LMFDB - Embedded newform 650.2.n.b.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(49,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("650.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.n (of order $6$, 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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	650.199
Dual form			650.2.n.b.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(2.36603 + 1.36603i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.36603 - 1.36603i) q^{6} +(1.50000 + 2.59808i) q^{7} -1.00000 q^{8} +(2.23205 + 3.86603i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(2.36603 + 1.36603i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.36603 - 1.36603i) q^{6} +(1.50000 + 2.59808i) q^{7} -1.00000 q^{8} +(2.23205 + 3.86603i) q^{9} +(-2.59808 - 1.50000i) q^{11} -2.73205i q^{12} +(0.866025 + 3.50000i) q^{13} +3.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.90192 - 1.09808i) q^{17} +4.46410 q^{18} +(5.59808 - 3.23205i) q^{19} +8.19615i q^{21} +(-2.59808 + 1.50000i) q^{22} +(-2.19615 - 1.26795i) q^{23} +(-2.36603 - 1.36603i) q^{24} +(3.46410 + 1.00000i) q^{26} +4.00000i q^{27} +(1.50000 - 2.59808i) q^{28} +(-4.73205 + 8.19615i) q^{29} -1.26795i q^{31} +(0.500000 + 0.866025i) q^{32} +(-4.09808 - 7.09808i) q^{33} -2.19615i q^{34} +(2.23205 - 3.86603i) q^{36} +(5.59808 - 9.69615i) q^{37} -6.46410i q^{38} +(-2.73205 + 9.46410i) q^{39} +(-9.00000 - 5.19615i) q^{41} +(7.09808 + 4.09808i) q^{42} +(1.73205 - 1.00000i) q^{43} +3.00000i q^{44} +(-2.19615 + 1.26795i) q^{46} -3.00000 q^{47} +(-2.36603 + 1.36603i) q^{48} +(-1.00000 + 1.73205i) q^{49} +6.00000 q^{51} +(2.59808 - 2.50000i) q^{52} -6.46410i q^{53} +(3.46410 + 2.00000i) q^{54} +(-1.50000 - 2.59808i) q^{56} +17.6603 q^{57} +(4.73205 + 8.19615i) q^{58} +(-9.00000 + 5.19615i) q^{59} +(2.09808 + 3.63397i) q^{61} +(-1.09808 - 0.633975i) q^{62} +(-6.69615 + 11.5981i) q^{63} +1.00000 q^{64} -8.19615 q^{66} +(-1.90192 - 1.09808i) q^{68} +(-3.46410 - 6.00000i) q^{69} +(5.19615 - 3.00000i) q^{71} +(-2.23205 - 3.86603i) q^{72} -5.66025 q^{73} +(-5.59808 - 9.69615i) q^{74} +(-5.59808 - 3.23205i) q^{76} -9.00000i q^{77} +(6.83013 + 7.09808i) q^{78} -6.19615 q^{79} +(1.23205 - 2.13397i) q^{81} +(-9.00000 + 5.19615i) q^{82} +2.19615 q^{83} +(7.09808 - 4.09808i) q^{84} -2.00000i q^{86} +(-22.3923 + 12.9282i) q^{87} +(2.59808 + 1.50000i) q^{88} +(14.8923 + 8.59808i) q^{89} +(-7.79423 + 7.50000i) q^{91} +2.53590i q^{92} +(1.73205 - 3.00000i) q^{93} +(-1.50000 + 2.59808i) q^{94} +2.73205i q^{96} +(-7.56218 - 13.0981i) q^{97} +(1.00000 + 1.73205i) q^{98} -13.3923i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 6 q^{3} - 2 q^{4} + 6 q^{6} + 6 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 6 * q^3 - 2 * q^4 + 6 * q^6 + 6 * q^7 - 4 * q^8 + 2 * q^9	$ 4 q + 2 q^{2} + 6 q^{3} - 2 q^{4} + 6 q^{6} + 6 q^{7} - 4 q^{8} + 2 q^{9} + 12 q^{14} - 2 q^{16} + 18 q^{17} + 4 q^{18} + 12 q^{19} + 12 q^{23} - 6 q^{24} + 6 q^{28} - 12 q^{29} + 2 q^{32} - 6 q^{33} + 2 q^{36} + 12 q^{37} - 4 q^{39} - 36 q^{41} + 18 q^{42} + 12 q^{46} - 12 q^{47} - 6 q^{48} - 4 q^{49} + 24 q^{51} - 6 q^{56} + 36 q^{57} + 12 q^{58} - 36 q^{59} - 2 q^{61} + 6 q^{62} - 6 q^{63} + 4 q^{64} - 12 q^{66} - 18 q^{68} - 2 q^{72} + 12 q^{73} - 12 q^{74} - 12 q^{76} + 10 q^{78} - 4 q^{79} - 2 q^{81} - 36 q^{82} - 12 q^{83} + 18 q^{84} - 48 q^{87} + 18 q^{89} - 6 q^{94} - 6 q^{97} + 4 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 + 6 * q^3 - 2 * q^4 + 6 * q^6 + 6 * q^7 - 4 * q^8 + 2 * q^9 + 12 * q^14 - 2 * q^16 + 18 * q^17 + 4 * q^18 + 12 * q^19 + 12 * q^23 - 6 * q^24 + 6 * q^28 - 12 * q^29 + 2 * q^32 - 6 * q^33 + 2 * q^36 + 12 * q^37 - 4 * q^39 - 36 * q^41 + 18 * q^42 + 12 * q^46 - 12 * q^47 - 6 * q^48 - 4 * q^49 + 24 * q^51 - 6 * q^56 + 36 * q^57 + 12 * q^58 - 36 * q^59 - 2 * q^61 + 6 * q^62 - 6 * q^63 + 4 * q^64 - 12 * q^66 - 18 * q^68 - 2 * q^72 + 12 * q^73 - 12 * q^74 - 12 * q^76 + 10 * q^78 - 4 * q^79 - 2 * q^81 - 36 * q^82 - 12 * q^83 + 18 * q^84 - 48 * q^87 + 18 * q^89 - 6 * q^94 - 6 * q^97 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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
$3$	2.36603	+	1.36603i	1.36603	+	0.788675i	0.990418	−	0.138104i	$-0.0441007\pi$
$3$	2.36603	+	1.36603i	1.36603	+	0.788675i	0.375608	+	0.926779i	$0.377434\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	2.36603	−	1.36603i	0.965926	−	0.557678i
$7$	1.50000	+	2.59808i	0.566947	+	0.981981i	0.996866	+	0.0791130i	$0.0252088\pi$
$7$	1.50000	+	2.59808i	0.566947	+	0.981981i	−0.429919	+	0.902867i	$0.641458\pi$
$8$	−1.00000			−0.353553
$9$	2.23205	+	3.86603i	0.744017	+	1.28868i
$10$		0			0
$11$	−2.59808	−	1.50000i	−0.783349	−	0.452267i	0.0542666	−	0.998526i	$-0.482718\pi$
$11$	−2.59808	−	1.50000i	−0.783349	−	0.452267i	−0.837616	+	0.546259i	$0.816051\pi$
$12$		−	2.73205i		−	0.788675i
$13$	0.866025	+	3.50000i	0.240192	+	0.970725i
$13$	0.866025	+	3.50000i	0.240192	+	0.970725i
$14$	3.00000			0.801784
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.90192	−	1.09808i	0.461284	−	0.266323i	−0.251300	−	0.967909i	$-0.580858\pi$
$17$	1.90192	−	1.09808i	0.461284	−	0.266323i	0.712584	+	0.701587i	$0.247525\pi$
$18$	4.46410			1.05220
$19$	5.59808	−	3.23205i	1.28429	−	0.741483i	0.306658	−	0.951820i	$-0.400789\pi$
$19$	5.59808	−	3.23205i	1.28429	−	0.741483i	0.977629	+	0.210337i	$0.0674560\pi$
$20$		0			0
$21$			8.19615i			1.78855i
$22$	−2.59808	+	1.50000i	−0.553912	+	0.319801i
$23$	−2.19615	−	1.26795i	−0.457929	−	0.264386i	0.253244	−	0.967402i	$-0.418503\pi$
$23$	−2.19615	−	1.26795i	−0.457929	−	0.264386i	−0.711173	+	0.703017i	$0.751836\pi$
$24$	−2.36603	−	1.36603i	−0.482963	−	0.278839i
$25$		0			0
$26$	3.46410	+	1.00000i	0.679366	+	0.196116i
$27$			4.00000i			0.769800i
$28$	1.50000	−	2.59808i	0.283473	−	0.490990i
$29$	−4.73205	+	8.19615i	−0.878720	+	1.52199i	−0.0259731	+	0.999663i	$0.508268\pi$
$29$	−4.73205	+	8.19615i	−0.878720	+	1.52199i	−0.852747	+	0.522325i	$0.825065\pi$
$30$		0			0
$31$		−	1.26795i		−	0.227730i	−0.993496	−	0.113865i	$-0.963677\pi$
$31$		−	1.26795i		−	0.227730i	0.993496	−	0.113865i	$-0.0363232\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−4.09808	−	7.09808i	−0.713384	−	1.23562i
$34$		−	2.19615i		−	0.376637i
$35$		0			0
$36$	2.23205	−	3.86603i	0.372008	−	0.644338i
$37$	5.59808	−	9.69615i	0.920318	−	1.59404i	0.121395	−	0.992604i	$-0.461263\pi$
$37$	5.59808	−	9.69615i	0.920318	−	1.59404i	0.798923	−	0.601433i	$-0.205403\pi$
$38$		−	6.46410i		−	1.04862i
$39$	−2.73205	+	9.46410i	−0.437478	+	1.51547i
$40$		0			0
$41$	−9.00000	−	5.19615i	−1.40556	−	0.811503i	−0.410608	−	0.911812i	$-0.634683\pi$
$41$	−9.00000	−	5.19615i	−1.40556	−	0.811503i	−0.994956	+	0.100309i	$0.968017\pi$
$42$	7.09808	+	4.09808i	1.09526	+	0.632347i
$43$	1.73205	−	1.00000i	0.264135	−	0.152499i	−0.362084	−	0.932145i	$-0.617935\pi$
$43$	1.73205	−	1.00000i	0.264135	−	0.152499i	0.626219	+	0.779647i	$0.284601\pi$
$44$			3.00000i			0.452267i
$45$		0			0
$46$	−2.19615	+	1.26795i	−0.323805	+	0.186949i
$47$	−3.00000			−0.437595			−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000			−0.437595			−0.218797	+	0.975770i	$0.570213\pi$
$48$	−2.36603	+	1.36603i	−0.341506	+	0.197169i
$49$	−1.00000	+	1.73205i	−0.142857	+	0.247436i
$50$		0			0
$51$	6.00000			0.840168
$52$	2.59808	−	2.50000i	0.360288	−	0.346688i
$53$		−	6.46410i		−	0.887913i	−0.896048	−	0.443956i	$-0.853575\pi$
$53$		−	6.46410i		−	0.887913i	0.896048	−	0.443956i	$-0.146425\pi$
$54$	3.46410	+	2.00000i	0.471405	+	0.272166i
$55$		0			0
$56$	−1.50000	−	2.59808i	−0.200446	−	0.347183i
$57$	17.6603			2.33916
$58$	4.73205	+	8.19615i	0.621349	+	1.07621i
$59$	−9.00000	+	5.19615i	−1.17170	+	0.676481i	−0.954080	−	0.299552i	$-0.903163\pi$
$59$	−9.00000	+	5.19615i	−1.17170	+	0.676481i	−0.217620	+	0.976034i	$0.569829\pi$
$60$		0			0
$61$	2.09808	+	3.63397i	0.268631	+	0.465283i	0.968509	−	0.248980i	$-0.0800954\pi$
$61$	2.09808	+	3.63397i	0.268631	+	0.465283i	−0.699877	+	0.714263i	$0.746762\pi$
