LMFDB - Embedded newform 198.3.j.b.127.2

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)

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")

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);

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,-8] 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:	16.0.6879707136000000000000.7
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 15x^{12} - 56x^{10} + 209x^{8} - 56x^{6} + 15x^{4} - 4x^{2} + 1 $ x^16 - 4x^14 + 15x^12 - 56x^10 + 209x^8 - 56x^6 + 15x^4 - 4*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			127.2
Root			$1.13551 + 1.56290i$ of defining polynomial
Character	$\chi$	$=$	198.127
Dual form			198.3.j.b.145.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34500 + 0.437016i) q^{2} +(1.61803 - 1.17557i) q^{4} +(-0.109202 + 0.336090i) q^{5} +(0.464787 + 0.639725i) q^{7} +(-1.66251 + 2.28825i) q^{8} -0.499764i q^{10} +(10.9281 + 1.25540i) q^{11} +(0.198988 - 0.0646551i) q^{13} +(-0.904708 - 0.657309i) q^{14} +(1.23607 - 3.80423i) q^{16} +(14.2369 + 4.62586i) q^{17} +(-1.27522 + 1.75519i) q^{19} +(0.218405 + 0.672180i) q^{20} +(-15.2469 + 3.08725i) q^{22} +24.1342 q^{23} +(20.1244 + 14.6212i) q^{25} +(-0.239383 + 0.173922i) q^{26} +(1.50408 + 0.488706i) q^{28} +(10.4767 + 14.4199i) q^{29} +(10.4564 + 32.1814i) q^{31} +5.65685i q^{32} -21.1702 q^{34} +(-0.265761 + 0.0863510i) q^{35} +(48.6102 - 35.3174i) q^{37} +(0.948120 - 2.91801i) q^{38} +(-0.587507 - 0.808634i) q^{40} +(-31.4796 + 43.3280i) q^{41} +15.5727i q^{43} +(19.1579 - 10.8155i) q^{44} +(-32.4604 + 10.5470i) q^{46} +(-49.4759 - 35.9463i) q^{47} +(14.9486 - 46.0071i) q^{49} +(-33.4570 - 10.8708i) q^{50} +(0.245962 - 0.338538i) q^{52} +(-18.2219 - 56.0812i) q^{53} +(-1.61531 + 3.53574i) q^{55} -2.23656 q^{56} +(-20.3928 - 14.8163i) q^{58} +(-41.6528 + 30.2625i) q^{59} +(38.7576 + 12.5931i) q^{61} +(-28.1276 - 38.7143i) q^{62} +(-2.47214 - 7.60845i) q^{64} +0.0739383i q^{65} -72.9302 q^{67} +(28.4739 - 9.25172i) q^{68} +(0.319711 - 0.232284i) q^{70} +(29.3727 - 90.3998i) q^{71} +(-66.7272 - 91.8421i) q^{73} +(-49.9464 + 68.7453i) q^{74} +4.33906i q^{76} +(4.27614 + 7.57449i) q^{77} +(-139.926 + 45.4646i) q^{79} +(1.14358 + 0.830861i) q^{80} +(23.4050 - 72.0331i) q^{82} +(18.9025 + 6.14179i) q^{83} +(-3.10941 + 4.27974i) q^{85} +(-6.80554 - 20.9453i) q^{86} +(-21.0408 + 22.9191i) q^{88} +74.9710 q^{89} +(0.133848 + 0.0972466i) q^{91} +(39.0499 - 28.3714i) q^{92} +(82.2540 + 26.7260i) q^{94} +(-0.450645 - 0.620259i) q^{95} +(31.3671 + 96.5379i) q^{97} +68.4122i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 8 q^{5} + 60 q^{7} + 4 q^{11} - 60 q^{13} + 32 q^{14} - 16 q^{16} + 60 q^{17} + 16 q^{20} - 48 q^{22} + 8 q^{23} - 48 q^{25} - 48 q^{26} + 40 q^{28} + 160 q^{29} + 32 q^{31} - 64 q^{34}+ \cdots + 324 q^{97}+O(q^{100}) $ 16 * q + 8 * q^4 - 8 * q^5 + 60 * q^7 + 4 * q^11 - 60 * q^13 + 32 * q^14 - 16 * q^16 + 60 * q^17 + 16 * q^20 - 48 * q^22 + 8 * q^23 - 48 * q^25 - 48 * q^26 + 40 * q^28 + 160 * q^29 + 32 * q^31 - 64 * q^34 - 160 * q^35 - 84 * q^37 + 48 * q^38 - 80 * q^40 - 40 * q^41 - 168 * q^44 + 160 * q^46 - 372 * q^47 + 96 * q^49 - 160 * q^50 + 40 * q^52 + 124 * q^53 + 32 * q^55 + 96 * q^56 - 16 * q^58 + 172 * q^59 + 100 * q^61 + 40 * q^62 + 32 * q^64 + 248 * q^67 + 120 * q^68 + 8 * q^70 - 48 * q^71 + 160 * q^73 - 80 * q^74 + 172 * q^77 - 460 * q^79 + 48 * q^80 - 24 * q^82 + 420 * q^83 - 420 * q^85 + 456 * q^86 - 144 * q^88 + 360 * q^89 - 252 * q^91 + 64 * q^92 - 280 * q^94 - 180 * q^95 + 324 * q^97

Character values

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

$n$	$145$	$155$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

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
$5$	−0.109202	+	0.336090i	−0.0218405	+	0.0672180i	−0.961383	−	0.275215i	$-0.911251\pi$
$5$	−0.109202	+	0.336090i	−0.0218405	+	0.0672180i	0.939542	+	0.342433i	$0.111251\pi$
$6$		0			0
$7$	0.464787	+	0.639725i	0.0663982	+	0.0913893i	0.840925	−	0.541152i	$-0.182012\pi$
$7$	0.464787	+	0.639725i	0.0663982	+	0.0913893i	−0.774526	+	0.632542i	$0.782012\pi$
$8$	−1.66251	+	2.28825i	−0.207813	+	0.286031i
$9$		0			0
$10$		−	0.499764i		−	0.0499764i
$11$	10.9281	+	1.25540i	0.993466	+	0.114128i
$11$	10.9281	+	1.25540i	0.993466	+	0.114128i
$12$		0			0
$13$	0.198988	−	0.0646551i	0.0153068	−	0.00497347i	−0.301354	−	0.953512i	$-0.597438\pi$
$13$	0.198988	−	0.0646551i	0.0153068	−	0.00497347i	0.316660	+	0.948539i	$0.397438\pi$
$14$	−0.904708	−	0.657309i	−0.0646220	−	0.0469506i
$15$		0			0
$16$	1.23607	−	3.80423i	0.0772542	−	0.237764i
$17$	14.2369	+	4.62586i	0.837467	+	0.272109i	0.696187	−	0.717860i	$-0.254878\pi$
$17$	14.2369	+	4.62586i	0.837467	+	0.272109i	0.141280	+	0.989970i	$0.454878\pi$
$18$		0			0
$19$	−1.27522	+	1.75519i	−0.0671168	+	0.0923783i	−0.841256	−	0.540637i	$-0.818183\pi$
$19$	−1.27522	+	1.75519i	−0.0671168	+	0.0923783i	0.774139	+	0.633016i	$0.218183\pi$
$20$	0.218405	+	0.672180i	0.0109202	+	0.0336090i
$21$		0			0
$22$	−15.2469	+	3.08725i	−0.693042	+	0.140330i
$23$	24.1342			1.04931			0.524656	−	0.851314i	$-0.324194\pi$
$23$	24.1342			1.04931			0.524656	+	0.851314i	$0.324194\pi$
$24$		0			0
$25$	20.1244	+	14.6212i	0.804976	+	0.584849i
$26$	−0.239383	+	0.173922i	−0.00920703	+	0.00668930i
$27$		0			0
$28$	1.50408	+	0.488706i	0.0537173	+	0.0174538i
$29$	10.4767	+	14.4199i	0.361265	+	0.497239i	0.950501	−	0.310723i	$-0.100571\pi$
$29$	10.4767	+	14.4199i	0.361265	+	0.497239i	−0.589236	+	0.807961i	$0.700571\pi$
$30$		0			0
$31$	10.4564	+	32.1814i	0.337303	+	1.03811i	0.965577	+	0.260119i	$0.0837616\pi$
$31$	10.4564	+	32.1814i	0.337303	+	1.03811i	−0.628274	+	0.777992i	$0.716238\pi$
$32$			5.65685i			0.176777i
$33$		0			0
$34$	−21.1702			−0.622653
$35$	−0.265761	+	0.0863510i	−0.00759318	+	0.00246717i
$36$		0			0
$37$	48.6102	−	35.3174i	1.31379	−	0.954524i	0.313803	−	0.949488i	$-0.398397\pi$
$37$	48.6102	−	35.3174i	1.31379	−	0.954524i	0.999987	−	0.00503636i	$-0.00160313\pi$
$38$	0.948120	−	2.91801i	0.0249505	−	0.0767899i
$39$		0			0
$40$	−0.587507	−	0.808634i	−0.0146877	−	0.0202159i
$41$	−31.4796	+	43.3280i	−0.767796	+	1.05678i	0.228729	+	0.973490i	$0.426543\pi$
$41$	−31.4796	+	43.3280i	−0.767796	+	1.05678i	−0.996525	+	0.0832904i	$0.973457\pi$
$42$		0			0
$43$			15.5727i			0.362157i	0.983469	+	0.181078i	$0.0579588\pi$
$43$			15.5727i			0.362157i	−0.983469	+	0.181078i	$0.942041\pi$
$44$	19.1579	−	10.8155i	0.435407	−	0.245807i
$45$		0			0
$46$	−32.4604	+	10.5470i	−0.705661	+	0.229283i
$47$	−49.4759	−	35.9463i	−1.05268	−	0.764816i	−0.0799585	−	0.996798i	$-0.525479\pi$
$47$	−49.4759	−	35.9463i	−1.05268	−	0.764816i	−0.972720	+	0.231983i	$0.925479\pi$
$48$		0			0
$49$	14.9486	−	46.0071i	0.305074	−	0.938920i
$50$	−33.4570	−	10.8708i	−0.669139	−	0.217417i
$51$		0			0
$52$	0.245962	−	0.338538i	0.00473005	−	0.00651035i
$53$	−18.2219	−	56.0812i	−0.343809	−	1.05814i	−0.962218	−	0.272280i	$-0.912222\pi$
$53$	−18.2219	−	56.0812i	−0.343809	−	1.05814i	0.618409	−	0.785857i	$-0.287778\pi$
$54$		0			0
$55$	−1.61531	+	3.53574i	−0.0293692	+	0.0642863i
$56$	−2.23656			−0.0399386
$57$		0			0
$58$	−20.3928	−	14.8163i	−0.351601	−	0.255453i
$59$	−41.6528	+	30.2625i	−0.705980	+	0.512924i	−0.881874	−	0.471485i	$-0.843718\pi$
$59$	−41.6528	+	30.2625i	−0.705980	+	0.512924i	0.175894	+	0.984409i	$0.443718\pi$
$60$		0			0
$61$	38.7576	+	12.5931i	0.635371	+	0.206445i	0.608953	−	0.793206i	$-0.291590\pi$
$61$	38.7576	+	12.5931i	0.635371	+	0.206445i	0.0264182	+	0.999651i	$0.491590\pi$
$62$	−28.1276	−	38.7143i	−0.453671	−	0.624425i
$63$		0			0
$64$	−2.47214	−	7.60845i	−0.0386271	−	0.118882i
$65$			0.0739383i			0.00113751i
