LMFDB - Embedded newform 350.3.i.a.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,3,Mod(199,350)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			199.2
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	350.199
Dual form			350.3.i.a.299.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 0.707107i) q^{2} +(-0.358719 + 0.621320i) q^{3} +(1.00000 - 1.73205i) q^{4} -1.01461i q^{6} +(-3.16693 - 6.24264i) q^{7} +2.82843i q^{8} +(4.24264 + 7.34847i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 8 * q + 8 * q^4	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.919599	−	0.392859i	$-0.871486\pi$
$3$	−0.358719	+	0.621320i	−0.119573	+	0.207107i	0.800025	+	0.599966i	$0.204819\pi$
$4$	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	−0.737413	−	0.675442i	$-0.763953\pi$
$11$	2.37868	−	4.11999i	0.216244	−	0.374545i	0.953657	+	0.300897i	$0.0972861\pi$
$12$	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	−0.916023	−	0.401126i	$-0.868619\pi$
$17$	−1.88064	+	3.25736i	−0.110626	+	0.191609i	0.805397	+	0.592736i	$0.201952\pi$
$18$	−10.3923	−	6.00000i	−0.577350	−	0.333333i
$19$	−3.62132	+	2.09077i	−0.190596	+	0.110041i	−0.592261	−	0.805746i	$-0.701765\pi$
$19$	−3.62132	+	2.09077i	−0.190596	+	0.110041i	0.401666	+	0.915786i	$0.368431\pi$
$20$		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	−0.920977	−	0.389617i	$-0.872607\pi$
$23$	−24.0131	+	13.8640i	−1.04405	+	0.602781i	−0.123070	+	0.992398i	$0.539274\pi$
$24$	−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	−0.374850	−	0.927085i	$-0.622306\pi$
$31$	−42.3198	−	24.4334i	−1.36516	−	0.788173i	−0.990305	+	0.138913i	$0.955639\pi$
$32$	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	−0.465185	−	0.885214i	$-0.654012\pi$
$37$	2.54709	−	1.47056i	0.0688403	−	0.0397449i	0.534025	+	0.845469i	$0.320679\pi$
$38$	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	$-0.889247\pi$
$41$		−	27.9590i		−	0.681927i	0.940077	−	0.340963i	$-0.110753\pi$
$42$	−6.33386	+	3.21320i	−0.150806	+	0.0765048i
$43$		−	10.4853i		−	0.243844i	−0.992540	−	0.121922i	$-0.961094\pi$
$43$		−	10.4853i		−	0.243844i	0.992540	−	0.121922i	$-0.0389057\pi$
$44$	−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	−0.997460	−	0.0712271i	$-0.977309\pi$
$47$	−26.3395	−	45.6213i	−0.560415	−	0.970666i	0.437046	−	0.899439i	$-0.356025\pi$
$48$	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	−0.0326677	−	0.999466i	$-0.510400\pi$
$53$	−48.4719	−	27.9853i	−0.914565	−	0.528024i	−0.881897	+	0.471442i	$0.843734\pi$
$54$	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	0.188136	−	0.982143i	$-0.439755\pi$
$59$	−33.5330	−	19.3603i	−0.568356	−	0.328141i	−0.756492	+	0.654002i	$0.773089\pi$
$60$		0			0
$61$	−78.3823	+	45.2540i	−1.28495	+	0.741869i	−0.977750	−	0.209774i	$-0.932727\pi$
$61$	−78.3823	+	45.2540i	−1.28495	+	0.741869i	−0.307205	+	0.951643i	$0.599394\pi$
$62$	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	0.259134	−	0.965842i	$-0.416563\pi$
$67$	−29.9988	−	17.3198i	−0.447743	−	0.258505i	−0.706877	+	0.707337i	$0.749896\pi$
$68$	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	−0.988014	−	0.154367i	$-0.950666\pi$
$73$	−26.3034	+	45.5589i	−0.360321	+	0.624094i	0.627693	+	0.778461i	$0.283999\pi$
$74$	−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	0.739073	−	0.673626i	$-0.235264\pi$
$79$	−16.8934	−	29.2602i	−0.213840	−	0.370383i	−0.952913	+	0.303243i	$0.901931\pi$
$80$		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	−0.234717	−	0.972064i	$-0.575416\pi$
