LMFDB - Embedded newform 7942.2.a.by.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7942,2,Mod(1,7942)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7942, 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("7942.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7942 = 2 \cdot 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7942.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:	$63.4171892853$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 3 x^{14} - 33 x^{13} + 101 x^{12} + 408 x^{11} - 1314 x^{10} - 2271 x^{9} + 8292 x^{8} + \cdots - 3592 $ x^15 - 3x^14 - 33x^13 + 101x^12 + 408x^11 - 1314x^10 - 2271x^9 + 8292x^8 + 4944x^7 - 26254x^6 + 1401x^5 + 39318x^4 - 19069x^3 - 20118x^2 + 18180x - 3592
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-1.52164$ of defining polynomial
Character	$\chi$	$=$	7942.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +1.52164 q^{3} +1.00000 q^{4} -2.93560 q^{5} -1.52164 q^{6} -0.464814 q^{7} -1.00000 q^{8} -0.684609 q^{9} +2.93560 q^{10} -1.00000 q^{11} +1.52164 q^{12} -4.49956 q^{13} +0.464814 q^{14} -4.46693 q^{15} +1.00000 q^{16} +0.188812 q^{17} +0.684609 q^{18} -2.93560 q^{20} -0.707279 q^{21} +1.00000 q^{22} +2.91060 q^{23} -1.52164 q^{24} +3.61774 q^{25} +4.49956 q^{26} -5.60665 q^{27} -0.464814 q^{28} -1.72567 q^{29} +4.46693 q^{30} +1.87404 q^{31} -1.00000 q^{32} -1.52164 q^{33} -0.188812 q^{34} +1.36451 q^{35} -0.684609 q^{36} +6.48294 q^{37} -6.84672 q^{39} +2.93560 q^{40} +3.30129 q^{41} +0.707279 q^{42} -10.7036 q^{43} -1.00000 q^{44} +2.00974 q^{45} -2.91060 q^{46} -4.02946 q^{47} +1.52164 q^{48} -6.78395 q^{49} -3.61774 q^{50} +0.287304 q^{51} -4.49956 q^{52} +1.35935 q^{53} +5.60665 q^{54} +2.93560 q^{55} +0.464814 q^{56} +1.72567 q^{58} +5.50657 q^{59} -4.46693 q^{60} -10.9663 q^{61} -1.87404 q^{62} +0.318216 q^{63} +1.00000 q^{64} +13.2089 q^{65} +1.52164 q^{66} -5.56717 q^{67} +0.188812 q^{68} +4.42889 q^{69} -1.36451 q^{70} -3.98279 q^{71} +0.684609 q^{72} +10.9027 q^{73} -6.48294 q^{74} +5.50491 q^{75} +0.464814 q^{77} +6.84672 q^{78} -5.54536 q^{79} -2.93560 q^{80} -6.47748 q^{81} -3.30129 q^{82} -12.8465 q^{83} -0.707279 q^{84} -0.554277 q^{85} +10.7036 q^{86} -2.62586 q^{87} +1.00000 q^{88} -16.9412 q^{89} -2.00974 q^{90} +2.09146 q^{91} +2.91060 q^{92} +2.85161 q^{93} +4.02946 q^{94} -1.52164 q^{96} +12.1485 q^{97} +6.78395 q^{98} +0.684609 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{2} - 3 q^{3} + 15 q^{4} + 9 q^{5} + 3 q^{6} - 15 q^{8} + 30 q^{9} - 9 q^{10} - 15 q^{11} - 3 q^{12} - 21 q^{15} + 15 q^{16} + 21 q^{17} - 30 q^{18} + 9 q^{20} + 9 q^{21} + 15 q^{22} + 21 q^{23}+ \cdots - 30 q^{99}+O(q^{100}) $ 15 * q - 15 * q^2 - 3 * q^3 + 15 * q^4 + 9 * q^5 + 3 * q^6 - 15 * q^8 + 30 * q^9 - 9 * q^10 - 15 * q^11 - 3 * q^12 - 21 * q^15 + 15 * q^16 + 21 * q^17 - 30 * q^18 + 9 * q^20 + 9 * q^21 + 15 * q^22 + 21 * q^23 + 3 * q^24 + 24 * q^25 - 3 * q^27 + 9 * q^29 + 21 * q^30 - 18 * q^31 - 15 * q^32 + 3 * q^33 - 21 * q^34 + 18 * q^35 + 30 * q^36 + 9 * q^37 - 9 * q^40 - 15 * q^41 - 9 * q^42 + 3 * q^43 - 15 * q^44 + 54 * q^45 - 21 * q^46 + 39 * q^47 - 3 * q^48 + 33 * q^49 - 24 * q^50 - 30 * q^51 - 18 * q^53 + 3 * q^54 - 9 * q^55 - 9 * q^58 - 6 * q^59 - 21 * q^60 - 30 * q^61 + 18 * q^62 + 24 * q^63 + 15 * q^64 - 6 * q^65 - 3 * q^66 - 9 * q^67 + 21 * q^68 + 42 * q^69 - 18 * q^70 - 9 * q^71 - 30 * q^72 + 12 * q^73 - 9 * q^74 - 21 * q^75 - 12 * q^79 + 9 * q^80 + 63 * q^81 + 15 * q^82 + 30 * q^83 + 9 * q^84 - 3 * q^85 - 3 * q^86 + 9 * q^87 + 15 * q^88 + 6 * q^89 - 54 * q^90 - 96 * q^91 + 21 * q^92 + 102 * q^93 - 39 * q^94 + 3 * q^96 - 33 * q^98 - 30 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.52164	0.878520	0.439260	−	0.898360i	$-0.355241\pi$
$3$	1.52164	0.878520	0.439260	+	0.898360i	$0.355241\pi$
$4$	1.00000	0.500000
$5$	−2.93560	−1.31284	−0.656420	−	0.754396i	$-0.727930\pi$
$5$	−2.93560	−1.31284	−0.656420	+	0.754396i	$0.727930\pi$
$6$	−1.52164	−0.621207
$7$	−0.464814	−0.175683	−0.0878415	−	0.996134i	$-0.527997\pi$
$7$	−0.464814	−0.175683	−0.0878415	+	0.996134i	$0.527997\pi$
$8$	−1.00000	−0.353553
$9$	−0.684609	−0.228203
$10$	2.93560	0.928318
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.52164	0.439260
$13$	−4.49956	−1.24795	−0.623977	−	0.781443i	$-0.714484\pi$
$13$	−4.49956	−1.24795	−0.623977	+	0.781443i	$0.714484\pi$
$14$	0.464814	0.124227
$15$	−4.46693	−1.15336
$16$	1.00000	0.250000
$17$	0.188812	0.0457937	0.0228969	−	0.999738i	$-0.492711\pi$
$17$	0.188812	0.0457937	0.0228969	+	0.999738i	$0.492711\pi$
$18$	0.684609	0.161364
$19$	0	0
$19$	0	0
$20$	−2.93560	−0.656420
$21$	−0.707279	−0.154341
$22$	1.00000	0.213201
$23$	2.91060	0.606903	0.303451	−	0.952847i	$-0.401861\pi$
$23$	2.91060	0.606903	0.303451	+	0.952847i	$0.401861\pi$
$24$	−1.52164	−0.310604
$25$	3.61774	0.723549
$26$	4.49956	0.882437
$27$	−5.60665	−1.07900
$28$	−0.464814	−0.0878415
$29$	−1.72567	−0.320450	−0.160225	−	0.987081i	$-0.551222\pi$
$29$	−1.72567	−0.320450	−0.160225	+	0.987081i	$0.551222\pi$
$30$	4.46693	0.815546
$31$	1.87404	0.336587	0.168293	−	0.985737i	$-0.446174\pi$
$31$	1.87404	0.336587	0.168293	+	0.985737i	$0.446174\pi$
$32$	−1.00000	−0.176777
$33$	−1.52164	−0.264884
$34$	−0.188812	−0.0323810
$35$	1.36451	0.230644
$36$	−0.684609	−0.114102
$37$	6.48294	1.06579	0.532894	−	0.846182i	$-0.321104\pi$
$37$	6.48294	1.06579	0.532894	+	0.846182i	$0.321104\pi$
$38$	0	0
$39$	−6.84672	−1.09635
$40$	2.93560	0.464159
$41$	3.30129	0.515575	0.257788	−	0.966202i	$-0.417007\pi$
$41$	3.30129	0.515575	0.257788	+	0.966202i	$0.417007\pi$
$42$	0.707279	0.109136
$43$	−10.7036	−1.63229	−0.816145	−	0.577847i	$-0.803893\pi$
$43$	−10.7036	−1.63229	−0.816145	+	0.577847i	$0.803893\pi$
$44$	−1.00000	−0.150756
$45$	2.00974	0.299594
$46$	−2.91060	−0.429145
$47$	−4.02946	−0.587757	−0.293878	−	0.955843i	$-0.594946\pi$
