LMFDB - Embedded newform 841.4.a.i.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [841,4,Mod(1,841)] 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("841.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(841, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	841.a (trivial)

Newform invariants

comment:select newform

sage:traces = [21,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$49.6206063148$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	no (minimal twist has level 29)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	841.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.43388 q^{2} +9.14452 q^{3} +3.79157 q^{4} -5.89225 q^{5} -31.4012 q^{6} +28.3262 q^{7} +14.4513 q^{8} +56.6222 q^{9} +20.2333 q^{10} +19.6828 q^{11} +34.6720 q^{12} +9.96495 q^{13} -97.2688 q^{14} -53.8817 q^{15} -79.9566 q^{16} +55.5715 q^{17} -194.434 q^{18} +137.548 q^{19} -22.3408 q^{20} +259.029 q^{21} -67.5886 q^{22} +115.734 q^{23} +132.150 q^{24} -90.2814 q^{25} -34.2185 q^{26} +270.881 q^{27} +107.401 q^{28} +185.024 q^{30} -176.138 q^{31} +158.951 q^{32} +179.990 q^{33} -190.826 q^{34} -166.905 q^{35} +214.687 q^{36} +11.5698 q^{37} -472.323 q^{38} +91.1247 q^{39} -85.1505 q^{40} -326.005 q^{41} -889.476 q^{42} +132.620 q^{43} +74.6287 q^{44} -333.632 q^{45} -397.418 q^{46} -147.429 q^{47} -731.164 q^{48} +459.372 q^{49} +310.016 q^{50} +508.174 q^{51} +37.7828 q^{52} +206.394 q^{53} -930.173 q^{54} -115.976 q^{55} +409.350 q^{56} +1257.81 q^{57} +58.8115 q^{59} -204.296 q^{60} -355.632 q^{61} +604.839 q^{62} +1603.89 q^{63} +93.8318 q^{64} -58.7159 q^{65} -618.065 q^{66} -422.136 q^{67} +210.703 q^{68} +1058.33 q^{69} +573.132 q^{70} +308.924 q^{71} +818.263 q^{72} -1039.68 q^{73} -39.7294 q^{74} -825.580 q^{75} +521.521 q^{76} +557.539 q^{77} -312.912 q^{78} -372.510 q^{79} +471.124 q^{80} +948.273 q^{81} +1119.46 q^{82} +592.453 q^{83} +982.126 q^{84} -327.441 q^{85} -455.402 q^{86} +284.442 q^{88} +741.411 q^{89} +1145.65 q^{90} +282.269 q^{91} +438.814 q^{92} -1610.70 q^{93} +506.254 q^{94} -810.464 q^{95} +1453.53 q^{96} -850.276 q^{97} -1577.43 q^{98} +1114.48 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 6 q^{2} - q^{3} + 90 q^{4} + 35 q^{5} + 26 q^{6} + 37 q^{7} + 51 q^{8} + 188 q^{9} + 37 q^{10} - 7 q^{11} - 68 q^{12} + 97 q^{13} - 68 q^{14} - 330 q^{15} + 310 q^{16} + 70 q^{17} + 305 q^{18} - 73 q^{19}+ \cdots + 8702 q^{99}+O(q^{100}) $ 21 * q + 6 * q^2 - q^3 + 90 * q^4 + 35 * q^5 + 26 * q^6 + 37 * q^7 + 51 * q^8 + 188 * q^9 + 37 * q^10 - 7 * q^11 - 68 * q^12 + 97 * q^13 - 68 * q^14 - 330 * q^15 + 310 * q^16 + 70 * q^17 + 305 * q^18 - 73 * q^19 + 408 * q^20 + 169 * q^21 + 705 * q^22 + 375 * q^23 + 641 * q^24 + 402 * q^25 + 1144 * q^26 + 14 * q^27 + 178 * q^28 + 1087 * q^30 - 693 * q^31 + 449 * q^32 + 820 * q^33 + 53 * q^34 + 886 * q^35 + 1464 * q^36 - 243 * q^37 + 914 * q^38 + 244 * q^39 + 275 * q^40 - 552 * q^41 - 373 * q^42 + 1151 * q^43 - 1502 * q^44 + 1139 * q^45 + 2992 * q^46 - 403 * q^47 - 3329 * q^48 + 1078 * q^49 + 1317 * q^50 + 2272 * q^51 - 1267 * q^52 + 1505 * q^53 + 140 * q^54 + 588 * q^55 - 2549 * q^56 + 859 * q^57 + 3086 * q^59 - 4371 * q^60 - 39 * q^61 + 1356 * q^62 + 1527 * q^63 - 1993 * q^64 + 1132 * q^65 - 980 * q^66 + 413 * q^67 - 919 * q^68 + 6116 * q^69 + 6779 * q^70 + 4015 * q^71 + 5524 * q^72 - 2667 * q^73 + 3844 * q^74 + 3734 * q^75 + 438 * q^76 - 5252 * q^77 - 4128 * q^78 + 1441 * q^79 + 6887 * q^80 - 371 * q^81 + 3401 * q^82 + 2505 * q^83 - 140 * q^84 - 3340 * q^85 + 3412 * q^86 + 8149 * q^88 - 2757 * q^89 - 1740 * q^90 + 4824 * q^91 + 3957 * q^92 - 4278 * q^93 + 1507 * q^94 - 2496 * q^95 + 3663 * q^96 - 1223 * q^97 + 10921 * q^98 + 8702 * 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 $

$2$	−3.43388	−1.21406	−0.607031	−	0.794678i	$-0.707640\pi$
$2$	−3.43388	−1.21406	−0.607031	+	0.794678i	$0.707640\pi$
$3$	9.14452	1.75986	0.879932	−	0.475101i	$-0.157588\pi$
$3$	9.14452	1.75986	0.879932	+	0.475101i	$0.157588\pi$
$4$	3.79157	0.473946
$5$	−5.89225	−0.527018	−0.263509	−	0.964657i	$-0.584880\pi$
$5$	−5.89225	−0.527018	−0.263509	+	0.964657i	$0.584880\pi$
$6$	−31.4012	−2.13658
$7$	28.3262	1.52947	0.764735	−	0.644345i	$-0.222870\pi$
$7$	28.3262	1.52947	0.764735	+	0.644345i	$0.222870\pi$
$8$	14.4513	0.638662
$9$	56.6222	2.09712
$10$	20.2333	0.639833
$11$	19.6828	0.539509	0.269754	−	0.962929i	$-0.413057\pi$
$11$	19.6828	0.539509	0.269754	+	0.962929i	$0.413057\pi$
$12$	34.6720	0.834079
$13$	9.96495	0.212599	0.106299	−	0.994334i	$-0.466100\pi$
$13$	9.96495	0.212599	0.106299	+	0.994334i	$0.466100\pi$
$14$	−97.2688	−1.85687
$15$	−53.8817	−0.927480
$16$	−79.9566	−1.24932
$17$	55.5715	0.792827	0.396413	−	0.918072i	$-0.370255\pi$
$17$	55.5715	0.792827	0.396413	+	0.918072i	$0.370255\pi$
$18$	−194.434	−2.54603
$19$	137.548	1.66082	0.830410	−	0.557152i	$-0.188106\pi$
$19$	137.548	1.66082	0.830410	+	0.557152i	$0.188106\pi$
$20$	−22.3408	−0.249778
$21$	259.029	2.69166
$22$	−67.5886	−0.654997
$23$	115.734	1.04923	0.524614	−	0.851340i	$-0.324210\pi$
$23$	115.734	1.04923	0.524614	+	0.851340i	$0.324210\pi$
$24$	132.150	1.12396
$25$	−90.2814	−0.722252
$26$	−34.2185	−0.258108
$27$	270.881	1.93078
$28$	107.401	0.724886
$29$	0	0
$29$	0	0
$30$	185.024	1.12602
$31$	−176.138	−1.02050	−0.510248	−	0.860027i	$-0.670447\pi$
$31$	−176.138	−1.02050	−0.510248	+	0.860027i	$0.670447\pi$
$32$	158.951	0.878090
$33$	179.990	0.949461
$34$	−190.826	−0.962541
$35$	−166.905	−0.806059
$36$	214.687	0.993920
$37$	11.5698	0.0514071	0.0257036	−	0.999670i	$-0.491817\pi$
$37$	11.5698	0.0514071	0.0257036	+	0.999670i	$0.491817\pi$
$38$	−472.323	−2.01634
$39$	91.1247	0.374144
$40$	−85.1505	−0.336587
$41$	−326.005	−1.24179	−0.620895	−	0.783893i	$-0.713231\pi$
$41$	−326.005	−1.24179	−0.620895	+	0.783893i	$0.713231\pi$
$42$	−889.476	−3.26784
