LMFDB - Embedded newform 7935.2.a.n.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7935,2,Mod(1,7935)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("7935.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7935, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,-2,-2,4,-2,2,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$63.3612940039$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 345)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.73205$ of defining polynomial
Character	$\chi$	$=$	7935.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.73205 q^{2} -1.00000 q^{3} +5.46410 q^{4} -1.00000 q^{5} +2.73205 q^{6} +3.00000 q^{7} -9.46410 q^{8} +1.00000 q^{9} +2.73205 q^{10} +2.73205 q^{11} -5.46410 q^{12} +6.19615 q^{13} -8.19615 q^{14} +1.00000 q^{15} +14.9282 q^{16} +2.26795 q^{17} -2.73205 q^{18} +3.26795 q^{19} -5.46410 q^{20} -3.00000 q^{21} -7.46410 q^{22} +9.46410 q^{24} +1.00000 q^{25} -16.9282 q^{26} -1.00000 q^{27} +16.3923 q^{28} -3.73205 q^{29} -2.73205 q^{30} -9.92820 q^{31} -21.8564 q^{32} -2.73205 q^{33} -6.19615 q^{34} -3.00000 q^{35} +5.46410 q^{36} +1.92820 q^{37} -8.92820 q^{38} -6.19615 q^{39} +9.46410 q^{40} -3.73205 q^{41} +8.19615 q^{42} +11.4641 q^{43} +14.9282 q^{44} -1.00000 q^{45} +7.66025 q^{47} -14.9282 q^{48} +2.00000 q^{49} -2.73205 q^{50} -2.26795 q^{51} +33.8564 q^{52} +5.73205 q^{53} +2.73205 q^{54} -2.73205 q^{55} -28.3923 q^{56} -3.26795 q^{57} +10.1962 q^{58} +7.19615 q^{59} +5.46410 q^{60} +11.1244 q^{61} +27.1244 q^{62} +3.00000 q^{63} +29.8564 q^{64} -6.19615 q^{65} +7.46410 q^{66} +6.46410 q^{67} +12.3923 q^{68} +8.19615 q^{70} -3.73205 q^{71} -9.46410 q^{72} -7.66025 q^{73} -5.26795 q^{74} -1.00000 q^{75} +17.8564 q^{76} +8.19615 q^{77} +16.9282 q^{78} -6.92820 q^{79} -14.9282 q^{80} +1.00000 q^{81} +10.1962 q^{82} +13.7321 q^{83} -16.3923 q^{84} -2.26795 q^{85} -31.3205 q^{86} +3.73205 q^{87} -25.8564 q^{88} -2.53590 q^{89} +2.73205 q^{90} +18.5885 q^{91} +9.92820 q^{93} -20.9282 q^{94} -3.26795 q^{95} +21.8564 q^{96} +4.00000 q^{97} -5.46410 q^{98} +2.73205 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} + 6 q^{7} - 12 q^{8} + 2 q^{9} + 2 q^{10} + 2 q^{11} - 4 q^{12} + 2 q^{13} - 6 q^{14} + 2 q^{15} + 16 q^{16} + 8 q^{17} - 2 q^{18} + 10 q^{19} - 4 q^{20}+ \cdots + 2 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 + 6 * q^7 - 12 * q^8 + 2 * q^9 + 2 * q^10 + 2 * q^11 - 4 * q^12 + 2 * q^13 - 6 * q^14 + 2 * q^15 + 16 * q^16 + 8 * q^17 - 2 * q^18 + 10 * q^19 - 4 * q^20 - 6 * q^21 - 8 * q^22 + 12 * q^24 + 2 * q^25 - 20 * q^26 - 2 * q^27 + 12 * q^28 - 4 * q^29 - 2 * q^30 - 6 * q^31 - 16 * q^32 - 2 * q^33 - 2 * q^34 - 6 * q^35 + 4 * q^36 - 10 * q^37 - 4 * q^38 - 2 * q^39 + 12 * q^40 - 4 * q^41 + 6 * q^42 + 16 * q^43 + 16 * q^44 - 2 * q^45 - 2 * q^47 - 16 * q^48 + 4 * q^49 - 2 * q^50 - 8 * q^51 + 40 * q^52 + 8 * q^53 + 2 * q^54 - 2 * q^55 - 36 * q^56 - 10 * q^57 + 10 * q^58 + 4 * q^59 + 4 * q^60 - 2 * q^61 + 30 * q^62 + 6 * q^63 + 32 * q^64 - 2 * q^65 + 8 * q^66 + 6 * q^67 + 4 * q^68 + 6 * q^70 - 4 * q^71 - 12 * q^72 + 2 * q^73 - 14 * q^74 - 2 * q^75 + 8 * q^76 + 6 * q^77 + 20 * q^78 - 16 * q^80 + 2 * q^81 + 10 * q^82 + 24 * q^83 - 12 * q^84 - 8 * q^85 - 28 * q^86 + 4 * q^87 - 24 * q^88 - 12 * q^89 + 2 * q^90 + 6 * q^91 + 6 * q^93 - 28 * q^94 - 10 * q^95 + 16 * q^96 + 8 * q^97 - 4 * q^98 + 2 * 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 $

$2$	−2.73205	−1.93185	−0.965926	−	0.258819i	$-0.916667\pi$
$2$	−2.73205	−1.93185	−0.965926	+	0.258819i	$0.916667\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.46410	2.73205
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.73205	1.11536
$7$	3.00000	1.13389	0.566947	−	0.823754i	$-0.308125\pi$
$7$	3.00000	1.13389	0.566947	+	0.823754i	$0.308125\pi$
$8$	−9.46410	−3.34607
$9$	1.00000	0.333333
$10$	2.73205	0.863950
$11$	2.73205	0.823744	0.411872	−	0.911242i	$-0.364875\pi$
$11$	2.73205	0.823744	0.411872	+	0.911242i	$0.364875\pi$
$12$	−5.46410	−1.57735
$13$	6.19615	1.71850	0.859252	−	0.511553i	$-0.170930\pi$
$13$	6.19615	1.71850	0.859252	+	0.511553i	$0.170930\pi$
$14$	−8.19615	−2.19051
$15$	1.00000	0.258199
$16$	14.9282	3.73205
$17$	2.26795	0.550058	0.275029	−	0.961436i	$-0.411312\pi$
$17$	2.26795	0.550058	0.275029	+	0.961436i	$0.411312\pi$
$18$	−2.73205	−0.643951
$19$	3.26795	0.749719	0.374859	−	0.927082i	$-0.377691\pi$
$19$	3.26795	0.749719	0.374859	+	0.927082i	$0.377691\pi$
$20$	−5.46410	−1.22181
$21$	−3.00000	−0.654654
$22$	−7.46410	−1.59135
$23$	0	0
$23$	0	0
$24$	9.46410	1.93185
$25$	1.00000	0.200000
$26$	−16.9282	−3.31989
$27$	−1.00000	−0.192450
$28$	16.3923	3.09785
$29$	−3.73205	−0.693024	−0.346512	−	0.938045i	$-0.612634\pi$
$29$	−3.73205	−0.693024	−0.346512	+	0.938045i	$0.612634\pi$
$30$	−2.73205	−0.498802
$31$	−9.92820	−1.78316	−0.891579	−	0.452865i	$-0.850402\pi$
$31$	−9.92820	−1.78316	−0.891579	+	0.452865i	$0.850402\pi$
$32$	−21.8564	−3.86370
$33$	−2.73205	−0.475589
$34$	−6.19615	−1.06263
$35$	−3.00000	−0.507093
$36$	5.46410	0.910684
$37$	1.92820	0.316995	0.158497	−	0.987359i	$-0.449335\pi$
$37$	1.92820	0.316995	0.158497	+	0.987359i	$0.449335\pi$
$38$	−8.92820	−1.44835
$39$	−6.19615	−0.992178
$40$	9.46410	1.49641
$41$	−3.73205	−0.582848	−0.291424	−	0.956594i	$-0.594129\pi$
$41$	−3.73205	−0.582848	−0.291424	+	0.956594i	$0.594129\pi$
$42$	8.19615	1.26469
$43$	11.4641	1.74826	0.874130	−	0.485693i	$-0.161433\pi$
$43$	11.4641	1.74826	0.874130	+	0.485693i	$0.161433\pi$
$44$	14.9282	2.25051
$45$	−1.00000	−0.149071
$46$	0	0
$47$	7.66025	1.11736	0.558681	−	0.829382i	$-0.311307\pi$
$47$	7.66025	1.11736	0.558681	+	0.829382i	$0.311307\pi$
$48$	−14.9282	−2.15470
$49$	2.00000	0.285714
$50$	−2.73205	−0.386370
$51$	−2.26795	−0.317576
$52$	33.8564	4.69504
