LMFDB - Embedded newform 950.2.j.g.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(49,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("950.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.j (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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.49787136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.1
Root			$-0.228425 + 1.39564i$ of defining polynomial
Character	$\chi$	$=$	950.49
Dual form			950.2.j.g.349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-2.29129 - 1.32288i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.32288 + 2.29129i) q^{6} -1.64575i q^{7} -1.00000i q^{8} +(2.00000 + 3.46410i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-2.29129 - 1.32288i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.32288 + 2.29129i) q^{6} -1.64575i q^{7} -1.00000i q^{8} +(2.00000 + 3.46410i) q^{9} +0.645751 q^{11} -2.64575i q^{12} +(-1.73205 + 1.00000i) q^{13} +(-0.822876 + 1.42526i) q^{14} +(-0.500000 + 0.866025i) q^{16} -4.00000i q^{18} +(-4.32288 - 0.559237i) q^{19} +(-2.17712 + 3.77089i) q^{21} +(-0.559237 - 0.322876i) q^{22} +(-3.15731 + 1.82288i) q^{23} +(-1.32288 + 2.29129i) q^{24} +2.00000 q^{26} -2.64575i q^{27} +(1.42526 - 0.822876i) q^{28} +(-1.82288 - 3.15731i) q^{29} -0.354249 q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.47960 - 0.854249i) q^{33} +(-2.00000 + 3.46410i) q^{36} +5.64575i q^{37} +(3.46410 + 2.64575i) q^{38} +5.29150 q^{39} +(-5.14575 + 8.91270i) q^{41} +(3.77089 - 2.17712i) q^{42} +(0.613577 + 0.354249i) q^{43} +(0.322876 + 0.559237i) q^{44} +3.64575 q^{46} +(8.35347 - 4.82288i) q^{47} +(2.29129 - 1.32288i) q^{48} +4.29150 q^{49} +(-1.73205 - 1.00000i) q^{52} +(-7.43310 + 4.29150i) q^{53} +(-1.32288 + 2.29129i) q^{54} -1.64575 q^{56} +(9.16515 + 7.00000i) q^{57} +3.64575i q^{58} +(3.96863 - 6.87386i) q^{59} +(7.46863 + 12.9360i) q^{61} +(0.306788 + 0.177124i) q^{62} +(5.70105 - 3.29150i) q^{63} -1.00000 q^{64} +(0.854249 + 1.47960i) q^{66} +(-4.02334 + 2.32288i) q^{67} +9.64575 q^{69} +(6.64575 - 11.5108i) q^{71} +(3.46410 - 2.00000i) q^{72} +(10.6448 + 6.14575i) q^{73} +(2.82288 - 4.88936i) q^{74} +(-1.67712 - 4.02334i) q^{76} -1.06275i q^{77} +(-4.58258 - 2.64575i) q^{78} +(-2.00000 + 3.46410i) q^{79} +(2.50000 - 4.33013i) q^{81} +(8.91270 - 5.14575i) q^{82} +7.93725i q^{83} -4.35425 q^{84} +(-0.354249 - 0.613577i) q^{86} +9.64575i q^{87} -0.645751i q^{88} +(1.64575 + 2.85052i) q^{91} +(-3.15731 - 1.82288i) q^{92} +(0.811686 + 0.468627i) q^{93} -9.64575 q^{94} -2.64575 q^{96} +(12.3768 + 7.14575i) q^{97} +(-3.71655 - 2.14575i) q^{98} +(1.29150 + 2.23695i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 16 q^{9}+O(q^{10}) $ 8 * q + 4 * q^4 + 16 * q^9	$ 8 q + 4 q^{4} + 16 q^{9} - 16 q^{11} + 4 q^{14} - 4 q^{16} - 24 q^{19} - 28 q^{21} + 16 q^{26} - 4 q^{29} - 24 q^{31} - 16 q^{36} - 20 q^{41} - 8 q^{44} + 8 q^{46} - 8 q^{49} + 8 q^{56} + 28 q^{61} - 8 q^{64} + 28 q^{66} + 56 q^{69} + 32 q^{71} + 12 q^{74} - 24 q^{76} - 16 q^{79} + 20 q^{81} - 56 q^{84} - 24 q^{86} - 8 q^{91} - 56 q^{94} - 32 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 + 16 * q^9 - 16 * q^11 + 4 * q^14 - 4 * q^16 - 24 * q^19 - 28 * q^21 + 16 * q^26 - 4 * q^29 - 24 * q^31 - 16 * q^36 - 20 * q^41 - 8 * q^44 + 8 * q^46 - 8 * q^49 + 8 * q^56 + 28 * q^61 - 8 * q^64 + 28 * q^66 + 56 * q^69 + 32 * q^71 + 12 * q^74 - 24 * q^76 - 16 * q^79 + 20 * q^81 - 56 * q^84 - 24 * q^86 - 8 * q^91 - 56 * q^94 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−2.29129	−	1.32288i	−1.32288	−	0.763763i	−0.338689	−	0.940898i	$-0.609984\pi$
$3$	−2.29129	−	1.32288i	−1.32288	−	0.763763i	−0.984186	+	0.177136i	$0.943317\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	1.32288	+	2.29129i	0.540062	+	0.935414i
$7$		−	1.64575i		−	0.622036i	−0.950404	−	0.311018i	$-0.899330\pi$
$7$		−	1.64575i		−	0.622036i	0.950404	−	0.311018i	$-0.100670\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.00000	+	3.46410i	0.666667	+	1.15470i
$10$		0			0
$11$	0.645751			0.194701			0.0973507	−	0.995250i	$-0.468963\pi$
$11$	0.645751			0.194701			0.0973507	+	0.995250i	$0.468963\pi$
$12$		−	2.64575i		−	0.763763i
$13$	−1.73205	+	1.00000i	−0.480384	+	0.277350i	−0.720577	−	0.693375i	$-0.756123\pi$
$13$	−1.73205	+	1.00000i	−0.480384	+	0.277350i	0.240192	+	0.970725i	$0.422790\pi$
$14$	−0.822876	+	1.42526i	−0.219923	+	0.380917i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$17$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$18$		−	4.00000i		−	0.942809i
$19$	−4.32288	−	0.559237i	−0.991736	−	0.128298i
$19$	−4.32288	−	0.559237i	−0.991736	−	0.128298i
$20$		0			0
$21$	−2.17712	+	3.77089i	−0.475087	+	0.822876i
$22$	−0.559237	−	0.322876i	−0.119230	−	0.0688373i
$23$	−3.15731	+	1.82288i	−0.658345	+	0.380096i	−0.791646	−	0.610980i	$-0.790776\pi$
$23$	−3.15731	+	1.82288i	−0.658345	+	0.380096i	0.133301	+	0.991076i	$0.457442\pi$
$24$	−1.32288	+	2.29129i	−0.270031	+	0.467707i
$25$		0			0
$26$	2.00000			0.392232
$27$		−	2.64575i		−	0.509175i
$28$	1.42526	−	0.822876i	0.269349	−	0.155509i
$29$	−1.82288	−	3.15731i	−0.338500	−	0.586298i	0.645651	−	0.763632i	$-0.276586\pi$
$29$	−1.82288	−	3.15731i	−0.338500	−	0.586298i	−0.984151	+	0.177334i	$0.943253\pi$
$30$		0			0
$31$	−0.354249			−0.0636249			−0.0318125	−	0.999494i	$-0.510128\pi$
$31$	−0.354249			−0.0636249			−0.0318125	+	0.999494i	$0.510128\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−1.47960	−	0.854249i	−0.257566	−	0.148706i
$34$		0			0
$35$		0			0
$36$	−2.00000	+	3.46410i	−0.333333	+	0.577350i
$37$			5.64575i			0.928156i	0.885794	+	0.464078i	$0.153614\pi$
$37$			5.64575i			0.928156i	−0.885794	+	0.464078i	$0.846386\pi$
$38$	3.46410	+	2.64575i	0.561951	+	0.429198i
$39$	5.29150			0.847319
$40$		0			0
$41$	−5.14575	+	8.91270i	−0.803631	+	1.39193i	0.113580	+	0.993529i	$0.463768\pi$
$41$	−5.14575	+	8.91270i	−0.803631	+	1.39193i	−0.917211	+	0.398401i	$0.869565\pi$
$42$	3.77089	−	2.17712i	0.581861	−	0.335938i
$43$	0.613577	+	0.354249i	0.0935696	+	0.0540224i	0.546055	−	0.837750i	$-0.316129\pi$
$43$	0.613577	+	0.354249i	0.0935696	+	0.0540224i	−0.452485	+	0.891772i	$0.649462\pi$
$44$	0.322876	+	0.559237i	0.0486753	+	0.0843082i
$45$		0			0
$46$	3.64575			0.537537
$47$	8.35347	−	4.82288i	1.21848	−	0.703489i	0.253886	−	0.967234i	$-0.418291\pi$
$47$	8.35347	−	4.82288i	1.21848	−	0.703489i	0.964592	+	0.263745i	$0.0849579\pi$
$48$	2.29129	−	1.32288i	0.330719	−	0.190941i
$49$	4.29150			0.613072
$50$		0			0
$51$		0			0
$52$	−1.73205	−	1.00000i	−0.240192	−	0.138675i
$53$	−7.43310	+	4.29150i	−1.02101	+	0.589483i	−0.914398	−	0.404817i	$-0.867335\pi$
$53$	−7.43310	+	4.29150i	−1.02101	+	0.589483i	−0.106617	+	0.994300i	$0.534002\pi$
$54$	−1.32288	+	2.29129i	−0.180021	+	0.311805i
$55$		0			0
$56$	−1.64575			−0.219923
$57$	9.16515	+	7.00000i	1.21395	+	0.927173i
$58$			3.64575i			0.478711i
$59$	3.96863	−	6.87386i	0.516671	−	0.894901i	−0.483141	−	0.875542i	$-0.660504\pi$
$59$	3.96863	−	6.87386i	0.516671	−	0.894901i	0.999813	−	0.0193585i	$-0.00616237\pi$
$60$		0			0
$61$	7.46863	+	12.9360i	0.956260	+	1.65629i	0.731459	+	0.681886i	$0.238840\pi$
$61$	7.46863	+	12.9360i	0.956260	+	1.65629i	0.224801	+	0.974405i	$0.427827\pi$
$62$	0.306788	+	0.177124i	0.0389622	+	0.0224948i
$63$	5.70105	−	3.29150i	0.718265	−	0.414690i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	0.854249	+	1.47960i	0.105151	+	0.182126i
$67$	−4.02334	+	2.32288i	−0.491529	+	0.283784i	−0.725209	−	0.688529i	$-0.758257\pi$
$67$	−4.02334	+	2.32288i	−0.491529	+	0.283784i	0.233680	+	0.972314i	$0.424923\pi$
$68$		0			0
$69$	9.64575			1.16121
$70$		0			0
$71$	6.64575	−	11.5108i	0.788706	−	1.36608i	−0.138055	−	0.990425i	$-0.544085\pi$
$71$	6.64575	−	11.5108i	0.788706	−	1.36608i	0.926760	−	0.375654i	$-0.122582\pi$
