Properties

Label 29.18.a.b.1.16
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 1.16
Character \(\chi\) \(=\) 29.1

$q$-expansion

\(f(q)\) \(=\) \(q+361.094 q^{2} -2259.76 q^{3} -683.052 q^{4} -433238. q^{5} -815984. q^{6} -1.41185e7 q^{7} -4.75760e7 q^{8} -1.24034e8 q^{9} +O(q^{10})\) \(q+361.094 q^{2} -2259.76 q^{3} -683.052 q^{4} -433238. q^{5} -815984. q^{6} -1.41185e7 q^{7} -4.75760e7 q^{8} -1.24034e8 q^{9} -1.56440e8 q^{10} -2.28788e8 q^{11} +1.54353e6 q^{12} +4.30393e9 q^{13} -5.09809e9 q^{14} +9.79012e8 q^{15} -1.70899e10 q^{16} +3.47755e10 q^{17} -4.47878e10 q^{18} +4.54956e10 q^{19} +2.95924e8 q^{20} +3.19043e10 q^{21} -8.26139e10 q^{22} +7.89750e10 q^{23} +1.07510e11 q^{24} -5.75244e11 q^{25} +1.55413e12 q^{26} +5.72111e11 q^{27} +9.64364e9 q^{28} +5.00246e11 q^{29} +3.53515e11 q^{30} -1.07216e12 q^{31} +6.48253e10 q^{32} +5.17005e11 q^{33} +1.25572e13 q^{34} +6.11665e12 q^{35} +8.47215e10 q^{36} +2.06120e13 q^{37} +1.64282e13 q^{38} -9.72584e12 q^{39} +2.06117e13 q^{40} -5.29668e12 q^{41} +1.15204e13 q^{42} +4.56833e13 q^{43} +1.56274e11 q^{44} +5.37361e13 q^{45} +2.85174e13 q^{46} -5.43318e13 q^{47} +3.86189e13 q^{48} -3.32996e13 q^{49} -2.07717e14 q^{50} -7.85841e13 q^{51} -2.93981e12 q^{52} -1.49915e14 q^{53} +2.06586e14 q^{54} +9.91196e13 q^{55} +6.71699e14 q^{56} -1.02809e14 q^{57} +1.80636e14 q^{58} -2.63283e14 q^{59} -6.68716e11 q^{60} +6.02615e14 q^{61} -3.87151e14 q^{62} +1.75116e15 q^{63} +2.26341e15 q^{64} -1.86463e15 q^{65} +1.86687e14 q^{66} +1.53138e15 q^{67} -2.37535e13 q^{68} -1.78464e14 q^{69} +2.20869e15 q^{70} +9.32986e15 q^{71} +5.90102e15 q^{72} -9.89992e14 q^{73} +7.44287e15 q^{74} +1.29991e15 q^{75} -3.10758e13 q^{76} +3.23013e15 q^{77} -3.51194e15 q^{78} +6.42999e15 q^{79} +7.40398e15 q^{80} +1.47249e16 q^{81} -1.91260e15 q^{82} +2.58298e16 q^{83} -2.17923e13 q^{84} -1.50661e16 q^{85} +1.64960e16 q^{86} -1.13043e15 q^{87} +1.08848e16 q^{88} -4.98199e16 q^{89} +1.94038e16 q^{90} -6.07649e16 q^{91} -5.39440e13 q^{92} +2.42282e15 q^{93} -1.96189e16 q^{94} -1.97104e16 q^{95} -1.46489e14 q^{96} +4.02028e16 q^{97} -1.20243e16 q^{98} +2.83774e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q + 256q^{2} + 23966q^{3} + 1452522q^{4} + 998272q^{5} + 3411526q^{6} + 2193368q^{7} - 138137226q^{8} + 1264832799q^{9} + O(q^{10}) \) \( 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 361.094 0.997391 0.498695 0.866777i \(-0.333813\pi\)
0.498695 + 0.866777i \(0.333813\pi\)
\(3\) −2259.76 −0.198852 −0.0994262 0.995045i \(-0.531701\pi\)
−0.0994262 + 0.995045i \(0.531701\pi\)
\(4\) −683.052 −0.00521127
\(5\) −433238. −0.496000 −0.248000 0.968760i \(-0.579773\pi\)
−0.248000 + 0.968760i \(0.579773\pi\)
\(6\) −815984. −0.198334
\(7\) −1.41185e7 −0.925665 −0.462833 0.886446i \(-0.653167\pi\)
−0.462833 + 0.886446i \(0.653167\pi\)
\(8\) −4.75760e7 −1.00259
\(9\) −1.24034e8 −0.960458
\(10\) −1.56440e8 −0.494706
\(11\) −2.28788e8 −0.321807 −0.160903 0.986970i \(-0.551441\pi\)
−0.160903 + 0.986970i \(0.551441\pi\)
\(12\) 1.54353e6 0.00103627
\(13\) 4.30393e9 1.46335 0.731673 0.681656i \(-0.238740\pi\)
0.731673 + 0.681656i \(0.238740\pi\)
\(14\) −5.09809e9 −0.923250
\(15\) 9.79012e8 0.0986307
\(16\) −1.70899e10 −0.994762
\(17\) 3.47755e10 1.20909 0.604543 0.796572i \(-0.293356\pi\)
0.604543 + 0.796572i \(0.293356\pi\)
\(18\) −4.47878e10 −0.957952
\(19\) 4.54956e10 0.614559 0.307279 0.951619i \(-0.400581\pi\)
0.307279 + 0.951619i \(0.400581\pi\)
\(20\) 2.95924e8 0.00258479
\(21\) 3.19043e10 0.184071
\(22\) −8.26139e10 −0.320967
\(23\) 7.89750e10 0.210282 0.105141 0.994457i \(-0.466471\pi\)
0.105141 + 0.994457i \(0.466471\pi\)
\(24\) 1.07510e11 0.199367
\(25\) −5.75244e11 −0.753984
\(26\) 1.55413e12 1.45953
\(27\) 5.72111e11 0.389842
\(28\) 9.64364e9 0.00482389
\(29\) 5.00246e11 0.185695
\(30\) 3.53515e11 0.0983734
\(31\) −1.07216e12 −0.225780 −0.112890 0.993607i \(-0.536011\pi\)
−0.112890 + 0.993607i \(0.536011\pi\)
\(32\) 6.48253e10 0.0104224
\(33\) 5.17005e11 0.0639920
\(34\) 1.25572e13 1.20593
\(35\) 6.11665e12 0.459130
\(36\) 8.47215e10 0.00500521
\(37\) 2.06120e13 0.964729 0.482364 0.875971i \(-0.339778\pi\)
0.482364 + 0.875971i \(0.339778\pi\)
\(38\) 1.64282e13 0.612955
\(39\) −9.72584e12 −0.290990
\(40\) 2.06117e13 0.497284
\(41\) −5.29668e12 −0.103595 −0.0517977 0.998658i \(-0.516495\pi\)
−0.0517977 + 0.998658i \(0.516495\pi\)
\(42\) 1.15204e13 0.183590
\(43\) 4.56833e13 0.596040 0.298020 0.954560i \(-0.403674\pi\)
0.298020 + 0.954560i \(0.403674\pi\)
\(44\) 1.56274e11 0.00167702
\(45\) 5.37361e13 0.476387
\(46\) 2.85174e13 0.209734
\(47\) −5.43318e13 −0.332830 −0.166415 0.986056i \(-0.553219\pi\)
−0.166415 + 0.986056i \(0.553219\pi\)
\(48\) 3.86189e13 0.197811
\(49\) −3.32996e13 −0.143144
\(50\) −2.07717e14 −0.752017
\(51\) −7.85841e13 −0.240430
\(52\) −2.93981e12 −0.00762590
\(53\) −1.49915e14 −0.330750 −0.165375 0.986231i \(-0.552883\pi\)
−0.165375 + 0.986231i \(0.552883\pi\)
\(54\) 2.06586e14 0.388824
\(55\) 9.91196e13 0.159616
\(56\) 6.71699e14 0.928061
\(57\) −1.02809e14 −0.122206
\(58\) 1.80636e14 0.185211
\(59\) −2.63283e14 −0.233443 −0.116722 0.993165i \(-0.537239\pi\)
−0.116722 + 0.993165i \(0.537239\pi\)
\(60\) −6.68716e11 −0.000513992 0