$47$	−4.02946	−0.587757	−0.293878	+	0.955843i	$0.594946\pi$
$48$	1.52164	0.219630
$49$	−6.78395	−0.969135
$50$	−3.61774	−0.511626
$51$	0.287304	0.0402307
$52$	−4.49956	−0.623977
$53$	1.35935	0.186721	0.0933605	−	0.995632i	$-0.470239\pi$
$53$	1.35935	0.186721	0.0933605	+	0.995632i	$0.470239\pi$
$54$	5.60665	0.762969
$55$	2.93560	0.395836
$56$	0.464814	0.0621133
$57$	0	0
$58$	1.72567	0.226592
$59$	5.50657	0.716895	0.358447	−	0.933550i	$-0.383306\pi$
$59$	5.50657	0.716895	0.358447	+	0.933550i	$0.383306\pi$
$60$	−4.46693	−0.576678
$61$	−10.9663	−1.40409	−0.702046	−	0.712132i	$-0.747730\pi$
$61$	−10.9663	−1.40409	−0.702046	+	0.712132i	$0.747730\pi$
$62$	−1.87404	−0.238003
$63$	0.318216	0.0400914
$64$	1.00000	0.125000
$65$	13.2089	1.63836
$66$	1.52164	0.187301
$67$	−5.56717	−0.680138	−0.340069	−	0.940400i	$-0.610450\pi$
$67$	−5.56717	−0.680138	−0.340069	+	0.940400i	$0.610450\pi$
$68$	0.188812	0.0228969
$69$	4.42889	0.533176
$70$	−1.36451	−0.163090
$71$	−3.98279	−0.472670	−0.236335	−	0.971672i	$-0.575946\pi$
$71$	−3.98279	−0.472670	−0.236335	+	0.971672i	$0.575946\pi$
$72$	0.684609	0.0806820
$73$	10.9027	1.27607	0.638033	−	0.770009i	$-0.279748\pi$
$73$	10.9027	1.27607	0.638033	+	0.770009i	$0.279748\pi$
$74$	−6.48294	−0.753626
$75$	5.50491	0.635652
$76$	0	0
$77$	0.464814	0.0529704
$78$	6.84672	0.775238
$79$	−5.54536	−0.623902	−0.311951	−	0.950098i	$-0.600982\pi$
$79$	−5.54536	−0.623902	−0.311951	+	0.950098i	$0.600982\pi$
$80$	−2.93560	−0.328210
$81$	−6.47748	−0.719720
$82$	−3.30129	−0.364567
$83$	−12.8465	−1.41009	−0.705043	−	0.709164i	$-0.749073\pi$
$83$	−12.8465	−1.41009	−0.705043	+	0.709164i	$0.749073\pi$
$84$	−0.707279	−0.0771705
$85$	−0.554277	−0.0601198
$86$	10.7036	1.15420
$87$	−2.62586	−0.281521
$88$	1.00000	0.106600
$89$	−16.9412	−1.79577	−0.897884	−	0.440232i	$-0.854896\pi$
$89$	−16.9412	−1.79577	−0.897884	+	0.440232i	$0.854896\pi$
$90$	−2.00974	−0.211845
$91$	2.09146	0.219244
$92$	2.91060	0.303451
$93$	2.85161	0.295698
$94$	4.02946	0.415607
$95$	0	0
$96$	−1.52164	−0.155302
$97$	12.1485	1.23350	0.616748	−	0.787161i	$-0.288450\pi$
$97$	12.1485	1.23350	0.616748	+	0.787161i	$0.288450\pi$
$98$	6.78395	0.685282
$99$	0.684609	0.0688058
$100$	3.61774	0.361774
$101$	8.90820	0.886399	0.443200	−	0.896423i	$-0.353843\pi$
$101$	8.90820	0.886399	0.443200	+	0.896423i	$0.353843\pi$
$102$	−0.287304	−0.0284474
$103$	−1.74670	−0.172108	−0.0860539	−	0.996290i	$-0.527426\pi$
$103$	−1.74670	−0.172108	−0.0860539	+	0.996290i	$0.527426\pi$
$104$	4.49956	0.441218
$105$	2.07629	0.202625
$106$	−1.35935	−0.132032
$107$	0.0663443	0.00641374	0.00320687	−	0.999995i	$-0.498979\pi$
$107$	0.0663443	0.00641374	0.00320687	+	0.999995i	$0.498979\pi$
$108$	−5.60665	−0.539500
$109$	−3.81573	−0.365481	−0.182741	−	0.983161i	$-0.558497\pi$
$109$	−3.81573	−0.365481	−0.182741	+	0.983161i	$0.558497\pi$
$110$	−2.93560	−0.279898
$111$	9.86470	0.936316
$112$	−0.464814	−0.0439208
$113$	0.0177717	0.00167182	0.000835908	−	1.00000i	$-0.499734\pi$
$113$	0.0177717	0.00167182	0.000835908		1.00000i	$0.499734\pi$
$114$	0	0
$115$	−8.54437	−0.796766
$116$	−1.72567	−0.160225
$117$	3.08044	0.284787
$118$	−5.50657	−0.506921
$119$	−0.0877625	−0.00804518
$120$	4.46693	0.407773
$121$	1.00000	0.0909091
$122$	10.9663	0.992842
$123$	5.02338	0.452943
$124$	1.87404	0.168293
$125$	4.05775	0.362936
$126$	−0.318216	−0.0283489
$127$	−7.69028	−0.682402	−0.341201	−	0.939990i	$-0.610834\pi$
$127$	−7.69028	−0.682402	−0.341201	+	0.939990i	$0.610834\pi$
$128$	−1.00000	−0.0883883
$129$	−16.2871	−1.43400
$130$	−13.2089	−1.15850
$131$	22.1186	1.93251	0.966257	−	0.257578i	$-0.0829246\pi$
$131$	22.1186	1.93251	0.966257	+	0.257578i	$0.0829246\pi$
$132$	−1.52164	−0.132442
$133$	0	0
$134$	5.56717	0.480930
$135$	16.4589	1.41656
$136$	−0.188812	−0.0161905
$137$	3.98966	0.340860	0.170430	−	0.985370i	$-0.445484\pi$
$137$	3.98966	0.340860	0.170430	+	0.985370i	$0.445484\pi$
$138$	−4.42889	−0.377013
$139$	1.48693	0.126120	0.0630598	−	0.998010i	$-0.479914\pi$
$139$	1.48693	0.126120	0.0630598	+	0.998010i	$0.479914\pi$
$140$	1.36451	0.115322
$141$	−6.13139	−0.516356
$142$	3.98279	0.334228
$143$	4.49956	0.376272
$144$	−0.684609	−0.0570508
$145$	5.06589	0.420699
$146$	−10.9027	−0.902315
$147$	−10.3227	−0.851405
$148$	6.48294	0.532894
$149$	8.10477	0.663969	0.331984	−	0.943285i	$-0.392282\pi$
$149$	8.10477	0.663969	0.331984	+	0.943285i	$0.392282\pi$
$150$	−5.50491	−0.449474
$151$	16.0446	1.30569	0.652846	−	0.757490i	$-0.273575\pi$
$151$	16.0446	1.30569	0.652846	+	0.757490i	$0.273575\pi$
$152$	0	0
$153$	−0.129263	−0.0104503
$154$	−0.464814	−0.0374557
$155$	−5.50142	−0.441885
$156$	−6.84672	−0.548176
$157$	18.1493	1.44847	0.724234	−	0.689554i	$-0.242194\pi$
$157$	18.1493	1.44847	0.724234	+	0.689554i	$0.242194\pi$
$158$	5.54536	0.441165
$159$	2.06844	0.164038
$160$	2.93560	0.232080
$161$	−1.35289	−0.106623
$162$	6.47748	0.508919
$163$	21.3870	1.67516	0.837579	−	0.546316i	$-0.183970\pi$
$163$	21.3870	1.67516	0.837579	+	0.546316i	$0.183970\pi$
$164$	3.30129	0.257788
$165$	4.46693	0.347750
$166$	12.8465	0.997082
$167$	−11.0690	−0.856548	−0.428274	−	0.903649i	$-0.640878\pi$
$167$	−11.0690	−0.856548	−0.428274	+	0.903649i	$0.640878\pi$
$168$	0.707279	0.0545678
$169$	7.24605	0.557389
$170$	0.554277	0.0425111
$171$	0	0
$172$	−10.7036	−0.816145
$173$	8.71135	0.662311	0.331156	−	0.943576i	$-0.392561\pi$
$173$	8.71135	0.662311	0.331156	+	0.943576i	$0.392561\pi$
$174$	2.62586	0.199066
$175$	−1.68158	−0.127115
$176$	−1.00000	−0.0753778
$177$	8.37903	0.629806
$178$	16.9412	1.26980
$179$	9.62721	0.719572	0.359786	−	0.933035i	$-0.382850\pi$
$179$	9.62721	0.719572	0.359786	+	0.933035i	$0.382850\pi$
$180$	2.00974	0.149797
$181$	−17.8108	−1.32387	−0.661935	−	0.749561i	$-0.730264\pi$
$181$	−17.8108	−1.32387	−0.661935	+	0.749561i	$0.730264\pi$
$182$	−2.09146	−0.155029
$183$	−16.6868	−1.23352