$66$		0			0
$67$	−72.9302			−1.08851			−0.544255	−	0.838920i	$-0.683188\pi$
$67$	−72.9302			−1.08851			−0.544255	+	0.838920i	$0.683188\pi$
$68$	28.4739	−	9.25172i	0.418733	−	0.136055i
$69$		0			0
$70$	0.319711	−	0.232284i	0.00456730	−	0.00331834i
$71$	29.3727	−	90.3998i	0.413700	−	1.27324i	−0.499709	−	0.866193i	$-0.666560\pi$
$71$	29.3727	−	90.3998i	0.413700	−	1.27324i	0.913409	−	0.407043i	$-0.133440\pi$
$72$		0			0
$73$	−66.7272	−	91.8421i	−0.914071	−	1.25811i	−0.965757	−	0.259448i	$-0.916459\pi$
$73$	−66.7272	−	91.8421i	−0.914071	−	1.25811i	0.0516858	−	0.998663i	$-0.483541\pi$
$74$	−49.9464	+	68.7453i	−0.674951	+	0.928990i
$75$		0			0
$76$			4.33906i			0.0570930i
$77$	4.27614	+	7.57449i	0.0555343	+	0.0983700i
$78$		0			0
$79$	−139.926	+	45.4646i	−1.77121	+	0.575502i	−0.998260	−	0.0589621i	$-0.981221\pi$
$79$	−139.926	+	45.4646i	−1.77121	+	0.575502i	−0.772952	+	0.634464i	$0.781221\pi$
$80$	1.14358	+	0.830861i	0.0142948	+	0.0103858i
$81$		0			0
$82$	23.4050	−	72.0331i	0.285427	−	0.878453i
$83$	18.9025	+	6.14179i	0.227741	+	0.0739974i	0.420664	−	0.907216i	$-0.361797\pi$
$83$	18.9025	+	6.14179i	0.227741	+	0.0739974i	−0.192924	+	0.981214i	$0.561797\pi$
$84$		0			0
$85$	−3.10941	+	4.27974i	−0.0365813	+	0.0503499i
$86$	−6.80554	−	20.9453i	−0.0791342	−	0.243550i
$87$		0			0
$88$	−21.0408	+	22.9191i	−0.239100	+	0.260445i
$89$	74.9710			0.842371			0.421185	−	0.906975i	$-0.361614\pi$
$89$	74.9710			0.842371			0.421185	+	0.906975i	$0.361614\pi$
$90$		0			0
$91$	0.133848	+	0.0972466i	0.00147086	+	0.00106864i
$92$	39.0499	−	28.3714i	0.424456	−	0.308385i
$93$		0			0
$94$	82.2540	+	26.7260i	0.875043	+	0.284319i
$95$	−0.450645	−	0.620259i	−0.00474363	−	0.00652905i
$96$		0			0
$97$	31.3671	+	96.5379i	0.323372	+	0.995236i	0.972170	+	0.234276i	$0.0752719\pi$
$97$	31.3671	+	96.5379i	0.323372	+	0.995236i	−0.648798	+	0.760960i	$0.724728\pi$
$98$			68.4122i			0.698084i
$99$		0			0
$100$	49.7502			0.497502
$101$	−24.8088	+	8.06086i	−0.245631	+	0.0798105i	−0.429245	−	0.903188i	$-0.641220\pi$
$101$	−24.8088	+	8.06086i	−0.245631	+	0.0798105i	0.183614	+	0.982998i	$0.441220\pi$
$102$		0			0
$103$	25.5133	−	18.5365i	0.247702	−	0.179966i	−0.457006	−	0.889464i	$-0.651078\pi$
$103$	25.5133	−	18.5365i	0.247702	−	0.179966i	0.704708	+	0.709498i	$0.251078\pi$
$104$	−0.182872	+	0.562823i	−0.00175839	+	0.00541175i
$105$		0			0
$106$	49.0168	+	67.4658i	0.462423	+	0.636470i
$107$	−47.3389	+	65.1565i	−0.442420	+	0.608939i	−0.970748	−	0.240102i	$-0.922819\pi$
$107$	−47.3389	+	65.1565i	−0.442420	+	0.608939i	0.528328	+	0.849040i	$0.322819\pi$
$108$		0			0
$109$		−	32.1811i		−	0.295239i	−0.989044	−	0.147620i	$-0.952839\pi$
$109$		−	32.1811i		−	0.295239i	0.989044	−	0.147620i	$-0.0471612\pi$
$110$	0.627405	−	5.46148i	0.00570368	−	0.0496498i
$111$		0			0
$112$	3.00817	−	0.977413i	0.0268586	−	0.00872690i
$113$	−23.6264	−	17.1656i	−0.209083	−	0.151908i	0.478315	−	0.878188i	$-0.341248\pi$
$113$	−23.6264	−	17.1656i	−0.209083	−	0.151908i	−0.687399	+	0.726280i	$0.741248\pi$
$114$		0			0
$115$	−2.63551	+	8.11126i	−0.0229175	+	0.0705327i
$116$	33.9033	+	11.0158i	0.292270	+	0.0949641i
$117$		0			0
$118$	42.7977	−	58.9060i	0.362692	−	0.499203i
$119$	3.65787	+	11.2578i	0.0307384	+	0.0946031i
$120$		0			0
$121$	117.848	+	27.4384i	0.973950	+	0.226764i
$122$	−57.6323			−0.472396
$123$		0			0
$124$	54.7503	+	39.7784i	0.441535	+	0.320794i
$125$	−14.2591	+	10.3598i	−0.114073	+	0.0828786i
$126$		0			0
$127$	141.757	+	46.0595i	1.11619	+	0.362673i	0.808314	−	0.588752i	$-0.200380\pi$
$127$	141.757	+	46.0595i	1.11619	+	0.362673i	0.307880	+	0.951425i	$0.400380\pi$
$128$	6.65003	+	9.15298i	0.0519534	+	0.0715077i
$129$		0			0
$130$	−0.0323122	−	0.0994468i	−0.000248556	−	0.000764976i
$131$			165.965i			1.26691i	0.773780	+	0.633454i	$0.218364\pi$
$131$			165.965i			1.26691i	−0.773780	+	0.633454i	$0.781636\pi$
$132$		0			0
$133$	−1.71554			−0.0128988
$134$	98.0909	−	31.8717i	0.732021	−	0.237848i
$135$		0			0
$136$	−34.2541	+	24.8871i	−0.251869	+	0.182993i
$137$	45.3846	−	139.680i	0.331275	−	1.01956i	−0.637253	−	0.770654i	$-0.719930\pi$
$137$	45.3846	−	139.680i	0.331275	−	1.01956i	0.968528	−	0.248904i	$-0.0800705\pi$
$138$		0			0
$139$	−125.653	−	172.947i	−0.903982	−	1.24422i	−0.969180	−	0.246352i	$-0.920768\pi$
$139$	−125.653	−	172.947i	−0.903982	−	1.24422i	0.0651984	−	0.997872i	$-0.479232\pi$
$140$	−0.328499	+	0.452140i	−0.00234642	+	0.00322957i
$141$		0			0
$142$			134.424i			0.946646i
$143$	2.25573	−	0.456749i	0.0157744	−	0.00319405i
$144$		0			0
$145$	−5.99047	+	1.94642i	−0.0413136	+	0.0134236i
$146$	129.884	+	94.3665i	0.889619	+	0.646346i
$147$		0			0
$148$	37.1349	−	114.290i	0.250912	−	0.772227i
$149$	219.924	+	71.4578i	1.47600	+	0.479582i	0.932916	−	0.360094i	$-0.117255\pi$
$149$	219.924	+	71.4578i	1.47600	+	0.479582i	0.543087	+	0.839677i	$0.317255\pi$
$150$		0			0
$151$	−156.589	+	215.527i	−1.03701	+	1.42733i	−0.137467	+	0.990506i	$0.543896\pi$
$151$	−156.589	+	215.527i	−1.03701	+	1.42733i	−0.899548	+	0.436822i	$0.856104\pi$
$152$	−1.89624	−	5.83603i	−0.0124753	−	0.0383949i
$153$		0			0
$154$	−9.06157	−	8.31893i	−0.0588414	−	0.0540190i
$155$	−11.9577			−0.0771466
$156$		0			0
$157$	84.3629	+	61.2933i	0.537344	+	0.390403i	0.823098	−	0.567900i	$-0.192244\pi$
$157$	84.3629	+	61.2933i	0.537344	+	0.390403i	−0.285754	+	0.958303i	$0.592244\pi$
$158$	168.331	−	122.300i	1.06539	−	0.774048i
$159$		0			0
$160$	−1.90121	−	0.617742i	−0.0118826	−	0.00386089i
$161$	11.2173	+	15.4392i	0.0696724	+	0.0958959i
$162$		0			0
$163$	−86.4221	−	265.980i	−0.530197	−	1.63178i	−0.753804	−	0.657099i	$-0.771783\pi$
$163$	−86.4221	−	265.980i	−0.530197	−	1.63178i	0.223607	−	0.974679i	$-0.428217\pi$
$164$			107.113i			0.653126i
$165$		0			0
$166$	−28.1078			−0.169324
$167$	−244.370	+	79.4006i	−1.46329	+	0.475453i	−0.929074	−	0.369893i	$-0.879394\pi$
$167$	−244.370	+	79.4006i	−1.46329	+	0.475453i	−0.534219	+	0.845346i	$0.679394\pi$
$168$		0			0
$169$	−136.688	+	99.3100i	−0.808807	+	0.587633i
$170$	2.31184	−	7.11510i	0.0135990	−	0.0418535i
$171$		0			0
$172$	18.3069	+	25.1972i	0.106435	+	0.146496i
$173$	64.7673	−	89.1445i	0.374377	−	0.515286i	−0.579707	−	0.814825i	$-0.696833\pi$
$173$	64.7673	−	89.1445i	0.374377	−	0.515286i	0.954084	+	0.299539i	$0.0968329\pi$
$174$		0			0
$175$			19.6698i			0.112399i
$176$	18.2837	−	40.0213i	0.103885	−	0.227394i
$177$		0			0
$178$	−100.836	+	32.7635i	−0.566493	+	0.184065i
$179$	21.9460	+	15.9447i	0.122603	+	0.0890764i	0.647397	−	0.762153i	$-0.275858\pi$
$179$	21.9460	+	15.9447i	0.122603	+	0.0890764i	−0.524794	+	0.851229i	$0.675858\pi$
$180$		0			0
$181$	80.2120	−	246.867i	0.443160	−	1.36391i	−0.441329	−	0.897345i	$-0.645493\pi$
$181$	80.2120	−	246.867i	0.443160	−	1.36391i	0.884489	−	0.466561i	$-0.154507\pi$
$182$	−0.222524	−	0.0723025i	−0.00122266	−	0.000397266i
$183$		0			0
$184$	−40.1233	+	55.2249i	−0.218061	+	0.300135i
$185$	6.56148	+	20.1942i	0.0354675	+	0.109158i
$186$		0			0
$187$	149.776	+	68.4251i	0.800940	+	0.365910i
$188$	−122.311			−0.650591
$189$		0			0
$190$	0.877179	+	0.637308i	0.00461673	+	0.00335425i
$191$	−100.951	+	73.3452i	−0.528539	+	0.384006i	−0.819811	−	0.572634i	$-0.805922\pi$
$191$	−100.951	+	73.3452i	−0.528539	+	0.384006i	0.291272	+	0.956640i	$0.405922\pi$
$192$		0			0
$193$	39.9341	+	12.9754i	0.206912	+	0.0672299i	0.410639	−	0.911798i	$-0.365306\pi$
$193$	39.9341	+	12.9754i	0.206912	+	0.0672299i	−0.203727	+	0.979028i	$0.565306\pi$
$194$	−84.3772	−	116.135i	−0.434934	−	0.598635i
$195$		0			0
$196$	−29.8972	−	92.0142i	−0.152537	−	0.469460i
$197$		−	274.338i		−	1.39258i	−0.717760	−	0.696290i	$-0.754833\pi$
