LMFDB - Embedded newform 1950.2.f.d.649.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(649,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1950.649");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.f (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$2$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			649.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	1950.649
Dual form			1950.2.f.d.649.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +1.00000i q^{6} +2.00000 q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +1.00000i q^{6} +2.00000 q^{7} -1.00000 q^{8} -1.00000 q^{9} -1.00000i q^{12} +(-2.00000 + 3.00000i) q^{13} -2.00000 q^{14} +1.00000 q^{16} -2.00000i q^{17} +1.00000 q^{18} +6.00000i q^{19} -2.00000i q^{21} -4.00000i q^{23} +1.00000i q^{24} +(2.00000 - 3.00000i) q^{26} +1.00000i q^{27} +2.00000 q^{28} +10.0000 q^{29} +10.0000i q^{31} -1.00000 q^{32} +2.00000i q^{34} -1.00000 q^{36} -8.00000 q^{37} -6.00000i q^{38} +(3.00000 + 2.00000i) q^{39} +10.0000i q^{41} +2.00000i q^{42} -4.00000i q^{43} +4.00000i q^{46} +12.0000 q^{47} -1.00000i q^{48} -3.00000 q^{49} -2.00000 q^{51} +(-2.00000 + 3.00000i) q^{52} +6.00000i q^{53} -1.00000i q^{54} -2.00000 q^{56} +6.00000 q^{57} -10.0000 q^{58} -4.00000i q^{59} +2.00000 q^{61} -10.0000i q^{62} -2.00000 q^{63} +1.00000 q^{64} +2.00000 q^{67} -2.00000i q^{68} -4.00000 q^{69} +1.00000 q^{72} -4.00000 q^{73} +8.00000 q^{74} +6.00000i q^{76} +(-3.00000 - 2.00000i) q^{78} +1.00000 q^{81} -10.0000i q^{82} -4.00000 q^{83} -2.00000i q^{84} +4.00000i q^{86} -10.0000i q^{87} +6.00000i q^{89} +(-4.00000 + 6.00000i) q^{91} -4.00000i q^{92} +10.0000 q^{93} -12.0000 q^{94} +1.00000i q^{96} +12.0000 q^{97} +3.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} + 4 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^4 + 4 * q^7 - 2 * q^8 - 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{4} + 4 q^{7} - 2 q^{8} - 2 q^{9} - 4 q^{13} - 4 q^{14} + 2 q^{16} + 2 q^{18} + 4 q^{26} + 4 q^{28} + 20 q^{29} - 2 q^{32} - 2 q^{36} - 16 q^{37} + 6 q^{39} + 24 q^{47} - 6 q^{49} - 4 q^{51} - 4 q^{52} - 4 q^{56} + 12 q^{57} - 20 q^{58} + 4 q^{61} - 4 q^{63} + 2 q^{64} + 4 q^{67} - 8 q^{69} + 2 q^{72} - 8 q^{73} + 16 q^{74} - 6 q^{78} + 2 q^{81} - 8 q^{83} - 8 q^{91} + 20 q^{93} - 24 q^{94} + 24 q^{97} + 6 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 + 4 * q^7 - 2 * q^8 - 2 * q^9 - 4 * q^13 - 4 * q^14 + 2 * q^16 + 2 * q^18 + 4 * q^26 + 4 * q^28 + 20 * q^29 - 2 * q^32 - 2 * q^36 - 16 * q^37 + 6 * q^39 + 24 * q^47 - 6 * q^49 - 4 * q^51 - 4 * q^52 - 4 * q^56 + 12 * q^57 - 20 * q^58 + 4 * q^61 - 4 * q^63 + 2 * q^64 + 4 * q^67 - 8 * q^69 + 2 * q^72 - 8 * q^73 + 16 * q^74 - 6 * q^78 + 2 * q^81 - 8 * q^83 - 8 * q^91 + 20 * q^93 - 24 * q^94 + 24 * q^97 + 6 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$301$	$1301$	$1327$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.00000			0.500000
$5$		0			0
$5$		0			0
$6$			1.00000i			0.408248i
$7$	2.00000			0.755929			0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000			0.755929			0.377964	+	0.925820i	$0.376624\pi$
$8$	−1.00000			−0.353553
$9$	−1.00000			−0.333333
$10$		0			0
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$		−	1.00000i		−	0.288675i
$13$	−2.00000	+	3.00000i	−0.554700	+	0.832050i
$13$	−2.00000	+	3.00000i	−0.554700	+	0.832050i
$14$	−2.00000			−0.534522
$15$		0			0
$16$	1.00000			0.250000
$17$		−	2.00000i		−	0.485071i	−0.970143	−	0.242536i	$-0.922021\pi$
$17$		−	2.00000i		−	0.485071i	0.970143	−	0.242536i	$-0.0779791\pi$
$18$	1.00000			0.235702
$19$			6.00000i			1.37649i	0.725476	+	0.688247i	$0.241620\pi$
$19$			6.00000i			1.37649i	−0.725476	+	0.688247i	$0.758380\pi$
$20$		0			0
$21$		−	2.00000i		−	0.436436i
$22$		0			0
$23$		−	4.00000i		−	0.834058i	−0.908893	−	0.417029i	$-0.863071\pi$
$23$		−	4.00000i		−	0.834058i	0.908893	−	0.417029i	$-0.136929\pi$
$24$			1.00000i			0.204124i
$25$		0			0
$26$	2.00000	−	3.00000i	0.392232	−	0.588348i
$27$			1.00000i			0.192450i
$28$	2.00000			0.377964
$29$	10.0000			1.85695			0.928477	−	0.371391i	$-0.121119\pi$
$29$	10.0000			1.85695			0.928477	+	0.371391i	$0.121119\pi$
$30$		0			0
$31$			10.0000i			1.79605i	0.439941	+	0.898027i	$0.354999\pi$
$31$			10.0000i			1.79605i	−0.439941	+	0.898027i	$0.645001\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$			2.00000i			0.342997i
$35$		0			0
$36$	−1.00000			−0.166667
$37$	−8.00000			−1.31519			−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000			−1.31519			−0.657596	+	0.753371i	$0.728427\pi$
$38$		−	6.00000i		−	0.973329i
$39$	3.00000	+	2.00000i	0.480384	+	0.320256i
$40$		0			0
$41$			10.0000i			1.56174i	0.624695	+	0.780869i	$0.285223\pi$
$41$			10.0000i			1.56174i	−0.624695	+	0.780869i	$0.714777\pi$
$42$			2.00000i			0.308607i
$43$		−	4.00000i		−	0.609994i	−0.952353	−	0.304997i	$-0.901344\pi$
$43$		−	4.00000i		−	0.609994i	0.952353	−	0.304997i	$-0.0986555\pi$
$44$		0			0
$45$		0			0
$46$			4.00000i			0.589768i
$47$	12.0000			1.75038			0.875190	−	0.483779i	$-0.160736\pi$
$47$	12.0000			1.75038			0.875190	+	0.483779i	$0.160736\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−3.00000			−0.428571
$50$		0			0
$51$	−2.00000			−0.280056
$52$	−2.00000	+	3.00000i	−0.277350	+	0.416025i
$53$			6.00000i			0.824163i	0.911147	+	0.412082i	$0.135198\pi$
$53$			6.00000i			0.824163i	−0.911147	+	0.412082i	$0.864802\pi$
$54$		−	1.00000i		−	0.136083i
$55$		0			0
$56$	−2.00000			−0.267261
$57$	6.00000			0.794719
$58$	−10.0000			−1.31306
$59$		−	4.00000i		−	0.520756i	−0.965507	−	0.260378i	$-0.916153\pi$
$59$		−	4.00000i		−	0.520756i	0.965507	−	0.260378i	$-0.0838471\pi$
$60$		0			0
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$		−	10.0000i		−	1.27000i
$63$	−2.00000			−0.251976
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	2.00000			0.244339			0.122169	−	0.992509i	$-0.461015\pi$
$67$	2.00000			0.244339			0.122169	+	0.992509i	$0.461015\pi$
$68$		−	2.00000i		−	0.242536i
$69$	−4.00000			−0.481543
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	1.00000			0.117851
