LMFDB - Embedded newform 1950.2.i.m.601.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(451,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1950.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			601.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1950.601
Dual form			1950.2.i.m.451.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(1.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-3.00000 - 5.19615i) q^{11} -1.00000 q^{12} +(3.50000 - 0.866025i) q^{13} -2.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +1.00000 q^{18} +(-1.00000 + 1.73205i) q^{19} +2.00000 q^{21} +(-3.00000 + 5.19615i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-2.50000 - 2.59808i) q^{26} -1.00000 q^{27} +(1.00000 + 1.73205i) q^{28} +(-1.50000 - 2.59808i) q^{29} -4.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.00000 - 5.19615i) q^{33} +3.00000 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-3.50000 - 6.06218i) q^{37} +2.00000 q^{38} +(2.50000 + 2.59808i) q^{39} +(1.50000 + 2.59808i) q^{41} +(-1.00000 - 1.73205i) q^{42} +(-5.00000 + 8.66025i) q^{43} +6.00000 q^{44} +(-3.00000 + 5.19615i) q^{46} -6.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} -3.00000 q^{51} +(-1.00000 + 3.46410i) q^{52} -3.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(1.00000 - 1.73205i) q^{56} -2.00000 q^{57} +(-1.50000 + 2.59808i) q^{58} +(3.50000 - 6.06218i) q^{61} +(2.00000 + 3.46410i) q^{62} +(1.00000 + 1.73205i) q^{63} +1.00000 q^{64} -6.00000 q^{66} +(-5.00000 - 8.66025i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(3.00000 - 5.19615i) q^{69} +(-3.00000 + 5.19615i) q^{71} +(-0.500000 + 0.866025i) q^{72} +13.0000 q^{73} +(-3.50000 + 6.06218i) q^{74} +(-1.00000 - 1.73205i) q^{76} -12.0000 q^{77} +(1.00000 - 3.46410i) q^{78} -4.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(1.50000 - 2.59808i) q^{82} +6.00000 q^{83} +(-1.00000 + 1.73205i) q^{84} +10.0000 q^{86} +(1.50000 - 2.59808i) q^{87} +(-3.00000 - 5.19615i) q^{88} +(-9.00000 - 15.5885i) q^{89} +(2.00000 - 6.92820i) q^{91} +6.00000 q^{92} +(-2.00000 - 3.46410i) q^{93} +(3.00000 + 5.19615i) q^{94} -1.00000 q^{96} +(7.00000 - 12.1244i) q^{97} +(1.50000 - 2.59808i) q^{98} +6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{3} - q^{4} + q^{6} + 2 q^{7} + 2 q^{8} - q^{9} - 6 q^{11} - 2 q^{12} + 7 q^{13} - 4 q^{14} - q^{16} - 3 q^{17} + 2 q^{18} - 2 q^{19} + 4 q^{21} - 6 q^{22} - 6 q^{23} + q^{24} - 5 q^{26}+ \cdots + 12 q^{99}+O(q^{100}) $ 2 * q - q^2 + q^3 - q^4 + q^6 + 2 * q^7 + 2 * q^8 - q^9 - 6 * q^11 - 2 * q^12 + 7 * q^13 - 4 * q^14 - q^16 - 3 * q^17 + 2 * q^18 - 2 * q^19 + 4 * q^21 - 6 * q^22 - 6 * q^23 + q^24 - 5 * q^26 - 2 * q^27 + 2 * q^28 - 3 * q^29 - 8 * q^31 - q^32 + 6 * q^33 + 6 * q^34 - q^36 - 7 * q^37 + 4 * q^38 + 5 * q^39 + 3 * q^41 - 2 * q^42 - 10 * q^43 + 12 * q^44 - 6 * q^46 - 12 * q^47 + q^48 + 3 * q^49 - 6 * q^51 - 2 * q^52 - 6 * q^53 + q^54 + 2 * q^56 - 4 * q^57 - 3 * q^58 + 7 * q^61 + 4 * q^62 + 2 * q^63 + 2 * q^64 - 12 * q^66 - 10 * q^67 - 3 * q^68 + 6 * q^69 - 6 * q^71 - q^72 + 26 * q^73 - 7 * q^74 - 2 * q^76 - 24 * q^77 + 2 * q^78 - 8 * q^79 - q^81 + 3 * q^82 + 12 * q^83 - 2 * q^84 + 20 * q^86 + 3 * q^87 - 6 * q^88 - 18 * q^89 + 4 * q^91 + 12 * q^92 - 4 * q^93 + 6 * q^94 - 2 * q^96 + 14 * q^97 + 3 * q^98 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	−0.612801	−	0.790237i	$-0.709957\pi$
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	0.990766	+	0.135583i	$0.0432908\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−3.00000	−	5.19615i	−0.904534	−	1.56670i	−0.821541	−	0.570149i	$-0.806886\pi$
$11$	−3.00000	−	5.19615i	−0.904534	−	1.56670i	−0.0829925	−	0.996550i	$-0.526448\pi$
$12$	−1.00000			−0.288675
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$14$	−2.00000			−0.534522
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$	1.00000			0.235702
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$		0			0
$21$	2.00000			0.436436
$22$	−3.00000	+	5.19615i	−0.639602	+	1.10782i
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$		0			0
$26$	−2.50000	−	2.59808i	−0.490290	−	0.509525i
$27$	−1.00000			−0.192450
$28$	1.00000	+	1.73205i	0.188982	+	0.327327i
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	3.00000	−	5.19615i	0.522233	−	0.904534i
$34$	3.00000			0.514496
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	−0.995998	−	0.0893706i	$-0.971514\pi$
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	0.420602	−	0.907245i	$-0.361819\pi$
$38$	2.00000			0.324443
$39$	2.50000	+	2.59808i	0.400320	+	0.416025i
$40$		0			0
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	0.959058	−	0.283211i	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$	−1.00000	−	1.73205i	−0.154303	−	0.267261i
$43$	−5.00000	+	8.66025i	−0.762493	+	1.32068i	0.179069	+	0.983836i	$0.442691\pi$
$43$	−5.00000	+	8.66025i	−0.762493	+	1.32068i	−0.941562	+	0.336840i	$0.890642\pi$
$44$	6.00000			0.904534
$45$		0			0
$46$	−3.00000	+	5.19615i	−0.442326	+	0.766131i
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$		0			0
$51$	−3.00000			−0.420084
$52$	−1.00000	+	3.46410i	−0.138675	+	0.480384i
$53$	−3.00000			−0.412082			−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000			−0.412082			−0.206041	+	0.978543i	$0.566058\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$		0			0
$56$	1.00000	−	1.73205i	0.133631	−	0.231455i
$57$	−2.00000			−0.264906
$58$	−1.50000	+	2.59808i	−0.196960	+	0.341144i
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	−0.550135	−	0.835076i	$-0.685424\pi$
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	0.998264	+	0.0588933i	$0.0187572\pi$
$62$	2.00000	+	3.46410i	0.254000	+	0.439941i
$63$	1.00000	+	1.73205i	0.125988	+	0.218218i
$64$	1.00000			0.125000
$65$		0			0
$66$	−6.00000			−0.738549
$67$	−5.00000	−	8.66025i	−0.610847	−	1.05802i	−0.991098	−	0.133135i	$-0.957496\pi$
$67$	−5.00000	−	8.66025i	−0.610847	−	1.05802i	0.380251	−	0.924883i	$-0.375838\pi$
$68$	−1.50000	−	2.59808i	−0.181902	−	0.315063i
$69$	3.00000	−	5.19615i	0.361158	−	0.625543i
$70$		0			0
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	13.0000			1.52153			0.760767	−	0.649025i	$-0.224823\pi$
$73$	13.0000			1.52153			0.760767	+	0.649025i	$0.224823\pi$
$74$	−3.50000	+	6.06218i	−0.406867	+	0.704714i
$75$		0			0
$76$	−1.00000	−	1.73205i	−0.114708	−	0.198680i
$77$	−12.0000			−1.36753
$78$	1.00000	−	3.46410i	0.113228	−	0.392232i
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.50000	−	2.59808i	0.165647	−	0.286910i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$	−1.00000	+	1.73205i	−0.109109	+	0.188982i
$85$		0			0
$86$	10.0000			1.07833
$87$	1.50000	−	2.59808i	0.160817	−	0.278543i
$88$	−3.00000	−	5.19615i	−0.319801	−	0.553912i
$89$	−9.00000	−	15.5885i	−0.953998	−	1.65237i	−0.736644	−	0.676280i	$-0.763591\pi$
$89$	−9.00000	−	15.5885i	−0.953998	−	1.65237i	−0.217354	−	0.976093i	$-0.569742\pi$
$90$		0			0
$91$	2.00000	−	6.92820i	0.209657	−	0.726273i
$92$	6.00000			0.625543
$93$	−2.00000	−	3.46410i	−0.207390	−	0.359211i
$94$	3.00000	+	5.19615i	0.309426	+	0.535942i
$95$		0			0
$96$	−1.00000			−0.102062
$97$	7.00000	−	12.1244i	0.710742	−	1.23104i	−0.253837	−	0.967247i	$-0.581693\pi$
$97$	7.00000	−	12.1244i	0.710742	−	1.23104i	0.964579	−	0.263795i	$-0.0849741\pi$
$98$	1.50000	−	2.59808i	0.151523	−	0.262445i
$99$	6.00000			0.603023
$100$		0			0