$43$	132.620	0.470334	0.235167	−	0.971955i	$-0.424436\pi$
$43$	132.620	0.470334	0.235167	+	0.971955i	$0.424436\pi$
$44$	74.6287	0.255698
$45$	−333.632	−1.10522
$46$	−397.418	−1.27383
$47$	−147.429	−0.457548	−0.228774	−	0.973480i	$-0.573472\pi$
$47$	−147.429	−0.457548	−0.228774	+	0.973480i	$0.573472\pi$
$48$	−731.164	−2.19863
$49$	459.372	1.33928
$50$	310.016	0.876858
$51$	508.174	1.39527
$52$	37.7828	0.100760
$53$	206.394	0.534913	0.267456	−	0.963570i	$-0.413817\pi$
$53$	206.394	0.534913	0.267456	+	0.963570i	$0.413817\pi$
$54$	−930.173	−2.34408
$55$	−115.976	−0.284331
$56$	409.350	0.976815
$57$	1257.81	2.92282
$58$	0	0
$59$	58.8115	0.129773	0.0648865	−	0.997893i	$-0.479331\pi$
$59$	58.8115	0.129773	0.0648865	+	0.997893i	$0.479331\pi$
$60$	−204.296	−0.439575
$61$	−355.632	−0.746459	−0.373229	−	0.927739i	$-0.621750\pi$
$61$	−355.632	−0.746459	−0.373229	+	0.927739i	$0.621750\pi$
$62$	604.839	1.23895
$63$	1603.89	3.20748
$64$	93.8318	0.183265
$65$	−58.7159	−0.112043
$66$	−618.065	−1.15270
$67$	−422.136	−0.769733	−0.384866	−	0.922972i	$-0.625752\pi$
$67$	−422.136	−0.769733	−0.384866	+	0.922972i	$0.625752\pi$
$68$	210.703	0.375757
$69$	1058.33	1.84650
$70$	573.132	0.978605
$71$	308.924	0.516374	0.258187	−	0.966095i	$-0.416875\pi$
$71$	308.924	0.516374	0.258187	+	0.966095i	$0.416875\pi$
$72$	818.263	1.33935
$73$	−1039.68	−1.66692	−0.833461	−	0.552578i	$-0.813644\pi$
$73$	−1039.68	−1.66692	−0.833461	+	0.552578i	$0.813644\pi$
$74$	−39.7294	−0.0624114
$75$	−825.580	−1.27106
$76$	521.521	0.787139
$77$	557.539	0.825162
$78$	−312.912	−0.454234
$79$	−372.510	−0.530514	−0.265257	−	0.964178i	$-0.585457\pi$
$79$	−372.510	−0.530514	−0.265257	+	0.964178i	$0.585457\pi$
$80$	471.124	0.658415
$81$	948.273	1.30079
$82$	1119.46	1.50761
$83$	592.453	0.783497	0.391748	−	0.920072i	$-0.371870\pi$
$83$	592.453	0.783497	0.391748	+	0.920072i	$0.371870\pi$
$84$	982.126	1.27570
$85$	−327.441	−0.417834
$86$	−455.402	−0.571014
$87$	0	0
$88$	284.442	0.344564
$89$	741.411	0.883028	0.441514	−	0.897254i	$-0.354442\pi$
$89$	741.411	0.883028	0.441514	+	0.897254i	$0.354442\pi$
$90$	1145.65	1.34181
$91$	282.269	0.325163
$92$	438.814	0.497277
$93$	−1610.70	−1.79593
$94$	506.254	0.555491
$95$	−810.464	−0.875283
$96$	1453.53	1.54532
$97$	−850.276	−0.890026	−0.445013	−	0.895524i	$-0.646801\pi$
$97$	−850.276	−0.890026	−0.445013	+	0.895524i	$0.646801\pi$
$98$	−1577.43	−1.62597
$99$	1114.48	1.13141
$100$	−342.308	−0.342308
$101$	−1214.94	−1.19694	−0.598470	−	0.801145i	$-0.704225\pi$
$101$	−1214.94	−1.19694	−0.598470	+	0.801145i	$0.704225\pi$
$102$	−1745.01	−1.69394
$103$	1927.45	1.84386	0.921929	−	0.387359i	$-0.126613\pi$
$103$	1927.45	1.84386	0.921929	+	0.387359i	$0.126613\pi$
$104$	144.006	0.135779
$105$	−1526.26	−1.41855
$106$	−708.733	−0.649417
$107$	−1018.81	−0.920490	−0.460245	−	0.887792i	$-0.652238\pi$
$107$	−1018.81	−0.920490	−0.460245	+	0.887792i	$0.652238\pi$
$108$	1027.06	0.915084
$109$	454.707	0.399569	0.199784	−	0.979840i	$-0.435976\pi$
$109$	454.707	0.399569	0.199784	+	0.979840i	$0.435976\pi$
$110$	398.248	0.345195
$111$	105.800	0.0904695
$112$	−2264.86	−1.91080
$113$	231.494	0.192718	0.0963590	−	0.995347i	$-0.469280\pi$
$113$	231.494	0.192718	0.0963590	+	0.995347i	$0.469280\pi$
$114$	−4319.16	−3.54848
$115$	−681.934	−0.552962
$116$	0	0
$117$	564.237	0.445844
$118$	−201.952	−0.157552
$119$	1574.13	1.21260
$120$	−778.660	−0.592347
$121$	−943.586	−0.708930
$122$	1221.20	0.906247
$123$	−2981.16	−2.18538
$124$	−667.840	−0.483660
$125$	1268.49	0.907658
$126$	−5507.57	−3.89408
$127$	−25.4155	−0.0177580	−0.00887900	−	0.999961i	$-0.502826\pi$
$127$	−25.4155	−0.0177580	−0.00887900	+	0.999961i	$0.502826\pi$
$128$	−1593.82	−1.10059
$129$	1212.75	0.827723
$130$	201.624	0.136028
$131$	−625.214	−0.416986	−0.208493	−	0.978024i	$-0.566856\pi$
$131$	−625.214	−0.416986	−0.208493	+	0.978024i	$0.566856\pi$
$132$	682.444	0.449993
$133$	3896.20	2.54017
$134$	1449.57	0.934503
$135$	−1596.09	−1.01756
$136$	803.079	0.506349
$137$	1482.87	0.924743	0.462371	−	0.886686i	$-0.346999\pi$
$137$	1482.87	0.924743	0.462371	+	0.886686i	$0.346999\pi$
$138$	−3634.19	−2.24176
$139$	−1235.77	−0.754077	−0.377039	−	0.926197i	$-0.623058\pi$
$139$	−1235.77	−0.754077	−0.377039	+	0.926197i	$0.623058\pi$
$140$	−632.830	−0.382028
$141$	−1348.17	−0.805221
$142$	−1060.81	−0.626909
$143$	196.138	0.114699
$144$	−4527.31	−2.61997
$145$	0	0
$146$	3570.14	2.02375
$147$	4200.74	2.35695
$148$	43.8676	0.0243642
$149$	964.689	0.530405	0.265203	−	0.964193i	$-0.414561\pi$
$149$	964.689	0.530405	0.265203	+	0.964193i	$0.414561\pi$
$150$	2834.95	1.54315
$151$	94.3117	0.0508277	0.0254138	−	0.999677i	$-0.491910\pi$
$151$	94.3117	0.0508277	0.0254138	+	0.999677i	$0.491910\pi$
$152$	1987.74	1.06070
$153$	3146.58	1.66265
$154$	−1914.53	−1.00180
$155$	1037.85	0.537821
$156$	345.505	0.177324
$157$	−1304.76	−0.663255	−0.331627	−	0.943410i	$-0.607598\pi$
$157$	−1304.76	−0.663255	−0.331627	+	0.943410i	$0.607598\pi$
$158$	1279.16	0.644077
$159$	1887.37	0.941373
$160$	−936.580	−0.462770
$161$	3278.31	1.60476
$162$	−3256.26	−1.57923
$163$	912.133	0.438305	0.219153	−	0.975691i	$-0.429671\pi$
$163$	912.133	0.438305	0.219153	+	0.975691i	$0.429671\pi$
$164$	−1236.07	−0.588541
$165$	−1060.54	−0.500384
$166$	−2034.42	−0.951213
$167$	3777.65	1.75044	0.875220	−	0.483725i	$-0.160716\pi$
$167$	3777.65	1.75044	0.875220	+	0.483725i	$0.160716\pi$
$168$	3743.30	1.71906
$169$	−2097.70	−0.954802
$170$	1124.39	0.507277
$171$	7788.25	3.48294
$172$	502.837	0.222913
$173$	−1148.42	−0.504696	−0.252348	−	0.967637i	$-0.581203\pi$
$173$	−1148.42	−0.504696	−0.252348	+	0.967637i	$0.581203\pi$
$174$	0	0
$175$	−2557.33	−1.10466
$176$	−1573.77	−0.674020
$177$	537.803	0.228383
$178$	−2545.92	−1.07205
$179$	1850.72	0.772789	0.386395	−	0.922334i	$-0.373720\pi$
$179$	1850.72	0.772789	0.386395	+	0.922334i	$0.373720\pi$
$180$	−1264.99	−0.523814
