LMFDB - Embedded newform 1050.2.o.a.949.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(499,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1050.499");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.o (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:	$8.38429221223$
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 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			949.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1050.949
Dual form			1050.2.o.a.499.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(2.59808 - 0.500000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(2.59808 - 0.500000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.50000 + 4.33013i) q^{11} +(0.866025 - 0.500000i) q^{12} +(-2.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.46410 - 2.00000i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(4.00000 + 6.92820i) q^{19} +(2.50000 + 0.866025i) q^{21} -5.00000i q^{22} +(-3.46410 + 2.00000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +1.00000i q^{27} +(0.866025 - 2.50000i) q^{28} +5.00000 q^{29} +(-1.50000 + 2.59808i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.33013 + 2.50000i) q^{33} +4.00000 q^{34} +1.00000 q^{36} +(3.46410 - 2.00000i) q^{37} +(-6.92820 - 4.00000i) q^{38} +(-2.59808 + 0.500000i) q^{42} +2.00000i q^{43} +(2.50000 + 4.33013i) q^{44} +(2.00000 - 3.46410i) q^{46} +(5.19615 - 3.00000i) q^{47} -1.00000i q^{48} +(6.50000 - 2.59808i) q^{49} +(-2.00000 - 3.46410i) q^{51} +(7.79423 + 4.50000i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(0.500000 + 2.59808i) q^{56} +8.00000i q^{57} +(-4.33013 + 2.50000i) q^{58} +(-5.50000 + 9.52628i) q^{59} +(3.00000 + 5.19615i) q^{61} -3.00000i q^{62} +(1.73205 + 2.00000i) q^{63} -1.00000 q^{64} +(2.50000 - 4.33013i) q^{66} +(-1.73205 - 1.00000i) q^{67} +(-3.46410 + 2.00000i) q^{68} -4.00000 q^{69} +2.00000 q^{71} +(-0.866025 + 0.500000i) q^{72} +(-8.66025 - 5.00000i) q^{73} +(-2.00000 + 3.46410i) q^{74} +8.00000 q^{76} +(-4.33013 + 12.5000i) q^{77} +(1.50000 + 2.59808i) q^{79} +(-0.500000 + 0.866025i) q^{81} -7.00000i q^{83} +(2.00000 - 1.73205i) q^{84} +(-1.00000 - 1.73205i) q^{86} +(4.33013 + 2.50000i) q^{87} +(-4.33013 - 2.50000i) q^{88} +(-3.00000 - 5.19615i) q^{89} +4.00000i q^{92} +(-2.59808 + 1.50000i) q^{93} +(-3.00000 + 5.19615i) q^{94} +(0.500000 + 0.866025i) q^{96} -7.00000i q^{97} +(-4.33013 + 5.50000i) q^{98} -5.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 4 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 - 4 * q^6 + 2 * q^9	$ 4 q + 2 q^{4} - 4 q^{6} + 2 q^{9} - 10 q^{11} - 8 q^{14} - 2 q^{16} + 16 q^{19} + 10 q^{21} - 2 q^{24} + 20 q^{29} - 6 q^{31} + 16 q^{34} + 4 q^{36} + 10 q^{44} + 8 q^{46} + 26 q^{49} - 8 q^{51} - 2 q^{54} + 2 q^{56} - 22 q^{59} + 12 q^{61} - 4 q^{64} + 10 q^{66} - 16 q^{69} + 8 q^{71} - 8 q^{74} + 32 q^{76} + 6 q^{79} - 2 q^{81} + 8 q^{84} - 4 q^{86} - 12 q^{89} - 12 q^{94} + 2 q^{96} - 20 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 - 4 * q^6 + 2 * q^9 - 10 * q^11 - 8 * q^14 - 2 * q^16 + 16 * q^19 + 10 * q^21 - 2 * q^24 + 20 * q^29 - 6 * q^31 + 16 * q^34 + 4 * q^36 + 10 * q^44 + 8 * q^46 + 26 * q^49 - 8 * q^51 - 2 * q^54 + 2 * q^56 - 22 * q^59 + 12 * q^61 - 4 * q^64 + 10 * q^66 - 16 * q^69 + 8 * q^71 - 8 * q^74 + 32 * q^76 + 6 * q^79 - 2 * q^81 + 8 * q^84 - 4 * q^86 - 12 * q^89 - 12 * q^94 + 2 * q^96 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

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
$6$	−1.00000			−0.408248
$7$	2.59808	−	0.500000i	0.981981	−	0.188982i
$7$	2.59808	−	0.500000i	0.981981	−	0.188982i
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−2.50000	+	4.33013i	−0.753778	+	1.30558i	0.192201	+	0.981356i	$0.438437\pi$
$11$	−2.50000	+	4.33013i	−0.753778	+	1.30558i	−0.945979	+	0.324227i	$0.894896\pi$
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$	−2.00000	+	1.73205i	−0.534522	+	0.462910i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.46410	−	2.00000i	−0.840168	−	0.485071i	0.0171533	−	0.999853i	$-0.494540\pi$
$17$	−3.46410	−	2.00000i	−0.840168	−	0.485071i	−0.857321	+	0.514782i	$0.827873\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	4.00000	+	6.92820i	0.917663	+	1.58944i	0.802955	+	0.596040i	$0.203260\pi$
$19$	4.00000	+	6.92820i	0.917663	+	1.58944i	0.114708	+	0.993399i	$0.463407\pi$
$20$		0			0
$21$	2.50000	+	0.866025i	0.545545	+	0.188982i
$22$		−	5.00000i		−	1.06600i
$23$	−3.46410	+	2.00000i	−0.722315	+	0.417029i	−0.815604	−	0.578610i	$-0.803595\pi$
$23$	−3.46410	+	2.00000i	−0.722315	+	0.417029i	0.0932891	+	0.995639i	$0.470262\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$		0			0
$26$		0			0
$27$			1.00000i			0.192450i
$28$	0.866025	−	2.50000i	0.163663	−	0.472456i
$29$	5.00000			0.928477			0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000			0.928477			0.464238	+	0.885710i	$0.346328\pi$
$30$		0			0
$31$	−1.50000	+	2.59808i	−0.269408	+	0.466628i	−0.968709	−	0.248199i	$-0.920161\pi$
$31$	−1.50000	+	2.59808i	−0.269408	+	0.466628i	0.699301	+	0.714827i	$0.253495\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−4.33013	+	2.50000i	−0.753778	+	0.435194i
$34$	4.00000			0.685994
$35$		0			0
$36$	1.00000			0.166667
$37$	3.46410	−	2.00000i	0.569495	−	0.328798i	−0.187453	−	0.982274i	$-0.560023\pi$
$37$	3.46410	−	2.00000i	0.569495	−	0.328798i	0.756948	+	0.653476i	$0.226690\pi$
$38$	−6.92820	−	4.00000i	−1.12390	−	0.648886i
$39$		0			0
$40$		0			0
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$	−2.59808	+	0.500000i	−0.400892	+	0.0771517i
$43$			2.00000i			0.304997i	0.988304	+	0.152499i	$0.0487319\pi$
$43$			2.00000i			0.304997i	−0.988304	+	0.152499i	$0.951268\pi$
$44$	2.50000	+	4.33013i	0.376889	+	0.652791i
$45$		0			0
$46$	2.00000	−	3.46410i	0.294884	−	0.510754i
$47$	5.19615	−	3.00000i	0.757937	−	0.437595i	−0.0706177	−	0.997503i	$-0.522497\pi$
$47$	5.19615	−	3.00000i	0.757937	−	0.437595i	0.828554	+	0.559908i	$0.189164\pi$
$48$		−	1.00000i		−	0.144338i
$49$	6.50000	−	2.59808i	0.928571	−	0.371154i
$50$		0			0
$51$	−2.00000	−	3.46410i	−0.280056	−	0.485071i
$52$		0			0
$53$	7.79423	+	4.50000i	1.07062	+	0.618123i	0.928351	−	0.371706i	$-0.121227\pi$
$53$	7.79423	+	4.50000i	1.07062	+	0.618123i	0.142269	+	0.989828i	$0.454560\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$		0			0
$56$	0.500000	+	2.59808i	0.0668153	+	0.347183i
$57$			8.00000i			1.05963i
$58$	−4.33013	+	2.50000i	−0.568574	+	0.328266i
$59$	−5.50000	+	9.52628i	−0.716039	+	1.24022i	0.246518	+	0.969138i	$0.420713\pi$
$59$	−5.50000	+	9.52628i	−0.716039	+	1.24022i	−0.962557	+	0.271078i	$0.912620\pi$
$60$		0			0
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	0.991645	−	0.128994i	$-0.0411748\pi$
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	−0.607535	+	0.794293i	$0.707841\pi$
$62$		−	3.00000i		−	0.381000i
$63$	1.73205	+	2.00000i	0.218218	+	0.251976i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	2.50000	−	4.33013i	0.307729	−	0.533002i
$67$	−1.73205	−	1.00000i	−0.211604	−	0.122169i	0.390453	−	0.920623i	$-0.372318\pi$
$67$	−1.73205	−	1.00000i	−0.211604	−	0.122169i	−0.602056	+	0.798454i	$0.705652\pi$
$68$	−3.46410	+	2.00000i	−0.420084	+	0.242536i
$69$	−4.00000			−0.481543
$70$		0			0
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	−8.66025	−	5.00000i	−1.01361	−	0.585206i	−0.101361	−	0.994850i	$-0.532320\pi$
$73$	−8.66025	−	5.00000i	−1.01361	−	0.585206i	−0.912245	+	0.409644i	$0.865653\pi$
$74$	−2.00000	+	3.46410i	−0.232495	+	0.402694i
$75$		0			0
$76$	8.00000			0.917663
$77$	−4.33013	+	12.5000i	−0.493464	+	1.42451i
$78$		0			0
$79$	1.50000	+	2.59808i	0.168763	+	0.292306i	0.937985	−	0.346675i	$-0.112689\pi$
