LMFDB - Embedded newform 1600.2.j.a.1007.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(143,1600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 3]))

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

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

chi := DirichletCharacter("1600.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.j (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.7760643234$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1007.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	1600.1007
Dual form			1600.2.j.a.143.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{3} +(-3.00000 - 3.00000i) q^{7} -1.00000 q^{9} +O(q^{10})$	$q+2.00000i q^{3} +(-3.00000 - 3.00000i) q^{7} -1.00000 q^{9} +(1.00000 + 1.00000i) q^{11} +2.00000 q^{13} +(-1.00000 - 1.00000i) q^{17} +(-3.00000 - 3.00000i) q^{19} +(6.00000 - 6.00000i) q^{21} +(-1.00000 + 1.00000i) q^{23} +4.00000i q^{27} +(7.00000 - 7.00000i) q^{29} -2.00000i q^{31} +(-2.00000 + 2.00000i) q^{33} +6.00000 q^{37} +4.00000i q^{39} -4.00000i q^{41} +4.00000 q^{43} +(7.00000 - 7.00000i) q^{47} +11.0000i q^{49} +(2.00000 - 2.00000i) q^{51} -8.00000i q^{53} +(6.00000 - 6.00000i) q^{57} +(3.00000 - 3.00000i) q^{59} +(-1.00000 - 1.00000i) q^{61} +(3.00000 + 3.00000i) q^{63} +4.00000 q^{67} +(-2.00000 - 2.00000i) q^{69} +(3.00000 + 3.00000i) q^{73} -6.00000i q^{77} +8.00000 q^{79} -11.0000 q^{81} +2.00000i q^{83} +(14.0000 + 14.0000i) q^{87} +6.00000 q^{89} +(-6.00000 - 6.00000i) q^{91} +4.00000 q^{93} +(11.0000 + 11.0000i) q^{97} +(-1.00000 - 1.00000i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 6 q^{7} - 2 q^{9}+O(q^{10}) $ 2 * q - 6 * q^7 - 2 * q^9	$ 2 q - 6 q^{7} - 2 q^{9} + 2 q^{11} + 4 q^{13} - 2 q^{17} - 6 q^{19} + 12 q^{21} - 2 q^{23} + 14 q^{29} - 4 q^{33} + 12 q^{37} + 8 q^{43} + 14 q^{47} + 4 q^{51} + 12 q^{57} + 6 q^{59} - 2 q^{61} + 6 q^{63} + 8 q^{67} - 4 q^{69} + 6 q^{73} + 16 q^{79} - 22 q^{81} + 28 q^{87} + 12 q^{89} - 12 q^{91} + 8 q^{93} + 22 q^{97} - 2 q^{99}+O(q^{100}) $ 2 * q - 6 * q^7 - 2 * q^9 + 2 * q^11 + 4 * q^13 - 2 * q^17 - 6 * q^19 + 12 * q^21 - 2 * q^23 + 14 * q^29 - 4 * q^33 + 12 * q^37 + 8 * q^43 + 14 * q^47 + 4 * q^51 + 12 * q^57 + 6 * q^59 - 2 * q^61 + 6 * q^63 + 8 * q^67 - 4 * q^69 + 6 * q^73 + 16 * q^79 - 22 * q^81 + 28 * q^87 + 12 * q^89 - 12 * q^91 + 8 * q^93 + 22 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1151$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$			2.00000i			1.15470i	0.816497	+	0.577350i	$0.195913\pi$
$3$			2.00000i			1.15470i	−0.816497	+	0.577350i	$0.804087\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−3.00000	−	3.00000i	−1.13389	−	1.13389i	−0.989524	−	0.144370i	$-0.953885\pi$
$7$	−3.00000	−	3.00000i	−1.13389	−	1.13389i	−0.144370	−	0.989524i	$-0.546115\pi$
$8$		0			0
$9$	−1.00000			−0.333333
$10$		0			0
$11$	1.00000	+	1.00000i	0.301511	+	0.301511i	0.841605	−	0.540094i	$-0.181611\pi$
$11$	1.00000	+	1.00000i	0.301511	+	0.301511i	−0.540094	+	0.841605i	$0.681611\pi$
$12$		0			0
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.00000	−	1.00000i	−0.242536	−	0.242536i	0.575363	−	0.817898i	$-0.304861\pi$
$17$	−1.00000	−	1.00000i	−0.242536	−	0.242536i	−0.817898	+	0.575363i	$0.804861\pi$
$18$		0			0
$19$	−3.00000	−	3.00000i	−0.688247	−	0.688247i	0.273597	−	0.961844i	$-0.411786\pi$
$19$	−3.00000	−	3.00000i	−0.688247	−	0.688247i	−0.961844	+	0.273597i	$0.911786\pi$
$20$		0			0
$21$	6.00000	−	6.00000i	1.30931	−	1.30931i
$22$		0			0
$23$	−1.00000	+	1.00000i	−0.208514	+	0.208514i	−0.803636	−	0.595121i	$-0.797104\pi$
$23$	−1.00000	+	1.00000i	−0.208514	+	0.208514i	0.595121	+	0.803636i	$0.297104\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			4.00000i			0.769800i
$28$		0			0
$29$	7.00000	−	7.00000i	1.29987	−	1.29987i	0.371391	−	0.928477i	$-0.378881\pi$
$29$	7.00000	−	7.00000i	1.29987	−	1.29987i	0.928477	−	0.371391i	$-0.121119\pi$
$30$		0			0
$31$		−	2.00000i		−	0.359211i	−0.983739	−	0.179605i	$-0.942518\pi$
$31$		−	2.00000i		−	0.359211i	0.983739	−	0.179605i	$-0.0574821\pi$
$32$		0			0
$33$	−2.00000	+	2.00000i	−0.348155	+	0.348155i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	6.00000			0.986394			0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000			0.986394			0.493197	+	0.869918i	$0.335828\pi$
$38$		0			0
$39$			4.00000i			0.640513i
$40$		0			0
$41$		−	4.00000i		−	0.624695i	−0.949968	−	0.312348i	$-0.898885\pi$
$41$		−	4.00000i		−	0.624695i	0.949968	−	0.312348i	$-0.101115\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	7.00000	−	7.00000i	1.02105	−	1.02105i	0.0212814	−	0.999774i	$-0.493225\pi$
$47$	7.00000	−	7.00000i	1.02105	−	1.02105i	0.999774	−	0.0212814i	$-0.00677460\pi$
$48$		0			0
$49$			11.0000i			1.57143i
$50$		0			0
$51$	2.00000	−	2.00000i	0.280056	−	0.280056i
$52$		0			0
$53$		−	8.00000i		−	1.09888i	−0.835532	−	0.549442i	$-0.814840\pi$
$53$		−	8.00000i		−	1.09888i	0.835532	−	0.549442i	$-0.185160\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	6.00000	−	6.00000i	0.794719	−	0.794719i
$58$		0			0
$59$	3.00000	−	3.00000i	0.390567	−	0.390567i	−0.484323	−	0.874889i	$-0.660934\pi$
$59$	3.00000	−	3.00000i	0.390567	−	0.390567i	0.874889	+	0.484323i	$0.160934\pi$
$60$		0			0
$61$	−1.00000	−	1.00000i	−0.128037	−	0.128037i	0.640184	−	0.768221i	$-0.278858\pi$
$61$	−1.00000	−	1.00000i	−0.128037	−	0.128037i	−0.768221	+	0.640184i	$0.778858\pi$
$62$		0			0
$63$	3.00000	+	3.00000i	0.377964	+	0.377964i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$		0			0
$69$	−2.00000	−	2.00000i	−0.240772	−	0.240772i
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	3.00000	+	3.00000i	0.351123	+	0.351123i	0.860527	−	0.509404i	$-0.170134\pi$
$73$	3.00000	+	3.00000i	0.351123	+	0.351123i	−0.509404	+	0.860527i	$0.670134\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		−	6.00000i		−	0.683763i
$78$		0			0
