LMFDB - Embedded newform 787.2.a.b.1.20

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			1.20
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)

$f(q)$	$=$	\(q+0.563766 q^{2} +0.822843 q^{3} -1.68217 q^{4} +1.78681 q^{5} +0.463891 q^{6} -0.964492 q^{7} -2.07588 q^{8} -2.32293 q^{9} +1.00734 q^{10} +5.94832 q^{11} -1.38416 q^{12} +2.26830 q^{13} -0.543748 q^{14} +1.47026 q^{15} +2.19402 q^{16} +1.30602 q^{17} -1.30959 q^{18} +5.52478 q^{19} -3.00571 q^{20} -0.793626 q^{21} +3.35346 q^{22} +1.41654 q^{23} -1.70812 q^{24} -1.80732 q^{25} +1.27879 q^{26} -4.37994 q^{27} +1.62244 q^{28} +6.67544 q^{29} +0.828883 q^{30} +2.06915 q^{31} +5.38868 q^{32} +4.89453 q^{33} +0.736288 q^{34} -1.72336 q^{35} +3.90756 q^{36} +6.60785 q^{37} +3.11468 q^{38} +1.86646 q^{39} -3.70920 q^{40} -2.33755 q^{41} -0.447419 q^{42} +4.15921 q^{43} -10.0061 q^{44} -4.15062 q^{45} +0.798594 q^{46} -7.57989 q^{47} +1.80534 q^{48} -6.06975 q^{49} -1.01891 q^{50} +1.07465 q^{51} -3.81567 q^{52} -6.95874 q^{53} -2.46926 q^{54} +10.6285 q^{55} +2.00217 q^{56} +4.54603 q^{57} +3.76339 q^{58} -5.46213 q^{59} -2.47323 q^{60} -8.63477 q^{61} +1.16652 q^{62} +2.24045 q^{63} -1.35010 q^{64} +4.05302 q^{65} +2.75937 q^{66} +3.13225 q^{67} -2.19694 q^{68} +1.16559 q^{69} -0.971572 q^{70} +4.08053 q^{71} +4.82213 q^{72} +12.2156 q^{73} +3.72528 q^{74} -1.48714 q^{75} -9.29361 q^{76} -5.73711 q^{77} +1.05224 q^{78} -9.89181 q^{79} +3.92030 q^{80} +3.36479 q^{81} -1.31783 q^{82} -1.18766 q^{83} +1.33501 q^{84} +2.33360 q^{85} +2.34482 q^{86} +5.49284 q^{87} -12.3480 q^{88} -5.38368 q^{89} -2.33998 q^{90} -2.18776 q^{91} -2.38285 q^{92} +1.70259 q^{93} -4.27328 q^{94} +9.87171 q^{95} +4.43404 q^{96} +3.48567 q^{97} -3.42192 q^{98} -13.8175 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.563766	0.398643	0.199321	−	0.979934i	$-0.436126\pi$
$2$	0.563766	0.398643	0.199321	+	0.979934i	$0.436126\pi$
$3$	0.822843	0.475069	0.237534	−	0.971379i	$-0.423661\pi$
$3$	0.822843	0.475069	0.237534	+	0.971379i	$0.423661\pi$
$4$	−1.68217	−0.841084
$5$	1.78681	0.799084	0.399542	−	0.916715i	$-0.369169\pi$
$5$	1.78681	0.799084	0.399542	+	0.916715i	$0.369169\pi$
$6$	0.463891	0.189383
$7$	−0.964492	−0.364544	−0.182272	−	0.983248i	$-0.558345\pi$
$7$	−0.964492	−0.364544	−0.182272	+	0.983248i	$0.558345\pi$
$8$	−2.07588	−0.733935
$9$	−2.32293	−0.774310
$10$	1.00734	0.318549
$11$	5.94832	1.79349	0.896743	−	0.442551i	$-0.145927\pi$
$11$	5.94832	1.79349	0.896743	+	0.442551i	$0.145927\pi$
$12$	−1.38416	−0.399573
$13$	2.26830	0.629114	0.314557	−	0.949239i	$-0.398144\pi$
$13$	2.26830	0.629114	0.314557	+	0.949239i	$0.398144\pi$
$14$	−0.543748	−0.145323
$15$	1.47026	0.379620
$16$	2.19402	0.548506
$17$	1.30602	0.316756	0.158378	−	0.987379i	$-0.449374\pi$
$17$	1.30602	0.316756	0.158378	+	0.987379i	$0.449374\pi$
$18$	−1.30959	−0.308673
$19$	5.52478	1.26747	0.633736	−	0.773550i	$-0.281521\pi$
$19$	5.52478	1.26747	0.633736	+	0.773550i	$0.281521\pi$
$20$	−3.00571	−0.672097
$21$	−0.793626	−0.173183
$22$	3.35346	0.714960
$23$	1.41654	0.295368	0.147684	−	0.989035i	$-0.452818\pi$
$23$	1.41654	0.295368	0.147684	+	0.989035i	$0.452818\pi$
$24$	−1.70812	−0.348669
$25$	−1.80732	−0.361465
$26$	1.27879	0.250792
$27$	−4.37994	−0.842919
$28$	1.62244	0.306612
$29$	6.67544	1.23960	0.619799	−	0.784760i	$-0.287214\pi$
$29$	6.67544	1.23960	0.619799	+	0.784760i	$0.287214\pi$
$30$	0.828883	0.151333
$31$	2.06915	0.371631	0.185815	−	0.982585i	$-0.440507\pi$
$31$	2.06915	0.371631	0.185815	+	0.982585i	$0.440507\pi$
$32$	5.38868	0.952593
$33$	4.89453	0.852029
$34$	0.736288	0.126272
$35$	−1.72336	−0.291301
$36$	3.90756	0.651260
$37$	6.60785	1.08632	0.543162	−	0.839628i	$-0.317227\pi$
$37$	6.60785	1.08632	0.543162	+	0.839628i	$0.317227\pi$
$38$	3.11468	0.505268
$39$	1.86646	0.298872
$40$	−3.70920	−0.586476
$41$	−2.33755	−0.365064	−0.182532	−	0.983200i	$-0.558429\pi$
$41$	−2.33755	−0.365064	−0.182532	+	0.983200i	$0.558429\pi$
$42$	−0.447419	−0.0690383
$43$	4.15921	0.634273	0.317137	−	0.948380i	$-0.397279\pi$
$43$	4.15921	0.634273	0.317137	+	0.948380i	$0.397279\pi$
$44$	−10.0061	−1.50847
$45$	−4.15062	−0.618739
$46$	0.798594	0.117746
$47$	−7.57989	−1.10564	−0.552820	−	0.833301i	$-0.686448\pi$
$47$	−7.57989	−1.10564	−0.552820	+	0.833301i	$0.686448\pi$
$48$	1.80534	0.260578
$49$	−6.06975	−0.867108
$50$	−1.01891	−0.144095
$51$	1.07465	0.150481
$52$	−3.81567	−0.529138
$53$	−6.95874	−0.955856	−0.477928	−	0.878399i	$-0.658612\pi$
$53$	−6.95874	−0.955856	−0.477928	+	0.878399i	$0.658612\pi$
$54$	−2.46926	−0.336024
$55$	10.6285	1.43315
$56$	2.00217	0.267551
$57$	4.54603	0.602136
$58$	3.76339	0.494157
$59$	−5.46213	−0.711109	−0.355554	−	0.934656i	$-0.615708\pi$
$59$	−5.46213	−0.711109	−0.355554	+	0.934656i	$0.615708\pi$
$60$	−2.47323	−0.319292
$61$	−8.63477	−1.10557	−0.552784	−	0.833324i	$-0.686435\pi$
$61$	−8.63477	−1.10557	−0.552784	+	0.833324i	$0.686435\pi$
$62$	1.16652	0.148148
$63$	2.24045	0.282270
$64$	−1.35010	−0.168762
$65$	4.05302	0.502715
$66$	2.75937	0.339655
$67$	3.13225	0.382666	0.191333	−	0.981525i	$-0.438719\pi$
$67$	3.13225	0.382666	0.191333	+	0.981525i	$0.438719\pi$
$68$	−2.19694	−0.266418
$69$	1.16559	0.140320
$70$	−0.971572	−0.116125
$71$	4.08053	0.484270	0.242135	−	0.970243i	$-0.422152\pi$
$71$	4.08053	0.484270	0.242135	+	0.970243i	$0.422152\pi$
$72$	4.82213	0.568293
$73$	12.2156	1.42973	0.714864	−	0.699263i	$-0.246488\pi$
$73$	12.2156	1.42973	0.714864	+	0.699263i	$0.246488\pi$
$74$	3.72528	0.433055
$75$	−1.48714	−0.171721
$76$	−9.29361	−1.06605
$77$	−5.73711	−0.653804
