LMFDB - Embedded newform 1530.2.f.e.1189.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1530,2,Mod(1189,1530)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1530, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1530.1189");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1530.f (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:	$12.2171115093$
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:	no (minimal twist has level 170)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1189.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	1530.1189
Dual form			1530.2.f.e.1189.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} -2.00000 q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} -2.00000 q^{7} -1.00000i q^{8} +(-1.00000 + 2.00000i) q^{10} -1.00000i q^{13} -2.00000i q^{14} +1.00000 q^{16} +(1.00000 + 4.00000i) q^{17} -5.00000 q^{19} +(-2.00000 - 1.00000i) q^{20} -4.00000 q^{23} +(3.00000 + 4.00000i) q^{25} +1.00000 q^{26} +2.00000 q^{28} +9.00000i q^{29} +5.00000i q^{31} +1.00000i q^{32} +(-4.00000 + 1.00000i) q^{34} +(-4.00000 - 2.00000i) q^{35} -2.00000 q^{37} -5.00000i q^{38} +(1.00000 - 2.00000i) q^{40} +10.0000i q^{41} -6.00000i q^{43} -4.00000i q^{46} -7.00000i q^{47} -3.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} +1.00000i q^{52} +1.00000i q^{53} +2.00000i q^{56} -9.00000 q^{58} +5.00000 q^{59} +5.00000i q^{61} -5.00000 q^{62} -1.00000 q^{64} +(1.00000 - 2.00000i) q^{65} +2.00000i q^{67} +(-1.00000 - 4.00000i) q^{68} +(2.00000 - 4.00000i) q^{70} -5.00000i q^{71} -11.0000 q^{73} -2.00000i q^{74} +5.00000 q^{76} +16.0000i q^{79} +(2.00000 + 1.00000i) q^{80} -10.0000 q^{82} +6.00000i q^{83} +(-2.00000 + 9.00000i) q^{85} +6.00000 q^{86} -5.00000 q^{89} +2.00000i q^{91} +4.00000 q^{92} +7.00000 q^{94} +(-10.0000 - 5.00000i) q^{95} -7.00000 q^{97} -3.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} + 4 q^{5} - 4 q^{7}+O(q^{10}) $ 2 * q - 2 * q^4 + 4 * q^5 - 4 * q^7	$ 2 q - 2 q^{4} + 4 q^{5} - 4 q^{7} - 2 q^{10} + 2 q^{16} + 2 q^{17} - 10 q^{19} - 4 q^{20} - 8 q^{23} + 6 q^{25} + 2 q^{26} + 4 q^{28} - 8 q^{34} - 8 q^{35} - 4 q^{37} + 2 q^{40} - 6 q^{49} - 8 q^{50} - 18 q^{58} + 10 q^{59} - 10 q^{62} - 2 q^{64} + 2 q^{65} - 2 q^{68} + 4 q^{70} - 22 q^{73} + 10 q^{76} + 4 q^{80} - 20 q^{82} - 4 q^{85} + 12 q^{86} - 10 q^{89} + 8 q^{92} + 14 q^{94} - 20 q^{95} - 14 q^{97}+O(q^{100}) $ 2 * q - 2 * q^4 + 4 * q^5 - 4 * q^7 - 2 * q^10 + 2 * q^16 + 2 * q^17 - 10 * q^19 - 4 * q^20 - 8 * q^23 + 6 * q^25 + 2 * q^26 + 4 * q^28 - 8 * q^34 - 8 * q^35 - 4 * q^37 + 2 * q^40 - 6 * q^49 - 8 * q^50 - 18 * q^58 + 10 * q^59 - 10 * q^62 - 2 * q^64 + 2 * q^65 - 2 * q^68 + 4 * q^70 - 22 * q^73 + 10 * q^76 + 4 * q^80 - 20 * q^82 - 4 * q^85 + 12 * q^86 - 10 * q^89 + 8 * q^92 + 14 * q^94 - 20 * q^95 - 14 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1530\mathbb{Z}\right)^\times$.

$n$	$307$	$1261$	$1361$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$6$		0			0
$7$	−2.00000			−0.755929			−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000			−0.755929			−0.377964	+	0.925820i	$0.623376\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−1.00000	+	2.00000i	−0.316228	+	0.632456i
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$		0			0
$13$		−	1.00000i		−	0.277350i	−0.990338	−	0.138675i	$-0.955716\pi$
$13$		−	1.00000i		−	0.277350i	0.990338	−	0.138675i	$-0.0442844\pi$
$14$		−	2.00000i		−	0.534522i
$15$		0			0
$16$	1.00000			0.250000
$17$	1.00000	+	4.00000i	0.242536	+	0.970143i
$17$	1.00000	+	4.00000i	0.242536	+	0.970143i
$18$		0			0
$19$	−5.00000			−1.14708			−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000			−1.14708			−0.573539	+	0.819178i	$0.694430\pi$
$20$	−2.00000	−	1.00000i	−0.447214	−	0.223607i
$21$		0			0
$22$		0			0
$23$	−4.00000			−0.834058			−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000			−0.834058			−0.417029	+	0.908893i	$0.636929\pi$
$24$		0			0
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$	1.00000			0.196116
$27$		0			0
$28$	2.00000			0.377964
$29$			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
$31$			5.00000i			0.898027i	0.893525	+	0.449013i	$0.148224\pi$
$31$			5.00000i			0.898027i	−0.893525	+	0.449013i	$0.851776\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−4.00000	+	1.00000i	−0.685994	+	0.171499i
$35$	−4.00000	−	2.00000i	−0.676123	−	0.338062i
$36$		0			0
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$		−	5.00000i		−	0.811107i
$39$		0			0
$40$	1.00000	−	2.00000i	0.158114	−	0.316228i
$41$			10.0000i			1.56174i	0.624695	+	0.780869i	$0.285223\pi$
$41$			10.0000i			1.56174i	−0.624695	+	0.780869i	$0.714777\pi$
$42$		0			0
$43$		−	6.00000i		−	0.914991i	−0.889212	−	0.457496i	$-0.848747\pi$
$43$		−	6.00000i		−	0.914991i	0.889212	−	0.457496i	$-0.151253\pi$
$44$		0			0
$45$		0			0
$46$		−	4.00000i		−	0.589768i
$47$		−	7.00000i		−	1.02105i	−0.859861	−	0.510527i	$-0.829450\pi$
$47$		−	7.00000i		−	1.02105i	0.859861	−	0.510527i	$-0.170550\pi$
$48$		0			0
$49$	−3.00000			−0.428571
$50$	−4.00000	+	3.00000i	−0.565685	+	0.424264i
$51$		0			0
$52$			1.00000i			0.138675i
$53$			1.00000i			0.137361i	0.997639	+	0.0686803i	$0.0218788\pi$
$53$			1.00000i			0.137361i	−0.997639	+	0.0686803i	$0.978121\pi$
$54$		0			0
$55$		0			0
$56$			2.00000i			0.267261i
$57$		0			0
$58$	−9.00000			−1.18176
$59$	5.00000			0.650945			0.325472	−	0.945552i	$-0.394477\pi$
$59$	5.00000			0.650945			0.325472	+	0.945552i	$0.394477\pi$
$60$		0			0
$61$			5.00000i			0.640184i	0.947386	+	0.320092i	$0.103714\pi$
$61$			5.00000i			0.640184i	−0.947386	+	0.320092i	$0.896286\pi$
$62$	−5.00000			−0.635001
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.00000	−	2.00000i	0.124035	−	0.248069i
$66$		0			0
$67$			2.00000i			0.244339i	0.992509	+	0.122169i	$0.0389851\pi$
$67$			2.00000i			0.244339i	−0.992509	+	0.122169i	$0.961015\pi$
$68$	−1.00000	−	4.00000i	−0.121268	−	0.485071i
$69$		0			0
