LMFDB - Embedded newform 378.3.o.a.181.8

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			181.8
Character	$\chi$	$=$	378.181
Dual form			378.3.o.a.307.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(6.78854 - 3.91937i) q^{5} +(-6.99901 + 0.117453i) q^{7} +2.82843 q^{8} +11.0856i q^{10} +(1.05393 - 1.82546i) q^{11} +(8.95661 - 5.17110i) q^{13} +(4.80520 - 8.65506i) q^{14} +(-2.00000 + 3.46410i) q^{16} -9.44215i q^{17} +7.01239i q^{19} +(-13.5771 - 7.83874i) q^{20} +(1.49048 + 2.58159i) q^{22} +(-22.7785 - 39.4534i) q^{23} +(18.2229 - 31.5630i) q^{25} +14.6261i q^{26} +(7.20245 + 12.0052i) q^{28} +(9.93225 - 17.2032i) q^{29} +(-5.21387 + 3.01023i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(11.5642 + 6.67661i) q^{34} +(-47.0528 + 28.2290i) q^{35} -40.4151 q^{37} +(-8.58839 - 4.95851i) q^{38} +(19.2009 - 11.0856i) q^{40} +(52.9968 - 30.5977i) q^{41} +(34.3646 - 59.5213i) q^{43} -4.21571 q^{44} +64.4272 q^{46} +(59.5554 + 34.3843i) q^{47} +(48.9724 - 1.64411i) q^{49} +(25.7710 + 44.6368i) q^{50} +(-17.9132 - 10.3422i) q^{52} +64.4077 q^{53} -16.5229i q^{55} +(-19.7962 + 0.332208i) q^{56} +(14.0463 + 24.3290i) q^{58} +(-36.8068 + 21.2504i) q^{59} +(9.89468 + 5.71270i) q^{61} -8.51422i q^{62} +8.00000 q^{64} +(40.5349 - 70.2085i) q^{65} +(4.32856 + 7.49729i) q^{67} +(-16.3543 + 9.44215i) q^{68} +(-1.30205 - 77.5886i) q^{70} -56.4985 q^{71} +64.7908i q^{73} +(28.5778 - 49.4982i) q^{74} +(12.1458 - 7.01239i) q^{76} +(-7.16205 + 12.9002i) q^{77} +(-57.0864 + 98.8765i) q^{79} +31.3549i q^{80} +86.5433i q^{82} +(-86.5846 - 49.9896i) q^{83} +(-37.0073 - 64.0985i) q^{85} +(48.5989 + 84.1758i) q^{86} +(2.98096 - 5.16317i) q^{88} -90.9556i q^{89} +(-62.0801 + 37.2446i) q^{91} +(-45.5569 + 78.9069i) q^{92} +(-84.2240 + 48.6267i) q^{94} +(27.4841 + 47.6039i) q^{95} +(39.5328 + 22.8243i) q^{97} +(-32.6151 + 61.1413i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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
$5$	6.78854	−	3.91937i	1.35771	−	0.783874i	0.368394	−	0.929670i	$-0.379908\pi$
$5$	6.78854	−	3.91937i	1.35771	−	0.783874i	0.989315	+	0.145796i	$0.0465744\pi$
$6$		0			0
$7$	−6.99901	+	0.117453i	−0.999859	+	0.0167790i
$7$	−6.99901	+	0.117453i	−0.999859	+	0.0167790i
$8$	2.82843			0.353553
$9$		0			0
$10$			11.0856i			1.10856i
$11$	1.05393	−	1.82546i	0.0958116	−	0.165951i	−0.814135	−	0.580675i	$-0.802789\pi$
$11$	1.05393	−	1.82546i	0.0958116	−	0.165951i	0.909947	+	0.414724i	$0.136122\pi$
$12$		0			0
$13$	8.95661	−	5.17110i	0.688970	−	0.397777i	−0.114256	−	0.993451i	$-0.536448\pi$
$13$	8.95661	−	5.17110i	0.688970	−	0.397777i	0.803226	+	0.595674i	$0.203115\pi$
$14$	4.80520	−	8.65506i	0.343229	−	0.618219i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$		−	9.44215i		−	0.555421i	−0.960665	−	0.277710i	$-0.910424\pi$
$17$		−	9.44215i		−	0.555421i	0.960665	−	0.277710i	$-0.0895755\pi$
$18$		0			0
$19$			7.01239i			0.369073i	0.982826	+	0.184537i	$0.0590784\pi$
$19$			7.01239i			0.369073i	−0.982826	+	0.184537i	$0.940922\pi$
$20$	−13.5771	−	7.83874i	−0.678854	−	0.391937i
$21$		0			0
$22$	1.49048	+	2.58159i	0.0677490	+	0.117345i
$23$	−22.7785	−	39.4534i	−0.990367	−	1.71537i	−0.615097	−	0.788451i	$-0.710883\pi$
$23$	−22.7785	−	39.4534i	−0.990367	−	1.71537i	−0.375270	−	0.926915i	$-0.622450\pi$
$24$		0			0
$25$	18.2229	−	31.5630i	0.728915	−	1.26252i
$26$			14.6261i			0.562542i
$27$		0			0
$28$	7.20245	+	12.0052i	0.257230	+	0.428757i
$29$	9.93225	−	17.2032i	0.342491	−	0.593213i	−0.642403	−	0.766367i	$-0.722063\pi$
$29$	9.93225	−	17.2032i	0.342491	−	0.593213i	0.984895	+	0.173154i	$0.0553959\pi$
$30$		0			0
$31$	−5.21387	+	3.01023i	−0.168189	+	0.0971042i	−0.581732	−	0.813381i	$-0.697625\pi$
$31$	−5.21387	+	3.01023i	−0.168189	+	0.0971042i	0.413542	+	0.910485i	$0.364291\pi$
$32$	−2.82843	−	4.89898i	−0.0883883	−	0.153093i
$33$		0			0
$34$	11.5642	+	6.67661i	0.340124	+	0.196371i
$35$	−47.0528	+	28.2290i	−1.34436	+	0.806544i
$36$		0			0
$37$	−40.4151			−1.09230			−0.546151	−	0.837687i	$-0.683907\pi$
$37$	−40.4151			−1.09230			−0.546151	+	0.837687i	$0.683907\pi$
$38$	−8.58839	−	4.95851i	−0.226010	−	0.130487i
$39$		0			0
$40$	19.2009	−	11.0856i	0.480023	−	0.277141i
$41$	52.9968	−	30.5977i	1.29260	−	0.746285i	0.313489	−	0.949592i	$-0.398502\pi$
$41$	52.9968	−	30.5977i	1.29260	−	0.746285i	0.979115	+	0.203307i	$0.0651688\pi$
$42$		0			0
$43$	34.3646	−	59.5213i	0.799178	−	1.38422i	−0.120974	−	0.992656i	$-0.538602\pi$
$43$	34.3646	−	59.5213i	0.799178	−	1.38422i	0.920152	−	0.391561i	$-0.128065\pi$
$44$	−4.21571			−0.0958116
$45$		0			0
$46$	64.4272			1.40059
$47$	59.5554	+	34.3843i	1.26714	+	0.731581i	0.974445	−	0.224626i	$-0.0721162\pi$
$47$	59.5554	+	34.3843i	1.26714	+	0.731581i	0.292690	+	0.956207i	$0.405450\pi$
$48$		0			0
$49$	48.9724	−	1.64411i	0.999437	−	0.0335534i
$50$	25.7710	+	44.6368i	0.515421	+	0.892735i
$51$		0			0
$52$	−17.9132	−	10.3422i	−0.344485	−	0.198889i
$53$	64.4077			1.21524			0.607620	−	0.794228i	$-0.292125\pi$
$53$	64.4077			1.21524			0.607620	+	0.794228i	$0.292125\pi$
$54$		0			0
$55$		−	16.5229i		−	0.300417i
$56$	−19.7962	+	0.332208i	−0.353504	+	0.00593229i
$57$		0			0
$58$	14.0463	+	24.3290i	0.242178	+	0.419465i
$59$	−36.8068	+	21.2504i	−0.623844	+	0.360177i	−0.778364	−	0.627813i	$-0.783950\pi$
$59$	−36.8068	+	21.2504i	−0.623844	+	0.360177i	0.154520	+	0.987990i	$0.450617\pi$
$60$		0			0
$61$	9.89468	+	5.71270i	0.162208	+	0.0936508i	0.578907	−	0.815394i	$-0.303480\pi$
$61$	9.89468	+	5.71270i	0.162208	+	0.0936508i	−0.416699	+	0.909045i	$0.636813\pi$
$62$		−	8.51422i		−	0.137326i
$63$		0			0
$64$	8.00000			0.125000
$65$	40.5349	−	70.2085i	0.623614	−	1.08013i
$66$		0			0
$67$	4.32856	+	7.49729i	0.0646054	+	0.111900i	0.896519	−	0.443005i	$-0.146088\pi$
$67$	4.32856	+	7.49729i	0.0646054	+	0.111900i	−0.831913	+	0.554905i	$0.812754\pi$
$68$	−16.3543	+	9.44215i	−0.240504	+	0.138855i
$69$		0			0
$70$	−1.30205	−	77.5886i	−0.0186006	−	1.10841i
$71$	−56.4985			−0.795753			−0.397876	−	0.917439i	$-0.630253\pi$
$71$	−56.4985			−0.795753			−0.397876	+	0.917439i	$0.630253\pi$
$72$		0			0
$73$			64.7908i			0.887545i	0.896139	+	0.443773i	$0.146360\pi$
$73$			64.7908i			0.887545i	−0.896139	+	0.443773i	$0.853640\pi$
$74$	28.5778	−	49.4982i	0.386187	−	0.668895i
$75$		0			0
$76$	12.1458	−	7.01239i	0.159813	−	0.0922683i
$77$	−7.16205	+	12.9002i	−0.0930136	+	0.167535i
$78$		0			0
$79$	−57.0864	+	98.8765i	−0.722612	+	1.25160i	0.237337	+	0.971427i	$0.423725\pi$
$79$	−57.0864	+	98.8765i	−0.722612	+	1.25160i	−0.959949	+	0.280174i	$0.909608\pi$
$80$			31.3549i			0.391937i
$81$		0			0
$82$			86.5433i			1.05541i
$83$	−86.5846	−	49.9896i	−1.04319	−	0.602285i	−0.122453	−	0.992474i	$-0.539076\pi$
$83$	−86.5846	−	49.9896i	−1.04319	−	0.602285i	−0.920735	+	0.390190i	$0.872409\pi$
$84$		0			0
$85$	−37.0073	−	64.0985i	−0.435380	−	0.754100i
$86$	48.5989	+	84.1758i	0.565104	+	0.978789i
$87$		0			0
$88$	2.98096	−	5.16317i	0.0338745	−	0.0586724i
$89$		−	90.9556i		−	1.02197i	−0.859589	−	0.510986i	$-0.829280\pi$
$89$		−	90.9556i		−	1.02197i	0.859589	−	0.510986i	$-0.170720\pi$