$181$	−257.569	−0.105773	−0.0528865	−	0.998601i	$-0.516842\pi$
$181$	−257.569	−0.105773	−0.0528865	+	0.998601i	$0.516842\pi$
$182$	−969.279	−0.394768
$183$	−3252.08	−1.31367
$184$	1672.51	0.670102
$185$	−68.1721	−0.0270925
$186$	5530.96	2.18038
$187$	1093.80	0.427737
$188$	−558.987	−0.216853
$189$	7673.01	2.95307
$190$	2783.04	1.06265
$191$	291.002	0.110242	0.0551208	−	0.998480i	$-0.482446\pi$
$191$	291.002	0.110242	0.0551208	+	0.998480i	$0.482446\pi$
$192$	858.046	0.322522
$193$	−1005.81	−0.375127	−0.187564	−	0.982252i	$-0.560059\pi$
$193$	−1005.81	−0.375127	−0.187564	+	0.982252i	$0.560059\pi$
$194$	2919.75	1.08055
$195$	−536.929	−0.197181
$196$	1741.74	0.634745
$197$	1418.87	0.513149	0.256575	−	0.966524i	$-0.417406\pi$
$197$	1418.87	0.513149	0.256575	+	0.966524i	$0.417406\pi$
$198$	−3827.01	−1.37361
$199$	2510.56	0.894317	0.447159	−	0.894455i	$-0.352436\pi$
$199$	2510.56	0.894317	0.447159	+	0.894455i	$0.352436\pi$
$200$	−1304.68	−0.461275
$201$	−3860.23	−1.35462
$202$	4171.96	1.45316
$203$	0	0
$204$	1926.78	0.661281
$205$	1920.90	0.654447
$206$	−6618.64	−2.23856
$207$	6553.12	2.20035
$208$	−796.763	−0.265604
$209$	2707.33	0.896027
$210$	5241.01	1.72221
$211$	−2369.11	−0.772967	−0.386483	−	0.922296i	$-0.626310\pi$
$211$	−2369.11	−0.772967	−0.386483	+	0.922296i	$0.626310\pi$
$212$	782.556	0.253520
$213$	2824.96	0.908747
$214$	3498.49	1.11753
$215$	−781.430	−0.247875
$216$	3914.57	1.23311
$217$	−4989.33	−1.56082
$218$	−1561.41	−0.485101
$219$	−9507.37	−2.93356
$220$	−439.731	−0.134757
$221$	553.767	0.168554
$222$	−363.306	−0.109836
$223$	485.779	0.145875	0.0729375	−	0.997337i	$-0.476763\pi$
$223$	485.779	0.145875	0.0729375	+	0.997337i	$0.476763\pi$
$224$	4502.48	1.34301
$225$	−5111.93	−1.51465
$226$	−794.924	−0.233972
$227$	4520.61	1.32178	0.660889	−	0.750484i	$-0.270180\pi$
$227$	4520.61	1.32178	0.660889	+	0.750484i	$0.270180\pi$
$228$	4769.06	1.38526
$229$	4815.89	1.38971	0.694854	−	0.719151i	$-0.255469\pi$
$229$	4815.89	1.38971	0.694854	+	0.719151i	$0.255469\pi$
$230$	2341.68	0.671330
$231$	5098.43	1.45217
$232$	0	0
$233$	4969.07	1.39714	0.698571	−	0.715540i	$-0.253819\pi$
$233$	4969.07	1.39714	0.698571	+	0.715540i	$0.253819\pi$
$234$	−1937.53	−0.541282
$235$	868.688	0.241136
$236$	222.988	0.0615053
$237$	−3406.42	−0.933632
$238$	−5405.37	−1.47218
$239$	−1539.34	−0.416619	−0.208309	−	0.978063i	$-0.566796\pi$
$239$	−1539.34	−0.416619	−0.208309	+	0.978063i	$0.566796\pi$
$240$	4308.20	1.15872
$241$	−5010.06	−1.33911	−0.669557	−	0.742761i	$-0.733516\pi$
$241$	−5010.06	−1.33911	−0.669557	+	0.742761i	$0.733516\pi$
$242$	3240.17	0.860685
$243$	1357.72	0.358428
$244$	−1348.40	−0.353781
$245$	−2706.73	−0.705824
$246$	10237.0	2.65319
$247$	1370.66	0.353088
$248$	−2545.43	−0.651753
$249$	5417.70	1.37885
$250$	−4355.85	−1.10195
$251$	−1681.87	−0.422944	−0.211472	−	0.977384i	$-0.567826\pi$
$251$	−1681.87	−0.422944	−0.211472	+	0.977384i	$0.567826\pi$
$252$	6081.25	1.52017
$253$	2277.98	0.566068
$254$	87.2741	0.0215593
$255$	−2994.29	−0.735331
$256$	4722.33	1.15291
$257$	−1253.50	−0.304245	−0.152123	−	0.988362i	$-0.548611\pi$
$257$	−1253.50	−0.304245	−0.152123	+	0.988362i	$0.548611\pi$
$258$	−4164.43	−1.00491
$259$	327.728	0.0786256
$260$	−222.625	−0.0531025
$261$	0	0
$262$	2146.91	0.506247
$263$	58.1849	0.0136420	0.00682098	−	0.999977i	$-0.497829\pi$
$263$	58.1849	0.0136420	0.00682098	+	0.999977i	$0.497829\pi$
$264$	2601.09	0.606385
$265$	−1216.12	−0.281909
$266$	−13379.1	−3.08393
$267$	6779.85	1.55401
$268$	−1600.56	−0.364811
$269$	1957.16	0.443606	0.221803	−	0.975091i	$-0.428806\pi$
$269$	1957.16	0.443606	0.221803	+	0.975091i	$0.428806\pi$
$270$	5480.81	1.23537
$271$	6184.03	1.38617	0.693087	−	0.720854i	$-0.256250\pi$
$271$	6184.03	1.38617	0.693087	+	0.720854i	$0.256250\pi$
$272$	−4443.30	−0.990495
$273$	2581.21	0.572242
$274$	−5091.99	−1.12269
$275$	−1776.99	−0.389661
$276$	4012.74	0.875139
$277$	7534.40	1.63429	0.817145	−	0.576432i	$-0.195555\pi$
$277$	7534.40	1.63429	0.817145	+	0.576432i	$0.195555\pi$
$278$	4243.50	0.915496
$279$	−9973.34	−2.14010
$280$	−2411.99	−0.514799
$281$	−6800.85	−1.44379	−0.721894	−	0.692003i	$-0.756728\pi$
$281$	−6800.85	−1.44379	−0.721894	+	0.692003i	$0.756728\pi$
$282$	4629.45	0.977588
$283$	−4368.04	−0.917501	−0.458750	−	0.888565i	$-0.651703\pi$
$283$	−4368.04	−0.917501	−0.458750	+	0.888565i	$0.651703\pi$
$284$	1171.31	0.244733
$285$	−7411.31	−1.54038
$286$	−673.517	−0.139251
$287$	−9234.47	−1.89928
$288$	9000.17	1.84146
$289$	−1824.81	−0.371425
$290$	0	0
$291$	−7775.37	−1.56632
$292$	−3942.02	−0.790031
$293$	5707.24	1.13795	0.568977	−	0.822354i	$-0.307339\pi$
$293$	5707.24	1.13795	0.568977	+	0.822354i	$0.307339\pi$
$294$	−14424.8	−2.86148
$295$	−346.532	−0.0683928
$296$	167.198	0.0328318
$297$	5331.70	1.04167
$298$	−3312.63	−0.643945
$299$	1153.29	0.223064
$300$	−3130.24	−0.602415
$301$	3756.62	0.719362
$302$	−323.856	−0.0617079
$303$	−11110.0	−2.10645
$304$	−10997.8	−2.07490
$305$	2095.47	0.393398
$306$	−10805.0	−2.01856
$307$	1288.73	0.239582	0.119791	−	0.992799i	$-0.461778\pi$
$307$	1288.73	0.239582	0.119791	+	0.992799i	$0.461778\pi$
$308$	2113.95	0.391082
$309$	17625.6	3.24494
$310$	−3563.86	−0.652947
$311$	−8939.77	−1.62999	−0.814996	−	0.579466i	$-0.803261\pi$
$311$	−8939.77	−1.62999	−0.814996	+	0.579466i	$0.803261\pi$
$312$	1316.87	0.238952
$313$	3896.68	0.703685	0.351843	−	0.936059i	$-0.385555\pi$
$313$	3896.68	0.703685	0.351843	+	0.936059i	$0.385555\pi$
$314$	4480.39	0.805232
$315$	−9450.51	−1.69040
$316$	−1412.40	−0.251435
$317$	−1290.77	−0.228697	−0.114348	−	0.993441i	$-0.536478\pi$
$317$	−1290.77	−0.228697	−0.114348	+	0.993441i	$0.536478\pi$
$318$	−6481.02	−1.14288
$319$	0	0
$320$	−552.880	−0.0965841
$321$	−9316.55	−1.61994
$322$	−11257.3	−1.94828
$323$	7643.72	1.31674
$324$	3595.44	0.616502
$325$	−899.650	−0.153550
$326$	−3132.16	−0.532130
