LMFDB - Embedded newform 288.2.v.b.181.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(37,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("288.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.v (of order $8$, degree $4$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{8})$
Coefficient field:	8.0.18939904.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			181.2
Root			$0.500000 + 0.0297061i$ of defining polynomial
Character	$\chi$	$=$	288.181
Dual form			288.2.v.b.253.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40426 - 0.167452i) q^{2} +(1.94392 - 0.470294i) q^{4} +(0.707107 - 1.70711i) q^{5} +(-2.74912 - 2.74912i) q^{7} +(2.65103 - 0.985930i) q^{8} +O(q^{10})$	\(q+(1.40426 - 0.167452i) q^{2} +(1.94392 - 0.470294i) q^{4} +(0.707107 - 1.70711i) q^{5} +(-2.74912 - 2.74912i) q^{7} +(2.65103 - 0.985930i) q^{8} +(0.707107 - 2.51564i) q^{10} +(-0.135390 - 0.0560803i) q^{11} +(1.18073 + 2.85054i) q^{13} +(-4.32083 - 3.40014i) q^{14} +(3.55765 - 1.82843i) q^{16} +6.44549i q^{17} +(0.805198 + 1.94392i) q^{19} +(0.571717 - 3.65103i) q^{20} +(-0.199514 - 0.0560803i) q^{22} +(-0.749118 + 0.749118i) q^{23} +(1.12132 + 1.12132i) q^{25} +(2.13539 + 3.80520i) q^{26} +(-6.63696 - 4.05117i) q^{28} +(-4.32417 + 1.79113i) q^{29} +1.17157 q^{31} +(4.68971 - 3.16333i) q^{32} +(1.07931 + 9.05117i) q^{34} +(-6.63696 + 2.74912i) q^{35} +(1.73172 - 4.18073i) q^{37} +(1.45622 + 2.59495i) q^{38} +(0.191470 - 5.22274i) q^{40} +(2.49824 - 2.49824i) q^{41} +(-6.10725 - 2.52971i) q^{43} +(-0.289561 - 0.0453426i) q^{44} +(-0.926518 + 1.17740i) q^{46} -2.66981i q^{47} +8.11529i q^{49} +(1.76240 + 1.38686i) q^{50} +(3.63584 + 4.98593i) q^{52} +(-1.64769 - 0.682497i) q^{53} +(-0.191470 + 0.191470i) q^{55} +(-9.99842 - 4.57754i) q^{56} +(-5.77235 + 3.23931i) q^{58} +(-1.43744 + 3.47029i) q^{59} +(-3.46760 + 1.43633i) q^{61} +(1.64520 - 0.196182i) q^{62} +(6.05588 - 5.22746i) q^{64} +5.70108 q^{65} +(-14.0791 + 5.83176i) q^{67} +(3.03127 + 12.5295i) q^{68} +(-8.85970 + 4.97186i) q^{70} +(3.40950 + 3.40950i) q^{71} +(-0.442353 + 0.442353i) q^{73} +(1.73172 - 6.16084i) q^{74} +(2.47945 + 3.40014i) q^{76} +(0.218031 + 0.526374i) q^{77} -7.07550i q^{79} +(-0.605684 - 7.36618i) q^{80} +(3.08985 - 3.92652i) q^{82} +(-2.99862 - 7.23931i) q^{83} +(11.0031 + 4.55765i) q^{85} +(-8.99980 - 2.52971i) q^{86} +(-0.414214 - 0.0151854i) q^{88} +(4.21803 + 4.21803i) q^{89} +(4.59050 - 11.0824i) q^{91} +(-1.10392 + 1.80853i) q^{92} +(-0.447065 - 3.74912i) q^{94} +3.88784 q^{95} +10.3267 q^{97} +(1.35892 + 11.3960i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 4 q^{4} - 8 q^{7} + 4 q^{8}+O(q^{10}) $ 8 * q + 4 * q^2 + 4 * q^4 - 8 * q^7 + 4 * q^8	$ 8 q + 4 q^{2} + 4 q^{4} - 8 q^{7} + 4 q^{8} - 4 q^{11} - 8 q^{13} - 12 q^{14} + 4 q^{19} - 4 q^{20} + 4 q^{22} + 8 q^{23} - 8 q^{25} + 20 q^{26} - 16 q^{28} + 32 q^{31} + 24 q^{32} - 16 q^{35} - 8 q^{37} - 8 q^{38} + 16 q^{40} - 8 q^{41} - 12 q^{43} - 20 q^{44} + 12 q^{46} - 16 q^{50} + 12 q^{52} - 8 q^{53} - 16 q^{55} - 8 q^{56} - 12 q^{58} + 20 q^{59} + 24 q^{61} + 24 q^{62} - 8 q^{64} - 36 q^{67} - 16 q^{68} - 8 q^{70} + 24 q^{71} - 32 q^{73} - 8 q^{74} - 20 q^{76} - 16 q^{77} - 8 q^{80} - 20 q^{82} - 20 q^{83} + 8 q^{85} - 4 q^{86} + 8 q^{88} + 16 q^{89} + 40 q^{91} + 16 q^{92} - 24 q^{94} + 8 q^{95} + 32 q^{97} + 24 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 + 4 * q^4 - 8 * q^7 + 4 * q^8 - 4 * q^11 - 8 * q^13 - 12 * q^14 + 4 * q^19 - 4 * q^20 + 4 * q^22 + 8 * q^23 - 8 * q^25 + 20 * q^26 - 16 * q^28 + 32 * q^31 + 24 * q^32 - 16 * q^35 - 8 * q^37 - 8 * q^38 + 16 * q^40 - 8 * q^41 - 12 * q^43 - 20 * q^44 + 12 * q^46 - 16 * q^50 + 12 * q^52 - 8 * q^53 - 16 * q^55 - 8 * q^56 - 12 * q^58 + 20 * q^59 + 24 * q^61 + 24 * q^62 - 8 * q^64 - 36 * q^67 - 16 * q^68 - 8 * q^70 + 24 * q^71 - 32 * q^73 - 8 * q^74 - 20 * q^76 - 16 * q^77 - 8 * q^80 - 20 * q^82 - 20 * q^83 + 8 * q^85 - 4 * q^86 + 8 * q^88 + 16 * q^89 + 40 * q^91 + 16 * q^92 - 24 * q^94 + 8 * q^95 + 32 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$	$1$

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 $

$2$	1.40426	−	0.167452i	0.992965	−	0.118406i
$2$	1.40426	−	0.167452i	0.992965	−	0.118406i
$3$		0			0
$3$		0			0
$4$	1.94392	−	0.470294i	0.971960	−	0.235147i
$5$	0.707107	−	1.70711i	0.316228	−	0.763441i	−0.683220	−	0.730213i	$-0.739421\pi$
$5$	0.707107	−	1.70711i	0.316228	−	0.763441i	0.999448	−	0.0332288i	$-0.0105790\pi$
$6$		0			0
$7$	−2.74912	−	2.74912i	−1.03907	−	1.03907i	−0.999205	−	0.0398636i	$-0.987308\pi$
$7$	−2.74912	−	2.74912i	−1.03907	−	1.03907i	−0.0398636	−	0.999205i	$-0.512692\pi$
$8$	2.65103	−	0.985930i	0.937279	−	0.348579i
$9$		0			0
$10$	0.707107	−	2.51564i	0.223607	−	0.795514i
$11$	−0.135390	−	0.0560803i	−0.0408216	−	0.0169089i	0.362179	−	0.932108i	$-0.382033\pi$
$11$	−0.135390	−	0.0560803i	−0.0408216	−	0.0169089i	−0.403001	+	0.915200i	$0.632033\pi$
$12$		0			0
$13$	1.18073	+	2.85054i	0.327476	+	0.790598i	0.998778	+	0.0494138i	$0.0157353\pi$
$13$	1.18073	+	2.85054i	0.327476	+	0.790598i	−0.671302	+	0.741184i	$0.734265\pi$
$14$	−4.32083	−	3.40014i	−1.15479	−	0.908727i
$15$		0			0
$16$	3.55765	−	1.82843i	0.889412	−	0.457107i
$17$			6.44549i			1.56326i	0.623742	+	0.781630i	$0.285611\pi$
$17$			6.44549i			1.56326i	−0.623742	+	0.781630i	$0.714389\pi$
$18$		0			0
$19$	0.805198	+	1.94392i	0.184725	+	0.445966i	0.988929	−	0.148387i	$-0.0474082\pi$
$19$	0.805198	+	1.94392i	0.184725	+	0.445966i	−0.804204	+	0.594353i	$0.797408\pi$
$20$	0.571717	−	3.65103i	0.127840	−	0.816394i
$21$		0			0
$22$	−0.199514	−	0.0560803i	−0.0425365	−	0.0119564i
$23$	−0.749118	+	0.749118i	−0.156202	+	0.156202i	−0.780881	−	0.624679i	$-0.785230\pi$
$23$	−0.749118	+	0.749118i	−0.156202	+	0.156202i	0.624679	+	0.780881i	$0.285230\pi$
$24$		0			0
$25$	1.12132	+	1.12132i	0.224264	+	0.224264i
$26$	2.13539	+	3.80520i	0.418784	+	0.746261i
$27$		0			0
$28$	−6.63696	−	4.05117i	−1.25427	−	0.765599i
$29$	−4.32417	+	1.79113i	−0.802978	+	0.332604i	−0.746148	−	0.665780i	$-0.768099\pi$
$29$	−4.32417	+	1.79113i	−0.802978	+	0.332604i	−0.0568292	+	0.998384i	$0.518099\pi$
$30$		0			0
$31$	1.17157			0.210421			0.105210	−	0.994450i	$-0.466448\pi$
$31$	1.17157			0.210421			0.105210	+	0.994450i	$0.466448\pi$
$32$	4.68971	−	3.16333i	0.829031	−	0.559203i
$33$		0			0
$34$	1.07931	+	9.05117i	0.185100	+	1.55226i
$35$	−6.63696	+	2.74912i	−1.12185	+	0.464686i
$36$		0			0
$37$	1.73172	−	4.18073i	0.284692	−	0.687308i	−0.715241	−	0.698878i	$-0.753683\pi$
$37$	1.73172	−	4.18073i	0.284692	−	0.687308i	0.999933	+	0.0115700i	$0.00368293\pi$
$38$	1.45622	+	2.59495i	0.236231	+	0.420956i
$39$		0			0
$40$	0.191470	−	5.22274i	0.0302741	−	0.825788i
$41$	2.49824	−	2.49824i	0.390159	−	0.390159i	−0.484585	−	0.874744i	$-0.661029\pi$
$41$	2.49824	−	2.49824i	0.390159	−	0.390159i	0.874744	+	0.484585i	$0.161029\pi$
$42$		0			0
$43$	−6.10725	−	2.52971i	−0.931347	−	0.385777i	−0.135158	−	0.990824i	$-0.543154\pi$
$43$	−6.10725	−	2.52971i	−0.931347	−	0.385777i	−0.796189	+	0.605048i	$0.793154\pi$
$44$	−0.289561	−	0.0453426i	−0.0436530	−	0.00683566i
$45$		0			0
$46$	−0.926518	+	1.17740i	−0.136608	+	0.173598i
$47$		−	2.66981i		−	0.389432i	−0.980860	−	0.194716i	$-0.937622\pi$
$47$		−	2.66981i		−	0.389432i	0.980860	−	0.194716i	$-0.0623784\pi$
$48$		0			0
$49$			8.11529i			1.15933i
$50$	1.76240	+	1.38686i	0.249241	+	0.196132i
$51$		0			0
$52$	3.63584	+	4.98593i	0.504200	+	0.691424i
$53$	−1.64769	−	0.682497i	−0.226328	−	0.0937482i	0.266638	−	0.963797i	$-0.414087\pi$
$53$	−1.64769	−	0.682497i	−0.226328	−	0.0937482i	−0.492966	+	0.870049i	$0.664087\pi$
$54$		0			0
$55$	−0.191470	+	0.191470i	−0.0258178	+	0.0258178i
$56$	−9.99842	−	4.57754i	−1.33610	−	0.611700i
$57$		0			0
$58$	−5.77235	+	3.23931i	−0.757946	+	0.425342i
$59$	−1.43744	+	3.47029i	−0.187139	+	0.451794i	−0.989407	−	0.145171i	$-0.953627\pi$
$59$	−1.43744	+	3.47029i	−0.187139	+	0.451794i	0.802267	+	0.596965i	$0.203627\pi$
$60$		0			0
