LMFDB - Embedded newform 350.3.i.a.299.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [350,3,Mod(199,350)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(350, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("350.199"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	350.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$9.53680925261$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			299.2
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	350.299
Dual form			350.3.i.a.199.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22474 - 0.707107i) q^{2} +(-0.358719 - 0.621320i) q^{3} +(1.00000 + 1.73205i) q^{4} +1.01461i q^{6} +(-3.16693 + 6.24264i) q^{7} -2.82843i q^{8} +(4.24264 - 7.34847i) q^{9} +(2.37868 + 4.11999i) q^{11} +(0.717439 - 1.24264i) q^{12} -15.2913 q^{13} +(8.29289 - 5.40629i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-1.88064 - 3.25736i) q^{17} +(-10.3923 + 6.00000i) q^{18} +(-3.62132 - 2.09077i) q^{19} +(5.01472 - 0.271680i) q^{21} -6.72792i q^{22} +(-24.0131 - 13.8640i) q^{23} +(-1.75736 + 1.01461i) q^{24} +(18.7279 + 10.8126i) q^{26} -12.5446 q^{27} +(-13.9795 + 0.757359i) q^{28} -3.51472 q^{29} +(-42.3198 + 24.4334i) q^{31} +(4.89898 - 2.82843i) q^{32} +(1.70656 - 2.95584i) q^{33} +5.31925i q^{34} +16.9706 q^{36} +(2.54709 + 1.47056i) q^{37} +(2.95680 + 5.12132i) q^{38} +(5.48528 + 9.50079i) q^{39} +27.9590i q^{41} +(-6.33386 - 3.21320i) q^{42} +10.4853i q^{43} +(-4.75736 + 8.23999i) q^{44} +(19.6066 + 33.9596i) q^{46} +(-26.3395 + 45.6213i) q^{47} +2.86976 q^{48} +(-28.9411 - 39.5400i) q^{49} +(-1.34924 + 2.33696i) q^{51} +(-15.2913 - 26.4853i) q^{52} +(-48.4719 + 27.9853i) q^{53} +(15.3640 + 8.87039i) q^{54} +(17.6569 + 8.95743i) q^{56} +3.00000i q^{57} +(4.30463 + 2.48528i) q^{58} +(-33.5330 + 19.3603i) q^{59} +(-78.3823 - 45.2540i) q^{61} +69.1080 q^{62} +(32.4377 + 49.7574i) q^{63} -8.00000 q^{64} +(-4.18019 + 2.41344i) q^{66} +(-29.9988 + 17.3198i) q^{67} +(3.76127 - 6.51472i) q^{68} +19.8931i q^{69} +36.4264 q^{71} +(-20.7846 - 12.0000i) q^{72} +(-26.3034 - 45.5589i) q^{73} +(-2.07969 - 3.60213i) q^{74} -8.36308i q^{76} +(-33.2528 + 1.80152i) q^{77} -15.5147i q^{78} +(-16.8934 + 29.2602i) q^{79} +(-33.6838 - 58.3420i) q^{81} +(19.7700 - 34.2426i) q^{82} +127.577 q^{83} +(5.48528 + 8.41407i) q^{84} +(7.41421 - 12.8418i) q^{86} +(1.26080 + 2.18377i) q^{87} +(11.6531 - 6.72792i) q^{88} +(43.5883 + 25.1657i) q^{89} +(48.4264 - 95.4580i) q^{91} -55.4558i q^{92} +(30.3619 + 17.5294i) q^{93} +(64.5183 - 37.2497i) q^{94} +(-3.51472 - 2.02922i) q^{96} +101.792 q^{97} +(7.48650 + 68.8909i) q^{98} +40.3675 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} + 36 q^{11} + 72 q^{14} - 16 q^{16} - 12 q^{19} + 108 q^{21} - 48 q^{24} + 48 q^{26} - 96 q^{29} - 84 q^{31} - 24 q^{39} - 72 q^{44} + 72 q^{46} + 40 q^{49} + 108 q^{51} + 72 q^{54} + 96 q^{56}+ \cdots - 288 q^{99}+O(q^{100}) $ 8 * q + 8 * q^4 + 36 * q^11 + 72 * q^14 - 16 * q^16 - 12 * q^19 + 108 * q^21 - 48 * q^24 + 48 * q^26 - 96 * q^29 - 84 * q^31 - 24 * q^39 - 72 * q^44 + 72 * q^46 + 40 * q^49 + 108 * q^51 + 72 * q^54 + 96 * q^56 + 156 * q^59 - 84 * q^61 - 64 * q^64 - 288 * q^66 - 48 * q^71 - 192 * q^74 - 220 * q^79 + 36 * q^81 - 24 * q^84 + 48 * q^86 + 756 * q^89 + 48 * q^91 + 24 * q^94 - 96 * q^96 - 288 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$3$	−0.358719	−	0.621320i	−0.119573	−	0.207107i	0.800025	−	0.599966i	$-0.204819\pi$
$3$	−0.358719	−	0.621320i	−0.119573	−	0.207107i	−0.919599	+	0.392859i	$0.871486\pi$
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$			1.01461i			0.169102i
$7$	−3.16693	+	6.24264i	−0.452418	+	0.891806i
$7$	−3.16693	+	6.24264i	−0.452418	+	0.891806i
$8$		−	2.82843i		−	0.353553i
$9$	4.24264	−	7.34847i	0.471405	−	0.816497i
$10$		0			0
$11$	2.37868	+	4.11999i	0.216244	+	0.374545i	0.953657	−	0.300897i	$-0.0972861\pi$
$11$	2.37868	+	4.11999i	0.216244	+	0.374545i	−0.737413	+	0.675442i	$0.763953\pi$
$12$	0.717439	−	1.24264i	0.0597866	−	0.103553i
$13$	−15.2913			−1.17625			−0.588126	−	0.808769i	$-0.700134\pi$
$13$	−15.2913			−1.17625			−0.588126	+	0.808769i	$0.700134\pi$
$14$	8.29289	−	5.40629i	0.592350	−	0.386163i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−1.88064	−	3.25736i	−0.110626	−	0.191609i	0.805397	−	0.592736i	$-0.201952\pi$
$17$	−1.88064	−	3.25736i	−0.110626	−	0.191609i	−0.916023	+	0.401126i	$0.868619\pi$
$18$	−10.3923	+	6.00000i	−0.577350	+	0.333333i
$19$	−3.62132	−	2.09077i	−0.190596	−	0.110041i	0.401666	−	0.915786i	$-0.368431\pi$
$19$	−3.62132	−	2.09077i	−0.190596	−	0.110041i	−0.592261	+	0.805746i	$0.701765\pi$
$20$		0			0
$21$	5.01472	−	0.271680i	0.238796	−	0.0129371i
$22$		−	6.72792i		−	0.305815i
$23$	−24.0131	−	13.8640i	−1.04405	−	0.602781i	−0.123070	−	0.992398i	$-0.539274\pi$
$23$	−24.0131	−	13.8640i	−1.04405	−	0.602781i	−0.920977	+	0.389617i	$0.872607\pi$
$24$	−1.75736	+	1.01461i	−0.0732233	+	0.0422755i
$25$		0			0
$26$	18.7279	+	10.8126i	0.720305	+	0.415868i
$27$	−12.5446			−0.464616
$28$	−13.9795	+	0.757359i	−0.499268	+	0.0270485i
$29$	−3.51472			−0.121197			−0.0605986	−	0.998162i	$-0.519301\pi$
$29$	−3.51472			−0.121197			−0.0605986	+	0.998162i	$0.519301\pi$
$30$		0			0
$31$	−42.3198	+	24.4334i	−1.36516	+	0.788173i	−0.990305	−	0.138913i	$-0.955639\pi$
$31$	−42.3198	+	24.4334i	−1.36516	+	0.788173i	−0.374850	+	0.927085i	$0.622306\pi$
$32$	4.89898	−	2.82843i	0.153093	−	0.0883883i
$33$	1.70656	−	2.95584i	0.0517139	−	0.0895710i
$34$			5.31925i			0.156448i
$35$		0			0
$36$	16.9706			0.471405
$37$	2.54709	+	1.47056i	0.0688403	+	0.0397449i	0.534025	−	0.845469i	$-0.320679\pi$
$37$	2.54709	+	1.47056i	0.0688403	+	0.0397449i	−0.465185	+	0.885214i	$0.654012\pi$
$38$	2.95680	+	5.12132i	0.0778104	+	0.134772i
$39$	5.48528	+	9.50079i	0.140648	+	0.243610i
$40$		0			0
$41$			27.9590i			0.681927i	0.940077	+	0.340963i	$0.110753\pi$
$41$			27.9590i			0.681927i	−0.940077	+	0.340963i	$0.889247\pi$
$42$	−6.33386	−	3.21320i	−0.150806	−	0.0765048i
$43$			10.4853i			0.243844i	0.992540	+	0.121922i	$0.0389057\pi$
$43$			10.4853i			0.243844i	−0.992540	+	0.121922i	$0.961094\pi$
$44$	−4.75736	+	8.23999i	−0.108122	+	0.187272i
$45$		0			0
$46$	19.6066	+	33.9596i	0.426230	+	0.738253i
$47$	−26.3395	+	45.6213i	−0.560415	+	0.970666i	0.437046	+	0.899439i	$0.356025\pi$
$47$	−26.3395	+	45.6213i	−0.560415	+	0.970666i	−0.997460	+	0.0712271i	$0.977309\pi$
$48$	2.86976			0.0597866
$49$	−28.9411	−	39.5400i	−0.590635	−	0.806939i
$50$		0			0
$51$	−1.34924	+	2.33696i	−0.0264557	+	0.0458227i
$52$	−15.2913	−	26.4853i	−0.294063	−	0.509332i
$53$	−48.4719	+	27.9853i	−0.914565	+	0.528024i	−0.881897	−	0.471442i	$-0.843734\pi$
$53$	−48.4719	+	27.9853i	−0.914565	+	0.528024i	−0.0326677	+	0.999466i	$0.510400\pi$
$54$	15.3640	+	8.87039i	0.284518	+	0.164266i
$55$		0			0
$56$	17.6569	+	8.95743i	0.315301	+	0.159954i
$57$			3.00000i			0.0526316i
$58$	4.30463	+	2.48528i	0.0742178	+	0.0428497i
$59$	−33.5330	+	19.3603i	−0.568356	+	0.328141i	−0.756492	−	0.654002i	$-0.773089\pi$
$59$	−33.5330	+	19.3603i	−0.568356	+	0.328141i	0.188136	+	0.982143i	$0.439755\pi$
$60$		0			0
$61$	−78.3823	−	45.2540i	−1.28495	−	0.741869i	−0.307205	−	0.951643i	$-0.599394\pi$
$61$	−78.3823	−	45.2540i	−1.28495	−	0.741869i	−0.977750	+	0.209774i	$0.932727\pi$
$62$	69.1080			1.11464
$63$	32.4377	+	49.7574i	0.514884	+	0.789799i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	−4.18019	+	2.41344i	−0.0633363	+	0.0365672i
$67$	−29.9988	+	17.3198i	−0.447743	+	0.258505i	−0.706877	−	0.707337i	$-0.749896\pi$
$67$	−29.9988	+	17.3198i	−0.447743	+	0.258505i	0.259134	+	0.965842i	$0.416563\pi$
$68$	3.76127	−	6.51472i	0.0553129	−	0.0958047i
$69$			19.8931i			0.288306i
$70$		0			0
$71$	36.4264			0.513048			0.256524	−	0.966538i	$-0.417423\pi$
$71$	36.4264			0.513048			0.256524	+	0.966538i	$0.417423\pi$
$72$	−20.7846	−	12.0000i	−0.288675	−	0.166667i
$73$	−26.3034	−	45.5589i	−0.360321	−	0.624094i	0.627693	−	0.778461i	$-0.283999\pi$
$73$	−26.3034	−	45.5589i	−0.360321	−	0.624094i	−0.988014	+	0.154367i	$0.950666\pi$
