LMFDB - Embedded newform 650.2.m.a.251.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(101,650)]

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([0, 5]))

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

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

chi := DirichletCharacter("650.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.m (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.19027613138$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			251.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	650.251
Dual form			650.2.m.a.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−1.36603	+	2.36603i	−0.788675	+	1.36603i	0.138104	+	0.990418i	$0.455899\pi$
$3$	−1.36603	+	2.36603i	−0.788675	+	1.36603i	−0.926779	+	0.375608i	$0.877434\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	2.36603	−	1.36603i	0.965926	−	0.557678i
$7$	2.59808	−	1.50000i	0.981981	−	0.566947i	0.0791130	−	0.996866i	$-0.474791\pi$
$7$	2.59808	−	1.50000i	0.981981	−	0.566947i	0.902867	+	0.429919i	$0.141458\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−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	$0.816051\pi$
$12$	−2.73205			−0.788675
$13$	−3.50000	+	0.866025i	−0.970725	+	0.240192i
$13$	−3.50000	+	0.866025i	−0.970725	+	0.240192i
$14$	−3.00000			−0.801784
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.09808	−	1.90192i	−0.266323	−	0.461284i	0.701587	−	0.712584i	$-0.252475\pi$
$17$	−1.09808	−	1.90192i	−0.266323	−	0.461284i	−0.967909	+	0.251300i	$0.919142\pi$
$18$			4.46410i			1.05220i
$19$	−5.59808	+	3.23205i	−1.28429	+	0.741483i	−0.977629	−	0.210337i	$-0.932544\pi$
$19$	−5.59808	+	3.23205i	−1.28429	+	0.741483i	−0.306658	+	0.951820i	$0.599211\pi$
$20$		0			0
$21$			8.19615i			1.78855i
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$	1.26795	−	2.19615i	0.264386	−	0.457929i	−0.703017	−	0.711173i	$-0.748164\pi$
$23$	1.26795	−	2.19615i	0.264386	−	0.457929i	0.967402	+	0.253244i	$0.0814975\pi$
$24$	2.36603	+	1.36603i	0.482963	+	0.278839i
$25$		0			0
$26$	3.46410	+	1.00000i	0.679366	+	0.196116i
$27$	4.00000			0.769800
$28$	2.59808	+	1.50000i	0.490990	+	0.283473i
$29$	4.73205	−	8.19615i	0.878720	−	1.52199i	0.0259731	−	0.999663i	$-0.491732\pi$
$29$	4.73205	−	8.19615i	0.878720	−	1.52199i	0.852747	−	0.522325i	$-0.174935\pi$
$30$		0			0
$31$		−	1.26795i		−	0.227730i	−0.993496	−	0.113865i	$-0.963677\pi$
$31$		−	1.26795i		−	0.227730i	0.993496	−	0.113865i	$-0.0363232\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	7.09808	−	4.09808i	1.23562	−	0.713384i
$34$			2.19615i			0.376637i
$35$		0			0
$36$	2.23205	−	3.86603i	0.372008	−	0.644338i
$37$	−9.69615	−	5.59808i	−1.59404	−	0.920318i	−0.992604	−	0.121395i	$-0.961263\pi$
$37$	−9.69615	−	5.59808i	−1.59404	−	0.920318i	−0.601433	−	0.798923i	$-0.705403\pi$
$38$	6.46410			1.04862
$39$	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	$0.968017\pi$
$42$	4.09808	−	7.09808i	0.632347	−	1.09526i
$43$	1.00000	+	1.73205i	0.152499	+	0.264135i	0.932145	−	0.362084i	$-0.117935\pi$
$43$	1.00000	+	1.73205i	0.152499	+	0.264135i	−0.779647	+	0.626219i	$0.784601\pi$
$44$		−	3.00000i		−	0.452267i
$45$		0			0
$46$	−2.19615	+	1.26795i	−0.323805	+	0.186949i
$47$			3.00000i			0.437595i	0.975770	+	0.218797i	$0.0702134\pi$
$47$			3.00000i			0.437595i	−0.975770	+	0.218797i	$0.929787\pi$
$48$	−1.36603	−	2.36603i	−0.197169	−	0.341506i
$49$	1.00000	−	1.73205i	0.142857	−	0.247436i
$50$		0			0
$51$	6.00000			0.840168
$52$	−2.50000	−	2.59808i	−0.346688	−	0.360288i
$53$	6.46410			0.887913			0.443956	−	0.896048i	$-0.353575\pi$
$53$	6.46410			0.887913			0.443956	+	0.896048i	$0.353575\pi$
$54$	−3.46410	−	2.00000i	−0.471405	−	0.272166i
$55$		0			0
$56$	−1.50000	−	2.59808i	−0.200446	−	0.347183i
$57$		−	17.6603i		−	2.33916i
$58$	−8.19615	+	4.73205i	−1.07621	+	0.621349i
$59$	9.00000	−	5.19615i	1.17170	−	0.676481i	0.217620	−	0.976034i	$-0.430171\pi$
$59$	9.00000	−	5.19615i	1.17170	−	0.676481i	0.954080	+	0.299552i	$0.0968372\pi$
$60$		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	$0.746762\pi$
$62$	−0.633975	+	1.09808i	−0.0805149	+	0.139456i
$63$	−11.5981	−	6.69615i	−1.46122	−	0.843636i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−8.19615			−1.00888
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$	1.09808	−	1.90192i	0.133161	−	0.230642i
$69$	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	$0.217462\pi$
$72$	−3.86603	+	2.23205i	−0.455615	+	0.263050i
$73$		−	5.66025i		−	0.662483i	−0.943546	−	0.331241i	$-0.892533\pi$
$73$		−	5.66025i		−	0.662483i	0.943546	−	0.331241i	$-0.107467\pi$
$74$	5.59808	+	9.69615i	0.650763	+	1.12715i
$75$		0			0
$76$	−5.59808	−	3.23205i	−0.642143	−	0.370742i
$77$	−9.00000			−1.02565
$78$	−7.09808	+	6.83013i	−0.803699	+	0.773360i
$79$	6.19615			0.697122			0.348561	−	0.937286i	$-0.386670\pi$
$79$	6.19615			0.697122			0.348561	+	0.937286i	$0.386670\pi$
$80$		0			0
$81$	1.23205	−	2.13397i	0.136895	−	0.237108i
$82$	5.19615	+	9.00000i	0.573819	+	0.993884i
$83$			2.19615i			0.241059i	0.992710	+	0.120530i	$0.0384592\pi$
$83$			2.19615i			0.241059i	−0.992710	+	0.120530i	$0.961541\pi$
$84$	−7.09808	+	4.09808i	−0.774464	+	0.447137i
$85$		0			0
$86$		−	2.00000i		−	0.215666i
$87$	12.9282	+	22.3923i	1.38605	+	2.40071i
$88$	−1.50000	+	2.59808i	−0.159901	+	0.276956i
$89$	−14.8923	−	8.59808i	−1.57858	−	0.911394i	−0.995058	−	0.0992979i	$-0.968340\pi$
$89$	−14.8923	−	8.59808i	−1.57858	−	0.911394i	−0.583523	−	0.812096i	$-0.698326\pi$
$90$		0			0
$91$	−7.79423	+	7.50000i	−0.817057	+	0.786214i
$92$	2.53590			0.264386
$93$	3.00000	+	1.73205i	0.311086	+	0.179605i
$94$	1.50000	−	2.59808i	0.154713	−	0.267971i
$95$		0			0
$96$			2.73205i			0.278839i
$97$	−13.0981	+	7.56218i	−1.32991	+	0.767823i	−0.985285	−	0.170918i	$-0.945327\pi$
$97$	−13.0981	+	7.56218i	−1.32991	+	0.767823i	−0.344623	+	0.938741i	$0.611993\pi$
$98$	−1.73205	+	1.00000i	−0.174964	+	0.101015i
$99$			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	$0.284434\pi$
$102$	−5.19615	−	3.00000i	−0.514496	−	0.297044i
$103$	−1.19615			−0.117860			−0.0589302	−	0.998262i	$-0.518769\pi$
$103$	−1.19615			−0.117860			−0.0589302	+	0.998262i	$0.518769\pi$
$104$	0.866025	+	3.50000i	0.0849208	+	0.343203i
$105$		0			0
$106$	−5.59808	−	3.23205i	−0.543733	−	0.313925i
$107$	0.169873	−	0.294229i	0.0164222	−	0.0284442i	−0.857697	−	0.514155i	$-0.828106\pi$
$107$	0.169873	−	0.294229i	0.0164222	−	0.0284442i	0.874120	+	0.485710i	$0.161439\pi$
$108$	2.00000	+	3.46410i	0.192450	+	0.333333i
$109$			15.4641i			1.48119i	0.671950	+	0.740596i	$0.265457\pi$
