LMFDB - Embedded newform 1690.2.e.e.191.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1690,2,Mod(191,1690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1690, 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("1690.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.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:	$13.4947179416$
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 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			191.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1690.191
Dual form			1690.2.e.e.991.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(1.00000 + 1.73205i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(1.00000 + 1.73205i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(1.50000 - 2.59808i) q^{11} -2.00000 q^{12} +1.00000 q^{14} +(1.00000 - 1.73205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +1.00000 q^{18} +(2.50000 + 4.33013i) q^{19} +(-0.500000 - 0.866025i) q^{20} -2.00000 q^{21} +(1.50000 + 2.59808i) q^{22} +(1.00000 - 1.73205i) q^{24} +1.00000 q^{25} +4.00000 q^{27} +(-0.500000 + 0.866025i) q^{28} +(1.00000 + 1.73205i) q^{30} +4.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{33} -6.00000 q^{34} +(-0.500000 - 0.866025i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(5.50000 - 9.52628i) q^{37} -5.00000 q^{38} +1.00000 q^{40} +(3.00000 - 5.19615i) q^{41} +(1.00000 - 1.73205i) q^{42} +(-1.00000 - 1.73205i) q^{43} -3.00000 q^{44} +(-0.500000 - 0.866025i) q^{45} +3.00000 q^{47} +(1.00000 + 1.73205i) q^{48} +(3.00000 - 5.19615i) q^{49} +(-0.500000 + 0.866025i) q^{50} +12.0000 q^{51} -9.00000 q^{53} +(-2.00000 + 3.46410i) q^{54} +(1.50000 - 2.59808i) q^{55} +(-0.500000 - 0.866025i) q^{56} +10.0000 q^{57} -2.00000 q^{60} +(-4.00000 - 6.92820i) q^{61} +(-2.00000 + 3.46410i) q^{62} +(-0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +6.00000 q^{66} +(-8.00000 + 13.8564i) q^{67} +(3.00000 - 5.19615i) q^{68} +1.00000 q^{70} +(3.00000 + 5.19615i) q^{71} +(-0.500000 - 0.866025i) q^{72} -14.0000 q^{73} +(5.50000 + 9.52628i) q^{74} +(1.00000 - 1.73205i) q^{75} +(2.50000 - 4.33013i) q^{76} -3.00000 q^{77} -16.0000 q^{79} +(-0.500000 + 0.866025i) q^{80} +(5.50000 - 9.52628i) q^{81} +(3.00000 + 5.19615i) q^{82} +6.00000 q^{83} +(1.00000 + 1.73205i) q^{84} +(3.00000 + 5.19615i) q^{85} +2.00000 q^{86} +(1.50000 - 2.59808i) q^{88} +(4.50000 - 7.79423i) q^{89} +1.00000 q^{90} +(4.00000 - 6.92820i) q^{93} +(-1.50000 + 2.59808i) q^{94} +(2.50000 + 4.33013i) q^{95} -2.00000 q^{96} +(-5.00000 - 8.66025i) q^{97} +(3.00000 + 5.19615i) q^{98} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 2 q^{3} - q^{4} + 2 q^{5} + 2 q^{6} - q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 + 2 * q^3 - q^4 + 2 * q^5 + 2 * q^6 - q^7 + 2 * q^8 - q^9	$ 2 q - q^{2} + 2 q^{3} - q^{4} + 2 q^{5} + 2 q^{6} - q^{7} + 2 q^{8} - q^{9} - q^{10} + 3 q^{11} - 4 q^{12} + 2 q^{14} + 2 q^{15} - q^{16} + 6 q^{17} + 2 q^{18} + 5 q^{19} - q^{20} - 4 q^{21} + 3 q^{22} + 2 q^{24} + 2 q^{25} + 8 q^{27} - q^{28} + 2 q^{30} + 8 q^{31} - q^{32} - 6 q^{33} - 12 q^{34} - q^{35} - q^{36} + 11 q^{37} - 10 q^{38} + 2 q^{40} + 6 q^{41} + 2 q^{42} - 2 q^{43} - 6 q^{44} - q^{45} + 6 q^{47} + 2 q^{48} + 6 q^{49} - q^{50} + 24 q^{51} - 18 q^{53} - 4 q^{54} + 3 q^{55} - q^{56} + 20 q^{57} - 4 q^{60} - 8 q^{61} - 4 q^{62} - q^{63} + 2 q^{64} + 12 q^{66} - 16 q^{67} + 6 q^{68} + 2 q^{70} + 6 q^{71} - q^{72} - 28 q^{73} + 11 q^{74} + 2 q^{75} + 5 q^{76} - 6 q^{77} - 32 q^{79} - q^{80} + 11 q^{81} + 6 q^{82} + 12 q^{83} + 2 q^{84} + 6 q^{85} + 4 q^{86} + 3 q^{88} + 9 q^{89} + 2 q^{90} + 8 q^{93} - 3 q^{94} + 5 q^{95} - 4 q^{96} - 10 q^{97} + 6 q^{98} - 6 q^{99}+O(q^{100}) $ 2 * q - q^2 + 2 * q^3 - q^4 + 2 * q^5 + 2 * q^6 - q^7 + 2 * q^8 - q^9 - q^10 + 3 * q^11 - 4 * q^12 + 2 * q^14 + 2 * q^15 - q^16 + 6 * q^17 + 2 * q^18 + 5 * q^19 - q^20 - 4 * q^21 + 3 * q^22 + 2 * q^24 + 2 * q^25 + 8 * q^27 - q^28 + 2 * q^30 + 8 * q^31 - q^32 - 6 * q^33 - 12 * q^34 - q^35 - q^36 + 11 * q^37 - 10 * q^38 + 2 * q^40 + 6 * q^41 + 2 * q^42 - 2 * q^43 - 6 * q^44 - q^45 + 6 * q^47 + 2 * q^48 + 6 * q^49 - q^50 + 24 * q^51 - 18 * q^53 - 4 * q^54 + 3 * q^55 - q^56 + 20 * q^57 - 4 * q^60 - 8 * q^61 - 4 * q^62 - q^63 + 2 * q^64 + 12 * q^66 - 16 * q^67 + 6 * q^68 + 2 * q^70 + 6 * q^71 - q^72 - 28 * q^73 + 11 * q^74 + 2 * q^75 + 5 * q^76 - 6 * q^77 - 32 * q^79 - q^80 + 11 * q^81 + 6 * q^82 + 12 * q^83 + 2 * q^84 + 6 * q^85 + 4 * q^86 + 3 * q^88 + 9 * q^89 + 2 * q^90 + 8 * q^93 - 3 * q^94 + 5 * q^95 - 4 * q^96 - 10 * q^97 + 6 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1690\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	1.00000	−	1.73205i	0.577350	−	1.00000i	−0.418432	−	0.908248i	$-0.637420\pi$
$3$	1.00000	−	1.73205i	0.577350	−	1.00000i	0.995782	−	0.0917517i	$-0.0292466\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	1.00000	+	1.73205i	0.408248	+	0.707107i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	0.755929	−	0.654654i	$-0.227186\pi$
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	−0.944911	+	0.327327i	$0.893852\pi$
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$	−2.00000			−0.577350
$13$		0			0
$13$		0			0
$14$	1.00000			0.267261
$15$	1.00000	−	1.73205i	0.258199	−	0.447214i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	0.957892	+	0.287129i	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$	1.00000			0.235702
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	0.996199	+	0.0871106i	$0.0277634\pi$
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	−0.422659	+	0.906289i	$0.638903\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	−2.00000			−0.436436
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	1.00000	−	1.73205i	0.204124	−	0.353553i
$25$	1.00000			0.200000
$26$		0			0
$27$	4.00000			0.769800
$28$	−0.500000	+	0.866025i	−0.0944911	+	0.163663i
$29$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$29$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$30$	1.00000	+	1.73205i	0.182574	+	0.316228i
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−3.00000	−	5.19615i	−0.522233	−	0.904534i
$34$	−6.00000			−1.02899
$35$	−0.500000	−	0.866025i	−0.0845154	−	0.146385i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	5.50000	−	9.52628i	0.904194	−	1.56611i	0.0821995	−	0.996616i	$-0.473806\pi$
$37$	5.50000	−	9.52628i	0.904194	−	1.56611i	0.821995	−	0.569495i	$-0.192861\pi$
$38$	−5.00000			−0.811107
$39$		0			0
$40$	1.00000			0.158114
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	−0.530831	−	0.847477i	$-0.678120\pi$
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	0.999353	+	0.0359748i	$0.0114536\pi$
$42$	1.00000	−	1.73205i	0.154303	−	0.267261i
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	0.779647	−	0.626219i	$-0.215399\pi$
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	−0.932145	+	0.362084i	$0.882065\pi$
$44$	−3.00000			−0.452267
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$		0			0
$47$	3.00000			0.437595			0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000			0.437595			0.218797	+	0.975770i	$0.429787\pi$
$48$	1.00000	+	1.73205i	0.144338	+	0.250000i
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	12.0000			1.68034
$52$		0			0
$53$	−9.00000			−1.23625			−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000			−1.23625			−0.618123	+	0.786082i	$0.712106\pi$
$54$	−2.00000	+	3.46410i	−0.272166	+	0.471405i
$55$	1.50000	−	2.59808i	0.202260	−	0.350325i
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$	10.0000			1.32453
$58$		0			0
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$	−2.00000			−0.258199
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$	−2.00000	+	3.46410i	−0.254000	+	0.439941i
$63$	−0.500000	+	0.866025i	−0.0629941	+	0.109109i
$64$	1.00000			0.125000
$65$		0			0
$66$	6.00000			0.738549
$67$	−8.00000	+	13.8564i	−0.977356	+	1.69283i	−0.305424	+	0.952217i	$0.598798\pi$
