LMFDB - Embedded newform 370.2.e.c.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(121,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("370.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.e (of order $3$, degree $2$, 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:	$2.95446487479$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	370.121
Dual form			370.2.e.c.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.00000 q^{6} -1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.00000 q^{6} -1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +1.00000 q^{10} +2.00000 q^{11} +(1.50000 - 2.59808i) q^{12} +(0.500000 + 0.866025i) q^{13} +(-1.50000 + 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +(3.00000 + 5.19615i) q^{18} +(-1.00000 - 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{20} +(1.00000 - 1.73205i) q^{22} -6.00000 q^{23} +(-1.50000 - 2.59808i) q^{24} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{26} -9.00000 q^{27} +6.00000 q^{29} +(1.50000 + 2.59808i) q^{30} +5.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(3.00000 + 5.19615i) q^{33} +(-1.00000 - 1.73205i) q^{34} +6.00000 q^{36} +(-5.50000 - 2.59808i) q^{37} -2.00000 q^{38} +(-1.50000 + 2.59808i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-1.50000 - 2.59808i) q^{41} +7.00000 q^{43} +(-1.00000 - 1.73205i) q^{44} -6.00000 q^{45} +(-3.00000 + 5.19615i) q^{46} -8.00000 q^{47} -3.00000 q^{48} +(3.50000 - 6.06218i) q^{49} +(0.500000 + 0.866025i) q^{50} +6.00000 q^{51} +(0.500000 - 0.866025i) q^{52} +(5.50000 - 9.52628i) q^{53} +(-4.50000 + 7.79423i) q^{54} +(1.00000 + 1.73205i) q^{55} +(3.00000 - 5.19615i) q^{57} +(3.00000 - 5.19615i) q^{58} +(1.00000 - 1.73205i) q^{59} +3.00000 q^{60} +(-5.00000 - 8.66025i) q^{61} +(2.50000 - 4.33013i) q^{62} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +6.00000 q^{66} +(-2.00000 - 3.46410i) q^{67} -2.00000 q^{68} +(-9.00000 - 15.5885i) q^{69} +(3.00000 - 5.19615i) q^{72} -2.00000 q^{73} +(-5.00000 + 3.46410i) q^{74} -3.00000 q^{75} +(-1.00000 + 1.73205i) q^{76} +(1.50000 + 2.59808i) q^{78} +(2.00000 + 3.46410i) q^{79} -1.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} -3.00000 q^{82} +(-6.00000 + 10.3923i) q^{83} +2.00000 q^{85} +(3.50000 - 6.06218i) q^{86} +(9.00000 + 15.5885i) q^{87} -2.00000 q^{88} +(-1.00000 + 1.73205i) q^{89} +(-3.00000 + 5.19615i) q^{90} +(3.00000 + 5.19615i) q^{92} +(7.50000 + 12.9904i) q^{93} +(-4.00000 + 6.92820i) q^{94} +(1.00000 - 1.73205i) q^{95} +(-1.50000 + 2.59808i) q^{96} +18.0000 q^{97} +(-3.50000 - 6.06218i) q^{98} +(-6.00000 + 10.3923i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 3 q^{3} - q^{4} + q^{5} + 6 q^{6} - 2 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q + q^2 + 3 * q^3 - q^4 + q^5 + 6 * q^6 - 2 * q^8 - 6 * q^9	$ 2 q + q^{2} + 3 q^{3} - q^{4} + q^{5} + 6 q^{6} - 2 q^{8} - 6 q^{9} + 2 q^{10} + 4 q^{11} + 3 q^{12} + q^{13} - 3 q^{15} - q^{16} + 2 q^{17} + 6 q^{18} - 2 q^{19} + q^{20} + 2 q^{22} - 12 q^{23} - 3 q^{24} - q^{25} + 2 q^{26} - 18 q^{27} + 12 q^{29} + 3 q^{30} + 10 q^{31} + q^{32} + 6 q^{33} - 2 q^{34} + 12 q^{36} - 11 q^{37} - 4 q^{38} - 3 q^{39} - q^{40} - 3 q^{41} + 14 q^{43} - 2 q^{44} - 12 q^{45} - 6 q^{46} - 16 q^{47} - 6 q^{48} + 7 q^{49} + q^{50} + 12 q^{51} + q^{52} + 11 q^{53} - 9 q^{54} + 2 q^{55} + 6 q^{57} + 6 q^{58} + 2 q^{59} + 6 q^{60} - 10 q^{61} + 5 q^{62} + 2 q^{64} - q^{65} + 12 q^{66} - 4 q^{67} - 4 q^{68} - 18 q^{69} + 6 q^{72} - 4 q^{73} - 10 q^{74} - 6 q^{75} - 2 q^{76} + 3 q^{78} + 4 q^{79} - 2 q^{80} - 9 q^{81} - 6 q^{82} - 12 q^{83} + 4 q^{85} + 7 q^{86} + 18 q^{87} - 4 q^{88} - 2 q^{89} - 6 q^{90} + 6 q^{92} + 15 q^{93} - 8 q^{94} + 2 q^{95} - 3 q^{96} + 36 q^{97} - 7 q^{98} - 12 q^{99}+O(q^{100}) $ 2 * q + q^2 + 3 * q^3 - q^4 + q^5 + 6 * q^6 - 2 * q^8 - 6 * q^9 + 2 * q^10 + 4 * q^11 + 3 * q^12 + q^13 - 3 * q^15 - q^16 + 2 * q^17 + 6 * q^18 - 2 * q^19 + q^20 + 2 * q^22 - 12 * q^23 - 3 * q^24 - q^25 + 2 * q^26 - 18 * q^27 + 12 * q^29 + 3 * q^30 + 10 * q^31 + q^32 + 6 * q^33 - 2 * q^34 + 12 * q^36 - 11 * q^37 - 4 * q^38 - 3 * q^39 - q^40 - 3 * q^41 + 14 * q^43 - 2 * q^44 - 12 * q^45 - 6 * q^46 - 16 * q^47 - 6 * q^48 + 7 * q^49 + q^50 + 12 * q^51 + q^52 + 11 * q^53 - 9 * q^54 + 2 * q^55 + 6 * q^57 + 6 * q^58 + 2 * q^59 + 6 * q^60 - 10 * q^61 + 5 * q^62 + 2 * q^64 - q^65 + 12 * q^66 - 4 * q^67 - 4 * q^68 - 18 * q^69 + 6 * q^72 - 4 * q^73 - 10 * q^74 - 6 * q^75 - 2 * q^76 + 3 * q^78 + 4 * q^79 - 2 * q^80 - 9 * q^81 - 6 * q^82 - 12 * q^83 + 4 * q^85 + 7 * q^86 + 18 * q^87 - 4 * q^88 - 2 * q^89 - 6 * q^90 + 6 * q^92 + 15 * q^93 - 8 * q^94 + 2 * q^95 - 3 * q^96 + 36 * q^97 - 7 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	3.00000			1.22474
$7$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$7$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$8$	−1.00000			−0.353553
$9$	−3.00000	+	5.19615i	−1.00000	+	1.73205i
$10$	1.00000			0.316228
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$	1.50000	−	2.59808i	0.433013	−	0.750000i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	0.926995	−	0.375073i	$-0.122382\pi$
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	−0.788320	+	0.615265i	$0.789049\pi$
$14$		0			0
$15$	−1.50000	+	2.59808i	−0.387298	+	0.670820i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	−0.718900	−	0.695113i	$-0.755354\pi$
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	0.961436	+	0.275029i	$0.0886875\pi$
$18$	3.00000	+	5.19615i	0.707107	+	1.22474i
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	0.728219	−	0.685344i	$-0.240348\pi$
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	−0.957635	+	0.287984i	$0.907015\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$		0			0
$22$	1.00000	−	1.73205i	0.213201	−	0.369274i
$23$	−6.00000			−1.25109			−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000			−1.25109			−0.625543	+	0.780189i	$0.715123\pi$
$24$	−1.50000	−	2.59808i	−0.306186	−	0.530330i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.00000			0.196116
$27$	−9.00000			−1.73205
$28$		0			0
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$	1.50000	+	2.59808i	0.273861	+	0.474342i
$31$	5.00000			0.898027			0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000			0.898027			0.449013	+	0.893525i	$0.351776\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	3.00000	+	5.19615i	0.522233	+	0.904534i
$34$	−1.00000	−	1.73205i	−0.171499	−	0.297044i
$35$		0			0
$36$	6.00000			1.00000
$37$	−5.50000	−	2.59808i	−0.904194	−	0.427121i
$37$	−5.50000	−	2.59808i	−0.904194	−	0.427121i
$38$	−2.00000			−0.324443
$39$	−1.50000	+	2.59808i	−0.240192	+	0.416025i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	0.724797	−	0.688963i	$-0.241934\pi$
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	−0.959058	+	0.283211i	$0.908600\pi$
$42$		0			0
$43$	7.00000			1.06749			0.533745	−	0.845645i	$-0.320784\pi$
$43$	7.00000			1.06749			0.533745	+	0.845645i	$0.320784\pi$
$44$	−1.00000	−	1.73205i	−0.150756	−	0.261116i
$45$	−6.00000			−0.894427
$46$	−3.00000	+	5.19615i	−0.442326	+	0.766131i
$47$	−8.00000			−1.16692			−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000			−1.16692			−0.583460	+	0.812142i	$0.698301\pi$
$48$	−3.00000			−0.433013
$49$	3.50000	−	6.06218i	0.500000	−	0.866025i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	6.00000			0.840168
$52$	0.500000	−	0.866025i	0.0693375	−	0.120096i
$53$	5.50000	−	9.52628i	0.755483	−	1.30854i	−0.189651	−	0.981852i	$-0.560736\pi$
$53$	5.50000	−	9.52628i	0.755483	−	1.30854i	0.945134	−	0.326683i	$-0.105931\pi$
$54$	−4.50000	+	7.79423i	−0.612372	+	1.06066i
$55$	1.00000	+	1.73205i	0.134840	+	0.233550i
$56$		0			0
$57$	3.00000	−	5.19615i	0.397360	−	0.688247i
$58$	3.00000	−	5.19615i	0.393919	−	0.682288i
$59$	1.00000	−	1.73205i	0.130189	−	0.225494i	−0.793560	−	0.608492i	$-0.791775\pi$
$59$	1.00000	−	1.73205i	0.130189	−	0.225494i	0.923749	+	0.382998i	$0.125108\pi$
$60$	3.00000			0.387298
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	−0.985391	−	0.170305i	$-0.945525\pi$
