LMFDB - Embedded newform 1110.2.h.c.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(961,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("1110.961");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.h (of order $2$, degree $1$, 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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			961.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	1110.961
Dual form			1110.2.h.c.961.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} -1.00000i q^{6} +1.00000 q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} -1.00000i q^{6} +1.00000 q^{7} +1.00000i q^{8} +1.00000 q^{9} -1.00000 q^{10} +3.00000 q^{11} -1.00000 q^{12} -6.00000i q^{13} -1.00000i q^{14} -1.00000i q^{15} +1.00000 q^{16} -3.00000i q^{17} -1.00000i q^{18} +6.00000i q^{19} +1.00000i q^{20} +1.00000 q^{21} -3.00000i q^{22} +6.00000i q^{23} +1.00000i q^{24} -1.00000 q^{25} -6.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} -9.00000i q^{29} -1.00000 q^{30} +3.00000i q^{31} -1.00000i q^{32} +3.00000 q^{33} -3.00000 q^{34} -1.00000i q^{35} -1.00000 q^{36} +(1.00000 - 6.00000i) q^{37} +6.00000 q^{38} -6.00000i q^{39} +1.00000 q^{40} +9.00000 q^{41} -1.00000i q^{42} -9.00000i q^{43} -3.00000 q^{44} -1.00000i q^{45} +6.00000 q^{46} +1.00000 q^{48} -6.00000 q^{49} +1.00000i q^{50} -3.00000i q^{51} +6.00000i q^{52} +3.00000 q^{53} -1.00000i q^{54} -3.00000i q^{55} +1.00000i q^{56} +6.00000i q^{57} -9.00000 q^{58} +1.00000i q^{60} -9.00000i q^{61} +3.00000 q^{62} +1.00000 q^{63} -1.00000 q^{64} -6.00000 q^{65} -3.00000i q^{66} -14.0000 q^{67} +3.00000i q^{68} +6.00000i q^{69} -1.00000 q^{70} +6.00000 q^{71} +1.00000i q^{72} -2.00000 q^{73} +(-6.00000 - 1.00000i) q^{74} -1.00000 q^{75} -6.00000i q^{76} +3.00000 q^{77} -6.00000 q^{78} -1.00000i q^{80} +1.00000 q^{81} -9.00000i q^{82} -1.00000 q^{84} -3.00000 q^{85} -9.00000 q^{86} -9.00000i q^{87} +3.00000i q^{88} +12.0000i q^{89} -1.00000 q^{90} -6.00000i q^{91} -6.00000i q^{92} +3.00000i q^{93} +6.00000 q^{95} -1.00000i q^{96} +3.00000i q^{97} +6.00000i q^{98} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} - 2 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^3 - 2 * q^4 + 2 * q^7 + 2 * q^9	$ 2 q + 2 q^{3} - 2 q^{4} + 2 q^{7} + 2 q^{9} - 2 q^{10} + 6 q^{11} - 2 q^{12} + 2 q^{16} + 2 q^{21} - 2 q^{25} - 12 q^{26} + 2 q^{27} - 2 q^{28} - 2 q^{30} + 6 q^{33} - 6 q^{34} - 2 q^{36} + 2 q^{37} + 12 q^{38} + 2 q^{40} + 18 q^{41} - 6 q^{44} + 12 q^{46} + 2 q^{48} - 12 q^{49} + 6 q^{53} - 18 q^{58} + 6 q^{62} + 2 q^{63} - 2 q^{64} - 12 q^{65} - 28 q^{67} - 2 q^{70} + 12 q^{71} - 4 q^{73} - 12 q^{74} - 2 q^{75} + 6 q^{77} - 12 q^{78} + 2 q^{81} - 2 q^{84} - 6 q^{85} - 18 q^{86} - 2 q^{90} + 12 q^{95} + 6 q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 - 2 * q^4 + 2 * q^7 + 2 * q^9 - 2 * q^10 + 6 * q^11 - 2 * q^12 + 2 * q^16 + 2 * q^21 - 2 * q^25 - 12 * q^26 + 2 * q^27 - 2 * q^28 - 2 * q^30 + 6 * q^33 - 6 * q^34 - 2 * q^36 + 2 * q^37 + 12 * q^38 + 2 * q^40 + 18 * q^41 - 6 * q^44 + 12 * q^46 + 2 * q^48 - 12 * q^49 + 6 * q^53 - 18 * q^58 + 6 * q^62 + 2 * q^63 - 2 * q^64 - 12 * q^65 - 28 * q^67 - 2 * q^70 + 12 * q^71 - 4 * q^73 - 12 * q^74 - 2 * q^75 + 6 * q^77 - 12 * q^78 + 2 * q^81 - 2 * q^84 - 6 * q^85 - 18 * q^86 - 2 * q^90 + 12 * q^95 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−1.00000			−0.500000
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		−	1.00000i		−	0.408248i
$7$	1.00000			0.377964			0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000			0.377964			0.188982	+	0.981981i	$0.439481\pi$
$8$			1.00000i			0.353553i
$9$	1.00000			0.333333
$10$	−1.00000			−0.316228
$11$	3.00000			0.904534			0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000			0.904534			0.452267	+	0.891883i	$0.350615\pi$
$12$	−1.00000			−0.288675
$13$		−	6.00000i		−	1.66410i	−0.554700	−	0.832050i	$-0.687167\pi$
$13$		−	6.00000i		−	1.66410i	0.554700	−	0.832050i	$-0.312833\pi$
$14$		−	1.00000i		−	0.267261i
$15$		−	1.00000i		−	0.258199i
$16$	1.00000			0.250000
$17$		−	3.00000i		−	0.727607i	−0.931476	−	0.363803i	$-0.881478\pi$
$17$		−	3.00000i		−	0.727607i	0.931476	−	0.363803i	$-0.118522\pi$
$18$		−	1.00000i		−	0.235702i
$19$			6.00000i			1.37649i	0.725476	+	0.688247i	$0.241620\pi$
$19$			6.00000i			1.37649i	−0.725476	+	0.688247i	$0.758380\pi$
$20$			1.00000i			0.223607i
$21$	1.00000			0.218218
$22$		−	3.00000i		−	0.639602i
$23$			6.00000i			1.25109i	0.780189	+	0.625543i	$0.215123\pi$
$23$			6.00000i			1.25109i	−0.780189	+	0.625543i	$0.784877\pi$
$24$			1.00000i			0.204124i
$25$	−1.00000			−0.200000
$26$	−6.00000			−1.17670
$27$	1.00000			0.192450
$28$	−1.00000			−0.188982
$29$		−	9.00000i		−	1.67126i	−0.549294	−	0.835629i	$-0.685103\pi$
$29$		−	9.00000i		−	1.67126i	0.549294	−	0.835629i	$-0.314897\pi$
$30$	−1.00000			−0.182574
$31$			3.00000i			0.538816i	0.963026	+	0.269408i	$0.0868280\pi$
$31$			3.00000i			0.538816i	−0.963026	+	0.269408i	$0.913172\pi$
$32$		−	1.00000i		−	0.176777i
$33$	3.00000			0.522233
$34$	−3.00000			−0.514496
$35$		−	1.00000i		−	0.169031i
$36$	−1.00000			−0.166667
$37$	1.00000	−	6.00000i	0.164399	−	0.986394i
$37$	1.00000	−	6.00000i	0.164399	−	0.986394i
$38$	6.00000			0.973329
$39$		−	6.00000i		−	0.960769i
$40$	1.00000			0.158114
$41$	9.00000			1.40556			0.702782	−	0.711405i	$-0.251941\pi$
$41$	9.00000			1.40556			0.702782	+	0.711405i	$0.251941\pi$
$42$		−	1.00000i		−	0.154303i
$43$		−	9.00000i		−	1.37249i	−0.727372	−	0.686244i	$-0.759258\pi$
$43$		−	9.00000i		−	1.37249i	0.727372	−	0.686244i	$-0.240742\pi$
$44$	−3.00000			−0.452267
$45$		−	1.00000i		−	0.149071i
$46$	6.00000			0.884652
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$	1.00000			0.144338
$49$	−6.00000			−0.857143
$50$			1.00000i			0.141421i
$51$		−	3.00000i		−	0.420084i
$52$			6.00000i			0.832050i
$53$	3.00000			0.412082			0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000			0.412082			0.206041	+	0.978543i	$0.433942\pi$
$54$		−	1.00000i		−	0.136083i
$55$		−	3.00000i		−	0.404520i
$56$			1.00000i			0.133631i
$57$			6.00000i			0.794719i
$58$	−9.00000			−1.18176
$59$		0			0		1.00000			$0$
$59$		0			0		−1.00000			$\pi$
$60$			1.00000i			0.129099i
$61$		−	9.00000i		−	1.15233i	−0.817333	−	0.576166i	$-0.804548\pi$