$109$			15.4641i			1.48119i	−0.671950	+	0.740596i	$0.734543\pi$
$110$		0			0
$111$	26.4904	−	15.2942i	2.51436	−	1.45166i
$112$			3.00000i			0.283473i
$113$	−3.46410	−	6.00000i	−0.325875	−	0.564433i	0.655814	−	0.754923i	$-0.272326\pi$
$113$	−3.46410	−	6.00000i	−0.325875	−	0.564433i	−0.981689	+	0.190490i	$0.938992\pi$
$114$	−8.83013	+	15.2942i	−0.827017	+	1.43244i
$115$		0			0
$116$	9.46410			0.878720
$117$	11.1603	+	11.5981i	1.03177	+	1.07224i
$118$	−10.3923			−0.956689
$119$	−5.70577	−	3.29423i	−0.523047	−	0.301981i
$120$		0			0
$121$	−1.00000	−	1.73205i	−0.0909091	−	0.157459i
$122$		−	4.19615i		−	0.379902i
$123$	24.5885	−	14.1962i	2.21707	−	1.28002i
$124$	1.09808	−	0.633975i	0.0986102	−	0.0569326i
$125$		0			0
$126$	6.69615	+	11.5981i	0.596541	+	1.03324i
$127$	10.5981	−	18.3564i	0.940427	−	1.62887i	0.175769	−	0.984431i	$-0.443759\pi$
$127$	10.5981	−	18.3564i	0.940427	−	1.62887i	0.764658	−	0.644436i	$-0.222908\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−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	$0.790838\pi$
$132$	7.09808	+	4.09808i	0.617808	+	0.356692i
$133$	−9.69615	+	16.7942i	−0.840763	+	1.45624i
$134$		0			0
$135$		0			0
$136$	−1.90192	+	1.09808i	−0.163089	+	0.0941593i
$137$	−7.09808	+	4.09808i	−0.606430	+	0.350122i	−0.771567	−	0.636148i	$-0.780527\pi$
$137$	−7.09808	+	4.09808i	−0.606430	+	0.350122i	0.165137	+	0.986271i	$0.447193\pi$
$138$		−	6.92820i		−	0.589768i
$139$	4.59808	+	7.96410i	0.390004	+	0.675506i	0.992450	−	0.122653i	$-0.0391404\pi$
$139$	4.59808	+	7.96410i	0.390004	+	0.675506i	−0.602446	+	0.798160i	$0.705807\pi$
$140$		0			0
$141$	−7.09808	−	4.09808i	−0.597766	−	0.345120i
$142$	−6.00000			−0.503509
$143$	10.3923	+	3.00000i	0.869048	+	0.250873i
$144$	4.46410			0.372008
$145$		0			0
$146$	−2.83013	+	4.90192i	−0.234223	+	0.405686i
$147$	2.73205	+	4.73205i	0.225336	+	0.390293i
$148$		−	11.1962i		−	0.920318i
$149$	−5.19615	+	3.00000i	−0.425685	+	0.245770i	−0.697507	−	0.716578i	$-0.745707\pi$
$149$	−5.19615	+	3.00000i	−0.425685	+	0.245770i	0.271821	+	0.962348i	$0.412374\pi$
$150$		0			0
$151$			6.33975i			0.515921i	0.966155	+	0.257961i	$0.0830505\pi$
$151$			6.33975i			0.515921i	−0.966155	+	0.257961i	$0.916950\pi$
$152$	3.23205	+	5.59808i	0.262154	+	0.454064i
$153$	−4.90192	+	8.49038i	−0.396297	+	0.686407i
$154$	7.79423	+	4.50000i	0.628077	+	0.362620i
$155$		0			0
$156$	9.56218	−	2.36603i	0.765587	−	0.189434i
$157$	13.0000			1.03751			0.518756	−	0.854922i	$-0.326395\pi$
$157$	13.0000			1.03751			0.518756	+	0.854922i	$0.326395\pi$
$158$	−5.36603	−	3.09808i	−0.426898	−	0.246470i
$159$	−8.83013	+	15.2942i	−0.700275	+	1.21291i
$160$		0			0
$161$		−	7.60770i		−	0.599570i
$162$	−2.13397	+	1.23205i	−0.167661	+	0.0967991i
$163$	−6.29423	+	3.63397i	−0.493002	+	0.284635i	−0.725819	−	0.687886i	$-0.758539\pi$
$163$	−6.29423	+	3.63397i	−0.493002	+	0.284635i	0.232817	+	0.972521i	$0.425206\pi$
$164$		−	10.3923i		−	0.811503i
$165$		0			0
$166$	1.09808	−	1.90192i	0.0852272	−	0.147618i
$167$	2.59808	+	1.50000i	0.201045	+	0.116073i	0.597143	−	0.802135i	$-0.296303\pi$
$167$	2.59808	+	1.50000i	0.201045	+	0.116073i	−0.396098	+	0.918208i	$0.629636\pi$
$168$	8.19615			0.632347
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$		0			0
$171$	24.9904	+	14.4282i	1.91106	+	1.10335i
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	−7.50000	−	12.9904i	−0.570214	−	0.987640i	−0.996544	−	0.0830722i	$-0.973527\pi$
$173$	−7.50000	−	12.9904i	−0.570214	−	0.987640i	0.426329	−	0.904568i	$-0.359807\pi$
$174$		−	25.8564i		−	1.96017i
$175$		0			0
$176$	2.59808	−	1.50000i	0.195837	−	0.113067i
$177$			28.3923i			2.13410i
$178$	8.59808	+	14.8923i	0.644453	+	1.11623i
$179$	1.26795	−	2.19615i	0.0947710	−	0.164148i	−0.814742	−	0.579824i	$-0.803121\pi$
$179$	1.26795	−	2.19615i	0.0947710	−	0.164148i	0.909513	+	0.415675i	$0.136455\pi$
$180$		0			0
$181$	−16.5885			−1.23301			−0.616505	−	0.787351i	$-0.711452\pi$
$181$	−16.5885			−1.23301			−0.616505	+	0.787351i	$0.711452\pi$
$182$	10.5000	−	2.59808i	0.778312	−	0.192582i
$183$	−11.4641			−0.847451
$184$	−2.19615	−	1.26795i	−0.161903	−	0.0934745i
$185$		0			0
$186$	−1.73205	−	3.00000i	−0.127000	−	0.219971i
$187$			6.58846i			0.481796i
$188$	−2.59808	+	1.50000i	−0.189484	+	0.109399i
$189$	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	$0.587811\pi$
$192$	1.36603	−	2.36603i	0.0985844	−	0.170753i
$193$	3.80385	+	2.19615i	0.273807	+	0.158083i	0.630616	−	0.776095i	$-0.282802\pi$
$193$	3.80385	+	2.19615i	0.273807	+	0.158083i	−0.356809	+	0.934177i	$0.616135\pi$
$194$	15.1244			1.08587
$195$		0			0
$196$	2.00000			0.142857
$197$	−8.30385	−	4.79423i	−0.591625	−	0.341575i	0.174115	−	0.984725i	$-0.444294\pi$
$197$	−8.30385	−	4.79423i	−0.591625	−	0.341575i	−0.765740	+	0.643151i	$0.777627\pi$
$198$	6.69615	−	11.5981i	0.475875	−	0.824239i
$199$	−7.19615	−	12.4641i	−0.510122	−	0.883557i	−0.999931	−	0.0117273i	$-0.996267\pi$
$199$	−7.19615	−	12.4641i	−0.510122	−	0.883557i	0.489810	−	0.871829i	$-0.337066\pi$
$200$		0			0
$201$		0			0
$202$	6.29423	−	3.63397i	0.442860	−	0.255686i
$203$		−	28.3923i		−	1.99275i
$204$	3.00000	+	5.19615i	0.210042	+	0.363803i
$205$		0			0
$206$	1.03590	+	0.598076i	0.0721745	+	0.0416699i
$207$	−11.3205			−0.786830
$208$	1.00000	−	3.46410i	0.0693375	−	0.240192i
$209$	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	$0.321596\pi$
$212$	3.23205	+	5.59808i	0.221978	+	0.384477i
$213$			16.3923i			1.12318i
$214$	−0.294229	+	0.169873i	−0.0201131	+	0.0116123i
$215$		0			0
$216$		−	4.00000i		−	0.272166i
$217$	−1.90192	−	3.29423i	−0.129111	−	0.223627i
$218$	7.73205	−	13.3923i	0.523681	−	0.907041i
$219$	13.3923	+	7.73205i	0.904968	+	0.522484i
$220$		0			0
$221$	5.49038	+	5.70577i	0.369323	+	0.383812i
$222$	−30.5885			−2.05296
$223$	0.401924	+	0.232051i	0.0269148	+	0.0155393i	0.513397	−	0.858151i	$-0.328387\pi$
$223$	0.401924	+	0.232051i	0.0269148	+	0.0155393i	−0.486482	+	0.873690i	$0.661720\pi$
$224$	1.50000	−	2.59808i	0.100223	−	0.173591i
$225$		0			0
$226$			6.92820i			0.460857i
$227$	−3.80385	+	2.19615i	−0.252470	+	0.145764i	−0.620895	−	0.783894i	$-0.713231\pi$
$227$	−3.80385	+	2.19615i	−0.252470	+	0.145764i	0.368425	+	0.929658i	$0.379897\pi$
$228$	15.2942	−	8.83013i	1.01289	−	0.584789i
$229$			4.73205i			0.312703i	0.987701	+	0.156351i	$0.0499732\pi$
$229$			4.73205i			0.312703i	−0.987701	+	0.156351i	$0.950027\pi$
$230$		0			0
$231$	12.2942	−	21.2942i	0.808901	−	1.40106i
$232$	−8.19615	−	4.73205i	−0.538104	−	0.310674i
$233$	−1.26795			−0.0830661			−0.0415331	−	0.999137i	$-0.513224\pi$
