LMFDB - Embedded newform 591.2.a.e.1.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [591,2,Mod(1,591)] 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("591.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(591, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 591 = 3 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	591.a (trivial)

Newform invariants

comment:select newform

sage:traces = [14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$4.71915875946$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 24 x^{12} + 220 x^{10} - 958 x^{8} - 4 x^{7} + 2002 x^{6} + 28 x^{5} - 1792 x^{4} - 15 x^{3} + \cdots - 26 $ x^14 - 24x^12 + 220x^10 - 958x^8 - 4x^7 + 2002x^6 + 28x^5 - 1792x^4 - 15x^3 + 520x^2 + 40x - 26
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-0.507888$ of defining polynomial
Character	$\chi$	$=$	591.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.507888 q^{2} -1.00000 q^{3} -1.74205 q^{4} -3.87524 q^{5} -0.507888 q^{6} +1.74487 q^{7} -1.90054 q^{8} +1.00000 q^{9} -1.96819 q^{10} -4.22106 q^{11} +1.74205 q^{12} +5.10306 q^{13} +0.886200 q^{14} +3.87524 q^{15} +2.51883 q^{16} +7.21103 q^{17} +0.507888 q^{18} +3.54054 q^{19} +6.75087 q^{20} -1.74487 q^{21} -2.14383 q^{22} -0.786215 q^{23} +1.90054 q^{24} +10.0175 q^{25} +2.59179 q^{26} -1.00000 q^{27} -3.03965 q^{28} -8.18532 q^{29} +1.96819 q^{30} -5.37761 q^{31} +5.08037 q^{32} +4.22106 q^{33} +3.66240 q^{34} -6.76180 q^{35} -1.74205 q^{36} +3.37387 q^{37} +1.79820 q^{38} -5.10306 q^{39} +7.36507 q^{40} +4.87320 q^{41} -0.886200 q^{42} -2.35251 q^{43} +7.35329 q^{44} -3.87524 q^{45} -0.399310 q^{46} +5.49738 q^{47} -2.51883 q^{48} -3.95543 q^{49} +5.08778 q^{50} -7.21103 q^{51} -8.88978 q^{52} +11.8690 q^{53} -0.507888 q^{54} +16.3576 q^{55} -3.31620 q^{56} -3.54054 q^{57} -4.15723 q^{58} +11.9278 q^{59} -6.75087 q^{60} -12.2493 q^{61} -2.73123 q^{62} +1.74487 q^{63} -2.45741 q^{64} -19.7756 q^{65} +2.14383 q^{66} +13.4293 q^{67} -12.5620 q^{68} +0.786215 q^{69} -3.43424 q^{70} +2.80305 q^{71} -1.90054 q^{72} +10.5857 q^{73} +1.71355 q^{74} -10.0175 q^{75} -6.16780 q^{76} -7.36520 q^{77} -2.59179 q^{78} +5.74443 q^{79} -9.76110 q^{80} +1.00000 q^{81} +2.47504 q^{82} -14.8889 q^{83} +3.03965 q^{84} -27.9445 q^{85} -1.19481 q^{86} +8.18532 q^{87} +8.02230 q^{88} -1.54824 q^{89} -1.96819 q^{90} +8.90418 q^{91} +1.36963 q^{92} +5.37761 q^{93} +2.79205 q^{94} -13.7205 q^{95} -5.08037 q^{96} -2.98646 q^{97} -2.00892 q^{98} -4.22106 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{3} + 20 q^{4} + 7 q^{7} + 14 q^{9} + 8 q^{10} + 4 q^{11} - 20 q^{12} + 8 q^{13} + 6 q^{14} + 40 q^{16} + 4 q^{17} + 15 q^{19} - 6 q^{20} - 7 q^{21} + 12 q^{22} - 3 q^{23} + 40 q^{25} + 10 q^{26}+ \cdots + 4 q^{99}+O(q^{100}) $ 14 * q - 14 * q^3 + 20 * q^4 + 7 * q^7 + 14 * q^9 + 8 * q^10 + 4 * q^11 - 20 * q^12 + 8 * q^13 + 6 * q^14 + 40 * q^16 + 4 * q^17 + 15 * q^19 - 6 * q^20 - 7 * q^21 + 12 * q^22 - 3 * q^23 + 40 * q^25 + 10 * q^26 - 14 * q^27 + 22 * q^28 + 7 * q^29 - 8 * q^30 + 18 * q^31 - 4 * q^33 + 32 * q^34 - 8 * q^35 + 20 * q^36 + 21 * q^37 - 22 * q^38 - 8 * q^39 + 24 * q^40 + 23 * q^41 - 6 * q^42 + 27 * q^43 + 32 * q^44 + 32 * q^46 - 19 * q^47 - 40 * q^48 + 59 * q^49 - q^50 - 4 * q^51 + 12 * q^52 + 12 * q^53 + 12 * q^55 + 7 * q^56 - 15 * q^57 + 8 * q^58 - 16 * q^59 + 6 * q^60 + 7 * q^61 - 22 * q^62 + 7 * q^63 + 36 * q^64 + 36 * q^65 - 12 * q^66 + 22 * q^67 - 45 * q^68 + 3 * q^69 - 48 * q^70 - 4 * q^71 + 18 * q^73 + 10 * q^74 - 40 * q^75 - 14 * q^76 - 2 * q^77 - 10 * q^78 + 2 * q^79 - 68 * q^80 + 14 * q^81 - 48 * q^82 - 51 * q^83 - 22 * q^84 + 20 * q^85 - 15 * q^86 - 7 * q^87 - 28 * q^88 + 28 * q^89 + 8 * q^90 + 2 * q^91 - 2 * q^92 - 18 * q^93 - 54 * q^94 - 16 * q^95 + 54 * q^97 - 74 * q^98 + 4 * 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 $

$2$	0.507888	0.359131	0.179566	−	0.983746i	$-0.442531\pi$
$2$	0.507888	0.359131	0.179566	+	0.983746i	$0.442531\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.74205	−0.871025
$5$	−3.87524	−1.73306	−0.866531	−	0.499123i	$-0.833656\pi$
$5$	−3.87524	−1.73306	−0.866531	+	0.499123i	$0.833656\pi$
$6$	−0.507888	−0.207345
$7$	1.74487	0.659499	0.329750	−	0.944068i	$-0.393036\pi$
$7$	1.74487	0.659499	0.329750	+	0.944068i	$0.393036\pi$
$8$	−1.90054	−0.671944
$9$	1.00000	0.333333
$10$	−1.96819	−0.622397
$11$	−4.22106	−1.27270	−0.636348	−	0.771402i	$-0.719556\pi$
$11$	−4.22106	−1.27270	−0.636348	+	0.771402i	$0.719556\pi$
$12$	1.74205	0.502886
$13$	5.10306	1.41533	0.707667	−	0.706546i	$-0.249748\pi$
$13$	5.10306	1.41533	0.707667	+	0.706546i	$0.249748\pi$
$14$	0.886200	0.236847
$15$	3.87524	1.00058
$16$	2.51883	0.629709
$17$	7.21103	1.74893	0.874466	−	0.485088i	$-0.161212\pi$
$17$	7.21103	1.74893	0.874466	+	0.485088i	$0.161212\pi$
$18$	0.507888	0.119710
$19$	3.54054	0.812256	0.406128	−	0.913816i	$-0.366879\pi$
$19$	3.54054	0.812256	0.406128	+	0.913816i	$0.366879\pi$
$20$	6.75087	1.50954
$21$	−1.74487	−0.380762
$22$	−2.14383	−0.457065
$23$	−0.786215	−0.163937	−0.0819686	−	0.996635i	$-0.526121\pi$
$23$	−0.786215	−0.163937	−0.0819686	+	0.996635i	$0.526121\pi$
$24$	1.90054	0.387947
$25$	10.0175	2.00350
$26$	2.59179	0.508291
$27$	−1.00000	−0.192450
$28$	−3.03965	−0.574440
$29$	−8.18532	−1.51998	−0.759988	−	0.649937i	$-0.774795\pi$
$29$	−8.18532	−1.51998	−0.759988	+	0.649937i	$0.774795\pi$
$30$	1.96819	0.359341
$31$	−5.37761	−0.965848	−0.482924	−	0.875662i	$-0.660425\pi$
$31$	−5.37761	−0.965848	−0.482924	+	0.875662i	$0.660425\pi$
$32$	5.08037	0.898092
$33$	4.22106	0.734791
$34$	3.66240	0.628096
$35$	−6.76180	−1.14295
$36$	−1.74205	−0.290342
$37$	3.37387	0.554661	0.277331	−	0.960775i	$-0.410550\pi$
$37$	3.37387	0.554661	0.277331	+	0.960775i	$0.410550\pi$
$38$	1.79820	0.291707
$39$	−5.10306	−0.817144
$40$	7.36507	1.16452
$41$	4.87320	0.761065	0.380533	−	0.924767i	$-0.375741\pi$
$41$	4.87320	0.761065	0.380533	+	0.924767i	$0.375741\pi$