$72$	3.46410	−	2.00000i	0.408248	−	0.235702i
$73$	10.6448	+	6.14575i	1.24587	+	0.719306i	0.970284	−	0.241969i	$-0.0777934\pi$
$73$	10.6448	+	6.14575i	1.24587	+	0.719306i	0.275590	+	0.961275i	$0.411127\pi$
$74$	2.82288	−	4.88936i	0.328153	−	0.568377i
$75$		0			0
$76$	−1.67712	−	4.02334i	−0.192379	−	0.461509i
$77$		−	1.06275i		−	0.121111i
$78$	−4.58258	−	2.64575i	−0.518875	−	0.299572i
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	−0.956325	−	0.292306i	$-0.905577\pi$
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	0.731307	+	0.682048i	$0.238911\pi$
$80$		0			0
$81$	2.50000	−	4.33013i	0.277778	−	0.481125i
$82$	8.91270	−	5.14575i	0.984243	−	0.568253i
$83$			7.93725i			0.871227i	0.900134	+	0.435613i	$0.143469\pi$
$83$			7.93725i			0.871227i	−0.900134	+	0.435613i	$0.856531\pi$
$84$	−4.35425			−0.475087
$85$		0			0
$86$	−0.354249	−	0.613577i	−0.0381996	−	0.0661637i
$87$			9.64575i			1.03413i
$88$		−	0.645751i		−	0.0688373i
$89$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$89$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$90$		0			0
$91$	1.64575	+	2.85052i	0.172522	+	0.298816i
$92$	−3.15731	−	1.82288i	−0.329173	−	0.190048i
$93$	0.811686	+	0.468627i	0.0841679	+	0.0485944i
$94$	−9.64575			−0.994883
$95$		0			0
$96$	−2.64575			−0.270031
$97$	12.3768	+	7.14575i	1.25667	+	0.725541i	0.972426	−	0.233210i	$-0.0749229\pi$
$97$	12.3768	+	7.14575i	1.25667	+	0.725541i	0.284248	+	0.958751i	$0.408256\pi$
$98$	−3.71655	−	2.14575i	−0.375428	−	0.216754i
$99$	1.29150	+	2.23695i	0.129801	+	0.224822i
$100$		0			0
$101$	4.17712	+	7.23499i	0.415639	+	0.719909i	0.995495	−	0.0948105i	$-0.0302245\pi$
$101$	4.17712	+	7.23499i	0.415639	+	0.719909i	−0.579856	+	0.814719i	$0.696891\pi$
$102$		0			0
$103$			2.70850i			0.266876i	0.991057	+	0.133438i	$0.0426017\pi$
$103$			2.70850i			0.266876i	−0.991057	+	0.133438i	$0.957398\pi$
$104$	1.00000	+	1.73205i	0.0980581	+	0.169842i
$105$		0			0
$106$	8.58301			0.833655
$107$			4.70850i			0.455188i	0.973756	+	0.227594i	$0.0730858\pi$
$107$			4.70850i			0.455188i	−0.973756	+	0.227594i	$0.926914\pi$
$108$	2.29129	−	1.32288i	0.220479	−	0.127294i
$109$	−3.29150	+	5.70105i	−0.315269	+	0.546062i	−0.979495	−	0.201470i	$-0.935428\pi$
$109$	−3.29150	+	5.70105i	−0.315269	+	0.546062i	0.664226	+	0.747532i	$0.268761\pi$
$110$		0			0
$111$	7.46863	−	12.9360i	0.708891	−	1.22783i
$112$	1.42526	+	0.822876i	0.134675	+	0.0777544i
$113$		−	5.58301i		−	0.525205i	−0.964904	−	0.262602i	$-0.915419\pi$
$113$		−	5.58301i		−	0.525205i	0.964904	−	0.262602i	$-0.0845808\pi$
$114$	−4.43725	−	10.6448i	−0.415587	−	0.996973i
$115$		0			0
$116$	1.82288	−	3.15731i	0.169250	−	0.293149i
$117$	−6.92820	−	4.00000i	−0.640513	−	0.369800i
$118$	−6.87386	+	3.96863i	−0.632790	+	0.365342i
$119$		0			0
$120$		0			0
$121$	−10.5830			−0.962091
$122$		−	14.9373i		−	1.35236i
$123$	23.5808	−	13.6144i	2.12621	−	1.22757i
$124$	−0.177124	−	0.306788i	−0.0159062	−	0.0275504i
$125$		0			0
$126$	−6.58301			−0.586461
$127$	−2.34563	+	1.35425i	−0.208141	+	0.120170i	−0.600447	−	0.799665i	$-0.705011\pi$
$127$	−2.34563	+	1.35425i	−0.208141	+	0.120170i	0.392306	+	0.919835i	$0.371677\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−0.937254	−	1.62337i	−0.0825206	−	0.142930i
$130$		0			0
$131$	6.96863	−	12.0700i	0.608852	−	1.05456i	−0.382578	−	0.923923i	$-0.624964\pi$
$131$	6.96863	−	12.0700i	0.608852	−	1.05456i	0.991430	−	0.130639i	$-0.0417029\pi$
$132$		−	1.70850i		−	0.148706i
$133$	−0.920365	+	7.11438i	−0.0798058	+	0.616895i
$134$	4.64575			0.401332
$135$		0			0
$136$		0			0
$137$	−4.83502	+	2.79150i	−0.413084	+	0.238494i	−0.692114	−	0.721788i	$-0.743320\pi$
$137$	−4.83502	+	2.79150i	−0.413084	+	0.238494i	0.279030	+	0.960282i	$0.409987\pi$
$138$	−8.35347	−	4.82288i	−0.711094	−	0.410550i
$139$	6.67712	+	11.5651i	0.566346	+	0.980941i	0.996923	+	0.0783866i	$0.0249768\pi$
$139$	6.67712	+	11.5651i	0.566346	+	0.980941i	−0.430577	+	0.902554i	$0.641690\pi$
$140$		0			0
$141$	−25.5203			−2.14919
$142$	−11.5108	+	6.64575i	−0.965963	+	0.557699i
$143$	−1.11847	+	0.645751i	−0.0935315	+	0.0540004i
$144$	−4.00000			−0.333333
$145$		0			0
$146$	−6.14575	−	10.6448i	−0.508626	−	0.880966i
$147$	−9.83307	−	5.67712i	−0.811018	−	0.468241i
$148$	−4.88936	+	2.82288i	−0.401903	+	0.232039i
$149$	−2.46863	+	4.27579i	−0.202238	+	0.350286i	−0.949249	−	0.314525i	$-0.898155\pi$
$149$	−2.46863	+	4.27579i	−0.202238	+	0.350286i	0.747011	+	0.664811i	$0.231488\pi$
$150$		0			0
$151$	−2.93725			−0.239030			−0.119515	−	0.992832i	$-0.538134\pi$
$151$	−2.93725			−0.239030			−0.119515	+	0.992832i	$0.538134\pi$
$152$	−0.559237	+	4.32288i	−0.0453601	+	0.350632i
$153$		0			0
$154$	−0.531373	+	0.920365i	−0.0428193	+	0.0741651i
$155$		0			0
$156$	2.64575	+	4.58258i	0.211830	+	0.366900i
$157$	−9.16515	−	5.29150i	−0.731459	−	0.422308i	0.0874969	−	0.996165i	$-0.472113\pi$
$157$	−9.16515	−	5.29150i	−0.731459	−	0.422308i	−0.818956	+	0.573857i	$0.805447\pi$
$158$	3.46410	−	2.00000i	0.275589	−	0.159111i
$159$	22.7085			1.80090
$160$		0			0
$161$	3.00000	+	5.19615i	0.236433	+	0.409514i
$162$	−4.33013	+	2.50000i	−0.340207	+	0.196419i
$163$			11.9373i			0.934998i	0.883994	+	0.467499i	$0.154845\pi$
$163$			11.9373i			0.934998i	−0.883994	+	0.467499i	$0.845155\pi$
$164$	−10.2915			−0.803631
$165$		0			0
$166$	3.96863	−	6.87386i	0.308025	−	0.533515i
$167$	−10.3923	+	6.00000i	−0.804181	+	0.464294i	−0.844931	−	0.534875i	$-0.820359\pi$
$167$	−10.3923	+	6.00000i	−0.804181	+	0.464294i	0.0407502	+	0.999169i	$0.487025\pi$
$168$	3.77089	+	2.17712i	0.290930	+	0.167969i
$169$	−4.50000	+	7.79423i	−0.346154	+	0.599556i
$170$		0			0
$171$	−6.70850	−	16.0934i	−0.513012	−	1.23069i
$172$			0.708497i			0.0540224i
$173$	−5.19615	−	3.00000i	−0.395056	−	0.228086i	0.289292	−	0.957241i	$-0.406580\pi$
$173$	−5.19615	−	3.00000i	−0.395056	−	0.228086i	−0.684349	+	0.729155i	$0.739913\pi$
$174$	4.82288	−	8.35347i	0.365621	−	0.633275i
$175$		0			0
$176$	−0.322876	+	0.559237i	−0.0243377	+	0.0421541i
$177$	−18.1865	+	10.5000i	−1.36698	+	0.789228i
$178$		0			0
$179$	−19.9373			−1.49018			−0.745090	−	0.666964i	$-0.767594\pi$
$179$	−19.9373			−1.49018			−0.745090	+	0.666964i	$0.767594\pi$
$180$		0			0
$181$	2.11438	+	3.66221i	0.157160	+	0.272210i	0.933844	−	0.357682i	$-0.116433\pi$
$181$	2.11438	+	3.66221i	0.157160	+	0.272210i	−0.776683	+	0.629892i	$0.783099\pi$
$182$		−	3.29150i		−	0.243982i
$183$		−	39.5203i		−	2.92142i
$184$	1.82288	+	3.15731i	0.134384	+	0.232760i
$185$		0			0
$186$	−0.468627	−	0.811686i	−0.0343614	−	0.0595157i
$187$		0			0
$188$	8.35347	+	4.82288i	0.609239	+	0.351744i
$189$	−4.35425			−0.316725
$190$		0			0
$191$	−14.5830			−1.05519			−0.527595	−	0.849496i	$-0.676906\pi$
$191$	−14.5830			−1.05519			−0.527595	+	0.849496i	$0.676906\pi$
$192$	2.29129	+	1.32288i	0.165359	+	0.0954703i
$193$	−5.70105	−	3.29150i	−0.410371	−	0.236928i	0.280578	−	0.959831i	$-0.409474\pi$
$193$	−5.70105	−	3.29150i	−0.410371	−	0.236928i	−0.690949	+	0.722904i	$0.742807\pi$
$194$	−7.14575	−	12.3768i	−0.513035	−	0.888603i
$195$		0			0
$196$	2.14575	+	3.71655i	0.153268	+	0.265468i
$197$		−	2.35425i		−	0.167733i	−0.996477	−	0.0838666i	$-0.973273\pi$
$197$		−	2.35425i		−	0.167733i	0.996477	−	0.0838666i	$-0.0267270\pi$
$198$		−	2.58301i		−	0.183566i
$199$	5.93725	+	10.2836i	0.420881	+	0.728987i	0.996026	−	0.0890645i	$-0.0283877\pi$
$199$	5.93725	+	10.2836i	0.420881	+	0.728987i	−0.575145	+	0.818051i	$0.695054\pi$
$200$		0			0
$201$	12.2915			0.866976
$202$		−	8.35425i		−	0.587803i
$203$	−5.19615	+	3.00000i	−0.364698	+	0.210559i
$204$		0			0
$205$		0			0
$206$	1.35425	−	2.34563i	0.0943550	−	0.163428i
$207$	−12.6293	−	7.29150i	−0.877794	−	0.506794i
$208$		−	2.00000i		−	0.138675i
$209$	−2.79150	−	0.361128i	−0.193092	−	0.0249797i
$210$		0			0
$211$	1.35425	−	2.34563i	0.0932303	−	0.161480i	−0.815638	−	0.578562i	$-0.803614\pi$
