LMFDB - Embedded newform 1050.3.q.d.199.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(199,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("1050.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.q (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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.10
Character	$\chi$	$=$	1050.199
Dual form			1050.3.q.d.649.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-0.264136 - 6.99501i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-0.264136 - 6.99501i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(2.03457 - 3.52398i) q^{11} +(1.73205 + 3.00000i) q^{12} -11.1199 q^{13} +(-5.26972 - 8.38034i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-1.44803 + 2.50807i) q^{17} +(-3.67423 - 2.12132i) q^{18} +(-17.9363 + 10.3556i) q^{19} +(10.7213 + 5.66166i) q^{21} -5.75463i q^{22} +(-26.5348 + 15.3199i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-13.6190 + 7.86292i) q^{26} +5.19615 q^{27} +(-12.3799 - 6.53752i) q^{28} +5.75463 q^{29} +(3.32136 + 1.91759i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(3.52398 + 6.10371i) q^{33} +4.09566i q^{34} -6.00000 q^{36} +(7.72755 - 4.46151i) q^{37} +(-14.6450 + 25.3658i) q^{38} +(9.63007 - 16.6798i) q^{39} +56.2622i q^{41} +(17.1342 - 0.646999i) q^{42} +7.16364i q^{43} +(-4.06914 - 7.04796i) q^{44} +(-21.6656 + 37.5258i) q^{46} +(-23.8028 - 41.2277i) q^{47} +6.92820 q^{48} +(-48.8605 + 3.69527i) q^{49} +(-2.50807 - 4.34410i) q^{51} +(-11.1199 + 19.2601i) q^{52} +(-28.8610 - 16.6629i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-19.7849 + 0.747090i) q^{56} -35.8727i q^{57} +(7.04796 - 4.06914i) q^{58} +(38.3489 + 22.1407i) q^{59} +(-60.3282 + 34.8305i) q^{61} +5.42375 q^{62} +(-17.7774 + 11.1788i) q^{63} -8.00000 q^{64} +(8.63195 + 4.98366i) q^{66} +(-79.7722 - 46.0565i) q^{67} +(2.89607 + 5.01614i) q^{68} -53.0695i q^{69} +6.64679 q^{71} +(-7.34847 + 4.24264i) q^{72} +(-26.2108 + 45.3984i) q^{73} +(6.30952 - 10.9284i) q^{74} +41.4222i q^{76} +(-25.1877 - 13.3010i) q^{77} -27.2380i q^{78} +(-26.7215 - 46.2830i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(39.7834 + 68.9069i) q^{82} -116.101 q^{83} +(20.5275 - 12.9081i) q^{84} +(5.06546 + 8.77363i) q^{86} +(-4.98366 + 8.63195i) q^{87} +(-9.96732 - 5.75463i) q^{88} +(85.6511 - 49.4507i) q^{89} +(2.93716 + 77.7835i) q^{91} +61.2794i q^{92} +(-5.75276 + 3.32136i) q^{93} +(-58.3047 - 33.6623i) q^{94} +(8.48528 - 4.89898i) q^{96} -132.963 q^{97} +(-57.2286 + 39.0753i) q^{98} -12.2074 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4} - 36 q^{9}+O(q^{10}) $ 24 * q + 24 * q^4 - 36 * q^9	$ 24 q + 24 q^{4} - 36 q^{9} - 8 q^{11} - 16 q^{14} - 48 q^{16} - 24 q^{19} + 36 q^{21} - 48 q^{26} + 48 q^{29} - 396 q^{31} - 144 q^{36} + 72 q^{39} + 16 q^{44} + 64 q^{46} - 56 q^{49} - 48 q^{51} + 80 q^{56} + 96 q^{59} + 372 q^{61} - 192 q^{64} + 72 q^{66} - 272 q^{71} + 128 q^{74} + 140 q^{79} - 108 q^{81} + 24 q^{84} - 416 q^{86} - 336 q^{89} + 584 q^{91} + 408 q^{94} + 48 q^{99}+O(q^{100}) $ 24 * q + 24 * q^4 - 36 * q^9 - 8 * q^11 - 16 * q^14 - 48 * q^16 - 24 * q^19 + 36 * q^21 - 48 * q^26 + 48 * q^29 - 396 * q^31 - 144 * q^36 + 72 * q^39 + 16 * q^44 + 64 * q^46 - 56 * q^49 - 48 * q^51 + 80 * q^56 + 96 * q^59 + 372 * q^61 - 192 * q^64 + 72 * q^66 - 272 * q^71 + 128 * q^74 + 140 * q^79 - 108 * q^81 + 24 * q^84 - 416 * q^86 - 336 * q^89 + 584 * q^91 + 408 * q^94 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	−0.866025	+	1.50000i	−0.288675	+	0.500000i
$3$	−0.866025	+	1.50000i	−0.288675	+	0.500000i
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$			2.44949i			0.408248i
$7$	−0.264136	−	6.99501i	−0.0377338	−	0.999288i
$7$	−0.264136	−	6.99501i	−0.0377338	−	0.999288i
$8$		−	2.82843i		−	0.353553i
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$		0			0
$11$	2.03457	−	3.52398i	0.184961	−	0.320362i	−0.758602	−	0.651554i	$-0.774117\pi$
$11$	2.03457	−	3.52398i	0.184961	−	0.320362i	0.943563	+	0.331192i	$0.107451\pi$
$12$	1.73205	+	3.00000i	0.144338	+	0.250000i
$13$	−11.1199			−0.855373			−0.427687	−	0.903927i	$-0.640671\pi$
$13$	−11.1199			−0.855373			−0.427687	+	0.903927i	$0.640671\pi$
$14$	−5.26972	−	8.38034i	−0.376409	−	0.598595i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−1.44803	+	2.50807i	−0.0851785	+	0.147534i	−0.905467	−	0.424416i	$-0.860479\pi$
$17$	−1.44803	+	2.50807i	−0.0851785	+	0.147534i	0.820289	+	0.571950i	$0.193813\pi$
$18$	−3.67423	−	2.12132i	−0.204124	−	0.117851i
$19$	−17.9363	+	10.3556i	−0.944018	+	0.545029i	−0.891218	−	0.453576i	$-0.850148\pi$
$19$	−17.9363	+	10.3556i	−0.944018	+	0.545029i	−0.0528007	+	0.998605i	$0.516815\pi$
$20$		0			0
$21$	10.7213	+	5.66166i	0.510537	+	0.269603i
$22$		−	5.75463i		−	0.261574i
$23$	−26.5348	+	15.3199i	−1.15369	+	0.666081i	−0.949783	−	0.312910i	$-0.898696\pi$
$23$	−26.5348	+	15.3199i	−1.15369	+	0.666081i	−0.203903	+	0.978991i	$0.565363\pi$
$24$	4.24264	+	2.44949i	0.176777	+	0.102062i
$25$		0			0
$26$	−13.6190	+	7.86292i	−0.523807	+	0.302420i
$27$	5.19615			0.192450
$28$	−12.3799	−	6.53752i	−0.442138	−	0.233483i
$29$	5.75463			0.198436			0.0992178	−	0.995066i	$-0.468366\pi$
$29$	5.75463			0.198436			0.0992178	+	0.995066i	$0.468366\pi$
$30$		0			0
$31$	3.32136	+	1.91759i	0.107141	+	0.0618576i	0.552613	−	0.833438i	$-0.313631\pi$
$31$	3.32136	+	1.91759i	0.107141	+	0.0618576i	−0.445472	+	0.895296i	$0.646964\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$	3.52398	+	6.10371i	0.106787	+	0.184961i
$34$			4.09566i			0.120461i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	7.72755	−	4.46151i	0.208853	−	0.120581i	−0.391925	−	0.919997i	$-0.628191\pi$
$37$	7.72755	−	4.46151i	0.208853	−	0.120581i	0.600778	+	0.799416i	$0.294858\pi$
$38$	−14.6450	+	25.3658i	−0.385394	+	0.667522i
$39$	9.63007	−	16.6798i	0.246925	−	0.427687i
$40$		0			0
$41$			56.2622i			1.37225i	0.727484	+	0.686125i	$0.240689\pi$
$41$			56.2622i			1.37225i	−0.727484	+	0.686125i	$0.759311\pi$
$42$	17.1342	−	0.646999i	0.407958	−	0.0154047i
$43$			7.16364i			0.166596i	0.996525	+	0.0832982i	$0.0265454\pi$
$43$			7.16364i			0.166596i	−0.996525	+	0.0832982i	$0.973455\pi$
$44$	−4.06914	−	7.04796i	−0.0924805	−	0.160181i
$45$		0			0
$46$	−21.6656	+	37.5258i	−0.470990	+	0.815779i
$47$	−23.8028	−	41.2277i	−0.506443	−	0.877184i	−0.999972	−	0.00745542i	$-0.997627\pi$
$47$	−23.8028	−	41.2277i	−0.506443	−	0.877184i	0.493530	−	0.869729i	$-0.335706\pi$
$48$	6.92820			0.144338
$49$	−48.8605	+	3.69527i	−0.997152	+	0.0754138i
$50$		0			0
$51$	−2.50807	−	4.34410i	−0.0491778	−	0.0851785i
$52$	−11.1199	+	19.2601i	−0.213843	+	0.370387i
$53$	−28.8610	−	16.6629i	−0.544548	−	0.314395i	0.202372	−	0.979309i	$-0.435135\pi$
$53$	−28.8610	−	16.6629i	−0.544548	−	0.314395i	−0.746920	+	0.664914i	$0.768468\pi$
$54$	6.36396	−	3.67423i	0.117851	−	0.0680414i
$55$		0			0
$56$	−19.7849	+	0.747090i	−0.353302	+	0.0133409i
$57$		−	35.8727i		−	0.629346i
$58$	7.04796	−	4.06914i	0.121517	−	0.0701576i
$59$	38.3489	+	22.1407i	0.649981	+	0.375267i	0.788449	−	0.615100i	$-0.210884\pi$
$59$	38.3489	+	22.1407i	0.649981	+	0.375267i	−0.138468	+	0.990367i	$0.544218\pi$
$60$		0			0
$61$	−60.3282	+	34.8305i	−0.988987	+	0.570992i	−0.904971	−	0.425472i	$-0.860108\pi$
$61$	−60.3282	+	34.8305i	−0.988987	+	0.570992i	−0.0840158	+	0.996464i	$0.526775\pi$
$62$	5.42375			0.0874799
$63$	−17.7774	+	11.1788i	−0.282181	+	0.177441i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	8.63195	+	4.98366i	0.130787	+	0.0755100i
$67$	−79.7722	−	46.0565i	−1.19063	−	0.687410i	−0.232180	−	0.972673i	$-0.574586\pi$
$67$	−79.7722	−	46.0565i	−1.19063	−	0.687410i	−0.958449	+	0.285263i	$0.907919\pi$
$68$	2.89607	+	5.01614i	0.0425893	+	0.0737668i
$69$		−	53.0695i		−	0.769124i
$70$		0			0
$71$	6.64679			0.0936168			0.0468084	−	0.998904i	$-0.485095\pi$