$70$	2.00000	−	4.00000i	0.239046	−	0.478091i
$71$		−	5.00000i		−	0.593391i	−0.954972	−	0.296695i	$-0.904115\pi$
$71$		−	5.00000i		−	0.593391i	0.954972	−	0.296695i	$-0.0958846\pi$
$72$		0			0
$73$	−11.0000			−1.28745			−0.643726	−	0.765256i	$-0.722612\pi$
$73$	−11.0000			−1.28745			−0.643726	+	0.765256i	$0.722612\pi$
$74$		−	2.00000i		−	0.232495i
$75$		0			0
$76$	5.00000			0.573539
$77$		0			0
$78$		0			0
$79$			16.0000i			1.80014i	0.435745	+	0.900070i	$0.356485\pi$
$79$			16.0000i			1.80014i	−0.435745	+	0.900070i	$0.643515\pi$
$80$	2.00000	+	1.00000i	0.223607	+	0.111803i
$81$		0			0
$82$	−10.0000			−1.10432
$83$			6.00000i			0.658586i	0.944228	+	0.329293i	$0.106810\pi$
$83$			6.00000i			0.658586i	−0.944228	+	0.329293i	$0.893190\pi$
$84$		0			0
$85$	−2.00000	+	9.00000i	−0.216930	+	0.976187i
$86$	6.00000			0.646997
$87$		0			0
$88$		0			0
$89$	−5.00000			−0.529999			−0.264999	−	0.964249i	$-0.585372\pi$
$89$	−5.00000			−0.529999			−0.264999	+	0.964249i	$0.585372\pi$
$90$		0			0
$91$			2.00000i			0.209657i
$92$	4.00000			0.417029
$93$		0			0
$94$	7.00000			0.721995
$95$	−10.0000	−	5.00000i	−1.02598	−	0.512989i
$96$		0			0
$97$	−7.00000			−0.710742			−0.355371	−	0.934725i	$-0.615646\pi$
$97$	−7.00000			−0.710742			−0.355371	+	0.934725i	$0.615646\pi$
$98$		−	3.00000i		−	0.303046i
$99$		0			0
$100$	−3.00000	−	4.00000i	−0.300000	−	0.400000i
$101$	8.00000			0.796030			0.398015	−	0.917379i	$-0.369699\pi$
$101$	8.00000			0.796030			0.398015	+	0.917379i	$0.369699\pi$
$102$		0			0
$103$		−	16.0000i		−	1.57653i	−0.615338	−	0.788263i	$-0.710980\pi$
$103$		−	16.0000i		−	1.57653i	0.615338	−	0.788263i	$-0.289020\pi$
$104$	−1.00000			−0.0980581
$105$		0			0
$106$	−1.00000			−0.0971286
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$		0			0
$109$		−	9.00000i		−	0.862044i	−0.902342	−	0.431022i	$-0.858153\pi$
$109$		−	9.00000i		−	0.862044i	0.902342	−	0.431022i	$-0.141847\pi$
$110$		0			0
$111$		0			0
$112$	−2.00000			−0.188982
$113$	−9.00000			−0.846649			−0.423324	−	0.905978i	$-0.639137\pi$
$113$	−9.00000			−0.846649			−0.423324	+	0.905978i	$0.639137\pi$
$114$		0			0
$115$	−8.00000	−	4.00000i	−0.746004	−	0.373002i
$116$		−	9.00000i		−	0.835629i
$117$		0			0
$118$			5.00000i			0.460287i
$119$	−2.00000	−	8.00000i	−0.183340	−	0.733359i
$120$		0			0
$121$	11.0000			1.00000
$122$	−5.00000			−0.452679
$123$		0			0
$124$		−	5.00000i		−	0.449013i
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$		0			0
$127$			7.00000i			0.621150i	0.950549	+	0.310575i	$0.100522\pi$
$127$			7.00000i			0.621150i	−0.950549	+	0.310575i	$0.899478\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	2.00000	+	1.00000i	0.175412	+	0.0877058i
$131$			20.0000i			1.74741i	0.486458	+	0.873704i	$0.338289\pi$
$131$			20.0000i			1.74741i	−0.486458	+	0.873704i	$0.661711\pi$
$132$		0			0
$133$	10.0000			0.867110
$134$	−2.00000			−0.172774
$135$		0			0
$136$	4.00000	−	1.00000i	0.342997	−	0.0857493i
$137$		−	2.00000i		−	0.170872i	−0.996344	−	0.0854358i	$-0.972772\pi$
$137$		−	2.00000i		−	0.170872i	0.996344	−	0.0854358i	$-0.0272282\pi$
$138$		0			0
$139$		−	14.0000i		−	1.18746i	−0.804663	−	0.593732i	$-0.797654\pi$
$139$		−	14.0000i		−	1.18746i	0.804663	−	0.593732i	$-0.202346\pi$
$140$	4.00000	+	2.00000i	0.338062	+	0.169031i
$141$		0			0
$142$	5.00000			0.419591
$143$		0			0
$144$		0			0
$145$	−9.00000	+	18.0000i	−0.747409	+	1.49482i
$146$		−	11.0000i		−	0.910366i
$147$		0			0
$148$	2.00000			0.164399
$149$	−20.0000			−1.63846			−0.819232	−	0.573462i	$-0.805600\pi$
$149$	−20.0000			−1.63846			−0.819232	+	0.573462i	$0.805600\pi$
$150$		0			0
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$			5.00000i			0.405554i
$153$		0			0
$154$		0			0
$155$	−5.00000	+	10.0000i	−0.401610	+	0.803219i
$156$		0			0
$157$		−	18.0000i		−	1.43656i	−0.695756	−	0.718278i	$-0.744931\pi$
$157$		−	18.0000i		−	1.43656i	0.695756	−	0.718278i	$-0.255069\pi$
$158$	−16.0000			−1.27289
$159$		0			0
$160$	−1.00000	+	2.00000i	−0.0790569	+	0.158114i
$161$	8.00000			0.630488
$162$		0			0
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$		−	10.0000i		−	0.780869i
$165$		0			0
$166$	−6.00000			−0.465690
$167$	−18.0000			−1.39288			−0.696441	−	0.717614i	$-0.745234\pi$
$167$	−18.0000			−1.39288			−0.696441	+	0.717614i	$0.745234\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$	−9.00000	−	2.00000i	−0.690268	−	0.153393i
$171$		0			0
$172$			6.00000i			0.457496i
$173$	16.0000			1.21646			0.608229	−	0.793762i	$-0.291880\pi$
$173$	16.0000			1.21646			0.608229	+	0.793762i	$0.291880\pi$
$174$		0			0
$175$	−6.00000	−	8.00000i	−0.453557	−	0.604743i
$176$		0			0
$177$		0			0
$178$		−	5.00000i		−	0.374766i
$179$	−20.0000			−1.49487			−0.747435	−	0.664335i	$-0.768715\pi$
$179$	−20.0000			−1.49487			−0.747435	+	0.664335i	$0.768715\pi$
$180$		0			0
$181$			10.0000i			0.743294i	0.928374	+	0.371647i	$0.121207\pi$
$181$			10.0000i			0.743294i	−0.928374	+	0.371647i	$0.878793\pi$
$182$	−2.00000			−0.148250
$183$		0			0
$184$			4.00000i			0.294884i
$185$	−4.00000	−	2.00000i	−0.294086	−	0.147043i
$186$		0			0
$187$		0			0
$188$			7.00000i			0.510527i
$189$		0			0
$190$	5.00000	−	10.0000i	0.362738	−	0.725476i
$191$	18.0000			1.30243			0.651217	−	0.758891i	$-0.274259\pi$
$191$	18.0000			1.30243			0.651217	+	0.758891i	$0.274259\pi$
$192$		0			0
$193$	14.0000			1.00774			0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000			1.00774			0.503871	+	0.863779i	$0.331909\pi$
$194$		−	7.00000i		−	0.502571i
$195$		0			0
$196$	3.00000			0.214286
$197$	−8.00000			−0.569976			−0.284988	−	0.958531i	$-0.591990\pi$
$197$	−8.00000			−0.569976			−0.284988	+	0.958531i	$0.591990\pi$
$198$		0			0
$199$			1.00000i			0.0708881i	0.999372	+	0.0354441i	$0.0112846\pi$
$199$			1.00000i			0.0708881i	−0.999372	+	0.0354441i	$0.988715\pi$
$200$	4.00000	−	3.00000i	0.282843	−	0.212132i
$201$		0			0
$202$			8.00000i			0.562878i
$203$		−	18.0000i		−	1.26335i
$204$		0			0
