LMFDB - Embedded newform 3179.2.a.bi.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3179,2,Mod(1,3179)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3179, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3179.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3179 = 11 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3179.a (trivial)

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:	yes
Analytic conductor:	$25.3844428026$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	no (minimal twist has level 187)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	3179.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.86094 q^{2} -3.04898 q^{3} +1.46310 q^{4} +4.00111 q^{5} +5.67397 q^{6} +2.90599 q^{7} +0.999144 q^{8} +6.29627 q^{9} +O(q^{10})$	\(q-1.86094 q^{2} -3.04898 q^{3} +1.46310 q^{4} +4.00111 q^{5} +5.67397 q^{6} +2.90599 q^{7} +0.999144 q^{8} +6.29627 q^{9} -7.44583 q^{10} -1.00000 q^{11} -4.46095 q^{12} -0.505453 q^{13} -5.40787 q^{14} -12.1993 q^{15} -4.78554 q^{16} -11.7170 q^{18} +4.17343 q^{19} +5.85402 q^{20} -8.86030 q^{21} +1.86094 q^{22} -2.47628 q^{23} -3.04637 q^{24} +11.0089 q^{25} +0.940618 q^{26} -10.0503 q^{27} +4.25174 q^{28} -1.65651 q^{29} +22.7022 q^{30} +8.32386 q^{31} +6.90732 q^{32} +3.04898 q^{33} +11.6272 q^{35} +9.21206 q^{36} +4.40681 q^{37} -7.76650 q^{38} +1.54112 q^{39} +3.99769 q^{40} +7.26922 q^{41} +16.4885 q^{42} +3.03512 q^{43} -1.46310 q^{44} +25.1921 q^{45} +4.60822 q^{46} -6.44748 q^{47} +14.5910 q^{48} +1.44477 q^{49} -20.4869 q^{50} -0.739527 q^{52} +6.83865 q^{53} +18.7029 q^{54} -4.00111 q^{55} +2.90350 q^{56} -12.7247 q^{57} +3.08266 q^{58} +1.23093 q^{59} -17.8488 q^{60} -2.96347 q^{61} -15.4902 q^{62} +18.2969 q^{63} -3.28302 q^{64} -2.02238 q^{65} -5.67397 q^{66} -2.22966 q^{67} +7.55014 q^{69} -21.6375 q^{70} +2.27684 q^{71} +6.29088 q^{72} -2.33113 q^{73} -8.20082 q^{74} -33.5660 q^{75} +6.10613 q^{76} -2.90599 q^{77} -2.86792 q^{78} -8.84193 q^{79} -19.1475 q^{80} +11.7542 q^{81} -13.5276 q^{82} +1.95376 q^{83} -12.9635 q^{84} -5.64818 q^{86} +5.05065 q^{87} -0.999144 q^{88} +9.25188 q^{89} -46.8810 q^{90} -1.46884 q^{91} -3.62305 q^{92} -25.3793 q^{93} +11.9984 q^{94} +16.6984 q^{95} -21.0603 q^{96} +12.2584 q^{97} -2.68863 q^{98} -6.29627 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 8 q^{3} + 24 q^{4} + 16 q^{5} + 16 q^{6} + 12 q^{7} + 20 q^{9}+O(q^{10}) $ 28 * q + 8 * q^3 + 24 * q^4 + 16 * q^5 + 16 * q^6 + 12 * q^7 + 20 * q^9	$ 28 q + 8 q^{3} + 24 q^{4} + 16 q^{5} + 16 q^{6} + 12 q^{7} + 20 q^{9} + 24 q^{10} - 28 q^{11} + 24 q^{12} + 16 q^{14} - 16 q^{15} + 16 q^{16} + 32 q^{20} + 8 q^{23} - 8 q^{24} + 20 q^{25} - 24 q^{26} + 32 q^{27} + 32 q^{28} + 36 q^{29} + 40 q^{30} + 56 q^{31} + 40 q^{32} - 8 q^{33} + 16 q^{35} + 40 q^{36} + 64 q^{37} - 8 q^{38} + 32 q^{39} + 72 q^{40} + 28 q^{41} + 24 q^{42} + 16 q^{43} - 24 q^{44} + 24 q^{45} - 36 q^{47} + 56 q^{48} + 16 q^{49} + 56 q^{50} - 20 q^{53} + 64 q^{54} - 16 q^{55} + 48 q^{56} + 32 q^{57} - 16 q^{58} - 28 q^{59} + 8 q^{60} + 104 q^{61} - 8 q^{62} + 28 q^{63} + 32 q^{65} - 16 q^{66} - 12 q^{67} - 32 q^{69} + 40 q^{71} + 40 q^{72} + 76 q^{73} + 24 q^{74} - 16 q^{75} - 16 q^{76} - 12 q^{77} - 24 q^{78} + 24 q^{79} + 8 q^{80} + 12 q^{81} + 56 q^{82} + 32 q^{83} - 40 q^{84} - 16 q^{86} - 8 q^{87} - 52 q^{89} + 16 q^{90} + 80 q^{91} - 56 q^{92} + 24 q^{97} - 24 q^{98} - 20 q^{99}+O(q^{100}) $ 28 * q + 8 * q^3 + 24 * q^4 + 16 * q^5 + 16 * q^6 + 12 * q^7 + 20 * q^9 + 24 * q^10 - 28 * q^11 + 24 * q^12 + 16 * q^14 - 16 * q^15 + 16 * q^16 + 32 * q^20 + 8 * q^23 - 8 * q^24 + 20 * q^25 - 24 * q^26 + 32 * q^27 + 32 * q^28 + 36 * q^29 + 40 * q^30 + 56 * q^31 + 40 * q^32 - 8 * q^33 + 16 * q^35 + 40 * q^36 + 64 * q^37 - 8 * q^38 + 32 * q^39 + 72 * q^40 + 28 * q^41 + 24 * q^42 + 16 * q^43 - 24 * q^44 + 24 * q^45 - 36 * q^47 + 56 * q^48 + 16 * q^49 + 56 * q^50 - 20 * q^53 + 64 * q^54 - 16 * q^55 + 48 * q^56 + 32 * q^57 - 16 * q^58 - 28 * q^59 + 8 * q^60 + 104 * q^61 - 8 * q^62 + 28 * q^63 + 32 * q^65 - 16 * q^66 - 12 * q^67 - 32 * q^69 + 40 * q^71 + 40 * q^72 + 76 * q^73 + 24 * q^74 - 16 * q^75 - 16 * q^76 - 12 * q^77 - 24 * q^78 + 24 * q^79 + 8 * q^80 + 12 * q^81 + 56 * q^82 + 32 * q^83 - 40 * q^84 - 16 * q^86 - 8 * q^87 - 52 * q^89 + 16 * q^90 + 80 * q^91 - 56 * q^92 + 24 * q^97 - 24 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.86094	−1.31588	−0.657942	−	0.753069i	$-0.728573\pi$
$2$	−1.86094	−1.31588	−0.657942	+	0.753069i	$0.728573\pi$
$3$	−3.04898	−1.76033	−0.880164	−	0.474669i	$-0.842568\pi$
$3$	−3.04898	−1.76033	−0.880164	+	0.474669i	$0.842568\pi$
$4$	1.46310	0.731549
$5$	4.00111	1.78935	0.894676	−	0.446715i	$-0.147406\pi$
$5$	4.00111	1.78935	0.894676	+	0.446715i	$0.147406\pi$
$6$	5.67397	2.31639
$7$	2.90599	1.09836	0.549180	−	0.835704i	$-0.314940\pi$
$7$	2.90599	1.09836	0.549180	+	0.835704i	$0.314940\pi$
$8$	0.999144	0.353251
$9$	6.29627	2.09876
$10$	−7.44583	−2.35458
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−4.46095	−1.28777
$13$	−0.505453	−0.140187	−0.0700937	−	0.997540i	$-0.522330\pi$
$13$	−0.505453	−0.140187	−0.0700937	+	0.997540i	$0.522330\pi$
$14$	−5.40787	−1.44531
$15$	−12.1993	−3.14985
$16$	−4.78554	−1.19639
$17$	0	0
$17$	0	0
$18$	−11.7170	−2.76172
$19$	4.17343	0.957450	0.478725	−	0.877965i	$-0.341099\pi$
$19$	4.17343	0.957450	0.478725	+	0.877965i	$0.341099\pi$
$20$	5.85402	1.30900
$21$	−8.86030	−1.93347
$22$	1.86094	0.396754
$23$	−2.47628	−0.516341	−0.258171	−	0.966099i	$-0.583120\pi$
$23$	−2.47628	−0.516341	−0.258171	+	0.966099i	$0.583120\pi$
$24$	−3.04637	−0.621837
$25$	11.0089	2.20178
$26$	0.940618	0.184470
$27$	−10.0503	−1.93417
$28$	4.25174	0.803504
$29$	−1.65651	−0.307605	−0.153803	−	0.988102i	$-0.549152\pi$
$29$	−1.65651	−0.307605	−0.153803	+	0.988102i	$0.549152\pi$
$30$	22.7022	4.14483
$31$	8.32386	1.49501	0.747504	−	0.664257i	$-0.231252\pi$
$31$	8.32386	1.49501	0.747504	+	0.664257i	$0.231252\pi$
$32$	6.90732	1.22105
$33$	3.04898	0.530759
