LMFDB - Embedded newform 381.3.d.a.253.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [381,3,Mod(253,381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(381, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("381.253");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 381 = 3 \cdot 127 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	381.d (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:	$10.3814980721$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			253.2
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	381.253
Dual form			381.3.d.a.253.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} +1.73205i q^{3} +8.66025i q^{5} -3.46410i q^{6} -6.92820i q^{7} +8.00000 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +1.73205i q^{3} +8.66025i q^{5} -3.46410i q^{6} -6.92820i q^{7} +8.00000 q^{8} -3.00000 q^{9} -17.3205i q^{10} +10.0000 q^{11} +23.0000 q^{13} +13.8564i q^{14} -15.0000 q^{15} -16.0000 q^{16} +10.0000 q^{17} +6.00000 q^{18} +26.0000 q^{19} +12.0000 q^{21} -20.0000 q^{22} +8.66025i q^{23} +13.8564i q^{24} -50.0000 q^{25} -46.0000 q^{26} -5.19615i q^{27} +12.1244i q^{29} +30.0000 q^{30} -25.0000 q^{31} +17.3205i q^{33} -20.0000 q^{34} +60.0000 q^{35} -37.0000 q^{37} -52.0000 q^{38} +39.8372i q^{39} +69.2820i q^{40} +16.0000 q^{41} -24.0000 q^{42} +24.2487i q^{43} -25.9808i q^{45} -17.3205i q^{46} +82.0000 q^{47} -27.7128i q^{48} +1.00000 q^{49} +100.000 q^{50} +17.3205i q^{51} -77.9423i q^{53} +10.3923i q^{54} +86.6025i q^{55} -55.4256i q^{56} +45.0333i q^{57} -24.2487i q^{58} +91.7987i q^{59} -79.0000 q^{61} +50.0000 q^{62} +20.7846i q^{63} +64.0000 q^{64} +199.186i q^{65} -34.6410i q^{66} +79.6743i q^{67} -15.0000 q^{69} -120.000 q^{70} -26.0000 q^{71} -24.0000 q^{72} +17.0000 q^{73} +74.0000 q^{74} -86.6025i q^{75} -69.2820i q^{77} -79.6743i q^{78} +26.0000 q^{79} -138.564i q^{80} +9.00000 q^{81} -32.0000 q^{82} -60.6218i q^{83} +86.6025i q^{85} -48.4974i q^{86} -21.0000 q^{87} +80.0000 q^{88} +57.1577i q^{89} +51.9615i q^{90} -159.349i q^{91} -43.3013i q^{93} -164.000 q^{94} +225.167i q^{95} -121.244i q^{97} -2.00000 q^{98} -30.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} + 16 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q - 4 * q^2 + 16 * q^8 - 6 * q^9	$ 2 q - 4 q^{2} + 16 q^{8} - 6 q^{9} + 20 q^{11} + 46 q^{13} - 30 q^{15} - 32 q^{16} + 20 q^{17} + 12 q^{18} + 52 q^{19} + 24 q^{21} - 40 q^{22} - 100 q^{25} - 92 q^{26} + 60 q^{30} - 50 q^{31} - 40 q^{34} + 120 q^{35} - 74 q^{37} - 104 q^{38} + 32 q^{41} - 48 q^{42} + 164 q^{47} + 2 q^{49} + 200 q^{50} - 158 q^{61} + 100 q^{62} + 128 q^{64} - 30 q^{69} - 240 q^{70} - 52 q^{71} - 48 q^{72} + 34 q^{73} + 148 q^{74} + 52 q^{79} + 18 q^{81} - 64 q^{82} - 42 q^{87} + 160 q^{88} - 328 q^{94} - 4 q^{98} - 60 q^{99}+O(q^{100}) $ 2 * q - 4 * q^2 + 16 * q^8 - 6 * q^9 + 20 * q^11 + 46 * q^13 - 30 * q^15 - 32 * q^16 + 20 * q^17 + 12 * q^18 + 52 * q^19 + 24 * q^21 - 40 * q^22 - 100 * q^25 - 92 * q^26 + 60 * q^30 - 50 * q^31 - 40 * q^34 + 120 * q^35 - 74 * q^37 - 104 * q^38 + 32 * q^41 - 48 * q^42 + 164 * q^47 + 2 * q^49 + 200 * q^50 - 158 * q^61 + 100 * q^62 + 128 * q^64 - 30 * q^69 - 240 * q^70 - 52 * q^71 - 48 * q^72 + 34 * q^73 + 148 * q^74 + 52 * q^79 + 18 * q^81 - 64 * q^82 - 42 * q^87 + 160 * q^88 - 328 * q^94 - 4 * q^98 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/381\mathbb{Z}\right)^\times$.

$n$	$128$	$130$
$\chi(n)$	$1$	$-1$

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 $

$2$	−2.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$2$	−2.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$3$	1.73205i	0.577350i
$3$	1.73205i	0.577350i
$4$	0	0
$5$	8.66025i	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$5$	8.66025i	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$6$	− 3.46410i	− 0.577350i
$7$	− 6.92820i	− 0.989743i	−0.868966	−	0.494872i	$-0.835215\pi$
$7$	− 6.92820i	− 0.989743i	0.868966	−	0.494872i	$-0.164785\pi$
$8$	8.00000	1.00000
$9$	−3.00000	−0.333333
$10$	− 17.3205i	− 1.73205i
$11$	10.0000	0.909091	0.454545	−	0.890724i	$-0.349802\pi$
$11$	10.0000	0.909091	0.454545	+	0.890724i	$0.349802\pi$
$12$	0	0
$13$	23.0000	1.76923	0.884615	−	0.466321i	$-0.154421\pi$
$13$	23.0000	1.76923	0.884615	+	0.466321i	$0.154421\pi$
$14$	13.8564i	0.989743i
$15$	−15.0000	−1.00000
$16$	−16.0000	−1.00000
$17$	10.0000	0.588235	0.294118	−	0.955769i	$-0.404974\pi$
$17$	10.0000	0.588235	0.294118	+	0.955769i	$0.404974\pi$
$18$	6.00000	0.333333
$19$	26.0000	1.36842	0.684211	−	0.729285i	$-0.260147\pi$
$19$	26.0000	1.36842	0.684211	+	0.729285i	$0.260147\pi$
$20$	0	0
$21$	12.0000	0.571429
$22$	−20.0000	−0.909091
$23$	8.66025i	0.376533i	0.982118	+	0.188266i	$0.0602868\pi$
$23$	8.66025i	0.376533i	−0.982118	+	0.188266i	$0.939713\pi$
$24$	13.8564i	0.577350i
$25$	−50.0000	−2.00000
$26$	−46.0000	−1.76923
$27$	− 5.19615i	− 0.192450i
$28$	0	0
$29$	12.1244i	0.418081i	0.977907	+	0.209041i	$0.0670341\pi$
$29$	12.1244i	0.418081i	−0.977907	+	0.209041i	$0.932966\pi$
$30$	30.0000	1.00000
$31$	−25.0000	−0.806452	−0.403226	−	0.915101i	$-0.632111\pi$
$31$	−25.0000	−0.806452	−0.403226	+	0.915101i	$0.632111\pi$
$32$	0	0
$33$	17.3205i	0.524864i
$34$	−20.0000	−0.588235
$35$	60.0000	1.71429
$36$	0	0
$37$	−37.0000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$37$	−37.0000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$38$	−52.0000	−1.36842
$39$	39.8372i	1.02147i
$40$	69.2820i	1.73205i
$41$	16.0000	0.390244	0.195122	−	0.980779i	$-0.437490\pi$
$41$	16.0000	0.390244	0.195122	+	0.980779i	$0.437490\pi$
$42$	−24.0000	−0.571429
$43$	24.2487i	0.563924i	0.959426	+	0.281962i	$0.0909851\pi$
$43$	24.2487i	0.563924i	−0.959426	+	0.281962i	$0.909015\pi$
$44$	0	0
$45$	− 25.9808i	− 0.577350i
$46$	− 17.3205i	− 0.376533i