$53$	5.73205	0.787358	0.393679	−	0.919248i	$-0.371202\pi$
$53$	5.73205	0.787358	0.393679	+	0.919248i	$0.371202\pi$
$54$	2.73205	0.371785
$55$	−2.73205	−0.368390
$56$	−28.3923	−3.79408
$57$	−3.26795	−0.432850
$58$	10.1962	1.33882
$59$	7.19615	0.936859	0.468430	−	0.883501i	$-0.344820\pi$
$59$	7.19615	0.936859	0.468430	+	0.883501i	$0.344820\pi$
$60$	5.46410	0.705412
$61$	11.1244	1.42433	0.712164	−	0.702013i	$-0.247715\pi$
$61$	11.1244	1.42433	0.712164	+	0.702013i	$0.247715\pi$
$62$	27.1244	3.44480
$63$	3.00000	0.377964
$64$	29.8564	3.73205
$65$	−6.19615	−0.768538
$66$	7.46410	0.918767
$67$	6.46410	0.789716	0.394858	−	0.918742i	$-0.370794\pi$
$67$	6.46410	0.789716	0.394858	+	0.918742i	$0.370794\pi$
$68$	12.3923	1.50279
$69$	0	0
$70$	8.19615	0.979628
$71$	−3.73205	−0.442913	−0.221456	−	0.975170i	$-0.571081\pi$
$71$	−3.73205	−0.442913	−0.221456	+	0.975170i	$0.571081\pi$
$72$	−9.46410	−1.11536
$73$	−7.66025	−0.896565	−0.448282	−	0.893892i	$-0.647964\pi$
$73$	−7.66025	−0.896565	−0.448282	+	0.893892i	$0.647964\pi$
$74$	−5.26795	−0.612387
$75$	−1.00000	−0.115470
$76$	17.8564	2.04827
$77$	8.19615	0.934038
$78$	16.9282	1.91674
$79$	−6.92820	−0.779484	−0.389742	−	0.920924i	$-0.627436\pi$
$79$	−6.92820	−0.779484	−0.389742	+	0.920924i	$0.627436\pi$
$80$	−14.9282	−1.66902
$81$	1.00000	0.111111
$82$	10.1962	1.12598
$83$	13.7321	1.50729	0.753644	−	0.657283i	$-0.228294\pi$
$83$	13.7321	1.50729	0.753644	+	0.657283i	$0.228294\pi$
$84$	−16.3923	−1.78855
$85$	−2.26795	−0.245994
$86$	−31.3205	−3.37738
$87$	3.73205	0.400118
$88$	−25.8564	−2.75630
$89$	−2.53590	−0.268805	−0.134402	−	0.990927i	$-0.542911\pi$
$89$	−2.53590	−0.268805	−0.134402	+	0.990927i	$0.542911\pi$
$90$	2.73205	0.287983
$91$	18.5885	1.94860
$92$	0	0
$93$	9.92820	1.02951
$94$	−20.9282	−2.15858
$95$	−3.26795	−0.335285
$96$	21.8564	2.23071
$97$	4.00000	0.406138	0.203069	−	0.979164i	$-0.434908\pi$
$97$	4.00000	0.406138	0.203069	+	0.979164i	$0.434908\pi$
$98$	−5.46410	−0.551958
$99$	2.73205	0.274581
$100$	5.46410	0.546410
$101$	5.19615	0.517036	0.258518	−	0.966006i	$-0.416766\pi$
$101$	5.19615	0.517036	0.258518	+	0.966006i	$0.416766\pi$
$102$	6.19615	0.613511
$103$	−15.8564	−1.56238	−0.781189	−	0.624295i	$-0.785387\pi$
$103$	−15.8564	−1.56238	−0.781189	+	0.624295i	$0.785387\pi$
$104$	−58.6410	−5.75022
$105$	3.00000	0.292770
$106$	−15.6603	−1.52106
$107$	−6.12436	−0.592064	−0.296032	−	0.955178i	$-0.595663\pi$
$107$	−6.12436	−0.592064	−0.296032	+	0.955178i	$0.595663\pi$
$108$	−5.46410	−0.525783
$109$	−3.26795	−0.313013	−0.156506	−	0.987677i	$-0.550023\pi$
$109$	−3.26795	−0.313013	−0.156506	+	0.987677i	$0.550023\pi$
$110$	7.46410	0.711674
$111$	−1.92820	−0.183017
$112$	44.7846	4.23175
$113$	−1.19615	−0.112525	−0.0562623	−	0.998416i	$-0.517918\pi$
$113$	−1.19615	−0.112525	−0.0562623	+	0.998416i	$0.517918\pi$
$114$	8.92820	0.836203
$115$	0	0
$116$	−20.3923	−1.89338
$117$	6.19615	0.572834
$118$	−19.6603	−1.80987
$119$	6.80385	0.623708
$120$	−9.46410	−0.863950
$121$	−3.53590	−0.321445
$122$	−30.3923	−2.75159
$123$	3.73205	0.336508
$124$	−54.2487	−4.87168
$125$	−1.00000	−0.0894427
$126$	−8.19615	−0.730171
$127$	12.1962	1.08223	0.541117	−	0.840947i	$-0.318002\pi$
$127$	12.1962	1.08223	0.541117	+	0.840947i	$0.318002\pi$
$128$	−37.8564	−3.34607
$129$	−11.4641	−1.00936
$130$	16.9282	1.48470
$131$	18.9282	1.65376	0.826882	−	0.562375i	$-0.190112\pi$
$131$	18.9282	1.65376	0.826882	+	0.562375i	$0.190112\pi$
$132$	−14.9282	−1.29933
$133$	9.80385	0.850101
$134$	−17.6603	−1.52561
$135$	1.00000	0.0860663
$136$	−21.4641	−1.84053
$137$	20.7846	1.77575	0.887875	−	0.460086i	$-0.152181\pi$
$137$	20.7846	1.77575	0.887875	+	0.460086i	$0.152181\pi$
$138$	0	0
$139$	5.00000	0.424094	0.212047	−	0.977259i	$-0.431987\pi$
$139$	5.00000	0.424094	0.212047	+	0.977259i	$0.431987\pi$
$140$	−16.3923	−1.38540
$141$	−7.66025	−0.645110
$142$	10.1962	0.855642
$143$	16.9282	1.41561
$144$	14.9282	1.24402
$145$	3.73205	0.309930
$146$	20.9282	1.73203
$147$	−2.00000	−0.164957
$148$	10.5359	0.866046
$149$	5.80385	0.475470	0.237735	−	0.971330i	$-0.423595\pi$
$149$	5.80385	0.475470	0.237735	+	0.971330i	$0.423595\pi$
$150$	2.73205	0.223071
$151$	2.39230	0.194683	0.0973415	−	0.995251i	$-0.468966\pi$
$151$	2.39230	0.194683	0.0973415	+	0.995251i	$0.468966\pi$
$152$	−30.9282	−2.50861
$153$	2.26795	0.183353
$154$	−22.3923	−1.80442
$155$	9.92820	0.797452
$156$	−33.8564	−2.71068
$157$	0.0717968	0.00573001	0.00286500	−	0.999996i	$-0.499088\pi$
$157$	0.0717968	0.00573001	0.00286500	+	0.999996i	$0.499088\pi$
$158$	18.9282	1.50585
$159$	−5.73205	−0.454581
$160$	21.8564	1.72790
$161$	0	0
$162$	−2.73205	−0.214650
$163$	14.0000	1.09656	0.548282	−	0.836293i	$-0.315282\pi$
$163$	14.0000	1.09656	0.548282	+	0.836293i	$0.315282\pi$
$164$	−20.3923	−1.59237
$165$	2.73205	0.212690
$166$	−37.5167	−2.91186
$167$	−23.6603	−1.83089	−0.915443	−	0.402448i	$-0.868159\pi$
$167$	−23.6603	−1.83089	−0.915443	+	0.402448i	$0.868159\pi$
$168$	28.3923	2.19051
$169$	25.3923	1.95325
$170$	6.19615	0.475223
$171$	3.26795	0.249906
$172$	62.6410	4.77633
$173$	1.85641	0.141140	0.0705700	−	0.997507i	$-0.477518\pi$
$173$	1.85641	0.141140	0.0705700	+	0.997507i	$0.477518\pi$
$174$	−10.1962	−0.772968
$175$	3.00000	0.226779
$176$	40.7846	3.07426
$177$	−7.19615	−0.540896
$178$	6.92820	0.519291
$179$	4.53590	0.339029	0.169514	−	0.985528i	$-0.445780\pi$
$179$	4.53590	0.339029	0.169514	+	0.985528i	$0.445780\pi$
$180$	−5.46410	−0.407270
$181$	−12.3923	−0.921113	−0.460556	−	0.887630i	$-0.652350\pi$
$181$	−12.3923	−0.921113	−0.460556	+	0.887630i	$0.652350\pi$
$182$	−50.7846	−3.76441
$183$	−11.1244	−0.822336
$184$	0	0
$185$	−1.92820	−0.141764
$186$	−27.1244	−1.98885
$187$	6.19615	0.453108
$188$	41.8564	3.05269
$189$	−3.00000	−0.218218
$190$	8.92820	0.647720
$191$	−3.66025	−0.264847	−0.132423	−	0.991193i	$-0.542276\pi$
