LMFDB - Embedded newform 1950.2.i.b.451.1

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			451.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1950.451
Dual form			1950.2.i.b.601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(-1.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(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} +(-1.00000 + 1.73205i) q^{11} +1.00000 q^{12} +(-2.50000 - 2.59808i) q^{13} +2.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.50000 + 4.33013i) q^{17} +1.00000 q^{18} +(1.00000 + 1.73205i) q^{19} +2.00000 q^{21} +(-1.00000 - 1.73205i) q^{22} +(3.00000 - 5.19615i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(3.50000 - 0.866025i) q^{26} +1.00000 q^{27} +(-1.00000 + 1.73205i) q^{28} +(4.50000 - 7.79423i) q^{29} -4.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{33} -5.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-5.50000 + 9.52628i) q^{37} -2.00000 q^{38} +(3.50000 - 0.866025i) q^{39} +(-2.50000 + 4.33013i) q^{41} +(-1.00000 + 1.73205i) q^{42} +(5.00000 + 8.66025i) q^{43} +2.00000 q^{44} +(3.00000 + 5.19615i) q^{46} -2.00000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(1.50000 - 2.59808i) q^{49} -5.00000 q^{51} +(-1.00000 + 3.46410i) q^{52} +1.00000 q^{53} +(-0.500000 + 0.866025i) q^{54} +(-1.00000 - 1.73205i) q^{56} -2.00000 q^{57} +(4.50000 + 7.79423i) q^{58} +(4.00000 + 6.92820i) q^{59} +(5.50000 + 9.52628i) q^{61} +(2.00000 - 3.46410i) q^{62} +(-1.00000 + 1.73205i) q^{63} +1.00000 q^{64} +2.00000 q^{66} +(1.00000 - 1.73205i) q^{67} +(2.50000 - 4.33013i) q^{68} +(3.00000 + 5.19615i) q^{69} +(7.00000 + 12.1244i) q^{71} +(-0.500000 - 0.866025i) q^{72} +13.0000 q^{73} +(-5.50000 - 9.52628i) q^{74} +(1.00000 - 1.73205i) q^{76} +4.00000 q^{77} +(-1.00000 + 3.46410i) q^{78} -4.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-2.50000 - 4.33013i) q^{82} -6.00000 q^{83} +(-1.00000 - 1.73205i) q^{84} -10.0000 q^{86} +(4.50000 + 7.79423i) q^{87} +(-1.00000 + 1.73205i) q^{88} +(-1.00000 + 1.73205i) q^{89} +(-2.00000 + 6.92820i) q^{91} -6.00000 q^{92} +(2.00000 - 3.46410i) q^{93} +(1.00000 - 1.73205i) q^{94} +1.00000 q^{96} +(-1.00000 - 1.73205i) q^{97} +(1.50000 + 2.59808i) q^{98} +2.00000 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}+O(q^{10}) $ 2 * q - q^2 - q^3 - q^4 - q^6 - 2 * q^7 + 2 * q^8 - q^9	$ 2 q - q^{2} - q^{3} - q^{4} - q^{6} - 2 q^{7} + 2 q^{8} - q^{9} - 2 q^{11} + 2 q^{12} - 5 q^{13} + 4 q^{14} - q^{16} + 5 q^{17} + 2 q^{18} + 2 q^{19} + 4 q^{21} - 2 q^{22} + 6 q^{23} - q^{24} + 7 q^{26} + 2 q^{27} - 2 q^{28} + 9 q^{29} - 8 q^{31} - q^{32} - 2 q^{33} - 10 q^{34} - q^{36} - 11 q^{37} - 4 q^{38} + 7 q^{39} - 5 q^{41} - 2 q^{42} + 10 q^{43} + 4 q^{44} + 6 q^{46} - 4 q^{47} - q^{48} + 3 q^{49} - 10 q^{51} - 2 q^{52} + 2 q^{53} - q^{54} - 2 q^{56} - 4 q^{57} + 9 q^{58} + 8 q^{59} + 11 q^{61} + 4 q^{62} - 2 q^{63} + 2 q^{64} + 4 q^{66} + 2 q^{67} + 5 q^{68} + 6 q^{69} + 14 q^{71} - q^{72} + 26 q^{73} - 11 q^{74} + 2 q^{76} + 8 q^{77} - 2 q^{78} - 8 q^{79} - q^{81} - 5 q^{82} - 12 q^{83} - 2 q^{84} - 20 q^{86} + 9 q^{87} - 2 q^{88} - 2 q^{89} - 4 q^{91} - 12 q^{92} + 4 q^{93} + 2 q^{94} + 2 q^{96} - 2 q^{97} + 3 q^{98} + 4 q^{99}+O(q^{100}) $ 2 * q - q^2 - q^3 - q^4 - q^6 - 2 * q^7 + 2 * q^8 - q^9 - 2 * q^11 + 2 * q^12 - 5 * q^13 + 4 * q^14 - q^16 + 5 * q^17 + 2 * q^18 + 2 * q^19 + 4 * q^21 - 2 * q^22 + 6 * q^23 - q^24 + 7 * q^26 + 2 * q^27 - 2 * q^28 + 9 * q^29 - 8 * q^31 - q^32 - 2 * q^33 - 10 * q^34 - q^36 - 11 * q^37 - 4 * q^38 + 7 * q^39 - 5 * q^41 - 2 * q^42 + 10 * q^43 + 4 * q^44 + 6 * q^46 - 4 * q^47 - q^48 + 3 * q^49 - 10 * q^51 - 2 * q^52 + 2 * q^53 - q^54 - 2 * q^56 - 4 * q^57 + 9 * q^58 + 8 * q^59 + 11 * q^61 + 4 * q^62 - 2 * q^63 + 2 * q^64 + 4 * q^66 + 2 * q^67 + 5 * q^68 + 6 * q^69 + 14 * q^71 - q^72 + 26 * q^73 - 11 * q^74 + 2 * q^76 + 8 * q^77 - 2 * q^78 - 8 * q^79 - q^81 - 5 * q^82 - 12 * q^83 - 2 * q^84 - 20 * q^86 + 9 * q^87 - 2 * q^88 - 2 * q^89 - 4 * q^91 - 12 * q^92 + 4 * q^93 + 2 * q^94 + 2 * q^96 - 2 * q^97 + 3 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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	$-0.290043\pi$
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	−0.990766	+	0.135583i	$0.956709\pi$
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$	1.00000			0.288675
$13$	−2.50000	−	2.59808i	−0.693375	−	0.720577i
$13$	−2.50000	−	2.59808i	−0.693375	−	0.720577i
$14$	2.00000			0.534522
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.50000	+	4.33013i	0.606339	+	1.05021i	0.991838	+	0.127502i	$0.0406959\pi$
$17$	2.50000	+	4.33013i	0.606339	+	1.05021i	−0.385499	+	0.922708i	$0.625971\pi$
$18$	1.00000			0.235702
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	0.957635	−	0.287984i	$-0.0929851\pi$
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	−0.728219	+	0.685344i	$0.759652\pi$
$20$		0			0
$21$	2.00000			0.436436
$22$	−1.00000	−	1.73205i	−0.213201	−	0.369274i
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$		0			0
$26$	3.50000	−	0.866025i	0.686406	−	0.169842i
$27$	1.00000			0.192450
$28$	−1.00000	+	1.73205i	−0.188982	+	0.327327i
$29$	4.50000	−	7.79423i	0.835629	−	1.44735i	−0.0578882	−	0.998323i	$-0.518437\pi$
$29$	4.50000	−	7.79423i	0.835629	−	1.44735i	0.893517	−	0.449029i	$-0.148230\pi$
$30$		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
$33$	−1.00000	−	1.73205i	−0.174078	−	0.301511i
$34$	−5.00000			−0.857493
$35$		0			0
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−5.50000	+	9.52628i	−0.904194	+	1.56611i	−0.0821995	+	0.996616i	$0.526194\pi$
$37$	−5.50000	+	9.52628i	−0.904194	+	1.56611i	−0.821995	+	0.569495i	$0.807139\pi$
$38$	−2.00000			−0.324443
$39$	3.50000	−	0.866025i	0.560449	−	0.138675i
$40$		0			0
$41$	−2.50000	+	4.33013i	−0.390434	+	0.676252i	−0.992507	−	0.122189i	$-0.961009\pi$
$41$	−2.50000	+	4.33013i	−0.390434	+	0.676252i	0.602072	+	0.798441i	$0.294342\pi$
$42$	−1.00000	+	1.73205i	−0.154303	+	0.267261i
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	0.941562	+	0.336840i	$0.109358\pi$
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	−0.179069	+	0.983836i	$0.557309\pi$
$44$	2.00000			0.301511
$45$		0			0
$46$	3.00000	+	5.19615i	0.442326	+	0.766131i
$47$	−2.00000			−0.291730			−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000			−0.291730			−0.145865	+	0.989305i	$0.546597\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$		0			0
$51$	−5.00000			−0.700140
$52$	−1.00000	+	3.46410i	−0.138675	+	0.480384i
$53$	1.00000			0.137361			0.0686803	−	0.997639i	$-0.478121\pi$
$53$	1.00000			0.137361			0.0686803	+	0.997639i	$0.478121\pi$
$54$	−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
$58$	4.50000	+	7.79423i	0.590879	+	1.02343i
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	0.999709	+	0.0241347i	$0.00768307\pi$
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	−0.478953	+	0.877841i	$0.658984\pi$
$60$		0			0
$61$	5.50000	+	9.52628i	0.704203	+	1.21972i	0.966978	+	0.254858i	$0.0820288\pi$
$61$	5.50000	+	9.52628i	0.704203	+	1.21972i	−0.262776	+	0.964857i	$0.584638\pi$
$62$	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
$66$	2.00000			0.246183
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	−0.798454	−	0.602056i	$-0.794348\pi$
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	0.920623	+	0.390453i	$0.127682\pi$
$68$	2.50000	−	4.33013i	0.303170	−	0.525105i
$69$	3.00000	+	5.19615i	0.361158	+	0.625543i
$70$		0			0
$71$	7.00000	+	12.1244i	0.830747	+	1.43890i	0.897447	+	0.441123i	$0.145420\pi$
$71$	7.00000	+	12.1244i	0.830747	+	1.43890i	−0.0666994	+	0.997773i	$0.521247\pi$
$72$	−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	$0.224823\pi$
$74$	−5.50000	−	9.52628i	−0.639362	−	1.10741i
$75$		0			0
