LMFDB - Embedded newform 787.2.a.b.1.30

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [787,2,Mod(1,787)] 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("787.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(787, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 787 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	787.a (trivial)

Newform invariants

comment:select newform

sage:traces = [37] 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:	$6.28422663907$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.30
Character	$\chi$	$=$	787.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.15909 q^{2} -0.193646 q^{3} +2.66166 q^{4} +1.27973 q^{5} -0.418099 q^{6} +3.30692 q^{7} +1.42857 q^{8} -2.96250 q^{9} +2.76304 q^{10} +1.74233 q^{11} -0.515419 q^{12} +3.81881 q^{13} +7.13993 q^{14} -0.247814 q^{15} -2.23890 q^{16} -5.59990 q^{17} -6.39630 q^{18} +2.43802 q^{19} +3.40620 q^{20} -0.640373 q^{21} +3.76185 q^{22} +8.57475 q^{23} -0.276637 q^{24} -3.36230 q^{25} +8.24514 q^{26} +1.15462 q^{27} +8.80189 q^{28} -5.45908 q^{29} -0.535053 q^{30} -5.25017 q^{31} -7.69113 q^{32} -0.337396 q^{33} -12.0907 q^{34} +4.23196 q^{35} -7.88516 q^{36} +8.07141 q^{37} +5.26391 q^{38} -0.739497 q^{39} +1.82818 q^{40} +3.73448 q^{41} -1.38262 q^{42} -5.12895 q^{43} +4.63749 q^{44} -3.79120 q^{45} +18.5136 q^{46} +1.97994 q^{47} +0.433555 q^{48} +3.93574 q^{49} -7.25949 q^{50} +1.08440 q^{51} +10.1643 q^{52} -6.79390 q^{53} +2.49291 q^{54} +2.22971 q^{55} +4.72418 q^{56} -0.472114 q^{57} -11.7866 q^{58} +14.3592 q^{59} -0.659596 q^{60} -12.8742 q^{61} -11.3356 q^{62} -9.79677 q^{63} -12.1280 q^{64} +4.88703 q^{65} -0.728467 q^{66} -11.5181 q^{67} -14.9050 q^{68} -1.66047 q^{69} +9.13718 q^{70} -0.363435 q^{71} -4.23214 q^{72} -8.27175 q^{73} +17.4269 q^{74} +0.651095 q^{75} +6.48918 q^{76} +5.76176 q^{77} -1.59664 q^{78} -2.27371 q^{79} -2.86519 q^{80} +8.66392 q^{81} +8.06306 q^{82} -16.4140 q^{83} -1.70445 q^{84} -7.16635 q^{85} -11.0738 q^{86} +1.05713 q^{87} +2.48905 q^{88} +18.4490 q^{89} -8.18552 q^{90} +12.6285 q^{91} +22.8230 q^{92} +1.01668 q^{93} +4.27486 q^{94} +3.12001 q^{95} +1.48936 q^{96} -5.94452 q^{97} +8.49761 q^{98} -5.16166 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 12 q^{2} + 6 q^{3} + 42 q^{4} + 31 q^{5} + 4 q^{6} + 9 q^{7} + 36 q^{8} + 47 q^{9} + 4 q^{10} + 18 q^{11} + 15 q^{12} + 13 q^{13} + 8 q^{14} + 3 q^{15} + 48 q^{16} + 18 q^{17} + 17 q^{18} + 40 q^{20}+ \cdots - 35 q^{99}+O(q^{100}) $ 37 * q + 12 * q^2 + 6 * q^3 + 42 * q^4 + 31 * q^5 + 4 * q^6 + 9 * q^7 + 36 * q^8 + 47 * q^9 + 4 * q^10 + 18 * q^11 + 15 * q^12 + 13 * q^13 + 8 * q^14 + 3 * q^15 + 48 * q^16 + 18 * q^17 + 17 * q^18 + 40 * q^20 - 4 * q^21 - 4 * q^22 + 42 * q^23 - 10 * q^24 + 56 * q^25 - 4 * q^26 + 18 * q^27 + 3 * q^28 + 45 * q^29 - 32 * q^30 - 3 * q^31 + 59 * q^32 + 14 * q^33 - 22 * q^34 + 16 * q^35 + 28 * q^36 + 52 * q^37 - 5 * q^38 - 13 * q^39 - 11 * q^40 + 23 * q^41 - 16 * q^42 + 4 * q^43 + 23 * q^44 + 69 * q^45 - 5 * q^46 + 45 * q^47 - 5 * q^48 + 30 * q^49 + 13 * q^50 - 7 * q^51 + 3 * q^52 + 103 * q^53 - 23 * q^54 - 9 * q^55 + 4 * q^56 + 9 * q^57 + 8 * q^58 + 2 * q^59 - 47 * q^60 - 6 * q^61 + 20 * q^62 + 5 * q^63 + 28 * q^64 + 51 * q^65 - 48 * q^66 + 24 * q^67 - 9 * q^68 - 52 * q^70 + 32 * q^71 + 42 * q^72 + 5 * q^73 + 4 * q^74 - 35 * q^75 - 34 * q^76 + 97 * q^77 - 31 * q^78 - 27 * q^79 + 47 * q^80 + 29 * q^81 - q^82 + 23 * q^83 - 93 * q^84 + 27 * q^85 + 10 * q^86 - 46 * q^87 - 45 * q^88 + 9 * q^89 - 70 * q^90 - 48 * q^91 + 67 * q^92 + 72 * q^93 - 52 * q^94 - 20 * q^95 - 89 * q^96 - 7 * q^97 - 12 * q^98 - 35 * q^99

Coefficient data

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

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

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

$2$	2.15909	1.52670	0.763352	−	0.645982i	$-0.223552\pi$
$2$	2.15909	1.52670	0.763352	+	0.645982i	$0.223552\pi$
$3$	−0.193646	−0.111802	−0.0559008	−	0.998436i	$-0.517803\pi$
$3$	−0.193646	−0.111802	−0.0559008	+	0.998436i	$0.517803\pi$
$4$	2.66166	1.33083
$5$	1.27973	0.572312	0.286156	−	0.958183i	$-0.407622\pi$
$5$	1.27973	0.572312	0.286156	+	0.958183i	$0.407622\pi$
$6$	−0.418099	−0.170688
$7$	3.30692	1.24990	0.624950	−	0.780665i	$-0.285119\pi$
$7$	3.30692	1.24990	0.624950	+	0.780665i	$0.285119\pi$
$8$	1.42857	0.505076
$9$	−2.96250	−0.987500
$10$	2.76304	0.873751
$11$	1.74233	0.525333	0.262667	−	0.964887i	$-0.415398\pi$
$11$	1.74233	0.525333	0.262667	+	0.964887i	$0.415398\pi$
$12$	−0.515419	−0.148789
$13$	3.81881	1.05915	0.529573	−	0.848264i	$-0.322352\pi$
$13$	3.81881	1.05915	0.529573	+	0.848264i	$0.322352\pi$
$14$	7.13993	1.90823
$15$	−0.247814	−0.0639854
$16$	−2.23890	−0.559725
$17$	−5.59990	−1.35817	−0.679087	−	0.734057i	$-0.737624\pi$
$17$	−5.59990	−1.35817	−0.679087	+	0.734057i	$0.737624\pi$
$18$	−6.39630	−1.50762
$19$	2.43802	0.559321	0.279661	−	0.960099i	$-0.409778\pi$
$19$	2.43802	0.559321	0.279661	+	0.960099i	$0.409778\pi$
$20$	3.40620	0.761648
$21$	−0.640373	−0.139741
$22$	3.76185	0.802029
$23$	8.57475	1.78796	0.893979	−	0.448109i	$-0.147902\pi$
$23$	8.57475	1.78796	0.893979	+	0.448109i	$0.147902\pi$
$24$	−0.276637	−0.0564683
$25$	−3.36230	−0.672459
$26$	8.24514	1.61700
$27$	1.15462	0.222206
$28$	8.80189	1.66340
$29$	−5.45908	−1.01373	−0.506863	−	0.862027i	$-0.669195\pi$
$29$	−5.45908	−1.01373	−0.506863	+	0.862027i	$0.669195\pi$
$30$	−0.535053	−0.0976868
$31$	−5.25017	−0.942959	−0.471479	−	0.881877i	$-0.656280\pi$
$31$	−5.25017	−0.942959	−0.471479	+	0.881877i	$0.656280\pi$
$32$	−7.69113	−1.35961
$33$	−0.337396	−0.0587331
$34$	−12.0907	−2.07353
$35$	4.23196	0.715332
$36$	−7.88516	−1.31419
$37$	8.07141	1.32693	0.663466	−	0.748207i	$-0.269085\pi$
$37$	8.07141	1.32693	0.663466	+	0.748207i	$0.269085\pi$
$38$	5.26391	0.853919
$39$	−0.739497	−0.118414
$40$	1.82818	0.289061
$41$	3.73448	0.583227	0.291614	−	0.956536i	$-0.405808\pi$
$41$	3.73448	0.583227	0.291614	+	0.956536i	$0.405808\pi$