$101$	−7.50000	−	12.9904i	−0.746278	−	1.29259i	−0.949595	−	0.313478i	$-0.898506\pi$
$101$	−7.50000	−	12.9904i	−0.746278	−	1.29259i	0.203317	−	0.979113i	$-0.434828\pi$
$102$	1.50000	+	2.59808i	0.148522	+	0.257248i
$103$	−14.0000			−1.37946			−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000			−1.37946			−0.689730	+	0.724066i	$0.742271\pi$
$104$	3.50000	−	0.866025i	0.343203	−	0.0849208i
$105$		0			0
$106$	1.50000	+	2.59808i	0.145693	+	0.252347i
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	0.683793	−	0.729676i	$-0.260329\pi$
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	−0.973814	+	0.227345i	$0.926996\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	14.0000			1.34096			0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000			1.34096			0.670478	+	0.741929i	$0.266089\pi$
$110$		0			0
$111$	3.50000	−	6.06218i	0.332205	−	0.575396i
$112$	−2.00000			−0.188982
$113$	−1.50000	+	2.59808i	−0.141108	+	0.244406i	−0.927914	−	0.372794i	$-0.878400\pi$
$113$	−1.50000	+	2.59808i	−0.141108	+	0.244406i	0.786806	+	0.617200i	$0.211733\pi$
$114$	1.00000	+	1.73205i	0.0936586	+	0.162221i
$115$		0			0
$116$	3.00000			0.278543
$117$	−1.00000	+	3.46410i	−0.0924500	+	0.320256i
$118$		0			0
$119$	3.00000	+	5.19615i	0.275010	+	0.476331i
$120$		0			0
$121$	−12.5000	+	21.6506i	−1.13636	+	1.96824i
$122$	−7.00000			−0.633750
$123$	−1.50000	+	2.59808i	−0.135250	+	0.234261i
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$		0			0
$126$	1.00000	−	1.73205i	0.0890871	−	0.154303i
$127$	−2.00000	−	3.46410i	−0.177471	−	0.307389i	0.763542	−	0.645758i	$-0.223458\pi$
$127$	−2.00000	−	3.46410i	−0.177471	−	0.307389i	−0.941014	+	0.338368i	$0.890125\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−10.0000			−0.880451
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	3.00000	+	5.19615i	0.261116	+	0.452267i
$133$	2.00000	+	3.46410i	0.173422	+	0.300376i
$134$	−5.00000	+	8.66025i	−0.431934	+	0.748132i
$135$		0			0
$136$	−1.50000	+	2.59808i	−0.128624	+	0.222783i
$137$	4.50000	−	7.79423i	0.384461	−	0.665906i	−0.607233	−	0.794524i	$-0.707721\pi$
$137$	4.50000	−	7.79423i	0.384461	−	0.665906i	0.991694	+	0.128618i	$0.0410540\pi$
$138$	−6.00000			−0.510754
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	−0.768655	−	0.639664i	$-0.779074\pi$
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	0.938293	+	0.345843i	$0.112407\pi$
$140$		0			0
$141$	−3.00000	−	5.19615i	−0.252646	−	0.437595i
$142$	6.00000			0.503509
$143$	−15.0000	−	15.5885i	−1.25436	−	1.30357i
$144$	1.00000			0.0833333
$145$		0			0
$146$	−6.50000	−	11.2583i	−0.537944	−	0.931746i
$147$	−1.50000	+	2.59808i	−0.123718	+	0.214286i
$148$	7.00000			0.575396
$149$	4.50000	−	7.79423i	0.368654	−	0.638528i	−0.620701	−	0.784047i	$-0.713152\pi$
$149$	4.50000	−	7.79423i	0.368654	−	0.638528i	0.989355	+	0.145519i	$0.0464853\pi$
$150$		0			0
$151$	−10.0000			−0.813788			−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000			−0.813788			−0.406894	+	0.913475i	$0.633388\pi$
$152$	−1.00000	+	1.73205i	−0.0811107	+	0.140488i
$153$	−1.50000	−	2.59808i	−0.121268	−	0.210042i
$154$	6.00000	+	10.3923i	0.483494	+	0.837436i
$155$		0			0
$156$	−3.50000	+	0.866025i	−0.280224	+	0.0693375i
$157$	−5.00000			−0.399043			−0.199522	−	0.979893i	$-0.563939\pi$
$157$	−5.00000			−0.399043			−0.199522	+	0.979893i	$0.563939\pi$
$158$	2.00000	+	3.46410i	0.159111	+	0.275589i
$159$	−1.50000	−	2.59808i	−0.118958	−	0.206041i
$160$		0			0
$161$	−12.0000			−0.945732
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	−0.933659	−	0.358162i	$-0.883403\pi$
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	0.777007	+	0.629492i	$0.216737\pi$
$164$	−3.00000			−0.234261
$165$		0			0
$166$	−3.00000	−	5.19615i	−0.232845	−	0.403300i
$167$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$167$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$168$	2.00000			0.154303
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$		0			0
$171$	−1.00000	−	1.73205i	−0.0764719	−	0.132453i
$172$	−5.00000	−	8.66025i	−0.381246	−	0.660338i
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$	−3.00000			−0.227429
$175$		0			0
$176$	−3.00000	+	5.19615i	−0.226134	+	0.391675i
$177$		0			0
$178$	−9.00000	+	15.5885i	−0.674579	+	1.16840i
$179$	−3.00000	−	5.19615i	−0.224231	−	0.388379i	0.731858	−	0.681457i	$-0.238654\pi$
$179$	−3.00000	−	5.19615i	−0.224231	−	0.388379i	−0.956088	+	0.293079i	$0.905320\pi$
$180$		0			0
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$	−7.00000	+	1.73205i	−0.518875	+	0.128388i
$183$	7.00000			0.517455
$184$	−3.00000	−	5.19615i	−0.221163	−	0.383065i
$185$		0			0
$186$	−2.00000	+	3.46410i	−0.146647	+	0.254000i
$187$	18.0000			1.31629
$188$	3.00000	−	5.19615i	0.218797	−	0.378968i
$189$	−1.00000	+	1.73205i	−0.0727393	+	0.125988i
$190$		0			0
$191$	6.00000	−	10.3923i	0.434145	−	0.751961i	−0.563081	−	0.826402i	$-0.690384\pi$
$191$	6.00000	−	10.3923i	0.434145	−	0.751961i	0.997225	+	0.0744412i	$0.0237173\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	11.5000	+	19.9186i	0.827788	+	1.43377i	0.899770	+	0.436365i	$0.143734\pi$
$193$	11.5000	+	19.9186i	0.827788	+	1.43377i	−0.0719816	+	0.997406i	$0.522932\pi$
$194$	−14.0000			−1.00514
$195$		0			0
$196$	−3.00000			−0.214286
$197$	3.00000	+	5.19615i	0.213741	+	0.370211i	0.952882	−	0.303340i	$-0.0981018\pi$
$197$	3.00000	+	5.19615i	0.213741	+	0.370211i	−0.739141	+	0.673550i	$0.764768\pi$
$198$	−3.00000	−	5.19615i	−0.213201	−	0.369274i
$199$	5.00000	−	8.66025i	0.354441	−	0.613909i	−0.632581	−	0.774494i	$-0.718005\pi$
$199$	5.00000	−	8.66025i	0.354441	−	0.613909i	0.987022	+	0.160585i	$0.0513380\pi$
$200$		0			0
$201$	5.00000	−	8.66025i	0.352673	−	0.610847i
$202$	−7.50000	+	12.9904i	−0.527698	+	0.914000i
$203$	−6.00000			−0.421117
$204$	1.50000	−	2.59808i	0.105021	−	0.181902i
$205$		0			0
$206$	7.00000	+	12.1244i	0.487713	+	0.844744i
$207$	6.00000			0.417029
$208$	−2.50000	−	2.59808i	−0.173344	−	0.180144i
$209$	12.0000			0.830057
$210$		0			0
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	0.998221	+	0.0596196i	$0.0189888\pi$
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	−0.447478	+	0.894295i	$0.647678\pi$
$212$	1.50000	−	2.59808i	0.103020	−	0.178437i
$213$	−6.00000			−0.411113
$214$	−3.00000	+	5.19615i	−0.205076	+	0.355202i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$	−4.00000	+	6.92820i	−0.271538	+	0.470317i
$218$	−7.00000	−	12.1244i	−0.474100	−	0.821165i
$219$	6.50000	+	11.2583i	0.439229	+	0.760767i
$220$		0			0
$221$	−3.00000	+	10.3923i	−0.201802	+	0.699062i
$222$	−7.00000			−0.469809
$223$	4.00000	+	6.92820i	0.267860	+	0.463947i	0.968309	−	0.249756i	$-0.0803503\pi$
$223$	4.00000	+	6.92820i	0.267860	+	0.463947i	−0.700449	+	0.713702i	$0.747017\pi$
$224$	1.00000	+	1.73205i	0.0668153	+	0.115728i
$225$		0			0
$226$	3.00000			0.199557
$227$	9.00000	−	15.5885i	0.597351	−	1.03464i	−0.395860	−	0.918311i	$-0.629553\pi$
$227$	9.00000	−	15.5885i	0.597351	−	1.03464i	0.993210	−	0.116331i	$-0.0371134\pi$
$228$	1.00000	−	1.73205i	0.0662266	−	0.114708i
$229$	−22.0000			−1.45380			−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000			−1.45380			−0.726900	+	0.686743i	$0.759040\pi$
$230$		0			0
$231$	−6.00000	−	10.3923i	−0.394771	−	0.683763i
$232$	−1.50000	−	2.59808i	−0.0984798	−	0.170572i
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$	3.50000	−	0.866025i	0.228802	−	0.0566139i
$235$		0			0
$236$		0			0
$237$	−2.00000	−	3.46410i	−0.129914	−	0.225018i