$191$	−3.66025	−0.264847	−0.132423	+	0.991193i	$0.542276\pi$
$192$	−29.8564	−2.15470
$193$	10.5359	0.758391	0.379195	−	0.925317i	$-0.376201\pi$
$193$	10.5359	0.758391	0.379195	+	0.925317i	$0.376201\pi$
$194$	−10.9282	−0.784599
$195$	6.19615	0.443716
$196$	10.9282	0.780586
$197$	−1.60770	−0.114544	−0.0572718	−	0.998359i	$-0.518240\pi$
$197$	−1.60770	−0.114544	−0.0572718	+	0.998359i	$0.518240\pi$
$198$	−7.46410	−0.530451
$199$	11.4641	0.812669	0.406334	−	0.913724i	$-0.366807\pi$
$199$	11.4641	0.812669	0.406334	+	0.913724i	$0.366807\pi$
$200$	−9.46410	−0.669213
$201$	−6.46410	−0.455943
$202$	−14.1962	−0.998838
$203$	−11.1962	−0.785816
$204$	−12.3923	−0.867635
$205$	3.73205	0.260658
$206$	43.3205	3.01828
$207$	0	0
$208$	92.4974	6.41354
$209$	8.92820	0.617577
$210$	−8.19615	−0.565588
$211$	−21.7846	−1.49971	−0.749857	−	0.661600i	$-0.769878\pi$
$211$	−21.7846	−1.49971	−0.749857	+	0.661600i	$0.769878\pi$
$212$	31.3205	2.15110
$213$	3.73205	0.255716
$214$	16.7321	1.14378
$215$	−11.4641	−0.781845
$216$	9.46410	0.643951
$217$	−29.7846	−2.02191
$218$	8.92820	0.604694
$219$	7.66025	0.517632
$220$	−14.9282	−1.00646
$221$	14.0526	0.945277
$222$	5.26795	0.353562
$223$	2.00000	0.133930	0.0669650	−	0.997755i	$-0.478668\pi$
$223$	2.00000	0.133930	0.0669650	+	0.997755i	$0.478668\pi$
$224$	−65.5692	−4.38103
$225$	1.00000	0.0666667
$226$	3.26795	0.217381
$227$	−22.9282	−1.52180	−0.760899	−	0.648870i	$-0.775242\pi$
$227$	−22.9282	−1.52180	−0.760899	+	0.648870i	$0.775242\pi$
$228$	−17.8564	−1.18257
$229$	−23.3205	−1.54106	−0.770531	−	0.637402i	$-0.780009\pi$
$229$	−23.3205	−1.54106	−0.770531	+	0.637402i	$0.780009\pi$
$230$	0	0
$231$	−8.19615	−0.539267
$232$	35.3205	2.31890
$233$	−1.85641	−0.121617	−0.0608086	−	0.998149i	$-0.519368\pi$
$233$	−1.85641	−0.121617	−0.0608086	+	0.998149i	$0.519368\pi$
$234$	−16.9282	−1.10663
$235$	−7.66025	−0.499700
$236$	39.3205	2.55955
$237$	6.92820	0.450035
$238$	−18.5885	−1.20491
$239$	−17.0526	−1.10304	−0.551519	−	0.834162i	$-0.685952\pi$
$239$	−17.0526	−1.10304	−0.551519	+	0.834162i	$0.685952\pi$
$240$	14.9282	0.963611
$241$	27.2679	1.75648	0.878242	−	0.478217i	$-0.158717\pi$
$241$	27.2679	1.75648	0.878242	+	0.478217i	$0.158717\pi$
$242$	9.66025	0.620985
$243$	−1.00000	−0.0641500
$244$	60.7846	3.89134
$245$	−2.00000	−0.127775
$246$	−10.1962	−0.650083
$247$	20.2487	1.28839
$248$	93.9615	5.96656
$249$	−13.7321	−0.870233
$250$	2.73205	0.172790
$251$	7.85641	0.495892	0.247946	−	0.968774i	$-0.420244\pi$
$251$	7.85641	0.495892	0.247946	+	0.968774i	$0.420244\pi$
$252$	16.3923	1.03262
$253$	0	0
$254$	−33.3205	−2.09071
$255$	2.26795	0.142024
$256$	43.7128	2.73205
$257$	11.6603	0.727347	0.363673	−	0.931527i	$-0.381522\pi$
$257$	11.6603	0.727347	0.363673	+	0.931527i	$0.381522\pi$
$258$	31.3205	1.94993
$259$	5.78461	0.359438
$260$	−33.8564	−2.09969
$261$	−3.73205	−0.231008
$262$	−51.7128	−3.19483
$263$	−11.7321	−0.723429	−0.361715	−	0.932289i	$-0.617809\pi$
$263$	−11.7321	−0.723429	−0.361715	+	0.932289i	$0.617809\pi$
$264$	25.8564	1.59135
$265$	−5.73205	−0.352117
$266$	−26.7846	−1.64227
$267$	2.53590	0.155194
$268$	35.3205	2.15754
$269$	11.3397	0.691397	0.345698	−	0.938346i	$-0.387642\pi$
$269$	11.3397	0.691397	0.345698	+	0.938346i	$0.387642\pi$
$270$	−2.73205	−0.166267
$271$	−15.3923	−0.935016	−0.467508	−	0.883989i	$-0.654848\pi$
$271$	−15.3923	−0.935016	−0.467508	+	0.883989i	$0.654848\pi$
$272$	33.8564	2.05285
$273$	−18.5885	−1.12502
$274$	−56.7846	−3.43048
$275$	2.73205	0.164749
$276$	0	0
$277$	−26.7846	−1.60933	−0.804666	−	0.593728i	$-0.797655\pi$
$277$	−26.7846	−1.60933	−0.804666	+	0.593728i	$0.797655\pi$
$278$	−13.6603	−0.819288
$279$	−9.92820	−0.594386
$280$	28.3923	1.69676
$281$	−22.0526	−1.31555	−0.657773	−	0.753216i	$-0.728501\pi$
$281$	−22.0526	−1.31555	−0.657773	+	0.753216i	$0.728501\pi$
$282$	20.9282	1.24626
$283$	−0.464102	−0.0275880	−0.0137940	−	0.999905i	$-0.504391\pi$
$283$	−0.464102	−0.0275880	−0.0137940	+	0.999905i	$0.504391\pi$
$284$	−20.3923	−1.21006
$285$	3.26795	0.193577
$286$	−46.2487	−2.73474
$287$	−11.1962	−0.660888
$288$	−21.8564	−1.28790
$289$	−11.8564	−0.697436
$290$	−10.1962	−0.598739
$291$	−4.00000	−0.234484
$292$	−41.8564	−2.44946
$293$	4.26795	0.249336	0.124668	−	0.992198i	$-0.460213\pi$
$293$	4.26795	0.249336	0.124668	+	0.992198i	$0.460213\pi$
$294$	5.46410	0.318673
$295$	−7.19615	−0.418976
$296$	−18.2487	−1.06068
$297$	−2.73205	−0.158530
$298$	−15.8564	−0.918537
$299$	0	0
$300$	−5.46410	−0.315470
$301$	34.3923	1.98234
$302$	−6.53590	−0.376099
$303$	−5.19615	−0.298511
$304$	48.7846	2.79799
$305$	−11.1244	−0.636979
$306$	−6.19615	−0.354210
$307$	13.8038	0.787827	0.393914	−	0.919147i	$-0.371121\pi$
$307$	13.8038	0.787827	0.393914	+	0.919147i	$0.371121\pi$
$308$	44.7846	2.55184
$309$	15.8564	0.902039
$310$	−27.1244	−1.54056
$311$	−12.0000	−0.680458	−0.340229	−	0.940343i	$-0.610505\pi$
$311$	−12.0000	−0.680458	−0.340229	+	0.940343i	$0.610505\pi$
$312$	58.6410	3.31989
$313$	7.92820	0.448129	0.224064	−	0.974574i	$-0.428067\pi$
$313$	7.92820	0.448129	0.224064	+	0.974574i	$0.428067\pi$
$314$	−0.196152	−0.0110695
$315$	−3.00000	−0.169031
$316$	−37.8564	−2.12959
$317$	17.5167	0.983834	0.491917	−	0.870642i	$-0.336296\pi$
$317$	17.5167	0.983834	0.491917	+	0.870642i	$0.336296\pi$
$318$	15.6603	0.878183
$319$	−10.1962	−0.570875
$320$	−29.8564	−1.66902
$321$	6.12436	0.341828
$322$	0	0
$323$	7.41154	0.412389
$324$	5.46410	0.303561
$325$	6.19615	0.343701
$326$	−38.2487	−2.11840
$327$	3.26795	0.180718
$328$	35.3205	1.95025
$329$	22.9808	1.26697
$330$	−7.46410	−0.410885
$331$	20.3205	1.11692	0.558458	−	0.829533i	$-0.311393\pi$
$331$	20.3205	1.11692	0.558458	+	0.829533i	$0.311393\pi$
$332$	75.0333	4.11799
$333$	1.92820	0.105665
$334$	64.6410	3.53700