$184$	−2.91060	−0.214573
$185$	−19.0313	−1.39921
$186$	−2.85161	−0.209090
$187$	−0.188812	−0.0138073
$188$	−4.02946	−0.293878
$189$	2.60605	0.189562
$190$	0	0
$191$	25.2728	1.82868	0.914338	−	0.404952i	$-0.132712\pi$
$191$	25.2728	1.82868	0.914338	+	0.404952i	$0.132712\pi$
$192$	1.52164	0.109815
$193$	−16.7371	−1.20476	−0.602381	−	0.798209i	$-0.705781\pi$
$193$	−16.7371	−1.20476	−0.602381	+	0.798209i	$0.705781\pi$
$194$	−12.1485	−0.872214
$195$	20.0992	1.43933
$196$	−6.78395	−0.484568
$197$	8.52528	0.607401	0.303700	−	0.952768i	$-0.401778\pi$
$197$	8.52528	0.607401	0.303700	+	0.952768i	$0.401778\pi$
$198$	−0.684609	−0.0486531
$199$	21.7367	1.54087	0.770435	−	0.637518i	$-0.220039\pi$
$199$	21.7367	1.54087	0.770435	+	0.637518i	$0.220039\pi$
$200$	−3.61774	−0.255813
$201$	−8.47123	−0.597515
$202$	−8.90820	−0.626779
$203$	0.802117	0.0562976
$204$	0.287304	0.0201153
$205$	−9.69127	−0.676868
$206$	1.74670	0.121699
$207$	−1.99263	−0.138497
$208$	−4.49956	−0.311988
$209$	0	0
$210$	−2.07629	−0.143278
$211$	−8.82448	−0.607503	−0.303751	−	0.952751i	$-0.598239\pi$
$211$	−8.82448	−0.607503	−0.303751	+	0.952751i	$0.598239\pi$
$212$	1.35935	0.0933605
$213$	−6.06037	−0.415250
$214$	−0.0663443	−0.00453520
$215$	31.4216	2.14293
$216$	5.60665	0.381484
$217$	−0.871078	−0.0591326
$218$	3.81573	0.258434
$219$	16.5900	1.12105
$220$	2.93560	0.197918
$221$	−0.849573	−0.0571484
$222$	−9.86470	−0.662076
$223$	−6.40530	−0.428931	−0.214465	−	0.976732i	$-0.568801\pi$
$223$	−6.40530	−0.428931	−0.214465	+	0.976732i	$0.568801\pi$
$224$	0.464814	0.0310567
$225$	−2.47674	−0.165116
$226$	−0.0177717	−0.00118215
$227$	13.8824	0.921409	0.460705	−	0.887554i	$-0.347597\pi$
$227$	13.8824	0.921409	0.460705	+	0.887554i	$0.347597\pi$
$228$	0	0
$229$	−6.38691	−0.422059	−0.211030	−	0.977480i	$-0.567682\pi$
$229$	−6.38691	−0.422059	−0.211030	+	0.977480i	$0.567682\pi$
$230$	8.54437	0.563399
$231$	0.707279	0.0465356
$232$	1.72567	0.113296
$233$	−5.19556	−0.340372	−0.170186	−	0.985412i	$-0.554437\pi$
$233$	−5.19556	−0.340372	−0.170186	+	0.985412i	$0.554437\pi$
$234$	−3.08044	−0.201375
$235$	11.8289	0.771631
$236$	5.50657	0.358447
$237$	−8.43804	−0.548110
$238$	0.0877625	0.00568880
$239$	−8.20845	−0.530960	−0.265480	−	0.964116i	$-0.585530\pi$
$239$	−8.20845	−0.530960	−0.265480	+	0.964116i	$0.585530\pi$
$240$	−4.46693	−0.288339
$241$	17.8978	1.15290	0.576448	−	0.817134i	$-0.304438\pi$
$241$	17.8978	1.15290	0.576448	+	0.817134i	$0.304438\pi$
$242$	−1.00000	−0.0642824
$243$	6.96355	0.446712
$244$	−10.9663	−0.702046
$245$	19.9150	1.27232
$246$	−5.02338	−0.320279
$247$	0	0
$248$	−1.87404	−0.119001
$249$	−19.5478	−1.23879
$250$	−4.05775	−0.256635
$251$	11.9474	0.754111	0.377056	−	0.926191i	$-0.376937\pi$
$251$	11.9474	0.754111	0.377056	+	0.926191i	$0.376937\pi$
$252$	0.318216	0.0200457
$253$	−2.91060	−0.182988
$254$	7.69028	0.482531
$255$	−0.843411	−0.0528164
$256$	1.00000	0.0625000
$257$	−4.07347	−0.254096	−0.127048	−	0.991897i	$-0.540550\pi$
$257$	−4.07347	−0.254096	−0.127048	+	0.991897i	$0.540550\pi$
$258$	16.2871	1.01399
$259$	−3.01336	−0.187241
$260$	13.2089	0.819182
$261$	1.18141	0.0731276
$262$	−22.1186	−1.36649
$263$	7.22171	0.445310	0.222655	−	0.974897i	$-0.428528\pi$
$263$	7.22171	0.445310	0.222655	+	0.974897i	$0.428528\pi$
$264$	1.52164	0.0936505
$265$	−3.99050	−0.245135
$266$	0	0
$267$	−25.7785	−1.57762
$268$	−5.56717	−0.340069
$269$	31.8344	1.94098	0.970488	−	0.241149i	$-0.0775241\pi$
$269$	31.8344	1.94098	0.970488	+	0.241149i	$0.0775241\pi$
$270$	−16.4589	−1.00166
$271$	−31.2403	−1.89771	−0.948857	−	0.315706i	$-0.897759\pi$
$271$	−31.2403	−1.89771	−0.948857	+	0.315706i	$0.897759\pi$
$272$	0.188812	0.0114484
$273$	3.18245	0.192610
$274$	−3.98966	−0.241024
$275$	−3.61774	−0.218158
$276$	4.42889	0.266588
$277$	12.3578	0.742506	0.371253	−	0.928532i	$-0.378928\pi$
$277$	12.3578	0.742506	0.371253	+	0.928532i	$0.378928\pi$
$278$	−1.48693	−0.0891800
$279$	−1.28298	−0.0768102
$280$	−1.36451	−0.0815449
$281$	6.73851	0.401986	0.200993	−	0.979593i	$-0.435583\pi$
$281$	6.73851	0.401986	0.200993	+	0.979593i	$0.435583\pi$
$282$	6.13139	0.365119
$283$	3.67917	0.218704	0.109352	−	0.994003i	$-0.465122\pi$
$283$	3.67917	0.218704	0.109352	+	0.994003i	$0.465122\pi$
$284$	−3.98279	−0.236335
$285$	0	0
$286$	−4.49956	−0.266065
$287$	−1.53449	−0.0905778
$288$	0.684609	0.0403410
$289$	−16.9643	−0.997903
$290$	−5.06589	−0.297479
$291$	18.4857	1.08365
$292$	10.9027	0.638033
$293$	−2.79512	−0.163293	−0.0816464	−	0.996661i	$-0.526018\pi$
$293$	−2.79512	−0.163293	−0.0816464	+	0.996661i	$0.526018\pi$
$294$	10.3227	0.602034
$295$	−16.1651	−0.941168
$296$	−6.48294	−0.376813
$297$	5.60665	0.325331
$298$	−8.10477	−0.469497
$299$	−13.0964	−0.757387
$300$	5.50491	0.317826
$301$	4.97520	0.286766
$302$	−16.0446	−0.923264
$303$	13.5551	0.778719
$304$	0	0
$305$	32.1927	1.84335
$306$	0.129263	0.00738945
$307$	−11.8371	−0.675581	−0.337790	−	0.941221i	$-0.609679\pi$
$307$	−11.8371	−0.675581	−0.337790	+	0.941221i	$0.609679\pi$
$308$	0.464814	0.0264852
$309$	−2.65786	−0.151200
$310$	5.50142	0.312460
$311$	15.9983	0.907180	0.453590	−	0.891210i	$-0.350143\pi$
$311$	15.9983	0.907180	0.453590	+	0.891210i	$0.350143\pi$
$312$	6.84672	0.387619
$313$	−17.4536	−0.986539	−0.493269	−	0.869877i	$-0.664198\pi$
$313$	−17.4536	−0.986539	−0.493269	+	0.869877i	$0.664198\pi$
$314$	−18.1493	−1.02422
$315$	−0.934154	−0.0526336
$316$	−5.54536	−0.311951
$317$	22.7519	1.27787	0.638936	−	0.769260i	$-0.279375\pi$
$317$	22.7519	1.27787	0.638936	+	0.769260i	$0.279375\pi$
$318$	−2.06844	−0.115992
$319$	1.72567	0.0966192
$320$	−2.93560	−0.164105
$321$	0.100952	0.00563460
$322$	1.35289	0.0753935
$323$	0	0
$324$	−6.47748	−0.359860
$325$	−16.2783	−0.902955
$326$	−21.3870	−1.18452
$327$	−5.80618	−0.321082
$328$	−3.30129	−0.182283
$329$	1.87295	0.103259
$330$	−4.46693	−0.245896