$205$	−10.0000	+	20.0000i	−0.698430	+	1.39686i
$206$	16.0000			1.11477
$207$		0			0
$208$		−	1.00000i		−	0.0693375i
$209$		0			0
$210$		0			0
$211$		−	20.0000i		−	1.37686i	−0.725304	−	0.688428i	$-0.758301\pi$
$211$		−	20.0000i		−	1.37686i	0.725304	−	0.688428i	$-0.241699\pi$
$212$		−	1.00000i		−	0.0686803i
$213$		0			0
$214$			12.0000i			0.820303i
$215$	6.00000	−	12.0000i	0.409197	−	0.818393i
$216$		0			0
$217$		−	10.0000i		−	0.678844i
$218$	9.00000			0.609557
$219$		0			0
$220$		0			0
$221$	4.00000	−	1.00000i	0.269069	−	0.0672673i
$222$		0			0
$223$			9.00000i			0.602685i	0.953516	+	0.301342i	$0.0974347\pi$
$223$			9.00000i			0.602685i	−0.953516	+	0.301342i	$0.902565\pi$
$224$		−	2.00000i		−	0.133631i
$225$		0			0
$226$		−	9.00000i		−	0.598671i
$227$	27.0000			1.79205			0.896026	−	0.444001i	$-0.146441\pi$
$227$	27.0000			1.79205			0.896026	+	0.444001i	$0.146441\pi$
$228$		0			0
$229$		0			0			−	1.00000i	$-0.5\pi$
$229$		0			0				1.00000i	$0.5\pi$
$230$	4.00000	−	8.00000i	0.263752	−	0.527504i
$231$		0			0
$232$	9.00000			0.590879
$233$	21.0000			1.37576			0.687878	−	0.725826i	$-0.258542\pi$
$233$	21.0000			1.37576			0.687878	+	0.725826i	$0.258542\pi$
$234$		0			0
$235$	7.00000	−	14.0000i	0.456630	−	0.913259i
$236$	−5.00000			−0.325472
$237$		0			0
$238$	8.00000	−	2.00000i	0.518563	−	0.129641i
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$			10.0000i			0.644157i	0.946713	+	0.322078i	$0.104381\pi$
$241$			10.0000i			0.644157i	−0.946713	+	0.322078i	$0.895619\pi$
$242$			11.0000i			0.707107i
$243$		0			0
$244$		−	5.00000i		−	0.320092i
$245$	−6.00000	−	3.00000i	−0.383326	−	0.191663i
$246$		0			0
$247$			5.00000i			0.318142i
$248$	5.00000			0.317500
$249$		0			0
$250$	−11.0000	+	2.00000i	−0.695701	+	0.126491i
$251$	8.00000			0.504956			0.252478	−	0.967603i	$-0.418755\pi$
$251$	8.00000			0.504956			0.252478	+	0.967603i	$0.418755\pi$
$252$		0			0
$253$		0			0
$254$	−7.00000			−0.439219
$255$		0			0
$256$	1.00000			0.0625000
$257$			18.0000i			1.12281i	0.827541	+	0.561405i	$0.189739\pi$
$257$			18.0000i			1.12281i	−0.827541	+	0.561405i	$0.810261\pi$
$258$		0			0
$259$	4.00000			0.248548
$260$	−1.00000	+	2.00000i	−0.0620174	+	0.124035i
$261$		0			0
$262$	−20.0000			−1.23560
$263$			21.0000i			1.29492i	0.762101	+	0.647458i	$0.224168\pi$
$263$			21.0000i			1.29492i	−0.762101	+	0.647458i	$0.775832\pi$
$264$		0			0
$265$	−1.00000	+	2.00000i	−0.0614295	+	0.122859i
$266$			10.0000i			0.613139i
$267$		0			0
$268$		−	2.00000i		−	0.122169i
$269$		−	1.00000i		−	0.0609711i	−0.999535	−	0.0304855i	$-0.990295\pi$
$269$		−	1.00000i		−	0.0609711i	0.999535	−	0.0304855i	$-0.00970535\pi$
$270$		0			0
$271$	22.0000			1.33640			0.668202	−	0.743980i	$-0.267064\pi$
$271$	22.0000			1.33640			0.668202	+	0.743980i	$0.267064\pi$
$272$	1.00000	+	4.00000i	0.0606339	+	0.242536i
$273$		0			0
$274$	2.00000			0.120824
$275$		0			0
$276$		0			0
$277$	18.0000			1.08152			0.540758	−	0.841178i	$-0.318138\pi$
$277$	18.0000			1.08152			0.540758	+	0.841178i	$0.318138\pi$
$278$	14.0000			0.839664
$279$		0			0
$280$	−2.00000	+	4.00000i	−0.119523	+	0.239046i
$281$	23.0000			1.37206			0.686032	−	0.727571i	$-0.259351\pi$
$281$	23.0000			1.37206			0.686032	+	0.727571i	$0.259351\pi$
$282$		0			0
$283$	−21.0000			−1.24832			−0.624160	−	0.781296i	$-0.714559\pi$
$283$	−21.0000			−1.24832			−0.624160	+	0.781296i	$0.714559\pi$
$284$			5.00000i			0.296695i
$285$		0			0
$286$		0			0
$287$		−	20.0000i		−	1.18056i
$288$		0			0
$289$	−15.0000	+	8.00000i	−0.882353	+	0.470588i
$290$	−18.0000	−	9.00000i	−1.05700	−	0.528498i
$291$		0			0
$292$	11.0000			0.643726
$293$		−	29.0000i		−	1.69420i	−0.531435	−	0.847099i	$-0.678347\pi$
$293$		−	29.0000i		−	1.69420i	0.531435	−	0.847099i	$-0.321653\pi$
$294$		0			0
$295$	10.0000	+	5.00000i	0.582223	+	0.291111i
$296$			2.00000i			0.116248i
$297$		0			0
$298$		−	20.0000i		−	1.15857i
$299$			4.00000i			0.231326i
$300$		0			0
$301$			12.0000i			0.691669i
$302$		−	8.00000i		−	0.460348i
$303$		0			0
$304$	−5.00000			−0.286770
$305$	−5.00000	+	10.0000i	−0.286299	+	0.572598i
$306$		0			0
$307$			2.00000i			0.114146i	0.998370	+	0.0570730i	$0.0181768\pi$
$307$			2.00000i			0.114146i	−0.998370	+	0.0570730i	$0.981823\pi$
$308$		0			0
$309$		0			0
$310$	−10.0000	−	5.00000i	−0.567962	−	0.283981i
$311$		−	20.0000i		−	1.13410i	−0.823685	−	0.567048i	$-0.808085\pi$
$311$		−	20.0000i		−	1.13410i	0.823685	−	0.567048i	$-0.191915\pi$
$312$		0			0
$313$	14.0000			0.791327			0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000			0.791327			0.395663	+	0.918396i	$0.370515\pi$
$314$	18.0000			1.01580
$315$		0			0
$316$		−	16.0000i		−	0.900070i
$317$	12.0000			0.673987			0.336994	−	0.941507i	$-0.390590\pi$
$317$	12.0000			0.673987			0.336994	+	0.941507i	$0.390590\pi$
$318$		0			0
$319$		0			0
$320$	−2.00000	−	1.00000i	−0.111803	−	0.0559017i
$321$		0			0
$322$			8.00000i			0.445823i
$323$	−5.00000	−	20.0000i	−0.278207	−	1.11283i
$324$		0			0
$325$	4.00000	−	3.00000i	0.221880	−	0.166410i
$326$			4.00000i			0.221540i
$327$		0			0
$328$	10.0000			0.552158
$329$			14.0000i			0.771845i
$330$		0			0
$331$	7.00000			0.384755			0.192377	−	0.981321i	$-0.438380\pi$
$331$	7.00000			0.384755			0.192377	+	0.981321i	$0.438380\pi$
$332$		−	6.00000i		−	0.329293i
$333$		0			0
$334$		−	18.0000i		−	0.984916i
$335$	−2.00000	+	4.00000i	−0.109272	+	0.218543i
$336$		0			0
$337$	23.0000			1.25289			0.626445	−	0.779466i	$-0.284509\pi$
$337$	23.0000			1.25289			0.626445	+	0.779466i	$0.284509\pi$
$338$			12.0000i			0.652714i
$339$		0			0
$340$	2.00000	−	9.00000i	0.108465	−	0.488094i
$341$		0			0
$342$		0			0
$343$	20.0000			1.07990
$344$	−6.00000			−0.323498
$345$		0			0
$346$			16.0000i			0.860165i
$347$	−23.0000			−1.23470			−0.617352	−	0.786687i	$-0.711795\pi$
$347$	−23.0000			−1.23470			−0.617352	+	0.786687i	$0.711795\pi$
$348$		0			0
$349$	10.0000			0.535288			0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000			0.535288			0.267644	+	0.963518i	$0.413755\pi$