$79$	1.50000	+	2.59808i	0.168763	+	0.292306i	−0.769222	+	0.638982i	$0.779356\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	7.00000i		−	0.768350i	−0.923260	−	0.384175i	$-0.874486\pi$
$83$		−	7.00000i		−	0.768350i	0.923260	−	0.384175i	$-0.125514\pi$
$84$	2.00000	−	1.73205i	0.218218	−	0.188982i
$85$		0			0
$86$	−1.00000	−	1.73205i	−0.107833	−	0.186772i
$87$	4.33013	+	2.50000i	0.464238	+	0.268028i
$88$	−4.33013	−	2.50000i	−0.461593	−	0.266501i
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$		0			0
$91$		0			0
$92$			4.00000i			0.417029i
$93$	−2.59808	+	1.50000i	−0.269408	+	0.155543i
$94$	−3.00000	+	5.19615i	−0.309426	+	0.535942i
$95$		0			0
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$		−	7.00000i		−	0.710742i	−0.934725	−	0.355371i	$-0.884354\pi$
$97$		−	7.00000i		−	0.710742i	0.934725	−	0.355371i	$-0.115646\pi$
$98$	−4.33013	+	5.50000i	−0.437409	+	0.555584i
$99$	−5.00000			−0.502519
$100$		0			0
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	−0.999996	−	0.00286291i	$-0.999089\pi$
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	0.502477	+	0.864590i	$0.332422\pi$
$102$	3.46410	+	2.00000i	0.342997	+	0.198030i
$103$	6.92820	−	4.00000i	0.682656	−	0.394132i	−0.118199	−	0.992990i	$-0.537712\pi$
$103$	6.92820	−	4.00000i	0.682656	−	0.394132i	0.800855	+	0.598858i	$0.204379\pi$
$104$		0			0
$105$		0			0
$106$	−9.00000			−0.874157
$107$	−2.59808	+	1.50000i	−0.251166	+	0.145010i	−0.620298	−	0.784366i	$-0.712988\pi$
$107$	−2.59808	+	1.50000i	−0.251166	+	0.145010i	0.369132	+	0.929377i	$0.379655\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	−0.909935	−	0.414751i	$-0.863869\pi$
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	0.814152	+	0.580651i	$0.197202\pi$
$110$		0			0
$111$	4.00000			0.379663
$112$	−1.73205	−	2.00000i	−0.163663	−	0.188982i
$113$			16.0000i			1.50515i	0.658505	+	0.752577i	$0.271189\pi$
$113$			16.0000i			1.50515i	−0.658505	+	0.752577i	$0.728811\pi$
$114$	−4.00000	−	6.92820i	−0.374634	−	0.648886i
$115$		0			0
$116$	2.50000	−	4.33013i	0.232119	−	0.402042i
$117$		0			0
$118$		−	11.0000i		−	1.01263i
$119$	−10.0000	−	3.46410i	−0.916698	−	0.317554i
$120$		0			0
$121$	−7.00000	−	12.1244i	−0.636364	−	1.10221i
$122$	−5.19615	−	3.00000i	−0.470438	−	0.271607i
$123$		0			0
$124$	1.50000	+	2.59808i	0.134704	+	0.233314i
$125$		0			0
$126$	−2.50000	−	0.866025i	−0.222718	−	0.0771517i
$127$		−	9.00000i		−	0.798621i	−0.916816	−	0.399310i	$-0.869250\pi$
$127$		−	9.00000i		−	0.798621i	0.916816	−	0.399310i	$-0.130750\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−1.00000	+	1.73205i	−0.0880451	+	0.152499i
$130$		0			0
$131$	−0.500000	−	0.866025i	−0.0436852	−	0.0756650i	0.843356	−	0.537355i	$-0.180577\pi$
$131$	−0.500000	−	0.866025i	−0.0436852	−	0.0756650i	−0.887041	+	0.461690i	$0.847243\pi$
$132$			5.00000i			0.435194i
$133$	13.8564	+	16.0000i	1.20150	+	1.38738i
$134$	2.00000			0.172774
$135$		0			0
$136$	2.00000	−	3.46410i	0.171499	−	0.297044i
$137$	−1.73205	−	1.00000i	−0.147979	−	0.0854358i	0.424182	−	0.905577i	$-0.360562\pi$
$137$	−1.73205	−	1.00000i	−0.147979	−	0.0854358i	−0.572161	+	0.820141i	$0.693895\pi$
$138$	3.46410	−	2.00000i	0.294884	−	0.170251i
$139$	14.0000			1.18746			0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000			1.18746			0.593732	+	0.804663i	$0.297654\pi$
$140$		0			0
$141$	6.00000			0.505291
$142$	−1.73205	+	1.00000i	−0.145350	+	0.0839181i
$143$		0			0
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$		0			0
$146$	10.0000			0.827606
$147$	6.92820	+	1.00000i	0.571429	+	0.0824786i
$148$		−	4.00000i		−	0.328798i
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	−0.953703	−	0.300750i	$-0.902763\pi$
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	0.216394	−	0.976306i	$-0.430570\pi$
$150$		0			0
$151$	−9.50000	+	16.4545i	−0.773099	+	1.33905i	0.162758	+	0.986666i	$0.447961\pi$
$151$	−9.50000	+	16.4545i	−0.773099	+	1.33905i	−0.935857	+	0.352381i	$0.885372\pi$
$152$	−6.92820	+	4.00000i	−0.561951	+	0.324443i
$153$		−	4.00000i		−	0.323381i
$154$	−2.50000	−	12.9904i	−0.201456	−	1.04679i
$155$		0			0
$156$		0			0
$157$	−3.46410	−	2.00000i	−0.276465	−	0.159617i	0.355357	−	0.934731i	$-0.384359\pi$
$157$	−3.46410	−	2.00000i	−0.276465	−	0.159617i	−0.631822	+	0.775113i	$0.717693\pi$
$158$	−2.59808	−	1.50000i	−0.206692	−	0.119334i
$159$	4.50000	+	7.79423i	0.356873	+	0.618123i
$160$		0			0
$161$	−8.00000	+	6.92820i	−0.630488	+	0.546019i
$162$		−	1.00000i		−	0.0785674i
$163$	−3.46410	+	2.00000i	−0.271329	+	0.156652i	−0.629492	−	0.777007i	$-0.716737\pi$
$163$	−3.46410	+	2.00000i	−0.271329	+	0.156652i	0.358162	+	0.933659i	$0.383403\pi$
$164$		0			0
$165$		0			0
$166$	3.50000	+	6.06218i	0.271653	+	0.470516i
$167$			14.0000i			1.08335i	0.840587	+	0.541676i	$0.182210\pi$
$167$			14.0000i			1.08335i	−0.840587	+	0.541676i	$0.817790\pi$
$168$	−0.866025	+	2.50000i	−0.0668153	+	0.192879i
$169$	13.0000			1.00000
$170$		0			0
$171$	−4.00000	+	6.92820i	−0.305888	+	0.529813i
$172$	1.73205	+	1.00000i	0.132068	+	0.0762493i
$173$	19.0526	−	11.0000i	1.44854	−	0.836315i	0.450145	−	0.892956i	$-0.351372\pi$
$173$	19.0526	−	11.0000i	1.44854	−	0.836315i	0.998395	+	0.0566411i	$0.0180391\pi$
$174$	−5.00000			−0.379049
$175$		0			0
$176$	5.00000			0.376889
$177$	−9.52628	+	5.50000i	−0.716039	+	0.413405i
$178$	5.19615	+	3.00000i	0.389468	+	0.224860i
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$		0			0
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$			6.00000i			0.443533i
$184$	−2.00000	−	3.46410i	−0.147442	−	0.255377i
$185$		0			0
$186$	1.50000	−	2.59808i	0.109985	−	0.190500i
$187$	17.3205	−	10.0000i	1.26660	−	0.731272i
$188$		−	6.00000i		−	0.437595i
$189$	0.500000	+	2.59808i	0.0363696	+	0.188982i
$190$		0			0
$191$	−12.0000	−	20.7846i	−0.868290	−	1.50392i	−0.863743	−	0.503932i	$-0.831886\pi$
$191$	−12.0000	−	20.7846i	−0.868290	−	1.50392i	−0.00454614	−	0.999990i	$-0.501447\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	−4.33013	−	2.50000i	−0.311689	−	0.179954i	0.335993	−	0.941865i	$-0.390928\pi$
$193$	−4.33013	−	2.50000i	−0.311689	−	0.179954i	−0.647682	+	0.761911i	$0.724262\pi$
$194$	3.50000	+	6.06218i	0.251285	+	0.435239i
$195$		0			0
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$		−	2.00000i		−	0.142494i	−0.997459	−	0.0712470i	$-0.977302\pi$
$197$		−	2.00000i		−	0.142494i	0.997459	−	0.0712470i	$-0.0226979\pi$
$198$	4.33013	−	2.50000i	0.307729	−	0.177667i
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	−0.928166	−	0.372168i	$-0.878615\pi$
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	0.786389	+	0.617731i	$0.211948\pi$
$200$		0			0
$201$	−1.00000	−	1.73205i	−0.0705346	−	0.122169i
$202$		−	10.0000i		−	0.703598i
$203$	12.9904	−	2.50000i	0.911746	−	0.175466i
$204$	−4.00000			−0.280056
$205$		0			0
$206$	−4.00000	+	6.92820i	−0.278693	+	0.482711i
$207$	−3.46410	−	2.00000i	−0.240772	−	0.139010i
$208$		0			0
$209$	−40.0000			−2.76686
$210$		0			0
$211$	2.00000			0.137686			0.0688428	−	0.997628i	$-0.478069\pi$
$211$	2.00000			0.137686			0.0688428	+	0.997628i	$0.478069\pi$
$212$	7.79423	−	4.50000i	0.535310	−	0.309061i
$213$	1.73205	+	1.00000i	0.118678	+	0.0685189i
$214$	1.50000	−	2.59808i	0.102538	−	0.177601i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$	−2.59808	+	7.50000i	−0.176369	+	0.509133i
$218$		−	2.00000i		−	0.135457i
$219$	−5.00000	−	8.66025i	−0.337869	−	0.585206i
$220$		0			0
$221$		0			0
$222$	−3.46410	+	2.00000i	−0.232495	+	0.134231i
$223$		−	7.00000i		−	0.468755i	−0.972146	−	0.234377i	$-0.924695\pi$
$223$		−	7.00000i		−	0.468755i	0.972146	−	0.234377i	$-0.0753051\pi$