$47$	82.0000	1.74468	0.872340	−	0.488899i	$-0.162601\pi$
$47$	82.0000	1.74468	0.872340	+	0.488899i	$0.162601\pi$
$48$	− 27.7128i	− 0.577350i
$49$	1.00000	0.0204082
$50$	100.000	2.00000
$51$	17.3205i	0.339618i
$52$	0	0
$53$	− 77.9423i	− 1.47061i	−0.677737	−	0.735305i	$-0.737039\pi$
$53$	− 77.9423i	− 1.47061i	0.677737	−	0.735305i	$-0.262961\pi$
$54$	10.3923i	0.192450i
$55$	86.6025i	1.57459i
$56$	− 55.4256i	− 0.989743i
$57$	45.0333i	0.790058i
$58$	− 24.2487i	− 0.418081i
$59$	91.7987i	1.55591i	0.628320	+	0.777955i	$0.283743\pi$
$59$	91.7987i	1.55591i	−0.628320	+	0.777955i	$0.716257\pi$
$60$	0	0
$61$	−79.0000	−1.29508	−0.647541	−	0.762031i	$-0.724203\pi$
$61$	−79.0000	−1.29508	−0.647541	+	0.762031i	$0.724203\pi$
$62$	50.0000	0.806452
$63$	20.7846i	0.329914i
$64$	64.0000	1.00000
$65$	199.186i	3.06440i
$66$	− 34.6410i	− 0.524864i
$67$	79.6743i	1.18917i	0.804033	+	0.594585i	$0.202683\pi$
$67$	79.6743i	1.18917i	−0.804033	+	0.594585i	$0.797317\pi$
$68$	0	0
$69$	−15.0000	−0.217391
$70$	−120.000	−1.71429
$71$	−26.0000	−0.366197	−0.183099	−	0.983095i	$-0.558613\pi$
$71$	−26.0000	−0.366197	−0.183099	+	0.983095i	$0.558613\pi$
$72$	−24.0000	−0.333333
$73$	17.0000	0.232877	0.116438	−	0.993198i	$-0.462852\pi$
$73$	17.0000	0.232877	0.116438	+	0.993198i	$0.462852\pi$
$74$	74.0000	1.00000
$75$	− 86.6025i	− 1.15470i
$76$	0	0
$77$	− 69.2820i	− 0.899767i
$78$	− 79.6743i	− 1.02147i
$79$	26.0000	0.329114	0.164557	−	0.986368i	$-0.447381\pi$
$79$	26.0000	0.329114	0.164557	+	0.986368i	$0.447381\pi$
$80$	− 138.564i	− 1.73205i
$81$	9.00000	0.111111
$82$	−32.0000	−0.390244
$83$	− 60.6218i	− 0.730383i	−0.930932	−	0.365191i	$-0.881004\pi$
$83$	− 60.6218i	− 0.730383i	0.930932	−	0.365191i	$-0.118996\pi$
$84$	0	0
$85$	86.6025i	1.01885i
$86$	− 48.4974i	− 0.563924i
$87$	−21.0000	−0.241379
$88$	80.0000	0.909091
$89$	57.1577i	0.642221i	0.947042	+	0.321111i	$0.104056\pi$
$89$	57.1577i	0.642221i	−0.947042	+	0.321111i	$0.895944\pi$
$90$	51.9615i	0.577350i
$91$	− 159.349i	− 1.75108i
$92$	0	0
$93$	− 43.3013i	− 0.465605i
$94$	−164.000	−1.74468
$95$	225.167i	2.37017i
$96$	0	0
$97$	− 121.244i	− 1.24993i	−0.780651	−	0.624967i	$-0.785113\pi$
$97$	− 121.244i	− 1.24993i	0.780651	−	0.624967i	$-0.214887\pi$
$98$	−2.00000	−0.0204082
$99$	−30.0000	−0.303030
$100$	0	0
$101$	− 29.4449i	− 0.291533i	−0.989319	−	0.145767i	$-0.953435\pi$
$101$	− 29.4449i	− 0.291533i	0.989319	−	0.145767i	$-0.0465649\pi$
$102$	− 34.6410i	− 0.339618i
$103$	110.000	1.06796	0.533981	−	0.845497i	$-0.320696\pi$
$103$	110.000	1.06796	0.533981	+	0.845497i	$0.320696\pi$
$104$	184.000	1.76923
$105$	103.923i	0.989743i
$106$	155.885i	1.47061i
$107$	−128.000	−1.19626	−0.598131	−	0.801398i	$-0.704090\pi$
$107$	−128.000	−1.19626	−0.598131	+	0.801398i	$0.704090\pi$
$108$	0	0
$109$	31.1769i	0.286027i	0.989721	+	0.143013i	$0.0456792\pi$
$109$	31.1769i	0.286027i	−0.989721	+	0.143013i	$0.954321\pi$
$110$	− 173.205i	− 1.57459i
$111$	− 64.0859i	− 0.577350i
$112$	110.851i	0.989743i
$113$	−110.000	−0.973451	−0.486726	−	0.873555i	$-0.661809\pi$
$113$	−110.000	−0.973451	−0.486726	+	0.873555i	$0.661809\pi$
$114$	− 90.0666i	− 0.790058i
$115$	−75.0000	−0.652174
$116$	0	0
$117$	−69.0000	−0.589744
$118$	− 183.597i	− 1.55591i
$119$	− 69.2820i	− 0.582202i
$120$	−120.000	−1.00000
$121$	−21.0000	−0.173554
$122$	158.000	1.29508
$123$	27.7128i	0.225307i
$124$	0	0
$125$	− 216.506i	− 1.73205i
$126$	− 41.5692i	− 0.329914i
$127$	127.000	1.00000
$127$	127.000	1.00000
$128$	−128.000	−1.00000
$129$	−42.0000	−0.325581
$130$	− 398.372i	− 3.06440i
$131$	124.000	0.946565	0.473282	−	0.880911i	$-0.343069\pi$
$131$	124.000	0.946565	0.473282	+	0.880911i	$0.343069\pi$
$132$	0	0
$133$	− 180.133i	− 1.35439i
$134$	− 159.349i	− 1.18917i
$135$	45.0000	0.333333
$136$	80.0000	0.588235
$137$	188.794i	1.37806i	0.724735	+	0.689028i	$0.241962\pi$
$137$	188.794i	1.37806i	−0.724735	+	0.689028i	$0.758038\pi$
$138$	30.0000	0.217391
$139$	− 242.487i	− 1.74451i	−0.489050	−	0.872256i	$-0.662656\pi$
$139$	− 242.487i	− 1.74451i	0.489050	−	0.872256i	$-0.337344\pi$
$140$	0	0
$141$	142.028i	1.00729i
$142$	52.0000	0.366197
$143$	230.000	1.60839
$144$	48.0000	0.333333
$145$	−105.000	−0.724138
$146$	−34.0000	−0.232877
$147$	1.73205i	0.0117827i
$148$	0	0
$149$	−2.00000	−0.0134228	−0.00671141	−	0.999977i	$-0.502136\pi$
$149$	−2.00000	−0.0134228	−0.00671141	+	0.999977i	$0.502136\pi$
$150$	173.205i	1.15470i
$151$	− 17.3205i	− 0.114705i	−0.998354	−	0.0573527i	$-0.981734\pi$
$151$	− 17.3205i	− 0.114705i	0.998354	−	0.0573527i	$-0.0182659\pi$
$152$	208.000	1.36842
$153$	−30.0000	−0.196078
$154$	138.564i	0.899767i
$155$	− 216.506i	− 1.39682i
$156$	0	0
$157$	−214.000	−1.36306	−0.681529	−	0.731791i	$-0.738685\pi$
$157$	−214.000	−1.36306	−0.681529	+	0.731791i	$0.738685\pi$
$158$	−52.0000	−0.329114
$159$	135.000	0.849057
$160$	0	0
$161$	60.0000	0.372671
$162$	−18.0000	−0.111111
$163$	−163.000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$163$	−163.000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$164$	0	0
$165$	−150.000	−0.909091
$166$	121.244i	0.730383i
$167$	242.487i	1.45202i	0.687685	+	0.726009i	$0.258627\pi$
$167$	242.487i	1.45202i	−0.687685	+	0.726009i	$0.741373\pi$
$168$	96.0000	0.571429
$169$	360.000	2.13018
$170$	− 173.205i	− 1.01885i
$171$	−78.0000	−0.456140
$172$	0	0
$173$	214.774i	1.24147i	0.784020	+	0.620735i	$0.213166\pi$
$173$	214.774i	1.24147i	−0.784020	+	0.620735i	$0.786834\pi$
$174$	42.0000	0.241379
$175$	346.410i	1.97949i
$176$	−160.000	−0.909091
$177$	−159.000	−0.898305
$178$	− 114.315i	− 0.642221i
$179$	−116.000	−0.648045	−0.324022	−	0.946049i	$-0.605035\pi$
$179$	−116.000	−0.648045	−0.324022	+	0.946049i	$0.605035\pi$
$180$	0	0
$181$	− 290.985i	− 1.60765i	−0.594866	−	0.803825i	$-0.702795\pi$
$181$	− 290.985i	− 1.60765i	0.594866	−	0.803825i	$-0.297205\pi$