$331$	9.94526	0.546641	0.273320	−	0.961923i	$-0.411878\pi$
$331$	9.94526	0.546641	0.273320	+	0.961923i	$0.411878\pi$
$332$	−12.8465	−0.705043
$333$	−4.43828	−0.243216
$334$	11.0690	0.605671
$335$	16.3430	0.892912
$336$	−0.707279	−0.0385853
$337$	27.0670	1.47443	0.737216	−	0.675658i	$-0.236140\pi$
$337$	27.0670	1.47443	0.737216	+	0.675658i	$0.236140\pi$
$338$	−7.24605	−0.394133
$339$	0.0270421	0.00146872
$340$	−0.554277	−0.0300599
$341$	−1.87404	−0.101485
$342$	0	0
$343$	6.40697	0.345944
$344$	10.7036	0.577102
$345$	−13.0015	−0.699975
$346$	−8.71135	−0.468325
$347$	19.4414	1.04367	0.521834	−	0.853047i	$-0.325248\pi$
$347$	19.4414	1.04367	0.521834	+	0.853047i	$0.325248\pi$
$348$	−2.62586	−0.140761
$349$	22.6056	1.21005	0.605025	−	0.796206i	$-0.293163\pi$
$349$	22.6056	1.21005	0.605025	+	0.796206i	$0.293163\pi$
$350$	1.68158	0.0898840
$351$	25.2275	1.34654
$352$	1.00000	0.0533002
$353$	24.0961	1.28251	0.641254	−	0.767328i	$-0.278414\pi$
$353$	24.0961	1.28251	0.641254	+	0.767328i	$0.278414\pi$
$354$	−8.37903	−0.445340
$355$	11.6919	0.620540
$356$	−16.9412	−0.897884
$357$	−0.133543	−0.00706785
$358$	−9.62721	−0.508814
$359$	25.6187	1.35210	0.676052	−	0.736854i	$-0.263689\pi$
$359$	25.6187	1.35210	0.676052	+	0.736854i	$0.263689\pi$
$360$	−2.00974	−0.105923
$361$	0	0
$362$	17.8108	0.936117
$363$	1.52164	0.0798654
$364$	2.09146	0.109622
$365$	−32.0060	−1.67527
$366$	16.6868	0.872232
$367$	−1.01974	−0.0532300	−0.0266150	−	0.999646i	$-0.508473\pi$
$367$	−1.01974	−0.0532300	−0.0266150	+	0.999646i	$0.508473\pi$
$368$	2.91060	0.151726
$369$	−2.26010	−0.117656
$370$	19.0313	0.989391
$371$	−0.631844	−0.0328037
$372$	2.85161	0.147849
$373$	31.7363	1.64325	0.821623	−	0.570031i	$-0.193069\pi$
$373$	31.7363	1.64325	0.821623	+	0.570031i	$0.193069\pi$
$374$	0.188812	0.00976325
$375$	6.17444	0.318847
$376$	4.02946	0.207803
$377$	7.76478	0.399906
$378$	−2.60605	−0.134041
$379$	19.0665	0.979382	0.489691	−	0.871896i	$-0.337110\pi$
$379$	19.0665	0.979382	0.489691	+	0.871896i	$0.337110\pi$
$380$	0	0
$381$	−11.7018	−0.599504
$382$	−25.2728	−1.29307
$383$	18.1444	0.927137	0.463568	−	0.886061i	$-0.346569\pi$
$383$	18.1444	0.927137	0.463568	+	0.886061i	$0.346569\pi$
$384$	−1.52164	−0.0776509
$385$	−1.36451	−0.0695417
$386$	16.7371	0.851895
$387$	7.32781	0.372494
$388$	12.1485	0.616748
$389$	3.88312	0.196882	0.0984411	−	0.995143i	$-0.468614\pi$
$389$	3.88312	0.196882	0.0984411	+	0.995143i	$0.468614\pi$
$390$	−20.0992	−1.01776
$391$	0.549558	0.0277923
$392$	6.78395	0.342641
$393$	33.6566	1.69775
$394$	−8.52528	−0.429497
$395$	16.2790	0.819083
$396$	0.684609	0.0344029
$397$	17.8589	0.896311	0.448155	−	0.893956i	$-0.352081\pi$
$397$	17.8589	0.896311	0.448155	+	0.893956i	$0.352081\pi$
$398$	−21.7367	−1.08956
$399$	0	0
$400$	3.61774	0.180887
$401$	−33.5041	−1.67311	−0.836557	−	0.547880i	$-0.815435\pi$
$401$	−33.5041	−1.67311	−0.836557	+	0.547880i	$0.815435\pi$
$402$	8.47123	0.422507
$403$	−8.43234	−0.420045
$404$	8.90820	0.443200
$405$	19.0153	0.944877
$406$	−0.802117	−0.0398084
$407$	−6.48294	−0.321347
$408$	−0.287304	−0.0142237
$409$	−26.3286	−1.30186	−0.650932	−	0.759136i	$-0.725622\pi$
$409$	−26.3286	−1.30186	−0.650932	+	0.759136i	$0.725622\pi$
$410$	9.69127	0.478618
$411$	6.07083	0.299452
$412$	−1.74670	−0.0860539
$413$	−2.55953	−0.125946
$414$	1.99263	0.0979323
$415$	37.7122	1.85122
$416$	4.49956	0.220609
$417$	2.26257	0.110799
$418$	0	0
$419$	−32.1866	−1.57242	−0.786209	−	0.617961i	$-0.787959\pi$
$419$	−32.1866	−1.57242	−0.786209	+	0.617961i	$0.787959\pi$
$420$	2.07629	0.101313
$421$	−20.0204	−0.975733	−0.487867	−	0.872918i	$-0.662225\pi$
$421$	−20.0204	−0.975733	−0.487867	+	0.872918i	$0.662225\pi$
$422$	8.82448	0.429569
$423$	2.75860	0.134128
$424$	−1.35935	−0.0660158
$425$	0.683074	0.0331340
$426$	6.06037	0.293626
$427$	5.09729	0.246675
$428$	0.0663443	0.00320687
$429$	6.84672	0.330563
$430$	−31.4216	−1.51528
$431$	−29.2413	−1.40850	−0.704252	−	0.709950i	$-0.748717\pi$
$431$	−29.2413	−1.40850	−0.704252	+	0.709950i	$0.748717\pi$
$432$	−5.60665	−0.269750
$433$	−21.8706	−1.05103	−0.525516	−	0.850784i	$-0.676128\pi$
$433$	−21.8706	−1.05103	−0.525516	+	0.850784i	$0.676128\pi$
$434$	0.871078	0.0418131
$435$	7.70846	0.369593
$436$	−3.81573	−0.182741
$437$	0	0
$438$	−16.5900	−0.792702
$439$	−25.8255	−1.23258	−0.616291	−	0.787518i	$-0.711366\pi$
$439$	−25.8255	−1.23258	−0.616291	+	0.787518i	$0.711366\pi$
$440$	−2.93560	−0.139949
$441$	4.64435	0.221160
$442$	0.849573	0.0404100
$443$	7.15530	0.339958	0.169979	−	0.985448i	$-0.445630\pi$
$443$	7.15530	0.339958	0.169979	+	0.985448i	$0.445630\pi$
$444$	9.86470	0.468158
$445$	49.7327	2.35756
$446$	6.40530	0.303300
$447$	12.3326	0.583310
$448$	−0.464814	−0.0219604
$449$	−14.0318	−0.662202	−0.331101	−	0.943595i	$-0.607420\pi$
$449$	−14.0318	−0.662202	−0.331101	+	0.943595i	$0.607420\pi$
$450$	2.47674	0.116755
$451$	−3.30129	−0.155452
$452$	0.0177717	0.000835908 0
$453$	24.4141	1.14708
$454$	−13.8824	−0.651535
$455$	−6.13968	−0.287833
$456$	0	0
$457$	−31.3113	−1.46468	−0.732340	−	0.680940i	$-0.761572\pi$
$457$	−31.3113	−1.46468	−0.732340	+	0.680940i	$0.761572\pi$
$458$	6.38691	0.298441
$459$	−1.05860	−0.0494114
$460$	−8.54437	−0.398383
$461$	12.2299	0.569603	0.284802	−	0.958586i	$-0.408072\pi$
$461$	12.2299	0.569603	0.284802	+	0.958586i	$0.408072\pi$
$462$	−0.707279	−0.0329056
$463$	−23.2772	−1.08178	−0.540892	−	0.841092i	$-0.681913\pi$
$463$	−23.2772	−1.08178	−0.540892	+	0.841092i	$0.681913\pi$
$464$	−1.72567	−0.0801124
$465$	−8.37119	−0.388205
$466$	5.19556	0.240680
$467$	17.2913	0.800146	0.400073	−	0.916483i	$-0.368985\pi$
$467$	17.2913	0.800146	0.400073	+	0.916483i	$0.368985\pi$
$468$	3.08044	0.142393
$469$	2.58770	0.119489
$470$	−11.8289	−0.545625
$471$	27.6166	1.27251
$472$	−5.50657	−0.253461
$473$	10.7036	0.492154
$474$	8.43804	0.387572
$475$	0	0
$476$	−0.0877625	−0.00402259