$61$		−	9.00000i		−	1.15233i	0.817333	−	0.576166i	$-0.195452\pi$
$62$	3.00000			0.381000
$63$	1.00000			0.125988
$64$	−1.00000			−0.125000
$65$	−6.00000			−0.744208
$66$		−	3.00000i		−	0.369274i
$67$	−14.0000			−1.71037			−0.855186	−	0.518321i	$-0.826557\pi$
$67$	−14.0000			−1.71037			−0.855186	+	0.518321i	$0.826557\pi$
$68$			3.00000i			0.363803i
$69$			6.00000i			0.722315i
$70$	−1.00000			−0.119523
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$			1.00000i			0.117851i
$73$	−2.00000			−0.234082			−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000			−0.234082			−0.117041	+	0.993127i	$0.537341\pi$
$74$	−6.00000	−	1.00000i	−0.697486	−	0.116248i
$75$	−1.00000			−0.115470
$76$		−	6.00000i		−	0.688247i
$77$	3.00000			0.341882
$78$	−6.00000			−0.679366
$79$		0			0		1.00000			$0$
$79$		0			0		−1.00000			$\pi$
$80$		−	1.00000i		−	0.111803i
$81$	1.00000			0.111111
$82$		−	9.00000i		−	0.993884i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$	−1.00000			−0.109109
$85$	−3.00000			−0.325396
$86$	−9.00000			−0.970495
$87$		−	9.00000i		−	0.964901i
$88$			3.00000i			0.319801i
$89$			12.0000i			1.27200i	0.771690	+	0.635999i	$0.219412\pi$
$89$			12.0000i			1.27200i	−0.771690	+	0.635999i	$0.780588\pi$
$90$	−1.00000			−0.105409
$91$		−	6.00000i		−	0.628971i
$92$		−	6.00000i		−	0.625543i
$93$			3.00000i			0.311086i
$94$		0			0
$95$	6.00000			0.615587
$96$		−	1.00000i		−	0.102062i
$97$			3.00000i			0.304604i	0.988334	+	0.152302i	$0.0486686\pi$
$97$			3.00000i			0.304604i	−0.988334	+	0.152302i	$0.951331\pi$
$98$			6.00000i			0.606092i
$99$	3.00000			0.301511
$100$	1.00000			0.100000
$101$	12.0000			1.19404			0.597022	−	0.802225i	$-0.296350\pi$
$101$	12.0000			1.19404			0.597022	+	0.802225i	$0.296350\pi$
$102$	−3.00000			−0.297044
$103$			6.00000i			0.591198i	0.955312	+	0.295599i	$0.0955191\pi$
$103$			6.00000i			0.591198i	−0.955312	+	0.295599i	$0.904481\pi$
$104$	6.00000			0.588348
$105$		−	1.00000i		−	0.0975900i
$106$		−	3.00000i		−	0.291386i
$107$	−6.00000			−0.580042			−0.290021	−	0.957020i	$-0.593662\pi$
$107$	−6.00000			−0.580042			−0.290021	+	0.957020i	$0.593662\pi$
$108$	−1.00000			−0.0962250
$109$			9.00000i			0.862044i	0.902342	+	0.431022i	$0.141847\pi$
$109$			9.00000i			0.862044i	−0.902342	+	0.431022i	$0.858153\pi$
$110$	−3.00000			−0.286039
$111$	1.00000	−	6.00000i	0.0949158	−	0.569495i
$112$	1.00000			0.0944911
$113$			9.00000i			0.846649i	0.905978	+	0.423324i	$0.139137\pi$
$113$			9.00000i			0.846649i	−0.905978	+	0.423324i	$0.860863\pi$
$114$	6.00000			0.561951
$115$	6.00000			0.559503
$116$			9.00000i			0.835629i
$117$		−	6.00000i		−	0.554700i
$118$		0			0
$119$		−	3.00000i		−	0.275010i
$120$	1.00000			0.0912871
$121$	−2.00000			−0.181818
$122$	−9.00000			−0.814822
$123$	9.00000			0.811503
$124$		−	3.00000i		−	0.269408i
$125$			1.00000i			0.0894427i
$126$		−	1.00000i		−	0.0890871i
$127$	20.0000			1.77471			0.887357	−	0.461084i	$-0.152539\pi$
$127$	20.0000			1.77471			0.887357	+	0.461084i	$0.152539\pi$
$128$			1.00000i			0.0883883i
$129$		−	9.00000i		−	0.792406i
$130$			6.00000i			0.526235i
$131$			12.0000i			1.04844i	0.851581	+	0.524222i	$0.175644\pi$
$131$			12.0000i			1.04844i	−0.851581	+	0.524222i	$0.824356\pi$
$132$	−3.00000			−0.261116
$133$			6.00000i			0.520266i
$134$			14.0000i			1.20942i
$135$		−	1.00000i		−	0.0860663i
$136$	3.00000			0.257248
$137$	12.0000			1.02523			0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000			1.02523			0.512615	+	0.858619i	$0.328677\pi$
$138$	6.00000			0.510754
$139$	−5.00000			−0.424094			−0.212047	−	0.977259i	$-0.568013\pi$
$139$	−5.00000			−0.424094			−0.212047	+	0.977259i	$0.568013\pi$
$140$			1.00000i			0.0845154i
$141$		0			0
$142$		−	6.00000i		−	0.503509i
$143$		−	18.0000i		−	1.50524i
$144$	1.00000			0.0833333
$145$	−9.00000			−0.747409
$146$			2.00000i			0.165521i
$147$	−6.00000			−0.494872
$148$	−1.00000	+	6.00000i	−0.0821995	+	0.493197i
$149$	−18.0000			−1.47462			−0.737309	−	0.675556i	$-0.763904\pi$
$149$	−18.0000			−1.47462			−0.737309	+	0.675556i	$0.763904\pi$
$150$			1.00000i			0.0816497i
$151$	−10.0000			−0.813788			−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000			−0.813788			−0.406894	+	0.913475i	$0.633388\pi$
$152$	−6.00000			−0.486664
$153$		−	3.00000i		−	0.242536i
$154$		−	3.00000i		−	0.241747i
$155$	3.00000			0.240966
$156$			6.00000i			0.480384i
$157$	−5.00000			−0.399043			−0.199522	−	0.979893i	$-0.563939\pi$
$157$	−5.00000			−0.399043			−0.199522	+	0.979893i	$0.563939\pi$
$158$		0			0
$159$	3.00000			0.237915
$160$	−1.00000			−0.0790569
$161$			6.00000i			0.472866i
$162$		−	1.00000i		−	0.0785674i
$163$			9.00000i			0.704934i	0.935824	+	0.352467i	$0.114657\pi$
$163$			9.00000i			0.704934i	−0.935824	+	0.352467i	$0.885343\pi$
$164$	−9.00000			−0.702782
$165$		−	3.00000i		−	0.233550i
$166$		0			0
$167$		−	6.00000i		−	0.464294i	−0.972681	−	0.232147i	$-0.925425\pi$
$167$		−	6.00000i		−	0.464294i	0.972681	−	0.232147i	$-0.0745750\pi$
$168$			1.00000i			0.0771517i
$169$	−23.0000			−1.76923
$170$			3.00000i			0.230089i
$171$			6.00000i			0.458831i
$172$			9.00000i			0.686244i
$173$	−3.00000			−0.228086			−0.114043	−	0.993476i	$-0.536380\pi$
$173$	−3.00000			−0.228086			−0.114043	+	0.993476i	$0.536380\pi$
$174$	−9.00000			−0.682288
$175$	−1.00000			−0.0755929
$176$	3.00000			0.226134
$177$		0			0
$178$	12.0000			0.899438
$179$			18.0000i			1.34538i	0.739923	+	0.672692i	$0.234862\pi$
$179$			18.0000i			1.34538i	−0.739923	+	0.672692i	$0.765138\pi$
$180$			1.00000i			0.0745356i
$181$	16.0000			1.18927			0.594635	−	0.803996i	$-0.297296\pi$
$181$	16.0000			1.18927			0.594635	+	0.803996i	$0.297296\pi$
$182$	−6.00000			−0.444750
$183$		−	9.00000i		−	0.665299i
$184$	−6.00000			−0.442326
$185$	−6.00000	−	1.00000i	−0.441129	−	0.0735215i
$186$	3.00000			0.219971
$187$		−	9.00000i		−	0.658145i
$188$		0			0
$189$	1.00000			0.0727393
$190$		−	6.00000i		−	0.435286i
$191$			27.0000i			1.95365i	0.214036	+	0.976826i	$0.431339\pi$
$191$			27.0000i			1.95365i	−0.214036	+	0.976826i	$0.568661\pi$
$192$	−1.00000			−0.0721688
$193$		−	18.0000i		−	1.29567i	−0.761781	−	0.647834i	$-0.775675\pi$
$193$		−	18.0000i		−	1.29567i	0.761781	−	0.647834i	$-0.224325\pi$
$194$	3.00000			0.215387
$195$	−6.00000			−0.429669