$42$	−1.38262	−0.213343
$43$	−5.12895	−0.782157	−0.391078	−	0.920357i	$-0.627898\pi$
$43$	−5.12895	−0.782157	−0.391078	+	0.920357i	$0.627898\pi$
$44$	4.63749	0.699128
$45$	−3.79120	−0.565158
$46$	18.5136	2.72968
$47$	1.97994	0.288804	0.144402	−	0.989519i	$-0.453874\pi$
$47$	1.97994	0.288804	0.144402	+	0.989519i	$0.453874\pi$
$48$	0.433555	0.0625782
$49$	3.93574	0.562249
$50$	−7.25949	−1.02665
$51$	1.08440	0.151846
$52$	10.1643	1.40954
$53$	−6.79390	−0.933214	−0.466607	−	0.884465i	$-0.654524\pi$
$53$	−6.79390	−0.933214	−0.466607	+	0.884465i	$0.654524\pi$
$54$	2.49291	0.339243
$55$	2.22971	0.300654
$56$	4.72418	0.631295
$57$	−0.472114	−0.0625330
$58$	−11.7866	−1.54766
$59$	14.3592	1.86940	0.934702	−	0.355433i	$-0.115667\pi$
$59$	14.3592	1.86940	0.934702	+	0.355433i	$0.115667\pi$
$60$	−0.659596	−0.0851535
$61$	−12.8742	−1.64838	−0.824189	−	0.566315i	$-0.808368\pi$
$61$	−12.8742	−1.64838	−0.824189	+	0.566315i	$0.808368\pi$
$62$	−11.3356	−1.43962
$63$	−9.79677	−1.23428
$64$	−12.1280	−1.51600
$65$	4.88703	0.606162
$66$	−0.728467	−0.0896681
$67$	−11.5181	−1.40716	−0.703582	−	0.710615i	$-0.748417\pi$
$67$	−11.5181	−1.40716	−0.703582	+	0.710615i	$0.748417\pi$
$68$	−14.9050	−1.80750
$69$	−1.66047	−0.199897
$70$	9.13718	1.09210
$71$	−0.363435	−0.0431318	−0.0215659	−	0.999767i	$-0.506865\pi$
$71$	−0.363435	−0.0431318	−0.0215659	+	0.999767i	$0.506865\pi$
$72$	−4.23214	−0.498763
$73$	−8.27175	−0.968136	−0.484068	−	0.875030i	$-0.660841\pi$
$73$	−8.27175	−0.968136	−0.484068	+	0.875030i	$0.660841\pi$
$74$	17.4269	2.02583
$75$	0.651095	0.0751820
$76$	6.48918	0.744360
$77$	5.76176	0.656614
$78$	−1.59664	−0.180784
$79$	−2.27371	−0.255812	−0.127906	−	0.991786i	$-0.540826\pi$
$79$	−2.27371	−0.255812	−0.127906	+	0.991786i	$0.540826\pi$
$80$	−2.86519	−0.320337
$81$	8.66392	0.962657
$82$	8.06306	0.890416
$83$	−16.4140	−1.80167	−0.900836	−	0.434161i	$-0.857045\pi$
$83$	−16.4140	−1.80167	−0.900836	+	0.434161i	$0.857045\pi$
$84$	−1.70445	−0.185971
$85$	−7.16635	−0.777299
$86$	−11.0738	−1.19412
$87$	1.05713	0.113336
$88$	2.48905	0.265333
$89$	18.4490	1.95559	0.977797	−	0.209553i	$-0.0672007\pi$
$89$	18.4490	1.95559	0.977797	+	0.209553i	$0.0672007\pi$
$90$	−8.18552	−0.862830
$91$	12.6285	1.32383
$92$	22.8230	2.37946
$93$	1.01668	0.105424
$94$	4.27486	0.440918
$95$	3.12001	0.320106
$96$	1.48936	0.152007
$97$	−5.94452	−0.603574	−0.301787	−	0.953375i	$-0.597583\pi$
$97$	−5.94452	−0.603574	−0.301787	+	0.953375i	$0.597583\pi$
$98$	8.49761	0.858388
$99$	−5.16166	−0.518767
$100$	−8.94927	−0.894927
$101$	2.03367	0.202358	0.101179	−	0.994868i	$-0.467739\pi$
$101$	2.03367	0.202358	0.101179	+	0.994868i	$0.467739\pi$
$102$	2.34131	0.231824
$103$	3.44297	0.339246	0.169623	−	0.985509i	$-0.445745\pi$
$103$	3.44297	0.339246	0.169623	+	0.985509i	$0.445745\pi$
$104$	5.45544	0.534950
$105$	−0.819503	−0.0799753
$106$	−14.6686	−1.42474
$107$	−7.10757	−0.687114	−0.343557	−	0.939132i	$-0.611632\pi$
$107$	−7.10757	−0.687114	−0.343557	+	0.939132i	$0.611632\pi$
$108$	3.07319	0.295718
$109$	−1.59260	−0.152544	−0.0762719	−	0.997087i	$-0.524302\pi$
$109$	−1.59260	−0.152544	−0.0762719	+	0.997087i	$0.524302\pi$
$110$	4.81414	0.459010
$111$	−1.56300	−0.148353
$112$	−7.40388	−0.699601
$113$	12.7500	1.19942	0.599709	−	0.800218i	$-0.295283\pi$
$113$	12.7500	1.19942	0.599709	+	0.800218i	$0.295283\pi$
$114$	−1.01934	−0.0954695
$115$	10.9733	1.02327
$116$	−14.5302	−1.34909
$117$	−11.3132	−1.04591
$118$	31.0027	2.85403
$119$	−18.5184	−1.69758
$120$	−0.354020	−0.0323175
$121$	−7.96428	−0.724025
$122$	−27.7966	−2.51659
$123$	−0.723167	−0.0652058
$124$	−13.9741	−1.25492
$125$	−10.7015	−0.957168
$126$	−21.1521	−1.88438
$127$	−2.27878	−0.202209	−0.101105	−	0.994876i	$-0.532238\pi$
$127$	−2.27878	−0.202209	−0.101105	+	0.994876i	$0.532238\pi$
$128$	−10.8032	−0.954873
$129$	0.993200	0.0874464
$130$	10.5515	0.925431
$131$	−12.1033	−1.05747	−0.528736	−	0.848787i	$-0.677334\pi$
$131$	−12.1033	−1.05747	−0.528736	+	0.848787i	$0.677334\pi$
$132$	−0.898032	−0.0781636
$133$	8.06236	0.699095
$134$	−24.8686	−2.14832
$135$	1.47759	0.127171
$136$	−7.99985	−0.685982
$137$	11.1001	0.948345	0.474172	−	0.880432i	$-0.342747\pi$
$137$	11.1001	0.948345	0.474172	+	0.880432i	$0.342747\pi$
$138$	−3.58509	−0.305183
$139$	−8.54741	−0.724981	−0.362491	−	0.931987i	$-0.618074\pi$
$139$	−8.54741	−0.724981	−0.362491	+	0.931987i	$0.618074\pi$
$140$	11.2640	0.951984
$141$	−0.383408	−0.0322887
$142$	−0.784688	−0.0658496
$143$	6.65363	0.556405
$144$	6.63275	0.552729
$145$	−6.98614	−0.580167
$146$	−17.8594	−1.47806
$147$	−0.762141	−0.0628604
$148$	21.4833	1.76592
$149$	20.7127	1.69685	0.848427	−	0.529312i	$-0.177550\pi$
$149$	20.7127	1.69685	0.848427	+	0.529312i	$0.177550\pi$
$150$	1.40577	0.114781
$151$	−4.34623	−0.353691	−0.176846	−	0.984239i	$-0.556589\pi$
$151$	−4.34623	−0.353691	−0.176846	+	0.984239i	$0.556589\pi$
$152$	3.48289	0.282500
$153$	16.5897	1.34120
$154$	12.4401	1.00246
$155$	−6.71879	−0.539666
$156$	−1.96829	−0.157589
$157$	−15.0456	−1.20077	−0.600386	−	0.799710i	$-0.704986\pi$
$157$	−15.0456	−1.20077	−0.600386	+	0.799710i	$0.704986\pi$
$158$	−4.90913	−0.390549
$159$	1.31561	0.104335
$160$	−9.84255	−0.778122
$161$	28.3560	2.23477
$162$	18.7061	1.46969
$163$	23.1107	1.81017	0.905085	−	0.425231i	$-0.139807\pi$
$163$	23.1107	1.81017	0.905085	+	0.425231i	$0.139807\pi$
$164$	9.93989	0.776175
$165$	−0.431775	−0.0336136
$166$	−35.4393	−2.75062
$167$	−12.9195	−0.999740	−0.499870	−	0.866100i	$-0.666619\pi$
$167$	−12.9195	−0.999740	−0.499870	+	0.866100i	$0.666619\pi$
$168$	−0.914818	−0.0705798
$169$	1.58329	0.121791
$170$	−15.4728	−1.18671
$171$	−7.22265	−0.552330
$172$	−13.6515	−1.04092
$173$	−20.7368	−1.57659	−0.788296	−	0.615297i	$-0.789036\pi$
$173$	−20.7368	−1.57659	−0.788296	+	0.615297i	$0.789036\pi$
$174$	2.28243	0.173031
$175$	−11.1189	−0.840507
$176$	−3.90091	−0.294042
$177$	−2.78059	−0.209002
$178$	39.8331	2.98562
$179$	18.7708	1.40300	0.701499	−	0.712671i	$-0.252515\pi$