\(61\) 6.02615e14 0.402472 0.201236 0.979543i \(-0.435504\pi\)
0.201236 + 0.979543i \(0.435504\pi\)
\(62\) −3.87151e14 −0.225191
\(63\) 1.75116e15 0.889062
\(64\) 2.26341e15 1.00516
\(65\) −1.86463e15 −0.725819
\(66\) 1.86687e14 0.0638251
\(67\) 1.53138e15 0.460730 0.230365 0.973104i \(-0.426008\pi\)
0.230365 + 0.973104i \(0.426008\pi\)
\(68\) −2.37535e13 −0.00630088
\(69\) −1.78464e14 −0.0418152
\(70\) 2.20869e15 0.457932
\(71\) 9.32986e15 1.71466 0.857332 0.514763i \(-0.172120\pi\)
0.857332 + 0.514763i \(0.172120\pi\)
\(72\) 5.90102e15 0.962944
\(73\) −9.89992e14 −0.143677 −0.0718385 0.997416i \(-0.522887\pi\)
−0.0718385 + 0.997416i \(0.522887\pi\)
\(74\) 7.44287e15 0.962212
\(75\) 1.29991e15 0.149932
\(76\) −3.10758e13 −0.00320263
\(77\) 3.23013e15 0.297885
\(78\) −3.51194e15 −0.290231
\(79\) 6.42999e15 0.476848 0.238424 0.971161i \(-0.423369\pi\)
0.238424 + 0.971161i \(0.423369\pi\)
\(80\) 7.40398e15 0.493402
\(81\) 1.47249e16 0.882937
\(82\) −1.91260e15 −0.103325
\(83\) 2.58298e16 1.25880 0.629401 0.777080i \(-0.283300\pi\)
0.629401 + 0.777080i \(0.283300\pi\)
\(84\) −2.17923e13 −0.000959243 0
\(85\) −1.50661e16 −0.599707
\(86\) 1.64960e16 0.594485
\(87\) −1.13043e15 −0.0369260
\(88\) 1.08848e16 0.322640
\(89\) −4.98199e16 −1.34149 −0.670745 0.741688i \(-0.734026\pi\)
−0.670745 + 0.741688i \(0.734026\pi\)
\(90\) 1.94038e16 0.475144
\(91\) −6.07649e16 −1.35457
\(92\) −5.39440e13 −0.00109584
\(93\) 2.42282e15 0.0448969
\(94\) −1.96189e16 −0.331961
\(95\) −1.97104e16 −0.304821
\(96\) −1.46489e14 −0.00207253
\(97\) 4.02028e16 0.520831 0.260415 0.965497i \(-0.416140\pi\)
0.260415 + 0.965497i \(0.416140\pi\)
\(98\) −1.20243e16 −0.142770
\(99\) 2.83774e16 0.309082
\(100\) 3.92922e14 0.00392922
\(101\) −1.37975e17 −1.26785 −0.633925 0.773395i \(-0.718557\pi\)
−0.633925 + 0.773395i \(0.718557\pi\)
\(102\) −2.83763e16 −0.239802
\(103\) 4.22562e16 0.328681 0.164340 0.986404i \(-0.447450\pi\)
0.164340 + 0.986404i \(0.447450\pi\)
\(104\) −2.04764e17 −1.46713
\(105\) −1.38221e16 −0.0912990
\(106\) −5.41334e16 −0.329887
\(107\) −2.50719e17 −1.41067 −0.705335 0.708874i \(-0.749204\pi\)
−0.705335 + 0.708874i \(0.749204\pi\)
\(108\) −3.90782e14 −0.00203157
\(109\) −3.12026e16 −0.149991 −0.0749956 0.997184i \(-0.523894\pi\)
−0.0749956 + 0.997184i \(0.523894\pi\)
\(110\) 3.57915e16 0.159200
\(111\) −4.65780e16 −0.191839
\(112\) 2.41283e17 0.920816
\(113\) 3.91401e17 1.38502 0.692509 0.721409i \(-0.256505\pi\)
0.692509 + 0.721409i \(0.256505\pi\)
\(114\) −3.71237e16 −0.121888
\(115\) −3.42150e16 −0.104300
\(116\) −3.41694e14 −0.000967709 0
\(117\) −5.33833e17 −1.40548
\(118\) −9.50701e16 −0.232834
\(119\) −4.90976e17 −1.11921
\(120\) −4.65774e16 −0.0988860
\(121\) −4.53103e17 −0.896440
\(122\) 2.17601e17 0.401422
\(123\) 1.19692e16 0.0206002
\(124\) 7.32342e14 0.00117660
\(125\) 5.79752e17 0.869976
\(126\) 6.32335e17 0.886743
\(127\) 8.79572e17 1.15329 0.576647 0.816994i \(-0.304361\pi\)
0.576647 + 0.816994i \(0.304361\pi\)
\(128\) 8.08808e17 0.992112
\(129\) −1.03233e17 −0.118524
\(130\) −6.73306e17 −0.723926
\(131\) −1.06964e18 −1.07753 −0.538767 0.842455i \(-0.681110\pi\)
−0.538767 + 0.842455i \(0.681110\pi\)
\(132\) −3.53141e14 −0.000333480 0
\(133\) −6.42327e17 −0.568876
\(134\) 5.52971e17 0.459528
\(135\) −2.47860e17 −0.193361
\(136\) −1.65448e18 −1.21222
\(137\) 1.96077e18 1.34990 0.674949 0.737864i \(-0.264166\pi\)
0.674949 + 0.737864i \(0.264166\pi\)
\(138\) −6.44423e16 −0.0417061
\(139\) −7.92486e17 −0.482354 −0.241177 0.970481i \(-0.577533\pi\)
−0.241177 + 0.970481i \(0.577533\pi\)
\(140\) −4.17799e15 −0.00239265
\(141\) 1.22776e17 0.0661840
\(142\) 3.36896e18 1.71019
\(143\) −9.84688e17 −0.470915
\(144\) 2.11972e18 0.955426
\(145\) −2.16726e17 −0.0921049
\(146\) −3.57480e17 −0.143302
\(147\) 7.52490e16 0.0284645
\(148\) −1.40791e16 −0.00502747
\(149\) −2.70437e18 −0.911975 −0.455987 0.889986i \(-0.650714\pi\)
−0.455987 + 0.889986i \(0.650714\pi\)
\(150\) 4.69390e17 0.149540
\(151\) 9.73683e17 0.293166 0.146583 0.989198i \(-0.453172\pi\)
0.146583 + 0.989198i \(0.453172\pi\)
\(152\) −2.16450e18 −0.616150
\(153\) −4.31333e18 −1.16128
\(154\) 1.16638e18 0.297108
\(155\) 4.64501e17 0.111987
\(156\) 6.64325e15 0.00151643
\(157\) 6.54835e18 1.41574 0.707872 0.706341i \(-0.249655\pi\)
0.707872 + 0.706341i \(0.249655\pi\)
\(158\) 2.32183e18 0.475604
\(159\) 3.38771e17 0.0657704
\(160\) −2.80848e16 −0.00516953
\(161\) −1.11501e18 −0.194651
\(162\) 5.31707e18 0.880633
\(163\) 2.56556e18 0.403263 0.201631 0.979461i \(-0.435376\pi\)
0.201631 + 0.979461i \(0.435376\pi\)
\(164\) 3.61791e15 0.000539864 0
\(165\) −2.23986e17 −0.0317400
\(166\) 9.32700e18 1.25552
\(167\) 4.57045e18 0.584614 0.292307 0.956325i \(-0.405577\pi\)
0.292307 + 0.956325i \(0.405577\pi\)
\(168\) −1.51788e18 −0.184547
\(169\) 9.87343e18 1.14138
\(170\) −5.44027e18 −0.598142
\(171\) −5.64298e18 −0.590258
\(172\) −3.12040e16 −0.00310613
\(173\) 4.67606e18 0.443086 0.221543 0.975151i \(-0.428891\pi\)
0.221543 + 0.975151i \(0.428891\pi\)
\(174\) −4.08193e17 −0.0368296
\(175\) 8.12156e18 0.697937
\(176\) 3.90996e18 0.320121
\(177\) 5.94956e17 0.0464207
\(178\) −1.79897e19 −1.33799
\(179\) 1.66722e19 1.18234 0.591171 0.806546i \(-0.298666\pi\)