$76$	1.00000	−	1.73205i	0.114708	−	0.198680i
$77$	4.00000			0.455842
$78$	−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
$82$	−2.50000	−	4.33013i	−0.276079	−	0.478183i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$	−1.00000	−	1.73205i	−0.109109	−	0.188982i
$85$		0			0
$86$	−10.0000			−1.07833
$87$	4.50000	+	7.79423i	0.482451	+	0.835629i
$88$	−1.00000	+	1.73205i	−0.106600	+	0.184637i
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	−0.914146	−	0.405385i	$-0.867138\pi$
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	0.808146	+	0.588982i	$0.200471\pi$
$90$		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
$94$	1.00000	−	1.73205i	0.103142	−	0.178647i
$95$		0			0
$96$	1.00000			0.102062
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$	1.50000	+	2.59808i	0.151523	+	0.262445i
$99$	2.00000			0.201008
$100$		0			0
$101$	2.50000	−	4.33013i	0.248759	−	0.430864i	−0.714423	−	0.699715i	$-0.753311\pi$
$101$	2.50000	−	4.33013i	0.248759	−	0.430864i	0.963182	+	0.268851i	$0.0866439\pi$
$102$	2.50000	−	4.33013i	0.247537	−	0.428746i
$103$	−10.0000			−0.985329			−0.492665	−	0.870219i	$-0.663977\pi$
$103$	−10.0000			−0.985329			−0.492665	+	0.870219i	$0.663977\pi$
$104$	−2.50000	−	2.59808i	−0.245145	−	0.254762i
$105$		0			0
$106$	−0.500000	+	0.866025i	−0.0485643	+	0.0841158i
$107$	−9.00000	+	15.5885i	−0.870063	+	1.50699i	−0.00813215	+	0.999967i	$0.502589\pi$
$107$	−9.00000	+	15.5885i	−0.870063	+	1.50699i	−0.861931	+	0.507026i	$0.830745\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$	−5.50000	−	9.52628i	−0.522037	−	0.904194i
$112$	2.00000			0.188982
$113$	−1.50000	−	2.59808i	−0.141108	−	0.244406i	0.786806	−	0.617200i	$-0.211733\pi$
$113$	−1.50000	−	2.59808i	−0.141108	−	0.244406i	−0.927914	+	0.372794i	$0.878400\pi$
$114$	1.00000	−	1.73205i	0.0936586	−	0.162221i
$115$		0			0
$116$	−9.00000			−0.835629
$117$	−1.00000	+	3.46410i	−0.0924500	+	0.320256i
$118$	−8.00000			−0.736460
$119$	5.00000	−	8.66025i	0.458349	−	0.793884i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−11.0000			−0.995893
$123$	−2.50000	−	4.33013i	−0.225417	−	0.390434i
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$		0			0
$126$	−1.00000	−	1.73205i	−0.0890871	−	0.154303i
$127$	−6.00000	+	10.3923i	−0.532414	+	0.922168i	0.466870	+	0.884326i	$0.345382\pi$
$127$	−6.00000	+	10.3923i	−0.532414	+	0.922168i	−0.999284	+	0.0378419i	$0.987952\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−10.0000			−0.880451
$130$		0			0
$131$	−8.00000			−0.698963			−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−8.00000			−0.698963			−0.349482	+	0.936943i	$0.613642\pi$
$132$	−1.00000	+	1.73205i	−0.0870388	+	0.150756i
$133$	2.00000	−	3.46410i	0.173422	−	0.300376i
$134$	1.00000	+	1.73205i	0.0863868	+	0.149626i
$135$		0			0
$136$	2.50000	+	4.33013i	0.214373	+	0.371305i
$137$	8.50000	+	14.7224i	0.726204	+	1.25782i	0.958477	+	0.285171i	$0.0920506\pi$
$137$	8.50000	+	14.7224i	0.726204	+	1.25782i	−0.232273	+	0.972651i	$0.574616\pi$
$138$	−6.00000			−0.510754
$139$	6.00000	+	10.3923i	0.508913	+	0.881464i	0.999947	+	0.0103230i	$0.00328598\pi$
$139$	6.00000	+	10.3923i	0.508913	+	0.881464i	−0.491033	+	0.871141i	$0.663381\pi$
$140$		0			0
$141$	1.00000	−	1.73205i	0.0842152	−	0.145865i
$142$	−14.0000			−1.17485
$143$	7.00000	−	1.73205i	0.585369	−	0.144841i
$144$	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
$148$	11.0000			0.904194
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	0.798019	−	0.602632i	$-0.205881\pi$
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	−0.920904	+	0.389789i	$0.872548\pi$
$150$		0			0
$151$	−6.00000			−0.488273			−0.244137	−	0.969741i	$-0.578505\pi$
$151$	−6.00000			−0.488273			−0.244137	+	0.969741i	$0.578505\pi$
$152$	1.00000	+	1.73205i	0.0811107	+	0.140488i
$153$	2.50000	−	4.33013i	0.202113	−	0.350070i
$154$	−2.00000	+	3.46410i	−0.161165	+	0.279145i
$155$		0			0
$156$	−2.50000	−	2.59808i	−0.200160	−	0.208013i
$157$	7.00000			0.558661			0.279330	−	0.960195i	$-0.409888\pi$
$157$	7.00000			0.558661			0.279330	+	0.960195i	$0.409888\pi$
$158$	2.00000	−	3.46410i	0.159111	−	0.275589i
$159$	−0.500000	+	0.866025i	−0.0396526	+	0.0686803i
$160$		0			0
$161$	−12.0000			−0.945732
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	10.0000	+	17.3205i	0.783260	+	1.35665i	0.930033	+	0.367477i	$0.119778\pi$
$163$	10.0000	+	17.3205i	0.783260	+	1.35665i	−0.146772	+	0.989170i	$0.546888\pi$
$164$	5.00000			0.390434
$165$		0			0
$166$	3.00000	−	5.19615i	0.232845	−	0.403300i
$167$	12.0000	−	20.7846i	0.928588	−	1.60836i	0.142901	−	0.989737i	$-0.454357\pi$
$167$	12.0000	−	20.7846i	0.928588	−	1.60836i	0.785687	−	0.618624i	$-0.212310\pi$
$168$	2.00000			0.154303
$169$	−0.500000	+	12.9904i	−0.0384615	+	0.999260i
$170$		0			0
$171$	1.00000	−	1.73205i	0.0764719	−	0.132453i
$172$	5.00000	−	8.66025i	0.381246	−	0.660338i
$173$	−11.0000	−	19.0526i	−0.836315	−	1.44854i	−0.892956	−	0.450145i	$-0.851372\pi$
$173$	−11.0000	−	19.0526i	−0.836315	−	1.44854i	0.0566411	−	0.998395i	$-0.481961\pi$
$174$	−9.00000			−0.682288
$175$		0			0
$176$	−1.00000	−	1.73205i	−0.0753778	−	0.130558i
$177$	−8.00000			−0.601317
$178$	−1.00000	−	1.73205i	−0.0749532	−	0.129823i
$179$	3.00000	−	5.19615i	0.224231	−	0.388379i	−0.731858	−	0.681457i	$-0.761346\pi$
$179$	3.00000	−	5.19615i	0.224231	−	0.388379i	0.956088	+	0.293079i	$0.0946798\pi$
$180$		0			0
$181$	5.00000			0.371647			0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000			0.371647			0.185824	+	0.982583i	$0.440505\pi$
$182$	−5.00000	−	5.19615i	−0.370625	−	0.385164i
$183$	−11.0000			−0.813143
$184$	3.00000	−	5.19615i	0.221163	−	0.383065i
$185$		0			0
$186$	2.00000	+	3.46410i	0.146647	+	0.254000i
$187$	−10.0000			−0.731272
$188$	1.00000	+	1.73205i	0.0729325	+	0.126323i
$189$	−1.00000	−	1.73205i	−0.0727393	−	0.125988i
$190$		0			0
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	0.784552	−	0.620063i	$-0.212893\pi$
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	−0.929267	+	0.369410i	$0.879560\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−8.50000	+	14.7224i	−0.611843	+	1.05974i	0.379086	+	0.925361i	$0.376238\pi$
$193$	−8.50000	+	14.7224i	−0.611843	+	1.05974i	−0.990930	+	0.134382i	$0.957095\pi$
$194$	2.00000			0.143592
$195$		0			0
$196$	−3.00000			−0.214286
$197$	3.00000	−	5.19615i	0.213741	−	0.370211i	−0.739141	−	0.673550i	$-0.764768\pi$
$197$	3.00000	−	5.19615i	0.213741	−	0.370211i	0.952882	+	0.303340i	$0.0981018\pi$
$198$	−1.00000	+	1.73205i	−0.0710669	+	0.123091i
$199$	−5.00000	−	8.66025i	−0.354441	−	0.613909i	0.632581	−	0.774494i	$-0.281995\pi$
$199$	−5.00000	−	8.66025i	−0.354441	−	0.613909i	−0.987022	+	0.160585i	$0.948662\pi$
$200$		0			0
$201$	1.00000	+	1.73205i	0.0705346	+	0.122169i
$202$	2.50000	+	4.33013i	0.175899	+	0.304667i
$203$	−18.0000			−1.26335
$204$	2.50000	+	4.33013i	0.175035	+	0.303170i
$205$		0			0
$206$	5.00000	−	8.66025i	0.348367	−	0.603388i
$207$	−6.00000			−0.417029
$208$	3.50000	−	0.866025i	0.242681	−	0.0600481i
$209$	−4.00000			−0.276686
$210$		0			0
$211$	−12.0000	+	20.7846i	−0.826114	+	1.43087i	0.0749508	+	0.997187i	$0.476120\pi$
$211$	−12.0000	+	20.7846i	−0.826114	+	1.43087i	−0.901065	+	0.433684i	$0.857213\pi$
$212$	−0.500000	−	0.866025i	−0.0343401	−	0.0594789i
$213$	−14.0000			−0.959264
$214$	−9.00000	−	15.5885i	−0.615227	−	1.06561i
$215$		0			0
$216$	1.00000			0.0680414
$217$	4.00000	+	6.92820i	0.271538	+	0.470317i
$218$	1.00000	−	1.73205i	0.0677285	−	0.117309i
$219$	−6.50000	+	11.2583i	−0.439229	+	0.760767i
$220$		0			0
$221$	5.00000	−	17.3205i	0.336336	−	1.16510i
$222$	11.0000			0.738272
$223$	−8.00000	+	13.8564i	−0.535720	+	0.927894i	0.463409	+	0.886145i	$0.346626\pi$
$223$	−8.00000	+	13.8564i	−0.535720	+	0.927894i	−0.999128	+	0.0417488i	$0.986707\pi$