$238$	3.00000	−	5.19615i	0.194461	−	0.336817i
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$		0			0
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	−0.849472	−	0.527633i	$-0.823079\pi$
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	0.881680	+	0.471848i	$0.156413\pi$
$242$	25.0000			1.60706
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	3.50000	+	6.06218i	0.224065	+	0.388091i
$245$		0			0
$246$	3.00000			0.191273
$247$	−2.00000	+	6.92820i	−0.127257	+	0.440831i
$248$	−4.00000			−0.254000
$249$	3.00000	+	5.19615i	0.190117	+	0.329293i
$250$		0			0
$251$	6.00000	−	10.3923i	0.378717	−	0.655956i	−0.612159	−	0.790735i	$-0.709699\pi$
$251$	6.00000	−	10.3923i	0.378717	−	0.655956i	0.990876	+	0.134778i	$0.0430322\pi$
$252$	−2.00000			−0.125988
$253$	−18.0000	+	31.1769i	−1.13165	+	1.96008i
$254$	−2.00000	+	3.46410i	−0.125491	+	0.217357i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.50000	−	2.59808i	−0.0935674	−	0.162064i	0.815442	−	0.578838i	$-0.196494\pi$
$257$	−1.50000	−	2.59808i	−0.0935674	−	0.162064i	−0.909010	+	0.416775i	$0.863160\pi$
$258$	5.00000	+	8.66025i	0.311286	+	0.539164i
$259$	−14.0000			−0.869918
$260$		0			0
$261$	3.00000			0.185695
$262$		0			0
$263$	−3.00000	−	5.19615i	−0.184988	−	0.320408i	0.758585	−	0.651575i	$-0.225891\pi$
$263$	−3.00000	−	5.19615i	−0.184988	−	0.320408i	−0.943572	+	0.331166i	$0.892558\pi$
$264$	3.00000	−	5.19615i	0.184637	−	0.319801i
$265$		0			0
$266$	2.00000	−	3.46410i	0.122628	−	0.212398i
$267$	9.00000	−	15.5885i	0.550791	−	0.953998i
$268$	10.0000			0.610847
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	0.449622	+	0.893219i	$0.351559\pi$
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	−0.998361	+	0.0572259i	$0.981774\pi$
$270$		0			0
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	0.999870	−	0.0161307i	$-0.00513477\pi$
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	−0.513905	+	0.857847i	$0.671801\pi$
$272$	3.00000			0.181902
$273$	7.00000	−	1.73205i	0.423659	−	0.104828i
$274$	−9.00000			−0.543710
$275$		0			0
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	8.50000	−	14.7224i	0.510716	−	0.884585i	−0.489207	−	0.872167i	$-0.662714\pi$
$277$	8.50000	−	14.7224i	0.510716	−	0.884585i	0.999923	−	0.0124177i	$-0.00395278\pi$
$278$	−4.00000			−0.239904
$279$	2.00000	−	3.46410i	0.119737	−	0.207390i
$280$		0			0
$281$	9.00000			0.536895			0.268447	−	0.963294i	$-0.413489\pi$
$281$	9.00000			0.536895			0.268447	+	0.963294i	$0.413489\pi$
$282$	−3.00000	+	5.19615i	−0.178647	+	0.309426i
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	0.995544	−	0.0942988i	$-0.0300609\pi$
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	−0.579437	+	0.815017i	$0.696728\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$		0			0
$286$	−6.00000	+	20.7846i	−0.354787	+	1.22902i
$287$	6.00000			0.354169
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	14.0000			0.820695
$292$	−6.50000	+	11.2583i	−0.380384	+	0.658844i
$293$	−10.5000	+	18.1865i	−0.613417	+	1.06247i	0.377244	+	0.926114i	$0.376872\pi$
$293$	−10.5000	+	18.1865i	−0.613417	+	1.06247i	−0.990660	+	0.136355i	$0.956461\pi$
$294$	3.00000			0.174964
$295$		0			0
$296$	−3.50000	−	6.06218i	−0.203433	−	0.352357i
$297$	3.00000	+	5.19615i	0.174078	+	0.301511i
$298$	−9.00000			−0.521356
$299$	−15.0000	−	15.5885i	−0.867472	−	0.901504i
$300$		0			0
$301$	10.0000	+	17.3205i	0.576390	+	0.998337i
$302$	5.00000	+	8.66025i	0.287718	+	0.498342i
$303$	7.50000	−	12.9904i	0.430864	−	0.746278i
$304$	2.00000			0.114708
$305$		0			0
$306$	−1.50000	+	2.59808i	−0.0857493	+	0.148522i
$307$	10.0000			0.570730			0.285365	−	0.958419i	$-0.407885\pi$
$307$	10.0000			0.570730			0.285365	+	0.958419i	$0.407885\pi$
$308$	6.00000	−	10.3923i	0.341882	−	0.592157i
$309$	−7.00000	−	12.1244i	−0.398216	−	0.689730i
$310$		0			0
$311$	−30.0000			−1.70114			−0.850572	−	0.525859i	$-0.823744\pi$
$311$	−30.0000			−1.70114			−0.850572	+	0.525859i	$0.823744\pi$
$312$	2.50000	+	2.59808i	0.141535	+	0.147087i
$313$	10.0000			0.565233			0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000			0.565233			0.282617	+	0.959233i	$0.408798\pi$
$314$	2.50000	+	4.33013i	0.141083	+	0.244363i
$315$		0			0
$316$	2.00000	−	3.46410i	0.112509	−	0.194871i
$317$	−3.00000			−0.168497			−0.0842484	−	0.996445i	$-0.526849\pi$
$317$	−3.00000			−0.168497			−0.0842484	+	0.996445i	$0.526849\pi$
$318$	−1.50000	+	2.59808i	−0.0841158	+	0.145693i
$319$	−9.00000	+	15.5885i	−0.503903	+	0.872786i
$320$		0			0
$321$	3.00000	−	5.19615i	0.167444	−	0.290021i
$322$	6.00000	+	10.3923i	0.334367	+	0.579141i
$323$	−3.00000	−	5.19615i	−0.166924	−	0.289122i
$324$	1.00000			0.0555556
$325$		0			0
$326$	4.00000			0.221540
$327$	7.00000	+	12.1244i	0.387101	+	0.670478i
$328$	1.50000	+	2.59808i	0.0828236	+	0.143455i
$329$	−6.00000	+	10.3923i	−0.330791	+	0.572946i
$330$		0			0
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$	−3.00000	+	5.19615i	−0.164646	+	0.285176i
$333$	7.00000			0.383598
$334$		0			0
$335$		0			0
$336$	−1.00000	−	1.73205i	−0.0545545	−	0.0944911i
$337$	−23.0000			−1.25289			−0.626445	−	0.779466i	$-0.715491\pi$
$337$	−23.0000			−1.25289			−0.626445	+	0.779466i	$0.715491\pi$
$338$	−11.0000	−	6.92820i	−0.598321	−	0.376845i
$339$	−3.00000			−0.162938
$340$		0			0
$341$	12.0000	+	20.7846i	0.649836	+	1.12555i
$342$	−1.00000	+	1.73205i	−0.0540738	+	0.0936586i
$343$	20.0000			1.07990
$344$	−5.00000	+	8.66025i	−0.269582	+	0.466930i
$345$		0			0
$346$	6.00000			0.322562
$347$	−15.0000	+	25.9808i	−0.805242	+	1.39472i	0.110885	+	0.993833i	$0.464631\pi$
$347$	−15.0000	+	25.9808i	−0.805242	+	1.39472i	−0.916127	+	0.400887i	$0.868702\pi$
$348$	1.50000	+	2.59808i	0.0804084	+	0.139272i
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	0.968253	−	0.249973i	$-0.0804216\pi$
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	−0.700609	+	0.713545i	$0.747088\pi$
$350$		0			0
$351$	−3.50000	+	0.866025i	−0.186816	+	0.0462250i
$352$	6.00000			0.319801
$353$	−7.50000	−	12.9904i	−0.399185	−	0.691408i	0.594441	−	0.804139i	$-0.297373\pi$
$353$	−7.50000	−	12.9904i	−0.399185	−	0.691408i	−0.993626	+	0.112731i	$0.964040\pi$
$354$		0			0
$355$		0			0
$356$	18.0000			0.953998
$357$	−3.00000	+	5.19615i	−0.158777	+	0.275010i
$358$	−3.00000	+	5.19615i	−0.158555	+	0.274625i
$359$	6.00000			0.316668			0.158334	−	0.987386i	$-0.449388\pi$
$359$	6.00000			0.316668			0.158334	+	0.987386i	$0.449388\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	3.50000	+	6.06218i	0.183956	+	0.318621i
$363$	−25.0000			−1.31216
$364$	5.00000	+	5.19615i	0.262071	+	0.272352i
$365$		0			0
$366$	−3.50000	−	6.06218i	−0.182948	−	0.316875i
$367$	1.00000	+	1.73205i	0.0521996	+	0.0904123i	0.890945	−	0.454112i	$-0.150043\pi$
$367$	1.00000	+	1.73205i	0.0521996	+	0.0904123i	−0.838745	+	0.544524i	$0.816710\pi$
$368$	−3.00000	+	5.19615i	−0.156386	+	0.270868i
$369$	−3.00000			−0.156174
$370$		0			0
$371$	−3.00000	+	5.19615i	−0.155752	+	0.269771i
$372$	4.00000			0.207390
$373$	14.5000	−	25.1147i	0.750782	−	1.30039i	−0.196663	−	0.980471i	$-0.563010\pi$
$373$	14.5000	−	25.1147i	0.750782	−	1.30039i	0.947444	−	0.319921i	$-0.103656\pi$
$374$	−9.00000	−	15.5885i	−0.465379	−	0.806060i
$375$		0			0
$376$	−6.00000			−0.309426
$377$	−7.50000	−	7.79423i	−0.386270	−	0.401423i
$378$	2.00000			0.102869
$379$	−10.0000	−	17.3205i	−0.513665	−	0.889695i	−0.999874	−	0.0158521i	$-0.994954\pi$