$233$	−1.26795			−0.0830661			−0.0415331	+	0.999137i	$0.513224\pi$
$234$	−3.86603	−	15.6244i	−0.252730	−	1.02140i
$235$		0			0
$236$	9.00000	+	5.19615i	0.585850	+	0.338241i
$237$	−8.46410	+	14.6603i	−0.549802	+	0.952286i
$238$	3.29423	+	5.70577i	0.213533	+	0.369850i
$239$			8.19615i			0.530165i	0.964226	+	0.265083i	$0.0853992\pi$
$239$			8.19615i			0.530165i	−0.964226	+	0.265083i	$0.914601\pi$
$240$		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	$0.423312\pi$
$242$			2.00000i			0.128565i
$243$	9.36603	+	16.2224i	0.600831	+	1.04067i
$244$	−2.09808	+	3.63397i	−0.134316	+	0.232641i
$245$		0			0
$246$	−28.3923			−1.81023
$247$	16.7942	−	16.1603i	1.06859	−	1.02825i
$248$	−1.26795			−0.0805149
$249$	−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	$0.902220\pi$
$252$		−	13.3923i		−	0.843636i
$253$	−6.58846	+	3.80385i	−0.414213	+	0.239146i
$254$	−18.3564	+	10.5981i	−1.15178	+	0.664982i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.92820	−	12.0000i	0.432169	−	0.748539i	−0.564890	−	0.825166i	$-0.691082\pi$
$257$	6.92820	−	12.0000i	0.432169	−	0.748539i	0.997060	+	0.0766265i	$0.0244149\pi$
$258$	4.73205	+	2.73205i	0.294605	+	0.170090i
$259$	−33.5885			−2.08709
$260$		0			0
$261$	−42.2487			−2.61513
$262$	15.6962	+	9.06218i	0.969712	+	0.559863i
$263$	−13.7942	+	23.8923i	−0.850589	+	1.47326i	0.0300894	+	0.999547i	$0.490421\pi$
$263$	−13.7942	+	23.8923i	−0.850589	+	1.47326i	−0.880678	+	0.473715i	$0.842913\pi$
$264$	−4.09808	−	7.09808i	−0.252219	−	0.436856i
$265$		0			0
$266$	16.7942	−	9.69615i	1.02972	−	0.594509i
$267$	40.6865	−	23.4904i	2.48998	−	1.43759i
$268$		0			0
$269$	1.43782	+	2.49038i	0.0876656	+	0.151841i	0.906524	−	0.422154i	$-0.138726\pi$
$269$	1.43782	+	2.49038i	0.0876656	+	0.151841i	−0.818858	+	0.573996i	$0.805393\pi$
$270$		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	$0.691208\pi$
$272$	2.19615			0.133161
$273$	−7.09808	−	28.6865i	−0.429595	−	1.73619i
$274$	8.19615			0.495148
$275$		0			0
$276$	−3.46410	+	6.00000i	−0.208514	+	0.361158i
$277$	−0.500000	−	0.866025i	−0.0300421	−	0.0520344i	0.850613	−	0.525792i	$-0.176231\pi$
$277$	−0.500000	−	0.866025i	−0.0300421	−	0.0520344i	−0.880656	+	0.473757i	$0.842897\pi$
$278$		−	9.19615i		−	0.551549i
$279$	−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	$-0.100321\pi$
$282$	4.09808	+	7.09808i	0.244037	+	0.422684i
$283$	−15.1962	+	26.3205i	−0.903317	+	1.56459i	−0.0801576	+	0.996782i	$0.525542\pi$
$283$	−15.1962	+	26.3205i	−0.903317	+	1.56459i	−0.823160	+	0.567810i	$0.807791\pi$
$284$	5.19615	+	3.00000i	0.308335	+	0.178017i
$285$		0			0
$286$	−7.50000	−	7.79423i	−0.443484	−	0.460882i
$287$	−31.1769			−1.84032
$288$	−3.86603	−	2.23205i	−0.227808	−	0.131525i
$289$	6.08846	−	10.5455i	0.358145	−	0.620325i
$290$		0			0
$291$		−	41.3205i		−	2.42225i
$292$	4.90192	−	2.83013i	0.286863	−	0.165621i
$293$	0.696152	−	0.401924i	0.0406697	−	0.0234806i	−0.479527	−	0.877527i	$-0.659192\pi$
$293$	0.696152	−	0.401924i	0.0406697	−	0.0234806i	0.520197	+	0.854046i	$0.325859\pi$
$294$		−	5.46410i		−	0.318673i
$295$		0			0
$296$	−5.59808	+	9.69615i	−0.325382	+	0.563577i
$297$	−10.3923	−	6.00000i	−0.603023	−	0.348155i
$298$	6.00000			0.347571
$299$	−2.53590	+	8.78461i	−0.146655	+	0.508027i
$300$		0			0
$301$	5.19615	+	3.00000i	0.299501	+	0.172917i
$302$	3.16987	−	5.49038i	0.182406	−	0.315936i
$303$	−9.92820	−	17.1962i	−0.570360	−	0.987893i
$304$		−	6.46410i		−	0.370742i
$305$		0			0
$306$	8.49038	−	4.90192i	0.485363	−	0.280224i
$307$		−	20.5359i		−	1.17205i	−0.810295	−	0.586023i	$-0.800693\pi$
$307$		−	20.5359i		−	1.17205i	0.810295	−	0.586023i	$-0.199307\pi$
$308$	−4.50000	−	7.79423i	−0.256411	−	0.444117i
$309$	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	$0.358932\pi$
$312$	−9.46410	−	2.73205i	−0.535799	−	0.154672i
$313$	−5.60770			−0.316966			−0.158483	−	0.987362i	$-0.550660\pi$
$313$	−5.60770			−0.316966			−0.158483	+	0.987362i	$0.550660\pi$
$314$	−11.2583	−	6.50000i	−0.635344	−	0.366816i
$315$		0			0
$316$	3.09808	+	5.36603i	0.174280	+	0.301863i
$317$		−	12.8038i		−	0.719136i	−0.933119	−	0.359568i	$-0.882924\pi$
$317$		−	12.8038i		−	0.719136i	0.933119	−	0.359568i	$-0.117076\pi$
$318$	15.2942	−	8.83013i	0.857658	−	0.495169i
$319$	−24.5885	+	14.1962i	−1.37669	+	0.794832i
$320$		0			0
$321$	0.464102	+	0.803848i	0.0259036	+	0.0448664i
$322$	−3.80385	+	6.58846i	−0.211980	+	0.367160i
$323$	12.2942	+	7.09808i	0.684069	+	0.394948i
$324$	2.46410			0.136895
$325$		0			0
$326$	7.26795			0.402534
$327$	−36.5885	−	21.1244i	−2.02335	−	1.16818i
$328$	−5.19615	+	9.00000i	−0.286910	+	0.496942i
$329$	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	$0.325213\pi$
$332$	−1.90192	+	1.09808i	−0.104382	+	0.0602648i
$333$			49.9808i			2.73893i
$334$	−1.50000	−	2.59808i	−0.0820763	−	0.142160i
$335$		0			0
$336$	−7.09808	−	4.09808i	−0.387232	−	0.223568i
$337$	4.19615			0.228579			0.114289	−	0.993447i	$-0.463541\pi$
$337$	4.19615			0.228579			0.114289	+	0.993447i	$0.463541\pi$
$338$	−12.9904	−	0.500000i	−0.706584	−	0.0271964i
$339$	18.9282			1.02804
$340$		0			0
$341$	−1.90192	+	3.29423i	−0.102995	+	0.178392i
$342$	−14.4282	−	24.9904i	−0.780188	−	1.35133i
$343$			15.0000i			0.809924i
$344$	1.73205	−	1.00000i	0.0933859	−	0.0539164i
$345$		0			0
$346$			15.0000i			0.806405i
$347$	−12.6340	−	21.8827i	−0.678227	−	1.17472i	−0.975514	−	0.219936i	$-0.929415\pi$
$347$	−12.6340	−	21.8827i	−0.678227	−	1.17472i	0.297287	−	0.954788i	$-0.403918\pi$
$348$	−12.9282	+	22.3923i	−0.693024	+	1.20035i
$349$	−29.4904	−	17.0263i	−1.57858	−	0.911396i	−0.995057	−	0.0993018i	$-0.968339\pi$
$349$	−29.4904	−	17.0263i	−1.57858	−	0.911396i	−0.583527	−	0.812094i	$-0.698328\pi$
$350$		0			0
$351$	−14.0000	+	3.46410i	−0.747265	+	0.184900i
$352$	−3.00000			−0.159901
$353$	17.4904	+	10.0981i	0.930919	+	0.537466i	0.887102	−	0.461573i	$-0.152715\pi$
$353$	17.4904	+	10.0981i	0.930919	+	0.537466i	0.0438169	+	0.999040i	$0.486048\pi$
$354$	14.1962	−	24.5885i	0.754517	−	1.30686i
$355$		0			0
$356$		−	17.1962i		−	0.911394i
$357$	15.5885	−	9.00000i	0.825029	−	0.476331i
$358$	−2.19615	+	1.26795i	−0.116070	+	0.0670132i
$359$		−	22.3923i		−	1.18182i	−0.806737	−	0.590910i	$-0.798769\pi$
$359$		−	22.3923i		−	1.18182i	0.806737	−	0.590910i	$-0.201231\pi$
$360$		0			0
$361$	11.3923	−	19.7321i	0.599595	−	1.03853i
$362$	14.3660	+	8.29423i	0.755062	+	0.435935i
$363$	5.46410			0.286791
$364$	−10.3923	−	3.00000i	−0.544705	−	0.157243i
$365$		0			0
$366$	9.92820	+	5.73205i	0.518955	+	0.299619i
$367$	−13.1962	+	22.8564i	−0.688834	+	1.19309i	0.283382	+	0.959007i	$0.408544\pi$