$224$	−1.00000	+	1.73205i	−0.0668153	+	0.115728i
$225$		0			0
$226$	3.00000			0.199557
$227$	7.00000	+	12.1244i	0.464606	+	0.804722i	0.999184	−	0.0403978i	$-0.0128625\pi$
$227$	7.00000	+	12.1244i	0.464606	+	0.804722i	−0.534577	+	0.845120i	$0.679529\pi$
$228$	1.00000	+	1.73205i	0.0662266	+	0.114708i
$229$	10.0000			0.660819			0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000			0.660819			0.330409	+	0.943838i	$0.392813\pi$
$230$		0			0
$231$	−2.00000	+	3.46410i	−0.131590	+	0.227921i
$232$	4.50000	−	7.79423i	0.295439	−	0.511716i
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$	−2.50000	−	2.59808i	−0.163430	−	0.169842i
$235$		0			0
$236$	4.00000	−	6.92820i	0.260378	−	0.450988i
$237$	2.00000	−	3.46410i	0.129914	−	0.225018i
$238$	5.00000	+	8.66025i	0.324102	+	0.561361i
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$		0			0
$241$	−3.50000	−	6.06218i	−0.225455	−	0.390499i	0.731001	−	0.682376i	$-0.239053\pi$
$241$	−3.50000	−	6.06218i	−0.225455	−	0.390499i	−0.956456	+	0.291877i	$0.905720\pi$
$242$	−7.00000			−0.449977
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	5.50000	−	9.52628i	0.352101	−	0.609858i
$245$		0			0
$246$	5.00000			0.318788
$247$	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
$251$	−2.00000	−	3.46410i	−0.126239	−	0.218652i	0.795978	−	0.605326i	$-0.206957\pi$
$251$	−2.00000	−	3.46410i	−0.126239	−	0.218652i	−0.922217	+	0.386674i	$0.873624\pi$
$252$	2.00000			0.125988
$253$	6.00000	+	10.3923i	0.377217	+	0.653359i
$254$	−6.00000	−	10.3923i	−0.376473	−	0.652071i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.50000	+	2.59808i	−0.0935674	+	0.162064i	−0.909010	−	0.416775i	$-0.863160\pi$
$257$	−1.50000	+	2.59808i	−0.0935674	+	0.162064i	0.815442	+	0.578838i	$0.196494\pi$
$258$	5.00000	−	8.66025i	0.311286	−	0.539164i
$259$	22.0000			1.36701
$260$		0			0
$261$	−9.00000			−0.557086
$262$	4.00000	−	6.92820i	0.247121	−	0.428026i
$263$	7.00000	−	12.1244i	0.431638	−	0.747620i	−0.565376	−	0.824833i	$-0.691269\pi$
$263$	7.00000	−	12.1244i	0.431638	−	0.747620i	0.997015	+	0.0772134i	$0.0246023\pi$
$264$	−1.00000	−	1.73205i	−0.0615457	−	0.106600i
$265$		0			0
$266$	2.00000	+	3.46410i	0.122628	+	0.212398i
$267$	−1.00000	−	1.73205i	−0.0611990	−	0.106000i
$268$	−2.00000			−0.122169
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	0.996586	−	0.0825561i	$-0.0263084\pi$
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	−0.569789	+	0.821791i	$0.692975\pi$
$270$		0			0
$271$	−4.00000	+	6.92820i	−0.242983	+	0.420858i	−0.961563	−	0.274586i	$-0.911459\pi$
$271$	−4.00000	+	6.92820i	−0.242983	+	0.420858i	0.718580	+	0.695444i	$0.244792\pi$
$272$	−5.00000			−0.303170
$273$	−5.00000	−	5.19615i	−0.302614	−	0.314485i
$274$	−17.0000			−1.02701
$275$		0			0
$276$	3.00000	−	5.19615i	0.180579	−	0.312772i
$277$	−5.50000	−	9.52628i	−0.330463	−	0.572379i	0.652140	−	0.758099i	$-0.273872\pi$
$277$	−5.50000	−	9.52628i	−0.330463	−	0.572379i	−0.982603	+	0.185720i	$0.940538\pi$
$278$	−12.0000			−0.719712
$279$	2.00000	+	3.46410i	0.119737	+	0.207390i
$280$		0			0
$281$	25.0000			1.49137			0.745687	−	0.666296i	$-0.232121\pi$
$281$	25.0000			1.49137			0.745687	+	0.666296i	$0.232121\pi$
$282$	1.00000	+	1.73205i	0.0595491	+	0.103142i
$283$	13.0000	−	22.5167i	0.772770	−	1.33848i	−0.163270	−	0.986581i	$-0.552204\pi$
$283$	13.0000	−	22.5167i	0.772770	−	1.33848i	0.936039	−	0.351895i	$-0.114463\pi$
$284$	7.00000	−	12.1244i	0.415374	−	0.719448i
$285$		0			0
$286$	−2.00000	+	6.92820i	−0.118262	+	0.409673i
$287$	10.0000			0.590281
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	−4.00000	+	6.92820i	−0.235294	+	0.407541i
$290$		0			0
$291$	2.00000			0.117242
$292$	−6.50000	−	11.2583i	−0.380384	−	0.658844i
$293$	−0.500000	−	0.866025i	−0.0292103	−	0.0505937i	0.851051	−	0.525084i	$-0.175966\pi$
$293$	−0.500000	−	0.866025i	−0.0292103	−	0.0505937i	−0.880261	+	0.474490i	$0.842633\pi$
$294$	−3.00000			−0.174964
$295$		0			0
$296$	−5.50000	+	9.52628i	−0.319681	+	0.553704i
$297$	−1.00000	+	1.73205i	−0.0580259	+	0.100504i
$298$	3.00000			0.173785
$299$	−21.0000	+	5.19615i	−1.21446	+	0.300501i
$300$		0			0
$301$	10.0000	−	17.3205i	0.576390	−	0.998337i
$302$	3.00000	−	5.19615i	0.172631	−	0.299005i
$303$	2.50000	+	4.33013i	0.143621	+	0.248759i
$304$	−2.00000			−0.114708
$305$		0			0
$306$	2.50000	+	4.33013i	0.142915	+	0.247537i
$307$	14.0000			0.799022			0.399511	−	0.916728i	$-0.369180\pi$
$307$	14.0000			0.799022			0.399511	+	0.916728i	$0.369180\pi$
$308$	−2.00000	−	3.46410i	−0.113961	−	0.197386i
$309$	5.00000	−	8.66025i	0.284440	−	0.492665i
$310$		0			0
$311$	6.00000			0.340229			0.170114	−	0.985424i	$-0.445586\pi$
$311$	6.00000			0.340229			0.170114	+	0.985424i	$0.445586\pi$
$312$	3.50000	−	0.866025i	0.198148	−	0.0490290i
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$	−3.50000	+	6.06218i	−0.197516	+	0.342108i
$315$		0			0
$316$	2.00000	+	3.46410i	0.112509	+	0.194871i
$317$	33.0000			1.85346			0.926732	−	0.375722i	$-0.122605\pi$
$317$	33.0000			1.85346			0.926732	+	0.375722i	$0.122605\pi$
$318$	−0.500000	−	0.866025i	−0.0280386	−	0.0485643i
$319$	9.00000	+	15.5885i	0.503903	+	0.872786i
$320$		0			0
$321$	−9.00000	−	15.5885i	−0.502331	−	0.870063i
$322$	6.00000	−	10.3923i	0.334367	−	0.579141i
$323$	−5.00000	+	8.66025i	−0.278207	+	0.481869i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−20.0000			−1.10770
$327$	1.00000	−	1.73205i	0.0553001	−	0.0957826i
$328$	−2.50000	+	4.33013i	−0.138039	+	0.239091i
$329$	2.00000	+	3.46410i	0.110264	+	0.190982i
$330$		0			0
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	0.937829	+	0.347097i	$0.112833\pi$
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	−0.168320	+	0.985732i	$0.553834\pi$
$332$	3.00000	+	5.19615i	0.164646	+	0.285176i
$333$	11.0000			0.602796
$334$	12.0000	+	20.7846i	0.656611	+	1.13728i
$335$		0			0
$336$	−1.00000	+	1.73205i	−0.0545545	+	0.0944911i
$337$	9.00000			0.490261			0.245131	−	0.969490i	$-0.421169\pi$
$337$	9.00000			0.490261			0.245131	+	0.969490i	$0.421169\pi$
$338$	−11.0000	−	6.92820i	−0.598321	−	0.376845i
$339$	3.00000			0.162938
$340$		0			0
$341$	4.00000	−	6.92820i	0.216612	−	0.375183i
$342$	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
$346$	22.0000			1.18273
$347$	3.00000	+	5.19615i	0.161048	+	0.278944i	0.935245	−	0.354001i	$-0.115179\pi$
$347$	3.00000	+	5.19615i	0.161048	+	0.278944i	−0.774197	+	0.632945i	$0.781846\pi$
$348$	4.50000	−	7.79423i	0.241225	−	0.417815i
$349$	−3.00000	+	5.19615i	−0.160586	+	0.278144i	−0.935079	−	0.354439i	$-0.884672\pi$
$349$	−3.00000	+	5.19615i	−0.160586	+	0.278144i	0.774493	+	0.632583i	$0.218005\pi$
$350$		0			0
$351$	−2.50000	−	2.59808i	−0.133440	−	0.138675i
$352$	2.00000			0.106600
$353$	8.50000	−	14.7224i	0.452409	−	0.783596i	−0.546126	−	0.837703i	$-0.683898\pi$
$353$	8.50000	−	14.7224i	0.452409	−	0.783596i	0.998535	+	0.0541072i	$0.0172313\pi$
$354$	4.00000	−	6.92820i	0.212598	−	0.368230i
$355$		0			0
$356$	2.00000			0.106000
$357$	5.00000	+	8.66025i	0.264628	+	0.458349i
$358$	3.00000	+	5.19615i	0.158555	+	0.274625i
$359$	−30.0000			−1.58334			−0.791670	−	0.610949i	$-0.790788\pi$
$359$	−30.0000			−1.58334			−0.791670	+	0.610949i	$0.790788\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	−2.50000	+	4.33013i	−0.131397	+	0.227586i
$363$	−7.00000			−0.367405
$364$	7.00000	−	1.73205i	0.366900	−	0.0907841i
$365$		0			0
$366$	5.50000	−	9.52628i	0.287490	−	0.497947i
$367$	−1.00000	+	1.73205i	−0.0521996	+	0.0904123i	−0.890945	−	0.454112i	$-0.849957\pi$
$367$	−1.00000	+	1.73205i	−0.0521996	+	0.0904123i	0.838745	+	0.544524i	$0.183290\pi$
$368$	3.00000	+	5.19615i	0.156386	+	0.270868i
$369$	5.00000			0.260290
$370$		0			0
$371$	−1.00000	−	1.73205i	−0.0519174	−	0.0899236i
$372$	−4.00000			−0.207390
$373$	4.50000	+	7.79423i	0.233001	+	0.403570i	0.958690	−	0.284453i	$-0.0918121\pi$
