Properties

Label 29.18.a.b.1.9
Level $29$
Weight $18$
Character 29.1
Self dual yes
Analytic conductor $53.134$
Analytic rank $0$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 18 \)
Character orbit: \([\chi]\) \(=\) 29.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(53.1344053299\)
Analytic rank: \(0\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) \(=\) 29.1

$q$-expansion

\(f(q)\) \(=\) \(q-65.9873 q^{2} +22515.6 q^{3} -126718. q^{4} +342266. q^{5} -1.48575e6 q^{6} +1.63719e7 q^{7} +1.70108e7 q^{8} +3.77814e8 q^{9} +O(q^{10})\) \(q-65.9873 q^{2} +22515.6 q^{3} -126718. q^{4} +342266. q^{5} -1.48575e6 q^{6} +1.63719e7 q^{7} +1.70108e7 q^{8} +3.77814e8 q^{9} -2.25852e7 q^{10} +1.38186e8 q^{11} -2.85313e9 q^{12} -3.21553e9 q^{13} -1.08034e9 q^{14} +7.70633e9 q^{15} +1.54866e10 q^{16} +3.77540e10 q^{17} -2.49309e10 q^{18} -6.09675e10 q^{19} -4.33711e10 q^{20} +3.68625e11 q^{21} -9.11855e9 q^{22} +2.42040e11 q^{23} +3.83010e11 q^{24} -6.45794e11 q^{25} +2.12184e11 q^{26} +5.59905e12 q^{27} -2.07461e12 q^{28} +5.00246e11 q^{29} -5.08520e11 q^{30} -1.83676e12 q^{31} -3.25157e12 q^{32} +3.11136e12 q^{33} -2.49128e12 q^{34} +5.60355e12 q^{35} -4.78757e13 q^{36} +1.75933e13 q^{37} +4.02308e12 q^{38} -7.23998e13 q^{39} +5.82223e12 q^{40} +1.19591e13 q^{41} -2.43246e13 q^{42} -5.09731e13 q^{43} -1.75107e13 q^{44} +1.29313e14 q^{45} -1.59716e13 q^{46} +5.99637e13 q^{47} +3.48692e14 q^{48} +3.54101e13 q^{49} +4.26142e13 q^{50} +8.50055e14 q^{51} +4.07465e14 q^{52} +8.34952e14 q^{53} -3.69466e14 q^{54} +4.72965e13 q^{55} +2.78501e14 q^{56} -1.37272e15 q^{57} -3.30099e13 q^{58} -9.87609e14 q^{59} -9.76528e14 q^{60} -5.79160e14 q^{61} +1.21203e14 q^{62} +6.18555e15 q^{63} -1.81530e15 q^{64} -1.10057e15 q^{65} -2.05310e14 q^{66} +5.24224e15 q^{67} -4.78410e15 q^{68} +5.44969e15 q^{69} -3.69763e14 q^{70} +9.25752e15 q^{71} +6.42693e15 q^{72} -1.03766e16 q^{73} -1.16093e15 q^{74} -1.45405e16 q^{75} +7.72566e15 q^{76} +2.26238e15 q^{77} +4.77747e15 q^{78} +1.94267e16 q^{79} +5.30054e15 q^{80} +7.72752e16 q^{81} -7.89146e14 q^{82} -1.07716e16 q^{83} -4.67113e16 q^{84} +1.29219e16 q^{85} +3.36358e15 q^{86} +1.12634e16 q^{87} +2.35067e15 q^{88} +5.92817e15 q^{89} -8.53300e15 q^{90} -5.26446e16 q^{91} -3.06708e16 q^{92} -4.13559e16 q^{93} -3.95685e15 q^{94} -2.08671e16 q^{95} -7.32111e16 q^{96} +7.11503e16 q^{97} -2.33662e15 q^{98} +5.22088e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q + 256q^{2} + 23966q^{3} + 1452522q^{4} + 998272q^{5} + 3411526q^{6} + 2193368q^{7} - 138137226q^{8} + 1264832799q^{9} + O(q^{10}) \) \( 21q + 256q^{2} + 23966q^{3} + 1452522q^{4} + 998272q^{5} + 3411526q^{6} + 2193368q^{7} - 138137226q^{8} + 1264832799q^{9} - 224469478q^{10} + 1203139534q^{11} - 5164251122q^{12} + 3854339312q^{13} + 25262272904q^{14} + 28324474306q^{15} + 196520815922q^{16} + 76444714794q^{17} + 75758949126q^{18} + 246497292428q^{19} - 46900976670q^{20} + 360937126704q^{21} - 275001533522q^{22} + 213498528140q^{23} - 451123453870q^{24} + 3898884886997q^{25} - 3609347694206q^{26} - 2718903745978q^{27} - 5946174617200q^{28} + 10505174672181q^{29} - 20237658929454q^{30} + 16670029895798q^{31} - 42141001912046q^{32} - 7157109761394q^{33} + 12785761151136q^{34} + 46677934312888q^{35} + 132137824374868q^{36} + 53445659988410q^{37} + 76581637956388q^{38} + 79233849032530q^{39} + 193617444734146q^{40} - 20814769309298q^{41} + 76690667258352q^{42} + 185498647364454q^{43} + 315429066899678q^{44} - 486270821438526q^{45} + 261474367677132q^{46} + 389503471719450q^{47} - 101509672247630q^{48} + 730079062141437q^{49} + 1482269666368354q^{50} + 718238208473988q^{51} + 1966802817157170q^{52} + 747441265526156q^{53} + 5692893333117030q^{54} + 1639109418219546q^{55} + 5657219329125240q^{56} + 4694352396864932q^{57} + 128063081718016q^{58} + 5280258638332960q^{59} + 15251367906033378q^{60} + 5813675353074254q^{61} + 6242066590947250q^{62} + 10947760075450368q^{63} + 24583792057508902q^{64} + 19190799243789974q^{65} + 41877805444482390q^{66} + 13420580230958268q^{67} + 24771837384165388q^{68} + 30973047049935252q^{69} + 8505088080182440q^{70} + 4824462822979508q^{71} + 1180071997284592q^{72} + 11228916281304662q^{73} - 89132715356772q^{74} + 59161419576630296q^{75} + 57466858643173460q^{76} + 58741564492720064q^{77} + 142050530910210210q^{78} + 71718598015696758q^{79} + 48350023652407550q^{80} + 75805931446703569q^{81} + 188661890754420812q^{82} + 50769377111735608q^{83} + 198832046985593048q^{84} + 53422044849490784q^{85} + 35014892323844118q^{86} + 11988905533023326q^{87} + 37459283979085258q^{88} - 70981414576978018q^{89} + 57211029866143724q^{90} + 112933943315157320q^{91} - 103019729095759724q^{92} - 350358290646906646q^{93} - 150286322409612578q^{94} - 102561321856584476q^{95} - 213770098354021866q^{96} - 130930167251505210q^{97} - 537387515497557296q^{98} - 95267700931431064q^{99} + O(q^{100}) \)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −65.9873 −0.182266 −0.0911330 0.995839i \(-0.529049\pi\)
−0.0911330 + 0.995839i \(0.529049\pi\)
\(3\) 22515.6 1.98132 0.990658 0.136372i \(-0.0435442\pi\)
0.990658 + 0.136372i \(0.0435442\pi\)
\(4\) −126718. −0.966779
\(5\) 342266. 0.391849 0.195924 0.980619i \(-0.437229\pi\)
0.195924 + 0.980619i \(0.437229\pi\)
\(6\) −1.48575e6 −0.361126
\(7\) 1.63719e7 1.07341 0.536707 0.843769i \(-0.319668\pi\)
0.536707 + 0.843769i \(0.319668\pi\)
\(8\) 1.70108e7 0.358477
\(9\) 3.77814e8 2.92561
\(10\) −2.25852e7 −0.0714206
\(11\) 1.38186e8 0.194369 0.0971846 0.995266i \(-0.469016\pi\)
0.0971846 + 0.995266i \(0.469016\pi\)
\(12\) −2.85313e9 −1.91549
\(13\) −3.21553e9 −1.09329 −0.546644 0.837365i \(-0.684095\pi\)
−0.546644 + 0.837365i \(0.684095\pi\)
\(14\) −1.08034e9 −0.195647
\(15\) 7.70633e9 0.776376
\(16\) 1.54866e10 0.901441
