LMFDB - Embedded newform 855.2.c.d.514.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(514,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("855.514");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.16516096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 9x^{4} + 13x^{2} + 1 $ x^6 + 9x^4 + 13x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			514.1
Root			$1.30397i$ of defining polynomial
Character	$\chi$	$=$	855.514
Dual form			855.2.c.d.514.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41987i q^{2} -3.85577 q^{4} +(2.07772 + 0.826491i) q^{5} +3.18676i q^{7} +4.49073i q^{8} +O(q^{10})$	\(q-2.41987i q^{2} -3.85577 q^{4} +(2.07772 + 0.826491i) q^{5} +3.18676i q^{7} +4.49073i q^{8} +(2.00000 - 5.02781i) q^{10} -4.15544 q^{11} +2.07086i q^{13} +7.71155 q^{14} +3.15544 q^{16} +5.79470i q^{17} +1.00000 q^{19} +(-8.01121 - 3.18676i) q^{20} +10.0556i q^{22} +2.60794i q^{23} +(3.63383 + 3.43443i) q^{25} +5.01121 q^{26} -12.2874i q^{28} +6.00000 q^{29} +2.59933 q^{31} +1.34571i q^{32} +14.0224 q^{34} +(-2.63383 + 6.62119i) q^{35} -4.30266i q^{37} -2.41987i q^{38} +(-3.71155 + 9.33047i) q^{40} +0.599328 q^{41} +3.18676i q^{43} +16.0224 q^{44} +6.31087 q^{46} +11.7086i q^{47} -3.15544 q^{49} +(8.31087 - 8.79339i) q^{50} -7.98476i q^{52} -11.7503i q^{53} +(-8.63383 - 3.43443i) q^{55} -14.3109 q^{56} -14.5192i q^{58} -1.71155 q^{59} -8.75476 q^{61} -6.29004i q^{62} +9.56732 q^{64} +(-1.71155 + 4.30266i) q^{65} -4.76228i q^{67} -22.3430i q^{68} +(16.0224 + 6.37352i) q^{70} -13.7115 q^{71} -2.72714i q^{73} -10.4119 q^{74} -3.85577 q^{76} -13.2424i q^{77} +1.40067 q^{79} +(6.55611 + 2.60794i) q^{80} -1.45030i q^{82} +7.07154i q^{83} +(-4.78926 + 12.0398i) q^{85} +7.71155 q^{86} -18.6609i q^{88} +16.5353 q^{89} -6.59933 q^{91} -10.0556i q^{92} +28.3333 q^{94} +(2.07772 + 0.826491i) q^{95} -2.07086i q^{97} +7.63575i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 8 q^{4} + q^{5}+O(q^{10}) $ 6 * q - 8 * q^4 + q^5	$ 6 q - 8 q^{4} + q^{5} + 12 q^{10} - 2 q^{11} + 16 q^{14} - 4 q^{16} + 6 q^{19} - 10 q^{20} + 3 q^{25} - 8 q^{26} + 36 q^{29} + 8 q^{34} + 3 q^{35} + 8 q^{40} - 12 q^{41} + 20 q^{44} - 8 q^{46} + 4 q^{49} + 4 q^{50} - 33 q^{55} - 40 q^{56} + 20 q^{59} - 14 q^{61} + 12 q^{64} + 20 q^{65} + 20 q^{70} - 52 q^{71} - 40 q^{74} - 8 q^{76} + 24 q^{79} + 32 q^{80} + 13 q^{85} + 16 q^{86} + 24 q^{89} - 24 q^{91} + 48 q^{94} + q^{95}+O(q^{100}) $ 6 * q - 8 * q^4 + q^5 + 12 * q^10 - 2 * q^11 + 16 * q^14 - 4 * q^16 + 6 * q^19 - 10 * q^20 + 3 * q^25 - 8 * q^26 + 36 * q^29 + 8 * q^34 + 3 * q^35 + 8 * q^40 - 12 * q^41 + 20 * q^44 - 8 * q^46 + 4 * q^49 + 4 * q^50 - 33 * q^55 - 40 * q^56 + 20 * q^59 - 14 * q^61 + 12 * q^64 + 20 * q^65 + 20 * q^70 - 52 * q^71 - 40 * q^74 - 8 * q^76 + 24 * q^79 + 32 * q^80 + 13 * q^85 + 16 * q^86 + 24 * q^89 - 24 * q^91 + 48 * q^94 + q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$		−	2.41987i		−	1.71111i	−0.517715	−	0.855553i	$-0.673217\pi$
$2$		−	2.41987i		−	1.71111i	0.517715	−	0.855553i	$-0.326783\pi$
$3$		0			0
$3$		0			0
$4$	−3.85577			−1.92789
$5$	2.07772	+	0.826491i	0.929184	+	0.369618i
$5$	2.07772	+	0.826491i	0.929184	+	0.369618i
$6$		0			0
$7$			3.18676i			1.20448i	0.798314	+	0.602241i	$0.205725\pi$
$7$			3.18676i			1.20448i	−0.798314	+	0.602241i	$0.794275\pi$
$8$			4.49073i			1.58771i
$9$		0			0
$10$	2.00000	−	5.02781i	0.632456	−	1.58993i
$11$	−4.15544			−1.25291			−0.626456	−	0.779457i	$-0.715495\pi$
$11$	−4.15544			−1.25291			−0.626456	+	0.779457i	$0.715495\pi$
$12$		0			0
$13$			2.07086i			0.574353i	0.957878	+	0.287176i	$0.0927166\pi$
$13$			2.07086i			0.574353i	−0.957878	+	0.287176i	$0.907283\pi$
$14$	7.71155			2.06100
$15$		0			0
$16$	3.15544			0.788859
$17$			5.79470i			1.40542i	0.711476	+	0.702710i	$0.248027\pi$
$17$			5.79470i			1.40542i	−0.711476	+	0.702710i	$0.751973\pi$
$18$		0			0
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	−8.01121	−	3.18676i	−1.79136	−	0.712581i
$21$		0			0
$22$			10.0556i			2.14386i
$23$			2.60794i			0.543793i	0.962327	+	0.271896i	$0.0876508\pi$
$23$			2.60794i			0.543793i	−0.962327	+	0.271896i	$0.912349\pi$
$24$		0			0
$25$	3.63383	+	3.43443i	0.726765	+	0.686886i
$26$	5.01121			0.982779
$27$		0			0
$28$		−	12.2874i		−	2.32210i
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$	2.59933			0.466853			0.233427	−	0.972374i	$-0.425006\pi$
$31$	2.59933			0.466853			0.233427	+	0.972374i	$0.425006\pi$
$32$			1.34571i			0.237890i
$33$		0			0
$34$	14.0224			2.40482
$35$	−2.63383	+	6.62119i	−0.445198	+	1.11919i
$36$		0			0
$37$		−	4.30266i		−	0.707353i	−0.935368	−	0.353677i	$-0.884931\pi$
$37$		−	4.30266i		−	0.707353i	0.935368	−	0.353677i	$-0.115069\pi$
$38$		−	2.41987i		−	0.392555i
$39$		0			0
$40$	−3.71155	+	9.33047i	−0.586847	+	1.47528i
$41$	0.599328			0.0935993			0.0467997	−	0.998904i	$-0.485098\pi$
$41$	0.599328			0.0935993			0.0467997	+	0.998904i	$0.485098\pi$
$42$		0			0
$43$			3.18676i			0.485976i	0.970029	+	0.242988i	$0.0781276\pi$
$43$			3.18676i			0.485976i	−0.970029	+	0.242988i	$0.921872\pi$
$44$	16.0224			2.41547
$45$		0			0
$46$	6.31087			0.930487
$47$			11.7086i			1.70787i	0.520376	+	0.853937i	$0.325792\pi$
$47$			11.7086i			1.70787i	−0.520376	+	0.853937i	$0.674208\pi$
$48$		0			0
$49$	−3.15544			−0.450777
$50$	8.31087	−	8.79339i	1.17533	−	1.24357i
$51$		0			0
$52$		−	7.98476i		−	1.10729i
$53$		−	11.7503i		−	1.61403i	−0.590529	−	0.807017i	$-0.701081\pi$
$53$		−	11.7503i		−	1.61403i	0.590529	−	0.807017i	$-0.298919\pi$
$54$		0			0
$55$	−8.63383	−	3.43443i	−1.16418	−	0.463098i
$56$	−14.3109			−1.91237
$57$		0			0
$58$		−	14.5192i		−	1.90647i
$59$	−1.71155			−0.222824			−0.111412	−	0.993774i	$-0.535537\pi$
$59$	−1.71155			−0.222824			−0.111412	+	0.993774i	$0.535537\pi$
$60$		0			0
$61$	−8.75476			−1.12093			−0.560466	−	0.828177i	$-0.689378\pi$
$61$	−8.75476			−1.12093			−0.560466	+	0.828177i	$0.689378\pi$
$62$		−	6.29004i		−	0.798836i
$63$		0			0
$64$	9.56732			1.19591
$65$	−1.71155	+	4.30266i	−0.212291	+	0.533679i
$66$		0			0
$67$		−	4.76228i		−	0.581805i	−0.956753	−	0.290902i	$-0.906044\pi$