$71$	6.64679			0.0936168			0.0468084	+	0.998904i	$0.485095\pi$
$72$	−7.34847	+	4.24264i	−0.102062	+	0.0589256i
$73$	−26.2108	+	45.3984i	−0.359052	+	0.621896i	−0.987803	−	0.155711i	$-0.950233\pi$
$73$	−26.2108	+	45.3984i	−0.359052	+	0.621896i	0.628751	+	0.777607i	$0.283566\pi$
$74$	6.30952	−	10.9284i	0.0852638	−	0.147681i
$75$		0			0
$76$			41.4222i			0.545029i
$77$	−25.1877	−	13.3010i	−0.327113	−	0.172741i
$78$		−	27.2380i		−	0.349205i
$79$	−26.7215	−	46.2830i	−0.338247	−	0.585861i	0.645856	−	0.763459i	$-0.276501\pi$
$79$	−26.7215	−	46.2830i	−0.338247	−	0.585861i	−0.984103	+	0.177598i	$0.943167\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	39.7834	+	68.9069i	0.485163	+	0.840327i
$83$	−116.101			−1.39880			−0.699402	−	0.714729i	$-0.746550\pi$
$83$	−116.101			−1.39880			−0.699402	+	0.714729i	$0.746550\pi$
$84$	20.5275	−	12.9081i	0.244376	−	0.153668i
$85$		0			0
$86$	5.06546	+	8.77363i	0.0589007	+	0.102019i
$87$	−4.98366	+	8.63195i	−0.0572834	+	0.0992178i
$88$	−9.96732	−	5.75463i	−0.113265	−	0.0653936i
$89$	85.6511	−	49.4507i	0.962372	−	0.555626i	0.0654695	−	0.997855i	$-0.479145\pi$
$89$	85.6511	−	49.4507i	0.962372	−	0.555626i	0.896902	+	0.442229i	$0.145812\pi$
$90$		0			0
$91$	2.93716	+	77.7835i	0.0322764	+	0.854764i
$92$			61.2794i			0.666081i
$93$	−5.75276	+	3.32136i	−0.0618576	+	0.0357135i
$94$	−58.3047	−	33.6623i	−0.620263	−	0.358109i
$95$		0			0
$96$	8.48528	−	4.89898i	0.0883883	−	0.0510310i
$97$	−132.963			−1.37075			−0.685377	−	0.728189i	$-0.740362\pi$
$97$	−132.963			−1.37075			−0.685377	+	0.728189i	$0.740362\pi$
$98$	−57.2286	+	39.0753i	−0.583966	+	0.398728i
$99$	−12.2074			−0.123307
$100$		0			0
$101$	−52.3294	−	30.2124i	−0.518113	−	0.299133i	0.218049	−	0.975938i	$-0.430031\pi$
$101$	−52.3294	−	30.2124i	−0.518113	−	0.299133i	−0.736162	+	0.676805i	$0.763364\pi$
$102$	−6.14349	−	3.54695i	−0.0602303	−	0.0347740i
$103$	15.6572	+	27.1191i	0.152012	+	0.263293i	0.931967	−	0.362543i	$-0.118091\pi$
$103$	15.6572	+	27.1191i	0.152012	+	0.263293i	−0.779955	+	0.625836i	$0.784758\pi$
$104$			31.4517i			0.302420i
$105$		0			0
$106$	−47.1299			−0.444622
$107$	−40.7378	+	23.5200i	−0.380727	+	0.219813i	−0.678135	−	0.734938i	$-0.737211\pi$
$107$	−40.7378	+	23.5200i	−0.380727	+	0.219813i	0.297407	+	0.954751i	$0.403878\pi$
$108$	5.19615	−	9.00000i	0.0481125	−	0.0833333i
$109$	100.779	−	174.554i	0.924576	−	1.60141i	0.132335	−	0.991205i	$-0.457753\pi$
$109$	100.779	−	174.554i	0.924576	−	1.60141i	0.792242	−	0.610208i	$-0.208914\pi$
$110$		0			0
$111$			15.4551i			0.139235i
$112$	−23.7032	+	14.9050i	−0.211635	+	0.133081i
$113$		−	168.422i		−	1.49046i	−0.666807	−	0.745230i	$-0.732339\pi$
$113$		−	168.422i		−	1.49046i	0.666807	−	0.745230i	$-0.267661\pi$
$114$	−25.3658	−	43.9349i	−0.222507	−	0.385394i
$115$		0			0
$116$	5.75463	−	9.96732i	0.0496089	−	0.0859252i
$117$	16.6798	+	28.8902i	0.142562	+	0.246925i
$118$	62.6234			0.530707
$119$	17.9265	+	9.46655i	0.150643	+	0.0795509i
$120$		0			0
$121$	52.2210	+	90.4495i	0.431579	+	0.747517i
$122$	−49.2578	+	85.3170i	−0.403752	+	0.699320i
$123$	−84.3933	−	48.7245i	−0.686125	−	0.396134i
$124$	6.64271	−	3.83517i	0.0535703	−	0.0309288i
$125$		0			0
$126$	−13.8682	+	26.2616i	−0.110065	+	0.208426i
$127$		−	29.1799i		−	0.229763i	−0.993379	−	0.114882i	$-0.963351\pi$
$127$		−	29.1799i		−	0.229763i	0.993379	−	0.114882i	$-0.0366489\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$	−10.7455	−	6.20390i	−0.0832982	−	0.0480922i
$130$		0			0
$131$	123.441	−	71.2688i	0.942299	−	0.544037i	0.0516187	−	0.998667i	$-0.483562\pi$
$131$	123.441	−	71.2688i	0.942299	−	0.544037i	0.890680	+	0.454630i	$0.150229\pi$
$132$	14.0959			0.106787
$133$	77.1749	+	122.730i	0.580262	+	0.922780i
$134$	−130.267			−0.972145
$135$		0			0
$136$	7.09389	+	4.09566i	0.0521610	+	0.0301152i
$137$	−180.648	−	104.297i	−1.31860	−	0.761295i	−0.335098	−	0.942183i	$-0.608769\pi$
$137$	−180.648	−	104.297i	−1.31860	−	0.761295i	−0.983504	+	0.180889i	$0.942103\pi$
$138$	−37.5258	−	64.9967i	−0.271926	−	0.470990i
$139$			152.491i			1.09706i	0.836132	+	0.548528i	$0.184812\pi$
$139$			152.491i			1.09706i	−0.836132	+	0.548528i	$0.815188\pi$
$140$		0			0
$141$	82.4553			0.584790
$142$	8.14062	−	4.69999i	0.0573283	−	0.0330985i
$143$	−22.6241	+	39.1861i	−0.158211	+	0.274029i
$144$	−6.00000	+	10.3923i	−0.0416667	+	0.0721688i
$145$		0			0
$146$			74.1353i			0.507776i
$147$	36.7715	−	76.4909i	0.250146	−	0.520346i
$148$		−	17.8460i		−	0.120581i
$149$	68.2572	+	118.225i	0.458102	+	0.793456i	0.998861	−	0.0477221i	$-0.0151962\pi$
$149$	68.2572	+	118.225i	0.458102	+	0.793456i	−0.540759	+	0.841178i	$0.681863\pi$
$150$		0			0
$151$	−64.7993	+	112.236i	−0.429134	+	0.743282i	−0.996797	−	0.0799793i	$-0.974515\pi$
$151$	−64.7993	+	112.236i	−0.429134	+	0.743282i	0.567662	+	0.823261i	$0.307848\pi$
$152$	29.2899	+	50.7317i	0.192697	+	0.333761i
$153$	8.68821			0.0567857
$154$	−40.2538	+	1.52001i	−0.261388	+	0.00987018i
$155$		0			0
$156$	−19.2601	−	33.3596i	−0.123462	−	0.213843i
$157$	67.1273	−	116.268i	0.427562	−	0.740560i	−0.569094	−	0.822273i	$-0.692706\pi$
$157$	67.1273	−	116.268i	0.427562	−	0.740560i	0.996656	+	0.0817131i	$0.0260391\pi$
$158$	−65.4540	−	37.7899i	−0.414266	−	0.239177i
$159$	49.9888	−	28.8610i	0.314395	−	0.181516i
$160$		0			0
$161$	114.171	+	181.565i	0.709139	+	1.12773i
$162$			12.7279i			0.0785674i
$163$	139.972	−	80.8126i	0.858721	−	0.495783i	−0.00486254	−	0.999988i	$-0.501548\pi$
$163$	139.972	−	80.8126i	0.858721	−	0.495783i	0.863584	+	0.504205i	$0.168214\pi$
$164$	97.4490	+	56.2622i	0.594201	+	0.343062i
$165$		0			0
$166$	−142.194	+	82.0956i	−0.856589	+	0.494552i
$167$	−166.987			−0.999920			−0.499960	−	0.866049i	$-0.666652\pi$
$167$	−166.987			−0.999920			−0.499960	+	0.866049i	$0.666652\pi$
$168$	16.0136	−	30.3243i	0.0953189	−	0.180502i
$169$	−45.3489			−0.268337
$170$		0			0
$171$	53.8090	+	31.0667i	0.314673	+	0.181676i
$172$	12.4078	+	7.16364i	0.0721383	+	0.0416491i
$173$	−5.84719	−	10.1276i	−0.0337988	−	0.0585412i	0.848631	−	0.528985i	$-0.177427\pi$
$173$	−5.84719	−	10.1276i	−0.0337988	−	0.0585412i	−0.882430	+	0.470444i	$0.844094\pi$
$174$			14.0959i			0.0810110i
$175$		0			0
$176$	−16.2766			−0.0924805
$177$	−66.4222	+	38.3489i	−0.375267	+	0.216660i
$178$	69.9338	−	121.129i	0.392887	−	0.680500i
$179$	66.8799	−	115.839i	0.373631	−	0.647147i	−0.616490	−	0.787363i	$-0.711446\pi$
$179$	66.8799	−	115.839i	0.373631	−	0.647147i	0.990121	+	0.140215i	$0.0447794\pi$
$180$		0			0
$181$			113.035i			0.624501i	0.950000	+	0.312251i	$0.101083\pi$
$181$			113.035i			0.624501i	−0.950000	+	0.312251i	$0.898917\pi$
$182$	58.5985	+	93.1881i	0.321970	+	0.512022i
$183$		−	120.656i		−	0.659325i
$184$	43.3311	+	75.0517i	0.235495	+	0.407890i
$185$		0			0
$186$	−4.69711	+	8.13563i	−0.0252533	+	0.0437399i
$187$	5.89226	+	10.2057i	0.0315094	+	0.0545759i
$188$	−95.2112			−0.506443
$189$	−1.37249	−	36.3472i	−0.00726187	−	0.192313i
$190$		0			0
$191$	−125.518	−	217.404i	−0.657163	−	1.13824i	−0.981347	−	0.192245i	$-0.938423\pi$
$191$	−125.518	−	217.404i	−0.657163	−	1.13824i	0.324184	−	0.945994i	$-0.394910\pi$
$192$	6.92820	−	12.0000i	0.0360844	−	0.0625000i
$193$	309.163	+	178.495i	1.60188	+	0.924846i	0.991111	+	0.133038i	$0.0424731\pi$
$193$	309.163	+	178.495i	1.60188	+	0.924846i	0.610769	+	0.791809i	$0.290860\pi$
$194$	−162.846	+	94.0191i	−0.839412	+	0.484635i
$195$		0			0
$196$	−42.4601	+	88.3241i	−0.216633	+	0.450633i
$197$			35.1268i			0.178309i	0.996018	+	0.0891543i	$0.0284164\pi$
$197$			35.1268i			0.178309i	−0.996018	+	0.0891543i	$0.971584\pi$
$198$	−14.9510	+	8.63195i	−0.0755100	+	0.0435957i
$199$	79.3368	+	45.8051i	0.398677	+	0.230177i	0.685913	−	0.727683i	$-0.259403\pi$
$199$	79.3368	+	45.8051i	0.398677	+	0.230177i	−0.287236	+	0.957860i	$0.592736\pi$
$200$		0			0
$201$	138.169	−	79.7722i	0.687410	−	0.396876i
$202$	−85.4536			−0.423038