$350$	8.00000	−	6.00000i	0.427618	−	0.320713i
$351$		0			0
$352$		0			0
$353$		−	4.00000i		−	0.212899i	−0.994318	−	0.106449i	$-0.966052\pi$
$353$		−	4.00000i		−	0.212899i	0.994318	−	0.106449i	$-0.0339482\pi$
$354$		0			0
$355$	5.00000	−	10.0000i	0.265372	−	0.530745i
$356$	5.00000			0.264999
$357$		0			0
$358$		−	20.0000i		−	1.05703i
$359$	30.0000			1.58334			0.791670	−	0.610949i	$-0.209212\pi$
$359$	30.0000			1.58334			0.791670	+	0.610949i	$0.209212\pi$
$360$		0			0
$361$	6.00000			0.315789
$362$	−10.0000			−0.525588
$363$		0			0
$364$		−	2.00000i		−	0.104828i
$365$	−22.0000	−	11.0000i	−1.15153	−	0.575766i
$366$		0			0
$367$	−2.00000			−0.104399			−0.0521996	−	0.998637i	$-0.516623\pi$
$367$	−2.00000			−0.104399			−0.0521996	+	0.998637i	$0.516623\pi$
$368$	−4.00000			−0.208514
$369$		0			0
$370$	2.00000	−	4.00000i	0.103975	−	0.207950i
$371$		−	2.00000i		−	0.103835i
$372$		0			0
$373$			34.0000i			1.76045i	0.474554	+	0.880227i	$0.342610\pi$
$373$			34.0000i			1.76045i	−0.474554	+	0.880227i	$0.657390\pi$
$374$		0			0
$375$		0			0
$376$	−7.00000			−0.360997
$377$	9.00000			0.463524
$378$		0			0
$379$		−	4.00000i		−	0.205466i	−0.994709	−	0.102733i	$-0.967241\pi$
$379$		−	4.00000i		−	0.205466i	0.994709	−	0.102733i	$-0.0327588\pi$
$380$	10.0000	+	5.00000i	0.512989	+	0.256495i
$381$		0			0
$382$			18.0000i			0.920960i
$383$			31.0000i			1.58403i	0.610504	+	0.792013i	$0.290967\pi$
$383$			31.0000i			1.58403i	−0.610504	+	0.792013i	$0.709033\pi$
$384$		0			0
$385$		0			0
$386$			14.0000i			0.712581i
$387$		0			0
$388$	7.00000			0.355371
$389$	10.0000			0.507020			0.253510	−	0.967333i	$-0.418415\pi$
$389$	10.0000			0.507020			0.253510	+	0.967333i	$0.418415\pi$
$390$		0			0
$391$	−4.00000	−	16.0000i	−0.202289	−	0.809155i
$392$			3.00000i			0.151523i
$393$		0			0
$394$		−	8.00000i		−	0.403034i
$395$	−16.0000	+	32.0000i	−0.805047	+	1.61009i
$396$		0			0
$397$	18.0000			0.903394			0.451697	−	0.892171i	$-0.350819\pi$
$397$	18.0000			0.903394			0.451697	+	0.892171i	$0.350819\pi$
$398$	−1.00000			−0.0501255
$399$		0			0
$400$	3.00000	+	4.00000i	0.150000	+	0.200000i
$401$			10.0000i			0.499376i	0.968326	+	0.249688i	$0.0803281\pi$
$401$			10.0000i			0.499376i	−0.968326	+	0.249688i	$0.919672\pi$
$402$		0			0
$403$	5.00000			0.249068
$404$	−8.00000			−0.398015
$405$		0			0
$406$	18.0000			0.893325
$407$		0			0
$408$		0			0
$409$	−25.0000			−1.23617			−0.618085	−	0.786111i	$-0.712091\pi$
$409$	−25.0000			−1.23617			−0.618085	+	0.786111i	$0.712091\pi$
$410$	−20.0000	−	10.0000i	−0.987730	−	0.493865i
$411$		0			0
$412$			16.0000i			0.788263i
$413$	−10.0000			−0.492068
$414$		0			0
$415$	−6.00000	+	12.0000i	−0.294528	+	0.589057i
$416$	1.00000			0.0490290
$417$		0			0
$418$		0			0
$419$			24.0000i			1.17248i	0.810139	+	0.586238i	$0.199392\pi$
$419$			24.0000i			1.17248i	−0.810139	+	0.586238i	$0.800608\pi$
$420$		0			0
$421$	2.00000			0.0974740			0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000			0.0974740			0.0487370	+	0.998812i	$0.484480\pi$
$422$	20.0000			0.973585
$423$		0			0
$424$	1.00000			0.0485643
$425$	−13.0000	+	16.0000i	−0.630593	+	0.776114i
$426$		0			0
$427$		−	10.0000i		−	0.483934i
$428$	−12.0000			−0.580042
$429$		0			0
$430$	12.0000	+	6.00000i	0.578691	+	0.289346i
$431$		0			0		1.00000			$0$
$431$		0			0		−1.00000			$\pi$
$432$		0			0
$433$		−	6.00000i		−	0.288342i	−0.989553	−	0.144171i	$-0.953949\pi$
$433$		−	6.00000i		−	0.288342i	0.989553	−	0.144171i	$-0.0460515\pi$
$434$	10.0000			0.480015
$435$		0			0
$436$			9.00000i			0.431022i
$437$	20.0000			0.956730
$438$		0			0
$439$		−	24.0000i		−	1.14546i	−0.819745	−	0.572729i	$-0.805885\pi$
$439$		−	24.0000i		−	1.14546i	0.819745	−	0.572729i	$-0.194115\pi$
$440$		0			0
$441$		0			0
$442$	1.00000	+	4.00000i	0.0475651	+	0.190261i
$443$			26.0000i			1.23530i	0.786454	+	0.617649i	$0.211915\pi$
$443$			26.0000i			1.23530i	−0.786454	+	0.617649i	$0.788085\pi$
$444$		0			0
$445$	−10.0000	−	5.00000i	−0.474045	−	0.237023i
$446$	−9.00000			−0.426162
$447$		0			0
$448$	2.00000			0.0944911
$449$		−	16.0000i		−	0.755087i	−0.925992	−	0.377543i	$-0.876769\pi$
$449$		−	16.0000i		−	0.755087i	0.925992	−	0.377543i	$-0.123231\pi$
$450$		0			0
$451$		0			0
$452$	9.00000			0.423324
$453$		0			0
$454$			27.0000i			1.26717i
$455$	−2.00000	+	4.00000i	−0.0937614	+	0.187523i
$456$		0			0
$457$		−	18.0000i		−	0.842004i	−0.907060	−	0.421002i	$-0.861678\pi$
$457$		−	18.0000i		−	0.842004i	0.907060	−	0.421002i	$-0.138322\pi$
$458$		0			0
$459$		0			0
$460$	8.00000	+	4.00000i	0.373002	+	0.186501i
$461$	−32.0000			−1.49039			−0.745194	−	0.666847i	$-0.767643\pi$
$461$	−32.0000			−1.49039			−0.745194	+	0.666847i	$0.767643\pi$
$462$		0			0
$463$			29.0000i			1.34774i	0.738848	+	0.673872i	$0.235370\pi$
$463$			29.0000i			1.34774i	−0.738848	+	0.673872i	$0.764630\pi$
$464$			9.00000i			0.417815i
$465$		0			0
$466$			21.0000i			0.972806i
$467$		−	12.0000i		−	0.555294i	−0.960683	−	0.277647i	$-0.910445\pi$
$467$		−	12.0000i		−	0.555294i	0.960683	−	0.277647i	$-0.0895545\pi$
$468$		0			0
$469$		−	4.00000i		−	0.184703i
$470$	14.0000	+	7.00000i	0.645772	+	0.322886i
$471$		0			0
$472$		−	5.00000i		−	0.230144i
$473$		0			0
$474$		0			0
$475$	−15.0000	−	20.0000i	−0.688247	−	0.917663i
$476$	2.00000	+	8.00000i	0.0916698	+	0.366679i
$477$		0			0
$478$		0			0
$479$		−	21.0000i		−	0.959514i	−0.877401	−	0.479757i	$-0.840725\pi$
$479$		−	21.0000i		−	0.959514i	0.877401	−	0.479757i	$-0.159275\pi$
$480$		0			0
$481$			2.00000i			0.0911922i
$482$	−10.0000			−0.455488
$483$		0			0
$484$	−11.0000			−0.500000
$485$	−14.0000	−	7.00000i	−0.635707	−	0.317854i
$486$		0			0
$487$	−32.0000			−1.45006			−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000			−1.45006			−0.725029	+	0.688718i	$0.758174\pi$
$488$	5.00000			0.226339
$489$		0			0
$490$	3.00000	−	6.00000i	0.135526	−	0.271052i
$491$	33.0000			1.48927			0.744635	−	0.667472i	$-0.232624\pi$