$61$	−3.46760	+	1.43633i	−0.443981	+	0.183903i	−0.593462	−	0.804862i	$-0.702239\pi$
$61$	−3.46760	+	1.43633i	−0.443981	+	0.183903i	0.149482	+	0.988764i	$0.452239\pi$
$62$	1.64520	−	0.196182i	0.208940	−	0.0249152i
$63$		0			0
$64$	6.05588	−	5.22746i	0.756985	−	0.653432i
$65$	5.70108			0.707132
$66$		0			0
$67$	−14.0791	+	5.83176i	−1.72004	+	0.712463i	−0.720212	+	0.693754i	$0.755956\pi$
$67$	−14.0791	+	5.83176i	−1.72004	+	0.712463i	−0.999825	+	0.0187090i	$0.994044\pi$
$68$	3.03127	+	12.5295i	0.367596	+	1.51943i
$69$		0			0
$70$	−8.85970	+	4.97186i	−1.05894	+	0.594251i
$71$	3.40950	+	3.40950i	0.404633	+	0.404633i	0.879862	−	0.475229i	$-0.157635\pi$
$71$	3.40950	+	3.40950i	0.404633	+	0.404633i	−0.475229	+	0.879862i	$0.657635\pi$
$72$		0			0
$73$	−0.442353	+	0.442353i	−0.0517735	+	0.0517735i	−0.732520	−	0.680746i	$-0.761656\pi$
$73$	−0.442353	+	0.442353i	−0.0517735	+	0.0517735i	0.680746	+	0.732520i	$0.261656\pi$
$74$	1.73172	−	6.16084i	0.201308	−	0.716183i
$75$		0			0
$76$	2.47945	+	3.40014i	0.284413	+	0.390023i
$77$	0.218031	+	0.526374i	0.0248470	+	0.0599859i
$78$		0			0
$79$		−	7.07550i		−	0.796056i	−0.917373	−	0.398028i	$-0.869695\pi$
$79$		−	7.07550i		−	0.796056i	0.917373	−	0.398028i	$-0.130305\pi$
$80$	−0.605684	−	7.36618i	−0.0677175	−	0.823564i
$81$		0			0
$82$	3.08985	−	3.92652i	0.341217	−	0.433611i
$83$	−2.99862	−	7.23931i	−0.329141	−	0.794617i	−0.998656	−	0.0518190i	$-0.983498\pi$
$83$	−2.99862	−	7.23931i	−0.329141	−	0.794617i	0.669515	−	0.742798i	$-0.266502\pi$
$84$		0			0
$85$	11.0031	+	4.55765i	1.19346	+	0.494346i
$86$	−8.99980	−	2.52971i	−0.970474	−	0.272785i
$87$		0			0
$88$	−0.414214	−	0.0151854i	−0.0441553	−	0.00161877i
$89$	4.21803	+	4.21803i	0.447110	+	0.447110i	0.894393	−	0.447282i	$-0.147608\pi$
$89$	4.21803	+	4.21803i	0.447110	+	0.447110i	−0.447282	+	0.894393i	$0.647608\pi$
$90$		0			0
$91$	4.59050	−	11.0824i	0.481215	−	1.16176i
$92$	−1.10392	+	1.80853i	−0.115092	+	0.188552i
$93$		0			0
$94$	−0.447065	−	3.74912i	−0.0461112	−	0.386692i
$95$	3.88784			0.398884
$96$		0			0
$97$	10.3267			1.04851			0.524257	−	0.851560i	$-0.324343\pi$
$97$	10.3267			1.04851			0.524257	+	0.851560i	$0.324343\pi$
$98$	1.35892	+	11.3960i	0.137272	+	1.15117i
$99$		0			0
$100$	2.70711	+	1.65241i	0.270711	+	0.165241i
$101$	4.31750	−	10.4234i	0.429608	−	1.03716i	−0.549805	−	0.835293i	$-0.685298\pi$
$101$	4.31750	−	10.4234i	0.429608	−	1.03716i	0.979412	−	0.201871i	$-0.0647022\pi$
$102$		0			0
$103$	13.3134	+	13.3134i	1.31181	+	1.31181i	0.920080	+	0.391732i	$0.128124\pi$
$103$	13.3134	+	13.3134i	1.31181	+	1.31181i	0.391732	+	0.920080i	$0.371876\pi$
$104$	5.94059	+	6.39274i	0.582523	+	0.626860i
$105$		0			0
$106$	−2.42809	−	0.682497i	−0.235836	−	0.0662900i
$107$	−13.2507	−	5.48861i	−1.28099	−	0.530604i	−0.364704	−	0.931124i	$-0.618830\pi$
$107$	−13.2507	−	5.48861i	−1.28099	−	0.530604i	−0.916288	+	0.400519i	$0.868830\pi$
$108$		0			0
$109$	−4.87515	−	11.7697i	−0.466955	−	1.12733i	−0.965486	−	0.260456i	$-0.916127\pi$
$109$	−4.87515	−	11.7697i	−0.466955	−	1.12733i	0.498531	−	0.866872i	$-0.333873\pi$
$110$	−0.236813	+	0.300937i	−0.0225792	+	0.0286932i
$111$		0			0
$112$	−14.8070	−	4.75383i	−1.39913	−	0.449195i
$113$			5.88118i			0.553254i	0.960977	+	0.276627i	$0.0892167\pi$
$113$			5.88118i			0.553254i	−0.960977	+	0.276627i	$0.910783\pi$
$114$		0			0
$115$	0.749118	+	1.80853i	0.0698556	+	0.168646i
$116$	−7.56348	+	5.51544i	−0.702251	+	0.512096i
$117$		0			0
$118$	−1.43744	+	5.11391i	−0.132327	+	0.470774i
$119$	17.7194	−	17.7194i	1.62433	−	1.62433i
$120$		0			0
$121$	−7.76299	−	7.76299i	−0.705726	−	0.705726i
$122$	−4.62891	+	2.59764i	−0.419082	+	0.235179i
$123$		0			0
$124$	2.27744	−	0.550984i	0.204520	−	0.0494798i
$125$	11.2426	−	4.65685i	1.00557	−	0.416522i
$126$		0			0
$127$	−15.4022			−1.36672			−0.683360	−	0.730081i	$-0.739482\pi$
$127$	−15.4022			−1.36672			−0.683360	+	0.730081i	$0.739482\pi$
$128$	7.62872	−	8.35480i	0.674290	−	0.738467i
$129$		0			0
$130$	8.00583	−	0.954657i	0.702158	−	0.0837290i
$131$	2.96382	−	1.22765i	0.258950	−	0.107261i	−0.249432	−	0.968392i	$-0.580244\pi$
$131$	2.96382	−	1.22765i	0.258950	−	0.107261i	0.508382	+	0.861132i	$0.330244\pi$
$132$		0			0
$133$	3.13048	−	7.55765i	0.271447	−	0.655331i
$134$	−18.7943	+	10.5469i	−1.62358	+	0.911114i
$135$		0			0
$136$	6.35480	+	17.0872i	0.544920	+	1.46521i
$137$	−10.7757	+	10.7757i	−0.920628	+	0.920628i	−0.997074	−	0.0764454i	$-0.975643\pi$
$137$	−10.7757	+	10.7757i	−0.920628	+	0.920628i	0.0764454	+	0.997074i	$0.475643\pi$
$138$		0			0
$139$	4.78372	+	1.98148i	0.405750	+	0.168067i	0.576218	−	0.817296i	$-0.304528\pi$
$139$	4.78372	+	1.98148i	0.405750	+	0.168067i	−0.170468	+	0.985363i	$0.554528\pi$
$140$	−11.6088	+	8.46538i	−0.981124	+	0.715456i
$141$		0			0
$142$	5.35877	+	4.21692i	0.449698	+	0.353876i
$143$		−	0.452150i		−	0.0378107i
$144$		0			0
$145$			8.64833i			0.718205i
$146$	−0.547108	+	0.695253i	−0.0452789	+	0.0575396i
$147$		0			0
$148$	1.40014	−	8.94142i	0.115091	−	0.734981i
$149$	−4.32417	−	1.79113i	−0.354250	−	0.146735i	0.198460	−	0.980109i	$-0.436406\pi$
$149$	−4.32417	−	1.79113i	−0.354250	−	0.146735i	−0.552709	+	0.833374i	$0.686406\pi$
$150$		0			0
$151$	13.2344	−	13.2344i	1.07700	−	1.07700i	0.0802232	−	0.996777i	$-0.474437\pi$
$151$	13.2344	−	13.2344i	1.07700	−	1.07700i	0.996777	−	0.0802232i	$-0.0255633\pi$
$152$	4.05117	+	4.35951i	0.328593	+	0.353603i
$153$		0			0
$154$	0.394316	+	0.702659i	0.0317749	+	0.0566219i
$155$	0.828427	−	2.00000i	0.0665409	−	0.160644i
$156$		0			0
$157$	−15.9529	+	6.60790i	−1.27318	+	0.527368i	−0.913929	−	0.405874i	$-0.866967\pi$
$157$	−15.9529	+	6.60790i	−1.27318	+	0.527368i	−0.359249	+	0.933242i	$0.616967\pi$
$158$	−1.18481	−	9.93588i	−0.0942581	−	0.790456i
$159$		0			0
$160$	−2.08402	−	10.2426i	−0.164756	−	0.809752i
$161$	4.11882			0.324609
$162$		0			0
$163$	10.6488	−	4.41088i	0.834079	−	0.345487i	0.0755629	−	0.997141i	$-0.475925\pi$
$163$	10.6488	−	4.41088i	0.834079	−	0.345487i	0.758516	+	0.651654i	$0.225925\pi$
$164$	3.68146	−	6.03127i	0.287474	−	0.470963i
$165$		0			0
$166$	−5.42309	−	9.66378i	−0.420914	−	0.750055i
$167$	2.98677	+	2.98677i	0.231123	+	0.231123i	0.813161	−	0.582038i	$-0.197745\pi$
$167$	2.98677	+	2.98677i	0.231123	+	0.231123i	−0.582038	+	0.813161i	$0.697745\pi$
$168$		0			0
$169$	2.46094	−	2.46094i	0.189303	−	0.189303i
$170$	16.2145	+	4.55765i	1.24360	+	0.349556i
$171$		0			0
$172$	−13.0617	−	2.04534i	−0.995946	−	0.155956i
$173$	−7.85054	−	18.9529i	−0.596866	−	1.44096i	−0.876759	−	0.480930i	$-0.840299\pi$
$173$	−7.85054	−	18.9529i	−0.596866	−	1.44096i	0.279894	−	0.960031i	$-0.409701\pi$
$174$		0			0
$175$		−	6.16528i		−	0.466052i
$176$	−0.584208	+	0.0480365i	−0.0440364	+	0.00362089i
$177$		0			0
$178$	6.62955	+	5.21692i	0.496906	+	0.391024i
$179$	9.60549	+	23.1897i	0.717948	+	1.73328i	0.679113	+	0.734033i	$0.262364\pi$
$179$	9.60549	+	23.1897i	0.717948	+	1.73328i	0.0388344	+	0.999246i	$0.487636\pi$
$180$		0			0
$181$	1.87868	+	0.778175i	0.139641	+	0.0578413i	0.451410	−	0.892317i	$-0.350921\pi$
$181$	1.87868	+	0.778175i	0.139641	+	0.0578413i	−0.311768	+	0.950158i	$0.600921\pi$
$182$	4.59050	−	16.3314i	0.340270	−	1.21056i
$183$		0			0
$184$	−1.24735	+	2.72451i	−0.0919561	+	0.200853i
$185$	−5.91245	−	5.91245i	−0.434692	−	0.434692i
$186$		0			0
$187$	0.361465	−	0.872654i	0.0264329	−	0.0638148i
$188$	−1.25559	−	5.18989i	−0.0915736	−	0.378512i
$189$		0			0
$190$	5.45956	−	0.651026i	0.396078	−	0.0472304i
$191$	−9.05902			−0.655487			−0.327744	−	0.944767i	$-0.606288\pi$
$191$	−9.05902			−0.655487			−0.327744	+	0.944767i	$0.606288\pi$
$192$		0			0
$193$	6.24707			0.449674			0.224837	−	0.974396i	$-0.427815\pi$
$193$	6.24707			0.449674			0.224837	+	0.974396i	$0.427815\pi$
$194$	14.5014	−	1.72922i	1.04114	−	0.124151i
$195$		0			0
$196$	3.81657	+	15.7755i	0.272612	+	1.12682i
$197$	1.81298	−	4.37691i	0.129169	−	0.311842i	−0.846043	−	0.533115i	$-0.821021\pi$
$197$	1.81298	−	4.37691i	0.129169	−	0.311842i	0.975212	+	0.221273i	$0.0710212\pi$
$198$		0			0