$373$	4.50000	+	7.79423i	0.233001	+	0.403570i	−0.725689	+	0.688023i	$0.758479\pi$
$374$	5.00000	−	8.66025i	0.258544	−	0.447811i
$375$		0			0
$376$	−2.00000			−0.103142
$377$	−31.5000	+	7.79423i	−1.62233	+	0.401423i
$378$	2.00000			0.102869
$379$	−6.00000	+	10.3923i	−0.308199	+	0.533817i	−0.977969	−	0.208752i	$-0.933060\pi$
$379$	−6.00000	+	10.3923i	−0.308199	+	0.533817i	0.669769	+	0.742569i	$0.266393\pi$
$380$		0			0
$381$	−6.00000	−	10.3923i	−0.307389	−	0.532414i
$382$	4.00000			0.204658
$383$	12.0000	+	20.7846i	0.613171	+	1.06204i	0.990702	+	0.136047i	$0.0434398\pi$
$383$	12.0000	+	20.7846i	0.613171	+	1.06204i	−0.377531	+	0.925997i	$0.623227\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$		0			0
$386$	−8.50000	−	14.7224i	−0.432639	−	0.749352i
$387$	5.00000	−	8.66025i	0.254164	−	0.440225i
$388$	−1.00000	+	1.73205i	−0.0507673	+	0.0879316i
$389$	19.0000			0.963338			0.481669	−	0.876353i	$-0.340031\pi$
$389$	19.0000			0.963338			0.481669	+	0.876353i	$0.340031\pi$
$390$		0			0
$391$	30.0000			1.51717
$392$	1.50000	−	2.59808i	0.0757614	−	0.131223i
$393$	4.00000	−	6.92820i	0.201773	−	0.349482i
$394$	3.00000	+	5.19615i	0.151138	+	0.261778i
$395$		0			0
$396$	−1.00000	−	1.73205i	−0.0502519	−	0.0870388i
$397$	−9.00000	−	15.5885i	−0.451697	−	0.782362i	0.546795	−	0.837267i	$-0.315848\pi$
$397$	−9.00000	−	15.5885i	−0.451697	−	0.782362i	−0.998492	+	0.0549046i	$0.982515\pi$
$398$	10.0000			0.501255
$399$	2.00000	+	3.46410i	0.100125	+	0.173422i
$400$		0			0
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	−0.302556	−	0.953131i	$-0.597840\pi$
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	0.976714	−	0.214544i	$-0.0688266\pi$
$402$	−2.00000			−0.0997509
$403$	10.0000	+	10.3923i	0.498135	+	0.517678i
$404$	−5.00000			−0.248759
$405$		0			0
$406$	9.00000	−	15.5885i	0.446663	−	0.773642i
$407$	−11.0000	−	19.0526i	−0.545250	−	0.944400i
$408$	−5.00000			−0.247537
$409$	−11.5000	−	19.9186i	−0.568638	−	0.984911i	−0.996701	−	0.0811615i	$-0.974137\pi$
$409$	−11.5000	−	19.9186i	−0.568638	−	0.984911i	0.428063	−	0.903749i	$-0.359196\pi$
$410$		0			0
$411$	−17.0000			−0.838548
$412$	5.00000	+	8.66025i	0.246332	+	0.426660i
$413$	8.00000	−	13.8564i	0.393654	−	0.681829i
$414$	3.00000	−	5.19615i	0.147442	−	0.255377i
$415$		0			0
$416$	−1.00000	+	3.46410i	−0.0490290	+	0.169842i
$417$	−12.0000			−0.587643
$418$	2.00000	−	3.46410i	0.0978232	−	0.169435i
$419$	16.0000	−	27.7128i	0.781651	−	1.35386i	−0.149328	−	0.988788i	$-0.547711\pi$
$419$	16.0000	−	27.7128i	0.781651	−	1.35386i	0.930979	−	0.365072i	$-0.118956\pi$
$420$		0			0
$421$	−23.0000			−1.12095			−0.560476	−	0.828171i	$-0.689382\pi$
$421$	−23.0000			−1.12095			−0.560476	+	0.828171i	$0.689382\pi$
$422$	−12.0000	−	20.7846i	−0.584151	−	1.01178i
$423$	1.00000	+	1.73205i	0.0486217	+	0.0842152i
$424$	1.00000			0.0485643
$425$		0			0
$426$	7.00000	−	12.1244i	0.339151	−	0.587427i
$427$	11.0000	−	19.0526i	0.532327	−	0.922018i
$428$	18.0000			0.870063
$429$	−2.00000	+	6.92820i	−0.0965609	+	0.334497i
$430$		0			0
$431$	1.00000	−	1.73205i	0.0481683	−	0.0834300i	−0.840936	−	0.541135i	$-0.817995\pi$
$431$	1.00000	−	1.73205i	0.0481683	−	0.0834300i	0.889104	+	0.457705i	$0.151328\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−10.5000	−	18.1865i	−0.504598	−	0.873989i	−0.999986	−	0.00531724i	$-0.998307\pi$
$433$	−10.5000	−	18.1865i	−0.504598	−	0.873989i	0.495388	−	0.868672i	$-0.335026\pi$
$434$	−8.00000			−0.384012
$435$		0			0
$436$	1.00000	+	1.73205i	0.0478913	+	0.0829502i
$437$	12.0000			0.574038
$438$	−6.50000	−	11.2583i	−0.310582	−	0.537944i
$439$	−5.00000	+	8.66025i	−0.238637	+	0.413331i	−0.960323	−	0.278889i	$-0.910034\pi$
$439$	−5.00000	+	8.66025i	−0.238637	+	0.413331i	0.721686	+	0.692220i	$0.243367\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$	12.5000	+	12.9904i	0.594564	+	0.617889i
$443$	−20.0000			−0.950229			−0.475114	−	0.879924i	$-0.657593\pi$
$443$	−20.0000			−0.950229			−0.475114	+	0.879924i	$0.657593\pi$
$444$	−5.50000	+	9.52628i	−0.261018	+	0.452097i
$445$		0			0
$446$	−8.00000	−	13.8564i	−0.378811	−	0.656120i
$447$	3.00000			0.141895
$448$	−1.00000	−	1.73205i	−0.0472456	−	0.0818317i
$449$	15.0000	+	25.9808i	0.707894	+	1.22611i	0.965637	+	0.259895i	$0.0836878\pi$
$449$	15.0000	+	25.9808i	0.707894	+	1.22611i	−0.257743	+	0.966213i	$0.582979\pi$
$450$		0			0
$451$	−5.00000	−	8.66025i	−0.235441	−	0.407795i
$452$	−1.50000	+	2.59808i	−0.0705541	+	0.122203i
$453$	3.00000	−	5.19615i	0.140952	−	0.244137i
$454$	−14.0000			−0.657053
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	1.50000	−	2.59808i	0.0701670	−	0.121533i	−0.828807	−	0.559534i	$-0.810980\pi$
$457$	1.50000	−	2.59808i	0.0701670	−	0.121533i	0.898974	+	0.438001i	$0.144313\pi$
$458$	−5.00000	+	8.66025i	−0.233635	+	0.404667i
$459$	2.50000	+	4.33013i	0.116690	+	0.202113i
$460$		0			0
$461$	−1.50000	−	2.59808i	−0.0698620	−	0.121004i	0.828978	−	0.559281i	$-0.188923\pi$
$461$	−1.50000	−	2.59808i	−0.0698620	−	0.121004i	−0.898840	+	0.438276i	$0.855589\pi$
$462$	−2.00000	−	3.46410i	−0.0930484	−	0.161165i
$463$	14.0000			0.650635			0.325318	−	0.945605i	$-0.394529\pi$
$463$	14.0000			0.650635			0.325318	+	0.945605i	$0.394529\pi$
$464$	4.50000	+	7.79423i	0.208907	+	0.361838i
$465$		0			0
$466$	−3.00000	+	5.19615i	−0.138972	+	0.240707i
$467$	22.0000			1.01804			0.509019	−	0.860755i	$-0.330008\pi$
$467$	22.0000			1.01804			0.509019	+	0.860755i	$0.330008\pi$
$468$	3.50000	−	0.866025i	0.161788	−	0.0400320i
$469$	−4.00000			−0.184703
$470$		0			0
$471$	−3.50000	+	6.06218i	−0.161271	+	0.279330i
$472$	4.00000	+	6.92820i	0.184115	+	0.318896i
$473$	−20.0000			−0.919601
$474$	2.00000	+	3.46410i	0.0918630	+	0.159111i
$475$		0			0
$476$	−10.0000			−0.458349
$477$	−0.500000	−	0.866025i	−0.0228934	−	0.0396526i
$478$	3.00000	−	5.19615i	0.137217	−	0.237666i
$479$	−16.0000	+	27.7128i	−0.731059	+	1.26623i	0.225372	+	0.974273i	$0.427640\pi$
$479$	−16.0000	+	27.7128i	−0.731059	+	1.26623i	−0.956431	+	0.291958i	$0.905693\pi$
$480$		0			0
$481$	38.5000	−	9.52628i	1.75545	−	0.434361i
$482$	7.00000			0.318841
$483$	6.00000	−	10.3923i	0.273009	−	0.472866i
$484$	3.50000	−	6.06218i	0.159091	−	0.275554i
$485$		0			0
$486$	1.00000			0.0453609
$487$	−13.0000	−	22.5167i	−0.589086	−	1.02033i	−0.994352	−	0.106129i	$-0.966154\pi$
$487$	−13.0000	−	22.5167i	−0.589086	−	1.02033i	0.405266	−	0.914199i	$-0.367179\pi$
$488$	5.50000	+	9.52628i	0.248973	+	0.431234i
$489$	−20.0000			−0.904431
$490$		0			0
$491$	15.0000	−	25.9808i	0.676941	−	1.17250i	−0.298957	−	0.954267i	$-0.596639\pi$
$491$	15.0000	−	25.9808i	0.676941	−	1.17250i	0.975898	−	0.218229i	$-0.0700279\pi$
$492$	−2.50000	+	4.33013i	−0.112709	+	0.195217i
$493$	45.0000			2.02670
$494$	5.00000	+	5.19615i	0.224961	+	0.233786i
$495$		0			0
$496$	2.00000	−	3.46410i	0.0898027	−	0.155543i
$497$	14.0000	−	24.2487i	0.627986	−	1.08770i
$498$	3.00000	+	5.19615i	0.134433	+	0.232845i
$499$		0			0			−	1.00000i	$-0.5\pi$
$499$		0			0				1.00000i	$0.5\pi$
$500$		0			0
$501$	12.0000	+	20.7846i	0.536120	+	0.928588i
$502$	4.00000			0.178529
$503$	−7.00000	−	12.1244i	−0.312115	−	0.540598i	0.666705	−	0.745321i	$-0.267704\pi$
$503$	−7.00000	−	12.1244i	−0.312115	−	0.540598i	−0.978820	+	0.204723i	$0.934371\pi$
$504$	−1.00000	+	1.73205i	−0.0445435	+	0.0771517i
$505$		0			0
$506$	−12.0000			−0.533465
$507$	−11.0000	−	6.92820i	−0.488527	−	0.307692i
$508$	12.0000			0.532414
$509$	−7.50000	+	12.9904i	−0.332432	+	0.575789i	−0.982988	−	0.183669i	$-0.941202\pi$
$509$	−7.50000	+	12.9904i	−0.332432	+	0.575789i	0.650556	+	0.759458i	$0.274536\pi$
$510$		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
$517$	2.00000	−	3.46410i	0.0879599	−	0.152351i
$518$	−11.0000	+	19.0526i	−0.483312	+	0.837121i
$519$	22.0000			0.965693