$73$	−4.00000			−0.468165			−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000			−0.468165			−0.234082	+	0.972217i	$0.575209\pi$
$74$	8.00000			0.929981
$75$		0			0
$76$			6.00000i			0.688247i
$77$		0			0
$78$	−3.00000	−	2.00000i	−0.339683	−	0.226455i
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		−	10.0000i		−	1.10432i
$83$	−4.00000			−0.439057			−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000			−0.439057			−0.219529	+	0.975606i	$0.570452\pi$
$84$		−	2.00000i		−	0.218218i
$85$		0			0
$86$			4.00000i			0.431331i
$87$		−	10.0000i		−	1.07211i
$88$		0			0
$89$			6.00000i			0.635999i	0.948091	+	0.317999i	$0.103011\pi$
$89$			6.00000i			0.635999i	−0.948091	+	0.317999i	$0.896989\pi$
$90$		0			0
$91$	−4.00000	+	6.00000i	−0.419314	+	0.628971i
$92$		−	4.00000i		−	0.417029i
$93$	10.0000			1.03695
$94$	−12.0000			−1.23771
$95$		0			0
$96$			1.00000i			0.102062i
$97$	12.0000			1.21842			0.609208	−	0.793011i	$-0.291488\pi$
$97$	12.0000			1.21842			0.609208	+	0.793011i	$0.291488\pi$
$98$	3.00000			0.303046
$99$		0			0
$100$		0			0
$101$	2.00000			0.199007			0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000			0.199007			0.0995037	+	0.995037i	$0.468274\pi$
$102$	2.00000			0.198030
$103$			16.0000i			1.57653i	0.615338	+	0.788263i	$0.289020\pi$
$103$			16.0000i			1.57653i	−0.615338	+	0.788263i	$0.710980\pi$
$104$	2.00000	−	3.00000i	0.196116	−	0.294174i
$105$		0			0
$106$		−	6.00000i		−	0.582772i
$107$			8.00000i			0.773389i	0.922208	+	0.386695i	$0.126383\pi$
$107$			8.00000i			0.773389i	−0.922208	+	0.386695i	$0.873617\pi$
$108$			1.00000i			0.0962250i
$109$		−	4.00000i		−	0.383131i	−0.981480	−	0.191565i	$-0.938644\pi$
$109$		−	4.00000i		−	0.383131i	0.981480	−	0.191565i	$-0.0613564\pi$
$110$		0			0
$111$			8.00000i			0.759326i
$112$	2.00000			0.188982
$113$		−	14.0000i		−	1.31701i	−0.752577	−	0.658505i	$-0.771189\pi$
$113$		−	14.0000i		−	1.31701i	0.752577	−	0.658505i	$-0.228811\pi$
$114$	−6.00000			−0.561951
$115$		0			0
$116$	10.0000			0.928477
$117$	2.00000	−	3.00000i	0.184900	−	0.277350i
$118$			4.00000i			0.368230i
$119$		−	4.00000i		−	0.366679i
$120$		0			0
$121$	11.0000			1.00000
$122$	−2.00000			−0.181071
$123$	10.0000			0.901670
$124$			10.0000i			0.898027i
$125$		0			0
$126$	2.00000			0.178174
$127$			8.00000i			0.709885i	0.934888	+	0.354943i	$0.115500\pi$
$127$			8.00000i			0.709885i	−0.934888	+	0.354943i	$0.884500\pi$
$128$	−1.00000			−0.0883883
$129$	−4.00000			−0.352180
$130$		0			0
$131$	−8.00000			−0.698963			−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−8.00000			−0.698963			−0.349482	+	0.936943i	$0.613642\pi$
$132$		0			0
$133$			12.0000i			1.04053i
$134$	−2.00000			−0.172774
$135$		0			0
$136$			2.00000i			0.171499i
$137$	2.00000			0.170872			0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000			0.170872			0.0854358	+	0.996344i	$0.472772\pi$
$138$	4.00000			0.340503
$139$	20.0000			1.69638			0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000			1.69638			0.848189	+	0.529694i	$0.177693\pi$
$140$		0			0
$141$		−	12.0000i		−	1.01058i
$142$		0			0
$143$		0			0
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	4.00000			0.331042
$147$			3.00000i			0.247436i
$148$	−8.00000			−0.657596
$149$		−	14.0000i		−	1.14692i	−0.819232	−	0.573462i	$-0.805600\pi$
$149$		−	14.0000i		−	1.14692i	0.819232	−	0.573462i	$-0.194400\pi$
$150$		0			0
$151$			10.0000i			0.813788i	0.913475	+	0.406894i	$0.133388\pi$
$151$			10.0000i			0.813788i	−0.913475	+	0.406894i	$0.866612\pi$
$152$		−	6.00000i		−	0.486664i
$153$			2.00000i			0.161690i
$154$		0			0
$155$		0			0
$156$	3.00000	+	2.00000i	0.240192	+	0.160128i
$157$		−	2.00000i		−	0.159617i	−0.996810	−	0.0798087i	$-0.974569\pi$
$157$		−	2.00000i		−	0.159617i	0.996810	−	0.0798087i	$-0.0254309\pi$
$158$		0			0
$159$	6.00000			0.475831
$160$		0			0
$161$		−	8.00000i		−	0.630488i
$162$	−1.00000			−0.0785674
$163$	−14.0000			−1.09656			−0.548282	−	0.836293i	$-0.684718\pi$
$163$	−14.0000			−1.09656			−0.548282	+	0.836293i	$0.684718\pi$
$164$			10.0000i			0.780869i
$165$		0			0
$166$	4.00000			0.310460
$167$	12.0000			0.928588			0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000			0.928588			0.464294	+	0.885681i	$0.346308\pi$
$168$			2.00000i			0.154303i
$169$	−5.00000	−	12.0000i	−0.384615	−	0.923077i
$170$		0			0
$171$		−	6.00000i		−	0.458831i
$172$		−	4.00000i		−	0.304997i
$173$			6.00000i			0.456172i	0.973641	+	0.228086i	$0.0732467\pi$
$173$			6.00000i			0.456172i	−0.973641	+	0.228086i	$0.926753\pi$
$174$			10.0000i			0.758098i
$175$		0			0
$176$		0			0
$177$	−4.00000			−0.300658
$178$		−	6.00000i		−	0.449719i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		0			0
$181$	22.0000			1.63525			0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000			1.63525			0.817624	+	0.575753i	$0.195291\pi$
$182$	4.00000	−	6.00000i	0.296500	−	0.444750i
$183$		−	2.00000i		−	0.147844i
$184$			4.00000i			0.294884i
$185$		0			0
$186$	−10.0000			−0.733236
$187$		0			0
$188$	12.0000			0.875190
$189$			2.00000i			0.145479i
$190$		0			0
$191$	12.0000			0.868290			0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000			0.868290			0.434145	+	0.900843i	$0.357051\pi$
$192$		−	1.00000i		−	0.0721688i
$193$	16.0000			1.15171			0.575853	−	0.817554i	$-0.304670\pi$
$193$	16.0000			1.15171			0.575853	+	0.817554i	$0.304670\pi$
$194$	−12.0000			−0.861550
$195$		0			0
$196$	−3.00000			−0.214286
$197$	22.0000			1.56744			0.783718	−	0.621117i	$-0.213321\pi$
$197$	22.0000			1.56744			0.783718	+	0.621117i	$0.213321\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$		0			0
$201$		−	2.00000i		−	0.141069i
$202$	−2.00000			−0.140720
$203$	20.0000			1.40372
$204$	−2.00000			−0.140028
$205$		0			0
$206$		−	16.0000i		−	1.11477i
$207$			4.00000i			0.278019i
$208$	−2.00000	+	3.00000i	−0.138675	+	0.208013i
$209$		0			0
$210$		0			0
$211$	12.0000			0.826114			0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$212$			6.00000i			0.412082i
$213$		0			0
$214$		−	8.00000i		−	0.546869i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$			20.0000i			1.35769i
$218$			4.00000i			0.270914i