$78$	1.05224	0.119143
$79$	−9.89181	−1.11292	−0.556458	−	0.830876i	$-0.687840\pi$
$79$	−9.89181	−1.11292	−0.556458	+	0.830876i	$0.687840\pi$
$80$	3.92030	0.438302
$81$	3.36479	0.373866
$82$	−1.31783	−0.145530
$83$	−1.18766	−0.130362	−0.0651812	−	0.997873i	$-0.520763\pi$
$83$	−1.18766	−0.130362	−0.0651812	+	0.997873i	$0.520763\pi$
$84$	1.33501	0.145662
$85$	2.33360	0.253114
$86$	2.34482	0.252848
$87$	5.49284	0.588894
$88$	−12.3480	−1.31630
$89$	−5.38368	−0.570669	−0.285334	−	0.958428i	$-0.592105\pi$
$89$	−5.38368	−0.570669	−0.285334	+	0.958428i	$0.592105\pi$
$90$	−2.33998	−0.246656
$91$	−2.18776	−0.229340
$92$	−2.38285	−0.248429
$93$	1.70259	0.176550
$94$	−4.27328	−0.440755
$95$	9.87171	1.01282
$96$	4.43404	0.452547
$97$	3.48567	0.353916	0.176958	−	0.984218i	$-0.443374\pi$
$97$	3.48567	0.353916	0.176958	+	0.984218i	$0.443374\pi$
$98$	−3.42192	−0.345666
$99$	−13.8175	−1.38871
$100$	3.04022	0.304022
$101$	−0.965037	−0.0960248	−0.0480124	−	0.998847i	$-0.515289\pi$
$101$	−0.965037	−0.0960248	−0.0480124	+	0.998847i	$0.515289\pi$
$102$	0.605849	0.0599880
$103$	14.7118	1.44959	0.724797	−	0.688963i	$-0.241934\pi$
$103$	14.7118	1.44959	0.724797	+	0.688963i	$0.241934\pi$
$104$	−4.70873	−0.461729
$105$	−1.41806	−0.138388
$106$	−3.92310	−0.381045
$107$	−5.93695	−0.573947	−0.286973	−	0.957939i	$-0.592649\pi$
$107$	−5.93695	−0.573947	−0.286973	+	0.957939i	$0.592649\pi$
$108$	7.36779	0.708966
$109$	−0.713069	−0.0682996	−0.0341498	−	0.999417i	$-0.510872\pi$
$109$	−0.713069	−0.0682996	−0.0341498	+	0.999417i	$0.510872\pi$
$110$	5.99199	0.571313
$111$	5.43722	0.516078
$112$	−2.11612	−0.199955
$113$	3.08478	0.290192	0.145096	−	0.989418i	$-0.453651\pi$
$113$	3.08478	0.290192	0.145096	+	0.989418i	$0.453651\pi$
$114$	2.56290	0.240037
$115$	2.53107	0.236024
$116$	−11.2292	−1.04261
$117$	−5.26911	−0.487129
$118$	−3.07936	−0.283478
$119$	−1.25964	−0.115471
$120$	−3.05209	−0.278616
$121$	24.3825	2.21659
$122$	−4.86799	−0.440727
$123$	−1.92344	−0.173431
$124$	−3.48066	−0.312573
$125$	−12.1634	−1.08792
$126$	1.26309	0.112525
$127$	−5.75870	−0.511002	−0.255501	−	0.966809i	$-0.582240\pi$
$127$	−5.75870	−0.511002	−0.255501	+	0.966809i	$0.582240\pi$
$128$	−11.5385	−1.01987
$129$	3.42238	0.301323
$130$	2.28495	0.200404
$131$	4.10474	0.358632	0.179316	−	0.983791i	$-0.442611\pi$
$131$	4.10474	0.358632	0.179316	+	0.983791i	$0.442611\pi$
$132$	−8.23343	−0.716628
$133$	−5.32861	−0.462049
$134$	1.76586	0.152547
$135$	−7.82609	−0.673563
$136$	−2.71113	−0.232478
$137$	−19.2478	−1.64445	−0.822227	−	0.569159i	$-0.807269\pi$
$137$	−19.2478	−1.64445	−0.822227	+	0.569159i	$0.807269\pi$
$138$	0.657118	0.0559376
$139$	−13.7806	−1.16886	−0.584429	−	0.811445i	$-0.698681\pi$
$139$	−13.7806	−1.16886	−0.584429	+	0.811445i	$0.698681\pi$
$140$	2.89898	0.245009
$141$	−6.23706	−0.525255
$142$	2.30047	0.193051
$143$	13.4926	1.12831
$144$	−5.09656	−0.424714
$145$	11.9277	0.990543
$146$	6.88674	0.569951
$147$	−4.99445	−0.411936
$148$	−11.1155	−0.913689
$149$	4.60811	0.377511	0.188755	−	0.982024i	$-0.439555\pi$
$149$	4.60811	0.377511	0.188755	+	0.982024i	$0.439555\pi$
$150$	−0.838401	−0.0684552
$151$	−2.29186	−0.186509	−0.0932544	−	0.995642i	$-0.529727\pi$
$151$	−2.29186	−0.186509	−0.0932544	+	0.995642i	$0.529727\pi$
$152$	−11.4688	−0.930241
$153$	−3.03378	−0.245267
$154$	−3.23439	−0.260634
$155$	3.69717	0.296964
$156$	−3.13969	−0.251377
$157$	0.863544	0.0689183	0.0344592	−	0.999406i	$-0.489029\pi$
$157$	0.863544	0.0689183	0.0344592	+	0.999406i	$0.489029\pi$
$158$	−5.57666	−0.443656
$159$	−5.72595	−0.454097
$160$	9.62852	0.761202
$161$	−1.36624	−0.107675
$162$	1.89695	0.149039
$163$	−12.9687	−1.01579	−0.507895	−	0.861419i	$-0.669576\pi$
$163$	−12.9687	−1.01579	−0.507895	+	0.861419i	$0.669576\pi$
$164$	3.93215	0.307050
$165$	8.74558	0.680843
$166$	−0.669561	−0.0519680
$167$	−1.89301	−0.146486	−0.0732429	−	0.997314i	$-0.523335\pi$
$167$	−1.89301	−0.146486	−0.0732429	+	0.997314i	$0.523335\pi$
$168$	1.64747	0.127105
$169$	−7.85481	−0.604216
$170$	1.31560	0.100902
$171$	−12.8337	−0.981416
$172$	−6.99649	−0.533477
$173$	13.3774	1.01706	0.508532	−	0.861043i	$-0.330188\pi$
$173$	13.3774	1.01706	0.508532	+	0.861043i	$0.330188\pi$
$174$	3.09668	0.234759
$175$	1.74315	0.131770
$176$	13.0508	0.983738
$177$	−4.49447	−0.337825
$178$	−3.03514	−0.227493
$179$	−22.8068	−1.70466	−0.852330	−	0.523005i	$-0.824811\pi$
$179$	−22.8068	−1.70466	−0.852330	+	0.523005i	$0.824811\pi$
$180$	6.98205	0.520411
$181$	−12.2888	−0.913422	−0.456711	−	0.889615i	$-0.650973\pi$
$181$	−12.2888	−0.913422	−0.456711	+	0.889615i	$0.650973\pi$
$182$	−1.23338	−0.0914246
$183$	−7.10506	−0.525221
$184$	−2.94056	−0.216781
$185$	11.8069	0.868064
$186$	0.959861	0.0703804
$187$	7.76861	0.568097
$188$	12.7506	0.929936
$189$	4.22441	0.307281
$190$	5.56533	0.403752
$191$	17.8977	1.29503	0.647514	−	0.762053i	$-0.275809\pi$
$191$	17.8977	1.29503	0.647514	+	0.762053i	$0.275809\pi$
$192$	−1.11092	−0.0801735
$193$	8.36294	0.601978	0.300989	−	0.953628i	$-0.402683\pi$
$193$	8.36294	0.601978	0.300989	+	0.953628i	$0.402683\pi$
$194$	1.96510	0.141086
$195$	3.33500	0.238824
$196$	10.2103	0.729310
$197$	8.73271	0.622180	0.311090	−	0.950381i	$-0.399306\pi$
$197$	8.73271	0.622180	0.311090	+	0.950381i	$0.399306\pi$
$198$	−7.78985	−0.553601
$199$	−21.9950	−1.55918	−0.779592	−	0.626288i	$-0.784574\pi$
$199$	−21.9950	−1.55918	−0.779592	+	0.626288i	$0.784574\pi$
$200$	3.75179	0.265292
$201$	2.57735	0.181793
$202$	−0.544055	−0.0382796
$203$	−6.43841	−0.451888
$204$	−1.80774	−0.126567
$205$	−4.17675	−0.291717
$206$	8.29399	0.577870