$477$	−0.930623	−0.0426103
$478$	8.20845	0.375446
$479$	−13.2757	−0.606584	−0.303292	−	0.952898i	$-0.598086\pi$
$479$	−13.2757	−0.606584	−0.303292	+	0.952898i	$0.598086\pi$
$480$	4.46693	0.203886
$481$	−29.1704	−1.33005
$482$	−17.8978	−0.815221
$483$	−2.05861	−0.0936700
$484$	1.00000	0.0454545
$485$	−35.6632	−1.61938
$486$	−6.96355	−0.315873
$487$	27.2081	1.23292	0.616459	−	0.787387i	$-0.288566\pi$
$487$	27.2081	1.23292	0.616459	+	0.787387i	$0.288566\pi$
$488$	10.9663	0.496421
$489$	32.5433	1.47166
$490$	−19.9150	−0.899666
$491$	35.5134	1.60270	0.801348	−	0.598198i	$-0.204116\pi$
$491$	35.5134	1.60270	0.801348	+	0.598198i	$0.204116\pi$
$492$	5.02338	0.226471
$493$	−0.325829	−0.0146746
$494$	0	0
$495$	−2.00974	−0.0903310
$496$	1.87404	0.0841467
$497$	1.85125	0.0830401
$498$	19.5478	0.875956
$499$	−9.33762	−0.418009	−0.209005	−	0.977915i	$-0.567022\pi$
$499$	−9.33762	−0.418009	−0.209005	+	0.977915i	$0.567022\pi$
$500$	4.05775	0.181468
$501$	−16.8431	−0.752495
$502$	−11.9474	−0.533237
$503$	14.2368	0.634787	0.317393	−	0.948294i	$-0.397192\pi$
$503$	14.2368	0.634787	0.317393	+	0.948294i	$0.397192\pi$
$504$	−0.318216	−0.0141745
$505$	−26.1509	−1.16370
$506$	2.91060	0.129392
$507$	11.0259	0.489677
$508$	−7.69028	−0.341201
$509$	−20.5706	−0.911778	−0.455889	−	0.890037i	$-0.650679\pi$
$509$	−20.5706	−0.911778	−0.455889	+	0.890037i	$0.650679\pi$
$510$	0.843411	0.0373469
$511$	−5.06773	−0.224183
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	4.07347	0.179673
$515$	5.12762	0.225950
$516$	−16.2871	−0.716999
$517$	4.02946	0.177215
$518$	3.01336	0.132399
$519$	13.2555	0.581854
$520$	−13.2089	−0.579249
$521$	−36.0695	−1.58024	−0.790118	−	0.612955i	$-0.789981\pi$
$521$	−36.0695	−1.58024	−0.790118	+	0.612955i	$0.789981\pi$
$522$	−1.18141	−0.0517090
$523$	28.4282	1.24308	0.621539	−	0.783383i	$-0.286508\pi$
$523$	28.4282	1.24308	0.621539	+	0.783383i	$0.286508\pi$
$524$	22.1186	0.966257
$525$	−2.55875	−0.111673
$526$	−7.22171	−0.314881
$527$	0.353841	0.0154136
$528$	−1.52164	−0.0662209
$529$	−14.5284	−0.631669
$530$	3.99050	0.173336
$531$	−3.76985	−0.163598
$532$	0	0
$533$	−14.8544	−0.643414
$534$	25.7785	1.11554
$535$	−0.194760	−0.00842022
$536$	5.56717	0.240465
$537$	14.6492	0.632158
$538$	−31.8344	−1.37248
$539$	6.78395	0.292205
$540$	16.4589	0.708278
$541$	−13.5875	−0.584173	−0.292086	−	0.956392i	$-0.594350\pi$
$541$	−13.5875	−0.584173	−0.292086	+	0.956392i	$0.594350\pi$
$542$	31.2403	1.34189
$543$	−27.1017	−1.16305
$544$	−0.188812	−0.00809526
$545$	11.2015	0.479818
$546$	−3.18245	−0.136196
$547$	−21.3894	−0.914544	−0.457272	−	0.889327i	$-0.651173\pi$
$547$	−21.3894	−0.914544	−0.457272	+	0.889327i	$0.651173\pi$
$548$	3.98966	0.170430
$549$	7.50763	0.320418
$550$	3.61774	0.154261
$551$	0	0
$552$	−4.42889	−0.188506
$553$	2.57756	0.109609
$554$	−12.3578	−0.525031
$555$	−28.9588	−1.22923
$556$	1.48693	0.0630598
$557$	−21.3938	−0.906484	−0.453242	−	0.891387i	$-0.649733\pi$
$557$	−21.3938	−0.906484	−0.453242	+	0.891387i	$0.649733\pi$
$558$	1.28298	0.0543130
$559$	48.1617	2.03702
$560$	1.36451	0.0576609
$561$	−0.287304	−0.0121300
$562$	−6.73851	−0.284247
$563$	−20.1053	−0.847337	−0.423669	−	0.905817i	$-0.639258\pi$
$563$	−20.1053	−0.847337	−0.423669	+	0.905817i	$0.639258\pi$
$564$	−6.13139	−0.258178
$565$	−0.0521705	−0.00219483
$566$	−3.67917	−0.154647
$567$	3.01082	0.126443
$568$	3.98279	0.167114
$569$	12.2391	0.513089	0.256544	−	0.966532i	$-0.417416\pi$
$569$	12.2391	0.513089	0.256544	+	0.966532i	$0.417416\pi$
$570$	0	0
$571$	−8.38225	−0.350786	−0.175393	−	0.984498i	$-0.556120\pi$
$571$	−8.38225	−0.350786	−0.175393	+	0.984498i	$0.556120\pi$
$572$	4.49956	0.188136
$573$	38.4561	1.60653
$574$	1.53449	0.0640482
$575$	10.5298	0.439124
$576$	−0.684609	−0.0285254
$577$	20.3140	0.845683	0.422841	−	0.906204i	$-0.361033\pi$
$577$	20.3140	0.845683	0.422841	+	0.906204i	$0.361033\pi$
$578$	16.9643	0.705624
$579$	−25.4678	−1.05841
$580$	5.06589	0.210350
$581$	5.97123	0.247728
$582$	−18.4857	−0.766257
$583$	−1.35935	−0.0562985
$584$	−10.9027	−0.451158
$585$	−9.04294	−0.373880
$586$	2.79512	0.115465
$587$	−6.13299	−0.253136	−0.126568	−	0.991958i	$-0.540396\pi$
$587$	−6.13299	−0.253136	−0.126568	+	0.991958i	$0.540396\pi$
$588$	−10.3227	−0.425702
$589$	0	0
$590$	16.1651	0.665507
$591$	12.9724	0.533614
$592$	6.48294	0.266447
$593$	43.8711	1.80157	0.900785	−	0.434266i	$-0.142992\pi$
$593$	43.8711	1.80157	0.900785	+	0.434266i	$0.142992\pi$
$594$	−5.60665	−0.230044
$595$	0.257636	0.0105620
$596$	8.10477	0.331984
$597$	33.0754	1.35369
$598$	13.0964	0.535553
$599$	−36.7077	−1.49984	−0.749919	−	0.661530i	$-0.769907\pi$
$599$	−36.7077	−1.49984	−0.749919	+	0.661530i	$0.769907\pi$
$600$	−5.50491	−0.224737
$601$	−25.0723	−1.02272	−0.511361	−	0.859366i	$-0.670858\pi$
$601$	−25.0723	−1.02272	−0.511361	+	0.859366i	$0.670858\pi$
$602$	−4.97520	−0.202774
$603$	3.81134	0.155210
$604$	16.0446	0.652846
$605$	−2.93560	−0.119349
$606$	−13.5551	−0.550638
$607$	−11.3520	−0.460765	−0.230382	−	0.973100i	$-0.573998\pi$
$607$	−11.3520	−0.460765	−0.230382	+	0.973100i	$0.573998\pi$
$608$	0	0
$609$	1.22053	0.0494585
$610$	−32.1927	−1.30344
$611$	18.1308	0.733493
$612$	−0.129263	−0.00522513
$613$	−19.4685	−0.786325	−0.393162	−	0.919469i	$-0.628619\pi$
$613$	−19.4685	−0.786325	−0.393162	+	0.919469i	$0.628619\pi$
$614$	11.8371	0.477708
$615$	−14.7466	−0.594642
$616$	−0.464814	−0.0187279
$617$	−25.2893	−1.01811	−0.509055	−	0.860734i	$-0.670005\pi$
$617$	−25.2893	−1.01811	−0.509055	+	0.860734i	$0.670005\pi$
$618$	2.65786	0.106915
$619$	11.1209	0.446986	0.223493	−	0.974705i	$-0.428254\pi$
$619$	11.1209	0.446986	0.223493	+	0.974705i	$0.428254\pi$
$620$	−5.50142	−0.220942
$621$	−16.3187	−0.654849
$622$	−15.9983	−0.641473
$623$	7.87452	0.315486
$624$	−6.84672	−0.274088
$625$	−30.0007	−1.20003
$626$	17.4536	0.697588
$627$	0	0