$197$		−	274.338i		−	1.39258i	0.717760	−	0.696290i	$-0.245167\pi$
$198$		0			0
$199$	−150.979			−0.758690			−0.379345	−	0.925255i	$-0.623851\pi$
$199$	−150.979			−0.758690			−0.379345	+	0.925255i	$0.623851\pi$
$200$	−66.9139	+	21.7417i	−0.334570	+	0.108708i
$201$		0			0
$202$	29.8450	−	21.6837i	0.147748	−	0.107345i
$203$	−4.35535	+	13.4044i	−0.0214549	+	0.0660315i
$204$		0			0
$205$	−11.1245	−	15.3115i	−0.0542657	−	0.0746903i
$206$	−26.2146	+	36.0813i	−0.127255	+	0.175152i
$207$		0			0
$208$		−	0.836913i		−	0.00402362i
$209$	−16.1392	+	17.5800i	−0.0772212	+	0.0841149i
$210$		0			0
$211$	−17.7693	+	5.77360i	−0.0842147	+	0.0273630i	−0.350821	−	0.936442i	$-0.614098\pi$
$211$	−17.7693	+	5.77360i	−0.0842147	+	0.0273630i	0.266607	+	0.963805i	$0.414098\pi$
$212$	−95.4111	−	69.3202i	−0.450052	−	0.326982i
$213$		0			0
$214$	35.1963	−	108.323i	0.164469	−	0.506183i
$215$	−5.23385	−	1.70058i	−0.0243435	−	0.00790968i
$216$		0			0
$217$	−15.7273	+	21.6467i	−0.0724759	+	0.0997545i
$218$	14.0637	+	43.2835i	0.0645122	+	0.198548i
$219$		0			0
$220$	1.54290	+	7.61986i	0.00701317	+	0.0346357i
$221$	3.13206			0.0141722
$222$		0			0
$223$	76.2747	+	55.4168i	0.342039	+	0.248506i	0.745522	−	0.666481i	$-0.232200\pi$
$223$	76.2747	+	55.4168i	0.342039	+	0.248506i	−0.403483	+	0.914987i	$0.632200\pi$
$224$	−3.61883	+	2.62923i	−0.0161555	+	0.0117377i
$225$		0			0
$226$	39.2791	+	12.7626i	0.173801	+	0.0564715i
$227$	−170.335	−	234.446i	−0.750374	−	1.03280i	−0.997954	−	0.0639340i	$-0.979635\pi$
$227$	−170.335	−	234.446i	−0.750374	−	1.03280i	0.247580	−	0.968867i	$-0.420365\pi$
$228$		0			0
$229$	−70.5265	−	217.058i	−0.307976	−	0.947852i	−0.978550	−	0.206010i	$-0.933952\pi$
$229$	−70.5265	−	217.058i	−0.307976	−	0.947852i	0.670574	−	0.741843i	$-0.266048\pi$
$230$		−	12.0614i		−	0.0524408i
$231$		0			0
$232$	−50.4139			−0.217301
$233$	−284.201	+	92.3427i	−1.21975	+	0.396320i	−0.846990	−	0.531608i	$-0.821588\pi$
$233$	−284.201	+	92.3427i	−1.21975	+	0.396320i	−0.372758	+	0.927928i	$0.621588\pi$
$234$		0			0
$235$	17.4841	−	12.7029i	0.0744004	−	0.0540551i
$236$	−31.8199	+	97.9317i	−0.134830	+	0.414965i
$237$		0			0
$238$	−9.83965	−	13.5431i	−0.0413431	−	0.0569038i
$239$	144.554	−	198.961i	0.604827	−	0.832473i	−0.391313	−	0.920258i	$-0.627979\pi$
$239$	144.554	−	198.961i	0.604827	−	0.832473i	0.996139	+	0.0877850i	$0.0279789\pi$
$240$		0			0
$241$			373.418i			1.54945i	0.632297	+	0.774726i	$0.282112\pi$
$241$			373.418i			1.54945i	−0.632297	+	0.774726i	$0.717888\pi$
$242$	−170.496	+	14.5969i	−0.704529	+	0.0603176i
$243$		0			0
$244$	77.5153	−	25.1862i	0.317686	−	0.103222i
$245$	13.8301	+	10.0482i	0.0564494	+	0.0410129i
$246$		0			0
$247$	−0.140271	+	0.431710i	−0.000567900	+	0.00174782i
$248$	−91.0228	−	29.5751i	−0.367028	−	0.119254i
$249$		0			0
$250$	14.6510	−	20.1654i	0.0586040	−	0.0806615i
$251$	111.067	+	341.831i	0.442500	+	1.36187i	0.885202	+	0.465206i	$0.154020\pi$
$251$	111.067	+	341.831i	0.442500	+	1.36187i	−0.442702	+	0.896669i	$0.645980\pi$
$252$		0			0
$253$	263.741	+	30.2981i	1.04246	+	0.119755i
$254$	−210.791			−0.829886
$255$		0			0
$256$	−12.9443	−	9.40456i	−0.0505636	−	0.0367366i
$257$	−28.9501	+	21.0334i	−0.112646	+	0.0818422i	−0.642682	−	0.766133i	$-0.722178\pi$
$257$	−28.9501	+	21.0334i	−0.112646	+	0.0818422i	0.530036	+	0.847975i	$0.322178\pi$
$258$		0			0
$259$	45.1869	+	14.6821i	0.174467	+	0.0566876i
$260$	0.0869197	+	0.119635i	0.000334307	+	0.000460134i
$261$		0			0
$262$	−72.5294	−	223.222i	−0.276830	−	0.851994i
$263$		−	364.668i		−	1.38657i	−0.720663	−	0.693286i	$-0.756162\pi$
$263$		−	364.668i		−	1.38657i	0.720663	−	0.693286i	$-0.243838\pi$
$264$		0			0
$265$	20.8382			0.0786348
$266$	2.30740	−	0.749720i	0.00867444	−	0.00281850i
$267$		0			0
$268$	−118.004	+	85.7346i	−0.440312	+	0.319905i
$269$	4.13369	−	12.7222i	0.0153669	−	0.0472944i	−0.943079	−	0.332569i	$-0.892085\pi$
$269$	4.13369	−	12.7222i	0.0153669	−	0.0472944i	0.958446	+	0.285274i	$0.0920847\pi$
$270$		0			0
$271$	41.6402	+	57.3128i	0.153654	+	0.211486i	0.878904	−	0.477000i	$-0.158276\pi$
$271$	41.6402	+	57.3128i	0.153654	+	0.211486i	−0.725250	+	0.688486i	$0.758276\pi$
$272$	35.1956	−	48.4426i	0.129396	−	0.178098i
$273$		0			0
$274$			207.702i			0.758038i
$275$	201.566	+	185.047i	0.732969	+	0.672898i
$276$		0			0
$277$	−75.4632	+	24.5195i	−0.272430	+	0.0885179i	−0.442046	−	0.896992i	$-0.645747\pi$
$277$	−75.4632	+	24.5195i	−0.272430	+	0.0885179i	0.169616	+	0.985510i	$0.445747\pi$
$278$	244.584	+	177.701i	0.879800	+	0.639212i
$279$		0			0
$280$	0.244238	−	0.751686i	0.000872277	−	0.00268459i
$281$	326.300	+	106.021i	1.16121	+	0.377300i	0.825355	−	0.564614i	$-0.190975\pi$
$281$	326.300	+	106.021i	1.16121	+	0.377300i	0.335854	+	0.941914i	$0.390975\pi$
$282$		0			0
$283$	−70.3457	+	96.8225i	−0.248571	+	0.342129i	−0.915010	−	0.403430i	$-0.867818\pi$
$283$	−70.3457	+	96.8225i	−0.248571	+	0.342129i	0.666439	+	0.745560i	$0.267818\pi$
$284$	−58.7453	−	180.800i	−0.206850	−	0.636618i
$285$		0			0
$286$	−2.83435	+	1.60012i	−0.00991030	+	0.00559481i
$287$	−42.3493			−0.147559
$288$		0			0
$289$	−52.5141	−	38.1538i	−0.181710	−	0.132020i
$290$	7.20655	−	5.23586i	0.0248502	−	0.0180547i
$291$		0			0
$292$	−215.934	−	70.1611i	−0.739499	−	0.240278i
$293$	−6.76900	−	9.31673i	−0.0231024	−	0.0317977i	0.797310	−	0.603571i	$-0.206256\pi$
$293$	−6.76900	−	9.31673i	−0.0231024	−	0.0317977i	−0.820412	+	0.571773i	$0.806256\pi$
$294$		0			0
$295$	−5.62236	−	17.3038i	−0.0190588	−	0.0586571i
$296$			169.948i			0.574147i
$297$		0			0
$298$	−327.026			−1.09740
$299$	4.80241	−	1.56040i	0.0160616	−	0.00521872i
$300$		0			0
$301$	−9.96228	+	7.23802i	−0.0330973	+	0.0240466i
$302$	116.423	−	358.315i	0.385508	−	1.18647i
$303$		0			0
$304$	5.10088	+	7.02075i	0.0167792	+	0.0230946i
$305$	−8.46485	+	11.6509i	−0.0277536	+	0.0381996i
$306$		0			0
$307$		−	196.858i		−	0.641231i	−0.947210	−	0.320615i	$-0.896110\pi$
$307$		−	196.858i		−	0.641231i	0.947210	−	0.320615i	$-0.103890\pi$
$308$	15.8233	+	7.22888i	0.0513743	+	0.0234704i
$309$		0			0
$310$	16.0831	−	5.22572i	0.0518810	−	0.0168572i
$311$	218.771	+	158.946i	0.703443	+	0.511082i	0.881052	−	0.473020i	$-0.156836\pi$
$311$	218.771	+	158.946i	0.703443	+	0.511082i	−0.177608	+	0.984101i	$0.556836\pi$
$312$		0			0
$313$	106.490	−	327.743i	0.340224	−	1.04710i	−0.623867	−	0.781531i	$-0.714439\pi$
$313$	106.490	−	327.743i	0.340224	−	1.04710i	0.964091	−	0.265572i	$-0.0855608\pi$
$314$	−140.254	−	45.5713i	−0.446669	−	0.145132i
$315$		0			0
$316$	−172.958	+	238.056i	−0.547335	+	0.753342i
$317$	−20.2627	−	62.3621i	−0.0639201	−	0.196726i	0.913996	−	0.405723i	$-0.132980\pi$
$317$	−20.2627	−	62.3621i	−0.0639201	−	0.196726i	−0.977916	+	0.208997i	$0.932980\pi$
$318$		0			0
$319$	96.3877	+	170.735i	0.302156	+	0.535220i
$320$	2.82709			0.00883465
$321$		0			0
$322$	−21.8344	−	15.8636i	−0.0678086	−	0.0492659i
$323$	−26.2745	+	19.0895i	−0.0813451	+	0.0591007i
$324$		0			0
$325$	4.94985	+	1.60830i	0.0152303	+	0.00494862i
$326$	232.475	+	319.974i	0.713113	+	0.981516i
$327$		0			0
$328$	−46.8100	−	144.066i	−0.142713	−	0.439226i
$329$		−	48.3584i		−	0.146986i
$330$		0			0
$331$	105.818			0.319693			0.159847	−	0.987142i	$-0.448900\pi$
$331$	105.818			0.319693			0.159847	+	0.987142i	$0.448900\pi$
$332$	37.8050	−	12.2836i	0.113870	−	0.0369987i
$333$		0			0
$334$	293.978	−	213.587i	0.880172	−	0.639483i
$335$	7.96415	−	24.5111i	0.0237736	−	0.0731675i
$336$		0			0
$337$	132.617	+	182.531i	0.393521	+	0.541635i	0.959103	−	0.283057i	$-0.0913485\pi$
$337$	132.617	+	182.531i	0.393521	+	0.541635i	−0.565582	+	0.824692i	$0.691348\pi$
$338$	140.446	−	193.307i	0.415519	−	0.571913i
$339$		0			0