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$		0			0
$81$	−11.0000			−1.22222
$82$		0			0
$83$			2.00000i			0.219529i	0.993958	+	0.109764i	$0.0350096\pi$
$83$			2.00000i			0.219529i	−0.993958	+	0.109764i	$0.964990\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	14.0000	+	14.0000i	1.50096	+	1.50096i
$88$		0			0
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$		0			0
$91$	−6.00000	−	6.00000i	−0.628971	−	0.628971i
$92$		0			0
$93$	4.00000			0.414781
$94$		0			0
$95$		0			0
$96$		0			0
$97$	11.0000	+	11.0000i	1.11688	+	1.11688i	0.992196	+	0.124684i	$0.0397918\pi$
$97$	11.0000	+	11.0000i	1.11688	+	1.11688i	0.124684	+	0.992196i	$0.460208\pi$
$98$		0			0
$99$	−1.00000	−	1.00000i	−0.100504	−	0.100504i
$100$		0			0
$101$	−5.00000	+	5.00000i	−0.497519	+	0.497519i	−0.910665	−	0.413146i	$-0.864430\pi$
$101$	−5.00000	+	5.00000i	−0.497519	+	0.497519i	0.413146	+	0.910665i	$0.364430\pi$
$102$		0			0
$103$	−5.00000	+	5.00000i	−0.492665	+	0.492665i	−0.909145	−	0.416480i	$-0.863264\pi$
$103$	−5.00000	+	5.00000i	−0.492665	+	0.492665i	0.416480	+	0.909145i	$0.363264\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	6.00000i		−	0.580042i	−0.957020	−	0.290021i	$-0.906338\pi$
$107$		−	6.00000i		−	0.580042i	0.957020	−	0.290021i	$-0.0936623\pi$
$108$		0			0
$109$	−5.00000	+	5.00000i	−0.478913	+	0.478913i	−0.904784	−	0.425871i	$-0.859968\pi$
$109$	−5.00000	+	5.00000i	−0.478913	+	0.478913i	0.425871	+	0.904784i	$0.359968\pi$
$110$		0			0
$111$			12.0000i			1.13899i
$112$		0			0
$113$	−13.0000	+	13.0000i	−1.22294	+	1.22294i	−0.256354	+	0.966583i	$0.582521\pi$
$113$	−13.0000	+	13.0000i	−1.22294	+	1.22294i	−0.966583	+	0.256354i	$0.917479\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−2.00000			−0.184900
$118$		0			0
$119$			6.00000i			0.550019i
$120$		0			0
$121$		−	9.00000i		−	0.818182i
$122$		0			0
$123$	8.00000			0.721336
$124$		0			0
$125$		0			0
$126$		0			0
$127$	7.00000	−	7.00000i	0.621150	−	0.621150i	−0.324676	−	0.945825i	$-0.605255\pi$
$127$	7.00000	−	7.00000i	0.621150	−	0.621150i	0.945825	+	0.324676i	$0.105255\pi$
$128$		0			0
$129$			8.00000i			0.704361i
$130$		0			0
$131$	7.00000	−	7.00000i	0.611593	−	0.611593i	−0.331768	−	0.943361i	$-0.607645\pi$
$131$	7.00000	−	7.00000i	0.611593	−	0.611593i	0.943361	+	0.331768i	$0.107645\pi$
$132$		0			0
$133$			18.0000i			1.56080i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−9.00000	+	9.00000i	−0.768922	+	0.768922i	−0.977917	−	0.208995i	$-0.932981\pi$
$137$	−9.00000	+	9.00000i	−0.768922	+	0.768922i	0.208995	+	0.977917i	$0.432981\pi$
$138$		0			0
$139$	−9.00000	+	9.00000i	−0.763370	+	0.763370i	−0.976930	−	0.213560i	$-0.931494\pi$
$139$	−9.00000	+	9.00000i	−0.763370	+	0.763370i	0.213560	+	0.976930i	$0.431494\pi$
$140$		0			0
$141$	14.0000	+	14.0000i	1.17901	+	1.17901i
$142$		0			0
$143$	2.00000	+	2.00000i	0.167248	+	0.167248i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−22.0000			−1.81453
$148$		0			0
$149$	−1.00000	−	1.00000i	−0.0819232	−	0.0819232i	0.664958	−	0.746881i	$-0.268450\pi$
$149$	−1.00000	−	1.00000i	−0.0819232	−	0.0819232i	−0.746881	+	0.664958i	$0.768450\pi$
$150$		0			0
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$		0			0
$153$	1.00000	+	1.00000i	0.0808452	+	0.0808452i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		−	20.0000i		−	1.59617i	−0.602542	−	0.798087i	$-0.705846\pi$
$157$		−	20.0000i		−	1.59617i	0.602542	−	0.798087i	$-0.294154\pi$
$158$		0			0
$159$	16.0000			1.26888
$160$		0			0
$161$	6.00000			0.472866
$162$		0			0
$163$		−	14.0000i		−	1.09656i	−0.836293	−	0.548282i	$-0.815282\pi$
$163$		−	14.0000i		−	1.09656i	0.836293	−	0.548282i	$-0.184718\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.00000	−	3.00000i	−0.232147	−	0.232147i	0.581441	−	0.813588i	$-0.302489\pi$
$167$	−3.00000	−	3.00000i	−0.232147	−	0.232147i	−0.813588	+	0.581441i	$0.802489\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$	3.00000	+	3.00000i	0.229416	+	0.229416i
$172$		0			0
$173$	6.00000			0.456172			0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000			0.456172			0.228086	+	0.973641i	$0.426753\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	6.00000	+	6.00000i	0.450988	+	0.450988i
$178$		0			0
$179$	5.00000	+	5.00000i	0.373718	+	0.373718i	0.868829	−	0.495112i	$-0.164873\pi$
$179$	5.00000	+	5.00000i	0.373718	+	0.373718i	−0.495112	+	0.868829i	$0.664873\pi$
$180$		0			0
$181$	3.00000	−	3.00000i	0.222988	−	0.222988i	−0.586767	−	0.809756i	$-0.699600\pi$
$181$	3.00000	−	3.00000i	0.222988	−	0.222988i	0.809756	+	0.586767i	$0.199600\pi$
$182$		0			0
$183$	2.00000	−	2.00000i	0.147844	−	0.147844i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		−	2.00000i		−	0.146254i
$188$		0			0
$189$	12.0000	−	12.0000i	0.872872	−	0.872872i
$190$		0			0
$191$		−	18.0000i		−	1.30243i	−0.758891	−	0.651217i	$-0.774259\pi$
$191$		−	18.0000i		−	1.30243i	0.758891	−	0.651217i	$-0.225741\pi$
$192$		0			0
$193$	15.0000	−	15.0000i	1.07972	−	1.07972i	0.0831899	−	0.996534i	$-0.473489\pi$
$193$	15.0000	−	15.0000i	1.07972	−	1.07972i	0.996534	−	0.0831899i	$-0.0265108\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$		0			0
$199$		−	10.0000i		−	0.708881i	−0.935079	−	0.354441i	$-0.884671\pi$
$199$		−	10.0000i		−	0.708881i	0.935079	−	0.354441i	$-0.115329\pi$
$200$		0			0
$201$			8.00000i			0.564276i
$202$		0			0
$203$	−42.0000			−2.94782
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.00000	−	1.00000i	0.0695048	−	0.0695048i
$208$		0			0
$209$		−	6.00000i		−	0.415029i
$210$		0			0
$211$	19.0000	−	19.0000i	1.30801	−	1.30801i	0.385167	−	0.922847i	$-0.374144\pi$
$211$	19.0000	−	19.0000i	1.30801	−	1.30801i	0.922847	−	0.385167i	$-0.125856\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−6.00000	+	6.00000i	−0.407307	+	0.407307i
$218$		0			0
$219$	−6.00000	+	6.00000i	−0.405442	+	0.405442i
$220$		0			0
$221$	−2.00000	−	2.00000i	−0.134535	−	0.134535i
$222$		0			0
