LMFDB - Embedded newform 3971.2.a.t.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3971,2,Mod(1,3971)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3971, 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("3971.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3971 = 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3971.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:	$31.7085946427$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	no (minimal twist has level 209)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	3971.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.40278 q^{2} +2.92541 q^{3} -0.0322206 q^{4} +1.23149 q^{5} -4.10370 q^{6} +3.91477 q^{7} +2.85075 q^{8} +5.55805 q^{9} -1.72751 q^{10} +1.00000 q^{11} -0.0942587 q^{12} +5.37366 q^{13} -5.49155 q^{14} +3.60263 q^{15} -3.93452 q^{16} +2.82070 q^{17} -7.79670 q^{18} -0.0396795 q^{20} +11.4523 q^{21} -1.40278 q^{22} -3.08937 q^{23} +8.33962 q^{24} -3.48342 q^{25} -7.53804 q^{26} +7.48335 q^{27} -0.126136 q^{28} +2.28200 q^{29} -5.05369 q^{30} +5.31111 q^{31} -0.182249 q^{32} +2.92541 q^{33} -3.95681 q^{34} +4.82102 q^{35} -0.179084 q^{36} +2.40677 q^{37} +15.7202 q^{39} +3.51068 q^{40} -10.2660 q^{41} -16.0650 q^{42} +7.91544 q^{43} -0.0322206 q^{44} +6.84471 q^{45} +4.33369 q^{46} -3.81292 q^{47} -11.5101 q^{48} +8.32544 q^{49} +4.88646 q^{50} +8.25172 q^{51} -0.173143 q^{52} -8.12625 q^{53} -10.4975 q^{54} +1.23149 q^{55} +11.1600 q^{56} -3.20113 q^{58} +7.77647 q^{59} -0.116079 q^{60} -9.84295 q^{61} -7.45029 q^{62} +21.7585 q^{63} +8.12470 q^{64} +6.61764 q^{65} -4.10370 q^{66} +2.30646 q^{67} -0.0908847 q^{68} -9.03768 q^{69} -6.76281 q^{70} +9.18711 q^{71} +15.8446 q^{72} -10.1223 q^{73} -3.37615 q^{74} -10.1904 q^{75} +3.91477 q^{77} -22.0519 q^{78} -8.62894 q^{79} -4.84534 q^{80} +5.21776 q^{81} +14.4009 q^{82} -13.3973 q^{83} -0.369001 q^{84} +3.47368 q^{85} -11.1036 q^{86} +6.67579 q^{87} +2.85075 q^{88} -10.3481 q^{89} -9.60159 q^{90} +21.0367 q^{91} +0.0995413 q^{92} +15.5372 q^{93} +5.34866 q^{94} -0.533155 q^{96} -7.25726 q^{97} -11.6787 q^{98} +5.55805 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 6 q^{2} + 15 q^{3} + 18 q^{4} + 6 q^{5} - 6 q^{6} + 6 q^{7} + 15 q^{8} + 18 q^{9} - 6 q^{10} + 21 q^{11} + 30 q^{12} + 36 q^{13} + 12 q^{14} + 12 q^{15} + 12 q^{16} + 21 q^{17} + 6 q^{18} + 15 q^{20}+ \cdots + 18 q^{99}+O(q^{100}) $ 21 * q + 6 * q^2 + 15 * q^3 + 18 * q^4 + 6 * q^5 - 6 * q^6 + 6 * q^7 + 15 * q^8 + 18 * q^9 - 6 * q^10 + 21 * q^11 + 30 * q^12 + 36 * q^13 + 12 * q^14 + 12 * q^15 + 12 * q^16 + 21 * q^17 + 6 * q^18 + 15 * q^20 - 3 * q^21 + 6 * q^22 + 6 * q^23 - 18 * q^24 + 3 * q^25 + 6 * q^26 + 24 * q^27 + 27 * q^29 - 30 * q^30 + 54 * q^31 + 21 * q^32 + 15 * q^33 + 39 * q^34 - 33 * q^35 + 54 * q^36 + 57 * q^37 - 27 * q^40 + 24 * q^41 + 6 * q^42 + 12 * q^43 + 18 * q^44 - 3 * q^45 + 15 * q^46 + 12 * q^47 - 39 * q^48 + 21 * q^49 + 33 * q^50 - 18 * q^51 - 18 * q^52 + 39 * q^53 + 30 * q^54 + 6 * q^55 + 57 * q^56 + 30 * q^58 + 27 * q^59 + 12 * q^60 - 30 * q^61 + 21 * q^62 - 18 * q^63 - 15 * q^64 - 24 * q^65 - 6 * q^66 + 27 * q^67 - 48 * q^68 + 54 * q^69 + 51 * q^70 + 42 * q^71 + 15 * q^72 + 6 * q^73 + 84 * q^74 + 27 * q^75 + 6 * q^77 - 48 * q^78 + 39 * q^79 - 27 * q^80 - 27 * q^81 - 15 * q^82 + 12 * q^83 - 48 * q^84 - 42 * q^85 - 45 * q^86 + 75 * q^87 + 15 * q^88 + 75 * q^89 - 87 * q^90 + 45 * q^91 + 12 * q^92 + 66 * q^93 + 42 * q^94 - 3 * q^96 + 39 * q^97 - 45 * q^98 + 18 * q^99

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 $

$2$	−1.40278	−0.991912	−0.495956	−	0.868348i	$-0.665182\pi$
$2$	−1.40278	−0.991912	−0.495956	+	0.868348i	$0.665182\pi$
$3$	2.92541	1.68899	0.844494	−	0.535564i	$-0.179901\pi$
$3$	2.92541	1.68899	0.844494	+	0.535564i	$0.179901\pi$
$4$	−0.0322206	−0.0161103
$5$	1.23149	0.550741	0.275371	−	0.961338i	$-0.411199\pi$
$5$	1.23149	0.550741	0.275371	+	0.961338i	$0.411199\pi$
$6$	−4.10370	−1.67533
$7$	3.91477	1.47964	0.739822	−	0.672802i	$-0.234910\pi$
$7$	3.91477	1.47964	0.739822	+	0.672802i	$0.234910\pi$
$8$	2.85075	1.00789
$9$	5.55805	1.85268
$10$	−1.72751	−0.546287
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.0942587	−0.0272101
$13$	5.37366	1.49039	0.745193	−	0.666849i	$-0.232357\pi$
$13$	5.37366	1.49039	0.745193	+	0.666849i	$0.232357\pi$
$14$	−5.49155	−1.46768
$15$	3.60263	0.930196
$16$	−3.93452	−0.983630
$17$	2.82070	0.684120	0.342060	−	0.939678i	$-0.388875\pi$
$17$	2.82070	0.684120	0.342060	+	0.939678i	$0.388875\pi$
$18$	−7.79670	−1.83770
$19$	0	0
$19$	0	0
$20$	−0.0396795	−0.00887261
$21$	11.4523	2.49910
$22$	−1.40278	−0.299073
$23$	−3.08937	−0.644178	−0.322089	−	0.946709i	$-0.604385\pi$
$23$	−3.08937	−0.644178	−0.322089	+	0.946709i	$0.604385\pi$
$24$	8.33962	1.70232
$25$	−3.48342	−0.696684
$26$	−7.53804	−1.47833
$27$	7.48335	1.44017
$28$	−0.126136	−0.0238375
$29$	2.28200	0.423757	0.211878	−	0.977296i	$-0.432042\pi$
$29$	2.28200	0.423757	0.211878	+	0.977296i	$0.432042\pi$
$30$	−5.05369	−0.922672
$31$	5.31111	0.953903	0.476952	−	0.878930i	$-0.341742\pi$
$31$	5.31111	0.953903	0.476952	+	0.878930i	$0.341742\pi$
$32$	−0.182249	−0.0322175
$33$	2.92541	0.509249
$34$	−3.95681	−0.678587
$35$	4.82102	0.814901
$36$	−0.179084	−0.0298473
$37$	2.40677	0.395670	0.197835	−	0.980235i	$-0.436609\pi$
$37$	2.40677	0.395670	0.197835	+	0.980235i	$0.436609\pi$
$38$	0	0
$39$	15.7202	2.51724
$40$	3.51068	0.555088
$41$	−10.2660	−1.60328	−0.801642	−	0.597805i	$-0.796040\pi$
$41$	−10.2660	−1.60328	−0.801642	+	0.597805i	$0.796040\pi$
$42$	−16.0650	−2.47889
$43$	7.91544	1.20709	0.603547	−	0.797328i	$-0.293754\pi$
$43$	7.91544	1.20709	0.603547	+	0.797328i	$0.293754\pi$
$44$	−0.0322206	−0.00485744
$45$	6.84471	1.02035
$46$	4.33369	0.638968
$47$	−3.81292	−0.556171	−0.278085	−	0.960556i	$-0.589700\pi$