$520$		0			0
$521$	25.0000			1.09527			0.547635	−	0.836717i	$-0.315528\pi$
$521$	25.0000			1.09527			0.547635	+	0.836717i	$0.315528\pi$
$522$	4.50000	−	7.79423i	0.196960	−	0.341144i
$523$	−19.0000	+	32.9090i	−0.830812	+	1.43901i	0.0665832	+	0.997781i	$0.478790\pi$
$523$	−19.0000	+	32.9090i	−0.830812	+	1.43901i	−0.897395	+	0.441228i	$0.854543\pi$
$524$	4.00000	+	6.92820i	0.174741	+	0.302660i
$525$		0			0
$526$	7.00000	+	12.1244i	0.305215	+	0.528647i
$527$	−10.0000	−	17.3205i	−0.435607	−	0.754493i
$528$	2.00000			0.0870388
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$		0			0
$531$	4.00000	−	6.92820i	0.173585	−	0.300658i
$532$	−4.00000			−0.173422
$533$	17.5000	−	4.33013i	0.758009	−	0.187559i
$534$	2.00000			0.0865485
$535$		0			0
$536$	1.00000	−	1.73205i	0.0431934	−	0.0748132i
$537$	3.00000	+	5.19615i	0.129460	+	0.224231i
$538$	−14.0000			−0.603583
$539$	3.00000	+	5.19615i	0.129219	+	0.223814i
$540$		0			0
$541$	−7.00000			−0.300954			−0.150477	−	0.988614i	$-0.548081\pi$
$541$	−7.00000			−0.300954			−0.150477	+	0.988614i	$0.548081\pi$
$542$	−4.00000	−	6.92820i	−0.171815	−	0.297592i
$543$	−2.50000	+	4.33013i	−0.107285	+	0.185824i
$544$	2.50000	−	4.33013i	0.107187	−	0.185653i
$545$		0			0
$546$	7.00000	−	1.73205i	0.299572	−	0.0741249i
$547$	−2.00000			−0.0855138			−0.0427569	−	0.999086i	$-0.513614\pi$
$547$	−2.00000			−0.0855138			−0.0427569	+	0.999086i	$0.513614\pi$
$548$	8.50000	−	14.7224i	0.363102	−	0.628911i
$549$	5.50000	−	9.52628i	0.234734	−	0.406572i
$550$		0			0
$551$	18.0000			0.766826
$552$	3.00000	+	5.19615i	0.127688	+	0.221163i
$553$	4.00000	+	6.92820i	0.170097	+	0.294617i
$554$	11.0000			0.467345
$555$		0			0
$556$	6.00000	−	10.3923i	0.254457	−	0.440732i
$557$	−4.50000	+	7.79423i	−0.190671	+	0.330252i	−0.945473	−	0.325701i	$-0.894400\pi$
$557$	−4.50000	+	7.79423i	−0.190671	+	0.330252i	0.754802	+	0.655953i	$0.227733\pi$
$558$	−4.00000			−0.169334
$559$	10.0000	−	34.6410i	0.422955	−	1.46516i
$560$		0			0
$561$	5.00000	−	8.66025i	0.211100	−	0.365636i
$562$	−12.5000	+	21.6506i	−0.527281	+	0.913277i
$563$	20.0000	+	34.6410i	0.842900	+	1.45994i	0.887433	+	0.460937i	$0.152487\pi$
$563$	20.0000	+	34.6410i	0.842900	+	1.45994i	−0.0445334	+	0.999008i	$0.514180\pi$
$564$	−2.00000			−0.0842152
$565$		0			0
$566$	13.0000	+	22.5167i	0.546431	+	0.946446i
$567$	2.00000			0.0839921
$568$	7.00000	+	12.1244i	0.293713	+	0.508727i
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	−0.922032	−	0.387113i	$-0.873472\pi$
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	0.796266	+	0.604947i	$0.206806\pi$
$570$		0			0
$571$	−2.00000			−0.0836974			−0.0418487	−	0.999124i	$-0.513325\pi$
$571$	−2.00000			−0.0836974			−0.0418487	+	0.999124i	$0.513325\pi$
$572$	−5.00000	−	5.19615i	−0.209061	−	0.217262i
$573$	4.00000			0.167102
$574$	−5.00000	+	8.66025i	−0.208696	+	0.361472i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−27.0000			−1.12402			−0.562012	−	0.827129i	$-0.689973\pi$
$577$	−27.0000			−1.12402			−0.562012	+	0.827129i	$0.689973\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$	−8.50000	−	14.7224i	−0.353248	−	0.611843i
$580$		0			0
$581$	6.00000	+	10.3923i	0.248922	+	0.431145i
$582$	−1.00000	+	1.73205i	−0.0414513	+	0.0717958i
$583$	−1.00000	+	1.73205i	−0.0414158	+	0.0717342i
$584$	13.0000			0.537944
$585$		0			0
$586$	1.00000			0.0413096
$587$	−16.0000	+	27.7128i	−0.660391	+	1.14383i	0.320122	+	0.947376i	$0.396276\pi$
$587$	−16.0000	+	27.7128i	−0.660391	+	1.14383i	−0.980513	+	0.196454i	$0.937057\pi$
$588$	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
$592$	−5.50000	−	9.52628i	−0.226049	−	0.391528i
$593$	39.0000			1.60154			0.800769	−	0.598973i	$-0.204424\pi$
$593$	39.0000			1.60154			0.800769	+	0.598973i	$0.204424\pi$
$594$	−1.00000	−	1.73205i	−0.0410305	−	0.0710669i
$595$		0			0
$596$	−1.50000	+	2.59808i	−0.0614424	+	0.106421i
$597$	10.0000			0.409273
$598$	6.00000	−	20.7846i	0.245358	−	0.849946i
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	−5.50000	+	9.52628i	−0.224350	+	0.388585i	−0.956124	−	0.292962i	$-0.905359\pi$
$601$	−5.50000	+	9.52628i	−0.224350	+	0.388585i	0.731774	+	0.681547i	$0.238692\pi$
$602$	10.0000	+	17.3205i	0.407570	+	0.705931i
$603$	−2.00000			−0.0814463
$604$	3.00000	+	5.19615i	0.122068	+	0.211428i
$605$		0			0
$606$	−5.00000			−0.203111
$607$	16.0000	+	27.7128i	0.649420	+	1.12483i	0.983262	+	0.182199i	$0.0583216\pi$
$607$	16.0000	+	27.7128i	0.649420	+	1.12483i	−0.333842	+	0.942629i	$0.608345\pi$
$608$	1.00000	−	1.73205i	0.0405554	−	0.0702439i
$609$	9.00000	−	15.5885i	0.364698	−	0.631676i
$610$		0			0
$611$	5.00000	+	5.19615i	0.202278	+	0.210214i
$612$	−5.00000			−0.202113
$613$	6.50000	−	11.2583i	0.262533	−	0.454720i	−0.704382	−	0.709821i	$-0.748776\pi$
$613$	6.50000	−	11.2583i	0.262533	−	0.454720i	0.966914	+	0.255102i	$0.0821090\pi$
$614$	−7.00000	+	12.1244i	−0.282497	+	0.489299i
$615$		0			0
$616$	4.00000			0.161165
$617$	−7.50000	−	12.9904i	−0.301939	−	0.522973i	0.674636	−	0.738150i	$-0.264300\pi$
$617$	−7.50000	−	12.9904i	−0.301939	−	0.522973i	−0.976575	+	0.215177i	$0.930967\pi$
$618$	5.00000	+	8.66025i	0.201129	+	0.348367i
$619$	32.0000			1.28619			0.643094	−	0.765787i	$-0.277650\pi$
$619$	32.0000			1.28619			0.643094	+	0.765787i	$0.277650\pi$
$620$		0			0
$621$	3.00000	−	5.19615i	0.120386	−	0.208514i
$622$	−3.00000	+	5.19615i	−0.120289	+	0.208347i
$623$	4.00000			0.160257
$624$	−1.00000	+	3.46410i	−0.0400320	+	0.138675i
$625$		0			0
$626$	3.00000	−	5.19615i	0.119904	−	0.207680i
$627$	2.00000	−	3.46410i	0.0798723	−	0.138343i
$628$	−3.50000	−	6.06218i	−0.139665	−	0.241907i
$629$	−55.0000			−2.19299
$630$		0			0
$631$	−6.00000	−	10.3923i	−0.238856	−	0.413711i	0.721530	−	0.692383i	$-0.243439\pi$
$631$	−6.00000	−	10.3923i	−0.238856	−	0.413711i	−0.960386	+	0.278672i	$0.910106\pi$
$632$	−4.00000			−0.159111
$633$	−12.0000	−	20.7846i	−0.476957	−	0.826114i
$634$	−16.5000	+	28.5788i	−0.655299	+	1.13501i
$635$		0			0
$636$	1.00000			0.0396526
$637$	−10.5000	+	2.59808i	−0.416025	+	0.102940i
$638$	−18.0000			−0.712627
$639$	7.00000	−	12.1244i	0.276916	−	0.479632i
$640$		0			0
$641$	−2.50000	−	4.33013i	−0.0987441	−	0.171030i	0.812421	−	0.583071i	$-0.198149\pi$
$641$	−2.50000	−	4.33013i	−0.0987441	−	0.171030i	−0.911165	+	0.412042i	$0.864816\pi$
$642$	18.0000			0.710403
$643$	4.00000	+	6.92820i	0.157745	+	0.273222i	0.934055	−	0.357129i	$-0.116244\pi$
$643$	4.00000	+	6.92820i	0.157745	+	0.273222i	−0.776310	+	0.630351i	$0.782911\pi$
$644$	6.00000	+	10.3923i	0.236433	+	0.409514i
$645$		0			0
$646$	−5.00000	−	8.66025i	−0.196722	−	0.340733i
$647$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$647$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−16.0000			−0.628055
$650$		0			0
$651$	−8.00000			−0.313545
$652$	10.0000	−	17.3205i	0.391630	−	0.678323i
$653$	−11.0000	+	19.0526i	−0.430463	+	0.745584i	−0.996913	−	0.0785119i	$-0.974983\pi$
$653$	−11.0000	+	19.0526i	−0.430463	+	0.745584i	0.566450	+	0.824096i	$0.308316\pi$
$654$	1.00000	+	1.73205i	0.0391031	+	0.0677285i
$655$		0			0
$656$	−2.50000	−	4.33013i	−0.0976086	−	0.169063i
$657$	−6.50000	−	11.2583i	−0.253589	−	0.439229i
$658$	−4.00000			−0.155936
$659$	−12.0000	−	20.7846i	−0.467454	−	0.809653i	0.531855	−	0.846836i	$-0.321495\pi$
$659$	−12.0000	−	20.7846i	−0.467454	−	0.809653i	−0.999309	+	0.0371821i	$0.988162\pi$
$660$		0			0
$661$	−12.5000	+	21.6506i	−0.486194	+	0.842112i	−0.999874	−	0.0158695i	$-0.994948\pi$
$661$	−12.5000	+	21.6506i	−0.486194	+	0.842112i	0.513680	+	0.857982i	$0.328282\pi$
$662$	−28.0000			−1.08825
$663$	12.5000	+	12.9904i	0.485460	+	0.504505i
$664$	−6.00000			−0.232845
$665$		0			0
$666$	−5.50000	+	9.52628i	−0.213121	+	0.369136i
$667$	−27.0000	−	46.7654i	−1.04544	−	1.81076i
$668$	−24.0000			−0.928588
$669$	−8.00000	−	13.8564i	−0.309298	−	0.535720i