$42$	−0.886200	−0.136744
$43$	−2.35251	−0.358755	−0.179377	−	0.983780i	$-0.557408\pi$
$43$	−2.35251	−0.358755	−0.179377	+	0.983780i	$0.557408\pi$
$44$	7.35329	1.10855
$45$	−3.87524	−0.577687
$46$	−0.399310	−0.0588750
$47$	5.49738	0.801875	0.400937	−	0.916105i	$-0.368684\pi$
$47$	5.49738	0.801875	0.400937	+	0.916105i	$0.368684\pi$
$48$	−2.51883	−0.363562
$49$	−3.95543	−0.565061
$50$	5.08778	0.719521
$51$	−7.21103	−1.00975
$52$	−8.88978	−1.23279
$53$	11.8690	1.63033	0.815164	−	0.579230i	$-0.196647\pi$
$53$	11.8690	1.63033	0.815164	+	0.579230i	$0.196647\pi$
$54$	−0.507888	−0.0691149
$55$	16.3576	2.20566
$56$	−3.31620	−0.443146
$57$	−3.54054	−0.468956
$58$	−4.15723	−0.545871
$59$	11.9278	1.55287	0.776433	−	0.630200i	$-0.217027\pi$
$59$	11.9278	1.55287	0.776433	+	0.630200i	$0.217027\pi$
$60$	−6.75087	−0.871533
$61$	−12.2493	−1.56836	−0.784180	−	0.620534i	$-0.786916\pi$
$61$	−12.2493	−1.56836	−0.784180	+	0.620534i	$0.786916\pi$
$62$	−2.73123	−0.346866
$63$	1.74487	0.219833
$64$	−2.45741	−0.307176
$65$	−19.7756	−2.45286
$66$	2.14383	0.263887
$67$	13.4293	1.64065	0.820326	−	0.571896i	$-0.193792\pi$
$67$	13.4293	1.64065	0.820326	+	0.571896i	$0.193792\pi$
$68$	−12.5620	−1.52336
$69$	0.786215	0.0946492
$70$	−3.43424	−0.410470
$71$	2.80305	0.332661	0.166330	−	0.986070i	$-0.446808\pi$
$71$	2.80305	0.332661	0.166330	+	0.986070i	$0.446808\pi$
$72$	−1.90054	−0.223981
$73$	10.5857	1.23896	0.619482	−	0.785011i	$-0.287343\pi$
$73$	10.5857	1.23896	0.619482	+	0.785011i	$0.287343\pi$
$74$	1.71355	0.199196
$75$	−10.0175	−1.15672
$76$	−6.16780	−0.707495
$77$	−7.36520	−0.839342
$78$	−2.59179	−0.293462
$79$	5.74443	0.646299	0.323149	−	0.946348i	$-0.395258\pi$
$79$	5.74443	0.646299	0.323149	+	0.946348i	$0.395258\pi$
$80$	−9.76110	−1.09132
$81$	1.00000	0.111111
$82$	2.47504	0.273322
$83$	−14.8889	−1.63427	−0.817134	−	0.576448i	$-0.804438\pi$
$83$	−14.8889	−1.63427	−0.817134	+	0.576448i	$0.804438\pi$
$84$	3.03965	0.331653
$85$	−27.9445	−3.03101
$86$	−1.19481	−0.128840
$87$	8.18532	0.877558
$88$	8.02230	0.855180
$89$	−1.54824	−0.164113	−0.0820563	−	0.996628i	$-0.526149\pi$
$89$	−1.54824	−0.164113	−0.0820563	+	0.996628i	$0.526149\pi$
$90$	−1.96819	−0.207466
$91$	8.90418	0.933412
$92$	1.36963	0.142793
$93$	5.37761	0.557632
$94$	2.79205	0.287978
$95$	−13.7205	−1.40769
$96$	−5.08037	−0.518514
$97$	−2.98646	−0.303229	−0.151615	−	0.988440i	$-0.548447\pi$
$97$	−2.98646	−0.303229	−0.151615	+	0.988440i	$0.548447\pi$
$98$	−2.00892	−0.202931
$99$	−4.22106	−0.424232
$100$	−17.4510	−1.74510
$101$	6.19360	0.616287	0.308143	−	0.951340i	$-0.400292\pi$
$101$	6.19360	0.616287	0.308143	+	0.951340i	$0.400292\pi$
$102$	−3.66240	−0.362631
$103$	5.59688	0.551477	0.275739	−	0.961233i	$-0.411078\pi$
$103$	5.59688	0.551477	0.275739	+	0.961233i	$0.411078\pi$
$104$	−9.69859	−0.951025
$105$	6.76180	0.659884
$106$	6.02811	0.585502
$107$	1.30505	0.126164	0.0630821	−	0.998008i	$-0.479907\pi$
$107$	1.30505	0.126164	0.0630821	+	0.998008i	$0.479907\pi$
$108$	1.74205	0.167629
$109$	9.71705	0.930725	0.465362	−	0.885120i	$-0.345924\pi$
$109$	9.71705	0.930725	0.465362	+	0.885120i	$0.345924\pi$
$110$	8.30785	0.792122
$111$	−3.37387	−0.320234
$112$	4.39504	0.415292
$113$	14.4373	1.35814	0.679072	−	0.734072i	$-0.262383\pi$
$113$	14.4373	1.35814	0.679072	+	0.734072i	$0.262383\pi$
$114$	−1.79820	−0.168417
$115$	3.04678	0.284113
$116$	14.2592	1.32394
$117$	5.10306	0.471778
$118$	6.05799	0.557683
$119$	12.5823	1.15342
$120$	−7.36507	−0.672336
$121$	6.81731	0.619755
$122$	−6.22127	−0.563247
$123$	−4.87320	−0.439401
$124$	9.36806	0.841277
$125$	−19.4441	−1.73913
$126$	0.886200	0.0789489
$127$	3.65387	0.324229	0.162114	−	0.986772i	$-0.448169\pi$
$127$	3.65387	0.324229	0.162114	+	0.986772i	$0.448169\pi$
$128$	−11.4088	−1.00841
$129$	2.35251	0.207127
$130$	−10.0438	−0.880900
$131$	−11.7673	−1.02811	−0.514056	−	0.857756i	$-0.671858\pi$
$131$	−11.7673	−1.02811	−0.514056	+	0.857756i	$0.671858\pi$
$132$	−7.35329	−0.640021
$133$	6.17779	0.535682
$134$	6.82059	0.589210
$135$	3.87524	0.333528
$136$	−13.7049	−1.17518
$137$	15.4294	1.31822	0.659111	−	0.752045i	$-0.270933\pi$
$137$	15.4294	1.31822	0.659111	+	0.752045i	$0.270933\pi$
$138$	0.399310	0.0339915
$139$	4.37359	0.370963	0.185481	−	0.982648i	$-0.440616\pi$
$139$	4.37359	0.370963	0.185481	+	0.982648i	$0.440616\pi$
$140$	11.7794	0.995540
$141$	−5.49738	−0.462963
$142$	1.42364	0.119469
$143$	−21.5403	−1.80129
$144$	2.51883	0.209903
$145$	31.7201	2.63421
$146$	5.37636	0.444951
$147$	3.95543	0.326238
$148$	−5.87745	−0.483124
$149$	−20.1278	−1.64893	−0.824467	−	0.565910i	$-0.808525\pi$
$149$	−20.1278	−1.64893	−0.824467	+	0.565910i	$0.808525\pi$
$150$	−5.08778	−0.415416
$151$	−15.1523	−1.23307	−0.616536	−	0.787326i	$-0.711465\pi$
$151$	−15.1523	−1.23307	−0.616536	+	0.787326i	$0.711465\pi$
$152$	−6.72896	−0.545790
$153$	7.21103	0.582977
$154$	−3.74070	−0.301434
$155$	20.8396	1.67387
$156$	8.88978	0.711752
$157$	0.652471	0.0520728	0.0260364	−	0.999661i	$-0.491711\pi$
$157$	0.652471	0.0520728	0.0260364	+	0.999661i	$0.491711\pi$
$158$	2.91753	0.232106
$159$	−11.8690	−0.941271
$160$	−19.6877	−1.55645
$161$	−1.37184	−0.108116
$162$	0.507888	0.0399035
$163$	−14.4535	−1.13208	−0.566041	−	0.824377i	$-0.691526\pi$
$163$	−14.4535	−1.13208	−0.566041	+	0.824377i	$0.691526\pi$
$164$	−8.48935	−0.662907
$165$	−16.3576	−1.27344
$166$	−7.56189	−0.586917
$167$	−10.4070	−0.805320	−0.402660	−	0.915350i	$-0.631914\pi$
$167$	−10.4070	−0.805320	−0.402660	+	0.915350i	$0.631914\pi$
$168$	3.31620	0.255851
$169$	13.0412	1.00317
$170$	−14.1927	−1.08853
$171$	3.54054	0.270752
$172$	4.09819	0.312484
$173$	13.4897	1.02560	0.512801	−	0.858507i	$-0.328608\pi$
$173$	13.4897	1.02560	0.512801	+	0.858507i	$0.328608\pi$
$174$	4.15723	0.315159
$175$	17.4793	1.32131
$176$	−10.6321	−0.801428
$177$	−11.9278	−0.896548
$178$	−0.786331	−0.0589380
$179$	21.4402	1.60252	0.801259	−	0.598317i	$-0.204164\pi$