0.591171 + 0.806546i \(0.298666\pi\)
\(180\) −3.67046e16 −0.00248258
\(181\) −1.62147e19 −1.04627 −0.523133 0.852251i \(-0.675237\pi\)
−0.523133 + 0.852251i \(0.675237\pi\)
\(182\) −2.19419e19 −1.35103
\(183\) −1.36176e18 −0.0800326
\(184\) −3.75731e18 −0.210827
\(185\) −8.92990e18 −0.478505
\(186\) 8.74867e17 0.0447798
\(187\) −7.95621e18 −0.389092
\(188\) 3.71114e16 0.00173447
\(189\) −8.07732e18 −0.360863
\(190\) −7.11731e18 −0.304026
\(191\) 1.79651e19 0.733916 0.366958 0.930237i \(-0.380399\pi\)
0.366958 + 0.930237i \(0.380399\pi\)
\(192\) −5.11476e18 −0.199878
\(193\) −1.49005e19 −0.557139 −0.278569 0.960416i \(-0.589860\pi\)
−0.278569 + 0.960416i \(0.589860\pi\)
\(194\) 1.45170e19 0.519472
\(195\) 4.21360e18 0.144331
\(196\) 2.27454e16 0.000745962 0
\(197\) −3.35319e19 −1.05316 −0.526581 0.850125i \(-0.676526\pi\)
−0.526581 + 0.850125i \(0.676526\pi\)
\(198\) 1.02469e19 0.308275
\(199\) −5.61225e19 −1.61765 −0.808827 0.588046i \(-0.799897\pi\)
−0.808827 + 0.588046i \(0.799897\pi\)
\(200\) 2.73678e19 0.755936
\(201\) −3.46054e18 −0.0916172
\(202\) −4.98218e19 −1.26454
\(203\) −7.06271e18 −0.171892
\(204\) 5.36770e16 0.00125295
\(205\) 2.29472e18 0.0513833
\(206\) 1.52585e19 0.327823
\(207\) −9.79556e18 −0.201967
\(208\) −7.35537e19 −1.45568
\(209\) −1.04088e19 −0.197769
\(210\) −4.99109e18 −0.0910608
\(211\) 4.79947e19 0.840994 0.420497 0.907294i \(-0.361856\pi\)
0.420497 + 0.907294i \(0.361856\pi\)
\(212\) 1.02400e17 0.00172363
\(213\) −2.10832e19 −0.340965
\(214\) −9.05332e19 −1.40699
\(215\) −1.97917e19 −0.295636
\(216\) −2.72187e19 −0.390851
\(217\) 1.51373e19 0.208997
\(218\) −1.12671e19 −0.149600
\(219\) 2.23714e18 0.0285705
\(220\) −6.77038e16 −0.000831803 0
\(221\) 1.49671e20 1.76931
\(222\) −1.68191e19 −0.191338
\(223\) 1.61706e20 1.77066 0.885328 0.464967i \(-0.153934\pi\)
0.885328 + 0.464967i \(0.153934\pi\)
\(224\) −9.15233e17 −0.00964769
\(225\) 7.13497e19 0.724170
\(226\) 1.41333e20 1.38140
\(227\) 4.30189e19 0.404986 0.202493 0.979284i \(-0.435096\pi\)
0.202493 + 0.979284i \(0.435096\pi\)
\(228\) 7.02238e16 0.000636851 0
\(229\) 1.72831e20 1.51015 0.755075 0.655638i \(-0.227600\pi\)
0.755075 + 0.655638i \(0.227600\pi\)
\(230\) −1.23548e19 −0.104028
\(231\) −7.29931e18 −0.0592352
\(232\) −2.37997e19 −0.186176
\(233\) 2.22248e20 1.67615 0.838076 0.545554i \(-0.183681\pi\)
0.838076 + 0.545554i \(0.183681\pi\)
\(234\) −1.92764e20 −1.40182
\(235\) 2.35386e19 0.165083
\(236\) 1.79836e17 0.00121654
\(237\) −1.45302e19 −0.0948223
\(238\) −1.77289e20 −1.11629
\(239\) 1.44050e20 0.875246 0.437623 0.899158i \(-0.355820\pi\)
0.437623 + 0.899158i \(0.355820\pi\)
\(240\) −1.67312e19 −0.0981141
\(241\) 3.10781e19 0.175917 0.0879587 0.996124i \(-0.471966\pi\)
0.0879587 + 0.996124i \(0.471966\pi\)
\(242\) −1.63613e20 −0.894102
\(243\) −1.07157e20 −0.565416
\(244\) −4.11617e17 −0.00209739
\(245\) 1.44267e19 0.0709993
\(246\) 4.32201e18 0.0205465
\(247\) 1.95810e20 0.899312
\(248\) 5.10091e19 0.226365
\(249\) −5.83691e19 −0.250316
\(250\) 2.09345e20 0.867706
\(251\) 9.49597e19 0.380463 0.190232 0.981739i \(-0.439076\pi\)
0.190232 + 0.981739i \(0.439076\pi\)
\(252\) −1.19614e18 −0.00463315
\(253\) −1.80685e19 −0.0676703
\(254\) 3.17608e20 1.15028
\(255\) 3.40456e19 0.119253
\(256\) −4.61416e18 −0.0156334
\(257\) 3.95433e20 1.29611 0.648053 0.761595i \(-0.275583\pi\)
0.648053 + 0.761595i \(0.275583\pi\)
\(258\) −3.72768e19 −0.118215
\(259\) −2.91010e20 −0.893016
\(260\) 1.27364e18 0.00378244
\(261\) −6.20474e19 −0.178353
\(262\) −3.86240e20 −1.07472
\(263\) −5.83802e20 −1.57268 −0.786342 0.617791i \(-0.788028\pi\)
−0.786342 + 0.617791i \(0.788028\pi\)
\(264\) −2.45970e19 −0.0641577
\(265\) 6.49488e19 0.164052
\(266\) −2.31941e20 −0.567391
\(267\) 1.12581e20 0.266758
\(268\) −1.04601e18 −0.00240099
\(269\) 1.41736e20 0.315200 0.157600 0.987503i \(-0.449624\pi\)
0.157600 + 0.987503i \(0.449624\pi\)
\(270\) −8.95008e19 −0.192857
\(271\) −8.28766e20 −1.73058 −0.865292 0.501268i \(-0.832867\pi\)
−0.865292 + 0.501268i \(0.832867\pi\)
\(272\) −5.94309e20 −1.20275
\(273\) 1.37314e20 0.269359
\(274\) 7.08021e20 1.34638
\(275\) 1.31609e20 0.242637
\(276\) 1.21900e17 0.000217910 0
\(277\) 5.35448e20 0.928194 0.464097 0.885784i \(-0.346379\pi\)
0.464097 + 0.885784i \(0.346379\pi\)
\(278\) −2.86162e20 −0.481095
\(279\) 1.32984e20 0.216852
\(280\) −2.91006e20 −0.460318
\(281\) −1.64188e20 −0.251963 −0.125982 0.992033i \(-0.540208\pi\)
−0.125982 + 0.992033i \(0.540208\pi\)
\(282\) 4.43339e19 0.0660113
\(283\) 4.18506e18 0.00604668 0.00302334 0.999995i \(-0.499038\pi\)
0.00302334 + 0.999995i \(0.499038\pi\)
\(284\) −6.37278e18 −0.00893559
\(285\) 4.45407e19 0.0606144
\(286\) −3.55565e20 −0.469686
\(287\) 7.47809e19 0.0958947
\(288\) −8.04051e18 −0.0100103
\(289\) 3.82095e20 0.461891
\(290\) −7.82584e19 −0.0918645
\(291\) −9.08485e19 −0.103568
\(292\) 6.76216e17 0.000748740 0
\(293\) 5.14492e20 0.553355 0.276677 0.960963i \(-0.410767\pi\)
0.276677 + 0.960963i \(0.410767\pi\)
\(294\) 2.71720e19 0.0283902
\(295\) 1.14064e20 0.115788
\(296\) −9.80635e20 −0.967226
\(297\) −1.30892e20 −0.125454
\(298\) −9.76532e20 −0.909595
\(299\) 3.39903e20 0.307716
\(300\) −8.87907e17 −0.000781334 0
