(9.46263 + 3.07459i) q^{46} +(-24.1721 + 17.5620i) q^{47} +(-21.1364 - 65.0511i) q^{49} +(9.88460 - 3.21170i) q^{50} +(-5.29343 - 7.28578i) q^{52} +(4.79618 - 14.7611i) q^{53} +(31.1748 - 54.2437i) q^{55} +30.6462 q^{56} +(62.0466 - 45.0795i) q^{58} +(-31.3552 - 22.7809i) q^{59} +(-38.9028 + 12.6403i) q^{61} +(31.9880 - 44.0278i) q^{62} +(-2.47214 + 7.60845i) q^{64} +25.6106i q^{65} -33.1092 q^{67} +(-33.1990 - 10.7870i) q^{68} +(-70.5076 - 51.2268i) q^{70} +(-26.7010 - 82.1772i) q^{71} +(59.4667 - 81.8488i) q^{73} +(-16.6845 - 22.9643i) q^{74} +67.3036i q^{76} +(-118.508 + 12.6927i) q^{77} +(-47.6389 - 15.4788i) q^{79} +(18.4056 - 13.3724i) q^{80} +(-6.56656 - 20.2098i) q^{82} +(13.9686 - 4.53869i) q^{83} +(58.3497 + 80.3114i) q^{85} +(-29.5284 + 90.8791i) q^{86} +(6.40851 - 30.4455i) q^{88} +81.0524 q^{89} +(39.4710 - 28.6774i) q^{91} +(-11.3836 - 8.27064i) q^{92} +(40.1862 - 13.0573i) q^{94} +(112.502 - 154.845i) q^{95} +(7.64123 - 23.5173i) q^{97} +96.7305i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 60 q^{7} + 60 q^{13} - 16 q^{16} + 96 q^{25} + 40 q^{28} - 160 q^{31} - 64 q^{34} + 60 q^{37} - 80 q^{40} + 160 q^{46} + 96 q^{49} + 40 q^{52} + 224 q^{55} + 80 q^{58} - 500 q^{61} + 32 q^{64}+ \cdots - 1020 q^{97}+O(q^{100}) $ 16 * q + 8 * q^4 - 60 * q^7 + 60 * q^13 - 16 * q^16 + 96 * q^25 + 40 * q^28 - 160 * q^31 - 64 * q^34 + 60 * q^37 - 80 * q^40 + 160 * q^46 + 96 * q^49 + 40 * q^52 + 224 * q^55 + 80 * q^58 - 500 * q^61 + 32 * q^64 - 280 * q^67 - 424 * q^70 - 200 * q^73 - 100 * q^79 - 120 * q^82 + 1020 * q^85 + 240 * q^88 + 828 * q^91 + 440 * q^94 - 1020 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$

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 $

$2$	−1.34500	−	0.437016i	−0.672499	−	0.218508i
$2$	−1.34500	−	0.437016i	−0.672499	−	0.218508i
$3$		0			0
$3$		0			0
$4$	1.61803	+	1.17557i	0.404508	+	0.293893i
$5$	−1.75757	−	5.40926i	−0.351515	−	1.08185i	−0.958003	−	0.286759i	$-0.907422\pi$
$5$	−1.75757	−	5.40926i	−0.351515	−	1.08185i	0.606488	−	0.795093i	$-0.292578\pi$
$6$		0			0
$7$	−6.36870	+	8.76576i	−0.909814	+	1.25225i	0.0574167	+	0.998350i	$0.481714\pi$
$7$	−6.36870	+	8.76576i	−0.909814	+	1.25225i	−0.967230	+	0.253901i	$0.918286\pi$
$8$	−1.66251	−	2.28825i	−0.207813	−	0.286031i
$9$		0			0
$10$			8.04353i			0.804353i
$11$	7.37659	+	8.16002i	0.670599	+	0.741820i
$11$	7.37659	+	8.16002i	0.670599	+	0.741820i
$12$		0			0
$13$	−4.28248	−	1.39146i	−0.329421	−	0.107035i	0.139637	−	0.990203i	$-0.455406\pi$
$13$	−4.28248	−	1.39146i	−0.329421	−	0.107035i	−0.469058	+	0.883167i	$0.655406\pi$
$14$	12.3967	−	9.00670i	0.885475	−	0.643335i
$15$		0			0
$16$	1.23607	+	3.80423i	0.0772542	+	0.237764i
$17$	−16.5995	+	5.39350i	−0.976440	+	0.317265i	−0.753413	−	0.657548i	$-0.771594\pi$
$17$	−16.5995	+	5.39350i	−0.976440	+	0.317265i	−0.223027	+	0.974812i	$0.571594\pi$
$18$		0			0
$19$	19.7800	+	27.2249i	1.04105	+	1.43289i	0.896315	+	0.443419i	$0.146235\pi$
$19$	19.7800	+	27.2249i	1.04105	+	1.43289i	0.144740	+	0.989470i	$0.453765\pi$
$20$	3.51515	−	10.8185i	0.175757	−	0.540926i
$21$		0			0
$22$	−6.35542	−	14.1989i	−0.288883	−	0.645404i
$23$	−7.03543			−0.305888			−0.152944	−	0.988235i	$-0.548875\pi$
$23$	−7.03543			−0.305888			−0.152944	+	0.988235i	$0.548875\pi$
$24$		0			0
$25$	−5.94559	+	4.31973i	−0.237824	+	0.172789i
$26$	5.15183	+	3.74302i	0.198147	+	0.143962i
$27$		0			0
$28$	−20.6095	+	6.69644i	−0.736055	+	0.239159i
$29$	−31.8760	+	43.8736i	−1.09917	+	1.51288i	−0.262698	+	0.964878i	$0.584612\pi$
$29$	−31.8760	+	43.8736i	−1.09917	+	1.51288i	−0.836476	+	0.548004i	$0.815388\pi$
$30$		0			0
$31$	−11.8915	+	36.5982i	−0.383596	+	1.18059i	0.553897	+	0.832585i	$0.313140\pi$
$31$	−11.8915	+	36.5982i	−0.383596	+	1.18059i	−0.937493	+	0.348003i	$0.886860\pi$
$32$		−	5.65685i		−	0.176777i
$33$		0			0
$34$	24.6833			0.725979
$35$	58.6097	+	19.0435i	1.67456	+	0.544099i
$36$		0			0
$37$	16.2382	+	11.7977i	0.438870	+	0.318858i	0.785186	−	0.619260i	$-0.212567\pi$
$37$	16.2382	+	11.7977i	0.438870	+	0.318858i	−0.346315	+	0.938118i	$0.612567\pi$
$38$	−14.7064	−	45.2616i	−0.387010	−	1.19109i
$39$		0			0
$40$	−9.45573	+	13.0147i	−0.236393	+	0.325367i
$41$	8.83200	+	12.1562i	0.215415	+	0.296493i	0.903026	−	0.429586i	$-0.141341\pi$
$41$	8.83200	+	12.1562i	0.215415	+	0.296493i	−0.687611	+	0.726079i	$0.741341\pi$
$42$		0			0
$43$		−	67.5682i		−	1.57135i	−0.618637	−	0.785677i	$-0.712315\pi$
$43$		−	67.5682i		−	1.57135i	0.618637	−	0.785677i	$-0.287685\pi$
$44$	2.34288	+	21.8749i	0.0532473	+	0.497157i
$45$		0			0
$46$	9.46263	+	3.07459i	0.205709	+	0.0668390i
$47$	−24.1721	+	17.5620i	−0.514299	+	0.373660i	−0.814452	−	0.580231i	$-0.802962\pi$
$47$	−24.1721	+	17.5620i	−0.514299	+	0.373660i	0.300153	+	0.953891i	$0.402962\pi$
$48$		0			0
$49$	−21.1364	−	65.0511i	−0.431355	−	1.32757i
$50$	9.88460	−	3.21170i	0.197692	−	0.0642340i
$51$		0			0
$52$	−5.29343	−	7.28578i	−0.101797	−	0.140111i
$53$	4.79618	−	14.7611i	0.0904940	−	0.278512i	−0.895559	−	0.444942i	$-0.853224\pi$
$53$	4.79618	−	14.7611i	0.0904940	−	0.278512i	0.986053	+	0.166430i	$0.0532241\pi$
$54$		0			0
$55$	31.1748	−	54.2437i	0.566814	−	0.986249i
$56$	30.6462			0.547254
$57$		0			0
$58$	62.0466	−	45.0795i	1.06977	−	0.777233i
$59$	−31.3552	−	22.7809i	−0.531444	−	0.386117i	0.289454	−	0.957192i	$-0.406526\pi$
$59$	−31.3552	−	22.7809i	−0.531444	−	0.386117i	−0.820898	+	0.571075i	$0.806526\pi$
$60$		0			0
$61$	−38.9028	+	12.6403i	−0.637751	+	0.207218i	−0.610005	−	0.792397i	$-0.708833\pi$
$61$	−38.9028	+	12.6403i	−0.637751	+	0.207218i	−0.0277454	+	0.999615i	$0.508833\pi$
$62$	31.9880	−	44.0278i	0.515936	−	0.710125i
$63$		0			0
$64$	−2.47214	+	7.60845i	−0.0386271	+	0.118882i
$65$			25.6106i			0.394010i
$66$		0			0
$67$	−33.1092			−0.494167			−0.247083	−	0.968994i	$-0.579472\pi$
$67$	−33.1092			−0.494167			−0.247083	+	0.968994i	$0.579472\pi$
$68$	−33.1990	−	10.7870i	−0.488220	−	0.158632i
$69$		0			0
$70$	−70.5076	−	51.2268i	−1.00725	−	0.731811i
$71$	−26.7010	−	82.1772i	−0.376070	−	1.15743i	−0.942754	−	0.333490i	$-0.891774\pi$
$71$	−26.7010	−	82.1772i	−0.376070	−	1.15743i	0.566683	−	0.823936i	$-0.308226\pi$
$72$		0			0
$73$	59.4667	−	81.8488i	0.814612	−	1.12122i	−0.175984	−	0.984393i	$-0.556311\pi$
$73$	59.4667	−	81.8488i	0.814612	−	1.12122i	0.990595	−	0.136824i	$-0.0436894\pi$
$74$	−16.6845	−	22.9643i	−0.225467	−	0.310328i
$75$		0			0
$76$			67.3036i			0.885574i
$77$	−118.508	+	12.6927i	−1.53907	+	0.164840i
$78$		0			0
$79$	−47.6389	−	15.4788i	−0.603024	−	0.195934i	−0.00843539	−	0.999964i	$-0.502685\pi$
$79$	−47.6389	−	15.4788i	−0.603024	−	0.195934i	−0.594589	+	0.804030i	$0.702685\pi$
$80$	18.4056	−	13.3724i	0.230070	−	0.167155i
$81$		0			0
$82$	−6.56656	−	20.2098i	−0.0800800	−	0.246461i
$83$	13.9686	−	4.53869i	0.168297	−	0.0546830i	−0.223657	−	0.974668i	$-0.571799\pi$
$83$	13.9686	−	4.53869i	0.168297	−	0.0546830i	0.391954	+	0.919985i	$0.371799\pi$
$84$		0			0
$85$	58.3497	+	80.3114i	0.686467	+	0.944840i
$86$	−29.5284	+	90.8791i	−0.343354	+	1.05673i
$87$		0			0
$88$	6.40851	−	30.4455i	0.0728239	−	0.345972i
$89$	81.0524			0.910701			0.455350	−	0.890312i	$-0.349514\pi$
$89$	81.0524			0.910701			0.455350	+	0.890312i	$0.349514\pi$
$90$		0			0
$91$	39.4710	−	28.6774i	0.433747	−	0.315136i
$92$	−11.3836	−	8.27064i	−0.123734	−	0.0898983i
