LMFDB - Embedded newform 1950.2.z.b.1849.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(1699,1950)]

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, 3, 4]))

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

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

chi := DirichletCharacter("1950.1699");

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.z (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1849.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1950.1849
Dual form			1950.2.z.b.1699.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(1.73205 + 1.00000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(1.73205 + 1.00000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{11} -1.00000i q^{12} +(-2.59808 - 2.50000i) q^{13} -2.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.33013 - 2.50000i) q^{17} +1.00000i q^{18} +(-1.00000 + 1.73205i) q^{19} +2.00000 q^{21} +(1.73205 + 1.00000i) q^{22} +(-5.19615 + 3.00000i) q^{23} +(0.500000 + 0.866025i) q^{24} +(3.50000 + 0.866025i) q^{26} -1.00000i q^{27} +(1.73205 - 1.00000i) q^{28} +(-4.50000 - 7.79423i) q^{29} -4.00000 q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.73205 - 1.00000i) q^{33} +5.00000 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-9.52628 + 5.50000i) q^{37} -2.00000i q^{38} +(-3.50000 - 0.866025i) q^{39} +(-2.50000 - 4.33013i) q^{41} +(-1.73205 + 1.00000i) q^{42} +(8.66025 + 5.00000i) q^{43} -2.00000 q^{44} +(3.00000 - 5.19615i) q^{46} +2.00000i q^{47} +(-0.866025 - 0.500000i) q^{48} +(-1.50000 - 2.59808i) q^{49} -5.00000 q^{51} +(-3.46410 + 1.00000i) q^{52} +1.00000i q^{53} +(0.500000 + 0.866025i) q^{54} +(-1.00000 + 1.73205i) q^{56} +2.00000i q^{57} +(7.79423 + 4.50000i) q^{58} +(-4.00000 + 6.92820i) q^{59} +(5.50000 - 9.52628i) q^{61} +(3.46410 - 2.00000i) q^{62} +(1.73205 - 1.00000i) q^{63} -1.00000 q^{64} +2.00000 q^{66} +(1.73205 - 1.00000i) q^{67} +(-4.33013 + 2.50000i) q^{68} +(-3.00000 + 5.19615i) q^{69} +(7.00000 - 12.1244i) q^{71} +(0.866025 + 0.500000i) q^{72} +13.0000i q^{73} +(5.50000 - 9.52628i) q^{74} +(1.00000 + 1.73205i) q^{76} -4.00000i q^{77} +(3.46410 - 1.00000i) q^{78} +4.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(4.33013 + 2.50000i) q^{82} -6.00000i q^{83} +(1.00000 - 1.73205i) q^{84} -10.0000 q^{86} +(-7.79423 - 4.50000i) q^{87} +(1.73205 - 1.00000i) q^{88} +(1.00000 + 1.73205i) q^{89} +(-2.00000 - 6.92820i) q^{91} +6.00000i q^{92} +(-3.46410 + 2.00000i) q^{93} +(-1.00000 - 1.73205i) q^{94} +1.00000 q^{96} +(1.73205 + 1.00000i) q^{97} +(2.59808 + 1.50000i) q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 2 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 - 2 * q^6 + 2 * q^9	$ 4 q + 2 q^{4} - 2 q^{6} + 2 q^{9} - 4 q^{11} - 8 q^{14} - 2 q^{16} - 4 q^{19} + 8 q^{21} + 2 q^{24} + 14 q^{26} - 18 q^{29} - 16 q^{31} + 20 q^{34} - 2 q^{36} - 14 q^{39} - 10 q^{41} - 8 q^{44} + 12 q^{46} - 6 q^{49} - 20 q^{51} + 2 q^{54} - 4 q^{56} - 16 q^{59} + 22 q^{61} - 4 q^{64} + 8 q^{66} - 12 q^{69} + 28 q^{71} + 22 q^{74} + 4 q^{76} + 16 q^{79} - 2 q^{81} + 4 q^{84} - 40 q^{86} + 4 q^{89} - 8 q^{91} - 4 q^{94} + 4 q^{96} - 8 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 - 2 * q^6 + 2 * q^9 - 4 * q^11 - 8 * q^14 - 2 * q^16 - 4 * q^19 + 8 * q^21 + 2 * q^24 + 14 * q^26 - 18 * q^29 - 16 * q^31 + 20 * q^34 - 2 * q^36 - 14 * q^39 - 10 * q^41 - 8 * q^44 + 12 * q^46 - 6 * q^49 - 20 * q^51 + 2 * q^54 - 4 * q^56 - 16 * q^59 + 22 * q^61 - 4 * q^64 + 8 * q^66 - 12 * q^69 + 28 * q^71 + 22 * q^74 + 4 * q^76 + 16 * q^79 - 2 * q^81 + 4 * q^84 - 40 * q^86 + 4 * q^89 - 8 * q^91 - 4 * q^94 + 4 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	1.73205	+	1.00000i	0.654654	+	0.377964i	0.790237	−	0.612801i	$-0.209957\pi$
$7$	1.73205	+	1.00000i	0.654654	+	0.377964i	−0.135583	+	0.990766i	$0.543291\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$		−	1.00000i		−	0.288675i
$13$	−2.59808	−	2.50000i	−0.720577	−	0.693375i
$13$	−2.59808	−	2.50000i	−0.720577	−	0.693375i
$14$	−2.00000			−0.534522
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−4.33013	−	2.50000i	−1.05021	−	0.606339i	−0.127502	−	0.991838i	$-0.540696\pi$
$17$	−4.33013	−	2.50000i	−1.05021	−	0.606339i	−0.922708	+	0.385499i	$0.874029\pi$
$18$			1.00000i			0.235702i
$19$	−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
$22$	1.73205	+	1.00000i	0.369274	+	0.213201i
$23$	−5.19615	+	3.00000i	−1.08347	+	0.625543i	−0.931831	−	0.362892i	$-0.881789\pi$
$23$	−5.19615	+	3.00000i	−1.08347	+	0.625543i	−0.151642	+	0.988436i	$0.548456\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$		0			0
$26$	3.50000	+	0.866025i	0.686406	+	0.169842i
$27$		−	1.00000i		−	0.192450i
$28$	1.73205	−	1.00000i	0.327327	−	0.188982i
$29$	−4.50000	−	7.79423i	−0.835629	−	1.44735i	−0.893517	−	0.449029i	$-0.851770\pi$
$29$	−4.50000	−	7.79423i	−0.835629	−	1.44735i	0.0578882	−	0.998323i	$-0.481563\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−1.73205	−	1.00000i	−0.301511	−	0.174078i
$34$	5.00000			0.857493
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−9.52628	+	5.50000i	−1.56611	+	0.904194i	−0.569495	+	0.821995i	$0.692861\pi$
$37$	−9.52628	+	5.50000i	−1.56611	+	0.904194i	−0.996616	+	0.0821995i	$0.973806\pi$
$38$		−	2.00000i		−	0.324443i
$39$	−3.50000	−	0.866025i	−0.560449	−	0.138675i
$40$		0			0
$41$	−2.50000	−	4.33013i	−0.390434	−	0.676252i	0.602072	−	0.798441i	$-0.294342\pi$
$41$	−2.50000	−	4.33013i	−0.390434	−	0.676252i	−0.992507	+	0.122189i	$0.961009\pi$
$42$	−1.73205	+	1.00000i	−0.267261	+	0.154303i
$43$	8.66025	+	5.00000i	1.32068	+	0.762493i	0.983836	−	0.179069i	$-0.0573086\pi$
$43$	8.66025	+	5.00000i	1.32068	+	0.762493i	0.336840	+	0.941562i	$0.390642\pi$
$44$	−2.00000			−0.301511
$45$		0			0
$46$	3.00000	−	5.19615i	0.442326	−	0.766131i
$47$			2.00000i			0.291730i	0.989305	+	0.145865i	$0.0465965\pi$
$47$			2.00000i			0.291730i	−0.989305	+	0.145865i	$0.953403\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	−1.50000	−	2.59808i	−0.214286	−	0.371154i
$50$		0			0
$51$	−5.00000			−0.700140
$52$	−3.46410	+	1.00000i	−0.480384	+	0.138675i
$53$			1.00000i			0.137361i	0.997639	+	0.0686803i	$0.0218788\pi$
$53$			1.00000i			0.137361i	−0.997639	+	0.0686803i	$0.978121\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$		0			0
$56$	−1.00000	+	1.73205i	−0.133631	+	0.231455i
$57$			2.00000i			0.264906i
$58$	7.79423	+	4.50000i	1.02343	+	0.590879i
$59$	−4.00000	+	6.92820i	−0.520756	+	0.901975i	0.478953	+	0.877841i	$0.341016\pi$
$59$	−4.00000	+	6.92820i	−0.520756	+	0.901975i	−0.999709	+	0.0241347i	$0.992317\pi$
$60$		0			0
$61$	5.50000	−	9.52628i	0.704203	−	1.21972i	−0.262776	−	0.964857i	$-0.584638\pi$
$61$	5.50000	−	9.52628i	0.704203	−	1.21972i	0.966978	−	0.254858i	$-0.0820288\pi$
$62$	3.46410	−	2.00000i	0.439941	−	0.254000i
$63$	1.73205	−	1.00000i	0.218218	−	0.125988i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	2.00000			0.246183
$67$	1.73205	−	1.00000i	0.211604	−	0.122169i	−0.390453	−	0.920623i	$-0.627682\pi$
$67$	1.73205	−	1.00000i	0.211604	−	0.122169i	0.602056	+	0.798454i	$0.294348\pi$
$68$	−4.33013	+	2.50000i	−0.525105	+	0.303170i
$69$	−3.00000	+	5.19615i	−0.361158	+	0.625543i
$70$		0			0
$71$	7.00000	−	12.1244i	0.830747	−	1.43890i	−0.0666994	−	0.997773i	$-0.521247\pi$
$71$	7.00000	−	12.1244i	0.830747	−	1.43890i	0.897447	−	0.441123i	$-0.145420\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$			13.0000i			1.52153i	0.649025	+	0.760767i	$0.275177\pi$
$73$			13.0000i			1.52153i	−0.649025	+	0.760767i	$0.724823\pi$
$74$	5.50000	−	9.52628i	0.639362	−	1.10741i
$75$		0			0
$76$	1.00000	+	1.73205i	0.114708	+	0.198680i
