LMFDB - Embedded newform 1078.2.e.f.177.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(67,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("1078.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.e (of order $3$, 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:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1078.177
Dual form			1078.2.e.f.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} -3.00000 q^{6} +1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} -3.00000 q^{6} +1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +(1.00000 + 1.73205i) q^{10} +(0.500000 + 0.866025i) q^{11} +(1.50000 - 2.59808i) q^{12} +7.00000 q^{13} +6.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(-3.00000 - 5.19615i) q^{18} -2.00000 q^{20} -1.00000 q^{22} +(4.00000 - 6.92820i) q^{23} +(1.50000 + 2.59808i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-3.50000 + 6.06218i) q^{26} -9.00000 q^{27} -5.00000 q^{29} +(-3.00000 + 5.19615i) q^{30} +(2.00000 + 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} -2.00000 q^{34} +6.00000 q^{36} +(-2.00000 + 3.46410i) q^{37} +(10.5000 + 18.1865i) q^{39} +(1.00000 - 1.73205i) q^{40} -4.00000 q^{41} -8.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(6.00000 + 10.3923i) q^{45} +(4.00000 + 6.92820i) q^{46} +(1.00000 - 1.73205i) q^{47} -3.00000 q^{48} -1.00000 q^{50} +(-3.00000 + 5.19615i) q^{51} +(-3.50000 - 6.06218i) q^{52} +(3.00000 + 5.19615i) q^{53} +(4.50000 - 7.79423i) q^{54} +2.00000 q^{55} +(2.50000 - 4.33013i) q^{58} +(1.50000 + 2.59808i) q^{59} +(-3.00000 - 5.19615i) q^{60} +(0.500000 - 0.866025i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(7.00000 - 12.1244i) q^{65} +(-1.50000 - 2.59808i) q^{66} +(-4.50000 - 7.79423i) q^{67} +(1.00000 - 1.73205i) q^{68} +24.0000 q^{69} -2.00000 q^{71} +(-3.00000 + 5.19615i) q^{72} +(2.00000 + 3.46410i) q^{73} +(-2.00000 - 3.46410i) q^{74} +(-1.50000 + 2.59808i) q^{75} -21.0000 q^{78} +(-4.50000 + 7.79423i) q^{79} +(1.00000 + 1.73205i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(2.00000 - 3.46410i) q^{82} -6.00000 q^{83} +4.00000 q^{85} +(4.00000 - 6.92820i) q^{86} +(-7.50000 - 12.9904i) q^{87} +(0.500000 + 0.866025i) q^{88} +(3.00000 - 5.19615i) q^{89} -12.0000 q^{90} -8.00000 q^{92} +(-6.00000 + 10.3923i) q^{93} +(1.00000 + 1.73205i) q^{94} +(1.50000 - 2.59808i) q^{96} -7.00000 q^{97} -6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 3 q^{3} - q^{4} + 2 q^{5} - 6 q^{6} + 2 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q - q^2 + 3 * q^3 - q^4 + 2 * q^5 - 6 * q^6 + 2 * q^8 - 6 * q^9	$ 2 q - q^{2} + 3 q^{3} - q^{4} + 2 q^{5} - 6 q^{6} + 2 q^{8} - 6 q^{9} + 2 q^{10} + q^{11} + 3 q^{12} + 14 q^{13} + 12 q^{15} - q^{16} + 2 q^{17} - 6 q^{18} - 4 q^{20} - 2 q^{22} + 8 q^{23} + 3 q^{24} + q^{25} - 7 q^{26} - 18 q^{27} - 10 q^{29} - 6 q^{30} + 4 q^{31} - q^{32} - 3 q^{33} - 4 q^{34} + 12 q^{36} - 4 q^{37} + 21 q^{39} + 2 q^{40} - 8 q^{41} - 16 q^{43} + q^{44} + 12 q^{45} + 8 q^{46} + 2 q^{47} - 6 q^{48} - 2 q^{50} - 6 q^{51} - 7 q^{52} + 6 q^{53} + 9 q^{54} + 4 q^{55} + 5 q^{58} + 3 q^{59} - 6 q^{60} + q^{61} - 8 q^{62} + 2 q^{64} + 14 q^{65} - 3 q^{66} - 9 q^{67} + 2 q^{68} + 48 q^{69} - 4 q^{71} - 6 q^{72} + 4 q^{73} - 4 q^{74} - 3 q^{75} - 42 q^{78} - 9 q^{79} + 2 q^{80} - 9 q^{81} + 4 q^{82} - 12 q^{83} + 8 q^{85} + 8 q^{86} - 15 q^{87} + q^{88} + 6 q^{89} - 24 q^{90} - 16 q^{92} - 12 q^{93} + 2 q^{94} + 3 q^{96} - 14 q^{97} - 12 q^{99}+O(q^{100}) $ 2 * q - q^2 + 3 * q^3 - q^4 + 2 * q^5 - 6 * q^6 + 2 * q^8 - 6 * q^9 + 2 * q^10 + q^11 + 3 * q^12 + 14 * q^13 + 12 * q^15 - q^16 + 2 * q^17 - 6 * q^18 - 4 * q^20 - 2 * q^22 + 8 * q^23 + 3 * q^24 + q^25 - 7 * q^26 - 18 * q^27 - 10 * q^29 - 6 * q^30 + 4 * q^31 - q^32 - 3 * q^33 - 4 * q^34 + 12 * q^36 - 4 * q^37 + 21 * q^39 + 2 * q^40 - 8 * q^41 - 16 * q^43 + q^44 + 12 * q^45 + 8 * q^46 + 2 * q^47 - 6 * q^48 - 2 * q^50 - 6 * q^51 - 7 * q^52 + 6 * q^53 + 9 * q^54 + 4 * q^55 + 5 * q^58 + 3 * q^59 - 6 * q^60 + q^61 - 8 * q^62 + 2 * q^64 + 14 * q^65 - 3 * q^66 - 9 * q^67 + 2 * q^68 + 48 * q^69 - 4 * q^71 - 6 * q^72 + 4 * q^73 - 4 * q^74 - 3 * q^75 - 42 * q^78 - 9 * q^79 + 2 * q^80 - 9 * q^81 + 4 * q^82 - 12 * q^83 + 8 * q^85 + 8 * q^86 - 15 * q^87 + q^88 + 6 * q^89 - 24 * q^90 - 16 * q^92 - 12 * q^93 + 2 * q^94 + 3 * q^96 - 14 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.50000	+	2.59808i	0.866025	+	1.50000i	0.866025	+	0.500000i	$0.166667\pi$
$3$	1.50000	+	2.59808i	0.866025	+	1.50000i			1.00000i	$0.5\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	−0.550990	−	0.834512i	$-0.685750\pi$
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	0.998203	+	0.0599153i	$0.0190830\pi$
$6$	−3.00000			−1.22474
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−3.00000	+	5.19615i	−1.00000	+	1.73205i
$10$	1.00000	+	1.73205i	0.316228	+	0.547723i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	1.50000	−	2.59808i	0.433013	−	0.750000i
$13$	7.00000			1.94145			0.970725	−	0.240192i	$-0.0772105\pi$
$13$	7.00000			1.94145			0.970725	+	0.240192i	$0.0772105\pi$
$14$		0			0
$15$	6.00000			1.54919
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$	−3.00000	−	5.19615i	−0.707107	−	1.22474i
$19$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$19$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$20$	−2.00000			−0.447214
$21$		0			0
$22$	−1.00000			−0.213201
$23$	4.00000	−	6.92820i	0.834058	−	1.44463i	−0.0607377	−	0.998154i	$-0.519345\pi$
$23$	4.00000	−	6.92820i	0.834058	−	1.44463i	0.894795	−	0.446476i	$-0.147321\pi$
$24$	1.50000	+	2.59808i	0.306186	+	0.530330i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−3.50000	+	6.06218i	−0.686406	+	1.18889i
$27$	−9.00000			−1.73205
$28$		0			0
$29$	−5.00000			−0.928477			−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000			−0.928477			−0.464238	+	0.885710i	$0.653672\pi$
$30$	−3.00000	+	5.19615i	−0.547723	+	0.948683i
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.50000	+	2.59808i	−0.261116	+	0.452267i
$34$	−2.00000			−0.342997
$35$		0			0
$36$	6.00000			1.00000
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	−0.982274	−	0.187453i	$-0.939977\pi$
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	0.653476	+	0.756948i	$0.273310\pi$
$38$		0			0
$39$	10.5000	+	18.1865i	1.68135	+	2.91218i
$40$	1.00000	−	1.73205i	0.158114	−	0.273861i
$41$	−4.00000			−0.624695			−0.312348	−	0.949968i	$-0.601115\pi$
$41$	−4.00000			−0.624695			−0.312348	+	0.949968i	$0.601115\pi$
$42$		0			0
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$	6.00000	+	10.3923i	0.894427	+	1.54919i
$46$	4.00000	+	6.92820i	0.589768	+	1.02151i
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	−0.783830	−	0.620975i	$-0.786737\pi$
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	0.929695	+	0.368329i	$0.120070\pi$
$48$	−3.00000			−0.433013
$49$		0			0
$50$	−1.00000			−0.141421
$51$	−3.00000	+	5.19615i	−0.420084	+	0.727607i
$52$	−3.50000	−	6.06218i	−0.485363	−	0.840673i
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	0.995117	−	0.0987002i	$-0.0314685\pi$
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	−0.583036	+	0.812447i	$0.698135\pi$
$54$	4.50000	−	7.79423i	0.612372	−	1.06066i
$55$	2.00000			0.269680
$56$		0			0
$57$		0			0
$58$	2.50000	−	4.33013i	0.328266	−	0.568574i
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	0.946993	−	0.321253i	$-0.104104\pi$
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	−0.751710	+	0.659494i	$0.770771\pi$
$60$	−3.00000	−	5.19615i	−0.387298	−	0.670820i
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	0.896258	+	0.443533i	$0.146275\pi$
$62$	−4.00000			−0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	7.00000	−	12.1244i	0.868243	−	1.50384i
