LMFDB - Embedded newform 1512.2.c.b.757.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(757,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1512.757");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			757.2
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	1512.757
Dual form			1512.2.c.b.757.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{4} -2.00000i q^{5} -1.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{4} -2.00000i q^{5} -1.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} +(2.00000 - 2.00000i) q^{10} +5.00000i q^{13} +(-1.00000 - 1.00000i) q^{14} -4.00000 q^{16} -1.00000 q^{17} +4.00000i q^{19} +4.00000 q^{20} +5.00000 q^{23} +1.00000 q^{25} +(-5.00000 + 5.00000i) q^{26} -2.00000i q^{28} +9.00000i q^{29} -7.00000 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-1.00000 - 1.00000i) q^{34} +2.00000i q^{35} +2.00000i q^{37} +(-4.00000 + 4.00000i) q^{38} +(4.00000 + 4.00000i) q^{40} -2.00000 q^{41} +5.00000i q^{43} +(5.00000 + 5.00000i) q^{46} +1.00000 q^{49} +(1.00000 + 1.00000i) q^{50} -10.0000 q^{52} +9.00000i q^{53} +(2.00000 - 2.00000i) q^{56} +(-9.00000 + 9.00000i) q^{58} -1.00000i q^{59} +6.00000i q^{61} +(-7.00000 - 7.00000i) q^{62} -8.00000i q^{64} +10.0000 q^{65} -9.00000i q^{67} -2.00000i q^{68} +(-2.00000 + 2.00000i) q^{70} +15.0000 q^{71} +(-2.00000 + 2.00000i) q^{74} -8.00000 q^{76} -14.0000 q^{79} +8.00000i q^{80} +(-2.00000 - 2.00000i) q^{82} -4.00000i q^{83} +2.00000i q^{85} +(-5.00000 + 5.00000i) q^{86} +13.0000 q^{89} -5.00000i q^{91} +10.0000i q^{92} +8.00000 q^{95} -14.0000 q^{97} +(1.00000 + 1.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{7} - 4 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^7 - 4 * q^8	$ 2 q + 2 q^{2} - 2 q^{7} - 4 q^{8} + 4 q^{10} - 2 q^{14} - 8 q^{16} - 2 q^{17} + 8 q^{20} + 10 q^{23} + 2 q^{25} - 10 q^{26} - 14 q^{31} - 8 q^{32} - 2 q^{34} - 8 q^{38} + 8 q^{40} - 4 q^{41} + 10 q^{46} + 2 q^{49} + 2 q^{50} - 20 q^{52} + 4 q^{56} - 18 q^{58} - 14 q^{62} + 20 q^{65} - 4 q^{70} + 30 q^{71} - 4 q^{74} - 16 q^{76} - 28 q^{79} - 4 q^{82} - 10 q^{86} + 26 q^{89} + 16 q^{95} - 28 q^{97} + 2 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^7 - 4 * q^8 + 4 * q^10 - 2 * q^14 - 8 * q^16 - 2 * q^17 + 8 * q^20 + 10 * q^23 + 2 * q^25 - 10 * q^26 - 14 * q^31 - 8 * q^32 - 2 * q^34 - 8 * q^38 + 8 * q^40 - 4 * q^41 + 10 * q^46 + 2 * q^49 + 2 * q^50 - 20 * q^52 + 4 * q^56 - 18 * q^58 - 14 * q^62 + 20 * q^65 - 4 * q^70 + 30 * q^71 - 4 * q^74 - 16 * q^76 - 28 * q^79 - 4 * q^82 - 10 * q^86 + 26 * q^89 + 16 * q^95 - 28 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$1$	$1$	$1$

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	+	1.00000i	0.707107	+	0.707107i
$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$3$		0			0
$3$		0			0
$4$			2.00000i			1.00000i
$5$		−	2.00000i		−	0.894427i	−0.894427	−	0.447214i	$-0.852416\pi$
$5$		−	2.00000i		−	0.894427i	0.894427	−	0.447214i	$-0.147584\pi$
$6$		0			0
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$		0			0
$10$	2.00000	−	2.00000i	0.632456	−	0.632456i
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$		0			0
$13$			5.00000i			1.38675i	0.720577	+	0.693375i	$0.243877\pi$
$13$			5.00000i			1.38675i	−0.720577	+	0.693375i	$0.756123\pi$
$14$	−1.00000	−	1.00000i	−0.267261	−	0.267261i
$15$		0			0
$16$	−4.00000			−1.00000
$17$	−1.00000			−0.242536			−0.121268	−	0.992620i	$-0.538696\pi$
$17$	−1.00000			−0.242536			−0.121268	+	0.992620i	$0.538696\pi$
$18$		0			0
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$	4.00000			0.894427
$21$		0			0
$22$		0			0
$23$	5.00000			1.04257			0.521286	−	0.853382i	$-0.325452\pi$
$23$	5.00000			1.04257			0.521286	+	0.853382i	$0.325452\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−5.00000	+	5.00000i	−0.980581	+	0.980581i
$27$		0			0
$28$		−	2.00000i		−	0.377964i
$29$			9.00000i			1.67126i	0.549294	+	0.835629i	$0.314897\pi$
$29$			9.00000i			1.67126i	−0.549294	+	0.835629i	$0.685103\pi$
$30$		0			0
$31$	−7.00000			−1.25724			−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000			−1.25724			−0.628619	+	0.777714i	$0.716379\pi$
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$		0			0
$34$	−1.00000	−	1.00000i	−0.171499	−	0.171499i
$35$			2.00000i			0.338062i
$36$		0			0
$37$			2.00000i			0.328798i	0.986394	+	0.164399i	$0.0525685\pi$
$37$			2.00000i			0.328798i	−0.986394	+	0.164399i	$0.947432\pi$
$38$	−4.00000	+	4.00000i	−0.648886	+	0.648886i
$39$		0			0
$40$	4.00000	+	4.00000i	0.632456	+	0.632456i
$41$	−2.00000			−0.312348			−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$		0			0
$43$			5.00000i			0.762493i	0.924473	+	0.381246i	$0.124505\pi$
$43$			5.00000i			0.762493i	−0.924473	+	0.381246i	$0.875495\pi$
$44$		0			0
$45$		0			0
$46$	5.00000	+	5.00000i	0.737210	+	0.737210i
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	1.00000	+	1.00000i	0.141421	+	0.141421i
$51$		0			0
$52$	−10.0000			−1.38675
$53$			9.00000i			1.23625i	0.786082	+	0.618123i	$0.212106\pi$
$53$			9.00000i			1.23625i	−0.786082	+	0.618123i	$0.787894\pi$
$54$		0			0
$55$		0			0
$56$	2.00000	−	2.00000i	0.267261	−	0.267261i
$57$		0			0
$58$	−9.00000	+	9.00000i	−1.18176	+	1.18176i
$59$		−	1.00000i		−	0.130189i	−0.997879	−	0.0650945i	$-0.979265\pi$
$59$		−	1.00000i		−	0.130189i	0.997879	−	0.0650945i	$-0.0207349\pi$
$60$		0			0
$61$			6.00000i			0.768221i	0.923287	+	0.384111i	$0.125492\pi$
$61$			6.00000i			0.768221i	−0.923287	+	0.384111i	$0.874508\pi$
$62$	−7.00000	−	7.00000i	−0.889001	−	0.889001i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$	10.0000			1.24035
$66$		0			0
$67$		−	9.00000i		−	1.09952i	−0.835321	−	0.549762i	$-0.814718\pi$
$67$		−	9.00000i		−	1.09952i	0.835321	−	0.549762i	$-0.185282\pi$
$68$		−	2.00000i		−	0.242536i
$69$		0			0
$70$	−2.00000	+	2.00000i	−0.239046	+	0.239046i
$71$	15.0000			1.78017			0.890086	−	0.455792i	$-0.150644\pi$
