LMFDB - Embedded newform 2394.2.e.b.1063.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2394,2,Mod(1063,2394)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2394, 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("2394.1063");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2394.e (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:	$19.1161862439$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} + 54x^{8} - 114x^{7} + 120x^{6} + 46x^{5} + 9x^{4} - 4x^{3} + 8x^{2} + 4x + 1 $ x^12 - 2x^11 + 2x^10 + 54x^8 - 114x^7 + 120x^6 + 46x^5 + 9x^4 - 4x^3 + 8x^2 + 4x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 798)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1063.4
Root			$0.382656 - 0.382656i$ of defining polynomial
Character	$\chi$	$=$	2394.1063
Dual form			2394.2.e.b.1063.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +0.765312i q^{5} +(-2.29245 + 1.32086i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +0.765312i q^{5} +(-2.29245 + 1.32086i) q^{7} +1.00000i q^{8} +0.765312 q^{10} -4.09356 q^{11} +1.23469 q^{13} +(1.32086 + 2.29245i) q^{14} +1.00000 q^{16} -3.96246i q^{17} +(3.29983 + 2.84800i) q^{19} -0.765312i q^{20} +4.09356i q^{22} -2.23644 q^{23} +4.41430 q^{25} -1.23469i q^{26} +(2.29245 - 1.32086i) q^{28} -3.54539i q^{29} -8.42378 q^{31} -1.00000i q^{32} -3.96246 q^{34} +(-1.01087 - 1.75444i) q^{35} +5.83888i q^{37} +(2.84800 - 3.29983i) q^{38} -0.765312 q^{40} +5.62174 q^{41} +11.3395 q^{43} +4.09356 q^{44} +2.23644i q^{46} -10.9149i q^{47} +(3.51063 - 6.05603i) q^{49} -4.41430i q^{50} -1.23469 q^{52} +8.28090i q^{53} -3.13285i q^{55} +(-1.32086 - 2.29245i) q^{56} -3.54539 q^{58} -6.22487 q^{59} -5.64349i q^{61} +8.42378i q^{62} -1.00000 q^{64} +0.944922i q^{65} -13.7327i q^{67} +3.96246i q^{68} +(-1.75444 + 1.01087i) q^{70} -11.2414i q^{71} -9.01653i q^{73} +5.83888 q^{74} +(-3.29983 - 2.84800i) q^{76} +(9.38428 - 5.40704i) q^{77} -6.21470i q^{79} +0.765312i q^{80} -5.62174i q^{82} -2.03860i q^{83} +3.03252 q^{85} -11.3395i q^{86} -4.09356i q^{88} +16.3174 q^{89} +(-2.83046 + 1.63086i) q^{91} +2.23644 q^{92} -10.9149 q^{94} +(-2.17961 + 2.52540i) q^{95} +1.90563 q^{97} +(-6.05603 - 3.51063i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4}+O(q^{10}) $ 12 * q - 12 * q^4	$ 12 q - 12 q^{4} + 4 q^{10} - 12 q^{11} + 20 q^{13} + 4 q^{14} + 12 q^{16} - 8 q^{19} + 12 q^{23} - 12 q^{25} + 24 q^{31} + 4 q^{34} - 4 q^{35} - 4 q^{40} + 16 q^{41} + 12 q^{44} + 4 q^{49} - 20 q^{52} - 4 q^{56} + 8 q^{58} - 40 q^{59} - 12 q^{64} - 24 q^{70} + 8 q^{76} - 8 q^{77} + 8 q^{85} + 16 q^{89} + 24 q^{91} - 12 q^{92} + 44 q^{95} - 60 q^{97} + 16 q^{98}+O(q^{100}) $ 12 * q - 12 * q^4 + 4 * q^10 - 12 * q^11 + 20 * q^13 + 4 * q^14 + 12 * q^16 - 8 * q^19 + 12 * q^23 - 12 * q^25 + 24 * q^31 + 4 * q^34 - 4 * q^35 - 4 * q^40 + 16 * q^41 + 12 * q^44 + 4 * q^49 - 20 * q^52 - 4 * q^56 + 8 * q^58 - 40 * q^59 - 12 * q^64 - 24 * q^70 + 8 * q^76 - 8 * q^77 + 8 * q^85 + 16 * q^89 + 24 * q^91 - 12 * q^92 + 44 * q^95 - 60 * q^97 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times$.

$n$	$533$	$1009$	$1711$
$\chi(n)$	$1$	$-1$	$-1$

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
$5$			0.765312i			0.342258i	0.985249	+	0.171129i	$0.0547415\pi$
$5$			0.765312i			0.342258i	−0.985249	+	0.171129i	$0.945259\pi$
$6$		0			0
$7$	−2.29245	+	1.32086i	−0.866464	+	0.499240i
$7$	−2.29245	+	1.32086i	−0.866464	+	0.499240i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.765312			0.242013
$11$	−4.09356			−1.23426			−0.617128	−	0.786863i	$-0.711704\pi$
$11$	−4.09356			−1.23426			−0.617128	+	0.786863i	$0.711704\pi$
$12$		0			0
$13$	1.23469			0.342441			0.171220	−	0.985233i	$-0.445229\pi$
$13$	1.23469			0.342441			0.171220	+	0.985233i	$0.445229\pi$
$14$	1.32086	+	2.29245i	0.353016	+	0.612682i
$15$		0			0
$16$	1.00000			0.250000
$17$		−	3.96246i		−	0.961039i	−0.876984	−	0.480519i	$-0.840448\pi$
$17$		−	3.96246i		−	0.961039i	0.876984	−	0.480519i	$-0.159552\pi$
$18$		0			0
$19$	3.29983	+	2.84800i	0.757034	+	0.653376i
$19$	3.29983	+	2.84800i	0.757034	+	0.653376i
$20$		−	0.765312i		−	0.171129i
$21$		0			0
$22$			4.09356i			0.872750i
$23$	−2.23644			−0.466331			−0.233165	−	0.972437i	$-0.574908\pi$
$23$	−2.23644			−0.466331			−0.233165	+	0.972437i	$0.574908\pi$
$24$		0			0
$25$	4.41430			0.882859
$26$		−	1.23469i		−	0.242142i
$27$		0			0
$28$	2.29245	−	1.32086i	0.433232	−	0.249620i
$29$		−	3.54539i		−	0.658363i	−0.944267	−	0.329182i	$-0.893227\pi$
$29$		−	3.54539i		−	0.658363i	0.944267	−	0.329182i	$-0.106773\pi$
$30$		0			0
$31$	−8.42378			−1.51296			−0.756478	−	0.654020i	$-0.773081\pi$
$31$	−8.42378			−1.51296			−0.756478	+	0.654020i	$0.773081\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−3.96246			−0.679557
$35$	−1.01087	−	1.75444i	−0.170869	−	0.296554i
$36$		0			0
$37$			5.83888i			0.959906i	0.877294	+	0.479953i	$0.159346\pi$
$37$			5.83888i			0.959906i	−0.877294	+	0.479953i	$0.840654\pi$
$38$	2.84800	−	3.29983i	0.462007	−	0.535304i
$39$		0			0
$40$	−0.765312			−0.121006
$41$	5.62174			0.877968			0.438984	−	0.898495i	$-0.355338\pi$
$41$	5.62174			0.877968			0.438984	+	0.898495i	$0.355338\pi$
$42$		0			0
$43$	11.3395			1.72926			0.864628	−	0.502413i	$-0.167554\pi$
$43$	11.3395			1.72926			0.864628	+	0.502413i	$0.167554\pi$
$44$	4.09356			0.617128
$45$		0			0
$46$			2.23644i			0.329746i
$47$		−	10.9149i		−	1.59210i	−0.605230	−	0.796051i	$-0.706919\pi$
$47$		−	10.9149i		−	1.59210i	0.605230	−	0.796051i	$-0.293081\pi$
$48$		0			0
$49$	3.51063	−	6.05603i	0.501519	−	0.865147i
$50$		−	4.41430i		−	0.624276i
$51$		0			0
$52$	−1.23469			−0.171220
$53$			8.28090i			1.13747i	0.822521	+	0.568734i	$0.192567\pi$
$53$			8.28090i			1.13747i	−0.822521	+	0.568734i	$0.807433\pi$
$54$		0			0
$55$		−	3.13285i		−	0.422434i
$56$	−1.32086	−	2.29245i	−0.176508	−	0.306341i
$57$		0			0
$58$	−3.54539			−0.465533
$59$	−6.22487			−0.810409			−0.405204	−	0.914226i	$-0.632800\pi$
$59$	−6.22487			−0.810409			−0.405204	+	0.914226i	$0.632800\pi$
$60$		0			0
$61$		−	5.64349i		−	0.722574i	−0.932455	−	0.361287i	$-0.882337\pi$