$491$	33.0000			1.48927			0.744635	+	0.667472i	$0.232624\pi$
$492$		0			0
$493$	−36.0000	+	9.00000i	−1.62136	+	0.405340i
$494$	−5.00000			−0.224961
$495$		0			0
$496$			5.00000i			0.224507i
$497$			10.0000i			0.448561i
$498$		0			0
$499$			6.00000i			0.268597i	0.990941	+	0.134298i	$0.0428781\pi$
$499$			6.00000i			0.268597i	−0.990941	+	0.134298i	$0.957122\pi$
$500$	−2.00000	−	11.0000i	−0.0894427	−	0.491935i
$501$		0			0
$502$			8.00000i			0.357057i
$503$	6.00000			0.267527			0.133763	−	0.991013i	$-0.457294\pi$
$503$	6.00000			0.267527			0.133763	+	0.991013i	$0.457294\pi$
$504$		0			0
$505$	16.0000	+	8.00000i	0.711991	+	0.355995i
$506$		0			0
$507$		0			0
$508$		−	7.00000i		−	0.310575i
$509$	20.0000			0.886484			0.443242	−	0.896402i	$-0.353828\pi$
$509$	20.0000			0.886484			0.443242	+	0.896402i	$0.353828\pi$
$510$		0			0
$511$	22.0000			0.973223
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−18.0000			−0.793946
$515$	16.0000	−	32.0000i	0.705044	−	1.41009i
$516$		0			0
$517$		0			0
$518$			4.00000i			0.175750i
$519$		0			0
$520$	−2.00000	−	1.00000i	−0.0877058	−	0.0438529i
$521$			40.0000i			1.75243i	0.481919	+	0.876216i	$0.339940\pi$
$521$			40.0000i			1.75243i	−0.481919	+	0.876216i	$0.660060\pi$
$522$		0			0
$523$			34.0000i			1.48672i	0.668894	+	0.743358i	$0.266768\pi$
$523$			34.0000i			1.48672i	−0.668894	+	0.743358i	$0.733232\pi$
$524$		−	20.0000i		−	0.873704i
$525$		0			0
$526$	−21.0000			−0.915644
$527$	−20.0000	+	5.00000i	−0.871214	+	0.217803i
$528$		0			0
$529$	−7.00000			−0.304348
$530$	−2.00000	−	1.00000i	−0.0868744	−	0.0434372i
$531$		0			0
$532$	−10.0000			−0.433555
$533$	10.0000			0.433148
$534$		0			0
$535$	24.0000	+	12.0000i	1.03761	+	0.518805i
$536$	2.00000			0.0863868
$537$		0			0
$538$	1.00000			0.0431131
$539$		0			0
$540$		0			0
$541$		−	10.0000i		−	0.429934i	−0.976621	−	0.214967i	$-0.931036\pi$
$541$		−	10.0000i		−	0.429934i	0.976621	−	0.214967i	$-0.0689643\pi$
$542$			22.0000i			0.944981i
$543$		0			0
$544$	−4.00000	+	1.00000i	−0.171499	+	0.0428746i
$545$	9.00000	−	18.0000i	0.385518	−	0.771035i
$546$		0			0
$547$	13.0000			0.555840			0.277920	−	0.960604i	$-0.410355\pi$
$547$	13.0000			0.555840			0.277920	+	0.960604i	$0.410355\pi$
$548$			2.00000i			0.0854358i
$549$		0			0
$550$		0			0
$551$		−	45.0000i		−	1.91706i
$552$		0			0
$553$		−	32.0000i		−	1.36078i
$554$			18.0000i			0.764747i
$555$		0			0
$556$			14.0000i			0.593732i
$557$			3.00000i			0.127114i	0.997978	+	0.0635570i	$0.0202445\pi$
$557$			3.00000i			0.127114i	−0.997978	+	0.0635570i	$0.979756\pi$
$558$		0			0
$559$	−6.00000			−0.253773
$560$	−4.00000	−	2.00000i	−0.169031	−	0.0845154i
$561$		0			0
$562$			23.0000i			0.970196i
$563$		−	24.0000i		−	1.01148i	−0.862686	−	0.505740i	$-0.831220\pi$
$563$		−	24.0000i		−	1.01148i	0.862686	−	0.505740i	$-0.168780\pi$
$564$		0			0
$565$	−18.0000	−	9.00000i	−0.757266	−	0.378633i
$566$		−	21.0000i		−	0.882696i
$567$		0			0
$568$	−5.00000			−0.209795
$569$	−15.0000			−0.628833			−0.314416	−	0.949285i	$-0.601809\pi$
$569$	−15.0000			−0.628833			−0.314416	+	0.949285i	$0.601809\pi$
$570$		0			0
$571$		−	20.0000i		−	0.836974i	−0.908223	−	0.418487i	$-0.862561\pi$
$571$		−	20.0000i		−	0.836974i	0.908223	−	0.418487i	$-0.137439\pi$
$572$		0			0
$573$		0			0
$574$	20.0000			0.834784
$575$	−12.0000	−	16.0000i	−0.500435	−	0.667246i
$576$		0			0
$577$		−	28.0000i		−	1.16566i	−0.812596	−	0.582828i	$-0.801946\pi$
$577$		−	28.0000i		−	1.16566i	0.812596	−	0.582828i	$-0.198054\pi$
$578$	−8.00000	−	15.0000i	−0.332756	−	0.623918i
$579$		0			0
$580$	9.00000	−	18.0000i	0.373705	−	0.747409i
$581$		−	12.0000i		−	0.497844i
$582$		0			0
$583$		0			0
$584$			11.0000i			0.455183i
$585$		0			0
$586$	29.0000			1.19798
$587$		−	12.0000i		−	0.495293i	−0.968850	−	0.247647i	$-0.920343\pi$
$587$		−	12.0000i		−	0.495293i	0.968850	−	0.247647i	$-0.0796572\pi$
$588$		0			0
$589$		−	25.0000i		−	1.03011i
$590$	−5.00000	+	10.0000i	−0.205847	+	0.411693i
$591$		0			0
$592$	−2.00000			−0.0821995
$593$			6.00000i			0.246390i	0.992382	+	0.123195i	$0.0393141\pi$
$593$			6.00000i			0.246390i	−0.992382	+	0.123195i	$0.960686\pi$
$594$		0			0
$595$	4.00000	−	18.0000i	0.163984	−	0.737928i
$596$	20.0000			0.819232
$597$		0			0
$598$	−4.00000			−0.163572
$599$	−20.0000			−0.817178			−0.408589	−	0.912719i	$-0.633979\pi$
$599$	−20.0000			−0.817178			−0.408589	+	0.912719i	$0.633979\pi$
$600$		0			0
$601$		−	30.0000i		−	1.22373i	−0.790964	−	0.611863i	$-0.790420\pi$
$601$		−	30.0000i		−	1.22373i	0.790964	−	0.611863i	$-0.209580\pi$
$602$	−12.0000			−0.489083
$603$		0			0
$604$	8.00000			0.325515
$605$	22.0000	+	11.0000i	0.894427	+	0.447214i
$606$		0			0
$607$	38.0000			1.54237			0.771186	−	0.636610i	$-0.219664\pi$
$607$	38.0000			1.54237			0.771186	+	0.636610i	$0.219664\pi$
$608$		−	5.00000i		−	0.202777i
$609$		0			0
$610$	−10.0000	−	5.00000i	−0.404888	−	0.202444i
$611$	−7.00000			−0.283190
$612$		0			0
$613$		−	41.0000i		−	1.65597i	−0.560747	−	0.827987i	$-0.689486\pi$
$613$		−	41.0000i		−	1.65597i	0.560747	−	0.827987i	$-0.310514\pi$
$614$	−2.00000			−0.0807134
$615$		0			0
$616$		0			0
$617$	−33.0000			−1.32853			−0.664265	−	0.747497i	$-0.731255\pi$
$617$	−33.0000			−1.32853			−0.664265	+	0.747497i	$0.731255\pi$
$618$		0			0
$619$			26.0000i			1.04503i	0.852631	+	0.522514i	$0.175006\pi$
$619$			26.0000i			1.04503i	−0.852631	+	0.522514i	$0.824994\pi$
$620$	5.00000	−	10.0000i	0.200805	−	0.401610i
$621$		0			0
$622$	20.0000			0.801927
$623$	10.0000			0.400642
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$			14.0000i			0.559553i
$627$		0			0
$628$			18.0000i			0.718278i
$629$	−2.00000	−	8.00000i	−0.0797452	−	0.318981i
$630$		0			0
$631$	2.00000			0.0796187			0.0398094	−	0.999207i	$-0.487325\pi$
$631$	2.00000			0.0796187			0.0398094	+	0.999207i	$0.487325\pi$
$632$	16.0000			0.636446
$633$		0			0
$634$			12.0000i			0.476581i
$635$	−7.00000	+	14.0000i	−0.277787	+	0.555573i
$636$		0			0