$66$	−1.50000	−	2.59808i	−0.184637	−	0.319801i
$67$	−4.50000	−	7.79423i	−0.549762	−	0.952217i	−0.998290	−	0.0584478i	$-0.981385\pi$
$67$	−4.50000	−	7.79423i	−0.549762	−	0.952217i	0.448528	−	0.893769i	$-0.351948\pi$
$68$	1.00000	−	1.73205i	0.121268	−	0.210042i
$69$	24.0000			2.88926
$70$		0			0
$71$	−2.00000			−0.237356			−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000			−0.237356			−0.118678	+	0.992933i	$0.537866\pi$
$72$	−3.00000	+	5.19615i	−0.353553	+	0.612372i
$73$	2.00000	+	3.46410i	0.234082	+	0.405442i	0.959006	−	0.283387i	$-0.0914581\pi$
$73$	2.00000	+	3.46410i	0.234082	+	0.405442i	−0.724923	+	0.688830i	$0.758125\pi$
$74$	−2.00000	−	3.46410i	−0.232495	−	0.402694i
$75$	−1.50000	+	2.59808i	−0.173205	+	0.300000i
$76$		0			0
$77$		0			0
$78$	−21.0000			−2.37778
$79$	−4.50000	+	7.79423i	−0.506290	+	0.876919i	0.493684	+	0.869641i	$0.335650\pi$
$79$	−4.50000	+	7.79423i	−0.506290	+	0.876919i	−0.999974	+	0.00727784i	$0.997683\pi$
$80$	1.00000	+	1.73205i	0.111803	+	0.193649i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	2.00000	−	3.46410i	0.220863	−	0.382546i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$		0			0
$85$	4.00000			0.433861
$86$	4.00000	−	6.92820i	0.431331	−	0.747087i
$87$	−7.50000	−	12.9904i	−0.804084	−	1.39272i
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$	−12.0000			−1.26491
$91$		0			0
$92$	−8.00000			−0.834058
$93$	−6.00000	+	10.3923i	−0.622171	+	1.07763i
$94$	1.00000	+	1.73205i	0.103142	+	0.178647i
$95$		0			0
$96$	1.50000	−	2.59808i	0.153093	−	0.265165i
$97$	−7.00000			−0.710742			−0.355371	−	0.934725i	$-0.615646\pi$
$97$	−7.00000			−0.710742			−0.355371	+	0.934725i	$0.615646\pi$
$98$		0			0
$99$	−6.00000			−0.603023
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	0.550474	−	0.834853i	$-0.314447\pi$
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	−0.998240	+	0.0592978i	$0.981114\pi$
$102$	−3.00000	−	5.19615i	−0.297044	−	0.514496i
$103$	9.00000	−	15.5885i	0.886796	−	1.53598i	0.0431555	−	0.999068i	$-0.486259\pi$
$103$	9.00000	−	15.5885i	0.886796	−	1.53598i	0.843641	−	0.536908i	$-0.180408\pi$
$104$	7.00000			0.686406
$105$		0			0
$106$	−6.00000			−0.582772
$107$	−1.00000	+	1.73205i	−0.0966736	+	0.167444i	−0.910306	−	0.413936i	$-0.864154\pi$
$107$	−1.00000	+	1.73205i	−0.0966736	+	0.167444i	0.813632	+	0.581380i	$0.197487\pi$
$108$	4.50000	+	7.79423i	0.433013	+	0.750000i
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	0.909935	−	0.414751i	$-0.136131\pi$
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	−0.814152	+	0.580651i	$0.802798\pi$
$110$	−1.00000	+	1.73205i	−0.0953463	+	0.165145i
$111$	−12.0000			−1.13899
$112$		0			0
$113$	5.00000			0.470360			0.235180	−	0.971952i	$-0.424432\pi$
$113$	5.00000			0.470360			0.235180	+	0.971952i	$0.424432\pi$
$114$		0			0
$115$	−8.00000	−	13.8564i	−0.746004	−	1.29212i
$116$	2.50000	+	4.33013i	0.232119	+	0.402042i
$117$	−21.0000	+	36.3731i	−1.94145	+	3.36269i
$118$	−3.00000			−0.276172
$119$		0			0
$120$	6.00000			0.547723
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	0.500000	+	0.866025i	0.0452679	+	0.0784063i
$123$	−6.00000	−	10.3923i	−0.541002	−	0.937043i
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$	12.0000			1.07331
$126$		0			0
$127$	−19.0000			−1.68598			−0.842989	−	0.537931i	$-0.819206\pi$
$127$	−19.0000			−1.68598			−0.842989	+	0.537931i	$0.819206\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−12.0000	−	20.7846i	−1.05654	−	1.82998i
$130$	7.00000	+	12.1244i	0.613941	+	1.06338i
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$	3.00000			0.261116
$133$		0			0
$134$	9.00000			0.777482
$135$	−9.00000	+	15.5885i	−0.774597	+	1.34164i
$136$	1.00000	+	1.73205i	0.0857493	+	0.148522i
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	0.794808	−	0.606861i	$-0.207572\pi$
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	−0.922961	+	0.384893i	$0.874238\pi$
$138$	−12.0000	+	20.7846i	−1.02151	+	1.76930i
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	6.00000			0.505291
$142$	1.00000	−	1.73205i	0.0839181	−	0.145350i
$143$	3.50000	+	6.06218i	0.292685	+	0.506945i
$144$	−3.00000	−	5.19615i	−0.250000	−	0.433013i
$145$	−5.00000	+	8.66025i	−0.415227	+	0.719195i
$146$	−4.00000			−0.331042
$147$		0			0
$148$	4.00000			0.328798
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	−0.585231	−	0.810867i	$-0.698996\pi$
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	0.994847	+	0.101391i	$0.0323294\pi$
$150$	−1.50000	−	2.59808i	−0.122474	−	0.212132i
$151$	1.50000	+	2.59808i	0.122068	+	0.211428i	0.920583	−	0.390547i	$-0.127714\pi$
$151$	1.50000	+	2.59808i	0.122068	+	0.211428i	−0.798515	+	0.601975i	$0.794381\pi$
$152$		0			0
$153$	−12.0000			−0.970143
$154$		0			0
$155$	8.00000			0.642575
$156$	10.5000	−	18.1865i	0.840673	−	1.45609i
$157$	8.00000	+	13.8564i	0.638470	+	1.10586i	0.985769	+	0.168107i	$0.0537655\pi$
$157$	8.00000	+	13.8564i	0.638470	+	1.10586i	−0.347299	+	0.937754i	$0.612901\pi$
$158$	−4.50000	−	7.79423i	−0.358001	−	0.620076i
$159$	−9.00000	+	15.5885i	−0.713746	+	1.23625i
$160$	−2.00000			−0.158114
$161$		0			0
$162$	9.00000			0.707107
$163$	8.50000	−	14.7224i	0.665771	−	1.15315i	−0.313304	−	0.949653i	$-0.601436\pi$
$163$	8.50000	−	14.7224i	0.665771	−	1.15315i	0.979076	−	0.203497i	$-0.0652307\pi$
$164$	2.00000	+	3.46410i	0.156174	+	0.270501i
$165$	3.00000	+	5.19615i	0.233550	+	0.404520i
$166$	3.00000	−	5.19615i	0.232845	−	0.403300i
$167$	−19.0000			−1.47026			−0.735132	−	0.677924i	$-0.762880\pi$
$167$	−19.0000			−1.47026			−0.735132	+	0.677924i	$0.762880\pi$
$168$		0			0
$169$	36.0000			2.76923
$170$	−2.00000	+	3.46410i	−0.153393	+	0.265684i
$171$		0			0
$172$	4.00000	+	6.92820i	0.304997	+	0.528271i
$173$	12.5000	−	21.6506i	0.950357	−	1.64607i	0.205706	−	0.978614i	$-0.434051\pi$
$173$	12.5000	−	21.6506i	0.950357	−	1.64607i	0.744652	−	0.667453i	$-0.232616\pi$
$174$	15.0000			1.13715
$175$		0			0
$176$	−1.00000			−0.0753778
$177$	−4.50000	+	7.79423i	−0.338241	+	0.585850i
$178$	3.00000	+	5.19615i	0.224860	+	0.389468i
$179$	−9.50000	−	16.4545i	−0.710063	−	1.22987i	−0.964833	−	0.262864i	$-0.915333\pi$
$179$	−9.50000	−	16.4545i	−0.710063	−	1.22987i	0.254770	−	0.967002i	$-0.418000\pi$
$180$	6.00000	−	10.3923i	0.447214	−	0.774597i
$181$	22.0000			1.63525			0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000			1.63525			0.817624	+	0.575753i	$0.195291\pi$
$182$		0			0
$183$	3.00000			0.221766
$184$	4.00000	−	6.92820i	0.294884	−	0.510754i
$185$	4.00000	+	6.92820i	0.294086	+	0.509372i
$186$	−6.00000	−	10.3923i	−0.439941	−	0.762001i
$187$	−1.00000	+	1.73205i	−0.0731272	+	0.126660i
$188$	−2.00000			−0.145865
$189$		0			0
$190$		0			0
$191$	−1.00000	+	1.73205i	−0.0723575	+	0.125327i	−0.899934	−	0.436026i	$-0.856386\pi$
$191$	−1.00000	+	1.73205i	−0.0723575	+	0.125327i	0.827577	+	0.561353i	$0.189719\pi$
$192$	1.50000	+	2.59808i	0.108253	+	0.187500i
$193$	−4.00000	−	6.92820i	−0.287926	−	0.498703i	0.685388	−	0.728178i	$-0.259632\pi$
$193$	−4.00000	−	6.92820i	−0.287926	−	0.498703i	−0.973315	+	0.229475i	$0.926299\pi$
$194$	3.50000	−	6.06218i	0.251285	−	0.435239i
$195$	42.0000			3.00768
$196$		0			0
$197$	15.0000			1.06871			0.534353	−	0.845262i	$-0.320555\pi$
$197$	15.0000			1.06871			0.534353	+	0.845262i	$0.320555\pi$
$198$	3.00000	−	5.19615i	0.213201	−	0.369274i
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	0.928166	−	0.372168i	$-0.121385\pi$
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	−0.786389	+	0.617731i	$0.788052\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	13.5000	−	23.3827i	0.952217	−	1.64929i
$202$	9.00000			0.633238
$203$		0			0
$204$	6.00000			0.420084
$205$	−4.00000	+	6.92820i	−0.279372	+	0.483887i
$206$	9.00000	+	15.5885i	0.627060	+	1.08610i