$61$		−	5.64349i		−	0.722574i	0.932455	−	0.361287i	$-0.117663\pi$
$62$			8.42378i			1.06982i
$63$		0			0
$64$	−1.00000			−0.125000
$65$			0.944922i			0.117203i
$66$		0			0
$67$		−	13.7327i		−	1.67772i	−0.544347	−	0.838860i	$-0.683223\pi$
$67$		−	13.7327i		−	1.67772i	0.544347	−	0.838860i	$-0.316777\pi$
$68$			3.96246i			0.480519i
$69$		0			0
$70$	−1.75444	+	1.01087i	−0.209695	+	0.120823i
$71$		−	11.2414i		−	1.33411i	−0.745009	−	0.667054i	$-0.767555\pi$
$71$		−	11.2414i		−	1.33411i	0.745009	−	0.667054i	$-0.232445\pi$
$72$		0			0
$73$		−	9.01653i		−	1.05530i	−0.849460	−	0.527652i	$-0.823072\pi$
$73$		−	9.01653i		−	1.05530i	0.849460	−	0.527652i	$-0.176928\pi$
$74$	5.83888			0.678756
$75$		0			0
$76$	−3.29983	−	2.84800i	−0.378517	−	0.326688i
$77$	9.38428	−	5.40704i	1.06944	−	0.616190i
$78$		0			0
$79$		−	6.21470i		−	0.699208i	−0.936898	−	0.349604i	$-0.886316\pi$
$79$		−	6.21470i		−	0.699208i	0.936898	−	0.349604i	$-0.113684\pi$
$80$			0.765312i			0.0855645i
$81$		0			0
$82$		−	5.62174i		−	0.620817i
$83$		−	2.03860i		−	0.223765i	−0.993721	−	0.111883i	$-0.964312\pi$
$83$		−	2.03860i		−	0.223765i	0.993721	−	0.111883i	$-0.0356881\pi$
$84$		0			0
$85$	3.03252			0.328923
$86$		−	11.3395i		−	1.22277i
$87$		0			0
$88$		−	4.09356i		−	0.436375i
$89$	16.3174			1.72964			0.864821	−	0.502080i	$-0.167432\pi$
$89$	16.3174			1.72964			0.864821	+	0.502080i	$0.167432\pi$
$90$		0			0
$91$	−2.83046	+	1.63086i	−0.296713	+	0.170960i
$92$	2.23644			0.233165
$93$		0			0
$94$	−10.9149			−1.12579
$95$	−2.17961	+	2.52540i	−0.223623	+	0.259101i
$96$		0			0
$97$	1.90563			0.193487			0.0967437	−	0.995309i	$-0.469157\pi$
$97$	1.90563			0.193487			0.0967437	+	0.995309i	$0.469157\pi$
$98$	−6.05603	−	3.51063i	−0.611751	−	0.354627i
$99$		0			0
$100$	−4.41430			−0.441430
$101$		−	11.8561i		−	1.17973i	−0.807503	−	0.589863i	$-0.799182\pi$
$101$		−	11.8561i		−	1.17973i	0.807503	−	0.589863i	$-0.200818\pi$
$102$		0			0
$103$	0.00772432			0.000761100			0.000380550	−	1.00000i	$-0.499879\pi$
$103$	0.00772432			0.000761100			0.000380550		1.00000i	$0.499879\pi$
$104$			1.23469i			0.121071i
$105$		0			0
$106$	8.28090			0.804312
$107$			13.2084i			1.27690i	0.769662	+	0.638452i	$0.220425\pi$
$107$			13.2084i			1.27690i	−0.769662	+	0.638452i	$0.779575\pi$
$108$		0			0
$109$			5.93963i			0.568914i	0.958689	+	0.284457i	$0.0918132\pi$
$109$			5.93963i			0.568914i	−0.958689	+	0.284457i	$0.908187\pi$
$110$	−3.13285			−0.298706
$111$		0			0
$112$	−2.29245	+	1.32086i	−0.216616	+	0.124810i
$113$			4.56747i			0.429671i	0.976650	+	0.214836i	$0.0689216\pi$
$113$			4.56747i			0.429671i	−0.976650	+	0.214836i	$0.931078\pi$
$114$		0			0
$115$		−	1.71158i		−	0.159605i
$116$			3.54539i			0.329182i
$117$		0			0
$118$			6.22487i			0.573046i
$119$	5.23388	+	9.08374i	0.479789	+	0.832705i
$120$		0			0
$121$	5.75725			0.523386
$122$	−5.64349			−0.510937
$123$		0			0
$124$	8.42378			0.756478
$125$			7.20488i			0.644424i
$126$		0			0
$127$		−	2.92024i		−	0.259129i	−0.991571	−	0.129565i	$-0.958642\pi$
$127$		−	2.92024i		−	0.259129i	0.991571	−	0.129565i	$-0.0413580\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	0.944922			0.0828751
$131$		−	10.9795i		−	0.959280i	−0.877465	−	0.479640i	$-0.840767\pi$
$131$		−	10.9795i		−	0.959280i	0.877465	−	0.479640i	$-0.159233\pi$
$132$		0			0
$133$	−11.3265	−	2.17026i	−0.982134	−	0.188185i
$134$	−13.7327			−1.18633
$135$		0			0
$136$	3.96246			0.339779
$137$	16.2479			1.38815			0.694075	−	0.719902i	$-0.255813\pi$
$137$	16.2479			1.38815			0.694075	+	0.719902i	$0.255813\pi$
$138$		0			0
$139$		−	1.75338i		−	0.148720i	−0.997231	−	0.0743600i	$-0.976309\pi$
$139$		−	1.75338i		−	0.148720i	0.997231	−	0.0743600i	$-0.0236914\pi$
$140$	1.01087	+	1.75444i	0.0854344	+	0.148277i
$141$		0			0
$142$	−11.2414			−0.943357
$143$	−5.05427			−0.422659
$144$		0			0
$145$	2.71333			0.225330
$146$	−9.01653			−0.746213
$147$		0			0
$148$		−	5.83888i		−	0.479953i
$149$	13.3695			1.09527			0.547636	−	0.836716i	$-0.315528\pi$
$149$	13.3695			1.09527			0.547636	+	0.836716i	$0.315528\pi$
$150$		0			0
$151$		−	14.0410i		−	1.14264i	−0.820728	−	0.571320i	$-0.806432\pi$
$151$		−	14.0410i		−	1.14264i	0.820728	−	0.571320i	$-0.193568\pi$
$152$	−2.84800	+	3.29983i	−0.231003	+	0.267652i
$153$		0			0
$154$	−5.40704	−	9.38428i	−0.435712	−	0.756207i
$155$		−	6.44682i		−	0.517821i
$156$		0			0
$157$		−	20.2233i		−	1.61399i	−0.590557	−	0.806996i	$-0.701092\pi$
$157$		−	20.2233i		−	1.61399i	0.590557	−	0.806996i	$-0.298908\pi$
$158$	−6.21470			−0.494415
$159$		0			0
$160$	0.765312			0.0605032
$161$	5.12693	−	2.95404i	0.404059	−	0.232811i
$162$		0			0
$163$	14.1471			1.10809			0.554045	−	0.832487i	$-0.313084\pi$
$163$	14.1471			1.10809			0.554045	+	0.832487i	$0.313084\pi$
$164$	−5.62174			−0.438984
$165$		0			0
$166$	−2.03860			−0.158226
$167$	3.09425			0.239441			0.119720	−	0.992808i	$-0.461800\pi$
$167$	3.09425			0.239441			0.119720	+	0.992808i	$0.461800\pi$
$168$		0			0
$169$	−11.4755			−0.882734
$170$		−	3.03252i		−	0.232584i
$171$		0			0
$172$	−11.3395			−0.864628
$173$	−13.7442			−1.04495			−0.522477	−	0.852653i	$-0.674992\pi$
$173$	−13.7442			−1.04495			−0.522477	+	0.852653i	$0.674992\pi$
$174$		0			0
$175$	−10.1195	+	5.83069i	−0.764966	+	0.440759i
$176$	−4.09356			−0.308564
$177$		0			0
$178$		−	16.3174i		−	1.22304i
$179$			18.6774i			1.39602i	0.716089	+	0.698009i	$0.245930\pi$
$179$			18.6774i			1.39602i	−0.716089	+	0.698009i	$0.754070\pi$
$180$		0			0
$181$	8.23590			0.612169			0.306085	−	0.952004i	$-0.400981\pi$
$181$	8.23590			0.612169			0.306085	+	0.952004i	$0.400981\pi$
$182$	1.63086	+	2.83046i	0.120887	+	0.209807i
$183$		0			0
$184$		−	2.23644i		−	0.164873i
$185$	−4.46857			−0.328536
$186$		0			0
$187$			16.2206i			1.18617i
$188$			10.9149i			0.796051i
$189$		0			0
$190$	2.52540	+	2.17961i	0.183212	+	0.158125i
$191$	−3.13660			−0.226956			−0.113478	−	0.993541i	$-0.536199\pi$
$191$	−3.13660			−0.226956			−0.113478	+	0.993541i	$0.536199\pi$
$192$		0			0
$193$		−	17.3387i		−	1.24807i	−0.781398	−	0.624033i	$-0.785493\pi$
$193$		−	17.3387i		−	1.24807i	0.781398	−	0.624033i	$-0.214507\pi$
$194$		−	1.90563i		−	0.136816i