$367$	−13.1962	+	22.8564i	−0.688834	+	1.19309i	−0.972216	+	0.234088i	$0.924790\pi$
$368$	1.26795	+	2.19615i	0.0660964	+	0.114482i
$369$			46.3923i			2.41509i
$370$		0			0
$371$	16.7942	−	9.69615i	0.871913	−	0.503399i
$372$			3.46410i			0.179605i
$373$	10.1962	+	17.6603i	0.527937	+	0.914413i	0.999470	+	0.0325648i	$0.0103675\pi$
$373$	10.1962	+	17.6603i	0.527937	+	0.914413i	−0.471533	+	0.881848i	$0.656299\pi$
$374$	3.29423	−	5.70577i	0.170341	−	0.295038i
$375$		0			0
$376$	3.00000			0.154713
$377$	−9.46410	+	32.7846i	−0.487426	+	1.68849i
$378$	−12.0000			−0.617213
$379$	10.2058	+	5.89230i	0.524235	+	0.302667i	0.738666	−	0.674072i	$-0.235456\pi$
$379$	10.2058	+	5.89230i	0.524235	+	0.302667i	−0.214430	+	0.976739i	$0.568790\pi$
$380$		0			0
$381$	28.9545	+	50.1506i	1.48338	+	2.56929i
$382$		−	19.2679i		−	0.985834i
$383$	1.39230	−	0.803848i	0.0711435	−	0.0410747i	−0.464006	−	0.885832i	$-0.653589\pi$
$383$	1.39230	−	0.803848i	0.0711435	−	0.0410747i	0.535150	+	0.844757i	$0.320255\pi$
$384$	−2.36603	+	1.36603i	−0.120741	+	0.0697097i
$385$		0			0
$386$	−2.19615	−	3.80385i	−0.111781	−	0.193611i
$387$	4.46410	−	7.73205i	0.226923	−	0.393042i
$388$	−13.0981	−	7.56218i	−0.664954	−	0.383911i
$389$	19.2679			0.976924			0.488462	−	0.872585i	$-0.337558\pi$
$389$	19.2679			0.976924			0.488462	+	0.872585i	$0.337558\pi$
$390$		0			0
$391$	−5.56922			−0.281648
$392$	−1.73205	−	1.00000i	−0.0874818	−	0.0505076i
$393$	24.7583	−	42.8827i	1.24889	−	2.16315i
$394$	4.79423	+	8.30385i	0.241530	+	0.418342i
$395$		0			0
$396$	−11.5981	+	6.69615i	−0.582825	+	0.336494i
$397$	−0.696152	+	0.401924i	−0.0349389	+	0.0201720i	−0.517368	−	0.855763i	$-0.673088\pi$
$397$	−0.696152	+	0.401924i	−0.0349389	+	0.0201720i	0.482429	+	0.875935i	$0.339755\pi$
$398$			14.3923i			0.721421i
$399$	−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
$403$	1.09808	+	4.43782i	0.0546991	+	0.221064i
$404$	−7.26795			−0.361594
$405$		0			0
$406$	−14.1962	+	24.5885i	−0.704543	+	1.22030i
$407$	16.7942	+	29.0885i	0.832459	+	1.44186i
$408$		−	6.00000i		−	0.297044i
$409$	17.0885	−	9.86603i	0.844970	−	0.487844i	−0.0139806	−	0.999902i	$-0.504450\pi$
$409$	17.0885	−	9.86603i	0.844970	−	0.487844i	0.858950	+	0.512059i	$0.171117\pi$
$410$		0			0
$411$		−	22.3923i		−	1.10453i
$412$	−0.598076	−	1.03590i	−0.0294651	−	0.0510351i
$413$	15.5885	−	27.0000i	0.767058	−	1.32858i
$414$	9.80385	+	5.66025i	0.481833	+	0.278186i
$415$		0			0
$416$	−2.59808	+	2.50000i	−0.127381	+	0.122573i
$417$	−25.1244			−1.23034
$418$	−16.7942	−	9.69615i	−0.821433	−	0.474254i
$419$	−8.66025	+	15.0000i	−0.423081	+	0.732798i	−0.996239	−	0.0866469i	$-0.972385\pi$
$419$	−8.66025	+	15.0000i	−0.423081	+	0.732798i	0.573158	+	0.819445i	$0.305718\pi$
$420$		0			0
$421$		−	27.1244i		−	1.32196i	−0.750403	−	0.660980i	$-0.770141\pi$
$421$		−	27.1244i		−	1.32196i	0.750403	−	0.660980i	$-0.229859\pi$
$422$	11.7679	−	6.79423i	0.572855	−	0.330738i
$423$	11.5981	−	6.69615i	0.563918	−	0.325578i
$424$		−	6.46410i		−	0.313925i
$425$		0			0
$426$	8.19615	−	14.1962i	0.397105	−	0.687806i
$427$	10.9019	+	6.29423i	0.527581	+	0.304599i
$428$	0.339746			0.0164222
$429$	−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	$0.683511\pi$
$432$	−2.00000	+	3.46410i	−0.0962250	+	0.166667i
$433$	−6.19615	−	10.7321i	−0.297768	−	0.515749i	0.677857	−	0.735194i	$-0.262909\pi$
$433$	−6.19615	−	10.7321i	−0.297768	−	0.515749i	−0.975625	+	0.219444i	$0.929576\pi$
$434$			3.80385i			0.182591i
$435$		0			0
$436$	−13.3923	+	7.73205i	−0.641375	+	0.370298i
$437$			16.3923i			0.784150i
$438$	−7.73205	−	13.3923i	−0.369452	−	0.639909i
$439$	17.2942	−	29.9545i	0.825408	−	1.42965i	−0.0761982	−	0.997093i	$-0.524278\pi$
$439$	17.2942	−	29.9545i	0.825408	−	1.42965i	0.901607	−	0.432557i	$-0.142388\pi$
$440$		0			0
$441$	−8.92820			−0.425153
$442$	−1.90192	−	7.68653i	−0.0904653	−	0.365611i
$443$	1.60770			0.0763839			0.0381920	−	0.999270i	$-0.487840\pi$
$443$	1.60770			0.0763839			0.0381920	+	0.999270i	$0.487840\pi$
$444$	26.4904	+	15.2942i	1.25718	+	0.725832i
$445$		0			0
$446$	−0.232051	−	0.401924i	−0.0109879	−	0.0190316i
$447$		−	16.3923i		−	0.775329i
$448$	−2.59808	+	1.50000i	−0.122748	+	0.0708683i
$449$	13.5000	−	7.79423i	0.637104	−	0.367832i	−0.146394	−	0.989226i	$-0.546767\pi$
$449$	13.5000	−	7.79423i	0.637104	−	0.367832i	0.783498	+	0.621394i	$0.213433\pi$
$450$		0			0
$451$	15.5885	+	27.0000i	0.734032	+	1.27138i
$452$	3.46410	−	6.00000i	0.162938	−	0.282216i
$453$	−15.0000	−	8.66025i	−0.704761	−	0.406894i
$454$	4.39230			0.206141
$455$		0			0
$456$	−17.6603			−0.827017
$457$	30.8827	+	17.8301i	1.44463	+	0.834058i	0.998154	−	0.0607368i	$-0.0193450\pi$
$457$	30.8827	+	17.8301i	1.44463	+	0.834058i	0.446477	+	0.894795i	$0.352678\pi$
$458$	2.36603	−	4.09808i	0.110557	−	0.191491i
$459$	−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	$0.337695\pi$
$462$	−21.2942	+	12.2942i	−0.990697	+	0.571979i
$463$		−	0.928203i		−	0.0431373i	−0.999767	−	0.0215686i	$-0.993134\pi$
$463$		−	0.928203i		−	0.0431373i	0.999767	−	0.0215686i	$-0.00686604\pi$
$464$	4.73205	+	8.19615i	0.219680	+	0.380497i
$465$		0			0
$466$	1.09808	+	0.633975i	0.0508674	+	0.0293683i
$467$	10.1436			0.469390			0.234695	−	0.972069i	$-0.424591\pi$
$467$	10.1436			0.469390			0.234695	+	0.972069i	$0.424591\pi$
$468$	−4.46410	+	15.4641i	−0.206353	+	0.714828i
$469$		0			0
$470$		0			0
$471$	−17.7583	+	30.7583i	−0.818261	+	1.41727i
$472$	−5.19615	−	9.00000i	−0.239172	−	0.414259i
$473$		−	6.00000i		−	0.275880i
$474$	14.6603	−	8.46410i	0.673368	−	0.388769i
$475$		0			0
$476$		−	6.58846i		−	0.301981i
$477$	−14.4282	−	24.9904i	−0.660622	−	1.14423i
$478$	4.09808	−	7.09808i	0.187442	−	0.324658i
$479$	−9.50962	−	5.49038i	−0.434506	−	0.250862i	0.266759	−	0.963763i	$-0.414047\pi$
$479$	−9.50962	−	5.49038i	−0.434506	−	0.250862i	−0.701264	+	0.712901i	$0.747381\pi$
$480$		0			0
$481$	38.7846	+	11.1962i	1.76843	+	0.510501i
$482$	8.66025			0.394464
$483$	18.0000	+	10.3923i	0.819028	+	0.472866i
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$		0			0
$486$		−	18.7321i		−	0.849703i
$487$	28.7942	−	16.6244i	1.30479	−	0.753321i	0.323569	−	0.946204i	$-0.395117\pi$
$487$	28.7942	−	16.6244i	1.30479	−	0.753321i	0.981222	+	0.192883i	$0.0617838\pi$
$488$	3.63397	−	2.09808i	0.164502	−	0.0949754i
$489$		−	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	$0.190677\pi$
$492$	24.5885	+	14.1962i	1.10853	+	0.640012i
$493$	−20.7846			−0.936092
$494$	−22.6244	+	5.59808i	−1.01792	+	0.251869i
$495$		0			0
$496$	1.09808	+	0.633975i	0.0493051	+	0.0284663i
$497$	9.00000	−	15.5885i	0.403705	−	0.699238i