$196$	6.00000			0.428571
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		−	3.00000i		−	0.213201i
$199$			12.0000i			0.850657i	0.905039	+	0.425329i	$0.139842\pi$
$199$			12.0000i			0.850657i	−0.905039	+	0.425329i	$0.860158\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	−14.0000			−0.987484
$202$		−	12.0000i		−	0.844317i
$203$		−	9.00000i		−	0.631676i
$204$			3.00000i			0.210042i
$205$		−	9.00000i		−	0.628587i
$206$	6.00000			0.418040
$207$			6.00000i			0.417029i
$208$		−	6.00000i		−	0.416025i
$209$			18.0000i			1.24509i
$210$	−1.00000			−0.0690066
$211$	23.0000			1.58339			0.791693	−	0.610920i	$-0.209200\pi$
$211$	23.0000			1.58339			0.791693	+	0.610920i	$0.209200\pi$
$212$	−3.00000			−0.206041
$213$	6.00000			0.411113
$214$			6.00000i			0.410152i
$215$	−9.00000			−0.613795
$216$			1.00000i			0.0680414i
$217$			3.00000i			0.203653i
$218$	9.00000			0.609557
$219$	−2.00000			−0.135147
$220$			3.00000i			0.202260i
$221$	−18.0000			−1.21081
$222$	−6.00000	−	1.00000i	−0.402694	−	0.0671156i
$223$	−1.00000			−0.0669650			−0.0334825	−	0.999439i	$-0.510660\pi$
$223$	−1.00000			−0.0669650			−0.0334825	+	0.999439i	$0.510660\pi$
$224$		−	1.00000i		−	0.0668153i
$225$	−1.00000			−0.0666667
$226$	9.00000			0.598671
$227$			21.0000i			1.39382i	0.717159	+	0.696909i	$0.245442\pi$
$227$			21.0000i			1.39382i	−0.717159	+	0.696909i	$0.754558\pi$
$228$		−	6.00000i		−	0.397360i
$229$	−22.0000			−1.45380			−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000			−1.45380			−0.726900	+	0.686743i	$0.759040\pi$
$230$		−	6.00000i		−	0.395628i
$231$	3.00000			0.197386
$232$	9.00000			0.590879
$233$	24.0000			1.57229			0.786146	−	0.618041i	$-0.212073\pi$
$233$	24.0000			1.57229			0.786146	+	0.618041i	$0.212073\pi$
$234$	−6.00000			−0.392232
$235$		0			0
$236$		0			0
$237$		0			0
$238$	−3.00000			−0.194461
$239$			15.0000i			0.970269i	0.874439	+	0.485135i	$0.161229\pi$
$239$			15.0000i			0.970269i	−0.874439	+	0.485135i	$0.838771\pi$
$240$		−	1.00000i		−	0.0645497i
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$			2.00000i			0.128565i
$243$	1.00000			0.0641500
$244$			9.00000i			0.576166i
$245$			6.00000i			0.383326i
$246$		−	9.00000i		−	0.573819i
$247$	36.0000			2.29063
$248$	−3.00000			−0.190500
$249$		0			0
$250$	1.00000			0.0632456
$251$		−	12.0000i		−	0.757433i	−0.925513	−	0.378717i	$-0.876365\pi$
$251$		−	12.0000i		−	0.757433i	0.925513	−	0.378717i	$-0.123635\pi$
$252$	−1.00000			−0.0629941
$253$			18.0000i			1.13165i
$254$		−	20.0000i		−	1.25491i
$255$	−3.00000			−0.187867
$256$	1.00000			0.0625000
$257$			6.00000i			0.374270i	0.982334	+	0.187135i	$0.0599201\pi$
$257$			6.00000i			0.374270i	−0.982334	+	0.187135i	$0.940080\pi$
$258$	−9.00000			−0.560316
$259$	1.00000	−	6.00000i	0.0621370	−	0.372822i
$260$	6.00000			0.372104
$261$		−	9.00000i		−	0.557086i
$262$	12.0000			0.741362
$263$	9.00000			0.554964			0.277482	−	0.960731i	$-0.410500\pi$
$263$	9.00000			0.554964			0.277482	+	0.960731i	$0.410500\pi$
$264$			3.00000i			0.184637i
$265$		−	3.00000i		−	0.184289i
$266$	6.00000			0.367884
$267$			12.0000i			0.734388i
$268$	14.0000			0.855186
$269$		0			0			−	1.00000i	$-0.5\pi$
$269$		0			0				1.00000i	$0.5\pi$
$270$	−1.00000			−0.0608581
$271$	−20.0000			−1.21491			−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−20.0000			−1.21491			−0.607457	+	0.794353i	$0.707810\pi$
$272$		−	3.00000i		−	0.181902i
$273$		−	6.00000i		−	0.363137i
$274$		−	12.0000i		−	0.724947i
$275$	−3.00000			−0.180907
$276$		−	6.00000i		−	0.361158i
$277$			12.0000i			0.721010i	0.932757	+	0.360505i	$0.117396\pi$
$277$			12.0000i			0.721010i	−0.932757	+	0.360505i	$0.882604\pi$
$278$			5.00000i			0.299880i
$279$			3.00000i			0.179605i
$280$	1.00000			0.0597614
$281$			18.0000i			1.07379i	0.843649	+	0.536895i	$0.180403\pi$
$281$			18.0000i			1.07379i	−0.843649	+	0.536895i	$0.819597\pi$
$282$		0			0
$283$		−	24.0000i		−	1.42665i	−0.700832	−	0.713326i	$-0.747188\pi$
$283$		−	24.0000i		−	1.42665i	0.700832	−	0.713326i	$-0.252812\pi$
$284$	−6.00000			−0.356034
$285$	6.00000			0.355409
$286$	−18.0000			−1.06436
$287$	9.00000			0.531253
$288$		−	1.00000i		−	0.0589256i
$289$	8.00000			0.470588
$290$			9.00000i			0.528498i
$291$			3.00000i			0.175863i
$292$	2.00000			0.117041
$293$	21.0000			1.22683			0.613417	−	0.789760i	$-0.289795\pi$
$293$	21.0000			1.22683			0.613417	+	0.789760i	$0.289795\pi$
$294$			6.00000i			0.349927i
$295$		0			0
$296$	6.00000	+	1.00000i	0.348743	+	0.0581238i
$297$	3.00000			0.174078
$298$			18.0000i			1.04271i
$299$	36.0000			2.08193
$300$	1.00000			0.0577350
$301$		−	9.00000i		−	0.518751i
$302$			10.0000i			0.575435i
$303$	12.0000			0.689382
$304$			6.00000i			0.344124i
$305$	−9.00000			−0.515339
$306$	−3.00000			−0.171499
$307$	−16.0000			−0.913168			−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000			−0.913168			−0.456584	+	0.889680i	$0.650927\pi$
$308$	−3.00000			−0.170941
$309$			6.00000i			0.341328i
$310$		−	3.00000i		−	0.170389i
$311$		−	27.0000i		−	1.53103i	−0.643418	−	0.765515i	$-0.722484\pi$
$311$		−	27.0000i		−	1.53103i	0.643418	−	0.765515i	$-0.277516\pi$
$312$	6.00000			0.339683
$313$			18.0000i			1.01742i	0.860938	+	0.508710i	$0.169877\pi$
$313$			18.0000i			1.01742i	−0.860938	+	0.508710i	$0.830123\pi$
$314$			5.00000i			0.282166i
$315$		−	1.00000i		−	0.0563436i
$316$		0			0
$317$	−27.0000			−1.51647			−0.758236	−	0.651981i	$-0.773938\pi$
$317$	−27.0000			−1.51647			−0.758236	+	0.651981i	$0.773938\pi$
$318$		−	3.00000i		−	0.168232i
$319$		−	27.0000i		−	1.51171i
$320$			1.00000i			0.0559017i
$321$	−6.00000			−0.334887
$322$	6.00000			0.334367
$323$	18.0000			1.00155
$324$	−1.00000			−0.0555556
$325$			6.00000i			0.332820i
$326$	9.00000			0.498464
$327$			9.00000i			0.497701i
$328$			9.00000i			0.496942i
$329$		0			0
$330$	−3.00000			−0.165145
$331$			18.0000i			0.989369i	0.869072	+	0.494685i	$0.164716\pi$
$331$			18.0000i			0.989369i	−0.869072	+	0.494685i	$0.835284\pi$
$332$		0			0
$333$	1.00000	−	6.00000i	0.0547997	−	0.328798i
$334$	−6.00000			−0.328305
$335$			14.0000i			0.764902i
$336$	1.00000			0.0545545
$337$	−4.00000			−0.217894			−0.108947	−	0.994048i	$-0.534748\pi$
$337$	−4.00000			−0.217894			−0.108947	+	0.994048i	$0.534748\pi$
$338$			23.0000i			1.25104i