$203$	−1.52001	−	40.2538i	−0.00748772	−	0.198294i
$204$	−10.0323			−0.0491778
$205$		0			0
$206$	38.3523	+	22.1427i	0.186176	+	0.107489i
$207$	79.6043	+	45.9596i	0.384562	+	0.222027i
$208$	22.2397	+	38.5203i	0.106922	+	0.185194i
$209$			84.2764i			0.403237i
$210$		0			0
$211$	8.70268			0.0412449			0.0206225	−	0.999787i	$-0.493435\pi$
$211$	8.70268			0.0412449			0.0206225	+	0.999787i	$0.493435\pi$
$212$	−57.7221	+	33.3259i	−0.272274	+	0.157197i
$213$	−5.75629	+	9.97019i	−0.0270248	+	0.0468084i
$214$	−33.2623	+	57.6120i	−0.155431	+	0.269215i
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	12.5363	−	23.7394i	0.0577708	−	0.109398i
$218$		−	285.045i		−	1.30755i
$219$	−45.3984	−	78.6323i	−0.207299	−	0.359052i
$220$		0			0
$221$	16.1019	−	27.8894i	0.0728594	−	0.126196i
$222$	10.9284	+	18.9286i	0.0492271	+	0.0852638i
$223$	158.414			0.710375			0.355187	−	0.934795i	$-0.384417\pi$
$223$	158.414			0.710375			0.355187	+	0.934795i	$0.384417\pi$
$224$	−18.4909	+	35.0155i	−0.0825486	+	0.156319i
$225$		0			0
$226$	−119.092	−	206.274i	−0.526957	−	0.912717i
$227$	198.211	−	343.311i	0.873176	−	1.51239i	0.0144830	−	0.999895i	$-0.495390\pi$
$227$	198.211	−	343.311i	0.873176	−	1.51239i	0.858693	−	0.512490i	$-0.171277\pi$
$228$	−62.1333	−	35.8727i	−0.272515	−	0.157336i
$229$	−178.548	+	103.085i	−0.779685	+	0.450151i	−0.836319	−	0.548244i	$-0.815297\pi$
$229$	−178.548	+	103.085i	−0.779685	+	0.450151i	0.0566339	+	0.998395i	$0.481963\pi$
$230$		0			0
$231$	41.7647	−	26.2625i	0.180800	−	0.113690i
$232$		−	16.2766i		−	0.0701576i
$233$	−96.3981	+	55.6555i	−0.413726	+	0.238865i	−0.692389	−	0.721524i	$-0.743442\pi$
$233$	−96.3981	+	55.6555i	−0.413726	+	0.238865i	0.278664	+	0.960389i	$0.410109\pi$
$234$	40.8569	+	23.5888i	0.174602	+	0.100807i
$235$		0			0
$236$	76.6977	−	44.2815i	0.324990	−	0.187633i
$237$	92.5660			0.390574
$238$	28.6492	−	1.08181i	0.120375	−	0.00454543i
$239$	258.839			1.08301			0.541504	−	0.840698i	$-0.317855\pi$
$239$	258.839			1.08301			0.541504	+	0.840698i	$0.317855\pi$
$240$		0			0
$241$	264.996	+	152.995i	1.09957	+	0.634835i	0.936107	−	0.351715i	$-0.114401\pi$
$241$	264.996	+	152.995i	1.09957	+	0.634835i	0.163460	+	0.986550i	$0.447735\pi$
$242$	127.915	+	73.8517i	0.528574	+	0.305172i
$243$	−7.79423	−	13.5000i	−0.0320750	−	0.0555556i
$244$			139.322i			0.570992i
$245$		0			0
$246$	−137.814			−0.560218
$247$	199.450	−	115.152i	0.807488	−	0.466203i
$248$	5.42375	−	9.39422i	0.0218700	−	0.0378799i
$249$	100.546	−	174.151i	0.403800	−	0.699402i
$250$		0			0
$251$		−	415.878i		−	1.65688i	−0.560076	−	0.828441i	$-0.689228\pi$
$251$		−	415.878i		−	1.65688i	0.560076	−	0.828441i	$-0.310772\pi$
$252$	1.58482	+	41.9701i	0.00628896	+	0.166548i
$253$			124.677i			0.492796i
$254$	−20.6333	−	35.7380i	−0.0812336	−	0.140701i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	156.624	+	271.280i	0.609430	+	1.05556i	0.991334	+	0.131362i	$0.0419350\pi$
$257$	156.624	+	271.280i	0.609430	+	1.05556i	−0.381904	+	0.924202i	$0.624732\pi$
$258$	−17.5473			−0.0680127
$259$	−33.2494	−	52.8759i	−0.128376	−	0.204154i
$260$		0			0
$261$	−8.63195	−	14.9510i	−0.0330726	−	0.0572834i
$262$	100.789	−	174.572i	0.384692	−	0.666306i
$263$	−76.6921	−	44.2782i	−0.291605	−	0.168358i	0.347061	−	0.937843i	$-0.387180\pi$
$263$	−76.6921	−	44.2782i	−0.291605	−	0.168358i	−0.638665	+	0.769485i	$0.720513\pi$
$264$	17.2639	−	9.96732i	0.0653936	−	0.0377550i
$265$		0			0
$266$	181.303	+	95.7417i	0.681589	+	0.359931i
$267$			171.302i			0.641581i
$268$	−159.544	+	92.1130i	−0.595315	+	0.343705i
$269$	70.7545	+	40.8501i	0.263028	+	0.151859i	0.625715	−	0.780052i	$-0.284807\pi$
$269$	70.7545	+	40.8501i	0.263028	+	0.151859i	−0.362687	+	0.931911i	$0.618141\pi$
$270$		0			0
$271$	254.904	−	147.169i	0.940604	−	0.543058i	0.0504543	−	0.998726i	$-0.483933\pi$
$271$	254.904	−	147.169i	0.940604	−	0.543058i	0.890150	+	0.455668i	$0.150600\pi$
$272$	11.5843			0.0425893
$273$	−119.219	−	62.9568i	−0.436699	−	0.230611i
$274$	−294.998			−1.07663
$275$		0			0
$276$	−91.9192	−	53.0695i	−0.333040	−	0.192281i
$277$	−351.817	−	203.122i	−1.27010	−	0.733292i	−0.295092	−	0.955469i	$-0.595350\pi$
$277$	−351.817	−	203.122i	−1.27010	−	0.733292i	−0.975006	+	0.222177i	$0.928684\pi$
$278$	107.827	+	186.762i	0.387868	+	0.671807i
$279$		−	11.5055i		−	0.0412384i
$280$		0			0
$281$	−234.304			−0.833823			−0.416912	−	0.908947i	$-0.636888\pi$
$281$	−234.304			−0.833823			−0.416912	+	0.908947i	$0.636888\pi$
$282$	100.987	−	58.3047i	0.358109	−	0.206754i
$283$	−137.164	+	237.575i	−0.484678	+	0.839488i	−0.999845	−	0.0176023i	$-0.994397\pi$
$283$	−137.164	+	237.575i	−0.484678	+	0.839488i	0.515167	+	0.857090i	$0.327730\pi$
$284$	6.64679	−	11.5126i	0.0234042	−	0.0405372i
$285$		0			0
$286$			63.9907i			0.223744i
$287$	393.555	−	14.8609i	1.37127	−	0.0517801i
$288$			16.9706i			0.0589256i
$289$	140.306	+	243.018i	0.485489	+	0.840892i
$290$		0			0
$291$	115.149	−	199.445i	0.395702	−	0.685377i
$292$	52.4215	+	90.7968i	0.179526	+	0.310948i
$293$	64.7274			0.220913			0.110456	−	0.993881i	$-0.464769\pi$
$293$	64.7274			0.220913			0.110456	+	0.993881i	$0.464769\pi$
$294$	−9.05154	−	119.683i	−0.0307875	−	0.407086i
$295$		0			0
$296$	−12.6190	−	21.8568i	−0.0426319	−	0.0738406i
$297$	10.5719	−	18.3111i	0.0355958	−	0.0616537i
$298$	167.195	+	96.5302i	0.561058	+	0.323927i
$299$	295.063	−	170.355i	0.986832	−	0.569748i
$300$		0			0
$301$	50.1098	−	1.89218i	0.166478	−	0.00628631i
$302$			183.280i			0.606887i
$303$	90.6372	−	52.3294i	0.299133	−	0.172704i
$304$	71.7454	+	41.4222i	0.236005	+	0.136257i
$305$		0			0
$306$	10.6408	−	6.14349i	0.0347740	−	0.0200768i
$307$	−164.065			−0.534413			−0.267207	−	0.963639i	$-0.586101\pi$
$307$	−164.065			−0.534413			−0.267207	+	0.963639i	$0.586101\pi$
$308$	−48.2258	+	30.3253i	−0.156577	+	0.0984588i
$309$	−54.2383			−0.175528
$310$		0			0
$311$	−197.874	−	114.243i	−0.636252	−	0.367340i	0.146918	−	0.989149i	$-0.453065\pi$
$311$	−197.874	−	114.243i	−0.636252	−	0.367340i	−0.783169	+	0.621809i	$0.786398\pi$
$312$	−47.1775	−	27.2380i	−0.151210	−	0.0873012i
$313$	258.738	+	448.148i	0.826640	+	1.43178i	0.900659	+	0.434526i	$0.143084\pi$
$313$	258.738	+	448.148i	0.826640	+	1.43178i	−0.0740194	+	0.997257i	$0.523583\pi$
$314$		−	189.865i		−	0.604664i
$315$		0			0
$316$	−106.886			−0.338247
$317$	255.744	−	147.654i	0.806764	−	0.465785i	−0.0390670	−	0.999237i	$-0.512439\pi$
$317$	255.744	−	147.654i	0.806764	−	0.465785i	0.845831	+	0.533451i	$0.179105\pi$
$318$	40.8157	−	70.6948i	0.128351	−	0.222311i
$319$	11.7082	−	20.2792i	0.0367029	−	0.0635712i
$320$		0			0
$321$		−	81.4756i		−	0.253818i
$322$	268.216	+	141.639i	0.832970	+	0.439872i
$323$		−	59.9808i		−	0.185699i
$324$	9.00000	+	15.5885i	0.0277778	+	0.0481125i
$325$		0			0
$326$	114.286	−	197.950i	0.350572	−	0.607208i
$327$	174.554	+	302.336i	0.533804	+	0.924576i
$328$	159.134			0.485163
$329$	−282.101	+	177.391i	−0.857450	+	0.539181i
$330$		0			0
$331$	−311.691	−	539.864i	−0.941663	−	1.63101i	−0.762298	−	0.647226i	$-0.775929\pi$
$331$	−311.691	−	539.864i	−0.941663	−	1.63101i	−0.179366	−	0.983782i	$-0.557404\pi$
$332$	−116.101	+	201.092i	−0.349701	+	0.605700i
$333$	−23.1827	−	13.3845i	−0.0696176	−	0.0401937i
$334$	−204.516	+	118.077i	−0.612323	+	0.353525i
$335$		0			0
$336$	−1.82999	−	48.4629i	−0.00544640	−	0.144235i
$337$		−	0.0404399i		−	0.000120000i	−1.00000		5.99998e-5i	$-0.999981\pi$
$337$		−	0.0404399i		−	0.000120000i	1.00000		5.99998e-5i	$-1.90985e-5\pi$
$338$	−55.5408	+	32.0665i	−0.164322	+	0.0948714i
$339$	252.633	+	145.858i	0.745230	+	0.430259i
$340$		0			0
$341$	13.5151	−	7.80293i	0.0396336	−	0.0228825i
$342$	87.8698			0.256929
$343$	38.7543	+	340.804i	0.112986	+	0.993597i
$344$	20.2618			0.0589007
$345$		0			0
$346$	−14.3226	−	8.26918i	−0.0413949	−	0.0238994i
$347$	−105.353	−	60.8256i	−0.303611	−	0.175290i	0.340453	−	0.940262i	$-0.389420\pi$