$637$			3.00000i			0.118864i
$638$		0			0
$639$		0			0
$640$	1.00000	−	2.00000i	0.0395285	−	0.0790569i
$641$			10.0000i			0.394976i	0.980305	+	0.197488i	$0.0632784\pi$
$641$			10.0000i			0.394976i	−0.980305	+	0.197488i	$0.936722\pi$
$642$		0			0
$643$	−36.0000			−1.41970			−0.709851	−	0.704352i	$-0.751238\pi$
$643$	−36.0000			−1.41970			−0.709851	+	0.704352i	$0.751238\pi$
$644$	−8.00000			−0.315244
$645$		0			0
$646$	20.0000	−	5.00000i	0.786889	−	0.196722i
$647$		−	37.0000i		−	1.45462i	−0.686309	−	0.727310i	$-0.740770\pi$
$647$		−	37.0000i		−	1.45462i	0.686309	−	0.727310i	$-0.259230\pi$
$648$		0			0
$649$		0			0
$650$	3.00000	+	4.00000i	0.117670	+	0.156893i
$651$		0			0
$652$	−4.00000			−0.156652
$653$	−24.0000			−0.939193			−0.469596	−	0.882881i	$-0.655601\pi$
$653$	−24.0000			−0.939193			−0.469596	+	0.882881i	$0.655601\pi$
$654$		0			0
$655$	−20.0000	+	40.0000i	−0.781465	+	1.56293i
$656$			10.0000i			0.390434i
$657$		0			0
$658$	−14.0000			−0.545777
$659$	5.00000			0.194772			0.0973862	−	0.995247i	$-0.468952\pi$
$659$	5.00000			0.194772			0.0973862	+	0.995247i	$0.468952\pi$
$660$		0			0
$661$	−8.00000			−0.311164			−0.155582	−	0.987823i	$-0.549725\pi$
$661$	−8.00000			−0.311164			−0.155582	+	0.987823i	$0.549725\pi$
$662$			7.00000i			0.272063i
$663$		0			0
$664$	6.00000			0.232845
$665$	20.0000	+	10.0000i	0.775567	+	0.387783i
$666$		0			0
$667$		−	36.0000i		−	1.39393i
$668$	18.0000			0.696441
$669$		0			0
$670$	−4.00000	−	2.00000i	−0.154533	−	0.0772667i
$671$		0			0
$672$		0			0
$673$	−1.00000			−0.0385472			−0.0192736	−	0.999814i	$-0.506135\pi$
$673$	−1.00000			−0.0385472			−0.0192736	+	0.999814i	$0.506135\pi$
$674$			23.0000i			0.885927i
$675$		0			0
$676$	−12.0000			−0.461538
$677$	2.00000			0.0768662			0.0384331	−	0.999261i	$-0.487763\pi$
$677$	2.00000			0.0768662			0.0384331	+	0.999261i	$0.487763\pi$
$678$		0			0
$679$	14.0000			0.537271
$680$	9.00000	+	2.00000i	0.345134	+	0.0766965i
$681$		0			0
$682$		0			0
$683$	−39.0000			−1.49229			−0.746147	−	0.665782i	$-0.768098\pi$
$683$	−39.0000			−1.49229			−0.746147	+	0.665782i	$0.768098\pi$
$684$		0			0
$685$	2.00000	−	4.00000i	0.0764161	−	0.152832i
$686$			20.0000i			0.763604i
$687$		0			0
$688$		−	6.00000i		−	0.228748i
$689$	1.00000			0.0380970
$690$		0			0
$691$			30.0000i			1.14125i	0.821209	+	0.570627i	$0.193300\pi$
$691$			30.0000i			1.14125i	−0.821209	+	0.570627i	$0.806700\pi$
$692$	−16.0000			−0.608229
$693$		0			0
$694$		−	23.0000i		−	0.873068i
$695$	14.0000	−	28.0000i	0.531050	−	1.06210i
$696$		0			0
$697$	−40.0000	+	10.0000i	−1.51511	+	0.378777i
$698$			10.0000i			0.378506i
$699$		0			0
$700$	6.00000	+	8.00000i	0.226779	+	0.302372i
$701$	48.0000			1.81293			0.906467	−	0.422276i	$-0.138769\pi$
$701$	48.0000			1.81293			0.906467	+	0.422276i	$0.138769\pi$
$702$		0			0
$703$	10.0000			0.377157
$704$		0			0
$705$		0			0
$706$	4.00000			0.150542
$707$	−16.0000			−0.601742
$708$		0			0
$709$			31.0000i			1.16423i	0.813107	+	0.582115i	$0.197775\pi$
$709$			31.0000i			1.16423i	−0.813107	+	0.582115i	$0.802225\pi$
$710$	10.0000	+	5.00000i	0.375293	+	0.187647i
$711$		0			0
$712$			5.00000i			0.187383i
$713$		−	20.0000i		−	0.749006i
$714$		0			0
$715$		0			0
$716$	20.0000			0.747435
$717$		0			0
$718$			30.0000i			1.11959i
$719$		−	51.0000i		−	1.90198i	−0.309223	−	0.950990i	$-0.600069\pi$
$719$		−	51.0000i		−	1.90198i	0.309223	−	0.950990i	$-0.399931\pi$
$720$		0			0
$721$			32.0000i			1.19174i
$722$			6.00000i			0.223297i
$723$		0			0
$724$		−	10.0000i		−	0.371647i
$725$	−36.0000	+	27.0000i	−1.33701	+	1.00275i
$726$		0			0
$727$		−	33.0000i		−	1.22390i	−0.790896	−	0.611951i	$-0.790385\pi$
$727$		−	33.0000i		−	1.22390i	0.790896	−	0.611951i	$-0.209615\pi$
$728$	2.00000			0.0741249
$729$		0			0
$730$	11.0000	−	22.0000i	0.407128	−	0.814257i
$731$	24.0000	−	6.00000i	0.887672	−	0.221918i
$732$		0			0
$733$		−	6.00000i		−	0.221615i	−0.993842	−	0.110808i	$-0.964656\pi$
$733$		−	6.00000i		−	0.221615i	0.993842	−	0.110808i	$-0.0353437\pi$
$734$		−	2.00000i		−	0.0738213i
$735$		0			0
$736$		−	4.00000i		−	0.147442i
$737$		0			0
$738$		0			0
$739$	−15.0000			−0.551784			−0.275892	−	0.961189i	$-0.588973\pi$
$739$	−15.0000			−0.551784			−0.275892	+	0.961189i	$0.588973\pi$
$740$	4.00000	+	2.00000i	0.147043	+	0.0735215i
$741$		0			0
$742$	2.00000			0.0734223
$743$	−34.0000			−1.24734			−0.623670	−	0.781688i	$-0.714359\pi$
$743$	−34.0000			−1.24734			−0.623670	+	0.781688i	$0.714359\pi$
$744$		0			0
$745$	−40.0000	−	20.0000i	−1.46549	−	0.732743i
$746$	−34.0000			−1.24483
$747$		0			0
$748$		0			0
$749$	−24.0000			−0.876941
$750$		0			0
$751$		−	25.0000i		−	0.912263i	−0.889912	−	0.456131i	$-0.849235\pi$
$751$		−	25.0000i		−	0.912263i	0.889912	−	0.456131i	$-0.150765\pi$
$752$		−	7.00000i		−	0.255264i
$753$		0			0
$754$			9.00000i			0.327761i
$755$	−16.0000	−	8.00000i	−0.582300	−	0.291150i
$756$		0			0
$757$		−	13.0000i		−	0.472493i	−0.971693	−	0.236247i	$-0.924083\pi$
$757$		−	13.0000i		−	0.472493i	0.971693	−	0.236247i	$-0.0759173\pi$
$758$	4.00000			0.145287
$759$		0			0
$760$	−5.00000	+	10.0000i	−0.181369	+	0.362738i
$761$	−22.0000			−0.797499			−0.398750	−	0.917060i	$-0.630556\pi$
$761$	−22.0000			−0.797499			−0.398750	+	0.917060i	$0.630556\pi$
$762$		0			0
$763$			18.0000i			0.651644i
$764$	−18.0000			−0.651217
$765$		0			0
$766$	−31.0000			−1.12008
$767$		−	5.00000i		−	0.180540i
$768$		0			0
$769$	35.0000			1.26213			0.631066	−	0.775729i	$-0.282618\pi$
$769$	35.0000			1.26213			0.631066	+	0.775729i	$0.282618\pi$
$770$		0			0
$771$		0			0
$772$	−14.0000			−0.503871
$773$			26.0000i			0.935155i	0.883952	+	0.467578i	$0.154873\pi$
$773$			26.0000i			0.935155i	−0.883952	+	0.467578i	$0.845127\pi$
$774$		0			0
$775$	−20.0000	+	15.0000i	−0.718421	+	0.538816i
$776$			7.00000i			0.251285i
$777$		0			0
$778$			10.0000i			0.358517i
$779$		−	50.0000i		−	1.79144i
$780$		0			0
$781$		0			0
$782$	16.0000	−	4.00000i	0.572159	−	0.143040i
$783$		0			0