\(301\) −6.44977e20 −0.551733
\(302\) 3.51591e20 0.292401
\(303\) 3.11789e20 0.252115
\(304\) −7.77513e20 −0.611339
\(305\) −2.61076e20 −0.199626
\(306\) −1.55752e21 −1.15825
\(307\) −2.96318e19 −0.0214330 −0.0107165 0.999943i \(-0.503411\pi\)
−0.0107165 + 0.999943i \(0.503411\pi\)
\(308\) −2.20635e18 −0.00155236
\(309\) −9.54886e19 −0.0653589
\(310\) 1.67729e20 0.111695
\(311\) 3.00263e21 1.94553 0.972767 0.231786i \(-0.0744568\pi\)
0.972767 + 0.231786i \(0.0744568\pi\)
\(312\) 4.62716e20 0.291743
\(313\) −1.80401e21 −1.10691 −0.553454 0.832880i \(-0.686691\pi\)
−0.553454 + 0.832880i \(0.686691\pi\)
\(314\) 2.36457e21 1.41205
\(315\) −7.58671e20 −0.440975
\(316\) −4.39202e18 −0.00248498
\(317\) 4.23700e20 0.233375 0.116688 0.993169i \(-0.462772\pi\)
0.116688 + 0.993169i \(0.462772\pi\)
\(318\) 1.22328e20 0.0655988
\(319\) −1.14450e20 −0.0597580
\(320\) −9.80596e20 −0.498558
\(321\) 5.66564e20 0.280515
\(322\) −4.02622e20 −0.194143
\(323\) 1.58213e21 0.743055
\(324\) −1.00579e19 −0.00460123
\(325\) −2.47581e21 −1.10334
\(326\) 9.26409e20 0.402210
\(327\) 7.05103e19 0.0298261
\(328\) 2.51995e20 0.103864
\(329\) 7.67081e20 0.308089
\(330\) −8.08800e19 −0.0316572
\(331\) 7.74777e20 0.295555 0.147778 0.989021i \(-0.452788\pi\)
0.147778 + 0.989021i \(0.452788\pi\)
\(332\) −1.76431e19 −0.00655996
\(333\) −2.55658e21 −0.926581
\(334\) 1.65036e21 0.583089
\(335\) −6.63451e20 −0.228522
\(336\) −5.45240e20 −0.183106
\(337\) −4.66708e21 −1.52824 −0.764119 0.645075i \(-0.776826\pi\)
−0.764119 + 0.645075i \(0.776826\pi\)
\(338\) 3.56524e21 1.13840
\(339\) −8.84471e20 −0.275414
\(340\) 1.02909e19 0.00312524
\(341\) 2.45298e20 0.0726576
\(342\) −2.03765e21 −0.588718
\(343\) 3.75452e21 1.05817
\(344\) −2.17343e21 −0.597583
\(345\) 7.73174e19 0.0207403
\(346\) 1.68850e21 0.441930
\(347\) 2.40172e21 0.613368 0.306684 0.951811i \(-0.400781\pi\)
0.306684 + 0.951811i \(0.400781\pi\)
\(348\) 7.72146e17 0.000192431 0
\(349\) 3.18348e21 0.774257 0.387129 0.922026i \(-0.373467\pi\)
0.387129 + 0.922026i \(0.373467\pi\)
\(350\) 2.93265e21 0.696116
\(351\) 2.46233e21 0.570473
\(352\) −1.48312e19 −0.00335401
\(353\) 5.75633e21 1.27075 0.635376 0.772203i \(-0.280845\pi\)
0.635376 + 0.772203i \(0.280845\pi\)
\(354\) 2.14835e20 0.0462996
\(355\) −4.04205e21 −0.850473
\(356\) 3.40296e19 0.00699087
\(357\) 1.10949e21 0.222557
\(358\) 6.02025e21 1.17926
\(359\) 4.54608e21 0.869630 0.434815 0.900520i \(-0.356814\pi\)
0.434815 + 0.900520i \(0.356814\pi\)
\(360\) −2.55655e21 −0.477620
\(361\) −3.41054e21 −0.622318
\(362\) −5.85505e21 −1.04354
\(363\) 1.02390e21 0.178259
\(364\) 4.15056e19 0.00705903
\(365\) 4.28902e20 0.0712638
\(366\) −4.91724e20 −0.0798238
\(367\) 9.39502e21 1.49017 0.745086 0.666968i \(-0.232408\pi\)
0.745086 + 0.666968i \(0.232408\pi\)
\(368\) −1.34967e21 −0.209181
\(369\) 6.56966e20 0.0994991
\(370\) −3.22453e21 −0.477257
\(371\) 2.11657e21 0.306164
\(372\) −1.65491e18 −0.000233970 0
\(373\) 4.92376e21 0.680412 0.340206 0.940351i \(-0.389503\pi\)
0.340206 + 0.940351i \(0.389503\pi\)
\(374\) −2.87294e21 −0.388077
\(375\) −1.31010e21 −0.172997
\(376\) 2.58489e21 0.333691
\(377\) 2.15303e21 0.271737
\(378\) −2.91667e21 −0.359921
\(379\) −1.20746e22 −1.45694 −0.728468 0.685079i \(-0.759767\pi\)
−0.728468 + 0.685079i \(0.759767\pi\)
\(380\) 1.34632e19 0.00158851
\(381\) −1.98762e21 −0.229335
\(382\) 6.48710e21 0.732002
\(383\) 6.75134e21 0.745076 0.372538 0.928017i \(-0.378488\pi\)
0.372538 + 0.928017i \(0.378488\pi\)
\(384\) −1.82771e21 −0.197284
\(385\) −1.39942e21 −0.147751
\(386\) −5.38048e21 −0.555685
\(387\) −5.66626e21 −0.572471
\(388\) −2.74606e19 −0.00271419
\(389\) −7.82790e21 −0.756961 −0.378481 0.925609i \(-0.623553\pi\)
−0.378481 + 0.925609i \(0.623553\pi\)
\(390\) 1.52151e21 0.143954
\(391\) 2.74639e21 0.254250
\(392\) 1.58426e21 0.143514
\(393\) 2.41712e21 0.214270
\(394\) −1.21082e22 −1.05041
\(395\) −2.78571e21 −0.236516
\(396\) −1.93832e19 −0.00161071
\(397\) 1.23438e20 0.0100399 0.00501997 0.999987i \(-0.498402\pi\)
0.00501997 + 0.999987i \(0.498402\pi\)
\(398\) −2.02655e22 −1.61343
\(399\) 1.45150e21 0.113122
\(400\) 9.83085e21 0.750034
\(401\) −1.62453e22 −1.21339 −0.606694 0.794935i \(-0.707505\pi\)
−0.606694 + 0.794935i \(0.707505\pi\)
\(402\) −1.24958e21 −0.0913782
\(403\) −4.61451e21 −0.330395
\(404\) 9.42439e19 0.00660711
\(405\) −6.37939e21 −0.437937
\(406\) −2.55030e21 −0.171443
\(407\) −4.71577e21 −0.310456
\(408\) 3.73871e21 0.241052
\(409\) 6.74538e20 0.0425950 0.0212975 0.999773i \(-0.493220\pi\)
0.0212975 + 0.999773i \(0.493220\pi\)
\(410\) 8.28611e20 0.0512493
\(411\) −4.43085e21 −0.268430
\(412\) −2.88632e19 −0.00171284
\(413\) 3.71716e21 0.216090
\(414\) −3.53712e21 −0.201440
\(415\) −1.11905e22 −0.624366
\(416\) 2.79004e20 0.0152516
\(417\) 1.79082e21 0.0959172
\(418\) −3.75857e21 −0.197253
\(419\) −2.65087e22 −1.36323 −0.681614 0.731712i \(-0.738722\pi\)
−0.681614 + 0.731712i \(0.738722\pi\)
\(420\) 9.44124e18 0.000475784 0
\(421\) 7.51157e21 0.370965 0.185483 0.982648i \(-0.440615\pi\)
0.185483 + 0.982648i \(0.440615\pi\)
\(422\) 1.73306e22 0.838800
\(423\) 6.73897e21 0.319669
\(424\) 7.13234e21 0.331606
\(425\) −2.00044e22 −0.911632