$77$		−	4.00000i		−	0.455842i
$78$	3.46410	−	1.00000i	0.392232	−	0.113228i
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.33013	+	2.50000i	0.478183	+	0.276079i
$83$		−	6.00000i		−	0.658586i	−0.944228	−	0.329293i	$-0.893190\pi$
$83$		−	6.00000i		−	0.658586i	0.944228	−	0.329293i	$-0.106810\pi$
$84$	1.00000	−	1.73205i	0.109109	−	0.188982i
$85$		0			0
$86$	−10.0000			−1.07833
$87$	−7.79423	−	4.50000i	−0.835629	−	0.482451i
$88$	1.73205	−	1.00000i	0.184637	−	0.106600i
$89$	1.00000	+	1.73205i	0.106000	+	0.183597i	0.914146	−	0.405385i	$-0.132862\pi$
$89$	1.00000	+	1.73205i	0.106000	+	0.183597i	−0.808146	+	0.588982i	$0.799529\pi$
$90$		0			0
$91$	−2.00000	−	6.92820i	−0.209657	−	0.726273i
$92$			6.00000i			0.625543i
$93$	−3.46410	+	2.00000i	−0.359211	+	0.207390i
$94$	−1.00000	−	1.73205i	−0.103142	−	0.178647i
$95$		0			0
$96$	1.00000			0.102062
$97$	1.73205	+	1.00000i	0.175863	+	0.101535i	0.585348	−	0.810782i	$-0.300958\pi$
$97$	1.73205	+	1.00000i	0.175863	+	0.101535i	−0.409484	+	0.912317i	$0.634291\pi$
$98$	2.59808	+	1.50000i	0.262445	+	0.151523i
$99$	−2.00000			−0.201008
$100$		0			0
$101$	2.50000	+	4.33013i	0.248759	+	0.430864i	0.963182	−	0.268851i	$-0.0866439\pi$
$101$	2.50000	+	4.33013i	0.248759	+	0.430864i	−0.714423	+	0.699715i	$0.753311\pi$
$102$	4.33013	−	2.50000i	0.428746	−	0.247537i
$103$		−	10.0000i		−	0.985329i	−0.870219	−	0.492665i	$-0.836023\pi$
$103$		−	10.0000i		−	0.985329i	0.870219	−	0.492665i	$-0.163977\pi$
$104$	2.50000	−	2.59808i	0.245145	−	0.254762i
$105$		0			0
$106$	−0.500000	−	0.866025i	−0.0485643	−	0.0841158i
$107$	−15.5885	+	9.00000i	−1.50699	+	0.870063i	−0.507026	+	0.861931i	$0.669255\pi$
$107$	−15.5885	+	9.00000i	−1.50699	+	0.870063i	−0.999967	+	0.00813215i	$0.997411\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$	−5.50000	+	9.52628i	−0.522037	+	0.904194i
$112$		−	2.00000i		−	0.188982i
$113$	−2.59808	−	1.50000i	−0.244406	−	0.141108i	0.372794	−	0.927914i	$-0.378400\pi$
$113$	−2.59808	−	1.50000i	−0.244406	−	0.141108i	−0.617200	+	0.786806i	$0.711733\pi$
$114$	−1.00000	−	1.73205i	−0.0936586	−	0.162221i
$115$		0			0
$116$	−9.00000			−0.835629
$117$	−3.46410	+	1.00000i	−0.320256	+	0.0924500i
$118$		−	8.00000i		−	0.736460i
$119$	−5.00000	−	8.66025i	−0.458349	−	0.793884i
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$			11.0000i			0.995893i
$123$	−4.33013	−	2.50000i	−0.390434	−	0.225417i
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$		0			0
$126$	−1.00000	+	1.73205i	−0.0890871	+	0.154303i
$127$	−10.3923	+	6.00000i	−0.922168	+	0.532414i	−0.884326	−	0.466870i	$-0.845382\pi$
$127$	−10.3923	+	6.00000i	−0.922168	+	0.532414i	−0.0378419	+	0.999284i	$0.512048\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	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	$0.613642\pi$
$132$	−1.73205	+	1.00000i	−0.150756	+	0.0870388i
$133$	−3.46410	+	2.00000i	−0.300376	+	0.173422i
$134$	−1.00000	+	1.73205i	−0.0863868	+	0.149626i
$135$		0			0
$136$	2.50000	−	4.33013i	0.214373	−	0.371305i
$137$	−14.7224	−	8.50000i	−1.25782	−	0.726204i	−0.285171	−	0.958477i	$-0.592051\pi$
$137$	−14.7224	−	8.50000i	−1.25782	−	0.726204i	−0.972651	+	0.232273i	$0.925384\pi$
$138$		−	6.00000i		−	0.510754i
$139$	−6.00000	+	10.3923i	−0.508913	+	0.881464i	0.491033	+	0.871141i	$0.336619\pi$
$139$	−6.00000	+	10.3923i	−0.508913	+	0.881464i	−0.999947	+	0.0103230i	$0.996714\pi$
$140$		0			0
$141$	1.00000	+	1.73205i	0.0842152	+	0.145865i
$142$			14.0000i			1.17485i
$143$	−1.73205	+	7.00000i	−0.144841	+	0.585369i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	−6.50000	−	11.2583i	−0.537944	−	0.931746i
$147$	−2.59808	−	1.50000i	−0.214286	−	0.123718i
$148$			11.0000i			0.904194i
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	−0.798019	−	0.602632i	$-0.794119\pi$
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	0.920904	+	0.389789i	$0.127452\pi$
$150$		0			0
$151$	−6.00000			−0.488273			−0.244137	−	0.969741i	$-0.578505\pi$
$151$	−6.00000			−0.488273			−0.244137	+	0.969741i	$0.578505\pi$
$152$	−1.73205	−	1.00000i	−0.140488	−	0.0811107i
$153$	−4.33013	+	2.50000i	−0.350070	+	0.202113i
$154$	2.00000	+	3.46410i	0.161165	+	0.279145i
$155$		0			0
$156$	−2.50000	+	2.59808i	−0.200160	+	0.208013i
$157$		−	7.00000i		−	0.558661i	−0.960195	−	0.279330i	$-0.909888\pi$
$157$		−	7.00000i		−	0.558661i	0.960195	−	0.279330i	$-0.0901125\pi$
$158$	−3.46410	+	2.00000i	−0.275589	+	0.159111i
$159$	0.500000	+	0.866025i	0.0396526	+	0.0686803i
$160$		0			0
$161$	−12.0000			−0.945732
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	17.3205	+	10.0000i	1.35665	+	0.783260i	0.989170	−	0.146772i	$-0.0468885\pi$
$163$	17.3205	+	10.0000i	1.35665	+	0.783260i	0.367477	+	0.930033i	$0.380222\pi$
$164$	−5.00000			−0.390434
$165$		0			0
$166$	3.00000	+	5.19615i	0.232845	+	0.403300i
$167$	20.7846	−	12.0000i	1.60836	−	0.928588i	0.618624	−	0.785687i	$-0.287690\pi$
$167$	20.7846	−	12.0000i	1.60836	−	0.928588i	0.989737	−	0.142901i	$-0.0456431\pi$
$168$			2.00000i			0.154303i
$169$	0.500000	+	12.9904i	0.0384615	+	0.999260i
$170$		0			0
$171$	1.00000	+	1.73205i	0.0764719	+	0.132453i
$172$	8.66025	−	5.00000i	0.660338	−	0.381246i
$173$	−19.0526	−	11.0000i	−1.44854	−	0.836315i	−0.450145	−	0.892956i	$-0.648628\pi$
$173$	−19.0526	−	11.0000i	−1.44854	−	0.836315i	−0.998395	+	0.0566411i	$0.981961\pi$
$174$	9.00000			0.682288
$175$		0			0
$176$	−1.00000	+	1.73205i	−0.0753778	+	0.130558i
$177$			8.00000i			0.601317i
$178$	−1.73205	−	1.00000i	−0.129823	−	0.0749532i
$179$	−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
$181$	5.00000			0.371647			0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000			0.371647			0.185824	+	0.982583i	$0.440505\pi$
$182$	5.19615	+	5.00000i	0.385164	+	0.370625i
$183$		−	11.0000i		−	0.813143i
$184$	−3.00000	−	5.19615i	−0.221163	−	0.383065i
$185$		0			0
$186$	2.00000	−	3.46410i	0.146647	−	0.254000i
$187$			10.0000i			0.731272i
$188$	1.73205	+	1.00000i	0.126323	+	0.0729325i
$189$	1.00000	−	1.73205i	0.0727393	−	0.125988i
$190$		0			0
$191$	−2.00000	+	3.46410i	−0.144715	+	0.250654i	−0.929267	−	0.369410i	$-0.879560\pi$
$191$	−2.00000	+	3.46410i	−0.144715	+	0.250654i	0.784552	+	0.620063i	$0.212893\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	14.7224	−	8.50000i	1.05974	−	0.611843i	0.134382	−	0.990930i	$-0.457095\pi$
$193$	14.7224	−	8.50000i	1.05974	−	0.611843i	0.925361	+	0.379086i	$0.123762\pi$
$194$	−2.00000			−0.143592
$195$		0			0
$196$	−3.00000			−0.214286
$197$	5.19615	−	3.00000i	0.370211	−	0.213741i	−0.303340	−	0.952882i	$-0.598102\pi$
$197$	5.19615	−	3.00000i	0.370211	−	0.213741i	0.673550	+	0.739141i	$0.264768\pi$
$198$	1.73205	−	1.00000i	0.123091	−	0.0710669i
$199$	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
$201$	1.00000	−	1.73205i	0.0705346	−	0.122169i
$202$	−4.33013	−	2.50000i	−0.304667	−	0.175899i
$203$		−	18.0000i		−	1.26335i
$204$	−2.50000	+	4.33013i	−0.175035	+	0.303170i
$205$		0			0
$206$	5.00000	+	8.66025i	0.348367	+	0.603388i
$207$			6.00000i			0.417029i
$208$	−0.866025	+	3.50000i	−0.0600481	+	0.242681i
$209$	4.00000			0.276686
$210$		0			0
$211$	−12.0000	−	20.7846i	−0.826114	−	1.43087i	−0.901065	−	0.433684i	$-0.857213\pi$
$211$	−12.0000	−	20.7846i	−0.826114	−	1.43087i	0.0749508	−	0.997187i	$-0.476120\pi$
$212$	0.866025	+	0.500000i	0.0594789	+	0.0343401i
$213$		−	14.0000i		−	0.959264i
$214$	9.00000	−	15.5885i	0.615227	−	1.06561i
$215$		0			0
$216$	1.00000			0.0680414
$217$	−6.92820	−	4.00000i	−0.470317	−	0.271538i
$218$	−1.73205	+	1.00000i	−0.117309	+	0.0677285i
$219$	6.50000	+	11.2583i	0.439229	+	0.760767i
$220$		0			0
$221$	5.00000	+	17.3205i	0.336336	+	1.16510i
$222$		−	11.0000i		−	0.738272i
