LMFDB - Embedded newform 686.2.c.c.361.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [686,2,Mod(361,686)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(686, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("686.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 686 = 2 \cdot 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	686.c (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:	$5.47773757866$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.3
Root			$-0.623490 - 1.07992i$ of defining polynomial
Character	$\chi$	$=$	686.361
Dual form			686.2.c.c.667.3

$q$-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} +(0.623490 - 1.07992i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.678448 - 1.17511i) q^{5} +1.24698 q^{6} -1.00000 q^{8} +(0.722521 + 1.25144i) q^{9} +(0.678448 - 1.17511i) q^{10} +(0.167563 - 0.290227i) q^{11} +(0.623490 + 1.07992i) q^{12} +6.38404 q^{13} -1.69202 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.48039 - 2.56410i) q^{17} +(-0.722521 + 1.25144i) q^{18} +(-2.05496 - 3.55929i) q^{19} +1.35690 q^{20} +0.335126 q^{22} +(1.82640 + 3.16341i) q^{23} +(-0.623490 + 1.07992i) q^{24} +(1.57942 - 2.73563i) q^{25} +(3.19202 + 5.52874i) q^{26} +5.54288 q^{27} +4.04892 q^{29} +(-0.846011 - 1.46533i) q^{30} +(-0.352052 + 0.609771i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.208947 - 0.361908i) q^{33} +2.96077 q^{34} -1.44504 q^{36} +(-3.37047 - 5.83782i) q^{37} +(2.05496 - 3.55929i) q^{38} +(3.98039 - 6.89423i) q^{39} +(0.678448 + 1.17511i) q^{40} +6.60388 q^{41} -4.91185 q^{43} +(0.167563 + 0.290227i) q^{44} +(0.980386 - 1.69808i) q^{45} +(-1.82640 + 3.16341i) q^{46} +(0.431468 + 0.747325i) q^{47} -1.24698 q^{48} +3.15883 q^{50} +(-1.84601 - 3.19738i) q^{51} +(-3.19202 + 5.52874i) q^{52} +(-6.44385 + 11.1611i) q^{53} +(2.77144 + 4.80027i) q^{54} -0.454731 q^{55} -5.12498 q^{57} +(2.02446 + 3.50647i) q^{58} +(-4.52930 + 7.84498i) q^{59} +(0.846011 - 1.46533i) q^{60} +(-6.57942 - 11.3959i) q^{61} -0.704103 q^{62} +1.00000 q^{64} +(-4.33124 - 7.50193i) q^{65} +(0.208947 - 0.361908i) q^{66} +(-1.57457 + 2.72724i) q^{67} +(1.48039 + 2.56410i) q^{68} +4.55496 q^{69} +10.5700 q^{71} +(-0.722521 - 1.25144i) q^{72} +(-5.01089 + 8.67911i) q^{73} +(3.37047 - 5.83782i) q^{74} +(-1.96950 - 3.41127i) q^{75} +4.10992 q^{76} +7.96077 q^{78} +(4.43147 + 7.67553i) q^{79} +(-0.678448 + 1.17511i) q^{80} +(1.28836 - 2.23151i) q^{81} +(3.30194 + 5.71912i) q^{82} -17.4426 q^{83} -4.01746 q^{85} +(-2.45593 - 4.25379i) q^{86} +(2.52446 - 4.37249i) q^{87} +(-0.167563 + 0.290227i) q^{88} +(0.312823 + 0.541825i) q^{89} +1.96077 q^{90} -3.65279 q^{92} +(0.439001 + 0.760372i) q^{93} +(-0.431468 + 0.747325i) q^{94} +(-2.78836 + 4.82959i) q^{95} +(-0.623490 - 1.07992i) q^{96} +3.24698 q^{97} +0.484271 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - q^{3} - 3 q^{4} - 2 q^{6} - 6 q^{8} + 4 q^{9} - q^{12} + 18 q^{13} - 3 q^{16} - 4 q^{17} - 4 q^{18} - 13 q^{19} - 7 q^{23} + q^{24} + q^{25} + 9 q^{26} - 4 q^{27} + 6 q^{29} - 16 q^{31}+ \cdots + 28 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - q^3 - 3 * q^4 - 2 * q^6 - 6 * q^8 + 4 * q^9 - q^12 + 18 * q^13 - 3 * q^16 - 4 * q^17 - 4 * q^18 - 13 * q^19 - 7 * q^23 + q^24 + q^25 + 9 * q^26 - 4 * q^27 + 6 * q^29 - 16 * q^31 + 3 * q^32 - 7 * q^33 - 8 * q^34 - 8 * q^36 - 6 * q^37 + 13 * q^38 + 11 * q^39 + 22 * q^41 - 22 * q^43 - 7 * q^45 + 7 * q^46 + 8 * q^47 + 2 * q^48 + 2 * q^50 - 6 * q^51 - 9 * q^52 + 3 * q^53 - 2 * q^54 + 42 * q^55 + 18 * q^57 + 3 * q^58 + 4 * q^59 - 31 * q^61 - 32 * q^62 + 6 * q^64 + 14 * q^65 + 7 * q^66 - 23 * q^67 - 4 * q^68 + 28 * q^69 + 14 * q^71 - 4 * q^72 - 27 * q^73 + 6 * q^74 - 2 * q^75 + 26 * q^76 + 22 * q^78 + 32 * q^79 + 5 * q^81 + 11 * q^82 - 22 * q^83 - 56 * q^85 - 11 * q^86 + 6 * q^87 - 10 * q^89 - 14 * q^90 + 14 * q^92 - 17 * q^93 - 8 * q^94 - 14 * q^95 + q^96 + 10 * q^97 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/686\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.623490	−	1.07992i	0.359972	−	0.623490i	−0.627984	−	0.778226i	$-0.716120\pi$
$3$	0.623490	−	1.07992i	0.359972	−	0.623490i	0.987956	+	0.154737i	$0.0494529\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.678448	−	1.17511i	−0.303411	−	0.525524i	0.673495	−	0.739192i	$-0.264792\pi$
$5$	−0.678448	−	1.17511i	−0.303411	−	0.525524i	−0.976906	+	0.213668i	$0.931459\pi$
$6$	1.24698			0.509077
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	0.722521	+	1.25144i	0.240840	+	0.417148i
$10$	0.678448	−	1.17511i	0.214544	−	0.371601i
$11$	0.167563	−	0.290227i	0.0505221	−	0.0875068i	−0.839658	−	0.543115i	$-0.817245\pi$
$11$	0.167563	−	0.290227i	0.0505221	−	0.0875068i	0.890180	+	0.455608i	$0.150578\pi$
$12$	0.623490	+	1.07992i	0.179986	+	0.311745i
$13$	6.38404			1.77061			0.885307	−	0.465006i	$-0.153948\pi$
$13$	6.38404			1.77061			0.885307	+	0.465006i	$0.153948\pi$
$14$		0			0
$15$	−1.69202			−0.436878
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.48039	−	2.56410i	0.359046	−	0.621886i	−0.628755	−	0.777603i	$-0.716435\pi$
$17$	1.48039	−	2.56410i	0.359046	−	0.621886i	0.987802	+	0.155717i	$0.0497687\pi$
$18$	−0.722521	+	1.25144i	−0.170300	+	0.294968i
$19$	−2.05496	−	3.55929i	−0.471440	−	0.816558i	0.528026	−	0.849228i	$-0.322932\pi$
$19$	−2.05496	−	3.55929i	−0.471440	−	0.816558i	−0.999466	+	0.0326704i	$0.989599\pi$
$20$	1.35690			0.303411
$21$		0			0
$22$	0.335126			0.0714490
$23$	1.82640	+	3.16341i	0.380830	+	0.659617i	0.991181	−	0.132514i	$-0.0423050\pi$
$23$	1.82640	+	3.16341i	0.380830	+	0.659617i	−0.610351	+	0.792131i	$0.708972\pi$
$24$	−0.623490	+	1.07992i	−0.127269	+	0.220437i
$25$	1.57942	−	2.73563i	0.315883	−	0.547126i
$26$	3.19202	+	5.52874i	0.626007	+	1.08428i
$27$	5.54288			1.06673
$28$		0			0
$29$	4.04892			0.751865			0.375933	−	0.926647i	$-0.377322\pi$
$29$	4.04892			0.751865			0.375933	+	0.926647i	$0.377322\pi$
$30$	−0.846011	−	1.46533i	−0.154460	−	0.267532i
$31$	−0.352052	+	0.609771i	−0.0632303	+	0.109518i	−0.895908	−	0.444240i	$-0.853474\pi$
$31$	−0.352052	+	0.609771i	−0.0632303	+	0.109518i	0.832677	+	0.553759i	$0.186807\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−0.208947	−	0.361908i	−0.0363731	−	0.0630000i
$34$	2.96077			0.507768
$35$		0			0
$36$	−1.44504			−0.240840
$37$	−3.37047	−	5.83782i	−0.554102	−	0.959732i	−0.997973	−	0.0636417i	$-0.979729\pi$
$37$	−3.37047	−	5.83782i	−0.554102	−	0.959732i	0.443871	−	0.896091i	$-0.353605\pi$
$38$	2.05496	−	3.55929i	0.333358	−	0.577393i
$39$	3.98039	−	6.89423i	0.637372	−	1.10396i
$40$	0.678448	+	1.17511i	0.107272	+	0.185801i
$41$	6.60388			1.03135			0.515676	−	0.856784i	$-0.327541\pi$
$41$	6.60388			1.03135			0.515676	+	0.856784i	$0.327541\pi$
$42$		0			0
$43$	−4.91185			−0.749051			−0.374525	−	0.927217i	$-0.622194\pi$
$43$	−4.91185			−0.749051			−0.374525	+	0.927217i	$0.622194\pi$
$44$	0.167563	+	0.290227i	0.0252610	+	0.0437534i
$45$	0.980386	−	1.69808i	0.146147	−	0.253134i
$46$	−1.82640	+	3.16341i	−0.269287	+	0.466420i
$47$	0.431468	+	0.747325i	0.0629361	+	0.109009i	0.895777	−	0.444504i	$-0.146620\pi$
$47$	0.431468	+	0.747325i	0.0629361	+	0.109009i	−0.832840	+	0.553513i	$0.813287\pi$
$48$	−1.24698			−0.179986
$49$		0			0
$50$	3.15883			0.446727
$51$	−1.84601	−	3.19738i	−0.258493	−	0.447723i
$52$	−3.19202	+	5.52874i	−0.442654	+	0.766699i
$53$	−6.44385	+	11.1611i	−0.885130	+	1.53309i	−0.0395659	+	0.999217i	$0.512598\pi$
$53$	−6.44385	+	11.1611i	−0.885130	+	1.53309i	−0.845564	+	0.533874i	$0.820736\pi$
$54$	2.77144	+	4.80027i	0.377145	+	0.653234i
$55$	−0.454731			−0.0613159
$56$		0			0
$57$	−5.12498			−0.678820
$58$	2.02446	+	3.50647i	0.265824	+	0.460421i
$59$	−4.52930	+	7.84498i	−0.589665	+	1.02133i	0.404611	+	0.914489i	$0.367407\pi$
$59$	−4.52930	+	7.84498i	−0.589665	+	1.02133i	−0.994276	+	0.106841i	$0.965926\pi$
$60$	0.846011	−	1.46533i	0.109220	−	0.189174i
$61$	−6.57942	−	11.3959i	−0.842408	−	1.45909i	−0.887853	−	0.460127i	$-0.847804\pi$
$61$	−6.57942	−	11.3959i	−0.842408	−	1.45909i	0.0454453	−	0.998967i	$-0.485529\pi$