$89$	43.5883	−	25.1657i	0.489756	−	0.282761i	0.724473	+	0.689303i	$0.242083\pi$
$90$		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	0.221820	−	0.975088i	$-0.428800\pi$
$101$	−51.6838	−	29.8396i	−0.511720	−	0.295442i	−0.733541	+	0.679646i	$0.762134\pi$
$102$	3.30496	+	1.90812i	0.0324015	+	0.0187070i
$103$	60.0890	+	104.077i	0.583388	+	1.01046i	0.995074	+	0.0991322i	$0.0316067\pi$
$103$	60.0890	+	104.077i	0.583388	+	1.01046i	−0.411686	+	0.911326i	$0.635060\pi$
$104$		−	43.2503i		−	0.415868i
$105$		0			0
$106$	79.1543			0.746739
$107$	98.3893	−	56.8051i	0.919526	−	0.530889i	0.0360423	−	0.999350i	$-0.488525\pi$
$107$	98.3893	−	56.8051i	0.919526	−	0.530889i	0.883484	+	0.468462i	$0.155192\pi$
$108$	−12.5446	+	21.7279i	−0.116154	+	0.201184i
$109$	−72.6543	+	125.841i	−0.666553	+	1.15450i	0.312308	+	0.949981i	$0.398898\pi$
$109$	−72.6543	+	125.841i	−0.666553	+	1.15450i	−0.978862	+	0.204524i	$0.934435\pi$
$110$		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	$0.0488452\pi$
$113$			34.5442i			0.305700i	−0.988249	+	0.152850i	$0.951155\pi$
$114$	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	$0.426936\pi$
$127$			247.338i			1.94754i	−0.227526	+	0.973772i	$0.573064\pi$
$128$	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	−0.901079	−	0.433656i	$-0.857223\pi$
$131$	−127.864	+	73.8223i	−0.976061	+	0.563529i	−0.0749822	+	0.997185i	$0.523890\pi$
$132$	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	0.393500	−	0.919325i	$-0.371264\pi$
$137$	−28.2096	−	16.2868i	−0.205909	−	0.118882i	−0.599409	+	0.800443i	$0.704598\pi$
$138$	14.0665	+	24.3640i	0.101931	+	0.176550i
$139$		−	68.5857i		−	0.493422i	−0.969089	−	0.246711i	$-0.920650\pi$
$139$		−	68.5857i		−	0.493422i	0.969089	−	0.246711i	$-0.0793499\pi$
$140$		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	0.978374	−	0.206842i	$-0.0663185\pi$
$149$	46.1985	+	80.0181i	0.310057	+	0.537034i	−0.668317	+	0.743876i	$0.732985\pi$
$150$		0			0
$151$	45.8934	−	79.4897i	0.303930	−	0.526422i	−0.673093	−	0.739558i	$-0.735035\pi$
$151$	45.8934	−	79.4897i	0.303930	−	0.526422i	0.977022	+	0.213136i	$0.0683678\pi$
$152$	−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	−0.852246	−	0.523142i	$-0.824760\pi$
$157$	4.22815	−	7.32338i	0.0269309	−	0.0466457i	0.879177	+	0.476496i	$0.158093\pi$
$158$	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	0.223506	−	0.974703i	$-0.428250\pi$
$163$	192.238	−	110.989i	1.17938	−	0.680913i	0.955870	+	0.293789i	$0.0949164\pi$
$164$	−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	0.524616	−	0.851339i	$-0.324209\pi$
$173$	−82.1704	−	142.323i	−0.474974	−	0.822678i	−0.999589	+	0.0286608i	$0.990876\pi$
$174$			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	−0.482526	−	0.875882i	$-0.660280\pi$
$179$	92.5919	−	160.374i	0.517273	−	0.895943i	0.999799	−	0.0200614i	$-0.00638618\pi$
$180$		0			0
$181$		−	155.086i		−	0.856830i	−0.903582	−	0.428415i	$-0.859072\pi$
$181$		−	155.086i		−	0.856830i	0.903582	−	0.428415i	$-0.140928\pi$
$182$	−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	−0.983251	−	0.182257i	$-0.941660\pi$
$191$	−124.048	−	214.857i	−0.649465	−	1.12491i	0.333786	−	0.942649i	$-0.391674\pi$
$192$	2.86976	−	4.97056i	0.0149466	−	0.0258883i
$193$	−133.661	−	77.1690i	−0.692543	−	0.399840i	0.112021	−	0.993706i	$-0.464268\pi$
$193$	−133.661	−	77.1690i	−0.692543	−	0.399840i	−0.804564	+	0.593866i	$0.797601\pi$
$194$	−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	$0.152026\pi$
