LMFDB - Embedded newform 1050.2.i.l.751.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(151,1050)]

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, 0, 4]))

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

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

chi := DirichletCharacter("1050.151");

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.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.38429221223$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			751.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1050.751
Dual form			1050.2.i.l.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.50000 - 4.33013i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(2.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-4.00000 + 6.92820i) q^{19} +(2.50000 - 0.866025i) q^{21} -5.00000 q^{22} +(-2.00000 + 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{24} +1.00000 q^{27} +(2.50000 - 0.866025i) q^{28} -5.00000 q^{29} +(-1.50000 - 2.59808i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.50000 + 4.33013i) q^{33} -4.00000 q^{34} +1.00000 q^{36} +(-2.00000 + 3.46410i) q^{37} +(4.00000 + 6.92820i) q^{38} +(0.500000 - 2.59808i) q^{42} -2.00000 q^{43} +(-2.50000 + 4.33013i) q^{44} +(2.00000 + 3.46410i) q^{46} +(-3.00000 + 5.19615i) q^{47} +1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} +(-2.00000 + 3.46410i) q^{51} +(-4.50000 - 7.79423i) q^{53} +(0.500000 - 0.866025i) q^{54} +(0.500000 - 2.59808i) q^{56} +8.00000 q^{57} +(-2.50000 + 4.33013i) q^{58} +(5.50000 + 9.52628i) q^{59} +(3.00000 - 5.19615i) q^{61} -3.00000 q^{62} +(-2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(2.50000 + 4.33013i) q^{66} +(-1.00000 - 1.73205i) q^{67} +(-2.00000 + 3.46410i) q^{68} +4.00000 q^{69} +2.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(5.00000 + 8.66025i) q^{73} +(2.00000 + 3.46410i) q^{74} +8.00000 q^{76} +(12.5000 - 4.33013i) q^{77} +(-1.50000 + 2.59808i) q^{79} +(-0.500000 - 0.866025i) q^{81} +7.00000 q^{83} +(-2.00000 - 1.73205i) q^{84} +(-1.00000 + 1.73205i) q^{86} +(2.50000 + 4.33013i) q^{87} +(2.50000 + 4.33013i) q^{88} +(3.00000 - 5.19615i) q^{89} +4.00000 q^{92} +(-1.50000 + 2.59808i) q^{93} +(3.00000 + 5.19615i) q^{94} +(0.500000 - 0.866025i) q^{96} -7.00000 q^{97} +(-5.50000 + 4.33013i) q^{98} +5.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} - q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 - q^3 - q^4 - 2 * q^6 - q^7 - 2 * q^8 - q^9	$ 2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} - q^{7} - 2 q^{8} - q^{9} - 5 q^{11} - q^{12} + 4 q^{14} - q^{16} - 4 q^{17} + q^{18} - 8 q^{19} + 5 q^{21} - 10 q^{22} - 4 q^{23} + q^{24} + 2 q^{27} + 5 q^{28} - 10 q^{29} - 3 q^{31} + q^{32} - 5 q^{33} - 8 q^{34} + 2 q^{36} - 4 q^{37} + 8 q^{38} + q^{42} - 4 q^{43} - 5 q^{44} + 4 q^{46} - 6 q^{47} + 2 q^{48} - 13 q^{49} - 4 q^{51} - 9 q^{53} + q^{54} + q^{56} + 16 q^{57} - 5 q^{58} + 11 q^{59} + 6 q^{61} - 6 q^{62} - 4 q^{63} + 2 q^{64} + 5 q^{66} - 2 q^{67} - 4 q^{68} + 8 q^{69} + 4 q^{71} + q^{72} + 10 q^{73} + 4 q^{74} + 16 q^{76} + 25 q^{77} - 3 q^{79} - q^{81} + 14 q^{83} - 4 q^{84} - 2 q^{86} + 5 q^{87} + 5 q^{88} + 6 q^{89} + 8 q^{92} - 3 q^{93} + 6 q^{94} + q^{96} - 14 q^{97} - 11 q^{98} + 10 q^{99}+O(q^{100}) $ 2 * q + q^2 - q^3 - q^4 - 2 * q^6 - q^7 - 2 * q^8 - q^9 - 5 * q^11 - q^12 + 4 * q^14 - q^16 - 4 * q^17 + q^18 - 8 * q^19 + 5 * q^21 - 10 * q^22 - 4 * q^23 + q^24 + 2 * q^27 + 5 * q^28 - 10 * q^29 - 3 * q^31 + q^32 - 5 * q^33 - 8 * q^34 + 2 * q^36 - 4 * q^37 + 8 * q^38 + q^42 - 4 * q^43 - 5 * q^44 + 4 * q^46 - 6 * q^47 + 2 * q^48 - 13 * q^49 - 4 * q^51 - 9 * q^53 + q^54 + q^56 + 16 * q^57 - 5 * q^58 + 11 * q^59 + 6 * q^61 - 6 * q^62 - 4 * q^63 + 2 * q^64 + 5 * q^66 - 2 * q^67 - 4 * q^68 + 8 * q^69 + 4 * q^71 + q^72 + 10 * q^73 + 4 * q^74 + 16 * q^76 + 25 * q^77 - 3 * q^79 - q^81 + 14 * q^83 - 4 * q^84 - 2 * q^86 + 5 * q^87 + 5 * q^88 + 6 * q^89 + 8 * q^92 - 3 * q^93 + 6 * q^94 + q^96 - 14 * q^97 - 11 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.00000			−0.408248
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	−0.945979	−	0.324227i	$-0.894896\pi$
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	0.192201	−	0.981356i	$-0.438437\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$	2.00000	+	1.73205i	0.534522	+	0.462910i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	0.514782	−	0.857321i	$-0.327873\pi$
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	−0.999853	+	0.0171533i	$0.994540\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−4.00000	+	6.92820i	−0.917663	+	1.58944i	−0.114708	+	0.993399i	$0.536593\pi$
$19$	−4.00000	+	6.92820i	−0.917663	+	1.58944i	−0.802955	+	0.596040i	$0.796740\pi$
$20$		0			0
$21$	2.50000	−	0.866025i	0.545545	−	0.188982i
$22$	−5.00000			−1.06600
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$		0			0
$26$		0			0
$27$	1.00000			0.192450
$28$	2.50000	−	0.866025i	0.472456	−	0.163663i
$29$	−5.00000			−0.928477			−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000			−0.928477			−0.464238	+	0.885710i	$0.653672\pi$
$30$		0			0
$31$	−1.50000	−	2.59808i	−0.269408	−	0.466628i	0.699301	−	0.714827i	$-0.253495\pi$
$31$	−1.50000	−	2.59808i	−0.269408	−	0.466628i	−0.968709	+	0.248199i	$0.920161\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−2.50000	+	4.33013i	−0.435194	+	0.753778i
$34$	−4.00000			−0.685994
$35$		0			0
$36$	1.00000			0.166667
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	−0.982274	−	0.187453i	$-0.939977\pi$
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	0.653476	+	0.756948i	$0.273310\pi$
$38$	4.00000	+	6.92820i	0.648886	+	1.12390i
$39$		0			0
$40$		0			0
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$	0.500000	−	2.59808i	0.0771517	−	0.400892i
$43$	−2.00000			−0.304997			−0.152499	−	0.988304i	$-0.548732\pi$
$43$	−2.00000			−0.304997			−0.152499	+	0.988304i	$0.548732\pi$
$44$	−2.50000	+	4.33013i	−0.376889	+	0.652791i
$45$		0			0
$46$	2.00000	+	3.46410i	0.294884	+	0.510754i
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	−0.997503	−	0.0706177i	$-0.977503\pi$
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	0.559908	+	0.828554i	$0.310836\pi$
$48$	1.00000			0.144338
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$		0			0
$51$	−2.00000	+	3.46410i	−0.280056	+	0.485071i
$52$		0			0
$53$	−4.50000	−	7.79423i	−0.618123	−	1.07062i	−0.989828	−	0.142269i	$-0.954560\pi$
$53$	−4.50000	−	7.79423i	−0.618123	−	1.07062i	0.371706	−	0.928351i	$-0.378773\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$		0			0
$56$	0.500000	−	2.59808i	0.0668153	−	0.347183i
$57$	8.00000			1.05963
$58$	−2.50000	+	4.33013i	−0.328266	+	0.568574i
$59$	5.50000	+	9.52628i	0.716039	+	1.24022i	0.962557	+	0.271078i	$0.0873801\pi$
$59$	5.50000	+	9.52628i	0.716039	+	1.24022i	−0.246518	+	0.969138i	$0.579287\pi$
$60$		0			0
$61$	3.00000	−	5.19615i	0.384111	−	0.665299i	−0.607535	−	0.794293i	$-0.707841\pi$
$61$	3.00000	−	5.19615i	0.384111	−	0.665299i	0.991645	+	0.128994i	$0.0411748\pi$
$62$	−3.00000			−0.381000
$63$	−2.00000	−	1.73205i	−0.251976	−	0.218218i
$64$	1.00000			0.125000
$65$		0			0
$66$	2.50000	+	4.33013i	0.307729	+	0.533002i
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	0.798454	−	0.602056i	$-0.205652\pi$
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	−0.920623	+	0.390453i	$0.872318\pi$
$68$	−2.00000	+	3.46410i	−0.242536	+	0.420084i