$62$	−0.704103			−0.0894212
$63$		0			0
$64$	1.00000			0.125000
$65$	−4.33124	−	7.50193i	−0.537224	−	0.930500i
$66$	0.208947	−	0.361908i	0.0257196	−	0.0445477i
$67$	−1.57457	+	2.72724i	−0.192365	+	0.333185i	−0.946033	−	0.324069i	$-0.894949\pi$
$67$	−1.57457	+	2.72724i	−0.192365	+	0.333185i	0.753669	+	0.657254i	$0.228282\pi$
$68$	1.48039	+	2.56410i	0.179523	+	0.310943i
$69$	4.55496			0.548353
$70$		0			0
$71$	10.5700			1.25443			0.627216	−	0.778846i	$-0.284195\pi$
$71$	10.5700			1.25443			0.627216	+	0.778846i	$0.284195\pi$
$72$	−0.722521	−	1.25144i	−0.0851499	−	0.147484i
$73$	−5.01089	+	8.67911i	−0.586480	+	1.01581i	0.408209	+	0.912888i	$0.366153\pi$
$73$	−5.01089	+	8.67911i	−0.586480	+	1.01581i	−0.994689	+	0.102924i	$0.967180\pi$
$74$	3.37047	−	5.83782i	0.391809	−	0.678633i
$75$	−1.96950	−	3.41127i	−0.227418	−	0.393900i
$76$	4.10992			0.471440
$77$		0			0
$78$	7.96077			0.901380
$79$	4.43147	+	7.67553i	0.498579	+	0.863564i	0.999999	−	0.00163989i	$-0.000521994\pi$
$79$	4.43147	+	7.67553i	0.498579	+	0.863564i	−0.501420	+	0.865204i	$0.667189\pi$
$80$	−0.678448	+	1.17511i	−0.0758528	+	0.131381i
$81$	1.28836	−	2.23151i	0.143152	−	0.247946i
$82$	3.30194	+	5.71912i	0.364638	+	0.631572i
$83$	−17.4426			−1.91458			−0.957290	−	0.289130i	$-0.906634\pi$
$83$	−17.4426			−1.91458			−0.957290	+	0.289130i	$0.906634\pi$
$84$		0			0
$85$	−4.01746			−0.435755
$86$	−2.45593	−	4.25379i	−0.264829	−	0.458698i
$87$	2.52446	−	4.37249i	0.270650	−	0.468780i
$88$	−0.167563	+	0.290227i	−0.0178623	+	0.0309383i
$89$	0.312823	+	0.541825i	0.0331592	+	0.0574333i	0.882129	−	0.471008i	$-0.156110\pi$
$89$	0.312823	+	0.541825i	0.0331592	+	0.0574333i	−0.848970	+	0.528442i	$0.822777\pi$
$90$	1.96077			0.206683
$91$		0			0
$92$	−3.65279			−0.380830
$93$	0.439001	+	0.760372i	0.0455223	+	0.0788469i
$94$	−0.431468	+	0.747325i	−0.0445026	+	0.0770807i
$95$	−2.78836	+	4.82959i	−0.286080	+	0.495505i
$96$	−0.623490	−	1.07992i	−0.0636347	−	0.110218i
$97$	3.24698			0.329681			0.164840	−	0.986320i	$-0.447289\pi$
$97$	3.24698			0.329681			0.164840	+	0.986320i	$0.447289\pi$
$98$		0			0
$99$	0.484271			0.0486710
$100$	1.57942	+	2.73563i	0.157942	+	0.273563i
$101$	−0.887395	+	1.53701i	−0.0882991	+	0.152939i	−0.906792	−	0.421578i	$-0.861476\pi$
$101$	−0.887395	+	1.53701i	−0.0882991	+	0.152939i	0.818493	+	0.574516i	$0.194810\pi$
$102$	1.84601	−	3.19738i	0.182782	−	0.316588i
$103$	−7.85839	−	13.6111i	−0.774310	−	1.34114i	−0.935181	−	0.354169i	$-0.884764\pi$
$103$	−7.85839	−	13.6111i	−0.774310	−	1.34114i	0.160872	−	0.986975i	$-0.448570\pi$
$104$	−6.38404			−0.626007
$105$		0			0
$106$	−12.8877			−1.25176
$107$	8.71528	+	15.0953i	0.842538	+	1.45932i	0.887742	+	0.460341i	$0.152273\pi$
$107$	8.71528	+	15.0953i	0.842538	+	1.45932i	−0.0452037	+	0.998978i	$0.514394\pi$
$108$	−2.77144	+	4.80027i	−0.266682	+	0.461906i
$109$	−3.54623	+	6.14225i	−0.339667	+	0.588321i	−0.984370	−	0.176112i	$-0.943648\pi$
$109$	−3.54623	+	6.14225i	−0.339667	+	0.588321i	0.644703	+	0.764433i	$0.276981\pi$
$110$	−0.227365	−	0.393808i	−0.0216784	−	0.0375481i
$111$	−8.40581			−0.797844
$112$		0			0
$113$	−12.9433			−1.21760			−0.608802	−	0.793322i	$-0.708350\pi$
$113$	−12.9433			−1.21760			−0.608802	+	0.793322i	$0.708350\pi$
$114$	−2.56249	−	4.43836i	−0.239999	−	0.415691i
$115$	2.47823	−	4.29242i	0.231096	−	0.400270i
$116$	−2.02446	+	3.50647i	−0.187966	+	0.325567i
$117$	4.61260	+	7.98927i	0.426435	+	0.738608i
$118$	−9.05861			−0.833912
$119$		0			0
$120$	1.69202			0.154460
$121$	5.44385	+	9.42902i	0.494895	+	0.857183i
$122$	6.57942	−	11.3959i	0.595672	−	1.03173i
$123$	4.11745	−	7.13163i	0.371258	−	0.643038i
$124$	−0.352052	−	0.609771i	−0.0316152	−	0.0547591i
$125$	−11.0707			−0.990192
$126$		0			0
$127$	10.9487			0.971539			0.485770	−	0.874087i	$-0.338539\pi$
$127$	10.9487			0.971539			0.485770	+	0.874087i	$0.338539\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−3.06249	+	5.30439i	−0.269637	+	0.467025i
$130$	4.33124	−	7.50193i	0.379875	−	0.657963i
$131$	2.21983	+	3.84486i	0.193948	+	0.335927i	0.946555	−	0.322542i	$-0.104537\pi$
$131$	2.21983	+	3.84486i	0.193948	+	0.335927i	−0.752607	+	0.658470i	$0.771204\pi$
$132$	0.417895			0.0363731
$133$		0			0
$134$	−3.14914			−0.272045
$135$	−3.76055	−	6.51347i	−0.323657	−	0.560590i
$136$	−1.48039	+	2.56410i	−0.126942	+	0.219870i
$137$	7.88135	−	13.6509i	0.673350	−	1.16628i	−0.303599	−	0.952800i	$-0.598188\pi$
$137$	7.88135	−	13.6509i	0.673350	−	1.16628i	0.976948	−	0.213476i	$-0.0684784\pi$
$138$	2.27748	+	3.94471i	0.193872	+	0.335796i
$139$	−17.9584			−1.52321			−0.761605	−	0.648042i	$-0.775588\pi$
$139$	−17.9584			−1.52321			−0.761605	+	0.648042i	$0.775588\pi$
$140$		0			0
$141$	1.07606			0.0906210
$142$	5.28501	+	9.15391i	0.443508	+	0.768179i
$143$	1.06973	−	1.85282i	0.0894552	−	0.154941i
$144$	0.722521	−	1.25144i	0.0602101	−	0.104287i
$145$	−2.74698	−	4.75791i	−0.228124	−	0.395123i
$146$	−10.0218			−0.829408
$147$		0			0
$148$	6.74094			0.554102
$149$	−7.04556	−	12.2033i	−0.577195	−	0.999731i	−0.995799	−	0.0915626i	$-0.970814\pi$
$149$	−7.04556	−	12.2033i	−0.577195	−	0.999731i	0.418604	−	0.908169i	$-0.362519\pi$
$150$	1.96950	−	3.41127i	0.160809	−	0.278529i
$151$	−6.12833	+	10.6146i	−0.498717	+	0.863803i	−0.999999	−	0.00148113i	$-0.999529\pi$
$151$	−6.12833	+	10.6146i	−0.498717	+	0.863803i	0.501282	+	0.865284i	$0.332862\pi$
$152$	2.05496	+	3.55929i	0.166679	+	0.288697i
$153$	4.27844			0.345891
$154$		0			0
$155$	0.955395			0.0767391
$156$	3.98039	+	6.89423i	0.318686	+	0.551980i
$157$	10.6027	−	18.3644i	0.846186	−	1.46564i	−0.0384014	−	0.999262i	$-0.512227\pi$
$157$	10.6027	−	18.3644i	0.846186	−	1.46564i	0.884587	−	0.466375i	$-0.154440\pi$
$158$	−4.43147	+	7.67553i	−0.352549	+	0.610632i
$159$	8.03534	+	13.9176i	0.637244	+	1.10374i
$160$	−1.35690			−0.107272
$161$		0			0
$162$	2.57673			0.202447
$163$	−9.24309	−	16.0095i	−0.723975	−	1.25396i	−0.959394	−	0.282068i	$-0.908980\pi$
$163$	−9.24309	−	16.0095i	−0.723975	−	1.25396i	0.235419	−	0.971894i	$-0.424354\pi$
$164$	−3.30194	+	5.71912i	−0.257838	+	0.446589i
$165$	−0.283520	+	0.491071i	−0.0220720	+	0.0382298i
$166$	−8.72132	−	15.1058i	−0.676906	−	1.17244i
$167$	−20.2741			−1.56886			−0.784430	−	0.620218i	$-0.787044\pi$
$167$	−20.2741			−1.56886			−0.784430	+	0.620218i	$0.787044\pi$
$168$		0			0
$169$	27.7560			2.13508
$170$	−2.00873	−	3.47922i	−0.154062	−	0.266844i
$171$	2.96950	−	5.14333i	0.227083	−	0.393320i
$172$	2.45593	−	4.25379i	0.187263	−	0.324348i
$173$	3.17845	+	5.50523i	0.241653	+	0.418555i	0.961185	−	0.275904i	$-0.0889771\pi$
$173$	3.17845	+	5.50523i	0.241653	+	0.418555i	−0.719532	+	0.694459i	$0.755644\pi$
$174$	5.04892			0.382757
$175$		0			0
$176$	−0.335126			−0.0252610
$177$	5.64795	+	9.78253i	0.424526	+	0.735300i
$178$	−0.312823	+	0.541825i	−0.0234471	+	0.0406115i
$179$	−1.73005	+	2.99654i	−0.129310	+	0.223972i	−0.923410	−	0.383816i	$-0.874610\pi$
$179$	−1.73005	+	2.99654i	−0.129310	+	0.223972i	0.794099	+	0.607788i	$0.207943\pi$
$180$	0.980386	+	1.69808i	0.0730736	+	0.126567i
$181$	13.7071			1.01884			0.509420	−	0.860518i	$-0.329860\pi$
$181$	13.7071			1.01884			0.509420	+	0.860518i	$0.329860\pi$
$182$		0			0
$183$	−16.4088			−1.21297
$184$	−1.82640	−	3.16341i	−0.134644	−	0.233210i
$185$	−4.57338	+	7.92132i	−0.336241	+	0.582387i
$186$	−0.439001	+	0.760372i	−0.0321891	+	0.0557532i
$187$	−0.496115	−	0.859297i	−0.0362795	−	0.0628380i
$188$	−0.862937			−0.0629361
$189$		0			0
$190$	−5.57673			−0.404578
$191$	3.46466	+	6.00096i	0.250694	+	0.434214i	0.963717	−	0.266926i	$-0.0860080\pi$
$191$	3.46466	+	6.00096i	0.250694	+	0.434214i	−0.713023	+	0.701140i	$0.752675\pi$
$192$	0.623490	−	1.07992i	0.0449965	−	0.0779362i
$193$	0.358092	−	0.620234i	0.0257760	−	0.0446454i	−0.852850	−	0.522157i	$-0.825128\pi$
$193$	0.358092	−	0.620234i	0.0257760	−	0.0446454i	0.878626	+	0.477511i	$0.158461\pi$
$194$	1.62349	+	2.81197i	0.116560	+	0.201887i
$195$	−10.8019			−0.773543
$196$		0			0
$197$	2.06100			0.146840			0.0734200	−	0.997301i	$-0.476609\pi$
$197$	2.06100			0.146840			0.0734200	+	0.997301i	$0.476609\pi$