$71$	15.0000			1.78017			0.890086	+	0.455792i	$0.150644\pi$
$72$		0			0
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$	−2.00000	+	2.00000i	−0.232495	+	0.232495i
$75$		0			0
$76$	−8.00000			−0.917663
$77$		0			0
$78$		0			0
$79$	−14.0000			−1.57512			−0.787562	−	0.616236i	$-0.788657\pi$
$79$	−14.0000			−1.57512			−0.787562	+	0.616236i	$0.788657\pi$
$80$			8.00000i			0.894427i
$81$		0			0
$82$	−2.00000	−	2.00000i	−0.220863	−	0.220863i
$83$		−	4.00000i		−	0.439057i	−0.975606	−	0.219529i	$-0.929548\pi$
$83$		−	4.00000i		−	0.439057i	0.975606	−	0.219529i	$-0.0704519\pi$
$84$		0			0
$85$			2.00000i			0.216930i
$86$	−5.00000	+	5.00000i	−0.539164	+	0.539164i
$87$		0			0
$88$		0			0
$89$	13.0000			1.37800			0.688999	−	0.724763i	$-0.258051\pi$
$89$	13.0000			1.37800			0.688999	+	0.724763i	$0.258051\pi$
$90$		0			0
$91$		−	5.00000i		−	0.524142i
$92$			10.0000i			1.04257i
$93$		0			0
$94$		0			0
$95$	8.00000			0.820783
$96$		0			0
$97$	−14.0000			−1.42148			−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000			−1.42148			−0.710742	+	0.703452i	$0.751641\pi$
$98$	1.00000	+	1.00000i	0.101015	+	0.101015i
$99$		0			0
$100$			2.00000i			0.200000i
$101$		−	8.00000i		−	0.796030i	−0.917379	−	0.398015i	$-0.869699\pi$
$101$		−	8.00000i		−	0.796030i	0.917379	−	0.398015i	$-0.130301\pi$
$102$		0			0
$103$	−3.00000			−0.295599			−0.147799	−	0.989017i	$-0.547219\pi$
$103$	−3.00000			−0.295599			−0.147799	+	0.989017i	$0.547219\pi$
$104$	−10.0000	−	10.0000i	−0.980581	−	0.980581i
$105$		0			0
$106$	−9.00000	+	9.00000i	−0.874157	+	0.874157i
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$		0			0
$109$			16.0000i			1.53252i	0.642529	+	0.766261i	$0.277885\pi$
$109$			16.0000i			1.53252i	−0.642529	+	0.766261i	$0.722115\pi$
$110$		0			0
$111$		0			0
$112$	4.00000			0.377964
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$		0			0
$115$		−	10.0000i		−	0.932505i
$116$	−18.0000			−1.67126
$117$		0			0
$118$	1.00000	−	1.00000i	0.0920575	−	0.0920575i
$119$	1.00000			0.0916698
$120$		0			0
$121$	11.0000			1.00000
$122$	−6.00000	+	6.00000i	−0.543214	+	0.543214i
$123$		0			0
$124$		−	14.0000i		−	1.25724i
$125$		−	12.0000i		−	1.07331i
$126$		0			0
$127$	−8.00000			−0.709885			−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000			−0.709885			−0.354943	+	0.934888i	$0.615500\pi$
$128$	8.00000	−	8.00000i	0.707107	−	0.707107i
$129$		0			0
$130$	10.0000	+	10.0000i	0.877058	+	0.877058i
$131$		−	13.0000i		−	1.13582i	−0.823092	−	0.567908i	$-0.807753\pi$
$131$		−	13.0000i		−	1.13582i	0.823092	−	0.567908i	$-0.192247\pi$
$132$		0			0
$133$		−	4.00000i		−	0.346844i
$134$	9.00000	−	9.00000i	0.777482	−	0.777482i
$135$		0			0
$136$	2.00000	−	2.00000i	0.171499	−	0.171499i
$137$	12.0000			1.02523			0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000			1.02523			0.512615	+	0.858619i	$0.328677\pi$
$138$		0			0
$139$		−	20.0000i		−	1.69638i	−0.529694	−	0.848189i	$-0.677693\pi$
$139$		−	20.0000i		−	1.69638i	0.529694	−	0.848189i	$-0.322307\pi$
$140$	−4.00000			−0.338062
$141$		0			0
$142$	15.0000	+	15.0000i	1.25877	+	1.25877i
$143$		0			0
$144$		0			0
$145$	18.0000			1.49482
$146$		0			0
$147$		0			0
$148$	−4.00000			−0.328798
$149$		−	9.00000i		−	0.737309i	−0.929567	−	0.368654i	$-0.879819\pi$
$149$		−	9.00000i		−	0.737309i	0.929567	−	0.368654i	$-0.120181\pi$
$150$		0			0
$151$	12.0000			0.976546			0.488273	−	0.872691i	$-0.337627\pi$
$151$	12.0000			0.976546			0.488273	+	0.872691i	$0.337627\pi$
$152$	−8.00000	−	8.00000i	−0.648886	−	0.648886i
$153$		0			0
$154$		0			0
$155$			14.0000i			1.12451i
$156$		0			0
$157$		−	13.0000i		−	1.03751i	−0.854922	−	0.518756i	$-0.826395\pi$
$157$		−	13.0000i		−	1.03751i	0.854922	−	0.518756i	$-0.173605\pi$
$158$	−14.0000	−	14.0000i	−1.11378	−	1.11378i
$159$		0			0
$160$	−8.00000	+	8.00000i	−0.632456	+	0.632456i
$161$	−5.00000			−0.394055
$162$		0			0
$163$			11.0000i			0.861586i	0.902451	+	0.430793i	$0.141766\pi$
$163$			11.0000i			0.861586i	−0.902451	+	0.430793i	$0.858234\pi$
$164$		−	4.00000i		−	0.312348i
$165$		0			0
$166$	4.00000	−	4.00000i	0.310460	−	0.310460i
$167$	4.00000			0.309529			0.154765	−	0.987951i	$-0.450538\pi$
$167$	4.00000			0.309529			0.154765	+	0.987951i	$0.450538\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$	−2.00000	+	2.00000i	−0.153393	+	0.153393i
$171$		0			0
$172$	−10.0000			−0.762493
$173$		−	6.00000i		−	0.456172i	−0.973641	−	0.228086i	$-0.926753\pi$
$173$		−	6.00000i		−	0.456172i	0.973641	−	0.228086i	$-0.0732467\pi$
$174$		0			0
$175$	−1.00000			−0.0755929
$176$		0			0
$177$		0			0
$178$	13.0000	+	13.0000i	0.974391	+	0.974391i
$179$		−	10.0000i		−	0.747435i	−0.927543	−	0.373718i	$-0.878083\pi$
$179$		−	10.0000i		−	0.747435i	0.927543	−	0.373718i	$-0.121917\pi$
$180$		0			0
$181$			19.0000i			1.41226i	0.708083	+	0.706129i	$0.249560\pi$
$181$			19.0000i			1.41226i	−0.708083	+	0.706129i	$0.750440\pi$
$182$	5.00000	−	5.00000i	0.370625	−	0.370625i
$183$		0			0
$184$	−10.0000	+	10.0000i	−0.737210	+	0.737210i
$185$	4.00000			0.294086
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	8.00000	+	8.00000i	0.580381	+	0.580381i
$191$	−4.00000			−0.289430			−0.144715	−	0.989473i	$-0.546227\pi$
$191$	−4.00000			−0.289430			−0.144715	+	0.989473i	$0.546227\pi$
$192$		0			0
$193$	9.00000			0.647834			0.323917	−	0.946085i	$-0.395000\pi$
$193$	9.00000			0.647834			0.323917	+	0.946085i	$0.395000\pi$
$194$	−14.0000	−	14.0000i	−1.00514	−	1.00514i
$195$		0			0
$196$			2.00000i			0.142857i
$197$			14.0000i			0.997459i	0.866758	+	0.498729i	$0.166200\pi$
$197$			14.0000i			0.997459i	−0.866758	+	0.498729i	$0.833800\pi$
$198$		0			0
$199$	13.0000			0.921546			0.460773	−	0.887518i	$-0.347572\pi$
$199$	13.0000			0.921546			0.460773	+	0.887518i	$0.347572\pi$
$200$	−2.00000	+	2.00000i	−0.141421	+	0.141421i
$201$		0			0
$202$	8.00000	−	8.00000i	0.562878	−	0.562878i
$203$		−	9.00000i		−	0.631676i
$204$		0			0
$205$			4.00000i			0.279372i