$199$	6.14186	+	6.14186i	0.435385	+	0.435385i	0.890455	−	0.455071i	$-0.150386\pi$
$199$	6.14186	+	6.14186i	0.435385	+	0.435385i	−0.455071	+	0.890455i	$0.650386\pi$
$200$	4.07819	+	1.86711i	0.288372	+	0.132024i
$201$		0			0
$202$	4.31750	−	15.3602i	0.303778	−	1.08074i
$203$	16.8117	+	6.96362i	1.17995	+	0.488750i
$204$		0			0
$205$	−2.49824	−	6.03127i	−0.174484	−	0.421242i
$206$	20.9249	+	16.4662i	1.45791	+	1.14726i
$207$		0			0
$208$	9.41264	+	7.98233i	0.652649	+	0.553475i
$209$		−	0.308343i		−	0.0213285i
$210$		0			0
$211$	5.21588	+	12.5923i	0.359076	+	0.866886i	0.995430	+	0.0954895i	$0.0304416\pi$
$211$	5.21588	+	12.5923i	0.359076	+	0.866886i	−0.636354	+	0.771397i	$0.719558\pi$
$212$	−3.52396	−	0.551819i	−0.242027	−	0.0378991i
$213$		0			0
$214$	−19.5265	−	5.48861i	−1.33481	−	0.375194i
$215$	−8.63696	+	8.63696i	−0.589036	+	0.589036i
$216$		0			0
$217$	−3.22079	−	3.22079i	−0.218642	−	0.218642i
$218$	−8.81685	−	15.7114i	−0.597153	−	1.06411i
$219$		0			0
$220$	−0.282156	+	0.462250i	−0.0190229	+	0.0311649i
$221$	−18.3731	+	7.61040i	−1.23591	+	0.511931i
$222$		0			0
$223$	−0.960579			−0.0643251			−0.0321626	−	0.999483i	$-0.510239\pi$
$223$	−0.960579			−0.0643251			−0.0321626	+	0.999483i	$0.510239\pi$
$224$	−21.5889	−	4.19618i	−1.44247	−	0.280369i
$225$		0			0
$226$	0.984815	+	8.25873i	0.0655089	+	0.549362i
$227$	−14.1698	+	5.86932i	−0.940482	+	0.389561i	−0.799646	−	0.600472i	$-0.794979\pi$
$227$	−14.1698	+	5.86932i	−0.940482	+	0.389561i	−0.140837	+	0.990033i	$0.544979\pi$
$228$		0			0
$229$	1.80408	−	4.35544i	0.119217	−	0.287816i	−0.852994	−	0.521920i	$-0.825216\pi$
$229$	1.80408	−	4.35544i	0.119217	−	0.287816i	0.972211	+	0.234105i	$0.0752159\pi$
$230$	1.35480	+	2.41421i	0.0893330	+	0.159189i
$231$		0			0
$232$	−9.69755	+	9.01166i	−0.636675	+	0.591644i
$233$	16.7918	−	16.7918i	1.10007	−	1.10007i	0.105663	−	0.994402i	$-0.466303\pi$
$233$	16.7918	−	16.7918i	1.10007	−	1.10007i	0.994402	−	0.105663i	$-0.0336965\pi$
$234$		0			0
$235$	−4.55765	−	1.88784i	−0.297308	−	0.123149i
$236$	−1.16222	+	7.42199i	−0.0756538	+	0.483131i
$237$		0			0
$238$	21.9156	−	27.8499i	1.42058	−	1.80524i
$239$		−	15.8414i		−	1.02469i	−0.858779	−	0.512347i	$-0.828776\pi$
$239$		−	15.8414i		−	1.02469i	0.858779	−	0.512347i	$-0.171224\pi$
$240$		0			0
$241$			0.313335i			0.0201837i	0.999949	+	0.0100918i	$0.00321239\pi$
$241$			0.313335i			0.0201837i	−0.999949	+	0.0100918i	$0.996788\pi$
$242$	−12.2012	−	9.60136i	−0.784324	−	0.617199i
$243$		0			0
$244$	−6.06524	+	4.42290i	−0.388287	+	0.283147i
$245$	13.8537	+	5.73838i	0.885079	+	0.366612i
$246$		0			0
$247$	−4.59050	+	4.59050i	−0.292086	+	0.292086i
$248$	3.10587	−	1.15509i	0.197223	−	0.0733482i
$249$		0			0
$250$	15.0078	−	8.42206i	0.949180	−	0.532658i
$251$	3.55903	−	8.59225i	0.224644	−	0.542338i	−0.770866	−	0.636997i	$-0.780176\pi$
$251$	3.55903	−	8.59225i	0.224644	−	0.542338i	0.995510	+	0.0946593i	$0.0301762\pi$
$252$		0			0
$253$	0.143434	−	0.0594122i	0.00901760	−	0.00373521i
$254$	−21.6287	+	2.57912i	−1.35711	+	0.161829i
$255$		0			0
$256$	9.31371	−	13.0098i	0.582107	−	0.813112i
$257$	−18.9043			−1.17922			−0.589609	−	0.807689i	$-0.700718\pi$
$257$	−18.9043			−1.17922			−0.589609	+	0.807689i	$0.700718\pi$
$258$		0			0
$259$	−16.2540	+	6.73263i	−1.00998	+	0.418346i
$260$	11.0824	−	2.68118i	0.687304	−	0.166280i
$261$		0			0
$262$	3.95641	−	2.22025i	0.244428	−	0.137167i
$263$	16.6366	+	16.6366i	1.02585	+	1.02585i	0.999657	+	0.0261975i	$0.00833988\pi$
$263$	16.6366	+	16.6366i	1.02585	+	1.02585i	0.0261975	+	0.999657i	$0.491660\pi$
$264$		0			0
$265$	−2.33019	+	2.33019i	−0.143143	+	0.143143i
$266$	3.13048	−	11.1371i	0.191942	−	0.682862i
$267$		0			0
$268$	−24.6260	+	17.9578i	−1.50427	+	1.09695i
$269$	5.01046	+	12.0963i	0.305493	+	0.737525i	0.999840	+	0.0178850i	$0.00569329\pi$
$269$	5.01046	+	12.0963i	0.305493	+	0.737525i	−0.694347	+	0.719640i	$0.744307\pi$
$270$		0			0
$271$			28.2141i			1.71388i	0.515412	+	0.856942i	$0.327639\pi$
$271$			28.2141i			1.71388i	−0.515412	+	0.856942i	$0.672361\pi$
$272$	11.7851	+	22.9308i	0.714577	+	1.39038i
$273$		0			0
$274$	−13.3275	+	16.9363i	−0.805144	+	1.02316i
$275$	−0.0889314	−	0.214699i	−0.00536277	−	0.0129469i
$276$		0			0
$277$	−21.8246	−	9.04006i	−1.31132	−	0.543165i	−0.386047	−	0.922479i	$-0.626160\pi$
$277$	−21.8246	−	9.04006i	−1.31132	−	0.543165i	−0.925268	+	0.379314i	$0.876160\pi$
$278$	7.04942	+	1.98148i	0.422796	+	0.118841i
$279$		0			0
$280$	−14.8843	+	13.8316i	−0.889508	+	0.826594i
$281$	−3.00666	−	3.00666i	−0.179363	−	0.179363i	0.611715	−	0.791078i	$-0.290480\pi$
$281$	−3.00666	−	3.00666i	−0.179363	−	0.179363i	−0.791078	+	0.611715i	$0.790480\pi$
$282$		0			0
$283$	0.709521	−	1.71293i	0.0421766	−	0.101823i	−0.901387	−	0.433014i	$-0.857450\pi$
$283$	0.709521	−	1.71293i	0.0421766	−	0.101823i	0.943564	+	0.331190i	$0.107450\pi$
$284$	8.23127	+	5.02433i	0.488436	+	0.298139i
$285$		0			0
$286$	−0.0757135	−	0.634939i	−0.00447703	−	0.0375447i
$287$	−13.7359			−0.810804
$288$		0			0
$289$	−24.5443			−1.44378
$290$	1.44818	+	12.1445i	0.0850401	+	0.713153i
$291$		0			0
$292$	−0.651862	+	1.06793i	−0.0381474	+	0.0624961i
$293$	−10.5176	+	25.3917i	−0.614444	+	1.48340i	0.243627	+	0.969869i	$0.421663\pi$
$293$	−10.5176	+	25.3917i	−0.614444	+	1.48340i	−0.858071	+	0.513530i	$0.828337\pi$
$294$		0			0
$295$	4.90774	+	4.90774i	0.285739	+	0.285739i
$296$	0.468914	−	12.7906i	0.0272551	−	0.743438i
$297$		0			0
$298$	−6.37220	−	1.79113i	−0.369132	−	0.103757i
$299$	−3.01990	−	1.25088i	−0.174645	−	0.0723404i
$300$		0			0
$301$	9.83509	+	23.7440i	0.566885	+	1.36858i
$302$	16.3685	−	20.8007i	0.941900	−	1.19695i
$303$		0			0
$304$	6.41893	+	5.44353i	0.368151	+	0.312208i
$305$			6.93520i			0.397108i
$306$		0			0
$307$	5.80167	+	14.0065i	0.331119	+	0.799391i	0.998504	+	0.0546786i	$0.0174134\pi$
$307$	5.80167	+	14.0065i	0.331119	+	0.799391i	−0.667385	+	0.744713i	$0.732587\pi$
$308$	0.671386	+	0.920690i	0.0382558	+	0.0524612i
$309$		0			0
$310$	0.828427	−	2.94725i	0.0470515	−	0.167393i
$311$	−7.15481	+	7.15481i	−0.405712	+	0.405712i	−0.880240	−	0.474528i	$-0.842619\pi$
$311$	−7.15481	+	7.15481i	−0.405712	+	0.405712i	0.474528	+	0.880240i	$0.342619\pi$
$312$		0			0
$313$	−11.8512	−	11.8512i	−0.669868	−	0.669868i	0.287817	−	0.957685i	$-0.407070\pi$
$313$	−11.8512	−	11.8512i	−0.669868	−	0.669868i	−0.957685	+	0.287817i	$0.907070\pi$
$314$	−21.2956	+	11.9506i	−1.20178	+	0.674410i
$315$		0			0
$316$	−3.32756	−	13.7542i	−0.187190	−	0.773734i
$317$	−18.9377	+	7.84425i	−1.06365	+	0.440577i	−0.844745	−	0.535170i	$-0.820248\pi$
$317$	−18.9377	+	7.84425i	−1.06365	+	0.440577i	−0.218902	+	0.975747i	$0.570248\pi$
$318$		0			0
$319$	0.685896			0.0384028
$320$	−4.64167	−	14.0344i	−0.259477	−	0.784547i
$321$		0			0
$322$	5.78392	−	0.689705i	0.322325	−	0.0384358i
$323$	−12.5295	+	5.18989i	−0.697160	+	0.288773i
$324$		0			0
$325$	−1.87239	+	4.52035i	−0.103861	+	0.250744i
$326$	14.2151	−	7.97721i	0.787304	−	0.441817i
$327$		0			0
$328$	4.15980	−	9.08597i	0.229687	−	0.501689i
$329$	−7.33962	+	7.33962i	−0.404646	+	0.404646i
$330$		0			0
$331$	9.91107	+	4.10530i	0.544762	+	0.225648i	0.638055	−	0.769991i	$-0.279739\pi$
$331$	9.91107	+	4.10530i	0.544762	+	0.225648i	−0.0932931	+	0.995639i	$0.529739\pi$
$332$	−9.23368	−	12.6624i	−0.506764	−	0.694940i
$333$		0			0
$334$	4.69435	+	3.69407i	0.256863	+	0.202131i
$335$			28.1582i			1.53845i
$336$		0			0
$337$			3.23412i			0.176174i	0.996113	+	0.0880868i	$0.0280753\pi$
$337$			3.23412i			0.176174i	−0.996113	+	0.0880868i	$0.971925\pi$
$338$	3.04372	−	3.86790i	0.165556	−	0.210386i
$339$		0			0
$340$	23.5326	+	3.68499i	1.27624	+	0.199847i
$341$	−0.158619	−	0.0657022i	−0.00858971	−	0.00355797i
$342$		0			0
$343$	3.06608	−	3.06608i	0.165553	−	0.165553i
$344$	−18.6846	−	0.684993i	−1.00741	−	0.0369324i
$345$		0			0
$346$	−14.1979	−	25.3003i	−0.763286	−	1.36015i
$347$	9.82705	−	23.7246i	0.527544	−	1.27360i	−0.405584	−	0.914058i	$-0.632932\pi$
$347$	9.82705	−	23.7246i	0.527544	−	1.27360i	0.933128	−	0.359545i	$-0.117068\pi$