$198$	0.242135	+	0.419391i	0.0172078	+	0.0298048i
$199$	−0.0108851	+	0.0188536i	−0.000771627	+	0.00133650i	−0.866411	−	0.499332i	$-0.833579\pi$
$199$	−0.0108851	+	0.0188536i	−0.000771627	+	0.00133650i	0.865639	+	0.500668i	$0.166912\pi$
$200$	−1.57942	+	2.73563i	−0.111682	+	0.193438i
$201$	1.96346	+	3.40081i	0.138492	+	0.239875i
$202$	−1.77479			−0.124874
$203$		0			0
$204$	3.69202			0.258493
$205$	−4.48039	−	7.76026i	−0.312924	−	0.542000i
$206$	7.85839	−	13.6111i	0.547520	−	0.948332i
$207$	−2.63922	+	4.57126i	−0.183438	+	0.317725i
$208$	−3.19202	−	5.52874i	−0.221327	−	0.383349i
$209$	−1.37734			−0.0952725
$210$		0			0
$211$	−27.7875			−1.91297			−0.956484	−	0.291785i	$-0.905751\pi$
$211$	−27.7875			−1.91297			−0.956484	+	0.291785i	$0.905751\pi$
$212$	−6.44385	−	11.1611i	−0.442565	−	0.766545i
$213$	6.59030	−	11.4147i	0.451560	−	0.782125i
$214$	−8.71528	+	15.0953i	−0.595765	+	1.03189i
$215$	3.33244	+	5.77195i	0.227270	+	0.393644i
$216$	−5.54288			−0.377145
$217$		0			0
$218$	−7.09246			−0.480362
$219$	6.24847	+	10.8227i	0.422233	+	0.731328i
$220$	0.227365	−	0.393808i	0.0153290	−	0.0265505i
$221$	9.45085	−	16.3693i	0.635733	−	1.10112i
$222$	−4.20291	−	7.27965i	−0.282081	−	0.488578i
$223$	−12.7017			−0.850569			−0.425285	−	0.905060i	$-0.639826\pi$
$223$	−12.7017			−0.850569			−0.425285	+	0.905060i	$0.639826\pi$
$224$		0			0
$225$	4.56465			0.304310
$226$	−6.47166	−	11.2092i	−0.430488	−	0.745627i
$227$	3.24818	−	5.62601i	0.215589	−	0.373411i	−0.737866	−	0.674948i	$-0.764166\pi$
$227$	3.24818	−	5.62601i	0.215589	−	0.373411i	0.953455	+	0.301537i	$0.0974995\pi$
$228$	2.56249	−	4.43836i	0.169705	−	0.293938i
$229$	−4.85086	−	8.40193i	−0.320554	−	0.555215i	0.660049	−	0.751223i	$-0.270536\pi$
$229$	−4.85086	−	8.40193i	−0.320554	−	0.555215i	−0.980602	+	0.196008i	$0.937202\pi$
$230$	4.95646			0.326819
$231$		0			0
$232$	−4.04892			−0.265824
$233$	−0.909698	−	1.57564i	−0.0595963	−	0.103224i	0.834688	−	0.550723i	$-0.185648\pi$
$233$	−0.909698	−	1.57564i	−0.0595963	−	0.103224i	−0.894284	+	0.447499i	$0.852315\pi$
$234$	−4.61260	+	7.98927i	−0.301535	+	0.522275i
$235$	0.585458	−	1.01404i	0.0381910	−	0.0661488i
$236$	−4.52930	−	7.84498i	−0.294833	−	0.510665i
$237$	11.0519			0.717898
$238$		0			0
$239$	8.19567			0.530134			0.265067	−	0.964230i	$-0.414606\pi$
$239$	8.19567			0.530134			0.265067	+	0.964230i	$0.414606\pi$
$240$	0.846011	+	1.46533i	0.0546098	+	0.0945869i
$241$	−2.61865	+	4.53563i	−0.168682	+	0.292165i	−0.937957	−	0.346753i	$-0.887284\pi$
$241$	−2.61865	+	4.53563i	−0.168682	+	0.292165i	0.769275	+	0.638918i	$0.220618\pi$
$242$	−5.44385	+	9.42902i	−0.349944	+	0.606120i
$243$	6.70775	+	11.6182i	0.430302	+	0.745306i
$244$	13.1588			0.842408
$245$		0			0
$246$	8.23490			0.525038
$247$	−13.1189	−	22.7227i	−0.834738	−	1.44581i
$248$	0.352052	−	0.609771i	0.0223553	−	0.0387205i
$249$	−10.8753	+	18.8366i	−0.689195	+	1.19372i
$250$	−5.53534	−	9.58750i	−0.350086	−	0.606367i
$251$	0.972853			0.0614059			0.0307030	−	0.999529i	$-0.490225\pi$
$251$	0.972853			0.0614059			0.0307030	+	0.999529i	$0.490225\pi$
$252$		0			0
$253$	1.22414			0.0769613
$254$	5.47434	+	9.48184i	0.343491	+	0.594944i
$255$	−2.50484	+	4.33852i	−0.156859	+	0.271689i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.85839	+	13.6111i	0.490193	+	0.849039i	0.999936	−	0.0112876i	$-0.00359304\pi$
$257$	7.85839	+	13.6111i	0.490193	+	0.849039i	−0.509744	+	0.860326i	$0.670260\pi$
$258$	−6.12498			−0.381325
$259$		0			0
$260$	8.66248			0.537224
$261$	2.92543	+	5.06699i	0.181079	+	0.313639i
$262$	−2.21983	+	3.84486i	−0.137142	+	0.237536i
$263$	9.28113	−	16.0754i	0.572299	−	0.991251i	−0.424031	−	0.905648i	$-0.639385\pi$
$263$	9.28113	−	16.0754i	0.572299	−	0.991251i	0.996329	−	0.0856027i	$-0.0272816\pi$
$264$	0.208947	+	0.361908i	0.0128598	+	0.0222739i
$265$	17.4873			1.07423
$266$		0			0
$267$	0.780167			0.0477455
$268$	−1.57457	−	2.72724i	−0.0961823	−	0.166593i
$269$	−5.56518	+	9.63917i	−0.339315	+	0.587711i	−0.984304	−	0.176481i	$-0.943529\pi$
$269$	−5.56518	+	9.63917i	−0.339315	+	0.587711i	0.644989	+	0.764192i	$0.276862\pi$
$270$	3.76055	−	6.51347i	0.228860	−	0.396397i
$271$	−10.0625	−	17.4287i	−0.611253	−	1.05872i	−0.991030	−	0.133643i	$-0.957333\pi$
$271$	−10.0625	−	17.4287i	−0.611253	−	1.05872i	0.379777	−	0.925078i	$-0.376001\pi$
$272$	−2.96077			−0.179523
$273$		0			0
$274$	15.7627			0.952260
$275$	−0.529303	−	0.916780i	−0.0319182	−	0.0552839i
$276$	−2.27748	+	3.94471i	−0.137088	+	0.237444i
$277$	12.9242	−	22.3854i	0.776542	−	1.34501i	−0.157382	−	0.987538i	$-0.550305\pi$
$277$	12.9242	−	22.3854i	0.776542	−	1.34501i	0.933924	−	0.357472i	$-0.116361\pi$
$278$	−8.97919	−	15.5524i	−0.538536	−	0.932772i
$279$	−1.01746			−0.0609136
$280$		0			0
$281$	−13.0737			−0.779910			−0.389955	−	0.920834i	$-0.627509\pi$
$281$	−13.0737			−0.779910			−0.389955	+	0.920834i	$0.627509\pi$
$282$	0.538032	+	0.931899i	0.0320394	+	0.0554938i
$283$	−2.88859	+	5.00319i	−0.171709	+	0.297409i	−0.939017	−	0.343870i	$-0.888262\pi$
$283$	−2.88859	+	5.00319i	−0.171709	+	0.297409i	0.767308	+	0.641278i	$0.221596\pi$
$284$	−5.28501	+	9.15391i	−0.313608	+	0.543185i
$285$	3.47703	+	6.02240i	0.205962	+	0.356736i
$286$	2.13946			0.126509
$287$		0			0
$288$	1.44504			0.0851499
$289$	4.11692	+	7.13071i	0.242172	+	0.419453i
$290$	2.74698	−	4.75791i	0.161308	−	0.279394i
$291$	2.02446	−	3.50647i	0.118676	−	0.205553i
$292$	−5.01089	−	8.67911i	−0.293240	−	0.507906i
$293$	20.5200			1.19879			0.599397	−	0.800452i	$-0.295407\pi$
$293$	20.5200			1.19879			0.599397	+	0.800452i	$0.295407\pi$
$294$		0			0
$295$	12.2916			0.715644
$296$	3.37047	+	5.83782i	0.195905	+	0.339317i
$297$	0.928780	−	1.60869i	0.0538933	−	0.0933459i
$298$	7.04556	−	12.2033i	0.408139	−	0.706917i
$299$	11.6598	+	20.1954i	0.674303	+	1.16793i
$300$	3.93900			0.227418
$301$		0			0
$302$	−12.2567			−0.705292
$303$	1.10656	+	1.91662i	0.0635704	+	0.110107i
$304$	−2.05496	+	3.55929i	−0.117860	+	0.204139i
$305$	−8.92758	+	15.4630i	−0.511192	+	0.885410i
$306$	2.13922	+	3.70524i	0.122291	+	0.211814i
$307$	10.2446			0.584689			0.292345	−	0.956313i	$-0.405565\pi$
$307$	10.2446			0.584689			0.292345	+	0.956313i	$0.405565\pi$
$308$		0			0
$309$	−19.5985			−1.11492
$310$	0.477697	+	0.827396i	0.0271314	+	0.0469929i
$311$	−17.3339	+	30.0232i	−0.982917	+	1.70246i	−0.332067	+	0.943256i	$0.607746\pi$
$311$	−17.3339	+	30.0232i	−0.982917	+	1.70246i	−0.650850	+	0.759206i	$0.725587\pi$
$312$	−3.98039	+	6.89423i	−0.225345	+	0.390309i
$313$	5.84966	+	10.1319i	0.330642	+	0.572689i	0.982638	−	0.185533i	$-0.0594013\pi$
$313$	5.84966	+	10.1319i	0.330642	+	0.572689i	−0.651996	+	0.758223i	$0.726068\pi$
$314$	21.2054			1.19669
$315$		0			0
$316$	−8.86294			−0.498579
$317$	3.41454	+	5.91416i	0.191780	+	0.332172i	0.945840	−	0.324633i	$-0.105241\pi$
$317$	3.41454	+	5.91416i	0.191780	+	0.332172i	−0.754060	+	0.656805i	$0.771907\pi$
$318$	−8.03534	+	13.9176i	−0.450600	+	0.780462i
$319$	0.678448	−	1.17511i	0.0379858	−	0.0657933i
$320$	−0.678448	−	1.17511i	−0.0379264	−	0.0656904i
$321$	21.7356			1.21316
$322$		0			0
$323$	−12.1685			−0.677075
$324$	1.28836	+	2.23151i	0.0715758	+	0.123973i
$325$	10.0831	−	17.4644i	0.559308	−	0.968750i
$326$	9.24309	−	16.0095i	0.511928	−	0.886685i
$327$	4.42208	+	7.65926i	0.244541	+	0.423558i
$328$	−6.60388			−0.364638
$329$		0			0
$330$	−0.567040			−0.0312145
$331$	7.63318	+	13.2211i	0.419557	+	0.726695i	0.995895	−	0.0905170i	$-0.0288519\pi$
$331$	7.63318	+	13.2211i	0.419557	+	0.726695i	−0.576337	+	0.817212i	$0.695519\pi$
$332$	8.72132	−	15.1058i	0.478645	−	0.829037i
$333$	4.87047	−	8.43590i	0.266900	−	0.462284i
$334$	−10.1371	−	17.5579i	−0.554675	−	0.960726i
$335$	4.27306			0.233462
$336$		0			0
$337$	−0.0163935			−0.000893008			−0.000446504	−	1.00000i	$-0.500142\pi$
$337$	−0.0163935			−0.000893008			−0.000446504		1.00000i	$0.500142\pi$
$338$	13.8780	+	24.0374i	0.754864	+	1.30746i
$339$	−8.07002	+	13.9777i	−0.438304	+	0.759164i
$340$	2.00873	−	3.47922i	0.108939	−	0.188687i
$341$	0.117981	+	0.204350i	0.00638906	+	0.0110662i