$784$	−3.00000			−0.107143
$785$	18.0000	−	36.0000i	0.642448	−	1.28490i
$786$		0			0
$787$	−7.00000			−0.249523			−0.124762	−	0.992187i	$-0.539817\pi$
$787$	−7.00000			−0.249523			−0.124762	+	0.992187i	$0.539817\pi$
$788$	8.00000			0.284988
$789$		0			0
$790$	−32.0000	−	16.0000i	−1.13851	−	0.569254i
$791$	18.0000			0.640006
$792$		0			0
$793$	5.00000			0.177555
$794$			18.0000i			0.638796i
$795$		0			0
$796$		−	1.00000i		−	0.0354441i
$797$		−	2.00000i		−	0.0708436i	−0.999372	−	0.0354218i	$-0.988723\pi$
$797$		−	2.00000i		−	0.0708436i	0.999372	−	0.0354218i	$-0.0112775\pi$
$798$		0			0
$799$	28.0000	−	7.00000i	0.990569	−	0.247642i
$800$	−4.00000	+	3.00000i	−0.141421	+	0.106066i
$801$		0			0
$802$	−10.0000			−0.353112
$803$		0			0
$804$		0			0
$805$	16.0000	+	8.00000i	0.563926	+	0.281963i
$806$			5.00000i			0.176117i
$807$		0			0
$808$		−	8.00000i		−	0.281439i
$809$			24.0000i			0.843795i	0.906644	+	0.421898i	$0.138636\pi$
$809$			24.0000i			0.843795i	−0.906644	+	0.421898i	$0.861364\pi$
$810$		0			0
$811$			30.0000i			1.05344i	0.850038	+	0.526721i	$0.176579\pi$
$811$			30.0000i			1.05344i	−0.850038	+	0.526721i	$0.823421\pi$
$812$			18.0000i			0.631676i
$813$		0			0
$814$		0			0
$815$	8.00000	+	4.00000i	0.280228	+	0.140114i
$816$		0			0
$817$			30.0000i			1.04957i
$818$		−	25.0000i		−	0.874105i
$819$		0			0
$820$	10.0000	−	20.0000i	0.349215	−	0.698430i
$821$		−	15.0000i		−	0.523504i	−0.965135	−	0.261752i	$-0.915700\pi$
$821$		−	15.0000i		−	0.523504i	0.965135	−	0.261752i	$-0.0843002\pi$
$822$		0			0
$823$	−46.0000			−1.60346			−0.801730	−	0.597687i	$-0.796087\pi$
$823$	−46.0000			−1.60346			−0.801730	+	0.597687i	$0.796087\pi$
$824$	−16.0000			−0.557386
$825$		0			0
$826$		−	10.0000i		−	0.347945i
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	10.0000			0.347314			0.173657	−	0.984806i	$-0.444442\pi$
$829$	10.0000			0.347314			0.173657	+	0.984806i	$0.444442\pi$
$830$	−12.0000	−	6.00000i	−0.416526	−	0.208263i
$831$		0			0
$832$			1.00000i			0.0346688i
$833$	−3.00000	−	12.0000i	−0.103944	−	0.415775i
$834$		0			0
$835$	−36.0000	−	18.0000i	−1.24583	−	0.622916i
$836$		0			0
$837$		0			0
$838$	−24.0000			−0.829066
$839$			9.00000i			0.310715i	0.987858	+	0.155357i	$0.0496529\pi$
$839$			9.00000i			0.310715i	−0.987858	+	0.155357i	$0.950347\pi$
$840$		0			0
$841$	−52.0000			−1.79310
$842$			2.00000i			0.0689246i
$843$		0			0
$844$			20.0000i			0.688428i
$845$	24.0000	+	12.0000i	0.825625	+	0.412813i
$846$		0			0
$847$	−22.0000			−0.755929
$848$			1.00000i			0.0343401i
$849$		0			0
$850$	−16.0000	−	13.0000i	−0.548795	−	0.445896i
$851$	8.00000			0.274236
$852$		0			0
$853$	−16.0000			−0.547830			−0.273915	−	0.961754i	$-0.588319\pi$
$853$	−16.0000			−0.547830			−0.273915	+	0.961754i	$0.588319\pi$
$854$	10.0000			0.342193
$855$		0			0
$856$		−	12.0000i		−	0.410152i
$857$	17.0000			0.580709			0.290354	−	0.956919i	$-0.406227\pi$
$857$	17.0000			0.580709			0.290354	+	0.956919i	$0.406227\pi$
$858$		0			0
$859$	−25.0000			−0.852989			−0.426494	−	0.904490i	$-0.640252\pi$
$859$	−25.0000			−0.852989			−0.426494	+	0.904490i	$0.640252\pi$
$860$	−6.00000	+	12.0000i	−0.204598	+	0.409197i
$861$		0			0
$862$		0			0
$863$			36.0000i			1.22545i	0.790295	+	0.612727i	$0.209928\pi$
$863$			36.0000i			1.22545i	−0.790295	+	0.612727i	$0.790072\pi$
$864$		0			0
$865$	32.0000	+	16.0000i	1.08803	+	0.544016i
$866$	6.00000			0.203888
$867$		0			0
$868$			10.0000i			0.339422i
$869$		0			0
$870$		0			0
$871$	2.00000			0.0677674
$872$	−9.00000			−0.304778
$873$		0			0
$874$			20.0000i			0.676510i
$875$	−4.00000	−	22.0000i	−0.135225	−	0.743736i
$876$		0			0
$877$	−32.0000			−1.08056			−0.540282	−	0.841484i	$-0.681682\pi$
$877$	−32.0000			−1.08056			−0.540282	+	0.841484i	$0.681682\pi$
$878$	24.0000			0.809961
$879$		0			0
$880$		0			0
$881$		−	30.0000i		−	1.01073i	−0.862907	−	0.505363i	$-0.831359\pi$
$881$		−	30.0000i		−	1.01073i	0.862907	−	0.505363i	$-0.168641\pi$
$882$		0			0
$883$			44.0000i			1.48072i	0.672212	+	0.740359i	$0.265344\pi$
$883$			44.0000i			1.48072i	−0.672212	+	0.740359i	$0.734656\pi$
$884$	−4.00000	+	1.00000i	−0.134535	+	0.0336336i
$885$		0			0
$886$	−26.0000			−0.873487
$887$	−8.00000			−0.268614			−0.134307	−	0.990940i	$-0.542881\pi$
$887$	−8.00000			−0.268614			−0.134307	+	0.990940i	$0.542881\pi$
$888$		0			0
$889$		−	14.0000i		−	0.469545i
$890$	5.00000	−	10.0000i	0.167600	−	0.335201i
$891$		0			0
$892$		−	9.00000i		−	0.301342i
$893$			35.0000i			1.17123i
$894$		0			0
$895$	−40.0000	−	20.0000i	−1.33705	−	0.668526i
$896$			2.00000i			0.0668153i
$897$		0			0
$898$	16.0000			0.533927
$899$	−45.0000			−1.50083
$900$		0			0
$901$	−4.00000	+	1.00000i	−0.133259	+	0.0333148i
$902$		0			0
$903$		0			0
$904$			9.00000i			0.299336i
$905$	−10.0000	+	20.0000i	−0.332411	+	0.664822i
$906$		0			0
$907$	−7.00000			−0.232431			−0.116216	−	0.993224i	$-0.537076\pi$
$907$	−7.00000			−0.232431			−0.116216	+	0.993224i	$0.537076\pi$
$908$	−27.0000			−0.896026
$909$		0			0
$910$	−4.00000	−	2.00000i	−0.132599	−	0.0662994i
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$	18.0000			0.595387
$915$		0			0
$916$		0			0
$917$		−	40.0000i		−	1.32092i
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$	−4.00000	+	8.00000i	−0.131876	+	0.263752i
$921$		0			0
$922$		−	32.0000i		−	1.05386i
$923$	−5.00000			−0.164577
$924$		0			0
$925$	−6.00000	−	8.00000i	−0.197279	−	0.263038i
$926$	−29.0000			−0.952999
$927$		0			0
$928$	−9.00000			−0.295439
$929$			24.0000i			0.787414i	0.919236	+	0.393707i	$0.128808\pi$
$929$			24.0000i			0.787414i	−0.919236	+	0.393707i	$0.871192\pi$
$930$		0			0
$931$	15.0000			0.491605
$932$	−21.0000			−0.687878
$933$		0			0
$934$	12.0000			0.392652
$935$		0			0
$936$		0			0
$937$			22.0000i			0.718709i	0.933201	+	0.359354i	$0.117003\pi$
$937$			22.0000i			0.718709i	−0.933201	+	0.359354i	$0.882997\pi$
$938$	4.00000			0.130605
$939$		0			0
$940$	−7.00000	+	14.0000i	−0.228315	+	0.456630i