$223$	13.8564	−	8.00000i	0.927894	−	0.535720i	0.0417488	−	0.999128i	$-0.486707\pi$
$223$	13.8564	−	8.00000i	0.927894	−	0.535720i	0.886145	+	0.463409i	$0.153374\pi$
$224$	1.00000	+	1.73205i	0.0668153	+	0.115728i
$225$		0			0
$226$	3.00000			0.199557
$227$	−12.1244	−	7.00000i	−0.804722	−	0.464606i	0.0403978	−	0.999184i	$-0.487137\pi$
$227$	−12.1244	−	7.00000i	−0.804722	−	0.464606i	−0.845120	+	0.534577i	$0.820471\pi$
$228$	1.73205	+	1.00000i	0.114708	+	0.0662266i
$229$	−10.0000			−0.660819			−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000			−0.660819			−0.330409	+	0.943838i	$0.607187\pi$
$230$		0			0
$231$	−2.00000	−	3.46410i	−0.131590	−	0.227921i
$232$	7.79423	−	4.50000i	0.511716	−	0.295439i
$233$			6.00000i			0.393073i	0.980497	+	0.196537i	$0.0629694\pi$
$233$			6.00000i			0.393073i	−0.980497	+	0.196537i	$0.937031\pi$
$234$	2.50000	−	2.59808i	0.163430	−	0.169842i
$235$		0			0
$236$	4.00000	+	6.92820i	0.260378	+	0.450988i
$237$	3.46410	−	2.00000i	0.225018	−	0.129914i
$238$	8.66025	+	5.00000i	0.561361	+	0.324102i
$239$	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
$241$	−3.50000	+	6.06218i	−0.225455	+	0.390499i	−0.956456	−	0.291877i	$-0.905720\pi$
$241$	−3.50000	+	6.06218i	−0.225455	+	0.390499i	0.731001	+	0.682376i	$0.239053\pi$
$242$			7.00000i			0.449977i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−5.50000	−	9.52628i	−0.352101	−	0.609858i
$245$		0			0
$246$	5.00000			0.318788
$247$	6.92820	−	2.00000i	0.440831	−	0.127257i
$248$		−	4.00000i		−	0.254000i
$249$	−3.00000	−	5.19615i	−0.190117	−	0.329293i
$250$		0			0
$251$	−2.00000	+	3.46410i	−0.126239	+	0.218652i	−0.922217	−	0.386674i	$-0.873624\pi$
$251$	−2.00000	+	3.46410i	−0.126239	+	0.218652i	0.795978	+	0.605326i	$0.206957\pi$
$252$		−	2.00000i		−	0.125988i
$253$	10.3923	+	6.00000i	0.653359	+	0.377217i
$254$	6.00000	−	10.3923i	0.376473	−	0.652071i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.59808	+	1.50000i	−0.162064	+	0.0935674i	−0.578838	−	0.815442i	$-0.696494\pi$
$257$	−2.59808	+	1.50000i	−0.162064	+	0.0935674i	0.416775	+	0.909010i	$0.363160\pi$
$258$	−8.66025	+	5.00000i	−0.539164	+	0.311286i
$259$	−22.0000			−1.36701
$260$		0			0
$261$	−9.00000			−0.557086
$262$	6.92820	−	4.00000i	0.428026	−	0.247121i
$263$	−12.1244	+	7.00000i	−0.747620	+	0.431638i	−0.824833	−	0.565376i	$-0.808731\pi$
$263$	−12.1244	+	7.00000i	−0.747620	+	0.431638i	0.0772134	+	0.997015i	$0.475398\pi$
$264$	1.00000	−	1.73205i	0.0615457	−	0.106600i
$265$		0			0
$266$	2.00000	−	3.46410i	0.122628	−	0.212398i
$267$	1.73205	+	1.00000i	0.106000	+	0.0611990i
$268$		−	2.00000i		−	0.122169i
$269$	−7.00000	+	12.1244i	−0.426798	+	0.739235i	−0.996586	−	0.0825561i	$-0.973692\pi$
$269$	−7.00000	+	12.1244i	−0.426798	+	0.739235i	0.569789	+	0.821791i	$0.307025\pi$
$270$		0			0
$271$	−4.00000	−	6.92820i	−0.242983	−	0.420858i	0.718580	−	0.695444i	$-0.244792\pi$
$271$	−4.00000	−	6.92820i	−0.242983	−	0.420858i	−0.961563	+	0.274586i	$0.911459\pi$
$272$			5.00000i			0.303170i
$273$	−5.19615	−	5.00000i	−0.314485	−	0.302614i
$274$	17.0000			1.02701
$275$		0			0
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	9.52628	+	5.50000i	0.572379	+	0.330463i	0.758099	−	0.652140i	$-0.226128\pi$
$277$	9.52628	+	5.50000i	0.572379	+	0.330463i	−0.185720	+	0.982603i	$0.559462\pi$
$278$		−	12.0000i		−	0.719712i
$279$	−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	$0.232121\pi$
$282$	−1.73205	−	1.00000i	−0.103142	−	0.0595491i
$283$	−22.5167	+	13.0000i	−1.33848	+	0.772770i	−0.986581	−	0.163270i	$-0.947796\pi$
$283$	−22.5167	+	13.0000i	−1.33848	+	0.772770i	−0.351895	+	0.936039i	$0.614463\pi$
$284$	−7.00000	−	12.1244i	−0.415374	−	0.719448i
$285$		0			0
$286$	−2.00000	−	6.92820i	−0.118262	−	0.409673i
$287$		−	10.0000i		−	0.590281i
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	2.00000			0.117242
$292$	11.2583	+	6.50000i	0.658844	+	0.380384i
$293$	−0.866025	−	0.500000i	−0.0505937	−	0.0292103i	0.474490	−	0.880261i	$-0.342633\pi$
$293$	−0.866025	−	0.500000i	−0.0505937	−	0.0292103i	−0.525084	+	0.851051i	$0.675966\pi$
$294$	3.00000			0.174964
$295$		0			0
$296$	−5.50000	−	9.52628i	−0.319681	−	0.553704i
$297$	−1.73205	+	1.00000i	−0.100504	+	0.0580259i
$298$			3.00000i			0.173785i
$299$	21.0000	+	5.19615i	1.21446	+	0.300501i
$300$		0			0
$301$	10.0000	+	17.3205i	0.576390	+	0.998337i
$302$	5.19615	−	3.00000i	0.299005	−	0.172631i
$303$	4.33013	+	2.50000i	0.248759	+	0.143621i
$304$	2.00000			0.114708
$305$		0			0
$306$	2.50000	−	4.33013i	0.142915	−	0.247537i
$307$		−	14.0000i		−	0.799022i	−0.916728	−	0.399511i	$-0.869180\pi$
$307$		−	14.0000i		−	0.799022i	0.916728	−	0.399511i	$-0.130820\pi$
$308$	−3.46410	−	2.00000i	−0.197386	−	0.113961i
$309$	−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	$0.445586\pi$
$312$	0.866025	−	3.50000i	0.0490290	−	0.198148i
$313$		−	6.00000i		−	0.339140i	−0.985518	−	0.169570i	$-0.945762\pi$
$313$		−	6.00000i		−	0.339140i	0.985518	−	0.169570i	$-0.0542379\pi$
$314$	3.50000	+	6.06218i	0.197516	+	0.342108i
$315$		0			0
$316$	2.00000	−	3.46410i	0.112509	−	0.194871i
$317$		−	33.0000i		−	1.85346i	−0.375722	−	0.926732i	$-0.622605\pi$
$317$		−	33.0000i		−	1.85346i	0.375722	−	0.926732i	$-0.377395\pi$
$318$	−0.866025	−	0.500000i	−0.0485643	−	0.0280386i
$319$	−9.00000	+	15.5885i	−0.503903	+	0.872786i
$320$		0			0
$321$	−9.00000	+	15.5885i	−0.502331	+	0.870063i
$322$	10.3923	−	6.00000i	0.579141	−	0.334367i
$323$	8.66025	−	5.00000i	0.481869	−	0.278207i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−20.0000			−1.10770
$327$	1.73205	−	1.00000i	0.0957826	−	0.0553001i
$328$	4.33013	−	2.50000i	0.239091	−	0.138039i
$329$	−2.00000	+	3.46410i	−0.110264	+	0.190982i
$330$		0			0
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	−0.168320	−	0.985732i	$-0.553834\pi$
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	0.937829	−	0.347097i	$-0.112833\pi$
$332$	−5.19615	−	3.00000i	−0.285176	−	0.164646i
$333$			11.0000i			0.602796i
$334$	−12.0000	+	20.7846i	−0.656611	+	1.13728i
$335$		0			0
$336$	−1.00000	−	1.73205i	−0.0545545	−	0.0944911i
$337$		−	9.00000i		−	0.490261i	−0.969490	−	0.245131i	$-0.921169\pi$
$337$		−	9.00000i		−	0.490261i	0.969490	−	0.245131i	$-0.0788309\pi$
$338$	−6.92820	−	11.0000i	−0.376845	−	0.598321i
$339$	−3.00000			−0.162938
$340$		0			0
$341$	4.00000	+	6.92820i	0.216612	+	0.375183i
$342$	−1.73205	−	1.00000i	−0.0936586	−	0.0540738i
$343$		−	20.0000i		−	1.07990i
$344$	−5.00000	+	8.66025i	−0.269582	+	0.466930i
$345$		0			0
$346$	22.0000			1.18273
$347$	−5.19615	−	3.00000i	−0.278944	−	0.161048i	0.354001	−	0.935245i	$-0.384821\pi$
$347$	−5.19615	−	3.00000i	−0.278944	−	0.161048i	−0.632945	+	0.774197i	$0.718154\pi$
$348$	−7.79423	+	4.50000i	−0.417815	+	0.241225i
$349$	3.00000	+	5.19615i	0.160586	+	0.278144i	0.935079	−	0.354439i	$-0.115328\pi$
$349$	3.00000	+	5.19615i	0.160586	+	0.278144i	−0.774493	+	0.632583i	$0.781995\pi$
$350$		0			0
$351$	−2.50000	+	2.59808i	−0.133440	+	0.138675i
$352$		−	2.00000i		−	0.106600i
$353$	−14.7224	+	8.50000i	−0.783596	+	0.452409i	−0.837703	−	0.546126i	$-0.816102\pi$
$353$	−14.7224	+	8.50000i	−0.783596	+	0.452409i	0.0541072	+	0.998535i	$0.482769\pi$
$354$	−4.00000	−	6.92820i	−0.212598	−	0.368230i
$355$		0			0
$356$	2.00000			0.106000
$357$	−8.66025	−	5.00000i	−0.458349	−	0.264628i
$358$	5.19615	+	3.00000i	0.274625	+	0.158555i
$359$	30.0000			1.58334			0.791670	−	0.610949i	$-0.209212\pi$
$359$	30.0000			1.58334			0.791670	+	0.610949i	$0.209212\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−4.33013	+	2.50000i	−0.227586	+	0.131397i
$363$		−	7.00000i		−	0.367405i
$364$	−7.00000	−	1.73205i	−0.366900	−	0.0907841i
$365$		0			0