$340$			10.5801i			0.0311179i
$341$	73.8680	+	364.810i	0.216622	+	1.06982i
$342$		0			0
$343$	73.2299	−	23.7938i	0.213498	−	0.0693698i
$344$	−35.6343	−	25.8898i	−0.103588	−	0.0752611i
$345$		0			0
$346$	−48.1542	+	148.203i	−0.139174	+	0.428334i
$347$	−128.933	−	41.8930i	−0.371566	−	0.120729i	0.117281	−	0.993099i	$-0.462582\pi$
$347$	−128.933	−	41.8930i	−0.371566	−	0.120729i	−0.488847	+	0.872370i	$0.662582\pi$
$348$		0			0
$349$	293.983	−	404.633i	0.842358	−	1.15941i	−0.143137	−	0.989703i	$-0.545719\pi$
$349$	293.983	−	404.633i	0.842358	−	1.15941i	0.985495	−	0.169704i	$-0.0542811\pi$
$350$	−8.59603	−	26.4559i	−0.0245601	−	0.0755882i
$351$		0			0
$352$	−7.10163	+	61.8188i	−0.0201751	+	0.175622i
$353$	−320.592			−0.908192			−0.454096	−	0.890953i	$-0.650038\pi$
$353$	−320.592			−0.908192			−0.454096	+	0.890953i	$0.650038\pi$
$354$		0			0
$355$	27.1749	+	19.7437i	0.0765491	+	0.0556162i
$356$	121.306	−	88.1337i	0.340746	−	0.247567i
$357$		0			0
$358$	−36.4853	−	11.8548i	−0.101914	−	0.0331140i
$359$	−66.6745	−	91.7696i	−0.185723	−	0.255626i	0.705996	−	0.708216i	$-0.250500\pi$
$359$	−66.6745	−	91.7696i	−0.185723	−	0.255626i	−0.891718	+	0.452591i	$0.850500\pi$
$360$		0			0
$361$	110.101	+	338.855i	0.304988	+	0.938656i
$362$			367.089i			1.01406i
$363$		0			0
$364$	0.330892			0.000909043
$365$	38.1540	−	12.3970i	0.104532	−	0.0339644i
$366$		0			0
$367$	−72.4621	+	52.6468i	−0.197444	+	0.143452i	−0.682115	−	0.731245i	$-0.738940\pi$
$367$	−72.4621	+	52.6468i	−0.197444	+	0.143452i	0.484670	+	0.874697i	$0.338940\pi$
$368$	29.8315	−	91.8119i	0.0810638	−	0.249489i
$369$		0			0
$370$	−17.6504	−	24.2936i	−0.0477037	−	0.0656584i
$371$	27.4073	−	37.7228i	0.0738740	−	0.101679i
$372$		0			0
$373$		−	275.552i		−	0.738744i	−0.929282	−	0.369372i	$-0.879573\pi$
$373$		−	275.552i		−	0.738744i	0.929282	−	0.369372i	$-0.120427\pi$
$374$	−231.351	−	26.5771i	−0.618585	−	0.0710619i
$375$		0			0
$376$	164.508	−	53.4519i	0.437522	−	0.142159i
$377$	3.01705	+	2.19202i	0.00800279	+	0.00581437i
$378$		0			0
$379$	−54.2463	+	166.953i	−0.143130	+	0.440509i	−0.996766	−	0.0803612i	$-0.974393\pi$
$379$	−54.2463	+	166.953i	−0.143130	+	0.440509i	0.853636	+	0.520871i	$0.174393\pi$
$380$	−1.45832	−	0.473836i	−0.00383768	−	0.00124694i
$381$		0			0
$382$	103.726	−	142.766i	0.271533	−	0.373733i
$383$	15.8151	+	48.6740i	0.0412928	+	0.127086i	0.969578	−	0.244783i	$-0.0787169\pi$
$383$	15.8151	+	48.6740i	0.0412928	+	0.127086i	−0.928285	+	0.371870i	$0.878717\pi$
$384$		0			0
$385$	−3.01268	+	0.610018i	−0.00782514	+	0.00158446i
$386$	−59.3817			−0.153838
$387$		0			0
$388$	164.240	+	119.327i	0.423299	+	0.307545i
$389$	−18.5317	+	13.4641i	−0.0476393	+	0.0346120i	−0.611350	−	0.791360i	$-0.709373\pi$
$389$	−18.5317	+	13.4641i	−0.0476393	+	0.0346120i	0.563711	+	0.825972i	$0.309373\pi$
$390$		0			0
$391$	343.597	+	111.641i	0.878764	+	0.285528i
$392$	80.4234	+	110.693i	0.205162	+	0.282381i
$393$		0			0
$394$	119.890	+	368.984i	0.304290	+	0.936509i
$395$		−	51.9925i		−	0.131627i
$396$		0			0
$397$	131.054			0.330112			0.165056	−	0.986284i	$-0.447220\pi$
$397$	131.054			0.330112			0.165056	+	0.986284i	$0.447220\pi$
$398$	203.067	−	65.9804i	0.510218	−	0.165780i
$399$		0			0
$400$	80.4976	−	58.4849i	0.201244	−	0.146212i
$401$	−239.751	+	737.877i	−0.597882	+	1.84009i	−0.0580587	+	0.998313i	$0.518491\pi$
$401$	−239.751	+	737.877i	−0.597882	+	1.84009i	−0.539823	+	0.841778i	$0.681509\pi$
$402$		0			0
$403$	4.16138	+	5.72765i	0.0103260	+	0.0142125i
$404$	−30.6653	+	42.2072i	−0.0759043	+	0.104473i
$405$		0			0
$406$		−	19.9322i		−	0.0490942i
$407$	575.556	−	324.928i	1.41414	−	0.798348i
$408$		0			0
$409$	−710.800	+	230.953i	−1.73790	+	0.564677i	−0.994553	−	0.104232i	$-0.966762\pi$
$409$	−710.800	+	230.953i	−1.73790	+	0.564677i	−0.743345	+	0.668909i	$0.766762\pi$
$410$	21.6538	+	15.7324i	0.0528140	+	0.0383716i
$411$		0			0
$412$	19.4904	−	59.9854i	0.0473069	−	0.145596i
$413$	−38.7194	−	12.5807i	−0.0937516	−	0.0304617i
$414$		0			0
$415$	−4.12839	+	5.68224i	−0.00994793	+	0.0136921i
$416$	0.365744	+	1.12565i	0.000879193	+	0.00270588i
$417$		0			0
$418$	14.0245	−	30.6982i	0.0335513	−	0.0734406i
$419$	408.427			0.974765			0.487383	−	0.873189i	$-0.337952\pi$
$419$	408.427			0.974765			0.487383	+	0.873189i	$0.337952\pi$
$420$		0			0
$421$	−84.5514	−	61.4302i	−0.200835	−	0.145915i	0.482823	−	0.875718i	$-0.339612\pi$
$421$	−84.5514	−	61.4302i	−0.200835	−	0.145915i	−0.683657	+	0.729803i	$0.739612\pi$
$422$	21.3765	−	15.5309i	0.0506552	−	0.0368032i
$423$		0			0
$424$	158.622	+	51.5393i	0.374108	+	0.121555i
$425$	218.874	+	301.254i	0.514998	+	0.708833i
$426$		0			0
$427$	9.95793	+	30.6473i	0.0233207	+	0.0717737i
$428$			161.076i			0.376345i
$429$		0			0
$430$	7.78269			0.0180993
$431$	274.915	−	89.3253i	0.637854	−	0.207251i	0.0278030	−	0.999613i	$-0.491149\pi$
$431$	274.915	−	89.3253i	0.637854	−	0.207251i	0.610051	+	0.792362i	$0.291149\pi$
$432$		0			0
$433$	−445.768	+	323.869i	−1.02949	+	0.747966i	−0.968206	−	0.250154i	$-0.919519\pi$
$433$	−445.768	+	323.869i	−1.02949	+	0.747966i	−0.0612810	+	0.998121i	$0.519519\pi$
$434$	11.6932	−	35.9879i	0.0269428	−	0.0829213i
$435$		0			0
$436$	−37.8311	−	52.0701i	−0.0867687	−	0.119427i
$437$	−30.7764	+	42.3600i	−0.0704265	+	0.0969337i
$438$		0			0
$439$		−	576.891i		−	1.31410i	−0.753846	−	0.657051i	$-0.771804\pi$
$439$		−	576.891i		−	1.31410i	0.753846	−	0.657051i	$-0.228196\pi$
$440$	−5.40519	−	9.57442i	−0.0122845	−	0.0217600i
$441$		0			0
$442$	−4.21261	+	1.36876i	−0.00953080	+	0.00309675i
$443$	−144.200	−	104.767i	−0.325508	−	0.236495i	0.413014	−	0.910724i	$-0.364476\pi$
$443$	−144.200	−	104.767i	−0.325508	−	0.236495i	−0.738522	+	0.674229i	$0.764476\pi$
$444$		0			0
$445$	−8.18701	+	25.1970i	−0.0183978	+	0.0566225i
$446$	−126.807	−	41.2022i	−0.284321	−	0.0923816i
$447$		0			0
$448$	3.71830	−	5.11780i	0.00829977	−	0.0114237i
$449$	−192.428	−	592.233i	−0.428570	−	1.31900i	−0.899534	−	0.436851i	$-0.856094\pi$
$449$	−192.428	−	592.233i	−0.428570	−	1.31900i	0.470963	−	0.882153i	$-0.343906\pi$
$450$		0			0
$451$	−398.408	+	433.974i	−0.883387	+	0.962249i
$452$	−58.4078			−0.129221
$453$		0			0
$454$	331.557	+	240.890i	0.730301	+	0.530595i
$455$	−0.0473002	+	0.0343656i	−0.000103956	+	7.55288e-5i
$456$		0			0
$457$	−749.250	−	243.446i	−1.63950	−	0.532704i	−0.663070	−	0.748557i	$-0.730747\pi$
$457$	−749.250	−	243.446i	−1.63950	−	0.532704i	−0.976426	+	0.215853i	$0.930747\pi$
$458$	189.716	+	261.121i	0.414227	+	0.570134i
$459$		0			0
$460$	5.27102	+	16.2225i	0.0114587	+	0.0352664i
$461$		−	377.985i		−	0.819924i	−0.912103	−	0.409962i	$-0.865542\pi$
$461$		−	377.985i		−	0.819924i	0.912103	−	0.409962i	$-0.134458\pi$
$462$		0			0
$463$	−49.3159			−0.106514			−0.0532569	−	0.998581i	$-0.516960\pi$
$463$	−49.3159			−0.106514			−0.0532569	+	0.998581i	$0.516960\pi$
$464$	67.8065	−	22.0317i	0.146135	−	0.0474821i
$465$		0			0
$466$	341.895	−	248.401i	0.733680	−	0.533050i
$467$	36.2129	−	111.452i	0.0775436	−	0.238655i	−0.904769	−	0.425902i	$-0.859957\pi$
$467$	36.2129	−	111.452i	0.0775436	−	0.238655i	0.982313	+	0.187248i	$0.0599567\pi$
$468$		0			0
$469$	−33.8970	−	46.6553i	−0.0722751	−	0.0994782i
$470$	−17.9647	+	24.7262i	−0.0382227	+	0.0526090i
$471$		0			0
$472$		−	145.624i		−	0.308525i
$473$	−19.5501	+	170.181i	−0.0413321	+	0.359791i
$474$		0			0
$475$	−51.3260	+	16.6768i	−0.108055	+	0.0351091i
$476$	19.1529	+	13.9154i	0.0402371	+	0.0292340i
$477$		0			0
$478$	−107.475	+	330.774i	−0.224843	+	0.691996i
$479$	−875.668	−	284.522i	−1.82812	−	0.593991i	−0.999411	−	0.0343053i	$-0.989078\pi$
$479$	−875.668	−	284.522i	−1.82812	−	0.593991i	−0.828705	−	0.559686i	$-0.810922\pi$