$179$	18.7708	1.40300	0.701499	+	0.712671i	$0.252515\pi$
$180$	−10.0909	−0.752128
$181$	−6.33864	−0.471147	−0.235574	−	0.971856i	$-0.575697\pi$
$181$	−6.33864	−0.471147	−0.235574	+	0.971856i	$0.575697\pi$
$182$	27.2660	2.02109
$183$	2.49305	0.184291
$184$	12.2496	0.903055
$185$	10.3292	0.759419
$186$	2.19509	0.160952
$187$	−9.75689	−0.713494
$188$	5.26992	0.384348
$189$	3.81822	0.277735
$190$	6.73637	0.488708
$191$	−4.40076	−0.318428	−0.159214	−	0.987244i	$-0.550896\pi$
$191$	−4.40076	−0.318428	−0.159214	+	0.987244i	$0.550896\pi$
$192$	2.34854	0.169491
$193$	5.27295	0.379555	0.189778	−	0.981827i	$-0.439223\pi$
$193$	5.27295	0.379555	0.189778	+	0.981827i	$0.439223\pi$
$194$	−12.8347	−0.921480
$195$	−0.946355	−0.0677699
$196$	10.4756	0.748257
$197$	13.1085	0.933945	0.466973	−	0.884272i	$-0.345345\pi$
$197$	13.1085	0.933945	0.466973	+	0.884272i	$0.345345\pi$
$198$	−11.1445	−0.792003
$199$	10.8387	0.768337	0.384168	−	0.923263i	$-0.374488\pi$
$199$	10.8387	0.768337	0.384168	+	0.923263i	$0.374488\pi$
$200$	−4.80328	−0.339643
$201$	2.23044	0.157323
$202$	4.39087	0.308941
$203$	−18.0528	−1.26706
$204$	2.88629	0.202081
$205$	4.77911	0.333788
$206$	7.43368	0.517929
$207$	−25.4027	−1.76561
$208$	−8.54993	−0.592831
$209$	4.24785	0.293830
$210$	−1.76938	−0.122099
$211$	−1.27964	−0.0880938	−0.0440469	−	0.999029i	$-0.514025\pi$
$211$	−1.27964	−0.0880938	−0.0440469	+	0.999029i	$0.514025\pi$
$212$	−18.0830	−1.24195
$213$	0.0703778	0.00482221
$214$	−15.3459	−1.04902
$215$	−6.56366	−0.447638
$216$	1.64945	0.112231
$217$	−17.3619	−1.17860
$218$	−3.43857	−0.232889
$219$	1.60179	0.108239
$220$	5.93472	0.400119
$221$	−21.3849	−1.43851
$222$	−3.37465	−0.226491
$223$	24.7788	1.65931	0.829657	−	0.558273i	$-0.188536\pi$
$223$	24.7788	1.65931	0.829657	+	0.558273i	$0.188536\pi$
$224$	−25.4340	−1.69938
$225$	9.96081	0.664054
$226$	27.5283	1.83116
$227$	8.97561	0.595732	0.297866	−	0.954608i	$-0.403725\pi$
$227$	8.97561	0.595732	0.297866	+	0.954608i	$0.403725\pi$
$228$	−1.25660	−0.0832207
$229$	25.7318	1.70040	0.850202	−	0.526457i	$-0.176480\pi$
$229$	25.7318	1.70040	0.850202	+	0.526457i	$0.176480\pi$
$230$	23.6924	1.56223
$231$	−1.11574	−0.0734105
$232$	−7.79868	−0.512009
$233$	16.8337	1.10281	0.551406	−	0.834237i	$-0.314092\pi$
$233$	16.8337	1.10281	0.551406	+	0.834237i	$0.314092\pi$
$234$	−24.4262	−1.59679
$235$	2.53378	0.165286
$236$	38.2191	2.48785
$237$	0.440294	0.0286002
$238$	−39.9829	−2.59171
$239$	−18.2138	−1.17815	−0.589075	−	0.808078i	$-0.700508\pi$
$239$	−18.2138	−1.17815	−0.589075	+	0.808078i	$0.700508\pi$
$240$	0.554832	0.0358142
$241$	2.89730	0.186632	0.0933158	−	0.995637i	$-0.470253\pi$
$241$	2.89730	0.186632	0.0933158	+	0.995637i	$0.470253\pi$
$242$	−17.1956	−1.10537
$243$	−5.14158	−0.329832
$244$	−34.2668	−2.19371
$245$	5.03668	0.321782
$246$	−1.56138	−0.0995499
$247$	9.31035	0.592403
$248$	−7.50024	−0.476266
$249$	3.17851	0.201430
$250$	−23.1054	−1.46131
$251$	15.2014	0.959502	0.479751	−	0.877405i	$-0.340727\pi$
$251$	15.2014	0.959502	0.479751	+	0.877405i	$0.340727\pi$
$252$	−26.0756	−1.64261
$253$	14.9401	0.939273
$254$	−4.92009	−0.308714
$255$	1.38774	0.0869033
$256$	0.931049	0.0581906
$257$	18.5312	1.15595	0.577974	−	0.816055i	$-0.303844\pi$
$257$	18.5312	1.15595	0.577974	+	0.816055i	$0.303844\pi$
$258$	2.14441	0.133505
$259$	26.6915	1.65853
$260$	13.0076	0.806697
$261$	16.1725	1.00105
$262$	−26.1321	−1.61445
$263$	−7.87351	−0.485501	−0.242751	−	0.970089i	$-0.578050\pi$
$263$	−7.87351	−0.485501	−0.242751	+	0.970089i	$0.578050\pi$
$264$	−0.481994	−0.0296647
$265$	−8.69435	−0.534089
$266$	17.4073	1.06731
$267$	−3.57259	−0.218639
$268$	−30.6573	−1.87269
$269$	23.1808	1.41336	0.706678	−	0.707535i	$-0.250193\pi$
$269$	23.1808	1.41336	0.706678	+	0.707535i	$0.250193\pi$
$270$	3.19025	0.194153
$271$	5.00036	0.303750	0.151875	−	0.988400i	$-0.451469\pi$
$271$	5.00036	0.303750	0.151875	+	0.988400i	$0.451469\pi$
$272$	12.5376	0.760205
$273$	−2.44546	−0.148006
$274$	23.9661	1.44784
$275$	−5.85824	−0.353265
$276$	−4.41959	−0.266028
$277$	−2.86202	−0.171962	−0.0859812	−	0.996297i	$-0.527402\pi$
$277$	−2.86202	−0.171962	−0.0859812	+	0.996297i	$0.527402\pi$
$278$	−18.4546	−1.10683
$279$	15.5536	0.931172
$280$	6.04566	0.361297
$281$	21.8710	1.30471	0.652356	−	0.757913i	$-0.273781\pi$
$281$	21.8710	1.30471	0.652356	+	0.757913i	$0.273781\pi$
$282$	−0.827810	−0.0492954
$283$	27.0630	1.60873	0.804364	−	0.594136i	$-0.202506\pi$
$283$	27.0630	1.60873	0.804364	+	0.594136i	$0.202506\pi$
$284$	−0.967339	−0.0574010
$285$	−0.604178	−0.0357884
$286$	14.3658	0.849466
$287$	12.3496	0.728976
$288$	22.7850	1.34262
$289$	14.3589	0.844639
$290$	−15.0837	−0.885744
$291$	1.15113	0.0674806
$292$	−22.0166	−1.28842
$293$	0.378130	0.0220906	0.0110453	−	0.999939i	$-0.496484\pi$
$293$	0.378130	0.0220906	0.0110453	+	0.999939i	$0.496484\pi$
$294$	−1.64553	−0.0959692
$295$	18.3758	1.06988
$296$	11.5306	0.670202
$297$	2.01172	0.116732
$298$	44.7206	2.59060
$299$	32.7453	1.89371
$300$	1.73299	0.100054
$301$	−16.9610	−0.977618
$302$	−9.38389	−0.539982
$303$	−0.393812	−0.0226239
$304$	−5.45850	−0.313066
$305$	−16.4755	−0.943386
$306$	35.8186	2.04761
$307$	−6.52202	−0.372231	−0.186116	−	0.982528i	$-0.559590\pi$
$307$	−6.52202	−0.372231	−0.186116	+	0.982528i	$0.559590\pi$
$308$	15.3358	0.873840
$309$	−0.666718	−0.0379283
$310$	−14.5065	−0.823911
$311$	−27.5348	−1.56136	−0.780678	−	0.624934i	$-0.785126\pi$
$311$	−27.5348	−1.56136	−0.780678	+	0.624934i	$0.785126\pi$
$312$	−1.05642	−0.0598082
$313$	0.580082	0.0327882	0.0163941	−	0.999866i	$-0.494781\pi$
$313$	0.580082	0.0327882	0.0163941	+	0.999866i	$0.494781\pi$
$314$	−32.4848	−1.83322
$315$	−12.5372	−0.706391
$316$	−6.05182	−0.340442
$317$	−23.9543	−1.34541	−0.672704	−	0.739912i	$-0.734867\pi$
$317$	−23.9543	−1.34541	−0.672704	+	0.739912i	$0.734867\pi$
$318$	2.84052	0.159289
$319$	−9.51153	−0.532544
$320$	−15.5205	−0.867625
$321$	1.37635	0.0768205