$47$	−3.81292	−0.556171	−0.278085	+	0.960556i	$0.589700\pi$
$48$	−11.5101	−1.66134
$49$	8.32544	1.18935
$50$	4.88646	0.691049
$51$	8.25172	1.15547
$52$	−0.173143	−0.0240106
$53$	−8.12625	−1.11623	−0.558113	−	0.829765i	$-0.688475\pi$
$53$	−8.12625	−1.11623	−0.558113	+	0.829765i	$0.688475\pi$
$54$	−10.4975	−1.42852
$55$	1.23149	0.166055
$56$	11.1600	1.49132
$57$	0	0
$58$	−3.20113	−0.420329
$59$	7.77647	1.01241	0.506205	−	0.862413i	$-0.331048\pi$
$59$	7.77647	1.01241	0.506205	+	0.862413i	$0.331048\pi$
$60$	−0.116079	−0.0149857
$61$	−9.84295	−1.26026	−0.630130	−	0.776489i	$-0.716999\pi$
$61$	−9.84295	−1.26026	−0.630130	+	0.776489i	$0.716999\pi$
$62$	−7.45029	−0.946188
$63$	21.7585	2.74131
$64$	8.12470	1.01559
$65$	6.61764	0.820817
$66$	−4.10370	−0.505131
$67$	2.30646	0.281779	0.140889	−	0.990025i	$-0.455004\pi$
$67$	2.30646	0.281779	0.140889	+	0.990025i	$0.455004\pi$
$68$	−0.0908847	−0.0110214
$69$	−9.03768	−1.08801
$70$	−6.76281	−0.808311
$71$	9.18711	1.09031	0.545155	−	0.838335i	$-0.316471\pi$
$71$	9.18711	1.09031	0.545155	+	0.838335i	$0.316471\pi$
$72$	15.8446	1.86730
$73$	−10.1223	−1.18472	−0.592361	−	0.805672i	$-0.701804\pi$
$73$	−10.1223	−1.18472	−0.592361	+	0.805672i	$0.701804\pi$
$74$	−3.37615	−0.392470
$75$	−10.1904	−1.17669
$76$	0	0
$77$	3.91477	0.446130
$78$	−22.0519	−2.49689
$79$	−8.62894	−0.970831	−0.485416	−	0.874283i	$-0.661332\pi$
$79$	−8.62894	−0.970831	−0.485416	+	0.874283i	$0.661332\pi$
$80$	−4.84534	−0.541726
$81$	5.21776	0.579752
$82$	14.4009	1.59032
$83$	−13.3973	−1.47055	−0.735275	−	0.677769i	$-0.762947\pi$
$83$	−13.3973	−1.47055	−0.735275	+	0.677769i	$0.762947\pi$
$84$	−0.369001	−0.0402613
$85$	3.47368	0.376773
$86$	−11.1036	−1.19733
$87$	6.67579	0.715720
$88$	2.85075	0.303891
$89$	−10.3481	−1.09689	−0.548447	−	0.836185i	$-0.684781\pi$
$89$	−10.3481	−1.09689	−0.548447	+	0.836185i	$0.684781\pi$
$90$	−9.60159	−1.01210
$91$	21.0367	2.20524
$92$	0.0995413	0.0103779
$93$	15.5372	1.61113
$94$	5.34866	0.551673
$95$	0	0
$96$	−0.533155	−0.0544149
$97$	−7.25726	−0.736863	−0.368431	−	0.929655i	$-0.620105\pi$
$97$	−7.25726	−0.736863	−0.368431	+	0.929655i	$0.620105\pi$
$98$	−11.6787	−1.17973
$99$	5.55805	0.558605
$100$	0.112238	0.0112238
$101$	−14.7770	−1.47037	−0.735185	−	0.677867i	$-0.762905\pi$
$101$	−14.7770	−1.47037	−0.735185	+	0.677867i	$0.762905\pi$
$102$	−11.5753	−1.14613
$103$	−15.0223	−1.48019	−0.740093	−	0.672504i	$-0.765219\pi$
$103$	−15.0223	−1.48019	−0.740093	+	0.672504i	$0.765219\pi$
$104$	15.3190	1.50215
$105$	14.1035	1.37636
$106$	11.3993	1.10720
$107$	4.50182	0.435207	0.217604	−	0.976037i	$-0.430176\pi$
$107$	4.50182	0.435207	0.217604	+	0.976037i	$0.430176\pi$
$108$	−0.241118	−0.0232016
$109$	−0.881799	−0.0844610	−0.0422305	−	0.999108i	$-0.513446\pi$
$109$	−0.881799	−0.0844610	−0.0422305	+	0.999108i	$0.513446\pi$
$110$	−1.72751	−0.164712
$111$	7.04079	0.668282
$112$	−15.4028	−1.45542
$113$	6.85435	0.644803	0.322402	−	0.946603i	$-0.395510\pi$
$113$	6.85435	0.644803	0.322402	+	0.946603i	$0.395510\pi$
$114$	0	0
$115$	−3.80454	−0.354775
$116$	−0.0735274	−0.00682685
$117$	29.8671	2.76121
$118$	−10.9086	−1.00422
$119$	11.0424	1.01225
$120$	10.2702	0.937537
$121$	1.00000	0.0909091
$122$	13.8075	1.25007
$123$	−30.0324	−2.70793
$124$	−0.171127	−0.0153677
$125$	−10.4473	−0.934434
$126$	−30.5223	−2.71914
$127$	−8.87549	−0.787572	−0.393786	−	0.919202i	$-0.628835\pi$
$127$	−8.87549	−0.787572	−0.393786	+	0.919202i	$0.628835\pi$
$128$	−11.0326	−0.975156
$129$	23.1559	2.03877
$130$	−9.28306	−0.814178
$131$	3.22314	0.281607	0.140803	−	0.990038i	$-0.455031\pi$
$131$	3.22314	0.281607	0.140803	+	0.990038i	$0.455031\pi$
$132$	−0.0942587	−0.00820416
$133$	0	0
$134$	−3.23544	−0.279500
$135$	9.21571	0.793162
$136$	8.04111	0.689519
$137$	−16.7290	−1.42925	−0.714626	−	0.699506i	$-0.753403\pi$
$137$	−16.7290	−1.42925	−0.714626	+	0.699506i	$0.753403\pi$
$138$	12.6778	1.07921
$139$	−11.1077	−0.942142	−0.471071	−	0.882095i	$-0.656132\pi$
$139$	−11.1077	−0.942142	−0.471071	+	0.882095i	$0.656132\pi$
$140$	−0.155336	−0.0131283
$141$	−11.1544	−0.939366
$142$	−12.8875	−1.08149
$143$	5.37366	0.449368
$144$	−21.8683	−1.82235
$145$	2.81027	0.233380
$146$	14.1993	1.17514
$147$	24.3554	2.00880
$148$	−0.0775475	−0.00637436
$149$	−22.3503	−1.83101	−0.915505	−	0.402307i	$-0.868208\pi$
$149$	−22.3503	−1.83101	−0.915505	+	0.402307i	$0.868208\pi$
$150$	14.2949	1.16717
$151$	−6.65528	−0.541599	−0.270800	−	0.962636i	$-0.587288\pi$
$151$	−6.65528	−0.541599	−0.270800	+	0.962636i	$0.587288\pi$
$152$	0	0
$153$	15.6776	1.26746
$154$	−5.49155	−0.442521
$155$	6.54060	0.525354
$156$	−0.506514	−0.0405536
$157$	−10.3795	−0.828377	−0.414189	−	0.910191i	$-0.635935\pi$
$157$	−10.3795	−0.828377	−0.414189	+	0.910191i	$0.635935\pi$
$158$	12.1045	0.962979
$159$	−23.7727	−1.88529
$160$	−0.224439	−0.0177435
$161$	−12.0942	−0.953154
$162$	−7.31935	−0.575063
$163$	−5.15647	−0.403886	−0.201943	−	0.979397i	$-0.564726\pi$
$163$	−5.15647	−0.403886	−0.201943	+	0.979397i	$0.564726\pi$
$164$	0.330778	0.0258294
$165$	3.60263	0.280465
$166$	18.7935	1.45866
$167$	6.66683	0.515895	0.257948	−	0.966159i	$-0.416954\pi$
$167$	6.66683	0.515895	0.257948	+	0.966159i	$0.416954\pi$
$168$	32.6477	2.51883
$169$	15.8762	1.22125
$170$	−4.87279	−0.373726
$171$	0	0
$172$	−0.255040	−0.0194466
$173$	10.3638	0.787947	0.393974	−	0.919122i	$-0.371100\pi$
$173$	10.3638	0.787947	0.393974	+	0.919122i	$0.371100\pi$
$174$	−9.36464	−0.709932
$175$	−13.6368	−1.03084
$176$	−3.93452	−0.296576
$177$	22.7494	1.70995
$178$	14.5160	1.08802
$179$	14.0614	1.05100	0.525501	−	0.850793i	$-0.323878\pi$
$179$	14.0614	1.05100	0.525501	+	0.850793i	$0.323878\pi$
$180$	−0.220541	−0.0164381
$181$	13.6259	1.01281	0.506404	−	0.862296i	$-0.330974\pi$
$181$	13.6259	1.01281	0.506404	+	0.862296i	$0.330974\pi$
$182$	−29.5097	−2.18741
$183$	−28.7947	−2.12857
$184$	−8.80701	−0.649262