$74$	−2.07969	−	3.60213i	−0.0281039	−	0.0486774i
$75$		0			0
$76$		−	8.36308i		−	0.110041i
$77$	−33.2528	+	1.80152i	−0.431854	+	0.0233963i
$78$		−	15.5147i		−	0.198907i
$79$	−16.8934	+	29.2602i	−0.213840	+	0.370383i	−0.952913	−	0.303243i	$-0.901931\pi$
$79$	−16.8934	+	29.2602i	−0.213840	+	0.370383i	0.739073	+	0.673626i	$0.235264\pi$
$80$		0			0
$81$	−33.6838	−	58.3420i	−0.415849	−	0.720272i
$82$	19.7700	−	34.2426i	0.241098	−	0.417593i
$83$	127.577			1.53708			0.768539	−	0.639803i	$-0.220984\pi$
$83$	127.577			1.53708			0.768539	+	0.639803i	$0.220984\pi$
$84$	5.48528	+	8.41407i	0.0653010	+	0.100167i
$85$		0			0
$86$	7.41421	−	12.8418i	0.0862118	−	0.149323i
$87$	1.26080	+	2.18377i	0.0144919	+	0.0251008i
$88$	11.6531	−	6.72792i	0.132422	−	0.0764537i
$89$	43.5883	+	25.1657i	0.489756	+	0.282761i	0.724473	−	0.689303i	$-0.242083\pi$
$89$	43.5883	+	25.1657i	0.489756	+	0.282761i	−0.234717	+	0.972064i	$0.575416\pi$
$90$		0			0
$91$	48.4264	−	95.4580i	0.532158	−	1.04899i
$92$		−	55.4558i		−	0.602781i
$93$	30.3619	+	17.5294i	0.326472	+	0.188489i
$94$	64.5183	−	37.2497i	0.686365	−	0.396273i
$95$		0			0
$96$	−3.51472	−	2.02922i	−0.0366117	−	0.0211377i
$97$	101.792			1.04940			0.524700	−	0.851287i	$-0.324177\pi$
$97$	101.792			1.04940			0.524700	+	0.851287i	$0.324177\pi$
$98$	7.48650	+	68.8909i	0.0763928	+	0.702968i
$99$	40.3675			0.407753
$100$		0			0
$101$	−51.6838	+	29.8396i	−0.511720	+	0.295442i	−0.733541	−	0.679646i	$-0.762134\pi$
$101$	−51.6838	+	29.8396i	−0.511720	+	0.295442i	0.221820	+	0.975088i	$0.428800\pi$
$102$	3.30496	−	1.90812i	0.0324015	−	0.0187070i
$103$	60.0890	−	104.077i	0.583388	−	1.01046i	−0.411686	−	0.911326i	$-0.635060\pi$
$103$	60.0890	−	104.077i	0.583388	−	1.01046i	0.995074	−	0.0991322i	$-0.0316067\pi$
$104$			43.2503i			0.415868i
$105$		0			0
$106$	79.1543			0.746739
$107$	98.3893	+	56.8051i	0.919526	+	0.530889i	0.883484	−	0.468462i	$-0.155192\pi$
$107$	98.3893	+	56.8051i	0.919526	+	0.530889i	0.0360423	+	0.999350i	$0.488525\pi$
$108$	−12.5446	−	21.7279i	−0.116154	−	0.201184i
$109$	−72.6543	−	125.841i	−0.666553	−	1.15450i	−0.978862	−	0.204524i	$-0.934435\pi$
$109$	−72.6543	−	125.841i	−0.666553	−	1.15450i	0.312308	−	0.949981i	$-0.398898\pi$
$110$		0			0
$111$		−	2.11008i		−	0.0190097i
$112$	−15.2913	−	23.4558i	−0.136529	−	0.209427i
$113$		−	34.5442i		−	0.305700i	−0.988249	−	0.152850i	$-0.951155\pi$
$113$		−	34.5442i		−	0.305700i	0.988249	−	0.152850i	$-0.0488452\pi$
$114$	2.12132	−	3.67423i	0.0186081	−	0.0322301i
$115$		0			0
$116$	−3.51472	−	6.08767i	−0.0302993	−	0.0524799i
$117$	−64.8754	+	112.368i	−0.554491	+	0.960406i
$118$	54.7592			0.464061
$119$	26.2904	−	1.42432i	0.220927	−	0.0119691i
$120$		0			0
$121$	49.1838	−	85.1888i	0.406477	−	0.704040i
$122$	63.9988	+	110.849i	0.524581	+	0.908600i
$123$	17.3715	−	10.0294i	0.141232	−	0.0815401i
$124$	−84.6396	−	48.8667i	−0.682578	−	0.394086i
$125$		0			0
$126$	−4.54416	−	83.8770i	−0.0360647	−	0.665690i
$127$		−	247.338i		−	1.94754i	−0.227526	−	0.973772i	$-0.573064\pi$
$127$		−	247.338i		−	1.94754i	0.227526	−	0.973772i	$-0.426936\pi$
$128$	9.79796	+	5.65685i	0.0765466	+	0.0441942i
$129$	6.51472	−	3.76127i	0.0505017	−	0.0291572i
$130$		0			0
$131$	−127.864	−	73.8223i	−0.976061	−	0.563529i	−0.0749822	−	0.997185i	$-0.523890\pi$
$131$	−127.864	−	73.8223i	−0.976061	−	0.563529i	−0.901079	+	0.433656i	$0.857223\pi$
$132$	6.82623			0.0517139
$133$	24.5204	−	15.9853i	0.184364	−	0.120190i
$134$	48.9878			0.365581
$135$		0			0
$136$	−9.21320	+	5.31925i	−0.0677441	+	0.0391121i
$137$	−28.2096	+	16.2868i	−0.205909	+	0.118882i	−0.599409	−	0.800443i	$-0.704598\pi$
$137$	−28.2096	+	16.2868i	−0.205909	+	0.118882i	0.393500	+	0.919325i	$0.371264\pi$
$138$	14.0665	−	24.3640i	0.101931	−	0.176550i
$139$			68.5857i			0.493422i	0.969089	+	0.246711i	$0.0793499\pi$
$139$			68.5857i			0.493422i	−0.969089	+	0.246711i	$0.920650\pi$
$140$		0			0
$141$	37.7939			0.268042
$142$	−44.6131	−	25.7574i	−0.314176	−	0.181390i
$143$	−36.3731	−	63.0000i	−0.254357	−	0.440559i
$144$	16.9706	+	29.3939i	0.117851	+	0.204124i
$145$		0			0
$146$			74.3973i			0.509571i
$147$	−14.1853	+	32.1655i	−0.0964984	+	0.218813i
$148$			5.88225i			0.0397449i
$149$	46.1985	−	80.0181i	0.310057	−	0.537034i	−0.668317	−	0.743876i	$-0.732985\pi$
$149$	46.1985	−	80.0181i	0.310057	−	0.537034i	0.978374	+	0.206842i	$0.0663185\pi$
$150$		0			0
$151$	45.8934	+	79.4897i	0.303930	+	0.526422i	0.977022	−	0.213136i	$-0.0683678\pi$
$151$	45.8934	+	79.4897i	0.303930	+	0.526422i	−0.673093	+	0.739558i	$0.735035\pi$
$152$	−5.91359	+	10.2426i	−0.0389052	+	0.0673858i
$153$	−31.9155			−0.208598
$154$	42.0000	+	21.3068i	0.272727	+	0.138356i
$155$		0			0
$156$	−10.9706	+	19.0016i	−0.0703241	+	0.121805i
$157$	4.22815	+	7.32338i	0.0269309	+	0.0466457i	0.879177	−	0.476496i	$-0.158093\pi$
$157$	4.22815	+	7.32338i	0.0269309	+	0.0466457i	−0.852246	+	0.523142i	$0.824760\pi$
$158$	41.3802	−	23.8909i	0.261900	−	0.151208i
$159$	34.7756	+	20.0777i	0.218715	+	0.126275i
$160$		0			0
$161$	162.595	−	105.999i	1.00991	−	0.658378i
$162$			95.2721i			0.588099i
$163$	192.238	+	110.989i	1.17938	+	0.680913i	0.955870	−	0.293789i	$-0.0949164\pi$
$163$	192.238	+	110.989i	1.17938	+	0.680913i	0.223506	+	0.974703i	$0.428250\pi$
$164$	−48.4264	+	27.9590i	−0.295283	+	0.170482i
$165$		0			0
$166$	−156.250	−	90.2109i	−0.941264	−	0.543439i
$167$	168.841			1.01102			0.505511	−	0.862820i	$-0.331304\pi$
$167$	168.841			1.01102			0.505511	+	0.862820i	$0.331304\pi$
$168$	−0.768426	−	14.1838i	−0.00457396	−	0.0844272i
$169$	64.8234			0.383570
$170$		0			0
$171$	−30.7279	+	17.7408i	−0.179695	+	0.103747i
$172$	−18.1610	+	10.4853i	−0.105587	+	0.0609609i
$173$	−82.1704	+	142.323i	−0.474974	+	0.822678i	−0.999589	−	0.0286608i	$-0.990876\pi$
$173$	−82.1704	+	142.323i	−0.474974	+	0.822678i	0.524616	+	0.851339i	$0.324209\pi$
$174$		−	3.56608i		−	0.0204947i
$175$		0			0
$176$	−19.0294			−0.108122
$177$	24.0579	+	13.8898i	0.135920	+	0.0784736i
$178$	−35.5897	−	61.6432i	−0.199942	−	0.346310i
$179$	92.5919	+	160.374i	0.517273	+	0.895943i	0.999799	+	0.0200614i	$0.00638618\pi$
$179$	92.5919	+	160.374i	0.517273	+	0.895943i	−0.482526	+	0.875882i	$0.660280\pi$
$180$		0			0
$181$			155.086i			0.856830i	0.903582	+	0.428415i	$0.140928\pi$
$181$			155.086i			0.856830i	−0.903582	+	0.428415i	$0.859072\pi$
$182$	−126.809	+	82.6690i	−0.696753	+	0.454226i
$183$			64.9340i			0.354831i
$184$	−39.2132	+	67.9193i	−0.213115	+	0.369126i
$185$		0			0
$186$	−24.7904	−	42.9382i	−0.133282	−	0.230850i
$187$	8.94687	−	15.4964i	0.0478442	−	0.0828686i
$188$	−105.358			−0.560415
$189$	39.7279	−	78.3116i	0.210201	−	0.414347i
$190$		0			0
$191$	−124.048	+	214.857i	−0.649465	+	1.12491i	0.333786	+	0.942649i	$0.391674\pi$
$191$	−124.048	+	214.857i	−0.649465	+	1.12491i	−0.983251	+	0.182257i	$0.941660\pi$
$192$	2.86976	+	4.97056i	0.0149466	+	0.0258883i
$193$	−133.661	+	77.1690i	−0.692543	+	0.399840i	−0.804564	−	0.593866i	$-0.797601\pi$
$193$	−133.661	+	77.1690i	−0.692543	+	0.399840i	0.112021	+	0.993706i	$0.464268\pi$
$194$	−124.669	−	71.9777i	−0.642624	−	0.371019i
$195$		0			0
$196$	39.5442	−	89.6675i	0.201756	−	0.457487i
$197$		−	181.103i		−	0.919303i	−0.888099	−	0.459651i	$-0.847974\pi$
$197$		−	181.103i		−	0.919303i	0.888099	−	0.459651i	$-0.152026\pi$
$198$	−49.4399	−	28.5442i	−0.249697	−	0.144162i
$199$	−301.989	+	174.353i	−1.51753	+	0.876147i	−0.517744	+	0.855535i	$0.673228\pi$
$199$	−301.989	+	174.353i	−1.51753	+	0.876147i	−0.999788	+	0.0206121i	$0.993439\pi$
$200$		0			0
$201$	21.5223	+	12.4259i	0.107076	+	0.0618204i
$202$	84.3992			0.417818
$203$	11.1309	−	21.9411i	0.0548318	−	0.108084i
$204$	−5.39697			−0.0264557
$205$		0			0
$206$	−147.187	+	84.9786i	−0.714502	+	0.412518i
$207$	−203.758	+	117.640i	−0.984337	+	0.568307i
$208$	30.5826	−	52.9706i	0.147032	−	0.254666i
$209$		−	19.8931i		−	0.0951823i
$210$		0			0
$211$	364.073			1.72547			0.862733	−	0.505660i	$-0.168751\pi$
$211$	364.073			1.72547			0.862733	+	0.505660i	$0.168751\pi$