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	0.345207	−	0.938527i	$-0.387809\pi$
$62$	2.50000	−	4.33013i	0.317500	−	0.549927i
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$	6.00000			0.738549
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	0.717607	−	0.696449i	$-0.245238\pi$
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	−0.961946	+	0.273241i	$0.911904\pi$
$68$	−2.00000			−0.242536
$69$	−9.00000	−	15.5885i	−1.08347	−	1.87663i
$70$		0			0
$71$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$71$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$72$	3.00000	−	5.19615i	0.353553	−	0.612372i
$73$	−2.00000			−0.234082			−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000			−0.234082			−0.117041	+	0.993127i	$0.537341\pi$
$74$	−5.00000	+	3.46410i	−0.581238	+	0.402694i
$75$	−3.00000			−0.346410
$76$	−1.00000	+	1.73205i	−0.114708	+	0.198680i
$77$		0			0
$78$	1.50000	+	2.59808i	0.169842	+	0.294174i
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	−0.731307	+	0.682048i	$0.761089\pi$
$80$	−1.00000			−0.111803
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−3.00000			−0.331295
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	0.322396	+	0.946605i	$0.395512\pi$
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	−0.980982	+	0.194099i	$0.937822\pi$
$84$		0			0
$85$	2.00000			0.216930
$86$	3.50000	−	6.06218i	0.377415	−	0.653701i
$87$	9.00000	+	15.5885i	0.964901	+	1.67126i
$88$	−2.00000			−0.213201
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	−0.914146	−	0.405385i	$-0.867138\pi$
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	0.808146	+	0.588982i	$0.200471\pi$
$90$	−3.00000	+	5.19615i	−0.316228	+	0.547723i
$91$		0			0
$92$	3.00000	+	5.19615i	0.312772	+	0.541736i
$93$	7.50000	+	12.9904i	0.777714	+	1.34704i
$94$	−4.00000	+	6.92820i	−0.412568	+	0.714590i
$95$	1.00000	−	1.73205i	0.102598	−	0.177705i
$96$	−1.50000	+	2.59808i	−0.153093	+	0.265165i
$97$	18.0000			1.82762			0.913812	−	0.406138i	$-0.133125\pi$
$97$	18.0000			1.82762			0.913812	+	0.406138i	$0.133125\pi$
$98$	−3.50000	−	6.06218i	−0.353553	−	0.612372i
$99$	−6.00000	+	10.3923i	−0.603023	+	1.04447i
$100$	1.00000			0.100000
$101$	−18.0000			−1.79107			−0.895533	−	0.444994i	$-0.853206\pi$
$101$	−18.0000			−1.79107			−0.895533	+	0.444994i	$0.853206\pi$
$102$	3.00000	−	5.19615i	0.297044	−	0.514496i
$103$	−18.0000			−1.77359			−0.886796	−	0.462160i	$-0.847074\pi$
$103$	−18.0000			−1.77359			−0.886796	+	0.462160i	$0.847074\pi$
$104$	−0.500000	−	0.866025i	−0.0490290	−	0.0849208i
$105$		0			0
$106$	−5.50000	−	9.52628i	−0.534207	−	0.925274i
$107$	8.50000	+	14.7224i	0.821726	+	1.42327i	0.904396	+	0.426694i	$0.140322\pi$
$107$	8.50000	+	14.7224i	0.821726	+	1.42327i	−0.0826699	+	0.996577i	$0.526345\pi$
$108$	4.50000	+	7.79423i	0.433013	+	0.750000i
$109$	9.00000	−	15.5885i	0.862044	−	1.49310i	−0.00790932	−	0.999969i	$-0.502518\pi$
$109$	9.00000	−	15.5885i	0.862044	−	1.49310i	0.869953	−	0.493135i	$-0.164149\pi$
$110$	2.00000			0.190693
$111$	−1.50000	−	18.1865i	−0.142374	−	1.72619i
$112$		0			0
$113$	−10.0000	+	17.3205i	−0.940721	+	1.62938i	−0.176620	+	0.984279i	$0.556517\pi$
$113$	−10.0000	+	17.3205i	−0.940721	+	1.62938i	−0.764100	+	0.645097i	$0.776817\pi$
$114$	−3.00000	−	5.19615i	−0.280976	−	0.486664i
$115$	−3.00000	−	5.19615i	−0.279751	−	0.484544i
$116$	−3.00000	−	5.19615i	−0.278543	−	0.482451i
$117$	−6.00000			−0.554700
$118$	−1.00000	−	1.73205i	−0.0920575	−	0.159448i
$119$		0			0
$120$	1.50000	−	2.59808i	0.136931	−	0.237171i
$121$	−7.00000			−0.636364
$122$	−10.0000			−0.905357
$123$	4.50000	−	7.79423i	0.405751	−	0.702782i
$124$	−2.50000	−	4.33013i	−0.224507	−	0.388857i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	2.00000	−	3.46410i	0.177471	−	0.307389i	−0.763542	−	0.645758i	$-0.776542\pi$
$127$	2.00000	−	3.46410i	0.177471	−	0.307389i	0.941014	+	0.338368i	$0.109875\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	10.5000	+	18.1865i	0.924473	+	1.60123i
$130$	0.500000	+	0.866025i	0.0438529	+	0.0759555i
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	−0.704692	−	0.709514i	$-0.748915\pi$
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	0.966803	+	0.255524i	$0.0822479\pi$
$132$	3.00000	−	5.19615i	0.261116	−	0.452267i
$133$		0			0
$134$	−4.00000			−0.345547
$135$	−4.50000	−	7.79423i	−0.387298	−	0.670820i
$136$	−1.00000	+	1.73205i	−0.0857493	+	0.148522i
$137$	−6.00000			−0.512615			−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000			−0.512615			−0.256307	+	0.966595i	$0.582506\pi$
$138$	−18.0000			−1.53226
$139$	−7.00000	+	12.1244i	−0.593732	+	1.02837i	0.399992	+	0.916519i	$0.369013\pi$
$139$	−7.00000	+	12.1244i	−0.593732	+	1.02837i	−0.993724	+	0.111856i	$0.964321\pi$
$140$		0			0
$141$	−12.0000	−	20.7846i	−1.01058	−	1.75038i
$142$		0			0
$143$	1.00000	+	1.73205i	0.0836242	+	0.144841i
$144$	−3.00000	−	5.19615i	−0.250000	−	0.433013i
$145$	3.00000	+	5.19615i	0.249136	+	0.431517i
$146$	−1.00000	+	1.73205i	−0.0827606	+	0.143346i
$147$	21.0000			1.73205
$148$	0.500000	+	6.06218i	0.0410997	+	0.498308i
$149$	−4.00000			−0.327693			−0.163846	−	0.986486i	$-0.552390\pi$
$149$	−4.00000			−0.327693			−0.163846	+	0.986486i	$0.552390\pi$
$150$	−1.50000	+	2.59808i	−0.122474	+	0.212132i
$151$	4.50000	+	7.79423i	0.366205	+	0.634285i	0.988969	−	0.148124i	$-0.0473236\pi$
$151$	4.50000	+	7.79423i	0.366205	+	0.634285i	−0.622764	+	0.782410i	$0.713990\pi$
$152$	1.00000	+	1.73205i	0.0811107	+	0.140488i
$153$	6.00000	+	10.3923i	0.485071	+	0.840168i
$154$		0			0
$155$	2.50000	+	4.33013i	0.200805	+	0.347804i
$156$	3.00000			0.240192
$157$	−1.50000	+	2.59808i	−0.119713	+	0.207349i	−0.919654	−	0.392730i	$-0.871531\pi$
$157$	−1.50000	+	2.59808i	−0.119713	+	0.207349i	0.799941	+	0.600079i	$0.204864\pi$
$158$	4.00000			0.318223
$159$	33.0000			2.61707
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$		0			0
$162$	−9.00000			−0.707107
$163$	0.500000	−	0.866025i	0.0391630	−	0.0678323i	−0.845780	−	0.533533i	$-0.820864\pi$
$163$	0.500000	−	0.866025i	0.0391630	−	0.0678323i	0.884943	+	0.465700i	$0.154198\pi$
$164$	−1.50000	+	2.59808i	−0.117130	+	0.202876i
$165$	−3.00000	+	5.19615i	−0.233550	+	0.404520i
$166$	6.00000	+	10.3923i	0.465690	+	0.806599i
$167$	5.00000	+	8.66025i	0.386912	+	0.670151i	0.992032	−	0.125983i	$-0.0402085\pi$
$167$	5.00000	+	8.66025i	0.386912	+	0.670151i	−0.605121	+	0.796134i	$0.706875\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$	1.00000	−	1.73205i	0.0766965	−	0.132842i
$171$	12.0000			0.917663
$172$	−3.50000	−	6.06218i	−0.266872	−	0.462237i
$173$	−11.0000	+	19.0526i	−0.836315	+	1.44854i	0.0566411	+	0.998395i	$0.481961\pi$
$173$	−11.0000	+	19.0526i	−0.836315	+	1.44854i	−0.892956	+	0.450145i	$0.851372\pi$
$174$	18.0000			1.36458
$175$		0			0
$176$	−1.00000	+	1.73205i	−0.0753778	+	0.130558i
$177$	6.00000			0.450988
$178$	1.00000	+	1.73205i	0.0749532	+	0.129823i
$179$	4.00000			0.298974			0.149487	−	0.988764i	$-0.452238\pi$
$179$	4.00000			0.298974			0.149487	+	0.988764i	$0.452238\pi$
$180$	3.00000	+	5.19615i	0.223607	+	0.387298i
$181$	−8.00000	−	13.8564i	−0.594635	−	1.02994i	−0.993598	−	0.112972i	$-0.963963\pi$
$181$	−8.00000	−	13.8564i	−0.594635	−	1.02994i	0.398963	−	0.916967i	$-0.369370\pi$
$182$		0			0
$183$	15.0000	−	25.9808i	1.10883	−	1.92055i
$184$	6.00000			0.442326
$185$	−0.500000	−	6.06218i	−0.0367607	−	0.445700i
$186$	15.0000			1.09985
$187$	2.00000	−	3.46410i	0.146254	−	0.253320i
$188$	4.00000	+	6.92820i	0.291730	+	0.505291i
$189$		0			0
$190$	−1.00000	−	1.73205i	−0.0725476	−	0.125656i
$191$	−3.00000			−0.217072			−0.108536	−	0.994092i	$-0.534616\pi$
$191$	−3.00000			−0.217072			−0.108536	+	0.994092i	$0.534616\pi$
$192$	1.50000	+	2.59808i	0.108253	+	0.187500i
$193$	26.0000			1.87152			0.935760	−	0.352636i	$-0.114715\pi$
$193$	26.0000			1.87152			0.935760	+	0.352636i	$0.114715\pi$
$194$	9.00000	−	15.5885i	0.646162	−	1.11919i
$195$	−3.00000			−0.214834
$196$	−7.00000			−0.500000
$197$	−5.50000	+	9.52628i	−0.391859	+	0.678719i	−0.992695	−	0.120653i	$-0.961501\pi$