$379$	−10.0000	−	17.3205i	−0.513665	−	0.889695i	0.486209	−	0.873843i	$-0.338379\pi$
$380$		0			0
$381$	2.00000	−	3.46410i	0.102463	−	0.177471i
$382$	−12.0000			−0.613973
$383$	12.0000	−	20.7846i	0.613171	−	1.06204i	−0.377531	−	0.925997i	$-0.623227\pi$
$383$	12.0000	−	20.7846i	0.613171	−	1.06204i	0.990702	−	0.136047i	$-0.0434398\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$		0			0
$386$	11.5000	−	19.9186i	0.585335	−	1.01383i
$387$	−5.00000	−	8.66025i	−0.254164	−	0.440225i
$388$	7.00000	+	12.1244i	0.355371	+	0.615521i
$389$	39.0000			1.97738			0.988689	−	0.149979i	$-0.0479205\pi$
$389$	39.0000			1.97738			0.988689	+	0.149979i	$0.0479205\pi$
$390$		0			0
$391$	18.0000			0.910299
$392$	1.50000	+	2.59808i	0.0757614	+	0.131223i
$393$		0			0
$394$	3.00000	−	5.19615i	0.151138	−	0.261778i
$395$		0			0
$396$	−3.00000	+	5.19615i	−0.150756	+	0.261116i
$397$	7.00000	−	12.1244i	0.351320	−	0.608504i	−0.635161	−	0.772380i	$-0.719066\pi$
$397$	7.00000	−	12.1244i	0.351320	−	0.608504i	0.986481	+	0.163876i	$0.0523996\pi$
$398$	−10.0000			−0.501255
$399$	−2.00000	+	3.46410i	−0.100125	+	0.173422i
$400$		0			0
$401$	1.50000	+	2.59808i	0.0749064	+	0.129742i	0.901046	−	0.433724i	$-0.142801\pi$
$401$	1.50000	+	2.59808i	0.0749064	+	0.129742i	−0.826139	+	0.563466i	$0.809468\pi$
$402$	−10.0000			−0.498755
$403$	−14.0000	+	3.46410i	−0.697390	+	0.172559i
$404$	15.0000			0.746278
$405$		0			0
$406$	3.00000	+	5.19615i	0.148888	+	0.257881i
$407$	−21.0000	+	36.3731i	−1.04093	+	1.80295i
$408$	−3.00000			−0.148522
$409$	0.500000	−	0.866025i	0.0247234	−	0.0428222i	−0.853399	−	0.521258i	$-0.825463\pi$
$409$	0.500000	−	0.866025i	0.0247234	−	0.0428222i	0.878122	+	0.478436i	$0.158796\pi$
$410$		0			0
$411$	9.00000			0.443937
$412$	7.00000	−	12.1244i	0.344865	−	0.597324i
$413$		0			0
$414$	−3.00000	−	5.19615i	−0.147442	−	0.255377i
$415$		0			0
$416$	−1.00000	+	3.46410i	−0.0490290	+	0.169842i
$417$	4.00000			0.195881
$418$	−6.00000	−	10.3923i	−0.293470	−	0.508304i
$419$	−12.0000	−	20.7846i	−0.586238	−	1.01539i	−0.994720	−	0.102628i	$-0.967275\pi$
$419$	−12.0000	−	20.7846i	−0.586238	−	1.01539i	0.408481	−	0.912767i	$-0.366058\pi$
$420$		0			0
$421$	29.0000			1.41337			0.706687	−	0.707527i	$-0.250189\pi$
$421$	29.0000			1.41337			0.706687	+	0.707527i	$0.250189\pi$
$422$	8.00000	−	13.8564i	0.389434	−	0.674519i
$423$	3.00000	−	5.19615i	0.145865	−	0.252646i
$424$	−3.00000			−0.145693
$425$		0			0
$426$	3.00000	+	5.19615i	0.145350	+	0.251754i
$427$	−7.00000	−	12.1244i	−0.338754	−	0.586739i
$428$	6.00000			0.290021
$429$	6.00000	−	20.7846i	0.289683	−	1.00349i
$430$		0			0
$431$	3.00000	+	5.19615i	0.144505	+	0.250290i	0.929188	−	0.369607i	$-0.120508\pi$
$431$	3.00000	+	5.19615i	0.144505	+	0.250290i	−0.784683	+	0.619897i	$0.787174\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−6.50000	+	11.2583i	−0.312370	+	0.541041i	−0.978875	−	0.204460i	$-0.934456\pi$
$433$	−6.50000	+	11.2583i	−0.312370	+	0.541041i	0.666505	+	0.745501i	$0.267790\pi$
$434$	8.00000			0.384012
$435$		0			0
$436$	−7.00000	+	12.1244i	−0.335239	+	0.580651i
$437$	12.0000			0.574038
$438$	6.50000	−	11.2583i	0.310582	−	0.537944i
$439$	−7.00000	−	12.1244i	−0.334092	−	0.578664i	0.649218	−	0.760602i	$-0.275096\pi$
$439$	−7.00000	−	12.1244i	−0.334092	−	0.578664i	−0.983310	+	0.181938i	$0.941763\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$	10.5000	−	2.59808i	0.499434	−	0.123578i
$443$	36.0000			1.71041			0.855206	−	0.518289i	$-0.173431\pi$
$443$	36.0000			1.71041			0.855206	+	0.518289i	$0.173431\pi$
$444$	3.50000	+	6.06218i	0.166103	+	0.287698i
$445$		0			0
$446$	4.00000	−	6.92820i	0.189405	−	0.328060i
$447$	9.00000			0.425685
$448$	1.00000	−	1.73205i	0.0472456	−	0.0818317i
$449$	−9.00000	+	15.5885i	−0.424736	+	0.735665i	−0.996396	−	0.0848262i	$-0.972967\pi$
$449$	−9.00000	+	15.5885i	−0.424736	+	0.735665i	0.571660	+	0.820491i	$0.306300\pi$
$450$		0			0
$451$	9.00000	−	15.5885i	0.423793	−	0.734032i
$452$	−1.50000	−	2.59808i	−0.0705541	−	0.122203i
$453$	−5.00000	−	8.66025i	−0.234920	−	0.406894i
$454$	−18.0000			−0.844782
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	5.50000	+	9.52628i	0.257279	+	0.445621i	0.965512	−	0.260358i	$-0.0838407\pi$
$457$	5.50000	+	9.52628i	0.257279	+	0.445621i	−0.708233	+	0.705979i	$0.750507\pi$
$458$	11.0000	+	19.0526i	0.513996	+	0.890268i
$459$	1.50000	−	2.59808i	0.0700140	−	0.121268i
$460$		0			0
$461$	−7.50000	+	12.9904i	−0.349310	+	0.605022i	−0.986127	−	0.165992i	$-0.946917\pi$
$461$	−7.50000	+	12.9904i	−0.349310	+	0.605022i	0.636817	+	0.771015i	$0.280251\pi$
$462$	−6.00000	+	10.3923i	−0.279145	+	0.483494i
$463$	−38.0000			−1.76601			−0.883005	−	0.469364i	$-0.844483\pi$
$463$	−38.0000			−1.76601			−0.883005	+	0.469364i	$0.844483\pi$
$464$	−1.50000	+	2.59808i	−0.0696358	+	0.120613i
$465$		0			0
$466$	−3.00000	−	5.19615i	−0.138972	−	0.240707i
$467$	18.0000			0.832941			0.416470	−	0.909149i	$-0.363267\pi$
$467$	18.0000			0.832941			0.416470	+	0.909149i	$0.363267\pi$
$468$	−2.50000	−	2.59808i	−0.115563	−	0.120096i
$469$	−20.0000			−0.923514
$470$		0			0
$471$	−2.50000	−	4.33013i	−0.115194	−	0.199522i
$472$		0			0
$473$	60.0000			2.75880
$474$	−2.00000	+	3.46410i	−0.0918630	+	0.159111i
$475$		0			0
$476$	−6.00000			−0.275010
$477$	1.50000	−	2.59808i	0.0686803	−	0.118958i
$478$	−3.00000	−	5.19615i	−0.137217	−	0.237666i
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$		0			0
$481$	−17.5000	−	18.1865i	−0.797931	−	0.829235i
$482$	−1.00000			−0.0455488
$483$	−6.00000	−	10.3923i	−0.273009	−	0.472866i
$484$	−12.5000	−	21.6506i	−0.568182	−	0.984120i
$485$		0			0
$486$	−1.00000			−0.0453609
$487$	1.00000	−	1.73205i	0.0453143	−	0.0784867i	−0.842479	−	0.538730i	$-0.818904\pi$
$487$	1.00000	−	1.73205i	0.0453143	−	0.0784867i	0.887793	+	0.460243i	$0.152238\pi$
$488$	3.50000	−	6.06218i	0.158438	−	0.274422i
$489$	−4.00000			−0.180886
$490$		0			0
$491$	9.00000	+	15.5885i	0.406164	+	0.703497i	0.994456	−	0.105151i	$-0.0335327\pi$
$491$	9.00000	+	15.5885i	0.406164	+	0.703497i	−0.588292	+	0.808649i	$0.700199\pi$
$492$	−1.50000	−	2.59808i	−0.0676252	−	0.117130i
$493$	9.00000			0.405340
$494$	7.00000	−	1.73205i	0.314945	−	0.0779287i
$495$		0			0
$496$	2.00000	+	3.46410i	0.0898027	+	0.155543i
$497$	6.00000	+	10.3923i	0.269137	+	0.466159i
$498$	3.00000	−	5.19615i	0.134433	−	0.232845i
$499$	32.0000			1.43252			0.716258	−	0.697835i	$-0.245853\pi$
$499$	32.0000			1.43252			0.716258	+	0.697835i	$0.245853\pi$
$500$		0			0
$501$		0			0
$502$	−12.0000			−0.535586
$503$	3.00000	−	5.19615i	0.133763	−	0.231685i	−0.791361	−	0.611349i	$-0.790627\pi$
$503$	3.00000	−	5.19615i	0.133763	−	0.231685i	0.925124	+	0.379664i	$0.123960\pi$
$504$	1.00000	+	1.73205i	0.0445435	+	0.0771517i
$505$		0			0
$506$	36.0000			1.60040
$507$	11.0000	+	6.92820i	0.488527	+	0.307692i
$508$	4.00000			0.177471
$509$	−1.50000	−	2.59808i	−0.0664863	−	0.115158i	0.830866	−	0.556473i	$-0.187846\pi$
$509$	−1.50000	−	2.59808i	−0.0664863	−	0.115158i	−0.897352	+	0.441315i	$0.854512\pi$
$510$		0			0
$511$	13.0000	−	22.5167i	0.575086	−	0.996078i
$512$	1.00000			0.0441942
$513$	1.00000	−	1.73205i	0.0441511	−	0.0764719i
$514$	−1.50000	+	2.59808i	−0.0661622	+	0.114596i
$515$		0			0
$516$	5.00000	−	8.66025i	0.220113	−	0.381246i
$517$	18.0000	+	31.1769i	0.791639	+	1.37116i
$518$	7.00000	+	12.1244i	0.307562	+	0.532714i
$519$	−6.00000			−0.263371
$520$		0			0
$521$	33.0000			1.44576			0.722878	−	0.690976i	$-0.242819\pi$