$197$			181.103i			0.919303i	−0.888099	+	0.459651i	$0.847974\pi$
$198$	−49.4399	+	28.5442i	−0.249697	+	0.144162i
$199$	−301.989	−	174.353i	−1.51753	−	0.876147i	−0.999788	−	0.0206121i	$-0.993439\pi$
$199$	−301.989	−	174.353i	−1.51753	−	0.876147i	−0.517744	−	0.855535i	$-0.673228\pi$
$200$		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	−0.937797	−	0.347184i	$-0.887138\pi$
$227$	−38.1878	+	66.1432i	−0.168228	+	0.291380i	0.769569	+	0.638564i	$0.220471\pi$
$228$	−5.19615	−	3.00000i	−0.0227901	−	0.0131579i
$229$	−309.419	+	178.643i	−1.35117	+	0.780101i	−0.988414	−	0.151782i	$-0.951499\pi$
$229$	−309.419	+	178.643i	−1.35117	+	0.780101i	−0.362760	+	0.931883i	$0.618166\pi$
$230$		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	−0.912643	−	0.408757i	$-0.865962\pi$
$233$	−236.488	+	136.537i	−1.01497	+	0.585994i	−0.102328	+	0.994751i	$0.532629\pi$
$234$	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	0.334203	−	0.942501i	$-0.391533\pi$
$241$	−75.8970	−	43.8191i	−0.314925	−	0.181822i	−0.649128	+	0.760679i	$0.724866\pi$
$242$	−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	$-0.550663\pi$
$251$		−	495.655i		−	1.97472i	0.158491	−	0.987360i	$-0.449337\pi$
$252$	−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	−0.932372	−	0.361499i	$-0.882265\pi$
$257$	−200.268	−	346.875i	−0.779254	−	1.34971i	0.153119	−	0.988208i	$-0.451068\pi$
$258$	−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	0.552308	−	0.833640i	$-0.313747\pi$
$263$	28.0118	+	16.1726i	0.106509	+	0.0614928i	−0.445799	+	0.895133i	$0.647081\pi$
$264$	−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	0.904749	−	0.425944i	$-0.140058\pi$
$269$	265.838	+	153.482i	0.988246	+	0.570564i	0.0834963	+	0.996508i	$0.473391\pi$
$270$		0			0
$271$	−65.8051	+	37.9926i	−0.242823	+	0.140194i	−0.616474	−	0.787376i	$-0.711439\pi$
$271$	−65.8051	+	37.9926i	−0.242823	+	0.140194i	0.373650	+	0.927570i	$0.378106\pi$
$272$	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	0.867494	−	0.497448i	$-0.165730\pi$
$277$	241.111	+	139.206i	0.870438	+	0.502547i	0.00294398	+	0.999996i	$0.499063\pi$
$278$	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	−0.965881	−	0.258988i	$-0.916611\pi$
$283$	−73.1981	+	126.783i	−0.258650	+	0.447996i	0.707230	+	0.706983i	$0.249944\pi$
$284$	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	0.731565	−	0.681772i	$-0.238790\pi$
$311$	157.651	+	91.0197i	0.506916	+	0.292668i	−0.224649	+	0.974440i	$0.572124\pi$
$312$	26.8723	+	15.5147i	0.0861291	+	0.0497267i
$313$	−48.9643	−	84.8087i	−0.156435	−	0.270954i	0.777145	−	0.629321i	$-0.216667\pi$
$313$	−48.9643	−	84.8087i	−0.156435	−	0.270954i	−0.933581	+	0.358367i	$0.883334\pi$
$314$			11.9590i			0.0380861i
$315$		0			0
$316$	−67.5736			−0.213840
$317$	417.399	−	240.985i	1.31672	−	0.760206i	0.333517	−	0.942744i	$-0.391765\pi$
$317$	417.399	−	240.985i	1.31672	−	0.760206i	0.983199	+	0.182538i	$0.0584314\pi$
$318$	−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	0.644522	−	0.764586i	$-0.277056\pi$
$331$	−112.504	−	194.862i	−0.339890	−	0.588707i	−0.984412	+	0.175879i	$0.943723\pi$
$332$	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	$0.128299\pi$
$337$			264.368i			0.784473i	−0.919864	+	0.392237i	$0.871701\pi$
$338$	−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	0.241973	−	0.970283i	$-0.422205\pi$
$347$	−165.633	−	95.6285i	−0.477330	−	0.275586i	−0.719303	+	0.694697i	$0.755539\pi$
$348$	−2.52160	−	4.36753i	−0.00724597	−	0.0125504i
$349$		−	135.448i		−	0.388104i	−0.980991	−	0.194052i	$-0.937837\pi$