$219$			4.00000i			0.270295i
$220$		0			0
$221$	6.00000	+	4.00000i	0.403604	+	0.269069i
$222$		−	8.00000i		−	0.536925i
$223$	−14.0000			−0.937509			−0.468755	−	0.883328i	$-0.655297\pi$
$223$	−14.0000			−0.937509			−0.468755	+	0.883328i	$0.655297\pi$
$224$	−2.00000			−0.133631
$225$		0			0
$226$			14.0000i			0.931266i
$227$	−8.00000			−0.530979			−0.265489	−	0.964114i	$-0.585534\pi$
$227$	−8.00000			−0.530979			−0.265489	+	0.964114i	$0.585534\pi$
$228$	6.00000			0.397360
$229$		−	4.00000i		−	0.264327i	−0.991228	−	0.132164i	$-0.957808\pi$
$229$		−	4.00000i		−	0.264327i	0.991228	−	0.132164i	$-0.0421925\pi$
$230$		0			0
$231$		0			0
$232$	−10.0000			−0.656532
$233$			6.00000i			0.393073i	0.980497	+	0.196537i	$0.0629694\pi$
$233$			6.00000i			0.393073i	−0.980497	+	0.196537i	$0.937031\pi$
$234$	−2.00000	+	3.00000i	−0.130744	+	0.196116i
$235$		0			0
$236$		−	4.00000i		−	0.260378i
$237$		0			0
$238$			4.00000i			0.259281i
$239$			16.0000i			1.03495i	0.855697	+	0.517477i	$0.173129\pi$
$239$			16.0000i			1.03495i	−0.855697	+	0.517477i	$0.826871\pi$
$240$		0			0
$241$			20.0000i			1.28831i	0.764894	+	0.644157i	$0.222792\pi$
$241$			20.0000i			1.28831i	−0.764894	+	0.644157i	$0.777208\pi$
$242$	−11.0000			−0.707107
$243$		−	1.00000i		−	0.0641500i
$244$	2.00000			0.128037
$245$		0			0
$246$	−10.0000			−0.637577
$247$	−18.0000	−	12.0000i	−1.14531	−	0.763542i
$248$		−	10.0000i		−	0.635001i
$249$			4.00000i			0.253490i
$250$		0			0
$251$	−28.0000			−1.76734			−0.883672	−	0.468106i	$-0.844936\pi$
$251$	−28.0000			−1.76734			−0.883672	+	0.468106i	$0.844936\pi$
$252$	−2.00000			−0.125988
$253$		0			0
$254$		−	8.00000i		−	0.501965i
$255$		0			0
$256$	1.00000			0.0625000
$257$			18.0000i			1.12281i	0.827541	+	0.561405i	$0.189739\pi$
$257$			18.0000i			1.12281i	−0.827541	+	0.561405i	$0.810261\pi$
$258$	4.00000			0.249029
$259$	−16.0000			−0.994192
$260$		0			0
$261$	−10.0000			−0.618984
$262$	8.00000			0.494242
$263$		−	24.0000i		−	1.47990i	−0.672660	−	0.739952i	$-0.734848\pi$
$263$		−	24.0000i		−	1.47990i	0.672660	−	0.739952i	$-0.265152\pi$
$264$		0			0
$265$		0			0
$266$		−	12.0000i		−	0.735767i
$267$	6.00000			0.367194
$268$	2.00000			0.122169
$269$	10.0000			0.609711			0.304855	−	0.952399i	$-0.401392\pi$
$269$	10.0000			0.609711			0.304855	+	0.952399i	$0.401392\pi$
$270$		0			0
$271$		−	10.0000i		−	0.607457i	−0.952759	−	0.303728i	$-0.901768\pi$
$271$		−	10.0000i		−	0.607457i	0.952759	−	0.303728i	$-0.0982315\pi$
$272$		−	2.00000i		−	0.121268i
$273$	6.00000	+	4.00000i	0.363137	+	0.242091i
$274$	−2.00000			−0.120824
$275$		0			0
$276$	−4.00000			−0.240772
$277$		−	2.00000i		−	0.120168i	−0.998193	−	0.0600842i	$-0.980863\pi$
$277$		−	2.00000i		−	0.120168i	0.998193	−	0.0600842i	$-0.0191369\pi$
$278$	−20.0000			−1.19952
$279$		−	10.0000i		−	0.598684i
$280$		0			0
$281$		−	10.0000i		−	0.596550i	−0.954480	−	0.298275i	$-0.903589\pi$
$281$		−	10.0000i		−	0.596550i	0.954480	−	0.298275i	$-0.0964112\pi$
$282$			12.0000i			0.714590i
$283$		−	4.00000i		−	0.237775i	−0.992908	−	0.118888i	$-0.962067\pi$
$283$		−	4.00000i		−	0.237775i	0.992908	−	0.118888i	$-0.0379328\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			20.0000i			1.18056i
$288$	1.00000			0.0589256
$289$	13.0000			0.764706
$290$		0			0
$291$		−	12.0000i		−	0.703452i
$292$	−4.00000			−0.234082
$293$	−14.0000			−0.817889			−0.408944	−	0.912559i	$-0.634103\pi$
$293$	−14.0000			−0.817889			−0.408944	+	0.912559i	$0.634103\pi$
$294$		−	3.00000i		−	0.174964i
$295$		0			0
$296$	8.00000			0.464991
$297$		0			0
$298$			14.0000i			0.810998i
$299$	12.0000	+	8.00000i	0.693978	+	0.462652i
$300$		0			0
$301$		−	8.00000i		−	0.461112i
$302$		−	10.0000i		−	0.575435i
$303$		−	2.00000i		−	0.114897i
$304$			6.00000i			0.344124i
$305$		0			0
$306$		−	2.00000i		−	0.114332i
$307$	2.00000			0.114146			0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000			0.114146			0.0570730	+	0.998370i	$0.481823\pi$
$308$		0			0
$309$	16.0000			0.910208
$310$		0			0
$311$	−28.0000			−1.58773			−0.793867	−	0.608091i	$-0.791935\pi$
$311$	−28.0000			−1.58773			−0.793867	+	0.608091i	$0.791935\pi$
$312$	−3.00000	−	2.00000i	−0.169842	−	0.113228i
$313$			26.0000i			1.46961i	0.678280	+	0.734803i	$0.262726\pi$
$313$			26.0000i			1.46961i	−0.678280	+	0.734803i	$0.737274\pi$
$314$			2.00000i			0.112867i
$315$		0			0
$316$		0			0
$317$	−18.0000			−1.01098			−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000			−1.01098			−0.505490	+	0.862832i	$0.668688\pi$
$318$	−6.00000			−0.336463
$319$		0			0
$320$		0			0
$321$	8.00000			0.446516
$322$			8.00000i			0.445823i
$323$	12.0000			0.667698
$324$	1.00000			0.0555556
$325$		0			0
$326$	14.0000			0.775388
$327$	−4.00000			−0.221201
$328$		−	10.0000i		−	0.552158i
$329$	24.0000			1.32316
$330$		0			0
$331$		−	10.0000i		−	0.549650i	−0.961494	−	0.274825i	$-0.911380\pi$
$331$		−	10.0000i		−	0.549650i	0.961494	−	0.274825i	$-0.0886199\pi$
$332$	−4.00000			−0.219529
$333$	8.00000			0.438397
$334$	−12.0000			−0.656611
$335$		0			0
$336$		−	2.00000i		−	0.109109i
$337$		−	2.00000i		−	0.108947i	−0.998515	−	0.0544735i	$-0.982652\pi$
$337$		−	2.00000i		−	0.108947i	0.998515	−	0.0544735i	$-0.0173480\pi$
$338$	5.00000	+	12.0000i	0.271964	+	0.652714i
$339$	−14.0000			−0.760376
$340$		0			0
$341$		0			0
$342$			6.00000i			0.324443i
$343$	−20.0000			−1.07990
$344$			4.00000i			0.215666i
$345$		0			0
$346$		−	6.00000i		−	0.322562i
$347$		−	12.0000i		−	0.644194i	−0.946707	−	0.322097i	$-0.895612\pi$
$347$		−	12.0000i		−	0.644194i	0.946707	−	0.322097i	$-0.104388\pi$
$348$		−	10.0000i		−	0.536056i
$349$			16.0000i			0.856460i	0.903670	+	0.428230i	$0.140863\pi$
$349$			16.0000i			0.856460i	−0.903670	+	0.428230i	$0.859137\pi$
$350$		0			0
$351$	−3.00000	−	2.00000i	−0.160128	−	0.106752i
$352$		0			0
$353$	26.0000			1.38384			0.691920	−	0.721974i	$-0.256765\pi$
$353$	26.0000			1.38384			0.691920	+	0.721974i	$0.256765\pi$
$354$	4.00000			0.212598
$355$		0			0
$356$			6.00000i			0.317999i
$357$	−4.00000			−0.211702
$358$		0			0
$359$		−	4.00000i		−	0.211112i	−0.994413	−	0.105556i	$-0.966338\pi$