$197$	−5.50000	+	9.52628i	−0.391859	+	0.678719i	0.600836	+	0.799372i	$0.294834\pi$
$198$	6.00000	+	10.3923i	0.426401	+	0.738549i
$199$	25.0000			1.77220			0.886102	−	0.463491i	$-0.153403\pi$
$199$	25.0000			1.77220			0.886102	+	0.463491i	$0.153403\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	6.00000	−	10.3923i	0.423207	−	0.733017i
$202$	−9.00000	+	15.5885i	−0.633238	+	1.09680i
$203$		0			0
$204$	−3.00000	−	5.19615i	−0.210042	−	0.363803i
$205$	1.50000	−	2.59808i	0.104765	−	0.181458i
$206$	−9.00000	+	15.5885i	−0.627060	+	1.08610i
$207$	18.0000	−	31.1769i	1.25109	−	2.16695i
$208$	−1.00000			−0.0693375
$209$	−2.00000	−	3.46410i	−0.138343	−	0.239617i
$210$		0			0
$211$	−2.00000			−0.137686			−0.0688428	−	0.997628i	$-0.521931\pi$
$211$	−2.00000			−0.137686			−0.0688428	+	0.997628i	$0.521931\pi$
$212$	−11.0000			−0.755483
$213$		0			0
$214$	17.0000			1.16210
$215$	3.50000	+	6.06218i	0.238698	+	0.413437i
$216$	9.00000			0.612372
$217$		0			0
$218$	−9.00000	−	15.5885i	−0.609557	−	1.05578i
$219$	−3.00000	−	5.19615i	−0.202721	−	0.351123i
$220$	1.00000	−	1.73205i	0.0674200	−	0.116775i
$221$	2.00000			0.134535
$222$	−16.5000	−	7.79423i	−1.10741	−	0.523114i
$223$	2.00000			0.133930			0.0669650	−	0.997755i	$-0.478668\pi$
$223$	2.00000			0.133930			0.0669650	+	0.997755i	$0.478668\pi$
$224$		0			0
$225$	−3.00000	−	5.19615i	−0.200000	−	0.346410i
$226$	10.0000	+	17.3205i	0.665190	+	1.15214i
$227$	12.5000	+	21.6506i	0.829654	+	1.43700i	0.898310	+	0.439363i	$0.144796\pi$
$227$	12.5000	+	21.6506i	0.829654	+	1.43700i	−0.0686556	+	0.997640i	$0.521871\pi$
$228$	−6.00000			−0.397360
$229$	6.00000	+	10.3923i	0.396491	+	0.686743i	0.993290	−	0.115648i	$-0.0368944\pi$
$229$	6.00000	+	10.3923i	0.396491	+	0.686743i	−0.596799	+	0.802391i	$0.703561\pi$
$230$	−6.00000			−0.395628
$231$		0			0
$232$	−6.00000			−0.393919
$233$	−16.0000			−1.04819			−0.524097	−	0.851658i	$-0.675597\pi$
$233$	−16.0000			−1.04819			−0.524097	+	0.851658i	$0.675597\pi$
$234$	−3.00000	+	5.19615i	−0.196116	+	0.339683i
$235$	−4.00000	−	6.92820i	−0.260931	−	0.451946i
$236$	−2.00000			−0.130189
$237$	−6.00000	+	10.3923i	−0.389742	+	0.675053i
$238$		0			0
$239$	−12.0000	+	20.7846i	−0.776215	+	1.34444i	0.157893	+	0.987456i	$0.449530\pi$
$239$	−12.0000	+	20.7846i	−0.776215	+	1.34444i	−0.934109	+	0.356988i	$0.883804\pi$
$240$	−1.50000	−	2.59808i	−0.0968246	−	0.167705i
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	0.980917	−	0.194429i	$-0.0622852\pi$
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	−0.658838	+	0.752285i	$0.728952\pi$
$242$	−3.50000	+	6.06218i	−0.224989	+	0.389692i
$243$		0			0
$244$	−5.00000	+	8.66025i	−0.320092	+	0.554416i
$245$	7.00000			0.447214
$246$	−4.50000	−	7.79423i	−0.286910	−	0.496942i
$247$	1.00000	−	1.73205i	0.0636285	−	0.110208i
$248$	−5.00000			−0.317500
$249$	−36.0000			−2.28141
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	−10.0000			−0.631194			−0.315597	−	0.948893i	$-0.602205\pi$
$251$	−10.0000			−0.631194			−0.315597	+	0.948893i	$0.602205\pi$
$252$		0			0
$253$	−12.0000			−0.754434
$254$	−2.00000	−	3.46410i	−0.125491	−	0.217357i
$255$	3.00000	+	5.19615i	0.187867	+	0.325396i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	8.00000	−	13.8564i	0.499026	−	0.864339i	−0.500973	−	0.865463i	$-0.667024\pi$
$257$	8.00000	−	13.8564i	0.499026	−	0.864339i	0.999999	+	0.00112398i	$0.000357774\pi$
$258$	21.0000			1.30740
$259$		0			0
$260$	1.00000			0.0620174
$261$	−18.0000	+	31.1769i	−1.11417	+	1.92980i
$262$	−3.00000	−	5.19615i	−0.185341	−	0.321019i
$263$	−8.00000	−	13.8564i	−0.493301	−	0.854423i	0.506669	−	0.862141i	$-0.330877\pi$
$263$	−8.00000	−	13.8564i	−0.493301	−	0.854423i	−0.999970	+	0.00771799i	$0.997543\pi$
$264$	−3.00000	−	5.19615i	−0.184637	−	0.319801i
$265$	11.0000			0.675725
$266$		0			0
$267$	−6.00000			−0.367194
$268$	−2.00000	+	3.46410i	−0.122169	+	0.211604i
$269$	2.00000			0.121942			0.0609711	−	0.998140i	$-0.480580\pi$
$269$	2.00000			0.121942			0.0609711	+	0.998140i	$0.480580\pi$
$270$	−9.00000			−0.547723
$271$	−0.500000	+	0.866025i	−0.0303728	+	0.0526073i	−0.880812	−	0.473466i	$-0.843003\pi$
$271$	−0.500000	+	0.866025i	−0.0303728	+	0.0526073i	0.850439	+	0.526073i	$0.176336\pi$
$272$	1.00000	+	1.73205i	0.0606339	+	0.105021i
$273$		0			0
$274$	−3.00000	+	5.19615i	−0.181237	+	0.313911i
$275$	−1.00000	+	1.73205i	−0.0603023	+	0.104447i
$276$	−9.00000	+	15.5885i	−0.541736	+	0.938315i
$277$	−14.5000	−	25.1147i	−0.871221	−	1.50900i	−0.860735	−	0.509053i	$-0.829996\pi$
$277$	−14.5000	−	25.1147i	−0.871221	−	1.50900i	−0.0104855	−	0.999945i	$-0.503338\pi$
$278$	7.00000	+	12.1244i	0.419832	+	0.727171i
$279$	−15.0000	+	25.9808i	−0.898027	+	1.55543i
$280$		0			0
$281$	9.50000	−	16.4545i	0.566722	−	0.981592i	−0.430165	−	0.902750i	$-0.641545\pi$
$281$	9.50000	−	16.4545i	0.566722	−	0.981592i	0.996887	−	0.0788417i	$-0.0251222\pi$
$282$	−24.0000			−1.42918
$283$	5.50000	+	9.52628i	0.326941	+	0.566279i	0.981903	−	0.189383i	$-0.0606488\pi$
$283$	5.50000	+	9.52628i	0.326941	+	0.566279i	−0.654962	+	0.755662i	$0.727315\pi$
$284$		0			0
$285$	6.00000			0.355409
$286$	2.00000			0.118262
$287$		0			0
$288$	−6.00000			−0.353553
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	6.00000			0.352332
$291$	27.0000	+	46.7654i	1.58277	+	2.74143i
$292$	1.00000	+	1.73205i	0.0585206	+	0.101361i
$293$	−13.5000	−	23.3827i	−0.788678	−	1.36603i	−0.926777	−	0.375613i	$-0.877432\pi$
$293$	−13.5000	−	23.3827i	−0.788678	−	1.36603i	0.138098	−	0.990419i	$-0.455901\pi$
$294$	10.5000	−	18.1865i	0.612372	−	1.06066i
$295$	2.00000			0.116445
$296$	5.50000	+	2.59808i	0.319681	+	0.151010i
$297$	−18.0000			−1.04447
$298$	−2.00000	+	3.46410i	−0.115857	+	0.200670i
$299$	−3.00000	−	5.19615i	−0.173494	−	0.300501i
$300$	1.50000	+	2.59808i	0.0866025	+	0.150000i
$301$		0			0
$302$	9.00000			0.517892
$303$	−27.0000	−	46.7654i	−1.55111	−	2.68660i
$304$	2.00000			0.114708
$305$	5.00000	−	8.66025i	0.286299	−	0.495885i
$306$	12.0000			0.685994
$307$	−23.0000			−1.31268			−0.656340	−	0.754466i	$-0.727896\pi$
$307$	−23.0000			−1.31268			−0.656340	+	0.754466i	$0.727896\pi$
$308$		0			0
$309$	−27.0000	−	46.7654i	−1.53598	−	2.66039i
$310$	5.00000			0.283981
$311$	−1.50000	+	2.59808i	−0.0850572	+	0.147323i	−0.905416	−	0.424526i	$-0.860441\pi$
$311$	−1.50000	+	2.59808i	−0.0850572	+	0.147323i	0.820358	+	0.571850i	$0.193774\pi$
$312$	1.50000	−	2.59808i	0.0849208	−	0.147087i
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	−0.993186	−	0.116543i	$-0.962819\pi$
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	0.597522	+	0.801852i	$0.296152\pi$
$314$	1.50000	+	2.59808i	0.0846499	+	0.146618i
$315$		0			0
$316$	2.00000	−	3.46410i	0.112509	−	0.194871i
$317$	−8.50000	+	14.7224i	−0.477408	+	0.826894i	−0.999665	−	0.0258939i	$-0.991757\pi$
$317$	−8.50000	+	14.7224i	−0.477408	+	0.826894i	0.522257	+	0.852788i	$0.325090\pi$
$318$	16.5000	−	28.5788i	0.925274	−	1.60262i
$319$	12.0000			0.671871
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	−25.5000	+	44.1673i	−1.42327	+	2.46518i
$322$		0			0
$323$	−4.00000			−0.222566
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	−1.00000			−0.0554700
$326$	−0.500000	−	0.866025i	−0.0276924	−	0.0479647i
$327$	54.0000			2.98621
$328$	1.50000	+	2.59808i	0.0828236	+	0.143455i
$329$		0			0
$330$	3.00000	+	5.19615i	0.165145	+	0.286039i
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	0.448649	+	0.893708i	$0.351905\pi$
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	−0.998298	+	0.0583130i	$0.981428\pi$
$332$	12.0000			0.658586
$333$	30.0000	−	20.7846i	1.64399	−	1.13899i
$334$	10.0000			0.547176
$335$	2.00000	−	3.46410i	0.109272	−	0.189264i
$336$		0			0
$337$	−5.00000	−	8.66025i	−0.272367	−	0.471754i	0.697100	−	0.716974i	$-0.254473\pi$
$337$	−5.00000	−	8.66025i	−0.272367	−	0.471754i	−0.969468	+	0.245220i	$0.921140\pi$
$338$	−6.00000	−	10.3923i	−0.326357	−	0.565267i
$339$	−60.0000			−3.25875
$340$	−1.00000	−	1.73205i	−0.0542326	−	0.0939336i
$341$	10.0000			0.541530