$62$	−1.09808	−	0.633975i	−0.139456	−	0.0805149i
$63$	−6.69615	+	11.5981i	−0.843636	+	1.46122i
$64$	1.00000			0.125000
$65$		0			0
$66$	−8.19615			−1.00888
$67$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$67$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$68$	−1.90192	−	1.09808i	−0.230642	−	0.133161i
$69$	−3.46410	−	6.00000i	−0.417029	−	0.722315i
$70$		0			0
$71$	5.19615	−	3.00000i	0.616670	−	0.356034i	−0.158901	−	0.987294i	$-0.550795\pi$
$71$	5.19615	−	3.00000i	0.616670	−	0.356034i	0.775571	+	0.631260i	$0.217462\pi$
$72$	−2.23205	−	3.86603i	−0.263050	−	0.455615i
$73$	−5.66025			−0.662483			−0.331241	−	0.943546i	$-0.607467\pi$
$73$	−5.66025			−0.662483			−0.331241	+	0.943546i	$0.607467\pi$
$74$	−5.59808	−	9.69615i	−0.650763	−	1.12715i
$75$		0			0
$76$	−5.59808	−	3.23205i	−0.642143	−	0.370742i
$77$		−	9.00000i		−	1.02565i
$78$	6.83013	+	7.09808i	0.773360	+	0.803699i
$79$	−6.19615			−0.697122			−0.348561	−	0.937286i	$-0.613330\pi$
$79$	−6.19615			−0.697122			−0.348561	+	0.937286i	$0.613330\pi$
$80$		0			0
$81$	1.23205	−	2.13397i	0.136895	−	0.237108i
$82$	−9.00000	+	5.19615i	−0.993884	+	0.573819i
$83$	2.19615			0.241059			0.120530	−	0.992710i	$-0.461541\pi$
$83$	2.19615			0.241059			0.120530	+	0.992710i	$0.461541\pi$
$84$	7.09808	−	4.09808i	0.774464	−	0.447137i
$85$		0			0
$86$		−	2.00000i		−	0.215666i
$87$	−22.3923	+	12.9282i	−2.40071	+	1.38605i
$88$	2.59808	+	1.50000i	0.276956	+	0.159901i
$89$	14.8923	+	8.59808i	1.57858	+	0.911394i	0.995058	+	0.0992979i	$0.0316597\pi$
$89$	14.8923	+	8.59808i	1.57858	+	0.911394i	0.583523	+	0.812096i	$0.301674\pi$
$90$		0			0
$91$	−7.79423	+	7.50000i	−0.817057	+	0.786214i
$92$			2.53590i			0.264386i
$93$	1.73205	−	3.00000i	0.179605	−	0.311086i
$94$	−1.50000	+	2.59808i	−0.154713	+	0.267971i
$95$		0			0
$96$			2.73205i			0.278839i
$97$	−7.56218	−	13.0981i	−0.767823	−	1.32991i	−0.938741	−	0.344623i	$-0.888007\pi$
$97$	−7.56218	−	13.0981i	−0.767823	−	1.32991i	0.170918	−	0.985285i	$-0.445327\pi$
$98$	1.00000	+	1.73205i	0.101015	+	0.174964i
$99$		−	13.3923i		−	1.34598i
$100$		0			0
$101$	−3.63397	+	6.29423i	−0.361594	+	0.626299i	−0.988223	−	0.153018i	$-0.951101\pi$
$101$	−3.63397	+	6.29423i	−0.361594	+	0.626299i	0.626629	+	0.779317i	$0.284434\pi$
$102$	3.00000	−	5.19615i	0.297044	−	0.514496i
$103$			1.19615i			0.117860i	0.998262	+	0.0589302i	$0.0187689\pi$
$103$			1.19615i			0.117860i	−0.998262	+	0.0589302i	$0.981231\pi$
$104$	−0.866025	−	3.50000i	−0.0849208	−	0.343203i
$105$		0			0
$106$	−5.59808	−	3.23205i	−0.543733	−	0.313925i
$107$	0.294229	+	0.169873i	0.0284442	+	0.0164222i	0.514155	−	0.857697i	$-0.328106\pi$
$107$	0.294229	+	0.169873i	0.0284442	+	0.0164222i	−0.485710	+	0.874120i	$0.661439\pi$
$108$	3.46410	−	2.00000i	0.333333	−	0.192450i
$109$		−	15.4641i		−	1.48119i	−0.671950	−	0.740596i	$-0.734543\pi$
$109$		−	15.4641i		−	1.48119i	0.671950	−	0.740596i	$-0.265457\pi$
$110$		0			0
$111$	26.4904	−	15.2942i	2.51436	−	1.45166i
$112$	−3.00000			−0.283473
$113$	−6.00000	+	3.46410i	−0.564433	+	0.325875i	−0.754923	−	0.655814i	$-0.772326\pi$
$113$	−6.00000	+	3.46410i	−0.564433	+	0.325875i	0.190490	+	0.981689i	$0.438992\pi$
$114$	8.83013	−	15.2942i	0.827017	−	1.43244i
$115$		0			0
$116$	9.46410			0.878720
$117$	−11.5981	+	11.1603i	−1.07224	+	1.03177i
$118$			10.3923i			0.956689i
$119$	5.70577	+	3.29423i	0.523047	+	0.301981i
$120$		0			0
$121$	−1.00000	−	1.73205i	−0.0909091	−	0.157459i
$122$	4.19615			0.379902
$123$	−14.1962	−	24.5885i	−1.28002	−	2.21707i
$124$	−1.09808	+	0.633975i	−0.0986102	+	0.0569326i
$125$		0			0
$126$	6.69615	+	11.5981i	0.596541	+	1.03324i
$127$	18.3564	+	10.5981i	1.62887	+	0.940427i	0.984431	+	0.175769i	$0.0562412\pi$
$127$	18.3564	+	10.5981i	1.62887	+	0.940427i	0.644436	+	0.764658i	$0.277092\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	5.46410			0.481087
$130$		0			0
$131$	−18.1244			−1.58353			−0.791766	−	0.610824i	$-0.790838\pi$
$131$	−18.1244			−1.58353			−0.791766	+	0.610824i	$0.790838\pi$
$132$	−4.09808	+	7.09808i	−0.356692	+	0.617808i
$133$	16.7942	+	9.69615i	1.45624	+	0.840763i
$134$		0			0
$135$		0			0
$136$	−1.90192	+	1.09808i	−0.163089	+	0.0941593i
$137$	−4.09808	−	7.09808i	−0.350122	−	0.606430i	0.636148	−	0.771567i	$-0.280527\pi$
$137$	−4.09808	−	7.09808i	−0.350122	−	0.606430i	−0.986271	+	0.165137i	$0.947193\pi$
$138$	−6.92820			−0.589768
$139$	−4.59808	−	7.96410i	−0.390004	−	0.675506i	0.602446	−	0.798160i	$-0.294193\pi$
$139$	−4.59808	−	7.96410i	−0.390004	−	0.675506i	−0.992450	+	0.122653i	$0.960860\pi$
$140$		0			0
$141$	−7.09808	−	4.09808i	−0.597766	−	0.345120i
$142$		−	6.00000i		−	0.503509i
$143$	3.00000	−	10.3923i	0.250873	−	0.869048i
$144$	−4.46410			−0.372008
$145$		0			0
$146$	−2.83013	+	4.90192i	−0.234223	+	0.405686i
$147$	−4.73205	+	2.73205i	−0.390293	+	0.225336i
$148$	−11.1962			−0.920318
$149$	5.19615	−	3.00000i	0.425685	−	0.245770i	−0.271821	−	0.962348i	$-0.587626\pi$
$149$	5.19615	−	3.00000i	0.425685	−	0.245770i	0.697507	+	0.716578i	$0.254293\pi$
$150$		0			0
$151$			6.33975i			0.515921i	0.966155	+	0.257961i	$0.0830505\pi$
$151$			6.33975i			0.515921i	−0.966155	+	0.257961i	$0.916950\pi$
$152$	−5.59808	+	3.23205i	−0.454064	+	0.262154i
$153$	8.49038	+	4.90192i	0.686407	+	0.396297i
$154$	−7.79423	−	4.50000i	−0.628077	−	0.362620i
$155$		0			0
$156$	9.56218	−	2.36603i	0.765587	−	0.189434i
$157$			13.0000i			1.03751i	0.854922	+	0.518756i	$0.173605\pi$
$157$			13.0000i			1.03751i	−0.854922	+	0.518756i	$0.826395\pi$
$158$	−3.09808	+	5.36603i	−0.246470	+	0.426898i
$159$	8.83013	−	15.2942i	0.700275	−	1.21291i
$160$		0			0
$161$		−	7.60770i		−	0.599570i
$162$	−1.23205	−	2.13397i	−0.0967991	−	0.167661i
$163$	3.63397	+	6.29423i	0.284635	+	0.493002i	0.972521	−	0.232817i	$-0.0747943\pi$
$163$	3.63397	+	6.29423i	0.284635	+	0.493002i	−0.687886	+	0.725819i	$0.741461\pi$
$164$			10.3923i			0.811503i
$165$		0			0
$166$	1.09808	−	1.90192i	0.0852272	−	0.147618i
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	−0.918208	−	0.396098i	$-0.870364\pi$
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	0.802135	+	0.597143i	$0.203697\pi$
$168$		−	8.19615i		−	0.632347i
$169$	−11.5000	+	6.06218i	−0.884615	+	0.466321i
$170$		0			0
$171$	24.9904	+	14.4282i	1.91106	+	1.10335i
$172$	−1.73205	−	1.00000i	−0.132068	−	0.0762493i
$173$	−12.9904	+	7.50000i	−0.987640	+	0.570214i	−0.904568	−	0.426329i	$-0.859807\pi$
$173$	−12.9904	+	7.50000i	−0.987640	+	0.570214i	−0.0830722	+	0.996544i	$0.526473\pi$
$174$			25.8564i			1.96017i
$175$		0			0
$176$	2.59808	−	1.50000i	0.195837	−	0.113067i
$177$	−28.3923			−2.13410
$178$	14.8923	−	8.59808i	1.11623	−	0.644453i
$179$	−1.26795	+	2.19615i	−0.0947710	+	0.164148i	−0.909513	−	0.415675i	$-0.863545\pi$
$179$	−1.26795	+	2.19615i	−0.0947710	+	0.164148i	0.814742	+	0.579824i	$0.196879\pi$
$180$		0			0
$181$	−16.5885			−1.23301			−0.616505	−	0.787351i	$-0.711452\pi$
$181$	−16.5885			−1.23301			−0.616505	+	0.787351i	$0.711452\pi$
$182$	2.59808	+	10.5000i	0.192582	+	0.778312i
$183$			11.4641i			0.847451i
$184$	2.19615	+	1.26795i	0.161903	+	0.0934745i
$185$		0			0
$186$	−1.73205	−	3.00000i	−0.127000	−	0.219971i
$187$	−6.58846			−0.481796
$188$	1.50000	+	2.59808i	0.109399	+	0.189484i
$189$	−10.3923	+	6.00000i	−0.755929	+	0.436436i
$190$		0			0
$191$	9.63397	+	16.6865i	0.697090	+	1.20740i	0.969471	+	0.245206i	$0.0788555\pi$
$191$	9.63397	+	16.6865i	0.697090	+	1.20740i	−0.272381	+	0.962189i	$0.587811\pi$
$192$	2.36603	+	1.36603i	0.170753	+	0.0985844i
$193$	2.19615	−	3.80385i	0.158083	−	0.273807i	−0.776095	−	0.630616i	$-0.782802\pi$
$193$	2.19615	−	3.80385i	0.158083	−	0.273807i	0.934177	+	0.356809i	$0.116135\pi$
$194$	−15.1244			−1.08587
$195$		0			0
$196$	2.00000			0.142857
$197$	4.79423	−	8.30385i	0.341575	−	0.591625i	−0.643151	−	0.765740i	$-0.722373\pi$
$197$	4.79423	−	8.30385i	0.341575	−	0.591625i	0.984725	+	0.174115i	$0.0557064\pi$
$198$	−11.5981	−	6.69615i	−0.824239	−	0.475875i
$199$	7.19615	+	12.4641i	0.510122	+	0.883557i	0.999931	+	0.0117273i	$0.00373299\pi$
$199$	7.19615	+	12.4641i	0.510122	+	0.883557i	−0.489810	+	0.871829i	$0.662934\pi$