$195$		0			0
$196$	−3.51063	+	6.05603i	−0.250759	+	0.432573i
$197$	−21.1245			−1.50505			−0.752527	−	0.658561i	$-0.771165\pi$
$197$	−21.1245			−1.50505			−0.752527	+	0.658561i	$0.771165\pi$
$198$		0			0
$199$		−	4.25847i		−	0.301875i	−0.988543	−	0.150937i	$-0.951771\pi$
$199$		−	4.25847i		−	0.301875i	0.988543	−	0.150937i	$-0.0482292\pi$
$200$			4.41430i			0.312138i
$201$		0			0
$202$	−11.8561			−0.834192
$203$	4.68299	+	8.12763i	0.328681	+	0.570448i
$204$		0			0
$205$			4.30238i			0.300492i
$206$		−	0.00772432i		−	0.000538179i
$207$		0			0
$208$	1.23469			0.0856102
$209$	−13.5081	−	11.6585i	−0.934373	−	0.806433i
$210$		0			0
$211$			24.9211i			1.71564i	0.513953	+	0.857818i	$0.328181\pi$
$211$			24.9211i			1.71564i	−0.513953	+	0.857818i	$0.671819\pi$
$212$		−	8.28090i		−	0.568734i
$213$		0			0
$214$	13.2084			0.902907
$215$			8.67825i			0.591852i
$216$		0			0
$217$	19.3111	−	11.1267i	1.31092	−	0.755328i
$218$	5.93963			0.402283
$219$		0			0
$220$			3.13285i			0.211217i
$221$		−	4.89241i		−	0.329099i
$222$		0			0
$223$	−10.6895			−0.715821			−0.357910	−	0.933756i	$-0.616511\pi$
$223$	−10.6895			−0.715821			−0.357910	+	0.933756i	$0.616511\pi$
$224$	1.32086	+	2.29245i	0.0882540	+	0.153171i
$225$		0			0
$226$	4.56747			0.303823
$227$	−18.2992			−1.21456			−0.607280	−	0.794488i	$-0.707739\pi$
$227$	−18.2992			−1.21456			−0.607280	+	0.794488i	$0.707739\pi$
$228$		0			0
$229$			10.3769i			0.685725i	0.939386	+	0.342863i	$0.111397\pi$
$229$			10.3769i			0.685725i	−0.939386	+	0.342863i	$0.888603\pi$
$230$	−1.71158			−0.112858
$231$		0			0
$232$	3.54539			0.232767
$233$	−1.50567			−0.0986397			−0.0493198	−	0.998783i	$-0.515705\pi$
$233$	−1.50567			−0.0986397			−0.0493198	+	0.998783i	$0.515705\pi$
$234$		0			0
$235$	8.35331			0.544910
$236$	6.22487			0.405204
$237$		0			0
$238$	9.08374	−	5.23388i	0.588812	−	0.339262i
$239$	8.59215			0.555780			0.277890	−	0.960613i	$-0.410365\pi$
$239$	8.59215			0.555780			0.277890	+	0.960613i	$0.410365\pi$
$240$		0			0
$241$	−16.4908			−1.06226			−0.531132	−	0.847289i	$-0.678233\pi$
$241$	−16.4908			−1.06226			−0.531132	+	0.847289i	$0.678233\pi$
$242$		−	5.75725i		−	0.370090i
$243$		0			0
$244$			5.64349i			0.361287i
$245$	4.63475	+	2.68673i	0.296103	+	0.171649i
$246$		0			0
$247$	4.07426	+	3.51639i	0.259239	+	0.223743i
$248$		−	8.42378i		−	0.534910i
$249$		0			0
$250$	7.20488			0.455676
$251$		−	1.47028i		−	0.0928031i	−0.998923	−	0.0464016i	$-0.985225\pi$
$251$		−	1.47028i		−	0.0928031i	0.998923	−	0.0464016i	$-0.0147754\pi$
$252$		0			0
$253$	9.15502			0.575571
$254$	−2.92024			−0.183232
$255$		0			0
$256$	1.00000			0.0625000
$257$	19.2597			1.20139			0.600693	−	0.799480i	$-0.294891\pi$
$257$	19.2597			1.20139			0.600693	+	0.799480i	$0.294891\pi$
$258$		0			0
$259$	−7.71237	−	13.3853i	−0.479224	−	0.831724i
$260$		−	0.944922i		−	0.0586016i
$261$		0			0
$262$	−10.9795			−0.678313
$263$	−2.32602			−0.143429			−0.0717144	−	0.997425i	$-0.522847\pi$
$263$	−2.32602			−0.143429			−0.0717144	+	0.997425i	$0.522847\pi$
$264$		0			0
$265$	−6.33747			−0.389308
$266$	−2.17026	+	11.3265i	−0.133067	+	0.694473i
$267$		0			0
$268$			13.7327i			0.838860i
$269$	26.1715			1.59571			0.797854	−	0.602851i	$-0.205969\pi$
$269$	26.1715			1.59571			0.797854	+	0.602851i	$0.205969\pi$
$270$		0			0
$271$		−	24.5470i		−	1.49113i	−0.666436	−	0.745563i	$-0.732181\pi$
$271$		−	24.5470i		−	1.49113i	0.666436	−	0.745563i	$-0.267819\pi$
$272$		−	3.96246i		−	0.240260i
$273$		0			0
$274$		−	16.2479i		−	0.981571i
$275$	−18.0702			−1.08967
$276$		0			0
$277$	−24.5064			−1.47244			−0.736222	−	0.676740i	$-0.763392\pi$
$277$	−24.5064			−1.47244			−0.736222	+	0.676740i	$0.763392\pi$
$278$	−1.75338			−0.105161
$279$		0			0
$280$	1.75444	−	1.01087i	0.104848	−	0.0604113i
$281$			0.686453i			0.0409503i	0.999790	+	0.0204752i	$0.00651790\pi$
$281$			0.686453i			0.0409503i	−0.999790	+	0.0204752i	$0.993482\pi$
$282$		0			0
$283$		−	20.7294i		−	1.23224i	−0.787654	−	0.616118i	$-0.788705\pi$
$283$		−	20.7294i		−	1.23224i	0.787654	−	0.616118i	$-0.211295\pi$
$284$			11.2414i			0.667054i
$285$		0			0
$286$			5.05427i			0.298865i
$287$	−12.8875	+	7.42556i	−0.760727	+	0.438317i
$288$		0			0
$289$	1.29887			0.0764043
$290$		−	2.71333i		−	0.159332i
$291$		0			0
$292$			9.01653i			0.527652i
$293$	−2.43374			−0.142181			−0.0710903	−	0.997470i	$-0.522648\pi$
$293$	−2.43374			−0.142181			−0.0710903	+	0.997470i	$0.522648\pi$
$294$		0			0
$295$		−	4.76397i		−	0.277369i
$296$	−5.83888			−0.339378
$297$		0			0
$298$		−	13.3695i		−	0.774475i
$299$	−2.76131			−0.159691
$300$		0			0
$301$	−25.9952	+	14.9779i	−1.49834	+	0.863313i
$302$	−14.0410			−0.807968
$303$		0			0
$304$	3.29983	+	2.84800i	0.189258	+	0.163344i
$305$	4.31903			0.247307
$306$		0			0
$307$	16.1689			0.922807			0.461404	−	0.887190i	$-0.347346\pi$
$307$	16.1689			0.922807			0.461404	+	0.887190i	$0.347346\pi$
$308$	−9.38428	+	5.40704i	−0.534719	+	0.308095i
$309$		0			0
$310$	−6.44682			−0.366155
$311$			32.0665i			1.81832i	0.416445	+	0.909161i	$0.363276\pi$
$311$			32.0665i			1.81832i	−0.416445	+	0.909161i	$0.636724\pi$
$312$		0			0
$313$			27.1690i			1.53568i	0.640641	+	0.767841i	$0.278669\pi$
$313$			27.1690i			1.53568i	−0.640641	+	0.767841i	$0.721331\pi$
$314$	−20.2233			−1.14126
$315$		0			0
$316$			6.21470i			0.349604i
$317$		−	23.6041i		−	1.32574i	−0.748736	−	0.662869i	$-0.769339\pi$
$317$		−	23.6041i		−	1.32574i	0.748736	−	0.662869i	$-0.230661\pi$
$318$		0			0
$319$			14.5133i			0.812588i
$320$		−	0.765312i		−	0.0427823i
$321$		0			0
$322$	−2.95404	−	5.12693i	−0.164622	−	0.285713i
$323$	11.2851	−	13.0755i	0.627920	−	0.727539i
$324$		0			0
$325$	5.45028			0.302327
$326$		−	14.1471i		−	0.783538i
$327$		0			0
$328$			5.62174i			0.310409i
$329$	14.4171	+	25.0218i	0.794841	+	1.37950i
$330$		0			0
$331$			0.995116i			0.0546965i	0.999626	+	0.0273483i	$0.00870631\pi$
$331$			0.995116i			0.0546965i	−0.999626	+	0.0273483i	$0.991294\pi$
$332$			2.03860i			0.111883i
$333$		0			0
$334$		−	3.09425i		−	0.169310i
$335$	10.5098			0.574213
$336$		0			0
$337$			27.5073i			1.49842i	0.662335	+	0.749208i	$0.269566\pi$