$212$	−96.9439	−	55.9706i	−0.457282	−	0.264012i
$213$	−13.0669	−	22.6325i	−0.0613468	−	0.106256i
$214$	−80.3345	−	139.143i	−0.375395	−	0.650203i
$215$		0			0
$216$			35.4815i			0.164266i
$217$	−18.5048	−	341.566i	−0.0852757	−	1.57404i
$218$			205.497i			0.942649i
$219$	−18.8711	+	32.6857i	−0.0861694	+	0.149250i
$220$		0			0
$221$	28.7574	+	49.8092i	0.130124	+	0.225381i
$222$	−1.49205	+	2.58431i	−0.00672095	+	0.0116410i
$223$	−123.231			−0.552603			−0.276302	−	0.961071i	$-0.589109\pi$
$223$	−123.231			−0.552603			−0.276302	+	0.961071i	$0.589109\pi$
$224$	2.14214	+	39.5400i	0.00956311	+	0.176518i
$225$		0			0
$226$	−24.4264	+	42.3078i	−0.108081	+	0.187203i
$227$	−38.1878	−	66.1432i	−0.168228	−	0.291380i	0.769569	−	0.638564i	$-0.220471\pi$
$227$	−38.1878	−	66.1432i	−0.168228	−	0.291380i	−0.937797	+	0.347184i	$0.887138\pi$
$228$	−5.19615	+	3.00000i	−0.0227901	+	0.0131579i
$229$	−309.419	−	178.643i	−1.35117	−	0.780101i	−0.362760	−	0.931883i	$-0.618166\pi$
$229$	−309.419	−	178.643i	−1.35117	−	0.780101i	−0.988414	+	0.151782i	$0.951499\pi$
$230$		0			0
$231$	13.0477	+	20.0144i	0.0564837	+	0.0866423i
$232$			9.94113i			0.0428497i
$233$	−236.488	−	136.537i	−1.01497	−	0.585994i	−0.102328	−	0.994751i	$-0.532629\pi$
$233$	−236.488	−	136.537i	−1.01497	−	0.585994i	−0.912643	+	0.408757i	$0.865962\pi$
$234$	158.912	−	91.7477i	0.679110	−	0.392084i
$235$		0			0
$236$	−67.0660	−	38.7206i	−0.284178	−	0.164070i
$237$	24.2400			0.102278
$238$	−33.2061	−	16.8457i	−0.139522	−	0.0707801i
$239$	265.103			1.10922			0.554608	−	0.832112i	$-0.312868\pi$
$239$	265.103			1.10922			0.554608	+	0.832112i	$0.312868\pi$
$240$		0			0
$241$	−75.8970	+	43.8191i	−0.314925	+	0.181822i	−0.649128	−	0.760679i	$-0.724866\pi$
$241$	−75.8970	+	43.8191i	−0.314925	+	0.181822i	0.334203	+	0.942501i	$0.391533\pi$
$242$	−120.475	+	69.5563i	−0.497831	+	0.287423i
$243$	−80.6168	+	139.632i	−0.331757	+	0.574619i
$244$		−	181.016i		−	0.741869i
$245$		0			0
$246$	−28.3675			−0.115315
$247$	55.3746	+	31.9706i	0.224189	+	0.129435i
$248$	69.1080	+	119.698i	0.278661	+	0.482655i
$249$	−45.7645	−	79.2664i	−0.183793	−	0.318339i
$250$		0			0
$251$			495.655i			1.97472i	0.158491	+	0.987360i	$0.449337\pi$
$251$			495.655i			1.97472i	−0.158491	+	0.987360i	$0.550663\pi$
$252$	−53.7446	+	105.941i	−0.213272	+	0.420401i
$253$		−	131.912i		−	0.521390i
$254$	−174.894	+	302.926i	−0.688561	+	1.19262i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−200.268	+	346.875i	−0.779254	+	1.34971i	0.153119	+	0.988208i	$0.451068\pi$
$257$	−200.268	+	346.875i	−0.779254	+	1.34971i	−0.932372	+	0.361499i	$0.882265\pi$
$258$	−10.6385			−0.0412345
$259$	−17.2466	+	11.2434i	−0.0665894	+	0.0434108i
$260$		0			0
$261$	−14.9117	+	25.8278i	−0.0571329	+	0.0989571i
$262$	104.400	+	180.827i	0.398475	+	0.690179i
$263$	28.0118	−	16.1726i	0.106509	−	0.0614928i	−0.445799	−	0.895133i	$-0.647081\pi$
$263$	28.0118	−	16.1726i	0.106509	−	0.0614928i	0.552308	+	0.833640i	$0.313747\pi$
$264$	−8.36039	−	4.82687i	−0.0316681	−	0.0182836i
$265$		0			0
$266$	−41.3345	+	2.23936i	−0.155393	+	0.00841863i
$267$		−	36.1097i		−	0.135242i
$268$	−59.9976	−	34.6396i	−0.223872	−	0.129252i
$269$	265.838	−	153.482i	0.988246	−	0.570564i	0.0834963	−	0.996508i	$-0.473391\pi$
$269$	265.838	−	153.482i	0.988246	−	0.570564i	0.904749	+	0.425944i	$0.140058\pi$
$270$		0			0
$271$	−65.8051	−	37.9926i	−0.242823	−	0.140194i	0.373650	−	0.927570i	$-0.378106\pi$
$271$	−65.8051	−	37.9926i	−0.242823	−	0.140194i	−0.616474	+	0.787376i	$0.711439\pi$
$272$	15.0451			0.0553129
$273$	−76.6815	+	4.15433i	−0.280885	+	0.0152173i
$274$	46.0660			0.168124
$275$		0			0
$276$	−34.4558	+	19.8931i	−0.124840	+	0.0720764i
$277$	241.111	−	139.206i	0.870438	−	0.502547i	0.00294398	−	0.999996i	$-0.499063\pi$
$277$	241.111	−	139.206i	0.870438	−	0.502547i	0.867494	+	0.497448i	$0.165730\pi$
$278$	48.4974	−	84.0000i	0.174451	−	0.302158i
$279$			414.648i			1.48619i
$280$		0			0
$281$	394.690			1.40459			0.702296	−	0.711885i	$-0.252158\pi$
$281$	394.690			1.40459			0.702296	+	0.711885i	$0.252158\pi$
$282$	−46.2879	−	26.7244i	−0.164142	−	0.0947672i
$283$	−73.1981	−	126.783i	−0.258650	−	0.447996i	0.707230	−	0.706983i	$-0.249944\pi$
$283$	−73.1981	−	126.783i	−0.258650	−	0.447996i	−0.965881	+	0.258988i	$0.916611\pi$
$284$	36.4264	+	63.0924i	0.128262	+	0.222156i
$285$		0			0
$286$			102.879i			0.359715i
$287$	−174.538	−	88.5442i	−0.608146	−	0.308516i
$288$		−	48.0000i		−	0.166667i
$289$	137.426	−	238.030i	0.475524	−	0.823632i
$290$		0			0
$291$	−36.5147	−	63.2453i	−0.125480	−	0.217338i
$292$	52.6069	−	91.1177i	0.180160	−	0.312047i
$293$	−299.678			−1.02279			−0.511396	−	0.859345i	$-0.670872\pi$
$293$	−299.678			−1.02279			−0.511396	+	0.859345i	$0.670872\pi$
$294$	40.1177	−	29.3640i	0.136455	−	0.0998776i
$295$		0			0
$296$	4.15938	−	7.20426i	0.0140520	−	0.0243387i
$297$	−29.8396	−	51.6838i	−0.100470	−	0.174019i
$298$	−113.163	+	65.3345i	−0.379741	+	0.219243i
$299$	367.191	+	211.998i	1.22806	+	0.709023i
$300$		0			0
$301$	−65.4558	−	33.2061i	−0.217461	−	0.110319i
$302$		−	129.806i		−	0.429822i
$303$	37.0799	+	21.4081i	0.122376	+	0.0706539i
$304$	14.4853	−	8.36308i	0.0476490	−	0.0275101i
$305$		0			0
$306$	39.0883	+	22.5676i	0.127740	+	0.0737505i
$307$	−20.9886			−0.0683666			−0.0341833	−	0.999416i	$-0.510883\pi$
$307$	−20.9886			−0.0683666			−0.0341833	+	0.999416i	$0.510883\pi$
$308$	−36.3731	−	55.7939i	−0.118094	−	0.181149i
$309$	−86.2203			−0.279030
$310$		0			0
$311$	157.651	−	91.0197i	0.506916	−	0.292668i	−0.224649	−	0.974440i	$-0.572124\pi$
$311$	157.651	−	91.0197i	0.506916	−	0.292668i	0.731565	+	0.681772i	$0.238790\pi$
$312$	26.8723	−	15.5147i	0.0861291	−	0.0497267i
$313$	−48.9643	+	84.8087i	−0.156435	+	0.270954i	−0.933581	−	0.358367i	$-0.883334\pi$
$313$	−48.9643	+	84.8087i	−0.156435	+	0.270954i	0.777145	+	0.629321i	$0.216667\pi$
$314$		−	11.9590i		−	0.0380861i
$315$		0			0
$316$	−67.5736			−0.213840
$317$	417.399	+	240.985i	1.31672	+	0.760206i	0.983199	−	0.182538i	$-0.0584314\pi$
$317$	417.399	+	240.985i	1.31672	+	0.760206i	0.333517	+	0.942744i	$0.391765\pi$
$318$	−28.3942	−	49.1802i	−0.0892899	−	0.154655i
$319$	−8.36039	−	14.4806i	−0.0262081	−	0.0453938i
$320$		0			0
$321$		−	81.5084i		−	0.253920i
$322$	−274.090	+	14.8492i	−0.851213	+	0.0461157i
$323$			15.7279i			0.0486933i
$324$	67.3675	−	116.684i	0.207924	−	0.360136i
$325$		0			0
$326$	−156.962	−	271.866i	−0.481478	−	0.833945i
$327$	−52.1250	+	90.2832i	−0.159404	+	0.276095i
$328$	79.0800			0.241098
$329$	−201.382	−	308.907i	−0.612104	−	0.938928i
$330$		0			0
$331$	−112.504	+	194.862i	−0.339890	+	0.588707i	−0.984412	−	0.175879i	$-0.943723\pi$
$331$	−112.504	+	194.862i	−0.339890	+	0.588707i	0.644522	+	0.764586i	$0.277056\pi$
$332$	127.577	+	220.971i	0.384269	+	0.665574i
$333$	21.6128	−	12.4781i	0.0649032	−	0.0374719i
$334$	−206.787	−	119.388i	−0.619122	−	0.357450i
$335$		0			0
$336$	−9.08831	+	17.9149i	−0.0270485	+	0.0533180i
$337$		−	264.368i		−	0.784473i	−0.919864	−	0.392237i	$-0.871701\pi$
$337$		−	264.368i		−	0.784473i	0.919864	−	0.392237i	$-0.128299\pi$
$338$	−79.3921	−	45.8370i	−0.234888	−	0.135613i
$339$	−21.4630	+	12.3917i	−0.0633126	+	0.0365536i
$340$		0			0
$341$	−201.331	−	116.238i	−0.590412	−	0.340875i
$342$	50.1785			0.146721
$343$	338.488	−	55.4487i	0.986847	−	0.161658i
$344$	29.6569			0.0862118
$345$		0			0
$346$	201.276	−	116.207i	0.581722	−	0.335857i
$347$	−165.633	+	95.6285i	−0.477330	+	0.275586i	−0.719303	−	0.694697i	$-0.755539\pi$
$347$	−165.633	+	95.6285i	−0.477330	+	0.275586i	0.241973	+	0.970283i	$0.422205\pi$
$348$	−2.52160	+	4.36753i	−0.00724597	+	0.0125504i
$349$			135.448i			0.388104i	0.980991	+	0.194052i	$0.0621630\pi$
$349$			135.448i			0.388104i	−0.980991	+	0.194052i	$0.937837\pi$
$350$		0			0
$351$	191.823			0.546505
$352$	23.3062	+	13.4558i	0.0662108	+	0.0382268i
$353$	174.245	+	301.802i	0.493612	+	0.854962i	0.999973	−	0.00736010i	$-0.00234281\pi$
$353$	174.245	+	301.802i	0.493612	+	0.854962i	−0.506360	+	0.862322i	$0.669009\pi$