\(426\) −7.61302e21 −0.340075
\(427\) −8.50799e21 −0.372555
\(428\) 1.71254e20 0.00735139
\(429\) 2.22515e21 0.0936425
\(430\) −7.14667e21 −0.294864
\(431\) 4.21364e22 1.70451 0.852256 0.523124i \(-0.175234\pi\)
0.852256 + 0.523124i \(0.175234\pi\)
\(432\) −9.77730e21 −0.387799
\(433\) −1.20126e22 −0.467187 −0.233594 0.972334i \(-0.575049\pi\)
−0.233594 + 0.972334i \(0.575049\pi\)
\(434\) 5.46598e21 0.208452
\(435\) 4.89747e20 0.0183153
\(436\) 2.13130e19 0.000781645 0
\(437\) 3.59301e21 0.129231
\(438\) 8.07817e20 0.0284960
\(439\) 1.85211e22 0.640792 0.320396 0.947284i \(-0.396184\pi\)
0.320396 + 0.947284i \(0.396184\pi\)
\(440\) −4.71571e21 −0.160029
\(441\) 4.13028e21 0.137484
\(442\) 5.40455e22 1.76470
\(443\) −2.08979e22 −0.669377 −0.334689 0.942329i \(-0.608631\pi\)
−0.334689 + 0.942329i \(0.608631\pi\)
\(444\) 3.18152e19 0.000999723 0
\(445\) 2.15839e22 0.665379
\(446\) 5.83910e22 1.76604
\(447\) 6.11121e21 0.181348
\(448\) −3.19559e22 −0.930439
\(449\) −7.53146e21 −0.215172 −0.107586 0.994196i \(-0.534312\pi\)
−0.107586 + 0.994196i \(0.534312\pi\)
\(450\) 2.57639e22 0.722281
\(451\) 1.21182e21 0.0333377
\(452\) −2.67348e20 −0.00721771
\(453\) −2.20029e21 −0.0582968
\(454\) 1.55339e22 0.403929
\(455\) 2.63257e22 0.671866
\(456\) 4.89123e21 0.122523
\(457\) 6.48078e22 1.59345 0.796727 0.604339i \(-0.206563\pi\)
0.796727 + 0.604339i \(0.206563\pi\)
\(458\) 6.24083e22 1.50621
\(459\) 1.98954e22 0.471352
\(460\) 2.33706e19 0.000543536 0
\(461\) −5.69183e22 −1.29955 −0.649777 0.760125i \(-0.725138\pi\)
−0.649777 + 0.760125i \(0.725138\pi\)
\(462\) −2.63574e21 −0.0590806
\(463\) −3.85663e22 −0.848730 −0.424365 0.905491i \(-0.639503\pi\)
−0.424365 + 0.905491i \(0.639503\pi\)
\(464\) −8.54915e21 −0.184723
\(465\) −1.04966e21 −0.0222689
\(466\) 8.02526e22 1.67178
\(467\) −5.50901e22 −1.12689 −0.563443 0.826155i \(-0.690524\pi\)
−0.563443 + 0.826155i \(0.690524\pi\)
\(468\) 3.64636e20 0.00732435
\(469\) −2.16207e22 −0.426482
\(470\) 8.49964e21 0.164653
\(471\) −1.47977e22 −0.281524
\(472\) 1.25260e22 0.234048
\(473\) −1.04518e22 −0.191810
\(474\) −5.24677e21 −0.0945749
\(475\) −2.61711e22 −0.463368
\(476\) 3.35362e20 0.00583251
\(477\) 1.85945e22 0.317671
\(478\) 5.20155e22 0.872963
\(479\) −7.25612e22 −1.19633 −0.598167 0.801371i \(-0.704104\pi\)
−0.598167 + 0.801371i \(0.704104\pi\)
\(480\) 6.34647e19 0.00102797
\(481\) 8.87126e22 1.41173
\(482\) 1.12221e22 0.175458
\(483\) 2.51964e21 0.0387068
\(484\) 3.09493e20 0.00467160
\(485\) −1.74174e22 −0.258332
\(486\) −3.86938e22 −0.563940
\(487\) −9.08930e22 −1.30177 −0.650885 0.759177i \(-0.725602\pi\)
−0.650885 + 0.759177i \(0.725602\pi\)
\(488\) −2.86700e22 −0.403514
\(489\) −5.79754e21 −0.0801897
\(490\) 5.20938e21 0.0708141
\(491\) −8.39289e22 −1.12129 −0.560646 0.828055i \(-0.689447\pi\)
−0.560646 + 0.828055i \(0.689447\pi\)
\(492\) −8.17558e18 −0.000107353 0
\(493\) 1.73963e22 0.224522
\(494\) 7.07058e22 0.896966
\(495\) −1.22942e22 −0.153305
\(496\) 1.83231e22 0.224598
\(497\) −1.31723e23 −1.58721
\(498\) −2.10767e22 −0.249663
\(499\) 3.02223e22 0.351943 0.175972 0.984395i \(-0.443693\pi\)
0.175972 + 0.984395i \(0.443693\pi\)
\(500\) −3.96001e20 −0.00453368
\(501\) −1.03281e22 −0.116252
\(502\) 3.42894e22 0.379471
\(503\) 1.25963e22 0.137062 0.0685308 0.997649i \(-0.478169\pi\)
0.0685308 + 0.997649i \(0.478169\pi\)
\(504\) −8.33133e22 −0.891364
\(505\) 5.97759e22 0.628853
\(506\) −6.52444e21 −0.0674937
\(507\) −2.23115e22 −0.226966
\(508\) −6.00793e20 −0.00601013
\(509\) −1.27820e23 −1.25747 −0.628735 0.777619i \(-0.716427\pi\)
−0.628735 + 0.777619i \(0.716427\pi\)
\(510\) 1.22937e22 0.118942
\(511\) 1.39772e22 0.132997
\(512\) −1.07678e23 −1.00770
\(513\) 2.60285e22 0.239581
\(514\) 1.42788e23 1.29273
\(515\) −1.83070e22 −0.163025
\(516\) 7.05135e19 0.000617660 0
\(517\) 1.24304e22 0.107107
\(518\) −1.05082e23 −0.890686
\(519\) −1.05668e22 −0.0881088
\(520\) 8.87115e22 0.727698
\(521\) 8.24007e22 0.664983 0.332491 0.943106i \(-0.392111\pi\)
0.332491 + 0.943106i \(0.392111\pi\)
\(522\) −2.24049e22 −0.177887
\(523\) 1.66840e23 1.30327 0.651636 0.758532i \(-0.274083\pi\)
0.651636 + 0.758532i \(0.274083\pi\)
\(524\) 7.30619e20 0.00561532
\(525\) −1.83527e22 −0.138786
\(526\) −2.10807e23 −1.56858
\(527\) −3.72850e22 −0.272988
\(528\) −8.83554e21 −0.0636568
\(529\) −1.34813e23 −0.955781
\(530\) 2.34526e22 0.163624
\(531\) 3.26560e22 0.224212
\(532\) 4.38743e20 0.00296457
\(533\) −2.27965e22 −0.151596
\(534\) 4.06522e22 0.266062
\(535\) 1.08621e23 0.699692
\(536\) −7.28568e22 −0.461923
\(537\) −3.76752e22 −0.235111
\(538\) 5.11801e22 0.314378
\(539\) 7.61855e21 0.0460647
\(540\) 1.69301e20 0.00100766
\(541\) 1.28619e23 0.753578 0.376789 0.926299i \(-0.377028\pi\)
0.376789 + 0.926299i \(0.377028\pi\)
\(542\) −2.99262e23 −1.72607
\(543\) 3.66413e22 0.208052
\(544\) 2.25433e21 0.0126016
\(545\) 1.35182e22 0.0743956
\(546\) 4.95832e22 0.268656
\(547\) 1.36246e23 0.726826 0.363413 0.931628i \(-0.381611\pi\)
0.363413 + 0.931628i \(0.381611\pi\)
\(548\) −1.33931e21 −0.00703469
\(549\) −7.47445e22 −0.386558
\(550\) 4.75232e22 0.242004
\(551\) 2.27590e22 0.114121
\(552\) 8.49060e21 0.0419234
\(553\) −9.07815e22 −0.441401
\(554\) 1.93347e23 0.925773