$211$	1.35425	−	2.34563i	0.0932303	−	0.161480i	0.908869	+	0.417082i	$0.136947\pi$
$212$	−7.43310	−	4.29150i	−0.510507	−	0.294742i
$213$	−30.4547	+	17.5830i	−2.08672	+	1.20477i
$214$	2.35425	−	4.07768i	0.160933	−	0.278744i
$215$		0			0
$216$	−2.64575			−0.180021
$217$			0.583005i			0.0395770i
$218$	5.70105	−	3.29150i	0.386124	−	0.222929i
$219$	−16.2601	−	28.1634i	−1.09876	−	1.90310i
$220$		0			0
$221$		0			0
$222$	−12.9360	+	7.46863i	−0.868210	+	0.501261i
$223$	24.9517	+	14.4059i	1.67089	+	0.964689i	0.967141	+	0.254241i	$0.0818257\pi$
$223$	24.9517	+	14.4059i	1.67089	+	0.964689i	0.703750	+	0.710448i	$0.251508\pi$
$224$	−0.822876	−	1.42526i	−0.0549807	−	0.0952294i
$225$		0			0
$226$	−2.79150	+	4.83502i	−0.185688	+	0.321621i
$227$		−	12.6458i		−	0.839328i	−0.907680	−	0.419664i	$-0.862148\pi$
$227$		−	12.6458i		−	0.839328i	0.907680	−	0.419664i	$-0.137852\pi$
$228$	−1.47960	+	11.4373i	−0.0979890	+	0.757451i
$229$	−20.0000			−1.32164			−0.660819	−	0.750546i	$-0.729791\pi$
$229$	−20.0000			−1.32164			−0.660819	+	0.750546i	$0.729791\pi$
$230$		0			0
$231$	−1.40588	+	2.43506i	−0.0925002	+	0.160215i
$232$	−3.15731	+	1.82288i	−0.207288	+	0.119678i
$233$	−11.1497	−	6.43725i	−0.730438	−	0.421719i	0.0881444	−	0.996108i	$-0.471906\pi$
$233$	−11.1497	−	6.43725i	−0.730438	−	0.421719i	−0.818582	+	0.574389i	$0.805240\pi$
$234$	4.00000	+	6.92820i	0.261488	+	0.452911i
$235$		0			0
$236$	7.93725			0.516671
$237$	9.16515	−	5.29150i	0.595341	−	0.343720i
$238$		0			0
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$		0			0
$241$	−6.79150	−	11.7632i	−0.437479	−	0.757736i	0.560015	−	0.828482i	$-0.310795\pi$
$241$	−6.79150	−	11.7632i	−0.437479	−	0.757736i	−0.997494	+	0.0707462i	$0.977462\pi$
$242$	9.16515	+	5.29150i	0.589158	+	0.340151i
$243$	−18.3303	+	10.5830i	−1.17589	+	0.678900i
$244$	−7.46863	+	12.9360i	−0.478130	+	0.828145i
$245$		0			0
$246$	−27.2288			−1.73604
$247$	8.04668	−	3.35425i	0.511998	−	0.213426i
$248$			0.354249i			0.0224948i
$249$	10.5000	−	18.1865i	0.665410	−	1.15252i
$250$		0			0
$251$	−1.38562	−	2.39997i	−0.0874597	−	0.151485i	0.818977	−	0.573826i	$-0.194542\pi$
$251$	−1.38562	−	2.39997i	−0.0874597	−	0.151485i	−0.906437	+	0.422342i	$0.861208\pi$
$252$	5.70105	+	3.29150i	0.359132	+	0.207345i
$253$	−2.03884	+	1.17712i	−0.128181	+	0.0740052i
$254$	2.70850			0.169946
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.47960	−	0.854249i	0.0922950	−	0.0532866i	−0.453142	−	0.891438i	$-0.649697\pi$
$257$	1.47960	−	0.854249i	0.0922950	−	0.0532866i	0.545437	+	0.838152i	$0.316364\pi$
$258$			1.87451i			0.116702i
$259$	9.29150			0.577346
$260$		0			0
$261$	7.29150	−	12.6293i	0.451333	−	0.781731i
$262$	−12.0700	+	6.96863i	−0.745688	+	0.430523i
$263$	4.27579	+	2.46863i	0.263656	+	0.152222i	0.626001	−	0.779822i	$-0.284690\pi$
$263$	4.27579	+	2.46863i	0.263656	+	0.152222i	−0.362345	+	0.932044i	$0.618024\pi$
$264$	−0.854249	+	1.47960i	−0.0525754	+	0.0910632i
$265$		0			0
$266$	4.35425	−	5.70105i	0.266976	−	0.349554i
$267$		0			0
$268$	−4.02334	−	2.32288i	−0.245765	−	0.141892i
$269$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$269$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$270$		0			0
$271$	−8.82288	+	15.2817i	−0.535952	+	0.928295i	0.463165	+	0.886272i	$0.346714\pi$
$271$	−8.82288	+	15.2817i	−0.535952	+	0.928295i	−0.999117	+	0.0420233i	$0.986620\pi$
$272$		0			0
$273$		−	8.70850i		−	0.527062i
$274$	5.58301			0.337282
$275$		0			0
$276$	4.82288	+	8.35347i	0.290303	+	0.502820i
$277$			9.52026i			0.572017i	0.958227	+	0.286008i	$0.0923285\pi$
$277$			9.52026i			0.572017i	−0.958227	+	0.286008i	$0.907671\pi$
$278$		−	13.3542i		−	0.800935i
$279$	−0.708497	−	1.22715i	−0.0424166	−	0.0734678i
$280$		0			0
$281$	13.7288	+	23.7789i	0.818989	+	1.41853i	0.906428	+	0.422361i	$0.138798\pi$
$281$	13.7288	+	23.7789i	0.818989	+	1.41853i	−0.0874389	+	0.996170i	$0.527868\pi$
$282$	22.1012	+	12.7601i	1.31611	+	0.759855i
$283$	21.9574	+	12.6771i	1.30523	+	0.753577i	0.981297	−	0.192502i	$-0.0616602\pi$
$283$	21.9574	+	12.6771i	1.30523	+	0.753577i	0.323937	+	0.946079i	$0.394993\pi$
$284$	13.2915			0.788706
$285$		0			0
$286$	1.29150			0.0763682
$287$	14.6681	+	8.46863i	0.865830	+	0.499887i
$288$	3.46410	+	2.00000i	0.204124	+	0.117851i
$289$	−8.50000	−	14.7224i	−0.500000	−	0.866025i
$290$		0			0
$291$	−18.9059	−	32.7459i	−1.10828	−	1.91960i
$292$			12.2915i			0.719306i
$293$		−	13.0627i		−	0.763134i	−0.924341	−	0.381567i	$-0.875385\pi$
$293$		−	13.0627i		−	0.763134i	0.924341	−	0.381567i	$-0.124615\pi$
$294$	5.67712	+	9.83307i	0.331097	+	0.573476i
$295$		0			0
$296$	5.64575			0.328153
$297$		−	1.70850i		−	0.0991371i
$298$	4.27579	−	2.46863i	0.247690	−	0.143004i
$299$	3.64575	−	6.31463i	0.210839	−	0.365184i
$300$		0			0
$301$	0.583005	−	1.00979i	0.0336039	−	0.0582036i
$302$	2.54374	+	1.46863i	0.146376	+	0.0845100i
$303$		−	22.1033i		−	1.26980i
$304$	2.64575	−	3.46410i	0.151744	−	0.198680i
$305$		0			0
$306$		0			0
$307$	4.02334	+	2.32288i	0.229624	+	0.132574i	0.610399	−	0.792094i	$-0.291009\pi$
$307$	4.02334	+	2.32288i	0.229624	+	0.132574i	−0.380775	+	0.924668i	$0.624343\pi$
$308$	0.920365	−	0.531373i	0.0524427	−	0.0302778i
$309$	3.58301	−	6.20595i	0.203830	−	0.353044i
$310$		0			0
$311$	8.35425			0.473726			0.236863	−	0.971543i	$-0.423881\pi$
$311$	8.35425			0.473726			0.236863	+	0.971543i	$0.423881\pi$
$312$		−	5.29150i		−	0.299572i
$313$	19.8099	−	11.4373i	1.11972	−	0.646472i	0.178392	−	0.983959i	$-0.442910\pi$
$313$	19.8099	−	11.4373i	1.11972	−	0.646472i	0.941330	+	0.337488i	$0.109577\pi$
$314$	5.29150	+	9.16515i	0.298617	+	0.517219i
$315$		0			0
$316$	−4.00000			−0.225018
$317$	−5.19615	+	3.00000i	−0.291845	+	0.168497i	−0.638774	−	0.769395i	$-0.720558\pi$
$317$	−5.19615	+	3.00000i	−0.291845	+	0.168497i	0.346929	+	0.937892i	$0.387225\pi$
$318$	−19.6661	−	11.3542i	−1.10282	−	0.636715i
$319$	−1.17712	−	2.03884i	−0.0659063	−	0.114153i
$320$		0			0
$321$	6.22876	−	10.7885i	0.347655	−	0.602157i
$322$		−	6.00000i		−	0.334367i
$323$		0			0
$324$	5.00000			0.277778
$325$		0			0
$326$	5.96863	−	10.3380i	0.330572	−	0.572567i
$327$	15.0836	−	8.70850i	0.834123	−	0.481581i
$328$	8.91270	+	5.14575i	0.492122	+	0.284127i
$329$	−7.93725	−	13.7477i	−0.437595	−	0.757937i
$330$		0			0
$331$	−27.8118			−1.52867			−0.764336	−	0.644818i	$-0.776933\pi$
$331$	−27.8118			−1.52867			−0.764336	+	0.644818i	$0.776933\pi$
$332$	−6.87386	+	3.96863i	−0.377252	+	0.217807i
$333$	−19.5575	+	11.2915i	−1.07174	+	0.618771i
$334$	12.0000			0.656611
$335$		0			0
$336$	−2.17712	−	3.77089i	−0.118772	−	0.205719i
$337$	17.5730	+	10.1458i	0.957260	+	0.552674i	0.895329	−	0.445406i	$-0.146941\pi$
$337$	17.5730	+	10.1458i	0.957260	+	0.552674i	0.0619313	+	0.998080i	$0.480274\pi$
$338$	7.79423	−	4.50000i	0.423950	−	0.244768i
$339$	−7.38562	+	12.7923i	−0.401132	+	0.694781i
$340$		0			0
$341$	−0.228757			−0.0123879
$342$	−2.23695	+	17.2915i	−0.120960	+	0.935017i
$343$		−	18.5830i		−	1.00339i
$344$	0.354249	−	0.613577i	0.0190998	−	0.0330818i
$345$		0			0
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	−2.79619	−	1.61438i	−0.150107	−	0.0866644i	0.423065	−	0.906099i	$-0.360954\pi$
$347$	−2.79619	−	1.61438i	−0.150107	−	0.0866644i	−0.573172	+	0.819435i	$0.694287\pi$
$348$	−8.35347	+	4.82288i	−0.447793	+	0.258533i
$349$	21.1660			1.13299			0.566495	−	0.824065i	$-0.308299\pi$
$349$	21.1660			1.13299			0.566495	+	0.824065i	$0.308299\pi$
$350$		0			0
$351$	2.64575	+	4.58258i	0.141220	+	0.244600i
$352$	0.559237	−	0.322876i	0.0298074	−	0.0172093i
$353$			18.8745i			1.00459i	0.864697	+	0.502294i	$0.167511\pi$
$353$			18.8745i			1.00459i	−0.864697	+	0.502294i	$0.832489\pi$
$354$	21.0000			1.11614
$355$		0			0
$356$		0			0
$357$		0			0
$358$	17.2662	+	9.96863i	0.912545	+	0.526858i
