LMFDB - Embedded newform 529.4.a.m.1.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [529,4,Mod(1,529)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(529, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("529.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 529 = 23^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	529.a (trivial)

Newform invariants

comment:select newform

sage:traces = [25,0,-1,80,-51] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$31.2120103930$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 23)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	529.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.15026 q^{2} +9.55258 q^{3} -3.37638 q^{4} -17.5072 q^{5} -20.5405 q^{6} +3.15231 q^{7} +24.4622 q^{8} +64.2518 q^{9} +37.6451 q^{10} -12.8819 q^{11} -32.2531 q^{12} +2.45445 q^{13} -6.77829 q^{14} -167.239 q^{15} -25.5890 q^{16} -62.6503 q^{17} -138.158 q^{18} +39.6603 q^{19} +59.1111 q^{20} +30.1127 q^{21} +27.6994 q^{22} +233.677 q^{24} +181.504 q^{25} -5.27771 q^{26} +355.851 q^{27} -10.6434 q^{28} -187.506 q^{29} +359.608 q^{30} +3.14887 q^{31} -140.674 q^{32} -123.055 q^{33} +134.714 q^{34} -55.1883 q^{35} -216.938 q^{36} -132.244 q^{37} -85.2801 q^{38} +23.4463 q^{39} -428.265 q^{40} +54.1707 q^{41} -64.7502 q^{42} -235.739 q^{43} +43.4942 q^{44} -1124.87 q^{45} -128.295 q^{47} -244.441 q^{48} -333.063 q^{49} -390.280 q^{50} -598.472 q^{51} -8.28715 q^{52} -189.516 q^{53} -765.172 q^{54} +225.527 q^{55} +77.1124 q^{56} +378.859 q^{57} +403.186 q^{58} -503.522 q^{59} +564.664 q^{60} +48.0229 q^{61} -6.77088 q^{62} +202.542 q^{63} +507.199 q^{64} -42.9707 q^{65} +264.601 q^{66} +490.926 q^{67} +211.531 q^{68} +118.669 q^{70} -994.675 q^{71} +1571.74 q^{72} -235.311 q^{73} +284.358 q^{74} +1733.83 q^{75} -133.908 q^{76} -40.6077 q^{77} -50.4157 q^{78} -1338.36 q^{79} +447.993 q^{80} +1664.49 q^{81} -116.481 q^{82} -1067.95 q^{83} -101.672 q^{84} +1096.83 q^{85} +506.901 q^{86} -1791.16 q^{87} -315.119 q^{88} +1326.88 q^{89} +2418.77 q^{90} +7.73719 q^{91} +30.0798 q^{93} +275.867 q^{94} -694.344 q^{95} -1343.80 q^{96} +1126.82 q^{97} +716.172 q^{98} -827.685 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19}+ \cdots - 7317 q^{99}+O(q^{100}) $ 25 * q - q^3 + 80 * q^4 - 51 * q^5 + 86 * q^6 - 73 * q^7 + 3 * q^8 + 166 * q^9 - 139 * q^10 - 221 * q^11 - 191 * q^12 - 27 * q^13 - 372 * q^14 - 310 * q^15 + 152 * q^16 - 365 * q^17 - 538 * q^18 - 405 * q^19 - 578 * q^20 - 352 * q^21 - 155 * q^22 + 803 * q^24 + 90 * q^25 - 850 * q^26 + 368 * q^27 - 459 * q^28 + 175 * q^29 - 893 * q^30 + 287 * q^31 + 164 * q^32 - 1020 * q^33 - 335 * q^34 + 462 * q^35 - 1092 * q^36 - 471 * q^37 - 810 * q^38 - 822 * q^39 - 1405 * q^40 - 73 * q^41 - 556 * q^42 - 901 * q^43 - 2073 * q^44 - 1384 * q^45 + 1452 * q^47 - 4028 * q^48 - 1092 * q^49 + 364 * q^50 - 2214 * q^51 + 1287 * q^52 - 2071 * q^53 + 2052 * q^54 + 1006 * q^55 - 4879 * q^56 - 418 * q^57 + 2796 * q^58 - 2713 * q^59 - 2805 * q^60 - 1225 * q^61 - 2852 * q^62 - 4003 * q^63 + 217 * q^64 - 2030 * q^65 - 2933 * q^66 - 767 * q^67 - 4175 * q^68 + 4851 * q^70 - 1683 * q^71 - 5265 * q^72 + 2203 * q^73 - 3089 * q^74 + 2333 * q^75 - 5252 * q^76 + 2760 * q^77 - 692 * q^78 - 5425 * q^79 - 4689 * q^80 + 1929 * q^81 - 2725 * q^82 - 5425 * q^83 - 4317 * q^84 - 912 * q^85 - 4359 * q^86 - 4404 * q^87 - 2610 * q^88 - 4933 * q^89 - 2695 * q^90 - 3619 * q^91 + 6375 * q^93 - 5117 * q^94 - 1338 * q^95 + 20 * q^96 - 2085 * q^97 + 5951 * q^98 - 7317 * q^99