$322$	61.2231	3.41183
$323$	−13.6527	−0.759656
$324$	23.0604	1.28113
$325$	−12.8400	−0.712233
$326$	49.8980	2.76359
$327$	0.308402	0.0170547
$328$	5.33497	0.294574
$329$	6.54751	0.360976
$330$	−0.932240	−0.0513181
$331$	−12.1366	−0.667088	−0.333544	−	0.942734i	$-0.608245\pi$
$331$	−12.1366	−0.667088	−0.333544	+	0.942734i	$0.608245\pi$
$332$	−43.6884	−2.39771
$333$	−23.9116	−1.31035
$334$	−27.8943	−1.52631
$335$	−14.7401	−0.805336
$336$	1.43373	0.0782165
$337$	33.2107	1.80910	0.904552	−	0.426363i	$-0.140205\pi$
$337$	33.2107	1.80910	0.904552	+	0.426363i	$0.140205\pi$
$338$	3.41846	0.185940
$339$	−2.46899	−0.134097
$340$	−19.0743	−1.03445
$341$	−9.14754	−0.495367
$342$	−15.5943	−0.843245
$343$	−10.1333	−0.547145
$344$	−7.32706	−0.395049
$345$	−2.12495	−0.114403
$346$	−44.7726	−2.40699
$347$	8.72501	0.468383	0.234192	−	0.972190i	$-0.424756\pi$
$347$	8.72501	0.468383	0.234192	+	0.972190i	$0.424756\pi$
$348$	2.81371	0.150831
$349$	−5.11786	−0.273953	−0.136976	−	0.990574i	$-0.543738\pi$
$349$	−5.11786	−0.273953	−0.136976	+	0.990574i	$0.543738\pi$
$350$	−24.0066	−1.28321
$351$	4.40925	0.235348
$352$	−13.4005	−0.714249
$353$	−30.7524	−1.63679	−0.818393	−	0.574660i	$-0.805134\pi$
$353$	−30.7524	−1.63679	−0.818393	+	0.574660i	$0.805134\pi$
$354$	−6.00355	−0.319085
$355$	−0.465098	−0.0246849
$356$	49.1050	2.60256
$357$	3.58602	0.189792
$358$	40.5278	2.14196
$359$	27.2437	1.43787	0.718935	−	0.695078i	$-0.244630\pi$
$359$	27.2437	1.43787	0.718935	+	0.695078i	$0.244630\pi$
$360$	−5.41599	−0.285448
$361$	−13.0560	−0.687160
$362$	−13.6857	−0.719303
$363$	1.54225	0.0809472
$364$	33.6127	1.76179
$365$	−10.5856	−0.554075
$366$	5.38270	0.281358
$367$	1.12382	0.0586631	0.0293315	−	0.999570i	$-0.490662\pi$
$367$	1.12382	0.0586631	0.0293315	+	0.999570i	$0.490662\pi$
$368$	−19.1980	−1.00077
$369$	−11.0634	−0.575937
$370$	22.3017	1.15941
$371$	−22.4669	−1.16642
$372$	2.70604	0.140302
$373$	13.7738	0.713181	0.356590	−	0.934261i	$-0.383939\pi$
$373$	13.7738	0.713181	0.356590	+	0.934261i	$0.383939\pi$
$374$	−21.0660	−1.08929
$375$	2.07230	0.107013
$376$	2.82848	0.145868
$377$	−20.8472	−1.07368
$378$	8.24388	0.424019
$379$	25.2518	1.29710	0.648548	−	0.761174i	$-0.275377\pi$
$379$	25.2518	1.29710	0.648548	+	0.761174i	$0.275377\pi$
$380$	8.30439	0.426006
$381$	0.441277	0.0226073
$382$	−9.50161	−0.486145
$383$	16.3911	0.837547	0.418773	−	0.908091i	$-0.362460\pi$
$383$	16.3911	0.837547	0.418773	+	0.908091i	$0.362460\pi$
$384$	2.09199	0.106756
$385$	7.37349	0.375788
$386$	11.3848	0.579469
$387$	15.1945	0.772380
$388$	−15.8223	−0.803254
$389$	32.9159	1.66890	0.834452	−	0.551081i	$-0.185785\pi$
$389$	32.9159	1.66890	0.834452	+	0.551081i	$0.185785\pi$
$390$	−2.04326	−0.103465
$391$	−48.0177	−2.42836
$392$	5.62249	0.283979
$393$	2.34376	0.118227
$394$	28.3025	1.42586
$395$	−2.90973	−0.146404
$396$	−13.7386	−0.690389
$397$	−8.73821	−0.438558	−0.219279	−	0.975662i	$-0.570371\pi$
$397$	−8.73821	−0.438558	−0.219279	+	0.975662i	$0.570371\pi$
$398$	23.4017	1.17302
$399$	−1.56124	−0.0781600
$400$	7.52785	0.376392
$401$	32.8523	1.64057	0.820283	−	0.571958i	$-0.193816\pi$
$401$	32.8523	1.64057	0.820283	+	0.571958i	$0.193816\pi$
$402$	4.81571	0.240186
$403$	−20.0494	−0.998731
$404$	5.41293	0.269303
$405$	11.0875	0.550940
$406$	−38.9775	−1.93442
$407$	14.0631	0.697081
$408$	1.54914	0.0766939
$409$	−27.2692	−1.34837	−0.674187	−	0.738561i	$-0.735506\pi$
$409$	−27.2692	−1.34837	−0.674187	+	0.738561i	$0.735506\pi$
$410$	10.3185	0.509596
$411$	−2.14949	−0.106027
$412$	9.16400	0.451478
$413$	47.4846	2.33657
$414$	−54.8466	−2.69556
$415$	−21.0055	−1.03112
$416$	−29.3709	−1.44003
$417$	1.65517	0.0810541
$418$	9.17148	0.448592
$419$	−3.28648	−0.160555	−0.0802775	−	0.996773i	$-0.525581\pi$
$419$	−3.28648	−0.160555	−0.0802775	+	0.996773i	$0.525581\pi$
$420$	−2.18123	−0.106433
$421$	28.0183	1.36553	0.682764	−	0.730639i	$-0.260778\pi$
$421$	28.0183	1.36553	0.682764	+	0.730639i	$0.260778\pi$
$422$	−2.76284	−0.134493
$423$	−5.86557	−0.285194
$424$	−9.70557	−0.471344
$425$	18.8285	0.913317
$426$	0.151952	0.00736209
$427$	−42.5741	−2.06031
$428$	−18.9179	−0.914431
$429$	−1.28845	−0.0622069
$430$	−14.1715	−0.683411
$431$	−21.1666	−1.01956	−0.509781	−	0.860304i	$-0.670273\pi$
$431$	−21.1666	−1.01956	−0.509781	+	0.860304i	$0.670273\pi$
$432$	−2.58507	−0.124374
$433$	4.67196	0.224520	0.112260	−	0.993679i	$-0.464191\pi$
$433$	4.67196	0.224520	0.112260	+	0.993679i	$0.464191\pi$
$434$	−37.4859	−1.79938
$435$	1.35284	0.0648636
$436$	−4.23897	−0.203010
$437$	20.9054	1.00004
$438$	3.45841	0.165249
$439$	−21.6416	−1.03290	−0.516449	−	0.856318i	$-0.672746\pi$
$439$	−21.6416	−1.03290	−0.516449	+	0.856318i	$0.672746\pi$
$440$	3.18530	0.151853
$441$	−11.6596	−0.555221
$442$	−46.1719	−2.19617
$443$	17.9066	0.850770	0.425385	−	0.905013i	$-0.360139\pi$
$443$	17.9066	0.850770	0.425385	+	0.905013i	$0.360139\pi$
$444$	−4.16016	−0.197432
$445$	23.6098	1.11921
$446$	53.4997	2.53328
$447$	−4.01094	−0.189711
$448$	−40.1064	−1.89485
$449$	−12.6465	−0.596824	−0.298412	−	0.954437i	$-0.596457\pi$
$449$	−12.6465	−0.596824	−0.298412	+	0.954437i	$0.596457\pi$
$450$	21.5062	1.01381
$451$	6.50670	0.306389
$452$	33.9361	1.59622
$453$	0.841630	0.0395432
$454$	19.3791	0.909507
$455$	16.1611	0.757642
$456$	−0.674448	−0.0315839
$457$	−17.7165	−0.828742	−0.414371	−	0.910108i	$-0.635998\pi$
$457$	−17.7165	−0.828742	−0.414371	+	0.910108i	$0.635998\pi$
$458$	55.5571	2.59601
$459$	−6.46573	−0.301794
$460$	29.2073	1.36180
$461$	5.25330	0.244671	0.122335	−	0.992489i	$-0.460962\pi$
$461$	5.25330	0.244671	0.122335	+	0.992489i	$0.460962\pi$
$462$	−2.40898	−0.112076
$463$	−7.04488	−0.327404	−0.163702	−	0.986510i	$-0.552343\pi$
$463$	−7.04488	−0.327404	−0.163702	+	0.986510i	$0.552343\pi$
$464$	12.2223	0.567408
$465$	1.30107	0.0603356
$466$	36.3454	1.68367
$467$	−35.1002	−1.62425	−0.812123	−	0.583487i	$-0.801688\pi$
$467$	−35.1002	−1.62425	−0.812123	+	0.583487i	$0.801688\pi$
$468$	−30.1119	−1.39192