$366$	5.50000	+	9.52628i	0.287490	+	0.497947i
$367$	−1.73205	+	1.00000i	−0.0904123	+	0.0521996i	−0.544524	−	0.838745i	$-0.683290\pi$
$367$	−1.73205	+	1.00000i	−0.0904123	+	0.0521996i	0.454112	+	0.890945i	$0.349957\pi$
$368$	5.19615	+	3.00000i	0.270868	+	0.156386i
$369$	−5.00000			−0.260290
$370$		0			0
$371$	−1.00000	+	1.73205i	−0.0519174	+	0.0899236i
$372$			4.00000i			0.207390i
$373$	7.79423	+	4.50000i	0.403570	+	0.233001i	0.688023	−	0.725689i	$-0.258479\pi$
$373$	7.79423	+	4.50000i	0.403570	+	0.233001i	−0.284453	+	0.958690i	$0.591812\pi$
$374$	−5.00000	−	8.66025i	−0.258544	−	0.447811i
$375$		0			0
$376$	−2.00000			−0.103142
$377$	−7.79423	+	31.5000i	−0.401423	+	1.62233i
$378$			2.00000i			0.102869i
$379$	6.00000	+	10.3923i	0.308199	+	0.533817i	0.977969	−	0.208752i	$-0.0669403\pi$
$379$	6.00000	+	10.3923i	0.308199	+	0.533817i	−0.669769	+	0.742569i	$0.733607\pi$
$380$		0			0
$381$	−6.00000	+	10.3923i	−0.307389	+	0.532414i
$382$		−	4.00000i		−	0.204658i
$383$	20.7846	+	12.0000i	1.06204	+	0.613171i	0.925997	−	0.377531i	$-0.123227\pi$
$383$	20.7846	+	12.0000i	1.06204	+	0.613171i	0.136047	+	0.990702i	$0.456560\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$		0			0
$386$	−8.50000	+	14.7224i	−0.432639	+	0.749352i
$387$	8.66025	−	5.00000i	0.440225	−	0.254164i
$388$	1.73205	−	1.00000i	0.0879316	−	0.0507673i
$389$	−19.0000			−0.963338			−0.481669	−	0.876353i	$-0.659969\pi$
$389$	−19.0000			−0.963338			−0.481669	+	0.876353i	$0.659969\pi$
$390$		0			0
$391$	30.0000			1.51717
$392$	2.59808	−	1.50000i	0.131223	−	0.0757614i
$393$	−6.92820	+	4.00000i	−0.349482	+	0.201773i
$394$	−3.00000	+	5.19615i	−0.151138	+	0.261778i
$395$		0			0
$396$	−1.00000	+	1.73205i	−0.0502519	+	0.0870388i
$397$	15.5885	+	9.00000i	0.782362	+	0.451697i	0.837267	−	0.546795i	$-0.184152\pi$
$397$	15.5885	+	9.00000i	0.782362	+	0.451697i	−0.0549046	+	0.998492i	$0.517485\pi$
$398$			10.0000i			0.501255i
$399$	−2.00000	+	3.46410i	−0.100125	+	0.173422i
$400$		0			0
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	0.976714	+	0.214544i	$0.0688266\pi$
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	−0.302556	+	0.953131i	$0.597840\pi$
$402$			2.00000i			0.0997509i
$403$	10.3923	+	10.0000i	0.517678	+	0.498135i
$404$	5.00000			0.248759
$405$		0			0
$406$	9.00000	+	15.5885i	0.446663	+	0.773642i
$407$	19.0526	+	11.0000i	0.944400	+	0.545250i
$408$		−	5.00000i		−	0.247537i
$409$	11.5000	−	19.9186i	0.568638	−	0.984911i	−0.428063	−	0.903749i	$-0.640804\pi$
$409$	11.5000	−	19.9186i	0.568638	−	0.984911i	0.996701	−	0.0811615i	$-0.0258630\pi$
$410$		0			0
$411$	−17.0000			−0.838548
$412$	−8.66025	−	5.00000i	−0.426660	−	0.246332i
$413$	−13.8564	+	8.00000i	−0.681829	+	0.393654i
$414$	−3.00000	−	5.19615i	−0.147442	−	0.255377i
$415$		0			0
$416$	−1.00000	−	3.46410i	−0.0490290	−	0.169842i
$417$			12.0000i			0.587643i
$418$	−3.46410	+	2.00000i	−0.169435	+	0.0978232i
$419$	−16.0000	−	27.7128i	−0.781651	−	1.35386i	−0.930979	−	0.365072i	$-0.881044\pi$
$419$	−16.0000	−	27.7128i	−0.781651	−	1.35386i	0.149328	−	0.988788i	$-0.452289\pi$
$420$		0			0
$421$	−23.0000			−1.12095			−0.560476	−	0.828171i	$-0.689382\pi$
$421$	−23.0000			−1.12095			−0.560476	+	0.828171i	$0.689382\pi$
$422$	20.7846	+	12.0000i	1.01178	+	0.584151i
$423$	1.73205	+	1.00000i	0.0842152	+	0.0486217i
$424$	−1.00000			−0.0485643
$425$		0			0
$426$	7.00000	+	12.1244i	0.339151	+	0.587427i
$427$	19.0526	−	11.0000i	0.922018	−	0.532327i
$428$			18.0000i			0.870063i
$429$	2.00000	+	6.92820i	0.0965609	+	0.334497i
$430$		0			0
$431$	1.00000	+	1.73205i	0.0481683	+	0.0834300i	0.889104	−	0.457705i	$-0.151328\pi$
$431$	1.00000	+	1.73205i	0.0481683	+	0.0834300i	−0.840936	+	0.541135i	$0.817995\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	−18.1865	−	10.5000i	−0.873989	−	0.504598i	−0.00531724	−	0.999986i	$-0.501693\pi$
$433$	−18.1865	−	10.5000i	−0.873989	−	0.504598i	−0.868672	+	0.495388i	$0.835026\pi$
$434$	8.00000			0.384012
$435$		0			0
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$		−	12.0000i		−	0.574038i
$438$	−11.2583	−	6.50000i	−0.537944	−	0.310582i
$439$	5.00000	+	8.66025i	0.238637	+	0.413331i	0.960323	−	0.278889i	$-0.0899661\pi$
$439$	5.00000	+	8.66025i	0.238637	+	0.413331i	−0.721686	+	0.692220i	$0.756633\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$	−12.9904	−	12.5000i	−0.617889	−	0.594564i
$443$		−	20.0000i		−	0.950229i	−0.879924	−	0.475114i	$-0.842407\pi$
$443$		−	20.0000i		−	0.950229i	0.879924	−	0.475114i	$-0.157593\pi$
$444$	5.50000	+	9.52628i	0.261018	+	0.452097i
$445$		0			0
$446$	−8.00000	+	13.8564i	−0.378811	+	0.656120i
$447$		−	3.00000i		−	0.141895i
$448$	−1.73205	−	1.00000i	−0.0818317	−	0.0472456i
$449$	−15.0000	+	25.9808i	−0.707894	+	1.22611i	0.257743	+	0.966213i	$0.417021\pi$
$449$	−15.0000	+	25.9808i	−0.707894	+	1.22611i	−0.965637	+	0.259895i	$0.916312\pi$
$450$		0			0
$451$	−5.00000	+	8.66025i	−0.235441	+	0.407795i
$452$	−2.59808	+	1.50000i	−0.122203	+	0.0705541i
$453$	−5.19615	+	3.00000i	−0.244137	+	0.140952i
$454$	14.0000			0.657053
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	2.59808	−	1.50000i	0.121533	−	0.0701670i	−0.438001	−	0.898974i	$-0.644313\pi$
$457$	2.59808	−	1.50000i	0.121533	−	0.0701670i	0.559534	+	0.828807i	$0.310980\pi$
$458$	8.66025	−	5.00000i	0.404667	−	0.233635i
$459$	−2.50000	+	4.33013i	−0.116690	+	0.202113i
$460$		0			0
$461$	−1.50000	+	2.59808i	−0.0698620	+	0.121004i	−0.898840	−	0.438276i	$-0.855589\pi$
$461$	−1.50000	+	2.59808i	−0.0698620	+	0.121004i	0.828978	+	0.559281i	$0.188923\pi$
$462$	3.46410	+	2.00000i	0.161165	+	0.0930484i
$463$			14.0000i			0.650635i	0.945605	+	0.325318i	$0.105471\pi$
$463$			14.0000i			0.650635i	−0.945605	+	0.325318i	$0.894529\pi$
$464$	−4.50000	+	7.79423i	−0.208907	+	0.361838i
$465$		0			0
$466$	−3.00000	−	5.19615i	−0.138972	−	0.240707i
$467$		−	22.0000i		−	1.01804i	−0.860755	−	0.509019i	$-0.830008\pi$
$467$		−	22.0000i		−	1.01804i	0.860755	−	0.509019i	$-0.169992\pi$
$468$	−0.866025	+	3.50000i	−0.0400320	+	0.161788i
$469$	4.00000			0.184703
$470$		0			0
$471$	−3.50000	−	6.06218i	−0.161271	−	0.279330i
$472$	−6.92820	−	4.00000i	−0.318896	−	0.184115i
$473$		−	20.0000i		−	0.919601i
$474$	−2.00000	+	3.46410i	−0.0918630	+	0.159111i
$475$		0			0
$476$	−10.0000			−0.458349
$477$	0.866025	+	0.500000i	0.0396526	+	0.0228934i
$478$	−5.19615	+	3.00000i	−0.237666	+	0.137217i
$479$	16.0000	+	27.7128i	0.731059	+	1.26623i	0.956431	+	0.291958i	$0.0943068\pi$
$479$	16.0000	+	27.7128i	0.731059	+	1.26623i	−0.225372	+	0.974273i	$0.572360\pi$
$480$		0			0
$481$	38.5000	+	9.52628i	1.75545	+	0.434361i
$482$		−	7.00000i		−	0.318841i
$483$	−10.3923	+	6.00000i	−0.472866	+	0.273009i
$484$	−3.50000	−	6.06218i	−0.159091	−	0.275554i
$485$		0			0
$486$	1.00000			0.0453609
$487$	22.5167	+	13.0000i	1.02033	+	0.589086i	0.914199	−	0.405266i	$-0.132821\pi$
$487$	22.5167	+	13.0000i	1.02033	+	0.589086i	0.106129	+	0.994352i	$0.466154\pi$
$488$	9.52628	+	5.50000i	0.431234	+	0.248973i
$489$	20.0000			0.904431
$490$		0			0
$491$	15.0000	+	25.9808i	0.676941	+	1.17250i	0.975898	+	0.218229i	$0.0700279\pi$
$491$	15.0000	+	25.9808i	0.676941	+	1.17250i	−0.298957	+	0.954267i	$0.596639\pi$
$492$	−4.33013	+	2.50000i	−0.195217	+	0.112709i
$493$			45.0000i			2.02670i
$494$	−5.00000	+	5.19615i	−0.224961	+	0.233786i
$495$		0			0
$496$	2.00000	+	3.46410i	0.0898027	+	0.155543i
$497$	24.2487	−	14.0000i	1.08770	−	0.627986i
$498$	5.19615	+	3.00000i	0.232845	+	0.134433i
$499$		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
$502$		−	4.00000i		−	0.178529i
$503$	−12.1244	−	7.00000i	−0.540598	−	0.312115i	0.204723	−	0.978820i	$-0.434371\pi$