$185$	2.96392	0.217912
$186$	−21.7952	−1.59810
$187$	2.82070	0.206270
$188$	0.122854	0.00896008
$189$	29.2956	2.13094
$190$	0	0
$191$	−17.0015	−1.23019	−0.615093	−	0.788455i	$-0.710881\pi$
$191$	−17.0015	−1.23019	−0.615093	+	0.788455i	$0.710881\pi$
$192$	23.7681	1.71532
$193$	23.3659	1.68192	0.840959	−	0.541099i	$-0.181992\pi$
$193$	23.3659	1.68192	0.840959	+	0.541099i	$0.181992\pi$
$194$	10.1803	0.730903
$195$	19.3593	1.38635
$196$	−0.268251	−0.0191608
$197$	1.57194	0.111996	0.0559979	−	0.998431i	$-0.482166\pi$
$197$	1.57194	0.111996	0.0559979	+	0.998431i	$0.482166\pi$
$198$	−7.79670	−0.554087
$199$	12.0279	0.852635	0.426318	−	0.904573i	$-0.359811\pi$
$199$	12.0279	0.852635	0.426318	+	0.904573i	$0.359811\pi$
$200$	−9.93036	−0.702182
$201$	6.74735	0.475921
$202$	20.7289	1.45848
$203$	8.93351	0.627009
$204$	−0.265875	−0.0186150
$205$	−12.6426	−0.882994
$206$	21.0728	1.46821
$207$	−17.1709	−1.19346
$208$	−21.1428	−1.46599
$209$	0	0
$210$	−19.7840	−1.36523
$211$	2.18051	0.150112	0.0750562	−	0.997179i	$-0.476086\pi$
$211$	2.18051	0.150112	0.0750562	+	0.997179i	$0.476086\pi$
$212$	0.261833	0.0179828
$213$	26.8761	1.84152
$214$	−6.31504	−0.431687
$215$	9.74782	0.664796
$216$	21.3332	1.45154
$217$	20.7918	1.41144
$218$	1.23697	0.0837779
$219$	−29.6119	−2.00098
$220$	−0.0396795	−0.00267519
$221$	15.1575	1.01960
$222$	−9.87665	−0.662877
$223$	18.9897	1.27164	0.635822	−	0.771836i	$-0.280661\pi$
$223$	18.9897	1.27164	0.635822	+	0.771836i	$0.280661\pi$
$224$	−0.713465	−0.0476704
$225$	−19.3610	−1.29073
$226$	−9.61512	−0.639588
$227$	−7.88502	−0.523347	−0.261674	−	0.965156i	$-0.584274\pi$
$227$	−7.88502	−0.523347	−0.261674	+	0.965156i	$0.584274\pi$
$228$	0	0
$229$	18.2466	1.20577	0.602886	−	0.797828i	$-0.294017\pi$
$229$	18.2466	1.20577	0.602886	+	0.797828i	$0.294017\pi$
$230$	5.33692	0.351906
$231$	11.4523	0.753508
$232$	6.50541	0.427101
$233$	−7.99531	−0.523790	−0.261895	−	0.965096i	$-0.584347\pi$
$233$	−7.99531	−0.523790	−0.261895	+	0.965096i	$0.584347\pi$
$234$	−41.8968	−2.73888
$235$	−4.69559	−0.306306
$236$	−0.250563	−0.0163102
$237$	−25.2432	−1.63972
$238$	−15.4900	−1.00407
$239$	4.41716	0.285722	0.142861	−	0.989743i	$-0.454370\pi$
$239$	4.41716	0.285722	0.142861	+	0.989743i	$0.454370\pi$
$240$	−14.1746	−0.914969
$241$	15.7501	1.01455	0.507277	−	0.861783i	$-0.330652\pi$
$241$	15.7501	1.01455	0.507277	+	0.861783i	$0.330652\pi$
$242$	−1.40278	−0.0901738
$243$	−7.18594	−0.460978
$244$	0.317146	0.0203032
$245$	10.2527	0.655023
$246$	42.1287	2.68603
$247$	0	0
$248$	15.1406	0.961431
$249$	−39.1928	−2.48374
$250$	14.6552	0.926876
$251$	−0.942823	−0.0595105	−0.0297552	−	0.999557i	$-0.509473\pi$
$251$	−0.942823	−0.0595105	−0.0297552	+	0.999557i	$0.509473\pi$
$252$	−0.701072	−0.0441634
$253$	−3.08937	−0.194227
$254$	12.4503	0.781203
$255$	10.1619	0.636366
$256$	−0.773093	−0.0483183
$257$	21.0419	1.31256	0.656278	−	0.754519i	$-0.272130\pi$
$257$	21.0419	1.31256	0.656278	+	0.754519i	$0.272130\pi$
$258$	−32.4826	−2.02228
$259$	9.42194	0.585451
$260$	−0.213224	−0.0132236
$261$	12.6835	0.785087
$262$	−4.52134	−0.279329
$263$	3.22056	0.198589	0.0992943	−	0.995058i	$-0.468341\pi$
$263$	3.22056	0.198589	0.0992943	+	0.995058i	$0.468341\pi$
$264$	8.33962	0.513268
$265$	−10.0074	−0.614752
$266$	0	0
$267$	−30.2724	−1.85264
$268$	−0.0743155	−0.00453954
$269$	0.599650	0.0365613	0.0182806	−	0.999833i	$-0.494181\pi$
$269$	0.599650	0.0365613	0.0182806	+	0.999833i	$0.494181\pi$
$270$	−12.9276	−0.786747
$271$	−0.720756	−0.0437828	−0.0218914	−	0.999760i	$-0.506969\pi$
$271$	−0.720756	−0.0437828	−0.0218914	+	0.999760i	$0.506969\pi$
$272$	−11.0981	−0.672921
$273$	61.5409	3.72463
$274$	23.4670	1.41769
$275$	−3.48342	−0.210058
$276$	0.291200	0.0175282
$277$	19.4370	1.16786	0.583928	−	0.811806i	$-0.301515\pi$
$277$	19.4370	1.16786	0.583928	+	0.811806i	$0.301515\pi$
$278$	15.5816	0.934522
$279$	29.5194	1.76728
$280$	13.7435	0.821333
$281$	−9.44434	−0.563402	−0.281701	−	0.959502i	$-0.590899\pi$
$281$	−9.44434	−0.563402	−0.281701	+	0.959502i	$0.590899\pi$
$282$	15.6471	0.931769
$283$	−14.0148	−0.833090	−0.416545	−	0.909115i	$-0.636759\pi$
$283$	−14.0148	−0.833090	−0.416545	+	0.909115i	$0.636759\pi$
$284$	−0.296014	−0.0175652
$285$	0	0
$286$	−7.53804	−0.445734
$287$	−40.1891	−2.37229
$288$	−1.01295	−0.0596887
$289$	−9.04365	−0.531979
$290$	−3.94218	−0.231493
$291$	−21.2305	−1.24455
$292$	0.326146	0.0190863
$293$	−16.6707	−0.973915	−0.486957	−	0.873426i	$-0.661893\pi$
$293$	−16.6707	−0.973915	−0.486957	+	0.873426i	$0.661893\pi$
$294$	−34.1651	−1.99255
$295$	9.57668	0.557576
$296$	6.86109	0.398793
$297$	7.48335	0.434228
$298$	31.3525	1.81620
$299$	−16.6012	−0.960073
$300$	0.328343	0.0189569
$301$	30.9871	1.78607
$302$	9.33587	0.537219
$303$	−43.2289	−2.48344
$304$	0	0
$305$	−12.1215	−0.694078
$306$	−21.9921	−1.25721
$307$	14.5754	0.831863	0.415932	−	0.909396i	$-0.363456\pi$
$307$	14.5754	0.831863	0.415932	+	0.909396i	$0.363456\pi$
$308$	−0.126136	−0.00718729
$309$	−43.9463	−2.50002
$310$	−9.17500	−0.521105
$311$	11.0502	0.626602	0.313301	−	0.949654i	$-0.398565\pi$
$311$	11.0502	0.626602	0.313301	+	0.949654i	$0.398565\pi$
$312$	44.8143	2.53711
$313$	1.70007	0.0960934	0.0480467	−	0.998845i	$-0.484700\pi$
$313$	1.70007	0.0960934	0.0480467	+	0.998845i	$0.484700\pi$
$314$	14.5602	0.821677
$315$	26.7955	1.50975
$316$	0.278030	0.0156404
$317$	4.73755	0.266088	0.133044	−	0.991110i	$-0.457525\pi$
$317$	4.73755	0.266088	0.133044	+	0.991110i	$0.457525\pi$
$318$	33.3477	1.87005
$319$	2.28200	0.127767
$320$	10.0055	0.559326
$321$	13.1697	0.735060
$322$	16.9654	0.945445
$323$	0	0
$324$	−0.168120	−0.00933998
$325$	−18.7187	−1.03833
$326$	7.23337	0.400619
$327$	−2.57963	−0.142654
$328$	−29.2659	−1.61594
$329$	−14.9267	−0.822935
$330$	−5.05369	−0.278196
$331$	−4.16549	−0.228956	−0.114478	−	0.993426i	$-0.536520\pi$