$469$	−38.0896	−1.75881
$470$	5.47066	0.252343
$471$	2.91353	0.134248
$472$	20.5131	0.944191
$473$	−8.93633	−0.410893
$474$	0.950634	0.0436640
$475$	−8.19736	−0.376121
$476$	−49.2897	−2.25919
$477$	20.1269	0.921549
$478$	−39.3251	−1.79869
$479$	−1.53619	−0.0701904	−0.0350952	−	0.999384i	$-0.511173\pi$
$479$	−1.53619	−0.0701904	−0.0350952	+	0.999384i	$0.511173\pi$
$480$	1.90597	0.0869953
$481$	30.8232	1.40542
$482$	6.25552	0.284931
$483$	−5.49103	−0.249851
$484$	−21.1982	−0.963553
$485$	−7.60737	−0.345433
$486$	−11.1011	−0.503557
$487$	5.71734	0.259077	0.129539	−	0.991574i	$-0.458650\pi$
$487$	5.71734	0.259077	0.129539	+	0.991574i	$0.458650\pi$
$488$	−18.3918	−0.832556
$489$	−4.47530	−0.202380
$490$	10.8746	0.491266
$491$	−35.5648	−1.60502	−0.802510	−	0.596639i	$-0.796502\pi$
$491$	−35.5648	−1.60502	−0.802510	+	0.596639i	$0.796502\pi$
$492$	−1.92482	−0.0867776
$493$	30.5703	1.37682
$494$	20.1018	0.904425
$495$	−6.60552	−0.296896
$496$	11.7546	0.527798
$497$	−1.20185	−0.0539105
$498$	6.86267	0.307524
$499$	34.4678	1.54299	0.771496	−	0.636234i	$-0.219509\pi$
$499$	34.4678	1.54299	0.771496	+	0.636234i	$0.219509\pi$
$500$	−28.4836	−1.27383
$501$	2.50181	0.111773
$502$	32.8211	1.46488
$503$	−16.6728	−0.743402	−0.371701	−	0.928352i	$-0.621225\pi$
$503$	−16.6728	−0.743402	−0.371701	+	0.928352i	$0.621225\pi$
$504$	−13.9954	−0.623404
$505$	2.60254	0.115812
$506$	32.2569	1.43399
$507$	−0.306598	−0.0136165
$508$	−6.06533	−0.269106
$509$	20.0796	0.890015	0.445007	−	0.895527i	$-0.353201\pi$
$509$	20.0796	0.890015	0.445007	+	0.895527i	$0.353201\pi$
$510$	2.99624	0.132676
$511$	−27.3541	−1.21007
$512$	23.6165	1.04371
$513$	2.81498	0.124284
$514$	40.0106	1.76479
$515$	4.40607	0.194155
$516$	2.64356	0.116376
$517$	3.44971	0.151718
$518$	57.6293	2.53209
$519$	4.01560	0.176265
$520$	6.98148	0.306158
$521$	−27.7877	−1.21740	−0.608701	−	0.793400i	$-0.708309\pi$
$521$	−27.7877	−1.21740	−0.608701	+	0.793400i	$0.708309\pi$
$522$	34.9179	1.52831
$523$	−32.3282	−1.41361	−0.706806	−	0.707407i	$-0.749865\pi$
$523$	−32.3282	−1.41361	−0.706806	+	0.707407i	$0.749865\pi$
$524$	−32.2148	−1.40731
$525$	2.15312	0.0939700
$526$	−16.9996	−0.741217
$527$	29.4004	1.28070
$528$	0.755396	0.0328744
$529$	50.5263	2.19679
$530$	−18.7718	−0.815397
$531$	−42.5390	−1.84604
$532$	21.4592	0.930376
$533$	14.2612	0.617723
$534$	−7.71352	−0.333797
$535$	−9.09575	−0.393244
$536$	−16.4545	−0.710725
$537$	−3.63490	−0.156857
$538$	50.0493	2.15778
$539$	6.85738	0.295368
$540$	3.93284	0.169243
$541$	−2.84846	−0.122465	−0.0612324	−	0.998124i	$-0.519503\pi$
$541$	−2.84846	−0.122465	−0.0612324	+	0.998124i	$0.519503\pi$
$542$	10.7962	0.463737
$543$	1.22745	0.0526750
$544$	43.0695	1.84659
$545$	−2.03810	−0.0873027
$546$	−5.27996	−0.225961
$547$	10.6130	0.453781	0.226890	−	0.973920i	$-0.427144\pi$
$547$	10.6130	0.453781	0.226890	+	0.973920i	$0.427144\pi$
$548$	29.5446	1.26208
$549$	38.1399	1.62777
$550$	−12.6484	−0.539331
$551$	−13.3094	−0.566998
$552$	−2.37209	−0.100963
$553$	−7.51897	−0.319739
$554$	−6.17936	−0.262536
$555$	−2.00021	−0.0849043
$556$	−22.7502	−0.964825
$557$	5.43745	0.230392	0.115196	−	0.993343i	$-0.463250\pi$
$557$	5.43745	0.230392	0.115196	+	0.993343i	$0.463250\pi$
$558$	33.5817	1.42162
$559$	−19.5865	−0.828419
$560$	−9.47495	−0.400390
$561$	1.88938	0.0797698
$562$	47.2213	1.99191
$563$	28.9486	1.22004	0.610018	−	0.792387i	$-0.291162\pi$
$563$	28.9486	1.22004	0.610018	+	0.792387i	$0.291162\pi$
$564$	−1.02050	−0.0429708
$565$	16.3165	0.686441
$566$	58.4314	2.45605
$567$	28.6509	1.20323
$568$	−0.519193	−0.0217849
$569$	−42.7950	−1.79406	−0.897029	−	0.441971i	$-0.854279\pi$
$569$	−42.7950	−1.79406	−0.897029	+	0.441971i	$0.854279\pi$
$570$	−1.30447	−0.0546383
$571$	2.09656	0.0877383	0.0438691	−	0.999037i	$-0.486032\pi$
$571$	2.09656	0.0877383	0.0438691	+	0.999037i	$0.486032\pi$
$572$	17.7097	0.740479
$573$	0.852189	0.0356007
$574$	26.6639	1.11293
$575$	−28.8308	−1.20233
$576$	35.9292	1.49705
$577$	−13.4387	−0.559461	−0.279731	−	0.960079i	$-0.590245\pi$
$577$	−13.4387	−0.559461	−0.279731	+	0.960079i	$0.590245\pi$
$578$	31.0020	1.28951
$579$	−1.02109	−0.0424349
$580$	−18.5947	−0.772102
$581$	−54.2799	−2.25191
$582$	2.48540	0.103023
$583$	−11.8372	−0.490248
$584$	−11.8168	−0.488982
$585$	−14.4778	−0.598585
$586$	0.816416	0.0337258
$587$	19.4864	0.804290	0.402145	−	0.915576i	$-0.368265\pi$
$587$	19.4864	0.804290	0.402145	+	0.915576i	$0.368265\pi$
$588$	−2.02856	−0.0836563
$589$	−12.8000	−0.527417
$590$	39.6750	1.63339
$591$	−2.53842	−0.104417
$592$	−18.0711	−0.742717
$593$	25.1742	1.03378	0.516889	−	0.856052i	$-0.327090\pi$
$593$	25.1742	1.03378	0.516889	+	0.856052i	$0.327090\pi$
$594$	4.34349	0.178215
$595$	−23.6986	−0.971546
$596$	55.1302	2.25822
$597$	−2.09888	−0.0859013
$598$	70.6999	2.89114
$599$	12.3649	0.505215	0.252607	−	0.967569i	$-0.418712\pi$
$599$	12.3649	0.505215	0.252607	+	0.967569i	$0.418712\pi$
$600$	0.930136	0.0379727
$601$	−21.7122	−0.885660	−0.442830	−	0.896606i	$-0.646025\pi$
$601$	−21.7122	−0.885660	−0.442830	+	0.896606i	$0.646025\pi$
$602$	−36.6203	−1.49253
$603$	34.1225	1.38957
$604$	−11.5682	−0.470702
$605$	−10.1921	−0.414368
$606$	−0.850275	−0.0345401
$607$	−13.9905	−0.567855	−0.283927	−	0.958846i	$-0.591637\pi$
$607$	−13.9905	−0.567855	−0.283927	+	0.958846i	$0.591637\pi$
$608$	−18.7512	−0.760460
$609$	3.49585	0.141659
$610$	−35.5721	−1.44027
$611$	7.56101	0.305886
$612$	44.1561	1.78490
$613$	−1.85000	−0.0747207	−0.0373603	−	0.999302i	$-0.511895\pi$
$613$	−1.85000	−0.0747207	−0.0373603	+	0.999302i	$0.511895\pi$
$614$	−14.0816	−0.568287
$615$	−0.925457	−0.0373180
$616$	8.23109	0.331640
$617$	−17.7233	−0.713513	−0.356757	−	0.934197i	$-0.616117\pi$
$617$	−17.7233	−0.713513	−0.356757	+	0.934197i	$0.616117\pi$
$618$	−1.43950	−0.0579053
$619$	−23.1662	−0.931127	−0.465564	−	0.885014i	$-0.654148\pi$
$619$	−23.1662	−0.931127	−0.465564	+	0.885014i	$0.654148\pi$
$620$	−17.8831	−0.718203
$621$	9.90053	0.397295