$207$	−3.29051	−0.228706
$208$	4.97671	0.345073
$209$	32.8632	2.27319
$210$	−0.799451	−0.0551674
$211$	−2.23785	−0.154060	−0.0770300	−	0.997029i	$-0.524544\pi$
$211$	−2.23785	−0.154060	−0.0770300	+	0.997029i	$0.524544\pi$
$212$	11.7058	0.803955
$213$	3.35764	0.230062
$214$	−3.34705	−0.228800
$215$	7.43170	0.506838
$216$	9.09222	0.618648
$217$	−1.99568	−0.135476
$218$	−0.402004	−0.0272272
$219$	10.0515	0.679219
$220$	−17.8789	−1.20540
$221$	2.96244	0.199275
$222$	3.06532	0.205731
$223$	−17.0149	−1.13940	−0.569702	−	0.821851i	$-0.692941\pi$
$223$	−17.0149	−1.13940	−0.569702	+	0.821851i	$0.692941\pi$
$224$	−5.19734	−0.347262
$225$	4.19829	0.279886
$226$	1.73910	0.115683
$227$	−9.65276	−0.640676	−0.320338	−	0.947303i	$-0.603797\pi$
$227$	−9.65276	−0.640676	−0.320338	+	0.947303i	$0.603797\pi$
$228$	−7.64718	−0.506447
$229$	2.33099	0.154036	0.0770179	−	0.997030i	$-0.475460\pi$
$229$	2.33099	0.154036	0.0770179	+	0.997030i	$0.475460\pi$
$230$	1.42693	0.0940892
$231$	−4.72074	−0.310602
$232$	−13.8574	−0.909785
$233$	5.60954	0.367493	0.183747	−	0.982974i	$-0.441177\pi$
$233$	5.60954	0.367493	0.183747	+	0.982974i	$0.441177\pi$
$234$	−2.97054	−0.194190
$235$	−13.5438	−0.883499
$236$	9.18822	0.598102
$237$	−8.13940	−0.528711
$238$	−0.710144	−0.0460318
$239$	−22.6692	−1.46635	−0.733174	−	0.680041i	$-0.761962\pi$
$239$	−22.6692	−1.46635	−0.733174	+	0.680041i	$0.761962\pi$
$240$	3.22579	0.208224
$241$	26.8664	1.73062	0.865308	−	0.501241i	$-0.167123\pi$
$241$	26.8664	1.73062	0.865308	+	0.501241i	$0.167123\pi$
$242$	13.7460	0.883629
$243$	15.9085	1.02053
$244$	14.5251	0.929876
$245$	−10.8455	−0.692892
$246$	−1.08437	−0.0691368
$247$	12.5319	0.797384
$248$	−4.29531	−0.272753
$249$	−0.977256	−0.0619311
$250$	−6.85729	−0.433693
$251$	5.27636	0.333041	0.166520	−	0.986038i	$-0.446747\pi$
$251$	5.27636	0.333041	0.166520	+	0.986038i	$0.446747\pi$
$252$	−3.76881	−0.237413
$253$	8.42601	0.529738
$254$	−3.24656	−0.203707
$255$	1.92018	0.120247
$256$	−3.80482	−0.237801
$257$	−3.21059	−0.200271	−0.100136	−	0.994974i	$-0.531928\pi$
$257$	−3.21059	−0.200271	−0.100136	+	0.994974i	$0.531928\pi$
$258$	1.92942	0.120120
$259$	−6.37322	−0.396013
$260$	−6.81785	−0.422825
$261$	−15.5066	−0.959833
$262$	2.31411	0.142966
$263$	14.6644	0.904245	0.452123	−	0.891956i	$-0.350667\pi$
$263$	14.6644	0.904245	0.452123	+	0.891956i	$0.350667\pi$
$264$	−10.1605	−0.625334
$265$	−12.4339	−0.763809
$266$	−3.00409	−0.184192
$267$	−4.42992	−0.271107
$268$	−5.26898	−0.321854
$269$	10.4240	0.635561	0.317781	−	0.948164i	$-0.397062\pi$
$269$	10.4240	0.635561	0.317781	+	0.948164i	$0.397062\pi$
$270$	−4.41209	−0.268511
$271$	−11.7659	−0.714728	−0.357364	−	0.933965i	$-0.616324\pi$
$271$	−11.7659	−0.714728	−0.357364	+	0.933965i	$0.616324\pi$
$272$	2.86543	0.173742
$273$	−1.80018	−0.108952
$274$	−10.8513	−0.655550
$275$	−10.7505	−0.648282
$276$	−1.96071	−0.118021
$277$	23.9203	1.43723	0.718616	−	0.695407i	$-0.244776\pi$
$277$	23.9203	1.43723	0.718616	+	0.695407i	$0.244776\pi$
$278$	−7.76905	−0.465956
$279$	−4.80649	−0.287757
$280$	3.57749	0.213796
$281$	18.7229	1.11691	0.558457	−	0.829533i	$-0.311393\pi$
$281$	18.7229	1.11691	0.558457	+	0.829533i	$0.311393\pi$
$282$	−3.51624	−0.209389
$283$	−25.0061	−1.48646	−0.743229	−	0.669037i	$-0.766707\pi$
$283$	−25.0061	−1.48646	−0.743229	+	0.669037i	$0.766707\pi$
$284$	−6.86414	−0.407312
$285$	8.12287	0.481157
$286$	7.60666	0.449791
$287$	2.25455	0.133082
$288$	−12.5175	−0.737602
$289$	−15.2943	−0.899666
$290$	6.72444	0.394873
$291$	2.86816	0.168135
$292$	−20.5487	−1.20252
$293$	14.4268	0.842825	0.421413	−	0.906869i	$-0.361534\pi$
$293$	14.4268	0.842825	0.421413	+	0.906869i	$0.361534\pi$
$294$	−2.81570	−0.164215
$295$	−9.75976	−0.568235
$296$	−13.7171	−0.797291
$297$	−26.0533	−1.51176
$298$	2.59789	0.150492
$299$	3.21313	0.185820
$300$	2.50163	0.144431
$301$	−4.01152	−0.231220
$302$	−1.29207	−0.0743503
$303$	−0.794074	−0.0456183
$304$	12.1215	0.695216
$305$	−15.4287	−0.883442
$306$	−1.71034	−0.0977739
$307$	−4.91196	−0.280340	−0.140170	−	0.990127i	$-0.544765\pi$
$307$	−4.91196	−0.280340	−0.140170	+	0.990127i	$0.544765\pi$
$308$	9.65078	0.549904
$309$	12.1055	0.688656
$310$	2.08434	0.118383
$311$	14.6387	0.830087	0.415043	−	0.909802i	$-0.363766\pi$
$311$	14.6387	0.830087	0.415043	+	0.909802i	$0.363766\pi$
$312$	−3.87454	−0.219353
$313$	−16.2271	−0.917211	−0.458606	−	0.888640i	$-0.651651\pi$
$313$	−16.2271	−0.917211	−0.458606	+	0.888640i	$0.651651\pi$
$314$	0.486837	0.0274738
$315$	4.00325	0.225557
$316$	16.6397	0.936055
$317$	−18.5174	−1.04004	−0.520019	−	0.854155i	$-0.674075\pi$
$317$	−18.5174	−1.04004	−0.520019	+	0.854155i	$0.674075\pi$
$318$	−3.22810	−0.181023
$319$	39.7077	2.22320
$320$	−2.41236	−0.134855
$321$	−4.88518	−0.272664
$322$	−0.770238	−0.0429237
$323$	7.21545	0.401479
$324$	−5.66014	−0.314452
$325$	−4.09956	−0.227403
$326$	−7.31133	−0.404937
$327$	−0.586744	−0.0324470
$328$	4.85248	0.267933
$329$	7.31074	0.403054
$330$	4.93046	0.271413
$331$	−29.6554	−1.63001	−0.815004	−	0.579455i	$-0.803265\pi$
$331$	−29.6554	−1.63001	−0.815004	+	0.579455i	$0.803265\pi$
$332$	1.99784	0.109646
$333$	−15.3496	−0.841151
$334$	−1.06722	−0.0583955
$335$	5.59673	0.305782
$336$	−1.74123	−0.0949921
$337$	−0.738933	−0.0402523	−0.0201261	−	0.999797i	$-0.506407\pi$
$337$	−0.738933	−0.0402523	−0.0201261	+	0.999797i	$0.506407\pi$
$338$	−4.42827	−0.240866
$339$	2.53829	0.137861
$340$	−3.92550	−0.212890
$341$	12.3080	0.666515
$342$	−7.23519	−0.391234
$343$	12.6057	0.680643
$344$	−8.63402	−0.465515
$345$	2.08268	0.112128