$335$	−6.46410	−0.353172
$336$	−44.7846	−2.44320
$337$	−18.7846	−1.02326	−0.511631	−	0.859205i	$-0.670959\pi$
$337$	−18.7846	−1.02326	−0.511631	+	0.859205i	$0.670959\pi$
$338$	−69.3731	−3.77340
$339$	1.19615	0.0649661
$340$	−12.3923	−0.672067
$341$	−27.1244	−1.46887
$342$	−8.92820	−0.482782
$343$	−15.0000	−0.809924
$344$	−108.497	−5.84979
$345$	0	0
$346$	−5.07180	−0.272661
$347$	−27.3205	−1.46664	−0.733321	−	0.679883i	$-0.762031\pi$
$347$	−27.3205	−1.46664	−0.733321	+	0.679883i	$0.762031\pi$
$348$	20.3923	1.09314
$349$	−4.32051	−0.231271	−0.115636	−	0.993292i	$-0.536891\pi$
$349$	−4.32051	−0.231271	−0.115636	+	0.993292i	$0.536891\pi$
$350$	−8.19615	−0.438103
$351$	−6.19615	−0.330726
$352$	−59.7128	−3.18270
$353$	4.73205	0.251862	0.125931	−	0.992039i	$-0.459808\pi$
$353$	4.73205	0.251862	0.125931	+	0.992039i	$0.459808\pi$
$354$	19.6603	1.04493
$355$	3.73205	0.198077
$356$	−13.8564	−0.734388
$357$	−6.80385	−0.360098
$358$	−12.3923	−0.654954
$359$	2.87564	0.151771	0.0758854	−	0.997117i	$-0.475822\pi$
$359$	2.87564	0.151771	0.0758854	+	0.997117i	$0.475822\pi$
$360$	9.46410	0.498802
$361$	−8.32051	−0.437921
$362$	33.8564	1.77945
$363$	3.53590	0.185587
$364$	101.569	5.32367
$365$	7.66025	0.400956
$366$	30.3923	1.58863
$367$	15.0000	0.782994	0.391497	−	0.920179i	$-0.371957\pi$
$367$	15.0000	0.782994	0.391497	+	0.920179i	$0.371957\pi$
$368$	0	0
$369$	−3.73205	−0.194283
$370$	5.26795	0.273868
$371$	17.1962	0.892780
$372$	54.2487	2.81266
$373$	−11.6077	−0.601024	−0.300512	−	0.953778i	$-0.597157\pi$
$373$	−11.6077	−0.601024	−0.300512	+	0.953778i	$0.597157\pi$
$374$	−16.9282	−0.875337
$375$	1.00000	0.0516398
$376$	−72.4974	−3.73877
$377$	−23.1244	−1.19096
$378$	8.19615	0.421565
$379$	−4.00000	−0.205466	−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000	−0.205466	−0.102733	+	0.994709i	$0.532759\pi$
$380$	−17.8564	−0.916014
$381$	−12.1962	−0.624828
$382$	10.0000	0.511645
$383$	33.5885	1.71629	0.858145	−	0.513407i	$-0.171617\pi$
$383$	33.5885	1.71629	0.858145	+	0.513407i	$0.171617\pi$
$384$	37.8564	1.93185
$385$	−8.19615	−0.417715
$386$	−28.7846	−1.46510
$387$	11.4641	0.582753
$388$	21.8564	1.10959
$389$	3.46410	0.175637	0.0878185	−	0.996136i	$-0.472010\pi$
$389$	3.46410	0.175637	0.0878185	+	0.996136i	$0.472010\pi$
$390$	−16.9282	−0.857193
$391$	0	0
$392$	−18.9282	−0.956019
$393$	−18.9282	−0.954802
$394$	4.39230	0.221281
$395$	6.92820	0.348596
$396$	14.9282	0.750170
$397$	−16.7846	−0.842395	−0.421198	−	0.906969i	$-0.638390\pi$
$397$	−16.7846	−0.842395	−0.421198	+	0.906969i	$0.638390\pi$
$398$	−31.3205	−1.56996
$399$	−9.80385	−0.490806
$400$	14.9282	0.746410
$401$	29.3205	1.46420	0.732098	−	0.681199i	$-0.238541\pi$
$401$	29.3205	1.46420	0.732098	+	0.681199i	$0.238541\pi$
$402$	17.6603	0.880813
$403$	−61.5167	−3.06436
$404$	28.3923	1.41257
$405$	−1.00000	−0.0496904
$406$	30.5885	1.51808
$407$	5.26795	0.261123
$408$	21.4641	1.06263
$409$	9.39230	0.464420	0.232210	−	0.972666i	$-0.425404\pi$
$409$	9.39230	0.464420	0.232210	+	0.972666i	$0.425404\pi$
$410$	−10.1962	−0.503552
$411$	−20.7846	−1.02523
$412$	−86.6410	−4.26850
$413$	21.5885	1.06230
$414$	0	0
$415$	−13.7321	−0.674080
$416$	−135.426	−6.63979
$417$	−5.00000	−0.244851
$418$	−24.3923	−1.19307
$419$	−14.7321	−0.719708	−0.359854	−	0.933009i	$-0.617173\pi$
$419$	−14.7321	−0.719708	−0.359854	+	0.933009i	$0.617173\pi$
$420$	16.3923	0.799863
$421$	−4.33975	−0.211506	−0.105753	−	0.994392i	$-0.533725\pi$
$421$	−4.33975	−0.211506	−0.105753	+	0.994392i	$0.533725\pi$
$422$	59.5167	2.89723
$423$	7.66025	0.372454
$424$	−54.2487	−2.63455
$425$	2.26795	0.110012
$426$	−10.1962	−0.494005
$427$	33.3731	1.61504
$428$	−33.4641	−1.61755
$429$	−16.9282	−0.817301
$430$	31.3205	1.51041
$431$	−4.39230	−0.211570	−0.105785	−	0.994389i	$-0.533736\pi$
$431$	−4.39230	−0.211570	−0.105785	+	0.994389i	$0.533736\pi$
$432$	−14.9282	−0.718234
$433$	−37.9282	−1.82271	−0.911357	−	0.411618i	$-0.864964\pi$
$433$	−37.9282	−1.82271	−0.911357	+	0.411618i	$0.864964\pi$
$434$	81.3731	3.90603
$435$	−3.73205	−0.178938
$436$	−17.8564	−0.855167
$437$	0	0
$438$	−20.9282	−0.999988
$439$	−26.0000	−1.24091	−0.620456	−	0.784241i	$-0.713053\pi$
$439$	−26.0000	−1.24091	−0.620456	+	0.784241i	$0.713053\pi$
$440$	25.8564	1.23266
$441$	2.00000	0.0952381
$442$	−38.3923	−1.82614
$443$	−25.5167	−1.21233	−0.606167	−	0.795338i	$-0.707294\pi$
$443$	−25.5167	−1.21233	−0.606167	+	0.795338i	$0.707294\pi$
$444$	−10.5359	−0.500012
$445$	2.53590	0.120213
$446$	−5.46410	−0.258733
$447$	−5.80385	−0.274513
$448$	89.5692	4.23175
$449$	9.05256	0.427217	0.213608	−	0.976919i	$-0.431478\pi$
$449$	9.05256	0.427217	0.213608	+	0.976919i	$0.431478\pi$
$450$	−2.73205	−0.128790
$451$	−10.1962	−0.480118
$452$	−6.53590	−0.307423
$453$	−2.39230	−0.112400
$454$	62.6410	2.93989
$455$	−18.5885	−0.871440
$456$	30.9282	1.44835
$457$	10.0718	0.471139	0.235569	−	0.971858i	$-0.424305\pi$
$457$	10.0718	0.471139	0.235569	+	0.971858i	$0.424305\pi$
$458$	63.7128	2.97710
$459$	−2.26795	−0.105859
$460$	0	0
$461$	−20.5359	−0.956452	−0.478226	−	0.878237i	$-0.658720\pi$
$461$	−20.5359	−0.956452	−0.478226	+	0.878237i	$0.658720\pi$
$462$	22.3923	1.04178
$463$	0.339746	0.0157893	0.00789467	−	0.999969i	$-0.497487\pi$
$463$	0.339746	0.0157893	0.00789467	+	0.999969i	$0.497487\pi$
$464$	−55.7128	−2.58640
$465$	−9.92820	−0.460409
$466$	5.07180	0.234946
$467$	15.7321	0.727992	0.363996	−	0.931400i	$-0.381412\pi$
$467$	15.7321	0.727992	0.363996	+	0.931400i	$0.381412\pi$
$468$	33.8564	1.56501
$469$	19.3923	0.895453
$470$	20.9282	0.965346
$471$	−0.0717968	−0.00330822
$472$	−68.1051	−3.13479
$473$	31.3205	1.44012
$474$	−18.9282	−0.869401
$475$	3.26795	0.149944
$476$	37.1769	1.70400
$477$	5.73205	0.262453
$478$	46.5885	2.13091
$479$	−20.4449	−0.934150	−0.467075	−	0.884218i	$-0.654692\pi$