$327$	4158.07	0.703186
$328$	−4711.19	−0.793085
$329$	−4176.10	−0.699805
$330$	3641.79	0.607497
$331$	−5596.52	−0.929343	−0.464671	−	0.885483i	$-0.653828\pi$
$331$	−5596.52	−0.929343	−0.464671	+	0.885483i	$0.653828\pi$
$332$	2246.33	0.371335
$333$	655.107	0.107807
$334$	−12972.0	−2.12514
$335$	2487.33	0.405663
$336$	−20711.1	−3.36274
$337$	6821.81	1.10269	0.551347	−	0.834276i	$-0.314114\pi$
$337$	6821.81	1.10269	0.551347	+	0.834276i	$0.314114\pi$
$338$	7203.26	1.15919
$339$	2116.90	0.339157
$340$	−1241.51	−0.198031
$341$	−3466.90	−0.550567
$342$	−26743.9	−4.22850
$343$	3296.38	0.518915
$344$	1916.53	0.300385
$345$	−6235.96	−0.973138
$346$	3943.53	0.612732
$347$	11277.8	1.74473	0.872366	−	0.488854i	$-0.162585\pi$
$347$	11277.8	1.74473	0.872366	+	0.488854i	$0.162585\pi$
$348$	0	0
$349$	−8979.20	−1.37721	−0.688604	−	0.725138i	$-0.741776\pi$
$349$	−8979.20	−1.37721	−0.688604	+	0.725138i	$0.741776\pi$
$350$	8781.57	1.34113
$351$	2699.31	0.410480
$352$	3128.61	0.473737
$353$	10858.5	1.63722	0.818611	−	0.574348i	$-0.194744\pi$
$353$	10858.5	1.63722	0.818611	+	0.574348i	$0.194744\pi$
$354$	−1846.75	−0.277271
$355$	−1820.26	−0.272138
$356$	2811.11	0.418507
$357$	14394.6	2.13402
$358$	−6355.16	−0.938214
$359$	−9053.50	−1.33099	−0.665495	−	0.746402i	$-0.731780\pi$
$359$	−9053.50	−1.33099	−0.665495	+	0.746402i	$0.731780\pi$
$360$	−4821.41	−0.705862
$361$	12060.4	1.75832
$362$	884.461	0.128415
$363$	−8628.64	−1.24762
$364$	1070.24	0.154110
$365$	6126.05	0.878499
$366$	11167.3	1.59487
$367$	−3972.57	−0.565031	−0.282516	−	0.959263i	$-0.591169\pi$
$367$	−3972.57	−0.565031	−0.282516	+	0.959263i	$0.591169\pi$
$368$	−9253.70	−1.31082
$369$	−18459.1	−2.60418
$370$	234.095	0.0328920
$371$	5846.35	0.818133
$372$	−6107.08	−0.851175
$373$	3915.58	0.543541	0.271771	−	0.962362i	$-0.412391\pi$
$373$	3915.58	0.543541	0.271771	+	0.962362i	$0.412391\pi$
$374$	−3755.99	−0.519299
$375$	11599.7	1.59735
$376$	−2130.54	−0.292218
$377$	0	0
$378$	−26348.2	−3.58520
$379$	−13509.4	−1.83096	−0.915479	−	0.402365i	$-0.868188\pi$
$379$	−13509.4	−1.83096	−0.915479	+	0.402365i	$0.868188\pi$
$380$	−3072.93	−0.414837
$381$	−232.413	−0.0312516
$382$	−999.266	−0.133840
$383$	−11893.5	−1.58676	−0.793381	−	0.608725i	$-0.791681\pi$
$383$	−11893.5	−1.58676	−0.793381	+	0.608725i	$0.791681\pi$
$384$	−14574.7	−1.93688
$385$	−3285.16	−0.434876
$386$	3453.83	0.455428
$387$	7509.23	0.986346
$388$	−3223.88	−0.421824
$389$	−4540.73	−0.591836	−0.295918	−	0.955213i	$-0.595625\pi$
$389$	−4540.73	−0.591836	−0.295918	+	0.955213i	$0.595625\pi$
$390$	1843.75	0.239390
$391$	6431.52	0.831856
$392$	6638.52	0.855346
$393$	−5717.28	−0.733839
$394$	−4872.24	−0.622995
$395$	2194.92	0.279591
$396$	4225.64	0.536228
$397$	7642.39	0.966147	0.483073	−	0.875580i	$-0.339520\pi$
$397$	7642.39	0.966147	0.483073	+	0.875580i	$0.339520\pi$
$398$	−8620.98	−1.08576
$399$	35628.9	4.47036
$400$	7218.59	0.902324
$401$	−4834.08	−0.602001	−0.301000	−	0.953624i	$-0.597321\pi$
$401$	−4834.08	−0.602001	−0.301000	+	0.953624i	$0.597321\pi$
$402$	13255.6	1.64460
$403$	−1755.21	−0.216956
$404$	−4606.52	−0.567285
$405$	−5587.46	−0.685538
$406$	0	0
$407$	227.726	0.0277346
$408$	7343.77	0.891104
$409$	−10510.8	−1.27072	−0.635362	−	0.772215i	$-0.719149\pi$
$409$	−10510.8	−1.27072	−0.635362	+	0.772215i	$0.719149\pi$
$410$	−6596.15	−0.794539
$411$	13560.1	1.62742
$412$	7308.06	0.873889
$413$	1665.91	0.198484
$414$	−22502.7	−2.67137
$415$	−3490.88	−0.412917
$416$	1583.94	0.186681
$417$	−11300.5	−1.32707
$418$	−9296.65	−1.08783
$419$	−10935.5	−1.27502	−0.637509	−	0.770443i	$-0.720035\pi$
$419$	−10935.5	−1.27502	−0.637509	+	0.770443i	$0.720035\pi$
$420$	−5786.93	−0.672317
$421$	1379.57	0.159706	0.0798531	−	0.996807i	$-0.474555\pi$
$421$	1379.57	0.159706	0.0798531	+	0.996807i	$0.474555\pi$
$422$	8135.24	0.938429
$423$	−8347.76	−0.959531
$424$	2982.65	0.341629
$425$	−5017.07	−0.572620
$426$	−9700.59	−1.10327
$427$	−10073.7	−1.14169
$428$	−3862.90	−0.436262
$429$	1793.59	0.201854
$430$	2683.34	0.300935
$431$	1861.59	0.208051	0.104025	−	0.994575i	$-0.466828\pi$
$431$	1861.59	0.208051	0.104025	+	0.994575i	$0.466828\pi$
$432$	−21658.7	−2.41216
$433$	7954.51	0.882840	0.441420	−	0.897301i	$-0.354475\pi$
$433$	7954.51	0.882840	0.441420	+	0.897301i	$0.354475\pi$
$434$	17132.8	1.89493
$435$	0	0
$436$	1724.05	0.189374
$437$	15919.0	1.74258
$438$	32647.2	3.56152
$439$	−10283.9	−1.11805	−0.559027	−	0.829149i	$-0.688825\pi$
$439$	−10283.9	−1.11805	−0.559027	+	0.829149i	$0.688825\pi$
$440$	−1676.00	−0.181592
$441$	26010.7	2.80862
$442$	−1901.57	−0.204635
$443$	−4700.61	−0.504137	−0.252069	−	0.967709i	$-0.581111\pi$
$443$	−4700.61	−0.504137	−0.252069	+	0.967709i	$0.581111\pi$
$444$	401.148	0.0428776
$445$	−4368.58	−0.465372
$446$	−1668.11	−0.177101
$447$	8821.61	0.933440
$448$	2657.90	0.280299
$449$	11839.3	1.24439	0.622193	−	0.782864i	$-0.286242\pi$
$449$	11839.3	1.24439	0.622193	+	0.782864i	$0.286242\pi$
$450$	17553.8	1.83887
$451$	−6416.70	−0.669957
$452$	877.725	0.0913379
$453$	862.435	0.0894497
$454$	−15523.3	−1.60472
$455$	−1663.20	−0.171367
$456$	18176.9	1.86669
$457$	−18534.6	−1.89719	−0.948593	−	0.316498i	$-0.897493\pi$
$457$	−18534.6	−1.89719	−0.948593	+	0.316498i	$0.897493\pi$
$458$	−16537.2	−1.68719
$459$	15053.2	1.53077
$460$	−2585.60	−0.262074
$461$	5810.52	0.587035	0.293517	−	0.955954i	$-0.405174\pi$
$461$	5810.52	0.587035	0.293517	+	0.955954i	$0.405174\pi$
$462$	−17507.4	−1.76303
$463$	−16949.4	−1.70131	−0.850655	−	0.525725i	$-0.823794\pi$
$463$	−16949.4	−1.70131	−0.850655	+	0.525725i	$0.823794\pi$
$464$	0	0
$465$	9490.65	0.946491
$466$	−17063.2	−1.69622
$467$	−12229.5	−1.21181	−0.605903	−	0.795539i	$-0.707188\pi$
$467$	−12229.5	−1.21181	−0.605903	+	0.795539i	$0.707188\pi$
$468$	2139.34	0.211306
$469$	−11957.5	−1.17728
$470$	−2982.98	−0.292754
$471$	−11931.4	−1.16724
$472$	849.902	0.0828811