$93$		0			0
$94$	40.1862	−	13.0573i	0.427513	−	0.138907i
$95$	112.502	−	154.845i	1.18423	−	1.62995i
$96$		0			0
$97$	7.64123	−	23.5173i	0.0787756	−	0.242446i	−0.903911	−	0.427720i	$-0.859317\pi$
$97$	7.64123	−	23.5173i	0.0787756	−	0.242446i	0.982687	+	0.185273i	$0.0593171\pi$
$98$			96.7305i			0.987046i
$99$		0			0
$100$	−14.6983			−0.146983
$101$	107.535	+	34.9404i	1.06471	+	0.345944i	0.788424	−	0.615132i	$-0.210897\pi$
$101$	107.535	+	34.9404i	1.06471	+	0.345944i	0.276283	+	0.961076i	$0.410897\pi$
$102$		0			0
$103$	29.7882	+	21.6424i	0.289206	+	0.210121i	0.722923	−	0.690929i	$-0.242798\pi$
$103$	29.7882	+	21.6424i	0.289206	+	0.210121i	−0.433717	+	0.901049i	$0.642798\pi$
$104$	3.93565	+	12.1127i	0.0378427	+	0.116468i
$105$		0			0
$106$	−12.9017	+	17.7577i	−0.121714	+	0.167525i
$107$	118.164	+	162.638i	1.10433	+	1.51998i	0.829513	+	0.558487i	$0.188618\pi$
$107$	118.164	+	162.638i	1.10433	+	1.51998i	0.274819	+	0.961496i	$0.411382\pi$
$108$		0			0
$109$			116.981i			1.07322i	0.843831	+	0.536608i	$0.180295\pi$
$109$			116.981i			1.07322i	−0.843831	+	0.536608i	$0.819705\pi$
$110$	−65.6354	+	59.3338i	−0.596685	+	0.539398i
$111$		0			0
$112$	−41.2191	−	13.3929i	−0.368027	−	0.119579i
$113$	−157.729	+	114.597i	−1.39583	+	1.01413i	−0.400635	+	0.916238i	$0.631211\pi$
$113$	−157.729	+	114.597i	−1.39583	+	1.01413i	−0.995197	+	0.0978937i	$0.968789\pi$
$114$		0			0
$115$	12.3653	+	38.0565i	0.107524	+	0.330926i
$116$	−103.153	+	33.5164i	−0.889250	+	0.288935i
$117$		0			0
$118$	32.2170	+	44.3429i	0.273026	+	0.375788i
$119$	58.4389	−	179.857i	0.491084	−	1.51140i
$120$		0			0
$121$	−12.1720	+	120.386i	−0.100595	+	0.994927i
$122$	57.8482			0.474165
$123$		0			0
$124$	−62.2647	+	45.2379i	−0.502134	+	0.364822i
$125$	−81.2184	−	59.0086i	−0.649747	−	0.472069i
$126$		0			0
$127$	−76.8059	+	24.9558i	−0.604771	+	0.196502i	−0.595367	−	0.803454i	$-0.702993\pi$
$127$	−76.8059	+	24.9558i	−0.604771	+	0.196502i	−0.00940389	+	0.999956i	$0.502993\pi$
$128$	6.65003	−	9.15298i	0.0519534	−	0.0715077i
$129$		0			0
$130$	11.1923	−	34.4462i	0.0860942	−	0.264971i
$131$		−	14.5488i		−	0.111060i	−0.998457	−	0.0555298i	$-0.982315\pi$
$131$		−	14.5488i		−	0.111060i	0.998457	−	0.0555298i	$-0.0176848\pi$
$132$		0			0
$133$	−364.620			−2.74150
$134$	44.5318	+	14.4692i	0.332327	+	0.107979i
$135$		0			0
$136$	39.9384	+	29.0170i	0.293665	+	0.213360i
$137$	−34.8631	−	107.298i	−0.254475	−	0.783194i	−0.993933	−	0.109991i	$-0.964918\pi$
$137$	−34.8631	−	107.298i	−0.254475	−	0.783194i	0.739457	−	0.673203i	$-0.235082\pi$
$138$		0			0
$139$	21.4006	−	29.4553i	0.153961	−	0.211909i	−0.725068	−	0.688677i	$-0.758192\pi$
$139$	21.4006	−	29.4553i	0.153961	−	0.211909i	0.879029	+	0.476768i	$0.158192\pi$
$140$	72.4456	+	99.7128i	0.517469	+	0.712234i
$141$		0			0
$142$			122.197i			0.860541i
$143$	−20.2357	−	45.2093i	−0.141508	−	0.316149i
$144$		0			0
$145$	293.348	+	95.3146i	2.02309	+	0.657342i
$146$	−115.752	+	84.0985i	−0.792820	+	0.576017i
$147$		0			0
$148$	12.4049	+	38.1783i	0.0838168	+	0.257962i
$149$	−259.594	+	84.3473i	−1.74224	+	0.566090i	−0.995127	−	0.0986025i	$-0.968563\pi$
$149$	−259.594	+	84.3473i	−1.74224	+	0.566090i	−0.747118	+	0.664692i	$0.768563\pi$
$150$		0			0
$151$	23.8667	+	32.8497i	0.158058	+	0.217548i	0.880700	−	0.473674i	$-0.157073\pi$
$151$	23.8667	+	32.8497i	0.158058	+	0.217548i	−0.722642	+	0.691222i	$0.757073\pi$
$152$	29.4128	−	90.5232i	0.193505	−	0.595547i
$153$		0			0
$154$	164.940	+	34.7183i	1.07104	+	0.225444i
$155$	218.870			1.41206
$156$		0			0
$157$	133.661	−	97.1107i	0.851347	−	0.618539i	−0.0741704	−	0.997246i	$-0.523631\pi$
$157$	133.661	−	97.1107i	0.851347	−	0.618539i	0.925517	+	0.378706i	$0.123631\pi$
$158$	57.3097	+	41.6379i	0.362720	+	0.263531i
$159$		0			0
$160$	−30.5994	+	9.94235i	−0.191246	+	0.0621397i
$161$	44.8065	−	61.6709i	0.278301	−	0.383049i
$162$		0			0
$163$	−68.2702	+	210.114i	−0.418836	+	1.28904i	0.489939	+	0.871757i	$0.337019\pi$
$163$	−68.2702	+	210.114i	−0.418836	+	1.28904i	−0.908775	+	0.417287i	$0.862981\pi$
$164$			30.0518i			0.183243i
$165$		0			0
$166$	−20.7713			−0.125128
$167$	193.953	+	63.0190i	1.16139	+	0.377360i	0.825424	−	0.564513i	$-0.190936\pi$
$167$	193.953	+	63.0190i	1.16139	+	0.377360i	0.335969	+	0.941873i	$0.390936\pi$
$168$		0			0
$169$	−120.320	−	87.4179i	−0.711955	−	0.517266i
$170$	−43.3827	−	133.518i	−0.255193	−	0.785402i
$171$		0			0
$172$	79.4312	−	109.328i	0.461809	−	0.635626i
$173$	−165.214	−	227.397i	−0.954992	−	1.31443i	−0.949274	−	0.314450i	$-0.898180\pi$
$173$	−165.214	−	227.397i	−0.954992	−	1.31443i	−0.00571804	−	0.999984i	$-0.501820\pi$
$174$		0			0
$175$		−	79.6287i		−	0.455021i
$176$	−21.9246	+	38.1485i	−0.124572	+	0.216753i
$177$		0			0
$178$	−109.015	−	35.4212i	−0.612445	−	0.198995i
$179$	117.682	−	85.5013i	0.657444	−	0.477661i	−0.208355	−	0.978053i	$-0.566811\pi$
$179$	117.682	−	85.5013i	0.657444	−	0.477661i	0.865799	+	0.500393i	$0.166811\pi$
$180$		0			0
$181$	69.5569	+	214.074i	0.384292	+	1.18273i	0.936992	+	0.349350i	$0.113597\pi$
$181$	69.5569	+	214.074i	0.384292	+	1.18273i	−0.552700	+	0.833380i	$0.686403\pi$
$182$	−65.6208	+	21.3215i	−0.360554	+	0.117151i
$183$		0			0
$184$	11.6965	+	16.0988i	0.0635677	+	0.0874934i
$185$	35.2772	−	108.572i	0.190688	−	0.586876i
$186$		0			0
$187$	−166.459	−	95.6666i	−0.890153	−	0.511586i
$188$	−59.7566			−0.317854
$189$		0			0
$190$	−218.984	+	159.101i	−1.15255	+	0.837375i
$191$	202.127	+	146.854i	1.05826	+	0.768869i	0.973765	−	0.227555i	$-0.0730730\pi$
$191$	202.127	+	146.854i	1.05826	+	0.768869i	0.0844927	+	0.996424i	$0.473073\pi$
$192$		0			0
$193$	−6.36296	+	2.06745i	−0.0329687	+	0.0107122i	−0.325455	−	0.945558i	$-0.605517\pi$
$193$	−6.36296	+	2.06745i	−0.0329687	+	0.0107122i	0.292486	+	0.956270i	$0.405517\pi$
$194$	−20.5549	+	28.2913i	−0.105953	+	0.145832i
$195$		0			0
$196$	42.2728	−	130.102i	0.215677	−	0.663787i
$197$			258.538i			1.31237i	0.754598	+	0.656187i	$0.227832\pi$
$197$			258.538i			1.31237i	−0.754598	+	0.656187i	$0.772168\pi$
$198$		0			0
$199$	235.298			1.18240			0.591200	−	0.806525i	$-0.298654\pi$
$199$	235.298			1.18240			0.591200	+	0.806525i	$0.298654\pi$
$200$	19.7692	+	6.42340i	0.0988460	+	0.0321170i
$201$		0			0
$202$	−129.365	−	93.9894i	−0.640422	−	0.465294i
$203$	−181.577	−	558.835i	−0.894466	−	2.75288i
$204$		0			0
$205$	50.2332	−	69.1400i	0.245040	−	0.337268i
$206$	−30.6070	−	42.1269i	−0.148578	−	0.204500i
$207$		0			0
$208$		−	18.0114i		−	0.0865935i
$209$	−76.2466	+	362.232i	−0.364816	+	1.73317i
$210$		0			0
$211$	30.5915	+	9.93979i	0.144984	+	0.0471080i	0.380610	−	0.924736i	$-0.375714\pi$
$211$	30.5915	+	9.93979i	0.144984	+	0.0471080i	−0.235626	+	0.971844i	$0.575714\pi$
$212$	25.1131	−	18.2458i	0.118458	−	0.0860649i
$213$		0			0
$214$	−87.8542	−	270.387i	−0.410533	−	1.26349i
$215$	−365.494	+	118.756i	−1.69997	+	0.552355i
$216$		0			0
$217$	−245.078	−	337.321i	−1.12939	−	1.55447i
$218$	51.1224	−	157.339i	0.234506	−	0.721737i
$219$		0			0
$220$	114.209	−	51.1200i	0.519133	−	0.232364i
$221$	78.5917			0.355619
$222$		0			0
$223$	140.206	−	101.866i	0.628726	−	0.456796i	−0.227233	−	0.973840i	$-0.572968\pi$
$223$	140.206	−	101.866i	0.628726	−	0.456796i	0.855959	+	0.517044i	$0.172968\pi$
$224$	49.5866	+	36.0268i	0.221369	+	0.160834i
$225$		0			0