$339$			9.00000i			0.488813i
$340$	3.00000			0.162698
$341$			9.00000i			0.487377i
$342$	6.00000			0.324443
$343$	−13.0000			−0.701934
$344$	9.00000			0.485247
$345$	6.00000			0.323029
$346$			3.00000i			0.161281i
$347$			12.0000i			0.644194i	0.946707	+	0.322097i	$0.104388\pi$
$347$			12.0000i			0.644194i	−0.946707	+	0.322097i	$0.895612\pi$
$348$			9.00000i			0.482451i
$349$	−26.0000			−1.39175			−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000			−1.39175			−0.695874	+	0.718164i	$0.744983\pi$
$350$			1.00000i			0.0534522i
$351$		−	6.00000i		−	0.320256i
$352$		−	3.00000i		−	0.159901i
$353$		−	21.0000i		−	1.11772i	−0.829263	−	0.558859i	$-0.811239\pi$
$353$		−	21.0000i		−	1.11772i	0.829263	−	0.558859i	$-0.188761\pi$
$354$		0			0
$355$		−	6.00000i		−	0.318447i
$356$		−	12.0000i		−	0.635999i
$357$		−	3.00000i		−	0.158777i
$358$	18.0000			0.951330
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$	1.00000			0.0527046
$361$	−17.0000			−0.894737
$362$		−	16.0000i		−	0.840941i
$363$	−2.00000			−0.104973
$364$			6.00000i			0.314485i
$365$			2.00000i			0.104685i
$366$	−9.00000			−0.470438
$367$	17.0000			0.887393			0.443696	−	0.896177i	$-0.353667\pi$
$367$	17.0000			0.887393			0.443696	+	0.896177i	$0.353667\pi$
$368$			6.00000i			0.312772i
$369$	9.00000			0.468521
$370$	−1.00000	+	6.00000i	−0.0519875	+	0.311925i
$371$	3.00000			0.155752
$372$		−	3.00000i		−	0.155543i
$373$	22.0000			1.13912			0.569558	−	0.821951i	$-0.307114\pi$
$373$	22.0000			1.13912			0.569558	+	0.821951i	$0.307114\pi$
$374$	−9.00000			−0.465379
$375$			1.00000i			0.0516398i
$376$		0			0
$377$	−54.0000			−2.78114
$378$		−	1.00000i		−	0.0514344i
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$	−6.00000			−0.307794
$381$	20.0000			1.02463
$382$	27.0000			1.38144
$383$			18.0000i			0.919757i	0.887982	+	0.459879i	$0.152107\pi$
$383$			18.0000i			0.919757i	−0.887982	+	0.459879i	$0.847893\pi$
$384$			1.00000i			0.0510310i
$385$		−	3.00000i		−	0.152894i
$386$	−18.0000			−0.916176
$387$		−	9.00000i		−	0.457496i
$388$		−	3.00000i		−	0.152302i
$389$		−	21.0000i		−	1.06474i	−0.846511	−	0.532371i	$-0.821301\pi$
$389$		−	21.0000i		−	1.06474i	0.846511	−	0.532371i	$-0.178699\pi$
$390$			6.00000i			0.303822i
$391$	18.0000			0.910299
$392$		−	6.00000i		−	0.303046i
$393$			12.0000i			0.605320i
$394$		−	18.0000i		−	0.906827i
$395$		0			0
$396$	−3.00000			−0.150756
$397$	34.0000			1.70641			0.853206	−	0.521575i	$-0.174655\pi$
$397$	34.0000			1.70641			0.853206	+	0.521575i	$0.174655\pi$
$398$	12.0000			0.601506
$399$			6.00000i			0.300376i
$400$	−1.00000			−0.0500000
$401$			18.0000i			0.898877i	0.893311	+	0.449439i	$0.148376\pi$
$401$			18.0000i			0.898877i	−0.893311	+	0.449439i	$0.851624\pi$
$402$			14.0000i			0.698257i
$403$	18.0000			0.896644
$404$	−12.0000			−0.597022
$405$		−	1.00000i		−	0.0496904i
$406$	−9.00000			−0.446663
$407$	3.00000	−	18.0000i	0.148704	−	0.892227i
$408$	3.00000			0.148522
$409$		0			0		1.00000			$0$
$409$		0			0		−1.00000			$\pi$
$410$	−9.00000			−0.444478
$411$	12.0000			0.591916
$412$		−	6.00000i		−	0.295599i
$413$		0			0
$414$	6.00000			0.294884
$415$		0			0
$416$	−6.00000			−0.294174
$417$	−5.00000			−0.244851
$418$	18.0000			0.880409
$419$	−24.0000			−1.17248			−0.586238	−	0.810139i	$-0.699392\pi$
$419$	−24.0000			−1.17248			−0.586238	+	0.810139i	$0.699392\pi$
$420$			1.00000i			0.0487950i
$421$			30.0000i			1.46211i	0.682318	+	0.731055i	$0.260972\pi$
$421$			30.0000i			1.46211i	−0.682318	+	0.731055i	$0.739028\pi$
$422$		−	23.0000i		−	1.11962i
$423$		0			0
$424$			3.00000i			0.145693i
$425$			3.00000i			0.145521i
$426$		−	6.00000i		−	0.290701i
$427$		−	9.00000i		−	0.435541i
$428$	6.00000			0.290021
$429$		−	18.0000i		−	0.869048i
$430$			9.00000i			0.434019i
$431$			9.00000i			0.433515i	0.976226	+	0.216757i	$0.0695480\pi$
$431$			9.00000i			0.433515i	−0.976226	+	0.216757i	$0.930452\pi$
$432$	1.00000			0.0481125
$433$	−38.0000			−1.82616			−0.913082	−	0.407777i	$-0.866304\pi$
$433$	−38.0000			−1.82616			−0.913082	+	0.407777i	$0.866304\pi$
$434$	3.00000			0.144005
$435$	−9.00000			−0.431517
$436$		−	9.00000i		−	0.431022i
$437$	−36.0000			−1.72211
$438$			2.00000i			0.0955637i
$439$			33.0000i			1.57500i	0.616312	+	0.787502i	$0.288626\pi$
$439$			33.0000i			1.57500i	−0.616312	+	0.787502i	$0.711374\pi$
$440$	3.00000			0.143019
$441$	−6.00000			−0.285714
$442$			18.0000i			0.856173i
$443$	−12.0000			−0.570137			−0.285069	−	0.958507i	$-0.592016\pi$
$443$	−12.0000			−0.570137			−0.285069	+	0.958507i	$0.592016\pi$
$444$	−1.00000	+	6.00000i	−0.0474579	+	0.284747i
$445$	12.0000			0.568855
$446$			1.00000i			0.0473514i
$447$	−18.0000			−0.851371
$448$	−1.00000			−0.0472456
$449$		−	30.0000i		−	1.41579i	−0.706319	−	0.707894i	$-0.749646\pi$
$449$		−	30.0000i		−	1.41579i	0.706319	−	0.707894i	$-0.250354\pi$
$450$			1.00000i			0.0471405i
$451$	27.0000			1.27138
$452$		−	9.00000i		−	0.423324i
$453$	−10.0000			−0.469841
$454$	21.0000			0.985579
$455$	−6.00000			−0.281284
$456$	−6.00000			−0.280976
$457$			39.0000i			1.82434i	0.409809	+	0.912172i	$0.365595\pi$
$457$			39.0000i			1.82434i	−0.409809	+	0.912172i	$0.634405\pi$
$458$			22.0000i			1.02799i
$459$		−	3.00000i		−	0.140028i
$460$	−6.00000			−0.279751
$461$		−	9.00000i		−	0.419172i	−0.977790	−	0.209586i	$-0.932788\pi$
$461$		−	9.00000i		−	0.419172i	0.977790	−	0.209586i	$-0.0672116\pi$
$462$		−	3.00000i		−	0.139573i
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$		−	9.00000i		−	0.417815i
$465$	3.00000			0.139122
$466$		−	24.0000i		−	1.11178i
$467$		−	33.0000i		−	1.52706i	−0.645774	−	0.763529i	$-0.723465\pi$
$467$		−	33.0000i		−	1.52706i	0.645774	−	0.763529i	$-0.276535\pi$
$468$			6.00000i			0.277350i
$469$	−14.0000			−0.646460
$470$		0			0
$471$	−5.00000			−0.230388
$472$		0			0
$473$		−	27.0000i		−	1.24146i
$474$		0			0
$475$		−	6.00000i		−	0.275299i
$476$			3.00000i			0.137505i
$477$	3.00000			0.137361
$478$	15.0000			0.686084
$479$		0			0		1.00000			$0$
$479$		0			0		−1.00000			$\pi$
$480$	−1.00000			−0.0456435
$481$	−36.0000	−	6.00000i	−1.64146	−	0.273576i
$482$		0			0
$483$			6.00000i			0.273009i
$484$	2.00000			0.0909091
$485$	3.00000			0.136223
$486$		−	1.00000i		−	0.0453609i
$487$		−	12.0000i		−	0.543772i	−0.962329	−	0.271886i	$-0.912353\pi$