$69$	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	$0.462134\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	5.00000	+	8.66025i	0.585206	+	1.01361i	0.994850	+	0.101361i	$0.0323196\pi$
$73$	5.00000	+	8.66025i	0.585206	+	1.01361i	−0.409644	+	0.912245i	$0.634347\pi$
$74$	2.00000	+	3.46410i	0.232495	+	0.402694i
$75$		0			0
$76$	8.00000			0.917663
$77$	12.5000	−	4.33013i	1.42451	−	0.493464i
$78$		0			0
$79$	−1.50000	+	2.59808i	−0.168763	+	0.292306i	−0.937985	−	0.346675i	$-0.887311\pi$
$79$	−1.50000	+	2.59808i	−0.168763	+	0.292306i	0.769222	+	0.638982i	$0.220644\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	7.00000			0.768350			0.384175	−	0.923260i	$-0.374486\pi$
$83$	7.00000			0.768350			0.384175	+	0.923260i	$0.374486\pi$
$84$	−2.00000	−	1.73205i	−0.218218	−	0.188982i
$85$		0			0
$86$	−1.00000	+	1.73205i	−0.107833	+	0.186772i
$87$	2.50000	+	4.33013i	0.268028	+	0.464238i
$88$	2.50000	+	4.33013i	0.266501	+	0.461593i
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$		0			0
$91$		0			0
$92$	4.00000			0.417029
$93$	−1.50000	+	2.59808i	−0.155543	+	0.269408i
$94$	3.00000	+	5.19615i	0.309426	+	0.535942i
$95$		0			0
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	−7.00000			−0.710742			−0.355371	−	0.934725i	$-0.615646\pi$
$97$	−7.00000			−0.710742			−0.355371	+	0.934725i	$0.615646\pi$
$98$	−5.50000	+	4.33013i	−0.555584	+	0.437409i
$99$	5.00000			0.502519
$100$		0			0
$101$	−5.00000	−	8.66025i	−0.497519	−	0.861727i	0.502477	−	0.864590i	$-0.332422\pi$
$101$	−5.00000	−	8.66025i	−0.497519	−	0.861727i	−0.999996	+	0.00286291i	$0.999089\pi$
$102$	2.00000	+	3.46410i	0.198030	+	0.342997i
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	−0.598858	−	0.800855i	$-0.704379\pi$
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	0.992990	+	0.118199i	$0.0377120\pi$
$104$		0			0
$105$		0			0
$106$	−9.00000			−0.874157
$107$	1.50000	−	2.59808i	0.145010	−	0.251166i	−0.784366	−	0.620298i	$-0.787012\pi$
$107$	1.50000	−	2.59808i	0.145010	−	0.251166i	0.929377	+	0.369132i	$0.120345\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	0.909935	−	0.414751i	$-0.136131\pi$
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	−0.814152	+	0.580651i	$0.802798\pi$
$110$		0			0
$111$	4.00000			0.379663
$112$	−2.00000	−	1.73205i	−0.188982	−	0.163663i
$113$	−16.0000			−1.50515			−0.752577	−	0.658505i	$-0.771189\pi$
$113$	−16.0000			−1.50515			−0.752577	+	0.658505i	$0.771189\pi$
$114$	4.00000	−	6.92820i	0.374634	−	0.648886i
$115$		0			0
$116$	2.50000	+	4.33013i	0.232119	+	0.402042i
$117$		0			0
$118$	11.0000			1.01263
$119$	10.0000	−	3.46410i	0.916698	−	0.317554i
$120$		0			0
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$	−3.00000	−	5.19615i	−0.271607	−	0.470438i
$123$		0			0
$124$	−1.50000	+	2.59808i	−0.134704	+	0.233314i
$125$		0			0
$126$	−2.50000	+	0.866025i	−0.222718	+	0.0771517i
$127$	−9.00000			−0.798621			−0.399310	−	0.916816i	$-0.630750\pi$
$127$	−9.00000			−0.798621			−0.399310	+	0.916816i	$0.630750\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	1.00000	+	1.73205i	0.0880451	+	0.152499i
$130$		0			0
$131$	−0.500000	+	0.866025i	−0.0436852	+	0.0756650i	−0.887041	−	0.461690i	$-0.847243\pi$
$131$	−0.500000	+	0.866025i	−0.0436852	+	0.0756650i	0.843356	+	0.537355i	$0.180577\pi$
$132$	5.00000			0.435194
$133$	−16.0000	−	13.8564i	−1.38738	−	1.20150i
$134$	−2.00000			−0.172774
$135$		0			0
$136$	2.00000	+	3.46410i	0.171499	+	0.297044i
$137$	−1.00000	−	1.73205i	−0.0854358	−	0.147979i	0.820141	−	0.572161i	$-0.193895\pi$
$137$	−1.00000	−	1.73205i	−0.0854358	−	0.147979i	−0.905577	+	0.424182i	$0.860562\pi$
$138$	2.00000	−	3.46410i	0.170251	−	0.294884i
$139$	−14.0000			−1.18746			−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−14.0000			−1.18746			−0.593732	+	0.804663i	$0.702346\pi$
$140$		0			0
$141$	6.00000			0.505291
$142$	1.00000	−	1.73205i	0.0839181	−	0.145350i
$143$		0			0
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$		0			0
$146$	10.0000			0.827606
$147$	1.00000	+	6.92820i	0.0824786	+	0.571429i
$148$	4.00000			0.328798
$149$	9.00000	−	15.5885i	0.737309	−	1.27706i	−0.216394	−	0.976306i	$-0.569430\pi$
$149$	9.00000	−	15.5885i	0.737309	−	1.27706i	0.953703	−	0.300750i	$-0.0972370\pi$
$150$		0			0
$151$	−9.50000	−	16.4545i	−0.773099	−	1.33905i	−0.935857	−	0.352381i	$-0.885372\pi$
$151$	−9.50000	−	16.4545i	−0.773099	−	1.33905i	0.162758	−	0.986666i	$-0.447961\pi$
$152$	4.00000	−	6.92820i	0.324443	−	0.561951i
$153$	4.00000			0.323381
$154$	2.50000	−	12.9904i	0.201456	−	1.04679i
$155$		0			0
$156$		0			0
$157$	−2.00000	−	3.46410i	−0.159617	−	0.276465i	0.775113	−	0.631822i	$-0.217693\pi$
$157$	−2.00000	−	3.46410i	−0.159617	−	0.276465i	−0.934731	+	0.355357i	$0.884359\pi$
$158$	1.50000	+	2.59808i	0.119334	+	0.206692i
$159$	−4.50000	+	7.79423i	−0.356873	+	0.618123i
$160$		0			0
$161$	−8.00000	−	6.92820i	−0.630488	−	0.546019i
$162$	−1.00000			−0.0785674
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	−0.933659	−	0.358162i	$-0.883403\pi$
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	0.777007	+	0.629492i	$0.216737\pi$
$164$		0			0
$165$		0			0
$166$	3.50000	−	6.06218i	0.271653	−	0.470516i
$167$	14.0000			1.08335			0.541676	−	0.840587i	$-0.317790\pi$
$167$	14.0000			1.08335			0.541676	+	0.840587i	$0.317790\pi$
$168$	−2.50000	+	0.866025i	−0.192879	+	0.0668153i
$169$	−13.0000			−1.00000
$170$		0			0
$171$	−4.00000	−	6.92820i	−0.305888	−	0.529813i
$172$	1.00000	+	1.73205i	0.0762493	+	0.132068i
$173$	11.0000	−	19.0526i	0.836315	−	1.44854i	−0.0566411	−	0.998395i	$-0.518039\pi$
$173$	11.0000	−	19.0526i	0.836315	−	1.44854i	0.892956	−	0.450145i	$-0.148628\pi$
$174$	5.00000			0.379049
$175$		0			0
$176$	5.00000			0.376889
$177$	5.50000	−	9.52628i	0.413405	−	0.716039i
$178$	−3.00000	−	5.19615i	−0.224860	−	0.389468i
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	0.549825	−	0.835280i	$-0.314694\pi$
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	−0.998286	+	0.0585225i	$0.981361\pi$
$180$		0			0
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$	−6.00000			−0.443533
$184$	2.00000	−	3.46410i	0.147442	−	0.255377i
$185$		0			0
$186$	1.50000	+	2.59808i	0.109985	+	0.190500i
$187$	−10.0000	+	17.3205i	−0.731272	+	1.26660i
$188$	6.00000			0.437595
$189$	−0.500000	+	2.59808i	−0.0363696	+	0.188982i
$190$		0			0
$191$	−12.0000	+	20.7846i	−0.868290	+	1.50392i	−0.00454614	+	0.999990i	$0.501447\pi$
$191$	−12.0000	+	20.7846i	−0.868290	+	1.50392i	−0.863743	+	0.503932i	$0.831886\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	2.50000	+	4.33013i	0.179954	+	0.311689i	0.941865	−	0.335993i	$-0.109072\pi$
$193$	2.50000	+	4.33013i	0.179954	+	0.311689i	−0.761911	+	0.647682i	$0.775738\pi$
$194$	−3.50000	+	6.06218i	−0.251285	+	0.435239i
$195$		0			0
$196$	1.00000	+	6.92820i	0.0714286	+	0.494872i
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$	2.50000	−	4.33013i	0.177667	−	0.307729i
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	0.928166	−	0.372168i	$-0.121385\pi$
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	−0.786389	+	0.617731i	$0.788052\pi$
$200$		0			0
$201$	−1.00000	+	1.73205i	−0.0705346	+	0.122169i
$202$	−10.0000			−0.703598
$203$	2.50000	−	12.9904i	0.175466	−	0.911746i
$204$	4.00000			0.280056
$205$		0			0
$206$	−4.00000	−	6.92820i	−0.278693	−	0.482711i
$207$	−2.00000	−	3.46410i	−0.139010	−	0.240772i
$208$		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	$0.478069\pi$
$212$	−4.50000	+	7.79423i	−0.309061	+	0.535310i
$213$	−1.00000	−	1.73205i	−0.0685189	−	0.118678i
$214$	−1.50000	−	2.59808i	−0.102538	−	0.177601i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$	7.50000	−	2.59808i	0.509133	−	0.176369i