$207$	24.0000	+	41.5692i	1.66812	+	2.88926i
$208$	−3.50000	+	6.06218i	−0.242681	+	0.420336i
$209$		0			0
$210$		0			0
$211$	−20.0000			−1.37686			−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000			−1.37686			−0.688428	+	0.725304i	$0.741699\pi$
$212$	3.00000	−	5.19615i	0.206041	−	0.356873i
$213$	−3.00000	−	5.19615i	−0.205557	−	0.356034i
$214$	−1.00000	−	1.73205i	−0.0683586	−	0.118401i
$215$	−8.00000	+	13.8564i	−0.545595	+	0.944999i
$216$	−9.00000			−0.612372
$217$		0			0
$218$	−2.00000			−0.135457
$219$	−6.00000	+	10.3923i	−0.405442	+	0.702247i
$220$	−1.00000	−	1.73205i	−0.0674200	−	0.116775i
$221$	7.00000	+	12.1244i	0.470871	+	0.815572i
$222$	6.00000	−	10.3923i	0.402694	−	0.697486i
$223$	−4.00000			−0.267860			−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000			−0.267860			−0.133930	+	0.990991i	$0.542760\pi$
$224$		0			0
$225$	−6.00000			−0.400000
$226$	−2.50000	+	4.33013i	−0.166298	+	0.288036i
$227$	−1.00000	−	1.73205i	−0.0663723	−	0.114960i	0.830930	−	0.556378i	$-0.187809\pi$
$227$	−1.00000	−	1.73205i	−0.0663723	−	0.114960i	−0.897302	+	0.441417i	$0.854476\pi$
$228$		0			0
$229$	−14.0000	+	24.2487i	−0.925146	+	1.60240i	−0.133820	+	0.991006i	$0.542724\pi$
$229$	−14.0000	+	24.2487i	−0.925146	+	1.60240i	−0.791326	+	0.611394i	$0.790609\pi$
$230$	16.0000			1.05501
$231$		0			0
$232$	−5.00000			−0.328266
$233$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$233$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$234$	−21.0000	−	36.3731i	−1.37281	−	2.37778i
$235$	−2.00000	−	3.46410i	−0.130466	−	0.225973i
$236$	1.50000	−	2.59808i	0.0976417	−	0.169120i
$237$	−27.0000			−1.75384
$238$		0			0
$239$	−5.00000			−0.323423			−0.161712	−	0.986838i	$-0.551701\pi$
$239$	−5.00000			−0.323423			−0.161712	+	0.986838i	$0.551701\pi$
$240$	−3.00000	+	5.19615i	−0.193649	+	0.335410i
$241$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$241$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$242$	−0.500000	−	0.866025i	−0.0321412	−	0.0556702i
$243$		0			0
$244$	−1.00000			−0.0640184
$245$		0			0
$246$	12.0000			0.765092
$247$		0			0
$248$	2.00000	+	3.46410i	0.127000	+	0.219971i
$249$	−9.00000	−	15.5885i	−0.570352	−	0.987878i
$250$	−6.00000	+	10.3923i	−0.379473	+	0.657267i
$251$	24.0000			1.51487			0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000			1.51487			0.757433	+	0.652913i	$0.226453\pi$
$252$		0			0
$253$	8.00000			0.502956
$254$	9.50000	−	16.4545i	0.596083	−	1.03245i
$255$	6.00000	+	10.3923i	0.375735	+	0.650791i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.50000	−	2.59808i	0.0935674	−	0.162064i	−0.815442	−	0.578838i	$-0.803506\pi$
$257$	1.50000	−	2.59808i	0.0935674	−	0.162064i	0.909010	+	0.416775i	$0.136840\pi$
$258$	24.0000			1.49417
$259$		0			0
$260$	−14.0000			−0.868243
$261$	15.0000	−	25.9808i	0.928477	−	1.60817i
$262$		0			0
$263$	−13.5000	−	23.3827i	−0.832446	−	1.44184i	−0.896093	−	0.443866i	$-0.853607\pi$
$263$	−13.5000	−	23.3827i	−0.832446	−	1.44184i	0.0636476	−	0.997972i	$-0.479727\pi$
$264$	−1.50000	+	2.59808i	−0.0923186	+	0.159901i
$265$	12.0000			0.737154
$266$		0			0
$267$	18.0000			1.10158
$268$	−4.50000	+	7.79423i	−0.274881	+	0.476108i
$269$	−12.0000	−	20.7846i	−0.731653	−	1.26726i	−0.956176	−	0.292791i	$-0.905416\pi$
$269$	−12.0000	−	20.7846i	−0.731653	−	1.26726i	0.224523	−	0.974469i	$-0.427917\pi$
$270$	−9.00000	−	15.5885i	−0.547723	−	0.948683i
$271$	−5.50000	+	9.52628i	−0.334101	+	0.578680i	−0.983312	−	0.181928i	$-0.941766\pi$
$271$	−5.50000	+	9.52628i	−0.334101	+	0.578680i	0.649211	+	0.760609i	$0.275099\pi$
$272$	−2.00000			−0.121268
$273$		0			0
$274$	3.00000			0.181237
$275$	−0.500000	+	0.866025i	−0.0301511	+	0.0522233i
$276$	−12.0000	−	20.7846i	−0.722315	−	1.25109i
$277$	4.50000	+	7.79423i	0.270379	+	0.468310i	0.968959	−	0.247222i	$-0.0795177\pi$
$277$	4.50000	+	7.79423i	0.270379	+	0.468310i	−0.698580	+	0.715532i	$0.746184\pi$
$278$	−2.00000	+	3.46410i	−0.119952	+	0.207763i
$279$	−24.0000			−1.43684
$280$		0			0
$281$	−28.0000			−1.67034			−0.835170	−	0.549992i	$-0.814631\pi$
$281$	−28.0000			−1.67034			−0.835170	+	0.549992i	$0.814631\pi$
$282$	−3.00000	+	5.19615i	−0.178647	+	0.309426i
$283$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$283$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$284$	1.00000	+	1.73205i	0.0593391	+	0.102778i
$285$		0			0
$286$	−7.00000			−0.413919
$287$		0			0
$288$	6.00000			0.353553
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$	−5.00000	−	8.66025i	−0.293610	−	0.508548i
$291$	−10.5000	−	18.1865i	−0.615521	−	1.06611i
$292$	2.00000	−	3.46410i	0.117041	−	0.202721i
$293$	18.0000			1.05157			0.525786	−	0.850617i	$-0.323771\pi$
$293$	18.0000			1.05157			0.525786	+	0.850617i	$0.323771\pi$
$294$		0			0
$295$	6.00000			0.349334
$296$	−2.00000	+	3.46410i	−0.116248	+	0.201347i
$297$	−4.50000	−	7.79423i	−0.261116	−	0.452267i
$298$	5.00000	+	8.66025i	0.289642	+	0.501675i
$299$	28.0000	−	48.4974i	1.61928	−	2.80468i
$300$	3.00000			0.173205
$301$		0			0
$302$	−3.00000			−0.172631
$303$	13.5000	−	23.3827i	0.775555	−	1.34330i
$304$		0			0
$305$	−1.00000	−	1.73205i	−0.0572598	−	0.0991769i
$306$	6.00000	−	10.3923i	0.342997	−	0.594089i
$307$	−2.00000			−0.114146			−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000			−0.114146			−0.0570730	+	0.998370i	$0.518177\pi$
$308$		0			0
$309$	54.0000			3.07195
$310$	−4.00000	+	6.92820i	−0.227185	+	0.393496i
$311$	−5.00000	−	8.66025i	−0.283524	−	0.491078i	0.688726	−	0.725022i	$-0.258170\pi$
$311$	−5.00000	−	8.66025i	−0.283524	−	0.491078i	−0.972250	+	0.233944i	$0.924837\pi$
$312$	10.5000	+	18.1865i	0.594445	+	1.02961i
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	−0.851549	−	0.524276i	$-0.824336\pi$
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	0.879810	+	0.475325i	$0.157669\pi$
$314$	−16.0000			−0.902932
$315$		0			0
$316$	9.00000			0.506290
$317$	6.00000	−	10.3923i	0.336994	−	0.583690i	−0.646872	−	0.762598i	$-0.723923\pi$
$317$	6.00000	−	10.3923i	0.336994	−	0.583690i	0.983866	+	0.178908i	$0.0572566\pi$
$318$	−9.00000	−	15.5885i	−0.504695	−	0.874157i
$319$	−2.50000	−	4.33013i	−0.139973	−	0.242441i
$320$	1.00000	−	1.73205i	0.0559017	−	0.0968246i
$321$	−6.00000			−0.334887
$322$		0			0
$323$		0			0
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	3.50000	+	6.06218i	0.194145	+	0.336269i
$326$	8.50000	+	14.7224i	0.470771	+	0.815400i
$327$	−3.00000	+	5.19615i	−0.165900	+	0.287348i
$328$	−4.00000			−0.220863
$329$		0			0
$330$	−6.00000			−0.330289
$331$	−6.50000	+	11.2583i	−0.357272	+	0.618814i	−0.987504	−	0.157593i	$-0.949627\pi$
$331$	−6.50000	+	11.2583i	−0.357272	+	0.618814i	0.630232	+	0.776407i	$0.282960\pi$
$332$	3.00000	+	5.19615i	0.164646	+	0.285176i
$333$	−12.0000	−	20.7846i	−0.657596	−	1.13899i
$334$	9.50000	−	16.4545i	0.519817	−	0.900349i
$335$	−18.0000			−0.983445
$336$		0			0
$337$	−12.0000			−0.653682			−0.326841	−	0.945079i	$-0.605984\pi$
$337$	−12.0000			−0.653682			−0.326841	+	0.945079i	$0.605984\pi$
$338$	−18.0000	+	31.1769i	−0.979071	+	1.69580i
$339$	7.50000	+	12.9904i	0.407344	+	0.705541i
$340$	−2.00000	−	3.46410i	−0.108465	−	0.187867i
$341$	−2.00000	+	3.46410i	−0.108306	+	0.187592i
$342$		0			0
$343$		0			0
$344$	−8.00000			−0.431331
$345$	24.0000	−	41.5692i	1.29212	−	2.23801i
$346$	12.5000	+	21.6506i	0.672004	+	1.16395i
$347$	11.0000	+	19.0526i	0.590511	+	1.02279i	0.994164	+	0.107883i	$0.0344071\pi$
$347$	11.0000	+	19.0526i	0.590511	+	1.02279i	−0.403653	+	0.914912i	$0.632260\pi$
$348$	−7.50000	+	12.9904i	−0.402042	+	0.696358i
$349$	−2.00000			−0.107058			−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000			−0.107058			−0.0535288	+	0.998566i	$0.517047\pi$
$350$		0			0
$351$	−63.0000			−3.36269
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	0.520689	−	0.853746i	$-0.325675\pi$