$359$	5.46863	−	9.47194i	0.288623	−	0.499910i	−0.684858	−	0.728676i	$-0.740136\pi$
$359$	5.46863	−	9.47194i	0.288623	−	0.499910i	0.973481	+	0.228766i	$0.0734692\pi$
$360$		0			0
$361$	18.3745	+	4.83502i	0.967079	+	0.254475i
$362$		−	4.22876i		−	0.222259i
$363$	24.2487	+	14.0000i	1.27273	+	0.734809i
$364$	−1.64575	+	2.85052i	−0.0862608	+	0.149408i
$365$		0			0
$366$	−19.7601	+	34.2255i	−1.03288	+	1.78900i
$367$	−8.85836	+	5.11438i	−0.462403	+	0.266968i	−0.713054	−	0.701109i	$-0.752689\pi$
$367$	−8.85836	+	5.11438i	−0.462403	+	0.266968i	0.250651	+	0.968077i	$0.419355\pi$
$368$		−	3.64575i		−	0.190048i
$369$	−41.1660			−2.14302
$370$		0			0
$371$	7.06275	+	12.2330i	0.366680	+	0.635108i
$372$			0.937254i			0.0485944i
$373$			4.00000i			0.207112i	0.994624	+	0.103556i	$0.0330221\pi$
$373$			4.00000i			0.207112i	−0.994624	+	0.103556i	$0.966978\pi$
$374$		0			0
$375$		0			0
$376$	−4.82288	−	8.35347i	−0.248721	−	0.430797i
$377$	6.31463	+	3.64575i	0.325220	+	0.187766i
$378$	3.77089	+	2.17712i	0.193954	+	0.111979i
$379$	−21.2915			−1.09367			−0.546836	−	0.837240i	$-0.684168\pi$
$379$	−21.2915			−1.09367			−0.546836	+	0.837240i	$0.684168\pi$
$380$		0			0
$381$	7.16601			0.367126
$382$	12.6293	+	7.29150i	0.646169	+	0.373066i
$383$	−27.2973	−	15.7601i	−1.39483	−	0.805305i	−0.400984	−	0.916085i	$-0.631332\pi$
$383$	−27.2973	−	15.7601i	−1.39483	−	0.805305i	−0.993845	+	0.110780i	$0.964665\pi$
$384$	−1.32288	−	2.29129i	−0.0675077	−	0.116927i
$385$		0			0
$386$	3.29150	+	5.70105i	0.167533	+	0.290176i
$387$			2.83399i			0.144060i
$388$			14.2915i			0.725541i
$389$	6.00000	+	10.3923i	0.304212	+	0.526911i	0.977086	−	0.212847i	$-0.0682735\pi$
$389$	6.00000	+	10.3923i	0.304212	+	0.526911i	−0.672874	+	0.739758i	$0.734940\pi$
$390$		0			0
$391$		0			0
$392$		−	4.29150i		−	0.216754i
$393$	−31.9343	+	18.4373i	−1.61087	+	0.930036i
$394$	−1.17712	+	2.03884i	−0.0593027	+	0.102715i
$395$		0			0
$396$	−1.29150	+	2.23695i	−0.0649004	+	0.112411i
$397$	−31.9886	−	18.4686i	−1.60546	−	0.926914i	−0.990368	−	0.138460i	$-0.955785\pi$
$397$	−31.9886	−	18.4686i	−1.60546	−	0.926914i	−0.615094	−	0.788454i	$-0.710882\pi$
$398$		−	11.8745i		−	0.595215i
$399$	11.5203	−	15.0836i	0.576734	−	0.755122i
$400$		0			0
$401$	−3.20850	+	5.55728i	−0.160225	+	0.277517i	−0.934949	−	0.354782i	$-0.884555\pi$
$401$	−3.20850	+	5.55728i	−0.160225	+	0.277517i	0.774724	+	0.632299i	$0.217889\pi$
$402$	−10.6448	−	6.14575i	−0.530912	−	0.306522i
$403$	0.613577	−	0.354249i	0.0305644	−	0.0176464i
$404$	−4.17712	+	7.23499i	−0.207820	+	0.359954i
$405$		0			0
$406$	6.00000			0.297775
$407$			3.64575i			0.180713i
$408$		0			0
$409$	6.79150	+	11.7632i	0.335818	+	0.581654i	0.983642	−	0.180136i	$-0.0576539\pi$
$409$	6.79150	+	11.7632i	0.335818	+	0.581654i	−0.647823	+	0.761790i	$0.724321\pi$
$410$		0			0
$411$	14.7712			0.728612
$412$	−2.34563	+	1.35425i	−0.115561	+	0.0667190i
$413$	−11.3127	−	6.53137i	−0.556660	−	0.321388i
$414$	7.29150	+	12.6293i	0.358358	+	0.620694i
$415$		0			0
$416$	−1.00000	+	1.73205i	−0.0490290	+	0.0849208i
$417$		−	35.3320i		−	1.73022i
$418$	2.23695	+	1.70850i	0.109413	+	0.0835653i
$419$	−31.7490			−1.55104			−0.775520	−	0.631322i	$-0.782512\pi$
$419$	−31.7490			−1.55104			−0.775520	+	0.631322i	$0.782512\pi$
$420$		0			0
$421$	−11.4059	+	19.7556i	−0.555889	+	0.962827i	0.441945	+	0.897042i	$0.354289\pi$
$421$	−11.4059	+	19.7556i	−0.555889	+	0.962827i	−0.997834	+	0.0657853i	$0.979045\pi$
$422$	−2.34563	+	1.35425i	−0.114183	+	0.0659238i
$423$	33.4139	+	19.2915i	1.62464	+	0.937985i
$424$	4.29150	+	7.43310i	0.208414	+	0.360983i
$425$		0			0
$426$	35.1660			1.70380
$427$	21.2895	−	12.2915i	1.03027	−	0.594828i
$428$	−4.07768	+	2.35425i	−0.197102	+	0.113797i
$429$	3.41699			0.164974
$430$		0			0
$431$	1.93725	+	3.35542i	0.0933142	+	0.161625i	0.908904	−	0.417006i	$-0.136921\pi$
$431$	1.93725	+	3.35542i	0.0933142	+	0.161625i	−0.815590	+	0.578631i	$0.803587\pi$
$432$	2.29129	+	1.32288i	0.110240	+	0.0636469i
$433$	12.0157	−	6.93725i	0.577437	−	0.333383i	−0.182677	−	0.983173i	$-0.558476\pi$
$433$	12.0157	−	6.93725i	0.577437	−	0.333383i	0.760114	+	0.649790i	$0.225143\pi$
$434$	0.291503	−	0.504897i	0.0139926	−	0.0242358i
$435$		0			0
$436$	−6.58301			−0.315269
$437$	14.6681	−	6.11438i	0.701670	−	0.292490i
$438$			32.5203i			1.55388i
$439$	−18.4059	+	31.8799i	−0.878465	+	1.52155i	−0.0254393	+	0.999676i	$0.508098\pi$
$439$	−18.4059	+	31.8799i	−0.878465	+	1.52155i	−0.853025	+	0.521869i	$0.825235\pi$
$440$		0			0
$441$	8.58301	+	14.8662i	0.408715	+	0.707914i
$442$		0			0
$443$	−4.63692	+	2.67712i	−0.220306	+	0.127194i	−0.606092	−	0.795394i	$-0.707264\pi$
$443$	−4.63692	+	2.67712i	−0.220306	+	0.127194i	0.385786	+	0.922588i	$0.373930\pi$
$444$	14.9373			0.708891
$445$		0			0
$446$	−14.4059	−	24.9517i	−0.682138	−	1.18150i
$447$	11.3127	−	6.53137i	0.535071	−	0.308923i
$448$			1.64575i			0.0777544i
$449$	13.7085			0.646944			0.323472	−	0.946238i	$-0.395150\pi$
$449$	13.7085			0.646944			0.323472	+	0.946238i	$0.395150\pi$
$450$		0			0
$451$	−3.32288	+	5.75539i	−0.156468	+	0.271011i
$452$	4.83502	−	2.79150i	0.227420	−	0.131301i
$453$	6.73009	+	3.88562i	0.316207	+	0.182562i
$454$	−6.32288	+	10.9515i	−0.296747	+	0.513981i
$455$		0			0
$456$	7.00000	−	9.16515i	0.327805	−	0.429198i
$457$			1.12549i			0.0526483i	0.999653	+	0.0263242i	$0.00838021\pi$
$457$			1.12549i			0.0526483i	−0.999653	+	0.0263242i	$0.991620\pi$
$458$	17.3205	+	10.0000i	0.809334	+	0.467269i
$459$		0			0
$460$		0			0
$461$	11.5830	−	20.0624i	0.539474	−	0.934397i	−0.459458	−	0.888200i	$-0.651956\pi$
$461$	11.5830	−	20.0624i	0.539474	−	0.934397i	0.998932	−	0.0461975i	$-0.0147103\pi$
$462$	2.43506	−	1.40588i	0.113289	−	0.0654075i
$463$		−	14.4575i		−	0.671898i	−0.941880	−	0.335949i	$-0.890943\pi$
$463$		−	14.4575i		−	0.671898i	0.941880	−	0.335949i	$-0.109057\pi$
$464$	3.64575			0.169250
$465$		0			0
$466$	6.43725	+	11.1497i	0.298200	+	0.516498i
$467$		−	24.6458i		−	1.14047i	−0.821482	−	0.570235i	$-0.806852\pi$
$467$		−	24.6458i		−	1.14047i	0.821482	−	0.570235i	$-0.193148\pi$
$468$		−	8.00000i		−	0.369800i
$469$	3.82288	+	6.62141i	0.176524	+	0.305749i
$470$		0			0
$471$	14.0000	+	24.2487i	0.645086	+	1.11732i
$472$	−6.87386	−	3.96863i	−0.316395	−	0.182671i
$473$	0.396218	+	0.228757i	0.0182181	+	0.0105182i
$474$	−10.5830			−0.486094
$475$		0			0
$476$		0			0
$477$	−29.7324	−	17.1660i	−1.36135	−	0.785978i
$478$	−10.3923	−	6.00000i	−0.475333	−	0.274434i
$479$	−7.29150	−	12.6293i	−0.333157	−	0.577045i	0.649972	−	0.759958i	$-0.274781\pi$
$479$	−7.29150	−	12.6293i	−0.333157	−	0.577045i	−0.983129	+	0.182913i	$0.941447\pi$
$480$		0			0
$481$	−5.64575	−	9.77873i	−0.257424	−	0.445872i
$482$			13.5830i			0.618689i
$483$		−	15.8745i		−	0.722315i
$484$	−5.29150	−	9.16515i	−0.240523	−	0.416598i
$485$		0			0
$486$	21.1660			0.960110
$487$		−	22.2288i		−	1.00728i	−0.863913	−	0.503641i	$-0.831994\pi$
$487$		−	22.2288i		−	1.00728i	0.863913	−	0.503641i	$-0.168006\pi$
$488$	12.9360	−	7.46863i	0.585587	−	0.338089i
$489$	15.7915	−	27.3517i	0.714116	−	1.23689i
$490$		0			0
$491$	−14.3542	+	24.8623i	−0.647798	+	1.12202i	0.335849	+	0.941916i	$0.390977\pi$
$491$	−14.3542	+	24.8623i	−0.647798	+	1.12202i	−0.983648	+	0.180104i	$0.942357\pi$
$492$	23.5808	+	13.6144i	1.06310	+	0.613784i
$493$		0			0
$494$	−8.64575	−	1.11847i	−0.388991	−	0.0503225i
$495$		0			0
$496$	0.177124	−	0.306788i	0.00795312	−	0.0137752i
$497$	−18.9439	−	10.9373i	−0.849749	−	0.490603i
$498$	−18.1865	+	10.5000i	−0.814958	+	0.470516i
$499$	−15.6144	+	27.0449i	−0.698996	+	1.21070i	0.269819	+	0.962911i	$0.413036\pi$
$499$	−15.6144	+	27.0449i	−0.698996	+	1.21070i	−0.968815	+	0.247785i	$0.920297\pi$
$500$		0			0
$501$	31.7490			1.41844
$502$			2.77124i			0.123687i
$503$	21.7050	−	12.5314i	0.967777	−	0.558746i	0.0692192	−	0.997601i	$-0.477949\pi$