$354$	−19.6432	−	34.0230i	−0.0554892	−	0.0961101i
$355$		0			0
$356$			100.663i			0.282761i
$357$	−10.3158	−	15.8238i	−0.0288959	−	0.0443244i
$358$		−	261.889i		−	0.731535i
$359$	152.415	−	263.991i	0.424555	−	0.735351i	−0.571824	−	0.820377i	$-0.693764\pi$
$359$	152.415	−	263.991i	0.424555	−	0.735351i	0.996379	+	0.0850256i	$0.0270972\pi$
$360$		0			0
$361$	−171.757	−	297.492i	−0.475782	−	0.824079i
$362$	109.663	−	189.941i	0.302935	−	0.524699i
$363$	−70.5727			−0.194415
$364$	213.765	−	11.5810i	0.587265	−	0.0318159i
$365$		0			0
$366$	45.9153	−	79.5276i	0.125452	−	0.217288i
$367$	−47.5021	−	82.2761i	−0.129434	−	0.224186i	0.794024	−	0.607887i	$-0.207983\pi$
$367$	−47.5021	−	82.2761i	−0.129434	−	0.224186i	−0.923457	+	0.383701i	$0.874649\pi$
$368$	96.0523	−	55.4558i	0.261012	−	0.150695i
$369$	205.456	+	118.620i	0.556791	+	0.321463i
$370$		0			0
$371$	−21.1949	−	391.220i	−0.0571291	−	1.05450i
$372$			70.1177i			0.188489i
$373$	219.588	+	126.779i	0.588708	+	0.339891i	0.764586	−	0.644521i	$-0.222943\pi$
$373$	219.588	+	126.779i	0.588708	+	0.339891i	−0.175879	+	0.984412i	$0.556277\pi$
$374$	−21.9153	+	12.6528i	−0.0585970	+	0.0338310i
$375$		0			0
$376$	129.037	+	74.4993i	0.343182	+	0.198136i
$377$	53.7446			0.142559
$378$	−104.031	+	67.8198i	−0.275215	+	0.179417i
$379$	−508.250			−1.34103			−0.670514	−	0.741897i	$-0.733926\pi$
$379$	−508.250			−1.34103			−0.670514	+	0.741897i	$0.733926\pi$
$380$		0			0
$381$	−153.676	+	88.7250i	−0.403350	+	0.232874i
$382$	303.854	−	175.430i	0.795428	−	0.459241i
$383$	238.881	−	413.753i	0.623709	−	1.08030i	−0.365080	−	0.930976i	$-0.618958\pi$
$383$	238.881	−	413.753i	0.623709	−	1.08030i	0.988789	−	0.149320i	$-0.0477084\pi$
$384$		−	8.11689i		−	0.0211377i
$385$		0			0
$386$	218.267			0.565459
$387$	77.0508	+	44.4853i	0.199098	+	0.114949i
$388$	101.792	+	176.309i	0.262350	+	0.454404i
$389$	85.1102	+	147.415i	0.218792	+	0.378959i	0.954439	−	0.298406i	$-0.0964550\pi$
$389$	85.1102	+	147.415i	0.218792	+	0.378959i	−0.735647	+	0.677365i	$0.763122\pi$
$390$		0			0
$391$			104.292i			0.266732i
$392$	−111.836	+	81.8579i	−0.285296	+	0.208821i
$393$			105.926i			0.269532i
$394$	−128.059	+	221.804i	−0.325023	+	0.562956i
$395$		0			0
$396$	40.3675	+	69.9186i	0.101938	+	0.176562i
$397$	−122.275	+	211.786i	−0.307997	+	0.533467i	−0.977924	−	0.208960i	$-0.932992\pi$
$397$	−122.275	+	211.786i	−0.307997	+	0.533467i	0.669927	+	0.742427i	$0.266325\pi$
$398$	493.146			1.23906
$399$	−18.7279	−	9.50079i	−0.0469371	−	0.0238115i
$400$		0			0
$401$	208.786	−	361.629i	0.520664	−	0.901817i	−0.479047	−	0.877789i	$-0.659018\pi$
$401$	208.786	−	361.629i	0.520664	−	0.901817i	0.999711	−	0.0240277i	$-0.00764899\pi$
$402$	−17.5729	−	30.4371i	−0.0437136	−	0.0757142i
$403$	647.124	−	373.617i	1.60577	−	0.927090i
$404$	−103.368	−	59.6793i	−0.255860	−	0.147721i
$405$		0			0
$406$	−29.1472	+	19.0016i	−0.0717911	+	0.0468019i
$407$			13.9920i			0.0343784i
$408$	6.60991	+	3.81623i	0.0162008	+	0.00935351i
$409$	−266.919	+	154.106i	−0.652614	+	0.376787i	−0.789457	−	0.613806i	$-0.789638\pi$
$409$	−266.919	+	154.106i	−0.652614	+	0.376787i	0.136843	+	0.990593i	$0.456304\pi$
$410$		0			0
$411$	20.2386	+	11.6848i	0.0492424	+	0.0284301i
$412$	240.356			0.583388
$413$	−14.6627	−	270.647i	−0.0355029	−	0.655320i
$414$	332.735			0.803708
$415$		0			0
$416$	−74.9117	+	43.2503i	−0.180076	+	0.103967i
$417$	42.6137	−	24.6030i	0.102191	−	0.0590001i
$418$	−14.0665	+	24.3640i	−0.0336520	+	0.0582870i
$419$		−	103.142i		−	0.246163i	−0.992397	−	0.123081i	$-0.960722\pi$
$419$		−	103.142i		−	0.246163i	0.992397	−	0.123081i	$-0.0392776\pi$
$420$		0			0
$421$	−165.220			−0.392447			−0.196224	−	0.980559i	$-0.562868\pi$
$421$	−165.220			−0.392447			−0.196224	+	0.980559i	$0.562868\pi$
$422$	−445.897	−	257.439i	−1.05663	−	0.610044i
$423$	223.498	+	387.110i	0.528364	+	0.915153i
$424$	79.1543	+	137.099i	0.186685	+	0.323347i
$425$		0			0
$426$			36.9587i			0.0867574i
$427$	530.736	−	345.996i	1.24294	−	0.810295i
$428$			227.220i			0.530889i
$429$	−26.0955	+	45.1987i	−0.0608286	+	0.105358i
$430$		0			0
$431$	−297.268	−	514.883i	−0.689717	−	1.19463i	−0.971929	−	0.235273i	$-0.924402\pi$
$431$	−297.268	−	514.883i	−0.689717	−	1.19463i	0.282212	−	0.959352i	$-0.408932\pi$
$432$	25.0892	−	43.4558i	0.0580770	−	0.100592i
$433$	40.6267			0.0938261			0.0469131	−	0.998899i	$-0.485062\pi$
$433$	40.6267			0.0938261			0.0469131	+	0.998899i	$0.485062\pi$
$434$	−218.860	+	431.416i	−0.504286	+	0.994046i
$435$		0			0
$436$	145.309	−	251.682i	0.333277	−	0.577252i
$437$	57.9727	+	100.412i	0.132661	+	0.229775i
$438$	46.2246	−	26.6878i	0.105536	−	0.0609310i
$439$	−126.959	−	73.3001i	−0.289201	−	0.166971i	0.348380	−	0.937353i	$-0.386732\pi$
$439$	−126.959	−	73.3001i	−0.289201	−	0.166971i	−0.637582	+	0.770383i	$0.720065\pi$
$440$		0			0
$441$	−413.345	+	44.9190i	−0.937291	+	0.101857i
$442$		−	81.3381i		−	0.184023i
$443$	92.9768	+	53.6802i	0.209880	+	0.121174i	0.601256	−	0.799057i	$-0.294667\pi$
$443$	92.9768	+	53.6802i	0.209880	+	0.121174i	−0.391376	+	0.920231i	$0.628001\pi$
$444$	3.65476	−	2.11008i	0.00823145	−	0.00475243i
$445$		0			0
$446$	150.926	+	87.1372i	0.338399	+	0.195375i
$447$	−66.2892			−0.148298
$448$	25.3354	−	49.9411i	0.0565523	−	0.111476i
$449$	−135.161			−0.301028			−0.150514	−	0.988608i	$-0.548093\pi$
$449$	−135.161			−0.301028			−0.150514	+	0.988608i	$0.548093\pi$
$450$		0			0
$451$	−115.191	+	66.5055i	−0.255412	+	0.147462i
$452$	59.8322	−	34.5442i	0.132372	−	0.0764251i
$453$	32.9257	−	57.0290i	0.0726837	−	0.125892i
$454$			108.011i			0.237910i
$455$		0			0
$456$	8.48528			0.0186081
$457$	−138.335	−	79.8675i	−0.302702	−	0.174765i	0.340954	−	0.940080i	$-0.389250\pi$
$457$	−138.335	−	79.8675i	−0.302702	−	0.174765i	−0.643656	+	0.765315i	$0.722583\pi$
$458$	252.639	+	437.584i	0.551614	+	0.955424i
$459$	23.5919	+	40.8623i	0.0513984	+	0.0890247i
$460$		0			0
$461$		−	310.250i		−	0.672993i	−0.941685	−	0.336497i	$-0.890758\pi$
$461$		−	310.250i		−	0.672993i	0.941685	−	0.336497i	$-0.109242\pi$
$462$	−1.82784	−	33.7386i	−0.00395636	−	0.0730274i
$463$			326.014i			0.704135i	0.935975	+	0.352067i	$0.114521\pi$
$463$			326.014i			0.704135i	−0.935975	+	0.352067i	$0.885479\pi$
$464$	7.02944	−	12.1753i	0.0151496	−	0.0262400i
$465$		0			0
$466$	193.092	+	334.445i	0.414360	+	0.717693i
$467$	−297.779	+	515.769i	−0.637643	+	1.10443i	0.348306	+	0.937381i	$0.386757\pi$
$467$	−297.779	+	515.769i	−0.637643	+	1.10443i	−0.985949	+	0.167048i	$0.946576\pi$
$468$	−259.502			−0.554491
$469$	−13.1173	−	242.122i	−0.0279687	−	0.516252i
$470$		0			0
$471$	3.03344	−	5.25408i	0.00644043	−	0.0111551i
$472$	54.7592	+	94.8457i	0.116015	+	0.200944i
$473$	−43.1993	+	24.9411i	−0.0913304	+	0.0527297i
$474$	−29.6878	−	17.1402i	−0.0626324	−	0.0361608i
$475$		0			0
$476$	28.7574	+	44.1119i	0.0604146	+	0.0926721i
$477$			474.926i			0.995652i
$478$	−324.683	−	187.456i	−0.679253	−	0.392167i
$479$	−438.798	+	253.340i	−0.916071	+	0.528894i	−0.882379	−	0.470539i	$-0.844060\pi$
$479$	−438.798	+	253.340i	−0.916071	+	0.528894i	−0.0336914	+	0.999432i	$0.510726\pi$
$480$		0			0
$481$	−38.9483	−	22.4868i	−0.0809735	−	0.0467501i
$482$	123.939			0.257135
$483$	−124.185	−	63.0000i	−0.257113	−	0.130435i
$484$	196.735			0.406477
$485$		0			0
$486$	197.470	−	114.009i	0.406317	−	0.234587i
$487$	182.992	−	105.651i	0.375755	−	0.216942i	−0.300215	−	0.953872i	$-0.597058\pi$
$487$	182.992	−	105.651i	0.375755	−	0.216942i	0.675970	+	0.736930i	$0.263725\pi$
$488$	−127.998	+	221.698i	−0.262290	+	0.454300i
$489$		−	159.255i		−	0.325676i
$490$		0			0
$491$	−784.161			−1.59707			−0.798534	−	0.601949i	$-0.794391\pi$
$491$	−784.161			−1.59707			−0.798534	+	0.601949i	$0.794391\pi$
$492$	34.7430	+	20.0589i	0.0706158	+	0.0407701i
$493$	6.60991	+	11.4487i	0.0134075	+	0.0232225i
$494$	−45.2132	−	78.3116i	−0.0915247	−	0.158525i
$495$		0			0
$496$		−	195.467i		−	0.394086i
$497$	−115.360	+	227.397i	−0.232112	+	0.457539i
$498$			129.442i			0.259923i