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	−0.999711	+	0.0240566i	$0.992342\pi$
$354$	−4.50000	−	7.79423i	−0.239172	−	0.414259i
$355$	−2.00000	+	3.46410i	−0.106149	+	0.183855i
$356$	−6.00000			−0.317999
$357$		0			0
$358$	19.0000			1.00418
$359$	9.50000	−	16.4545i	0.501391	−	0.868434i	−0.498608	−	0.866828i	$-0.666155\pi$
$359$	9.50000	−	16.4545i	0.501391	−	0.868434i	0.999999	−	0.00160673i	$-0.000511438\pi$
$360$	6.00000	+	10.3923i	0.316228	+	0.547723i
$361$	9.50000	+	16.4545i	0.500000	+	0.866025i
$362$	−11.0000	+	19.0526i	−0.578147	+	1.00138i
$363$	−3.00000			−0.157459
$364$		0			0
$365$	8.00000			0.418739
$366$	−1.50000	+	2.59808i	−0.0784063	+	0.135804i
$367$	2.00000	+	3.46410i	0.104399	+	0.180825i	0.913493	−	0.406855i	$-0.133375\pi$
$367$	2.00000	+	3.46410i	0.104399	+	0.180825i	−0.809093	+	0.587680i	$0.800041\pi$
$368$	4.00000	+	6.92820i	0.208514	+	0.361158i
$369$	12.0000	−	20.7846i	0.624695	−	1.08200i
$370$	−8.00000			−0.415900
$371$		0			0
$372$	12.0000			0.622171
$373$	−5.50000	+	9.52628i	−0.284779	+	0.493252i	−0.972556	−	0.232671i	$-0.925254\pi$
$373$	−5.50000	+	9.52628i	−0.284779	+	0.493252i	0.687776	+	0.725923i	$0.258587\pi$
$374$	−1.00000	−	1.73205i	−0.0517088	−	0.0895622i
$375$	18.0000	+	31.1769i	0.929516	+	1.60997i
$376$	1.00000	−	1.73205i	0.0515711	−	0.0893237i
$377$	−35.0000			−1.80259
$378$		0			0
$379$	1.00000			0.0513665			0.0256833	−	0.999670i	$-0.491824\pi$
$379$	1.00000			0.0513665			0.0256833	+	0.999670i	$0.491824\pi$
$380$		0			0
$381$	−28.5000	−	49.3634i	−1.46010	−	2.52897i
$382$	−1.00000	−	1.73205i	−0.0511645	−	0.0886194i
$383$	13.0000	−	22.5167i	0.664269	−	1.15055i	−0.315214	−	0.949021i	$-0.602076\pi$
$383$	13.0000	−	22.5167i	0.664269	−	1.15055i	0.979483	−	0.201527i	$-0.0645904\pi$
$384$	−3.00000			−0.153093
$385$		0			0
$386$	8.00000			0.407189
$387$	24.0000	−	41.5692i	1.21999	−	2.11308i
$388$	3.50000	+	6.06218i	0.177686	+	0.307760i
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	0.542445	−	0.840091i	$-0.317499\pi$
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	−0.998763	+	0.0497253i	$0.984165\pi$
$390$	−21.0000	+	36.3731i	−1.06338	+	1.84182i
$391$	16.0000			0.809155
$392$		0			0
$393$		0			0
$394$	−7.50000	+	12.9904i	−0.377845	+	0.654446i
$395$	9.00000	+	15.5885i	0.452839	+	0.784340i
$396$	3.00000	+	5.19615i	0.150756	+	0.261116i
$397$	3.00000	−	5.19615i	0.150566	−	0.260787i	−0.780870	−	0.624694i	$-0.785224\pi$
$397$	3.00000	−	5.19615i	0.150566	−	0.260787i	0.931436	+	0.363906i	$0.118557\pi$
$398$	−4.00000			−0.200502
$399$		0			0
$400$	−1.00000			−0.0500000
$401$	4.50000	−	7.79423i	0.224719	−	0.389225i	−0.731516	−	0.681824i	$-0.761187\pi$
$401$	4.50000	−	7.79423i	0.224719	−	0.389225i	0.956235	+	0.292599i	$0.0945202\pi$
$402$	13.5000	+	23.3827i	0.673319	+	1.16622i
$403$	14.0000	+	24.2487i	0.697390	+	1.20791i
$404$	−4.50000	+	7.79423i	−0.223883	+	0.387777i
$405$	−18.0000			−0.894427
$406$		0			0
$407$	−4.00000			−0.198273
$408$	−3.00000	+	5.19615i	−0.148522	+	0.257248i
$409$	11.0000	+	19.0526i	0.543915	+	0.942088i	0.998674	+	0.0514740i	$0.0163919\pi$
$409$	11.0000	+	19.0526i	0.543915	+	0.942088i	−0.454759	+	0.890614i	$0.650275\pi$
$410$	−4.00000	−	6.92820i	−0.197546	−	0.342160i
$411$	4.50000	−	7.79423i	0.221969	−	0.384461i
$412$	−18.0000			−0.886796
$413$		0			0
$414$	−48.0000			−2.35907
$415$	−6.00000	+	10.3923i	−0.294528	+	0.510138i
$416$	−3.50000	−	6.06218i	−0.171602	−	0.297223i
$417$	6.00000	+	10.3923i	0.293821	+	0.508913i
$418$		0			0
$419$	−16.0000			−0.781651			−0.390826	−	0.920465i	$-0.627810\pi$
$419$	−16.0000			−0.781651			−0.390826	+	0.920465i	$0.627810\pi$
$420$		0			0
$421$	−20.0000			−0.974740			−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000			−0.974740			−0.487370	+	0.873195i	$0.662044\pi$
$422$	10.0000	−	17.3205i	0.486792	−	0.843149i
$423$	6.00000	+	10.3923i	0.291730	+	0.505291i
$424$	3.00000	+	5.19615i	0.145693	+	0.252347i
$425$	−1.00000	+	1.73205i	−0.0485071	+	0.0840168i
$426$	6.00000			0.290701
$427$		0			0
$428$	2.00000			0.0966736
$429$	−10.5000	+	18.1865i	−0.506945	+	0.878054i
$430$	−8.00000	−	13.8564i	−0.385794	−	0.668215i
$431$	−12.5000	−	21.6506i	−0.602104	−	1.04287i	−0.992502	−	0.122228i	$-0.960996\pi$
$431$	−12.5000	−	21.6506i	−0.602104	−	1.04287i	0.390398	−	0.920646i	$-0.372337\pi$
$432$	4.50000	−	7.79423i	0.216506	−	0.375000i
$433$	34.0000			1.63394			0.816968	−	0.576683i	$-0.195653\pi$
$433$	34.0000			1.63394			0.816968	+	0.576683i	$0.195653\pi$
$434$		0			0
$435$	−30.0000			−1.43839
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$		0			0
$438$	−6.00000	−	10.3923i	−0.286691	−	0.496564i
$439$	−2.50000	+	4.33013i	−0.119318	+	0.206666i	−0.919498	−	0.393095i	$-0.871404\pi$
$439$	−2.50000	+	4.33013i	−0.119318	+	0.206666i	0.800179	+	0.599761i	$0.204738\pi$
$440$	2.00000			0.0953463
$441$		0			0
$442$	−14.0000			−0.665912
$443$	−18.0000	+	31.1769i	−0.855206	+	1.48126i	0.0212481	+	0.999774i	$0.493236\pi$
$443$	−18.0000	+	31.1769i	−0.855206	+	1.48126i	−0.876454	+	0.481486i	$0.840097\pi$
$444$	6.00000	+	10.3923i	0.284747	+	0.493197i
$445$	−6.00000	−	10.3923i	−0.284427	−	0.492642i
$446$	2.00000	−	3.46410i	0.0947027	−	0.164030i
$447$	30.0000			1.41895
$448$		0			0
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$	3.00000	−	5.19615i	0.141421	−	0.244949i
$451$	−2.00000	−	3.46410i	−0.0941763	−	0.163118i
$452$	−2.50000	−	4.33013i	−0.117590	−	0.203672i
$453$	−4.50000	+	7.79423i	−0.211428	+	0.366205i
$454$	2.00000			0.0938647
$455$		0			0
$456$		0			0
$457$	−7.00000	+	12.1244i	−0.327446	+	0.567153i	−0.982004	−	0.188858i	$-0.939521\pi$
$457$	−7.00000	+	12.1244i	−0.327446	+	0.567153i	0.654558	+	0.756012i	$0.272855\pi$
$458$	−14.0000	−	24.2487i	−0.654177	−	1.13307i
$459$	−9.00000	−	15.5885i	−0.420084	−	0.727607i
$460$	−8.00000	+	13.8564i	−0.373002	+	0.646058i
$461$	−27.0000			−1.25752			−0.628758	−	0.777601i	$-0.716436\pi$
$461$	−27.0000			−1.25752			−0.628758	+	0.777601i	$0.716436\pi$
$462$		0			0
$463$	−2.00000			−0.0929479			−0.0464739	−	0.998920i	$-0.514798\pi$
$463$	−2.00000			−0.0929479			−0.0464739	+	0.998920i	$0.514798\pi$
$464$	2.50000	−	4.33013i	0.116060	−	0.201021i
$465$	12.0000	+	20.7846i	0.556487	+	0.963863i
$466$		0			0
$467$	6.00000	−	10.3923i	0.277647	−	0.480899i	−0.693153	−	0.720791i	$-0.743779\pi$
$467$	6.00000	−	10.3923i	0.277647	−	0.480899i	0.970799	+	0.239892i	$0.0771121\pi$
$468$	42.0000			1.94145
$469$		0			0
$470$	4.00000			0.184506
$471$	−24.0000	+	41.5692i	−1.10586	+	1.91541i
$472$	1.50000	+	2.59808i	0.0690431	+	0.119586i
$473$	−4.00000	−	6.92820i	−0.183920	−	0.318559i
$474$	13.5000	−	23.3827i	0.620076	−	1.07400i
$475$		0			0
$476$		0			0
$477$	−36.0000			−1.64833
$478$	2.50000	−	4.33013i	0.114347	−	0.198055i
$479$	−0.500000	−	0.866025i	−0.0228456	−	0.0395697i	0.854377	−	0.519654i	$-0.173939\pi$
$479$	−0.500000	−	0.866025i	−0.0228456	−	0.0395697i	−0.877222	+	0.480085i	$0.840606\pi$
$480$	−3.00000	−	5.19615i	−0.136931	−	0.237171i
$481$	−14.0000	+	24.2487i	−0.638345	+	1.10565i
$482$		0			0
$483$		0			0
$484$	1.00000			0.0454545
$485$	−7.00000	+	12.1244i	−0.317854	+	0.550539i
$486$		0			0
$487$	20.0000	+	34.6410i	0.906287	+	1.56973i	0.819181	+	0.573535i	$0.194428\pi$
$487$	20.0000	+	34.6410i	0.906287	+	1.56973i	0.0871056	+	0.996199i	$0.472238\pi$
$488$	0.500000	−	0.866025i	0.0226339	−	0.0392031i
$489$	51.0000			2.30630
$490$		0			0
$491$	30.0000			1.35388			0.676941	−	0.736038i	$-0.263305\pi$
$491$	30.0000			1.35388			0.676941	+	0.736038i	$0.263305\pi$
$492$	−6.00000	+	10.3923i	−0.270501	+	0.468521i
$493$	−5.00000	−	8.66025i	−0.225189	−	0.390038i
$494$		0			0
$495$	−6.00000	+	10.3923i	−0.269680	+	0.467099i
$496$	−4.00000			−0.179605
$497$		0			0
$498$	18.0000			0.806599