Coefficient data

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

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

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

$2$	−2.15026	−0.760232	−0.380116	−	0.924939i	$-0.624116\pi$
$2$	−2.15026	−0.760232	−0.380116	+	0.924939i	$0.624116\pi$
$3$	9.55258	1.83839	0.919197	−	0.393797i	$-0.128839\pi$
$3$	9.55258	1.83839	0.919197	+	0.393797i	$0.128839\pi$
$4$	−3.37638	−0.422047
$5$	−17.5072	−1.56590	−0.782948	−	0.622087i	$-0.786285\pi$
$5$	−17.5072	−1.56590	−0.782948	+	0.622087i	$0.786285\pi$
$6$	−20.5405	−1.39761
$7$	3.15231	0.170209	0.0851044	−	0.996372i	$-0.472878\pi$
$7$	3.15231	0.170209	0.0851044	+	0.996372i	$0.472878\pi$
$8$	24.4622	1.08109
$9$	64.2518	2.37970
$10$	37.6451	1.19044
$11$	−12.8819	−0.353094	−0.176547	−	0.984292i	$-0.556493\pi$
$11$	−12.8819	−0.353094	−0.176547	+	0.984292i	$0.556493\pi$
$12$	−32.2531	−0.775890
$13$	2.45445	0.0523648	0.0261824	−	0.999657i	$-0.491665\pi$
$13$	2.45445	0.0523648	0.0261824	+	0.999657i	$0.491665\pi$
$14$	−6.77829	−0.129398
$15$	−167.239	−2.87874
$16$	−25.5890	−0.399829
$17$	−62.6503	−0.893819	−0.446909	−	0.894579i	$-0.647475\pi$
$17$	−62.6503	−0.893819	−0.446909	+	0.894579i	$0.647475\pi$
$18$	−138.158	−1.80912
$19$	39.6603	0.478879	0.239440	−	0.970911i	$-0.423036\pi$
$19$	39.6603	0.478879	0.239440	+	0.970911i	$0.423036\pi$
$20$	59.1111	0.660882
$21$	30.1127	0.312911
$22$	27.6994	0.268434
$23$	0	0
$23$	0	0
$24$	233.677	1.98746
$25$	181.504	1.45203
$26$	−5.27771	−0.0398094
$27$	355.851	2.53643
$28$	−10.6434	−0.0718362
$29$	−187.506	−1.20065	−0.600327	−	0.799755i	$-0.704963\pi$
$29$	−187.506	−1.20065	−0.600327	+	0.799755i	$0.704963\pi$
$30$	359.608	2.18851
$31$	3.14887	0.0182436	0.00912182	−	0.999958i	$-0.497096\pi$
$31$	3.14887	0.0182436	0.00912182	+	0.999958i	$0.497096\pi$
$32$	−140.674	−0.777123
$33$	−123.055	−0.649127
$34$	134.714	0.679510
$35$	−55.1883	−0.266529
$36$	−216.938	−1.00434
$37$	−132.244	−0.587587	−0.293793	−	0.955869i	$-0.594918\pi$
$37$	−132.244	−0.587587	−0.293793	+	0.955869i	$0.594918\pi$
$38$	−85.2801	−0.364059
$39$	23.4463	0.0962671
$40$	−428.265	−1.69287
$41$	54.1707	0.206343	0.103171	−	0.994664i	$-0.467101\pi$
$41$	54.1707	0.206343	0.103171	+	0.994664i	$0.467101\pi$
$42$	−64.7502	−0.237885
$43$	−235.739	−0.836044	−0.418022	−	0.908437i	$-0.637276\pi$
$43$	−235.739	−0.836044	−0.418022	+	0.908437i	$0.637276\pi$
$44$	43.4942	0.149023
$45$	−1124.87	−3.72636
$46$	0	0
$47$	−128.295	−0.398164	−0.199082	−	0.979983i	$-0.563796\pi$
$47$	−128.295	−0.398164	−0.199082	+	0.979983i	$0.563796\pi$
$48$	−244.441	−0.735043
$49$	−333.063	−0.971029
$50$	−390.280	−1.10388
$51$	−598.472	−1.64319
$52$	−8.28715	−0.0221004
$53$	−189.516	−0.491171	−0.245585	−	0.969375i	$-0.578980\pi$
$53$	−189.516	−0.491171	−0.245585	+	0.969375i	$0.578980\pi$
$54$	−765.172	−1.92827
$55$	225.527	0.552909
$56$	77.1124	0.184010
$57$	378.859	0.880369
$58$	403.186	0.912775
$59$	−503.522	−1.11107	−0.555534	−	0.831494i	$-0.687486\pi$
$59$	−503.522	−1.11107	−0.555534	+	0.831494i	$0.687486\pi$
$60$	564.664	1.21496
$61$	48.0229	0.100798	0.0503992	−	0.998729i	$-0.483951\pi$
$61$	48.0229	0.100798	0.0503992	+	0.998729i	$0.483951\pi$
$62$	−6.77088	−0.0138694
$63$	202.542	0.405045
$64$	507.199	0.990623
$65$	−42.9707	−0.0819978
$66$	264.601	0.493487
$67$	490.926	0.895166	0.447583	−	0.894242i	$-0.352285\pi$
$67$	490.926	0.895166	0.447583	+	0.894242i	$0.352285\pi$
$68$	211.531	0.377234
$69$	0	0
$70$	118.669	0.202624
$71$	−994.675	−1.66262	−0.831312	−	0.555807i	$-0.812410\pi$
$71$	−994.675	−1.66262	−0.831312	+	0.555807i	$0.812410\pi$
$72$	1571.74	2.57266
$73$	−235.311	−0.377275	−0.188638	−	0.982047i	$-0.560407\pi$
$73$	−235.311	−0.377275	−0.188638	+	0.982047i	$0.560407\pi$
$74$	284.358	0.446702
$75$	1733.83	2.66940
$76$	−133.908	−0.202110
$77$	−40.6077	−0.0600998
$78$	−50.4157	−0.0731853
$79$	−1338.36	−1.90604	−0.953018	−	0.302914i	$-0.902041\pi$
$79$	−1338.36	−1.90604	−0.953018	+	0.302914i	$0.902041\pi$
$80$	447.993	0.626090
$81$	1664.49	2.28326
$82$	−116.481	−0.156868
$83$	−1067.95	−1.41232	−0.706161	−	0.708051i	$-0.749575\pi$
$83$	−1067.95	−1.41232	−0.706161	+	0.708051i	$0.749575\pi$
$84$	−101.672	−0.132063
$85$	1096.83	1.39963
$86$	506.901	0.635587
$87$	−1791.16	−2.20727
$88$	−315.119	−0.381725
$89$	1326.88	1.58033	0.790165	−	0.612894i	$-0.209995\pi$
$89$	1326.88	1.58033	0.790165	+	0.612894i	$0.209995\pi$
$90$	2418.77	2.83289
$91$	7.73719	0.00891294
$92$	0	0
$93$	30.0798	0.0335390
$94$	275.867	0.302697
$95$	−694.344	−0.749875
$96$	−1343.80	−1.42866
$97$	1126.82	1.17949	0.589746	−	0.807589i	$-0.299228\pi$
$97$	1126.82	1.17949	0.589746	+	0.807589i	$0.299228\pi$
$98$	716.172	0.738207
$99$	−827.685	−0.840257
$100$	−612.826	−0.612826
$101$	660.124	0.650344	0.325172	−	0.945655i	$-0.394578\pi$
$101$	660.124	0.650344	0.325172	+	0.945655i	$0.394578\pi$
$102$	1286.87	1.24921
$103$	−1071.59	−1.02512	−0.512560	−	0.858651i	$-0.671303\pi$
$103$	−1071.59	−1.02512	−0.512560	+	0.858651i	$0.671303\pi$
$104$	60.0412	0.0566108
$105$	−527.191	−0.489986
$106$	407.509	0.373404
$107$	703.100	0.635245	0.317622	−	0.948217i	$-0.397116\pi$
$107$	703.100	0.635245	0.317622	+	0.948217i	$0.397116\pi$
$108$	−1201.49	−1.07049
$109$	−1465.25	−1.28757	−0.643787	−	0.765205i	$-0.722638\pi$
$109$	−1465.25	−1.28757	−0.643787	+	0.765205i	$0.722638\pi$
$110$	−484.941	−0.420339
$111$	−1263.27	−1.08022
$112$	−80.6646	−0.0680543
$113$	−1302.54	−1.08436	−0.542180	−	0.840263i	$-0.682401\pi$
$113$	−1302.54	−1.08436	−0.542180	+	0.840263i	$0.682401\pi$
$114$	−814.645	−0.669285
$115$	0	0
$116$	633.091	0.506733
$117$	157.703	0.124612
$118$	1082.70	0.844669
$119$	−197.493	−0.152136
$120$	−4091.04	−3.11216
$121$	−1165.06	−0.875324
$122$	−103.262	−0.0766302
$123$	517.470	0.379339
$124$	−10.6318	−0.00769968
$125$	−989.225	−0.707832
$126$	−435.517	−0.307928
$127$	1947.63	1.36082	0.680409	−	0.732833i	$-0.261802\pi$
$127$	1947.63	1.36082	0.680409	+	0.732833i	$0.261802\pi$
$128$	34.7855	0.0240206
$129$	−2251.92	−1.53698
$130$	92.3981	0.0623373
$131$	1062.71	0.708775	0.354387	−	0.935099i	$-0.384689\pi$
$131$	1062.71	0.708775	0.354387	+	0.935099i	$0.384689\pi$
$132$	415.482	0.273962
$133$	125.022	0.0815095
$134$	−1055.62	−0.680534
$135$	−6229.97	−3.97178
$136$	−1532.56	−0.966295
$137$	−1054.06	−0.657331	−0.328665	−	0.944446i	$-0.606599\pi$
$137$	−1054.06	−0.657331	−0.328665	+	0.944446i	$0.606599\pi$
$138$	0	0
$139$	1091.53	0.666063	0.333032	−	0.942916i	$-0.391928\pi$
$139$	1091.53	0.666063	0.333032	+	0.942916i	$0.391928\pi$
$140$	186.337	0.112488
$141$	−1225.54	−0.731982
$142$	2138.81	1.26398
$143$	−31.6180	−0.0184897