$182$	318.697i	1.75108i
$183$	− 136.832i	− 0.747716i
$184$	69.2820i	0.376533i
$185$	− 320.429i	− 1.73205i
$186$	86.6025i	0.465605i
$187$	100.000	0.534759
$188$	0	0
$189$	−36.0000	−0.190476
$190$	− 450.333i	− 2.37017i
$191$	−254.000	−1.32984	−0.664921	−	0.746913i	$-0.731535\pi$
$191$	−254.000	−1.32984	−0.664921	+	0.746913i	$0.731535\pi$
$192$	110.851i	0.577350i
$193$	225.167i	1.16667i	0.812233	+	0.583333i	$0.198252\pi$
$193$	225.167i	1.16667i	−0.812233	+	0.583333i	$0.801748\pi$
$194$	242.487i	1.24993i
$195$	−345.000	−1.76923
$196$	0	0
$197$	268.000	1.36041	0.680203	−	0.733024i	$-0.261892\pi$
$197$	268.000	1.36041	0.680203	+	0.733024i	$0.261892\pi$
$198$	60.0000	0.303030
$199$	−109.000	−0.547739	−0.273869	−	0.961767i	$-0.588304\pi$
$199$	−109.000	−0.547739	−0.273869	+	0.961767i	$0.588304\pi$
$200$	−400.000	−2.00000
$201$	−138.000	−0.686567
$202$	58.8897i	0.291533i
$203$	84.0000	0.413793
$204$	0	0
$205$	138.564i	0.675922i
$206$	−220.000	−1.06796
$207$	− 25.9808i	− 0.125511i
$208$	−368.000	−1.76923
$209$	260.000	1.24402
$210$	− 207.846i	− 0.989743i
$211$	191.000	0.905213	0.452607	−	0.891710i	$-0.350494\pi$
$211$	191.000	0.905213	0.452607	+	0.891710i	$0.350494\pi$
$212$	0	0
$213$	− 45.0333i	− 0.211424i
$214$	256.000	1.19626
$215$	−210.000	−0.976744
$216$	− 41.5692i	− 0.192450i
$217$	173.205i	0.798180i
$218$	− 62.3538i	− 0.286027i
$219$	29.4449i	0.134451i
$220$	0	0
$221$	230.000	1.04072
$222$	128.172i	0.577350i
$223$	242.487i	1.08739i	0.839284	+	0.543693i	$0.182974\pi$
$223$	242.487i	1.08739i	−0.839284	+	0.543693i	$0.817026\pi$
$224$	0	0
$225$	150.000	0.666667
$226$	220.000	0.973451
$227$	−200.000	−0.881057	−0.440529	−	0.897739i	$-0.645209\pi$
$227$	−200.000	−0.881057	−0.440529	+	0.897739i	$0.645209\pi$
$228$	0	0
$229$	− 367.195i	− 1.60347i	−0.597679	−	0.801735i	$-0.703910\pi$
$229$	− 367.195i	− 1.60347i	0.597679	−	0.801735i	$-0.296090\pi$
$230$	150.000	0.652174
$231$	120.000	0.519481
$232$	96.9948i	0.418081i
$233$	348.142i	1.49417i	0.664727	+	0.747086i	$0.268548\pi$
$233$	348.142i	1.49417i	−0.664727	+	0.747086i	$0.731452\pi$
$234$	138.000	0.589744
$235$	710.141i	3.02188i
$236$	0	0
$237$	45.0333i	0.190014i
$238$	138.564i	0.582202i
$239$	133.368i	0.558025i	0.960288	+	0.279012i	$0.0900070\pi$
$239$	133.368i	0.558025i	−0.960288	+	0.279012i	$0.909993\pi$
$240$	240.000	1.00000
$241$	− 17.3205i	− 0.0718693i	−0.999354	−	0.0359347i	$-0.988559\pi$
$241$	− 17.3205i	− 0.0718693i	0.999354	−	0.0359347i	$-0.0114408\pi$
$242$	42.0000	0.173554
$243$	15.5885i	0.0641500i
$244$	0	0
$245$	8.66025i	0.0353480i
$246$	− 55.4256i	− 0.225307i
$247$	598.000	2.42105
$248$	−200.000	−0.806452
$249$	105.000	0.421687
$250$	433.013i	1.73205i
$251$	226.000	0.900398	0.450199	−	0.892928i	$-0.351353\pi$
$251$	226.000	0.900398	0.450199	+	0.892928i	$0.351353\pi$
$252$	0	0
$253$	86.6025i	0.342303i
$254$	−254.000	−1.00000
$255$	−150.000	−0.588235
$256$	0	0
$257$	− 136.832i	− 0.532420i	−0.963915	−	0.266210i	$-0.914228\pi$
$257$	− 136.832i	− 0.532420i	0.963915	−	0.266210i	$-0.0857715\pi$
$258$	84.0000	0.325581
$259$	256.344i	0.989743i
$260$	0	0
$261$	− 36.3731i	− 0.139360i
$262$	−248.000	−0.946565
$263$	10.0000	0.0380228	0.0190114	−	0.999819i	$-0.493948\pi$
$263$	10.0000	0.0380228	0.0190114	+	0.999819i	$0.493948\pi$
$264$	138.564i	0.524864i
$265$	675.000	2.54717
$266$	360.267i	1.35439i
$267$	−99.0000	−0.370787
$268$	0	0
$269$	304.000	1.13011	0.565056	−	0.825053i	$-0.308855\pi$
$269$	304.000	1.13011	0.565056	+	0.825053i	$0.308855\pi$
$270$	−90.0000	−0.333333
$271$	341.000	1.25830	0.629151	−	0.777283i	$-0.283403\pi$
$271$	341.000	1.25830	0.629151	+	0.777283i	$0.283403\pi$
$272$	−160.000	−0.588235
$273$	276.000	1.01099
$274$	− 377.587i	− 1.37806i
$275$	−500.000	−1.81818
$276$	0	0
$277$	− 235.559i	− 0.850393i	−0.905101	−	0.425197i	$-0.860205\pi$
$277$	− 235.559i	− 0.850393i	0.905101	−	0.425197i	$-0.139795\pi$
$278$	484.974i	1.74451i
$279$	75.0000	0.268817
$280$	480.000	1.71429
$281$	− 533.472i	− 1.89848i	−0.314559	−	0.949238i	$-0.601857\pi$
$281$	− 533.472i	− 1.89848i	0.314559	−	0.949238i	$-0.398143\pi$
$282$	− 284.056i	− 1.00729i
$283$	− 138.564i	− 0.489626i	−0.969570	−	0.244813i	$-0.921273\pi$
$283$	− 138.564i	− 0.489626i	0.969570	−	0.244813i	$-0.0787265\pi$
$284$	0	0
$285$	−390.000	−1.36842
$286$	−460.000	−1.60839
$287$	− 110.851i	− 0.386241i
$288$	0	0
$289$	−189.000	−0.653979
$290$	210.000	0.724138
$291$	210.000	0.721649
$292$	0	0
$293$	96.9948i	0.331040i	0.986206	+	0.165520i	$0.0529303\pi$
$293$	96.9948i	0.331040i	−0.986206	+	0.165520i	$0.947070\pi$
$294$	− 3.46410i	− 0.0117827i
$295$	−795.000	−2.69492
$296$	−296.000	−1.00000
$297$	− 51.9615i	− 0.174955i
$298$	4.00000	0.0134228
$299$	199.186i	0.666173i
$300$	0	0
$301$	168.000	0.558140
$302$	34.6410i	0.114705i
$303$	51.0000	0.168317
$304$	−416.000	−1.36842
$305$	− 684.160i	− 2.24315i
$306$	60.0000	0.196078
$307$	581.969i	1.89566i	0.318769	+	0.947832i	$0.396731\pi$
$307$	581.969i	1.89566i	−0.318769	+	0.947832i	$0.603269\pi$
$308$	0	0
$309$	190.526i	0.616588i
$310$	433.013i	1.39682i
$311$	− 199.186i	− 0.640469i	−0.947338	−	0.320234i	$-0.896238\pi$
$311$	− 199.186i	− 0.640469i	0.947338	−	0.320234i	$-0.103762\pi$
$312$	318.697i	1.02147i
$313$	336.018i	1.07354i	0.843729	+	0.536770i	$0.180356\pi$
$313$	336.018i	1.07354i	−0.843729	+	0.536770i	$0.819644\pi$
$314$	428.000	1.36306
$315$	−180.000	−0.571429
$316$	0	0
$317$	− 76.2102i	− 0.240411i	−0.992749	−	0.120205i	$-0.961645\pi$
$317$	− 76.2102i	− 0.240411i	0.992749	−	0.120205i	$-0.0383553\pi$
$318$	−270.000	−0.849057
$319$	121.244i	0.380074i
$320$	554.256i	1.73205i
$321$	− 221.703i	− 0.690662i
$322$	−120.000	−0.372671
$323$	260.000	0.804954
$324$	0	0
$325$	−1150.00	−3.53846
$326$	326.000	1.00000
$327$	−54.0000	−0.165138
$328$	128.000	0.390244
$329$	− 568.113i	− 1.72679i
$330$	300.000	0.909091