$499$	−10.0000	+	17.3205i	−0.447661	+	0.775372i	−0.998233	−	0.0594153i	$-0.981076\pi$
$499$	−10.0000	+	17.3205i	−0.447661	+	0.775372i	0.550572	+	0.834788i	$0.314410\pi$
$500$	−6.00000	−	10.3923i	−0.268328	−	0.464758i
$501$	−28.5000	−	49.3634i	−1.27329	−	2.20540i
$502$	−12.0000	+	20.7846i	−0.535586	+	0.927663i
$503$	−3.00000			−0.133763			−0.0668817	−	0.997761i	$-0.521305\pi$
$503$	−3.00000			−0.133763			−0.0668817	+	0.997761i	$0.521305\pi$
$504$		0			0
$505$	−18.0000			−0.800989
$506$	−4.00000	+	6.92820i	−0.177822	+	0.307996i
$507$	54.0000	+	93.5307i	2.39822	+	4.15385i
$508$	9.50000	+	16.4545i	0.421494	+	0.730050i
$509$	−11.0000	+	19.0526i	−0.487566	+	0.844490i	−0.999898	−	0.0142980i	$-0.995449\pi$
$509$	−11.0000	+	19.0526i	−0.487566	+	0.844490i	0.512331	+	0.858788i	$0.328782\pi$
$510$	−12.0000			−0.531369
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	1.50000	+	2.59808i	0.0661622	+	0.114596i
$515$	−18.0000	−	31.1769i	−0.793175	−	1.37382i
$516$	−12.0000	+	20.7846i	−0.528271	+	0.914991i
$517$	2.00000			0.0879599
$518$		0			0
$519$	75.0000			3.29213
$520$	7.00000	−	12.1244i	0.306970	−	0.531688i
$521$	5.00000	+	8.66025i	0.219054	+	0.379413i	0.954519	−	0.298150i	$-0.0963696\pi$
$521$	5.00000	+	8.66025i	0.219054	+	0.379413i	−0.735465	+	0.677563i	$0.763036\pi$
$522$	15.0000	+	25.9808i	0.656532	+	1.13715i
$523$	−5.00000	+	8.66025i	−0.218635	+	0.378686i	−0.954391	−	0.298560i	$-0.903494\pi$
$523$	−5.00000	+	8.66025i	−0.218635	+	0.378686i	0.735756	+	0.677247i	$0.236827\pi$
$524$		0			0
$525$		0			0
$526$	27.0000			1.17726
$527$	−4.00000	+	6.92820i	−0.174243	+	0.301797i
$528$	−1.50000	−	2.59808i	−0.0652791	−	0.113067i
$529$	−20.5000	−	35.5070i	−0.891304	−	1.54378i
$530$	−6.00000	+	10.3923i	−0.260623	+	0.451413i
$531$	−18.0000			−0.781133
$532$		0			0
$533$	−28.0000			−1.21281
$534$	−9.00000	+	15.5885i	−0.389468	+	0.674579i
$535$	2.00000	+	3.46410i	0.0864675	+	0.149766i
$536$	−4.50000	−	7.79423i	−0.194370	−	0.336659i
$537$	28.5000	−	49.3634i	1.22987	−	2.13019i
$538$	24.0000			1.03471
$539$		0			0
$540$	18.0000			0.774597
$541$	−2.50000	+	4.33013i	−0.107483	+	0.186167i	−0.914750	−	0.404020i	$-0.867613\pi$
$541$	−2.50000	+	4.33013i	−0.107483	+	0.186167i	0.807267	+	0.590187i	$0.200946\pi$
$542$	−5.50000	−	9.52628i	−0.236245	−	0.409189i
$543$	33.0000	+	57.1577i	1.41617	+	2.45287i
$544$	1.00000	−	1.73205i	0.0428746	−	0.0742611i
$545$	4.00000			0.171341
$546$		0			0
$547$	30.0000			1.28271			0.641354	−	0.767245i	$-0.278373\pi$
$547$	30.0000			1.28271			0.641354	+	0.767245i	$0.278373\pi$
$548$	−1.50000	+	2.59808i	−0.0640768	+	0.110984i
$549$	3.00000	+	5.19615i	0.128037	+	0.221766i
$550$	−0.500000	−	0.866025i	−0.0213201	−	0.0369274i
$551$		0			0
$552$	24.0000			1.02151
$553$		0			0
$554$	−9.00000			−0.382373
$555$	−12.0000	+	20.7846i	−0.509372	+	0.882258i
$556$	−2.00000	−	3.46410i	−0.0848189	−	0.146911i
$557$	−13.0000	−	22.5167i	−0.550828	−	0.954062i	−0.998215	−	0.0597213i	$-0.980979\pi$
$557$	−13.0000	−	22.5167i	−0.550828	−	0.954062i	0.447387	−	0.894340i	$-0.352355\pi$
$558$	12.0000	−	20.7846i	0.508001	−	0.879883i
$559$	−56.0000			−2.36855
$560$		0			0
$561$	−6.00000			−0.253320
$562$	14.0000	−	24.2487i	0.590554	−	1.02287i
$563$	10.0000	+	17.3205i	0.421450	+	0.729972i	0.996082	−	0.0884397i	$-0.0281881\pi$
$563$	10.0000	+	17.3205i	0.421450	+	0.729972i	−0.574632	+	0.818412i	$0.694855\pi$
$564$	−3.00000	−	5.19615i	−0.126323	−	0.218797i
$565$	5.00000	−	8.66025i	0.210352	−	0.364340i
$566$		0			0
$567$		0			0
$568$	−2.00000			−0.0839181
$569$	6.00000	−	10.3923i	0.251533	−	0.435668i	−0.712415	−	0.701758i	$-0.752399\pi$
$569$	6.00000	−	10.3923i	0.251533	−	0.435668i	0.963948	+	0.266090i	$0.0857319\pi$
$570$		0			0
$571$	−11.0000	−	19.0526i	−0.460336	−	0.797325i	0.538642	−	0.842535i	$-0.318938\pi$
$571$	−11.0000	−	19.0526i	−0.460336	−	0.797325i	−0.998978	+	0.0452101i	$0.985604\pi$
$572$	3.50000	−	6.06218i	0.146342	−	0.253472i
$573$	−6.00000			−0.250654
$574$		0			0
$575$	8.00000			0.333623
$576$	−3.00000	+	5.19615i	−0.125000	+	0.216506i
$577$	−21.5000	−	37.2391i	−0.895057	−	1.55028i	−0.833734	−	0.552166i	$-0.813802\pi$
$577$	−21.5000	−	37.2391i	−0.895057	−	1.55028i	−0.0613223	−	0.998118i	$-0.519532\pi$
$578$	6.50000	+	11.2583i	0.270364	+	0.468285i
$579$	12.0000	−	20.7846i	0.498703	−	0.863779i
$580$	10.0000			0.415227
$581$		0			0
$582$	21.0000			0.870478
$583$	−3.00000	+	5.19615i	−0.124247	+	0.215203i
$584$	2.00000	+	3.46410i	0.0827606	+	0.143346i
$585$	42.0000	+	72.7461i	1.73649	+	3.00768i
$586$	−9.00000	+	15.5885i	−0.371787	+	0.643953i
$587$	−27.0000			−1.11441			−0.557205	−	0.830375i	$-0.688126\pi$
$587$	−27.0000			−1.11441			−0.557205	+	0.830375i	$0.688126\pi$
$588$		0			0
$589$		0			0
$590$	−3.00000	+	5.19615i	−0.123508	+	0.213922i
$591$	22.5000	+	38.9711i	0.925526	+	1.60306i
$592$	−2.00000	−	3.46410i	−0.0821995	−	0.142374i
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	−0.797831	−	0.602881i	$-0.794019\pi$
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	0.921026	+	0.389501i	$0.127353\pi$
$594$	9.00000			0.369274
$595$		0			0
$596$	−10.0000			−0.409616
$597$	−6.00000	+	10.3923i	−0.245564	+	0.425329i
$598$	28.0000	+	48.4974i	1.14501	+	1.98321i
$599$	−18.0000	−	31.1769i	−0.735460	−	1.27385i	−0.954521	−	0.298143i	$-0.903633\pi$
$599$	−18.0000	−	31.1769i	−0.735460	−	1.27385i	0.219061	−	0.975711i	$-0.429701\pi$
$600$	−1.50000	+	2.59808i	−0.0612372	+	0.106066i
$601$	−26.0000			−1.06056			−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000			−1.06056			−0.530281	+	0.847822i	$0.677914\pi$
$602$		0			0
$603$	54.0000			2.19905
$604$	1.50000	−	2.59808i	0.0610341	−	0.105714i
$605$	1.00000	+	1.73205i	0.0406558	+	0.0704179i
$606$	13.5000	+	23.3827i	0.548400	+	0.949857i
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	−0.773358	−	0.633970i	$-0.781424\pi$
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	0.935713	+	0.352763i	$0.114758\pi$
$608$		0			0
$609$		0			0
$610$	2.00000			0.0809776
$611$	7.00000	−	12.1244i	0.283190	−	0.490499i
$612$	6.00000	+	10.3923i	0.242536	+	0.420084i
$613$	19.0000	+	32.9090i	0.767403	+	1.32918i	0.938967	+	0.344008i	$0.111785\pi$
$613$	19.0000	+	32.9090i	0.767403	+	1.32918i	−0.171564	+	0.985173i	$0.554882\pi$
$614$	1.00000	−	1.73205i	0.0403567	−	0.0698999i
$615$	−24.0000			−0.967773
$616$		0			0
$617$	−15.0000			−0.603877			−0.301939	−	0.953327i	$-0.597634\pi$
$617$	−15.0000			−0.603877			−0.301939	+	0.953327i	$0.597634\pi$
$618$	−27.0000	+	46.7654i	−1.08610	+	1.88118i
$619$	−14.0000	−	24.2487i	−0.562708	−	0.974638i	−0.997259	−	0.0739910i	$-0.976426\pi$
$619$	−14.0000	−	24.2487i	−0.562708	−	0.974638i	0.434551	−	0.900647i	$-0.356907\pi$
$620$	−4.00000	−	6.92820i	−0.160644	−	0.278243i
$621$	−36.0000	+	62.3538i	−1.44463	+	2.50217i
$622$	10.0000			0.400963
$623$		0			0
$624$	−21.0000			−0.840673
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$	0.500000	+	0.866025i	0.0199840	+	0.0346133i
$627$		0			0
$628$	8.00000	−	13.8564i	0.319235	−	0.552931i
$629$	−8.00000			−0.318981
$630$		0			0
$631$	−18.0000			−0.716569			−0.358284	−	0.933613i	$-0.616638\pi$
$631$	−18.0000			−0.716569			−0.358284	+	0.933613i	$0.616638\pi$
$632$	−4.50000	+	7.79423i	−0.179000	+	0.310038i
$633$	−30.0000	−	51.9615i	−1.19239	−	2.06529i
$634$	6.00000	+	10.3923i	0.238290	+	0.412731i
$635$	−19.0000	+	32.9090i	−0.753992	+	1.30595i
$636$	18.0000			0.713746
$637$		0			0
$638$	5.00000			0.197952
$639$	6.00000	−	10.3923i	0.237356	−	0.411113i
$640$	1.00000	+	1.73205i	0.0395285	+	0.0684653i
$641$	13.5000	+	23.3827i	0.533218	+	0.923561i	0.999247	+	0.0387913i	$0.0123508\pi$
$641$	13.5000	+	23.3827i	0.533218	+	0.923561i	−0.466029	+	0.884769i	$0.654316\pi$
$642$	3.00000	−	5.19615i	0.118401	−	0.205076i
$643$	−31.0000			−1.22252			−0.611260	−	0.791430i	$-0.709337\pi$