$941$			45.0000i			1.46696i	0.679712	+	0.733479i	$0.262105\pi$
$941$			45.0000i			1.46696i	−0.679712	+	0.733479i	$0.737895\pi$
$942$		0			0
$943$		−	40.0000i		−	1.30258i
$944$	5.00000			0.162736
$945$		0			0
$946$		0			0
$947$	−3.00000			−0.0974869			−0.0487435	−	0.998811i	$-0.515522\pi$
$947$	−3.00000			−0.0974869			−0.0487435	+	0.998811i	$0.515522\pi$
$948$		0			0
$949$			11.0000i			0.357075i
$950$	20.0000	−	15.0000i	0.648886	−	0.486664i
$951$		0			0
$952$	−8.00000	+	2.00000i	−0.259281	+	0.0648204i
$953$			46.0000i			1.49009i	0.667016	+	0.745043i	$0.267571\pi$
$953$			46.0000i			1.49009i	−0.667016	+	0.745043i	$0.732429\pi$
$954$		0			0
$955$	36.0000	+	18.0000i	1.16493	+	0.582466i
$956$		0			0
$957$		0			0
$958$	21.0000			0.678479
$959$			4.00000i			0.129167i
$960$		0			0
$961$	6.00000			0.193548
$962$	−2.00000			−0.0644826
$963$		0			0
$964$		−	10.0000i		−	0.322078i
$965$	28.0000	+	14.0000i	0.901352	+	0.450676i
$966$		0			0
$967$		−	8.00000i		−	0.257263i	−0.991692	−	0.128631i	$-0.958942\pi$
$967$		−	8.00000i		−	0.257263i	0.991692	−	0.128631i	$-0.0410584\pi$
$968$		−	11.0000i		−	0.353553i
$969$		0			0
$970$	7.00000	−	14.0000i	0.224756	−	0.449513i
$971$	−57.0000			−1.82922			−0.914609	−	0.404341i	$-0.867501\pi$
$971$	−57.0000			−1.82922			−0.914609	+	0.404341i	$0.867501\pi$
$972$		0			0
$973$			28.0000i			0.897639i
$974$		−	32.0000i		−	1.02535i
$975$		0			0
$976$			5.00000i			0.160046i
$977$			8.00000i			0.255943i	0.991778	+	0.127971i	$0.0408466\pi$
$977$			8.00000i			0.255943i	−0.991778	+	0.127971i	$0.959153\pi$
$978$		0			0
$979$		0			0
$980$	6.00000	+	3.00000i	0.191663	+	0.0958315i
$981$		0			0
$982$			33.0000i			1.05307i
$983$	−24.0000			−0.765481			−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000			−0.765481			−0.382741	+	0.923856i	$0.625020\pi$
$984$		0			0
$985$	−16.0000	−	8.00000i	−0.509802	−	0.254901i
$986$	−9.00000	−	36.0000i	−0.286618	−	1.14647i
$987$		0			0
$988$		−	5.00000i		−	0.159071i
$989$			24.0000i			0.763156i
$990$		0			0
$991$		−	35.0000i		−	1.11181i	−0.831245	−	0.555906i	$-0.812372\pi$
$991$		−	35.0000i		−	1.11181i	0.831245	−	0.555906i	$-0.187628\pi$
$992$	−5.00000			−0.158750
$993$		0			0
$994$	−10.0000			−0.317181
$995$	−1.00000	+	2.00000i	−0.0317021	+	0.0634043i
$996$		0			0
$997$	18.0000			0.570066			0.285033	−	0.958518i	$-0.407995\pi$
$997$	18.0000			0.570066			0.285033	+	0.958518i	$0.407995\pi$
$998$	−6.00000			−0.189927
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1530.2.f.e.1189.2		2
3.2	odd	2		170.2.d.a.169.1	✓	2
5.4	even	2		1530.2.f.b.1189.1		2
12.11	even	2		1360.2.o.b.849.1		2
15.2	even	4		850.2.b.i.101.2		2
15.8	even	4		850.2.b.c.101.1		2
15.14	odd	2		170.2.d.b.169.2	yes	2
17.16	even	2		1530.2.f.b.1189.2		2
51.50	odd	2		170.2.d.b.169.1	yes	2
60.59	even	2		1360.2.o.a.849.1		2
85.84	even	2	inner	1530.2.f.e.1189.1		2
204.203	even	2		1360.2.o.a.849.2		2
255.152	even	4		850.2.b.i.101.1		2
255.203	even	4		850.2.b.c.101.2		2
255.254	odd	2		170.2.d.a.169.2	yes	2
1020.1019	even	2		1360.2.o.b.849.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.d.a.169.1	✓	2	3.2	odd	2
170.2.d.a.169.2	yes	2	255.254	odd	2
170.2.d.b.169.1	yes	2	51.50	odd	2
170.2.d.b.169.2	yes	2	15.14	odd	2
850.2.b.c.101.1		2	15.8	even	4
850.2.b.c.101.2		2	255.203	even	4
850.2.b.i.101.1		2	255.152	even	4
850.2.b.i.101.2		2	15.2	even	4
1360.2.o.a.849.1		2	60.59	even	2
1360.2.o.a.849.2		2	204.203	even	2
1360.2.o.b.849.1		2	12.11	even	2
1360.2.o.b.849.2		2	1020.1019	even	2
1530.2.f.b.1189.1		2	5.4	even	2
1530.2.f.b.1189.2		2	17.16	even	2
1530.2.f.e.1189.1		2	85.84	even	2	inner
1530.2.f.e.1189.2		2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1530.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} -2.00000 q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} -2.00000 q^{7} -1.00000i q^{8} +(-1.00000 + 2.00000i) q^{10} -1.00000i q^{13} -2.00000i q^{14} +1.00000 q^{16} +(1.00000 + 4.00000i) q^{17} -5.00000 q^{19} +(-2.00000 - 1.00000i) q^{20} -4.00000 q^{23} +(3.00000 + 4.00000i) q^{25} +1.00000 q^{26} +2.00000 q^{28} +9.00000i q^{29} +5.00000i q^{31} +1.00000i q^{32} +(-4.00000 + 1.00000i) q^{34} +(-4.00000 - 2.00000i) q^{35} -2.00000 q^{37} -5.00000i q^{38} +(1.00000 - 2.00000i) q^{40} +10.0000i q^{41} -6.00000i q^{43} -4.00000i q^{46} -7.00000i q^{47} -3.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} +1.00000i q^{52} +1.00000i q^{53} +2.00000i q^{56} -9.00000 q^{58} +5.00000 q^{59} +5.00000i q^{61} -5.00000 q^{62} -1.00000 q^{64} +(1.00000 - 2.00000i) q^{65} +2.00000i q^{67} +(-1.00000 - 4.00000i) q^{68} +(2.00000 - 4.00000i) q^{70} -5.00000i q^{71} -11.0000 q^{73} -2.00000i q^{74} +5.00000 q^{76} +16.0000i q^{79} +(2.00000 + 1.00000i) q^{80} -10.0000 q^{82} +6.00000i q^{83} +(-2.00000 + 9.00000i) q^{85} +6.00000 q^{86} -5.00000 q^{89} +2.00000i q^{91} +4.00000 q^{92} +7.00000 q^{94} +(-10.0000 - 5.00000i) q^{95} -7.00000 q^{97} -3.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} + 4 q^{5} - 4 q^{7}+O(q^{10}) \) 2 * q - 2 * q^4 + 4 * q^5 - 4 * q^7	\( 2 q - 2 q^{4} + 4 q^{5} - 4 q^{7} - 2 q^{10} + 2 q^{16} + 2 q^{17} - 10 q^{19} - 4 q^{20} - 8 q^{23} + 6 q^{25} + 2 q^{26} + 4 q^{28} - 8 q^{34} - 8 q^{35} - 4 q^{37} + 2 q^{40} - 6 q^{49} - 8 q^{50} - 18 q^{58} + 10 q^{59} - 10 q^{62} - 2 q^{64} + 2 q^{65} - 2 q^{68} + 4 q^{70} - 22 q^{73} + 10 q^{76} + 4 q^{80} - 20 q^{82} - 4 q^{85} + 12 q^{86} - 10 q^{89} + 8 q^{92} + 14 q^{94} - 20 q^{95} - 14 q^{97}+O(q^{100}) \) 2 * q - 2 * q^4 + 4 * q^5 - 4 * q^7 - 2 * q^10 + 2 * q^16 + 2 * q^17 - 10 * q^19 - 4 * q^20 - 8 * q^23 + 6 * q^25 + 2 * q^26 + 4 * q^28 - 8 * q^34 - 8 * q^35 - 4 * q^37 + 2 * q^40 - 6 * q^49 - 8 * q^50 - 18 * q^58 + 10 * q^59 - 10 * q^62 - 2 * q^64 + 2 * q^65 - 2 * q^68 + 4 * q^70 - 22 * q^73 + 10 * q^76 + 4 * q^80 - 20 * q^82 - 4 * q^85 + 12 * q^86 - 10 * q^89 + 8 * q^92 + 14 * q^94 - 20 * q^95 - 14 * q^97

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