$503$	−12.1244	−	7.00000i	−0.540598	−	0.312115i	−0.745321	+	0.666705i	$0.767704\pi$
$504$	1.00000	+	1.73205i	0.0445435	+	0.0771517i
$505$		0			0
$506$	−12.0000			−0.533465
$507$	6.92820	+	11.0000i	0.307692	+	0.488527i
$508$			12.0000i			0.532414i
$509$	7.50000	+	12.9904i	0.332432	+	0.575789i	0.982988	−	0.183669i	$-0.0587976\pi$
$509$	7.50000	+	12.9904i	0.332432	+	0.575789i	−0.650556	+	0.759458i	$0.725464\pi$
$510$		0			0
$511$	−13.0000	+	22.5167i	−0.575086	+	0.996078i
$512$		−	1.00000i		−	0.0441942i
$513$	1.73205	+	1.00000i	0.0764719	+	0.0441511i
$514$	1.50000	−	2.59808i	0.0661622	−	0.114596i
$515$		0			0
$516$	5.00000	−	8.66025i	0.220113	−	0.381246i
$517$	3.46410	−	2.00000i	0.152351	−	0.0879599i
$518$	19.0526	−	11.0000i	0.837121	−	0.483312i
$519$	−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	$0.315528\pi$
$522$	7.79423	−	4.50000i	0.341144	−	0.196960i
$523$	32.9090	−	19.0000i	1.43901	−	0.830812i	0.441228	−	0.897395i	$-0.354543\pi$
$523$	32.9090	−	19.0000i	1.43901	−	0.830812i	0.997781	+	0.0665832i	$0.0212098\pi$
$524$	−4.00000	+	6.92820i	−0.174741	+	0.302660i
$525$		0			0
$526$	7.00000	−	12.1244i	0.305215	−	0.528647i
$527$	17.3205	+	10.0000i	0.754493	+	0.435607i
$528$			2.00000i			0.0870388i
$529$	6.50000	−	11.2583i	0.282609	−	0.489493i
$530$		0			0
$531$	4.00000	+	6.92820i	0.173585	+	0.300658i
$532$			4.00000i			0.173422i
$533$	−4.33013	+	17.5000i	−0.187559	+	0.758009i
$534$	−2.00000			−0.0865485
$535$		0			0
$536$	1.00000	+	1.73205i	0.0431934	+	0.0748132i
$537$	−5.19615	−	3.00000i	−0.224231	−	0.129460i
$538$		−	14.0000i		−	0.603583i
$539$	−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	$0.548081\pi$
$542$	6.92820	+	4.00000i	0.297592	+	0.171815i
$543$	4.33013	−	2.50000i	0.185824	−	0.107285i
$544$	−2.50000	−	4.33013i	−0.107187	−	0.185653i
$545$		0			0
$546$	7.00000	+	1.73205i	0.299572	+	0.0741249i
$547$			2.00000i			0.0855138i	0.999086	+	0.0427569i	$0.0136141\pi$
$547$			2.00000i			0.0855138i	−0.999086	+	0.0427569i	$0.986386\pi$
$548$	−14.7224	+	8.50000i	−0.628911	+	0.363102i
$549$	−5.50000	−	9.52628i	−0.234734	−	0.406572i
$550$		0			0
$551$	18.0000			0.766826
$552$	−5.19615	−	3.00000i	−0.221163	−	0.127688i
$553$	6.92820	+	4.00000i	0.294617	+	0.170097i
$554$	−11.0000			−0.467345
$555$		0			0
$556$	6.00000	+	10.3923i	0.254457	+	0.440732i
$557$	−7.79423	+	4.50000i	−0.330252	+	0.190671i	−0.655953	−	0.754802i	$-0.727733\pi$
$557$	−7.79423	+	4.50000i	−0.330252	+	0.190671i	0.325701	+	0.945473i	$0.394400\pi$
$558$		−	4.00000i		−	0.169334i
$559$	−10.0000	−	34.6410i	−0.422955	−	1.46516i
$560$		0			0
$561$	5.00000	+	8.66025i	0.211100	+	0.365636i
$562$	−21.6506	+	12.5000i	−0.913277	+	0.527281i
$563$	34.6410	+	20.0000i	1.45994	+	0.842900i	0.999008	−	0.0445334i	$-0.0141801\pi$
$563$	34.6410	+	20.0000i	1.45994	+	0.842900i	0.460937	+	0.887433i	$0.347513\pi$
$564$	2.00000			0.0842152
$565$		0			0
$566$	13.0000	−	22.5167i	0.546431	−	0.946446i
$567$		−	2.00000i		−	0.0839921i
$568$	12.1244	+	7.00000i	0.508727	+	0.293713i
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$		0			0
$571$	−2.00000			−0.0836974			−0.0418487	−	0.999124i	$-0.513325\pi$
$571$	−2.00000			−0.0836974			−0.0418487	+	0.999124i	$0.513325\pi$
$572$	5.19615	+	5.00000i	0.217262	+	0.209061i
$573$			4.00000i			0.167102i
$574$	5.00000	+	8.66025i	0.208696	+	0.361472i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$			27.0000i			1.12402i	0.827129	+	0.562012i	$0.189973\pi$
$577$			27.0000i			1.12402i	−0.827129	+	0.562012i	$0.810027\pi$
$578$	−6.92820	−	4.00000i	−0.288175	−	0.166378i
$579$	8.50000	−	14.7224i	0.353248	−	0.611843i
$580$		0			0
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$	−1.73205	+	1.00000i	−0.0717958	+	0.0414513i
$583$	1.73205	−	1.00000i	0.0717342	−	0.0414158i
$584$	−13.0000			−0.537944
$585$		0			0
$586$	1.00000			0.0413096
$587$	−27.7128	+	16.0000i	−1.14383	+	0.660391i	−0.947376	−	0.320122i	$-0.896276\pi$
$587$	−27.7128	+	16.0000i	−1.14383	+	0.660391i	−0.196454	+	0.980513i	$0.562943\pi$
$588$	−2.59808	+	1.50000i	−0.107143	+	0.0618590i
$589$	4.00000	−	6.92820i	0.164817	−	0.285472i
$590$		0			0
$591$	3.00000	−	5.19615i	0.123404	−	0.213741i
$592$	9.52628	+	5.50000i	0.391528	+	0.226049i
$593$			39.0000i			1.60154i	0.598973	+	0.800769i	$0.295576\pi$
$593$			39.0000i			1.60154i	−0.598973	+	0.800769i	$0.704424\pi$
$594$	1.00000	−	1.73205i	0.0410305	−	0.0710669i
$595$		0			0
$596$	−1.50000	−	2.59808i	−0.0614424	−	0.106421i
$597$		−	10.0000i		−	0.409273i
$598$	−20.7846	+	6.00000i	−0.849946	+	0.245358i
$599$		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	0.731774	−	0.681547i	$-0.238692\pi$
$601$	−5.50000	−	9.52628i	−0.224350	−	0.388585i	−0.956124	+	0.292962i	$0.905359\pi$
$602$	−17.3205	−	10.0000i	−0.705931	−	0.407570i
$603$		−	2.00000i		−	0.0814463i
$604$	−3.00000	+	5.19615i	−0.122068	+	0.211428i
$605$		0			0
$606$	−5.00000			−0.203111
$607$	−27.7128	−	16.0000i	−1.12483	−	0.649420i	−0.182199	−	0.983262i	$-0.558322\pi$
$607$	−27.7128	−	16.0000i	−1.12483	−	0.649420i	−0.942629	+	0.333842i	$0.891655\pi$
$608$	−1.73205	+	1.00000i	−0.0702439	+	0.0405554i
$609$	−9.00000	−	15.5885i	−0.364698	−	0.631676i
$610$		0			0
$611$	5.00000	−	5.19615i	0.202278	−	0.210214i
$612$			5.00000i			0.202113i
$613$	−11.2583	+	6.50000i	−0.454720	+	0.262533i	−0.709821	−	0.704382i	$-0.751224\pi$
$613$	−11.2583	+	6.50000i	−0.454720	+	0.262533i	0.255102	+	0.966914i	$0.417891\pi$
$614$	7.00000	+	12.1244i	0.282497	+	0.489299i
$615$		0			0
$616$	4.00000			0.161165
$617$	12.9904	+	7.50000i	0.522973	+	0.301939i	0.738150	−	0.674636i	$-0.235700\pi$
$617$	12.9904	+	7.50000i	0.522973	+	0.301939i	−0.215177	+	0.976575i	$0.569033\pi$
$618$	8.66025	+	5.00000i	0.348367	+	0.201129i
$619$	−32.0000			−1.28619			−0.643094	−	0.765787i	$-0.722350\pi$
$619$	−32.0000			−1.28619			−0.643094	+	0.765787i	$0.722350\pi$
$620$		0			0
$621$	3.00000	+	5.19615i	0.120386	+	0.208514i
$622$	−5.19615	+	3.00000i	−0.208347	+	0.120289i
$623$			4.00000i			0.160257i
$624$	1.00000	+	3.46410i	0.0400320	+	0.138675i
$625$		0			0
$626$	3.00000	+	5.19615i	0.119904	+	0.207680i
$627$	3.46410	−	2.00000i	0.138343	−	0.0798723i
$628$	−6.06218	−	3.50000i	−0.241907	−	0.139665i
$629$	55.0000			2.19299
$630$		0			0
$631$	−6.00000	+	10.3923i	−0.238856	+	0.413711i	−0.960386	−	0.278672i	$-0.910106\pi$
$631$	−6.00000	+	10.3923i	−0.238856	+	0.413711i	0.721530	+	0.692383i	$0.243439\pi$
$632$			4.00000i			0.159111i
$633$	−20.7846	−	12.0000i	−0.826114	−	0.476957i
$634$	16.5000	+	28.5788i	0.655299	+	1.13501i
$635$		0			0
$636$	1.00000			0.0396526
$637$	−2.59808	+	10.5000i	−0.102940	+	0.416025i
$638$		−	18.0000i		−	0.712627i
$639$	−7.00000	−	12.1244i	−0.276916	−	0.479632i
$640$		0			0
$641$	−2.50000	+	4.33013i	−0.0987441	+	0.171030i	−0.911165	−	0.412042i	$-0.864816\pi$
$641$	−2.50000	+	4.33013i	−0.0987441	+	0.171030i	0.812421	+	0.583071i	$0.198149\pi$
$642$		−	18.0000i		−	0.710403i
$643$	6.92820	+	4.00000i	0.273222	+	0.157745i	0.630351	−	0.776310i	$-0.282911\pi$
$643$	6.92820	+	4.00000i	0.273222	+	0.157745i	−0.357129	+	0.934055i	$0.616244\pi$
$644$	−6.00000	+	10.3923i	−0.236433	+	0.409514i
$645$		0			0
$646$	−5.00000	+	8.66025i	−0.196722	+	0.340733i
$647$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$647$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	16.0000			0.628055
$650$		0			0
$651$	−8.00000			−0.313545
$652$	17.3205	−	10.0000i	0.678323	−	0.391630i
$653$	19.0526	−	11.0000i	0.745584	−	0.430463i	−0.0785119	−	0.996913i	$-0.525017\pi$
$653$	19.0526	−	11.0000i	0.745584	−	0.430463i	0.824096	+	0.566450i	$0.191684\pi$
$654$	−1.00000	+	1.73205i	−0.0391031	+	0.0677285i
$655$		0			0
$656$	−2.50000	+	4.33013i	−0.0976086	+	0.169063i