$342$	6.00000	−	10.3923i	0.324443	−	0.561951i
$343$		0			0
$344$	−7.00000			−0.377415
$345$	9.00000	−	15.5885i	0.484544	−	0.839254i
$346$	11.0000	+	19.0526i	0.591364	+	1.02427i
$347$	4.00000			0.214731			0.107366	−	0.994220i	$-0.465758\pi$
$347$	4.00000			0.214731			0.107366	+	0.994220i	$0.465758\pi$
$348$	9.00000	−	15.5885i	0.482451	−	0.835629i
$349$	3.00000	−	5.19615i	0.160586	−	0.278144i	−0.774493	−	0.632583i	$-0.781995\pi$
$349$	3.00000	−	5.19615i	0.160586	−	0.278144i	0.935079	+	0.354439i	$0.115328\pi$
$350$		0			0
$351$	−4.50000	−	7.79423i	−0.240192	−	0.416025i
$352$	1.00000	+	1.73205i	0.0533002	+	0.0923186i
$353$	−12.0000	+	20.7846i	−0.638696	+	1.10625i	0.347024	+	0.937856i	$0.387192\pi$
$353$	−12.0000	+	20.7846i	−0.638696	+	1.10625i	−0.985719	+	0.168397i	$0.946141\pi$
$354$	3.00000	−	5.19615i	0.159448	−	0.276172i
$355$		0			0
$356$	2.00000			0.106000
$357$		0			0
$358$	2.00000	−	3.46410i	0.105703	−	0.183083i
$359$	21.0000			1.10834			0.554169	−	0.832404i	$-0.313036\pi$
$359$	21.0000			1.10834			0.554169	+	0.832404i	$0.313036\pi$
$360$	6.00000			0.316228
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	−16.0000			−0.840941
$363$	−10.5000	−	18.1865i	−0.551107	−	0.954545i
$364$		0			0
$365$	−1.00000	−	1.73205i	−0.0523424	−	0.0906597i
$366$	−15.0000	−	25.9808i	−0.784063	−	1.35804i
$367$	−13.0000	−	22.5167i	−0.678594	−	1.17536i	−0.975404	−	0.220423i	$-0.929256\pi$
$367$	−13.0000	−	22.5167i	−0.678594	−	1.17536i	0.296810	−	0.954937i	$-0.404077\pi$
$368$	3.00000	−	5.19615i	0.156386	−	0.270868i
$369$	18.0000			0.937043
$370$	−5.50000	−	2.59808i	−0.285931	−	0.135068i
$371$		0			0
$372$	7.50000	−	12.9904i	0.388857	−	0.673520i
$373$	8.50000	+	14.7224i	0.440113	+	0.762299i	0.997697	−	0.0678218i	$-0.0216049\pi$
$373$	8.50000	+	14.7224i	0.440113	+	0.762299i	−0.557584	+	0.830120i	$0.688272\pi$
$374$	−2.00000	−	3.46410i	−0.103418	−	0.179124i
$375$	−1.50000	−	2.59808i	−0.0774597	−	0.134164i
$376$	8.00000			0.412568
$377$	3.00000	+	5.19615i	0.154508	+	0.267615i
$378$		0			0
$379$	5.00000	−	8.66025i	0.256833	−	0.444847i	−0.708559	−	0.705652i	$-0.750654\pi$
$379$	5.00000	−	8.66025i	0.256833	−	0.444847i	0.965392	+	0.260804i	$0.0839877\pi$
$380$	−2.00000			−0.102598
$381$	12.0000			0.614779
$382$	−1.50000	+	2.59808i	−0.0767467	+	0.132929i
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	0.977613	−	0.210411i	$-0.0674801\pi$
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	−0.671027	+	0.741433i	$0.734147\pi$
$384$	3.00000			0.153093
$385$		0			0
$386$	13.0000	−	22.5167i	0.661683	−	1.14607i
$387$	−21.0000	+	36.3731i	−1.06749	+	1.84895i
$388$	−9.00000	−	15.5885i	−0.456906	−	0.791384i
$389$	−8.00000	−	13.8564i	−0.405616	−	0.702548i	0.588777	−	0.808296i	$-0.299610\pi$
$389$	−8.00000	−	13.8564i	−0.405616	−	0.702548i	−0.994393	+	0.105748i	$0.966276\pi$
$390$	−1.50000	+	2.59808i	−0.0759555	+	0.131559i
$391$	−6.00000	+	10.3923i	−0.303433	+	0.525561i
$392$	−3.50000	+	6.06218i	−0.176777	+	0.306186i
$393$	18.0000			0.907980
$394$	5.50000	+	9.52628i	0.277086	+	0.479927i
$395$	−2.00000	+	3.46410i	−0.100631	+	0.174298i
$396$	12.0000			0.603023
$397$	25.0000			1.25471			0.627357	−	0.778732i	$-0.284137\pi$
$397$	25.0000			1.25471			0.627357	+	0.778732i	$0.284137\pi$
$398$	12.5000	−	21.6506i	0.626568	−	1.08525i
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	2.00000			0.0998752			0.0499376	−	0.998752i	$-0.484098\pi$
$401$	2.00000			0.0998752			0.0499376	+	0.998752i	$0.484098\pi$
$402$	−6.00000	−	10.3923i	−0.299253	−	0.518321i
$403$	2.50000	+	4.33013i	0.124534	+	0.215699i
$404$	9.00000	+	15.5885i	0.447767	+	0.775555i
$405$	4.50000	−	7.79423i	0.223607	−	0.387298i
$406$		0			0
$407$	−11.0000	−	5.19615i	−0.545250	−	0.257564i
$408$	−6.00000			−0.297044
$409$	−14.5000	+	25.1147i	−0.716979	+	1.24184i	0.245212	+	0.969469i	$0.421142\pi$
$409$	−14.5000	+	25.1147i	−0.716979	+	1.24184i	−0.962191	+	0.272374i	$0.912191\pi$
$410$	−1.50000	−	2.59808i	−0.0740797	−	0.128310i
$411$	−9.00000	−	15.5885i	−0.443937	−	0.768922i
$412$	9.00000	+	15.5885i	0.443398	+	0.767988i
$413$		0			0
$414$	−18.0000	−	31.1769i	−0.884652	−	1.53226i
$415$	−12.0000			−0.589057
$416$	−0.500000	+	0.866025i	−0.0245145	+	0.0424604i
$417$	−42.0000			−2.05675
$418$	−4.00000			−0.195646
$419$	7.00000	−	12.1244i	0.341972	−	0.592314i	−0.642827	−	0.766012i	$-0.722238\pi$
$419$	7.00000	−	12.1244i	0.341972	−	0.592314i	0.984799	+	0.173698i	$0.0555717\pi$
$420$		0			0
$421$		0			0			−	1.00000i	$-0.5\pi$
$421$		0			0				1.00000i	$0.5\pi$
$422$	−1.00000	+	1.73205i	−0.0486792	+	0.0843149i
$423$	24.0000	−	41.5692i	1.16692	−	2.02116i
$424$	−5.50000	+	9.52628i	−0.267104	+	0.462637i
$425$	1.00000	+	1.73205i	0.0485071	+	0.0840168i
$426$		0			0
$427$		0			0
$428$	8.50000	−	14.7224i	0.410863	−	0.711636i
$429$	−3.00000	+	5.19615i	−0.144841	+	0.250873i
$430$	7.00000			0.337570
$431$	−6.50000	−	11.2583i	−0.313094	−	0.542295i	0.665937	−	0.746008i	$-0.268032\pi$
$431$	−6.50000	−	11.2583i	−0.313094	−	0.542295i	−0.979030	+	0.203714i	$0.934699\pi$
$432$	4.50000	−	7.79423i	0.216506	−	0.375000i
$433$	16.0000			0.768911			0.384455	−	0.923144i	$-0.374389\pi$
$433$	16.0000			0.768911			0.384455	+	0.923144i	$0.374389\pi$
$434$		0			0
$435$	−9.00000	+	15.5885i	−0.431517	+	0.747409i
$436$	−18.0000			−0.862044
$437$	6.00000	+	10.3923i	0.287019	+	0.497131i
$438$	−6.00000			−0.286691
$439$	−3.50000	−	6.06218i	−0.167046	−	0.289332i	0.770334	−	0.637641i	$-0.220089\pi$
$439$	−3.50000	−	6.06218i	−0.167046	−	0.289332i	−0.937380	+	0.348309i	$0.886756\pi$
$440$	−1.00000	−	1.73205i	−0.0476731	−	0.0825723i
$441$	21.0000	+	36.3731i	1.00000	+	1.73205i
$442$	1.00000	−	1.73205i	0.0475651	−	0.0823853i
$443$	−21.0000			−0.997740			−0.498870	−	0.866677i	$-0.666252\pi$
$443$	−21.0000			−0.997740			−0.498870	+	0.866677i	$0.666252\pi$
$444$	−15.0000	+	10.3923i	−0.711868	+	0.493197i
$445$	−2.00000			−0.0948091
$446$	1.00000	−	1.73205i	0.0473514	−	0.0820150i
$447$	−6.00000	−	10.3923i	−0.283790	−	0.491539i
$448$		0			0
$449$	−10.5000	−	18.1865i	−0.495526	−	0.858276i	0.504461	−	0.863434i	$-0.331691\pi$
$449$	−10.5000	−	18.1865i	−0.495526	−	0.858276i	−0.999987	+	0.00515887i	$0.998358\pi$
$450$	−6.00000			−0.282843
$451$	−3.00000	−	5.19615i	−0.141264	−	0.244677i
$452$	20.0000			0.940721
$453$	−13.5000	+	23.3827i	−0.634285	+	1.09861i
$454$	25.0000			1.17331
$455$		0			0
$456$	−3.00000	+	5.19615i	−0.140488	+	0.243332i
$457$	−6.00000	−	10.3923i	−0.280668	−	0.486132i	0.690881	−	0.722968i	$-0.257223\pi$
$457$	−6.00000	−	10.3923i	−0.280668	−	0.486132i	−0.971549	+	0.236837i	$0.923889\pi$
$458$	12.0000			0.560723
$459$	−9.00000	+	15.5885i	−0.420084	+	0.727607i
$460$	−3.00000	+	5.19615i	−0.139876	+	0.242272i
$461$	7.00000	−	12.1244i	0.326023	−	0.564688i	−0.655696	−	0.755025i	$-0.727625\pi$
$461$	7.00000	−	12.1244i	0.326023	−	0.564688i	0.981719	+	0.190337i	$0.0609581\pi$
$462$		0			0
$463$	−10.0000	−	17.3205i	−0.464739	−	0.804952i	0.534450	−	0.845200i	$-0.320519\pi$
$463$	−10.0000	−	17.3205i	−0.464739	−	0.804952i	−0.999190	+	0.0402476i	$0.987185\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$	−7.50000	+	12.9904i	−0.347804	+	0.602414i
$466$	−8.00000	+	13.8564i	−0.370593	+	0.641886i
$467$	−23.0000			−1.06431			−0.532157	−	0.846646i	$-0.678618\pi$
$467$	−23.0000			−1.06431			−0.532157	+	0.846646i	$0.678618\pi$
$468$	3.00000	+	5.19615i	0.138675	+	0.240192i
$469$		0			0
$470$	−8.00000			−0.369012
$471$	−9.00000			−0.414698
$472$	−1.00000	+	1.73205i	−0.0460287	+	0.0797241i
$473$	14.0000			0.643721
$474$	6.00000	+	10.3923i	0.275589	+	0.477334i
$475$	2.00000			0.0917663
$476$		0			0
$477$	33.0000	+	57.1577i	1.51097	+	2.61707i
$478$	12.0000	+	20.7846i	0.548867	+	0.950666i
$479$	−3.50000	+	6.06218i	−0.159919	+	0.276988i	−0.934839	−	0.355071i	$-0.884457\pi$
$479$	−3.50000	+	6.06218i	−0.159919	+	0.276988i	0.774920	+	0.632059i	$0.217790\pi$
$480$	−3.00000			−0.136931
$481$	−0.500000	−	6.06218i	−0.0227980	−	0.276412i
$482$	10.0000			0.455488
$483$		0			0
$484$	3.50000	+	6.06218i	0.159091	+	0.275554i
$485$	9.00000	+	15.5885i	0.408669	+	0.707835i