$643$	−31.0000			−1.22252			−0.611260	+	0.791430i	$0.709337\pi$
$644$		0			0
$645$	−48.0000			−1.89000
$646$		0			0
$647$	15.0000	+	25.9808i	0.589711	+	1.02141i	0.994270	+	0.106897i	$0.0340916\pi$
$647$	15.0000	+	25.9808i	0.589711	+	1.02141i	−0.404559	+	0.914512i	$0.632575\pi$
$648$	−4.50000	−	7.79423i	−0.176777	−	0.306186i
$649$	−1.50000	+	2.59808i	−0.0588802	+	0.101983i
$650$	−7.00000			−0.274563
$651$		0			0
$652$	−17.0000			−0.665771
$653$	−20.0000	+	34.6410i	−0.782660	+	1.35561i	0.147726	+	0.989028i	$0.452805\pi$
$653$	−20.0000	+	34.6410i	−0.782660	+	1.35561i	−0.930387	+	0.366579i	$0.880529\pi$
$654$	−3.00000	−	5.19615i	−0.117309	−	0.203186i
$655$		0			0
$656$	2.00000	−	3.46410i	0.0780869	−	0.135250i
$657$	−24.0000			−0.936329
$658$		0			0
$659$	28.0000			1.09073			0.545363	−	0.838200i	$-0.316392\pi$
$659$	28.0000			1.09073			0.545363	+	0.838200i	$0.316392\pi$
$660$	3.00000	−	5.19615i	0.116775	−	0.202260i
$661$	−11.0000	−	19.0526i	−0.427850	−	0.741059i	0.568831	−	0.822454i	$-0.307396\pi$
$661$	−11.0000	−	19.0526i	−0.427850	−	0.741059i	−0.996682	+	0.0813955i	$0.974062\pi$
$662$	−6.50000	−	11.2583i	−0.252630	−	0.437567i
$663$	−21.0000	+	36.3731i	−0.815572	+	1.41261i
$664$	−6.00000			−0.232845
$665$		0			0
$666$	24.0000			0.929981
$667$	−20.0000	+	34.6410i	−0.774403	+	1.34131i
$668$	9.50000	+	16.4545i	0.367566	+	0.636643i
$669$	−6.00000	−	10.3923i	−0.231973	−	0.401790i
$670$	9.00000	−	15.5885i	0.347700	−	0.602235i
$671$	1.00000			0.0386046
$672$		0			0
$673$	34.0000			1.31060			0.655302	−	0.755367i	$-0.272541\pi$
$673$	34.0000			1.31060			0.655302	+	0.755367i	$0.272541\pi$
$674$	6.00000	−	10.3923i	0.231111	−	0.400297i
$675$	−4.50000	−	7.79423i	−0.173205	−	0.300000i
$676$	−18.0000	−	31.1769i	−0.692308	−	1.19911i
$677$	7.00000	−	12.1244i	0.269032	−	0.465977i	−0.699580	−	0.714554i	$-0.746630\pi$
$677$	7.00000	−	12.1244i	0.269032	−	0.465977i	0.968612	+	0.248577i	$0.0799630\pi$
$678$	−15.0000			−0.576072
$679$		0			0
$680$	4.00000			0.153393
$681$	3.00000	−	5.19615i	0.114960	−	0.199117i
$682$	−2.00000	−	3.46410i	−0.0765840	−	0.132647i
$683$	−10.5000	−	18.1865i	−0.401771	−	0.695888i	0.592168	−	0.805814i	$-0.298272\pi$
$683$	−10.5000	−	18.1865i	−0.401771	−	0.695888i	−0.993940	+	0.109926i	$0.964939\pi$
$684$		0			0
$685$	−6.00000			−0.229248
$686$		0			0
$687$	−84.0000			−3.20480
$688$	4.00000	−	6.92820i	0.152499	−	0.264135i
$689$	21.0000	+	36.3731i	0.800036	+	1.38570i
$690$	24.0000	+	41.5692i	0.913664	+	1.58251i
$691$	16.5000	−	28.5788i	0.627690	−	1.08719i	−0.360325	−	0.932827i	$-0.617334\pi$
$691$	16.5000	−	28.5788i	0.627690	−	1.08719i	0.988014	−	0.154363i	$-0.0493326\pi$
$692$	−25.0000			−0.950357
$693$		0			0
$694$	−22.0000			−0.835109
$695$	4.00000	−	6.92820i	0.151729	−	0.262802i
$696$	−7.50000	−	12.9904i	−0.284287	−	0.492399i
$697$	−4.00000	−	6.92820i	−0.151511	−	0.262424i
$698$	1.00000	−	1.73205i	0.0378506	−	0.0655591i
$699$		0			0
$700$		0			0
$701$	−27.0000			−1.01978			−0.509888	−	0.860241i	$-0.670313\pi$
$701$	−27.0000			−1.01978			−0.509888	+	0.860241i	$0.670313\pi$
$702$	31.5000	−	54.5596i	1.18889	−	2.05922i
$703$		0			0
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$	6.00000	−	10.3923i	0.225973	−	0.391397i
$706$	18.0000			0.677439
$707$		0			0
$708$	9.00000			0.338241
$709$	24.0000	−	41.5692i	0.901339	−	1.56116i	0.0755813	−	0.997140i	$-0.475919\pi$
$709$	24.0000	−	41.5692i	0.901339	−	1.56116i	0.825758	−	0.564025i	$-0.190748\pi$
$710$	−2.00000	−	3.46410i	−0.0750587	−	0.130005i
$711$	−27.0000	−	46.7654i	−1.01258	−	1.75384i
$712$	3.00000	−	5.19615i	0.112430	−	0.194734i
$713$	32.0000			1.19841
$714$		0			0
$715$	14.0000			0.523570
$716$	−9.50000	+	16.4545i	−0.355032	+	0.614933i
$717$	−7.50000	−	12.9904i	−0.280093	−	0.485135i
$718$	9.50000	+	16.4545i	0.354537	+	0.614076i
$719$	−19.0000	+	32.9090i	−0.708580	+	1.22730i	0.256803	+	0.966464i	$0.417331\pi$
$719$	−19.0000	+	32.9090i	−0.708580	+	1.22730i	−0.965384	+	0.260834i	$0.916003\pi$
$720$	−12.0000			−0.447214
$721$		0			0
$722$	−19.0000			−0.707107
$723$		0			0
$724$	−11.0000	−	19.0526i	−0.408812	−	0.708083i
$725$	−2.50000	−	4.33013i	−0.0928477	−	0.160817i
$726$	1.50000	−	2.59808i	0.0556702	−	0.0964237i
$727$	22.0000			0.815935			0.407967	−	0.912996i	$-0.366238\pi$
$727$	22.0000			0.815935			0.407967	+	0.912996i	$0.366238\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	−4.00000	+	6.92820i	−0.148047	+	0.256424i
$731$	−8.00000	−	13.8564i	−0.295891	−	0.512498i
$732$	−1.50000	−	2.59808i	−0.0554416	−	0.0960277i
$733$	−9.50000	+	16.4545i	−0.350891	+	0.607760i	−0.986406	−	0.164328i	$-0.947454\pi$
$733$	−9.50000	+	16.4545i	−0.350891	+	0.607760i	0.635515	+	0.772088i	$0.280788\pi$
$734$	−4.00000			−0.147643
$735$		0			0
$736$	−8.00000			−0.294884
$737$	4.50000	−	7.79423i	0.165760	−	0.287104i
$738$	12.0000	+	20.7846i	0.441726	+	0.765092i
$739$	−21.0000	−	36.3731i	−0.772497	−	1.33800i	−0.936190	−	0.351494i	$-0.885674\pi$
$739$	−21.0000	−	36.3731i	−0.772497	−	1.33800i	0.163693	−	0.986511i	$-0.447659\pi$
$740$	4.00000	−	6.92820i	0.147043	−	0.254686i
$741$		0			0
$742$		0			0
$743$	12.0000			0.440237			0.220119	−	0.975473i	$-0.429356\pi$
$743$	12.0000			0.440237			0.220119	+	0.975473i	$0.429356\pi$
$744$	−6.00000	+	10.3923i	−0.219971	+	0.381000i
$745$	−10.0000	−	17.3205i	−0.366372	−	0.634574i
$746$	−5.50000	−	9.52628i	−0.201369	−	0.348782i
$747$	18.0000	−	31.1769i	0.658586	−	1.14070i
$748$	2.00000			0.0731272
$749$		0			0
$750$	−36.0000			−1.31453
$751$	−14.0000	+	24.2487i	−0.510867	+	0.884848i	0.489053	+	0.872254i	$0.337342\pi$
$751$	−14.0000	+	24.2487i	−0.510867	+	0.884848i	−0.999921	+	0.0125942i	$0.995991\pi$
$752$	1.00000	+	1.73205i	0.0364662	+	0.0631614i
$753$	36.0000	+	62.3538i	1.31191	+	2.27230i
$754$	17.5000	−	30.3109i	0.637312	−	1.10386i
$755$	6.00000			0.218362
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$	−0.500000	+	0.866025i	−0.0181608	+	0.0314555i
$759$	12.0000	+	20.7846i	0.435572	+	0.754434i
$760$		0			0
$761$	−3.00000	+	5.19615i	−0.108750	+	0.188360i	−0.915264	−	0.402854i	$-0.868018\pi$
$761$	−3.00000	+	5.19615i	−0.108750	+	0.188360i	0.806514	+	0.591215i	$0.201351\pi$
$762$	57.0000			2.06489
$763$		0			0
$764$	2.00000			0.0723575
$765$	−12.0000	+	20.7846i	−0.433861	+	0.751469i
$766$	13.0000	+	22.5167i	0.469709	+	0.813560i
$767$	10.5000	+	18.1865i	0.379133	+	0.656678i
$768$	1.50000	−	2.59808i	0.0541266	−	0.0937500i
$769$	14.0000			0.504853			0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000			0.504853			0.252426	+	0.967616i	$0.418771\pi$
$770$		0			0
$771$	9.00000			0.324127
$772$	−4.00000	+	6.92820i	−0.143963	+	0.249351i
$773$	12.0000	+	20.7846i	0.431610	+	0.747570i	0.997012	−	0.0772449i	$-0.0246123\pi$
$773$	12.0000	+	20.7846i	0.431610	+	0.747570i	−0.565402	+	0.824815i	$0.691279\pi$
$774$	24.0000	+	41.5692i	0.862662	+	1.49417i
$775$	−2.00000	+	3.46410i	−0.0718421	+	0.124434i
$776$	−7.00000			−0.251285
$777$		0			0
$778$	18.0000			0.645331
$779$		0			0
$780$	−21.0000	−	36.3731i	−0.751921	−	1.30236i
$781$	−1.00000	−	1.73205i	−0.0357828	−	0.0619777i
$782$	−8.00000	+	13.8564i	−0.286079	+	0.495504i
$783$	45.0000			1.60817
$784$		0			0
$785$	32.0000			1.14213
$786$		0			0
$787$	−20.0000	−	34.6410i	−0.712923	−	1.23482i	−0.963755	−	0.266788i	$-0.914038\pi$
$787$	−20.0000	−	34.6410i	−0.712923	−	1.23482i	0.250832	−	0.968031i	$-0.419296\pi$
$788$	−7.50000	−	12.9904i	−0.267176	−	0.462763i
$789$	40.5000	−	70.1481i	1.44184	−	2.49734i
$790$	−18.0000			−0.640411
$791$		0			0
$792$	−6.00000			−0.213201
$793$	3.50000	−	6.06218i	0.124289	−	0.215274i
$794$	3.00000	+	5.19615i	0.106466	+	0.184405i
$795$	18.0000	+	31.1769i	0.638394	+	1.10573i
$796$	2.00000	−	3.46410i	0.0708881	−	0.122782i
$797$	−50.0000			−1.77109			−0.885545	−	0.464553i	$-0.846215\pi$