$67$	−8.00000	+	13.8564i	−0.977356	+	1.69283i	−0.671932	+	0.740613i	$0.734535\pi$
$68$	3.00000	−	5.19615i	0.363803	−	0.630126i
$69$		0			0
$70$	1.00000			0.119523
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	0.987294	−	0.158901i	$-0.0507952\pi$
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	−0.631260	+	0.775571i	$0.717462\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−14.0000			−1.63858			−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000			−1.63858			−0.819288	+	0.573382i	$0.805631\pi$
$74$	5.50000	+	9.52628i	0.639362	+	1.10741i
$75$	1.00000	−	1.73205i	0.115470	−	0.200000i
$76$	2.50000	−	4.33013i	0.286770	−	0.496700i
$77$	−3.00000			−0.341882
$78$		0			0
$79$	−16.0000			−1.80014			−0.900070	−	0.435745i	$-0.856485\pi$
$79$	−16.0000			−1.80014			−0.900070	+	0.435745i	$0.856485\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$	3.00000	+	5.19615i	0.331295	+	0.573819i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$	1.00000	+	1.73205i	0.109109	+	0.188982i
$85$	3.00000	+	5.19615i	0.325396	+	0.563602i
$86$	2.00000			0.215666
$87$		0			0
$88$	1.50000	−	2.59808i	0.159901	−	0.276956i
$89$	4.50000	−	7.79423i	0.476999	−	0.826187i	−0.522654	−	0.852545i	$-0.675058\pi$
$89$	4.50000	−	7.79423i	0.476999	−	0.826187i	0.999653	+	0.0263586i	$0.00839118\pi$
$90$	1.00000			0.105409
$91$		0			0
$92$		0			0
$93$	4.00000	−	6.92820i	0.414781	−	0.718421i
$94$	−1.50000	+	2.59808i	−0.154713	+	0.267971i
$95$	2.50000	+	4.33013i	0.256495	+	0.444262i
$96$	−2.00000			−0.204124
$97$	−5.00000	−	8.66025i	−0.507673	−	0.879316i	−0.999961	−	0.00888289i	$-0.997172\pi$
$97$	−5.00000	−	8.66025i	−0.507673	−	0.879316i	0.492287	−	0.870433i	$-0.336161\pi$
$98$	3.00000	+	5.19615i	0.303046	+	0.524891i
$99$	−3.00000			−0.301511
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	−0.677284	−	0.735721i	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$	−6.00000	+	10.3923i	−0.594089	+	1.02899i
$103$	5.00000			0.492665			0.246332	−	0.969185i	$-0.420775\pi$
$103$	5.00000			0.492665			0.246332	+	0.969185i	$0.420775\pi$
$104$		0			0
$105$	−2.00000			−0.195180
$106$	4.50000	−	7.79423i	0.437079	−	0.757042i
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	−0.415432	−	0.909624i	$-0.636370\pi$
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	0.995474	−	0.0950377i	$-0.0302972\pi$
$108$	−2.00000	−	3.46410i	−0.192450	−	0.333333i
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$	1.50000	+	2.59808i	0.143019	+	0.247717i
$111$	−11.0000	−	19.0526i	−1.04407	−	1.80839i
$112$	1.00000			0.0944911
$113$	6.00000	+	10.3923i	0.564433	+	0.977626i	0.997102	+	0.0760733i	$0.0242383\pi$
$113$	6.00000	+	10.3923i	0.564433	+	0.977626i	−0.432670	+	0.901553i	$0.642428\pi$
$114$	−5.00000	+	8.66025i	−0.468293	+	0.811107i
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$	3.00000	−	5.19615i	0.275010	−	0.476331i
$120$	1.00000	−	1.73205i	0.0912871	−	0.158114i
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	8.00000			0.724286
$123$	−6.00000	−	10.3923i	−0.541002	−	0.937043i
$124$	−2.00000	−	3.46410i	−0.179605	−	0.311086i
$125$	1.00000			0.0894427
$126$	−0.500000	−	0.866025i	−0.0445435	−	0.0771517i
$127$	0.500000	−	0.866025i	0.0443678	−	0.0768473i	−0.842989	−	0.537931i	$-0.819206\pi$
$127$	0.500000	−	0.866025i	0.0443678	−	0.0768473i	0.887357	+	0.461084i	$0.152539\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−4.00000			−0.352180
$130$		0			0
$131$	−9.00000			−0.786334			−0.393167	−	0.919467i	$-0.628621\pi$
$131$	−9.00000			−0.786334			−0.393167	+	0.919467i	$0.628621\pi$
$132$	−3.00000	+	5.19615i	−0.261116	+	0.452267i
$133$	2.50000	−	4.33013i	0.216777	−	0.375470i
$134$	−8.00000	−	13.8564i	−0.691095	−	1.19701i
$135$	4.00000			0.344265
$136$	3.00000	+	5.19615i	0.257248	+	0.445566i
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	0.965250	−	0.261329i	$-0.0841608\pi$
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	−0.708942	+	0.705266i	$0.750827\pi$
$138$		0			0
$139$	9.50000	+	16.4545i	0.805779	+	1.39565i	0.915764	+	0.401718i	$0.131587\pi$
$139$	9.50000	+	16.4545i	0.805779	+	1.39565i	−0.109984	+	0.993933i	$0.535080\pi$
$140$	−0.500000	+	0.866025i	−0.0422577	+	0.0731925i
$141$	3.00000	−	5.19615i	0.252646	−	0.437595i
$142$	−6.00000			−0.503509
$143$		0			0
$144$	1.00000			0.0833333
$145$		0			0
$146$	7.00000	−	12.1244i	0.579324	−	1.00342i
$147$	−6.00000	−	10.3923i	−0.494872	−	0.857143i
$148$	−11.0000			−0.904194
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	−0.953703	−	0.300750i	$-0.902763\pi$
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	0.216394	−	0.976306i	$-0.430570\pi$
$150$	1.00000	+	1.73205i	0.0816497	+	0.141421i
$151$	16.0000			1.30206			0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000			1.30206			0.651031	+	0.759051i	$0.274337\pi$
$152$	2.50000	+	4.33013i	0.202777	+	0.351220i
$153$	3.00000	−	5.19615i	0.242536	−	0.420084i
$154$	1.50000	−	2.59808i	0.120873	−	0.209359i
$155$	4.00000			0.321288
$156$		0			0
$157$	17.0000			1.35675			0.678374	−	0.734717i	$-0.262685\pi$
$157$	17.0000			1.35675			0.678374	+	0.734717i	$0.262685\pi$
$158$	8.00000	−	13.8564i	0.636446	−	1.10236i
$159$	−9.00000	+	15.5885i	−0.713746	+	1.23625i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$		0			0
$162$	5.50000	+	9.52628i	0.432121	+	0.748455i
$163$	1.00000	+	1.73205i	0.0783260	+	0.135665i	0.902528	−	0.430632i	$-0.141709\pi$
$163$	1.00000	+	1.73205i	0.0783260	+	0.135665i	−0.824202	+	0.566296i	$0.808376\pi$
$164$	−6.00000			−0.468521
$165$	−3.00000	−	5.19615i	−0.233550	−	0.404520i
$166$	−3.00000	+	5.19615i	−0.232845	+	0.403300i
$167$	−7.50000	+	12.9904i	−0.580367	+	1.00523i	0.415068	+	0.909790i	$0.363758\pi$
$167$	−7.50000	+	12.9904i	−0.580367	+	1.00523i	−0.995436	+	0.0954356i	$0.969576\pi$
$168$	−2.00000			−0.154303
$169$		0			0
$170$	−6.00000			−0.460179
$171$	2.50000	−	4.33013i	0.191180	−	0.331133i
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	−7.50000	−	12.9904i	−0.570214	−	0.987640i	−0.996544	−	0.0830722i	$-0.973527\pi$
$173$	−7.50000	−	12.9904i	−0.570214	−	0.987640i	0.426329	−	0.904568i	$-0.359807\pi$
$174$		0			0
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$	1.50000	+	2.59808i	0.113067	+	0.195837i
$177$		0			0
$178$	4.50000	+	7.79423i	0.337289	+	0.584202i
$179$	12.0000	−	20.7846i	0.896922	−	1.55351i	0.0655145	−	0.997852i	$-0.479131\pi$
$179$	12.0000	−	20.7846i	0.896922	−	1.55351i	0.831408	−	0.555663i	$-0.187536\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$		0			0
$183$	−16.0000			−1.18275
$184$		0			0
$185$	5.50000	−	9.52628i	0.404368	−	0.700386i
$186$	4.00000	+	6.92820i	0.293294	+	0.508001i
$187$	18.0000			1.31629
$188$	−1.50000	−	2.59808i	−0.109399	−	0.189484i
$189$	−2.00000	−	3.46410i	−0.145479	−	0.251976i
$190$	−5.00000			−0.362738
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$	1.00000	−	1.73205i	0.0721688	−	0.125000i
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	−0.928986	−	0.370116i	$-0.879318\pi$
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	0.785022	+	0.619467i	$0.212651\pi$
$194$	10.0000			0.717958
$195$		0			0
$196$	−6.00000			−0.428571
$197$	−13.5000	+	23.3827i	−0.961835	+	1.66595i	−0.243947	+	0.969788i	$0.578442\pi$
$197$	−13.5000	+	23.3827i	−0.961835	+	1.66595i	−0.717888	+	0.696159i	$0.754891\pi$
$198$	1.50000	−	2.59808i	0.106600	−	0.184637i
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	0.987022	−	0.160585i	$-0.0513380\pi$
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	−0.632581	+	0.774494i	$0.718005\pi$
$200$	1.00000			0.0707107
$201$	16.0000	+	27.7128i	1.12855	+	1.95471i
$202$	3.00000	+	5.19615i	0.211079	+	0.365600i
$203$		0			0
$204$	−6.00000	−	10.3923i	−0.420084	−	0.727607i
$205$	3.00000	−	5.19615i	0.209529	−	0.362915i
$206$	−2.50000	+	4.33013i	−0.174183	+	0.301694i
$207$		0			0
$208$		0			0
$209$	15.0000			1.03757
$210$	1.00000	−	1.73205i	0.0690066	−	0.119523i
$211$	−11.5000	+	19.9186i	−0.791693	+	1.37125i	0.133226	+	0.991086i	$0.457467\pi$