$498$	3.00000	+	5.19615i	0.134433	+	0.232845i
$499$			1.85641i			0.0831042i	0.999136	+	0.0415521i	$0.0132302\pi$
$499$			1.85641i			0.0831042i	−0.999136	+	0.0415521i	$0.986770\pi$
$500$		0			0
$501$	−7.09808	+	4.09808i	−0.317119	+	0.183089i
$502$			6.80385i			0.303671i
$503$	−4.66987	−	8.08846i	−0.208219	−	0.360646i	0.742934	−	0.669364i	$-0.233433\pi$
$503$	−4.66987	−	8.08846i	−0.208219	−	0.360646i	−0.951154	+	0.308718i	$0.900100\pi$
$504$	−6.69615	+	11.5981i	−0.298270	+	0.516619i
$505$		0			0
$506$	7.60770			0.338203
$507$	−1.36603	+	35.4904i	−0.0606673	+	1.57618i
$508$	21.1962			0.940427
$509$	1.39230	+	0.803848i	0.0617128	+	0.0356299i	0.530539	−	0.847661i	$-0.321990\pi$
$509$	1.39230	+	0.803848i	0.0617128	+	0.0356299i	−0.468826	+	0.883290i	$0.655323\pi$
$510$		0			0
$511$	−8.49038	−	14.7058i	−0.375592	−	0.650545i
$512$			1.00000i			0.0441942i
$513$	−22.3923	+	12.9282i	−0.988644	+	0.570794i
$514$	−12.0000	+	6.92820i	−0.529297	+	0.305590i
$515$		0			0
$516$	−2.73205	−	4.73205i	−0.120272	−	0.208317i
$517$	4.50000	−	7.79423i	0.197910	−	0.342790i
$518$	29.0885	+	16.7942i	1.27807	+	0.737896i
$519$	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	$0.503236\pi$
$522$	36.5885	+	21.1244i	1.60143	+	0.924588i
$523$	9.19615	−	15.9282i	0.402120	−	0.696492i	−0.591862	−	0.806039i	$-0.701607\pi$
$523$	9.19615	−	15.9282i	0.402120	−	0.696492i	0.993982	+	0.109548i	$0.0349402\pi$
$524$	−9.06218	−	15.6962i	−0.395883	−	0.685690i
$525$		0			0
$526$	23.8923	−	13.7942i	1.04175	−	0.601457i
$527$	−2.41154	+	1.39230i	−0.105048	+	0.0606498i
$528$			8.19615i			0.356692i
$529$	8.28461	+	14.3494i	0.360200	+	0.623885i
$530$		0			0
$531$	−40.1769	−	23.1962i	−1.74353	−	1.00663i
$532$	−19.3923			−0.840763
$533$	36.0000	+	10.3923i	1.55933	+	0.450141i
$534$	−46.9808			−2.03306
$535$		0			0
$536$		0			0
$537$	3.46410	+	6.00000i	0.149487	+	0.258919i
$538$		−	2.87564i		−	0.123978i
$539$	−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	$0.887853\pi$
$542$	1.26795	+	2.19615i	0.0544631	+	0.0943328i
$543$	22.6603	−	39.2487i	0.972445	−	1.68432i
$544$	−1.90192	−	1.09808i	−0.0815443	−	0.0470796i
$545$		0			0
$546$	−8.19615	+	28.3923i	−0.350763	+	1.21508i
$547$	−34.7846			−1.48728			−0.743641	−	0.668579i	$-0.766903\pi$
$547$	−34.7846			−1.48728			−0.743641	+	0.668579i	$0.766903\pi$
$548$	−7.09808	−	4.09808i	−0.303215	−	0.175061i
$549$	9.36603	−	16.2224i	0.399732	−	0.692357i
$550$		0			0
$551$			61.1769i			2.60622i
$552$	6.00000	−	3.46410i	0.255377	−	0.147442i
$553$	16.0981	−	9.29423i	0.684560	−	0.395231i
$554$			1.00000i			0.0424859i
$555$		0			0
$556$	−4.59808	+	7.96410i	−0.195002	+	0.337753i
$557$	−14.8923	−	8.59808i	−0.631007	−	0.364312i	0.150135	−	0.988666i	$-0.452029\pi$
$557$	−14.8923	−	8.59808i	−0.631007	−	0.364312i	−0.781142	+	0.624353i	$0.785363\pi$
$558$	5.66025			0.239618
$559$	−5.00000	−	5.19615i	−0.211477	−	0.219774i
$560$		0			0
$561$	−15.5885	−	9.00000i	−0.658145	−	0.379980i
$562$	−5.19615	+	9.00000i	−0.219186	+	0.379642i
$563$	10.7321	+	18.5885i	0.452302	+	0.783410i	0.998529	−	0.0542274i	$-0.0172696\pi$
$563$	10.7321	+	18.5885i	0.452302	+	0.783410i	−0.546227	+	0.837637i	$0.683936\pi$
$564$		−	8.19615i		−	0.345120i
$565$		0			0
$566$	26.3205	−	15.1962i	1.10633	−	0.638742i
$567$		−	7.39230i		−	0.310448i
$568$	−3.00000	−	5.19615i	−0.125877	−	0.218026i
$569$	−10.6244	+	18.4019i	−0.445396	+	0.771449i	−0.998080	−	0.0619424i	$-0.980270\pi$
$569$	−10.6244	+	18.4019i	−0.445396	+	0.771449i	0.552684	+	0.833391i	$0.313604\pi$
$570$		0			0
$571$	34.3731			1.43847			0.719234	−	0.694768i	$-0.244493\pi$
$571$	34.3731			1.43847			0.719234	+	0.694768i	$0.244493\pi$
$572$	2.59808	+	10.5000i	0.108631	+	0.439027i
$573$	−52.6410			−2.19911
$574$	27.0000	+	15.5885i	1.12696	+	0.650650i
$575$		0			0
$576$	2.23205	+	3.86603i	0.0930021	+	0.161084i
$577$			32.4449i			1.35070i	0.737499	+	0.675349i	$0.236007\pi$
$577$			32.4449i			1.35070i	−0.737499	+	0.675349i	$0.763993\pi$
$578$	−10.5455	+	6.08846i	−0.438636	+	0.253246i
$579$	−10.3923	+	6.00000i	−0.431889	+	0.249351i
$580$		0			0
$581$	3.29423	+	5.70577i	0.136668	+	0.236715i
$582$	−20.6603	+	35.7846i	−0.856395	+	1.48332i
$583$	−16.7942	−	9.69615i	−0.695546	−	0.401574i
$584$	−5.66025			−0.234223
$585$		0			0
$586$	−0.803848			−0.0332066
$587$	25.9808	+	15.0000i	1.07234	+	0.619116i	0.928820	−	0.370531i	$-0.120824\pi$
$587$	25.9808	+	15.0000i	1.07234	+	0.619116i	0.143521	+	0.989647i	$0.454158\pi$
$588$	−2.73205	+	4.73205i	−0.112668	+	0.195146i
$589$	4.09808	+	7.09808i	0.168858	+	0.292471i
$590$		0			0
$591$	22.6865	−	13.0981i	0.933199	−	0.538783i
$592$	9.69615	−	5.59808i	0.398509	−	0.230080i
$593$			20.7846i			0.853522i	0.904365	+	0.426761i	$0.140345\pi$
$593$			20.7846i			0.853522i	−0.904365	+	0.426761i	$0.859655\pi$
$594$	6.00000	+	10.3923i	0.246183	+	0.426401i
$595$		0			0
$596$	−5.19615	−	3.00000i	−0.212843	−	0.122885i
$597$	39.3205			1.60928
$598$	6.58846	−	6.33975i	0.269422	−	0.259251i
$599$	7.85641			0.321004			0.160502	−	0.987036i	$-0.448689\pi$
$599$	7.85641			0.321004			0.160502	+	0.987036i	$0.448689\pi$
$600$		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	$0.191261\pi$
$602$	−3.00000	−	5.19615i	−0.122271	−	0.211779i
$603$		0			0
$604$	−5.49038	+	3.16987i	−0.223400	+	0.128980i
$605$		0			0
$606$			19.8564i			0.806611i
$607$	−3.20577	−	5.55256i	−0.130118	−	0.225371i	0.793604	−	0.608435i	$-0.208202\pi$
$607$	−3.20577	−	5.55256i	−0.130118	−	0.225371i	−0.923722	+	0.383064i	$0.874869\pi$
$608$	−3.23205	+	5.59808i	−0.131077	+	0.227032i
$609$	67.1769	+	38.7846i	2.72215	+	1.57163i
$610$		0			0
$611$	−2.59808	−	10.5000i	−0.105107	−	0.424785i
$612$	−9.80385			−0.396297
$613$	−23.3038	−	13.4545i	−0.941234	−	0.543421i	−0.0508868	−	0.998704i	$-0.516205\pi$
$613$	−23.3038	−	13.4545i	−0.941234	−	0.543421i	−0.890347	+	0.455283i	$0.849538\pi$
$614$	−10.2679	+	17.7846i	−0.414381	+	0.717728i
$615$		0			0
$616$			9.00000i			0.362620i
$617$	15.5885	−	9.00000i	0.627568	−	0.362326i	−0.152242	−	0.988343i	$-0.548649\pi$
$617$	15.5885	−	9.00000i	0.627568	−	0.362326i	0.779809	+	0.626017i	$0.215316\pi$
$618$	−2.83013	+	1.63397i	−0.113844	+	0.0657281i
$619$			10.6077i			0.426359i	0.977013	+	0.213180i	$0.0683820\pi$
$619$			10.6077i			0.426359i	−0.977013	+	0.213180i	$0.931618\pi$
$620$		0			0
$621$	5.07180	−	8.78461i	0.203524	−	0.352514i
$622$	−13.0981	−	7.56218i	−0.525185	−	0.303216i
$623$	−51.5885			−2.06685
$624$	6.83013	+	7.09808i	0.273424	+	0.284150i
$625$		0			0
$626$	4.85641	+	2.80385i	0.194101	+	0.112064i
$627$	−26.4904	+	45.8827i	−1.05792	+	1.83238i