$224$	2.50000	+	0.866025i	0.167038	+	0.0578638i
$225$		0			0
$226$	−8.00000	−	13.8564i	−0.532152	−	0.921714i
$227$	2.59808	+	1.50000i	0.172440	+	0.0995585i	0.583736	−	0.811943i	$-0.301590\pi$
$227$	2.59808	+	1.50000i	0.172440	+	0.0995585i	−0.411296	+	0.911502i	$0.634924\pi$
$228$	6.92820	+	4.00000i	0.458831	+	0.264906i
$229$	−10.0000	−	17.3205i	−0.660819	−	1.14457i	−0.980401	−	0.197013i	$-0.936876\pi$
$229$	−10.0000	−	17.3205i	−0.660819	−	1.14457i	0.319582	−	0.947559i	$-0.396457\pi$
$230$		0			0
$231$	−10.0000	+	8.66025i	−0.657952	+	0.569803i
$232$			5.00000i			0.328266i
$233$	−3.46410	+	2.00000i	−0.226941	+	0.131024i	−0.609160	−	0.793047i	$-0.708493\pi$
$233$	−3.46410	+	2.00000i	−0.226941	+	0.131024i	0.382219	+	0.924072i	$0.375160\pi$
$234$		0			0
$235$		0			0
$236$	5.50000	+	9.52628i	0.358020	+	0.620108i
$237$			3.00000i			0.194871i
$238$	10.3923	−	2.00000i	0.673633	−	0.129641i
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$		0			0
$241$	12.5000	−	21.6506i	0.805196	−	1.39464i	−0.110963	−	0.993825i	$-0.535394\pi$
$241$	12.5000	−	21.6506i	0.805196	−	1.39464i	0.916159	−	0.400815i	$-0.131273\pi$
$242$	12.1244	+	7.00000i	0.779383	+	0.449977i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	6.00000			0.384111
$245$		0			0
$246$		0			0
$247$		0			0
$248$	−2.59808	−	1.50000i	−0.164978	−	0.0952501i
$249$	3.50000	−	6.06218i	0.221803	−	0.384175i
$250$		0			0
$251$	21.0000			1.32551			0.662754	−	0.748837i	$-0.269387\pi$
$251$	21.0000			1.32551			0.662754	+	0.748837i	$0.269387\pi$
$252$	2.59808	−	0.500000i	0.163663	−	0.0314970i
$253$		−	20.0000i		−	1.25739i
$254$	4.50000	+	7.79423i	0.282355	+	0.489053i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.19615	−	3.00000i	0.324127	−	0.187135i	−0.329104	−	0.944294i	$-0.606747\pi$
$257$	5.19615	−	3.00000i	0.324127	−	0.187135i	0.653231	+	0.757159i	$0.273413\pi$
$258$		−	2.00000i		−	0.124515i
$259$	8.00000	−	6.92820i	0.497096	−	0.430498i
$260$		0			0
$261$	2.50000	+	4.33013i	0.154746	+	0.268028i
$262$	0.866025	+	0.500000i	0.0535032	+	0.0308901i
$263$	25.9808	+	15.0000i	1.60204	+	0.924940i	0.991078	+	0.133281i	$0.0425514\pi$
$263$	25.9808	+	15.0000i	1.60204	+	0.924940i	0.610964	+	0.791658i	$0.290782\pi$
$264$	−2.50000	−	4.33013i	−0.153864	−	0.266501i
$265$		0			0
$266$	−20.0000	−	6.92820i	−1.22628	−	0.424795i
$267$		−	6.00000i		−	0.367194i
$268$	−1.73205	+	1.00000i	−0.105802	+	0.0610847i
$269$	15.5000	−	26.8468i	0.945052	−	1.63688i	0.189404	−	0.981899i	$-0.439344\pi$
$269$	15.5000	−	26.8468i	0.945052	−	1.63688i	0.755648	−	0.654978i	$-0.227322\pi$
$270$		0			0
$271$	−7.50000	−	12.9904i	−0.455593	−	0.789109i	0.543130	−	0.839649i	$-0.317239\pi$
$271$	−7.50000	−	12.9904i	−0.455593	−	0.789109i	−0.998722	+	0.0505395i	$0.983906\pi$
$272$			4.00000i			0.242536i
$273$		0			0
$274$	2.00000			0.120824
$275$		0			0
$276$	−2.00000	+	3.46410i	−0.120386	+	0.208514i
$277$	−13.8564	−	8.00000i	−0.832551	−	0.480673i	0.0221745	−	0.999754i	$-0.492941\pi$
$277$	−13.8564	−	8.00000i	−0.832551	−	0.480673i	−0.854725	+	0.519081i	$0.826274\pi$
$278$	−12.1244	+	7.00000i	−0.727171	+	0.419832i
$279$	−3.00000			−0.179605
$280$		0			0
$281$	2.00000			0.119310			0.0596550	−	0.998219i	$-0.481000\pi$
$281$	2.00000			0.119310			0.0596550	+	0.998219i	$0.481000\pi$
$282$	−5.19615	+	3.00000i	−0.309426	+	0.178647i
$283$	−8.66025	−	5.00000i	−0.514799	−	0.297219i	0.220005	−	0.975499i	$-0.429393\pi$
$283$	−8.66025	−	5.00000i	−0.514799	−	0.297219i	−0.734804	+	0.678280i	$0.762726\pi$
$284$	1.00000	−	1.73205i	0.0593391	−	0.102778i
$285$		0			0
$286$		0			0
$287$		0			0
$288$			1.00000i			0.0589256i
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$		0			0
$291$	3.50000	−	6.06218i	0.205174	−	0.355371i
$292$	−8.66025	+	5.00000i	−0.506803	+	0.292603i
$293$		−	21.0000i		−	1.22683i	−0.789760	−	0.613417i	$-0.789795\pi$
$293$		−	21.0000i		−	1.22683i	0.789760	−	0.613417i	$-0.210205\pi$
$294$	−6.50000	+	2.59808i	−0.379088	+	0.151523i
$295$		0			0
$296$	2.00000	+	3.46410i	0.116248	+	0.201347i
$297$	−4.33013	−	2.50000i	−0.251259	−	0.145065i
$298$	15.5885	+	9.00000i	0.903015	+	0.521356i
$299$		0			0
$300$		0			0
$301$	1.00000	+	5.19615i	0.0576390	+	0.299501i
$302$		−	19.0000i		−	1.09333i
$303$	−8.66025	+	5.00000i	−0.497519	+	0.287242i
$304$	4.00000	−	6.92820i	0.229416	−	0.397360i
$305$		0			0
$306$	2.00000	+	3.46410i	0.114332	+	0.198030i
$307$		−	28.0000i		−	1.59804i	−0.601302	−	0.799022i	$-0.705351\pi$
$307$		−	28.0000i		−	1.59804i	0.601302	−	0.799022i	$-0.294649\pi$
$308$	8.66025	+	10.0000i	0.493464	+	0.569803i
$309$	8.00000			0.455104
$310$		0			0
$311$	16.0000	−	27.7128i	0.907277	−	1.57145i	0.0894452	−	0.995992i	$-0.471491\pi$
$311$	16.0000	−	27.7128i	0.907277	−	1.57145i	0.817832	−	0.575458i	$-0.195176\pi$
$312$		0			0
$313$	0.866025	−	0.500000i	0.0489506	−	0.0282617i	−0.475325	−	0.879810i	$-0.657669\pi$
$313$	0.866025	−	0.500000i	0.0489506	−	0.0282617i	0.524276	+	0.851549i	$0.324336\pi$
$314$	4.00000			0.225733
$315$		0			0
$316$	3.00000			0.168763
$317$	−2.59808	+	1.50000i	−0.145922	+	0.0842484i	−0.571184	−	0.820822i	$-0.693516\pi$
$317$	−2.59808	+	1.50000i	−0.145922	+	0.0842484i	0.425261	+	0.905071i	$0.360182\pi$
$318$	−7.79423	−	4.50000i	−0.437079	−	0.252347i
$319$	−12.5000	+	21.6506i	−0.699866	+	1.21220i
$320$		0			0
$321$	−3.00000			−0.167444
$322$	3.46410	−	10.0000i	0.193047	−	0.557278i
$323$		−	32.0000i		−	1.78053i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$		0			0
$326$	2.00000	−	3.46410i	0.110770	−	0.191859i
$327$	−1.73205	+	1.00000i	−0.0957826	+	0.0553001i
$328$		0			0
$329$	12.0000	−	10.3923i	0.661581	−	0.572946i
$330$		0			0
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	0.915742	−	0.401768i	$-0.131604\pi$
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	−0.805812	+	0.592172i	$0.798271\pi$
$332$	−6.06218	−	3.50000i	−0.332705	−	0.192087i
$333$	3.46410	+	2.00000i	0.189832	+	0.109599i
$334$	−7.00000	−	12.1244i	−0.383023	−	0.663415i
$335$		0			0
$336$	−0.500000	−	2.59808i	−0.0272772	−	0.141737i
$337$		−	9.00000i		−	0.490261i	−0.969490	−	0.245131i	$-0.921169\pi$
$337$		−	9.00000i		−	0.490261i	0.969490	−	0.245131i	$-0.0788309\pi$
$338$	−11.2583	+	6.50000i	−0.612372	+	0.353553i
$339$	−8.00000	+	13.8564i	−0.434500	+	0.752577i
$340$		0			0
$341$	−7.50000	−	12.9904i	−0.406148	−	0.703469i
$342$		−	8.00000i		−	0.432590i
$343$	15.5885	−	10.0000i	0.841698	−	0.539949i
$344$	−2.00000			−0.107833
$345$		0			0
$346$	−11.0000	+	19.0526i	−0.591364	+	1.02427i
$347$	10.3923	+	6.00000i	0.557888	+	0.322097i	0.752297	−	0.658824i	$-0.228946\pi$
$347$	10.3923	+	6.00000i	0.557888	+	0.322097i	−0.194409	+	0.980921i	$0.562279\pi$
$348$	4.33013	−	2.50000i	0.232119	−	0.134014i
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$		0			0
$351$		0			0
$352$	−4.33013	+	2.50000i	−0.230797	+	0.133250i
$353$	−20.7846	−	12.0000i	−1.10625	−	0.638696i	−0.168397	−	0.985719i	$-0.553859\pi$
$353$	−20.7846	−	12.0000i	−1.10625	−	0.638696i	−0.937856	+	0.347024i	$0.887192\pi$
$354$	5.50000	−	9.52628i	0.292322	−	0.506316i
$355$		0			0
$356$	−6.00000			−0.317999
$357$	−6.92820	−	8.00000i	−0.366679	−	0.423405i
$358$			12.0000i			0.634220i
$359$	5.00000	+	8.66025i	0.263890	+	0.457071i	0.967272	−	0.253741i	$-0.0816611\pi$
$359$	5.00000	+	8.66025i	0.263890	+	0.457071i	−0.703382	+	0.710812i	$0.748328\pi$
$360$		0			0
$361$	−22.5000	+	38.9711i	−1.18421	+	2.05111i
$362$		0			0
$363$		−	14.0000i		−	0.734809i
$364$		0			0
$365$		0			0
$366$	−3.00000	−	5.19615i	−0.156813	−	0.271607i
$367$	14.7224	+	8.50000i	0.768505	+	0.443696i	0.832341	−	0.554264i	$-0.187000\pi$
$367$	14.7224	+	8.50000i	0.768505	+	0.443696i	−0.0638362	+	0.997960i	$0.520334\pi$