$34$	0	0
$35$	11.6272	1.96535
$36$	9.21206	1.53534
$37$	4.40681	0.724476	0.362238	−	0.932086i	$-0.382013\pi$
$37$	4.40681	0.724476	0.362238	+	0.932086i	$0.382013\pi$
$38$	−7.76650	−1.25989
$39$	1.54112	0.246776
$40$	3.99769	0.632090
$41$	7.26922	1.13526	0.567631	−	0.823283i	$-0.307860\pi$
$41$	7.26922	1.13526	0.567631	+	0.823283i	$0.307860\pi$
$42$	16.4885	2.54423
$43$	3.03512	0.462851	0.231426	−	0.972853i	$-0.425661\pi$
$43$	3.03512	0.462851	0.231426	+	0.972853i	$0.425661\pi$
$44$	−1.46310	−0.220570
$45$	25.1921	3.75542
$46$	4.60822	0.679444
$47$	−6.44748	−0.940461	−0.470231	−	0.882544i	$-0.655829\pi$
$47$	−6.44748	−0.940461	−0.470231	+	0.882544i	$0.655829\pi$
$48$	14.5910	2.10603
$49$	1.44477	0.206395
$50$	−20.4869	−2.89729
$51$	0	0
$52$	−0.739527	−0.102554
$53$	6.83865	0.939360	0.469680	−	0.882837i	$-0.344369\pi$
$53$	6.83865	0.939360	0.469680	+	0.882837i	$0.344369\pi$
$54$	18.7029	2.54515
$55$	−4.00111	−0.539510
$56$	2.90350	0.387996
$57$	−12.7247	−1.68543
$58$	3.08266	0.404773
$59$	1.23093	0.160254	0.0801269	−	0.996785i	$-0.474467\pi$
$59$	1.23093	0.160254	0.0801269	+	0.996785i	$0.474467\pi$
$60$	−17.8488	−2.30427
$61$	−2.96347	−0.379433	−0.189717	−	0.981839i	$-0.560757\pi$
$61$	−2.96347	−0.379433	−0.189717	+	0.981839i	$0.560757\pi$
$62$	−15.4902	−1.96726
$63$	18.2969	2.30519
$64$	−3.28302	−0.410377
$65$	−2.02238	−0.250845
$66$	−5.67397	−0.698417
$67$	−2.22966	−0.272396	−0.136198	−	0.990682i	$-0.543488\pi$
$67$	−2.22966	−0.272396	−0.136198	+	0.990682i	$0.543488\pi$
$68$	0	0
$69$	7.55014	0.908930
$70$	−21.6375	−2.58618
$71$	2.27684	0.270211	0.135106	−	0.990831i	$-0.456863\pi$
$71$	2.27684	0.270211	0.135106	+	0.990831i	$0.456863\pi$
$72$	6.29088	0.741387
$73$	−2.33113	−0.272838	−0.136419	−	0.990651i	$-0.543559\pi$
$73$	−2.33113	−0.272838	−0.136419	+	0.990651i	$0.543559\pi$
$74$	−8.20082	−0.953325
$75$	−33.5660	−3.87586
$76$	6.10613	0.700421
$77$	−2.90599	−0.331168
$78$	−2.86792	−0.324728
$79$	−8.84193	−0.994795	−0.497398	−	0.867523i	$-0.665711\pi$
$79$	−8.84193	−0.994795	−0.497398	+	0.867523i	$0.665711\pi$
$80$	−19.1475	−2.14076
$81$	11.7542	1.30602
$82$	−13.5276	−1.49387
$83$	1.95376	0.214453	0.107226	−	0.994235i	$-0.465803\pi$
$83$	1.95376	0.214453	0.107226	+	0.994235i	$0.465803\pi$
$84$	−12.9635	−1.41443
$85$	0	0
$86$	−5.64818	−0.609058
$87$	5.05065	0.541487
$88$	−0.999144	−0.106509
$89$	9.25188	0.980697	0.490348	−	0.871526i	$-0.336870\pi$
$89$	9.25188	0.980697	0.490348	+	0.871526i	$0.336870\pi$
$90$	−46.8810	−4.94169
$91$	−1.46884	−0.153976
$92$	−3.62305	−0.377729
$93$	−25.3793	−2.63171
$94$	11.9984	1.23754
$95$	16.6984	1.71322
$96$	−21.0603	−2.14945
$97$	12.2584	1.24466	0.622328	−	0.782757i	$-0.286187\pi$
$97$	12.2584	1.24466	0.622328	+	0.782757i	$0.286187\pi$
$98$	−2.68863	−0.271592
$99$	−6.29627	−0.632799
$100$	16.1071	1.61071
$101$	−0.925257	−0.0920665	−0.0460333	−	0.998940i	$-0.514658\pi$
$101$	−0.925257	−0.0920665	−0.0460333	+	0.998940i	$0.514658\pi$
$102$	0	0
$103$	−17.6838	−1.74243	−0.871217	−	0.490898i	$-0.836669\pi$
$103$	−17.6838	−1.74243	−0.871217	+	0.490898i	$0.836669\pi$
$104$	−0.505020	−0.0495213
$105$	−35.4511	−3.45967
$106$	−12.7263	−1.23609
$107$	4.37072	0.422533	0.211267	−	0.977428i	$-0.432241\pi$
$107$	4.37072	0.422533	0.211267	+	0.977428i	$0.432241\pi$
$108$	−14.7045	−1.41494
$109$	12.6456	1.21123	0.605614	−	0.795758i	$-0.292927\pi$
$109$	12.6456	1.21123	0.605614	+	0.795758i	$0.292927\pi$
$110$	7.44583	0.709932
$111$	−13.4363	−1.27532
$112$	−13.9067	−1.31406
$113$	11.2346	1.05686	0.528431	−	0.848977i	$-0.322781\pi$
$113$	11.2346	1.05686	0.528431	+	0.848977i	$0.322781\pi$
$114$	23.6799	2.21782
$115$	−9.90790	−0.923916
$116$	−2.42363	−0.225028
$117$	−3.18247	−0.294219
$118$	−2.29069	−0.210875
$119$	0	0
$120$	−12.1889	−1.11269
$121$	1.00000	0.0909091
$122$	5.51484	0.499290
$123$	−22.1637	−1.99843
$124$	12.1786	1.09367
$125$	24.0424	2.15042
$126$	−34.0494	−3.03336
$127$	−3.01484	−0.267524	−0.133762	−	0.991014i	$-0.542706\pi$
$127$	−3.01484	−0.267524	−0.133762	+	0.991014i	$0.542706\pi$
$128$	−7.70513	−0.681044
$129$	−9.25402	−0.814771
$130$	3.76352	0.330083
$131$	2.91351	0.254554	0.127277	−	0.991867i	$-0.459376\pi$
$131$	2.91351	0.254554	0.127277	+	0.991867i	$0.459376\pi$
$132$	4.46095	0.388276
$133$	12.1279	1.05162
$134$	4.14926	0.358442
$135$	−40.2122	−3.46092
$136$	0	0
$137$	−3.13630	−0.267952	−0.133976	−	0.990985i	$-0.542775\pi$
$137$	−3.13630	−0.267952	−0.133976	+	0.990985i	$0.542775\pi$
$138$	−14.0504	−1.19605
$139$	8.03173	0.681243	0.340621	−	0.940201i	$-0.389363\pi$
$139$	8.03173	0.681243	0.340621	+	0.940201i	$0.389363\pi$
$140$	17.0117	1.43775
$141$	19.6582	1.65552
$142$	−4.23706	−0.355566
$143$	0.505453	0.0422681
$144$	−30.1311	−2.51092
$145$	−6.62787	−0.550415
$146$	4.33809	0.359023
$147$	−4.40506	−0.363324
$148$	6.44760	0.529989
$149$	5.02880	0.411975	0.205988	−	0.978555i	$-0.433959\pi$
$149$	5.02880	0.411975	0.205988	+	0.978555i	$0.433959\pi$
$150$	62.4642	5.10018
$151$	−12.7918	−1.04098	−0.520492	−	0.853866i	$-0.674252\pi$
$151$	−12.7918	−1.04098	−0.520492	+	0.853866i	$0.674252\pi$
$152$	4.16985	0.338220
$153$	0	0
$154$	5.40787	0.435779
$155$	33.3047	2.67510
$156$	2.25480	0.180529
$157$	−15.1696	−1.21067	−0.605333	−	0.795973i	$-0.706960\pi$
$157$	−15.1696	−1.21067	−0.605333	+	0.795973i	$0.706960\pi$
$158$	16.4543	1.30903
$159$	−20.8509	−1.65358
$160$	27.6370	2.18489
$161$	−7.19605	−0.567128
$162$	−21.8739	−1.71857
$163$	−2.76834	−0.216833	−0.108416	−	0.994106i	$-0.534578\pi$
$163$	−2.76834	−0.216833	−0.108416	+	0.994106i	$0.534578\pi$
$164$	10.6356	0.830499
$165$	12.1993	0.949715
$166$	−3.63582	−0.282195
$167$	−6.53156	−0.505427	−0.252714	−	0.967541i	$-0.581323\pi$
$167$	−6.53156	−0.505427	−0.252714	+	0.967541i	$0.581323\pi$
$168$	−8.85271	−0.683001
$169$	−12.7445	−0.980347
$170$	0	0
$171$	26.2770	2.00945
$172$	4.44068	0.338598
$173$	−24.9019	−1.89326	−0.946630	−	0.322323i	$-0.895536\pi$
$173$	−24.9019	−1.89326	−0.946630	+	0.322323i	$0.895536\pi$
$174$	−9.39896	−0.712533