$90$		0			0
$91$	−62.0801	+	37.2446i	−0.682199	+	0.409281i
$92$	−45.5569	+	78.9069i	−0.495184	+	0.857683i
$93$		0			0
$94$	−84.2240	+	48.6267i	−0.896000	+	0.517306i
$95$	27.4841	+	47.6039i	0.289307	+	0.501094i
$96$		0			0
$97$	39.5328	+	22.8243i	0.407555	+	0.235302i	0.689738	−	0.724059i	$-0.257726\pi$
$97$	39.5328	+	22.8243i	0.407555	+	0.235302i	−0.282184	+	0.959360i	$0.591059\pi$
$98$	−32.6151	+	61.1413i	−0.332807	+	0.623891i
$99$		0			0
$100$	−72.8915			−0.728915
$101$	−0.526801	−	0.304149i	−0.00521585	−	0.00301137i	0.497390	−	0.867527i	$-0.334292\pi$
$101$	−0.526801	−	0.304149i	−0.00521585	−	0.00301137i	−0.502606	+	0.864516i	$0.667625\pi$
$102$		0			0
$103$	84.7729	−	48.9437i	0.823038	−	0.475181i	−0.0284251	−	0.999596i	$-0.509049\pi$
$103$	84.7729	−	48.9437i	0.823038	−	0.475181i	0.851463	+	0.524415i	$0.175716\pi$
$104$	25.3331	−	14.6261i	0.243588	−	0.140635i
$105$		0			0
$106$	−45.5431	+	78.8830i	−0.429652	+	0.744179i
$107$	65.2642			0.609946			0.304973	−	0.952361i	$-0.401353\pi$
$107$	65.2642			0.609946			0.304973	+	0.952361i	$0.401353\pi$
$108$		0			0
$109$	−197.677			−1.81355			−0.906776	−	0.421612i	$-0.861464\pi$
$109$	−197.677			−1.81355			−0.906776	+	0.421612i	$0.861464\pi$
$110$	20.2364	+	11.6835i	0.183967	+	0.106213i
$111$		0			0
$112$	13.5912	−	24.4802i	0.121350	−	0.218573i
$113$	−25.1877	−	43.6264i	−0.222900	−	0.386074i	0.732787	−	0.680458i	$-0.238219\pi$
$113$	−25.1877	−	43.6264i	−0.222900	−	0.386074i	−0.955687	+	0.294384i	$0.904886\pi$
$114$		0			0
$115$	−309.265	−	178.554i	−2.68926	−	1.55265i
$116$	−39.7290			−0.342491
$117$		0			0
$118$		−	60.1053i		−	0.509367i
$119$	1.10901	+	66.0858i	0.00931943	+	0.555342i
$120$		0			0
$121$	58.2785	+	100.941i	0.481640	+	0.834225i
$122$	−13.9932	+	8.07898i	−0.114698	+	0.0662211i
$123$		0			0
$124$	10.4277	+	6.02046i	0.0840947	+	0.0485521i
$125$		−	89.7203i		−	0.717763i
$126$		0			0
$127$	118.295			0.931457			0.465729	−	0.884928i	$-0.345792\pi$
$127$	118.295			0.931457			0.465729	+	0.884928i	$0.345792\pi$
$128$	−5.65685	+	9.79796i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	57.3250	+	99.2898i	0.440962	+	0.763768i
$131$	−111.014	+	64.0941i	−0.847438	+	0.489268i	−0.859785	−	0.510655i	$-0.829403\pi$
$131$	−111.014	+	64.0941i	−0.847438	+	0.489268i	0.0123479	+	0.999924i	$0.496069\pi$
$132$		0			0
$133$	−0.823628	−	49.0798i	−0.00619269	−	0.369021i
$134$	−12.2430			−0.0913659
$135$		0			0
$136$		−	26.7064i		−	0.196371i
$137$	−110.979	+	192.221i	−0.810063	+	1.40307i	0.102757	+	0.994706i	$0.467234\pi$
$137$	−110.979	+	192.221i	−0.810063	+	1.40307i	−0.912820	+	0.408363i	$0.866100\pi$
$138$		0			0
$139$	206.757	−	119.371i	1.48746	−	0.858788i	0.487566	−	0.873086i	$-0.337885\pi$
$139$	206.757	−	119.371i	1.48746	−	0.858788i	0.999898	+	0.0142986i	$0.00455153\pi$
$140$	95.9469	+	53.2687i	0.685335	+	0.380491i
$141$		0			0
$142$	39.9504	−	69.1962i	0.281341	−	0.487297i
$143$		−	21.7999i		−	0.152447i
$144$		0			0
$145$		−	155.713i		−	1.07388i
$146$	−79.3522	−	45.8140i	−0.543508	−	0.313795i
$147$		0			0
$148$	40.4151	+	70.0011i	0.273075	+	0.472980i
$149$	−51.5809	−	89.3407i	−0.346180	−	0.599602i	0.639387	−	0.768885i	$-0.279188\pi$
$149$	−51.5809	−	89.3407i	−0.346180	−	0.599602i	−0.985567	+	0.169283i	$0.945855\pi$
$150$		0			0
$151$	−100.671	+	174.368i	−0.666697	+	1.15475i	0.312126	+	0.950041i	$0.398959\pi$
$151$	−100.671	+	174.368i	−0.666697	+	1.15475i	−0.978822	+	0.204712i	$0.934374\pi$
$152$			19.8340i			0.130487i
$153$		0			0
$154$	−10.7351	−	17.8935i	−0.0697084	−	0.116191i
$155$	−23.5964	+	40.8702i	−0.152235	+	0.263679i
$156$		0			0
$157$	−81.5336	+	47.0735i	−0.519322	+	0.299831i	−0.736657	−	0.676266i	$-0.763597\pi$
$157$	−81.5336	+	47.0735i	−0.519322	+	0.299831i	0.217335	+	0.976097i	$0.430264\pi$
$158$	−80.7323	−	139.832i	−0.510964	−	0.885016i
$159$		0			0
$160$	−38.4018	−	22.1713i	−0.240011	−	0.138571i
$161$	164.061	+	273.460i	1.01901	+	1.69851i
$162$		0			0
$163$	9.85556			0.0604636			0.0302318	−	0.999543i	$-0.490375\pi$
$163$	9.85556			0.0604636			0.0302318	+	0.999543i	$0.490375\pi$
$164$	−105.994	−	61.1954i	−0.646302	−	0.373143i
$165$		0			0
$166$	122.449	−	70.6960i	0.737645	−	0.425880i
$167$	106.856	−	61.6935i	0.639858	−	0.369422i	−0.144702	−	0.989475i	$-0.546222\pi$
$167$	106.856	−	61.6935i	0.639858	−	0.369422i	0.784560	+	0.620053i	$0.212889\pi$
$168$		0			0
$169$	−31.0194	+	53.7272i	−0.183547	+	0.317912i
$170$	104.672			0.615720
$171$		0			0
$172$	−137.459			−0.799178
$173$	224.321	+	129.512i	1.29666	+	0.748624i	0.979825	−	0.199858i	$-0.0640481\pi$
$173$	224.321	+	129.512i	1.29666	+	0.748624i	0.316830	+	0.948482i	$0.397381\pi$
$174$		0			0
$175$	−123.835	+	223.050i	−0.707629	+	1.27457i
$176$	4.21571	+	7.30183i	0.0239529	+	0.0414876i
$177$		0			0
$178$	111.397	+	64.3153i	0.625828	+	0.361322i
$179$	−23.4639			−0.131083			−0.0655416	−	0.997850i	$-0.520878\pi$
$179$	−23.4639			−0.131083			−0.0655416	+	0.997850i	$0.520878\pi$
$180$		0			0
$181$			173.634i			0.959304i	0.877459	+	0.479652i	$0.159237\pi$
$181$			173.634i			0.959304i	−0.877459	+	0.479652i	$0.840763\pi$
$182$	−1.71788	−	102.368i	−0.00943891	−	0.562463i
$183$		0			0
$184$	−64.4272	−	111.591i	−0.350148	−	0.606474i
$185$	−274.360	+	158.402i	−1.48303	+	0.856226i
$186$		0			0
$187$	−17.2362	−	9.95135i	−0.0921724	−	0.0532157i
$188$		−	137.537i		−	0.731581i
$189$		0			0
$190$	−77.7369			−0.409141
$191$	−121.207	+	209.936i	−0.634590	+	1.09914i	0.352011	+	0.935996i	$0.385498\pi$
$191$	−121.207	+	209.936i	−0.634590	+	1.09914i	−0.986602	+	0.163147i	$0.947835\pi$
$192$		0			0
$193$	−124.323	−	215.333i	−0.644159	−	1.11572i	−0.984495	−	0.175412i	$-0.943874\pi$
$193$	−124.323	−	215.333i	−0.644159	−	1.11572i	0.340336	−	0.940304i	$-0.389459\pi$
$194$	−55.9078	+	32.2784i	−0.288185	+	0.166383i
$195$		0			0
$196$	−51.8201	−	83.1786i	−0.264388	−	0.424381i
$197$	6.15551			0.0312462			0.0156231	−	0.999878i	$-0.495027\pi$
$197$	6.15551			0.0312462			0.0156231	+	0.999878i	$0.495027\pi$
$198$		0			0
$199$			293.738i			1.47607i	0.674761	+	0.738036i	$0.264247\pi$
$199$			293.738i			1.47607i	−0.674761	+	0.738036i	$0.735753\pi$
$200$	51.5421	−	89.2735i	0.257710	−	0.446368i
$201$		0			0
$202$	0.745009	−	0.430131i	0.00368817	−	0.00212936i
$203$	−67.4954	+	121.572i	−0.332490	+	0.598876i
$204$		0			0
$205$	239.847	−	415.428i	1.16999	−	2.02648i
$206$			138.434i			0.672008i
$207$		0			0
$208$			41.3688i			0.198889i
$209$	12.8008	+	7.39055i	0.0612479	+	0.0353615i
$210$		0			0
$211$	37.0792	+	64.2230i	0.175731	+	0.304374i	0.940414	−	0.340032i	$-0.110438\pi$
$211$	37.0792	+	64.2230i	0.175731	+	0.304374i	−0.764683	+	0.644406i	$0.777105\pi$
$212$	−64.4077	−	111.557i	−0.303810	−	0.526214i
$213$		0			0
$214$	−46.1488	+	79.9320i	−0.215649	+	0.373514i
$215$		−	538.751i		−	2.50582i
$216$		0			0
$217$	36.1384	−	21.6810i	0.166536	−	0.0999126i
$218$	139.779	−	242.104i	0.641188	−	1.11057i
$219$		0			0
$220$	−28.6185	+	16.5229i	−0.130084	+	0.0751042i
$221$	−48.8263	−	84.5697i	−0.220934	−	0.382668i
$222$		0			0