$368$	3.46410	+	2.00000i	0.180579	+	0.104257i
$369$		0			0
$370$		0			0
$371$	22.5000	+	7.79423i	1.16814	+	0.404656i
$372$			3.00000i			0.155543i
$373$	−27.7128	+	16.0000i	−1.43492	+	0.828449i	−0.997490	−	0.0708063i	$-0.977443\pi$
$373$	−27.7128	+	16.0000i	−1.43492	+	0.828449i	−0.437425	+	0.899255i	$0.644109\pi$
$374$	−10.0000	+	17.3205i	−0.517088	+	0.895622i
$375$		0			0
$376$	3.00000	+	5.19615i	0.154713	+	0.267971i
$377$		0			0
$378$	−1.73205	−	2.00000i	−0.0890871	−	0.102869i
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$		0			0
$381$	4.50000	−	7.79423i	0.230542	−	0.399310i
$382$	20.7846	+	12.0000i	1.06343	+	0.613973i
$383$	−29.4449	+	17.0000i	−1.50456	+	0.868659i	−0.504576	+	0.863367i	$0.668351\pi$
$383$	−29.4449	+	17.0000i	−1.50456	+	0.868659i	−0.999986	+	0.00529229i	$0.998315\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	5.00000			0.254493
$387$	−1.73205	+	1.00000i	−0.0880451	+	0.0508329i
$388$	−6.06218	−	3.50000i	−0.307760	−	0.177686i
$389$	−1.00000	+	1.73205i	−0.0507020	+	0.0878185i	−0.890263	−	0.455448i	$-0.849479\pi$
$389$	−1.00000	+	1.73205i	−0.0507020	+	0.0878185i	0.839561	+	0.543266i	$0.182813\pi$
$390$		0			0
$391$	16.0000			0.809155
$392$	2.59808	+	6.50000i	0.131223	+	0.328300i
$393$		−	1.00000i		−	0.0504433i
$394$	1.00000	+	1.73205i	0.0503793	+	0.0872595i
$395$		0			0
$396$	−2.50000	+	4.33013i	−0.125630	+	0.217597i
$397$	−31.1769	+	18.0000i	−1.56472	+	0.903394i	−0.567957	+	0.823058i	$0.692266\pi$
$397$	−31.1769	+	18.0000i	−1.56472	+	0.903394i	−0.996768	+	0.0803356i	$0.974401\pi$
$398$		−	4.00000i		−	0.200502i
$399$	4.00000	+	20.7846i	0.200250	+	1.04053i
$400$		0			0
$401$	−12.0000	−	20.7846i	−0.599251	−	1.03793i	−0.992932	−	0.118686i	$-0.962132\pi$
$401$	−12.0000	−	20.7846i	−0.599251	−	1.03793i	0.393680	−	0.919247i	$-0.371202\pi$
$402$	1.73205	+	1.00000i	0.0863868	+	0.0498755i
$403$		0			0
$404$	5.00000	+	8.66025i	0.248759	+	0.430864i
$405$		0			0
$406$	−10.0000	+	8.66025i	−0.496292	+	0.429801i
$407$			20.0000i			0.991363i
$408$	3.46410	−	2.00000i	0.171499	−	0.0990148i
$409$	−12.5000	+	21.6506i	−0.618085	+	1.07056i	0.371750	+	0.928333i	$0.378758\pi$
$409$	−12.5000	+	21.6506i	−0.618085	+	1.07056i	−0.989835	+	0.142222i	$0.954575\pi$
$410$		0			0
$411$	−1.00000	−	1.73205i	−0.0493264	−	0.0854358i
$412$		−	8.00000i		−	0.394132i
$413$	−9.52628	+	27.5000i	−0.468758	+	1.35319i
$414$	4.00000			0.196589
$415$		0			0
$416$		0			0
$417$	12.1244	+	7.00000i	0.593732	+	0.342791i
$418$	34.6410	−	20.0000i	1.69435	−	0.978232i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	30.0000			1.46211			0.731055	−	0.682318i	$-0.239028\pi$
$421$	30.0000			1.46211			0.731055	+	0.682318i	$0.239028\pi$
$422$	−1.73205	+	1.00000i	−0.0843149	+	0.0486792i
$423$	5.19615	+	3.00000i	0.252646	+	0.145865i
$424$	−4.50000	+	7.79423i	−0.218539	+	0.378521i
$425$		0			0
$426$	−2.00000			−0.0969003
$427$	10.3923	+	12.0000i	0.502919	+	0.580721i
$428$			3.00000i			0.145010i
$429$		0			0
$430$		0			0
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	−0.973574	−	0.228373i	$-0.926659\pi$
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	0.684564	+	0.728953i	$0.259993\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$			14.0000i			0.672797i	0.941720	+	0.336399i	$0.109209\pi$
$433$			14.0000i			0.672797i	−0.941720	+	0.336399i	$0.890791\pi$
$434$	−1.50000	−	7.79423i	−0.0720023	−	0.374135i
$435$		0			0
$436$	1.00000	+	1.73205i	0.0478913	+	0.0829502i
$437$	−27.7128	−	16.0000i	−1.32568	−	0.765384i
$438$	8.66025	+	5.00000i	0.413803	+	0.238909i
$439$	7.50000	+	12.9904i	0.357955	+	0.619997i	0.987619	−	0.156871i	$-0.0501406\pi$
$439$	7.50000	+	12.9904i	0.357955	+	0.619997i	−0.629664	+	0.776868i	$0.716807\pi$
$440$		0			0
$441$	5.50000	+	4.33013i	0.261905	+	0.206197i
$442$		0			0
$443$	14.7224	−	8.50000i	0.699484	−	0.403847i	−0.107671	−	0.994187i	$-0.534339\pi$
$443$	14.7224	−	8.50000i	0.699484	−	0.403847i	0.807155	+	0.590339i	$0.201006\pi$
$444$	2.00000	−	3.46410i	0.0949158	−	0.164399i
$445$		0			0
$446$	3.50000	+	6.06218i	0.165730	+	0.287052i
$447$		−	18.0000i		−	0.851371i
$448$	−2.59808	+	0.500000i	−0.122748	+	0.0236228i
$449$	−16.0000			−0.755087			−0.377543	−	0.925992i	$-0.623231\pi$
$449$	−16.0000			−0.755087			−0.377543	+	0.925992i	$0.623231\pi$
$450$		0			0
$451$		0			0
$452$	13.8564	+	8.00000i	0.651751	+	0.376288i
$453$	−16.4545	+	9.50000i	−0.773099	+	0.446349i
$454$	−3.00000			−0.140797
$455$		0			0
$456$	−8.00000			−0.374634
$457$	−26.8468	+	15.5000i	−1.25584	+	0.725059i	−0.972263	−	0.233890i	$-0.924854\pi$
$457$	−26.8468	+	15.5000i	−1.25584	+	0.725059i	−0.283577	+	0.958950i	$0.591521\pi$
$458$	17.3205	+	10.0000i	0.809334	+	0.467269i
$459$	2.00000	−	3.46410i	0.0933520	−	0.161690i
$460$		0			0
$461$	−14.0000			−0.652045			−0.326023	−	0.945362i	$-0.605709\pi$
$461$	−14.0000			−0.652045			−0.326023	+	0.945362i	$0.605709\pi$
$462$	4.33013	−	12.5000i	0.201456	−	0.581553i
$463$			16.0000i			0.743583i	0.928316	+	0.371792i	$0.121256\pi$
$463$			16.0000i			0.743583i	−0.928316	+	0.371792i	$0.878744\pi$
$464$	−2.50000	−	4.33013i	−0.116060	−	0.201021i
$465$		0			0
$466$	2.00000	−	3.46410i	0.0926482	−	0.160471i
$467$	17.3205	−	10.0000i	0.801498	−	0.462745i	−0.0424970	−	0.999097i	$-0.513531\pi$
$467$	17.3205	−	10.0000i	0.801498	−	0.462745i	0.843995	+	0.536352i	$0.180198\pi$
$468$		0			0
$469$	−5.00000	−	1.73205i	−0.230879	−	0.0799787i
$470$		0			0
$471$	−2.00000	−	3.46410i	−0.0921551	−	0.159617i
$472$	−9.52628	−	5.50000i	−0.438483	−	0.253158i
$473$	−8.66025	−	5.00000i	−0.398199	−	0.229900i
$474$	−1.50000	−	2.59808i	−0.0688973	−	0.119334i
$475$		0			0
$476$	−8.00000	+	6.92820i	−0.366679	+	0.317554i
$477$			9.00000i			0.412082i
$478$	−10.3923	+	6.00000i	−0.475333	+	0.274434i
$479$	19.0000	−	32.9090i	0.868132	−	1.50365i	0.00422900	−	0.999991i	$-0.498654\pi$
$479$	19.0000	−	32.9090i	0.868132	−	1.50365i	0.863903	−	0.503658i	$-0.168013\pi$
$480$		0			0
$481$		0			0
$482$			25.0000i			1.13872i
$483$	−10.3923	+	2.00000i	−0.472866	+	0.0910032i
$484$	−14.0000			−0.636364
$485$		0			0
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	4.33013	+	2.50000i	0.196217	+	0.113286i	0.594890	−	0.803807i	$-0.297196\pi$
$487$	4.33013	+	2.50000i	0.196217	+	0.113286i	−0.398673	+	0.917093i	$0.630529\pi$
$488$	−5.19615	+	3.00000i	−0.235219	+	0.135804i
$489$	−4.00000			−0.180886
$490$		0			0
$491$	9.00000			0.406164			0.203082	−	0.979162i	$-0.434904\pi$
$491$	9.00000			0.406164			0.203082	+	0.979162i	$0.434904\pi$
$492$		0			0
$493$	−17.3205	−	10.0000i	−0.780076	−	0.450377i
$494$		0			0
$495$		0			0
$496$	3.00000			0.134704
$497$	5.19615	−	1.00000i	0.233079	−	0.0448561i
$498$			7.00000i			0.313678i
$499$	5.00000	+	8.66025i	0.223831	+	0.387686i	0.955968	−	0.293471i	$-0.0948104\pi$
$499$	5.00000	+	8.66025i	0.223831	+	0.387686i	−0.732137	+	0.681157i	$0.761477\pi$
$500$		0			0
$501$	−7.00000	+	12.1244i	−0.312737	+	0.541676i
$502$	−18.1865	+	10.5000i	−0.811705	+	0.468638i
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$	−2.00000	+	1.73205i	−0.0890871	+	0.0771517i
$505$		0			0
$506$	10.0000	+	17.3205i	0.444554	+	0.769991i
$507$	11.2583	+	6.50000i	0.500000	+	0.288675i
$508$	−7.79423	−	4.50000i	−0.345813	−	0.199655i
$509$	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
$511$	−25.0000	−	8.66025i	−1.10593	−	0.383107i
$512$		−	1.00000i		−	0.0441942i
$513$	−6.92820	+	4.00000i	−0.305888	+	0.176604i
$514$	−3.00000	+	5.19615i	−0.132324	+	0.229192i
$515$		0			0
$516$	1.00000	+	1.73205i	0.0440225	+	0.0762493i
$517$			30.0000i			1.31940i
$518$	−3.46410	+	10.0000i	−0.152204	+	0.439375i
$519$	22.0000			0.965693
$520$		0			0