$179$	21.4402	1.60252	0.801259	+	0.598317i	$0.204164\pi$
$180$	6.75087	0.503180
$181$	0.730083	0.0542667	0.0271333	−	0.999632i	$-0.491362\pi$
$181$	0.730083	0.0542667	0.0271333	+	0.999632i	$0.491362\pi$
$182$	4.52233	0.335217
$183$	12.2493	0.905493
$184$	1.49424	0.110157
$185$	−13.0746	−0.961262
$186$	2.73123	0.200263
$187$	−30.4381	−2.22586
$188$	−9.57670	−0.698453
$189$	−1.74487	−0.126921
$190$	−6.96847	−0.505546
$191$	−6.92113	−0.500796	−0.250398	−	0.968143i	$-0.580561\pi$
$191$	−6.92113	−0.500796	−0.250398	+	0.968143i	$0.580561\pi$
$192$	2.45741	0.177348
$193$	21.2432	1.52912	0.764558	−	0.644555i	$-0.222957\pi$
$193$	21.2432	1.52912	0.764558	+	0.644555i	$0.222957\pi$
$194$	−1.51679	−0.108899
$195$	19.7756	1.41616
$196$	6.89055	0.492182
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	−2.14383	−0.152355
$199$	10.5620	0.748718	0.374359	−	0.927284i	$-0.377863\pi$
$199$	10.5620	0.748718	0.374359	+	0.927284i	$0.377863\pi$
$200$	−19.0387	−1.34624
$201$	−13.4293	−0.947231
$202$	3.14566	0.221328
$203$	−14.2823	−1.00242
$204$	12.5620	0.879514
$205$	−18.8848	−1.31897
$206$	2.84259	0.198053
$207$	−0.786215	−0.0546457
$208$	12.8538	0.891248
$209$	−14.9448	−1.03376
$210$	3.43424	0.236985
$211$	−8.14376	−0.560639	−0.280320	−	0.959907i	$-0.590440\pi$
$211$	−8.14376	−0.560639	−0.280320	+	0.959907i	$0.590440\pi$
$212$	−20.6763	−1.42006
$213$	−2.80305	−0.192062
$214$	0.662821	0.0453095
$215$	9.11656	0.621744
$216$	1.90054	0.129316
$217$	−9.38324	−0.636976
$218$	4.93518	0.334252
$219$	−10.5857	−0.715316
$220$	−28.4958	−1.92119
$221$	36.7983	2.47532
$222$	−1.71355	−0.115006
$223$	25.0228	1.67565	0.837827	−	0.545936i	$-0.183826\pi$
$223$	25.0228	1.67565	0.837827	+	0.545936i	$0.183826\pi$
$224$	8.86460	0.592291
$225$	10.0175	0.667835
$226$	7.33252	0.487752
$227$	−13.8495	−0.919226	−0.459613	−	0.888119i	$-0.652012\pi$
$227$	−13.8495	−0.919226	−0.459613	+	0.888119i	$0.652012\pi$
$228$	6.16780	0.408473
$229$	17.3127	1.14405	0.572027	−	0.820235i	$-0.306157\pi$
$229$	17.3127	1.14405	0.572027	+	0.820235i	$0.306157\pi$
$230$	1.54742	0.102034
$231$	7.36520	0.484594
$232$	15.5566	1.02134
$233$	15.1037	0.989476	0.494738	−	0.869042i	$-0.335264\pi$
$233$	15.1037	0.989476	0.494738	+	0.869042i	$0.335264\pi$
$234$	2.59179	0.169430
$235$	−21.3037	−1.38970
$236$	−20.7788	−1.35258
$237$	−5.74443	−0.373141
$238$	6.39041	0.414229
$239$	9.33833	0.604047	0.302023	−	0.953301i	$-0.402338\pi$
$239$	9.33833	0.604047	0.302023	+	0.953301i	$0.402338\pi$
$240$	9.76110	0.630076
$241$	−12.6052	−0.811970	−0.405985	−	0.913880i	$-0.633072\pi$
$241$	−12.6052	−0.811970	−0.405985	+	0.913880i	$0.633072\pi$
$242$	3.46243	0.222574
$243$	−1.00000	−0.0641500
$244$	21.3388	1.36608
$245$	15.3282	0.979286
$246$	−2.47504	−0.157803
$247$	18.0676	1.14961
$248$	10.2204	0.648995
$249$	14.8889	0.943545
$250$	−9.87544	−0.624578
$251$	6.14687	0.387987	0.193994	−	0.981003i	$-0.437856\pi$
$251$	6.14687	0.387987	0.193994	+	0.981003i	$0.437856\pi$
$252$	−3.03965	−0.191480
$253$	3.31866	0.208642
$254$	1.85576	0.116441
$255$	27.9445	1.74995
$256$	−0.879604	−0.0549752
$257$	−14.7480	−0.919957	−0.459978	−	0.887930i	$-0.652143\pi$
$257$	−14.7480	−0.919957	−0.459978	+	0.887930i	$0.652143\pi$
$258$	1.19481	0.0743858
$259$	5.88697	0.365799
$260$	34.4501	2.13650
$261$	−8.18532	−0.506659
$262$	−5.97647	−0.369227
$263$	6.33007	0.390329	0.195165	−	0.980771i	$-0.437476\pi$
$263$	6.33007	0.390329	0.195165	+	0.980771i	$0.437476\pi$
$264$	−8.02230	−0.493738
$265$	−45.9952	−2.82546
$266$	3.13763	0.192380
$267$	1.54824	0.0947505
$268$	−23.3945	−1.42905
$269$	−0.463551	−0.0282632	−0.0141316	−	0.999900i	$-0.504498\pi$
$269$	−0.463551	−0.0282632	−0.0141316	+	0.999900i	$0.504498\pi$
$270$	1.96819	0.119780
$271$	−6.49925	−0.394801	−0.197401	−	0.980323i	$-0.563250\pi$
$271$	−6.49925	−0.394801	−0.197401	+	0.980323i	$0.563250\pi$
$272$	18.1634	1.10132
$273$	−8.90418	−0.538906
$274$	7.83641	0.473415
$275$	−42.2845	−2.54985
$276$	−1.36963	−0.0824418
$277$	−22.1114	−1.32855	−0.664273	−	0.747490i	$-0.731259\pi$
$277$	−22.1114	−1.32855	−0.664273	+	0.747490i	$0.731259\pi$
$278$	2.22129	0.133224
$279$	−5.37761	−0.321949
$280$	12.8511	0.768000
$281$	8.76446	0.522844	0.261422	−	0.965225i	$-0.415809\pi$
$281$	8.76446	0.522844	0.261422	+	0.965225i	$0.415809\pi$
$282$	−2.79205	−0.166264
$283$	−10.8794	−0.646716	−0.323358	−	0.946277i	$-0.604812\pi$
$283$	−10.8794	−0.646716	−0.323358	+	0.946277i	$0.604812\pi$
$284$	−4.88305	−0.289756
$285$	13.7205	0.812731
$286$	−10.9401	−0.646900
$287$	8.50310	0.501922
$288$	5.08037	0.299364
$289$	34.9989	2.05876
$290$	16.1103	0.946028
$291$	2.98646	0.175069
$292$	−18.4408	−1.07917
$293$	18.5628	1.08445	0.542226	−	0.840233i	$-0.317582\pi$
$293$	18.5628	1.08445	0.542226	+	0.840233i	$0.317582\pi$
$294$	2.00892	0.117162
$295$	−46.2231	−2.69121
$296$	−6.41219	−0.372701
$297$	4.22106	0.244930
$298$	−10.2227	−0.592184
$299$	−4.01211	−0.232026
$300$	17.4510	1.00753
$301$	−4.10483	−0.236598
$302$	−7.69565	−0.442835
$303$	−6.19360	−0.355813
$304$	8.91804	0.511485
$305$	47.4689	2.71806
$306$	3.66240	0.209365
$307$	−28.2122	−1.61015	−0.805077	−	0.593170i	$-0.797876\pi$
$307$	−28.2122	−1.61015	−0.805077	+	0.593170i	$0.797876\pi$
$308$	12.8305	0.731088
$309$	−5.59688	−0.318396
$310$	10.5842	0.601141
$311$	−17.9758	−1.01932	−0.509658	−	0.860377i	$-0.670228\pi$
$311$	−17.9758	−1.01932	−0.509658	+	0.860377i	$0.670228\pi$
$312$	9.69859	0.549075
$313$	−23.2208	−1.31252	−0.656258	−	0.754536i	$-0.727862\pi$
$313$	−23.2208	−1.31252	−0.656258	+	0.754536i	$0.727862\pi$
$314$	0.331382	0.0187010
$315$	−6.76180	−0.380984
$316$	−10.0071	−0.562942
$317$	15.1085	0.848580	0.424290	−	0.905526i	$-0.360524\pi$
$317$	15.1085	0.848580	0.424290	+	0.905526i	$0.360524\pi$
$318$	−6.02811	−0.338040
$319$	34.5507	1.93447
$320$	9.52305	0.532355
$321$	−1.30505	−0.0728409
$322$	−0.696744	−0.0388280
$323$	25.5310	1.42058
$324$	−1.74205	−0.0967805
$325$	51.1200	2.83563
$326$	−7.34075	−0.406566