$223$	240.774	+	139.011i	1.07970	+	0.623366i	0.930816	−	0.365488i	$-0.119098\pi$
$223$	240.774	+	139.011i	1.07970	+	0.623366i	0.148886	+	0.988854i	$0.452431\pi$
$224$	20.3716	+	33.9558i	0.0909447	+	0.151588i
$225$		0			0
$226$	71.2416			0.315228
$227$	87.4980	+	50.5170i	0.385454	+	0.222542i	0.680188	−	0.733037i	$-0.261898\pi$
$227$	87.4980	+	50.5170i	0.385454	+	0.222542i	−0.294735	+	0.955579i	$0.595231\pi$
$228$		0			0
$229$	−51.0727	+	29.4869i	−0.223025	+	0.128764i	−0.607350	−	0.794434i	$-0.707767\pi$
$229$	−51.0727	+	29.4869i	−0.223025	+	0.128764i	0.384325	+	0.923198i	$0.374434\pi$
$230$	437.367	−	252.514i	1.90159	−	1.09789i
$231$		0			0
$232$	28.0927	−	48.6579i	0.121089	−	0.209732i
$233$	179.497			0.770374			0.385187	−	0.922839i	$-0.374137\pi$
$233$	179.497			0.770374			0.385187	+	0.922839i	$0.374137\pi$
$234$		0			0
$235$	539.059			2.29387
$236$	73.6136	+	42.5008i	0.311922	+	0.180088i
$237$		0			0
$238$	−81.7224	−	45.3714i	−0.343371	−	0.190636i
$239$	91.2575	+	158.063i	0.381831	+	0.661350i	0.991324	−	0.131441i	$-0.0419604\pi$
$239$	91.2575	+	158.063i	0.381831	+	0.661350i	−0.609493	+	0.792791i	$0.708627\pi$
$240$		0			0
$241$	4.89842	+	2.82810i	0.0203254	+	0.0117349i	0.510128	−	0.860098i	$-0.329598\pi$
$241$	4.89842	+	2.82810i	0.0203254	+	0.0117349i	−0.489803	+	0.871833i	$0.662931\pi$
$242$	−164.836			−0.681142
$243$		0			0
$244$		−	22.8508i		−	0.0936508i
$245$	326.007	−	203.102i	1.33064	−	0.828988i
$246$		0			0
$247$	36.2618	+	62.8072i	0.146809	+	0.254280i
$248$	−14.7471	+	8.51422i	−0.0594640	+	0.0343315i
$249$		0			0
$250$	109.885	+	63.4419i	0.439538	+	0.253767i
$251$		−	150.523i		−	0.599693i	−0.953987	−	0.299847i	$-0.903064\pi$
$251$		−	150.523i		−	0.599693i	0.953987	−	0.299847i	$-0.0969355\pi$
$252$		0			0
$253$	−96.0274			−0.379555
$254$	−83.6472	+	144.881i	−0.329320	+	0.570399i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	88.3013	−	50.9808i	0.343585	−	0.198369i	−0.318271	−	0.948000i	$-0.603102\pi$
$257$	88.3013	−	50.9808i	0.343585	−	0.198369i	0.661856	+	0.749631i	$0.269769\pi$
$258$		0			0
$259$	282.866	−	4.74689i	1.09215	−	0.0183278i
$260$	−162.140			−0.623614
$261$		0			0
$262$		−	181.286i		−	0.691930i
$263$	56.3682	−	97.6325i	0.214328	−	0.371226i	−0.738737	−	0.673994i	$-0.764577\pi$
$263$	56.3682	−	97.6325i	0.214328	−	0.371226i	0.953064	+	0.302768i	$0.0979106\pi$
$264$		0			0
$265$	437.234	−	252.437i	1.64994	−	0.952594i
$266$	60.6926	+	33.6959i	0.228168	+	0.126676i
$267$		0			0
$268$	8.65713	−	14.9946i	0.0323027	−	0.0559499i
$269$		−	67.6480i		−	0.251479i	−0.992063	−	0.125740i	$-0.959870\pi$
$269$		−	67.6480i		−	0.251479i	0.992063	−	0.125740i	$-0.0401304\pi$
$270$		0			0
$271$		−	144.406i		−	0.532863i	−0.963854	−	0.266431i	$-0.914155\pi$
$271$		−	144.406i		−	0.532863i	0.963854	−	0.266431i	$-0.0858446\pi$
$272$	32.7086	+	18.8843i	0.120252	+	0.0694276i
$273$		0			0
$274$	−156.947	−	271.841i	−0.572801	−	0.992120i
$275$	−38.4112	−	66.5302i	−0.139677	−	0.241928i
$276$		0			0
$277$	128.720	−	222.949i	0.464692	−	0.804871i	−0.534495	−	0.845171i	$-0.679498\pi$
$277$	128.720	−	222.949i	0.464692	−	0.804871i	0.999188	+	0.0403008i	$0.0128316\pi$
$278$			337.634i			1.21451i
$279$		0			0
$280$	−133.085	+	79.8438i	−0.475305	+	0.285156i
$281$	146.075	−	253.010i	0.519840	−	0.900390i	−0.479894	−	0.877327i	$-0.659325\pi$
$281$	146.075	−	253.010i	0.519840	−	0.900390i	0.999734	−	0.0230634i	$-0.00734196\pi$
$282$		0			0
$283$	−287.137	+	165.778i	−1.01462	+	0.585790i	−0.912540	−	0.408987i	$-0.865882\pi$
$283$	−287.137	+	165.778i	−1.01462	+	0.585790i	−0.102077	+	0.994776i	$0.532549\pi$
$284$	56.4985	+	97.8582i	0.198938	+	0.344571i
$285$		0			0
$286$	26.6993	+	15.4148i	0.0933541	+	0.0538980i
$287$	−367.331	+	220.378i	−1.27990	+	0.767869i
$288$		0			0
$289$	199.846			0.691508
$290$	190.708	+	110.105i	0.657615	+	0.379674i
$291$		0			0
$292$	112.221	−	64.7908i	0.384318	−	0.221886i
$293$	−128.607	+	74.2511i	−0.438931	+	0.253417i	−0.703144	−	0.711047i	$-0.748221\pi$
$293$	−128.607	+	74.2511i	−0.438931	+	0.253417i	0.264213	+	0.964464i	$0.414888\pi$
$294$		0			0
$295$	−166.576	+	288.519i	−0.564666	+	0.978030i
$296$	−114.311			−0.386187
$297$		0			0
$298$	145.893			0.489573
$299$	−408.036	−	235.579i	−1.36467	−	0.787891i
$300$		0			0
$301$	−233.528	+	420.627i	−0.775839	+	1.39743i
$302$	−142.371	−	246.593i	−0.471426	−	0.816533i
$303$		0			0
$304$	−24.2916	−	14.0248i	−0.0799067	−	0.0461341i
$305$	89.5607			0.293642
$306$		0			0
$307$		−	47.5917i		−	0.155022i	−0.996992	−	0.0775109i	$-0.975303\pi$
$307$		−	47.5917i		−	0.155022i	0.996992	−	0.0775109i	$-0.0246973\pi$
$308$	29.5058	−	0.495149i	0.0957981	−	0.00160763i
$309$		0			0
$310$	−33.3704	−	57.7992i	−0.107646	−	0.186449i
$311$	13.1863	−	7.61311i	0.0423996	−	0.0244794i	−0.478650	−	0.878006i	$-0.658874\pi$
$311$	13.1863	−	7.61311i	0.0423996	−	0.0244794i	0.521050	+	0.853526i	$0.325541\pi$
$312$		0			0
$313$	135.158	+	78.0334i	0.431814	+	0.249308i	0.700119	−	0.714026i	$-0.253130\pi$
$313$	135.158	+	78.0334i	0.431814	+	0.249308i	−0.268305	+	0.963334i	$0.586464\pi$
$314$		−	133.144i		−	0.424025i
$315$		0			0
$316$	228.345			0.722612
$317$	−148.788	+	257.709i	−0.469363	+	0.812961i	−0.999387	−	0.0350219i	$-0.988850\pi$
$317$	−148.788	+	257.709i	−0.469363	+	0.812961i	0.530023	+	0.847983i	$0.322183\pi$
$318$		0			0
$319$	−20.9358	−	36.2618i	−0.0656293	−	0.113673i
$320$	54.3083	−	31.3549i	0.169714	−	0.0979842i
$321$		0			0
$322$	−450.927	+	7.56718i	−1.40039	+	0.0235006i
$323$	66.2120			0.204991
$324$		0			0
$325$		−	376.930i		−	1.15978i
$326$	−6.96893	+	12.0705i	−0.0213771	+	0.0370262i
$327$		0			0
$328$	149.897	−	86.5433i	0.457005	−	0.263852i
$329$	−420.867	−	233.661i	−1.27923	−	0.710217i
$330$		0			0
$331$	−151.889	+	263.079i	−0.458878	+	0.794800i	−0.998902	−	0.0468498i	$-0.985082\pi$
$331$	−151.889	+	263.079i	−0.458878	+	0.794800i	0.540024	+	0.841650i	$0.318415\pi$
$332$			199.959i			0.602285i
$333$		0			0
$334$			174.496i			0.522442i
$335$	58.7693	+	33.9305i	0.175431	+	0.101285i
$336$		0			0
$337$	−150.144	−	260.057i	−0.445531	−	0.771682i	0.552558	−	0.833474i	$-0.313652\pi$
$337$	−150.144	−	260.057i	−0.445531	−	0.771682i	−0.998089	+	0.0617925i	$0.980318\pi$
$338$	−43.8681	−	75.9817i	−0.129787	−	0.224798i
$339$		0			0
$340$	−74.0145	+	128.197i	−0.217690	+	0.377050i
$341$			12.6903i			0.0372148i
$342$		0			0
$343$	−342.565	+	17.2591i	−0.998733	+	0.0503182i
$344$	97.1979	−	168.352i	0.282552	−	0.489394i
$345$		0			0
$346$	−317.238	+	183.158i	−0.916874	+	0.529357i
$347$	−19.6093	−	33.9643i	−0.0565110	−	0.0978799i	0.836386	−	0.548141i	$-0.184664\pi$
$347$	−19.6093	−	33.9643i	−0.0565110	−	0.0978799i	−0.892897	+	0.450261i	$0.851331\pi$
$348$		0			0
$349$	391.985	+	226.313i	1.12317	+	0.648460i	0.942207	−	0.335030i	$-0.108747\pi$
$349$	391.985	+	226.313i	1.12317	+	0.648460i	0.180959	+	0.983491i	$0.442080\pi$
$350$	−185.615	−	309.386i	−0.530328	−	0.883961i
$351$		0			0
$352$	−11.9238			−0.0338745
$353$	364.417	+	210.396i	1.03234	+	0.596024i	0.917655	−	0.397378i	$-0.130080\pi$
$353$	364.417	+	210.396i	1.03234	+	0.596024i	0.114688	+	0.993402i	$0.463413\pi$