$331$	− 173.205i	− 0.523278i	−0.965166	−	0.261639i	$-0.915737\pi$
$331$	− 173.205i	− 0.523278i	0.965166	−	0.261639i	$-0.0842630\pi$
$332$	0	0
$333$	111.000	0.333333
$334$	− 484.974i	− 1.45202i
$335$	−690.000	−2.05970
$336$	−192.000	−0.571429
$337$	− 460.726i	− 1.36714i	−0.729886	−	0.683569i	$-0.760427\pi$
$337$	− 460.726i	− 1.36714i	0.729886	−	0.683569i	$-0.239573\pi$
$338$	−720.000	−2.13018
$339$	− 190.526i	− 0.562022i
$340$	0	0
$341$	−250.000	−0.733138
$342$	156.000	0.456140
$343$	− 346.410i	− 1.00994i
$344$	193.990i	0.563924i
$345$	− 129.904i	− 0.376533i
$346$	− 429.549i	− 1.24147i
$347$	164.545i	0.474193i	0.971486	+	0.237096i	$0.0761957\pi$
$347$	164.545i	0.474193i	−0.971486	+	0.237096i	$0.923804\pi$
$348$	0	0
$349$	− 121.244i	− 0.347403i	−0.984798	−	0.173701i	$-0.944427\pi$
$349$	− 121.244i	− 0.347403i	0.984798	−	0.173701i	$-0.0555727\pi$
$350$	− 692.820i	− 1.97949i
$351$	− 119.512i	− 0.340489i
$352$	0	0
$353$	388.000	1.09915	0.549575	−	0.835444i	$-0.314790\pi$
$353$	388.000	1.09915	0.549575	+	0.835444i	$0.314790\pi$
$354$	318.000	0.898305
$355$	− 225.167i	− 0.634272i
$356$	0	0
$357$	120.000	0.336134
$358$	232.000	0.648045
$359$	20.7846i	0.0578958i	0.999581	+	0.0289479i	$0.00921570\pi$
$359$	20.7846i	0.0578958i	−0.999581	+	0.0289479i	$0.990784\pi$
$360$	− 207.846i	− 0.577350i
$361$	315.000	0.872576
$362$	581.969i	1.60765i
$363$	− 36.3731i	− 0.100201i
$364$	0	0
$365$	147.224i	0.403354i
$366$	273.664i	0.747716i
$367$	−403.000	−1.09809	−0.549046	−	0.835792i	$-0.685009\pi$
$367$	−403.000	−1.09809	−0.549046	+	0.835792i	$0.685009\pi$
$368$	− 138.564i	− 0.376533i
$369$	−48.0000	−0.130081
$370$	640.859i	1.73205i
$371$	−540.000	−1.45553
$372$	0	0
$373$	− 658.179i	− 1.76456i	−0.470729	−	0.882278i	$-0.656009\pi$
$373$	− 658.179i	− 1.76456i	0.470729	−	0.882278i	$-0.343991\pi$
$374$	−200.000	−0.534759
$375$	375.000	1.00000
$376$	656.000	1.74468
$377$	278.860i	0.739682i
$378$	72.0000	0.190476
$379$	72.7461i	0.191942i	0.995384	+	0.0959712i	$0.0305957\pi$
$379$	72.7461i	0.191942i	−0.995384	+	0.0959712i	$0.969404\pi$
$380$	0	0
$381$	219.970i	0.577350i
$382$	508.000	1.32984
$383$	−128.000	−0.334204	−0.167102	−	0.985940i	$-0.553441\pi$
$383$	−128.000	−0.334204	−0.167102	+	0.985940i	$0.553441\pi$
$384$	− 221.703i	− 0.577350i
$385$	600.000	1.55844
$386$	− 450.333i	− 1.16667i
$387$	− 72.7461i	− 0.187975i
$388$	0	0
$389$	−116.000	−0.298201	−0.149100	−	0.988822i	$-0.547638\pi$
$389$	−116.000	−0.298201	−0.149100	+	0.988822i	$0.547638\pi$
$390$	690.000	1.76923
$391$	86.6025i	0.221490i
$392$	8.00000	0.0204082
$393$	214.774i	0.546499i
$394$	−536.000	−1.36041
$395$	225.167i	0.570042i
$396$	0	0
$397$	−163.000	−0.410579	−0.205290	−	0.978701i	$-0.565814\pi$
$397$	−163.000	−0.410579	−0.205290	+	0.978701i	$0.565814\pi$
$398$	218.000	0.547739
$399$	312.000	0.781955
$400$	800.000	2.00000
$401$	8.66025i	0.0215966i	0.999942	+	0.0107983i	$0.00343728\pi$
$401$	8.66025i	0.0215966i	−0.999942	+	0.0107983i	$0.996563\pi$
$402$	276.000	0.686567
$403$	−575.000	−1.42680
$404$	0	0
$405$	77.9423i	0.192450i
$406$	−168.000	−0.413793
$407$	−370.000	−0.909091
$408$	138.564i	0.339618i
$409$	− 429.549i	− 1.05024i	−0.851028	−	0.525121i	$-0.824020\pi$
$409$	− 429.549i	− 1.05024i	0.851028	−	0.525121i	$-0.175980\pi$
$410$	− 277.128i	− 0.675922i
$411$	−327.000	−0.795620
$412$	0	0
$413$	636.000	1.53995
$414$	51.9615i	0.125511i
$415$	525.000	1.26506
$416$	0	0
$417$	420.000	1.00719
$418$	−520.000	−1.24402
$419$	−110.000	−0.262530	−0.131265	−	0.991347i	$-0.541904\pi$
$419$	−110.000	−0.262530	−0.131265	+	0.991347i	$0.541904\pi$
$420$	0	0
$421$	− 557.720i	− 1.32475i	−0.749172	−	0.662376i	$-0.769548\pi$
$421$	− 557.720i	− 1.32475i	0.749172	−	0.662376i	$-0.230452\pi$
$422$	−382.000	−0.905213
$423$	−246.000	−0.581560
$424$	− 623.538i	− 1.47061i
$425$	−500.000	−1.17647
$426$	90.0666i	0.211424i
$427$	547.328i	1.28180i
$428$	0	0
$429$	398.372i	0.928605i
$430$	420.000	0.976744
$431$	766.000	1.77726	0.888631	−	0.458623i	$-0.151657\pi$
$431$	766.000	1.77726	0.888631	+	0.458623i	$0.151657\pi$
$432$	83.1384i	0.192450i
$433$	−82.0000	−0.189376	−0.0946882	−	0.995507i	$-0.530185\pi$
$433$	−82.0000	−0.189376	−0.0946882	+	0.995507i	$0.530185\pi$
$434$	− 346.410i	− 0.798180i
$435$	− 181.865i	− 0.418081i
$436$	0	0
$437$	225.167i	0.515255i
$438$	− 58.8897i	− 0.134451i
$439$	− 173.205i	− 0.394545i	−0.980349	−	0.197272i	$-0.936792\pi$
$439$	− 173.205i	− 0.394545i	0.980349	−	0.197272i	$-0.0632083\pi$
$440$	692.820i	1.57459i
$441$	−3.00000	−0.00680272
$442$	−460.000	−1.04072
$443$	−170.000	−0.383747	−0.191874	−	0.981420i	$-0.561456\pi$
$443$	−170.000	−0.383747	−0.191874	+	0.981420i	$0.561456\pi$
$444$	0	0
$445$	−495.000	−1.11236
$446$	− 484.974i	− 1.08739i
$447$	− 3.46410i	− 0.00774967i
$448$	− 443.405i	− 0.989743i
$449$	−530.000	−1.18040	−0.590200	−	0.807257i	$-0.700951\pi$
$449$	−530.000	−1.18040	−0.590200	+	0.807257i	$0.700951\pi$
$450$	−300.000	−0.666667
$451$	160.000	0.354767
$452$	0	0
$453$	30.0000	0.0662252
$454$	400.000	0.881057
$455$	1380.00	3.03297
$456$	360.267i	0.790058i
$457$	215.000	0.470460	0.235230	−	0.971940i	$-0.424416\pi$
$457$	215.000	0.470460	0.235230	+	0.971940i	$0.424416\pi$
$458$	734.390i	1.60347i
$459$	− 51.9615i	− 0.113206i
$460$	0	0
$461$	193.990i	0.420802i	0.977615	+	0.210401i	$0.0674769\pi$
$461$	193.990i	0.420802i	−0.977615	+	0.210401i	$0.932523\pi$
$462$	−240.000	−0.519481
$463$	−103.000	−0.222462	−0.111231	−	0.993795i	$-0.535479\pi$
$463$	−103.000	−0.222462	−0.111231	+	0.993795i	$0.535479\pi$
$464$	− 193.990i	− 0.418081i
$465$	375.000	0.806452
$466$	− 696.284i	− 1.49417i
$467$	− 233.827i	− 0.500700i	−0.968155	−	0.250350i	$-0.919454\pi$
$467$	− 233.827i	− 0.500700i	0.968155	−	0.250350i	$-0.0805457\pi$
$468$	0	0
$469$	552.000	1.17697
$470$	− 1420.28i	− 3.02188i