$503$	21.7050	−	12.5314i	0.967777	−	0.558746i	0.898558	+	0.438855i	$0.144616\pi$
$504$	−3.29150	−	5.70105i	−0.146615	−	0.253945i
$505$		0			0
$506$	2.35425			0.104659
$507$	20.6216	−	11.9059i	0.915837	−	0.528759i
$508$	−2.34563	−	1.35425i	−0.104070	−	0.0600851i
$509$	15.8745	+	27.4955i	0.703625	+	1.21871i	0.967185	+	0.254072i	$0.0817699\pi$
$509$	15.8745	+	27.4955i	0.703625	+	1.21871i	−0.263560	+	0.964643i	$0.584897\pi$
$510$		0			0
$511$	10.1144	−	17.5186i	0.447434	−	0.774978i
$512$			1.00000i			0.0441942i
$513$	−1.47960	+	11.4373i	−0.0653260	+	0.504967i
$514$	−1.70850			−0.0753586
$515$		0			0
$516$	0.937254	−	1.62337i	0.0412603	−	0.0714649i
$517$	5.39426	−	3.11438i	0.237239	−	0.136970i
$518$	−8.04668	−	4.64575i	−0.353551	−	0.204123i
$519$	7.93725	+	13.7477i	0.348407	+	0.603458i
$520$		0			0
$521$	−22.2915			−0.976608			−0.488304	−	0.872673i	$-0.662384\pi$
$521$	−22.2915			−0.976608			−0.488304	+	0.872673i	$0.662384\pi$
$522$	−12.6293	+	7.29150i	−0.552767	+	0.319140i
$523$	−25.8721	+	14.9373i	−1.13131	+	0.653161i	−0.944263	−	0.329191i	$-0.893224\pi$
$523$	−25.8721	+	14.9373i	−1.13131	+	0.653161i	−0.187044	+	0.982352i	$0.559891\pi$
$524$	13.9373			0.608852
$525$		0			0
$526$	−2.46863	−	4.27579i	−0.107637	−	0.186433i
$527$		0			0
$528$	1.47960	−	0.854249i	0.0643914	−	0.0371764i
$529$	−4.85425	+	8.40781i	−0.211054	+	0.365557i
$530$		0			0
$531$	31.7490			1.37779
$532$	−6.62141	+	2.76013i	−0.287075	+	0.119667i
$533$		−	20.5830i		−	0.891549i
$534$		0			0
$535$		0			0
$536$	2.32288	+	4.02334i	0.100333	+	0.173782i
$537$	45.6820	+	26.3745i	1.97132	+	1.13814i
$538$		0			0
$539$	2.77124			0.119366
$540$		0			0
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	0.767136	−	0.641484i	$-0.221681\pi$
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	−0.939110	+	0.343617i	$0.888348\pi$
$542$	15.2817	−	8.82288i	0.656404	−	0.378975i
$543$		−	11.1882i		−	0.480133i
$544$		0			0
$545$		0			0
$546$	−4.35425	+	7.54178i	−0.186345	+	0.322758i
$547$	0.613577	−	0.354249i	0.0262346	−	0.0151466i	−0.486825	−	0.873499i	$-0.661845\pi$
$547$	0.613577	−	0.354249i	0.0262346	−	0.0151466i	0.513060	+	0.858353i	$0.328512\pi$
$548$	−4.83502	−	2.79150i	−0.206542	−	0.119247i
$549$	−29.8745	+	51.7442i	−1.27501	+	2.20839i
$550$		0			0
$551$	6.11438	+	14.6681i	0.260481	+	0.624882i
$552$		−	9.64575i		−	0.410550i
$553$	5.70105	+	3.29150i	0.242433	+	0.139969i
$554$	4.76013	−	8.24479i	0.202239	−	0.350287i
$555$		0			0
$556$	−6.67712	+	11.5651i	−0.283173	+	0.490470i
$557$	−23.0216	+	13.2915i	−0.975455	+	0.563179i	−0.900895	−	0.434037i	$-0.857089\pi$
$557$	−23.0216	+	13.2915i	−0.975455	+	0.563179i	−0.0745599	+	0.997217i	$0.523755\pi$
$558$			1.41699i			0.0599862i
$559$	−1.41699			−0.0599325
$560$		0			0
$561$		0			0
$562$		−	27.4575i		−	1.15823i
$563$		−	25.9373i		−	1.09312i	−0.837418	−	0.546562i	$-0.815936\pi$
$563$		−	25.9373i		−	1.09312i	0.837418	−	0.546562i	$-0.184064\pi$
$564$	−12.7601	−	22.1012i	−0.537298	−	0.930628i
$565$		0			0
$566$	−12.6771	−	21.9574i	−0.532859	−	0.922939i
$567$	−7.12631	−	4.11438i	−0.299277	−	0.172788i
$568$	−11.5108	−	6.64575i	−0.482982	−	0.278850i
$569$	14.5830			0.611351			0.305676	−	0.952136i	$-0.401118\pi$
$569$	14.5830			0.611351			0.305676	+	0.952136i	$0.401118\pi$
$570$		0			0
$571$	−39.8118			−1.66607			−0.833035	−	0.553220i	$-0.813399\pi$
$571$	−39.8118			−1.66607			−0.833035	+	0.553220i	$0.813399\pi$
$572$	−1.11847	−	0.645751i	−0.0467658	−	0.0270002i
$573$	33.4139	+	19.2915i	1.39588	+	0.805914i
$574$	−8.46863	−	14.6681i	−0.353474	−	0.612234i
$575$		0			0
$576$	−2.00000	−	3.46410i	−0.0833333	−	0.144338i
$577$			11.0000i			0.457936i	0.973434	+	0.228968i	$0.0735351\pi$
$577$			11.0000i			0.457936i	−0.973434	+	0.228968i	$0.926465\pi$
$578$			17.0000i			0.707107i
$579$	8.70850	+	15.0836i	0.361913	+	0.626851i
$580$		0			0
$581$	13.0627			0.541934
$582$			37.8118i			1.56735i
$583$	−4.79993	+	2.77124i	−0.198793	+	0.114773i
$584$	6.14575	−	10.6448i	0.254313	−	0.440483i
$585$		0			0
$586$	−6.53137	+	11.3127i	−0.269809	+	0.467322i
$587$	39.7285	+	22.9373i	1.63977	+	0.946722i	0.980911	+	0.194455i	$0.0622939\pi$
$587$	39.7285	+	22.9373i	1.63977	+	0.946722i	0.658859	+	0.752267i	$0.271039\pi$
$588$		−	11.3542i		−	0.468241i
$589$	1.53137	+	0.198109i	0.0630991	+	0.00816294i
$590$		0			0
$591$	−3.11438	+	5.39426i	−0.128108	+	0.221890i
$592$	−4.88936	−	2.82288i	−0.200952	−	0.116019i
$593$	−34.8935	+	20.1458i	−1.43290	+	0.827287i	−0.997341	−	0.0728721i	$-0.976784\pi$
$593$	−34.8935	+	20.1458i	−1.43290	+	0.827287i	−0.435562	+	0.900159i	$0.643450\pi$
$594$	−0.854249	+	1.47960i	−0.0350502	+	0.0607088i
$595$		0			0
$596$	−4.93725			−0.202238
$597$		−	31.4170i		−	1.28581i
$598$	−6.31463	+	3.64575i	−0.258224	+	0.149086i
$599$	−0.531373	−	0.920365i	−0.0217113	−	0.0376051i	0.854966	−	0.518685i	$-0.173578\pi$
$599$	−0.531373	−	0.920365i	−0.0217113	−	0.0376051i	−0.876677	+	0.481080i	$0.840245\pi$
$600$		0			0
$601$	31.5830			1.28830			0.644149	−	0.764900i	$-0.277212\pi$
$601$	31.5830			1.28830			0.644149	+	0.764900i	$0.277212\pi$
$602$	−1.00979	+	0.583005i	−0.0411562	+	0.0237615i
$603$	−16.0934	−	9.29150i	−0.655372	−	0.378379i
$604$	−1.46863	−	2.54374i	−0.0597576	−	0.103503i
$605$		0			0
$606$	−11.0516	+	19.1420i	−0.448942	+	0.777590i
$607$		−	8.93725i		−	0.362752i	−0.983414	−	0.181376i	$-0.941945\pi$
$607$		−	8.93725i		−	0.362752i	0.983414	−	0.181376i	$-0.0580551\pi$
$608$	−4.02334	+	1.67712i	−0.163168	+	0.0680164i
$609$	15.8745			0.643268
$610$		0			0
$611$	−9.64575	+	16.7069i	−0.390225	+	0.675890i
$612$		0			0
$613$	24.7536	+	14.2915i	0.999789	+	0.577228i	0.908186	−	0.418567i	$-0.137468\pi$
$613$	24.7536	+	14.2915i	0.999789	+	0.577228i	0.0916030	+	0.995796i	$0.470801\pi$
$614$	−2.32288	−	4.02334i	−0.0937436	−	0.162369i
$615$		0			0
$616$	−1.06275			−0.0428193
$617$	0.757346	−	0.437254i	0.0304896	−	0.0176032i	−0.484678	−	0.874693i	$-0.661063\pi$
$617$	0.757346	−	0.437254i	0.0304896	−	0.0176032i	0.515167	+	0.857090i	$0.327730\pi$
$618$	−6.20595	+	3.58301i	−0.249640	+	0.144130i
$619$	−44.4575			−1.78690			−0.893449	−	0.449164i	$-0.851722\pi$
$619$	−44.4575			−1.78690			−0.893449	+	0.449164i	$0.851722\pi$
$620$		0			0
$621$	4.82288	+	8.35347i	0.193535	+	0.335213i
$622$	−7.23499	−	4.17712i	−0.290097	−	0.167487i
$623$		0			0
$624$	−2.64575	+	4.58258i	−0.105915	+	0.183450i
$625$		0			0
$626$	−22.8745			−0.914249
$627$	5.91841	+	4.52026i	0.236358	+	0.180522i
$628$		−	10.5830i		−	0.422308i
$629$		0			0
$630$		0			0
$631$	−11.4059	−	19.7556i	−0.454061	−	0.786457i	0.544573	−	0.838714i	$-0.316692\pi$
$631$	−11.4059	−	19.7556i	−0.454061	−	0.786457i	−0.998634	+	0.0522570i	$0.983359\pi$
$632$	3.46410	+	2.00000i	0.137795	+	0.0795557i
$633$	−6.20595	+	3.58301i	−0.246664	+	0.142412i
$634$	6.00000			0.238290
$635$		0			0
$636$	11.3542	+	19.6661i	0.450225	+	0.779813i
$637$	−7.43310	+	4.29150i	−0.294510	+	0.170036i
$638$			2.35425i			0.0932056i
$639$	53.1660			2.10321
$640$		0			0
$641$	9.43725	−	16.3458i	0.372749	−	0.645620i	−0.617238	−	0.786776i	$-0.711749\pi$
$641$	9.43725	−	16.3458i	0.372749	−	0.645620i	0.989987	+	0.141156i	$0.0450819\pi$
$642$	−10.7885	+	6.22876i	−0.425789	+	0.245829i
$643$	26.4313	+	15.2601i	1.04235	+	0.601801i	0.920498	−	0.390748i	$-0.127783\pi$
$643$	26.4313	+	15.2601i	1.04235	+	0.601801i	0.121852	+	0.992548i	$0.461117\pi$
$644$	−3.00000	+	5.19615i	−0.118217	+	0.204757i
$645$		0			0
$646$		0			0
$647$			30.4575i			1.19741i	0.800970	+	0.598704i	$0.204317\pi$
$647$			30.4575i			1.19741i	−0.800970	+	0.598704i	$0.795683\pi$
$648$	−4.33013	−	2.50000i	−0.170103	−	0.0982093i
$649$	2.56275	−	4.43881i	0.100597	−	0.174238i
$650$		0			0
$651$	0.771243	−	1.33583i	0.0302274	−	0.0523554i
$652$	−10.3380	+	5.96863i	−0.404866	+	0.233749i
$653$		−	24.0000i		−	0.939193i	−0.882881	−	0.469596i	$-0.844399\pi$