$200$		0			0
$201$		0			0
$202$	3.63397	+	6.29423i	0.255686	+	0.442860i
$203$	−28.3923			−1.99275
$204$	−3.00000	−	5.19615i	−0.210042	−	0.363803i
$205$		0			0
$206$	1.03590	+	0.598076i	0.0721745	+	0.0416699i
$207$		−	11.3205i		−	0.786830i
$208$	−3.46410	−	1.00000i	−0.240192	−	0.0693375i
$209$	−19.3923			−1.34139
$210$		0			0
$211$	−6.79423	+	11.7679i	−0.467734	+	0.810139i	−0.999320	−	0.0368651i	$-0.988263\pi$
$211$	−6.79423	+	11.7679i	−0.467734	+	0.810139i	0.531586	+	0.847004i	$0.321596\pi$
$212$	−5.59808	+	3.23205i	−0.384477	+	0.221978i
$213$	16.3923			1.12318
$214$	0.294229	−	0.169873i	0.0201131	−	0.0116123i
$215$		0			0
$216$		−	4.00000i		−	0.272166i
$217$	3.29423	−	1.90192i	0.223627	−	0.129111i
$218$	−13.3923	−	7.73205i	−0.907041	−	0.523681i
$219$	−13.3923	−	7.73205i	−0.904968	−	0.522484i
$220$		0			0
$221$	5.49038	+	5.70577i	0.369323	+	0.383812i
$222$		−	30.5885i		−	2.05296i
$223$	0.232051	−	0.401924i	0.0155393	−	0.0269148i	−0.858151	−	0.513397i	$-0.828387\pi$
$223$	0.232051	−	0.401924i	0.0155393	−	0.0269148i	0.873690	+	0.486482i	$0.161720\pi$
$224$	−1.50000	+	2.59808i	−0.100223	+	0.173591i
$225$		0			0
$226$			6.92820i			0.460857i
$227$	−2.19615	−	3.80385i	−0.145764	−	0.252470i	0.783894	−	0.620895i	$-0.213231\pi$
$227$	−2.19615	−	3.80385i	−0.145764	−	0.252470i	−0.929658	+	0.368425i	$0.879897\pi$
$228$	−8.83013	−	15.2942i	−0.584789	−	1.01289i
$229$		−	4.73205i		−	0.312703i	−0.987701	−	0.156351i	$-0.950027\pi$
$229$		−	4.73205i		−	0.312703i	0.987701	−	0.156351i	$-0.0499732\pi$
$230$		0			0
$231$	12.2942	−	21.2942i	0.808901	−	1.40106i
$232$	4.73205	−	8.19615i	0.310674	−	0.538104i
$233$			1.26795i			0.0830661i	0.999137	+	0.0415331i	$0.0132242\pi$
$233$			1.26795i			0.0830661i	−0.999137	+	0.0415331i	$0.986776\pi$
$234$	3.86603	+	15.6244i	0.252730	+	1.02140i
$235$		0			0
$236$	9.00000	+	5.19615i	0.585850	+	0.338241i
$237$	−14.6603	−	8.46410i	−0.952286	−	0.549802i
$238$	5.70577	−	3.29423i	0.369850	−	0.213533i
$239$		−	8.19615i		−	0.530165i	−0.964226	−	0.265083i	$-0.914601\pi$
$239$		−	8.19615i		−	0.530165i	0.964226	−	0.265083i	$-0.0853992\pi$
$240$		0			0
$241$	−7.50000	+	4.33013i	−0.483117	+	0.278928i	−0.721715	−	0.692191i	$-0.756646\pi$
$241$	−7.50000	+	4.33013i	−0.483117	+	0.278928i	0.238597	+	0.971119i	$0.423312\pi$
$242$	−2.00000			−0.128565
$243$	16.2224	−	9.36603i	1.04067	−	0.600831i
$244$	2.09808	−	3.63397i	0.134316	−	0.232641i
$245$		0			0
$246$	−28.3923			−1.81023
$247$	16.1603	+	16.7942i	1.02825	+	1.06859i
$248$			1.26795i			0.0805149i
$249$	5.19615	+	3.00000i	0.329293	+	0.190117i
$250$		0			0
$251$	−3.40192	−	5.89230i	−0.214728	−	0.371919i	0.738461	−	0.674296i	$-0.235553\pi$
$251$	−3.40192	−	5.89230i	−0.214728	−	0.371919i	−0.953188	+	0.302378i	$0.902220\pi$
$252$	13.3923			0.843636
$253$	3.80385	+	6.58846i	0.239146	+	0.414213i
$254$	18.3564	−	10.5981i	1.15178	−	0.664982i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	12.0000	+	6.92820i	0.748539	+	0.432169i	0.825166	−	0.564890i	$-0.191082\pi$
$257$	12.0000	+	6.92820i	0.748539	+	0.432169i	−0.0766265	+	0.997060i	$0.524415\pi$
$258$	2.73205	−	4.73205i	0.170090	−	0.294605i
$259$	33.5885			2.08709
$260$		0			0
$261$	−42.2487			−2.61513
$262$	−9.06218	+	15.6962i	−0.559863	+	0.969712i
$263$	23.8923	+	13.7942i	1.47326	+	0.850589i	0.999547	−	0.0300894i	$-0.00957920\pi$
$263$	23.8923	+	13.7942i	1.47326	+	0.850589i	0.473715	+	0.880678i	$0.342913\pi$
$264$	4.09808	+	7.09808i	0.252219	+	0.436856i
$265$		0			0
$266$	16.7942	−	9.69615i	1.02972	−	0.594509i
$267$	23.4904	+	40.6865i	1.43759	+	2.48998i
$268$		0			0
$269$	−1.43782	−	2.49038i	−0.0876656	−	0.151841i	0.818858	−	0.573996i	$-0.194607\pi$
$269$	−1.43782	−	2.49038i	−0.0876656	−	0.151841i	−0.906524	+	0.422154i	$0.861274\pi$
$270$		0			0
$271$	−2.19615	−	1.26795i	−0.133407	−	0.0770224i	0.431811	−	0.901964i	$-0.357875\pi$
$271$	−2.19615	−	1.26795i	−0.133407	−	0.0770224i	−0.565218	+	0.824942i	$0.691208\pi$
$272$			2.19615i			0.133161i
$273$	−28.6865	+	7.09808i	−1.73619	+	0.429595i
$274$	−8.19615			−0.495148
$275$		0			0
$276$	−3.46410	+	6.00000i	−0.208514	+	0.361158i
$277$	0.866025	−	0.500000i	0.0520344	−	0.0300421i	−0.473757	−	0.880656i	$-0.657103\pi$
$277$	0.866025	−	0.500000i	0.0520344	−	0.0300421i	0.525792	+	0.850613i	$0.323769\pi$
$278$	−9.19615			−0.551549
$279$	4.90192	−	2.83013i	0.293471	−	0.169435i
$280$		0			0
$281$		−	10.3923i		−	0.619953i	−0.950744	−	0.309976i	$-0.899679\pi$
$281$		−	10.3923i		−	0.619953i	0.950744	−	0.309976i	$-0.100321\pi$
$282$	−7.09808	+	4.09808i	−0.422684	+	0.244037i
$283$	26.3205	+	15.1962i	1.56459	+	0.903317i	0.996782	+	0.0801576i	$0.0255424\pi$
$283$	26.3205	+	15.1962i	1.56459	+	0.903317i	0.567810	+	0.823160i	$0.307791\pi$
$284$	−5.19615	−	3.00000i	−0.308335	−	0.178017i
$285$		0			0
$286$	−7.50000	−	7.79423i	−0.443484	−	0.460882i
$287$		−	31.1769i		−	1.84032i
$288$	−2.23205	+	3.86603i	−0.131525	+	0.227808i
$289$	−6.08846	+	10.5455i	−0.358145	+	0.620325i
$290$		0			0
$291$		−	41.3205i		−	2.42225i
$292$	2.83013	+	4.90192i	0.165621	+	0.286863i
$293$	−0.401924	−	0.696152i	−0.0234806	−	0.0406697i	0.854046	−	0.520197i	$-0.174141\pi$
$293$	−0.401924	−	0.696152i	−0.0234806	−	0.0406697i	−0.877527	+	0.479527i	$0.840808\pi$
$294$			5.46410i			0.318673i
$295$		0			0
$296$	−5.59808	+	9.69615i	−0.325382	+	0.563577i
$297$	6.00000	−	10.3923i	0.348155	−	0.603023i
$298$		−	6.00000i		−	0.347571i
$299$	2.53590	−	8.78461i	0.146655	−	0.508027i
$300$		0			0
$301$	5.19615	+	3.00000i	0.299501	+	0.172917i
$302$	5.49038	+	3.16987i	0.315936	+	0.182406i
$303$	−17.1962	+	9.92820i	−0.987893	+	0.570360i
$304$			6.46410i			0.370742i
$305$		0			0
$306$	8.49038	−	4.90192i	0.485363	−	0.280224i
$307$	20.5359			1.17205			0.586023	−	0.810295i	$-0.300693\pi$
$307$	20.5359			1.17205			0.586023	+	0.810295i	$0.300693\pi$
$308$	−7.79423	+	4.50000i	−0.444117	+	0.256411i
$309$	−1.63397	+	2.83013i	−0.0929536	+	0.161000i
$310$		0			0
$311$	15.1244			0.857624			0.428812	−	0.903394i	$-0.358932\pi$
$311$	15.1244			0.857624			0.428812	+	0.903394i	$0.358932\pi$
$312$	2.73205	−	9.46410i	0.154672	−	0.535799i
$313$			5.60770i			0.316966i	0.987362	+	0.158483i	$0.0506603\pi$
$313$			5.60770i			0.316966i	−0.987362	+	0.158483i	$0.949340\pi$
$314$	11.2583	+	6.50000i	0.635344	+	0.366816i
$315$		0			0
$316$	3.09808	+	5.36603i	0.174280	+	0.301863i
$317$	12.8038			0.719136			0.359568	−	0.933119i	$-0.382924\pi$
$317$	12.8038			0.719136			0.359568	+	0.933119i	$0.382924\pi$
$318$	−8.83013	−	15.2942i	−0.495169	−	0.857658i
$319$	24.5885	−	14.1962i	1.37669	−	0.794832i
$320$		0			0
$321$	0.464102	+	0.803848i	0.0259036	+	0.0448664i
$322$	−6.58846	−	3.80385i	−0.367160	−	0.211980i
$323$	7.09808	−	12.2942i	0.394948	−	0.684069i
$324$	−2.46410			−0.136895
$325$		0			0
$326$	7.26795			0.402534
$327$	21.1244	−	36.5885i	1.16818	−	2.02335i
$328$	9.00000	+	5.19615i	0.496942	+	0.286910i
$329$	−4.50000	−	7.79423i	−0.248093	−	0.429710i
$330$		0			0
$331$	0.803848	−	0.464102i	0.0441835	−	0.0255093i	−0.477746	−	0.878498i	$-0.658546\pi$
$331$	0.803848	−	0.464102i	0.0441835	−	0.0255093i	0.521929	+	0.852989i	$0.325213\pi$
$332$	−1.09808	−	1.90192i	−0.0602648	−	0.104382i
$333$	49.9808			2.73893
$334$	1.50000	+	2.59808i	0.0820763	+	0.142160i
$335$		0			0
$336$	−7.09808	−	4.09808i	−0.387232	−	0.223568i
$337$			4.19615i			0.228579i	0.993447	+	0.114289i	$0.0364591\pi$
$337$			4.19615i			0.228579i	−0.993447	+	0.114289i	$0.963541\pi$
$338$	−0.500000	+	12.9904i	−0.0271964	+	0.706584i
$339$	−18.9282			−1.02804
$340$		0			0
$341$	−1.90192	+	3.29423i	−0.102995	+	0.178392i
$342$	24.9904	−	14.4282i	1.35133	−	0.780188i
$343$	15.0000			0.809924
$344$	−1.73205	+	1.00000i	−0.0933859	+	0.0539164i
$345$		0			0
$346$			15.0000i			0.806405i
$347$	21.8827	−	12.6340i	1.17472	−	0.678227i	0.219936	−	0.975514i	$-0.429415\pi$
$347$	21.8827	−	12.6340i	1.17472	−	0.678227i	0.954788	+	0.297287i	$0.0960818\pi$
$348$	22.3923	+	12.9282i	1.20035	+	0.693024i
$349$	29.4904	+	17.0263i	1.57858	+	0.911396i	0.995057	+	0.0993018i	$0.0316609\pi$