$349$		−	135.448i		−	0.388104i	0.980991	−	0.194052i	$-0.0621630\pi$
$350$		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	−0.506360	−	0.862322i	$-0.669009\pi$
$353$	174.245	−	301.802i	0.493612	−	0.854962i	0.999973	+	0.00736010i	$0.00234281\pi$
$354$	−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	0.996379	−	0.0850256i	$-0.0270972\pi$
$359$	152.415	+	263.991i	0.424555	+	0.735351i	−0.571824	+	0.820377i	$0.693764\pi$
$360$		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	−0.923457	−	0.383701i	$-0.874649\pi$
$367$	−47.5021	+	82.2761i	−0.129434	+	0.224186i	0.794024	+	0.607887i	$0.207983\pi$
$368$	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	−0.175879	−	0.984412i	$-0.556277\pi$
$373$	219.588	−	126.779i	0.588708	−	0.339891i	0.764586	+	0.644521i	$0.222943\pi$
$374$	−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	0.988789	+	0.149320i	$0.0477084\pi$
$383$	238.881	+	413.753i	0.623709	+	1.08030i	−0.365080	+	0.930976i	$0.618958\pi$
$384$			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	−0.735647	−	0.677365i	$-0.763122\pi$
$389$	85.1102	−	147.415i	0.218792	−	0.378959i	0.954439	+	0.298406i	$0.0964550\pi$
$390$		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	0.669927	−	0.742427i	$-0.266325\pi$
$397$	−122.275	−	211.786i	−0.307997	−	0.533467i	−0.977924	+	0.208960i	$0.932992\pi$
$398$	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	0.999711	+	0.0240277i	$0.00764899\pi$
$401$	208.786	+	361.629i	0.520664	+	0.901817i	−0.479047	+	0.877789i	$0.659018\pi$
$402$	−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	0.136843	−	0.990593i	$-0.456304\pi$
$409$	−266.919	−	154.106i	−0.652614	−	0.376787i	−0.789457	+	0.613806i	$0.789638\pi$
$410$		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	$0.0392776\pi$
$419$			103.142i			0.246163i	−0.992397	+	0.123081i	$0.960722\pi$
$420$		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	0.282212	+	0.959352i	$0.408932\pi$
$431$	−297.268	+	514.883i	−0.689717	+	1.19463i	−0.971929	+	0.235273i	$0.924402\pi$
$432$	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	−0.637582	−	0.770383i	$-0.720065\pi$
$439$	−126.959	+	73.3001i	−0.289201	+	0.166971i	0.348380	+	0.937353i	$0.386732\pi$
$440$		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	−0.391376	−	0.920231i	$-0.628001\pi$
$443$	92.9768	−	53.6802i	0.209880	−	0.121174i	0.601256	+	0.799057i	$0.294667\pi$
$444$	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	−0.643656	−	0.765315i	$-0.722583\pi$
$457$	−138.335	+	79.8675i	−0.302702	+	0.174765i	0.340954	+	0.940080i	$0.389250\pi$
$458$	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	$0.109242\pi$
$461$			310.250i			0.672993i	−0.941685	+	0.336497i	$0.890758\pi$
$462$	−1.82784	+	33.7386i	−0.00395636	+	0.0730274i
$463$		−	326.014i		−	0.704135i	−0.935975	−	0.352067i	$-0.885479\pi$
$463$		−	326.014i		−	0.704135i	0.935975	−	0.352067i	$-0.114521\pi$
$464$	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	−0.985949	−	0.167048i	$-0.946576\pi$
$467$	−297.779	−	515.769i	−0.637643	−	1.10443i	0.348306	−	0.937381i	$-0.386757\pi$
$468$	−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	−0.0336914	−	0.999432i	$-0.510726\pi$
$479$	−438.798	−	253.340i	−0.916071	−	0.528894i	−0.882379	+	0.470539i	$0.844060\pi$
$480$		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	0.675970	−	0.736930i	$-0.263725\pi$
$487$	182.992	+	105.651i	0.375755	+	0.216942i	−0.300215	+	0.953872i	$0.597058\pi$