$331$	−4.16549	−0.228956	−0.114478	+	0.993426i	$0.536520\pi$
$332$	0.431671	0.0236910
$333$	13.3769	0.733051
$334$	−9.35207	−0.511723
$335$	2.84039	0.155187
$336$	−45.0594	−2.45819
$337$	−17.7615	−0.967531	−0.483765	−	0.875198i	$-0.660731\pi$
$337$	−17.7615	−0.967531	−0.483765	+	0.875198i	$0.660731\pi$
$338$	−22.2708	−1.21137
$339$	20.0518	1.08907
$340$	−0.111924	−0.00606993
$341$	5.31111	0.287613
$342$	0	0
$343$	5.18879	0.280168
$344$	22.5649	1.21662
$345$	−11.1299	−0.599211
$346$	−14.5381	−0.781574
$347$	15.4698	0.830463	0.415232	−	0.909716i	$-0.363700\pi$
$347$	15.4698	0.830463	0.415232	+	0.909716i	$0.363700\pi$
$348$	−0.215098	−0.0115305
$349$	−33.4319	−1.78957	−0.894783	−	0.446500i	$-0.852670\pi$
$349$	−33.4319	−1.78957	−0.894783	+	0.446500i	$0.852670\pi$
$350$	19.1294	1.02251
$351$	40.2130	2.14641
$352$	−0.182249	−0.00971393
$353$	22.4639	1.19563	0.597815	−	0.801634i	$-0.296036\pi$
$353$	22.4639	1.19563	0.597815	+	0.801634i	$0.296036\pi$
$354$	−31.9123	−1.69612
$355$	11.3139	0.600478
$356$	0.333422	0.0176713
$357$	32.3036	1.70969
$358$	−19.7251	−1.04250
$359$	−10.3166	−0.544490	−0.272245	−	0.962228i	$-0.587766\pi$
$359$	−10.3166	−0.544490	−0.272245	+	0.962228i	$0.587766\pi$
$360$	19.5126	1.02840
$361$	0	0
$362$	−19.1141	−1.00462
$363$	2.92541	0.153544
$364$	−0.677814	−0.0355271
$365$	−12.4655	−0.652476
$366$	40.3925	2.11135
$367$	35.9073	1.87434	0.937172	−	0.348867i	$-0.113433\pi$
$367$	35.9073	1.87434	0.937172	+	0.348867i	$0.113433\pi$
$368$	12.1552	0.633633
$369$	−57.0591	−2.97038
$370$	−4.15771	−0.216149
$371$	−31.8124	−1.65162
$372$	−0.500618	−0.0259558
$373$	−21.8700	−1.13238	−0.566192	−	0.824273i	$-0.691584\pi$
$373$	−21.8700	−1.13238	−0.566192	+	0.824273i	$0.691584\pi$
$374$	−3.95681	−0.204602
$375$	−30.5626	−1.57825
$376$	−10.8697	−0.560560
$377$	12.2627	0.631561
$378$	−41.0952	−2.11371
$379$	−17.9961	−0.924400	−0.462200	−	0.886776i	$-0.652940\pi$
$379$	−17.9961	−0.924400	−0.462200	+	0.886776i	$0.652940\pi$
$380$	0	0
$381$	−25.9645	−1.33020
$382$	23.8493	1.22024
$383$	−27.3586	−1.39796	−0.698980	−	0.715142i	$-0.746362\pi$
$383$	−27.3586	−1.39796	−0.698980	+	0.715142i	$0.746362\pi$
$384$	−32.2750	−1.64703
$385$	4.82102	0.245702
$386$	−32.7772	−1.66831
$387$	43.9944	2.23636
$388$	0.233833	0.0118711
$389$	−7.48438	−0.379473	−0.189737	−	0.981835i	$-0.560763\pi$
$389$	−7.48438	−0.379473	−0.189737	+	0.981835i	$0.560763\pi$
$390$	−27.1568	−1.37514
$391$	−8.71418	−0.440695
$392$	23.7337	1.19873
$393$	9.42901	0.475631
$394$	−2.20507	−0.111090
$395$	−10.6265	−0.534677
$396$	−0.179084	−0.00899930
$397$	23.0994	1.15933	0.579663	−	0.814856i	$-0.303184\pi$
$397$	23.0994	1.15933	0.579663	+	0.814856i	$0.303184\pi$
$398$	−16.8724	−0.845739
$399$	0	0
$400$	13.7056	0.685279
$401$	6.62056	0.330615	0.165307	−	0.986242i	$-0.447138\pi$
$401$	6.62056	0.330615	0.165307	+	0.986242i	$0.447138\pi$
$402$	−9.46501	−0.472072
$403$	28.5401	1.42168
$404$	0.476125	0.0236881
$405$	6.42565	0.319293
$406$	−12.5317	−0.621938
$407$	2.40677	0.119299
$408$	23.5236	1.16459
$409$	20.9494	1.03588	0.517942	−	0.855416i	$-0.326698\pi$
$409$	20.9494	1.03588	0.517942	+	0.855416i	$0.326698\pi$
$410$	17.7347	0.875853
$411$	−48.9392	−2.41399
$412$	0.484026	0.0238463
$413$	30.4431	1.49801
$414$	24.0869	1.18380
$415$	−16.4988	−0.809892
$416$	−0.979347	−0.0480164
$417$	−32.4946	−1.59127
$418$	0	0
$419$	−6.91321	−0.337732	−0.168866	−	0.985639i	$-0.554011\pi$
$419$	−6.91321	−0.337732	−0.168866	+	0.985639i	$0.554011\pi$
$420$	−0.454423	−0.0221736
$421$	11.0499	0.538538	0.269269	−	0.963065i	$-0.413218\pi$
$421$	11.0499	0.538538	0.269269	+	0.963065i	$0.413218\pi$
$422$	−3.05876	−0.148898
$423$	−21.1924	−1.03041
$424$	−23.1659	−1.12504
$425$	−9.82568	−0.476616
$426$	−37.7011	−1.82663
$427$	−38.5329	−1.86474
$428$	−0.145051	−0.00701132
$429$	15.7202	0.758978
$430$	−13.6740	−0.659419
$431$	−5.22802	−0.251825	−0.125912	−	0.992041i	$-0.540186\pi$
$431$	−5.22802	−0.251825	−0.125912	+	0.992041i	$0.540186\pi$
$432$	−29.4434	−1.41660
$433$	30.7094	1.47580	0.737900	−	0.674910i	$-0.235818\pi$
$433$	30.7094	1.47580	0.737900	+	0.674910i	$0.235818\pi$
$434$	−29.1662	−1.40002
$435$	8.22121	0.394177
$436$	0.0284121	0.00136069
$437$	0	0
$438$	41.5388	1.98480
$439$	25.5773	1.22074	0.610368	−	0.792118i	$-0.291022\pi$
$439$	25.5773	1.22074	0.610368	+	0.792118i	$0.291022\pi$
$440$	3.51068	0.167365
$441$	46.2732	2.20349
$442$	−21.2626	−1.01136
$443$	38.9565	1.85088	0.925438	−	0.378898i	$-0.123697\pi$
$443$	38.9565	1.85088	0.925438	+	0.378898i	$0.123697\pi$
$444$	−0.226859	−0.0107662
$445$	−12.7436	−0.604105
$446$	−26.6383	−1.26136
$447$	−65.3839	−3.09255
$448$	31.8063	1.50271
$449$	23.7119	1.11903	0.559517	−	0.828819i	$-0.310987\pi$
$449$	23.7119	1.11903	0.559517	+	0.828819i	$0.310987\pi$
$450$	27.1592	1.28030
$451$	−10.2660	−0.483408
$452$	−0.220852	−0.0103880
$453$	−19.4695	−0.914755
$454$	11.0609	0.519114
$455$	25.9065	1.21452
$456$	0	0
$457$	41.3053	1.93218	0.966090	−	0.258205i	$-0.0831310\pi$
$457$	41.3053	1.93218	0.966090	+	0.258205i	$0.0831310\pi$
$458$	−25.5959	−1.19602
$459$	21.1083	0.985251
$460$	0.122585	0.00571554
$461$	0.545980	0.0254288	0.0127144	−	0.999919i	$-0.495953\pi$
$461$	0.545980	0.0254288	0.0127144	+	0.999919i	$0.495953\pi$
$462$	−16.0650	−0.747414
$463$	−3.52927	−0.164019	−0.0820095	−	0.996632i	$-0.526134\pi$
$463$	−3.52927	−0.164019	−0.0820095	+	0.996632i	$0.526134\pi$
$464$	−8.97857	−0.416820
$465$	19.1340	0.887317
$466$	11.2156	0.519554
$467$	6.72604	0.311244	0.155622	−	0.987817i	$-0.450262\pi$
$467$	6.72604	0.311244	0.155622	+	0.987817i	$0.450262\pi$
$468$	−0.962336	−0.0444840
$469$	9.02926	0.416932
$470$	6.58685	0.303829
$471$	−30.3644	−1.39912
$472$	22.1688	1.02040
$473$	7.91544	0.363952
$474$	35.4106	1.62646
$475$	0	0
$476$	−0.355793	−0.0163077
$477$	−45.1661	−2.06801