$349$	29.4904	+	17.0263i	1.57858	+	0.911396i	0.583527	+	0.812094i	$0.301672\pi$
$350$		0			0
$351$	−14.0000	+	3.46410i	−0.747265	+	0.184900i
$352$		−	3.00000i		−	0.159901i
$353$	10.0981	−	17.4904i	0.537466	−	0.930919i	−0.461573	−	0.887102i	$-0.652715\pi$
$353$	10.0981	−	17.4904i	0.537466	−	0.930919i	0.999040	−	0.0438169i	$-0.0139518\pi$
$354$	−14.1962	+	24.5885i	−0.754517	+	1.30686i
$355$		0			0
$356$		−	17.1962i		−	0.911394i
$357$	9.00000	+	15.5885i	0.476331	+	0.825029i
$358$	1.26795	+	2.19615i	0.0670132	+	0.116070i
$359$			22.3923i			1.18182i	0.806737	+	0.590910i	$0.201231\pi$
$359$			22.3923i			1.18182i	−0.806737	+	0.590910i	$0.798769\pi$
$360$		0			0
$361$	11.3923	−	19.7321i	0.599595	−	1.03853i
$362$	−8.29423	+	14.3660i	−0.435935	+	0.755062i
$363$		−	5.46410i		−	0.286791i
$364$	10.3923	+	3.00000i	0.544705	+	0.157243i
$365$		0			0
$366$	9.92820	+	5.73205i	0.518955	+	0.299619i
$367$	−22.8564	−	13.1962i	−1.19309	−	0.688834i	−0.234088	−	0.972216i	$-0.575210\pi$
$367$	−22.8564	−	13.1962i	−1.19309	−	0.688834i	−0.959007	+	0.283382i	$0.908544\pi$
$368$	2.19615	−	1.26795i	0.114482	−	0.0660964i
$369$		−	46.3923i		−	2.41509i
$370$		0			0
$371$	16.7942	−	9.69615i	0.871913	−	0.503399i
$372$	−3.46410			−0.179605
$373$	17.6603	−	10.1962i	0.914413	−	0.527937i	0.0325648	−	0.999470i	$-0.489632\pi$
$373$	17.6603	−	10.1962i	0.914413	−	0.527937i	0.881848	+	0.471533i	$0.156299\pi$
$374$	−3.29423	+	5.70577i	−0.170341	+	0.295038i
$375$		0			0
$376$	3.00000			0.154713
$377$	−32.7846	−	9.46410i	−1.68849	−	0.487426i
$378$			12.0000i			0.617213i
$379$	−10.2058	−	5.89230i	−0.524235	−	0.302667i	0.214430	−	0.976739i	$-0.431210\pi$
$379$	−10.2058	−	5.89230i	−0.524235	−	0.302667i	−0.738666	+	0.674072i	$0.764544\pi$
$380$		0			0
$381$	28.9545	+	50.1506i	1.48338	+	2.56929i
$382$	19.2679			0.985834
$383$	−0.803848	−	1.39230i	−0.0410747	−	0.0711435i	0.844757	−	0.535150i	$-0.179745\pi$
$383$	−0.803848	−	1.39230i	−0.0410747	−	0.0711435i	−0.885832	+	0.464006i	$0.846411\pi$
$384$	2.36603	−	1.36603i	0.120741	−	0.0697097i
$385$		0			0
$386$	−2.19615	−	3.80385i	−0.111781	−	0.193611i
$387$	7.73205	+	4.46410i	0.393042	+	0.226923i
$388$	−7.56218	+	13.0981i	−0.383911	+	0.664954i
$389$	−19.2679			−0.976924			−0.488462	−	0.872585i	$-0.662442\pi$
$389$	−19.2679			−0.976924			−0.488462	+	0.872585i	$0.662442\pi$
$390$		0			0
$391$	−5.56922			−0.281648
$392$	1.00000	−	1.73205i	0.0505076	−	0.0874818i
$393$	−42.8827	−	24.7583i	−2.16315	−	1.24889i
$394$	−4.79423	−	8.30385i	−0.241530	−	0.418342i
$395$		0			0
$396$	−11.5981	+	6.69615i	−0.582825	+	0.336494i
$397$	−0.401924	−	0.696152i	−0.0201720	−	0.0349389i	0.855763	−	0.517368i	$-0.173088\pi$
$397$	−0.401924	−	0.696152i	−0.0201720	−	0.0349389i	−0.875935	+	0.482429i	$0.839755\pi$
$398$	14.3923			0.721421
$399$	26.4904	+	45.8827i	1.32618	+	2.29701i
$400$		0			0
$401$	−4.50000	−	2.59808i	−0.224719	−	0.129742i	0.383414	−	0.923576i	$-0.374748\pi$
$401$	−4.50000	−	2.59808i	−0.224719	−	0.129742i	−0.608134	+	0.793835i	$0.708081\pi$
$402$		0			0
$403$	4.43782	−	1.09808i	0.221064	−	0.0546991i
$404$	7.26795			0.361594
$405$		0			0
$406$	−14.1962	+	24.5885i	−0.704543	+	1.22030i
$407$	−29.0885	+	16.7942i	−1.44186	+	0.832459i
$408$	−6.00000			−0.297044
$409$	−17.0885	+	9.86603i	−0.844970	+	0.487844i	−0.858950	−	0.512059i	$-0.828883\pi$
$409$	−17.0885	+	9.86603i	−0.844970	+	0.487844i	0.0139806	+	0.999902i	$0.495550\pi$
$410$		0			0
$411$		−	22.3923i		−	1.10453i
$412$	1.03590	−	0.598076i	0.0510351	−	0.0294651i
$413$	−27.0000	−	15.5885i	−1.32858	−	0.767058i
$414$	−9.80385	−	5.66025i	−0.481833	−	0.278186i
$415$		0			0
$416$	−2.59808	+	2.50000i	−0.127381	+	0.122573i
$417$		−	25.1244i		−	1.23034i
$418$	−9.69615	+	16.7942i	−0.474254	+	0.821433i
$419$	8.66025	−	15.0000i	0.423081	−	0.732798i	−0.573158	−	0.819445i	$-0.694282\pi$
$419$	8.66025	−	15.0000i	0.423081	−	0.732798i	0.996239	+	0.0866469i	$0.0276152\pi$
$420$		0			0
$421$		−	27.1244i		−	1.32196i	−0.750403	−	0.660980i	$-0.770141\pi$
$421$		−	27.1244i		−	1.32196i	0.750403	−	0.660980i	$-0.229859\pi$
$422$	6.79423	+	11.7679i	0.330738	+	0.572855i
$423$	−6.69615	−	11.5981i	−0.325578	−	0.563918i
$424$			6.46410i			0.313925i
$425$		0			0
$426$	8.19615	−	14.1962i	0.397105	−	0.687806i
$427$	−6.29423	+	10.9019i	−0.304599	+	0.527581i
$428$		−	0.339746i		−	0.0164222i
$429$	21.2942	−	20.4904i	1.02810	−	0.989285i
$430$		0			0
$431$	−1.90192	−	1.09808i	−0.0916124	−	0.0528925i	0.453494	−	0.891259i	$-0.350177\pi$
$431$	−1.90192	−	1.09808i	−0.0916124	−	0.0528925i	−0.545106	+	0.838367i	$0.683511\pi$
$432$	−3.46410	−	2.00000i	−0.166667	−	0.0962250i
$433$	−10.7321	+	6.19615i	−0.515749	+	0.297768i	−0.735194	−	0.677857i	$-0.762909\pi$
$433$	−10.7321	+	6.19615i	−0.515749	+	0.297768i	0.219444	+	0.975625i	$0.429576\pi$
$434$		−	3.80385i		−	0.182591i
$435$		0			0
$436$	−13.3923	+	7.73205i	−0.641375	+	0.370298i
$437$	−16.3923			−0.784150
$438$	−13.3923	+	7.73205i	−0.639909	+	0.369452i
$439$	−17.2942	+	29.9545i	−0.825408	+	1.42965i	0.0761982	+	0.997093i	$0.475722\pi$
$439$	−17.2942	+	29.9545i	−0.825408	+	1.42965i	−0.901607	+	0.432557i	$0.857612\pi$
$440$		0			0
$441$	−8.92820			−0.425153
$442$	7.68653	−	1.90192i	0.365611	−	0.0904653i
$443$		−	1.60770i		−	0.0763839i	−0.999270	−	0.0381920i	$-0.987840\pi$
$443$		−	1.60770i		−	0.0763839i	0.999270	−	0.0381920i	$-0.0121598\pi$
$444$	−26.4904	−	15.2942i	−1.25718	−	0.725832i
$445$		0			0
$446$	−0.232051	−	0.401924i	−0.0109879	−	0.0190316i
$447$	16.3923			0.775329
$448$	1.50000	+	2.59808i	0.0708683	+	0.122748i
$449$	−13.5000	+	7.79423i	−0.637104	+	0.367832i	−0.783498	−	0.621394i	$-0.786567\pi$
$449$	−13.5000	+	7.79423i	−0.637104	+	0.367832i	0.146394	+	0.989226i	$0.453233\pi$
$450$		0			0
$451$	15.5885	+	27.0000i	0.734032	+	1.27138i
$452$	6.00000	+	3.46410i	0.282216	+	0.162938i
$453$	−8.66025	+	15.0000i	−0.406894	+	0.704761i
$454$	−4.39230			−0.206141
$455$		0			0
$456$	−17.6603			−0.827017
$457$	−17.8301	+	30.8827i	−0.834058	+	1.44463i	0.0607368	+	0.998154i	$0.480655\pi$
$457$	−17.8301	+	30.8827i	−0.834058	+	1.44463i	−0.894795	+	0.446477i	$0.852678\pi$
$458$	−4.09808	−	2.36603i	−0.191491	−	0.110557i
$459$	4.39230	+	7.60770i	0.205015	+	0.355097i
$460$		0			0
$461$	−0.509619	+	0.294229i	−0.0237353	+	0.0137036i	−0.511821	−	0.859092i	$-0.671029\pi$
$461$	−0.509619	+	0.294229i	−0.0237353	+	0.0137036i	0.488085	+	0.872796i	$0.337695\pi$
$462$	−12.2942	−	21.2942i	−0.571979	−	0.990697i
$463$	−0.928203			−0.0431373			−0.0215686	−	0.999767i	$-0.506866\pi$
$463$	−0.928203			−0.0431373			−0.0215686	+	0.999767i	$0.506866\pi$
$464$	−4.73205	−	8.19615i	−0.219680	−	0.380497i
$465$		0			0
$466$	1.09808	+	0.633975i	0.0508674	+	0.0293683i
$467$			10.1436i			0.469390i	0.972069	+	0.234695i	$0.0754091\pi$
$467$			10.1436i			0.469390i	−0.972069	+	0.234695i	$0.924591\pi$
$468$	15.4641	+	4.46410i	0.714828	+	0.206353i
$469$		0			0
$470$		0			0
$471$	−17.7583	+	30.7583i	−0.818261	+	1.41727i
$472$	9.00000	−	5.19615i	0.414259	−	0.239172i
$473$	−6.00000			−0.275880
$474$	−14.6603	+	8.46410i	−0.673368	+	0.388769i
$475$		0			0
$476$		−	6.58846i		−	0.301981i
$477$	24.9904	−	14.4282i	1.14423	−	0.660622i
$478$	−7.09808	−	4.09808i	−0.324658	−	0.187442i
$479$	9.50962	+	5.49038i	0.434506	+	0.250862i	0.701264	−	0.712901i	$-0.252619\pi$
$479$	9.50962	+	5.49038i	0.434506	+	0.250862i	−0.266759	+	0.963763i	$0.585953\pi$
$480$		0			0
$481$	38.7846	+	11.1962i	1.76843	+	0.510501i
$482$			8.66025i			0.394464i
$483$	10.3923	−	18.0000i	0.472866	−	0.819028i
$484$	−1.00000	+	1.73205i	−0.0454545	+	0.0787296i
$485$		0			0
$486$		−	18.7321i		−	0.849703i
$487$	16.6244	+	28.7942i	0.753321	+	1.30479i	0.946204	+	0.323569i	$0.104883\pi$
$487$	16.6244	+	28.7942i	0.753321	+	1.30479i	−0.192883	+	0.981222i	$0.561784\pi$
$488$	−2.09808	−	3.63397i	−0.0949754	−	0.164502i
$489$			19.8564i			0.897938i
$490$		0			0
$491$	−1.66987	+	2.89230i	−0.0753603	+	0.130528i	−0.901243	−	0.433314i	$-0.857344\pi$
$491$	−1.66987	+	2.89230i	−0.0753603	+	0.130528i	0.825883	+	0.563842i	$0.190677\pi$