$499$	−85.7462	+	148.517i	−0.171836	+	0.297629i	−0.939062	−	0.343748i	$-0.888303\pi$
$499$	−85.7462	+	148.517i	−0.171836	+	0.297629i	0.767226	+	0.641377i	$0.221637\pi$
$500$		0			0
$501$	−60.5665	−	104.904i	−0.120891	−	0.209390i
$502$	350.481	−	607.051i	0.698169	−	1.20926i
$503$	20.0883			0.0399370			0.0199685	−	0.999801i	$-0.493643\pi$
$503$	20.0883			0.0399370			0.0199685	+	0.999801i	$0.493643\pi$
$504$	140.735	−	91.7477i	0.279236	−	0.182039i
$505$		0			0
$506$	−93.2756	+	161.558i	−0.184339	+	0.319285i
$507$	−23.2534	−	40.2761i	−0.0458647	−	0.0794400i
$508$	428.402	−	247.338i	0.843311	−	0.486886i
$509$	412.890	+	238.382i	0.811178	+	0.468334i	0.847365	−	0.531011i	$-0.178188\pi$
$509$	412.890	+	238.382i	0.811178	+	0.468334i	−0.0361865	+	0.999345i	$0.511521\pi$
$510$		0			0
$511$	367.709	−	19.9211i	0.719587	−	0.0389846i
$512$			22.6274i			0.0441942i
$513$	45.4281	+	26.2279i	0.0885538	+	0.0511266i
$514$	490.555	−	283.222i	0.954387	−	0.551016i
$515$		0			0
$516$	13.0294	+	7.52255i	0.0252508	+	0.0145786i
$517$	−250.613			−0.484744
$518$	29.0730	−	1.57507i	0.0561255	−	0.00304068i
$519$	117.905			0.227176
$520$		0			0
$521$	739.823	−	427.137i	1.42001	−	0.819841i	0.423707	−	0.905799i	$-0.360729\pi$
$521$	739.823	−	427.137i	1.42001	−	0.819841i	0.996299	+	0.0859587i	$0.0273953\pi$
$522$	36.5260	−	21.0883i	0.0699732	−	0.0403991i
$523$	−296.501	+	513.554i	−0.566923	+	0.981940i	0.429945	+	0.902855i	$0.358533\pi$
$523$	−296.501	+	513.554i	−0.566923	+	0.981940i	−0.996868	+	0.0790845i	$0.974800\pi$
$524$		−	295.289i		−	0.563529i
$525$		0			0
$526$	−45.7431			−0.0869640
$527$	159.176	+	91.9005i	0.302043	+	0.174384i
$528$	6.82623	+	11.8234i	0.0129285	+	0.0223928i
$529$	119.919	+	207.706i	0.226690	+	0.392638i
$530$		0			0
$531$			328.555i			0.618748i
$532$	52.2077	+	26.4853i	0.0981348	+	0.0497844i
$533$		−	427.529i		−	0.802118i
$534$	−25.5334	+	44.2252i	−0.0478154	+	0.0828188i
$535$		0			0
$536$	48.9878	+	84.8494i	0.0913952	+	0.158301i
$537$	66.4290	−	115.058i	0.123704	−	0.214262i
$538$	−434.112			−0.806899
$539$	94.0629	−	213.290i	0.174514	−	0.395715i
$540$		0			0
$541$	−427.595	+	740.617i	−0.790380	+	1.36898i	0.135352	+	0.990798i	$0.456783\pi$
$541$	−427.595	+	740.617i	−0.790380	+	1.36898i	−0.925732	+	0.378180i	$0.876550\pi$
$542$	53.7296	+	93.0624i	0.0991322	+	0.171702i
$543$	96.3583	−	55.6325i	0.177455	−	0.102454i
$544$	−18.4264	−	10.6385i	−0.0338721	−	0.0195560i
$545$		0			0
$546$	96.8528	+	49.1340i	0.177386	+	0.0899890i
$547$			415.897i			0.760323i	0.924920	+	0.380161i	$0.124132\pi$
$547$			415.897i			0.760323i	−0.924920	+	0.380161i	$0.875868\pi$
$548$	−56.4191	−	32.5736i	−0.102955	−	0.0594409i
$549$	−665.095	+	383.993i	−1.21147	+	0.699441i
$550$		0			0
$551$	12.7279	+	7.34847i	0.0230997	+	0.0133366i
$552$	56.2662			0.101931
$553$	−129.161	−	198.124i	−0.233564	−	0.358272i
$554$	−393.733			−0.710709
$555$		0			0
$556$	−118.794	+	68.5857i	−0.213658	+	0.123356i
$557$	−505.950	+	292.110i	−0.908348	+	0.524435i	−0.879899	−	0.475160i	$-0.842390\pi$
$557$	−505.950	+	292.110i	−0.908348	+	0.524435i	−0.0284485	+	0.999595i	$0.509057\pi$
$558$	293.200	−	507.838i	0.525448	−	0.910103i
$559$		−	160.333i		−	0.286822i
$560$		0			0
$561$	−12.8377			−0.0228835
$562$	−483.395	−	279.088i	−0.860134	−	0.496598i
$563$	−455.573	−	789.076i	−0.809189	−	1.40156i	−0.913426	−	0.407004i	$-0.866573\pi$
$563$	−455.573	−	789.076i	−0.809189	−	1.40156i	0.104237	−	0.994552i	$-0.466760\pi$
$564$	37.7939	+	65.4610i	0.0670105	+	0.116066i
$565$		0			0
$566$			207.035i			0.365787i
$567$	470.882	−	25.5107i	0.830480	−	0.0449924i
$568$		−	103.029i		−	0.181390i
$569$	350.000	−	606.217i	0.615113	−	1.06541i	−0.375251	−	0.926923i	$-0.622444\pi$
$569$	350.000	−	606.217i	0.615113	−	1.06541i	0.990365	−	0.138485i	$-0.0442231\pi$
$570$		0			0
$571$	281.231	+	487.107i	0.492525	+	0.853077i	0.999963	−	0.00861055i	$-0.00274086\pi$
$571$	281.231	+	487.107i	0.492525	+	0.853077i	−0.507438	+	0.861688i	$0.669408\pi$
$572$	72.7461	−	126.000i	0.127179	−	0.220280i
$573$	177.993			0.310634
$574$	151.154	+	231.861i	0.263335	+	0.403939i
$575$		0			0
$576$	−33.9411	+	58.7878i	−0.0589256	+	0.102062i
$577$	−330.830	−	573.014i	−0.573362	−	0.993092i	−0.996218	−	0.0868946i	$-0.972306\pi$
$577$	−330.830	−	573.014i	−0.573362	−	0.993092i	0.422856	−	0.906197i	$-0.361028\pi$
$578$	−336.625	+	194.350i	−0.582395	+	0.336246i
$579$	95.8934	+	55.3641i	0.165619	+	0.0956202i
$580$		0			0
$581$	−404.029	+	796.420i	−0.695402	+	1.37077i
$582$			103.279i			0.177456i
$583$	−230.598	−	133.136i	−0.395538	−	0.228364i
$584$	−128.860	+	74.3973i	−0.220651	+	0.127393i
$585$		0			0
$586$	367.029	+	211.905i	0.626330	+	0.361612i
$587$	−823.029			−1.40209			−0.701046	−	0.713116i	$-0.747283\pi$
$587$	−823.029			−1.40209			−0.701046	+	0.713116i	$0.747283\pi$
$588$	−69.8975	+	7.59589i	−0.118873	+	0.0129182i
$589$	204.338			0.346924
$590$		0			0
$591$	−112.523	+	64.9650i	−0.190394	+	0.109924i
$592$	−10.1884	+	5.88225i	−0.0172101	+	0.00993623i
$593$	−311.128	+	538.890i	−0.524668	+	0.908752i	0.474919	+	0.880029i	$0.342477\pi$
$593$	−311.128	+	538.890i	−0.524668	+	0.908752i	−0.999587	+	0.0287225i	$0.990856\pi$
$594$			84.3992i			0.142086i
$595$		0			0
$596$	184.794			0.310057
$597$	216.659	+	125.088i	0.362912	+	0.209527i
$598$	−299.810	−	519.286i	−0.501355	−	0.868372i
$599$	−256.422	−	444.137i	−0.428084	−	0.741463i	0.568619	−	0.822601i	$-0.307478\pi$
$599$	−256.422	−	444.137i	−0.428084	−	0.741463i	−0.996703	+	0.0811377i	$0.974145\pi$
$600$		0			0
$601$		−	680.160i		−	1.13171i	−0.824504	−	0.565857i	$-0.808546\pi$
$601$		−	680.160i		−	1.13171i	0.824504	−	0.565857i	$-0.191454\pi$
$602$	56.6864	+	86.9533i	0.0941635	+	0.144441i
$603$			293.927i			0.487441i
$604$	−91.7868	+	158.979i	−0.151965	+	0.263211i
$605$		0			0
$606$	−30.2756	−	52.4390i	−0.0499598	−	0.0865329i
$607$	−19.3690	+	33.5482i	−0.0319095	+	0.0552688i	−0.881539	−	0.472111i	$-0.843492\pi$
$607$	−19.3690	+	33.5482i	−0.0319095	+	0.0552688i	0.849630	+	0.527380i	$0.176825\pi$
$608$	−23.6544			−0.0389052
$609$	−17.6253	+	0.954877i	−0.0289414	+	0.00156794i
$610$		0			0
$611$	402.765	−	697.609i	0.659189	−	1.14175i
$612$	−31.9155	−	55.2792i	−0.0521495	−	0.0903255i
$613$	−347.366	+	200.552i	−0.566665	+	0.327164i	−0.755816	−	0.654784i	$-0.772760\pi$
$613$	−347.366	+	200.552i	−0.566665	+	0.327164i	0.189151	+	0.981948i	$0.439426\pi$
$614$	25.7056	+	14.8412i	0.0418658	+	0.0241713i
$615$		0			0
$616$	5.09545	+	94.0530i	0.00827184	+	0.152683i
$617$		−	959.044i		−	1.55437i	−0.629275	−	0.777183i	$-0.716648\pi$
$617$		−	959.044i		−	1.55437i	0.629275	−	0.777183i	$-0.283352\pi$
$618$	105.598	+	60.9670i	0.170870	+	0.0986521i
$619$	869.951	−	502.267i	1.40541	−	0.811416i	0.410473	−	0.911873i	$-0.365364\pi$
$619$	869.951	−	502.267i	1.40541	−	0.811416i	0.994941	+	0.100457i	$0.0320303\pi$
$620$		0			0
$621$	301.235	+	173.918i	0.485081	+	0.280061i
$622$	−257.443			−0.413895
$623$	−295.142	+	192.408i	−0.473743	+	0.308841i
$624$	−43.8823			−0.0703241
$625$		0			0
$626$	119.938	−	69.2460i	0.191594	−	0.110617i
$627$	−12.3600	+	7.13604i	−0.0197129	+	0.0113812i
$628$	−8.45631	+	14.6468i	−0.0134655	+	0.0233229i
$629$		−	11.0624i		−	0.0175873i
$630$		0			0
$631$	−386.514			−0.612542			−0.306271	−	0.951944i	$-0.599081\pi$
$631$	−386.514			−0.612542			−0.306271	+	0.951944i	$0.599081\pi$
$632$	82.7604	+	47.7817i	0.130950	+	0.0756040i
$633$	−130.600	−	226.206i	−0.206319	−	0.357356i
$634$	−340.805	−	590.291i	−0.537547	−	0.931058i
$635$		0			0
$636$			80.3109i			0.126275i
$637$	442.547	+	604.617i	0.694736	+	0.949164i
$638$			23.6468i			0.0370639i
$639$	154.544	−	267.678i	0.241853	−	0.418902i
$640$		0			0
$641$	496.074	+	859.225i	0.773906	+	1.34044i	0.935407	+	0.353572i	$0.115033\pi$
$641$	496.074	+	859.225i	0.773906	+	1.34044i	−0.161502	+	0.986872i	$0.551634\pi$
$642$	−57.6351	+	99.8269i	−0.0897743	+	0.155494i
$643$	−944.986			−1.46965			−0.734826	−	0.678256i	$-0.762736\pi$
$643$	−944.986			−1.46965			−0.734826	+	0.678256i	$0.762736\pi$
