LMFDB - Embedded newform 378.3.o.a.307.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,3,Mod(181,378)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(378, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 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("378.181"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	378.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$10.2997539928$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			307.7
Character	$\chi$	$=$	378.307
Dual form			378.3.o.a.181.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(4.98058 + 2.87554i) q^{5} +(5.06966 - 4.82685i) q^{7} +2.82843 q^{8} -8.13325i q^{10} +(8.66094 + 15.0012i) q^{11} +(-11.7856 - 6.80443i) q^{13} +(-9.49646 - 2.79594i) q^{14} +(-2.00000 - 3.46410i) q^{16} +10.4941i q^{17} +23.0584i q^{19} +(-9.96116 + 5.75108i) q^{20} +(12.2484 - 21.2149i) q^{22} +(13.5925 - 23.5429i) q^{23} +(4.03745 + 6.99307i) q^{25} +19.2458i q^{26} +(3.29069 + 13.6078i) q^{28} +(22.7948 + 39.4817i) q^{29} +(0.774381 + 0.447089i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(12.8526 - 7.42048i) q^{34} +(39.1297 - 9.46251i) q^{35} +51.1625 q^{37} +(28.2407 - 16.3048i) q^{38} +(14.0872 + 8.13325i) q^{40} +(-21.1730 - 12.2242i) q^{41} +(-5.94767 - 10.3017i) q^{43} -34.6438 q^{44} -38.4454 q^{46} +(14.4813 - 8.36076i) q^{47} +(2.40298 - 48.9410i) q^{49} +(5.70982 - 9.88970i) q^{50} +(23.5712 - 13.6089i) q^{52} +79.0686 q^{53} +99.6195i q^{55} +(14.3392 - 13.6524i) q^{56} +(32.2367 - 55.8355i) q^{58} +(-37.5149 - 21.6592i) q^{59} +(42.3562 - 24.4543i) q^{61} -1.26456i q^{62} +8.00000 q^{64} +(-39.1328 - 67.7800i) q^{65} +(-5.17274 + 8.95945i) q^{67} +(-18.1764 - 10.4941i) q^{68} +(-39.2580 - 41.2329i) q^{70} -42.0936 q^{71} -109.752i q^{73} +(-36.1774 - 62.6610i) q^{74} +(-39.9383 - 23.0584i) q^{76} +(116.317 + 34.2459i) q^{77} +(56.6624 + 98.1421i) q^{79} -23.0043i q^{80} +34.5753i q^{82} +(-82.8440 + 47.8300i) q^{83} +(-30.1763 + 52.2669i) q^{85} +(-8.41128 + 14.5688i) q^{86} +(24.4968 + 42.4298i) q^{88} +123.188i q^{89} +(-92.5931 + 22.3913i) q^{91} +(27.1850 + 47.0858i) q^{92} +(-20.4796 - 11.8239i) q^{94} +(-66.3053 + 114.844i) q^{95} +(-20.9168 + 12.0763i) q^{97} +(-61.6395 + 31.6635i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{4} - 2 q^{7} + 12 q^{11} + 12 q^{14} - 64 q^{16} - 12 q^{23} + 80 q^{25} + 8 q^{28} + 48 q^{29} - 348 q^{35} - 88 q^{37} + 32 q^{43} - 48 q^{44} + 48 q^{46} + 50 q^{49} - 48 q^{50} + 864 q^{53}+ \cdots - 624 q^{98}+O(q^{100}) $ 32 * q - 32 * q^4 - 2 * q^7 + 12 * q^11 + 12 * q^14 - 64 * q^16 - 12 * q^23 + 80 * q^25 + 8 * q^28 + 48 * q^29 - 348 * q^35 - 88 * q^37 + 32 * q^43 - 48 * q^44 + 48 * q^46 + 50 * q^49 - 48 * q^50 + 864 * q^53 + 24 * q^56 + 48 * q^58 + 256 * q^64 - 120 * q^65 - 140 * q^67 - 108 * q^70 - 552 * q^71 - 144 * q^74 + 258 * q^77 - 176 * q^79 - 60 * q^85 - 96 * q^86 + 372 * q^91 - 24 * q^92 - 528 * q^95 - 624 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	4.98058	+	2.87554i	0.996116	+	0.575108i	0.907097	−	0.420922i	$-0.138293\pi$
$5$	4.98058	+	2.87554i	0.996116	+	0.575108i	0.0890192	+	0.996030i	$0.471627\pi$
$6$		0			0
$7$	5.06966	−	4.82685i	0.724238	−	0.689550i
$7$	5.06966	−	4.82685i	0.724238	−	0.689550i
$8$	2.82843			0.353553
$9$		0			0
$10$		−	8.13325i		−	0.813325i
$11$	8.66094	+	15.0012i	0.787358	+	1.36374i	0.927580	+	0.373625i	$0.121885\pi$
$11$	8.66094	+	15.0012i	0.787358	+	1.36374i	−0.140222	+	0.990120i	$0.544782\pi$
$12$		0			0
$13$	−11.7856	−	6.80443i	−0.906586	−	0.523418i	−0.0272552	−	0.999629i	$-0.508677\pi$
$13$	−11.7856	−	6.80443i	−0.906586	−	0.523418i	−0.879331	+	0.476211i	$0.842010\pi$
$14$	−9.49646	−	2.79594i	−0.678318	−	0.199710i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$			10.4941i			0.617302i	0.951175	+	0.308651i	$0.0998776\pi$
$17$			10.4941i			0.617302i	−0.951175	+	0.308651i	$0.900122\pi$
$18$		0			0
$19$			23.0584i			1.21360i	0.794855	+	0.606800i	$0.207547\pi$
$19$			23.0584i			1.21360i	−0.794855	+	0.606800i	$0.792453\pi$
$20$	−9.96116	+	5.75108i	−0.498058	+	0.287554i
$21$		0			0
$22$	12.2484	−	21.2149i	0.556746	−	0.964313i
$23$	13.5925	−	23.5429i	0.590978	−	1.02360i	−0.403123	−	0.915146i	$-0.632075\pi$
$23$	13.5925	−	23.5429i	0.590978	−	1.02360i	0.994101	−	0.108458i	$-0.0345912\pi$
$24$		0			0
$25$	4.03745	+	6.99307i	0.161498	+	0.279723i
$26$			19.2458i			0.740225i
$27$		0			0
$28$	3.29069	+	13.6078i	0.117525	+	0.485992i
$29$	22.7948	+	39.4817i	0.786026	+	1.36144i	0.928384	+	0.371622i	$0.121198\pi$
$29$	22.7948	+	39.4817i	0.786026	+	1.36144i	−0.142357	+	0.989815i	$0.545468\pi$
$30$		0			0
$31$	0.774381	+	0.447089i	0.0249800	+	0.0144222i	0.512438	−	0.858724i	$-0.328742\pi$
$31$	0.774381	+	0.447089i	0.0249800	+	0.0144222i	−0.487458	+	0.873146i	$0.662076\pi$
$32$	−2.82843	+	4.89898i	−0.0883883	+	0.153093i
$33$		0			0
$34$	12.8526	−	7.42048i	0.378019	−	0.218249i
$35$	39.1297	−	9.46251i	1.11799	−	0.270357i
$36$		0			0
$37$	51.1625			1.38277			0.691386	−	0.722486i	$-0.257001\pi$
$37$	51.1625			1.38277			0.691386	+	0.722486i	$0.257001\pi$
$38$	28.2407	−	16.3048i	0.743175	−	0.429072i
$39$		0			0
$40$	14.0872	+	8.13325i	0.352180	+	0.203331i
$41$	−21.1730	−	12.2242i	−0.516413	−	0.298151i	0.219053	−	0.975713i	$-0.429703\pi$
$41$	−21.1730	−	12.2242i	−0.516413	−	0.298151i	−0.735466	+	0.677562i	$0.763037\pi$
$42$		0			0
$43$	−5.94767	−	10.3017i	−0.138318	−	0.239574i	0.788542	−	0.614981i	$-0.210836\pi$
$43$	−5.94767	−	10.3017i	−0.138318	−	0.239574i	−0.926860	+	0.375407i	$0.877503\pi$
$44$	−34.6438			−0.787358
$45$		0			0
$46$	−38.4454			−0.835769
$47$	14.4813	−	8.36076i	0.308112	−	0.177888i	−0.337969	−	0.941157i	$-0.609740\pi$
$47$	14.4813	−	8.36076i	0.308112	−	0.177888i	0.646081	+	0.763269i	$0.276407\pi$
$48$		0			0
$49$	2.40298	−	48.9410i	0.0490403	−	0.998797i
$50$	5.70982	−	9.88970i	0.114196	−	0.197794i
$51$		0			0
$52$	23.5712	−	13.6089i	0.453293	−	0.261709i
$53$	79.0686			1.49186			0.745930	−	0.666024i	$-0.232005\pi$
$53$	79.0686			1.49186			0.745930	+	0.666024i	$0.232005\pi$
$54$		0			0
$55$			99.6195i			1.81126i
$56$	14.3392	−	13.6524i	0.256057	−	0.243793i
$57$		0			0
$58$	32.2367	−	55.8355i	0.555805	−	0.962682i
$59$	−37.5149	−	21.6592i	−0.635846	−	0.367106i	0.147167	−	0.989112i	$-0.452985\pi$
$59$	−37.5149	−	21.6592i	−0.635846	−	0.367106i	−0.783012	+	0.622006i	$0.786318\pi$
$60$		0			0
$61$	42.3562	−	24.4543i	0.694363	−	0.400891i	−0.110881	−	0.993834i	$-0.535367\pi$
$61$	42.3562	−	24.4543i	0.694363	−	0.400891i	0.805245	+	0.592943i	$0.202034\pi$
$62$		−	1.26456i		−	0.0203961i
$63$		0			0
$64$	8.00000			0.125000
$65$	−39.1328	−	67.7800i	−0.602043	−	1.04277i
$66$		0			0
$67$	−5.17274	+	8.95945i	−0.0772051	+	0.133723i	−0.902043	−	0.431646i	$-0.857933\pi$
$67$	−5.17274	+	8.95945i	−0.0772051	+	0.133723i	0.824838	+	0.565369i	$0.191266\pi$
$68$	−18.1764	−	10.4941i	−0.267300	−	0.154326i
$69$		0			0
$70$	−39.2580	−	41.2329i	−0.560829	−	0.589041i
$71$	−42.0936			−0.592868			−0.296434	−	0.955053i	$-0.595797\pi$
$71$	−42.0936			−0.592868			−0.296434	+	0.955053i	$0.595797\pi$
$72$		0			0
$73$		−	109.752i		−	1.50345i	−0.659476	−	0.751726i	$-0.729222\pi$
$73$		−	109.752i		−	1.50345i	0.659476	−	0.751726i	$-0.270778\pi$