$492$	−14.1962	+	24.5885i	−0.640012	+	1.10853i
$493$			20.7846i			0.936092i
$494$	22.6244	−	5.59808i	1.01792	−	0.251869i
$495$		0			0
$496$	1.09808	+	0.633975i	0.0493051	+	0.0284663i
$497$	15.5885	+	9.00000i	0.699238	+	0.403705i
$498$	5.19615	−	3.00000i	0.232845	−	0.134433i
$499$		−	1.85641i		−	0.0831042i	−0.999136	−	0.0415521i	$-0.986770\pi$
$499$		−	1.85641i		−	0.0831042i	0.999136	−	0.0415521i	$-0.0132302\pi$
$500$		0			0
$501$	−7.09808	+	4.09808i	−0.317119	+	0.183089i
$502$	−6.80385			−0.303671
$503$	−8.08846	+	4.66987i	−0.360646	+	0.208219i	−0.669364	−	0.742934i	$-0.733433\pi$
$503$	−8.08846	+	4.66987i	−0.360646	+	0.208219i	0.308718	+	0.951154i	$0.400100\pi$
$504$	6.69615	−	11.5981i	0.298270	−	0.516619i
$505$		0			0
$506$	7.60770			0.338203
$507$	−35.4904	−	1.36603i	−1.57618	−	0.0606673i
$508$		−	21.1962i		−	0.940427i
$509$	−1.39230	−	0.803848i	−0.0617128	−	0.0356299i	0.468826	−	0.883290i	$-0.344677\pi$
$509$	−1.39230	−	0.803848i	−0.0617128	−	0.0356299i	−0.530539	+	0.847661i	$0.678010\pi$
$510$		0			0
$511$	−8.49038	−	14.7058i	−0.375592	−	0.650545i
$512$	−1.00000			−0.0441942
$513$	12.9282	+	22.3923i	0.570794	+	0.988644i
$514$	12.0000	−	6.92820i	0.529297	−	0.305590i
$515$		0			0
$516$	−2.73205	−	4.73205i	−0.120272	−	0.208317i
$517$	7.79423	+	4.50000i	0.342790	+	0.197910i
$518$	16.7942	−	29.0885i	0.737896	−	1.27807i
$519$	−40.9808			−1.79886
$520$		0			0
$521$	−0.464102			−0.0203327			−0.0101663	−	0.999948i	$-0.503236\pi$
$521$	−0.464102			−0.0203327			−0.0101663	+	0.999948i	$0.503236\pi$
$522$	−21.1244	+	36.5885i	−0.924588	+	1.60143i
$523$	−15.9282	−	9.19615i	−0.696492	−	0.402120i	0.109548	−	0.993982i	$-0.465060\pi$
$523$	−15.9282	−	9.19615i	−0.696492	−	0.402120i	−0.806039	+	0.591862i	$0.798393\pi$
$524$	9.06218	+	15.6962i	0.395883	+	0.685690i
$525$		0			0
$526$	23.8923	−	13.7942i	1.04175	−	0.601457i
$527$	−1.39230	−	2.41154i	−0.0606498	−	0.105048i
$528$	8.19615			0.356692
$529$	−8.28461	−	14.3494i	−0.360200	−	0.623885i
$530$		0			0
$531$	−40.1769	−	23.1962i	−1.74353	−	1.00663i
$532$		−	19.3923i		−	0.840763i
$533$	10.3923	−	36.0000i	0.450141	−	1.55933i
$534$	46.9808			2.03306
$535$		0			0
$536$		0			0
$537$	−6.00000	+	3.46410i	−0.258919	+	0.149487i
$538$	−2.87564			−0.123978
$539$	5.19615	−	3.00000i	0.223814	−	0.129219i
$540$		0			0
$541$			16.0526i			0.690153i	0.938574	+	0.345077i	$0.112147\pi$
$541$			16.0526i			0.690153i	−0.938574	+	0.345077i	$0.887853\pi$
$542$	−2.19615	+	1.26795i	−0.0943328	+	0.0544631i
$543$	−39.2487	−	22.6603i	−1.68432	−	0.972445i
$544$	1.90192	+	1.09808i	0.0815443	+	0.0470796i
$545$		0			0
$546$	−8.19615	+	28.3923i	−0.350763	+	1.21508i
$547$		−	34.7846i		−	1.48728i	−0.668579	−	0.743641i	$-0.733097\pi$
$547$		−	34.7846i		−	1.48728i	0.668579	−	0.743641i	$-0.266903\pi$
$548$	−4.09808	+	7.09808i	−0.175061	+	0.303215i
$549$	−9.36603	+	16.2224i	−0.399732	+	0.692357i
$550$		0			0
$551$			61.1769i			2.60622i
$552$	3.46410	+	6.00000i	0.147442	+	0.255377i
$553$	−9.29423	−	16.0981i	−0.395231	−	0.684560i
$554$		−	1.00000i		−	0.0424859i
$555$		0			0
$556$	−4.59808	+	7.96410i	−0.195002	+	0.337753i
$557$	8.59808	−	14.8923i	0.364312	−	0.631007i	−0.624353	−	0.781142i	$-0.714637\pi$
$557$	8.59808	−	14.8923i	0.364312	−	0.631007i	0.988666	+	0.150135i	$0.0479708\pi$
$558$		−	5.66025i		−	0.239618i
$559$	5.00000	+	5.19615i	0.211477	+	0.219774i
$560$		0			0
$561$	−15.5885	−	9.00000i	−0.658145	−	0.379980i
$562$	−9.00000	−	5.19615i	−0.379642	−	0.219186i
$563$	18.5885	−	10.7321i	0.783410	−	0.452302i	−0.0542274	−	0.998529i	$-0.517270\pi$
$563$	18.5885	−	10.7321i	0.783410	−	0.452302i	0.837637	+	0.546227i	$0.183936\pi$
$564$			8.19615i			0.345120i
$565$		0			0
$566$	26.3205	−	15.1962i	1.10633	−	0.638742i
$567$	7.39230			0.310448
$568$	−5.19615	+	3.00000i	−0.218026	+	0.125877i
$569$	10.6244	−	18.4019i	0.445396	−	0.771449i	−0.552684	−	0.833391i	$-0.686396\pi$
$569$	10.6244	−	18.4019i	0.445396	−	0.771449i	0.998080	+	0.0619424i	$0.0197295\pi$
$570$		0			0
$571$	34.3731			1.43847			0.719234	−	0.694768i	$-0.244493\pi$
$571$	34.3731			1.43847			0.719234	+	0.694768i	$0.244493\pi$
$572$	−10.5000	+	2.59808i	−0.439027	+	0.108631i
$573$			52.6410i			2.19911i
$574$	−27.0000	−	15.5885i	−1.12696	−	0.650650i
$575$		0			0
$576$	2.23205	+	3.86603i	0.0930021	+	0.161084i
$577$	−32.4449			−1.35070			−0.675349	−	0.737499i	$-0.736007\pi$
$577$	−32.4449			−1.35070			−0.675349	+	0.737499i	$0.736007\pi$
$578$	6.08846	+	10.5455i	0.253246	+	0.438636i
$579$	10.3923	−	6.00000i	0.431889	−	0.249351i
$580$		0			0
$581$	3.29423	+	5.70577i	0.136668	+	0.236715i
$582$	−35.7846	−	20.6603i	−1.48332	−	0.856395i
$583$	−9.69615	+	16.7942i	−0.401574	+	0.695546i
$584$	5.66025			0.234223
$585$		0			0
$586$	−0.803848			−0.0332066
$587$	−15.0000	+	25.9808i	−0.619116	+	1.07234i	0.370531	+	0.928820i	$0.379176\pi$
$587$	−15.0000	+	25.9808i	−0.619116	+	1.07234i	−0.989647	+	0.143521i	$0.954158\pi$
$588$	4.73205	+	2.73205i	0.195146	+	0.112668i
$589$	−4.09808	−	7.09808i	−0.168858	−	0.292471i
$590$		0			0
$591$	22.6865	−	13.0981i	0.933199	−	0.538783i
$592$	5.59808	+	9.69615i	0.230080	+	0.398509i
$593$	20.7846			0.853522			0.426761	−	0.904365i	$-0.359655\pi$
$593$	20.7846			0.853522			0.426761	+	0.904365i	$0.359655\pi$
$594$	−6.00000	−	10.3923i	−0.246183	−	0.426401i
$595$		0			0
$596$	−5.19615	−	3.00000i	−0.212843	−	0.122885i
$597$			39.3205i			1.60928i
$598$	−6.33975	−	6.58846i	−0.259251	−	0.269422i
$599$	−7.85641			−0.321004			−0.160502	−	0.987036i	$-0.551311\pi$
$599$	−7.85641			−0.321004			−0.160502	+	0.987036i	$0.551311\pi$
$600$		0			0
$601$	−1.89230	+	3.27757i	−0.0771887	+	0.133695i	−0.902036	−	0.431661i	$-0.857928\pi$
$601$	−1.89230	+	3.27757i	−0.0771887	+	0.133695i	0.824847	+	0.565356i	$0.191261\pi$
$602$	5.19615	−	3.00000i	0.211779	−	0.122271i
$603$		0			0
$604$	5.49038	−	3.16987i	0.223400	−	0.128980i
$605$		0			0
$606$			19.8564i			0.806611i
$607$	5.55256	−	3.20577i	0.225371	−	0.130118i	−0.383064	−	0.923722i	$-0.625131\pi$
$607$	5.55256	−	3.20577i	0.225371	−	0.130118i	0.608435	+	0.793604i	$0.291798\pi$
$608$	5.59808	+	3.23205i	0.227032	+	0.131077i
$609$	−67.1769	−	38.7846i	−2.72215	−	1.57163i
$610$		0			0
$611$	−2.59808	−	10.5000i	−0.105107	−	0.424785i
$612$		−	9.80385i		−	0.396297i
$613$	−13.4545	+	23.3038i	−0.543421	+	0.941234i	0.455283	+	0.890347i	$0.349538\pi$
$613$	−13.4545	+	23.3038i	−0.543421	+	0.941234i	−0.998704	+	0.0508868i	$0.983795\pi$
$614$	10.2679	−	17.7846i	0.414381	−	0.717728i
$615$		0			0
$616$			9.00000i			0.362620i
$617$	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	$0.715316\pi$
$618$	1.63397	+	2.83013i	0.0657281	+	0.113844i
$619$		−	10.6077i		−	0.426359i	−0.977013	−	0.213180i	$-0.931618\pi$
$619$		−	10.6077i		−	0.426359i	0.977013	−	0.213180i	$-0.0683820\pi$
$620$		0			0
$621$	5.07180	−	8.78461i	0.203524	−	0.352514i
$622$	7.56218	−	13.0981i	0.303216	−	0.525185i
$623$			51.5885i			2.06685i
$624$	−6.83013	−	7.09808i	−0.273424	−	0.284150i
$625$		0			0
$626$	4.85641	+	2.80385i	0.194101	+	0.112064i
$627$	−45.8827	−	26.4904i	−1.83238	−	1.05792i
$628$	11.2583	−	6.50000i	0.449256	−	0.259378i
$629$		−	24.5885i		−	0.980406i
$630$		0			0
$631$	−18.0000	+	10.3923i	−0.716569	+	0.413711i	−0.813488	−	0.581581i	$-0.802434\pi$
$631$	−18.0000	+	10.3923i	−0.716569	+	0.413711i	0.0969198	+	0.995292i	$0.469101\pi$
$632$	6.19615			0.246470
$633$	−32.1506	+	18.5622i	−1.27787	+	0.737780i
$634$	6.40192	−	11.0885i	0.254253	−	0.440379i
$635$		0			0
$636$	−17.6603			−0.700275
$637$	−6.92820	−	2.00000i	−0.274505	−	0.0792429i
$638$		−	28.3923i		−	1.12406i
$639$	23.1962	+	13.3923i	0.917626	+	0.529791i
$640$		0			0
$641$	−22.9641	−	39.7750i	−0.907027	−	1.57102i	−0.818172	−	0.574973i	$-0.805012\pi$
$641$	−22.9641	−	39.7750i	−0.907027	−	1.57102i	−0.0888552	−	0.996045i	$-0.528321\pi$
$642$	0.928203			0.0366333
$643$	3.63397	+	6.29423i	0.143310	+	0.248220i	0.928741	−	0.370729i	$-0.120892\pi$
$643$	3.63397	+	6.29423i	0.143310	+	0.248220i	−0.785431	+	0.618949i	$0.787559\pi$
$644$	−6.58846	+	3.80385i	−0.259622	+	0.149893i
$645$		0			0