$488$	−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	0.767226	−	0.641377i	$-0.221637\pi$
$499$	−85.7462	−	148.517i	−0.171836	−	0.297629i	−0.939062	+	0.343748i	$0.888303\pi$
$500$		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	−0.0361865	−	0.999345i	$-0.511521\pi$
$509$	412.890	−	238.382i	0.811178	−	0.468334i	0.847365	+	0.531011i	$0.178188\pi$
$510$		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	0.996299	−	0.0859587i	$-0.0273953\pi$
$521$	739.823	+	427.137i	1.42001	+	0.819841i	0.423707	+	0.905799i	$0.360729\pi$
$522$	36.5260	+	21.0883i	0.0699732	+	0.0403991i
$523$	−296.501	−	513.554i	−0.566923	−	0.981940i	−0.996868	−	0.0790845i	$-0.974800\pi$
$523$	−296.501	−	513.554i	−0.566923	−	0.981940i	0.429945	−	0.902855i	$-0.358533\pi$
$524$			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	−0.925732	−	0.378180i	$-0.876550\pi$
$541$	−427.595	−	740.617i	−0.790380	−	1.36898i	0.135352	−	0.990798i	$-0.456783\pi$
$542$	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	$-0.875868\pi$
$547$		−	415.897i		−	0.760323i	0.924920	−	0.380161i	$-0.124132\pi$
$548$	−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	−0.0284485	−	0.999595i	$-0.509057\pi$
$557$	−505.950	−	292.110i	−0.908348	−	0.524435i	−0.879899	+	0.475160i	$0.842390\pi$
$558$	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	0.104237	+	0.994552i	$0.466760\pi$
$563$	−455.573	+	789.076i	−0.809189	+	1.40156i	−0.913426	+	0.407004i	$0.866573\pi$
$564$	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	0.990365	+	0.138485i	$0.0442231\pi$
$569$	350.000	+	606.217i	0.615113	+	1.06541i	−0.375251	+	0.926923i	$0.622444\pi$
$570$		0			0
$571$	281.231	−	487.107i	0.492525	−	0.853077i	−0.507438	−	0.861688i	$-0.669408\pi$
$571$	281.231	−	487.107i	0.492525	−	0.853077i	0.999963	+	0.00861055i	$0.00274086\pi$
$572$	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	0.422856	+	0.906197i	$0.361028\pi$
$577$	−330.830	+	573.014i	−0.573362	+	0.993092i	−0.996218	+	0.0868946i	$0.972306\pi$
$578$	−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	−0.999587	−	0.0287225i	$-0.990856\pi$
$593$	−311.128	−	538.890i	−0.524668	−	0.908752i	0.474919	−	0.880029i	$-0.342477\pi$
$594$		−	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	−0.996703	−	0.0811377i	$-0.974145\pi$
$599$	−256.422	+	444.137i	−0.428084	+	0.741463i	0.568619	+	0.822601i	$0.307478\pi$
$600$		0			0
$601$			680.160i			1.13171i	0.824504	+	0.565857i	$0.191454\pi$
$601$			680.160i			1.13171i	−0.824504	+	0.565857i	$0.808546\pi$
$602$	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	0.849630	−	0.527380i	$-0.176825\pi$
$607$	−19.3690	−	33.5482i	−0.0319095	−	0.0552688i	−0.881539	+	0.472111i	$0.843492\pi$
$608$	−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	0.189151	−	0.981948i	$-0.439426\pi$
$613$	−347.366	−	200.552i	−0.566665	−	0.327164i	−0.755816	+	0.654784i	$0.772760\pi$
$614$	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	$0.283352\pi$
$617$			959.044i			1.55437i	−0.629275	+	0.777183i	$0.716648\pi$
$618$	105.598	−	60.9670i	0.170870	−	0.0986521i
$619$	869.951	+	502.267i	1.40541	+	0.811416i	0.994941	−	0.100457i	$-0.0320303\pi$
$619$	869.951	+	502.267i	1.40541	+	0.811416i	0.410473	+	0.911873i	$0.365364\pi$
$620$		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	−0.161502	−	0.986872i	$-0.551634\pi$
$641$	496.074	−	859.225i	0.773906	−	1.34044i	0.935407	−	0.353572i	$-0.115033\pi$
$642$	−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	−0.864906	−	0.501934i	$-0.832622\pi$
$647$	1.44544	−	2.50357i	0.00223406	−	0.00386951i	0.867140	+	0.498064i	$0.165956\pi$