$354$		0			0
$355$	−383.542	+	221.438i	−1.08040	+	0.623770i
$356$	−157.540	+	90.9556i	−0.442527	+	0.255493i
$357$		0			0
$358$	16.5915	−	28.7373i	0.0463449	−	0.0802718i
$359$	−268.070			−0.746714			−0.373357	−	0.927688i	$-0.621793\pi$
$359$	−268.070			−0.746714			−0.373357	+	0.927688i	$0.621793\pi$
$360$		0			0
$361$	311.826			0.863785
$362$	−212.657	−	122.778i	−0.587451	−	0.339165i
$363$		0			0
$364$	126.590	+	70.2813i	0.347774	+	0.193080i
$365$	253.939	+	439.835i	0.695723	+	1.20503i
$366$		0			0
$367$	−24.1481	−	13.9419i	−0.0657986	−	0.0379889i	0.466740	−	0.884395i	$-0.345428\pi$
$367$	−24.1481	−	13.9419i	−0.0657986	−	0.0379889i	−0.532538	+	0.846406i	$0.678762\pi$
$368$	182.228			0.495184
$369$		0			0
$370$		−	448.028i		−	1.21089i
$371$	−450.790	+	7.56489i	−1.21507	+	0.0203905i
$372$		0			0
$373$	62.6374	+	108.491i	0.167929	+	0.290861i	0.937691	−	0.347469i	$-0.112959\pi$
$373$	62.6374	+	108.491i	0.167929	+	0.290861i	−0.769763	+	0.638330i	$0.779625\pi$
$374$	24.3757	−	14.0733i	0.0651757	−	0.0376292i
$375$		0			0
$376$	168.448	+	97.2535i	0.448000	+	0.258653i
$377$		−	205.443i		−	0.544941i
$378$		0			0
$379$	56.1639			0.148190			0.0740949	−	0.997251i	$-0.476393\pi$
$379$	56.1639			0.148190			0.0740949	+	0.997251i	$0.476393\pi$
$380$	54.9683	−	95.2078i	0.144653	−	0.250547i
$381$		0			0
$382$	−171.412	−	296.895i	−0.448723	−	0.777211i
$383$	491.936	−	284.020i	1.28443	−	0.741565i	0.306774	−	0.951782i	$-0.400750\pi$
$383$	491.936	−	284.020i	1.28443	−	0.741565i	0.977655	+	0.210217i	$0.0674170\pi$
$384$		0			0
$385$	1.94067	+	115.644i	0.00504070	+	0.300374i
$386$	351.638			0.910979
$387$		0			0
$388$		−	91.2971i		−	0.235302i
$389$	−146.522	+	253.784i	−0.376664	+	0.652401i	−0.990575	−	0.136974i	$-0.956262\pi$
$389$	−146.522	+	253.784i	−0.376664	+	0.652401i	0.613911	+	0.789376i	$0.289596\pi$
$390$		0			0
$391$	−372.525	+	215.078i	−0.952750	+	0.550071i
$392$	138.515	−	4.65026i	0.353354	−	0.0118629i
$393$		0			0
$394$	−4.35260	+	7.53893i	−0.0110472	+	0.0191343i
$395$			894.970i			2.26575i
$396$		0			0
$397$		−	507.654i		−	1.27873i	−0.768905	−	0.639363i	$-0.779198\pi$
$397$		−	507.654i		−	1.27873i	0.768905	−	0.639363i	$-0.220802\pi$
$398$	−359.755	−	207.704i	−0.903906	−	0.521870i
$399$		0			0
$400$	72.8915	+	126.252i	0.182229	+	0.315630i
$401$	−69.4682	−	120.322i	−0.173237	−	0.300056i	0.766313	−	0.642468i	$-0.222089\pi$
$401$	−69.4682	−	120.322i	−0.173237	−	0.300056i	−0.939550	+	0.342412i	$0.888756\pi$
$402$		0			0
$403$	−31.1324	+	53.9229i	−0.0772517	+	0.133804i
$404$			1.21660i			0.00301137i
$405$		0			0
$406$	−101.168	−	168.629i	−0.249182	−	0.415342i
$407$	−42.5946	+	73.7761i	−0.104655	+	0.181268i
$408$		0			0
$409$	416.051	−	240.207i	1.01724	−	0.587303i	0.103936	−	0.994584i	$-0.466856\pi$
$409$	416.051	−	240.207i	1.01724	−	0.587303i	0.913303	+	0.407281i	$0.133523\pi$
$410$	339.195	+	587.503i	0.827305	+	1.43293i
$411$		0			0
$412$	−169.546	−	97.8873i	−0.411519	−	0.237591i
$413$	255.115	−	153.055i	0.617713	−	0.370593i
$414$		0			0
$415$	−783.711			−1.88846
$416$	−50.6662	−	29.2522i	−0.121794	−	0.0703177i
$417$		0			0
$418$	−18.1031	+	10.4518i	−0.0433088	+	0.0250043i
$419$	385.429	−	222.527i	0.919878	−	0.531092i	0.0362816	−	0.999342i	$-0.488449\pi$
$419$	385.429	−	222.527i	0.919878	−	0.531092i	0.883596	+	0.468250i	$0.155115\pi$
$420$		0			0
$421$	−283.010	+	490.188i	−0.672233	+	1.16434i	0.305036	+	0.952341i	$0.401331\pi$
$421$	−283.010	+	490.188i	−0.672233	+	1.16434i	−0.977269	+	0.212001i	$0.932002\pi$
$422$	−104.876			−0.248521
$423$		0			0
$424$	182.172			0.429652
$425$	−298.022	−	172.063i	−0.701229	−	0.404855i
$426$		0			0
$427$	−69.9240	−	38.8211i	−0.163756	−	0.0909159i
$428$	−65.2642	−	113.041i	−0.152487	−	0.264114i
$429$		0			0
$430$	659.832	+	380.954i	1.53449	+	0.885940i
$431$	474.624			1.10121			0.550607	−	0.834764i	$-0.314396\pi$
$431$	474.624			1.10121			0.550607	+	0.834764i	$0.314396\pi$
$432$		0			0
$433$			1.62996i			0.00376435i	0.999998	+	0.00188217i	$0.000599115\pi$
$433$			1.62996i			0.00376435i	−0.999998	+	0.00188217i	$0.999401\pi$
$434$	1.00002	+	59.5911i	0.00230420	+	0.137307i
$435$		0			0
$436$	197.677	+	342.387i	0.453388	+	0.785291i
$437$	276.663	−	159.731i	0.633096	−	0.365518i
$438$		0			0
$439$	−541.613	−	312.700i	−1.23374	−	0.712302i	−0.265935	−	0.963991i	$-0.585681\pi$
$439$	−541.613	−	312.700i	−1.23374	−	0.712302i	−0.967808	+	0.251689i	$0.919014\pi$
$440$		−	46.7339i		−	0.106213i
$441$		0			0
$442$	138.102			0.312447
$443$	−148.901	+	257.904i	−0.336119	+	0.582175i	−0.983699	−	0.179822i	$-0.942448\pi$
$443$	−148.901	+	257.904i	−0.336119	+	0.582175i	0.647580	+	0.761997i	$0.275781\pi$
$444$		0			0
$445$	−356.488	−	617.456i	−0.801097	−	1.38754i
$446$	−340.505	+	196.591i	−0.763465	+	0.440787i
$447$		0			0
$448$	−55.9921	+	0.939626i	−0.124982	+	0.00209738i
$449$	−191.361			−0.426194			−0.213097	−	0.977031i	$-0.568355\pi$
$449$	−191.361			−0.426194			−0.213097	+	0.977031i	$0.568355\pi$
$450$		0			0
$451$		−	128.991i		−	0.286011i
$452$	−50.3754	+	87.2528i	−0.111450	+	0.193037i
$453$		0			0
$454$	−123.741	+	71.4418i	−0.272557	+	0.157361i
$455$	−275.458	+	496.151i	−0.605403	+	1.09044i
$456$		0			0
$457$	106.962	−	185.264i	0.234053	−	0.405392i	−0.724944	−	0.688808i	$-0.758134\pi$
$457$	106.962	−	185.264i	0.234053	−	0.405392i	0.958997	+	0.283416i	$0.0914676\pi$
$458$		−	83.4014i		−	0.182099i
$459$		0			0
$460$			714.217i			1.55265i
$461$	268.859	+	155.226i	0.583207	+	0.336715i	0.762407	−	0.647098i	$-0.224017\pi$
$461$	268.859	+	155.226i	0.583207	+	0.336715i	−0.179200	+	0.983813i	$0.557351\pi$
$462$		0			0
$463$	83.7628	+	145.081i	0.180913	+	0.313351i	0.942192	−	0.335074i	$-0.108761\pi$
$463$	83.7628	+	145.081i	0.180913	+	0.313351i	−0.761279	+	0.648425i	$0.775428\pi$
$464$	39.7290	+	68.8127i	0.0856229	+	0.148303i
$465$		0			0
$466$	−126.924	+	219.838i	−0.272368	+	0.471756i
$467$			315.106i			0.674744i	0.941371	+	0.337372i	$0.109538\pi$
$467$			315.106i			0.674744i	−0.941371	+	0.337372i	$0.890462\pi$
$468$		0			0
$469$	−31.1763	−	51.9653i	−0.0664739	−	0.110800i
$470$	−381.172	+	660.210i	−0.811005	+	1.40470i
$471$		0			0
$472$	−104.105	+	60.1053i	−0.220562	+	0.127342i
$473$	−72.4357	−	125.462i	−0.153141	−	0.265248i
$474$		0			0
$475$	221.332	+	127.786i	0.465962	+	0.269023i
$476$	113.355	−	68.0066i	0.238140	−	0.142871i
$477$		0			0
$478$	−258.115			−0.539990
$479$	−778.130	−	449.253i	−1.62449	−	0.937898i	−0.985699	−	0.168516i	$-0.946102\pi$
$479$	−778.130	−	449.253i	−1.62449	−	0.937898i	−0.638789	−	0.769382i	$-0.720564\pi$
$480$		0			0
$481$	−361.983	+	208.991i	−0.752563	+	0.434492i
$482$	−6.92741	+	3.99954i	−0.0143722	+	0.00829780i
$483$		0			0
$484$	116.557	−	201.883i	0.240820	−	0.417113i
$485$	357.827			0.737787
$486$		0			0
$487$	328.435			0.674404			0.337202	−	0.941432i	$-0.390519\pi$
$487$	328.435			0.674404			0.337202	+	0.941432i	$0.390519\pi$
$488$	27.9864	+	16.1580i	0.0573492	+	0.0331106i
$489$		0			0
$490$	18.2261	+	542.891i	0.0371961	+	1.10794i
$491$	165.906	+	287.358i	0.337894	+	0.585250i	0.984036	−	0.177967i	$-0.0569520\pi$