$478$	−6.19628	−0.283411
$479$	−16.1469	−0.737768	−0.368884	−	0.929475i	$-0.620260\pi$
$479$	−16.1469	−0.737768	−0.368884	+	0.929475i	$0.620260\pi$
$480$	−0.656578	−0.0299685
$481$	12.9331	0.589701
$482$	−22.0939	−1.00635
$483$	−35.3805	−1.60987
$484$	−0.0322206	−0.00146457
$485$	−8.93727	−0.405821
$486$	10.0803	0.457250
$487$	35.5726	1.61195	0.805975	−	0.591949i	$-0.201641\pi$
$487$	35.5726	1.61195	0.805975	+	0.591949i	$0.201641\pi$
$488$	−28.0598	−1.27021
$489$	−15.0848	−0.682159
$490$	−14.3823	−0.649725
$491$	7.45209	0.336308	0.168154	−	0.985761i	$-0.446219\pi$
$491$	7.45209	0.336308	0.168154	+	0.985761i	$0.446219\pi$
$492$	0.967662	0.0436256
$493$	6.43684	0.289901
$494$	0	0
$495$	6.84471	0.307647
$496$	−20.8967	−0.938288
$497$	35.9654	1.61327
$498$	54.9787	2.46365
$499$	7.99022	0.357691	0.178846	−	0.983877i	$-0.442764\pi$
$499$	7.99022	0.357691	0.178846	+	0.983877i	$0.442764\pi$
$500$	0.336618	0.0150540
$501$	19.5033	0.871341
$502$	1.32257	0.0590291
$503$	35.3181	1.57476	0.787379	−	0.616469i	$-0.211437\pi$
$503$	35.3181	1.57476	0.787379	+	0.616469i	$0.211437\pi$
$504$	62.0280	2.76295
$505$	−18.1978	−0.809793
$506$	4.33369	0.192656
$507$	46.4446	2.06268
$508$	0.285974	0.0126880
$509$	−5.05595	−0.224101	−0.112050	−	0.993703i	$-0.535742\pi$
$509$	−5.05595	−0.224101	−0.112050	+	0.993703i	$0.535742\pi$
$510$	−14.2549	−0.631219
$511$	−39.6264	−1.75297
$512$	23.1497	1.02308
$513$	0	0
$514$	−29.5170	−1.30194
$515$	−18.4998	−0.815200
$516$	−0.746099	−0.0328452
$517$	−3.81292	−0.167692
$518$	−13.2169	−0.580716
$519$	30.3185	1.33083
$520$	18.8652	0.827295
$521$	−22.5556	−0.988178	−0.494089	−	0.869411i	$-0.664498\pi$
$521$	−22.5556	−0.988178	−0.494089	+	0.869411i	$0.664498\pi$
$522$	−17.7921	−0.778737
$523$	−6.22268	−0.272099	−0.136049	−	0.990702i	$-0.543441\pi$
$523$	−6.22268	−0.272099	−0.136049	+	0.990702i	$0.543441\pi$
$524$	−0.103851	−0.00453677
$525$	−39.8933	−1.74109
$526$	−4.51773	−0.196982
$527$	14.9810	0.652584
$528$	−11.5101	−0.500913
$529$	−13.4558	−0.585035
$530$	14.0382	0.609780
$531$	43.2220	1.87567
$532$	0	0
$533$	−55.1661	−2.38951
$534$	42.4654	1.83766
$535$	5.54397	0.239687
$536$	6.57513	0.284003
$537$	41.1356	1.77513
$538$	−0.841174	−0.0362656
$539$	8.32544	0.358602
$540$	−0.296936	−0.0127781
$541$	−1.01541	−0.0436559	−0.0218280	−	0.999762i	$-0.506949\pi$
$541$	−1.01541	−0.0436559	−0.0218280	+	0.999762i	$0.506949\pi$
$542$	1.01106	0.0434287
$543$	39.8615	1.71062
$544$	−0.514071	−0.0220406
$545$	−1.08593	−0.0465162
$546$	−86.3281	−3.69450
$547$	9.95547	0.425665	0.212833	−	0.977089i	$-0.431731\pi$
$547$	9.95547	0.425665	0.212833	+	0.977089i	$0.431731\pi$
$548$	0.539018	0.0230257
$549$	−54.7076	−2.33486
$550$	4.88646	0.208359
$551$	0	0
$552$	−25.7642	−1.09660
$553$	−33.7803	−1.43649
$554$	−27.2657	−1.15841
$555$	8.67069	0.368050
$556$	0.357897	0.0151782
$557$	−20.6689	−0.875770	−0.437885	−	0.899031i	$-0.644272\pi$
$557$	−20.6689	−0.875770	−0.437885	+	0.899031i	$0.644272\pi$
$558$	−41.4091	−1.75299
$559$	42.5349	1.79903
$560$	−18.9684	−0.801562
$561$	8.25172	0.348388
$562$	13.2483	0.558845
$563$	24.5283	1.03374	0.516872	−	0.856063i	$-0.327096\pi$
$563$	24.5283	1.03374	0.516872	+	0.856063i	$0.327096\pi$
$564$	0.359400	0.0151335
$565$	8.44110	0.355120
$566$	19.6596	0.826353
$567$	20.4264	0.857826
$568$	26.1902	1.09891
$569$	−14.2252	−0.596350	−0.298175	−	0.954511i	$-0.596378\pi$
$569$	−14.2252	−0.596350	−0.298175	+	0.954511i	$0.596378\pi$
$570$	0	0
$571$	34.1997	1.43121	0.715607	−	0.698503i	$-0.246150\pi$
$571$	34.1997	1.43121	0.715607	+	0.698503i	$0.246150\pi$
$572$	−0.173143	−0.00723946
$573$	−49.7364	−2.07777
$574$	56.3764	2.35310
$575$	10.7616	0.448788
$576$	45.1575	1.88156
$577$	−32.2034	−1.34064	−0.670322	−	0.742070i	$-0.733844\pi$
$577$	−32.2034	−1.34064	−0.670322	+	0.742070i	$0.733844\pi$
$578$	12.6862	0.527677
$579$	68.3551	2.84074
$580$	−0.0905487	−0.00375983
$581$	−52.4475	−2.17589
$582$	29.7816	1.23449
$583$	−8.12625	−0.336555
$584$	−28.8561	−1.19407
$585$	36.7811	1.52071
$586$	23.3853	0.966038
$587$	5.77516	0.238366	0.119183	−	0.992872i	$-0.461972\pi$
$587$	5.77516	0.238366	0.119183	+	0.992872i	$0.461972\pi$
$588$	−0.784745	−0.0323623
$589$	0	0
$590$	−13.4339	−0.553066
$591$	4.59857	0.189160
$592$	−9.46947	−0.389193
$593$	−14.6792	−0.602802	−0.301401	−	0.953498i	$-0.597454\pi$
$593$	−14.6792	−0.602802	−0.301401	+	0.953498i	$0.597454\pi$
$594$	−10.4975	−0.430716
$595$	13.5987	0.557491
$596$	0.720141	0.0294981
$597$	35.1866	1.44009
$598$	23.2878	0.952308
$599$	−10.6836	−0.436520	−0.218260	−	0.975891i	$-0.570038\pi$
$599$	−10.6836	−0.436520	−0.218260	+	0.975891i	$0.570038\pi$
$600$	−29.0504	−1.18598
$601$	34.6301	1.41259	0.706295	−	0.707917i	$-0.250365\pi$
$601$	34.6301	1.41259	0.706295	+	0.707917i	$0.250365\pi$
$602$	−43.4680	−1.77162
$603$	12.8194	0.522047
$604$	0.214437	0.00872533
$605$	1.23149	0.0500674
$606$	60.6405	2.46335
$607$	34.9573	1.41887	0.709436	−	0.704770i	$-0.248950\pi$
$607$	34.9573	1.41887	0.709436	+	0.704770i	$0.248950\pi$
$608$	0	0
$609$	26.1342	1.05901
$610$	17.0038	0.688464
$611$	−20.4893	−0.828909
$612$	−0.505142	−0.0204191
$613$	−21.3740	−0.863289	−0.431645	−	0.902044i	$-0.642067\pi$
$613$	−21.3740	−0.863289	−0.431645	+	0.902044i	$0.642067\pi$
$614$	−20.4460	−0.825135
$615$	−36.9847	−1.49137
$616$	11.1600	0.449651
$617$	42.2937	1.70268	0.851341	−	0.524613i	$-0.175790\pi$
$617$	42.2937	1.70268	0.851341	+	0.524613i	$0.175790\pi$
$618$	61.6468	2.47980
$619$	9.79343	0.393631	0.196816	−	0.980441i	$-0.436940\pi$
$619$	9.79343	0.393631	0.196816	+	0.980441i	$0.436940\pi$
$620$	−0.210742	−0.00846361
$621$	−23.1188	−0.927727
$622$	−15.5010	−0.621534
$623$	−40.5104	−1.62301
$624$	−61.8514	−2.47604
$625$	4.55132	0.182053
$626$	−2.38481	−0.0953162
$627$	0	0
$628$	0.334435	0.0133454
$629$	6.78877	0.270686
$630$	−37.5880	−1.49754