$67$		−	4.76228i		−	0.581805i	0.956753	−	0.290902i	$-0.0939555\pi$
$68$		−	22.3430i		−	2.70949i
$69$		0			0
$70$	16.0224	+	6.37352i	1.91505	+	0.761781i
$71$	−13.7115			−1.62726			−0.813631	−	0.581382i	$-0.802512\pi$
$71$	−13.7115			−1.62726			−0.813631	+	0.581382i	$0.802512\pi$
$72$		0			0
$73$		−	2.72714i		−	0.319188i	−0.987183	−	0.159594i	$-0.948982\pi$
$73$		−	2.72714i		−	0.319188i	0.987183	−	0.159594i	$-0.0510185\pi$
$74$	−10.4119			−1.21036
$75$		0			0
$76$	−3.85577			−0.442287
$77$		−	13.2424i		−	1.50911i
$78$		0			0
$79$	1.40067			0.157588			0.0787939	−	0.996891i	$-0.474893\pi$
$79$	1.40067			0.157588			0.0787939	+	0.996891i	$0.474893\pi$
$80$	6.55611	+	2.60794i	0.732995	+	0.291576i
$81$		0			0
$82$		−	1.45030i		−	0.160158i
$83$			7.07154i			0.776203i	0.921617	+	0.388101i	$0.126869\pi$
$83$			7.07154i			0.776203i	−0.921617	+	0.388101i	$0.873131\pi$
$84$		0			0
$85$	−4.78926	+	12.0398i	−0.519469	+	1.30589i
$86$	7.71155			0.831557
$87$		0			0
$88$		−	18.6609i		−	1.98926i
$89$	16.5353			1.75274			0.876370	−	0.481639i	$-0.159958\pi$
$89$	16.5353			1.75274			0.876370	+	0.481639i	$0.159958\pi$
$90$		0			0
$91$	−6.59933			−0.691798
$92$		−	10.0556i		−	1.04837i
$93$		0			0
$94$	28.3333			2.92236
$95$	2.07772	+	0.826491i	0.213169	+	0.0847961i
$96$		0			0
$97$		−	2.07086i		−	0.210264i	−0.994458	−	0.105132i	$-0.966474\pi$
$97$		−	2.07086i		−	0.210264i	0.994458	−	0.105132i	$-0.0335265\pi$
$98$			7.63575i			0.771327i
$99$		0			0
$100$	−14.0112	−	13.2424i	−1.40112	−	1.32424i
$101$	1.71155			0.170305			0.0851525	−	0.996368i	$-0.472862\pi$
$101$	1.71155			0.170305			0.0851525	+	0.996368i	$0.472862\pi$
$102$		0			0
$103$			5.75296i			0.566856i	0.958994	+	0.283428i	$0.0914716\pi$
$103$			5.75296i			0.566856i	−0.958994	+	0.283428i	$0.908528\pi$
$104$	−9.29966			−0.911907
$105$		0			0
$106$	−28.4343			−2.76178
$107$		−	15.4324i		−	1.49191i	−0.665996	−	0.745955i	$-0.731993\pi$
$107$		−	15.4324i		−	1.49191i	0.665996	−	0.745955i	$-0.268007\pi$
$108$		0			0
$109$	−11.7115			−1.12176			−0.560881	−	0.827896i	$-0.689538\pi$
$109$	−11.7115			−1.12176			−0.560881	+	0.827896i	$0.689538\pi$
$110$	−8.31087	+	20.8927i	−0.792411	+	1.99204i
$111$		0			0
$112$			10.0556i			0.950167i
$113$			10.5927i			0.996477i	0.867040	+	0.498239i	$0.166020\pi$
$113$			10.5927i			0.996477i	−0.867040	+	0.498239i	$0.833980\pi$
$114$		0			0
$115$	−2.15544	+	5.41856i	−0.200996	+	0.505283i
$116$	−23.1346			−2.14800
$117$		0			0
$118$			4.14172i			0.381276i
$119$	−18.4663			−1.69280
$120$		0			0
$121$	6.26765			0.569787
$122$			21.1854i			1.91804i
$123$		0			0
$124$	−10.0224			−0.900040
$125$	4.71155	+	10.1391i	0.421413	+	0.906869i
$126$		0			0
$127$			6.07484i			0.539055i	0.962993	+	0.269528i	$0.0868676\pi$
$127$			6.07484i			0.539055i	−0.962993	+	0.269528i	$0.913132\pi$
$128$		−	20.4602i		−	1.80845i
$129$		0			0
$130$	10.4119	+	4.14172i	0.913182	+	0.363253i
$131$	13.5785			1.18636			0.593181	−	0.805069i	$-0.297872\pi$
$131$	13.5785			1.18636			0.593181	+	0.805069i	$0.297872\pi$
$132$		0			0
$133$			3.18676i			0.276327i
$134$	−11.5241			−0.995530
$135$		0			0
$136$	−26.0224			−2.23140
$137$		−	7.94302i		−	0.678618i	−0.940675	−	0.339309i	$-0.889807\pi$
$137$		−	7.94302i		−	0.678618i	0.940675	−	0.339309i	$-0.110193\pi$
$138$		0			0
$139$	−3.26765			−0.277159			−0.138579	−	0.990351i	$-0.544254\pi$
$139$	−3.26765			−0.277159			−0.138579	+	0.990351i	$0.544254\pi$
$140$	10.1554	−	25.5298i	0.858291	−	2.15766i
$141$		0			0
$142$			33.1802i			2.78442i
$143$		−	8.60532i		−	0.719613i
$144$		0			0
$145$	12.4663	+	4.95894i	1.03527	+	0.411818i
$146$	−6.59933			−0.546164
$147$		0			0
$148$			16.5901i			1.36370i
$149$	8.44389			0.691751			0.345875	−	0.938280i	$-0.387582\pi$
$149$	8.44389			0.691751			0.345875	+	0.938280i	$0.387582\pi$
$150$		0			0
$151$	0.887783			0.0722468			0.0361234	−	0.999347i	$-0.488499\pi$
$151$	0.887783			0.0722468			0.0361234	+	0.999347i	$0.488499\pi$
$152$			4.49073i			0.364246i
$153$		0			0
$154$	−32.0448			−2.58225
$155$	5.40067	+	2.14832i	0.433792	+	0.172557i
$156$		0			0
$157$		−	4.14172i		−	0.330545i	−0.986248	−	0.165273i	$-0.947150\pi$
$157$		−	4.14172i		−	0.330545i	0.986248	−	0.165273i	$-0.0528504\pi$
$158$		−	3.38944i		−	0.269650i
$159$		0			0
$160$	−1.11222	+	2.79601i	−0.0879285	+	0.221044i
$161$	−8.31087			−0.654989
$162$		0			0
$163$		−	24.7126i		−	1.93564i	−0.251647	−	0.967819i	$-0.580972\pi$
$163$		−	24.7126i		−	1.93564i	0.251647	−	0.967819i	$-0.419028\pi$
$164$	−2.31087			−0.180449
$165$		0			0
$166$	17.1122			1.32817
$167$		−	3.60464i		−	0.278935i	−0.990227	−	0.139468i	$-0.955461\pi$
$167$		−	3.60464i		−	0.278935i	0.990227	−	0.139468i	$-0.0445391\pi$
$168$		0			0
$169$	8.71155			0.670119
$170$	29.1346	+	11.5894i	2.23452	+	0.888866i
$171$		0			0
$172$		−	12.2874i		−	0.936907i
$173$			22.4205i			1.70460i	0.523054	+	0.852300i	$0.324793\pi$
$173$			22.4205i			1.70460i	−0.523054	+	0.852300i	$0.675207\pi$
$174$		0			0
$175$	−10.9447	+	11.5801i	−0.827342	+	0.875376i
$176$	−13.1122			−0.988371
$177$		0			0
$178$		−	40.0133i		−	2.99912i
$179$	−5.13464			−0.383781			−0.191890	−	0.981416i	$-0.561462\pi$
$179$	−5.13464			−0.383781			−0.191890	+	0.981416i	$0.561462\pi$
$180$		0			0
$181$	20.8462			1.54948			0.774742	−	0.632277i	$-0.217880\pi$
$181$	20.8462			1.54948			0.774742	+	0.632277i	$0.217880\pi$
$182$			15.9695i			1.18374i
$183$		0			0
$184$	−11.7115			−0.863387
$185$	3.55611	−	8.93972i	0.261450	−	0.657261i
$186$		0			0
$187$		−	24.0795i		−	1.76087i
$188$		−	45.1457i		−	3.29259i
$189$		0			0
$190$	2.00000	−	5.02781i	0.145095	−	0.364756i
$191$	5.26765			0.381154			0.190577	−	0.981672i	$-0.438964\pi$
$191$	5.26765			0.381154			0.190577	+	0.981672i	$0.438964\pi$
$192$		0			0
$193$			2.07086i			0.149064i	0.997219	+	0.0745318i	$0.0237462\pi$
$193$			2.07086i			0.149064i	−0.997219	+	0.0745318i	$0.976254\pi$
$194$	−5.01121			−0.359784
$195$		0			0
$196$	12.1666			0.869046
$197$			10.4318i			0.743232i	0.928387	+	0.371616i	$0.121196\pi$
$197$			10.4318i			0.743232i	−0.928387	+	0.371616i	$0.878804\pi$
$198$		0			0
$199$	2.73235			0.193691			0.0968455	−	0.995299i	$-0.469125\pi$