$521$	33.0000			1.44576			0.722878	+	0.690976i	$0.242819\pi$
$522$	−1.50000	−	2.59808i	−0.0656532	−	0.113715i
$523$	−17.0000	−	29.4449i	−0.743358	−	1.28753i	−0.950958	−	0.309320i	$-0.899899\pi$
$523$	−17.0000	−	29.4449i	−0.743358	−	1.28753i	0.207600	−	0.978214i	$-0.433435\pi$
$524$		0			0
$525$		0			0
$526$	−3.00000	+	5.19615i	−0.130806	+	0.226563i
$527$	6.00000	−	10.3923i	0.261364	−	0.452696i
$528$	−6.00000			−0.261116
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$		0			0
$531$		0			0
$532$	−4.00000			−0.173422
$533$	7.50000	+	7.79423i	0.324861	+	0.337606i
$534$	−18.0000			−0.778936
$535$		0			0
$536$	−5.00000	−	8.66025i	−0.215967	−	0.374066i
$537$	3.00000	−	5.19615i	0.129460	−	0.224231i
$538$	18.0000			0.776035
$539$	9.00000	−	15.5885i	0.387657	−	0.671442i
$540$		0			0
$541$	29.0000			1.24681			0.623404	−	0.781900i	$-0.285749\pi$
$541$	29.0000			1.24681			0.623404	+	0.781900i	$0.285749\pi$
$542$	8.00000	−	13.8564i	0.343629	−	0.595184i
$543$	−3.50000	−	6.06218i	−0.150199	−	0.260153i
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$		0			0
$546$	−5.00000	−	5.19615i	−0.213980	−	0.222375i
$547$	34.0000			1.45374			0.726868	−	0.686778i	$-0.240975\pi$
$547$	34.0000			1.45374			0.726868	+	0.686778i	$0.240975\pi$
$548$	4.50000	+	7.79423i	0.192230	+	0.332953i
$549$	3.50000	+	6.06218i	0.149376	+	0.258727i
$550$		0			0
$551$	6.00000			0.255609
$552$	3.00000	−	5.19615i	0.127688	−	0.221163i
$553$	−4.00000	+	6.92820i	−0.170097	+	0.294617i
$554$	−17.0000			−0.722261
$555$		0			0
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	1.50000	+	2.59808i	0.0635570	+	0.110084i	0.896053	−	0.443947i	$-0.146422\pi$
$557$	1.50000	+	2.59808i	0.0635570	+	0.110084i	−0.832496	+	0.554031i	$0.813089\pi$
$558$	−4.00000			−0.169334
$559$	−10.0000	+	34.6410i	−0.422955	+	1.46516i
$560$		0			0
$561$	9.00000	+	15.5885i	0.379980	+	0.658145i
$562$	−4.50000	−	7.79423i	−0.189821	−	0.328780i
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$	6.00000			0.252646
$565$		0			0
$566$	7.00000	−	12.1244i	0.294232	−	0.509625i
$567$	−2.00000			−0.0839921
$568$	−3.00000	+	5.19615i	−0.125877	+	0.218026i
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	0.796266	−	0.604947i	$-0.206806\pi$
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	−0.922032	+	0.387113i	$0.873472\pi$
$570$		0			0
$571$	−22.0000			−0.920671			−0.460336	−	0.887745i	$-0.652271\pi$
$571$	−22.0000			−0.920671			−0.460336	+	0.887745i	$0.652271\pi$
$572$	21.0000	−	5.19615i	0.878054	−	0.217262i
$573$	12.0000			0.501307
$574$	−3.00000	−	5.19615i	−0.125218	−	0.216883i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−11.0000			−0.457936			−0.228968	−	0.973434i	$-0.573535\pi$
$577$	−11.0000			−0.457936			−0.228968	+	0.973434i	$0.573535\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$	−11.5000	+	19.9186i	−0.477924	+	0.827788i
$580$		0			0
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$	−7.00000	−	12.1244i	−0.290159	−	0.502571i
$583$	9.00000	+	15.5885i	0.372742	+	0.645608i
$584$	13.0000			0.537944
$585$		0			0
$586$	21.0000			0.867502
$587$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$587$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$588$	−1.50000	−	2.59808i	−0.0618590	−	0.107143i
$589$	4.00000	−	6.92820i	0.164817	−	0.285472i
$590$		0			0
$591$	−3.00000	+	5.19615i	−0.123404	+	0.213741i
$592$	−3.50000	+	6.06218i	−0.143849	+	0.249154i
$593$	−9.00000			−0.369586			−0.184793	−	0.982777i	$-0.559161\pi$
$593$	−9.00000			−0.369586			−0.184793	+	0.982777i	$0.559161\pi$
$594$	3.00000	−	5.19615i	0.123091	−	0.213201i
$595$		0			0
$596$	4.50000	+	7.79423i	0.184327	+	0.319264i
$597$	10.0000			0.409273
$598$	−6.00000	+	20.7846i	−0.245358	+	0.849946i
$599$	24.0000			0.980613			0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000			0.980613			0.490307	+	0.871550i	$0.336885\pi$
$600$		0			0
$601$	18.5000	+	32.0429i	0.754631	+	1.30706i	0.945558	+	0.325455i	$0.105517\pi$
$601$	18.5000	+	32.0429i	0.754631	+	1.30706i	−0.190927	+	0.981604i	$0.561149\pi$
$602$	10.0000	−	17.3205i	0.407570	−	0.705931i
$603$	10.0000			0.407231
$604$	5.00000	−	8.66025i	0.203447	−	0.352381i
$605$		0			0
$606$	−15.0000			−0.609333
$607$	16.0000	−	27.7128i	0.649420	−	1.12483i	−0.333842	−	0.942629i	$-0.608345\pi$
$607$	16.0000	−	27.7128i	0.649420	−	1.12483i	0.983262	−	0.182199i	$-0.0583216\pi$
$608$	−1.00000	−	1.73205i	−0.0405554	−	0.0702439i
$609$	−3.00000	−	5.19615i	−0.121566	−	0.210559i
$610$		0			0
$611$	−21.0000	+	5.19615i	−0.849569	+	0.210214i
$612$	3.00000			0.121268
$613$	−15.5000	−	26.8468i	−0.626039	−	1.08433i	−0.988339	−	0.152270i	$-0.951342\pi$
$613$	−15.5000	−	26.8468i	−0.626039	−	1.08433i	0.362300	−	0.932062i	$-0.381992\pi$
$614$	−5.00000	−	8.66025i	−0.201784	−	0.349499i
$615$		0			0
$616$	−12.0000			−0.483494
$617$	−7.50000	+	12.9904i	−0.301939	+	0.522973i	−0.976575	−	0.215177i	$-0.930967\pi$
$617$	−7.50000	+	12.9904i	−0.301939	+	0.522973i	0.674636	+	0.738150i	$0.264300\pi$
$618$	−7.00000	+	12.1244i	−0.281581	+	0.487713i
$619$	8.00000			0.321547			0.160774	−	0.986991i	$-0.448601\pi$
$619$	8.00000			0.321547			0.160774	+	0.986991i	$0.448601\pi$
$620$		0			0
$621$	3.00000	+	5.19615i	0.120386	+	0.208514i
$622$	15.0000	+	25.9808i	0.601445	+	1.04173i
$623$	−36.0000			−1.44231
$624$	1.00000	−	3.46410i	0.0400320	−	0.138675i
$625$		0			0
$626$	−5.00000	−	8.66025i	−0.199840	−	0.346133i
$627$	6.00000	+	10.3923i	0.239617	+	0.415029i
$628$	2.50000	−	4.33013i	0.0997609	−	0.172791i
$629$	21.0000			0.837325
$630$		0			0
$631$	−10.0000	+	17.3205i	−0.398094	+	0.689519i	−0.993491	−	0.113913i	$-0.963661\pi$
$631$	−10.0000	+	17.3205i	−0.398094	+	0.689519i	0.595397	+	0.803432i	$0.296995\pi$
$632$	−4.00000			−0.159111
$633$	−8.00000	+	13.8564i	−0.317971	+	0.550743i
$634$	1.50000	+	2.59808i	0.0595726	+	0.103183i
$635$		0			0
$636$	3.00000			0.118958
$637$	7.50000	+	7.79423i	0.297161	+	0.308819i
$638$	18.0000			0.712627
$639$	−3.00000	−	5.19615i	−0.118678	−	0.205557i
$640$		0			0
$641$	1.50000	−	2.59808i	0.0592464	−	0.102618i	−0.834881	−	0.550431i	$-0.814464\pi$
$641$	1.50000	−	2.59808i	0.0592464	−	0.102618i	0.894127	+	0.447813i	$0.147797\pi$
$642$	−6.00000			−0.236801
$643$	−8.00000	+	13.8564i	−0.315489	+	0.546443i	−0.979541	−	0.201243i	$-0.935502\pi$
$643$	−8.00000	+	13.8564i	−0.315489	+	0.546443i	0.664052	+	0.747686i	$0.268835\pi$
$644$	6.00000	−	10.3923i	0.236433	−	0.409514i
$645$		0			0
$646$	−3.00000	+	5.19615i	−0.118033	+	0.204440i
$647$	12.0000	+	20.7846i	0.471769	+	0.817127i	0.999478	−	0.0322975i	$-0.0102824\pi$
$647$	12.0000	+	20.7846i	0.471769	+	0.817127i	−0.527710	+	0.849425i	$0.676949\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$		0			0
$650$		0			0
$651$	−8.00000			−0.313545
$652$	−2.00000	−	3.46410i	−0.0783260	−	0.135665i
$653$	21.0000	+	36.3731i	0.821794	+	1.42339i	0.904345	+	0.426801i	$0.140360\pi$
$653$	21.0000	+	36.3731i	0.821794	+	1.42339i	−0.0825519	+	0.996587i	$0.526307\pi$
$654$	7.00000	−	12.1244i	0.273722	−	0.474100i
$655$		0			0
$656$	1.50000	−	2.59808i	0.0585652	−	0.101438i
$657$	−6.50000	+	11.2583i	−0.253589	+	0.439229i
$658$	12.0000			0.467809
$659$	−12.0000	+	20.7846i	−0.467454	+	0.809653i	−0.999309	−	0.0371821i	$-0.988162\pi$
$659$	−12.0000	+	20.7846i	−0.467454	+	0.809653i	0.531855	+	0.846836i	$0.321495\pi$
$660$		0			0
$661$	−2.50000	−	4.33013i	−0.0972387	−	0.168422i	0.813302	−	0.581842i	$-0.197668\pi$