$486$		0			0
$487$	−22.0000			−0.996915			−0.498458	−	0.866914i	$-0.666100\pi$
$487$	−22.0000			−0.996915			−0.498458	+	0.866914i	$0.666100\pi$
$488$	5.00000	+	8.66025i	0.226339	+	0.392031i
$489$	3.00000			0.135665
$490$	3.50000	−	6.06218i	0.158114	−	0.273861i
$491$	2.00000			0.0902587			0.0451294	−	0.998981i	$-0.485630\pi$
$491$	2.00000			0.0902587			0.0451294	+	0.998981i	$0.485630\pi$
$492$	−9.00000			−0.405751
$493$	6.00000	−	10.3923i	0.270226	−	0.468046i
$494$	−1.00000	−	1.73205i	−0.0449921	−	0.0779287i
$495$	−12.0000			−0.539360
$496$	−2.50000	+	4.33013i	−0.112253	+	0.194428i
$497$		0			0
$498$	−18.0000	+	31.1769i	−0.806599	+	1.39707i
$499$	10.0000	+	17.3205i	0.447661	+	0.775372i	0.998233	−	0.0594153i	$-0.0189236\pi$
$499$	10.0000	+	17.3205i	0.447661	+	0.775372i	−0.550572	+	0.834788i	$0.685590\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	−15.0000	+	25.9808i	−0.670151	+	1.16073i
$502$	−5.00000	+	8.66025i	−0.223161	+	0.386526i
$503$	−12.0000	+	20.7846i	−0.535054	+	0.926740i	0.464107	+	0.885779i	$0.346375\pi$
$503$	−12.0000	+	20.7846i	−0.535054	+	0.926740i	−0.999161	+	0.0409609i	$0.986958\pi$
$504$		0			0
$505$	−9.00000	−	15.5885i	−0.400495	−	0.693677i
$506$	−6.00000	+	10.3923i	−0.266733	+	0.461994i
$507$	36.0000			1.59882
$508$	−4.00000			−0.177471
$509$	12.0000	−	20.7846i	0.531891	−	0.921262i	−0.467416	−	0.884037i	$-0.654815\pi$
$509$	12.0000	−	20.7846i	0.531891	−	0.921262i	0.999307	−	0.0372243i	$-0.0118516\pi$
$510$	6.00000			0.265684
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	9.00000	+	15.5885i	0.397360	+	0.688247i
$514$	−8.00000	−	13.8564i	−0.352865	−	0.611180i
$515$	−9.00000	−	15.5885i	−0.396587	−	0.686909i
$516$	10.5000	−	18.1865i	0.462237	−	0.800617i
$517$	−16.0000			−0.703679
$518$		0			0
$519$	−66.0000			−2.89708
$520$	0.500000	−	0.866025i	0.0219265	−	0.0379777i
$521$	−12.5000	−	21.6506i	−0.547635	−	0.948532i	−0.998436	−	0.0559071i	$-0.982195\pi$
$521$	−12.5000	−	21.6506i	−0.547635	−	0.948532i	0.450801	−	0.892624i	$-0.351138\pi$
$522$	18.0000	+	31.1769i	0.787839	+	1.36458i
$523$	4.50000	+	7.79423i	0.196771	+	0.340818i	0.947480	−	0.319816i	$-0.103621\pi$
$523$	4.50000	+	7.79423i	0.196771	+	0.340818i	−0.750708	+	0.660634i	$0.770288\pi$
$524$	−6.00000			−0.262111
$525$		0			0
$526$	−16.0000			−0.697633
$527$	5.00000	−	8.66025i	0.217803	−	0.377247i
$528$	−6.00000			−0.261116
$529$	13.0000			0.565217
$530$	5.50000	−	9.52628i	0.238905	−	0.413795i
$531$	6.00000	+	10.3923i	0.260378	+	0.450988i
$532$		0			0
$533$	1.50000	−	2.59808i	0.0649722	−	0.112535i
$534$	−3.00000	+	5.19615i	−0.129823	+	0.224860i
$535$	−8.50000	+	14.7224i	−0.367487	+	0.636506i
$536$	2.00000	+	3.46410i	0.0863868	+	0.149626i
$537$	6.00000	+	10.3923i	0.258919	+	0.448461i
$538$	1.00000	−	1.73205i	0.0431131	−	0.0746740i
$539$	7.00000	−	12.1244i	0.301511	−	0.522233i
$540$	−4.50000	+	7.79423i	−0.193649	+	0.335410i
$541$	6.00000			0.257960			0.128980	−	0.991647i	$-0.458830\pi$
$541$	6.00000			0.257960			0.128980	+	0.991647i	$0.458830\pi$
$542$	0.500000	+	0.866025i	0.0214768	+	0.0371990i
$543$	24.0000	−	41.5692i	1.02994	−	1.78391i
$544$	2.00000			0.0857493
$545$	18.0000			0.771035
$546$		0			0
$547$	−11.0000			−0.470326			−0.235163	−	0.971956i	$-0.575562\pi$
$547$	−11.0000			−0.470326			−0.235163	+	0.971956i	$0.575562\pi$
$548$	3.00000	+	5.19615i	0.128154	+	0.221969i
$549$	60.0000			2.56074
$550$	1.00000	+	1.73205i	0.0426401	+	0.0738549i
$551$	−6.00000	−	10.3923i	−0.255609	−	0.442727i
$552$	9.00000	+	15.5885i	0.383065	+	0.663489i
$553$		0			0
$554$	−29.0000			−1.23209
$555$	15.0000	−	10.3923i	0.636715	−	0.441129i
$556$	14.0000			0.593732
$557$	12.5000	−	21.6506i	0.529642	−	0.917367i	−0.469760	−	0.882794i	$-0.655660\pi$
$557$	12.5000	−	21.6506i	0.529642	−	0.917367i	0.999402	−	0.0345728i	$-0.0110071\pi$
$558$	15.0000	+	25.9808i	0.635001	+	1.09985i
$559$	3.50000	+	6.06218i	0.148034	+	0.256403i
$560$		0			0
$561$	12.0000			0.506640
$562$	−9.50000	−	16.4545i	−0.400733	−	0.694090i
$563$		0			0			−	1.00000i	$-0.5\pi$
$563$		0			0				1.00000i	$0.5\pi$
$564$	−12.0000	+	20.7846i	−0.505291	+	0.875190i
$565$	−20.0000			−0.841406
$566$	11.0000			0.462364
$567$		0			0
$568$		0			0
$569$	21.0000			0.880366			0.440183	−	0.897908i	$-0.354914\pi$
$569$	21.0000			0.880366			0.440183	+	0.897908i	$0.354914\pi$
$570$	3.00000	−	5.19615i	0.125656	−	0.217643i
$571$	6.00000	−	10.3923i	0.251092	−	0.434904i	−0.712735	−	0.701434i	$-0.752544\pi$
$571$	6.00000	−	10.3923i	0.251092	−	0.434904i	0.963827	+	0.266529i	$0.0858769\pi$
$572$	1.00000	−	1.73205i	0.0418121	−	0.0724207i
$573$	−4.50000	−	7.79423i	−0.187990	−	0.325609i
$574$		0			0
$575$	3.00000	−	5.19615i	0.125109	−	0.216695i
$576$	−3.00000	+	5.19615i	−0.125000	+	0.216506i
$577$	16.0000	−	27.7128i	0.666089	−	1.15370i	−0.312900	−	0.949786i	$-0.601301\pi$
$577$	16.0000	−	27.7128i	0.666089	−	1.15370i	0.978989	−	0.203913i	$-0.0653661\pi$
$578$	13.0000			0.540729
$579$	39.0000	+	67.5500i	1.62078	+	2.80728i
$580$	3.00000	−	5.19615i	0.124568	−	0.215758i
$581$		0			0
$582$	54.0000			2.23837
$583$	11.0000	−	19.0526i	0.455573	−	0.789076i
$584$	2.00000			0.0827606
$585$	−3.00000	−	5.19615i	−0.124035	−	0.214834i
$586$	−27.0000			−1.11536
$587$	7.50000	+	12.9904i	0.309558	+	0.536170i	0.978266	−	0.207355i	$-0.0664855\pi$
$587$	7.50000	+	12.9904i	0.309558	+	0.536170i	−0.668708	+	0.743525i	$0.733152\pi$
$588$	−10.5000	−	18.1865i	−0.433013	−	0.750000i
$589$	−5.00000	−	8.66025i	−0.206021	−	0.356840i
$590$	1.00000	−	1.73205i	0.0411693	−	0.0713074i
$591$	−33.0000			−1.35744
$592$	5.00000	−	3.46410i	0.205499	−	0.142374i
$593$	34.0000			1.39621			0.698106	−	0.715994i	$-0.254026\pi$
$593$	34.0000			1.39621			0.698106	+	0.715994i	$0.254026\pi$
$594$	−9.00000	+	15.5885i	−0.369274	+	0.639602i
$595$		0			0
$596$	2.00000	+	3.46410i	0.0819232	+	0.141895i
$597$	37.5000	+	64.9519i	1.53477	+	2.65830i
$598$	−6.00000			−0.245358
$599$	7.50000	+	12.9904i	0.306442	+	0.530773i	0.977581	−	0.210558i	$-0.0675282\pi$
$599$	7.50000	+	12.9904i	0.306442	+	0.530773i	−0.671140	+	0.741331i	$0.734195\pi$
$600$	3.00000			0.122474
$601$	17.5000	−	30.3109i	0.713840	−	1.23641i	−0.249565	−	0.968358i	$-0.580288\pi$
$601$	17.5000	−	30.3109i	0.713840	−	1.23641i	0.963405	−	0.268049i	$-0.0863789\pi$
$602$		0			0
$603$	24.0000			0.977356
$604$	4.50000	−	7.79423i	0.183102	−	0.317143i
$605$	−3.50000	−	6.06218i	−0.142295	−	0.246463i
$606$	−54.0000			−2.19360
$607$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$607$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$608$	1.00000	−	1.73205i	0.0405554	−	0.0702439i
$609$		0			0
$610$	−5.00000	−	8.66025i	−0.202444	−	0.350643i
$611$	−4.00000	−	6.92820i	−0.161823	−	0.280285i
$612$	6.00000	−	10.3923i	0.242536	−	0.420084i
$613$	−3.00000	+	5.19615i	−0.121169	+	0.209871i	−0.920229	−	0.391381i	$-0.871998\pi$
$613$	−3.00000	+	5.19615i	−0.121169	+	0.209871i	0.799060	+	0.601251i	$0.205331\pi$
$614$	−11.5000	+	19.9186i	−0.464102	+	0.803849i
$615$	9.00000			0.362915
$616$		0			0
$617$	3.00000	−	5.19615i	0.120775	−	0.209189i	−0.799298	−	0.600935i	$-0.794795\pi$
$617$	3.00000	−	5.19615i	0.120775	−	0.209189i	0.920074	+	0.391745i	$0.128129\pi$
$618$	−54.0000			−2.17220
$619$	−26.0000			−1.04503			−0.522514	−	0.852631i	$-0.675006\pi$
$619$	−26.0000			−1.04503			−0.522514	+	0.852631i	$0.675006\pi$
$620$	2.50000	−	4.33013i	0.100402	−	0.173902i
$621$	54.0000			2.16695
$622$	1.50000	+	2.59808i	0.0601445	+	0.104173i
$623$		0			0
$624$	−1.50000	−	2.59808i	−0.0600481	−	0.104006i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	7.00000	+	12.1244i	0.279776	+	0.484587i
$627$	6.00000	−	10.3923i	0.239617	−	0.415029i
$628$	3.00000			0.119713
$629$	−10.0000	+	6.92820i	−0.398726	+	0.276246i
$630$		0			0
$631$	−7.50000	+	12.9904i	−0.298570	+	0.517139i	−0.975809	−	0.218624i	$-0.929843\pi$
$631$	−7.50000	+	12.9904i	−0.298570	+	0.517139i	0.677239	+	0.735763i	$0.263176\pi$
$632$	−2.00000	−	3.46410i	−0.0795557	−	0.137795i
$633$	−3.00000	−	5.19615i	−0.119239	−	0.206529i
$634$	8.50000	+	14.7224i	0.337578	+	0.584702i
$635$	4.00000			0.158735