$199$	2.73235			0.193691			0.0968455	+	0.995299i	$0.469125\pi$
$200$	−15.4231	+	16.3185i	−1.09058	+	1.15389i
$201$		0			0
$202$		−	4.14172i		−	0.291410i
$203$			19.1206i			1.34200i
$204$		0			0
$205$	1.24524	+	0.495339i	0.0869710	+	0.0345960i
$206$	13.9214			0.969951
$207$		0			0
$208$			6.53446i			0.453083i
$209$	−4.15544			−0.287438
$210$		0			0
$211$	−15.7340			−1.08317			−0.541585	−	0.840646i	$-0.682176\pi$
$211$	−15.7340			−1.08317			−0.541585	+	0.840646i	$0.682176\pi$
$212$			45.3066i			3.11167i
$213$		0			0
$214$	−37.3445			−2.55282
$215$	−2.63383	+	6.62119i	−0.179625	+	0.451561i
$216$		0			0
$217$			8.28343i			0.562316i
$218$			28.3404i			1.91946i
$219$		0			0
$220$	33.2901	+	13.2424i	2.24442	+	0.892801i
$221$	−12.0000			−0.807207
$222$		0			0
$223$			18.8219i			1.26041i	0.776430	+	0.630203i	$0.217028\pi$
$223$			18.8219i			1.26041i	−0.776430	+	0.630203i	$0.782972\pi$
$224$	−4.28845			−0.286534
$225$		0			0
$226$	25.6330			1.70508
$227$		−	14.4418i		−	0.958533i	−0.877669	−	0.479267i	$-0.840903\pi$
$227$		−	14.4418i		−	0.958533i	0.877669	−	0.479267i	$-0.159097\pi$
$228$		0			0
$229$	4.17785			0.276080			0.138040	−	0.990427i	$-0.455920\pi$
$229$	4.17785			0.276080			0.138040	+	0.990427i	$0.455920\pi$
$230$	13.1122	+	5.21588i	0.864594	+	0.343925i
$231$		0			0
$232$			26.9444i			1.76898i
$233$		−	12.0847i		−	0.791697i	−0.918316	−	0.395849i	$-0.870450\pi$
$233$		−	12.0847i		−	0.791697i	0.918316	−	0.395849i	$-0.129550\pi$
$234$		0			0
$235$	−9.67705	+	24.3272i	−0.631261	+	1.58693i
$236$	6.59933			0.429580
$237$		0			0
$238$			44.6861i			2.89657i
$239$	−11.3541			−0.734435			−0.367218	−	0.930135i	$-0.619690\pi$
$239$	−11.3541			−0.734435			−0.367218	+	0.930135i	$0.619690\pi$
$240$		0			0
$241$	−3.40067			−0.219057			−0.109528	−	0.993984i	$-0.534934\pi$
$241$	−3.40067			−0.219057			−0.109528	+	0.993984i	$0.534934\pi$
$242$		−	15.1669i		−	0.974966i
$243$		0			0
$244$	33.7564			2.16103
$245$	−6.55611	−	2.60794i	−0.418854	−	0.166615i
$246$		0			0
$247$			2.07086i			0.131766i
$248$			11.6729i			0.741229i
$249$		0			0
$250$	24.5353	−	11.4013i	1.55175	−	0.721083i
$251$	−3.04322			−0.192086			−0.0960432	−	0.995377i	$-0.530619\pi$
$251$	−3.04322			−0.192086			−0.0960432	+	0.995377i	$0.530619\pi$
$252$		0			0
$253$		−	10.8371i		−	0.681324i
$254$	14.7003			0.922381
$255$		0			0
$256$	−30.3765			−1.89853
$257$			17.2881i			1.07840i	0.842177	+	0.539201i	$0.181274\pi$
$257$			17.2881i			1.07840i	−0.842177	+	0.539201i	$0.818726\pi$
$258$		0			0
$259$	13.7115			0.851994
$260$	6.59933	−	16.5901i	0.409273	−	1.02887i
$261$		0			0
$262$		−	32.8583i		−	2.02999i
$263$			1.19336i			0.0735859i	0.999323	+	0.0367930i	$0.0117142\pi$
$263$			1.19336i			0.0735859i	−0.999323	+	0.0367930i	$0.988286\pi$
$264$		0			0
$265$	9.71155	−	24.4139i	0.596575	−	1.49973i
$266$	7.71155			0.472825
$267$		0			0
$268$			18.3623i			1.12165i
$269$	22.1089			1.34800			0.674000	−	0.738731i	$-0.264575\pi$
$269$	22.1089			1.34800			0.674000	+	0.738731i	$0.264575\pi$
$270$		0			0
$271$	−4.08644			−0.248234			−0.124117	−	0.992268i	$-0.539610\pi$
$271$	−4.08644			−0.248234			−0.124117	+	0.992268i	$0.539610\pi$
$272$			18.2848i			1.10868i
$273$		0			0
$274$	−19.2211			−1.16119
$275$	−15.1001	−	14.2716i	−0.910572	−	0.860607i
$276$		0			0
$277$			10.0199i			0.602037i	0.953618	+	0.301019i	$0.0973266\pi$
$277$			10.0199i			0.602037i	−0.953618	+	0.301019i	$0.902673\pi$
$278$			7.90730i			0.474248i
$279$		0			0
$280$	−29.7340	−	11.8278i	−1.77694	−	0.706846i
$281$	−0.599328			−0.0357529			−0.0178765	−	0.999840i	$-0.505691\pi$
$281$	−0.599328			−0.0357529			−0.0178765	+	0.999840i	$0.505691\pi$
$282$		0			0
$283$			5.41856i			0.322100i	0.986946	+	0.161050i	$0.0514880\pi$
$283$			5.41856i			0.322100i	−0.986946	+	0.161050i	$0.948512\pi$
$284$	52.8686			3.13717
$285$		0			0
$286$	−20.8238			−1.23133
$287$			1.90991i			0.112739i
$288$		0			0
$289$	−16.5785			−0.975207
$290$	12.0000	−	30.1669i	0.704664	−	1.77146i
$291$		0			0
$292$			10.5152i			0.615358i
$293$		−	3.46691i		−	0.202539i	−0.994859	−	0.101269i	$-0.967710\pi$
$293$		−	3.46691i		−	0.202539i	0.994859	−	0.101269i	$-0.0322904\pi$
$294$		0			0
$295$	−3.55611	−	1.41458i	−0.207045	−	0.0823598i
$296$	19.3221			1.12307
$297$		0			0
$298$		−	20.4331i		−	1.18366i
$299$	−5.40067			−0.312329
$300$		0			0
$301$	−10.1554			−0.585350
$302$		−	2.14832i		−	0.123622i
$303$		0			0
$304$	3.15544			0.180977
$305$	−18.1899	−	7.23573i	−1.04155	−	0.414317i
$306$		0			0
$307$			16.5901i			0.946846i	0.880835	+	0.473423i	$0.156982\pi$
$307$			16.5901i			0.946846i	−0.880835	+	0.473423i	$0.843018\pi$
$308$			51.0596i			2.90939i
$309$		0			0
$310$	5.19866	−	13.0689i	0.295264	−	0.742265i
$311$	4.15544			0.235633			0.117817	−	0.993035i	$-0.462411\pi$
$311$	4.15544			0.235633			0.117817	+	0.993035i	$0.462411\pi$
$312$		0			0
$313$		−	0.919237i		−	0.0519583i	−0.999662	−	0.0259792i	$-0.991730\pi$
$313$		−	0.919237i		−	0.0519583i	0.999662	−	0.0259792i	$-0.00827036\pi$
$314$	−10.0224			−0.565598
$315$		0			0
$316$	−5.40067			−0.303812
$317$		−	26.7292i		−	1.50126i	−0.660723	−	0.750630i	$-0.729750\pi$
$317$		−	26.7292i		−	1.50126i	0.660723	−	0.750630i	$-0.270250\pi$
$318$		0			0
$319$	−24.9326			−1.39596
$320$	19.8782	+	7.90730i	1.11122	+	0.442031i
$321$		0			0
$322$			20.1112i			1.12076i
$323$			5.79470i			0.322426i
$324$		0			0
$325$	−7.11222	+	7.52514i	−0.394515	+	0.417420i
$326$	−59.8012			−3.31208
$327$		0			0
$328$			2.69142i			0.148609i
$329$	−37.3125			−2.05710
$330$		0			0
$331$	8.00000			0.439720			0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000			0.439720			0.219860	+	0.975531i	$0.429440\pi$
$332$		−	27.2663i		−	1.49643i
$333$		0			0
$334$	−8.72275			−0.477288
$335$	3.93598	−	9.89467i	0.215045	−	0.540604i
$336$		0			0
$337$		−	22.5040i		−	1.22587i	−0.790133	−	0.612935i	$-0.789989\pi$
$337$		−	22.5040i		−	1.22587i	0.790133	−	0.612935i	$-0.210011\pi$
$338$		−	21.0808i		−	1.14664i
$339$		0			0
$340$	18.4663	−	46.4225i	1.00148	−	2.51762i
$341$	−10.8013			−0.584926
$342$		0			0
$343$			12.2517i			0.661530i
$344$	−14.3109			−0.771591
$345$		0			0
$346$	54.2547			2.91675