$346$	7.54171	0.405445
$347$	5.91866	0.317730	0.158865	−	0.987300i	$-0.449217\pi$
$347$	5.91866	0.317730	0.158865	+	0.987300i	$0.449217\pi$
$348$	−9.23988	−0.495310
$349$	24.2054	1.29569	0.647843	−	0.761774i	$-0.275671\pi$
$349$	24.2054	1.29569	0.647843	+	0.761774i	$0.275671\pi$
$350$	0.982729	0.0525291
$351$	−9.93502	−0.530292
$352$	32.0536	1.70846
$353$	3.94926	0.210198	0.105099	−	0.994462i	$-0.466484\pi$
$353$	3.94926	0.210198	0.105099	+	0.994462i	$0.466484\pi$
$354$	−2.53383	−0.134672
$355$	7.29112	0.386972
$356$	9.05625	0.479980
$357$	−1.03649	−0.0548568
$358$	−12.8577	−0.679550
$359$	2.95226	0.155814	0.0779072	−	0.996961i	$-0.475176\pi$
$359$	2.95226	0.155814	0.0779072	+	0.996961i	$0.475176\pi$
$360$	8.61620	0.454114
$361$	11.5232	0.606484
$362$	−6.92803	−0.364129
$363$	20.0630	1.05303
$364$	3.68018	0.192894
$365$	21.8269	1.14247
$366$	−4.00559	−0.209376
$367$	19.8504	1.03618	0.518092	−	0.855325i	$-0.326642\pi$
$367$	19.8504	1.03618	0.518092	+	0.855325i	$0.326642\pi$
$368$	3.10791	0.162011
$369$	5.42997	0.282673
$370$	6.65635	0.346047
$371$	6.71165	0.348451
$372$	−2.86404	−0.148493
$373$	0.348621	0.0180509	0.00902546	−	0.999959i	$-0.497127\pi$
$373$	0.348621	0.0180509	0.00902546	+	0.999959i	$0.497127\pi$
$374$	4.37968	0.226468
$375$	−10.0085	−0.516839
$376$	15.7349	0.811468
$377$	15.1419	0.779849
$378$	2.38158	0.122495
$379$	26.9713	1.38542	0.692712	−	0.721214i	$-0.256416\pi$
$379$	26.9713	1.38542	0.692712	+	0.721214i	$0.256416\pi$
$380$	−16.6059	−0.851863
$381$	−4.73851	−0.242761
$382$	10.0901	0.516254
$383$	19.8014	1.01181	0.505903	−	0.862590i	$-0.331159\pi$
$383$	19.8014	1.01181	0.505903	+	0.862590i	$0.331159\pi$
$384$	−9.49437	−0.484508
$385$	−10.2511	−0.522445
$386$	4.71474	0.239974
$387$	−9.66155	−0.491124
$388$	−5.86349	−0.297673
$389$	19.2163	0.974303	0.487152	−	0.873317i	$-0.338036\pi$
$389$	19.2163	0.974303	0.487152	+	0.873317i	$0.338036\pi$
$390$	1.88016	0.0952055
$391$	1.85002	0.0935594
$392$	12.6001	0.636401
$393$	3.37755	0.170375
$394$	4.92320	0.248027
$395$	−17.6747	−0.889313
$396$	23.2434	1.16803
$397$	−18.5683	−0.931915	−0.465957	−	0.884807i	$-0.654290\pi$
$397$	−18.5683	−0.931915	−0.465957	+	0.884807i	$0.654290\pi$
$398$	−12.4000	−0.621558
$399$	−4.38461	−0.219505
$400$	−3.96531	−0.198266
$401$	−15.5059	−0.774329	−0.387164	−	0.922011i	$-0.626545\pi$
$401$	−15.5059	−0.774329	−0.387164	+	0.922011i	$0.626545\pi$
$402$	1.45302	0.0724703
$403$	4.69346	0.233798
$404$	1.62335	0.0807649
$405$	6.01223	0.298750
$406$	−3.62976	−0.180142
$407$	39.3056	1.94831
$408$	−2.23084	−0.110443
$409$	−22.7977	−1.12727	−0.563636	−	0.826023i	$-0.690598\pi$
$409$	−22.7977	−1.12727	−0.563636	+	0.826023i	$0.690598\pi$
$410$	−2.35471	−0.116291
$411$	−15.8380	−0.781229
$412$	−24.7477	−1.21923
$413$	5.26818	0.259230
$414$	−1.85508	−0.0911721
$415$	−2.12211	−0.104170
$416$	12.2232	0.599289
$417$	−11.3393	−0.555287
$418$	18.5271	0.906192
$419$	22.0813	1.07874	0.539371	−	0.842068i	$-0.318662\pi$
$419$	22.0813	1.07874	0.539371	+	0.842068i	$0.318662\pi$
$420$	2.38541	0.116396
$421$	−31.2186	−1.52150	−0.760751	−	0.649043i	$-0.775169\pi$
$421$	−31.2186	−1.52150	−0.760751	+	0.649043i	$0.775169\pi$
$422$	−1.26162	−0.0614149
$423$	17.6075	0.856108
$424$	14.4455	0.701536
$425$	−2.36040	−0.114496
$426$	1.89292	0.0917124
$427$	8.32817	0.403028
$428$	9.98695	0.482737
$429$	11.1023	0.536023
$430$	4.18974	0.202047
$431$	−23.3351	−1.12401	−0.562007	−	0.827133i	$-0.689971\pi$
$431$	−23.3351	−1.12401	−0.562007	+	0.827133i	$0.689971\pi$
$432$	−9.60968	−0.462346
$433$	1.17144	0.0562959	0.0281479	−	0.999604i	$-0.491039\pi$
$433$	1.17144	0.0562959	0.0281479	+	0.999604i	$0.491039\pi$
$434$	−1.12510	−0.0540064
$435$	9.81464	0.470576
$436$	1.19950	0.0574457
$437$	7.82605	0.374371
$438$	5.66671	0.270766
$439$	10.7328	0.512247	0.256123	−	0.966644i	$-0.417555\pi$
$439$	10.7328	0.512247	0.256123	+	0.966644i	$0.417555\pi$
$440$	−22.0635	−1.05184
$441$	14.0996	0.671410
$442$	1.67012	0.0794396
$443$	−10.8312	−0.514604	−0.257302	−	0.966331i	$-0.582833\pi$
$443$	−10.8312	−0.514604	−0.257302	+	0.966331i	$0.582833\pi$
$444$	−9.14632	−0.434065
$445$	−9.61959	−0.456012
$446$	−9.59244	−0.454215
$447$	3.79175	0.179344
$448$	1.30216	0.0615211
$449$	32.4116	1.52960	0.764799	−	0.644269i	$-0.222838\pi$
$449$	32.4116	1.52960	0.764799	+	0.644269i	$0.222838\pi$
$450$	2.36685	0.111574
$451$	−13.9045	−0.654738
$452$	−5.18913	−0.244076
$453$	−1.88584	−0.0886044
$454$	−5.44190	−0.255401
$455$	−3.90910	−0.183262
$456$	−9.43701	−0.441929
$457$	13.7438	0.642906	0.321453	−	0.946925i	$-0.395829\pi$
$457$	13.7438	0.642906	0.321453	+	0.946925i	$0.395829\pi$
$458$	1.31413	0.0614053
$459$	−5.72027	−0.266999
$460$	−4.25769	−0.198516
$461$	14.7757	0.688171	0.344085	−	0.938938i	$-0.388189\pi$
$461$	14.7757	0.688171	0.344085	+	0.938938i	$0.388189\pi$
$462$	−2.66139	−0.123819
$463$	−8.16583	−0.379498	−0.189749	−	0.981833i	$-0.560767\pi$
$463$	−8.16583	−0.379498	−0.189749	+	0.981833i	$0.560767\pi$
$464$	14.6461	0.679928
$465$	3.04219	0.141078
$466$	3.16247	0.146498
$467$	29.7679	1.37750	0.688748	−	0.725001i	$-0.258161\pi$
$467$	29.7679	1.37750	0.688748	+	0.725001i	$0.258161\pi$
$468$	8.86352	0.409716
$469$	−3.02104	−0.139498
$470$	−7.63553	−0.352201
$471$	0.710561	0.0327409
$472$	11.3387	0.521907
$473$	24.7403	1.13756
$474$	−4.58872	−0.210767
$475$	−9.98507	−0.458146
$476$	2.11893	0.0971210
$477$	16.1647	0.740129
$478$	−12.7801	−0.584549
$479$	−6.77788	−0.309689	−0.154845	−	0.987939i	$-0.549488\pi$
$479$	−6.77788	−0.309689	−0.154845	+	0.987939i	$0.549488\pi$