$348$		0			0
$349$	−12.5762	+	5.20925i	−0.673190	+	0.278845i	−0.692977	−	0.720960i	$-0.743701\pi$
$349$	−12.5762	+	5.20925i	−0.673190	+	0.278845i	0.0197868	+	0.999804i	$0.493701\pi$
$350$	−1.03239	−	8.65769i	−0.0551835	−	0.462773i
$351$		0			0
$352$	−0.812340	+	0.165283i	−0.0432978	+	0.00880961i
$353$	8.67371			0.461655			0.230828	−	0.972995i	$-0.425857\pi$
$353$	8.67371			0.461655			0.230828	+	0.972995i	$0.425857\pi$
$354$		0			0
$355$	8.23127	−	3.40950i	0.436870	−	0.180958i
$356$	10.1832	+	6.21580i	0.539710	+	0.329437i
$357$		0			0
$358$	17.3718	+	30.9560i	0.918129	+	1.63608i
$359$	−13.6307	−	13.6307i	−0.719399	−	0.719399i	0.249083	−	0.968482i	$-0.419871\pi$
$359$	−13.6307	−	13.6307i	−0.719399	−	0.719399i	−0.968482	+	0.249083i	$0.919871\pi$
$360$		0			0
$361$	10.3045	−	10.3045i	0.542345	−	0.542345i
$362$	2.76847	+	0.778175i	0.145508	+	0.0408999i
$363$		0			0
$364$	3.71155	−	23.7023i	0.194538	−	1.24234i
$365$	0.442353	+	1.06793i	0.0231538	+	0.0558982i
$366$		0			0
$367$		−	28.9800i		−	1.51274i	−0.654142	−	0.756371i	$-0.726970\pi$
$367$		−	28.9800i		−	1.51274i	0.654142	−	0.756371i	$-0.273030\pi$
$368$	−1.29539	+	4.03480i	−0.0675268	+	0.210329i
$369$		0			0
$370$	−9.29270	−	7.31259i	−0.483104	−	0.380164i
$371$	2.65344	+	6.40597i	0.137760	+	0.332581i
$372$		0			0
$373$	−5.56367	−	2.30455i	−0.288076	−	0.119325i	0.233966	−	0.972245i	$-0.424830\pi$
$373$	−5.56367	−	2.30455i	−0.288076	−	0.119325i	−0.522042	+	0.852920i	$0.674830\pi$
$374$	0.361465	−	1.28597i	0.0186909	−	0.0664957i
$375$		0			0
$376$	−2.63224	−	7.07773i	−0.135748	−	0.365006i
$377$	−10.2114	−	10.2114i	−0.525912	−	0.525912i
$378$		0			0
$379$	8.55274	−	20.6481i	0.439325	−	1.06062i	−0.536858	−	0.843673i	$-0.680389\pi$
$379$	8.55274	−	20.6481i	0.439325	−	1.06062i	0.976183	−	0.216951i	$-0.0696111\pi$
$380$	7.55765	−	1.82843i	0.387699	−	0.0937963i
$381$		0			0
$382$	−12.7213	+	1.51695i	−0.650876	+	0.0776139i
$383$	30.5667			1.56188			0.780942	−	0.624603i	$-0.214739\pi$
$383$	30.5667			1.56188			0.780942	+	0.624603i	$0.214739\pi$
$384$		0			0
$385$	1.05275			0.0536530
$386$	8.77254	−	1.04608i	0.446511	−	0.0532443i
$387$		0			0
$388$	20.0742	−	4.85657i	1.01911	−	0.246555i
$389$	7.06634	−	17.0597i	0.358278	−	0.864959i	−0.637265	−	0.770645i	$-0.719934\pi$
$389$	7.06634	−	17.0597i	0.358278	−	0.864959i	0.995543	−	0.0943139i	$-0.0300657\pi$
$390$		0			0
$391$	−4.82843	−	4.82843i	−0.244184	−	0.244184i
$392$	8.00112	+	21.5139i	0.404117	+	1.08661i
$393$		0			0
$394$	1.81298	−	6.44993i	0.0913365	−	0.324943i
$395$	−12.0786	−	5.00313i	−0.607742	−	0.251735i
$396$		0			0
$397$	7.15759	+	17.2799i	0.359229	+	0.867255i	0.995409	+	0.0957146i	$0.0305136\pi$
$397$	7.15759	+	17.2799i	0.359229	+	0.867255i	−0.636180	+	0.771541i	$0.719486\pi$
$398$	9.65326	+	7.59633i	0.483874	+	0.380769i
$399$		0			0
$400$	6.03951	+	1.93901i	0.301976	+	0.0969505i
$401$		−	11.0004i		−	0.549332i	−0.961540	−	0.274666i	$-0.911433\pi$
$401$		−	11.0004i		−	0.549332i	0.961540	−	0.274666i	$-0.0885674\pi$
$402$		0			0
$403$	1.38331	+	3.33962i	0.0689078	+	0.166358i
$404$	3.49083	−	22.2927i	0.173675	−	1.10910i
$405$		0			0
$406$	24.7741	+	6.96362i	1.22952	+	0.345599i
$407$	−0.468914	+	0.468914i	−0.0232432	+	0.0232432i
$408$		0			0
$409$	−1.15862	−	1.15862i	−0.0572900	−	0.0572900i	0.677881	−	0.735171i	$-0.262898\pi$
$409$	−1.15862	−	1.15862i	−0.0572900	−	0.0572900i	−0.735171	+	0.677881i	$0.762898\pi$
$410$	−4.51813	−	8.05117i	−0.223135	−	0.397619i
$411$		0			0
$412$	32.1415	+	19.6190i	1.58350	+	0.966559i
$413$	13.4919	−	5.58855i	0.663895	−	0.274994i
$414$		0			0
$415$	−14.4786			−0.710727
$416$	14.5545	+	9.63315i	0.713593	+	0.472304i
$417$		0			0
$418$	−0.0516326	−	0.432995i	−0.00252543	−	0.0211785i
$419$	32.0362	−	13.2698i	1.56507	−	0.648273i	0.579108	−	0.815251i	$-0.303401\pi$
$419$	32.0362	−	13.2698i	1.56507	−	0.648273i	0.985961	+	0.166978i	$0.0534009\pi$
$420$		0			0
$421$	9.34602	−	22.5633i	0.455497	−	1.09967i	−0.514705	−	0.857368i	$-0.672098\pi$
$421$	9.34602	−	22.5633i	0.455497	−	1.09967i	0.970202	−	0.242299i	$-0.0779016\pi$
$422$	9.43308	+	16.8094i	0.459195	+	0.818271i
$423$		0			0
$424$	−5.04098	−	0.184807i	−0.244811	−	0.00897500i
$425$	−7.22746	+	7.22746i	−0.350583	+	0.350583i
$426$		0			0
$427$	13.4815	+	5.58421i	0.652414	+	0.270239i
$428$	−28.3395	−	4.43771i	−1.36984	−	0.214505i
$429$		0			0
$430$	−10.6823	+	13.5749i	−0.515146	+	0.654637i
$431$		−	4.47586i		−	0.215594i	−0.994173	−	0.107797i	$-0.965620\pi$
$431$		−	4.47586i		−	0.215594i	0.994173	−	0.107797i	$-0.0343797\pi$
$432$		0			0
$433$			1.44196i			0.0692960i	0.999400	+	0.0346480i	$0.0110310\pi$
$433$			1.44196i			0.0692960i	−0.999400	+	0.0346480i	$0.988969\pi$
$434$	−5.06217	−	3.98352i	−0.242992	−	0.191215i
$435$		0			0
$436$	−15.0121	−	20.5865i	−0.718949	−	0.985915i
$437$	−2.05941	−	0.853036i	−0.0985150	−	0.0408063i
$438$		0			0
$439$	0.854615	−	0.854615i	0.0407885	−	0.0407885i	−0.686418	−	0.727207i	$-0.740818\pi$
$439$	0.854615	−	0.854615i	0.0407885	−	0.0407885i	0.727207	+	0.686418i	$0.240818\pi$
$440$	−0.318816	+	0.696369i	−0.0151990	+	0.0331981i
$441$		0			0
$442$	−24.5264	+	13.7636i	−1.16660	+	0.654669i
$443$	−4.68913	+	11.3206i	−0.222787	+	0.537857i	−0.995266	−	0.0971838i	$-0.969017\pi$
$443$	−4.68913	+	11.3206i	−0.222787	+	0.537857i	0.772479	+	0.635040i	$0.219017\pi$
$444$		0			0
$445$	10.1832	−	4.21803i	0.482731	−	0.199954i
$446$	−1.34891	+	0.160851i	−0.0638726	+	0.00761651i
$447$		0			0
$448$	−31.0192	−	2.27744i	−1.46552	−	0.107599i
$449$	24.5573			1.15893			0.579464	−	0.814998i	$-0.303262\pi$
$449$	24.5573			1.15893			0.579464	+	0.814998i	$0.303262\pi$
$450$		0			0
$451$	−0.478338	+	0.198134i	−0.0225240	+	0.00932976i
$452$	2.76588	+	11.4325i	0.130096	+	0.537741i
$453$		0			0
$454$	−18.9153	+	10.6148i	−0.887740	+	0.498179i
$455$	−15.6729	−	15.6729i	−0.734759	−	0.734759i
$456$		0			0
$457$	14.1684	−	14.1684i	0.662771	−	0.662771i	−0.293262	−	0.956032i	$-0.594741\pi$
$457$	14.1684	−	14.1684i	0.662771	−	0.662771i	0.956032	+	0.293262i	$0.0947407\pi$
$458$	1.80408	−	6.41829i	0.0842992	−	0.299907i
$459$		0			0
$460$	2.30676	+	3.16333i	0.107553	+	0.147491i
$461$	11.7965	+	28.4793i	0.549417	+	1.32641i	0.917913	+	0.396782i	$0.129873\pi$
$461$	11.7965	+	28.4793i	0.549417	+	1.32641i	−0.368496	+	0.929630i	$0.620127\pi$
$462$		0			0
$463$			14.8190i			0.688697i	0.938842	+	0.344349i	$0.111900\pi$
$463$			14.8190i			0.688697i	−0.938842	+	0.344349i	$0.888100\pi$
$464$	−12.1089	+	14.2786i	−0.562142	+	0.662869i
$465$		0			0
$466$	20.7683	−	26.3919i	0.962072	−	1.22258i
$467$	−5.43521	−	13.1218i	−0.251512	−	0.607203i	0.746815	−	0.665032i	$-0.231582\pi$
$467$	−5.43521	−	13.1218i	−0.251512	−	0.607203i	−0.998326	+	0.0578293i	$0.981582\pi$
$468$		0			0
$469$	54.7373	+	22.6729i	2.52753	+	1.04694i
$470$	−6.71627	−	1.88784i	−0.309798	−	0.0870795i
$471$		0			0
$472$	−0.389231	+	10.6171i	−0.0179158	+	0.488690i
$473$	0.684993	+	0.684993i	0.0314960	+	0.0314960i
$474$		0			0
$475$	−1.27687	+	3.08264i	−0.0585869	+	0.141441i
$476$	26.1118	−	42.7784i	1.19683	−	1.96075i
$477$		0			0
$478$	−2.65267	−	22.2455i	−0.121330	−	1.01749i
$479$	−32.3727			−1.47915			−0.739574	−	0.673076i	$-0.764973\pi$
$479$	−32.3727			−1.47915			−0.739574	+	0.673076i	$0.764973\pi$
$480$		0			0
$481$	13.9620			0.636614
$482$	0.0524685	+	0.440005i	0.00238988	+	0.0200417i
$483$		0			0
$484$	−18.7415	−	11.4397i	−0.851887	−	0.519988i
$485$	7.30205	−	17.6287i	0.331569	−	0.800479i
$486$		0			0
$487$	−1.89478	−	1.89478i	−0.0858608	−	0.0858608i	0.662872	−	0.748733i	$-0.269337\pi$
$487$	−1.89478	−	1.89478i	−0.0858608	−	0.0858608i	−0.748733	+	0.662872i	$0.769337\pi$
$488$	−7.77658	+	7.22655i	−0.352029	+	0.327131i
$489$		0			0
$490$	20.4151	+	5.73838i	0.922262	+	0.259234i
$491$	18.2886	+	7.57539i	0.825354	+	0.341873i	0.755062	−	0.655654i	$-0.227607\pi$
$491$	18.2886	+	7.57539i	0.825354	+	0.341873i	0.0702922	+	0.997526i	$0.477607\pi$
$492$		0			0
$493$	−11.5447	−	27.8714i	−0.519947	−	1.25526i