$218$	2.00000			0.135457
$219$	5.00000	−	8.66025i	0.337869	−	0.585206i
$220$		0			0
$221$		0			0
$222$	2.00000	−	3.46410i	0.134231	−	0.232495i
$223$	7.00000			0.468755			0.234377	−	0.972146i	$-0.424695\pi$
$223$	7.00000			0.468755			0.234377	+	0.972146i	$0.424695\pi$
$224$	−2.50000	+	0.866025i	−0.167038	+	0.0578638i
$225$		0			0
$226$	−8.00000	+	13.8564i	−0.532152	+	0.921714i
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	0.911502	−	0.411296i	$-0.134924\pi$
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	−0.811943	+	0.583736i	$0.801590\pi$
$228$	−4.00000	−	6.92820i	−0.264906	−	0.458831i
$229$	10.0000	−	17.3205i	0.660819	−	1.14457i	−0.319582	−	0.947559i	$-0.603543\pi$
$229$	10.0000	−	17.3205i	0.660819	−	1.14457i	0.980401	−	0.197013i	$-0.0631241\pi$
$230$		0			0
$231$	−10.0000	−	8.66025i	−0.657952	−	0.569803i
$232$	5.00000			0.328266
$233$	−2.00000	+	3.46410i	−0.131024	+	0.226941i	−0.924072	−	0.382219i	$-0.875160\pi$
$233$	−2.00000	+	3.46410i	−0.131024	+	0.226941i	0.793047	+	0.609160i	$0.208493\pi$
$234$		0			0
$235$		0			0
$236$	5.50000	−	9.52628i	0.358020	−	0.620108i
$237$	3.00000			0.194871
$238$	2.00000	−	10.3923i	0.129641	−	0.673633i
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$		0			0
$241$	12.5000	+	21.6506i	0.805196	+	1.39464i	0.916159	+	0.400815i	$0.131273\pi$
$241$	12.5000	+	21.6506i	0.805196	+	1.39464i	−0.110963	+	0.993825i	$0.535394\pi$
$242$	7.00000	+	12.1244i	0.449977	+	0.779383i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−6.00000			−0.384111
$245$		0			0
$246$		0			0
$247$		0			0
$248$	1.50000	+	2.59808i	0.0952501	+	0.164978i
$249$	−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	$0.269387\pi$
$252$	−0.500000	+	2.59808i	−0.0314970	+	0.163663i
$253$	20.0000			1.25739
$254$	−4.50000	+	7.79423i	−0.282355	+	0.489053i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	−0.944294	−	0.329104i	$-0.893253\pi$
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	0.757159	+	0.653231i	$0.226587\pi$
$258$	2.00000			0.124515
$259$	−8.00000	−	6.92820i	−0.497096	−	0.430498i
$260$		0			0
$261$	2.50000	−	4.33013i	0.154746	−	0.268028i
$262$	0.500000	+	0.866025i	0.0308901	+	0.0535032i
$263$	−15.0000	−	25.9808i	−0.924940	−	1.60204i	−0.791658	−	0.610964i	$-0.790782\pi$
$263$	−15.0000	−	25.9808i	−0.924940	−	1.60204i	−0.133281	−	0.991078i	$-0.542551\pi$
$264$	2.50000	−	4.33013i	0.153864	−	0.266501i
$265$		0			0
$266$	−20.0000	+	6.92820i	−1.22628	+	0.424795i
$267$	−6.00000			−0.367194
$268$	−1.00000	+	1.73205i	−0.0610847	+	0.105802i
$269$	−15.5000	−	26.8468i	−0.945052	−	1.63688i	−0.755648	−	0.654978i	$-0.772678\pi$
$269$	−15.5000	−	26.8468i	−0.945052	−	1.63688i	−0.189404	−	0.981899i	$-0.560656\pi$
$270$		0			0
$271$	−7.50000	+	12.9904i	−0.455593	+	0.789109i	−0.998722	−	0.0505395i	$-0.983906\pi$
$271$	−7.50000	+	12.9904i	−0.455593	+	0.789109i	0.543130	+	0.839649i	$0.317239\pi$
$272$	4.00000			0.242536
$273$		0			0
$274$	−2.00000			−0.120824
$275$		0			0
$276$	−2.00000	−	3.46410i	−0.120386	−	0.208514i
$277$	−8.00000	−	13.8564i	−0.480673	−	0.832551i	0.519081	−	0.854725i	$-0.326274\pi$
$277$	−8.00000	−	13.8564i	−0.480673	−	0.832551i	−0.999754	+	0.0221745i	$0.992941\pi$
$278$	−7.00000	+	12.1244i	−0.419832	+	0.727171i
$279$	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	$0.481000\pi$
$282$	3.00000	−	5.19615i	0.178647	−	0.309426i
$283$	5.00000	+	8.66025i	0.297219	+	0.514799i	0.975499	−	0.220005i	$-0.0706075\pi$
$283$	5.00000	+	8.66025i	0.297219	+	0.514799i	−0.678280	+	0.734804i	$0.737274\pi$
$284$	−1.00000	−	1.73205i	−0.0593391	−	0.102778i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−1.00000			−0.0589256
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$		0			0
$291$	3.50000	+	6.06218i	0.205174	+	0.355371i
$292$	5.00000	−	8.66025i	0.292603	−	0.506803i
$293$	21.0000			1.22683			0.613417	−	0.789760i	$-0.289795\pi$
$293$	21.0000			1.22683			0.613417	+	0.789760i	$0.289795\pi$
$294$	6.50000	+	2.59808i	0.379088	+	0.151523i
$295$		0			0
$296$	2.00000	−	3.46410i	0.116248	−	0.201347i
$297$	−2.50000	−	4.33013i	−0.145065	−	0.251259i
$298$	−9.00000	−	15.5885i	−0.521356	−	0.903015i
$299$		0			0
$300$		0			0
$301$	1.00000	−	5.19615i	0.0576390	−	0.299501i
$302$	−19.0000			−1.09333
$303$	−5.00000	+	8.66025i	−0.287242	+	0.497519i
$304$	−4.00000	−	6.92820i	−0.229416	−	0.397360i
$305$		0			0
$306$	2.00000	−	3.46410i	0.114332	−	0.198030i
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$	−10.0000	−	8.66025i	−0.569803	−	0.493464i
$309$	−8.00000			−0.455104
$310$		0			0
$311$	16.0000	+	27.7128i	0.907277	+	1.57145i	0.817832	+	0.575458i	$0.195176\pi$
$311$	16.0000	+	27.7128i	0.907277	+	1.57145i	0.0894452	+	0.995992i	$0.471491\pi$
$312$		0			0
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	−0.851549	−	0.524276i	$-0.824336\pi$
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	0.879810	+	0.475325i	$0.157669\pi$
$314$	−4.00000			−0.225733
$315$		0			0
$316$	3.00000			0.168763
$317$	1.50000	−	2.59808i	0.0842484	−	0.145922i	−0.820822	−	0.571184i	$-0.806484\pi$
$317$	1.50000	−	2.59808i	0.0842484	−	0.145922i	0.905071	+	0.425261i	$0.139818\pi$
$318$	4.50000	+	7.79423i	0.252347	+	0.437079i
$319$	12.5000	+	21.6506i	0.699866	+	1.21220i
$320$		0			0
$321$	−3.00000			−0.167444
$322$	−10.0000	+	3.46410i	−0.557278	+	0.193047i
$323$	32.0000			1.78053
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$		0			0
$326$	2.00000	+	3.46410i	0.110770	+	0.191859i
$327$	1.00000	−	1.73205i	0.0553001	−	0.0957826i
$328$		0			0
$329$	−12.0000	−	10.3923i	−0.661581	−	0.572946i
$330$		0			0
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$	−3.50000	−	6.06218i	−0.192087	−	0.332705i
$333$	−2.00000	−	3.46410i	−0.109599	−	0.189832i
$334$	7.00000	−	12.1244i	0.383023	−	0.663415i
$335$		0			0
$336$	−0.500000	+	2.59808i	−0.0272772	+	0.141737i
$337$	−9.00000			−0.490261			−0.245131	−	0.969490i	$-0.578831\pi$
$337$	−9.00000			−0.490261			−0.245131	+	0.969490i	$0.578831\pi$
$338$	−6.50000	+	11.2583i	−0.353553	+	0.612372i
$339$	8.00000	+	13.8564i	0.434500	+	0.752577i
$340$		0			0
$341$	−7.50000	+	12.9904i	−0.406148	+	0.703469i
$342$	−8.00000			−0.432590
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	2.00000			0.107833
$345$		0			0
$346$	−11.0000	−	19.0526i	−0.591364	−	1.02427i
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	0.980921	−	0.194409i	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$	2.50000	−	4.33013i	0.134014	−	0.232119i
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$		0			0
$352$	2.50000	−	4.33013i	0.133250	−	0.230797i
$353$	12.0000	+	20.7846i	0.638696	+	1.10625i	0.985719	+	0.168397i	$0.0538590\pi$
$353$	12.0000	+	20.7846i	0.638696	+	1.10625i	−0.347024	+	0.937856i	$0.612808\pi$
$354$	−5.50000	−	9.52628i	−0.292322	−	0.506316i
$355$		0			0
$356$	−6.00000			−0.317999
$357$	−8.00000	−	6.92820i	−0.423405	−	0.366679i
$358$	−12.0000			−0.634220
$359$	−5.00000	+	8.66025i	−0.263890	+	0.457071i	−0.967272	−	0.253741i	$-0.918339\pi$
$359$	−5.00000	+	8.66025i	−0.263890	+	0.457071i	0.703382	+	0.710812i	$0.251672\pi$
$360$		0			0
$361$	−22.5000	−	38.9711i	−1.18421	−	2.05111i
$362$		0			0
$363$	14.0000			0.734809
$364$		0			0
$365$		0			0
$366$	−3.00000	+	5.19615i	−0.156813	+	0.271607i
$367$	8.50000	+	14.7224i	0.443696	+	0.768505i	0.997960	−	0.0638362i	$-0.0203335\pi$
$367$	8.50000	+	14.7224i	0.443696	+	0.768505i	−0.554264	+	0.832341i	$0.687000\pi$
$368$	−2.00000	−	3.46410i	−0.104257	−	0.180579i
$369$		0			0
$370$		0			0