$337$			27.5073i			1.49842i	−0.662335	+	0.749208i	$0.730434\pi$
$338$			11.4755i			0.624187i
$339$		0			0
$340$	−3.03252			−0.164462
$341$	34.4833			1.86737
$342$		0			0
$343$	−0.0487486	+	18.5202i	−0.00263218	+	0.999997i
$344$			11.3395i			0.611384i
$345$		0			0
$346$			13.7442i			0.738895i
$347$	−7.19341			−0.386162			−0.193081	−	0.981183i	$-0.561848\pi$
$347$	−7.19341			−0.386162			−0.193081	+	0.981183i	$0.561848\pi$
$348$		0			0
$349$		−	36.0586i		−	1.93017i	−0.261932	−	0.965086i	$-0.584360\pi$
$349$		−	36.0586i		−	1.93017i	0.261932	−	0.965086i	$-0.415640\pi$
$350$	5.83069	+	10.1195i	0.311663	+	0.540912i
$351$		0			0
$352$			4.09356i			0.218188i
$353$		−	6.51821i		−	0.346930i	−0.984840	−	0.173465i	$-0.944504\pi$
$353$		−	6.51821i		−	0.346930i	0.984840	−	0.173465i	$-0.0554963\pi$
$354$		0			0
$355$	8.60318			0.456609
$356$	−16.3174			−0.864821
$357$		0			0
$358$	18.6774			0.987133
$359$	−31.9680			−1.68721			−0.843604	−	0.536966i	$-0.819570\pi$
$359$	−31.9680			−1.68721			−0.843604	+	0.536966i	$0.819570\pi$
$360$		0			0
$361$	2.77779	+	18.7958i	0.146199	+	0.989255i
$362$		−	8.23590i		−	0.432869i
$363$		0			0
$364$	2.83046	−	1.63086i	0.148356	−	0.0854801i
$365$	6.90046			0.361186
$366$		0			0
$367$			24.2110i			1.26380i	0.775049	+	0.631901i	$0.217725\pi$
$367$			24.2110i			1.26380i	−0.775049	+	0.631901i	$0.782275\pi$
$368$	−2.23644			−0.116583
$369$		0			0
$370$			4.46857i			0.232310i
$371$	−10.9379	−	18.9835i	−0.567870	−	0.985575i
$372$		0			0
$373$		−	7.25956i		−	0.375886i	−0.982180	−	0.187943i	$-0.939818\pi$
$373$		−	7.25956i		−	0.375886i	0.982180	−	0.187943i	$-0.0601820\pi$
$374$	16.2206			0.838747
$375$		0			0
$376$	10.9149			0.562893
$377$		−	4.37745i		−	0.225450i
$378$		0			0
$379$			17.8834i			0.918608i	0.888279	+	0.459304i	$0.151901\pi$
$379$			17.8834i			0.918608i	−0.888279	+	0.459304i	$0.848099\pi$
$380$	2.17961	−	2.52540i	0.111812	−	0.129550i
$381$		0			0
$382$			3.13660i			0.160482i
$383$	5.90529			0.301746			0.150873	−	0.988553i	$-0.451791\pi$
$383$	5.90529			0.301746			0.150873	+	0.988553i	$0.451791\pi$
$384$		0			0
$385$	4.13808	+	7.18190i	0.210896	+	0.366024i
$386$	−17.3387			−0.882515
$387$		0			0
$388$	−1.90563			−0.0967437
$389$	26.0156			1.31904			0.659521	−	0.751686i	$-0.270759\pi$
$389$	26.0156			1.31904			0.659521	+	0.751686i	$0.270759\pi$
$390$		0			0
$391$			8.86183i			0.448162i
$392$	6.05603	+	3.51063i	0.305876	+	0.177314i
$393$		0			0
$394$			21.1245i			1.06423i
$395$	4.75618			0.239310
$396$		0			0
$397$		−	20.3829i		−	1.02299i	−0.859286	−	0.511495i	$-0.829092\pi$
$397$		−	20.3829i		−	1.02299i	0.859286	−	0.511495i	$-0.170908\pi$
$398$	−4.25847			−0.213458
$399$		0			0
$400$	4.41430			0.220715
$401$		−	6.26305i		−	0.312762i	−0.987697	−	0.156381i	$-0.950017\pi$
$401$		−	6.26305i		−	0.312762i	0.987697	−	0.156381i	$-0.0499827\pi$
$402$		0			0
$403$	−10.4007			−0.518098
$404$			11.8561i			0.589863i
$405$		0			0
$406$	8.12763	−	4.68299i	0.403368	−	0.232413i
$407$		−	23.9018i		−	1.18477i
$408$		0			0
$409$	9.08055			0.449004			0.224502	−	0.974474i	$-0.427924\pi$
$409$	9.08055			0.449004			0.224502	+	0.974474i	$0.427924\pi$
$410$	4.30238			0.212480
$411$		0			0
$412$	−0.00772432			−0.000380550
$413$	14.2702	−	8.22221i	0.702190	−	0.404589i
$414$		0			0
$415$	1.56016			0.0765854
$416$		−	1.23469i		−	0.0605355i
$417$		0			0
$418$	−11.6585	+	13.5081i	−0.570234	+	0.660701i
$419$		−	20.3578i		−	0.994544i	−0.867595	−	0.497272i	$-0.834335\pi$
$419$		−	20.3578i		−	0.994544i	0.867595	−	0.497272i	$-0.165665\pi$
$420$		0			0
$421$			14.6067i			0.711888i	0.934507	+	0.355944i	$0.115841\pi$
$421$			14.6067i			0.711888i	−0.934507	+	0.355944i	$0.884159\pi$
$422$	24.9211			1.21314
$423$		0			0
$424$	−8.28090			−0.402156
$425$		−	17.4915i		−	0.848462i
$426$		0			0
$427$	7.45428	+	12.9374i	0.360738	+	0.626084i
$428$		−	13.2084i		−	0.638452i
$429$		0			0
$430$	8.67825			0.418502
$431$			1.86831i			0.0899933i	0.998987	+	0.0449966i	$0.0143277\pi$
$431$			1.86831i			0.0899933i	−0.998987	+	0.0449966i	$0.985672\pi$
$432$		0			0
$433$	−31.0009			−1.48981			−0.744903	−	0.667172i	$-0.767504\pi$
$433$	−31.0009			−1.48981			−0.744903	+	0.667172i	$0.767504\pi$
$434$	−11.1267	−	19.3111i	−0.534097	−	0.926961i
$435$		0			0
$436$		−	5.93963i		−	0.284457i
$437$	−7.37989	−	6.36939i	−0.353028	−	0.304689i
$438$		0			0
$439$	26.8712			1.28249			0.641246	−	0.767336i	$-0.278418\pi$
$439$	26.8712			1.28249			0.641246	+	0.767336i	$0.278418\pi$
$440$	3.13285			0.149353
$441$		0			0
$442$	−4.89241			−0.232708
$443$	8.07575			0.383690			0.191845	−	0.981425i	$-0.438553\pi$
$443$	8.07575			0.383690			0.191845	+	0.981425i	$0.438553\pi$
$444$		0			0
$445$			12.4879i			0.591984i
$446$			10.6895i			0.506162i
$447$		0			0
$448$	2.29245	−	1.32086i	0.108308	−	0.0624050i
$449$		−	7.13077i		−	0.336522i	−0.985742	−	0.168261i	$-0.946185\pi$
$449$		−	7.13077i		−	0.336522i	0.985742	−	0.168261i	$-0.0538151\pi$
$450$		0			0
$451$	−23.0129			−1.08364
$452$		−	4.56747i		−	0.214836i
$453$		0			0
$454$			18.2992i			0.858823i
$455$	−1.24811	−	2.16618i	−0.0585125	−	0.101552i
$456$		0			0
$457$	−4.94992			−0.231547			−0.115774	−	0.993276i	$-0.536935\pi$
$457$	−4.94992			−0.231547			−0.115774	+	0.993276i	$0.536935\pi$
$458$	10.3769			0.484881
$459$		0			0
$460$			1.71158i			0.0798027i
$461$			12.3884i			0.576983i	0.957482	+	0.288492i	$0.0931537\pi$
$461$			12.3884i			0.576983i	−0.957482	+	0.288492i	$0.906846\pi$
$462$		0			0
$463$	0.203161			0.00944167			0.00472084	−	0.999989i	$-0.498497\pi$
$463$	0.203161			0.00944167			0.00472084	+	0.999989i	$0.498497\pi$
$464$		−	3.54539i		−	0.164591i
$465$		0			0
$466$			1.50567i			0.0697488i
$467$			39.7312i			1.83854i	0.393629	+	0.919269i	$0.371220\pi$
$467$			39.7312i			1.83854i	−0.393629	+	0.919269i	$0.628780\pi$
$468$		0			0
$469$	18.1391	+	31.4816i	0.837585	+	1.45368i
$470$		−	8.35331i		−	0.385309i
$471$		0			0
$472$		−	6.22487i		−	0.286523i
$473$	−46.4189			−2.13434
$474$		0			0
$475$	14.5664	+	12.5719i	0.668354	+	0.576839i
$476$	−5.23388	−	9.08374i	−0.239895	−	0.416353i
$477$		0			0
$478$		−	8.59215i		−	0.392996i