$211$	−11.5000	+	19.9186i	−0.791693	+	1.37125i	−0.924918	+	0.380166i	$0.875867\pi$
$212$	4.50000	+	7.79423i	0.309061	+	0.535310i
$213$	12.0000			0.822226
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$	−1.00000	−	1.73205i	−0.0681994	−	0.118125i
$216$	4.00000			0.272166
$217$	−2.00000	−	3.46410i	−0.135769	−	0.235159i
$218$	1.00000	−	1.73205i	0.0677285	−	0.117309i
$219$	−14.0000	+	24.2487i	−0.946032	+	1.63858i
$220$	−3.00000			−0.202260
$221$		0			0
$222$	22.0000			1.47654
$223$	−9.50000	+	16.4545i	−0.636167	+	1.10187i	0.350100	+	0.936713i	$0.386148\pi$
$223$	−9.50000	+	16.4545i	−0.636167	+	1.10187i	−0.986267	+	0.165161i	$0.947186\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	−12.0000			−0.798228
$227$	−12.0000	−	20.7846i	−0.796468	−	1.37952i	−0.921903	−	0.387421i	$-0.873366\pi$
$227$	−12.0000	−	20.7846i	−0.796468	−	1.37952i	0.125435	−	0.992102i	$-0.459967\pi$
$228$	−5.00000	−	8.66025i	−0.331133	−	0.573539i
$229$	4.00000			0.264327			0.132164	−	0.991228i	$-0.457808\pi$
$229$	4.00000			0.264327			0.132164	+	0.991228i	$0.457808\pi$
$230$		0			0
$231$	−3.00000	+	5.19615i	−0.197386	+	0.341882i
$232$		0			0
$233$	−24.0000			−1.57229			−0.786146	−	0.618041i	$-0.787927\pi$
$233$	−24.0000			−1.57229			−0.786146	+	0.618041i	$0.787927\pi$
$234$		0			0
$235$	3.00000			0.195698
$236$		0			0
$237$	−16.0000	+	27.7128i	−1.03931	+	1.80014i
$238$	3.00000	+	5.19615i	0.194461	+	0.336817i
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$	1.00000	+	1.73205i	0.0645497	+	0.111803i
$241$	11.5000	+	19.9186i	0.740780	+	1.28307i	0.952141	+	0.305661i	$0.0988773\pi$
$241$	11.5000	+	19.9186i	0.740780	+	1.28307i	−0.211360	+	0.977408i	$0.567789\pi$
$242$	−2.00000			−0.128565
$243$	−5.00000	−	8.66025i	−0.320750	−	0.555556i
$244$	−4.00000	+	6.92820i	−0.256074	+	0.443533i
$245$	3.00000	−	5.19615i	0.191663	−	0.331970i
$246$	12.0000			0.765092
$247$		0			0
$248$	4.00000			0.254000
$249$	6.00000	−	10.3923i	0.380235	−	0.658586i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	7.50000	+	12.9904i	0.473396	+	0.819946i	0.999536	−	0.0304521i	$-0.00969471\pi$
$251$	7.50000	+	12.9904i	0.473396	+	0.819946i	−0.526140	+	0.850398i	$0.676361\pi$
$252$	1.00000			0.0629941
$253$		0			0
$254$	0.500000	+	0.866025i	0.0313728	+	0.0543393i
$255$	12.0000			0.751469
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	−0.990217	−	0.139533i	$-0.955440\pi$
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	0.615948	+	0.787787i	$0.288773\pi$
$258$	2.00000	−	3.46410i	0.124515	−	0.215666i
$259$	−11.0000			−0.683507
$260$		0			0
$261$		0			0
$262$	4.50000	−	7.79423i	0.278011	−	0.481529i
$263$	−4.50000	+	7.79423i	−0.277482	+	0.480613i	−0.970758	−	0.240059i	$-0.922833\pi$
$263$	−4.50000	+	7.79423i	−0.277482	+	0.480613i	0.693276	+	0.720672i	$0.256167\pi$
$264$	−3.00000	−	5.19615i	−0.184637	−	0.319801i
$265$	−9.00000			−0.552866
$266$	2.50000	+	4.33013i	0.153285	+	0.265497i
$267$	−9.00000	−	15.5885i	−0.550791	−	0.953998i
$268$	16.0000			0.977356
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	0.759958	−	0.649972i	$-0.225219\pi$
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	−0.942871	+	0.333157i	$0.891886\pi$
$270$	−2.00000	+	3.46410i	−0.121716	+	0.210819i
$271$	10.0000	−	17.3205i	0.607457	−	1.05215i	−0.384201	−	0.923249i	$-0.625523\pi$
$271$	10.0000	−	17.3205i	0.607457	−	1.05215i	0.991658	−	0.128897i	$-0.0411435\pi$
$272$	−6.00000			−0.363803
$273$		0			0
$274$	−6.00000			−0.362473
$275$	1.50000	−	2.59808i	0.0904534	−	0.156670i
$276$		0			0
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	0.880656	−	0.473757i	$-0.157103\pi$
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	−0.850613	+	0.525792i	$0.823769\pi$
$278$	−19.0000			−1.13954
$279$	−2.00000	−	3.46410i	−0.119737	−	0.207390i
$280$	−0.500000	−	0.866025i	−0.0298807	−	0.0517549i
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$	3.00000	+	5.19615i	0.178647	+	0.309426i
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	−0.995544	−	0.0942988i	$-0.969939\pi$
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	0.579437	+	0.815017i	$0.303272\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$	10.0000			0.592349
$286$		0			0
$287$	−6.00000			−0.354169
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$	−20.0000			−1.17242
$292$	7.00000	+	12.1244i	0.409644	+	0.709524i
$293$	4.50000	+	7.79423i	0.262893	+	0.455344i	0.967009	−	0.254741i	$-0.0819901\pi$
$293$	4.50000	+	7.79423i	0.262893	+	0.455344i	−0.704117	+	0.710084i	$0.748657\pi$
$294$	12.0000			0.699854
$295$		0			0
$296$	5.50000	−	9.52628i	0.319681	−	0.553704i
$297$	6.00000	−	10.3923i	0.348155	−	0.603023i
$298$	18.0000			1.04271
$299$		0			0
$300$	−2.00000			−0.115470
$301$	−1.00000	+	1.73205i	−0.0576390	+	0.0998337i
$302$	−8.00000	+	13.8564i	−0.460348	+	0.797347i
$303$	−6.00000	−	10.3923i	−0.344691	−	0.597022i
$304$	−5.00000			−0.286770
$305$	−4.00000	−	6.92820i	−0.229039	−	0.396708i
$306$	3.00000	+	5.19615i	0.171499	+	0.297044i
$307$	−2.00000			−0.114146			−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000			−0.114146			−0.0570730	+	0.998370i	$0.518177\pi$
$308$	1.50000	+	2.59808i	0.0854704	+	0.148039i
$309$	5.00000	−	8.66025i	0.284440	−	0.492665i
$310$	−2.00000	+	3.46410i	−0.113592	+	0.196748i
$311$	30.0000			1.70114			0.850572	−	0.525859i	$-0.176256\pi$
$311$	30.0000			1.70114			0.850572	+	0.525859i	$0.176256\pi$
$312$		0			0
$313$	14.0000			0.791327			0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000			0.791327			0.395663	+	0.918396i	$0.370515\pi$
$314$	−8.50000	+	14.7224i	−0.479683	+	0.830835i
$315$	−0.500000	+	0.866025i	−0.0281718	+	0.0487950i
$316$	8.00000	+	13.8564i	0.450035	+	0.779484i
$317$	−15.0000			−0.842484			−0.421242	−	0.906948i	$-0.638406\pi$
$317$	−15.0000			−0.842484			−0.421242	+	0.906948i	$0.638406\pi$
$318$	−9.00000	−	15.5885i	−0.504695	−	0.874157i
$319$		0			0
$320$	1.00000			0.0559017
$321$	−12.0000	−	20.7846i	−0.669775	−	1.16008i
$322$		0			0
$323$	−15.0000	+	25.9808i	−0.834622	+	1.44561i
$324$	−11.0000			−0.611111
$325$		0			0
$326$	−2.00000			−0.110770
$327$	−2.00000	+	3.46410i	−0.110600	+	0.191565i
$328$	3.00000	−	5.19615i	0.165647	−	0.286910i
$329$	−1.50000	−	2.59808i	−0.0826977	−	0.143237i
$330$	6.00000			0.330289
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	0.998298	+	0.0583130i	$0.0185721\pi$
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	−0.448649	+	0.893708i	$0.648095\pi$
$332$	−3.00000	−	5.19615i	−0.164646	−	0.285176i
$333$	−11.0000			−0.602796
$334$	−7.50000	−	12.9904i	−0.410382	−	0.710802i
$335$	−8.00000	+	13.8564i	−0.437087	+	0.757056i
$336$	1.00000	−	1.73205i	0.0545545	−	0.0944911i
$337$	−16.0000			−0.871576			−0.435788	−	0.900049i	$-0.643530\pi$
$337$	−16.0000			−0.871576			−0.435788	+	0.900049i	$0.643530\pi$
$338$		0			0
$339$	24.0000			1.30350
$340$	3.00000	−	5.19615i	0.162698	−	0.281801i
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$	2.50000	+	4.33013i	0.135185	+	0.234146i
$343$	−13.0000			−0.701934
$344$	−1.00000	−	1.73205i	−0.0539164	−	0.0933859i
$345$		0			0
$346$	15.0000			0.806405
$347$	−3.00000	−	5.19615i	−0.161048	−	0.278944i	0.774197	−	0.632945i	$-0.218154\pi$
$347$	−3.00000	−	5.19615i	−0.161048	−	0.278944i	−0.935245	+	0.354001i	$0.884821\pi$
$348$		0			0
$349$	1.00000	−	1.73205i	0.0535288	−	0.0927146i	−0.838019	−	0.545640i	$-0.816286\pi$
$349$	1.00000	−	1.73205i	0.0535288	−	0.0927146i	0.891548	+	0.452926i	$0.149620\pi$
$350$	1.00000			0.0534522
$351$		0			0
$352$	−3.00000			−0.159901
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	−0.775077	−	0.631867i	$-0.782289\pi$
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	0.934751	+	0.355303i	$0.115622\pi$
$354$		0			0
$355$	3.00000	+	5.19615i	0.159223	+	0.275783i
$356$	−9.00000			−0.476999
$357$	−6.00000	−	10.3923i	−0.317554	−	0.550019i
$358$	12.0000	+	20.7846i	0.634220	+	1.09850i
$359$	6.00000			0.316668			0.158334	−	0.987386i	$-0.449388\pi$