\(17\) 3.77540e10 1.31264 0.656322 0.754481i \(-0.272111\pi\)
0.656322 + 0.754481i \(0.272111\pi\)
\(18\) −2.49309e10 −0.533239
\(19\) −6.09675e10 −0.823556 −0.411778 0.911284i \(-0.635092\pi\)
−0.411778 + 0.911284i \(0.635092\pi\)
\(20\) −4.33711e10 −0.378831
\(21\) 3.68625e11 2.12677
\(22\) −9.11855e9 −0.0354269
\(23\) 2.42040e11 0.644468 0.322234 0.946660i \(-0.395566\pi\)
0.322234 + 0.946660i \(0.395566\pi\)
\(24\) 3.83010e11 0.710256
\(25\) −6.45794e11 −0.846455
\(26\) 2.12184e11 0.199269
\(27\) 5.59905e12 3.81524
\(28\) −2.07461e12 −1.03775
\(29\) 5.00246e11 0.185695
\(30\) −5.08520e11 −0.141507
\(31\) −1.83676e12 −0.386793 −0.193397 0.981121i \(-0.561950\pi\)
−0.193397 + 0.981121i \(0.561950\pi\)
\(32\) −3.25157e12 −0.522779
\(33\) 3.11136e12 0.385107
\(34\) −2.49128e12 −0.239250
\(35\) 5.60355e12 0.420615
\(36\) −4.78757e13 −2.82842
\(37\) 1.75933e13 0.823440 0.411720 0.911310i \(-0.364928\pi\)
0.411720 + 0.911310i \(0.364928\pi\)
\(38\) 4.02308e12 0.150106
\(39\) −7.23998e13 −2.16615
\(40\) 5.82223e12 0.140469
\(41\) 1.19591e13 0.233902 0.116951 0.993138i \(-0.462688\pi\)
0.116951 + 0.993138i \(0.462688\pi\)
\(42\) −2.43246e13 −0.387638
\(43\) −5.09731e13 −0.665058 −0.332529 0.943093i \(-0.607902\pi\)
−0.332529 + 0.943093i \(0.607902\pi\)
\(44\) −1.75107e13 −0.187912
\(45\) 1.29313e14 1.14640
\(46\) −1.59716e13 −0.117464
\(47\) 5.99637e13 0.367330 0.183665 0.982989i \(-0.441204\pi\)
0.183665 + 0.982989i \(0.441204\pi\)
\(48\) 3.48692e14 1.78604
\(49\) 3.54101e13 0.152216
\(50\) 4.26142e13 0.154280
\(51\) 8.50055e14 2.60076
\(52\) 4.07465e14 1.05697
\(53\) 8.34952e14 1.84212 0.921058 0.389426i \(-0.127327\pi\)
0.921058 + 0.389426i \(0.127327\pi\)
\(54\) −3.69466e14 −0.695389
\(55\) 4.72965e13 0.0761633
\(56\) 2.78501e14 0.384794
\(57\) −1.37272e15 −1.63172
\(58\) −3.30099e13 −0.0338459
\(59\) −9.87609e14 −0.875675 −0.437838 0.899054i \(-0.644255\pi\)
−0.437838 + 0.899054i \(0.644255\pi\)
\(60\) −9.76528e14 −0.750584
\(61\) −5.79160e14 −0.386807 −0.193404 0.981119i \(-0.561953\pi\)
−0.193404 + 0.981119i \(0.561953\pi\)
\(62\) 1.21203e14 0.0704992
\(63\) 6.18555e15 3.14039
\(64\) −1.81530e15 −0.806156
\(65\) −1.10057e15 −0.428403
\(66\) −2.05310e14 −0.0701919
\(67\) 5.24224e15 1.57718 0.788589 0.614921i \(-0.210812\pi\)
0.788589 + 0.614921i \(0.210812\pi\)
\(68\) −4.78410e15 −1.26904
\(69\) 5.44969e15 1.27689
\(70\) −3.69763e14 −0.0766639
\(71\) 9.25752e15 1.70137 0.850685 0.525676i \(-0.176187\pi\)
0.850685 + 0.525676i \(0.176187\pi\)
\(72\) 6.42693e15 1.04876
\(73\) −1.03766e16 −1.50595 −0.752973 0.658052i \(-0.771381\pi\)
−0.752973 + 0.658052i \(0.771381\pi\)
\(74\) −1.16093e15 −0.150085
\(75\) −1.45405e16 −1.67709
\(76\) 7.72566e15 0.796196
\(77\) 2.26238e15 0.208639
\(78\) 4.77747e15 0.394815
\(79\) 1.94267e16 1.44068 0.720341 0.693620i \(-0.243985\pi\)
0.720341 + 0.693620i \(0.243985\pi\)
\(80\) 5.30054e15 0.353228
\(81\) 7.72752e16 4.63359
\(82\) −7.89146e14 −0.0426324
\(83\) −1.07716e16 −0.524948 −0.262474 0.964939i \(-0.584538\pi\)
−0.262474 + 0.964939i \(0.584538\pi\)
\(84\) −4.67113e16 −2.05612
\(85\) 1.29219e16 0.514358
\(86\) 3.36358e15 0.121217
\(87\) 1.12634e16 0.367921
\(88\) 2.35067e15 0.0696769
\(89\) 5.92817e15 0.159627 0.0798133 0.996810i \(-0.474568\pi\)
0.0798133 + 0.996810i \(0.474568\pi\)
\(90\) −8.53300e15 −0.208949
\(91\) −5.26446e16 −1.17355
\(92\) −3.06708e16 −0.623058
\(93\) −4.13559e16 −0.766360
\(94\) −3.95685e15 −0.0669518
\(95\) −2.08671e16 −0.322709
\(96\) −7.32111e16 −1.03579
\(97\) 7.11503e16 0.921758 0.460879 0.887463i \(-0.347534\pi\)
0.460879 + 0.887463i \(0.347534\pi\)
\(98\) −2.33662e15 −0.0277438
\(99\) 5.22088e16 0.568649
\(100\) 8.18335e16 0.818335
\(101\) −3.90210e16 −0.358564 −0.179282 0.983798i \(-0.557377\pi\)
−0.179282 + 0.983798i \(0.557377\pi\)
\(102\) −5.60929e16 −0.474030
\(103\) −1.05247e17 −0.818642 −0.409321 0.912390i \(-0.634234\pi\)
−0.409321 + 0.912390i \(0.634234\pi\)
\(104\) −5.46990e16 −0.391918
\(105\) 1.26168e17 0.833372
\(106\) −5.50963e16 −0.335755
\(107\) 8.88125e16 0.499703 0.249851 0.968284i \(-0.419618\pi\)
0.249851 + 0.968284i \(0.419618\pi\)
\(108\) −7.09498e17 −3.68850
\(109\) −1.95228e17 −0.938462 −0.469231 0.883076i \(-0.655469\pi\)
−0.469231 + 0.883076i \(0.655469\pi\)
\(110\) −3.12097e15 −0.0138820
\(111\) 3.96124e17 1.63150
\(112\) 2.53546e17 0.967619
\(113\) 3.31667e17 1.17364 0.586821 0.809716i \(-0.300379\pi\)
0.586821 + 0.809716i \(0.300379\pi\)
\(114\) 9.05823e16 0.297408
\(115\) 8.28421e16 0.252534
\(116\) −6.33901e16 −0.179526
\(117\) −1.21487e18 −3.19854
\(118\) 6.51697e16 0.159606
\(119\) 6.18106e17 1.40901
\(120\) 1.31091e17 0.278313
\(121\) −4.86352e17 −0.962221
\(122\) 3.82172e16 0.0705018
\(123\) 2.69266e17 0.463434
\(124\) 2.32750e17 0.373944
\(125\) −4.82161e17 −0.723531
\(126\) −4.08168e17 −0.572386
\(127\) −9.02041e17 −1.18276 −0.591378 0.806395i \(-0.701416\pi\)
−0.591378 + 0.806395i \(0.701416\pi\)
\(128\) 5.45976e17 0.669714
\(129\) −1.14769e18 −1.31769
\(130\) 7.26234e16 0.0780833
\(131\) 1.14535e18 1.15380 0.576902 0.816814i \(-0.304262\pi\)
0.576902 + 0.816814i \(0.304262\pi\)
\(132\) −3.94264e17 −0.372313
\(133\) −9.98157e17 −0.884015
\(134\) −3.45921e17 −0.287466
\(135\) 1.91636e18 1.49500
\(136\) 6.42227e17 0.470553
\(137\) −1.40517e18 −0.967398 −0.483699 0.875234i \(-0.660707\pi\)
−0.483699 + 0.875234i \(0.660707\pi\)
\(138\) −3.59611e17 −0.232734
\(139\) −3.85585e17 −0.234690 −0.117345 0.993091i \(-0.537438\pi\)
−0.117345 + 0.993091i \(0.537438\pi\)
\(140\) −7.10069e17 −0.406642
\(141\) 1.35012e18 0.727798
\(142\) −6.10879e17 −0.310102
\(143\) −4.44343e17 −0.212502
\(144\) 5.85107e18 2.63727
\(145\) 1.71217e17 0.0727645
\(146\) 6.84721e17 0.274482
\(147\) 7.97281e17 0.301588
\(148\) −2.22938e18 −0.796085
\(149\) −1.18889e17 −0.0400921 −0.0200460 0.999799i \(-0.506381\pi\)