$480$	7.92276	0.361623
$481$	14.9886	0.683421
$482$	15.1464	0.689898
$483$	−1.12420	−0.0511528
$484$	−41.0155	−1.86434
$485$	6.22822	0.282809
$486$	8.96867	0.406827
$487$	31.9530	1.44793	0.723964	−	0.689838i	$-0.242318\pi$
$487$	31.9530	1.44793	0.723964	+	0.689838i	$0.242318\pi$
$488$	17.9247	0.811415
$489$	−10.6712	−0.482570
$490$	−6.11431	−0.276216
$491$	−32.5786	−1.47025	−0.735125	−	0.677931i	$-0.762877\pi$
$491$	−32.5786	−1.47025	−0.735125	+	0.677931i	$0.762877\pi$
$492$	3.23555	0.145870
$493$	8.71824	0.392650
$494$	7.06504	0.317871
$495$	−24.6892	−1.10970
$496$	4.53977	0.203842
$497$	−3.93564	−0.176538
$498$	−0.550944	−0.0246884
$499$	−1.60801	−0.0719845	−0.0359923	−	0.999352i	$-0.511459\pi$
$499$	−1.60801	−0.0719845	−0.0359923	+	0.999352i	$0.511459\pi$
$500$	20.4608	0.915036
$501$	−1.55765	−0.0695908
$502$	2.97463	0.132764
$503$	−37.2126	−1.65923	−0.829615	−	0.558337i	$-0.811440\pi$
$503$	−37.2126	−1.65923	−0.829615	+	0.558337i	$0.811440\pi$
$504$	−4.65090	−0.207168
$505$	−1.72433	−0.0767318
$506$	4.75030	0.211176
$507$	−6.46327	−0.287044
$508$	9.68710	0.429796
$509$	23.0310	1.02083	0.510415	−	0.859928i	$-0.329492\pi$
$509$	23.0310	1.02083	0.510415	+	0.859928i	$0.329492\pi$
$510$	1.08253	0.0479355
$511$	−11.7819	−0.521199
$512$	20.9320	0.925071
$513$	−24.1982	−1.06838
$514$	−1.81002	−0.0798366
$515$	26.2871	1.15835
$516$	−5.75701	−0.253438
$517$	−45.0876	−1.98295
$518$	−3.59300	−0.157868
$519$	11.0075	0.483175
$520$	−8.41358	−0.368960
$521$	32.5635	1.42663	0.713317	−	0.700841i	$-0.247192\pi$
$521$	32.5635	1.42663	0.713317	+	0.700841i	$0.247192\pi$
$522$	−8.74209	−0.382631
$523$	6.32841	0.276722	0.138361	−	0.990382i	$-0.455817\pi$
$523$	6.32841	0.276722	0.138361	+	0.990382i	$0.455817\pi$
$524$	−6.90486	−0.301640
$525$	1.43434	0.0625997
$526$	8.26729	0.360471
$527$	2.70235	0.117716
$528$	10.7387	0.467343
$529$	−20.9934	−0.912758
$530$	−7.00982	−0.304487
$531$	12.6881	0.550618
$532$	8.96361	0.388622
$533$	−5.30227	−0.229667
$534$	−2.49744	−0.108075
$535$	−10.6082	−0.458632
$536$	−6.50219	−0.280852
$537$	−18.7664	−0.809830
$538$	5.87668	0.253362
$539$	−36.1049	−1.55515
$540$	13.1648	0.566523
$541$	−21.1262	−0.908285	−0.454142	−	0.890929i	$-0.650054\pi$
$541$	−21.1262	−0.908285	−0.454142	+	0.890929i	$0.650054\pi$
$542$	−6.63322	−0.284921
$543$	−10.1118	−0.433938
$544$	7.03770	0.301739
$545$	−1.27412	−0.0545771
$546$	−1.01488	−0.0434329
$547$	−44.5357	−1.90421	−0.952104	−	0.305773i	$-0.901085\pi$
$547$	−44.5357	−1.90421	−0.952104	+	0.305773i	$0.901085\pi$
$548$	32.3781	1.38312
$549$	20.0580	0.856053
$550$	−6.06079	−0.258433
$551$	36.8804	1.57116
$552$	−2.41962	−0.102986
$553$	9.54057	0.405706
$554$	13.4855	0.572942
$555$	9.71526	0.412390
$556$	23.1813	0.983107
$557$	−15.9218	−0.674627	−0.337313	−	0.941392i	$-0.609518\pi$
$557$	−15.9218	−0.674627	−0.337313	+	0.941392i	$0.609518\pi$
$558$	−2.70974	−0.114712
$559$	9.43434	0.399030
$560$	−3.78110	−0.159780
$561$	6.39234	0.269885
$562$	10.5553	0.445250
$563$	6.21090	0.261758	0.130879	−	0.991398i	$-0.458220\pi$
$563$	6.21090	0.261758	0.130879	+	0.991398i	$0.458220\pi$
$564$	10.4918	0.441783
$565$	5.51191	0.231888
$566$	−14.0976	−0.592566
$567$	−3.24531	−0.136290
$568$	−8.47070	−0.355423
$569$	37.8833	1.58815	0.794074	−	0.607820i	$-0.207956\pi$
$569$	37.8833	1.58815	0.794074	+	0.607820i	$0.207956\pi$
$570$	4.57940	0.191810
$571$	19.6363	0.821752	0.410876	−	0.911691i	$-0.365223\pi$
$571$	19.6363	0.821752	0.410876	+	0.911691i	$0.365223\pi$
$572$	−22.6968	−0.949001
$573$	14.7270	0.615227
$574$	1.27104	0.0530521
$575$	−2.56014	−0.106765
$576$	3.13618	0.130674
$577$	−18.9167	−0.787513	−0.393757	−	0.919215i	$-0.628825\pi$
$577$	−18.9167	−0.787513	−0.393757	+	0.919215i	$0.628825\pi$
$578$	−8.62242	−0.358645
$579$	6.88139	0.285981
$580$	−20.0644	−0.833130
$581$	1.14549	0.0475228
$582$	1.61697	0.0670256
$583$	−41.3928	−1.71431
$584$	−25.3581	−1.04933
$585$	−9.41487	−0.389257
$586$	8.13337	0.335986
$587$	−43.0668	−1.77756	−0.888779	−	0.458336i	$-0.848446\pi$
$587$	−43.0668	−1.77756	−0.888779	+	0.458336i	$0.848446\pi$
$588$	8.40151	0.346472
$589$	11.4316	0.471031
$590$	−5.50222	−0.226523
$591$	7.18565	0.295578
$592$	14.4978	0.595855
$593$	−32.7597	−1.34528	−0.672640	−	0.739970i	$-0.734840\pi$
$593$	−32.7597	−1.34528	−0.672640	+	0.739970i	$0.734840\pi$
$594$	−14.6879	−0.602654
$595$	−2.25074	−0.0922712
$596$	−7.75161	−0.317518
$597$	−18.0984	−0.740720
$598$	1.81145	0.0740758
$599$	−47.9098	−1.95754	−0.978772	−	0.204954i	$-0.934295\pi$
$599$	−47.9098	−1.95754	−0.978772	+	0.204954i	$0.934295\pi$
$600$	3.08713	0.126032
$601$	−29.4929	−1.20304	−0.601520	−	0.798858i	$-0.705438\pi$
$601$	−29.4929	−1.20304	−0.601520	+	0.798858i	$0.705438\pi$
$602$	−2.26156	−0.0921743
$603$	−7.27601	−0.296302
$604$	3.85529	0.156869
$605$	43.5668	1.77124
$606$	−0.447672	−0.0181854
$607$	10.0240	0.406861	0.203430	−	0.979089i	$-0.434791\pi$
$607$	10.0240	0.406861	0.203430	+	0.979089i	$0.434791\pi$
$608$	29.7713	1.20738
$609$	−5.29780	−0.214678
$610$	−8.69815	−0.352178
$611$	−17.1935	−0.695574
$612$	5.10333	0.206290
$613$	−3.46352	−0.139890	−0.0699450	−	0.997551i	$-0.522282\pi$
$613$	−3.46352	−0.139890	−0.0699450	+	0.997551i	$0.522282\pi$
$614$	−2.76920	−0.111756
$615$	−3.43681	−0.138586
$616$	11.9096	0.479850
$617$	33.9350	1.36617	0.683085	−	0.730339i	$-0.260638\pi$
$617$	33.9350	1.36617	0.683085	+	0.730339i	$0.260638\pi$
$618$	6.82465	0.274528
$619$	−37.1102	−1.49158	−0.745792	−	0.666179i	$-0.767929\pi$
$619$	−37.1102	−1.49158	−0.745792	+	0.666179i	$0.767929\pi$
$620$	−6.21927	−0.249772