$646$	−7.09808	−	12.2942i	−0.279270	−	0.483710i
$647$	−9.69615	−	5.59808i	−0.381195	−	0.220083i	0.297143	−	0.954833i	$-0.403966\pi$
$647$	−9.69615	−	5.59808i	−0.381195	−	0.220083i	−0.678338	+	0.734750i	$0.737300\pi$
$648$	−1.23205	+	2.13397i	−0.0483995	+	0.0838304i
$649$	31.1769			1.22380
$650$		0			0
$651$	10.3923			0.407307
$652$	3.63397	−	6.29423i	0.142317	−	0.246501i
$653$	16.7942	+	9.69615i	0.657209	+	0.379440i	0.791213	−	0.611541i	$-0.209450\pi$
$653$	16.7942	+	9.69615i	0.657209	+	0.379440i	−0.134004	+	0.990981i	$0.542783\pi$
$654$	−21.1244	−	36.5885i	−0.826028	−	1.43072i
$655$		0			0
$656$	9.00000	−	5.19615i	0.351391	−	0.202876i
$657$	−12.6340	−	21.8827i	−0.492898	−	0.853725i
$658$	−9.00000			−0.350857
$659$	14.6603	+	25.3923i	0.571082	+	0.989144i	0.996455	+	0.0841255i	$0.0268097\pi$
$659$	14.6603	+	25.3923i	0.571082	+	0.989144i	−0.425373	+	0.905018i	$0.639857\pi$
$660$		0			0
$661$	25.9019	+	14.9545i	1.00747	+	0.581662i	0.910449	−	0.413621i	$-0.135736\pi$
$661$	25.9019	+	14.9545i	1.00747	+	0.581662i	0.0970187	+	0.995283i	$0.469069\pi$
$662$		−	0.928203i		−	0.0360756i
$663$	5.19615	+	21.0000i	0.201802	+	0.815572i
$664$	−2.19615			−0.0852272
$665$		0			0
$666$	24.9904	−	43.2846i	0.968358	−	1.67724i
$667$	20.7846	−	12.0000i	0.804783	−	0.464642i
$668$	3.00000			0.116073
$669$	1.09808	−	0.633975i	0.0424541	−	0.0245109i
$670$		0			0
$671$		−	12.5885i		−	0.485972i
$672$	−7.09808	+	4.09808i	−0.273814	+	0.158087i
$673$	−3.12436	−	1.80385i	−0.120435	−	0.0695332i	0.438572	−	0.898696i	$-0.355484\pi$
$673$	−3.12436	−	1.80385i	−0.120435	−	0.0695332i	−0.559007	+	0.829163i	$0.688818\pi$
$674$	3.63397	+	2.09808i	0.139975	+	0.0808149i
$675$		0			0
$676$	11.0000	+	6.92820i	0.423077	+	0.266469i
$677$		−	1.85641i		−	0.0713475i	−0.999363	−	0.0356737i	$-0.988642\pi$
$677$		−	1.85641i		−	0.0713475i	0.999363	−	0.0356737i	$-0.0113577\pi$
$678$	−9.46410	+	16.3923i	−0.363467	+	0.629543i
$679$	22.6865	−	39.2942i	0.870629	−	1.50797i
$680$		0			0
$681$		−	12.0000i		−	0.459841i
$682$	1.90192	+	3.29423i	0.0728284	+	0.126143i
$683$	15.5885	+	27.0000i	0.596476	+	1.03313i	0.993337	+	0.115248i	$0.0367661\pi$
$683$	15.5885	+	27.0000i	0.596476	+	1.03313i	−0.396861	+	0.917879i	$0.629901\pi$
$684$		−	28.8564i		−	1.10335i
$685$		0			0
$686$	7.50000	−	12.9904i	0.286351	−	0.495975i
$687$	6.46410	−	11.1962i	0.246621	−	0.427160i
$688$			2.00000i			0.0762493i
$689$	22.6244	−	5.59808i	0.861919	−	0.213270i
$690$		0			0
$691$	−16.2058	−	9.35641i	−0.616497	−	0.355934i	0.159007	−	0.987277i	$-0.449171\pi$
$691$	−16.2058	−	9.35641i	−0.616497	−	0.355934i	−0.775504	+	0.631343i	$0.782504\pi$
$692$	12.9904	+	7.50000i	0.493820	+	0.285107i
$693$	34.7942	−	20.0885i	1.32172	−	0.763097i
$694$		−	25.2679i		−	0.959158i
$695$		0			0
$696$	22.3923	−	12.9282i	0.848778	−	0.490042i
$697$	−22.8231			−0.864486
$698$	29.4904	−	17.0263i	1.11623	−	0.644454i
$699$	−1.73205	+	3.00000i	−0.0655122	+	0.113470i
$700$		0			0
$701$	−29.9090			−1.12965			−0.564823	−	0.825212i	$-0.691056\pi$
$701$	−29.9090			−1.12965			−0.564823	+	0.825212i	$0.691056\pi$
$702$	−4.00000	+	13.8564i	−0.150970	+	0.522976i
$703$		−	72.3731i		−	2.72960i
$704$	−2.59808	−	1.50000i	−0.0979187	−	0.0565334i
$705$		0			0
$706$	−10.0981	−	17.4904i	−0.380046	−	0.658259i
$707$	−21.8038			−0.820018
$708$	14.1962	+	24.5885i	0.533524	+	0.924091i
$709$	−35.4904	+	20.4904i	−1.33287	+	0.769532i	−0.985738	−	0.168284i	$-0.946177\pi$
$709$	−35.4904	+	20.4904i	−1.33287	+	0.769532i	−0.347131	+	0.937817i	$0.612844\pi$
$710$		0			0
$711$	−13.8301	−	23.9545i	−0.518670	−	0.898363i
$712$	−14.8923	−	8.59808i	−0.558113	−	0.322227i
$713$	−1.60770	+	2.78461i	−0.0602087	+	0.104284i
$714$	18.0000			0.673633
$715$		0			0
$716$	2.53590			0.0947710
$717$	11.1962	−	19.3923i	0.418128	−	0.724219i
$718$	19.3923	+	11.1962i	0.723714	+	0.417837i
$719$	−0.928203	−	1.60770i	−0.0346161	−	0.0599569i	0.848198	−	0.529679i	$-0.177688\pi$
$719$	−0.928203	−	1.60770i	−0.0346161	−	0.0599569i	−0.882814	+	0.469722i	$0.844354\pi$
$720$		0			0
$721$	−3.10770	+	1.79423i	−0.115737	+	0.0668206i
$722$	−11.3923	−	19.7321i	−0.423978	−	0.734351i
$723$	−23.6603			−0.879934
$724$	8.29423	+	14.3660i	0.308253	+	0.533909i
$725$		0			0
$726$	−4.73205	−	2.73205i	−0.175623	−	0.101396i
$727$			38.3731i			1.42318i	0.702596	+	0.711589i	$0.252024\pi$
$727$			38.3731i			1.42318i	−0.702596	+	0.711589i	$0.747976\pi$
$728$	7.79423	−	7.50000i	0.288873	−	0.277968i
$729$	43.7846			1.62165
$730$		0			0
$731$	2.19615	−	3.80385i	0.0812276	−	0.140690i
$732$	9.92820	−	5.73205i	0.366957	−	0.211863i
$733$	−50.9090			−1.88037			−0.940183	−	0.340670i	$-0.889346\pi$
$733$	−50.9090			−1.88037			−0.940183	+	0.340670i	$0.889346\pi$
$734$	−22.8564	+	13.1962i	−0.843645	+	0.487079i
$735$		0			0
$736$		−	2.53590i		−	0.0934745i
$737$		0			0
$738$	−40.1769	−	23.1962i	−1.47893	−	0.853862i
$739$	−43.7942	−	25.2846i	−1.61100	−	0.930109i	−0.989140	−	0.146979i	$-0.953045\pi$
$739$	−43.7942	−	25.2846i	−1.61100	−	0.930109i	−0.621857	−	0.783131i	$-0.713622\pi$
$740$		0			0
$741$	15.2942	+	61.8109i	0.561848	+	2.27068i
$742$		−	19.3923i		−	0.711914i
$743$	−17.1962	+	29.7846i	−0.630866	+	1.09269i	0.356509	+	0.934292i	$0.383967\pi$
$743$	−17.1962	+	29.7846i	−0.630866	+	1.09269i	−0.987375	+	0.158400i	$0.949367\pi$
$744$	−1.73205	+	3.00000i	−0.0635001	+	0.109985i
$745$		0			0
$746$		−	20.3923i		−	0.746615i
$747$	4.90192	+	8.49038i	0.179352	+	0.310647i
$748$	3.29423	+	5.70577i	0.120449	+	0.208624i
$749$			1.01924i			0.0372421i
$750$		0			0
$751$	−0.196152	+	0.339746i	−0.00715770	+	0.0123975i	−0.869582	−	0.493788i	$-0.835612\pi$
$751$	−0.196152	+	0.339746i	−0.00715770	+	0.0123975i	0.862424	+	0.506186i	$0.168945\pi$
$752$	1.50000	−	2.59808i	0.0546994	−	0.0947421i
$753$		−	18.5885i		−	0.677401i
$754$	−24.5885	+	23.6603i	−0.895459	+	0.861656i
$755$		0			0
$756$	10.3923	+	6.00000i	0.377964	+	0.218218i
$757$	3.27757	+	1.89230i	0.119125	+	0.0687770i	0.558379	−	0.829586i	$-0.311424\pi$
$757$	3.27757	+	1.89230i	0.119125	+	0.0687770i	−0.439253	+	0.898363i	$0.644757\pi$
$758$	−10.2058	+	5.89230i	−0.370690	+	0.214018i
$759$			20.7846i			0.754434i
$760$		0			0
$761$	−25.2846	+	14.5981i	−0.916566	+	0.529180i	−0.882538	−	0.470241i	$-0.844167\pi$
$761$	−25.2846	+	14.5981i	−0.916566	+	0.529180i	−0.0340283	+	0.999421i	$0.510834\pi$
$762$	57.9090			2.09782
$763$	40.1769	−	23.1962i	1.45450	−	0.839757i
$764$	9.63397	−	16.6865i	0.348545	−	0.603698i
$765$		0			0
$766$	−1.60770			−0.0580884
$767$	−25.9808	−	27.0000i	−0.938111	−	0.974913i
$768$		−	2.73205i		−	0.0985844i
$769$	33.0000	+	19.0526i	1.19001	+	0.687053i	0.958309	−	0.285734i	$-0.0922374\pi$
$769$	33.0000	+	19.0526i	1.19001	+	0.687053i	0.231701	+	0.972787i	$0.425571\pi$
$770$		0			0
$771$	18.9282	+	32.7846i	0.681683	+	1.18071i
$772$	−4.39230			−0.158083
$773$	−16.7942	−	29.0885i	−0.604046	−	1.04624i	−0.992201	−	0.124645i	$-0.960221\pi$
$773$	−16.7942	−	29.0885i	−0.604046	−	1.04624i	0.388155	−	0.921594i	$-0.373113\pi$
$774$	7.73205	−	4.46410i	0.277923	−	0.160459i
$775$		0			0
$776$	7.56218	+	13.0981i	0.271466	+	0.470194i
$777$	79.4711	+	45.8827i	2.85101	+	1.64603i
$778$	−9.63397	+	16.6865i	−0.345395	+	0.598241i
$779$	−67.1769			−2.40686
$780$		0			0
$781$	−18.0000			−0.644091
$782$	−2.78461	+	4.82309i	−0.0995774	+	0.172473i
$783$	−32.7846	−	18.9282i	−1.17163	−	0.676439i
$784$	−1.00000	−	1.73205i	−0.0357143	−	0.0618590i
$785$		0			0
$786$	−42.8827	+	24.7583i	−1.52957	+	0.883100i
$787$	18.4186	+	31.9019i	0.656552	+	1.13718i	0.981502	+	0.191450i	$0.0613189\pi$
$787$	18.4186	+	31.9019i	0.656552	+	1.13718i	−0.324951	+	0.945731i	$0.605348\pi$
$788$	−9.58846			−0.341575
$789$	37.6865	+	65.2750i	1.34168	+	2.32385i
$790$		0			0
$791$	−18.0000	−	10.3923i	−0.640006	−	0.369508i
$792$			13.3923i			0.475875i
$793$	−10.9019	+	10.4904i	−0.387139	+	0.372524i
$794$	−0.803848			−0.0285275
$795$		0			0
$796$	7.19615	−	12.4641i	0.255061	−	0.441778i
$797$	−0.803848	+	0.464102i	−0.0284737	+	0.0164393i	−0.514169	−	0.857689i	$-0.671900\pi$
$797$	−0.803848	+	0.464102i	−0.0284737	+	0.0164393i	0.485696	+	0.874128i	$0.338566\pi$