$644$	346.191	+	175.625i	0.537564	+	0.272709i
$645$		0			0
$646$	11.1213	−	19.2627i	0.0172157	−	0.0298184i
$647$	1.44544	+	2.50357i	0.00223406	+	0.00386951i	0.867140	−	0.498064i	$-0.165956\pi$
$647$	1.44544	+	2.50357i	0.00223406	+	0.00386951i	−0.864906	+	0.501934i	$0.832622\pi$
$648$	−165.016	+	95.2721i	−0.254654	+	0.147025i
$649$	−159.529	−	92.1039i	−0.245807	−	0.141917i
$650$		0			0
$651$	−205.584	+	134.024i	−0.315797	+	0.205874i
$652$			443.955i			0.680913i
$653$	−279.777	−	161.529i	−0.428449	−	0.247365i	0.270237	−	0.962794i	$-0.412898\pi$
$653$	−279.777	−	161.529i	−0.428449	−	0.247365i	−0.698686	+	0.715429i	$0.746231\pi$
$654$	127.680	−	73.7159i	0.195229	−	0.112716i
$655$		0			0
$656$	−96.8528	−	55.9180i	−0.147641	−	0.0852409i
$657$	−446.384			−0.679428
$658$	28.2114	+	520.731i	0.0428744	+	0.791385i
$659$	−295.955			−0.449098			−0.224549	−	0.974463i	$-0.572091\pi$
$659$	−295.955			−0.449098			−0.224549	+	0.974463i	$0.572091\pi$
$660$		0			0
$661$	17.9710	−	10.3756i	0.0271876	−	0.0156968i	−0.486345	−	0.873767i	$-0.661670\pi$
$661$	17.9710	−	10.3756i	0.0271876	−	0.0156968i	0.513532	+	0.858070i	$0.328337\pi$
$662$	275.576	−	159.104i	0.416278	−	0.240338i
$663$	20.6316	−	35.7351i	0.0311186	−	0.0538990i
$664$		−	360.843i		−	0.543439i
$665$		0			0
$666$	−35.2935			−0.0529933
$667$	84.3992	+	48.7279i	0.126536	+	0.0730554i
$668$	168.841	+	292.441i	0.252756	+	0.437785i
$669$	44.2052	+	76.5656i	0.0660765	+	0.114448i
$670$		0			0
$671$		−	430.579i		−	0.641698i
$672$	23.7986	−	15.5147i	0.0354146	−	0.0230874i
$673$		−	627.044i		−	0.931714i	−0.884860	−	0.465857i	$-0.845746\pi$
$673$		−	627.044i		−	0.931714i	0.884860	−	0.465857i	$-0.154254\pi$
$674$	−186.936	+	323.783i	−0.277353	+	0.480390i
$675$		0			0
$676$	64.8234	+	112.277i	0.0958926	+	0.166091i
$677$	54.6230	−	94.6097i	0.0806838	−	0.139749i	−0.822860	−	0.568244i	$-0.807623\pi$
$677$	54.6230	−	94.6097i	0.0806838	−	0.139749i	0.903544	+	0.428496i	$0.140956\pi$
$678$	35.0489			0.0516946
$679$	−322.368	+	635.450i	−0.474768	+	0.935861i
$680$		0			0
$681$	−27.3974	+	47.4537i	−0.0402311	+	0.0696824i
$682$	164.386	+	284.724i	0.241035	+	0.417484i
$683$	−687.248	+	396.783i	−1.00622	+	0.580941i	−0.910083	−	0.414427i	$-0.863982\pi$
$683$	−687.248	+	396.783i	−1.00622	+	0.580941i	−0.0961370	+	0.995368i	$0.530649\pi$
$684$	−61.4558	−	35.4815i	−0.0898477	−	0.0518736i
$685$		0			0
$686$	−453.770	−	171.437i	−0.661473	−	0.249908i
$687$			256.331i			0.373116i
$688$	−36.3221	−	20.9706i	−0.0527937	−	0.0304805i
$689$	741.198	−	427.931i	1.07576	−	0.621090i
$690$		0			0
$691$	159.253	+	91.9447i	0.230467	+	0.133060i	0.610788	−	0.791794i	$-0.290853\pi$
$691$	159.253	+	91.9447i	0.230467	+	0.133060i	−0.380320	+	0.924855i	$0.624186\pi$
$692$	−328.682			−0.474974
$693$	−127.841	+	252.000i	−0.184475	+	0.363636i
$694$	270.478			0.389738
$695$		0			0
$696$	6.17662	−	3.56608i	0.00887446	−	0.00512367i
$697$	91.0725	−	52.5807i	0.130664	−	0.0754386i
$698$	95.7763	−	165.889i	0.137215	−	0.237664i
$699$			195.913i			0.280277i
$700$		0			0
$701$	−1043.82			−1.48905			−0.744525	−	0.667595i	$-0.767324\pi$
$701$	−1043.82			−1.48905			−0.744525	+	0.667595i	$0.767324\pi$
$702$	−234.935	−	135.640i	−0.334665	−	0.193219i
$703$	−6.14922	−	10.6508i	−0.00874711	−	0.0151504i
$704$	−19.0294	−	32.9600i	−0.0270305	−	0.0468181i
$705$		0			0
$706$		−	492.840i		−	0.698073i
$707$	−22.5993	−	417.143i	−0.0319651	−	0.590019i
$708$			55.5593i			0.0784736i
$709$	−490.279	+	849.188i	−0.691507	+	1.19773i	0.279836	+	0.960048i	$0.409720\pi$
$709$	−490.279	+	849.188i	−0.691507	+	1.19773i	−0.971344	+	0.237678i	$0.923614\pi$
$710$		0			0
$711$	143.345	+	248.281i	0.201611	+	0.349200i
$712$	71.1794	−	123.286i	0.0999711	−	0.173155i
$713$	1354.97			1.90038
$714$	1.44513	+	26.6745i	0.00202399	+	0.0373593i
$715$		0			0
$716$	−185.184	+	320.748i	−0.258637	+	0.447972i
$717$	−95.0975	−	164.714i	−0.132632	−	0.229726i
$718$	−373.340	+	215.548i	−0.519972	+	0.300206i
$719$	674.187	+	389.242i	0.937673	+	0.541366i	0.889230	−	0.457460i	$-0.151241\pi$
$719$	674.187	+	389.242i	0.937673	+	0.541366i	0.0484429	+	0.998826i	$0.484574\pi$
$720$		0			0
$721$	459.419	+	704.719i	0.637197	+	0.977419i
$722$			485.803i			0.672858i
$723$	54.4514	+	31.4376i	0.0753132	+	0.0434821i
$724$	−268.617	+	155.086i	−0.371018	+	0.214208i
$725$		0			0
$726$	86.4335	+	49.9024i	0.119054	+	0.0687361i
$727$	−735.255			−1.01135			−0.505677	−	0.862723i	$-0.668757\pi$
$727$	−735.255			−1.01135			−0.505677	+	0.862723i	$0.668757\pi$
$728$	−269.996	−	136.971i	−0.370874	−	0.188146i
$729$	−490.632			−0.673021
$730$		0			0
$731$	34.1543	−	19.7190i	0.0467227	−	0.0269754i
$732$	−112.469	+	64.9340i	−0.153646	+	0.0887076i
$733$	−239.430	+	414.705i	−0.326644	+	0.565764i	−0.981844	−	0.189692i	$-0.939251\pi$
$733$	−239.430	+	414.705i	−0.326644	+	0.565764i	0.655200	+	0.755456i	$0.272585\pi$
$734$			134.356i			0.183047i
$735$		0			0
$736$	−156.853			−0.213115
$737$	−142.715	−	82.3965i	−0.193643	−	0.111800i
$738$	−167.754	−	290.558i	−0.227309	−	0.393711i
$739$	−9.95227	−	17.2378i	−0.0134672	−	0.0233259i	0.859213	−	0.511618i	$-0.170954\pi$
$739$	−9.95227	−	17.2378i	−0.0134672	−	0.0233259i	−0.872680	+	0.488292i	$0.837620\pi$
$740$		0			0
$741$		−	45.8739i		−	0.0619080i
$742$	−250.676	+	494.132i	−0.337838	+	0.665946i
$743$		−	43.3095i		−	0.0582901i	−0.999575	−	0.0291450i	$-0.990722\pi$
$743$		−	43.3095i		−	0.0582901i	0.999575	−	0.0291450i	$-0.00927847\pi$
$744$	49.5807	−	85.8764i	0.0666408	−	0.115425i
$745$		0			0
$746$	−179.293	−	310.544i	−0.240339	−	0.416279i
$747$	541.265	−	937.499i	0.724585	−	1.25502i
$748$	35.7875			0.0478442
$749$	−666.206	+	434.311i	−0.889460	+	0.579855i
$750$		0			0
$751$	−112.665	+	195.142i	−0.150020	+	0.259842i	−0.931235	−	0.364420i	$-0.881267\pi$
$751$	−112.665	+	195.142i	−0.150020	+	0.259842i	0.781215	+	0.624263i	$0.214600\pi$
$752$	−105.358	−	182.485i	−0.140104	−	0.242667i
$753$	307.961	−	177.801i	0.408978	−	0.236124i
$754$	−65.8234	−	38.0031i	−0.0872989	−	0.0504020i
$755$		0			0
$756$	175.368	−	9.50079i	0.231968	−	0.0125672i
$757$			935.779i			1.23617i	0.786112	+	0.618084i	$0.212091\pi$
$757$			935.779i			1.23617i	−0.786112	+	0.618084i	$0.787909\pi$
$758$	622.476	+	359.387i	0.821209	+	0.474125i
$759$	−81.9594	+	47.3193i	−0.107983	+	0.0623443i
$760$		0			0
$761$	1214.79	+	701.357i	1.59630	+	0.921625i	0.992191	+	0.124724i	$0.0398046\pi$
$761$	1214.79	+	701.357i	1.59630	+	0.921625i	0.604110	+	0.796901i	$0.293529\pi$
$762$	250.952			0.329334
$763$	1015.67	−	55.0254i	1.33115	−	0.0721172i
$764$	−496.191			−0.649465
$765$		0			0
$766$	−585.136	+	337.828i	−0.763885	+	0.441029i
$767$	512.763	−	296.044i	0.668530	−	0.385976i
$768$	−5.73951	+	9.94113i	−0.00747332	+	0.0129442i
$769$			1.72330i			0.00224097i	0.999999	+	0.00112048i	$0.000356661\pi$
$769$			1.72330i			0.00224097i	−0.999999	+	0.00112048i	$0.999643\pi$
$770$		0			0
$771$	287.360			0.372711
$772$	−267.321	−	154.338i	−0.346271	−	0.199920i
$773$	−112.129	−	194.213i	−0.145057	−	0.251245i	0.784337	−	0.620334i	$-0.213003\pi$
$773$	−112.129	−	194.213i	−0.145057	−	0.251245i	−0.929394	+	0.369089i	$0.879670\pi$
$774$	−62.9117	−	108.966i	−0.0812813	−	0.140783i
$775$		0			0
$776$		−	287.911i		−	0.371019i
$777$	13.1725	+	6.68247i	0.0169530	+	0.00860034i
$778$		−	240.728i		−	0.309419i
$779$	58.4558	−	101.248i	0.0750396	−	0.129972i
$780$		0			0
$781$	86.6468	+	150.077i	0.110943	+	0.192160i
$782$	73.7458	−	127.731i	0.0943041	−	0.163340i
$783$	44.0908			0.0563101
$784$	194.853	−	21.1750i	0.248537	−	0.0270089i
$785$		0			0
$786$	74.9010	−	129.732i	0.0952939	−	0.165054i
$787$	35.1017	+	60.7979i	0.0446019	+	0.0772528i	0.887465	−	0.460876i	$-0.152465\pi$
$787$	35.1017	+	60.7979i	0.0446019	+	0.0772528i	−0.842863	+	0.538129i	$0.819131\pi$
$788$	313.679	−	181.103i	0.398070	−	0.229826i
$789$	−20.0968	−	11.6029i	−0.0254712	−	0.0147058i
$790$		0			0
$791$	215.647	+	109.399i	0.272625	+	0.138305i
$792$		−	114.177i		−	0.144162i
$793$	1198.57	+	691.992i	1.51143	+	0.872625i
$794$	299.511	−	172.923i	0.377218	−	0.217787i