$175$	31.9918	2.41835
$176$	4.78554	0.360724
$177$	−3.75309	−0.282099
$178$	−17.2172	−1.29048
$179$	−7.22307	−0.539877	−0.269939	−	0.962878i	$-0.587003\pi$
$179$	−7.22307	−0.539877	−0.269939	+	0.962878i	$0.587003\pi$
$180$	36.8585	2.74727
$181$	25.7250	1.91212	0.956062	−	0.293166i	$-0.0947088\pi$
$181$	25.7250	1.91212	0.956062	+	0.293166i	$0.0947088\pi$
$182$	2.73342	0.202615
$183$	9.03556	0.667928
$184$	−2.47416	−0.182398
$185$	17.6322	1.29634
$186$	47.2293	3.46302
$187$	0	0
$188$	−9.43329	−0.687993
$189$	−29.2059	−2.12442
$190$	−31.0746	−2.25439
$191$	−9.33409	−0.675391	−0.337696	−	0.941255i	$-0.609647\pi$
$191$	−9.33409	−0.675391	−0.337696	+	0.941255i	$0.609647\pi$
$192$	10.0099	0.722399
$193$	23.2881	1.67632	0.838158	−	0.545428i	$-0.183633\pi$
$193$	23.2881	1.67632	0.838158	+	0.545428i	$0.183633\pi$
$194$	−22.8122	−1.63782
$195$	6.16618	0.441569
$196$	2.11384	0.150988
$197$	−3.63294	−0.258836	−0.129418	−	0.991590i	$-0.541311\pi$
$197$	−3.63294	−0.258836	−0.129418	+	0.991590i	$0.541311\pi$
$198$	11.7170	0.832689
$199$	−0.169676	−0.0120280	−0.00601401	−	0.999982i	$-0.501914\pi$
$199$	−0.169676	−0.0120280	−0.00601401	+	0.999982i	$0.501914\pi$
$200$	10.9995	0.777781
$201$	6.79818	0.479507
$202$	1.72185	0.121149
$203$	−4.81379	−0.337862
$204$	0	0
$205$	29.0850	2.03138
$206$	32.9084	2.29284
$207$	−15.5914	−1.08367
$208$	2.41887	0.167718
$209$	−4.17343	−0.288682
$210$	65.9723	4.55252
$211$	20.1468	1.38696	0.693480	−	0.720476i	$-0.256077\pi$
$211$	20.1468	1.38696	0.693480	+	0.720476i	$0.256077\pi$
$212$	10.0056	0.687188
$213$	−6.94203	−0.475660
$214$	−8.13365	−0.556005
$215$	12.1439	0.828205
$216$	−10.0416	−0.683248
$217$	24.1890	1.64206
$218$	−23.5327	−1.59384
$219$	7.10756	0.480284
$220$	−5.85402	−0.394678
$221$	0	0
$222$	25.0041	1.67817
$223$	1.14419	0.0766206	0.0383103	−	0.999266i	$-0.487802\pi$
$223$	1.14419	0.0766206	0.0383103	+	0.999266i	$0.487802\pi$
$224$	20.0726	1.34116
$225$	69.3151	4.62101
$226$	−20.9069	−1.39071
$227$	−13.8390	−0.918524	−0.459262	−	0.888301i	$-0.651886\pi$
$227$	−13.8390	−0.918524	−0.459262	+	0.888301i	$0.651886\pi$
$228$	−18.6175	−1.23297
$229$	−23.3479	−1.54287	−0.771435	−	0.636308i	$-0.780461\pi$
$229$	−23.3479	−1.54287	−0.771435	+	0.636308i	$0.780461\pi$
$230$	18.4380	1.21577
$231$	8.86030	0.582965
$232$	−1.65509	−0.108662
$233$	−2.03396	−0.133249	−0.0666247	−	0.997778i	$-0.521223\pi$
$233$	−2.03396	−0.133249	−0.0666247	+	0.997778i	$0.521223\pi$
$234$	5.92238	0.387158
$235$	−25.7971	−1.68282
$236$	1.80097	0.117233
$237$	26.9589	1.75117
$238$	0	0
$239$	−29.9599	−1.93795	−0.968974	−	0.247163i	$-0.920502\pi$
$239$	−29.9599	−1.93795	−0.968974	+	0.247163i	$0.920502\pi$
$240$	58.3803	3.76843
$241$	25.4539	1.63963	0.819815	−	0.572629i	$-0.194076\pi$
$241$	25.4539	1.63963	0.819815	+	0.572629i	$0.194076\pi$
$242$	−1.86094	−0.119626
$243$	−5.68755	−0.364856
$244$	−4.33584	−0.277574
$245$	5.78068	0.369314
$246$	41.2453	2.62970
$247$	−2.10947	−0.134222
$248$	8.31673	0.528113
$249$	−5.95696	−0.377507
$250$	−44.7414	−2.82970
$251$	−14.3640	−0.906648	−0.453324	−	0.891346i	$-0.649762\pi$
$251$	−14.3640	−0.906648	−0.453324	+	0.891346i	$0.649762\pi$
$252$	26.7701	1.68636
$253$	2.47628	0.155683
$254$	5.61043	0.352030
$255$	0	0
$256$	20.9048	1.30655
$257$	−15.9573	−0.995390	−0.497695	−	0.867352i	$-0.665820\pi$
$257$	−15.9573	−0.995390	−0.497695	+	0.867352i	$0.665820\pi$
$258$	17.2212	1.07214
$259$	12.8061	0.795735
$260$	−2.95893	−0.183505
$261$	−10.4298	−0.645589
$262$	−5.42186	−0.334964
$263$	−18.2415	−1.12482	−0.562410	−	0.826859i	$-0.690126\pi$
$263$	−18.2415	−1.12482	−0.562410	+	0.826859i	$0.690126\pi$
$264$	3.04637	0.187491
$265$	27.3622	1.68085
$266$	−22.5693	−1.38382
$267$	−28.2088	−1.72635
$268$	−3.26221	−0.199271
$269$	4.91299	0.299550	0.149775	−	0.988720i	$-0.452145\pi$
$269$	4.91299	0.299550	0.149775	+	0.988720i	$0.452145\pi$
$270$	74.8325	4.55416
$271$	30.2021	1.83465	0.917324	−	0.398142i	$-0.130345\pi$
$271$	30.2021	1.83465	0.917324	+	0.398142i	$0.130345\pi$
$272$	0	0
$273$	4.47846	0.271049
$274$	5.83647	0.352594
$275$	−11.0089	−0.663863
$276$	11.0466	0.664926
$277$	12.2230	0.734409	0.367205	−	0.930140i	$-0.380315\pi$
$277$	12.2230	0.734409	0.367205	+	0.930140i	$0.380315\pi$
$278$	−14.9466	−0.896436
$279$	52.4092	3.13766
$280$	11.6172	0.694263
$281$	5.99198	0.357452	0.178726	−	0.983899i	$-0.442802\pi$
$281$	5.99198	0.357452	0.178726	+	0.983899i	$0.442802\pi$
$282$	−36.5828	−2.17847
$283$	−14.1316	−0.840038	−0.420019	−	0.907515i	$-0.637977\pi$
$283$	−14.1316	−0.840038	−0.420019	+	0.907515i	$0.637977\pi$
$284$	3.33124	0.197673
$285$	−50.9129	−3.01582
$286$	−0.940618	−0.0556199
$287$	21.1243	1.24693
$288$	43.4903	2.56269
$289$	0	0
$290$	12.3341	0.724281
$291$	−37.3757	−2.19100
$292$	−3.41067	−0.199594
$293$	30.5759	1.78626	0.893132	−	0.449794i	$-0.148503\pi$
$293$	30.5759	1.78626	0.893132	+	0.449794i	$0.148503\pi$
$294$	8.19756	0.478091
$295$	4.92510	0.286751
$296$	4.40304	0.255922
$297$	10.0503	0.583175
$298$	−9.35829	−0.542111
$299$	1.25165	0.0723845
$300$	−49.1103	−2.83538
$301$	8.82002	0.508378
$302$	23.8048	1.36981
$303$	2.82109	0.162067
$304$	−19.9721	−1.14548
$305$	−11.8572	−0.678940
$306$	0	0
$307$	−1.89438	−0.108118	−0.0540589	−	0.998538i	$-0.517216\pi$
$307$	−1.89438	−0.108118	−0.0540589	+	0.998538i	$0.517216\pi$
$308$	−4.25174	−0.242266
$309$	53.9174	3.06726
$310$	−61.9780	−3.52012
$311$	−17.0293	−0.965643	−0.482822	−	0.875719i	$-0.660388\pi$
$311$	−17.0293	−0.965643	−0.482822	+	0.875719i	$0.660388\pi$
$312$	1.53980	0.0871738
$313$	5.20757	0.294349	0.147175	−	0.989111i	$-0.452982\pi$
$313$	5.20757	0.294349	0.147175	+	0.989111i	$0.452982\pi$
$314$	28.2297	1.59309
$315$	73.2079	4.12480
$316$	−12.9366	−0.727741
$317$	−10.3714	−0.582516	−0.291258	−	0.956645i	$-0.594074\pi$
$317$	−10.3714	−0.582516	−0.291258	+	0.956645i	$0.594074\pi$
$318$	38.8022	2.17592
$319$	1.65651	0.0927465
$320$	−13.1357	−0.734310
$321$	−13.3262	−0.743798
$322$	13.3914	0.746275
$323$	0	0