$206$	−3.00000	−	3.00000i	−0.209020	−	0.209020i
$207$		0			0
$208$		−	20.0000i		−	1.38675i
$209$		0			0
$210$		0			0
$211$		−	1.00000i		−	0.0688428i	−0.999407	−	0.0344214i	$-0.989041\pi$
$211$		−	1.00000i		−	0.0688428i	0.999407	−	0.0344214i	$-0.0109588\pi$
$212$	−18.0000			−1.23625
$213$		0			0
$214$		0			0
$215$	10.0000			0.681994
$216$		0			0
$217$	7.00000			0.475191
$218$	−16.0000	+	16.0000i	−1.08366	+	1.08366i
$219$		0			0
$220$		0			0
$221$		−	5.00000i		−	0.336336i
$222$		0			0
$223$	−16.0000			−1.07144			−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000			−1.07144			−0.535720	+	0.844396i	$0.679960\pi$
$224$	4.00000	+	4.00000i	0.267261	+	0.267261i
$225$		0			0
$226$	−6.00000	−	6.00000i	−0.399114	−	0.399114i
$227$			25.0000i			1.65931i	0.558278	+	0.829654i	$0.311462\pi$
$227$			25.0000i			1.65931i	−0.558278	+	0.829654i	$0.688538\pi$
$228$		0			0
$229$			10.0000i			0.660819i	0.943838	+	0.330409i	$0.107187\pi$
$229$			10.0000i			0.660819i	−0.943838	+	0.330409i	$0.892813\pi$
$230$	10.0000	−	10.0000i	0.659380	−	0.659380i
$231$		0			0
$232$	−18.0000	−	18.0000i	−1.18176	−	1.18176i
$233$	10.0000			0.655122			0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000			0.655122			0.327561	+	0.944830i	$0.393773\pi$
$234$		0			0
$235$		0			0
$236$	2.00000			0.130189
$237$		0			0
$238$	1.00000	+	1.00000i	0.0648204	+	0.0648204i
$239$	−24.0000			−1.55243			−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000			−1.55243			−0.776215	+	0.630468i	$0.782863\pi$
$240$		0			0
$241$	26.0000			1.67481			0.837404	−	0.546585i	$-0.184072\pi$
$241$	26.0000			1.67481			0.837404	+	0.546585i	$0.184072\pi$
$242$	11.0000	+	11.0000i	0.707107	+	0.707107i
$243$		0			0
$244$	−12.0000			−0.768221
$245$		−	2.00000i		−	0.127775i
$246$		0			0
$247$	−20.0000			−1.27257
$248$	14.0000	−	14.0000i	0.889001	−	0.889001i
$249$		0			0
$250$	12.0000	−	12.0000i	0.758947	−	0.758947i
$251$		−	12.0000i		−	0.757433i	−0.925513	−	0.378717i	$-0.876365\pi$
$251$		−	12.0000i		−	0.757433i	0.925513	−	0.378717i	$-0.123635\pi$
$252$		0			0
$253$		0			0
$254$	−8.00000	−	8.00000i	−0.501965	−	0.501965i
$255$		0			0
$256$	16.0000			1.00000
$257$	6.00000			0.374270			0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000			0.374270			0.187135	+	0.982334i	$0.440080\pi$
$258$		0			0
$259$		−	2.00000i		−	0.124274i
$260$			20.0000i			1.24035i
$261$		0			0
$262$	13.0000	−	13.0000i	0.803143	−	0.803143i
$263$	31.0000			1.91154			0.955771	−	0.294112i	$-0.0950239\pi$
$263$	31.0000			1.91154			0.955771	+	0.294112i	$0.0950239\pi$
$264$		0			0
$265$	18.0000			1.10573
$266$	4.00000	−	4.00000i	0.245256	−	0.245256i
$267$		0			0
$268$	18.0000			1.09952
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$		0			0
$271$	−15.0000			−0.911185			−0.455593	−	0.890188i	$-0.650573\pi$
$271$	−15.0000			−0.911185			−0.455593	+	0.890188i	$0.650573\pi$
$272$	4.00000			0.242536
$273$		0			0
$274$	12.0000	+	12.0000i	0.724947	+	0.724947i
$275$		0			0
$276$		0			0
$277$		−	26.0000i		−	1.56219i	−0.624413	−	0.781094i	$-0.714662\pi$
$277$		−	26.0000i		−	1.56219i	0.624413	−	0.781094i	$-0.285338\pi$
$278$	20.0000	−	20.0000i	1.19952	−	1.19952i
$279$		0			0
$280$	−4.00000	−	4.00000i	−0.239046	−	0.239046i
$281$	12.0000			0.715860			0.357930	−	0.933748i	$-0.383483\pi$
$281$	12.0000			0.715860			0.357930	+	0.933748i	$0.383483\pi$
$282$		0			0
$283$		−	16.0000i		−	0.951101i	−0.879688	−	0.475551i	$-0.842249\pi$
$283$		−	16.0000i		−	0.951101i	0.879688	−	0.475551i	$-0.157751\pi$
$284$			30.0000i			1.78017i
$285$		0			0
$286$		0			0
$287$	2.00000			0.118056
$288$		0			0
$289$	−16.0000			−0.941176
$290$	18.0000	+	18.0000i	1.05700	+	1.05700i
$291$		0			0
$292$		0			0
$293$			12.0000i			0.701047i	0.936554	+	0.350524i	$0.113996\pi$
$293$			12.0000i			0.701047i	−0.936554	+	0.350524i	$0.886004\pi$
$294$		0			0
$295$	−2.00000			−0.116445
$296$	−4.00000	−	4.00000i	−0.232495	−	0.232495i
$297$		0			0
$298$	9.00000	−	9.00000i	0.521356	−	0.521356i
$299$			25.0000i			1.44579i
$300$		0			0
$301$		−	5.00000i		−	0.288195i
$302$	12.0000	+	12.0000i	0.690522	+	0.690522i
$303$		0			0
$304$		−	16.0000i		−	0.917663i
$305$	12.0000			0.687118
$306$		0			0
$307$			6.00000i			0.342438i	0.985233	+	0.171219i	$0.0547706\pi$
$307$			6.00000i			0.342438i	−0.985233	+	0.171219i	$0.945229\pi$
$308$		0			0
$309$		0			0
$310$	−14.0000	+	14.0000i	−0.795147	+	0.795147i
$311$	−34.0000			−1.92796			−0.963982	−	0.265969i	$-0.914308\pi$
$311$	−34.0000			−1.92796			−0.963982	+	0.265969i	$0.914308\pi$
$312$		0			0
$313$	32.0000			1.80875			0.904373	−	0.426742i	$-0.140339\pi$
$313$	32.0000			1.80875			0.904373	+	0.426742i	$0.140339\pi$
$314$	13.0000	−	13.0000i	0.733632	−	0.733632i
$315$		0			0
$316$		−	28.0000i		−	1.57512i
$317$		−	14.0000i		−	0.786318i	−0.919470	−	0.393159i	$-0.871382\pi$
$317$		−	14.0000i		−	0.786318i	0.919470	−	0.393159i	$-0.128618\pi$
$318$		0			0
$319$		0			0
$320$	−16.0000			−0.894427
$321$		0			0
$322$	−5.00000	−	5.00000i	−0.278639	−	0.278639i
$323$		−	4.00000i		−	0.222566i
$324$		0			0
$325$			5.00000i			0.277350i
$326$	−11.0000	+	11.0000i	−0.609234	+	0.609234i
$327$		0			0
$328$	4.00000	−	4.00000i	0.220863	−	0.220863i
$329$		0			0
$330$		0			0
$331$		−	13.0000i		−	0.714545i	−0.934000	−	0.357272i	$-0.883707\pi$
$331$		−	13.0000i		−	0.714545i	0.934000	−	0.357272i	$-0.116293\pi$
$332$	8.00000			0.439057
$333$		0			0
$334$	4.00000	+	4.00000i	0.218870	+	0.218870i
$335$	−18.0000			−0.983445
$336$		0			0
$337$	19.0000			1.03500			0.517498	−	0.855684i	$-0.326864\pi$
$337$	19.0000			1.03500			0.517498	+	0.855684i	$0.326864\pi$
$338$	−12.0000	−	12.0000i	−0.652714	−	0.652714i
$339$		0			0
$340$	−4.00000			−0.216930
$341$		0			0
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	−10.0000	−	10.0000i	−0.539164	−	0.539164i
$345$		0			0
$346$	6.00000	−	6.00000i	0.322562	−	0.322562i
$347$			16.0000i			0.858925i	0.903085	+	0.429463i	$0.141297\pi$