$473$	2610.34	0.253749
$474$	11697.3	1.13349
$475$	−12418.0	−1.19953
$476$	5968.40	0.574709
$477$	11686.5	1.12177
$478$	5285.93	0.505801
$479$	−18960.5	−1.80862	−0.904311	−	0.426875i	$-0.859614\pi$
$479$	−18960.5	−1.80862	−0.904311	+	0.426875i	$0.859614\pi$
$480$	−8564.57	−0.814412
$481$	115.293	0.0109291
$482$	17204.0	1.62577
$483$	29978.5	2.82416
$484$	−3577.67	−0.335994
$485$	5010.04	0.469060
$486$	−4662.26	−0.435153
$487$	1025.75	0.0954438	0.0477219	−	0.998861i	$-0.484804\pi$
$487$	1025.75	0.0954438	0.0477219	+	0.998861i	$0.484804\pi$
$488$	−5139.34	−0.476735
$489$	8341.01	0.771357
$490$	9294.61	0.856914
$491$	11448.9	1.05231	0.526154	−	0.850389i	$-0.323633\pi$
$491$	11448.9	1.05231	0.526154	+	0.850389i	$0.323633\pi$
$492$	−11303.3	−1.03575
$493$	0	0
$494$	−4706.67	−0.428671
$495$	−6566.82	−0.596276
$496$	14083.4	1.27493
$497$	8750.63	0.789778
$498$	−18603.8	−1.67400
$499$	4178.52	0.374862	0.187431	−	0.982278i	$-0.439984\pi$
$499$	4178.52	0.374862	0.187431	+	0.982278i	$0.439984\pi$
$500$	4809.57	0.430181
$501$	34544.8	3.08054
$502$	5775.36	0.513480
$503$	−15795.2	−1.40014	−0.700072	−	0.714072i	$-0.746849\pi$
$503$	−15795.2	−1.40014	−0.700072	+	0.714072i	$0.746849\pi$
$504$	23178.3	2.04850
$505$	7158.72	0.630810
$506$	−7822.31	−0.687241
$507$	−19182.5	−1.68032
$508$	−96.3647	−0.00841632
$509$	−1938.84	−0.168837	−0.0844183	−	0.996430i	$-0.526903\pi$
$509$	−1938.84	−0.168837	−0.0844183	+	0.996430i	$0.526903\pi$
$510$	10282.0	0.892738
$511$	−29450.2	−2.54951
$512$	−3465.41	−0.299123
$513$	37259.0	3.20667
$514$	4304.37	0.369372
$515$	−11357.0	−0.971747
$516$	4598.21	0.392296
$517$	−2901.82	−0.246851
$518$	−1125.38	−0.0954564
$519$	−10501.7	−0.888196
$520$	−848.521	−0.0715579
$521$	1479.09	0.124377	0.0621884	−	0.998064i	$-0.480192\pi$
$521$	1479.09	0.124377	0.0621884	+	0.998064i	$0.480192\pi$
$522$	0	0
$523$	2891.84	0.241781	0.120891	−	0.992666i	$-0.461425\pi$
$523$	2891.84	0.241781	0.120891	+	0.992666i	$0.461425\pi$
$524$	−2370.54	−0.197629
$525$	−23385.5	−1.94405
$526$	−199.800	−0.0165622
$527$	−9788.27	−0.809077
$528$	−14391.4	−1.18618
$529$	1227.40	0.100879
$530$	4176.03	0.342255
$531$	3330.04	0.272149
$532$	14772.7	1.20390
$533$	−3248.62	−0.264003
$534$	−23281.2	−1.88666
$535$	6003.10	0.485115
$536$	−6100.40	−0.491599
$537$	16923.9	1.36000
$538$	−6720.66	−0.538565
$539$	9041.74	0.722552
$540$	−6051.70	−0.482266
$541$	−18063.0	−1.43547	−0.717735	−	0.696316i	$-0.754821\pi$
$541$	−18063.0	−1.43547	−0.717735	+	0.696316i	$0.754821\pi$
$542$	−21235.2	−1.68290
$543$	−2355.34	−0.186146
$544$	8833.16	0.696174
$545$	−2679.24	−0.210580
$546$	−8863.59	−0.694737
$547$	−23720.3	−1.85413	−0.927063	−	0.374906i	$-0.877675\pi$
$547$	−23720.3	−1.85413	−0.927063	+	0.374906i	$0.877675\pi$
$548$	5622.38	0.438278
$549$	−20136.7	−1.56541
$550$	6101.99	0.473072
$551$	0	0
$552$	15294.3	1.17929
$553$	−10551.8	−0.811405
$554$	−25872.3	−1.98413
$555$	−623.401	−0.0476791
$556$	−4685.51	−0.357392
$557$	−6055.38	−0.460637	−0.230319	−	0.973115i	$-0.573977\pi$
$557$	−6055.38	−0.460637	−0.230319	+	0.973115i	$0.573977\pi$
$558$	34247.3	2.59822
$559$	1321.55	0.0999923
$560$	13345.1	1.00703
$561$	10002.3	0.752759
$562$	23353.3	1.75285
$563$	16045.1	1.20110	0.600550	−	0.799587i	$-0.294948\pi$
$563$	16045.1	1.20110	0.600550	+	0.799587i	$0.294948\pi$
$564$	−5111.66	−0.381631
$565$	−1364.02	−0.101566
$566$	14999.3	1.11390
$567$	26860.9	1.98951
$568$	4464.35	0.329788
$569$	−22591.5	−1.66447	−0.832237	−	0.554420i	$-0.812940\pi$
$569$	−22591.5	−1.66447	−0.832237	+	0.554420i	$0.812940\pi$
$570$	25449.6	1.87011
$571$	−1965.79	−0.144073	−0.0720365	−	0.997402i	$-0.522950\pi$
$571$	−1965.79	−0.144073	−0.0720365	+	0.997402i	$0.522950\pi$
$572$	743.672	0.0543610
$573$	2661.07	0.194010
$574$	31710.1	2.30584
$575$	−10448.6	−0.757806
$576$	5312.96	0.384329
$577$	17428.7	1.25748	0.628741	−	0.777614i	$-0.283570\pi$
$577$	17428.7	1.25748	0.628741	+	0.777614i	$0.283570\pi$
$578$	6266.20	0.450933
$579$	−9197.62	−0.660173
$580$	0	0
$581$	16781.9	1.19833
$582$	26699.7	1.90161
$583$	4062.41	0.288590
$584$	−15024.7	−1.06460
$585$	−3324.63	−0.234968
$586$	−19598.0	−1.38155
$587$	13435.1	0.944680	0.472340	−	0.881416i	$-0.343409\pi$
$587$	13435.1	0.944680	0.472340	+	0.881416i	$0.343409\pi$
$588$	15927.4	1.11706
$589$	−24227.4	−1.69486
$590$	1189.95	0.0830330
$591$	12974.9	0.903073
$592$	−925.081	−0.0642240
$593$	−445.800	−0.0308715	−0.0154358	−	0.999881i	$-0.504914\pi$
$593$	−445.800	−0.0308715	−0.0154358	+	0.999881i	$0.504914\pi$
$594$	−18308.4	−1.26465
$595$	−9275.14	−0.639065
$596$	3657.68	0.251383
$597$	22957.9	1.57388
$598$	−3960.25	−0.270814
$599$	1118.95	0.0763260	0.0381630	−	0.999272i	$-0.487849\pi$
$599$	1118.95	0.0763260	0.0381630	+	0.999272i	$0.487849\pi$
$600$	−11930.7	−0.811781
$601$	−5612.21	−0.380910	−0.190455	−	0.981696i	$-0.560996\pi$
$601$	−5612.21	−0.380910	−0.190455	+	0.981696i	$0.560996\pi$
$602$	−12899.8	−0.873349
$603$	−23902.2	−1.61422
$604$	357.589	0.0240896
$605$	5559.84	0.373619
$606$	38150.6	2.55736
$607$	25588.5	1.71105	0.855524	−	0.517763i	$-0.173235\pi$
$607$	25588.5	1.71105	0.855524	+	0.517763i	$0.173235\pi$
$608$	21863.4	1.45835
$609$	0	0
$610$	−7195.60	−0.477609
$611$	−1469.12	−0.0972739
$612$	11930.5	0.788006
$613$	6647.94	0.438023	0.219011	−	0.975722i	$-0.429717\pi$
$613$	6647.94	0.438023	0.219011	+	0.975722i	$0.429717\pi$
$614$	−4425.35	−0.290867
$615$	17565.7	1.15174
$616$	8057.16	0.527000
$617$	9549.74	0.623109	0.311554	−	0.950228i	$-0.399150\pi$
$617$	9549.74	0.623109	0.311554	+	0.950228i	$0.399150\pi$
$618$	−60524.3	−3.93955
$619$	−5672.19	−0.368311	−0.184156	−	0.982897i	$-0.558955\pi$
$619$	−5672.19	−0.368311	−0.184156	+	0.982897i	$0.558955\pi$
$620$	3935.08	0.254898
$621$	31350.1	2.02583
$622$	30698.1	1.97891
$623$	21001.3	1.35056
$624$	−7286.02	−0.467426
$625$	3810.92	0.243899
$626$	−13380.8	−0.854317