$636$	−16.5000	−	28.5788i	−0.654268	−	1.13322i
$637$	7.00000			0.277350
$638$	6.00000	−	10.3923i	0.237542	−	0.411435i
$639$		0			0
$640$	1.00000			0.0395285
$641$	0.500000	−	0.866025i	0.0197488	−	0.0342059i	−0.855982	−	0.517005i	$-0.827047\pi$
$641$	0.500000	−	0.866025i	0.0197488	−	0.0342059i	0.875731	+	0.482800i	$0.160380\pi$
$642$	25.5000	+	44.1673i	1.00640	+	1.74314i
$643$	1.00000			0.0394362			0.0197181	−	0.999806i	$-0.493723\pi$
$643$	1.00000			0.0394362			0.0197181	+	0.999806i	$0.493723\pi$
$644$		0			0
$645$	−10.5000	+	18.1865i	−0.413437	+	0.716094i
$646$	−2.00000	+	3.46410i	−0.0786889	+	0.136293i
$647$	8.00000	+	13.8564i	0.314512	+	0.544752i	0.979334	−	0.202251i	$-0.0648256\pi$
$647$	8.00000	+	13.8564i	0.314512	+	0.544752i	−0.664821	+	0.747002i	$0.731492\pi$
$648$	4.50000	+	7.79423i	0.176777	+	0.306186i
$649$	2.00000	−	3.46410i	0.0785069	−	0.135978i
$650$	−0.500000	+	0.866025i	−0.0196116	+	0.0339683i
$651$		0			0
$652$	−1.00000			−0.0391630
$653$	2.50000	+	4.33013i	0.0978326	+	0.169451i	0.910787	−	0.412876i	$-0.135476\pi$
$653$	2.50000	+	4.33013i	0.0978326	+	0.169451i	−0.812955	+	0.582327i	$0.802142\pi$
$654$	27.0000	−	46.7654i	1.05578	−	1.82867i
$655$	6.00000			0.234439
$656$	3.00000			0.117130
$657$	6.00000	−	10.3923i	0.234082	−	0.405442i
$658$		0			0
$659$	20.0000	+	34.6410i	0.779089	+	1.34942i	0.932467	+	0.361255i	$0.117652\pi$
$659$	20.0000	+	34.6410i	0.779089	+	1.34942i	−0.153378	+	0.988168i	$0.549015\pi$
$660$	6.00000			0.233550
$661$	14.0000	+	24.2487i	0.544537	+	0.943166i	0.998636	+	0.0522143i	$0.0166279\pi$
$661$	14.0000	+	24.2487i	0.544537	+	0.943166i	−0.454099	+	0.890951i	$0.650039\pi$
$662$	10.0000	+	17.3205i	0.388661	+	0.673181i
$663$	3.00000	+	5.19615i	0.116510	+	0.201802i
$664$	6.00000	−	10.3923i	0.232845	−	0.403300i
$665$		0			0
$666$	−3.00000	−	36.3731i	−0.116248	−	1.40943i
$667$	−36.0000			−1.39393
$668$	5.00000	−	8.66025i	0.193456	−	0.335075i
$669$	3.00000	+	5.19615i	0.115987	+	0.200895i
$670$	−2.00000	−	3.46410i	−0.0772667	−	0.133830i
$671$	−10.0000	−	17.3205i	−0.386046	−	0.668651i
$672$		0			0
$673$	−14.0000	−	24.2487i	−0.539660	−	0.934719i	−0.998922	−	0.0464181i	$-0.985219\pi$
$673$	−14.0000	−	24.2487i	−0.539660	−	0.934719i	0.459262	−	0.888301i	$-0.348114\pi$
$674$	−10.0000			−0.385186
$675$	4.50000	−	7.79423i	0.173205	−	0.300000i
$676$	−12.0000			−0.461538
$677$	2.00000			0.0768662			0.0384331	−	0.999261i	$-0.487763\pi$
$677$	2.00000			0.0768662			0.0384331	+	0.999261i	$0.487763\pi$
$678$	−30.0000	+	51.9615i	−1.15214	+	1.99557i
$679$		0			0
$680$	−2.00000			−0.0766965
$681$	−37.5000	+	64.9519i	−1.43700	+	2.48896i
$682$	5.00000	−	8.66025i	0.191460	−	0.331618i
$683$	19.5000	−	33.7750i	0.746147	−	1.29236i	−0.203510	−	0.979073i	$-0.565235\pi$
$683$	19.5000	−	33.7750i	0.746147	−	1.29236i	0.949657	−	0.313291i	$-0.101432\pi$
$684$	−6.00000	−	10.3923i	−0.229416	−	0.397360i
$685$	−3.00000	−	5.19615i	−0.114624	−	0.198535i
$686$		0			0
$687$	−18.0000	+	31.1769i	−0.686743	+	1.18947i
$688$	−3.50000	+	6.06218i	−0.133436	+	0.231118i
$689$	11.0000			0.419067
$690$	−9.00000	−	15.5885i	−0.342624	−	0.593442i
$691$	10.0000	−	17.3205i	0.380418	−	0.658903i	−0.610704	−	0.791859i	$-0.709113\pi$
$691$	10.0000	−	17.3205i	0.380418	−	0.658903i	0.991122	+	0.132956i	$0.0424468\pi$
$692$	22.0000			0.836315
$693$		0			0
$694$	2.00000	−	3.46410i	0.0759190	−	0.131495i
$695$	−14.0000			−0.531050
$696$	−9.00000	−	15.5885i	−0.341144	−	0.590879i
$697$	−6.00000			−0.227266
$698$	−3.00000	−	5.19615i	−0.113552	−	0.196677i
$699$	−24.0000	−	41.5692i	−0.907763	−	1.57229i
$700$		0			0
$701$	11.0000	−	19.0526i	0.415464	−	0.719605i	−0.580013	−	0.814607i	$-0.696952\pi$
$701$	11.0000	−	19.0526i	0.415464	−	0.719605i	0.995477	+	0.0950021i	$0.0302858\pi$
$702$	−9.00000			−0.339683
$703$	1.00000	+	12.1244i	0.0377157	+	0.457279i
$704$	2.00000			0.0753778
$705$	12.0000	−	20.7846i	0.451946	−	0.782794i
$706$	12.0000	+	20.7846i	0.451626	+	0.782239i
$707$		0			0
$708$	−3.00000	−	5.19615i	−0.112747	−	0.195283i
$709$	24.0000			0.901339			0.450669	−	0.892691i	$-0.351185\pi$
$709$	24.0000			0.901339			0.450669	+	0.892691i	$0.351185\pi$
$710$		0			0
$711$	−24.0000			−0.900070
$712$	1.00000	−	1.73205i	0.0374766	−	0.0649113i
$713$	−30.0000			−1.12351
$714$		0			0
$715$	−1.00000	+	1.73205i	−0.0373979	+	0.0647750i
$716$	−2.00000	−	3.46410i	−0.0747435	−	0.129460i
$717$	−72.0000			−2.68889
$718$	10.5000	−	18.1865i	0.391857	−	0.678715i
$719$	18.5000	−	32.0429i	0.689934	−	1.19500i	−0.281925	−	0.959436i	$-0.590973\pi$
$719$	18.5000	−	32.0429i	0.689934	−	1.19500i	0.971859	−	0.235564i	$-0.0756936\pi$
$720$	3.00000	−	5.19615i	0.111803	−	0.193649i
$721$		0			0
$722$	−7.50000	−	12.9904i	−0.279121	−	0.483452i
$723$	−15.0000	+	25.9808i	−0.557856	+	0.966235i
$724$	−8.00000	+	13.8564i	−0.297318	+	0.514969i
$725$	−3.00000	+	5.19615i	−0.111417	+	0.192980i
$726$	−21.0000			−0.779383
$727$	−26.0000	−	45.0333i	−0.964287	−	1.67019i	−0.711520	−	0.702666i	$-0.751993\pi$
$727$	−26.0000	−	45.0333i	−0.964287	−	1.67019i	−0.252767	−	0.967527i	$-0.581341\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	−2.00000			−0.0740233
$731$	7.00000	−	12.1244i	0.258904	−	0.448435i
$732$	−30.0000			−1.10883
$733$	7.00000	+	12.1244i	0.258551	+	0.447823i	0.965854	−	0.259087i	$-0.0834217\pi$
$733$	7.00000	+	12.1244i	0.258551	+	0.447823i	−0.707303	+	0.706910i	$0.750088\pi$
$734$	−26.0000			−0.959678
$735$	10.5000	+	18.1865i	0.387298	+	0.670820i
$736$	−3.00000	−	5.19615i	−0.110581	−	0.191533i
$737$	−4.00000	−	6.92820i	−0.147342	−	0.255204i
$738$	9.00000	−	15.5885i	0.331295	−	0.573819i
$739$	−6.00000			−0.220714			−0.110357	−	0.993892i	$-0.535199\pi$
$739$	−6.00000			−0.220714			−0.110357	+	0.993892i	$0.535199\pi$
$740$	−5.00000	+	3.46410i	−0.183804	+	0.127343i
$741$	6.00000			0.220416
$742$		0			0
$743$	21.0000	+	36.3731i	0.770415	+	1.33440i	0.937336	+	0.348428i	$0.113284\pi$
$743$	21.0000	+	36.3731i	0.770415	+	1.33440i	−0.166920	+	0.985970i	$0.553382\pi$
$744$	−7.50000	−	12.9904i	−0.274963	−	0.476250i
$745$	−2.00000	−	3.46410i	−0.0732743	−	0.126915i
$746$	17.0000			0.622414
$747$	−36.0000	−	62.3538i	−1.31717	−	2.28141i
$748$	−4.00000			−0.146254
$749$		0			0
$750$	−3.00000			−0.109545
$751$	11.0000			0.401396			0.200698	−	0.979653i	$-0.435679\pi$
$751$	11.0000			0.401396			0.200698	+	0.979653i	$0.435679\pi$
$752$	4.00000	−	6.92820i	0.145865	−	0.252646i
$753$	−15.0000	−	25.9808i	−0.546630	−	0.946792i
$754$	6.00000			0.218507
$755$	−4.50000	+	7.79423i	−0.163772	+	0.283661i
$756$		0			0
$757$	23.5000	−	40.7032i	0.854122	−	1.47938i	−0.0233351	−	0.999728i	$-0.507428\pi$
$757$	23.5000	−	40.7032i	0.854122	−	1.47938i	0.877457	−	0.479655i	$-0.159238\pi$
$758$	−5.00000	−	8.66025i	−0.181608	−	0.314555i
$759$	−18.0000	−	31.1769i	−0.653359	−	1.13165i
$760$	−1.00000	+	1.73205i	−0.0362738	+	0.0628281i
$761$	−21.0000	+	36.3731i	−0.761249	+	1.31852i	0.180957	+	0.983491i	$0.442080\pi$
$761$	−21.0000	+	36.3731i	−0.761249	+	1.31852i	−0.942207	+	0.335032i	$0.891253\pi$
$762$	6.00000	−	10.3923i	0.217357	−	0.376473i
$763$		0			0
$764$	1.50000	+	2.59808i	0.0542681	+	0.0939951i
$765$	−6.00000	+	10.3923i	−0.216930	+	0.375735i
$766$	12.0000			0.433578
$767$	2.00000			0.0722158
$768$	1.50000	−	2.59808i	0.0541266	−	0.0937500i
$769$	30.0000			1.08183			0.540914	−	0.841078i	$-0.318079\pi$
$769$	30.0000			1.08183			0.540914	+	0.841078i	$0.318079\pi$
$770$		0			0
$771$	48.0000			1.72868
$772$	−13.0000	−	22.5167i	−0.467880	−	0.810392i
$773$	3.50000	+	6.06218i	0.125886	+	0.218041i	0.922079	−	0.387002i	$-0.126489\pi$
$773$	3.50000	+	6.06218i	0.125886	+	0.218041i	−0.796193	+	0.605043i	$0.793156\pi$
$774$	21.0000	+	36.3731i	0.754829	+	1.30740i
$775$	−2.50000	+	4.33013i	−0.0898027	+	0.155543i
$776$	−18.0000			−0.646162
$777$		0			0
$778$	−16.0000			−0.573628
$779$	−3.00000	+	5.19615i	−0.107486	+	0.186171i
$780$	1.50000	+	2.59808i	0.0537086	+	0.0930261i
$781$		0			0
$782$	6.00000	+	10.3923i	0.214560	+	0.371628i
$783$	−54.0000			−1.92980
$784$	3.50000	+	6.06218i	0.125000	+	0.216506i
$785$	−3.00000			−0.107075