$223$	9.00000	+	9.00000i	0.602685	+	0.602685i	0.941024	−	0.338340i	$-0.109865\pi$
$223$	9.00000	+	9.00000i	0.602685	+	0.602685i	−0.338340	+	0.941024i	$0.609865\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	12.0000			0.796468			0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000			0.796468			0.398234	+	0.917284i	$0.369623\pi$
$228$		0			0
$229$	−1.00000	−	1.00000i	−0.0660819	−	0.0660819i	0.673293	−	0.739375i	$-0.264879\pi$
$229$	−1.00000	−	1.00000i	−0.0660819	−	0.0660819i	−0.739375	+	0.673293i	$0.764879\pi$
$230$		0			0
$231$	12.0000			0.789542
$232$		0			0
$233$	−9.00000	−	9.00000i	−0.589610	−	0.589610i	0.347916	−	0.937526i	$-0.386889\pi$
$233$	−9.00000	−	9.00000i	−0.589610	−	0.589610i	−0.937526	+	0.347916i	$0.886889\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$			16.0000i			1.03931i
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	−14.0000			−0.901819			−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000			−0.901819			−0.450910	+	0.892570i	$0.648900\pi$
$242$		0			0
$243$		−	10.0000i		−	0.641500i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−6.00000	−	6.00000i	−0.381771	−	0.381771i
$248$		0			0
$249$	−4.00000			−0.253490
$250$		0			0
$251$	−11.0000	−	11.0000i	−0.694314	−	0.694314i	0.268864	−	0.963178i	$-0.413352\pi$
$251$	−11.0000	−	11.0000i	−0.694314	−	0.694314i	−0.963178	+	0.268864i	$0.913352\pi$
$252$		0			0
$253$	−2.00000			−0.125739
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−13.0000	−	13.0000i	−0.810918	−	0.810918i	0.173854	−	0.984771i	$-0.444378\pi$
$257$	−13.0000	−	13.0000i	−0.810918	−	0.810918i	−0.984771	+	0.173854i	$0.944378\pi$
$258$		0			0
$259$	−18.0000	−	18.0000i	−1.11847	−	1.11847i
$260$		0			0
$261$	−7.00000	+	7.00000i	−0.433289	+	0.433289i
$262$		0			0
$263$	7.00000	−	7.00000i	0.431638	−	0.431638i	−0.457547	−	0.889185i	$-0.651272\pi$
$263$	7.00000	−	7.00000i	0.431638	−	0.431638i	0.889185	+	0.457547i	$0.151272\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			12.0000i			0.734388i
$268$		0			0
$269$	−1.00000	+	1.00000i	−0.0609711	+	0.0609711i	−0.736935	−	0.675964i	$-0.763728\pi$
$269$	−1.00000	+	1.00000i	−0.0609711	+	0.0609711i	0.675964	+	0.736935i	$0.263728\pi$
$270$		0			0
$271$			30.0000i			1.82237i	0.411997	+	0.911185i	$0.364831\pi$
$271$			30.0000i			1.82237i	−0.411997	+	0.911185i	$0.635169\pi$
$272$		0			0
$273$	12.0000	−	12.0000i	0.726273	−	0.726273i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−18.0000			−1.08152			−0.540758	−	0.841178i	$-0.681862\pi$
$277$	−18.0000			−1.08152			−0.540758	+	0.841178i	$0.681862\pi$
$278$		0			0
$279$			2.00000i			0.119737i
$280$		0			0
$281$			16.0000i			0.954480i	0.878773	+	0.477240i	$0.158363\pi$
$281$			16.0000i			0.954480i	−0.878773	+	0.477240i	$0.841637\pi$
$282$		0			0
$283$	12.0000			0.713326			0.356663	−	0.934233i	$-0.383914\pi$
$283$	12.0000			0.713326			0.356663	+	0.934233i	$0.383914\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−12.0000	+	12.0000i	−0.708338	+	0.708338i
$288$		0			0
$289$		−	15.0000i		−	0.882353i
$290$		0			0
$291$	−22.0000	+	22.0000i	−1.28966	+	1.28966i
$292$		0			0
$293$		−	12.0000i		−	0.701047i	−0.936554	−	0.350524i	$-0.886004\pi$
$293$		−	12.0000i		−	0.701047i	0.936554	−	0.350524i	$-0.113996\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−4.00000	+	4.00000i	−0.232104	+	0.232104i
$298$		0			0
$299$	−2.00000	+	2.00000i	−0.115663	+	0.115663i
$300$		0			0
$301$	−12.0000	−	12.0000i	−0.691669	−	0.691669i
$302$		0			0
$303$	−10.0000	−	10.0000i	−0.574485	−	0.574485i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−4.00000			−0.228292			−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000			−0.228292			−0.114146	+	0.993464i	$0.536413\pi$
$308$		0			0
$309$	−10.0000	−	10.0000i	−0.568880	−	0.568880i
$310$		0			0
$311$	−16.0000			−0.907277			−0.453638	−	0.891186i	$-0.649874\pi$
$311$	−16.0000			−0.907277			−0.453638	+	0.891186i	$0.649874\pi$
$312$		0			0
$313$	−13.0000	−	13.0000i	−0.734803	−	0.734803i	0.236764	−	0.971567i	$-0.423913\pi$
$313$	−13.0000	−	13.0000i	−0.734803	−	0.734803i	−0.971567	+	0.236764i	$0.923913\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	8.00000i		−	0.449325i	−0.974437	−	0.224662i	$-0.927872\pi$
$317$		−	8.00000i		−	0.449325i	0.974437	−	0.224662i	$-0.0721279\pi$
$318$		0			0
$319$	14.0000			0.783850
$320$		0			0
$321$	12.0000			0.669775
$322$		0			0
$323$			6.00000i			0.333849i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−10.0000	−	10.0000i	−0.553001	−	0.553001i
$328$		0			0
$329$	−42.0000			−2.31553
$330$		0			0
$331$	21.0000	+	21.0000i	1.15426	+	1.15426i	0.985689	+	0.168576i	$0.0539168\pi$
$331$	21.0000	+	21.0000i	1.15426	+	1.15426i	0.168576	+	0.985689i	$0.446083\pi$
$332$		0			0
$333$	−6.00000			−0.328798
$334$		0			0
$335$		0			0
$336$		0			0
$337$	11.0000	+	11.0000i	0.599208	+	0.599208i	0.940102	−	0.340894i	$-0.110730\pi$
$337$	11.0000	+	11.0000i	0.599208	+	0.599208i	−0.340894	+	0.940102i	$0.610730\pi$
$338$		0			0
$339$	−26.0000	−	26.0000i	−1.41213	−	1.41213i
$340$		0			0
$341$	2.00000	−	2.00000i	0.108306	−	0.108306i
$342$		0			0
$343$	12.0000	−	12.0000i	0.647939	−	0.647939i
$344$		0			0
$345$		0			0
$346$		0			0
$347$			2.00000i			0.107366i	0.998558	+	0.0536828i	$0.0170960\pi$
$347$			2.00000i			0.107366i	−0.998558	+	0.0536828i	$0.982904\pi$
$348$		0			0
$349$	3.00000	−	3.00000i	0.160586	−	0.160586i	−0.622240	−	0.782826i	$-0.713777\pi$
$349$	3.00000	−	3.00000i	0.160586	−	0.160586i	0.782826	+	0.622240i	$0.213777\pi$
$350$		0			0
$351$			8.00000i			0.427008i
$352$		0			0
$353$	−13.0000	+	13.0000i	−0.691920	+	0.691920i	−0.962654	−	0.270734i	$-0.912734\pi$
$353$	−13.0000	+	13.0000i	−0.691920	+	0.691920i	0.270734	+	0.962654i	$0.412734\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−12.0000			−0.635107
$358$		0			0
$359$			14.0000i			0.738892i	0.929252	+	0.369446i	$0.120452\pi$