$342$	5.93900			0.321144
$343$		0			0
$344$	4.91185			0.264829
$345$	−3.09030	−	5.35256i	−0.166376	−	0.288172i
$346$	−3.17845	+	5.50523i	−0.170874	+	0.295963i
$347$	−9.75667	+	16.8990i	−0.523765	+	0.907188i	0.475852	+	0.879525i	$0.342140\pi$
$347$	−9.75667	+	16.8990i	−0.523765	+	0.907188i	−0.999617	+	0.0276629i	$0.991194\pi$
$348$	2.52446	+	4.37249i	0.135325	+	0.234390i
$349$	11.7778			0.630450			0.315225	−	0.949017i	$-0.397920\pi$
$349$	11.7778			0.630450			0.315225	+	0.949017i	$0.397920\pi$
$350$		0			0
$351$	35.3860			1.88876
$352$	−0.167563	−	0.290227i	−0.00893113	−	0.0154692i
$353$	−17.0836	+	29.5897i	−0.909268	+	1.57490i	−0.0941849	+	0.995555i	$0.530024\pi$
$353$	−17.0836	+	29.5897i	−0.909268	+	1.57490i	−0.815083	+	0.579344i	$0.803309\pi$
$354$	−5.64795	+	9.78253i	−0.300185	+	0.519936i
$355$	−7.17121	−	12.4209i	−0.380608	−	0.659233i
$356$	−0.625646			−0.0331592
$357$		0			0
$358$	−3.46011			−0.182872
$359$	−5.32789	−	9.22817i	−0.281195	−	0.487044i	0.690484	−	0.723347i	$-0.257398\pi$
$359$	−5.32789	−	9.22817i	−0.281195	−	0.487044i	−0.971679	+	0.236303i	$0.924064\pi$
$360$	−0.980386	+	1.69808i	−0.0516709	+	0.0894966i
$361$	1.05429	−	1.82609i	0.0554892	−	0.0961101i
$362$	6.85354	+	11.8707i	0.360214	+	0.623909i
$363$	13.5767			0.712593
$364$		0			0
$365$	13.5985			0.711778
$366$	−8.20440	−	14.2104i	−0.428851	−	0.742791i
$367$	16.5489	−	28.6636i	0.863846	−	1.49623i	−0.00434158	−	0.999991i	$-0.501382\pi$
$367$	16.5489	−	28.6636i	0.863846	−	1.49623i	0.868188	−	0.496235i	$-0.165285\pi$
$368$	1.82640	−	3.16341i	0.0952075	−	0.164904i
$369$	4.77144	+	8.26437i	0.248391	+	0.430226i
$370$	−9.14675			−0.475517
$371$		0			0
$372$	−0.878002			−0.0455223
$373$	9.28770	+	16.0868i	0.480899	+	0.832941i	0.999760	−	0.0219174i	$-0.00697708\pi$
$373$	9.28770	+	16.0868i	0.480899	+	0.832941i	−0.518861	+	0.854859i	$0.673644\pi$
$374$	0.496115	−	0.859297i	0.0256535	−	0.0444332i
$375$	−6.90246	+	11.9554i	−0.356442	+	0.617375i
$376$	−0.431468	−	0.747325i	−0.0222513	−	0.0385403i
$377$	25.8485			1.33126
$378$		0			0
$379$	8.85517			0.454859			0.227430	−	0.973795i	$-0.426968\pi$
$379$	8.85517			0.454859			0.227430	+	0.973795i	$0.426968\pi$
$380$	−2.78836	−	4.82959i	−0.143040	−	0.247753i
$381$	6.82640	−	11.8237i	0.349727	−	0.605745i
$382$	−3.46466	+	6.00096i	−0.177267	+	0.307036i
$383$	15.3485	+	26.5843i	0.784270	+	1.35840i	0.929434	+	0.368988i	$0.120296\pi$
$383$	15.3485	+	26.5843i	0.784270	+	1.35840i	−0.145165	+	0.989408i	$0.546371\pi$
$384$	1.24698			0.0636347
$385$		0			0
$386$	0.716185			0.0364528
$387$	−3.54892	−	6.14691i	−0.180402	−	0.312465i
$388$	−1.62349	+	2.81197i	−0.0824202	+	0.142756i
$389$	0.631023	−	1.09296i	0.0319941	−	0.0554154i	−0.849585	−	0.527452i	$-0.823148\pi$
$389$	0.631023	−	1.09296i	0.0319941	−	0.0554154i	0.881579	+	0.472036i	$0.156481\pi$
$390$	−5.40097	−	9.35475i	−0.273489	−	0.473696i
$391$	10.8151			0.546942
$392$		0			0
$393$	5.53617			0.279263
$394$	1.03050	+	1.78488i	0.0519158	+	0.0899208i
$395$	6.01304	−	10.4149i	0.302549	−	0.524030i
$396$	−0.242135	+	0.419391i	−0.0121678	+	0.0210752i
$397$	6.22790	+	10.7870i	0.312569	+	0.541386i	0.978918	−	0.204255i	$-0.0654770\pi$
$397$	6.22790	+	10.7870i	0.312569	+	0.541386i	−0.666349	+	0.745640i	$0.732144\pi$
$398$	−0.0217703			−0.00109124
$399$		0			0
$400$	−3.15883			−0.157942
$401$	5.91335	+	10.2422i	0.295298	+	0.511472i	0.975054	−	0.221967i	$-0.0712476\pi$
$401$	5.91335	+	10.2422i	0.295298	+	0.511472i	−0.679756	+	0.733438i	$0.737914\pi$
$402$	−1.96346	+	3.40081i	−0.0979285	+	0.169617i
$403$	−2.24751	+	3.89281i	−0.111957	+	0.193914i
$404$	−0.887395	−	1.53701i	−0.0441496	−	0.0764693i
$405$	−3.49635			−0.173735
$406$		0			0
$407$	−2.25906			−0.111978
$408$	1.84601	+	3.19738i	0.0913911	+	0.158294i
$409$	−9.20291	+	15.9399i	−0.455054	+	0.788177i	−0.998691	−	0.0511431i	$-0.983714\pi$
$409$	−9.20291	+	15.9399i	−0.455054	+	0.788177i	0.543637	+	0.839321i	$0.317047\pi$
$410$	4.48039	−	7.76026i	0.221270	−	0.383252i
$411$	−9.82789	−	17.0224i	−0.484774	−	0.839653i
$412$	15.7168			0.774310
$413$		0			0
$414$	−5.27844			−0.259421
$415$	11.8339	+	20.4970i	0.580905	+	1.00616i
$416$	3.19202	−	5.52874i	0.156502	−	0.271069i
$417$	−11.1969	+	19.3935i	−0.548313	+	0.949706i
$418$	−0.688669	−	1.19281i	−0.0336839	−	0.0583422i
$419$	−5.12067			−0.250161			−0.125081	−	0.992147i	$-0.539919\pi$
$419$	−5.12067			−0.250161			−0.125081	+	0.992147i	$0.539919\pi$
$420$		0			0
$421$	−16.4034			−0.799454			−0.399727	−	0.916634i	$-0.630895\pi$
$421$	−16.4034			−0.799454			−0.399727	+	0.916634i	$0.630895\pi$
$422$	−13.8937	−	24.0646i	−0.676336	−	1.17145i
$423$	−0.623490	+	1.07992i	−0.0303151	+	0.0525073i
$424$	6.44385	−	11.1611i	0.312941	−	0.542029i
$425$	−4.67629	−	8.09958i	−0.226833	−	0.392887i
$426$	13.1806			0.638602
$427$		0			0
$428$	−17.4306			−0.842538
$429$	−1.33393	−	2.31043i	−0.0644027	−	0.111549i
$430$	−3.33244	+	5.77195i	−0.160704	+	0.278348i
$431$	0.165407	−	0.286493i	0.00796737	−	0.0137999i	−0.862014	−	0.506884i	$-0.830797\pi$
$431$	0.165407	−	0.286493i	0.00796737	−	0.0137999i	0.869982	+	0.493084i	$0.164131\pi$
$432$	−2.77144	−	4.80027i	−0.133341	−	0.230953i
$433$	−2.45042			−0.117760			−0.0588798	−	0.998265i	$-0.518753\pi$
$433$	−2.45042			−0.117760			−0.0588798	+	0.998265i	$0.518753\pi$
$434$		0			0
$435$	−6.85086			−0.328473
$436$	−3.54623	−	6.14225i	−0.169834	−	0.294160i
$437$	7.50634	−	13.0014i	0.359077	−	0.621939i
$438$	−6.24847	+	10.8227i	−0.298564	+	0.517127i
$439$	−1.34601	−	2.33136i	−0.0642416	−	0.111270i	0.832116	−	0.554602i	$-0.187129\pi$
$439$	−1.34601	−	2.33136i	−0.0642416	−	0.111270i	−0.896357	+	0.443332i	$0.853796\pi$
$440$	0.454731			0.0216784
$441$		0			0
$442$	18.9017			0.899062
$443$	−18.2763	−	31.6555i	−0.868332	−	1.50400i	−0.863700	−	0.504007i	$-0.831859\pi$
$443$	−18.2763	−	31.6555i	−0.868332	−	1.50400i	−0.00463256	−	0.999989i	$-0.501475\pi$
$444$	4.20291	−	7.27965i	0.199461	−	0.345477i
$445$	0.424468	−	0.735200i	0.0201217	−	0.0348518i
$446$	−6.35086	−	11.0000i	−0.300722	−	0.520865i
$447$	−17.5714			−0.831096
$448$		0			0
$449$	−3.48427			−0.164433			−0.0822164	−	0.996614i	$-0.526200\pi$
$449$	−3.48427			−0.164433			−0.0822164	+	0.996614i	$0.526200\pi$
$450$	2.28232	+	3.95310i	0.107590	+	0.186351i
$451$	1.10656	−	1.91662i	0.0521061	−	0.0902503i
$452$	6.47166	−	11.2092i	0.304401	−	0.527238i
$453$	7.64191	+	13.2362i	0.359048	+	0.621890i
$454$	6.49635			0.304889
$455$		0			0
$456$	5.12498			0.239999
$457$	11.5591	+	20.0210i	0.540714	+	0.936544i	0.998863	+	0.0476684i	$0.0151791\pi$
$457$	11.5591	+	20.0210i	0.540714	+	0.936544i	−0.458150	+	0.888875i	$0.651488\pi$
$458$	4.85086	−	8.40193i	0.226666	−	0.392596i
$459$	8.20560	−	14.2125i	0.383004	−	0.663383i
$460$	2.47823	+	4.29242i	0.115548	+	0.200135i
$461$	9.69501			0.451541			0.225771	−	0.974180i	$-0.427510\pi$
$461$	9.69501			0.451541			0.225771	+	0.974180i	$0.427510\pi$
$462$		0			0
$463$	−5.84654			−0.271712			−0.135856	−	0.990729i	$-0.543378\pi$
$463$	−5.84654			−0.271712			−0.135856	+	0.990729i	$0.543378\pi$
$464$	−2.02446	−	3.50647i	−0.0939831	−	0.162784i
$465$	0.595679	−	1.03175i	0.0276239	−	0.0478461i
$466$	0.909698	−	1.57564i	0.0421409	−	0.0729903i
$467$	12.8916	+	22.3289i	0.596551	+	1.03326i	0.993326	+	0.115341i	$0.0367960\pi$
$467$	12.8916	+	22.3289i	0.596551	+	1.03326i	−0.396775	+	0.917916i	$0.629871\pi$
$468$	−9.22521			−0.426435
$469$		0			0
$470$	1.17092			0.0540103
$471$	−13.2213	−	22.9000i	−0.609206	−	1.05518i
$472$	4.52930	−	7.84498i	0.208478	−	0.361095i
$473$	−0.823044	+	1.42555i	−0.0378436	+	0.0655470i
$474$	5.52595	+	9.57123i	0.253815	+	0.439621i
$475$	−12.9825			−0.595680
$476$		0			0
$477$	−18.6233			−0.852700
$478$	4.09783	+	7.09766i	0.187431	+	0.324639i
$479$	−10.4400	+	18.0825i	−0.477014	+	0.826212i	−0.999653	−	0.0263416i	$-0.991614\pi$
$479$	−10.4400	+	18.0825i	−0.477014	+	0.826212i	0.522639	+	0.852554i	$0.324948\pi$
$480$	−0.846011	+	1.46533i	−0.0386149	+	0.0668830i
$481$	−21.5172	−	37.2689i	−0.981101	−	1.69932i
$482$	−5.23729			−0.238552