$324$	17.1975	0.955419
$325$	−5.56449	−0.308662
$326$	5.15171	0.285327
$327$	−38.5562	−2.13216
$328$	7.26300	0.401032
$329$	−18.7363	−1.03297
$330$	−22.7022	−1.24971
$331$	32.5474	1.78897	0.894484	−	0.447099i	$-0.147543\pi$
$331$	32.5474	1.78897	0.894484	+	0.447099i	$0.147543\pi$
$332$	2.85853	0.156882
$333$	27.7465	1.52050
$334$	12.1548	0.665083
$335$	−8.92112	−0.487413
$336$	42.4013	2.31318
$337$	−34.6842	−1.88937	−0.944685	−	0.327978i	$-0.893633\pi$
$337$	−34.6842	−1.88937	−0.944685	+	0.327978i	$0.893633\pi$
$338$	23.7168	1.29002
$339$	−34.2540	−1.86042
$340$	0	0
$341$	−8.32386	−0.450762
$342$	−48.9000	−2.64421
$343$	−16.1434	−0.871664
$344$	3.03252	0.163503
$345$	30.2090	1.62640
$346$	46.3410	2.49131
$347$	−12.9443	−0.694889	−0.347444	−	0.937701i	$-0.612950\pi$
$347$	−12.9443	−0.694889	−0.347444	+	0.937701i	$0.612950\pi$
$348$	7.38959	0.396124
$349$	11.1405	0.596336	0.298168	−	0.954513i	$-0.403624\pi$
$349$	11.1405	0.596336	0.298168	+	0.954513i	$0.403624\pi$
$350$	−59.5348	−3.18227
$351$	5.07993	0.271147
$352$	−6.90732	−0.368161
$353$	−32.3097	−1.71967	−0.859835	−	0.510573i	$-0.829433\pi$
$353$	−32.3097	−1.71967	−0.859835	+	0.510573i	$0.829433\pi$
$354$	6.98427	0.371210
$355$	9.10989	0.483503
$356$	13.5364	0.717427
$357$	0	0
$358$	13.4417	0.710415
$359$	29.3562	1.54936	0.774679	−	0.632354i	$-0.217911\pi$
$359$	29.3562	1.54936	0.774679	+	0.632354i	$0.217911\pi$
$360$	25.1705	1.32660
$361$	−1.58251	−0.0832899
$362$	−47.8727	−2.51613
$363$	−3.04898	−0.160030
$364$	−2.14906	−0.112641
$365$	−9.32711	−0.488203
$366$	−16.8146	−0.878915
$367$	1.53295	0.0800195	0.0400098	−	0.999199i	$-0.487261\pi$
$367$	1.53295	0.0800195	0.0400098	+	0.999199i	$0.487261\pi$
$368$	11.8504	0.617743
$369$	45.7690	2.38264
$370$	−32.8124	−1.70584
$371$	19.8730	1.03176
$372$	−37.1323	−1.92522
$373$	10.3262	0.534670	0.267335	−	0.963604i	$-0.413857\pi$
$373$	10.3262	0.534670	0.267335	+	0.963604i	$0.413857\pi$
$374$	0	0
$375$	−73.3047	−3.78544
$376$	−6.44196	−0.332219
$377$	0.837286	0.0431224
$378$	54.3505	2.79549
$379$	9.49436	0.487692	0.243846	−	0.969814i	$-0.421591\pi$
$379$	9.49436	0.487692	0.243846	+	0.969814i	$0.421591\pi$
$380$	24.4313	1.25330
$381$	9.19217	0.470929
$382$	17.3702	0.888736
$383$	3.78242	0.193273	0.0966363	−	0.995320i	$-0.469192\pi$
$383$	3.78242	0.193273	0.0966363	+	0.995320i	$0.469192\pi$
$384$	23.4928	1.19886
$385$	−11.6272	−0.592577
$386$	−43.3378	−2.20584
$387$	19.1099	0.971413
$388$	17.9353	0.910526
$389$	34.3213	1.74016	0.870079	−	0.492912i	$-0.164068\pi$
$389$	34.3213	1.74016	0.870079	+	0.492912i	$0.164068\pi$
$390$	−11.4749	−0.581054
$391$	0	0
$392$	1.44353	0.0729093
$393$	−8.88321	−0.448099
$394$	6.76068	0.340598
$395$	−35.3776	−1.78004
$396$	−9.21206	−0.462923
$397$	15.5434	0.780100	0.390050	−	0.920794i	$-0.372458\pi$
$397$	15.5434	0.780100	0.390050	+	0.920794i	$0.372458\pi$
$398$	0.315757	0.0158275
$399$	−36.9778	−1.85121
$400$	−52.6836	−2.63418
$401$	−25.8110	−1.28894	−0.644469	−	0.764631i	$-0.722921\pi$
$401$	−25.8110	−1.28894	−0.644469	+	0.764631i	$0.722921\pi$
$402$	−12.6510	−0.630975
$403$	−4.20732	−0.209581
$404$	−1.35374	−0.0673511
$405$	47.0299	2.33694
$406$	8.95817	0.444586
$407$	−4.40681	−0.218438
$408$	0	0
$409$	−15.2246	−0.752809	−0.376405	−	0.926455i	$-0.622840\pi$
$409$	−15.2246	−0.752809	−0.376405	+	0.926455i	$0.622840\pi$
$410$	−54.1254	−2.67306
$411$	9.56252	0.471684
$412$	−25.8731	−1.27467
$413$	3.57708	0.176016
$414$	29.0146	1.42599
$415$	7.81720	0.383731
$416$	−3.49132	−0.171176
$417$	−24.4886	−1.19921
$418$	7.76650	0.379872
$419$	−20.2468	−0.989121	−0.494561	−	0.869143i	$-0.664671\pi$
$419$	−20.2468	−0.989121	−0.494561	+	0.869143i	$0.664671\pi$
$420$	−51.8683	−2.53092
$421$	19.4317	0.947041	0.473521	−	0.880783i	$-0.342983\pi$
$421$	19.4317	0.947041	0.473521	+	0.880783i	$0.342983\pi$
$422$	−37.4919	−1.82508
$423$	−40.5951	−1.97380
$424$	6.83279	0.331830
$425$	0	0
$426$	12.9187	0.625913
$427$	−8.61181	−0.416755
$428$	6.39479	0.309104
$429$	−1.54112	−0.0744058
$430$	−22.5990	−1.08982
$431$	36.1054	1.73913	0.869567	−	0.493815i	$-0.164398\pi$
$431$	36.1054	1.73913	0.869567	+	0.493815i	$0.164398\pi$
$432$	48.0959	2.31402
$433$	−9.54605	−0.458754	−0.229377	−	0.973338i	$-0.573669\pi$
$433$	−9.54605	−0.458754	−0.229377	+	0.973338i	$0.573669\pi$
$434$	−45.0143	−2.16076
$435$	20.2082	0.968910
$436$	18.5017	0.886073
$437$	−10.3346	−0.494371
$438$	−13.2267	−0.631998
$439$	17.6079	0.840380	0.420190	−	0.907436i	$-0.361963\pi$
$439$	17.6079	0.840380	0.420190	+	0.907436i	$0.361963\pi$
$440$	−3.99769	−0.190582
$441$	9.09665	0.433174
$442$	0	0
$443$	6.24098	0.296518	0.148259	−	0.988949i	$-0.452633\pi$
$443$	6.24098	0.296518	0.148259	+	0.988949i	$0.452633\pi$
$444$	−19.6586	−0.932955
$445$	37.0178	1.75481
$446$	−2.12927	−0.100824
$447$	−15.3327	−0.725212
$448$	−9.54041	−0.450742
$449$	−14.1915	−0.669738	−0.334869	−	0.942265i	$-0.608692\pi$
$449$	−14.1915	−0.669738	−0.334869	+	0.942265i	$0.608692\pi$
$450$	−128.991	−6.08071
$451$	−7.26922	−0.342294
$452$	16.4373	0.773145
$453$	39.0020	1.83247
$454$	25.7535	1.20867
$455$	−5.87700	−0.275518
$456$	−12.7138	−0.595378
$457$	−1.76410	−0.0825213	−0.0412607	−	0.999148i	$-0.513137\pi$
$457$	−1.76410	−0.0825213	−0.0412607	+	0.999148i	$0.513137\pi$
$458$	43.4490	2.03024
$459$	0	0
$460$	−14.4962	−0.675890
$461$	25.4202	1.18394	0.591969	−	0.805961i	$-0.298351\pi$
$461$	25.4202	1.18394	0.591969	+	0.805961i	$0.298351\pi$
$462$	−16.4885	−0.767113
$463$	39.0926	1.81679	0.908393	−	0.418117i	$-0.137310\pi$
$463$	39.0926	1.81679	0.908393	+	0.418117i	$0.137310\pi$
$464$	7.92728	0.368015
$465$	−101.545	−4.70905
$466$	3.78509	0.175341
$467$	−7.39175	−0.342049	−0.171025	−	0.985267i	$-0.554708\pi$
$467$	−7.39175	−0.342049	−0.171025	+	0.985267i	$0.554708\pi$
$468$	−4.65626	−0.215236
$469$	−6.47937	−0.299189
$470$	48.0068	2.21439
$471$	46.2518	2.13117
$472$	1.22988	0.0566097
$473$	−3.03512	−0.139555
$474$	−50.1688	−2.30433
$475$	45.9449	2.10810
$476$	0	0
$477$	43.0580	1.97149