$494$	−5.67759	+	7.21496i	−0.255447	+	0.324617i
$495$		0			0
$496$	4.16804	−	2.14214i	0.187151	−	0.0961847i
$497$		−	18.7462i		−	0.840884i
$498$		0			0
$499$	−9.54921	−	23.0538i	−0.427481	−	1.03203i	−0.980083	−	0.198586i	$-0.936365\pi$
$499$	−9.54921	−	23.0538i	−0.427481	−	1.03203i	0.552602	−	0.833445i	$-0.313635\pi$
$500$	19.6647	−	14.3399i	0.879432	−	0.641300i
$501$		0			0
$502$	3.55903	−	12.6618i	0.158847	−	0.565122i
$503$	−22.6436	+	22.6436i	−1.00963	+	1.00963i	−0.00967595	+	0.999953i	$0.503080\pi$
$503$	−22.6436	+	22.6436i	−1.00963	+	1.00963i	−0.999953	+	0.00967595i	$0.996920\pi$
$504$		0			0
$505$	−14.7409	−	14.7409i	−0.655960	−	0.655960i
$506$	0.191470	−	0.107449i	0.00851189	−	0.00477668i
$507$		0			0
$508$	−29.9406	+	7.24354i	−1.32840	+	0.321380i
$509$	21.3715	−	8.85238i	0.947276	−	0.392375i	0.145070	−	0.989421i	$-0.453659\pi$
$509$	21.3715	−	8.85238i	0.947276	−	0.392375i	0.802206	+	0.597047i	$0.203659\pi$
$510$		0			0
$511$	2.43216			0.107592
$512$	10.9004	−	19.8288i	0.481734	−	0.876317i
$513$		0			0
$514$	−26.5466	+	3.16556i	−1.17092	+	0.139627i
$515$	32.1415	−	13.3134i	1.41632	−	0.586660i
$516$		0			0
$517$	−0.149724	+	0.361465i	−0.00658484	+	0.0158972i
$518$	−21.6976	+	12.1762i	−0.953336	+	0.534990i
$519$		0			0
$520$	15.1137	−	5.62087i	0.662780	−	0.246491i
$521$	9.76588	−	9.76588i	0.427851	−	0.427851i	−0.460045	−	0.887896i	$-0.652167\pi$
$521$	9.76588	−	9.76588i	0.427851	−	0.427851i	0.887896	+	0.460045i	$0.152167\pi$
$522$		0			0
$523$	−16.9370	−	7.01552i	−0.740601	−	0.306767i	−0.0197010	−	0.999806i	$-0.506271\pi$
$523$	−16.9370	−	7.01552i	−0.740601	−	0.306767i	−0.720900	+	0.693039i	$0.756271\pi$
$524$	5.18406	−	3.78032i	0.226467	−	0.165144i
$525$		0			0
$526$	26.1480	+	20.5763i	1.14011	+	0.897170i
$527$			7.55136i			0.328942i
$528$		0			0
$529$			21.8776i			0.951202i
$530$	−2.88201	+	3.66240i	−0.125187	+	0.159085i
$531$		0			0
$532$	2.53109	−	16.1637i	0.109737	−	0.700785i
$533$	10.0711	+	4.17157i	0.436226	+	0.180691i
$534$		0			0
$535$	−18.7393	+	18.7393i	−0.810170	+	0.810170i
$536$	−31.5744	+	29.3412i	−1.36381	+	1.26735i
$537$		0			0
$538$	9.06156	+	16.1474i	0.390672	+	0.696165i
$539$	0.455108	−	1.09873i	0.0196029	−	0.0473256i
$540$		0			0
$541$	14.2214	−	5.89071i	0.611427	−	0.253261i	−0.0554115	−	0.998464i	$-0.517647\pi$
$541$	14.2214	−	5.89071i	0.611427	−	0.253261i	0.666839	+	0.745202i	$0.267647\pi$
$542$	4.72451	+	39.6201i	0.202935	+	1.70183i
$543$		0			0
$544$	20.3892	+	30.2274i	0.874180	+	1.29599i
$545$	−23.5393			−1.00831
$546$		0			0
$547$	−9.67342	+	4.00686i	−0.413606	+	0.171321i	−0.579776	−	0.814776i	$-0.696860\pi$
$547$	−9.67342	+	4.00686i	−0.413606	+	0.171321i	0.166170	+	0.986097i	$0.446860\pi$
$548$	−15.8793	+	26.0148i	−0.678331	+	1.11130i
$549$		0			0
$550$	−0.160835	−	0.286603i	−0.00685803	−	0.0122208i
$551$	−6.96362	−	6.96362i	−0.296660	−	0.296660i
$552$		0			0
$553$	−19.4514	+	19.4514i	−0.827157	+	0.827157i
$554$	−32.1613	−	9.04006i	−1.36640	−	0.384075i
$555$		0			0
$556$	10.2311	+	1.60209i	0.433893	+	0.0679437i
$557$	3.08965	+	7.45908i	0.130913	+	0.316051i	0.975721	−	0.219018i	$-0.0702854\pi$
$557$	3.08965	+	7.45908i	0.130913	+	0.316051i	−0.844808	+	0.535070i	$0.820285\pi$
$558$		0			0
$559$		−	20.3959i		−	0.862653i
$560$	−18.5854	+	21.9156i	−0.785376	+	0.926102i
$561$		0			0
$562$	−4.72562	−	3.71868i	−0.199338	−	0.156863i
$563$	−10.1815	−	24.5802i	−0.429097	−	1.03593i	−0.979574	−	0.201082i	$-0.935554\pi$
$563$	−10.1815	−	24.5802i	−0.429097	−	1.03593i	0.550477	−	0.834850i	$-0.314446\pi$
$564$		0			0
$565$	10.0398	+	4.15862i	0.422377	+	0.174954i
$566$	0.709521	−	2.52422i	0.0298234	−	0.106101i
$567$		0			0
$568$	12.4002	+	5.67715i	0.520301	+	0.238208i
$569$	−8.12862	−	8.12862i	−0.340770	−	0.340770i	0.515887	−	0.856657i	$-0.327462\pi$
$569$	−8.12862	−	8.12862i	−0.340770	−	0.340770i	−0.856657	+	0.515887i	$0.827462\pi$
$570$		0			0
$571$	−7.40930	+	17.8876i	−0.310070	+	0.748574i	0.689632	+	0.724160i	$0.257772\pi$
$571$	−7.40930	+	17.8876i	−0.310070	+	0.748574i	−0.999702	+	0.0244147i	$0.992228\pi$
$572$	−0.212644	−	0.878944i	−0.00889107	−	0.0367505i
$573$		0			0
$574$	−19.2888	+	2.30010i	−0.805100	+	0.0960044i
$575$	−1.68000			−0.0700609
$576$		0			0
$577$	−11.9134			−0.495959			−0.247980	−	0.968765i	$-0.579767\pi$
$577$	−11.9134			−0.495959			−0.247980	+	0.968765i	$0.579767\pi$
$578$	−34.4667	+	4.10999i	−1.43363	+	0.170953i
$579$		0			0
$580$	4.06726	+	16.8117i	0.168884	+	0.698066i
$581$	−11.6582	+	28.1453i	−0.483662	+	1.16766i
$582$		0			0
$583$	0.184807	+	0.184807i	0.00765391	+	0.00765391i
$584$	−0.736560	+	1.60882i	−0.0304791	+	0.0665734i
$585$		0			0
$586$	−10.5176	+	37.4179i	−0.434478	+	1.54572i
$587$	23.6011	+	9.77588i	0.974120	+	0.403494i	0.812244	−	0.583318i	$-0.198246\pi$
$587$	23.6011	+	9.77588i	0.974120	+	0.403494i	0.161876	+	0.986811i	$0.448246\pi$
$588$		0			0
$589$	0.943348	+	2.27744i	0.0388700	+	0.0938404i
$590$	7.71357	+	6.06995i	0.317563	+	0.249896i
$591$		0			0
$592$	−1.48333	−	18.0399i	−0.0609645	−	0.741435i
$593$		−	12.5549i		−	0.515567i	−0.966203	−	0.257784i	$-0.917008\pi$
$593$		−	12.5549i		−	0.515567i	0.966203	−	0.257784i	$-0.0829922\pi$
$594$		0			0
$595$	−17.7194	−	42.7784i	−0.726425	−	1.75374i
$596$	−9.24819	−	1.44818i	−0.378821	−	0.0593198i
$597$		0			0
$598$	−4.45020	−	1.25088i	−0.181982	−	0.0511524i
$599$	6.66010	−	6.66010i	0.272124	−	0.272124i	−0.557830	−	0.829955i	$-0.688366\pi$
$599$	6.66010	−	6.66010i	0.272124	−	0.272124i	0.829955	+	0.557830i	$0.188366\pi$
$600$		0			0
$601$	27.4318	+	27.4318i	1.11896	+	1.11896i	0.991894	+	0.127071i	$0.0405577\pi$
$601$	27.4318	+	27.4318i	1.11896	+	1.11896i	0.127071	+	0.991894i	$0.459442\pi$
$602$	17.7871	+	31.6960i	0.724946	+	1.29183i
$603$		0			0
$604$	19.5026	−	31.9507i	0.793548	−	1.30005i
$605$	−18.7415	+	7.76299i	−0.761951	+	0.315610i
$606$		0			0
$607$	−20.3361			−0.825416			−0.412708	−	0.910863i	$-0.635417\pi$
$607$	−20.3361			−0.825416			−0.412708	+	0.910863i	$0.635417\pi$
$608$	9.92540	+	6.56930i	0.402528	+	0.266420i
$609$		0			0
$610$	1.16131	+	9.73886i	0.0470202	+	0.394315i
$611$	7.61040	−	3.15233i	0.307884	−	0.127530i
$612$		0			0
$613$	−13.3277	+	32.1759i	−0.538301	+	1.29957i	0.387608	+	0.921824i	$0.373301\pi$
$613$	−13.3277	+	32.1759i	−0.538301	+	1.29957i	−0.925908	+	0.377748i	$0.876699\pi$
$614$	10.4925	+	18.6973i	0.423442	+	0.754561i
$615$		0			0
$616$	1.09698	+	1.18047i	0.0441984	+	0.0475624i
$617$	11.3168	−	11.3168i	0.455599	−	0.455599i	−0.441609	−	0.897208i	$-0.645592\pi$
$617$	11.3168	−	11.3168i	0.455599	−	0.455599i	0.897208	+	0.441609i	$0.145592\pi$
$618$		0			0
$619$	−0.224799	−	0.0931149i	−0.00903545	−	0.00374260i	0.378161	−	0.925740i	$-0.376557\pi$
$619$	−0.224799	−	0.0931149i	−0.00903545	−	0.00374260i	−0.387197	+	0.921997i	$0.626557\pi$
$620$	0.669808	−	4.27744i	0.0269001	−	0.171786i
$621$		0			0
$622$	−8.84916	+	11.2453i	−0.354819	+	0.450897i
$623$		−	23.1917i		−	0.929157i
$624$		0			0
$625$		−	14.5563i		−	0.582254i
$626$	−18.6267	−	14.6577i	−0.744473	−	0.585839i
$627$		0			0
$628$	−27.9035	+	20.3478i	−1.11347	+	0.811964i
$629$	26.9469	+	11.1618i	1.07444	+	0.445048i
$630$		0			0
$631$	1.15481	−	1.15481i	0.0459722	−	0.0459722i	−0.683747	−	0.729719i	$-0.739651\pi$
$631$	1.15481	−	1.15481i	0.0459722	−	0.0459722i	0.729719	+	0.683747i	$0.239651\pi$
$632$	−6.97595	−	18.7573i	−0.277488	−	0.746127i
$633$		0			0
$634$	−25.2800	+	14.1866i	−1.00400	+	0.563420i
$635$	−10.8910	+	26.2931i	−0.432195	+	1.04341i
$636$		0			0
$637$	−23.1330	+	9.58199i	−0.916562	+	0.379652i
$638$	0.963179	−	0.114855i	0.0381326	−	0.00454714i
$639$		0			0
$640$	−8.86822	−	18.9308i	−0.350547	−	0.748304i
$641$	14.1953			0.560679			0.280339	−	0.959901i	$-0.409553\pi$
$641$	14.1953			0.560679			0.280339	+	0.959901i	$0.409553\pi$
$642$		0			0
$643$	33.9334	−	14.0557i	1.33820	−	0.554302i	0.405219	−	0.914219i	$-0.367195\pi$
$643$	33.9334	−	14.0557i	1.33820	−	0.554302i	0.932984	+	0.359917i	$0.117195\pi$
$644$	8.00666	−	1.93706i	0.315507	−	0.0763308i
$645$		0			0