$483$		0			0
$484$	−10.8877			−0.494895
$485$	−2.20291	−	3.81555i	−0.100029	−	0.173255i
$486$	−6.70775	+	11.6182i	−0.304270	+	0.527011i
$487$	0.314979	−	0.545559i	0.0142731	−	0.0247217i	−0.858801	−	0.512310i	$-0.828790\pi$
$487$	0.314979	−	0.545559i	0.0142731	−	0.0247217i	0.873074	+	0.487588i	$0.162123\pi$
$488$	6.57942	+	11.3959i	0.297836	+	0.515867i
$489$	−23.0519			−1.04244
$490$		0			0
$491$	−7.19269			−0.324601			−0.162301	−	0.986741i	$-0.551891\pi$
$491$	−7.19269			−0.324601			−0.162301	+	0.986741i	$0.551891\pi$
$492$	4.11745	+	7.13163i	0.185629	+	0.321519i
$493$	5.99396	−	10.3818i	0.269954	−	0.467575i
$494$	13.1189	−	22.7227i	0.590249	−	1.02234i
$495$	−0.328552	−	0.569069i	−0.0147673	−	0.0255778i
$496$	0.704103			0.0316152
$497$		0			0
$498$	−21.7506			−0.974669
$499$	−10.6283	−	18.4088i	−0.475790	−	0.824092i	0.523826	−	0.851825i	$-0.324504\pi$
$499$	−10.6283	−	18.4088i	−0.475790	−	0.824092i	−0.999615	+	0.0277337i	$0.991171\pi$
$500$	5.53534	−	9.58750i	0.247548	−	0.428766i
$501$	−12.6407	+	21.8944i	−0.564745	+	0.978168i
$502$	0.486426	+	0.842515i	0.0217103	+	0.0376033i
$503$	25.7614			1.14864			0.574322	−	0.818630i	$-0.305266\pi$
$503$	25.7614			1.14864			0.574322	+	0.818630i	$0.305266\pi$
$504$		0			0
$505$	2.40821			0.107164
$506$	0.612072	+	1.06014i	0.0272099	+	0.0471290i
$507$	17.3056	−	29.9742i	0.768568	−	1.33120i
$508$	−5.47434	+	9.48184i	−0.242885	+	0.420689i
$509$	−8.59837	−	14.8928i	−0.381116	−	0.660112i	0.610106	−	0.792320i	$-0.291127\pi$
$509$	−8.59837	−	14.8928i	−0.381116	−	0.660112i	−0.991222	+	0.132208i	$0.957793\pi$
$510$	−5.00969			−0.221833
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−11.3904	−	19.7287i	−0.502898	−	0.871044i
$514$	−7.85839	+	13.6111i	−0.346619	+	0.600361i
$515$	−10.6630	+	18.4689i	−0.469869	+	0.813836i
$516$	−3.06249	−	5.30439i	−0.134819	−	0.233513i
$517$	0.289192			0.0127187
$518$		0			0
$519$	7.92692			0.347953
$520$	4.33124	+	7.50193i	0.189937	+	0.328981i
$521$	0.216480	−	0.374955i	0.00948417	−	0.0164271i	−0.861244	−	0.508191i	$-0.830314\pi$
$521$	0.216480	−	0.374955i	0.00948417	−	0.0164271i	0.870729	+	0.491764i	$0.163648\pi$
$522$	−2.92543	+	5.06699i	−0.128042	+	0.221776i
$523$	−16.4535	−	28.4984i	−0.719463	−	1.24615i	−0.961213	−	0.275808i	$-0.911055\pi$
$523$	−16.4535	−	28.4984i	−0.719463	−	1.24615i	0.241750	−	0.970339i	$-0.422279\pi$
$524$	−4.43967			−0.193948
$525$		0			0
$526$	18.5623			0.809353
$527$	1.04234	+	1.80539i	0.0454052	+	0.0786441i
$528$	−0.208947	+	0.361908i	−0.00909327	+	0.0157500i
$529$	4.82855	−	8.36330i	0.209937	−	0.363622i
$530$	8.74363	+	15.1444i	0.379799	+	0.657831i
$531$	−13.0901			−0.568060
$532$		0			0
$533$	42.1594			1.82613
$534$	0.390084	+	0.675645i	0.0168806	+	0.0292380i
$535$	11.8257	−	20.4828i	0.511271	−	0.885547i
$536$	1.57457	−	2.72724i	0.0680112	−	0.117799i
$537$	2.15734	+	3.73663i	0.0930962	+	0.161247i
$538$	−11.1304			−0.479864
$539$		0			0
$540$	7.52111			0.323657
$541$	−5.15279	−	8.92490i	−0.221536	−	0.383711i	0.733739	−	0.679432i	$-0.237774\pi$
$541$	−5.15279	−	8.92490i	−0.221536	−	0.383711i	−0.955275	+	0.295720i	$0.904440\pi$
$542$	10.0625	−	17.4287i	0.432221	−	0.748629i
$543$	8.54623	−	14.8025i	0.366754	−	0.635236i
$544$	−1.48039	−	2.56410i	−0.0634710	−	0.109935i
$545$	9.62373			0.412235
$546$		0			0
$547$	4.55363			0.194699			0.0973496	−	0.995250i	$-0.468964\pi$
$547$	4.55363			0.194699			0.0973496	+	0.995250i	$0.468964\pi$
$548$	7.88135	+	13.6509i	0.336675	+	0.583138i
$549$	9.50753	−	16.4675i	0.405772	−	0.702817i
$550$	0.529303	−	0.916780i	0.0225696	−	0.0390916i
$551$	−8.32036	−	14.4113i	−0.354459	−	0.613941i
$552$	−4.55496			−0.193872
$553$		0			0
$554$	25.8485			1.09820
$555$	5.70291	+	9.87772i	0.242075	+	0.419286i
$556$	8.97919	−	15.5524i	0.380802	−	0.659569i
$557$	14.1456	−	24.5008i	0.599366	−	1.03813i	−0.393548	−	0.919304i	$-0.628753\pi$
$557$	14.1456	−	24.5008i	0.599366	−	1.03813i	0.992915	−	0.118829i	$-0.0379141\pi$
$558$	−0.508729	−	0.881145i	−0.0215362	−	0.0373018i
$559$	−31.3575			−1.32628
$560$		0			0
$561$	−1.23729			−0.0522385
$562$	−6.53684	−	11.3221i	−0.275740	−	0.477595i
$563$	−13.0531	+	22.6086i	−0.550122	+	0.952840i	0.448143	+	0.893962i	$0.352086\pi$
$563$	−13.0531	+	22.6086i	−0.550122	+	0.952840i	−0.998265	+	0.0588781i	$0.981248\pi$
$564$	−0.538032	+	0.931899i	−0.0226552	+	0.0392400i
$565$	8.78136	+	15.2098i	0.369435	+	0.639880i
$566$	−5.77718			−0.242833
$567$		0			0
$568$	−10.5700			−0.443508
$569$	4.83124	+	8.36795i	0.202536	+	0.350803i	0.949345	−	0.314236i	$-0.101748\pi$
$569$	4.83124	+	8.36795i	0.202536	+	0.350803i	−0.746809	+	0.665039i	$0.768415\pi$
$570$	−3.47703	+	6.02240i	−0.145637	+	0.252251i
$571$	8.77077	−	15.1914i	0.367045	−	0.635741i	−0.622057	−	0.782972i	$-0.713703\pi$
$571$	8.77077	−	15.1914i	0.367045	−	0.635741i	0.989102	+	0.147231i	$0.0470360\pi$
$572$	1.06973	+	1.85282i	0.0447276	+	0.0774704i
$573$	8.64071			0.360971
$574$		0			0
$575$	11.5386			0.481191
$576$	0.722521	+	1.25144i	0.0301050	+	0.0521435i
$577$	2.52297	−	4.36991i	0.105032	−	0.181922i	−0.808719	−	0.588195i	$-0.799839\pi$
$577$	2.52297	−	4.36991i	0.105032	−	0.181922i	0.913751	+	0.406274i	$0.133172\pi$
$578$	−4.11692	+	7.13071i	−0.171241	+	0.296598i
$579$	−0.446534	−	0.773419i	−0.0185573	−	0.0321422i
$580$	5.49396			0.228124
$581$		0			0
$582$	4.04892			0.167833
$583$	2.15950	+	3.74036i	0.0894373	+	0.154910i
$584$	5.01089	−	8.67911i	0.207352	−	0.359144i
$585$	6.25882	−	10.8406i	0.258771	−	0.448204i
$586$	10.2600	+	17.7709i	0.423838	+	0.734108i
$587$	−23.3787			−0.964941			−0.482470	−	0.875912i	$-0.660260\pi$
$587$	−23.3787			−0.964941			−0.482470	+	0.875912i	$0.660260\pi$
$588$		0			0
$589$	2.89380			0.119237
$590$	6.14579	+	10.6448i	0.253018	+	0.438241i
$591$	1.28501	−	2.22571i	0.0528583	−	0.0915533i
$592$	−3.37047	+	5.83782i	−0.138525	+	0.239933i
$593$	−10.7165	−	18.5615i	−0.440073	−	0.762229i	0.557621	−	0.830095i	$-0.311714\pi$
$593$	−10.7165	−	18.5615i	−0.440073	−	0.762229i	−0.997694	+	0.0678665i	$0.978381\pi$
$594$	1.85756			0.0762166
$595$		0			0
$596$	14.0911			0.577195
$597$	0.0135735	+	0.0235101i	0.000555528	+	0.000962203i
$598$	−11.6598	+	20.1954i	−0.476804	+	0.825849i
$599$	16.9085	−	29.2864i	0.690863	−	1.19661i	−0.280693	−	0.959798i	$-0.590564\pi$
$599$	16.9085	−	29.2864i	0.690863	−	1.19661i	0.971556	−	0.236812i	$-0.0761024\pi$
$600$	1.96950	+	3.41127i	0.0804045	+	0.139265i
$601$	−44.4161			−1.81177			−0.905885	−	0.423524i	$-0.860793\pi$
$601$	−44.4161			−1.81177			−0.905885	+	0.423524i	$0.860793\pi$
$602$		0			0
$603$	−4.55065			−0.185317
$604$	−6.12833	−	10.6146i	−0.249358	−	0.431901i
$605$	7.38673	−	12.7942i	0.300313	−	0.520158i
$606$	−1.10656	+	1.91662i	−0.0449511	+	0.0778576i
$607$	−2.87263	−	4.97553i	−0.116596	−	0.201951i	0.801820	−	0.597565i	$-0.203865\pi$
$607$	−2.87263	−	4.97553i	−0.116596	−	0.201951i	−0.918417	+	0.395614i	$0.870532\pi$
$608$	−4.10992			−0.166679
$609$		0			0
$610$	−17.8552			−0.722935
$611$	2.75451	+	4.77096i	0.111436	+	0.193012i
$612$	−2.13922	+	3.70524i	−0.0864728	+	0.149775i
$613$	−20.2371	+	35.0516i	−0.817367	+	1.41572i	0.0902489	+	0.995919i	$0.471234\pi$
$613$	−20.2371	+	35.0516i	−0.817367	+	1.41572i	−0.907616	+	0.419802i	$0.862100\pi$
$614$	5.12229	+	8.87207i	0.206719	+	0.358048i
$615$	−11.1739			−0.450575
$616$		0			0
$617$	−35.3706			−1.42397			−0.711984	−	0.702196i	$-0.752203\pi$
$617$	−35.3706			−1.42397			−0.711984	+	0.702196i	$0.752203\pi$
$618$	−9.79925	−	16.9728i	−0.394184	−	0.682746i
$619$	−13.5641	+	23.4937i	−0.545188	+	0.944293i	0.453407	+	0.891303i	$0.350208\pi$
$619$	−13.5641	+	23.4937i	−0.545188	+	0.944293i	−0.998595	+	0.0529895i	$0.983125\pi$
$620$	−0.477697	+	0.827396i	−0.0191848	+	0.0332290i
$621$	10.1235	+	17.5344i	0.406242	+	0.703631i
$622$	−34.6679			−1.39005
$623$		0			0
$624$	−7.96077			−0.318686
$625$	−0.386199	−	0.668916i	−0.0154480	−	0.0267566i
$626$	−5.84966	+	10.1319i	−0.233799	+	0.404952i
$627$	−0.858756	+	1.48741i	−0.0342954	+	0.0594014i
$628$	10.6027	+	18.3644i	0.423093	+	0.732818i
$629$	−19.9584			−0.795793