$226$	262.226	−	85.2023i	1.16029	−	0.377001i
$227$	1.30881	−	1.80142i	0.00576569	−	0.00793579i	−0.806124	−	0.591746i	$-0.798439\pi$
$227$	1.30881	−	1.80142i	0.00576569	−	0.00793579i	0.811890	+	0.583810i	$0.198439\pi$
$228$		0			0
$229$	97.1079	−	298.867i	0.424052	−	1.30510i	−0.479847	−	0.877352i	$-0.659308\pi$
$229$	97.1079	−	298.867i	0.424052	−	1.30510i	0.903899	−	0.427745i	$-0.140692\pi$
$230$		−	56.5896i		−	0.246042i
$231$		0			0
$232$	153.388			0.661154
$233$	120.967	+	39.3045i	0.519171	+	0.168689i	0.556869	−	0.830600i	$-0.312003\pi$
$233$	120.967	+	39.3045i	0.519171	+	0.168689i	−0.0376982	+	0.999289i	$0.512003\pi$
$234$		0			0
$235$	137.482	+	99.8864i	0.585029	+	0.425048i
$236$	−23.9532	−	73.7205i	−0.101497	−	0.312375i
$237$		0			0
$238$	−157.200	+	216.368i	−0.660506	+	0.909108i
$239$	93.6343	+	128.876i	0.391775	+	0.539232i	0.958656	−	0.284568i	$-0.0918500\pi$
$239$	93.6343	+	128.876i	0.391775	+	0.539232i	−0.566881	+	0.823800i	$0.691850\pi$
$240$		0			0
$241$		−	265.125i		−	1.10010i	−0.835131	−	0.550051i	$-0.814608\pi$
$241$		−	265.125i		−	1.10010i	0.835131	−	0.550051i	$-0.185392\pi$
$242$	68.9820	−	156.600i	0.285049	−	0.647106i
$243$		0			0
$244$	−77.8056	−	25.2806i	−0.318875	−	0.103609i
$245$	−314.730	+	228.664i	−1.28461	+	0.933324i
$246$		0			0
$247$	−46.8252	−	144.113i	−0.189576	−	0.583454i
$248$	103.515	−	33.6342i	0.417401	−	0.135622i
$249$		0			0
$250$	83.4508	+	114.860i	0.333803	+	0.459441i
$251$	−58.1919	+	179.096i	−0.231840	+	0.713531i	0.765685	+	0.643216i	$0.222400\pi$
$251$	−58.1919	+	179.096i	−0.231840	+	0.713531i	−0.997525	+	0.0703145i	$0.977600\pi$
$252$		0			0
$253$	−51.8974	−	57.4093i	−0.205128	−	0.226914i
$254$	114.210			0.449645
$255$		0			0
$256$	−12.9443	+	9.40456i	−0.0505636	+	0.0367366i
$257$	243.853	+	177.170i	0.948844	+	0.689376i	0.950533	−	0.310623i	$-0.100538\pi$
$257$	243.853	+	177.170i	0.948844	+	0.689376i	−0.00168883	+	0.999999i	$0.500538\pi$
$258$		0			0
$259$	−206.832	+	67.2039i	−0.798581	+	0.259475i
$260$	−30.1071	+	41.4389i	−0.115796	+	0.159380i
$261$		0			0
$262$	−6.35806	+	19.5681i	−0.0242674	+	0.0746874i
$263$			409.440i			1.55681i	0.627764	+	0.778404i	$0.283970\pi$
$263$			409.440i			1.55681i	−0.627764	+	0.778404i	$0.716030\pi$
$264$		0			0
$265$	−88.2765			−0.333119
$266$	490.412	+	159.345i	1.84366	+	0.599040i
$267$		0			0
$268$	−53.5718	−	38.9222i	−0.199895	−	0.145232i
$269$	−60.5446	−	186.337i	−0.225073	−	0.692704i	−0.998284	−	0.0585549i	$-0.981351\pi$
$269$	−60.5446	−	186.337i	−0.225073	−	0.692704i	0.773211	−	0.634149i	$-0.218649\pi$
$270$		0			0
$271$	−64.3416	+	88.5586i	−0.237423	+	0.326784i	−0.911057	−	0.412281i	$-0.864732\pi$
$271$	−64.3416	+	88.5586i	−0.237423	+	0.326784i	0.673634	+	0.739065i	$0.264732\pi$
$272$	−41.0362	−	56.4814i	−0.150868	−	0.207652i
$273$		0			0
$274$			159.551i			0.582302i
$275$	−79.1073	−	16.6514i	−0.287663	−	0.0605504i
$276$		0			0
$277$	−192.491	−	62.5442i	−0.694915	−	0.225791i	−0.0598011	−	0.998210i	$-0.519047\pi$
$277$	−192.491	−	62.5442i	−0.694915	−	0.225791i	−0.635113	+	0.772419i	$0.719047\pi$
$278$	−41.6562	+	30.2650i	−0.149842	+	0.108867i
$279$		0			0
$280$	−53.8630	−	165.773i	−0.192368	−	0.592048i
$281$	206.422	−	67.0706i	0.734598	−	0.238685i	0.0822574	−	0.996611i	$-0.473787\pi$
$281$	206.422	−	67.0706i	0.734598	−	0.238685i	0.652341	+	0.757926i	$0.273787\pi$
$282$		0			0
$283$	106.843	+	147.056i	0.377536	+	0.519633i	0.954930	−	0.296832i	$-0.0959303\pi$
$283$	106.843	+	147.056i	0.377536	+	0.519633i	−0.577394	+	0.816466i	$0.695930\pi$
$284$	53.4020	−	164.354i	0.188035	−	0.578713i
$285$		0			0
$286$	7.45975	+	69.6497i	0.0260830	+	0.243531i
$287$	−162.807			−0.567271
$288$		0			0
$289$	12.6470	−	9.18860i	0.0437613	−	0.0317945i
$290$	−352.898	−	256.396i	−1.21689	−	0.884123i
$291$		0			0
$292$	192.438	−	62.5269i	0.659035	−	0.214133i
$293$	−38.9360	+	53.5908i	−0.132887	+	0.182904i	−0.870275	−	0.492566i	$-0.836059\pi$
$293$	−38.9360	+	53.5908i	−0.132887	+	0.182904i	0.737388	+	0.675470i	$0.236059\pi$
$294$		0			0
$295$	−68.1186	+	209.647i	−0.230910	+	0.710669i
$296$		−	56.7709i		−	0.191793i
$297$		0			0
$298$	386.015			1.29535
$299$	30.1290	+	9.78952i	0.100766	+	0.0327409i
$300$		0			0
$301$	592.287	+	430.322i	1.96773	+	1.42964i
$302$	−17.7448	−	54.6129i	−0.0587576	−	0.180837i
$303$		0			0
$304$	−79.1201	+	108.900i	−0.260264	+	0.358222i
$305$	136.749	+	188.219i	0.448358	+	0.617112i
$306$		0			0
$307$		−	596.201i		−	1.94202i	−0.239034	−	0.971011i	$-0.576831\pi$
$307$		−	596.201i		−	1.94202i	0.239034	−	0.971011i	$-0.423169\pi$
$308$	−206.671	−	118.777i	−0.671010	−	0.385641i
$309$		0			0
$310$	−294.379	−	95.6495i	−0.949610	−	0.308547i
$311$	134.219	−	97.5159i	0.431573	−	0.313556i	−0.350705	−	0.936486i	$-0.614058\pi$
$311$	134.219	−	97.5159i	0.431573	−	0.313556i	0.782277	+	0.622930i	$0.214058\pi$
$312$		0			0
$313$	108.157	+	332.872i	0.345549	+	1.06349i	0.961289	+	0.275541i	$0.0888570\pi$
$313$	108.157	+	332.872i	0.345549	+	1.06349i	−0.615741	+	0.787949i	$0.711143\pi$
$314$	−222.213	+	72.2014i	−0.707685	+	0.229941i
$315$		0			0
$316$	−58.8849	−	81.0481i	−0.186345	−	0.256481i
$317$	23.5247	−	72.4017i	0.0742106	−	0.228397i	−0.907070	−	0.420980i	$-0.861686\pi$
$317$	23.5247	−	72.4017i	0.0742106	−	0.228397i	0.981281	+	0.192583i	$0.0616864\pi$
$318$		0			0
$319$	−593.146	+	63.5281i	−1.85939	+	0.199148i
$320$	45.5011			0.142191
$321$		0			0
$322$	−87.2158	+	63.3660i	−0.270856	+	0.196789i
$323$	−475.176	−	345.235i	−1.47113	−	1.06884i
$324$		0			0
$325$	31.4726	−	10.2261i	0.0968388	−	0.0314648i
$326$	183.647	−	252.768i	0.563333	−	0.775361i
$327$		0			0
$328$	13.1331	−	40.4196i	0.0400400	−	0.123230i
$329$		−	323.734i		−	0.983993i
$330$		0			0
$331$	498.082			1.50478			0.752390	−	0.658718i	$-0.228901\pi$
$331$	498.082			1.50478			0.752390	+	0.658718i	$0.228901\pi$
$332$	27.9373	+	9.07738i	0.0841485	+	0.0273415i
$333$		0			0
$334$	−233.325	−	169.521i	−0.698579	−	0.507547i
$335$	58.1919	+	179.096i	0.173707	+	0.534615i
$336$		0			0
$337$	−165.917	+	228.365i	−0.492335	+	0.677641i	−0.980817	−	0.194933i	$-0.937551\pi$
$337$	−165.917	+	228.365i	−0.492335	+	0.677641i	0.488481	+	0.872574i	$0.337551\pi$
$338$	123.628	+	170.159i	0.365762	+	0.503428i
$339$		0			0
$340$			198.541i			0.583943i
$341$	−386.361	+	172.935i	−1.13302	+	0.507141i
$342$		0			0
$343$	199.900	+	64.9514i	0.582798	+	0.189363i
$344$	−154.613	+	112.333i	−0.449456	+	0.326549i
$345$		0			0
$346$	122.836	+	378.049i	0.355016	+	1.09263i
$347$	−187.789	+	61.0163i	−0.541179	+	0.175840i	−0.566835	−	0.823831i	$-0.691832\pi$
$347$	−187.789	+	61.0163i	−0.541179	+	0.175840i	0.0256566	+	0.999671i	$0.491832\pi$
$348$		0			0
$349$	−125.873	−	173.249i	−0.360667	−	0.496416i	0.589667	−	0.807646i	$-0.299259\pi$
$349$	−125.873	−	173.249i	−0.360667	−	0.496416i	−0.950335	+	0.311230i	$0.899259\pi$
$350$	−34.7990	+	107.100i	−0.0994257	+	0.306001i
$351$		0			0
$352$	46.1601	−	41.7283i	0.131137	−	0.118546i
$353$	610.069			1.72824			0.864120	−	0.503285i	$-0.167876\pi$
$353$	610.069			1.72824			0.864120	+	0.503285i	$0.167876\pi$
$354$		0			0
$355$	−397.589	+	288.865i	−1.11997	+	0.813705i
$356$	131.145	+	95.2828i	0.368386	+	0.267648i
$357$		0			0
$358$	−195.648	+	63.5699i	−0.546503	+	0.177569i
$359$	344.015	−	473.496i	0.958260	−	1.31893i	0.0105005	−	0.999945i	$-0.496658\pi$