$359$		−	4.00000i		−	0.211112i	0.994413	−	0.105556i	$-0.0336622\pi$
$360$		0			0
$361$	−17.0000			−0.894737
$362$	−22.0000			−1.15629
$363$		−	11.0000i		−	0.577350i
$364$	−4.00000	+	6.00000i	−0.209657	+	0.314485i
$365$		0			0
$366$			2.00000i			0.104542i
$367$			8.00000i			0.417597i	0.977959	+	0.208798i	$0.0669552\pi$
$367$			8.00000i			0.417597i	−0.977959	+	0.208798i	$0.933045\pi$
$368$		−	4.00000i		−	0.208514i
$369$		−	10.0000i		−	0.520579i
$370$		0			0
$371$			12.0000i			0.623009i
$372$	10.0000			0.518476
$373$			6.00000i			0.310668i	0.987862	+	0.155334i	$0.0496454\pi$
$373$			6.00000i			0.310668i	−0.987862	+	0.155334i	$0.950355\pi$
$374$		0			0
$375$		0			0
$376$	−12.0000			−0.618853
$377$	−20.0000	+	30.0000i	−1.03005	+	1.54508i
$378$		−	2.00000i		−	0.102869i
$379$		−	34.0000i		−	1.74646i	−0.487306	−	0.873231i	$-0.662020\pi$
$379$		−	34.0000i		−	1.74646i	0.487306	−	0.873231i	$-0.337980\pi$
$380$		0			0
$381$	8.00000			0.409852
$382$	−12.0000			−0.613973
$383$	−4.00000			−0.204390			−0.102195	−	0.994764i	$-0.532587\pi$
$383$	−4.00000			−0.204390			−0.102195	+	0.994764i	$0.532587\pi$
$384$			1.00000i			0.0510310i
$385$		0			0
$386$	−16.0000			−0.814379
$387$			4.00000i			0.203331i
$388$	12.0000			0.609208
$389$	−30.0000			−1.52106			−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000			−1.52106			−0.760530	+	0.649303i	$0.775061\pi$
$390$		0			0
$391$	−8.00000			−0.404577
$392$	3.00000			0.151523
$393$			8.00000i			0.403547i
$394$	−22.0000			−1.10834
$395$		0			0
$396$		0			0
$397$	−8.00000			−0.401508			−0.200754	−	0.979642i	$-0.564339\pi$
$397$	−8.00000			−0.401508			−0.200754	+	0.979642i	$0.564339\pi$
$398$		0			0
$399$	12.0000			0.600751
$400$		0			0
$401$		−	30.0000i		−	1.49813i	−0.662497	−	0.749064i	$-0.730503\pi$
$401$		−	30.0000i		−	1.49813i	0.662497	−	0.749064i	$-0.269497\pi$
$402$			2.00000i			0.0997509i
$403$	−30.0000	−	20.0000i	−1.49441	−	0.996271i
$404$	2.00000			0.0995037
$405$		0			0
$406$	−20.0000			−0.992583
$407$		0			0
$408$	2.00000			0.0990148
$409$		−	4.00000i		−	0.197787i	−0.995098	−	0.0988936i	$-0.968470\pi$
$409$		−	4.00000i		−	0.197787i	0.995098	−	0.0988936i	$-0.0315304\pi$
$410$		0			0
$411$		−	2.00000i		−	0.0986527i
$412$			16.0000i			0.788263i
$413$		−	8.00000i		−	0.393654i
$414$		−	4.00000i		−	0.196589i
$415$		0			0
$416$	2.00000	−	3.00000i	0.0980581	−	0.147087i
$417$		−	20.0000i		−	0.979404i
$418$		0			0
$419$	−40.0000			−1.95413			−0.977064	−	0.212946i	$-0.931694\pi$
$419$	−40.0000			−1.95413			−0.977064	+	0.212946i	$0.931694\pi$
$420$		0			0
$421$			20.0000i			0.974740i	0.873195	+	0.487370i	$0.162044\pi$
$421$			20.0000i			0.974740i	−0.873195	+	0.487370i	$0.837956\pi$
$422$	−12.0000			−0.584151
$423$	−12.0000			−0.583460
$424$		−	6.00000i		−	0.291386i
$425$		0			0
$426$		0			0
$427$	4.00000			0.193574
$428$			8.00000i			0.386695i
$429$		0			0
$430$		0			0
$431$		−	20.0000i		−	0.963366i	−0.876346	−	0.481683i	$-0.840026\pi$
$431$		−	20.0000i		−	0.963366i	0.876346	−	0.481683i	$-0.159974\pi$
$432$			1.00000i			0.0481125i
$433$			26.0000i			1.24948i	0.780833	+	0.624740i	$0.214795\pi$
$433$			26.0000i			1.24948i	−0.780833	+	0.624740i	$0.785205\pi$
$434$		−	20.0000i		−	0.960031i
$435$		0			0
$436$		−	4.00000i		−	0.191565i
$437$	24.0000			1.14808
$438$		−	4.00000i		−	0.191127i
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$		0			0
$441$	3.00000			0.142857
$442$	−6.00000	−	4.00000i	−0.285391	−	0.190261i
$443$			16.0000i			0.760183i	0.924949	+	0.380091i	$0.124107\pi$
$443$			16.0000i			0.760183i	−0.924949	+	0.380091i	$0.875893\pi$
$444$			8.00000i			0.379663i
$445$		0			0
$446$	14.0000			0.662919
$447$	−14.0000			−0.662177
$448$	2.00000			0.0944911
$449$			6.00000i			0.283158i	0.989927	+	0.141579i	$0.0452178\pi$
$449$			6.00000i			0.283158i	−0.989927	+	0.141579i	$0.954782\pi$
$450$		0			0
$451$		0			0
$452$		−	14.0000i		−	0.658505i
$453$	10.0000			0.469841
$454$	8.00000			0.375459
$455$		0			0
$456$	−6.00000			−0.280976
$457$	−28.0000			−1.30978			−0.654892	−	0.755722i	$-0.727286\pi$
$457$	−28.0000			−1.30978			−0.654892	+	0.755722i	$0.727286\pi$
$458$			4.00000i			0.186908i
$459$	2.00000			0.0933520
$460$		0			0
$461$		−	30.0000i		−	1.39724i	−0.715493	−	0.698620i	$-0.753798\pi$
$461$		−	30.0000i		−	1.39724i	0.715493	−	0.698620i	$-0.246202\pi$
$462$		0			0
$463$	6.00000			0.278844			0.139422	−	0.990233i	$-0.455476\pi$
$463$	6.00000			0.278844			0.139422	+	0.990233i	$0.455476\pi$
$464$	10.0000			0.464238
$465$		0			0
$466$		−	6.00000i		−	0.277945i
$467$		−	12.0000i		−	0.555294i	−0.960683	−	0.277647i	$-0.910445\pi$
$467$		−	12.0000i		−	0.555294i	0.960683	−	0.277647i	$-0.0895545\pi$
$468$	2.00000	−	3.00000i	0.0924500	−	0.138675i
$469$	4.00000			0.184703
$470$		0			0
$471$	−2.00000			−0.0921551
$472$			4.00000i			0.184115i
$473$		0			0
$474$		0			0
$475$		0			0
$476$		−	4.00000i		−	0.183340i
$477$		−	6.00000i		−	0.274721i
$478$		−	16.0000i		−	0.731823i
$479$		−	24.0000i		−	1.09659i	−0.836286	−	0.548294i	$-0.815277\pi$
$479$		−	24.0000i		−	1.09659i	0.836286	−	0.548294i	$-0.184723\pi$
$480$		0			0
$481$	16.0000	−	24.0000i	0.729537	−	1.09431i
$482$		−	20.0000i		−	0.910975i
$483$	−8.00000			−0.364013
$484$	11.0000			0.500000
$485$		0			0
$486$			1.00000i			0.0453609i
$487$	−18.0000			−0.815658			−0.407829	−	0.913058i	$-0.633714\pi$
$487$	−18.0000			−0.815658			−0.407829	+	0.913058i	$0.633714\pi$
$488$	−2.00000			−0.0905357
$489$			14.0000i			0.633102i
$490$		0			0
$491$	−28.0000			−1.26362			−0.631811	−	0.775122i	$-0.717688\pi$
$491$	−28.0000			−1.26362			−0.631811	+	0.775122i	$0.717688\pi$
$492$	10.0000			0.450835
$493$		−	20.0000i		−	0.900755i
$494$	18.0000	+	12.0000i	0.809858	+	0.539906i
$495$		0			0
$496$			10.0000i			0.449013i
$497$		0			0
$498$		−	4.00000i		−	0.179244i
$499$		−	14.0000i		−	0.626726i	−0.949633	−	0.313363i	$-0.898544\pi$
$499$		−	14.0000i		−	0.626726i	0.949633	−	0.313363i	$-0.101456\pi$
$500$		0			0
$501$		−	12.0000i		−	0.536120i
$502$	28.0000			1.24970
$503$		−	24.0000i		−	1.07011i	−0.844818	−	0.535054i	$-0.820291\pi$
$503$		−	24.0000i		−	1.07011i	0.844818	−	0.535054i	$-0.179709\pi$