$327$	−9.71705	−0.537354
$328$	−9.26172	−0.511393
$329$	9.59221	0.528836
$330$	−8.30785	−0.457332
$331$	21.6433	1.18963	0.594813	−	0.803864i	$-0.297226\pi$
$331$	21.6433	1.18963	0.594813	+	0.803864i	$0.297226\pi$
$332$	25.9372	1.42349
$333$	3.37387	0.184887
$334$	−5.28561	−0.289216
$335$	−52.0419	−2.84335
$336$	−4.39504	−0.239769
$337$	10.2754	0.559736	0.279868	−	0.960038i	$-0.409709\pi$
$337$	10.2754	0.559736	0.279868	+	0.960038i	$0.409709\pi$
$338$	6.62349	0.360270
$339$	−14.4373	−0.784125
$340$	48.6807	2.64008
$341$	22.6992	1.22923
$342$	1.79820	0.0972356
$343$	−19.1158	−1.03216
$344$	4.47105	0.241063
$345$	−3.04678	−0.164033
$346$	6.85126	0.368326
$347$	−2.75521	−0.147908	−0.0739538	−	0.997262i	$-0.523562\pi$
$347$	−2.75521	−0.147908	−0.0739538	+	0.997262i	$0.523562\pi$
$348$	−14.2592	−0.764375
$349$	7.94937	0.425520	0.212760	−	0.977105i	$-0.431755\pi$
$349$	7.94937	0.425520	0.212760	+	0.977105i	$0.431755\pi$
$350$	8.87752	0.474524
$351$	−5.10306	−0.272381
$352$	−21.4445	−1.14300
$353$	17.0858	0.909384	0.454692	−	0.890649i	$-0.349749\pi$
$353$	17.0858	0.909384	0.454692	+	0.890649i	$0.349749\pi$
$354$	−6.05799	−0.321978
$355$	−10.8625	−0.576522
$356$	2.69710	0.142946
$357$	−12.5823	−0.665926
$358$	10.8892	0.575515
$359$	−22.6716	−1.19656	−0.598280	−	0.801287i	$-0.704149\pi$
$359$	−22.6716	−1.19656	−0.598280	+	0.801287i	$0.704149\pi$
$360$	7.36507	0.388173
$361$	−6.46455	−0.340240
$362$	0.370801	0.0194889
$363$	−6.81731	−0.357816
$364$	−15.5115	−0.813025
$365$	−41.0222	−2.14720
$366$	6.22127	0.325191
$367$	−1.17680	−0.0614287	−0.0307143	−	0.999528i	$-0.509778\pi$
$367$	−1.17680	−0.0614287	−0.0307143	+	0.999528i	$0.509778\pi$
$368$	−1.98035	−0.103233
$369$	4.87320	0.253688
$370$	−6.64043	−0.345219
$371$	20.7098	1.07520
$372$	−9.36806	−0.485712
$373$	−26.0858	−1.35067	−0.675335	−	0.737511i	$-0.736001\pi$
$373$	−26.0858	−1.35067	−0.675335	+	0.737511i	$0.736001\pi$
$374$	−15.4592	−0.799375
$375$	19.4441	1.00409
$376$	−10.4480	−0.538815
$377$	−41.7702	−2.15127
$378$	−0.886200	−0.0455812
$379$	−0.744035	−0.0382185	−0.0191093	−	0.999817i	$-0.506083\pi$
$379$	−0.744035	−0.0382185	−0.0191093	+	0.999817i	$0.506083\pi$
$380$	23.9017	1.22613
$381$	−3.65387	−0.187194
$382$	−3.51516	−0.179851
$383$	−33.4359	−1.70849	−0.854247	−	0.519867i	$-0.825982\pi$
$383$	−33.4359	−1.70849	−0.854247	+	0.519867i	$0.825982\pi$
$384$	11.4088	0.582205
$385$	28.5419	1.45463
$386$	10.7892	0.549153
$387$	−2.35251	−0.119585
$388$	5.20256	0.264120
$389$	15.2125	0.771302	0.385651	−	0.922645i	$-0.373977\pi$
$389$	15.2125	0.771302	0.385651	+	0.922645i	$0.373977\pi$
$390$	10.0438	0.508588
$391$	−5.66942	−0.286715
$392$	7.51746	0.379689
$393$	11.7673	0.593581
$394$	0.507888	0.0255870
$395$	−22.2611	−1.12008
$396$	7.35329	0.369517
$397$	13.0861	0.656774	0.328387	−	0.944543i	$-0.393495\pi$
$397$	13.0861	0.656774	0.328387	+	0.944543i	$0.393495\pi$
$398$	5.36430	0.268888
$399$	−6.17779	−0.309276
$400$	25.2325	1.26162
$401$	24.0711	1.20205	0.601027	−	0.799229i	$-0.294758\pi$
$401$	24.0711	1.20205	0.601027	+	0.799229i	$0.294758\pi$
$402$	−6.82059	−0.340180
$403$	−27.4423	−1.36700
$404$	−10.7896	−0.536801
$405$	−3.87524	−0.192562
$406$	−7.25383	−0.360001
$407$	−14.2413	−0.705915
$408$	13.7049	0.678492
$409$	−7.15990	−0.354034	−0.177017	−	0.984208i	$-0.556645\pi$
$409$	−7.15990	−0.354034	−0.177017	+	0.984208i	$0.556645\pi$
$410$	−9.59138	−0.473685
$411$	−15.4294	−0.761076
$412$	−9.75005	−0.480350
$413$	20.8125	1.02411
$414$	−0.399310	−0.0196250
$415$	57.6981	2.83229
$416$	25.9255	1.27110
$417$	−4.37359	−0.214175
$418$	−7.59031	−0.371254
$419$	22.8993	1.11870	0.559351	−	0.828931i	$-0.311050\pi$
$419$	22.8993	1.11870	0.559351	+	0.828931i	$0.311050\pi$
$420$	−11.7794	−0.574775
$421$	−3.08401	−0.150306	−0.0751528	−	0.997172i	$-0.523944\pi$
$421$	−3.08401	−0.150306	−0.0751528	+	0.997172i	$0.523944\pi$
$422$	−4.13612	−0.201343
$423$	5.49738	0.267292
$424$	−22.5575	−1.09549
$425$	72.2366	3.50399
$426$	−1.42364	−0.0689754
$427$	−21.3734	−1.03433
$428$	−2.27347	−0.109892
$429$	21.5403	1.03998
$430$	4.63019	0.223288
$431$	14.2950	0.688565	0.344283	−	0.938866i	$-0.388122\pi$
$431$	14.2950	0.688565	0.344283	+	0.938866i	$0.388122\pi$
$432$	−2.51883	−0.121187
$433$	12.8831	0.619122	0.309561	−	0.950880i	$-0.399818\pi$
$433$	12.8831	0.619122	0.309561	+	0.950880i	$0.399818\pi$
$434$	−4.76564	−0.228758
$435$	−31.7201	−1.52086
$436$	−16.9276	−0.810684
$437$	−2.78363	−0.133159
$438$	−5.37636	−0.256892
$439$	−8.19967	−0.391349	−0.195675	−	0.980669i	$-0.562690\pi$
$439$	−8.19967	−0.391349	−0.195675	+	0.980669i	$0.562690\pi$
$440$	−31.0884	−1.48208
$441$	−3.95543	−0.188354
$442$	18.6894	0.888966
$443$	28.7053	1.36383	0.681915	−	0.731432i	$-0.261148\pi$
$443$	28.7053	1.36383	0.681915	+	0.731432i	$0.261148\pi$
$444$	5.87745	0.278931
$445$	5.99979	0.284417
$446$	12.7088	0.601780
$447$	20.1278	0.952013
$448$	−4.28786	−0.202582
$449$	−8.72830	−0.411914	−0.205957	−	0.978561i	$-0.566031\pi$
$449$	−8.72830	−0.411914	−0.205957	+	0.978561i	$0.566031\pi$
$450$	5.08778	0.239840
$451$	−20.5700	−0.968605
$452$	−25.1504	−1.18298
$453$	15.1523	0.711915
$454$	−7.03402	−0.330123
$455$	−34.5059	−1.61766
$456$	6.72896	0.315112
$457$	11.0307	0.515997	0.257998	−	0.966145i	$-0.416937\pi$
$457$	11.0307	0.515997	0.257998	+	0.966145i	$0.416937\pi$
$458$	8.79291	0.410866
$459$	−7.21103	−0.336582
$460$	−5.30764	−0.247470
$461$	−22.4098	−1.04373	−0.521865	−	0.853028i	$-0.674763\pi$
$461$	−22.4098	−1.04373	−0.521865	+	0.853028i	$0.674763\pi$
$462$	3.74070	0.174033
$463$	16.9812	0.789183	0.394592	−	0.918857i	$-0.370886\pi$
$463$	16.9812	0.789183	0.394592	+	0.918857i	$0.370886\pi$
$464$	−20.6175	−0.957142
$465$	−20.8396	−0.966411
$466$	7.67099	0.355352
$467$	−21.4828	−0.994104	−0.497052	−	0.867721i	$-0.665584\pi$
$467$	−21.4828	−0.994104	−0.497052	+	0.867721i	$0.665584\pi$
$468$	−8.88978	−0.410930
$469$	23.4324	1.08201
$470$	−10.8199	−0.499084