$359$	344.015	−	473.496i	0.958260	−	1.31893i	0.947759	−	0.318987i	$-0.103342\pi$
$360$		0			0
$361$	−238.389	+	733.687i	−0.660358	+	2.03237i
$362$		−	318.327i		−	0.879355i
$363$		0			0
$364$	97.5776			0.268070
$365$	−547.259	−	177.815i	−1.49934	−	0.487165i
$366$		0			0
$367$	198.028	+	143.876i	0.539585	+	0.392032i	0.823931	−	0.566690i	$-0.191776\pi$
$367$	198.028	+	143.876i	0.539585	+	0.392032i	−0.284346	+	0.958722i	$0.591776\pi$
$368$	−8.69627	−	26.7644i	−0.0236312	−	0.0727292i
$369$		0			0
$370$	−94.8955	+	130.612i	−0.256474	+	0.353007i
$371$	98.8471	+	136.051i	0.266434	+	0.366715i
$372$		0			0
$373$		−	141.374i		−	0.379017i	−0.981879	−	0.189509i	$-0.939310\pi$
$373$		−	141.374i		−	0.379017i	0.981879	−	0.189509i	$-0.0606895\pi$
$374$	182.078	+	201.416i	0.486841	+	0.538546i
$375$		0			0
$376$	80.3725	+	26.1146i	0.213757	+	0.0694537i
$377$	197.557	−	143.533i	0.524023	−	0.380725i
$378$		0			0
$379$	−1.92262	−	5.91721i	−0.00507287	−	0.0156127i	0.948488	−	0.316813i	$-0.102613\pi$
$379$	−1.92262	−	5.91721i	−0.00507287	−	0.0156127i	−0.953561	+	0.301200i	$0.902613\pi$
$380$	364.063	−	118.291i	0.958060	−	0.311292i
$381$		0			0
$382$	−207.683	−	285.851i	−0.543673	−	0.748301i
$383$	−103.664	+	319.045i	−0.270663	+	0.833014i	0.719672	+	0.694315i	$0.244292\pi$
$383$	−103.664	+	319.045i	−0.270663	+	0.833014i	−0.990334	+	0.138700i	$0.955708\pi$
$384$		0			0
$385$	276.945	+	618.732i	0.719337	+	1.60710i
$386$	9.46166			0.0245121
$387$		0			0
$388$	40.0100	−	29.0690i	0.103119	−	0.0749200i
$389$	−104.105	−	75.6364i	−0.267621	−	0.194438i	0.445879	−	0.895093i	$-0.352891\pi$
$389$	−104.105	−	75.6364i	−0.267621	−	0.194438i	−0.713500	+	0.700655i	$0.752891\pi$
$390$		0			0
$391$	116.784	−	37.9456i	0.298681	−	0.0970475i
$392$	−113.713	+	156.513i	−0.290085	+	0.399268i
$393$		0			0
$394$	112.985	−	347.732i	0.286764	−	0.882570i
$395$			284.896i			0.721257i
$396$		0			0
$397$	−386.412			−0.973331			−0.486666	−	0.873588i	$-0.661787\pi$
$397$	−386.412			−0.973331			−0.486666	+	0.873588i	$0.661787\pi$
$398$	−316.474	−	102.829i	−0.795162	−	0.258364i
$399$		0			0
$400$	−23.7824	−	17.2789i	−0.0594559	−	0.0431973i
$401$	22.4682	+	69.1499i	0.0560303	+	0.172444i	0.975155	−	0.221523i	$-0.0711027\pi$
$401$	22.4682	+	69.1499i	0.0560303	+	0.172444i	−0.919125	+	0.393966i	$0.871103\pi$
$402$		0			0
$403$	101.850	−	140.185i	0.252730	−	0.347852i
$404$	132.921	+	182.950i	0.329013	+	0.452847i
$405$		0			0
$406$			830.983i			2.04676i
$407$	23.5126	+	219.531i	0.0577706	+	0.539389i
$408$		0			0
$409$	376.017	+	122.175i	0.919358	+	0.298718i	0.730203	−	0.683230i	$-0.239425\pi$
$409$	376.017	+	122.175i	0.919358	+	0.298718i	0.189155	+	0.981947i	$0.439425\pi$
$410$	−97.7788	+	71.0404i	−0.238485	+	0.173269i
$411$		0			0
$412$	22.7562	+	70.0363i	0.0552335	+	0.169991i
$413$	399.383	−	129.768i	0.967030	−	0.314207i
$414$		0			0
$415$	−49.1019	−	67.5829i	−0.118318	−	0.162850i
$416$	−7.87129	+	24.2253i	−0.0189214	+	0.0582340i
$417$		0			0
$418$	260.853	−	453.880i	0.624049	−	1.08584i
$419$	−33.9782			−0.0810936			−0.0405468	−	0.999178i	$-0.512910\pi$
$419$	−33.9782			−0.0810936			−0.0405468	+	0.999178i	$0.512910\pi$
$420$		0			0
$421$	−13.4240	+	9.75312i	−0.0318860	+	0.0231665i	−0.603614	−	0.797277i	$-0.706273\pi$
$421$	−13.4240	+	9.75312i	−0.0318860	+	0.0231665i	0.571728	+	0.820443i	$0.306273\pi$
$422$	−36.8017	−	26.7380i	−0.0872078	−	0.0633602i
$423$		0			0
$424$	−41.7508	+	13.5657i	−0.0984689	+	0.0319945i
$425$	75.3953	−	103.773i	0.177401	−	0.244171i
$426$		0			0
$427$	136.958	−	421.515i	0.320746	−	0.987154i
$428$			402.064i			0.939401i
$429$		0			0
$430$	543.487			1.26392
$431$	117.596	+	38.2092i	0.272844	+	0.0886524i	0.442243	−	0.896895i	$-0.354183\pi$
$431$	117.596	+	38.2092i	0.272844	+	0.0886524i	−0.169399	+	0.985548i	$0.554183\pi$
$432$		0			0
$433$	−276.496	−	200.886i	−0.638559	−	0.463941i	0.220796	−	0.975320i	$-0.429135\pi$
$433$	−276.496	−	200.886i	−0.638559	−	0.463941i	−0.859355	+	0.511380i	$0.829135\pi$
$434$	182.215	+	560.799i	0.419849	+	1.29216i
$435$		0			0
$436$	−137.519	+	189.279i	−0.315410	+	0.434125i
$437$	−139.161	−	191.539i	−0.318446	−	0.438304i
$438$		0			0
$439$		−	552.255i		−	1.25798i	−0.777412	−	0.628992i	$-0.783468\pi$
$439$		−	552.255i		−	1.25798i	0.777412	−	0.628992i	$-0.216532\pi$
$440$	−175.951	+	18.8450i	−0.399889	+	0.0428296i
$441$		0			0
$442$	−105.706	−	34.3458i	−0.239153	−	0.0777055i
$443$	4.12842	−	2.99947i	0.00931923	−	0.00677082i	−0.583116	−	0.812389i	$-0.698167\pi$
$443$	4.12842	−	2.99947i	0.00931923	−	0.00677082i	0.592435	+	0.805618i	$0.298167\pi$
$444$		0			0
$445$	−142.456	−	438.433i	−0.320125	−	0.985243i
$446$	−233.093	+	75.7366i	−0.522631	+	0.169813i
$447$		0			0
$448$	−50.9496	−	70.1261i	−0.113727	−	0.156531i
$449$	82.7028	−	254.533i	0.184193	−	0.566888i	−0.815740	−	0.578418i	$-0.803670\pi$
$449$	82.7028	−	254.533i	0.184193	−	0.566888i	0.999934	+	0.0115299i	$0.00367015\pi$
$450$		0			0
$451$	−34.0449	+	161.741i	−0.0754876	+	0.358627i
$452$	−389.928			−0.862672
$453$		0			0
$454$	−2.54760	+	1.85094i	−0.00561145	+	0.00407696i
$455$	−224.496	−	163.106i	−0.493399	−	0.358475i
$456$		0			0
$457$	199.543	−	64.8354i	0.436636	−	0.141872i	−0.0824468	−	0.996595i	$-0.526273\pi$
$457$	199.543	−	64.8354i	0.436636	−	0.141872i	0.519083	+	0.854724i	$0.326273\pi$
$458$	−261.220	+	359.538i	−0.570348	+	0.785017i
$459$		0			0
$460$	−24.7306	+	76.1129i	−0.0537621	+	0.165463i
$461$		−	710.734i		−	1.54172i	−0.637003	−	0.770862i	$-0.719826\pi$
$461$		−	710.734i		−	1.54172i	0.637003	−	0.770862i	$-0.280174\pi$
$462$		0			0
$463$	−546.690			−1.18076			−0.590378	−	0.807127i	$-0.701021\pi$
$463$	−546.690			−1.18076			−0.590378	+	0.807127i	$0.701021\pi$
$464$	−206.306	−	67.0329i	−0.444625	−	0.144467i
$465$		0			0
$466$	−145.523	−	105.729i	−0.312282	−	0.226886i
$467$	98.2195	+	302.289i	0.210320	+	0.647299i	0.999453	+	0.0330761i	$0.0105304\pi$
$467$	98.2195	+	302.289i	0.210320	+	0.647299i	−0.789133	+	0.614223i	$0.789470\pi$
$468$		0			0
$469$	210.862	−	290.227i	0.449600	−	0.618821i
$470$	−141.261	−	194.429i	−0.300555	−	0.413678i
$471$		0			0
$472$			109.622i			0.232250i
$473$	551.358	−	498.423i	1.16566	−	1.05375i
$474$		0			0
$475$	−235.208	−	76.4238i	−0.495175	−	0.160892i
$476$	305.990	−	222.315i	0.642837	−	0.467048i
$477$		0			0
$478$	−69.6167	−	214.258i	−0.145642	−	0.448239i
$479$	7.48699	−	2.43267i	0.0156305	−	0.00507865i	−0.301191	−	0.953564i	$-0.597384\pi$
$479$	7.48699	−	2.43267i	0.0156305	−	0.00507865i	0.316822	+	0.948485i	$0.397384\pi$
$480$		0			0
$481$	−53.1236	−	73.1184i	−0.110444	−	0.152013i
$482$	−115.864	+	356.592i	−0.240381	+	0.739818i
$483$		0			0
$484$	−161.217	+	180.480i	−0.333093	+	0.372893i
$485$	−140.641			−0.289982
$486$		0			0
$487$	−227.941	+	165.609i	−0.468052	+	0.340060i	−0.796682	−	0.604399i	$-0.793413\pi$
$487$	−227.941	+	165.609i	−0.468052	+	0.340060i	0.328630	+	0.944459i	$0.393413\pi$
$488$	93.6003	+	68.0046i	0.191804	+	0.139354i
$489$		0			0
$490$	523.240	−	170.011i	1.06784	−	0.346961i
$491$	−481.751	+	663.073i	−0.981162	+	1.35045i	−0.0449615	+	0.998989i	$0.514317\pi$
$491$	−481.751	+	663.073i	−0.981162	+	1.35045i	−0.936201	+	0.351465i	$0.885683\pi$
$492$		0			0
$493$	292.493	−	900.202i	0.593293	−	1.82597i
$494$			214.295i			0.433795i