$359$	6.00000			0.316668			0.158334	+	0.987386i	$0.449388\pi$
$360$	−0.500000	−	0.866025i	−0.0263523	−	0.0456435i
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$	−4.00000	+	6.92820i	−0.210235	+	0.364138i
$363$	4.00000			0.209946
$364$		0			0
$365$	−14.0000			−0.732793
$366$	8.00000	−	13.8564i	0.418167	−	0.724286i
$367$	−16.0000	+	27.7128i	−0.835193	+	1.44660i	0.0586798	+	0.998277i	$0.481311\pi$
$367$	−16.0000	+	27.7128i	−0.835193	+	1.44660i	−0.893873	+	0.448320i	$0.852022\pi$
$368$		0			0
$369$	−6.00000			−0.312348
$370$	5.50000	+	9.52628i	0.285931	+	0.495248i
$371$	4.50000	+	7.79423i	0.233628	+	0.404656i
$372$	−8.00000			−0.414781
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	0.625917	−	0.779890i	$-0.284725\pi$
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	−0.988363	+	0.152115i	$0.951392\pi$
$374$	−9.00000	+	15.5885i	−0.465379	+	0.806060i
$375$	1.00000	−	1.73205i	0.0516398	−	0.0894427i
$376$	3.00000			0.154713
$377$		0			0
$378$	4.00000			0.205738
$379$	−9.50000	+	16.4545i	−0.487982	+	0.845210i	−0.999904	−	0.0138218i	$-0.995600\pi$
$379$	−9.50000	+	16.4545i	−0.487982	+	0.845210i	0.511922	+	0.859032i	$0.328934\pi$
$380$	2.50000	−	4.33013i	0.128247	−	0.222131i
$381$	−1.00000	−	1.73205i	−0.0512316	−	0.0887357i
$382$		0			0
$383$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$383$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$384$	1.00000	+	1.73205i	0.0510310	+	0.0883883i
$385$	−3.00000			−0.152894
$386$	−2.00000	−	3.46410i	−0.101797	−	0.176318i
$387$	−1.00000	+	1.73205i	−0.0508329	+	0.0880451i
$388$	−5.00000	+	8.66025i	−0.253837	+	0.439658i
$389$	−30.0000			−1.52106			−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000			−1.52106			−0.760530	+	0.649303i	$0.775061\pi$
$390$		0			0
$391$		0			0
$392$	3.00000	−	5.19615i	0.151523	−	0.262445i
$393$	−9.00000	+	15.5885i	−0.453990	+	0.786334i
$394$	−13.5000	−	23.3827i	−0.680120	−	1.17800i
$395$	−16.0000			−0.805047
$396$	1.50000	+	2.59808i	0.0753778	+	0.130558i
$397$	−6.50000	−	11.2583i	−0.326226	−	0.565039i	0.655534	−	0.755166i	$-0.272444\pi$
$397$	−6.50000	−	11.2583i	−0.326226	−	0.565039i	−0.981760	+	0.190126i	$0.939110\pi$
$398$	−10.0000			−0.501255
$399$	−5.00000	−	8.66025i	−0.250313	−	0.433555i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−7.50000	+	12.9904i	−0.374532	+	0.648709i	−0.990257	−	0.139253i	$-0.955530\pi$
$401$	−7.50000	+	12.9904i	−0.374532	+	0.648709i	0.615725	+	0.787961i	$0.288863\pi$
$402$	−32.0000			−1.59601
$403$		0			0
$404$	−6.00000			−0.298511
$405$	5.50000	−	9.52628i	0.273297	−	0.473365i
$406$		0			0
$407$	−16.5000	−	28.5788i	−0.817875	−	1.41660i
$408$	12.0000			0.594089
$409$	2.50000	+	4.33013i	0.123617	+	0.214111i	0.921192	−	0.389109i	$-0.127217\pi$
$409$	2.50000	+	4.33013i	0.123617	+	0.214111i	−0.797574	+	0.603220i	$0.793884\pi$
$410$	3.00000	+	5.19615i	0.148159	+	0.256620i
$411$	12.0000			0.591916
$412$	−2.50000	−	4.33013i	−0.123166	−	0.213330i
$413$		0			0
$414$		0			0
$415$	6.00000			0.294528
$416$		0			0
$417$	38.0000			1.86087
$418$	−7.50000	+	12.9904i	−0.366837	+	0.635380i
$419$	18.0000	−	31.1769i	0.879358	−	1.52309i	0.0273103	−	0.999627i	$-0.491306\pi$
$419$	18.0000	−	31.1769i	0.879358	−	1.52309i	0.852047	−	0.523465i	$-0.175361\pi$
$420$	1.00000	+	1.73205i	0.0487950	+	0.0845154i
$421$	10.0000			0.487370			0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000			0.487370			0.243685	+	0.969854i	$0.421644\pi$
$422$	−11.5000	−	19.9186i	−0.559811	−	0.969622i
$423$	−1.50000	−	2.59808i	−0.0729325	−	0.126323i
$424$	−9.00000			−0.437079
$425$	3.00000	+	5.19615i	0.145521	+	0.252050i
$426$	−6.00000	+	10.3923i	−0.290701	+	0.503509i
$427$	−4.00000	+	6.92820i	−0.193574	+	0.335279i
$428$	−12.0000			−0.580042
$429$		0			0
$430$	2.00000			0.0964486
$431$	15.0000	−	25.9808i	0.722525	−	1.25145i	−0.237460	−	0.971397i	$-0.576315\pi$
$431$	15.0000	−	25.9808i	0.722525	−	1.25145i	0.959985	−	0.280052i	$-0.0903517\pi$
$432$	−2.00000	+	3.46410i	−0.0962250	+	0.166667i
$433$	8.00000	+	13.8564i	0.384455	+	0.665896i	0.991693	−	0.128624i	$-0.0410559\pi$
$433$	8.00000	+	13.8564i	0.384455	+	0.665896i	−0.607238	+	0.794520i	$0.707723\pi$
$434$	4.00000			0.192006
$435$		0			0
$436$	1.00000	+	1.73205i	0.0478913	+	0.0829502i
$437$		0			0
$438$	−14.0000	−	24.2487i	−0.668946	−	1.15865i
$439$	−10.0000	+	17.3205i	−0.477274	+	0.826663i	−0.999661	−	0.0260459i	$-0.991708\pi$
$439$	−10.0000	+	17.3205i	−0.477274	+	0.826663i	0.522387	+	0.852709i	$0.325042\pi$
$440$	1.50000	−	2.59808i	0.0715097	−	0.123858i
$441$	−6.00000			−0.285714
$442$		0			0
$443$	−18.0000			−0.855206			−0.427603	−	0.903967i	$-0.640642\pi$
$443$	−18.0000			−0.855206			−0.427603	+	0.903967i	$0.640642\pi$
$444$	−11.0000	+	19.0526i	−0.522037	+	0.904194i
$445$	4.50000	−	7.79423i	0.213320	−	0.369482i
$446$	−9.50000	−	16.4545i	−0.449838	−	0.779142i
$447$	−36.0000			−1.70274
$448$	−0.500000	−	0.866025i	−0.0236228	−	0.0409159i
$449$	4.50000	+	7.79423i	0.212368	+	0.367832i	0.952455	−	0.304679i	$-0.0985491\pi$
$449$	4.50000	+	7.79423i	0.212368	+	0.367832i	−0.740087	+	0.672511i	$0.765216\pi$
$450$	1.00000			0.0471405
$451$	−9.00000	−	15.5885i	−0.423793	−	0.734032i
$452$	6.00000	−	10.3923i	0.282216	−	0.488813i
$453$	16.0000	−	27.7128i	0.751746	−	1.30206i
$454$	24.0000			1.12638
$455$		0			0
$456$	10.0000			0.468293
$457$	−2.00000	+	3.46410i	−0.0935561	+	0.162044i	−0.909005	−	0.416785i	$-0.863157\pi$
$457$	−2.00000	+	3.46410i	−0.0935561	+	0.162044i	0.815449	+	0.578829i	$0.196490\pi$
$458$	−2.00000	+	3.46410i	−0.0934539	+	0.161867i
$459$	12.0000	+	20.7846i	0.560112	+	0.970143i
$460$		0			0
$461$	−21.0000	−	36.3731i	−0.978068	−	1.69406i	−0.669417	−	0.742887i	$-0.733456\pi$
$461$	−21.0000	−	36.3731i	−0.978068	−	1.69406i	−0.308651	−	0.951175i	$-0.599877\pi$
$462$	−3.00000	−	5.19615i	−0.139573	−	0.241747i
$463$	−8.00000			−0.371792			−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000			−0.371792			−0.185896	+	0.982569i	$0.559519\pi$
$464$		0			0
$465$	4.00000	−	6.92820i	0.185496	−	0.321288i
$466$	12.0000	−	20.7846i	0.555889	−	0.962828i
$467$	−12.0000			−0.555294			−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000			−0.555294			−0.277647	+	0.960683i	$0.589555\pi$
$468$		0			0
$469$	16.0000			0.738811
$470$	−1.50000	+	2.59808i	−0.0691898	+	0.119840i
$471$	17.0000	−	29.4449i	0.783319	−	1.35675i
$472$		0			0
$473$	−6.00000			−0.275880
$474$	−16.0000	−	27.7128i	−0.734904	−	1.27289i
$475$	2.50000	+	4.33013i	0.114708	+	0.198680i
$476$	−6.00000			−0.275010
$477$	4.50000	+	7.79423i	0.206041	+	0.356873i
$478$		0			0
$479$	−15.0000	+	25.9808i	−0.685367	+	1.18709i	0.287954	+	0.957644i	$0.407025\pi$
$479$	−15.0000	+	25.9808i	−0.685367	+	1.18709i	−0.973321	+	0.229447i	$0.926308\pi$
$480$	−2.00000			−0.0912871
$481$		0			0
$482$	−23.0000			−1.04762
$483$		0			0
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	−5.00000	−	8.66025i	−0.227038	−	0.393242i
$486$	10.0000			0.453609
$487$	−9.50000	−	16.4545i	−0.430486	−	0.745624i	0.566429	−	0.824110i	$-0.308325\pi$
$487$	−9.50000	−	16.4545i	−0.430486	−	0.745624i	−0.996915	+	0.0784867i	$0.974991\pi$
$488$	−4.00000	−	6.92820i	−0.181071	−	0.313625i
$489$	4.00000			0.180886
$490$	3.00000	+	5.19615i	0.135526	+	0.234738i
$491$	−13.5000	+	23.3827i	−0.609246	+	1.05525i	0.382118	+	0.924113i	$0.375195\pi$
$491$	−13.5000	+	23.3827i	−0.609246	+	1.05525i	−0.991365	+	0.131132i	$0.958139\pi$
$492$	−6.00000	+	10.3923i	−0.270501	+	0.468521i
$493$		0			0
$494$		0			0
$495$	−3.00000			−0.134840
$496$	−2.00000	+	3.46410i	−0.0898027	+	0.155543i
$497$	3.00000	−	5.19615i	0.134568	−	0.233079i
$498$	6.00000	+	10.3923i	0.268866	+	0.465690i
$499$	4.00000			0.179065			0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000			0.179065			0.0895323	+	0.995984i	$0.471463\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	15.0000	+	25.9808i	0.670151	+	1.16073i
$502$	−15.0000			−0.669483
$503$	−4.50000	−	7.79423i	−0.200645	−	0.347527i	0.748091	−	0.663596i	$-0.230970\pi$