$347$	−105.353	−	60.8256i	−0.303611	−	0.175290i	−0.644064	+	0.764972i	$0.722753\pi$
$348$	9.96732	+	17.2639i	0.0286417	+	0.0496089i
$349$			457.192i			1.31001i	0.755626	+	0.655003i	$0.227333\pi$
$349$			457.192i			1.31001i	−0.755626	+	0.655003i	$0.772667\pi$
$350$		0			0
$351$	−57.7804			−0.164617
$352$	−19.9346	+	11.5093i	−0.0566325	+	0.0326968i
$353$	−13.6656	+	23.6695i	−0.0387128	+	0.0670525i	−0.884733	−	0.466099i	$-0.845659\pi$
$353$	−13.6656	+	23.6695i	−0.0387128	+	0.0670525i	0.846020	+	0.533151i	$0.178992\pi$
$354$	−54.2335	+	93.9352i	−0.153202	+	0.265354i
$355$		0			0
$356$		−	197.803i		−	0.555626i
$357$	−29.7246	+	18.6914i	−0.0832622	+	0.0523569i
$358$		−	189.165i		−	0.528394i
$359$	−231.018	−	400.135i	−0.643504	−	1.11458i	−0.984645	−	0.174569i	$-0.944147\pi$
$359$	−231.018	−	400.135i	−0.643504	−	1.11458i	0.341141	−	0.940012i	$-0.389187\pi$
$360$		0			0
$361$	33.9751	−	58.8466i	0.0941138	−	0.163010i
$362$	79.9276	+	138.439i	0.220794	+	0.382427i
$363$	−180.899			−0.498344
$364$	137.662	+	72.6962i	0.378193	+	0.199715i
$365$		0			0
$366$	−85.3170	−	147.773i	−0.233107	−	0.403752i
$367$	215.013	−	372.413i	0.585865	−	1.01475i	−0.408902	−	0.912578i	$-0.634088\pi$
$367$	215.013	−	372.413i	0.585865	−	1.01475i	0.994767	−	0.102170i	$-0.0325786\pi$
$368$	106.139	+	61.2794i	0.288421	+	0.166520i
$369$	146.174	−	84.3933i	0.396134	−	0.228708i
$370$		0			0
$371$	−108.934	+	206.285i	−0.293623	+	0.556024i
$372$			13.2854i			0.0357135i
$373$	580.179	−	334.967i	1.55544	−	0.898034i	0.557757	−	0.830004i	$-0.311662\pi$
$373$	580.179	−	334.967i	1.55544	−	0.898034i	0.997683	−	0.0680300i	$-0.0216714\pi$
$374$	14.4330	+	8.33291i	0.0385910	+	0.0222805i
$375$		0			0
$376$	−116.609	+	67.3245i	−0.310132	+	0.179055i
$377$	−63.9907			−0.169737
$378$	−27.3823	−	43.5455i	−0.0724399	−	0.115200i
$379$	−704.346			−1.85843			−0.929216	−	0.369536i	$-0.879517\pi$
$379$	−704.346			−1.85843			−0.929216	+	0.369536i	$0.879517\pi$
$380$		0			0
$381$	43.7699	+	25.2706i	0.114882	+	0.0663269i
$382$	−307.455	−	177.509i	−0.804857	−	0.464684i
$383$	14.8185	+	25.6663i	0.0386905	+	0.0670139i	0.884722	−	0.466119i	$-0.154348\pi$
$383$	14.8185	+	25.6663i	0.0386905	+	0.0670139i	−0.846032	+	0.533133i	$0.821015\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	504.861			1.30793
$387$	18.6117	−	10.7455i	0.0480922	−	0.0277661i
$388$	−132.963	+	230.299i	−0.342688	+	0.593554i
$389$	−18.4085	+	31.8844i	−0.0473225	+	0.0819650i	−0.888716	−	0.458457i	$-0.848402\pi$
$389$	−18.4085	+	31.8844i	−0.0473225	+	0.0819650i	0.841394	+	0.540422i	$0.181736\pi$
$390$		0			0
$391$		−	88.7348i		−	0.226943i
$392$	10.4518	+	138.198i	0.0266628	+	0.352547i
$393$			246.882i			0.628199i
$394$	24.8384	+	43.0213i	0.0630416	+	0.109191i
$395$		0			0
$396$	−12.2074	+	21.1439i	−0.0308268	+	0.0533936i
$397$	45.9937	+	79.6635i	0.115853	+	0.200664i	0.918121	−	0.396301i	$-0.129706\pi$
$397$	45.9937	+	79.6635i	0.115853	+	0.200664i	−0.802267	+	0.596965i	$0.796373\pi$
$398$	129.556			0.325519
$399$	−250.930	+	9.47528i	−0.628897	+	0.0237476i
$400$		0			0
$401$	−178.114	−	308.502i	−0.444174	−	0.769332i	0.553820	−	0.832636i	$-0.313170\pi$
$401$	−178.114	−	308.502i	−0.444174	−	0.769332i	−0.997994	+	0.0633041i	$0.979836\pi$
$402$	112.815	−	195.401i	0.280634	−	0.486072i
$403$	−36.9330	−	21.3233i	−0.0916451	−	0.0529113i
$404$	−104.659	+	60.4248i	−0.259057	+	0.149566i
$405$		0			0
$406$	−30.3253	−	48.2258i	−0.0746929	−	0.118783i
$407$		−	36.3090i		−	0.0892113i
$408$	−12.2870	+	7.09389i	−0.0301152	+	0.0173870i
$409$	20.9491	+	12.0950i	0.0512203	+	0.0295720i	0.525391	−	0.850861i	$-0.323919\pi$
$409$	20.9491	+	12.0950i	0.0512203	+	0.0295720i	−0.474171	+	0.880433i	$0.657252\pi$
$410$		0			0
$411$	312.892	−	180.648i	0.761295	−	0.439534i
$412$	62.6290			0.152012
$413$	144.745	−	274.099i	0.350473	−	0.663678i
$414$	129.993			0.313994
$415$		0			0
$416$	54.4759	+	31.4517i	0.130952	+	0.0756050i
$417$	−228.736	−	132.061i	−0.548528	−	0.316693i
$418$	59.5924	+	103.217i	0.142566	+	0.246931i
$419$		−	537.398i		−	1.28257i	−0.767302	−	0.641286i	$-0.778401\pi$
$419$		−	537.398i		−	1.28257i	0.767302	−	0.641286i	$-0.221599\pi$
$420$		0			0
$421$	−644.404			−1.53065			−0.765326	−	0.643643i	$-0.777422\pi$
$421$	−644.404			−1.53065			−0.765326	+	0.643643i	$0.777422\pi$
$422$	10.6586	−	6.15372i	0.0252573	−	0.0145823i
$423$	−71.4084	+	123.683i	−0.168814	+	0.292395i
$424$	−47.1299	+	81.6314i	−0.111155	+	0.192527i
$425$		0			0
$426$			16.2812i			0.0382189i
$427$	259.575	+	412.797i	0.607904	+	0.966737i
$428$			94.0799i			0.219813i
$429$	−39.1861	−	67.8724i	−0.0913430	−	0.158211i
$430$		0			0
$431$	233.686	−	404.756i	0.542195	−	0.939109i	−0.456583	−	0.889681i	$-0.650927\pi$
$431$	233.686	−	404.756i	0.542195	−	0.939109i	0.998778	−	0.0494278i	$-0.0157398\pi$
$432$	−10.3923	−	18.0000i	−0.0240563	−	0.0416667i
$433$	33.2022			0.0766794			0.0383397	−	0.999265i	$-0.487793\pi$
$433$	33.2022			0.0766794			0.0383397	+	0.999265i	$0.487793\pi$
$434$	−1.43261	−	37.9392i	−0.00330094	−	0.0874176i
$435$		0			0
$436$	−201.558	−	349.108i	−0.462288	−	0.800706i
$437$	317.291	−	549.565i	0.726067	−	1.25759i
$438$	−111.203	−	64.2030i	−0.253888	−	0.146582i
$439$	44.2179	−	25.5292i	0.100724	−	0.0581531i	−0.448792	−	0.893636i	$-0.648145\pi$
$439$	44.2179	−	25.5292i	0.100724	−	0.0581531i	0.549516	+	0.835483i	$0.314812\pi$
$440$		0			0
$441$	82.8913	+	121.400i	0.187962	+	0.275284i
$442$		−	45.5431i		−	0.103039i
$443$	686.462	−	396.329i	1.54958	−	0.894648i	0.551401	−	0.834240i	$-0.314093\pi$
$443$	686.462	−	396.329i	1.54958	−	0.894648i	0.998174	−	0.0604076i	$-0.0192401\pi$
$444$	26.7690	+	15.4551i	0.0602906	+	0.0348088i
$445$		0			0
$446$	194.016	−	112.015i	0.435014	−	0.251155i
$447$	−236.450			−0.528970
$448$	2.11309	+	55.9601i	0.00471672	+	0.124911i
$449$	−71.7539			−0.159808			−0.0799041	−	0.996803i	$-0.525461\pi$
$449$	−71.7539			−0.159808			−0.0799041	+	0.996803i	$0.525461\pi$
$450$		0			0
$451$	198.267	+	114.469i	0.439616	+	0.253812i
$452$	−291.716	−	168.422i	−0.645388	−	0.372615i
$453$	−112.236	−	194.398i	−0.247761	−	0.429134i
$454$		−	560.625i		−	1.23486i
$455$		0			0
$456$	−101.463			−0.222507
$457$	−543.886	+	314.013i	−1.19012	+	0.687117i	−0.958334	−	0.285649i	$-0.907791\pi$
$457$	−543.886	+	314.013i	−1.19012	+	0.687117i	−0.231787	+	0.972766i	$0.574457\pi$
$458$	−145.784	+	252.505i	−0.318305	+	0.551320i
$459$	−7.52421	+	13.0323i	−0.0163926	+	0.0283928i
$460$		0			0
$461$		−	475.402i		−	1.03124i	−0.856817	−	0.515621i	$-0.827561\pi$
$461$		−	475.402i		−	1.03124i	0.856817	−	0.515621i	$-0.172439\pi$
$462$	32.5808	−	61.6970i	0.0705211	−	0.133543i
$463$			342.588i			0.739931i	0.929045	+	0.369966i	$0.120631\pi$
$463$			342.588i			0.739931i	−0.929045	+	0.369966i	$0.879369\pi$
$464$	−11.5093	−	19.9346i	−0.0248045	−	0.0429626i
$465$		0			0
$466$	−78.7087	+	136.327i	−0.168903	+	0.292548i
$467$	127.049	+	220.056i	0.272054	+	0.471211i	0.969388	−	0.245535i	$-0.0789638\pi$
$467$	127.049	+	220.056i	0.272054	+	0.471211i	−0.697334	+	0.716747i	$0.745630\pi$
$468$	66.7191			0.142562
$469$	−301.095	+	570.173i	−0.641994	+	1.21572i
$470$		0			0
$471$	116.268	+	201.382i	0.246853	+	0.427562i
$472$	62.6234	−	108.467i	0.132677	−	0.229803i
$473$	25.2445	+	14.5749i	0.0533711	+	0.0308138i
$474$	113.370	−	65.4540i	0.239177	−	0.138089i
$475$		0			0
$476$	34.3230	−	21.5830i	0.0721072	−	0.0453424i
$477$			99.9776i			0.209597i
$478$	317.012	−	183.027i	0.663204	−	0.382901i
$479$	278.924	+	161.037i	0.582305	+	0.336194i	0.762049	−	0.647519i	$-0.224194\pi$
$479$	278.924	+	161.037i	0.582305	+	0.336194i	−0.179744	+	0.983713i	$0.557527\pi$
$480$		0			0
$481$	−85.9293	+	49.6113i	−0.178647	+	0.103142i
$482$	432.736			0.897793
$483$	−371.222	+	14.0176i	−0.768576	+	0.0290219i
$484$	208.884			0.431579
$485$		0			0
$486$	−19.0919	−	11.0227i	−0.0392837	−	0.0226805i