$646$	−16.7257	+	9.38607i	−0.658063	+	0.369290i
$647$	−8.73969	−	8.73969i	−0.343593	−	0.343593i	0.514123	−	0.857716i	$-0.328117\pi$
$647$	−8.73969	−	8.73969i	−0.343593	−	0.343593i	−0.857716	+	0.514123i	$0.828117\pi$
$648$		0			0
$649$	0.389231	−	0.389231i	0.0152786	−	0.0152786i
$650$	−1.87239	+	6.66130i	−0.0734412	+	0.261278i
$651$		0			0
$652$	18.6260	−	13.5825i	0.729451	−	0.531931i
$653$	−16.1182	−	38.9127i	−0.630753	−	1.52277i	−0.838679	−	0.544627i	$-0.816671\pi$
$653$	−16.1182	−	38.9127i	−0.630753	−	1.52277i	0.207926	−	0.978145i	$-0.433329\pi$
$654$		0			0
$655$		−	5.92763i		−	0.231612i
$656$	4.32000	−	13.4557i	0.168668	−	0.525356i
$657$		0			0
$658$	−9.07773	+	11.5358i	−0.353887	+	0.449712i
$659$	8.93958	+	21.5821i	0.348237	+	0.840718i	0.996828	+	0.0795812i	$0.0253583\pi$
$659$	8.93958	+	21.5821i	0.348237	+	0.840718i	−0.648592	+	0.761136i	$0.724642\pi$
$660$		0			0
$661$	−22.0088	−	9.11633i	−0.856042	−	0.354584i	−0.0888835	−	0.996042i	$-0.528330\pi$
$661$	−22.0088	−	9.11633i	−0.856042	−	0.354584i	−0.767158	+	0.641458i	$0.778330\pi$
$662$	14.6052	+	4.10530i	0.567647	+	0.159557i
$663$		0			0
$664$	−15.0869	−	16.2352i	−0.585484	−	0.630047i
$665$	−10.6881	−	10.6881i	−0.414468	−	0.414468i
$666$		0			0
$667$	1.89754	−	4.58107i	0.0734732	−	0.177380i
$668$	7.21069	+	4.40138i	0.278990	+	0.170294i
$669$		0			0
$670$	4.71515	+	39.5416i	0.182162	+	1.52763i
$671$	0.550028			0.0212336
$672$		0			0
$673$	45.0980			1.73840			0.869200	−	0.494460i	$-0.164634\pi$
$673$	45.0980			1.73840			0.869200	+	0.494460i	$0.164634\pi$
$674$	0.541560	+	4.54156i	0.0208601	+	0.174934i
$675$		0			0
$676$	3.62650	−	5.94123i	0.139481	−	0.228509i
$677$	−13.6058	+	32.8474i	−0.522915	+	1.26243i	0.413170	+	0.910654i	$0.364421\pi$
$677$	−13.6058	+	32.8474i	−0.522915	+	1.26243i	−0.936085	+	0.351774i	$0.885579\pi$
$678$		0			0
$679$	−28.3892	−	28.3892i	−1.08948	−	1.08948i
$680$	33.6631	+	1.23412i	1.29092	+	0.0473263i
$681$		0			0
$682$	−0.233745	−	0.0657022i	−0.00895057	−	0.00251587i
$683$	−18.8141	−	7.79305i	−0.719901	−	0.298193i	−0.00750651	−	0.999972i	$-0.502389\pi$
$683$	−18.8141	−	7.79305i	−0.719901	−	0.298193i	−0.712395	+	0.701779i	$0.752389\pi$
$684$		0			0
$685$	10.7757	+	26.0148i	0.411718	+	0.993974i
$686$	3.79216	−	4.81900i	0.144785	−	0.183990i
$687$		0			0
$688$	−26.3528	+	2.16686i	−1.00469	+	0.0826108i
$689$		−	5.50267i		−	0.209635i
$690$		0			0
$691$	12.6322	+	30.4967i	0.480550	+	1.16015i	0.959348	+	0.282226i	$0.0910726\pi$
$691$	12.6322	+	30.4967i	0.480550	+	1.16015i	−0.478798	+	0.877925i	$0.658927\pi$
$692$	−24.1742	−	33.1508i	−0.918967	−	1.26020i
$693$		0			0
$694$	9.82705	−	34.9612i	0.373030	−	1.32711i
$695$	6.76521	−	6.76521i	0.256619	−	0.256619i
$696$		0			0
$697$	16.1023	+	16.1023i	0.609920	+	0.609920i
$698$	−16.7881	+	9.42108i	−0.635437	+	0.356593i
$699$		0			0
$700$	−2.89949	−	11.9848i	−0.109591	−	0.452983i
$701$	−0.915341	+	0.379146i	−0.0345719	+	0.0143202i	−0.399902	−	0.916558i	$-0.630956\pi$
$701$	−0.915341	+	0.379146i	−0.0345719	+	0.0143202i	0.365330	+	0.930878i	$0.380956\pi$
$702$		0			0
$703$	9.52138			0.359106
$704$	−1.11306	+	0.368129i	−0.0419501	+	0.0138744i
$705$		0			0
$706$	12.1802	−	1.45243i	0.458407	−	0.0546629i
$707$	−40.5244	+	16.7858i	−1.52408	+	0.631293i
$708$		0			0
$709$	−18.9677	+	45.7920i	−0.712346	+	1.71975i	−0.0182911	+	0.999833i	$0.505823\pi$
$709$	−18.9677	+	45.7920i	−0.712346	+	1.71975i	−0.694055	+	0.719922i	$0.744177\pi$
$710$	10.9879	−	6.16619i	0.412370	−	0.231413i
$711$		0			0
$712$	15.3408	+	7.02343i	0.574921	+	0.263214i
$713$	−0.877646	+	0.877646i	−0.0328681	+	0.0328681i
$714$		0			0
$715$	−0.771869	−	0.319719i	−0.0288663	−	0.0119568i
$716$	29.5783	+	40.5615i	1.10539	+	1.51585i
$717$		0			0
$718$	−21.4235	−	16.8586i	−0.799520	−	0.629157i
$719$			12.7931i			0.477102i	0.971130	+	0.238551i	$0.0766724\pi$
$719$			12.7931i			0.477102i	−0.971130	+	0.238551i	$0.923328\pi$
$720$		0			0
$721$		−	73.2004i		−	2.72612i
$722$	12.7448	−	16.1958i	0.474312	−	0.602746i
$723$		0			0
$724$	4.01797	+	0.629177i	0.149327	+	0.0233832i
$725$	−6.85720	−	2.84035i	−0.254670	−	0.105488i
$726$		0			0
$727$	−0.466154	+	0.466154i	−0.0172887	+	0.0172887i	−0.715698	−	0.698410i	$-0.753891\pi$
$727$	−0.466154	+	0.466154i	−0.0172887	+	0.0172887i	0.698410	+	0.715698i	$0.253891\pi$
$728$	1.24301	−	33.9058i	0.0460692	−	1.25663i
$729$		0			0
$730$	0.800008	+	1.42559i	0.0296096	+	0.0527634i
$731$	16.3052	−	39.3642i	0.603069	−	1.45594i
$732$		0			0
$733$	34.0271	−	14.0945i	1.25682	−	0.520591i	0.347887	−	0.937536i	$-0.386899\pi$
$733$	34.0271	−	14.0945i	1.25682	−	0.520591i	0.908932	+	0.416945i	$0.136899\pi$
$734$	−4.85276	−	40.6956i	−0.179119	−	1.50210i
$735$		0			0
$736$	−1.14343	+	5.88285i	−0.0421475	+	0.216845i
$737$	2.23322			0.0822616
$738$		0			0
$739$	8.25825	−	3.42068i	0.303785	−	0.125832i	−0.225584	−	0.974224i	$-0.572429\pi$
$739$	8.25825	−	3.42068i	0.303785	−	0.125832i	0.529368	+	0.848392i	$0.322429\pi$
$740$	−14.2739	−	8.71274i	−0.524720	−	0.320287i
$741$		0			0
$742$	4.79883	+	8.55136i	0.176170	+	0.313930i
$743$	32.4060	+	32.4060i	1.18886	+	1.18886i	0.977383	+	0.211477i	$0.0678273\pi$
$743$	32.4060	+	32.4060i	1.18886	+	1.18886i	0.211477	+	0.977383i	$0.432173\pi$
$744$		0			0
$745$	−6.11529	+	6.11529i	−0.224047	+	0.224047i
$746$	−8.19877	−	2.30455i	−0.300178	−	0.0843755i
$747$		0			0
$748$	0.292255	−	1.86636i	0.0106859	−	0.0682410i
$749$	21.3388	+	51.5165i	0.779704	+	1.88237i
$750$		0			0
$751$			21.5108i			0.784939i	0.919765	+	0.392470i	$0.128379\pi$
$751$			21.5108i			0.784939i	−0.919765	+	0.392470i	$0.871621\pi$
$752$	−4.88155	−	9.49824i	−0.178012	−	0.346365i
$753$		0			0
$754$	−16.0494	−	12.6296i	−0.584484	−	0.459941i
$755$	−13.2344	−	31.9507i	−0.481649	−	1.16280i
$756$		0			0
$757$	−17.3649	−	7.19276i	−0.631137	−	0.261425i	0.0440993	−	0.999027i	$-0.485958\pi$
$757$	−17.3649	−	7.19276i	−0.631137	−	0.261425i	−0.675236	+	0.737602i	$0.735958\pi$
$758$	8.55274	−	30.4276i	0.310649	−	1.10518i
$759$		0			0
$760$	10.3068	−	3.83314i	0.373866	−	0.139043i
$761$	37.8574	+	37.8574i	1.37233	+	1.37233i	0.856977	+	0.515354i	$0.172340\pi$
$761$	37.8574	+	37.8574i	1.37233	+	1.37233i	0.515354	+	0.856977i	$0.327660\pi$
$762$		0			0
$763$	−18.9538	+	45.7585i	−0.686174	+	1.65657i
$764$	−17.6100	+	4.26040i	−0.637107	+	0.154136i
$765$		0			0
$766$	42.9237	−	5.11845i	1.55090	−	0.184937i
$767$	−11.5894			−0.418471
$768$		0			0
$769$	3.07370			0.110840			0.0554201	−	0.998463i	$-0.482350\pi$
$769$	3.07370			0.110840			0.0554201	+	0.998463i	$0.482350\pi$
$770$	1.47834	−	0.176285i	0.0532756	−	0.00635286i
$771$		0			0
$772$	12.1438	−	2.93796i	0.437065	−	0.105740i
$773$	6.55831	−	15.8332i	0.235886	−	0.569479i	−0.760964	−	0.648795i	$-0.775273\pi$
$773$	6.55831	−	15.8332i	0.235886	−	0.569479i	0.996850	+	0.0793155i	$0.0252735\pi$
$774$		0			0
$775$	1.31371	+	1.31371i	0.0471898	+	0.0471898i
$776$	27.3763	−	10.1814i	0.982750	−	0.365490i
$777$		0			0
$778$	7.06634	−	25.1395i	0.253341	−	0.901296i
$779$	6.86794	+	2.84479i	0.246070	+	0.101925i
$780$		0			0
$781$	−0.270406	−	0.652818i	−0.00967589	−	0.0233597i
$782$	−7.58892	−	5.97186i	−0.271379	−	0.213553i
$783$		0			0
$784$	14.8382	+	28.8714i	0.529937	+	1.03112i
$785$			31.9058i			1.13877i
$786$		0			0
$787$	−6.77706	−	16.3613i	−0.241576	−	0.583216i	0.755864	−	0.654729i	$-0.227217\pi$
$787$	−6.77706	−	16.3613i	−0.241576	−	0.583216i	−0.997440	+	0.0715129i	$0.977217\pi$
$788$	1.46585	−	9.36100i	0.0522186	−	0.333472i
$789$		0			0
$790$	−17.7994	−	5.00313i	−0.633274	−	0.178004i
$791$	16.1680	−	16.1680i	0.574869	−	0.574869i
$792$		0			0
$793$	−8.18862	−	8.18862i	−0.290786	−	0.290786i
$794$	12.9447	+	23.0671i	0.459390	+	0.818619i
$795$		0			0
$796$	14.8278	+	9.05080i	0.525556	+	0.320797i
$797$	32.4476	−	13.4402i	1.14935	−	0.476077i	0.275036	−	0.961434i	$-0.411310\pi$
$797$	32.4476	−	13.4402i	1.14935	−	0.476077i	0.874316	+	0.485356i	$0.161310\pi$
$798$		0			0
$799$	17.2082			0.608783
$800$	8.80577	+	1.71155i	0.311331	+	0.0605126i