$628$	6.50000	+	11.2583i	0.259378	+	0.449256i
$629$			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	$0.469101\pi$
$632$		−	6.19615i		−	0.246470i
$633$	−18.5622	−	32.1506i	−0.737780	−	1.27787i
$634$	−6.40192	+	11.0885i	−0.254253	+	0.440379i
$635$		0			0
$636$	−17.6603			−0.700275
$637$	−2.00000	+	6.92820i	−0.0792429	+	0.274505i
$638$	28.3923			1.12406
$639$	−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	$-0.528321\pi$
$642$		−	0.928203i		−	0.0366333i
$643$	−6.29423	+	3.63397i	−0.248220	+	0.143310i	−0.618949	−	0.785431i	$-0.712441\pi$
$643$	−6.29423	+	3.63397i	−0.248220	+	0.143310i	0.370729	+	0.928741i	$0.379108\pi$
$644$	6.58846	−	3.80385i	0.259622	−	0.149893i
$645$		0			0
$646$	−7.09808	−	12.2942i	−0.279270	−	0.483710i
$647$	−5.59808	+	9.69615i	−0.220083	+	0.381195i	−0.954833	−	0.297143i	$-0.903966\pi$
$647$	−5.59808	+	9.69615i	−0.220083	+	0.381195i	0.734750	+	0.678338i	$0.237300\pi$
$648$	−2.13397	−	1.23205i	−0.0838304	−	0.0483995i
$649$	−31.1769			−1.22380
$650$		0			0
$651$	10.3923			0.407307
$652$	−6.29423	−	3.63397i	−0.246501	−	0.142317i
$653$	−9.69615	+	16.7942i	−0.379440	+	0.657209i	−0.990981	−	0.134004i	$-0.957217\pi$
$653$	−9.69615	+	16.7942i	−0.379440	+	0.657209i	0.611541	+	0.791213i	$0.290550\pi$
$654$	21.1244	+	36.5885i	0.826028	+	1.43072i
$655$		0			0
$656$	9.00000	−	5.19615i	0.351391	−	0.202876i
$657$	−21.8827	+	12.6340i	−0.853725	+	0.492898i
$658$		−	9.00000i		−	0.350857i
$659$	−14.6603	−	25.3923i	−0.571082	−	0.989144i	−0.996455	−	0.0841255i	$-0.973190\pi$
$659$	−14.6603	−	25.3923i	−0.571082	−	0.989144i	0.425373	−	0.905018i	$-0.360143\pi$
$660$		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	$0.469069\pi$
$662$	−0.928203			−0.0360756
$663$	−21.0000	+	5.19615i	−0.815572	+	0.201802i
$664$	2.19615			0.0852272
$665$		0			0
$666$	24.9904	−	43.2846i	0.968358	−	1.67724i
$667$	−12.0000	−	20.7846i	−0.464642	−	0.804783i
$668$			3.00000i			0.116073i
$669$	−1.09808	+	0.633975i	−0.0424541	+	0.0245109i
$670$		0			0
$671$		−	12.5885i		−	0.485972i
$672$	4.09808	+	7.09808i	0.158087	+	0.273814i
$673$	1.80385	−	3.12436i	0.0695332	−	0.120435i	−0.829163	−	0.559007i	$-0.811182\pi$
$673$	1.80385	−	3.12436i	0.0695332	−	0.120435i	0.898696	+	0.438572i	$0.144516\pi$
$674$	−3.63397	−	2.09808i	−0.139975	−	0.0808149i
$675$		0			0
$676$	11.0000	+	6.92820i	0.423077	+	0.266469i
$677$	−1.85641			−0.0713475			−0.0356737	−	0.999363i	$-0.511358\pi$
$677$	−1.85641			−0.0713475			−0.0356737	+	0.999363i	$0.511358\pi$
$678$	−16.3923	−	9.46410i	−0.629543	−	0.363467i
$679$	−22.6865	+	39.2942i	−0.870629	+	1.50797i
$680$		0			0
$681$		−	12.0000i		−	0.459841i
$682$	3.29423	−	1.90192i	0.126143	−	0.0728284i
$683$	−27.0000	+	15.5885i	−1.03313	+	0.596476i	−0.917879	−	0.396861i	$-0.870099\pi$
$683$	−27.0000	+	15.5885i	−1.03313	+	0.596476i	−0.115248	+	0.993337i	$0.536766\pi$
$684$			28.8564i			1.10335i
$685$		0			0
$686$	7.50000	−	12.9904i	0.286351	−	0.495975i
$687$	−11.1962	−	6.46410i	−0.427160	−	0.246621i
$688$	−2.00000			−0.0762493
$689$	−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	$0.782504\pi$
$692$	7.50000	−	12.9904i	0.285107	−	0.493820i
$693$	20.0885	+	34.7942i	0.763097	+	1.32172i
$694$			25.2679i			0.959158i
$695$		0			0
$696$	22.3923	−	12.9282i	0.848778	−	0.490042i
$697$			22.8231i			0.864486i
$698$	17.0263	+	29.4904i	0.644454	+	1.11623i
$699$	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	$0.691056\pi$
$702$	13.8564	+	4.00000i	0.522976	+	0.150970i
$703$	72.3731			2.72960
$704$	2.59808	+	1.50000i	0.0979187	+	0.0565334i
$705$		0			0
$706$	−10.0981	−	17.4904i	−0.380046	−	0.658259i
$707$			21.8038i			0.820018i
$708$	−24.5885	+	14.1962i	−0.924091	+	0.533524i
$709$	35.4904	−	20.4904i	1.33287	−	0.769532i	0.347131	−	0.937817i	$-0.387156\pi$
$709$	35.4904	−	20.4904i	1.33287	−	0.769532i	0.985738	+	0.168284i	$0.0538227\pi$
$710$		0			0
$711$	−13.8301	−	23.9545i	−0.518670	−	0.898363i
$712$	−8.59808	+	14.8923i	−0.322227	+	0.558113i
$713$	−2.78461	−	1.60770i	−0.104284	−	0.0602087i
$714$	−18.0000			−0.673633
$715$		0			0
$716$	2.53590			0.0947710
$717$	−19.3923	−	11.1962i	−0.724219	−	0.418128i
$718$	−11.1962	+	19.3923i	−0.417837	+	0.723714i
$719$	0.928203	+	1.60770i	0.0346161	+	0.0599569i	0.882814	−	0.469722i	$-0.155646\pi$
$719$	0.928203	+	1.60770i	0.0346161	+	0.0599569i	−0.848198	+	0.529679i	$0.822312\pi$
$720$		0			0
$721$	−3.10770	+	1.79423i	−0.115737	+	0.0668206i
$722$	−19.7321	+	11.3923i	−0.734351	+	0.423978i
$723$		−	23.6603i		−	0.879934i
$724$	−8.29423	−	14.3660i	−0.308253	−	0.533909i
$725$		0			0
$726$	−4.73205	−	2.73205i	−0.175623	−	0.101396i
$727$	38.3731			1.42318			0.711589	−	0.702596i	$-0.247976\pi$
$727$	38.3731			1.42318			0.711589	+	0.702596i	$0.247976\pi$
$728$	7.50000	+	7.79423i	0.277968	+	0.288873i
$729$	−43.7846			−1.62165
$730$		0			0
$731$	2.19615	−	3.80385i	0.0812276	−	0.140690i
$732$	−5.73205	−	9.92820i	−0.211863	−	0.366957i
$733$		−	50.9090i		−	1.88037i	−0.340670	−	0.940183i	$-0.610654\pi$
$733$		−	50.9090i		−	1.88037i	0.340670	−	0.940183i	$-0.389346\pi$
$734$	22.8564	−	13.1962i	0.843645	−	0.487079i
$735$		0			0
$736$		−	2.53590i		−	0.0934745i
$737$		0			0
$738$	23.1962	−	40.1769i	0.853862	−	1.47893i
$739$	43.7942	+	25.2846i	1.61100	+	0.930109i	0.989140	+	0.146979i	$0.0469549\pi$
$739$	43.7942	+	25.2846i	1.61100	+	0.930109i	0.621857	+	0.783131i	$0.286378\pi$
$740$		0			0
$741$	15.2942	+	61.8109i	0.561848	+	2.27068i
$742$	−19.3923			−0.711914
$743$	−29.7846	−	17.1962i	−1.09269	−	0.630866i	−0.158400	−	0.987375i	$-0.550633\pi$
$743$	−29.7846	−	17.1962i	−1.09269	−	0.630866i	−0.934292	+	0.356509i	$0.883967\pi$
$744$	1.73205	−	3.00000i	0.0635001	−	0.109985i
$745$		0			0
$746$		−	20.3923i		−	0.746615i
$747$	8.49038	−	4.90192i	0.310647	−	0.179352i
$748$	−5.70577	+	3.29423i	−0.208624	+	0.120449i
$749$		−	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	$0.168945\pi$
$752$	−2.59808	−	1.50000i	−0.0947421	−	0.0546994i
$753$	18.5885			0.677401
$754$	24.5885	−	23.6603i	0.895459	−	0.861656i
$755$		0			0
$756$	10.3923	+	6.00000i	0.377964	+	0.218218i
$757$	1.89230	−	3.27757i	0.0687770	−	0.119125i	−0.829586	−	0.558379i	$-0.811424\pi$
$757$	1.89230	−	3.27757i	0.0687770	−	0.119125i	0.898363	+	0.439253i	$0.144757\pi$
$758$	−5.89230	−	10.2058i	−0.214018	−	0.370690i
$759$		−	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	$0.510834\pi$
$762$		−	57.9090i		−	2.09782i
$763$	23.1962	+	40.1769i	0.839757	+	1.45450i
$764$	−9.63397	+	16.6865i	−0.348545	+	0.603698i
$765$		0			0
$766$	−1.60770			−0.0580884
$767$	−27.0000	+	25.9808i	−0.974913	+	0.938111i