$653$		−	24.0000i		−	0.939193i	0.882881	−	0.469596i	$-0.155601\pi$
$654$	−17.4170			−0.681058
$655$		0			0
$656$	−5.14575	−	8.91270i	−0.200908	−	0.347983i
$657$			49.1660i			1.91815i
$658$			15.8745i			0.618853i
$659$	1.29150	+	2.23695i	0.0503098	+	0.0871391i	0.890084	−	0.455797i	$-0.150646\pi$
$659$	1.29150	+	2.23695i	0.0503098	+	0.0871391i	−0.839774	+	0.542936i	$0.817312\pi$
$660$		0			0
$661$	5.11438	+	8.85836i	0.198926	+	0.344550i	0.948181	−	0.317732i	$-0.102921\pi$
$661$	5.11438	+	8.85836i	0.198926	+	0.344550i	−0.749254	+	0.662282i	$0.769588\pi$
$662$	24.0857	+	13.9059i	0.936117	+	0.540467i
$663$		0			0
$664$	7.93725			0.308025
$665$		0			0
$666$	22.5830			0.875074
$667$	11.5108	+	6.64575i	0.445699	+	0.257325i
$668$	−10.3923	−	6.00000i	−0.402090	−	0.232147i
$669$	−38.1144	−	66.0160i	−1.47359	−	2.55233i
$670$		0			0
$671$	4.82288	+	8.35347i	0.186185	+	0.322482i
$672$			4.35425i			0.167969i
$673$		−	17.8745i		−	0.689012i	−0.938784	−	0.344506i	$-0.888046\pi$
$673$		−	17.8745i		−	0.689012i	0.938784	−	0.344506i	$-0.111954\pi$
$674$	−10.1458	−	17.5730i	−0.390800	−	0.676885i
$675$		0			0
$676$	−9.00000			−0.346154
$677$		−	32.5830i		−	1.25227i	−0.779716	−	0.626133i	$-0.784637\pi$
$677$		−	32.5830i		−	1.25227i	0.779716	−	0.626133i	$-0.215363\pi$
$678$	12.7923	−	7.38562i	0.491284	−	0.283643i
$679$	11.7601	−	20.3691i	0.451312	−	0.781696i
$680$		0			0
$681$	−16.7288	+	28.9751i	−0.641047	+	1.11033i
$682$	0.198109	+	0.114378i	0.00758599	+	0.00437977i
$683$			26.5830i			1.01717i	0.861012	+	0.508585i	$0.169831\pi$
$683$			26.5830i			1.01717i	−0.861012	+	0.508585i	$0.830169\pi$
$684$	10.5830	−	13.8564i	0.404651	−	0.529813i
$685$		0			0
$686$	−9.29150	+	16.0934i	−0.354751	+	0.614447i
$687$	45.8258	+	26.4575i	1.74836	+	1.00942i
$688$	−0.613577	+	0.354249i	−0.0233924	+	0.0135056i
$689$	8.58301	−	14.8662i	0.326986	−	0.566357i
$690$		0			0
$691$	−18.5830			−0.706931			−0.353465	−	0.935448i	$-0.614997\pi$
$691$	−18.5830			−0.706931			−0.353465	+	0.935448i	$0.614997\pi$
$692$		−	6.00000i		−	0.228086i
$693$	3.68146	−	2.12549i	0.139847	−	0.0807408i
$694$	1.61438	+	2.79619i	0.0612810	+	0.106142i
$695$		0			0
$696$	9.64575			0.365621
$697$		0			0
$698$	−18.3303	−	10.5830i	−0.693812	−	0.400573i
$699$	17.0314	+	29.4992i	0.644186	+	1.11576i
$700$		0			0
$701$	−7.82288	+	13.5496i	−0.295466	+	0.511762i	−0.975093	−	0.221796i	$-0.928808\pi$
$701$	−7.82288	+	13.5496i	−0.295466	+	0.511762i	0.679627	+	0.733558i	$0.262142\pi$
$702$		−	5.29150i		−	0.199715i
$703$	3.15731	−	24.4059i	0.119080	−	0.920485i
$704$	−0.645751			−0.0243377
$705$		0			0
$706$	9.43725	−	16.3458i	0.355176	−	0.615182i
$707$	11.9070	−	6.87451i	0.447809	−	0.258542i
$708$	−18.1865	−	10.5000i	−0.683492	−	0.394614i
$709$	−0.822876	−	1.42526i	−0.0309037	−	0.0535269i	0.850160	−	0.526525i	$-0.176505\pi$
$709$	−0.822876	−	1.42526i	−0.0309037	−	0.0535269i	−0.881064	+	0.472998i	$0.843172\pi$
$710$		0			0
$711$	−16.0000			−0.600047
$712$		0			0
$713$	1.11847	−	0.645751i	0.0418872	−	0.0241836i
$714$		0			0
$715$		0			0
$716$	−9.96863	−	17.2662i	−0.372545	−	0.645267i
$717$	−27.4955	−	15.8745i	−1.02684	−	0.592844i
$718$	−9.47194	+	5.46863i	−0.353490	+	0.204087i
$719$	6.64575	−	11.5108i	0.247845	−	0.429280i	−0.715083	−	0.699040i	$-0.753611\pi$
$719$	6.64575	−	11.5108i	0.247845	−	0.429280i	0.962928	+	0.269760i	$0.0869444\pi$
$720$		0			0
$721$	4.45751			0.166006
$722$	−13.4953	−	13.3745i	−0.502242	−	0.497748i
$723$			35.9373i			1.33652i
$724$	−2.11438	+	3.66221i	−0.0785802	+	0.136105i
$725$		0			0
$726$	−14.0000	−	24.2487i	−0.519589	−	0.899954i
$727$	−19.5575	−	11.2915i	−0.725346	−	0.418779i	0.0913712	−	0.995817i	$-0.470875\pi$
$727$	−19.5575	−	11.2915i	−0.725346	−	0.418779i	−0.816717	+	0.577038i	$0.804208\pi$
$728$	2.85052	−	1.64575i	0.105647	−	0.0609956i
$729$	41.0000			1.51852
$730$		0			0
$731$		0			0
$732$	34.2255	−	19.7601i	1.26501	−	0.730355i
$733$		−	42.1033i		−	1.55512i	−0.628809	−	0.777560i	$-0.716457\pi$
$733$		−	42.1033i		−	1.55512i	0.628809	−	0.777560i	$-0.283543\pi$
$734$	10.2288			0.377550
$735$		0			0
$736$	−1.82288	+	3.15731i	−0.0671921	+	0.116380i
$737$	−2.59808	+	1.50000i	−0.0957014	+	0.0552532i
$738$	35.6508	+	20.5830i	1.31232	+	0.757671i
$739$	6.90588	−	11.9613i	0.254037	−	0.440005i	−0.710597	−	0.703600i	$-0.751575\pi$
$739$	6.90588	−	11.9613i	0.254037	−	0.440005i	0.964633	+	0.263595i	$0.0849082\pi$
$740$		0			0
$741$	−22.8745	−	2.95920i	−0.840316	−	0.108709i
$742$		−	14.1255i		−	0.518563i
$743$	−9.07572	−	5.23987i	−0.332956	−	0.192232i	0.324197	−	0.945990i	$-0.394906\pi$
$743$	−9.07572	−	5.23987i	−0.332956	−	0.192232i	−0.657153	+	0.753757i	$0.728239\pi$
$744$	0.468627	−	0.811686i	0.0171807	−	0.0297578i
$745$		0			0
$746$	2.00000	−	3.46410i	0.0732252	−	0.126830i
$747$	−27.4955	+	15.8745i	−1.00601	+	0.580818i
$748$		0			0
$749$	7.74902			0.283143
$750$		0			0
$751$	−11.9373	−	20.6759i	−0.435597	−	0.754475i	0.561748	−	0.827309i	$-0.310129\pi$
$751$	−11.9373	−	20.6759i	−0.435597	−	0.754475i	−0.997344	+	0.0728333i	$0.976796\pi$
$752$			9.64575i			0.351744i
$753$			7.33202i			0.267194i
$754$	−3.64575	−	6.31463i	−0.132770	−	0.229965i
$755$		0			0
$756$	−2.17712	−	3.77089i	−0.0791812	−	0.137146i
$757$	−14.3613	−	8.29150i	−0.521970	−	0.301360i	0.215770	−	0.976444i	$-0.430774\pi$
$757$	−14.3613	−	8.29150i	−0.521970	−	0.301360i	−0.737740	+	0.675084i	$0.764107\pi$
$758$	18.4390	+	10.6458i	0.669734	+	0.386671i
$759$	6.22876			0.226090
$760$		0			0
$761$	11.1255			0.403299			0.201649	−	0.979458i	$-0.435370\pi$
$761$	11.1255			0.403299			0.201649	+	0.979458i	$0.435370\pi$
$762$	−6.20595	−	3.58301i	−0.224818	−	0.129799i
$763$	9.38251	+	5.41699i	0.339670	+	0.196108i
$764$	−7.29150	−	12.6293i	−0.263797	−	0.456910i
$765$		0			0
$766$	15.7601	+	27.2973i	0.569437	+	0.986293i
$767$			15.8745i			0.573195i
$768$			2.64575i			0.0954703i
$769$	12.3542	+	21.3982i	0.445506	+	0.771638i	0.998087	−	0.0618204i	$-0.0196906\pi$
$769$	12.3542	+	21.3982i	0.445506	+	0.771638i	−0.552582	+	0.833459i	$0.686357\pi$
$770$		0			0
$771$	−4.52026			−0.162793
$772$		−	6.58301i		−	0.236928i
$773$	−9.47194	+	5.46863i	−0.340682	+	0.196693i	−0.660574	−	0.750761i	$-0.729687\pi$
$773$	−9.47194	+	5.46863i	−0.340682	+	0.196693i	0.319892	+	0.947454i	$0.396354\pi$
$774$	1.41699	−	2.45431i	0.0509328	−	0.0882182i
$775$		0			0
$776$	7.14575	−	12.3768i	0.256518	−	0.444301i
$777$	−21.2895	−	12.2915i	−0.763757	−	0.440955i
$778$		−	12.0000i		−	0.430221i
$779$	27.2288	−	35.6508i	0.975571	−	1.27732i
$780$		0			0
$781$	4.29150	−	7.43310i	0.153562	−	0.265977i
$782$		0			0
$783$	−8.35347	+	4.82288i	−0.298529	+	0.172356i
$784$	−2.14575	+	3.71655i	−0.0766340	+	0.132734i
$785$		0			0
$786$	36.8745			1.31527
$787$		−	5.47974i		−	0.195332i	−0.995219	−	0.0976658i	$-0.968862\pi$
$787$		−	5.47974i		−	0.195332i	0.995219	−	0.0976658i	$-0.0311376\pi$
$788$	2.03884	−	1.17712i	0.0726306	−	0.0419333i
$789$	−6.53137	−	11.3127i	−0.232523	−	0.402742i
$790$		0			0
$791$	−9.18824			−0.326696
$792$	2.23695	−	1.29150i	0.0794865	−	0.0458915i
$793$	−25.8721	−	14.9373i	−0.918745	−	0.530437i
$794$	18.4686	+	31.9886i	0.655427	+	1.13523i
$795$		0			0
$796$	−5.93725	+	10.2836i	−0.210440	+	0.364493i
$797$			2.81176i			0.0995977i	0.998759	+	0.0497989i	$0.0158580\pi$
$797$			2.81176i			0.0995977i	−0.998759	+	0.0497989i	$0.984142\pi$
$798$	−17.5186	+	7.30262i	−0.620152	+	0.258510i
$799$		0			0
$800$		0			0
$801$		0			0
$802$	5.55728	−	3.20850i	0.196234	−	0.113296i
$803$	6.87386	+	3.96863i	0.242573	+	0.140050i
$804$	6.14575	+	10.6448i	0.216744	+	0.375412i
$805$		0			0
$806$	−0.708497			−0.0249558
$807$		0			0
$808$	7.23499	−	4.17712i	0.254526	−	0.146951i
$809$	9.00000			0.316423			0.158212	−	0.987405i	$-0.449427\pi$
$809$	9.00000			0.316423			0.158212	+	0.987405i	$0.449427\pi$
$810$		0			0