$479$		−	42.8715i		−	1.95885i	−0.201813	−	0.979424i	$-0.564683\pi$
$479$		−	42.8715i		−	1.95885i	0.201813	−	0.979424i	$-0.435317\pi$
$480$		0			0
$481$			7.20920i			0.328711i
$482$			16.4908i			0.751135i
$483$		0			0
$484$	−5.75725			−0.261693
$485$			1.45840i			0.0662226i
$486$		0			0
$487$		−	25.8373i		−	1.17080i	−0.810744	−	0.585400i	$-0.800937\pi$
$487$		−	25.8373i		−	1.17080i	0.810744	−	0.585400i	$-0.199063\pi$
$488$	5.64349			0.255469
$489$		0			0
$490$	2.68673	−	4.63475i	0.121374	−	0.209377i
$491$	0.388503			0.0175329			0.00876645	−	0.999962i	$-0.497210\pi$
$491$	0.388503			0.0175329			0.00876645	+	0.999962i	$0.497210\pi$
$492$		0			0
$493$	−14.0485			−0.632713
$494$	3.51639	−	4.07426i	0.158210	−	0.183310i
$495$		0			0
$496$	−8.42378			−0.378239
$497$	14.8484	+	25.7703i	0.666040	+	1.15596i
$498$		0			0
$499$	3.56308			0.159505			0.0797527	−	0.996815i	$-0.474587\pi$
$499$	3.56308			0.159505			0.0797527	+	0.996815i	$0.474587\pi$
$500$		−	7.20488i		−	0.322212i
$501$		0			0
$502$	−1.47028			−0.0656217
$503$		−	8.38590i		−	0.373909i	−0.982369	−	0.186954i	$-0.940138\pi$
$503$		−	8.38590i		−	0.373909i	0.982369	−	0.186954i	$-0.0598617\pi$
$504$		0			0
$505$	9.07362			0.403771
$506$		−	9.15502i		−	0.406990i
$507$		0			0
$508$			2.92024i			0.129565i
$509$	27.1248			1.20229			0.601143	−	0.799141i	$-0.294712\pi$
$509$	27.1248			1.20229			0.601143	+	0.799141i	$0.294712\pi$
$510$		0			0
$511$	11.9096	+	20.6699i	0.526850	+	0.914383i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$		−	19.2597i		−	0.849508i
$515$			0.00591152i			0.000260493i
$516$		0			0
$517$			44.6808i			1.96506i
$518$	−13.3853	+	7.71237i	−0.588118	+	0.338862i
$519$		0			0
$520$	−0.944922			−0.0414376
$521$	−6.02707			−0.264051			−0.132025	−	0.991246i	$-0.542148\pi$
$521$	−6.02707			−0.264051			−0.132025	+	0.991246i	$0.542148\pi$
$522$		0			0
$523$	18.5396			0.810681			0.405341	−	0.914166i	$-0.367153\pi$
$523$	18.5396			0.810681			0.405341	+	0.914166i	$0.367153\pi$
$524$			10.9795i			0.479640i
$525$		0			0
$526$			2.32602i			0.101420i
$527$			33.3789i			1.45401i
$528$		0			0
$529$	−17.9983			−0.782536
$530$			6.33747i			0.275282i
$531$		0			0
$532$	11.3265	+	2.17026i	0.491067	+	0.0940926i
$533$	6.94109			0.300652
$534$		0			0
$535$	−10.1085			−0.437030
$536$	13.7327			0.593164
$537$		0			0
$538$		−	26.1715i		−	1.12834i
$539$	−14.3710	+	24.7907i	−0.619002	+	1.06781i
$540$		0			0
$541$	−13.8956			−0.597421			−0.298710	−	0.954344i	$-0.596556\pi$
$541$	−13.8956			−0.597421			−0.298710	+	0.954344i	$0.596556\pi$
$542$	−24.5470			−1.05438
$543$		0			0
$544$	−3.96246			−0.169889
$545$	−4.54567			−0.194715
$546$		0			0
$547$			16.6550i			0.712118i	0.934463	+	0.356059i	$0.115880\pi$
$547$			16.6550i			0.712118i	−0.934463	+	0.356059i	$0.884120\pi$
$548$	−16.2479			−0.694075
$549$		0			0
$550$			18.0702i			0.770516i
$551$	10.0973	−	11.6992i	0.430159	−	0.498403i
$552$		0			0
$553$	8.20877	+	14.2469i	0.349073	+	0.605838i
$554$			24.5064i			1.04118i
$555$		0			0
$556$			1.75338i			0.0743600i
$557$	34.7999			1.47452			0.737259	−	0.675610i	$-0.236120\pi$
$557$	34.7999			1.47452			0.737259	+	0.675610i	$0.236120\pi$
$558$		0			0
$559$	14.0007			0.592168
$560$	−1.01087	−	1.75444i	−0.0427172	−	0.0741385i
$561$		0			0
$562$	0.686453			0.0289563
$563$	7.55182			0.318271			0.159136	−	0.987257i	$-0.449129\pi$
$563$	7.55182			0.318271			0.159136	+	0.987257i	$0.449129\pi$
$564$		0			0
$565$	−3.49554			−0.147058
$566$	−20.7294			−0.871322
$567$		0			0
$568$	11.2414			0.471678
$569$			26.5621i			1.11354i	0.830666	+	0.556770i	$0.187960\pi$
$569$			26.5621i			1.11354i	−0.830666	+	0.556770i	$0.812040\pi$
$570$		0			0
$571$	−8.69844			−0.364018			−0.182009	−	0.983297i	$-0.558260\pi$
$571$	−8.69844			−0.364018			−0.182009	+	0.983297i	$0.558260\pi$
$572$	5.05427			0.211330
$573$		0			0
$574$	7.42556	+	12.8875i	0.309937	+	0.537915i
$575$	−9.87233			−0.411704
$576$		0			0
$577$		−	27.5019i		−	1.14492i	−0.819933	−	0.572460i	$-0.805989\pi$
$577$		−	27.5019i		−	1.14492i	0.819933	−	0.572460i	$-0.194011\pi$
$578$		−	1.29887i		−	0.0540260i
$579$		0			0
$580$	−2.71333			−0.112665
$581$	2.69271	+	4.67338i	0.111713	+	0.193884i
$582$		0			0
$583$		−	33.8984i		−	1.40393i
$584$	9.01653			0.373106
$585$		0			0
$586$			2.43374i			0.100537i
$587$		−	0.132209i		−	0.00545686i	−0.999996	−	0.00272843i	$-0.999132\pi$
$587$		−	0.132209i		−	0.00545686i	0.999996	−	0.00272843i	$-0.000868488\pi$
$588$		0			0
$589$	−27.7971	−	23.9909i	−1.14536	−	0.988529i
$590$	−4.76397			−0.196129
$591$		0			0
$592$			5.83888i			0.239977i
$593$		−	9.08659i		−	0.373142i	−0.982442	−	0.186571i	$-0.940263\pi$
$593$		−	9.08659i		−	0.373142i	0.982442	−	0.186571i	$-0.0597374\pi$
$594$		0			0
$595$	−6.95190	+	4.00555i	−0.285000	+	0.164212i
$596$	−13.3695			−0.547636
$597$		0			0
$598$			2.76131i			0.112918i
$599$			1.77247i			0.0724213i	0.999344	+	0.0362106i	$0.0115287\pi$
$599$			1.77247i			0.0724213i	−0.999344	+	0.0362106i	$0.988471\pi$
$600$		0			0
$601$	4.71929			0.192504			0.0962520	−	0.995357i	$-0.469315\pi$
$601$	4.71929			0.192504			0.0962520	+	0.995357i	$0.469315\pi$
$602$	14.9779	+	25.9952i	0.610455	+	1.05948i
$603$		0			0
$604$			14.0410i			0.571320i
$605$			4.40609i			0.179133i
$606$		0			0
$607$	40.5330			1.64519			0.822593	−	0.568631i	$-0.192527\pi$
$607$	40.5330			1.64519			0.822593	+	0.568631i	$0.192527\pi$
$608$	2.84800	−	3.29983i	0.115502	−	0.133826i
$609$		0			0
$610$		−	4.31903i		−	0.174872i
$611$		−	13.4765i		−	0.545201i
$612$		0			0
$613$	4.97167			0.200804			0.100402	−	0.994947i	$-0.467987\pi$
$613$	4.97167			0.200804			0.100402	+	0.994947i	$0.467987\pi$
$614$		−	16.1689i		−	0.652523i
$615$		0			0
$616$	5.40704	+	9.38428i	0.217856	+	0.378103i
$617$	−11.0803			−0.446078			−0.223039	−	0.974810i	$-0.571598\pi$
$617$	−11.0803			−0.446078			−0.223039	+	0.974810i	$0.571598\pi$
$618$		0			0
$619$		−	36.7817i		−	1.47838i	−0.673497	−	0.739190i	$-0.735209\pi$
$619$		−	36.7817i		−	1.47838i	0.673497	−	0.739190i	$-0.264791\pi$
$620$			6.44682i			0.258911i
$621$		0			0
$622$	32.0665			1.28575
$623$	−37.4068	+	21.5531i	−1.49867	+	0.863507i
$624$		0			0