$504$	2.00000			0.0890871
$505$		0			0
$506$		0			0
$507$	−12.0000	+	5.00000i	−0.532939	+	0.222058i
$508$			8.00000i			0.354943i
$509$			6.00000i			0.265945i	0.991120	+	0.132973i	$0.0424523\pi$
$509$			6.00000i			0.265945i	−0.991120	+	0.132973i	$0.957548\pi$
$510$		0			0
$511$	−8.00000			−0.353899
$512$	−1.00000			−0.0441942
$513$	−6.00000			−0.264906
$514$		−	18.0000i		−	0.793946i
$515$		0			0
$516$	−4.00000			−0.176090
$517$		0			0
$518$	16.0000			0.703000
$519$	6.00000			0.263371
$520$		0			0
$521$	−18.0000			−0.788594			−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000			−0.788594			−0.394297	+	0.918983i	$0.629012\pi$
$522$	10.0000			0.437688
$523$		−	4.00000i		−	0.174908i	−0.996169	−	0.0874539i	$-0.972127\pi$
$523$		−	4.00000i		−	0.174908i	0.996169	−	0.0874539i	$-0.0278730\pi$
$524$	−8.00000			−0.349482
$525$		0			0
$526$			24.0000i			1.04645i
$527$	20.0000			0.871214
$528$		0			0
$529$	7.00000			0.304348
$530$		0			0
$531$			4.00000i			0.173585i
$532$			12.0000i			0.520266i
$533$	−30.0000	−	20.0000i	−1.29944	−	0.866296i
$534$	−6.00000			−0.259645
$535$		0			0
$536$	−2.00000			−0.0863868
$537$		0			0
$538$	−10.0000			−0.431131
$539$		0			0
$540$		0			0
$541$		−	20.0000i		−	0.859867i	−0.902861	−	0.429934i	$-0.858537\pi$
$541$		−	20.0000i		−	0.859867i	0.902861	−	0.429934i	$-0.141463\pi$
$542$			10.0000i			0.429537i
$543$		−	22.0000i		−	0.944110i
$544$			2.00000i			0.0857493i
$545$		0			0
$546$	−6.00000	−	4.00000i	−0.256776	−	0.171184i
$547$			28.0000i			1.19719i	0.801050	+	0.598597i	$0.204275\pi$
$547$			28.0000i			1.19719i	−0.801050	+	0.598597i	$0.795725\pi$
$548$	2.00000			0.0854358
$549$	−2.00000			−0.0853579
$550$		0			0
$551$			60.0000i			2.55609i
$552$	4.00000			0.170251
$553$		0			0
$554$			2.00000i			0.0849719i
$555$		0			0
$556$	20.0000			0.848189
$557$	−18.0000			−0.762684			−0.381342	−	0.924434i	$-0.624538\pi$
$557$	−18.0000			−0.762684			−0.381342	+	0.924434i	$0.624538\pi$
$558$			10.0000i			0.423334i
$559$	12.0000	+	8.00000i	0.507546	+	0.338364i
$560$		0			0
$561$		0			0
$562$			10.0000i			0.421825i
$563$			16.0000i			0.674320i	0.941447	+	0.337160i	$0.109466\pi$
$563$			16.0000i			0.674320i	−0.941447	+	0.337160i	$0.890534\pi$
$564$		−	12.0000i		−	0.505291i
$565$		0			0
$566$			4.00000i			0.168133i
$567$	2.00000			0.0839921
$568$		0			0
$569$	−10.0000			−0.419222			−0.209611	−	0.977785i	$-0.567220\pi$
$569$	−10.0000			−0.419222			−0.209611	+	0.977785i	$0.567220\pi$
$570$		0			0
$571$	−28.0000			−1.17176			−0.585882	−	0.810397i	$-0.699252\pi$
$571$	−28.0000			−1.17176			−0.585882	+	0.810397i	$0.699252\pi$
$572$		0			0
$573$		−	12.0000i		−	0.501307i
$574$		−	20.0000i		−	0.834784i
$575$		0			0
$576$	−1.00000			−0.0416667
$577$	−8.00000			−0.333044			−0.166522	−	0.986038i	$-0.553254\pi$
$577$	−8.00000			−0.333044			−0.166522	+	0.986038i	$0.553254\pi$
$578$	−13.0000			−0.540729
$579$		−	16.0000i		−	0.664937i
$580$		0			0
$581$	−8.00000			−0.331896
$582$			12.0000i			0.497416i
$583$		0			0
$584$	4.00000			0.165521
$585$		0			0
$586$	14.0000			0.578335
$587$	−28.0000			−1.15568			−0.577842	−	0.816149i	$-0.696105\pi$
$587$	−28.0000			−1.15568			−0.577842	+	0.816149i	$0.696105\pi$
$588$			3.00000i			0.123718i
$589$	−60.0000			−2.47226
$590$		0			0
$591$		−	22.0000i		−	0.904959i
$592$	−8.00000			−0.328798
$593$	26.0000			1.06769			0.533846	−	0.845582i	$-0.320746\pi$
$593$	26.0000			1.06769			0.533846	+	0.845582i	$0.320746\pi$
$594$		0			0
$595$		0			0
$596$		−	14.0000i		−	0.573462i
$597$		0			0
$598$	−12.0000	−	8.00000i	−0.490716	−	0.327144i
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	22.0000			0.897399			0.448699	−	0.893683i	$-0.351887\pi$
$601$	22.0000			0.897399			0.448699	+	0.893683i	$0.351887\pi$
$602$			8.00000i			0.326056i
$603$	−2.00000			−0.0814463
$604$			10.0000i			0.406894i
$605$		0			0
$606$			2.00000i			0.0812444i
$607$		−	32.0000i		−	1.29884i	−0.760430	−	0.649420i	$-0.775012\pi$
$607$		−	32.0000i		−	1.29884i	0.760430	−	0.649420i	$-0.224988\pi$
$608$		−	6.00000i		−	0.243332i
$609$		−	20.0000i		−	0.810441i
$610$		0			0
$611$	−24.0000	+	36.0000i	−0.970936	+	1.45640i
$612$			2.00000i			0.0808452i
$613$	16.0000			0.646234			0.323117	−	0.946359i	$-0.395269\pi$
$613$	16.0000			0.646234			0.323117	+	0.946359i	$0.395269\pi$
$614$	−2.00000			−0.0807134
$615$		0			0
$616$		0			0
$617$	22.0000			0.885687			0.442843	−	0.896599i	$-0.353970\pi$
$617$	22.0000			0.885687			0.442843	+	0.896599i	$0.353970\pi$
$618$	−16.0000			−0.643614
$619$			26.0000i			1.04503i	0.852631	+	0.522514i	$0.175006\pi$
$619$			26.0000i			1.04503i	−0.852631	+	0.522514i	$0.824994\pi$
$620$		0			0
$621$	4.00000			0.160514
$622$	28.0000			1.12270
$623$			12.0000i			0.480770i
$624$	3.00000	+	2.00000i	0.120096	+	0.0800641i
$625$		0			0
$626$		−	26.0000i		−	1.03917i
$627$		0			0
$628$		−	2.00000i		−	0.0798087i
$629$			16.0000i			0.637962i
$630$		0			0
$631$			10.0000i			0.398094i	0.979990	+	0.199047i	$0.0637846\pi$
$631$			10.0000i			0.398094i	−0.979990	+	0.199047i	$0.936215\pi$
$632$		0			0
$633$		−	12.0000i		−	0.476957i
$634$	18.0000			0.714871
$635$		0			0
$636$	6.00000			0.237915
$637$	6.00000	−	9.00000i	0.237729	−	0.356593i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−18.0000			−0.710957			−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000			−0.710957			−0.355479	+	0.934684i	$0.615682\pi$
$642$	−8.00000			−0.315735
$643$	6.00000			0.236617			0.118308	−	0.992977i	$-0.462253\pi$
$643$	6.00000			0.236617			0.118308	+	0.992977i	$0.462253\pi$
$644$		−	8.00000i		−	0.315244i
$645$		0			0
$646$	−12.0000			−0.472134
$647$		−	32.0000i		−	1.25805i	−0.777385	−	0.629025i	$-0.783454\pi$
$647$		−	32.0000i		−	1.25805i	0.777385	−	0.629025i	$-0.216546\pi$
$648$	−1.00000			−0.0392837
$649$		0			0
$650$		0			0
$651$	20.0000			0.783862
$652$	−14.0000			−0.548282
$653$			26.0000i			1.01746i	0.860927	+	0.508729i	$0.169885\pi$
$653$			26.0000i			1.01746i	−0.860927	+	0.508729i	$0.830115\pi$
$654$	4.00000			0.156412
$655$		0			0
$656$			10.0000i			0.390434i
$657$	4.00000			0.156055