$661$	−2.50000	−	4.33013i	−0.0972387	−	0.168422i	−0.910541	+	0.413419i	$0.864334\pi$
$662$	−4.00000			−0.155464
$663$	−10.5000	+	2.59808i	−0.407786	+	0.100901i
$664$	6.00000			0.232845
$665$		0			0
$666$	−3.50000	−	6.06218i	−0.135622	−	0.234905i
$667$	−9.00000	+	15.5885i	−0.348481	+	0.603587i
$668$		0			0
$669$	−4.00000	+	6.92820i	−0.154649	+	0.267860i
$670$		0			0
$671$	−42.0000			−1.62139
$672$	−1.00000	+	1.73205i	−0.0385758	+	0.0668153i
$673$	−6.50000	−	11.2583i	−0.250557	−	0.433977i	0.713123	−	0.701039i	$-0.247280\pi$
$673$	−6.50000	−	11.2583i	−0.250557	−	0.433977i	−0.963679	+	0.267063i	$0.913947\pi$
$674$	11.5000	+	19.9186i	0.442963	+	0.767235i
$675$		0			0
$676$	−0.500000	+	12.9904i	−0.0192308	+	0.499630i
$677$	−18.0000			−0.691796			−0.345898	−	0.938272i	$-0.612426\pi$
$677$	−18.0000			−0.691796			−0.345898	+	0.938272i	$0.612426\pi$
$678$	1.50000	+	2.59808i	0.0576072	+	0.0997785i
$679$	−14.0000	−	24.2487i	−0.537271	−	0.930580i
$680$		0			0
$681$	18.0000			0.689761
$682$	12.0000	−	20.7846i	0.459504	−	0.795884i
$683$	−24.0000	+	41.5692i	−0.918334	+	1.59060i	−0.116390	+	0.993204i	$0.537132\pi$
$683$	−24.0000	+	41.5692i	−0.918334	+	1.59060i	−0.801945	+	0.597398i	$0.796201\pi$
$684$	2.00000			0.0764719
$685$		0			0
$686$	−10.0000	−	17.3205i	−0.381802	−	0.661300i
$687$	−11.0000	−	19.0526i	−0.419676	−	0.726900i
$688$	10.0000			0.381246
$689$	−10.5000	+	2.59808i	−0.400018	+	0.0989788i
$690$		0			0
$691$	−13.0000	−	22.5167i	−0.494543	−	0.856574i	0.505437	−	0.862864i	$-0.331331\pi$
$691$	−13.0000	−	22.5167i	−0.494543	−	0.856574i	−0.999980	+	0.00628943i	$0.997998\pi$
$692$	−3.00000	−	5.19615i	−0.114043	−	0.197528i
$693$	6.00000	−	10.3923i	0.227921	−	0.394771i
$694$	30.0000			1.13878
$695$		0			0
$696$	1.50000	−	2.59808i	0.0568574	−	0.0984798i
$697$	−9.00000			−0.340899
$698$	5.00000	−	8.66025i	0.189253	−	0.327795i
$699$	3.00000	+	5.19615i	0.113470	+	0.196537i
$700$		0			0
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$	2.50000	+	2.59808i	0.0943564	+	0.0980581i
$703$	14.0000			0.528020
$704$	−3.00000	−	5.19615i	−0.113067	−	0.195837i
$705$		0			0
$706$	−7.50000	+	12.9904i	−0.282266	+	0.488899i
$707$	−30.0000			−1.12827
$708$		0			0
$709$	−2.50000	+	4.33013i	−0.0938895	+	0.162621i	−0.909145	−	0.416481i	$-0.863263\pi$
$709$	−2.50000	+	4.33013i	−0.0938895	+	0.162621i	0.815255	+	0.579102i	$0.196597\pi$
$710$		0			0
$711$	2.00000	−	3.46410i	0.0750059	−	0.129914i
$712$	−9.00000	−	15.5885i	−0.337289	−	0.584202i
$713$	12.0000	+	20.7846i	0.449404	+	0.778390i
$714$	6.00000			0.224544
$715$		0			0
$716$	6.00000			0.224231
$717$	3.00000	+	5.19615i	0.112037	+	0.194054i
$718$	−3.00000	−	5.19615i	−0.111959	−	0.193919i
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$		0			0
$721$	−14.0000	+	24.2487i	−0.521387	+	0.903069i
$722$	7.50000	−	12.9904i	0.279121	−	0.483452i
$723$	1.00000			0.0371904
$724$	3.50000	−	6.06218i	0.130076	−	0.225299i
$725$		0			0
$726$	12.5000	+	21.6506i	0.463919	+	0.803530i
$727$	−14.0000			−0.519231			−0.259616	−	0.965712i	$-0.583596\pi$
$727$	−14.0000			−0.519231			−0.259616	+	0.965712i	$0.583596\pi$
$728$	2.00000	−	6.92820i	0.0741249	−	0.256776i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−15.0000	−	25.9808i	−0.554795	−	0.960933i
$732$	−3.50000	+	6.06218i	−0.129364	+	0.224065i
$733$	31.0000			1.14501			0.572506	−	0.819901i	$-0.305971\pi$
$733$	31.0000			1.14501			0.572506	+	0.819901i	$0.305971\pi$
$734$	1.00000	−	1.73205i	0.0369107	−	0.0639312i
$735$		0			0
$736$	6.00000			0.221163
$737$	−30.0000	+	51.9615i	−1.10506	+	1.91403i
$738$	1.50000	+	2.59808i	0.0552158	+	0.0956365i
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	0.974818	−	0.223001i	$-0.0715853\pi$
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	−0.680534	+	0.732717i	$0.738252\pi$
$740$		0			0
$741$	−7.00000	+	1.73205i	−0.257151	+	0.0636285i
$742$	6.00000			0.220267
$743$	−18.0000	−	31.1769i	−0.660356	−	1.14377i	−0.980522	−	0.196409i	$-0.937072\pi$
$743$	−18.0000	−	31.1769i	−0.660356	−	1.14377i	0.320166	−	0.947361i	$-0.396261\pi$
$744$	−2.00000	−	3.46410i	−0.0733236	−	0.127000i
$745$		0			0
$746$	−29.0000			−1.06177
$747$	−3.00000	+	5.19615i	−0.109764	+	0.190117i
$748$	−9.00000	+	15.5885i	−0.329073	+	0.569970i
$749$	−12.0000			−0.438470
$750$		0			0
$751$	−7.00000	−	12.1244i	−0.255434	−	0.442424i	0.709580	−	0.704625i	$-0.248885\pi$
$751$	−7.00000	−	12.1244i	−0.255434	−	0.442424i	−0.965013	+	0.262201i	$0.915552\pi$
$752$	3.00000	+	5.19615i	0.109399	+	0.189484i
$753$	12.0000			0.437304
$754$	−3.00000	+	10.3923i	−0.109254	+	0.378465i
$755$		0			0
$756$	−1.00000	−	1.73205i	−0.0363696	−	0.0629941i
$757$	−17.0000	−	29.4449i	−0.617876	−	1.07019i	−0.989873	−	0.141958i	$-0.954660\pi$
$757$	−17.0000	−	29.4449i	−0.617876	−	1.07019i	0.371997	−	0.928234i	$-0.378673\pi$
$758$	−10.0000	+	17.3205i	−0.363216	+	0.629109i
$759$	−36.0000			−1.30672
$760$		0			0
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	−0.454935	−	0.890525i	$-0.650337\pi$
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	0.998684	−	0.0512772i	$-0.0163292\pi$
$762$	−4.00000			−0.144905
$763$	14.0000	−	24.2487i	0.506834	−	0.877862i
$764$	6.00000	+	10.3923i	0.217072	+	0.375980i
$765$		0			0
$766$	−24.0000			−0.867155
$767$		0			0
$768$	−1.00000			−0.0360844
$769$	−7.00000	−	12.1244i	−0.252426	−	0.437215i	0.711767	−	0.702416i	$-0.247895\pi$
$769$	−7.00000	−	12.1244i	−0.252426	−	0.437215i	−0.964193	+	0.265200i	$0.914562\pi$
$770$		0			0
$771$	1.50000	−	2.59808i	0.0540212	−	0.0935674i
$772$	−23.0000			−0.827788
$773$	−15.0000	+	25.9808i	−0.539513	+	0.934463i	0.459418	+	0.888220i	$0.348058\pi$
$773$	−15.0000	+	25.9808i	−0.539513	+	0.934463i	−0.998930	+	0.0462427i	$0.985275\pi$
$774$	−5.00000	+	8.66025i	−0.179721	+	0.311286i
$775$		0			0
$776$	7.00000	−	12.1244i	0.251285	−	0.435239i
$777$	−7.00000	−	12.1244i	−0.251124	−	0.434959i
$778$	−19.5000	−	33.7750i	−0.699109	−	1.21089i
$779$	−6.00000			−0.214972
$780$		0			0
$781$	36.0000			1.28818
$782$	−9.00000	−	15.5885i	−0.321839	−	0.557442i
$783$	1.50000	+	2.59808i	0.0536056	+	0.0928477i
$784$	1.50000	−	2.59808i	0.0535714	−	0.0927884i
$785$		0			0
$786$		0			0
$787$	−14.0000	+	24.2487i	−0.499046	+	0.864373i	−0.999999	−	0.00110111i	$-0.999650\pi$
$787$	−14.0000	+	24.2487i	−0.499046	+	0.864373i	0.500953	+	0.865474i	$0.332983\pi$
$788$	−6.00000			−0.213741
$789$	3.00000	−	5.19615i	0.106803	−	0.184988i
$790$		0			0
$791$	3.00000	+	5.19615i	0.106668	+	0.184754i
$792$	6.00000			0.213201
$793$	7.00000	−	24.2487i	0.248577	−	0.861097i
$794$	−14.0000			−0.496841
$795$		0			0
$796$	5.00000	+	8.66025i	0.177220	+	0.306955i
$797$	15.0000	−	25.9808i	0.531327	−	0.920286i	−0.468004	−	0.883726i	$-0.655027\pi$
$797$	15.0000	−	25.9808i	0.531327	−	0.920286i	0.999331	−	0.0365596i	$-0.0116399\pi$
$798$	4.00000			0.141598
$799$	9.00000	−	15.5885i	0.318397	−	0.551480i
$800$		0			0
$801$	18.0000			0.635999
$802$	1.50000	−	2.59808i	0.0529668	−	0.0917413i
$803$	−39.0000	−	67.5500i	−1.37628	−	2.38379i
$804$	5.00000	+	8.66025i	0.176336	+	0.305424i
$805$		0			0
$806$	10.0000	+	10.3923i	0.352235	+	0.366053i
$807$	−18.0000			−0.633630
$808$	−7.50000	−	12.9904i	−0.263849	−	0.457000i
$809$	25.5000	+	44.1673i	0.896532	+	1.55284i	0.831897	+	0.554930i	$0.187255\pi$
$809$	25.5000	+	44.1673i	0.896532	+	1.55284i	0.0646355	+	0.997909i	$0.479412\pi$
$810$		0			0
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$	3.00000	−	5.19615i	0.105279	−	0.182349i