$521$	9.00000	−	15.5885i	0.394297	−	0.682943i	−0.598714	−	0.800963i	$-0.704321\pi$
$521$	9.00000	−	15.5885i	0.394297	−	0.682943i	0.993011	+	0.118020i	$0.0376547\pi$
$522$	−4.33013	−	2.50000i	−0.189525	−	0.109422i
$523$	6.92820	−	4.00000i	0.302949	−	0.174908i	−0.340818	−	0.940129i	$-0.610704\pi$
$523$	6.92820	−	4.00000i	0.302949	−	0.174908i	0.643767	+	0.765222i	$0.277371\pi$
$524$	−1.00000			−0.0436852
$525$		0			0
$526$	−30.0000			−1.30806
$527$	10.3923	−	6.00000i	0.452696	−	0.261364i
$528$	4.33013	+	2.50000i	0.188445	+	0.108799i
$529$	−3.50000	+	6.06218i	−0.152174	+	0.263573i
$530$		0			0
$531$	−11.0000			−0.477359
$532$	20.7846	−	4.00000i	0.901127	−	0.173422i
$533$		0			0
$534$	3.00000	+	5.19615i	0.129823	+	0.224860i
$535$		0			0
$536$	1.00000	−	1.73205i	0.0431934	−	0.0748132i
$537$	10.3923	−	6.00000i	0.448461	−	0.258919i
$538$			31.0000i			1.33650i
$539$	−5.00000	+	34.6410i	−0.215365	+	1.49209i
$540$		0			0
$541$	9.00000	+	15.5885i	0.386940	+	0.670200i	0.992036	−	0.125952i	$-0.0401986\pi$
$541$	9.00000	+	15.5885i	0.386940	+	0.670200i	−0.605096	+	0.796152i	$0.706865\pi$
$542$	12.9904	+	7.50000i	0.557985	+	0.322153i
$543$		0			0
$544$	−2.00000	−	3.46410i	−0.0857493	−	0.148522i
$545$		0			0
$546$		0			0
$547$			12.0000i			0.513083i	0.966533	+	0.256541i	$0.0825830\pi$
$547$			12.0000i			0.513083i	−0.966533	+	0.256541i	$0.917417\pi$
$548$	−1.73205	+	1.00000i	−0.0739895	+	0.0427179i
$549$	−3.00000	+	5.19615i	−0.128037	+	0.221766i
$550$		0			0
$551$	20.0000	+	34.6410i	0.852029	+	1.47576i
$552$		−	4.00000i		−	0.170251i
$553$	5.19615	+	6.00000i	0.220963	+	0.255146i
$554$	16.0000			0.679775
$555$		0			0
$556$	7.00000	−	12.1244i	0.296866	−	0.514187i
$557$	−19.9186	−	11.5000i	−0.843978	−	0.487271i	0.0146368	−	0.999893i	$-0.495341\pi$
$557$	−19.9186	−	11.5000i	−0.843978	−	0.487271i	−0.858614	+	0.512622i	$0.828674\pi$
$558$	2.59808	−	1.50000i	0.109985	−	0.0635001i
$559$		0			0
$560$		0			0
$561$	20.0000			0.844401
$562$	−1.73205	+	1.00000i	−0.0730622	+	0.0421825i
$563$	−14.7224	−	8.50000i	−0.620477	−	0.358232i	0.156578	−	0.987666i	$-0.449954\pi$
$563$	−14.7224	−	8.50000i	−0.620477	−	0.358232i	−0.777055	+	0.629433i	$0.783287\pi$
$564$	3.00000	−	5.19615i	0.126323	−	0.218797i
$565$		0			0
$566$	10.0000			0.420331
$567$	−0.866025	+	2.50000i	−0.0363696	+	0.104990i
$568$			2.00000i			0.0839181i
$569$	12.0000	+	20.7846i	0.503066	+	0.871336i	0.999994	+	0.00354413i	$0.00112814\pi$
$569$	12.0000	+	20.7846i	0.503066	+	0.871336i	−0.496928	+	0.867792i	$0.665539\pi$
$570$		0			0
$571$	15.0000	−	25.9808i	0.627730	−	1.08726i	−0.360276	−	0.932846i	$-0.617317\pi$
$571$	15.0000	−	25.9808i	0.627730	−	1.08726i	0.988006	−	0.154415i	$-0.0493493\pi$
$572$		0			0
$573$		−	24.0000i		−	1.00261i
$574$		0			0
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	26.8468	+	15.5000i	1.11765	+	0.645273i	0.940799	−	0.338965i	$-0.110077\pi$
$577$	26.8468	+	15.5000i	1.11765	+	0.645273i	0.176847	+	0.984238i	$0.443410\pi$
$578$	0.866025	+	0.500000i	0.0360219	+	0.0207973i
$579$	−2.50000	−	4.33013i	−0.103896	−	0.179954i
$580$		0			0
$581$	−3.50000	−	18.1865i	−0.145204	−	0.754505i
$582$			7.00000i			0.290159i
$583$	−38.9711	+	22.5000i	−1.61402	+	0.931855i
$584$	5.00000	−	8.66025i	0.206901	−	0.358364i
$585$		0			0
$586$	10.5000	+	18.1865i	0.433751	+	0.751279i
$587$		−	35.0000i		−	1.44460i	−0.691577	−	0.722302i	$-0.743084\pi$
$587$		−	35.0000i		−	1.44460i	0.691577	−	0.722302i	$-0.256916\pi$
$588$	4.33013	−	5.50000i	0.178571	−	0.226816i
$589$	−24.0000			−0.988903
$590$		0			0
$591$	1.00000	−	1.73205i	0.0411345	−	0.0712470i
$592$	−3.46410	−	2.00000i	−0.142374	−	0.0821995i
$593$	31.1769	−	18.0000i	1.28028	−	0.739171i	0.303383	−	0.952869i	$-0.401884\pi$
$593$	31.1769	−	18.0000i	1.28028	−	0.739171i	0.976900	+	0.213697i	$0.0685507\pi$
$594$	5.00000			0.205152
$595$		0			0
$596$	−18.0000			−0.737309
$597$	−3.46410	+	2.00000i	−0.141776	+	0.0818546i
$598$		0			0
$599$	−15.0000	+	25.9808i	−0.612883	+	1.06155i	0.377869	+	0.925859i	$0.376657\pi$
$599$	−15.0000	+	25.9808i	−0.612883	+	1.06155i	−0.990752	+	0.135686i	$0.956676\pi$
$600$		0			0
$601$	35.0000			1.42768			0.713840	−	0.700309i	$-0.246954\pi$
$601$	35.0000			1.42768			0.713840	+	0.700309i	$0.246954\pi$
$602$	−3.46410	−	4.00000i	−0.141186	−	0.163028i
$603$		−	2.00000i		−	0.0814463i
$604$	9.50000	+	16.4545i	0.386550	+	0.669523i
$605$		0			0
$606$	5.00000	−	8.66025i	0.203111	−	0.351799i
$607$	23.3827	−	13.5000i	0.949074	−	0.547948i	0.0562808	−	0.998415i	$-0.482076\pi$
$607$	23.3827	−	13.5000i	0.949074	−	0.547948i	0.892793	+	0.450467i	$0.148742\pi$
$608$			8.00000i			0.324443i
$609$	12.5000	+	4.33013i	0.506526	+	0.175466i
$610$		0			0
$611$		0			0
$612$	−3.46410	−	2.00000i	−0.140028	−	0.0808452i
$613$	−10.3923	−	6.00000i	−0.419741	−	0.242338i	0.275225	−	0.961380i	$-0.411248\pi$
$613$	−10.3923	−	6.00000i	−0.419741	−	0.242338i	−0.694967	+	0.719042i	$0.744581\pi$
$614$	14.0000	+	24.2487i	0.564994	+	0.978598i
$615$		0			0
$616$	−12.5000	−	4.33013i	−0.503639	−	0.174466i
$617$		−	2.00000i		−	0.0805170i	−0.999189	−	0.0402585i	$-0.987182\pi$
$617$		−	2.00000i		−	0.0805170i	0.999189	−	0.0402585i	$-0.0128181\pi$
$618$	−6.92820	+	4.00000i	−0.278693	+	0.160904i
$619$	5.00000	−	8.66025i	0.200967	−	0.348085i	−0.747873	−	0.663842i	$-0.768925\pi$
$619$	5.00000	−	8.66025i	0.200967	−	0.348085i	0.948840	+	0.315757i	$0.102258\pi$
$620$		0			0
$621$	−2.00000	−	3.46410i	−0.0802572	−	0.139010i
$622$			32.0000i			1.28308i
$623$	−10.3923	−	12.0000i	−0.416359	−	0.480770i
$624$		0			0
$625$		0			0
$626$	−0.500000	+	0.866025i	−0.0199840	+	0.0346133i
$627$	−34.6410	−	20.0000i	−1.38343	−	0.798723i
$628$	−3.46410	+	2.00000i	−0.138233	+	0.0798087i
$629$	−16.0000			−0.637962
$630$		0			0
$631$	−19.0000			−0.756378			−0.378189	−	0.925728i	$-0.623453\pi$
$631$	−19.0000			−0.756378			−0.378189	+	0.925728i	$0.623453\pi$
$632$	−2.59808	+	1.50000i	−0.103346	+	0.0596668i
$633$	1.73205	+	1.00000i	0.0688428	+	0.0397464i
$634$	1.50000	−	2.59808i	0.0595726	−	0.103183i
$635$		0			0
$636$	9.00000			0.356873
$637$		0			0
$638$		−	25.0000i		−	0.989759i
$639$	1.00000	+	1.73205i	0.0395594	+	0.0685189i
$640$		0			0
$641$	−13.0000	+	22.5167i	−0.513469	+	0.889355i	0.486409	+	0.873731i	$0.338307\pi$
$641$	−13.0000	+	22.5167i	−0.513469	+	0.889355i	−0.999878	+	0.0156233i	$0.995027\pi$
$642$	2.59808	−	1.50000i	0.102538	−	0.0592003i
$643$			14.0000i			0.552106i	0.961142	+	0.276053i	$0.0890266\pi$
$643$			14.0000i			0.552106i	−0.961142	+	0.276053i	$0.910973\pi$
$644$	2.00000	+	10.3923i	0.0788110	+	0.409514i
$645$		0			0
$646$	16.0000	+	27.7128i	0.629512	+	1.09035i
$647$	−15.5885	−	9.00000i	−0.612845	−	0.353827i	0.161233	−	0.986916i	$-0.448453\pi$
$647$	−15.5885	−	9.00000i	−0.612845	−	0.353827i	−0.774078	+	0.633090i	$0.781786\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−27.5000	−	47.6314i	−1.07947	−	1.86970i
$650$		0			0
$651$	−6.00000	+	5.19615i	−0.235159	+	0.203653i
$652$			4.00000i			0.156652i
$653$	−33.7750	+	19.5000i	−1.32172	+	0.763094i	−0.984003	−	0.178154i	$-0.942987\pi$
$653$	−33.7750	+	19.5000i	−1.32172	+	0.763094i	−0.337715	+	0.941248i	$0.609654\pi$
$654$	1.00000	−	1.73205i	0.0391031	−	0.0677285i
$655$		0			0
$656$		0			0
$657$		−	10.0000i		−	0.390137i
$658$	−5.19615	+	15.0000i	−0.202567	+	0.584761i
$659$	40.0000			1.55818			0.779089	−	0.626913i	$-0.215682\pi$
$659$	40.0000			1.55818			0.779089	+	0.626913i	$0.215682\pi$
$660$		0			0
$661$	−5.00000	+	8.66025i	−0.194477	+	0.336845i	−0.946729	−	0.322031i	$-0.895634\pi$
$661$	−5.00000	+	8.66025i	−0.194477	+	0.336845i	0.752252	+	0.658876i	$0.228968\pi$
$662$	−3.46410	−	2.00000i	−0.134636	−	0.0777322i
$663$		0			0