$622$	−59.4500	−2.38373
$623$	61.0096	2.44430
$624$	1.65566	0.0662795
$625$	3.11651	0.124661
$626$	1.25245	0.0500579
$627$	−0.822580	−0.0328507
$628$	−40.0463	−1.59802
$629$	−45.1991	−1.80221
$630$	−27.0689	−1.07845
$631$	33.8699	1.34834	0.674170	−	0.738577i	$-0.264502\pi$
$631$	33.8699	1.34834	0.674170	+	0.738577i	$0.264502\pi$
$632$	−3.24815	−0.129205
$633$	0.247797	0.00984903
$634$	−51.7194	−2.05404
$635$	−2.91622	−0.115727
$636$	3.50171	0.138852
$637$	15.0298	0.595504
$638$	−20.5362	−0.813037
$639$	1.07668	0.0425927
$640$	−13.8251	−0.546485
$641$	18.5019	0.730780	0.365390	−	0.930855i	$-0.380936\pi$
$641$	18.5019	0.730780	0.365390	+	0.930855i	$0.380936\pi$
$642$	2.97166	0.117282
$643$	−19.7557	−0.779090	−0.389545	−	0.921007i	$-0.627368\pi$
$643$	−19.7557	−0.779090	−0.389545	+	0.921007i	$0.627368\pi$
$644$	75.4740	2.97409
$645$	1.27103	0.0500466
$646$	−29.4773	−1.15977
$647$	−16.6612	−0.655018	−0.327509	−	0.944848i	$-0.606209\pi$
$647$	−16.6612	−0.655018	−0.327509	+	0.944848i	$0.606209\pi$
$648$	12.3770	0.486215
$649$	25.0184	0.982059
$650$	−27.7226	−1.08737
$651$	3.36207	0.131770
$652$	61.5127	2.40902
$653$	27.5613	1.07856	0.539279	−	0.842127i	$-0.318697\pi$
$653$	27.5613	1.07856	0.539279	+	0.842127i	$0.318697\pi$
$654$	0.665866	0.0260374
$655$	−15.4889	−0.605203
$656$	−8.36113	−0.326447
$657$	24.5051	0.956034
$658$	14.1366	0.551104
$659$	24.9583	0.972236	0.486118	−	0.873893i	$-0.338412\pi$
$659$	24.9583	0.972236	0.486118	+	0.873893i	$0.338412\pi$
$660$	−1.14924	−0.0447340
$661$	−37.2817	−1.45009	−0.725045	−	0.688702i	$-0.758181\pi$
$661$	−37.2817	−1.45009	−0.725045	+	0.688702i	$0.758181\pi$
$662$	−26.2040	−1.01845
$663$	4.14111	0.160827
$664$	−23.4486	−0.909981
$665$	10.3176	0.400101
$666$	−51.6271	−2.00051
$667$	−46.8102	−1.81250
$668$	−34.3872	−1.33048
$669$	−4.79833	−0.185514
$670$	−31.8251	−1.22951
$671$	−22.4312	−0.865947
$672$	4.92519	0.189993
$673$	−9.90519	−0.381817	−0.190908	−	0.981608i	$-0.561143\pi$
$673$	−9.90519	−0.381817	−0.190908	+	0.981608i	$0.561143\pi$
$674$	71.7049	2.76197
$675$	−3.88216	−0.149424
$676$	4.21417	0.162083
$677$	3.87119	0.148782	0.0743909	−	0.997229i	$-0.476299\pi$
$677$	3.87119	0.148782	0.0743909	+	0.997229i	$0.476299\pi$
$678$	−5.33076	−0.204726
$679$	−19.6581	−0.754408
$680$	−10.2376	−0.392595
$681$	−1.73809	−0.0666038
$682$	−19.7503	−0.756280
$683$	22.3232	0.854172	0.427086	−	0.904211i	$-0.359540\pi$
$683$	22.3232	0.854172	0.427086	+	0.904211i	$0.359540\pi$
$684$	−19.2242	−0.735056
$685$	14.2051	0.542749
$686$	−21.8786	−0.835328
$687$	−4.98286	−0.190108
$688$	11.4832	0.437793
$689$	−25.9446	−0.988411
$690$	−4.58794	−0.174660
$691$	−5.20738	−0.198098	−0.0990490	−	0.995083i	$-0.531580\pi$
$691$	−5.20738	−0.198098	−0.0990490	+	0.995083i	$0.531580\pi$
$692$	−55.1943	−2.09817
$693$	−17.0692	−0.648406
$694$	18.8381	0.715083
$695$	−10.9384	−0.414915
$696$	1.51018	0.0572434
$697$	−20.9127	−0.792125
$698$	−11.0499	−0.418245
$699$	−3.25978	−0.123296
$700$	−29.5946	−1.11857
$701$	10.8659	0.410398	0.205199	−	0.978720i	$-0.434216\pi$
$701$	10.8659	0.410398	0.205199	+	0.978720i	$0.434216\pi$
$702$	9.51996	0.359308
$703$	19.6783	0.742181
$704$	−21.1310	−0.796405
$705$	−0.490657	−0.0184792
$706$	−66.3971	−2.49889
$707$	6.72519	0.252927
$708$	−7.40099	−0.278146
$709$	−33.5779	−1.26105	−0.630523	−	0.776171i	$-0.717159\pi$
$709$	−33.5779	−1.26105	−0.630523	+	0.776171i	$0.717159\pi$
$710$	−1.00419	−0.0376865
$711$	6.73586	0.252614
$712$	26.3558	0.987724
$713$	−45.0189	−1.68597
$714$	7.74253	0.289757
$715$	8.51484	0.318437
$716$	49.9615	1.86715
$717$	3.52703	0.131719
$718$	58.8216	2.19520
$719$	−10.3749	−0.386917	−0.193459	−	0.981108i	$-0.561971\pi$
$719$	−10.3749	−0.386917	−0.193459	+	0.981108i	$0.561971\pi$
$720$	8.48811	0.316333
$721$	11.3856	0.424024
$722$	−28.1891	−1.04909
$723$	−0.561051	−0.0208657
$724$	−16.8713	−0.627016
$725$	18.3550	0.681689
$726$	3.32985	0.123582
$727$	−1.90364	−0.0706019	−0.0353010	−	0.999377i	$-0.511239\pi$
$727$	−1.90364	−0.0706019	−0.0353010	+	0.999377i	$0.511239\pi$
$728$	18.0407	0.668633
$729$	−24.9961	−0.925782
$730$	−22.8552	−0.845910
$731$	28.7216	1.06231
$732$	6.63563	0.245260
$733$	−11.6644	−0.430836	−0.215418	−	0.976522i	$-0.569111\pi$
$733$	−11.6644	−0.430836	−0.215418	+	0.976522i	$0.569111\pi$
$734$	2.42643	0.0895612
$735$	−0.975334	−0.0359757
$736$	−65.9494	−2.43093
$737$	−20.0684	−0.739229
$738$	−23.8868	−0.879286
$739$	14.8776	0.547282	0.273641	−	0.961832i	$-0.411772\pi$
$739$	14.8776	0.547282	0.273641	+	0.961832i	$0.411772\pi$
$740$	27.4928	1.01066
$741$	−1.80291	−0.0662316
$742$	−48.5080	−1.78079
$743$	−16.3598	−0.600184	−0.300092	−	0.953910i	$-0.597017\pi$
$743$	−16.3598	−0.600184	−0.300092	+	0.953910i	$0.597017\pi$
$744$	1.45239	0.0532473
$745$	26.5067	0.971130
$746$	29.7389	1.08882
$747$	48.6265	1.77915
$748$	−25.9695	−0.949538
$749$	−23.5042	−0.858824
$750$	4.47427	0.163377
$751$	−32.6208	−1.19035	−0.595175	−	0.803596i	$-0.702917\pi$
$751$	−32.6208	−1.19035	−0.595175	+	0.803596i	$0.702917\pi$
$752$	−4.43289	−0.161651
$753$	−2.94369	−0.107274
$754$	−45.0108	−1.63920
$755$	−5.56199	−0.202422
$756$	10.1628	0.369617
$757$	17.2372	0.626497	0.313248	−	0.949671i	$-0.398583\pi$
$757$	17.2372	0.626497	0.313248	+	0.949671i	$0.398583\pi$
$758$	54.5207	1.98028
$759$	−2.89308	−0.105012
$760$	4.45716	0.161678
$761$	−40.3618	−1.46311	−0.731557	−	0.681780i	$-0.761206\pi$
$761$	−40.3618	−1.46311	−0.731557	+	0.681780i	$0.761206\pi$
$762$	0.952756	0.0345147
$763$	−5.26662	−0.190665
$764$	−11.7133	−0.423772
$765$	21.2303	0.767584
$766$	35.3898	1.27869
$767$	54.8349	1.97997
$768$	−0.180294	−0.00650580
$769$	−47.1226	−1.69929	−0.849643	−	0.527359i	$-0.823182\pi$
$769$	−47.1226	−1.69929	−0.849643	+	0.527359i	$0.823182\pi$
$770$	15.9200	0.573717
$771$	−3.58850	−0.129237
$772$	14.0348	0.505122
$773$	21.3608	0.768293	0.384146	−	0.923272i	$-0.374496\pi$
$773$	21.3608	0.768293	0.384146	+	0.923272i	$0.374496\pi$
$774$	32.8063	1.17920