$625$	16.5575			0.662300
$626$	27.1690			1.08589
$627$		0			0
$628$			20.2233i			0.806996i
$629$	23.1364			0.922507
$630$		0			0
$631$	1.31188			0.0522251			0.0261126	−	0.999659i	$-0.491687\pi$
$631$	1.31188			0.0522251			0.0261126	+	0.999659i	$0.491687\pi$
$632$	6.21470			0.247207
$633$		0			0
$634$	−23.6041			−0.937438
$635$	2.23489			0.0886891
$636$		0			0
$637$	4.33453	−	7.47730i	0.171741	−	0.296261i
$638$	14.5133			0.574587
$639$		0			0
$640$	−0.765312			−0.0302516
$641$			31.5076i			1.24447i	0.782829	+	0.622237i	$0.213776\pi$
$641$			31.5076i			1.24447i	−0.782829	+	0.622237i	$0.786224\pi$
$642$		0			0
$643$		−	27.6317i		−	1.08969i	−0.838538	−	0.544844i	$-0.816589\pi$
$643$		−	27.6317i		−	1.08969i	0.838538	−	0.544844i	$-0.183411\pi$
$644$	−5.12693	+	2.95404i	−0.202029	+	0.116405i
$645$		0			0
$646$	−13.0755	−	11.2851i	−0.514448	−	0.444006i
$647$		−	2.13843i		−	0.0840705i	−0.999116	−	0.0420353i	$-0.986616\pi$
$647$		−	2.13843i		−	0.0840705i	0.999116	−	0.0420353i	$-0.0133842\pi$
$648$		0			0
$649$	25.4819			1.00025
$650$		−	5.45028i		−	0.213778i
$651$		0			0
$652$	−14.1471			−0.554045
$653$	−22.8181			−0.892942			−0.446471	−	0.894798i	$-0.647319\pi$
$653$	−22.8181			−0.892942			−0.446471	+	0.894798i	$0.647319\pi$
$654$		0			0
$655$	8.40271			0.328321
$656$	5.62174			0.219492
$657$		0			0
$658$	25.0218	−	14.4171i	0.975453	−	0.562037i
$659$			14.4903i			0.564463i	0.959346	+	0.282231i	$0.0910746\pi$
$659$			14.4903i			0.564463i	−0.959346	+	0.282231i	$0.908925\pi$
$660$		0			0
$661$	−12.7242			−0.494915			−0.247458	−	0.968899i	$-0.579595\pi$
$661$	−12.7242			−0.494915			−0.247458	+	0.968899i	$0.579595\pi$
$662$	0.995116			0.0386763
$663$		0			0
$664$	2.03860			0.0791130
$665$	1.66093	−	8.66832i	0.0644079	−	0.336143i
$666$		0			0
$667$			7.92907i			0.307015i
$668$	−3.09425			−0.119720
$669$		0			0
$670$		−	10.5098i		−	0.406030i
$671$			23.1020i			0.891841i
$672$		0			0
$673$		−	31.9711i		−	1.23239i	−0.787592	−	0.616197i	$-0.788672\pi$
$673$		−	31.9711i		−	1.23239i	0.787592	−	0.616197i	$-0.211328\pi$
$674$	27.5073			1.05954
$675$		0			0
$676$	11.4755			0.441367
$677$	1.23340			0.0474035			0.0237018	−	0.999719i	$-0.492455\pi$
$677$	1.23340			0.0474035			0.0237018	+	0.999719i	$0.492455\pi$
$678$		0			0
$679$	−4.36856	+	2.51708i	−0.167650	+	0.0965967i
$680$			3.03252i			0.116292i
$681$		0			0
$682$		−	34.4833i		−	1.32043i
$683$		−	15.2483i		−	0.583460i	−0.956501	−	0.291730i	$-0.905769\pi$
$683$		−	15.2483i		−	0.583460i	0.956501	−	0.291730i	$-0.0942308\pi$
$684$		0			0
$685$			12.4347i			0.475106i
$686$	18.5202	+	0.0487486i	0.707104	+	0.00186123i
$687$		0			0
$688$	11.3395			0.432314
$689$			10.2243i			0.389516i
$690$		0			0
$691$			40.6678i			1.54708i	0.633750	+	0.773538i	$0.281515\pi$
$691$			40.6678i			1.54708i	−0.633750	+	0.773538i	$0.718485\pi$
$692$	13.7442			0.522477
$693$		0			0
$694$			7.19341i			0.273058i
$695$	1.34189			0.0509006
$696$		0			0
$697$		−	22.2759i		−	0.843761i
$698$	−36.0586			−1.36484
$699$		0			0
$700$	10.1195	−	5.83069i	0.382483	−	0.220379i
$701$	10.6740			0.403151			0.201576	−	0.979473i	$-0.435394\pi$
$701$	10.6740			0.403151			0.201576	+	0.979473i	$0.435394\pi$
$702$		0			0
$703$	−16.6291	+	19.2673i	−0.627180	+	0.726681i
$704$	4.09356			0.154282
$705$		0			0
$706$	−6.51821			−0.245316
$707$	15.6603	+	27.1795i	0.588966	+	1.02219i
$708$		0			0
$709$	35.0499			1.31633			0.658163	−	0.752876i	$-0.271334\pi$
$709$	35.0499			1.31633			0.658163	+	0.752876i	$0.271334\pi$
$710$		−	8.60318i		−	0.322871i
$711$		0			0
$712$			16.3174i			0.611521i
$713$	18.8393			0.705537
$714$		0			0
$715$		−	3.86810i		−	0.144659i
$716$		−	18.6774i		−	0.698009i
$717$		0			0
$718$			31.9680i			1.19304i
$719$			17.5697i			0.655240i	0.944810	+	0.327620i	$0.106247\pi$
$719$			17.5697i			0.655240i	−0.944810	+	0.327620i	$0.893753\pi$
$720$		0			0
$721$	−0.0177076	+	0.0102028i	−0.000659466	+	0.000379972i
$722$	18.7958	−	2.77779i	0.699509	−	0.103379i
$723$		0			0
$724$	−8.23590			−0.306085
$725$		−	15.6504i		−	0.581242i
$726$		0			0
$727$		−	4.00613i		−	0.148579i	−0.997237	−	0.0742896i	$-0.976331\pi$
$727$		−	4.00613i		−	0.148579i	0.997237	−	0.0742896i	$-0.0236689\pi$
$728$	−1.63086	−	2.83046i	−0.0604435	−	0.104904i
$729$		0			0
$730$		−	6.90046i		−	0.255397i
$731$		−	44.9323i		−	1.66188i
$732$		0			0
$733$		−	17.6070i		−	0.650328i	−0.945658	−	0.325164i	$-0.894580\pi$
$733$		−	17.6070i		−	0.650328i	0.945658	−	0.325164i	$-0.105420\pi$
$734$	24.2110			0.893643
$735$		0			0
$736$			2.23644i			0.0824364i
$737$			56.2158i			2.07073i
$738$		0			0
$739$	−25.3500			−0.932514			−0.466257	−	0.884649i	$-0.654398\pi$
$739$	−25.3500			−0.932514			−0.466257	+	0.884649i	$0.654398\pi$
$740$	4.46857			0.164268
$741$		0			0
$742$	−18.9835	+	10.9379i	−0.696907	+	0.401545i
$743$			1.29589i			0.0475416i	0.999717	+	0.0237708i	$0.00756719\pi$
$743$			1.29589i			0.0475416i	−0.999717	+	0.0237708i	$0.992433\pi$
$744$		0			0
$745$			10.2318i			0.374866i
$746$	−7.25956			−0.265792
$747$		0			0
$748$		−	16.2206i		−	0.593084i
$749$	−17.4465	−	30.2795i	−0.637481	−	1.10639i
$750$		0			0
$751$			4.84765i			0.176893i	0.996081	+	0.0884466i	$0.0281903\pi$
$751$			4.84765i			0.176893i	−0.996081	+	0.0884466i	$0.971810\pi$
$752$		−	10.9149i		−	0.398025i
$753$		0			0
$754$	−4.37745			−0.159418
$755$	10.7457			0.391077
$756$		0			0
$757$	14.6530			0.532572			0.266286	−	0.963894i	$-0.414203\pi$
$757$	14.6530			0.532572			0.266286	+	0.963894i	$0.414203\pi$
$758$	17.8834			0.649554
$759$		0			0
$760$	−2.52540	−	2.17961i	−0.0916060	−	0.0790627i
$761$		−	33.0860i		−	1.19937i	−0.800237	−	0.599684i	$-0.795293\pi$
$761$		−	33.0860i		−	1.19937i	0.800237	−	0.599684i	$-0.204707\pi$
$762$		0			0
$763$	−7.84545	−	13.6163i	−0.284024	−	0.492943i
$764$	3.13660			0.113478
$765$		0			0
$766$		−	5.90529i		−	0.213367i
$767$	−7.68577			−0.277517
$768$		0			0
$769$		−	11.2141i		−	0.404391i	−0.979345	−	0.202195i	$-0.935192\pi$
$769$		−	11.2141i		−	0.404391i	0.979345	−	0.202195i	$-0.0648076\pi$
$770$	7.18190	−	4.13808i	0.258818	−	0.149126i
$771$		0			0
$772$			17.3387i			0.624033i