\(555\) 2.01794e22 0.0951519
\(556\) 5.41309e20 0.00251368
\(557\) −1.80838e23 −0.827031 −0.413515 0.910497i \(-0.635699\pi\)
−0.413515 + 0.910497i \(0.635699\pi\)
\(558\) 4.80198e22 0.216287
\(559\) 1.96618e23 0.872212
\(560\) −1.04533e23 −0.456725
\(561\) 1.79791e22 0.0773719
\(562\) −5.92872e22 −0.251306
\(563\) 9.08213e22 0.379198 0.189599 0.981862i \(-0.439281\pi\)
0.189599 + 0.981862i \(0.439281\pi\)
\(564\) −8.38627e19 −0.000344903 0
\(565\) −1.69570e23 −0.686969
\(566\) 1.51120e21 0.00603091
\(567\) −2.07893e23 −0.817304
\(568\) −4.43877e23 −1.71910
\(569\) 1.95996e23 0.747813 0.373906 0.927466i \(-0.378018\pi\)
0.373906 + 0.927466i \(0.378018\pi\)
\(570\) 1.60834e22 0.0604562
\(571\) 3.40549e23 1.26117 0.630583 0.776121i \(-0.282816\pi\)
0.630583 + 0.776121i \(0.282816\pi\)
\(572\) 6.72593e20 0.00245407
\(573\) −4.05968e22 −0.145941
\(574\) 2.70030e22 0.0956445
\(575\) −4.54299e22 −0.158550
\(576\) −2.80739e23 −0.965411
\(577\) 5.07118e23 1.71836 0.859181 0.511672i \(-0.170974\pi\)
0.859181 + 0.511672i \(0.170974\pi\)
\(578\) 1.37972e23 0.460686
\(579\) 3.36715e22 0.110788
\(580\) 1.48035e20 0.000479984 0
\(581\) −3.64677e23 −1.16523
\(582\) −3.28049e22 −0.103298
\(583\) 3.42987e22 0.106438
\(584\) 4.70998e22 0.144049
\(585\) 2.31277e23 0.697119
\(586\) 1.85780e23 0.551911
\(587\) 5.19155e23 1.52010 0.760052 0.649862i \(-0.225174\pi\)
0.760052 + 0.649862i \(0.225174\pi\)
\(588\) −5.13990e19 −0.000148336 0
\(589\) −4.87786e22 −0.138755
\(590\) 4.11880e22 0.115486
\(591\) 7.57739e22 0.209424
\(592\) −3.52256e23 −0.959675
\(593\) −1.48323e23 −0.398332 −0.199166 0.979966i \(-0.563823\pi\)
−0.199166 + 0.979966i \(0.563823\pi\)
\(594\) −4.72643e22 −0.125126
\(595\) 2.12710e23 0.555128
\(596\) 1.84723e21 0.00475255
\(597\) 1.26823e23 0.321674
\(598\) 1.22737e23 0.306913
\(599\) −3.86765e23 −0.953497 −0.476748 0.879040i \(-0.658185\pi\)
−0.476748 + 0.879040i \(0.658185\pi\)
\(600\) −6.18445e22 −0.150320
\(601\) 4.34922e23 1.04227 0.521133 0.853475i \(-0.325510\pi\)
0.521133 + 0.853475i \(0.325510\pi\)
\(602\) −2.32897e23 −0.550294
\(603\) −1.89942e23 −0.442512
\(604\) −6.65076e20 −0.00152777
\(605\) 1.96302e23 0.444634
\(606\) 1.12585e23 0.251457
\(607\) 1.19494e23 0.263175 0.131587 0.991305i \(-0.457993\pi\)
0.131587 + 0.991305i \(0.457993\pi\)
\(608\) 2.94926e21 0.00640520
\(609\) 1.59600e22 0.0341811
\(610\) −9.42728e22 −0.199105
\(611\) −2.33840e23 −0.487045
\(612\) 2.94623e21 0.00605173
\(613\) 6.79381e23 1.37626 0.688128 0.725589i \(-0.258433\pi\)
0.688128 + 0.725589i \(0.258433\pi\)
\(614\) −1.06999e22 −0.0213771
\(615\) −5.18551e21 −0.0102177
\(616\) −1.53677e23 −0.298656
\(617\) 4.92283e22 0.0943606 0.0471803 0.998886i \(-0.484976\pi\)
0.0471803 + 0.998886i \(0.484976\pi\)
\(618\) −3.44804e22 −0.0651884
\(619\) −4.65769e23 −0.868560 −0.434280 0.900778i \(-0.642997\pi\)
−0.434280 + 0.900778i \(0.642997\pi\)
\(620\) −3.17279e20 −0.000583595 0
\(621\) 4.51824e22 0.0819768
\(622\) 1.08423e24 1.94046
\(623\) 7.03380e23 1.24177
\(624\) 1.66213e23 0.289465
\(625\) 1.87706e23 0.322476
\(626\) −6.51417e23 −1.10402
\(627\) 2.35214e22 0.0393269
\(628\) −4.47286e21 −0.00737783
\(629\) 7.16792e23 1.16644
\(630\) −2.73952e23 −0.439824
\(631\) 6.56020e23 1.03912 0.519562 0.854433i \(-0.326095\pi\)
0.519562 + 0.854433i \(0.326095\pi\)
\(632\) −3.05913e23 −0.478082
\(633\) −1.08456e23 −0.167234
\(634\) 1.52996e23 0.232766
\(635\) −3.81064e23 −0.572033
\(636\) −2.31398e20 −0.000342748 0
\(637\) −1.43319e23 −0.209469
\(638\) −4.13273e22 −0.0596021
\(639\) −1.15722e24 −1.64686
\(640\) −3.50406e23 −0.492087
\(641\) −3.45513e23 −0.478819 −0.239409 0.970919i \(-0.576954\pi\)
−0.239409 + 0.970919i \(0.576954\pi\)
\(642\) 2.04583e23 0.279783
\(643\) 1.30958e23 0.176742 0.0883711 0.996088i \(-0.471834\pi\)
0.0883711 + 0.996088i \(0.471834\pi\)
\(644\) 7.61607e20 0.00101438
\(645\) 4.47244e22 0.0587878
\(646\) 5.71298e23 0.741116
\(647\) −1.84975e23 −0.236825 −0.118413 0.992964i \(-0.537781\pi\)
−0.118413 + 0.992964i \(0.537781\pi\)
\(648\) −7.00551e23 −0.885222
\(649\) 6.02361e22 0.0751236
\(650\) −8.94002e23 −1.10046
\(651\) −3.42065e22 −0.0415595
\(652\) −1.75241e21 −0.00210151
\(653\) 1.66260e23 0.196800 0.0984002 0.995147i \(-0.468627\pi\)
0.0984002 + 0.995147i \(0.468627\pi\)
\(654\) 2.54608e22 0.0297483
\(655\) 4.63408e23 0.534457
\(656\) 9.05196e22 0.103053
\(657\) 1.22792e23 0.137996
\(658\) 2.76988e23 0.307285
\(659\) −4.00812e23 −0.438949 −0.219475 0.975618i \(-0.570434\pi\)
−0.219475 + 0.975618i \(0.570434\pi\)
\(660\) 1.52994e20 0.000165406 0
\(661\) −1.35342e24 −1.44451 −0.722256 0.691626i \(-0.756895\pi\)
−0.722256 + 0.691626i \(0.756895\pi\)
\(662\) 2.79767e23 0.294784
\(663\) −3.38221e23 −0.351832
\(664\) −1.22888e24 −1.26206
\(665\) 2.78281e23 0.282162
\(666\) −9.23166e23 −0.924164
\(667\) 3.95070e22 0.0390485
\(668\) −3.12186e21 −0.00304658
\(669\) −3.65415e23 −0.352099
\(670\) −2.39568e23 −0.227926
\(671\) −1.37871e23 −0.129518
\(672\) 2.06820e21 0.00191847
\(673\) 8.66002e23 0.793215 0.396608 0.917988i \(-0.370187\pi\)
0.396608 + 0.917988i \(0.370187\pi\)
\(674\) −1.68526e24 −1.52425
\(675\) −3.29103e23 −0.293934
\(676\) −6.74407e21 −0.00594805