$347$			16.0000i			0.858925i	−0.903085	+	0.429463i	$0.858703\pi$
$348$		0			0
$349$			23.0000i			1.23116i	0.788074	+	0.615581i	$0.211079\pi$
$349$			23.0000i			1.23116i	−0.788074	+	0.615581i	$0.788921\pi$
$350$	−1.00000	−	1.00000i	−0.0534522	−	0.0534522i
$351$		0			0
$352$		0			0
$353$	33.0000			1.75641			0.878206	−	0.478282i	$-0.158740\pi$
$353$	33.0000			1.75641			0.878206	+	0.478282i	$0.158740\pi$
$354$		0			0
$355$		−	30.0000i		−	1.59223i
$356$			26.0000i			1.37800i
$357$		0			0
$358$	10.0000	−	10.0000i	0.528516	−	0.528516i
$359$	−1.00000			−0.0527780			−0.0263890	−	0.999652i	$-0.508401\pi$
$359$	−1.00000			−0.0527780			−0.0263890	+	0.999652i	$0.508401\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	−19.0000	+	19.0000i	−0.998618	+	0.998618i
$363$		0			0
$364$	10.0000			0.524142
$365$		0			0
$366$		0			0
$367$	21.0000			1.09619			0.548096	−	0.836416i	$-0.315353\pi$
$367$	21.0000			1.09619			0.548096	+	0.836416i	$0.315353\pi$
$368$	−20.0000			−1.04257
$369$		0			0
$370$	4.00000	+	4.00000i	0.207950	+	0.207950i
$371$		−	9.00000i		−	0.467257i
$372$		0			0
$373$			22.0000i			1.13912i	0.821951	+	0.569558i	$0.192886\pi$
$373$			22.0000i			1.13912i	−0.821951	+	0.569558i	$0.807114\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−45.0000			−2.31762
$378$		0			0
$379$			16.0000i			0.821865i	0.911666	+	0.410932i	$0.134797\pi$
$379$			16.0000i			0.821865i	−0.911666	+	0.410932i	$0.865203\pi$
$380$			16.0000i			0.820783i
$381$		0			0
$382$	−4.00000	−	4.00000i	−0.204658	−	0.204658i
$383$	24.0000			1.22634			0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000			1.22634			0.613171	+	0.789950i	$0.289894\pi$
$384$		0			0
$385$		0			0
$386$	9.00000	+	9.00000i	0.458088	+	0.458088i
$387$		0			0
$388$		−	28.0000i		−	1.42148i
$389$		−	10.0000i		−	0.507020i	−0.967333	−	0.253510i	$-0.918415\pi$
$389$		−	10.0000i		−	0.507020i	0.967333	−	0.253510i	$-0.0815851\pi$
$390$		0			0
$391$	−5.00000			−0.252861
$392$	−2.00000	+	2.00000i	−0.101015	+	0.101015i
$393$		0			0
$394$	−14.0000	+	14.0000i	−0.705310	+	0.705310i
$395$			28.0000i			1.40883i
$396$		0			0
$397$			10.0000i			0.501886i	0.968002	+	0.250943i	$0.0807406\pi$
$397$			10.0000i			0.501886i	−0.968002	+	0.250943i	$0.919259\pi$
$398$	13.0000	+	13.0000i	0.651631	+	0.651631i
$399$		0			0
$400$	−4.00000			−0.200000
$401$	−24.0000			−1.19850			−0.599251	−	0.800561i	$-0.704535\pi$
$401$	−24.0000			−1.19850			−0.599251	+	0.800561i	$0.704535\pi$
$402$		0			0
$403$		−	35.0000i		−	1.74347i
$404$	16.0000			0.796030
$405$		0			0
$406$	9.00000	−	9.00000i	0.446663	−	0.446663i
$407$		0			0
$408$		0			0
$409$	−32.0000			−1.58230			−0.791149	−	0.611623i	$-0.790517\pi$
$409$	−32.0000			−1.58230			−0.791149	+	0.611623i	$0.790517\pi$
$410$	−4.00000	+	4.00000i	−0.197546	+	0.197546i
$411$		0			0
$412$		−	6.00000i		−	0.295599i
$413$			1.00000i			0.0492068i
$414$		0			0
$415$	−8.00000			−0.392705
$416$	20.0000	−	20.0000i	0.980581	−	0.980581i
$417$		0			0
$418$		0			0
$419$		−	15.0000i		−	0.732798i	−0.930458	−	0.366399i	$-0.880591\pi$
$419$		−	15.0000i		−	0.732798i	0.930458	−	0.366399i	$-0.119409\pi$
$420$		0			0
$421$			4.00000i			0.194948i	0.995238	+	0.0974740i	$0.0310763\pi$
$421$			4.00000i			0.194948i	−0.995238	+	0.0974740i	$0.968924\pi$
$422$	1.00000	−	1.00000i	0.0486792	−	0.0486792i
$423$		0			0
$424$	−18.0000	−	18.0000i	−0.874157	−	0.874157i
$425$	−1.00000			−0.0485071
$426$		0			0
$427$		−	6.00000i		−	0.290360i
$428$		0			0
$429$		0			0
$430$	10.0000	+	10.0000i	0.482243	+	0.482243i
$431$	12.0000			0.578020			0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000			0.578020			0.289010	+	0.957326i	$0.406674\pi$
$432$		0			0
$433$	8.00000			0.384455			0.192228	−	0.981350i	$-0.438429\pi$
$433$	8.00000			0.384455			0.192228	+	0.981350i	$0.438429\pi$
$434$	7.00000	+	7.00000i	0.336011	+	0.336011i
$435$		0			0
$436$	−32.0000			−1.53252
$437$			20.0000i			0.956730i
$438$		0			0
$439$	9.00000			0.429547			0.214773	−	0.976664i	$-0.431099\pi$
$439$	9.00000			0.429547			0.214773	+	0.976664i	$0.431099\pi$
$440$		0			0
$441$		0			0
$442$	5.00000	−	5.00000i	0.237826	−	0.237826i
$443$			6.00000i			0.285069i	0.989790	+	0.142534i	$0.0455251\pi$
$443$			6.00000i			0.285069i	−0.989790	+	0.142534i	$0.954475\pi$
$444$		0			0
$445$		−	26.0000i		−	1.23252i
$446$	−16.0000	−	16.0000i	−0.757622	−	0.757622i
$447$		0			0
$448$			8.00000i			0.377964i
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$		0			0
$451$		0			0
$452$		−	12.0000i		−	0.564433i
$453$		0			0
$454$	−25.0000	+	25.0000i	−1.17331	+	1.17331i
$455$	−10.0000			−0.468807
$456$		0			0
$457$	5.00000			0.233890			0.116945	−	0.993138i	$-0.462690\pi$
$457$	5.00000			0.233890			0.116945	+	0.993138i	$0.462690\pi$
$458$	−10.0000	+	10.0000i	−0.467269	+	0.467269i
$459$		0			0
$460$	20.0000			0.932505
$461$			12.0000i			0.558896i	0.960161	+	0.279448i	$0.0901514\pi$
$461$			12.0000i			0.558896i	−0.960161	+	0.279448i	$0.909849\pi$
$462$		0			0
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$		−	36.0000i		−	1.67126i
$465$		0			0
$466$	10.0000	+	10.0000i	0.463241	+	0.463241i
$467$		−	32.0000i		−	1.48078i	−0.672176	−	0.740392i	$-0.734640\pi$
$467$		−	32.0000i		−	1.48078i	0.672176	−	0.740392i	$-0.265360\pi$
$468$		0			0
$469$			9.00000i			0.415581i
$470$		0			0
$471$		0			0
$472$	2.00000	+	2.00000i	0.0920575	+	0.0920575i
$473$		0			0
$474$		0			0
$475$			4.00000i			0.183533i
$476$			2.00000i			0.0916698i
$477$		0			0
$478$	−24.0000	−	24.0000i	−1.09773	−	1.09773i
$479$	−26.0000			−1.18797			−0.593985	−	0.804476i	$-0.702446\pi$
$479$	−26.0000			−1.18797			−0.593985	+	0.804476i	$0.702446\pi$
$480$		0			0
$481$	−10.0000			−0.455961
$482$	26.0000	+	26.0000i	1.18427	+	1.18427i
$483$		0			0
$484$			22.0000i			1.00000i
$485$			28.0000i			1.27141i
$486$		0			0
$487$	−16.0000			−0.725029			−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000			−0.725029			−0.362515	+	0.931978i	$0.618082\pi$