$491$	165.906	+	287.358i	0.337894	+	0.585250i	−0.646142	+	0.763217i	$0.723619\pi$
$492$		0			0
$493$	−162.435	−	93.7818i	−0.329483	−	0.190227i
$494$	−102.564			−0.207619
$495$		0			0
$496$		−	24.0818i		−	0.0485521i
$497$	395.434	−	6.63593i	0.795641	−	0.0133520i
$498$		0			0
$499$	−63.7291	−	110.382i	−0.127714	−	0.221206i	0.795077	−	0.606509i	$-0.207430\pi$
$499$	−63.7291	−	110.382i	−0.127714	−	0.221206i	−0.922790	+	0.385302i	$0.874097\pi$
$500$	−155.400	+	89.7203i	−0.310800	+	0.179441i
$501$		0			0
$502$	184.352	+	106.436i	0.367236	+	0.212024i
$503$			147.803i			0.293844i	0.989148	+	0.146922i	$0.0469366\pi$
$503$			147.803i			0.293844i	−0.989148	+	0.146922i	$0.953063\pi$
$504$		0			0
$505$	−4.76828			−0.00944215
$506$	67.9016	−	117.609i	0.134193	−	0.232429i
$507$		0			0
$508$	−118.295	−	204.893i	−0.232864	−	0.403333i
$509$	211.358	−	122.028i	0.415242	−	0.239740i	−0.277798	−	0.960640i	$-0.589604\pi$
$509$	211.358	−	122.028i	0.415242	−	0.239740i	0.693039	+	0.720900i	$0.256271\pi$
$510$		0			0
$511$	−7.60989	−	453.472i	−0.0148922	−	0.887420i
$512$	22.6274			0.0441942
$513$		0			0
$514$			144.195i			0.280536i
$515$	383.656	−	664.512i	0.744964	−	1.29032i
$516$		0			0
$517$	125.534	−	72.4771i	0.242813	−	0.140188i
$518$	−194.203	+	349.795i	−0.374909	+	0.675281i
$519$		0			0
$520$	114.650	−	198.580i	0.220481	−	0.381884i
$521$		−	147.106i		−	0.282354i	−0.989984	−	0.141177i	$-0.954911\pi$
$521$		−	147.106i		−	0.282354i	0.989984	−	0.141177i	$-0.0450886\pi$
$522$		0			0
$523$		−	62.8703i		−	0.120211i	−0.998192	−	0.0601055i	$-0.980856\pi$
$523$		−	62.8703i		−	0.120211i	0.998192	−	0.0601055i	$-0.0191437\pi$
$524$	222.029	+	128.188i	0.423719	+	0.244634i
$525$		0			0
$526$	79.7166	+	138.073i	0.151553	+	0.262497i
$527$	28.4231	+	49.2302i	0.0539337	+	0.0934159i
$528$		0			0
$529$	−773.216	+	1339.25i	−1.46166	+	2.53166i
$530$			714.001i			1.34717i
$531$		0			0
$532$	−84.1851	+	50.5064i	−0.158243	+	0.0949368i
$533$	316.448	−	548.103i	0.593710	−	1.02834i
$534$		0			0
$535$	443.049	−	255.795i	0.828129	−	0.478121i
$536$	12.2430	+	21.2055i	0.0228415	+	0.0395626i
$537$		0			0
$538$	82.8515	+	47.8343i	0.153999	+	0.0889114i
$539$	48.6121	−	91.1298i	0.0901895	−	0.169072i
$540$		0			0
$541$	9.15847			0.0169288			0.00846439	−	0.999964i	$-0.497306\pi$
$541$	9.15847			0.0169288			0.00846439	+	0.999964i	$0.497306\pi$
$542$	176.860	+	102.110i	0.326311	+	0.188395i
$543$		0			0
$544$	−46.2569	+	26.7064i	−0.0850311	+	0.0490927i
$545$	−1341.94	+	774.770i	−2.46228	+	1.42160i
$546$		0			0
$547$	394.904	−	683.994i	0.721945	−	1.25045i	−0.238274	−	0.971198i	$-0.576582\pi$
$547$	394.904	−	683.994i	0.721945	−	1.25045i	0.960219	−	0.279247i	$-0.0900849\pi$
$548$	443.914			0.810063
$549$		0			0
$550$	108.643			0.197533
$551$	120.635	+	69.6488i	0.218939	+	0.126404i
$552$		0			0
$553$	387.935	−	698.743i	0.701510	−	1.26355i
$554$	182.037	+	315.298i	0.328587	+	0.569129i
$555$		0			0
$556$	−413.515	−	238.743i	−0.743732	−	0.429394i
$557$	−676.050			−1.21373			−0.606867	−	0.794803i	$-0.707574\pi$
$557$	−676.050			−1.21373			−0.606867	+	0.794803i	$0.707574\pi$
$558$		0			0
$559$		−	710.812i		−	1.27158i
$560$	−3.68274	−	219.454i	−0.00657632	−	0.391882i
$561$		0			0
$562$	206.581	+	357.810i	0.367583	+	0.636672i
$563$	317.573	−	183.351i	0.564074	−	0.325668i	−0.190705	−	0.981647i	$-0.561077\pi$
$563$	317.573	−	183.351i	0.564074	−	0.325668i	0.754779	+	0.655979i	$0.227744\pi$
$564$		0			0
$565$	−341.976	−	197.440i	−0.605267	−	0.349451i
$566$		−	468.892i		−	0.828432i
$567$		0			0
$568$	−159.802			−0.281341
$569$	111.553	−	193.216i	0.196051	−	0.339570i	−0.751193	−	0.660082i	$-0.770521\pi$
$569$	111.553	−	193.216i	0.196051	−	0.339570i	0.947245	+	0.320512i	$0.103855\pi$
$570$		0			0
$571$	191.237	+	331.233i	0.334917	+	0.580093i	0.983469	−	0.181077i	$-0.0579585\pi$
$571$	191.237	+	331.233i	0.334917	+	0.580093i	−0.648552	+	0.761170i	$0.724625\pi$
$572$	−37.7585	+	21.7999i	−0.0660113	+	0.0381117i
$573$		0			0
$574$	−10.1648	−	605.718i	−0.0177087	−	1.05526i
$575$	−1660.36			−2.88758
$576$		0			0
$577$			591.373i			1.02491i	0.858714	+	0.512455i	$0.171264\pi$
$577$			591.373i			1.02491i	−0.858714	+	0.512455i	$0.828736\pi$
$578$	−141.312	+	244.760i	−0.244485	+	0.423460i
$579$		0			0
$580$	−269.702	+	155.713i	−0.465004	+	0.268470i
$581$	611.878	+	339.708i	1.05315	+	0.584696i
$582$		0			0
$583$	67.8810	−	117.573i	0.116434	−	0.201670i
$584$			183.256i			0.313795i
$585$		0			0
$586$		−	210.014i		−	0.358386i
$587$	309.364	+	178.611i	0.527025	+	0.304278i	0.739804	−	0.672822i	$-0.234918\pi$
$587$	309.364	+	178.611i	0.527025	+	0.304278i	−0.212779	+	0.977100i	$0.568251\pi$
$588$		0			0
$589$	−21.1089	−	36.5617i	−0.0358386	−	0.0620742i
$590$	−235.575	−	408.027i	−0.399279	−	0.691572i
$591$		0			0
$592$	80.8303	−	140.002i	0.136538	−	0.236490i
$593$		−	755.558i		−	1.27413i	−0.770811	−	0.637064i	$-0.780149\pi$
$593$		−	755.558i		−	1.27413i	0.770811	−	0.637064i	$-0.219851\pi$
$594$		0			0
$595$	266.543	+	444.279i	0.447971	+	0.746688i
$596$	−103.162	+	178.681i	−0.173090	+	0.299801i
$597$		0			0
$598$	577.049	−	333.160i	0.964965	−	0.557123i
$599$	−496.902	−	860.660i	−0.829553	−	1.43683i	−0.898389	−	0.439200i	$-0.855262\pi$
$599$	−496.902	−	860.660i	−0.829553	−	1.43683i	0.0688358	−	0.997628i	$-0.478072\pi$
$600$		0			0
$601$	−203.743	−	117.631i	−0.339006	−	0.195725i	0.320826	−	0.947138i	$-0.396039\pi$
$601$	−203.743	−	117.631i	−0.339006	−	0.195725i	−0.659832	+	0.751413i	$0.729373\pi$
$602$	−350.031	−	583.440i	−0.581448	−	0.969169i
$603$		0			0
$604$	402.685			0.666697
$605$	791.252	+	456.830i	1.30785	+	0.755090i
$606$		0			0
$607$	467.352	−	269.826i	0.769937	−	0.444523i	−0.0629152	−	0.998019i	$-0.520040\pi$
$607$	467.352	−	269.826i	0.769937	−	0.444523i	0.832852	+	0.553496i	$0.186706\pi$
$608$	34.3535	−	19.8340i	0.0565025	−	0.0326218i
$609$		0			0
$610$	−63.3289	+	109.689i	−0.103818	+	0.179818i
$611$	711.219			1.16402
$612$		0			0
$613$	−261.237			−0.426161			−0.213081	−	0.977035i	$-0.568350\pi$
$613$	−261.237			−0.426161			−0.213081	+	0.977035i	$0.568350\pi$
$614$	58.2877	+	33.6524i	0.0949311	+	0.0548085i
$615$		0			0
$616$	−20.2573	+	36.4872i	−0.0328853	+	0.0592325i
$617$	−333.055	−	576.868i	−0.539797	−	0.934956i	−0.998915	−	0.0465807i	$-0.985168\pi$
$617$	−333.055	−	576.868i	−0.539797	−	0.934956i	0.459117	−	0.888376i	$-0.348166\pi$
$618$		0			0
$619$	581.338	+	335.636i	0.939157	+	0.542223i	0.889696	−	0.456553i	$-0.150916\pi$
$619$	581.338	+	335.636i	0.939157	+	0.542223i	0.0494614	+	0.998776i	$0.484250\pi$
$620$	94.3856			0.152235
$621$		0			0
$622$			21.5331i			0.0346192i
$623$	10.6830	+	636.599i	0.0171477	+	1.02183i
$624$		0			0
$625$	103.925	+	180.004i	0.166280	+	0.288006i
$626$	−191.142	+	110.356i	−0.305339	+	0.176287i
$627$		0			0
$628$	163.067	+	94.1469i	0.259661	+	0.149915i
$629$			381.606i			0.606687i
$630$		0			0
$631$	252.355			0.399929			0.199965	−	0.979803i	$-0.435917\pi$
$631$	252.355			0.399929			0.199965	+	0.979803i	$0.435917\pi$
$632$	−161.465	+	279.665i	−0.255482	+	0.442508i