\(677\) −4.16997e23 −0.363186 −0.181593 0.983374i \(-0.558125\pi\)
−0.181593 + 0.983374i \(0.558125\pi\)
\(678\) −3.19377e23 −0.274696
\(679\) −5.67602e23 −0.482115
\(680\) 7.16783e23 0.601259
\(681\) −9.72122e22 −0.0805323
\(682\) 8.85755e22 0.0724681
\(683\) 2.20244e23 0.177962 0.0889812 0.996033i \(-0.471639\pi\)
0.0889812 + 0.996033i \(0.471639\pi\)
\(684\) 3.85445e21 0.00307599
\(685\) −8.49478e23 −0.669549
\(686\) 1.35574e24 1.05541
\(687\) −3.90556e23 −0.300297
\(688\) −7.80721e23 −0.592917
\(689\) −6.45223e23 −0.484002
\(690\) 2.79189e22 0.0206862
\(691\) 1.77459e24 1.29878 0.649389 0.760456i \(-0.275025\pi\)
0.649389 + 0.760456i \(0.275025\pi\)
\(692\) −3.19399e21 −0.00230904
\(693\) −4.00645e23 −0.286106
\(694\) 8.67245e23 0.611768
\(695\) 3.43335e23 0.239247
\(696\) 5.37815e22 0.0370215
\(697\) −1.84195e23 −0.125256
\(698\) 1.14953e24 0.772237
\(699\) −5.02227e23 −0.333307
\(700\) −5.54745e21 −0.00363714
\(701\) −6.81837e23 −0.441649 −0.220825 0.975314i \(-0.570875\pi\)
−0.220825 + 0.975314i \(0.570875\pi\)
\(702\) 8.89132e23 0.568985
\(703\) 9.37754e23 0.592882
\(704\) −5.17841e23 −0.323466
\(705\) −5.31914e22 −0.0328272
\(706\) 2.07858e24 1.26744
\(707\) 1.94799e24 1.17360
\(708\) −4.06386e20 −0.000241911 0
\(709\) −2.52327e24 −1.48413 −0.742063 0.670330i \(-0.766153\pi\)
−0.742063 + 0.670330i \(0.766153\pi\)
\(710\) −1.45956e24 −0.848254
\(711\) −7.97535e23 −0.457992
\(712\) 2.37023e24 1.34496
\(713\) −8.46740e22 −0.0474776
\(714\) 4.00629e23 0.221977
\(715\) 4.26604e23 0.233574
\(716\) −1.13880e22 −0.00616151
\(717\) −3.25517e23 −0.174045
\(718\) 1.64156e24 0.867361
\(719\) −1.14410e24 −0.597406 −0.298703 0.954346i \(-0.596554\pi\)
−0.298703 + 0.954346i \(0.596554\pi\)
\(720\) −9.18343e23 −0.473891
\(721\) −5.96592e23 −0.304248
\(722\) −1.23153e24 −0.620694
\(723\) −7.02288e22 −0.0349816
\(724\) 1.10755e22 0.00545238
\(725\) −2.87764e23 −0.140011
\(726\) 3.69725e23 0.177794
\(727\) 1.05434e24 0.501118 0.250559 0.968101i \(-0.419386\pi\)
0.250559 + 0.968101i \(0.419386\pi\)
\(728\) 2.89095e24 1.35808
\(729\) −1.65943e24 −0.770503
\(730\) 1.54874e23 0.0710778
\(731\) 1.58866e24 0.720664
\(732\) 9.30154e20 0.000417072 0
\(733\) 3.85209e24 1.70731 0.853656 0.520838i \(-0.174380\pi\)
0.853656 + 0.520838i \(0.174380\pi\)
\(734\) 3.39249e24 1.48628
\(735\) −3.26007e22 −0.0141184
\(736\) 5.11957e21 0.00219166
\(737\) −3.50361e23 −0.148266
\(738\) 2.37227e23 0.0992395
\(739\) −1.44868e24 −0.599093 −0.299546 0.954082i \(-0.596835\pi\)
−0.299546 + 0.954082i \(0.596835\pi\)
\(740\) 6.09958e21 0.00249362
\(741\) −4.42482e23 −0.178830
\(742\) 7.64280e23 0.305365
\(743\) 3.95298e24 1.56142 0.780709 0.624894i \(-0.214858\pi\)
0.780709 + 0.624894i \(0.214858\pi\)
\(744\) −1.15268e23 −0.0450132
\(745\) 1.17164e24 0.452339
\(746\) 1.77794e24 0.678637
\(747\) −3.20377e24 −1.20903
\(748\) 5.43451e21 0.00202767
\(749\) 3.53977e24 1.30581
\(750\) −4.73069e23 −0.172545
\(751\) 3.34972e24 1.20800 0.604002 0.796983i \(-0.293572\pi\)
0.604002 + 0.796983i \(0.293572\pi\)
\(752\) 9.28523e23 0.331086
\(753\) −2.14586e23 −0.0756560
\(754\) 7.77445e23 0.271028
\(755\) −4.21837e23 −0.145410
\(756\) 5.51723e21 0.00188055
\(757\) −5.40799e24 −1.82272 −0.911362 0.411605i \(-0.864968\pi\)
−0.911362 + 0.411605i \(0.864968\pi\)
\(758\) −4.36008e24 −1.45314
\(759\) 4.08304e22 0.0134564
\(760\) 9.37742e23 0.305610
\(761\) 4.57639e24 1.47487 0.737434 0.675419i \(-0.236037\pi\)
0.737434 + 0.675419i \(0.236037\pi\)
\(762\) −7.17717e23 −0.228737
\(763\) 4.40533e23 0.138842
\(764\) −1.22711e22 −0.00382464
\(765\) 1.86870e24 0.575993
\(766\) 2.43787e24 0.743132
\(767\) −1.13315e24 −0.341608
\(768\) 1.04269e22 0.00310874
\(769\) −4.78476e24 −1.41087 −0.705433 0.708776i \(-0.749248\pi\)
−0.705433 + 0.708776i \(0.749248\pi\)
\(770\) −5.05321e23 −0.147366
\(771\) −8.93581e23 −0.257734
\(772\) 1.01778e22 0.00290340
\(773\) −2.88301e24 −0.813431 −0.406715 0.913555i \(-0.633326\pi\)
−0.406715 + 0.913555i \(0.633326\pi\)
\(774\) −2.04605e24 −0.570977
\(775\) 6.16755e23 0.170235
\(776\) −1.91269e24 −0.522179
\(777\) 6.57610e23 0.177578
\(778\) −2.82661e24 −0.754986
\(779\) −2.40975e23 −0.0636655
\(780\) −2.87811e21 −0.000752148 0
\(781\) −2.13456e24 −0.551791
\(782\) 9.91707e23 0.253586
\(783\) 2.86196e23 0.0723918
\(784\) 5.69087e23 0.142394
\(785\) −2.83699e24 −0.702209
\(786\) 8.72808e23 0.213711
\(787\) −5.78719e24 −1.40179 −0.700894 0.713265i \(-0.747216\pi\)
−0.700894 + 0.713265i \(0.747216\pi\)
\(788\) 2.29040e22 0.00548831
\(789\) 1.31925e24 0.312732
\(790\) −1.00591e24 −0.235899
\(791\) −5.52598e24 −1.28206
\(792\) −1.35008e24 −0.309882
\(793\) 2.59361e24 0.588956
\(794\) 4.45729e22 0.0100137
\(795\) −1.46768e23 −0.0326221
\(796\) 3.83346e22 0.00843004
\(797\) −3.86589e24 −0.841112 −0.420556 0.907267i \(-0.638165\pi\)
−0.420556 + 0.907267i \(0.638165\pi\)
\(798\) 5.24129e23 0.112827
\(799\) −1.88941e24 −0.402420
\(800\) −3.72904e22 −0.00785836
\(801\) 6.17934e24 1.28844
\(802\) −5.86607e24 −1.21022
\(803\) 2.26498e23 0.0462362
\(804\) 2.36373e21 0.000477442 0
\(805\) 4.83063e23 0.0965469
\(806\) −1.66627e24 −0.329533
\(807\) −3.20289e23 −0.0626782
\(808\) 6.56428e24 1.27113
\(809\) −7.76614e24 −1.48814 −0.744069 0.668103i \(-0.767106\pi\)