$813$	−8.00000	+	13.8564i	−0.280572	+	0.485965i
$814$	42.0000			1.47210
$815$		0			0
$816$	1.50000	+	2.59808i	0.0525105	+	0.0909509i
$817$	−10.0000	−	17.3205i	−0.349856	−	0.605968i
$818$	−1.00000			−0.0349642
$819$	5.00000	+	5.19615i	0.174714	+	0.181568i
$820$		0			0
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	0.665144	−	0.746715i	$-0.268370\pi$
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	−0.979246	+	0.202674i	$0.935037\pi$
$822$	−4.50000	−	7.79423i	−0.156956	−	0.271855i
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	0.272292	+	0.962215i	$0.412218\pi$
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	−0.969448	+	0.245295i	$0.921115\pi$
$824$	−14.0000			−0.487713
$825$		0			0
$826$		0			0
$827$	48.0000			1.66912			0.834562	−	0.550914i	$-0.185721\pi$
$827$	48.0000			1.66912			0.834562	+	0.550914i	$0.185721\pi$
$828$	−3.00000	+	5.19615i	−0.104257	+	0.180579i
$829$	−8.50000	−	14.7224i	−0.295217	−	0.511331i	0.679818	−	0.733381i	$-0.262059\pi$
$829$	−8.50000	−	14.7224i	−0.295217	−	0.511331i	−0.975035	+	0.222049i	$0.928725\pi$
$830$		0			0
$831$	17.0000			0.589723
$832$	3.50000	−	0.866025i	0.121341	−	0.0300240i
$833$	−9.00000			−0.311832
$834$	−2.00000	−	3.46410i	−0.0692543	−	0.119952i
$835$		0			0
$836$	−6.00000	+	10.3923i	−0.207514	+	0.359425i
$837$	4.00000			0.138260
$838$	−12.0000	+	20.7846i	−0.414533	+	0.717992i
$839$	6.00000	−	10.3923i	0.207143	−	0.358782i	−0.743670	−	0.668546i	$-0.766917\pi$
$839$	6.00000	−	10.3923i	0.207143	−	0.358782i	0.950813	+	0.309764i	$0.100250\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−14.5000	−	25.1147i	−0.499703	−	0.865511i
$843$	4.50000	+	7.79423i	0.154988	+	0.268447i
$844$	−16.0000			−0.550743
$845$		0			0
$846$	−6.00000			−0.206284
$847$	25.0000	+	43.3013i	0.859010	+	1.48785i
$848$	1.50000	+	2.59808i	0.0515102	+	0.0892183i
$849$	−7.00000	+	12.1244i	−0.240239	+	0.416107i
$850$		0			0
$851$	−21.0000	+	36.3731i	−0.719871	+	1.24685i
$852$	3.00000	−	5.19615i	0.102778	−	0.178017i
$853$	19.0000			0.650548			0.325274	−	0.945620i	$-0.394544\pi$
$853$	19.0000			0.650548			0.325274	+	0.945620i	$0.394544\pi$
$854$	−7.00000	+	12.1244i	−0.239535	+	0.414887i
$855$		0			0
$856$	−3.00000	−	5.19615i	−0.102538	−	0.177601i
$857$	−21.0000			−0.717346			−0.358673	−	0.933463i	$-0.616771\pi$
$857$	−21.0000			−0.717346			−0.358673	+	0.933463i	$0.616771\pi$
$858$	−21.0000	+	5.19615i	−0.716928	+	0.177394i
$859$	26.0000			0.887109			0.443554	−	0.896248i	$-0.353717\pi$
$859$	26.0000			0.887109			0.443554	+	0.896248i	$0.353717\pi$
$860$		0			0
$861$	3.00000	+	5.19615i	0.102240	+	0.177084i
$862$	3.00000	−	5.19615i	0.102180	−	0.176982i
$863$	−18.0000			−0.612727			−0.306364	−	0.951915i	$-0.599112\pi$
$863$	−18.0000			−0.612727			−0.306364	+	0.951915i	$0.599112\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$		0			0
$866$	13.0000			0.441758
$867$	−4.00000	+	6.92820i	−0.135847	+	0.235294i
$868$	−4.00000	−	6.92820i	−0.135769	−	0.235159i
$869$	12.0000	+	20.7846i	0.407072	+	0.705070i
$870$		0			0
$871$	−25.0000	−	25.9808i	−0.847093	−	0.880325i
$872$	14.0000			0.474100
$873$	7.00000	+	12.1244i	0.236914	+	0.410347i
$874$	−6.00000	−	10.3923i	−0.202953	−	0.351525i
$875$		0			0
$876$	−13.0000			−0.439229
$877$	20.5000	−	35.5070i	0.692236	−	1.19899i	−0.278868	−	0.960329i	$-0.589959\pi$
$877$	20.5000	−	35.5070i	0.692236	−	1.19899i	0.971104	−	0.238658i	$-0.0767075\pi$
$878$	−7.00000	+	12.1244i	−0.236239	+	0.409177i
$879$	−21.0000			−0.708312
$880$		0			0
$881$	−16.5000	−	28.5788i	−0.555899	−	0.962846i	−0.997833	−	0.0657979i	$-0.979041\pi$
$881$	−16.5000	−	28.5788i	−0.555899	−	0.962846i	0.441934	−	0.897048i	$-0.354293\pi$
$882$	1.50000	+	2.59808i	0.0505076	+	0.0874818i
$883$	−8.00000			−0.269221			−0.134611	−	0.990899i	$-0.542978\pi$
$883$	−8.00000			−0.269221			−0.134611	+	0.990899i	$0.542978\pi$
$884$	−7.50000	−	7.79423i	−0.252252	−	0.262148i
$885$		0			0
$886$	−18.0000	−	31.1769i	−0.604722	−	1.04741i
$887$	−24.0000	−	41.5692i	−0.805841	−	1.39576i	−0.915722	−	0.401813i	$-0.868380\pi$
$887$	−24.0000	−	41.5692i	−0.805841	−	1.39576i	0.109881	−	0.993945i	$-0.464953\pi$
$888$	3.50000	−	6.06218i	0.117452	−	0.203433i
$889$	−8.00000			−0.268311
$890$		0			0
$891$	−3.00000	+	5.19615i	−0.100504	+	0.174078i
$892$	−8.00000			−0.267860
$893$	6.00000	−	10.3923i	0.200782	−	0.347765i
$894$	−4.50000	−	7.79423i	−0.150503	−	0.260678i
$895$		0			0
$896$	−2.00000			−0.0668153
$897$	6.00000	−	20.7846i	0.200334	−	0.693978i
$898$	18.0000			0.600668
$899$	6.00000	+	10.3923i	0.200111	+	0.346603i
$900$		0			0
$901$	4.50000	−	7.79423i	0.149917	−	0.259663i
$902$	−18.0000			−0.599334
$903$	−10.0000	+	17.3205i	−0.332779	+	0.576390i
$904$	−1.50000	+	2.59808i	−0.0498893	+	0.0864107i
$905$		0			0
$906$	−5.00000	+	8.66025i	−0.166114	+	0.287718i
$907$	22.0000	+	38.1051i	0.730498	+	1.26526i	0.956671	+	0.291172i	$0.0940453\pi$
$907$	22.0000	+	38.1051i	0.730498	+	1.26526i	−0.226173	+	0.974087i	$0.572621\pi$
$908$	9.00000	+	15.5885i	0.298675	+	0.517321i
$909$	15.0000			0.497519
$910$		0			0
$911$	−24.0000			−0.795155			−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000			−0.795155			−0.397578	+	0.917568i	$0.630149\pi$
$912$	1.00000	+	1.73205i	0.0331133	+	0.0573539i
$913$	−18.0000	−	31.1769i	−0.595713	−	1.03181i
$914$	5.50000	−	9.52628i	0.181924	−	0.315101i
$915$		0			0
$916$	11.0000	−	19.0526i	0.363450	−	0.629514i
$917$		0			0
$918$	−3.00000			−0.0990148
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	−0.703378	−	0.710816i	$-0.748326\pi$
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	0.967274	+	0.253735i	$0.0816592\pi$
$920$		0			0
$921$	5.00000	+	8.66025i	0.164756	+	0.285365i
$922$	15.0000			0.493999
$923$	−6.00000	+	20.7846i	−0.197492	+	0.684134i
$924$	12.0000			0.394771
$925$		0			0
$926$	19.0000	+	32.9090i	0.624379	+	1.08146i
$927$	7.00000	−	12.1244i	0.229910	−	0.398216i
$928$	3.00000			0.0984798
$929$	−16.5000	+	28.5788i	−0.541347	+	0.937641i	0.457480	+	0.889220i	$0.348752\pi$
$929$	−16.5000	+	28.5788i	−0.541347	+	0.937641i	−0.998827	+	0.0484211i	$0.984581\pi$
$930$		0			0
$931$	−6.00000			−0.196642
$932$	−3.00000	+	5.19615i	−0.0982683	+	0.170206i
$933$	−15.0000	−	25.9808i	−0.491078	−	0.850572i
$934$	−9.00000	−	15.5885i	−0.294489	−	0.510070i
$935$		0			0
$936$	−1.00000	+	3.46410i	−0.0326860	+	0.113228i
$937$	−47.0000			−1.53542			−0.767712	−	0.640796i	$-0.778605\pi$
$937$	−47.0000			−1.53542			−0.767712	+	0.640796i	$0.778605\pi$
$938$	10.0000	+	17.3205i	0.326512	+	0.565535i
$939$	5.00000	+	8.66025i	0.163169	+	0.282617i
$940$		0			0
$941$	42.0000			1.36916			0.684580	−	0.728937i	$-0.259985\pi$
$941$	42.0000			1.36916			0.684580	+	0.728937i	$0.259985\pi$
$942$	−2.50000	+	4.33013i	−0.0814544	+	0.141083i
$943$	9.00000	−	15.5885i	0.293080	−	0.507630i
$944$		0			0
$945$		0			0
$946$	−30.0000	−	51.9615i	−0.975384	−	1.68941i
$947$	12.0000	+	20.7846i	0.389948	+	0.675409i	0.992442	−	0.122714i	$-0.0391598\pi$
$947$	12.0000	+	20.7846i	0.389948	+	0.675409i	−0.602494	+	0.798123i	$0.705826\pi$
$948$	4.00000			0.129914
$949$	45.5000	−	11.2583i	1.47699	−	0.365461i
$950$		0			0
$951$	−1.50000	−	2.59808i	−0.0486408	−	0.0842484i
$952$	3.00000	+	5.19615i	0.0972306	+	0.168408i
$953$	27.0000	−	46.7654i	0.874616	−	1.51488i	0.0174443	−	0.999848i	$-0.494447\pi$
$953$	27.0000	−	46.7654i	0.874616	−	1.51488i	0.857171	−	0.515031i	$-0.172220\pi$
$954$	−3.00000			−0.0971286
$955$		0			0