$503$	−4.50000	−	7.79423i	−0.200645	−	0.347527i	−0.948736	+	0.316068i	$0.897637\pi$
$504$	−0.500000	+	0.866025i	−0.0222718	+	0.0385758i
$505$	3.00000	−	5.19615i	0.133498	−	0.231226i
$506$		0			0
$507$		0			0
$508$	−1.00000			−0.0443678
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	−0.791849	−	0.610718i	$-0.790881\pi$
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	0.924821	+	0.380402i	$0.124214\pi$
$510$	−6.00000	+	10.3923i	−0.265684	+	0.460179i
$511$	7.00000	+	12.1244i	0.309662	+	0.536350i
$512$	1.00000			0.0441942
$513$	10.0000	+	17.3205i	0.441511	+	0.764719i
$514$	−6.00000	−	10.3923i	−0.264649	−	0.458385i
$515$	5.00000			0.220326
$516$	2.00000	+	3.46410i	0.0880451	+	0.152499i
$517$	4.50000	−	7.79423i	0.197910	−	0.342790i
$518$	5.50000	−	9.52628i	0.241656	−	0.418561i
$519$	−30.0000			−1.31685
$520$		0			0
$521$	−27.0000			−1.18289			−0.591446	−	0.806345i	$-0.701443\pi$
$521$	−27.0000			−1.18289			−0.591446	+	0.806345i	$0.701443\pi$
$522$		0			0
$523$	−7.00000	+	12.1244i	−0.306089	+	0.530161i	−0.977503	−	0.210921i	$-0.932354\pi$
$523$	−7.00000	+	12.1244i	−0.306089	+	0.530161i	0.671414	+	0.741082i	$0.265687\pi$
$524$	4.50000	+	7.79423i	0.196583	+	0.340492i
$525$	−2.00000			−0.0872872
$526$	−4.50000	−	7.79423i	−0.196209	−	0.339845i
$527$	12.0000	+	20.7846i	0.522728	+	0.905392i
$528$	6.00000			0.261116
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	4.50000	−	7.79423i	0.195468	−	0.338560i
$531$		0			0
$532$	−5.00000			−0.216777
$533$		0			0
$534$	18.0000			0.778936
$535$	6.00000	−	10.3923i	0.259403	−	0.449299i
$536$	−8.00000	+	13.8564i	−0.345547	+	0.598506i
$537$	−24.0000	−	41.5692i	−1.03568	−	1.79384i
$538$	6.00000			0.258678
$539$	−9.00000	−	15.5885i	−0.387657	−	0.671442i
$540$	−2.00000	−	3.46410i	−0.0860663	−	0.149071i
$541$	−20.0000			−0.859867			−0.429934	−	0.902861i	$-0.641463\pi$
$541$	−20.0000			−0.859867			−0.429934	+	0.902861i	$0.641463\pi$
$542$	10.0000	+	17.3205i	0.429537	+	0.743980i
$543$	8.00000	−	13.8564i	0.343313	−	0.594635i
$544$	3.00000	−	5.19615i	0.128624	−	0.222783i
$545$	−2.00000			−0.0856706
$546$		0			0
$547$	−34.0000			−1.45374			−0.726868	−	0.686778i	$-0.759025\pi$
$547$	−34.0000			−1.45374			−0.726868	+	0.686778i	$0.759025\pi$
$548$	3.00000	−	5.19615i	0.128154	−	0.221969i
$549$	−4.00000	+	6.92820i	−0.170716	+	0.295689i
$550$	1.50000	+	2.59808i	0.0639602	+	0.110782i
$551$		0			0
$552$		0			0
$553$	8.00000	+	13.8564i	0.340195	+	0.589234i
$554$	−1.00000			−0.0424859
$555$	−11.0000	−	19.0526i	−0.466924	−	0.808736i
$556$	9.50000	−	16.4545i	0.402890	−	0.697826i
$557$	10.5000	−	18.1865i	0.444899	−	0.770588i	−0.553146	−	0.833084i	$-0.686573\pi$
$557$	10.5000	−	18.1865i	0.444899	−	0.770588i	0.998045	+	0.0624962i	$0.0199061\pi$
$558$	4.00000			0.169334
$559$		0			0
$560$	1.00000			0.0422577
$561$	18.0000	−	31.1769i	0.759961	−	1.31629i
$562$	−3.00000	+	5.19615i	−0.126547	+	0.219186i
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	0.943560	+	0.331202i	$0.107454\pi$
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	−0.184950	+	0.982748i	$0.559212\pi$
$564$	−6.00000			−0.252646
$565$	6.00000	+	10.3923i	0.252422	+	0.437208i
$566$	−7.00000	−	12.1244i	−0.294232	−	0.509625i
$567$	−11.0000			−0.461957
$568$	3.00000	+	5.19615i	0.125877	+	0.218026i
$569$	−4.50000	+	7.79423i	−0.188650	+	0.326751i	−0.944800	−	0.327647i	$-0.893744\pi$
$569$	−4.50000	+	7.79423i	−0.188650	+	0.326751i	0.756151	+	0.654398i	$0.227078\pi$
$570$	−5.00000	+	8.66025i	−0.209427	+	0.362738i
$571$	17.0000			0.711428			0.355714	−	0.934595i	$-0.384238\pi$
$571$	17.0000			0.711428			0.355714	+	0.934595i	$0.384238\pi$
$572$		0			0
$573$		0			0
$574$	3.00000	−	5.19615i	0.125218	−	0.216883i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−32.0000			−1.33218			−0.666089	−	0.745873i	$-0.732033\pi$
$577$	−32.0000			−1.33218			−0.666089	+	0.745873i	$0.732033\pi$
$578$	−9.50000	−	16.4545i	−0.395148	−	0.684416i
$579$	4.00000	+	6.92820i	0.166234	+	0.287926i
$580$		0			0
$581$	−3.00000	−	5.19615i	−0.124461	−	0.215573i
$582$	10.0000	−	17.3205i	0.414513	−	0.717958i
$583$	−13.5000	+	23.3827i	−0.559113	+	0.968412i
$584$	−14.0000			−0.579324
$585$		0			0
$586$	−9.00000			−0.371787
$587$	−3.00000	+	5.19615i	−0.123823	+	0.214468i	−0.921272	−	0.388918i	$-0.872849\pi$
$587$	−3.00000	+	5.19615i	−0.123823	+	0.214468i	0.797449	+	0.603386i	$0.206182\pi$
$588$	−6.00000	+	10.3923i	−0.247436	+	0.428571i
$589$	10.0000	+	17.3205i	0.412043	+	0.713679i
$590$		0			0
$591$	27.0000	+	46.7654i	1.11063	+	1.92367i
$592$	5.50000	+	9.52628i	0.226049	+	0.391528i
$593$	−24.0000			−0.985562			−0.492781	−	0.870153i	$-0.664020\pi$
$593$	−24.0000			−0.985562			−0.492781	+	0.870153i	$0.664020\pi$
$594$	6.00000	+	10.3923i	0.246183	+	0.426401i
$595$	3.00000	−	5.19615i	0.122988	−	0.213021i
$596$	−9.00000	+	15.5885i	−0.368654	+	0.638528i
$597$	20.0000			0.818546
$598$		0			0
$599$	−18.0000			−0.735460			−0.367730	−	0.929933i	$-0.619865\pi$
$599$	−18.0000			−0.735460			−0.367730	+	0.929933i	$0.619865\pi$
$600$	1.00000	−	1.73205i	0.0408248	−	0.0707107i
$601$	9.50000	−	16.4545i	0.387513	−	0.671192i	−0.604601	−	0.796528i	$-0.706668\pi$
$601$	9.50000	−	16.4545i	0.387513	−	0.671192i	0.992114	+	0.125336i	$0.0400009\pi$
$602$	−1.00000	−	1.73205i	−0.0407570	−	0.0705931i
$603$	16.0000			0.651570
$604$	−8.00000	−	13.8564i	−0.325515	−	0.563809i
$605$	1.00000	+	1.73205i	0.0406558	+	0.0704179i
$606$	12.0000			0.487467
$607$	6.50000	+	11.2583i	0.263827	+	0.456962i	0.967256	−	0.253804i	$-0.0816819\pi$
$607$	6.50000	+	11.2583i	0.263827	+	0.456962i	−0.703429	+	0.710766i	$0.748349\pi$
$608$	2.50000	−	4.33013i	0.101388	−	0.175610i
$609$		0			0
$610$	8.00000			0.323911
$611$		0			0
$612$	−6.00000			−0.242536
$613$	−6.50000	+	11.2583i	−0.262533	+	0.454720i	−0.966914	−	0.255102i	$-0.917891\pi$
$613$	−6.50000	+	11.2583i	−0.262533	+	0.454720i	0.704382	+	0.709821i	$0.251224\pi$
$614$	1.00000	−	1.73205i	0.0403567	−	0.0698999i
$615$	−6.00000	−	10.3923i	−0.241943	−	0.419058i
$616$	−3.00000			−0.120873
$617$	9.00000	+	15.5885i	0.362326	+	0.627568i	0.988343	−	0.152242i	$-0.0486493\pi$
$617$	9.00000	+	15.5885i	0.362326	+	0.627568i	−0.626017	+	0.779809i	$0.715316\pi$
$618$	5.00000	+	8.66025i	0.201129	+	0.348367i
$619$	1.00000			0.0401934			0.0200967	−	0.999798i	$-0.493603\pi$
$619$	1.00000			0.0401934			0.0200967	+	0.999798i	$0.493603\pi$
$620$	−2.00000	−	3.46410i	−0.0803219	−	0.139122i
$621$		0			0
$622$	−15.0000	+	25.9808i	−0.601445	+	1.04173i
$623$	−9.00000			−0.360577
$624$		0			0
$625$	1.00000			0.0400000
$626$	−7.00000	+	12.1244i	−0.279776	+	0.484587i
$627$	15.0000	−	25.9808i	0.599042	−	1.03757i
$628$	−8.50000	−	14.7224i	−0.339187	−	0.587489i
$629$	66.0000			2.63159
$630$	−0.500000	−	0.866025i	−0.0199205	−	0.0345033i
$631$	−14.0000	−	24.2487i	−0.557331	−	0.965326i	−0.997718	−	0.0675178i	$-0.978492\pi$
$631$	−14.0000	−	24.2487i	−0.557331	−	0.965326i	0.440387	−	0.897808i	$-0.354841\pi$
$632$	−16.0000			−0.636446
$633$	23.0000	+	39.8372i	0.914168	+	1.58339i
$634$	7.50000	−	12.9904i	0.297863	−	0.515914i
$635$	0.500000	−	0.866025i	0.0198419	−	0.0343672i
$636$	18.0000			0.713746
$637$		0			0
$638$		0			0
$639$	3.00000	−	5.19615i	0.118678	−	0.205557i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	4.50000	+	7.79423i	0.177739	+	0.307854i	0.941106	−	0.338112i	$-0.109788\pi$
$641$	4.50000	+	7.79423i	0.177739	+	0.307854i	−0.763367	+	0.645966i	$0.776455\pi$
$642$	24.0000			0.947204
$643$	1.00000	+	1.73205i	0.0394362	+	0.0683054i	0.885070	−	0.465458i	$-0.154110\pi$
$643$	1.00000	+	1.73205i	0.0394362	+	0.0683054i	−0.845634	+	0.533764i	$0.820777\pi$
$644$		0			0
$645$	−4.00000			−0.157500
$646$	−15.0000	−	25.9808i	−0.590167	−	1.02220i
$647$	4.50000	−	7.79423i	0.176913	−	0.306423i	−0.763908	−	0.645325i	$-0.776722\pi$
$647$	4.50000	−	7.79423i	0.176913	−	0.306423i	0.940822	+	0.338902i	$0.110055\pi$
$648$	5.50000	−	9.52628i	0.216060	−	0.374228i
$649$		0			0
$650$		0			0
$651$	−8.00000			−0.313545