$658$	−24.0000			−0.935617
$659$	−20.0000			−0.779089			−0.389545	−	0.921008i	$-0.627368\pi$
$659$	−20.0000			−0.779089			−0.389545	+	0.921008i	$0.627368\pi$
$660$		0			0
$661$		−	40.0000i		−	1.55582i	−0.628376	−	0.777910i	$-0.716280\pi$
$661$		−	40.0000i		−	1.55582i	0.628376	−	0.777910i	$-0.283720\pi$
$662$			10.0000i			0.388661i
$663$	4.00000	−	6.00000i	0.155347	−	0.233021i
$664$	4.00000			0.155230
$665$		0			0
$666$	−8.00000			−0.309994
$667$		−	40.0000i		−	1.54881i
$668$	12.0000			0.464294
$669$			14.0000i			0.541271i
$670$		0			0
$671$		0			0
$672$			2.00000i			0.0771517i
$673$			6.00000i			0.231283i	0.993291	+	0.115642i	$0.0368924\pi$
$673$			6.00000i			0.231283i	−0.993291	+	0.115642i	$0.963108\pi$
$674$			2.00000i			0.0770371i
$675$		0			0
$676$	−5.00000	−	12.0000i	−0.192308	−	0.461538i
$677$			18.0000i			0.691796i	0.938272	+	0.345898i	$0.112426\pi$
$677$			18.0000i			0.691796i	−0.938272	+	0.345898i	$0.887574\pi$
$678$	14.0000			0.537667
$679$	24.0000			0.921035
$680$		0			0
$681$			8.00000i			0.306561i
$682$		0			0
$683$	−24.0000			−0.918334			−0.459167	−	0.888350i	$-0.651852\pi$
$683$	−24.0000			−0.918334			−0.459167	+	0.888350i	$0.651852\pi$
$684$		−	6.00000i		−	0.229416i
$685$		0			0
$686$	20.0000			0.763604
$687$	−4.00000			−0.152610
$688$		−	4.00000i		−	0.152499i
$689$	−18.0000	−	12.0000i	−0.685745	−	0.457164i
$690$		0			0
$691$		−	10.0000i		−	0.380418i	−0.981744	−	0.190209i	$-0.939083\pi$
$691$		−	10.0000i		−	0.380418i	0.981744	−	0.190209i	$-0.0609166\pi$
$692$			6.00000i			0.228086i
$693$		0			0
$694$			12.0000i			0.455514i
$695$		0			0
$696$			10.0000i			0.379049i
$697$	20.0000			0.757554
$698$		−	16.0000i		−	0.605609i
$699$	6.00000			0.226941
$700$		0			0
$701$	22.0000			0.830929			0.415464	−	0.909610i	$-0.363619\pi$
$701$	22.0000			0.830929			0.415464	+	0.909610i	$0.363619\pi$
$702$	3.00000	+	2.00000i	0.113228	+	0.0754851i
$703$		−	48.0000i		−	1.81035i
$704$		0			0
$705$		0			0
$706$	−26.0000			−0.978523
$707$	4.00000			0.150435
$708$	−4.00000			−0.150329
$709$			36.0000i			1.35201i	0.736898	+	0.676004i	$0.236290\pi$
$709$			36.0000i			1.35201i	−0.736898	+	0.676004i	$0.763710\pi$
$710$		0			0
$711$		0			0
$712$		−	6.00000i		−	0.224860i
$713$	40.0000			1.49801
$714$	4.00000			0.149696
$715$		0			0
$716$		0			0
$717$	16.0000			0.597531
$718$			4.00000i			0.149279i
$719$	−20.0000			−0.745874			−0.372937	−	0.927857i	$-0.621649\pi$
$719$	−20.0000			−0.745874			−0.372937	+	0.927857i	$0.621649\pi$
$720$		0			0
$721$			32.0000i			1.19174i
$722$	17.0000			0.632674
$723$	20.0000			0.743808
$724$	22.0000			0.817624
$725$		0			0
$726$			11.0000i			0.408248i
$727$			8.00000i			0.296704i	0.988935	+	0.148352i	$0.0473968\pi$
$727$			8.00000i			0.296704i	−0.988935	+	0.148352i	$0.952603\pi$
$728$	4.00000	−	6.00000i	0.148250	−	0.222375i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−8.00000			−0.295891
$732$		−	2.00000i		−	0.0739221i
$733$	−44.0000			−1.62518			−0.812589	−	0.582838i	$-0.801942\pi$
$733$	−44.0000			−1.62518			−0.812589	+	0.582838i	$0.801942\pi$
$734$		−	8.00000i		−	0.295285i
$735$		0			0
$736$			4.00000i			0.147442i
$737$		0			0
$738$			10.0000i			0.368105i
$739$			26.0000i			0.956425i	0.878244	+	0.478213i	$0.158715\pi$
$739$			26.0000i			0.956425i	−0.878244	+	0.478213i	$0.841285\pi$
$740$		0			0
$741$	−12.0000	+	18.0000i	−0.440831	+	0.661247i
$742$		−	12.0000i		−	0.440534i
$743$	16.0000			0.586983			0.293492	−	0.955962i	$-0.405183\pi$
$743$	16.0000			0.586983			0.293492	+	0.955962i	$0.405183\pi$
$744$	−10.0000			−0.366618
$745$		0			0
$746$		−	6.00000i		−	0.219676i
$747$	4.00000			0.146352
$748$		0			0
$749$			16.0000i			0.584627i
$750$		0			0
$751$	32.0000			1.16770			0.583848	−	0.811863i	$-0.301546\pi$
$751$	32.0000			1.16770			0.583848	+	0.811863i	$0.301546\pi$
$752$	12.0000			0.437595
$753$			28.0000i			1.02038i
$754$	20.0000	−	30.0000i	0.728357	−	1.09254i
$755$		0			0
$756$			2.00000i			0.0727393i
$757$		−	22.0000i		−	0.799604i	−0.916602	−	0.399802i	$-0.869079\pi$
$757$		−	22.0000i		−	0.799604i	0.916602	−	0.399802i	$-0.130921\pi$
$758$			34.0000i			1.23494i
$759$		0			0
$760$		0			0
$761$			30.0000i			1.08750i	0.839248	+	0.543750i	$0.182996\pi$
$761$			30.0000i			1.08750i	−0.839248	+	0.543750i	$0.817004\pi$
$762$	−8.00000			−0.289809
$763$		−	8.00000i		−	0.289619i
$764$	12.0000			0.434145
$765$		0			0
$766$	4.00000			0.144526
$767$	12.0000	+	8.00000i	0.433295	+	0.288863i
$768$		−	1.00000i		−	0.0360844i
$769$		−	24.0000i		−	0.865462i	−0.901523	−	0.432731i	$-0.857550\pi$
$769$		−	24.0000i		−	0.865462i	0.901523	−	0.432731i	$-0.142450\pi$
$770$		0			0
$771$	18.0000			0.648254
$772$	16.0000			0.575853
$773$	6.00000			0.215805			0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000			0.215805			0.107903	+	0.994161i	$0.465587\pi$
$774$		−	4.00000i		−	0.143777i
$775$		0			0
$776$	−12.0000			−0.430775
$777$			16.0000i			0.573997i
$778$	30.0000			1.07555
$779$	−60.0000			−2.14972
$780$		0			0
$781$		0			0
$782$	8.00000			0.286079
$783$			10.0000i			0.357371i
$784$	−3.00000			−0.107143
$785$		0			0
$786$		−	8.00000i		−	0.285351i
$787$	−38.0000			−1.35455			−0.677277	−	0.735728i	$-0.736840\pi$
$787$	−38.0000			−1.35455			−0.677277	+	0.735728i	$0.736840\pi$
$788$	22.0000			0.783718
$789$	−24.0000			−0.854423
$790$		0			0
$791$		−	28.0000i		−	0.995565i
$792$		0			0
$793$	−4.00000	+	6.00000i	−0.142044	+	0.213066i
$794$	8.00000			0.283909
$795$		0			0
$796$		0			0
$797$		−	2.00000i		−	0.0708436i	−0.999372	−	0.0354218i	$-0.988723\pi$
$797$		−	2.00000i		−	0.0708436i	0.999372	−	0.0354218i	$-0.0112775\pi$
$798$	−12.0000			−0.424795
$799$		−	24.0000i		−	0.849059i
$800$		0			0
$801$		−	6.00000i		−	0.212000i
$802$			30.0000i			1.05934i
$803$		0			0
$804$		−	2.00000i		−	0.0705346i
$805$		0			0
$806$	30.0000	+	20.0000i	1.05670	+	0.704470i
$807$		−	10.0000i		−	0.352017i
$808$	−2.00000			−0.0703598
$809$	50.0000			1.75791			0.878953	−	0.476908i	$-0.158243\pi$
$809$	50.0000			1.75791			0.878953	+	0.476908i	$0.158243\pi$
$810$		0			0
$811$			10.0000i			0.351147i	0.984466	+	0.175574i	$0.0561780\pi$