$487$		−	12.0000i		−	0.543772i	0.962329	−	0.271886i	$-0.0876473\pi$
$488$	9.00000			0.407411
$489$			9.00000i			0.406994i
$490$	6.00000			0.271052
$491$	−36.0000			−1.62466			−0.812329	−	0.583200i	$-0.801800\pi$
$491$	−36.0000			−1.62466			−0.812329	+	0.583200i	$0.801800\pi$
$492$	−9.00000			−0.405751
$493$	−27.0000			−1.21602
$494$		−	36.0000i		−	1.61972i
$495$		−	3.00000i		−	0.134840i
$496$			3.00000i			0.134704i
$497$	6.00000			0.269137
$498$		0			0
$499$		−	6.00000i		−	0.268597i	−0.990941	−	0.134298i	$-0.957122\pi$
$499$		−	6.00000i		−	0.268597i	0.990941	−	0.134298i	$-0.0428781\pi$
$500$		−	1.00000i		−	0.0447214i
$501$		−	6.00000i		−	0.268060i
$502$	−12.0000			−0.535586
$503$		−	24.0000i		−	1.07011i	−0.844818	−	0.535054i	$-0.820291\pi$
$503$		−	24.0000i		−	1.07011i	0.844818	−	0.535054i	$-0.179709\pi$
$504$			1.00000i			0.0445435i
$505$		−	12.0000i		−	0.533993i
$506$	18.0000			0.800198
$507$	−23.0000			−1.02147
$508$	−20.0000			−0.887357
$509$	36.0000			1.59567			0.797836	−	0.602875i	$-0.205978\pi$
$509$	36.0000			1.59567			0.797836	+	0.602875i	$0.205978\pi$
$510$			3.00000i			0.132842i
$511$	−2.00000			−0.0884748
$512$		−	1.00000i		−	0.0441942i
$513$			6.00000i			0.264906i
$514$	6.00000			0.264649
$515$	6.00000			0.264392
$516$			9.00000i			0.396203i
$517$		0			0
$518$	−6.00000	−	1.00000i	−0.263625	−	0.0439375i
$519$	−3.00000			−0.131685
$520$		−	6.00000i		−	0.263117i
$521$	3.00000			0.131432			0.0657162	−	0.997838i	$-0.479067\pi$
$521$	3.00000			0.131432			0.0657162	+	0.997838i	$0.479067\pi$
$522$	−9.00000			−0.393919
$523$		−	36.0000i		−	1.57417i	−0.616844	−	0.787085i	$-0.711589\pi$
$523$		−	36.0000i		−	1.57417i	0.616844	−	0.787085i	$-0.288411\pi$
$524$		−	12.0000i		−	0.524222i
$525$	−1.00000			−0.0436436
$526$		−	9.00000i		−	0.392419i
$527$	9.00000			0.392046
$528$	3.00000			0.130558
$529$	−13.0000			−0.565217
$530$	−3.00000			−0.130312
$531$		0			0
$532$		−	6.00000i		−	0.260133i
$533$		−	54.0000i		−	2.33900i
$534$	12.0000			0.519291
$535$			6.00000i			0.259403i
$536$		−	14.0000i		−	0.604708i
$537$			18.0000i			0.776757i
$538$		0			0
$539$	−18.0000			−0.775315
$540$			1.00000i			0.0430331i
$541$		−	6.00000i		−	0.257960i	−0.991647	−	0.128980i	$-0.958830\pi$
$541$		−	6.00000i		−	0.257960i	0.991647	−	0.128980i	$-0.0411703\pi$
$542$			20.0000i			0.859074i
$543$	16.0000			0.686626
$544$	−3.00000			−0.128624
$545$	9.00000			0.385518
$546$	−6.00000			−0.256776
$547$			21.0000i			0.897895i	0.893558	+	0.448948i	$0.148201\pi$
$547$			21.0000i			0.897895i	−0.893558	+	0.448948i	$0.851799\pi$
$548$	−12.0000			−0.512615
$549$		−	9.00000i		−	0.384111i
$550$			3.00000i			0.127920i
$551$	54.0000			2.30048
$552$	−6.00000			−0.255377
$553$		0			0
$554$	12.0000			0.509831
$555$	−6.00000	−	1.00000i	−0.254686	−	0.0424476i
$556$	5.00000			0.212047
$557$			12.0000i			0.508456i	0.967144	+	0.254228i	$0.0818214\pi$
$557$			12.0000i			0.508456i	−0.967144	+	0.254228i	$0.918179\pi$
$558$	3.00000			0.127000
$559$	−54.0000			−2.28396
$560$		−	1.00000i		−	0.0422577i
$561$		−	9.00000i		−	0.379980i
$562$	18.0000			0.759284
$563$		−	27.0000i		−	1.13791i	−0.822367	−	0.568957i	$-0.807347\pi$
$563$		−	27.0000i		−	1.13791i	0.822367	−	0.568957i	$-0.192653\pi$
$564$		0			0
$565$	9.00000			0.378633
$566$	−24.0000			−1.00880
$567$	1.00000			0.0419961
$568$			6.00000i			0.251754i
$569$		−	12.0000i		−	0.503066i	−0.967849	−	0.251533i	$-0.919065\pi$
$569$		−	12.0000i		−	0.503066i	0.967849	−	0.251533i	$-0.0809347\pi$
$570$		−	6.00000i		−	0.251312i
$571$	−5.00000			−0.209243			−0.104622	−	0.994512i	$-0.533363\pi$
$571$	−5.00000			−0.209243			−0.104622	+	0.994512i	$0.533363\pi$
$572$			18.0000i			0.752618i
$573$			27.0000i			1.12794i
$574$		−	9.00000i		−	0.375653i
$575$		−	6.00000i		−	0.250217i
$576$	−1.00000			−0.0416667
$577$			18.0000i			0.749350i	0.927156	+	0.374675i	$0.122246\pi$
$577$			18.0000i			0.749350i	−0.927156	+	0.374675i	$0.877754\pi$
$578$		−	8.00000i		−	0.332756i
$579$		−	18.0000i		−	0.748054i
$580$	9.00000			0.373705
$581$		0			0
$582$	3.00000			0.124354
$583$	9.00000			0.372742
$584$		−	2.00000i		−	0.0827606i
$585$	−6.00000			−0.248069
$586$		−	21.0000i		−	0.867502i
$587$		−	3.00000i		−	0.123823i	−0.998082	−	0.0619116i	$-0.980280\pi$
$587$		−	3.00000i		−	0.123823i	0.998082	−	0.0619116i	$-0.0197197\pi$
$588$	6.00000			0.247436
$589$	−18.0000			−0.741677
$590$		0			0
$591$	18.0000			0.740421
$592$	1.00000	−	6.00000i	0.0410997	−	0.246598i
$593$	−12.0000			−0.492781			−0.246390	−	0.969171i	$-0.579245\pi$
$593$	−12.0000			−0.492781			−0.246390	+	0.969171i	$0.579245\pi$
$594$		−	3.00000i		−	0.123091i
$595$	−3.00000			−0.122988
$596$	18.0000			0.737309
$597$			12.0000i			0.491127i
$598$		−	36.0000i		−	1.47215i
$599$	−6.00000			−0.245153			−0.122577	−	0.992459i	$-0.539116\pi$
$599$	−6.00000			−0.245153			−0.122577	+	0.992459i	$0.539116\pi$
$600$		−	1.00000i		−	0.0408248i
$601$	−35.0000			−1.42768			−0.713840	−	0.700309i	$-0.753046\pi$
$601$	−35.0000			−1.42768			−0.713840	+	0.700309i	$0.753046\pi$
$602$	−9.00000			−0.366813
$603$	−14.0000			−0.570124
$604$	10.0000			0.406894
$605$			2.00000i			0.0813116i
$606$		−	12.0000i		−	0.487467i
$607$		−	24.0000i		−	0.974130i	−0.873366	−	0.487065i	$-0.838067\pi$
$607$		−	24.0000i		−	0.974130i	0.873366	−	0.487065i	$-0.161933\pi$
$608$	6.00000			0.243332
$609$		−	9.00000i		−	0.364698i
$610$			9.00000i			0.364399i
$611$		0			0
$612$			3.00000i			0.121268i
$613$	−25.0000			−1.00974			−0.504870	−	0.863195i	$-0.668460\pi$
$613$	−25.0000			−1.00974			−0.504870	+	0.863195i	$0.668460\pi$
$614$			16.0000i			0.645707i
$615$		−	9.00000i		−	0.362915i
$616$			3.00000i			0.120873i
$617$	12.0000			0.483102			0.241551	−	0.970388i	$-0.422344\pi$
$617$	12.0000			0.483102			0.241551	+	0.970388i	$0.422344\pi$
$618$	6.00000			0.241355
$619$	35.0000			1.40677			0.703384	−	0.710810i	$-0.251671\pi$
$619$	35.0000			1.40677			0.703384	+	0.710810i	$0.251671\pi$
$620$	−3.00000			−0.120483
$621$			6.00000i			0.240772i
$622$	−27.0000			−1.08260
$623$			12.0000i			0.480770i
$624$		−	6.00000i		−	0.240192i
$625$	1.00000			0.0400000
$626$	18.0000			0.719425
$627$			18.0000i			0.718851i
$628$	5.00000			0.199522
$629$	−18.0000	−	3.00000i	−0.717707	−	0.119618i
$630$	−1.00000			−0.0398410