$670$		0			0
$671$	−22.0000			−0.849301
$672$	−1.00000	−	1.73205i	−0.0385758	−	0.0668153i
$673$	21.5000	−	37.2391i	0.828764	−	1.43546i	−0.0702442	−	0.997530i	$-0.522378\pi$
$673$	21.5000	−	37.2391i	0.828764	−	1.43546i	0.899008	−	0.437932i	$-0.144289\pi$
$674$	−4.50000	+	7.79423i	−0.173334	+	0.300222i
$675$		0			0
$676$	11.5000	−	6.06218i	0.442308	−	0.233161i
$677$	46.0000			1.76792			0.883962	−	0.467559i	$-0.154866\pi$
$677$	46.0000			1.76792			0.883962	+	0.467559i	$0.154866\pi$
$678$	−1.50000	+	2.59808i	−0.0576072	+	0.0997785i
$679$	−2.00000	+	3.46410i	−0.0767530	+	0.132940i
$680$		0			0
$681$	−14.0000			−0.536481
$682$	4.00000	+	6.92820i	0.153168	+	0.265295i
$683$	−20.0000	−	34.6410i	−0.765279	−	1.32550i	−0.940099	−	0.340901i	$-0.889268\pi$
$683$	−20.0000	−	34.6410i	−0.765279	−	1.32550i	0.174820	−	0.984600i	$-0.444066\pi$
$684$	−2.00000			−0.0764719
$685$		0			0
$686$	10.0000	−	17.3205i	0.381802	−	0.661300i
$687$	−5.00000	+	8.66025i	−0.190762	+	0.330409i
$688$	−10.0000			−0.381246
$689$	−2.50000	−	2.59808i	−0.0952424	−	0.0989788i
$690$		0			0
$691$	1.00000	−	1.73205i	0.0380418	−	0.0658903i	−0.846378	−	0.532583i	$-0.821221\pi$
$691$	1.00000	−	1.73205i	0.0380418	−	0.0658903i	0.884419	+	0.466693i	$0.154555\pi$
$692$	−11.0000	+	19.0526i	−0.418157	+	0.724270i
$693$	−2.00000	−	3.46410i	−0.0759737	−	0.131590i
$694$	−6.00000			−0.227757
$695$		0			0
$696$	4.50000	+	7.79423i	0.170572	+	0.295439i
$697$	−25.0000			−0.946943
$698$	−3.00000	−	5.19615i	−0.113552	−	0.196677i
$699$	−3.00000	+	5.19615i	−0.113470	+	0.196537i
$700$		0			0
$701$	34.0000			1.28416			0.642081	−	0.766637i	$-0.278071\pi$
$701$	34.0000			1.28416			0.642081	+	0.766637i	$0.278071\pi$
$702$	3.50000	−	0.866025i	0.132099	−	0.0326860i
$703$	−22.0000			−0.829746
$704$	−1.00000	+	1.73205i	−0.0376889	+	0.0652791i
$705$		0			0
$706$	8.50000	+	14.7224i	0.319902	+	0.554086i
$707$	−10.0000			−0.376089
$708$	4.00000	+	6.92820i	0.150329	+	0.260378i
$709$	7.50000	+	12.9904i	0.281668	+	0.487864i	0.971796	−	0.235824i	$-0.0757789\pi$
$709$	7.50000	+	12.9904i	0.281668	+	0.487864i	−0.690127	+	0.723688i	$0.742446\pi$
$710$		0			0
$711$	2.00000	+	3.46410i	0.0750059	+	0.129914i
$712$	−1.00000	+	1.73205i	−0.0374766	+	0.0649113i
$713$	−12.0000	+	20.7846i	−0.449404	+	0.778390i
$714$	−10.0000			−0.374241
$715$		0			0
$716$	−6.00000			−0.224231
$717$	3.00000	−	5.19615i	0.112037	−	0.194054i
$718$	15.0000	−	25.9808i	0.559795	−	0.969593i
$719$	−12.0000	−	20.7846i	−0.447524	−	0.775135i	0.550700	−	0.834703i	$-0.314361\pi$
$719$	−12.0000	−	20.7846i	−0.447524	−	0.775135i	−0.998224	+	0.0595683i	$0.981028\pi$
$720$		0			0
$721$	10.0000	+	17.3205i	0.372419	+	0.645049i
$722$	7.50000	+	12.9904i	0.279121	+	0.483452i
$723$	7.00000			0.260333
$724$	−2.50000	−	4.33013i	−0.0929118	−	0.160928i
$725$		0			0
$726$	3.50000	−	6.06218i	0.129897	−	0.224989i
$727$	−2.00000			−0.0741759			−0.0370879	−	0.999312i	$-0.511808\pi$
$727$	−2.00000			−0.0741759			−0.0370879	+	0.999312i	$0.511808\pi$
$728$	−2.00000	+	6.92820i	−0.0741249	+	0.256776i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−25.0000	+	43.3013i	−0.924658	+	1.60156i
$732$	5.50000	+	9.52628i	0.203286	+	0.352101i
$733$	−13.0000			−0.480166			−0.240083	−	0.970752i	$-0.577175\pi$
$733$	−13.0000			−0.480166			−0.240083	+	0.970752i	$0.577175\pi$
$734$	−1.00000	−	1.73205i	−0.0369107	−	0.0639312i
$735$		0			0
$736$	−6.00000			−0.221163
$737$	2.00000	+	3.46410i	0.0736709	+	0.127602i
$738$	−2.50000	+	4.33013i	−0.0920263	+	0.159394i
$739$	−8.00000	+	13.8564i	−0.294285	+	0.509716i	−0.974818	−	0.223001i	$-0.928415\pi$
$739$	−8.00000	+	13.8564i	−0.294285	+	0.509716i	0.680534	+	0.732717i	$0.261748\pi$
$740$		0			0
$741$	5.00000	+	5.19615i	0.183680	+	0.190885i
$742$	2.00000			0.0734223
$743$	−6.00000	+	10.3923i	−0.220119	+	0.381257i	−0.954844	−	0.297108i	$-0.903978\pi$
$743$	−6.00000	+	10.3923i	−0.220119	+	0.381257i	0.734725	+	0.678365i	$0.237311\pi$
$744$	2.00000	−	3.46410i	0.0733236	−	0.127000i
$745$		0			0
$746$	−9.00000			−0.329513
$747$	3.00000	+	5.19615i	0.109764	+	0.190117i
$748$	5.00000	+	8.66025i	0.182818	+	0.316650i
$749$	36.0000			1.31541
$750$		0			0
$751$	−13.0000	+	22.5167i	−0.474377	+	0.821645i	−0.999570	−	0.0293387i	$-0.990660\pi$
$751$	−13.0000	+	22.5167i	−0.474377	+	0.821645i	0.525193	+	0.850983i	$0.323993\pi$
$752$	1.00000	−	1.73205i	0.0364662	−	0.0631614i
$753$	4.00000			0.145768
$754$	9.00000	−	31.1769i	0.327761	−	1.13540i
$755$		0			0
$756$	−1.00000	+	1.73205i	−0.0363696	+	0.0629941i
$757$	−9.00000	+	15.5885i	−0.327111	+	0.566572i	−0.981937	−	0.189207i	$-0.939408\pi$
$757$	−9.00000	+	15.5885i	−0.327111	+	0.566572i	0.654827	+	0.755779i	$0.272742\pi$
$758$	−6.00000	−	10.3923i	−0.217930	−	0.377466i
$759$	−12.0000			−0.435572
$760$		0			0
$761$	−17.0000	−	29.4449i	−0.616250	−	1.06738i	−0.990164	−	0.139912i	$-0.955318\pi$
$761$	−17.0000	−	29.4449i	−0.616250	−	1.06738i	0.373914	−	0.927463i	$-0.378015\pi$
$762$	12.0000			0.434714
$763$	2.00000	+	3.46410i	0.0724049	+	0.125409i
$764$	−2.00000	+	3.46410i	−0.0723575	+	0.125327i
$765$		0			0
$766$	−24.0000			−0.867155
$767$	8.00000	−	27.7128i	0.288863	−	1.00065i
$768$	1.00000			0.0360844
$769$	17.0000	−	29.4449i	0.613036	−	1.06181i	−0.377690	−	0.925932i	$-0.623282\pi$
$769$	17.0000	−	29.4449i	0.613036	−	1.06181i	0.990726	−	0.135877i	$-0.0433852\pi$
$770$		0			0
$771$	−1.50000	−	2.59808i	−0.0540212	−	0.0935674i
$772$	17.0000			0.611843
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	0.981250	−	0.192740i	$-0.0617373\pi$
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	−0.657542	+	0.753418i	$0.728404\pi$
$774$	5.00000	+	8.66025i	0.179721	+	0.311286i
$775$		0			0
$776$	−1.00000	−	1.73205i	−0.0358979	−	0.0621770i
$777$	−11.0000	+	19.0526i	−0.394623	+	0.683507i
$778$	−9.50000	+	16.4545i	−0.340592	+	0.589922i
$779$	−10.0000			−0.358287
$780$		0			0
$781$	−28.0000			−1.00192
$782$	−15.0000	+	25.9808i	−0.536399	+	0.929070i
$783$	4.50000	−	7.79423i	0.160817	−	0.278543i
$784$	1.50000	+	2.59808i	0.0535714	+	0.0927884i
$785$		0			0
$786$	4.00000	+	6.92820i	0.142675	+	0.247121i
$787$	2.00000	+	3.46410i	0.0712923	+	0.123482i	0.899468	−	0.436987i	$-0.143954\pi$
$787$	2.00000	+	3.46410i	0.0712923	+	0.123482i	−0.828176	+	0.560469i	$0.810621\pi$
$788$	−6.00000			−0.213741
$789$	7.00000	+	12.1244i	0.249207	+	0.431638i
$790$		0			0
$791$	−3.00000	+	5.19615i	−0.106668	+	0.184754i
$792$	2.00000			0.0710669
$793$	11.0000	−	38.1051i	0.390621	−	1.35315i
$794$	18.0000			0.638796
$795$		0			0
$796$	−5.00000	+	8.66025i	−0.177220	+	0.306955i
$797$	−1.00000	−	1.73205i	−0.0354218	−	0.0613524i	0.847771	−	0.530362i	$-0.177944\pi$
$797$	−1.00000	−	1.73205i	−0.0354218	−	0.0613524i	−0.883193	+	0.469010i	$0.844611\pi$
$798$	−4.00000			−0.141598
$799$	−5.00000	−	8.66025i	−0.176887	−	0.306378i
$800$		0			0
$801$	2.00000			0.0706665
$802$	13.5000	+	23.3827i	0.476702	+	0.825671i
$803$	−13.0000	+	22.5167i	−0.458760	+	0.794596i
$804$	1.00000	−	1.73205i	0.0352673	−	0.0610847i
$805$		0			0
$806$	−14.0000	+	3.46410i	−0.493129	+	0.122018i
$807$	−14.0000			−0.492823
$808$	2.50000	−	4.33013i	0.0879497	−	0.152333i
$809$	−2.50000	+	4.33013i	−0.0878953	+	0.152239i	−0.906621	−	0.421945i	$-0.861347\pi$
$809$	−2.50000	+	4.33013i	−0.0878953	+	0.152239i	0.818726	+	0.574184i	$0.194681\pi$
$810$		0			0
$811$	−36.0000			−1.26413			−0.632065	−	0.774915i	$-0.717793\pi$
$811$	−36.0000			−1.26413			−0.632065	+	0.774915i	$0.717793\pi$
$812$	9.00000	+	15.5885i	0.315838	+	0.547048i
$813$	−4.00000	−	6.92820i	−0.140286	−	0.242983i
$814$	22.0000			0.771100
$815$		0			0
$816$	2.50000	−	4.33013i	0.0875175	−	0.151585i
$817$	−10.0000	+	17.3205i	−0.349856	+	0.605968i
$818$	23.0000			0.804176
$819$	7.00000	−	1.73205i	0.244600	−	0.0605228i
$820$		0			0