$495$		0			0
$496$	−153.927			−0.310336
$497$	890.396	+	289.307i	1.79154	+	0.582107i
$498$		0			0
$499$	−8.08796	−	5.87625i	−0.0162083	−	0.0117761i	0.579652	−	0.814864i	$-0.303189\pi$
$499$	−8.08796	−	5.87625i	−0.0162083	−	0.0117761i	−0.595860	+	0.803088i	$0.703189\pi$
$500$	−62.0454	−	190.956i	−0.124091	−	0.381912i
$501$		0			0
$502$	156.536	−	215.453i	0.311824	−	0.429189i
$503$	−147.116	−	202.488i	−0.292477	−	0.402560i	0.637340	−	0.770583i	$-0.280035\pi$
$503$	−147.116	−	202.488i	−0.292477	−	0.402560i	−0.929817	+	0.368023i	$0.880035\pi$
$504$		0			0
$505$		−	643.097i		−	1.27346i
$506$	44.7131	+	99.8953i	0.0883659	+	0.197422i
$507$		0			0
$508$	−153.612	−	49.9115i	−0.302386	−	0.0982510i
$509$	−18.9127	+	13.7409i	−0.0371566	+	0.0269958i	−0.606209	−	0.795306i	$-0.707310\pi$
$509$	−18.9127	+	13.7409i	−0.0371566	+	0.0269958i	0.569052	+	0.822302i	$0.307310\pi$
$510$		0			0
$511$	338.742	+	1042.54i	0.662900	+	2.04020i
$512$	21.5200	−	6.99226i	0.0420312	−	0.0136568i
$513$		0			0
$514$	−250.556	−	344.860i	−0.487462	−	0.670934i
$515$	64.7144	−	199.170i	0.125659	−	0.386739i
$516$		0			0
$517$	−321.614	−	67.6968i	−0.622077	−	0.130942i
$518$	307.558			0.593742
$519$		0			0
$520$	58.6034	−	42.5779i	0.112699	−	0.0818805i
$521$	424.959	+	308.751i	0.815661	+	0.592612i	0.915466	−	0.402395i	$-0.131822\pi$
$521$	424.959	+	308.751i	0.815661	+	0.592612i	−0.0998053	+	0.995007i	$0.531822\pi$
$522$		0			0
$523$	405.485	−	131.750i	0.775305	−	0.251912i	0.105471	−	0.994422i	$-0.466365\pi$
$523$	405.485	−	131.750i	0.775305	−	0.251912i	0.669835	+	0.742510i	$0.266365\pi$
$524$	17.1031	−	23.5405i	0.0326396	−	0.0449245i
$525$		0			0
$526$	178.932	−	550.696i	0.340175	−	1.04695i
$527$		−	671.649i		−	1.27448i
$528$		0			0
$529$	−479.503			−0.906432
$530$	118.732	+	38.5782i	0.224022	+	0.0727891i
$531$		0			0
$532$	−589.967	−	428.636i	−1.10896	−	0.805707i
$533$	−20.9079	−	64.3480i	−0.0392269	−	0.120728i
$534$		0			0
$535$	672.071	−	925.026i	1.25621	−	1.72902i
$536$	55.0443	+	75.7619i	0.102695	+	0.141347i
$537$		0			0
$538$			277.082i			0.515022i
$539$	374.904	−	652.328i	0.695555	−	1.21026i
$540$		0			0
$541$	544.329	+	176.863i	1.00615	+	0.326919i	0.765322	−	0.643648i	$-0.222580\pi$
$541$	544.329	+	176.863i	1.00615	+	0.326919i	0.240831	+	0.970567i	$0.422580\pi$
$542$	125.241	−	90.9927i	0.231071	−	0.167883i
$543$		0			0
$544$	30.5102	+	93.9008i	0.0560850	+	0.172612i
$545$	632.779	−	205.602i	1.16106	−	0.377252i
$546$		0			0
$547$	104.694	+	144.098i	0.191396	+	0.263434i	0.893921	−	0.448225i	$-0.147944\pi$
$547$	104.694	+	144.098i	0.191396	+	0.263434i	−0.702524	+	0.711660i	$0.747944\pi$
$548$	69.7262	−	214.595i	0.127238	−	0.391597i
$549$		0			0
$550$	99.1221	+	56.9672i	0.180222	+	0.103577i
$551$	−1824.96			−3.31209
$552$		0			0
$553$	439.081	−	319.011i	0.793999	−	0.576874i
$554$	231.567	+	168.244i	0.417992	+	0.303689i
$555$		0			0
$556$	69.2537	−	22.5019i	0.124557	−	0.0404710i
$557$	−237.768	+	327.260i	−0.426873	+	0.587540i	−0.967232	−	0.253895i	$-0.918288\pi$
$557$	−237.768	+	327.260i	−0.426873	+	0.587540i	0.540359	+	0.841434i	$0.318288\pi$
$558$		0			0
$559$	−94.0186	+	289.359i	−0.168191	+	0.517637i
$560$			246.504i			0.440185i
$561$		0			0
$562$	−306.948			−0.546171
$563$	−968.783	−	314.777i	−1.72075	−	0.559106i	−0.728687	−	0.684846i	$-0.759869\pi$
$563$	−968.783	−	314.777i	−1.72075	−	0.559106i	−0.992063	+	0.125741i	$0.959869\pi$
$564$		0			0
$565$	897.105	+	651.785i	1.58780	+	1.15360i
$566$	−79.4371	−	244.482i	−0.140348	−	0.431947i
$567$		0			0
$568$	−143.651	+	197.719i	−0.252907	+	0.348096i
$569$	−433.829	−	597.114i	−0.762441	−	1.04941i	−0.997007	−	0.0773095i	$-0.975367\pi$
$569$	−433.829	−	597.114i	−0.762441	−	1.04941i	0.234566	−	0.972100i	$-0.424633\pi$
$570$		0			0
$571$			650.748i			1.13966i	0.821762	+	0.569832i	$0.192992\pi$
$571$			650.748i			1.13966i	−0.821762	+	0.569832i	$0.807008\pi$
$572$	20.4047	−	96.9387i	0.0356726	−	0.169473i
$573$		0			0
$574$	218.974	+	71.1491i	0.381489	+	0.123953i
$575$	41.8298	−	30.3911i	0.0727475	−	0.0528541i
$576$		0			0
$577$	−256.196	−	788.492i	−0.444015	−	1.36654i	−0.883561	−	0.468317i	$-0.844861\pi$
$577$	−256.196	−	788.492i	−0.444015	−	1.36654i	0.439546	−	0.898220i	$-0.355139\pi$
$578$	−21.0258	+	6.83169i	−0.0363768	+	0.0118195i
$579$		0			0
$580$	362.598	+	499.074i	0.625169	+	0.860472i
$581$	−49.1770	+	151.351i	−0.0846420	+	0.260501i
$582$		0			0
$583$	155.831	−	69.7498i	0.267291	−	0.119639i
$584$	−286.154			−0.489990
$585$		0			0
$586$	75.7888	−	55.0638i	0.129332	−	0.0939655i
$587$	600.701	+	436.435i	1.02334	+	0.743501i	0.966965	−	0.254908i	$-0.0820453\pi$
$587$	600.701	+	436.435i	1.02334	+	0.743501i	0.0563763	+	0.998410i	$0.482045\pi$
$588$		0			0
$589$	−1231.60	+	400.170i	−2.09100	+	0.679406i
$590$	183.239	−	252.206i	0.310574	−	0.427468i
$591$		0			0
$592$	−24.8098	+	76.3566i	−0.0419084	+	0.128981i
$593$			360.480i			0.607891i	0.952689	+	0.303946i	$0.0983041\pi$
$593$			360.480i			0.607891i	−0.952689	+	0.303946i	$0.901696\pi$
$594$		0			0
$595$	−1075.60			−1.80773
$596$	−519.189	−	168.695i	−0.871122	−	0.283045i
$597$		0			0
$598$	−36.2453	−	26.3338i	−0.0606109	−	0.0440364i
$599$	90.2125	+	277.646i	0.150605	+	0.463515i	0.997689	−	0.0679440i	$-0.0216439\pi$
$599$	90.2125	+	277.646i	0.150605	+	0.463515i	−0.847084	+	0.531459i	$0.821644\pi$
$600$		0			0
$601$	−473.815	+	652.151i	−0.788378	+	1.08511i	0.205930	+	0.978567i	$0.433978\pi$
$601$	−473.815	+	652.151i	−0.788378	+	1.08511i	−0.994308	+	0.106543i	$0.966022\pi$
$602$	−608.567	−	837.620i	−1.01091	−	1.39140i
$603$		0			0
$604$			81.2089i			0.134452i
$605$	672.593	−	145.746i	1.11172	−	0.240903i
$606$		0			0
$607$	−136.092	−	44.2190i	−0.224204	−	0.0728484i	0.194761	−	0.980851i	$-0.437607\pi$
$607$	−136.092	−	44.2190i	−0.224204	−	0.0728484i	−0.418965	+	0.908002i	$0.637607\pi$
$608$	154.007	−	111.893i	0.253301	−	0.184034i
$609$		0			0
$610$	−101.672	−	312.916i	−0.166676	−	0.512977i
$611$	127.953	−	41.5745i	0.209416	−	0.0680434i
$612$		0			0
$613$	−235.002	−	323.452i	−0.383363	−	0.527654i	0.573108	−	0.819480i	$-0.305737\pi$
$613$	−235.002	−	323.452i	−0.383363	−	0.527654i	−0.956472	+	0.291825i	$0.905737\pi$
$614$	−260.549	+	801.888i	−0.424347	+	1.30601i
$615$		0			0
$616$	226.064	+	250.074i	0.366988	+	0.405964i
$617$	366.869			0.594602			0.297301	−	0.954784i	$-0.403914\pi$
$617$	366.869			0.594602			0.297301	+	0.954784i	$0.403914\pi$
$618$		0			0
$619$	677.581	−	492.291i	1.09464	−	0.795301i	0.114461	−	0.993428i	$-0.463486\pi$
$619$	677.581	−	492.291i	1.09464	−	0.795301i	0.980176	+	0.198127i	$0.0634858\pi$
$620$	354.138	+	257.297i	0.571191	+	0.414995i
$621$		0			0
$622$	−223.140	+	72.5027i	−0.358746	+	0.116564i
$623$	−516.198	+	710.485i	−0.828568	+	1.14043i
$624$		0			0
$625$	−233.221	+	717.780i	−0.373154	+	1.14845i
$626$		−	494.979i		−	0.790701i
$627$		0			0
$628$	330.429			0.526161
$629$	−333.177	−	108.256i	−0.529693	−	0.172108i
$630$		0			0
$631$	−359.387	−	261.110i	−0.569551	−	0.413803i	0.265391	−	0.964141i	$-0.414499\pi$
$631$	−359.387	−	261.110i	−0.569551	−	0.413803i	−0.834942	+	0.550338i	$0.814499\pi$
$632$	43.7807	+	134.743i	0.0692733	+	0.213201i
$633$		0			0
$634$	−63.2814	+	87.0994i	−0.0998130	+	0.137381i
$635$	269.984	+	371.602i	0.425172	+	0.585199i
$636$		0			0
$637$			307.990i			0.483501i