$487$	168.278	+	97.1552i	0.345539	+	0.199497i	0.662719	−	0.748868i	$-0.269402\pi$
$487$	168.278	+	97.1552i	0.345539	+	0.199497i	−0.317180	+	0.948366i	$0.602736\pi$
$488$	98.5156	+	170.634i	0.201876	+	0.349660i
$489$			279.943i			0.572481i
$490$		0			0
$491$	−491.719			−1.00146			−0.500732	−	0.865602i	$-0.666936\pi$
$491$	−491.719			−1.00146			−0.500732	+	0.865602i	$0.666936\pi$
$492$	−168.787	+	97.4490i	−0.343062	+	0.198067i
$493$	−8.33291	+	14.4330i	−0.0169025	+	0.0292759i
$494$	162.850	−	282.064i	0.329656	−	0.570980i
$495$		0			0
$496$		−	15.3407i		−	0.0309288i
$497$	−1.75566	−	46.4944i	−0.00353251	−	0.0935501i
$498$		−	284.388i		−	0.571059i
$499$	38.5757	+	66.8150i	0.0773060	+	0.133898i	0.902087	−	0.431555i	$-0.142035\pi$
$499$	38.5757	+	66.8150i	0.0773060	+	0.133898i	−0.824781	+	0.565453i	$0.808702\pi$
$500$		0			0
$501$	144.615	−	250.480i	0.288652	−	0.499960i
$502$	−294.070	−	509.344i	−0.585797	−	1.01463i
$503$	−772.176			−1.53514			−0.767571	−	0.640965i	$-0.778535\pi$
$503$	−772.176			−1.53514			−0.767571	+	0.640965i	$0.778535\pi$
$504$	31.6183	+	50.2820i	0.0627348	+	0.0997659i
$505$		0			0
$506$	88.1602	+	152.698i	0.174230	+	0.301775i
$507$	39.2733	−	68.0234i	0.0774621	−	0.134168i
$508$	−50.5411	−	29.1799i	−0.0994904	−	0.0574408i
$509$	−583.669	+	336.981i	−1.14670	+	0.662046i	−0.948080	−	0.318032i	$-0.896978\pi$
$509$	−583.669	+	336.981i	−1.14670	+	0.662046i	−0.198617	+	0.980077i	$0.563645\pi$
$510$		0			0
$511$	324.486	+	171.353i	0.635001	+	0.335329i
$512$			22.6274i			0.0441942i
$513$	−93.2000	+	53.8090i	−0.181676	+	0.104891i
$514$	383.648	+	221.499i	0.746396	+	0.430932i
$515$		0			0
$516$	−21.4909	+	12.4078i	−0.0416491	+	0.0240461i
$517$	−193.714			−0.374689
$518$	−78.1110	−	41.2486i	−0.150793	−	0.0796305i
$519$	20.2553			0.0390275
$520$		0			0
$521$	275.030	+	158.788i	0.527888	+	0.304776i	0.740156	−	0.672435i	$-0.234752\pi$
$521$	275.030	+	158.788i	0.527888	+	0.304776i	−0.212268	+	0.977211i	$0.568085\pi$
$522$	−21.1439	−	12.2074i	−0.0405055	−	0.0233859i
$523$	−350.273	−	606.691i	−0.669739	−	1.16002i	−0.977977	−	0.208713i	$-0.933073\pi$
$523$	−350.273	−	606.691i	−0.669739	−	1.16002i	0.308238	−	0.951309i	$-0.400261\pi$
$524$		−	285.075i		−	0.544037i
$525$		0			0
$526$	−125.238			−0.238094
$527$	−9.61888	+	5.55346i	−0.0182521	+	0.0105379i
$528$	14.0959	−	24.4148i	0.0266968	−	0.0462402i
$529$	204.896	−	354.891i	0.387327	−	0.670871i
$530$		0			0
$531$		−	132.844i		−	0.250178i
$532$	289.749	−	10.9411i	0.544641	−	0.0205660i
$533$		−	625.627i		−	1.17379i
$534$	121.129	+	209.801i	0.226833	+	0.392887i
$535$		0			0
$536$	−130.267	+	225.630i	−0.243036	+	0.420951i
$537$	115.839	+	200.640i	0.215716	+	0.373631i
$538$	115.542			0.214761
$539$	−86.3880	+	179.702i	−0.160275	+	0.333398i
$540$		0			0
$541$	−23.3027	−	40.3614i	−0.0430733	−	0.0746052i	0.843685	−	0.536839i	$-0.180382\pi$
$541$	−23.3027	−	40.3614i	−0.0430733	−	0.0746052i	−0.886758	+	0.462233i	$0.847048\pi$
$542$	208.128	−	360.488i	0.384000	−	0.665107i
$543$	−169.552	−	97.8909i	−0.312251	−	0.180278i
$544$	14.1878	−	8.19132i	0.0260805	−	0.0150576i
$545$		0			0
$546$	−190.530	+	7.19454i	−0.348956	+	0.0131768i
$547$			886.307i			1.62031i	0.586219	+	0.810153i	$0.300616\pi$
$547$			886.307i			1.62031i	−0.586219	+	0.810153i	$0.699384\pi$
$548$	−361.297	+	208.595i	−0.659301	+	0.380647i
$549$	180.985	+	104.492i	0.329662	+	0.190331i
$550$		0			0
$551$	−103.217	+	59.5924i	−0.187327	+	0.108153i
$552$	−150.103			−0.271926
$553$	−316.692	+	199.142i	−0.572680	+	0.360113i
$554$	−574.515			−1.03703
$555$		0			0
$556$	264.122	+	152.491i	0.475039	+	0.274264i
$557$	−500.743	−	289.104i	−0.899000	−	0.519038i	−0.0221246	−	0.999755i	$-0.507043\pi$
$557$	−500.743	−	289.104i	−0.899000	−	0.519038i	−0.876876	+	0.480717i	$0.840376\pi$
$558$	−8.13563	−	14.0913i	−0.0145800	−	0.0252533i
$559$		−	79.6586i		−	0.142502i
$560$		0			0
$561$	−20.4114			−0.0363839
$562$	−286.963	+	165.678i	−0.510610	+	0.294801i
$563$	74.7467	−	129.465i	0.132765	−	0.229956i	−0.791976	−	0.610552i	$-0.790948\pi$
$563$	74.7467	−	129.465i	0.132765	−	0.229956i	0.924741	+	0.380596i	$0.124281\pi$
$564$	82.4553	−	142.817i	0.146197	−	0.253221i
$565$		0			0
$566$			387.958i			0.685439i
$567$	55.7094	+	29.4188i	0.0982528	+	0.0518851i
$568$		−	18.8000i		−	0.0330985i
$569$	79.3178	+	137.382i	0.139399	+	0.241446i	0.927269	−	0.374395i	$-0.122150\pi$
$569$	79.3178	+	137.382i	0.139399	+	0.241446i	−0.787871	+	0.615841i	$0.788816\pi$
$570$		0			0
$571$	7.86886	−	13.6293i	0.0137808	−	0.0238691i	−0.859053	−	0.511887i	$-0.828947\pi$
$571$	7.86886	−	13.6293i	0.0137808	−	0.0238691i	0.872834	+	0.488018i	$0.162280\pi$
$572$	45.2482	+	78.3723i	0.0791053	+	0.137014i
$573$	434.807			0.758826
$574$	471.496	−	296.486i	0.821422	−	0.516526i
$575$		0			0
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	−82.8557	+	143.510i	−0.143597	+	0.248718i	−0.928849	−	0.370459i	$-0.879200\pi$
$577$	−82.8557	+	143.510i	−0.143597	+	0.248718i	0.785251	+	0.619177i	$0.212534\pi$
$578$	343.679	+	198.423i	0.594600	+	0.343293i
$579$	−535.486	+	309.163i	−0.924846	+	0.533960i
$580$		0			0
$581$	30.6664	+	812.126i	0.0527821	+	1.39781i
$582$		−	325.692i		−	0.559608i
$583$	−117.440	+	67.8038i	−0.201440	+	0.116302i
$584$	128.406	+	74.1353i	0.219873	+	0.126944i
$585$		0			0
$586$	79.2745	−	45.7692i	0.135281	−	0.0781044i
$587$	466.624			0.794929			0.397465	−	0.917617i	$-0.369890\pi$
$587$	466.624			0.794929			0.397465	+	0.917617i	$0.369890\pi$
$588$	−95.7146	−	140.181i	−0.162780	−	0.238403i
$589$	−79.4307			−0.134857
$590$		0			0
$591$	−52.6902	−	30.4207i	−0.0891543	−	0.0514732i
$592$	−30.9102	−	17.8460i	−0.0522132	−	0.0301453i
$593$	111.713	+	193.493i	0.188386	+	0.326295i	0.944712	−	0.327900i	$-0.106341\pi$
$593$	111.713	+	193.493i	0.188386	+	0.326295i	−0.756326	+	0.654195i	$0.773008\pi$
$594$		−	29.9020i		−	0.0503400i
$595$		0			0
$596$	273.029			0.458102
$597$	−137.415	+	79.3368i	−0.230177	+	0.132892i
$598$	240.918	−	417.282i	0.402872	−	0.697796i
$599$	389.927	−	675.373i	0.650963	−	1.12750i	−0.331926	−	0.943305i	$-0.607699\pi$
$599$	389.927	−	675.373i	0.650963	−	1.12750i	0.982890	−	0.184196i	$-0.0589681\pi$
$600$		0			0
$601$			917.029i			1.52584i	0.646494	+	0.762919i	$0.276234\pi$
$601$			917.029i			1.52584i	−0.646494	+	0.762919i	$0.723766\pi$
$602$	60.0337	−	37.7504i	0.0997238	−	0.0627083i
$603$			276.339i			0.458273i
$604$	129.599	+	224.471i	0.214567	+	0.371641i
$605$		0			0
$606$	74.0050	−	128.180i	0.122120	−	0.211519i
$607$	109.365	+	189.426i	0.180174	+	0.312070i	0.941940	−	0.335783i	$-0.109001\pi$
$607$	109.365	+	189.426i	0.180174	+	0.312070i	−0.761766	+	0.647852i	$0.775667\pi$
$608$	117.160			0.192697
$609$	61.6970	+	32.5808i	0.101309	+	0.0534988i
$610$		0			0
$611$	264.684	+	458.446i	0.433197	+	0.750320i
$612$	8.68821	−	15.0484i	0.0141964	−	0.0245889i
$613$	777.010	+	448.607i	1.26755	+	0.731822i	0.974524	−	0.224282i	$-0.0720036\pi$
$613$	777.010	+	448.607i	1.26755	+	0.731822i	0.293029	+	0.956104i	$0.405337\pi$
$614$	−200.938	+	116.011i	−0.327260	+	0.188944i
$615$		0			0
$616$	−37.6210	+	71.2416i	−0.0610731	+	0.115652i
$617$			1227.93i			1.99016i	0.0990738	+	0.995080i	$0.468412\pi$
$617$			1227.93i			1.99016i	−0.0990738	+	0.995080i	$0.531588\pi$
$618$	−66.4281	+	38.3523i	−0.107489	+	0.0620587i
$619$	−359.910	−	207.794i	−0.581437	−	0.335693i	0.180267	−	0.983618i	$-0.442304\pi$
$619$	−359.910	−	207.794i	−0.581437	−	0.335693i	−0.761704	+	0.647925i	$0.775637\pi$
$620$		0			0
$621$	−137.879	+	79.6043i	−0.222027	+	0.128187i
$622$	−323.127			−0.519497
$623$	−368.532	−	586.069i	−0.591544	−	0.940720i
$624$	−77.0406			−0.123462
$625$		0			0
$626$	633.777	+	365.911i	1.01242	+	0.584523i
$627$	−126.415	−	72.9855i	−0.201618	−	0.116404i
$628$	−134.255	−	232.536i	−0.213781	−	0.370280i
$629$			25.8417i			0.0410837i
$630$		0			0
$631$	−67.1152			−0.106363			−0.0531816	−	0.998585i	$-0.516936\pi$