$471$	−0.652471	−0.0300643
$472$	−22.6693	−1.04344
$473$	9.93008	0.456586
$474$	−2.91753	−0.134007
$475$	35.4675	1.62736
$476$	−21.9190	−1.00466
$477$	11.8690	0.543443
$478$	4.74283	0.216932
$479$	8.77656	0.401011	0.200506	−	0.979693i	$-0.435742\pi$
$479$	8.77656	0.401011	0.200506	+	0.979693i	$0.435742\pi$
$480$	19.6877	0.898616
$481$	17.2171	0.785031
$482$	−6.40202	−0.291604
$483$	1.37184	0.0624211
$484$	−11.8761	−0.539822
$485$	11.5733	0.525515
$486$	−0.507888	−0.0230383
$487$	27.2078	1.23290	0.616451	−	0.787394i	$-0.288570\pi$
$487$	27.2078	1.23290	0.616451	+	0.787394i	$0.288570\pi$
$488$	23.2803	1.05385
$489$	14.4535	0.653608
$490$	7.78504	0.351692
$491$	0.852587	0.0384767	0.0192384	−	0.999815i	$-0.493876\pi$
$491$	0.852587	0.0384767	0.0192384	+	0.999815i	$0.493876\pi$
$492$	8.48935	0.382729
$493$	−59.0246	−2.65833
$494$	9.17633	0.412863
$495$	16.3576	0.735220
$496$	−13.5453	−0.608203
$497$	4.89096	0.219390
$498$	7.56189	0.338857
$499$	−3.00160	−0.134370	−0.0671850	−	0.997741i	$-0.521402\pi$
$499$	−3.00160	−0.134370	−0.0671850	+	0.997741i	$0.521402\pi$
$500$	33.8726	1.51483
$501$	10.4070	0.464952
$502$	3.12193	0.139338
$503$	−16.8007	−0.749105	−0.374552	−	0.927206i	$-0.622204\pi$
$503$	−16.8007	−0.749105	−0.374552	+	0.927206i	$0.622204\pi$
$504$	−3.31620	−0.147715
$505$	−24.0017	−1.06806
$506$	1.68551	0.0749300
$507$	−13.0412	−0.579182
$508$	−6.36523	−0.282411
$509$	9.57205	0.424274	0.212137	−	0.977240i	$-0.431958\pi$
$509$	9.57205	0.424274	0.212137	+	0.977240i	$0.431958\pi$
$510$	14.1927	0.628463
$511$	18.4707	0.817096
$512$	22.3709	0.988665
$513$	−3.54054	−0.156319
$514$	−7.49035	−0.330385
$515$	−21.6893	−0.955744
$516$	−4.09819	−0.180413
$517$	−23.2047	−1.02054
$518$	2.98992	0.131370
$519$	−13.4897	−0.592132
$520$	37.5844	1.64819
$521$	−7.40942	−0.324613	−0.162306	−	0.986740i	$-0.551893\pi$
$521$	−7.40942	−0.324613	−0.162306	+	0.986740i	$0.551893\pi$
$522$	−4.15723	−0.181957
$523$	−11.7495	−0.513769	−0.256885	−	0.966442i	$-0.582696\pi$
$523$	−11.7495	−0.513769	−0.256885	+	0.966442i	$0.582696\pi$
$524$	20.4992	0.895511
$525$	−17.4793	−0.762858
$526$	3.21497	0.140179
$527$	−38.7781	−1.68920
$528$	10.6321	0.462705
$529$	−22.3819	−0.973125
$530$	−23.3604	−1.01471
$531$	11.9278	0.517622
$532$	−10.7620	−0.466593
$533$	24.8682	1.07716
$534$	0.786331	0.0340279
$535$	−5.05740	−0.218650
$536$	−25.5230	−1.10243
$537$	−21.4402	−0.925215
$538$	−0.235432	−0.0101502
$539$	16.6961	0.719151
$540$	−6.75087	−0.290511
$541$	−25.1858	−1.08282	−0.541411	−	0.840758i	$-0.682110\pi$
$541$	−25.1858	−1.08282	−0.541411	+	0.840758i	$0.682110\pi$
$542$	−3.30089	−0.141785
$543$	−0.730083	−0.0313309
$544$	36.6347	1.57070
$545$	−37.6559	−1.61300
$546$	−4.52233	−0.193538
$547$	−5.01027	−0.214224	−0.107112	−	0.994247i	$-0.534160\pi$
$547$	−5.01027	−0.214224	−0.107112	+	0.994247i	$0.534160\pi$
$548$	−26.8788	−1.14820
$549$	−12.2493	−0.522786
$550$	−21.4758	−0.915732
$551$	−28.9805	−1.23461
$552$	−1.49424	−0.0635989
$553$	10.0233	0.426233
$554$	−11.2301	−0.477123
$555$	13.0746	0.554985
$556$	−7.61900	−0.323118
$557$	13.3412	0.565284	0.282642	−	0.959225i	$-0.408789\pi$
$557$	13.3412	0.565284	0.282642	+	0.959225i	$0.408789\pi$
$558$	−2.73123	−0.115622
$559$	−12.0050	−0.507758
$560$	−17.0319	−0.719727
$561$	30.4381	1.28510
$562$	4.45137	0.187770
$563$	−15.9846	−0.673670	−0.336835	−	0.941564i	$-0.609356\pi$
$563$	−15.9846	−0.673670	−0.336835	+	0.941564i	$0.609356\pi$
$564$	9.57670	0.403252
$565$	−55.9479	−2.35375
$566$	−5.52554	−0.232256
$567$	1.74487	0.0732777
$568$	−5.32732	−0.223529
$569$	32.6744	1.36978	0.684891	−	0.728646i	$-0.259850\pi$
$569$	32.6744	1.36978	0.684891	+	0.728646i	$0.259850\pi$
$570$	6.96847	0.291877
$571$	−8.21244	−0.343680	−0.171840	−	0.985125i	$-0.554971\pi$
$571$	−8.21244	−0.343680	−0.171840	+	0.985125i	$0.554971\pi$
$572$	37.5243	1.56897
$573$	6.92113	0.289135
$574$	4.31862	0.180256
$575$	−7.87593	−0.328449
$576$	−2.45741	−0.102392
$577$	10.2414	0.426354	0.213177	−	0.977014i	$-0.431619\pi$
$577$	10.2414	0.426354	0.213177	+	0.977014i	$0.431619\pi$
$578$	17.7755	0.739365
$579$	−21.2432	−0.882835
$580$	−55.2580	−2.29446
$581$	−25.9792	−1.07780
$582$	1.51679	0.0628729
$583$	−50.0996	−2.07491
$584$	−20.1186	−0.832514
$585$	−19.7756	−0.817621
$586$	9.42785	0.389461
$587$	−7.61757	−0.314411	−0.157205	−	0.987566i	$-0.550248\pi$
$587$	−7.61757	−0.314411	−0.157205	+	0.987566i	$0.550248\pi$
$588$	−6.89055	−0.284161
$589$	−19.0397	−0.784516
$590$	−23.4762	−0.966499
$591$	−1.00000	−0.0411345
$592$	8.49823	0.349275
$593$	−36.6921	−1.50676	−0.753382	−	0.657584i	$-0.771579\pi$
$593$	−36.6921	−1.50676	−0.753382	+	0.657584i	$0.771579\pi$
$594$	2.14383	0.0879622
$595$	−48.7595	−1.99895
$596$	35.0636	1.43626
$597$	−10.5620	−0.432273
$598$	−2.03770	−0.0833278
$599$	−19.7280	−0.806063	−0.403032	−	0.915186i	$-0.632044\pi$
$599$	−19.7280	−0.806063	−0.403032	+	0.915186i	$0.632044\pi$
$600$	19.0387	0.777253
$601$	−2.54191	−0.103686	−0.0518432	−	0.998655i	$-0.516510\pi$
$601$	−2.54191	−0.103686	−0.0518432	+	0.998655i	$0.516510\pi$
$602$	−2.08480	−0.0849699
$603$	13.4293	0.546884
$604$	26.3960	1.07404
$605$	−26.4187	−1.07407
$606$	−3.14566	−0.127784
$607$	13.2925	0.539525	0.269763	−	0.962927i	$-0.413055\pi$
$607$	13.2925	0.539525	0.269763	+	0.962927i	$0.413055\pi$
$608$	17.9873	0.729481
$609$	14.2823	0.578749
$610$	24.1089	0.976142
$611$	28.0534	1.13492
$612$	−12.5620	−0.507787
$613$	5.38710	0.217583	0.108791	−	0.994065i	$-0.465302\pi$
$613$	5.38710	0.217583	0.108791	+	0.994065i	$0.465302\pi$
$614$	−14.3286	−0.578257
$615$	18.8848	0.761510
$616$	13.9979	0.563990
$617$	29.6708	1.19450	0.597250	−	0.802055i	$-0.296260\pi$
$617$	29.6708	1.19450	0.597250	+	0.802055i	$0.296260\pi$
$618$	−2.84259	−0.114346
$619$	−5.77137	−0.231971	−0.115986	−	0.993251i	$-0.537003\pi$
$619$	−5.77137	−0.231971	−0.115986	+	0.993251i	$0.537003\pi$
$620$	−36.3035	−1.45799
$621$	0.786215	0.0315497