$631$			27.0000i			1.07485i	0.843311	+	0.537427i	$0.180603\pi$
$631$			27.0000i			1.07485i	−0.843311	+	0.537427i	$0.819397\pi$
$632$		0			0
$633$	23.0000			0.914168
$634$			27.0000i			1.07231i
$635$		−	20.0000i		−	0.793676i
$636$	−3.00000			−0.118958
$637$			36.0000i			1.42637i
$638$	−27.0000			−1.06894
$639$	6.00000			0.237356
$640$	1.00000			0.0395285
$641$	−33.0000			−1.30342			−0.651711	−	0.758468i	$-0.725948\pi$
$641$	−33.0000			−1.30342			−0.651711	+	0.758468i	$0.725948\pi$
$642$			6.00000i			0.236801i
$643$		−	27.0000i		−	1.06478i	−0.846500	−	0.532388i	$-0.821295\pi$
$643$		−	27.0000i		−	1.06478i	0.846500	−	0.532388i	$-0.178705\pi$
$644$		−	6.00000i		−	0.236433i
$645$	−9.00000			−0.354375
$646$		−	18.0000i		−	0.708201i
$647$		−	18.0000i		−	0.707653i	−0.935311	−	0.353827i	$-0.884880\pi$
$647$		−	18.0000i		−	0.707653i	0.935311	−	0.353827i	$-0.115120\pi$
$648$			1.00000i			0.0392837i
$649$		0			0
$650$	6.00000			0.235339
$651$			3.00000i			0.117579i
$652$		−	9.00000i		−	0.352467i
$653$		−	42.0000i		−	1.64359i	−0.569785	−	0.821794i	$-0.692974\pi$
$653$		−	42.0000i		−	1.64359i	0.569785	−	0.821794i	$-0.307026\pi$
$654$	9.00000			0.351928
$655$	12.0000			0.468879
$656$	9.00000			0.351391
$657$	−2.00000			−0.0780274
$658$		0			0
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$			3.00000i			0.116775i
$661$		−	15.0000i		−	0.583432i	−0.956505	−	0.291716i	$-0.905774\pi$
$661$		−	15.0000i		−	0.583432i	0.956505	−	0.291716i	$-0.0942263\pi$
$662$	18.0000			0.699590
$663$	−18.0000			−0.699062
$664$		0			0
$665$	6.00000			0.232670
$666$	−6.00000	−	1.00000i	−0.232495	−	0.0387492i
$667$	54.0000			2.09089
$668$			6.00000i			0.232147i
$669$	−1.00000			−0.0386622
$670$	14.0000			0.540867
$671$		−	27.0000i		−	1.04232i
$672$		−	1.00000i		−	0.0385758i
$673$	−26.0000			−1.00223			−0.501113	−	0.865382i	$-0.667076\pi$
$673$	−26.0000			−1.00223			−0.501113	+	0.865382i	$0.667076\pi$
$674$			4.00000i			0.154074i
$675$	−1.00000			−0.0384900
$676$	23.0000			0.884615
$677$	6.00000			0.230599			0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000			0.230599			0.115299	+	0.993331i	$0.463217\pi$
$678$	9.00000			0.345643
$679$			3.00000i			0.115129i
$680$		−	3.00000i		−	0.115045i
$681$			21.0000i			0.804722i
$682$	9.00000			0.344628
$683$			9.00000i			0.344375i	0.985064	+	0.172188i	$0.0550836\pi$
$683$			9.00000i			0.344375i	−0.985064	+	0.172188i	$0.944916\pi$
$684$		−	6.00000i		−	0.229416i
$685$		−	12.0000i		−	0.458496i
$686$			13.0000i			0.496342i
$687$	−22.0000			−0.839352
$688$		−	9.00000i		−	0.343122i
$689$		−	18.0000i		−	0.685745i
$690$		−	6.00000i		−	0.228416i
$691$	37.0000			1.40755			0.703773	−	0.710425i	$-0.251497\pi$
$691$	37.0000			1.40755			0.703773	+	0.710425i	$0.251497\pi$
$692$	3.00000			0.114043
$693$	3.00000			0.113961
$694$	12.0000			0.455514
$695$			5.00000i			0.189661i
$696$	9.00000			0.341144
$697$		−	27.0000i		−	1.02270i
$698$			26.0000i			0.984115i
$699$	24.0000			0.907763
$700$	1.00000			0.0377964
$701$			30.0000i			1.13308i	0.824033	+	0.566542i	$0.191719\pi$
$701$			30.0000i			1.13308i	−0.824033	+	0.566542i	$0.808281\pi$
$702$	−6.00000			−0.226455
$703$	36.0000	+	6.00000i	1.35777	+	0.226294i
$704$	−3.00000			−0.113067
$705$		0			0
$706$	−21.0000			−0.790345
$707$	12.0000			0.451306
$708$		0			0
$709$		−	39.0000i		−	1.46468i	−0.680941	−	0.732338i	$-0.738429\pi$
$709$		−	39.0000i		−	1.46468i	0.680941	−	0.732338i	$-0.261571\pi$
$710$	−6.00000			−0.225176
$711$		0			0
$712$	−12.0000			−0.449719
$713$	−18.0000			−0.674105
$714$	−3.00000			−0.112272
$715$	−18.0000			−0.673162
$716$		−	18.0000i		−	0.672692i
$717$			15.0000i			0.560185i
$718$		0			0
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		−	1.00000i		−	0.0372678i
$721$			6.00000i			0.223452i
$722$			17.0000i			0.632674i
$723$		0			0
$724$	−16.0000			−0.594635
$725$			9.00000i			0.334252i
$726$			2.00000i			0.0742270i
$727$		−	30.0000i		−	1.11264i	−0.830969	−	0.556319i	$-0.812213\pi$
$727$		−	30.0000i		−	1.11264i	0.830969	−	0.556319i	$-0.187787\pi$
$728$	6.00000			0.222375
$729$	1.00000			0.0370370
$730$	2.00000			0.0740233
$731$	−27.0000			−0.998631
$732$			9.00000i			0.332650i
$733$	23.0000			0.849524			0.424762	−	0.905305i	$-0.360358\pi$
$733$	23.0000			0.849524			0.424762	+	0.905305i	$0.360358\pi$
$734$		−	17.0000i		−	0.627481i
$735$			6.00000i			0.221313i
$736$	6.00000			0.221163
$737$	−42.0000			−1.54709
$738$		−	9.00000i		−	0.331295i
$739$	11.0000			0.404642			0.202321	−	0.979319i	$-0.435152\pi$
$739$	11.0000			0.404642			0.202321	+	0.979319i	$0.435152\pi$
$740$	6.00000	+	1.00000i	0.220564	+	0.0367607i
$741$	36.0000			1.32249
$742$		−	3.00000i		−	0.110133i
$743$	−15.0000			−0.550297			−0.275148	−	0.961402i	$-0.588727\pi$
$743$	−15.0000			−0.550297			−0.275148	+	0.961402i	$0.588727\pi$
$744$	−3.00000			−0.109985
$745$			18.0000i			0.659469i
$746$		−	22.0000i		−	0.805477i
$747$		0			0
$748$			9.00000i			0.329073i
$749$	−6.00000			−0.219235
$750$	1.00000			0.0365148
$751$	−50.0000			−1.82453			−0.912263	−	0.409605i	$-0.865667\pi$
$751$	−50.0000			−1.82453			−0.912263	+	0.409605i	$0.865667\pi$
$752$		0			0
$753$		−	12.0000i		−	0.437304i
$754$			54.0000i			1.96656i
$755$			10.0000i			0.363937i
$756$	−1.00000			−0.0363696
$757$			36.0000i			1.30844i	0.756303	+	0.654221i	$0.227003\pi$
$757$			36.0000i			1.30844i	−0.756303	+	0.654221i	$0.772997\pi$
$758$			20.0000i			0.726433i
$759$			18.0000i			0.653359i
$760$			6.00000i			0.217643i
$761$	−3.00000			−0.108750			−0.0543750	−	0.998521i	$-0.517317\pi$
$761$	−3.00000			−0.108750			−0.0543750	+	0.998521i	$0.517317\pi$
$762$		−	20.0000i		−	0.724524i
$763$			9.00000i			0.325822i
$764$		−	27.0000i		−	0.976826i
$765$	−3.00000			−0.108465
$766$	18.0000			0.650366
$767$		0			0
$768$	1.00000			0.0360844
$769$		−	24.0000i		−	0.865462i	−0.901523	−	0.432731i	$-0.857550\pi$
$769$		−	24.0000i		−	0.865462i	0.901523	−	0.432731i	$-0.142450\pi$
$770$	−3.00000			−0.108112
$771$			6.00000i			0.216085i
$772$			18.0000i			0.647834i
$773$	−3.00000			−0.107903			−0.0539513	−	0.998544i	$-0.517182\pi$
$773$	−3.00000			−0.107903			−0.0539513	+	0.998544i	$0.517182\pi$
$774$	−9.00000			−0.323498
$775$		−	3.00000i		−	0.107763i
$776$	−3.00000			−0.107694
$777$	1.00000	−	6.00000i	0.0358748	−	0.215249i