$480$		0			0
$481$	7.38940	−	10.1706i	0.0153626	−	0.0211448i
$482$	−163.190	−	502.246i	−0.338568	−	1.04200i
$483$		0			0
$484$	222.938	−	94.1423i	0.460615	−	0.194509i
$485$	−35.8708			−0.0739604
$486$		0			0
$487$	−313.986	−	228.124i	−0.644735	−	0.468427i	0.216739	−	0.976230i	$-0.430458\pi$
$487$	−313.986	−	228.124i	−0.644735	−	0.468427i	−0.861474	+	0.507802i	$0.830458\pi$
$488$	−93.2510	+	67.7508i	−0.191088	+	0.138834i
$489$		0			0
$490$	−22.9927	−	7.47077i	−0.0469238	−	0.0152465i
$491$	−214.526	−	295.270i	−0.436917	−	0.601365i	0.532607	−	0.846363i	$-0.321213\pi$
$491$	−214.526	−	295.270i	−0.436917	−	0.601365i	−0.969523	+	0.244998i	$0.921213\pi$
$492$		0			0
$493$	82.4513	+	253.759i	0.167244	+	0.514724i
$494$		−	0.641950i		−	0.00129949i
$495$		0			0
$496$	135.350			0.272884
$497$	71.4830	−	23.2262i	0.143829	−	0.0467329i
$498$		0			0
$499$	198.310	−	144.081i	0.397415	−	0.288739i	−0.371072	−	0.928604i	$-0.621010\pi$
$499$	198.310	−	144.081i	0.397415	−	0.288739i	0.768487	+	0.639865i	$0.221010\pi$
$500$	−10.8930	+	33.5251i	−0.0217859	+	0.0670502i
$501$		0			0
$502$	−298.771	−	411.223i	−0.595161	−	0.819169i
$503$	−172.959	+	238.058i	−0.343855	+	0.473276i	−0.945563	−	0.325440i	$-0.894487\pi$
$503$	−172.959	+	238.058i	−0.343855	+	0.473276i	0.601707	+	0.798717i	$0.294487\pi$
$504$		0			0
$505$		−	9.21825i		−	0.0182540i
$506$	−367.972	+	74.5083i	−0.727218	+	0.147250i
$507$		0			0
$508$	283.513	−	92.1190i	0.558097	−	0.181337i
$509$	−691.862	−	502.667i	−1.35926	−	0.987558i	−0.998492	−	0.0549019i	$-0.982515\pi$
$509$	−691.862	−	502.667i	−1.35926	−	0.987558i	−0.360766	−	0.932656i	$-0.617485\pi$
$510$		0			0
$511$	27.7397	−	85.3741i	0.0542852	−	0.167073i
$512$	21.5200	+	6.99226i	0.0420312	+	0.0136568i
$513$		0			0
$514$	29.7458	−	40.9416i	0.0578712	−	0.0796528i
$515$	3.44383	+	10.5990i	0.00668704	+	0.0205806i
$516$		0			0
$517$	−495.552	−	454.938i	−0.958514	−	0.879958i
$518$	−67.1925			−0.129715
$519$		0			0
$520$	−0.169189	−	0.122923i	−0.000325364	−	0.000236391i
$521$	−491.143	+	356.836i	−0.942693	+	0.684907i	−0.949068	−	0.315073i	$-0.897971\pi$
$521$	−491.143	+	356.836i	−0.942693	+	0.684907i	0.00637404	+	0.999980i	$0.497971\pi$
$522$		0			0
$523$	641.901	+	208.566i	1.22734	+	0.398788i	0.849752	−	0.527183i	$-0.176752\pi$
$523$	641.901	+	208.566i	1.22734	+	0.398788i	0.377593	+	0.925972i	$0.376752\pi$
$524$	195.104	+	268.537i	0.372335	+	0.512475i
$525$		0			0
$526$	159.366	+	490.478i	0.302977	+	0.932467i
$527$			506.535i			0.961166i
$528$		0			0
$529$	53.4586			0.101056
$530$	−28.0274	+	9.10664i	−0.0528818	+	0.0171823i
$531$		0			0
$532$	−2.77581	+	2.01674i	−0.00521768	+	0.00379087i
$533$	−3.46269	+	10.6571i	−0.00649660	+	0.0199945i
$534$		0			0
$535$	−16.7289	−	23.0254i	−0.0312690	−	0.0430381i
$536$	121.247	−	166.882i	0.226207	−	0.311347i
$537$		0			0
$538$			18.9178i			0.0351632i
$539$	221.118	−	484.005i	0.410237	−	0.897968i
$540$		0			0
$541$	−222.251	+	72.2137i	−0.410815	+	0.133482i	−0.507131	−	0.861869i	$-0.669294\pi$
$541$	−222.251	+	72.2137i	−0.410815	+	0.133482i	0.0963161	+	0.995351i	$0.469294\pi$
$542$	−81.0525	−	58.8881i	−0.149543	−	0.108650i
$543$		0			0
$544$	−26.1678	+	80.5363i	−0.0481026	+	0.148045i
$545$	10.8157	+	3.51425i	0.0198454	+	0.00644816i
$546$		0			0
$547$	560.308	−	771.198i	1.02433	−	1.40987i	0.115207	−	0.993342i	$-0.463247\pi$
$547$	560.308	−	771.198i	1.02433	−	1.40987i	0.909123	−	0.416527i	$-0.136753\pi$
$548$	−90.7693	−	279.359i	−0.165637	−	0.509779i
$549$		0			0
$550$	−351.975	−	160.800i	−0.639954	−	0.292363i
$551$	−38.6697			−0.0701810
$552$		0			0
$553$	−94.1206	−	68.3826i	−0.170200	−	0.123658i
$554$	90.7823	−	65.9572i	0.163867	−	0.119056i
$555$		0			0
$556$	−406.623	−	132.120i	−0.731337	−	0.237626i
$557$	−264.552	−	364.125i	−0.474959	−	0.653725i	0.502567	−	0.864538i	$-0.332389\pi$
$557$	−264.552	−	364.125i	−0.474959	−	0.653725i	−0.977526	+	0.210813i	$0.932389\pi$
$558$		0			0
$559$	1.00686	+	3.09879i	0.00180118	+	0.00554345i
$560$			1.11775i			0.00199598i
$561$		0			0
$562$	−485.205			−0.863354
$563$	−297.055	+	96.5192i	−0.527630	+	0.171437i	−0.560705	−	0.828016i	$-0.689470\pi$
$563$	−297.055	+	96.5192i	−0.527630	+	0.171437i	0.0330754	+	0.999453i	$0.489470\pi$
$564$		0			0
$565$	8.34926	−	6.06609i	0.0147774	−	0.0107364i
$566$	52.3017	−	160.968i	0.0924059	−	0.284396i
$567$		0			0
$568$	158.025	+	217.502i	0.278212	+	0.382926i
$569$	−331.841	+	456.740i	−0.583200	+	0.802706i	−0.994042	−	0.109000i	$-0.965235\pi$
$569$	−331.841	+	456.740i	−0.583200	+	0.802706i	0.410841	+	0.911707i	$0.365235\pi$
$570$		0			0
$571$		−	224.552i		−	0.393260i	−0.980478	−	0.196630i	$-0.937000\pi$
$571$		−	224.552i		−	0.393260i	0.980478	−	0.196630i	$-0.0629998\pi$
$572$	3.11291	−	3.39081i	0.00544215	−	0.00592798i
$573$		0			0
$574$	56.9597	−	18.5073i	0.0992330	−	0.0322428i
$575$	485.686	+	352.871i	0.844671	+	0.613689i
$576$		0			0
$577$	−326.124	+	1003.71i	−0.565207	+	1.73953i	0.102130	+	0.994771i	$0.467434\pi$
$577$	−326.124	+	1003.71i	−0.565207	+	1.73953i	−0.667337	+	0.744756i	$0.732566\pi$
$578$	87.3052	+	28.3672i	0.151047	+	0.0490782i
$579$		0			0
$580$	−7.40463	+	10.1916i	−0.0127666	+	0.0175717i
$581$	4.85658	+	14.9470i	0.00835900	+	0.0257264i
$582$		0			0
$583$	−128.727	−	635.739i	−0.220800	−	1.09046i
$584$	321.092			0.549815
$585$		0			0
$586$	13.1759	+	9.57282i	0.0224844	+	0.0163359i
$587$	−64.2470	+	46.6782i	−0.109450	+	0.0795200i	−0.641164	−	0.767404i	$-0.721548\pi$
$587$	−64.2470	+	46.6782i	−0.109450	+	0.0795200i	0.531714	+	0.846924i	$0.321548\pi$
$588$		0			0
$589$	−69.8186	−	22.6855i	−0.118538	−	0.0385152i
$590$	15.1241	+	20.8166i	0.0256341	+	0.0352823i
$591$		0			0
$592$	−74.2698	−	228.579i	−0.125456	−	0.386113i
$593$		−	709.519i		−	1.19649i	−0.801313	−	0.598245i	$-0.795865\pi$
$593$		−	709.519i		−	1.19649i	0.801313	−	0.598245i	$-0.204135\pi$
$594$		0			0
$595$	−4.18307			−0.00703037
$596$	439.849	−	142.916i	0.738001	−	0.239791i
$597$		0			0
$598$	−5.77731	+	4.19746i	−0.00966105	+	0.00701916i
$599$	−215.771	+	664.076i	−0.360219	+	1.10864i	0.592702	+	0.805422i	$0.298061\pi$
$599$	−215.771	+	664.076i	−0.360219	+	1.10864i	−0.952921	+	0.303219i	$0.901939\pi$
$600$		0			0
$601$	131.365	+	180.808i	0.218577	+	0.300845i	0.904198	−	0.427113i	$-0.140469\pi$
$601$	131.365	+	180.808i	0.218577	+	0.300845i	−0.685621	+	0.727958i	$0.740469\pi$
$602$	10.2361	−	14.0888i	0.0170035	−	0.0234033i
$603$		0			0
$604$			532.811i			0.882137i
$605$	−22.0911	+	36.6112i	−0.0365141	+	0.0605144i
$606$		0			0
$607$	906.706	−	294.607i	1.49375	−	0.485348i	0.555561	−	0.831476i	$-0.312503\pi$
$607$	906.706	−	294.607i	1.49375	−	0.485348i	0.938188	+	0.346127i	$0.112503\pi$
$608$	−9.92885	−	7.21373i	−0.0163303	−	0.0118647i
$609$		0			0
$610$	6.29358	−	19.3697i	0.0103173	−	0.0317535i
$611$	−12.1692	−	3.95402i	−0.0199169	−	0.00647139i
$612$		0			0
$613$	−16.3918	+	22.5614i	−0.0267403	+	0.0368049i	−0.822178	−	0.569231i	$-0.807241\pi$
$613$	−16.3918	+	22.5614i	−0.0267403	+	0.0368049i	0.795438	+	0.606036i	$0.207241\pi$
$614$	86.0300	+	264.773i	0.140114	+	0.431227i
$615$		0			0
$616$	−24.4414	−	2.80778i	−0.0396776	−	0.00455809i
$617$	997.165			1.61615			0.808075	−	0.589079i	$-0.200509\pi$
$617$	997.165			1.61615			0.808075	+	0.589079i	$0.200509\pi$
$618$		0			0
$619$	18.8208	+	13.6741i	0.0304052	+	0.0220907i	0.602884	−	0.797829i	$-0.294018\pi$
$619$	18.8208	+	13.6741i	0.0304052	+	0.0220907i	−0.572479	+	0.819919i	$0.694018\pi$
$620$	−19.3480	+	14.0571i	−0.0312065	+	0.0226728i
$621$		0			0
$622$	−363.708	−	118.176i	−0.584740	−	0.189994i
$623$	34.8456	+	47.9608i	0.0559319	+	0.0769837i
$624$		0			0
$625$	190.246	+	585.517i	0.304394	+	0.936828i