$821$	15.0000	−	25.9808i	0.523504	−	0.906735i	−0.476122	−	0.879379i	$-0.657958\pi$
$821$	15.0000	−	25.9808i	0.523504	−	0.906735i	0.999626	−	0.0273557i	$-0.00870868\pi$
$822$	8.50000	−	14.7224i	0.296472	−	0.513504i
$823$	−8.00000	−	13.8564i	−0.278862	−	0.483004i	0.692240	−	0.721668i	$-0.256624\pi$
$823$	−8.00000	−	13.8564i	−0.278862	−	0.483004i	−0.971102	+	0.238664i	$0.923291\pi$
$824$	−10.0000			−0.348367
$825$		0			0
$826$	8.00000	+	13.8564i	0.278356	+	0.482126i
$827$	8.00000			0.278187			0.139094	−	0.990279i	$-0.455581\pi$
$827$	8.00000			0.278187			0.139094	+	0.990279i	$0.455581\pi$
$828$	3.00000	+	5.19615i	0.104257	+	0.180579i
$829$	17.5000	−	30.3109i	0.607800	−	1.05274i	−0.383802	−	0.923415i	$-0.625386\pi$
$829$	17.5000	−	30.3109i	0.607800	−	1.05274i	0.991602	−	0.129325i	$-0.0412811\pi$
$830$		0			0
$831$	11.0000			0.381586
$832$	−2.50000	−	2.59808i	−0.0866719	−	0.0900721i
$833$	15.0000			0.519719
$834$	6.00000	−	10.3923i	0.207763	−	0.359856i
$835$		0			0
$836$	2.00000	+	3.46410i	0.0691714	+	0.119808i
$837$	−4.00000			−0.138260
$838$	16.0000	+	27.7128i	0.552711	+	0.957323i
$839$	−22.0000	−	38.1051i	−0.759524	−	1.31553i	−0.943093	−	0.332528i	$-0.892098\pi$
$839$	−22.0000	−	38.1051i	−0.759524	−	1.31553i	0.183569	−	0.983007i	$-0.441235\pi$
$840$		0			0
$841$	−26.0000	−	45.0333i	−0.896552	−	1.55287i
$842$	11.5000	−	19.9186i	0.396316	−	0.686440i
$843$	−12.5000	+	21.6506i	−0.430523	+	0.745687i
$844$	24.0000			0.826114
$845$		0			0
$846$	−2.00000			−0.0687614
$847$	7.00000	−	12.1244i	0.240523	−	0.416598i
$848$	−0.500000	+	0.866025i	−0.0171701	+	0.0297394i
$849$	13.0000	+	22.5167i	0.446159	+	0.772770i
$850$		0			0
$851$	33.0000	+	57.1577i	1.13123	+	1.95934i
$852$	7.00000	+	12.1244i	0.239816	+	0.415374i
$853$	−49.0000			−1.67773			−0.838864	−	0.544341i	$-0.816780\pi$
$853$	−49.0000			−1.67773			−0.838864	+	0.544341i	$0.816780\pi$
$854$	11.0000	+	19.0526i	0.376412	+	0.651965i
$855$		0			0
$856$	−9.00000	+	15.5885i	−0.307614	+	0.532803i
$857$	−45.0000			−1.53717			−0.768585	−	0.639747i	$-0.779039\pi$
$857$	−45.0000			−1.53717			−0.768585	+	0.639747i	$0.779039\pi$
$858$	−5.00000	−	5.19615i	−0.170697	−	0.177394i
$859$	−50.0000			−1.70598			−0.852989	−	0.521929i	$-0.825213\pi$
$859$	−50.0000			−1.70598			−0.852989	+	0.521929i	$0.825213\pi$
$860$		0			0
$861$	−5.00000	+	8.66025i	−0.170400	+	0.295141i
$862$	1.00000	+	1.73205i	0.0340601	+	0.0589939i
$863$	−46.0000			−1.56586			−0.782929	−	0.622111i	$-0.786275\pi$
$863$	−46.0000			−1.56586			−0.782929	+	0.622111i	$0.786275\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$		0			0
$866$	21.0000			0.713609
$867$	−4.00000	−	6.92820i	−0.135847	−	0.235294i
$868$	4.00000	−	6.92820i	0.135769	−	0.235159i
$869$	4.00000	−	6.92820i	0.135691	−	0.235023i
$870$		0			0
$871$	−7.00000	+	1.73205i	−0.237186	+	0.0586883i
$872$	−2.00000			−0.0677285
$873$	−1.00000	+	1.73205i	−0.0338449	+	0.0586210i
$874$	−6.00000	+	10.3923i	−0.202953	+	0.351525i
$875$		0			0
$876$	13.0000			0.439229
$877$	18.5000	+	32.0429i	0.624701	+	1.08201i	0.988599	+	0.150574i	$0.0481123\pi$
$877$	18.5000	+	32.0429i	0.624701	+	1.08201i	−0.363898	+	0.931439i	$0.618554\pi$
$878$	−5.00000	−	8.66025i	−0.168742	−	0.292269i
$879$	1.00000			0.0337292
$880$		0			0
$881$	−8.50000	+	14.7224i	−0.286372	+	0.496011i	−0.972941	−	0.231054i	$-0.925783\pi$
$881$	−8.50000	+	14.7224i	−0.286372	+	0.496011i	0.686569	+	0.727065i	$0.259116\pi$
$882$	1.50000	−	2.59808i	0.0505076	−	0.0874818i
$883$	8.00000			0.269221			0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000			0.269221			0.134611	+	0.990899i	$0.457022\pi$
$884$	−17.5000	+	4.33013i	−0.588589	+	0.145638i
$885$		0			0
$886$	10.0000	−	17.3205i	0.335957	−	0.581894i
$887$	12.0000	−	20.7846i	0.402921	−	0.697879i	−0.591156	−	0.806557i	$-0.701328\pi$
$887$	12.0000	−	20.7846i	0.402921	−	0.697879i	0.994077	+	0.108678i	$0.0346618\pi$
$888$	−5.50000	−	9.52628i	−0.184568	−	0.319681i
$889$	24.0000			0.804934
$890$		0			0
$891$	−1.00000	−	1.73205i	−0.0335013	−	0.0580259i
$892$	16.0000			0.535720
$893$	−2.00000	−	3.46410i	−0.0669274	−	0.115922i
$894$	−1.50000	+	2.59808i	−0.0501675	+	0.0868927i
$895$		0			0
$896$	2.00000			0.0668153
$897$	6.00000	−	20.7846i	0.200334	−	0.693978i
$898$	−30.0000			−1.00111
$899$	−18.0000	+	31.1769i	−0.600334	+	1.03981i
$900$		0			0
$901$	2.50000	+	4.33013i	0.0832871	+	0.144257i
$902$	10.0000			0.332964
$903$	10.0000	+	17.3205i	0.332779	+	0.576390i
$904$	−1.50000	−	2.59808i	−0.0498893	−	0.0864107i
$905$		0			0
$906$	3.00000	+	5.19615i	0.0996683	+	0.172631i
$907$	−22.0000	+	38.1051i	−0.730498	+	1.26526i	0.226173	+	0.974087i	$0.427379\pi$
$907$	−22.0000	+	38.1051i	−0.730498	+	1.26526i	−0.956671	+	0.291172i	$0.905955\pi$
$908$	7.00000	−	12.1244i	0.232303	−	0.402361i
$909$	−5.00000			−0.165840
$910$		0			0
$911$	−32.0000			−1.06021			−0.530104	−	0.847933i	$-0.677847\pi$
$911$	−32.0000			−1.06021			−0.530104	+	0.847933i	$0.677847\pi$
$912$	1.00000	−	1.73205i	0.0331133	−	0.0573539i
$913$	6.00000	−	10.3923i	0.198571	−	0.343935i
$914$	1.50000	+	2.59808i	0.0496156	+	0.0859367i
$915$		0			0
$916$	−5.00000	−	8.66025i	−0.165205	−	0.286143i
$917$	8.00000	+	13.8564i	0.264183	+	0.457579i
$918$	−5.00000			−0.165025
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	0.967274	−	0.253735i	$-0.0816592\pi$
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	−0.703378	+	0.710816i	$0.748326\pi$
$920$		0			0
$921$	−7.00000	+	12.1244i	−0.230658	+	0.399511i
$922$	3.00000			0.0987997
$923$	14.0000	−	48.4974i	0.460816	−	1.59631i
$924$	4.00000			0.131590
$925$		0			0
$926$	−7.00000	+	12.1244i	−0.230034	+	0.398431i
$927$	5.00000	+	8.66025i	0.164222	+	0.284440i
$928$	−9.00000			−0.295439
$929$	11.5000	+	19.9186i	0.377303	+	0.653508i	0.990669	−	0.136291i	$-0.0435183\pi$
$929$	11.5000	+	19.9186i	0.377303	+	0.653508i	−0.613366	+	0.789799i	$0.710185\pi$
$930$		0			0
$931$	6.00000			0.196642
$932$	−3.00000	−	5.19615i	−0.0982683	−	0.170206i
$933$	−3.00000	+	5.19615i	−0.0982156	+	0.170114i
$934$	−11.0000	+	19.0526i	−0.359931	+	0.623419i
$935$		0			0
$936$	−1.00000	+	3.46410i	−0.0326860	+	0.113228i
$937$	1.00000			0.0326686			0.0163343	−	0.999867i	$-0.494800\pi$
$937$	1.00000			0.0326686			0.0163343	+	0.999867i	$0.494800\pi$
$938$	2.00000	−	3.46410i	0.0653023	−	0.113107i
$939$	3.00000	−	5.19615i	0.0979013	−	0.169570i
$940$		0			0
$941$	−22.0000			−0.717180			−0.358590	−	0.933495i	$-0.616742\pi$
$941$	−22.0000			−0.717180			−0.358590	+	0.933495i	$0.616742\pi$
$942$	−3.50000	−	6.06218i	−0.114036	−	0.197516i
$943$	15.0000	+	25.9808i	0.488467	+	0.846050i
$944$	−8.00000			−0.260378
$945$		0			0
$946$	10.0000	−	17.3205i	0.325128	−	0.563138i
$947$	4.00000	−	6.92820i	0.129983	−	0.225136i	−0.793687	−	0.608326i	$-0.791841\pi$
$947$	4.00000	−	6.92820i	0.129983	−	0.225136i	0.923670	+	0.383190i	$0.125175\pi$
$948$	−4.00000			−0.129914
$949$	−32.5000	−	33.7750i	−1.05499	−	1.09638i
$950$		0			0
$951$	−16.5000	+	28.5788i	−0.535049	+	0.926732i
$952$	5.00000	−	8.66025i	0.162051	−	0.280680i
$953$	27.0000	+	46.7654i	0.874616	+	1.51488i	0.857171	+	0.515031i	$0.172220\pi$
$953$	27.0000	+	46.7654i	0.874616	+	1.51488i	0.0174443	+	0.999848i	$0.494447\pi$
$954$	1.00000			0.0323762
$955$		0			0
$956$	3.00000	+	5.19615i	0.0970269	+	0.168056i
$957$	−18.0000			−0.581857
$958$	−16.0000	−	27.7128i	−0.516937	−	0.895360i
$959$	17.0000	−	29.4449i	0.548959	−	0.950824i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	−11.0000	+	38.1051i	−0.354654	+	1.22856i
$963$	18.0000			0.580042
$964$	−3.50000	+	6.06218i	−0.112727	+	0.195250i
$965$		0			0
$966$	6.00000	+	10.3923i	0.193047	+	0.334367i
$967$	50.0000			1.60789			0.803946	−	0.594703i	$-0.202730\pi$
$967$	50.0000			1.60789			0.803946	+	0.594703i	$0.202730\pi$
$968$	3.50000	+	6.06218i	0.112494	+	0.194846i