$768$	2.73205			0.0985844
$769$	−33.0000	−	19.0526i	−1.19001	−	0.687053i	−0.231701	−	0.972787i	$-0.574429\pi$
$769$	−33.0000	−	19.0526i	−1.19001	−	0.687053i	−0.958309	+	0.285734i	$0.907763\pi$
$770$		0			0
$771$	18.9282	+	32.7846i	0.681683	+	1.18071i
$772$			4.39230i			0.158083i
$773$	29.0885	−	16.7942i	1.04624	−	0.604046i	0.124645	−	0.992201i	$-0.460221\pi$
$773$	29.0885	−	16.7942i	1.04624	−	0.604046i	0.921594	+	0.388155i	$0.126887\pi$
$774$	−7.73205	+	4.46410i	−0.277923	+	0.160459i
$775$		0			0
$776$	7.56218	+	13.0981i	0.271466	+	0.470194i
$777$	45.8827	−	79.4711i	1.64603	−	2.85101i
$778$	−16.6865	−	9.63397i	−0.598241	−	0.345395i
$779$	67.1769			2.40686
$780$		0			0
$781$	−18.0000			−0.644091
$782$	4.82309	+	2.78461i	0.172473	+	0.0995774i
$783$	18.9282	−	32.7846i	0.676439	−	1.17163i
$784$	1.00000	+	1.73205i	0.0357143	+	0.0618590i
$785$		0			0
$786$	−42.8827	+	24.7583i	−1.52957	+	0.883100i
$787$	31.9019	−	18.4186i	1.13718	−	0.656552i	0.191450	−	0.981502i	$-0.438681\pi$
$787$	31.9019	−	18.4186i	1.13718	−	0.656552i	0.945731	+	0.324951i	$0.105348\pi$
$788$		−	9.58846i		−	0.341575i
$789$	−37.6865	−	65.2750i	−1.34168	−	2.32385i
$790$		0			0
$791$	−18.0000	−	10.3923i	−0.640006	−	0.369508i
$792$	13.3923			0.475875
$793$	−10.4904	−	10.9019i	−0.372524	−	0.387139i
$794$	0.803848			0.0285275
$795$		0			0
$796$	7.19615	−	12.4641i	0.255061	−	0.441778i
$797$	0.464102	+	0.803848i	0.0164393	+	0.0284737i	0.874128	−	0.485696i	$-0.161434\pi$
$797$	0.464102	+	0.803848i	0.0164393	+	0.0284737i	−0.857689	+	0.514169i	$0.828100\pi$
$798$			52.9808i			1.87550i
$799$	5.70577	−	3.29423i	0.201856	−	0.116541i
$800$		0			0
$801$			76.7654i			2.71237i
$802$	2.59808	+	4.50000i	0.0917413	+	0.158901i
$803$	−8.49038	+	14.7058i	−0.299619	+	0.518955i
$804$		0			0
$805$		0			0
$806$	1.26795	−	4.39230i	0.0446616	−	0.154712i
$807$	−7.85641			−0.276559
$808$	6.29423	+	3.63397i	0.221430	+	0.127843i
$809$	−12.0000	+	20.7846i	−0.421898	+	0.730748i	−0.996125	−	0.0879478i	$-0.971969\pi$
$809$	−12.0000	+	20.7846i	−0.421898	+	0.730748i	0.574228	+	0.818696i	$0.305302\pi$
$810$		0			0
$811$		−	22.6077i		−	0.793864i	−0.917848	−	0.396932i	$-0.870075\pi$
$811$		−	22.6077i		−	0.793864i	0.917848	−	0.396932i	$-0.129925\pi$
$812$	24.5885	−	14.1962i	0.862886	−	0.498187i
$813$	6.00000	−	3.46410i	0.210429	−	0.121491i
$814$		−	33.5885i		−	1.17727i
$815$		0			0
$816$	−3.00000	+	5.19615i	−0.105021	+	0.181902i
$817$	−11.1962	−	6.46410i	−0.391704	−	0.226150i
$818$	−19.7321			−0.689915
$819$	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	$0.721392\pi$
$822$	−11.1962	+	19.3923i	−0.390511	+	0.676384i
$823$	−8.40192	−	14.5526i	−0.292873	−	0.507270i	0.681615	−	0.731711i	$-0.261278\pi$
$823$	−8.40192	−	14.5526i	−0.292873	−	0.507270i	−0.974488	+	0.224441i	$0.927945\pi$
$824$			1.19615i			0.0416699i
$825$		0			0
$826$	−27.0000	+	15.5885i	−0.939450	+	0.542392i
$827$		−	11.4115i		−	0.396818i	−0.980119	−	0.198409i	$-0.936423\pi$
$827$		−	11.4115i		−	0.396818i	0.980119	−	0.198409i	$-0.0635775\pi$
$828$	−5.66025	−	9.80385i	−0.196707	−	0.340707i
$829$	10.0000	−	17.3205i	0.347314	−	0.601566i	−0.638457	−	0.769657i	$-0.720427\pi$
$829$	10.0000	−	17.3205i	0.347314	−	0.601566i	0.985771	+	0.168091i	$0.0537604\pi$
$830$		0			0
$831$	2.73205			0.0947738
$832$	3.50000	−	0.866025i	0.121341	−	0.0300240i
$833$	−4.39230			−0.152184
$834$	21.7583	+	12.5622i	0.753429	+	0.434993i
$835$		0			0
$836$	9.69615	+	16.7942i	0.335348	+	0.580841i
$837$		−	5.07180i		−	0.175307i
$838$	15.0000	−	8.66025i	0.518166	−	0.299164i
$839$	−27.8827	+	16.0981i	−0.962617	+	0.555767i	−0.896978	−	0.442076i	$-0.854242\pi$
$839$	−27.8827	+	16.0981i	−0.962617	+	0.555767i	−0.0656397	+	0.997843i	$0.520909\pi$
$840$		0			0
$841$	−30.2846	−	52.4545i	−1.04430	−	1.80878i
$842$	−13.5622	+	23.4904i	−0.467384	+	0.809532i
$843$	24.5885	+	14.1962i	0.846871	+	0.488941i
$844$	−13.5885			−0.467734
$845$		0			0
$846$	−13.3923			−0.460437
$847$	−5.19615	−	3.00000i	−0.178542	−	0.103081i
$848$	−3.23205	+	5.59808i	−0.110989	+	0.192239i
$849$	−41.5167	−	71.9090i	−1.42485	−	2.46791i
$850$		0			0
$851$	−24.5885	+	14.1962i	−0.842881	+	0.486638i
$852$	−14.1962	+	8.19615i	−0.486352	+	0.280796i
$853$		−	13.8564i		−	0.474434i	−0.971457	−	0.237217i	$-0.923765\pi$
$853$		−	13.8564i		−	0.474434i	0.971457	−	0.237217i	$-0.0762353\pi$
$854$	−6.29423	−	10.9019i	−0.215384	−	0.373056i
$855$		0			0
$856$	−0.294229	−	0.169873i	−0.0100565	−	0.00580614i
$857$	13.2679			0.453225			0.226612	−	0.973985i	$-0.427235\pi$
$857$	13.2679			0.453225			0.226612	+	0.973985i	$0.427235\pi$
$858$	28.6865	−	7.09808i	0.979342	−	0.242324i
$859$	52.3731			1.78695			0.893473	−	0.449117i	$-0.148261\pi$
$859$	52.3731			1.78695			0.893473	+	0.449117i	$0.148261\pi$
$860$		0			0
$861$	42.5885	−	73.7654i	1.45141	−	2.51392i
$862$	1.09808	+	1.90192i	0.0374006	+	0.0647798i
$863$		−	19.1769i		−	0.652790i	−0.945234	−	0.326395i	$-0.894166\pi$
$863$		−	19.1769i		−	0.652790i	0.945234	−	0.326395i	$-0.105834\pi$
$864$	3.46410	−	2.00000i	0.117851	−	0.0680414i
$865$		0			0
$866$			12.3923i			0.421108i
$867$	16.6340	+	28.8109i	0.564919	+	0.978469i
$868$	1.90192	−	3.29423i	0.0645555	−	0.111813i
$869$	−16.0981	−	9.29423i	−0.546090	−	0.315285i
$870$		0			0
$871$		0			0
$872$	15.4641			0.523681
$873$	58.4711	+	33.7583i	1.97895	+	1.14255i
$874$	8.19615	−	14.1962i	0.277239	−	0.480192i
$875$		0			0
$876$			15.4641i			0.522484i
$877$	−17.7846	+	10.2679i	−0.600544	+	0.346724i	−0.769255	−	0.638941i	$-0.779373\pi$
$877$	−17.7846	+	10.2679i	−0.600544	+	0.346724i	0.168712	+	0.985665i	$0.446039\pi$
$878$	−29.9545	+	17.2942i	−1.01091	+	0.583652i
$879$			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	$0.121904\pi$
$882$	7.73205	+	4.46410i	0.260352	+	0.150314i
$883$	26.5885			0.894773			0.447386	−	0.894341i	$-0.352355\pi$
$883$	26.5885			0.894773			0.447386	+	0.894341i	$0.352355\pi$
$884$	−2.19615	+	7.60770i	−0.0738646	+	0.255874i
$885$		0			0
$886$	−1.39230	−	0.803848i	−0.0467754	−	0.0270058i
$887$	26.3827	−	45.6962i	0.885844	−	1.53433i	0.0411005	−	0.999155i	$-0.486914\pi$
$887$	26.3827	−	45.6962i	0.885844	−	1.53433i	0.844743	−	0.535172i	$-0.179753\pi$
$888$	−15.2942	−	26.4904i	−0.513241	−	0.888959i
$889$		−	63.5885i		−	2.13269i
$890$		0			0
$891$	−6.40192	+	3.69615i	−0.214473	+	0.123826i
$892$			0.464102i			0.0155393i
$893$	−9.69615	−	16.7942i	−0.324469	−	0.561997i
$894$	−8.19615	+	14.1962i	−0.274120	+	0.474790i
$895$		0			0
$896$	3.00000			0.100223
$897$	−17.3205	−	18.0000i	−0.578315	−	0.601003i
$898$	−15.5885			−0.520194
$899$	−10.3923	−	6.00000i	−0.346603	−	0.200111i