$479$	−20.4449	−0.934150	−0.467075	+	0.884218i	$0.654692\pi$
$480$	−21.8564	−0.997604
$481$	11.9474	0.544756
$482$	−74.4974	−3.39326
$483$	0	0
$484$	−19.3205	−0.878205
$485$	−4.00000	−0.181631
$486$	2.73205	0.123928
$487$	−9.66025	−0.437748	−0.218874	−	0.975753i	$-0.570238\pi$
$487$	−9.66025	−0.437748	−0.218874	+	0.975753i	$0.570238\pi$
$488$	−105.282	−4.76589
$489$	−14.0000	−0.633102
$490$	5.46410	0.246843
$491$	33.4449	1.50935	0.754673	−	0.656101i	$-0.227796\pi$
$491$	33.4449	1.50935	0.754673	+	0.656101i	$0.227796\pi$
$492$	20.3923	0.919356
$493$	−8.46410	−0.381204
$494$	−55.3205	−2.48899
$495$	−2.73205	−0.122797
$496$	−148.210	−6.65484
$497$	−11.1962	−0.502216
$498$	37.5167	1.68116
$499$	35.3923	1.58438	0.792189	−	0.610276i	$-0.208942\pi$
$499$	35.3923	1.58438	0.792189	+	0.610276i	$0.208942\pi$
$500$	−5.46410	−0.244362
$501$	23.6603	1.05706
$502$	−21.4641	−0.957990
$503$	22.6603	1.01037	0.505185	−	0.863011i	$-0.331424\pi$
$503$	22.6603	1.01037	0.505185	+	0.863011i	$0.331424\pi$
$504$	−28.3923	−1.26469
$505$	−5.19615	−0.231226
$506$	0	0
$507$	−25.3923	−1.12771
$508$	66.6410	2.95672
$509$	−21.0718	−0.933991	−0.466995	−	0.884260i	$-0.654664\pi$
$509$	−21.0718	−0.933991	−0.466995	+	0.884260i	$0.654664\pi$
$510$	−6.19615	−0.274370
$511$	−22.9808	−1.01661
$512$	−43.7128	−1.93185
$513$	−3.26795	−0.144283
$514$	−31.8564	−1.40513
$515$	15.8564	0.698717
$516$	−62.6410	−2.75762
$517$	20.9282	0.920421
$518$	−15.8038	−0.694381
$519$	−1.85641	−0.0814872
$520$	58.6410	2.57158
$521$	9.26795	0.406036	0.203018	−	0.979175i	$-0.434925\pi$
$521$	9.26795	0.406036	0.203018	+	0.979175i	$0.434925\pi$
$522$	10.1962	0.446273
$523$	20.0000	0.874539	0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000	0.874539	0.437269	+	0.899331i	$0.355946\pi$
$524$	103.426	4.51817
$525$	−3.00000	−0.130931
$526$	32.0526	1.39756
$527$	−22.5167	−0.980841
$528$	−40.7846	−1.77492
$529$	0	0
$530$	15.6603	0.680238
$531$	7.19615	0.312286
$532$	53.5692	2.32252
$533$	−23.1244	−1.00163
$534$	−6.92820	−0.299813
$535$	6.12436	0.264779
$536$	−61.1769	−2.64244
$537$	−4.53590	−0.195738
$538$	−30.9808	−1.33568
$539$	5.46410	0.235356
$540$	5.46410	0.235137
$541$	25.8564	1.11165	0.555827	−	0.831298i	$-0.312402\pi$
$541$	25.8564	1.11165	0.555827	+	0.831298i	$0.312402\pi$
$542$	42.0526	1.80631
$543$	12.3923	0.531805
$544$	−49.5692	−2.12526
$545$	3.26795	0.139984
$546$	50.7846	2.17338
$547$	21.0718	0.900965	0.450482	−	0.892785i	$-0.351252\pi$
$547$	21.0718	0.900965	0.450482	+	0.892785i	$0.351252\pi$
$548$	113.569	4.85144
$549$	11.1244	0.474776
$550$	−7.46410	−0.318270
$551$	−12.1962	−0.519574
$552$	0	0
$553$	−20.7846	−0.883852
$554$	73.1769	3.10899
$555$	1.92820	0.0818477
$556$	27.3205	1.15865
$557$	27.5885	1.16896	0.584480	−	0.811408i	$-0.301298\pi$
$557$	27.5885	1.16896	0.584480	+	0.811408i	$0.301298\pi$
$558$	27.1244	1.14827
$559$	71.0333	3.00439
$560$	−44.7846	−1.89250
$561$	−6.19615	−0.261602
$562$	60.2487	2.54144
$563$	−40.5167	−1.70757	−0.853787	−	0.520623i	$-0.825700\pi$
$563$	−40.5167	−1.70757	−0.853787	+	0.520623i	$0.825700\pi$
$564$	−41.8564	−1.76247
$565$	1.19615	0.0503225
$566$	1.26795	0.0532959
$567$	3.00000	0.125988
$568$	35.3205	1.48202
$569$	−17.3205	−0.726113	−0.363057	−	0.931767i	$-0.618267\pi$
$569$	−17.3205	−0.726113	−0.363057	+	0.931767i	$0.618267\pi$
$570$	−8.92820	−0.373961
$571$	16.5885	0.694205	0.347103	−	0.937827i	$-0.387166\pi$
$571$	16.5885	0.694205	0.347103	+	0.937827i	$0.387166\pi$
$572$	92.4974	3.86751
$573$	3.66025	0.152909
$574$	30.5885	1.27674
$575$	0	0
$576$	29.8564	1.24402
$577$	2.92820	0.121903	0.0609513	−	0.998141i	$-0.480587\pi$
$577$	2.92820	0.121903	0.0609513	+	0.998141i	$0.480587\pi$
$578$	32.3923	1.34734
$579$	−10.5359	−0.437857
$580$	20.3923	0.846744
$581$	41.1962	1.70910
$582$	10.9282	0.452989
$583$	15.6603	0.648581
$584$	72.4974	2.99996
$585$	−6.19615	−0.256179
$586$	−11.6603	−0.481681
$587$	−7.85641	−0.324269	−0.162134	−	0.986769i	$-0.551838\pi$
$587$	−7.85641	−0.324269	−0.162134	+	0.986769i	$0.551838\pi$
$588$	−10.9282	−0.450672
$589$	−32.4449	−1.33687
$590$	19.6603	0.809400
$591$	1.60770	0.0661317
$592$	28.7846	1.18304
$593$	−26.5885	−1.09186	−0.545929	−	0.837832i	$-0.683823\pi$
$593$	−26.5885	−1.09186	−0.545929	+	0.837832i	$0.683823\pi$
$594$	7.46410	0.306256
$595$	−6.80385	−0.278931
$596$	31.7128	1.29901
$597$	−11.4641	−0.469194
$598$	0	0
$599$	−7.32051	−0.299108	−0.149554	−	0.988754i	$-0.547784\pi$
$599$	−7.32051	−0.299108	−0.149554	+	0.988754i	$0.547784\pi$
$600$	9.46410	0.386370
$601$	−4.46410	−0.182095	−0.0910473	−	0.995847i	$-0.529021\pi$
$601$	−4.46410	−0.182095	−0.0910473	+	0.995847i	$0.529021\pi$
$602$	−93.9615	−3.82959
$603$	6.46410	0.263239
$604$	13.0718	0.531884
$605$	3.53590	0.143755
$606$	14.1962	0.576679
$607$	12.8756	0.522606	0.261303	−	0.965257i	$-0.415848\pi$
$607$	12.8756	0.522606	0.261303	+	0.965257i	$0.415848\pi$
$608$	−71.4256	−2.89669
$609$	11.1962	0.453691
$610$	30.3923	1.23055
$611$	47.4641	1.92019
$612$	12.3923	0.500929
$613$	−47.8564	−1.93290	−0.966451	−	0.256851i	$-0.917315\pi$
$613$	−47.8564	−1.93290	−0.966451	+	0.256851i	$0.917315\pi$
$614$	−37.7128	−1.52197
$615$	−3.73205	−0.150491
$616$	−77.5692	−3.12535
$617$	−4.51666	−0.181834	−0.0909170	−	0.995858i	$-0.528980\pi$
$617$	−4.51666	−0.181834	−0.0909170	+	0.995858i	$0.528980\pi$
$618$	−43.3205	−1.74261
$619$	0.784610	0.0315361	0.0157681	−	0.999876i	$-0.494981\pi$
$619$	0.784610	0.0315361	0.0157681	+	0.999876i	$0.494981\pi$
$620$	54.2487	2.17868
$621$	0	0
$622$	32.7846	1.31454
$623$	−7.60770	−0.304796
$624$	−92.4974	−3.70286
$625$	1.00000	0.0400000
$626$	−21.6603	−0.865718
$627$	−8.92820	−0.356558
$628$	0.392305	0.0156547
$629$	4.37307	0.174366
$630$	8.19615	0.326543
$631$	−7.12436	−0.283616	−0.141808	−	0.989894i	$-0.545292\pi$