$633$		0			0
$634$	−210.418	−	364.455i	−0.331890	−	0.574850i
$635$	803.051	−	463.642i	1.26465	−	0.730145i
$636$		0			0
$637$	430.125	−	267.967i	0.675235	−	0.420670i
$638$	59.2153			0.0928139
$639$		0			0
$640$			88.6852i			0.138571i
$641$	−287.254	+	497.539i	−0.448135	+	0.776192i	−0.998265	−	0.0588868i	$-0.981245\pi$
$641$	−287.254	+	497.539i	−0.448135	+	0.776192i	0.550130	+	0.835079i	$0.314578\pi$
$642$		0			0
$643$	128.360	−	74.1086i	0.199626	−	0.115254i	−0.396855	−	0.917881i	$-0.629898\pi$
$643$	128.360	−	74.1086i	0.199626	−	0.115254i	0.596481	+	0.802627i	$0.296565\pi$
$644$	309.586	−	557.621i	0.480723	−	0.865871i
$645$		0			0
$646$	−46.8190	+	81.0929i	−0.0724752	+	0.125531i
$647$		−	904.316i		−	1.39771i	−0.715265	−	0.698853i	$-0.753694\pi$
$647$		−	904.316i		−	1.39771i	0.715265	−	0.698853i	$-0.246306\pi$
$648$		0			0
$649$			89.5856i			0.138036i
$650$	461.643	+	266.529i	0.710219	+	0.410045i
$651$		0			0
$652$	−9.85556	−	17.0703i	−0.0151159	−	0.0261815i
$653$	−43.6173	−	75.5473i	−0.0667952	−	0.115693i	0.830694	−	0.556730i	$-0.187944\pi$
$653$	−43.6173	−	75.5473i	−0.0667952	−	0.115693i	−0.897489	+	0.441037i	$0.854611\pi$
$654$		0			0
$655$	−502.417	+	870.212i	−0.767049	+	1.32857i
$656$			244.782i			0.373143i
$657$		0			0
$658$	583.774	−	350.232i	0.887194	−	0.532267i
$659$	225.512	−	390.598i	0.342203	−	0.592713i	−0.642639	−	0.766170i	$-0.722160\pi$
$659$	225.512	−	390.598i	0.342203	−	0.592713i	0.984842	+	0.173457i	$0.0554936\pi$
$660$		0			0
$661$	−227.522	+	131.360i	−0.344209	+	0.198729i	−0.662132	−	0.749388i	$-0.730348\pi$
$661$	−227.522	+	131.360i	−0.344209	+	0.198729i	0.317923	+	0.948117i	$0.397015\pi$
$662$	−214.803	−	372.050i	−0.324476	−	0.562008i
$663$		0			0
$664$	−244.898	−	141.392i	−0.368823	−	0.212940i
$665$	−197.953	−	329.952i	−0.297674	−	0.496169i
$666$		0			0
$667$	−904.965			−1.35677
$668$	−213.713	−	123.387i	−0.319929	−	0.184711i
$669$		0			0
$670$	−83.1123	+	47.9849i	−0.124048	+	0.0716193i
$671$	20.8566	−	12.0415i	0.0310828	−	0.0179457i
$672$		0			0
$673$	294.210	−	509.587i	0.437162	−	0.757187i	−0.560307	−	0.828285i	$-0.689317\pi$
$673$	294.210	−	509.587i	0.437162	−	0.757187i	0.997469	+	0.0710979i	$0.0226503\pi$
$674$	424.671			0.630075
$675$		0			0
$676$	124.078			0.183547
$677$	−923.740	−	533.321i	−1.36446	−	0.787772i	−0.374247	−	0.927329i	$-0.622099\pi$
$677$	−923.740	−	533.321i	−1.36446	−	0.787772i	−0.990214	+	0.139557i	$0.955432\pi$
$678$		0			0
$679$	−279.371	−	155.104i	−0.411445	−	0.228430i
$680$	−104.672	−	181.298i	−0.153930	−	0.266614i
$681$		0			0
$682$	−15.5423	−	8.97337i	−0.0227893	−	0.0131574i
$683$	91.4075			0.133832			0.0669162	−	0.997759i	$-0.478684\pi$
$683$	91.4075			0.133832			0.0669162	+	0.997759i	$0.478684\pi$
$684$		0			0
$685$			1739.86i			2.53995i
$686$	221.092	−	431.759i	0.322292	−	0.629387i
$687$		0			0
$688$	137.459	+	238.085i	0.199794	+	0.346054i
$689$	576.875	−	333.059i	0.837264	−	0.483394i
$690$		0			0
$691$	−17.8222	−	10.2897i	−0.0257920	−	0.0148910i	0.487049	−	0.873375i	$-0.338073\pi$
$691$	−17.8222	−	10.2897i	−0.0257920	−	0.0148910i	−0.512841	+	0.858484i	$0.671407\pi$
$692$		−	518.048i		−	0.748624i
$693$		0			0
$694$	55.4635			0.0799186
$695$	935.721	−	1620.72i	1.34636	−	2.33197i
$696$		0			0
$697$	−288.908	−	500.403i	−0.414502	−	0.717939i
$698$	−554.351	+	320.054i	−0.794199	+	0.458531i
$699$		0			0
$700$	510.169	−	8.56135i	0.728813	−	0.0122305i
$701$	509.822			0.727278			0.363639	−	0.931540i	$-0.381534\pi$
$701$	509.822			0.727278			0.363639	+	0.931540i	$0.381534\pi$
$702$		0			0
$703$		−	283.407i		−	0.403139i
$704$	8.43142	−	14.6037i	0.0119765	−	0.0207438i
$705$		0			0
$706$	−515.364	+	297.545i	−0.729977	+	0.421452i
$707$	3.72281	+	2.06687i	0.00526565	+	0.00292343i
$708$		0			0
$709$	596.846	−	1033.77i	0.841814	−	1.45806i	−0.0465457	−	0.998916i	$-0.514821\pi$
$709$	596.846	−	1033.77i	0.841814	−	1.45806i	0.888360	−	0.459148i	$-0.151845\pi$
$710$		−	626.322i		−	0.882144i
$711$		0			0
$712$		−	257.261i		−	0.361322i
$713$	237.528	+	137.137i	0.333139	+	0.192338i
$714$		0			0
$715$	−85.4417	−	147.989i	−0.119499	−	0.206978i
$716$	23.4639	+	40.6407i	0.0327708	+	0.0567607i
$717$		0			0
$718$	189.554	−	328.318i	0.264003	−	0.457267i
$719$			721.258i			1.00314i	0.865117	+	0.501571i	$0.167244\pi$
$719$			721.258i			1.00314i	−0.865117	+	0.501571i	$0.832756\pi$
$720$		0			0
$721$	−587.578	+	352.514i	−0.814949	+	0.488924i
$722$	−220.495	+	381.908i	−0.305394	+	0.528958i
$723$		0			0
$724$	300.743	−	173.634i	0.415391	−	0.239826i
$725$	−361.989	−	626.983i	−0.499295	−	0.864804i
$726$		0			0
$727$	−127.774	−	73.7701i	−0.175754	−	0.101472i	0.409542	−	0.912291i	$-0.365689\pi$
$727$	−127.774	−	73.7701i	−0.175754	−	0.101472i	−0.585296	+	0.810819i	$0.699022\pi$
$728$	−175.589	+	105.344i	−0.241194	+	0.144703i
$729$		0			0
$730$	−718.248			−0.983901
$731$	−562.009	−	324.476i	−0.768822	−	0.443880i
$732$		0			0
$733$	−597.569	+	345.006i	−0.815237	+	0.470677i	−0.848771	−	0.528760i	$-0.822657\pi$
$733$	−597.569	+	345.006i	−0.815237	+	0.470677i	0.0335343	+	0.999438i	$0.489324\pi$
$734$	34.1506	−	19.7168i	0.0465267	−	0.0268622i
$735$		0			0
$736$	−128.854	+	223.182i	−0.175074	+	0.303237i
$737$	18.2480			0.0247598
$738$		0			0
$739$	456.471			0.617687			0.308844	−	0.951113i	$-0.400058\pi$
$739$	456.471			0.617687			0.308844	+	0.951113i	$0.400058\pi$
$740$	548.720	+	316.804i	0.741513	+	0.428113i
$741$		0			0
$742$	309.492	−	557.452i	0.417105	−	0.751283i
$743$	−35.6377	−	61.7263i	−0.0479646	−	0.0830772i	0.841046	−	0.540963i	$-0.181940\pi$
$743$	−35.6377	−	61.7263i	−0.0479646	−	0.0830772i	−0.889011	+	0.457886i	$0.848607\pi$
$744$		0			0
$745$	−700.318	−	404.329i	−0.940024	−	0.542723i
$746$	−177.165			−0.237487
$747$		0			0
$748$			39.8054i			0.0532157i
$749$	−456.785	+	7.66550i	−0.609860	+	0.0102343i
$750$		0			0
$751$	678.540	+	1175.27i	0.903515	+	1.56493i	0.822898	+	0.568189i	$0.192356\pi$
$751$	678.540	+	1175.27i	0.903515	+	1.56493i	0.0806166	+	0.996745i	$0.474311\pi$
$752$	−238.221	+	137.537i	−0.316784	+	0.182895i
$753$		0			0
$754$	251.615	+	145.270i	0.333707	+	0.192666i
$755$			1578.27i			2.09042i
$756$		0			0
$757$	310.769			0.410527			0.205264	−	0.978707i	$-0.434195\pi$
$757$	310.769			0.410527			0.205264	+	0.978707i	$0.434195\pi$
$758$	−39.7139	+	68.7865i	−0.0523930	+	0.0907473i
$759$		0			0
$760$	77.7369	+	134.644i	0.102285	+	0.177163i
$761$	−231.955	+	133.919i	−0.304803	+	0.175978i	−0.644599	−	0.764521i	$-0.722975\pi$
$761$	−231.955	+	133.919i	−0.304803	+	0.175978i	0.339795	+	0.940499i	$0.389642\pi$
$762$		0			0
$763$	1383.55	−	23.2178i	1.81330	−	0.0304297i
$764$	484.827			0.634590
$765$		0			0
$766$			803.329i			1.04873i
$767$	−219.776	+	380.664i	−0.286540	+	0.496302i
$768$		0			0
$769$	−1021.03	+	589.492i	−1.32774	+	0.766569i	−0.984949	−	0.172844i	$-0.944704\pi$
$769$	−1021.03	+	589.492i	−1.32774	+	0.766569i	−0.342788	+	0.939413i	$0.611371\pi$
$770$	−143.007	−	79.3959i	−0.185723	−	0.103112i
$771$		0			0
$772$	−248.645	+	430.667i	−0.322080	+	0.557858i