$630$		0			0
$631$	−43.8418			−1.74531			−0.872656	−	0.488335i	$-0.837605\pi$
$631$	−43.8418			−1.74531			−0.872656	+	0.488335i	$0.837605\pi$
$632$	−4.43147	−	7.67553i	−0.176274	−	0.305316i
$633$	−17.3252	+	30.0081i	−0.688615	+	1.19272i
$634$	−3.41454	+	5.91416i	−0.135609	+	0.234881i
$635$	−7.42812	−	12.8659i	−0.294776	−	0.510567i
$636$	−16.0707			−0.637244
$637$		0			0
$638$	1.35690			0.0537200
$639$	7.63706	+	13.2278i	0.302118	+	0.523283i
$640$	0.678448	−	1.17511i	0.0268180	−	0.0464502i
$641$	−12.7383	+	22.0633i	−0.503131	+	0.871448i	0.496863	+	0.867829i	$0.334485\pi$
$641$	−12.7383	+	22.0633i	−0.503131	+	0.871448i	−0.999993	+	0.00361873i	$0.998848\pi$
$642$	10.8678	+	18.8235i	0.428917	+	0.742906i
$643$	−4.20344			−0.165767			−0.0828837	−	0.996559i	$-0.526413\pi$
$643$	−4.20344			−0.165767			−0.0828837	+	0.996559i	$0.526413\pi$
$644$		0			0
$645$	8.31096			0.327244
$646$	−6.08426	−	10.5382i	−0.239382	−	0.414622i
$647$	18.2141	−	31.5477i	0.716070	−	1.24027i	−0.246476	−	0.969149i	$-0.579273\pi$
$647$	18.2141	−	31.5477i	0.716070	−	1.24027i	0.962546	−	0.271120i	$-0.0873941\pi$
$648$	−1.28836	+	2.23151i	−0.0506117	+	0.0876621i
$649$	1.51789	+	2.62905i	0.0595822	+	0.103199i
$650$	20.1661			0.790981
$651$		0			0
$652$	18.4862			0.723975
$653$	18.0269	+	31.2235i	0.705448	+	1.22187i	0.966530	+	0.256554i	$0.0825873\pi$
$653$	18.0269	+	31.2235i	0.705448	+	1.22187i	−0.261082	+	0.965317i	$0.584079\pi$
$654$	−4.42208	+	7.65926i	−0.172917	+	0.299501i
$655$	3.01208	−	5.21708i	0.117692	−	0.203848i
$656$	−3.30194	−	5.71912i	−0.128919	−	0.223294i
$657$	−14.4819			−0.564992
$658$		0			0
$659$	−29.5881			−1.15259			−0.576294	−	0.817243i	$-0.695502\pi$
$659$	−29.5881			−1.15259			−0.576294	+	0.817243i	$0.695502\pi$
$660$	−0.283520	−	0.491071i	−0.0110360	−	0.0191149i
$661$	6.67025	−	11.5532i	0.259443	−	0.449368i	−0.706650	−	0.707563i	$-0.749794\pi$
$661$	6.67025	−	11.5532i	0.259443	−	0.449368i	0.966093	+	0.258195i	$0.0831278\pi$
$662$	−7.63318	+	13.2211i	−0.296672	+	0.513851i
$663$	−11.7850	−	20.4122i	−0.457692	−	0.792746i
$664$	17.4426			0.676906
$665$		0			0
$666$	9.74094			0.377454
$667$	7.39493	+	12.8084i	0.286333	+	0.495943i
$668$	10.1371	−	17.5579i	0.392215	−	0.679336i
$669$	−7.91939	+	13.7168i	−0.306181	+	0.530321i
$670$	2.13653	+	3.70058i	0.0825414	+	0.142966i
$671$	−4.40986			−0.170241
$672$		0			0
$673$	22.5332			0.868591			0.434295	−	0.900771i	$-0.356997\pi$
$673$	22.5332			0.868591			0.434295	+	0.900771i	$0.356997\pi$
$674$	−0.00819673	−	0.0141971i	−0.000315726	−	0.000546854i
$675$	8.75451	−	15.1633i	0.336961	−	0.583634i
$676$	−13.8780	+	24.0374i	−0.533769	+	0.924516i
$677$	−12.7962	−	22.1637i	−0.491798	−	0.851818i	0.508158	−	0.861264i	$-0.330327\pi$
$677$	−12.7962	−	22.1637i	−0.491798	−	0.851818i	−0.999955	+	0.00944553i	$0.996993\pi$
$678$	−16.1400			−0.619855
$679$		0			0
$680$	4.01746			0.154062
$681$	−4.05041	−	7.01551i	−0.155212	−	0.268835i
$682$	−0.117981	+	0.204350i	−0.00451774	+	0.00782496i
$683$	1.08695	−	1.88265i	0.0415910	−	0.0720377i	−0.844481	−	0.535586i	$-0.820091\pi$
$683$	1.08695	−	1.88265i	0.0415910	−	0.0720377i	0.886072	+	0.463549i	$0.153424\pi$
$684$	2.96950	+	5.14333i	0.113542	+	0.196660i
$685$	−21.3884			−0.817207
$686$		0			0
$687$	−12.0978			−0.461561
$688$	2.45593	+	4.25379i	0.0936313	+	0.162174i
$689$	−41.1378	+	71.2527i	−1.56722	+	2.71451i
$690$	3.09030	−	5.35256i	0.117646	−	0.203768i
$691$	10.2758	+	17.7981i	0.390908	+	0.677072i	0.992570	−	0.121679i	$-0.0388277\pi$
$691$	10.2758	+	17.7981i	0.390908	+	0.677072i	−0.601662	+	0.798751i	$0.705494\pi$
$692$	−6.35690			−0.241653
$693$		0			0
$694$	−19.5133			−0.740716
$695$	12.1838	+	21.1030i	0.462159	+	0.800483i
$696$	−2.52446	+	4.37249i	−0.0956894	+	0.165739i
$697$	9.77628	−	16.9330i	0.370303	−	0.641384i
$698$	5.88889	+	10.1999i	0.222898	+	0.386070i
$699$	−2.26875			−0.0858120
$700$		0			0
$701$	20.8170			0.786247			0.393124	−	0.919486i	$-0.371394\pi$
$701$	20.8170			0.786247			0.393124	+	0.919486i	$0.371394\pi$
$702$	17.6930	+	30.6451i	0.667779	+	1.15663i
$703$	−13.8523	+	23.9930i	−0.522451	+	0.904912i
$704$	0.167563	−	0.290227i	0.00631526	−	0.0109384i
$705$	−0.730054	−	1.26449i	−0.0274954	−	0.0476235i
$706$	−34.1672			−1.28590
$707$		0			0
$708$	−11.2959			−0.424526
$709$	−4.33340	−	7.50566i	−0.162744	−	0.281881i	0.773108	−	0.634275i	$-0.218701\pi$
$709$	−4.33340	−	7.50566i	−0.162744	−	0.281881i	−0.935852	+	0.352394i	$0.885368\pi$
$710$	7.17121	−	12.4209i	0.269131	−	0.466148i
$711$	−6.40366	+	11.0915i	−0.240156	+	0.415962i
$712$	−0.312823	−	0.541825i	−0.0117235	−	0.0203058i
$713$	−2.57194			−0.0963200
$714$		0			0
$715$	−2.90302			−0.108567
$716$	−1.73005	−	2.99654i	−0.0646551	−	0.111986i
$717$	5.10992	−	8.85063i	0.190833	−	0.330533i
$718$	5.32789	−	9.22817i	0.198835	−	0.344392i
$719$	13.1773	+	22.8237i	0.491429	+	0.851179i	0.999951	−	0.00986933i	$-0.00314156\pi$
$719$	13.1773	+	22.8237i	0.491429	+	0.851179i	−0.508523	+	0.861049i	$0.669808\pi$
$720$	−1.96077			−0.0730736
$721$		0			0
$722$	2.10859			0.0784735
$723$	3.26540	+	5.65583i	0.121441	+	0.210343i
$724$	−6.85354	+	11.8707i	−0.254710	+	0.441171i
$725$	6.39493	−	11.0763i	0.237502	−	0.411365i
$726$	6.78836	+	11.7578i	0.251940	+	0.436373i
$727$	16.8931			0.626529			0.313265	−	0.949666i	$-0.398577\pi$
$727$	16.8931			0.626529			0.313265	+	0.949666i	$0.398577\pi$
$728$		0			0
$729$	24.4590			0.905890
$730$	6.79925	+	11.7766i	0.251652	+	0.435873i
$731$	−7.27144	+	12.5945i	−0.268944	+	0.465824i
$732$	8.20440	−	14.2104i	0.303243	−	0.525233i
$733$	−8.52930	−	14.7732i	−0.315037	−	0.545660i	0.664408	−	0.747370i	$-0.268684\pi$
$733$	−8.52930	−	14.7732i	−0.315037	−	0.545660i	−0.979445	+	0.201710i	$0.935350\pi$
$734$	33.0978			1.22166
$735$		0			0
$736$	3.65279			0.134644
$737$	0.527680	+	0.913968i	0.0194373	+	0.0336664i
$738$	−4.77144	+	8.26437i	−0.175639	+	0.304216i
$739$	18.1722	−	31.4751i	0.668474	−	1.15783i	−0.309857	−	0.950783i	$-0.600281\pi$
$739$	18.1722	−	31.4751i	0.668474	−	1.15783i	0.978331	−	0.207048i	$-0.0663856\pi$
$740$	−4.57338	−	7.92132i	−0.168121	−	0.291194i
$741$	−32.7181			−1.20193
$742$		0			0
$743$	34.1890			1.25427			0.627136	−	0.778910i	$-0.284227\pi$
$743$	34.1890			1.25427			0.627136	+	0.778910i	$0.284227\pi$
$744$	−0.439001	−	0.760372i	−0.0160946	−	0.0278766i
$745$	−9.56010	+	16.5586i	−0.350255	+	0.606659i
$746$	−9.28770	+	16.0868i	−0.340047	+	0.588978i
$747$	−12.6027	−	21.8285i	−0.461108	−	0.798662i
$748$	0.992230			0.0362795
$749$		0			0
$750$	−13.8049			−0.504084
$751$	4.83273	+	8.37054i	0.176349	+	0.305445i	0.940627	−	0.339441i	$-0.110238\pi$
$751$	4.83273	+	8.37054i	0.176349	+	0.305445i	−0.764278	+	0.644887i	$0.776905\pi$
$752$	0.431468	−	0.747325i	0.0157340	−	0.0272521i
$753$	0.606564	−	1.05060i	0.0221044	−	0.0382860i
$754$	12.9242	+	22.3854i	0.470673	+	0.815229i
$755$	16.6310			0.605265
$756$		0			0
$757$	2.97584			0.108159			0.0540793	−	0.998537i	$-0.482778\pi$
$757$	2.97584			0.108159			0.0540793	+	0.998537i	$0.482778\pi$
$758$	4.42758	+	7.66880i	0.160817	+	0.278543i
$759$	0.763242	−	1.32197i	0.0277039	−	0.0479846i
$760$	2.78836	−	4.82959i	0.101145	−	0.175188i
$761$	−11.0942	−	19.2157i	−0.402164	−	0.696568i	0.591823	−	0.806068i	$-0.298408\pi$
$761$	−11.0942	−	19.2157i	−0.402164	−	0.696568i	−0.993987	+	0.109500i	$0.965075\pi$
$762$	13.6528			0.494588
$763$		0			0
$764$	−6.92931			−0.250694
$765$	−2.90270	−	5.02762i	−0.104947	−	0.181774i
$766$	−15.3485	+	26.5843i	−0.554562	+	0.960530i
$767$	−28.9153	+	50.0827i	−1.04407	+	1.80838i
$768$	0.623490	+	1.07992i	0.0224983	+	0.0389681i
$769$	−27.5803			−0.994571			−0.497286	−	0.867587i	$-0.665670\pi$
$769$	−27.5803			−0.994571			−0.497286	+	0.867587i	$0.665670\pi$
$770$		0			0
$771$	19.5985			0.705823
$772$	0.358092	+	0.620234i	0.0128880	+	0.0223227i
$773$	18.2664	−	31.6383i	0.656995	−	1.13795i	−0.324394	−	0.945922i	$-0.605161\pi$
$773$	18.2664	−	31.6383i	0.656995	−	1.13795i	0.981390	−	0.192027i	$-0.0615062\pi$
$774$	3.54892	−	6.14691i	0.127563	−	0.220946i
$775$	1.11207	+	1.92617i	0.0399468	+	0.0691899i