$626$			487.352i			0.778517i
$627$		0			0
$628$	208.557			0.332097
$629$	855.434	−	277.947i	1.35999	−	0.441888i
$630$		0			0
$631$	423.736	−	307.862i	0.671531	−	0.487896i	−0.199006	−	0.979998i	$-0.563771\pi$
$631$	423.736	−	307.862i	0.671531	−	0.487896i	0.870537	+	0.492103i	$0.163771\pi$
$632$	128.593	−	395.770i	0.203471	−	0.626218i
$633$		0			0
$634$	54.5065	+	75.0218i	0.0859724	+	0.118331i
$635$	−30.9603	+	42.6132i	−0.0487564	+	0.0671074i
$636$		0			0
$637$		−	10.1214i		−	0.0158891i
$638$	−204.255	−	187.515i	−0.320149	−	0.293911i
$639$		0			0
$640$	−3.80243	+	1.23548i	−0.00594129	+	0.00193044i
$641$	−54.5371	−	39.6235i	−0.0850813	−	0.0618152i	0.544431	−	0.838805i	$-0.316745\pi$
$641$	−54.5371	−	39.6235i	−0.0850813	−	0.0618152i	−0.629513	+	0.776990i	$0.716745\pi$
$642$		0			0
$643$	−249.209	+	766.988i	−0.387573	+	1.19283i	0.547024	+	0.837117i	$0.315761\pi$
$643$	−249.209	+	766.988i	−0.387573	+	1.19283i	−0.934597	+	0.355710i	$0.884239\pi$
$644$	36.2998	+	11.7945i	0.0563662	+	0.0183145i
$645$		0			0
$646$	26.9967	−	37.1577i	0.0417905	−	0.0575197i
$647$	300.028	+	923.392i	0.463722	+	1.42719i	0.860582	+	0.509311i	$0.170100\pi$
$647$	300.028	+	923.392i	0.463722	+	1.42719i	−0.396860	+	0.917879i	$0.629900\pi$
$648$		0			0
$649$	−493.179	+	278.422i	−0.759906	+	0.429001i
$650$	−7.36038			−0.0113237
$651$		0			0
$652$	−452.512	−	328.769i	−0.694037	−	0.504247i
$653$	22.6871	−	16.4831i	0.0347429	−	0.0252422i	−0.570278	−	0.821452i	$-0.693165\pi$
$653$	22.6871	−	16.4831i	0.0347429	−	0.0252422i	0.605021	+	0.796209i	$0.293165\pi$
$654$		0			0
$655$	−55.7792	−	18.1238i	−0.0851591	−	0.0276699i
$656$	125.919	+	173.312i	0.191949	+	0.264195i
$657$		0			0
$658$	21.1334	+	65.0419i	0.0321176	+	0.0988478i
$659$		−	570.449i		−	0.865628i	−0.901483	−	0.432814i	$-0.857521\pi$
$659$		−	570.449i		−	0.865628i	0.901483	−	0.432814i	$-0.142479\pi$
$660$		0			0
$661$	854.772			1.29315			0.646575	−	0.762851i	$-0.276201\pi$
$661$	854.772			1.29315			0.646575	+	0.762851i	$0.276201\pi$
$662$	−142.325	+	46.2443i	−0.214993	+	0.0698555i
$663$		0			0
$664$	−45.4794	+	33.0427i	−0.0684931	+	0.0497632i
$665$	0.187341	−	0.576577i	0.000281716	−	0.000867034i
$666$		0			0
$667$	252.846	+	348.013i	0.379080	+	0.521758i
$668$	−302.058	+	415.747i	−0.452182	+	0.622376i
$669$		0			0
$670$			36.4478i			0.0543998i
$671$	407.739	+	186.276i	0.607659	+	0.277609i
$672$		0			0
$673$	336.109	−	109.208i	0.499418	−	0.162271i	−0.0484662	−	0.998825i	$-0.515433\pi$
$673$	336.109	−	109.208i	0.499418	−	0.162271i	0.547885	+	0.836554i	$0.315433\pi$
$674$	−258.138	−	187.548i	−0.382994	−	0.278261i
$675$		0			0
$676$	−104.421	+	321.374i	−0.154468	+	0.475405i
$677$	1181.53	+	383.903i	1.74525	+	0.567065i	0.995509	−	0.0946695i	$-0.0301794\pi$
$677$	1181.53	+	383.903i	1.74525	+	0.567065i	0.749738	+	0.661735i	$0.230179\pi$
$678$		0			0
$679$	−47.1787	+	64.9359i	−0.0694826	+	0.0956346i
$680$	−4.62367	−	14.2302i	−0.00679952	−	0.0209268i
$681$		0			0
$682$	−258.780	−	458.386i	−0.379443	−	0.672121i
$683$	818.617			1.19856			0.599281	−	0.800539i	$-0.295453\pi$
$683$	818.617			1.19856			0.599281	+	0.800539i	$0.295453\pi$
$684$		0			0
$685$	41.9888	+	30.5067i	0.0612975	+	0.0445353i
$686$	−88.0957	+	64.0052i	−0.128419	+	0.0933021i
$687$		0			0
$688$	59.2423	+	19.2490i	0.0861079	+	0.0279782i
$689$	−7.25187	−	9.98134i	−0.0105252	−	0.0144867i
$690$		0			0
$691$	84.5050	+	260.080i	0.122294	+	0.376381i	0.993398	−	0.114716i	$-0.0365959\pi$
$691$	84.5050	+	260.080i	0.122294	+	0.376381i	−0.871105	+	0.491098i	$0.836596\pi$
$692$		−	220.377i		−	0.318464i
$693$		0			0
$694$	191.723			0.276258
$695$	71.8475	−	23.3447i	0.103378	−	0.0335895i
$696$		0			0
$697$	−648.603	+	471.238i	−0.930564	+	0.676094i
$698$	−218.575	+	672.705i	−0.313145	+	0.963761i
$699$		0			0
$700$	23.1233	+	31.8265i	0.0330333	+	0.0454664i
$701$	298.072	−	410.262i	0.425210	−	0.585252i	−0.541635	−	0.840614i	$-0.682195\pi$
$701$	298.072	−	410.262i	0.425210	−	0.585252i	0.966846	+	0.255362i	$0.0821946\pi$
$702$		0			0
$703$			130.358i			0.185430i
$704$	−17.4641	−	86.2497i	−0.0248070	−	0.122514i
$705$		0			0
$706$	431.195	−	140.104i	0.610758	−	0.198447i
$707$	−16.6875	−	12.1242i	−0.0236033	−	0.0171488i
$708$		0			0
$709$	178.793	−	550.269i	0.252177	−	0.776119i	−0.742196	−	0.670183i	$-0.766216\pi$
$709$	178.793	−	550.269i	0.252177	−	0.776119i	0.994373	−	0.105937i	$-0.0337842\pi$
$710$	−45.1785	−	14.6794i	−0.0636317	−	0.0206752i
$711$		0			0
$712$	−124.640	+	171.552i	−0.175056	+	0.240944i
$713$	252.356	+	776.672i	0.353936	+	1.08930i
$714$		0			0
$715$	−0.0928224	+	0.808008i	−0.000129822	+	0.00113008i
$716$	54.2534			0.0757729
$717$		0			0
$718$	129.782	+	94.2920i	0.180755	+	0.131326i
$719$	31.7569	−	23.0727i	0.0441681	−	0.0320900i	−0.565482	−	0.824761i	$-0.691310\pi$
$719$	31.7569	−	23.0727i	0.0441681	−	0.0320900i	0.609650	+	0.792671i	$0.291310\pi$
$720$		0			0
$721$	23.7165	+	7.70597i	0.0328940	+	0.0106879i
$722$	−296.170	−	407.643i	−0.410208	−	0.564603i
$723$		0			0
$724$	−160.424	−	493.734i	−0.221580	−	0.681953i
$725$			443.374i			0.611550i
$726$		0			0
$727$	918.828			1.26386			0.631932	−	0.775024i	$-0.282262\pi$
$727$	918.828			1.26386			0.631932	+	0.775024i	$0.282262\pi$
$728$	−0.445048	+	0.144605i	−0.000611330	+	0.000198633i
$729$		0			0
$730$	−45.8993	+	33.3478i	−0.0628758	+	0.0456820i
$731$	−72.0374	+	221.708i	−0.0985463	+	0.303294i
$732$		0			0
$733$	434.317	+	597.786i	0.592520	+	0.815534i	0.994998	−	0.0998958i	$-0.0318509\pi$
$733$	434.317	+	597.786i	0.592520	+	0.815534i	−0.402478	+	0.915430i	$0.631851\pi$
$734$	74.4538	−	102.477i	0.101436	−	0.139614i
$735$		0			0
$736$			136.524i			0.185494i
$737$	−796.990	−	91.5568i	−1.08140	−	0.124229i
$738$		0			0
$739$	1082.21	−	351.633i	1.46443	−	0.475822i	0.535011	−	0.844845i	$-0.320308\pi$
$739$	1082.21	−	351.633i	1.46443	−	0.475822i	0.929420	+	0.369023i	$0.120308\pi$
$740$	34.3564	+	24.9614i	0.0464275	+	0.0337316i
$741$		0			0
$742$	−20.3772	+	62.7145i	−0.0274625	+	0.0845209i
$743$	−179.099	−	58.1929i	−0.241049	−	0.0783215i	0.186001	−	0.982550i	$-0.440447\pi$
$743$	−179.099	−	58.1929i	−0.241049	−	0.0783215i	−0.427050	+	0.904228i	$0.640447\pi$
$744$		0			0
$745$	−48.0325	+	66.1111i	−0.0644732	+	0.0887397i
$746$	120.421	+	370.616i	0.161422	+	0.496805i
$747$		0			0
$748$	322.781	−	65.3578i	0.431525	−	0.0873767i
$749$	−63.6848			−0.0850264
$750$		0			0
$751$	−489.777	−	355.844i	−0.652166	−	0.473827i	0.211842	−	0.977304i	$-0.432054\pi$
$751$	−489.777	−	355.844i	−0.652166	−	0.473827i	−0.864008	+	0.503477i	$0.832054\pi$
$752$	−197.904	+	143.785i	−0.263170	+	0.191204i
$753$		0			0
$754$	−5.01587	−	1.62976i	−0.00665235	−	0.00216148i
$755$	−55.3365	−	76.1641i	−0.0732933	−	0.100880i
$756$		0			0
$757$	−120.088	−	369.594i	−0.158637	−	0.488235i	0.839874	−	0.542781i	$-0.182629\pi$
$757$	−120.088	−	369.594i	−0.158637	−	0.488235i	−0.998511	+	0.0545462i	$0.982629\pi$
$758$		−	248.258i		−	0.327517i
$759$		0			0
$760$	2.16851			0.00285330
$761$	−664.937	+	216.051i	−0.873768	+	0.283904i	−0.711367	−	0.702821i	$-0.751924\pi$
$761$	−664.937	+	216.051i	−0.873768	+	0.283904i	−0.162400	+	0.986725i	$0.551924\pi$
$762$		0			0
$763$	20.5870	−	14.9574i	0.0269817	−	0.0196034i
$764$	−77.1197	+	237.350i	−0.100942	+	0.310667i
$765$		0			0
$766$	−42.5426	−	58.5549i	−0.0555387	−	0.0764424i
$767$	−6.33178	+	8.71494i	−0.00825525	+	0.0113624i
$768$		0			0
$769$			337.074i			0.438328i	0.975688	+	0.219164i	$0.0703330\pi$
$769$			337.074i			0.438328i	−0.975688	+	0.219164i	$0.929667\pi$
$770$	3.78545	−	2.13706i	0.00491617	−	0.00277540i
$771$		0			0
$772$	79.8682	−	25.9507i	0.103456	−	0.0336149i