$631$	−67.1152			−0.106363			−0.0531816	+	0.998585i	$0.516936\pi$
$632$	−130.908	+	75.5798i	−0.207133	+	0.119588i
$633$	−7.53674	+	13.0540i	−0.0119064	+	0.0206225i
$634$	208.814	−	361.677i	0.329360	−	0.570468i
$635$		0			0
$636$		−	115.444i		−	0.181516i
$637$	543.321	−	41.0909i	0.852937	−	0.0645069i
$638$		−	33.1158i		−	0.0519057i
$639$	−9.97019	−	17.2689i	−0.0156028	−	0.0270248i
$640$		0			0
$641$	−459.366	+	795.645i	−0.716639	+	1.24126i	0.245685	+	0.969350i	$0.420987\pi$
$641$	−459.366	+	795.645i	−0.716639	+	1.24126i	−0.962324	+	0.271905i	$0.912346\pi$
$642$	−57.6120	−	99.7868i	−0.0897383	−	0.155431i
$643$	−881.952			−1.37162			−0.685810	−	0.727780i	$-0.740552\pi$
$643$	−881.952			−1.37162			−0.685810	+	0.727780i	$0.740552\pi$
$644$	428.651	−	16.1861i	0.665606	−	0.0251337i
$645$		0			0
$646$	−42.4129	−	73.4612i	−0.0656546	−	0.113717i
$647$	443.493	−	768.152i	0.685460	−	1.18725i	−0.287832	−	0.957681i	$-0.592934\pi$
$647$	443.493	−	768.152i	0.685460	−	1.18725i	0.973292	−	0.229571i	$-0.0737323\pi$
$648$	22.0454	+	12.7279i	0.0340207	+	0.0196419i
$649$	156.047	−	90.0938i	0.240442	−	0.138819i
$650$		0			0
$651$	24.7525	+	39.3633i	0.0380222	+	0.0604660i
$652$		−	323.251i		−	0.495783i
$653$	866.151	−	500.073i	1.32642	−	0.765808i	0.341675	−	0.939818i	$-0.389006\pi$
$653$	866.151	−	500.073i	1.32642	−	0.765808i	0.984744	+	0.174010i	$0.0556726\pi$
$654$	427.568	+	246.857i	0.653774	+	0.377457i
$655$		0			0
$656$	194.898	−	112.524i	0.297101	−	0.171531i
$657$	157.265			0.239368
$658$	−220.068	+	416.734i	−0.334449	+	0.633334i
$659$	825.607			1.25282			0.626409	−	0.779495i	$-0.284524\pi$
$659$	825.607			1.25282			0.626409	+	0.779495i	$0.284524\pi$
$660$		0			0
$661$	923.294	+	533.064i	1.39681	+	0.806451i	0.994058	−	0.108856i	$-0.0347188\pi$
$661$	923.294	+	533.064i	1.39681	+	0.806451i	0.402757	+	0.915307i	$0.368052\pi$
$662$	−763.483	−	440.797i	−1.15330	−	0.665857i
$663$	27.8894	+	48.3058i	0.0420654	+	0.0728594i
$664$			328.382i			0.494552i
$665$		0			0
$666$	−37.8571			−0.0568425
$667$	−152.698	+	88.1602i	−0.228932	+	0.132174i
$668$	−166.987	+	289.229i	−0.249980	+	0.432978i
$669$	−137.190	+	237.620i	−0.205068	+	0.355187i
$670$		0			0
$671$			283.461i			0.422445i
$672$	−36.5097	−	58.0607i	−0.0543299	−	0.0863998i
$673$		−	115.190i		−	0.171159i	−0.996331	−	0.0855796i	$-0.972726\pi$
$673$		−	115.190i		−	0.171159i	0.996331	−	0.0855796i	$-0.0272742\pi$
$674$	−0.0285953	−	0.0495285i	−4.24263e−5	−	7.34845e-5i
$675$		0			0
$676$	−45.3489	+	78.5466i	−0.0670842	+	0.116193i
$677$	−283.420	−	490.897i	−0.418641	−	0.725107i	0.577162	−	0.816629i	$-0.304160\pi$
$677$	−283.420	−	490.897i	−0.418641	−	0.725107i	−0.995803	+	0.0915226i	$0.970827\pi$
$678$	412.548			0.608478
$679$	35.1204	+	930.079i	0.0517237	+	1.36978i
$680$		0			0
$681$	343.311	+	594.633i	0.504128	+	0.873176i
$682$	11.0350	−	19.1132i	0.0161804	−	0.0280252i
$683$	20.5001	+	11.8357i	0.0300147	+	0.0173290i	0.514932	−	0.857231i	$-0.327817\pi$
$683$	20.5001	+	11.8357i	0.0300147	+	0.0173290i	−0.484918	+	0.874560i	$0.661150\pi$
$684$	107.618	−	62.1333i	0.157336	−	0.0908382i
$685$		0			0
$686$	288.449	+	389.994i	0.420479	+	0.568504i
$687$		−	357.096i		−	0.519790i
$688$	24.8156	−	14.3273i	0.0360692	−	0.0208245i
$689$	320.931	+	185.289i	0.465792	+	0.268925i
$690$		0			0
$691$	−922.771	+	532.762i	−1.33541	+	0.771002i	−0.986124	−	0.166013i	$-0.946911\pi$
$691$	−922.771	+	532.762i	−1.33541	+	0.771002i	−0.349290	+	0.937014i	$0.613577\pi$
$692$	−23.3888			−0.0337988
$693$	3.22442	+	85.3911i	0.00465285	+	0.123219i
$694$	−172.041			−0.247897
$695$		0			0
$696$	24.4148	+	14.0959i	0.0350788	+	0.0202528i
$697$	−141.110	−	81.4696i	−0.202453	−	0.116886i
$698$	323.284	+	559.944i	0.463157	+	0.802212i
$699$		−	192.796i		−	0.275817i
$700$		0			0
$701$	−1086.46			−1.54987			−0.774936	−	0.632040i	$-0.782218\pi$
$701$	−1086.46			−1.54987			−0.774936	+	0.632040i	$0.782218\pi$
$702$	−70.7663	+	40.8569i	−0.100807	+	0.0582008i
$703$	−92.4027	+	160.046i	−0.131441	+	0.227662i
$704$	−16.2766	+	28.1918i	−0.0231201	+	0.0400452i
$705$		0			0
$706$			38.6522i			0.0547481i
$707$	−197.514	+	374.025i	−0.279369	+	0.529032i
$708$			153.395i			0.216660i
$709$	−299.823	−	519.309i	−0.422881	−	0.732452i	0.573339	−	0.819319i	$-0.305648\pi$
$709$	−299.823	−	519.309i	−0.422881	−	0.732452i	−0.996220	+	0.0868665i	$0.972315\pi$
$710$		0			0
$711$	−80.1645	+	138.849i	−0.112749	+	0.195287i
$712$	−139.868	−	242.258i	−0.196443	−	0.340250i
$713$	−117.509			−0.164809
$714$	−23.1882	+	43.9107i	−0.0324765	+	0.0614996i
$715$		0			0
$716$	−133.760	−	231.679i	−0.186815	−	0.323574i
$717$	−224.161	+	388.258i	−0.312637	+	0.541504i
$718$	−565.876	−	326.709i	−0.788128	−	0.455026i
$719$	−286.589	+	165.462i	−0.398594	+	0.230128i	−0.685877	−	0.727717i	$-0.740581\pi$
$719$	−286.589	+	165.462i	−0.398594	+	0.230128i	0.287283	+	0.957846i	$0.407248\pi$
$720$		0			0
$721$	185.563	−	116.686i	0.257369	−	0.161839i
$722$		−	96.0961i		−	0.133097i
$723$	−458.986	+	264.996i	−0.634835	+	0.366522i
$724$	195.782	+	113.035i	0.270417	+	0.156125i
$725$		0			0
$726$	−221.555	+	127.915i	−0.305172	+	0.176191i
$727$	−1104.90			−1.51980			−0.759901	−	0.650039i	$-0.774753\pi$
$727$	−1104.90			−1.51980			−0.759901	+	0.650039i	$0.774753\pi$
$728$	220.005	−	8.30753i	0.302205	−	0.0114114i
$729$	27.0000			0.0370370
$730$		0			0
$731$	−17.9669	−	10.3732i	−0.0245785	−	0.0141904i
$732$	−208.983	−	120.656i	−0.285496	−	0.164831i
$733$	−502.205	−	869.845i	−0.685137	−	1.18669i	−0.973394	−	0.229138i	$-0.926409\pi$
$733$	−502.205	−	869.845i	−0.685137	−	1.18669i	0.288257	−	0.957553i	$-0.406924\pi$
$734$		−	608.147i		−	0.828539i
$735$		0			0
$736$	173.324			0.235495
$737$	−324.604	+	187.410i	−0.440440	+	0.254288i
$738$	119.350	−	206.721i	0.161721	−	0.280109i
$739$	545.640	−	945.075i	0.738348	−	1.27886i	−0.214890	−	0.976638i	$-0.568939\pi$
$739$	545.640	−	945.075i	0.738348	−	1.27886i	0.953239	−	0.302219i	$-0.0977273\pi$
$740$		0			0
$741$			398.899i			0.538325i
$742$	12.4487	+	329.674i	0.0167772	+	0.444305i
$743$		−	876.833i		−	1.18013i	−0.807358	−	0.590063i	$-0.799103\pi$
$743$		−	876.833i		−	1.18013i	0.807358	−	0.590063i	$-0.200897\pi$
$744$	9.39422	+	16.2713i	0.0126266	+	0.0218700i
$745$		0			0
$746$	473.714	−	820.498i	0.635006	−	1.09986i
$747$	174.151	+	301.639i	0.233134	+	0.403800i
$748$	23.5690			0.0315094
$749$	175.283	+	278.749i	0.234023	+	0.372162i
$750$		0			0
$751$	56.4095	+	97.7042i	0.0751126	+	0.130099i	0.901135	−	0.433538i	$-0.142735\pi$
$751$	56.4095	+	97.7042i	0.0751126	+	0.130099i	−0.826023	+	0.563637i	$0.809402\pi$
$752$	−95.2112	+	164.911i	−0.126611	+	0.219296i
$753$	623.816	+	360.161i	0.828441	+	0.478301i
$754$	−78.3723	+	45.2482i	−0.103942	+	0.0600109i
$755$		0			0
$756$	−64.3276	−	33.9699i	−0.0850895	−	0.0449338i
$757$			1279.08i			1.68966i	0.535032	+	0.844832i	$0.320300\pi$
$757$			1279.08i			1.68966i	−0.535032	+	0.844832i	$0.679700\pi$
$758$	−862.644	+	498.048i	−1.13805	+	0.657055i
$759$	−187.016	−	107.974i	−0.246398	−	0.142258i
$760$		0			0
$761$	−794.534	+	458.724i	−1.04407	+	0.602791i	−0.920982	−	0.389605i	$-0.872612\pi$
$761$	−794.534	+	458.724i	−1.04407	+	0.602791i	−0.123083	+	0.992396i	$0.539278\pi$
$762$	71.4759			0.0938004
$763$	−1247.63	−	658.843i	−1.63516	−	0.863490i
$764$	−502.072			−0.657163
$765$		0			0
$766$	36.2977	+	20.9565i	0.0473860	+	0.0273583i
$767$	−426.434	−	246.202i	−0.555976	−	0.320993i
$768$	−13.8564	−	24.0000i	−0.0180422	−	0.0312500i
$769$			187.311i			0.243577i	0.992556	+	0.121789i	$0.0388630\pi$
$769$			187.311i			0.243577i	−0.992556	+	0.121789i	$0.961137\pi$
$770$		0			0
$771$	−542.560			−0.703709
$772$	618.326	−	356.991i	0.800940	−	0.462423i
$773$	−97.7567	+	169.320i	−0.126464	+	0.219042i	−0.922304	−	0.386464i	$-0.873696\pi$
$773$	−97.7567	+	169.320i	−0.126464	+	0.219042i	0.795840	+	0.605507i	$0.207030\pi$