$144$	−1644.14	−0.951470
$145$	3282.71	1.88010
$146$	505.980	0.286817
$147$	−3181.61	−1.78513
$148$	446.505	0.247990
$149$	−1619.85	−0.890626	−0.445313	−	0.895375i	$-0.646908\pi$
$149$	−1619.85	−0.890626	−0.445313	+	0.895375i	$0.646908\pi$
$150$	−3728.18	−2.02937
$151$	234.828	0.126556	0.0632782	−	0.997996i	$-0.479844\pi$
$151$	234.828	0.126556	0.0632782	+	0.997996i	$0.479844\pi$
$152$	970.179	0.517710
$153$	−4025.39	−2.12702
$154$	87.3172	0.0456898
$155$	−55.1280	−0.0285676
$156$	−79.1637	−0.0406293
$157$	2029.08	1.03145	0.515726	−	0.856753i	$-0.327522\pi$
$157$	2029.08	1.03145	0.515726	+	0.856753i	$0.327522\pi$
$158$	2877.81	1.44903
$159$	−1810.37	−0.902966
$160$	2462.82	1.21689
$161$	0	0
$162$	−3579.10	−1.73580
$163$	1638.54	0.787362	0.393681	−	0.919247i	$-0.371201\pi$
$163$	1638.54	0.787362	0.393681	+	0.919247i	$0.371201\pi$
$164$	−182.901	−0.0870863
$165$	2154.36	1.01646
$166$	2296.37	1.07369
$167$	1896.64	0.878842	0.439421	−	0.898281i	$-0.355184\pi$
$167$	1896.64	0.878842	0.439421	+	0.898281i	$0.355184\pi$
$168$	736.622	0.338284
$169$	−2190.98	−0.997258
$170$	−2358.48	−1.06404
$171$	2548.25	1.13959
$172$	795.945	0.352850
$173$	−3817.88	−1.67785	−0.838926	−	0.544246i	$-0.816816\pi$
$173$	−3817.88	−1.67785	−0.838926	+	0.544246i	$0.816816\pi$
$174$	3851.47	1.67804
$175$	572.156	0.247148
$176$	329.635	0.141177
$177$	−4809.93	−2.04258
$178$	−2853.15	−1.20142
$179$	−590.451	−0.246550	−0.123275	−	0.992373i	$-0.539340\pi$
$179$	−590.451	−0.246550	−0.123275	+	0.992373i	$0.539340\pi$
$180$	3797.99	1.57270
$181$	2531.37	1.03953	0.519765	−	0.854309i	$-0.326019\pi$
$181$	2531.37	1.03953	0.519765	+	0.854309i	$0.326019\pi$
$182$	−16.6370	−0.00677590
$183$	458.743	0.185307
$184$	0	0
$185$	2315.22	0.920100
$186$	−64.6794	−0.0254974
$187$	807.054	0.315602
$188$	433.171	0.168044
$189$	1121.75	0.431722
$190$	1493.02	0.570079
$191$	324.857	0.123067	0.0615336	−	0.998105i	$-0.480401\pi$
$191$	324.857	0.123067	0.0615336	+	0.998105i	$0.480401\pi$
$192$	4845.06	1.82116
$193$	2714.01	1.01222	0.506111	−	0.862468i	$-0.331082\pi$
$193$	2714.01	1.01222	0.506111	+	0.862468i	$0.331082\pi$
$194$	−2422.95	−0.896688
$195$	−410.481	−0.150744
$196$	1124.55	0.409820
$197$	−2683.66	−0.970572	−0.485286	−	0.874355i	$-0.661285\pi$
$197$	−2683.66	−0.970572	−0.485286	+	0.874355i	$0.661285\pi$
$198$	1779.74	0.638790
$199$	1104.09	0.393302	0.196651	−	0.980474i	$-0.436993\pi$
$199$	1104.09	0.393302	0.196651	+	0.980474i	$0.436993\pi$
$200$	4439.98	1.56977
$201$	4689.61	1.64567
$202$	−1419.44	−0.494412
$203$	−591.077	−0.204362
$204$	2020.67	0.693505
$205$	−948.380	−0.323111
$206$	2304.21	0.779329
$207$	0	0
$208$	−62.8070	−0.0209369
$209$	−510.900	−0.169090
$210$	1133.60	0.372503
$211$	−3023.60	−0.986507	−0.493254	−	0.869886i	$-0.664193\pi$
$211$	−3023.60	−0.986507	−0.493254	+	0.869886i	$0.664193\pi$
$212$	639.879	0.207297
$213$	−9501.72	−3.05656
$214$	−1511.85	−0.482933
$215$	4127.14	1.30916
$216$	8704.88	2.74209
$217$	9.92621	0.00310523
$218$	3150.67	0.978854
$219$	−2247.83	−0.693581
$220$	−761.463	−0.233354
$221$	−153.772	−0.0468046
$222$	2716.35	0.821215
$223$	−1320.89	−0.396652	−0.198326	−	0.980136i	$-0.563550\pi$
$223$	−1320.89	−0.396652	−0.198326	+	0.980136i	$0.563550\pi$
$224$	−443.449	−0.132273
$225$	11661.9	3.45539
$226$	2800.80	0.824365
$227$	−1614.53	−0.472071	−0.236035	−	0.971744i	$-0.575848\pi$
$227$	−1614.53	−0.472071	−0.236035	+	0.971744i	$0.575848\pi$
$228$	−1279.17	−0.371558
$229$	3389.10	0.977983	0.488991	−	0.872289i	$-0.337365\pi$
$229$	3389.10	0.977983	0.488991	+	0.872289i	$0.337365\pi$
$230$	0	0
$231$	−387.909	−0.110487
$232$	−4586.80	−1.29801
$233$	−5564.15	−1.56446	−0.782231	−	0.622989i	$-0.785918\pi$
$233$	−5564.15	−1.56446	−0.782231	+	0.622989i	$0.785918\pi$
$234$	−339.102	−0.0947342
$235$	2246.09	0.623483
$236$	1700.08	0.468923
$237$	−12784.8	−3.50405
$238$	424.662	0.115659
$239$	−199.085	−0.0538819	−0.0269409	−	0.999637i	$-0.508577\pi$
$239$	−199.085	−0.0538819	−0.0269409	+	0.999637i	$0.508577\pi$
$240$	4279.49	1.15100
$241$	4244.76	1.13456	0.567280	−	0.823525i	$-0.307996\pi$
$241$	4244.76	1.13456	0.567280	+	0.823525i	$0.307996\pi$
$242$	2505.18	0.665450
$243$	6292.24	1.66110
$244$	−162.144	−0.0425417
$245$	5831.02	1.52053
$246$	−1112.70	−0.288386
$247$	97.3443	0.0250764
$248$	77.0281	0.0197229
$249$	−10201.7	−2.59641
$250$	2127.09	0.538116
$251$	5259.08	1.32251	0.661256	−	0.750160i	$-0.270024\pi$
$251$	5259.08	1.32251	0.661256	+	0.750160i	$0.270024\pi$
$252$	−683.857	−0.170948
$253$	0	0
$254$	−4187.90	−1.03454
$255$	10477.6	2.57307
$256$	−4132.39	−1.00888
$257$	135.768	0.0329531	0.0164766	−	0.999864i	$-0.494755\pi$
$257$	135.768	0.0329531	0.0164766	+	0.999864i	$0.494755\pi$
$258$	4842.21	1.16846
$259$	−416.873	−0.100012
$260$	145.085	0.0346069
$261$	−12047.6	−2.85719
$262$	−2285.11	−0.538833
$263$	−437.170	−0.102498	−0.0512492	−	0.998686i	$-0.516320\pi$
$263$	−437.170	−0.102498	−0.0512492	+	0.998686i	$0.516320\pi$
$264$	−3010.20	−0.701762
$265$	3317.91	0.769123
$266$	−268.829	−0.0619661
$267$	12675.2	2.90527
$268$	−1657.55	−0.377803
$269$	2332.26	0.528626	0.264313	−	0.964437i	$-0.414855\pi$
$269$	2332.26	0.528626	0.264313	+	0.964437i	$0.414855\pi$
$270$	13396.1	3.01947
$271$	1128.81	0.253027	0.126514	−	0.991965i	$-0.459621\pi$
$271$	1128.81	0.253027	0.126514	+	0.991965i	$0.459621\pi$
$272$	1603.16	0.357374
$273$	73.9101	0.0163855
$274$	2266.50	0.499724
$275$	−2338.11	−0.512704
$276$	0	0
$277$	1526.61	0.331137	0.165568	−	0.986198i	$-0.447054\pi$
$277$	1526.61	0.331137	0.165568	+	0.986198i	$0.447054\pi$
$278$	−2347.08	−0.506362
$279$	202.320	0.0434143
$280$	−1350.03	−0.288141
$281$	8922.62	1.89423	0.947115	−	0.320894i	$-0.103983\pi$
$281$	8922.62	1.89423	0.947115	+	0.320894i	$0.103983\pi$
$282$	2635.24	0.556476
$283$	6062.16	1.27335	0.636675	−	0.771132i	$-0.280309\pi$
$283$	6062.16	1.27335	0.636675	+	0.771132i	$0.280309\pi$
$284$	3358.40	0.701706
$285$	−6632.77	−1.37857
$286$	67.9869	0.0140565
$287$	170.763	0.0351213
$288$	−9038.58	−1.84932
$289$	−987.944	−0.201088
$290$	−7058.68	−1.42931
$291$	10764.0	2.16837
$292$	794.500	0.159228
$293$	−4042.56	−0.806038	−0.403019	−	0.915192i	$-0.632039\pi$
$293$	−4042.56	−0.806038	−0.403019	+	0.915192i	$0.632039\pi$
$294$	6841.29	1.35712
$295$	8815.28	1.73982
$296$	−3234.97	−0.635232
$297$	−4584.03	−0.895597
$298$	3483.10	0.677082
$299$	0	0
$300$	−5854.07	−1.12662
$301$	−743.123	−0.142302
$302$	−504.941	−0.0962122
$303$	6305.89	1.19559
$304$	−1014.87	−0.191470
$305$	−840.749	−0.157840
$306$	8655.64	1.61703
$307$	8641.34	1.60647	0.803236	−	0.595660i	$-0.203110\pi$
$307$	8641.34	1.60647	0.803236	+	0.595660i	$0.203110\pi$