$811$	10.3542	+	17.9341i	0.363587	+	0.629751i	0.988548	−	0.150905i	$-0.0482187\pi$
$811$	10.3542	+	17.9341i	0.363587	+	0.629751i	−0.624961	+	0.780656i	$0.714885\pi$
$812$	−5.19615	−	3.00000i	−0.182349	−	0.105279i
$813$	40.4315	−	23.3431i	1.41799	−	0.818679i
$814$	1.82288	−	3.15731i	0.0638918	−	0.110664i
$815$		0			0
$816$		0			0
$817$	−2.45431	−	1.87451i	−0.0858653	−	0.0655807i
$818$		−	13.5830i		−	0.474919i
$819$	−6.58301	+	11.4021i	−0.230029	+	0.398422i
$820$		0			0
$821$	3.00000	+	5.19615i	0.104701	+	0.181347i	0.913616	−	0.406578i	$-0.133278\pi$
$821$	3.00000	+	5.19615i	0.104701	+	0.181347i	−0.808915	+	0.587925i	$0.799945\pi$
$822$	−12.7923	−	7.38562i	−0.446182	−	0.257603i
$823$	0.108679	−	0.0627461i	0.00378832	−	0.00218719i	−0.498105	−	0.867117i	$-0.665970\pi$
$823$	0.108679	−	0.0627461i	0.00378832	−	0.00218719i	0.501893	+	0.864930i	$0.332637\pi$
$824$	2.70850			0.0943550
$825$		0			0
$826$	6.53137	+	11.3127i	0.227256	+	0.393618i
$827$	−41.0100	+	23.6771i	−1.42606	+	0.823334i	−0.996807	−	0.0798514i	$-0.974555\pi$
$827$	−41.0100	+	23.6771i	−1.42606	+	0.823334i	−0.429250	+	0.903186i	$0.641222\pi$
$828$		−	14.5830i		−	0.506794i
$829$	−25.1660			−0.874052			−0.437026	−	0.899449i	$-0.643968\pi$
$829$	−25.1660			−0.874052			−0.437026	+	0.899449i	$0.643968\pi$
$830$		0			0
$831$	12.5941	−	21.8137i	0.436885	−	0.756707i
$832$	1.73205	−	1.00000i	0.0600481	−	0.0346688i
$833$		0			0
$834$	−17.6660	+	30.5984i	−0.611724	+	1.05954i
$835$		0			0
$836$	−1.08301	−	2.59808i	−0.0374565	−	0.0898563i
$837$			0.937254i			0.0323962i
$838$	27.4955	+	15.8745i	0.949815	+	0.548376i
$839$	−2.23987	+	3.87957i	−0.0773289	+	0.133938i	−0.902097	−	0.431534i	$-0.857972\pi$
$839$	−2.23987	+	3.87957i	−0.0773289	+	0.133938i	0.824768	+	0.565472i	$0.191306\pi$
$840$		0			0
$841$	7.85425	−	13.6040i	0.270836	−	0.469102i
$842$	19.7556	−	11.4059i	0.680822	−	0.393073i
$843$		−	72.6458i		−	2.50205i
$844$	2.70850			0.0932303
$845$		0			0
$846$	−19.2915	−	33.4139i	−0.663256	−	1.14879i
$847$			17.4170i			0.598455i
$848$		−	8.58301i		−	0.294742i
$849$	−33.5405	−	58.0939i	−1.15111	−	1.99378i
$850$		0			0
$851$	−10.2915	−	17.8254i	−0.352788	−	0.611047i
$852$	−30.4547	−	17.5830i	−1.04336	−	0.602384i
$853$	−10.8972	−	6.29150i	−0.373113	−	0.215417i	0.301705	−	0.953401i	$-0.402444\pi$
$853$	−10.8972	−	6.29150i	−0.373113	−	0.215417i	−0.674818	+	0.737985i	$0.735778\pi$
$854$	−24.5830			−0.841213
$855$		0			0
$856$	4.70850			0.160933
$857$	−18.1865	−	10.5000i	−0.621240	−	0.358673i	0.156112	−	0.987739i	$-0.450104\pi$
$857$	−18.1865	−	10.5000i	−0.621240	−	0.358673i	−0.777352	+	0.629066i	$0.783437\pi$
$858$	−2.95920	−	1.70850i	−0.101026	−	0.0583271i
$859$	−6.61438	−	11.4564i	−0.225680	−	0.390889i	0.730843	−	0.682545i	$-0.239127\pi$
$859$	−6.61438	−	11.4564i	−0.225680	−	0.390889i	−0.956523	+	0.291656i	$0.905794\pi$
$860$		0			0
$861$	−22.4059	−	38.8081i	−0.763590	−	1.32258i
$862$		−	3.87451i		−	0.131966i
$863$			46.9373i			1.59776i	0.601489	+	0.798881i	$0.294575\pi$
$863$			46.9373i			1.59776i	−0.601489	+	0.798881i	$0.705425\pi$
$864$	−1.32288	−	2.29129i	−0.0450051	−	0.0779512i
$865$		0			0
$866$	−13.8745			−0.471475
$867$			44.9778i			1.52753i
$868$	−0.504897	+	0.291503i	−0.0171373	+	0.00989424i
$869$	−1.29150	+	2.23695i	−0.0438112	+	0.0758833i
$870$		0			0
$871$	4.64575	−	8.04668i	0.157415	−	0.272651i
$872$	5.70105	+	3.29150i	0.193062	+	0.111464i
$873$			57.1660i			1.93478i
$874$	−15.7601	−	2.03884i	−0.533094	−	0.0689648i
$875$		0			0
$876$	16.2601	−	28.1634i	0.549379	−	0.951552i
$877$	31.4837	+	18.1771i	1.06313	+	0.613798i	0.926296	−	0.376796i	$-0.122974\pi$
$877$	31.4837	+	18.1771i	1.06313	+	0.613798i	0.136833	+	0.990594i	$0.456308\pi$
$878$	31.8799	−	18.4059i	1.07590	−	0.621168i
$879$	−17.2804	+	29.9305i	−0.582853	+	1.00953i
$880$		0			0
$881$	−5.12549			−0.172682			−0.0863411	−	0.996266i	$-0.527517\pi$
$881$	−5.12549			−0.172682			−0.0863411	+	0.996266i	$0.527517\pi$
$882$		−	17.1660i		−	0.578010i
$883$	−34.9829	+	20.1974i	−1.17727	+	0.679696i	−0.955381	−	0.295376i	$-0.904555\pi$
$883$	−34.9829	+	20.1974i	−1.17727	+	0.679696i	−0.221887	+	0.975072i	$0.571222\pi$
$884$		0			0
$885$		0			0
$886$	5.35425			0.179880
$887$	−33.4139	+	19.2915i	−1.12193	+	0.647745i	−0.941892	−	0.335915i	$-0.890955\pi$
$887$	−33.4139	+	19.2915i	−1.12193	+	0.647745i	−0.180035	+	0.983660i	$0.557621\pi$
$888$	−12.9360	−	7.46863i	−0.434105	−	0.250631i
$889$	2.22876	+	3.86032i	0.0747501	+	0.129471i
$890$		0			0
$891$	1.61438	−	2.79619i	0.0540837	−	0.0936757i
$892$			28.8118i			0.964689i
$893$	−38.8081	+	16.1771i	−1.29866	+	0.541347i
$894$	−13.0627			−0.436884
$895$		0			0
$896$	0.822876	−	1.42526i	0.0274903	−	0.0476147i
$897$	−16.7069	+	9.64575i	−0.557828	+	0.322062i
$898$	−11.8719	−	6.85425i	−0.396171	−	0.228729i
$899$	0.645751	+	1.11847i	0.0215370	+	0.0373032i
$900$		0			0
$901$		0			0
$902$	5.75539	−	3.32288i	0.191634	−	0.110640i
$903$	−2.67167	+	1.54249i	−0.0889075	+	0.0513307i
$904$	−5.58301			−0.185688
$905$		0			0
$906$	−3.88562	−	6.73009i	−0.129091	−	0.223592i
$907$	−20.8389	−	12.0314i	−0.691946	−	0.399495i	0.112395	−	0.993664i	$-0.464148\pi$
$907$	−20.8389	−	12.0314i	−0.691946	−	0.399495i	−0.804341	+	0.594168i	$0.797481\pi$
$908$	10.9515	−	6.32288i	0.363440	−	0.209832i
$909$	−16.7085	+	28.9400i	−0.554186	+	0.959878i
$910$		0			0
$911$	1.06275			0.0352103			0.0176052	−	0.999845i	$-0.494396\pi$
$911$	1.06275			0.0352103			0.0176052	+	0.999845i	$0.494396\pi$
$912$	−10.6448	+	4.43725i	−0.352483	+	0.146932i
$913$			5.12549i			0.169629i
$914$	0.562746	−	0.974705i	0.0186140	−	0.0322404i
$915$		0			0
$916$	−10.0000	−	17.3205i	−0.330409	−	0.572286i
$917$	−19.8642	−	11.4686i	−0.655975	−	0.378727i
$918$		0			0
$919$	−11.8745			−0.391704			−0.195852	−	0.980633i	$-0.562747\pi$
$919$	−11.8745			−0.391704			−0.195852	+	0.980633i	$0.562747\pi$
$920$		0			0
$921$	−6.14575	−	10.6448i	−0.202509	−	0.350757i
$922$	−20.0624	+	11.5830i	−0.660718	+	0.381466i
$923$			26.5830i			0.874990i
$924$	−2.81176			−0.0925002
$925$		0			0
$926$	−7.22876	+	12.5206i	−0.237552	+	0.411452i
$927$	−9.38251	+	5.41699i	−0.308162	+	0.177917i
$928$	−3.15731	−	1.82288i	−0.103644	−	0.0598388i
$929$	5.79150	−	10.0312i	0.190013	−	0.329112i	−0.755241	−	0.655447i	$-0.772480\pi$
$929$	5.79150	−	10.0312i	0.190013	−	0.329112i	0.945254	+	0.326335i	$0.105814\pi$
$930$		0			0
$931$	−18.5516	−	2.39997i	−0.608005	−	0.0786557i
$932$		−	12.8745i		−	0.421719i
$933$	−19.1420	−	11.0516i	−0.626681	−	0.361814i
$934$	−12.3229	+	21.3438i	−0.403217	+	0.698392i
$935$		0			0
$936$	−4.00000	+	6.92820i	−0.130744	+	0.226455i
$937$	33.6663	−	19.4373i	1.09983	−	0.634987i	0.163654	−	0.986518i	$-0.447672\pi$
$937$	33.6663	−	19.4373i	1.09983	−	0.634987i	0.936176	+	0.351530i	$0.114339\pi$
$938$		−	7.64575i		−	0.249643i
$939$	−60.5203			−1.97500
$940$		0			0
$941$	−29.5830	−	51.2393i	−0.964378	−	1.67035i	−0.711276	−	0.702913i	$-0.751882\pi$
$941$	−29.5830	−	51.2393i	−0.964378	−	1.67035i	−0.253103	−	0.967439i	$-0.581451\pi$
$942$		−	28.0000i		−	0.912289i
$943$		−	37.5203i		−	1.22183i
$944$	3.96863	+	6.87386i	0.129168	+	0.223725i
$945$		0			0
$946$	−0.228757	−	0.396218i	−0.00743752	−	0.0128822i
$947$	−48.2801	−	27.8745i	−1.56889	−	0.905800i	−0.996299	−	0.0859598i	$-0.972604\pi$
$947$	−48.2801	−	27.8745i	−1.56889	−	0.905800i	−0.572593	−	0.819840i	$-0.694062\pi$
$948$	9.16515	+	5.29150i	0.297670	+	0.171860i
$949$	−24.5830			−0.797998
$950$		0			0
$951$	15.8745			0.514766
$952$		0			0
$953$	34.1712	+	19.7288i	1.10691	+	0.639077i	0.938028	−	0.346559i	$-0.112650\pi$
$953$	34.1712	+	19.7288i	1.10691	+	0.639077i	0.168886	+	0.985636i	$0.445983\pi$
$954$	17.1660	+	29.7324i	0.555770	+	0.962622i
$955$		0			0
$956$	6.00000	+	10.3923i	0.194054	+	0.336111i
$957$			6.22876i			0.201347i
$958$			14.5830i			0.471156i