$648$	−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	−0.698686	−	0.715429i	$-0.746231\pi$
$653$	−279.777	+	161.529i	−0.428449	+	0.247365i	0.270237	+	0.962794i	$0.412898\pi$
$654$	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	0.513532	−	0.858070i	$-0.328337\pi$
$661$	17.9710	+	10.3756i	0.0271876	+	0.0156968i	−0.486345	+	0.873767i	$0.661670\pi$
$662$	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	$0.154254\pi$
$673$			627.044i			0.931714i	−0.884860	+	0.465857i	$0.845746\pi$
$674$	−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	0.903544	−	0.428496i	$-0.140956\pi$
$677$	54.6230	+	94.6097i	0.0806838	+	0.139749i	−0.822860	+	0.568244i	$0.807623\pi$
$678$	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	−0.0961370	−	0.995368i	$-0.530649\pi$
$683$	−687.248	−	396.783i	−1.00622	−	0.580941i	−0.910083	+	0.414427i	$0.863982\pi$
$684$	−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	−0.380320	−	0.924855i	$-0.624186\pi$
$691$	159.253	−	91.9447i	0.230467	−	0.133060i	0.610788	+	0.791794i	$0.290853\pi$
$692$	−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	−0.971344	−	0.237678i	$-0.923614\pi$
$709$	−490.279	−	849.188i	−0.691507	−	1.19773i	0.279836	−	0.960048i	$-0.409720\pi$
$710$		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	0.0484429	−	0.998826i	$-0.484574\pi$
$719$	674.187	−	389.242i	0.937673	−	0.541366i	0.889230	+	0.457460i	$0.151241\pi$
$720$		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	0.655200	−	0.755456i	$-0.272585\pi$
$733$	−239.430	−	414.705i	−0.326644	−	0.565764i	−0.981844	+	0.189692i	$0.939251\pi$
$734$		−	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	−0.872680	−	0.488292i	$-0.837620\pi$
$739$	−9.95227	+	17.2378i	−0.0134672	+	0.0233259i	0.859213	+	0.511618i	$0.170954\pi$
$740$		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	$0.00927847\pi$
$743$			43.3095i			0.0582901i	−0.999575	+	0.0291450i	$0.990722\pi$
$744$	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	0.781215	−	0.624263i	$-0.214600\pi$
$751$	−112.665	−	195.142i	−0.150020	−	0.259842i	−0.931235	+	0.364420i	$0.881267\pi$
$752$	−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	$-0.787909\pi$
$757$		−	935.779i		−	1.23617i	0.786112	−	0.618084i	$-0.212091\pi$
$758$	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	0.604110	−	0.796901i	$-0.293529\pi$
$761$	1214.79	−	701.357i	1.59630	−	0.921625i	0.992191	−	0.124724i	$-0.0398046\pi$
$762$	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	$-0.999643\pi$
$769$		−	1.72330i		−	0.00224097i	0.999999	−	0.00112048i	$-0.000356661\pi$
$770$		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	−0.929394	−	0.369089i	$-0.879670\pi$
$773$	−112.129	+	194.213i	−0.145057	+	0.251245i	0.784337	+	0.620334i	$0.213003\pi$
$774$	−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	−0.842863	−	0.538129i	$-0.819131\pi$
$787$	35.1017	−	60.7979i	0.0446019	−	0.0772528i	0.887465	+	0.460876i	$0.152465\pi$
$788$	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	−0.528041	−	0.849219i	$-0.677073\pi$
$809$	381.382	−	660.573i	0.471424	−	0.816531i	0.999466	+	0.0326879i	$0.0104067\pi$
$810$		0			0
$811$			1214.98i			1.49813i	0.662498	+	0.749064i	$0.269496\pi$
$811$			1214.98i			1.49813i	−0.662498	+	0.749064i	$0.730504\pi$
$812$	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	0.987166	−	0.159700i	$-0.0510527\pi$
$821$	291.684	+	505.211i	0.355279	+	0.615361i	−0.631887	+	0.775061i	$0.717719\pi$