$628$	18.1493	0.724234
$629$	1.22406	0.0488064
$630$	0.934154	0.0372176
$631$	32.3028	1.28596	0.642978	−	0.765885i	$-0.277699\pi$
$631$	32.3028	1.28596	0.642978	+	0.765885i	$0.277699\pi$
$632$	5.54536	0.220583
$633$	−13.4277	−0.533703
$634$	−22.7519	−0.903591
$635$	22.5756	0.895885
$636$	2.06844	0.0820190
$637$	30.5248	1.20944
$638$	−1.72567	−0.0683201
$639$	2.72665	0.107865
$640$	2.93560	0.116040
$641$	38.5887	1.52416	0.762080	−	0.647483i	$-0.224178\pi$
$641$	38.5887	1.52416	0.762080	+	0.647483i	$0.224178\pi$
$642$	−0.100952	−0.00398426
$643$	−41.6452	−1.64233	−0.821163	−	0.570693i	$-0.806675\pi$
$643$	−41.6452	−1.64233	−0.821163	+	0.570693i	$0.806675\pi$
$644$	−1.35289	−0.0533113
$645$	47.8124	1.88261
$646$	0	0
$647$	11.2852	0.443667	0.221834	−	0.975085i	$-0.428796\pi$
$647$	11.2852	0.443667	0.221834	+	0.975085i	$0.428796\pi$
$648$	6.47748	0.254460
$649$	−5.50657	−0.216152
$650$	16.2783	0.638486
$651$	−1.32547	−0.0519492
$652$	21.3870	0.837579
$653$	6.98352	0.273286	0.136643	−	0.990620i	$-0.456369\pi$
$653$	6.98352	0.273286	0.136643	+	0.990620i	$0.456369\pi$
$654$	5.80618	0.227039
$655$	−64.9315	−2.53708
$656$	3.30129	0.128894
$657$	−7.46410	−0.291202
$658$	−1.87295	−0.0730151
$659$	34.6339	1.34915	0.674573	−	0.738208i	$-0.264328\pi$
$659$	34.6339	1.34915	0.674573	+	0.738208i	$0.264328\pi$
$660$	4.46693	0.173875
$661$	4.29030	0.166873	0.0834367	−	0.996513i	$-0.473410\pi$
$661$	4.29030	0.166873	0.0834367	+	0.996513i	$0.473410\pi$
$662$	−9.94526	−0.386533
$663$	−1.29274	−0.0502060
$664$	12.8465	0.498541
$665$	0	0
$666$	4.43828	0.171980
$667$	−5.02276	−0.194482
$668$	−11.0690	−0.428274
$669$	−9.74657	−0.376824
$670$	−16.3430	−0.631384
$671$	10.9663	0.423349
$672$	0.707279	0.0272839
$673$	−45.7513	−1.76358	−0.881792	−	0.471638i	$-0.843663\pi$
$673$	−45.7513	−1.76358	−0.881792	+	0.471638i	$0.843663\pi$
$674$	−27.0670	−1.04258
$675$	−20.2834	−0.780709
$676$	7.24605	0.278694
$677$	−6.11715	−0.235101	−0.117551	−	0.993067i	$-0.537504\pi$
$677$	−6.11715	−0.235101	−0.117551	+	0.993067i	$0.537504\pi$
$678$	−0.0270421	−0.00103854
$679$	−5.64680	−0.216704
$680$	0.554277	0.0212556
$681$	21.1241	0.809476
$682$	1.87404	0.0717606
$683$	−8.43385	−0.322712	−0.161356	−	0.986896i	$-0.551587\pi$
$683$	−8.43385	−0.322712	−0.161356	+	0.986896i	$0.551587\pi$
$684$	0	0
$685$	−11.7120	−0.447494
$686$	−6.40697	−0.244619
$687$	−9.71859	−0.370787
$688$	−10.7036	−0.408072
$689$	−6.11647	−0.233019
$690$	13.0015	0.494957
$691$	0.287350	0.0109313	0.00546566	−	0.999985i	$-0.498260\pi$
$691$	0.287350	0.0109313	0.00546566	+	0.999985i	$0.498260\pi$
$692$	8.71135	0.331156
$693$	−0.318216	−0.0120880
$694$	−19.4414	−0.737985
$695$	−4.36503	−0.165575
$696$	2.62586	0.0995328
$697$	0.623324	0.0236101
$698$	−22.6056	−0.855635
$699$	−7.90578	−0.299024
$700$	−1.68158	−0.0635576
$701$	−2.87902	−0.108739	−0.0543696	−	0.998521i	$-0.517315\pi$
$701$	−2.87902	−0.108739	−0.0543696	+	0.998521i	$0.517315\pi$
$702$	−25.2275	−0.952150
$703$	0	0
$704$	−1.00000	−0.0376889
$705$	17.9993	0.677893
$706$	−24.0961	−0.906870
$707$	−4.14065	−0.155725
$708$	8.37903	0.314903
$709$	−37.7391	−1.41732	−0.708662	−	0.705548i	$-0.750701\pi$
$709$	−37.7391	−1.41732	−0.708662	+	0.705548i	$0.750701\pi$
$710$	−11.6919	−0.438788
$711$	3.79640	0.142376
$712$	16.9412	0.634900
$713$	5.45458	0.204276
$714$	0.133543	0.00499772
$715$	−13.2089	−0.493985
$716$	9.62721	0.359786
$717$	−12.4903	−0.466459
$718$	−25.6187	−0.956082
$719$	44.2686	1.65094	0.825469	−	0.564447i	$-0.190911\pi$
$719$	44.2686	1.65094	0.825469	+	0.564447i	$0.190911\pi$
$720$	2.00974	0.0748985
$721$	0.811892	0.0302364
$722$	0	0
$723$	27.2340	1.01284
$724$	−17.8108	−0.661935
$725$	−6.24305	−0.231861
$726$	−1.52164	−0.0564734
$727$	−10.9177	−0.404917	−0.202458	−	0.979291i	$-0.564893\pi$
$727$	−10.9177	−0.404917	−0.202458	+	0.979291i	$0.564893\pi$
$728$	−2.09146	−0.0775146
$729$	30.0285	1.11217
$730$	32.0060	1.18460
$731$	−2.02098	−0.0747486
$732$	−16.6868	−0.616761
$733$	35.3266	1.30482	0.652409	−	0.757867i	$-0.273758\pi$
$733$	35.3266	1.30482	0.652409	+	0.757867i	$0.273758\pi$
$734$	1.01974	0.0376393
$735$	30.3034	1.11776
$736$	−2.91060	−0.107286
$737$	5.56717	0.205069
$738$	2.26010	0.0831952
$739$	1.14794	0.0422276	0.0211138	−	0.999777i	$-0.493279\pi$
$739$	1.14794	0.0422276	0.0211138	+	0.999777i	$0.493279\pi$
$740$	−19.0313	−0.699605
$741$	0	0
$742$	0.631844	0.0231957
$743$	−10.9608	−0.402114	−0.201057	−	0.979580i	$-0.564438\pi$
$743$	−10.9608	−0.402114	−0.201057	+	0.979580i	$0.564438\pi$
$744$	−2.85161	−0.104545
$745$	−23.7924	−0.871685
$746$	−31.7363	−1.16195
$747$	8.79484	0.321786
$748$	−0.188812	−0.00690366
$749$	−0.0308377	−0.00112679
$750$	−6.17444	−0.225459
$751$	−20.6039	−0.751847	−0.375923	−	0.926651i	$-0.622674\pi$
$751$	−20.6039	−0.751847	−0.375923	+	0.926651i	$0.622674\pi$
$752$	−4.02946	−0.146939
$753$	18.1796	0.662502
$754$	−7.76478	−0.282777
$755$	−47.1006	−1.71417
$756$	2.60605	0.0947810
$757$	34.2368	1.24436	0.622178	−	0.782875i	$-0.286248\pi$
$757$	34.2368	1.24436	0.622178	+	0.782875i	$0.286248\pi$
$758$	−19.0665	−0.692527
$759$	−4.42889	−0.160759
$760$	0	0
$761$	−43.6051	−1.58069	−0.790343	−	0.612665i	$-0.790097\pi$
$761$	−43.6051	−1.58069	−0.790343	+	0.612665i	$0.790097\pi$
$762$	11.7018	0.423913
$763$	1.77360	0.0642088
$764$	25.2728	0.914338
$765$	0.379463	0.0137195
$766$	−18.1444	−0.655585
$767$	−24.7772	−0.894652
$768$	1.52164	0.0549075
$769$	36.4963	1.31609	0.658045	−	0.752979i	$-0.271384\pi$
$769$	36.4963	1.31609	0.658045	+	0.752979i	$0.271384\pi$
$770$	1.36451	0.0491734
$771$	−6.19836	−0.223228
$772$	−16.7371	−0.602381
$773$	−46.1555	−1.66010	−0.830049	−	0.557690i	$-0.811688\pi$
$773$	−46.1555	−1.66010	−0.830049	+	0.557690i	$0.811688\pi$
$774$	−7.32781	−0.263393
$775$	6.77978	0.243537
$776$	−12.1485	−0.436107
$777$	−4.58525	−0.164495
$778$	−3.88312	−0.139217