$956$	−3.00000	+	5.19615i	−0.0970269	+	0.168056i
$957$	−18.0000			−0.581857
$958$		0			0
$959$	−9.00000	−	15.5885i	−0.290625	−	0.503378i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	−7.00000	+	24.2487i	−0.225689	+	0.781810i
$963$	6.00000			0.193347
$964$	0.500000	+	0.866025i	0.0161039	+	0.0278928i
$965$		0			0
$966$	−6.00000	+	10.3923i	−0.193047	+	0.334367i
$967$	22.0000			0.707472			0.353736	−	0.935345i	$-0.384911\pi$
$967$	22.0000			0.707472			0.353736	+	0.935345i	$0.384911\pi$
$968$	−12.5000	+	21.6506i	−0.401765	+	0.695878i
$969$	3.00000	−	5.19615i	0.0963739	−	0.166924i
$970$		0			0
$971$	−30.0000	+	51.9615i	−0.962746	+	1.66752i	−0.247193	+	0.968966i	$0.579508\pi$
$971$	−30.0000	+	51.9615i	−0.962746	+	1.66752i	−0.715553	+	0.698558i	$0.753825\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−4.00000	−	6.92820i	−0.128234	−	0.222108i
$974$	−2.00000			−0.0640841
$975$		0			0
$976$	−7.00000			−0.224065
$977$	−1.50000	−	2.59808i	−0.0479893	−	0.0831198i	0.841033	−	0.540984i	$-0.181948\pi$
$977$	−1.50000	−	2.59808i	−0.0479893	−	0.0831198i	−0.889022	+	0.457864i	$0.848615\pi$
$978$	2.00000	+	3.46410i	0.0639529	+	0.110770i
$979$	−54.0000	+	93.5307i	−1.72585	+	2.98926i
$980$		0			0
$981$	−7.00000	+	12.1244i	−0.223493	+	0.387101i
$982$	9.00000	−	15.5885i	0.287202	−	0.497448i
$983$	36.0000			1.14822			0.574111	−	0.818778i	$-0.305348\pi$
$983$	36.0000			1.14822			0.574111	+	0.818778i	$0.305348\pi$
$984$	−1.50000	+	2.59808i	−0.0478183	+	0.0828236i
$985$		0			0
$986$	−4.50000	−	7.79423i	−0.143309	−	0.248219i
$987$	−12.0000			−0.381964
$988$	−5.00000	−	5.19615i	−0.159071	−	0.165312i
$989$	60.0000			1.90789
$990$		0			0
$991$	−19.0000	−	32.9090i	−0.603555	−	1.04539i	−0.992278	−	0.124033i	$-0.960417\pi$
$991$	−19.0000	−	32.9090i	−0.603555	−	1.04539i	0.388723	−	0.921355i	$-0.372916\pi$
$992$	2.00000	−	3.46410i	0.0635001	−	0.109985i
$993$	4.00000			0.126936
$994$	6.00000	−	10.3923i	0.190308	−	0.329624i
$995$		0			0
$996$	−6.00000			−0.190117
$997$	2.50000	−	4.33013i	0.0791758	−	0.137136i	−0.823719	−	0.566999i	$-0.808104\pi$
$997$	2.50000	−	4.33013i	0.0791758	−	0.137136i	0.902895	+	0.429862i	$0.141438\pi$
$998$	−16.0000	−	27.7128i	−0.506471	−	0.877234i
$999$	3.50000	+	6.06218i	0.110735	+	0.191799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.i.m.601.1		2
5.2	odd	4		1950.2.z.g.1849.2		4
5.3	odd	4		1950.2.z.g.1849.1		4
5.4	even	2		78.2.e.a.55.1	✓	2
13.9	even	3	inner	1950.2.i.m.451.1		2
15.14	odd	2		234.2.h.a.55.1		2
20.19	odd	2		624.2.q.g.289.1		2
60.59	even	2		1872.2.t.c.289.1		2
65.4	even	6		1014.2.e.a.529.1		2
65.9	even	6		78.2.e.a.61.1	yes	2
65.19	odd	12		1014.2.i.b.823.1		4
65.22	odd	12		1950.2.z.g.1699.1		4
65.24	odd	12		1014.2.b.c.337.1		2
65.29	even	6		1014.2.a.c.1.1		1
65.34	odd	4		1014.2.i.b.361.1		4
65.44	odd	4		1014.2.i.b.361.2		4
65.48	odd	12		1950.2.z.g.1699.2		4
65.49	even	6		1014.2.a.f.1.1		1
65.54	odd	12		1014.2.b.c.337.2		2
65.59	odd	12		1014.2.i.b.823.2		4
65.64	even	2		1014.2.e.a.991.1		2
195.29	odd	6		3042.2.a.i.1.1		1
195.74	odd	6		234.2.h.a.217.1		2
195.89	even	12		3042.2.b.h.1351.2		2
195.119	even	12		3042.2.b.h.1351.1		2
195.179	odd	6		3042.2.a.h.1.1		1
260.139	odd	6		624.2.q.g.529.1		2
260.159	odd	6		8112.2.a.m.1.1		1
260.179	odd	6		8112.2.a.c.1.1		1
780.659	even	6		1872.2.t.c.1153.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.e.a.55.1	✓	2	5.4	even	2
78.2.e.a.61.1	yes	2	65.9	even	6
234.2.h.a.55.1		2	15.14	odd	2
234.2.h.a.217.1		2	195.74	odd	6
624.2.q.g.289.1		2	20.19	odd	2
624.2.q.g.529.1		2	260.139	odd	6
1014.2.a.c.1.1		1	65.29	even	6
1014.2.a.f.1.1		1	65.49	even	6
1014.2.b.c.337.1		2	65.24	odd	12
1014.2.b.c.337.2		2	65.54	odd	12
1014.2.e.a.529.1		2	65.4	even	6
1014.2.e.a.991.1		2	65.64	even	2
1014.2.i.b.361.1		4	65.34	odd	4
1014.2.i.b.361.2		4	65.44	odd	4
1014.2.i.b.823.1		4	65.19	odd	12
1014.2.i.b.823.2		4	65.59	odd	12
1872.2.t.c.289.1		2	60.59	even	2
1872.2.t.c.1153.1		2	780.659	even	6
1950.2.i.m.451.1		2	13.9	even	3	inner
1950.2.i.m.601.1		2	1.1	even	1	trivial
1950.2.z.g.1699.1		4	65.22	odd	12
1950.2.z.g.1699.2		4	65.48	odd	12
1950.2.z.g.1849.1		4	5.3	odd	4
1950.2.z.g.1849.2		4	5.2	odd	4
3042.2.a.h.1.1		1	195.179	odd	6
3042.2.a.i.1.1		1	195.29	odd	6
3042.2.b.h.1351.1		2	195.119	even	12
3042.2.b.h.1351.2		2	195.89	even	12
8112.2.a.c.1.1		1	260.179	odd	6
8112.2.a.m.1.1		1	260.159	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(1.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-3.00000 - 5.19615i) q^{11} -1.00000 q^{12} +(3.50000 - 0.866025i) q^{13} -2.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +1.00000 q^{18} +(-1.00000 + 1.73205i) q^{19} +2.00000 q^{21} +(-3.00000 + 5.19615i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-2.50000 - 2.59808i) q^{26} -1.00000 q^{27} +(1.00000 + 1.73205i) q^{28} +(-1.50000 - 2.59808i) q^{29} -4.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.00000 - 5.19615i) q^{33} +3.00000 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-3.50000 - 6.06218i) q^{37} +2.00000 q^{38} +(2.50000 + 2.59808i) q^{39} +(1.50000 + 2.59808i) q^{41} +(-1.00000 - 1.73205i) q^{42} +(-5.00000 + 8.66025i) q^{43} +6.00000 q^{44} +(-3.00000 + 5.19615i) q^{46} -6.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} -3.00000 q^{51} +(-1.00000 + 3.46410i) q^{52} -3.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(1.00000 - 1.73205i) q^{56} -2.00000 q^{57} +(-1.50000 + 2.59808i) q^{58} +(3.50000 - 6.06218i) q^{61} +(2.00000 + 3.46410i) q^{62} +(1.00000 + 1.73205i) q^{63} +1.00000 q^{64} -6.00000 q^{66} +(-5.00000 - 8.66025i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(3.00000 - 5.19615i) q^{69} +(-3.00000 + 5.19615i) q^{71} +(-0.500000 + 0.866025i) q^{72} +13.0000 q^{73} +(-3.50000 + 6.06218i) q^{74} +(-1.00000 - 1.73205i) q^{76} -12.0000 q^{77} +(1.00000 - 3.46410i) q^{78} -4.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(1.50000 - 2.59808i) q^{82} +6.00000 q^{83} +(-1.00000 + 1.73205i) q^{84} +10.0000 q^{86} +(1.50000 - 2.59808i) q^{87} +(-3.00000 - 5.19615i) q^{88} +(-9.00000 - 15.5885i) q^{89} +(2.00000 - 6.92820i) q^{91} +6.00000 q^{92} +(-2.00000 - 3.46410i) q^{93} +(3.00000 + 5.19615i) q^{94} -1.00000 q^{96} +(7.00000 - 12.1244i) q^{97} +(1.50000 - 2.59808i) q^{98} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} - q^{4} + q^{6} + 2 q^{7} + 2 q^{8} - q^{9} - 6 q^{11} - 2 q^{12} + 7 q^{13} - 4 q^{14} - q^{16} - 3 q^{17} + 2 q^{18} - 2 q^{19} + 4 q^{21} - 6 q^{22} - 6 q^{23} + q^{24} - 5 q^{26}+ \cdots + 12 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 + q^6 + 2 * q^7 + 2 * q^8 - q^9 - 6 * q^11 - 2 * q^12 + 7 * q^13 - 4 * q^14 - q^16 - 3 * q^17 + 2 * q^18 - 2 * q^19 + 4 * q^21 - 6 * q^22 - 6 * q^23 + q^24 - 5 * q^26 - 2 * q^27 + 2 * q^28 - 3 * q^29 - 8 * q^31 - q^32 + 6 * q^33 + 6 * q^34 - q^36 - 7 * q^37 + 4 * q^38 + 5 * q^39 + 3 * q^41 - 2 * q^42 - 10 * q^43 + 12 * q^44 - 6 * q^46 - 12 * q^47 + q^48 + 3 * q^49 - 6 * q^51 - 2 * q^52 - 6 * q^53 + q^54 + 2 * q^56 - 4 * q^57 - 3 * q^58 + 7 * q^61 + 4 * q^62 + 2 * q^63 + 2 * q^64 - 12 * q^66 - 10 * q^67 - 3 * q^68 + 6 * q^69 - 6 * q^71 - q^72 + 26 * q^73 - 7 * q^74 - 2 * q^76 - 24 * q^77 + 2 * q^78 - 8 * q^79 - q^81 + 3 * q^82 + 12 * q^83 - 2 * q^84 + 20 * q^86 + 3 * q^87 - 6 * q^88 - 18 * q^89 + 4 * q^91 + 12 * q^92 - 4 * q^93 + 6 * q^94 - 2 * q^96 + 14 * q^97 + 3 * q^98 + 12 * q^99

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