$347$		−	14.4543i		−	0.775946i	−0.921671	−	0.387973i	$-0.873175\pi$
$347$		−	14.4543i		−	0.775946i	0.921671	−	0.387973i	$-0.126825\pi$
$348$		0			0
$349$	13.3541			0.714828			0.357414	−	0.933946i	$-0.383658\pi$
$349$	13.3541			0.714828			0.357414	+	0.933946i	$0.383658\pi$
$350$	28.0224	+	26.4848i	1.49786	+	1.41567i
$351$		0			0
$352$		−	5.59201i		−	0.298055i
$353$		−	17.6410i		−	0.938937i	−0.882949	−	0.469469i	$-0.844446\pi$
$353$		−	17.6410i		−	0.938937i	0.882949	−	0.469469i	$-0.155554\pi$
$354$		0			0
$355$	−28.4887	−	11.3325i	−1.51202	−	0.601465i
$356$	−63.7564			−3.37908
$357$		0			0
$358$			12.4252i			0.656690i
$359$	12.4663			0.657947			0.328973	−	0.944339i	$-0.393297\pi$
$359$	12.4663			0.657947			0.328973	+	0.944339i	$0.393297\pi$
$360$		0			0
$361$	1.00000			0.0526316
$362$		−	50.4451i		−	2.65133i
$363$		0			0
$364$	25.4455			1.33371
$365$	2.25396	−	5.66623i	0.117977	−	0.296584i
$366$		0			0
$367$			16.4291i			0.857594i	0.903401	+	0.428797i	$0.141062\pi$
$367$			16.4291i			0.857594i	−0.903401	+	0.428797i	$0.858938\pi$
$368$			8.22918i			0.428976i
$369$		0			0
$370$	−21.6330	−	8.60532i	−1.12464	−	0.447369i
$371$	37.4455			1.94407
$372$		0			0
$373$		−	5.29334i		−	0.274079i	−0.990566	−	0.137039i	$-0.956241\pi$
$373$		−	5.29334i		−	0.274079i	0.990566	−	0.137039i	$-0.0437587\pi$
$374$	−58.2693			−3.01303
$375$		0			0
$376$	−52.5801			−2.71161
$377$			12.4252i			0.639928i
$378$		0			0
$379$	−14.5353			−0.746629			−0.373314	−	0.927705i	$-0.621779\pi$
$379$	−14.5353			−0.746629			−0.373314	+	0.927705i	$0.621779\pi$
$380$	−8.01121	−	3.18676i	−0.410966	−	0.163477i
$381$		0			0
$382$		−	12.7470i		−	0.652195i
$383$		−	0.453598i		−	0.0231778i	−0.999933	−	0.0115889i	$-0.996311\pi$
$383$		−	0.453598i		−	0.0231778i	0.999933	−	0.0115889i	$-0.00368894\pi$
$384$		0			0
$385$	10.9447	−	27.5139i	0.557794	−	1.40224i
$386$	5.01121			0.255064
$387$		0			0
$388$			7.98476i			0.405365i
$389$	16.1554			0.819113			0.409557	−	0.912285i	$-0.365683\pi$
$389$	16.1554			0.819113			0.409557	+	0.912285i	$0.365683\pi$
$390$		0			0
$391$	−15.1122			−0.764258
$392$		−	14.1702i		−	0.715704i
$393$		0			0
$394$	25.2435			1.27175
$395$	2.91020	+	1.15764i	0.146428	+	0.0582473i
$396$		0			0
$397$		−	32.7563i		−	1.64399i	−0.569495	−	0.821995i	$-0.692861\pi$
$397$		−	32.7563i		−	1.64399i	0.569495	−	0.821995i	$-0.307139\pi$
$398$		−	6.61192i		−	0.331426i
$399$		0			0
$400$	11.4663	+	10.8371i	0.573315	+	0.541856i
$401$	−12.0864			−0.603568			−0.301784	−	0.953376i	$-0.597582\pi$
$401$	−12.0864			−0.603568			−0.301784	+	0.953376i	$0.597582\pi$
$402$		0			0
$403$			5.38284i			0.268138i
$404$	−6.59933			−0.328329
$405$		0			0
$406$	46.2693			2.29631
$407$			17.8794i			0.886251i
$408$		0			0
$409$	19.1346			0.946147			0.473073	−	0.881023i	$-0.343145\pi$
$409$	19.1346			0.946147			0.473073	+	0.881023i	$0.343145\pi$
$410$	1.19866	−	3.01331i	0.0591974	−	0.148817i
$411$		0			0
$412$		−	22.1821i		−	1.09283i
$413$		−	5.45428i		−	0.268388i
$414$		0			0
$415$	−5.84456	+	14.6927i	−0.286898	+	0.721235i
$416$	−2.78678			−0.136633
$417$		0			0
$418$			10.0556i			0.491836i
$419$	8.04484			0.393016			0.196508	−	0.980502i	$-0.437040\pi$
$419$	8.04484			0.393016			0.196508	+	0.980502i	$0.437040\pi$
$420$		0			0
$421$	−29.3591			−1.43087			−0.715437	−	0.698678i	$-0.753772\pi$
$421$	−29.3591			−1.43087			−0.715437	+	0.698678i	$0.753772\pi$
$422$			38.0742i			1.85342i
$423$		0			0
$424$	52.7676			2.56262
$425$	−19.9015	+	21.0569i	−0.965364	+	1.02141i
$426$		0			0
$427$		−	27.8993i		−	1.35014i
$428$			59.5040i			2.87623i
$429$		0			0
$430$	16.0224	+	6.37352i	0.772670	+	0.307358i
$431$	32.0448			1.54355			0.771773	−	0.635898i	$-0.219370\pi$
$431$	32.0448			1.54355			0.771773	+	0.635898i	$0.219370\pi$
$432$		0			0
$433$			0.482831i			0.0232034i	0.999933	+	0.0116017i	$0.00369301\pi$
$433$			0.482831i			0.0232034i	−0.999933	+	0.0116017i	$0.996307\pi$
$434$	20.0448			0.962183
$435$		0			0
$436$	45.1571			2.16263
$437$			2.60794i			0.124755i
$438$		0			0
$439$	27.3591			1.30578			0.652889	−	0.757454i	$-0.273557\pi$
$439$	27.3591			1.30578			0.652889	+	0.757454i	$0.273557\pi$
$440$	15.4231	−	38.7722i	0.735267	−	1.84839i
$441$		0			0
$442$			29.0384i			1.38122i
$443$		−	23.3815i		−	1.11089i	−0.831554	−	0.555444i	$-0.812548\pi$
$443$		−	23.3815i		−	1.11089i	0.831554	−	0.555444i	$-0.187452\pi$
$444$		0			0
$445$	34.3557	+	13.6663i	1.62862	+	0.647844i
$446$	45.5465			2.15669
$447$		0			0
$448$			30.4887i			1.44046i
$449$	23.1346			1.09179			0.545895	−	0.837853i	$-0.316190\pi$
$449$	23.1346			1.09179			0.545895	+	0.837853i	$0.316190\pi$
$450$		0			0
$451$	−2.49047			−0.117272
$452$		−	40.8430i		−	1.92109i
$453$		0			0
$454$	−34.9472			−1.64015
$455$	−13.7115	−	5.45428i	−0.642807	−	0.255701i
$456$		0			0
$457$		−	21.2503i		−	0.994049i	−0.867736	−	0.497025i	$-0.834426\pi$
$457$		−	21.2503i		−	0.994049i	0.867736	−	0.497025i	$-0.165574\pi$
$458$		−	10.1099i		−	0.472403i
$459$		0			0
$460$	8.31087	−	20.8927i	0.387496	−	0.974129i
$461$	−31.5785			−1.47076			−0.735379	−	0.677656i	$-0.762996\pi$
$461$	−31.5785			−1.47076			−0.735379	+	0.677656i	$0.762996\pi$
$462$		0			0
$463$		−	15.6119i		−	0.725547i	−0.931877	−	0.362774i	$-0.881830\pi$
$463$		−	15.6119i		−	0.725547i	0.931877	−	0.362774i	$-0.118170\pi$
$464$	18.9326			0.878925
$465$		0			0
$466$	−29.2435			−1.35468
$467$		−	29.8264i		−	1.38020i	−0.723713	−	0.690101i	$-0.757566\pi$
$467$		−	29.8264i		−	1.38020i	0.723713	−	0.690101i	$-0.242434\pi$
$468$		0			0
$469$	15.1762			0.700774
$470$	58.8686	+	23.4172i	2.71541	+	1.08015i
$471$		0			0
$472$		−	7.68608i		−	0.353781i
$473$		−	13.2424i		−	0.608885i
$474$		0			0
$475$	3.63383	+	3.43443i	0.166731	+	0.157582i
$476$	71.2019			3.26353
$477$		0			0
$478$			27.4754i			1.25670i
$479$	4.53531			0.207223			0.103612	−	0.994618i	$-0.466960\pi$
$479$	4.53531			0.207223			0.103612	+	0.994618i	$0.466960\pi$
$480$		0			0
$481$	8.91020			0.406270
$482$			8.22918i			0.374829i
$483$		0			0
$484$	−24.1666			−1.09848
$485$	1.71155	−	4.30266i	0.0777173	−	0.195374i
$486$		0			0
$487$		−	39.2550i		−	1.77881i	−0.457116	−	0.889407i	$-0.651118\pi$