$74$	−36.1774	−	62.6610i	−0.488883	−	0.846771i
$75$		0			0
$76$	−39.9383	−	23.0584i	−0.525504	−	0.303400i
$77$	116.317	+	34.2459i	1.51061	+	0.444752i
$78$		0			0
$79$	56.6624	+	98.1421i	0.717245	+	1.24231i	0.962087	+	0.272742i	$0.0879306\pi$
$79$	56.6624	+	98.1421i	0.717245	+	1.24231i	−0.244842	+	0.969563i	$0.578736\pi$
$80$		−	23.0043i		−	0.287554i
$81$		0			0
$82$			34.5753i			0.421650i
$83$	−82.8440	+	47.8300i	−0.998121	+	0.576265i	−0.907692	−	0.419638i	$-0.862157\pi$
$83$	−82.8440	+	47.8300i	−0.998121	+	0.576265i	−0.0904289	+	0.995903i	$0.528824\pi$
$84$		0			0
$85$	−30.1763	+	52.2669i	−0.355016	+	0.614905i
$86$	−8.41128	+	14.5688i	−0.0978056	+	0.169404i
$87$		0			0
$88$	24.4968	+	42.4298i	0.278373	+	0.482157i
$89$			123.188i			1.38414i	0.721831	+	0.692070i	$0.243301\pi$
$89$			123.188i			1.38414i	−0.721831	+	0.692070i	$0.756699\pi$
$90$		0			0
$91$	−92.5931	+	22.3913i	−1.01751	+	0.246058i
$92$	27.1850	+	47.0858i	0.295489	+	0.511802i
$93$		0			0
$94$	−20.4796	−	11.8239i	−0.217868	−	0.125786i
$95$	−66.3053	+	114.844i	−0.697951	+	1.20889i
$96$		0			0
$97$	−20.9168	+	12.0763i	−0.215637	+	0.124498i	−0.603929	−	0.797038i	$-0.706399\pi$
$97$	−20.9168	+	12.0763i	−0.215637	+	0.124498i	0.388291	+	0.921537i	$0.373065\pi$
$98$	−61.6395	+	31.6635i	−0.628974	+	0.323097i
$99$		0			0
$100$	−16.1498			−0.161498
$101$	21.0830	−	12.1723i	0.208743	−	0.120518i	−0.391984	−	0.919972i	$-0.628211\pi$
$101$	21.0830	−	12.1723i	0.208743	−	0.120518i	0.600727	+	0.799454i	$0.294878\pi$
$102$		0			0
$103$	−126.643	−	73.1173i	−1.22954	−	0.709876i	−0.262608	−	0.964903i	$-0.584583\pi$
$103$	−126.643	−	73.1173i	−1.22954	−	0.709876i	−0.966934	+	0.255026i	$0.917916\pi$
$104$	−33.3348	−	19.2458i	−0.320527	−	0.185056i
$105$		0			0
$106$	−55.9099	−	96.8388i	−0.527452	−	0.913574i
$107$	−39.3576			−0.367828			−0.183914	−	0.982942i	$-0.558877\pi$
$107$	−39.3576			−0.367828			−0.183914	+	0.982942i	$0.558877\pi$
$108$		0			0
$109$	84.9847			0.779676			0.389838	−	0.920884i	$-0.372531\pi$
$109$	84.9847			0.779676			0.389838	+	0.920884i	$0.372531\pi$
$110$	122.008	−	70.4416i	1.10917	−	0.640378i
$111$		0			0
$112$	−26.8600	−	7.90812i	−0.239822	−	0.0706082i
$113$	25.6093	−	44.3566i	0.226631	−	0.392536i	−0.730177	−	0.683258i	$-0.760562\pi$
$113$	25.6093	−	44.3566i	0.226631	−	0.392536i	0.956807	+	0.290722i	$0.0938956\pi$
$114$		0			0
$115$	135.397	−	78.1715i	1.17736	−	0.679752i
$116$	−91.1791			−0.786026
$117$		0			0
$118$			61.2616i			0.519166i
$119$	50.6537	+	53.2018i	0.425661	+	0.447074i
$120$		0			0
$121$	−89.5238	+	155.060i	−0.739866	+	1.28149i
$122$	−59.9007	−	34.5837i	−0.490989	−	0.283473i
$123$		0			0
$124$	−1.54876	+	0.894178i	−0.0124900	+	0.00721111i
$125$		−	97.3376i		−	0.778700i
$126$		0			0
$127$	−139.901			−1.10158			−0.550790	−	0.834644i	$-0.685673\pi$
$127$	−139.901			−1.10158			−0.550790	+	0.834644i	$0.685673\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−55.3422	+	95.8555i	−0.425709	+	0.737350i
$131$	−36.7121	−	21.1958i	−0.280245	−	0.161800i	0.353289	−	0.935514i	$-0.385063\pi$
$131$	−36.7121	−	21.1958i	−0.280245	−	0.161800i	−0.633534	+	0.773714i	$0.718397\pi$
$132$		0			0
$133$	111.300	+	116.898i	0.836838	+	0.878935i
$134$	14.6307			0.109184
$135$		0			0
$136$			29.6819i			0.218249i
$137$	−45.9094	−	79.5175i	−0.335105	−	0.580420i	0.648400	−	0.761300i	$-0.275439\pi$
$137$	−45.9094	−	79.5175i	−0.335105	−	0.580420i	−0.983505	+	0.180881i	$0.942105\pi$
$138$		0			0
$139$	43.1971	+	24.9399i	0.310771	+	0.179423i	0.647271	−	0.762260i	$-0.275910\pi$
$139$	43.1971	+	24.9399i	0.310771	+	0.179423i	−0.336501	+	0.941683i	$0.609243\pi$
$140$	−22.7401	+	77.2371i	−0.162429	+	0.551693i
$141$		0			0
$142$	29.7647	+	51.5540i	0.209611	+	0.363056i
$143$		−	235.731i		−	1.64847i
$144$		0			0
$145$			262.189i			1.80820i
$146$	−134.418	+	77.6063i	−0.920672	+	0.531550i
$147$		0			0
$148$	−51.1625	+	88.6161i	−0.345693	+	0.598757i
$149$	−35.3502	+	61.2284i	−0.237250	+	0.410929i	−0.959924	−	0.280260i	$-0.909579\pi$
$149$	−35.3502	+	61.2284i	−0.237250	+	0.410929i	0.722674	+	0.691189i	$0.242913\pi$
$150$		0			0
$151$	−57.5780	−	99.7279i	−0.381311	−	0.660450i	0.609939	−	0.792448i	$-0.291194\pi$
$151$	−57.5780	−	99.7279i	−0.381311	−	0.660450i	−0.991250	+	0.131998i	$0.957861\pi$
$152$			65.2190i			0.429072i
$153$		0			0
$154$	−40.3058	−	166.674i	−0.261726	−	1.08230i
$155$	2.57124	+	4.45353i	0.0165887	+	0.0287324i
$156$		0			0
$157$	−177.402	−	102.423i	−1.12995	−	0.652376i	−0.186026	−	0.982545i	$-0.559561\pi$
$157$	−177.402	−	102.423i	−1.12995	−	0.652376i	−0.943922	+	0.330169i	$0.892894\pi$
$158$	80.1327	−	138.794i	0.507169	−	0.878442i
$159$		0			0
$160$	−28.1744	+	16.2665i	−0.176090	+	0.101666i
$161$	−44.7287	−	184.963i	−0.277818	−	1.14884i
$162$		0			0
$163$	−200.360			−1.22920			−0.614601	−	0.788838i	$-0.710683\pi$
$163$	−200.360			−1.22920			−0.614601	+	0.788838i	$0.710683\pi$
$164$	42.3459	−	24.4484i	0.258207	−	0.149076i
$165$		0			0
$166$	117.159	+	67.6418i	0.705778	+	0.407481i
$167$	−20.5934	−	11.8896i	−0.123314	−	0.0711953i	0.437074	−	0.899425i	$-0.356015\pi$
$167$	−20.5934	−	11.8896i	−0.123314	−	0.0711953i	−0.560388	+	0.828230i	$0.689348\pi$
$168$		0			0
$169$	8.10061	+	14.0307i	0.0479326	+	0.0830217i
$170$	85.3515			0.502068
$171$		0			0
$172$	23.7907			0.138318
$173$	−141.525	+	81.7094i	−0.818062	+	0.472309i	−0.849748	−	0.527189i	$-0.823246\pi$
$173$	−141.525	+	81.7094i	−0.818062	+	0.472309i	0.0316855	+	0.999498i	$0.489913\pi$
$174$		0			0
$175$	54.2230	+	15.9643i	0.309846	+	0.0912248i
$176$	34.6438	−	60.0048i	0.196840	−	0.340936i
$177$		0			0
$178$	150.874	−	87.1074i	0.847609	−	0.489367i
$179$	−189.491			−1.05861			−0.529304	−	0.848432i	$-0.677547\pi$
$179$	−189.491			−1.05861			−0.529304	+	0.848432i	$0.677547\pi$
$180$		0			0
$181$			162.121i			0.895698i	0.894109	+	0.447849i	$0.147810\pi$
$181$			162.121i			0.895698i	−0.894109	+	0.447849i	$0.852190\pi$
$182$	92.8969	+	97.5699i	0.510422	+	0.536099i
$183$		0			0
$184$	38.4454	−	66.5893i	0.208942	−	0.361898i
$185$	254.819	+	147.120i	1.37740	+	0.795243i
$186$		0			0
$187$	−157.425	+	90.8892i	−0.841843	+	0.486038i
$188$			33.4430i			0.177888i
$189$		0			0
$190$	187.540			0.987052
$191$	−48.8766	−	84.6567i	−0.255898	−	0.443229i	0.709241	−	0.704966i	$-0.249038\pi$
$191$	−48.8766	−	84.6567i	−0.255898	−	0.443229i	−0.965139	+	0.261737i	$0.915705\pi$
$192$		0			0
$193$	173.476	−	300.468i	0.898837	−	1.55683i	0.0698539	−	0.997557i	$-0.477747\pi$
$193$	173.476	−	300.468i	0.898837	−	1.55683i	0.828983	−	0.559274i	$-0.188920\pi$
$194$	29.5808	+	17.0785i	0.152479	+	0.0880335i
$195$		0			0
$196$	82.3654	+	53.1031i	0.420232	+	0.270934i
$197$	−15.5388			−0.0788769			−0.0394385	−	0.999222i	$-0.512557\pi$
$197$	−15.5388			−0.0788769			−0.0394385	+	0.999222i	$0.512557\pi$
$198$		0			0
$199$		−	286.352i		−	1.43895i	−0.694516	−	0.719477i	$-0.744381\pi$
$199$		−	286.352i		−	1.43895i	0.694516	−	0.719477i	$-0.255619\pi$
$200$	11.4196	+	19.7794i	0.0570982	+	0.0988970i
$201$		0			0
$202$	−29.8159	−	17.2142i	−0.147604	−	0.0852190i
$203$	306.134	+	90.1319i	1.50805	+	0.444000i
$204$		0			0
$205$	−70.3024	−	121.767i	−0.342938	−	0.593987i
$206$			206.807i			1.00392i
$207$		0			0
$208$			54.4355i			0.261709i