$775$	17.6526	0.634101
$776$	−8.49217	−0.304851
$777$	−5.16871	−0.185427
$778$	71.0683	2.54792
$779$	9.10475	0.326211
$780$	−2.51887	−0.0901901
$781$	−0.633225	−0.0226586
$782$	−103.674	−3.70739
$783$	−6.30313	−0.225256
$784$	−8.81174	−0.314705
$785$	−19.2543	−0.687216
$786$	5.06038	0.180498
$787$	1.00000	0.0356462
$787$	1.00000	0.0356462
$788$	34.8904	1.24292
$789$	1.52467	0.0542798
$790$	−6.28235	−0.223516
$791$	42.1633	1.49915
$792$	−7.37380	−0.262017
$793$	−49.1642	−1.74587
$794$	−18.8666	−0.669549
$795$	1.68363	0.0597121
$796$	28.8489	1.02252
$797$	−7.66956	−0.271670	−0.135835	−	0.990731i	$-0.543372\pi$
$797$	−7.66956	−0.271670	−0.135835	+	0.990731i	$0.543372\pi$
$798$	−3.37086	−0.119327
$799$	−11.0875	−0.392246
$800$	25.8598	0.914283
$801$	−54.6553	−1.93115
$802$	70.9310	2.50466
$803$	−14.4121	−0.508594
$804$	5.93666	0.209370
$805$	36.2880	1.27898
$806$	−43.2884	−1.52477
$807$	−4.48886	−0.158016
$808$	2.90524	0.102206
$809$	52.9003	1.85987	0.929937	−	0.367718i	$-0.119861\pi$
$809$	52.9003	1.85987	0.929937	+	0.367718i	$0.119861\pi$
$810$	23.9388	0.841123
$811$	−11.2280	−0.394270	−0.197135	−	0.980376i	$-0.563164\pi$
$811$	−11.2280	−0.394270	−0.197135	+	0.980376i	$0.563164\pi$
$812$	−48.0502	−1.68623
$813$	−0.968299	−0.0339597
$814$	30.3634	1.06424
$815$	29.5754	1.03598
$816$	−2.42786	−0.0849921
$817$	−12.5045	−0.437477
$818$	−58.8765	−2.05857
$819$	−37.4120	−1.30728
$820$	12.7204	0.444214
$821$	21.4199	0.747560	0.373780	−	0.927517i	$-0.378061\pi$
$821$	21.4199	0.747560	0.373780	+	0.927517i	$0.378061\pi$
$822$	−4.64093	−0.161871
$823$	−48.5723	−1.69312	−0.846562	−	0.532290i	$-0.821332\pi$
$823$	−48.5723	−1.69312	−0.846562	+	0.532290i	$0.821332\pi$
$824$	4.91853	0.171345
$825$	1.13442	0.0394956
$826$	102.523	3.56725
$827$	−11.0889	−0.385598	−0.192799	−	0.981238i	$-0.561756\pi$
$827$	−11.0889	−0.385598	−0.192799	+	0.981238i	$0.561756\pi$
$828$	−67.6132	−2.34972
$829$	−16.7957	−0.583338	−0.291669	−	0.956519i	$-0.594211\pi$
$829$	−16.7957	−0.583338	−0.291669	+	0.956519i	$0.594211\pi$
$830$	−45.3526	−1.57421
$831$	0.554220	0.0192257
$832$	−46.3145	−1.60567
$833$	−22.0398	−0.763633
$834$	3.57366	0.123746
$835$	−16.5334	−0.572163
$836$	11.3063	0.391037
$837$	−6.06193	−0.209531
$838$	−7.09579	−0.245120
$839$	−1.99146	−0.0687530	−0.0343765	−	0.999409i	$-0.510945\pi$
$839$	−1.99146	−0.0687530	−0.0343765	+	0.999409i	$0.510945\pi$
$840$	−1.17072	−0.0403936
$841$	0.801541	0.0276394
$842$	60.4939	2.08476
$843$	−4.23523	−0.145869
$844$	−3.40595	−0.117238
$845$	2.02618	0.0697027
$846$	−12.6643	−0.435407
$847$	−26.3373	−0.904959
$848$	15.2109	0.522344
$849$	−5.24065	−0.179858
$850$	40.6524	1.39437
$851$	69.2103	2.37250
$852$	0.187322	0.00641753
$853$	17.1801	0.588234	0.294117	−	0.955769i	$-0.404974\pi$
$853$	17.1801	0.588234	0.294117	+	0.955769i	$0.404974\pi$
$854$	−91.9212	−3.14548
$855$	−9.24303	−0.316105
$856$	−10.1537	−0.347045
$857$	23.9809	0.819172	0.409586	−	0.912271i	$-0.365673\pi$
$857$	23.9809	0.819172	0.409586	+	0.912271i	$0.365673\pi$
$858$	−2.78188	−0.0949716
$859$	−35.6130	−1.21510	−0.607549	−	0.794282i	$-0.707847\pi$
$859$	−35.6130	−1.21510	−0.607549	+	0.794282i	$0.707847\pi$
$860$	−17.4702	−0.595729
$861$	−2.39146	−0.0815007
$862$	−45.7006	−1.55657
$863$	−36.8747	−1.25523	−0.627615	−	0.778524i	$-0.715969\pi$
$863$	−36.8747	−1.25523	−0.627615	+	0.778524i	$0.715969\pi$
$864$	−8.88029	−0.302114
$865$	−26.5375	−0.902302
$866$	10.0872	0.342776
$867$	−2.78054	−0.0944320
$868$	−46.2114	−1.56852
$869$	−3.96155	−0.134386
$870$	2.92089	0.0990276
$871$	−43.9855	−1.49039
$872$	−2.27515	−0.0770463
$873$	17.6106	0.596030
$874$	45.1367	1.52677
$875$	−35.3889	−1.19636
$876$	4.26342	0.144048
$877$	−24.0104	−0.810773	−0.405387	−	0.914145i	$-0.632863\pi$
$877$	−24.0104	−0.810773	−0.405387	+	0.914145i	$0.632863\pi$
$878$	−46.7261	−1.57693
$879$	−0.0732234	−0.00246976
$880$	−4.99211	−0.168284
$881$	37.4071	1.26028	0.630138	−	0.776483i	$-0.282998\pi$
$881$	37.4071	1.26028	0.630138	+	0.776483i	$0.282998\pi$
$882$	−25.1742	−0.847659
$883$	−45.8331	−1.54241	−0.771203	−	0.636589i	$-0.780345\pi$
$883$	−45.8331	−1.54241	−0.771203	+	0.636589i	$0.780345\pi$
$884$	−56.9193	−1.91440
$885$	−3.55841	−0.119614
$886$	38.6620	1.29887
$887$	−0.469943	−0.0157791	−0.00788957	−	0.999969i	$-0.502511\pi$
$887$	−0.469943	−0.0157791	−0.00788957	+	0.999969i	$0.502511\pi$
$888$	−2.23285	−0.0749296
$889$	−7.53576	−0.252741
$890$	50.9755	1.70870
$891$	15.0954	0.505716
$892$	65.9527	2.20826
$893$	4.82714	0.161534
$894$	−8.65997	−0.289633
$895$	24.0216	0.802952
$896$	−35.7252	−1.19350
$897$	−6.34100	−0.211720
$898$	−27.3048	−0.911174
$899$	28.6611	0.955901
$900$	26.5122	0.883741
$901$	38.0452	1.26747
$902$	14.0485	0.467765
$903$	3.28444	0.109299
$904$	18.2143	0.605798
$905$	−8.11174	−0.269643
$906$	1.81715	0.0603709
$907$	31.1793	1.03529	0.517646	−	0.855595i	$-0.326808\pi$
$907$	31.1793	1.03529	0.517646	+	0.855595i	$0.326808\pi$
$908$	23.8900	0.792817
$909$	−6.02475	−0.199828
$910$	34.8931	1.15670
$911$	−42.9428	−1.42276	−0.711379	−	0.702808i	$-0.751929\pi$
$911$	−42.9428	−1.42276	−0.711379	+	0.702808i	$0.751929\pi$
$912$	1.05702	0.0350013
$913$	−28.5987	−0.946477
$914$	−38.2514	−1.26524
$915$	3.19042	0.105472
$916$	68.4891	2.26294
$917$	−40.0247	−1.32173
$918$	−13.9601	−0.460751
$919$	44.2525	1.45976	0.729878	−	0.683577i	$-0.239577\pi$
$919$	44.2525	1.45976	0.729878	+	0.683577i	$0.239577\pi$
$920$	15.6762	0.516829
$921$	1.26296	0.0416160
$922$	11.3423	0.373540
$923$	−1.38789	−0.0456829
$924$	−2.96972	−0.0976967
$925$	−27.1385	−0.892307
$926$	−15.2105	−0.499849
$927$	−10.1998	−0.335006
$928$	41.9865	1.37827
$929$	−28.7183	−0.942217	−0.471108	−	0.882075i	$-0.656146\pi$
$929$	−28.7183	−0.942217	−0.471108	+	0.882075i	$0.656146\pi$
$930$	2.80912	0.0921146
$931$	9.59544	0.314478
$932$	44.8055	1.46765
$933$	5.33201	0.174562
$934$	−75.7845	−2.47974
$935$	−12.4862	−0.408341
$936$	−16.1617	−0.528263
$937$	27.3722	0.894212	0.447106	−	0.894481i	$-0.352455\pi$