$795$		0			0
$796$	−603.978	−	348.707i	−0.758766	−	0.438074i
$797$	1305.38			1.63787			0.818933	−	0.573889i	$-0.194566\pi$
$797$	1305.38			1.63787			0.818933	+	0.573889i	$0.194566\pi$
$798$	16.2189	+	24.8787i	0.0203244	+	0.0311763i
$799$	198.140			0.247985
$800$		0			0
$801$	369.859	−	213.538i	0.461747	−	0.266590i
$802$	−511.420	+	295.269i	−0.637681	+	0.368165i
$803$	125.135	−	216.740i	0.155834	−	0.269913i
$804$			49.7036i			0.0618204i
$805$		0			0
$806$	−1056.75			−1.31110
$807$	−190.723	−	110.114i	−0.236335	−	0.136448i
$808$	84.3992	+	146.184i	0.104455	+	0.180921i
$809$	381.382	+	660.573i	0.471424	+	0.816531i	0.999466	−	0.0326879i	$-0.0104067\pi$
$809$	381.382	+	660.573i	0.471424	+	0.816531i	−0.528041	+	0.849219i	$0.677073\pi$
$810$		0			0
$811$		−	1214.98i		−	1.49813i	−0.662498	−	0.749064i	$-0.730504\pi$
$811$		−	1214.98i		−	1.49813i	0.662498	−	0.749064i	$-0.269496\pi$
$812$	49.1340	−	2.66190i	0.0605099	−	0.00327821i
$813$			54.5147i			0.0670538i
$814$	9.89383	−	17.1366i	0.0121546	−	0.0210524i
$815$		0			0
$816$	−5.39697	−	9.34783i	−0.00661393	−	0.0114557i
$817$	21.9223	−	37.9706i	0.0268327	−	0.0464756i
$818$	435.877			0.532857
$819$	−496.014	−	760.854i	−0.605634	−	0.929004i
$820$		0			0
$821$	291.684	−	505.211i	0.355279	−	0.615361i	−0.631887	−	0.775061i	$-0.717719\pi$
$821$	291.684	−	505.211i	0.355279	−	0.615361i	0.987166	+	0.159700i	$0.0510527\pi$
$822$	−16.5248	−	28.6218i	−0.0201031	−	0.0348197i
$823$	−892.648	+	515.371i	−1.08463	+	0.626210i	−0.932141	−	0.362096i	$-0.882061\pi$
$823$	−892.648	+	515.371i	−1.08463	+	0.626210i	−0.152486	+	0.988306i	$0.548728\pi$
$824$	−294.375	−	169.957i	−0.357251	−	0.206259i
$825$		0			0
$826$	−173.418	+	341.842i	−0.209950	+	0.413852i
$827$			152.102i			0.183920i	0.995763	+	0.0919599i	$0.0293132\pi$
$827$			152.102i			0.183920i	−0.995763	+	0.0919599i	$0.970687\pi$
$828$	−407.516	−	235.279i	−0.492169	−	0.284154i
$829$	−532.095	+	307.205i	−0.641852	+	0.370573i	−0.785327	−	0.619081i	$-0.787505\pi$
$829$	−532.095	+	307.205i	−0.641852	+	0.370573i	0.143476	+	0.989654i	$0.454172\pi$
$830$		0			0
$831$	−172.983	−	99.8715i	−0.208162	−	0.120182i
$832$	122.330			0.147032
$833$	−74.3682	+	168.632i	−0.0892776	+	0.202439i
$834$	−69.5879			−0.0834387
$835$		0			0
$836$	34.4558	−	19.8931i	0.0412151	−	0.0237956i
$837$	530.886	−	306.507i	0.634272	−	0.366197i
$838$	−72.9326	+	126.323i	−0.0870317	+	0.150743i
$839$		−	1546.14i		−	1.84284i	−0.388568	−	0.921420i	$-0.627030\pi$
$839$		−	1546.14i		−	1.84284i	0.388568	−	0.921420i	$-0.372970\pi$
$840$		0			0
$841$	−828.647			−0.985311
$842$	202.353	+	116.828i	0.240324	+	0.138751i
$843$	−141.583	−	245.229i	−0.167952	−	0.290901i
$844$	364.073	+	630.593i	0.431366	+	0.747148i
$845$		0			0
$846$		−	632.148i		−	0.747219i
$847$	376.041	+	576.823i	0.443969	+	0.681019i
$848$		−	223.882i		−	0.264012i
$849$	−52.5152	+	90.9589i	−0.0618553	+	0.107137i
$850$		0			0
$851$	−40.7756	−	70.6255i	−0.0479150	−	0.0829912i
$852$	26.1337	−	45.2649i	0.0306734	−	0.0531279i
$853$	1235.15			1.44800			0.724002	−	0.689798i	$-0.242301\pi$
$853$	1235.15			1.44800			0.724002	+	0.689798i	$0.242301\pi$
$854$	−894.672	+	48.4701i	−1.04763	+	0.0567566i
$855$		0			0
$856$	160.669	−	278.287i	0.187697	−	0.325102i
$857$	−550.341	−	953.219i	−0.642172	−	1.11227i	−0.984947	−	0.172857i	$-0.944700\pi$
$857$	−550.341	−	953.219i	−0.642172	−	1.11227i	0.342775	−	0.939417i	$-0.388633\pi$
$858$	63.9205	−	36.9045i	0.0744995	−	0.0430123i
$859$	−512.488	−	295.885i	−0.596610	−	0.344453i	0.171096	−	0.985254i	$-0.445269\pi$
$859$	−512.488	−	295.885i	−0.596610	−	0.344453i	−0.767707	+	0.640801i	$0.778602\pi$
$860$		0			0
$861$	7.59589	+	140.207i	0.00882217	+	0.162841i
$862$			840.801i			0.975407i
$863$	−56.0553	−	32.3635i	−0.0649540	−	0.0375012i	0.467171	−	0.884167i	$-0.345273\pi$
$863$	−56.0553	−	32.3635i	−0.0649540	−	0.0375012i	−0.532125	+	0.846666i	$0.678606\pi$
$864$	−61.4558	+	35.4815i	−0.0711294	+	0.0410666i
$865$		0			0
$866$	−49.7574	−	28.7274i	−0.0574565	−	0.0331725i
$867$	−197.190			−0.227440
$868$	573.105	−	373.617i	0.660259	−	0.430435i
$869$	−160.736			−0.184967
$870$		0			0
$871$	458.720	−	264.842i	0.526659	−	0.304067i
$872$	−355.932	+	205.497i	−0.408179	+	0.235662i
$873$	431.866	−	748.014i	0.494692	−	0.856832i
$874$		−	163.972i		−	0.187611i
$875$		0			0
$876$	−75.4844			−0.0861694
$877$	263.438	+	152.096i	0.300385	+	0.173427i	0.642616	−	0.766188i	$-0.277849\pi$
$877$	263.438	+	152.096i	0.300385	+	0.173427i	−0.342231	+	0.939616i	$0.611182\pi$
$878$	103.662	+	179.548i	0.118066	+	0.204496i
$879$	107.500	+	186.196i	0.122299	+	0.211827i
$880$		0			0
$881$		−	863.732i		−	0.980400i	−0.871610	−	0.490200i	$-0.836924\pi$
$881$		−	863.732i		−	0.980400i	0.871610	−	0.490200i	$-0.163076\pi$
$882$	538.005	+	237.265i	0.609983	+	0.269008i
$883$			567.456i			0.642645i	0.946970	+	0.321323i	$0.104127\pi$
$883$			567.456i			0.642645i	−0.946970	+	0.321323i	$0.895873\pi$
$884$	−57.5147	+	99.6184i	−0.0650619	+	0.112691i
$885$		0			0
$886$	−75.9153	−	131.489i	−0.0856831	−	0.148408i
$887$	444.880	−	770.555i	0.501556	−	0.868721i	−0.498442	−	0.866923i	$-0.666094\pi$
$887$	444.880	−	770.555i	0.501556	−	0.868721i	0.999998	−	0.00179783i	$-0.000572267\pi$
$888$	−5.96820			−0.00672095
$889$	1544.04	+	783.302i	1.73683	+	0.881105i
$890$		0			0
$891$	160.246	−	277.554i	0.179849	−	0.311508i
$892$	−123.231	−	213.442i	−0.138151	−	0.239284i
$893$	190.767	−	110.140i	0.213625	−	0.123337i
$894$	81.1873	+	46.8735i	0.0908136	+	0.0524312i
$895$		0			0
$896$	−66.3431	+	43.2503i	−0.0740437	+	0.0482704i
$897$		−	304.191i		−	0.339120i
$898$	165.538	+	95.5736i	0.184341	+	0.106429i
$899$	148.742	−	85.8764i	0.165453	−	0.0955243i
$900$		0			0
$901$	182.316	+	105.260i	0.202349	+	0.116826i
$902$	188.106			0.208543
$903$	2.84864	+	52.5807i	0.00315464	+	0.0582289i
$904$	−97.7056			−0.108081
$905$		0			0
$906$	−80.6512	+	46.5640i	−0.0890190	+	0.0513951i
$907$	323.874	−	186.989i	0.357083	−	0.206162i	−0.310717	−	0.950502i	$-0.600569\pi$
$907$	323.874	−	186.989i	0.357083	−	0.206162i	0.667800	+	0.744340i	$0.267236\pi$
$908$	76.3756	−	132.286i	0.0841141	−	0.145690i
$909$			506.395i			0.557091i
$910$		0			0
$911$	1133.75			1.24451			0.622256	−	0.782814i	$-0.286216\pi$
$911$	1133.75			1.24451			0.622256	+	0.782814i	$0.286216\pi$
$912$	−10.3923	−	6.00000i	−0.0113951	−	0.00657895i
$913$	303.466	+	525.618i	0.332383	+	0.575704i
$914$	112.950	+	195.635i	0.123577	+	0.214042i
$915$		0			0
$916$		−	714.572i		−	0.780101i
$917$	865.782	−	564.419i	0.944146	−	0.615506i
$918$		−	66.7279i		−	0.0726884i
$919$	228.151	−	395.169i	0.248260	−	0.429999i	−0.714783	−	0.699346i	$-0.753475\pi$
$919$	228.151	−	395.169i	0.248260	−	0.429999i	0.963043	+	0.269347i	$0.0868078\pi$
$920$		0			0
$921$	7.52900	+	13.0406i	0.00817481	+	0.0141592i
$922$	−219.380	+	379.977i	−0.237939	+	0.412122i
$923$	−557.007			−0.603474
$924$	−21.6182	+	42.6137i	−0.0233963	+	0.0461187i
$925$		0			0
$926$	230.527	−	399.284i	0.248949	−	0.431193i
$927$	−509.872	−	883.124i	−0.550024	−	0.952669i
$928$	−17.2185	+	9.94113i	−0.0185545	+	0.0107124i
$929$	824.058	+	475.770i	0.887037	+	0.512131i	0.872972	−	0.487770i	$-0.162189\pi$
$929$	824.058	+	475.770i	0.887037	+	0.512131i	0.0140650	+	0.999901i	$0.495523\pi$
$930$		0			0
$931$	22.1360	+	203.696i	0.0237766	+	0.218793i
$932$		−	546.146i		−	0.585994i
$933$	−113.105	−	65.3011i	−0.121227	−	0.0699904i
$934$	729.407	−	421.123i	0.780949	−	0.450881i
$935$		0			0
$936$	317.823	+	183.495i	0.339555	+	0.196042i
$937$	−1295.71			−1.38283			−0.691413	−	0.722460i	$-0.743011\pi$
$937$	−1295.71			−1.38283			−0.691413	+	0.722460i	$0.743011\pi$
$938$	−155.141	+	305.813i	−0.165395	+	0.326027i
$939$	70.2578			0.0748219
$940$		0			0
$941$	−1175.10	+	678.446i	−1.24878	+	0.720984i	−0.970866	−	0.239622i	$-0.922977\pi$
$941$	−1175.10	+	678.446i	−1.24878	+	0.720984i	−0.277915	+	0.960606i	$0.589643\pi$
$942$	−7.43038	+	4.28993i	−0.00788788	+	0.00455407i
$943$	387.622	−	671.382i	0.411052	−	0.711964i