$779$	0	0
$780$	20.0992	0.719667
$781$	3.98279	0.142515
$782$	−0.549558	−0.0196522
$783$	9.67526	0.345765
$784$	−6.78395	−0.242284
$785$	−53.2789	−1.90161
$786$	−33.6566	−1.20049
$787$	−29.8430	−1.06379	−0.531893	−	0.846811i	$-0.678519\pi$
$787$	−29.8430	−1.06379	−0.531893	+	0.846811i	$0.678519\pi$
$788$	8.52528	0.303700
$789$	10.9888	0.391213
$790$	−16.2790	−0.579179
$791$	−0.00826051	−0.000293710 0
$792$	−0.684609	−0.0243265
$793$	49.3436	1.75224
$794$	−17.8589	−0.633787
$795$	−6.07211	−0.215356
$796$	21.7367	0.770435
$797$	26.9999	0.956386	0.478193	−	0.878255i	$-0.341292\pi$
$797$	26.9999	0.956386	0.478193	+	0.878255i	$0.341292\pi$
$798$	0	0
$799$	−0.760811	−0.0269156
$800$	−3.61774	−0.127907
$801$	11.5981	0.409800
$802$	33.5041	1.18307
$803$	−10.9027	−0.384749
$804$	−8.47123	−0.298757
$805$	3.97154	0.139978
$806$	8.43234	0.297017
$807$	48.4405	1.70519
$808$	−8.90820	−0.313390
$809$	41.6163	1.46315	0.731575	−	0.681761i	$-0.238786\pi$
$809$	41.6163	1.46315	0.731575	+	0.681761i	$0.238786\pi$
$810$	−19.0153	−0.668129
$811$	−17.0281	−0.597937	−0.298968	−	0.954263i	$-0.596643\pi$
$811$	−17.0281	−0.597937	−0.298968	+	0.954263i	$0.596643\pi$
$812$	0.802117	0.0281488
$813$	−47.5365	−1.66718
$814$	6.48294	0.227227
$815$	−62.7836	−2.19921
$816$	0.287304	0.0100577
$817$	0	0
$818$	26.3286	0.920556
$819$	−1.43183	−0.0500322
$820$	−9.69127	−0.338434
$821$	24.8643	0.867771	0.433885	−	0.900968i	$-0.357142\pi$
$821$	24.8643	0.867771	0.433885	+	0.900968i	$0.357142\pi$
$822$	−6.07083	−0.211745
$823$	38.2993	1.33503	0.667514	−	0.744597i	$-0.267358\pi$
$823$	38.2993	1.33503	0.667514	+	0.744597i	$0.267358\pi$
$824$	1.74670	0.0608493
$825$	−5.50491	−0.191656
$826$	2.55953	0.0890575
$827$	4.14004	0.143963	0.0719816	−	0.997406i	$-0.477068\pi$
$827$	4.14004	0.143963	0.0719816	+	0.997406i	$0.477068\pi$
$828$	−1.99263	−0.0692486
$829$	22.6282	0.785909	0.392955	−	0.919558i	$-0.371453\pi$
$829$	22.6282	0.785909	0.392955	+	0.919558i	$0.371453\pi$
$830$	−37.7122	−1.30901
$831$	18.8041	0.652306
$832$	−4.49956	−0.155994
$833$	−1.28089	−0.0443803
$834$	−2.26257	−0.0783464
$835$	32.4943	1.12451
$836$	0	0
$837$	−10.5071	−0.363178
$838$	32.1866	1.11187
$839$	15.4313	0.532746	0.266373	−	0.963870i	$-0.414175\pi$
$839$	15.4313	0.532746	0.266373	+	0.963870i	$0.414175\pi$
$840$	−2.07629	−0.0716388
$841$	−26.0220	−0.897312
$842$	20.0204	0.689948
$843$	10.2536	0.353152
$844$	−8.82448	−0.303751
$845$	−21.2715	−0.731762
$846$	−2.75860	−0.0948428
$847$	−0.464814	−0.0159712
$848$	1.35935	0.0466802
$849$	5.59838	0.192136
$850$	−0.683074	−0.0234293
$851$	18.8693	0.646830
$852$	−6.06037	−0.207625
$853$	−34.6022	−1.18476	−0.592379	−	0.805659i	$-0.701811\pi$
$853$	−34.6022	−1.18476	−0.592379	+	0.805659i	$0.701811\pi$
$854$	−5.09729	−0.174426
$855$	0	0
$856$	−0.0663443	−0.00226760
$857$	−47.4450	−1.62069	−0.810345	−	0.585953i	$-0.800720\pi$
$857$	−47.4450	−1.62069	−0.810345	+	0.585953i	$0.800720\pi$
$858$	−6.84672	−0.233743
$859$	41.6905	1.42246	0.711230	−	0.702959i	$-0.248138\pi$
$859$	41.6905	1.42246	0.711230	+	0.702959i	$0.248138\pi$
$860$	31.4216	1.07147
$861$	−2.33494	−0.0795744
$862$	29.2413	0.995963
$863$	39.0792	1.33027	0.665136	−	0.746722i	$-0.268374\pi$
$863$	39.0792	1.33027	0.665136	+	0.746722i	$0.268374\pi$
$864$	5.60665	0.190742
$865$	−25.5730	−0.869509
$866$	21.8706	0.743192
$867$	−25.8136	−0.876677
$868$	−0.871078	−0.0295663
$869$	5.54536	0.188113
$870$	−7.70846	−0.261341
$871$	25.0498	0.848781
$872$	3.81573	0.129217
$873$	−8.31700	−0.281488
$874$	0	0
$875$	−1.88610	−0.0637618
$876$	16.5900	0.560525
$877$	−5.61044	−0.189451	−0.0947255	−	0.995503i	$-0.530197\pi$
$877$	−5.61044	−0.189451	−0.0947255	+	0.995503i	$0.530197\pi$
$878$	25.8255	0.871567
$879$	−4.25317	−0.143456
$880$	2.93560	0.0989590
$881$	14.5597	0.490530	0.245265	−	0.969456i	$-0.421125\pi$
$881$	14.5597	0.490530	0.245265	+	0.969456i	$0.421125\pi$
$882$	−4.64435	−0.156384
$883$	0.760531	0.0255939	0.0127969	−	0.999918i	$-0.495926\pi$
$883$	0.760531	0.0255939	0.0127969	+	0.999918i	$0.495926\pi$
$884$	−0.849573	−0.0285742
$885$	−24.5975	−0.826835
$886$	−7.15530	−0.240387
$887$	−37.0738	−1.24482	−0.622409	−	0.782692i	$-0.713846\pi$
$887$	−37.0738	−1.24482	−0.622409	+	0.782692i	$0.713846\pi$
$888$	−9.86470	−0.331038
$889$	3.57455	0.119886
$890$	−49.7327	−1.66704
$891$	6.47748	0.217004
$892$	−6.40530	−0.214465
$893$	0	0
$894$	−12.3326	−0.412462
$895$	−28.2616	−0.944682
$896$	0.464814	0.0155283
$897$	−19.9281	−0.665379
$898$	14.0318	0.468248
$899$	−3.23398	−0.107859
$900$	−2.47674	−0.0825580
$901$	0.256662	0.00855064
$902$	3.30129	0.109921
$903$	7.57046	0.251929
$904$	−0.0177717	−0.000591077 0
$905$	52.2855	1.73803
$906$	−24.4141	−0.811106
$907$	16.2729	0.540333	0.270166	−	0.962814i	$-0.412921\pi$
$907$	16.2729	0.540333	0.270166	+	0.962814i	$0.412921\pi$
$908$	13.8824	0.460705
$909$	−6.09864	−0.202279
$910$	6.13968	0.203528
$911$	17.9183	0.593659	0.296830	−	0.954930i	$-0.404071\pi$
$911$	17.9183	0.593659	0.296830	+	0.954930i	$0.404071\pi$
$912$	0	0
$913$	12.8465	0.425157
$914$	31.3113	1.03568
$915$	48.9857	1.61942
$916$	−6.38691	−0.211030
$917$	−10.2810	−0.339510
$918$	1.05860	0.0349392
$919$	−34.5775	−1.14061	−0.570303	−	0.821435i	$-0.693174\pi$
$919$	−34.5775	−1.14061	−0.570303	+	0.821435i	$0.693174\pi$
$920$	8.54437	0.281699
$921$	−18.0119	−0.593511
$922$	−12.2299	−0.402770
$923$	17.9208	0.589870
$924$	0.707279	0.0232678
$925$	23.4536	0.771150
$926$	23.2772	0.764937
$927$	1.19581	0.0392756
$928$	1.72567	0.0566480
$929$	−19.0657	−0.625524	−0.312762	−	0.949831i	$-0.601254\pi$
$929$	−19.0657	−0.625524	−0.312762	+	0.949831i	$0.601254\pi$
$930$	8.37119	0.274502
$931$	0	0
$932$	−5.19556	−0.170186
$933$	24.3437	0.796976
$934$	−17.2913	−0.565789
$935$	0.554277	0.0181268
$936$	−3.08044	−0.100687
$937$	−49.0690	−1.60301	−0.801507	−	0.597985i	$-0.795968\pi$