$652$	1.00000	−	1.73205i	0.0391630	−	0.0678323i
$653$	13.5000	−	23.3827i	0.528296	−	0.915035i	−0.471160	−	0.882048i	$-0.656165\pi$
$653$	13.5000	−	23.3827i	0.528296	−	0.915035i	0.999456	−	0.0329874i	$-0.0105021\pi$
$654$	−2.00000	−	3.46410i	−0.0782062	−	0.135457i
$655$	−9.00000			−0.351659
$656$	3.00000	+	5.19615i	0.117130	+	0.202876i
$657$	7.00000	+	12.1244i	0.273096	+	0.473016i
$658$	3.00000			0.116952
$659$	−6.00000	−	10.3923i	−0.233727	−	0.404827i	0.725175	−	0.688565i	$-0.241759\pi$
$659$	−6.00000	−	10.3923i	−0.233727	−	0.404827i	−0.958902	+	0.283738i	$0.908425\pi$
$660$	−3.00000	+	5.19615i	−0.116775	+	0.202260i
$661$	−2.00000	+	3.46410i	−0.0777910	+	0.134738i	−0.902297	−	0.431116i	$-0.858120\pi$
$661$	−2.00000	+	3.46410i	−0.0777910	+	0.134738i	0.824506	+	0.565854i	$0.191453\pi$
$662$	−20.0000			−0.777322
$663$		0			0
$664$	6.00000			0.232845
$665$	2.50000	−	4.33013i	0.0969458	−	0.167915i
$666$	5.50000	−	9.52628i	0.213121	−	0.369136i
$667$		0			0
$668$	15.0000			0.580367
$669$	19.0000	+	32.9090i	0.734582	+	1.27233i
$670$	−8.00000	−	13.8564i	−0.309067	−	0.535320i
$671$	−24.0000			−0.926510
$672$	1.00000	+	1.73205i	0.0385758	+	0.0668153i
$673$	−10.0000	+	17.3205i	−0.385472	+	0.667657i	−0.991835	−	0.127532i	$-0.959295\pi$
$673$	−10.0000	+	17.3205i	−0.385472	+	0.667657i	0.606363	+	0.795188i	$0.292628\pi$
$674$	8.00000	−	13.8564i	0.308148	−	0.533729i
$675$	4.00000			0.153960
$676$		0			0
$677$	−18.0000			−0.691796			−0.345898	−	0.938272i	$-0.612426\pi$
$677$	−18.0000			−0.691796			−0.345898	+	0.938272i	$0.612426\pi$
$678$	−12.0000	+	20.7846i	−0.460857	+	0.798228i
$679$	−5.00000	+	8.66025i	−0.191882	+	0.332350i
$680$	3.00000	+	5.19615i	0.115045	+	0.199263i
$681$	−48.0000			−1.83936
$682$	6.00000	+	10.3923i	0.229752	+	0.397942i
$683$	−3.00000	−	5.19615i	−0.114792	−	0.198825i	0.802905	−	0.596107i	$-0.203287\pi$
$683$	−3.00000	−	5.19615i	−0.114792	−	0.198825i	−0.917697	+	0.397282i	$0.869953\pi$
$684$	−5.00000			−0.191180
$685$	3.00000	+	5.19615i	0.114624	+	0.198535i
$686$	6.50000	−	11.2583i	0.248171	−	0.429845i
$687$	4.00000	−	6.92820i	0.152610	−	0.264327i
$688$	2.00000			0.0762493
$689$		0			0
$690$		0			0
$691$	−6.50000	+	11.2583i	−0.247272	+	0.428287i	−0.962768	−	0.270330i	$-0.912867\pi$
$691$	−6.50000	+	11.2583i	−0.247272	+	0.428287i	0.715496	+	0.698617i	$0.246201\pi$
$692$	−7.50000	+	12.9904i	−0.285107	+	0.493820i
$693$	1.50000	+	2.59808i	0.0569803	+	0.0986928i
$694$	6.00000			0.227757
$695$	9.50000	+	16.4545i	0.360356	+	0.624154i
$696$		0			0
$697$	36.0000			1.36360
$698$	1.00000	+	1.73205i	0.0378506	+	0.0655591i
$699$	−24.0000	+	41.5692i	−0.907763	+	1.57229i
$700$	−0.500000	+	0.866025i	−0.0188982	+	0.0327327i
$701$	6.00000			0.226617			0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000			0.226617			0.113308	+	0.993560i	$0.463855\pi$
$702$		0			0
$703$	55.0000			2.07436
$704$	1.50000	−	2.59808i	0.0565334	−	0.0979187i
$705$	3.00000	−	5.19615i	0.112987	−	0.195698i
$706$	3.00000	+	5.19615i	0.112906	+	0.195560i
$707$	−6.00000			−0.225653
$708$		0			0
$709$	−5.00000	−	8.66025i	−0.187779	−	0.325243i	0.756730	−	0.653727i	$-0.226796\pi$
$709$	−5.00000	−	8.66025i	−0.187779	−	0.325243i	−0.944509	+	0.328484i	$0.893462\pi$
$710$	−6.00000			−0.225176
$711$	8.00000	+	13.8564i	0.300023	+	0.519656i
$712$	4.50000	−	7.79423i	0.168645	−	0.292101i
$713$		0			0
$714$	12.0000			0.449089
$715$		0			0
$716$	−24.0000			−0.896922
$717$		0			0
$718$	−3.00000	+	5.19615i	−0.111959	+	0.193919i
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$	1.00000			0.0372678
$721$	−2.50000	−	4.33013i	−0.0931049	−	0.161262i
$722$	−3.00000	−	5.19615i	−0.111648	−	0.193381i
$723$	46.0000			1.71076
$724$	−4.00000	−	6.92820i	−0.148659	−	0.257485i
$725$		0			0
$726$	−2.00000	+	3.46410i	−0.0742270	+	0.128565i
$727$	29.0000			1.07555			0.537775	−	0.843088i	$-0.319265\pi$
$727$	29.0000			1.07555			0.537775	+	0.843088i	$0.319265\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	7.00000	−	12.1244i	0.259082	−	0.448743i
$731$	6.00000	−	10.3923i	0.221918	−	0.384373i
$732$	8.00000	+	13.8564i	0.295689	+	0.512148i
$733$	25.0000			0.923396			0.461698	−	0.887037i	$-0.347240\pi$
$733$	25.0000			0.923396			0.461698	+	0.887037i	$0.347240\pi$
$734$	−16.0000	−	27.7128i	−0.590571	−	1.02290i
$735$	−6.00000	−	10.3923i	−0.221313	−	0.383326i
$736$		0			0
$737$	24.0000	+	41.5692i	0.884051	+	1.53122i
$738$	3.00000	−	5.19615i	0.110432	−	0.191273i
$739$	−3.50000	+	6.06218i	−0.128750	+	0.223001i	−0.923192	−	0.384338i	$-0.874430\pi$
$739$	−3.50000	+	6.06218i	−0.128750	+	0.223001i	0.794443	+	0.607339i	$0.207763\pi$
$740$	−11.0000			−0.404368
$741$		0			0
$742$	−9.00000			−0.330400
$743$	6.00000	−	10.3923i	0.220119	−	0.381257i	−0.734725	−	0.678365i	$-0.762689\pi$
$743$	6.00000	−	10.3923i	0.220119	−	0.381257i	0.954844	+	0.297108i	$0.0960222\pi$
$744$	4.00000	−	6.92820i	0.146647	−	0.254000i
$745$	−9.00000	−	15.5885i	−0.329734	−	0.571117i
$746$	14.0000			0.512576
$747$	−3.00000	−	5.19615i	−0.109764	−	0.190117i
$748$	−9.00000	−	15.5885i	−0.329073	−	0.569970i
$749$	−12.0000			−0.438470
$750$	1.00000	+	1.73205i	0.0365148	+	0.0632456i
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	−0.227153	−	0.973859i	$-0.572942\pi$
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	0.956963	−	0.290209i	$-0.0937250\pi$
$752$	−1.50000	+	2.59808i	−0.0546994	+	0.0947421i
$753$	30.0000			1.09326
$754$		0			0
$755$	16.0000			0.582300
$756$	−2.00000	+	3.46410i	−0.0727393	+	0.125988i
$757$	−11.5000	+	19.9186i	−0.417975	+	0.723953i	−0.995736	−	0.0922527i	$-0.970593\pi$
$757$	−11.5000	+	19.9186i	−0.417975	+	0.723953i	0.577761	+	0.816206i	$0.303927\pi$
$758$	−9.50000	−	16.4545i	−0.345056	−	0.597654i
$759$		0			0
$760$	2.50000	+	4.33013i	0.0906845	+	0.157070i
$761$	−1.50000	−	2.59808i	−0.0543750	−	0.0941802i	0.837557	−	0.546350i	$-0.183983\pi$
$761$	−1.50000	−	2.59808i	−0.0543750	−	0.0941802i	−0.891932	+	0.452170i	$0.850650\pi$
$762$	2.00000			0.0724524
$763$	1.00000	+	1.73205i	0.0362024	+	0.0627044i
$764$		0			0
$765$	3.00000	−	5.19615i	0.108465	−	0.187867i
$766$		0			0
$767$		0			0
$768$	−2.00000			−0.0721688
$769$	−17.0000	+	29.4449i	−0.613036	+	1.06181i	0.377690	+	0.925932i	$0.376718\pi$
$769$	−17.0000	+	29.4449i	−0.613036	+	1.06181i	−0.990726	+	0.135877i	$0.956615\pi$
$770$	1.50000	−	2.59808i	0.0540562	−	0.0936282i
$771$	12.0000	+	20.7846i	0.432169	+	0.748539i
$772$	4.00000			0.143963
$773$	19.5000	+	33.7750i	0.701366	+	1.21480i	0.967987	+	0.251000i	$0.0807596\pi$
$773$	19.5000	+	33.7750i	0.701366	+	1.21480i	−0.266621	+	0.963802i	$0.585907\pi$
$774$	−1.00000	−	1.73205i	−0.0359443	−	0.0622573i
$775$	4.00000			0.143684
$776$	−5.00000	−	8.66025i	−0.179490	−	0.310885i
$777$	−11.0000	+	19.0526i	−0.394623	+	0.683507i
$778$	15.0000	−	25.9808i	0.537776	−	0.931455i
$779$	30.0000			1.07486
$780$		0			0
$781$	18.0000			0.644091
$782$		0			0
$783$		0			0
$784$	3.00000	+	5.19615i	0.107143	+	0.185577i
$785$	17.0000			0.606756
$786$	−9.00000	−	15.5885i	−0.321019	−	0.556022i
$787$	−11.0000	−	19.0526i	−0.392108	−	0.679150i	0.600620	−	0.799535i	$-0.294921\pi$
$787$	−11.0000	−	19.0526i	−0.392108	−	0.679150i	−0.992727	+	0.120384i	$0.961587\pi$
$788$	27.0000			0.961835
$789$	9.00000	+	15.5885i	0.320408	+	0.554964i
$790$	8.00000	−	13.8564i	0.284627	−	0.492989i
$791$	6.00000	−	10.3923i	0.213335	−	0.369508i
$792$	−3.00000			−0.106600
$793$		0			0
$794$	13.0000			0.461353
$795$	−9.00000	+	15.5885i	−0.319197	+	0.552866i
$796$	5.00000	−	8.66025i	0.177220	−	0.306955i
$797$	−21.0000	−	36.3731i	−0.743858	−	1.28840i	−0.950726	−	0.310031i	$-0.899660\pi$
$797$	−21.0000	−	36.3731i	−0.743858	−	1.28840i	0.206868	−	0.978369i	$-0.433673\pi$
$798$	10.0000			0.353996
$799$	9.00000	+	15.5885i	0.318397	+	0.551480i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−9.00000			−0.317999
$802$	−7.50000	−	12.9904i	−0.264834	−	0.458706i
$803$	−21.0000	+	36.3731i	−0.741074	+	1.28358i
$804$	16.0000	−	27.7128i	0.564276	−	0.977356i