$774$	15.1964	−	26.3209i	0.0196336	−	0.0340063i
$775$		0			0
$776$			376.076i			0.484635i
$777$	108.109	−	4.08226i	0.139136	−	0.00525387i
$778$			52.0670i			0.0669241i
$779$	−582.626	−	1009.14i	−0.747916	−	1.29543i
$780$		0			0
$781$	13.5234	−	23.4232i	0.0173154	−	0.0299912i
$782$	−62.7450	−	108.677i	−0.0802365	−	0.138974i
$783$	29.9020			0.0381890
$784$	110.522	+	161.867i	0.140972	+	0.206463i
$785$		0			0
$786$	174.572	+	302.368i	0.222102	+	0.384692i
$787$	246.440	−	426.846i	0.313138	−	0.542371i	−0.665902	−	0.746040i	$-0.731953\pi$
$787$	246.440	−	426.846i	0.313138	−	0.542371i	0.979040	+	0.203668i	$0.0652863\pi$
$788$	60.8414	+	35.1268i	0.0772099	+	0.0445771i
$789$	132.835	−	76.6921i	0.168358	−	0.0972016i
$790$		0			0
$791$	−1178.11	+	44.4864i	−1.48940	+	0.0562407i
$792$			34.5278i			0.0435957i
$793$	670.841	−	387.310i	0.845953	−	0.488411i
$794$	112.661	+	65.0450i	0.141891	+	0.0819206i
$795$		0			0
$796$	158.674	−	91.6103i	0.199339	−	0.115088i
$797$	−283.436			−0.355629			−0.177814	−	0.984064i	$-0.556903\pi$
$797$	−283.436			−0.355629			−0.177814	+	0.984064i	$0.556903\pi$
$798$	−300.625	+	189.039i	−0.376723	+	0.236891i
$799$	137.869			0.172552
$800$		0			0
$801$	−256.953	−	148.352i	−0.320791	−	0.185209i
$802$	−436.288	−	251.891i	−0.544000	−	0.314079i
$803$	106.655	+	184.732i	0.132821	+	0.230053i
$804$		−	319.089i		−	0.396876i
$805$		0			0
$806$	−60.3113			−0.0748279
$807$	−122.550	+	70.7545i	−0.151859	+	0.0876759i
$808$	−85.4536	+	148.010i	−0.105759	+	0.183181i
$809$	−63.7961	+	110.498i	−0.0788580	+	0.136586i	−0.902757	−	0.430150i	$-0.858461\pi$
$809$	−63.7961	+	110.498i	−0.0788580	+	0.136586i	0.823899	+	0.566736i	$0.191794\pi$
$810$		0			0
$811$		−	1029.60i		−	1.26955i	−0.772697	−	0.634774i	$-0.781093\pi$
$811$		−	1029.60i		−	1.26955i	0.772697	−	0.634774i	$-0.218907\pi$
$812$	−71.2416	−	37.6210i	−0.0877359	−	0.0463313i
$813$			509.807i			0.627069i
$814$	−25.6743	−	44.4693i	−0.0315410	−	0.0546305i
$815$		0			0
$816$	−10.0323	+	17.3764i	−0.0122945	+	0.0212946i
$817$	−74.1835	−	128.490i	−0.0907999	−	0.157270i
$818$	34.2097			0.0418212
$819$	197.682	−	124.306i	0.241370	−	0.151778i
$820$		0			0
$821$	357.710	+	619.572i	0.435701	+	0.754656i	0.997353	−	0.0727181i	$-0.0231673\pi$
$821$	357.710	+	619.572i	0.435701	+	0.754656i	−0.561652	+	0.827374i	$0.689834\pi$
$822$	255.475	−	442.496i	0.310797	−	0.538317i
$823$	−1030.23	−	594.806i	−1.25180	−	0.722729i	−0.280336	−	0.959902i	$-0.590446\pi$
$823$	−1030.23	−	594.806i	−1.25180	−	0.722729i	−0.971467	+	0.237173i	$0.923779\pi$
$824$	76.7045	−	44.2854i	0.0930880	−	0.0537444i
$825$		0			0
$826$	−16.5411	−	438.052i	−0.0200256	−	0.530329i
$827$			764.411i			0.924318i	0.886797	+	0.462159i	$0.152925\pi$
$827$			764.411i			0.924318i	−0.886797	+	0.462159i	$0.847075\pi$
$828$	159.209	−	91.9192i	0.192281	−	0.111013i
$829$	−623.257	−	359.837i	−0.751818	−	0.434062i	0.0745327	−	0.997219i	$-0.476253\pi$
$829$	−623.257	−	359.837i	−0.751818	−	0.434062i	−0.826350	+	0.563156i	$0.809587\pi$
$830$		0			0
$831$	609.365	−	351.817i	0.733292	−	0.423366i
$832$	88.9588			0.106922
$833$	61.4837	−	127.896i	0.0738099	−	0.153537i
$834$	−373.525			−0.447871
$835$		0			0
$836$	145.971	+	84.2764i	0.174607	+	0.100809i
$837$	17.2583	+	9.96407i	0.0206192	+	0.0119045i
$838$	−379.997	−	658.175i	−0.453458	−	0.785412i
$839$		−	622.729i		−	0.742228i	−0.928587	−	0.371114i	$-0.878976\pi$
$839$		−	622.729i		−	0.742228i	0.928587	−	0.371114i	$-0.121024\pi$
$840$		0			0
$841$	−807.884			−0.960623
$842$	−789.231	+	455.663i	−0.937329	+	0.541167i
$843$	202.913	−	351.456i	0.240704	−	0.416912i
$844$	8.70268	−	15.0735i	0.0103112	−	0.0178596i
$845$		0			0
$846$			201.974i			0.238739i
$847$	618.902	−	389.178i	0.730699	−	0.459478i
$848$			133.303i			0.157197i
$849$	−237.575	−	411.492i	−0.279829	−	0.484678i
$850$		0			0
$851$	−136.699	+	236.770i	−0.160634	+	0.278226i
$852$	11.5126	+	19.9404i	0.0135124	+	0.0234042i
$853$	−748.971			−0.878044			−0.439022	−	0.898476i	$-0.644675\pi$
$853$	−748.971			−0.878044			−0.439022	+	0.898476i	$0.644675\pi$
$854$	609.804	+	322.024i	0.714057	+	0.377077i
$855$		0			0
$856$	66.5246	+	115.224i	0.0777156	+	0.134607i
$857$	521.013	−	902.421i	0.607950	−	1.05300i	−0.383628	−	0.923488i	$-0.625325\pi$
$857$	521.013	−	902.421i	0.607950	−	1.05300i	0.991578	−	0.129512i	$-0.0413412\pi$
$858$	−95.9860	−	55.4176i	−0.111872	−	0.0645892i
$859$	483.193	−	278.972i	0.562506	−	0.324763i	−0.191644	−	0.981464i	$-0.561382\pi$
$859$	483.193	−	278.972i	0.562506	−	0.324763i	0.754151	+	0.656701i	$0.228049\pi$
$860$		0			0
$861$	−318.537	+	603.202i	−0.369962	+	0.700584i
$862$		−	660.963i		−	0.766779i
$863$	−1263.08	+	729.238i	−1.46359	+	0.845004i	−0.999175	−	0.0406140i	$-0.987069\pi$
$863$	−1263.08	+	729.238i	−1.46359	+	0.845004i	−0.464415	+	0.885618i	$0.653735\pi$
$864$	−25.4558	−	14.6969i	−0.0294628	−	0.0170103i
$865$		0			0
$866$	40.6642	−	23.4775i	0.0469563	−	0.0271103i
$867$	−486.036			−0.560595
$868$	−28.5817	−	45.4529i	−0.0329282	−	0.0523651i
$869$	−217.467			−0.250250
$870$		0			0
$871$	887.055	+	512.141i	1.01843	+	0.587992i
$872$	−493.713	−	285.045i	−0.566185	−	0.326887i
$873$	199.445	+	345.448i	0.228459	+	0.395702i
$874$		−	897.435i		−	1.02681i
$875$		0			0
$876$	−181.594			−0.207299
$877$	602.267	−	347.719i	0.686736	−	0.396487i	−0.115652	−	0.993290i	$-0.536896\pi$
$877$	602.267	−	347.719i	0.686736	−	0.396487i	0.802388	+	0.596803i	$0.203563\pi$
$878$	36.1038	−	62.5336i	0.0411205	−	0.0712228i
$879$	−56.0556	+	97.0911i	−0.0637720	+	0.110456i
$880$		0			0
$881$		−	795.045i		−	0.902435i	−0.892414	−	0.451218i	$-0.850990\pi$
$881$		−	795.045i		−	0.902435i	0.892414	−	0.451218i	$-0.149010\pi$
$882$	187.364	+	90.0714i	0.212430	+	0.102122i
$883$			1060.28i			1.20077i	0.799712	+	0.600384i	$0.204986\pi$
$883$			1060.28i			1.20077i	−0.799712	+	0.600384i	$0.795014\pi$
$884$	−32.2039	−	55.7787i	−0.0364297	−	0.0630981i
$885$		0			0
$886$	560.494	−	970.804i	0.632611	−	1.09572i
$887$	580.285	+	1005.08i	0.654211	+	1.13313i	0.982091	+	0.188407i	$0.0603326\pi$
$887$	580.285	+	1005.08i	0.654211	+	1.13313i	−0.327880	+	0.944719i	$0.606334\pi$
$888$	43.7137			0.0492271
$889$	−204.114	+	7.70748i	−0.229600	+	0.00866983i
$890$		0			0
$891$	18.3111	+	31.7158i	0.0205512	+	0.0355958i
$892$	158.414	−	274.380i	0.177594	−	0.307601i
$893$	853.871	+	492.983i	0.956182	+	0.552052i
$894$	−289.591	+	167.195i	−0.323927	+	0.187019i
$895$		0			0
$896$	42.1578	+	67.0427i	0.0470511	+	0.0748244i
$897$			590.125i			0.657888i
$898$	−87.8802	+	50.7376i	−0.0978621	+	0.0565007i
$899$	19.1132	+	11.0350i	0.0212605	+	0.0122748i
$900$		0			0
$901$	83.5836	−	48.2570i	0.0927676	−	0.0535594i
$902$	323.768			0.358945
$903$	−40.5581	+	76.8034i	−0.0449148	+	0.0850535i
$904$	−476.370			−0.526957
$905$		0			0
$906$	−274.920	−	158.725i	−0.303444	−	0.175193i
$907$	−1255.71	−	724.984i	−1.38446	−	0.799320i	−0.391779	−	0.920059i	$-0.628140\pi$
$907$	−1255.71	−	724.984i	−1.38446	−	0.799320i	−0.992684	+	0.120739i	$0.961474\pi$
$908$	−396.422	−	686.623i	−0.436588	−	0.756193i
$909$			181.274i			0.199422i
$910$		0			0
$911$	803.838			0.882369			0.441185	−	0.897416i	$-0.354558\pi$
$911$	803.838			0.882369			0.441185	+	0.897416i	$0.354558\pi$
$912$	−124.267	+	71.7454i	−0.136257	+	0.0786682i
$913$	−236.215	+	409.137i	−0.258724	+	0.448123i
$914$	−444.081	+	769.170i	−0.485865	+	0.841543i
$915$		0			0
$916$			412.338i			0.450151i
$917$	−531.131	−	844.648i	−0.579206	−	0.921099i
$918$			21.2817i			0.0231827i
$919$	−190.607	−	330.140i	−0.207407	−	0.359239i	0.743490	−	0.668747i	$-0.233169\pi$
$919$	−190.607	−	330.140i	−0.207407	−	0.359239i	−0.950897	+	0.309508i	$0.899836\pi$
$920$		0			0
$921$	142.084	−	246.097i	0.154272	−	0.267207i
$922$	−336.160	−	582.247i	−0.364599	−	0.631504i
$923$	−73.9113			−0.0800773
$924$	−3.72324	−	98.6012i	−0.00402948	−	0.106711i