$798$	52.9808			1.87550
$799$	−5.70577	+	3.29423i	−0.201856	+	0.116541i
$800$		0			0
$801$			76.7654i			2.71237i
$802$	−4.50000	+	2.59808i	−0.158901	+	0.0917413i
$803$	14.7058	+	8.49038i	0.518955	+	0.299619i
$804$		0			0
$805$		0			0
$806$	1.26795	−	4.39230i	0.0446616	−	0.154712i
$807$		−	7.85641i		−	0.276559i
$808$	3.63397	−	6.29423i	0.127843	−	0.221430i
$809$	12.0000	−	20.7846i	0.421898	−	0.730748i	−0.574228	−	0.818696i	$-0.694698\pi$
$809$	12.0000	−	20.7846i	0.421898	−	0.730748i	0.996125	+	0.0879478i	$0.0280309\pi$
$810$		0			0
$811$		−	22.6077i		−	0.793864i	−0.917848	−	0.396932i	$-0.870075\pi$
$811$		−	22.6077i		−	0.793864i	0.917848	−	0.396932i	$-0.129925\pi$
$812$	14.1962	+	24.5885i	0.498187	+	0.862886i
$813$	−3.46410	−	6.00000i	−0.121491	−	0.210429i
$814$			33.5885i			1.17727i
$815$		0			0
$816$	−3.00000	+	5.19615i	−0.105021	+	0.181902i
$817$	6.46410	−	11.1962i	0.226150	−	0.391704i
$818$			19.7321i			0.689915i
$819$	−46.3923	−	13.3923i	−1.62108	−	0.467965i
$820$		0			0
$821$	−8.49038	−	4.90192i	−0.296316	−	0.171078i	0.344471	−	0.938797i	$-0.388058\pi$
$821$	−8.49038	−	4.90192i	−0.296316	−	0.171078i	−0.640787	+	0.767719i	$0.721392\pi$
$822$	−19.3923	−	11.1962i	−0.676384	−	0.390511i
$823$	−14.5526	+	8.40192i	−0.507270	+	0.292873i	−0.731711	−	0.681615i	$-0.761278\pi$
$823$	−14.5526	+	8.40192i	−0.507270	+	0.292873i	0.224441	+	0.974488i	$0.427945\pi$
$824$		−	1.19615i		−	0.0416699i
$825$		0			0
$826$	−27.0000	+	15.5885i	−0.939450	+	0.542392i
$827$	11.4115			0.396818			0.198409	−	0.980119i	$-0.436423\pi$
$827$	11.4115			0.396818			0.198409	+	0.980119i	$0.436423\pi$
$828$	−9.80385	+	5.66025i	−0.340707	+	0.196707i
$829$	−10.0000	+	17.3205i	−0.347314	+	0.601566i	−0.985771	−	0.168091i	$-0.946240\pi$
$829$	−10.0000	+	17.3205i	−0.347314	+	0.601566i	0.638457	+	0.769657i	$0.279573\pi$
$830$		0			0
$831$	2.73205			0.0947738
$832$	0.866025	+	3.50000i	0.0300240	+	0.121341i
$833$			4.39230i			0.152184i
$834$	−21.7583	−	12.5622i	−0.753429	−	0.434993i
$835$		0			0
$836$	9.69615	+	16.7942i	0.335348	+	0.580841i
$837$	5.07180			0.175307
$838$	−8.66025	−	15.0000i	−0.299164	−	0.518166i
$839$	27.8827	−	16.0981i	0.962617	−	0.555767i	0.0656397	−	0.997843i	$-0.479091\pi$
$839$	27.8827	−	16.0981i	0.962617	−	0.555767i	0.896978	+	0.442076i	$0.145758\pi$
$840$		0			0
$841$	−30.2846	−	52.4545i	−1.04430	−	1.80878i
$842$	−23.4904	−	13.5622i	−0.809532	−	0.467384i
$843$	14.1962	−	24.5885i	0.488941	−	0.846871i
$844$	13.5885			0.467734
$845$		0			0
$846$	−13.3923			−0.460437
$847$	3.00000	−	5.19615i	0.103081	−	0.178542i
$848$	5.59808	+	3.23205i	0.192239	+	0.110989i
$849$	41.5167	+	71.9090i	1.42485	+	2.46791i
$850$		0			0
$851$	−24.5885	+	14.1962i	−0.842881	+	0.486638i
$852$	−8.19615	−	14.1962i	−0.280796	−	0.486352i
$853$	−13.8564			−0.474434			−0.237217	−	0.971457i	$-0.576235\pi$
$853$	−13.8564			−0.474434			−0.237217	+	0.971457i	$0.576235\pi$
$854$	6.29423	+	10.9019i	0.215384	+	0.373056i
$855$		0			0
$856$	−0.294229	−	0.169873i	−0.0100565	−	0.00580614i
$857$			13.2679i			0.453225i	0.973985	+	0.226612i	$0.0727650\pi$
$857$			13.2679i			0.453225i	−0.973985	+	0.226612i	$0.927235\pi$
$858$	−7.09808	−	28.6865i	−0.242324	−	0.979342i
$859$	−52.3731			−1.78695			−0.893473	−	0.449117i	$-0.851739\pi$
$859$	−52.3731			−1.78695			−0.893473	+	0.449117i	$0.851739\pi$
$860$		0			0
$861$	42.5885	−	73.7654i	1.45141	−	2.51392i
$862$	−1.90192	+	1.09808i	−0.0647798	+	0.0374006i
$863$	−19.1769			−0.652790			−0.326395	−	0.945234i	$-0.605834\pi$
$863$	−19.1769			−0.652790			−0.326395	+	0.945234i	$0.605834\pi$
$864$	−3.46410	+	2.00000i	−0.117851	+	0.0680414i
$865$		0			0
$866$			12.3923i			0.421108i
$867$	−28.8109	+	16.6340i	−0.978469	+	0.564919i
$868$	−3.29423	−	1.90192i	−0.111813	−	0.0645555i
$869$	16.0981	+	9.29423i	0.546090	+	0.315285i
$870$		0			0
$871$		0			0
$872$			15.4641i			0.523681i
$873$	33.7583	−	58.4711i	1.14255	−	1.97895i
$874$	−8.19615	+	14.1962i	−0.277239	+	0.480192i
$875$		0			0
$876$			15.4641i			0.522484i
$877$	−10.2679	−	17.7846i	−0.346724	−	0.600544i	0.638941	−	0.769255i	$-0.279373\pi$
$877$	−10.2679	−	17.7846i	−0.346724	−	0.600544i	−0.985665	+	0.168712i	$0.946039\pi$
$878$	17.2942	+	29.9545i	0.583652	+	1.01091i
$879$		−	2.19615i		−	0.0740744i
$880$		0			0
$881$	4.16025	−	7.20577i	0.140163	−	0.242769i	−0.787395	−	0.616449i	$-0.788571\pi$
$881$	4.16025	−	7.20577i	0.140163	−	0.242769i	0.927558	+	0.373680i	$0.121904\pi$
$882$	−4.46410	+	7.73205i	−0.150314	+	0.260352i
$883$		−	26.5885i		−	0.894773i	−0.894341	−	0.447386i	$-0.852355\pi$
$883$		−	26.5885i		−	0.894773i	0.894341	−	0.447386i	$-0.147645\pi$
$884$	2.19615	−	7.60770i	0.0738646	−	0.255874i
$885$		0			0
$886$	−1.39230	−	0.803848i	−0.0467754	−	0.0270058i
$887$	45.6962	+	26.3827i	1.53433	+	0.885844i	0.999155	+	0.0411005i	$0.0130864\pi$
$887$	45.6962	+	26.3827i	1.53433	+	0.885844i	0.535172	+	0.844743i	$0.320247\pi$
$888$	−26.4904	+	15.2942i	−0.888959	+	0.513241i
$889$			63.5885i			2.13269i
$890$		0			0
$891$	−6.40192	+	3.69615i	−0.214473	+	0.123826i
$892$	−0.464102			−0.0155393
$893$	−16.7942	+	9.69615i	−0.561997	+	0.324469i
$894$	8.19615	−	14.1962i	0.274120	−	0.474790i
$895$		0			0
$896$	3.00000			0.100223
$897$	18.0000	−	17.3205i	0.601003	−	0.578315i
$898$			15.5885i			0.520194i
$899$	10.3923	+	6.00000i	0.346603	+	0.200111i
$900$		0			0
$901$	−7.09808	−	12.2942i	−0.236471	−	0.409580i
$902$	31.1769			1.03808
$903$	8.19615	+	14.1962i	0.272751	+	0.472418i
$904$	6.00000	−	3.46410i	0.199557	−	0.115214i
$905$		0			0
$906$	8.66025	+	15.0000i	0.287718	+	0.498342i
$907$	−23.0263	−	13.2942i	−0.764575	−	0.441428i	0.0663609	−	0.997796i	$-0.478861\pi$
$907$	−23.0263	−	13.2942i	−0.764575	−	0.441428i	−0.830936	+	0.556368i	$0.812194\pi$
$908$	−2.19615	+	3.80385i	−0.0728819	+	0.126235i
$909$	−32.4449			−1.07613
$910$		0			0
$911$	−14.5359			−0.481596			−0.240798	−	0.970575i	$-0.577409\pi$
$911$	−14.5359			−0.481596			−0.240798	+	0.970575i	$0.577409\pi$
$912$	−8.83013	+	15.2942i	−0.292395	+	0.506443i
$913$	−5.70577	−	3.29423i	−0.188833	−	0.109023i
$914$	17.8301	+	30.8827i	0.589768	+	1.02151i
$915$		0			0
$916$	−4.09808	+	2.36603i	−0.135404	+	0.0781757i
$917$	−27.1865	−	47.0885i	−0.897778	−	1.55500i
$918$	8.78461			0.289935
$919$	−5.39230	−	9.33975i	−0.177876	−	0.308090i	0.763277	−	0.646071i	$-0.223589\pi$
$919$	−5.39230	−	9.33975i	−0.177876	−	0.308090i	−0.941153	+	0.337982i	$0.890256\pi$
$920$		0			0
$921$	48.5885	+	28.0526i	1.60104	+	0.924363i
$922$			0.588457i			0.0193798i
$923$	15.0000	+	15.5885i	0.493731	+	0.513100i
$924$	−24.5885			−0.808901
$925$		0			0
$926$	−0.464102	+	0.803848i	−0.0152513	+	0.0264161i
$927$	−4.62436	+	2.66987i	−0.151884	+	0.0876901i
$928$	−9.46410			−0.310674
$929$	−38.7846	+	22.3923i	−1.27248	+	0.734668i	−0.975454	−	0.220201i	$-0.929329\pi$
$929$	−38.7846	+	22.3923i	−1.27248	+	0.734668i	−0.297027	+	0.954869i	$0.595995\pi$
$930$		0			0
$931$			12.9282i			0.423705i
$932$	1.09808	−	0.633975i	0.0359687	−	0.0207665i
$933$	35.7846	+	20.6603i	1.17154	+	0.676386i
$934$	8.78461	+	5.07180i	0.287441	+	0.165954i
$935$		0			0
$936$	11.5981	−	11.1603i	0.379095	−	0.364784i
$937$			30.3923i			0.992873i	0.868073	+	0.496437i	$0.165359\pi$
$937$			30.3923i			0.992873i	−0.868073	+	0.496437i	$0.834641\pi$
$938$		0			0
$939$	−7.66025	+	13.2679i	−0.249983	+	0.432983i
$940$		0			0
$941$		−	44.7846i		−	1.45994i	−0.683481	−	0.729968i	$-0.739535\pi$
$941$		−	44.7846i		−	1.45994i	0.683481	−	0.729968i	$-0.260465\pi$
$942$	17.7583	+	30.7583i	0.578598	+	1.00216i
$943$	13.1769	+	22.8231i	0.429099	+	0.743222i
$944$		−	10.3923i		−	0.338241i
$945$		0			0
$946$	−3.00000	+	5.19615i	−0.0975384	+	0.168941i
$947$	28.6865	−	49.6865i	0.932187	−	1.61460i	0.152612	−	0.988286i	$-0.451231\pi$
$947$	28.6865	−	49.6865i	0.932187	−	1.61460i	0.779575	−	0.626309i	$-0.215435\pi$
$948$			16.9282i			0.549802i
$949$	−4.90192	−	19.8109i	−0.159123	−	0.643089i
$950$		0			0
$951$	30.2942	+	17.4904i	0.982358	+	0.567164i
$952$	−5.70577	−	3.29423i	−0.184925	−	0.106767i