$805$		0			0
$806$		0			0
$807$	−12.0000			−0.422420
$808$	3.00000	−	5.19615i	0.105540	−	0.182800i
$809$	9.00000	−	15.5885i	0.316423	−	0.548061i	−0.663316	−	0.748340i	$-0.730851\pi$
$809$	9.00000	−	15.5885i	0.316423	−	0.548061i	0.979739	+	0.200279i	$0.0641847\pi$
$810$	5.50000	+	9.52628i	0.193250	+	0.334719i
$811$	49.0000			1.72062			0.860311	−	0.509769i	$-0.170269\pi$
$811$	49.0000			1.72062			0.860311	+	0.509769i	$0.170269\pi$
$812$		0			0
$813$	−20.0000	−	34.6410i	−0.701431	−	1.21491i
$814$	33.0000			1.15665
$815$	1.00000	+	1.73205i	0.0350285	+	0.0606711i
$816$	−6.00000	+	10.3923i	−0.210042	+	0.363803i
$817$	5.00000	−	8.66025i	0.174928	−	0.302984i
$818$	−5.00000			−0.174821
$819$		0			0
$820$	−6.00000			−0.209529
$821$	18.0000	−	31.1769i	0.628204	−	1.08808i	−0.359708	−	0.933065i	$-0.617124\pi$
$821$	18.0000	−	31.1769i	0.628204	−	1.08808i	0.987912	−	0.155017i	$-0.0495431\pi$
$822$	−6.00000	+	10.3923i	−0.209274	+	0.362473i
$823$	21.5000	+	37.2391i	0.749443	+	1.29807i	0.948090	+	0.318002i	$0.103012\pi$
$823$	21.5000	+	37.2391i	0.749443	+	1.29807i	−0.198647	+	0.980071i	$0.563655\pi$
$824$	5.00000			0.174183
$825$	−3.00000	−	5.19615i	−0.104447	−	0.180907i
$826$		0			0
$827$	−36.0000			−1.25184			−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000			−1.25184			−0.625921	+	0.779886i	$0.715277\pi$
$828$		0			0
$829$	20.0000	−	34.6410i	0.694629	−	1.20313i	−0.275677	−	0.961250i	$-0.588902\pi$
$829$	20.0000	−	34.6410i	0.694629	−	1.20313i	0.970306	−	0.241882i	$-0.0777647\pi$
$830$	−3.00000	+	5.19615i	−0.104132	+	0.180361i
$831$	2.00000			0.0693792
$832$		0			0
$833$	36.0000			1.24733
$834$	−19.0000	+	32.9090i	−0.657916	+	1.13954i
$835$	−7.50000	+	12.9904i	−0.259548	+	0.449551i
$836$	−7.50000	−	12.9904i	−0.259393	−	0.449282i
$837$	16.0000			0.553041
$838$	18.0000	+	31.1769i	0.621800	+	1.07699i
$839$	−12.0000	−	20.7846i	−0.414286	−	0.717564i	0.581067	−	0.813856i	$-0.302635\pi$
$839$	−12.0000	−	20.7846i	−0.414286	−	0.717564i	−0.995353	+	0.0962912i	$0.969302\pi$
$840$	−2.00000			−0.0690066
$841$	14.5000	+	25.1147i	0.500000	+	0.866025i
$842$	−5.00000	+	8.66025i	−0.172311	+	0.298452i
$843$	6.00000	−	10.3923i	0.206651	−	0.357930i
$844$	23.0000			0.791693
$845$		0			0
$846$	3.00000			0.103142
$847$	1.00000	−	1.73205i	0.0343604	−	0.0595140i
$848$	4.50000	−	7.79423i	0.154531	−	0.267655i
$849$	14.0000	+	24.2487i	0.480479	+	0.832214i
$850$	−6.00000			−0.205798
$851$		0			0
$852$	−6.00000	−	10.3923i	−0.205557	−	0.356034i
$853$	46.0000			1.57501			0.787505	−	0.616308i	$-0.211372\pi$
$853$	46.0000			1.57501			0.787505	+	0.616308i	$0.211372\pi$
$854$	−4.00000	−	6.92820i	−0.136877	−	0.237078i
$855$	2.50000	−	4.33013i	0.0854982	−	0.148087i
$856$	6.00000	−	10.3923i	0.205076	−	0.355202i
$857$	−12.0000			−0.409912			−0.204956	−	0.978771i	$-0.565705\pi$
$857$	−12.0000			−0.409912			−0.204956	+	0.978771i	$0.565705\pi$
$858$		0			0
$859$	−31.0000			−1.05771			−0.528853	−	0.848713i	$-0.677378\pi$
$859$	−31.0000			−1.05771			−0.528853	+	0.848713i	$0.677378\pi$
$860$	−1.00000	+	1.73205i	−0.0340997	+	0.0590624i
$861$	−6.00000	+	10.3923i	−0.204479	+	0.354169i
$862$	15.0000	+	25.9808i	0.510902	+	0.884908i
$863$	−36.0000			−1.22545			−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000			−1.22545			−0.612727	+	0.790295i	$0.709928\pi$
$864$	−2.00000	−	3.46410i	−0.0680414	−	0.117851i
$865$	−7.50000	−	12.9904i	−0.255008	−	0.441686i
$866$	−16.0000			−0.543702
$867$	19.0000	+	32.9090i	0.645274	+	1.11765i
$868$	−2.00000	+	3.46410i	−0.0678844	+	0.117579i
$869$	−24.0000	+	41.5692i	−0.814144	+	1.41014i
$870$		0			0
$871$		0			0
$872$	−2.00000			−0.0677285
$873$	−5.00000	+	8.66025i	−0.169224	+	0.293105i
$874$		0			0
$875$	−0.500000	−	0.866025i	−0.0169031	−	0.0292770i
$876$	28.0000			0.946032
$877$	−5.00000	−	8.66025i	−0.168838	−	0.292436i	0.769174	−	0.639040i	$-0.220668\pi$
$877$	−5.00000	−	8.66025i	−0.168838	−	0.292436i	−0.938012	+	0.346604i	$0.887335\pi$
$878$	−10.0000	−	17.3205i	−0.337484	−	0.584539i
$879$	18.0000			0.607125
$880$	1.50000	+	2.59808i	0.0505650	+	0.0875811i
$881$	7.50000	−	12.9904i	0.252681	−	0.437657i	−0.711582	−	0.702603i	$-0.752021\pi$
$881$	7.50000	−	12.9904i	0.252681	−	0.437657i	0.964263	+	0.264946i	$0.0853542\pi$
$882$	3.00000	−	5.19615i	0.101015	−	0.174964i
$883$	−52.0000			−1.74994			−0.874970	−	0.484178i	$-0.839119\pi$
$883$	−52.0000			−1.74994			−0.874970	+	0.484178i	$0.839119\pi$
$884$		0			0
$885$		0			0
$886$	9.00000	−	15.5885i	0.302361	−	0.523704i
$887$	13.5000	−	23.3827i	0.453286	−	0.785114i	−0.545302	−	0.838240i	$-0.683585\pi$
$887$	13.5000	−	23.3827i	0.453286	−	0.785114i	0.998588	+	0.0531258i	$0.0169184\pi$
$888$	−11.0000	−	19.0526i	−0.369136	−	0.639362i
$889$	−1.00000			−0.0335389
$890$	4.50000	+	7.79423i	0.150840	+	0.261263i
$891$	−16.5000	−	28.5788i	−0.552771	−	0.957427i
$892$	19.0000			0.636167
$893$	7.50000	+	12.9904i	0.250978	+	0.434707i
$894$	18.0000	−	31.1769i	0.602010	−	1.04271i
$895$	12.0000	−	20.7846i	0.401116	−	0.694753i
$896$	1.00000			0.0334077
$897$		0			0
$898$	−9.00000			−0.300334
$899$		0			0
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−27.0000	−	46.7654i	−0.899500	−	1.55798i
$902$	18.0000			0.599334
$903$	2.00000	+	3.46410i	0.0665558	+	0.115278i
$904$	6.00000	+	10.3923i	0.199557	+	0.345643i
$905$	8.00000			0.265929
$906$	16.0000	+	27.7128i	0.531564	+	0.920697i
$907$	−4.00000	+	6.92820i	−0.132818	+	0.230047i	−0.924762	−	0.380547i	$-0.875736\pi$
$907$	−4.00000	+	6.92820i	−0.132818	+	0.230047i	0.791944	+	0.610594i	$0.209069\pi$
$908$	−12.0000	+	20.7846i	−0.398234	+	0.689761i
$909$	−6.00000			−0.199007
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$	−5.00000	+	8.66025i	−0.165567	+	0.286770i
$913$	9.00000	−	15.5885i	0.297857	−	0.515903i
$914$	−2.00000	−	3.46410i	−0.0661541	−	0.114582i
$915$	−16.0000			−0.528944
$916$	−2.00000	−	3.46410i	−0.0660819	−	0.114457i
$917$	4.50000	+	7.79423i	0.148603	+	0.257388i
$918$	−24.0000			−0.792118
$919$	17.0000	+	29.4449i	0.560778	+	0.971296i	0.997429	+	0.0716652i	$0.0228313\pi$
$919$	17.0000	+	29.4449i	0.560778	+	0.971296i	−0.436650	+	0.899631i	$0.643835\pi$
$920$		0			0
$921$	−2.00000	+	3.46410i	−0.0659022	+	0.114146i
$922$	42.0000			1.38320
$923$		0			0
$924$	6.00000			0.197386
$925$	5.50000	−	9.52628i	0.180839	−	0.313222i
$926$	4.00000	−	6.92820i	0.131448	−	0.227675i
$927$	−2.50000	−	4.33013i	−0.0821108	−	0.142220i
$928$		0			0
$929$	21.0000	+	36.3731i	0.688988	+	1.19336i	0.972166	+	0.234294i	$0.0752779\pi$
$929$	21.0000	+	36.3731i	0.688988	+	1.19336i	−0.283178	+	0.959067i	$0.591389\pi$
$930$	4.00000	+	6.92820i	0.131165	+	0.227185i
$931$	30.0000			0.983210
$932$	12.0000	+	20.7846i	0.393073	+	0.680823i
$933$	30.0000	−	51.9615i	0.982156	−	1.70114i
$934$	6.00000	−	10.3923i	0.196326	−	0.340047i
$935$	18.0000			0.588663
$936$		0			0
$937$	50.0000			1.63343			0.816714	−	0.577042i	$-0.195793\pi$
$937$	50.0000			1.63343			0.816714	+	0.577042i	$0.195793\pi$
$938$	−8.00000	+	13.8564i	−0.261209	+	0.452428i
$939$	14.0000	−	24.2487i	0.456873	−	0.791327i
$940$	−1.50000	−	2.59808i	−0.0489246	−	0.0847399i
$941$		0			0			−	1.00000i	$-0.5\pi$
$941$		0			0				1.00000i	$0.5\pi$
$942$	17.0000	+	29.4449i	0.553890	+	0.959366i
$943$		0			0
$944$		0			0
$945$	−2.00000	−	3.46410i	−0.0650600	−	0.112687i
$946$	3.00000	−	5.19615i	0.0975384	−	0.168941i
$947$	24.0000	−	41.5692i	0.779895	−	1.35082i	−0.152106	−	0.988364i	$-0.548606\pi$
$947$	24.0000	−	41.5692i	0.779895	−	1.35082i	0.932002	−	0.362454i	$-0.118061\pi$
$948$	32.0000			1.03931
$949$		0			0
$950$	−5.00000			−0.162221
$951$	−15.0000	+	25.9808i	−0.486408	+	0.842484i
$952$	3.00000	−	5.19615i	0.0972306	−	0.168408i
$953$	−12.0000	−	20.7846i	−0.388718	−	0.673280i	0.603559	−	0.797318i	$-0.293749\pi$
$953$	−12.0000	−	20.7846i	−0.388718	−	0.673280i	−0.992277	+	0.124039i	$0.960415\pi$
$954$	−9.00000			−0.291386
$955$		0			0
$956$		0			0
$957$		0			0
$958$	−15.0000	−	25.9808i	−0.484628	−	0.839400i
$959$	3.00000	−	5.19615i	0.0968751	−	0.167793i