$925$		0			0
$926$	242.246	+	419.583i	0.261605	+	0.453114i
$927$	46.9717	−	81.3574i	0.0506707	−	0.0877642i
$928$	−28.1918	−	16.2766i	−0.0303791	−	0.0175394i
$929$	−1182.30	+	682.603i	−1.27266	+	0.734772i	−0.975488	−	0.220051i	$-0.929378\pi$
$929$	−1182.30	+	682.603i	−1.27266	+	0.734772i	−0.297174	+	0.954823i	$0.596044\pi$
$930$		0			0
$931$	838.112	−	572.257i	0.900227	−	0.614669i
$932$			222.622i			0.238865i
$933$	342.728	−	197.874i	0.367340	−	0.212084i
$934$	311.206	+	179.675i	0.333197	+	0.192371i
$935$		0			0
$936$	81.7139	−	47.1775i	0.0873012	−	0.0504033i
$937$	836.234			0.892459			0.446230	−	0.894918i	$-0.352766\pi$
$937$	836.234			0.892459			0.446230	+	0.894918i	$0.352766\pi$
$938$	34.4083	+	911.222i	0.0366827	+	0.971452i
$939$	−896.296			−0.954522
$940$		0			0
$941$	−846.732	−	488.861i	−0.899822	−	0.519512i	−0.0226794	−	0.999743i	$-0.507220\pi$
$941$	−846.732	−	488.861i	−0.899822	−	0.519512i	−0.877142	+	0.480230i	$0.840553\pi$
$942$	284.797	+	164.428i	0.302332	+	0.174552i
$943$	−861.929	−	1492.91i	−0.914029	−	1.58314i
$944$		−	177.126i		−	0.187633i
$945$		0			0
$946$	41.2241			0.0435773
$947$	−827.780	+	477.919i	−0.874108	+	0.504667i	−0.868711	−	0.495319i	$-0.835051\pi$
$947$	−827.780	+	477.919i	−0.874108	+	0.504667i	−0.00539682	+	0.999985i	$0.501718\pi$
$948$	92.5660	−	160.329i	0.0976435	−	0.169123i
$949$	291.460	−	504.823i	0.307123	−	0.531953i
$950$		0			0
$951$			511.488i			0.537843i
$952$	26.7755	−	50.7037i	0.0281255	−	0.0532602i
$953$			156.597i			0.164320i	0.996619	+	0.0821598i	$0.0261818\pi$
$953$			156.597i			0.164320i	−0.996619	+	0.0821598i	$0.973818\pi$
$954$	70.6948	+	122.447i	0.0741036	+	0.128351i
$955$		0			0
$956$	258.839	−	448.322i	0.270752	−	0.468956i
$957$	20.2792	+	35.1246i	0.0211904	+	0.0367029i
$958$	455.481			0.475450
$959$	−681.846	+	1291.19i	−0.710997	+	1.34639i
$960$		0			0
$961$	−473.146	−	819.512i	−0.492347	−	0.852770i
$962$	−70.1609	+	121.522i	−0.0729324	+	0.126323i
$963$	122.213	+	70.5600i	0.126909	+	0.0732710i
$964$	529.991	−	305.991i	0.549784	−	0.317418i
$965$		0			0
$966$	−444.741	+	279.662i	−0.460394	+	0.289505i
$967$			1344.56i			1.39045i	0.718793	+	0.695224i	$0.244695\pi$
$967$			1344.56i			1.39045i	−0.718793	+	0.695224i	$0.755305\pi$
$968$	255.830	−	147.703i	0.264287	−	0.152586i
$969$	89.9712	+	51.9449i	0.0928496	+	0.0536067i
$970$		0			0
$971$	−1311.13	+	756.983i	−1.35029	+	0.779591i	−0.988290	−	0.152586i	$-0.951240\pi$
$971$	−1311.13	+	756.983i	−1.35029	+	0.779591i	−0.362001	+	0.932178i	$0.617906\pi$
$972$	−31.1769			−0.0320750
$973$	1066.68	−	40.2784i	1.09627	−	0.0413961i
$974$	274.796			0.282132
$975$		0			0
$976$	241.313	+	139.322i	0.247247	+	0.142748i
$977$	−28.9055	−	16.6886i	−0.0295860	−	0.0170815i	0.485134	−	0.874440i	$-0.338771\pi$
$977$	−28.9055	−	16.6886i	−0.0295860	−	0.0170815i	−0.514720	+	0.857358i	$0.672104\pi$
$978$	197.950	+	342.859i	0.202403	+	0.350572i
$979$		−	402.444i		−	0.411076i
$980$		0			0
$981$	−604.673			−0.616384
$982$	−602.230	+	347.698i	−0.613269	+	0.354071i
$983$	−965.345	+	1672.03i	−0.982039	+	1.70094i	−0.327621	+	0.944809i	$0.606247\pi$
$983$	−965.345	+	1672.03i	−0.982039	+	1.70094i	−0.654418	+	0.756133i	$0.727086\pi$
$984$	−137.814	+	238.700i	−0.140055	+	0.242582i
$985$		0			0
$986$			23.5690i			0.0239037i
$987$	−21.7794	−	576.776i	−0.0220663	−	0.584373i
$988$		−	460.609i		−	0.466203i
$989$	−109.746	−	190.086i	−0.110967	−	0.192200i
$990$		0			0
$991$	670.602	−	1161.52i	0.676692	−	1.17206i	−0.299279	−	0.954166i	$-0.596746\pi$
$991$	670.602	−	1161.52i	0.676692	−	1.17206i	0.975971	−	0.217899i	$-0.0699205\pi$
$992$	−10.8475	−	18.7884i	−0.0109350	−	0.0189400i
$993$	1079.73			1.08734
$994$	−35.0267	−	55.7023i	−0.0352382	−	0.0560386i
$995$		0			0
$996$	−201.092	−	348.302i	−0.201900	−	0.349701i
$997$	−92.1525	+	159.613i	−0.0924298	+	0.160093i	−0.908533	−	0.417813i	$-0.862797\pi$
$997$	−92.1525	+	159.613i	−0.0924298	+	0.160093i	0.816103	+	0.577906i	$0.196130\pi$
$998$	94.4907	+	54.5542i	0.0946801	+	0.0546636i
$999$	40.1536	−	23.1827i	0.0401937	−	0.0232059i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.q.d.199.10		24
5.2	odd	4		1050.3.p.f.451.6	yes	12
5.3	odd	4		1050.3.p.e.451.1	✓	12
5.4	even	2	inner	1050.3.q.d.199.4		24
7.5	odd	6	inner	1050.3.q.d.649.4		24
35.12	even	12		1050.3.p.f.901.6	yes	12
35.19	odd	6	inner	1050.3.q.d.649.10		24
35.33	even	12		1050.3.p.e.901.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.p.e.451.1	✓	12	5.3	odd	4
1050.3.p.e.901.1	yes	12	35.33	even	12
1050.3.p.f.451.6	yes	12	5.2	odd	4
1050.3.p.f.901.6	yes	12	35.12	even	12
1050.3.q.d.199.4		24	5.4	even	2	inner
1050.3.q.d.199.10		24	1.1	even	1	trivial
1050.3.q.d.649.4		24	7.5	odd	6	inner
1050.3.q.d.649.10		24	35.19	odd	6	inner

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-0.264136 - 6.99501i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-0.264136 - 6.99501i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(2.03457 - 3.52398i) q^{11} +(1.73205 + 3.00000i) q^{12} -11.1199 q^{13} +(-5.26972 - 8.38034i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-1.44803 + 2.50807i) q^{17} +(-3.67423 - 2.12132i) q^{18} +(-17.9363 + 10.3556i) q^{19} +(10.7213 + 5.66166i) q^{21} -5.75463i q^{22} +(-26.5348 + 15.3199i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-13.6190 + 7.86292i) q^{26} +5.19615 q^{27} +(-12.3799 - 6.53752i) q^{28} +5.75463 q^{29} +(3.32136 + 1.91759i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(3.52398 + 6.10371i) q^{33} +4.09566i q^{34} -6.00000 q^{36} +(7.72755 - 4.46151i) q^{37} +(-14.6450 + 25.3658i) q^{38} +(9.63007 - 16.6798i) q^{39} +56.2622i q^{41} +(17.1342 - 0.646999i) q^{42} +7.16364i q^{43} +(-4.06914 - 7.04796i) q^{44} +(-21.6656 + 37.5258i) q^{46} +(-23.8028 - 41.2277i) q^{47} +6.92820 q^{48} +(-48.8605 + 3.69527i) q^{49} +(-2.50807 - 4.34410i) q^{51} +(-11.1199 + 19.2601i) q^{52} +(-28.8610 - 16.6629i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-19.7849 + 0.747090i) q^{56} -35.8727i q^{57} +(7.04796 - 4.06914i) q^{58} +(38.3489 + 22.1407i) q^{59} +(-60.3282 + 34.8305i) q^{61} +5.42375 q^{62} +(-17.7774 + 11.1788i) q^{63} -8.00000 q^{64} +(8.63195 + 4.98366i) q^{66} +(-79.7722 - 46.0565i) q^{67} +(2.89607 + 5.01614i) q^{68} -53.0695i q^{69} +6.64679 q^{71} +(-7.34847 + 4.24264i) q^{72} +(-26.2108 + 45.3984i) q^{73} +(6.30952 - 10.9284i) q^{74} +41.4222i q^{76} +(-25.1877 - 13.3010i) q^{77} -27.2380i q^{78} +(-26.7215 - 46.2830i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(39.7834 + 68.9069i) q^{82} -116.101 q^{83} +(20.5275 - 12.9081i) q^{84} +(5.06546 + 8.77363i) q^{86} +(-4.98366 + 8.63195i) q^{87} +(-9.96732 - 5.75463i) q^{88} +(85.6511 - 49.4507i) q^{89} +(2.93716 + 77.7835i) q^{91} +61.2794i q^{92} +(-5.75276 + 3.32136i) q^{93} +(-58.3047 - 33.6623i) q^{94} +(8.48528 - 4.89898i) q^{96} -132.963 q^{97} +(-57.2286 + 39.0753i) q^{98} -12.2074 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} - 36 q^{9}+O(q^{10}) \) 24 * q + 24 * q^4 - 36 * q^9	\( 24 q + 24 q^{4} - 36 q^{9} - 8 q^{11} - 16 q^{14} - 48 q^{16} - 24 q^{19} + 36 q^{21} - 48 q^{26} + 48 q^{29} - 396 q^{31} - 144 q^{36} + 72 q^{39} + 16 q^{44} + 64 q^{46} - 56 q^{49} - 48 q^{51} + 80 q^{56} + 96 q^{59} + 372 q^{61} - 192 q^{64} + 72 q^{66} - 272 q^{71} + 128 q^{74} + 140 q^{79} - 108 q^{81} + 24 q^{84} - 416 q^{86} - 336 q^{89} + 584 q^{91} + 408 q^{94} + 48 q^{99}+O(q^{100}) \) 24 * q + 24 * q^4 - 36 * q^9 - 8 * q^11 - 16 * q^14 - 48 * q^16 - 24 * q^19 + 36 * q^21 - 48 * q^26 + 48 * q^29 - 396 * q^31 - 144 * q^36 + 72 * q^39 + 16 * q^44 + 64 * q^46 - 56 * q^49 - 48 * q^51 + 80 * q^56 + 96 * q^59 + 372 * q^61 - 192 * q^64 + 72 * q^66 - 272 * q^71 + 128 * q^74 + 140 * q^79 - 108 * q^81 + 24 * q^84 - 416 * q^86 - 336 * q^89 + 584 * q^91 + 408 * q^94 + 48 * q^99

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