$937$	27.3722	0.894212	0.447106	+	0.894481i	$0.352455\pi$
$938$	−82.2387	−2.68519
$939$	−0.112331	−0.00366577
$940$	6.74406	0.219967
$941$	36.9446	1.20436	0.602181	−	0.798360i	$-0.294299\pi$
$941$	36.9446	1.20436	0.602181	+	0.798360i	$0.294299\pi$
$942$	6.29056	0.204958
$943$	32.0222	1.04279
$944$	−32.1487	−1.04635
$945$	4.88629	0.158951
$946$	−19.2943	−0.627312
$947$	−44.7793	−1.45513	−0.727565	−	0.686039i	$-0.759348\pi$
$947$	−44.7793	−1.45513	−0.727565	+	0.686039i	$0.759348\pi$
$948$	1.17191	0.0380619
$949$	−31.5882	−1.02540
$950$	−17.6988	−0.574225
$951$	4.63866	0.150419
$952$	−26.4549	−0.857408
$953$	−13.7123	−0.444185	−0.222093	−	0.975026i	$-0.571289\pi$
$953$	−13.7123	−0.444185	−0.222093	+	0.975026i	$0.571289\pi$
$954$	43.4558	1.40693
$955$	−5.63177	−0.182240
$956$	−48.4788	−1.56792
$957$	1.84187	0.0595392
$958$	−3.31677	−0.107160
$959$	36.7072	1.18534
$960$	3.00549	0.0970019
$961$	−3.43570	−0.110829
$962$	66.5499	2.14565
$963$	21.0562	0.678526
$964$	7.71162	0.248374
$965$	6.74794	0.217224
$966$	−11.8556	−0.381448
$967$	16.8642	0.542316	0.271158	−	0.962535i	$-0.412593\pi$
$967$	16.8642	0.542316	0.271158	+	0.962535i	$0.412593\pi$
$968$	−11.3775	−0.365688
$969$	2.64379	0.0849308
$970$	−16.4250	−0.527374
$971$	−7.66424	−0.245957	−0.122979	−	0.992409i	$-0.539245\pi$
$971$	−7.66424	−0.245957	−0.122979	+	0.992409i	$0.539245\pi$
$972$	−13.6851	−0.438950
$973$	−28.2656	−0.906154
$974$	12.3442	0.395535
$975$	2.48641	0.0796288
$976$	28.8242	0.922639
$977$	38.1198	1.21956	0.609780	−	0.792571i	$-0.291258\pi$
$977$	38.1198	1.21956	0.609780	+	0.792571i	$0.291258\pi$
$978$	−9.66255	−0.308974
$979$	32.1444	1.02734
$980$	13.4059	0.428236
$981$	4.71809	0.150637
$982$	−76.7876	−2.45039
$983$	−22.9318	−0.731410	−0.365705	−	0.930731i	$-0.619172\pi$
$983$	−22.9318	−0.731410	−0.365705	+	0.930731i	$0.619172\pi$
$984$	−1.03310	−0.0329339
$985$	16.7754	0.534508
$986$	66.0039	2.10199
$987$	−1.26790	−0.0403577
$988$	24.7809	0.788387
$989$	−43.9794	−1.39846
$990$	−14.2619	−0.453273
$991$	50.5666	1.60630	0.803151	−	0.595776i	$-0.203155\pi$
$991$	50.5666	1.60630	0.803151	+	0.595776i	$0.203155\pi$
$992$	40.3797	1.28206
$993$	2.35021	0.0745815
$994$	−2.59490	−0.0823054
$995$	13.8706	0.439728
$996$	8.46009	0.268068
$997$	−5.03571	−0.159482	−0.0797412	−	0.996816i	$-0.525409\pi$
$997$	−5.03571	−0.159482	−0.0797412	+	0.996816i	$0.525409\pi$
$998$	74.4190	2.35569
$999$	9.31937	0.294852

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	787.2.a.b.1.30	✓	37
3.2	odd	2		7083.2.a.g.1.8		37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
787.2.a.b.1.30	✓	37	1.1	even	1	trivial
7083.2.a.g.1.8		37	3.2	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:	\( N \)	\(=\)	\( 787 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	787.a (trivial)

\(f(q)\)	\(=\)	\(q+2.15909 q^{2} -0.193646 q^{3} +2.66166 q^{4} +1.27973 q^{5} -0.418099 q^{6} +3.30692 q^{7} +1.42857 q^{8} -2.96250 q^{9} +2.76304 q^{10} +1.74233 q^{11} -0.515419 q^{12} +3.81881 q^{13} +7.13993 q^{14} -0.247814 q^{15} -2.23890 q^{16} -5.59990 q^{17} -6.39630 q^{18} +2.43802 q^{19} +3.40620 q^{20} -0.640373 q^{21} +3.76185 q^{22} +8.57475 q^{23} -0.276637 q^{24} -3.36230 q^{25} +8.24514 q^{26} +1.15462 q^{27} +8.80189 q^{28} -5.45908 q^{29} -0.535053 q^{30} -5.25017 q^{31} -7.69113 q^{32} -0.337396 q^{33} -12.0907 q^{34} +4.23196 q^{35} -7.88516 q^{36} +8.07141 q^{37} +5.26391 q^{38} -0.739497 q^{39} +1.82818 q^{40} +3.73448 q^{41} -1.38262 q^{42} -5.12895 q^{43} +4.63749 q^{44} -3.79120 q^{45} +18.5136 q^{46} +1.97994 q^{47} +0.433555 q^{48} +3.93574 q^{49} -7.25949 q^{50} +1.08440 q^{51} +10.1643 q^{52} -6.79390 q^{53} +2.49291 q^{54} +2.22971 q^{55} +4.72418 q^{56} -0.472114 q^{57} -11.7866 q^{58} +14.3592 q^{59} -0.659596 q^{60} -12.8742 q^{61} -11.3356 q^{62} -9.79677 q^{63} -12.1280 q^{64} +4.88703 q^{65} -0.728467 q^{66} -11.5181 q^{67} -14.9050 q^{68} -1.66047 q^{69} +9.13718 q^{70} -0.363435 q^{71} -4.23214 q^{72} -8.27175 q^{73} +17.4269 q^{74} +0.651095 q^{75} +6.48918 q^{76} +5.76176 q^{77} -1.59664 q^{78} -2.27371 q^{79} -2.86519 q^{80} +8.66392 q^{81} +8.06306 q^{82} -16.4140 q^{83} -1.70445 q^{84} -7.16635 q^{85} -11.0738 q^{86} +1.05713 q^{87} +2.48905 q^{88} +18.4490 q^{89} -8.18552 q^{90} +12.6285 q^{91} +22.8230 q^{92} +1.01668 q^{93} +4.27486 q^{94} +3.12001 q^{95} +1.48936 q^{96} -5.94452 q^{97} +8.49761 q^{98} -5.16166 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 12 q^{2} + 6 q^{3} + 42 q^{4} + 31 q^{5} + 4 q^{6} + 9 q^{7} + 36 q^{8} + 47 q^{9} + 4 q^{10} + 18 q^{11} + 15 q^{12} + 13 q^{13} + 8 q^{14} + 3 q^{15} + 48 q^{16} + 18 q^{17} + 17 q^{18} + 40 q^{20}+ \cdots - 35 q^{99}+O(q^{100}) \) 37 * q + 12 * q^2 + 6 * q^3 + 42 * q^4 + 31 * q^5 + 4 * q^6 + 9 * q^7 + 36 * q^8 + 47 * q^9 + 4 * q^10 + 18 * q^11 + 15 * q^12 + 13 * q^13 + 8 * q^14 + 3 * q^15 + 48 * q^16 + 18 * q^17 + 17 * q^18 + 40 * q^20 - 4 * q^21 - 4 * q^22 + 42 * q^23 - 10 * q^24 + 56 * q^25 - 4 * q^26 + 18 * q^27 + 3 * q^28 + 45 * q^29 - 32 * q^30 - 3 * q^31 + 59 * q^32 + 14 * q^33 - 22 * q^34 + 16 * q^35 + 28 * q^36 + 52 * q^37 - 5 * q^38 - 13 * q^39 - 11 * q^40 + 23 * q^41 - 16 * q^42 + 4 * q^43 + 23 * q^44 + 69 * q^45 - 5 * q^46 + 45 * q^47 - 5 * q^48 + 30 * q^49 + 13 * q^50 - 7 * q^51 + 3 * q^52 + 103 * q^53 - 23 * q^54 - 9 * q^55 + 4 * q^56 + 9 * q^57 + 8 * q^58 + 2 * q^59 - 47 * q^60 - 6 * q^61 + 20 * q^62 + 5 * q^63 + 28 * q^64 + 51 * q^65 - 48 * q^66 + 24 * q^67 - 9 * q^68 - 52 * q^70 + 32 * q^71 + 42 * q^72 + 5 * q^73 + 4 * q^74 - 35 * q^75 - 34 * q^76 + 97 * q^77 - 31 * q^78 - 27 * q^79 + 47 * q^80 + 29 * q^81 - q^82 + 23 * q^83 - 93 * q^84 + 27 * q^85 + 10 * q^86 - 46 * q^87 - 45 * q^88 + 9 * q^89 - 70 * q^90 - 48 * q^91 + 67 * q^92 + 72 * q^93 - 52 * q^94 - 20 * q^95 - 89 * q^96 - 7 * q^97 - 12 * q^98 - 35 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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