$801$		0			0
$802$	−1.84203	−	15.4474i	−0.0650445	−	0.545468i
$803$	0.0846974	−	0.0350828i	0.00298891	−	0.00123805i
$804$		0			0
$805$	2.91245	−	7.03127i	0.102650	−	0.247820i
$806$	2.50176	+	4.45807i	0.0881209	+	0.157029i
$807$		0			0
$808$	1.16909	−	31.8894i	0.0411285	−	1.12187i
$809$	−11.2704	+	11.2704i	−0.396246	+	0.396246i	−0.876907	−	0.480661i	$-0.840397\pi$
$809$	−11.2704	+	11.2704i	−0.396246	+	0.396246i	0.480661	+	0.876907i	$0.340397\pi$
$810$		0			0
$811$	−16.3328	−	6.76529i	−0.573524	−	0.237561i	0.0770206	−	0.997029i	$-0.475459\pi$
$811$	−16.3328	−	6.76529i	−0.573524	−	0.237561i	−0.650545	+	0.759468i	$0.725459\pi$
$812$	35.9555	+	5.63029i	1.26179	+	0.197585i
$813$		0			0
$814$	−0.579959	+	0.737000i	−0.0203275	+	0.0258318i
$815$		−	21.2976i		−	0.746023i
$816$		0			0
$817$		−	13.9089i		−	0.486611i
$818$	−1.82102	−	1.43300i	−0.0636705	−	0.0501035i
$819$		0			0
$820$	−7.69284	−	10.5494i	−0.268646	−	0.368401i
$821$	−29.5124	−	12.2244i	−1.02999	−	0.426636i	−0.197281	−	0.980347i	$-0.563211\pi$
$821$	−29.5124	−	12.2244i	−1.02999	−	0.426636i	−0.832709	+	0.553711i	$0.813211\pi$
$822$		0			0
$823$	1.00381	−	1.00381i	0.0349906	−	0.0349906i	−0.689395	−	0.724386i	$-0.742124\pi$
$823$	1.00381	−	1.00381i	0.0349906	−	0.0349906i	0.724386	+	0.689395i	$0.242124\pi$
$824$	48.4204	+	22.1681i	1.68680	+	0.772264i
$825$		0			0
$826$	18.0105	−	10.1071i	0.626664	−	0.351669i
$827$	−15.7060	+	37.9176i	−0.546151	+	1.31852i	0.374170	+	0.927360i	$0.377928\pi$
$827$	−15.7060	+	37.9176i	−0.546151	+	1.31852i	−0.920321	+	0.391165i	$0.872072\pi$
$828$		0			0
$829$	31.9806	−	13.2468i	1.11073	−	0.460081i	0.249543	−	0.968364i	$-0.419720\pi$
$829$	31.9806	−	13.2468i	1.11073	−	0.460081i	0.861190	+	0.508283i	$0.169720\pi$
$830$	−20.3318	+	2.42447i	−0.705728	+	0.0841547i
$831$		0			0
$832$	22.0515	+	11.0903i	0.764496	+	0.384487i
$833$	−52.3070			−1.81233
$834$		0			0
$835$	7.21069	−	2.98677i	0.249536	−	0.103361i
$836$	−0.145012	−	0.599394i	−0.00501534	−	0.0207305i
$837$		0			0
$838$	42.7652	−	23.9989i	1.47730	−	0.829027i
$839$	−3.42599	−	3.42599i	−0.118278	−	0.118278i	0.645490	−	0.763768i	$-0.276653\pi$
$839$	−3.42599	−	3.42599i	−0.118278	−	0.118278i	−0.763768	+	0.645490i	$0.776653\pi$
$840$		0			0
$841$	−5.01582	+	5.01582i	−0.172959	+	0.172959i
$842$	9.34602	−	33.2498i	0.322085	−	1.14586i
$843$		0			0
$844$	16.0613	+	22.0253i	0.552853	+	0.758143i
$845$	−2.46094	−	5.94123i	−0.0846588	−	0.204384i
$846$		0			0
$847$			42.6827i			1.46660i
$848$	−7.10981	+	0.584604i	−0.244152	+	0.0200754i
$849$		0			0
$850$	−8.93901	+	11.3595i	−0.306606	+	0.389628i
$851$	1.83460	+	4.42912i	0.0628893	+	0.151828i
$852$		0			0
$853$	−33.4739	−	13.8653i	−1.14612	−	0.474740i	−0.272892	−	0.962045i	$-0.587980\pi$
$853$	−33.4739	−	13.8653i	−1.14612	−	0.474740i	−0.873232	+	0.487305i	$0.837980\pi$
$854$	19.8666	+	5.58421i	0.679823	+	0.191088i
$855$		0			0
$856$	−40.5393	−	1.48621i	−1.38560	−	0.0507975i
$857$	−19.6667	−	19.6667i	−0.671800	−	0.671800i	0.286331	−	0.958131i	$-0.407564\pi$
$857$	−19.6667	−	19.6667i	−0.671800	−	0.671800i	−0.958131	+	0.286331i	$0.907564\pi$
$858$		0			0
$859$	15.0121	−	36.2424i	0.512207	−	1.23658i	−0.430390	−	0.902643i	$-0.641624\pi$
$859$	15.0121	−	36.2424i	0.512207	−	1.23658i	0.942597	−	0.333933i	$-0.108376\pi$
$860$	−12.7276	+	20.8515i	−0.434009	+	0.711029i
$861$		0			0
$862$	−0.749491	−	6.28529i	−0.0255278	−	0.214078i
$863$	−28.3727			−0.965819			−0.482909	−	0.875670i	$-0.660420\pi$
$863$	−28.3727			−0.965819			−0.482909	+	0.875670i	$0.660420\pi$
$864$		0			0
$865$	−37.9058			−1.28883
$866$	0.241459	+	2.02489i	0.00820510	+	0.0688085i
$867$		0			0
$868$	−7.77568	−	4.74624i	−0.263924	−	0.161098i
$869$	−0.396796	+	0.957951i	−0.0134604	+	0.0324963i
$870$		0			0
$871$	−33.2473	−	33.2473i	−1.12654	−	1.12654i
$872$	−24.5282	−	26.3951i	−0.830630	−	0.893851i
$873$		0			0
$874$	−3.03480	−	0.853036i	−0.102654	−	0.0288544i
$875$	−43.7096	−	18.1051i	−1.47765	−	0.612064i
$876$		0			0
$877$	−10.1396	−	24.4793i	−0.342391	−	0.826606i	−0.997473	−	0.0710476i	$-0.977366\pi$
$877$	−10.1396	−	24.4793i	−0.342391	−	0.826606i	0.655082	−	0.755558i	$-0.272634\pi$
$878$	1.05700	−	1.34321i	0.0356720	−	0.0453312i
$879$		0			0
$880$	−0.331094	+	1.03127i	−0.0111612	+	0.0347642i
$881$		−	9.35846i		−	0.315295i	−0.987495	−	0.157647i	$-0.949609\pi$
$881$		−	9.35846i		−	0.315295i	0.987495	−	0.157647i	$-0.0503909\pi$
$882$		0			0
$883$	7.09207	+	17.1218i	0.238667	+	0.576193i	0.997145	−	0.0755050i	$-0.0240569\pi$
$883$	7.09207	+	17.1218i	0.238667	+	0.576193i	−0.758478	+	0.651698i	$0.774057\pi$
$884$	−32.1367	+	23.4348i	−1.08088	+	0.788196i
$885$		0			0
$886$	−4.68913	+	16.6823i	−0.157535	+	0.560452i
$887$	−30.8931	+	30.8931i	−1.03729	+	1.03729i	−0.0380100	+	0.999277i	$0.512102\pi$
$887$	−30.8931	+	30.8931i	−1.03729	+	1.03729i	−0.999277	+	0.0380100i	$0.987898\pi$
$888$		0			0
$889$	42.3424	+	42.3424i	1.42012	+	1.42012i
$890$	13.5936	−	7.62844i	0.455660	−	0.255706i
$891$		0			0
$892$	−1.86729	+	0.451754i	−0.0625214	+	0.0151259i
$893$	5.18989	−	2.14972i	0.173673	−	0.0719378i
$894$		0			0
$895$	46.3794			1.55029
$896$	−43.9406	+	1.99610i	−1.46795	+	0.0666849i
$897$		0			0
$898$	34.4849	−	4.11216i	1.15078	−	0.137225i
$899$	−5.06608	+	2.09844i	−0.168963	+	0.0699868i
$900$		0			0
$901$	4.39903	−	10.6202i	0.146553	−	0.353810i
$902$	−0.638535	+	0.358331i	−0.0212609	+	0.0119311i
$903$		0			0
$904$	5.79843	+	15.5912i	0.192853	+	0.518554i
$905$	2.65685	−	2.65685i	0.0883168	−	0.0883168i
$906$		0			0
$907$	12.6479	+	5.23891i	0.419965	+	0.173955i	0.582651	−	0.812723i	$-0.302016\pi$
$907$	12.6479	+	5.23891i	0.419965	+	0.173955i	−0.162686	+	0.986678i	$0.552016\pi$
$908$	−24.7846	+	18.0735i	−0.822507	+	0.599789i
$909$		0			0
$910$	−24.6334	−	19.3845i	−0.816590	−	0.642590i
$911$			35.3498i			1.17119i	0.810604	+	0.585595i	$0.199139\pi$
$911$			35.3498i			1.17119i	−0.810604	+	0.585595i	$0.800861\pi$
$912$		0			0
$913$			1.14829i			0.0380030i
$914$	17.5237	−	22.2687i	0.579632	−	0.736584i
$915$		0			0
$916$	1.45865	−	9.31507i	0.0481953	−	0.307779i
$917$	−11.5228	−	4.77292i	−0.380518	−	0.157616i
$918$		0			0
$919$	−30.0652	+	30.0652i	−0.991759	+	0.991759i	−0.999966	−	0.00820720i	$-0.997388\pi$
$919$	−30.0652	+	30.0652i	−0.991759	+	0.991759i	0.00820720	+	0.999966i	$0.497388\pi$
$920$	3.76901	+	4.05588i	0.124261	+	0.133718i
$921$		0			0
$922$	21.3343	+	38.0171i	0.702608	+	1.25203i
$923$	−5.69321	+	13.7446i	−0.187394	+	0.452410i
$924$		0			0
$925$	6.62975	−	2.74613i	0.217985	−	0.0902923i
$926$	2.48147	+	20.8098i	0.0815462	+	0.683853i
$927$		0			0
$928$	−14.6131	+	22.0786i	−0.479700	+	0.724767i
$929$	−7.62858			−0.250286			−0.125143	−	0.992139i	$-0.539939\pi$
$929$	−7.62858			−0.250286			−0.125143	+	0.992139i	$0.539939\pi$
$930$		0			0
$931$	−15.7755	+	6.53442i	−0.517020	+	0.214157i
$932$	24.7448	−	40.5389i	0.810542	−	1.32790i
$933$		0			0
$934$	−9.82974	−	17.5163i	−0.321639	−	0.573151i
$935$	−1.23412	−	1.23412i	−0.0403600	−	0.0403600i
$936$		0			0
$937$	−21.2074	+	21.2074i	−0.692817	+	0.692817i	−0.962851	−	0.270034i	$-0.912965\pi$
$937$	−21.2074	+	21.2074i	−0.692817	+	0.692817i	0.270034	+	0.962851i	$0.412965\pi$
$938$	80.6623	+	22.6729i	2.63372	+	0.740298i
$939$		0			0
$940$	−9.74754	−	1.52637i	−0.317930	−	0.0497848i
$941$	−13.0249	−	31.4448i	−0.424599	−	1.02507i	−0.980974	−	0.194141i	$-0.937808\pi$
$941$	−13.0249	−	31.4448i	−0.424599	−	1.02507i	0.556375	−	0.830931i	$-0.312192\pi$
$942$		0			0
$943$			3.74294i			0.121887i
$944$	1.23127	+	14.9743i	0.0400743	+	0.487373i
$945$		0			0
$946$	1.07662	+	0.847209i	0.0350038	+	0.0275451i
$947$	18.6229	+	44.9596i	0.605162	+	1.46099i	0.868205	+	0.496206i	$0.165274\pi$
$947$	18.6229	+	44.9596i	0.605162	+	1.46099i	−0.263043	+	0.964784i	$0.584726\pi$
$948$		0			0
$949$	−1.78324	−	0.738644i	−0.0578866	−	0.0239774i
$950$	−1.27687	+	4.54266i	−0.0414272	+	0.147383i
$951$		0			0
$952$	29.5045	−	64.4447i	0.956246	−	2.08866i
$953$	33.7784	+	33.7784i	1.09419	+	1.09419i	0.995076	+	0.0991142i	$0.0316009\pi$