$811$			10.0000i			0.351147i	−0.984466	+	0.175574i	$0.943822\pi$
$812$	20.0000			0.701862
$813$	−10.0000			−0.350715
$814$		0			0
$815$		0			0
$816$	−2.00000			−0.0700140
$817$	24.0000			0.839654
$818$			4.00000i			0.139857i
$819$	4.00000	−	6.00000i	0.139771	−	0.209657i
$820$		0			0
$821$			30.0000i			1.04701i	0.852023	+	0.523504i	$0.175375\pi$
$821$			30.0000i			1.04701i	−0.852023	+	0.523504i	$0.824625\pi$
$822$			2.00000i			0.0697580i
$823$		−	24.0000i		−	0.836587i	−0.908312	−	0.418294i	$-0.862628\pi$
$823$		−	24.0000i		−	0.836587i	0.908312	−	0.418294i	$-0.137372\pi$
$824$		−	16.0000i		−	0.557386i
$825$		0			0
$826$			8.00000i			0.278356i
$827$	−48.0000			−1.66912			−0.834562	−	0.550914i	$-0.814279\pi$
$827$	−48.0000			−1.66912			−0.834562	+	0.550914i	$0.814279\pi$
$828$			4.00000i			0.139010i
$829$	30.0000			1.04194			0.520972	−	0.853574i	$-0.325570\pi$
$829$	30.0000			1.04194			0.520972	+	0.853574i	$0.325570\pi$
$830$		0			0
$831$	−2.00000			−0.0693792
$832$	−2.00000	+	3.00000i	−0.0693375	+	0.104006i
$833$			6.00000i			0.207888i
$834$			20.0000i			0.692543i
$835$		0			0
$836$		0			0
$837$	−10.0000			−0.345651
$838$	40.0000			1.38178
$839$			16.0000i			0.552381i	0.961103	+	0.276191i	$0.0890721\pi$
$839$			16.0000i			0.552381i	−0.961103	+	0.276191i	$0.910928\pi$
$840$		0			0
$841$	71.0000			2.44828
$842$		−	20.0000i		−	0.689246i
$843$	−10.0000			−0.344418
$844$	12.0000			0.413057
$845$		0			0
$846$	12.0000			0.412568
$847$	22.0000			0.755929
$848$			6.00000i			0.206041i
$849$	−4.00000			−0.137280
$850$		0			0
$851$			32.0000i			1.09695i
$852$		0			0
$853$	56.0000			1.91740			0.958702	−	0.284413i	$-0.0917988\pi$
$853$	56.0000			1.91740			0.958702	+	0.284413i	$0.0917988\pi$
$854$	−4.00000			−0.136877
$855$		0			0
$856$		−	8.00000i		−	0.273434i
$857$		−	22.0000i		−	0.751506i	−0.926720	−	0.375753i	$-0.877384\pi$
$857$		−	22.0000i		−	0.751506i	0.926720	−	0.375753i	$-0.122616\pi$
$858$		0			0
$859$	20.0000			0.682391			0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000			0.682391			0.341196	+	0.939992i	$0.389168\pi$
$860$		0			0
$861$	20.0000			0.681598
$862$			20.0000i			0.681203i
$863$	−44.0000			−1.49778			−0.748889	−	0.662696i	$-0.769412\pi$
$863$	−44.0000			−1.49778			−0.748889	+	0.662696i	$0.769412\pi$
$864$		−	1.00000i		−	0.0340207i
$865$		0			0
$866$		−	26.0000i		−	0.883516i
$867$		−	13.0000i		−	0.441503i
$868$			20.0000i			0.678844i
$869$		0			0
$870$		0			0
$871$	−4.00000	+	6.00000i	−0.135535	+	0.203302i
$872$			4.00000i			0.135457i
$873$	−12.0000			−0.406138
$874$	−24.0000			−0.811812
$875$		0			0
$876$			4.00000i			0.135147i
$877$	−8.00000			−0.270141			−0.135070	−	0.990836i	$-0.543126\pi$
$877$	−8.00000			−0.270141			−0.135070	+	0.990836i	$0.543126\pi$
$878$		0			0
$879$			14.0000i			0.472208i
$880$		0			0
$881$	42.0000			1.41502			0.707508	−	0.706705i	$-0.249819\pi$
$881$	42.0000			1.41502			0.707508	+	0.706705i	$0.249819\pi$
$882$	−3.00000			−0.101015
$883$			36.0000i			1.21150i	0.795656	+	0.605748i	$0.207126\pi$
$883$			36.0000i			1.21150i	−0.795656	+	0.605748i	$0.792874\pi$
$884$	6.00000	+	4.00000i	0.201802	+	0.134535i
$885$		0			0
$886$		−	16.0000i		−	0.537531i
$887$		−	12.0000i		−	0.402921i	−0.979497	−	0.201460i	$-0.935431\pi$
$887$		−	12.0000i		−	0.402921i	0.979497	−	0.201460i	$-0.0645687\pi$
$888$		−	8.00000i		−	0.268462i
$889$			16.0000i			0.536623i
$890$		0			0
$891$		0			0
$892$	−14.0000			−0.468755
$893$			72.0000i			2.40939i
$894$	14.0000			0.468230
$895$		0			0
$896$	−2.00000			−0.0668153
$897$	8.00000	−	12.0000i	0.267112	−	0.400668i
$898$		−	6.00000i		−	0.200223i
$899$			100.000i			3.33519i
$900$		0			0
$901$	12.0000			0.399778
$902$		0			0
$903$	−8.00000			−0.266223
$904$			14.0000i			0.465633i
$905$		0			0
$906$	−10.0000			−0.332228
$907$			28.0000i			0.929725i	0.885383	+	0.464862i	$0.153896\pi$
$907$			28.0000i			0.929725i	−0.885383	+	0.464862i	$0.846104\pi$
$908$	−8.00000			−0.265489
$909$	−2.00000			−0.0663358
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	6.00000			0.198680
$913$		0			0
$914$	28.0000			0.926158
$915$		0			0
$916$		−	4.00000i		−	0.132164i
$917$	−16.0000			−0.528367
$918$	−2.00000			−0.0660098
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$		0			0
$921$		−	2.00000i		−	0.0659022i
$922$			30.0000i			0.987997i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−6.00000			−0.197172
$927$		−	16.0000i		−	0.525509i
$928$	−10.0000			−0.328266
$929$			6.00000i			0.196854i	0.995144	+	0.0984268i	$0.0313810\pi$
$929$			6.00000i			0.196854i	−0.995144	+	0.0984268i	$0.968619\pi$
$930$		0			0
$931$		−	18.0000i		−	0.589926i
$932$			6.00000i			0.196537i
$933$			28.0000i			0.916679i
$934$			12.0000i			0.392652i
$935$		0			0
$936$	−2.00000	+	3.00000i	−0.0653720	+	0.0980581i
$937$		−	2.00000i		−	0.0653372i	−0.999466	−	0.0326686i	$-0.989599\pi$
$937$		−	2.00000i		−	0.0653372i	0.999466	−	0.0326686i	$-0.0104006\pi$
$938$	−4.00000			−0.130605
$939$	26.0000			0.848478
$940$		0			0
$941$		−	10.0000i		−	0.325991i	−0.986627	−	0.162995i	$-0.947884\pi$
$941$		−	10.0000i		−	0.325991i	0.986627	−	0.162995i	$-0.0521156\pi$
$942$	2.00000			0.0651635
$943$	40.0000			1.30258
$944$		−	4.00000i		−	0.130189i
$945$		0			0
$946$		0			0
$947$	52.0000			1.68977			0.844886	−	0.534946i	$-0.179668\pi$
$947$	52.0000			1.68977			0.844886	+	0.534946i	$0.179668\pi$
$948$		0			0
$949$	8.00000	−	12.0000i	0.259691	−	0.389536i
$950$		0			0
$951$			18.0000i			0.583690i
$952$			4.00000i			0.129641i
$953$			6.00000i			0.194359i	0.995267	+	0.0971795i	$0.0309821\pi$
$953$			6.00000i			0.194359i	−0.995267	+	0.0971795i	$0.969018\pi$
$954$			6.00000i			0.194257i
$955$		0			0
$956$			16.0000i			0.517477i
$957$		0			0
$958$			24.0000i			0.775405i
$959$	4.00000			0.129167
$960$		0			0
$961$	−69.0000			−2.22581
$962$	−16.0000	+	24.0000i	−0.515861	+	0.773791i
$963$		−	8.00000i		−	0.257796i
$964$			20.0000i			0.644157i
$965$		0			0
$966$	8.00000			0.257396
$967$	22.0000			0.707472			0.353736	−	0.935345i	$-0.384911\pi$
$967$	22.0000			0.707472			0.353736	+	0.935345i	$0.384911\pi$
$968$	−11.0000			−0.353553