$773$	−45.7715			−1.64629			−0.823144	−	0.567833i	$-0.807782\pi$
$773$	−45.7715			−1.64629			−0.823144	+	0.567833i	$0.807782\pi$
$774$		0			0
$775$	−37.1851			−1.33573
$776$			1.90563i			0.0684081i
$777$		0			0
$778$		−	26.0156i		−	0.932703i
$779$	18.5508	+	16.0107i	0.664651	+	0.573643i
$780$		0			0
$781$			46.0173i			1.64663i
$782$	8.86183			0.316898
$783$		0			0
$784$	3.51063	−	6.05603i	0.125380	−	0.216287i
$785$	15.4771			0.552402
$786$		0			0
$787$	13.9600			0.497621			0.248810	−	0.968552i	$-0.419960\pi$
$787$	13.9600			0.497621			0.248810	+	0.968552i	$0.419960\pi$
$788$	21.1245			0.752527
$789$		0			0
$790$		−	4.75618i		−	0.169217i
$791$	−6.03301	−	10.4707i	−0.214509	−	0.372294i
$792$		0			0
$793$		−	6.96794i		−	0.247439i
$794$	−20.3829			−0.723363
$795$		0			0
$796$			4.25847i			0.150937i
$797$	−13.9410			−0.493815			−0.246907	−	0.969039i	$-0.579414\pi$
$797$	−13.9410			−0.493815			−0.246907	+	0.969039i	$0.579414\pi$
$798$		0			0
$799$	−43.2499			−1.53007
$800$		−	4.41430i		−	0.156069i
$801$		0			0
$802$	−6.26305			−0.221156
$803$			36.9097i			1.30252i
$804$		0			0
$805$	2.26076	+	3.92370i	0.0796814	+	0.138292i
$806$			10.4007i			0.366350i
$807$		0			0
$808$	11.8561			0.417096
$809$	−6.97307			−0.245160			−0.122580	−	0.992459i	$-0.539117\pi$
$809$	−6.97307			−0.245160			−0.122580	+	0.992459i	$0.539117\pi$
$810$		0			0
$811$	8.17371			0.287018			0.143509	−	0.989649i	$-0.454161\pi$
$811$	8.17371			0.287018			0.143509	+	0.989649i	$0.454161\pi$
$812$	−4.68299	−	8.12763i	−0.164341	−	0.285224i
$813$		0			0
$814$	−23.9018			−0.837759
$815$			10.8270i			0.379253i
$816$		0			0
$817$	37.4184	+	32.2949i	1.30910	+	1.12985i
$818$		−	9.08055i		−	0.317494i
$819$		0			0
$820$		−	4.30238i		−	0.150246i
$821$	−16.3649			−0.571138			−0.285569	−	0.958358i	$-0.592183\pi$
$821$	−16.3649			−0.571138			−0.285569	+	0.958358i	$0.592183\pi$
$822$		0			0
$823$	27.7362			0.966822			0.483411	−	0.875394i	$-0.339398\pi$
$823$	27.7362			0.966822			0.483411	+	0.875394i	$0.339398\pi$
$824$			0.00772432i			0.000269090i
$825$		0			0
$826$	−8.22221	−	14.2702i	−0.286087	−	0.496523i
$827$			46.1901i			1.60619i	0.595852	+	0.803094i	$0.296814\pi$
$827$			46.1901i			1.60619i	−0.595852	+	0.803094i	$0.703186\pi$
$828$		0			0
$829$	5.51500			0.191544			0.0957719	−	0.995403i	$-0.469468\pi$
$829$	5.51500			0.191544			0.0957719	+	0.995403i	$0.469468\pi$
$830$		−	1.56016i		−	0.0541541i
$831$		0			0
$832$	−1.23469			−0.0428051
$833$	−23.9968	−	13.9108i	−0.831440	−	0.481979i
$834$		0			0
$835$			2.36807i			0.0819505i
$836$	13.5081	+	11.6585i	0.467186	+	0.403216i
$837$		0			0
$838$	−20.3578			−0.703249
$839$	−31.9140			−1.10179			−0.550896	−	0.834574i	$-0.685714\pi$
$839$	−31.9140			−1.10179			−0.550896	+	0.834574i	$0.685714\pi$
$840$		0			0
$841$	16.4302			0.566558
$842$	14.6067			0.503380
$843$		0			0
$844$		−	24.9211i		−	0.857818i
$845$		−	8.78238i		−	0.302123i
$846$		0			0
$847$	−13.1982	+	7.60455i	−0.453495	+	0.261295i
$848$			8.28090i			0.284367i
$849$		0			0
$850$	−17.4915			−0.599953
$851$		−	13.0583i		−	0.447634i
$852$		0			0
$853$		−	21.6794i		−	0.742289i	−0.928575	−	0.371145i	$-0.878965\pi$
$853$		−	21.6794i		−	0.742289i	0.928575	−	0.371145i	$-0.121035\pi$
$854$	12.9374	−	7.45428i	0.442709	−	0.255080i
$855$		0			0
$856$	−13.2084			−0.451453
$857$	−39.9212			−1.36368			−0.681841	−	0.731501i	$-0.738820\pi$
$857$	−39.9212			−1.36368			−0.681841	+	0.731501i	$0.738820\pi$
$858$		0			0
$859$		−	4.68934i		−	0.159998i	−0.996795	−	0.0799991i	$-0.974508\pi$
$859$		−	4.68934i		−	0.159998i	0.996795	−	0.0799991i	$-0.0254918\pi$
$860$		−	8.67825i		−	0.295926i
$861$		0			0
$862$	1.86831			0.0636349
$863$		−	44.3151i		−	1.50850i	−0.656585	−	0.754252i	$-0.728000\pi$
$863$		−	44.3151i		−	1.50850i	0.656585	−	0.754252i	$-0.272000\pi$
$864$		0			0
$865$		−	10.5186i		−	0.357644i
$866$			31.0009i			1.05345i
$867$		0			0
$868$	−19.3111	+	11.1267i	−0.655460	+	0.377664i
$869$			25.4402i			0.863001i
$870$		0			0
$871$		−	16.9556i		−	0.574520i
$872$	−5.93963			−0.201141
$873$		0			0
$874$	−6.36939	+	7.37989i	−0.215448	+	0.249628i
$875$	−9.51667	−	16.5168i	−0.321722	−	0.558370i
$876$		0			0
$877$		−	55.3577i		−	1.86930i	−0.355572	−	0.934649i	$-0.615714\pi$
$877$		−	55.3577i		−	1.86930i	0.355572	−	0.934649i	$-0.384286\pi$
$878$		−	26.8712i		−	0.906858i
$879$		0			0
$880$		−	3.13285i		−	0.105608i
$881$			11.5455i			0.388977i	0.980905	+	0.194488i	$0.0623047\pi$
$881$			11.5455i			0.388977i	−0.980905	+	0.194488i	$0.937695\pi$
$882$		0			0
$883$	−55.5239			−1.86853			−0.934264	−	0.356582i	$-0.883942\pi$
$883$	−55.5239			−1.86853			−0.934264	+	0.356582i	$0.883942\pi$
$884$			4.89241i			0.164549i
$885$		0			0
$886$		−	8.07575i		−	0.271310i
$887$	−14.8432			−0.498386			−0.249193	−	0.968454i	$-0.580165\pi$
$887$	−14.8432			−0.498386			−0.249193	+	0.968454i	$0.580165\pi$
$888$		0			0
$889$	3.85724	+	6.69449i	0.129368	+	0.224526i
$890$	12.4879			0.418596
$891$		0			0
$892$	10.6895			0.357910
$893$	31.0856	−	36.0173i	1.04024	−	1.20527i
$894$		0			0
$895$	−14.2941			−0.477798
$896$	−1.32086	−	2.29245i	−0.0441270	−	0.0765853i
$897$		0			0
$898$	−7.13077			−0.237957
$899$			29.8656i			0.996074i
$900$		0			0
$901$	32.8128			1.09315
$902$			23.0129i			0.766247i
$903$		0			0
$904$	−4.56747			−0.151912
$905$			6.30303i			0.209520i
$906$		0			0
$907$		−	3.44122i		−	0.114264i	−0.998367	−	0.0571320i	$-0.981804\pi$
$907$		−	3.44122i		−	0.114264i	0.998367	−	0.0571320i	$-0.0181956\pi$
$908$	18.2992			0.607280
$909$		0			0
$910$	−2.16618	+	1.24811i	−0.0718083	+	0.0413746i
$911$		−	31.1234i		−	1.03116i	−0.856840	−	0.515582i	$-0.827576\pi$
$911$		−	31.1234i		−	1.03116i	0.856840	−	0.515582i	$-0.172424\pi$
$912$		0			0
$913$			8.34513i			0.276183i
$914$			4.94992i			0.163729i
$915$		0			0
$916$		−	10.3769i		−	0.342863i
$917$	14.5024	+	25.1698i	0.478911	+	0.831181i
$918$		0			0
$919$	−0.282023			−0.00930306			−0.00465153	−	0.999989i	$-0.501481\pi$
$919$	−0.282023			−0.00930306			−0.00465153	+	0.999989i	$0.501481\pi$
$920$	1.71158			0.0564290
$921$		0			0
$922$	12.3884			0.407989
$923$		−	13.8796i		−	0.456853i
$924$		0			0
$925$			25.7746i			0.847462i