$638$	825.542	+	173.769i	1.29395	+	0.272365i
$639$		0			0
$640$	−61.1988	−	19.8847i	−0.0956231	−	0.0310698i
$641$	908.387	−	659.982i	1.41714	−	1.02961i	0.424906	−	0.905238i	$-0.360307\pi$
$641$	908.387	−	659.982i	1.41714	−	1.02961i	0.992235	−	0.124376i	$-0.0396928\pi$
$642$		0			0
$643$	238.694	+	734.624i	0.371219	+	1.14249i	0.945994	+	0.324183i	$0.105089\pi$
$643$	238.694	+	734.624i	0.371219	+	1.14249i	−0.574776	+	0.818311i	$0.694911\pi$
$644$	144.997	−	47.1123i	0.225150	−	0.0731558i
$645$		0			0
$646$	488.236	+	672.000i	0.755784	+	1.04025i
$647$	−115.544	+	355.609i	−0.178585	+	0.549627i	−0.999779	−	0.0210213i	$-0.993308\pi$
$647$	−115.544	+	355.609i	−0.178585	+	0.549627i	0.821194	+	0.570649i	$0.193308\pi$
$648$		0			0
$649$	−45.4017	−	423.904i	−0.0699565	−	0.653165i
$650$	−46.7995			−0.0719992
$651$		0			0
$652$	−357.468	+	259.715i	−0.548263	+	0.398336i
$653$	−199.717	−	145.103i	−0.305845	−	0.222209i	0.424267	−	0.905537i	$-0.360532\pi$
$653$	−199.717	−	145.103i	−0.305845	−	0.222209i	−0.730112	+	0.683328i	$0.760532\pi$
$654$		0			0
$655$	−78.6982	+	25.5706i	−0.120150	+	0.0390391i
$656$	−35.3280	+	48.6248i	−0.0538537	+	0.0741232i
$657$		0			0
$658$	−141.477	+	435.421i	−0.215010	+	0.661734i
$659$			609.418i			0.924762i	0.886681	+	0.462381i	$0.153005\pi$
$659$			609.418i			0.924762i	−0.886681	+	0.462381i	$0.846995\pi$
$660$		0			0
$661$	1129.61			1.70893			0.854467	−	0.519506i	$-0.173884\pi$
$661$	1129.61			1.70893			0.854467	+	0.519506i	$0.173884\pi$
$662$	−669.919	−	217.670i	−1.01196	−	0.328806i
$663$		0			0
$664$	−33.6086	−	24.4181i	−0.0506154	−	0.0367742i
$665$	640.846	+	1972.32i	0.963679	+	2.96590i
$666$		0			0
$667$	224.261	−	308.669i	0.336224	−	0.462773i
$668$	239.739	+	329.972i	0.358890	+	0.493970i
$669$		0			0
$670$		−	266.315i		−	0.397484i
$671$	−390.115	−	224.206i	−0.581393	−	0.334137i
$672$		0			0
$673$	415.483	+	134.999i	0.617359	+	0.200592i	0.600967	−	0.799274i	$-0.294782\pi$
$673$	415.483	+	134.999i	0.617359	+	0.200592i	0.0163917	+	0.999866i	$0.494782\pi$
$674$	322.957	−	234.642i	0.479165	−	0.348134i
$675$		0			0
$676$	−91.9166	−	282.890i	−0.135971	−	0.418477i
$677$	−455.564	+	148.022i	−0.672915	+	0.218643i	−0.625491	−	0.780231i	$-0.715101\pi$
$677$	−455.564	+	148.022i	−0.672915	+	0.218643i	−0.0474244	+	0.998875i	$0.515101\pi$
$678$		0			0
$679$	157.482	+	216.756i	0.231933	+	0.319228i
$680$	86.7655	−	267.037i	0.127596	−	0.392701i
$681$		0			0
$682$	595.230	−	63.7514i	0.872771	−	0.0934771i
$683$	614.419			0.899588			0.449794	−	0.893132i	$-0.351497\pi$
$683$	614.419			0.899588			0.449794	+	0.893132i	$0.351497\pi$
$684$		0			0
$685$	−519.126	+	377.167i	−0.757848	+	0.550609i
$686$	−240.480	−	174.719i	−0.350554	−	0.254692i
$687$		0			0
$688$	257.045	−	83.5189i	0.373612	−	0.121394i
$689$	−41.0791	+	56.5405i	−0.0596213	+	0.0820617i
$690$		0			0
$691$	−296.082	+	911.247i	−0.428484	+	1.31874i	0.471135	+	0.882061i	$0.343844\pi$
$691$	−296.082	+	911.247i	−0.428484	+	1.31874i	−0.899619	+	0.436676i	$0.856156\pi$
$692$		−	562.156i		−	0.812365i
$693$		0			0
$694$	279.241			0.402364
$695$	−196.945	−	63.9912i	−0.283374	−	0.0920737i
$696$		0			0
$697$	−212.171	−	154.151i	−0.304406	−	0.221164i
$698$	93.5860	+	288.028i	0.134077	+	0.412648i
$699$		0			0
$700$	93.6091	−	128.842i	0.133727	−	0.184060i
$701$	−113.833	−	156.678i	−0.162387	−	0.223507i	0.720068	−	0.693904i	$-0.244111\pi$
$701$	−113.833	−	156.678i	−0.162387	−	0.223507i	−0.882455	+	0.470397i	$0.844111\pi$
$702$		0			0
$703$			675.443i			0.960801i
$704$	−80.3211	+	35.9517i	−0.114092	+	0.0510678i
$705$		0			0
$706$	−820.541	−	266.610i	−1.16224	−	0.377634i
$707$	−991.139	+	720.105i	−1.40189	+	1.01854i
$708$		0			0
$709$	9.14132	+	28.1341i	0.0128933	+	0.0396814i	0.957296	−	0.289109i	$-0.0933590\pi$
$709$	9.14132	+	28.1341i	0.0128933	+	0.0396814i	−0.944403	+	0.328790i	$0.893359\pi$
$710$	660.995	−	214.770i	0.930978	−	0.302493i
$711$		0			0
$712$	−134.750	−	185.468i	−0.189256	−	0.260488i
$713$	83.6617	−	257.484i	0.117338	−	0.361128i
$714$		0			0
$715$	−208.983	+	188.919i	−0.292284	+	0.264222i
$716$	290.927			0.406323
$717$		0			0
$718$	−669.625	+	486.511i	−0.932625	+	0.677592i
$719$	24.8732	+	18.0715i	0.0345942	+	0.0251341i	0.604948	−	0.796265i	$-0.293194\pi$
$719$	24.8732	+	18.0715i	0.0345942	+	0.0251341i	−0.570354	+	0.821399i	$0.693194\pi$
$720$		0			0
$721$	−379.424	+	123.282i	−0.526247	+	0.170988i
$722$	641.266	−	882.627i	0.888180	−	1.22247i
$723$		0			0
$724$	−139.114	+	428.148i	−0.192146	+	0.591365i
$725$		−	398.550i		−	0.549725i
$726$		0			0
$727$	252.046			0.346694			0.173347	−	0.984861i	$-0.444542\pi$
$727$	252.046			0.346694			0.173347	+	0.984861i	$0.444542\pi$
$728$	−131.242	−	42.6430i	−0.180277	−	0.0585755i
$729$		0			0
$730$	658.353	+	478.322i	0.901854	+	0.655235i
$731$	364.429	+	1121.60i	0.498535	+	1.53433i
$732$		0			0
$733$	−532.114	+	732.392i	−0.725940	+	0.999171i	0.273366	+	0.961910i	$0.411863\pi$
$733$	−532.114	+	732.392i	−0.725940	+	0.999171i	−0.999306	+	0.0372605i	$0.988137\pi$
$734$	−203.471	−	280.054i	−0.277208	−	0.381544i
$735$		0			0
$736$			39.7984i			0.0540739i
$737$	−244.233	−	270.172i	−0.331388	−	0.366583i
$738$		0			0
$739$	−239.639	−	77.8633i	−0.324274	−	0.105363i	0.142356	−	0.989815i	$-0.454532\pi$
$739$	−239.639	−	77.8633i	−0.324274	−	0.105363i	−0.466630	+	0.884452i	$0.654532\pi$
$740$	184.714	−	134.203i	0.249613	−	0.181355i
$741$		0			0
$742$	−73.4924	−	226.186i	−0.0990464	−	0.304833i
$743$	531.450	−	172.678i	0.715275	−	0.232407i	0.0713018	−	0.997455i	$-0.477285\pi$
$743$	531.450	−	172.678i	0.715275	−	0.232407i	0.643974	+	0.765048i	$0.277285\pi$
$744$		0			0
$745$	912.513	+	1255.97i	1.22485	+	1.68586i
$746$	−61.7825	+	190.147i	−0.0828184	+	0.254889i
$747$		0			0
$748$	−156.873	−	350.476i	−0.209723	−	0.468550i
$749$	−2178.19			−2.90814
$750$		0			0
$751$	739.744	−	537.456i	0.985012	−	0.715653i	0.0261890	−	0.999657i	$-0.491663\pi$
$751$	739.744	−	537.456i	0.985012	−	0.715653i	0.958823	+	0.284004i	$0.0916628\pi$
$752$	−96.6883	−	70.2481i	−0.128575	−	0.0934151i
$753$		0			0
$754$	−328.440	+	106.716i	−0.435596	+	0.141534i
$755$	135.745	−	186.837i	0.179795	−	0.247466i
$756$		0			0
$757$	−77.6831	+	239.084i	−0.102620	+	0.315831i	−0.989164	−	0.146812i	$-0.953099\pi$
$757$	−77.6831	+	239.084i	−0.102620	+	0.315831i	0.886545	+	0.462643i	$0.153099\pi$
$758$			8.79885i			0.0116080i
$759$		0			0
$760$	−541.358			−0.712314
$761$	−589.527	−	191.549i	−0.774675	−	0.251707i	−0.105110	−	0.994461i	$-0.533519\pi$
$761$	−589.527	−	191.549i	−0.774675	−	0.251707i	−0.669565	+	0.742754i	$0.733519\pi$
$762$		0			0
$763$	−1025.42	−	745.014i	−1.34394	−	0.976427i
$764$	154.411	+	475.230i	0.202109	+	0.622028i
$765$		0			0
$766$	278.855	−	383.811i	0.364041	−	0.501059i
$767$	102.579	+	141.188i	0.133741	+	0.184078i
$768$		0			0
$769$		−	298.190i		−	0.387763i	−0.981025	−	0.193882i	$-0.937892\pi$
$769$		−	298.190i		−	0.387763i	0.981025	−	0.193882i	$-0.0621078\pi$
$770$	−102.094	−	953.222i	−0.132589	−	1.23795i
$771$		0			0
$772$	−12.7259	−	4.13490i	−0.0164843	−	0.00535609i
$773$	−490.878	+	356.643i	−0.635029	+	0.461376i	−0.858139	−	0.513418i	$-0.828379\pi$
$773$	−490.878	+	356.643i	−0.635029	+	0.461376i	0.223110	+	0.974793i	$0.428379\pi$
$774$		0			0
$775$	−87.3925	−	268.966i	−0.112764	−	0.347053i