−0.0200460 + 0.999799i \(0.506381\pi\)
\(150\) 9.59486e17 0.305677
\(151\) −5.97320e18 −1.79847 −0.899235 0.437466i \(-0.855876\pi\)
−0.899235 + 0.437466i \(0.855876\pi\)
\(152\) −1.03711e18 −0.295226
\(153\) 1.42640e19 3.84029
\(154\) −1.49288e17 −0.0380277
\(155\) −6.28661e17 −0.151564
\(156\) 9.17434e18 2.09419
\(157\) −3.79849e18 −0.821229 −0.410614 0.911809i \(-0.634686\pi\)
−0.410614 + 0.911809i \(0.634686\pi\)
\(158\) −1.28191e18 −0.262587
\(159\) 1.87995e19 3.64981
\(160\) −1.11290e18 −0.204850
\(161\) 3.96267e18 0.691780
\(162\) −5.09918e18 −0.844545
\(163\) −1.06189e19 −1.66910 −0.834552 0.550929i \(-0.814274\pi\)
−0.834552 + 0.550929i \(0.814274\pi\)
\(164\) −1.51542e18 −0.226132
\(165\) 1.06491e18 0.150904
\(166\) 7.10789e17 0.0956802
\(167\) 2.59417e17 0.0331824 0.0165912 0.999862i \(-0.494719\pi\)
0.0165912 + 0.999862i \(0.494719\pi\)
\(168\) 6.27062e18 0.762398
\(169\) 1.68925e18 0.195279
\(170\) −8.52681e17 −0.0937499
\(171\) −2.30344e19 −2.40940
\(172\) 6.45920e18 0.642964
\(173\) −3.94225e18 −0.373553 −0.186776 0.982402i \(-0.559804\pi\)
−0.186776 + 0.982402i \(0.559804\pi\)
\(174\) −7.43239e17 −0.0670595
\(175\) −1.05729e19 −0.908596
\(176\) 2.14004e18 0.175212
\(177\) −2.22366e19 −1.73499
\(178\) −3.91184e17 −0.0290945
\(179\) 1.98644e19 1.40872 0.704360 0.709843i \(-0.251234\pi\)
0.704360 + 0.709843i \(0.251234\pi\)
\(180\) −1.63862e19 −1.10831
\(181\) −2.32630e19 −1.50106 −0.750531 0.660835i \(-0.770202\pi\)
−0.750531 + 0.660835i \(0.770202\pi\)
\(182\) 3.47387e18 0.213898
\(183\) −1.30402e19 −0.766388
\(184\) 4.11731e18 0.231027
\(185\) 6.02158e18 0.322664
\(186\) 2.72897e18 0.139681
\(187\) 5.21709e18 0.255138
\(188\) −7.59847e18 −0.355127
\(189\) 9.16673e19 4.09533
\(190\) 1.37696e18 0.0588189
\(191\) −3.80256e19 −1.55343 −0.776717 0.629850i \(-0.783116\pi\)
−0.776717 + 0.629850i \(0.783116\pi\)
\(192\) −4.08727e19 −1.59725
\(193\) 1.89543e19 0.708712 0.354356 0.935111i \(-0.384700\pi\)
0.354356 + 0.935111i \(0.384700\pi\)
\(194\) −4.69502e18 −0.168005
\(195\) −2.47800e19 −0.848802
\(196\) −4.48709e18 −0.147159
\(197\) −5.59698e19 −1.75789 −0.878943 0.476926i \(-0.841751\pi\)
−0.878943 + 0.476926i \(0.841751\pi\)
\(198\) −3.44512e18 −0.103645
\(199\) 1.86947e19 0.538849 0.269424 0.963022i \(-0.413167\pi\)
0.269424 + 0.963022i \(0.413167\pi\)
\(200\) −1.09855e19 −0.303434
\(201\) 1.18032e20 3.12489
\(202\) 2.57489e18 0.0653540
\(203\) 8.19001e18 0.199328
\(204\) −1.07717e20 −2.51436
\(205\) 4.09317e18 0.0916542
\(206\) 6.94498e18 0.149211
\(207\) 9.14462e19 1.88546
\(208\) −4.97978e19 −0.985535
\(209\) −8.42489e18 −0.160074
\(210\) −8.32546e18 −0.151895
\(211\) 1.83677e19 0.321851 0.160926 0.986967i \(-0.448552\pi\)
0.160926 + 0.986967i \(0.448552\pi\)
\(212\) −1.05803e20 −1.78092
\(213\) 2.08439e20 3.37095
\(214\) −5.86050e18 −0.0910788
\(215\) −1.74464e19 −0.260602
\(216\) 9.52445e19 1.36768
\(217\) −3.00714e19 −0.415189
\(218\) 1.28826e19 0.171050
\(219\) −2.33635e20 −2.98375
\(220\) −5.99330e18 −0.0736331
\(221\) −1.21399e20 −1.43510
\(222\) −2.61392e19 −0.297366
\(223\) −8.87499e18 −0.0971799 −0.0485900 0.998819i \(-0.515473\pi\)
−0.0485900 + 0.998819i \(0.515473\pi\)
\(224\) −5.32345e19 −0.561158
\(225\) −2.43990e20 −2.47640
\(226\) −2.18858e19 −0.213915
\(227\) −6.49039e19 −0.611014 −0.305507 0.952190i \(-0.598826\pi\)
−0.305507 + 0.952190i \(0.598826\pi\)
\(228\) 1.73948e20 1.57752
\(229\) −8.59117e19 −0.750673 −0.375336 0.926889i \(-0.622473\pi\)
−0.375336 + 0.926889i \(0.622473\pi\)
\(230\) −5.46653e18 −0.0460283
\(231\) 5.09390e19 0.413379
\(232\) 8.50961e18 0.0665675
\(233\) 1.92886e20 1.45471 0.727354 0.686263i \(-0.240750\pi\)
0.727354 + 0.686263i \(0.240750\pi\)
\(234\) 8.01662e19 0.582984
\(235\) 2.05235e19 0.143938
\(236\) 1.25148e20 0.846584
\(237\) 4.37404e20 2.85445
\(238\) −4.07872e19 −0.256814
\(239\) 6.89822e18 0.0419136 0.0209568 0.999780i \(-0.493329\pi\)
0.0209568 + 0.999780i \(0.493329\pi\)
\(240\) 1.19345e20 0.699857
\(241\) −2.63569e20 −1.49193 −0.745966 0.665983i \(-0.768012\pi\)
−0.745966 + 0.665983i \(0.768012\pi\)
\(242\) 3.20930e19 0.175380
\(243\) 1.01684e21 5.36536
\(244\) 7.33898e19 0.373957
\(245\) 1.21197e19 0.0596457
\(246\) −1.77681e19 −0.0844682
\(247\) 1.96043e20 0.900384
\(248\) −3.12449e19 −0.138656
\(249\) −2.42529e20 −1.04009
\(250\) 3.18165e19 0.131875
\(251\) −1.94638e20 −0.779831 −0.389916 0.920851i \(-0.627496\pi\)
−0.389916 + 0.920851i \(0.627496\pi\)
\(252\) −7.83818e20 −3.03606
\(253\) 3.34467e19 0.125265
\(254\) 5.95233e19 0.215576
\(255\) 2.90945e20 1.01911
\(256\) 2.01908e20 0.684090
\(257\) −2.59950e20 −0.852035 −0.426018 0.904715i \(-0.640084\pi\)
−0.426018 + 0.904715i \(0.640084\pi\)
\(258\) 7.57332e19 0.240170
\(259\) 2.88036e20 0.883892
\(260\) 1.39461e20 0.414171
\(261\) 1.89000e20 0.543272
\(262\) −7.55785e19 −0.210299
\(263\) −6.08855e20 −1.64017 −0.820087 0.572239i \(-0.806075\pi\)
−0.820087 + 0.572239i \(0.806075\pi\)
\(264\) 5.29268e19 0.138052
\(265\) 2.85775e20 0.721830
\(266\) 6.58657e19 0.161126
\(267\) 1.33476e20 0.316271
\(268\) −6.64284e20 −1.52478
\(269\) 2.10139e20 0.467319 0.233659 0.972319i \(-0.424930\pi\)
0.233659 + 0.972319i \(0.424930\pi\)
\(270\) −1.26456e20 −0.272487
\(271\) −5.03341e20 −1.05105 −0.525525 0.850778i \(-0.676131\pi\)
−0.525525 + 0.850778i \(0.676131\pi\)
\(272\) 5.84683e20 1.18327
\(273\) −1.18533e21 −2.32517
\(274\) 9.27236e19 0.176324
\(275\) −8.92399e19 −0.164525
\(276\) −6.90572e20 −1.23447
\(277\) 4.95306e20 0.858609 0.429304 0.903160i \(-0.358759\pi\)
0.429304 + 0.903160i \(0.358759\pi\)
\(278\) 2.54437e19 0.0427760
\(279\) −6.93955e20 −1.13161
\(280\) 9.53212e19 0.150781
\(281\) −9.17961e19 −0.140871 −0.0704353 0.997516i \(-0.522439\pi\)
−0.0704353 + 0.997516i \(0.522439\pi\)
\(282\) −8.90909e19 −0.132653
\(283\) −2.56229e20 −0.370205 −0.185103 0.982719i \(-0.559262\pi\)