$371$	22.5000	−	7.79423i	1.16814	−	0.404656i
$372$	3.00000			0.155543
$373$	−16.0000	+	27.7128i	−0.828449	+	1.43492i	0.0708063	+	0.997490i	$0.477443\pi$
$373$	−16.0000	+	27.7128i	−0.828449	+	1.43492i	−0.899255	+	0.437425i	$0.855891\pi$
$374$	10.0000	+	17.3205i	0.517088	+	0.895622i
$375$		0			0
$376$	3.00000	−	5.19615i	0.154713	−	0.267971i
$377$		0			0
$378$	2.00000	+	1.73205i	0.102869	+	0.0890871i
$379$	16.0000			0.821865			0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000			0.821865			0.410932	+	0.911666i	$0.365203\pi$
$380$		0			0
$381$	4.50000	+	7.79423i	0.230542	+	0.399310i
$382$	12.0000	+	20.7846i	0.613973	+	1.06343i
$383$	−17.0000	+	29.4449i	−0.868659	+	1.50456i	−0.00529229	+	0.999986i	$0.501685\pi$
$383$	−17.0000	+	29.4449i	−0.868659	+	1.50456i	−0.863367	+	0.504576i	$0.831649\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	5.00000			0.254493
$387$	1.00000	−	1.73205i	0.0508329	−	0.0880451i
$388$	3.50000	+	6.06218i	0.177686	+	0.307760i
$389$	1.00000	+	1.73205i	0.0507020	+	0.0878185i	0.890263	−	0.455448i	$-0.150521\pi$
$389$	1.00000	+	1.73205i	0.0507020	+	0.0878185i	−0.839561	+	0.543266i	$0.817187\pi$
$390$		0			0
$391$	16.0000			0.809155
$392$	6.50000	+	2.59808i	0.328300	+	0.131223i
$393$	1.00000			0.0504433
$394$	−1.00000	+	1.73205i	−0.0503793	+	0.0872595i
$395$		0			0
$396$	−2.50000	−	4.33013i	−0.125630	−	0.217597i
$397$	18.0000	−	31.1769i	0.903394	−	1.56472i	0.0803356	−	0.996768i	$-0.474401\pi$
$397$	18.0000	−	31.1769i	0.903394	−	1.56472i	0.823058	−	0.567957i	$-0.192266\pi$
$398$	4.00000			0.200502
$399$	−4.00000	+	20.7846i	−0.200250	+	1.04053i
$400$		0			0
$401$	−12.0000	+	20.7846i	−0.599251	+	1.03793i	0.393680	+	0.919247i	$0.371202\pi$
$401$	−12.0000	+	20.7846i	−0.599251	+	1.03793i	−0.992932	+	0.118686i	$0.962132\pi$
$402$	1.00000	+	1.73205i	0.0498755	+	0.0863868i
$403$		0			0
$404$	−5.00000	+	8.66025i	−0.248759	+	0.430864i
$405$		0			0
$406$	−10.0000	−	8.66025i	−0.496292	−	0.429801i
$407$	20.0000			0.991363
$408$	2.00000	−	3.46410i	0.0990148	−	0.171499i
$409$	12.5000	+	21.6506i	0.618085	+	1.07056i	0.989835	+	0.142222i	$0.0454247\pi$
$409$	12.5000	+	21.6506i	0.618085	+	1.07056i	−0.371750	+	0.928333i	$0.621242\pi$
$410$		0			0
$411$	−1.00000	+	1.73205i	−0.0493264	+	0.0854358i
$412$	−8.00000			−0.394132
$413$	−27.5000	+	9.52628i	−1.35319	+	0.468758i
$414$	−4.00000			−0.196589
$415$		0			0
$416$		0			0
$417$	7.00000	+	12.1244i	0.342791	+	0.593732i
$418$	20.0000	−	34.6410i	0.978232	−	1.69435i
$419$		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	$0.239028\pi$
$422$	1.00000	−	1.73205i	0.0486792	−	0.0843149i
$423$	−3.00000	−	5.19615i	−0.145865	−	0.252646i
$424$	4.50000	+	7.79423i	0.218539	+	0.378521i
$425$		0			0
$426$	−2.00000			−0.0969003
$427$	12.0000	+	10.3923i	0.580721	+	0.502919i
$428$	−3.00000			−0.145010
$429$		0			0
$430$		0			0
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	0.684564	−	0.728953i	$-0.259993\pi$
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	−0.973574	+	0.228373i	$0.926659\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$	1.50000	−	7.79423i	0.0720023	−	0.374135i
$435$		0			0
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$	−16.0000	−	27.7128i	−0.765384	−	1.32568i
$438$	−5.00000	−	8.66025i	−0.238909	−	0.413803i
$439$	−7.50000	+	12.9904i	−0.357955	+	0.619997i	−0.987619	−	0.156871i	$-0.949859\pi$
$439$	−7.50000	+	12.9904i	−0.357955	+	0.619997i	0.629664	+	0.776868i	$0.283193\pi$
$440$		0			0
$441$	5.50000	−	4.33013i	0.261905	−	0.206197i
$442$		0			0
$443$	8.50000	−	14.7224i	0.403847	−	0.699484i	−0.590339	−	0.807155i	$-0.701006\pi$
$443$	8.50000	−	14.7224i	0.403847	−	0.699484i	0.994187	+	0.107671i	$0.0343394\pi$
$444$	−2.00000	−	3.46410i	−0.0949158	−	0.164399i
$445$		0			0
$446$	3.50000	−	6.06218i	0.165730	−	0.287052i
$447$	−18.0000			−0.851371
$448$	−0.500000	+	2.59808i	−0.0236228	+	0.122748i
$449$	16.0000			0.755087			0.377543	−	0.925992i	$-0.376769\pi$
$449$	16.0000			0.755087			0.377543	+	0.925992i	$0.376769\pi$
$450$		0			0
$451$		0			0
$452$	8.00000	+	13.8564i	0.376288	+	0.651751i
$453$	−9.50000	+	16.4545i	−0.446349	+	0.773099i
$454$	3.00000			0.140797
$455$		0			0
$456$	−8.00000			−0.374634
$457$	15.5000	−	26.8468i	0.725059	−	1.25584i	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	15.5000	−	26.8468i	0.725059	−	1.25584i	0.958950	−	0.283577i	$-0.0915211\pi$
$458$	−10.0000	−	17.3205i	−0.467269	−	0.809334i
$459$	−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	$0.605709\pi$
$462$	−12.5000	+	4.33013i	−0.581553	+	0.201456i
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$	2.50000	−	4.33013i	0.116060	−	0.201021i
$465$		0			0
$466$	2.00000	+	3.46410i	0.0926482	+	0.160471i
$467$	−10.0000	+	17.3205i	−0.462745	+	0.801498i	−0.999097	−	0.0424970i	$-0.986469\pi$
$467$	−10.0000	+	17.3205i	−0.462745	+	0.801498i	0.536352	+	0.843995i	$0.319802\pi$
$468$		0			0
$469$	5.00000	−	1.73205i	0.230879	−	0.0799787i
$470$		0			0
$471$	−2.00000	+	3.46410i	−0.0921551	+	0.159617i
$472$	−5.50000	−	9.52628i	−0.253158	−	0.438483i
$473$	5.00000	+	8.66025i	0.229900	+	0.398199i
$474$	1.50000	−	2.59808i	0.0688973	−	0.119334i
$475$		0			0
$476$	−8.00000	−	6.92820i	−0.366679	−	0.317554i
$477$	9.00000			0.412082
$478$	−6.00000	+	10.3923i	−0.274434	+	0.475333i
$479$	−19.0000	−	32.9090i	−0.868132	−	1.50365i	−0.863903	−	0.503658i	$-0.831987\pi$
$479$	−19.0000	−	32.9090i	−0.868132	−	1.50365i	−0.00422900	−	0.999991i	$-0.501346\pi$
$480$		0			0
$481$		0			0
$482$	25.0000			1.13872
$483$	−2.00000	+	10.3923i	−0.0910032	+	0.472866i
$484$	14.0000			0.636364
$485$		0			0
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	2.50000	+	4.33013i	0.113286	+	0.196217i	0.917093	−	0.398673i	$-0.130529\pi$
$487$	2.50000	+	4.33013i	0.113286	+	0.196217i	−0.803807	+	0.594890i	$0.797196\pi$
$488$	−3.00000	+	5.19615i	−0.135804	+	0.235219i
$489$	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
$493$	10.0000	+	17.3205i	0.450377	+	0.780076i
$494$		0			0
$495$		0			0
$496$	3.00000			0.134704
$497$	−1.00000	+	5.19615i	−0.0448561	+	0.233079i
$498$	−7.00000			−0.313678
$499$	−5.00000	+	8.66025i	−0.223831	+	0.387686i	−0.955968	−	0.293471i	$-0.905190\pi$
$499$	−5.00000	+	8.66025i	−0.223831	+	0.387686i	0.732137	+	0.681157i	$0.238523\pi$
$500$		0			0
$501$	−7.00000	−	12.1244i	−0.312737	−	0.541676i
$502$	10.5000	−	18.1865i	0.468638	−	0.811705i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$	2.00000	+	1.73205i	0.0890871	+	0.0771517i
$505$		0			0
$506$	10.0000	−	17.3205i	0.444554	−	0.769991i
$507$	6.50000	+	11.2583i	0.288675	+	0.500000i
$508$	4.50000	+	7.79423i	0.199655	+	0.345813i
$509$	−7.50000	+	12.9904i	−0.332432	+	0.575789i	−0.982988	−	0.183669i	$-0.941202\pi$
$509$	−7.50000	+	12.9904i	−0.332432	+	0.575789i	0.650556	+	0.759458i	$0.274536\pi$
$510$		0			0
$511$	−25.0000	+	8.66025i	−1.10593	+	0.383107i
$512$	−1.00000			−0.0441942
$513$	−4.00000	+	6.92820i	−0.176604	+	0.305888i
$514$	3.00000	+	5.19615i	0.132324	+	0.229192i
$515$		0			0
$516$	1.00000	−	1.73205i	0.0440225	−	0.0762493i
$517$	30.0000			1.31940
$518$	−10.0000	+	3.46410i	−0.439375	+	0.152204i
$519$	−22.0000			−0.965693
$520$		0			0
$521$	9.00000	+	15.5885i	0.394297	+	0.682943i	0.993011	−	0.118020i	$-0.0376547\pi$
$521$	9.00000	+	15.5885i	0.394297	+	0.682943i	−0.598714	+	0.800963i	$0.704321\pi$
$522$	−2.50000	−	4.33013i	−0.109422	−	0.189525i
$523$	4.00000	−	6.92820i	0.174908	−	0.302949i	−0.765222	−	0.643767i	$-0.777371\pi$
$523$	4.00000	−	6.92820i	0.174908	−	0.302949i	0.940129	+	0.340818i	$0.110704\pi$