$631$	−7.12436	−0.283616	−0.141808	+	0.989894i	$0.545292\pi$
$632$	65.5692	2.60820
$633$	21.7846	0.865861
$634$	−47.8564	−1.90062
$635$	−12.1962	−0.483990
$636$	−31.3205	−1.24194
$637$	12.3923	0.491001
$638$	27.8564	1.10285
$639$	−3.73205	−0.147638
$640$	37.8564	1.49641
$641$	−19.5167	−0.770862	−0.385431	−	0.922737i	$-0.625947\pi$
$641$	−19.5167	−0.770862	−0.385431	+	0.922737i	$0.625947\pi$
$642$	−16.7321	−0.660361
$643$	−25.6410	−1.01118	−0.505591	−	0.862773i	$-0.668726\pi$
$643$	−25.6410	−1.01118	−0.505591	+	0.862773i	$0.668726\pi$
$644$	0	0
$645$	11.4641	0.451399
$646$	−20.2487	−0.796675
$647$	−21.6603	−0.851552	−0.425776	−	0.904828i	$-0.639999\pi$
$647$	−21.6603	−0.851552	−0.425776	+	0.904828i	$0.639999\pi$
$648$	−9.46410	−0.371785
$649$	19.6603	0.771732
$650$	−16.9282	−0.663979
$651$	29.7846	1.16735
$652$	76.4974	2.99587
$653$	40.5885	1.58835	0.794175	−	0.607690i	$-0.207904\pi$
$653$	40.5885	1.58835	0.794175	+	0.607690i	$0.207904\pi$
$654$	−8.92820	−0.349120
$655$	−18.9282	−0.739586
$656$	−55.7128	−2.17522
$657$	−7.66025	−0.298855
$658$	−62.7846	−2.44760
$659$	−16.1962	−0.630913	−0.315456	−	0.948940i	$-0.602158\pi$
$659$	−16.1962	−0.630913	−0.315456	+	0.948940i	$0.602158\pi$
$660$	14.9282	0.581080
$661$	25.3205	0.984854	0.492427	−	0.870354i	$-0.336110\pi$
$661$	25.3205	0.984854	0.492427	+	0.870354i	$0.336110\pi$
$662$	−55.5167	−2.15772
$663$	−14.0526	−0.545756
$664$	−129.962	−5.04349
$665$	−9.80385	−0.380177
$666$	−5.26795	−0.204129
$667$	0	0
$668$	−129.282	−5.00207
$669$	−2.00000	−0.0773245
$670$	17.6603	0.682275
$671$	30.3923	1.17328
$672$	65.5692	2.52939
$673$	6.33975	0.244379	0.122190	−	0.992507i	$-0.461008\pi$
$673$	6.33975	0.244379	0.122190	+	0.992507i	$0.461008\pi$
$674$	51.3205	1.97679
$675$	−1.00000	−0.0384900
$676$	138.746	5.33639
$677$	39.8372	1.53107	0.765533	−	0.643396i	$-0.222475\pi$
$677$	39.8372	1.53107	0.765533	+	0.643396i	$0.222475\pi$
$678$	−3.26795	−0.125505
$679$	12.0000	0.460518
$680$	21.4641	0.823111
$681$	22.9282	0.878611
$682$	74.1051	2.83763
$683$	−28.0526	−1.07340	−0.536701	−	0.843773i	$-0.680330\pi$
$683$	−28.0526	−1.07340	−0.536701	+	0.843773i	$0.680330\pi$
$684$	17.8564	0.682757
$685$	−20.7846	−0.794139
$686$	40.9808	1.56465
$687$	23.3205	0.889733
$688$	171.138	6.52459
$689$	35.5167	1.35308
$690$	0	0
$691$	−37.3205	−1.41974	−0.709870	−	0.704333i	$-0.751246\pi$
$691$	−37.3205	−1.41974	−0.709870	+	0.704333i	$0.751246\pi$
$692$	10.1436	0.385602
$693$	8.19615	0.311346
$694$	74.6410	2.83333
$695$	−5.00000	−0.189661
$696$	−35.3205	−1.33882
$697$	−8.46410	−0.320601
$698$	11.8038	0.446782
$699$	1.85641	0.0702157
$700$	16.3923	0.619571
$701$	−29.5167	−1.11483	−0.557414	−	0.830234i	$-0.688207\pi$
$701$	−29.5167	−1.11483	−0.557414	+	0.830234i	$0.688207\pi$
$702$	16.9282	0.638914
$703$	6.30127	0.237657
$704$	81.5692	3.07426
$705$	7.66025	0.288502
$706$	−12.9282	−0.486559
$707$	15.5885	0.586264
$708$	−39.3205	−1.47776
$709$	−9.66025	−0.362798	−0.181399	−	0.983410i	$-0.558063\pi$
$709$	−9.66025	−0.362798	−0.181399	+	0.983410i	$0.558063\pi$
$710$	−10.1962	−0.382655
$711$	−6.92820	−0.259828
$712$	24.0000	0.899438
$713$	0	0
$714$	18.5885	0.695656
$715$	−16.9282	−0.633079
$716$	24.7846	0.926244
$717$	17.0526	0.636839
$718$	−7.85641	−0.293198
$719$	−5.19615	−0.193784	−0.0968919	−	0.995295i	$-0.530890\pi$
$719$	−5.19615	−0.193784	−0.0968919	+	0.995295i	$0.530890\pi$
$720$	−14.9282	−0.556341
$721$	−47.5692	−1.77157
$722$	22.7321	0.845999
$723$	−27.2679	−1.01411
$724$	−67.7128	−2.51653
$725$	−3.73205	−0.138605
$726$	−9.66025	−0.358526
$727$	−12.1769	−0.451617	−0.225808	−	0.974172i	$-0.572502\pi$
$727$	−12.1769	−0.451617	−0.225808	+	0.974172i	$0.572502\pi$
$728$	−175.923	−6.52014
$729$	1.00000	0.0370370
$730$	−20.9282	−0.774588
$731$	26.0000	0.961645
$732$	−60.7846	−2.24666
$733$	−49.1051	−1.81374	−0.906869	−	0.421412i	$-0.861535\pi$
$733$	−49.1051	−1.81374	−0.906869	+	0.421412i	$0.861535\pi$
$734$	−40.9808	−1.51263
$735$	2.00000	0.0737711
$736$	0	0
$737$	17.6603	0.650524
$738$	10.1962	0.375326
$739$	13.6795	0.503208	0.251604	−	0.967830i	$-0.419042\pi$
$739$	13.6795	0.503208	0.251604	+	0.967830i	$0.419042\pi$
$740$	−10.5359	−0.387307
$741$	−20.2487	−0.743855
$742$	−46.9808	−1.72472
$743$	28.0000	1.02722	0.513610	−	0.858024i	$-0.328308\pi$
$743$	28.0000	1.02722	0.513610	+	0.858024i	$0.328308\pi$
$744$	−93.9615	−3.44480
$745$	−5.80385	−0.212637
$746$	31.7128	1.16109
$747$	13.7321	0.502429
$748$	33.8564	1.23791
$749$	−18.3731	−0.671337
$750$	−2.73205	−0.0997604
$751$	−8.73205	−0.318637	−0.159319	−	0.987227i	$-0.550930\pi$
$751$	−8.73205	−0.318637	−0.159319	+	0.987227i	$0.550930\pi$
$752$	114.354	4.17006
$753$	−7.85641	−0.286303
$754$	63.1769	2.30077
$755$	−2.39230	−0.0870649
$756$	−16.3923	−0.596182
$757$	39.3923	1.43174	0.715869	−	0.698235i	$-0.246031\pi$
$757$	39.3923	1.43174	0.715869	+	0.698235i	$0.246031\pi$
$758$	10.9282	0.396930
$759$	0	0
$760$	30.9282	1.12188
$761$	−20.6603	−0.748934	−0.374467	−	0.927240i	$-0.622174\pi$
$761$	−20.6603	−0.748934	−0.374467	+	0.927240i	$0.622174\pi$
$762$	33.3205	1.20707
$763$	−9.80385	−0.354923
$764$	−20.0000	−0.723575
$765$	−2.26795	−0.0819979
$766$	−91.7654	−3.31562
$767$	44.5885	1.61000
$768$	−43.7128	−1.57735
$769$	12.1962	0.439805	0.219902	−	0.975522i	$-0.429426\pi$
$769$	12.1962	0.439805	0.219902	+	0.975522i	$0.429426\pi$
$770$	22.3923	0.806963
$771$	−11.6603	−0.419934
$772$	57.5692	2.07196
$773$	−8.53590	−0.307015	−0.153507	−	0.988147i	$-0.549057\pi$
$773$	−8.53590	−0.307015	−0.153507	+	0.988147i	$0.549057\pi$
$774$	−31.3205	−1.12579
$775$	−9.92820	−0.356632
$776$	−37.8564	−1.35897
$777$	−5.78461	−0.207522
$778$	−9.46410	−0.339304
$779$	−12.1962	−0.436973
$780$	33.8564	1.21225
$781$	−10.1962	−0.364847
$782$	0	0
$783$	3.73205	0.133373