−0.185103 + 0.982719i \(0.559262\pi\)
\(284\) −1.17309e21 −1.64485
\(285\) −4.69836e20 −0.639388
\(286\) 2.93210e19 0.0387318
\(287\) 1.95793e20 0.251074
\(288\) −1.22849e21 −1.52945
\(289\) 5.98124e20 0.723036
\(290\) −1.12982e19 −0.0132625
\(291\) 1.60199e21 1.82629
\(292\) 1.31489e21 1.45592
\(293\) 1.42832e21 1.53621 0.768105 0.640324i \(-0.221200\pi\)
0.768105 + 0.640324i \(0.221200\pi\)
\(294\) −5.26104e19 −0.0549692
\(295\) −3.38025e20 −0.343132
\(296\) 2.99277e20 0.295184
\(297\) 7.73713e20 0.741566
\(298\) 7.84517e18 0.00730742
\(299\) −7.78289e20 −0.704589
\(300\) 1.84253e21 1.62138
\(301\) −8.34529e20 −0.713882
\(302\) 3.94156e20 0.327800
\(303\) −8.78582e20 −0.710428
\(304\) −9.44182e20 −0.742387
\(305\) −1.98226e20 −0.151570
\(306\) −9.41242e20 −0.699953
\(307\) 1.09544e21 0.792342 0.396171 0.918177i \(-0.370339\pi\)
0.396171 + 0.918177i \(0.370339\pi\)
\(308\) −2.86684e20 −0.201707
\(309\) −2.36971e21 −1.62199
\(310\) 4.14837e19 0.0276250
\(311\) −8.72677e20 −0.565445 −0.282723 0.959202i \(-0.591238\pi\)
−0.282723 + 0.959202i \(0.591238\pi\)
\(312\) −1.23158e21 −0.776514
\(313\) 2.31722e21 1.42181 0.710903 0.703290i \(-0.248286\pi\)
0.710903 + 0.703290i \(0.248286\pi\)
\(314\) 2.50652e20 0.149682
\(315\) 2.11710e21 1.23056
\(316\) −2.46170e21 −1.39282
\(317\) 2.00368e21 1.10363 0.551816 0.833966i \(-0.313935\pi\)
0.551816 + 0.833966i \(0.313935\pi\)
\(318\) −1.24053e21 −0.665236
\(319\) 6.91273e19 0.0360935
\(320\) −6.21316e20 −0.315891
\(321\) 1.99967e21 0.990069
\(322\) −2.61486e20 −0.126088
\(323\) −2.30177e21 −1.08104
\(324\) −9.79213e21 −4.47966
\(325\) 2.07657e21 0.925419
\(326\) 7.00710e20 0.304221
\(327\) −4.39568e21 −1.85939
\(328\) 2.03434e20 0.0838485
\(329\) 9.81723e20 0.394297
\(330\) −7.02706e19 −0.0275046
\(331\) 1.98894e20 0.0758725 0.0379362 0.999280i \(-0.487922\pi\)
0.0379362 + 0.999280i \(0.487922\pi\)
\(332\) 1.36495e21 0.507509
\(333\) 6.64699e21 2.40907
\(334\) −1.71182e19 −0.00604803
\(335\) 1.79424e21 0.618015
\(336\) 5.70876e21 1.91716
\(337\) 5.06276e21 1.65780 0.828901 0.559395i \(-0.188966\pi\)
0.828901 + 0.559395i \(0.188966\pi\)
\(338\) −1.11469e20 −0.0355927
\(339\) 7.46770e21 2.32536
\(340\) −1.63743e21 −0.497270
\(341\) −2.53816e20 −0.0751807
\(342\) 1.51998e21 0.439152
\(343\) −3.22888e21 −0.910023
\(344\) −8.67096e20 −0.238408
\(345\) 1.86524e21 0.500349
\(346\) 2.60138e20 0.0680859
\(347\) −3.81221e20 −0.0973589 −0.0486795 0.998814i \(-0.515501\pi\)
−0.0486795 + 0.998814i \(0.515501\pi\)
\(348\) −1.42727e21 −0.355698
\(349\) 6.19750e21 1.50730 0.753652 0.657274i \(-0.228291\pi\)
0.753652 + 0.657274i \(0.228291\pi\)
\(350\) 6.97677e20 0.165606
\(351\) −1.80039e22 −4.17116
\(352\) −4.49323e20 −0.101612
\(353\) 7.56185e21 1.66933 0.834667 0.550755i \(-0.185660\pi\)
0.834667 + 0.550755i \(0.185660\pi\)
\(354\) 1.46734e21 0.316229
\(355\) 3.16853e21 0.666679
\(356\) −7.51203e20 −0.154324
\(357\) 1.39171e22 2.79169
\(358\) −1.31080e21 −0.256762
\(359\) −6.32890e21 −1.21067 −0.605334 0.795971i \(-0.706961\pi\)
−0.605334 + 0.795971i \(0.706961\pi\)
\(360\) 2.19972e21 0.410957
\(361\) −1.76335e21 −0.321756
\(362\) 1.53507e21 0.273592
\(363\) −1.09505e22 −1.90646
\(364\) 6.67100e21 1.13456
\(365\) −3.55154e21 −0.590102
\(366\) 8.60485e20 0.139686
\(367\) 2.22304e21 0.352603 0.176301 0.984336i \(-0.443587\pi\)
0.176301 + 0.984336i \(0.443587\pi\)
\(368\) 3.74839e21 0.580950
\(369\) 4.51830e21 0.684307
\(370\) −3.97348e20 −0.0588106
\(371\) 1.36698e22 1.97735
\(372\) 5.24053e21 0.740900
\(373\) −1.03913e22 −1.43597 −0.717985 0.696059i \(-0.754935\pi\)
−0.717985 + 0.696059i \(0.754935\pi\)
\(374\) −3.44262e20 −0.0465029
\(375\) −1.08562e22 −1.43354
\(376\) 1.02003e21 0.131679
\(377\) −1.60856e21 −0.203019
\(378\) −6.04888e21 −0.746439
\(379\) −9.65759e21 −1.16529 −0.582647 0.812725i \(-0.697983\pi\)
−0.582647 + 0.812725i \(0.697983\pi\)
\(380\) 2.64423e21 0.311988
\(381\) −2.03100e22 −2.34341
\(382\) 2.50921e21 0.283138
\(383\) −1.49999e22 −1.65539 −0.827693 0.561182i \(-0.810347\pi\)
−0.827693 + 0.561182i \(0.810347\pi\)
\(384\) 1.22930e22 1.32691
\(385\) 7.74335e20 0.0817547
\(386\) −1.25074e21 −0.129174
\(387\) −1.92584e22 −1.94570
\(388\) −9.01600e21 −0.891137
\(389\) 2.53264e21 0.244908 0.122454 0.992474i \(-0.460924\pi\)
0.122454 + 0.992474i \(0.460924\pi\)
\(390\) 1.63516e21 0.154708
\(391\) 9.13799e21 0.845957
\(392\) 6.02356e20 0.0545659
\(393\) 2.57883e22 2.28605
\(394\) 3.69330e21 0.320403
\(395\) 6.64909e21 0.564530
\(396\) −6.61577e21 −0.549758
\(397\) −6.77939e21 −0.551406 −0.275703 0.961243i \(-0.588911\pi\)
−0.275703 + 0.961243i \(0.588911\pi\)
\(398\) −1.23361e21 −0.0982138
\(399\) −2.24741e22 −1.75151
\(400\) −1.00012e22 −0.763029
\(401\) −1.41959e22 −1.06032 −0.530159 0.847898i \(-0.677868\pi\)
−0.530159 + 0.847898i \(0.677868\pi\)
\(402\) −7.78863e21 −0.569560
\(403\) 5.90618e21 0.422877
\(404\) 4.94465e21 0.346652
\(405\) 2.64486e22 1.81566
\(406\) −5.40437e20 −0.0363307
\(407\) 2.43115e21 0.160052
\(408\) 1.44602e22 0.932313
\(409\) 9.66139e20 0.0610087 0.0305043 0.999535i \(-0.490289\pi\)
0.0305043 + 0.999535i \(0.490289\pi\)
\(410\) −2.70098e20 −0.0167054
\(411\) −3.16384e22 −1.91672
\(412\) 1.33367e22 0.791446
\(413\) −1.61691e22 −0.939961
\(414\) −6.03429e21 −0.343655
\(415\) −3.68675e21 −0.205700
\(416\) 1.04555e22 0.571548
\(417\) −8.68169e21 −0.464995
\(418\) 5.55935e20 0.0291760
\(419\) 7.73948e21 0.398009 0.199004 0.979999i \(-0.436229\pi\)
0.199004 + 0.979999i \(0.436229\pi\)
\(420\) −1.59877e22 −0.805687
\(421\) 1.25042e22 0.617532 0.308766 0.951138i \(-0.400084\pi\)
0.308766 + 0.951138i \(0.400084\pi\)
\(422\) −1.21204e21 −0.0586625
\(423\) 2.26551e22 1.07467
\(424\) 1.42032e22 0.660356
\(425\) −2.43813e22 −1.11109
\(426\) −1.37543e22 −0.614409
\(427\) −9.48197e21 −0.415204