$524$	1.00000			0.0436852
$525$		0			0
$526$	−30.0000			−1.30806
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$	−2.50000	−	4.33013i	−0.108799	−	0.188445i
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$		0			0
$531$	−11.0000			−0.477359
$532$	−4.00000	+	20.7846i	−0.173422	+	0.901127i
$533$		0			0
$534$	−3.00000	+	5.19615i	−0.129823	+	0.224860i
$535$		0			0
$536$	1.00000	+	1.73205i	0.0431934	+	0.0748132i
$537$	−6.00000	+	10.3923i	−0.258919	+	0.448461i
$538$	−31.0000			−1.33650
$539$	5.00000	+	34.6410i	0.215365	+	1.49209i
$540$		0			0
$541$	9.00000	−	15.5885i	0.386940	−	0.670200i	−0.605096	−	0.796152i	$-0.706865\pi$
$541$	9.00000	−	15.5885i	0.386940	−	0.670200i	0.992036	+	0.125952i	$0.0401986\pi$
$542$	7.50000	+	12.9904i	0.322153	+	0.557985i
$543$		0			0
$544$	2.00000	−	3.46410i	0.0857493	−	0.148522i
$545$		0			0
$546$		0			0
$547$	12.0000			0.513083			0.256541	−	0.966533i	$-0.417417\pi$
$547$	12.0000			0.513083			0.256541	+	0.966533i	$0.417417\pi$
$548$	−1.00000	+	1.73205i	−0.0427179	+	0.0739895i
$549$	3.00000	+	5.19615i	0.128037	+	0.221766i
$550$		0			0
$551$	20.0000	−	34.6410i	0.852029	−	1.47576i
$552$	−4.00000			−0.170251
$553$	−6.00000	−	5.19615i	−0.255146	−	0.220963i
$554$	−16.0000			−0.679775
$555$		0			0
$556$	7.00000	+	12.1244i	0.296866	+	0.514187i
$557$	−11.5000	−	19.9186i	−0.487271	−	0.843978i	0.512622	−	0.858614i	$-0.328674\pi$
$557$	−11.5000	−	19.9186i	−0.487271	−	0.843978i	−0.999893	+	0.0146368i	$0.995341\pi$
$558$	1.50000	−	2.59808i	0.0635001	−	0.109985i
$559$		0			0
$560$		0			0
$561$	20.0000			0.844401
$562$	1.00000	−	1.73205i	0.0421825	−	0.0730622i
$563$	8.50000	+	14.7224i	0.358232	+	0.620477i	0.987666	−	0.156578i	$-0.0500463\pi$
$563$	8.50000	+	14.7224i	0.358232	+	0.620477i	−0.629433	+	0.777055i	$0.716713\pi$
$564$	−3.00000	−	5.19615i	−0.126323	−	0.218797i
$565$		0			0
$566$	10.0000			0.420331
$567$	2.50000	−	0.866025i	0.104990	−	0.0363696i
$568$	−2.00000			−0.0839181
$569$	−12.0000	+	20.7846i	−0.503066	+	0.871336i	0.496928	+	0.867792i	$0.334461\pi$
$569$	−12.0000	+	20.7846i	−0.503066	+	0.871336i	−0.999994	+	0.00354413i	$0.998872\pi$
$570$		0			0
$571$	15.0000	+	25.9808i	0.627730	+	1.08726i	0.988006	+	0.154415i	$0.0493493\pi$
$571$	15.0000	+	25.9808i	0.627730	+	1.08726i	−0.360276	+	0.932846i	$0.617317\pi$
$572$		0			0
$573$	24.0000			1.00261
$574$		0			0
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	15.5000	+	26.8468i	0.645273	+	1.11765i	0.984238	+	0.176847i	$0.0565899\pi$
$577$	15.5000	+	26.8468i	0.645273	+	1.11765i	−0.338965	+	0.940799i	$0.610077\pi$
$578$	−0.500000	−	0.866025i	−0.0207973	−	0.0360219i
$579$	2.50000	−	4.33013i	0.103896	−	0.179954i
$580$		0			0
$581$	−3.50000	+	18.1865i	−0.145204	+	0.754505i
$582$	7.00000			0.290159
$583$	−22.5000	+	38.9711i	−0.931855	+	1.61402i
$584$	−5.00000	−	8.66025i	−0.206901	−	0.358364i
$585$		0			0
$586$	10.5000	−	18.1865i	0.433751	−	0.751279i
$587$	−35.0000			−1.44460			−0.722302	−	0.691577i	$-0.756916\pi$
$587$	−35.0000			−1.44460			−0.722302	+	0.691577i	$0.756916\pi$
$588$	5.50000	−	4.33013i	0.226816	−	0.178571i
$589$	24.0000			0.988903
$590$		0			0
$591$	1.00000	+	1.73205i	0.0411345	+	0.0712470i
$592$	−2.00000	−	3.46410i	−0.0821995	−	0.142374i
$593$	18.0000	−	31.1769i	0.739171	−	1.28028i	−0.213697	−	0.976900i	$-0.568551\pi$
$593$	18.0000	−	31.1769i	0.739171	−	1.28028i	0.952869	−	0.303383i	$-0.0981160\pi$
$594$	−5.00000			−0.205152
$595$		0			0
$596$	−18.0000			−0.737309
$597$	2.00000	−	3.46410i	0.0818546	−	0.141776i
$598$		0			0
$599$	15.0000	+	25.9808i	0.612883	+	1.06155i	0.990752	+	0.135686i	$0.0433238\pi$
$599$	15.0000	+	25.9808i	0.612883	+	1.06155i	−0.377869	+	0.925859i	$0.623343\pi$
$600$		0			0
$601$	35.0000			1.42768			0.713840	−	0.700309i	$-0.246954\pi$
$601$	35.0000			1.42768			0.713840	+	0.700309i	$0.246954\pi$
$602$	−4.00000	−	3.46410i	−0.163028	−	0.141186i
$603$	2.00000			0.0814463
$604$	−9.50000	+	16.4545i	−0.386550	+	0.669523i
$605$		0			0
$606$	5.00000	+	8.66025i	0.203111	+	0.351799i
$607$	−13.5000	+	23.3827i	−0.547948	+	0.949074i	0.450467	+	0.892793i	$0.351258\pi$
$607$	−13.5000	+	23.3827i	−0.547948	+	0.949074i	−0.998415	+	0.0562808i	$0.982076\pi$
$608$	−8.00000			−0.324443
$609$	−12.5000	+	4.33013i	−0.506526	+	0.175466i
$610$		0			0
$611$		0			0
$612$	−2.00000	−	3.46410i	−0.0808452	−	0.140028i
$613$	6.00000	+	10.3923i	0.242338	+	0.419741i	0.961380	−	0.275225i	$-0.0887525\pi$
$613$	6.00000	+	10.3923i	0.242338	+	0.419741i	−0.719042	+	0.694967i	$0.755419\pi$
$614$	−14.0000	+	24.2487i	−0.564994	+	0.978598i
$615$		0			0
$616$	−12.5000	+	4.33013i	−0.503639	+	0.174466i
$617$	−2.00000			−0.0805170			−0.0402585	−	0.999189i	$-0.512818\pi$
$617$	−2.00000			−0.0805170			−0.0402585	+	0.999189i	$0.512818\pi$
$618$	−4.00000	+	6.92820i	−0.160904	+	0.278693i
$619$	−5.00000	−	8.66025i	−0.200967	−	0.348085i	0.747873	−	0.663842i	$-0.231075\pi$
$619$	−5.00000	−	8.66025i	−0.200967	−	0.348085i	−0.948840	+	0.315757i	$0.897742\pi$
$620$		0			0
$621$	−2.00000	+	3.46410i	−0.0802572	+	0.139010i
$622$	32.0000			1.28308
$623$	12.0000	+	10.3923i	0.480770	+	0.416359i
$624$		0			0
$625$		0			0
$626$	−0.500000	−	0.866025i	−0.0199840	−	0.0346133i
$627$	−20.0000	−	34.6410i	−0.798723	−	1.38343i
$628$	−2.00000	+	3.46410i	−0.0798087	+	0.138233i
$629$	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	$0.623453\pi$
$632$	1.50000	−	2.59808i	0.0596668	−	0.103346i
$633$	−1.00000	−	1.73205i	−0.0397464	−	0.0688428i
$634$	−1.50000	−	2.59808i	−0.0595726	−	0.103183i
$635$		0			0
$636$	9.00000			0.356873
$637$		0			0
$638$	25.0000			0.989759
$639$	−1.00000	+	1.73205i	−0.0395594	+	0.0685189i
$640$		0			0
$641$	−13.0000	−	22.5167i	−0.513469	−	0.889355i	−0.999878	−	0.0156233i	$-0.995027\pi$
$641$	−13.0000	−	22.5167i	−0.513469	−	0.889355i	0.486409	−	0.873731i	$-0.338307\pi$
$642$	−1.50000	+	2.59808i	−0.0592003	+	0.102538i
$643$	−14.0000			−0.552106			−0.276053	−	0.961142i	$-0.589027\pi$
$643$	−14.0000			−0.552106			−0.276053	+	0.961142i	$0.589027\pi$
$644$	−2.00000	+	10.3923i	−0.0788110	+	0.409514i
$645$		0			0
$646$	16.0000	−	27.7128i	0.629512	−	1.09035i
$647$	−9.00000	−	15.5885i	−0.353827	−	0.612845i	0.633090	−	0.774078i	$-0.281786\pi$
$647$	−9.00000	−	15.5885i	−0.353827	−	0.612845i	−0.986916	+	0.161233i	$0.948453\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	27.5000	−	47.6314i	1.07947	−	1.86970i
$650$		0			0
$651$	−6.00000	−	5.19615i	−0.235159	−	0.203653i
$652$	4.00000			0.156652
$653$	−19.5000	+	33.7750i	−0.763094	+	1.32172i	0.178154	+	0.984003i	$0.442987\pi$
$653$	−19.5000	+	33.7750i	−0.763094	+	1.32172i	−0.941248	+	0.337715i	$0.890346\pi$
$654$	−1.00000	−	1.73205i	−0.0391031	−	0.0677285i
$655$		0			0
$656$		0			0
$657$	−10.0000			−0.390137
$658$	−15.0000	+	5.19615i	−0.584761	+	0.202567i
$659$	−40.0000			−1.55818			−0.779089	−	0.626913i	$-0.784318\pi$
$659$	−40.0000			−1.55818			−0.779089	+	0.626913i	$0.784318\pi$
$660$		0			0
$661$	−5.00000	−	8.66025i	−0.194477	−	0.336845i	0.752252	−	0.658876i	$-0.228968\pi$
$661$	−5.00000	−	8.66025i	−0.194477	−	0.336845i	−0.946729	+	0.322031i	$0.895634\pi$
$662$	−2.00000	−	3.46410i	−0.0777322	−	0.134636i
$663$		0			0
$664$	−7.00000			−0.271653
$665$		0			0
$666$	−4.00000			−0.154997
$667$	10.0000	−	17.3205i	0.387202	−	0.670653i
$668$	−7.00000	−	12.1244i	−0.270838	−	0.469105i
$669$	−3.50000	−	6.06218i	−0.135318	−	0.234377i
$670$		0			0
$671$	−30.0000			−1.15814
$672$	2.00000	+	1.73205i	0.0771517	+	0.0668153i
$673$	19.0000			0.732396			0.366198	−	0.930537i	$-0.380659\pi$