$627$	24757.2	1.57689
$628$	−4947.07	−0.314347
$629$	642.951	0.0407569
$630$	32452.0	2.05225
$631$	−25006.0	−1.57761	−0.788805	−	0.614644i	$-0.789300\pi$
$631$	−25006.0	−1.57761	−0.788805	+	0.614644i	$0.789300\pi$
$632$	−5383.24	−0.338819
$633$	−21664.3	−1.36032
$634$	4432.35	0.277652
$635$	149.755	0.00935879
$636$	7156.09	0.446160
$637$	4577.62	0.284728
$638$	0	0
$639$	17491.9	1.08290
$640$	9391.17	0.580029
$641$	−11884.0	−0.732275	−0.366138	−	0.930561i	$-0.619320\pi$
$641$	−11884.0	−0.732275	−0.366138	+	0.930561i	$0.619320\pi$
$642$	31992.0	1.96670
$643$	2994.14	0.183635	0.0918175	−	0.995776i	$-0.470732\pi$
$643$	2994.14	0.183635	0.0918175	+	0.995776i	$0.470732\pi$
$644$	12429.9	0.760570
$645$	−7145.80	−0.436226
$646$	−26247.7	−1.59861
$647$	7641.25	0.464310	0.232155	−	0.972679i	$-0.425422\pi$
$647$	7641.25	0.464310	0.232155	+	0.972679i	$0.425422\pi$
$648$	13703.8	0.830763
$649$	1157.58	0.0700137
$650$	3089.30	0.186419
$651$	−45625.0	−2.74683
$652$	3458.41	0.207733
$653$	30822.9	1.84716	0.923578	−	0.383411i	$-0.125251\pi$
$653$	30822.9	1.84716	0.923578	+	0.383411i	$0.125251\pi$
$654$	−14278.3	−0.853712
$655$	3683.92	0.219760
$656$	26066.2	1.55140
$657$	−58869.0	−3.49573
$658$	14340.3	0.849607
$659$	27525.0	1.62704	0.813521	−	0.581535i	$-0.197548\pi$
$659$	27525.0	1.62704	0.813521	+	0.581535i	$0.197548\pi$
$660$	−4021.13	−0.237155
$661$	6548.53	0.385338	0.192669	−	0.981264i	$-0.438286\pi$
$661$	6548.53	0.385338	0.192669	+	0.981264i	$0.438286\pi$
$662$	19217.8	1.12828
$663$	5063.93	0.296632
$664$	8561.71	0.500390
$665$	−22957.4	−1.33872
$666$	−2249.56	−0.130884
$667$	0	0
$668$	14323.2	0.829614
$669$	4442.21	0.256720
$670$	−8541.20	−0.492500
$671$	−6999.84	−0.402721
$672$	41173.0	2.36352
$673$	−14112.1	−0.808291	−0.404145	−	0.914695i	$-0.632431\pi$
$673$	−14112.1	−0.808291	−0.404145	+	0.914695i	$0.632431\pi$
$674$	−23425.3	−1.33874
$675$	−24455.5	−1.39451
$676$	−7953.57	−0.452524
$677$	9323.80	0.529310	0.264655	−	0.964343i	$-0.414742\pi$
$677$	9323.80	0.529310	0.264655	+	0.964343i	$0.414742\pi$
$678$	−7269.20	−0.411758
$679$	−24085.1	−1.36127
$680$	−4731.94	−0.266855
$681$	41338.8	2.32615
$682$	11904.9	0.668422
$683$	−4863.66	−0.272478	−0.136239	−	0.990676i	$-0.543502\pi$
$683$	−4863.66	−0.272478	−0.136239	+	0.990676i	$0.543502\pi$
$684$	29529.6	1.65072
$685$	−8737.41	−0.487357
$686$	−11319.4	−0.629995
$687$	44039.0	2.44569
$688$	−10603.8	−0.587598
$689$	2056.70	0.113722
$690$	21413.6	1.18145
$691$	8256.67	0.454557	0.227278	−	0.973830i	$-0.427017\pi$
$691$	8256.67	0.454557	0.227278	+	0.973830i	$0.427017\pi$
$692$	−4354.29	−0.239198
$693$	31569.1	1.73046
$694$	−38726.5	−2.11821
$695$	7281.47	0.397413
$696$	0	0
$697$	−18116.6	−0.984525
$698$	30833.5	1.67201
$699$	45439.7	2.45878
$700$	−9696.28	−0.523550
$701$	17710.8	0.954250	0.477125	−	0.878835i	$-0.341679\pi$
$701$	17710.8	0.954250	0.477125	+	0.878835i	$0.341679\pi$
$702$	−9269.13	−0.498349
$703$	1591.40	0.0853780
$704$	1846.87	0.0988732
$705$	7943.73	0.424366
$706$	−37286.8	−1.98769
$707$	−34414.6	−1.83068
$708$	2039.11	0.108241
$709$	−11407.4	−0.604252	−0.302126	−	0.953268i	$-0.597696\pi$
$709$	−11407.4	−0.604252	−0.302126	+	0.953268i	$0.597696\pi$
$710$	6250.55	0.330393
$711$	−21092.3	−1.11255
$712$	10714.3	0.563957
$713$	−20385.2	−1.07073
$714$	−49429.5	−2.59083
$715$	−1155.70	−0.0604484
$716$	7017.13	0.366260
$717$	−14076.6	−0.733192
$718$	31088.7	1.61590
$719$	24212.7	1.25589	0.627943	−	0.778259i	$-0.283897\pi$
$719$	24212.7	1.25589	0.627943	+	0.778259i	$0.283897\pi$
$720$	26676.0	1.38077
$721$	54597.3	2.82013
$722$	−41413.9	−2.13471
$723$	−45814.6	−2.35666
$724$	−976.588	−0.0501307
$725$	0	0
$726$	29629.8	1.51469
$727$	−26557.9	−1.35485	−0.677425	−	0.735591i	$-0.736904\pi$
$727$	−26557.9	−1.35485	−0.677425	+	0.735591i	$0.736904\pi$
$728$	4079.15	0.207669
$729$	−13187.7	−0.670002
$730$	−21036.2	−1.06655
$731$	7369.89	0.372893
$732$	−12330.5	−0.622606
$733$	−15621.7	−0.787176	−0.393588	−	0.919287i	$-0.628766\pi$
$733$	−15621.7	−0.787176	−0.393588	+	0.919287i	$0.628766\pi$
$734$	13641.3	0.685983
$735$	−24751.8	−1.24215
$736$	18396.1	0.921317
$737$	−8308.83	−0.415277
$738$	63386.5	3.16164
$739$	−30757.7	−1.53104	−0.765521	−	0.643411i	$-0.777519\pi$
$739$	−30757.7	−1.53104	−0.765521	+	0.643411i	$0.777519\pi$
$740$	−258.479	−0.0128404
$741$	12534.0	0.621387
$742$	−20075.7	−0.993263
$743$	19540.0	0.964810	0.482405	−	0.875948i	$-0.339763\pi$
$743$	19540.0	0.964810	0.482405	+	0.875948i	$0.339763\pi$
$744$	−23276.7	−1.14700
$745$	−5684.18	−0.279533
$746$	−13445.6	−0.659893
$747$	33546.0	1.64308
$748$	4147.23	0.202724
$749$	−28859.1	−1.40786
$750$	−39832.2	−1.93929
$751$	−12946.6	−0.629068	−0.314534	−	0.949246i	$-0.601848\pi$
$751$	−12946.6	−0.629068	−0.314534	+	0.949246i	$0.601848\pi$
$752$	11787.9	0.571624
$753$	−15379.9	−0.744324
$754$	0	0
$755$	−555.708	−0.0267871
$756$	29092.7	1.39959
$757$	15108.3	0.725393	0.362696	−	0.931907i	$-0.381856\pi$
$757$	15108.3	0.725393	0.362696	+	0.931907i	$0.381856\pi$
$758$	46389.9	2.22290
$759$	20831.0	0.996201
$760$	−11712.2	−0.559010
$761$	15009.9	0.714990	0.357495	−	0.933915i	$-0.383631\pi$
$761$	15009.9	0.714990	0.357495	+	0.933915i	$0.383631\pi$
$762$	798.079	0.0379414
$763$	12880.1	0.611128
$764$	1103.35	0.0522485
$765$	−18540.4	−0.876248
$766$	40840.9	1.92643
$767$	586.054	0.0275895
$768$	43183.5	2.02897
$769$	19787.6	0.927907	0.463953	−	0.885860i	$-0.346431\pi$
$769$	19787.6	0.927907	0.463953	+	0.885860i	$0.346431\pi$
$770$	11280.9	0.527966
$771$	−11462.6	−0.535430
$772$	−3813.58	−0.177790
$773$	2093.89	0.0974281	0.0487140	−	0.998813i	$-0.484488\pi$
$773$	2093.89	0.0974281	0.0487140	+	0.998813i	$0.484488\pi$
$774$	−25785.8	−1.19748
$775$	15902.0	0.737055
$776$	−12287.6	−0.568426
$777$	2996.92	0.138370
$778$	15592.3	0.718525
$779$	−44841.2	−2.06239
$780$	−2035.80	−0.0934530
$781$	6080.50	0.278588