\(428\) −1.12541e22 −0.483102
\(429\) −1.00047e22 −0.421033
\(430\) 1.15124e21 0.0474989
\(431\) 9.32674e21 0.377288 0.188644 0.982046i \(-0.439591\pi\)
0.188644 + 0.982046i \(0.439591\pi\)
\(432\) 8.67104e22 3.43922
\(433\) 2.93512e22 1.14151 0.570753 0.821121i \(-0.306651\pi\)
0.570753 + 0.821121i \(0.306651\pi\)
\(434\) 1.98433e21 0.0756748
\(435\) 3.85506e21 0.144169
\(436\) 2.47388e22 0.907285
\(437\) −1.47566e22 −0.530755
\(438\) 1.54169e22 0.543836
\(439\) 4.39578e21 0.152086 0.0760428 0.997105i \(-0.475771\pi\)
0.0760428 + 0.997105i \(0.475771\pi\)
\(440\) 8.04553e20 0.0273028
\(441\) 1.33784e22 0.445325
\(442\) 8.01081e21 0.261570
\(443\) −3.38423e21 −0.108400 −0.0541999 0.998530i \(-0.517261\pi\)
−0.0541999 + 0.998530i \(0.517261\pi\)
\(444\) −5.01959e22 −1.57730
\(445\) 2.02901e21 0.0625495
\(446\) 5.85637e20 0.0177126
\(447\) −2.67686e21 −0.0794350
\(448\) −2.97200e22 −0.865339
\(449\) −3.94737e22 −1.12775 −0.563876 0.825859i \(-0.690691\pi\)
−0.563876 + 0.825859i \(0.690691\pi\)
\(450\) 1.61002e22 0.451363
\(451\) 1.65258e21 0.0454634
\(452\) −4.20281e22 −1.13465
\(453\) −1.34491e23 −3.56334
\(454\) 4.28283e21 0.111367
\(455\) −1.80184e22 −0.459854
\(456\) −2.33512e22 −0.584935
\(457\) 9.39007e21 0.230877 0.115439 0.993315i \(-0.463173\pi\)
0.115439 + 0.993315i \(0.463173\pi\)
\(458\) 5.66908e21 0.136822
\(459\) 2.11386e23 5.00806
\(460\) −1.04976e22 −0.244144
\(461\) 1.66822e22 0.380888 0.190444 0.981698i \(-0.439007\pi\)
0.190444 + 0.981698i \(0.439007\pi\)
\(462\) −3.36132e21 −0.0753449
\(463\) −3.15330e22 −0.693948 −0.346974 0.937875i \(-0.612791\pi\)
−0.346974 + 0.937875i \(0.612791\pi\)
\(464\) 7.74714e21 0.167393
\(465\) −1.41547e22 −0.300297
\(466\) −1.27280e22 −0.265144
\(467\) −5.13437e22 −1.05025 −0.525126 0.851024i \(-0.675982\pi\)
−0.525126 + 0.851024i \(0.675982\pi\)
\(468\) 1.53946e23 3.09228
\(469\) 8.58256e22 1.69296
\(470\) −1.35429e21 −0.0262350
\(471\) −8.55255e22 −1.62711
\(472\) −1.68001e22 −0.313909
\(473\) −7.04380e21 −0.129267
\(474\) −2.88631e22 −0.520268
\(475\) 3.93724e22 0.697102
\(476\) −7.83250e22 −1.36220
\(477\) 3.15457e23 5.38931
\(478\) −4.55195e20 −0.00763942
\(479\) 3.32260e22 0.547805 0.273902 0.961758i \(-0.411686\pi\)
0.273902 + 0.961758i \(0.411686\pi\)
\(480\) −2.50577e22 −0.405873
\(481\) −5.65718e22 −0.900258
\(482\) 1.73922e22 0.271929
\(483\) 8.92221e22 1.37063
\(484\) 6.16293e22 0.930255
\(485\) 2.43523e22 0.361190
\(486\) −6.70984e22 −0.977922
\(487\) 2.03886e21 0.0292005 0.0146003 0.999893i \(-0.495352\pi\)
0.0146003 + 0.999893i \(0.495352\pi\)
\(488\) −9.85200e21 −0.138661
\(489\) −2.39091e23 −3.30702
\(490\) −7.99744e20 −0.0108714
\(491\) −5.86767e22 −0.783922 −0.391961 0.919982i \(-0.628203\pi\)
−0.391961 + 0.919982i \(0.628203\pi\)
\(492\) −3.41207e22 −0.448038
\(493\) 1.88863e22 0.243752
\(494\) −1.29364e22 −0.164109
\(495\) 1.78693e22 0.222824
\(496\) −2.84453e22 −0.348671
\(497\) 1.51564e23 1.82627
\(498\) 1.60039e22 0.189573
\(499\) −6.29044e22 −0.732532 −0.366266 0.930510i \(-0.619364\pi\)
−0.366266 + 0.930510i \(0.619364\pi\)
\(500\) 6.10983e22 0.699494
\(501\) 5.84094e21 0.0657449
\(502\) 1.28436e22 0.142137
\(503\) −5.80357e22 −0.631491 −0.315746 0.948844i \(-0.602255\pi\)
−0.315746 + 0.948844i \(0.602255\pi\)
\(504\) 1.05221e23 1.12576
\(505\) −1.33555e22 −0.140503
\(506\) −2.20706e21 −0.0228315
\(507\) 3.80344e22 0.386909
\(508\) 1.14305e23 1.14346
\(509\) 7.27184e22 0.715391 0.357695 0.933838i \(-0.383563\pi\)
0.357695 + 0.933838i \(0.383563\pi\)
\(510\) −1.91987e22 −0.185748
\(511\) −1.69884e23 −1.61650
\(512\) −8.48856e22 −0.794400
\(513\) −3.41360e23 −3.14206
\(514\) 1.71534e22 0.155297
\(515\) −3.60225e22 −0.320784
\(516\) 1.45433e23 1.27391
\(517\) 8.28618e21 0.0713978
\(518\) −1.90067e22 −0.161103
\(519\) −8.87622e22 −0.740126
\(520\) −1.87216e22 −0.153573
\(521\) 6.46306e22 0.521576 0.260788 0.965396i \(-0.416018\pi\)
0.260788 + 0.965396i \(0.416018\pi\)
\(522\) −1.24716e22 −0.0990200
\(523\) −6.52155e21 −0.0509433 −0.0254716 0.999676i \(-0.508109\pi\)
−0.0254716 + 0.999676i \(0.508109\pi\)
\(524\) −1.45136e23 −1.11547
\(525\) −2.38056e23 −1.80021
\(526\) 4.01767e22 0.298948
\(527\) −6.93452e22 −0.507722
\(528\) 4.81845e22 0.347151
\(529\) −8.24665e22 −0.584661
\(530\) −1.88576e22 −0.131565
\(531\) −3.73132e23 −2.56188
\(532\) 1.26484e23 0.854648
\(533\) −3.84548e22 −0.255722
\(534\) −8.80775e21 −0.0576454
\(535\) 3.03975e22 0.195808
\(536\) 8.91749e22 0.565382
\(537\) 4.47260e23 2.79112
\(538\) −1.38665e22 −0.0851763
\(539\) 4.89320e21 0.0295861
\(540\) −2.42837e23 −1.44533
\(541\) −1.77640e23 −1.04079 −0.520396 0.853925i \(-0.674216\pi\)
−0.520396 + 0.853925i \(0.674216\pi\)
\(542\) 3.32141e22 0.191570
\(543\) −5.23782e23 −2.97408
\(544\) −1.22760e23 −0.686223
\(545\) −6.68198e22 −0.367735
\(546\) 7.82165e22 0.423800
\(547\) 2.55242e23 1.36163 0.680817 0.732454i \(-0.261625\pi\)
0.680817 + 0.732454i \(0.261625\pi\)
\(548\) 1.78060e23 0.935260
\(549\) −2.18815e23 −1.13165
\(550\) 5.88870e21 0.0299873
\(551\) −3.04988e22 −0.152930
\(552\) 9.27039e22 0.457737
\(553\) 3.18053e23 1.54645
\(554\) −3.26839e22 −0.156495
\(555\) 1.35580e23 0.639299
\(556\) 4.88604e22 0.226893
\(557\) 4.34159e22 0.198554 0.0992772 0.995060i \(-0.468347\pi\)
0.0992772 + 0.995060i \(0.468347\pi\)
\(558\) 4.57922e22 0.206253
\(559\) 1.63906e23 0.727100
\(560\) 8.67802e22 0.379160
\(561\) 1.17466e23 0.505508
\(562\) 6.05738e21 0.0256759
\(563\) 3.78966e23 1.58226 0.791132 0.611645i \(-0.209492\pi\)
0.791132 + 0.611645i \(0.209492\pi\)
\(564\) −1.71084e23 −0.703619
\(565\) 1.13518e23 0.459890
\(566\) 1.69078e22 0.0674758
\(567\) 1.26515e24 4.97376
\(568\) 1.57478e23 0.609902
\(569\) −6.99505e22 −0.266893 −0.133446 0.991056i \(-0.542604\pi\)
−0.133446 + 0.991056i \(0.542604\pi\)
\(570\) 3.10032e22 0.116539