$471$	− 370.659i	− 0.786962i
$472$	734.390i	1.55591i
$473$	242.487i	0.512658i
$474$	− 90.0666i	− 0.190014i
$475$	−1300.00	−2.73684
$476$	0	0
$477$	233.827i	0.490203i
$478$	− 266.736i	− 0.558025i
$479$	304.000	0.634656	0.317328	−	0.948316i	$-0.397214\pi$
$479$	304.000	0.634656	0.317328	+	0.948316i	$0.397214\pi$
$480$	0	0
$481$	−851.000	−1.76923
$482$	34.6410i	0.0718693i
$483$	103.923i	0.215162i
$484$	0	0
$485$	1050.00	2.16495
$486$	− 31.1769i	− 0.0641500i
$487$	− 259.808i	− 0.533486i	−0.963768	−	0.266743i	$-0.914053\pi$
$487$	− 259.808i	− 0.533486i	0.963768	−	0.266743i	$-0.0859475\pi$
$488$	−632.000	−1.29508
$489$	− 282.324i	− 0.577350i
$490$	− 17.3205i	− 0.0353480i
$491$	− 921.451i	− 1.87668i	−0.345711	−	0.938341i	$-0.612362\pi$
$491$	− 921.451i	− 1.87668i	0.345711	−	0.938341i	$-0.387638\pi$
$492$	0	0
$493$	121.244i	0.245930i
$494$	−1196.00	−2.42105
$495$	− 259.808i	− 0.524864i
$496$	400.000	0.806452
$497$	180.133i	0.362441i
$498$	−210.000	−0.421687
$499$	869.490i	1.74246i	0.490872	+	0.871232i	$0.336678\pi$
$499$	869.490i	1.74246i	−0.490872	+	0.871232i	$0.663322\pi$
$500$	0	0
$501$	−420.000	−0.838323
$502$	−452.000	−0.900398
$503$	772.000	1.53479	0.767396	−	0.641174i	$-0.221552\pi$
$503$	772.000	1.53479	0.767396	+	0.641174i	$0.221552\pi$
$504$	166.277i	0.329914i
$505$	255.000	0.504950
$506$	− 173.205i	− 0.342303i
$507$	623.538i	1.22986i
$508$	0	0
$509$	124.000	0.243615	0.121807	−	0.992554i	$-0.461131\pi$
$509$	124.000	0.243615	0.121807	+	0.992554i	$0.461131\pi$
$510$	300.000	0.588235
$511$	− 117.779i	− 0.230488i
$512$	512.000	1.00000
$513$	− 135.100i	− 0.263353i
$514$	273.664i	0.532420i
$515$	952.628i	1.84976i
$516$	0	0
$517$	820.000	1.58607
$518$	− 512.687i	− 0.989743i
$519$	−372.000	−0.716763
$520$	1593.49i	3.06440i
$521$	136.000	0.261036	0.130518	−	0.991446i	$-0.458336\pi$
$521$	136.000	0.261036	0.130518	+	0.991446i	$0.458336\pi$
$522$	72.7461i	0.139360i
$523$	−163.000	−0.311663	−0.155832	−	0.987784i	$-0.549806\pi$
$523$	−163.000	−0.311663	−0.155832	+	0.987784i	$0.549806\pi$
$524$	0	0
$525$	−600.000	−1.14286
$526$	−20.0000	−0.0380228
$527$	−250.000	−0.474383
$528$	− 277.128i	− 0.524864i
$529$	454.000	0.858223
$530$	−1350.00	−2.54717
$531$	− 275.396i	− 0.518637i
$532$	0	0
$533$	368.000	0.690432
$534$	198.000	0.370787
$535$	− 1108.51i	− 2.07199i
$536$	637.395i	1.18917i
$537$	− 200.918i	− 0.374149i
$538$	−608.000	−1.13011
$539$	10.0000	0.0185529
$540$	0	0
$541$	1039.23i	1.92094i	0.278377	+	0.960472i	$0.410203\pi$
$541$	1039.23i	1.92094i	−0.278377	+	0.960472i	$0.589797\pi$
$542$	−682.000	−1.25830
$543$	504.000	0.928177
$544$	0	0
$545$	−270.000	−0.495413
$546$	−552.000	−1.01099
$547$	24.2487i	0.0443304i	0.999754	+	0.0221652i	$0.00705598\pi$
$547$	24.2487i	0.0443304i	−0.999754	+	0.0221652i	$0.992944\pi$
$548$	0	0
$549$	237.000	0.431694
$550$	1000.00	1.81818
$551$	315.233i	0.572111i
$552$	−120.000	−0.217391
$553$	− 180.133i	− 0.325738i
$554$	471.118i	0.850393i
$555$	555.000	1.00000
$556$	0	0
$557$	−578.000	−1.03770	−0.518851	−	0.854865i	$-0.673640\pi$
$557$	−578.000	−1.03770	−0.518851	+	0.854865i	$0.673640\pi$
$558$	−150.000	−0.268817
$559$	557.720i	0.997711i
$560$	−960.000	−1.71429
$561$	173.205i	0.308743i
$562$	1066.94i	1.89848i
$563$	− 963.020i	− 1.71052i	−0.518203	−	0.855258i	$-0.673399\pi$
$563$	− 963.020i	− 1.71052i	0.518203	−	0.855258i	$-0.326601\pi$
$564$	0	0
$565$	− 952.628i	− 1.68607i
$566$	277.128i	0.489626i
$567$	− 62.3538i	− 0.109971i
$568$	−208.000	−0.366197
$569$	−884.000	−1.55360	−0.776801	−	0.629746i	$-0.783159\pi$
$569$	−884.000	−1.55360	−0.776801	+	0.629746i	$0.783159\pi$
$570$	780.000	1.36842
$571$	661.643i	1.15875i	0.815063	+	0.579373i	$0.196702\pi$
$571$	661.643i	1.15875i	−0.815063	+	0.579373i	$0.803298\pi$
$572$	0	0
$573$	− 439.941i	− 0.767785i
$574$	221.703i	0.386241i
$575$	− 433.013i	− 0.753066i
$576$	−192.000	−0.333333
$577$	17.0000	0.0294627	0.0147314	−	0.999891i	$-0.495311\pi$
$577$	17.0000	0.0294627	0.0147314	+	0.999891i	$0.495311\pi$
$578$	378.000	0.653979
$579$	−390.000	−0.673575
$580$	0	0
$581$	−420.000	−0.722892
$582$	−420.000	−0.721649
$583$	− 779.423i	− 1.33692i
$584$	136.000	0.232877
$585$	− 597.558i	− 1.02147i
$586$	− 193.990i	− 0.331040i
$587$	−908.000	−1.54685	−0.773424	−	0.633889i	$-0.781458\pi$
$587$	−908.000	−1.54685	−0.773424	+	0.633889i	$0.781458\pi$
$588$	0	0
$589$	−650.000	−1.10357
$590$	1590.00	2.69492
$591$	464.190i	0.785431i
$592$	592.000	1.00000
$593$	857.365i	1.44581i	0.690948	+	0.722905i	$0.257194\pi$
$593$	857.365i	1.44581i	−0.690948	+	0.722905i	$0.742806\pi$
$594$	103.923i	0.174955i
$595$	600.000	1.00840
$596$	0	0
$597$	− 188.794i	− 0.316237i
$598$	− 398.372i	− 0.666173i
$599$	164.545i	0.274699i	0.990523	+	0.137350i	$0.0438584\pi$
$599$	164.545i	0.274699i	−0.990523	+	0.137350i	$0.956142\pi$
$600$	− 692.820i	− 1.15470i
$601$	− 557.720i	− 0.927987i	−0.885839	−	0.463994i	$-0.846416\pi$
$601$	− 557.720i	− 0.927987i	0.885839	−	0.463994i	$-0.153584\pi$
$602$	−336.000	−0.558140
$603$	− 239.023i	− 0.396390i
$604$	0	0
$605$	− 181.865i	− 0.300604i
$606$	−102.000	−0.168317
$607$	383.000	0.630972	0.315486	−	0.948930i	$-0.397832\pi$
$607$	383.000	0.630972	0.315486	+	0.948930i	$0.397832\pi$
$608$	0	0
$609$	145.492i	0.238904i
$610$	1368.32i	2.24315i
$611$	1886.00	3.08674
$612$	0	0
$613$	− 841.777i	− 1.37321i	−0.727031	−	0.686604i	$-0.759101\pi$
$613$	− 841.777i	− 1.37321i	0.727031	−	0.686604i	$-0.240899\pi$
$614$	− 1163.94i	− 1.89566i
$615$	−240.000	−0.390244
$616$	− 554.256i	− 0.899767i
$617$	60.6218i	0.0982525i	0.998793	+	0.0491262i	$0.0156437\pi$
$617$	60.6218i	0.0982525i	−0.998793	+	0.0491262i	$0.984356\pi$
$618$	− 381.051i	− 0.616588i
$619$	− 744.782i	− 1.20320i	−0.798797	−	0.601601i	$-0.794530\pi$
$619$	− 744.782i	− 1.20320i	0.798797	−	0.601601i	$-0.205470\pi$
$620$	0	0