$631$	29.9291	1.19146	0.595729	−	0.803186i	$-0.296863\pi$
$631$	29.9291	1.19146	0.595729	+	0.803186i	$0.296863\pi$
$632$	−24.5989	−0.978493
$633$	6.37889	0.253538
$634$	−6.64573	−0.263935
$635$	−10.9301	−0.433749
$636$	0.765970	0.0303727
$637$	44.7381	1.77259
$638$	−3.20113	−0.126734
$639$	51.0624	2.02000
$640$	−13.5866	−0.537058
$641$	−3.14428	−0.124192	−0.0620958	−	0.998070i	$-0.519778\pi$
$641$	−3.14428	−0.124192	−0.0620958	+	0.998070i	$0.519778\pi$
$642$	−18.4741	−0.729115
$643$	−5.55270	−0.218977	−0.109489	−	0.993988i	$-0.534921\pi$
$643$	−5.55270	−0.218977	−0.109489	+	0.993988i	$0.534921\pi$
$644$	0.389682	0.0153556
$645$	28.5164	1.12283
$646$	0	0
$647$	7.16024	0.281498	0.140749	−	0.990045i	$-0.455049\pi$
$647$	7.16024	0.281498	0.140749	+	0.990045i	$0.455049\pi$
$648$	14.8745	0.584327
$649$	7.77647	0.305253
$650$	26.2582	1.02993
$651$	60.8246	2.38390
$652$	0.166145	0.00650673
$653$	17.8855	0.699915	0.349957	−	0.936766i	$-0.386196\pi$
$653$	17.8855	0.699915	0.349957	+	0.936766i	$0.386196\pi$
$654$	3.61864	0.141500
$655$	3.96928	0.155093
$656$	40.3919	1.57704
$657$	−56.2601	−2.19492
$658$	20.9388	0.816279
$659$	−38.7207	−1.50834	−0.754172	−	0.656677i	$-0.771962\pi$
$659$	−38.7207	−1.50834	−0.754172	+	0.656677i	$0.771962\pi$
$660$	−0.116079	−0.00451837
$661$	47.7529	1.85737	0.928686	−	0.370867i	$-0.120939\pi$
$661$	47.7529	1.85737	0.928686	+	0.370867i	$0.120939\pi$
$662$	5.84325	0.227104
$663$	44.3419	1.72210
$664$	−38.1925	−1.48216
$665$	0	0
$666$	−18.7648	−0.727122
$667$	−7.04994	−0.272975
$668$	−0.214809	−0.00831123
$669$	55.5527	2.14779
$670$	−3.98443	−0.153932
$671$	−9.84295	−0.379983
$672$	−2.08718	−0.0805148
$673$	29.4901	1.13676	0.568380	−	0.822766i	$-0.307570\pi$
$673$	29.4901	1.13676	0.568380	+	0.822766i	$0.307570\pi$
$674$	24.9154	0.959705
$675$	−26.0677	−1.00335
$676$	−0.511542	−0.0196747
$677$	−2.54519	−0.0978194	−0.0489097	−	0.998803i	$-0.515575\pi$
$677$	−2.54519	−0.0978194	−0.0489097	+	0.998803i	$0.515575\pi$
$678$	−28.1282	−1.08026
$679$	−28.4105	−1.09030
$680$	9.90259	0.379747
$681$	−23.0670	−0.883928
$682$	−7.45029	−0.285286
$683$	−34.3857	−1.31573	−0.657866	−	0.753135i	$-0.728541\pi$
$683$	−34.3857	−1.31573	−0.657866	+	0.753135i	$0.728541\pi$
$684$	0	0
$685$	−20.6016	−0.787148
$686$	−7.27871	−0.277902
$687$	53.3790	2.03653
$688$	−31.1435	−1.18733
$689$	−43.6677	−1.66361
$690$	15.6127	0.594365
$691$	−39.5183	−1.50335	−0.751674	−	0.659535i	$-0.770753\pi$
$691$	−39.5183	−1.50335	−0.751674	+	0.659535i	$0.770753\pi$
$692$	−0.333929	−0.0126941
$693$	21.7585	0.826537
$694$	−21.7007	−0.823747
$695$	−13.6791	−0.518876
$696$	19.0310	0.721369
$697$	−28.9574	−1.09684
$698$	46.8974	1.77509
$699$	−23.3896	−0.884676
$700$	0.439386	0.0166072
$701$	−9.85853	−0.372352	−0.186176	−	0.982516i	$-0.559609\pi$
$701$	−9.85853	−0.372352	−0.186176	+	0.982516i	$0.559609\pi$
$702$	−56.4098	−2.12905
$703$	0	0
$704$	8.12470	0.306211
$705$	−13.7365	−0.517348
$706$	−31.5118	−1.18596
$707$	−57.8487	−2.17562
$708$	−0.732999	−0.0275478
$709$	7.08012	0.265900	0.132950	−	0.991123i	$-0.457555\pi$
$709$	7.08012	0.265900	0.132950	+	0.991123i	$0.457555\pi$
$710$	−15.8708	−0.595622
$711$	−47.9601	−1.79864
$712$	−29.4998	−1.10555
$713$	−16.4080	−0.614483
$714$	−45.3147	−1.69586
$715$	6.61764	0.247486
$716$	−0.453069	−0.0169320
$717$	12.9220	0.482581
$718$	14.4719	0.540086
$719$	3.26599	0.121801	0.0609005	−	0.998144i	$-0.480603\pi$
$719$	3.26599	0.121801	0.0609005	+	0.998144i	$0.480603\pi$
$720$	−26.9306	−1.00365
$721$	−58.8087	−2.19015
$722$	0	0
$723$	46.0756	1.71357
$724$	−0.439036	−0.0163167
$725$	−7.94916	−0.295225
$726$	−4.10370	−0.152303
$727$	11.6227	0.431060	0.215530	−	0.976497i	$-0.430852\pi$
$727$	11.6227	0.431060	0.215530	+	0.976497i	$0.430852\pi$
$728$	59.9702	2.22265
$729$	−36.6751	−1.35834
$730$	17.4863	0.647199
$731$	22.3271	0.825797
$732$	0.927783	0.0342919
$733$	−2.35950	−0.0871502	−0.0435751	−	0.999050i	$-0.513875\pi$
$733$	−2.35950	−0.0871502	−0.0435751	+	0.999050i	$0.513875\pi$
$734$	−50.3699	−1.85919
$735$	29.9935	1.10633
$736$	0.563036	0.0207538
$737$	2.30646	0.0849595
$738$	80.0411	2.94635
$739$	−30.3769	−1.11743	−0.558716	−	0.829359i	$-0.688706\pi$
$739$	−30.3769	−1.11743	−0.558716	+	0.829359i	$0.688706\pi$
$740$	−0.0954993	−0.00351063
$741$	0	0
$742$	44.6257	1.63826
$743$	31.7192	1.16366	0.581832	−	0.813309i	$-0.302336\pi$
$743$	31.7192	1.16366	0.581832	+	0.813309i	$0.302336\pi$
$744$	44.2926	1.62385
$745$	−27.5243	−1.00841
$746$	30.6787	1.12323
$747$	−74.4631	−2.72446
$748$	−0.0908847	−0.00332307
$749$	17.6236	0.643952
$750$	42.8725	1.56548
$751$	−14.1710	−0.517108	−0.258554	−	0.965997i	$-0.583246\pi$
$751$	−14.1710	−0.517108	−0.258554	+	0.965997i	$0.583246\pi$
$752$	15.0020	0.547066
$753$	−2.75815	−0.100512
$754$	−17.2018	−0.626453
$755$	−8.19595	−0.298281
$756$	−0.943923	−0.0343301
$757$	−24.3944	−0.886628	−0.443314	−	0.896366i	$-0.646197\pi$
$757$	−24.3944	−0.886628	−0.443314	+	0.896366i	$0.646197\pi$
$758$	25.2446	0.916924
$759$	−9.03768	−0.328047
$760$	0	0
$761$	39.7159	1.43970	0.719851	−	0.694129i	$-0.244210\pi$
$761$	39.7159	1.43970	0.719851	+	0.694129i	$0.244210\pi$
$762$	36.4223	1.31944
$763$	−3.45204	−0.124972
$764$	0.547799	0.0198187
$765$	19.3069	0.698041
$766$	38.3780	1.38665
$767$	41.7881	1.50888
$768$	−2.26162	−0.0816091
$769$	−1.90327	−0.0686337	−0.0343169	−	0.999411i	$-0.510926\pi$
$769$	−1.90327	−0.0686337	−0.0343169	+	0.999411i	$0.510926\pi$
$770$	−6.76281	−0.243715
$771$	61.5562	2.21689
$772$	−0.752865	−0.0270962
$773$	30.1296	1.08369	0.541843	−	0.840479i	$-0.317727\pi$
$773$	30.1296	1.08369	0.541843	+	0.840479i	$0.317727\pi$
$774$	−61.7143	−2.21827
$775$	−18.5008	−0.664569
$776$	−20.6886	−0.742678
$777$	27.5631	0.988820
$778$	10.4989	0.376404
$779$	0	0
$780$	−0.623769	−0.0223345
$781$	9.18711	0.328741
$782$	12.2240	0.437131