\(571\) 2.29202e23 0.848813 0.424406 0.905472i \(-0.360483\pi\)
0.424406 + 0.905472i \(0.360483\pi\)
\(572\) 5.63061e22 0.205442
\(573\) −8.56171e23 −3.07784
\(574\) −1.29199e22 −0.0457622
\(575\) −1.56308e23 −0.545513
\(576\) −6.85846e23 −2.35850
\(577\) 4.59513e23 1.55705 0.778527 0.627612i \(-0.215967\pi\)
0.778527 + 0.627612i \(0.215967\pi\)
\(578\) −3.94686e22 −0.131785
\(579\) 4.26768e23 1.40418
\(580\) −2.16962e22 −0.0703472
\(581\) −1.76352e23 −0.563486
\(582\) −1.05711e23 −0.332871
\(583\) 1.15379e23 0.358051
\(584\) −1.76514e23 −0.539846
\(585\) −4.15809e23 −1.25334
\(586\) −9.42510e22 −0.279999
\(587\) 4.56546e23 1.33678 0.668391 0.743810i \(-0.266983\pi\)
0.668391 + 0.743810i \(0.266983\pi\)
\(588\) −1.01030e23 −0.291569
\(589\) 1.11983e23 0.318546
\(590\) 2.23053e22 0.0625413
\(591\) −1.26020e24 −3.48293
\(592\) 2.72461e23 0.742283
\(593\) −4.07180e23 −1.09351 −0.546754 0.837294i \(-0.684137\pi\)
−0.546754 + 0.837294i \(0.684137\pi\)
\(594\) −5.10552e22 −0.135162
\(595\) 2.11557e23 0.552119
\(596\) 1.50653e22 0.0387602
\(597\) 4.20923e23 1.06763
\(598\) 5.13572e22 0.128423
\(599\) −1.39283e23 −0.343376 −0.171688 0.985151i \(-0.554922\pi\)
−0.171688 + 0.985151i \(0.554922\pi\)
\(600\) −2.47345e23 −0.601199
\(601\) −1.16683e23 −0.279623 −0.139812 0.990178i \(-0.544650\pi\)
−0.139812 + 0.990178i \(0.544650\pi\)
\(602\) 5.50684e22 0.130116
\(603\) 1.98059e24 4.61421
\(604\) 7.56911e23 1.73872
\(605\) −1.66461e23 −0.377045
\(606\) 5.79753e22 0.129487
\(607\) −4.55704e23 −1.00364 −0.501821 0.864972i \(-0.667336\pi\)
−0.501821 + 0.864972i \(0.667336\pi\)
\(608\) 1.98240e23 0.430537
\(609\) 1.84403e23 0.394931
\(610\) 1.30804e22 0.0276260
\(611\) −1.92815e23 −0.401598
\(612\) −1.80750e24 −3.71271
\(613\) −1.48674e23 −0.301176 −0.150588 0.988597i \(-0.548117\pi\)
−0.150588 + 0.988597i \(0.548117\pi\)
\(614\) −7.22851e22 −0.144417
\(615\) 9.21604e22 0.181596
\(616\) 3.84850e22 0.0747921
\(617\) −9.12127e23 −1.74836 −0.874181 0.485600i \(-0.838601\pi\)
−0.874181 + 0.485600i \(0.838601\pi\)
\(618\) 1.56371e23 0.295633
\(619\) 2.35729e23 0.439584 0.219792 0.975547i \(-0.429462\pi\)
0.219792 + 0.975547i \(0.429462\pi\)
\(620\) 7.96625e22 0.146529
\(621\) 1.35520e24 2.45880
\(622\) 5.75856e22 0.103061
\(623\) 9.70556e22 0.171345
\(624\) −1.12123e24 −1.95266
\(625\) 3.27674e23 0.562940
\(626\) −1.52907e23 −0.259147
\(627\) −1.89692e23 −0.317157
\(628\) 4.81336e23 0.793947
\(629\) 6.64217e23 1.08088
\(630\) −1.39702e23 −0.224289
\(631\) 1.22019e23 0.193276 0.0966381 0.995320i \(-0.469191\pi\)
0.0966381 + 0.995320i \(0.469191\pi\)
\(632\) 3.30464e23 0.516451
\(633\) 4.13561e23 0.637688
\(634\) −1.32217e23 −0.201154
\(635\) −3.08738e23 −0.463461
\(636\) −2.38223e24 −3.52856
\(637\) −1.13862e23 −0.166416
\(638\) −4.56152e21 −0.00657861
\(639\) 3.49762e24 4.97755
\(640\) 1.86869e23 0.262426
\(641\) −8.85231e23 −1.22677 −0.613385 0.789784i \(-0.710193\pi\)
−0.613385 + 0.789784i \(0.710193\pi\)
\(642\) −1.31953e23 −0.180456
\(643\) 2.08225e23 0.281021 0.140511 0.990079i \(-0.455126\pi\)
0.140511 + 0.990079i \(0.455126\pi\)
\(644\) −5.02141e23 −0.668799
\(645\) −3.92816e23 −0.516335
\(646\) 1.51887e23 0.197036
\(647\) 1.36987e24 1.75386 0.876928 0.480622i \(-0.159589\pi\)
0.876928 + 0.480622i \(0.159589\pi\)
\(648\) 1.31452e24 1.66103
\(649\) −1.36474e23 −0.170204
\(650\) −1.37027e23 −0.168672
\(651\) −6.77077e23 −0.822621
\(652\) 1.34560e24 1.61366
\(653\) −6.01921e22 −0.0712488 −0.0356244 0.999365i \(-0.511342\pi\)
−0.0356244 + 0.999365i \(0.511342\pi\)
\(654\) 2.90059e23 0.338903
\(655\) 3.92014e23 0.452116
\(656\) 1.85206e23 0.210849
\(657\) −3.92041e24 −4.40581
\(658\) −6.47813e22 −0.0718670
\(659\) −9.41383e23 −1.03096 −0.515478 0.856903i \(-0.672386\pi\)
−0.515478 + 0.856903i \(0.672386\pi\)
\(660\) −1.34943e23 −0.145890
\(661\) 9.26012e23 0.988335 0.494168 0.869367i \(-0.335473\pi\)
0.494168 + 0.869367i \(0.335473\pi\)
\(662\) −1.31245e22 −0.0138290
\(663\) −2.73338e24 −2.84338
\(664\) −1.83234e23 −0.188182
\(665\) −3.41635e23 −0.346400
\(666\) −4.38617e23 −0.439091
\(667\) 1.21080e23 0.119675
\(668\) −3.28727e22 −0.0320801
\(669\) −1.99826e23 −0.192544
\(670\) −1.18397e23 −0.112643
\(671\) −8.00320e22 −0.0751835
\(672\) −1.19861e24 −1.11183
\(673\) 2.41956e23 0.221619 0.110810 0.993842i \(-0.464656\pi\)
0.110810 + 0.993842i \(0.464656\pi\)
\(674\) −3.34078e23 −0.302161
\(675\) −3.61583e24 −3.22943
\(676\) −2.14057e23 −0.188792
\(677\) 8.03744e23 0.700026 0.350013 0.936745i \(-0.386177\pi\)
0.350013 + 0.936745i \(0.386177\pi\)
\(678\) −4.92774e23 −0.423833
\(679\) 1.16487e24 0.989428
\(680\) 2.19812e23 0.184385
\(681\) −1.46135e24 −1.21061
\(682\) 1.67486e22 0.0137029
\(683\) 1.66430e24 1.34480 0.672398 0.740190i \(-0.265265\pi\)
0.672398 + 0.740190i \(0.265265\pi\)
\(684\) 2.91886e24 2.32936
\(685\) −4.80943e23 −0.379074
\(686\) 2.13065e23 0.165866
\(687\) −1.93436e24 −1.48732
\(688\) −7.89403e23 −0.599511
\(689\) −2.68482e24 −2.01396
\(690\) −1.23082e23 −0.0911966
\(691\) 1.12823e24 0.825724 0.412862 0.910794i \(-0.364529\pi\)
0.412862 + 0.910794i \(0.364529\pi\)
\(692\) 4.99552e23 0.361143
\(693\) 8.54759e23 0.610395
\(694\) 2.51557e22 0.0177452
\(695\) −1.31973e23 −0.0919629
\(696\) 1.91599e23 0.131891
\(697\) 4.51502e23 0.307030
\(698\) −4.08957e23 −0.274730
\(699\) 4.34295e24 2.88223
\(700\) 1.33977e24 0.878411
\(701\) −1.63857e24 −1.06136 −0.530679 0.847573i \(-0.678063\pi\)
−0.530679 + 0.847573i \(0.678063\pi\)
\(702\) 1.18803e24 0.760260
\(703\) −1.07262e24 −0.678149
\(704\) −2.50850e23 −0.156692
\(705\) 4.62100e23 0.285186
\(706\) −4.98986e23 −0.304263
\(707\) −6.38849e23 −0.384887
\(708\) 2.81778e24 1.67735
\(709\) −7.20175e22 −0.0423590 −0.0211795 0.999776i \(-0.506742\pi\)
−0.0211795 + 0.999776i \(0.506742\pi\)
\(710\) −2.09083e23 −0.121513
\(711\) 7.33967e24 4.21488