$673$	19.0000			0.732396			0.366198	+	0.930537i	$0.380659\pi$
$674$	−4.50000	+	7.79423i	−0.173334	+	0.300222i
$675$		0			0
$676$	6.50000	+	11.2583i	0.250000	+	0.433013i
$677$	−13.5000	+	23.3827i	−0.518847	+	0.898670i	0.480913	+	0.876768i	$0.340305\pi$
$677$	−13.5000	+	23.3827i	−0.518847	+	0.898670i	−0.999760	+	0.0219013i	$0.993028\pi$
$678$	16.0000			0.614476
$679$	3.50000	−	18.1865i	0.134318	−	0.697935i
$680$		0			0
$681$	1.50000	−	2.59808i	0.0574801	−	0.0995585i
$682$	7.50000	+	12.9904i	0.287190	+	0.497427i
$683$	−4.50000	−	7.79423i	−0.172188	−	0.298238i	0.766997	−	0.641651i	$-0.221750\pi$
$683$	−4.50000	−	7.79423i	−0.172188	−	0.298238i	−0.939184	+	0.343413i	$0.888417\pi$
$684$	−4.00000	+	6.92820i	−0.152944	+	0.264906i
$685$		0			0
$686$	−8.50000	−	16.4545i	−0.324532	−	0.628235i
$687$	−20.0000			−0.763048
$688$	1.00000	−	1.73205i	0.0381246	−	0.0660338i
$689$		0			0
$690$		0			0
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	−0.932024	−	0.362397i	$-0.881959\pi$
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	0.779857	+	0.625958i	$0.215292\pi$
$692$	−22.0000			−0.836315
$693$	−2.50000	+	12.9904i	−0.0949671	+	0.493464i
$694$	12.0000			0.455514
$695$		0			0
$696$	−2.50000	−	4.33013i	−0.0947623	−	0.164133i
$697$		0			0
$698$	−7.00000	+	12.1244i	−0.264954	+	0.458914i
$699$	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
$703$	−16.0000	−	27.7128i	−0.603451	−	1.04521i
$704$	−2.50000	−	4.33013i	−0.0942223	−	0.163198i
$705$		0			0
$706$	24.0000			0.903252
$707$	25.0000	−	8.66025i	0.940222	−	0.325702i
$708$	−11.0000			−0.413405
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	0.249952	+	0.968258i	$0.419585\pi$
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	−0.963512	+	0.267664i	$0.913748\pi$
$710$		0			0
$711$	−1.50000	−	2.59808i	−0.0562544	−	0.0974355i
$712$	−3.00000	+	5.19615i	−0.112430	+	0.194734i
$713$	12.0000			0.449404
$714$	−10.0000	+	3.46410i	−0.374241	+	0.129641i
$715$		0			0
$716$	−6.00000	+	10.3923i	−0.224231	+	0.388379i
$717$	6.00000	+	10.3923i	0.224074	+	0.388108i
$718$	5.00000	+	8.66025i	0.186598	+	0.323198i
$719$	3.00000	−	5.19615i	0.111881	−	0.193784i	−0.804648	−	0.593753i	$-0.797646\pi$
$719$	3.00000	−	5.19615i	0.111881	−	0.193784i	0.916529	+	0.399969i	$0.130979\pi$
$720$		0			0
$721$	16.0000	+	13.8564i	0.595871	+	0.516040i
$722$	−45.0000			−1.67473
$723$	12.5000	−	21.6506i	0.464880	−	0.805196i
$724$		0			0
$725$		0			0
$726$	7.00000	−	12.1244i	0.259794	−	0.449977i
$727$	−7.00000			−0.259616			−0.129808	−	0.991539i	$-0.541436\pi$
$727$	−7.00000			−0.259616			−0.129808	+	0.991539i	$0.541436\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	4.00000	+	6.92820i	0.147945	+	0.256249i
$732$	3.00000	+	5.19615i	0.110883	+	0.192055i
$733$	−3.00000	+	5.19615i	−0.110808	+	0.191924i	−0.916096	−	0.400959i	$-0.868677\pi$
$733$	−3.00000	+	5.19615i	−0.110808	+	0.191924i	0.805289	+	0.592883i	$0.202010\pi$
$734$	17.0000			0.627481
$735$		0			0
$736$	−4.00000			−0.147442
$737$	−5.00000	+	8.66025i	−0.184177	+	0.319005i
$738$		0			0
$739$	15.0000	+	25.9808i	0.551784	+	0.955718i	0.998146	+	0.0608653i	$0.0193860\pi$
$739$	15.0000	+	25.9808i	0.551784	+	0.955718i	−0.446362	+	0.894852i	$0.647281\pi$
$740$		0			0
$741$		0			0
$742$	4.50000	−	23.3827i	0.165200	−	0.858405i
$743$	−30.0000			−1.10059			−0.550297	−	0.834969i	$-0.685485\pi$
$743$	−30.0000			−1.10059			−0.550297	+	0.834969i	$0.685485\pi$
$744$	1.50000	−	2.59808i	0.0549927	−	0.0952501i
$745$		0			0
$746$	16.0000	+	27.7128i	0.585802	+	1.01464i
$747$	−3.50000	+	6.06218i	−0.128058	+	0.221803i
$748$	20.0000			0.731272
$749$	6.00000	+	5.19615i	0.219235	+	0.189863i
$750$		0			0
$751$	−22.5000	+	38.9711i	−0.821037	+	1.42208i	0.0838743	+	0.996476i	$0.473271\pi$
$751$	−22.5000	+	38.9711i	−0.821037	+	1.42208i	−0.904911	+	0.425601i	$0.860063\pi$
$752$	−3.00000	−	5.19615i	−0.109399	−	0.189484i
$753$	−10.5000	−	18.1865i	−0.382641	−	0.662754i
$754$		0			0
$755$		0			0
$756$	2.50000	−	0.866025i	0.0909241	−	0.0314970i
$757$	54.0000			1.96266			0.981332	−	0.192323i	$-0.0616021\pi$
$757$	54.0000			1.96266			0.981332	+	0.192323i	$0.0616021\pi$
$758$	8.00000	−	13.8564i	0.290573	−	0.503287i
$759$	−10.0000	−	17.3205i	−0.362977	−	0.628695i
$760$		0			0
$761$	−4.00000	+	6.92820i	−0.145000	+	0.251147i	−0.929373	−	0.369142i	$-0.879652\pi$
$761$	−4.00000	+	6.92820i	−0.145000	+	0.251147i	0.784373	+	0.620289i	$0.212985\pi$
$762$	9.00000			0.326036
$763$	−5.00000	+	1.73205i	−0.181012	+	0.0627044i
$764$	24.0000			0.868290
$765$		0			0
$766$	17.0000	+	29.4449i	0.614235	+	1.06389i
$767$		0			0
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	−35.0000			−1.26213			−0.631066	−	0.775729i	$-0.717382\pi$
$769$	−35.0000			−1.26213			−0.631066	+	0.775729i	$0.717382\pi$
$770$		0			0
$771$	6.00000			0.216085
$772$	2.50000	−	4.33013i	0.0899770	−	0.155845i
$773$	5.00000	+	8.66025i	0.179838	+	0.311488i	0.941825	−	0.336104i	$-0.109109\pi$
$773$	5.00000	+	8.66025i	0.179838	+	0.311488i	−0.761987	+	0.647592i	$0.775776\pi$
$774$	−1.00000	−	1.73205i	−0.0359443	−	0.0622573i
$775$		0			0
$776$	7.00000			0.251285
$777$	−2.00000	+	10.3923i	−0.0717496	+	0.372822i
$778$	2.00000			0.0717035
$779$		0			0
$780$		0			0
$781$	−5.00000	−	8.66025i	−0.178914	−	0.309888i
$782$	8.00000	−	13.8564i	0.286079	−	0.495504i
$783$	−5.00000			−0.178685
$784$	5.50000	−	4.33013i	0.196429	−	0.154647i
$785$		0			0
$786$	0.500000	−	0.866025i	0.0178344	−	0.0308901i
$787$	−9.00000	−	15.5885i	−0.320815	−	0.555668i	0.659841	−	0.751405i	$-0.270624\pi$
$787$	−9.00000	−	15.5885i	−0.320815	−	0.555668i	−0.980656	+	0.195737i	$0.937290\pi$
$788$	1.00000	+	1.73205i	0.0356235	+	0.0617018i
$789$	−15.0000	+	25.9808i	−0.534014	+	0.924940i
$790$		0			0
$791$	8.00000	−	41.5692i	0.284447	−	1.47803i
$792$	−5.00000			−0.177667
$793$		0			0
$794$	−18.0000	−	31.1769i	−0.638796	−	1.10643i
$795$		0			0
$796$	2.00000	−	3.46410i	0.0708881	−	0.122782i
$797$	−21.0000			−0.743858			−0.371929	−	0.928261i	$-0.621304\pi$
$797$	−21.0000			−0.743858			−0.371929	+	0.928261i	$0.621304\pi$
$798$	16.0000	+	13.8564i	0.566394	+	0.490511i
$799$	24.0000			0.849059
$800$		0			0
$801$	3.00000	+	5.19615i	0.106000	+	0.183597i
$802$	12.0000	+	20.7846i	0.423735	+	0.733930i
$803$	25.0000	−	43.3013i	0.882231	−	1.52807i
$804$	2.00000			0.0705346
$805$		0			0
$806$		0			0
$807$	−15.5000	+	26.8468i	−0.545626	+	0.945052i
$808$	5.00000	+	8.66025i	0.175899	+	0.304667i
$809$	−20.0000	−	34.6410i	−0.703163	−	1.21791i	−0.967351	−	0.253442i	$-0.918437\pi$
$809$	−20.0000	−	34.6410i	−0.703163	−	1.21791i	0.264188	−	0.964471i	$-0.414896\pi$
$810$		0			0
$811$	−14.0000			−0.491606			−0.245803	−	0.969320i	$-0.579052\pi$
$811$	−14.0000			−0.491606			−0.245803	+	0.969320i	$0.579052\pi$
$812$	−12.5000	+	4.33013i	−0.438664	+	0.151958i
$813$	15.0000			0.526073
$814$	10.0000	−	17.3205i	0.350500	−	0.607083i
$815$		0			0
$816$	−2.00000	−	3.46410i	−0.0700140	−	0.121268i
$817$	8.00000	−	13.8564i	0.279885	−	0.484774i
$818$	25.0000			0.874105
$819$		0			0
$820$		0			0
$821$	12.5000	−	21.6506i	0.436253	−	0.755612i	−0.561144	−	0.827718i	$-0.689639\pi$
$821$	12.5000	−	21.6506i	0.436253	−	0.755612i	0.997397	+	0.0721058i	$0.0229719\pi$
$822$	1.00000	+	1.73205i	0.0348790	+	0.0604122i
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	0.969448	+	0.245295i	$0.0788849\pi$
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	−0.272292	+	0.962215i	$0.587782\pi$
$824$	−4.00000	+	6.92820i	−0.139347	+	0.241355i
$825$		0			0
$826$	−5.50000	+	28.5788i	−0.191369	+	0.994385i