$622$	−9.12971	−0.366068
$623$	−2.70147	−0.108232
$624$	−12.8538	−0.514563
$625$	25.2631	1.01052
$626$	−11.7936	−0.471366
$627$	14.9448	0.596839
$628$	−1.13664	−0.0453567
$629$	24.3291	0.970064
$630$	−3.43424	−0.136823
$631$	−47.2099	−1.87940	−0.939698	−	0.342005i	$-0.888894\pi$
$631$	−47.2099	−1.87940	−0.939698	+	0.342005i	$0.888894\pi$
$632$	−10.9175	−0.434276
$633$	8.14376	0.323685
$634$	7.67345	0.304752
$635$	−14.1597	−0.561909
$636$	20.6763	0.819870
$637$	−20.1848	−0.799750
$638$	17.5479	0.694728
$639$	2.80305	0.110887
$640$	44.2120	1.74763
$641$	16.5361	0.653135	0.326567	−	0.945174i	$-0.394108\pi$
$641$	16.5361	0.653135	0.326567	+	0.945174i	$0.394108\pi$
$642$	−0.662821	−0.0261595
$643$	45.5661	1.79695	0.898475	−	0.439025i	$-0.144676\pi$
$643$	45.5661	1.79695	0.898475	+	0.439025i	$0.144676\pi$
$644$	2.38982	0.0941721
$645$	−9.11656	−0.358964
$646$	12.9669	0.510175
$647$	−29.1494	−1.14598	−0.572991	−	0.819562i	$-0.694217\pi$
$647$	−29.1494	−1.14598	−0.572991	+	0.819562i	$0.694217\pi$
$648$	−1.90054	−0.0746604
$649$	−50.3479	−1.97633
$650$	25.9633	1.01836
$651$	9.38324	0.367758
$652$	25.1786	0.986072
$653$	20.6527	0.808204	0.404102	−	0.914714i	$-0.367584\pi$
$653$	20.6527	0.808204	0.404102	+	0.914714i	$0.367584\pi$
$654$	−4.93518	−0.192981
$655$	45.6011	1.78178
$656$	12.2748	0.479249
$657$	10.5857	0.412988
$658$	4.87177	0.189921
$659$	−12.2614	−0.477636	−0.238818	−	0.971064i	$-0.576760\pi$
$659$	−12.2614	−0.477636	−0.238818	+	0.971064i	$0.576760\pi$
$660$	28.4958	1.10920
$661$	−41.5946	−1.61784	−0.808921	−	0.587918i	$-0.799948\pi$
$661$	−41.5946	−1.61784	−0.808921	+	0.587918i	$0.799948\pi$
$662$	10.9924	0.427232
$663$	−36.7983	−1.42913
$664$	28.2970	1.09814
$665$	−23.9404	−0.928371
$666$	1.71355	0.0663987
$667$	6.43542	0.249181
$668$	18.1296	0.701454
$669$	−25.0228	−0.967439
$670$	−26.4315	−1.02114
$671$	51.7049	1.99604
$672$	−8.86460	−0.341959
$673$	33.1385	1.27740	0.638698	−	0.769458i	$-0.279474\pi$
$673$	33.1385	1.27740	0.638698	+	0.769458i	$0.279474\pi$
$674$	5.21875	0.201019
$675$	−10.0175	−0.385575
$676$	−22.7185	−0.873788
$677$	−0.810846	−0.0311633	−0.0155817	−	0.999879i	$-0.504960\pi$
$677$	−0.810846	−0.0311633	−0.0155817	+	0.999879i	$0.504960\pi$
$678$	−7.33252	−0.281604
$679$	−5.21099	−0.199979
$680$	53.1097	2.03667
$681$	13.8495	0.530715
$682$	11.5287	0.441455
$683$	−22.6705	−0.867462	−0.433731	−	0.901042i	$-0.642803\pi$
$683$	−22.6705	−0.867462	−0.433731	+	0.901042i	$0.642803\pi$
$684$	−6.16780	−0.235832
$685$	−59.7927	−2.28456
$686$	−9.70869	−0.370680
$687$	−17.3127	−0.660520
$688$	−5.92559	−0.225911
$689$	60.5681	2.30746
$690$	−1.54742	−0.0589094
$691$	40.8647	1.55457	0.777283	−	0.629152i	$-0.216598\pi$
$691$	40.8647	1.55457	0.777283	+	0.629152i	$0.216598\pi$
$692$	−23.4997	−0.893325
$693$	−7.36520	−0.279781
$694$	−1.39934	−0.0531182
$695$	−16.9487	−0.642901
$696$	−15.5566	−0.589670
$697$	35.1407	1.33105
$698$	4.03739	0.152818
$699$	−15.1037	−0.571274
$700$	−30.4498	−1.15089
$701$	−37.2339	−1.40631	−0.703153	−	0.711039i	$-0.748225\pi$
$701$	−37.2339	−1.40631	−0.703153	+	0.711039i	$0.748225\pi$
$702$	−2.59179	−0.0978207
$703$	11.9453	0.450527
$704$	10.3728	0.390941
$705$	21.3037	0.802343
$706$	8.67767	0.326588
$707$	10.8070	0.406441
$708$	20.7788	0.780915
$709$	21.2722	0.798895	0.399448	−	0.916756i	$-0.369202\pi$
$709$	21.2722	0.798895	0.399448	+	0.916756i	$0.369202\pi$
$710$	−5.51694	−0.207047
$711$	5.74443	0.215433
$712$	2.94249	0.110274
$713$	4.22796	0.158338
$714$	−6.39041	−0.239155
$715$	83.4739	3.12175
$716$	−37.3500	−1.39583
$717$	−9.33833	−0.348746
$718$	−11.5146	−0.429722
$719$	−19.1782	−0.715227	−0.357613	−	0.933870i	$-0.616409\pi$
$719$	−19.1782	−0.715227	−0.357613	+	0.933870i	$0.616409\pi$
$720$	−9.76110	−0.363775
$721$	9.76584	0.363699
$722$	−3.28327	−0.122191
$723$	12.6052	0.468791
$724$	−1.27184	−0.0472676
$725$	−81.9966	−3.04528
$726$	−3.46243	−0.128503
$727$	−7.92808	−0.294036	−0.147018	−	0.989134i	$-0.546968\pi$
$727$	−7.92808	−0.294036	−0.147018	+	0.989134i	$0.546968\pi$
$728$	−16.9228	−0.627200
$729$	1.00000	0.0370370
$730$	−20.8347	−0.771127
$731$	−16.9640	−0.627437
$732$	−21.3388	−0.788706
$733$	36.4914	1.34784	0.673921	−	0.738803i	$-0.264609\pi$
$733$	36.4914	1.34784	0.673921	+	0.738803i	$0.264609\pi$
$734$	−0.597685	−0.0220610
$735$	−15.3282	−0.565391
$736$	−3.99427	−0.147231
$737$	−56.6859	−2.08805
$738$	2.47504	0.0911075
$739$	−46.2736	−1.70220	−0.851101	−	0.525002i	$-0.824065\pi$
$739$	−46.2736	−1.70220	−0.851101	+	0.525002i	$0.824065\pi$
$740$	22.7766	0.837283
$741$	−18.0676	−0.663730
$742$	10.5183	0.386138
$743$	−13.5188	−0.495955	−0.247978	−	0.968766i	$-0.579766\pi$
$743$	−13.5188	−0.495955	−0.247978	+	0.968766i	$0.579766\pi$
$744$	−10.2204	−0.374697
$745$	78.0002	2.85771
$746$	−13.2487	−0.485068
$747$	−14.8889	−0.544756
$748$	53.0248	1.93878
$749$	2.27715	0.0832052
$750$	9.87544	0.360600
$751$	12.2198	0.445908	0.222954	−	0.974829i	$-0.428430\pi$
$751$	12.2198	0.445908	0.222954	+	0.974829i	$0.428430\pi$
$752$	13.8470	0.504947
$753$	−6.14687	−0.224004
$754$	−21.2146	−0.772590
$755$	58.7187	2.13699
$756$	3.03965	0.110551
$757$	1.89559	0.0688963	0.0344481	−	0.999406i	$-0.489033\pi$
$757$	1.89559	0.0688963	0.0344481	+	0.999406i	$0.489033\pi$
$758$	−0.377887	−0.0137255
$759$	−3.31866	−0.120460
$760$	26.0764	0.945889
$761$	40.4538	1.46645	0.733224	−	0.679987i	$-0.238015\pi$
$761$	40.4538	1.46645	0.733224	+	0.679987i	$0.238015\pi$
$762$	−1.85576	−0.0672271
$763$	16.9550	0.613812
$764$	12.0570	0.436205
$765$	−27.9445	−1.01034
$766$	−16.9817	−0.613574
$767$	60.8683	2.19783
$768$	0.879604	0.0317400
$769$	−36.1808	−1.30471	−0.652357	−	0.757912i	$-0.726220\pi$
$769$	−36.1808	−1.30471	−0.652357	+	0.757912i	$0.726220\pi$
$770$	14.4961	0.522404
$771$	14.7480	0.531137
$772$	−37.0066	−1.33190
$773$	−9.95164	−0.357936	−0.178968	−	0.983855i	$-0.557276\pi$
$773$	−9.95164	−0.357936	−0.178968	+	0.983855i	$0.557276\pi$