$782$	−22085.1	−1.00992
$783$	0	0
$784$	−36729.8	−1.67319
$785$	7687.95	0.349548
$786$	19632.5	0.890926
$787$	26192.6	1.18636	0.593180	−	0.805070i	$-0.297872\pi$
$787$	26192.6	1.18636	0.593180	+	0.805070i	$0.297872\pi$
$788$	5379.74	0.243205
$789$	532.073	0.0240080
$790$	−7537.10	−0.339440
$791$	6557.34	0.294756
$792$	16105.7	0.722591
$793$	−3543.85	−0.158696
$794$	−26243.1	−1.17296
$795$	−11120.9	−0.496121
$796$	9518.96	0.423858
$797$	−43480.7	−1.93246	−0.966228	−	0.257690i	$-0.917039\pi$
$797$	−43480.7	−1.93246	−0.966228	+	0.257690i	$0.917039\pi$
$798$	−122345.	−5.42729
$799$	−8192.85	−0.362756
$800$	−14350.4	−0.634202
$801$	41980.3	1.85181
$802$	16599.7	0.730866
$803$	−20463.8	−0.899319
$804$	−14636.3	−0.642018
$805$	−19316.6	−0.845739
$806$	6027.19	0.263398
$807$	17897.3	0.780686
$808$	−17557.4	−0.764441
$809$	33975.7	1.47654	0.738272	−	0.674504i	$-0.235642\pi$
$809$	33975.7	1.47654	0.738272	+	0.674504i	$0.235642\pi$
$810$	19186.7	0.832286
$811$	−3732.02	−0.161589	−0.0807947	−	0.996731i	$-0.525746\pi$
$811$	−3732.02	−0.161589	−0.0807947	+	0.996731i	$0.525746\pi$
$812$	0	0
$813$	56549.9	2.43948
$814$	−781.986	−0.0336715
$815$	−5374.51	−0.230995
$816$	−40631.9	−1.74314
$817$	18241.6	0.781140
$818$	36092.9	1.54274
$819$	15982.7	0.681905
$820$	7283.22	0.310172
$821$	9169.96	0.389810	0.194905	−	0.980822i	$-0.437560\pi$
$821$	9169.96	0.389810	0.194905	+	0.980822i	$0.437560\pi$
$822$	−46563.8	−1.97579
$823$	35897.6	1.52043	0.760214	−	0.649673i	$-0.225094\pi$
$823$	35897.6	1.52043	0.760214	+	0.649673i	$0.225094\pi$
$824$	27854.1	1.17760
$825$	−16249.8	−0.685750
$826$	−5720.53	−0.240972
$827$	−32487.3	−1.36601	−0.683007	−	0.730412i	$-0.739328\pi$
$827$	−32487.3	−1.36601	−0.683007	+	0.730412i	$0.739328\pi$
$828$	24846.6	1.04285
$829$	1759.23	0.0737040	0.0368520	−	0.999321i	$-0.488267\pi$
$829$	1759.23	0.0737040	0.0368520	+	0.999321i	$0.488267\pi$
$830$	11987.3	0.501307
$831$	68898.5	2.87613
$832$	935.029	0.0389619
$833$	25528.0	1.06182
$834$	38804.7	1.61115
$835$	−22258.9	−0.922514
$836$	10265.0	0.424668
$837$	−47712.5	−1.97035
$838$	37551.1	1.54795
$839$	−12137.9	−0.499462	−0.249731	−	0.968315i	$-0.580342\pi$
$839$	−12137.9	−0.499462	−0.249731	+	0.968315i	$0.580342\pi$
$840$	−22056.5	−0.905976
$841$	0	0
$842$	−4737.30	−0.193893
$843$	−62190.5	−2.54087
$844$	−8982.62	−0.366344
$845$	12360.2	0.503198
$846$	28665.2	1.16493
$847$	−26728.2	−1.08429
$848$	−16502.5	−0.668278
$849$	−39943.6	−1.61468
$850$	17228.0	0.695197
$851$	1339.02	0.0539378
$852$	10711.0	0.430697
$853$	79.0685	0.00317380	0.00158690	−	0.999999i	$-0.499495\pi$
$853$	79.0685	0.00317380	0.00158690	+	0.999999i	$0.499495\pi$
$854$	34591.9	1.38608
$855$	−45890.3	−1.83557
$856$	−14723.2	−0.587882
$857$	21292.0	0.848682	0.424341	−	0.905503i	$-0.360506\pi$
$857$	21292.0	0.848682	0.424341	+	0.905503i	$0.360506\pi$
$858$	−6158.99	−0.245063
$859$	−15943.1	−0.633259	−0.316630	−	0.948549i	$-0.602551\pi$
$859$	−15943.1	−0.633259	−0.316630	+	0.948549i	$0.602551\pi$
$860$	−2962.84	−0.117479
$861$	−84444.8	−3.34247
$862$	−6392.50	−0.252586
$863$	3459.63	0.136462	0.0682312	−	0.997670i	$-0.478264\pi$
$863$	3459.63	0.136462	0.0682312	+	0.997670i	$0.478264\pi$
$864$	43056.8	1.69540
$865$	6766.74	0.265984
$866$	−27314.9	−1.07182
$867$	−16687.0	−0.653658
$868$	−18917.4	−0.739743
$869$	−7332.05	−0.286217
$870$	0	0
$871$	−4206.56	−0.163644
$872$	6571.09	0.255190
$873$	−48144.5	−1.86649
$874$	−54663.9	−2.11560
$875$	35931.5	1.38824
$876$	−36047.8	−1.39035
$877$	−27923.1	−1.07514	−0.537569	−	0.843220i	$-0.680657\pi$
$877$	−27923.1	−1.07514	−0.537569	+	0.843220i	$0.680657\pi$
$878$	35313.9	1.35739
$879$	52189.9	2.00264
$880$	9273.05	0.355221
$881$	−20958.0	−0.801468	−0.400734	−	0.916194i	$-0.631245\pi$
$881$	−20958.0	−0.801468	−0.400734	+	0.916194i	$0.631245\pi$
$882$	−89317.6	−3.40984
$883$	−33203.3	−1.26544	−0.632719	−	0.774382i	$-0.718061\pi$
$883$	−33203.3	−1.26544	−0.632719	+	0.774382i	$0.718061\pi$
$884$	2099.64	0.0798854
$885$	−3168.87	−0.120362
$886$	16141.4	0.612054
$887$	−8053.49	−0.304859	−0.152429	−	0.988314i	$-0.548710\pi$
$887$	−8053.49	−0.304859	−0.152429	+	0.988314i	$0.548710\pi$
$888$	1528.95	0.0577795
$889$	−719.925	−0.0271603
$890$	15001.2	0.564990
$891$	18664.7	0.701785
$892$	1841.86	0.0691369
$893$	−20278.5	−0.759904
$894$	−30292.4	−1.13325
$895$	−10904.9	−0.407274
$896$	−45146.8	−1.68331
$897$	10546.2	0.392563
$898$	−40654.7	−1.51076
$899$	0	0
$900$	−19382.2	−0.717860
$901$	11469.6	0.424093
$902$	22034.2	0.813369
$903$	34352.5	1.26598
$904$	3345.39	0.123082
$905$	1517.66	0.0557444
$906$	−2961.50	−0.108598
$907$	−6295.01	−0.230455	−0.115227	−	0.993339i	$-0.536760\pi$
$907$	−6295.01	−0.230455	−0.115227	+	0.993339i	$0.536760\pi$
$908$	17140.2	0.626451
$909$	−68792.5	−2.51013
$910$	5711.23	0.208050
$911$	−36317.6	−1.32081	−0.660404	−	0.750910i	$-0.729615\pi$
$911$	−36317.6	−1.32081	−0.660404	+	0.750910i	$0.729615\pi$
$912$	−100570.	−3.65154
$913$	11661.2	0.422703
$914$	63645.8	2.30330
$915$	19162.1	0.692326
$916$	18259.8	0.658646
$917$	−17709.9	−0.637768
$918$	−51691.1	−1.85845
$919$	42181.6	1.51408	0.757042	−	0.653366i	$-0.226644\pi$
$919$	42181.6	1.51408	0.757042	+	0.653366i	$0.226644\pi$
$920$	−9854.82	−0.353156
$921$	11784.8	0.421632
$922$	−19952.7	−0.712696
$923$	3078.41	0.109780
$924$	19331.0	0.688251
$925$	−1044.54	−0.0371289
$926$	58202.4	2.06549
$927$	109136.	3.86679
$928$	0	0
$929$	−48418.9	−1.70998	−0.854991	−	0.518643i	$-0.826437\pi$
$929$	−48418.9	−1.70998	−0.854991	+	0.518643i	$0.826437\pi$
$930$	−32589.8	−1.14910
$931$	63185.6	2.22430
$932$	18840.5	0.662170
$933$	−81749.8	−2.86856
$934$	41994.6	1.47121
$935$	−6444.96	−0.225425
$936$	8153.95	0.284744
$937$	−33006.0	−1.15076	−0.575379	−	0.817887i	$-0.695145\pi$
$937$	−33006.0	−1.15076	−0.575379	+	0.817887i	$0.695145\pi$
$938$	41060.6	1.42929
$939$	35633.3	1.23839