$773$	−643.324	−	467.403i	−0.832244	−	0.604660i	0.0879495	−	0.996125i	$-0.471969\pi$
$773$	−643.324	−	467.403i	−0.832244	−	0.604660i	−0.920193	+	0.391464i	$0.871969\pi$
$774$		0			0
$775$	−260.104	+	800.517i	−0.335618	+	1.03292i
$776$	−273.050	−	88.7195i	−0.351869	−	0.114329i
$777$		0			0
$778$	19.0410	−	26.2078i	0.0244744	−	0.0336861i
$779$	−35.9054	−	110.505i	−0.0460916	−	0.141855i
$780$		0			0
$781$	434.476	−	951.026i	0.556308	−	1.21770i
$782$	−510.926			−0.653358
$783$		0			0
$784$	−156.544	−	113.736i	−0.199673	−	0.145071i
$785$	−29.8127	+	21.6602i	−0.0379780	+	0.0275926i
$786$		0			0
$787$	−508.815	−	165.324i	−0.646525	−	0.210069i	−0.0326436	−	0.999467i	$-0.510393\pi$
$787$	−508.815	−	165.324i	−0.646525	−	0.210069i	−0.613881	+	0.789398i	$0.710393\pi$
$788$	−322.504	−	443.889i	−0.409269	−	0.563311i
$789$		0			0
$790$	22.7216	+	69.9298i	0.0287615	+	0.0885188i
$791$		−	23.0928i		−	0.0291944i
$792$		0			0
$793$	8.52651			0.0107522
$794$	−176.268	+	57.2729i	−0.222000	+	0.0721321i
$795$		0			0
$796$	−244.290	+	177.487i	−0.306897	+	0.222974i
$797$	219.724	−	676.242i	0.275689	−	0.848484i	−0.713347	−	0.700811i	$-0.752822\pi$
$797$	219.724	−	676.242i	0.275689	−	0.848484i	0.989036	−	0.147673i	$-0.0471783\pi$
$798$		0			0
$799$	−538.102	−	740.634i	−0.673470	−	0.926952i
$800$	−82.7102	+	113.841i	−0.103388	+	0.142301i
$801$		0			0
$802$		−	1097.22i		−	1.36810i
$803$	−613.905	−	1087.43i	−0.764514	−	1.35421i
$804$		0			0
$805$	−6.41393	+	2.08401i	−0.00796761	+	0.00258883i
$806$	−8.10013	−	5.88509i	−0.0100498	−	0.00730160i
$807$		0			0
$808$	22.7996	−	70.1698i	0.0282173	−	0.0868438i
$809$	102.321	+	33.2462i	0.126479	+	0.0410954i	0.371572	−	0.928404i	$-0.378819\pi$
$809$	102.321	+	33.2462i	0.126479	+	0.0410954i	−0.245094	+	0.969499i	$0.578819\pi$
$810$		0			0
$811$	−738.698	+	1016.73i	−0.910848	+	1.25368i	0.0560279	+	0.998429i	$0.482156\pi$
$811$	−738.698	+	1016.73i	−0.910848	+	1.25368i	−0.966876	+	0.255246i	$0.917844\pi$
$812$	8.71070	+	26.8088i	0.0107275	+	0.0330157i
$813$		0			0
$814$	−632.123	+	688.554i	−0.776564	+	0.845890i
$815$	98.8308			0.121265
$816$		0			0
$817$	−27.3331	−	19.8587i	−0.0334555	−	0.0243068i
$818$	855.094	−	621.262i	1.04535	−	0.759489i
$819$		0			0
$820$	−35.9995	−	11.6970i	−0.0439019	−	0.0142646i
$821$	608.067	+	836.933i	0.740642	+	1.01941i	0.998581	+	0.0532455i	$0.0169566\pi$
$821$	608.067	+	836.933i	0.740642	+	1.01941i	−0.257939	+	0.966161i	$0.583043\pi$
$822$		0			0
$823$	−165.580	−	509.603i	−0.201191	−	0.619202i	−0.999848	−	0.0174160i	$-0.994456\pi$
$823$	−165.580	−	509.603i	−0.201191	−	0.619202i	0.798657	−	0.601786i	$-0.205544\pi$
$824$			89.1979i			0.108250i
$825$		0			0
$826$	57.5755			0.0697039
$827$	−131.119	+	42.6030i	−0.158547	+	0.0515151i	−0.387215	−	0.921989i	$-0.626563\pi$
$827$	−131.119	+	42.6030i	−0.158547	+	0.0515151i	0.228668	+	0.973504i	$0.426563\pi$
$828$		0			0
$829$	7.75076	−	5.63126i	0.00934954	−	0.00679283i	−0.583101	−	0.812400i	$-0.698161\pi$
$829$	7.75076	−	5.63126i	0.00934954	−	0.00679283i	0.592450	+	0.805607i	$0.298161\pi$
$830$	3.06944	−	9.44677i	0.00369812	−	0.0113817i
$831$		0			0
$832$	−0.983850	−	1.35415i	−0.00118251	−	0.00162759i
$833$	425.645	−	585.850i	0.510978	−	0.703301i
$834$		0			0
$835$		−	90.8011i		−	0.108744i
$836$	−5.44727	+	47.4178i	−0.00651588	+	0.0567199i
$837$		0			0
$838$	−549.333	+	178.489i	−0.655528	+	0.212994i
$839$	−388.855	−	282.520i	−0.463474	−	0.336734i	0.331418	−	0.943484i	$-0.392473\pi$
$839$	−388.855	−	282.520i	−0.463474	−	0.336734i	−0.794893	+	0.606750i	$0.792473\pi$
$840$		0			0
$841$	161.710	−	497.693i	0.192283	−	0.591787i
$842$	140.567	+	45.6731i	0.166945	+	0.0542436i
$843$		0			0
$844$	−21.9641	+	30.2309i	−0.0260238	+	0.0358186i
$845$	−18.4504	−	56.7845i	−0.0218348	−	0.0672006i
$846$		0			0
$847$	37.2212	+	88.1433i	0.0439447	+	0.104065i
$848$	−235.869			−0.278148
$849$		0			0
$850$	−426.038	−	309.534i	−0.501221	−	0.364158i
$851$	1173.17	−	852.357i	1.37858	−	1.00159i
$852$		0			0
$853$	−1443.72	−	469.094i	−1.69252	−	0.549934i	−0.705248	−	0.708960i	$-0.749165\pi$
$853$	−1443.72	−	469.094i	−1.69252	−	0.549934i	−0.987274	+	0.159026i	$0.949165\pi$
$854$	−26.7868	−	36.8688i	−0.0313662	−	0.0431719i
$855$		0			0
$856$	−70.3926	−	216.646i	−0.0822344	−	0.253091i
$857$			229.336i			0.267603i	0.991008	+	0.133802i	$0.0427185\pi$
$857$			229.336i			0.267603i	−0.991008	+	0.133802i	$0.957282\pi$
$858$		0			0
$859$	−308.792			−0.359478			−0.179739	−	0.983714i	$-0.557525\pi$
$859$	−308.792			−0.359478			−0.179739	+	0.983714i	$0.557525\pi$
$860$	−10.4677	+	3.40116i	−0.0121717	+	0.00395484i
$861$		0			0
$862$	−330.723	+	240.285i	−0.383670	+	0.278752i
$863$	−159.802	+	491.821i	−0.185171	+	0.569897i	−0.999951	−	0.00987257i	$-0.996857\pi$
$863$	−159.802	+	491.821i	−0.185171	+	0.569897i	0.814781	+	0.579770i	$0.196857\pi$
$864$		0			0
$865$	22.8879	+	31.5024i	0.0264600	+	0.0364190i
$866$	458.020	−	630.411i	0.528892	−	0.727957i
$867$		0			0
$868$			53.5137i			0.0616517i
$869$	−1586.20	+	321.180i	−1.82532	+	0.369597i
$870$		0			0
$871$	−14.5122	+	4.71530i	−0.0166616	+	0.00541367i
$872$	73.6382	+	53.5013i	0.0844475	+	0.0613547i
$873$		0			0
$874$	22.8821	−	70.4239i	0.0261809	−	0.0805765i
$875$	−13.2549	−	4.30677i	−0.0151484	−	0.00492202i
$876$		0			0
$877$	148.255	−	204.056i	0.169048	−	0.232675i	−0.716084	−	0.698014i	$-0.754067\pi$
$877$	148.255	−	204.056i	0.169048	−	0.232675i	0.885133	+	0.465339i	$0.154067\pi$
$878$	252.111	+	775.916i	0.287142	+	0.883732i
$879$		0			0
$880$	11.4541	+	10.5154i	0.0130161	+	0.0119493i
$881$	−830.794			−0.943012			−0.471506	−	0.881863i	$-0.656289\pi$
$881$	−830.794			−0.943012			−0.471506	+	0.881863i	$0.656289\pi$
$882$		0			0
$883$	−435.210	−	316.199i	−0.492877	−	0.358096i	0.313413	−	0.949617i	$-0.398528\pi$
$883$	−435.210	−	316.199i	−0.492877	−	0.358096i	−0.806290	+	0.591521i	$0.798528\pi$
$884$	5.06778	−	3.68196i	0.00573279	−	0.00416511i
$885$		0			0
$886$	239.733	+	77.8941i	0.270579	+	0.0879166i
$887$	−840.566	−	1156.94i	−0.947651	−	1.30433i	−0.952563	−	0.304341i	$-0.901564\pi$
$887$	−840.566	−	1156.94i	−0.947651	−	1.30433i	0.00491261	−	0.999988i	$-0.498436\pi$
$888$		0			0
$889$	36.4213	+	112.093i	0.0409688	+	0.126089i
$890$		−	37.4678i		−	0.0420986i
$891$		0			0
$892$	188.562			0.211392
$893$	126.185	−	41.0001i	0.141305	−	0.0459127i
$894$		0			0
$895$	−7.75540	+	5.63463i	−0.00866525	+	0.00629567i
$896$	−2.76454	+	8.50838i	−0.00308543	+	0.00949596i
$897$		0			0
$898$	517.630	+	712.457i	0.576426	+	0.793382i
$899$	−354.505	+	487.935i	−0.394333	+	0.542753i
$900$		0			0
$901$		−	882.717i		−	0.979708i
$902$	346.203	−	757.805i	0.383817	−	0.840138i
$903$		0			0
$904$	78.5583	−	25.5251i	0.0869007	−	0.0282358i
$905$	74.2103	+	53.9169i	0.0820003	+	0.0595767i
$906$		0			0
$907$	−418.026	+	1286.55i	−0.460889	+	1.41847i	0.403191	+	0.915116i	$0.367901\pi$
$907$	−418.026	+	1286.55i	−0.460889	+	1.41847i	−0.864080	+	0.503355i	$0.832099\pi$
$908$	−551.215	−	179.101i	−0.607065	−	0.197248i
$909$		0			0
$910$	0.0486003	−	0.0668926i	5.34069e−5	−	7.35083e-5i
$911$	263.965	+	812.400i	0.289753	+	0.891768i	0.984934	+	0.172933i	$0.0553243\pi$
$911$	263.965	+	812.400i	0.289753	+	0.891768i	−0.695181	+	0.718835i	$0.744676\pi$
$912$		0			0
$913$	198.858	+	90.8485i	0.217808	+	0.0995054i
$914$	1114.13			1.21896
$915$		0			0
$916$	−369.281	−	268.299i	−0.403146	−	0.292902i
$917$	−106.172	+	77.1385i	−0.115782	+	0.0841204i
$918$		0			0
$919$	−314.056	−	102.043i	−0.341737	−	0.111037i	0.133120	−	0.991100i	$-0.457500\pi$
$919$	−314.056	−	102.043i	−0.341737	−	0.111037i	−0.474857	+	0.880063i	$0.657500\pi$
$920$	−14.1790	−	19.5157i	−0.0154120	−	0.0212127i
$921$		0			0