$776$	−3.24698			−0.116560
$777$		0			0
$778$	1.26205			0.0452465
$779$	−13.5707	−	23.5051i	−0.486220	−	0.842158i
$780$	5.40097	−	9.35475i	0.193386	−	0.334954i
$781$	1.77114	−	3.06771i	0.0633765	−	0.109771i
$782$	5.40754	+	9.36614i	0.193373	+	0.334932i
$783$	22.4426			0.802035
$784$		0			0
$785$	−28.7735			−1.02697
$786$	2.76809	+	4.79447i	0.0987344	+	0.171013i
$787$	7.19351	−	12.4595i	0.256421	−	0.444134i	−0.708859	−	0.705350i	$-0.750790\pi$
$787$	7.19351	−	12.4595i	0.256421	−	0.444134i	0.965281	+	0.261215i	$0.0841233\pi$
$788$	−1.03050	+	1.78488i	−0.0367100	+	0.0635836i
$789$	−11.5734	−	20.0457i	−0.412023	−	0.713645i
$790$	12.0261			0.427869
$791$		0			0
$792$	−0.484271			−0.0172078
$793$	−42.0033	−	72.7518i	−1.49158	−	2.58349i
$794$	−6.22790	+	10.7870i	−0.221020	+	0.382818i
$795$	10.9031	−	18.8848i	0.386694	−	0.669774i
$796$	−0.0108851	−	0.0188536i	−0.000385813	−	0.000668248i
$797$	−19.1564			−0.678556			−0.339278	−	0.940686i	$-0.610183\pi$
$797$	−19.1564			−0.678556			−0.339278	+	0.940686i	$0.610183\pi$
$798$		0			0
$799$	2.55496			0.0903879
$800$	−1.57942	−	2.73563i	−0.0558408	−	0.0967191i
$801$	−0.452042	+	0.782960i	−0.0159721	+	0.0276645i
$802$	−5.91335	+	10.2422i	−0.208808	+	0.361665i
$803$	1.67928	+	2.90859i	0.0592604	+	0.102642i
$804$	−3.92692			−0.138492
$805$		0			0
$806$	−4.49502			−0.158330
$807$	6.93967	+	12.0199i	0.244288	+	0.423119i
$808$	0.887395	−	1.53701i	0.0312185	−	0.0540720i
$809$	23.6386	−	40.9432i	0.831087	−	1.43949i	−0.0660893	−	0.997814i	$-0.521052\pi$
$809$	23.6386	−	40.9432i	0.831087	−	1.43949i	0.897177	−	0.441672i	$-0.145614\pi$
$810$	−1.74818	−	3.02793i	−0.0614246	−	0.106391i
$811$	35.9691			1.26305			0.631524	−	0.775357i	$-0.282430\pi$
$811$	35.9691			1.26305			0.631524	+	0.775357i	$0.282430\pi$
$812$		0			0
$813$	−25.0954			−0.880136
$814$	−1.12953	−	1.95640i	−0.0395900	−	0.0685719i
$815$	−12.5419	+	21.7232i	−0.439324	+	0.760932i
$816$	−1.84601	+	3.19738i	−0.0646233	+	0.111931i
$817$	10.0937	+	17.4827i	0.353132	+	0.611643i
$818$	−18.4058			−0.643544
$819$		0			0
$820$	8.96077			0.312924
$821$	7.97770	+	13.8178i	0.278424	+	0.482244i	0.970993	−	0.239107i	$-0.0768548\pi$
$821$	7.97770	+	13.8178i	0.278424	+	0.482244i	−0.692570	+	0.721351i	$0.743521\pi$
$822$	9.82789	−	17.0224i	0.342787	−	0.593724i
$823$	−16.2905	+	28.2160i	−0.567852	+	0.983548i	0.428926	+	0.903340i	$0.358892\pi$
$823$	−16.2905	+	28.2160i	−0.567852	+	0.983548i	−0.996778	+	0.0802087i	$0.974441\pi$
$824$	7.85839	+	13.6111i	0.273760	+	0.474166i
$825$	−1.32006			−0.0459586
$826$		0			0
$827$	18.6300			0.647827			0.323914	−	0.946087i	$-0.395001\pi$
$827$	18.6300			0.647827			0.323914	+	0.946087i	$0.395001\pi$
$828$	−2.63922	−	4.57126i	−0.0917192	−	0.158862i
$829$	8.48307	−	14.6931i	0.294629	−	0.510313i	−0.680269	−	0.732962i	$-0.738137\pi$
$829$	8.48307	−	14.6931i	0.294629	−	0.510313i	0.974899	+	0.222649i	$0.0714705\pi$
$830$	−11.8339	+	20.4970i	−0.410762	+	0.711460i
$831$	−16.1163	−	27.9142i	−0.559067	−	0.968332i
$832$	6.38404			0.221327
$833$		0			0
$834$	−22.3937			−0.775432
$835$	13.7549	+	23.8243i	0.476009	+	0.824472i
$836$	0.688669	−	1.19281i	0.0238181	−	0.0412542i
$837$	−1.95138	+	3.37989i	−0.0674495	+	0.116826i
$838$	−2.56033	−	4.43463i	−0.0884453	−	0.153192i
$839$	−9.12365			−0.314984			−0.157492	−	0.987520i	$-0.550341\pi$
$839$	−9.12365			−0.314984			−0.157492	+	0.987520i	$0.550341\pi$
$840$		0			0
$841$	−12.6063			−0.434699
$842$	−8.20171	−	14.2058i	−0.282650	−	0.489563i
$843$	−8.15130	+	14.1185i	−0.280746	+	0.486266i
$844$	13.8937	−	24.0646i	0.478242	−	0.828339i
$845$	−18.8310	−	32.6163i	−0.647806	−	1.12203i
$846$	−1.24698			−0.0428720
$847$		0			0
$848$	12.8877			0.442565
$849$	3.60202	+	6.23887i	0.123621	+	0.214118i
$850$	4.67629	−	8.09958i	0.160395	−	0.277813i
$851$	12.3116	−	21.3244i	0.422037	−	0.730990i
$852$	6.59030	+	11.4147i	0.225780	+	0.391062i
$853$	−10.2620			−0.351366			−0.175683	−	0.984447i	$-0.556213\pi$
$853$	−10.2620			−0.351366			−0.175683	+	0.984447i	$0.556213\pi$
$854$		0			0
$855$	−8.05861			−0.275599
$856$	−8.71528	−	15.0953i	−0.297882	−	0.515947i
$857$	−5.64161	+	9.77156i	−0.192714	+	0.333790i	−0.946149	−	0.323732i	$-0.895062\pi$
$857$	−5.64161	+	9.77156i	−0.192714	+	0.333790i	0.753435	+	0.657523i	$0.228396\pi$
$858$	1.33393	−	2.31043i	0.0455396	−	0.0788769i
$859$	−10.0121	−	17.3414i	−0.341608	−	0.591682i	0.643124	−	0.765762i	$-0.277638\pi$
$859$	−10.0121	−	17.3414i	−0.341608	−	0.591682i	−0.984731	+	0.174080i	$0.944305\pi$
$860$	−6.66487			−0.227270
$861$		0			0
$862$	0.330814			0.0112676
$863$	−20.7298	−	35.9051i	−0.705651	−	1.22222i	−0.966456	−	0.256832i	$-0.917321\pi$
$863$	−20.7298	−	35.9051i	−0.705651	−	1.22222i	0.260805	−	0.965392i	$-0.416012\pi$
$864$	2.77144	−	4.80027i	0.0942862	−	0.163309i
$865$	4.31282	−	7.47003i	0.146640	−	0.253989i
$866$	−1.22521	−	2.12212i	−0.0416343	−	0.0721127i
$867$	10.2674			0.348700
$868$		0			0
$869$	2.97020			0.100757
$870$	−3.42543	−	5.93301i	−0.116133	−	0.201148i
$871$	−10.0521	+	17.4108i	−0.340604	+	0.589943i
$872$	3.54623	−	6.14225i	0.120090	−	0.208003i
$873$	2.34601	+	4.06341i	0.0794004	+	0.137526i
$874$	15.0127			0.507811
$875$		0			0
$876$	−12.4969			−0.422233
$877$	−12.1017	−	20.9608i	−0.408646	−	0.707796i	0.586092	−	0.810244i	$-0.300666\pi$
$877$	−12.1017	−	20.9608i	−0.408646	−	0.707796i	−0.994738	+	0.102449i	$0.967332\pi$
$878$	1.34601	−	2.33136i	0.0454257	−	0.0786796i
$879$	12.7940	−	22.1599i	0.431532	−	0.747436i
$880$	0.227365	+	0.393808i	0.00766448	+	0.0132753i
$881$	37.3793			1.25934			0.629670	−	0.776863i	$-0.283190\pi$
$881$	37.3793			1.25934			0.629670	+	0.776863i	$0.283190\pi$
$882$		0			0
$883$	0.550172			0.0185148			0.00925739	−	0.999957i	$-0.497053\pi$
$883$	0.550172			0.0185148			0.00925739	+	0.999957i	$0.497053\pi$
$884$	9.45085	+	16.3693i	0.317866	+	0.550561i
$885$	7.66368	−	13.2739i	0.257612	−	0.446197i
$886$	18.2763	−	31.6555i	0.614004	−	1.06349i
$887$	−12.6761	−	21.9556i	−0.425620	−	0.737196i	0.570858	−	0.821049i	$-0.306611\pi$
$887$	−12.6761	−	21.9556i	−0.425620	−	0.737196i	−0.996478	+	0.0838530i	$0.973277\pi$
$888$	8.40581			0.282081
$889$		0			0
$890$	0.848936			0.0284564
$891$	−0.431764	−	0.747837i	−0.0144646	−	0.0250535i
$892$	6.35086	−	11.0000i	0.212642	−	0.368307i
$893$	1.77330	−	3.07144i	0.0593412	−	0.102782i
$894$	−8.78568	−	15.2172i	−0.293837	−	0.508941i
$895$	4.69501			0.156937
$896$		0			0
$897$	29.0790			0.970921
$898$	−1.74214	−	3.01747i	−0.0581358	−	0.100694i
$899$	−1.42543	+	2.46891i	−0.0475407	+	0.0823429i
$900$	−2.28232	+	3.95310i	−0.0760774	+	0.131770i
$901$	19.0788	+	33.0454i	0.635605	+	1.10090i
$902$	2.21313			0.0736891
$903$		0			0
$904$	12.9433			0.430488
$905$	−9.29954	−	16.1073i	−0.309127	−	0.535424i
$906$	−7.64191	+	13.2362i	−0.253885	+	0.439742i
$907$	−26.9756	+	46.7231i	−0.895710	+	1.55142i	−0.0627868	+	0.998027i	$0.519999\pi$
$907$	−26.9756	+	46.7231i	−0.895710	+	1.55142i	−0.832923	+	0.553388i	$0.813335\pi$
$908$	3.24818	+	5.62601i	0.107795	+	0.186706i
$909$	−2.56465			−0.0850640
$910$		0			0
$911$	13.2433			0.438769			0.219384	−	0.975639i	$-0.429595\pi$
$911$	13.2433			0.438769			0.219384	+	0.975639i	$0.429595\pi$
$912$	2.56249	+	4.43836i	0.0848526	+	0.146969i
$913$	−2.92274	+	5.06233i	−0.0967285	+	0.167539i
$914$	−11.5591	+	20.0210i	−0.382342	+	0.662236i
$915$	11.1325	+	19.2821i	0.368030	+	0.637446i
$916$	9.70171			0.320554
$917$		0			0
$918$	16.4112			0.541650
$919$	12.1195	+	20.9915i	0.399785	+	0.692447i	0.993699	−	0.112081i	$-0.0357516\pi$
$919$	12.1195	+	20.9915i	0.399785	+	0.692447i	−0.593915	+	0.804528i	$0.702418\pi$
$920$	−2.47823	+	4.29242i	−0.0817048	+	0.141517i
$921$	6.38740	−	11.0633i	0.210472	−	0.364548i
$922$	4.84750	+	8.39612i	0.159644	+	0.276512i
$923$	67.4795			2.22111
$924$		0			0
$925$	−21.2935			−0.700126
$926$	−2.92327	−	5.06325i	−0.0960647	−	0.166389i
$927$	11.3557	−	19.6686i	0.372970	−	0.646003i
$928$	2.02446	−	3.50647i	0.0664561	−	0.115105i
$929$	6.21475	+	10.7643i	0.203899	+	0.353164i	0.949782	−	0.312914i	$-0.101305\pi$