$969$	−5.00000	−	8.66025i	−0.160623	−	0.278207i
$970$		0			0
$971$	−10.0000	−	17.3205i	−0.320915	−	0.555842i	0.659762	−	0.751475i	$-0.270657\pi$
$971$	−10.0000	−	17.3205i	−0.320915	−	0.555842i	−0.980677	+	0.195633i	$0.937324\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	12.0000	−	20.7846i	0.384702	−	0.666324i
$974$	26.0000			0.833094
$975$		0			0
$976$	−11.0000			−0.352101
$977$	10.5000	−	18.1865i	0.335925	−	0.581839i	−0.647737	−	0.761864i	$-0.724285\pi$
$977$	10.5000	−	18.1865i	0.335925	−	0.581839i	0.983662	+	0.180025i	$0.0576179\pi$
$978$	10.0000	−	17.3205i	0.319765	−	0.553849i
$979$	−2.00000	−	3.46410i	−0.0639203	−	0.110713i
$980$		0			0
$981$	1.00000	+	1.73205i	0.0319275	+	0.0553001i
$982$	15.0000	+	25.9808i	0.478669	+	0.829079i
$983$	−60.0000			−1.91370			−0.956851	−	0.290578i	$-0.906153\pi$
$983$	−60.0000			−1.91370			−0.956851	+	0.290578i	$0.906153\pi$
$984$	−2.50000	−	4.33013i	−0.0796971	−	0.138039i
$985$		0			0
$986$	−22.5000	+	38.9711i	−0.716546	+	1.24109i
$987$	−4.00000			−0.127321
$988$	−7.00000	+	1.73205i	−0.222700	+	0.0551039i
$989$	60.0000			1.90789
$990$		0			0
$991$	−9.00000	+	15.5885i	−0.285894	+	0.495184i	−0.972826	−	0.231539i	$-0.925624\pi$
$991$	−9.00000	+	15.5885i	−0.285894	+	0.495184i	0.686931	+	0.726722i	$0.258957\pi$
$992$	2.00000	+	3.46410i	0.0635001	+	0.109985i
$993$	−28.0000			−0.888553
$994$	14.0000	+	24.2487i	0.444053	+	0.769122i
$995$		0			0
$996$	−6.00000			−0.190117
$997$	−11.5000	−	19.9186i	−0.364209	−	0.630828i	0.624440	−	0.781073i	$-0.285327\pi$
$997$	−11.5000	−	19.9186i	−0.364209	−	0.630828i	−0.988649	+	0.150245i	$0.951994\pi$
$998$		0			0
$999$	−5.50000	+	9.52628i	−0.174012	+	0.301398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.i.b.451.1		2
5.2	odd	4		1950.2.z.b.1699.1		4
5.3	odd	4		1950.2.z.b.1699.2		4
5.4	even	2		78.2.e.b.61.1	yes	2
13.3	even	3	inner	1950.2.i.b.601.1		2
15.14	odd	2		234.2.h.b.217.1		2
20.19	odd	2		624.2.q.b.529.1		2
60.59	even	2		1872.2.t.i.1153.1		2
65.3	odd	12		1950.2.z.b.1849.1		4
65.4	even	6		1014.2.a.e.1.1		1
65.9	even	6		1014.2.a.a.1.1		1
65.19	odd	12		1014.2.b.a.337.2		2
65.24	odd	12		1014.2.i.e.361.1		4
65.29	even	6		78.2.e.b.55.1	✓	2
65.34	odd	4		1014.2.i.e.823.2		4
65.42	odd	12		1950.2.z.b.1849.2		4
65.44	odd	4		1014.2.i.e.823.1		4
65.49	even	6		1014.2.e.d.991.1		2
65.54	odd	12		1014.2.i.e.361.2		4
65.59	odd	12		1014.2.b.a.337.1		2
65.64	even	2		1014.2.e.d.529.1		2
195.29	odd	6		234.2.h.b.55.1		2
195.59	even	12		3042.2.b.d.1351.2		2
195.74	odd	6		3042.2.a.m.1.1		1
195.134	odd	6		3042.2.a.d.1.1		1
195.149	even	12		3042.2.b.d.1351.1		2
260.139	odd	6		8112.2.a.x.1.1		1
260.159	odd	6		624.2.q.b.289.1		2
260.199	odd	6		8112.2.a.bb.1.1		1
780.419	even	6		1872.2.t.i.289.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.e.b.55.1	✓	2	65.29	even	6
78.2.e.b.61.1	yes	2	5.4	even	2
234.2.h.b.55.1		2	195.29	odd	6
234.2.h.b.217.1		2	15.14	odd	2
624.2.q.b.289.1		2	260.159	odd	6
624.2.q.b.529.1		2	20.19	odd	2
1014.2.a.a.1.1		1	65.9	even	6
1014.2.a.e.1.1		1	65.4	even	6
1014.2.b.a.337.1		2	65.59	odd	12
1014.2.b.a.337.2		2	65.19	odd	12
1014.2.e.d.529.1		2	65.64	even	2
1014.2.e.d.991.1		2	65.49	even	6
1014.2.i.e.361.1		4	65.24	odd	12
1014.2.i.e.361.2		4	65.54	odd	12
1014.2.i.e.823.1		4	65.44	odd	4
1014.2.i.e.823.2		4	65.34	odd	4
1872.2.t.i.289.1		2	780.419	even	6
1872.2.t.i.1153.1		2	60.59	even	2
1950.2.i.b.451.1		2	1.1	even	1	trivial
1950.2.i.b.601.1		2	13.3	even	3	inner
1950.2.z.b.1699.1		4	5.2	odd	4
1950.2.z.b.1699.2		4	5.3	odd	4
1950.2.z.b.1849.1		4	65.3	odd	12
1950.2.z.b.1849.2		4	65.42	odd	12
3042.2.a.d.1.1		1	195.134	odd	6
3042.2.a.m.1.1		1	195.74	odd	6
3042.2.b.d.1351.1		2	195.149	even	12
3042.2.b.d.1351.2		2	195.59	even	12
8112.2.a.x.1.1		1	260.139	odd	6
8112.2.a.bb.1.1		1	260.199	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(-1.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(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} +(-1.00000 + 1.73205i) q^{11} +1.00000 q^{12} +(-2.50000 - 2.59808i) q^{13} +2.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.50000 + 4.33013i) q^{17} +1.00000 q^{18} +(1.00000 + 1.73205i) q^{19} +2.00000 q^{21} +(-1.00000 - 1.73205i) q^{22} +(3.00000 - 5.19615i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(3.50000 - 0.866025i) q^{26} +1.00000 q^{27} +(-1.00000 + 1.73205i) q^{28} +(4.50000 - 7.79423i) q^{29} -4.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{33} -5.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-5.50000 + 9.52628i) q^{37} -2.00000 q^{38} +(3.50000 - 0.866025i) q^{39} +(-2.50000 + 4.33013i) q^{41} +(-1.00000 + 1.73205i) q^{42} +(5.00000 + 8.66025i) q^{43} +2.00000 q^{44} +(3.00000 + 5.19615i) q^{46} -2.00000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(1.50000 - 2.59808i) q^{49} -5.00000 q^{51} +(-1.00000 + 3.46410i) q^{52} +1.00000 q^{53} +(-0.500000 + 0.866025i) q^{54} +(-1.00000 - 1.73205i) q^{56} -2.00000 q^{57} +(4.50000 + 7.79423i) q^{58} +(4.00000 + 6.92820i) q^{59} +(5.50000 + 9.52628i) q^{61} +(2.00000 - 3.46410i) q^{62} +(-1.00000 + 1.73205i) q^{63} +1.00000 q^{64} +2.00000 q^{66} +(1.00000 - 1.73205i) q^{67} +(2.50000 - 4.33013i) q^{68} +(3.00000 + 5.19615i) q^{69} +(7.00000 + 12.1244i) q^{71} +(-0.500000 - 0.866025i) q^{72} +13.0000 q^{73} +(-5.50000 - 9.52628i) q^{74} +(1.00000 - 1.73205i) q^{76} +4.00000 q^{77} +(-1.00000 + 3.46410i) q^{78} -4.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-2.50000 - 4.33013i) q^{82} -6.00000 q^{83} +(-1.00000 - 1.73205i) q^{84} -10.0000 q^{86} +(4.50000 + 7.79423i) q^{87} +(-1.00000 + 1.73205i) q^{88} +(-1.00000 + 1.73205i) q^{89} +(-2.00000 + 6.92820i) q^{91} -6.00000 q^{92} +(2.00000 - 3.46410i) q^{93} +(1.00000 - 1.73205i) q^{94} +1.00000 q^{96} +(-1.00000 - 1.73205i) q^{97} +(1.50000 + 2.59808i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{3} - q^{4} - q^{6} - 2 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 - q^3 - q^4 - q^6 - 2 * q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} - q^{3} - q^{4} - q^{6} - 2 q^{7} + 2 q^{8} - q^{9} - 2 q^{11} + 2 q^{12} - 5 q^{13} + 4 q^{14} - q^{16} + 5 q^{17} + 2 q^{18} + 2 q^{19} + 4 q^{21} - 2 q^{22} + 6 q^{23} - q^{24} + 7 q^{26} + 2 q^{27} - 2 q^{28} + 9 q^{29} - 8 q^{31} - q^{32} - 2 q^{33} - 10 q^{34} - q^{36} - 11 q^{37} - 4 q^{38} + 7 q^{39} - 5 q^{41} - 2 q^{42} + 10 q^{43} + 4 q^{44} + 6 q^{46} - 4 q^{47} - q^{48} + 3 q^{49} - 10 q^{51} - 2 q^{52} + 2 q^{53} - q^{54} - 2 q^{56} - 4 q^{57} + 9 q^{58} + 8 q^{59} + 11 q^{61} + 4 q^{62} - 2 q^{63} + 2 q^{64} + 4 q^{66} + 2 q^{67} + 5 q^{68} + 6 q^{69} + 14 q^{71} - q^{72} + 26 q^{73} - 11 q^{74} + 2 q^{76} + 8 q^{77} - 2 q^{78} - 8 q^{79} - q^{81} - 5 q^{82} - 12 q^{83} - 2 q^{84} - 20 q^{86} + 9 q^{87} - 2 q^{88} - 2 q^{89} - 4 q^{91} - 12 q^{92} + 4 q^{93} + 2 q^{94} + 2 q^{96} - 2 q^{97} + 3 q^{98} + 4 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^3 - q^4 - q^6 - 2 * q^7 + 2 * q^8 - q^9 - 2 * q^11 + 2 * q^12 - 5 * q^13 + 4 * q^14 - q^16 + 5 * q^17 + 2 * q^18 + 2 * q^19 + 4 * q^21 - 2 * q^22 + 6 * q^23 - q^24 + 7 * q^26 + 2 * q^27 - 2 * q^28 + 9 * q^29 - 8 * q^31 - q^32 - 2 * q^33 - 10 * q^34 - q^36 - 11 * q^37 - 4 * q^38 + 7 * q^39 - 5 * q^41 - 2 * q^42 + 10 * q^43 + 4 * q^44 + 6 * q^46 - 4 * q^47 - q^48 + 3 * q^49 - 10 * q^51 - 2 * q^52 + 2 * q^53 - q^54 - 2 * q^56 - 4 * q^57 + 9 * q^58 + 8 * q^59 + 11 * q^61 + 4 * q^62 - 2 * q^63 + 2 * q^64 + 4 * q^66 + 2 * q^67 + 5 * q^68 + 6 * q^69 + 14 * q^71 - q^72 + 26 * q^73 - 11 * q^74 + 2 * q^76 + 8 * q^77 - 2 * q^78 - 8 * q^79 - q^81 - 5 * q^82 - 12 * q^83 - 2 * q^84 - 20 * q^86 + 9 * q^87 - 2 * q^88 - 2 * q^89 - 4 * q^91 - 12 * q^92 + 4 * q^93 + 2 * q^94 + 2 * q^96 - 2 * q^97 + 3 * q^98 + 4 * q^99

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