$478$	55.7537	2.55011
$479$	8.54573	0.390464	0.195232	−	0.980757i	$-0.437454\pi$
$479$	8.54573	0.390464	0.195232	+	0.980757i	$0.437454\pi$
$480$	−84.2645	−3.84613
$481$	−2.22744	−0.101562
$482$	−47.3682	−2.15756
$483$	21.9406	0.998332
$484$	1.46310	0.0665044
$485$	49.0474	2.22713
$486$	10.5842	0.480108
$487$	−8.12020	−0.367961	−0.183981	−	0.982930i	$-0.558898\pi$
$487$	−8.12020	−0.367961	−0.183981	+	0.982930i	$0.558898\pi$
$488$	−2.96093	−0.134035
$489$	8.44060	0.381697
$490$	−10.7575	−0.485974
$491$	17.8440	0.805290	0.402645	−	0.915356i	$-0.368091\pi$
$491$	17.8440	0.805290	0.402645	+	0.915356i	$0.368091\pi$
$492$	−32.4276	−1.46195
$493$	0	0
$494$	3.92560	0.176621
$495$	−25.1921	−1.13230
$496$	−39.8342	−1.78861
$497$	6.61647	0.296789
$498$	11.0855	0.496755
$499$	−2.49485	−0.111685	−0.0558424	−	0.998440i	$-0.517784\pi$
$499$	−2.49485	−0.111685	−0.0558424	+	0.998440i	$0.517784\pi$
$500$	35.1763	1.57313
$501$	19.9146	0.889718
$502$	26.7306	1.19304
$503$	14.0458	0.626272	0.313136	−	0.949708i	$-0.398621\pi$
$503$	14.0458	0.626272	0.313136	+	0.949708i	$0.398621\pi$
$504$	18.2812	0.814310
$505$	−3.70206	−0.164739
$506$	−4.60822	−0.204860
$507$	38.8578	1.72573
$508$	−4.41100	−0.195706
$509$	−26.4685	−1.17319	−0.586597	−	0.809879i	$-0.699533\pi$
$509$	−26.4685	−1.17319	−0.586597	+	0.809879i	$0.699533\pi$
$510$	0	0
$511$	−6.77423	−0.299674
$512$	−23.4924	−1.03823
$513$	−41.9440	−1.85187
$514$	29.6956	1.30982
$515$	−70.7548	−3.11783
$516$	−13.5395	−0.596044
$517$	6.44748	0.283560
$518$	−23.8315	−1.04709
$519$	75.9255	3.33276
$520$	−2.02064	−0.0886111
$521$	14.8774	0.651791	0.325896	−	0.945406i	$-0.394334\pi$
$521$	14.8774	0.651791	0.325896	+	0.945406i	$0.394334\pi$
$522$	19.4092	0.849519
$523$	−43.6952	−1.91066	−0.955330	−	0.295541i	$-0.904500\pi$
$523$	−43.6952	−1.91066	−0.955330	+	0.295541i	$0.904500\pi$
$524$	4.26274	0.186219
$525$	−97.5423	−4.25709
$526$	33.9464	1.48013
$527$	0	0
$528$	−14.5910	−0.634992
$529$	−16.8680	−0.733392
$530$	−50.9194	−2.21180
$531$	7.75028	0.336334
$532$	17.7443	0.769315
$533$	−3.67425	−0.159149
$534$	52.4948	2.27167
$535$	17.4878	0.756061
$536$	−2.22775	−0.0962242
$537$	22.0230	0.950361
$538$	−9.14277	−0.394173
$539$	−1.44477	−0.0622305
$540$	−58.8344	−2.53183
$541$	17.4846	0.751723	0.375861	−	0.926676i	$-0.377347\pi$
$541$	17.4846	0.751723	0.375861	+	0.926676i	$0.377347\pi$
$542$	−56.2043	−2.41418
$543$	−78.4349	−3.36596
$544$	0	0
$545$	50.5965	2.16732
$546$	−8.33415	−0.356669
$547$	34.8810	1.49140	0.745702	−	0.666279i	$-0.232114\pi$
$547$	34.8810	1.49140	0.745702	+	0.666279i	$0.232114\pi$
$548$	−4.58872	−0.196020
$549$	−18.6588	−0.796338
$550$	20.4869	0.873566
$551$	−6.91331	−0.294517
$552$	7.54367	0.321080
$553$	−25.6946	−1.09264
$554$	−22.7463	−0.966397
$555$	−53.7601	−2.28199
$556$	11.7512	0.498362
$557$	−3.97182	−0.168292	−0.0841458	−	0.996453i	$-0.526816\pi$
$557$	−3.97182	−0.168292	−0.0841458	+	0.996453i	$0.526816\pi$
$558$	−97.5304	−4.12879
$559$	−1.53411	−0.0648860
$560$	−55.6424	−2.35132
$561$	0	0
$562$	−11.1507	−0.470365
$563$	−7.42900	−0.313095	−0.156547	−	0.987670i	$-0.550036\pi$
$563$	−7.42900	−0.313095	−0.156547	+	0.987670i	$0.550036\pi$
$564$	28.7619	1.21109
$565$	44.9509	1.89110
$566$	26.2981	1.10539
$567$	34.1576	1.43448
$568$	2.27489	0.0954522
$569$	25.8805	1.08497	0.542483	−	0.840066i	$-0.317484\pi$
$569$	25.8805	1.08497	0.542483	+	0.840066i	$0.317484\pi$
$570$	94.7459	3.96847
$571$	17.8749	0.748042	0.374021	−	0.927420i	$-0.377979\pi$
$571$	17.8749	0.748042	0.374021	+	0.927420i	$0.377979\pi$
$572$	0.739527	0.0309212
$573$	28.4595	1.18891
$574$	−39.3110	−1.64081
$575$	−27.2612	−1.13687
$576$	−20.6708	−0.861282
$577$	18.1277	0.754665	0.377332	−	0.926078i	$-0.376841\pi$
$577$	18.1277	0.754665	0.377332	+	0.926078i	$0.376841\pi$
$578$	0	0
$579$	−71.0050	−2.95087
$580$	−9.69722	−0.402655
$581$	5.67759	0.235546
$582$	69.5540	2.88310
$583$	−6.83865	−0.283228
$584$	−2.32913	−0.0963802
$585$	−12.7334	−0.526462
$586$	−56.9000	−2.35052
$587$	−22.8668	−0.943815	−0.471908	−	0.881648i	$-0.656434\pi$
$587$	−22.8668	−0.943815	−0.471908	+	0.881648i	$0.656434\pi$
$588$	−6.44504	−0.265789
$589$	34.7390	1.43140
$590$	−9.16532	−0.377330
$591$	11.0768	0.455637
$592$	−21.0890	−0.866752
$593$	9.85959	0.404885	0.202442	−	0.979294i	$-0.435112\pi$
$593$	9.85959	0.404885	0.202442	+	0.979294i	$0.435112\pi$
$594$	−18.7029	−0.767390
$595$	0	0
$596$	7.35762	0.301380
$597$	0.517339	0.0211733
$598$	−2.32924	−0.0952496
$599$	−37.6577	−1.53865	−0.769325	−	0.638857i	$-0.779407\pi$
$599$	−37.6577	−1.53865	−0.769325	+	0.638857i	$0.779407\pi$
$600$	−33.5372	−1.36915
$601$	15.4564	0.630481	0.315241	−	0.949012i	$-0.397915\pi$
$601$	15.4564	0.630481	0.315241	+	0.949012i	$0.397915\pi$
$602$	−16.4135	−0.668966
$603$	−14.0385	−0.571694
$604$	−18.7157	−0.761531
$605$	4.00111	0.162668
$606$	−5.24988	−0.213262
$607$	−15.1764	−0.615991	−0.307995	−	0.951388i	$-0.599658\pi$
$607$	−15.1764	−0.615991	−0.307995	+	0.951388i	$0.599658\pi$
$608$	28.8272	1.16910
$609$	14.6771	0.594747
$610$	22.0655	0.893406
$611$	3.25890	0.131841
$612$	0	0
$613$	−8.45011	−0.341297	−0.170648	−	0.985332i	$-0.554586\pi$
$613$	−8.45011	−0.341297	−0.170648	+	0.985332i	$0.554586\pi$
$614$	3.52532	0.142270
$615$	−88.6795	−3.57590
$616$	−2.90350	−0.116985
$617$	23.1193	0.930750	0.465375	−	0.885114i	$-0.345920\pi$
$617$	23.1193	0.930750	0.465375	+	0.885114i	$0.345920\pi$
$618$	−100.337	−4.03615
$619$	−41.4539	−1.66617	−0.833086	−	0.553143i	$-0.813428\pi$
$619$	−41.4539	−1.66617	−0.833086	+	0.553143i	$0.813428\pi$
$620$	48.7280	1.95696
$621$	24.8873	0.998693
$622$	31.6905	1.27067
$623$	26.8858	1.07716
$624$	−7.37507	−0.295239
$625$	41.1517	1.64607
$626$	−9.69097	−0.387329
$627$	12.7247	0.508175
$628$	−22.1946	−0.885661
$629$	0	0
$630$	−136.236	−5.42776
$631$	−47.7823	−1.90218	−0.951092	−	0.308908i	$-0.900036\pi$
$631$	−47.7823	−1.90218	−0.951092	+	0.308908i	$0.900036\pi$
$632$	−8.83436	−0.351412
$633$	−61.4270	−2.44151
$634$	19.3006	0.766523