$776$	−66.5169	+	21.6127i	−0.0857177	+	0.0278514i
$777$		0			0
$778$	106.966	+	147.226i	0.137488	+	0.189237i
$779$	−156.254	+	480.900i	−0.200583	+	0.617330i
$780$		0			0
$781$	473.606	−	824.068i	0.606410	−	1.05514i
$782$	−173.658			−0.222068
$783$		0			0
$784$	221.343	−	160.815i	0.282325	−	0.205121i
$785$	−760.217	−	552.330i	−0.968429	−	0.703605i
$786$		0			0
$787$	56.8552	−	18.4734i	0.0722430	−	0.0234732i	−0.272673	−	0.962107i	$-0.587908\pi$
$787$	56.8552	−	18.4734i	0.0722430	−	0.0234732i	0.344916	+	0.938634i	$0.387908\pi$
$788$	−303.929	+	418.323i	−0.385697	+	0.530867i
$789$		0			0
$790$	124.504	−	383.185i	0.157600	−	0.485044i
$791$		−	2112.45i		−	2.67060i
$792$		0			0
$793$	184.189			0.232268
$794$	519.724	+	168.868i	0.654564	+	0.212681i
$795$		0			0
$796$	380.719	+	276.609i	0.478291	+	0.347499i
$797$	281.843	+	867.424i	0.353630	+	1.08836i	0.956800	+	0.290748i	$0.0939041\pi$
$797$	281.843	+	867.424i	0.353630	+	1.08836i	−0.603170	+	0.797613i	$0.706096\pi$
$798$		0			0
$799$	306.523	−	421.893i	0.383633	−	0.528026i
$800$	24.4361	+	33.6334i	0.0305451	+	0.0420417i
$801$		0			0
$802$		−	102.825i		−	0.128211i
$803$	1106.55	−	118.516i	1.37802	−	0.147591i
$804$		0			0
$805$	−412.344	−	133.979i	−0.512229	−	0.166433i
$806$	−198.251	+	144.038i	−0.245969	+	0.178707i
$807$		0			0
$808$	−98.8263	−	304.156i	−0.122310	−	0.376431i
$809$	892.191	−	289.890i	1.10283	−	0.358332i	0.299640	−	0.954052i	$-0.403133\pi$
$809$	892.191	−	289.890i	1.10283	−	0.358332i	0.803192	+	0.595721i	$0.203133\pi$
$810$		0			0
$811$	224.757	+	309.351i	0.277136	+	0.381444i	0.924782	−	0.380496i	$-0.124247\pi$
$811$	224.757	+	309.351i	0.277136	+	0.381444i	−0.647647	+	0.761941i	$0.724247\pi$
$812$	363.153	−	1117.67i	0.447233	−	1.37644i
$813$		0			0
$814$	64.3143	−	305.544i	0.0790102	−	0.375362i
$815$	1256.55			1.54178
$816$		0			0
$817$	1839.54	−	1336.50i	2.25158	−	1.63587i
$818$	−452.350	−	328.651i	−0.552995	−	0.401774i
$819$		0			0
$820$	162.558	−	52.8183i	0.198241	−	0.0644125i
$821$	367.969	−	506.465i	0.448196	−	0.616888i	−0.523813	−	0.851833i	$-0.675491\pi$
$821$	367.969	−	506.465i	0.448196	−	0.616888i	0.972009	+	0.234945i	$0.0754909\pi$
$822$		0			0
$823$	13.2495	−	40.7778i	0.0160990	−	0.0495478i	−0.942684	−	0.333686i	$-0.891707\pi$
$823$	13.2495	−	40.7778i	0.0160990	−	0.0495478i	0.958783	+	0.284138i	$0.0917075\pi$
$824$		−	104.143i		−	0.126388i
$825$		0			0
$826$	−593.880			−0.718983
$827$	−1030.89	−	334.955i	−1.24654	−	0.405025i	−0.389859	−	0.920875i	$-0.627476\pi$
$827$	−1030.89	−	334.955i	−1.24654	−	0.405025i	−0.856679	+	0.515850i	$0.827476\pi$
$828$		0			0
$829$	1140.35	+	828.512i	1.37557	+	0.999412i	0.997279	+	0.0737262i	$0.0234891\pi$
$829$	1140.35	+	828.512i	1.37557	+	0.999412i	0.378294	+	0.925686i	$0.376511\pi$
$830$	36.5071	+	112.357i	0.0439844	+	0.135370i
$831$		0			0
$832$	21.1737	−	29.1431i	0.0254492	−	0.0350278i
$833$	701.706	+	965.815i	0.842384	+	1.15944i
$834$		0			0
$835$		−	1159.90i		−	1.38910i
$836$	−549.199	+	496.471i	−0.656937	+	0.593865i
$837$		0			0
$838$	45.7006	+	14.8490i	0.0545353	+	0.0177196i
$839$	719.538	−	522.775i	0.857614	−	0.623093i	−0.0696206	−	0.997574i	$-0.522179\pi$
$839$	719.538	−	522.775i	0.857614	−	0.623093i	0.927235	+	0.374480i	$0.122179\pi$
$840$		0			0
$841$	−648.927	−	1997.19i	−0.771614	−	2.37478i
$842$	22.3175	−	7.25140i	0.0265054	−	0.00861212i
$843$		0			0
$844$	37.8132	+	52.0454i	0.0448024	+	0.0616652i
$845$	−261.394	+	804.488i	−0.309342	+	0.952057i
$846$		0			0
$847$	−977.757	−	873.400i	−1.15438	−	1.03117i
$848$	62.0831			0.0732112
$849$		0			0
$850$	−146.757	+	106.625i	−0.172655	+	0.125441i
$851$	−114.243	−	83.0022i	−0.134245	−	0.0975349i
$852$		0			0
$853$	−1386.20	+	450.405i	−1.62509	+	0.528025i	−0.973136	−	0.230232i	$-0.926052\pi$
$853$	−1386.20	+	450.405i	−1.62509	+	0.528025i	−0.651957	+	0.758256i	$0.726052\pi$
$854$	−368.417	+	507.083i	−0.431402	+	0.593774i
$855$		0			0
$856$	175.708	−	540.775i	0.205267	−	0.631746i
$857$			731.392i			0.853433i	0.904385	+	0.426716i	$0.140330\pi$
$857$			731.392i			0.853433i	−0.904385	+	0.426716i	$0.859670\pi$
$858$		0			0
$859$	85.1091			0.0990792			0.0495396	−	0.998772i	$-0.484225\pi$
$859$	85.1091			0.0990792			0.0495396	+	0.998772i	$0.484225\pi$
$860$	−730.988	−	237.513i	−0.849986	−	0.276177i
$861$		0			0
$862$	−141.468	−	102.783i	−0.164116	−	0.119237i
$863$	183.125	+	563.602i	0.212196	+	0.653073i	0.999341	+	0.0363044i	$0.0115586\pi$
$863$	183.125	+	563.602i	0.212196	+	0.653073i	−0.787144	+	0.616769i	$0.788441\pi$
$864$		0			0
$865$	−939.674	+	1293.35i	−1.08633	+	1.49520i
$866$	284.096	+	391.025i	0.328056	+	0.451530i
$867$		0			0
$868$		−	833.903i		−	0.960718i
$869$	−225.105	−	502.915i	−0.259039	−	0.578729i
$870$		0			0
$871$	141.789	+	46.0701i	0.162789	+	0.0528934i
$872$	267.680	−	194.481i	0.306973	−	0.223029i
$873$		0			0
$874$	103.466	+	318.435i	0.118382	+	0.364342i
$875$	1034.51	−	336.133i	1.18230	−	0.384152i
$876$		0			0
$877$	−476.604	−	655.989i	−0.543448	−	0.747992i	0.445657	−	0.895204i	$-0.352970\pi$
$877$	−476.604	−	655.989i	−0.543448	−	0.747992i	−0.989105	+	0.147212i	$0.952970\pi$
$878$	−241.344	+	742.781i	−0.274880	+	0.845992i
$879$		0			0
$880$	244.890	+	51.5470i	0.278284	+	0.0585761i
$881$	−162.880			−0.184881			−0.0924404	−	0.995718i	$-0.529467\pi$
$881$	−162.880			−0.184881			−0.0924404	+	0.995718i	$0.529467\pi$
$882$		0			0
$883$	−697.072	+	506.452i	−0.789436	+	0.573559i	−0.907796	−	0.419412i	$-0.862236\pi$
$883$	−697.072	+	506.452i	−0.789436	+	0.573559i	0.118360	+	0.992971i	$0.462236\pi$
$884$	127.164	+	92.3901i	0.143851	+	0.104514i
$885$		0			0
$886$	−6.86353	+	2.23010i	−0.00774665	+	0.00251704i
$887$	−14.7932	+	20.3611i	−0.0166778	+	0.0229551i	−0.817274	−	0.576249i	$-0.804516\pi$
$887$	−14.7932	+	20.3611i	−0.0166778	+	0.0229551i	0.800597	+	0.599204i	$0.204516\pi$
$888$		0			0
$889$	270.397	−	832.198i	0.304159	−	0.936105i
$890$			651.947i			0.732524i
$891$		0			0
$892$	346.608			0.388574
$893$	−956.249	−	310.704i	−1.07083	−	0.347933i
$894$		0			0
$895$	−669.334	−	486.300i	−0.747859	−	0.543352i
$896$	37.8808	+	116.585i	0.0422777	+	0.130117i
$897$		0			0
$898$	−222.470	+	306.204i	−0.247739	+	0.340984i
$899$	−1226.64	−	1688.33i	−1.36445	−	1.87801i
$900$		0			0
$901$			270.895i			0.300661i
$902$	116.474	−	202.662i	0.129128	−	0.224681i
$903$		0			0
$904$	524.451	+	170.405i	0.580145	+	0.188501i
$905$	1035.73	−	752.503i	1.14445	−	0.831495i
$906$		0			0
$907$	224.068	+	689.610i	0.247043	+	0.760319i	0.995294	+	0.0969036i	$0.0308938\pi$
$907$	224.068	+	689.610i	0.247043	+	0.760319i	−0.748251	+	0.663416i	$0.769106\pi$
$908$	4.23540	−	1.37617i	0.00466454	−	0.00151560i
$909$		0			0
$910$	230.667	+	317.486i	0.253480	+	0.348886i
$911$	−264.290	+	813.400i	−0.290109	+	0.892865i	0.694711	+	0.719289i	$0.255532\pi$
$911$	−264.290	+	813.400i	−0.290109	+	0.892865i	−0.984820	+	0.173576i	$0.944468\pi$
$912$		0			0
$913$	140.077	+	80.5045i	0.153425	+	0.0881757i
$914$	−296.719			−0.324637
$915$		0			0
$916$	508.463	−	369.420i	0.555091	−	0.403297i
$917$	127.531	+	92.6569i	0.139074	+	0.101043i
$918$		0			0
$919$	1362.32	−	442.644i	1.48239	−	0.481658i	0.547564	−	0.836764i	$-0.315555\pi$
$919$	1362.32	−	442.644i	1.48239	−	0.481658i	0.934826	+	0.355106i	$0.115555\pi$
$920$	66.5251	−	91.5640i	0.0723099	−	0.0995261i