$926$		−	0.203161i		−	0.00667627i
$927$		0			0
$928$	−3.54539			−0.116383
$929$		−	22.0598i		−	0.723758i	−0.932225	−	0.361879i	$-0.882135\pi$
$929$		−	22.0598i		−	0.723758i	0.932225	−	0.361879i	$-0.117865\pi$
$930$		0			0
$931$	28.8321	−	9.98559i	0.944933	−	0.327265i
$932$	1.50567			0.0493198
$933$		0			0
$934$	39.7312			1.30004
$935$	−12.4138			−0.405975
$936$		0			0
$937$		−	4.59462i		−	0.150100i	−0.997180	−	0.0750499i	$-0.976088\pi$
$937$		−	4.59462i		−	0.150100i	0.997180	−	0.0750499i	$-0.0239116\pi$
$938$	31.4816	−	18.1391i	1.02791	−	0.592262i
$939$		0			0
$940$	−8.35331			−0.272455
$941$	20.2344			0.659623			0.329812	−	0.944047i	$-0.393015\pi$
$941$	20.2344			0.659623			0.329812	+	0.944047i	$0.393015\pi$
$942$		0			0
$943$	−12.5727			−0.409423
$944$	−6.22487			−0.202602
$945$		0			0
$946$			46.4189i			1.50921i
$947$	13.6923			0.444941			0.222470	−	0.974939i	$-0.428588\pi$
$947$	13.6923			0.444941			0.222470	+	0.974939i	$0.428588\pi$
$948$		0			0
$949$		−	11.1326i		−	0.361379i
$950$	12.5719	−	14.5664i	0.407887	−	0.472598i
$951$		0			0
$952$	−9.08374	+	5.23388i	−0.294406	+	0.169631i
$953$			23.1598i			0.750218i	0.926981	+	0.375109i	$0.122395\pi$
$953$			23.1598i			0.750218i	−0.926981	+	0.375109i	$0.877605\pi$
$954$		0			0
$955$		−	2.40048i		−	0.0776776i
$956$	−8.59215			−0.277890
$957$		0			0
$958$	−42.8715			−1.38511
$959$	−37.2474	+	21.4613i	−1.20278	+	0.693020i
$960$		0			0
$961$	39.9600			1.28903
$962$	7.20920			0.232434
$963$		0			0
$964$	16.4908			0.531132
$965$	13.2695			0.427160
$966$		0			0
$967$	−21.9102			−0.704584			−0.352292	−	0.935890i	$-0.614598\pi$
$967$	−21.9102			−0.704584			−0.352292	+	0.935890i	$0.614598\pi$
$968$			5.75725i			0.185045i
$969$		0			0
$970$	1.45840			0.0468265
$971$	−20.8725			−0.669831			−0.334915	−	0.942248i	$-0.608708\pi$
$971$	−20.8725			−0.669831			−0.334915	+	0.942248i	$0.608708\pi$
$972$		0			0
$973$	2.31598	+	4.01954i	0.0742470	+	0.128861i
$974$	−25.8373			−0.827881
$975$		0			0
$976$		−	5.64349i		−	0.180644i
$977$		−	10.9734i		−	0.351069i	−0.984473	−	0.175535i	$-0.943835\pi$
$977$		−	10.9734i		−	0.351069i	0.984473	−	0.175535i	$-0.0561654\pi$
$978$		0			0
$979$	−66.7963			−2.13482
$980$	−4.63475	−	2.68673i	−0.148052	−	0.0858244i
$981$		0			0
$982$		−	0.388503i		−	0.0123976i
$983$	−48.0126			−1.53136			−0.765682	−	0.643219i	$-0.777598\pi$
$983$	−48.0126			−1.53136			−0.765682	+	0.643219i	$0.777598\pi$
$984$		0			0
$985$		−	16.1668i		−	0.515117i
$986$			14.0485i			0.447395i
$987$		0			0
$988$	−4.07426	−	3.51639i	−0.129620	−	0.111871i
$989$	−25.3601			−0.806405
$990$		0			0
$991$			14.0953i			0.447752i	0.974618	+	0.223876i	$0.0718710\pi$
$991$			14.0953i			0.447752i	−0.974618	+	0.223876i	$0.928129\pi$
$992$			8.42378i			0.267455i
$993$		0			0
$994$	25.7703	−	14.8484i	0.817385	−	0.470961i
$995$	3.25906			0.103319
$996$		0			0
$997$		−	17.3893i		−	0.550726i	−0.961340	−	0.275363i	$-0.911202\pi$
$997$		−	17.3893i		−	0.550726i	0.961340	−	0.275363i	$-0.0887980\pi$
$998$		−	3.56308i		−	0.112787i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2394.2.e.b.1063.4		12
3.2	odd	2		798.2.e.b.265.9	yes	12
7.6	odd	2		2394.2.e.a.1063.3		12
19.18	odd	2		2394.2.e.a.1063.10		12
21.20	even	2		798.2.e.a.265.10	yes	12
57.56	even	2		798.2.e.a.265.3	✓	12
133.132	even	2	inner	2394.2.e.b.1063.9		12
399.398	odd	2		798.2.e.b.265.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.e.a.265.3	✓	12	57.56	even	2
798.2.e.a.265.10	yes	12	21.20	even	2
798.2.e.b.265.4	yes	12	399.398	odd	2
798.2.e.b.265.9	yes	12	3.2	odd	2
2394.2.e.a.1063.3		12	7.6	odd	2
2394.2.e.a.1063.10		12	19.18	odd	2
2394.2.e.b.1063.4		12	1.1	even	1	trivial
2394.2.e.b.1063.9		12	133.132	even	2	inner

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:	\( N \)	\(=\)	\( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2394.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +0.765312i q^{5} +(-2.29245 + 1.32086i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +0.765312i q^{5} +(-2.29245 + 1.32086i) q^{7} +1.00000i q^{8} +0.765312 q^{10} -4.09356 q^{11} +1.23469 q^{13} +(1.32086 + 2.29245i) q^{14} +1.00000 q^{16} -3.96246i q^{17} +(3.29983 + 2.84800i) q^{19} -0.765312i q^{20} +4.09356i q^{22} -2.23644 q^{23} +4.41430 q^{25} -1.23469i q^{26} +(2.29245 - 1.32086i) q^{28} -3.54539i q^{29} -8.42378 q^{31} -1.00000i q^{32} -3.96246 q^{34} +(-1.01087 - 1.75444i) q^{35} +5.83888i q^{37} +(2.84800 - 3.29983i) q^{38} -0.765312 q^{40} +5.62174 q^{41} +11.3395 q^{43} +4.09356 q^{44} +2.23644i q^{46} -10.9149i q^{47} +(3.51063 - 6.05603i) q^{49} -4.41430i q^{50} -1.23469 q^{52} +8.28090i q^{53} -3.13285i q^{55} +(-1.32086 - 2.29245i) q^{56} -3.54539 q^{58} -6.22487 q^{59} -5.64349i q^{61} +8.42378i q^{62} -1.00000 q^{64} +0.944922i q^{65} -13.7327i q^{67} +3.96246i q^{68} +(-1.75444 + 1.01087i) q^{70} -11.2414i q^{71} -9.01653i q^{73} +5.83888 q^{74} +(-3.29983 - 2.84800i) q^{76} +(9.38428 - 5.40704i) q^{77} -6.21470i q^{79} +0.765312i q^{80} -5.62174i q^{82} -2.03860i q^{83} +3.03252 q^{85} -11.3395i q^{86} -4.09356i q^{88} +16.3174 q^{89} +(-2.83046 + 1.63086i) q^{91} +2.23644 q^{92} -10.9149 q^{94} +(-2.17961 + 2.52540i) q^{95} +1.90563 q^{97} +(-6.05603 - 3.51063i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4}+O(q^{10}) \) 12 * q - 12 * q^4	\( 12 q - 12 q^{4} + 4 q^{10} - 12 q^{11} + 20 q^{13} + 4 q^{14} + 12 q^{16} - 8 q^{19} + 12 q^{23} - 12 q^{25} + 24 q^{31} + 4 q^{34} - 4 q^{35} - 4 q^{40} + 16 q^{41} + 12 q^{44} + 4 q^{49} - 20 q^{52} - 4 q^{56} + 8 q^{58} - 40 q^{59} - 12 q^{64} - 24 q^{70} + 8 q^{76} - 8 q^{77} + 8 q^{85} + 16 q^{89} + 24 q^{91} - 12 q^{92} + 44 q^{95} - 60 q^{97} + 16 q^{98}+O(q^{100}) \) 12 * q - 12 * q^4 + 4 * q^10 - 12 * q^11 + 20 * q^13 + 4 * q^14 + 12 * q^16 - 8 * q^19 + 12 * q^23 - 12 * q^25 + 24 * q^31 + 4 * q^34 - 4 * q^35 - 4 * q^40 + 16 * q^41 + 12 * q^44 + 4 * q^49 - 20 * q^52 - 4 * q^56 + 8 * q^58 - 40 * q^59 - 12 * q^64 - 24 * q^70 + 8 * q^76 - 8 * q^77 + 8 * q^85 + 16 * q^89 + 24 * q^91 - 12 * q^92 + 44 * q^95 - 60 * q^97 + 16 * q^98

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