$664$	7.00000			0.271653
$665$		0			0
$666$	−4.00000			−0.154997
$667$	−17.3205	+	10.0000i	−0.670653	+	0.387202i
$668$	12.1244	+	7.00000i	0.469105	+	0.270838i
$669$	3.50000	−	6.06218i	0.135318	−	0.234377i
$670$		0			0
$671$	−30.0000			−1.15814
$672$	1.73205	+	2.00000i	0.0668153	+	0.0771517i
$673$		−	19.0000i		−	0.732396i	−0.930537	−	0.366198i	$-0.880659\pi$
$673$		−	19.0000i		−	0.732396i	0.930537	−	0.366198i	$-0.119341\pi$
$674$	4.50000	+	7.79423i	0.173334	+	0.300222i
$675$		0			0
$676$	6.50000	−	11.2583i	0.250000	−	0.433013i
$677$	23.3827	−	13.5000i	0.898670	−	0.518847i	0.0219013	−	0.999760i	$-0.493028\pi$
$677$	23.3827	−	13.5000i	0.898670	−	0.518847i	0.876768	+	0.480913i	$0.159695\pi$
$678$		−	16.0000i		−	0.614476i
$679$	−3.50000	−	18.1865i	−0.134318	−	0.697935i
$680$		0			0
$681$	1.50000	+	2.59808i	0.0574801	+	0.0995585i
$682$	12.9904	+	7.50000i	0.497427	+	0.287190i
$683$	7.79423	+	4.50000i	0.298238	+	0.172188i	0.641651	−	0.766997i	$-0.278250\pi$
$683$	7.79423	+	4.50000i	0.298238	+	0.172188i	−0.343413	+	0.939184i	$0.611583\pi$
$684$	4.00000	+	6.92820i	0.152944	+	0.264906i
$685$		0			0
$686$	−8.50000	+	16.4545i	−0.324532	+	0.628235i
$687$		−	20.0000i		−	0.763048i
$688$	1.73205	−	1.00000i	0.0660338	−	0.0381246i
$689$		0			0
$690$		0			0
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	0.779857	−	0.625958i	$-0.215292\pi$
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	−0.932024	+	0.362397i	$0.881959\pi$
$692$		−	22.0000i		−	0.836315i
$693$	−12.9904	+	2.50000i	−0.493464	+	0.0949671i
$694$	−12.0000			−0.455514
$695$		0			0
$696$	−2.50000	+	4.33013i	−0.0947623	+	0.164133i
$697$		0			0
$698$	−12.1244	+	7.00000i	−0.458914	+	0.264954i
$699$	−4.00000			−0.151294
$700$		0			0
$701$	−5.00000			−0.188847			−0.0944237	−	0.995532i	$-0.530101\pi$
$701$	−5.00000			−0.188847			−0.0944237	+	0.995532i	$0.530101\pi$
$702$		0			0
$703$	27.7128	+	16.0000i	1.04521	+	0.603451i
$704$	2.50000	−	4.33013i	0.0942223	−	0.163198i
$705$		0			0
$706$	24.0000			0.903252
$707$	−8.66025	+	25.0000i	−0.325702	+	0.940222i
$708$			11.0000i			0.413405i
$709$	19.0000	+	32.9090i	0.713560	+	1.23592i	0.963512	+	0.267664i	$0.0862517\pi$
$709$	19.0000	+	32.9090i	0.713560	+	1.23592i	−0.249952	+	0.968258i	$0.580415\pi$
$710$		0			0
$711$	−1.50000	+	2.59808i	−0.0562544	+	0.0974355i
$712$	5.19615	−	3.00000i	0.194734	−	0.112430i
$713$		−	12.0000i		−	0.449404i
$714$	10.0000	+	3.46410i	0.374241	+	0.129641i
$715$		0			0
$716$	−6.00000	−	10.3923i	−0.224231	−	0.388379i
$717$	10.3923	+	6.00000i	0.388108	+	0.224074i
$718$	−8.66025	−	5.00000i	−0.323198	−	0.186598i
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	0.804648	−	0.593753i	$-0.202354\pi$
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	−0.916529	+	0.399969i	$0.869021\pi$
$720$		0			0
$721$	16.0000	−	13.8564i	0.595871	−	0.516040i
$722$		−	45.0000i		−	1.67473i
$723$	21.6506	−	12.5000i	0.805196	−	0.464880i
$724$		0			0
$725$		0			0
$726$	7.00000	+	12.1244i	0.259794	+	0.449977i
$727$		−	7.00000i		−	0.259616i	−0.991539	−	0.129808i	$-0.958564\pi$
$727$		−	7.00000i		−	0.259616i	0.991539	−	0.129808i	$-0.0414360\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	4.00000	−	6.92820i	0.147945	−	0.256249i
$732$	5.19615	+	3.00000i	0.192055	+	0.110883i
$733$	−5.19615	+	3.00000i	−0.191924	+	0.110808i	−0.592883	−	0.805289i	$-0.702010\pi$
$733$	−5.19615	+	3.00000i	−0.191924	+	0.110808i	0.400959	+	0.916096i	$0.368677\pi$
$734$	−17.0000			−0.627481
$735$		0			0
$736$	−4.00000			−0.147442
$737$	8.66025	−	5.00000i	0.319005	−	0.184177i
$738$		0			0
$739$	−15.0000	+	25.9808i	−0.551784	+	0.955718i	0.446362	+	0.894852i	$0.352719\pi$
$739$	−15.0000	+	25.9808i	−0.551784	+	0.955718i	−0.998146	+	0.0608653i	$0.980614\pi$
$740$		0			0
$741$		0			0
$742$	−23.3827	+	4.50000i	−0.858405	+	0.165200i
$743$			30.0000i			1.10059i	0.834969	+	0.550297i	$0.185485\pi$
$743$			30.0000i			1.10059i	−0.834969	+	0.550297i	$0.814515\pi$
$744$	−1.50000	−	2.59808i	−0.0549927	−	0.0952501i
$745$		0			0
$746$	16.0000	−	27.7128i	0.585802	−	1.01464i
$747$	6.06218	−	3.50000i	0.221803	−	0.128058i
$748$		−	20.0000i		−	0.731272i
$749$	−6.00000	+	5.19615i	−0.219235	+	0.189863i
$750$		0			0
$751$	−22.5000	−	38.9711i	−0.821037	−	1.42208i	−0.904911	−	0.425601i	$-0.860063\pi$
$751$	−22.5000	−	38.9711i	−0.821037	−	1.42208i	0.0838743	−	0.996476i	$-0.473271\pi$
$752$	−5.19615	−	3.00000i	−0.189484	−	0.109399i
$753$	18.1865	+	10.5000i	0.662754	+	0.382641i
$754$		0			0
$755$		0			0
$756$	2.50000	+	0.866025i	0.0909241	+	0.0314970i
$757$			54.0000i			1.96266i	0.192323	+	0.981332i	$0.438398\pi$
$757$			54.0000i			1.96266i	−0.192323	+	0.981332i	$0.561602\pi$
$758$	13.8564	−	8.00000i	0.503287	−	0.290573i
$759$	10.0000	−	17.3205i	0.362977	−	0.628695i
$760$		0			0
$761$	−4.00000	−	6.92820i	−0.145000	−	0.251147i	0.784373	−	0.620289i	$-0.212985\pi$
$761$	−4.00000	−	6.92820i	−0.145000	−	0.251147i	−0.929373	+	0.369142i	$0.879652\pi$
$762$			9.00000i			0.326036i
$763$	−1.73205	+	5.00000i	−0.0627044	+	0.181012i
$764$	−24.0000			−0.868290
$765$		0			0
$766$	17.0000	−	29.4449i	0.614235	−	1.06389i
$767$		0			0
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	35.0000			1.26213			0.631066	−	0.775729i	$-0.282618\pi$
$769$	35.0000			1.26213			0.631066	+	0.775729i	$0.282618\pi$
$770$		0			0
$771$	6.00000			0.216085
$772$	−4.33013	+	2.50000i	−0.155845	+	0.0899770i
$773$	−8.66025	−	5.00000i	−0.311488	−	0.179838i	0.336104	−	0.941825i	$-0.390891\pi$
$773$	−8.66025	−	5.00000i	−0.311488	−	0.179838i	−0.647592	+	0.761987i	$0.724224\pi$
$774$	1.00000	−	1.73205i	0.0359443	−	0.0622573i
$775$		0			0
$776$	7.00000			0.251285
$777$	10.3923	−	2.00000i	0.372822	−	0.0717496i
$778$		−	2.00000i		−	0.0717035i
$779$		0			0
$780$		0			0
$781$	−5.00000	+	8.66025i	−0.178914	+	0.309888i
$782$	−13.8564	+	8.00000i	−0.495504	+	0.286079i
$783$			5.00000i			0.178685i
$784$	−5.50000	−	4.33013i	−0.196429	−	0.154647i
$785$		0			0
$786$	0.500000	+	0.866025i	0.0178344	+	0.0308901i
$787$	−15.5885	−	9.00000i	−0.555668	−	0.320815i	0.195737	−	0.980656i	$-0.437290\pi$
$787$	−15.5885	−	9.00000i	−0.555668	−	0.320815i	−0.751405	+	0.659841i	$0.770624\pi$
$788$	−1.73205	−	1.00000i	−0.0617018	−	0.0356235i
$789$	15.0000	+	25.9808i	0.534014	+	0.924940i
$790$		0			0
$791$	8.00000	+	41.5692i	0.284447	+	1.47803i
$792$		−	5.00000i		−	0.177667i
$793$		0			0
$794$	18.0000	−	31.1769i	0.638796	−	1.10643i
$795$		0			0
$796$	2.00000	+	3.46410i	0.0708881	+	0.122782i
$797$		−	21.0000i		−	0.743858i	−0.928261	−	0.371929i	$-0.878696\pi$
$797$		−	21.0000i		−	0.743858i	0.928261	−	0.371929i	$-0.121304\pi$
$798$	−13.8564	−	16.0000i	−0.490511	−	0.566394i
$799$	−24.0000			−0.849059
$800$		0			0
$801$	3.00000	−	5.19615i	0.106000	−	0.183597i
$802$	20.7846	+	12.0000i	0.733930	+	0.423735i
$803$	43.3013	−	25.0000i	1.52807	−	0.882231i
$804$	−2.00000			−0.0705346
$805$		0			0
$806$		0			0
$807$	26.8468	−	15.5000i	0.945052	−	0.545626i
$808$	−8.66025	−	5.00000i	−0.304667	−	0.175899i
$809$	20.0000	−	34.6410i	0.703163	−	1.21791i	−0.264188	−	0.964471i	$-0.585104\pi$
$809$	20.0000	−	34.6410i	0.703163	−	1.21791i	0.967351	−	0.253442i	$-0.0815627\pi$
$810$		0			0
$811$	−14.0000			−0.491606			−0.245803	−	0.969320i	$-0.579052\pi$
$811$	−14.0000			−0.491606			−0.245803	+	0.969320i	$0.579052\pi$
$812$	4.33013	−	12.5000i	0.151958	−	0.438664i
$813$		−	15.0000i		−	0.526073i
$814$	−10.0000	−	17.3205i	−0.350500	−	0.607083i
$815$		0			0
$816$	−2.00000	+	3.46410i	−0.0700140	+	0.121268i
$817$	−13.8564	+	8.00000i	−0.484774	+	0.279885i
$818$		−	25.0000i		−	0.874105i
$819$		0			0
$820$		0			0
$821$	12.5000	+	21.6506i	0.436253	+	0.755612i	0.997397	−	0.0721058i	$-0.0229719\pi$