$773$		−	586.849i		−	0.759184i	−0.925154	−	0.379592i	$-0.876064\pi$
$773$		−	586.849i		−	0.759184i	0.925154	−	0.379592i	$-0.123936\pi$
$774$		0			0
$775$			219.420i			0.283123i
$776$	111.816	+	64.5568i	0.144092	+	0.0831917i
$777$		0			0
$778$	−207.214	−	358.905i	−0.266342	−	0.461317i
$779$	214.563	+	371.634i	0.275434	+	0.477065i
$780$		0			0
$781$	−59.5453	+	103.135i	−0.0762424	+	0.132056i
$782$		−	608.331i		−	0.777917i
$783$		0			0
$784$	−92.2494	+	172.934i	−0.117665	+	0.220579i
$785$	−368.996	+	639.120i	−0.470059	+	0.814166i
$786$		0			0
$787$	525.886	−	303.620i	0.668216	−	0.385795i	−0.127184	−	0.991879i	$-0.540594\pi$
$787$	525.886	−	303.620i	0.668216	−	0.385795i	0.795400	+	0.606084i	$0.207261\pi$
$788$	−6.15551	−	10.6617i	−0.00781156	−	0.0135300i
$789$		0			0
$790$	−1096.11	−	632.839i	−1.38748	−	0.801062i
$791$	181.413	+	302.383i	0.229347	+	0.382280i
$792$		0			0
$793$	118.164			0.149009
$794$	621.747	+	358.966i	0.783056	+	0.452098i
$795$		0			0
$796$	508.770	−	293.738i	0.639158	−	0.369018i
$797$	138.769	−	80.1182i	0.174114	−	0.100525i	−0.410410	−	0.911901i	$-0.634615\pi$
$797$	138.769	−	80.1182i	0.174114	−	0.100525i	0.584524	+	0.811376i	$0.301281\pi$
$798$		0			0
$799$	324.662	−	562.331i	0.406335	−	0.703793i
$800$	−206.168			−0.257710
$801$		0			0
$802$	196.486			0.244995
$803$	118.273	+	68.2848i	0.147289	+	0.0850371i
$804$		0			0
$805$	2185.52	+	1213.38i	2.71493	+	1.50730i
$806$	−44.0279	−	76.2586i	−0.0546252	−	0.0946136i
$807$		0			0
$808$	−1.49002	−	0.860263i	−0.00184408	−	0.00106468i
$809$	806.158			0.996487			0.498244	−	0.867037i	$-0.333978\pi$
$809$	806.158			0.996487			0.498244	+	0.867037i	$0.333978\pi$
$810$		0			0
$811$			19.2228i			0.0237026i	0.999930	+	0.0118513i	$0.00377248\pi$
$811$			19.2228i			0.0237026i	−0.999930	+	0.0118513i	$0.996228\pi$
$812$	278.064	−	4.66630i	0.342443	−	0.00574668i
$813$		0			0
$814$	−60.2379	−	104.335i	−0.0740023	−	0.128176i
$815$	66.9049	−	38.6276i	0.0820919	−	0.0473958i
$816$		0			0
$817$	417.387	+	240.978i	0.510877	+	0.294955i
$818$			679.408i			0.830572i
$819$		0			0
$820$	−959.389			−1.16999
$821$	−712.768	+	1234.55i	−0.868171	+	1.50372i	−0.00430682	+	0.999991i	$0.501371\pi$
$821$	−712.768	+	1234.55i	−0.868171	+	1.50372i	−0.863864	+	0.503725i	$0.831962\pi$
$822$		0			0
$823$	−307.257	−	532.185i	−0.373338	−	0.646641i	0.616739	−	0.787168i	$-0.288454\pi$
$823$	−307.257	−	532.185i	−0.373338	−	0.646641i	−0.990077	+	0.140527i	$0.955120\pi$
$824$	239.774	−	138.434i	0.290988	−	0.168002i
$825$		0			0
$826$	7.05956	+	420.678i	0.00854668	+	0.509295i
$827$	681.029			0.823494			0.411747	−	0.911298i	$-0.364919\pi$
$827$	681.029			0.823494			0.411747	+	0.911298i	$0.364919\pi$
$828$		0			0
$829$		−	1137.71i		−	1.37239i	−0.727419	−	0.686194i	$-0.759280\pi$
$829$		−	1137.71i		−	1.37239i	0.727419	−	0.686194i	$-0.240720\pi$
$830$	554.167	−	959.846i	0.667671	−	1.15644i
$831$		0			0
$832$	71.6529	−	41.3688i	0.0861213	−	0.0497221i
$833$	−15.5240	−	462.405i	−0.0186362	−	0.555108i
$834$		0			0
$835$	483.599	−	837.618i	0.579160	−	1.00314i
$836$		−	29.5622i		−	0.0353615i
$837$		0			0
$838$			629.402i			0.751077i
$839$	−470.831	−	271.834i	−0.561181	−	0.323998i	0.192438	−	0.981309i	$-0.438360\pi$
$839$	−470.831	−	271.834i	−0.561181	−	0.323998i	−0.753619	+	0.657311i	$0.771694\pi$
$840$		0			0
$841$	223.201	+	386.595i	0.265399	+	0.459685i
$842$	−400.237	−	693.230i	−0.475341	−	0.823314i
$843$		0			0
$844$	74.1583	−	128.446i	0.0878653	−	0.152187i
$845$			486.306i			0.575510i
$846$		0			0
$847$	−419.748	−	699.644i	−0.495570	−	0.826027i
$848$	−128.815	+	223.115i	−0.151905	+	0.263107i
$849$		0			0
$850$	421.467	−	243.334i	0.495844	−	0.286275i
$851$	920.594	+	1594.52i	1.08178	+	1.87370i
$852$		0			0
$853$	−1448.28	−	836.167i	−1.69787	−	0.980266i	−0.947777	−	0.318935i	$-0.896675\pi$
$853$	−1448.28	−	836.167i	−1.69787	−	0.980266i	−0.750094	−	0.661331i	$-0.769992\pi$
$854$	96.9897	−	58.1884i	0.113571	−	0.0681363i
$855$		0			0
$856$	184.595			0.215649
$857$	−828.715	−	478.459i	−0.966996	−	0.558295i	−0.0686767	−	0.997639i	$-0.521878\pi$
$857$	−828.715	−	478.459i	−0.966996	−	0.558295i	−0.898319	+	0.439344i	$0.855211\pi$
$858$		0			0
$859$	1415.32	−	817.134i	1.64763	−	0.951262i	0.669624	−	0.742700i	$-0.266455\pi$
$859$	1415.32	−	817.134i	1.64763	−	0.951262i	0.978009	−	0.208561i	$-0.0668781\pi$
$860$	−933.144	+	538.751i	−1.08505	+	0.626454i
$861$		0			0
$862$	−335.610	+	581.293i	−0.389338	+	0.674354i
$863$	−1264.39			−1.46511			−0.732555	−	0.680708i	$-0.761672\pi$
$863$	−1264.39			−1.46511			−0.732555	+	0.680708i	$0.761672\pi$
$864$		0			0
$865$	2030.42			2.34731
$866$	−1.99629	−	1.15256i	−0.00230518	−	0.00133090i
$867$		0			0
$868$	−73.6911	−	40.9125i	−0.0848976	−	0.0471343i
$869$	120.330	+	208.417i	0.138469	+	0.239836i
$870$		0			0
$871$	77.5385	+	44.7669i	0.0890224	+	0.0513971i
$872$	−559.116			−0.641188
$873$		0			0
$874$			451.788i			0.516920i
$875$	10.5379	+	627.954i	0.0120434	+	0.717662i
$876$		0			0
$877$	−157.796	−	273.311i	−0.179927	−	0.311643i	0.761928	−	0.647661i	$-0.224253\pi$
$877$	−157.796	−	273.311i	−0.179927	−	0.311643i	−0.941855	+	0.336019i	$0.890919\pi$
$878$	765.957	−	442.225i	0.872388	−	0.503673i
$879$		0			0
$880$	57.2371	+	33.0458i	0.0650421	+	0.0375521i
$881$			1325.05i			1.50403i	0.659148	+	0.752013i	$0.270917\pi$
$881$			1325.05i			1.50403i	−0.659148	+	0.752013i	$0.729083\pi$
$882$		0			0
$883$	53.0789			0.0601120			0.0300560	−	0.999548i	$-0.490431\pi$
$883$	53.0789			0.0601120			0.0300560	+	0.999548i	$0.490431\pi$
$884$	−97.6527	+	169.139i	−0.110467	+	0.191334i
$885$		0			0
$886$	−210.577	−	364.731i	−0.237672	−	0.411660i
$887$	−569.288	+	328.679i	−0.641813	+	0.370551i	−0.785313	−	0.619099i	$-0.787498\pi$
$887$	−569.288	+	328.679i	−0.641813	+	0.370551i	0.143499	+	0.989650i	$0.454165\pi$
$888$		0			0
$889$	−827.949	+	13.8941i	−0.931326	+	0.0156290i
$890$	1008.30			1.13292
$891$		0			0
$892$		−	556.043i		−	0.623366i
$893$	−241.116	+	417.625i	−0.270007	+	0.467665i
$894$		0			0
$895$	−159.286	+	91.9636i	−0.177973	+	0.102753i
$896$	38.4416	−	69.2405i	0.0429036	−	0.0772773i
$897$		0			0
$898$	135.313	−	234.369i	0.150682	−	0.260990i
$899$			119.594i			0.133029i
$900$		0			0
$901$		−	608.147i		−	0.674969i
$902$	157.981	+	91.2104i	0.175145	+	0.101120i
$903$		0			0
$904$	−71.2416	−	123.394i	−0.0788071	−	0.136498i
$905$	680.536	+	1178.72i	0.751973	+	1.30246i
$906$		0			0
$907$	254.110	−	440.131i	0.280165	−	0.485260i	−0.691260	−	0.722606i	$-0.742944\pi$
$907$	254.110	−	440.131i	0.280165	−	0.485260i	0.971425	+	0.237346i	$0.0762774\pi$
$908$		−	202.068i		−	0.222542i
$909$		0			0
$910$	−412.880	−	688.198i	−0.453715	−	0.756261i
$911$	615.535	−	1066.14i	0.675670	−	1.17029i	−0.300603	−	0.953749i	$-0.597188\pi$
$911$	615.535	−	1066.14i	0.675670	−	1.17029i	0.976273	−	0.216545i	$-0.0694787\pi$
$912$		0			0
$913$	−182.508	+	105.371i	−0.199899	+	0.115412i
$914$	151.268	+	262.003i	0.165501	+	0.286656i
$915$		0			0
$916$	102.145	+	58.9737i	0.111513	+	0.0643818i
$917$	769.463	−	461.635i	0.839109	−	0.503419i
$918$		0			0