$209$	−345.903	+	199.707i	−1.65504	+	0.955538i
$210$		0			0
$211$	71.1281	−	123.197i	0.337100	−	0.583874i	−0.646786	−	0.762672i	$-0.723887\pi$
$211$	71.1281	−	123.197i	0.337100	−	0.583874i	0.983886	+	0.178797i	$0.0572206\pi$
$212$	−79.0686	+	136.951i	−0.372965	+	0.645994i
$213$		0			0
$214$	27.8300	+	48.2030i	0.130047	+	0.225247i
$215$		−	68.4111i		−	0.318191i
$216$		0			0
$217$	6.08388	−	1.47123i	0.0280363	−	0.00677987i
$218$	−60.0932	−	104.085i	−0.275657	−	0.477452i
$219$		0			0
$220$	−172.546	−	99.6195i	−0.784300	−	0.452816i
$221$	71.4067	−	123.680i	0.323107	−	0.559638i
$222$		0			0
$223$	−98.4840	+	56.8598i	−0.441632	+	0.254977i	−0.704290	−	0.709913i	$-0.748734\pi$
$223$	−98.4840	+	56.8598i	−0.441632	+	0.254977i	0.262657	+	0.964889i	$0.415401\pi$
$224$	9.30748	+	38.4886i	0.0415513	+	0.171824i
$225$		0			0
$226$	−72.4340			−0.320504
$227$	130.245	−	75.1969i	0.573766	−	0.331264i	−0.184886	−	0.982760i	$-0.559192\pi$
$227$	130.245	−	75.1969i	0.573766	−	0.331264i	0.758652	+	0.651496i	$0.225858\pi$
$228$		0			0
$229$	31.0059	+	17.9012i	0.135397	+	0.0781714i	0.566168	−	0.824290i	$-0.308425\pi$
$229$	31.0059	+	17.9012i	0.135397	+	0.0781714i	−0.430772	+	0.902461i	$0.641759\pi$
$230$	−191.480	−	110.551i	−0.832522	−	0.480657i
$231$		0			0
$232$	64.4733	+	111.671i	0.277902	+	0.481341i
$233$	397.747			1.70707			0.853533	−	0.521038i	$-0.174455\pi$
$233$	397.747			1.70707			0.853533	+	0.521038i	$0.174455\pi$
$234$		0			0
$235$	96.1668			0.409220
$236$	75.0298	−	43.3185i	0.317923	−	0.183553i
$237$		0			0
$238$	29.3410	−	99.6572i	0.123282	−	0.418728i
$239$	−85.1346	+	147.458i	−0.356212	+	0.616977i	−0.987325	−	0.158714i	$-0.949265\pi$
$239$	−85.1346	+	147.458i	−0.356212	+	0.616977i	0.631113	+	0.775691i	$0.282599\pi$
$240$		0			0
$241$	62.5220	−	36.0971i	0.259427	−	0.149780i	−0.364646	−	0.931146i	$-0.618810\pi$
$241$	62.5220	−	36.0971i	0.259427	−	0.149780i	0.624073	+	0.781366i	$0.285477\pi$
$242$	253.212			1.04633
$243$		0			0
$244$			97.8174i			0.400891i
$245$	152.700	−	236.845i	0.623266	−	0.966714i
$246$		0			0
$247$	156.899	−	271.758i	0.635220	−	1.10023i
$248$	2.19028	+	1.26456i	0.00883177	+	0.00509903i
$249$		0			0
$250$	−119.214	+	68.8280i	−0.476855	+	0.275312i
$251$			220.918i			0.880153i	0.897960	+	0.440076i	$0.145049\pi$
$251$			220.918i			0.880153i	−0.897960	+	0.440076i	$0.854951\pi$
$252$		0			0
$253$	470.895			1.86124
$254$	98.9246	+	171.343i	0.389467	+	0.674577i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−307.432	−	177.496i	−1.19623	−	0.690645i	−0.236519	−	0.971627i	$-0.576006\pi$
$257$	−307.432	−	177.496i	−1.19623	−	0.690645i	−0.959713	+	0.280982i	$0.909340\pi$
$258$		0			0
$259$	259.377	−	246.954i	1.00145	−	0.953490i
$260$	156.531			0.602043
$261$		0			0
$262$			59.9507i			0.228819i
$263$	107.394	+	186.012i	0.408341	+	0.707268i	0.994704	−	0.102781i	$-0.0327740\pi$
$263$	107.394	+	186.012i	0.408341	+	0.707268i	−0.586363	+	0.810049i	$0.699441\pi$
$264$		0			0
$265$	393.807	+	227.365i	1.48607	+	0.857980i
$266$	64.4700	−	218.973i	0.242368	−	0.823207i
$267$		0			0
$268$	−10.3455	−	17.9189i	−0.0386025	−	0.0668615i
$269$		−	99.1640i		−	0.368639i	−0.982866	−	0.184320i	$-0.940992\pi$
$269$		−	99.1640i		−	0.368639i	0.982866	−	0.184320i	$-0.0590082\pi$
$270$		0			0
$271$		−	487.080i		−	1.79734i	−0.438622	−	0.898672i	$-0.644533\pi$
$271$		−	487.080i		−	1.79734i	0.438622	−	0.898672i	$-0.355467\pi$
$272$	36.3528	−	20.9883i	0.133650	−	0.0771628i
$273$		0			0
$274$	−64.9258	+	112.455i	−0.236955	+	0.410419i
$275$	−69.9363	+	121.133i	−0.254314	+	0.440484i
$276$		0			0
$277$	−161.811	−	280.265i	−0.584155	−	1.01179i	−0.994980	−	0.100072i	$-0.968093\pi$
$277$	−161.811	−	280.265i	−0.584155	−	1.01179i	0.410825	−	0.911714i	$-0.365241\pi$
$278$		−	70.5406i		−	0.253743i
$279$		0			0
$280$	110.675	−	26.7640i	0.395269	−	0.0955858i
$281$	−103.963	−	180.070i	−0.369976	−	0.640817i	0.619585	−	0.784929i	$-0.287301\pi$
$281$	−103.963	−	180.070i	−0.369976	−	0.640817i	−0.989561	+	0.144112i	$0.953967\pi$
$282$		0			0
$283$	235.533	+	135.985i	0.832273	+	0.480513i	0.854630	−	0.519237i	$-0.173784\pi$
$283$	235.533	+	135.985i	0.832273	+	0.480513i	−0.0223573	+	0.999750i	$0.507117\pi$
$284$	42.0936	−	72.9083i	0.148217	−	0.256719i
$285$		0			0
$286$	−288.711	+	166.687i	−1.00948	+	0.582822i
$287$	−166.344	+	40.2261i	−0.579597	+	0.140161i
$288$		0			0
$289$	178.873			0.618938
$290$	321.115	−	185.396i	1.10729	−	0.639295i
$291$		0			0
$292$	190.096	+	109.752i	0.651014	+	0.375863i
$293$	239.193	+	138.098i	0.816357	+	0.471324i	0.849158	−	0.528138i	$-0.177110\pi$
$293$	239.193	+	138.098i	0.816357	+	0.471324i	−0.0328018	+	0.999462i	$0.510443\pi$
$294$		0			0
$295$	−124.564	−	215.751i	−0.422251	−	0.731360i
$296$	144.709			0.488883
$297$		0			0
$298$	99.9855			0.335522
$299$	−320.392	+	184.978i	−1.07154	+	0.618657i
$300$		0			0
$301$	−79.8773	−	23.5175i	−0.265373	−	0.0781311i
$302$	−81.4275	+	141.037i	−0.269628	+	0.467009i
$303$		0			0
$304$	79.8766	−	46.1168i	0.262752	−	0.151700i
$305$	281.278			0.922222
$306$		0			0
$307$			418.849i			1.36433i	0.731199	+	0.682165i	$0.238961\pi$
$307$			418.849i			1.36433i	−0.731199	+	0.682165i	$0.761039\pi$
$308$	−175.632	+	167.220i	−0.570235	+	0.542923i
$309$		0			0
$310$	3.63629	−	6.29824i	0.0117300	−	0.0203169i
$311$	−168.685	−	97.3905i	−0.542397	−	0.313153i	0.203653	−	0.979043i	$-0.434719\pi$
$311$	−168.685	−	97.3905i	−0.542397	−	0.313153i	−0.746050	+	0.665890i	$0.768052\pi$
$312$		0			0
$313$	−82.2059	+	47.4616i	−0.262639	+	0.151634i	−0.625538	−	0.780194i	$-0.715120\pi$
$313$	−82.2059	+	47.4616i	−0.262639	+	0.151634i	0.362899	+	0.931828i	$0.381787\pi$
$314$			289.696i			0.922599i
$315$		0			0
$316$	−226.649			−0.717245
$317$	77.4057	+	134.071i	0.244182	+	0.422936i	0.961901	−	0.273397i	$-0.0881472\pi$
$317$	77.4057	+	134.071i	0.244182	+	0.422936i	−0.717719	+	0.696333i	$0.754814\pi$
$318$		0			0
$319$	−394.848	+	683.897i	−1.23777	+	2.14388i
$320$	39.8446	+	23.0043i	0.124515	+	0.0718885i
$321$		0			0
$322$	−194.905	+	185.570i	−0.605295	+	0.576305i
$323$	−241.978			−0.749158
$324$		0			0
$325$		−	109.890i		−	0.338124i
$326$	141.676	+	245.390i	0.434588	+	0.752729i
$327$		0			0
$328$	−59.8862	−	34.5753i	−0.182580	−	0.105412i
$329$	33.0590	−	112.285i	0.100483	−	0.341292i
$330$		0			0
$331$	−87.2053	−	151.044i	−0.263460	−	0.456326i	0.703699	−	0.710498i	$-0.251530\pi$
$331$	−87.2053	−	151.044i	−0.263460	−	0.456326i	−0.967159	+	0.254172i	$0.918197\pi$
$332$		−	191.320i		−	0.576265i
$333$		0			0
$334$			33.6289i			0.100685i
$335$	−51.5265	+	29.7488i	−0.153810	+	0.0888025i
$336$		0			0
$337$	−40.8311	+	70.7216i	−0.121161	+	0.209856i	−0.920226	−	0.391388i	$-0.871995\pi$
$337$	−40.8311	+	70.7216i	−0.121161	+	0.209856i	0.799065	+	0.601245i	$0.205328\pi$
$338$	11.4560	−	19.8424i	0.0338935	−	0.0587052i
$339$		0			0
$340$	−60.3526	−	104.534i	−0.177508	−	0.307452i
$341$			15.4888i			0.0454218i
$342$		0			0
$343$	−224.049	−	259.713i	−0.653204	−	0.757182i
$344$	−16.8226	−	29.1375i	−0.0489028	−	0.0847021i
$345$		0			0
$346$	200.146	+	115.555i	0.578457	+	0.333973i
$347$	−242.992	+	420.875i	−0.700266	+	1.21290i	0.268106	+	0.963389i	$0.413602\pi$
$347$	−242.992	+	420.875i	−0.700266	+	1.21290i	−0.968373	+	0.249508i	$0.919731\pi$