$657$	11.2583	+	6.50000i	0.439229	+	0.253589i
$658$		−	4.00000i		−	0.155936i
$659$	12.0000	−	20.7846i	0.467454	−	0.809653i	−0.531855	−	0.846836i	$-0.678505\pi$
$659$	12.0000	−	20.7846i	0.467454	−	0.809653i	0.999309	+	0.0371821i	$0.0118382\pi$
$660$		0			0
$661$	−12.5000	−	21.6506i	−0.486194	−	0.842112i	0.513680	−	0.857982i	$-0.328282\pi$
$661$	−12.5000	−	21.6506i	−0.486194	−	0.842112i	−0.999874	+	0.0158695i	$0.994948\pi$
$662$			28.0000i			1.08825i
$663$	12.9904	+	12.5000i	0.504505	+	0.485460i
$664$	6.00000			0.232845
$665$		0			0
$666$	−5.50000	−	9.52628i	−0.213121	−	0.369136i
$667$	46.7654	+	27.0000i	1.81076	+	1.04544i
$668$		−	24.0000i		−	0.928588i
$669$	8.00000	−	13.8564i	0.309298	−	0.535720i
$670$		0			0
$671$	−22.0000			−0.849301
$672$	1.73205	+	1.00000i	0.0668153	+	0.0385758i
$673$	−37.2391	+	21.5000i	−1.43546	+	0.828764i	−0.997530	−	0.0702442i	$-0.977622\pi$
$673$	−37.2391	+	21.5000i	−1.43546	+	0.828764i	−0.437932	+	0.899008i	$0.644289\pi$
$674$	4.50000	+	7.79423i	0.173334	+	0.300222i
$675$		0			0
$676$	11.5000	+	6.06218i	0.442308	+	0.233161i
$677$		−	46.0000i		−	1.76792i	−0.467559	−	0.883962i	$-0.654866\pi$
$677$		−	46.0000i		−	1.76792i	0.467559	−	0.883962i	$-0.345134\pi$
$678$	2.59808	−	1.50000i	0.0997785	−	0.0576072i
$679$	2.00000	+	3.46410i	0.0767530	+	0.132940i
$680$		0			0
$681$	−14.0000			−0.536481
$682$	−6.92820	−	4.00000i	−0.265295	−	0.153168i
$683$	−34.6410	−	20.0000i	−1.32550	−	0.765279i	−0.340901	−	0.940099i	$-0.610732\pi$
$683$	−34.6410	−	20.0000i	−1.32550	−	0.765279i	−0.984600	+	0.174820i	$0.944066\pi$
$684$	2.00000			0.0764719
$685$		0			0
$686$	10.0000	+	17.3205i	0.381802	+	0.661300i
$687$	−8.66025	+	5.00000i	−0.330409	+	0.190762i
$688$		−	10.0000i		−	0.381246i
$689$	2.50000	−	2.59808i	0.0952424	−	0.0989788i
$690$		0			0
$691$	1.00000	+	1.73205i	0.0380418	+	0.0658903i	0.884419	−	0.466693i	$-0.154555\pi$
$691$	1.00000	+	1.73205i	0.0380418	+	0.0658903i	−0.846378	+	0.532583i	$0.821221\pi$
$692$	−19.0526	+	11.0000i	−0.724270	+	0.418157i
$693$	−3.46410	−	2.00000i	−0.131590	−	0.0759737i
$694$	6.00000			0.227757
$695$		0			0
$696$	4.50000	−	7.79423i	0.170572	−	0.295439i
$697$			25.0000i			0.946943i
$698$	−5.19615	−	3.00000i	−0.196677	−	0.113552i
$699$	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	$0.278071\pi$
$702$	0.866025	−	3.50000i	0.0326860	−	0.132099i
$703$		−	22.0000i		−	0.829746i
$704$	1.00000	+	1.73205i	0.0376889	+	0.0652791i
$705$		0			0
$706$	8.50000	−	14.7224i	0.319902	−	0.554086i
$707$			10.0000i			0.376089i
$708$	6.92820	+	4.00000i	0.260378	+	0.150329i
$709$	−7.50000	+	12.9904i	−0.281668	+	0.487864i	−0.971796	−	0.235824i	$-0.924221\pi$
$709$	−7.50000	+	12.9904i	−0.281668	+	0.487864i	0.690127	+	0.723688i	$0.257554\pi$
$710$		0			0
$711$	2.00000	−	3.46410i	0.0750059	−	0.129914i
$712$	−1.73205	+	1.00000i	−0.0649113	+	0.0374766i
$713$	20.7846	−	12.0000i	0.778390	−	0.449404i
$714$	10.0000			0.374241
$715$		0			0
$716$	−6.00000			−0.224231
$717$	5.19615	−	3.00000i	0.194054	−	0.112037i
$718$	−25.9808	+	15.0000i	−0.969593	+	0.559795i
$719$	12.0000	−	20.7846i	0.447524	−	0.775135i	−0.550700	−	0.834703i	$-0.685639\pi$
$719$	12.0000	−	20.7846i	0.447524	−	0.775135i	0.998224	+	0.0595683i	$0.0189724\pi$
$720$		0			0
$721$	10.0000	−	17.3205i	0.372419	−	0.645049i
$722$	−12.9904	−	7.50000i	−0.483452	−	0.279121i
$723$			7.00000i			0.260333i
$724$	2.50000	−	4.33013i	0.0929118	−	0.160928i
$725$		0			0
$726$	3.50000	+	6.06218i	0.129897	+	0.224989i
$727$			2.00000i			0.0741759i	0.999312	+	0.0370879i	$0.0118082\pi$
$727$			2.00000i			0.0741759i	−0.999312	+	0.0370879i	$0.988192\pi$
$728$	6.92820	−	2.00000i	0.256776	−	0.0741249i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−25.0000	−	43.3013i	−0.924658	−	1.60156i
$732$	−9.52628	−	5.50000i	−0.352101	−	0.203286i
$733$		−	13.0000i		−	0.480166i	−0.970752	−	0.240083i	$-0.922825\pi$
$733$		−	13.0000i		−	0.480166i	0.970752	−	0.240083i	$-0.0771747\pi$
$734$	1.00000	−	1.73205i	0.0369107	−	0.0639312i
$735$		0			0
$736$	−6.00000			−0.221163
$737$	−3.46410	−	2.00000i	−0.127602	−	0.0736709i
$738$	4.33013	−	2.50000i	0.159394	−	0.0920263i
$739$	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
$741$	5.00000	−	5.19615i	0.183680	−	0.190885i
$742$		−	2.00000i		−	0.0734223i
$743$	10.3923	−	6.00000i	0.381257	−	0.220119i	−0.297108	−	0.954844i	$-0.596022\pi$
$743$	10.3923	−	6.00000i	0.381257	−	0.220119i	0.678365	+	0.734725i	$0.262689\pi$
$744$	−2.00000	−	3.46410i	−0.0733236	−	0.127000i
$745$		0			0
$746$	−9.00000			−0.329513
$747$	−5.19615	−	3.00000i	−0.190117	−	0.109764i
$748$	8.66025	+	5.00000i	0.316650	+	0.182818i
$749$	−36.0000			−1.31541
$750$		0			0
$751$	−13.0000	−	22.5167i	−0.474377	−	0.821645i	0.525193	−	0.850983i	$-0.323993\pi$
$751$	−13.0000	−	22.5167i	−0.474377	−	0.821645i	−0.999570	+	0.0293387i	$0.990660\pi$
$752$	1.73205	−	1.00000i	0.0631614	−	0.0364662i
$753$			4.00000i			0.145768i
$754$	−9.00000	−	31.1769i	−0.327761	−	1.13540i
$755$		0			0
$756$	−1.00000	−	1.73205i	−0.0363696	−	0.0629941i
$757$	−15.5885	+	9.00000i	−0.566572	+	0.327111i	−0.755779	−	0.654827i	$-0.772742\pi$
$757$	−15.5885	+	9.00000i	−0.566572	+	0.327111i	0.189207	+	0.981937i	$0.439408\pi$
$758$	−10.3923	−	6.00000i	−0.377466	−	0.217930i
$759$	12.0000			0.435572
$760$		0			0
$761$	−17.0000	+	29.4449i	−0.616250	+	1.06738i	0.373914	+	0.927463i	$0.378015\pi$
$761$	−17.0000	+	29.4449i	−0.616250	+	1.06738i	−0.990164	+	0.139912i	$0.955318\pi$
$762$		−	12.0000i		−	0.434714i
$763$	3.46410	+	2.00000i	0.125409	+	0.0724049i
$764$	2.00000	+	3.46410i	0.0723575	+	0.125327i
$765$		0			0
$766$	−24.0000			−0.867155
$767$	27.7128	−	8.00000i	1.00065	−	0.288863i
$768$			1.00000i			0.0360844i
$769$	−17.0000	−	29.4449i	−0.613036	−	1.06181i	−0.990726	−	0.135877i	$-0.956615\pi$
$769$	−17.0000	−	29.4449i	−0.613036	−	1.06181i	0.377690	−	0.925932i	$-0.376718\pi$
$770$		0			0
$771$	−1.50000	+	2.59808i	−0.0540212	+	0.0935674i
$772$		−	17.0000i		−	0.611843i
$773$	15.5885	+	9.00000i	0.560678	+	0.323708i	0.753418	−	0.657542i	$-0.228404\pi$
$773$	15.5885	+	9.00000i	0.560678	+	0.323708i	−0.192740	+	0.981250i	$0.561737\pi$
$774$	−5.00000	+	8.66025i	−0.179721	+	0.311286i
$775$		0			0
$776$	−1.00000	+	1.73205i	−0.0358979	+	0.0621770i
$777$	−19.0526	+	11.0000i	−0.683507	+	0.394623i
$778$	16.4545	−	9.50000i	0.589922	−	0.340592i
$779$	10.0000			0.358287
$780$		0			0
$781$	−28.0000			−1.00192
$782$	−25.9808	+	15.0000i	−0.929070	+	0.536399i
$783$	−7.79423	+	4.50000i	−0.278543	+	0.160817i
$784$	−1.50000	+	2.59808i	−0.0535714	+	0.0927884i
$785$		0			0
$786$	4.00000	−	6.92820i	0.142675	−	0.247121i
$787$	−3.46410	−	2.00000i	−0.123482	−	0.0712923i	0.436987	−	0.899468i	$-0.356046\pi$
$787$	−3.46410	−	2.00000i	−0.123482	−	0.0712923i	−0.560469	+	0.828176i	$0.689379\pi$
$788$		−	6.00000i		−	0.213741i
$789$	−7.00000	+	12.1244i	−0.249207	+	0.431638i
$790$		0			0
$791$	−3.00000	−	5.19615i	−0.106668	−	0.184754i
$792$		−	2.00000i		−	0.0710669i
$793$	−38.1051	+	11.0000i	−1.35315	+	0.390621i
$794$	−18.0000			−0.638796
$795$		0			0
$796$	−5.00000	−	8.66025i	−0.177220	−	0.306955i
$797$	1.73205	+	1.00000i	0.0613524	+	0.0354218i	0.530362	−	0.847771i	$-0.322056\pi$
$797$	1.73205	+	1.00000i	0.0613524	+	0.0354218i	−0.469010	+	0.883193i	$0.655389\pi$
$798$		−	4.00000i		−	0.141598i
$799$	5.00000	−	8.66025i	0.176887	−	0.306378i
$800$		0			0
$801$	2.00000			0.0706665
$802$	−23.3827	−	13.5000i	−0.825671	−	0.476702i
$803$	22.5167	−	13.0000i	0.794596	−	0.458760i
$804$	−1.00000	−	1.73205i	−0.0352673	−	0.0610847i
$805$		0			0
$806$	−14.0000	−	3.46410i	−0.493129	−	0.122018i
$807$			14.0000i			0.492823i
$808$	−4.33013	+	2.50000i	−0.152333	+	0.0879497i