$959$	4.59412	+	7.95725i	0.148352	+	0.256953i
$960$		0			0
$961$	−30.8745			−0.995952
$962$			11.2915i			0.364053i
$963$	−16.3107	+	9.41699i	−0.525605	+	0.303458i
$964$	6.79150	−	11.7632i	0.218740	−	0.378868i
$965$		0			0
$966$	−7.93725	+	13.7477i	−0.255377	+	0.442326i
$967$	2.34563	+	1.35425i	0.0754303	+	0.0435497i	0.537241	−	0.843429i	$-0.319467\pi$
$967$	2.34563	+	1.35425i	0.0754303	+	0.0435497i	−0.461810	+	0.886979i	$0.652800\pi$
$968$			10.5830i			0.340151i
$969$		0			0
$970$		0			0
$971$	−7.19738	+	12.4662i	−0.230975	+	0.400060i	−0.958095	−	0.286450i	$-0.907525\pi$
$971$	−7.19738	+	12.4662i	−0.230975	+	0.400060i	0.727120	+	0.686510i	$0.240858\pi$
$972$	−18.3303	−	10.5830i	−0.587945	−	0.339450i
$973$	19.0333	−	10.9889i	0.610180	−	0.352288i
$974$	−11.1144	+	19.2507i	−0.356128	+	0.616831i
$975$		0			0
$976$	−14.9373			−0.478130
$977$			45.4575i			1.45431i	0.686471	+	0.727157i	$0.259159\pi$
$977$			45.4575i			1.45431i	−0.686471	+	0.727157i	$0.740841\pi$
$978$	−27.3517	+	15.7915i	−0.874610	+	0.504957i
$979$		0			0
$980$		0			0
$981$	−26.3320			−0.840717
$982$	24.8623	−	14.3542i	0.793387	−	0.458062i
$983$	−27.4955	−	15.8745i	−0.876969	−	0.506318i	−0.00731102	−	0.999973i	$-0.502327\pi$
$983$	−27.4955	−	15.8745i	−0.876969	−	0.506318i	−0.869658	+	0.493655i	$0.835661\pi$
$984$	−13.6144	−	23.5808i	−0.434011	−	0.751728i
$985$		0			0
$986$		0			0
$987$			42.0000i			1.33687i
$988$	6.92820	+	5.29150i	0.220416	+	0.168345i
$989$	−2.58301			−0.0821348
$990$		0			0
$991$	22.5830	−	39.1149i	0.717373	−	1.24253i	−0.244664	−	0.969608i	$-0.578678\pi$
$991$	22.5830	−	39.1149i	0.717373	−	1.24253i	0.962037	−	0.272918i	$-0.0879889\pi$
$992$	−0.306788	+	0.177124i	−0.00974054	+	0.00562370i
$993$	63.7248	+	36.7915i	2.02224	+	1.16754i
$994$	10.9373	+	18.9439i	0.346909	+	0.600863i
$995$		0			0
$996$	21.0000			0.665410
$997$	−8.85836	+	5.11438i	−0.280547	+	0.161974i	−0.633671	−	0.773603i	$-0.718453\pi$
$997$	−8.85836	+	5.11438i	−0.280547	+	0.161974i	0.353124	+	0.935577i	$0.385119\pi$
$998$	27.0449	−	15.6144i	0.856091	−	0.494265i
$999$	14.9373			0.472594

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.j.g.49.1		8
5.2	odd	4		950.2.e.k.201.1		4
5.3	odd	4		38.2.c.b.11.2	yes	4
5.4	even	2	inner	950.2.j.g.49.4		8
15.8	even	4		342.2.g.f.163.2		4
19.7	even	3	inner	950.2.j.g.349.4		8
20.3	even	4		304.2.i.e.49.1		4
40.3	even	4		1216.2.i.k.961.2		4
40.13	odd	4		1216.2.i.l.961.1		4
60.23	odd	4		2736.2.s.v.1873.2		4
95.3	even	36		722.2.e.o.99.2		12
95.7	odd	12		950.2.e.k.501.1		4
95.8	even	12		722.2.a.g.1.2		2
95.13	even	36		722.2.e.o.415.1		12
95.18	even	4		722.2.c.j.429.1		4
95.23	odd	36		722.2.e.n.423.1		12
95.28	odd	36		722.2.e.n.245.1		12
95.33	even	36		722.2.e.o.389.2		12
95.43	odd	36		722.2.e.n.389.1		12
95.48	even	36		722.2.e.o.245.2		12
95.53	even	36		722.2.e.o.423.2		12
95.63	odd	36		722.2.e.n.415.2		12
95.64	even	6	inner	950.2.j.g.349.1		8
95.68	odd	12		722.2.a.j.1.1		2
95.73	odd	36		722.2.e.n.99.1		12
95.78	even	36		722.2.e.o.595.1		12
95.83	odd	12		38.2.c.b.7.2	✓	4
95.88	even	12		722.2.c.j.653.1		4
95.93	odd	36		722.2.e.n.595.2		12
285.8	odd	12		6498.2.a.bg.1.1		2
285.68	even	12		6498.2.a.ba.1.1		2
285.83	even	12		342.2.g.f.235.2		4
380.83	even	12		304.2.i.e.273.1		4
380.103	odd	12		5776.2.a.z.1.1		2
380.163	even	12		5776.2.a.ba.1.2		2
760.83	even	12		1216.2.i.k.577.2		4
760.653	odd	12		1216.2.i.l.577.1		4
1140.83	odd	12		2736.2.s.v.577.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.c.b.7.2	✓	4	95.83	odd	12
38.2.c.b.11.2	yes	4	5.3	odd	4
304.2.i.e.49.1		4	20.3	even	4
304.2.i.e.273.1		4	380.83	even	12
342.2.g.f.163.2		4	15.8	even	4
342.2.g.f.235.2		4	285.83	even	12
722.2.a.g.1.2		2	95.8	even	12
722.2.a.j.1.1		2	95.68	odd	12
722.2.c.j.429.1		4	95.18	even	4
722.2.c.j.653.1		4	95.88	even	12
722.2.e.n.99.1		12	95.73	odd	36
722.2.e.n.245.1		12	95.28	odd	36
722.2.e.n.389.1		12	95.43	odd	36
722.2.e.n.415.2		12	95.63	odd	36
722.2.e.n.423.1		12	95.23	odd	36
722.2.e.n.595.2		12	95.93	odd	36
722.2.e.o.99.2		12	95.3	even	36
722.2.e.o.245.2		12	95.48	even	36
722.2.e.o.389.2		12	95.33	even	36
722.2.e.o.415.1		12	95.13	even	36
722.2.e.o.423.2		12	95.53	even	36
722.2.e.o.595.1		12	95.78	even	36
950.2.e.k.201.1		4	5.2	odd	4
950.2.e.k.501.1		4	95.7	odd	12
950.2.j.g.49.1		8	1.1	even	1	trivial
950.2.j.g.49.4		8	5.4	even	2	inner
950.2.j.g.349.1		8	95.64	even	6	inner
950.2.j.g.349.4		8	19.7	even	3	inner
1216.2.i.k.577.2		4	760.83	even	12
1216.2.i.k.961.2		4	40.3	even	4
1216.2.i.l.577.1		4	760.653	odd	12
1216.2.i.l.961.1		4	40.13	odd	4
2736.2.s.v.577.2		4	1140.83	odd	12
2736.2.s.v.1873.2		4	60.23	odd	4
5776.2.a.z.1.1		2	380.103	odd	12
5776.2.a.ba.1.2		2	380.163	even	12
6498.2.a.ba.1.1		2	285.68	even	12
6498.2.a.bg.1.1		2	285.8	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-2.29129 - 1.32288i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.32288 + 2.29129i) q^{6} -1.64575i q^{7} -1.00000i q^{8} +(2.00000 + 3.46410i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-2.29129 - 1.32288i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.32288 + 2.29129i) q^{6} -1.64575i q^{7} -1.00000i q^{8} +(2.00000 + 3.46410i) q^{9} +0.645751 q^{11} -2.64575i q^{12} +(-1.73205 + 1.00000i) q^{13} +(-0.822876 + 1.42526i) q^{14} +(-0.500000 + 0.866025i) q^{16} -4.00000i q^{18} +(-4.32288 - 0.559237i) q^{19} +(-2.17712 + 3.77089i) q^{21} +(-0.559237 - 0.322876i) q^{22} +(-3.15731 + 1.82288i) q^{23} +(-1.32288 + 2.29129i) q^{24} +2.00000 q^{26} -2.64575i q^{27} +(1.42526 - 0.822876i) q^{28} +(-1.82288 - 3.15731i) q^{29} -0.354249 q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.47960 - 0.854249i) q^{33} +(-2.00000 + 3.46410i) q^{36} +5.64575i q^{37} +(3.46410 + 2.64575i) q^{38} +5.29150 q^{39} +(-5.14575 + 8.91270i) q^{41} +(3.77089 - 2.17712i) q^{42} +(0.613577 + 0.354249i) q^{43} +(0.322876 + 0.559237i) q^{44} +3.64575 q^{46} +(8.35347 - 4.82288i) q^{47} +(2.29129 - 1.32288i) q^{48} +4.29150 q^{49} +(-1.73205 - 1.00000i) q^{52} +(-7.43310 + 4.29150i) q^{53} +(-1.32288 + 2.29129i) q^{54} -1.64575 q^{56} +(9.16515 + 7.00000i) q^{57} +3.64575i q^{58} +(3.96863 - 6.87386i) q^{59} +(7.46863 + 12.9360i) q^{61} +(0.306788 + 0.177124i) q^{62} +(5.70105 - 3.29150i) q^{63} -1.00000 q^{64} +(0.854249 + 1.47960i) q^{66} +(-4.02334 + 2.32288i) q^{67} +9.64575 q^{69} +(6.64575 - 11.5108i) q^{71} +(3.46410 - 2.00000i) q^{72} +(10.6448 + 6.14575i) q^{73} +(2.82288 - 4.88936i) q^{74} +(-1.67712 - 4.02334i) q^{76} -1.06275i q^{77} +(-4.58258 - 2.64575i) q^{78} +(-2.00000 + 3.46410i) q^{79} +(2.50000 - 4.33013i) q^{81} +(8.91270 - 5.14575i) q^{82} +7.93725i q^{83} -4.35425 q^{84} +(-0.354249 - 0.613577i) q^{86} +9.64575i q^{87} -0.645751i q^{88} +(1.64575 + 2.85052i) q^{91} +(-3.15731 - 1.82288i) q^{92} +(0.811686 + 0.468627i) q^{93} -9.64575 q^{94} -2.64575 q^{96} +(12.3768 + 7.14575i) q^{97} +(-3.71655 - 2.14575i) q^{98} +(1.29150 + 2.23695i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 16 q^{9}+O(q^{10}) \) 8 * q + 4 * q^4 + 16 * q^9	\( 8 q + 4 q^{4} + 16 q^{9} - 16 q^{11} + 4 q^{14} - 4 q^{16} - 24 q^{19} - 28 q^{21} + 16 q^{26} - 4 q^{29} - 24 q^{31} - 16 q^{36} - 20 q^{41} - 8 q^{44} + 8 q^{46} - 8 q^{49} + 8 q^{56} + 28 q^{61} - 8 q^{64} + 28 q^{66} + 56 q^{69} + 32 q^{71} + 12 q^{74} - 24 q^{76} - 16 q^{79} + 20 q^{81} - 56 q^{84} - 24 q^{86} - 8 q^{91} - 56 q^{94} - 32 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 + 16 * q^9 - 16 * q^11 + 4 * q^14 - 4 * q^16 - 24 * q^19 - 28 * q^21 + 16 * q^26 - 4 * q^29 - 24 * q^31 - 16 * q^36 - 20 * q^41 - 8 * q^44 + 8 * q^46 - 8 * q^49 + 8 * q^56 + 28 * q^61 - 8 * q^64 + 28 * q^66 + 56 * q^69 + 32 * q^71 + 12 * q^74 - 24 * q^76 - 16 * q^79 + 20 * q^81 - 56 * q^84 - 24 * q^86 - 8 * q^91 - 56 * q^94 - 32 * q^99

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