$308$	137.107	0.0253650
$309$	−10236.5	−1.88457
$310$	118.540	0.0217180
$311$	2199.14	0.400970	0.200485	−	0.979697i	$-0.435748\pi$
$311$	2199.14	0.400970	0.200485	+	0.979697i	$0.435748\pi$
$312$	573.548	0.104073
$313$	−2165.82	−0.391117	−0.195558	−	0.980692i	$-0.562652\pi$
$313$	−2165.82	−0.391117	−0.195558	+	0.980692i	$0.562652\pi$
$314$	−4363.05	−0.784143
$315$	−3545.95	−0.634259
$316$	4518.80	0.804438
$317$	−4560.17	−0.807964	−0.403982	−	0.914767i	$-0.632374\pi$
$317$	−4560.17	−0.807964	−0.403982	+	0.914767i	$0.632374\pi$
$318$	3892.77	0.686464
$319$	2415.43	0.423944
$320$	−8879.65	−1.55121
$321$	6716.42	1.16783
$322$	0	0
$323$	−2484.73	−0.428031
$324$	−5619.96	−0.963642
$325$	445.492	0.0760352
$326$	−3523.28	−0.598578
$327$	−13996.9	−2.36707
$328$	1325.13	0.223074
$329$	−404.425	−0.0677710
$330$	−4632.44	−0.772749
$331$	−4702.98	−0.780965	−0.390482	−	0.920610i	$-0.627692\pi$
$331$	−4702.98	−0.780965	−0.390482	+	0.920610i	$0.627692\pi$
$332$	3605.81	0.596067
$333$	−8496.89	−1.39828
$334$	−4078.27	−0.668123
$335$	−8594.76	−1.40174
$336$	−770.555	−0.125111
$337$	4777.48	0.772243	0.386122	−	0.922448i	$-0.373814\pi$
$337$	4777.48	0.772243	0.386122	+	0.922448i	$0.373814\pi$
$338$	4711.17	0.758147
$339$	−12442.6	−1.99348
$340$	−3703.33	−0.590709
$341$	−40.5634	−0.00644173
$342$	−5479.40	−0.866350
$343$	−2131.16	−0.335487
$344$	−5766.69	−0.903835
$345$	0	0
$346$	8209.44	1.27556
$347$	2049.09	0.317006	0.158503	−	0.987358i	$-0.449333\pi$
$347$	2049.09	0.317006	0.158503	+	0.987358i	$0.449333\pi$
$348$	6047.65	0.931575
$349$	−7746.21	−1.18809	−0.594047	−	0.804430i	$-0.702471\pi$
$349$	−7746.21	−1.18809	−0.594047	+	0.804430i	$0.702471\pi$
$350$	−1230.29	−0.187890
$351$	873.417	0.132819
$352$	1812.15	0.274398
$353$	7598.47	1.14568	0.572841	−	0.819666i	$-0.305841\pi$
$353$	7598.47	1.14568	0.572841	+	0.819666i	$0.305841\pi$
$354$	10342.6	1.55283
$355$	17414.0	2.60349
$356$	−4480.06	−0.666974
$357$	−1886.57	−0.279686
$358$	1269.62	0.187435
$359$	3897.16	0.572936	0.286468	−	0.958090i	$-0.407519\pi$
$359$	3897.16	0.572936	0.286468	+	0.958090i	$0.407519\pi$
$360$	−27516.8	−4.02851
$361$	−5286.06	−0.770675
$362$	−5443.10	−0.790284
$363$	−11129.3	−1.60919
$364$	−26.1237	−0.00376168
$365$	4119.65	0.590774
$366$	−986.417	−0.140877
$367$	−1565.60	−0.222680	−0.111340	−	0.993782i	$-0.535514\pi$
$367$	−1565.60	−0.222680	−0.111340	+	0.993782i	$0.535514\pi$
$368$	0	0
$369$	3480.56	0.491032
$370$	−4978.33	−0.699489
$371$	−597.414	−0.0836016
$372$	−101.561	−0.0141551
$373$	−12141.5	−1.68542	−0.842712	−	0.538364i	$-0.819042\pi$
$373$	−12141.5	−1.68542	−0.842712	+	0.538364i	$0.819042\pi$
$374$	−1735.38	−0.239931
$375$	−9449.65	−1.30127
$376$	−3138.37	−0.430449
$377$	−460.223	−0.0628719
$378$	−2412.06	−0.328209
$379$	13545.2	1.83580	0.917901	−	0.396810i	$-0.129883\pi$
$379$	13545.2	1.83580	0.917901	+	0.396810i	$0.129883\pi$
$380$	2344.37	0.316483
$381$	18604.8	2.50172
$382$	−698.528	−0.0935596
$383$	−5087.87	−0.678794	−0.339397	−	0.940643i	$-0.610223\pi$
$383$	−5087.87	−0.678794	−0.339397	+	0.940643i	$0.610223\pi$
$384$	332.291	0.0441593
$385$	710.930	0.0941100
$386$	−5835.84	−0.769524
$387$	−15146.7	−1.98953
$388$	−3804.56	−0.497802
$389$	−1620.42	−0.211204	−0.105602	−	0.994408i	$-0.533677\pi$
$389$	−1620.42	−0.211204	−0.105602	+	0.994408i	$0.533677\pi$
$390$	882.640	0.114601
$391$	0	0
$392$	−8147.45	−1.04977
$393$	10151.6	1.30301
$394$	5770.56	0.737860
$395$	23430.9	2.98465
$396$	2794.58	0.354628
$397$	296.575	0.0374929	0.0187465	−	0.999824i	$-0.494032\pi$
$397$	296.575	0.0374929	0.0187465	+	0.999824i	$0.494032\pi$
$398$	−2374.09	−0.299000
$399$	1194.28	0.149847
$400$	−4644.50	−0.580563
$401$	−6313.70	−0.786262	−0.393131	−	0.919482i	$-0.628608\pi$
$401$	−6313.70	−0.786262	−0.393131	+	0.919482i	$0.628608\pi$
$402$	−10083.9	−1.25109
$403$	7.72873	0.000955324 0
$404$	−2228.83	−0.274476
$405$	−29140.7	−3.57534
$406$	1270.97	0.155362
$407$	1703.55	0.207474
$408$	−14639.9	−1.77643
$409$	−3596.16	−0.434765	−0.217382	−	0.976087i	$-0.569752\pi$
$409$	−3596.16	−0.434765	−0.217382	+	0.976087i	$0.569752\pi$
$410$	2039.26	0.245639
$411$	−10069.0	−1.20843
$412$	3618.11	0.432649
$413$	−1587.26	−0.189113
$414$	0	0
$415$	18696.9	2.21155
$416$	−345.278	−0.0406939
$417$	10427.0	1.22449
$418$	1098.57	0.128547
$419$	2762.70	0.322117	0.161058	−	0.986945i	$-0.448509\pi$
$419$	2762.70	0.322117	0.161058	+	0.986945i	$0.448509\pi$
$420$	1780.00	0.206797
$421$	11993.9	1.38848	0.694238	−	0.719746i	$-0.255742\pi$
$421$	11993.9	1.38848	0.694238	+	0.719746i	$0.255742\pi$
$422$	6501.52	0.749974
$423$	−8243.16	−0.947509
$424$	−4635.98	−0.530998
$425$	−11371.3	−1.29785
$426$	20431.2	2.32369
$427$	151.383	0.0171568
$428$	−2373.93	−0.268104
$429$	−302.033	−0.0339914
$430$	−8874.44	−0.995264
$431$	9502.90	1.06204	0.531019	−	0.847360i	$-0.321809\pi$
$431$	9502.90	1.06204	0.531019	+	0.847360i	$0.321809\pi$
$432$	−9105.87	−1.01414
$433$	−15343.5	−1.70292	−0.851459	−	0.524421i	$-0.824282\pi$
$433$	−15343.5	−1.70292	−0.851459	+	0.524421i	$0.824282\pi$
$434$	−21.3439	−0.00236069
$435$	31358.3	3.45636
$436$	4947.24	0.543417
$437$	0	0
$438$	4833.42	0.527282
$439$	8801.88	0.956926	0.478463	−	0.878108i	$-0.341194\pi$
$439$	8801.88	0.956926	0.478463	+	0.878108i	$0.341194\pi$
$440$	5516.87	0.597742
$441$	−21399.9	−2.31075
$442$	330.650	0.0355824
$443$	−3549.81	−0.380715	−0.190358	−	0.981715i	$-0.560965\pi$
$443$	−3549.81	−0.380715	−0.190358	+	0.981715i	$0.560965\pi$
$444$	4265.27	0.455903
$445$	−23230.1	−2.47463
$446$	2840.26	0.301547
$447$	−15473.7	−1.63732
$448$	1598.85	0.168613
$449$	8548.19	0.898472	0.449236	−	0.893413i	$-0.351696\pi$
$449$	8548.19	0.898472	0.449236	+	0.893413i	$0.351696\pi$
$450$	−25076.2	−2.62690
$451$	−697.821	−0.0728584
$452$	4397.87	0.457651
$453$	2243.21	0.232661
$454$	3471.66	0.358883
$455$	−135.457	−0.0139567
$456$	9267.71	0.951755
$457$	6103.64	0.624762	0.312381	−	0.949957i	$-0.398873\pi$
$457$	6103.64	0.624762	0.312381	+	0.949957i	$0.398873\pi$
$458$	−7287.45	−0.743494
$459$	−22294.1	−2.26711
$460$	0	0
$461$	−3590.11	−0.362707	−0.181354	−	0.983418i	$-0.558048\pi$
$461$	−3590.11	−0.362707	−0.181354	+	0.983418i	$0.558048\pi$
$462$	834.105	0.0839958
$463$	−6055.70	−0.607845	−0.303922	−	0.952697i	$-0.598296\pi$
$463$	−6055.70	−0.607845	−0.303922	+	0.952697i	$0.598296\pi$
$464$	4798.09	0.480055
$465$	−526.614	−0.0525186
$466$	11964.4	1.18935
$467$	−8601.84	−0.852346	−0.426173	−	0.904642i	$-0.640139\pi$
$467$	−8601.84	−0.852346	−0.426173	+	0.904642i	$0.640139\pi$
$468$	−532.464	−0.0525923
$469$	1547.55	0.152365
$470$	−4829.67	−0.473992
$471$	19382.9	1.89622
$472$	−12317.2	−1.20116