$900$		0			0
$901$	−7.09808	−	12.2942i	−0.236471	−	0.409580i
$902$		−	31.1769i		−	1.03808i
$903$	−14.1962	+	8.19615i	−0.472418	+	0.272751i
$904$	−6.00000	+	3.46410i	−0.199557	+	0.115214i
$905$		0			0
$906$	8.66025	+	15.0000i	0.287718	+	0.498342i
$907$	−13.2942	+	23.0263i	−0.441428	+	0.764575i	−0.997796	−	0.0663609i	$-0.978861\pi$
$907$	−13.2942	+	23.0263i	−0.441428	+	0.764575i	0.556368	+	0.830936i	$0.312194\pi$
$908$	−3.80385	−	2.19615i	−0.126235	−	0.0728819i
$909$	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	$0.577409\pi$
$912$	15.2942	+	8.83013i	0.506443	+	0.292395i
$913$	3.29423	−	5.70577i	0.109023	−	0.188833i
$914$	−17.8301	−	30.8827i	−0.589768	−	1.02151i
$915$		0			0
$916$	−4.09808	+	2.36603i	−0.135404	+	0.0781757i
$917$	−47.0885	+	27.1865i	−1.55500	+	0.897778i
$918$			8.78461i			0.289935i
$919$	5.39230	+	9.33975i	0.177876	+	0.308090i	0.941153	−	0.337982i	$-0.109744\pi$
$919$	5.39230	+	9.33975i	0.177876	+	0.308090i	−0.763277	+	0.646071i	$0.776411\pi$
$920$		0			0
$921$	48.5885	+	28.0526i	1.60104	+	0.924363i
$922$	0.588457			0.0193798
$923$	−15.5885	+	15.0000i	−0.513100	+	0.493731i
$924$	24.5885			0.808901
$925$		0			0
$926$	−0.464102	+	0.803848i	−0.0152513	+	0.0264161i
$927$	2.66987	+	4.62436i	0.0876901	+	0.151884i
$928$		−	9.46410i		−	0.310674i
$929$	38.7846	−	22.3923i	1.27248	−	0.734668i	0.297027	−	0.954869i	$-0.404005\pi$
$929$	38.7846	−	22.3923i	1.27248	−	0.734668i	0.975454	+	0.220201i	$0.0706714\pi$
$930$		0			0
$931$			12.9282i			0.423705i
$932$	−0.633975	−	1.09808i	−0.0207665	−	0.0359687i
$933$	−20.6603	+	35.7846i	−0.676386	+	1.17154i
$934$	−8.78461	−	5.07180i	−0.287441	−	0.165954i
$935$		0			0
$936$	11.5981	−	11.1603i	0.379095	−	0.364784i
$937$	30.3923			0.992873			0.496437	−	0.868073i	$-0.334641\pi$
$937$	30.3923			0.992873			0.496437	+	0.868073i	$0.334641\pi$
$938$		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	$-0.260465\pi$
$942$	30.7583	−	17.7583i	1.00216	−	0.578598i
$943$	−22.8231	+	13.1769i	−0.743222	+	0.429099i
$944$			10.3923i			0.338241i
$945$		0			0
$946$	−3.00000	+	5.19615i	−0.0975384	+	0.168941i
$947$	−49.6865	−	28.6865i	−1.61460	−	0.932187i	−0.988286	−	0.152612i	$-0.951231\pi$
$947$	−49.6865	−	28.6865i	−1.61460	−	0.932187i	−0.626309	−	0.779575i	$-0.715435\pi$
$948$	−16.9282			−0.549802
$949$	4.90192	+	19.8109i	0.159123	+	0.643089i
$950$		0			0
$951$	30.2942	+	17.4904i	0.982358	+	0.567164i
$952$	−3.29423	+	5.70577i	−0.106767	+	0.184925i
$953$	12.2942	+	21.2942i	0.398249	+	0.689788i	0.993510	−	0.113745i	$-0.0362846\pi$
$953$	12.2942	+	21.2942i	0.398249	+	0.689788i	−0.595261	+	0.803533i	$0.702951\pi$
$954$			28.8564i			0.934261i
$955$		0			0
$956$	−7.09808	+	4.09808i	−0.229568	+	0.132541i
$957$		−	77.5692i		−	2.50746i
$958$	5.49038	+	9.50962i	0.177386	+	0.307242i
$959$	−12.2942	+	21.2942i	−0.397001	+	0.687627i
$960$		0			0
$961$	29.3923			0.948139
$962$	−27.9904	−	29.0885i	−0.902446	−	0.937850i
$963$	−1.51666			−0.0488737
$964$	−7.50000	−	4.33013i	−0.241559	−	0.139464i
$965$		0			0
$966$	−10.3923	−	18.0000i	−0.334367	−	0.579141i
$967$			38.5692i			1.24030i	0.784482	+	0.620151i	$0.212929\pi$
$967$			38.5692i			1.24030i	−0.784482	+	0.620151i	$0.787071\pi$
$968$	−1.73205	+	1.00000i	−0.0556702	+	0.0321412i
$969$	−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	$0.563201\pi$
$972$	−9.36603	+	16.2224i	−0.300415	+	0.520335i
$973$	23.8923	+	13.7942i	0.765952	+	0.442223i
$974$	−33.2487			−1.06536
$975$		0			0
$976$	−4.19615			−0.134316
$977$	−3.80385	−	2.19615i	−0.121696	−	0.0702611i	0.437916	−	0.899016i	$-0.355717\pi$
$977$	−3.80385	−	2.19615i	−0.121696	−	0.0702611i	−0.559612	+	0.828755i	$0.689050\pi$
$978$	−9.92820	+	17.1962i	−0.317469	+	0.549872i
$979$	25.7942	+	44.6769i	0.824387	+	1.42788i
$980$		0			0
$981$	59.7846	−	34.5167i	1.90878	−	1.10203i
$982$	2.89230	−	1.66987i	0.0922972	−	0.0532878i
$983$		−	38.5692i		−	1.23017i	−0.788462	−	0.615084i	$-0.789122\pi$
$983$		−	38.5692i		−	1.23017i	0.788462	−	0.615084i	$-0.210878\pi$
$984$	−14.1962	−	24.5885i	−0.452557	−	0.783851i
$985$		0			0
$986$	18.0000	+	10.3923i	0.573237	+	0.330958i
$987$	−24.5885			−0.782659
$988$	22.3923	+	6.46410i	0.712394	+	0.205650i
$989$	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	$0.864585\pi$
$992$	−0.633975	−	1.09808i	−0.0201287	−	0.0348640i
$993$			2.53590i			0.0804743i
$994$	−15.5885	+	9.00000i	−0.494436	+	0.285463i
$995$		0			0
$996$		−	6.00000i		−	0.190117i
$997$	−21.2846	−	36.8660i	−0.674090	−	1.16756i	−0.976734	−	0.214455i	$-0.931202\pi$
$997$	−21.2846	−	36.8660i	−0.674090	−	1.16756i	0.302644	−	0.953104i	$-0.402131\pi$
$998$	0.928203	−	1.60770i	0.0293818	−	0.0508907i
$999$	−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.m.a.251.1		4
5.2	odd	4		650.2.n.b.199.2		4
5.3	odd	4		650.2.n.a.199.1		4
5.4	even	2		130.2.l.a.121.2	yes	4
13.6	odd	12		8450.2.a.bm.1.2		2
13.7	odd	12		8450.2.a.bf.1.2		2
13.10	even	6	inner	650.2.m.a.101.1		4
15.14	odd	2		1170.2.bs.c.901.1		4
20.19	odd	2		1040.2.da.a.641.1		4
65.4	even	6		1690.2.d.f.1351.3		4
65.9	even	6		1690.2.d.f.1351.1		4
65.19	odd	12		1690.2.a.j.1.1		2
65.23	odd	12		650.2.n.b.49.2		4
65.24	odd	12		1690.2.e.l.991.2		4
65.29	even	6		1690.2.l.g.361.1		4
65.34	odd	4		1690.2.e.l.191.2		4
65.44	odd	4		1690.2.e.n.191.2		4
65.49	even	6		130.2.l.a.101.2	✓	4
65.54	odd	12		1690.2.e.n.991.2		4
65.59	odd	12		1690.2.a.m.1.1		2
65.62	odd	12		650.2.n.a.49.1		4
65.64	even	2		1690.2.l.g.1161.1		4
195.179	odd	6		1170.2.bs.c.361.1		4
260.179	odd	6		1040.2.da.a.881.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.l.a.101.2	✓	4	65.49	even	6
130.2.l.a.121.2	yes	4	5.4	even	2
650.2.m.a.101.1		4	13.10	even	6	inner
650.2.m.a.251.1		4	1.1	even	1	trivial
650.2.n.a.49.1		4	65.62	odd	12
650.2.n.a.199.1		4	5.3	odd	4
650.2.n.b.49.2		4	65.23	odd	12
650.2.n.b.199.2		4	5.2	odd	4
1040.2.da.a.641.1		4	20.19	odd	2
1040.2.da.a.881.1		4	260.179	odd	6
1170.2.bs.c.361.1		4	195.179	odd	6
1170.2.bs.c.901.1		4	15.14	odd	2
1690.2.a.j.1.1		2	65.19	odd	12
1690.2.a.m.1.1		2	65.59	odd	12
1690.2.d.f.1351.1		4	65.9	even	6
1690.2.d.f.1351.3		4	65.4	even	6
1690.2.e.l.191.2		4	65.34	odd	4
1690.2.e.l.991.2		4	65.24	odd	12
1690.2.e.n.191.2		4	65.44	odd	4
1690.2.e.n.991.2		4	65.54	odd	12
1690.2.l.g.361.1		4	65.29	even	6
1690.2.l.g.1161.1		4	65.64	even	2
8450.2.a.bf.1.2		2	13.7	odd	12
8450.2.a.bm.1.2		2	13.6	odd	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.m (of order \(6\), degree \(2\), minimal)

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

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