$921$		0			0
$922$	−310.602	+	955.936i	−0.336879	+	1.03681i
$923$			389.075i			0.421533i
$924$		0			0
$925$	−147.509			−0.159469
$926$	735.296	+	238.912i	0.794057	+	0.258005i
$927$		0			0
$928$	248.186	+	180.318i	0.267442	+	0.194308i
$929$	−468.925	−	1443.20i	−0.504763	−	1.55350i	−0.801168	−	0.598440i	$-0.795788\pi$
$929$	−468.925	−	1443.20i	−0.504763	−	1.55350i	0.296404	−	0.955063i	$-0.404212\pi$
$930$		0			0
$931$	1352.93	−	1862.15i	1.45320	−	2.00016i
$932$	149.523	+	205.801i	0.160433	+	0.220817i
$933$		0			0
$934$		−	449.501i		−	0.481264i
$935$	−224.922	+	1068.56i	−0.240558	+	1.14284i
$936$		0			0
$937$	−178.500	−	57.9983i	−0.190502	−	0.0618978i	0.212212	−	0.977224i	$-0.431933\pi$
$937$	−178.500	−	57.9983i	−0.190502	−	0.0618978i	−0.402714	+	0.915326i	$0.631933\pi$
$938$	−410.443	+	298.204i	−0.437573	+	0.317915i
$939$		0			0
$940$	105.027	+	323.239i	0.111731	+	0.343871i
$941$	−419.370	+	136.262i	−0.445664	+	0.144805i	−0.523248	−	0.852181i	$-0.675280\pi$
$941$	−419.370	+	136.262i	−0.445664	+	0.144805i	0.0775831	+	0.996986i	$0.475280\pi$
$942$		0			0
$943$	−62.1369	−	85.5241i	−0.0658928	−	0.0906936i
$944$	47.9065	−	147.441i	0.0507484	−	0.156187i
$945$		0			0
$946$	−959.394	+	429.425i	−1.01416	+	0.453938i
$947$	−744.379			−0.786039			−0.393019	−	0.919530i	$-0.628569\pi$
$947$	−744.379			−0.786039			−0.393019	+	0.919530i	$0.628569\pi$
$948$		0			0
$949$	−368.554	+	267.770i	−0.388360	+	0.282160i
$950$	282.956	+	205.579i	0.297848	+	0.216399i
$951$		0			0
$952$	−508.711	+	165.290i	−0.534360	+	0.173624i
$953$	−235.027	+	323.487i	−0.246618	+	0.339440i	−0.914323	−	0.404985i	$-0.867277\pi$
$953$	−235.027	+	323.487i	−0.246618	+	0.339440i	0.667705	+	0.744426i	$0.267277\pi$
$954$		0			0
$955$	439.118	−	1351.47i	0.459809	−	1.41515i
$956$			318.600i			0.333264i
$957$		0			0
$958$	−11.1331			−0.0116212
$959$	1162.58	+	377.744i	1.21228	+	0.393894i
$960$		0			0
$961$	−420.559	−	305.554i	−0.437626	−	0.317954i
$962$	39.4972	+	121.560i	0.0410574	+	0.126362i
$963$		0			0
$964$	311.673	−	428.981i	0.323312	−	0.445001i
$965$	22.3667	+	30.7852i	0.0231780	+	0.0319017i
$966$		0			0
$967$			1646.99i			1.70320i	0.524196	+	0.851598i	$0.324366\pi$
$967$			1646.99i			1.70320i	−0.524196	+	0.851598i	$0.675634\pi$
$968$	295.709	−	172.291i	0.305485	−	0.177986i
$969$		0			0
$970$	189.162	+	61.4624i	0.195012	+	0.0633633i
$971$	535.994	−	389.423i	0.552003	−	0.401053i	−0.276521	−	0.961008i	$-0.589181\pi$
$971$	535.994	−	389.423i	0.552003	−	0.401053i	0.828523	+	0.559955i	$0.189181\pi$
$972$		0			0
$973$	121.905	+	375.184i	0.125288	+	0.385595i
$974$	378.954	−	123.130i	0.389070	−	0.126417i
$975$		0			0
$976$	−96.1730	−	132.371i	−0.0985379	−	0.135626i
$977$	−459.564	+	1414.39i	−0.470382	+	1.44769i	0.381703	+	0.924285i	$0.375338\pi$
$977$	−459.564	+	1414.39i	−0.470382	+	1.44769i	−0.852085	+	0.523403i	$0.824662\pi$
$978$		0			0
$979$	597.890	+	661.389i	0.610715	+	0.675576i
$980$	−778.054			−0.793933
$981$		0			0
$982$	937.727	−	681.298i	0.954915	−	0.693787i
$983$	303.127	+	220.235i	0.308369	+	0.224043i	0.731196	−	0.682167i	$-0.238962\pi$
$983$	303.127	+	220.235i	0.308369	+	0.224043i	−0.422827	+	0.906210i	$0.638962\pi$
$984$		0			0
$985$	1398.50	−	454.399i	1.41979	−	0.461319i
$986$	−786.805	+	1082.94i	−0.797977	+	1.09832i
$987$		0			0
$988$	93.6503	−	288.226i	0.0947878	−	0.291727i
$989$			475.371i			0.480659i
$990$		0			0
$991$	−455.590			−0.459727			−0.229864	−	0.973223i	$-0.573828\pi$
$991$	−455.590			−0.459727			−0.229864	+	0.973223i	$0.573828\pi$
$992$	207.031	+	67.2684i	0.208701	+	0.0678109i
$993$		0			0
$994$	−1071.15	−	778.235i	−1.07761	−	0.782932i
$995$	−413.553	−	1272.79i	−0.415631	−	1.27918i
$996$		0			0
$997$	−265.340	+	365.209i	−0.266138	+	0.366307i	−0.921081	−	0.389371i	$-0.872693\pi$
$997$	−265.340	+	365.209i	−0.266138	+	0.366307i	0.654943	+	0.755678i	$0.272693\pi$
$998$	8.31027	+	11.4381i	0.00832693	+	0.0114610i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.3.j.c.145.1	yes	16
3.2	odd	2	inner	198.3.j.c.145.4	yes	16
11.4	even	5		2178.3.d.n.1693.2		16
11.6	odd	10	inner	198.3.j.c.127.1	✓	16
11.7	odd	10		2178.3.d.n.1693.10		16
33.17	even	10	inner	198.3.j.c.127.4	yes	16
33.26	odd	10		2178.3.d.n.1693.15		16
33.29	even	10		2178.3.d.n.1693.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.3.j.c.127.1	✓	16	11.6	odd	10	inner
198.3.j.c.127.4	yes	16	33.17	even	10	inner
198.3.j.c.145.1	yes	16	1.1	even	1	trivial
198.3.j.c.145.4	yes	16	3.2	odd	2	inner
2178.3.d.n.1693.2		16	11.4	even	5
2178.3.d.n.1693.7		16	33.29	even	10
2178.3.d.n.1693.10		16	11.7	odd	10
2178.3.d.n.1693.15		16	33.26	odd	10

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:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	198.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34500 - 0.437016i) q^{2} +(1.61803 + 1.17557i) q^{4} +(-1.75757 - 5.40926i) q^{5} +(-6.36870 + 8.76576i) q^{7} +(-1.66251 - 2.28825i) q^{8} +8.04353i q^{10} +(7.37659 + 8.16002i) q^{11} +(-4.28248 - 1.39146i) q^{13} +(12.3967 - 9.00670i) q^{14} +(1.23607 + 3.80423i) q^{16} +(-16.5995 + 5.39350i) q^{17} +(19.7800 + 27.2249i) q^{19} +(3.51515 - 10.8185i) q^{20} +(-6.35542 - 14.1989i) q^{22} -7.03543 q^{23} +(-5.94559 + 4.31973i) q^{25} +(5.15183 + 3.74302i) q^{26} +(-20.6095 + 6.69644i) q^{28} +(-31.8760 + 43.8736i) q^{29} +(-11.8915 + 36.5982i) q^{31} -5.65685i q^{32} +24.6833 q^{34} +(58.6097 + 19.0435i) q^{35} +(16.2382 + 11.7977i) q^{37} +(-14.7064 - 45.2616i) q^{38} +(-9.45573 + 13.0147i) q^{40} +(8.83200 + 12.1562i) q^{41} -67.5682i q^{43} +(2.34288 + 21.8749i) q^{44} +(9.46263 + 3.07459i) q^{46} +(-24.1721 + 17.5620i) q^{47} +(-21.1364 - 65.0511i) q^{49} +(9.88460 - 3.21170i) q^{50} +(-5.29343 - 7.28578i) q^{52} +(4.79618 - 14.7611i) q^{53} +(31.1748 - 54.2437i) q^{55} +30.6462 q^{56} +(62.0466 - 45.0795i) q^{58} +(-31.3552 - 22.7809i) q^{59} +(-38.9028 + 12.6403i) q^{61} +(31.9880 - 44.0278i) q^{62} +(-2.47214 + 7.60845i) q^{64} +25.6106i q^{65} -33.1092 q^{67} +(-33.1990 - 10.7870i) q^{68} +(-70.5076 - 51.2268i) q^{70} +(-26.7010 - 82.1772i) q^{71} +(59.4667 - 81.8488i) q^{73} +(-16.6845 - 22.9643i) q^{74} +67.3036i q^{76} +(-118.508 + 12.6927i) q^{77} +(-47.6389 - 15.4788i) q^{79} +(18.4056 - 13.3724i) q^{80} +(-6.56656 - 20.2098i) q^{82} +(13.9686 - 4.53869i) q^{83} +(58.3497 + 80.3114i) q^{85} +(-29.5284 + 90.8791i) q^{86} +(6.40851 - 30.4455i) q^{88} +81.0524 q^{89} +(39.4710 - 28.6774i) q^{91} +(-11.3836 - 8.27064i) q^{92} +(40.1862 - 13.0573i) q^{94} +(112.502 - 154.845i) q^{95} +(7.64123 - 23.5173i) q^{97} +96.7305i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 60 q^{7} + 60 q^{13} - 16 q^{16} + 96 q^{25} + 40 q^{28} - 160 q^{31} - 64 q^{34} + 60 q^{37} - 80 q^{40} + 160 q^{46} + 96 q^{49} + 40 q^{52} + 224 q^{55} + 80 q^{58} - 500 q^{61} + 32 q^{64}+ \cdots - 1020 q^{97}+O(q^{100}) \) 16 * q + 8 * q^4 - 60 * q^7 + 60 * q^13 - 16 * q^16 + 96 * q^25 + 40 * q^28 - 160 * q^31 - 64 * q^34 + 60 * q^37 - 80 * q^40 + 160 * q^46 + 96 * q^49 + 40 * q^52 + 224 * q^55 + 80 * q^58 - 500 * q^61 + 32 * q^64 - 280 * q^67 - 424 * q^70 - 200 * q^73 - 100 * q^79 - 120 * q^82 + 1020 * q^85 + 240 * q^88 + 828 * q^91 + 440 * q^94 - 1020 * q^97

Introduction

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