$487$		−	39.2550i		−	1.77881i	0.457116	−	0.889407i	$-0.348882\pi$
$488$		−	39.3153i		−	1.77972i
$489$		0			0
$490$	−6.31087	+	15.8649i	−0.285096	+	0.716705i
$491$	−38.8910			−1.75513			−0.877564	−	0.479460i	$-0.840832\pi$
$491$	−38.8910			−1.75513			−0.877564	+	0.479460i	$0.840832\pi$
$492$		0			0
$493$			34.7682i			1.56588i
$494$	5.01121			0.225465
$495$		0			0
$496$	8.20202			0.368281
$497$		−	43.6954i		−	1.96001i
$498$		0			0
$499$	−4.73235			−0.211849			−0.105924	−	0.994374i	$-0.533780\pi$
$499$	−4.73235			−0.211849			−0.105924	+	0.994374i	$0.533780\pi$
$500$	−18.1666	−	39.0941i	−0.812437	−	1.74834i
$501$		0			0
$502$			7.36420i			0.328680i
$503$		−	1.85567i		−	0.0827400i	−0.999144	−	0.0413700i	$-0.986828\pi$
$503$		−	1.85567i		−	0.0827400i	0.999144	−	0.0413700i	$-0.0131722\pi$
$504$		0			0
$505$	3.55611	+	1.41458i	0.158245	+	0.0629478i
$506$	−26.2244			−1.16582
$507$		0			0
$508$		−	23.4232i		−	1.03924i
$509$	22.8878			1.01448			0.507242	−	0.861804i	$-0.330665\pi$
$509$	22.8878			1.01448			0.507242	+	0.861804i	$0.330665\pi$
$510$		0			0
$511$	8.69074			0.384456
$512$			32.5867i			1.44014i
$513$		0			0
$514$	41.8350			1.84526
$515$	−4.75476	+	11.9530i	−0.209520	+	0.526713i
$516$		0			0
$517$		−	48.6543i		−	2.13982i
$518$		−	33.1802i		−	1.45785i
$519$		0			0
$520$	−19.3221	−	7.68608i	−0.847329	−	0.337057i
$521$	29.7340			1.30267			0.651334	−	0.758791i	$-0.274210\pi$
$521$	29.7340			1.30267			0.651334	+	0.758791i	$0.274210\pi$
$522$		0			0
$523$			30.6497i			1.34022i	0.742263	+	0.670109i	$0.233752\pi$
$523$			30.6497i			1.34022i	−0.742263	+	0.670109i	$0.766248\pi$
$524$	−52.3557			−2.28717
$525$		0			0
$526$	2.88778			0.125913
$527$			15.0623i			0.656125i
$528$		0			0
$529$	16.1987			0.704289
$530$	−59.0785	−	23.5007i	−2.56620	−	1.02080i
$531$		0			0
$532$		−	12.2874i		−	0.532727i
$533$			1.24112i			0.0537590i
$534$		0			0
$535$	12.7548	−	32.0643i	0.551437	−	1.38626i
$536$	21.3861			0.923739
$537$		0			0
$538$		−	53.5006i		−	2.30657i
$539$	13.1122			0.564783
$540$		0			0
$541$	2.21946			0.0954220			0.0477110	−	0.998861i	$-0.484807\pi$
$541$	2.21946			0.0954220			0.0477110	+	0.998861i	$0.484807\pi$
$542$			9.88865i			0.424754i
$543$		0			0
$544$	−7.79798			−0.334336
$545$	−24.3333	−	9.67948i	−1.04232	−	0.414623i
$546$		0			0
$547$			14.4297i			0.616970i	0.951229	+	0.308485i	$0.0998220\pi$
$547$			14.4297i			0.616970i	−0.951229	+	0.308485i	$0.900178\pi$
$548$			30.6265i			1.30830i
$549$		0			0
$550$	−34.5353	+	36.5404i	−1.47259	+	1.55809i
$551$	6.00000			0.255609
$552$		0			0
$553$			4.46360i			0.189812i
$554$	24.2469			1.03015
$555$		0			0
$556$	12.5993			0.534331
$557$			19.4610i			0.824588i	0.911051	+	0.412294i	$0.135272\pi$
$557$			19.4610i			0.824588i	−0.911051	+	0.412294i	$0.864728\pi$
$558$		0			0
$559$	−6.59933			−0.279122
$560$	−8.31087	+	20.8927i	−0.351198	+	0.882879i
$561$		0			0
$562$			1.45030i			0.0611771i
$563$			12.3649i			0.521118i	0.965458	+	0.260559i	$0.0839068\pi$
$563$			12.3649i			0.521118i	−0.965458	+	0.260559i	$0.916093\pi$
$564$		0			0
$565$	−8.75476	+	22.0086i	−0.368316	+	0.925911i
$566$	13.1122			0.551148
$567$		0			0
$568$		−	61.5748i		−	2.58362i
$569$	15.0898			0.632597			0.316299	−	0.948660i	$-0.397560\pi$
$569$	15.0898			0.632597			0.316299	+	0.948660i	$0.397560\pi$
$570$		0			0
$571$	17.1571			0.718000			0.359000	−	0.933337i	$-0.383118\pi$
$571$	17.1571			0.718000			0.359000	+	0.933337i	$0.383118\pi$
$572$			33.1802i			1.38733i
$573$		0			0
$574$	4.62175			0.192908
$575$	−8.95678	+	9.47680i	−0.373524	+	0.395210i
$576$		0			0
$577$			22.5165i			0.937374i	0.883364	+	0.468687i	$0.155273\pi$
$577$			22.5165i			0.937374i	−0.883364	+	0.468687i	$0.844727\pi$
$578$			40.1179i			1.66868i
$579$		0			0
$580$	−48.0673	−	19.1206i	−1.99588	−	0.793938i
$581$	−22.5353			−0.934922
$582$		0			0
$583$			48.8278i			2.02224i
$584$	12.2469			0.506778
$585$		0			0
$586$	−8.38946			−0.346566
$587$			7.49544i			0.309370i	0.987964	+	0.154685i	$0.0494363\pi$
$587$			7.49544i			0.309370i	−0.987964	+	0.154685i	$0.950564\pi$
$588$		0			0
$589$	2.59933			0.107103
$590$	−3.42309	+	8.60532i	−0.140926	+	0.354275i
$591$		0			0
$592$		−	13.5768i		−	0.558002i
$593$		−	27.8094i		−	1.14199i	−0.820952	−	0.570997i	$-0.806557\pi$
$593$		−	27.8094i		−	1.14199i	0.820952	−	0.570997i	$-0.193443\pi$
$594$		0			0
$595$	−38.3678	−	15.2622i	−1.57293	−	0.625690i
$596$	−32.5577			−1.33362
$597$		0			0
$598$			13.0689i			0.534428i
$599$	−45.4903			−1.85869			−0.929343	−	0.369219i	$-0.879625\pi$
$599$	−45.4903			−1.85869			−0.929343	+	0.369219i	$0.879625\pi$
$600$		0			0
$601$	−16.5993			−0.677101			−0.338550	−	0.940948i	$-0.609937\pi$
$601$	−16.5993			−0.677101			−0.338550	+	0.940948i	$0.609937\pi$
$602$			24.5748i			1.00160i
$603$		0			0
$604$	−3.42309			−0.139284
$605$	13.0224	+	5.18016i	0.529437	+	0.210603i
$606$		0			0
$607$			5.08417i			0.206360i	0.994663	+	0.103180i	$0.0329018\pi$
$607$			5.08417i			0.206360i	−0.994663	+	0.103180i	$0.967098\pi$
$608$			1.34571i			0.0545758i
$609$		0			0
$610$	−17.5095	+	44.0173i	−0.708940	+	1.78221i
$611$	−24.2469			−0.980923
$612$		0			0
$613$			4.63706i			0.187289i	0.995606	+	0.0936445i	$0.0298517\pi$
$613$			4.63706i			0.187289i	−0.995606	+	0.0936445i	$0.970148\pi$
$614$	40.1458			1.62015
$615$		0			0
$616$	59.4679			2.39603
$617$			40.2874i			1.62191i	0.585108	+	0.810955i	$0.301052\pi$
$617$			40.2874i			1.62191i	−0.585108	+	0.810955i	$0.698948\pi$
$618$		0			0
$619$	43.3815			1.74365			0.871825	−	0.489818i	$-0.162937\pi$
$619$	43.3815			1.74365			0.871825	+	0.489818i	$0.162937\pi$
$620$	−20.8238	−	8.28343i	−0.836302	−	0.332671i
$621$		0			0
$622$		−	10.0556i		−	0.403194i
$623$			52.6940i			2.11114i
$624$		0			0
$625$	1.40939	+	24.9602i	0.0563757	+	0.998410i
$626$	−2.22443			−0.0889062
$627$		0			0
$628$			15.9695i			0.637253i
$629$	24.9326			0.994129
$630$		0			0
$631$	7.53369			0.299911			0.149956	−	0.988693i	$-0.452087\pi$
$631$	7.53369			0.299911			0.149956	+	0.988693i	$0.452087\pi$
$632$			6.29004i			0.250204i
$633$		0			0
$634$	−64.6812			−2.56882