$940$	3293.69	0.114285
$941$	31165.6	1.07967	0.539834	−	0.841771i	$-0.318487\pi$
$941$	31165.6	1.07967	0.539834	+	0.841771i	$0.318487\pi$
$942$	40971.0	1.41710
$943$	−37729.9	−1.30292
$944$	−4702.37	−0.162128
$945$	−45211.3	−1.55632
$946$	−8963.60	−0.308067
$947$	−41588.7	−1.42709	−0.713543	−	0.700612i	$-0.752911\pi$
$947$	−41588.7	−1.42709	−0.713543	+	0.700612i	$0.752911\pi$
$948$	−12915.7	−0.442491
$949$	−10360.4	−0.354385
$950$	42642.0	1.45630
$951$	−11803.5	−0.402475
$952$	22748.1	0.774445
$953$	35938.4	1.22157	0.610786	−	0.791796i	$-0.290854\pi$
$953$	35938.4	1.22157	0.610786	+	0.791796i	$0.290854\pi$
$954$	−40130.0	−1.36190
$955$	−1714.65	−0.0580993
$956$	−5836.52	−0.197455
$957$	0	0
$958$	65108.3	2.19578
$959$	42003.9	1.41437
$960$	−5055.82	−0.169975
$961$	1233.76	0.0414137
$962$	−395.901	−0.0132686
$963$	−57687.4	−1.93038
$964$	−18996.0	−0.634667
$965$	5926.46	0.197699
$966$	−102943.	−3.42871
$967$	2701.06	0.0898244	0.0449122	−	0.998991i	$-0.485699\pi$
$967$	2701.06	0.0898244	0.0449122	+	0.998991i	$0.485699\pi$
$968$	−13636.0	−0.452767
$969$	69898.1	2.31729
$970$	−17203.9	−0.569468
$971$	−18818.5	−0.621952	−0.310976	−	0.950418i	$-0.600656\pi$
$971$	−18818.5	−0.621952	−0.310976	+	0.950418i	$0.600656\pi$
$972$	5147.89	0.169875
$973$	−35004.7	−1.15334
$974$	−3522.31	−0.115875
$975$	−8226.87	−0.270226
$976$	28435.1	0.932567
$977$	36036.9	1.18007	0.590033	−	0.807379i	$-0.299115\pi$
$977$	36036.9	1.18007	0.590033	+	0.807379i	$0.299115\pi$
$978$	−28642.1	−0.936475
$979$	14593.1	0.476401
$980$	−10262.8	−0.334522
$981$	25746.5	0.837943
$982$	−39314.4	−1.27757
$983$	−44246.6	−1.43565	−0.717826	−	0.696222i	$-0.754863\pi$
$983$	−44246.6	−1.43565	−0.717826	+	0.696222i	$0.754863\pi$
$984$	−43081.5	−1.39572
$985$	−8360.34	−0.270439
$986$	0	0
$987$	−38188.4	−1.23156
$988$	5196.93	0.167345
$989$	15348.7	0.493488
$990$	22549.7	0.723915
$991$	48114.8	1.54230	0.771149	−	0.636654i	$-0.219682\pi$
$991$	48114.8	1.54230	0.771149	+	0.636654i	$0.219682\pi$
$992$	−27997.4	−0.896089
$993$	−51177.5	−1.63552
$994$	−30048.7	−0.958839
$995$	−14792.9	−0.471322
$996$	20541.6	0.653498
$997$	39263.2	1.24722	0.623609	−	0.781736i	$-0.285666\pi$
$997$	39263.2	1.24722	0.623609	+	0.781736i	$0.285666\pi$
$998$	−14348.6	−0.455106
$999$	3134.03	0.0992557

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.4.a.i.1.5		21
29.5	even	14		29.4.d.a.25.2	yes	42
29.6	even	14		29.4.d.a.7.2	✓	42
29.28	even	2		841.4.a.h.1.17		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.4.d.a.7.2	✓	42	29.6	even	14
29.4.d.a.25.2	yes	42	29.5	even	14
841.4.a.h.1.17		21	29.28	even	2
841.4.a.i.1.5		21	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	841.a (trivial)

\(f(q)\)	\(=\)	\(q-3.43388 q^{2} +9.14452 q^{3} +3.79157 q^{4} -5.89225 q^{5} -31.4012 q^{6} +28.3262 q^{7} +14.4513 q^{8} +56.6222 q^{9} +20.2333 q^{10} +19.6828 q^{11} +34.6720 q^{12} +9.96495 q^{13} -97.2688 q^{14} -53.8817 q^{15} -79.9566 q^{16} +55.5715 q^{17} -194.434 q^{18} +137.548 q^{19} -22.3408 q^{20} +259.029 q^{21} -67.5886 q^{22} +115.734 q^{23} +132.150 q^{24} -90.2814 q^{25} -34.2185 q^{26} +270.881 q^{27} +107.401 q^{28} +185.024 q^{30} -176.138 q^{31} +158.951 q^{32} +179.990 q^{33} -190.826 q^{34} -166.905 q^{35} +214.687 q^{36} +11.5698 q^{37} -472.323 q^{38} +91.1247 q^{39} -85.1505 q^{40} -326.005 q^{41} -889.476 q^{42} +132.620 q^{43} +74.6287 q^{44} -333.632 q^{45} -397.418 q^{46} -147.429 q^{47} -731.164 q^{48} +459.372 q^{49} +310.016 q^{50} +508.174 q^{51} +37.7828 q^{52} +206.394 q^{53} -930.173 q^{54} -115.976 q^{55} +409.350 q^{56} +1257.81 q^{57} +58.8115 q^{59} -204.296 q^{60} -355.632 q^{61} +604.839 q^{62} +1603.89 q^{63} +93.8318 q^{64} -58.7159 q^{65} -618.065 q^{66} -422.136 q^{67} +210.703 q^{68} +1058.33 q^{69} +573.132 q^{70} +308.924 q^{71} +818.263 q^{72} -1039.68 q^{73} -39.7294 q^{74} -825.580 q^{75} +521.521 q^{76} +557.539 q^{77} -312.912 q^{78} -372.510 q^{79} +471.124 q^{80} +948.273 q^{81} +1119.46 q^{82} +592.453 q^{83} +982.126 q^{84} -327.441 q^{85} -455.402 q^{86} +284.442 q^{88} +741.411 q^{89} +1145.65 q^{90} +282.269 q^{91} +438.814 q^{92} -1610.70 q^{93} +506.254 q^{94} -810.464 q^{95} +1453.53 q^{96} -850.276 q^{97} -1577.43 q^{98} +1114.48 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 6 q^{2} - q^{3} + 90 q^{4} + 35 q^{5} + 26 q^{6} + 37 q^{7} + 51 q^{8} + 188 q^{9} + 37 q^{10} - 7 q^{11} - 68 q^{12} + 97 q^{13} - 68 q^{14} - 330 q^{15} + 310 q^{16} + 70 q^{17} + 305 q^{18} - 73 q^{19}+ \cdots + 8702 q^{99}+O(q^{100}) \) 21 * q + 6 * q^2 - q^3 + 90 * q^4 + 35 * q^5 + 26 * q^6 + 37 * q^7 + 51 * q^8 + 188 * q^9 + 37 * q^10 - 7 * q^11 - 68 * q^12 + 97 * q^13 - 68 * q^14 - 330 * q^15 + 310 * q^16 + 70 * q^17 + 305 * q^18 - 73 * q^19 + 408 * q^20 + 169 * q^21 + 705 * q^22 + 375 * q^23 + 641 * q^24 + 402 * q^25 + 1144 * q^26 + 14 * q^27 + 178 * q^28 + 1087 * q^30 - 693 * q^31 + 449 * q^32 + 820 * q^33 + 53 * q^34 + 886 * q^35 + 1464 * q^36 - 243 * q^37 + 914 * q^38 + 244 * q^39 + 275 * q^40 - 552 * q^41 - 373 * q^42 + 1151 * q^43 - 1502 * q^44 + 1139 * q^45 + 2992 * q^46 - 403 * q^47 - 3329 * q^48 + 1078 * q^49 + 1317 * q^50 + 2272 * q^51 - 1267 * q^52 + 1505 * q^53 + 140 * q^54 + 588 * q^55 - 2549 * q^56 + 859 * q^57 + 3086 * q^59 - 4371 * q^60 - 39 * q^61 + 1356 * q^62 + 1527 * q^63 - 1993 * q^64 + 1132 * q^65 - 980 * q^66 + 413 * q^67 - 919 * q^68 + 6116 * q^69 + 6779 * q^70 + 4015 * q^71 + 5524 * q^72 - 2667 * q^73 + 3844 * q^74 + 3734 * q^75 + 438 * q^76 - 5252 * q^77 - 4128 * q^78 + 1441 * q^79 + 6887 * q^80 - 371 * q^81 + 3401 * q^82 + 2505 * q^83 - 140 * q^84 - 3340 * q^85 + 3412 * q^86 + 8149 * q^88 - 2757 * q^89 - 1740 * q^90 + 4824 * q^91 + 3957 * q^92 - 4278 * q^93 + 1507 * q^94 - 2496 * q^95 + 3663 * q^96 - 1223 * q^97 + 10921 * q^98 + 8702 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more