$621$	−6.20433	−0.248971
$622$	8.25282	0.330908
$623$	5.19252	0.208034
$624$	4.09505	0.163933
$625$	−12.6970	−0.507878
$626$	−9.14830	−0.365640
$627$	27.0412	1.07992
$628$	−1.45263	−0.0579661
$629$	8.62996	0.344099
$630$	2.25689	0.0899168
$631$	−14.5875	−0.580720	−0.290360	−	0.956917i	$-0.593775\pi$
$631$	−14.5875	−0.580720	−0.290360	+	0.956917i	$0.593775\pi$
$632$	20.5342	0.816807
$633$	−1.84140	−0.0731890
$634$	−10.4395	−0.414604
$635$	−10.2897	−0.408334
$636$	9.63201	0.381934
$637$	−13.7680	−0.545510
$638$	22.3858	0.886264
$639$	−9.47879	−0.374975
$640$	−20.6171	−0.814961
$641$	−8.25882	−0.326204	−0.163102	−	0.986609i	$-0.552150\pi$
$641$	−8.25882	−0.326204	−0.163102	+	0.986609i	$0.552150\pi$
$642$	−2.75410	−0.108696
$643$	−14.4390	−0.569418	−0.284709	−	0.958614i	$-0.591897\pi$
$643$	−14.4390	−0.569418	−0.284709	+	0.958614i	$0.591897\pi$
$644$	2.29824	0.0905634
$645$	6.11512	0.240783
$646$	4.06783	0.160047
$647$	28.5178	1.12115	0.560576	−	0.828103i	$-0.310580\pi$
$647$	28.5178	1.12115	0.560576	+	0.828103i	$0.310580\pi$
$648$	−6.98490	−0.274393
$649$	−32.4905	−1.27536
$650$	−2.31119	−0.0906524
$651$	−1.64213	−0.0643602
$652$	21.8156	0.854364
$653$	−34.5336	−1.35140	−0.675701	−	0.737175i	$-0.736159\pi$
$653$	−34.5336	−1.35140	−0.675701	+	0.737175i	$0.736159\pi$
$654$	−0.330786	−0.0129348
$655$	7.33437	0.286577
$656$	−5.12864	−0.200240
$657$	−28.3760	−1.10705
$658$	4.12155	0.160675
$659$	−10.7848	−0.420118	−0.210059	−	0.977689i	$-0.567366\pi$
$659$	−10.7848	−0.420118	−0.210059	+	0.977689i	$0.567366\pi$
$660$	−14.7115	−0.572646
$661$	18.5717	0.722354	0.361177	−	0.932497i	$-0.382375\pi$
$661$	18.5717	0.722354	0.361177	+	0.932497i	$0.382375\pi$
$662$	−16.7187	−0.649791
$663$	2.43762	0.0946694
$664$	2.46544	0.0956775
$665$	−9.52119	−0.369216
$666$	−8.65356	−0.335319
$667$	9.45600	0.366138
$668$	3.18437	0.123207
$669$	−14.0006	−0.541295
$670$	3.15525	0.121898
$671$	−51.3624	−1.98282
$672$	−4.27659	−0.164973
$673$	12.0496	0.464476	0.232238	−	0.972659i	$-0.425395\pi$
$673$	12.0496	0.464476	0.232238	+	0.972659i	$0.425395\pi$
$674$	−0.416586	−0.0160463
$675$	7.91596	0.304686
$676$	13.2131	0.508196
$677$	−15.4952	−0.595529	−0.297765	−	0.954639i	$-0.596241\pi$
$677$	−15.4952	−0.595529	−0.297765	+	0.954639i	$0.596241\pi$
$678$	1.43100	0.0549574
$679$	−3.36190	−0.129018
$680$	−4.84427	−0.185769
$681$	−7.94271	−0.304365
$682$	6.93882	0.265701
$683$	−11.9438	−0.457018	−0.228509	−	0.973542i	$-0.573385\pi$
$683$	−11.9438	−0.457018	−0.228509	+	0.973542i	$0.573385\pi$
$684$	21.5884	0.825453
$685$	−34.3922	−1.31406
$686$	7.10665	0.271333
$687$	1.91804	0.0731776
$688$	9.12540	0.347903
$689$	−15.7845	−0.601342
$690$	1.17414	0.0446988
$691$	0.886939	0.0337407	0.0168704	−	0.999858i	$-0.494630\pi$
$691$	0.886939	0.0337407	0.0168704	+	0.999858i	$0.494630\pi$
$692$	−22.5030	−0.855436
$693$	13.3269	0.506247
$694$	3.33674	0.126661
$695$	−24.6233	−0.934015
$696$	−11.4025	−0.432210
$697$	−3.05288	−0.115636
$698$	13.6462	0.516516
$699$	4.61577	0.174584
$700$	−2.93227	−0.110829
$701$	15.4593	0.583890	0.291945	−	0.956435i	$-0.405698\pi$
$701$	15.4593	0.583890	0.291945	+	0.956435i	$0.405698\pi$
$702$	−5.60102	−0.211397
$703$	36.5069	1.37688
$704$	−8.03080	−0.302672
$705$	−11.1444	−0.419723
$706$	2.22646	0.0837940
$707$	0.930771	0.0350052
$708$	7.56046	0.284139
$709$	−38.3069	−1.43864	−0.719322	−	0.694676i	$-0.755548\pi$
$709$	−38.3069	−1.43864	−0.719322	+	0.694676i	$0.755548\pi$
$710$	4.11049	0.154264
$711$	22.9780	0.861741
$712$	11.1759	0.418834
$713$	2.93103	0.109768
$714$	−0.584337	−0.0218683
$715$	24.1086	0.901612
$716$	38.3648	1.43376
$717$	−18.6532	−0.696616
$718$	1.66439	0.0621143
$719$	−13.4500	−0.501600	−0.250800	−	0.968039i	$-0.580694\pi$
$719$	−13.4500	−0.501600	−0.250800	+	0.968039i	$0.580694\pi$
$720$	−9.10657	−0.339382
$721$	−14.1894	−0.528440
$722$	6.49639	0.241770
$723$	22.1068	0.822161
$724$	20.6719	0.768265
$725$	−12.0647	−0.448071
$726$	11.3108	0.419784
$727$	−21.5259	−0.798352	−0.399176	−	0.916874i	$-0.630704\pi$
$727$	−21.5259	−0.798352	−0.399176	+	0.916874i	$0.630704\pi$
$728$	4.54153	0.168320
$729$	2.99583	0.110957
$730$	12.3053	0.455439
$731$	5.43199	0.200910
$732$	11.9519	0.441755
$733$	44.2760	1.63537	0.817685	−	0.575665i	$-0.195257\pi$
$733$	44.2760	1.63537	0.817685	+	0.575665i	$0.195257\pi$
$734$	11.1910	0.413067
$735$	−8.92412	−0.329171
$736$	7.63325	0.281365
$737$	18.6317	0.686306
$738$	3.06123	0.112685
$739$	−2.70594	−0.0995396	−0.0497698	−	0.998761i	$-0.515849\pi$
$739$	−2.70594	−0.0995396	−0.0497698	+	0.998761i	$0.515849\pi$
$740$	−19.8613	−0.730115
$741$	10.3118	0.378812
$742$	3.78380	0.138908
$743$	16.0120	0.587423	0.293711	−	0.955894i	$-0.405110\pi$
$743$	16.0120	0.587423	0.293711	+	0.955894i	$0.405110\pi$
$744$	−3.53437	−0.129576
$745$	8.23380	0.301663
$746$	0.196541	0.00719587
$747$	2.75884	0.100941
$748$	−13.0681	−0.477817
$749$	5.72614	0.209229
$750$	−5.64248	−0.206034
$751$	−10.8480	−0.395850	−0.197925	−	0.980217i	$-0.563420\pi$
$751$	−10.8480	−0.395850	−0.197925	+	0.980217i	$0.563420\pi$
$752$	−16.6305	−0.606450
$753$	4.34161	0.158217
$754$	8.53650	0.310881
$755$	−4.09510	−0.149036
$756$	−7.10617	−0.258449
$757$	41.0794	1.49306	0.746529	−	0.665353i	$-0.231719\pi$
$757$	41.0794	1.49306	0.746529	+	0.665353i	$0.231719\pi$
$758$	15.2055	0.552289
$759$	6.93328	0.251662
$760$	−20.4925	−0.743341
$761$	17.9713	0.651460	0.325730	−	0.945463i	$-0.394390\pi$
$761$	17.9713	0.651460	0.325730	+	0.945463i	$0.394390\pi$
$762$	−2.67141	−0.0967750
$763$	0.687750	0.0248982
$764$	−30.1069	−1.08923