$937$	−49.0690	−1.60301	−0.801507	+	0.597985i	$0.795968\pi$
$938$	−2.58770	−0.0844913
$939$	−26.5582	−0.866694
$940$	11.8289	0.385815
$941$	−26.1208	−0.851512	−0.425756	−	0.904838i	$-0.639992\pi$
$941$	−26.1208	−0.851512	−0.425756	+	0.904838i	$0.639992\pi$
$942$	−27.6166	−0.899799
$943$	9.60875	0.312904
$944$	5.50657	0.179224
$945$	−7.65031	−0.248865
$946$	−10.7036	−0.348005
$947$	16.5343	0.537294	0.268647	−	0.963239i	$-0.413424\pi$
$947$	16.5343	0.537294	0.268647	+	0.963239i	$0.413424\pi$
$948$	−8.43804	−0.274055
$949$	−49.0574	−1.59247
$950$	0	0
$951$	34.6201	1.12264
$952$	0.0877625	0.00284440
$953$	14.5445	0.471142	0.235571	−	0.971857i	$-0.424304\pi$
$953$	14.5445	0.471142	0.235571	+	0.971857i	$0.424304\pi$
$954$	0.930623	0.0301300
$955$	−74.1908	−2.40076
$956$	−8.20845	−0.265480
$957$	2.62586	0.0848819
$958$	13.2757	0.428919
$959$	−1.85445	−0.0598833
$960$	−4.46693	−0.144169
$961$	−27.4880	−0.886709
$962$	29.1704	0.940491
$963$	−0.0454199	−0.00146364
$964$	17.8978	0.576448
$965$	49.1334	1.58166
$966$	2.05861	0.0662347
$967$	−17.1147	−0.550371	−0.275186	−	0.961391i	$-0.588739\pi$
$967$	−17.1147	−0.550371	−0.275186	+	0.961391i	$0.588739\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	35.6632	1.14508
$971$	17.0715	0.547850	0.273925	−	0.961751i	$-0.411678\pi$
$971$	17.0715	0.547850	0.273925	+	0.961751i	$0.411678\pi$
$972$	6.96355	0.223356
$973$	−0.691145	−0.0221571
$974$	−27.2081	−0.871805
$975$	−24.7697	−0.793264
$976$	−10.9663	−0.351023
$977$	−21.8610	−0.699396	−0.349698	−	0.936862i	$-0.613716\pi$
$977$	−21.8610	−0.699396	−0.349698	+	0.936862i	$0.613716\pi$
$978$	−32.5433	−1.04062
$979$	16.9412	0.541444
$980$	19.9150	0.636160
$981$	2.61229	0.0834039
$982$	−35.5134	−1.13328
$983$	−29.5680	−0.943072	−0.471536	−	0.881847i	$-0.656300\pi$
$983$	−29.5680	−0.943072	−0.471536	+	0.881847i	$0.656300\pi$
$984$	−5.02338	−0.160140
$985$	−25.0268	−0.797420
$986$	0.325829	0.0103765
$987$	2.84995	0.0907150
$988$	0	0
$989$	−31.1541	−0.990641
$990$	2.00974	0.0638737
$991$	33.6392	1.06858	0.534292	−	0.845300i	$-0.320578\pi$
$991$	33.6392	1.06858	0.534292	+	0.845300i	$0.320578\pi$
$992$	−1.87404	−0.0595007
$993$	15.1331	0.480235
$994$	−1.85125	−0.0587182
$995$	−63.8101	−2.02292
$996$	−19.5478	−0.619395
$997$	50.8390	1.61009	0.805043	−	0.593216i	$-0.202142\pi$
$997$	50.8390	1.61009	0.805043	+	0.593216i	$0.202142\pi$
$998$	9.33762	0.295577
$999$	−36.3476	−1.14999

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7942.2.a.by.1.11		15
19.3	odd	18		418.2.j.d.199.2	✓	30
19.13	odd	18		418.2.j.d.397.2	yes	30
19.18	odd	2		7942.2.a.ca.1.5		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.j.d.199.2	✓	30	19.3	odd	18
418.2.j.d.397.2	yes	30	19.13	odd	18
7942.2.a.by.1.11		15	1.1	even	1	trivial
7942.2.a.ca.1.5		15	19.18	odd	2

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:	\( N \)	\(=\)	\( 7942 = 2 \cdot 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7942.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.52164 q^{3} +1.00000 q^{4} -2.93560 q^{5} -1.52164 q^{6} -0.464814 q^{7} -1.00000 q^{8} -0.684609 q^{9} +2.93560 q^{10} -1.00000 q^{11} +1.52164 q^{12} -4.49956 q^{13} +0.464814 q^{14} -4.46693 q^{15} +1.00000 q^{16} +0.188812 q^{17} +0.684609 q^{18} -2.93560 q^{20} -0.707279 q^{21} +1.00000 q^{22} +2.91060 q^{23} -1.52164 q^{24} +3.61774 q^{25} +4.49956 q^{26} -5.60665 q^{27} -0.464814 q^{28} -1.72567 q^{29} +4.46693 q^{30} +1.87404 q^{31} -1.00000 q^{32} -1.52164 q^{33} -0.188812 q^{34} +1.36451 q^{35} -0.684609 q^{36} +6.48294 q^{37} -6.84672 q^{39} +2.93560 q^{40} +3.30129 q^{41} +0.707279 q^{42} -10.7036 q^{43} -1.00000 q^{44} +2.00974 q^{45} -2.91060 q^{46} -4.02946 q^{47} +1.52164 q^{48} -6.78395 q^{49} -3.61774 q^{50} +0.287304 q^{51} -4.49956 q^{52} +1.35935 q^{53} +5.60665 q^{54} +2.93560 q^{55} +0.464814 q^{56} +1.72567 q^{58} +5.50657 q^{59} -4.46693 q^{60} -10.9663 q^{61} -1.87404 q^{62} +0.318216 q^{63} +1.00000 q^{64} +13.2089 q^{65} +1.52164 q^{66} -5.56717 q^{67} +0.188812 q^{68} +4.42889 q^{69} -1.36451 q^{70} -3.98279 q^{71} +0.684609 q^{72} +10.9027 q^{73} -6.48294 q^{74} +5.50491 q^{75} +0.464814 q^{77} +6.84672 q^{78} -5.54536 q^{79} -2.93560 q^{80} -6.47748 q^{81} -3.30129 q^{82} -12.8465 q^{83} -0.707279 q^{84} -0.554277 q^{85} +10.7036 q^{86} -2.62586 q^{87} +1.00000 q^{88} -16.9412 q^{89} -2.00974 q^{90} +2.09146 q^{91} +2.91060 q^{92} +2.85161 q^{93} +4.02946 q^{94} -1.52164 q^{96} +12.1485 q^{97} +6.78395 q^{98} +0.684609 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{2} - 3 q^{3} + 15 q^{4} + 9 q^{5} + 3 q^{6} - 15 q^{8} + 30 q^{9} - 9 q^{10} - 15 q^{11} - 3 q^{12} - 21 q^{15} + 15 q^{16} + 21 q^{17} - 30 q^{18} + 9 q^{20} + 9 q^{21} + 15 q^{22} + 21 q^{23}+ \cdots - 30 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - 3 * q^3 + 15 * q^4 + 9 * q^5 + 3 * q^6 - 15 * q^8 + 30 * q^9 - 9 * q^10 - 15 * q^11 - 3 * q^12 - 21 * q^15 + 15 * q^16 + 21 * q^17 - 30 * q^18 + 9 * q^20 + 9 * q^21 + 15 * q^22 + 21 * q^23 + 3 * q^24 + 24 * q^25 - 3 * q^27 + 9 * q^29 + 21 * q^30 - 18 * q^31 - 15 * q^32 + 3 * q^33 - 21 * q^34 + 18 * q^35 + 30 * q^36 + 9 * q^37 - 9 * q^40 - 15 * q^41 - 9 * q^42 + 3 * q^43 - 15 * q^44 + 54 * q^45 - 21 * q^46 + 39 * q^47 - 3 * q^48 + 33 * q^49 - 24 * q^50 - 30 * q^51 - 18 * q^53 + 3 * q^54 - 9 * q^55 - 9 * q^58 - 6 * q^59 - 21 * q^60 - 30 * q^61 + 18 * q^62 + 24 * q^63 + 15 * q^64 - 6 * q^65 - 3 * q^66 - 9 * q^67 + 21 * q^68 + 42 * q^69 - 18 * q^70 - 9 * q^71 - 30 * q^72 + 12 * q^73 - 9 * q^74 - 21 * q^75 - 12 * q^79 + 9 * q^80 + 63 * q^81 + 15 * q^82 + 30 * q^83 + 9 * q^84 - 3 * q^85 - 3 * q^86 + 9 * q^87 + 15 * q^88 + 6 * q^89 - 54 * q^90 - 96 * q^91 + 21 * q^92 + 102 * q^93 - 39 * q^94 + 3 * q^96 - 33 * q^98 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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