$774$	−1.19481	−0.0429467
$775$	−53.8703	−1.93508
$776$	5.67590	0.203753
$777$	−5.88697	−0.211194
$778$	7.72623	0.276999
$779$	17.2538	0.618180
$780$	−34.4501	−1.23351
$781$	−11.8318	−0.423376
$782$	−2.87943	−0.102968
$783$	8.18532	0.292519
$784$	−9.96306	−0.355824
$785$	−2.52848	−0.0902454
$786$	5.97647	0.213174
$787$	31.3670	1.11811	0.559057	−	0.829129i	$-0.311163\pi$
$787$	31.3670	1.11811	0.559057	+	0.829129i	$0.311163\pi$
$788$	−1.74205	−0.0620579
$789$	−6.33007	−0.225357
$790$	−11.3061	−0.402254
$791$	25.1912	0.895694
$792$	8.02230	0.285060
$793$	−62.5088	−2.21975
$794$	6.64629	0.235868
$795$	45.9952	1.63128
$796$	−18.3995	−0.652152
$797$	−15.3571	−0.543978	−0.271989	−	0.962300i	$-0.587681\pi$
$797$	−15.3571	−0.543978	−0.271989	+	0.962300i	$0.587681\pi$
$798$	−3.13763	−0.111071
$799$	39.6417	1.40242
$800$	50.8928	1.79933
$801$	−1.54824	−0.0547042
$802$	12.2254	0.431695
$803$	−44.6829	−1.57682
$804$	23.3945	0.825061
$805$	5.31623	0.187373
$806$	−13.9376	−0.490932
$807$	0.463551	0.0163178
$808$	−11.7712	−0.414110
$809$	9.82774	0.345525	0.172763	−	0.984964i	$-0.444731\pi$
$809$	9.82774	0.345525	0.172763	+	0.984964i	$0.444731\pi$
$810$	−1.96819	−0.0691552
$811$	35.9132	1.26108	0.630542	−	0.776155i	$-0.282833\pi$
$811$	35.9132	1.26108	0.630542	+	0.776155i	$0.282833\pi$
$812$	24.8805	0.873135
$813$	6.49925	0.227939
$814$	−7.23299	−0.253516
$815$	56.0107	1.96197
$816$	−18.1634	−0.635846
$817$	−8.32917	−0.291401
$818$	−3.63643	−0.127145
$819$	8.90418	0.311137
$820$	32.8983	1.14886
$821$	−35.8676	−1.25179	−0.625895	−	0.779908i	$-0.715266\pi$
$821$	−35.8676	−1.25179	−0.625895	+	0.779908i	$0.715266\pi$
$822$	−7.83641	−0.273326
$823$	−43.1858	−1.50536	−0.752680	−	0.658386i	$-0.771239\pi$
$823$	−43.1858	−1.50536	−0.752680	+	0.658386i	$0.771239\pi$
$824$	−10.6371	−0.370562
$825$	42.2845	1.47216
$826$	10.5704	0.367791
$827$	33.2194	1.15515	0.577576	−	0.816337i	$-0.303999\pi$
$827$	33.2194	1.15515	0.577576	+	0.816337i	$0.303999\pi$
$828$	1.36963	0.0475978
$829$	−12.7297	−0.442120	−0.221060	−	0.975260i	$-0.570952\pi$
$829$	−12.7297	−0.442120	−0.221060	+	0.975260i	$0.570952\pi$
$830$	29.3042	1.01716
$831$	22.1114	0.767037
$832$	−12.5403	−0.434756
$833$	−28.5227	−0.988253
$834$	−2.22129	−0.0769171
$835$	40.3298	1.39567
$836$	26.0346	0.900427
$837$	5.37761	0.185877
$838$	11.6303	0.401761
$839$	7.84886	0.270973	0.135486	−	0.990779i	$-0.456740\pi$
$839$	7.84886	0.270973	0.135486	+	0.990779i	$0.456740\pi$
$840$	−12.8511	−0.443405
$841$	37.9995	1.31033
$842$	−1.56634	−0.0539795
$843$	−8.76446	−0.301864
$844$	14.1868	0.488331
$845$	−50.5380	−1.73856
$846$	2.79205	0.0959928
$847$	11.8953	0.408728
$848$	29.8960	1.02663
$849$	10.8794	0.373382
$850$	36.6881	1.25839
$851$	−2.65259	−0.0909296
$852$	4.88305	0.167291
$853$	−24.7803	−0.848460	−0.424230	−	0.905554i	$-0.639455\pi$
$853$	−24.7803	−0.848460	−0.424230	+	0.905554i	$0.639455\pi$
$854$	−10.8553	−0.371461
$855$	−13.7205	−0.469230
$856$	−2.48031	−0.0847752
$857$	28.2845	0.966181	0.483090	−	0.875571i	$-0.339514\pi$
$857$	28.2845	0.966181	0.483090	+	0.875571i	$0.339514\pi$
$858$	10.9401	0.373488
$859$	42.8116	1.46071	0.730356	−	0.683066i	$-0.239354\pi$
$859$	42.8116	1.46071	0.730356	+	0.683066i	$0.239354\pi$
$860$	−15.8815	−0.541555
$861$	−8.50310	−0.289785
$862$	7.26026	0.247285
$863$	−34.4867	−1.17394	−0.586970	−	0.809609i	$-0.699679\pi$
$863$	−34.4867	−1.17394	−0.586970	+	0.809609i	$0.699679\pi$
$864$	−5.08037	−0.172838
$865$	−52.2758	−1.77743
$866$	6.54318	0.222346
$867$	−34.9989	−1.18863
$868$	16.3461	0.554821
$869$	−24.2476	−0.822542
$870$	−16.1103	−0.546190
$871$	68.5306	2.32207
$872$	−18.4677	−0.625394
$873$	−2.98646	−0.101076
$874$	−1.41377	−0.0478216
$875$	−33.9275	−1.14696
$876$	18.4408	0.623058
$877$	53.6975	1.81324	0.906619	−	0.421951i	$-0.138655\pi$
$877$	53.6975	1.81324	0.906619	+	0.421951i	$0.138655\pi$
$878$	−4.16452	−0.140546
$879$	−18.5628	−0.626109
$880$	41.2021	1.38892
$881$	10.6692	0.359455	0.179728	−	0.983716i	$-0.442478\pi$
$881$	10.6692	0.359455	0.179728	+	0.983716i	$0.442478\pi$
$882$	−2.00892	−0.0676437
$883$	−30.2821	−1.01907	−0.509536	−	0.860449i	$-0.670183\pi$
$883$	−30.2821	−1.01907	−0.509536	+	0.860449i	$0.670183\pi$
$884$	−64.1045	−2.15607
$885$	46.2231	1.55377
$886$	14.5791	0.489794
$887$	−8.27169	−0.277736	−0.138868	−	0.990311i	$-0.544346\pi$
$887$	−8.27169	−0.277736	−0.138868	+	0.990311i	$0.544346\pi$
$888$	6.41219	0.215179
$889$	6.37554	0.213829
$890$	3.04723	0.102143
$891$	−4.22106	−0.141411
$892$	−43.5910	−1.45954
$893$	19.4637	0.651328
$894$	10.2227	0.341898
$895$	−83.0862	−2.77726
$896$	−19.9069	−0.665044
$897$	4.01211	0.133960
$898$	−4.43300	−0.147931
$899$	44.0175	1.46806
$900$	−17.4510	−0.581701
$901$	85.5875	2.85133
$902$	−10.4473	−0.347856
$903$	4.10483	0.136600
$904$	−27.4386	−0.912596
$905$	−2.82925	−0.0940475
$906$	7.69565	0.255671
$907$	10.3820	0.344728	0.172364	−	0.985033i	$-0.444860\pi$
$907$	10.3820	0.344728	0.172364	+	0.985033i	$0.444860\pi$
$908$	24.1266	0.800668
$909$	6.19360	0.205429
$910$	−17.5251	−0.580953
$911$	18.6371	0.617476	0.308738	−	0.951147i	$-0.400093\pi$
$911$	18.6371	0.617476	0.308738	+	0.951147i	$0.400093\pi$
$912$	−8.91804	−0.295306
$913$	62.8468	2.07993
$914$	5.60239	0.185311
$915$	−47.4689	−1.56928
$916$	−30.1595	−0.996499
$917$	−20.5324	−0.678039
$918$	−3.66240	−0.120877
$919$	14.3615	0.473743	0.236871	−	0.971541i	$-0.423878\pi$
$919$	14.3615	0.473743	0.236871	+	0.971541i	$0.423878\pi$
$920$	−5.79053	−0.190908
$921$	28.2122	0.929623
$922$	−11.3817	−0.374836
$923$	14.3041	0.470826
$924$	−12.8305	−0.422094
$925$	33.7978	1.11127
$926$	8.62455	0.283420
$927$	5.59688	0.183826
$928$	−41.5845	−1.36508
$929$	35.1809	1.15425	0.577125	−	0.816656i	$-0.304175\pi$
$929$	35.1809	1.15425	0.577125	+	0.816656i	$0.304175\pi$
$930$	−10.5842	−0.347069
$931$	−14.0044	−0.458974
$932$	−26.3114	−0.861858
$933$	17.9758	0.588502
$934$	−10.9108	−0.357014
$935$	117.955	3.85755