$621$	45.0000	0.0724638
$622$	398.372i	0.640469i
$623$	396.000	0.635634
$624$	− 637.395i	− 1.02147i
$625$	625.000	1.00000
$626$	− 672.036i	− 1.07354i
$627$	450.333i	0.718235i
$628$	0	0
$629$	−370.000	−0.588235
$630$	360.000	0.571429
$631$	363.731i	0.576435i	0.957565	+	0.288218i	$0.0930627\pi$
$631$	363.731i	0.576435i	−0.957565	+	0.288218i	$0.906937\pi$
$632$	208.000	0.329114
$633$	330.822i	0.522625i
$634$	152.420i	0.240411i
$635$	1099.85i	1.73205i
$636$	0	0
$637$	23.0000	0.0361068
$638$	− 242.487i	− 0.380074i
$639$	78.0000	0.122066
$640$	− 1108.51i	− 1.73205i
$641$	− 138.564i	− 0.216169i	−0.994142	−	0.108084i	$-0.965528\pi$
$641$	− 138.564i	− 0.216169i	0.994142	−	0.108084i	$-0.0344716\pi$
$642$	443.405i	0.690662i
$643$	338.000	0.525661	0.262830	−	0.964842i	$-0.415344\pi$
$643$	338.000	0.525661	0.262830	+	0.964842i	$0.415344\pi$
$644$	0	0
$645$	− 363.731i	− 0.563924i
$646$	−520.000	−0.804954
$647$	795.011i	1.22877i	0.789008	+	0.614383i	$0.210595\pi$
$647$	795.011i	1.22877i	−0.789008	+	0.614383i	$0.789405\pi$
$648$	72.0000	0.111111
$649$	917.987i	1.41446i
$650$	2300.00	3.53846
$651$	−300.000	−0.460829
$652$	0	0
$653$	−968.000	−1.48239	−0.741194	−	0.671290i	$-0.765740\pi$
$653$	−968.000	−1.48239	−0.741194	+	0.671290i	$0.765740\pi$
$654$	108.000	0.165138
$655$	1073.87i	1.63950i
$656$	−256.000	−0.390244
$657$	−51.0000	−0.0776256
$658$	1136.23i	1.72679i
$659$	303.109i	0.459953i	0.973196	+	0.229976i	$0.0738649\pi$
$659$	303.109i	0.459953i	−0.973196	+	0.229976i	$0.926135\pi$
$660$	0	0
$661$	185.000	0.279879	0.139939	−	0.990160i	$-0.455309\pi$
$661$	185.000	0.279879	0.139939	+	0.990160i	$0.455309\pi$
$662$	346.410i	0.523278i
$663$	398.372i	0.600862i
$664$	− 484.974i	− 0.730383i
$665$	1560.00	2.34586
$666$	−222.000	−0.333333
$667$	−105.000	−0.157421
$668$	0	0
$669$	−420.000	−0.627803
$670$	1380.00	2.05970
$671$	−790.000	−1.17735
$672$	0	0
$673$	−523.000	−0.777117	−0.388559	−	0.921424i	$-0.627027\pi$
$673$	−523.000	−0.777117	−0.388559	+	0.921424i	$0.627027\pi$
$674$	921.451i	1.36714i
$675$	259.808i	0.384900i
$676$	0	0
$677$	82.0000	0.121123	0.0605613	−	0.998164i	$-0.480711\pi$
$677$	82.0000	0.121123	0.0605613	+	0.998164i	$0.480711\pi$
$678$	381.051i	0.562022i
$679$	−840.000	−1.23711
$680$	692.820i	1.01885i
$681$	− 346.410i	− 0.508679i
$682$	500.000	0.733138
$683$	103.923i	0.152157i	0.997102	+	0.0760784i	$0.0242399\pi$
$683$	103.923i	0.152157i	−0.997102	+	0.0760784i	$0.975760\pi$
$684$	0	0
$685$	−1635.00	−2.38686
$686$	692.820i	1.00994i
$687$	636.000	0.925764
$688$	− 387.979i	− 0.563924i
$689$	− 1792.67i	− 2.60185i
$690$	259.808i	0.376533i
$691$	− 973.413i	− 1.40870i	−0.709852	−	0.704351i	$-0.751238\pi$
$691$	− 973.413i	− 1.40870i	0.709852	−	0.704351i	$-0.248762\pi$
$692$	0	0
$693$	207.846i	0.299922i
$694$	− 329.090i	− 0.474193i
$695$	2100.00	3.02158
$696$	−168.000	−0.241379
$697$	160.000	0.229555
$698$	242.487i	0.347403i
$699$	−603.000	−0.862661
$700$	0	0
$701$	− 836.581i	− 1.19341i	−0.802461	−	0.596705i	$-0.796476\pi$
$701$	− 836.581i	− 1.19341i	0.802461	−	0.596705i	$-0.203524\pi$
$702$	239.023i	0.340489i
$703$	−962.000	−1.36842
$704$	640.000	0.909091
$705$	−1230.00	−1.74468
$706$	−776.000	−1.09915
$707$	−204.000	−0.288543
$708$	0	0
$709$	−730.000	−1.02962	−0.514810	−	0.857305i	$-0.672137\pi$
$709$	−730.000	−1.02962	−0.514810	+	0.857305i	$0.672137\pi$
$710$	450.333i	0.634272i
$711$	−78.0000	−0.109705
$712$	457.261i	0.642221i
$713$	− 216.506i	− 0.303655i
$714$	−240.000	−0.336134
$715$	1991.86i	2.78582i
$716$	0	0
$717$	−231.000	−0.322176
$718$	− 41.5692i	− 0.0578958i
$719$	−1304.00	−1.81363	−0.906815	−	0.421529i	$-0.861494\pi$
$719$	−1304.00	−1.81363	−0.906815	+	0.421529i	$0.861494\pi$
$720$	415.692i	0.577350i
$721$	− 762.102i	− 1.05701i
$722$	−630.000	−0.872576
$723$	30.0000	0.0414938
$724$	0	0
$725$	− 606.218i	− 0.836162i
$726$	72.7461i	0.100201i
$727$	− 121.244i	− 0.166772i	−0.996517	−	0.0833862i	$-0.973426\pi$
$727$	− 121.244i	− 0.166772i	0.996517	−	0.0833862i	$-0.0265735\pi$
$728$	− 1274.79i	− 1.75108i
$729$	−27.0000	−0.0370370
$730$	− 294.449i	− 0.403354i
$731$	242.487i	0.331720i
$732$	0	0
$733$	−835.000	−1.13915	−0.569577	−	0.821938i	$-0.692893\pi$
$733$	−835.000	−1.13915	−0.569577	+	0.821938i	$0.692893\pi$
$734$	806.000	1.09809
$735$	−15.0000	−0.0204082
$736$	0	0
$737$	796.743i	1.08106i
$738$	96.0000	0.130081
$739$	899.000	1.21651	0.608254	−	0.793742i	$-0.291870\pi$
$739$	899.000	1.21651	0.608254	+	0.793742i	$0.291870\pi$
$740$	0	0
$741$	1035.77i	1.39780i
$742$	1080.00	1.45553
$743$	− 812.332i	− 1.09331i	−0.837357	−	0.546657i	$-0.815900\pi$
$743$	− 812.332i	− 1.09331i	0.837357	−	0.546657i	$-0.184100\pi$
$744$	− 346.410i	− 0.465605i
$745$	− 17.3205i	− 0.0232490i
$746$	1316.36i	1.76456i
$747$	181.865i	0.243461i
$748$	0	0
$749$	886.810i	1.18399i
$750$	−750.000	−1.00000
$751$	− 658.179i	− 0.876404i	−0.898877	−	0.438202i	$-0.855615\pi$
$751$	− 658.179i	− 0.876404i	0.898877	−	0.438202i	$-0.144385\pi$
$752$	−1312.00	−1.74468
$753$	391.443i	0.519845i
$754$	− 557.720i	− 0.739682i
$755$	150.000	0.198675
$756$	0	0
$757$	989.000	1.30647	0.653236	−	0.757154i	$-0.273411\pi$
$757$	989.000	1.30647	0.653236	+	0.757154i	$0.273411\pi$
$758$	− 145.492i	− 0.191942i
$759$	−150.000	−0.197628
$760$	1801.33i	2.37017i
$761$	− 646.055i	− 0.848955i	−0.905438	−	0.424478i	$-0.860458\pi$
$761$	− 646.055i	− 0.848955i	0.905438	−	0.424478i	$-0.139542\pi$
$762$	− 439.941i	− 0.577350i
$763$	216.000	0.283093
$764$	0	0
$765$	− 259.808i	− 0.339618i
$766$	256.000	0.334204
$767$	2111.37i	2.75276i
$768$	0	0
$769$	− 533.472i	− 0.693721i	−0.937917	−	0.346861i	$-0.887248\pi$
$769$	− 533.472i	− 0.693721i	0.937917	−	0.346861i	$-0.112752\pi$
$770$	−1200.00	−1.55844
$771$	237.000	0.307393
$772$	0	0
$773$	10.0000	0.0129366	0.00646831	−	0.999979i	$-0.497941\pi$