$359$			14.0000i			0.738892i	−0.929252	+	0.369446i	$0.879548\pi$
$360$		0			0
$361$		−	1.00000i		−	0.0526316i
$362$		0			0
$363$	18.0000			0.944755
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−21.0000	+	21.0000i	−1.09619	+	1.09619i	−0.101339	+	0.994852i	$0.532313\pi$
$367$	−21.0000	+	21.0000i	−1.09619	+	1.09619i	−0.994852	+	0.101339i	$0.967687\pi$
$368$		0			0
$369$			4.00000i			0.208232i
$370$		0			0
$371$	−24.0000	+	24.0000i	−1.24602	+	1.24602i
$372$		0			0
$373$		−	4.00000i		−	0.207112i	−0.994624	−	0.103556i	$-0.966978\pi$
$373$		−	4.00000i		−	0.207112i	0.994624	−	0.103556i	$-0.0330221\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	14.0000	−	14.0000i	0.721037	−	0.721037i
$378$		0			0
$379$	15.0000	−	15.0000i	0.770498	−	0.770498i	−0.207695	−	0.978194i	$-0.566596\pi$
$379$	15.0000	−	15.0000i	0.770498	−	0.770498i	0.978194	+	0.207695i	$0.0665963\pi$
$380$		0			0
$381$	14.0000	+	14.0000i	0.717242	+	0.717242i
$382$		0			0
$383$	5.00000	+	5.00000i	0.255488	+	0.255488i	0.823216	−	0.567728i	$-0.192177\pi$
$383$	5.00000	+	5.00000i	0.255488	+	0.255488i	−0.567728	+	0.823216i	$0.692177\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−4.00000			−0.203331
$388$		0			0
$389$	23.0000	+	23.0000i	1.16615	+	1.16615i	0.983105	+	0.183041i	$0.0585941\pi$
$389$	23.0000	+	23.0000i	1.16615	+	1.16615i	0.183041	+	0.983105i	$0.441406\pi$
$390$		0			0
$391$	2.00000			0.101144
$392$		0			0
$393$	14.0000	+	14.0000i	0.706207	+	0.706207i
$394$		0			0
$395$		0			0
$396$		0			0
$397$			32.0000i			1.60603i	0.595956	+	0.803017i	$0.296773\pi$
$397$			32.0000i			1.60603i	−0.595956	+	0.803017i	$0.703227\pi$
$398$		0			0
$399$	−36.0000			−1.80225
$400$		0			0
$401$	−2.00000			−0.0998752			−0.0499376	−	0.998752i	$-0.515902\pi$
$401$	−2.00000			−0.0998752			−0.0499376	+	0.998752i	$0.515902\pi$
$402$		0			0
$403$		−	4.00000i		−	0.199254i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	6.00000	+	6.00000i	0.297409	+	0.297409i
$408$		0			0
$409$	38.0000			1.87898			0.939490	−	0.342578i	$-0.111300\pi$
$409$	38.0000			1.87898			0.939490	+	0.342578i	$0.111300\pi$
$410$		0			0
$411$	−18.0000	−	18.0000i	−0.887875	−	0.887875i
$412$		0			0
$413$	−18.0000			−0.885722
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−18.0000	−	18.0000i	−0.881464	−	0.881464i
$418$		0			0
$419$	17.0000	+	17.0000i	0.830504	+	0.830504i	0.987586	−	0.157081i	$-0.0502085\pi$
$419$	17.0000	+	17.0000i	0.830504	+	0.830504i	−0.157081	+	0.987586i	$0.550208\pi$
$420$		0			0
$421$	−5.00000	+	5.00000i	−0.243685	+	0.243685i	−0.818373	−	0.574688i	$-0.805124\pi$
$421$	−5.00000	+	5.00000i	−0.243685	+	0.243685i	0.574688	+	0.818373i	$0.305124\pi$
$422$		0			0
$423$	−7.00000	+	7.00000i	−0.340352	+	0.340352i
$424$		0			0
$425$		0			0
$426$		0			0
$427$			6.00000i			0.290360i
$428$		0			0
$429$	−4.00000	+	4.00000i	−0.193122	+	0.193122i
$430$		0			0
$431$		−	2.00000i		−	0.0963366i	−0.998839	−	0.0481683i	$-0.984662\pi$
$431$		−	2.00000i		−	0.0963366i	0.998839	−	0.0481683i	$-0.0153384\pi$
$432$		0			0
$433$	−5.00000	+	5.00000i	−0.240285	+	0.240285i	−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−5.00000	+	5.00000i	−0.240285	+	0.240285i	0.576683	+	0.816968i	$0.304347\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	6.00000			0.287019
$438$		0			0
$439$		−	26.0000i		−	1.24091i	−0.784241	−	0.620456i	$-0.786947\pi$
$439$		−	26.0000i		−	1.24091i	0.784241	−	0.620456i	$-0.213053\pi$
$440$		0			0
$441$		−	11.0000i		−	0.523810i
$442$		0			0
$443$	−4.00000			−0.190046			−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000			−0.190046			−0.0950229	+	0.995475i	$0.530292\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	2.00000	−	2.00000i	0.0945968	−	0.0945968i
$448$		0			0
$449$			24.0000i			1.13263i	0.824189	+	0.566315i	$0.191631\pi$
$449$			24.0000i			1.13263i	−0.824189	+	0.566315i	$0.808369\pi$
$450$		0			0
$451$	4.00000	−	4.00000i	0.188353	−	0.188353i
$452$		0			0
$453$		−	16.0000i		−	0.751746i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	7.00000	−	7.00000i	0.327446	−	0.327446i	−0.524168	−	0.851615i	$-0.675624\pi$
$457$	7.00000	−	7.00000i	0.327446	−	0.327446i	0.851615	+	0.524168i	$0.175624\pi$
$458$		0			0
$459$	4.00000	−	4.00000i	0.186704	−	0.186704i
$460$		0			0
$461$	−21.0000	−	21.0000i	−0.978068	−	0.978068i	0.0216971	−	0.999765i	$-0.493093\pi$
$461$	−21.0000	−	21.0000i	−0.978068	−	0.978068i	−0.999765	+	0.0216971i	$0.993093\pi$
$462$		0			0
$463$	−19.0000	−	19.0000i	−0.883005	−	0.883005i	0.110834	−	0.993839i	$-0.464648\pi$
$463$	−19.0000	−	19.0000i	−0.883005	−	0.883005i	−0.993839	+	0.110834i	$0.964648\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−28.0000			−1.29569			−0.647843	−	0.761774i	$-0.724329\pi$
$467$	−28.0000			−1.29569			−0.647843	+	0.761774i	$0.724329\pi$
$468$		0			0
$469$	−12.0000	−	12.0000i	−0.554109	−	0.554109i
$470$		0			0
$471$	40.0000			1.84310
$472$		0			0
$473$	4.00000	+	4.00000i	0.183920	+	0.183920i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			8.00000i			0.366295i
$478$		0			0
$479$	−32.0000			−1.46212			−0.731059	−	0.682315i	$-0.760973\pi$
$479$	−32.0000			−1.46212			−0.731059	+	0.682315i	$0.760973\pi$
$480$		0			0
$481$	12.0000			0.547153
$482$		0			0
$483$			12.0000i			0.546019i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−15.0000	−	15.0000i	−0.679715	−	0.679715i	0.280221	−	0.959936i	$-0.409592\pi$
$487$	−15.0000	−	15.0000i	−0.679715	−	0.679715i	−0.959936	+	0.280221i	$0.909592\pi$
$488$		0			0
$489$	28.0000			1.26620
$490$		0			0
$491$	9.00000	+	9.00000i	0.406164	+	0.406164i	0.880399	−	0.474234i	$-0.157275\pi$
$491$	9.00000	+	9.00000i	0.406164	+	0.406164i	−0.474234	+	0.880399i	$0.657275\pi$
$492$		0			0
$493$	−14.0000			−0.630528
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	29.0000	+	29.0000i	1.29822	+	1.29822i	0.929568	+	0.368650i	$0.120180\pi$
$499$	29.0000	+	29.0000i	1.29822	+	1.29822i	0.368650	+	0.929568i	$0.379820\pi$