$936$	−9.69859	−0.317008
$937$	−1.31084	−0.0428234	−0.0214117	−	0.999771i	$-0.506816\pi$
$937$	−1.31084	−0.0428234	−0.0214117	+	0.999771i	$0.506816\pi$
$938$	11.9011	0.388583
$939$	23.2208	0.757782
$940$	37.1121	1.21046
$941$	19.6544	0.640717	0.320358	−	0.947296i	$-0.396197\pi$
$941$	19.6544	0.640717	0.320358	+	0.947296i	$0.396197\pi$
$942$	−0.331382	−0.0107970
$943$	−3.83138	−0.124767
$944$	30.0441	0.977853
$945$	6.76180	0.219961
$946$	5.04337	0.163974
$947$	−29.2100	−0.949197	−0.474598	−	0.880203i	$-0.657407\pi$
$947$	−29.2100	−0.949197	−0.474598	+	0.880203i	$0.657407\pi$
$948$	10.0071	0.325015
$949$	54.0195	1.75355
$950$	18.0135	0.584436
$951$	−15.1085	−0.489928
$952$	−23.9132	−0.775032
$953$	−58.8054	−1.90490	−0.952448	−	0.304703i	$-0.901443\pi$
$953$	−58.8054	−1.90490	−0.952448	+	0.304703i	$0.901443\pi$
$954$	6.02811	0.195167
$955$	26.8211	0.867910
$956$	−16.2678	−0.526140
$957$	−34.5507	−1.11687
$958$	4.45751	0.144016
$959$	26.9223	0.869367
$960$	−9.52305	−0.307355
$961$	−2.08129	−0.0671385
$962$	8.74435	0.281929
$963$	1.30505	0.0420547
$964$	21.9588	0.707246
$965$	−82.3224	−2.65005
$966$	0.696744	0.0224174
$967$	−45.3531	−1.45846	−0.729228	−	0.684271i	$-0.760121\pi$
$967$	−45.3531	−1.45846	−0.729228	+	0.684271i	$0.760121\pi$
$968$	−12.9566	−0.416441
$969$	−25.5310	−0.820172
$970$	5.87793	0.188729
$971$	20.6246	0.661876	0.330938	−	0.943652i	$-0.392635\pi$
$971$	20.6246	0.661876	0.330938	+	0.943652i	$0.392635\pi$
$972$	1.74205	0.0558763
$973$	7.63134	0.244650
$974$	13.8185	0.442774
$975$	−51.1200	−1.63715
$976$	−30.8539	−0.987609
$977$	23.2450	0.743673	0.371837	−	0.928298i	$-0.378728\pi$
$977$	23.2450	0.743673	0.371837	+	0.928298i	$0.378728\pi$
$978$	7.34075	0.234731
$979$	6.53519	0.208866
$980$	−26.7026	−0.852982
$981$	9.71705	0.310242
$982$	0.433019	0.0138182
$983$	16.2850	0.519410	0.259705	−	0.965688i	$-0.416375\pi$
$983$	16.2850	0.519410	0.259705	+	0.965688i	$0.416375\pi$
$984$	9.26172	0.295253
$985$	−3.87524	−0.123476
$986$	−29.9779	−0.954691
$987$	−9.59221	−0.305323
$988$	−31.4747	−1.00134
$989$	1.84958	0.0588133
$990$	8.30785	0.264041
$991$	37.1058	1.17870	0.589352	−	0.807876i	$-0.299383\pi$
$991$	37.1058	1.17870	0.589352	+	0.807876i	$0.299383\pi$
$992$	−27.3203	−0.867420
$993$	−21.6433	−0.686830
$994$	2.48406	0.0787897
$995$	−40.9302	−1.29758
$996$	−25.9372	−0.821851
$997$	−6.52582	−0.206675	−0.103337	−	0.994646i	$-0.532952\pi$
$997$	−6.52582	−0.206675	−0.103337	+	0.994646i	$0.532952\pi$
$998$	−1.52448	−0.0482565
$999$	−3.37387	−0.106745

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	591.2.a.e.1.9	✓	14
3.2	odd	2		1773.2.a.h.1.6		14
4.3	odd	2		9456.2.a.bd.1.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
591.2.a.e.1.9	✓	14	1.1	even	1	trivial
1773.2.a.h.1.6		14	3.2	odd	2
9456.2.a.bd.1.2		14	4.3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 591 = 3 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	591.a (trivial)

\(f(q)\)	\(=\)	\(q+0.507888 q^{2} -1.00000 q^{3} -1.74205 q^{4} -3.87524 q^{5} -0.507888 q^{6} +1.74487 q^{7} -1.90054 q^{8} +1.00000 q^{9} -1.96819 q^{10} -4.22106 q^{11} +1.74205 q^{12} +5.10306 q^{13} +0.886200 q^{14} +3.87524 q^{15} +2.51883 q^{16} +7.21103 q^{17} +0.507888 q^{18} +3.54054 q^{19} +6.75087 q^{20} -1.74487 q^{21} -2.14383 q^{22} -0.786215 q^{23} +1.90054 q^{24} +10.0175 q^{25} +2.59179 q^{26} -1.00000 q^{27} -3.03965 q^{28} -8.18532 q^{29} +1.96819 q^{30} -5.37761 q^{31} +5.08037 q^{32} +4.22106 q^{33} +3.66240 q^{34} -6.76180 q^{35} -1.74205 q^{36} +3.37387 q^{37} +1.79820 q^{38} -5.10306 q^{39} +7.36507 q^{40} +4.87320 q^{41} -0.886200 q^{42} -2.35251 q^{43} +7.35329 q^{44} -3.87524 q^{45} -0.399310 q^{46} +5.49738 q^{47} -2.51883 q^{48} -3.95543 q^{49} +5.08778 q^{50} -7.21103 q^{51} -8.88978 q^{52} +11.8690 q^{53} -0.507888 q^{54} +16.3576 q^{55} -3.31620 q^{56} -3.54054 q^{57} -4.15723 q^{58} +11.9278 q^{59} -6.75087 q^{60} -12.2493 q^{61} -2.73123 q^{62} +1.74487 q^{63} -2.45741 q^{64} -19.7756 q^{65} +2.14383 q^{66} +13.4293 q^{67} -12.5620 q^{68} +0.786215 q^{69} -3.43424 q^{70} +2.80305 q^{71} -1.90054 q^{72} +10.5857 q^{73} +1.71355 q^{74} -10.0175 q^{75} -6.16780 q^{76} -7.36520 q^{77} -2.59179 q^{78} +5.74443 q^{79} -9.76110 q^{80} +1.00000 q^{81} +2.47504 q^{82} -14.8889 q^{83} +3.03965 q^{84} -27.9445 q^{85} -1.19481 q^{86} +8.18532 q^{87} +8.02230 q^{88} -1.54824 q^{89} -1.96819 q^{90} +8.90418 q^{91} +1.36963 q^{92} +5.37761 q^{93} +2.79205 q^{94} -13.7205 q^{95} -5.08037 q^{96} -2.98646 q^{97} -2.00892 q^{98} -4.22106 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{3} + 20 q^{4} + 7 q^{7} + 14 q^{9} + 8 q^{10} + 4 q^{11} - 20 q^{12} + 8 q^{13} + 6 q^{14} + 40 q^{16} + 4 q^{17} + 15 q^{19} - 6 q^{20} - 7 q^{21} + 12 q^{22} - 3 q^{23} + 40 q^{25} + 10 q^{26}+ \cdots + 4 q^{99}+O(q^{100}) \) 14 * q - 14 * q^3 + 20 * q^4 + 7 * q^7 + 14 * q^9 + 8 * q^10 + 4 * q^11 - 20 * q^12 + 8 * q^13 + 6 * q^14 + 40 * q^16 + 4 * q^17 + 15 * q^19 - 6 * q^20 - 7 * q^21 + 12 * q^22 - 3 * q^23 + 40 * q^25 + 10 * q^26 - 14 * q^27 + 22 * q^28 + 7 * q^29 - 8 * q^30 + 18 * q^31 - 4 * q^33 + 32 * q^34 - 8 * q^35 + 20 * q^36 + 21 * q^37 - 22 * q^38 - 8 * q^39 + 24 * q^40 + 23 * q^41 - 6 * q^42 + 27 * q^43 + 32 * q^44 + 32 * q^46 - 19 * q^47 - 40 * q^48 + 59 * q^49 - q^50 - 4 * q^51 + 12 * q^52 + 12 * q^53 + 12 * q^55 + 7 * q^56 - 15 * q^57 + 8 * q^58 - 16 * q^59 + 6 * q^60 + 7 * q^61 - 22 * q^62 + 7 * q^63 + 36 * q^64 + 36 * q^65 - 12 * q^66 + 22 * q^67 - 45 * q^68 + 3 * q^69 - 48 * q^70 - 4 * q^71 + 18 * q^73 + 10 * q^74 - 40 * q^75 - 14 * q^76 - 2 * q^77 - 10 * q^78 + 2 * q^79 - 68 * q^80 + 14 * q^81 - 48 * q^82 - 51 * q^83 - 22 * q^84 + 20 * q^85 - 15 * q^86 - 7 * q^87 - 28 * q^88 + 28 * q^89 + 8 * q^90 + 2 * q^91 - 2 * q^92 - 18 * q^93 - 54 * q^94 - 16 * q^95 + 54 * q^97 - 74 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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