$348$		0			0
$349$	−423.870	+	244.722i	−1.21453	+	0.701208i	−0.963742	−	0.266834i	$-0.914022\pi$
$349$	−423.870	+	244.722i	−1.21453	+	0.701208i	−0.250786	+	0.968043i	$0.580689\pi$
$350$	−18.7893	−	77.6979i	−0.0536836	−	0.221994i
$351$		0			0
$352$	−97.9874			−0.278373
$353$	−148.587	+	85.7870i	−0.420927	+	0.243023i	−0.695474	−	0.718551i	$-0.744806\pi$
$353$	−148.587	+	85.7870i	−0.420927	+	0.243023i	0.274547	+	0.961574i	$0.411472\pi$
$354$		0			0
$355$	−209.651	−	121.042i	−0.590565	−	0.340963i
$356$	−213.369	−	123.188i	−0.599350	−	0.346035i
$357$		0			0
$358$	133.990	+	232.078i	0.374275	+	0.648263i
$359$	111.557			0.310744			0.155372	−	0.987856i	$-0.450342\pi$
$359$	111.557			0.310744			0.155372	+	0.987856i	$0.450342\pi$
$360$		0			0
$361$	−170.690			−0.472825
$362$	198.557	−	114.637i	0.548501	−	0.316677i
$363$		0			0
$364$	53.8103	−	182.767i	0.147830	−	0.502108i
$365$	315.596	−	546.628i	0.864647	−	1.49761i
$366$		0			0
$367$	−502.284	+	289.994i	−1.36862	+	0.790174i	−0.990752	−	0.135686i	$-0.956676\pi$
$367$	−502.284	+	289.994i	−1.36862	+	0.790174i	−0.377869	+	0.925859i	$0.623343\pi$
$368$	−108.740			−0.295489
$369$		0			0
$370$		−	416.118i		−	1.12464i
$371$	400.851	−	381.652i	1.08046	−	1.02871i
$372$		0			0
$373$	159.831	−	276.835i	0.428501	−	0.742185i	−0.568240	−	0.822863i	$-0.692375\pi$
$373$	159.831	−	276.835i	0.428501	−	0.742185i	0.996740	+	0.0806784i	$0.0257087\pi$
$374$	222.632	+	128.537i	0.595273	+	0.343681i
$375$		0			0
$376$	40.9592	−	23.6478i	0.108934	−	0.0628931i
$377$		−	620.422i		−	1.64568i
$378$		0			0
$379$	105.877			0.279359			0.139679	−	0.990197i	$-0.455393\pi$
$379$	105.877			0.279359			0.139679	+	0.990197i	$0.455393\pi$
$380$	−132.611	−	229.688i	−0.348975	−	0.604443i
$381$		0			0
$382$	−69.1219	+	119.723i	−0.180947	+	0.313410i
$383$	111.394	+	64.3133i	0.290846	+	0.167920i	0.638323	−	0.769769i	$-0.279628\pi$
$383$	111.394	+	64.3133i	0.290846	+	0.167920i	−0.347478	+	0.937688i	$0.612962\pi$
$384$		0			0
$385$	480.849	+	505.037i	1.24896	+	1.31179i
$386$	−490.663			−1.27115
$387$		0			0
$388$		−	48.3053i		−	0.124498i
$389$	−75.0565	−	130.002i	−0.192947	−	0.334195i	0.753278	−	0.657702i	$-0.228471\pi$
$389$	−75.0565	−	130.002i	−0.192947	−	0.334195i	−0.946226	+	0.323507i	$0.895138\pi$
$390$		0			0
$391$	247.062	+	142.641i	0.631873	+	0.364812i
$392$	6.79664	−	138.426i	0.0173384	−	0.353128i
$393$		0			0
$394$	10.9876	+	19.0310i	0.0278872	+	0.0483021i
$395$			651.740i			1.64997i
$396$		0			0
$397$		−	305.431i		−	0.769347i	−0.923053	−	0.384674i	$-0.874314\pi$
$397$		−	305.431i		−	0.769347i	0.923053	−	0.384674i	$-0.125686\pi$
$398$	−350.708	+	202.481i	−0.881176	+	0.508747i
$399$		0			0
$400$	16.1498	−	27.9723i	0.0403745	−	0.0699307i
$401$	−131.258	+	227.346i	−0.327327	+	0.566947i	−0.981981	−	0.188982i	$-0.939481\pi$
$401$	−131.258	+	227.346i	−0.327327	+	0.566947i	0.654653	+	0.755929i	$0.272815\pi$
$402$		0			0
$403$	−6.08437	−	10.5384i	−0.0150977	−	0.0261500i
$404$			48.6892i			0.120518i
$405$		0			0
$406$	−106.081	−	438.669i	−0.261283	−	1.08047i
$407$	443.116	+	767.499i	1.08874	+	1.88575i
$408$		0			0
$409$	305.530	+	176.398i	0.747017	+	0.431291i	0.824615	−	0.565694i	$-0.191392\pi$
$409$	305.530	+	176.398i	0.747017	+	0.431291i	−0.0775980	+	0.996985i	$0.524725\pi$
$410$	−99.4226	+	172.205i	−0.242494	+	0.420012i
$411$		0			0
$412$	253.286	−	146.235i	0.614771	−	0.354938i
$413$	−294.734	+	71.2739i	−0.713641	+	0.172576i
$414$		0			0
$415$	−550.148			−1.32566
$416$	66.6696	−	38.4917i	0.160263	−	0.0925281i
$417$		0			0
$418$	489.181	+	282.429i	1.17029	+	0.675667i
$419$	−604.426	−	348.965i	−1.44254	−	0.832853i	−0.444524	−	0.895767i	$-0.646627\pi$
$419$	−604.426	−	348.965i	−1.44254	−	0.832853i	−0.998019	+	0.0629143i	$0.979961\pi$
$420$		0			0
$421$	−15.2619	−	26.4343i	−0.0362514	−	0.0627894i	0.847330	−	0.531066i	$-0.178208\pi$
$421$	−15.2619	−	26.4343i	−0.0362514	−	0.0627894i	−0.883582	+	0.468277i	$0.844875\pi$
$422$	−201.181			−0.476731
$423$		0			0
$424$	223.640			0.527452
$425$	−73.3863	+	42.3696i	−0.172674	+	0.0996932i
$426$		0			0
$427$	96.6940	−	328.422i	0.226450	−	0.769139i
$428$	39.3576	−	68.1693i	0.0919569	−	0.159274i
$429$		0			0
$430$	−83.7861	+	48.3739i	−0.194851	+	0.112497i
$431$	−214.726			−0.498205			−0.249103	−	0.968477i	$-0.580136\pi$
$431$	−214.726			−0.498205			−0.249103	+	0.968477i	$0.580136\pi$
$432$		0			0
$433$		−	49.9849i		−	0.115439i	−0.998333	−	0.0577193i	$-0.981617\pi$
$433$		−	49.9849i		−	0.115439i	0.998333	−	0.0577193i	$-0.0183828\pi$
$434$	−6.10384	−	6.41089i	−0.0140641	−	0.0147716i
$435$		0			0
$436$	−84.9847	+	147.198i	−0.194919	+	0.337609i
$437$	542.861	+	313.421i	1.24224	+	0.717210i
$438$		0			0
$439$	174.953	−	101.009i	0.398527	−	0.230090i	−0.287321	−	0.957834i	$-0.592765\pi$
$439$	174.953	−	101.009i	0.398527	−	0.230090i	0.685848	+	0.727745i	$0.259431\pi$
$440$			281.767i			0.640378i
$441$		0			0
$442$	−201.969			−0.456943
$443$	−410.792	−	711.513i	−0.927296	−	1.60612i	−0.787826	−	0.615898i	$-0.788793\pi$
$443$	−410.792	−	711.513i	−0.927296	−	1.60612i	−0.139470	−	0.990226i	$-0.544540\pi$
$444$		0			0
$445$	−354.233	+	613.550i	−0.796030	+	1.37876i
$446$	139.277	+	80.4119i	0.312281	+	0.180296i
$447$		0			0
$448$	40.5573	−	38.6148i	0.0905297	−	0.0861938i
$449$	−324.954			−0.723729			−0.361864	−	0.932231i	$-0.617860\pi$
$449$	−324.954			−0.723729			−0.361864	+	0.932231i	$0.617860\pi$
$450$		0			0
$451$		−	423.493i		−	0.939008i
$452$	51.2186	+	88.7132i	0.113315	+	0.196268i
$453$		0			0
$454$	−184.194	−	106.345i	−0.405714	−	0.234239i
$455$	−525.555	−	154.734i	−1.15507	−	0.340074i
$456$		0			0
$457$	370.766	+	642.186i	0.811305	+	1.40522i	0.911951	+	0.410298i	$0.134575\pi$
$457$	370.766	+	642.186i	0.811305	+	1.40522i	−0.100647	+	0.994922i	$0.532091\pi$
$458$		−	50.6324i		−	0.110551i
$459$		0			0
$460$			312.686i			0.679752i
$461$	573.356	−	331.027i	1.24372	−	0.718063i	0.273872	−	0.961766i	$-0.411695\pi$
$461$	573.356	−	331.027i	1.24372	−	0.718063i	0.969850	+	0.243703i	$0.0783621\pi$
$462$		0			0
$463$	−323.675	+	560.622i	−0.699083	+	1.21085i	0.269702	+	0.962944i	$0.413075\pi$
$463$	−323.675	+	560.622i	−0.699083	+	1.21085i	−0.968785	+	0.247903i	$0.920258\pi$
$464$	91.1791	−	157.927i	0.196507	−	0.340359i
$465$		0			0
$466$	−281.249	−	487.138i	−0.603539	−	1.04536i
$467$			17.5828i			0.0376506i	0.999823	+	0.0188253i	$0.00599263\pi$
$467$			17.5828i			0.0376506i	−0.999823	+	0.0188253i	$0.994007\pi$
$468$		0			0
$469$	17.0219	+	70.3894i	0.0362940	+	0.150084i
$470$	−68.0002	−	117.780i	−0.144681	−	0.250595i
$471$		0			0
$472$	−106.108	−	61.2616i	−0.224805	−	0.129791i
$473$	103.025	−	178.444i	0.217812	−	0.377261i
$474$		0			0
$475$	−161.249	+	93.0972i	−0.339472	+	0.195994i
$476$	−142.802	+	34.5330i	−0.300004	+	0.0725483i
$477$		0			0
$478$	240.797			0.503760
$479$	599.109	−	345.896i	1.25075	−	0.722121i	0.279491	−	0.960148i	$-0.409834\pi$
$479$	599.109	−	345.896i	1.25075	−	0.722121i	0.971258	+	0.238028i	$0.0765009\pi$
$480$		0			0
$481$	−602.982	−	348.132i	−1.25360	−	0.723767i
$482$	−88.4194	−	51.0490i	−0.183443	−	0.105911i
$483$		0			0
$484$	−179.048	−	310.120i	−0.369933	−	0.640743i
$485$	−138.904			−0.286400
$486$		0			0