$773$	10.0000	0.0129366	0.00646831	+	0.999979i	$0.497941\pi$
$774$	145.492i	0.187975i
$775$	1250.00	1.61290
$776$	− 969.948i	− 1.24993i
$777$	−444.000	−0.571429
$778$	232.000	0.298201
$779$	416.000	0.534018
$780$	0	0
$781$	−260.000	−0.332907
$782$	− 173.205i	− 0.221490i
$783$	63.0000	0.0804598
$784$	−16.0000	−0.0204082
$785$	− 1853.29i	− 2.36088i
$786$	− 429.549i	− 0.546499i
$787$	353.000	0.448539	0.224269	−	0.974527i	$-0.428000\pi$
$787$	353.000	0.448539	0.224269	+	0.974527i	$0.428000\pi$
$788$	0	0
$789$	17.3205i	0.0219525i
$790$	− 450.333i	− 0.570042i
$791$	762.102i	0.963467i
$792$	−240.000	−0.303030
$793$	−1817.00	−2.29130
$794$	326.000	0.410579
$795$	1169.13i	1.47061i
$796$	0	0
$797$	−362.000	−0.454203	−0.227102	−	0.973871i	$-0.572925\pi$
$797$	−362.000	−0.454203	−0.227102	+	0.973871i	$0.572925\pi$
$798$	−624.000	−0.781955
$799$	820.000	1.02628
$800$	0	0
$801$	− 171.473i	− 0.214074i
$802$	− 17.3205i	− 0.0215966i
$803$	170.000	0.211706
$804$	0	0
$805$	519.615i	0.645485i
$806$	1150.00	1.42680
$807$	526.543i	0.652470i
$808$	− 235.559i	− 0.291533i
$809$	640.000	0.791100	0.395550	−	0.918444i	$-0.370554\pi$
$809$	640.000	0.791100	0.395550	+	0.918444i	$0.370554\pi$
$810$	− 155.885i	− 0.192450i
$811$	191.000	0.235512	0.117756	−	0.993043i	$-0.462430\pi$
$811$	191.000	0.235512	0.117756	+	0.993043i	$0.462430\pi$
$812$	0	0
$813$	590.629i	0.726481i
$814$	740.000	0.909091
$815$	− 1411.62i	− 1.73205i
$816$	− 277.128i	− 0.339618i
$817$	630.466i	0.771685i
$818$	859.097i	1.05024i
$819$	478.046i	0.583695i
$820$	0	0
$821$	− 912.791i	− 1.11180i	−0.831248	−	0.555902i	$-0.812373\pi$
$821$	− 912.791i	− 1.11180i	0.831248	−	0.555902i	$-0.187627\pi$
$822$	654.000	0.795620
$823$	1046.00	1.27096	0.635480	−	0.772117i	$-0.280802\pi$
$823$	1046.00	1.27096	0.635480	+	0.772117i	$0.280802\pi$
$824$	880.000	1.06796
$825$	− 866.025i	− 1.04973i
$826$	−1272.00	−1.53995
$827$	909.327i	1.09955i	0.835313	+	0.549774i	$0.185286\pi$
$827$	909.327i	1.09955i	−0.835313	+	0.549774i	$0.814714\pi$
$828$	0	0
$829$	− 1278.25i	− 1.54192i	−0.636882	−	0.770961i	$-0.719776\pi$
$829$	− 1278.25i	− 1.54192i	0.636882	−	0.770961i	$-0.280224\pi$
$830$	−1050.00	−1.26506
$831$	408.000	0.490975
$832$	1472.00	1.76923
$833$	10.0000	0.0120048
$834$	−840.000	−1.00719
$835$	−2100.00	−2.51497
$836$	0	0
$837$	129.904i	0.155202i
$838$	220.000	0.262530
$839$	− 1515.54i	− 1.80637i	−0.429251	−	0.903185i	$-0.641223\pi$
$839$	− 1515.54i	− 1.80637i	0.429251	−	0.903185i	$-0.358777\pi$
$840$	831.384i	0.989743i
$841$	694.000	0.825208
$842$	1115.44i	1.32475i
$843$	924.000	1.09609
$844$	0	0
$845$	3117.69i	3.68958i
$846$	492.000	0.581560
$847$	145.492i	0.171774i
$848$	1247.08i	1.47061i
$849$	240.000	0.282686
$850$	1000.00	1.17647
$851$	− 320.429i	− 0.376533i
$852$	0	0
$853$	460.726i	0.540124i	0.962843	+	0.270062i	$0.0870442\pi$
$853$	460.726i	0.540124i	−0.962843	+	0.270062i	$0.912956\pi$
$854$	− 1094.66i	− 1.28180i
$855$	− 675.500i	− 0.790058i
$856$	−1024.00	−1.19626
$857$	625.270i	0.729604i	0.931085	+	0.364802i	$0.118863\pi$
$857$	625.270i	0.729604i	−0.931085	+	0.364802i	$0.881137\pi$
$858$	− 796.743i	− 0.928605i
$859$	869.490i	1.01221i	0.862471	+	0.506106i	$0.168915\pi$
$859$	869.490i	1.01221i	−0.862471	+	0.506106i	$0.831085\pi$
$860$	0	0
$861$	192.000	0.222997
$862$	−1532.00	−1.77726
$863$	− 743.050i	− 0.861008i	−0.902589	−	0.430504i	$-0.858336\pi$
$863$	− 743.050i	− 0.861008i	0.902589	−	0.430504i	$-0.141664\pi$
$864$	0	0
$865$	−1860.00	−2.15029
$866$	164.000	0.189376
$867$	− 327.358i	− 0.377575i
$868$	0	0
$869$	260.000	0.299194
$870$	363.731i	0.418081i
$871$	1832.51i	2.10391i
$872$	249.415i	0.286027i
$873$	363.731i	0.416645i
$874$	− 450.333i	− 0.515255i
$875$	−1500.00	−1.71429
$876$	0	0
$877$	110.000	0.125428	0.0627138	−	0.998032i	$-0.480024\pi$
$877$	110.000	0.125428	0.0627138	+	0.998032i	$0.480024\pi$
$878$	346.410i	0.394545i
$879$	−168.000	−0.191126
$880$	− 1385.64i	− 1.57459i
$881$	181.865i	0.206431i	0.994659	+	0.103215i	$0.0329131\pi$
$881$	181.865i	0.206431i	−0.994659	+	0.103215i	$0.967087\pi$
$882$	6.00000	0.00680272
$883$	947.000	1.07248	0.536240	−	0.844065i	$-0.319844\pi$
$883$	947.000	1.07248	0.536240	+	0.844065i	$0.319844\pi$
$884$	0	0
$885$	− 1376.98i	− 1.55591i
$886$	340.000	0.383747
$887$	8.66025i	0.00976353i	0.999988	+	0.00488177i	$0.00155392\pi$
$887$	8.66025i	0.00976353i	−0.999988	+	0.00488177i	$0.998446\pi$
$888$	− 512.687i	− 0.577350i
$889$	− 879.882i	− 0.989743i
$890$	990.000	1.11236
$891$	90.0000	0.101010
$892$	0	0
$893$	2132.00	2.38746
$894$	6.92820i	0.00774967i
$895$	− 1004.59i	− 1.12245i
$896$	886.810i	0.989743i
$897$	−345.000	−0.384615
$898$	1060.00	1.18040
$899$	− 303.109i	− 0.337162i
$900$	0	0
$901$	− 779.423i	− 0.865064i
$902$	−320.000	−0.354767
$903$	290.985i	0.322242i
$904$	−880.000	−0.973451
$905$	2520.00	2.78453
$906$	−60.0000	−0.0662252
$907$	−403.000	−0.444322	−0.222161	−	0.975010i	$-0.571311\pi$
$907$	−403.000	−0.444322	−0.222161	+	0.975010i	$0.571311\pi$
$908$	0	0
$909$	88.3346i	0.0971778i
$910$	−2760.00	−3.03297
$911$	−1496.00	−1.64215	−0.821076	−	0.570819i	$-0.806626\pi$
$911$	−1496.00	−1.64215	−0.821076	+	0.570819i	$0.806626\pi$
$912$	− 720.533i	− 0.790058i
$913$	− 606.218i	− 0.663984i
$914$	−430.000	−0.470460
$915$	1185.00	1.29508
$916$	0	0
$917$	− 859.097i	− 0.936856i
$918$	103.923i	0.113206i
$919$	−541.000	−0.588683	−0.294342	−	0.955700i	$-0.595100\pi$
$919$	−541.000	−0.588683	−0.294342	+	0.955700i	$0.595100\pi$
$920$	−600.000	−0.652174
$921$	−1008.00	−1.09446
$922$	− 387.979i	− 0.420802i
$923$	−598.000	−0.647887
$924$	0	0
$925$	1850.00	2.00000
$926$	206.000	0.222462
$927$	−330.000	−0.355987
$928$	0	0
$929$	796.743i	0.857635i	0.903391	+	0.428818i	$0.141070\pi$
$929$	796.743i	0.857635i	−0.903391	+	0.428818i	$0.858930\pi$
$930$	−750.000	−0.806452
$931$	26.0000	0.0279270
$932$	0	0