$929$	6.21475	+	10.7643i	0.203899	+	0.353164i	−0.745882	+	0.666078i	$0.767972\pi$
$930$	1.19136			0.0390662
$931$		0			0
$932$	1.81940			0.0595963
$933$	21.6151	+	37.4384i	0.707645	+	1.22568i
$934$	−12.8916	+	22.3289i	−0.421825	+	0.730623i
$935$	−0.673177	+	1.16598i	−0.0220152	+	0.0381315i
$936$	−4.61260	−	7.98927i	−0.150768	−	0.261137i
$937$	25.0672			0.818911			0.409455	−	0.912330i	$-0.365719\pi$
$937$	25.0672			0.818911			0.409455	+	0.912330i	$0.365719\pi$
$938$		0			0
$939$	14.5888			0.476088
$940$	0.585458	+	1.01404i	0.0190955	+	0.0330744i
$941$	20.9480	−	36.2830i	0.682886	−	1.18279i	−0.291210	−	0.956659i	$-0.594058\pi$
$941$	20.9480	−	36.2830i	0.682886	−	1.18279i	0.974096	−	0.226134i	$-0.0726088\pi$
$942$	13.2213	−	22.9000i	0.430774	−	0.746123i
$943$	12.0613	+	20.8908i	0.392770	+	0.680297i
$944$	9.05861			0.294833
$945$		0			0
$946$	−1.64609			−0.0535189
$947$	−6.98941	−	12.1060i	−0.227125	−	0.393393i	0.729830	−	0.683629i	$-0.239599\pi$
$947$	−6.98941	−	12.1060i	−0.227125	−	0.393393i	−0.956955	+	0.290236i	$0.906266\pi$
$948$	−5.52595	+	9.57123i	−0.179475	+	0.310859i
$949$	−31.9897	+	55.4078i	−1.03843	+	1.79861i
$950$	−6.49127	−	11.2432i	−0.210605	−	0.364778i
$951$	8.51573			0.276141
$952$		0			0
$953$	−14.9038			−0.482782			−0.241391	−	0.970428i	$-0.577604\pi$
$953$	−14.9038			−0.482782			−0.241391	+	0.970428i	$0.577604\pi$
$954$	−9.31163	−	16.1282i	−0.301475	−	0.522170i
$955$	4.70118	−	8.14268i	0.152127	−	0.263491i
$956$	−4.09783	+	7.09766i	−0.132533	+	0.229555i
$957$	−0.846011	−	1.46533i	−0.0273476	−	0.0473675i
$958$	−20.8799			−0.674600
$959$		0			0
$960$	−1.69202			−0.0546098
$961$	15.2521	+	26.4174i	0.492004	+	0.852176i
$962$	21.5172	−	37.2689i	0.693743	−	1.20160i
$963$	−12.5939	+	21.8134i	−0.405834	+	0.702926i
$964$	−2.61865	−	4.53563i	−0.0843409	−	0.146083i
$965$	−0.971788			−0.0312830
$966$		0			0
$967$	42.6469			1.37143			0.685717	−	0.727869i	$-0.259489\pi$
$967$	42.6469			1.37143			0.685717	+	0.727869i	$0.259489\pi$
$968$	−5.44385	−	9.42902i	−0.174972	−	0.303060i
$969$	−7.58695	+	13.1410i	−0.243728	+	0.422149i
$970$	2.20291	−	3.81555i	0.0707311	−	0.122510i
$971$	1.51895	+	2.63090i	0.0487454	+	0.0844296i	0.889369	−	0.457191i	$-0.151144\pi$
$971$	1.51895	+	2.63090i	0.0487454	+	0.0844296i	−0.840623	+	0.541620i	$0.817811\pi$
$972$	−13.4155			−0.430302
$973$		0			0
$974$	0.629958			0.0201851
$975$	−12.5734	−	21.7777i	−0.402670	−	0.697445i
$976$	−6.57942	+	11.3959i	−0.210602	+	0.364773i
$977$	−2.80045	+	4.85051i	−0.0895942	+	0.155182i	−0.907340	−	0.420398i	$-0.861890\pi$
$977$	−2.80045	+	4.85051i	−0.0895942	+	0.155182i	0.817745	+	0.575580i	$0.195224\pi$
$978$	−11.5260	−	19.9635i	−0.368559	−	0.638363i
$979$	0.209670			0.00670108
$980$		0			0
$981$	−10.2489			−0.327222
$982$	−3.59634	−	6.22905i	−0.114764	−	0.198777i
$983$	4.06800	−	7.04598i	0.129749	−	0.224732i	−0.793830	−	0.608139i	$-0.791916\pi$
$983$	4.06800	−	7.04598i	0.129749	−	0.224732i	0.923579	+	0.383407i	$0.125250\pi$
$984$	−4.11745	+	7.13163i	−0.131259	+	0.227348i
$985$	−1.39828	−	2.42189i	−0.0445529	−	0.0771679i
$986$	11.9879			0.381773
$987$		0			0
$988$	26.2379			0.834738
$989$	−8.97099	−	15.5382i	−0.285261	−	0.494086i
$990$	0.328552	−	0.569069i	0.0104421	−	0.0180862i
$991$	8.08187	−	13.9982i	0.256729	−	0.444668i	−0.708635	−	0.705576i	$-0.750689\pi$
$991$	8.08187	−	13.9982i	0.256729	−	0.444668i	0.965364	+	0.260908i	$0.0840219\pi$
$992$	0.352052	+	0.609771i	0.0111776	+	0.0193603i
$993$	19.0368			0.604116
$994$		0			0
$995$	0.0295400			0.000936480
$996$	−10.8753	−	18.8366i	−0.344598	−	0.596860i
$997$	15.8307	−	27.4196i	0.501364	−	0.868387i	−0.498635	−	0.866812i	$-0.666165\pi$
$997$	15.8307	−	27.4196i	0.501364	−	0.868387i	0.999999	−	0.00157522i	$-0.000501409\pi$
$998$	10.6283	−	18.4088i	0.336434	−	0.582721i
$999$	−18.6821	−	32.3583i	−0.591075	−	1.02377i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	686.2.c.c.361.3		6
7.2	even	3	inner	686.2.c.c.667.3		6
7.3	odd	6		686.2.a.a.1.3	✓	3
7.4	even	3		686.2.a.b.1.1	yes	3
7.5	odd	6		686.2.c.d.667.1		6
7.6	odd	2		686.2.c.d.361.1		6
21.11	odd	6		6174.2.a.l.1.2		3
21.17	even	6		6174.2.a.k.1.2		3
28.3	even	6		5488.2.a.e.1.1		3
28.11	odd	6		5488.2.a.b.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
686.2.a.a.1.3	✓	3	7.3	odd	6
686.2.a.b.1.1	yes	3	7.4	even	3
686.2.c.c.361.3		6	1.1	even	1	trivial
686.2.c.c.667.3		6	7.2	even	3	inner
686.2.c.d.361.1		6	7.6	odd	2
686.2.c.d.667.1		6	7.5	odd	6
5488.2.a.b.1.3		3	28.11	odd	6
5488.2.a.e.1.1		3	28.3	even	6
6174.2.a.k.1.2		3	21.17	even	6
6174.2.a.l.1.2		3	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 686 = 2 \cdot 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	686.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.623490 - 1.07992i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.678448 - 1.17511i) q^{5} +1.24698 q^{6} -1.00000 q^{8} +(0.722521 + 1.25144i) q^{9} +(0.678448 - 1.17511i) q^{10} +(0.167563 - 0.290227i) q^{11} +(0.623490 + 1.07992i) q^{12} +6.38404 q^{13} -1.69202 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.48039 - 2.56410i) q^{17} +(-0.722521 + 1.25144i) q^{18} +(-2.05496 - 3.55929i) q^{19} +1.35690 q^{20} +0.335126 q^{22} +(1.82640 + 3.16341i) q^{23} +(-0.623490 + 1.07992i) q^{24} +(1.57942 - 2.73563i) q^{25} +(3.19202 + 5.52874i) q^{26} +5.54288 q^{27} +4.04892 q^{29} +(-0.846011 - 1.46533i) q^{30} +(-0.352052 + 0.609771i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.208947 - 0.361908i) q^{33} +2.96077 q^{34} -1.44504 q^{36} +(-3.37047 - 5.83782i) q^{37} +(2.05496 - 3.55929i) q^{38} +(3.98039 - 6.89423i) q^{39} +(0.678448 + 1.17511i) q^{40} +6.60388 q^{41} -4.91185 q^{43} +(0.167563 + 0.290227i) q^{44} +(0.980386 - 1.69808i) q^{45} +(-1.82640 + 3.16341i) q^{46} +(0.431468 + 0.747325i) q^{47} -1.24698 q^{48} +3.15883 q^{50} +(-1.84601 - 3.19738i) q^{51} +(-3.19202 + 5.52874i) q^{52} +(-6.44385 + 11.1611i) q^{53} +(2.77144 + 4.80027i) q^{54} -0.454731 q^{55} -5.12498 q^{57} +(2.02446 + 3.50647i) q^{58} +(-4.52930 + 7.84498i) q^{59} +(0.846011 - 1.46533i) q^{60} +(-6.57942 - 11.3959i) q^{61} -0.704103 q^{62} +1.00000 q^{64} +(-4.33124 - 7.50193i) q^{65} +(0.208947 - 0.361908i) q^{66} +(-1.57457 + 2.72724i) q^{67} +(1.48039 + 2.56410i) q^{68} +4.55496 q^{69} +10.5700 q^{71} +(-0.722521 - 1.25144i) q^{72} +(-5.01089 + 8.67911i) q^{73} +(3.37047 - 5.83782i) q^{74} +(-1.96950 - 3.41127i) q^{75} +4.10992 q^{76} +7.96077 q^{78} +(4.43147 + 7.67553i) q^{79} +(-0.678448 + 1.17511i) q^{80} +(1.28836 - 2.23151i) q^{81} +(3.30194 + 5.71912i) q^{82} -17.4426 q^{83} -4.01746 q^{85} +(-2.45593 - 4.25379i) q^{86} +(2.52446 - 4.37249i) q^{87} +(-0.167563 + 0.290227i) q^{88} +(0.312823 + 0.541825i) q^{89} +1.96077 q^{90} -3.65279 q^{92} +(0.439001 + 0.760372i) q^{93} +(-0.431468 + 0.747325i) q^{94} +(-2.78836 + 4.82959i) q^{95} +(-0.623490 - 1.07992i) q^{96} +3.24698 q^{97} +0.484271 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - q^{3} - 3 q^{4} - 2 q^{6} - 6 q^{8} + 4 q^{9} - q^{12} + 18 q^{13} - 3 q^{16} - 4 q^{17} - 4 q^{18} - 13 q^{19} - 7 q^{23} + q^{24} + q^{25} + 9 q^{26} - 4 q^{27} + 6 q^{29} - 16 q^{31}+ \cdots + 28 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - q^3 - 3 * q^4 - 2 * q^6 - 6 * q^8 + 4 * q^9 - q^12 + 18 * q^13 - 3 * q^16 - 4 * q^17 - 4 * q^18 - 13 * q^19 - 7 * q^23 + q^24 + q^25 + 9 * q^26 - 4 * q^27 + 6 * q^29 - 16 * q^31 + 3 * q^32 - 7 * q^33 - 8 * q^34 - 8 * q^36 - 6 * q^37 + 13 * q^38 + 11 * q^39 + 22 * q^41 - 22 * q^43 - 7 * q^45 + 7 * q^46 + 8 * q^47 + 2 * q^48 + 2 * q^50 - 6 * q^51 - 9 * q^52 + 3 * q^53 - 2 * q^54 + 42 * q^55 + 18 * q^57 + 3 * q^58 + 4 * q^59 - 31 * q^61 - 32 * q^62 + 6 * q^64 + 14 * q^65 + 7 * q^66 - 23 * q^67 - 4 * q^68 + 28 * q^69 + 14 * q^71 - 4 * q^72 - 27 * q^73 + 6 * q^74 - 2 * q^75 + 26 * q^76 + 22 * q^78 + 32 * q^79 + 5 * q^81 + 11 * q^82 - 22 * q^83 - 56 * q^85 - 11 * q^86 + 6 * q^87 - 10 * q^89 - 14 * q^90 + 14 * q^92 - 17 * q^93 - 8 * q^94 - 14 * q^95 + q^96 + 10 * q^97 + 28 * q^99

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