\(712\) 1.00843e23 0.0572224
\(713\) −4.44571e23 −0.249276
\(714\) −9.18349e23 −0.508831
\(715\) −1.52083e23 −0.0832685
\(716\) −2.51717e24 −1.36192
\(717\) 1.55318e23 0.0830441
\(718\) 4.17627e23 0.220664
\(719\) −1.27896e24 −0.667821 −0.333910 0.942605i \(-0.608368\pi\)
−0.333910 + 0.942605i \(0.608368\pi\)
\(720\) 2.00262e24 1.03341
\(721\) −1.72310e24 −0.878741
\(722\) 1.16359e23 0.0586452
\(723\) −5.93442e24 −2.95599
\(724\) 2.94784e24 1.45120
\(725\) −3.23056e23 −0.157183
\(726\) 7.22595e23 0.347483
\(727\) −7.38880e23 −0.351181 −0.175591 0.984463i \(-0.556184\pi\)
−0.175591 + 0.984463i \(0.556184\pi\)
\(728\) −8.95528e23 −0.420690
\(729\) 1.29154e25 5.99688
\(730\) 2.34357e23 0.107556
\(731\) −1.92444e24 −0.872985
\(732\) 1.65242e24 0.740927
\(733\) 3.18090e24 1.40983 0.704915 0.709292i \(-0.250985\pi\)
0.704915 + 0.709292i \(0.250985\pi\)
\(734\) −1.46692e23 −0.0642675
\(735\) 2.72882e23 0.118177
\(736\) −7.87011e23 −0.336914
\(737\) 7.24406e23 0.306555
\(738\) −2.98150e23 −0.124726
\(739\) −1.82222e23 −0.0753570 −0.0376785 0.999290i \(-0.511996\pi\)
−0.0376785 + 0.999290i \(0.511996\pi\)
\(740\) −7.63040e23 −0.311945
\(741\) 4.41404e24 1.78394
\(742\) −9.02033e23 −0.360404
\(743\) −2.52156e24 −0.996010 −0.498005 0.867174i \(-0.665934\pi\)
−0.498005 + 0.867174i \(0.665934\pi\)
\(744\) −7.03499e23 −0.274722
\(745\) −4.06916e22 −0.0157100
\(746\) 6.85694e23 0.261728
\(747\) −4.06966e24 −1.53579
\(748\) −6.61098e23 −0.246662
\(749\) 1.45403e24 0.536388
\(750\) 7.16369e23 0.261286
\(751\) −1.63527e24 −0.589724 −0.294862 0.955540i \(-0.595274\pi\)
−0.294862 + 0.955540i \(0.595274\pi\)
\(752\) 9.28637e23 0.331127
\(753\) −4.38240e24 −1.54509
\(754\) 1.06145e23 0.0370034
\(755\) −2.04442e24 −0.704728
\(756\) −1.16159e25 −3.95928
\(757\) −1.57529e24 −0.530941 −0.265471 0.964119i \(-0.585527\pi\)
−0.265471 + 0.964119i \(0.585527\pi\)
\(758\) 6.37278e23 0.212393
\(759\) 7.53074e23 0.248189
\(760\) −3.54967e23 −0.115684
\(761\) −5.40935e24 −1.74331 −0.871656 0.490118i \(-0.836954\pi\)
−0.871656 + 0.490118i \(0.836954\pi\)
\(762\) 1.34020e24 0.427124
\(763\) −3.19626e24 −1.00736
\(764\) 4.81852e24 1.50183
\(765\) 4.88207e24 1.50481
\(766\) 9.89804e23 0.301720
\(767\) 3.17569e24 0.957365
\(768\) 4.54608e24 1.35540
\(769\) 1.04343e24 0.307673 0.153837 0.988096i \(-0.450837\pi\)
0.153837 + 0.988096i \(0.450837\pi\)
\(770\) −5.10963e22 −0.0149011
\(771\) −5.85293e24 −1.68815
\(772\) −2.40184e24 −0.685168
\(773\) −3.76662e24 −1.06274 −0.531369 0.847140i \(-0.678322\pi\)
−0.531369 + 0.847140i \(0.678322\pi\)
\(774\) 1.27081e24 0.354635
\(775\) 1.18617e24 0.327403
\(776\) 1.21033e24 0.330429
\(777\) 6.48532e24 1.75127
\(778\) −1.67122e23 −0.0446383
\(779\) −7.29114e23 −0.192631
\(780\) 3.14006e24 0.820604
\(781\) 1.27926e24 0.330694
\(782\) −6.02991e23 −0.154189
\(783\) 2.80090e24 0.708473
\(784\) 5.48383e23 0.137214
\(785\) −1.30009e24 −0.321797
\(786\) −1.70170e24 −0.416669
\(787\) 1.71201e22 0.00414687 0.00207343 0.999998i \(-0.499340\pi\)
0.00207343 + 0.999998i \(0.499340\pi\)
\(788\) 7.09236e24 1.69949
\(789\) −1.37088e25 −3.24970
\(790\) −4.38755e23 −0.102894
\(791\) 5.43004e24 1.25980
\(792\) 8.88115e23 0.203847
\(793\) 1.86231e24 0.422892
\(794\) 4.47354e23 0.100502
\(795\) 6.43442e24 1.43017
\(796\) −2.36895e24 −0.520948
\(797\) 1.29137e24 0.280968 0.140484 0.990083i \(-0.455134\pi\)
0.140484 + 0.990083i \(0.455134\pi\)
\(798\) 1.48301e24 0.319241
\(799\) 2.26387e24 0.482174
\(800\) 2.09984e24 0.442509
\(801\) 2.23974e24 0.467005
\(802\) 9.36750e23 0.193260
\(803\) −1.43390e24 −0.292709
\(804\) −1.49568e25 −3.02108
\(805\) 1.35629e24 0.271073
\(806\) −3.89733e23 −0.0770760
\(807\) 4.73143e24 0.925906
\(808\) −6.63780e23 −0.128537
\(809\) −8.56357e24 −1.64094 −0.820469 0.571691i \(-0.806288\pi\)
−0.820469 + 0.571691i \(0.806288\pi\)
\(810\) −1.74527e24 −0.330934
\(811\) 4.33814e24 0.814003 0.407001 0.913428i \(-0.366574\pi\)
0.407001 + 0.913428i \(0.366574\pi\)
\(812\) −1.03782e24 −0.192706
\(813\) −1.13330e25 −2.08246
\(814\) −1.60425e23 −0.0291719
\(815\) −3.63447e24 −0.654036
\(816\) 1.31645e25 2.34443
\(817\) 3.10771e24 0.547712
\(818\) −6.37529e22 −0.0111198
\(819\) −1.98898e25 −3.43335
\(820\) −5.18678e23 −0.0886094
\(821\) −2.76330e23 −0.0467209 −0.0233604 0.999727i \(-0.507437\pi\)
−0.0233604 + 0.999727i \(0.507437\pi\)
\(822\) 2.08773e24 0.349353
\(823\) 2.64106e23 0.0437401 0.0218700 0.999761i \(-0.493038\pi\)
0.0218700 + 0.999761i \(0.493038\pi\)
\(824\) −1.79034e24 −0.293464
\(825\) −2.00929e24 −0.325976
\(826\) 1.06695e24 0.171323
\(827\) 2.49849e24 0.397082 0.198541 0.980093i \(-0.436380\pi\)
0.198541 + 0.980093i \(0.436380\pi\)
\(828\) −1.15879e25 −1.82283
\(829\) −8.02963e24 −1.25021 −0.625104 0.780542i \(-0.714943\pi\)
−0.625104 + 0.780542i \(0.714943\pi\)
\(830\) 2.43279e23 0.0374921
\(831\) 1.11521e25 1.70117
\(832\) 5.83717e24 0.881361
\(833\) 1.33687e24 0.199806
\(834\) 5.72882e23 0.0847527
\(835\) 8.87895e22 0.0130025
\(836\) 1.06758e24 0.154756
\(837\) −1.02841e25 −1.47571
\(838\) −5.10708e23 −0.0725435
\(839\) 8.05504e24 1.13264 0.566319 0.824186i \(-0.308367\pi\)
0.566319 + 0.824186i \(0.308367\pi\)
\(840\) 2.14622e24 0.298744
\(841\) 2.50246e23 0.0344828
\(842\) −8.25121e23 −0.112555
\(843\) −2.06685e24 −0.279109
\(844\) −2.32752e24 −0.311159
\(845\) 5.78171e23 0.0765198
\(846\) −1.49495e24 −0.195875
\(847\) −7.96252e24 −1.03286
\(848\) 1.29306e25 1.66056
\(849\) −5.76915e24 −0.733494
\(850\) 1.60886e24 0.202515
\(851\) 4.25828e24 0.530681
\(852\) −2.64129e25 −3.25897
\(853\) 1.35706e25 1.65780 0.828898 0.559399i \(-0.188968\pi\)
0.828898 + 0.559399i \(0.188968\pi\)
\(854\) 6.25690e23 0.0756776
\(855\) −7.88387e24 −0.944121
\(856\) 1.51078e24 0.179132
\(857\) 1.63694e25 1.92174 0.960871 0.276995i \(-0.0893386\pi\)
0.960871 + 0.276995i \(0.0893386\pi\)