$765$	−5.42078	−0.195989
$766$	11.1634	0.403349
$767$	−12.3898	−0.447368
$768$	−3.13077	−0.112972
$769$	3.58238	0.129184	0.0645919	−	0.997912i	$-0.479425\pi$
$769$	3.58238	0.129184	0.0645919	+	0.997912i	$0.479425\pi$
$770$	−5.77922	−0.208269
$771$	−2.64181	−0.0951425
$772$	−14.0679	−0.506314
$773$	−35.3158	−1.27022	−0.635111	−	0.772421i	$-0.719046\pi$
$773$	−35.3158	−1.27022	−0.635111	+	0.772421i	$0.719046\pi$
$774$	−5.44685	−0.195783
$775$	−3.73963	−0.134331
$776$	−7.23584	−0.259752
$777$	−5.24416	−0.188133
$778$	10.8335	0.388399
$779$	−12.9145	−0.462708
$780$	−5.61002	−0.200871
$781$	24.2723	0.868532
$782$	1.04298	0.0372968
$783$	−29.2380	−1.04488
$784$	−13.3172	−0.475614
$785$	1.54299	0.0550715
$786$	1.90415	0.0679188
$787$	1.00000	0.0356462
$787$	1.00000	0.0356462
$788$	−14.6899	−0.523305
$789$	12.0665	0.429579
$790$	−9.96442	−0.354518
$791$	−2.97525	−0.105788
$792$	28.6836	1.01923
$793$	−19.5863	−0.695528
$794$	−10.4682	−0.371501
$795$	−10.2312	−0.362862
$796$	36.9993	1.31140
$797$	26.1947	0.927864	0.463932	−	0.885871i	$-0.346438\pi$
$797$	26.1947	0.927864	0.463932	+	0.885871i	$0.346438\pi$
$798$	−2.47189	−0.0875041
$799$	−9.89946	−0.350218
$800$	−9.73909	−0.344329
$801$	12.5059	0.441875
$802$	−8.74171	−0.308681
$803$	72.6624	2.56420
$804$	−4.33554	−0.152903
$805$	−2.44120	−0.0860410
$806$	2.64601	0.0932019
$807$	8.57730	0.301935
$808$	2.00330	0.0704759
$809$	44.3757	1.56017	0.780083	−	0.625676i	$-0.215177\pi$
$809$	44.3757	1.56017	0.780083	+	0.625676i	$0.215177\pi$
$810$	3.38949	0.119095
$811$	−40.6451	−1.42724	−0.713621	−	0.700532i	$-0.752946\pi$
$811$	−40.6451	−1.42724	−0.713621	+	0.700532i	$0.752946\pi$
$812$	10.8305	0.380076
$813$	−9.68150	−0.339545
$814$	22.1592	0.776678
$815$	−23.1726	−0.811701
$816$	2.35780	0.0825395
$817$	22.9787	0.803923
$818$	−12.8526	−0.449379
$819$	5.08201	0.177580
$820$	7.02600	0.245358
$821$	−17.8408	−0.622650	−0.311325	−	0.950304i	$-0.600773\pi$
$821$	−17.8408	−0.622650	−0.311325	+	0.950304i	$0.600773\pi$
$822$	−8.92890	−0.311431
$823$	21.7170	0.757006	0.378503	−	0.925600i	$-0.376439\pi$
$823$	21.7170	0.757006	0.378503	+	0.925600i	$0.376439\pi$
$824$	−30.5399	−1.06391
$825$	−8.84601	−0.307979
$826$	2.97002	0.103340
$827$	34.3025	1.19282	0.596408	−	0.802681i	$-0.296594\pi$
$827$	34.3025	1.19282	0.596408	+	0.802681i	$0.296594\pi$
$828$	5.53519	0.192361
$829$	50.9762	1.77048	0.885238	−	0.465137i	$-0.153995\pi$
$829$	50.9762	1.77048	0.885238	+	0.465137i	$0.153995\pi$
$830$	−1.19638	−0.0415268
$831$	19.6827	0.682784
$832$	−3.06242	−0.106170
$833$	−7.92720	−0.274661
$834$	−6.39271	−0.221361
$835$	−3.38245	−0.117055
$836$	−55.2814	−1.91195
$837$	−9.06275	−0.313255
$838$	12.4487	0.430033
$839$	−3.88375	−0.134082	−0.0670409	−	0.997750i	$-0.521356\pi$
$839$	−3.88375	−0.134082	−0.0670409	+	0.997750i	$0.521356\pi$
$840$	2.94371	0.101568
$841$	15.5615	0.536605
$842$	−17.6000	−0.606536
$843$	15.4060	0.530611
$844$	3.76444	0.129577
$845$	−14.0350	−0.482819
$846$	9.92653	0.341281
$847$	−23.5168	−0.808045
$848$	−15.2676	−0.524293
$849$	−20.5761	−0.706170
$850$	−1.33071	−0.0456430
$851$	9.36025	0.320865
$852$	−5.64811	−0.193501
$853$	−48.3238	−1.65458	−0.827288	−	0.561778i	$-0.810118\pi$
$853$	−48.3238	−1.65458	−0.827288	+	0.561778i	$0.810118\pi$
$854$	4.69514	0.160664
$855$	−22.9313	−0.784233
$856$	12.3244	0.421240
$857$	50.1708	1.71380	0.856901	−	0.515481i	$-0.172387\pi$
$857$	50.1708	1.71380	0.856901	+	0.515481i	$0.172387\pi$
$858$	6.25909	0.213682
$859$	−50.9676	−1.73899	−0.869496	−	0.493940i	$-0.835556\pi$
$859$	−50.9676	−1.73899	−0.869496	+	0.493940i	$0.835556\pi$
$860$	−12.5014	−0.426293
$861$	1.85514	0.0632230
$862$	−13.1556	−0.448080
$863$	−31.5730	−1.07476	−0.537379	−	0.843341i	$-0.680586\pi$
$863$	−31.5730	−1.07476	−0.537379	+	0.843341i	$0.680586\pi$
$864$	−23.6021	−0.802958
$865$	23.9028	0.812719
$866$	0.660419	0.0224419
$867$	−12.5848	−0.427403
$868$	3.35707	0.113946
$869$	−58.8396	−1.99600
$870$	5.53316	0.187592
$871$	7.10490	0.240740
$872$	1.48025	0.0501275
$873$	−8.09697	−0.274041
$874$	4.41206	0.149240
$875$	11.7315	0.396596
$876$	−16.9084	−0.571280
$877$	−32.4538	−1.09589	−0.547944	−	0.836515i	$-0.684589\pi$
$877$	−32.4538	−1.09589	−0.547944	+	0.836515i	$0.684589\pi$
$878$	6.05077	0.204204
$879$	11.8710	0.400400
$880$	23.3192	0.786089
$881$	−33.7444	−1.13688	−0.568439	−	0.822726i	$-0.692452\pi$
$881$	−33.7444	−1.13688	−0.568439	+	0.822726i	$0.692452\pi$
$882$	7.94888	0.267653
$883$	25.4446	0.856278	0.428139	−	0.903713i	$-0.359169\pi$
$883$	25.4446	0.856278	0.428139	+	0.903713i	$0.359169\pi$
$884$	−4.98332	−0.167607
$885$	−8.03075	−0.269951
$886$	−6.10624	−0.205143
$887$	−46.3958	−1.55782	−0.778910	−	0.627136i	$-0.784227\pi$
$887$	−46.3958	−1.55782	−0.778910	+	0.627136i	$0.784227\pi$
$888$	−11.2870	−0.378768
$889$	5.55422	0.186283
$890$	−5.42320	−0.181786
$891$	20.0148	0.670523
$892$	28.6220	0.958334
$893$	−41.8772	−1.40137
$894$	2.13766	0.0714940
$895$	−40.7513	−1.36217
$896$	11.1288	0.371787
$897$	2.64390	0.0882773
$898$	18.2726	0.609763
$899$	13.8125	0.460673
$900$	−7.06222	−0.235407
$901$	−9.08823	−0.302773
$902$	−7.83889	−0.261006
$903$	−3.30085	−0.109846
$904$	−6.40365	−0.212982
$905$	−21.9578	−0.729901
$906$	−1.06317	−0.0353215
$907$	48.6415	1.61511	0.807557	−	0.589789i	$-0.200789\pi$
$907$	48.6415	1.61511	0.807557	+	0.589789i	$0.200789\pi$
$908$	16.2376	0.538862
$909$	2.24171	0.0743529
$910$	−2.20382	−0.0730559
$911$	16.4768	0.545901	0.272950	−	0.962028i	$-0.412001\pi$
$911$	16.4768	0.545901	0.272950	+	0.962028i	$0.412001\pi$
$912$	9.97409	0.330275