$827$	−9.00000			−0.312961			−0.156480	−	0.987681i	$-0.550015\pi$
$827$	−9.00000			−0.312961			−0.156480	+	0.987681i	$0.550015\pi$
$828$	−2.00000	+	3.46410i	−0.0695048	+	0.120386i
$829$	16.0000	+	27.7128i	0.555703	+	0.962506i	0.997848	+	0.0655624i	$0.0208842\pi$
$829$	16.0000	+	27.7128i	0.555703	+	0.962506i	−0.442145	+	0.896943i	$0.645783\pi$
$830$		0			0
$831$	−8.00000	+	13.8564i	−0.277517	+	0.480673i
$832$		0			0
$833$	4.00000	+	27.7128i	0.138592	+	0.960192i
$834$	14.0000			0.484780
$835$		0			0
$836$	−20.0000	−	34.6410i	−0.691714	−	1.19808i
$837$	−1.50000	−	2.59808i	−0.0518476	−	0.0898027i
$838$		0			0
$839$	−28.0000			−0.966667			−0.483334	−	0.875436i	$-0.660574\pi$
$839$	−28.0000			−0.966667			−0.483334	+	0.875436i	$0.660574\pi$
$840$		0			0
$841$	−4.00000			−0.137931
$842$	15.0000	−	25.9808i	0.516934	−	0.895356i
$843$	−1.00000	−	1.73205i	−0.0344418	−	0.0596550i
$844$	−1.00000	−	1.73205i	−0.0344214	−	0.0596196i
$845$		0			0
$846$	−6.00000			−0.206284
$847$	−28.0000	−	24.2487i	−0.962091	−	0.833196i
$848$	9.00000			0.309061
$849$	5.00000	−	8.66025i	0.171600	−	0.297219i
$850$		0			0
$851$	−8.00000	−	13.8564i	−0.274236	−	0.474991i
$852$	−1.00000	+	1.73205i	−0.0342594	+	0.0593391i
$853$	−14.0000			−0.479351			−0.239675	−	0.970853i	$-0.577041\pi$
$853$	−14.0000			−0.479351			−0.239675	+	0.970853i	$0.577041\pi$
$854$	15.0000	−	5.19615i	0.513289	−	0.177809i
$855$		0			0
$856$	−1.50000	+	2.59808i	−0.0512689	+	0.0888004i
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	0.670366	−	0.742030i	$-0.266137\pi$
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	−0.977800	+	0.209539i	$0.932804\pi$
$858$		0			0
$859$	17.0000	−	29.4449i	0.580033	−	1.00465i	−0.415442	−	0.909620i	$-0.636373\pi$
$859$	17.0000	−	29.4449i	0.580033	−	1.00465i	0.995475	−	0.0950262i	$-0.0302935\pi$
$860$		0			0
$861$		0			0
$862$	−12.0000			−0.408722
$863$	5.00000	−	8.66025i	0.170202	−	0.294798i	−0.768288	−	0.640104i	$-0.778891\pi$
$863$	5.00000	−	8.66025i	0.170202	−	0.294798i	0.938490	+	0.345305i	$0.112225\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$		0			0
$866$	−7.00000	+	12.1244i	−0.237870	+	0.412002i
$867$	−1.00000			−0.0339618
$868$	−6.00000	−	5.19615i	−0.203653	−	0.176369i
$869$	15.0000			0.508840
$870$		0			0
$871$		0			0
$872$	−1.00000	−	1.73205i	−0.0338643	−	0.0586546i
$873$	3.50000	−	6.06218i	0.118457	−	0.205174i
$874$	−32.0000			−1.08242
$875$		0			0
$876$	−10.0000			−0.337869
$877$	−16.0000	+	27.7128i	−0.540282	+	0.935795i	0.458606	+	0.888640i	$0.348349\pi$
$877$	−16.0000	+	27.7128i	−0.540282	+	0.935795i	−0.998888	+	0.0471555i	$0.984984\pi$
$878$	7.50000	+	12.9904i	0.253113	+	0.438404i
$879$	−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	$0.750181\pi$
$882$	−1.00000	−	6.92820i	−0.0336718	−	0.233285i
$883$	40.0000			1.34611			0.673054	−	0.739594i	$-0.264982\pi$
$883$	40.0000			1.34611			0.673054	+	0.739594i	$0.264982\pi$
$884$		0			0
$885$		0			0
$886$	−8.50000	−	14.7224i	−0.285563	−	0.494610i
$887$	18.0000	−	31.1769i	0.604381	−	1.04682i	−0.387768	−	0.921757i	$-0.626754\pi$
$887$	18.0000	−	31.1769i	0.604381	−	1.04682i	0.992149	−	0.125061i	$-0.0399128\pi$
$888$	−4.00000			−0.134231
$889$	4.50000	−	23.3827i	0.150925	−	0.784230i
$890$		0			0
$891$	−2.50000	+	4.33013i	−0.0837532	+	0.145065i
$892$	−3.50000	−	6.06218i	−0.117189	−	0.202977i
$893$	−24.0000	−	41.5692i	−0.803129	−	1.39106i
$894$	−9.00000	+	15.5885i	−0.301005	+	0.521356i
$895$		0			0
$896$	2.00000	+	1.73205i	0.0668153	+	0.0578638i
$897$		0			0
$898$	8.00000	−	13.8564i	0.266963	−	0.462394i
$899$	7.50000	+	12.9904i	0.250139	+	0.433253i
$900$		0			0
$901$	−18.0000	+	31.1769i	−0.599667	+	1.03865i
$902$		0			0
$903$	−5.00000	+	1.73205i	−0.166390	+	0.0576390i
$904$	16.0000			0.532152
$905$		0			0
$906$	9.50000	+	16.4545i	0.315616	+	0.546664i
$907$	6.00000	+	10.3923i	0.199227	+	0.345071i	0.948278	−	0.317441i	$-0.102824\pi$
$907$	6.00000	+	10.3923i	0.199227	+	0.345071i	−0.749051	+	0.662512i	$0.769490\pi$
$908$	1.50000	−	2.59808i	0.0497792	−	0.0862202i
$909$	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	$0.334445\pi$
$912$	−4.00000	+	6.92820i	−0.132453	+	0.229416i
$913$	−17.5000	−	30.3109i	−0.579165	−	1.00314i
$914$	−15.5000	−	26.8468i	−0.512694	−	0.888013i
$915$		0			0
$916$	−20.0000			−0.660819
$917$	−2.00000	−	1.73205i	−0.0660458	−	0.0571974i
$918$	−4.00000			−0.132020
$919$	16.0000	−	27.7128i	0.527791	−	0.914161i	−0.471684	−	0.881768i	$-0.656354\pi$
$919$	16.0000	−	27.7128i	0.527791	−	0.914161i	0.999475	−	0.0323936i	$-0.0103130\pi$
$920$		0			0
$921$	14.0000	+	24.2487i	0.461316	+	0.799022i
$922$	−7.00000	+	12.1244i	−0.230533	+	0.399294i
$923$		0			0
$924$	−2.50000	+	12.9904i	−0.0822440	+	0.427352i
$925$		0			0
$926$	−8.00000	+	13.8564i	−0.262896	+	0.455350i
$927$	4.00000	+	6.92820i	0.131377	+	0.227552i
$928$	−2.50000	−	4.33013i	−0.0820665	−	0.142143i
$929$	3.00000	−	5.19615i	0.0984268	−	0.170480i	−0.812607	−	0.582812i	$-0.801952\pi$
$929$	3.00000	−	5.19615i	0.0984268	−	0.170480i	0.911034	+	0.412332i	$0.135286\pi$
$930$		0			0
$931$	44.0000	−	34.6410i	1.44204	−	1.13531i
$932$	4.00000			0.131024
$933$	16.0000	−	27.7128i	0.523816	−	0.907277i
$934$	10.0000	+	17.3205i	0.327210	+	0.566744i
$935$		0			0
$936$		0			0
$937$	−35.0000			−1.14340			−0.571700	−	0.820463i	$-0.693716\pi$
$937$	−35.0000			−1.14340			−0.571700	+	0.820463i	$0.693716\pi$
$938$	1.00000	−	5.19615i	0.0326512	−	0.169660i
$939$	−1.00000			−0.0326338
$940$		0			0
$941$	5.50000	+	9.52628i	0.179295	+	0.310548i	0.941639	−	0.336624i	$-0.109285\pi$
$941$	5.50000	+	9.52628i	0.179295	+	0.310548i	−0.762344	+	0.647172i	$0.775952\pi$
$942$	2.00000	+	3.46410i	0.0651635	+	0.112867i
$943$		0			0
$944$	−11.0000			−0.358020
$945$		0			0
$946$	10.0000			0.325128
$947$	−16.0000	+	27.7128i	−0.519930	+	0.900545i	0.479801	+	0.877377i	$0.340709\pi$
$947$	−16.0000	+	27.7128i	−0.519930	+	0.900545i	−0.999732	+	0.0231683i	$0.992625\pi$
$948$	−1.50000	−	2.59808i	−0.0487177	−	0.0843816i
$949$		0			0
$950$		0			0
$951$	−3.00000			−0.0972817
$952$	−10.0000	+	3.46410i	−0.324102	+	0.112272i
$953$	−2.00000			−0.0647864			−0.0323932	−	0.999475i	$-0.510313\pi$
$953$	−2.00000			−0.0647864			−0.0323932	+	0.999475i	$0.510313\pi$
$954$	4.50000	−	7.79423i	0.145693	−	0.252347i
$955$		0			0
$956$	6.00000	+	10.3923i	0.194054	+	0.336111i
$957$	12.5000	−	21.6506i	0.404068	−	0.699866i
$958$	−38.0000			−1.22772
$959$	5.00000	−	1.73205i	0.161458	−	0.0559308i
$960$		0			0
$961$	11.0000	−	19.0526i	0.354839	−	0.614599i
$962$		0			0
$963$	1.50000	+	2.59808i	0.0483368	+	0.0837218i
$964$	12.5000	−	21.6506i	0.402598	−	0.697320i
$965$		0			0
$966$	8.00000	+	6.92820i	0.257396	+	0.222911i
$967$	61.0000			1.96163			0.980814	−	0.194946i	$-0.0624533\pi$
$967$	61.0000			1.96163			0.980814	+	0.194946i	$0.0624533\pi$
$968$	7.00000	−	12.1244i	0.224989	−	0.389692i
$969$	−16.0000	−	27.7128i	−0.513994	−	0.890264i
$970$		0			0
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	−0.960910	−	0.276861i	$-0.910706\pi$
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	0.720224	+	0.693742i	$0.244039\pi$
$972$	1.00000			0.0320750
$973$	7.00000	−	36.3731i	0.224410	−	1.16607i
$974$	5.00000			0.160210
$975$		0			0
$976$	3.00000	+	5.19615i	0.0960277	+	0.166325i
$977$	−15.0000	−	25.9808i	−0.479893	−	0.831198i	0.519841	−	0.854263i	$-0.325991\pi$
$977$	−15.0000	−	25.9808i	−0.479893	−	0.831198i	−0.999734	+	0.0230645i	$0.992658\pi$
$978$	2.00000	−	3.46410i	0.0639529	−	0.110770i
$979$	−30.0000			−0.958804
$980$		0			0
$981$	−2.00000			−0.0638551
$982$	4.50000	−	7.79423i	0.143601	−	0.248724i