$969$		−	12.0000i		−	0.385496i
$970$		0			0
$971$	12.0000			0.385098			0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000			0.385098			0.192549	+	0.981287i	$0.438325\pi$
$972$		−	1.00000i		−	0.0320750i
$973$	40.0000			1.28234
$974$	18.0000			0.576757
$975$		0			0
$976$	2.00000			0.0640184
$977$	42.0000			1.34370			0.671850	−	0.740688i	$-0.265500\pi$
$977$	42.0000			1.34370			0.671850	+	0.740688i	$0.265500\pi$
$978$		−	14.0000i		−	0.447671i
$979$		0			0
$980$		0			0
$981$			4.00000i			0.127710i
$982$	28.0000			0.893516
$983$	−24.0000			−0.765481			−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000			−0.765481			−0.382741	+	0.923856i	$0.625020\pi$
$984$	−10.0000			−0.318788
$985$		0			0
$986$			20.0000i			0.636930i
$987$		−	24.0000i		−	0.763928i
$988$	−18.0000	−	12.0000i	−0.572656	−	0.381771i
$989$	−16.0000			−0.508770
$990$		0			0
$991$	−8.00000			−0.254128			−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000			−0.254128			−0.127064	+	0.991894i	$0.540555\pi$
$992$		−	10.0000i		−	0.317500i
$993$	−10.0000			−0.317340
$994$		0			0
$995$		0			0
$996$			4.00000i			0.126745i
$997$		−	42.0000i		−	1.33015i	−0.746775	−	0.665077i	$-0.768399\pi$
$997$		−	42.0000i		−	1.33015i	0.746775	−	0.665077i	$-0.231601\pi$
$998$			14.0000i			0.443162i
$999$		−	8.00000i		−	0.253109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.f.d.649.1		2
5.2	odd	4		1950.2.b.c.1351.1		2
5.3	odd	4		78.2.b.a.25.2	yes	2
5.4	even	2		1950.2.f.g.649.2		2
13.12	even	2		1950.2.f.g.649.1		2
15.8	even	4		234.2.b.a.181.1		2
20.3	even	4		624.2.c.a.337.2		2
35.13	even	4		3822.2.c.d.883.2		2
40.3	even	4		2496.2.c.m.961.1		2
40.13	odd	4		2496.2.c.f.961.1		2
60.23	odd	4		1872.2.c.b.1585.1		2
65.3	odd	12		1014.2.i.c.823.1		4
65.8	even	4		1014.2.a.b.1.1		1
65.12	odd	4		1950.2.b.c.1351.2		2
65.18	even	4		1014.2.a.g.1.1		1
65.23	odd	12		1014.2.i.c.823.2		4
65.28	even	12		1014.2.e.b.529.1		2
65.33	even	12		1014.2.e.e.991.1		2
65.38	odd	4		78.2.b.a.25.1	✓	2
65.43	odd	12		1014.2.i.c.361.1		4
65.48	odd	12		1014.2.i.c.361.2		4
65.58	even	12		1014.2.e.b.991.1		2
65.63	even	12		1014.2.e.e.529.1		2
65.64	even	2	inner	1950.2.f.d.649.2		2
195.8	odd	4		3042.2.a.n.1.1		1
195.38	even	4		234.2.b.a.181.2		2
195.83	odd	4		3042.2.a.c.1.1		1
260.83	odd	4		8112.2.a.j.1.1		1
260.103	even	4		624.2.c.a.337.1		2
260.203	odd	4		8112.2.a.g.1.1		1
455.363	even	4		3822.2.c.d.883.1		2
520.363	even	4		2496.2.c.m.961.2		2
520.493	odd	4		2496.2.c.f.961.2		2
780.623	odd	4		1872.2.c.b.1585.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.b.a.25.1	✓	2	65.38	odd	4
78.2.b.a.25.2	yes	2	5.3	odd	4
234.2.b.a.181.1		2	15.8	even	4
234.2.b.a.181.2		2	195.38	even	4
624.2.c.a.337.1		2	260.103	even	4
624.2.c.a.337.2		2	20.3	even	4
1014.2.a.b.1.1		1	65.8	even	4
1014.2.a.g.1.1		1	65.18	even	4
1014.2.e.b.529.1		2	65.28	even	12
1014.2.e.b.991.1		2	65.58	even	12
1014.2.e.e.529.1		2	65.63	even	12
1014.2.e.e.991.1		2	65.33	even	12
1014.2.i.c.361.1		4	65.43	odd	12
1014.2.i.c.361.2		4	65.48	odd	12
1014.2.i.c.823.1		4	65.3	odd	12
1014.2.i.c.823.2		4	65.23	odd	12
1872.2.c.b.1585.1		2	60.23	odd	4
1872.2.c.b.1585.2		2	780.623	odd	4
1950.2.b.c.1351.1		2	5.2	odd	4
1950.2.b.c.1351.2		2	65.12	odd	4
1950.2.f.d.649.1		2	1.1	even	1	trivial
1950.2.f.d.649.2		2	65.64	even	2	inner
1950.2.f.g.649.1		2	13.12	even	2
1950.2.f.g.649.2		2	5.4	even	2
2496.2.c.f.961.1		2	40.13	odd	4
2496.2.c.f.961.2		2	520.493	odd	4
2496.2.c.m.961.1		2	40.3	even	4
2496.2.c.m.961.2		2	520.363	even	4
3042.2.a.c.1.1		1	195.83	odd	4
3042.2.a.n.1.1		1	195.8	odd	4
3822.2.c.d.883.1		2	455.363	even	4
3822.2.c.d.883.2		2	35.13	even	4
8112.2.a.g.1.1		1	260.203	odd	4
8112.2.a.j.1.1		1	260.83	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +1.00000i q^{6} +2.00000 q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +1.00000i q^{6} +2.00000 q^{7} -1.00000 q^{8} -1.00000 q^{9} -1.00000i q^{12} +(-2.00000 + 3.00000i) q^{13} -2.00000 q^{14} +1.00000 q^{16} -2.00000i q^{17} +1.00000 q^{18} +6.00000i q^{19} -2.00000i q^{21} -4.00000i q^{23} +1.00000i q^{24} +(2.00000 - 3.00000i) q^{26} +1.00000i q^{27} +2.00000 q^{28} +10.0000 q^{29} +10.0000i q^{31} -1.00000 q^{32} +2.00000i q^{34} -1.00000 q^{36} -8.00000 q^{37} -6.00000i q^{38} +(3.00000 + 2.00000i) q^{39} +10.0000i q^{41} +2.00000i q^{42} -4.00000i q^{43} +4.00000i q^{46} +12.0000 q^{47} -1.00000i q^{48} -3.00000 q^{49} -2.00000 q^{51} +(-2.00000 + 3.00000i) q^{52} +6.00000i q^{53} -1.00000i q^{54} -2.00000 q^{56} +6.00000 q^{57} -10.0000 q^{58} -4.00000i q^{59} +2.00000 q^{61} -10.0000i q^{62} -2.00000 q^{63} +1.00000 q^{64} +2.00000 q^{67} -2.00000i q^{68} -4.00000 q^{69} +1.00000 q^{72} -4.00000 q^{73} +8.00000 q^{74} +6.00000i q^{76} +(-3.00000 - 2.00000i) q^{78} +1.00000 q^{81} -10.0000i q^{82} -4.00000 q^{83} -2.00000i q^{84} +4.00000i q^{86} -10.0000i q^{87} +6.00000i q^{89} +(-4.00000 + 6.00000i) q^{91} -4.00000i q^{92} +10.0000 q^{93} -12.0000 q^{94} +1.00000i q^{96} +12.0000 q^{97} +3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} + 4 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^4 + 4 * q^7 - 2 * q^8 - 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{4} + 4 q^{7} - 2 q^{8} - 2 q^{9} - 4 q^{13} - 4 q^{14} + 2 q^{16} + 2 q^{18} + 4 q^{26} + 4 q^{28} + 20 q^{29} - 2 q^{32} - 2 q^{36} - 16 q^{37} + 6 q^{39} + 24 q^{47} - 6 q^{49} - 4 q^{51} - 4 q^{52} - 4 q^{56} + 12 q^{57} - 20 q^{58} + 4 q^{61} - 4 q^{63} + 2 q^{64} + 4 q^{67} - 8 q^{69} + 2 q^{72} - 8 q^{73} + 16 q^{74} - 6 q^{78} + 2 q^{81} - 8 q^{83} - 8 q^{91} + 20 q^{93} - 24 q^{94} + 24 q^{97} + 6 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 + 4 * q^7 - 2 * q^8 - 2 * q^9 - 4 * q^13 - 4 * q^14 + 2 * q^16 + 2 * q^18 + 4 * q^26 + 4 * q^28 + 20 * q^29 - 2 * q^32 - 2 * q^36 - 16 * q^37 + 6 * q^39 + 24 * q^47 - 6 * q^49 - 4 * q^51 - 4 * q^52 - 4 * q^56 + 12 * q^57 - 20 * q^58 + 4 * q^61 - 4 * q^63 + 2 * q^64 + 4 * q^67 - 8 * q^69 + 2 * q^72 - 8 * q^73 + 16 * q^74 - 6 * q^78 + 2 * q^81 - 8 * q^83 - 8 * q^91 + 20 * q^93 - 24 * q^94 + 24 * q^97 + 6 * q^98

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