$783$	17.0770	0.610283
$784$	−32.7566	−1.16988
$785$	−12.7823	−0.456221
$786$	−13.2268	−0.471784
$787$	0.630871	0.0224881	0.0112441	−	0.999937i	$-0.496421\pi$
$787$	0.630871	0.0224881	0.0112441	+	0.999937i	$0.496421\pi$
$788$	−0.0506488	−0.00180429
$789$	9.42149	0.335414
$790$	14.9066	0.530352
$791$	26.8332	0.954080
$792$	15.8446	0.563014
$793$	−52.8927	−1.87827
$794$	−32.4033	−1.14995
$795$	−29.2759	−1.03831
$796$	−0.387546	−0.0137362
$797$	23.7794	0.842310	0.421155	−	0.906989i	$-0.361625\pi$
$797$	23.7794	0.842310	0.421155	+	0.906989i	$0.361625\pi$
$798$	0	0
$799$	−10.7551	−0.380488
$800$	0.634852	0.0224454
$801$	−57.5152	−2.03220
$802$	−9.28715	−0.327941
$803$	−10.1223	−0.357207
$804$	−0.217404	−0.00766723
$805$	−14.8939	−0.524941
$806$	−40.0353	−1.41018
$807$	1.75422	0.0617516
$808$	−42.1256	−1.48197
$809$	5.05779	0.177822	0.0889112	−	0.996040i	$-0.471661\pi$
$809$	5.05779	0.177822	0.0889112	+	0.996040i	$0.471661\pi$
$810$	−9.01374	−0.316711
$811$	4.91387	0.172549	0.0862746	−	0.996271i	$-0.472504\pi$
$811$	4.91387	0.172549	0.0862746	+	0.996271i	$0.472504\pi$
$812$	−0.287843	−0.0101013
$813$	−2.10851	−0.0739486
$814$	−3.37615	−0.118334
$815$	−6.35017	−0.222437
$816$	−32.4666	−1.13656
$817$	0	0
$818$	−29.3874	−1.02751
$819$	116.923	4.08561
$820$	0.407351	0.0142253
$821$	11.3250	0.395244	0.197622	−	0.980278i	$-0.436678\pi$
$821$	11.3250	0.395244	0.197622	+	0.980278i	$0.436678\pi$
$822$	68.6507	2.39447
$823$	29.7292	1.03630	0.518148	−	0.855291i	$-0.326622\pi$
$823$	29.7292	1.03630	0.518148	+	0.855291i	$0.326622\pi$
$824$	−42.8247	−1.49187
$825$	−10.1904	−0.354786
$826$	−42.7048	−1.48589
$827$	−43.9845	−1.52949	−0.764746	−	0.644332i	$-0.777135\pi$
$827$	−43.9845	−1.52949	−0.764746	+	0.644332i	$0.777135\pi$
$828$	0.553256	0.0192270
$829$	18.7590	0.651528	0.325764	−	0.945451i	$-0.394379\pi$
$829$	18.7590	0.651528	0.325764	+	0.945451i	$0.394379\pi$
$830$	23.1441	0.803342
$831$	56.8613	1.97250
$832$	43.6594	1.51362
$833$	23.4836	0.813657
$834$	45.5826	1.57840
$835$	8.21017	0.284125
$836$	0	0
$837$	39.7449	1.37378
$838$	9.69768	0.335001
$839$	−16.9384	−0.584779	−0.292390	−	0.956299i	$-0.594450\pi$
$839$	−16.9384	−0.584779	−0.292390	+	0.956299i	$0.594450\pi$
$840$	40.2055	1.38722
$841$	−23.7925	−0.820430
$842$	−15.5005	−0.534183
$843$	−27.6286	−0.951580
$844$	−0.0702573	−0.00241836
$845$	19.5515	0.672592
$846$	29.7281	1.02207
$847$	3.91477	0.134513
$848$	31.9729	1.09795
$849$	−40.9990	−1.40708
$850$	13.7832	0.472761
$851$	−7.43539	−0.254882
$852$	−0.865965	−0.0296675
$853$	−41.5873	−1.42392	−0.711961	−	0.702219i	$-0.752193\pi$
$853$	−41.5873	−1.42392	−0.711961	+	0.702219i	$0.752193\pi$
$854$	54.0530	1.84966
$855$	0	0
$856$	12.8336	0.438642
$857$	36.1838	1.23601	0.618007	−	0.786172i	$-0.287940\pi$
$857$	36.1838	1.23601	0.618007	+	0.786172i	$0.287940\pi$
$858$	−22.0519	−0.752839
$859$	23.2464	0.793157	0.396578	−	0.918001i	$-0.370198\pi$
$859$	23.2464	0.793157	0.396578	+	0.918001i	$0.370198\pi$
$860$	−0.314081	−0.0107101
$861$	−117.570	−4.00677
$862$	7.33374	0.249788
$863$	−10.9135	−0.371500	−0.185750	−	0.982597i	$-0.559471\pi$
$863$	−10.9135	−0.371500	−0.185750	+	0.982597i	$0.559471\pi$
$864$	−1.36384	−0.0463987
$865$	12.7630	0.433955
$866$	−43.0784	−1.46386
$867$	−26.4564	−0.898507
$868$	−0.669924	−0.0227387
$869$	−8.62894	−0.292717
$870$	−11.5325	−0.390989
$871$	12.3941	0.419959
$872$	−2.51379	−0.0851276
$873$	−40.3362	−1.36517
$874$	0	0
$875$	−40.8988	−1.38263
$876$	0.954112	0.0322365
$877$	−28.8304	−0.973534	−0.486767	−	0.873532i	$-0.661824\pi$
$877$	−28.8304	−0.973534	−0.486767	+	0.873532i	$0.661824\pi$
$878$	−35.8792	−1.21086
$879$	−48.7688	−1.64493
$880$	−4.84534	−0.163336
$881$	53.7267	1.81010	0.905049	−	0.425307i	$-0.139834\pi$
$881$	53.7267	1.81010	0.905049	+	0.425307i	$0.139834\pi$
$882$	−64.9109	−2.18566
$883$	30.1116	1.01334	0.506669	−	0.862141i	$-0.330877\pi$
$883$	30.1116	1.01334	0.506669	+	0.862141i	$0.330877\pi$
$884$	−0.488384	−0.0164261
$885$	28.0158	0.941739
$886$	−54.6472	−1.83591
$887$	−4.34515	−0.145896	−0.0729479	−	0.997336i	$-0.523241\pi$
$887$	−4.34515	−0.145896	−0.0729479	+	0.997336i	$0.523241\pi$
$888$	20.0715	0.673556
$889$	−34.7455	−1.16533
$890$	17.8764	0.599219
$891$	5.21776	0.174802
$892$	−0.611860	−0.0204866
$893$	0	0
$894$	91.7190	3.06754
$895$	17.3166	0.578830
$896$	−43.1902	−1.44288
$897$	−48.5654	−1.62155
$898$	−33.2625	−1.10998
$899$	12.1199	0.404223
$900$	0.623824	0.0207941
$901$	−22.9217	−0.763633
$902$	14.4009	0.479498
$903$	90.6502	3.01665
$904$	19.5400	0.649892
$905$	16.7803	0.557795
$906$	27.3113	0.907357
$907$	−16.0197	−0.531926	−0.265963	−	0.963983i	$-0.585690\pi$
$907$	−16.0197	−0.531926	−0.265963	+	0.963983i	$0.585690\pi$
$908$	0.254060	0.00843129
$909$	−82.1315	−2.72413
$910$	−36.3411	−1.20469
$911$	36.9160	1.22308	0.611540	−	0.791213i	$-0.290550\pi$
$911$	36.9160	1.22308	0.611540	+	0.791213i	$0.290550\pi$
$912$	0	0
$913$	−13.3973	−0.443387
$914$	−57.9421	−1.91655
$915$	−35.4605	−1.17229
$916$	−0.587918	−0.0194254
$917$	12.6178	0.416678
$918$	−29.6102	−0.977282
$919$	20.0040	0.659872	0.329936	−	0.944003i	$-0.392973\pi$
$919$	20.0040	0.659872	0.329936	+	0.944003i	$0.392973\pi$
$920$	−10.8458	−0.357575
$921$	42.6391	1.40501
$922$	−0.765888	−0.0252232
$923$	49.3684	1.62498
$924$	−0.369001	−0.0121392
$925$	−8.38378	−0.275657
$926$	4.95077	0.162692
$927$	−83.4944	−2.74232
$928$	−0.415893	−0.0136524
$929$	−37.1159	−1.21773	−0.608867	−	0.793273i	$-0.708375\pi$
$929$	−37.1159	−1.21773	−0.608867	+	0.793273i	$0.708375\pi$
$930$	−26.8407	−0.880140
$931$	0	0
$932$	0.257614	0.00843842
$933$	32.3265	1.05832
$934$	−9.43513	−0.308727
$935$	3.47368	0.113601
$936$	85.1435	2.78300
$937$	26.7942	0.875328	0.437664	−	0.899138i	$-0.355806\pi$
$937$	26.7942	0.875328	0.437664	+	0.899138i	$0.355806\pi$
$938$	−12.6660	−0.413560