$822$	−16.5248	+	28.6218i	−0.0201031	+	0.0348197i
$823$	−892.648	−	515.371i	−1.08463	−	0.626210i	−0.152486	−	0.988306i	$-0.548728\pi$
$823$	−892.648	−	515.371i	−1.08463	−	0.626210i	−0.932141	+	0.362096i	$0.882061\pi$
$824$	−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	$-0.970687\pi$
$827$		−	152.102i		−	0.183920i	0.995763	−	0.0919599i	$-0.0293132\pi$
$828$	−407.516	+	235.279i	−0.492169	+	0.284154i
$829$	−532.095	−	307.205i	−0.641852	−	0.370573i	0.143476	−	0.989654i	$-0.454172\pi$
$829$	−532.095	−	307.205i	−0.641852	−	0.370573i	−0.785327	+	0.619081i	$0.787505\pi$
$830$		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	$0.372970\pi$
$839$			1546.14i			1.84284i	−0.388568	+	0.921420i	$0.627030\pi$
$840$		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	0.342775	+	0.939417i	$0.388633\pi$
$857$	−550.341	+	953.219i	−0.642172	+	1.11227i	−0.984947	+	0.172857i	$0.944700\pi$
$858$	63.9205	+	36.9045i	0.0744995	+	0.0430123i
$859$	−512.488	+	295.885i	−0.596610	+	0.344453i	−0.767707	−	0.640801i	$-0.778602\pi$
$859$	−512.488	+	295.885i	−0.596610	+	0.344453i	0.171096	+	0.985254i	$0.445269\pi$
$860$		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	−0.532125	−	0.846666i	$-0.678606\pi$
$863$	−56.0553	+	32.3635i	−0.0649540	+	0.0375012i	0.467171	+	0.884167i	$0.345273\pi$
$864$	−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	−0.342231	−	0.939616i	$-0.611182\pi$
$877$	263.438	−	152.096i	0.300385	−	0.173427i	0.642616	+	0.766188i	$0.277849\pi$
$878$	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	$0.163076\pi$
$881$			863.732i			0.980400i	−0.871610	+	0.490200i	$0.836924\pi$
$882$	538.005	−	237.265i	0.609983	−	0.269008i
$883$		−	567.456i		−	0.642645i	−0.946970	−	0.321323i	$-0.895873\pi$
$883$		−	567.456i		−	0.642645i	0.946970	−	0.321323i	$-0.104127\pi$
$884$	−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	0.999998	+	0.00179783i	$0.000572267\pi$
$887$	444.880	+	770.555i	0.501556	+	0.868721i	−0.498442	+	0.866923i	$0.666094\pi$
$888$	−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	0.667800	−	0.744340i	$-0.267236\pi$
$907$	323.874	+	186.989i	0.357083	+	0.206162i	−0.310717	+	0.950502i	$0.600569\pi$
$908$	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	0.963043	−	0.269347i	$-0.0868078\pi$
$919$	228.151	+	395.169i	0.248260	+	0.429999i	−0.714783	+	0.699346i	$0.753475\pi$
$920$		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	0.0140650	−	0.999901i	$-0.495523\pi$
$929$	824.058	−	475.770i	0.887037	−	0.512131i	0.872972	+	0.487770i	$0.162189\pi$
$930$		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	−0.277915	−	0.960606i	$-0.589643\pi$
$941$	−1175.10	−	678.446i	−1.24878	−	0.720984i	−0.970866	+	0.239622i	$0.922977\pi$
$942$	−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	−0.139197	−	0.990265i	$-0.544452\pi$
$947$	614.412	−	354.731i	0.648799	−	0.374584i	0.787996	+	0.615681i	$0.211119\pi$
$948$	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	$0.163514\pi$
$953$			936.603i			0.982794i	−0.870936	+	0.491397i	$0.836486\pi$
$954$	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	$-0.748408\pi$
$967$		−	1374.37i		−	1.42127i	0.703561	−	0.710635i	$-0.251592\pi$
$968$	−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	−0.513965	−	0.857811i	$-0.671824\pi$
$971$	−27.2466	+	15.7309i	−0.0280604	+	0.0162007i	0.485904	+	0.874012i	$0.338490\pi$
$972$	−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	0.240215	−	0.970720i	$-0.422782\pi$
$977$	−469.297	−	270.949i	−0.480345	−	0.277327i	−0.720560	+	0.693392i	$0.756115\pi$