$473$	3036.77	0.295202
$474$	27490.6	2.66389
$475$	7198.50	0.695347
$476$	666.812	0.0642085
$477$	−12176.8	−1.16884
$478$	428.085	0.0409627
$479$	7110.53	0.678264	0.339132	−	0.940739i	$-0.389867\pi$
$479$	7110.53	0.678264	0.339132	+	0.940739i	$0.389867\pi$
$480$	23526.3	2.23713
$481$	−324.585	−0.0307688
$482$	−9127.34	−0.862529
$483$	0	0
$484$	3933.67	0.369428
$485$	−19727.4	−1.84696
$486$	−13530.0	−1.26282
$487$	−4560.49	−0.424344	−0.212172	−	0.977232i	$-0.568054\pi$
$487$	−4560.49	−0.424344	−0.212172	+	0.977232i	$0.568054\pi$
$488$	1174.75	0.108972
$489$	15652.2	1.44748
$490$	−12538.2	−1.15596
$491$	−10169.0	−0.934665	−0.467333	−	0.884082i	$-0.654785\pi$
$491$	−10169.0	−0.934665	−0.467333	+	0.884082i	$0.654785\pi$
$492$	−1747.18	−0.160099
$493$	11747.3	1.07317
$494$	−209.316	−0.0190639
$495$	14490.5	1.31576
$496$	−80.5764	−0.00729433
$497$	−3135.53	−0.282993
$498$	21936.3	1.97387
$499$	5785.66	0.519042	0.259521	−	0.965738i	$-0.416435\pi$
$499$	5785.66	0.519042	0.259521	+	0.965738i	$0.416435\pi$
$500$	3340.00	0.298739
$501$	18117.8	1.61566
$502$	−11308.4	−1.00542
$503$	−16030.4	−1.42099	−0.710496	−	0.703701i	$-0.751529\pi$
$503$	−16030.4	−1.42099	−0.710496	+	0.703701i	$0.751529\pi$
$504$	4954.61	0.437889
$505$	−11557.0	−1.01837
$506$	0	0
$507$	−20929.5	−1.83335
$508$	−6575.92	−0.574330
$509$	−5460.20	−0.475479	−0.237740	−	0.971329i	$-0.576406\pi$
$509$	−5460.20	−0.475479	−0.237740	+	0.971329i	$0.576406\pi$
$510$	−22529.6	−1.95613
$511$	−741.774	−0.0642156
$512$	8607.43	0.742965
$513$	14113.2	1.21464
$514$	−291.936	−0.0250520
$515$	18760.7	1.60523
$516$	7603.33	0.648678
$517$	1652.68	0.140589
$518$	896.386	0.0760327
$519$	−36470.6	−3.08455
$520$	−1051.16	−0.0886466
$521$	−18037.2	−1.51675	−0.758374	−	0.651820i	$-0.774006\pi$
$521$	−18037.2	−1.51675	−0.758374	+	0.651820i	$0.774006\pi$
$522$	25905.4	2.17213
$523$	15736.6	1.31571	0.657853	−	0.753147i	$-0.271465\pi$
$523$	15736.6	1.31571	0.657853	+	0.753147i	$0.271465\pi$
$524$	−3588.12	−0.299137
$525$	5465.57	0.454356
$526$	940.029	0.0779225
$527$	−197.277	−0.0163065
$528$	3148.87	0.259539
$529$	0	0
$530$	−7134.37	−0.584712
$531$	−32352.2	−2.64400
$532$	−422.121	−0.0344009
$533$	132.959	0.0108051
$534$	−27254.9	−2.20868
$535$	−12309.3	−0.994727
$536$	12009.1	0.967752
$537$	−5640.33	−0.453255
$538$	−5014.97	−0.401879
$539$	4290.48	0.342865
$540$	21034.7	1.67628
$541$	15101.6	1.20013	0.600064	−	0.799952i	$-0.295142\pi$
$541$	15101.6	1.20013	0.600064	+	0.799952i	$0.295142\pi$
$542$	−2427.24	−0.192359
$543$	24181.1	1.91107
$544$	8813.29	0.694608
$545$	25652.5	2.01621
$546$	−158.926	−0.0124568
$547$	13944.7	1.09000	0.545002	−	0.838435i	$-0.316529\pi$
$547$	13944.7	1.09000	0.545002	+	0.838435i	$0.316529\pi$
$548$	3558.90	0.277425
$549$	3085.56	0.239870
$550$	5027.55	0.389774
$551$	−7436.54	−0.574968
$552$	0	0
$553$	−4218.92	−0.324424
$554$	−3282.60	−0.251741
$555$	22116.3	1.69151
$556$	−3685.44	−0.281110
$557$	18183.2	1.38321	0.691604	−	0.722277i	$-0.256904\pi$
$557$	18183.2	1.38321	0.691604	+	0.722277i	$0.256904\pi$
$558$	−435.041	−0.0330050
$559$	−578.610	−0.0437792
$560$	1412.21	0.106566
$561$	7709.45	0.580202
$562$	−19186.0	−1.44005
$563$	932.071	0.0697728	0.0348864	−	0.999391i	$-0.488893\pi$
$563$	932.071	0.0697728	0.0348864	+	0.999391i	$0.488893\pi$
$564$	4137.90	0.308931
$565$	22803.9	1.69799
$566$	−13035.2	−0.968041
$567$	5247.00	0.388630
$568$	−24331.9	−1.79744
$569$	1911.06	0.140801	0.0704003	−	0.997519i	$-0.477572\pi$
$569$	1911.06	0.140801	0.0704003	+	0.997519i	$0.477572\pi$
$570$	14262.2	1.04803
$571$	9541.35	0.699287	0.349644	−	0.936883i	$-0.386303\pi$
$571$	9541.35	0.699287	0.349644	+	0.936883i	$0.386303\pi$
$572$	106.754	0.00780353
$573$	3103.22	0.226246
$574$	−367.185	−0.0267003
$575$	0	0
$576$	32588.4	2.35738
$577$	16377.5	1.18164	0.590819	−	0.806804i	$-0.298805\pi$
$577$	16377.5	1.18164	0.590819	+	0.806804i	$0.298805\pi$
$578$	2124.34	0.152873
$579$	25925.8	1.86087
$580$	−11083.7	−0.793491
$581$	−3366.51	−0.240390
$582$	−23145.4	−1.64847
$583$	2441.33	0.173430
$584$	−5756.22	−0.407867
$585$	−2760.94	−0.195130
$586$	8692.57	0.612776
$587$	−21713.5	−1.52677	−0.763385	−	0.645944i	$-0.776464\pi$
$587$	−21713.5	−1.52677	−0.763385	+	0.645944i	$0.776464\pi$
$588$	10742.3	0.753412
$589$	124.885	0.00873650
$590$	−18955.2	−1.32266
$591$	−25635.9	−1.78430
$592$	3383.98	0.234934
$593$	−2845.74	−0.197067	−0.0985333	−	0.995134i	$-0.531415\pi$
$593$	−2845.74	−0.197067	−0.0985333	+	0.995134i	$0.531415\pi$
$594$	9856.86	0.680862
$595$	3457.56	0.238229
$596$	5469.23	0.375886
$597$	10546.9	0.723044
$598$	0	0
$599$	−17924.9	−1.22269	−0.611344	−	0.791365i	$-0.709371\pi$
$599$	−17924.9	−1.22269	−0.611344	+	0.791365i	$0.709371\pi$
$600$	42413.2	2.88586
$601$	−13096.8	−0.888902	−0.444451	−	0.895803i	$-0.646601\pi$
$601$	−13096.8	−0.888902	−0.444451	+	0.895803i	$0.646601\pi$
$602$	1597.91	0.108183
$603$	31542.9	2.13022
$604$	−792.867	−0.0534128
$605$	20396.9	1.37067
$606$	−13559.3	−0.908925
$607$	−9181.77	−0.613965	−0.306982	−	0.951715i	$-0.599319\pi$
$607$	−9181.77	−0.613965	−0.306982	+	0.951715i	$0.599319\pi$
$608$	−5579.19	−0.372148
$609$	−5646.31	−0.375698
$610$	1807.83	0.119995
$611$	−314.893	−0.0208497
$612$	13591.2	0.897702
$613$	−10987.3	−0.723939	−0.361969	−	0.932190i	$-0.617895\pi$
$613$	−10987.3	−0.723939	−0.361969	+	0.932190i	$0.617895\pi$
$614$	−18581.1	−1.22129
$615$	−9059.48	−0.594005
$616$	−993.354	−0.0649730
$617$	−20870.9	−1.36180	−0.680900	−	0.732376i	$-0.738411\pi$
$617$	−20870.9	−1.36180	−0.680900	+	0.732376i	$0.738411\pi$
$618$	22011.1	1.43271
$619$	5747.50	0.373201	0.186601	−	0.982436i	$-0.440253\pi$
$619$	5747.50	0.373201	0.186601	+	0.982436i	$0.440253\pi$
$620$	186.133	0.0120569
$621$	0	0
$622$	−4728.72	−0.304830
$623$	4182.75	0.268986
$624$	−599.969	−0.0384903
$625$	−5369.36	−0.343639
$626$	4657.08	0.297339
$627$	−4880.42	−0.310853
$628$	−6850.94	−0.435322
$629$	8285.10	0.525196
$630$	7624.71	0.482184
$631$	7882.69	0.497314	0.248657	−	0.968592i	$-0.420011\pi$
$631$	7882.69	0.497314	0.248657	+	0.968592i	$0.420011\pi$
$632$	−32739.1	−2.06059
$633$	−28883.2	−1.81359
$634$	9805.55	0.614240
$635$	−34097.6	−2.13090
$636$	6112.49	0.381095
$637$	−817.486	−0.0508477
$638$	−5193.80	−0.322296
$639$	−63909.7	−3.95654
$640$	−608.998	−0.0376137
$641$	−15202.6	−0.936764	−0.468382	−	0.883526i	$-0.655163\pi$
$641$	−15202.6	−0.936764	−0.468382	+	0.883526i	$0.655163\pi$
$642$	−14442.0	−0.887822
$643$	−5844.75	−0.358468	−0.179234	−	0.983807i	$-0.557362\pi$
$643$	−5844.75	−0.358468	−0.179234	+	0.983807i	$0.557362\pi$
$644$	0	0
$645$	39424.9	2.40675
$646$	5342.82	0.325403