$922$	165.185	+	508.389i	0.179160	+	0.551398i
$923$		−	19.8875i		−	0.0215466i
$924$		0			0
$925$	1494.64			1.61582
$926$	66.3297	−	21.5518i	0.0716303	−	0.0232741i
$927$		0			0
$928$	−81.5714	+	59.2651i	−0.0879002	+	0.0638632i
$929$	35.3551	−	108.812i	0.0380572	−	0.117128i	−0.930223	−	0.366995i	$-0.880387\pi$
$929$	35.3551	−	108.812i	0.0380572	−	0.117128i	0.968280	+	0.249867i	$0.0803868\pi$
$930$		0			0
$931$	61.6884	+	84.9068i	0.0662603	+	0.0911995i
$932$	−351.292	+	483.512i	−0.376923	+	0.518790i
$933$		0			0
$934$			165.728i			0.177439i
$935$	−39.3529	+	42.8660i	−0.0420886	+	0.0458460i
$936$		0			0
$937$	1540.46	−	500.527i	1.64404	−	0.534181i	0.666603	−	0.745413i	$-0.267748\pi$
$937$	1540.46	−	500.527i	1.64404	−	0.534181i	0.977436	+	0.211233i	$0.0677478\pi$
$938$	65.9805	+	47.9376i	0.0703417	+	0.0511062i
$939$		0			0
$940$	13.3567	−	41.1076i	0.0142092	−	0.0437315i
$941$	−722.085	−	234.620i	−0.767359	−	0.249330i	−0.100925	−	0.994894i	$-0.532180\pi$
$941$	−722.085	−	234.620i	−0.767359	−	0.249330i	−0.666434	+	0.745564i	$0.732180\pi$
$942$		0			0
$943$	−759.735	+	1045.69i	−0.805658	+	1.10889i
$944$	63.6398	+	195.863i	0.0674151	+	0.207482i
$945$		0			0
$946$	−48.0770	−	237.437i	−0.0508214	−	0.250990i
$947$	−1855.32			−1.95915			−0.979575	−	0.201079i	$-0.935555\pi$
$947$	−1855.32			−1.95915			−0.979575	+	0.201079i	$0.935555\pi$
$948$		0			0
$949$	−19.2160	−	13.9612i	−0.0202486	−	0.0147115i
$950$	61.7453	−	44.8606i	0.0649951	−	0.0472217i
$951$		0			0
$952$	−31.8418	−	10.3460i	−0.0334472	−	0.0108677i
$953$	955.025	+	1314.48i	1.00212	+	1.37931i	0.924013	+	0.382361i	$0.124889\pi$
$953$	955.025	+	1314.48i	1.00212	+	1.37931i	0.0781115	+	0.996945i	$0.475111\pi$
$954$		0			0
$955$	−13.6265	−	41.9381i	−0.0142686	−	0.0439142i
$956$		−	491.859i		−	0.514496i
$957$		0			0
$958$	1302.11			1.35920
$959$	110.451	−	35.8876i	0.115173	−	0.0374219i
$960$		0			0
$961$	−148.843	+	108.141i	−0.154884	+	0.112530i
$962$	−5.49399	+	16.9088i	−0.00571101	+	0.0175767i
$963$		0			0
$964$	438.979	+	604.203i	0.455373	+	0.626767i
$965$	−8.72179	+	12.0045i	−0.00903812	+	0.0124399i
$966$		0			0
$967$		−	325.104i		−	0.336199i	−0.985770	−	0.168099i	$-0.946237\pi$
$967$		−	325.104i		−	0.336199i	0.985770	−	0.168099i	$-0.0537629\pi$
$968$	−258.709	+	224.048i	−0.267261	+	0.231455i
$969$		0			0
$970$	48.2461	−	15.6761i	0.0497383	−	0.0161609i
$971$	227.145	+	165.031i	0.233929	+	0.169960i	0.698574	−	0.715537i	$-0.253818\pi$
$971$	227.145	+	165.031i	0.233929	+	0.169960i	−0.464645	+	0.885497i	$0.653818\pi$
$972$		0			0
$973$	52.2365	−	160.767i	0.0536860	−	0.165229i
$974$	522.004	+	169.609i	0.535938	+	0.174137i
$975$		0			0
$976$	95.8141	−	131.877i	0.0981702	−	0.135120i
$977$	−497.452	−	1531.00i	−0.509163	−	1.56704i	−0.793658	−	0.608364i	$-0.791826\pi$
$977$	−497.452	−	1531.00i	−0.509163	−	1.56704i	0.284495	−	0.958678i	$-0.408174\pi$
$978$		0			0
$979$	819.293	+	94.1188i	0.836867	+	0.0961377i
$980$	34.1899			0.0348877
$981$		0			0
$982$	417.575	+	303.386i	0.425229	+	0.308947i
$983$	−302.881	+	220.056i	−0.308119	+	0.223862i	−0.731089	−	0.682282i	$-0.760988\pi$
$983$	−302.881	+	220.056i	−0.308119	+	0.223862i	0.422970	+	0.906144i	$0.360988\pi$
$984$		0			0
$985$	92.2025	+	29.9584i	0.0936066	+	0.0304146i
$986$	−221.794	−	305.273i	−0.224943	−	0.309607i
$987$		0			0
$988$	0.280542	+	0.863421i	0.000283950	+	0.000873908i
$989$			375.836i			0.380016i
$990$		0			0
$991$	−943.875			−0.952447			−0.476223	−	0.879324i	$-0.657995\pi$
$991$	−943.875			−0.952447			−0.476223	+	0.879324i	$0.657995\pi$
$992$	−182.046	+	59.1502i	−0.183514	+	0.0596272i
$993$		0			0
$994$	−85.9942	+	62.4785i	−0.0865133	+	0.0628556i
$995$	16.4873	−	50.7427i	0.0165702	−	0.0509977i
$996$		0			0
$997$	400.666	+	551.470i	0.401872	+	0.553129i	0.961213	−	0.275809i	$-0.0889457\pi$
$997$	400.666	+	551.470i	0.401872	+	0.553129i	−0.559341	+	0.828938i	$0.688946\pi$
$998$	−203.761	+	280.453i	−0.204169	+	0.281015i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.3.j.b.127.2		16
3.2	odd	2		66.3.f.a.61.4	yes	16
11.2	odd	10	inner	198.3.j.b.145.2		16
11.3	even	5		2178.3.d.m.1693.12		16
11.8	odd	10		2178.3.d.m.1693.4		16
12.11	even	2		528.3.bf.c.193.1		16
33.2	even	10		66.3.f.a.13.4	✓	16
33.8	even	10		726.3.d.e.241.10		16
33.14	odd	10		726.3.d.e.241.2		16
132.35	odd	10		528.3.bf.c.145.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.3.f.a.13.4	✓	16	33.2	even	10
66.3.f.a.61.4	yes	16	3.2	odd	2
198.3.j.b.127.2		16	1.1	even	1	trivial
198.3.j.b.145.2		16	11.2	odd	10	inner
528.3.bf.c.145.1		16	132.35	odd	10
528.3.bf.c.193.1		16	12.11	even	2
726.3.d.e.241.2		16	33.14	odd	10
726.3.d.e.241.10		16	33.8	even	10
2178.3.d.m.1693.4		16	11.8	odd	10
2178.3.d.m.1693.12		16	11.3	even	5

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)

\(f(q)\)	\(=\)	\(q+(-1.34500 + 0.437016i) q^{2} +(1.61803 - 1.17557i) q^{4} +(-0.109202 + 0.336090i) q^{5} +(0.464787 + 0.639725i) q^{7} +(-1.66251 + 2.28825i) q^{8} -0.499764i q^{10} +(10.9281 + 1.25540i) q^{11} +(0.198988 - 0.0646551i) q^{13} +(-0.904708 - 0.657309i) q^{14} +(1.23607 - 3.80423i) q^{16} +(14.2369 + 4.62586i) q^{17} +(-1.27522 + 1.75519i) q^{19} +(0.218405 + 0.672180i) q^{20} +(-15.2469 + 3.08725i) q^{22} +24.1342 q^{23} +(20.1244 + 14.6212i) q^{25} +(-0.239383 + 0.173922i) q^{26} +(1.50408 + 0.488706i) q^{28} +(10.4767 + 14.4199i) q^{29} +(10.4564 + 32.1814i) q^{31} +5.65685i q^{32} -21.1702 q^{34} +(-0.265761 + 0.0863510i) q^{35} +(48.6102 - 35.3174i) q^{37} +(0.948120 - 2.91801i) q^{38} +(-0.587507 - 0.808634i) q^{40} +(-31.4796 + 43.3280i) q^{41} +15.5727i q^{43} +(19.1579 - 10.8155i) q^{44} +(-32.4604 + 10.5470i) q^{46} +(-49.4759 - 35.9463i) q^{47} +(14.9486 - 46.0071i) q^{49} +(-33.4570 - 10.8708i) q^{50} +(0.245962 - 0.338538i) q^{52} +(-18.2219 - 56.0812i) q^{53} +(-1.61531 + 3.53574i) q^{55} -2.23656 q^{56} +(-20.3928 - 14.8163i) q^{58} +(-41.6528 + 30.2625i) q^{59} +(38.7576 + 12.5931i) q^{61} +(-28.1276 - 38.7143i) q^{62} +(-2.47214 - 7.60845i) q^{64} +0.0739383i q^{65} -72.9302 q^{67} +(28.4739 - 9.25172i) q^{68} +(0.319711 - 0.232284i) q^{70} +(29.3727 - 90.3998i) q^{71} +(-66.7272 - 91.8421i) q^{73} +(-49.9464 + 68.7453i) q^{74} +4.33906i q^{76} +(4.27614 + 7.57449i) q^{77} +(-139.926 + 45.4646i) q^{79} +(1.14358 + 0.830861i) q^{80} +(23.4050 - 72.0331i) q^{82} +(18.9025 + 6.14179i) q^{83} +(-3.10941 + 4.27974i) q^{85} +(-6.80554 - 20.9453i) q^{86} +(-21.0408 + 22.9191i) q^{88} +74.9710 q^{89} +(0.133848 + 0.0972466i) q^{91} +(39.0499 - 28.3714i) q^{92} +(82.2540 + 26.7260i) q^{94} +(-0.450645 - 0.620259i) q^{95} +(31.3671 + 96.5379i) q^{97} +68.4122i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 8 q^{5} + 60 q^{7} + 4 q^{11} - 60 q^{13} + 32 q^{14} - 16 q^{16} + 60 q^{17} + 16 q^{20} - 48 q^{22} + 8 q^{23} - 48 q^{25} - 48 q^{26} + 40 q^{28} + 160 q^{29} + 32 q^{31} - 64 q^{34}+ \cdots + 324 q^{97}+O(q^{100}) \) 16 * q + 8 * q^4 - 8 * q^5 + 60 * q^7 + 4 * q^11 - 60 * q^13 + 32 * q^14 - 16 * q^16 + 60 * q^17 + 16 * q^20 - 48 * q^22 + 8 * q^23 - 48 * q^25 - 48 * q^26 + 40 * q^28 + 160 * q^29 + 32 * q^31 - 64 * q^34 - 160 * q^35 - 84 * q^37 + 48 * q^38 - 80 * q^40 - 40 * q^41 - 168 * q^44 + 160 * q^46 - 372 * q^47 + 96 * q^49 - 160 * q^50 + 40 * q^52 + 124 * q^53 + 32 * q^55 + 96 * q^56 - 16 * q^58 + 172 * q^59 + 100 * q^61 + 40 * q^62 + 32 * q^64 + 248 * q^67 + 120 * q^68 + 8 * q^70 - 48 * q^71 + 160 * q^73 - 80 * q^74 + 172 * q^77 - 460 * q^79 + 48 * q^80 - 24 * q^82 + 420 * q^83 - 420 * q^85 + 456 * q^86 - 144 * q^88 + 360 * q^89 - 252 * q^91 + 64 * q^92 - 280 * q^94 - 180 * q^95 + 324 * q^97

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