$500$		0			0
$501$	6.00000	−	6.00000i	0.268060	−	0.268060i
$502$		0			0
$503$	−29.0000	+	29.0000i	−1.29305	+	1.29305i	−0.360153	+	0.932893i	$0.617275\pi$
$503$	−29.0000	+	29.0000i	−1.29305	+	1.29305i	−0.932893	+	0.360153i	$0.882725\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		−	18.0000i		−	0.799408i
$508$		0			0
$509$	−17.0000	+	17.0000i	−0.753512	+	0.753512i	−0.975133	−	0.221621i	$-0.928865\pi$
$509$	−17.0000	+	17.0000i	−0.753512	+	0.753512i	0.221621	+	0.975133i	$0.428865\pi$
$510$		0			0
$511$		−	18.0000i		−	0.796273i
$512$		0			0
$513$	12.0000	−	12.0000i	0.529813	−	0.529813i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	14.0000			0.615719
$518$		0			0
$519$			12.0000i			0.526742i
$520$		0			0
$521$		−	16.0000i		−	0.700973i	−0.936568	−	0.350486i	$-0.886016\pi$
$521$		−	16.0000i		−	0.700973i	0.936568	−	0.350486i	$-0.113984\pi$
$522$		0			0
$523$	20.0000			0.874539			0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000			0.874539			0.437269	+	0.899331i	$0.355946\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.00000	+	2.00000i	−0.0871214	+	0.0871214i
$528$		0			0
$529$			21.0000i			0.913043i
$530$		0			0
$531$	−3.00000	+	3.00000i	−0.130189	+	0.130189i
$532$		0			0
$533$		−	8.00000i		−	0.346518i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−10.0000	+	10.0000i	−0.431532	+	0.431532i
$538$		0			0
$539$	−11.0000	+	11.0000i	−0.473804	+	0.473804i
$540$		0			0
$541$	15.0000	+	15.0000i	0.644900	+	0.644900i	0.951756	−	0.306856i	$-0.0992769\pi$
$541$	15.0000	+	15.0000i	0.644900	+	0.644900i	−0.306856	+	0.951756i	$0.599277\pi$
$542$		0			0
$543$	6.00000	+	6.00000i	0.257485	+	0.257485i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$		0			0
$549$	1.00000	+	1.00000i	0.0426790	+	0.0426790i
$550$		0			0
$551$	−42.0000			−1.78926
$552$		0			0
$553$	−24.0000	−	24.0000i	−1.02058	−	1.02058i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	28.0000i		−	1.18640i	−0.805056	−	0.593199i	$-0.797865\pi$
$557$		−	28.0000i		−	1.18640i	0.805056	−	0.593199i	$-0.202135\pi$
$558$		0			0
$559$	8.00000			0.338364
$560$		0			0
$561$	4.00000			0.168880
$562$		0			0
$563$			18.0000i			0.758610i	0.925272	+	0.379305i	$0.123837\pi$
$563$			18.0000i			0.758610i	−0.925272	+	0.379305i	$0.876163\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	33.0000	+	33.0000i	1.38587	+	1.38587i
$568$		0			0
$569$	6.00000			0.251533			0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000			0.251533			0.125767	+	0.992060i	$0.459861\pi$
$570$		0			0
$571$	25.0000	+	25.0000i	1.04622	+	1.04622i	0.998879	+	0.0473385i	$0.0150740\pi$
$571$	25.0000	+	25.0000i	1.04622	+	1.04622i	0.0473385	+	0.998879i	$0.484926\pi$
$572$		0			0
$573$	36.0000			1.50392
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−9.00000	−	9.00000i	−0.374675	−	0.374675i	0.494502	−	0.869177i	$-0.335351\pi$
$577$	−9.00000	−	9.00000i	−0.374675	−	0.374675i	−0.869177	+	0.494502i	$0.835351\pi$
$578$		0			0
$579$	30.0000	+	30.0000i	1.24676	+	1.24676i
$580$		0			0
$581$	6.00000	−	6.00000i	0.248922	−	0.248922i
$582$		0			0
$583$	8.00000	−	8.00000i	0.331326	−	0.331326i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			2.00000i			0.0825488i	0.999148	+	0.0412744i	$0.0131418\pi$
$587$			2.00000i			0.0825488i	−0.999148	+	0.0412744i	$0.986858\pi$
$588$		0			0
$589$	−6.00000	+	6.00000i	−0.247226	+	0.247226i
$590$		0			0
$591$		−	12.0000i		−	0.493614i
$592$		0			0
$593$	−17.0000	+	17.0000i	−0.698106	+	0.698106i	−0.964002	−	0.265896i	$-0.914332\pi$
$593$	−17.0000	+	17.0000i	−0.698106	+	0.698106i	0.265896	+	0.964002i	$0.414332\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	20.0000			0.818546
$598$		0			0
$599$			30.0000i			1.22577i	0.790173	+	0.612883i	$0.209990\pi$
$599$			30.0000i			1.22577i	−0.790173	+	0.612883i	$0.790010\pi$
$600$		0			0
$601$			16.0000i			0.652654i	0.945257	+	0.326327i	$0.105811\pi$
$601$			16.0000i			0.652654i	−0.945257	+	0.326327i	$0.894189\pi$
$602$		0			0
$603$	−4.00000			−0.162893
$604$		0			0
$605$		0			0
$606$		0			0
$607$	23.0000	−	23.0000i	0.933541	−	0.933541i	−0.0643840	−	0.997925i	$-0.520508\pi$
$607$	23.0000	−	23.0000i	0.933541	−	0.933541i	0.997925	+	0.0643840i	$0.0205082\pi$
$608$		0			0
$609$		−	84.0000i		−	3.40385i
$610$		0			0
$611$	14.0000	−	14.0000i	0.566379	−	0.566379i
$612$		0			0
$613$			8.00000i			0.323117i	0.986863	+	0.161558i	$0.0516520\pi$
$613$			8.00000i			0.323117i	−0.986863	+	0.161558i	$0.948348\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−25.0000	+	25.0000i	−1.00646	+	1.00646i	−0.00648312	+	0.999979i	$0.502064\pi$
$617$	−25.0000	+	25.0000i	−1.00646	+	1.00646i	−0.999979	+	0.00648312i	$0.997936\pi$
$618$		0			0
$619$	7.00000	−	7.00000i	0.281354	−	0.281354i	−0.552295	−	0.833649i	$-0.686248\pi$
$619$	7.00000	−	7.00000i	0.281354	−	0.281354i	0.833649	+	0.552295i	$0.186248\pi$
$620$		0			0
$621$	−4.00000	−	4.00000i	−0.160514	−	0.160514i
$622$		0			0
$623$	−18.0000	−	18.0000i	−0.721155	−	0.721155i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	12.0000			0.479234
$628$		0			0
$629$	−6.00000	−	6.00000i	−0.239236	−	0.239236i
$630$		0			0
$631$	−24.0000			−0.955425			−0.477712	−	0.878516i	$-0.658534\pi$
$631$	−24.0000			−0.955425			−0.477712	+	0.878516i	$0.658534\pi$
$632$		0			0
$633$	38.0000	+	38.0000i	1.51036	+	1.51036i
$634$		0			0
$635$		0			0
$636$		0			0
$637$			22.0000i			0.871672i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−30.0000			−1.18493			−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000			−1.18493			−0.592464	+	0.805597i	$0.701845\pi$
$642$		0			0
$643$			26.0000i			1.02534i	0.858586	+	0.512670i	$0.171344\pi$
$643$			26.0000i			1.02534i	−0.858586	+	0.512670i	$0.828656\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−15.0000	−	15.0000i	−0.589711	−	0.589711i	0.347842	−	0.937553i	$-0.386914\pi$
$647$	−15.0000	−	15.0000i	−0.589711	−	0.589711i	−0.937553	+	0.347842i	$0.886914\pi$