$953$	21.2942	−	12.2942i	0.689788	−	0.398249i	−0.113745	−	0.993510i	$-0.536285\pi$
$953$	21.2942	−	12.2942i	0.689788	−	0.398249i	0.803533	+	0.595261i	$0.202951\pi$
$954$		−	28.8564i		−	0.934261i
$955$		0			0
$956$	−7.09808	+	4.09808i	−0.229568	+	0.132541i
$957$	77.5692			2.50746
$958$	9.50962	−	5.49038i	0.307242	−	0.177386i
$959$	12.2942	−	21.2942i	0.397001	−	0.687627i
$960$		0			0
$961$	29.3923			0.948139
$962$	29.0885	−	27.9904i	0.937850	−	0.902446i
$963$			1.51666i			0.0488737i
$964$	7.50000	+	4.33013i	0.241559	+	0.139464i
$965$		0			0
$966$	−10.3923	−	18.0000i	−0.334367	−	0.579141i
$967$	−38.5692			−1.24030			−0.620151	−	0.784482i	$-0.712929\pi$
$967$	−38.5692			−1.24030			−0.620151	+	0.784482i	$0.712929\pi$
$968$	1.00000	+	1.73205i	0.0321412	+	0.0556702i
$969$	33.5885	−	19.3923i	1.07902	−	0.622971i
$970$		0			0
$971$	23.3827	+	40.5000i	0.750386	+	1.29971i	0.947636	+	0.319354i	$0.103466\pi$
$971$	23.3827	+	40.5000i	0.750386	+	1.29971i	−0.197250	+	0.980353i	$0.563201\pi$
$972$	−16.2224	−	9.36603i	−0.520335	−	0.300415i
$973$	13.7942	−	23.8923i	0.442223	−	0.765952i
$974$	33.2487			1.06536
$975$		0			0
$976$	−4.19615			−0.134316
$977$	2.19615	−	3.80385i	0.0702611	−	0.121696i	−0.828755	−	0.559612i	$-0.810950\pi$
$977$	2.19615	−	3.80385i	0.0702611	−	0.121696i	0.899016	+	0.437916i	$0.144283\pi$
$978$	17.1962	+	9.92820i	0.549872	+	0.317469i
$979$	−25.7942	−	44.6769i	−0.824387	−	1.42788i
$980$		0			0
$981$	59.7846	−	34.5167i	1.90878	−	1.10203i
$982$	1.66987	+	2.89230i	0.0532878	+	0.0922972i
$983$	−38.5692			−1.23017			−0.615084	−	0.788462i	$-0.710878\pi$
$983$	−38.5692			−1.23017			−0.615084	+	0.788462i	$0.710878\pi$
$984$	14.1962	+	24.5885i	0.452557	+	0.783851i
$985$		0			0
$986$	18.0000	+	10.3923i	0.573237	+	0.330958i
$987$		−	24.5885i		−	0.782659i
$988$	6.46410	−	22.3923i	0.205650	−	0.712394i
$989$	−5.07180			−0.161274
$990$		0			0
$991$	−25.5885	+	44.3205i	−0.812844	+	1.40789i	0.0980215	+	0.995184i	$0.468749\pi$
$991$	−25.5885	+	44.3205i	−0.812844	+	1.40789i	−0.910866	+	0.412703i	$0.864585\pi$
$992$	1.09808	−	0.633975i	0.0348640	−	0.0201287i
$993$	2.53590			0.0804743
$994$	15.5885	−	9.00000i	0.494436	−	0.285463i
$995$		0			0
$996$		−	6.00000i		−	0.190117i
$997$	36.8660	−	21.2846i	1.16756	−	0.674090i	0.214455	−	0.976734i	$-0.431202\pi$
$997$	36.8660	−	21.2846i	1.16756	−	0.674090i	0.953104	+	0.302644i	$0.0978692\pi$
$998$	−1.60770	−	0.928203i	−0.0508907	−	0.0293818i
$999$	38.7846	+	22.3923i	1.22709	+	0.708461i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.n.b.199.2		4
5.2	odd	4		130.2.l.a.121.2	yes	4
5.3	odd	4		650.2.m.a.251.1		4
5.4	even	2		650.2.n.a.199.1		4
13.10	even	6		650.2.n.a.49.1		4
15.2	even	4		1170.2.bs.c.901.1		4
20.7	even	4		1040.2.da.a.641.1		4
65.2	even	12		1690.2.e.n.991.2		4
65.7	even	12		1690.2.a.m.1.1		2
65.12	odd	4		1690.2.l.g.1161.1		4
65.17	odd	12		1690.2.d.f.1351.3		4
65.22	odd	12		1690.2.d.f.1351.1		4
65.23	odd	12		650.2.m.a.101.1		4
65.32	even	12		1690.2.a.j.1.1		2
65.33	even	12		8450.2.a.bf.1.2		2
65.37	even	12		1690.2.e.l.991.2		4
65.42	odd	12		1690.2.l.g.361.1		4
65.47	even	4		1690.2.e.l.191.2		4
65.49	even	6	inner	650.2.n.b.49.2		4
65.57	even	4		1690.2.e.n.191.2		4
65.58	even	12		8450.2.a.bm.1.2		2
65.62	odd	12		130.2.l.a.101.2	✓	4
195.62	even	12		1170.2.bs.c.361.1		4
260.127	even	12		1040.2.da.a.881.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.l.a.101.2	✓	4	65.62	odd	12
130.2.l.a.121.2	yes	4	5.2	odd	4
650.2.m.a.101.1		4	65.23	odd	12
650.2.m.a.251.1		4	5.3	odd	4
650.2.n.a.49.1		4	13.10	even	6
650.2.n.a.199.1		4	5.4	even	2
650.2.n.b.49.2		4	65.49	even	6	inner
650.2.n.b.199.2		4	1.1	even	1	trivial
1040.2.da.a.641.1		4	20.7	even	4
1040.2.da.a.881.1		4	260.127	even	12
1170.2.bs.c.361.1		4	195.62	even	12
1170.2.bs.c.901.1		4	15.2	even	4
1690.2.a.j.1.1		2	65.32	even	12
1690.2.a.m.1.1		2	65.7	even	12
1690.2.d.f.1351.1		4	65.22	odd	12
1690.2.d.f.1351.3		4	65.17	odd	12
1690.2.e.l.191.2		4	65.47	even	4
1690.2.e.l.991.2		4	65.37	even	12
1690.2.e.n.191.2		4	65.57	even	4
1690.2.e.n.991.2		4	65.2	even	12
1690.2.l.g.361.1		4	65.42	odd	12
1690.2.l.g.1161.1		4	65.12	odd	4
8450.2.a.bf.1.2		2	65.33	even	12
8450.2.a.bm.1.2		2	65.58	even	12

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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(2.36603 + 1.36603i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.36603 - 1.36603i) q^{6} +(1.50000 + 2.59808i) q^{7} -1.00000 q^{8} +(2.23205 + 3.86603i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(2.36603 + 1.36603i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.36603 - 1.36603i) q^{6} +(1.50000 + 2.59808i) q^{7} -1.00000 q^{8} +(2.23205 + 3.86603i) q^{9} +(-2.59808 - 1.50000i) q^{11} -2.73205i q^{12} +(0.866025 + 3.50000i) q^{13} +3.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.90192 - 1.09808i) q^{17} +4.46410 q^{18} +(5.59808 - 3.23205i) q^{19} +8.19615i q^{21} +(-2.59808 + 1.50000i) q^{22} +(-2.19615 - 1.26795i) q^{23} +(-2.36603 - 1.36603i) q^{24} +(3.46410 + 1.00000i) q^{26} +4.00000i q^{27} +(1.50000 - 2.59808i) q^{28} +(-4.73205 + 8.19615i) q^{29} -1.26795i q^{31} +(0.500000 + 0.866025i) q^{32} +(-4.09808 - 7.09808i) q^{33} -2.19615i q^{34} +(2.23205 - 3.86603i) q^{36} +(5.59808 - 9.69615i) q^{37} -6.46410i q^{38} +(-2.73205 + 9.46410i) q^{39} +(-9.00000 - 5.19615i) q^{41} +(7.09808 + 4.09808i) q^{42} +(1.73205 - 1.00000i) q^{43} +3.00000i q^{44} +(-2.19615 + 1.26795i) q^{46} -3.00000 q^{47} +(-2.36603 + 1.36603i) q^{48} +(-1.00000 + 1.73205i) q^{49} +6.00000 q^{51} +(2.59808 - 2.50000i) q^{52} -6.46410i q^{53} +(3.46410 + 2.00000i) q^{54} +(-1.50000 - 2.59808i) q^{56} +17.6603 q^{57} +(4.73205 + 8.19615i) q^{58} +(-9.00000 + 5.19615i) q^{59} +(2.09808 + 3.63397i) q^{61} +(-1.09808 - 0.633975i) q^{62} +(-6.69615 + 11.5981i) q^{63} +1.00000 q^{64} -8.19615 q^{66} +(-1.90192 - 1.09808i) q^{68} +(-3.46410 - 6.00000i) q^{69} +(5.19615 - 3.00000i) q^{71} +(-2.23205 - 3.86603i) q^{72} -5.66025 q^{73} +(-5.59808 - 9.69615i) q^{74} +(-5.59808 - 3.23205i) q^{76} -9.00000i q^{77} +(6.83013 + 7.09808i) q^{78} -6.19615 q^{79} +(1.23205 - 2.13397i) q^{81} +(-9.00000 + 5.19615i) q^{82} +2.19615 q^{83} +(7.09808 - 4.09808i) q^{84} -2.00000i q^{86} +(-22.3923 + 12.9282i) q^{87} +(2.59808 + 1.50000i) q^{88} +(14.8923 + 8.59808i) q^{89} +(-7.79423 + 7.50000i) q^{91} +2.53590i q^{92} +(1.73205 - 3.00000i) q^{93} +(-1.50000 + 2.59808i) q^{94} +2.73205i q^{96} +(-7.56218 - 13.0981i) q^{97} +(1.00000 + 1.73205i) q^{98} -13.3923i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 6 q^{3} - 2 q^{4} + 6 q^{6} + 6 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 6 * q^3 - 2 * q^4 + 6 * q^6 + 6 * q^7 - 4 * q^8 + 2 * q^9	\( 4 q + 2 q^{2} + 6 q^{3} - 2 q^{4} + 6 q^{6} + 6 q^{7} - 4 q^{8} + 2 q^{9} + 12 q^{14} - 2 q^{16} + 18 q^{17} + 4 q^{18} + 12 q^{19} + 12 q^{23} - 6 q^{24} + 6 q^{28} - 12 q^{29} + 2 q^{32} - 6 q^{33} + 2 q^{36} + 12 q^{37} - 4 q^{39} - 36 q^{41} + 18 q^{42} + 12 q^{46} - 12 q^{47} - 6 q^{48} - 4 q^{49} + 24 q^{51} - 6 q^{56} + 36 q^{57} + 12 q^{58} - 36 q^{59} - 2 q^{61} + 6 q^{62} - 6 q^{63} + 4 q^{64} - 12 q^{66} - 18 q^{68} - 2 q^{72} + 12 q^{73} - 12 q^{74} - 12 q^{76} + 10 q^{78} - 4 q^{79} - 2 q^{81} - 36 q^{82} - 12 q^{83} + 18 q^{84} - 48 q^{87} + 18 q^{89} - 6 q^{94} - 6 q^{97} + 4 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 + 6 * q^3 - 2 * q^4 + 6 * q^6 + 6 * q^7 - 4 * q^8 + 2 * q^9 + 12 * q^14 - 2 * q^16 + 18 * q^17 + 4 * q^18 + 12 * q^19 + 12 * q^23 - 6 * q^24 + 6 * q^28 - 12 * q^29 + 2 * q^32 - 6 * q^33 + 2 * q^36 + 12 * q^37 - 4 * q^39 - 36 * q^41 + 18 * q^42 + 12 * q^46 - 12 * q^47 - 6 * q^48 - 4 * q^49 + 24 * q^51 - 6 * q^56 + 36 * q^57 + 12 * q^58 - 36 * q^59 - 2 * q^61 + 6 * q^62 - 6 * q^63 + 4 * q^64 - 12 * q^66 - 18 * q^68 - 2 * q^72 + 12 * q^73 - 12 * q^74 - 12 * q^76 + 10 * q^78 - 4 * q^79 - 2 * q^81 - 36 * q^82 - 12 * q^83 + 18 * q^84 - 48 * q^87 + 18 * q^89 - 6 * q^94 - 6 * q^97 + 4 * q^98

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