$647$	−21668.0	−1.31662	−0.658312	−	0.752745i	$-0.728729\pi$
$647$	−21668.0	−1.31662	−0.658312	+	0.752745i	$0.728729\pi$
$648$	40717.1	2.46840
$649$	6486.32	0.392312
$650$	−957.923	−0.0578044
$651$	94.8209	0.00570864
$652$	−5532.32	−0.332304
$653$	15985.0	0.957947	0.478974	−	0.877829i	$-0.341009\pi$
$653$	15985.0	0.957947	0.478974	+	0.877829i	$0.341009\pi$
$654$	30097.0	1.79952
$655$	−18605.1	−1.10987
$656$	−1386.18	−0.0825016
$657$	−15119.2	−0.897800
$658$	869.618	0.0515217
$659$	−22009.7	−1.30103	−0.650514	−	0.759495i	$-0.725446\pi$
$659$	−22009.7	−1.30103	−0.650514	+	0.759495i	$0.725446\pi$
$660$	−7273.94	−0.428996
$661$	−24770.7	−1.45759	−0.728795	−	0.684732i	$-0.759919\pi$
$661$	−24770.7	−1.45759	−0.728795	+	0.684732i	$0.759919\pi$
$662$	10112.6	0.593714
$663$	−1468.92	−0.0860453
$664$	−26124.4	−1.52684
$665$	−2188.79	−0.127635
$666$	18270.5	1.06302
$667$	0	0
$668$	−6403.78	−0.370913
$669$	−12617.9	−0.729203
$670$	18481.0	1.06565
$671$	−618.626	−0.0355914
$672$	−4236.09	−0.243170
$673$	−33896.7	−1.94149	−0.970745	−	0.240114i	$-0.922815\pi$
$673$	−33896.7	−1.94149	−0.970745	+	0.240114i	$0.922815\pi$
$674$	−10272.8	−0.587084
$675$	64588.2	3.68297
$676$	7397.57	0.420890
$677$	−28891.6	−1.64017	−0.820084	−	0.572243i	$-0.806073\pi$
$677$	−28891.6	−1.64017	−0.820084	+	0.572243i	$0.806073\pi$
$678$	26754.9	1.51551
$679$	3552.07	0.200760
$680$	26830.9	1.51312
$681$	−15422.9	−0.867852
$682$	87.2218	0.00489721
$683$	27504.0	1.54087	0.770433	−	0.637521i	$-0.220040\pi$
$683$	27504.0	1.54087	0.770433	+	0.637521i	$0.220040\pi$
$684$	−8603.85	−0.480960
$685$	18453.7	1.02931
$686$	4582.55	0.255048
$687$	32374.6	1.79792
$688$	6032.34	0.334274
$689$	−465.158	−0.0257200
$690$	0	0
$691$	−640.983	−0.0352882	−0.0176441	−	0.999844i	$-0.505617\pi$
$691$	−640.983	−0.0352882	−0.0176441	+	0.999844i	$0.505617\pi$
$692$	12890.6	0.708133
$693$	−2609.12	−0.143019
$694$	−4406.09	−0.240998
$695$	−19109.8	−1.04299
$696$	−43815.8	−2.38625
$697$	−3393.81	−0.184433
$698$	16656.4	0.903228
$699$	−53152.0	−2.87610
$700$	−1931.82	−0.104308
$701$	28422.6	1.53140	0.765698	−	0.643200i	$-0.222394\pi$
$701$	28422.6	1.53140	0.765698	+	0.643200i	$0.222394\pi$
$702$	−1878.08	−0.100973
$703$	−5244.83	−0.281383
$704$	−6533.68	−0.349783
$705$	21455.9	1.14621
$706$	−16338.7	−0.870984
$707$	2080.92	0.110694
$708$	16240.2	0.862066
$709$	3543.56	0.187703	0.0938513	−	0.995586i	$-0.470082\pi$
$709$	3543.56	0.187703	0.0938513	+	0.995586i	$0.470082\pi$
$710$	−37444.7	−1.97926
$711$	−85991.8	−4.53579
$712$	32458.5	1.70847
$713$	0	0
$714$	4056.62	0.212626
$715$	553.543	0.0289529
$716$	1993.59	0.104056
$717$	−1901.78	−0.0990561
$718$	−8379.90	−0.435564
$719$	6201.77	0.321679	0.160839	−	0.986981i	$-0.448580\pi$
$719$	6201.77	0.321679	0.160839	+	0.986981i	$0.448580\pi$
$720$	28784.4	1.48990
$721$	−3378.00	−0.174484
$722$	11366.4	0.585891
$723$	40548.4	2.08577
$724$	−8546.85	−0.438731
$725$	−34033.0	−1.74338
$726$	23930.9	1.22336
$727$	23846.5	1.21653	0.608266	−	0.793733i	$-0.291865\pi$
$727$	23846.5	1.21653	0.608266	+	0.793733i	$0.291865\pi$
$728$	189.269	0.00963566
$729$	15165.8	0.770503
$730$	−8858.32	−0.449125
$731$	14769.1	0.747272
$732$	−1548.89	−0.0782085
$733$	−2280.09	−0.114894	−0.0574469	−	0.998349i	$-0.518296\pi$
$733$	−2280.09	−0.114894	−0.0574469	+	0.998349i	$0.518296\pi$
$734$	3366.45	0.169289
$735$	55701.2	2.79534
$736$	0	0
$737$	−6324.06	−0.316078
$738$	−7484.12	−0.373299
$739$	27207.7	1.35433	0.677166	−	0.735830i	$-0.263208\pi$
$739$	27207.7	1.35433	0.677166	+	0.735830i	$0.263208\pi$
$740$	−7817.07	−0.388326
$741$	929.889	0.0461003
$742$	1284.60	0.0635566
$743$	−16617.5	−0.820509	−0.410254	−	0.911971i	$-0.634560\pi$
$743$	−16617.5	−0.820509	−0.410254	+	0.911971i	$0.634560\pi$
$744$	735.817	0.0362586
$745$	28359.1	1.39463
$746$	26107.4	1.28131
$747$	−68617.7	−3.36090
$748$	−2724.92	−0.133199
$749$	2216.39	0.108124
$750$	20319.2	0.989271
$751$	−18065.2	−0.877774	−0.438887	−	0.898542i	$-0.644627\pi$
$751$	−18065.2	−0.877774	−0.438887	+	0.898542i	$0.644627\pi$
$752$	3282.94	0.159197
$753$	50237.8	2.43130
$754$	989.600	0.0477972
$755$	−4111.19	−0.198174
$756$	−3787.46	−0.182207
$757$	−7974.14	−0.382860	−0.191430	−	0.981506i	$-0.561312\pi$
$757$	−7974.14	−0.382860	−0.191430	+	0.981506i	$0.561312\pi$
$758$	−29125.6	−1.39563
$759$	0	0
$760$	−16985.2	−0.810679
$761$	−12348.8	−0.588231	−0.294115	−	0.955770i	$-0.595025\pi$
$761$	−12348.8	−0.588231	−0.294115	+	0.955770i	$0.595025\pi$
$762$	−40005.3	−1.90189
$763$	−4618.92	−0.219156
$764$	−1096.84	−0.0519402
$765$	70473.5	3.33069
$766$	10940.2	0.516041
$767$	−1235.87	−0.0581808
$768$	−39475.0	−1.85473
$769$	−58.1546	−0.00272706	−0.00136353	−	0.999999i	$-0.500434\pi$
$769$	−58.1546	−0.00272706	−0.00136353	+	0.999999i	$0.500434\pi$
$770$	−1528.68	−0.0715454
$771$	1296.93	0.0605809
$772$	−9163.54	−0.427206
$773$	7820.85	0.363902	0.181951	−	0.983308i	$-0.441759\pi$
$773$	7820.85	0.363902	0.181951	+	0.983308i	$0.441759\pi$
$774$	32569.3	1.51250
$775$	571.531	0.0264903
$776$	27564.4	1.27513
$777$	−3982.21	−0.183862
$778$	3484.32	0.160564
$779$	2148.43	0.0988132
$780$	1385.94	0.0636212
$781$	12813.3	0.587063
$782$	0	0
$783$	−66724.0	−3.04537
$784$	8522.76	0.388245
$785$	−35523.6	−1.61515
$786$	−21828.7	−0.990588
$787$	−8623.14	−0.390574	−0.195287	−	0.980746i	$-0.562564\pi$
$787$	−8623.14	−0.390574	−0.195287	+	0.980746i	$0.562564\pi$
$788$	9061.05	0.409628
$789$	−4176.10	−0.188432
$790$	−50382.6	−2.26903
$791$	−4106.01	−0.184568
$792$	−20247.0	−0.908390
$793$	117.870	0.00527829
$794$	−637.714	−0.0285033
$795$	31694.6	1.41395
$796$	−3727.83	−0.165992
$797$	−16599.3	−0.737740	−0.368870	−	0.929481i	$-0.620255\pi$
$797$	−16599.3	−0.737740	−0.368870	+	0.929481i	$0.620255\pi$
$798$	−2568.01	−0.113918
$799$	8037.69	0.355886
$800$	−25532.9	−1.12841
$801$	85254.7	3.76071
$802$	13576.1	0.597742
$803$	3031.25	0.133214
$804$	−15833.9	−0.694550
$805$	0	0
$806$	−16.6188	−0.000726268 0
$807$	22279.1	0.971824
$808$	16148.1	0.703078
$809$	15615.4	0.678624	0.339312	−	0.940674i	$-0.389806\pi$
$809$	15615.4	0.678624	0.339312	+	0.940674i	$0.389806\pi$
$810$	62660.1	2.71809
$811$	23893.0	1.03452	0.517261	−	0.855828i	$-0.326952\pi$
$811$	23893.0	1.03452	0.517261	+	0.855828i	$0.326952\pi$
$812$	1995.70	0.0862504
$813$	10783.1	0.465164
$814$	−3663.07	−0.157728
$815$	−28686.3	−1.23293
$816$	15314.3	0.656995
$817$	−9349.50	−0.400364
$818$	7732.69	0.330522
$819$	497.128	0.0212101
$820$	3202.09	0.136368
$821$	−36505.2	−1.55182	−0.775908	−	0.630846i	$-0.782708\pi$
$821$	−36505.2	−1.55182	−0.775908	+	0.630846i	$0.782708\pi$
$822$	21650.9	0.918689
$823$	40053.3	1.69644	0.848220	−	0.529645i	$-0.177675\pi$