$778$	−21.0000			−0.752886
$779$			54.0000i			1.93475i
$780$	6.00000			0.214834
$781$	18.0000			0.644091
$782$		−	18.0000i		−	0.643679i
$783$		−	9.00000i		−	0.321634i
$784$	−6.00000			−0.214286
$785$			5.00000i			0.178458i
$786$	12.0000			0.428026
$787$	−22.0000			−0.784215			−0.392108	−	0.919919i	$-0.628254\pi$
$787$	−22.0000			−0.784215			−0.392108	+	0.919919i	$0.628254\pi$
$788$	−18.0000			−0.641223
$789$	9.00000			0.320408
$790$		0			0
$791$			9.00000i			0.320003i
$792$			3.00000i			0.106600i
$793$	−54.0000			−1.91760
$794$		−	34.0000i		−	1.20661i
$795$		−	3.00000i		−	0.106399i
$796$		−	12.0000i		−	0.425329i
$797$			12.0000i			0.425062i	0.977154	+	0.212531i	$0.0681706\pi$
$797$			12.0000i			0.425062i	−0.977154	+	0.212531i	$0.931829\pi$
$798$	6.00000			0.212398
$799$		0			0
$800$			1.00000i			0.0353553i
$801$			12.0000i			0.423999i
$802$	18.0000			0.635602
$803$	−6.00000			−0.211735
$804$	14.0000			0.493742
$805$	6.00000			0.211472
$806$		−	18.0000i		−	0.634023i
$807$		0			0
$808$			12.0000i			0.422159i
$809$			18.0000i			0.632846i	0.948618	+	0.316423i	$0.102482\pi$
$809$			18.0000i			0.632846i	−0.948618	+	0.316423i	$0.897518\pi$
$810$	−1.00000			−0.0351364
$811$	16.0000			0.561836			0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000			0.561836			0.280918	+	0.959732i	$0.409361\pi$
$812$			9.00000i			0.315838i
$813$	−20.0000			−0.701431
$814$	−18.0000	−	3.00000i	−0.630900	−	0.105150i
$815$	9.00000			0.315256
$816$		−	3.00000i		−	0.105021i
$817$	54.0000			1.88922
$818$		0			0
$819$		−	6.00000i		−	0.209657i
$820$			9.00000i			0.314294i
$821$	36.0000			1.25641			0.628204	−	0.778048i	$-0.283790\pi$
$821$	36.0000			1.25641			0.628204	+	0.778048i	$0.283790\pi$
$822$		−	12.0000i		−	0.418548i
$823$	32.0000			1.11545			0.557725	−	0.830026i	$-0.311674\pi$
$823$	32.0000			1.11545			0.557725	+	0.830026i	$0.311674\pi$
$824$	−6.00000			−0.209020
$825$	−3.00000			−0.104447
$826$		0			0
$827$		−	27.0000i		−	0.938882i	−0.882964	−	0.469441i	$-0.844455\pi$
$827$		−	27.0000i		−	0.938882i	0.882964	−	0.469441i	$-0.155545\pi$
$828$		−	6.00000i		−	0.208514i
$829$		−	9.00000i		−	0.312583i	−0.987711	−	0.156291i	$-0.950046\pi$
$829$		−	9.00000i		−	0.312583i	0.987711	−	0.156291i	$-0.0499539\pi$
$830$		0			0
$831$			12.0000i			0.416275i
$832$			6.00000i			0.208013i
$833$			18.0000i			0.623663i
$834$			5.00000i			0.173136i
$835$	−6.00000			−0.207639
$836$		−	18.0000i		−	0.622543i
$837$			3.00000i			0.103695i
$838$			24.0000i			0.829066i
$839$	30.0000			1.03572			0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000			1.03572			0.517858	+	0.855467i	$0.326730\pi$
$840$	1.00000			0.0345033
$841$	−52.0000			−1.79310
$842$	30.0000			1.03387
$843$			18.0000i			0.619953i
$844$	−23.0000			−0.791693
$845$			23.0000i			0.791224i
$846$		0			0
$847$	−2.00000			−0.0687208
$848$	3.00000			0.103020
$849$		−	24.0000i		−	0.823678i
$850$	3.00000			0.102899
$851$	36.0000	+	6.00000i	1.23406	+	0.205677i
$852$	−6.00000			−0.205557
$853$			6.00000i			0.205436i	0.994711	+	0.102718i	$0.0327539\pi$
$853$			6.00000i			0.205436i	−0.994711	+	0.102718i	$0.967246\pi$
$854$	−9.00000			−0.307974
$855$	6.00000			0.205196
$856$		−	6.00000i		−	0.205076i
$857$		−	21.0000i		−	0.717346i	−0.933463	−	0.358673i	$-0.883229\pi$
$857$		−	21.0000i		−	0.717346i	0.933463	−	0.358673i	$-0.116771\pi$
$858$	−18.0000			−0.614510
$859$			42.0000i			1.43302i	0.697576	+	0.716511i	$0.254262\pi$
$859$			42.0000i			1.43302i	−0.697576	+	0.716511i	$0.745738\pi$
$860$	9.00000			0.306897
$861$	9.00000			0.306719
$862$	9.00000			0.306541
$863$	−3.00000			−0.102121			−0.0510606	−	0.998696i	$-0.516260\pi$
$863$	−3.00000			−0.102121			−0.0510606	+	0.998696i	$0.516260\pi$
$864$		−	1.00000i		−	0.0340207i
$865$			3.00000i			0.102003i
$866$			38.0000i			1.29129i
$867$	8.00000			0.271694
$868$		−	3.00000i		−	0.101827i
$869$		0			0
$870$			9.00000i			0.305129i
$871$			84.0000i			2.84623i
$872$	−9.00000			−0.304778
$873$			3.00000i			0.101535i
$874$			36.0000i			1.21772i
$875$			1.00000i			0.0338062i
$876$	2.00000			0.0675737
$877$	−41.0000			−1.38447			−0.692236	−	0.721671i	$-0.743374\pi$
$877$	−41.0000			−1.38447			−0.692236	+	0.721671i	$0.743374\pi$
$878$	33.0000			1.11370
$879$	21.0000			0.708312
$880$		−	3.00000i		−	0.101130i
$881$	57.0000			1.92038			0.960189	−	0.279350i	$-0.0901189\pi$
$881$	57.0000			1.92038			0.960189	+	0.279350i	$0.0901189\pi$
$882$			6.00000i			0.202031i
$883$			39.0000i			1.31245i	0.754563	+	0.656227i	$0.227849\pi$
$883$			39.0000i			1.31245i	−0.754563	+	0.656227i	$0.772151\pi$
$884$	18.0000			0.605406
$885$		0			0
$886$			12.0000i			0.403148i
$887$	9.00000			0.302190			0.151095	−	0.988519i	$-0.451720\pi$
$887$	9.00000			0.302190			0.151095	+	0.988519i	$0.451720\pi$
$888$	6.00000	+	1.00000i	0.201347	+	0.0335578i
$889$	20.0000			0.670778
$890$		−	12.0000i		−	0.402241i
$891$	3.00000			0.100504
$892$	1.00000			0.0334825
$893$		0			0
$894$			18.0000i			0.602010i
$895$	18.0000			0.601674
$896$			1.00000i			0.0334077i
$897$	36.0000			1.20201
$898$	−30.0000			−1.00111
$899$	27.0000			0.900500
$900$	1.00000			0.0333333
$901$		−	9.00000i		−	0.299833i
$902$		−	27.0000i		−	0.899002i
$903$		−	9.00000i		−	0.299501i
$904$	−9.00000			−0.299336
$905$		−	16.0000i		−	0.531858i
$906$			10.0000i			0.332228i
$907$		−	36.0000i		−	1.19536i	−0.801735	−	0.597680i	$-0.796089\pi$
$907$		−	36.0000i		−	1.19536i	0.801735	−	0.597680i	$-0.203911\pi$
$908$		−	21.0000i		−	0.696909i
$909$	12.0000			0.398015
$910$			6.00000i			0.198898i
$911$		−	24.0000i		−	0.795155i	−0.917568	−	0.397578i	$-0.869851\pi$
$911$		−	24.0000i		−	0.795155i	0.917568	−	0.397578i	$-0.130149\pi$
$912$			6.00000i			0.198680i
$913$		0			0
$914$	39.0000			1.29001
$915$	−9.00000			−0.297531
$916$	22.0000			0.726900
$917$			12.0000i			0.396275i
$918$	−3.00000			−0.0990148
$919$		−	48.0000i		−	1.58337i	−0.610927	−	0.791687i	$-0.709203\pi$
$919$		−	48.0000i		−	1.58337i	0.610927	−	0.791687i	$-0.290797\pi$
$920$			6.00000i			0.197814i
$921$	−16.0000			−0.527218
$922$	−9.00000			−0.296399
$923$		−	36.0000i		−	1.18495i
$924$	−3.00000			−0.0986928
$925$	−1.00000	+	6.00000i	−0.0328798	+	0.197279i
$926$		0			0
$927$			6.00000i			0.197066i
$928$	−9.00000			−0.295439
$929$	39.0000			1.27955			0.639774	−	0.768563i	$-0.279028\pi$