$944$		−	154.882i		−	0.164070i
$945$		0			0
$946$	70.5442			0.0745710
$947$	614.412	+	354.731i	0.648799	+	0.374584i	0.787996	−	0.615681i	$-0.211119\pi$
$947$	614.412	+	354.731i	0.648799	+	0.374584i	−0.139197	+	0.990265i	$0.544452\pi$
$948$	24.2400	+	41.9848i	0.0255696	+	0.0442878i
$949$	402.213	+	696.654i	0.423828	+	0.734092i
$950$		0			0
$951$		−	345.784i		−	0.363601i
$952$	−4.02858	−	74.3604i	−0.00423170	−	0.0781097i
$953$		−	936.603i		−	0.982794i	−0.870936	−	0.491397i	$-0.836486\pi$
$953$		−	936.603i		−	0.982794i	0.870936	−	0.491397i	$-0.163514\pi$
$954$	335.823	−	581.663i	0.352016	−	0.609710i
$955$		0			0
$956$	265.103	+	459.171i	0.277304	+	0.480305i
$957$	−5.99807	+	10.3890i	−0.00626757	+	0.0108558i
$958$	716.554			0.747969
$959$	−12.3350	−	227.681i	−0.0128623	−	0.237415i
$960$		0			0
$961$	713.477	−	1235.78i	0.742432	−	1.28593i
$962$	31.8011	+	55.0812i	0.0330573	+	0.0572569i
$963$	834.861	−	482.007i	0.866938	−	0.500527i
$964$	−151.794	−	87.6383i	−0.157463	−	0.0909111i
$965$		0			0
$966$	107.548	+	164.971i	0.111333	+	0.170778i
$967$			1374.37i			1.42127i	0.703561	+	0.710635i	$0.251592\pi$
$967$			1374.37i			1.42127i	−0.703561	+	0.710635i	$0.748408\pi$
$968$	−240.950	−	139.113i	−0.248916	−	0.143711i
$969$	9.77208	−	5.64191i	0.0100847	−	0.00582241i
$970$		0			0
$971$	−27.2466	−	15.7309i	−0.0280604	−	0.0162007i	0.485904	−	0.874012i	$-0.338490\pi$
$971$	−27.2466	−	15.7309i	−0.0280604	−	0.0162007i	−0.513965	+	0.857811i	$0.671824\pi$
$972$	−322.467			−0.331757
$973$	−428.156	−	217.206i	−0.440037	−	0.223233i
$974$	−298.825			−0.306802
$975$		0			0
$976$	313.529	−	181.016i	0.321239	−	0.185467i
$977$	−469.297	+	270.949i	−0.480345	+	0.277327i	−0.720560	−	0.693392i	$-0.756115\pi$
$977$	−469.297	+	270.949i	−0.480345	+	0.277327i	0.240215	+	0.970720i	$0.422782\pi$
$978$	−112.611	+	195.047i	−0.115144	+	0.199435i
$979$			239.445i			0.244581i
$980$		0			0
$981$	−1232.98			−1.25687
$982$	960.397	+	554.485i	0.978001	+	0.564649i
$983$	−11.2099	−	19.4161i	−0.0114038	−	0.0197519i	0.860267	−	0.509843i	$-0.170297\pi$
$983$	−11.2099	−	19.4161i	−0.0114038	−	0.0197519i	−0.871671	+	0.490092i	$0.836963\pi$
$984$	−28.3675	−	49.1340i	−0.0288288	−	0.0499329i
$985$		0			0
$986$		−	18.6957i		−	0.0189611i
$987$	−119.691	+	235.934i	−0.121267	+	0.239042i
$988$			127.882i			0.129435i
$989$	145.368	−	251.784i	0.146984	−	0.254584i
$990$		0			0
$991$	−339.017	−	587.195i	−0.342096	−	0.592528i	0.642726	−	0.766097i	$-0.277804\pi$
$991$	−339.017	−	587.195i	−0.342096	−	0.592528i	−0.984822	+	0.173568i	$0.944470\pi$
$992$	−138.216	+	239.397i	−0.139331	+	0.241328i
$993$	161.429			0.162567
$994$	302.080	−	196.932i	0.303904	−	0.198120i
$995$		0			0
$996$	91.5290	−	158.533i	0.0918966	−	0.159170i
$997$	438.081	+	758.779i	0.439400	+	0.761062i	0.997643	−	0.0686147i	$-0.0218579\pi$
$997$	438.081	+	758.779i	0.439400	+	0.761062i	−0.558244	+	0.829677i	$0.688525\pi$
$998$	210.034	−	121.263i	0.210455	−	0.121506i
$999$	−31.9523	−	18.4477i	−0.0319843	−	0.0184661i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.3.i.a.299.2		8
5.2	odd	4		350.3.k.a.201.2		4
5.3	odd	4		14.3.d.a.5.1	yes	4
5.4	even	2	inner	350.3.i.a.299.3		8
7.3	odd	6	inner	350.3.i.a.199.3		8
15.8	even	4		126.3.n.c.19.2		4
20.3	even	4		112.3.s.b.33.1		4
35.3	even	12		14.3.d.a.3.1	✓	4
35.13	even	4		98.3.d.a.19.1		4
35.17	even	12		350.3.k.a.101.2		4
35.18	odd	12		98.3.d.a.31.1		4
35.23	odd	12		98.3.b.b.97.4		4
35.24	odd	6	inner	350.3.i.a.199.2		8
35.33	even	12		98.3.b.b.97.3		4
40.3	even	4		448.3.s.c.257.2		4
40.13	odd	4		448.3.s.d.257.1		4
60.23	odd	4		1008.3.cg.l.145.2		4
105.23	even	12		882.3.c.f.685.1		4
105.38	odd	12		126.3.n.c.73.2		4
105.53	even	12		882.3.n.b.325.2		4
105.68	odd	12		882.3.c.f.685.2		4
105.83	odd	4		882.3.n.b.19.2		4
140.3	odd	12		112.3.s.b.17.1		4
140.23	even	12		784.3.c.e.97.2		4
140.83	odd	4		784.3.s.c.705.2		4
140.103	odd	12		784.3.c.e.97.3		4
140.123	even	12		784.3.s.c.129.2		4
280.3	odd	12		448.3.s.c.129.2		4
280.213	even	12		448.3.s.d.129.1		4
420.143	even	12		1008.3.cg.l.577.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.3.d.a.3.1	✓	4	35.3	even	12
14.3.d.a.5.1	yes	4	5.3	odd	4
98.3.b.b.97.3		4	35.33	even	12
98.3.b.b.97.4		4	35.23	odd	12
98.3.d.a.19.1		4	35.13	even	4
98.3.d.a.31.1		4	35.18	odd	12
112.3.s.b.17.1		4	140.3	odd	12
112.3.s.b.33.1		4	20.3	even	4
126.3.n.c.19.2		4	15.8	even	4
126.3.n.c.73.2		4	105.38	odd	12
350.3.i.a.199.2		8	35.24	odd	6	inner
350.3.i.a.199.3		8	7.3	odd	6	inner
350.3.i.a.299.2		8	1.1	even	1	trivial
350.3.i.a.299.3		8	5.4	even	2	inner
350.3.k.a.101.2		4	35.17	even	12
350.3.k.a.201.2		4	5.2	odd	4
448.3.s.c.129.2		4	280.3	odd	12
448.3.s.c.257.2		4	40.3	even	4
448.3.s.d.129.1		4	280.213	even	12
448.3.s.d.257.1		4	40.13	odd	4
784.3.c.e.97.2		4	140.23	even	12
784.3.c.e.97.3		4	140.103	odd	12
784.3.s.c.129.2		4	140.123	even	12
784.3.s.c.705.2		4	140.83	odd	4
882.3.c.f.685.1		4	105.23	even	12
882.3.c.f.685.2		4	105.68	odd	12
882.3.n.b.19.2		4	105.83	odd	4
882.3.n.b.325.2		4	105.53	even	12
1008.3.cg.l.145.2		4	60.23	odd	4
1008.3.cg.l.577.2		4	420.143	even	12

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	350.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 0.707107i) q^{2} +(-0.358719 - 0.621320i) q^{3} +(1.00000 + 1.73205i) q^{4} +1.01461i q^{6} +(-3.16693 + 6.24264i) q^{7} -2.82843i q^{8} +(4.24264 - 7.34847i) q^{9} +(2.37868 + 4.11999i) q^{11} +(0.717439 - 1.24264i) q^{12} -15.2913 q^{13} +(8.29289 - 5.40629i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-1.88064 - 3.25736i) q^{17} +(-10.3923 + 6.00000i) q^{18} +(-3.62132 - 2.09077i) q^{19} +(5.01472 - 0.271680i) q^{21} -6.72792i q^{22} +(-24.0131 - 13.8640i) q^{23} +(-1.75736 + 1.01461i) q^{24} +(18.7279 + 10.8126i) q^{26} -12.5446 q^{27} +(-13.9795 + 0.757359i) q^{28} -3.51472 q^{29} +(-42.3198 + 24.4334i) q^{31} +(4.89898 - 2.82843i) q^{32} +(1.70656 - 2.95584i) q^{33} +5.31925i q^{34} +16.9706 q^{36} +(2.54709 + 1.47056i) q^{37} +(2.95680 + 5.12132i) q^{38} +(5.48528 + 9.50079i) q^{39} +27.9590i q^{41} +(-6.33386 - 3.21320i) q^{42} +10.4853i q^{43} +(-4.75736 + 8.23999i) q^{44} +(19.6066 + 33.9596i) q^{46} +(-26.3395 + 45.6213i) q^{47} +2.86976 q^{48} +(-28.9411 - 39.5400i) q^{49} +(-1.34924 + 2.33696i) q^{51} +(-15.2913 - 26.4853i) q^{52} +(-48.4719 + 27.9853i) q^{53} +(15.3640 + 8.87039i) q^{54} +(17.6569 + 8.95743i) q^{56} +3.00000i q^{57} +(4.30463 + 2.48528i) q^{58} +(-33.5330 + 19.3603i) q^{59} +(-78.3823 - 45.2540i) q^{61} +69.1080 q^{62} +(32.4377 + 49.7574i) q^{63} -8.00000 q^{64} +(-4.18019 + 2.41344i) q^{66} +(-29.9988 + 17.3198i) q^{67} +(3.76127 - 6.51472i) q^{68} +19.8931i q^{69} +36.4264 q^{71} +(-20.7846 - 12.0000i) q^{72} +(-26.3034 - 45.5589i) q^{73} +(-2.07969 - 3.60213i) q^{74} -8.36308i q^{76} +(-33.2528 + 1.80152i) q^{77} -15.5147i q^{78} +(-16.8934 + 29.2602i) q^{79} +(-33.6838 - 58.3420i) q^{81} +(19.7700 - 34.2426i) q^{82} +127.577 q^{83} +(5.48528 + 8.41407i) q^{84} +(7.41421 - 12.8418i) q^{86} +(1.26080 + 2.18377i) q^{87} +(11.6531 - 6.72792i) q^{88} +(43.5883 + 25.1657i) q^{89} +(48.4264 - 95.4580i) q^{91} -55.4558i q^{92} +(30.3619 + 17.5294i) q^{93} +(64.5183 - 37.2497i) q^{94} +(-3.51472 - 2.02922i) q^{96} +101.792 q^{97} +(7.48650 + 68.8909i) q^{98} +40.3675 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} + 36 q^{11} + 72 q^{14} - 16 q^{16} - 12 q^{19} + 108 q^{21} - 48 q^{24} + 48 q^{26} - 96 q^{29} - 84 q^{31} - 24 q^{39} - 72 q^{44} + 72 q^{46} + 40 q^{49} + 108 q^{51} + 72 q^{54} + 96 q^{56}+ \cdots - 288 q^{99}+O(q^{100}) \) 8 * q + 8 * q^4 + 36 * q^11 + 72 * q^14 - 16 * q^16 - 12 * q^19 + 108 * q^21 - 48 * q^24 + 48 * q^26 - 96 * q^29 - 84 * q^31 - 24 * q^39 - 72 * q^44 + 72 * q^46 + 40 * q^49 + 108 * q^51 + 72 * q^54 + 96 * q^56 + 156 * q^59 - 84 * q^61 - 64 * q^64 - 288 * q^66 - 48 * q^71 - 192 * q^74 - 220 * q^79 + 36 * q^81 - 24 * q^84 + 48 * q^86 + 756 * q^89 + 48 * q^91 + 24 * q^94 - 96 * q^96 - 288 * q^99

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