$919$	−953.211			−1.03723			−0.518613	−	0.855009i	$-0.673552\pi$
$919$	−953.211			−1.03723			−0.518613	+	0.855009i	$0.673552\pi$
$920$	−874.734	−	505.028i	−0.950797	−	0.548943i
$921$		0			0
$922$	−380.223	+	219.522i	−0.412390	+	0.238093i
$923$	−506.035	+	292.159i	−0.548250	+	0.316532i
$924$		0			0
$925$	−736.480	+	1275.62i	−0.796195	+	1.37905i
$926$	−236.917			−0.255850
$927$		0			0
$928$	−112.371			−0.121089
$929$	1161.63	+	670.670i	1.25041	+	0.721927i	0.971192	−	0.238300i	$-0.0765901\pi$
$929$	1161.63	+	670.670i	1.25041	+	0.721927i	0.279222	+	0.960227i	$0.409923\pi$
$930$		0			0
$931$	11.5292	+	343.414i	0.0123836	+	0.368865i
$932$	−179.497	−	310.898i	−0.192593	−	0.333582i
$933$		0			0
$934$	−385.924	−	222.813i	−0.413195	−	0.238558i
$935$	−156.012			−0.166858
$936$		0			0
$937$			1468.66i			1.56741i	0.621136	+	0.783703i	$0.286672\pi$
$937$			1468.66i			1.56741i	−0.621136	+	0.783703i	$0.713328\pi$
$938$	85.6891	−	1.43798i	0.0913530	−	0.00153303i
$939$		0			0
$940$	−539.059	−	933.677i	−0.573467	−	0.993274i
$941$	−466.720	+	269.461i	−0.495983	+	0.286356i	−0.727053	−	0.686581i	$-0.759111\pi$
$941$	−466.720	+	269.461i	−0.495983	+	0.286356i	0.231070	+	0.972937i	$0.425777\pi$
$942$		0			0
$943$	−2414.37	−	1393.94i	−2.56031	−	1.47819i
$944$		−	170.003i		−	0.180088i
$945$		0			0
$946$	204.879			0.216574
$947$	233.960	−	405.231i	0.247054	−	0.427910i	−0.715653	−	0.698456i	$-0.753871\pi$
$947$	233.960	−	405.231i	0.247054	−	0.427910i	0.962707	+	0.270546i	$0.0872041\pi$
$948$		0			0
$949$	335.040	+	580.306i	0.353045	+	0.611492i
$950$	−313.010	+	180.717i	−0.329485	+	0.190228i
$951$		0			0
$952$	3.13676	+	186.919i	0.00329491	+	0.196343i
$953$	−209.542			−0.219876			−0.109938	−	0.993938i	$-0.535065\pi$
$953$	−209.542			−0.219876			−0.109938	+	0.993938i	$0.535065\pi$
$954$		0			0
$955$			1900.22i			1.98975i
$956$	182.515	−	316.125i	0.190915	−	0.330675i
$957$		0			0
$958$	1100.44	−	635.340i	1.14869	−	0.663194i
$959$	754.164	−	1358.39i	0.786406	−	1.41646i
$960$		0			0
$961$	−462.377	+	800.860i	−0.481142	+	0.833362i
$962$		−	591.115i		−	0.614465i
$963$		0			0
$964$		−	11.3124i		−	0.0117349i
$965$	−1687.94	−	974.533i	−1.74916	−	1.00988i
$966$		0			0
$967$	−231.563	−	401.080i	−0.239466	−	0.414767i	0.721095	−	0.692836i	$-0.243639\pi$
$967$	−231.563	−	401.080i	−0.239466	−	0.414767i	−0.960561	+	0.278069i	$0.910306\pi$
$968$	164.836	+	285.505i	0.170286	+	0.294943i
$969$		0			0
$970$	−253.022	+	438.247i	−0.260847	+	0.451801i
$971$			20.0008i			0.0205981i	0.999947	+	0.0102991i	$0.00327835\pi$
$971$			20.0008i			0.0205981i	−0.999947	+	0.0102991i	$0.996722\pi$
$972$		0			0
$973$	−1433.08	+	859.767i	−1.47284	+	0.883625i
$974$	−232.238	+	402.249i	−0.238438	+	0.412986i
$975$		0			0
$976$	−39.5787	+	22.8508i	−0.0405520	+	0.0234127i
$977$	558.279	+	966.968i	0.571422	+	0.989732i	0.996420	+	0.0845376i	$0.0269413\pi$
$977$	558.279	+	966.968i	0.571422	+	0.989732i	−0.424998	+	0.905194i	$0.639725\pi$
$978$		0			0
$979$	−166.035	−	95.8606i	−0.169597	−	0.0979168i
$980$	−677.790	−	361.559i	−0.691623	−	0.368938i
$981$		0			0
$982$	−469.253			−0.477855
$983$	−595.403	−	343.756i	−0.605700	−	0.349701i	0.165581	−	0.986196i	$-0.447050\pi$
$983$	−595.403	−	343.756i	−0.605700	−	0.349701i	−0.771281	+	0.636495i	$0.780383\pi$
$984$		0			0
$985$	41.7869	−	24.1257i	0.0424233	−	0.0244931i
$986$	229.718	−	132.628i	0.232979	−	0.134511i
$987$		0			0
$988$	72.5236	−	125.614i	0.0734044	−	0.127140i
$989$	−3131.09			−3.16592
$990$		0			0
$991$	−470.055			−0.474324			−0.237162	−	0.971470i	$-0.576217\pi$
$991$	−470.055			−0.474324			−0.237162	+	0.971470i	$0.576217\pi$
$992$	29.4941	+	17.0284i	0.0297320	+	0.0171658i
$993$		0			0
$994$	−271.486	+	488.998i	−0.273125	+	0.491949i
$995$	1151.27	+	1994.06i	1.15705	+	2.00408i
$996$		0			0
$997$	1667.02	+	962.456i	1.67204	+	0.965353i	0.966494	+	0.256688i	$0.0826312\pi$
$997$	1667.02	+	962.456i	1.67204	+	0.965353i	0.705545	+	0.708665i	$0.250702\pi$
$998$	180.253			0.180614
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.3.o.a.181.8		32
3.2	odd	2		126.3.o.a.97.12	yes	32
7.6	odd	2	inner	378.3.o.a.181.1		32
9.2	odd	6		1134.3.c.e.811.1		16
9.4	even	3	inner	378.3.o.a.307.1		32
9.5	odd	6		126.3.o.a.13.13	yes	32
9.7	even	3		1134.3.c.d.811.16		16
21.20	even	2		126.3.o.a.97.13	yes	32
63.13	odd	6	inner	378.3.o.a.307.8		32
63.20	even	6		1134.3.c.e.811.8		16
63.34	odd	6		1134.3.c.d.811.9		16
63.41	even	6		126.3.o.a.13.12	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.o.a.13.12	✓	32	63.41	even	6
126.3.o.a.13.13	yes	32	9.5	odd	6
126.3.o.a.97.12	yes	32	3.2	odd	2
126.3.o.a.97.13	yes	32	21.20	even	2
378.3.o.a.181.1		32	7.6	odd	2	inner
378.3.o.a.181.8		32	1.1	even	1	trivial
378.3.o.a.307.1		32	9.4	even	3	inner
378.3.o.a.307.8		32	63.13	odd	6	inner
1134.3.c.d.811.9		16	63.34	odd	6
1134.3.c.d.811.16		16	9.7	even	3
1134.3.c.e.811.1		16	9.2	odd	6
1134.3.c.e.811.8		16	63.20	even	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(6.78854 - 3.91937i) q^{5} +(-6.99901 + 0.117453i) q^{7} +2.82843 q^{8} +11.0856i q^{10} +(1.05393 - 1.82546i) q^{11} +(8.95661 - 5.17110i) q^{13} +(4.80520 - 8.65506i) q^{14} +(-2.00000 + 3.46410i) q^{16} -9.44215i q^{17} +7.01239i q^{19} +(-13.5771 - 7.83874i) q^{20} +(1.49048 + 2.58159i) q^{22} +(-22.7785 - 39.4534i) q^{23} +(18.2229 - 31.5630i) q^{25} +14.6261i q^{26} +(7.20245 + 12.0052i) q^{28} +(9.93225 - 17.2032i) q^{29} +(-5.21387 + 3.01023i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(11.5642 + 6.67661i) q^{34} +(-47.0528 + 28.2290i) q^{35} -40.4151 q^{37} +(-8.58839 - 4.95851i) q^{38} +(19.2009 - 11.0856i) q^{40} +(52.9968 - 30.5977i) q^{41} +(34.3646 - 59.5213i) q^{43} -4.21571 q^{44} +64.4272 q^{46} +(59.5554 + 34.3843i) q^{47} +(48.9724 - 1.64411i) q^{49} +(25.7710 + 44.6368i) q^{50} +(-17.9132 - 10.3422i) q^{52} +64.4077 q^{53} -16.5229i q^{55} +(-19.7962 + 0.332208i) q^{56} +(14.0463 + 24.3290i) q^{58} +(-36.8068 + 21.2504i) q^{59} +(9.89468 + 5.71270i) q^{61} -8.51422i q^{62} +8.00000 q^{64} +(40.5349 - 70.2085i) q^{65} +(4.32856 + 7.49729i) q^{67} +(-16.3543 + 9.44215i) q^{68} +(-1.30205 - 77.5886i) q^{70} -56.4985 q^{71} +64.7908i q^{73} +(28.5778 - 49.4982i) q^{74} +(12.1458 - 7.01239i) q^{76} +(-7.16205 + 12.9002i) q^{77} +(-57.0864 + 98.8765i) q^{79} +31.3549i q^{80} +86.5433i q^{82} +(-86.5846 - 49.9896i) q^{83} +(-37.0073 - 64.0985i) q^{85} +(48.5989 + 84.1758i) q^{86} +(2.98096 - 5.16317i) q^{88} -90.9556i q^{89} +(-62.0801 + 37.2446i) q^{91} +(-45.5569 + 78.9069i) q^{92} +(-84.2240 + 48.6267i) q^{94} +(27.4841 + 47.6039i) q^{95} +(39.5328 + 22.8243i) q^{97} +(-32.6151 + 61.1413i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{4} - 2 q^{7} + 12 q^{11} + 12 q^{14} - 64 q^{16} - 12 q^{23} + 80 q^{25} + 8 q^{28} + 48 q^{29} - 348 q^{35} - 88 q^{37} + 32 q^{43} - 48 q^{44} + 48 q^{46} + 50 q^{49} - 48 q^{50} + 864 q^{53}+ \cdots - 624 q^{98}+O(q^{100}) \) 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

Fields

Representations

Groups

Database

Properties

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