$786$	9.00000	−	15.5885i	0.321019	−	0.556022i
$787$	−51.0000			−1.81795			−0.908977	−	0.416847i	$-0.863135\pi$
$787$	−51.0000			−1.81795			−0.908977	+	0.416847i	$0.863135\pi$
$788$	11.0000			0.391859
$789$	24.0000	−	41.5692i	0.854423	−	1.47990i
$790$	2.00000	+	3.46410i	0.0711568	+	0.123247i
$791$		0			0
$792$	6.00000	−	10.3923i	0.213201	−	0.369274i
$793$	5.00000	−	8.66025i	0.177555	−	0.307535i
$794$	12.5000	−	21.6506i	0.443608	−	0.768352i
$795$	16.5000	+	28.5788i	0.585195	+	1.01359i
$796$	−12.5000	−	21.6506i	−0.443051	−	0.767386i
$797$	−10.5000	+	18.1865i	−0.371929	+	0.644200i	−0.989862	−	0.142031i	$-0.954637\pi$
$797$	−10.5000	+	18.1865i	−0.371929	+	0.644200i	0.617933	+	0.786231i	$0.287970\pi$
$798$		0			0
$799$	−8.00000	+	13.8564i	−0.283020	+	0.490204i
$800$	−1.00000			−0.0353553
$801$	−6.00000	−	10.3923i	−0.212000	−	0.367194i
$802$	1.00000	−	1.73205i	0.0353112	−	0.0611608i
$803$	−4.00000			−0.141157
$804$	−12.0000			−0.423207
$805$		0			0
$806$	5.00000			0.176117
$807$	3.00000	+	5.19615i	0.105605	+	0.182913i
$808$	18.0000			0.633238
$809$	−5.50000	−	9.52628i	−0.193370	−	0.334926i	0.752995	−	0.658026i	$-0.228608\pi$
$809$	−5.50000	−	9.52628i	−0.193370	−	0.334926i	−0.946365	+	0.323100i	$0.895275\pi$
$810$	−4.50000	−	7.79423i	−0.158114	−	0.273861i
$811$	10.0000	+	17.3205i	0.351147	+	0.608205i	0.986451	−	0.164057i	$-0.0524582\pi$
$811$	10.0000	+	17.3205i	0.351147	+	0.608205i	−0.635303	+	0.772263i	$0.719125\pi$
$812$		0			0
$813$	−3.00000			−0.105215
$814$	−10.0000	+	6.92820i	−0.350500	+	0.242833i
$815$	1.00000			0.0350285
$816$	−3.00000	+	5.19615i	−0.105021	+	0.181902i
$817$	−7.00000	−	12.1244i	−0.244899	−	0.424178i
$818$	14.5000	+	25.1147i	0.506981	+	0.878116i
$819$		0			0
$820$	−3.00000			−0.104765
$821$	3.00000	+	5.19615i	0.104701	+	0.181347i	0.913616	−	0.406578i	$-0.133278\pi$
$821$	3.00000	+	5.19615i	0.104701	+	0.181347i	−0.808915	+	0.587925i	$0.799945\pi$
$822$	−18.0000			−0.627822
$823$	−28.0000	+	48.4974i	−0.976019	+	1.69051i	−0.299487	+	0.954100i	$0.596815\pi$
$823$	−28.0000	+	48.4974i	−0.976019	+	1.69051i	−0.676532	+	0.736413i	$0.736518\pi$
$824$	18.0000			0.627060
$825$	−6.00000			−0.208893
$826$		0			0
$827$	6.00000	+	10.3923i	0.208640	+	0.361376i	0.951286	−	0.308308i	$-0.0997628\pi$
$827$	6.00000	+	10.3923i	0.208640	+	0.361376i	−0.742646	+	0.669684i	$0.766429\pi$
$828$	−36.0000			−1.25109
$829$	−20.0000	+	34.6410i	−0.694629	+	1.20313i	0.275677	+	0.961250i	$0.411098\pi$
$829$	−20.0000	+	34.6410i	−0.694629	+	1.20313i	−0.970306	+	0.241882i	$0.922235\pi$
$830$	−6.00000	+	10.3923i	−0.208263	+	0.360722i
$831$	43.5000	−	75.3442i	1.50900	−	2.61366i
$832$	0.500000	+	0.866025i	0.0173344	+	0.0300240i
$833$	−7.00000	−	12.1244i	−0.242536	−	0.420084i
$834$	−21.0000	+	36.3731i	−0.727171	+	1.25950i
$835$	−5.00000	+	8.66025i	−0.173032	+	0.299700i
$836$	−2.00000	+	3.46410i	−0.0691714	+	0.119808i
$837$	−45.0000			−1.55543
$838$	−7.00000	−	12.1244i	−0.241811	−	0.418829i
$839$	19.5000	−	33.7750i	0.673215	−	1.16604i	−0.303773	−	0.952745i	$-0.598246\pi$
$839$	19.5000	−	33.7750i	0.673215	−	1.16604i	0.976987	−	0.213298i	$-0.0684204\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$	57.0000			1.96318
$844$	1.00000	+	1.73205i	0.0344214	+	0.0596196i
$845$	12.0000			0.412813
$846$	−24.0000	−	41.5692i	−0.825137	−	1.42918i
$847$		0			0
$848$	5.50000	+	9.52628i	0.188871	+	0.327134i
$849$	−16.5000	+	28.5788i	−0.566279	+	0.980823i
$850$	2.00000			0.0685994
$851$	33.0000	+	15.5885i	1.13123	+	0.534365i
$852$		0			0
$853$	−6.50000	+	11.2583i	−0.222556	+	0.385478i	−0.955583	−	0.294721i	$-0.904773\pi$
$853$	−6.50000	+	11.2583i	−0.222556	+	0.385478i	0.733028	+	0.680199i	$0.238107\pi$
$854$		0			0
$855$	6.00000	+	10.3923i	0.205196	+	0.355409i
$856$	−8.50000	−	14.7224i	−0.290524	−	0.503202i
$857$	30.0000			1.02478			0.512390	−	0.858753i	$-0.328760\pi$
$857$	30.0000			1.02478			0.512390	+	0.858753i	$0.328760\pi$
$858$	3.00000	+	5.19615i	0.102418	+	0.177394i
$859$	8.00000			0.272956			0.136478	−	0.990643i	$-0.456422\pi$
$859$	8.00000			0.272956			0.136478	+	0.990643i	$0.456422\pi$
$860$	3.50000	−	6.06218i	0.119349	−	0.206719i
$861$		0			0
$862$	−13.0000			−0.442782
$863$	18.0000	−	31.1769i	0.612727	−	1.06127i	−0.378052	−	0.925785i	$-0.623406\pi$
$863$	18.0000	−	31.1769i	0.612727	−	1.06127i	0.990779	−	0.135490i	$-0.0432609\pi$
$864$	−4.50000	−	7.79423i	−0.153093	−	0.265165i
$865$	−22.0000			−0.748022
$866$	8.00000	−	13.8564i	0.271851	−	0.470860i
$867$	−19.5000	+	33.7750i	−0.662255	+	1.14706i
$868$		0			0
$869$	4.00000	+	6.92820i	0.135691	+	0.235023i
$870$	9.00000	+	15.5885i	0.305129	+	0.528498i
$871$	2.00000	−	3.46410i	0.0677674	−	0.117377i
$872$	−9.00000	+	15.5885i	−0.304778	+	0.527892i
$873$	−54.0000	+	93.5307i	−1.82762	+	3.16554i
$874$	12.0000			0.405906
$875$		0			0
$876$	−3.00000	+	5.19615i	−0.101361	+	0.175562i
$877$	15.0000			0.506514			0.253257	−	0.967399i	$-0.418498\pi$
$877$	15.0000			0.506514			0.253257	+	0.967399i	$0.418498\pi$
$878$	−7.00000			−0.236239
$879$	40.5000	−	70.1481i	1.36603	−	2.36604i
$880$	−2.00000			−0.0674200
$881$	27.0000	+	46.7654i	0.909653	+	1.57557i	0.814546	+	0.580098i	$0.196986\pi$
$881$	27.0000	+	46.7654i	0.909653	+	1.57557i	0.0951067	+	0.995467i	$0.469681\pi$
$882$	42.0000			1.41421
$883$	9.50000	+	16.4545i	0.319700	+	0.553737i	0.980425	−	0.196891i	$-0.0630844\pi$
$883$	9.50000	+	16.4545i	0.319700	+	0.553737i	−0.660725	+	0.750628i	$0.729751\pi$
$884$	−1.00000	−	1.73205i	−0.0336336	−	0.0582552i
$885$	3.00000	+	5.19615i	0.100844	+	0.174667i
$886$	−10.5000	+	18.1865i	−0.352754	+	0.610989i
$887$	−34.0000			−1.14161			−0.570804	−	0.821086i	$-0.693368\pi$
$887$	−34.0000			−1.14161			−0.570804	+	0.821086i	$0.693368\pi$
$888$	1.50000	+	18.1865i	0.0503367	+	0.610300i
$889$		0			0
$890$	−1.00000	+	1.73205i	−0.0335201	+	0.0580585i
$891$	−9.00000	−	15.5885i	−0.301511	−	0.522233i
$892$	−1.00000	−	1.73205i	−0.0334825	−	0.0579934i
$893$	8.00000	+	13.8564i	0.267710	+	0.463687i
$894$	−12.0000			−0.401340
$895$	2.00000	+	3.46410i	0.0668526	+	0.115792i
$896$		0			0
$897$	9.00000	−	15.5885i	0.300501	−	0.520483i
$898$	−21.0000			−0.700779
$899$	30.0000			1.00056
$900$	−3.00000	+	5.19615i	−0.100000	+	0.173205i
$901$	−11.0000	−	19.0526i	−0.366463	−	0.634733i
$902$	−6.00000			−0.199778
$903$		0			0
$904$	10.0000	−	17.3205i	0.332595	−	0.576072i
$905$	8.00000	−	13.8564i	0.265929	−	0.460603i
$906$	13.5000	+	23.3827i	0.448507	+	0.776838i
$907$	−2.00000	−	3.46410i	−0.0664089	−	0.115024i	0.830909	−	0.556408i	$-0.187821\pi$
$907$	−2.00000	−	3.46410i	−0.0664089	−	0.115024i	−0.897318	+	0.441384i	$0.854488\pi$
$908$	12.5000	−	21.6506i	0.414827	−	0.718502i
$909$	54.0000	−	93.5307i	1.79107	−	3.10222i
$910$		0			0
$911$	57.0000			1.88849			0.944247	−	0.329238i	$-0.106792\pi$
$911$	57.0000			1.88849			0.944247	+	0.329238i	$0.106792\pi$
$912$	3.00000	+	5.19615i	0.0993399	+	0.172062i
$913$	−12.0000	+	20.7846i	−0.397142	+	0.687870i
$914$	−12.0000			−0.396925
$915$	30.0000			0.991769
$916$	6.00000	−	10.3923i	0.198246	−	0.343371i
$917$		0			0
$918$	9.00000	+	15.5885i	0.297044	+	0.514496i
$919$	−40.0000			−1.31948			−0.659739	−	0.751495i	$-0.729333\pi$
$919$	−40.0000			−1.31948			−0.659739	+	0.751495i	$0.729333\pi$
$920$	3.00000	+	5.19615i	0.0989071	+	0.171312i
$921$	−34.5000	−	59.7558i	−1.13681	−	1.96902i
$922$	−7.00000	−	12.1244i	−0.230533	−	0.399294i
$923$		0			0
$924$		0			0
$925$	5.00000	−	3.46410i	0.164399	−	0.113899i
$926$	−20.0000			−0.657241
$927$	54.0000	−	93.5307i	1.77359	−	3.07195i
$928$	3.00000	+	5.19615i	0.0984798	+	0.170572i
$929$	−10.5000	−	18.1865i	−0.344494	−	0.596681i	0.640768	−	0.767735i	$-0.278616\pi$
$929$	−10.5000	−	18.1865i	−0.344494	−	0.596681i	−0.985262	+	0.171054i	$0.945283\pi$
$930$	7.50000	+	12.9904i	0.245935	+	0.425971i
$931$	−14.0000			−0.458831
$932$	8.00000	+	13.8564i	0.262049	+	0.453882i
$933$	−9.00000			−0.294647
$934$	−11.5000	+	19.9186i	−0.376291	+	0.651756i
$935$	4.00000			0.130814
$936$	6.00000			0.196116
$937$	13.0000	−	22.5167i	0.424691	−	0.735587i	−0.571700	−	0.820463i	$-0.693716\pi$