$978$	−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	−0.871671	−	0.490092i	$-0.836963\pi$
$983$	−11.2099	+	19.4161i	−0.0114038	+	0.0197519i	0.860267	+	0.509843i	$0.170297\pi$
$984$	−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	−0.984822	−	0.173568i	$-0.944470\pi$
$991$	−339.017	+	587.195i	−0.342096	+	0.592528i	0.642726	+	0.766097i	$0.277804\pi$
$992$	−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	−0.558244	−	0.829677i	$-0.688525\pi$
$997$	438.081	−	758.779i	0.439400	−	0.761062i	0.997643	+	0.0686147i	$0.0218579\pi$
$998$	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.199.2		8
5.2	odd	4		14.3.d.a.3.1	✓	4
5.3	odd	4		350.3.k.a.101.2		4
5.4	even	2	inner	350.3.i.a.199.3		8
7.5	odd	6	inner	350.3.i.a.299.3		8
15.2	even	4		126.3.n.c.73.2		4
20.7	even	4		112.3.s.b.17.1		4
35.2	odd	12		98.3.d.a.19.1		4
35.12	even	12		14.3.d.a.5.1	yes	4
35.17	even	12		98.3.b.b.97.4		4
35.19	odd	6	inner	350.3.i.a.299.2		8
35.27	even	4		98.3.d.a.31.1		4
35.32	odd	12		98.3.b.b.97.3		4
35.33	even	12		350.3.k.a.201.2		4
40.27	even	4		448.3.s.c.129.2		4
40.37	odd	4		448.3.s.d.129.1		4
60.47	odd	4		1008.3.cg.l.577.2		4
105.2	even	12		882.3.n.b.19.2		4
105.17	odd	12		882.3.c.f.685.1		4
105.32	even	12		882.3.c.f.685.2		4
105.47	odd	12		126.3.n.c.19.2		4
105.62	odd	4		882.3.n.b.325.2		4
140.27	odd	4		784.3.s.c.129.2		4
140.47	odd	12		112.3.s.b.33.1		4
140.67	even	12		784.3.c.e.97.3		4
140.87	odd	12		784.3.c.e.97.2		4
140.107	even	12		784.3.s.c.705.2		4
280.117	even	12		448.3.s.d.257.1		4
280.187	odd	12		448.3.s.c.257.2		4
420.47	even	12		1008.3.cg.l.145.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.3.d.a.3.1	✓	4	5.2	odd	4
14.3.d.a.5.1	yes	4	35.12	even	12
98.3.b.b.97.3		4	35.32	odd	12
98.3.b.b.97.4		4	35.17	even	12
98.3.d.a.19.1		4	35.2	odd	12
98.3.d.a.31.1		4	35.27	even	4
112.3.s.b.17.1		4	20.7	even	4
112.3.s.b.33.1		4	140.47	odd	12
126.3.n.c.19.2		4	105.47	odd	12
126.3.n.c.73.2		4	15.2	even	4
350.3.i.a.199.2		8	1.1	even	1	trivial
350.3.i.a.199.3		8	5.4	even	2	inner
350.3.i.a.299.2		8	35.19	odd	6	inner
350.3.i.a.299.3		8	7.5	odd	6	inner
350.3.k.a.101.2		4	5.3	odd	4
350.3.k.a.201.2		4	35.33	even	12
448.3.s.c.129.2		4	40.27	even	4
448.3.s.c.257.2		4	280.187	odd	12
448.3.s.d.129.1		4	40.37	odd	4
448.3.s.d.257.1		4	280.117	even	12
784.3.c.e.97.2		4	140.87	odd	12
784.3.c.e.97.3		4	140.67	even	12
784.3.s.c.129.2		4	140.27	odd	4
784.3.s.c.705.2		4	140.107	even	12
882.3.c.f.685.1		4	105.17	odd	12
882.3.c.f.685.2		4	105.32	even	12
882.3.n.b.19.2		4	105.2	even	12
882.3.n.b.325.2		4	105.62	odd	4
1008.3.cg.l.145.2		4	420.47	even	12
1008.3.cg.l.577.2		4	60.47	odd	4

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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.358719 + 0.621320i) q^{3} +(1.00000 - 1.73205i) q^{4} -1.01461i q^{6} +(-3.16693 - 6.24264i) q^{7} +2.82843i q^{8} +(4.24264 + 7.34847i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4}+O(q^{10}) \) 8 * q + 8 * q^4	\( 8 q + 8 q^{4} + 36 q^{11} + 72 q^{14} - 16 q^{16} - 12 q^{19} + 108 q^{21} - 48 q^{24} + 48 q^{26} - 96 q^{29} - 84 q^{31} - 24 q^{39} - 72 q^{44} + 72 q^{46} + 40 q^{49} + 108 q^{51} + 72 q^{54} + 96 q^{56} + 156 q^{59} - 84 q^{61} - 64 q^{64} - 288 q^{66} - 48 q^{71} - 192 q^{74} - 220 q^{79} + 36 q^{81} - 24 q^{84} + 48 q^{86} + 756 q^{89} + 48 q^{91} + 24 q^{94} - 96 q^{96} - 288 q^{99}+O(q^{100}) \) 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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