$488$	−12.0000	−	12.0000i	−0.543214	−	0.543214i
$489$		0			0
$490$	2.00000	−	2.00000i	0.0903508	−	0.0903508i
$491$		−	4.00000i		−	0.180517i	−0.995918	−	0.0902587i	$-0.971231\pi$
$491$		−	4.00000i		−	0.180517i	0.995918	−	0.0902587i	$-0.0287694\pi$
$492$		0			0
$493$		−	9.00000i		−	0.405340i
$494$	−20.0000	−	20.0000i	−0.899843	−	0.899843i
$495$		0			0
$496$	28.0000			1.25724
$497$	−15.0000			−0.672842
$498$		0			0
$499$		−	24.0000i		−	1.07439i	−0.843459	−	0.537194i	$-0.819484\pi$
$499$		−	24.0000i		−	1.07439i	0.843459	−	0.537194i	$-0.180516\pi$
$500$	24.0000			1.07331
$501$		0			0
$502$	12.0000	−	12.0000i	0.535586	−	0.535586i
$503$	−6.00000			−0.267527			−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000			−0.267527			−0.133763	+	0.991013i	$0.542706\pi$
$504$		0			0
$505$	−16.0000			−0.711991
$506$		0			0
$507$		0			0
$508$		−	16.0000i		−	0.709885i
$509$		−	18.0000i		−	0.797836i	−0.916987	−	0.398918i	$-0.869386\pi$
$509$		−	18.0000i		−	0.797836i	0.916987	−	0.398918i	$-0.130614\pi$
$510$		0			0
$511$		0			0
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$		0			0
$514$	6.00000	+	6.00000i	0.264649	+	0.264649i
$515$			6.00000i			0.264392i
$516$		0			0
$517$		0			0
$518$	2.00000	−	2.00000i	0.0878750	−	0.0878750i
$519$		0			0
$520$	−20.0000	+	20.0000i	−0.877058	+	0.877058i
$521$	−39.0000			−1.70862			−0.854311	−	0.519763i	$-0.826020\pi$
$521$	−39.0000			−1.70862			−0.854311	+	0.519763i	$0.826020\pi$
$522$		0			0
$523$		−	36.0000i		−	1.57417i	−0.616844	−	0.787085i	$-0.711589\pi$
$523$		−	36.0000i		−	1.57417i	0.616844	−	0.787085i	$-0.288411\pi$
$524$	26.0000			1.13582
$525$		0			0
$526$	31.0000	+	31.0000i	1.35166	+	1.35166i
$527$	7.00000			0.304925
$528$		0			0
$529$	2.00000			0.0869565
$530$	18.0000	+	18.0000i	0.781870	+	0.781870i
$531$		0			0
$532$	8.00000			0.346844
$533$		−	10.0000i		−	0.433148i
$534$		0			0
$535$		0			0
$536$	18.0000	+	18.0000i	0.777482	+	0.777482i
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$			38.0000i			1.63375i	0.576816	+	0.816874i	$0.304295\pi$
$541$			38.0000i			1.63375i	−0.576816	+	0.816874i	$0.695705\pi$
$542$	−15.0000	−	15.0000i	−0.644305	−	0.644305i
$543$		0			0
$544$	4.00000	+	4.00000i	0.171499	+	0.171499i
$545$	32.0000			1.37073
$546$		0			0
$547$			28.0000i			1.19719i	0.801050	+	0.598597i	$0.204275\pi$
$547$			28.0000i			1.19719i	−0.801050	+	0.598597i	$0.795725\pi$
$548$			24.0000i			1.02523i
$549$		0			0
$550$		0			0
$551$	−36.0000			−1.53365
$552$		0			0
$553$	14.0000			0.595341
$554$	26.0000	−	26.0000i	1.10463	−	1.10463i
$555$		0			0
$556$	40.0000			1.69638
$557$			33.0000i			1.39825i	0.714997	+	0.699127i	$0.246428\pi$
$557$			33.0000i			1.39825i	−0.714997	+	0.699127i	$0.753572\pi$
$558$		0			0
$559$	−25.0000			−1.05739
$560$		−	8.00000i		−	0.338062i
$561$		0			0
$562$	12.0000	+	12.0000i	0.506189	+	0.506189i
$563$		−	15.0000i		−	0.632175i	−0.948730	−	0.316087i	$-0.897631\pi$
$563$		−	15.0000i		−	0.632175i	0.948730	−	0.316087i	$-0.102369\pi$
$564$		0			0
$565$			12.0000i			0.504844i
$566$	16.0000	−	16.0000i	0.672530	−	0.672530i
$567$		0			0
$568$	−30.0000	+	30.0000i	−1.25877	+	1.25877i
$569$	24.0000			1.00613			0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000			1.00613			0.503066	+	0.864248i	$0.332205\pi$
$570$		0			0
$571$			19.0000i			0.795125i	0.917575	+	0.397563i	$0.130144\pi$
$571$			19.0000i			0.795125i	−0.917575	+	0.397563i	$0.869856\pi$
$572$		0			0
$573$		0			0
$574$	2.00000	+	2.00000i	0.0834784	+	0.0834784i
$575$	5.00000			0.208514
$576$		0			0
$577$	30.0000			1.24892			0.624458	−	0.781058i	$-0.285320\pi$
$577$	30.0000			1.24892			0.624458	+	0.781058i	$0.285320\pi$
$578$	−16.0000	−	16.0000i	−0.665512	−	0.665512i
$579$		0			0
$580$			36.0000i			1.49482i
$581$			4.00000i			0.165948i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−12.0000	+	12.0000i	−0.495715	+	0.495715i
$587$			23.0000i			0.949312i	0.880172	+	0.474656i	$0.157427\pi$
$587$			23.0000i			0.949312i	−0.880172	+	0.474656i	$0.842573\pi$
$588$		0			0
$589$		−	28.0000i		−	1.15372i
$590$	−2.00000	−	2.00000i	−0.0823387	−	0.0823387i
$591$		0			0
$592$		−	8.00000i		−	0.328798i
$593$	−6.00000			−0.246390			−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000			−0.246390			−0.123195	+	0.992382i	$0.539314\pi$
$594$		0			0
$595$		−	2.00000i		−	0.0819920i
$596$	18.0000			0.737309
$597$		0			0
$598$	−25.0000	+	25.0000i	−1.02233	+	1.02233i
$599$	35.0000			1.43006			0.715031	−	0.699093i	$-0.246413\pi$
$599$	35.0000			1.43006			0.715031	+	0.699093i	$0.246413\pi$
$600$		0			0
$601$	38.0000			1.55005			0.775026	−	0.631929i	$-0.217737\pi$
$601$	38.0000			1.55005			0.775026	+	0.631929i	$0.217737\pi$
$602$	5.00000	−	5.00000i	0.203785	−	0.203785i
$603$		0			0
$604$			24.0000i			0.976546i
$605$		−	22.0000i		−	0.894427i
$606$		0			0
$607$	1.00000			0.0405887			0.0202944	−	0.999794i	$-0.493540\pi$
$607$	1.00000			0.0405887			0.0202944	+	0.999794i	$0.493540\pi$
$608$	16.0000	−	16.0000i	0.648886	−	0.648886i
$609$		0			0
$610$	12.0000	+	12.0000i	0.485866	+	0.485866i
$611$		0			0
$612$		0			0
$613$			16.0000i			0.646234i	0.946359	+	0.323117i	$0.104731\pi$
$613$			16.0000i			0.646234i	−0.946359	+	0.323117i	$0.895269\pi$
$614$	−6.00000	+	6.00000i	−0.242140	+	0.242140i
$615$		0			0
$616$		0			0
$617$	−46.0000			−1.85189			−0.925945	−	0.377658i	$-0.876729\pi$
$617$	−46.0000			−1.85189			−0.925945	+	0.377658i	$0.876729\pi$
$618$		0			0
$619$		0			0		1.00000			$0$
$619$		0			0		−1.00000			$\pi$
$620$	−28.0000			−1.12451
$621$		0			0
$622$	−34.0000	−	34.0000i	−1.36328	−	1.36328i
$623$	−13.0000			−0.520834
$624$		0			0
$625$	−19.0000			−0.760000
$626$	32.0000	+	32.0000i	1.27898	+	1.27898i
$627$		0			0
$628$	26.0000			1.03751
$629$		−	2.00000i		−	0.0797452i
$630$		0			0
$631$	34.0000			1.35352			0.676759	−	0.736204i	$-0.263384\pi$
$631$	34.0000			1.35352			0.676759	+	0.736204i	$0.263384\pi$
$632$	28.0000	−	28.0000i	1.11378	−	1.11378i
$633$		0			0