$635$	−5.02080	+	12.6218i	−0.199244	+	0.500881i
$636$		0			0
$637$		−	6.53446i		−	0.258905i
$638$			60.3337i			2.38863i
$639$		0			0
$640$	16.9102	−	42.5106i	0.668434	−	1.68038i
$641$	23.3075			0.920591			0.460296	−	0.887766i	$-0.347743\pi$
$641$	23.3075			0.920591			0.460296	+	0.887766i	$0.347743\pi$
$642$		0			0
$643$			1.87419i			0.0739110i	0.999317	+	0.0369555i	$0.0117660\pi$
$643$			1.87419i			0.0739110i	−0.999317	+	0.0369555i	$0.988234\pi$
$644$	32.0448			1.26274
$645$		0			0
$646$	14.0224			0.551705
$647$		−	47.0371i		−	1.84922i	−0.380917	−	0.924609i	$-0.624392\pi$
$647$		−	47.0371i		−	1.84922i	0.380917	−	0.924609i	$-0.375608\pi$
$648$		0			0
$649$	7.11222			0.279179
$650$	18.2099	+	17.2106i	0.714250	+	0.675057i
$651$		0			0
$652$			95.2861i			3.73169i
$653$		−	24.1630i		−	0.945571i	−0.881178	−	0.472785i	$-0.843249\pi$
$653$		−	24.1630i		−	0.945571i	0.881178	−	0.472785i	$-0.156751\pi$
$654$		0			0
$655$	28.2124	+	11.2225i	1.10235	+	0.438500i
$656$	1.89114			0.0738367
$657$		0			0
$658$			90.2914i			3.51992i
$659$	10.2885			0.400781			0.200391	−	0.979716i	$-0.435779\pi$
$659$	10.2885			0.400781			0.200391	+	0.979716i	$0.435779\pi$
$660$		0			0
$661$	5.93598			0.230883			0.115441	−	0.993314i	$-0.463172\pi$
$661$	5.93598			0.230883			0.115441	+	0.993314i	$0.463172\pi$
$662$		−	19.3590i		−	0.752407i
$663$		0			0
$664$	−31.7564			−1.23239
$665$	−2.63383	+	6.62119i	−0.102135	+	0.256759i
$666$		0			0
$667$			15.6476i			0.605879i
$668$			13.8987i			0.537755i
$669$		0			0
$670$	−23.9438	−	9.52456i	−0.925031	−	0.367966i
$671$	36.3799			1.40443
$672$		0			0
$673$		−	40.7053i		−	1.56907i	−0.620082	−	0.784537i	$-0.712901\pi$
$673$		−	40.7053i		−	1.56907i	0.620082	−	0.784537i	$-0.287099\pi$
$674$	−54.4567			−2.09759
$675$		0			0
$676$	−33.5897			−1.29191
$677$			18.8761i			0.725469i	0.931893	+	0.362734i	$0.118157\pi$
$677$			18.8761i			0.725469i	−0.931893	+	0.362734i	$0.881843\pi$
$678$		0			0
$679$	6.59933			0.253259
$680$	−54.0673	−	21.5073i	−2.07338	−	0.824767i
$681$		0			0
$682$			26.1379i			1.00087i
$683$			19.6576i			0.752179i	0.926583	+	0.376089i	$0.122731\pi$
$683$			19.6576i			0.752179i	−0.926583	+	0.376089i	$0.877269\pi$
$684$		0			0
$685$	6.56483	−	16.5034i	0.250829	−	0.630561i
$686$	29.6475			1.13195
$687$		0			0
$688$			10.0556i			0.383367i
$689$	24.3333			0.927025
$690$		0			0
$691$	−48.2451			−1.83533			−0.917665	−	0.397354i	$-0.869928\pi$
$691$	−48.2451			−1.83533			−0.917665	+	0.397354i	$0.869928\pi$
$692$		−	86.4483i		−	3.28627i
$693$		0			0
$694$	−34.9775			−1.32773
$695$	−6.78926	−	2.70068i	−0.257531	−	0.102443i
$696$		0			0
$697$			3.47293i			0.131546i
$698$		−	32.3152i		−	1.22315i
$699$		0			0
$700$	42.2003	−	44.6504i	1.59502	−	1.68762i
$701$	−0.512889			−0.0193715			−0.00968577	−	0.999953i	$-0.503083\pi$
$701$	−0.512889			−0.0193715			−0.00968577	+	0.999953i	$0.503083\pi$
$702$		0			0
$703$		−	4.30266i		−	0.162278i
$704$	−39.7564			−1.49838
$705$		0			0
$706$	−42.6890			−1.60662
$707$			5.45428i			0.205129i
$708$		0			0
$709$	8.84618			0.332225			0.166113	−	0.986107i	$-0.446878\pi$
$709$	8.84618			0.332225			0.166113	+	0.986107i	$0.446878\pi$
$710$	−27.4231	+	68.9390i	−1.02917	+	2.58724i
$711$		0			0
$712$			74.2556i			2.78285i
$713$			6.77889i			0.253871i
$714$		0			0
$715$	7.11222	−	17.8794i	0.265982	−	0.668653i
$716$	19.7980			0.739885
$717$		0			0
$718$		−	30.1669i		−	1.12582i
$719$	7.84456			0.292553			0.146276	−	0.989244i	$-0.453271\pi$
$719$	7.84456			0.292553			0.146276	+	0.989244i	$0.453271\pi$
$720$		0			0
$721$	−18.3333			−0.682767
$722$		−	2.41987i		−	0.0900582i
$723$		0			0
$724$	−80.3781			−2.98723
$725$	21.8030	+	20.6066i	0.809742	+	0.765309i
$726$		0			0
$727$			2.91130i			0.107974i	0.998542	+	0.0539870i	$0.0171930\pi$
$727$			2.91130i			0.107974i	−0.998542	+	0.0539870i	$0.982807\pi$
$728$		−	29.6358i		−	1.09838i
$729$		0			0
$730$	−13.7115	−	5.45428i	−0.507487	−	0.201872i
$731$	−18.4663			−0.683001
$732$		0			0
$733$		−	33.7775i		−	1.24760i	−0.781584	−	0.623800i	$-0.785588\pi$
$733$		−	33.7775i		−	1.24760i	0.781584	−	0.623800i	$-0.214412\pi$
$734$	39.7564			1.46743
$735$		0			0
$736$	−3.50953			−0.129363
$737$			19.7893i			0.728950i
$738$		0			0
$739$	35.8030			1.31703			0.658517	−	0.752566i	$-0.271184\pi$
$739$	35.8030			1.31703			0.658517	+	0.752566i	$0.271184\pi$
$740$	−13.7115	+	34.4695i	−0.504046	+	1.26712i
$741$		0			0
$742$		−	90.6133i		−	3.32652i
$743$			5.66948i			0.207993i	0.994578	+	0.103996i	$0.0331631\pi$
$743$			5.66948i			0.207993i	−0.994578	+	0.103996i	$0.966837\pi$
$744$		0			0
$745$	17.5440	+	6.97880i	0.642763	+	0.255683i
$746$	−12.8092			−0.468978
$747$		0			0
$748$			92.8451i			3.39475i
$749$	49.1795			1.79698
$750$		0			0
$751$	−27.4679			−1.00232			−0.501159	−	0.865355i	$-0.667093\pi$
$751$	−27.4679			−1.00232			−0.501159	+	0.865355i	$0.667093\pi$
$752$			36.9457i			1.34727i
$753$		0			0
$754$	30.0673			1.09498
$755$	1.84456	+	0.733744i	0.0671305	+	0.0267037i
$756$		0			0
$757$			41.6370i			1.51332i	0.653806	+	0.756662i	$0.273171\pi$
$757$			41.6370i			1.51332i	−0.653806	+	0.756662i	$0.726829\pi$
$758$			35.1736i			1.27756i
$759$		0			0
$760$	−3.71155	+	9.33047i	−0.134632	+	0.338452i
$761$	9.46967			0.343275			0.171638	−	0.985160i	$-0.445094\pi$
$761$	9.46967			0.343275			0.171638	+	0.985160i	$0.445094\pi$
$762$		0			0
$763$		−	37.3219i		−	1.35114i
$764$	−20.3109			−0.734822
$765$		0			0
$766$	−1.09765			−0.0396597
$767$		−	3.54437i		−	0.127980i
$768$		0			0
$769$	−1.90858			−0.0688253			−0.0344127	−	0.999408i	$-0.510956\pi$
$769$	−1.90858			−0.0688253			−0.0344127	+	0.999408i	$0.510956\pi$
$770$	−66.5801	−	26.4848i	−2.39938	−	0.954444i
$771$		0			0
$772$		−	7.98476i		−	0.287378i
$773$			28.4007i			1.02150i	0.859729	+	0.510751i	$0.170633\pi$
$773$			28.4007i			1.02150i	−0.859729	+	0.510751i	$0.829367\pi$
$774$		0			0
$775$	9.44551	+	8.92721i	0.339293	+	0.320675i
$776$	9.29966			0.333838
$777$		0			0
$778$		−	39.0941i		−	1.40159i
$779$	0.599328			0.0214732
$780$		0			0
$781$	56.9775			2.03881
$782$			36.5696i			1.30773i
$783$		0			0
$784$	−9.95678			−0.355599
$785$	3.42309	−	8.60532i	0.122175	−	0.307137i