$939$	4.97340	0.162301
$940$	0.151295	0.00493469
$941$	−42.4832	−1.38491	−0.692457	−	0.721459i	$-0.743472\pi$
$941$	−42.4832	−1.38491	−0.692457	+	0.721459i	$0.743472\pi$
$942$	42.5945	1.38780
$943$	31.7155	1.03280
$944$	−30.5967	−0.995837
$945$	36.0774	1.17360
$946$	−11.1036	−0.361009
$947$	15.3699	0.499454	0.249727	−	0.968316i	$-0.419659\pi$
$947$	15.3699	0.499454	0.249727	+	0.968316i	$0.419659\pi$
$948$	0.813352	0.0264164
$949$	−54.3937	−1.76569
$950$	0	0
$951$	13.8593	0.449419
$952$	31.4791	1.02024
$953$	−20.8377	−0.675000	−0.337500	−	0.941326i	$-0.609581\pi$
$953$	−20.8377	−0.675000	−0.337500	+	0.941326i	$0.609581\pi$
$954$	63.3579	2.05129
$955$	−20.9373	−0.677514
$956$	−0.142323	−0.00460307
$957$	6.67579	0.215798
$958$	22.6504	0.731802
$959$	−65.4901	−2.11479
$960$	29.2703	0.944695
$961$	−2.79214	−0.0900690
$962$	−18.1423	−0.584931
$963$	25.0213	0.806301
$964$	−0.507478	−0.0163448
$965$	28.7750	0.926301
$966$	49.6308	1.59685
$967$	19.1383	0.615447	0.307723	−	0.951476i	$-0.400433\pi$
$967$	19.1383	0.615447	0.307723	+	0.951476i	$0.400433\pi$
$968$	2.85075	0.0916266
$969$	0	0
$970$	12.5370	0.402539
$971$	−35.3028	−1.13292	−0.566460	−	0.824089i	$-0.691687\pi$
$971$	−35.3028	−1.13292	−0.566460	+	0.824089i	$0.691687\pi$
$972$	0.231535	0.00742650
$973$	−43.4841	−1.39404
$974$	−49.9004	−1.59891
$975$	−54.7600	−1.75372
$976$	38.7273	1.23963
$977$	−49.5200	−1.58429	−0.792143	−	0.610336i	$-0.791035\pi$
$977$	−49.5200	−1.58429	−0.792143	+	0.610336i	$0.791035\pi$
$978$	21.1606	0.676642
$979$	−10.3481	−0.330726
$980$	−0.330349	−0.0105526
$981$	−4.90108	−0.156479
$982$	−10.4536	−0.333588
$983$	−43.5302	−1.38840	−0.694199	−	0.719783i	$-0.744241\pi$
$983$	−43.5302	−1.38840	−0.694199	+	0.719783i	$0.744241\pi$
$984$	−85.6148	−2.72930
$985$	1.93583	0.0616807
$986$	−9.02944	−0.287556
$987$	−43.6668	−1.38993
$988$	0	0
$989$	−24.4537	−0.777582
$990$	−9.60159	−0.305159
$991$	−17.9848	−0.571306	−0.285653	−	0.958333i	$-0.592210\pi$
$991$	−17.9848	−0.571306	−0.285653	+	0.958333i	$0.592210\pi$
$992$	−0.967947	−0.0307323
$993$	−12.1858	−0.386704
$994$	−50.4514	−1.60022
$995$	14.8123	0.469582
$996$	1.26282	0.0400138
$997$	7.98108	0.252763	0.126382	−	0.991982i	$-0.459664\pi$
$997$	7.98108	0.252763	0.126382	+	0.991982i	$0.459664\pi$
$998$	−11.2085	−0.354798
$999$	18.0107	0.569833

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3971.2.a.t.1.6		21
19.6	even	9		209.2.j.b.188.2	✓	42
19.16	even	9		209.2.j.b.199.2	yes	42
19.18	odd	2		3971.2.a.s.1.16		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.j.b.188.2	✓	42	19.6	even	9
209.2.j.b.199.2	yes	42	19.16	even	9
3971.2.a.s.1.16		21	19.18	odd	2
3971.2.a.t.1.6		21	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:	\( N \)	\(=\)	\( 3971 = 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3971.a (trivial)

\(f(q)\)	\(=\)	\(q-1.40278 q^{2} +2.92541 q^{3} -0.0322206 q^{4} +1.23149 q^{5} -4.10370 q^{6} +3.91477 q^{7} +2.85075 q^{8} +5.55805 q^{9} -1.72751 q^{10} +1.00000 q^{11} -0.0942587 q^{12} +5.37366 q^{13} -5.49155 q^{14} +3.60263 q^{15} -3.93452 q^{16} +2.82070 q^{17} -7.79670 q^{18} -0.0396795 q^{20} +11.4523 q^{21} -1.40278 q^{22} -3.08937 q^{23} +8.33962 q^{24} -3.48342 q^{25} -7.53804 q^{26} +7.48335 q^{27} -0.126136 q^{28} +2.28200 q^{29} -5.05369 q^{30} +5.31111 q^{31} -0.182249 q^{32} +2.92541 q^{33} -3.95681 q^{34} +4.82102 q^{35} -0.179084 q^{36} +2.40677 q^{37} +15.7202 q^{39} +3.51068 q^{40} -10.2660 q^{41} -16.0650 q^{42} +7.91544 q^{43} -0.0322206 q^{44} +6.84471 q^{45} +4.33369 q^{46} -3.81292 q^{47} -11.5101 q^{48} +8.32544 q^{49} +4.88646 q^{50} +8.25172 q^{51} -0.173143 q^{52} -8.12625 q^{53} -10.4975 q^{54} +1.23149 q^{55} +11.1600 q^{56} -3.20113 q^{58} +7.77647 q^{59} -0.116079 q^{60} -9.84295 q^{61} -7.45029 q^{62} +21.7585 q^{63} +8.12470 q^{64} +6.61764 q^{65} -4.10370 q^{66} +2.30646 q^{67} -0.0908847 q^{68} -9.03768 q^{69} -6.76281 q^{70} +9.18711 q^{71} +15.8446 q^{72} -10.1223 q^{73} -3.37615 q^{74} -10.1904 q^{75} +3.91477 q^{77} -22.0519 q^{78} -8.62894 q^{79} -4.84534 q^{80} +5.21776 q^{81} +14.4009 q^{82} -13.3973 q^{83} -0.369001 q^{84} +3.47368 q^{85} -11.1036 q^{86} +6.67579 q^{87} +2.85075 q^{88} -10.3481 q^{89} -9.60159 q^{90} +21.0367 q^{91} +0.0995413 q^{92} +15.5372 q^{93} +5.34866 q^{94} -0.533155 q^{96} -7.25726 q^{97} -11.6787 q^{98} +5.55805 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 6 q^{2} + 15 q^{3} + 18 q^{4} + 6 q^{5} - 6 q^{6} + 6 q^{7} + 15 q^{8} + 18 q^{9} - 6 q^{10} + 21 q^{11} + 30 q^{12} + 36 q^{13} + 12 q^{14} + 12 q^{15} + 12 q^{16} + 21 q^{17} + 6 q^{18} + 15 q^{20}+ \cdots + 18 q^{99}+O(q^{100}) \) 21 * q + 6 * q^2 + 15 * q^3 + 18 * q^4 + 6 * q^5 - 6 * q^6 + 6 * q^7 + 15 * q^8 + 18 * q^9 - 6 * q^10 + 21 * q^11 + 30 * q^12 + 36 * q^13 + 12 * q^14 + 12 * q^15 + 12 * q^16 + 21 * q^17 + 6 * q^18 + 15 * q^20 - 3 * q^21 + 6 * q^22 + 6 * q^23 - 18 * q^24 + 3 * q^25 + 6 * q^26 + 24 * q^27 + 27 * q^29 - 30 * q^30 + 54 * q^31 + 21 * q^32 + 15 * q^33 + 39 * q^34 - 33 * q^35 + 54 * q^36 + 57 * q^37 - 27 * q^40 + 24 * q^41 + 6 * q^42 + 12 * q^43 + 18 * q^44 - 3 * q^45 + 15 * q^46 + 12 * q^47 - 39 * q^48 + 21 * q^49 + 33 * q^50 - 18 * q^51 - 18 * q^52 + 39 * q^53 + 30 * q^54 + 6 * q^55 + 57 * q^56 + 30 * q^58 + 27 * q^59 + 12 * q^60 - 30 * q^61 + 21 * q^62 - 18 * q^63 - 15 * q^64 - 24 * q^65 - 6 * q^66 + 27 * q^67 - 48 * q^68 + 54 * q^69 + 51 * q^70 + 42 * q^71 + 15 * q^72 + 6 * q^73 + 84 * q^74 + 27 * q^75 + 6 * q^77 - 48 * q^78 + 39 * q^79 - 27 * q^80 - 27 * q^81 - 15 * q^82 + 12 * q^83 - 48 * q^84 - 42 * q^85 - 45 * q^86 + 75 * q^87 + 15 * q^88 + 75 * q^89 - 87 * q^90 + 45 * q^91 + 12 * q^92 + 66 * q^93 + 42 * q^94 - 3 * q^96 + 39 * q^97 - 45 * q^98 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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