$823$	40053.3	1.69644	0.848220	+	0.529645i	$0.177675\pi$
$824$	−26213.5	−1.10824
$825$	−22335.0	−0.942552
$826$	3413.02	0.143770
$827$	−10952.2	−0.460513	−0.230257	−	0.973130i	$-0.573957\pi$
$827$	−10952.2	−0.460513	−0.230257	+	0.973130i	$0.573957\pi$
$828$	0	0
$829$	−26816.7	−1.12350	−0.561752	−	0.827306i	$-0.689872\pi$
$829$	−26816.7	−1.12350	−0.561752	+	0.827306i	$0.689872\pi$
$830$	−40203.2	−1.68129
$831$	14583.0	0.608761
$832$	1244.89	0.0518737
$833$	20866.5	0.867924
$834$	−22420.7	−0.930894
$835$	−33205.0	−1.37617
$836$	1724.99	0.0713638
$837$	1120.53	0.0462736
$838$	−5940.53	−0.244883
$839$	−28301.1	−1.16456	−0.582279	−	0.812989i	$-0.697839\pi$
$839$	−28301.1	−1.16456	−0.582279	+	0.812989i	$0.697839\pi$
$840$	−12896.2	−0.529717
$841$	10769.4	0.441568
$842$	−25790.1	−1.05556
$843$	85234.0	3.48234
$844$	10208.8	0.416353
$845$	38358.0	1.56160
$846$	17724.9	0.720326
$847$	−3672.62	−0.148988
$848$	4849.54	0.196384
$849$	57909.3	2.34092
$850$	24451.2	0.986668
$851$	0	0
$852$	32081.4	1.29001
$853$	3443.34	0.138215	0.0691076	−	0.997609i	$-0.477985\pi$
$853$	3443.34	0.138215	0.0691076	+	0.997609i	$0.477985\pi$
$854$	−325.513	−0.0130431
$855$	−44612.8	−1.78447
$856$	17199.4	0.686754
$857$	−18879.2	−0.752511	−0.376256	−	0.926516i	$-0.622789\pi$
$857$	−18879.2	−0.752511	−0.376256	+	0.926516i	$0.622789\pi$
$858$	649.450	0.0258413
$859$	7621.21	0.302715	0.151357	−	0.988479i	$-0.451636\pi$
$859$	7621.21	0.302715	0.151357	+	0.988479i	$0.451636\pi$
$860$	−13934.8	−0.552527
$861$	1631.23	0.0645669
$862$	−20433.7	−0.807396
$863$	36042.2	1.42166	0.710830	−	0.703364i	$-0.248320\pi$
$863$	36042.2	1.42166	0.710830	+	0.703364i	$0.248320\pi$
$864$	−50059.1	−1.97112
$865$	66840.6	2.62734
$866$	32992.6	1.29461
$867$	−9437.42	−0.369679
$868$	−33.5146	−0.00131055
$869$	17240.6	0.673010
$870$	−67428.6	−2.62764
$871$	1204.95	0.0468752
$872$	−35843.2	−1.39198
$873$	72399.9	2.80683
$874$	0	0
$875$	−3118.35	−0.120479
$876$	7589.52	0.292724
$877$	37728.5	1.45268	0.726341	−	0.687335i	$-0.241219\pi$
$877$	37728.5	1.45268	0.726341	+	0.687335i	$0.241219\pi$
$878$	−18926.3	−0.727486
$879$	−38616.9	−1.48182
$880$	−5771.00	−0.221069
$881$	20647.1	0.789579	0.394789	−	0.918772i	$-0.370818\pi$
$881$	20647.1	0.789579	0.394789	+	0.918772i	$0.370818\pi$
$882$	46015.3	1.75671
$883$	37529.7	1.43032	0.715160	−	0.698960i	$-0.246354\pi$
$883$	37529.7	1.43032	0.715160	+	0.698960i	$0.246354\pi$
$884$	519.192	0.0197538
$885$	84208.7	3.19847
$886$	7633.03	0.289432
$887$	−2367.18	−0.0896080	−0.0448040	−	0.998996i	$-0.514266\pi$
$887$	−2367.18	−0.0896080	−0.0448040	+	0.998996i	$0.514266\pi$
$888$	−30902.3	−1.16781
$889$	6139.52	0.231623
$890$	49950.7	1.88129
$891$	−21441.8	−0.806205
$892$	4459.83	0.167406
$893$	−5088.21	−0.190672
$894$	33272.6	1.24474
$895$	10337.2	0.386071
$896$	109.655	0.00408851
$897$	0	0
$898$	−18380.8	−0.683047
$899$	−590.430	−0.0219043
$900$	−39375.1	−1.45834
$901$	11873.2	0.439018
$902$	1500.50	0.0553893
$903$	−7098.75	−0.261607
$904$	−31863.0	−1.17229
$905$	−44317.2	−1.62780
$906$	−4823.49	−0.176876
$907$	1534.80	0.0561875	0.0280938	−	0.999605i	$-0.491056\pi$
$907$	1534.80	0.0561875	0.0280938	+	0.999605i	$0.491056\pi$
$908$	5451.26	0.199236
$909$	42414.1	1.54762
$910$	291.268	0.0106104
$911$	−39799.5	−1.44744	−0.723719	−	0.690095i	$-0.757569\pi$
$911$	−39799.5	−1.44744	−0.723719	+	0.690095i	$0.757569\pi$
$912$	−9694.62	−0.351997
$913$	13757.2	0.498683
$914$	−13124.4	−0.474964
$915$	−8031.33	−0.290172
$916$	−11442.9	−0.412755
$917$	3350.00	0.120640
$918$	47938.2	1.72353
$919$	−52801.4	−1.89527	−0.947637	−	0.319350i	$-0.896535\pi$
$919$	−52801.4	−1.89527	−0.947637	+	0.319350i	$0.896535\pi$
$920$	0	0
$921$	82547.1	2.95333
$922$	7719.67	0.275742
$923$	−2441.38	−0.0870629
$924$	1309.73	0.0466308
$925$	−24002.7	−0.853194
$926$	13021.3	0.462103
$927$	−68851.9	−2.43947
$928$	26377.3	0.933056
$929$	46580.9	1.64507	0.822535	−	0.568714i	$-0.192559\pi$
$929$	46580.9	1.64507	0.822535	+	0.568714i	$0.192559\pi$
$930$	1132.36	0.0399263
$931$	−13209.4	−0.465006
$932$	18786.7	0.660277
$933$	21007.4	0.737141
$934$	18496.2	0.647981
$935$	−14129.3	−0.494200
$936$	3857.75	0.134716
$937$	−30935.8	−1.07858	−0.539289	−	0.842121i	$-0.681307\pi$
$937$	−30935.8	−1.07858	−0.539289	+	0.842121i	$0.681307\pi$
$938$	−3327.64	−0.115833
$939$	−20689.2	−0.719027
$940$	−7583.64	−0.263139
$941$	−29008.4	−1.00494	−0.502470	−	0.864595i	$-0.667575\pi$
$941$	−29008.4	−1.00494	−0.502470	+	0.864595i	$0.667575\pi$
$942$	−41678.3	−1.44156
$943$	0	0
$944$	12884.6	0.444236
$945$	−19638.8	−0.676032
$946$	−6529.84	−0.224422
$947$	2389.80	0.0820044	0.0410022	−	0.999159i	$-0.486945\pi$
$947$	2389.80	0.0820044	0.0410022	+	0.999159i	$0.486945\pi$
$948$	43166.2	1.47887
$949$	−577.559	−0.0197559
$950$	−15478.7	−0.528625
$951$	−43561.4	−1.48536
$952$	−4831.11	−0.164472
$953$	46043.0	1.56504	0.782518	−	0.622628i	$-0.213935\pi$
$953$	46043.0	1.56504	0.782518	+	0.622628i	$0.213935\pi$
$954$	26183.2	0.888587
$955$	−5687.35	−0.192710
$956$	672.188	0.0227407
$957$	23073.6	0.779376
$958$	−15289.5	−0.515638
$959$	−3322.72	−0.111883
$960$	−84823.6	−2.85174
$961$	−29781.1	−0.999667
$962$	697.943	0.0233915
$963$	45175.4	1.51169
$964$	−14331.9	−0.478838
$965$	−47514.9	−1.58504
$966$	0	0
$967$	8457.00	0.281240	0.140620	−	0.990064i	$-0.455090\pi$
$967$	8457.00	0.281240	0.140620	+	0.990064i	$0.455090\pi$
$968$	−28499.8	−0.946301
$969$	−23735.6	−0.786891
$970$	42419.1	1.40412
$971$	21315.7	0.704485	0.352242	−	0.935909i	$-0.385419\pi$
$971$	21315.7	0.704485	0.352242	+	0.935909i	$0.385419\pi$
$972$	−21245.0	−0.701063
$973$	3440.86	0.113370
$974$	9806.23	0.322600
$975$	4255.60	0.139783
$976$	−1228.86	−0.0403021
$977$	26026.7	0.852269	0.426134	−	0.904660i	$-0.359875\pi$
$977$	26026.7	0.852269	0.426134	+	0.904660i	$0.359875\pi$
$978$	−33656.4	−1.10042
$979$	−17092.8	−0.558006
$980$	−19687.7	−0.641736
$981$	−94144.9	−3.06403
$982$	21866.0	0.710562
$983$	35252.5	1.14382	0.571912	−	0.820315i	$-0.306202\pi$
$983$	35252.5	1.14382	0.571912	+	0.820315i	$0.306202\pi$
$984$	12658.4	0.410098
$985$	46983.5	1.51982
$986$	−25259.7	−0.815855
$987$	−3863.30	−0.124590
$988$	−328.671	−0.0105834
$989$	0	0
$990$	−31158.3	−1.00028
$991$	37877.6	1.21415	0.607075	−	0.794645i	$-0.292343\pi$
$991$	37877.6	1.21415	0.607075	+	0.794645i	$0.292343\pi$
$992$	−442.965	−0.0141776
$993$	−44925.6	−1.43572
$994$	6742.20	0.215140
$995$	−19329.6	−0.615869
$996$	34444.8	1.09581
$997$	34456.5	1.09453	0.547266	−	0.836959i	$-0.315669\pi$
$997$	34456.5	1.09453	0.547266	+	0.836959i	$0.315669\pi$
$998$	−12440.7	−0.394592
$999$	−47059.0	−1.49037