$634$	14.0000	−	14.0000i	0.556011	−	0.556011i
$635$			16.0000i			0.634941i
$636$		0			0
$637$			5.00000i			0.198107i
$638$		0			0
$639$		0			0
$640$	−16.0000	−	16.0000i	−0.632456	−	0.632456i
$641$	26.0000			1.02694			0.513469	−	0.858108i	$-0.328360\pi$
$641$	26.0000			1.02694			0.513469	+	0.858108i	$0.328360\pi$
$642$		0			0
$643$			14.0000i			0.552106i	0.961142	+	0.276053i	$0.0890266\pi$
$643$			14.0000i			0.552106i	−0.961142	+	0.276053i	$0.910973\pi$
$644$		−	10.0000i		−	0.394055i
$645$		0			0
$646$	4.00000	−	4.00000i	0.157378	−	0.157378i
$647$	−18.0000			−0.707653			−0.353827	−	0.935311i	$-0.615120\pi$
$647$	−18.0000			−0.707653			−0.353827	+	0.935311i	$0.615120\pi$
$648$		0			0
$649$		0			0
$650$	−5.00000	+	5.00000i	−0.196116	+	0.196116i
$651$		0			0
$652$	−22.0000			−0.861586
$653$		−	21.0000i		−	0.821794i	−0.911682	−	0.410897i	$-0.865216\pi$
$653$		−	21.0000i		−	0.821794i	0.911682	−	0.410897i	$-0.134784\pi$
$654$		0			0
$655$	−26.0000			−1.01590
$656$	8.00000			0.312348
$657$		0			0
$658$		0			0
$659$		−	36.0000i		−	1.40236i	−0.712984	−	0.701180i	$-0.752657\pi$
$659$		−	36.0000i		−	1.40236i	0.712984	−	0.701180i	$-0.247343\pi$
$660$		0			0
$661$		−	22.0000i		−	0.855701i	−0.903850	−	0.427850i	$-0.859271\pi$
$661$		−	22.0000i		−	0.855701i	0.903850	−	0.427850i	$-0.140729\pi$
$662$	13.0000	−	13.0000i	0.505259	−	0.505259i
$663$		0			0
$664$	8.00000	+	8.00000i	0.310460	+	0.310460i
$665$	−8.00000			−0.310227
$666$		0			0
$667$			45.0000i			1.74241i
$668$			8.00000i			0.309529i
$669$		0			0
$670$	−18.0000	−	18.0000i	−0.695401	−	0.695401i
$671$		0			0
$672$		0			0
$673$	−37.0000			−1.42625			−0.713123	−	0.701039i	$-0.752720\pi$
$673$	−37.0000			−1.42625			−0.713123	+	0.701039i	$0.752720\pi$
$674$	19.0000	+	19.0000i	0.731853	+	0.731853i
$675$		0			0
$676$		−	24.0000i		−	0.923077i
$677$		−	12.0000i		−	0.461197i	−0.973049	−	0.230599i	$-0.925932\pi$
$677$		−	12.0000i		−	0.461197i	0.973049	−	0.230599i	$-0.0740685\pi$
$678$		0			0
$679$	14.0000			0.537271
$680$	−4.00000	−	4.00000i	−0.153393	−	0.153393i
$681$		0			0
$682$		0			0
$683$		−	46.0000i		−	1.76014i	−0.474843	−	0.880071i	$-0.657495\pi$
$683$		−	46.0000i		−	1.76014i	0.474843	−	0.880071i	$-0.342505\pi$
$684$		0			0
$685$		−	24.0000i		−	0.916993i
$686$	−1.00000	−	1.00000i	−0.0381802	−	0.0381802i
$687$		0			0
$688$		−	20.0000i		−	0.762493i
$689$	−45.0000			−1.71436
$690$		0			0
$691$		−	8.00000i		−	0.304334i	−0.988355	−	0.152167i	$-0.951375\pi$
$691$		−	8.00000i		−	0.304334i	0.988355	−	0.152167i	$-0.0486252\pi$
$692$	12.0000			0.456172
$693$		0			0
$694$	−16.0000	+	16.0000i	−0.607352	+	0.607352i
$695$	−40.0000			−1.51729
$696$		0			0
$697$	2.00000			0.0757554
$698$	−23.0000	+	23.0000i	−0.870563	+	0.870563i
$699$		0			0
$700$		−	2.00000i		−	0.0755929i
$701$			22.0000i			0.830929i	0.909610	+	0.415464i	$0.136381\pi$
$701$			22.0000i			0.830929i	−0.909610	+	0.415464i	$0.863619\pi$
$702$		0			0
$703$	−8.00000			−0.301726
$704$		0			0
$705$		0			0
$706$	33.0000	+	33.0000i	1.24197	+	1.24197i
$707$			8.00000i			0.300871i
$708$		0			0
$709$			16.0000i			0.600893i	0.953799	+	0.300446i	$0.0971356\pi$
$709$			16.0000i			0.600893i	−0.953799	+	0.300446i	$0.902864\pi$
$710$	30.0000	−	30.0000i	1.12588	−	1.12588i
$711$		0			0
$712$	−26.0000	+	26.0000i	−0.974391	+	0.974391i
$713$	−35.0000			−1.31076
$714$		0			0
$715$		0			0
$716$	20.0000			0.747435
$717$		0			0
$718$	−1.00000	−	1.00000i	−0.0373197	−	0.0373197i
$719$	14.0000			0.522112			0.261056	−	0.965324i	$-0.415929\pi$
$719$	14.0000			0.522112			0.261056	+	0.965324i	$0.415929\pi$
$720$		0			0
$721$	3.00000			0.111726
$722$	3.00000	+	3.00000i	0.111648	+	0.111648i
$723$		0			0
$724$	−38.0000			−1.41226
$725$			9.00000i			0.334252i
$726$		0			0
$727$	−33.0000			−1.22390			−0.611951	−	0.790896i	$-0.709615\pi$
$727$	−33.0000			−1.22390			−0.611951	+	0.790896i	$0.709615\pi$
$728$	10.0000	+	10.0000i	0.370625	+	0.370625i
$729$		0			0
$730$		0			0
$731$		−	5.00000i		−	0.184932i
$732$		0			0
$733$		−	49.0000i		−	1.80986i	−0.425564	−	0.904928i	$-0.639924\pi$
$733$		−	49.0000i		−	1.80986i	0.425564	−	0.904928i	$-0.360076\pi$
$734$	21.0000	+	21.0000i	0.775124	+	0.775124i
$735$		0			0
$736$	−20.0000	−	20.0000i	−0.737210	−	0.737210i
$737$		0			0
$738$		0			0
$739$			32.0000i			1.17714i	0.808447	+	0.588570i	$0.200309\pi$
$739$			32.0000i			1.17714i	−0.808447	+	0.588570i	$0.799691\pi$
$740$			8.00000i			0.294086i
$741$		0			0
$742$	9.00000	−	9.00000i	0.330400	−	0.330400i
$743$	−23.0000			−0.843788			−0.421894	−	0.906645i	$-0.638635\pi$
$743$	−23.0000			−0.843788			−0.421894	+	0.906645i	$0.638635\pi$
$744$		0			0
$745$	−18.0000			−0.659469
$746$	−22.0000	+	22.0000i	−0.805477	+	0.805477i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−46.0000			−1.67856			−0.839282	−	0.543696i	$-0.817024\pi$
$751$	−46.0000			−1.67856			−0.839282	+	0.543696i	$0.817024\pi$
$752$		0			0
$753$		0			0
$754$	−45.0000	−	45.0000i	−1.63880	−	1.63880i
$755$		−	24.0000i		−	0.873449i
$756$		0			0
$757$		−	24.0000i		−	0.872295i	−0.899875	−	0.436147i	$-0.856343\pi$
$757$		−	24.0000i		−	0.872295i	0.899875	−	0.436147i	$-0.143657\pi$
$758$	−16.0000	+	16.0000i	−0.581146	+	0.581146i
$759$		0			0
$760$	−16.0000	+	16.0000i	−0.580381	+	0.580381i
$761$	11.0000			0.398750			0.199375	−	0.979923i	$-0.436109\pi$
$761$	11.0000			0.398750			0.199375	+	0.979923i	$0.436109\pi$
$762$		0			0
$763$		−	16.0000i		−	0.579239i
$764$		−	8.00000i		−	0.289430i
$765$		0			0
$766$	24.0000	+	24.0000i	0.867155	+	0.867155i
$767$	5.00000			0.180540
$768$		0			0
$769$	−2.00000			−0.0721218			−0.0360609	−	0.999350i	$-0.511481\pi$
$769$	−2.00000			−0.0721218			−0.0360609	+	0.999350i	$0.511481\pi$
$770$		0			0
$771$		0			0
$772$			18.0000i			0.647834i
$773$		−	32.0000i		−	1.15096i	−0.817816	−	0.575480i	$-0.804815\pi$
$773$		−	32.0000i		−	1.15096i	0.817816	−	0.575480i	$-0.195185\pi$
$774$		0			0
$775$	−7.00000			−0.251447
$776$	28.0000	−	28.0000i	1.00514	−	1.00514i