$487$	782.871			1.60754			0.803769	−	0.594941i	$-0.202825\pi$
$487$	782.871			1.60754			0.803769	+	0.594941i	$0.202825\pi$
$488$	119.801	−	69.1673i	0.245495	−	0.141736i
$489$		0			0
$490$	−398.050	−	19.5440i	−0.812347	−	0.0398857i
$491$	169.949	−	294.361i	0.346129	−	0.599513i	−0.639429	−	0.768850i	$-0.720829\pi$
$491$	169.949	−	294.361i	0.346129	−	0.599513i	0.985558	+	0.169337i	$0.0541627\pi$
$492$		0			0
$493$	−414.327	+	239.212i	−0.840419	+	0.485216i
$494$	−443.778			−0.898337
$495$		0			0
$496$		−	3.57671i		−	0.00721111i
$497$	−213.401	+	203.180i	−0.429377	+	0.408812i
$498$		0			0
$499$	108.860	−	188.551i	0.218156	−	0.377857i	−0.736088	−	0.676885i	$-0.763329\pi$
$499$	108.860	−	188.551i	0.218156	−	0.377857i	0.954244	+	0.299028i	$0.0966626\pi$
$500$	168.594	+	97.3376i	0.337187	+	0.194675i
$501$		0			0
$502$	270.569	−	156.213i	0.538981	−	0.311181i
$503$			732.558i			1.45638i	0.685377	+	0.728189i	$0.259637\pi$
$503$			732.558i			1.45638i	−0.685377	+	0.728189i	$0.740363\pi$
$504$		0			0
$505$	140.008			0.277243
$506$	−332.973	−	576.726i	−0.658049	−	1.13977i
$507$		0			0
$508$	139.901	−	242.315i	0.275395	−	0.476998i
$509$	−22.4840	−	12.9812i	−0.0441730	−	0.0255033i	0.477751	−	0.878495i	$-0.341452\pi$
$509$	−22.4840	−	12.9812i	−0.0441730	−	0.0255033i	−0.521924	+	0.852992i	$0.674785\pi$
$510$		0			0
$511$	−529.757	−	556.405i	−1.03671	−	1.08886i
$512$	22.6274			0.0441942
$513$		0			0
$514$			502.034i			0.976719i
$515$	−420.503	−	728.333i	−0.816511	−	1.41424i
$516$		0			0
$517$	250.843	+	144.824i	0.485189	+	0.280124i
$518$	−485.863	−	143.048i	−0.937959	−	0.276154i
$519$		0			0
$520$	−110.684	−	191.711i	−0.212855	−	0.368675i
$521$		−	152.333i		−	0.292385i	−0.989256	−	0.146193i	$-0.953298\pi$
$521$		−	152.333i		−	0.292385i	0.989256	−	0.146193i	$-0.0467019\pi$
$522$		0			0
$523$			343.250i			0.656310i	0.944624	+	0.328155i	$0.106427\pi$
$523$			343.250i			0.656310i	−0.944624	+	0.328155i	$0.893573\pi$
$524$	73.4243	−	42.3915i	0.140123	−	0.0808999i
$525$		0			0
$526$	151.878	−	263.060i	0.288741	−	0.500114i
$527$	−4.69182	+	8.12646i	−0.00890288	+	0.0154202i
$528$		0			0
$529$	−105.011	−	181.885i	−0.198509	−	0.343828i
$530$		−	643.085i		−	1.21337i
$531$		0			0
$532$	−313.773	+	75.8781i	−0.589800	+	0.142628i
$533$	166.358	+	288.140i	0.312116	+	0.540600i
$534$		0			0
$535$	−196.023	−	113.174i	−0.366399	−	0.211541i
$536$	−14.6307	+	25.3411i	−0.0272961	+	0.0472782i
$537$		0			0
$538$	−121.451	+	70.1195i	−0.225745	+	0.130334i
$539$	754.986	−	387.828i	1.40072	−	0.719533i
$540$		0			0
$541$	−941.180			−1.73970			−0.869852	−	0.493313i	$-0.835786\pi$
$541$	−941.180			−1.73970			−0.869852	+	0.493313i	$0.835786\pi$
$542$	−596.549	+	344.418i	−1.10064	+	0.635457i
$543$		0			0
$544$	−51.4106	−	29.6819i	−0.0945048	−	0.0545623i
$545$	423.273	+	244.377i	0.776647	+	0.448398i
$546$		0			0
$547$	102.142	+	176.916i	0.186732	+	0.323429i	0.944159	−	0.329491i	$-0.106877\pi$
$547$	102.142	+	176.916i	0.186732	+	0.323429i	−0.757427	+	0.652920i	$0.773544\pi$
$548$	183.638			0.335105
$549$		0			0
$550$	197.810			0.359654
$551$	−910.385	+	525.611i	−1.65224	+	0.953922i
$552$		0			0
$553$	760.977	+	224.047i	1.37609	+	0.405147i
$554$	−228.835	+	396.354i	−0.413060	+	0.715441i
$555$		0			0
$556$	−86.3942	+	49.8797i	−0.155385	+	0.0897117i
$557$	693.807			1.24561			0.622807	−	0.782375i	$-0.285992\pi$
$557$	693.807			1.24561			0.622807	+	0.782375i	$0.285992\pi$
$558$		0			0
$559$			161.882i			0.289592i
$560$	−111.038	−	116.624i	−0.198283	−	0.208257i
$561$		0			0
$562$	−147.026	+	254.657i	−0.261613	+	0.453126i
$563$	−63.9135	−	36.9005i	−0.113523	−	0.0655426i	0.442163	−	0.896935i	$-0.354211\pi$
$563$	−63.9135	−	36.9005i	−0.113523	−	0.0655426i	−0.555686	+	0.831392i	$0.687544\pi$
$564$		0			0
$565$	255.098	−	147.281i	0.451501	−	0.260674i
$566$		−	384.624i		−	0.679548i
$567$		0			0
$568$	−119.059			−0.209611
$569$	490.396	+	849.391i	0.861856	+	1.49278i	0.870135	+	0.492813i	$0.164031\pi$
$569$	490.396	+	849.391i	0.861856	+	1.49278i	−0.00827871	+	0.999966i	$0.502635\pi$
$570$		0			0
$571$	−173.666	+	300.798i	−0.304143	+	0.526791i	−0.977070	−	0.212918i	$-0.931703\pi$
$571$	−173.666	+	300.798i	−0.304143	+	0.526791i	0.672927	+	0.739709i	$0.265037\pi$
$572$	408.298	+	235.731i	0.713808	+	0.412117i
$573$		0			0
$574$	166.890	+	175.285i	0.290749	+	0.305375i
$575$	219.516			0.381767
$576$		0			0
$577$			268.872i			0.465982i	0.972479	+	0.232991i	$0.0748512\pi$
$577$			268.872i			0.465982i	−0.972479	+	0.232991i	$0.925149\pi$
$578$	−126.482	−	219.074i	−0.218828	−	0.379020i
$579$		0			0
$580$	−454.125	−	262.189i	−0.782974	−	0.452050i
$581$	−189.123	+	642.358i	−0.325513	+	1.10561i
$582$		0			0
$583$	684.808	+	1186.12i	1.17463	+	2.03452i
$584$		−	310.425i		−	0.531550i
$585$		0			0
$586$		−	390.600i		−	0.666552i
$587$	822.447	−	474.840i	1.40110	−	0.808927i	0.406596	−	0.913608i	$-0.366716\pi$
$587$	822.447	−	474.840i	1.40110	−	0.808927i	0.994506	+	0.104681i	$0.0333823\pi$
$588$		0			0
$589$	−10.3092	+	17.8560i	−0.0175028	+	0.0303158i
$590$	−176.160	+	305.118i	−0.298576	+	0.517149i
$591$		0			0
$592$	−102.325	−	177.232i	−0.172846	−	0.299379i
$593$		−	738.022i		−	1.24456i	−0.782796	−	0.622278i	$-0.786207\pi$
$593$		−	738.022i		−	1.24456i	0.782796	−	0.622278i	$-0.213793\pi$
$594$		0			0
$595$	99.3010	+	410.632i	0.166892	+	0.690138i
$596$	−70.7004	−	122.457i	−0.118625	−	0.205464i
$597$		0			0
$598$	453.102	+	261.599i	0.757696	+	0.437456i
$599$	134.612	−	233.156i	0.224729	−	0.389241i	−0.731509	−	0.681831i	$-0.761184\pi$
$599$	134.612	−	233.156i	0.224729	−	0.389241i	0.956238	+	0.292590i	$0.0945171\pi$
$600$		0			0
$601$	669.416	−	386.488i	1.11384	−	0.643074i	0.174017	−	0.984743i	$-0.444325\pi$
$601$	669.416	−	386.488i	1.11384	−	0.643074i	0.939821	+	0.341668i	$0.110992\pi$
$602$	27.6789	+	114.459i	0.0459783	+	0.190131i
$603$		0			0
$604$	230.312			0.381311
$605$	−891.761	+	514.859i	−1.47399	+	0.851006i
$606$		0			0
$607$	341.516	+	197.174i	0.562629	+	0.324834i	0.754200	−	0.656645i	$-0.228025\pi$
$607$	341.516	+	197.174i	0.562629	+	0.324834i	−0.191571	+	0.981479i	$0.561358\pi$
$608$	−112.963	−	65.2190i	−0.185794	−	0.107268i
$609$		0			0
$610$	−198.893	−	344.493i	−0.326055	−	0.564743i
$611$	−227.561			−0.372440
$612$		0			0
$613$	855.275			1.39523			0.697614	−	0.716474i	$-0.254245\pi$
$613$	855.275			1.39523			0.697614	+	0.716474i	$0.254245\pi$
$614$	512.983	−	296.171i	0.835477	−	0.482363i
$615$		0			0
$616$	328.993	+	96.8620i	0.534080	+	0.157244i
$617$	187.827	−	325.326i	0.304420	−	0.527271i	−0.672712	−	0.739904i	$-0.734871\pi$
$617$	187.827	−	325.326i	0.304420	−	0.527271i	0.977132	+	0.212634i	$0.0682041\pi$
$618$		0			0
$619$	750.475	−	433.287i	1.21240	−	0.699979i	0.249118	−	0.968473i	$-0.419859\pi$
$619$	750.475	−	433.287i	1.21240	−	0.699979i	0.963281	+	0.268494i	$0.0865260\pi$
$620$	−10.2850			−0.0165887
$621$		0			0
$622$			275.462i			0.442865i
$623$	594.612	+	624.524i	0.954434	+	1.00245i
$624$		0			0
$625$	380.834	−	659.624i	0.609335	−	1.05540i
$626$	116.257	+	67.1208i	0.185713	+	0.107222i
$627$		0			0
$628$	354.804	−	204.846i	0.564974	−	0.326188i
$629$			536.907i			0.853588i
$630$		0			0
$631$	−1131.47			−1.79314			−0.896571	−	0.442900i	$-0.853950\pi$