$953$	33.7784	+	33.7784i	1.09419	+	1.09419i	0.0991142	+	0.995076i	$0.468399\pi$
$954$		0			0
$955$	−6.40569	+	15.4647i	−0.207283	+	0.500426i
$956$	−7.45010	−	30.7944i	−0.240954	−	0.995961i
$957$		0			0
$958$	−45.4599	+	5.42088i	−1.46874	+	0.175141i
$959$	59.2472			1.91319
$960$		0			0
$961$	−29.6274			−0.955723
$962$	19.6064	−	2.33797i	0.632136	−	0.0753792i
$963$		0			0
$964$	0.147359	+	0.609098i	0.00474613	+	0.0196177i
$965$	4.41735	−	10.6644i	0.142199	−	0.343300i
$966$		0			0
$967$	19.3234	+	19.3234i	0.621399	+	0.621399i	0.945889	−	0.324490i	$-0.105193\pi$
$967$	19.3234	+	19.3234i	0.621399	+	0.621399i	−0.324490	+	0.945889i	$0.605193\pi$
$968$	−28.2337	−	12.9261i	−0.907464	−	0.415461i
$969$		0			0
$970$	7.30205	−	25.9781i	0.234455	−	0.834107i
$971$	52.9160	+	21.9185i	1.69816	+	0.703399i	0.999922	−	0.0124699i	$-0.00396940\pi$
$971$	52.9160	+	21.9185i	1.69816	+	0.703399i	0.698234	+	0.715869i	$0.253969\pi$
$972$		0			0
$973$	−7.70369	−	18.5983i	−0.246969	−	0.596236i
$974$	−2.97806	−	2.34349i	−0.0954233	−	0.0750903i
$975$		0			0
$976$	−9.71028	+	11.4502i	−0.310818	+	0.366512i
$977$		−	12.2792i		−	0.392848i	−0.980519	−	0.196424i	$-0.937067\pi$
$977$		−	12.2792i		−	0.392848i	0.980519	−	0.196424i	$-0.0629329\pi$
$978$		0			0
$979$	−0.334530	−	0.807628i	−0.0106916	−	0.0258119i
$980$	29.6292	+	4.63965i	0.946469	+	0.148208i
$981$		0			0
$982$	26.9506	+	7.57539i	0.860028	+	0.241741i
$983$	14.1052	−	14.1052i	0.449887	−	0.449887i	−0.445430	−	0.895317i	$-0.646949\pi$
$983$	14.1052	−	14.1052i	0.449887	−	0.449887i	0.895317	+	0.445430i	$0.146949\pi$
$984$		0			0
$985$	−6.18989	−	6.18989i	−0.197226	−	0.197226i
$986$	−20.8789	−	37.2056i	−0.664920	−	1.18487i
$987$		0			0
$988$	−6.76468	+	11.0824i	−0.215213	+	0.352579i
$989$	6.47010	−	2.68000i	0.205737	−	0.0852191i
$990$		0			0
$991$	39.8015			1.26434			0.632169	−	0.774831i	$-0.282165\pi$
$991$	39.8015			1.26434			0.632169	+	0.774831i	$0.282165\pi$
$992$	5.49433	−	3.70607i	0.174445	−	0.117668i
$993$		0			0
$994$	−3.13910	−	26.3247i	−0.0995661	−	0.834968i
$995$	14.8278	−	6.14186i	0.470071	−	0.194710i
$996$		0			0
$997$	2.57111	−	6.20720i	0.0814278	−	0.196584i	−0.877922	−	0.478803i	$-0.841071\pi$
$997$	2.57111	−	6.20720i	0.0814278	−	0.196584i	0.959350	+	0.282219i	$0.0910706\pi$
$998$	−17.2700	−	30.7746i	−0.546673	−	0.974154i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.v.b.181.2		8
3.2	odd	2		32.2.g.b.21.1	✓	8
4.3	odd	2		1152.2.v.b.433.2		8
12.11	even	2		128.2.g.b.49.1		8
15.2	even	4		800.2.ba.c.149.1		8
15.8	even	4		800.2.ba.d.149.2		8
15.14	odd	2		800.2.y.b.501.2		8
24.5	odd	2		256.2.g.d.97.1		8
24.11	even	2		256.2.g.c.97.2		8
32.3	odd	8		1152.2.v.b.721.2		8
32.29	even	8	inner	288.2.v.b.253.2		8
48.5	odd	4		512.2.g.e.449.1		8
48.11	even	4		512.2.g.g.449.2		8
48.29	odd	4		512.2.g.h.449.2		8
48.35	even	4		512.2.g.f.449.1		8
96.5	odd	8		512.2.g.e.65.1		8
96.11	even	8		512.2.g.f.65.1		8
96.29	odd	8		32.2.g.b.29.1	yes	8
96.35	even	8		128.2.g.b.81.1		8
96.53	odd	8		512.2.g.h.65.2		8
96.59	even	8		512.2.g.g.65.2		8
96.77	odd	8		256.2.g.d.161.1		8
96.83	even	8		256.2.g.c.161.2		8
192.29	odd	16		4096.2.a.k.1.6		8
192.35	even	16		4096.2.a.q.1.3		8
192.125	odd	16		4096.2.a.k.1.3		8
192.131	even	16		4096.2.a.q.1.6		8
480.29	odd	8		800.2.y.b.701.2		8
480.317	even	8		800.2.ba.d.349.2		8
480.413	even	8		800.2.ba.c.349.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.2.g.b.21.1	✓	8	3.2	odd	2
32.2.g.b.29.1	yes	8	96.29	odd	8
128.2.g.b.49.1		8	12.11	even	2
128.2.g.b.81.1		8	96.35	even	8
256.2.g.c.97.2		8	24.11	even	2
256.2.g.c.161.2		8	96.83	even	8
256.2.g.d.97.1		8	24.5	odd	2
256.2.g.d.161.1		8	96.77	odd	8
288.2.v.b.181.2		8	1.1	even	1	trivial
288.2.v.b.253.2		8	32.29	even	8	inner
512.2.g.e.65.1		8	96.5	odd	8
512.2.g.e.449.1		8	48.5	odd	4
512.2.g.f.65.1		8	96.11	even	8
512.2.g.f.449.1		8	48.35	even	4
512.2.g.g.65.2		8	96.59	even	8
512.2.g.g.449.2		8	48.11	even	4
512.2.g.h.65.2		8	96.53	odd	8
512.2.g.h.449.2		8	48.29	odd	4
800.2.y.b.501.2		8	15.14	odd	2
800.2.y.b.701.2		8	480.29	odd	8
800.2.ba.c.149.1		8	15.2	even	4
800.2.ba.c.349.1		8	480.413	even	8
800.2.ba.d.149.2		8	15.8	even	4
800.2.ba.d.349.2		8	480.317	even	8
1152.2.v.b.433.2		8	4.3	odd	2
1152.2.v.b.721.2		8	32.3	odd	8
4096.2.a.k.1.3		8	192.125	odd	16
4096.2.a.k.1.6		8	192.29	odd	16
4096.2.a.q.1.3		8	192.35	even	16
4096.2.a.q.1.6		8	192.131	even	16

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40426 - 0.167452i) q^{2} +(1.94392 - 0.470294i) q^{4} +(0.707107 - 1.70711i) q^{5} +(-2.74912 - 2.74912i) q^{7} +(2.65103 - 0.985930i) q^{8} +O(q^{10})\)	\(q+(1.40426 - 0.167452i) q^{2} +(1.94392 - 0.470294i) q^{4} +(0.707107 - 1.70711i) q^{5} +(-2.74912 - 2.74912i) q^{7} +(2.65103 - 0.985930i) q^{8} +(0.707107 - 2.51564i) q^{10} +(-0.135390 - 0.0560803i) q^{11} +(1.18073 + 2.85054i) q^{13} +(-4.32083 - 3.40014i) q^{14} +(3.55765 - 1.82843i) q^{16} +6.44549i q^{17} +(0.805198 + 1.94392i) q^{19} +(0.571717 - 3.65103i) q^{20} +(-0.199514 - 0.0560803i) q^{22} +(-0.749118 + 0.749118i) q^{23} +(1.12132 + 1.12132i) q^{25} +(2.13539 + 3.80520i) q^{26} +(-6.63696 - 4.05117i) q^{28} +(-4.32417 + 1.79113i) q^{29} +1.17157 q^{31} +(4.68971 - 3.16333i) q^{32} +(1.07931 + 9.05117i) q^{34} +(-6.63696 + 2.74912i) q^{35} +(1.73172 - 4.18073i) q^{37} +(1.45622 + 2.59495i) q^{38} +(0.191470 - 5.22274i) q^{40} +(2.49824 - 2.49824i) q^{41} +(-6.10725 - 2.52971i) q^{43} +(-0.289561 - 0.0453426i) q^{44} +(-0.926518 + 1.17740i) q^{46} -2.66981i q^{47} +8.11529i q^{49} +(1.76240 + 1.38686i) q^{50} +(3.63584 + 4.98593i) q^{52} +(-1.64769 - 0.682497i) q^{53} +(-0.191470 + 0.191470i) q^{55} +(-9.99842 - 4.57754i) q^{56} +(-5.77235 + 3.23931i) q^{58} +(-1.43744 + 3.47029i) q^{59} +(-3.46760 + 1.43633i) q^{61} +(1.64520 - 0.196182i) q^{62} +(6.05588 - 5.22746i) q^{64} +5.70108 q^{65} +(-14.0791 + 5.83176i) q^{67} +(3.03127 + 12.5295i) q^{68} +(-8.85970 + 4.97186i) q^{70} +(3.40950 + 3.40950i) q^{71} +(-0.442353 + 0.442353i) q^{73} +(1.73172 - 6.16084i) q^{74} +(2.47945 + 3.40014i) q^{76} +(0.218031 + 0.526374i) q^{77} -7.07550i q^{79} +(-0.605684 - 7.36618i) q^{80} +(3.08985 - 3.92652i) q^{82} +(-2.99862 - 7.23931i) q^{83} +(11.0031 + 4.55765i) q^{85} +(-8.99980 - 2.52971i) q^{86} +(-0.414214 - 0.0151854i) q^{88} +(4.21803 + 4.21803i) q^{89} +(4.59050 - 11.0824i) q^{91} +(-1.10392 + 1.80853i) q^{92} +(-0.447065 - 3.74912i) q^{94} +3.88784 q^{95} +10.3267 q^{97} +(1.35892 + 11.3960i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 4 q^{4} - 8 q^{7} + 4 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 + 4 * q^4 - 8 * q^7 + 4 * q^8	\( 8 q + 4 q^{2} + 4 q^{4} - 8 q^{7} + 4 q^{8} - 4 q^{11} - 8 q^{13} - 12 q^{14} + 4 q^{19} - 4 q^{20} + 4 q^{22} + 8 q^{23} - 8 q^{25} + 20 q^{26} - 16 q^{28} + 32 q^{31} + 24 q^{32} - 16 q^{35} - 8 q^{37} - 8 q^{38} + 16 q^{40} - 8 q^{41} - 12 q^{43} - 20 q^{44} + 12 q^{46} - 16 q^{50} + 12 q^{52} - 8 q^{53} - 16 q^{55} - 8 q^{56} - 12 q^{58} + 20 q^{59} + 24 q^{61} + 24 q^{62} - 8 q^{64} - 36 q^{67} - 16 q^{68} - 8 q^{70} + 24 q^{71} - 32 q^{73} - 8 q^{74} - 20 q^{76} - 16 q^{77} - 8 q^{80} - 20 q^{82} - 20 q^{83} + 8 q^{85} - 4 q^{86} + 8 q^{88} + 16 q^{89} + 40 q^{91} + 16 q^{92} - 24 q^{94} + 8 q^{95} + 32 q^{97} + 24 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 + 4 * q^4 - 8 * q^7 + 4 * q^8 - 4 * q^11 - 8 * q^13 - 12 * q^14 + 4 * q^19 - 4 * q^20 + 4 * q^22 + 8 * q^23 - 8 * q^25 + 20 * q^26 - 16 * q^28 + 32 * q^31 + 24 * q^32 - 16 * q^35 - 8 * q^37 - 8 * q^38 + 16 * q^40 - 8 * q^41 - 12 * q^43 - 20 * q^44 + 12 * q^46 - 16 * q^50 + 12 * q^52 - 8 * q^53 - 16 * q^55 - 8 * q^56 - 12 * q^58 + 20 * q^59 + 24 * q^61 + 24 * q^62 - 8 * q^64 - 36 * q^67 - 16 * q^68 - 8 * q^70 + 24 * q^71 - 32 * q^73 - 8 * q^74 - 20 * q^76 - 16 * q^77 - 8 * q^80 - 20 * q^82 - 20 * q^83 + 8 * q^85 - 4 * q^86 + 8 * q^88 + 16 * q^89 + 40 * q^91 + 16 * q^92 - 24 * q^94 + 8 * q^95 + 32 * q^97 + 24 * q^98

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