$797$	−50.0000			−1.77109			−0.885545	+	0.464553i	$0.846215\pi$
$798$		0			0
$799$	4.00000			0.141510
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	18.0000	+	31.1769i	0.635999	+	1.10158i
$802$	4.50000	+	7.79423i	0.158901	+	0.275224i
$803$	−2.00000	+	3.46410i	−0.0705785	+	0.122245i
$804$	−27.0000			−0.952217
$805$		0			0
$806$	−28.0000			−0.986258
$807$	36.0000	−	62.3538i	1.26726	−	2.19496i
$808$	−4.50000	−	7.79423i	−0.158309	−	0.274200i
$809$	−6.00000	−	10.3923i	−0.210949	−	0.365374i	0.741063	−	0.671436i	$-0.234322\pi$
$809$	−6.00000	−	10.3923i	−0.210949	−	0.365374i	−0.952012	+	0.306062i	$0.900989\pi$
$810$	9.00000	−	15.5885i	0.316228	−	0.547723i
$811$	−8.00000			−0.280918			−0.140459	−	0.990086i	$-0.544858\pi$
$811$	−8.00000			−0.280918			−0.140459	+	0.990086i	$0.544858\pi$
$812$		0			0
$813$	−33.0000			−1.15736
$814$	2.00000	−	3.46410i	0.0701000	−	0.121417i
$815$	−17.0000	−	29.4449i	−0.595484	−	1.03141i
$816$	−3.00000	−	5.19615i	−0.105021	−	0.181902i
$817$		0			0
$818$	−22.0000			−0.769212
$819$		0			0
$820$	8.00000			0.279372
$821$	22.5000	−	38.9711i	0.785255	−	1.36010i	−0.143591	−	0.989637i	$-0.545865\pi$
$821$	22.5000	−	38.9711i	0.785255	−	1.36010i	0.928846	−	0.370465i	$-0.120802\pi$
$822$	4.50000	+	7.79423i	0.156956	+	0.271855i
$823$	−13.0000	−	22.5167i	−0.453152	−	0.784881i	0.545428	−	0.838157i	$-0.316367\pi$
$823$	−13.0000	−	22.5167i	−0.453152	−	0.784881i	−0.998580	+	0.0532760i	$0.983034\pi$
$824$	9.00000	−	15.5885i	0.313530	−	0.543050i
$825$	−3.00000			−0.104447
$826$		0			0
$827$	−4.00000			−0.139094			−0.0695468	−	0.997579i	$-0.522155\pi$
$827$	−4.00000			−0.139094			−0.0695468	+	0.997579i	$0.522155\pi$
$828$	24.0000	−	41.5692i	0.834058	−	1.44463i
$829$	−1.00000	−	1.73205i	−0.0347314	−	0.0601566i	0.848137	−	0.529777i	$-0.177724\pi$
$829$	−1.00000	−	1.73205i	−0.0347314	−	0.0601566i	−0.882869	+	0.469620i	$0.844391\pi$
$830$	−6.00000	−	10.3923i	−0.208263	−	0.360722i
$831$	−13.5000	+	23.3827i	−0.468310	+	0.811136i
$832$	7.00000			0.242681
$833$		0			0
$834$	−12.0000			−0.415526
$835$	−19.0000	+	32.9090i	−0.657522	+	1.13886i
$836$		0			0
$837$	−18.0000	−	31.1769i	−0.622171	−	1.07763i
$838$	8.00000	−	13.8564i	0.276355	−	0.478662i
$839$	18.0000			0.621429			0.310715	−	0.950503i	$-0.399432\pi$
$839$	18.0000			0.621429			0.310715	+	0.950503i	$0.399432\pi$
$840$		0			0
$841$	−4.00000			−0.137931
$842$	10.0000	−	17.3205i	0.344623	−	0.596904i
$843$	−42.0000	−	72.7461i	−1.44656	−	2.50551i
$844$	10.0000	+	17.3205i	0.344214	+	0.596196i
$845$	36.0000	−	62.3538i	1.23844	−	2.14504i
$846$	−12.0000			−0.412568
$847$		0			0
$848$	−6.00000			−0.206041
$849$		0			0
$850$	−1.00000	−	1.73205i	−0.0342997	−	0.0594089i
$851$	16.0000	+	27.7128i	0.548473	+	0.949983i
$852$	−3.00000	+	5.19615i	−0.102778	+	0.178017i
$853$	10.0000			0.342393			0.171197	−	0.985237i	$-0.445237\pi$
$853$	10.0000			0.342393			0.171197	+	0.985237i	$0.445237\pi$
$854$		0			0
$855$		0			0
$856$	−1.00000	+	1.73205i	−0.0341793	+	0.0592003i
$857$	22.0000	+	38.1051i	0.751506	+	1.30165i	0.947093	+	0.320960i	$0.104005\pi$
$857$	22.0000	+	38.1051i	0.751506	+	1.30165i	−0.195587	+	0.980686i	$0.562661\pi$
$858$	−10.5000	−	18.1865i	−0.358464	−	0.620878i
$859$	6.50000	−	11.2583i	0.221777	−	0.384129i	−0.733571	−	0.679613i	$-0.762148\pi$
$859$	6.50000	−	11.2583i	0.221777	−	0.384129i	0.955348	+	0.295484i	$0.0954809\pi$
$860$	16.0000			0.545595
$861$		0			0
$862$	25.0000			0.851503
$863$	−2.00000	+	3.46410i	−0.0680808	+	0.117919i	−0.898056	−	0.439880i	$-0.855021\pi$
$863$	−2.00000	+	3.46410i	−0.0680808	+	0.117919i	0.829976	+	0.557800i	$0.188354\pi$
$864$	4.50000	+	7.79423i	0.153093	+	0.265165i
$865$	−25.0000	−	43.3013i	−0.850026	−	1.47229i
$866$	−17.0000	+	29.4449i	−0.577684	+	1.00058i
$867$	39.0000			1.32451
$868$		0			0
$869$	−9.00000			−0.305304
$870$	15.0000	−	25.9808i	0.508548	−	0.880830i
$871$	−31.5000	−	54.5596i	−1.06734	−	1.84868i
$872$	1.00000	+	1.73205i	0.0338643	+	0.0586546i
$873$	21.0000	−	36.3731i	0.710742	−	1.23104i
$874$		0			0
$875$		0			0
$876$	12.0000			0.405442
$877$	14.5000	−	25.1147i	0.489630	−	0.848064i	−0.510299	−	0.859997i	$-0.670465\pi$
$877$	14.5000	−	25.1147i	0.489630	−	0.848064i	0.999929	+	0.0119329i	$0.00379845\pi$
$878$	−2.50000	−	4.33013i	−0.0843709	−	0.146135i
$879$	27.0000	+	46.7654i	0.910687	+	1.57736i
$880$	−1.00000	+	1.73205i	−0.0337100	+	0.0583874i
$881$	−21.0000			−0.707508			−0.353754	−	0.935339i	$-0.615095\pi$
$881$	−21.0000			−0.707508			−0.353754	+	0.935339i	$0.615095\pi$
$882$		0			0
$883$	−29.0000			−0.975928			−0.487964	−	0.872864i	$-0.662260\pi$
$883$	−29.0000			−0.975928			−0.487964	+	0.872864i	$0.662260\pi$
$884$	7.00000	−	12.1244i	0.235435	−	0.407786i
$885$	9.00000	+	15.5885i	0.302532	+	0.524000i
$886$	−18.0000	−	31.1769i	−0.604722	−	1.04741i
$887$	−20.5000	+	35.5070i	−0.688323	+	1.19221i	0.284058	+	0.958807i	$0.408319\pi$
$887$	−20.5000	+	35.5070i	−0.688323	+	1.19221i	−0.972380	+	0.233403i	$0.925014\pi$
$888$	−12.0000			−0.402694
$889$		0			0
$890$	12.0000			0.402241
$891$	4.50000	−	7.79423i	0.150756	−	0.261116i
$892$	2.00000	+	3.46410i	0.0669650	+	0.115987i
$893$		0			0
$894$	−15.0000	+	25.9808i	−0.501675	+	0.868927i
$895$	−38.0000			−1.27020
$896$		0			0
$897$	168.000			5.60936
$898$	3.00000	−	5.19615i	0.100111	−	0.173398i
$899$	−10.0000	−	17.3205i	−0.333519	−	0.577671i
$900$	3.00000	+	5.19615i	0.100000	+	0.173205i
$901$	−6.00000	+	10.3923i	−0.199889	+	0.346218i
$902$	4.00000			0.133185
$903$		0			0
$904$	5.00000			0.166298
$905$	22.0000	−	38.1051i	0.731305	−	1.26666i
$906$	−4.50000	−	7.79423i	−0.149502	−	0.258946i
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	0.999195	−	0.0401089i	$-0.0127705\pi$
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	−0.534333	+	0.845274i	$0.679437\pi$
$908$	−1.00000	+	1.73205i	−0.0331862	+	0.0574801i
$909$	54.0000			1.79107
$910$		0			0
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$		0			0
$913$	−3.00000	−	5.19615i	−0.0992855	−	0.171968i
$914$	−7.00000	−	12.1244i	−0.231539	−	0.401038i
$915$	3.00000	−	5.19615i	0.0991769	−	0.171780i
$916$	28.0000			0.925146
$917$		0			0
$918$	18.0000			0.594089
$919$	−18.0000	+	31.1769i	−0.593765	+	1.02843i	0.399955	+	0.916535i	$0.369026\pi$
$919$	−18.0000	+	31.1769i	−0.593765	+	1.02843i	−0.993720	+	0.111897i	$0.964307\pi$
$920$	−8.00000	−	13.8564i	−0.263752	−	0.456832i
$921$	−3.00000	−	5.19615i	−0.0988534	−	0.171219i
$922$	13.5000	−	23.3827i	0.444599	−	0.770068i
$923$	−14.0000			−0.460816
$924$		0			0
$925$	−4.00000			−0.131519
$926$	1.00000	−	1.73205i	0.0328620	−	0.0569187i
$927$	54.0000	+	93.5307i	1.77359	+	3.07195i
$928$	2.50000	+	4.33013i	0.0820665	+	0.142143i
$929$	7.50000	−	12.9904i	0.246067	−	0.426201i	−0.716364	−	0.697727i	$-0.754195\pi$
$929$	7.50000	−	12.9904i	0.246067	−	0.426201i	0.962431	+	0.271526i	$0.0875283\pi$
$930$	−24.0000			−0.786991
$931$		0			0
$932$		0			0
$933$	15.0000	−	25.9808i	0.491078	−	0.850572i
$934$	6.00000	+	10.3923i	0.196326	+	0.340047i
$935$	2.00000	+	3.46410i	0.0654070	+	0.113288i
$936$	−21.0000	+	36.3731i	−0.686406	+	1.18889i
$937$	30.0000			0.980057			0.490029	−	0.871706i	$-0.336986\pi$
$937$	30.0000			0.980057			0.490029	+	0.871706i	$0.336986\pi$
$938$		0			0
$939$	3.00000			0.0979013
$940$	−2.00000	+	3.46410i	−0.0652328	+	0.112987i
$941$	−5.50000	−	9.52628i	−0.179295	−	0.310548i	0.762344	−	0.647172i	$-0.224048\pi$
$941$	−5.50000	−	9.52628i	−0.179295	−	0.310548i	−0.941639	+	0.336624i	$0.890715\pi$
$942$	−24.0000	−	41.5692i	−0.781962	−	1.35440i
$943$	−16.0000	+	27.7128i	−0.521032	+	0.902453i
$944$	−3.00000			−0.0976417
$945$		0			0
$946$	8.00000			0.260102
$947$	2.00000	−	3.46410i	0.0649913	−	0.112568i	−0.831699	−	0.555227i	$-0.812631\pi$