$786$		0			0
$787$		−	15.6708i		−	0.558605i	−0.960203	−	0.279303i	$-0.909897\pi$
$787$		−	15.6708i		−	0.558605i	0.960203	−	0.279303i	$-0.0901033\pi$
$788$		−	40.2225i		−	1.43287i
$789$		0			0
$790$	2.80134	−	7.04231i	0.0996673	−	0.250554i
$791$	−33.7564			−1.20024
$792$		0			0
$793$		−	18.1299i		−	0.643811i
$794$	−79.2659			−2.81304
$795$		0			0
$796$	−10.5353			−0.373414
$797$		−	36.9225i		−	1.30786i	−0.756554	−	0.653932i	$-0.773118\pi$
$797$		−	36.9225i		−	1.30786i	0.756554	−	0.653932i	$-0.226882\pi$
$798$		0			0
$799$	−67.8478			−2.40028
$800$	−4.62175	+	4.89008i	−0.163403	+	0.172890i
$801$		0			0
$802$			29.2476i			1.03277i
$803$			11.3325i			0.399914i
$804$		0			0
$805$	−17.2677	−	6.86886i	−0.608605	−	0.242095i
$806$	13.0258			0.458813
$807$		0			0
$808$			7.68608i			0.270396i
$809$	43.0465			1.51343			0.756716	−	0.653743i	$-0.226802\pi$
$809$	43.0465			1.51343			0.756716	+	0.653743i	$0.226802\pi$
$810$		0			0
$811$	32.2469			1.13234			0.566170	−	0.824288i	$-0.308425\pi$
$811$	32.2469			1.13234			0.566170	+	0.824288i	$0.308425\pi$
$812$		−	73.7245i		−	2.58722i
$813$		0			0
$814$	43.2659			1.51647
$815$	20.4247	−	51.3458i	0.715446	−	1.79856i
$816$		0			0
$817$			3.18676i			0.111491i
$818$		−	46.3033i		−	1.61896i
$819$		0			0
$820$	−4.80134	−	1.90991i	−0.167670	−	0.0666971i
$821$	−5.18121			−0.180826			−0.0904128	−	0.995904i	$-0.528819\pi$
$821$	−5.18121			−0.180826			−0.0904128	+	0.995904i	$0.528819\pi$
$822$		0			0
$823$		−	25.8517i		−	0.901133i	−0.892743	−	0.450567i	$-0.851222\pi$
$823$		−	25.8517i		−	0.901133i	0.892743	−	0.450567i	$-0.148778\pi$
$824$	−25.8350			−0.900004
$825$		0			0
$826$	−13.1987			−0.459240
$827$		−	9.97816i		−	0.346974i	−0.984836	−	0.173487i	$-0.944496\pi$
$827$		−	9.97816i		−	0.346974i	0.984836	−	0.173487i	$-0.0555035\pi$
$828$		0			0
$829$	−21.9808			−0.763425			−0.381713	−	0.924281i	$-0.624666\pi$
$829$	−21.9808			−0.763425			−0.381713	+	0.924281i	$0.624666\pi$
$830$	35.5544	+	14.1431i	1.23411	+	0.490914i
$831$		0			0
$832$			19.8126i			0.686877i
$833$		−	18.2848i		−	0.633531i
$834$		0			0
$835$	2.97920	−	7.48942i	0.103099	−	0.259182i
$836$	16.0224			0.554147
$837$		0			0
$838$		−	19.4675i		−	0.672492i
$839$	−16.1089			−0.556140			−0.278070	−	0.960561i	$-0.589695\pi$
$839$	−16.1089			−0.556140			−0.278070	+	0.960561i	$0.589695\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$			71.0451i			2.44838i
$843$		0			0
$844$	60.6666			2.08823
$845$	18.1001	+	7.20001i	0.622664	+	0.247688i
$846$		0			0
$847$			19.9735i			0.686298i
$848$		−	37.0775i		−	1.27324i
$849$		0			0
$850$	50.9550	+	48.1590i	1.74774	+	1.65184i
$851$	11.2211			0.384653
$852$		0			0
$853$			44.9615i			1.53945i	0.638373	+	0.769727i	$0.279608\pi$
$853$			44.9615i			1.53945i	−0.638373	+	0.769727i	$0.720392\pi$
$854$	−67.5128			−2.31024
$855$		0			0
$856$	69.3029			2.36872
$857$		−	46.2431i		−	1.57963i	−0.613343	−	0.789817i	$-0.710176\pi$
$857$		−	46.2431i		−	1.57963i	0.613343	−	0.789817i	$-0.289824\pi$
$858$		0			0
$859$	10.7772			0.367713			0.183856	−	0.982953i	$-0.441142\pi$
$859$	10.7772			0.367713			0.183856	+	0.982953i	$0.441142\pi$
$860$	10.1554	−	25.5298i	0.346298	−	0.870559i
$861$		0			0
$862$		−	77.5443i		−	2.64117i
$863$		−	22.7966i		−	0.776007i	−0.921658	−	0.388003i	$-0.873165\pi$
$863$		−	22.7966i		−	0.776007i	0.921658	−	0.388003i	$-0.126835\pi$
$864$		0			0
$865$	−18.5303	+	46.5835i	−0.630050	+	1.58389i
$866$	1.16839			0.0397034
$867$		0			0
$868$		−	31.9390i		−	1.08408i
$869$	−5.82040			−0.197444
$870$		0			0
$871$	9.86201			0.334161
$872$		−	52.5934i		−	1.78104i
$873$		0			0
$874$	6.31087			0.213468
$875$	−32.3109	+	15.0146i	−1.09231	+	0.507585i
$876$		0			0
$877$			4.94644i			0.167029i	0.996507	+	0.0835146i	$0.0266145\pi$
$877$			4.94644i			0.167029i	−0.996507	+	0.0835146i	$0.973385\pi$
$878$		−	66.2054i		−	2.23432i
$879$		0			0
$880$	−27.2435	−	10.8371i	−0.918378	−	0.365319i
$881$	−2.53033			−0.0852490			−0.0426245	−	0.999091i	$-0.513572\pi$
$881$	−2.53033			−0.0852490			−0.0426245	+	0.999091i	$0.513572\pi$
$882$		0			0
$883$			29.7430i			1.00093i	0.865757	+	0.500465i	$0.166838\pi$
$883$			29.7430i			1.00093i	−0.865757	+	0.500465i	$0.833162\pi$
$884$	46.2693			1.55620
$885$		0			0
$886$	−56.5801			−1.90085
$887$			45.5450i			1.52925i	0.644474	+	0.764626i	$0.277076\pi$
$887$			45.5450i			1.52925i	−0.644474	+	0.764626i	$0.722924\pi$
$888$		0			0
$889$	−19.3591			−0.649282
$890$	33.0706	−	83.1364i	1.10853	−	2.78674i
$891$		0			0
$892$		−	72.5729i		−	2.42992i
$893$			11.7086i			0.391813i
$894$		0			0
$895$	−10.6683	−	4.24373i	−0.356603	−	0.141852i
$896$	65.2019			2.17824
$897$		0			0
$898$		−	55.9828i		−	1.86817i
$899$	15.5960			0.520155
$900$		0			0
$901$	68.0897			2.26840
$902$			6.02662i			0.200664i
$903$		0			0
$904$	−47.5689			−1.58212
$905$	43.3125	+	17.2292i	1.43976	+	0.572717i
$906$		0			0
$907$		−	33.2034i		−	1.10250i	−0.834340	−	0.551250i	$-0.814151\pi$
$907$		−	33.2034i		−	1.10250i	0.834340	−	0.551250i	$-0.185849\pi$
$908$			55.6841i			1.84794i
$909$		0			0
$910$	−13.1987	+	33.1802i	−0.437531	+	1.09991i
$911$	−55.7788			−1.84803			−0.924017	−	0.382351i	$-0.875114\pi$
$911$	−55.7788			−1.84803			−0.924017	+	0.382351i	$0.875114\pi$
$912$		0			0
$913$		−	29.3853i		−	0.972513i
$914$	−51.4231			−1.70092
$915$		0			0
$916$	−16.1089			−0.532252
$917$			43.2715i			1.42895i
$918$		0			0
$919$	28.5769			0.942665			0.471333	−	0.881956i	$-0.343773\pi$
$919$	28.5769			0.942665			0.471333	+	0.881956i	$0.343773\pi$
$920$	−24.3333	−	9.67948i	−0.802245	−	0.319123i
$921$		0			0
$922$			76.4159i			2.51662i
$923$		−	28.3947i		−	0.934622i
$924$		0			0
$925$	14.7772	−	15.6351i	0.485871	−	0.514080i
$926$	−37.7788			−1.24149
$927$		0			0
$928$			8.07426i			0.265051i
$929$	−54.4937			−1.78788			−0.893940	−	0.448186i	$-0.852070\pi$
$929$	−54.4937			−1.78788			−0.893940	+	0.448186i	$0.852070\pi$
$930$		0			0
$931$	−3.15544			−0.103415
$932$			46.5960i			1.52630i
$933$		0			0
$934$	−72.1761			−2.36167
$935$	19.9015	−	50.0304i	0.650848	−	1.63617i
$936$		0			0
$937$			37.1484i			1.21359i	0.794860	+	0.606793i	$0.207544\pi$