$648$		0			0
$649$	6.00000			0.235521
$650$		0			0
$651$	−12.0000	−	12.0000i	−0.470317	−	0.470317i
$652$		0			0
$653$	2.00000			0.0782660			0.0391330	−	0.999234i	$-0.487540\pi$
$653$	2.00000			0.0782660			0.0391330	+	0.999234i	$0.487540\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−3.00000	−	3.00000i	−0.117041	−	0.117041i
$658$		0			0
$659$	−11.0000	−	11.0000i	−0.428499	−	0.428499i	0.459618	−	0.888117i	$-0.347986\pi$
$659$	−11.0000	−	11.0000i	−0.428499	−	0.428499i	−0.888117	+	0.459618i	$0.847986\pi$
$660$		0			0
$661$	−25.0000	+	25.0000i	−0.972387	+	0.972387i	−0.999629	−	0.0272416i	$-0.991328\pi$
$661$	−25.0000	+	25.0000i	−0.972387	+	0.972387i	0.0272416	+	0.999629i	$0.491328\pi$
$662$		0			0
$663$	4.00000	−	4.00000i	0.155347	−	0.155347i
$664$		0			0
$665$		0			0
$666$		0			0
$667$			14.0000i			0.542082i
$668$		0			0
$669$	−18.0000	+	18.0000i	−0.695920	+	0.695920i
$670$		0			0
$671$		−	2.00000i		−	0.0772091i
$672$		0			0
$673$	−1.00000	+	1.00000i	−0.0385472	+	0.0385472i	−0.726118	−	0.687570i	$-0.758677\pi$
$673$	−1.00000	+	1.00000i	−0.0385472	+	0.0385472i	0.687570	+	0.726118i	$0.258677\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	42.0000			1.61419			0.807096	−	0.590421i	$-0.201038\pi$
$677$	42.0000			1.61419			0.807096	+	0.590421i	$0.201038\pi$
$678$		0			0
$679$		−	66.0000i		−	2.53285i
$680$		0			0
$681$			24.0000i			0.919682i
$682$		0			0
$683$	−4.00000			−0.153056			−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000			−0.153056			−0.0765279	+	0.997067i	$0.524383\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	2.00000	−	2.00000i	0.0763048	−	0.0763048i
$688$		0			0
$689$		−	16.0000i		−	0.609551i
$690$		0			0
$691$	−21.0000	+	21.0000i	−0.798878	+	0.798878i	−0.982919	−	0.184041i	$-0.941082\pi$
$691$	−21.0000	+	21.0000i	−0.798878	+	0.798878i	0.184041	+	0.982919i	$0.441082\pi$
$692$		0			0
$693$			6.00000i			0.227921i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−4.00000	+	4.00000i	−0.151511	+	0.151511i
$698$		0			0
$699$	18.0000	−	18.0000i	0.680823	−	0.680823i
$700$		0			0
$701$	−13.0000	−	13.0000i	−0.491003	−	0.491003i	0.417619	−	0.908622i	$-0.362865\pi$
$701$	−13.0000	−	13.0000i	−0.491003	−	0.491003i	−0.908622	+	0.417619i	$0.862865\pi$
$702$		0			0
$703$	−18.0000	−	18.0000i	−0.678883	−	0.678883i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	30.0000			1.12827
$708$		0			0
$709$	−1.00000	−	1.00000i	−0.0375558	−	0.0375558i	0.688080	−	0.725635i	$-0.258454\pi$
$709$	−1.00000	−	1.00000i	−0.0375558	−	0.0375558i	−0.725635	+	0.688080i	$0.758454\pi$
$710$		0			0
$711$	−8.00000			−0.300023
$712$		0			0
$713$	2.00000	+	2.00000i	0.0749006	+	0.0749006i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−32.0000			−1.19340			−0.596699	−	0.802465i	$-0.703521\pi$
$719$	−32.0000			−1.19340			−0.596699	+	0.802465i	$0.703521\pi$
$720$		0			0
$721$	30.0000			1.11726
$722$		0			0
$723$		−	28.0000i		−	1.04133i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−7.00000	−	7.00000i	−0.259616	−	0.259616i	0.565282	−	0.824898i	$-0.308767\pi$
$727$	−7.00000	−	7.00000i	−0.259616	−	0.259616i	−0.824898	+	0.565282i	$0.808767\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$		0			0
$731$	−4.00000	−	4.00000i	−0.147945	−	0.147945i
$732$		0			0
$733$	30.0000			1.10808			0.554038	−	0.832492i	$-0.313086\pi$
$733$	30.0000			1.10808			0.554038	+	0.832492i	$0.313086\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.00000	+	4.00000i	0.147342	+	0.147342i
$738$		0			0
$739$	21.0000	+	21.0000i	0.772497	+	0.772497i	0.978543	−	0.206045i	$-0.0660593\pi$
$739$	21.0000	+	21.0000i	0.772497	+	0.772497i	−0.206045	+	0.978543i	$0.566059\pi$
$740$		0			0
$741$	12.0000	−	12.0000i	0.440831	−	0.440831i
$742$		0			0
$743$	31.0000	−	31.0000i	1.13728	−	1.13728i	0.148344	−	0.988936i	$-0.452606\pi$
$743$	31.0000	−	31.0000i	1.13728	−	1.13728i	0.988936	−	0.148344i	$-0.0473942\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		−	2.00000i		−	0.0731762i
$748$		0			0
$749$	−18.0000	+	18.0000i	−0.657706	+	0.657706i
$750$		0			0
$751$		−	50.0000i		−	1.82453i	−0.409605	−	0.912263i	$-0.634333\pi$
$751$		−	50.0000i		−	1.82453i	0.409605	−	0.912263i	$-0.365667\pi$
$752$		0			0
$753$	22.0000	−	22.0000i	0.801725	−	0.801725i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−2.00000			−0.0726912			−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000			−0.0726912			−0.0363456	+	0.999339i	$0.511572\pi$
$758$		0			0
$759$		−	4.00000i		−	0.145191i
$760$		0			0
$761$			40.0000i			1.45000i	0.688749	+	0.724999i	$0.258160\pi$
$761$			40.0000i			1.45000i	−0.688749	+	0.724999i	$0.741840\pi$
$762$		0			0
$763$	30.0000			1.08607
$764$		0			0
$765$		0			0
$766$		0			0
$767$	6.00000	−	6.00000i	0.216647	−	0.216647i
$768$		0			0
$769$			4.00000i			0.144244i	0.997396	+	0.0721218i	$0.0229770\pi$
$769$			4.00000i			0.144244i	−0.997396	+	0.0721218i	$0.977023\pi$
$770$		0			0
$771$	26.0000	−	26.0000i	0.936367	−	0.936367i
$772$		0			0
$773$			48.0000i			1.72644i	0.504828	+	0.863220i	$0.331556\pi$
$773$			48.0000i			1.72644i	−0.504828	+	0.863220i	$0.668444\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	36.0000	−	36.0000i	1.29149	−	1.29149i
$778$		0			0
$779$	−12.0000	+	12.0000i	−0.429945	+	0.429945i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	28.0000	+	28.0000i	1.00064	+	1.00064i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−4.00000			−0.142585			−0.0712923	−	0.997455i	$-0.522712\pi$
$787$	−4.00000			−0.142585			−0.0712923	+	0.997455i	$0.522712\pi$
$788$		0			0
$789$	14.0000	+	14.0000i	0.498413	+	0.498413i
$790$		0			0
$791$	78.0000			2.77336
$792$		0			0
$793$	−2.00000	−	2.00000i	−0.0710221	−	0.0710221i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		1.00000			$0$
$797$		0			0		−1.00000			$\pi$
$798$		0			0
$799$	−14.0000			−0.495284
$800$		0			0
$801$	−6.00000			−0.212000
$802$		0			0