$635$	−12.0627	−0.478694
$636$	−30.5069	−1.20968
$637$	−0.730262	−0.0289340
$638$	−3.08266	−0.122044
$639$	14.3356	0.567107
$640$	−30.8291	−1.21863
$641$	15.8168	0.624727	0.312364	−	0.949963i	$-0.398879\pi$
$641$	15.8168	0.624727	0.312364	+	0.949963i	$0.398879\pi$
$642$	24.7993	0.978751
$643$	−20.4175	−0.805187	−0.402593	−	0.915379i	$-0.631891\pi$
$643$	−20.4175	−0.805187	−0.402593	+	0.915379i	$0.631891\pi$
$644$	−10.5285	−0.414882
$645$	−37.0264	−1.45791
$646$	0	0
$647$	4.63482	0.182213	0.0911067	−	0.995841i	$-0.470960\pi$
$647$	4.63482	0.182213	0.0911067	+	0.995841i	$0.470960\pi$
$648$	11.7441	0.461353
$649$	−1.23093	−0.0483183
$650$	10.3552	0.406164
$651$	−73.7518	−2.89056
$652$	−4.05035	−0.158624
$653$	−23.5256	−0.920627	−0.460314	−	0.887756i	$-0.652263\pi$
$653$	−23.5256	−0.920627	−0.460314	+	0.887756i	$0.652263\pi$
$654$	71.7507	2.80567
$655$	11.6573	0.455487
$656$	−34.7871	−1.35821
$657$	−14.6774	−0.572620
$658$	34.8671	1.35926
$659$	−7.49057	−0.291791	−0.145896	−	0.989300i	$-0.546606\pi$
$659$	−7.49057	−0.291791	−0.145896	+	0.989300i	$0.546606\pi$
$660$	17.8488	0.694763
$661$	40.4699	1.57410	0.787048	−	0.616892i	$-0.211609\pi$
$661$	40.4699	1.57410	0.787048	+	0.616892i	$0.211609\pi$
$662$	−60.5688	−2.35407
$663$	0	0
$664$	1.95208	0.0757555
$665$	48.5252	1.88173
$666$	−51.6345	−2.00080
$667$	4.10198	0.158829
$668$	−9.55631	−0.369745
$669$	−3.48861	−0.134877
$670$	16.6017	0.641379
$671$	2.96347	0.114403
$672$	−61.2009	−2.36087
$673$	−34.5369	−1.33130	−0.665650	−	0.746264i	$-0.731846\pi$
$673$	−34.5369	−1.33130	−0.665650	+	0.746264i	$0.731846\pi$
$674$	64.5453	2.48619
$675$	−110.642	−4.25863
$676$	−18.6465	−0.717172
$677$	−32.5829	−1.25226	−0.626131	−	0.779718i	$-0.715363\pi$
$677$	−32.5829	−1.25226	−0.626131	+	0.779718i	$0.715363\pi$
$678$	63.7447	2.44810
$679$	35.6229	1.36708
$680$	0	0
$681$	42.1947	1.61690
$682$	15.4902	0.593150
$683$	14.5889	0.558227	0.279114	−	0.960258i	$-0.409959\pi$
$683$	14.5889	0.558227	0.279114	+	0.960258i	$0.409959\pi$
$684$	38.4458	1.47001
$685$	−12.5487	−0.479461
$686$	30.0420	1.14701
$687$	71.1872	2.71596
$688$	−14.5247	−0.553749
$689$	−3.45662	−0.131687
$690$	−56.2171	−2.14015
$691$	22.9084	0.871475	0.435738	−	0.900074i	$-0.356488\pi$
$691$	22.9084	0.871475	0.435738	+	0.900074i	$0.356488\pi$
$692$	−36.4340	−1.38501
$693$	−18.2969	−0.695041
$694$	24.0886	0.914392
$695$	32.1359	1.21898
$696$	5.04633	0.191280
$697$	0	0
$698$	−20.7317	−0.784708
$699$	6.20152	0.234563
$700$	46.8071	1.76914
$701$	29.8956	1.12914	0.564570	−	0.825385i	$-0.309042\pi$
$701$	29.8956	1.12914	0.564570	+	0.825385i	$0.309042\pi$
$702$	−9.45345	−0.356797
$703$	18.3915	0.693649
$704$	3.28302	0.123733
$705$	78.6548	2.96231
$706$	60.1263	2.26288
$707$	−2.68879	−0.101122
$708$	−5.49113	−0.206369
$709$	−11.7221	−0.440233	−0.220117	−	0.975474i	$-0.570644\pi$
$709$	−11.7221	−0.440233	−0.220117	+	0.975474i	$0.570644\pi$
$710$	−16.9530	−0.636233
$711$	−55.6712	−2.08783
$712$	9.24395	0.346432
$713$	−20.6122	−0.771934
$714$	0	0
$715$	2.02238	0.0756326
$716$	−10.5680	−0.394946
$717$	91.3472	3.41142
$718$	−54.6301	−2.03878
$719$	25.3827	0.946616	0.473308	−	0.880897i	$-0.343060\pi$
$719$	25.3827	0.946616	0.473308	+	0.880897i	$0.343060\pi$
$720$	−120.558	−4.49292
$721$	−51.3888	−1.91382
$722$	2.94495	0.109600
$723$	−77.6084	−2.88629
$724$	37.6382	1.39881
$725$	−18.2363	−0.677280
$726$	5.67397	0.210581
$727$	43.7703	1.62335	0.811675	−	0.584110i	$-0.198556\pi$
$727$	43.7703	1.62335	0.811675	+	0.584110i	$0.198556\pi$
$728$	−1.46758	−0.0543922
$729$	−17.9214	−0.663756
$730$	17.3572	0.642419
$731$	0	0
$732$	13.2199	0.488621
$733$	−3.82048	−0.141112	−0.0705562	−	0.997508i	$-0.522477\pi$
$733$	−3.82048	−0.141112	−0.0705562	+	0.997508i	$0.522477\pi$
$734$	−2.85273	−0.105296
$735$	−17.6252	−0.650114
$736$	−17.1045	−0.630480
$737$	2.22966	0.0821306
$738$	−85.1733	−3.13527
$739$	28.8237	1.06030	0.530148	−	0.847905i	$-0.322136\pi$
$739$	28.8237	1.06030	0.530148	+	0.847905i	$0.322136\pi$
$740$	25.7976	0.948338
$741$	6.43173	0.236276
$742$	−36.9825	−1.35767
$743$	3.44279	0.126304	0.0631518	−	0.998004i	$-0.479885\pi$
$743$	3.44279	0.126304	0.0631518	+	0.998004i	$0.479885\pi$
$744$	−25.3575	−0.929652
$745$	20.1208	0.737169
$746$	−19.2164	−0.703564
$747$	12.3014	0.450084
$748$	0	0
$749$	12.7013	0.464094
$750$	136.416	4.98119
$751$	17.6340	0.643473	0.321737	−	0.946829i	$-0.395733\pi$
$751$	17.6340	0.643473	0.321737	+	0.946829i	$0.395733\pi$
$752$	30.8547	1.12515
$753$	43.7956	1.59600
$754$	−1.55814	−0.0567441
$755$	−51.1816	−1.86269
$756$	−42.7311	−1.55412
$757$	4.11948	0.149725	0.0748625	−	0.997194i	$-0.476148\pi$
$757$	4.11948	0.149725	0.0748625	+	0.997194i	$0.476148\pi$
$758$	−17.6684	−0.641746
$759$	−7.55014	−0.274053
$760$	16.6841	0.605194
$761$	−4.80735	−0.174266	−0.0871331	−	0.996197i	$-0.527771\pi$
$761$	−4.80735	−0.174266	−0.0871331	+	0.996197i	$0.527771\pi$
$762$	−17.1061	−0.619688
$763$	36.7480	1.33037
$764$	−13.6567	−0.494082
$765$	0	0
$766$	−7.03886	−0.254324
$767$	−0.622179	−0.0224656
$768$	−63.7384	−2.29996
$769$	32.8832	1.18580	0.592899	−	0.805277i	$-0.297983\pi$
$769$	32.8832	1.18580	0.592899	+	0.805277i	$0.297983\pi$
$770$	21.6375	0.779762
$771$	48.6535	1.75221
$772$	34.0728	1.22631
$773$	28.7069	1.03252	0.516258	−	0.856433i	$-0.327325\pi$
$773$	28.7069	1.03252	0.516258	+	0.856433i	$0.327325\pi$
$774$	−35.5624	−1.27827
$775$	91.6366	3.29169
$776$	12.2479	0.439675
$777$	−39.0457	−1.40076
$778$	−63.8698	−2.28985
$779$	30.3376	1.08696
$780$	9.02172	0.323029
$781$	−2.27684	−0.0814717
$782$	0	0
$783$	16.6483	0.594962
$784$	−6.91399	−0.246928
$785$	−60.6953	−2.16631
$786$	16.5311	0.589646
$787$	54.1191	1.92914	0.964569	−	0.263832i	$-0.0849865\pi$
$787$	54.1191	1.92914	0.964569	+	0.263832i	$0.0849865\pi$
$788$	−5.31534	−0.189351
$789$	55.6180	1.98005
$790$	65.8356	2.34232
$791$	32.6476	1.16081
$792$	−6.29088	−0.223537
$793$	1.49790	0.0531918
$794$	−28.9253	−1.02652
$795$	−83.4268	−2.95884
$796$	−0.248253	−0.00879909