$777$		0			0
$778$	10.0000	−	10.0000i	0.358517	−	0.358517i
$779$		−	8.00000i		−	0.286630i
$780$		0			0
$781$		0			0
$782$	−5.00000	−	5.00000i	−0.178800	−	0.178800i
$783$		0			0
$784$	−4.00000			−0.142857
$785$	−26.0000			−0.927980
$786$		0			0
$787$			48.0000i			1.71102i	0.517790	+	0.855508i	$0.326755\pi$
$787$			48.0000i			1.71102i	−0.517790	+	0.855508i	$0.673245\pi$
$788$	−28.0000			−0.997459
$789$		0			0
$790$	−28.0000	+	28.0000i	−0.996195	+	0.996195i
$791$	6.00000			0.213335
$792$		0			0
$793$	−30.0000			−1.06533
$794$	−10.0000	+	10.0000i	−0.354887	+	0.354887i
$795$		0			0
$796$			26.0000i			0.921546i
$797$			2.00000i			0.0708436i	0.999372	+	0.0354218i	$0.0112775\pi$
$797$			2.00000i			0.0708436i	−0.999372	+	0.0354218i	$0.988723\pi$
$798$		0			0
$799$		0			0
$800$	−4.00000	−	4.00000i	−0.141421	−	0.141421i
$801$		0			0
$802$	−24.0000	−	24.0000i	−0.847469	−	0.847469i
$803$		0			0
$804$		0			0
$805$			10.0000i			0.352454i
$806$	35.0000	−	35.0000i	1.23282	−	1.23282i
$807$		0			0
$808$	16.0000	+	16.0000i	0.562878	+	0.562878i
$809$	−6.00000			−0.210949			−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000			−0.210949			−0.105474	+	0.994422i	$0.533636\pi$
$810$		0			0
$811$			14.0000i			0.491606i	0.969320	+	0.245803i	$0.0790517\pi$
$811$			14.0000i			0.491606i	−0.969320	+	0.245803i	$0.920948\pi$
$812$	18.0000			0.631676
$813$		0			0
$814$		0			0
$815$	22.0000			0.770626
$816$		0			0
$817$	−20.0000			−0.699711
$818$	−32.0000	−	32.0000i	−1.11885	−	1.11885i
$819$		0			0
$820$	−8.00000			−0.279372
$821$		−	35.0000i		−	1.22151i	−0.791820	−	0.610754i	$-0.790866\pi$
$821$		−	35.0000i		−	1.22151i	0.791820	−	0.610754i	$-0.209134\pi$
$822$		0			0
$823$	44.0000			1.53374			0.766872	−	0.641800i	$-0.221812\pi$
$823$	44.0000			1.53374			0.766872	+	0.641800i	$0.221812\pi$
$824$	6.00000	−	6.00000i	0.209020	−	0.209020i
$825$		0			0
$826$	−1.00000	+	1.00000i	−0.0347945	+	0.0347945i
$827$			12.0000i			0.417281i	0.977992	+	0.208640i	$0.0669038\pi$
$827$			12.0000i			0.417281i	−0.977992	+	0.208640i	$0.933096\pi$
$828$		0			0
$829$			34.0000i			1.18087i	0.807086	+	0.590434i	$0.201044\pi$
$829$			34.0000i			1.18087i	−0.807086	+	0.590434i	$0.798956\pi$
$830$	−8.00000	−	8.00000i	−0.277684	−	0.277684i
$831$		0			0
$832$	40.0000			1.38675
$833$	−1.00000			−0.0346479
$834$		0			0
$835$		−	8.00000i		−	0.276851i
$836$		0			0
$837$		0			0
$838$	15.0000	−	15.0000i	0.518166	−	0.518166i
$839$	−44.0000			−1.51905			−0.759524	−	0.650479i	$-0.774568\pi$
$839$	−44.0000			−1.51905			−0.759524	+	0.650479i	$0.774568\pi$
$840$		0			0
$841$	−52.0000			−1.79310
$842$	−4.00000	+	4.00000i	−0.137849	+	0.137849i
$843$		0			0
$844$	2.00000			0.0688428
$845$			24.0000i			0.825625i
$846$		0			0
$847$	−11.0000			−0.377964
$848$		−	36.0000i		−	1.23625i
$849$		0			0
$850$	−1.00000	−	1.00000i	−0.0342997	−	0.0342997i
$851$			10.0000i			0.342796i
$852$		0			0
$853$			9.00000i			0.308154i	0.988059	+	0.154077i	$0.0492404\pi$
$853$			9.00000i			0.308154i	−0.988059	+	0.154077i	$0.950760\pi$
$854$	6.00000	−	6.00000i	0.205316	−	0.205316i
$855$		0			0
$856$		0			0
$857$	−9.00000			−0.307434			−0.153717	−	0.988115i	$-0.549124\pi$
$857$	−9.00000			−0.307434			−0.153717	+	0.988115i	$0.549124\pi$
$858$		0			0
$859$			2.00000i			0.0682391i	0.999418	+	0.0341196i	$0.0108627\pi$
$859$			2.00000i			0.0682391i	−0.999418	+	0.0341196i	$0.989137\pi$
$860$			20.0000i			0.681994i
$861$		0			0
$862$	12.0000	+	12.0000i	0.408722	+	0.408722i
$863$	45.0000			1.53182			0.765909	−	0.642949i	$-0.222289\pi$
$863$	45.0000			1.53182			0.765909	+	0.642949i	$0.222289\pi$
$864$		0			0
$865$	−12.0000			−0.408012
$866$	8.00000	+	8.00000i	0.271851	+	0.271851i
$867$		0			0
$868$			14.0000i			0.475191i
$869$		0			0
$870$		0			0
$871$	45.0000			1.52477
$872$	−32.0000	−	32.0000i	−1.08366	−	1.08366i
$873$		0			0
$874$	−20.0000	+	20.0000i	−0.676510	+	0.676510i
$875$			12.0000i			0.405674i
$876$		0			0
$877$			34.0000i			1.14810i	0.818821	+	0.574049i	$0.194628\pi$
$877$			34.0000i			1.14810i	−0.818821	+	0.574049i	$0.805372\pi$
$878$	9.00000	+	9.00000i	0.303735	+	0.303735i
$879$		0			0
$880$		0			0
$881$	−47.0000			−1.58347			−0.791735	−	0.610865i	$-0.790822\pi$
$881$	−47.0000			−1.58347			−0.791735	+	0.610865i	$0.790822\pi$
$882$		0			0
$883$			29.0000i			0.975928i	0.872864	+	0.487964i	$0.162260\pi$
$883$			29.0000i			0.975928i	−0.872864	+	0.487964i	$0.837740\pi$
$884$	10.0000			0.336336
$885$		0			0
$886$	−6.00000	+	6.00000i	−0.201574	+	0.201574i
$887$	12.0000			0.402921			0.201460	−	0.979497i	$-0.435431\pi$
$887$	12.0000			0.402921			0.201460	+	0.979497i	$0.435431\pi$
$888$		0			0
$889$	8.00000			0.268311
$890$	26.0000	−	26.0000i	0.871522	−	0.871522i
$891$		0			0
$892$		−	32.0000i		−	1.07144i
$893$		0			0
$894$		0			0
$895$	−20.0000			−0.668526
$896$	−8.00000	+	8.00000i	−0.267261	+	0.267261i
$897$		0			0
$898$	−30.0000	−	30.0000i	−1.00111	−	1.00111i
$899$		−	63.0000i		−	2.10117i
$900$		0			0
$901$		−	9.00000i		−	0.299833i
$902$		0			0
$903$		0			0
$904$	12.0000	−	12.0000i	0.399114	−	0.399114i
$905$	38.0000			1.26316
$906$		0			0
$907$			28.0000i			0.929725i	0.885383	+	0.464862i	$0.153896\pi$
$907$			28.0000i			0.929725i	−0.885383	+	0.464862i	$0.846104\pi$
$908$	−50.0000			−1.65931
$909$		0			0
$910$	−10.0000	−	10.0000i	−0.331497	−	0.331497i
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$		0			0
$914$	5.00000	+	5.00000i	0.165385	+	0.165385i
$915$		0			0
$916$	−20.0000			−0.660819
$917$			13.0000i			0.429298i
$918$		0			0
$919$	18.0000			0.593765			0.296883	−	0.954914i	$-0.404053\pi$
$919$	18.0000			0.593765			0.296883	+	0.954914i	$0.404053\pi$
$920$	20.0000	+	20.0000i	0.659380	+	0.659380i
$921$		0			0
$922$	−12.0000	+	12.0000i	−0.395199	+	0.395199i
$923$			75.0000i			2.46866i
$924$		0			0
$925$			2.00000i			0.0657596i
$926$	16.0000	+	16.0000i	0.525793	+	0.525793i
$927$		0			0
$928$	36.0000	−	36.0000i	1.18176	−	1.18176i