$929$	39.0000			1.27955			0.639774	+	0.768563i	$0.279028\pi$
$930$		−	3.00000i		−	0.0983739i
$931$		−	36.0000i		−	1.17985i
$932$	−24.0000			−0.786146
$933$		−	27.0000i		−	0.883940i
$934$	−33.0000			−1.07979
$935$	−9.00000			−0.294331
$936$	6.00000			0.196116
$937$	20.0000			0.653372			0.326686	−	0.945133i	$-0.394068\pi$
$937$	20.0000			0.653372			0.326686	+	0.945133i	$0.394068\pi$
$938$			14.0000i			0.457116i
$939$			18.0000i			0.587408i
$940$		0			0
$941$	−36.0000			−1.17357			−0.586783	−	0.809744i	$-0.699606\pi$
$941$	−36.0000			−1.17357			−0.586783	+	0.809744i	$0.699606\pi$
$942$			5.00000i			0.162909i
$943$			54.0000i			1.75848i
$944$		0			0
$945$		−	1.00000i		−	0.0325300i
$946$	−27.0000			−0.877846
$947$			21.0000i			0.682408i	0.939989	+	0.341204i	$0.110835\pi$
$947$			21.0000i			0.682408i	−0.939989	+	0.341204i	$0.889165\pi$
$948$		0			0
$949$			12.0000i			0.389536i
$950$	−6.00000			−0.194666
$951$	−27.0000			−0.875535
$952$	3.00000			0.0972306
$953$	54.0000			1.74923			0.874616	−	0.484817i	$-0.161114\pi$
$953$	54.0000			1.74923			0.874616	+	0.484817i	$0.161114\pi$
$954$		−	3.00000i		−	0.0971286i
$955$	27.0000			0.873699
$956$		−	15.0000i		−	0.485135i
$957$		−	27.0000i		−	0.872786i
$958$		0			0
$959$	12.0000			0.387500
$960$			1.00000i			0.0322749i
$961$	22.0000			0.709677
$962$	−6.00000	+	36.0000i	−0.193448	+	1.16069i
$963$	−6.00000			−0.193347
$964$		0			0
$965$	−18.0000			−0.579441
$966$	6.00000			0.193047
$967$			42.0000i			1.35063i	0.737530	+	0.675314i	$0.235992\pi$
$967$			42.0000i			1.35063i	−0.737530	+	0.675314i	$0.764008\pi$
$968$		−	2.00000i		−	0.0642824i
$969$	18.0000			0.578243
$970$		−	3.00000i		−	0.0963242i
$971$	−57.0000			−1.82922			−0.914609	−	0.404341i	$-0.867501\pi$
$971$	−57.0000			−1.82922			−0.914609	+	0.404341i	$0.867501\pi$
$972$	−1.00000			−0.0320750
$973$	−5.00000			−0.160293
$974$	−12.0000			−0.384505
$975$			6.00000i			0.192154i
$976$		−	9.00000i		−	0.288083i
$977$			3.00000i			0.0959785i	0.998848	+	0.0479893i	$0.0152813\pi$
$977$			3.00000i			0.0959785i	−0.998848	+	0.0479893i	$0.984719\pi$
$978$	9.00000			0.287788
$979$			36.0000i			1.15056i
$980$		−	6.00000i		−	0.191663i
$981$			9.00000i			0.287348i
$982$			36.0000i			1.14881i
$983$	−9.00000			−0.287055			−0.143528	−	0.989646i	$-0.545845\pi$
$983$	−9.00000			−0.287055			−0.143528	+	0.989646i	$0.545845\pi$
$984$			9.00000i			0.286910i
$985$		−	18.0000i		−	0.573528i
$986$			27.0000i			0.859855i
$987$		0			0
$988$	−36.0000			−1.14531
$989$	54.0000			1.71710
$990$	−3.00000			−0.0953463
$991$		−	27.0000i		−	0.857683i	−0.903380	−	0.428842i	$-0.858922\pi$
$991$		−	27.0000i		−	0.857683i	0.903380	−	0.428842i	$-0.141078\pi$
$992$	3.00000			0.0952501
$993$			18.0000i			0.571213i
$994$		−	6.00000i		−	0.190308i
$995$	12.0000			0.380426
$996$		0			0
$997$		0			0		1.00000			$0$
$997$		0			0		−1.00000			$\pi$
$998$	−6.00000			−0.189927
$999$	1.00000	−	6.00000i	0.0316386	−	0.189832i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.h.c.961.1	✓	2
3.2	odd	2		3330.2.h.f.2071.2		2
37.36	even	2	inner	1110.2.h.c.961.2	yes	2
111.110	odd	2		3330.2.h.f.2071.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.h.c.961.1	✓	2	1.1	even	1	trivial
1110.2.h.c.961.2	yes	2	37.36	even	2	inner
3330.2.h.f.2071.1		2	111.110	odd	2
3330.2.h.f.2071.2		2	3.2	odd	2

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} -1.00000i q^{6} +1.00000 q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} -1.00000i q^{6} +1.00000 q^{7} +1.00000i q^{8} +1.00000 q^{9} -1.00000 q^{10} +3.00000 q^{11} -1.00000 q^{12} -6.00000i q^{13} -1.00000i q^{14} -1.00000i q^{15} +1.00000 q^{16} -3.00000i q^{17} -1.00000i q^{18} +6.00000i q^{19} +1.00000i q^{20} +1.00000 q^{21} -3.00000i q^{22} +6.00000i q^{23} +1.00000i q^{24} -1.00000 q^{25} -6.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} -9.00000i q^{29} -1.00000 q^{30} +3.00000i q^{31} -1.00000i q^{32} +3.00000 q^{33} -3.00000 q^{34} -1.00000i q^{35} -1.00000 q^{36} +(1.00000 - 6.00000i) q^{37} +6.00000 q^{38} -6.00000i q^{39} +1.00000 q^{40} +9.00000 q^{41} -1.00000i q^{42} -9.00000i q^{43} -3.00000 q^{44} -1.00000i q^{45} +6.00000 q^{46} +1.00000 q^{48} -6.00000 q^{49} +1.00000i q^{50} -3.00000i q^{51} +6.00000i q^{52} +3.00000 q^{53} -1.00000i q^{54} -3.00000i q^{55} +1.00000i q^{56} +6.00000i q^{57} -9.00000 q^{58} +1.00000i q^{60} -9.00000i q^{61} +3.00000 q^{62} +1.00000 q^{63} -1.00000 q^{64} -6.00000 q^{65} -3.00000i q^{66} -14.0000 q^{67} +3.00000i q^{68} +6.00000i q^{69} -1.00000 q^{70} +6.00000 q^{71} +1.00000i q^{72} -2.00000 q^{73} +(-6.00000 - 1.00000i) q^{74} -1.00000 q^{75} -6.00000i q^{76} +3.00000 q^{77} -6.00000 q^{78} -1.00000i q^{80} +1.00000 q^{81} -9.00000i q^{82} -1.00000 q^{84} -3.00000 q^{85} -9.00000 q^{86} -9.00000i q^{87} +3.00000i q^{88} +12.0000i q^{89} -1.00000 q^{90} -6.00000i q^{91} -6.00000i q^{92} +3.00000i q^{93} +6.00000 q^{95} -1.00000i q^{96} +3.00000i q^{97} +6.00000i q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} - 2 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^3 - 2 * q^4 + 2 * q^7 + 2 * q^9	\( 2 q + 2 q^{3} - 2 q^{4} + 2 q^{7} + 2 q^{9} - 2 q^{10} + 6 q^{11} - 2 q^{12} + 2 q^{16} + 2 q^{21} - 2 q^{25} - 12 q^{26} + 2 q^{27} - 2 q^{28} - 2 q^{30} + 6 q^{33} - 6 q^{34} - 2 q^{36} + 2 q^{37} + 12 q^{38} + 2 q^{40} + 18 q^{41} - 6 q^{44} + 12 q^{46} + 2 q^{48} - 12 q^{49} + 6 q^{53} - 18 q^{58} + 6 q^{62} + 2 q^{63} - 2 q^{64} - 12 q^{65} - 28 q^{67} - 2 q^{70} + 12 q^{71} - 4 q^{73} - 12 q^{74} - 2 q^{75} + 6 q^{77} - 12 q^{78} + 2 q^{81} - 2 q^{84} - 6 q^{85} - 18 q^{86} - 2 q^{90} + 12 q^{95} + 6 q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 - 2 * q^4 + 2 * q^7 + 2 * q^9 - 2 * q^10 + 6 * q^11 - 2 * q^12 + 2 * q^16 + 2 * q^21 - 2 * q^25 - 12 * q^26 + 2 * q^27 - 2 * q^28 - 2 * q^30 + 6 * q^33 - 6 * q^34 - 2 * q^36 + 2 * q^37 + 12 * q^38 + 2 * q^40 + 18 * q^41 - 6 * q^44 + 12 * q^46 + 2 * q^48 - 12 * q^49 + 6 * q^53 - 18 * q^58 + 6 * q^62 + 2 * q^63 - 2 * q^64 - 12 * q^65 - 28 * q^67 - 2 * q^70 + 12 * q^71 - 4 * q^73 - 12 * q^74 - 2 * q^75 + 6 * q^77 - 12 * q^78 + 2 * q^81 - 2 * q^84 - 6 * q^85 - 18 * q^86 - 2 * q^90 + 12 * q^95 + 6 * q^99

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