$797$	−14.4068	−0.510315	−0.255157	−	0.966900i	$-0.582127\pi$
$797$	−14.4068	−0.510315	−0.255157	+	0.966900i	$0.582127\pi$
$798$	68.8135	2.43597
$799$	0	0
$800$	76.0421	2.68849
$801$	58.2523	2.05824
$802$	48.0326	1.69609
$803$	2.33113	0.0822637
$804$	9.94641	0.350783
$805$	−28.7922	−1.01479
$806$	7.82957	0.275785
$807$	−14.9796	−0.527307
$808$	−0.924465	−0.0325226
$809$	−35.9167	−1.26277	−0.631383	−	0.775472i	$-0.717512\pi$
$809$	−35.9167	−1.26277	−0.631383	+	0.775472i	$0.717512\pi$
$810$	−87.5198	−3.07513
$811$	23.1572	0.813159	0.406579	−	0.913615i	$-0.366721\pi$
$811$	23.1572	0.813159	0.406579	+	0.913615i	$0.366721\pi$
$812$	−7.04304	−0.247162
$813$	−92.0856	−3.22958
$814$	8.20082	0.287438
$815$	−11.0764	−0.387991
$816$	0	0
$817$	12.6669	0.443157
$818$	28.3321	0.990609
$819$	−9.24822	−0.323159
$820$	42.5542	1.48606
$821$	−2.65720	−0.0927370	−0.0463685	−	0.998924i	$-0.514765\pi$
$821$	−2.65720	−0.0927370	−0.0463685	+	0.998924i	$0.514765\pi$
$822$	−17.7953	−0.620681
$823$	−0.205673	−0.00716931	−0.00358466	−	0.999994i	$-0.501141\pi$
$823$	−0.205673	−0.00716931	−0.00358466	+	0.999994i	$0.501141\pi$
$824$	−17.6686	−0.615516
$825$	33.5660	1.16862
$826$	−6.65672	−0.231617
$827$	17.8653	0.621238	0.310619	−	0.950535i	$-0.399464\pi$
$827$	17.8653	0.621238	0.310619	+	0.950535i	$0.399464\pi$
$828$	−22.8117	−0.792760
$829$	−0.286953	−0.00996627	−0.00498314	−	0.999988i	$-0.501586\pi$
$829$	−0.286953	−0.00996627	−0.00498314	+	0.999988i	$0.501586\pi$
$830$	−14.5473	−0.504946
$831$	−37.2677	−1.29280
$832$	1.65941	0.0575298
$833$	0	0
$834$	45.5718	1.57802
$835$	−26.1335	−0.904388
$836$	−6.10613	−0.211185
$837$	−83.6569	−2.89160
$838$	37.6781	1.30157
$839$	52.1549	1.80059	0.900294	−	0.435282i	$-0.143351\pi$
$839$	52.1549	1.80059	0.900294	+	0.435282i	$0.143351\pi$
$840$	−35.4207	−1.22213
$841$	−26.2560	−0.905379
$842$	−36.1612	−1.24620
$843$	−18.2694	−0.629232
$844$	29.4767	1.01463
$845$	−50.9923	−1.75419
$846$	75.5450	2.59729
$847$	2.90599	0.0998509
$848$	−32.7266	−1.12384
$849$	43.0870	1.47874
$850$	0	0
$851$	−10.9125	−0.374077
$852$	−10.1569	−0.347969
$853$	−14.3946	−0.492861	−0.246430	−	0.969161i	$-0.579258\pi$
$853$	−14.3946	−0.492861	−0.246430	+	0.969161i	$0.579258\pi$
$854$	16.0261	0.548400
$855$	105.137	3.59562
$856$	4.36698	0.149260
$857$	−11.4511	−0.391162	−0.195581	−	0.980688i	$-0.562659\pi$
$857$	−11.4511	−0.391162	−0.195581	+	0.980688i	$0.562659\pi$
$858$	2.86792	0.0979093
$859$	29.7329	1.01447	0.507236	−	0.861807i	$-0.330667\pi$
$859$	29.7329	1.01447	0.507236	+	0.861807i	$0.330667\pi$
$860$	17.7677	0.605872
$861$	−64.4074	−2.19500
$862$	−67.1899	−2.28850
$863$	−0.284056	−0.00966939	−0.00483469	−	0.999988i	$-0.501539\pi$
$863$	−0.284056	−0.00966939	−0.00483469	+	0.999988i	$0.501539\pi$
$864$	−69.4203	−2.36173
$865$	−99.6355	−3.38771
$866$	17.7646	0.603666
$867$	0	0
$868$	35.3909	1.20125
$869$	8.84193	0.299942
$870$	−37.6063	−1.27497
$871$	1.12699	0.0381865
$872$	12.6348	0.427867
$873$	77.1824	2.61223
$874$	19.2321	0.650534
$875$	69.8668	2.36193
$876$	10.3991	0.351351
$877$	3.81451	0.128807	0.0644035	−	0.997924i	$-0.479486\pi$
$877$	3.81451	0.128807	0.0644035	+	0.997924i	$0.479486\pi$
$878$	−32.7673	−1.10584
$879$	−93.2254	−3.14441
$880$	19.1475	0.645462
$881$	−30.8186	−1.03831	−0.519153	−	0.854681i	$-0.673752\pi$
$881$	−30.8186	−1.03831	−0.519153	+	0.854681i	$0.673752\pi$
$882$	−16.9283	−0.570006
$883$	24.7589	0.833203	0.416602	−	0.909089i	$-0.363221\pi$
$883$	24.7589	0.833203	0.416602	+	0.909089i	$0.363221\pi$
$884$	0	0
$885$	−15.0165	−0.504775
$886$	−11.6141	−0.390183
$887$	15.4612	0.519137	0.259569	−	0.965725i	$-0.416420\pi$
$887$	15.4612	0.519137	0.259569	+	0.965725i	$0.416420\pi$
$888$	−13.4248	−0.450506
$889$	−8.76108	−0.293837
$890$	−68.8879	−2.30913
$891$	−11.7542	−0.393781
$892$	1.67406	0.0560517
$893$	−26.9081	−0.900444
$894$	28.5332	0.954294
$895$	−28.9003	−0.966031
$896$	−22.3910	−0.748032
$897$	−3.81624	−0.127421
$898$	26.4095	0.881297
$899$	−13.7885	−0.459873
$900$	101.415	3.38049
$901$	0	0
$902$	13.5276	0.450419
$903$	−26.8921	−0.894912
$904$	11.2250	0.373337
$905$	102.929	3.42146
$906$	−72.5804	−2.41132
$907$	−6.55569	−0.217678	−0.108839	−	0.994059i	$-0.534713\pi$
$907$	−6.55569	−0.217678	−0.108839	+	0.994059i	$0.534713\pi$
$908$	−20.2477	−0.671945
$909$	−5.82567	−0.193225
$910$	10.9367	0.362550
$911$	−33.9013	−1.12320	−0.561600	−	0.827409i	$-0.689814\pi$
$911$	−33.9013	−1.12320	−0.561600	+	0.827409i	$0.689814\pi$
$912$	60.8945	2.01642
$913$	−1.95376	−0.0646599
$914$	3.28289	0.108588
$915$	36.1523	1.19516
$916$	−34.1602	−1.12869
$917$	8.46661	0.279592
$918$	0	0
$919$	19.4750	0.642420	0.321210	−	0.947008i	$-0.395910\pi$
$919$	19.4750	0.642420	0.321210	+	0.947008i	$0.395910\pi$
$920$	−9.89941	−0.326374
$921$	5.77591	0.190323
$922$	−47.3055	−1.55792
$923$	−1.15084	−0.0378802
$924$	12.9635	0.426467
$925$	48.5143	1.59514
$926$	−72.7490	−2.39068
$927$	−111.342	−3.65694
$928$	−11.4420	−0.375602
$929$	−12.5063	−0.410318	−0.205159	−	0.978729i	$-0.565771\pi$
$929$	−12.5063	−0.410318	−0.205159	+	0.978729i	$0.565771\pi$
$930$	188.970	6.19656
$931$	6.02963	0.197613
$932$	−2.97589	−0.0974785
$933$	51.9220	1.69985
$934$	13.7556	0.450097
$935$	0	0
$936$	−3.17974	−0.103933
$937$	40.8756	1.33535	0.667673	−	0.744455i	$-0.267290\pi$
$937$	40.8756	1.33535	0.667673	+	0.744455i	$0.267290\pi$
$938$	12.0577	0.393698
$939$	−15.8778	−0.518151
$940$	−37.7437	−1.23106
$941$	11.7392	0.382687	0.191344	−	0.981523i	$-0.438715\pi$
$941$	11.7392	0.382687	0.191344	+	0.981523i	$0.438715\pi$
$942$	−86.0717	−2.80437
$943$	−18.0007	−0.586182
$944$	−5.89068	−0.191725
$945$	−116.856	−3.80133
$946$	5.64818	0.183638
$947$	40.4917	1.31580	0.657901	−	0.753104i	$-0.271444\pi$
$947$	40.4917	1.31580	0.657901	+	0.753104i	$0.271444\pi$
$948$	39.4434	1.28106
$949$	1.17828	0.0382485
$950$	−85.5007	−2.77401
$951$	31.6222	1.02542
$952$	0	0
$953$	19.9059	0.644817	0.322408	−	0.946601i	$-0.395508\pi$
$953$	19.9059	0.644817	0.322408	+	0.946601i	$0.395508\pi$