$631$	−1131.47			−1.79314			−0.896571	+	0.442900i	$0.853950\pi$
$632$	160.265	+	277.588i	0.253584	+	0.439221i
$633$		0			0
$634$	109.468	−	189.604i	0.172663	−	0.299061i
$635$	−696.786	−	402.290i	−1.09730	−	0.633527i
$636$		0			0
$637$	−361.337	+	560.450i	−0.567247	+	0.879827i
$638$	1116.80			1.75047
$639$		0			0
$640$		−	65.0660i		−	0.101666i
$641$	−205.779	−	356.420i	−0.321028	−	0.556038i	0.659672	−	0.751554i	$-0.270695\pi$
$641$	−205.779	−	356.420i	−0.321028	−	0.556038i	−0.980701	+	0.195516i	$0.937362\pi$
$642$		0			0
$643$	−984.048	−	568.140i	−1.53040	−	0.883577i	−0.999343	−	0.0362419i	$-0.988461\pi$
$643$	−984.048	−	568.140i	−1.53040	−	0.883577i	−0.531058	−	0.847336i	$-0.678205\pi$
$644$	365.095	+	107.491i	0.566917	+	0.166912i
$645$		0			0
$646$	171.104	+	296.361i	0.264867	+	0.458764i
$647$			52.9830i			0.0818902i	0.999161	+	0.0409451i	$0.0130369\pi$
$647$			52.9830i			0.0818902i	−0.999161	+	0.0409451i	$0.986963\pi$
$648$		0			0
$649$		−	750.357i		−	1.15617i
$650$	−134.588	+	77.7042i	−0.207058	+	0.119545i
$651$		0			0
$652$	200.360	−	347.034i	0.307300	−	0.532260i
$653$	24.9889	−	43.2821i	0.0382679	−	0.0662820i	−0.846257	−	0.532775i	$-0.821149\pi$
$653$	24.9889	−	43.2821i	0.0382679	−	0.0662820i	0.884525	+	0.466493i	$0.154483\pi$
$654$		0			0
$655$	−121.898	−	211.134i	−0.186105	−	0.322343i
$656$			97.7937i			0.149076i
$657$		0			0
$658$	−160.897	+	38.9088i	−0.244524	+	0.0591319i
$659$	226.144	+	391.692i	0.343162	+	0.594374i	0.985018	−	0.172451i	$-0.0551687\pi$
$659$	226.144	+	391.692i	0.343162	+	0.594374i	−0.641856	+	0.766825i	$0.721835\pi$
$660$		0			0
$661$	−472.830	−	272.988i	−0.715325	−	0.412993i	0.0977046	−	0.995215i	$-0.468850\pi$
$661$	−472.830	−	272.988i	−0.715325	−	0.412993i	−0.813030	+	0.582222i	$0.802183\pi$
$662$	−123.327	+	213.609i	−0.186294	+	0.322671i
$663$		0			0
$664$	−234.318	+	135.284i	−0.352889	+	0.203741i
$665$	218.190	+	902.268i	0.328106	+	1.35679i
$666$		0			0
$667$	1239.35			1.85810
$668$	41.1868	−	23.7792i	0.0616569	−	0.0355976i
$669$		0			0
$670$	72.8694	+	42.0712i	0.108760	+	0.0627928i
$671$	733.689	+	423.595i	1.09343	+	0.631290i
$672$		0			0
$673$	−208.424	−	361.001i	−0.309694	−	0.536406i	0.668601	−	0.743621i	$-0.266893\pi$
$673$	−208.424	−	361.001i	−0.309694	−	0.536406i	−0.978295	+	0.207215i	$0.933560\pi$
$674$	115.488			0.171347
$675$		0			0
$676$	−32.4024			−0.0479326
$677$	−423.242	+	244.359i	−0.625173	+	0.360944i	−0.778880	−	0.627173i	$-0.784212\pi$
$677$	−423.242	+	244.359i	−0.625173	+	0.360944i	0.153707	+	0.988116i	$0.450879\pi$
$678$		0			0
$679$	−47.7505	+	162.185i	−0.0703248	+	0.238859i
$680$	−85.3515	+	147.833i	−0.125517	+	0.217402i
$681$		0			0
$682$	18.9699	−	10.9523i	0.0278151	−	0.0160590i
$683$	546.916			0.800756			0.400378	−	0.916350i	$-0.368879\pi$
$683$	546.916			0.800756			0.400378	+	0.916350i	$0.368879\pi$
$684$		0			0
$685$		−	528.058i		−	0.770887i
$686$	−159.656	+	458.048i	−0.232735	+	0.667708i
$687$		0			0
$688$	−23.7907	+	41.2067i	−0.0345795	+	0.0598934i
$689$	−931.873	−	538.017i	−1.35250	−	0.780866i
$690$		0			0
$691$	−575.708	+	332.385i	−0.833152	+	0.481020i	−0.854931	−	0.518742i	$-0.826400\pi$
$691$	−575.708	+	332.385i	−0.833152	+	0.481020i	0.0217788	+	0.999763i	$0.493067\pi$
$692$		−	326.837i		−	0.472309i
$693$		0			0
$694$	687.286			0.990326
$695$	143.431	+	248.430i	0.206376	+	0.357453i
$696$		0			0
$697$	128.283	−	222.192i	0.184050	−	0.318783i
$698$	599.443	+	346.089i	0.858801	+	0.495829i
$699$		0			0
$700$	−81.8741	+	77.9527i	−0.116963	+	0.111361i
$701$	−125.029			−0.178358			−0.0891789	−	0.996016i	$-0.528424\pi$
$701$	−125.029			−0.178358			−0.0891789	+	0.996016i	$0.528424\pi$
$702$		0			0
$703$			1179.73i			1.67813i
$704$	69.2875	+	120.010i	0.0984198	+	0.170468i
$705$		0			0
$706$	210.134	+	121.321i	0.297641	+	0.171843i
$707$	48.1300	−	163.474i	0.0680764	−	0.231222i
$708$		0			0
$709$	−212.052	−	367.285i	−0.299086	−	0.518033i	0.676841	−	0.736129i	$-0.263349\pi$
$709$	−212.052	−	367.285i	−0.299086	−	0.518033i	−0.975927	+	0.218097i	$0.930015\pi$
$710$			342.358i			0.482195i
$711$		0			0
$712$			348.429i			0.489367i
$713$	21.0515	−	12.1541i	0.0295253	−	0.0170464i
$714$		0			0
$715$	677.854	−	1174.08i	0.948048	−	1.64207i
$716$	189.491	−	328.208i	0.264652	−	0.458391i
$717$		0			0
$718$	−78.8828	−	136.629i	−0.109865	−	0.190291i
$719$			852.338i			1.18545i	0.805405	+	0.592724i	$0.201948\pi$
$719$			852.338i			1.18545i	−0.805405	+	0.592724i	$0.798052\pi$
$720$		0			0
$721$	−994.963	+	240.606i	−1.37998	+	0.333712i
$722$	120.696	+	209.051i	0.167169	+	0.289545i
$723$		0			0
$724$	−280.802	−	162.121i	−0.387848	−	0.223924i
$725$	−184.066	+	318.811i	−0.253884	+	0.439739i
$726$		0			0
$727$	1127.09	−	650.723i	1.55032	−	0.895080i	0.552209	−	0.833705i	$-0.313785\pi$
$727$	1127.09	−	650.723i	1.55032	−	0.895080i	0.998115	−	0.0613747i	$-0.0195484\pi$
$728$	−261.893	+	63.3321i	−0.359743	+	0.0869947i
$729$		0			0
$730$	−892.640			−1.22280
$731$	108.107	−	62.4157i	0.147889	−	0.0853840i
$732$		0			0
$733$	−989.572	−	571.330i	−1.35003	−	0.779440i	−0.361777	−	0.932265i	$-0.617830\pi$
$733$	−989.572	−	571.330i	−1.35003	−	0.779440i	−0.988253	+	0.152825i	$0.951163\pi$
$734$	710.337	+	410.113i	0.967761	+	0.558737i
$735$		0			0
$736$	76.8907	+	133.179i	0.104471	+	0.180949i
$737$	−179.203			−0.243152
$738$		0			0
$739$	847.380			1.14666			0.573329	−	0.819325i	$-0.305652\pi$
$739$	847.380			1.14666			0.573329	+	0.819325i	$0.305652\pi$
$740$	−509.638	+	294.240i	−0.688700	+	0.397621i
$741$		0			0
$742$	−750.871	−	221.071i	−1.01196	−	0.297940i
$743$	74.5649	−	129.150i	0.100356	−	0.173823i	−0.811475	−	0.584387i	$-0.801335\pi$
$743$	74.5649	−	129.150i	0.100356	−	0.173823i	0.911832	+	0.410565i	$0.134668\pi$
$744$		0			0
$745$	−352.129	+	203.302i	−0.472656	+	0.272888i
$746$	−452.069			−0.605991
$747$		0			0
$748$		−	363.557i		−	0.486038i
$749$	−199.530	+	189.973i	−0.266395	+	0.253636i
$750$		0			0
$751$	−89.4819	+	154.987i	−0.119150	+	0.206374i	−0.919431	−	0.393251i	$-0.871350\pi$
$751$	−89.4819	+	154.987i	−0.119150	+	0.206374i	0.800281	+	0.599625i	$0.204684\pi$
$752$	−57.9250	−	33.4430i	−0.0770280	−	0.0444721i
$753$		0			0
$754$	−759.858	+	438.705i	−1.00777	+	0.581836i
$755$		−	662.271i		−	0.877180i
$756$		0			0
$757$	549.096			0.725358			0.362679	−	0.931914i	$-0.381862\pi$
$757$	549.096			0.725358			0.362679	+	0.931914i	$0.381862\pi$
$758$	−74.8663	−	129.672i	−0.0987682	−	0.171071i
$759$		0			0
$760$	−187.540	+	324.828i	−0.246763	+	0.427406i
$761$	1100.15	+	635.174i	1.44567	+	0.834657i	0.998219	−	0.0596526i	$-0.0189993\pi$
$761$	1100.15	+	635.174i	1.44567	+	0.834657i	0.447449	+	0.894309i	$0.352333\pi$
$762$		0			0
$763$	430.844	−	410.208i	0.564671	−	0.537626i
$764$	195.506			0.255898
$765$		0			0
$766$		−	181.905i		−	0.237474i
$767$	294.758	+	510.535i	0.384299	+	0.665626i
$768$		0			0
$769$	683.143	+	394.413i	0.888353	+	0.512891i	0.873403	−	0.486997i	$-0.161908\pi$
$769$	683.143	+	394.413i	0.888353	+	0.512891i	0.0149496	+	0.999888i	$0.495241\pi$
$770$	278.531	−	946.032i	0.361728	−	1.22861i
$771$		0			0
$772$	346.951	+	600.937i	0.449418	+	0.778416i
$773$			98.1910i			0.127026i	0.997981	+	0.0635130i	$0.0202304\pi$
$773$			98.1910i			0.127026i	−0.997981	+	0.0635130i	$0.979770\pi$