$809$	2.50000	+	4.33013i	0.0878953	+	0.152239i	0.906621	−	0.421945i	$-0.138653\pi$
$809$	2.50000	+	4.33013i	0.0878953	+	0.152239i	−0.818726	+	0.574184i	$0.805319\pi$
$810$		0			0
$811$	−36.0000			−1.26413			−0.632065	−	0.774915i	$-0.717793\pi$
$811$	−36.0000			−1.26413			−0.632065	+	0.774915i	$0.717793\pi$
$812$	−15.5885	−	9.00000i	−0.547048	−	0.315838i
$813$	−6.92820	−	4.00000i	−0.242983	−	0.140286i
$814$	−22.0000			−0.771100
$815$		0			0
$816$	2.50000	+	4.33013i	0.0875175	+	0.151585i
$817$	−17.3205	+	10.0000i	−0.605968	+	0.349856i
$818$			23.0000i			0.804176i
$819$	−7.00000	−	1.73205i	−0.244600	−	0.0605228i
$820$		0			0
$821$	15.0000	+	25.9808i	0.523504	+	0.906735i	0.999626	+	0.0273557i	$0.00870868\pi$
$821$	15.0000	+	25.9808i	0.523504	+	0.906735i	−0.476122	+	0.879379i	$0.657958\pi$
$822$	14.7224	−	8.50000i	0.513504	−	0.296472i
$823$	−13.8564	−	8.00000i	−0.483004	−	0.278862i	0.238664	−	0.971102i	$-0.423291\pi$
$823$	−13.8564	−	8.00000i	−0.483004	−	0.278862i	−0.721668	+	0.692240i	$0.756624\pi$
$824$	10.0000			0.348367
$825$		0			0
$826$	8.00000	−	13.8564i	0.278356	−	0.482126i
$827$		−	8.00000i		−	0.278187i	−0.990279	−	0.139094i	$-0.955581\pi$
$827$		−	8.00000i		−	0.278187i	0.990279	−	0.139094i	$-0.0444189\pi$
$828$	5.19615	+	3.00000i	0.180579	+	0.104257i
$829$	−17.5000	−	30.3109i	−0.607800	−	1.05274i	−0.991602	−	0.129325i	$-0.958719\pi$
$829$	−17.5000	−	30.3109i	−0.607800	−	1.05274i	0.383802	−	0.923415i	$-0.374614\pi$
$830$		0			0
$831$	11.0000			0.381586
$832$	2.59808	+	2.50000i	0.0900721	+	0.0866719i
$833$			15.0000i			0.519719i
$834$	−6.00000	−	10.3923i	−0.207763	−	0.359856i
$835$		0			0
$836$	2.00000	−	3.46410i	0.0691714	−	0.119808i
$837$			4.00000i			0.138260i
$838$	27.7128	+	16.0000i	0.957323	+	0.552711i
$839$	22.0000	−	38.1051i	0.759524	−	1.31553i	−0.183569	−	0.983007i	$-0.558765\pi$
$839$	22.0000	−	38.1051i	0.759524	−	1.31553i	0.943093	−	0.332528i	$-0.107902\pi$
$840$		0			0
$841$	−26.0000	+	45.0333i	−0.896552	+	1.55287i
$842$	19.9186	−	11.5000i	0.686440	−	0.396316i
$843$	21.6506	−	12.5000i	0.745687	−	0.430523i
$844$	−24.0000			−0.826114
$845$		0			0
$846$	−2.00000			−0.0687614
$847$	12.1244	−	7.00000i	0.416598	−	0.240523i
$848$	0.866025	−	0.500000i	0.0297394	−	0.0171701i
$849$	−13.0000	+	22.5167i	−0.446159	+	0.772770i
$850$		0			0
$851$	33.0000	−	57.1577i	1.13123	−	1.95934i
$852$	−12.1244	−	7.00000i	−0.415374	−	0.239816i
$853$		−	49.0000i		−	1.67773i	−0.544341	−	0.838864i	$-0.683220\pi$
$853$		−	49.0000i		−	1.67773i	0.544341	−	0.838864i	$-0.316780\pi$
$854$	−11.0000	+	19.0526i	−0.376412	+	0.651965i
$855$		0			0
$856$	−9.00000	−	15.5885i	−0.307614	−	0.532803i
$857$			45.0000i			1.53717i	0.639747	+	0.768585i	$0.279039\pi$
$857$			45.0000i			1.53717i	−0.639747	+	0.768585i	$0.720961\pi$
$858$	−5.19615	−	5.00000i	−0.177394	−	0.170697i
$859$	50.0000			1.70598			0.852989	−	0.521929i	$-0.174787\pi$
$859$	50.0000			1.70598			0.852989	+	0.521929i	$0.174787\pi$
$860$		0			0
$861$	−5.00000	−	8.66025i	−0.170400	−	0.295141i
$862$	−1.73205	−	1.00000i	−0.0589939	−	0.0340601i
$863$		−	46.0000i		−	1.56586i	−0.622111	−	0.782929i	$-0.713725\pi$
$863$		−	46.0000i		−	1.56586i	0.622111	−	0.782929i	$-0.286275\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$		0			0
$866$	21.0000			0.713609
$867$	6.92820	+	4.00000i	0.235294	+	0.135847i
$868$	−6.92820	+	4.00000i	−0.235159	+	0.135769i
$869$	−4.00000	−	6.92820i	−0.135691	−	0.235023i
$870$		0			0
$871$	−7.00000	−	1.73205i	−0.237186	−	0.0586883i
$872$			2.00000i			0.0677285i
$873$	1.73205	−	1.00000i	0.0586210	−	0.0338449i
$874$	6.00000	+	10.3923i	0.202953	+	0.351525i
$875$		0			0
$876$	13.0000			0.439229
$877$	−32.0429	−	18.5000i	−1.08201	−	0.624701i	−0.150574	−	0.988599i	$-0.548112\pi$
$877$	−32.0429	−	18.5000i	−1.08201	−	0.624701i	−0.931439	+	0.363898i	$0.881446\pi$
$878$	−8.66025	−	5.00000i	−0.292269	−	0.168742i
$879$	−1.00000			−0.0337292
$880$		0			0
$881$	−8.50000	−	14.7224i	−0.286372	−	0.496011i	0.686569	−	0.727065i	$-0.259116\pi$
$881$	−8.50000	−	14.7224i	−0.286372	−	0.496011i	−0.972941	+	0.231054i	$0.925783\pi$
$882$	2.59808	−	1.50000i	0.0874818	−	0.0505076i
$883$			8.00000i			0.269221i	0.990899	+	0.134611i	$0.0429784\pi$
$883$			8.00000i			0.269221i	−0.990899	+	0.134611i	$0.957022\pi$
$884$	17.5000	+	4.33013i	0.588589	+	0.145638i
$885$		0			0
$886$	10.0000	+	17.3205i	0.335957	+	0.581894i
$887$	20.7846	−	12.0000i	0.697879	−	0.402921i	−0.108678	−	0.994077i	$-0.534662\pi$
$887$	20.7846	−	12.0000i	0.697879	−	0.402921i	0.806557	+	0.591156i	$0.201328\pi$
$888$	−9.52628	−	5.50000i	−0.319681	−	0.184568i
$889$	−24.0000			−0.804934
$890$		0			0
$891$	−1.00000	+	1.73205i	−0.0335013	+	0.0580259i
$892$		−	16.0000i		−	0.535720i
$893$	−3.46410	−	2.00000i	−0.115922	−	0.0669274i
$894$	1.50000	+	2.59808i	0.0501675	+	0.0868927i
$895$		0			0
$896$	2.00000			0.0668153
$897$	20.7846	−	6.00000i	0.693978	−	0.200334i
$898$		−	30.0000i		−	1.00111i
$899$	18.0000	+	31.1769i	0.600334	+	1.03981i
$900$		0			0
$901$	2.50000	−	4.33013i	0.0832871	−	0.144257i
$902$		−	10.0000i		−	0.332964i
$903$	17.3205	+	10.0000i	0.576390	+	0.332779i
$904$	1.50000	−	2.59808i	0.0498893	−	0.0864107i
$905$		0			0
$906$	3.00000	−	5.19615i	0.0996683	−	0.172631i
$907$	−38.1051	+	22.0000i	−1.26526	+	0.730498i	−0.974087	−	0.226173i	$-0.927379\pi$
$907$	−38.1051	+	22.0000i	−1.26526	+	0.730498i	−0.291172	+	0.956671i	$0.594045\pi$
$908$	−12.1244	+	7.00000i	−0.402361	+	0.232303i
$909$	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	$0.677847\pi$
$912$	1.73205	−	1.00000i	0.0573539	−	0.0331133i
$913$	−10.3923	+	6.00000i	−0.343935	+	0.198571i
$914$	−1.50000	+	2.59808i	−0.0496156	+	0.0859367i
$915$		0			0
$916$	−5.00000	+	8.66025i	−0.165205	+	0.286143i
$917$	−13.8564	−	8.00000i	−0.457579	−	0.264183i
$918$		−	5.00000i		−	0.165025i
$919$	−8.00000	+	13.8564i	−0.263896	+	0.457081i	−0.967274	−	0.253735i	$-0.918341\pi$
$919$	−8.00000	+	13.8564i	−0.263896	+	0.457081i	0.703378	+	0.710816i	$0.251674\pi$
$920$		0			0
$921$	−7.00000	−	12.1244i	−0.230658	−	0.399511i
$922$		−	3.00000i		−	0.0987997i
$923$	−48.4974	+	14.0000i	−1.59631	+	0.460816i
$924$	−4.00000			−0.131590
$925$		0			0
$926$	−7.00000	−	12.1244i	−0.230034	−	0.398431i
$927$	−8.66025	−	5.00000i	−0.284440	−	0.164222i
$928$		−	9.00000i		−	0.295439i
$929$	−11.5000	+	19.9186i	−0.377303	+	0.653508i	−0.990669	−	0.136291i	$-0.956482\pi$
$929$	−11.5000	+	19.9186i	−0.377303	+	0.653508i	0.613366	+	0.789799i	$0.289815\pi$
$930$		0			0
$931$	6.00000			0.196642
$932$	5.19615	+	3.00000i	0.170206	+	0.0982683i
$933$	5.19615	−	3.00000i	0.170114	−	0.0982156i
$934$	11.0000	+	19.0526i	0.359931	+	0.623419i
$935$		0			0
$936$	−1.00000	−	3.46410i	−0.0326860	−	0.113228i
$937$		−	1.00000i		−	0.0326686i	−0.999867	−	0.0163343i	$-0.994800\pi$
$937$		−	1.00000i		−	0.0326686i	0.999867	−	0.0163343i	$-0.00519960\pi$
$938$	−3.46410	+	2.00000i	−0.113107	+	0.0653023i
$939$	−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	$0.616742\pi$
$942$	6.06218	+	3.50000i	0.197516	+	0.114036i
$943$	25.9808	+	15.0000i	0.846050	+	0.488467i
$944$	8.00000			0.260378
$945$		0			0
$946$	10.0000	+	17.3205i	0.325128	+	0.563138i
$947$	6.92820	−	4.00000i	0.225136	−	0.129983i	−0.383190	−	0.923670i	$-0.625175\pi$
$947$	6.92820	−	4.00000i	0.225136	−	0.129983i	0.608326	+	0.793687i	$0.291841\pi$
$948$		−	4.00000i		−	0.129914i
$949$	32.5000	−	33.7750i	1.05499	−	1.09638i
$950$		0			0
$951$	−16.5000	−	28.5788i	−0.535049	−	0.926732i
$952$	8.66025	−	5.00000i	0.280680	−	0.162051i
$953$	46.7654	+	27.0000i	1.51488	+	0.874616i	0.999848	+	0.0174443i	$0.00555298\pi$
$953$	46.7654	+	27.0000i	1.51488	+	0.874616i	0.515031	+	0.857171i	$0.327780\pi$