$933$	345.000	0.369775
$934$	467.654i	0.500700i
$935$	866.025i	0.926230i
$936$	−552.000	−0.589744
$937$	− 145.492i	− 0.155275i	−0.996982	−	0.0776373i	$-0.975262\pi$
$937$	− 145.492i	− 0.155275i	0.996982	−	0.0776373i	$-0.0247376\pi$
$938$	−1104.00	−1.17697
$939$	−582.000	−0.619808
$940$	0	0
$941$	1816.00	1.92986	0.964931	−	0.262504i	$-0.0845483\pi$
$941$	1816.00	1.92986	0.964931	+	0.262504i	$0.0845483\pi$
$942$	741.318i	0.786962i
$943$	138.564i	0.146940i
$944$	− 1468.78i	− 1.55591i
$945$	− 311.769i	− 0.329914i
$946$	− 484.974i	− 0.512658i
$947$	− 803.672i	− 0.848650i	−0.905510	−	0.424325i	$-0.860511\pi$
$947$	− 803.672i	− 0.848650i	0.905510	−	0.424325i	$-0.139489\pi$
$948$	0	0
$949$	391.000	0.412013
$950$	2600.00	2.73684
$951$	132.000	0.138801
$952$	− 554.256i	− 0.582202i
$953$	478.000	0.501574	0.250787	−	0.968042i	$-0.419311\pi$
$953$	478.000	0.501574	0.250787	+	0.968042i	$0.419311\pi$
$954$	− 467.654i	− 0.490203i
$955$	− 2199.70i	− 2.30336i
$956$	0	0
$957$	−210.000	−0.219436
$958$	−608.000	−0.634656
$959$	1308.00	1.36392
$960$	−960.000	−1.00000
$961$	−336.000	−0.349636
$962$	1702.00	1.76923
$963$	384.000	0.398754
$964$	0	0
$965$	−1950.00	−2.02073
$966$	− 207.846i	− 0.215162i
$967$	− 969.948i	− 1.00305i	−0.865143	−	0.501525i	$-0.832773\pi$
$967$	− 969.948i	− 1.00305i	0.865143	−	0.501525i	$-0.167227\pi$
$968$	−168.000	−0.173554
$969$	450.333i	0.464740i
$970$	−2100.00	−2.16495
$971$	−926.000	−0.953656	−0.476828	−	0.878997i	$-0.658214\pi$
$971$	−926.000	−0.953656	−0.476828	+	0.878997i	$0.658214\pi$
$972$	0	0
$973$	−1680.00	−1.72662
$974$	519.615i	0.533486i
$975$	− 1991.86i	− 2.04293i
$976$	1264.00	1.29508
$977$	−32.0000	−0.0327533	−0.0163767	−	0.999866i	$-0.505213\pi$
$977$	−32.0000	−0.0327533	−0.0163767	+	0.999866i	$0.505213\pi$
$978$	564.649i	0.577350i
$979$	571.577i	0.583837i
$980$	0	0
$981$	− 93.5307i	− 0.0953422i
$982$	1842.90i	1.87668i
$983$	−368.000	−0.374364	−0.187182	−	0.982325i	$-0.559935\pi$
$983$	−368.000	−0.374364	−0.187182	+	0.982325i	$0.559935\pi$
$984$	221.703i	0.225307i
$985$	2320.95i	2.35629i
$986$	− 242.487i	− 0.245930i
$987$	984.000	0.996960
$988$	0	0
$989$	−210.000	−0.212336
$990$	519.615i	0.524864i
$991$	831.384i	0.838935i	0.907770	+	0.419467i	$0.137783\pi$
$991$	831.384i	0.838935i	−0.907770	+	0.419467i	$0.862217\pi$
$992$	0	0
$993$	300.000	0.302115
$994$	− 360.267i	− 0.362441i
$995$	− 943.968i	− 0.948711i
$996$	0	0
$997$	1655.84i	1.66082i	0.557151	+	0.830412i	$0.311895\pi$
$997$	1655.84i	1.66082i	−0.557151	+	0.830412i	$0.688105\pi$
$998$	− 1738.98i	− 1.74246i
$999$	192.258i	0.192450i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	381.3.d.a.253.2	yes	2
127.126	odd	2	inner	381.3.d.a.253.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
381.3.d.a.253.1	✓	2	127.126	odd	2	inner
381.3.d.a.253.2	yes	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 381 = 3 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	381.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +1.73205i q^{3} +8.66025i q^{5} -3.46410i q^{6} -6.92820i q^{7} +8.00000 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +1.73205i q^{3} +8.66025i q^{5} -3.46410i q^{6} -6.92820i q^{7} +8.00000 q^{8} -3.00000 q^{9} -17.3205i q^{10} +10.0000 q^{11} +23.0000 q^{13} +13.8564i q^{14} -15.0000 q^{15} -16.0000 q^{16} +10.0000 q^{17} +6.00000 q^{18} +26.0000 q^{19} +12.0000 q^{21} -20.0000 q^{22} +8.66025i q^{23} +13.8564i q^{24} -50.0000 q^{25} -46.0000 q^{26} -5.19615i q^{27} +12.1244i q^{29} +30.0000 q^{30} -25.0000 q^{31} +17.3205i q^{33} -20.0000 q^{34} +60.0000 q^{35} -37.0000 q^{37} -52.0000 q^{38} +39.8372i q^{39} +69.2820i q^{40} +16.0000 q^{41} -24.0000 q^{42} +24.2487i q^{43} -25.9808i q^{45} -17.3205i q^{46} +82.0000 q^{47} -27.7128i q^{48} +1.00000 q^{49} +100.000 q^{50} +17.3205i q^{51} -77.9423i q^{53} +10.3923i q^{54} +86.6025i q^{55} -55.4256i q^{56} +45.0333i q^{57} -24.2487i q^{58} +91.7987i q^{59} -79.0000 q^{61} +50.0000 q^{62} +20.7846i q^{63} +64.0000 q^{64} +199.186i q^{65} -34.6410i q^{66} +79.6743i q^{67} -15.0000 q^{69} -120.000 q^{70} -26.0000 q^{71} -24.0000 q^{72} +17.0000 q^{73} +74.0000 q^{74} -86.6025i q^{75} -69.2820i q^{77} -79.6743i q^{78} +26.0000 q^{79} -138.564i q^{80} +9.00000 q^{81} -32.0000 q^{82} -60.6218i q^{83} +86.6025i q^{85} -48.4974i q^{86} -21.0000 q^{87} +80.0000 q^{88} +57.1577i q^{89} +51.9615i q^{90} -159.349i q^{91} -43.3013i q^{93} -164.000 q^{94} +225.167i q^{95} -121.244i q^{97} -2.00000 q^{98} -30.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} + 16 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q - 4 * q^2 + 16 * q^8 - 6 * q^9	\( 2 q - 4 q^{2} + 16 q^{8} - 6 q^{9} + 20 q^{11} + 46 q^{13} - 30 q^{15} - 32 q^{16} + 20 q^{17} + 12 q^{18} + 52 q^{19} + 24 q^{21} - 40 q^{22} - 100 q^{25} - 92 q^{26} + 60 q^{30} - 50 q^{31} - 40 q^{34} + 120 q^{35} - 74 q^{37} - 104 q^{38} + 32 q^{41} - 48 q^{42} + 164 q^{47} + 2 q^{49} + 200 q^{50} - 158 q^{61} + 100 q^{62} + 128 q^{64} - 30 q^{69} - 240 q^{70} - 52 q^{71} - 48 q^{72} + 34 q^{73} + 148 q^{74} + 52 q^{79} + 18 q^{81} - 64 q^{82} - 42 q^{87} + 160 q^{88} - 328 q^{94} - 4 q^{98} - 60 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 + 16 * q^8 - 6 * q^9 + 20 * q^11 + 46 * q^13 - 30 * q^15 - 32 * q^16 + 20 * q^17 + 12 * q^18 + 52 * q^19 + 24 * q^21 - 40 * q^22 - 100 * q^25 - 92 * q^26 + 60 * q^30 - 50 * q^31 - 40 * q^34 + 120 * q^35 - 74 * q^37 - 104 * q^38 + 32 * q^41 - 48 * q^42 + 164 * q^47 + 2 * q^49 + 200 * q^50 - 158 * q^61 + 100 * q^62 + 128 * q^64 - 30 * q^69 - 240 * q^70 - 52 * q^71 - 48 * q^72 + 34 * q^73 + 148 * q^74 + 52 * q^79 + 18 * q^81 - 64 * q^82 - 42 * q^87 + 160 * q^88 - 328 * q^94 - 4 * q^98 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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