$913$	−7.06457	−0.233803
$914$	7.74827	0.256290
$915$	−12.6954	−0.419696
$916$	−3.92111	−0.129557
$917$	−3.95899	−0.130737
$918$	−3.22489	−0.106437
$919$	−27.4858	−0.906672	−0.453336	−	0.891340i	$-0.649766\pi$
$919$	−27.4858	−0.906672	−0.453336	+	0.891340i	$0.649766\pi$
$920$	−5.25421	−0.173226
$921$	−4.04177	−0.133181
$922$	8.33001	0.274334
$923$	9.25588	0.304661
$924$	7.94108	0.261242
$925$	−11.9425	−0.392668
$926$	−4.60362	−0.151284
$927$	−34.1744	−1.12243
$928$	35.9718	1.18083
$929$	−36.6595	−1.20276	−0.601380	−	0.798963i	$-0.705382\pi$
$929$	−36.6595	−1.20276	−0.601380	+	0.798963i	$0.705382\pi$
$930$	1.71509	0.0562399
$931$	−33.5341	−1.09903
$932$	−9.43619	−0.309093
$933$	12.0454	0.394348
$934$	16.7822	0.549129
$935$	13.8810	0.453957
$936$	10.9380	0.357521
$937$	−17.5825	−0.574395	−0.287197	−	0.957871i	$-0.592724\pi$
$937$	−17.5825	−0.574395	−0.287197	+	0.957871i	$0.592724\pi$
$938$	−1.70316	−0.0556101
$939$	−13.3524	−0.435738
$940$	22.7829	0.743097
$941$	−7.96809	−0.259752	−0.129876	−	0.991530i	$-0.541458\pi$
$941$	−7.96809	−0.259752	−0.129876	+	0.991530i	$0.541458\pi$
$942$	0.400590	0.0130519
$943$	−3.31122	−0.107828
$944$	−11.9840	−0.390047
$945$	7.54821	0.245543
$946$	13.9477	0.453480
$947$	−42.1432	−1.36947	−0.684735	−	0.728792i	$-0.740082\pi$
$947$	−42.1432	−1.36947	−0.684735	+	0.728792i	$0.740082\pi$
$948$	13.6918	0.444690
$949$	27.7087	0.899462
$950$	−5.62924	−0.182637
$951$	−15.2369	−0.494089
$952$	2.61487	0.0847484
$953$	55.8926	1.81054	0.905270	−	0.424837i	$-0.139669\pi$
$953$	55.8926	1.81054	0.905270	+	0.424837i	$0.139669\pi$
$954$	9.11308	0.295047
$955$	31.9796	1.03484
$956$	38.1334	1.23332
$957$	32.6732	1.05617
$958$	−3.82114	−0.123455
$959$	18.5644	0.599476
$960$	−1.98499	−0.0640653
$961$	−26.7186	−0.861891
$962$	8.45006	0.272441
$963$	13.7911	0.444413
$964$	−45.1938	−1.45559
$965$	14.9430	0.481031
$966$	−0.633785	−0.0203917
$967$	57.5939	1.85210	0.926048	−	0.377407i	$-0.123184\pi$
$967$	57.5939	1.85210	0.926048	+	0.377407i	$0.123184\pi$
$968$	−50.6152	−1.62683
$969$	5.93719	0.190730
$970$	3.51126	0.112740
$971$	−10.4849	−0.336476	−0.168238	−	0.985746i	$-0.553808\pi$
$971$	−10.4849	−0.336476	−0.168238	+	0.985746i	$0.553808\pi$
$972$	−26.7608	−0.858352
$973$	13.2913	0.426100
$974$	18.0140	0.577206
$975$	−3.37329	−0.108032
$976$	−18.9449	−0.606411
$977$	21.8527	0.699129	0.349564	−	0.936912i	$-0.386330\pi$
$977$	21.8527	0.699129	0.349564	+	0.936912i	$0.386330\pi$
$978$	−6.01608	−0.192373
$979$	−32.0239	−1.02349
$980$	18.2439	0.582780
$981$	1.65641	0.0528851
$982$	−18.3667	−0.586105
$983$	28.9940	0.924764	0.462382	−	0.886681i	$-0.346995\pi$
$983$	28.9940	0.924764	0.462382	+	0.886681i	$0.346995\pi$
$984$	3.99283	0.127287
$985$	15.6037	0.497174
$986$	4.91505	0.156527
$987$	6.01559	0.191478
$988$	−21.0807	−0.670667
$989$	5.89166	0.187344
$990$	−13.9190	−0.442374
$991$	−24.7102	−0.784946	−0.392473	−	0.919764i	$-0.628380\pi$
$991$	−24.7102	−0.784946	−0.392473	+	0.919764i	$0.628380\pi$
$992$	11.1500	0.354013
$993$	−24.4017	−0.774366
$994$	−2.21878	−0.0703755
$995$	−39.3008	−1.24592
$996$	1.64391	0.0520892
$997$	−26.9722	−0.854219	−0.427110	−	0.904200i	$-0.640468\pi$
$997$	−26.9722	−0.854219	−0.427110	+	0.904200i	$0.640468\pi$
$998$	−0.906543	−0.0286961
$999$	−28.9420	−0.915683

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	787.2.a.b.1.20	✓	37
3.2	odd	2		7083.2.a.g.1.18		37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
787.2.a.b.1.20	✓	37	1.1	even	1	trivial
7083.2.a.g.1.18		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)

\(f(q)\)	\(=\)	\(q+0.563766 q^{2} +0.822843 q^{3} -1.68217 q^{4} +1.78681 q^{5} +0.463891 q^{6} -0.964492 q^{7} -2.07588 q^{8} -2.32293 q^{9} +1.00734 q^{10} +5.94832 q^{11} -1.38416 q^{12} +2.26830 q^{13} -0.543748 q^{14} +1.47026 q^{15} +2.19402 q^{16} +1.30602 q^{17} -1.30959 q^{18} +5.52478 q^{19} -3.00571 q^{20} -0.793626 q^{21} +3.35346 q^{22} +1.41654 q^{23} -1.70812 q^{24} -1.80732 q^{25} +1.27879 q^{26} -4.37994 q^{27} +1.62244 q^{28} +6.67544 q^{29} +0.828883 q^{30} +2.06915 q^{31} +5.38868 q^{32} +4.89453 q^{33} +0.736288 q^{34} -1.72336 q^{35} +3.90756 q^{36} +6.60785 q^{37} +3.11468 q^{38} +1.86646 q^{39} -3.70920 q^{40} -2.33755 q^{41} -0.447419 q^{42} +4.15921 q^{43} -10.0061 q^{44} -4.15062 q^{45} +0.798594 q^{46} -7.57989 q^{47} +1.80534 q^{48} -6.06975 q^{49} -1.01891 q^{50} +1.07465 q^{51} -3.81567 q^{52} -6.95874 q^{53} -2.46926 q^{54} +10.6285 q^{55} +2.00217 q^{56} +4.54603 q^{57} +3.76339 q^{58} -5.46213 q^{59} -2.47323 q^{60} -8.63477 q^{61} +1.16652 q^{62} +2.24045 q^{63} -1.35010 q^{64} +4.05302 q^{65} +2.75937 q^{66} +3.13225 q^{67} -2.19694 q^{68} +1.16559 q^{69} -0.971572 q^{70} +4.08053 q^{71} +4.82213 q^{72} +12.2156 q^{73} +3.72528 q^{74} -1.48714 q^{75} -9.29361 q^{76} -5.73711 q^{77} +1.05224 q^{78} -9.89181 q^{79} +3.92030 q^{80} +3.36479 q^{81} -1.31783 q^{82} -1.18766 q^{83} +1.33501 q^{84} +2.33360 q^{85} +2.34482 q^{86} +5.49284 q^{87} -12.3480 q^{88} -5.38368 q^{89} -2.33998 q^{90} -2.18776 q^{91} -2.38285 q^{92} +1.70259 q^{93} -4.27328 q^{94} +9.87171 q^{95} +4.43404 q^{96} +3.48567 q^{97} -3.42192 q^{98} -13.8175 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 12 q^{2} + 6 q^{3} + 42 q^{4} + 31 q^{5} + 4 q^{6} + 9 q^{7} + 36 q^{8} + 47 q^{9} + 4 q^{10} + 18 q^{11} + 15 q^{12} + 13 q^{13} + 8 q^{14} + 3 q^{15} + 48 q^{16} + 18 q^{17} + 17 q^{18} + 40 q^{20}+ \cdots - 35 q^{99}+O(q^{100}) \) 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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