$983$	−30.0000	−	51.9615i	−0.956851	−	1.65732i	−0.730073	−	0.683369i	$-0.760514\pi$
$983$	−30.0000	−	51.9615i	−0.956851	−	1.65732i	−0.226778	−	0.973946i	$-0.572819\pi$
$984$		0			0
$985$		0			0
$986$	20.0000			0.636930
$987$	−3.00000	+	15.5885i	−0.0954911	+	0.496186i
$988$		0			0
$989$	4.00000	−	6.92820i	0.127193	−	0.220304i
$990$		0			0
$991$	−23.5000	−	40.7032i	−0.746502	−	1.29298i	−0.949490	−	0.313798i	$-0.898398\pi$
$991$	−23.5000	−	40.7032i	−0.746502	−	1.29298i	0.202988	−	0.979181i	$-0.434935\pi$
$992$	1.50000	−	2.59808i	0.0476250	−	0.0824890i
$993$	−4.00000			−0.126936
$994$	4.00000	+	3.46410i	0.126872	+	0.109875i
$995$		0			0
$996$	−3.50000	+	6.06218i	−0.110902	+	0.192087i
$997$	19.0000	+	32.9090i	0.601736	+	1.04224i	0.992558	+	0.121771i	$0.0388574\pi$
$997$	19.0000	+	32.9090i	0.601736	+	1.04224i	−0.390822	+	0.920466i	$0.627809\pi$
$998$	5.00000	+	8.66025i	0.158272	+	0.274136i
$999$	−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.i.l.751.1		2
5.2	odd	4		1050.2.o.a.499.2		4
5.3	odd	4		1050.2.o.a.499.1		4
5.4	even	2		42.2.e.a.37.1	yes	2
7.2	even	3		7350.2.a.bl.1.1		1
7.4	even	3	inner	1050.2.i.l.151.1		2
7.5	odd	6		7350.2.a.q.1.1		1
15.14	odd	2		126.2.g.c.37.1		2
20.19	odd	2		336.2.q.b.289.1		2
35.4	even	6		42.2.e.a.25.1	✓	2
35.9	even	6		294.2.a.e.1.1		1
35.18	odd	12		1050.2.o.a.949.2		4
35.19	odd	6		294.2.a.f.1.1		1
35.24	odd	6		294.2.e.b.67.1		2
35.32	odd	12		1050.2.o.a.949.1		4
35.34	odd	2		294.2.e.b.79.1		2
40.19	odd	2		1344.2.q.s.961.1		2
40.29	even	2		1344.2.q.g.961.1		2
45.4	even	6		1134.2.h.e.541.1		2
45.14	odd	6		1134.2.h.l.541.1		2
45.29	odd	6		1134.2.e.e.919.1		2
45.34	even	6		1134.2.e.l.919.1		2
60.59	even	2		1008.2.s.k.289.1		2
105.44	odd	6		882.2.a.c.1.1		1
105.59	even	6		882.2.g.i.361.1		2
105.74	odd	6		126.2.g.c.109.1		2
105.89	even	6		882.2.a.d.1.1		1
105.104	even	2		882.2.g.i.667.1		2
140.19	even	6		2352.2.a.f.1.1		1
140.39	odd	6		336.2.q.b.193.1		2
140.59	even	6		2352.2.q.u.1537.1		2
140.79	odd	6		2352.2.a.t.1.1		1
140.139	even	2		2352.2.q.u.961.1		2
280.19	even	6		9408.2.a.cr.1.1		1
280.109	even	6		1344.2.q.g.193.1		2
280.149	even	6		9408.2.a.ce.1.1		1
280.179	odd	6		1344.2.q.s.193.1		2
280.219	odd	6		9408.2.a.q.1.1		1
280.229	odd	6		9408.2.a.z.1.1		1
315.4	even	6		1134.2.e.l.865.1		2
315.74	odd	6		1134.2.h.l.109.1		2
315.214	even	6		1134.2.h.e.109.1		2
315.284	odd	6		1134.2.e.e.865.1		2
420.179	even	6		1008.2.s.k.865.1		2
420.299	odd	6		7056.2.a.bl.1.1		1
420.359	even	6		7056.2.a.w.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.2.e.a.25.1	✓	2	35.4	even	6
42.2.e.a.37.1	yes	2	5.4	even	2
126.2.g.c.37.1		2	15.14	odd	2
126.2.g.c.109.1		2	105.74	odd	6
294.2.a.e.1.1		1	35.9	even	6
294.2.a.f.1.1		1	35.19	odd	6
294.2.e.b.67.1		2	35.24	odd	6
294.2.e.b.79.1		2	35.34	odd	2
336.2.q.b.193.1		2	140.39	odd	6
336.2.q.b.289.1		2	20.19	odd	2
882.2.a.c.1.1		1	105.44	odd	6
882.2.a.d.1.1		1	105.89	even	6
882.2.g.i.361.1		2	105.59	even	6
882.2.g.i.667.1		2	105.104	even	2
1008.2.s.k.289.1		2	60.59	even	2
1008.2.s.k.865.1		2	420.179	even	6
1050.2.i.l.151.1		2	7.4	even	3	inner
1050.2.i.l.751.1		2	1.1	even	1	trivial
1050.2.o.a.499.1		4	5.3	odd	4
1050.2.o.a.499.2		4	5.2	odd	4
1050.2.o.a.949.1		4	35.32	odd	12
1050.2.o.a.949.2		4	35.18	odd	12
1134.2.e.e.865.1		2	315.284	odd	6
1134.2.e.e.919.1		2	45.29	odd	6
1134.2.e.l.865.1		2	315.4	even	6
1134.2.e.l.919.1		2	45.34	even	6
1134.2.h.e.109.1		2	315.214	even	6
1134.2.h.e.541.1		2	45.4	even	6
1134.2.h.l.109.1		2	315.74	odd	6
1134.2.h.l.541.1		2	45.14	odd	6
1344.2.q.g.193.1		2	280.109	even	6
1344.2.q.g.961.1		2	40.29	even	2
1344.2.q.s.193.1		2	280.179	odd	6
1344.2.q.s.961.1		2	40.19	odd	2
2352.2.a.f.1.1		1	140.19	even	6
2352.2.a.t.1.1		1	140.79	odd	6
2352.2.q.u.961.1		2	140.139	even	2
2352.2.q.u.1537.1		2	140.59	even	6
7056.2.a.w.1.1		1	420.359	even	6
7056.2.a.bl.1.1		1	420.299	odd	6
7350.2.a.q.1.1		1	7.5	odd	6
7350.2.a.bl.1.1		1	7.2	even	3
9408.2.a.q.1.1		1	280.219	odd	6
9408.2.a.z.1.1		1	280.229	odd	6
9408.2.a.ce.1.1		1	280.149	even	6
9408.2.a.cr.1.1		1	280.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.50000 - 4.33013i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(2.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-4.00000 + 6.92820i) q^{19} +(2.50000 - 0.866025i) q^{21} -5.00000 q^{22} +(-2.00000 + 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{24} +1.00000 q^{27} +(2.50000 - 0.866025i) q^{28} -5.00000 q^{29} +(-1.50000 - 2.59808i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.50000 + 4.33013i) q^{33} -4.00000 q^{34} +1.00000 q^{36} +(-2.00000 + 3.46410i) q^{37} +(4.00000 + 6.92820i) q^{38} +(0.500000 - 2.59808i) q^{42} -2.00000 q^{43} +(-2.50000 + 4.33013i) q^{44} +(2.00000 + 3.46410i) q^{46} +(-3.00000 + 5.19615i) q^{47} +1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} +(-2.00000 + 3.46410i) q^{51} +(-4.50000 - 7.79423i) q^{53} +(0.500000 - 0.866025i) q^{54} +(0.500000 - 2.59808i) q^{56} +8.00000 q^{57} +(-2.50000 + 4.33013i) q^{58} +(5.50000 + 9.52628i) q^{59} +(3.00000 - 5.19615i) q^{61} -3.00000 q^{62} +(-2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(2.50000 + 4.33013i) q^{66} +(-1.00000 - 1.73205i) q^{67} +(-2.00000 + 3.46410i) q^{68} +4.00000 q^{69} +2.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(5.00000 + 8.66025i) q^{73} +(2.00000 + 3.46410i) q^{74} +8.00000 q^{76} +(12.5000 - 4.33013i) q^{77} +(-1.50000 + 2.59808i) q^{79} +(-0.500000 - 0.866025i) q^{81} +7.00000 q^{83} +(-2.00000 - 1.73205i) q^{84} +(-1.00000 + 1.73205i) q^{86} +(2.50000 + 4.33013i) q^{87} +(2.50000 + 4.33013i) q^{88} +(3.00000 - 5.19615i) q^{89} +4.00000 q^{92} +(-1.50000 + 2.59808i) q^{93} +(3.00000 + 5.19615i) q^{94} +(0.500000 - 0.866025i) q^{96} -7.00000 q^{97} +(-5.50000 + 4.33013i) q^{98} +5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} - q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 - q^3 - q^4 - 2 * q^6 - q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} - q^{7} - 2 q^{8} - q^{9} - 5 q^{11} - q^{12} + 4 q^{14} - q^{16} - 4 q^{17} + q^{18} - 8 q^{19} + 5 q^{21} - 10 q^{22} - 4 q^{23} + q^{24} + 2 q^{27} + 5 q^{28} - 10 q^{29} - 3 q^{31} + q^{32} - 5 q^{33} - 8 q^{34} + 2 q^{36} - 4 q^{37} + 8 q^{38} + q^{42} - 4 q^{43} - 5 q^{44} + 4 q^{46} - 6 q^{47} + 2 q^{48} - 13 q^{49} - 4 q^{51} - 9 q^{53} + q^{54} + q^{56} + 16 q^{57} - 5 q^{58} + 11 q^{59} + 6 q^{61} - 6 q^{62} - 4 q^{63} + 2 q^{64} + 5 q^{66} - 2 q^{67} - 4 q^{68} + 8 q^{69} + 4 q^{71} + q^{72} + 10 q^{73} + 4 q^{74} + 16 q^{76} + 25 q^{77} - 3 q^{79} - q^{81} + 14 q^{83} - 4 q^{84} - 2 q^{86} + 5 q^{87} + 5 q^{88} + 6 q^{89} + 8 q^{92} - 3 q^{93} + 6 q^{94} + q^{96} - 14 q^{97} - 11 q^{98} + 10 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 - 2 * q^6 - q^7 - 2 * q^8 - q^9 - 5 * q^11 - q^12 + 4 * q^14 - q^16 - 4 * q^17 + q^18 - 8 * q^19 + 5 * q^21 - 10 * q^22 - 4 * q^23 + q^24 + 2 * q^27 + 5 * q^28 - 10 * q^29 - 3 * q^31 + q^32 - 5 * q^33 - 8 * q^34 + 2 * q^36 - 4 * q^37 + 8 * q^38 + q^42 - 4 * q^43 - 5 * q^44 + 4 * q^46 - 6 * q^47 + 2 * q^48 - 13 * q^49 - 4 * q^51 - 9 * q^53 + q^54 + q^56 + 16 * q^57 - 5 * q^58 + 11 * q^59 + 6 * q^61 - 6 * q^62 - 4 * q^63 + 2 * q^64 + 5 * q^66 - 2 * q^67 - 4 * q^68 + 8 * q^69 + 4 * q^71 + q^72 + 10 * q^73 + 4 * q^74 + 16 * q^76 + 25 * q^77 - 3 * q^79 - q^81 + 14 * q^83 - 4 * q^84 - 2 * q^86 + 5 * q^87 + 5 * q^88 + 6 * q^89 + 8 * q^92 - 3 * q^93 + 6 * q^94 + q^96 - 14 * q^97 - 11 * q^98 + 10 * q^99

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