$947$	2.00000	−	3.46410i	0.0649913	−	0.112568i	0.896690	+	0.442659i	$0.145965\pi$
$948$	13.5000	+	23.3827i	0.438460	+	0.759434i
$949$	14.0000	+	24.2487i	0.454459	+	0.787146i
$950$		0			0
$951$	36.0000			1.16738
$952$		0			0
$953$	14.0000			0.453504			0.226752	−	0.973952i	$-0.427189\pi$
$953$	14.0000			0.453504			0.226752	+	0.973952i	$0.427189\pi$
$954$	18.0000	−	31.1769i	0.582772	−	1.00939i
$955$	2.00000	+	3.46410i	0.0647185	+	0.112096i
$956$	2.50000	+	4.33013i	0.0808558	+	0.140046i
$957$	7.50000	−	12.9904i	0.242441	−	0.419919i
$958$	1.00000			0.0323085
$959$		0			0
$960$	6.00000			0.193649
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	−14.0000	−	24.2487i	−0.451378	−	0.781810i
$963$	−6.00000	−	10.3923i	−0.193347	−	0.334887i
$964$		0			0
$965$	−16.0000			−0.515058
$966$		0			0
$967$	8.00000			0.257263			0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000			0.257263			0.128631	+	0.991692i	$0.458942\pi$
$968$	−0.500000	+	0.866025i	−0.0160706	+	0.0278351i
$969$		0			0
$970$	−7.00000	−	12.1244i	−0.224756	−	0.389290i
$971$	20.5000	−	35.5070i	0.657876	−	1.13948i	−0.323288	−	0.946301i	$-0.604788\pi$
$971$	20.5000	−	35.5070i	0.657876	−	1.13948i	0.981164	−	0.193175i	$-0.0618784\pi$
$972$		0			0
$973$		0			0
$974$	−40.0000			−1.28168
$975$	−10.5000	+	18.1865i	−0.336269	+	0.582435i
$976$	0.500000	+	0.866025i	0.0160046	+	0.0277208i
$977$	23.0000	+	39.8372i	0.735835	+	1.27450i	0.954356	+	0.298672i	$0.0965435\pi$
$977$	23.0000	+	39.8372i	0.735835	+	1.27450i	−0.218521	+	0.975832i	$0.570123\pi$
$978$	−25.5000	+	44.1673i	−0.815400	+	1.41231i
$979$	6.00000			0.191761
$980$		0			0
$981$	−12.0000			−0.383131
$982$	−15.0000	+	25.9808i	−0.478669	+	0.829079i
$983$	−9.00000	−	15.5885i	−0.287055	−	0.497195i	0.686050	−	0.727554i	$-0.259343\pi$
$983$	−9.00000	−	15.5885i	−0.287055	−	0.497195i	−0.973106	+	0.230360i	$0.926010\pi$
$984$	−6.00000	−	10.3923i	−0.191273	−	0.331295i
$985$	15.0000	−	25.9808i	0.477940	−	0.827816i
$986$	10.0000			0.318465
$987$		0			0
$988$		0			0
$989$	−32.0000	+	55.4256i	−1.01754	+	1.76243i
$990$	−6.00000	−	10.3923i	−0.190693	−	0.330289i
$991$	−5.00000	−	8.66025i	−0.158830	−	0.275102i	0.775617	−	0.631204i	$-0.217439\pi$
$991$	−5.00000	−	8.66025i	−0.158830	−	0.275102i	−0.934447	+	0.356102i	$0.884106\pi$
$992$	2.00000	−	3.46410i	0.0635001	−	0.109985i
$993$	−39.0000			−1.23763
$994$		0			0
$995$	8.00000			0.253617
$996$	−9.00000	+	15.5885i	−0.285176	+	0.493939i
$997$	−3.00000	−	5.19615i	−0.0950110	−	0.164564i	0.814602	−	0.580020i	$-0.196955\pi$
$997$	−3.00000	−	5.19615i	−0.0950110	−	0.164564i	−0.909613	+	0.415456i	$0.863622\pi$
$998$	−10.0000	−	17.3205i	−0.316544	−	0.548271i
$999$	18.0000	−	31.1769i	0.569495	−	0.986394i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.e.f.177.1		2
7.2	even	3		1078.2.a.g.1.1		1
7.3	odd	6		154.2.e.a.67.1	yes	2
7.4	even	3	inner	1078.2.e.f.67.1		2
7.5	odd	6		1078.2.a.m.1.1		1
7.6	odd	2		154.2.e.a.23.1	✓	2
21.2	odd	6		9702.2.a.y.1.1		1
21.5	even	6		9702.2.a.i.1.1		1
21.17	even	6		1386.2.k.o.991.1		2
21.20	even	2		1386.2.k.o.793.1		2
28.3	even	6		1232.2.q.e.529.1		2
28.19	even	6		8624.2.a.b.1.1		1
28.23	odd	6		8624.2.a.be.1.1		1
28.27	even	2		1232.2.q.e.177.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.e.a.23.1	✓	2	7.6	odd	2
154.2.e.a.67.1	yes	2	7.3	odd	6
1078.2.a.g.1.1		1	7.2	even	3
1078.2.a.m.1.1		1	7.5	odd	6
1078.2.e.f.67.1		2	7.4	even	3	inner
1078.2.e.f.177.1		2	1.1	even	1	trivial
1232.2.q.e.177.1		2	28.27	even	2
1232.2.q.e.529.1		2	28.3	even	6
1386.2.k.o.793.1		2	21.20	even	2
1386.2.k.o.991.1		2	21.17	even	6
8624.2.a.b.1.1		1	28.19	even	6
8624.2.a.be.1.1		1	28.23	odd	6
9702.2.a.i.1.1		1	21.5	even	6
9702.2.a.y.1.1		1	21.2	odd	6

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:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} -3.00000 q^{6} +1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} -3.00000 q^{6} +1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +(1.00000 + 1.73205i) q^{10} +(0.500000 + 0.866025i) q^{11} +(1.50000 - 2.59808i) q^{12} +7.00000 q^{13} +6.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(-3.00000 - 5.19615i) q^{18} -2.00000 q^{20} -1.00000 q^{22} +(4.00000 - 6.92820i) q^{23} +(1.50000 + 2.59808i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-3.50000 + 6.06218i) q^{26} -9.00000 q^{27} -5.00000 q^{29} +(-3.00000 + 5.19615i) q^{30} +(2.00000 + 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} -2.00000 q^{34} +6.00000 q^{36} +(-2.00000 + 3.46410i) q^{37} +(10.5000 + 18.1865i) q^{39} +(1.00000 - 1.73205i) q^{40} -4.00000 q^{41} -8.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(6.00000 + 10.3923i) q^{45} +(4.00000 + 6.92820i) q^{46} +(1.00000 - 1.73205i) q^{47} -3.00000 q^{48} -1.00000 q^{50} +(-3.00000 + 5.19615i) q^{51} +(-3.50000 - 6.06218i) q^{52} +(3.00000 + 5.19615i) q^{53} +(4.50000 - 7.79423i) q^{54} +2.00000 q^{55} +(2.50000 - 4.33013i) q^{58} +(1.50000 + 2.59808i) q^{59} +(-3.00000 - 5.19615i) q^{60} +(0.500000 - 0.866025i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(7.00000 - 12.1244i) q^{65} +(-1.50000 - 2.59808i) q^{66} +(-4.50000 - 7.79423i) q^{67} +(1.00000 - 1.73205i) q^{68} +24.0000 q^{69} -2.00000 q^{71} +(-3.00000 + 5.19615i) q^{72} +(2.00000 + 3.46410i) q^{73} +(-2.00000 - 3.46410i) q^{74} +(-1.50000 + 2.59808i) q^{75} -21.0000 q^{78} +(-4.50000 + 7.79423i) q^{79} +(1.00000 + 1.73205i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(2.00000 - 3.46410i) q^{82} -6.00000 q^{83} +4.00000 q^{85} +(4.00000 - 6.92820i) q^{86} +(-7.50000 - 12.9904i) q^{87} +(0.500000 + 0.866025i) q^{88} +(3.00000 - 5.19615i) q^{89} -12.0000 q^{90} -8.00000 q^{92} +(-6.00000 + 10.3923i) q^{93} +(1.00000 + 1.73205i) q^{94} +(1.50000 - 2.59808i) q^{96} -7.00000 q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 3 q^{3} - q^{4} + 2 q^{5} - 6 q^{6} + 2 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q - q^2 + 3 * q^3 - q^4 + 2 * q^5 - 6 * q^6 + 2 * q^8 - 6 * q^9	\( 2 q - q^{2} + 3 q^{3} - q^{4} + 2 q^{5} - 6 q^{6} + 2 q^{8} - 6 q^{9} + 2 q^{10} + q^{11} + 3 q^{12} + 14 q^{13} + 12 q^{15} - q^{16} + 2 q^{17} - 6 q^{18} - 4 q^{20} - 2 q^{22} + 8 q^{23} + 3 q^{24} + q^{25} - 7 q^{26} - 18 q^{27} - 10 q^{29} - 6 q^{30} + 4 q^{31} - q^{32} - 3 q^{33} - 4 q^{34} + 12 q^{36} - 4 q^{37} + 21 q^{39} + 2 q^{40} - 8 q^{41} - 16 q^{43} + q^{44} + 12 q^{45} + 8 q^{46} + 2 q^{47} - 6 q^{48} - 2 q^{50} - 6 q^{51} - 7 q^{52} + 6 q^{53} + 9 q^{54} + 4 q^{55} + 5 q^{58} + 3 q^{59} - 6 q^{60} + q^{61} - 8 q^{62} + 2 q^{64} + 14 q^{65} - 3 q^{66} - 9 q^{67} + 2 q^{68} + 48 q^{69} - 4 q^{71} - 6 q^{72} + 4 q^{73} - 4 q^{74} - 3 q^{75} - 42 q^{78} - 9 q^{79} + 2 q^{80} - 9 q^{81} + 4 q^{82} - 12 q^{83} + 8 q^{85} + 8 q^{86} - 15 q^{87} + q^{88} + 6 q^{89} - 24 q^{90} - 16 q^{92} - 12 q^{93} + 2 q^{94} + 3 q^{96} - 14 q^{97} - 12 q^{99}+O(q^{100}) \) 2 * q - q^2 + 3 * q^3 - q^4 + 2 * q^5 - 6 * q^6 + 2 * q^8 - 6 * q^9 + 2 * q^10 + q^11 + 3 * q^12 + 14 * q^13 + 12 * q^15 - q^16 + 2 * q^17 - 6 * q^18 - 4 * q^20 - 2 * q^22 + 8 * q^23 + 3 * q^24 + q^25 - 7 * q^26 - 18 * q^27 - 10 * q^29 - 6 * q^30 + 4 * q^31 - q^32 - 3 * q^33 - 4 * q^34 + 12 * q^36 - 4 * q^37 + 21 * q^39 + 2 * q^40 - 8 * q^41 - 16 * q^43 + q^44 + 12 * q^45 + 8 * q^46 + 2 * q^47 - 6 * q^48 - 2 * q^50 - 6 * q^51 - 7 * q^52 + 6 * q^53 + 9 * q^54 + 4 * q^55 + 5 * q^58 + 3 * q^59 - 6 * q^60 + q^61 - 8 * q^62 + 2 * q^64 + 14 * q^65 - 3 * q^66 - 9 * q^67 + 2 * q^68 + 48 * q^69 - 4 * q^71 - 6 * q^72 + 4 * q^73 - 4 * q^74 - 3 * q^75 - 42 * q^78 - 9 * q^79 + 2 * q^80 - 9 * q^81 + 4 * q^82 - 12 * q^83 + 8 * q^85 + 8 * q^86 - 15 * q^87 + q^88 + 6 * q^89 - 24 * q^90 - 16 * q^92 - 12 * q^93 + 2 * q^94 + 3 * q^96 - 14 * q^97 - 12 * q^99

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