$937$			37.1484i			1.21359i	−0.794860	+	0.606793i	$0.792456\pi$
$938$		−	36.7245i		−	1.19910i
$939$		0			0
$940$	37.3125	−	93.8000i	1.21700	−	3.05942i
$941$	−32.3973			−1.05612			−0.528061	−	0.849206i	$-0.677081\pi$
$941$	−32.3973			−1.05612			−0.528061	+	0.849206i	$0.677081\pi$
$942$		0			0
$943$			1.56301i			0.0508986i
$944$	−5.40067			−0.175777
$945$		0			0
$946$	−32.0448			−1.04187
$947$			35.4662i			1.15250i	0.817275	+	0.576249i	$0.195484\pi$
$947$			35.4662i			1.15250i	−0.817275	+	0.576249i	$0.804516\pi$
$948$		0			0
$949$	5.64752			0.183326
$950$	8.31087	−	8.79339i	0.269640	−	0.285295i
$951$		0			0
$952$		−	82.9272i		−	2.68769i
$953$			14.3411i			0.464553i	0.972650	+	0.232277i	$0.0746175\pi$
$953$			14.3411i			0.464553i	−0.972650	+	0.232277i	$0.925383\pi$
$954$		0			0
$955$	10.9447	+	4.35367i	0.354162	+	0.140881i
$956$	43.7788			1.41591
$957$		0			0
$958$		−	10.9749i		−	0.354581i
$959$	25.3125			0.817383
$960$		0			0
$961$	−24.2435			−0.782048
$962$		−	21.5615i		−	0.695172i
$963$		0			0
$964$	13.1122			0.422316
$965$	−1.71155	+	4.30266i	−0.0550966	+	0.138508i
$966$		0			0
$967$			27.9351i			0.898331i	0.893449	+	0.449165i	$0.148279\pi$
$967$			27.9351i			0.898331i	−0.893449	+	0.449165i	$0.851721\pi$
$968$			28.1463i			0.904657i
$969$		0			0
$970$	−10.4119	−	4.14172i	−0.334305	−	0.132983i
$971$	42.5993			1.36708			0.683539	−	0.729914i	$-0.260440\pi$
$971$	42.5993			1.36708			0.683539	+	0.729914i	$0.260440\pi$
$972$		0			0
$973$		−	10.4132i		−	0.333833i
$974$	−94.9920			−3.04374
$975$		0			0
$976$	−27.6251			−0.884258
$977$			39.5597i			1.26563i	0.774304	+	0.632813i	$0.218100\pi$
$977$			39.5597i			1.26563i	−0.774304	+	0.632813i	$0.781900\pi$
$978$		0			0
$979$	−68.7114			−2.19603
$980$	25.2789	+	10.0556i	0.807504	+	0.321215i
$981$		0			0
$982$			94.1112i			3.00321i
$983$			39.7689i			1.26843i	0.773157	+	0.634215i	$0.218677\pi$
$983$			39.7689i			1.26843i	−0.773157	+	0.634215i	$0.781323\pi$
$984$		0			0
$985$	−8.62175	+	21.6742i	−0.274712	+	0.690599i
$986$	84.1345			2.67939
$987$		0			0
$988$		−	7.98476i		−	0.254029i
$989$	−8.31087			−0.264270
$990$		0			0
$991$	55.2019			1.75355			0.876773	−	0.480905i	$-0.159692\pi$
$991$	55.2019			1.75355			0.876773	+	0.480905i	$0.159692\pi$
$992$			3.49794i			0.111060i
$993$		0			0
$994$	−105.737			−3.35378
$995$	5.67705	+	2.25826i	0.179974	+	0.0715916i
$996$		0			0
$997$			11.6543i			0.369097i	0.982823	+	0.184548i	$0.0590823\pi$
$997$			11.6543i			0.369097i	−0.982823	+	0.184548i	$0.940918\pi$
$998$			11.4517i			0.362496i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.c.d.514.1		6
3.2	odd	2		95.2.b.b.39.6	yes	6
5.2	odd	4		4275.2.a.br.1.6		6
5.3	odd	4		4275.2.a.br.1.1		6
5.4	even	2	inner	855.2.c.d.514.6		6
12.11	even	2		1520.2.d.h.609.3		6
15.2	even	4		475.2.a.j.1.1		6
15.8	even	4		475.2.a.j.1.6		6
15.14	odd	2		95.2.b.b.39.1	✓	6
57.56	even	2		1805.2.b.e.1084.1		6
60.23	odd	4		7600.2.a.ck.1.4		6
60.47	odd	4		7600.2.a.ck.1.3		6
60.59	even	2		1520.2.d.h.609.4		6
285.113	odd	4		9025.2.a.bx.1.1		6
285.227	odd	4		9025.2.a.bx.1.6		6
285.284	even	2		1805.2.b.e.1084.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.b.b.39.1	✓	6	15.14	odd	2
95.2.b.b.39.6	yes	6	3.2	odd	2
475.2.a.j.1.1		6	15.2	even	4
475.2.a.j.1.6		6	15.8	even	4
855.2.c.d.514.1		6	1.1	even	1	trivial
855.2.c.d.514.6		6	5.4	even	2	inner
1520.2.d.h.609.3		6	12.11	even	2
1520.2.d.h.609.4		6	60.59	even	2
1805.2.b.e.1084.1		6	57.56	even	2
1805.2.b.e.1084.6		6	285.284	even	2
4275.2.a.br.1.1		6	5.3	odd	4
4275.2.a.br.1.6		6	5.2	odd	4
7600.2.a.ck.1.3		6	60.47	odd	4
7600.2.a.ck.1.4		6	60.23	odd	4
9025.2.a.bx.1.1		6	285.113	odd	4
9025.2.a.bx.1.6		6	285.227	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.41987i q^{2} -3.85577 q^{4} +(2.07772 + 0.826491i) q^{5} +3.18676i q^{7} +4.49073i q^{8} +O(q^{10})\)	\(q-2.41987i q^{2} -3.85577 q^{4} +(2.07772 + 0.826491i) q^{5} +3.18676i q^{7} +4.49073i q^{8} +(2.00000 - 5.02781i) q^{10} -4.15544 q^{11} +2.07086i q^{13} +7.71155 q^{14} +3.15544 q^{16} +5.79470i q^{17} +1.00000 q^{19} +(-8.01121 - 3.18676i) q^{20} +10.0556i q^{22} +2.60794i q^{23} +(3.63383 + 3.43443i) q^{25} +5.01121 q^{26} -12.2874i q^{28} +6.00000 q^{29} +2.59933 q^{31} +1.34571i q^{32} +14.0224 q^{34} +(-2.63383 + 6.62119i) q^{35} -4.30266i q^{37} -2.41987i q^{38} +(-3.71155 + 9.33047i) q^{40} +0.599328 q^{41} +3.18676i q^{43} +16.0224 q^{44} +6.31087 q^{46} +11.7086i q^{47} -3.15544 q^{49} +(8.31087 - 8.79339i) q^{50} -7.98476i q^{52} -11.7503i q^{53} +(-8.63383 - 3.43443i) q^{55} -14.3109 q^{56} -14.5192i q^{58} -1.71155 q^{59} -8.75476 q^{61} -6.29004i q^{62} +9.56732 q^{64} +(-1.71155 + 4.30266i) q^{65} -4.76228i q^{67} -22.3430i q^{68} +(16.0224 + 6.37352i) q^{70} -13.7115 q^{71} -2.72714i q^{73} -10.4119 q^{74} -3.85577 q^{76} -13.2424i q^{77} +1.40067 q^{79} +(6.55611 + 2.60794i) q^{80} -1.45030i q^{82} +7.07154i q^{83} +(-4.78926 + 12.0398i) q^{85} +7.71155 q^{86} -18.6609i q^{88} +16.5353 q^{89} -6.59933 q^{91} -10.0556i q^{92} +28.3333 q^{94} +(2.07772 + 0.826491i) q^{95} -2.07086i q^{97} +7.63575i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 8 q^{4} + q^{5}+O(q^{10}) \) 6 * q - 8 * q^4 + q^5	\( 6 q - 8 q^{4} + q^{5} + 12 q^{10} - 2 q^{11} + 16 q^{14} - 4 q^{16} + 6 q^{19} - 10 q^{20} + 3 q^{25} - 8 q^{26} + 36 q^{29} + 8 q^{34} + 3 q^{35} + 8 q^{40} - 12 q^{41} + 20 q^{44} - 8 q^{46} + 4 q^{49} + 4 q^{50} - 33 q^{55} - 40 q^{56} + 20 q^{59} - 14 q^{61} + 12 q^{64} + 20 q^{65} + 20 q^{70} - 52 q^{71} - 40 q^{74} - 8 q^{76} + 24 q^{79} + 32 q^{80} + 13 q^{85} + 16 q^{86} + 24 q^{89} - 24 q^{91} + 48 q^{94} + q^{95}+O(q^{100}) \) 6 * q - 8 * q^4 + q^5 + 12 * q^10 - 2 * q^11 + 16 * q^14 - 4 * q^16 + 6 * q^19 - 10 * q^20 + 3 * q^25 - 8 * q^26 + 36 * q^29 + 8 * q^34 + 3 * q^35 + 8 * q^40 - 12 * q^41 + 20 * q^44 - 8 * q^46 + 4 * q^49 + 4 * q^50 - 33 * q^55 - 40 * q^56 + 20 * q^59 - 14 * q^61 + 12 * q^64 + 20 * q^65 + 20 * q^70 - 52 * q^71 - 40 * q^74 - 8 * q^76 + 24 * q^79 + 32 * q^80 + 13 * q^85 + 16 * q^86 + 24 * q^89 - 24 * q^91 + 48 * q^94 + q^95

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