$803$			6.00000i			0.211735i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−2.00000	−	2.00000i	−0.0704033	−	0.0704033i
$808$		0			0
$809$	26.0000			0.914111			0.457056	−	0.889438i	$-0.348904\pi$
$809$	26.0000			0.914111			0.457056	+	0.889438i	$0.348904\pi$
$810$		0			0
$811$	9.00000	+	9.00000i	0.316033	+	0.316033i	0.847241	−	0.531208i	$-0.178262\pi$
$811$	9.00000	+	9.00000i	0.316033	+	0.316033i	−0.531208	+	0.847241i	$0.678262\pi$
$812$		0			0
$813$	−60.0000			−2.10429
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−12.0000	−	12.0000i	−0.419827	−	0.419827i
$818$		0			0
$819$	6.00000	+	6.00000i	0.209657	+	0.209657i
$820$		0			0
$821$	15.0000	−	15.0000i	0.523504	−	0.523504i	−0.395124	−	0.918628i	$-0.629298\pi$
$821$	15.0000	−	15.0000i	0.523504	−	0.523504i	0.918628	+	0.395124i	$0.129298\pi$
$822$		0			0
$823$	−21.0000	+	21.0000i	−0.732014	+	0.732014i	−0.971018	−	0.239004i	$-0.923179\pi$
$823$	−21.0000	+	21.0000i	−0.732014	+	0.732014i	0.239004	+	0.971018i	$0.423179\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	54.0000i		−	1.87776i	−0.344239	−	0.938882i	$-0.611863\pi$
$827$		−	54.0000i		−	1.87776i	0.344239	−	0.938882i	$-0.388137\pi$
$828$		0			0
$829$	27.0000	−	27.0000i	0.937749	−	0.937749i	−0.0604240	−	0.998173i	$-0.519245\pi$
$829$	27.0000	−	27.0000i	0.937749	−	0.937749i	0.998173	+	0.0604240i	$0.0192453\pi$
$830$		0			0
$831$		−	36.0000i		−	1.24883i
$832$		0			0
$833$	11.0000	−	11.0000i	0.381127	−	0.381127i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	8.00000			0.276520
$838$		0			0
$839$		−	18.0000i		−	0.621429i	−0.950503	−	0.310715i	$-0.899432\pi$
$839$		−	18.0000i		−	0.621429i	0.950503	−	0.310715i	$-0.100568\pi$
$840$		0			0
$841$		−	69.0000i		−	2.37931i
$842$		0			0
$843$	−32.0000			−1.10214
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−27.0000	+	27.0000i	−0.927731	+	0.927731i
$848$		0			0
$849$			24.0000i			0.823678i
$850$		0			0
$851$	−6.00000	+	6.00000i	−0.205677	+	0.205677i
$852$		0			0
$853$			16.0000i			0.547830i	0.961754	+	0.273915i	$0.0883186\pi$
$853$			16.0000i			0.547830i	−0.961754	+	0.273915i	$0.911681\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	27.0000	−	27.0000i	0.922302	−	0.922302i	−0.0748894	−	0.997192i	$-0.523860\pi$
$857$	27.0000	−	27.0000i	0.922302	−	0.922302i	0.997192	+	0.0748894i	$0.0238604\pi$
$858$		0			0
$859$	19.0000	−	19.0000i	0.648272	−	0.648272i	−0.304303	−	0.952575i	$-0.598424\pi$
$859$	19.0000	−	19.0000i	0.648272	−	0.648272i	0.952575	+	0.304303i	$0.0984237\pi$
$860$		0			0
$861$	−24.0000	−	24.0000i	−0.817918	−	0.817918i
$862$		0			0
$863$	5.00000	+	5.00000i	0.170202	+	0.170202i	0.787068	−	0.616866i	$-0.211598\pi$
$863$	5.00000	+	5.00000i	0.170202	+	0.170202i	−0.616866	+	0.787068i	$0.711598\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	30.0000			1.01885
$868$		0			0
$869$	8.00000	+	8.00000i	0.271381	+	0.271381i
$870$		0			0
$871$	8.00000			0.271070
$872$		0			0
$873$	−11.0000	−	11.0000i	−0.372294	−	0.372294i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		−	4.00000i		−	0.135070i	−0.997717	−	0.0675352i	$-0.978487\pi$
$877$		−	4.00000i		−	0.135070i	0.997717	−	0.0675352i	$-0.0215135\pi$
$878$		0			0
$879$	24.0000			0.809500
$880$		0			0
$881$	46.0000			1.54978			0.774890	−	0.632096i	$-0.217805\pi$
$881$	46.0000			1.54978			0.774890	+	0.632096i	$0.217805\pi$
$882$		0			0
$883$		−	6.00000i		−	0.201916i	−0.994891	−	0.100958i	$-0.967809\pi$
$883$		−	6.00000i		−	0.201916i	0.994891	−	0.100958i	$-0.0321908\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−23.0000	−	23.0000i	−0.772264	−	0.772264i	0.206238	−	0.978502i	$-0.433878\pi$
$887$	−23.0000	−	23.0000i	−0.772264	−	0.772264i	−0.978502	+	0.206238i	$0.933878\pi$
$888$		0			0
$889$	−42.0000			−1.40863
$890$		0			0
$891$	−11.0000	−	11.0000i	−0.368514	−	0.368514i
$892$		0			0
$893$	−42.0000			−1.40548
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−4.00000	−	4.00000i	−0.133556	−	0.133556i
$898$		0			0
$899$	−14.0000	−	14.0000i	−0.466926	−	0.466926i
$900$		0			0
$901$	−8.00000	+	8.00000i	−0.266519	+	0.266519i
$902$		0			0
$903$	24.0000	−	24.0000i	0.798670	−	0.798670i
$904$		0			0
$905$		0			0
$906$		0			0
$907$			50.0000i			1.66022i	0.557598	+	0.830111i	$0.311723\pi$
$907$			50.0000i			1.66022i	−0.557598	+	0.830111i	$0.688277\pi$
$908$		0			0
$909$	5.00000	−	5.00000i	0.165840	−	0.165840i
$910$		0			0
$911$			38.0000i			1.25900i	0.777002	+	0.629498i	$0.216739\pi$
$911$			38.0000i			1.25900i	−0.777002	+	0.629498i	$0.783261\pi$
$912$		0			0
$913$	−2.00000	+	2.00000i	−0.0661903	+	0.0661903i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−42.0000			−1.38696
$918$		0			0
$919$			46.0000i			1.51740i	0.651440	+	0.758700i	$0.274165\pi$
$919$			46.0000i			1.51740i	−0.651440	+	0.758700i	$0.725835\pi$
$920$		0			0
$921$		−	8.00000i		−	0.263609i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$	5.00000	−	5.00000i	0.164222	−	0.164222i
$928$		0			0
$929$		−	16.0000i		−	0.524943i	−0.964940	−	0.262471i	$-0.915462\pi$
$929$		−	16.0000i		−	0.524943i	0.964940	−	0.262471i	$-0.0845376\pi$
$930$		0			0
$931$	33.0000	−	33.0000i	1.08153	−	1.08153i
$932$		0			0
$933$		−	32.0000i		−	1.04763i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	3.00000	−	3.00000i	0.0980057	−	0.0980057i	−0.656404	−	0.754410i	$-0.727923\pi$
$937$	3.00000	−	3.00000i	0.0980057	−	0.0980057i	0.754410	+	0.656404i	$0.227923\pi$
$938$		0			0
$939$	26.0000	−	26.0000i	0.848478	−	0.848478i
$940$		0			0
$941$	−1.00000	−	1.00000i	−0.0325991	−	0.0325991i	0.690619	−	0.723218i	$-0.257338\pi$
$941$	−1.00000	−	1.00000i	−0.0325991	−	0.0325991i	−0.723218	+	0.690619i	$0.757338\pi$
$942$		0			0
$943$	4.00000	+	4.00000i	0.130258	+	0.130258i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	28.0000			0.909878			0.454939	−	0.890523i	$-0.349661\pi$
$947$	28.0000			0.909878			0.454939	+	0.890523i	$0.349661\pi$
$948$		0			0