$954$	−1.00000			−0.0323762
$955$		0			0
$956$	3.00000	−	5.19615i	0.0970269	−	0.168056i
$957$			18.0000i			0.581857i
$958$	−27.7128	−	16.0000i	−0.895360	−	0.516937i
$959$	−17.0000	−	29.4449i	−0.548959	−	0.950824i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	−38.1051	+	11.0000i	−1.22856	+	0.354654i
$963$			18.0000i			0.580042i
$964$	3.50000	+	6.06218i	0.112727	+	0.195250i
$965$		0			0
$966$	6.00000	−	10.3923i	0.193047	−	0.334367i
$967$		−	50.0000i		−	1.60789i	−0.594703	−	0.803946i	$-0.702730\pi$
$967$		−	50.0000i		−	1.60789i	0.594703	−	0.803946i	$-0.297270\pi$
$968$	6.06218	+	3.50000i	0.194846	+	0.112494i
$969$	5.00000	−	8.66025i	0.160623	−	0.278207i
$970$		0			0
$971$	−10.0000	+	17.3205i	−0.320915	+	0.555842i	−0.980677	−	0.195633i	$-0.937324\pi$
$971$	−10.0000	+	17.3205i	−0.320915	+	0.555842i	0.659762	+	0.751475i	$0.270657\pi$
$972$	−0.866025	+	0.500000i	−0.0277778	+	0.0160375i
$973$	−20.7846	+	12.0000i	−0.666324	+	0.384702i
$974$	−26.0000			−0.833094
$975$		0			0
$976$	−11.0000			−0.352101
$977$	18.1865	−	10.5000i	0.581839	−	0.335925i	−0.180025	−	0.983662i	$-0.557618\pi$
$977$	18.1865	−	10.5000i	0.581839	−	0.335925i	0.761864	+	0.647737i	$0.224285\pi$
$978$	−17.3205	+	10.0000i	−0.553849	+	0.319765i
$979$	2.00000	−	3.46410i	0.0639203	−	0.110713i
$980$		0			0
$981$	1.00000	−	1.73205i	0.0319275	−	0.0553001i
$982$	−25.9808	−	15.0000i	−0.829079	−	0.478669i
$983$		−	60.0000i		−	1.91370i	−0.290578	−	0.956851i	$-0.593847\pi$
$983$		−	60.0000i		−	1.91370i	0.290578	−	0.956851i	$-0.406153\pi$
$984$	2.50000	−	4.33013i	0.0796971	−	0.138039i
$985$		0			0
$986$	−22.5000	−	38.9711i	−0.716546	−	1.24109i
$987$			4.00000i			0.127321i
$988$	1.73205	−	7.00000i	0.0551039	−	0.222700i
$989$	−60.0000			−1.90789
$990$		0			0
$991$	−9.00000	−	15.5885i	−0.285894	−	0.495184i	0.686931	−	0.726722i	$-0.258957\pi$
$991$	−9.00000	−	15.5885i	−0.285894	−	0.495184i	−0.972826	+	0.231539i	$0.925624\pi$
$992$	−3.46410	−	2.00000i	−0.109985	−	0.0635001i
$993$		−	28.0000i		−	0.888553i
$994$	−14.0000	+	24.2487i	−0.444053	+	0.769122i
$995$		0			0
$996$	−6.00000			−0.190117
$997$	19.9186	+	11.5000i	0.630828	+	0.364209i	0.781073	−	0.624440i	$-0.214673\pi$
$997$	19.9186	+	11.5000i	0.630828	+	0.364209i	−0.150245	+	0.988649i	$0.548006\pi$
$998$		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.z.b.1849.1		4
5.2	odd	4		1950.2.i.b.601.1		2
5.3	odd	4		78.2.e.b.55.1	✓	2
5.4	even	2	inner	1950.2.z.b.1849.2		4
13.9	even	3	inner	1950.2.z.b.1699.2		4
15.8	even	4		234.2.h.b.55.1		2
20.3	even	4		624.2.q.b.289.1		2
60.23	odd	4		1872.2.t.i.289.1		2
65.3	odd	12		1014.2.a.a.1.1		1
65.8	even	4		1014.2.i.e.361.1		4
65.9	even	6	inner	1950.2.z.b.1699.1		4
65.18	even	4		1014.2.i.e.361.2		4
65.22	odd	12		1950.2.i.b.451.1		2
65.23	odd	12		1014.2.a.e.1.1		1
65.28	even	12		1014.2.b.a.337.2		2
65.33	even	12		1014.2.i.e.823.2		4
65.38	odd	4		1014.2.e.d.991.1		2
65.43	odd	12		1014.2.e.d.529.1		2
65.48	odd	12		78.2.e.b.61.1	yes	2
65.58	even	12		1014.2.i.e.823.1		4
65.63	even	12		1014.2.b.a.337.1		2
195.23	even	12		3042.2.a.d.1.1		1
195.68	even	12		3042.2.a.m.1.1		1
195.113	even	12		234.2.h.b.217.1		2
195.128	odd	12		3042.2.b.d.1351.2		2
195.158	odd	12		3042.2.b.d.1351.1		2
260.3	even	12		8112.2.a.x.1.1		1
260.23	even	12		8112.2.a.bb.1.1		1
260.243	even	12		624.2.q.b.529.1		2
780.503	odd	12		1872.2.t.i.1153.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.e.b.55.1	✓	2	5.3	odd	4
78.2.e.b.61.1	yes	2	65.48	odd	12
234.2.h.b.55.1		2	15.8	even	4
234.2.h.b.217.1		2	195.113	even	12
624.2.q.b.289.1		2	20.3	even	4
624.2.q.b.529.1		2	260.243	even	12
1014.2.a.a.1.1		1	65.3	odd	12
1014.2.a.e.1.1		1	65.23	odd	12
1014.2.b.a.337.1		2	65.63	even	12
1014.2.b.a.337.2		2	65.28	even	12
1014.2.e.d.529.1		2	65.43	odd	12
1014.2.e.d.991.1		2	65.38	odd	4
1014.2.i.e.361.1		4	65.8	even	4
1014.2.i.e.361.2		4	65.18	even	4
1014.2.i.e.823.1		4	65.58	even	12
1014.2.i.e.823.2		4	65.33	even	12
1872.2.t.i.289.1		2	60.23	odd	4
1872.2.t.i.1153.1		2	780.503	odd	12
1950.2.i.b.451.1		2	65.22	odd	12
1950.2.i.b.601.1		2	5.2	odd	4
1950.2.z.b.1699.1		4	65.9	even	6	inner
1950.2.z.b.1699.2		4	13.9	even	3	inner
1950.2.z.b.1849.1		4	1.1	even	1	trivial
1950.2.z.b.1849.2		4	5.4	even	2	inner
3042.2.a.d.1.1		1	195.23	even	12
3042.2.a.m.1.1		1	195.68	even	12
3042.2.b.d.1351.1		2	195.158	odd	12
3042.2.b.d.1351.2		2	195.128	odd	12
8112.2.a.x.1.1		1	260.3	even	12
8112.2.a.bb.1.1		1	260.23	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.z (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(1.73205 + 1.00000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(1.73205 + 1.00000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{11} -1.00000i q^{12} +(-2.59808 - 2.50000i) q^{13} -2.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.33013 - 2.50000i) q^{17} +1.00000i q^{18} +(-1.00000 + 1.73205i) q^{19} +2.00000 q^{21} +(1.73205 + 1.00000i) q^{22} +(-5.19615 + 3.00000i) q^{23} +(0.500000 + 0.866025i) q^{24} +(3.50000 + 0.866025i) q^{26} -1.00000i q^{27} +(1.73205 - 1.00000i) q^{28} +(-4.50000 - 7.79423i) q^{29} -4.00000 q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.73205 - 1.00000i) q^{33} +5.00000 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-9.52628 + 5.50000i) q^{37} -2.00000i q^{38} +(-3.50000 - 0.866025i) q^{39} +(-2.50000 - 4.33013i) q^{41} +(-1.73205 + 1.00000i) q^{42} +(8.66025 + 5.00000i) q^{43} -2.00000 q^{44} +(3.00000 - 5.19615i) q^{46} +2.00000i q^{47} +(-0.866025 - 0.500000i) q^{48} +(-1.50000 - 2.59808i) q^{49} -5.00000 q^{51} +(-3.46410 + 1.00000i) q^{52} +1.00000i q^{53} +(0.500000 + 0.866025i) q^{54} +(-1.00000 + 1.73205i) q^{56} +2.00000i q^{57} +(7.79423 + 4.50000i) q^{58} +(-4.00000 + 6.92820i) q^{59} +(5.50000 - 9.52628i) q^{61} +(3.46410 - 2.00000i) q^{62} +(1.73205 - 1.00000i) q^{63} -1.00000 q^{64} +2.00000 q^{66} +(1.73205 - 1.00000i) q^{67} +(-4.33013 + 2.50000i) q^{68} +(-3.00000 + 5.19615i) q^{69} +(7.00000 - 12.1244i) q^{71} +(0.866025 + 0.500000i) q^{72} +13.0000i q^{73} +(5.50000 - 9.52628i) q^{74} +(1.00000 + 1.73205i) q^{76} -4.00000i q^{77} +(3.46410 - 1.00000i) q^{78} +4.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(4.33013 + 2.50000i) q^{82} -6.00000i q^{83} +(1.00000 - 1.73205i) q^{84} -10.0000 q^{86} +(-7.79423 - 4.50000i) q^{87} +(1.73205 - 1.00000i) q^{88} +(1.00000 + 1.73205i) q^{89} +(-2.00000 - 6.92820i) q^{91} +6.00000i q^{92} +(-3.46410 + 2.00000i) q^{93} +(-1.00000 - 1.73205i) q^{94} +1.00000 q^{96} +(1.73205 + 1.00000i) q^{97} +(2.59808 + 1.50000i) q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 2 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - 2 * q^6 + 2 * q^9	\( 4 q + 2 q^{4} - 2 q^{6} + 2 q^{9} - 4 q^{11} - 8 q^{14} - 2 q^{16} - 4 q^{19} + 8 q^{21} + 2 q^{24} + 14 q^{26} - 18 q^{29} - 16 q^{31} + 20 q^{34} - 2 q^{36} - 14 q^{39} - 10 q^{41} - 8 q^{44} + 12 q^{46} - 6 q^{49} - 20 q^{51} + 2 q^{54} - 4 q^{56} - 16 q^{59} + 22 q^{61} - 4 q^{64} + 8 q^{66} - 12 q^{69} + 28 q^{71} + 22 q^{74} + 4 q^{76} + 16 q^{79} - 2 q^{81} + 4 q^{84} - 40 q^{86} + 4 q^{89} - 8 q^{91} - 4 q^{94} + 4 q^{96} - 8 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 - 2 * q^6 + 2 * q^9 - 4 * q^11 - 8 * q^14 - 2 * q^16 - 4 * q^19 + 8 * q^21 + 2 * q^24 + 14 * q^26 - 18 * q^29 - 16 * q^31 + 20 * q^34 - 2 * q^36 - 14 * q^39 - 10 * q^41 - 8 * q^44 + 12 * q^46 - 6 * q^49 - 20 * q^51 + 2 * q^54 - 4 * q^56 - 16 * q^59 + 22 * q^61 - 4 * q^64 + 8 * q^66 - 12 * q^69 + 28 * q^71 + 22 * q^74 + 4 * q^76 + 16 * q^79 - 2 * q^81 + 4 * q^84 - 40 * q^86 + 4 * q^89 - 8 * q^91 - 4 * q^94 + 4 * q^96 - 8 * q^99

Introduction

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