$954$	−80.1283	−2.59425
$955$	−37.3468	−1.20851
$956$	−43.8343	−1.41770
$957$	−5.05065	−0.163264
$958$	−15.9031	−0.513805
$959$	−9.11406	−0.294308
$960$	40.0506	1.29263
$961$	38.2866	1.23505
$962$	4.14513	0.133644
$963$	27.5192	0.886795
$964$	37.2415	1.19947
$965$	93.1785	2.99952
$966$	−40.8302	−1.31369
$967$	−13.0216	−0.418745	−0.209372	−	0.977836i	$-0.567142\pi$
$967$	−13.0216	−0.418745	−0.209372	+	0.977836i	$0.567142\pi$
$968$	0.999144	0.0321137
$969$	0	0
$970$	−91.2743	−2.93064
$971$	−30.7026	−0.985293	−0.492647	−	0.870230i	$-0.663970\pi$
$971$	−30.7026	−0.985293	−0.492647	+	0.870230i	$0.663970\pi$
$972$	−8.32144	−0.266910
$973$	23.3401	0.748250
$974$	15.1112	0.484194
$975$	16.9660	0.543347
$976$	14.1818	0.453949
$977$	−39.7318	−1.27113	−0.635567	−	0.772046i	$-0.719234\pi$
$977$	−39.7318	−1.27113	−0.635567	+	0.772046i	$0.719234\pi$
$978$	−15.7074	−0.502269
$979$	−9.25188	−0.295691
$980$	8.45770	0.270171
$981$	79.6201	2.54207
$982$	−33.2067	−1.05967
$983$	−13.5692	−0.432789	−0.216394	−	0.976306i	$-0.569430\pi$
$983$	−13.5692	−0.432789	−0.216394	+	0.976306i	$0.569430\pi$
$984$	−22.1447	−0.705948
$985$	−14.5358	−0.463149
$986$	0	0
$987$	57.1266	1.81836
$988$	−3.08636	−0.0981903
$989$	−7.51582	−0.238989
$990$	46.8810	1.48998
$991$	45.8236	1.45564	0.727818	−	0.685771i	$-0.240535\pi$
$991$	45.8236	1.45564	0.727818	+	0.685771i	$0.240535\pi$
$992$	57.4955	1.82548
$993$	−99.2364	−3.14917
$994$	−12.3128	−0.390540
$995$	−0.678894	−0.0215224
$996$	−8.71561	−0.276165
$997$	14.1923	0.449474	0.224737	−	0.974419i	$-0.427848\pi$
$997$	14.1923	0.449474	0.224737	+	0.974419i	$0.427848\pi$
$998$	4.64276	0.146964
$999$	−44.2896	−1.40126

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3179.2.a.bi.1.6		28
17.3	odd	16		187.2.h.a.111.4	✓	56
17.6	odd	16		187.2.h.a.155.4	yes	56
17.16	even	2		3179.2.a.bh.1.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.h.a.111.4	✓	56	17.3	odd	16
187.2.h.a.155.4	yes	56	17.6	odd	16
3179.2.a.bh.1.6		28	17.16	even	2
3179.2.a.bi.1.6		28	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:	\( N \)	\(=\)	\( 3179 = 11 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3179.a (trivial)

\(f(q)\)	\(=\)	\(q-1.86094 q^{2} -3.04898 q^{3} +1.46310 q^{4} +4.00111 q^{5} +5.67397 q^{6} +2.90599 q^{7} +0.999144 q^{8} +6.29627 q^{9} +O(q^{10})\)	\(q-1.86094 q^{2} -3.04898 q^{3} +1.46310 q^{4} +4.00111 q^{5} +5.67397 q^{6} +2.90599 q^{7} +0.999144 q^{8} +6.29627 q^{9} -7.44583 q^{10} -1.00000 q^{11} -4.46095 q^{12} -0.505453 q^{13} -5.40787 q^{14} -12.1993 q^{15} -4.78554 q^{16} -11.7170 q^{18} +4.17343 q^{19} +5.85402 q^{20} -8.86030 q^{21} +1.86094 q^{22} -2.47628 q^{23} -3.04637 q^{24} +11.0089 q^{25} +0.940618 q^{26} -10.0503 q^{27} +4.25174 q^{28} -1.65651 q^{29} +22.7022 q^{30} +8.32386 q^{31} +6.90732 q^{32} +3.04898 q^{33} +11.6272 q^{35} +9.21206 q^{36} +4.40681 q^{37} -7.76650 q^{38} +1.54112 q^{39} +3.99769 q^{40} +7.26922 q^{41} +16.4885 q^{42} +3.03512 q^{43} -1.46310 q^{44} +25.1921 q^{45} +4.60822 q^{46} -6.44748 q^{47} +14.5910 q^{48} +1.44477 q^{49} -20.4869 q^{50} -0.739527 q^{52} +6.83865 q^{53} +18.7029 q^{54} -4.00111 q^{55} +2.90350 q^{56} -12.7247 q^{57} +3.08266 q^{58} +1.23093 q^{59} -17.8488 q^{60} -2.96347 q^{61} -15.4902 q^{62} +18.2969 q^{63} -3.28302 q^{64} -2.02238 q^{65} -5.67397 q^{66} -2.22966 q^{67} +7.55014 q^{69} -21.6375 q^{70} +2.27684 q^{71} +6.29088 q^{72} -2.33113 q^{73} -8.20082 q^{74} -33.5660 q^{75} +6.10613 q^{76} -2.90599 q^{77} -2.86792 q^{78} -8.84193 q^{79} -19.1475 q^{80} +11.7542 q^{81} -13.5276 q^{82} +1.95376 q^{83} -12.9635 q^{84} -5.64818 q^{86} +5.05065 q^{87} -0.999144 q^{88} +9.25188 q^{89} -46.8810 q^{90} -1.46884 q^{91} -3.62305 q^{92} -25.3793 q^{93} +11.9984 q^{94} +16.6984 q^{95} -21.0603 q^{96} +12.2584 q^{97} -2.68863 q^{98} -6.29627 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 8 q^{3} + 24 q^{4} + 16 q^{5} + 16 q^{6} + 12 q^{7} + 20 q^{9}+O(q^{10}) \) 28 * q + 8 * q^3 + 24 * q^4 + 16 * q^5 + 16 * q^6 + 12 * q^7 + 20 * q^9	\( 28 q + 8 q^{3} + 24 q^{4} + 16 q^{5} + 16 q^{6} + 12 q^{7} + 20 q^{9} + 24 q^{10} - 28 q^{11} + 24 q^{12} + 16 q^{14} - 16 q^{15} + 16 q^{16} + 32 q^{20} + 8 q^{23} - 8 q^{24} + 20 q^{25} - 24 q^{26} + 32 q^{27} + 32 q^{28} + 36 q^{29} + 40 q^{30} + 56 q^{31} + 40 q^{32} - 8 q^{33} + 16 q^{35} + 40 q^{36} + 64 q^{37} - 8 q^{38} + 32 q^{39} + 72 q^{40} + 28 q^{41} + 24 q^{42} + 16 q^{43} - 24 q^{44} + 24 q^{45} - 36 q^{47} + 56 q^{48} + 16 q^{49} + 56 q^{50} - 20 q^{53} + 64 q^{54} - 16 q^{55} + 48 q^{56} + 32 q^{57} - 16 q^{58} - 28 q^{59} + 8 q^{60} + 104 q^{61} - 8 q^{62} + 28 q^{63} + 32 q^{65} - 16 q^{66} - 12 q^{67} - 32 q^{69} + 40 q^{71} + 40 q^{72} + 76 q^{73} + 24 q^{74} - 16 q^{75} - 16 q^{76} - 12 q^{77} - 24 q^{78} + 24 q^{79} + 8 q^{80} + 12 q^{81} + 56 q^{82} + 32 q^{83} - 40 q^{84} - 16 q^{86} - 8 q^{87} - 52 q^{89} + 16 q^{90} + 80 q^{91} - 56 q^{92} + 24 q^{97} - 24 q^{98} - 20 q^{99}+O(q^{100}) \) 28 * q + 8 * q^3 + 24 * q^4 + 16 * q^5 + 16 * q^6 + 12 * q^7 + 20 * q^9 + 24 * q^10 - 28 * q^11 + 24 * q^12 + 16 * q^14 - 16 * q^15 + 16 * q^16 + 32 * q^20 + 8 * q^23 - 8 * q^24 + 20 * q^25 - 24 * q^26 + 32 * q^27 + 32 * q^28 + 36 * q^29 + 40 * q^30 + 56 * q^31 + 40 * q^32 - 8 * q^33 + 16 * q^35 + 40 * q^36 + 64 * q^37 - 8 * q^38 + 32 * q^39 + 72 * q^40 + 28 * q^41 + 24 * q^42 + 16 * q^43 - 24 * q^44 + 24 * q^45 - 36 * q^47 + 56 * q^48 + 16 * q^49 + 56 * q^50 - 20 * q^53 + 64 * q^54 - 16 * q^55 + 48 * q^56 + 32 * q^57 - 16 * q^58 - 28 * q^59 + 8 * q^60 + 104 * q^61 - 8 * q^62 + 28 * q^63 + 32 * q^65 - 16 * q^66 - 12 * q^67 - 32 * q^69 + 40 * q^71 + 40 * q^72 + 76 * q^73 + 24 * q^74 - 16 * q^75 - 16 * q^76 - 12 * q^77 - 24 * q^78 + 24 * q^79 + 8 * q^80 + 12 * q^81 + 56 * q^82 + 32 * q^83 - 40 * q^84 - 16 * q^86 - 8 * q^87 - 52 * q^89 + 16 * q^90 + 80 * q^91 - 56 * q^92 + 24 * q^97 - 24 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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