\(858\) 6.60181e23 0.0767399
\(859\) −1.24343e25 −1.43113 −0.715565 0.698546i \(-0.753831\pi\)
−0.715565 + 0.698546i \(0.753831\pi\)
\(860\) 2.21076e24 0.251945
\(861\) 4.40841e24 0.497456
\(862\) −6.15446e23 −0.0687667
\(863\) −1.29499e25 −1.43276 −0.716381 0.697709i \(-0.754203\pi\)
−0.716381 + 0.697709i \(0.754203\pi\)
\(864\) −1.82057e25 −1.99453
\(865\) −1.34930e24 −0.146376
\(866\) −1.93681e24 −0.208058
\(867\) 1.34671e25 1.43256
\(868\) 3.81058e24 0.401396
\(869\) 2.68450e24 0.280025
\(870\) −2.54385e23 −0.0262772
\(871\) −1.68566e25 −1.72431
\(872\) −3.32099e24 −0.336417
\(873\) 2.68816e25 2.69671
\(874\) 9.73748e23 0.0967385
\(875\) −7.89391e24 −0.776647
\(876\) 2.96057e25 2.88463
\(877\) −5.42683e24 −0.523660 −0.261830 0.965114i \(-0.584326\pi\)
−0.261830 + 0.965114i \(0.584326\pi\)
\(878\) −2.90066e23 −0.0277200
\(879\) 3.21595e25 3.04372
\(880\) 7.32463e23 0.0686568
\(881\) −6.05842e24 −0.562425 −0.281212 0.959646i \(-0.590737\pi\)
−0.281212 + 0.959646i \(0.590737\pi\)
\(882\) −8.82806e23 −0.0811676
\(883\) −1.01581e24 −0.0925011 −0.0462506 0.998930i \(-0.514727\pi\)
−0.0462506 + 0.998930i \(0.514727\pi\)
\(884\) 1.53834e25 1.38742
\(885\) −7.61084e24 −0.679853
\(886\) 2.23316e23 0.0197576
\(887\) 1.08483e25 0.950624 0.475312 0.879817i \(-0.342335\pi\)
0.475312 + 0.879817i \(0.342335\pi\)
\(888\) 6.73840e24 0.584853
\(889\) −1.47682e25 −1.26959
\(890\) −1.33889e23 −0.0114006
\(891\) 1.06784e25 0.900627
\(892\) 1.12462e24 0.0939515
\(893\) −3.65584e24 −0.302517
\(894\) 1.76639e23 0.0144783
\(895\) 6.79890e24 0.552005
\(896\) 8.93870e24 0.718879
\(897\) −1.75237e25 −1.39601
\(898\) 2.60476e24 0.205551
\(899\) −9.18835e23 −0.0718257
\(900\) 3.09178e25 2.39413
\(901\) 3.15228e25 2.41804
\(902\) −1.09049e23 −0.00828643
\(903\) −1.87900e25 −1.41443
\(904\) 5.64194e24 0.420724
\(905\) −7.96214e24 −0.588189
\(906\) 8.87467e24 0.649475
\(907\) −1.59876e24 −0.115910 −0.0579552 0.998319i \(-0.518458\pi\)
−0.0579552 + 0.998319i \(0.518458\pi\)
\(908\) 8.22447e24 0.590715
\(909\) −1.47427e25 −1.04902
\(910\) 1.18899e24 0.0838157
\(911\) 1.21604e25 0.849263 0.424631 0.905366i \(-0.360404\pi\)
0.424631 + 0.905366i \(0.360404\pi\)
\(912\) −2.12589e25 −1.47090
\(913\) −1.48849e24 −0.102034
\(914\) −6.19625e23 −0.0420810
\(915\) −4.46320e24 −0.300308
\(916\) 1.08865e25 0.725735
\(917\) 1.87516e25 1.23851
\(918\) −1.39488e25 −0.912798
\(919\) 7.39958e24 0.479761 0.239881 0.970802i \(-0.422892\pi\)
0.239881 + 0.970802i \(0.422892\pi\)
\(920\) 1.40921e24 0.0905275
\(921\) 2.46645e25 1.56988
\(922\) −1.10082e24 −0.0694228
\(923\) −2.97679e25 −1.86009
\(924\) −6.45487e24 −0.399646
\(925\) −1.13616e25 −0.697005
\(926\) 2.08078e24 0.126483
\(927\) −3.97638e25 −2.39503
\(928\) −1.62658e24 −0.0970776
\(929\) 1.08328e25 0.640627 0.320314 0.947312i \(-0.396212\pi\)
0.320314 + 0.947312i \(0.396212\pi\)
\(930\) 9.34031e23 0.0547339
\(931\) −2.15887e24 −0.125358
\(932\) −2.44421e25 −1.40638
\(933\) −1.96489e25 −1.12033
\(934\) 3.38803e24 0.191425
\(935\) 1.78563e24 0.0999754
\(936\) −2.06660e25 −1.14660
\(937\) 1.79869e24 0.0988940 0.0494470 0.998777i \(-0.484254\pi\)
0.0494470 + 0.998777i \(0.484254\pi\)
\(938\) −5.66340e24 −0.308570
\(939\) 5.21737e25 2.81705
\(940\) −2.60069e24 −0.139156
\(941\) −2.05865e25 −1.09162 −0.545808 0.837910i \(-0.683777\pi\)
−0.545808 + 0.837910i \(0.683777\pi\)
\(942\) 5.64359e24 0.296567
\(943\) 2.89457e24 0.150742
\(944\) −1.52947e25 −0.789369
\(945\) 3.13746e25 1.60475
\(946\) 4.64801e23 0.0235609
\(947\) 2.13339e25 1.07176 0.535878 0.844295i \(-0.319981\pi\)
0.535878 + 0.844295i \(0.319981\pi\)
\(948\) −5.54268e25 −2.75962
\(949\) 3.33662e25 1.64643
\(950\) −2.59808e24 −0.127058
\(951\) 4.51141e25 2.18664
\(952\) 1.05145e25 0.505097
\(953\) 4.12328e24 0.196315 0.0981574 0.995171i \(-0.468705\pi\)
0.0981574 + 0.995171i \(0.468705\pi\)
\(954\) −2.08161e25 −0.982288
\(955\) −1.30149e25 −0.608711
\(956\) −8.74127e23 −0.0405212
\(957\) 1.55644e24 0.0715126
\(958\) −2.19249e24 −0.0998461
\(959\) −2.30054e25 −1.03842
\(960\) −1.39893e25 −0.625880
\(961\) −1.91764e25 −0.850391
\(962\) 3.73302e24 0.164086
\(963\) 3.35546e25 1.46194
\(964\) 3.33988e25 1.44237
\(965\) 6.48740e24 0.277708
\(966\) −5.88753e24 −0.249820
\(967\) −4.17524e25 −1.75613 −0.878065 0.478542i \(-0.841165\pi\)
−0.878065 + 0.478542i \(0.841165\pi\)
\(968\) −8.27325e24 −0.344934
\(969\) −5.18258e25 −2.14187
\(970\) −1.60694e24 −0.0658326
\(971\) 3.87541e24 0.157382 0.0786909 0.996899i \(-0.474926\pi\)
0.0786909 + 0.996899i \(0.474926\pi\)
\(972\) −1.28851e26 −5.18712
\(973\) −6.31278e24 −0.251919
\(974\) −1.34539e23 −0.00532226
\(975\) 4.67553e25 1.83355
\(976\) −8.96924e24 −0.348684
\(977\) 3.59633e25 1.38598 0.692988 0.720949i \(-0.256294\pi\)
0.692988 + 0.720949i \(0.256294\pi\)
\(978\) 1.57769e25 0.602757
\(979\) 8.19192e23 0.0310265
\(980\) −1.53578e24 −0.0576642
\(981\) −7.37598e25 −2.74557
\(982\) 3.87192e24 0.142882
\(983\) 4.11968e25 1.50716 0.753578 0.657358i \(-0.228326\pi\)
0.753578 + 0.657358i \(0.228326\pi\)
\(984\) 4.58044e24 0.166130
\(985\) −1.91565e25 −0.688825
\(986\) −1.24626e24 −0.0444277
\(987\) 2.21041e25 0.781228
\(988\) −2.48421e25 −0.870472
\(989\) −1.23376e25 −0.428608
\(990\) −1.17914e24 −0.0406133
\(991\) −1.12200e24 −0.0383149 −0.0191574 0.999816i \(-0.506098\pi\)
−0.0191574 + 0.999816i \(0.506098\pi\)
\(992\) 5.97236e24 0.202207
\(993\) 4.47823e24 0.150327
\(994\) −1.00013e25 −0.332867
\(995\) 6.39855e24 0.211147
\(996\) 3.07328e25 1.00554
\(997\) −3.90220e25 −1.26590 −0.632952 0.774191i \(-0.718157\pi\)
−0.632952 + 0.774191i \(0.718157\pi\)
\(998\) 4.15089e24 0.133516
\(999\) 9.85056e25 3.14163
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 29.18.a.b.1.9 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.18.a.b.1.9 21 1.1 even 1 trivial