$774$		0			0
$775$			7.22040i			0.00931665i
$776$	−59.1617	+	34.1570i	−0.0762393	+	0.0440168i
$777$		0			0
$778$	−106.146	+	183.850i	−0.136434	+	0.236311i
$779$	281.871	−	488.214i	0.361837	−	0.626719i
$780$		0			0
$781$	−364.571	−	631.455i	−0.466800	−	0.808521i
$782$		−	403.451i		−	0.515922i
$783$		0			0
$784$	−174.343	+	89.5579i	−0.222376	+	0.114232i
$785$	−589.043	−	1020.25i	−0.750373	−	1.29968i
$786$		0			0
$787$	457.230	+	263.982i	0.580978	+	0.335428i	0.761522	−	0.648139i	$-0.224452\pi$
$787$	457.230	+	263.982i	0.580978	+	0.335428i	−0.180544	+	0.983567i	$0.557786\pi$
$788$	15.5388	−	26.9139i	0.0197192	−	0.0341547i
$789$		0			0
$790$	798.215	−	460.849i	1.01040	−	0.583354i
$791$	−84.2723	−	348.485i	−0.106539	−	0.440563i
$792$		0			0
$793$	−665.592			−0.839334
$794$	−374.075	+	215.972i	−0.471127	+	0.272005i
$795$		0			0
$796$	495.976	+	286.352i	0.623086	+	0.359739i
$797$	−455.600	−	263.041i	−0.571643	−	0.330038i	0.186162	−	0.982519i	$-0.440395\pi$
$797$	−455.600	−	263.041i	−0.571643	−	0.330038i	−0.757805	+	0.652481i	$0.773728\pi$
$798$		0			0
$799$	87.7390	+	151.968i	0.109811	+	0.190198i
$800$	−45.6786			−0.0570982
$801$		0			0
$802$	371.254			0.462910
$803$	1646.41	−	950.555i	2.05032	−	1.18375i
$804$		0			0
$805$	309.095	−	1049.84i	0.383969	−	1.30415i
$806$	−8.60460	+	14.9036i	−0.0106757	+	0.0184908i
$807$		0			0
$808$	59.6319	−	34.4285i	0.0738018	−	0.0426095i
$809$	−87.2827			−0.107890			−0.0539448	−	0.998544i	$-0.517180\pi$
$809$	−87.2827			−0.107890			−0.0539448	+	0.998544i	$0.517180\pi$
$810$		0			0
$811$		−	455.489i		−	0.561639i	−0.959761	−	0.280819i	$-0.909394\pi$
$811$		−	455.489i		−	0.561639i	0.959761	−	0.280819i	$-0.0906062\pi$
$812$	−462.247	+	440.108i	−0.569270	+	0.542005i
$813$		0			0
$814$	626.660	−	1085.41i	0.769853	−	1.33342i
$815$	−997.909	−	576.143i	−1.22443	−	0.706924i
$816$		0			0
$817$	237.540	−	137.144i	0.290747	−	0.167863i
$818$		−	498.928i		−	0.609937i
$819$		0			0
$820$	281.210			0.342938
$821$	−578.892	−	1002.67i	−0.705106	−	1.22128i	−0.966653	−	0.256089i	$-0.917566\pi$
$821$	−578.892	−	1002.67i	−0.705106	−	1.22128i	0.261547	−	0.965191i	$-0.415767\pi$
$822$		0			0
$823$	−288.372	+	499.474i	−0.350391	+	0.606895i	−0.986318	−	0.164855i	$-0.947285\pi$
$823$	−288.372	+	499.474i	−0.350391	+	0.606895i	0.635927	+	0.771749i	$0.280618\pi$
$824$	−358.200	−	206.807i	−0.434709	−	0.250979i
$825$		0			0
$826$	295.701	+	310.576i	0.357991	+	0.375999i
$827$	−1015.60			−1.22805			−0.614026	−	0.789286i	$-0.710451\pi$
$827$	−1015.60			−1.22805			−0.614026	+	0.789286i	$0.710451\pi$
$828$		0			0
$829$			1345.23i			1.62271i	0.584554	+	0.811355i	$0.301270\pi$
$829$			1345.23i			1.62271i	−0.584554	+	0.811355i	$0.698730\pi$
$830$	389.014	+	673.791i	0.468691	+	0.811797i
$831$		0			0
$832$	−94.2850	−	54.4355i	−0.113323	−	0.0654272i
$833$	513.594	+	25.2172i	0.616560	+	0.0302727i
$834$		0			0
$835$	−68.3781	−	118.434i	−0.0818899	−	0.141838i
$836$		−	798.830i		−	0.955538i
$837$		0			0
$838$			987.023i			1.17783i
$839$	1030.38	−	594.890i	1.22810	−	0.709047i	0.261472	−	0.965211i	$-0.415792\pi$
$839$	1030.38	−	594.890i	1.22810	−	0.709047i	0.966633	+	0.256165i	$0.0824589\pi$
$840$		0			0
$841$	−618.703	+	1071.62i	−0.735675	+	1.27423i
$842$	−21.5835	+	37.3838i	−0.0256336	+	0.0443988i
$843$		0			0
$844$	142.256	+	246.395i	0.168550	+	0.291937i
$845$			93.1745i			0.110266i
$846$		0			0
$847$	294.595	+	1218.22i	0.347810	+	1.43828i
$848$	−158.137	−	273.902i	−0.186483	−	0.322997i
$849$		0			0
$850$	103.784	+	59.9197i	0.122099	+	0.0704937i
$851$	695.426	−	1204.51i	0.817187	−	1.41541i
$852$		0			0
$853$	1394.66	−	805.206i	1.63500	−	0.943969i	0.652485	−	0.757802i	$-0.273727\pi$
$853$	1394.66	−	805.206i	1.63500	−	0.943969i	0.982518	−	0.186168i	$-0.0596068\pi$
$854$	−470.606	+	113.804i	−0.551061	+	0.133260i
$855$		0			0
$856$	−111.320			−0.130047
$857$	−637.918	+	368.302i	−0.744361	+	0.429757i	−0.823653	−	0.567094i	$-0.808068\pi$
$857$	−637.918	+	368.302i	−0.744361	+	0.429757i	0.0792915	+	0.996851i	$0.474734\pi$
$858$		0			0
$859$	449.010	+	259.236i	0.522712	+	0.301788i	0.738044	−	0.674753i	$-0.235750\pi$
$859$	449.010	+	259.236i	0.522712	+	0.301788i	−0.215331	+	0.976541i	$0.569083\pi$
$860$	118.491	+	68.4111i	0.137781	+	0.0795477i
$861$		0			0
$862$	151.835	+	262.985i	0.176142	+	0.305087i
$863$	−319.670			−0.370417			−0.185209	−	0.982699i	$-0.559296\pi$
$863$	−319.670			−0.370417			−0.185209	+	0.982699i	$0.559296\pi$
$864$		0			0
$865$	−939.834			−1.08651
$866$	−61.2187	+	35.3447i	−0.0706914	+	0.0408137i
$867$		0			0
$868$	−3.53563	+	12.0088i	−0.00407331	+	0.0138351i
$869$	−981.499	+	1700.01i	−1.12946	+	1.95628i
$870$		0			0
$871$	121.928	−	70.3951i	0.139986	−	0.0808210i
$872$	240.373			0.275657
$873$		0			0
$874$		−	886.488i		−	1.01429i
$875$	−469.834	−	493.469i	−0.536953	−	0.563964i
$876$		0			0
$877$	120.744	−	209.135i	0.137679	−	0.238467i	−0.788939	−	0.614472i	$-0.789369\pi$
$877$	120.744	−	209.135i	0.137679	−	0.238467i	0.926618	+	0.376005i	$0.122703\pi$
$878$	−247.422	−	142.849i	−0.281801	−	0.162698i
$879$		0			0
$880$	345.092	−	199.239i	0.392150	−	0.226408i
$881$		−	1263.93i		−	1.43466i	−0.696735	−	0.717328i	$-0.745365\pi$
$881$		−	1263.93i		−	1.43466i	0.696735	−	0.717328i	$-0.254635\pi$
$882$		0			0
$883$	84.6550			0.0958720			0.0479360	−	0.998850i	$-0.484736\pi$
$883$	84.6550			0.0958720			0.0479360	+	0.998850i	$0.484736\pi$
$884$	142.813	+	247.360i	0.161554	+	0.279819i
$885$		0			0
$886$	−580.948	+	1006.23i	−0.655697	+	1.13570i
$887$	−322.314	−	186.088i	−0.363375	−	0.209795i	0.307185	−	0.951650i	$-0.400613\pi$
$887$	−322.314	−	186.088i	−0.363375	−	0.209795i	−0.670560	+	0.741855i	$0.733946\pi$
$888$		0			0
$889$	−709.249	+	675.280i	−0.797805	+	0.759595i
$890$	1001.92			1.12576
$891$		0			0
$892$		−	227.439i		−	0.254977i
$893$	192.786	+	333.915i	0.215885	+	0.373925i
$894$		0			0
$895$	−943.775	−	544.889i	−1.05450	−	0.608814i
$896$	−75.9717	−	22.3675i	−0.0847898	−	0.0249638i
$897$		0			0
$898$	229.777	+	397.986i	0.255877	+	0.443192i
$899$			40.7652i			0.0453450i
$900$		0			0
$901$			829.757i			0.920929i
$902$	−518.670	+	299.455i	−0.575023	+	0.331990i
$903$		0			0
$904$	72.4340	−	125.459i	0.0801261	−	0.138783i
$905$	−466.186	+	807.458i	−0.515123	+	0.892219i
$906$		0			0
$907$	−680.264	−	1178.25i	−0.750015	−	1.29906i	−0.947815	−	0.318822i	$-0.896713\pi$
$907$	−680.264	−	1178.25i	−0.750015	−	1.29906i	0.197799	−	0.980243i	$-0.436621\pi$
$908$			300.788i			0.331264i
$909$		0			0
$910$	182.114	+	753.083i	0.200125	+	0.827564i
$911$	23.2739	+	40.3116i	0.0255477	+	0.0442498i	0.878517	−	0.477712i	$-0.158534\pi$
$911$	23.2739	+	40.3116i	0.0255477	+	0.0442498i	−0.852969	+	0.521962i	$0.825200\pi$
$912$		0			0
$913$	−1435.01	−	828.506i	−1.57176	−	0.907454i
$914$	524.343	−	908.188i	0.573679	−	0.993641i
$915$		0			0
$916$	−62.0117	+	35.8025i	−0.0676984	+	0.0390857i
$917$	−288.427	+	69.7487i	−0.314533	+	0.0760618i
$918$		0			0
$919$	−326.576			−0.355360			−0.177680	−	0.984088i	$-0.556859\pi$
$919$	−326.576			−0.355360			−0.177680	+	0.984088i	$0.556859\pi$
$920$	382.960	−	221.102i	0.416261	−	0.240329i
$921$		0			0
$922$	−810.848	−	468.143i	−0.879445	−	0.507748i
$923$	496.100	+	286.423i	0.537486	+	0.310318i