$821$	12.5000	+	21.6506i	0.436253	+	0.755612i	−0.561144	+	0.827718i	$0.689639\pi$
$822$	1.73205	+	1.00000i	0.0604122	+	0.0348790i
$823$	−34.6410	−	20.0000i	−1.20751	−	0.697156i	−0.245295	−	0.969448i	$-0.578885\pi$
$823$	−34.6410	−	20.0000i	−1.20751	−	0.697156i	−0.962215	+	0.272292i	$0.912218\pi$
$824$	4.00000	+	6.92820i	0.139347	+	0.241355i
$825$		0			0
$826$	−5.50000	−	28.5788i	−0.191369	−	0.994385i
$827$		−	9.00000i		−	0.312961i	−0.987681	−	0.156480i	$-0.949985\pi$
$827$		−	9.00000i		−	0.312961i	0.987681	−	0.156480i	$-0.0500148\pi$
$828$	−3.46410	+	2.00000i	−0.120386	+	0.0695048i
$829$	−16.0000	+	27.7128i	−0.555703	+	0.962506i	0.442145	+	0.896943i	$0.354217\pi$
$829$	−16.0000	+	27.7128i	−0.555703	+	0.962506i	−0.997848	+	0.0655624i	$0.979116\pi$
$830$		0			0
$831$	−8.00000	−	13.8564i	−0.277517	−	0.480673i
$832$		0			0
$833$	−27.7128	−	4.00000i	−0.960192	−	0.138592i
$834$	−14.0000			−0.484780
$835$		0			0
$836$	−20.0000	+	34.6410i	−0.691714	+	1.19808i
$837$	−2.59808	−	1.50000i	−0.0898027	−	0.0518476i
$838$		0			0
$839$	28.0000			0.966667			0.483334	−	0.875436i	$-0.339426\pi$
$839$	28.0000			0.966667			0.483334	+	0.875436i	$0.339426\pi$
$840$		0			0
$841$	−4.00000			−0.137931
$842$	−25.9808	+	15.0000i	−0.895356	+	0.516934i
$843$	1.73205	+	1.00000i	0.0596550	+	0.0344418i
$844$	1.00000	−	1.73205i	0.0344214	−	0.0596196i
$845$		0			0
$846$	−6.00000			−0.206284
$847$	−24.2487	−	28.0000i	−0.833196	−	0.962091i
$848$		−	9.00000i		−	0.309061i
$849$	−5.00000	−	8.66025i	−0.171600	−	0.297219i
$850$		0			0
$851$	−8.00000	+	13.8564i	−0.274236	+	0.474991i
$852$	1.73205	−	1.00000i	0.0593391	−	0.0342594i
$853$			14.0000i			0.479351i	0.970853	+	0.239675i	$0.0770410\pi$
$853$			14.0000i			0.479351i	−0.970853	+	0.239675i	$0.922959\pi$
$854$	−15.0000	−	5.19615i	−0.513289	−	0.177809i
$855$		0			0
$856$	−1.50000	−	2.59808i	−0.0512689	−	0.0888004i
$857$	−15.5885	−	9.00000i	−0.532492	−	0.307434i	0.209539	−	0.977800i	$-0.432804\pi$
$857$	−15.5885	−	9.00000i	−0.532492	−	0.307434i	−0.742030	+	0.670366i	$0.766137\pi$
$858$		0			0
$859$	−17.0000	−	29.4449i	−0.580033	−	1.00465i	−0.995475	−	0.0950262i	$-0.969707\pi$
$859$	−17.0000	−	29.4449i	−0.580033	−	1.00465i	0.415442	−	0.909620i	$-0.363627\pi$
$860$		0			0
$861$		0			0
$862$		−	12.0000i		−	0.408722i
$863$	8.66025	−	5.00000i	0.294798	−	0.170202i	−0.345305	−	0.938490i	$-0.612225\pi$
$863$	8.66025	−	5.00000i	0.294798	−	0.170202i	0.640104	+	0.768288i	$0.278891\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$		0			0
$866$	−7.00000	−	12.1244i	−0.237870	−	0.412002i
$867$		−	1.00000i		−	0.0339618i
$868$	5.19615	+	6.00000i	0.176369	+	0.203653i
$869$	−15.0000			−0.508840
$870$		0			0
$871$		0			0
$872$	−1.73205	−	1.00000i	−0.0586546	−	0.0338643i
$873$	6.06218	−	3.50000i	0.205174	−	0.118457i
$874$	32.0000			1.08242
$875$		0			0
$876$	−10.0000			−0.337869
$877$	27.7128	−	16.0000i	0.935795	−	0.540282i	0.0471555	−	0.998888i	$-0.484984\pi$
$877$	27.7128	−	16.0000i	0.935795	−	0.540282i	0.888640	+	0.458606i	$0.151651\pi$
$878$	−12.9904	−	7.50000i	−0.438404	−	0.253113i
$879$	10.5000	−	18.1865i	0.354156	−	0.613417i
$880$		0			0
$881$	−42.0000			−1.41502			−0.707508	−	0.706705i	$-0.750181\pi$
$881$	−42.0000			−1.41502			−0.707508	+	0.706705i	$0.750181\pi$
$882$	−6.92820	−	1.00000i	−0.233285	−	0.0336718i
$883$		−	40.0000i		−	1.34611i	−0.739594	−	0.673054i	$-0.764982\pi$
$883$		−	40.0000i		−	1.34611i	0.739594	−	0.673054i	$-0.235018\pi$
$884$		0			0
$885$		0			0
$886$	−8.50000	+	14.7224i	−0.285563	+	0.494610i
$887$	−31.1769	+	18.0000i	−1.04682	+	0.604381i	−0.921757	−	0.387768i	$-0.873246\pi$
$887$	−31.1769	+	18.0000i	−1.04682	+	0.604381i	−0.125061	+	0.992149i	$0.539913\pi$
$888$			4.00000i			0.134231i
$889$	−4.50000	−	23.3827i	−0.150925	−	0.784230i
$890$		0			0
$891$	−2.50000	−	4.33013i	−0.0837532	−	0.145065i
$892$	−6.06218	−	3.50000i	−0.202977	−	0.117189i
$893$	41.5692	+	24.0000i	1.39106	+	0.803129i
$894$	9.00000	+	15.5885i	0.301005	+	0.521356i
$895$		0			0
$896$	2.00000	−	1.73205i	0.0668153	−	0.0578638i
$897$		0			0
$898$	13.8564	−	8.00000i	0.462394	−	0.266963i
$899$	−7.50000	+	12.9904i	−0.250139	+	0.433253i
$900$		0			0
$901$	−18.0000	−	31.1769i	−0.599667	−	1.03865i
$902$		0			0
$903$	−1.73205	+	5.00000i	−0.0576390	+	0.166390i
$904$	−16.0000			−0.532152
$905$		0			0
$906$	9.50000	−	16.4545i	0.315616	−	0.546664i
$907$	10.3923	+	6.00000i	0.345071	+	0.199227i	0.662512	−	0.749051i	$-0.269490\pi$
$907$	10.3923	+	6.00000i	0.345071	+	0.199227i	−0.317441	+	0.948278i	$0.602824\pi$
$908$	2.59808	−	1.50000i	0.0862202	−	0.0497792i
$909$	−10.0000			−0.331679
$910$		0			0
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$	6.92820	−	4.00000i	0.229416	−	0.132453i
$913$	30.3109	+	17.5000i	1.00314	+	0.579165i
$914$	15.5000	−	26.8468i	0.512694	−	0.888013i
$915$		0			0
$916$	−20.0000			−0.660819
$917$	−1.73205	−	2.00000i	−0.0571974	−	0.0660458i
$918$			4.00000i			0.132020i
$919$	−16.0000	−	27.7128i	−0.527791	−	0.914161i	−0.999475	−	0.0323936i	$-0.989687\pi$
$919$	−16.0000	−	27.7128i	−0.527791	−	0.914161i	0.471684	−	0.881768i	$-0.343646\pi$
$920$		0			0
$921$	14.0000	−	24.2487i	0.461316	−	0.799022i
$922$	12.1244	−	7.00000i	0.399294	−	0.230533i
$923$		0			0
$924$	2.50000	+	12.9904i	0.0822440	+	0.427352i
$925$		0			0
$926$	−8.00000	−	13.8564i	−0.262896	−	0.455350i
$927$	6.92820	+	4.00000i	0.227552	+	0.131377i
$928$	4.33013	+	2.50000i	0.142143	+	0.0820665i
$929$	−3.00000	−	5.19615i	−0.0984268	−	0.170480i	0.812607	−	0.582812i	$-0.198048\pi$
$929$	−3.00000	−	5.19615i	−0.0984268	−	0.170480i	−0.911034	+	0.412332i	$0.864714\pi$
$930$		0			0
$931$	44.0000	+	34.6410i	1.44204	+	1.13531i
$932$			4.00000i			0.131024i
$933$	27.7128	−	16.0000i	0.907277	−	0.523816i
$934$	−10.0000	+	17.3205i	−0.327210	+	0.566744i
$935$		0			0
$936$		0			0
$937$		−	35.0000i		−	1.14340i	−0.820463	−	0.571700i	$-0.806284\pi$
$937$		−	35.0000i		−	1.14340i	0.820463	−	0.571700i	$-0.193716\pi$
$938$	5.19615	−	1.00000i	0.169660	−	0.0326512i
$939$	1.00000			0.0326338
$940$		0			0
$941$	5.50000	−	9.52628i	0.179295	−	0.310548i	−0.762344	−	0.647172i	$-0.775952\pi$
$941$	5.50000	−	9.52628i	0.179295	−	0.310548i	0.941639	+	0.336624i	$0.109285\pi$
$942$	3.46410	+	2.00000i	0.112867	+	0.0651635i
$943$		0			0
$944$	11.0000			0.358020
$945$		0			0
$946$	10.0000			0.325128
$947$	27.7128	−	16.0000i	0.900545	−	0.519930i	0.0231683	−	0.999732i	$-0.492625\pi$
$947$	27.7128	−	16.0000i	0.900545	−	0.519930i	0.877377	+	0.479801i	$0.159291\pi$
$948$	2.59808	+	1.50000i	0.0843816	+	0.0487177i
$949$		0			0
$950$		0			0
$951$	−3.00000			−0.0972817
$952$	3.46410	−	10.0000i	0.112272	−	0.324102i
$953$			2.00000i			0.0647864i	0.999475	+	0.0323932i	$0.0103129\pi$
$953$			2.00000i			0.0647864i	−0.999475	+	0.0323932i	$0.989687\pi$
$954$	−4.50000	−	7.79423i	−0.145693	−	0.252347i
$955$		0			0
$956$	6.00000	−	10.3923i	0.194054	−	0.336111i
$957$	−21.6506	+	12.5000i	−0.699866	+	0.404068i
$958$			38.0000i			1.22772i
$959$	−5.00000	−	1.73205i	−0.161458	−	0.0559308i
$960$		0			0
$961$	11.0000	+	19.0526i	0.354839	+	0.614599i
$962$		0			0
$963$	−2.59808	−	1.50000i	−0.0837218	−	0.0483368i
$964$	−12.5000	−	21.6506i	−0.402598	−	0.697320i
$965$		0			0
$966$	8.00000	−	6.92820i	0.257396	−	0.222911i
$967$			61.0000i			1.96163i	0.194946	+	0.980814i	$0.437547\pi$
$967$			61.0000i			1.96163i	−0.194946	+	0.980814i	$0.562453\pi$
$968$	12.1244	−	7.00000i	0.389692	−	0.224989i
$969$	16.0000	−	27.7128i	0.513994	−	0.890264i
$970$		0			0
$971$	−7.50000	−	12.9904i	−0.240686	−	0.416881i	0.720224	−	0.693742i	$-0.244039\pi$
$971$	−7.50000	−	12.9904i	−0.240686	−	0.416881i	−0.960910	+	0.276861i	$0.910706\pi$