$960$	1.00000	−	1.73205i	0.0322749	−	0.0559017i
$961$	−15.0000			−0.483871
$962$		0			0
$963$	−12.0000			−0.386695
$964$	11.5000	−	19.9186i	0.370390	−	0.641534i
$965$	−2.00000	+	3.46410i	−0.0643823	+	0.111513i
$966$		0			0
$967$	−5.00000			−0.160789			−0.0803946	−	0.996763i	$-0.525618\pi$
$967$	−5.00000			−0.160789			−0.0803946	+	0.996763i	$0.525618\pi$
$968$	1.00000	+	1.73205i	0.0321412	+	0.0556702i
$969$	30.0000	+	51.9615i	0.963739	+	1.66924i
$970$	10.0000			0.321081
$971$	−16.5000	−	28.5788i	−0.529510	−	0.917139i	−0.999408	−	0.0344175i	$-0.989042\pi$
$971$	−16.5000	−	28.5788i	−0.529510	−	0.917139i	0.469897	−	0.882721i	$-0.344291\pi$
$972$	−5.00000	+	8.66025i	−0.160375	+	0.277778i
$973$	9.50000	−	16.4545i	0.304556	−	0.527506i
$974$	19.0000			0.608799
$975$		0			0
$976$	8.00000			0.256074
$977$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$977$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$978$	−2.00000	+	3.46410i	−0.0639529	+	0.110770i
$979$	−13.5000	−	23.3827i	−0.431462	−	0.747314i
$980$	−6.00000			−0.191663
$981$	1.00000	+	1.73205i	0.0319275	+	0.0553001i
$982$	−13.5000	−	23.3827i	−0.430802	−	0.746171i
$983$	−39.0000			−1.24391			−0.621953	−	0.783054i	$-0.713661\pi$
$983$	−39.0000			−1.24391			−0.621953	+	0.783054i	$0.713661\pi$
$984$	−6.00000	−	10.3923i	−0.191273	−	0.331295i
$985$	−13.5000	+	23.3827i	−0.430146	+	0.745034i
$986$		0			0
$987$	−6.00000			−0.190982
$988$		0			0
$989$		0			0
$990$	1.50000	−	2.59808i	0.0476731	−	0.0825723i
$991$	11.0000	−	19.0526i	0.349427	−	0.605224i	−0.636721	−	0.771094i	$-0.719710\pi$
$991$	11.0000	−	19.0526i	0.349427	−	0.605224i	0.986148	+	0.165870i	$0.0530431\pi$
$992$	−2.00000	−	3.46410i	−0.0635001	−	0.109985i
$993$	40.0000			1.26936
$994$	3.00000	+	5.19615i	0.0951542	+	0.164812i
$995$	5.00000	+	8.66025i	0.158511	+	0.274549i
$996$	−12.0000			−0.380235
$997$	−20.5000	−	35.5070i	−0.649242	−	1.12452i	−0.983304	−	0.181968i	$-0.941753\pi$
$997$	−20.5000	−	35.5070i	−0.649242	−	1.12452i	0.334063	−	0.942551i	$-0.391580\pi$
$998$	−2.00000	+	3.46410i	−0.0633089	+	0.109654i
$999$	22.0000	−	38.1051i	0.696049	−	1.20559i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.e.e.191.1		2
13.2	odd	12		1690.2.l.i.361.1		4
13.3	even	3	inner	1690.2.e.e.991.1		2
13.4	even	6		1690.2.a.a.1.1		1
13.5	odd	4		1690.2.l.i.1161.2		4
13.6	odd	12		1690.2.d.a.1351.1		2
13.7	odd	12		1690.2.d.a.1351.2		2
13.8	odd	4		1690.2.l.i.1161.1		4
13.9	even	3		1690.2.a.g.1.1		1
13.10	even	6		130.2.e.b.81.1	yes	2
13.11	odd	12		1690.2.l.i.361.2		4
13.12	even	2		130.2.e.b.61.1	✓	2
39.23	odd	6		1170.2.i.f.991.1		2
39.38	odd	2		1170.2.i.f.451.1		2
52.23	odd	6		1040.2.q.c.81.1		2
52.51	odd	2		1040.2.q.c.321.1		2
65.4	even	6		8450.2.a.w.1.1		1
65.9	even	6		8450.2.a.k.1.1		1
65.12	odd	4		650.2.o.b.399.2		4
65.23	odd	12		650.2.o.b.549.2		4
65.38	odd	4		650.2.o.b.399.1		4
65.49	even	6		650.2.e.a.601.1		2
65.62	odd	12		650.2.o.b.549.1		4
65.64	even	2		650.2.e.a.451.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.e.b.61.1	✓	2	13.12	even	2
130.2.e.b.81.1	yes	2	13.10	even	6
650.2.e.a.451.1		2	65.64	even	2
650.2.e.a.601.1		2	65.49	even	6
650.2.o.b.399.1		4	65.38	odd	4
650.2.o.b.399.2		4	65.12	odd	4
650.2.o.b.549.1		4	65.62	odd	12
650.2.o.b.549.2		4	65.23	odd	12
1040.2.q.c.81.1		2	52.23	odd	6
1040.2.q.c.321.1		2	52.51	odd	2
1170.2.i.f.451.1		2	39.38	odd	2
1170.2.i.f.991.1		2	39.23	odd	6
1690.2.a.a.1.1		1	13.4	even	6
1690.2.a.g.1.1		1	13.9	even	3
1690.2.d.a.1351.1		2	13.6	odd	12
1690.2.d.a.1351.2		2	13.7	odd	12
1690.2.e.e.191.1		2	1.1	even	1	trivial
1690.2.e.e.991.1		2	13.3	even	3	inner
1690.2.l.i.361.1		4	13.2	odd	12
1690.2.l.i.361.2		4	13.11	odd	12
1690.2.l.i.1161.1		4	13.8	odd	4
1690.2.l.i.1161.2		4	13.5	odd	4
8450.2.a.k.1.1		1	65.9	even	6
8450.2.a.w.1.1		1	65.4	even	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:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(1.00000 + 1.73205i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(1.00000 + 1.73205i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(1.50000 - 2.59808i) q^{11} -2.00000 q^{12} +1.00000 q^{14} +(1.00000 - 1.73205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +1.00000 q^{18} +(2.50000 + 4.33013i) q^{19} +(-0.500000 - 0.866025i) q^{20} -2.00000 q^{21} +(1.50000 + 2.59808i) q^{22} +(1.00000 - 1.73205i) q^{24} +1.00000 q^{25} +4.00000 q^{27} +(-0.500000 + 0.866025i) q^{28} +(1.00000 + 1.73205i) q^{30} +4.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{33} -6.00000 q^{34} +(-0.500000 - 0.866025i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(5.50000 - 9.52628i) q^{37} -5.00000 q^{38} +1.00000 q^{40} +(3.00000 - 5.19615i) q^{41} +(1.00000 - 1.73205i) q^{42} +(-1.00000 - 1.73205i) q^{43} -3.00000 q^{44} +(-0.500000 - 0.866025i) q^{45} +3.00000 q^{47} +(1.00000 + 1.73205i) q^{48} +(3.00000 - 5.19615i) q^{49} +(-0.500000 + 0.866025i) q^{50} +12.0000 q^{51} -9.00000 q^{53} +(-2.00000 + 3.46410i) q^{54} +(1.50000 - 2.59808i) q^{55} +(-0.500000 - 0.866025i) q^{56} +10.0000 q^{57} -2.00000 q^{60} +(-4.00000 - 6.92820i) q^{61} +(-2.00000 + 3.46410i) q^{62} +(-0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +6.00000 q^{66} +(-8.00000 + 13.8564i) q^{67} +(3.00000 - 5.19615i) q^{68} +1.00000 q^{70} +(3.00000 + 5.19615i) q^{71} +(-0.500000 - 0.866025i) q^{72} -14.0000 q^{73} +(5.50000 + 9.52628i) q^{74} +(1.00000 - 1.73205i) q^{75} +(2.50000 - 4.33013i) q^{76} -3.00000 q^{77} -16.0000 q^{79} +(-0.500000 + 0.866025i) q^{80} +(5.50000 - 9.52628i) q^{81} +(3.00000 + 5.19615i) q^{82} +6.00000 q^{83} +(1.00000 + 1.73205i) q^{84} +(3.00000 + 5.19615i) q^{85} +2.00000 q^{86} +(1.50000 - 2.59808i) q^{88} +(4.50000 - 7.79423i) q^{89} +1.00000 q^{90} +(4.00000 - 6.92820i) q^{93} +(-1.50000 + 2.59808i) q^{94} +(2.50000 + 4.33013i) q^{95} -2.00000 q^{96} +(-5.00000 - 8.66025i) q^{97} +(3.00000 + 5.19615i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 2 q^{3} - q^{4} + 2 q^{5} + 2 q^{6} - q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 + 2 * q^3 - q^4 + 2 * q^5 + 2 * q^6 - q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} + 2 q^{3} - q^{4} + 2 q^{5} + 2 q^{6} - q^{7} + 2 q^{8} - q^{9} - q^{10} + 3 q^{11} - 4 q^{12} + 2 q^{14} + 2 q^{15} - q^{16} + 6 q^{17} + 2 q^{18} + 5 q^{19} - q^{20} - 4 q^{21} + 3 q^{22} + 2 q^{24} + 2 q^{25} + 8 q^{27} - q^{28} + 2 q^{30} + 8 q^{31} - q^{32} - 6 q^{33} - 12 q^{34} - q^{35} - q^{36} + 11 q^{37} - 10 q^{38} + 2 q^{40} + 6 q^{41} + 2 q^{42} - 2 q^{43} - 6 q^{44} - q^{45} + 6 q^{47} + 2 q^{48} + 6 q^{49} - q^{50} + 24 q^{51} - 18 q^{53} - 4 q^{54} + 3 q^{55} - q^{56} + 20 q^{57} - 4 q^{60} - 8 q^{61} - 4 q^{62} - q^{63} + 2 q^{64} + 12 q^{66} - 16 q^{67} + 6 q^{68} + 2 q^{70} + 6 q^{71} - q^{72} - 28 q^{73} + 11 q^{74} + 2 q^{75} + 5 q^{76} - 6 q^{77} - 32 q^{79} - q^{80} + 11 q^{81} + 6 q^{82} + 12 q^{83} + 2 q^{84} + 6 q^{85} + 4 q^{86} + 3 q^{88} + 9 q^{89} + 2 q^{90} + 8 q^{93} - 3 q^{94} + 5 q^{95} - 4 q^{96} - 10 q^{97} + 6 q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q - q^2 + 2 * q^3 - q^4 + 2 * q^5 + 2 * q^6 - q^7 + 2 * q^8 - q^9 - q^10 + 3 * q^11 - 4 * q^12 + 2 * q^14 + 2 * q^15 - q^16 + 6 * q^17 + 2 * q^18 + 5 * q^19 - q^20 - 4 * q^21 + 3 * q^22 + 2 * q^24 + 2 * q^25 + 8 * q^27 - q^28 + 2 * q^30 + 8 * q^31 - q^32 - 6 * q^33 - 12 * q^34 - q^35 - q^36 + 11 * q^37 - 10 * q^38 + 2 * q^40 + 6 * q^41 + 2 * q^42 - 2 * q^43 - 6 * q^44 - q^45 + 6 * q^47 + 2 * q^48 + 6 * q^49 - q^50 + 24 * q^51 - 18 * q^53 - 4 * q^54 + 3 * q^55 - q^56 + 20 * q^57 - 4 * q^60 - 8 * q^61 - 4 * q^62 - q^63 + 2 * q^64 + 12 * q^66 - 16 * q^67 + 6 * q^68 + 2 * q^70 + 6 * q^71 - q^72 - 28 * q^73 + 11 * q^74 + 2 * q^75 + 5 * q^76 - 6 * q^77 - 32 * q^79 - q^80 + 11 * q^81 + 6 * q^82 + 12 * q^83 + 2 * q^84 + 6 * q^85 + 4 * q^86 + 3 * q^88 + 9 * q^89 + 2 * q^90 + 8 * q^93 - 3 * q^94 + 5 * q^95 - 4 * q^96 - 10 * q^97 + 6 * q^98 - 6 * q^99

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