$784$	29.8564	1.06630
$785$	−0.0717968	−0.00256254
$786$	51.7128	1.84453
$787$	17.0000	0.605985	0.302992	−	0.952993i	$-0.402014\pi$
$787$	17.0000	0.605985	0.302992	+	0.952993i	$0.402014\pi$
$788$	−8.78461	−0.312939
$789$	11.7321	0.417672
$790$	−18.9282	−0.673435
$791$	−3.58846	−0.127591
$792$	−25.8564	−0.918767
$793$	68.9282	2.44771
$794$	45.8564	1.62738
$795$	5.73205	0.203295
$796$	62.6410	2.22025
$797$	21.9808	0.778599	0.389299	−	0.921111i	$-0.372717\pi$
$797$	21.9808	0.778599	0.389299	+	0.921111i	$0.372717\pi$
$798$	26.7846	0.948165
$799$	17.3731	0.614615
$800$	−21.8564	−0.772741
$801$	−2.53590	−0.0896016
$802$	−80.1051	−2.82861
$803$	−20.9282	−0.738540
$804$	−35.3205	−1.24566
$805$	0	0
$806$	168.067	5.91989
$807$	−11.3397	−0.399178
$808$	−49.1769	−1.73004
$809$	−14.1244	−0.496586	−0.248293	−	0.968685i	$-0.579870\pi$
$809$	−14.1244	−0.496586	−0.248293	+	0.968685i	$0.579870\pi$
$810$	2.73205	0.0959945
$811$	3.00000	0.105344	0.0526721	−	0.998612i	$-0.483226\pi$
$811$	3.00000	0.105344	0.0526721	+	0.998612i	$0.483226\pi$
$812$	−61.1769	−2.14689
$813$	15.3923	0.539832
$814$	−14.3923	−0.504450
$815$	−14.0000	−0.490399
$816$	−33.8564	−1.18521
$817$	37.4641	1.31070
$818$	−25.6603	−0.897190
$819$	18.5885	0.649533
$820$	20.3923	0.712130
$821$	15.7128	0.548381	0.274190	−	0.961675i	$-0.411590\pi$
$821$	15.7128	0.548381	0.274190	+	0.961675i	$0.411590\pi$
$822$	56.7846	1.98059
$823$	−33.0718	−1.15281	−0.576405	−	0.817164i	$-0.695545\pi$
$823$	−33.0718	−1.15281	−0.576405	+	0.817164i	$0.695545\pi$
$824$	150.067	5.22782
$825$	−2.73205	−0.0951178
$826$	−58.9808	−2.05220
$827$	40.3731	1.40391	0.701955	−	0.712222i	$-0.252311\pi$
$827$	40.3731	1.40391	0.701955	+	0.712222i	$0.252311\pi$
$828$	0	0
$829$	−14.0718	−0.488734	−0.244367	−	0.969683i	$-0.578580\pi$
$829$	−14.0718	−0.488734	−0.244367	+	0.969683i	$0.578580\pi$
$830$	37.5167	1.30222
$831$	26.7846	0.929148
$832$	184.995	6.41354
$833$	4.53590	0.157160
$834$	13.6603	0.473016
$835$	23.6603	0.818797
$836$	48.7846	1.68725
$837$	9.92820	0.343169
$838$	40.2487	1.39037
$839$	15.8564	0.547424	0.273712	−	0.961812i	$-0.411748\pi$
$839$	15.8564	0.547424	0.273712	+	0.961812i	$0.411748\pi$
$840$	−28.3923	−0.979628
$841$	−15.0718	−0.519717
$842$	11.8564	0.408599
$843$	22.0526	0.759530
$844$	−119.033	−4.09730
$845$	−25.3923	−0.873522
$846$	−20.9282	−0.719526
$847$	−10.6077	−0.364485
$848$	85.5692	2.93846
$849$	0.464102	0.0159279
$850$	−6.19615	−0.212526
$851$	0	0
$852$	20.3923	0.698629
$853$	8.53590	0.292264	0.146132	−	0.989265i	$-0.453318\pi$
$853$	8.53590	0.292264	0.146132	+	0.989265i	$0.453318\pi$
$854$	−91.1769	−3.12001
$855$	−3.26795	−0.111762
$856$	57.9615	1.98108
$857$	8.92820	0.304982	0.152491	−	0.988305i	$-0.451271\pi$
$857$	8.92820	0.304982	0.152491	+	0.988305i	$0.451271\pi$
$858$	46.2487	1.57890
$859$	49.9282	1.70353	0.851764	−	0.523925i	$-0.175533\pi$
$859$	49.9282	1.70353	0.851764	+	0.523925i	$0.175533\pi$
$860$	−62.6410	−2.13604
$861$	11.1962	0.381564
$862$	12.0000	0.408722
$863$	14.3923	0.489920	0.244960	−	0.969533i	$-0.421225\pi$
$863$	14.3923	0.489920	0.244960	+	0.969533i	$0.421225\pi$
$864$	21.8564	0.743570
$865$	−1.85641	−0.0631197
$866$	103.622	3.52121
$867$	11.8564	0.402665
$868$	−162.746	−5.52396
$869$	−18.9282	−0.642095
$870$	10.1962	0.345682
$871$	40.0526	1.35713
$872$	30.9282	1.04736
$873$	4.00000	0.135379
$874$	0	0
$875$	−3.00000	−0.101419
$876$	41.8564	1.41420
$877$	27.4641	0.927397	0.463698	−	0.885993i	$-0.346522\pi$
$877$	27.4641	0.927397	0.463698	+	0.885993i	$0.346522\pi$
$878$	71.0333	2.39726
$879$	−4.26795	−0.143954
$880$	−40.7846	−1.37485
$881$	13.8038	0.465063	0.232532	−	0.972589i	$-0.425299\pi$
$881$	13.8038	0.465063	0.232532	+	0.972589i	$0.425299\pi$
$882$	−5.46410	−0.183986
$883$	−5.94744	−0.200147	−0.100074	−	0.994980i	$-0.531908\pi$
$883$	−5.94744	−0.200147	−0.100074	+	0.994980i	$0.531908\pi$
$884$	76.7846	2.58255
$885$	7.19615	0.241896
$886$	69.7128	2.34205
$887$	3.46410	0.116313	0.0581566	−	0.998307i	$-0.481478\pi$
$887$	3.46410	0.116313	0.0581566	+	0.998307i	$0.481478\pi$
$888$	18.2487	0.612387
$889$	36.5885	1.22714
$890$	−6.92820	−0.232234
$891$	2.73205	0.0915271
$892$	10.9282	0.365903
$893$	25.0333	0.837708
$894$	15.8564	0.530318
$895$	−4.53590	−0.151618
$896$	−113.569	−3.79408
$897$	0	0
$898$	−24.7321	−0.825319
$899$	37.0526	1.23577
$900$	5.46410	0.182137
$901$	13.0000	0.433093
$902$	27.8564	0.927517
$903$	−34.3923	−1.14450
$904$	11.3205	0.376514
$905$	12.3923	0.411934
$906$	6.53590	0.217141
$907$	22.1769	0.736372	0.368186	−	0.929752i	$-0.379979\pi$
$907$	22.1769	0.736372	0.368186	+	0.929752i	$0.379979\pi$
$908$	−125.282	−4.15763
$909$	5.19615	0.172345
$910$	50.7846	1.68349
$911$	21.0718	0.698140	0.349070	−	0.937097i	$-0.386498\pi$
$911$	21.0718	0.698140	0.349070	+	0.937097i	$0.386498\pi$
$912$	−48.7846	−1.61542
$913$	37.5167	1.24162
$914$	−27.5167	−0.910170
$915$	11.1244	0.367760
$916$	−127.426	−4.21026
$917$	56.7846	1.87519
$918$	6.19615	0.204504
$919$	6.14359	0.202658	0.101329	−	0.994853i	$-0.467690\pi$
$919$	6.14359	0.202658	0.101329	+	0.994853i	$0.467690\pi$
$920$	0	0
$921$	−13.8038	−0.454852
$922$	56.1051	1.84772
$923$	−23.1244	−0.761147
$924$	−44.7846	−1.47331
$925$	1.92820	0.0633989
$926$	−0.928203	−0.0305027
$927$	−15.8564	−0.520793
$928$	81.5692	2.67764
$929$	−21.9808	−0.721165	−0.360583	−	0.932727i	$-0.617422\pi$
$929$	−21.9808	−0.721165	−0.360583	+	0.932727i	$0.617422\pi$
$930$	27.1244	0.889443
$931$	6.53590	0.214205
$932$	−10.1436	−0.332264
$933$	12.0000	0.392862
$934$	−42.9808	−1.40637
$935$	−6.19615	−0.202636
$936$	−58.6410	−1.91674
$937$	60.4974	1.97636	0.988182	−	0.153283i	$-0.0489846\pi$
$937$	60.4974	1.97636	0.988182	+	0.153283i	$0.0489846\pi$
$938$	−52.9808	−1.72988
$939$	−7.92820	−0.258727
$940$	−41.8564	−1.36521