$972$			1.00000i			0.0320750i
$973$	36.3731	−	7.00000i	1.16607	−	0.224410i
$974$	−5.00000			−0.160210
$975$		0			0
$976$	3.00000	−	5.19615i	0.0960277	−	0.166325i
$977$	−25.9808	−	15.0000i	−0.831198	−	0.479893i	0.0230645	−	0.999734i	$-0.492658\pi$
$977$	−25.9808	−	15.0000i	−0.831198	−	0.479893i	−0.854263	+	0.519841i	$0.825991\pi$
$978$	3.46410	−	2.00000i	0.110770	−	0.0639529i
$979$	30.0000			0.958804
$980$		0			0
$981$	−2.00000			−0.0638551
$982$	−7.79423	+	4.50000i	−0.248724	+	0.143601i
$983$	51.9615	+	30.0000i	1.65732	+	0.956851i	0.973946	+	0.226778i	$0.0728192\pi$
$983$	51.9615	+	30.0000i	1.65732	+	0.956851i	0.683369	+	0.730073i	$0.260514\pi$
$984$		0			0
$985$		0			0
$986$	20.0000			0.636930
$987$	15.5885	−	3.00000i	0.496186	−	0.0954911i
$988$		0			0
$989$	−4.00000	−	6.92820i	−0.127193	−	0.220304i
$990$		0			0
$991$	−23.5000	+	40.7032i	−0.746502	+	1.29298i	0.202988	+	0.979181i	$0.434935\pi$
$991$	−23.5000	+	40.7032i	−0.746502	+	1.29298i	−0.949490	+	0.313798i	$0.898398\pi$
$992$	−2.59808	+	1.50000i	−0.0824890	+	0.0476250i
$993$			4.00000i			0.126936i
$994$	−4.00000	+	3.46410i	−0.126872	+	0.109875i
$995$		0			0
$996$	−3.50000	−	6.06218i	−0.110902	−	0.192087i
$997$	32.9090	+	19.0000i	1.04224	+	0.601736i	0.920466	−	0.390822i	$-0.127809\pi$
$997$	32.9090	+	19.0000i	1.04224	+	0.601736i	0.121771	+	0.992558i	$0.461143\pi$
$998$	−8.66025	−	5.00000i	−0.274136	−	0.158272i
$999$	2.00000	+	3.46410i	0.0632772	+	0.109599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.o.a.949.1		4
5.2	odd	4		42.2.e.a.25.1	✓	2
5.3	odd	4		1050.2.i.l.151.1		2
5.4	even	2	inner	1050.2.o.a.949.2		4
7.2	even	3	inner	1050.2.o.a.499.2		4
15.2	even	4		126.2.g.c.109.1		2
20.7	even	4		336.2.q.b.193.1		2
35.2	odd	12		42.2.e.a.37.1	yes	2
35.3	even	12		7350.2.a.q.1.1		1
35.9	even	6	inner	1050.2.o.a.499.1		4
35.12	even	12		294.2.e.b.79.1		2
35.17	even	12		294.2.a.f.1.1		1
35.18	odd	12		7350.2.a.bl.1.1		1
35.23	odd	12		1050.2.i.l.751.1		2
35.27	even	4		294.2.e.b.67.1		2
35.32	odd	12		294.2.a.e.1.1		1
40.27	even	4		1344.2.q.s.193.1		2
40.37	odd	4		1344.2.q.g.193.1		2
45.2	even	12		1134.2.h.l.109.1		2
45.7	odd	12		1134.2.h.e.109.1		2
45.22	odd	12		1134.2.e.l.865.1		2
45.32	even	12		1134.2.e.e.865.1		2
60.47	odd	4		1008.2.s.k.865.1		2
105.2	even	12		126.2.g.c.37.1		2
105.17	odd	12		882.2.a.d.1.1		1
105.32	even	12		882.2.a.c.1.1		1
105.47	odd	12		882.2.g.i.667.1		2
105.62	odd	4		882.2.g.i.361.1		2
140.27	odd	4		2352.2.q.u.1537.1		2
140.47	odd	12		2352.2.q.u.961.1		2
140.67	even	12		2352.2.a.t.1.1		1
140.87	odd	12		2352.2.a.f.1.1		1
140.107	even	12		336.2.q.b.289.1		2
280.37	odd	12		1344.2.q.g.961.1		2
280.67	even	12		9408.2.a.q.1.1		1
280.107	even	12		1344.2.q.s.961.1		2
280.157	even	12		9408.2.a.z.1.1		1
280.227	odd	12		9408.2.a.cr.1.1		1
280.277	odd	12		9408.2.a.ce.1.1		1
315.2	even	12		1134.2.e.e.919.1		2
315.142	odd	12		1134.2.e.l.919.1		2
315.212	even	12		1134.2.h.l.541.1		2
315.247	odd	12		1134.2.h.e.541.1		2
420.107	odd	12		1008.2.s.k.289.1		2
420.227	even	12		7056.2.a.bl.1.1		1
420.347	odd	12		7056.2.a.w.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.2.e.a.25.1	✓	2	5.2	odd	4
42.2.e.a.37.1	yes	2	35.2	odd	12
126.2.g.c.37.1		2	105.2	even	12
126.2.g.c.109.1		2	15.2	even	4
294.2.a.e.1.1		1	35.32	odd	12
294.2.a.f.1.1		1	35.17	even	12
294.2.e.b.67.1		2	35.27	even	4
294.2.e.b.79.1		2	35.12	even	12
336.2.q.b.193.1		2	20.7	even	4
336.2.q.b.289.1		2	140.107	even	12
882.2.a.c.1.1		1	105.32	even	12
882.2.a.d.1.1		1	105.17	odd	12
882.2.g.i.361.1		2	105.62	odd	4
882.2.g.i.667.1		2	105.47	odd	12
1008.2.s.k.289.1		2	420.107	odd	12
1008.2.s.k.865.1		2	60.47	odd	4
1050.2.i.l.151.1		2	5.3	odd	4
1050.2.i.l.751.1		2	35.23	odd	12
1050.2.o.a.499.1		4	35.9	even	6	inner
1050.2.o.a.499.2		4	7.2	even	3	inner
1050.2.o.a.949.1		4	1.1	even	1	trivial
1050.2.o.a.949.2		4	5.4	even	2	inner
1134.2.e.e.865.1		2	45.32	even	12
1134.2.e.e.919.1		2	315.2	even	12
1134.2.e.l.865.1		2	45.22	odd	12
1134.2.e.l.919.1		2	315.142	odd	12
1134.2.h.e.109.1		2	45.7	odd	12
1134.2.h.e.541.1		2	315.247	odd	12
1134.2.h.l.109.1		2	45.2	even	12
1134.2.h.l.541.1		2	315.212	even	12
1344.2.q.g.193.1		2	40.37	odd	4
1344.2.q.g.961.1		2	280.37	odd	12
1344.2.q.s.193.1		2	40.27	even	4
1344.2.q.s.961.1		2	280.107	even	12
2352.2.a.f.1.1		1	140.87	odd	12
2352.2.a.t.1.1		1	140.67	even	12
2352.2.q.u.961.1		2	140.47	odd	12
2352.2.q.u.1537.1		2	140.27	odd	4
7056.2.a.w.1.1		1	420.347	odd	12
7056.2.a.bl.1.1		1	420.227	even	12
7350.2.a.q.1.1		1	35.3	even	12
7350.2.a.bl.1.1		1	35.18	odd	12
9408.2.a.q.1.1		1	280.67	even	12
9408.2.a.z.1.1		1	280.157	even	12
9408.2.a.ce.1.1		1	280.277	odd	12
9408.2.a.cr.1.1		1	280.227	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(2.59808 - 0.500000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(2.59808 - 0.500000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.50000 + 4.33013i) q^{11} +(0.866025 - 0.500000i) q^{12} +(-2.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.46410 - 2.00000i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(4.00000 + 6.92820i) q^{19} +(2.50000 + 0.866025i) q^{21} -5.00000i q^{22} +(-3.46410 + 2.00000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +1.00000i q^{27} +(0.866025 - 2.50000i) q^{28} +5.00000 q^{29} +(-1.50000 + 2.59808i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.33013 + 2.50000i) q^{33} +4.00000 q^{34} +1.00000 q^{36} +(3.46410 - 2.00000i) q^{37} +(-6.92820 - 4.00000i) q^{38} +(-2.59808 + 0.500000i) q^{42} +2.00000i q^{43} +(2.50000 + 4.33013i) q^{44} +(2.00000 - 3.46410i) q^{46} +(5.19615 - 3.00000i) q^{47} -1.00000i q^{48} +(6.50000 - 2.59808i) q^{49} +(-2.00000 - 3.46410i) q^{51} +(7.79423 + 4.50000i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(0.500000 + 2.59808i) q^{56} +8.00000i q^{57} +(-4.33013 + 2.50000i) q^{58} +(-5.50000 + 9.52628i) q^{59} +(3.00000 + 5.19615i) q^{61} -3.00000i q^{62} +(1.73205 + 2.00000i) q^{63} -1.00000 q^{64} +(2.50000 - 4.33013i) q^{66} +(-1.73205 - 1.00000i) q^{67} +(-3.46410 + 2.00000i) q^{68} -4.00000 q^{69} +2.00000 q^{71} +(-0.866025 + 0.500000i) q^{72} +(-8.66025 - 5.00000i) q^{73} +(-2.00000 + 3.46410i) q^{74} +8.00000 q^{76} +(-4.33013 + 12.5000i) q^{77} +(1.50000 + 2.59808i) q^{79} +(-0.500000 + 0.866025i) q^{81} -7.00000i q^{83} +(2.00000 - 1.73205i) q^{84} +(-1.00000 - 1.73205i) q^{86} +(4.33013 + 2.50000i) q^{87} +(-4.33013 - 2.50000i) q^{88} +(-3.00000 - 5.19615i) q^{89} +4.00000i q^{92} +(-2.59808 + 1.50000i) q^{93} +(-3.00000 + 5.19615i) q^{94} +(0.500000 + 0.866025i) q^{96} -7.00000i q^{97} +(-4.33013 + 5.50000i) q^{98} -5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 4 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - 4 * q^6 + 2 * q^9	\( 4 q + 2 q^{4} - 4 q^{6} + 2 q^{9} - 10 q^{11} - 8 q^{14} - 2 q^{16} + 16 q^{19} + 10 q^{21} - 2 q^{24} + 20 q^{29} - 6 q^{31} + 16 q^{34} + 4 q^{36} + 10 q^{44} + 8 q^{46} + 26 q^{49} - 8 q^{51} - 2 q^{54} + 2 q^{56} - 22 q^{59} + 12 q^{61} - 4 q^{64} + 10 q^{66} - 16 q^{69} + 8 q^{71} - 8 q^{74} + 32 q^{76} + 6 q^{79} - 2 q^{81} + 8 q^{84} - 4 q^{86} - 12 q^{89} - 12 q^{94} + 2 q^{96} - 20 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 - 4 * q^6 + 2 * q^9 - 10 * q^11 - 8 * q^14 - 2 * q^16 + 16 * q^19 + 10 * q^21 - 2 * q^24 + 20 * q^29 - 6 * q^31 + 16 * q^34 + 4 * q^36 + 10 * q^44 + 8 * q^46 + 26 * q^49 - 8 * q^51 - 2 * q^54 + 2 * q^56 - 22 * q^59 + 12 * q^61 - 4 * q^64 + 10 * q^66 - 16 * q^69 + 8 * q^71 - 8 * q^74 + 32 * q^76 + 6 * q^79 - 2 * q^81 + 8 * q^84 - 4 * q^86 - 12 * q^89 - 12 * q^94 + 2 * q^96 - 20 * q^99

Introduction

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