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.4.a.m.1.9		25
23.7	odd	22		23.4.c.a.3.4	✓	50
23.10	odd	22		23.4.c.a.8.4	yes	50
23.22	odd	2		529.4.a.n.1.9		25
69.53	even	22		207.4.i.a.118.2		50
69.56	even	22		207.4.i.a.100.2		50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.c.a.3.4	✓	50	23.7	odd	22
23.4.c.a.8.4	yes	50	23.10	odd	22
207.4.i.a.100.2		50	69.56	even	22
207.4.i.a.118.2		50	69.53	even	22
529.4.a.m.1.9		25	1.1	even	1	trivial
529.4.a.n.1.9		25	23.22	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:	\( N \)	\(=\)	\( 529 = 23^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	529.a (trivial)

\(f(q)\)	\(=\)	\(q-2.15026 q^{2} +9.55258 q^{3} -3.37638 q^{4} -17.5072 q^{5} -20.5405 q^{6} +3.15231 q^{7} +24.4622 q^{8} +64.2518 q^{9} +37.6451 q^{10} -12.8819 q^{11} -32.2531 q^{12} +2.45445 q^{13} -6.77829 q^{14} -167.239 q^{15} -25.5890 q^{16} -62.6503 q^{17} -138.158 q^{18} +39.6603 q^{19} +59.1111 q^{20} +30.1127 q^{21} +27.6994 q^{22} +233.677 q^{24} +181.504 q^{25} -5.27771 q^{26} +355.851 q^{27} -10.6434 q^{28} -187.506 q^{29} +359.608 q^{30} +3.14887 q^{31} -140.674 q^{32} -123.055 q^{33} +134.714 q^{34} -55.1883 q^{35} -216.938 q^{36} -132.244 q^{37} -85.2801 q^{38} +23.4463 q^{39} -428.265 q^{40} +54.1707 q^{41} -64.7502 q^{42} -235.739 q^{43} +43.4942 q^{44} -1124.87 q^{45} -128.295 q^{47} -244.441 q^{48} -333.063 q^{49} -390.280 q^{50} -598.472 q^{51} -8.28715 q^{52} -189.516 q^{53} -765.172 q^{54} +225.527 q^{55} +77.1124 q^{56} +378.859 q^{57} +403.186 q^{58} -503.522 q^{59} +564.664 q^{60} +48.0229 q^{61} -6.77088 q^{62} +202.542 q^{63} +507.199 q^{64} -42.9707 q^{65} +264.601 q^{66} +490.926 q^{67} +211.531 q^{68} +118.669 q^{70} -994.675 q^{71} +1571.74 q^{72} -235.311 q^{73} +284.358 q^{74} +1733.83 q^{75} -133.908 q^{76} -40.6077 q^{77} -50.4157 q^{78} -1338.36 q^{79} +447.993 q^{80} +1664.49 q^{81} -116.481 q^{82} -1067.95 q^{83} -101.672 q^{84} +1096.83 q^{85} +506.901 q^{86} -1791.16 q^{87} -315.119 q^{88} +1326.88 q^{89} +2418.77 q^{90} +7.73719 q^{91} +30.0798 q^{93} +275.867 q^{94} -694.344 q^{95} -1343.80 q^{96} +1126.82 q^{97} +716.172 q^{98} -827.685 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19}+ \cdots - 7317 q^{99}+O(q^{100}) \) 25 * q - q^3 + 80 * q^4 - 51 * q^5 + 86 * q^6 - 73 * q^7 + 3 * q^8 + 166 * q^9 - 139 * q^10 - 221 * q^11 - 191 * q^12 - 27 * q^13 - 372 * q^14 - 310 * q^15 + 152 * q^16 - 365 * q^17 - 538 * q^18 - 405 * q^19 - 578 * q^20 - 352 * q^21 - 155 * q^22 + 803 * q^24 + 90 * q^25 - 850 * q^26 + 368 * q^27 - 459 * q^28 + 175 * q^29 - 893 * q^30 + 287 * q^31 + 164 * q^32 - 1020 * q^33 - 335 * q^34 + 462 * q^35 - 1092 * q^36 - 471 * q^37 - 810 * q^38 - 822 * q^39 - 1405 * q^40 - 73 * q^41 - 556 * q^42 - 901 * q^43 - 2073 * q^44 - 1384 * q^45 + 1452 * q^47 - 4028 * q^48 - 1092 * q^49 + 364 * q^50 - 2214 * q^51 + 1287 * q^52 - 2071 * q^53 + 2052 * q^54 + 1006 * q^55 - 4879 * q^56 - 418 * q^57 + 2796 * q^58 - 2713 * q^59 - 2805 * q^60 - 1225 * q^61 - 2852 * q^62 - 4003 * q^63 + 217 * q^64 - 2030 * q^65 - 2933 * q^66 - 767 * q^67 - 4175 * q^68 + 4851 * q^70 - 1683 * q^71 - 5265 * q^72 + 2203 * q^73 - 3089 * q^74 + 2333 * q^75 - 5252 * q^76 + 2760 * q^77 - 692 * q^78 - 5425 * q^79 - 4689 * q^80 + 1929 * q^81 - 2725 * q^82 - 5425 * q^83 - 4317 * q^84 - 912 * q^85 - 4359 * q^86 - 4404 * q^87 - 2610 * q^88 - 4933 * q^89 - 2695 * q^90 - 3619 * q^91 + 6375 * q^93 - 5117 * q^94 - 1338 * q^95 + 20 * q^96 - 2085 * q^97 + 5951 * q^98 - 7317 * q^99

Introduction

L-functions

Modular forms

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Database

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