$929$	14.0000			0.459325			0.229663	−	0.973270i	$-0.426238\pi$
$929$	14.0000			0.459325			0.229663	+	0.973270i	$0.426238\pi$
$930$		0			0
$931$			4.00000i			0.131095i
$932$			20.0000i			0.655122i
$933$		0			0
$934$	32.0000	−	32.0000i	1.04707	−	1.04707i
$935$		0			0
$936$		0			0
$937$	−22.0000			−0.718709			−0.359354	−	0.933201i	$-0.617003\pi$
$937$	−22.0000			−0.718709			−0.359354	+	0.933201i	$0.617003\pi$
$938$	−9.00000	+	9.00000i	−0.293860	+	0.293860i
$939$		0			0
$940$		0			0
$941$			24.0000i			0.782378i	0.920310	+	0.391189i	$0.127936\pi$
$941$			24.0000i			0.782378i	−0.920310	+	0.391189i	$0.872064\pi$
$942$		0			0
$943$	−10.0000			−0.325645
$944$			4.00000i			0.130189i
$945$		0			0
$946$		0			0
$947$			12.0000i			0.389948i	0.980808	+	0.194974i	$0.0624622\pi$
$947$			12.0000i			0.389948i	−0.980808	+	0.194974i	$0.937538\pi$
$948$		0			0
$949$		0			0
$950$	−4.00000	+	4.00000i	−0.129777	+	0.129777i
$951$		0			0
$952$	−2.00000	+	2.00000i	−0.0648204	+	0.0648204i
$953$	36.0000			1.16615			0.583077	−	0.812417i	$-0.301849\pi$
$953$	36.0000			1.16615			0.583077	+	0.812417i	$0.301849\pi$
$954$		0			0
$955$			8.00000i			0.258874i
$956$		−	48.0000i		−	1.55243i
$957$		0			0
$958$	−26.0000	−	26.0000i	−0.840022	−	0.840022i
$959$	−12.0000			−0.387500
$960$		0			0
$961$	18.0000			0.580645
$962$	−10.0000	−	10.0000i	−0.322413	−	0.322413i
$963$		0			0
$964$			52.0000i			1.67481i
$965$		−	18.0000i		−	0.579441i
$966$		0			0
$967$	50.0000			1.60789			0.803946	−	0.594703i	$-0.202730\pi$
$967$	50.0000			1.60789			0.803946	+	0.594703i	$0.202730\pi$
$968$	−22.0000	+	22.0000i	−0.707107	+	0.707107i
$969$		0			0
$970$	−28.0000	+	28.0000i	−0.899026	+	0.899026i
$971$			33.0000i			1.05902i	0.848304	+	0.529510i	$0.177624\pi$
$971$			33.0000i			1.05902i	−0.848304	+	0.529510i	$0.822376\pi$
$972$		0			0
$973$			20.0000i			0.641171i
$974$	−16.0000	−	16.0000i	−0.512673	−	0.512673i
$975$		0			0
$976$		−	24.0000i		−	0.768221i
$977$	56.0000			1.79160			0.895799	−	0.444459i	$-0.146604\pi$
$977$	56.0000			1.79160			0.895799	+	0.444459i	$0.146604\pi$
$978$		0			0
$979$		0			0
$980$	4.00000			0.127775
$981$		0			0
$982$	4.00000	−	4.00000i	0.127645	−	0.127645i
$983$	−62.0000			−1.97749			−0.988746	−	0.149601i	$-0.952201\pi$
$983$	−62.0000			−1.97749			−0.988746	+	0.149601i	$0.952201\pi$
$984$		0			0
$985$	28.0000			0.892154
$986$	9.00000	−	9.00000i	0.286618	−	0.286618i
$987$		0			0
$988$		−	40.0000i		−	1.27257i
$989$			25.0000i			0.794954i
$990$		0			0
$991$	20.0000			0.635321			0.317660	−	0.948205i	$-0.397103\pi$
$991$	20.0000			0.635321			0.317660	+	0.948205i	$0.397103\pi$
$992$	28.0000	+	28.0000i	0.889001	+	0.889001i
$993$		0			0
$994$	−15.0000	−	15.0000i	−0.475771	−	0.475771i
$995$		−	26.0000i		−	0.824255i
$996$		0			0
$997$		−	57.0000i		−	1.80521i	−0.430472	−	0.902604i	$-0.641653\pi$
$997$		−	57.0000i		−	1.80521i	0.430472	−	0.902604i	$-0.358347\pi$
$998$	24.0000	−	24.0000i	0.759707	−	0.759707i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.c.b.757.2	yes	2
3.2	odd	2		1512.2.c.a.757.1	✓	2
4.3	odd	2		6048.2.c.a.3025.1		2
8.3	odd	2		6048.2.c.a.3025.2		2
8.5	even	2	inner	1512.2.c.b.757.1	yes	2
12.11	even	2		6048.2.c.b.3025.2		2
24.5	odd	2		1512.2.c.a.757.2	yes	2
24.11	even	2		6048.2.c.b.3025.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.c.a.757.1	✓	2	3.2	odd	2
1512.2.c.a.757.2	yes	2	24.5	odd	2
1512.2.c.b.757.1	yes	2	8.5	even	2	inner
1512.2.c.b.757.2	yes	2	1.1	even	1	trivial
6048.2.c.a.3025.1		2	4.3	odd	2
6048.2.c.a.3025.2		2	8.3	odd	2
6048.2.c.b.3025.1		2	24.11	even	2
6048.2.c.b.3025.2		2	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{4} -2.00000i q^{5} -1.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{4} -2.00000i q^{5} -1.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} +(2.00000 - 2.00000i) q^{10} +5.00000i q^{13} +(-1.00000 - 1.00000i) q^{14} -4.00000 q^{16} -1.00000 q^{17} +4.00000i q^{19} +4.00000 q^{20} +5.00000 q^{23} +1.00000 q^{25} +(-5.00000 + 5.00000i) q^{26} -2.00000i q^{28} +9.00000i q^{29} -7.00000 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-1.00000 - 1.00000i) q^{34} +2.00000i q^{35} +2.00000i q^{37} +(-4.00000 + 4.00000i) q^{38} +(4.00000 + 4.00000i) q^{40} -2.00000 q^{41} +5.00000i q^{43} +(5.00000 + 5.00000i) q^{46} +1.00000 q^{49} +(1.00000 + 1.00000i) q^{50} -10.0000 q^{52} +9.00000i q^{53} +(2.00000 - 2.00000i) q^{56} +(-9.00000 + 9.00000i) q^{58} -1.00000i q^{59} +6.00000i q^{61} +(-7.00000 - 7.00000i) q^{62} -8.00000i q^{64} +10.0000 q^{65} -9.00000i q^{67} -2.00000i q^{68} +(-2.00000 + 2.00000i) q^{70} +15.0000 q^{71} +(-2.00000 + 2.00000i) q^{74} -8.00000 q^{76} -14.0000 q^{79} +8.00000i q^{80} +(-2.00000 - 2.00000i) q^{82} -4.00000i q^{83} +2.00000i q^{85} +(-5.00000 + 5.00000i) q^{86} +13.0000 q^{89} -5.00000i q^{91} +10.0000i q^{92} +8.00000 q^{95} -14.0000 q^{97} +(1.00000 + 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{7} - 4 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^7 - 4 * q^8	\( 2 q + 2 q^{2} - 2 q^{7} - 4 q^{8} + 4 q^{10} - 2 q^{14} - 8 q^{16} - 2 q^{17} + 8 q^{20} + 10 q^{23} + 2 q^{25} - 10 q^{26} - 14 q^{31} - 8 q^{32} - 2 q^{34} - 8 q^{38} + 8 q^{40} - 4 q^{41} + 10 q^{46} + 2 q^{49} + 2 q^{50} - 20 q^{52} + 4 q^{56} - 18 q^{58} - 14 q^{62} + 20 q^{65} - 4 q^{70} + 30 q^{71} - 4 q^{74} - 16 q^{76} - 28 q^{79} - 4 q^{82} - 10 q^{86} + 26 q^{89} + 16 q^{95} - 28 q^{97} + 2 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^7 - 4 * q^8 + 4 * q^10 - 2 * q^14 - 8 * q^16 - 2 * q^17 + 8 * q^20 + 10 * q^23 + 2 * q^25 - 10 * q^26 - 14 * q^31 - 8 * q^32 - 2 * q^34 - 8 * q^38 + 8 * q^40 - 4 * q^41 + 10 * q^46 + 2 * q^49 + 2 * q^50 - 20 * q^52 + 4 * q^56 - 18 * q^58 - 14 * q^62 + 20 * q^65 - 4 * q^70 + 30 * q^71 - 4 * q^74 - 16 * q^76 - 28 * q^79 - 4 * q^82 - 10 * q^86 + 26 * q^89 + 16 * q^95 - 28 * q^97 + 2 * q^98

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