$924$		0			0
$925$	206.566	+	357.783i	0.223315	+	0.386793i
$926$	915.492			0.988653
$927$		0			0
$928$	−257.893			−0.277902
$929$	508.153	−	293.382i	0.546989	−	0.315804i	−0.200918	−	0.979608i	$-0.564392\pi$
$929$	508.153	−	293.382i	0.546989	−	0.315804i	0.747907	+	0.663804i	$0.231059\pi$
$930$		0			0
$931$	1128.50	+	55.4088i	1.21214	+	0.0595153i
$932$	−397.747	+	688.917i	−0.426767	+	0.739182i
$933$		0			0
$934$	21.5345	−	12.4329i	0.0230562	−	0.0133115i
$935$	−1045.42			−1.11810
$936$		0			0
$937$		−	858.055i		−	0.915747i	−0.889017	−	0.457873i	$-0.848611\pi$
$937$		−	858.055i		−	0.915747i	0.889017	−	0.457873i	$-0.151389\pi$
$938$	74.1728	−	70.6203i	0.0790755	−	0.0752882i
$939$		0			0
$940$	−96.1668	+	166.566i	−0.102305	+	0.177198i
$941$	−293.858	−	169.659i	−0.312283	−	0.180296i	0.335665	−	0.941981i	$-0.391039\pi$
$941$	−293.858	−	169.659i	−0.312283	−	0.180296i	−0.647947	+	0.761685i	$0.724372\pi$
$942$		0			0
$943$	−575.586	+	332.315i	−0.610378	+	0.352402i
$944$			173.274i			0.183553i
$945$		0			0
$946$	−291.398			−0.308032
$947$	−145.781	−	252.501i	−0.153940	−	0.266632i	0.778732	−	0.627356i	$-0.215863\pi$
$947$	−145.781	−	252.501i	−0.153940	−	0.266632i	−0.932673	+	0.360724i	$0.882530\pi$
$948$		0			0
$949$	−746.800	+	1293.50i	−0.786933	+	1.36301i
$950$	228.041	+	131.659i	0.240043	+	0.138589i
$951$		0			0
$952$	143.270	+	150.477i	0.150494	+	0.158064i
$953$	−1099.85			−1.15409			−0.577046	−	0.816712i	$-0.695795\pi$
$953$	−1099.85			−1.15409			−0.577046	+	0.816712i	$0.695795\pi$
$954$		0			0
$955$		−	562.186i		−	0.588676i
$956$	−170.269	−	294.915i	−0.178106	−	0.308489i
$957$		0			0
$958$	−847.268	−	489.171i	−0.884414	−	0.510616i
$959$	−616.565	−	181.529i	−0.642925	−	0.189290i
$960$		0			0
$961$	−480.100	−	831.558i	−0.499584	−	0.865305i
$962$			984.666i			1.02356i
$963$		0			0
$964$			144.388i			0.149780i
$965$	1728.02	−	997.671i	1.79069	−	1.03386i
$966$		0			0
$967$	−206.206	+	357.160i	−0.213243	+	0.369348i	−0.952728	−	0.303825i	$-0.901736\pi$
$967$	−206.206	+	357.160i	−0.213243	+	0.369348i	0.739484	+	0.673174i	$0.235069\pi$
$968$	−253.212	+	438.575i	−0.261582	+	0.453074i
$969$		0			0
$970$	98.2198	+	170.122i	0.101258	+	0.175383i
$971$			1193.06i			1.22869i	0.789038	+	0.614344i	$0.210579\pi$
$971$			1193.06i			1.22869i	−0.789038	+	0.614344i	$0.789421\pi$
$972$		0			0
$973$	339.376	−	82.0694i	0.348793	−	0.0843468i
$974$	−553.574	−	958.818i	−0.568351	−	0.984412i
$975$		0			0
$976$	−169.425	−	97.8174i	−0.173591	−	0.100223i
$977$	−962.075	+	1666.36i	−0.984723	+	1.70559i	−0.341564	+	0.939858i	$0.610957\pi$
$977$	−962.075	+	1666.36i	−0.984723	+	1.70559i	−0.643159	+	0.765733i	$0.722377\pi$
$978$		0			0
$979$	−1847.97	+	1066.93i	−1.88761	+	1.08981i
$980$	257.527	+	501.329i	0.262783	+	0.511560i
$981$		0			0
$982$	−480.689			−0.489500
$983$	−1122.96	+	648.340i	−1.14238	+	0.659552i	−0.947018	−	0.321180i	$-0.895921\pi$
$983$	−1122.96	+	648.340i	−1.14238	+	0.659552i	−0.195359	+	0.980732i	$0.562587\pi$
$984$		0			0
$985$	−77.3920	−	44.6823i	−0.0785706	−	0.0453627i
$986$	585.946	+	338.296i	0.594266	+	0.343100i
$987$		0			0
$988$	313.799	+	543.515i	0.317610	+	0.550117i
$989$	−323.375			−0.326971
$990$		0			0
$991$	232.207			0.234315			0.117158	−	0.993113i	$-0.462622\pi$
$991$	232.207			0.234315			0.117158	+	0.993113i	$0.462622\pi$
$992$	−4.38056	+	2.52912i	−0.00441589	+	0.00254951i
$993$		0			0
$994$	399.740	+	117.691i	0.402153	+	0.118402i
$995$	823.416	−	1426.20i	0.827554	−	1.43337i
$996$		0			0
$997$	1177.97	−	680.103i	1.18152	−	0.682149i	0.225152	−	0.974324i	$-0.427712\pi$
$997$	1177.97	−	680.103i	1.18152	−	0.682149i	0.956365	+	0.292174i	$0.0943787\pi$
$998$	−307.902			−0.308519
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.3.o.a.307.7		32
3.2	odd	2		126.3.o.a.13.9	✓	32
7.6	odd	2	inner	378.3.o.a.307.2		32
9.2	odd	6		126.3.o.a.97.16	yes	32
9.4	even	3		1134.3.c.d.811.10		16
9.5	odd	6		1134.3.c.e.811.7		16
9.7	even	3	inner	378.3.o.a.181.2		32
21.20	even	2		126.3.o.a.13.16	yes	32
63.13	odd	6		1134.3.c.d.811.15		16
63.20	even	6		126.3.o.a.97.9	yes	32
63.34	odd	6	inner	378.3.o.a.181.7		32
63.41	even	6		1134.3.c.e.811.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.o.a.13.9	✓	32	3.2	odd	2
126.3.o.a.13.16	yes	32	21.20	even	2
126.3.o.a.97.9	yes	32	63.20	even	6
126.3.o.a.97.16	yes	32	9.2	odd	6
378.3.o.a.181.2		32	9.7	even	3	inner
378.3.o.a.181.7		32	63.34	odd	6	inner
378.3.o.a.307.2		32	7.6	odd	2	inner
378.3.o.a.307.7		32	1.1	even	1	trivial
1134.3.c.d.811.10		16	9.4	even	3
1134.3.c.d.811.15		16	63.13	odd	6
1134.3.c.e.811.2		16	63.41	even	6
1134.3.c.e.811.7		16	9.5	odd	6

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	378.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(4.98058 + 2.87554i) q^{5} +(5.06966 - 4.82685i) q^{7} +2.82843 q^{8} -8.13325i q^{10} +(8.66094 + 15.0012i) q^{11} +(-11.7856 - 6.80443i) q^{13} +(-9.49646 - 2.79594i) q^{14} +(-2.00000 - 3.46410i) q^{16} +10.4941i q^{17} +23.0584i q^{19} +(-9.96116 + 5.75108i) q^{20} +(12.2484 - 21.2149i) q^{22} +(13.5925 - 23.5429i) q^{23} +(4.03745 + 6.99307i) q^{25} +19.2458i q^{26} +(3.29069 + 13.6078i) q^{28} +(22.7948 + 39.4817i) q^{29} +(0.774381 + 0.447089i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(12.8526 - 7.42048i) q^{34} +(39.1297 - 9.46251i) q^{35} +51.1625 q^{37} +(28.2407 - 16.3048i) q^{38} +(14.0872 + 8.13325i) q^{40} +(-21.1730 - 12.2242i) q^{41} +(-5.94767 - 10.3017i) q^{43} -34.6438 q^{44} -38.4454 q^{46} +(14.4813 - 8.36076i) q^{47} +(2.40298 - 48.9410i) q^{49} +(5.70982 - 9.88970i) q^{50} +(23.5712 - 13.6089i) q^{52} +79.0686 q^{53} +99.6195i q^{55} +(14.3392 - 13.6524i) q^{56} +(32.2367 - 55.8355i) q^{58} +(-37.5149 - 21.6592i) q^{59} +(42.3562 - 24.4543i) q^{61} -1.26456i q^{62} +8.00000 q^{64} +(-39.1328 - 67.7800i) q^{65} +(-5.17274 + 8.95945i) q^{67} +(-18.1764 - 10.4941i) q^{68} +(-39.2580 - 41.2329i) q^{70} -42.0936 q^{71} -109.752i q^{73} +(-36.1774 - 62.6610i) q^{74} +(-39.9383 - 23.0584i) q^{76} +(116.317 + 34.2459i) q^{77} +(56.6624 + 98.1421i) q^{79} -23.0043i q^{80} +34.5753i q^{82} +(-82.8440 + 47.8300i) q^{83} +(-30.1763 + 52.2669i) q^{85} +(-8.41128 + 14.5688i) q^{86} +(24.4968 + 42.4298i) q^{88} +123.188i q^{89} +(-92.5931 + 22.3913i) q^{91} +(27.1850 + 47.0858i) q^{92} +(-20.4796 - 11.8239i) q^{94} +(-66.3053 + 114.844i) q^{95} +(-20.9168 + 12.0763i) q^{97} +(-61.6395 + 31.6635i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{4} - 2 q^{7} + 12 q^{11} + 12 q^{14} - 64 q^{16} - 12 q^{23} + 80 q^{25} + 8 q^{28} + 48 q^{29} - 348 q^{35} - 88 q^{37} + 32 q^{43} - 48 q^{44} + 48 q^{46} + 50 q^{49} - 48 q^{50} + 864 q^{53}+ \cdots - 624 q^{98}+O(q^{100}) \) 32 * q - 32 * q^4 - 2 * q^7 + 12 * q^11 + 12 * q^14 - 64 * q^16 - 12 * q^23 + 80 * q^25 + 8 * q^28 + 48 * q^29 - 348 * q^35 - 88 * q^37 + 32 * q^43 - 48 * q^44 + 48 * q^46 + 50 * q^49 - 48 * q^50 + 864 * q^53 + 24 * q^56 + 48 * q^58 + 256 * q^64 - 120 * q^65 - 140 * q^67 - 108 * q^70 - 552 * q^71 - 144 * q^74 + 258 * q^77 - 176 * q^79 - 60 * q^85 - 96 * q^86 + 372 * q^91 - 24 * q^92 - 528 * q^95 - 624 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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