$937$	13.0000	−	22.5167i	0.424691	−	0.735587i	0.996392	+	0.0848755i	$0.0270492\pi$
$938$		0			0
$939$	−42.0000			−1.37062
$940$	−4.00000	+	6.92820i	−0.130466	+	0.225973i
$941$	−15.0000	+	25.9808i	−0.488986	+	0.846949i	−0.999920	−	0.0126715i	$-0.995966\pi$
$941$	−15.0000	+	25.9808i	−0.488986	+	0.846949i	0.510934	+	0.859620i	$0.329300\pi$
$942$	−4.50000	+	7.79423i	−0.146618	+	0.253950i
$943$	9.00000	+	15.5885i	0.293080	+	0.507630i
$944$	1.00000	+	1.73205i	0.0325472	+	0.0563735i
$945$		0			0
$946$	7.00000	−	12.1244i	0.227590	−	0.394197i
$947$	30.5000	−	52.8275i	0.991117	−	1.71666i	0.380382	−	0.924829i	$-0.375792\pi$
$947$	30.5000	−	52.8275i	0.991117	−	1.71666i	0.610735	−	0.791835i	$-0.290874\pi$
$948$	12.0000			0.389742
$949$	−1.00000	−	1.73205i	−0.0324614	−	0.0562247i
$950$	1.00000	−	1.73205i	0.0324443	−	0.0561951i
$951$	−51.0000			−1.65379
$952$		0			0
$953$	−15.0000	+	25.9808i	−0.485898	+	0.841599i	−0.999869	−	0.0162081i	$-0.994841\pi$
$953$	−15.0000	+	25.9808i	−0.485898	+	0.841599i	0.513971	+	0.857808i	$0.328174\pi$
$954$	66.0000			2.13683
$955$	−1.50000	−	2.59808i	−0.0485389	−	0.0840718i
$956$	24.0000			0.776215
$957$	18.0000	+	31.1769i	0.581857	+	1.00781i
$958$	3.50000	+	6.06218i	0.113080	+	0.195860i
$959$		0			0
$960$	−1.50000	+	2.59808i	−0.0484123	+	0.0838525i
$961$	−6.00000			−0.193548
$962$	−5.50000	−	2.59808i	−0.177327	−	0.0837653i
$963$	−102.000			−3.28690
$964$	5.00000	−	8.66025i	0.161039	−	0.278928i
$965$	13.0000	+	22.5167i	0.418485	+	0.724837i
$966$		0			0
$967$	10.0000	+	17.3205i	0.321578	+	0.556990i	0.980814	−	0.194946i	$-0.0624533\pi$
$967$	10.0000	+	17.3205i	0.321578	+	0.556990i	−0.659236	+	0.751936i	$0.729120\pi$
$968$	7.00000			0.224989
$969$	−6.00000	−	10.3923i	−0.192748	−	0.333849i
$970$	18.0000			0.577945
$971$	3.00000	−	5.19615i	0.0962746	−	0.166752i	−0.813865	−	0.581054i	$-0.802641\pi$
$971$	3.00000	−	5.19615i	0.0962746	−	0.166752i	0.910140	+	0.414301i	$0.135974\pi$
$972$		0			0
$973$		0			0
$974$	−11.0000	+	19.0526i	−0.352463	+	0.610483i
$975$	−1.50000	−	2.59808i	−0.0480384	−	0.0832050i
$976$	10.0000			0.320092
$977$	31.0000	−	53.6936i	0.991778	−	1.71781i	0.385063	−	0.922890i	$-0.374180\pi$
$977$	31.0000	−	53.6936i	0.991778	−	1.71781i	0.606715	−	0.794919i	$-0.292487\pi$
$978$	1.50000	−	2.59808i	0.0479647	−	0.0830773i
$979$	−2.00000	+	3.46410i	−0.0639203	+	0.110713i
$980$	−3.50000	−	6.06218i	−0.111803	−	0.193649i
$981$	54.0000	+	93.5307i	1.72409	+	2.98621i
$982$	1.00000	−	1.73205i	0.0319113	−	0.0552720i
$983$	−3.00000	+	5.19615i	−0.0956851	+	0.165732i	−0.909894	−	0.414840i	$-0.863838\pi$
$983$	−3.00000	+	5.19615i	−0.0956851	+	0.165732i	0.814209	+	0.580572i	$0.197171\pi$
$984$	−4.50000	+	7.79423i	−0.143455	+	0.248471i
$985$	−11.0000			−0.350489
$986$	−6.00000	−	10.3923i	−0.191079	−	0.330958i
$987$		0			0
$988$	−2.00000			−0.0636285
$989$	−42.0000			−1.33552
$990$	−6.00000	+	10.3923i	−0.190693	+	0.330289i
$991$	17.0000			0.540023			0.270011	−	0.962857i	$-0.412973\pi$
$991$	17.0000			0.540023			0.270011	+	0.962857i	$0.412973\pi$
$992$	2.50000	+	4.33013i	0.0793751	+	0.137482i
$993$	−60.0000			−1.90404
$994$		0			0
$995$	12.5000	+	21.6506i	0.396277	+	0.686371i
$996$	18.0000	+	31.1769i	0.570352	+	0.987878i
$997$	−27.5000	+	47.6314i	−0.870934	+	1.50850i	−0.00990158	+	0.999951i	$0.503152\pi$
$997$	−27.5000	+	47.6314i	−0.870934	+	1.50850i	−0.861032	+	0.508551i	$0.830182\pi$
$998$	20.0000			0.633089
$999$	49.5000	+	23.3827i	1.56611	+	0.739795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.e.c.121.1	✓	2
37.26	even	3	inner	370.2.e.c.211.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.e.c.121.1	✓	2	1.1	even	1	trivial
370.2.e.c.211.1	yes	2	37.26	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.00000 q^{6} -1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.00000 q^{6} -1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +1.00000 q^{10} +2.00000 q^{11} +(1.50000 - 2.59808i) q^{12} +(0.500000 + 0.866025i) q^{13} +(-1.50000 + 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +(3.00000 + 5.19615i) q^{18} +(-1.00000 - 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{20} +(1.00000 - 1.73205i) q^{22} -6.00000 q^{23} +(-1.50000 - 2.59808i) q^{24} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{26} -9.00000 q^{27} +6.00000 q^{29} +(1.50000 + 2.59808i) q^{30} +5.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(3.00000 + 5.19615i) q^{33} +(-1.00000 - 1.73205i) q^{34} +6.00000 q^{36} +(-5.50000 - 2.59808i) q^{37} -2.00000 q^{38} +(-1.50000 + 2.59808i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-1.50000 - 2.59808i) q^{41} +7.00000 q^{43} +(-1.00000 - 1.73205i) q^{44} -6.00000 q^{45} +(-3.00000 + 5.19615i) q^{46} -8.00000 q^{47} -3.00000 q^{48} +(3.50000 - 6.06218i) q^{49} +(0.500000 + 0.866025i) q^{50} +6.00000 q^{51} +(0.500000 - 0.866025i) q^{52} +(5.50000 - 9.52628i) q^{53} +(-4.50000 + 7.79423i) q^{54} +(1.00000 + 1.73205i) q^{55} +(3.00000 - 5.19615i) q^{57} +(3.00000 - 5.19615i) q^{58} +(1.00000 - 1.73205i) q^{59} +3.00000 q^{60} +(-5.00000 - 8.66025i) q^{61} +(2.50000 - 4.33013i) q^{62} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +6.00000 q^{66} +(-2.00000 - 3.46410i) q^{67} -2.00000 q^{68} +(-9.00000 - 15.5885i) q^{69} +(3.00000 - 5.19615i) q^{72} -2.00000 q^{73} +(-5.00000 + 3.46410i) q^{74} -3.00000 q^{75} +(-1.00000 + 1.73205i) q^{76} +(1.50000 + 2.59808i) q^{78} +(2.00000 + 3.46410i) q^{79} -1.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} -3.00000 q^{82} +(-6.00000 + 10.3923i) q^{83} +2.00000 q^{85} +(3.50000 - 6.06218i) q^{86} +(9.00000 + 15.5885i) q^{87} -2.00000 q^{88} +(-1.00000 + 1.73205i) q^{89} +(-3.00000 + 5.19615i) q^{90} +(3.00000 + 5.19615i) q^{92} +(7.50000 + 12.9904i) q^{93} +(-4.00000 + 6.92820i) q^{94} +(1.00000 - 1.73205i) q^{95} +(-1.50000 + 2.59808i) q^{96} +18.0000 q^{97} +(-3.50000 - 6.06218i) q^{98} +(-6.00000 + 10.3923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 3 q^{3} - q^{4} + q^{5} + 6 q^{6} - 2 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q + q^2 + 3 * q^3 - q^4 + q^5 + 6 * q^6 - 2 * q^8 - 6 * q^9	\( 2 q + q^{2} + 3 q^{3} - q^{4} + q^{5} + 6 q^{6} - 2 q^{8} - 6 q^{9} + 2 q^{10} + 4 q^{11} + 3 q^{12} + q^{13} - 3 q^{15} - q^{16} + 2 q^{17} + 6 q^{18} - 2 q^{19} + q^{20} + 2 q^{22} - 12 q^{23} - 3 q^{24} - q^{25} + 2 q^{26} - 18 q^{27} + 12 q^{29} + 3 q^{30} + 10 q^{31} + q^{32} + 6 q^{33} - 2 q^{34} + 12 q^{36} - 11 q^{37} - 4 q^{38} - 3 q^{39} - q^{40} - 3 q^{41} + 14 q^{43} - 2 q^{44} - 12 q^{45} - 6 q^{46} - 16 q^{47} - 6 q^{48} + 7 q^{49} + q^{50} + 12 q^{51} + q^{52} + 11 q^{53} - 9 q^{54} + 2 q^{55} + 6 q^{57} + 6 q^{58} + 2 q^{59} + 6 q^{60} - 10 q^{61} + 5 q^{62} + 2 q^{64} - q^{65} + 12 q^{66} - 4 q^{67} - 4 q^{68} - 18 q^{69} + 6 q^{72} - 4 q^{73} - 10 q^{74} - 6 q^{75} - 2 q^{76} + 3 q^{78} + 4 q^{79} - 2 q^{80} - 9 q^{81} - 6 q^{82} - 12 q^{83} + 4 q^{85} + 7 q^{86} + 18 q^{87} - 4 q^{88} - 2 q^{89} - 6 q^{90} + 6 q^{92} + 15 q^{93} - 8 q^{94} + 2 q^{95} - 3 q^{96} + 36 q^{97} - 7 q^{98} - 12 q^{99}+O(q^{100}) \) 2 * q + q^2 + 3 * q^3 - q^4 + q^5 + 6 * q^6 - 2 * q^8 - 6 * q^9 + 2 * q^10 + 4 * q^11 + 3 * q^12 + q^13 - 3 * q^15 - q^16 + 2 * q^17 + 6 * q^18 - 2 * q^19 + q^20 + 2 * q^22 - 12 * q^23 - 3 * q^24 - q^25 + 2 * q^26 - 18 * q^27 + 12 * q^29 + 3 * q^30 + 10 * q^31 + q^32 + 6 * q^33 - 2 * q^34 + 12 * q^36 - 11 * q^37 - 4 * q^38 - 3 * q^39 - q^40 - 3 * q^41 + 14 * q^43 - 2 * q^44 - 12 * q^45 - 6 * q^46 - 16 * q^47 - 6 * q^48 + 7 * q^49 + q^50 + 12 * q^51 + q^52 + 11 * q^53 - 9 * q^54 + 2 * q^55 + 6 * q^57 + 6 * q^58 + 2 * q^59 + 6 * q^60 - 10 * q^61 + 5 * q^62 + 2 * q^64 - q^65 + 12 * q^66 - 4 * q^67 - 4 * q^68 - 18 * q^69 + 6 * q^72 - 4 * q^73 - 10 * q^74 - 6 * q^75 - 2 * q^76 + 3 * q^78 + 4 * q^79 - 2 * q^80 - 9 * q^81 - 6 * q^82 - 12 * q^83 + 4 * q^85 + 7 * q^86 + 18 * q^87 - 4 * q^88 - 2 * q^89 - 6 * q^90 + 6 * q^92 + 15 * q^93 - 8 * q^94 + 2 * q^95 - 3 * q^96 + 36 * q^97 - 7 * q^98 - 12 * q^99

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