$949$	6.00000	+	6.00000i	0.194768	+	0.194768i
$950$		0			0
$951$	16.0000			0.518836
$952$		0			0
$953$	31.0000	+	31.0000i	1.00419	+	1.00419i	0.999991	+	0.00419731i	$0.00133605\pi$
$953$	31.0000	+	31.0000i	1.00419	+	1.00419i	0.00419731	+	0.999991i	$0.498664\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			28.0000i			0.905111i
$958$		0			0
$959$	54.0000			1.74375
$960$		0			0
$961$	27.0000			0.870968
$962$		0			0
$963$			6.00000i			0.193347i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	33.0000	+	33.0000i	1.06121	+	1.06121i	0.998000	+	0.0632081i	$0.0201332\pi$
$967$	33.0000	+	33.0000i	1.06121	+	1.06121i	0.0632081	+	0.998000i	$0.479867\pi$
$968$		0			0
$969$	−12.0000			−0.385496
$970$		0			0
$971$	−31.0000	−	31.0000i	−0.994837	−	0.994837i	0.00514940	−	0.999987i	$-0.498361\pi$
$971$	−31.0000	−	31.0000i	−0.994837	−	0.994837i	−0.999987	+	0.00514940i	$0.998361\pi$
$972$		0			0
$973$	54.0000			1.73116
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−17.0000	−	17.0000i	−0.543878	−	0.543878i	0.380785	−	0.924663i	$-0.375654\pi$
$977$	−17.0000	−	17.0000i	−0.543878	−	0.543878i	−0.924663	+	0.380785i	$0.875654\pi$
$978$		0			0
$979$	6.00000	+	6.00000i	0.191761	+	0.191761i
$980$		0			0
$981$	5.00000	−	5.00000i	0.159638	−	0.159638i
$982$		0			0
$983$	−5.00000	+	5.00000i	−0.159475	+	0.159475i	−0.782334	−	0.622859i	$-0.785971\pi$
$983$	−5.00000	+	5.00000i	−0.159475	+	0.159475i	0.622859	+	0.782334i	$0.285971\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		−	84.0000i		−	2.67375i
$988$		0			0
$989$	−4.00000	+	4.00000i	−0.127193	+	0.127193i
$990$		0			0
$991$		−	10.0000i		−	0.317660i	−0.987306	−	0.158830i	$-0.949228\pi$
$991$		−	10.0000i		−	0.317660i	0.987306	−	0.158830i	$-0.0507723\pi$
$992$		0			0
$993$	−42.0000	+	42.0000i	−1.33283	+	1.33283i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−22.0000			−0.696747			−0.348373	−	0.937356i	$-0.613266\pi$
$997$	−22.0000			−0.696747			−0.348373	+	0.937356i	$0.613266\pi$
$998$		0			0
$999$			24.0000i			0.759326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.j.a.1007.1		2
4.3	odd	2		400.2.j.a.307.1		2
5.2	odd	4		320.2.s.a.303.1		2
5.3	odd	4		1600.2.s.a.943.1		2
5.4	even	2		320.2.j.a.47.1		2
16.5	even	4		400.2.s.a.107.1		2
16.11	odd	4		1600.2.s.a.207.1		2
20.3	even	4		400.2.s.a.243.1		2
20.7	even	4		80.2.s.a.3.1	yes	2
20.19	odd	2		80.2.j.a.67.1	yes	2
40.19	odd	2		640.2.j.a.607.1		2
40.27	even	4		640.2.s.b.223.1		2
40.29	even	2		640.2.j.b.607.1		2
40.37	odd	4		640.2.s.a.223.1		2
60.47	odd	4		720.2.z.d.163.1		2
60.59	even	2		720.2.bd.a.307.1		2
80.19	odd	4		640.2.s.a.287.1		2
80.27	even	4		320.2.j.a.143.1		2
80.29	even	4		640.2.s.b.287.1		2
80.37	odd	4		80.2.j.a.43.1	✓	2
80.43	even	4	inner	1600.2.j.a.143.1		2
80.53	odd	4		400.2.j.a.43.1		2
80.59	odd	4		320.2.s.a.207.1		2
80.67	even	4		640.2.j.b.543.1		2
80.69	even	4		80.2.s.a.27.1	yes	2
80.77	odd	4		640.2.j.a.543.1		2
240.149	odd	4		720.2.z.d.667.1		2
240.197	even	4		720.2.bd.a.523.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.a.43.1	✓	2	80.37	odd	4
80.2.j.a.67.1	yes	2	20.19	odd	2
80.2.s.a.3.1	yes	2	20.7	even	4
80.2.s.a.27.1	yes	2	80.69	even	4
320.2.j.a.47.1		2	5.4	even	2
320.2.j.a.143.1		2	80.27	even	4
320.2.s.a.207.1		2	80.59	odd	4
320.2.s.a.303.1		2	5.2	odd	4
400.2.j.a.43.1		2	80.53	odd	4
400.2.j.a.307.1		2	4.3	odd	2
400.2.s.a.107.1		2	16.5	even	4
400.2.s.a.243.1		2	20.3	even	4
640.2.j.a.543.1		2	80.77	odd	4
640.2.j.a.607.1		2	40.19	odd	2
640.2.j.b.543.1		2	80.67	even	4
640.2.j.b.607.1		2	40.29	even	2
640.2.s.a.223.1		2	40.37	odd	4
640.2.s.a.287.1		2	80.19	odd	4
640.2.s.b.223.1		2	40.27	even	4
640.2.s.b.287.1		2	80.29	even	4
720.2.z.d.163.1		2	60.47	odd	4
720.2.z.d.667.1		2	240.149	odd	4
720.2.bd.a.307.1		2	60.59	even	2
720.2.bd.a.523.1		2	240.197	even	4
1600.2.j.a.143.1		2	80.43	even	4	inner
1600.2.j.a.1007.1		2	1.1	even	1	trivial
1600.2.s.a.207.1		2	16.11	odd	4
1600.2.s.a.943.1		2	5.3	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:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1600.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{3} +(-3.00000 - 3.00000i) q^{7} -1.00000 q^{9} +O(q^{10})\)	\(q+2.00000i q^{3} +(-3.00000 - 3.00000i) q^{7} -1.00000 q^{9} +(1.00000 + 1.00000i) q^{11} +2.00000 q^{13} +(-1.00000 - 1.00000i) q^{17} +(-3.00000 - 3.00000i) q^{19} +(6.00000 - 6.00000i) q^{21} +(-1.00000 + 1.00000i) q^{23} +4.00000i q^{27} +(7.00000 - 7.00000i) q^{29} -2.00000i q^{31} +(-2.00000 + 2.00000i) q^{33} +6.00000 q^{37} +4.00000i q^{39} -4.00000i q^{41} +4.00000 q^{43} +(7.00000 - 7.00000i) q^{47} +11.0000i q^{49} +(2.00000 - 2.00000i) q^{51} -8.00000i q^{53} +(6.00000 - 6.00000i) q^{57} +(3.00000 - 3.00000i) q^{59} +(-1.00000 - 1.00000i) q^{61} +(3.00000 + 3.00000i) q^{63} +4.00000 q^{67} +(-2.00000 - 2.00000i) q^{69} +(3.00000 + 3.00000i) q^{73} -6.00000i q^{77} +8.00000 q^{79} -11.0000 q^{81} +2.00000i q^{83} +(14.0000 + 14.0000i) q^{87} +6.00000 q^{89} +(-6.00000 - 6.00000i) q^{91} +4.00000 q^{93} +(11.0000 + 11.0000i) q^{97} +(-1.00000 - 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 6 q^{7} - 2 q^{9}+O(q^{10}) \) 2 * q - 6 * q^7 - 2 * q^9	\( 2 q - 6 q^{7} - 2 q^{9} + 2 q^{11} + 4 q^{13} - 2 q^{17} - 6 q^{19} + 12 q^{21} - 2 q^{23} + 14 q^{29} - 4 q^{33} + 12 q^{37} + 8 q^{43} + 14 q^{47} + 4 q^{51} + 12 q^{57} + 6 q^{59} - 2 q^{61} + 6 q^{63} + 8 q^{67} - 4 q^{69} + 6 q^{73} + 16 q^{79} - 22 q^{81} + 28 q^{87} + 12 q^{89} - 12 q^{91} + 8 q^{93} + 22 q^{97} - 2 q^{99}+O(q^{100}) \) 2 * q - 6 * q^7 - 2 * q^9 + 2 * q^11 + 4 * q^13 - 2 * q^17 - 6 * q^19 + 12 * q^21 - 2 * q^23 + 14 * q^29 - 4 * q^33 + 12 * q^37 + 8 * q^43 + 14 * q^47 + 4 * q^51 + 12 * q^57 + 6 * q^59 - 2 * q^61 + 6 * q^63 + 8 * q^67 - 4 * q^69 + 6 * q^73 + 16 * q^79 - 22 * q^81 + 28 * q^87 + 12 * q^89 - 12 * q^91 + 8 * q^93 + 22 * q^97 - 2 * q^99

Introduction

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