$941$	58.6936	1.91336	0.956678	−	0.291148i	$-0.0940373\pi$
$941$	58.6936	1.91336	0.956678	+	0.291148i	$0.0940373\pi$
$942$	0.196152	0.00639099
$943$	0	0
$944$	107.426	3.49641
$945$	3.00000	0.0975900
$946$	−85.5692	−2.78210
$947$	52.3923	1.70252	0.851261	−	0.524743i	$-0.175839\pi$
$947$	52.3923	1.70252	0.851261	+	0.524743i	$0.175839\pi$
$948$	37.8564	1.22952
$949$	−47.4641	−1.54075
$950$	−8.92820	−0.289669
$951$	−17.5167	−0.568017
$952$	−64.3923	−2.08697
$953$	−39.8564	−1.29108	−0.645538	−	0.763728i	$-0.723367\pi$
$953$	−39.8564	−1.29108	−0.645538	+	0.763728i	$0.723367\pi$
$954$	−15.6603	−0.507019
$955$	3.66025	0.118443
$956$	−93.1769	−3.01356
$957$	10.1962	0.329595
$958$	55.8564	1.80464
$959$	62.3538	2.01351
$960$	29.8564	0.963611
$961$	67.5692	2.17965
$962$	−32.6410	−1.05239
$963$	−6.12436	−0.197355
$964$	148.995	4.79880
$965$	−10.5359	−0.339163
$966$	0	0
$967$	16.1962	0.520833	0.260417	−	0.965496i	$-0.416140\pi$
$967$	16.1962	0.520833	0.260417	+	0.965496i	$0.416140\pi$
$968$	33.4641	1.07558
$969$	−7.41154	−0.238093
$970$	10.9282	0.350883
$971$	−9.46410	−0.303717	−0.151859	−	0.988402i	$-0.548526\pi$
$971$	−9.46410	−0.303717	−0.151859	+	0.988402i	$0.548526\pi$
$972$	−5.46410	−0.175261
$973$	15.0000	0.480878
$974$	26.3923	0.845664
$975$	−6.19615	−0.198436
$976$	166.067	5.31566
$977$	−8.12436	−0.259921	−0.129961	−	0.991519i	$-0.541485\pi$
$977$	−8.12436	−0.259921	−0.129961	+	0.991519i	$0.541485\pi$
$978$	38.2487	1.22306
$979$	−6.92820	−0.221426
$980$	−10.9282	−0.349089
$981$	−3.26795	−0.104338
$982$	−91.3731	−2.91583
$983$	−37.9808	−1.21140	−0.605699	−	0.795694i	$-0.707106\pi$
$983$	−37.9808	−1.21140	−0.605699	+	0.795694i	$0.707106\pi$
$984$	−35.3205	−1.12598
$985$	1.60770	0.0512254
$986$	23.1244	0.736430
$987$	−22.9808	−0.731486
$988$	110.641	3.51996
$989$	0	0
$990$	7.46410	0.237225
$991$	−25.0000	−0.794151	−0.397076	−	0.917786i	$-0.629975\pi$
$991$	−25.0000	−0.794151	−0.397076	+	0.917786i	$0.629975\pi$
$992$	216.995	6.88959
$993$	−20.3205	−0.644852
$994$	30.5885	0.970207
$995$	−11.4641	−0.363436
$996$	−75.0333	−2.37752
$997$	−50.5359	−1.60049	−0.800244	−	0.599675i	$-0.795297\pi$
$997$	−50.5359	−1.60049	−0.800244	+	0.599675i	$0.795297\pi$
$998$	−96.6936	−3.06078
$999$	−1.92820	−0.0610057

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.n.1.1		2
23.22	odd	2		345.2.a.g.1.1	✓	2
69.68	even	2		1035.2.a.l.1.2		2
92.91	even	2		5520.2.a.bu.1.2		2
115.22	even	4		1725.2.b.p.1174.1		4
115.68	even	4		1725.2.b.p.1174.4		4
115.114	odd	2		1725.2.a.bd.1.2		2
345.344	even	2		5175.2.a.bd.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.a.g.1.1	✓	2	23.22	odd	2
1035.2.a.l.1.2		2	69.68	even	2
1725.2.a.bd.1.2		2	115.114	odd	2
1725.2.b.p.1174.1		4	115.22	even	4
1725.2.b.p.1174.4		4	115.68	even	4
5175.2.a.bd.1.1		2	345.344	even	2
5520.2.a.bu.1.2		2	92.91	even	2
7935.2.a.n.1.1		2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q-2.73205 q^{2} -1.00000 q^{3} +5.46410 q^{4} -1.00000 q^{5} +2.73205 q^{6} +3.00000 q^{7} -9.46410 q^{8} +1.00000 q^{9} +2.73205 q^{10} +2.73205 q^{11} -5.46410 q^{12} +6.19615 q^{13} -8.19615 q^{14} +1.00000 q^{15} +14.9282 q^{16} +2.26795 q^{17} -2.73205 q^{18} +3.26795 q^{19} -5.46410 q^{20} -3.00000 q^{21} -7.46410 q^{22} +9.46410 q^{24} +1.00000 q^{25} -16.9282 q^{26} -1.00000 q^{27} +16.3923 q^{28} -3.73205 q^{29} -2.73205 q^{30} -9.92820 q^{31} -21.8564 q^{32} -2.73205 q^{33} -6.19615 q^{34} -3.00000 q^{35} +5.46410 q^{36} +1.92820 q^{37} -8.92820 q^{38} -6.19615 q^{39} +9.46410 q^{40} -3.73205 q^{41} +8.19615 q^{42} +11.4641 q^{43} +14.9282 q^{44} -1.00000 q^{45} +7.66025 q^{47} -14.9282 q^{48} +2.00000 q^{49} -2.73205 q^{50} -2.26795 q^{51} +33.8564 q^{52} +5.73205 q^{53} +2.73205 q^{54} -2.73205 q^{55} -28.3923 q^{56} -3.26795 q^{57} +10.1962 q^{58} +7.19615 q^{59} +5.46410 q^{60} +11.1244 q^{61} +27.1244 q^{62} +3.00000 q^{63} +29.8564 q^{64} -6.19615 q^{65} +7.46410 q^{66} +6.46410 q^{67} +12.3923 q^{68} +8.19615 q^{70} -3.73205 q^{71} -9.46410 q^{72} -7.66025 q^{73} -5.26795 q^{74} -1.00000 q^{75} +17.8564 q^{76} +8.19615 q^{77} +16.9282 q^{78} -6.92820 q^{79} -14.9282 q^{80} +1.00000 q^{81} +10.1962 q^{82} +13.7321 q^{83} -16.3923 q^{84} -2.26795 q^{85} -31.3205 q^{86} +3.73205 q^{87} -25.8564 q^{88} -2.53590 q^{89} +2.73205 q^{90} +18.5885 q^{91} +9.92820 q^{93} -20.9282 q^{94} -3.26795 q^{95} +21.8564 q^{96} +4.00000 q^{97} -5.46410 q^{98} +2.73205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} + 6 q^{7} - 12 q^{8} + 2 q^{9} + 2 q^{10} + 2 q^{11} - 4 q^{12} + 2 q^{13} - 6 q^{14} + 2 q^{15} + 16 q^{16} + 8 q^{17} - 2 q^{18} + 10 q^{19} - 4 q^{20}+ \cdots + 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 + 6 * q^7 - 12 * q^8 + 2 * q^9 + 2 * q^10 + 2 * q^11 - 4 * q^12 + 2 * q^13 - 6 * q^14 + 2 * q^15 + 16 * q^16 + 8 * q^17 - 2 * q^18 + 10 * q^19 - 4 * q^20 - 6 * q^21 - 8 * q^22 + 12 * q^24 + 2 * q^25 - 20 * q^26 - 2 * q^27 + 12 * q^28 - 4 * q^29 - 2 * q^30 - 6 * q^31 - 16 * q^32 - 2 * q^33 - 2 * q^34 - 6 * q^35 + 4 * q^36 - 10 * q^37 - 4 * q^38 - 2 * q^39 + 12 * q^40 - 4 * q^41 + 6 * q^42 + 16 * q^43 + 16 * q^44 - 2 * q^45 - 2 * q^47 - 16 * q^48 + 4 * q^49 - 2 * q^50 - 8 * q^51 + 40 * q^52 + 8 * q^53 + 2 * q^54 - 2 * q^55 - 36 * q^56 - 10 * q^57 + 10 * q^58 + 4 * q^59 + 4 * q^60 - 2 * q^61 + 30 * q^62 + 6 * q^63 + 32 * q^64 - 2 * q^65 + 8 * q^66 + 6 * q^67 + 4 * q^68 + 6 * q^70 - 4 * q^71 - 12 * q^72 + 2 * q^73 - 14 * q^74 - 2 * q^75 + 8 * q^76 + 6 * q^77 + 20 * q^78 - 16 * q^80 + 2 * q^81 + 10 * q^82 + 24 * q^83 - 12 * q^84 - 8 * q^85 - 28 * q^86 + 4 * q^87 - 24 * q^88 - 12 * q^89 + 2 * q^90 + 6 * q^91 + 6 * q^93 - 28 * q^94 - 10 * q^95 + 16 * q^96 + 8 * q^97 - 4 * q^98 + 2 * q^99

Introduction

L-functions

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