−0.744069 + 0.668103i \(0.767106\pi\)
\(810\) −2.30356e24 −0.436794
\(811\) 5.97255e24 1.12068 0.560341 0.828262i \(-0.310670\pi\)
0.560341 + 0.828262i \(0.310670\pi\)
\(812\) 4.82420e21 0.000895775 0
\(813\) 1.87281e24 0.344131
\(814\) −1.70284e24 −0.309646
\(815\) −1.11150e24 −0.200018
\(816\) 1.34299e24 0.239170
\(817\) 2.07839e24 0.366301
\(818\) 2.43572e23 0.0424838
\(819\) 7.53689e24 1.30101
\(820\) −1.56741e21 −0.000267773 0
\(821\) −3.79757e24 −0.642080 −0.321040 0.947066i \(-0.604032\pi\)
−0.321040 + 0.947066i \(0.604032\pi\)
\(822\) −1.59995e24 −0.267730
\(823\) −2.24155e24 −0.371235 −0.185618 0.982622i \(-0.559429\pi\)
−0.185618 + 0.982622i \(0.559429\pi\)
\(824\) −2.01038e24 −0.329531
\(825\) −2.97404e23 −0.0482490
\(826\) 1.34224e24 0.215527
\(827\) 5.49632e24 0.873525 0.436763 0.899577i \(-0.356125\pi\)
0.436763 + 0.899577i \(0.356125\pi\)
\(828\) 6.69088e21 0.00105251
\(829\) −3.94938e24 −0.614916 −0.307458 0.951562i \(-0.599478\pi\)
−0.307458 + 0.951562i \(0.599478\pi\)
\(830\) −4.04081e24 −0.622737
\(831\) −1.20998e24 −0.184574
\(832\) 9.74157e24 1.47089
\(833\) −1.15801e24 −0.173073
\(834\) 6.46656e23 0.0956669
\(835\) −1.98009e24 −0.289968
\(836\) 7.10977e21 0.00103063
\(837\) −6.13395e23 −0.0880185
\(838\) −9.57212e24 −1.35967
\(839\) −7.15524e24 −1.00611 −0.503057 0.864253i \(-0.667792\pi\)
−0.503057 + 0.864253i \(0.667792\pi\)
\(840\) 6.57602e23 0.0915354
\(841\) 2.50246e23 0.0344828
\(842\) 2.71238e24 0.369997
\(843\) 3.71024e23 0.0501035
\(844\) −3.27829e22 −0.00438265
\(845\) −4.27754e24 −0.566125
\(846\) 2.43340e24 0.318835
\(847\) 6.39712e24 0.829804
\(848\) 2.56203e24 0.329017
\(849\) −9.45721e21 −0.00120240
\(850\) −7.22347e24 −0.909254
\(851\) 1.62783e24 0.202866
\(852\) 1.44009e22 0.00177686
\(853\) −3.24126e24 −0.395956 −0.197978 0.980206i \(-0.563437\pi\)
−0.197978 + 0.980206i \(0.563437\pi\)
\(854\) −3.07218e24 −0.371583
\(855\) 2.44475e24 0.292768
\(856\) 1.19282e25 1.41432
\(857\) 4.49269e24 0.527436 0.263718 0.964600i \(-0.415051\pi\)
0.263718 + 0.964600i \(0.415051\pi\)
\(858\) 8.03490e23 0.0933982
\(859\) 6.87241e24 0.790983 0.395492 0.918470i \(-0.370574\pi\)
0.395492 + 0.918470i \(0.370574\pi\)
\(860\) 1.35188e22 0.00154064
\(861\) −1.68987e23 −0.0190689
\(862\) 1.52152e25 1.70007
\(863\) 8.68590e24 0.961000 0.480500 0.876995i \(-0.340455\pi\)
0.480500 + 0.876995i \(0.340455\pi\)
\(864\) 3.70872e22 0.00406310
\(865\) −2.02585e24 −0.219771
\(866\) −4.33769e24 −0.465968
\(867\) −8.63440e23 −0.0918481
\(868\) −1.03395e22 −0.00108914
\(869\) −1.47110e24 −0.153453
\(870\) 1.76845e23 0.0182675
\(871\) 6.59095e24 0.674207
\(872\) 1.48449e24 0.150379
\(873\) −4.98650e24 −0.500236
\(874\) 1.29742e24 0.128894
\(875\) −8.18521e24 −0.805306
\(876\) −1.52808e21 −0.000148889 0
\(877\) 7.40659e24 0.714697 0.357348 0.933971i \(-0.383681\pi\)
0.357348 + 0.933971i \(0.383681\pi\)
\(878\) 6.68784e24 0.639120
\(879\) −1.16263e24 −0.110036
\(880\) −1.69394e24 −0.158780
\(881\) −5.91827e24 −0.549414 −0.274707 0.961528i \(-0.588581\pi\)
−0.274707 + 0.961528i \(0.588581\pi\)
\(882\) 1.49142e24 0.137125
\(883\) 1.34375e25 1.22364 0.611818 0.790999i \(-0.290438\pi\)
0.611818 + 0.790999i \(0.290438\pi\)
\(884\) −1.02233e23 −0.00922037
\(885\) −2.57758e23 −0.0230247
\(886\) −7.54611e24 −0.667631
\(887\) −1.47109e25 −1.28910 −0.644552 0.764561i \(-0.722956\pi\)
−0.644552 + 0.764561i \(0.722956\pi\)
\(888\) 2.21600e24 0.192335
\(889\) −1.24182e25 −1.06756
\(890\) 7.79380e24 0.663643
\(891\) −3.36888e24 −0.284135
\(892\) −1.10453e23 −0.00922737
\(893\) −2.47185e24 −0.204543
\(894\) 2.20672e24 0.180875
\(895\) −7.22305e24 −0.586441
\(896\) −1.14191e25 −0.918363
\(897\) −7.68098e23 −0.0611900
\(898\) −2.71957e24 −0.214610
\(899\) −5.36345e23 −0.0419263
\(900\) −4.87355e22 −0.00377385
\(901\) −5.21336e24 −0.399905
\(902\) 4.37579e23 0.0332507
\(903\) 1.45749e24 0.109713
\(904\) −1.86213e25 −1.38860
\(905\) 7.02484e24 0.518948
\(906\) −7.94510e23 −0.0581447
\(907\) 2.49331e25 1.80765 0.903823 0.427905i \(-0.140748\pi\)
0.903823 + 0.427905i \(0.140748\pi\)
\(908\) −2.93842e22 −0.00211049
\(909\) 1.71135e25 1.21772
\(910\) 9.50604e24 0.670113
\(911\) −5.85002e24 −0.408556 −0.204278 0.978913i \(-0.565485\pi\)
−0.204278 + 0.978913i \(0.565485\pi\)
\(912\) 1.75699e24 0.121566
\(913\) −5.90955e24 −0.405091
\(914\) 2.34017e25 1.58930
\(915\) 5.89967e23 0.0396961
\(916\) −1.18053e23 −0.00786981
\(917\) 1.51016e25 0.997436
\(918\) 7.18413e24 0.470123
\(919\) 7.14568e24 0.463299 0.231650 0.972799i \(-0.425588\pi\)
0.231650 + 0.972799i \(0.425588\pi\)
\(920\) 1.62781e24 0.104570
\(921\) 6.69607e22 0.00426200
\(922\) −2.05529e25 −1.29616
\(923\) 4.01551e25 2.50915
\(924\) 4.98581e21 0.000308691 0
\(925\) −1.18569e25 −0.727390
\(926\) −1.39261e25 −0.846515
\(927\) −5.24119e24 −0.315684
\(928\) 3.24286e22 0.00193540
\(929\) −3.63609e24 −0.215031 −0.107516 0.994203i \(-0.534290\pi\)
−0.107516 + 0.994203i \(0.534290\pi\)
\(930\) −3.79026e23 −0.0222108
\(931\) −1.51499e24 −0.0879703
\(932\) −1.51807e23 −0.00873488
\(933\) −6.78521e24 −0.386874
\(934\) −1.98927e25 −1.12395
\(935\) 3.44693e24 0.192990
\(936\) 2.53976e25 1.40912
\(937\) −2.73327e25 −1.50278 −0.751392 0.659856i \(-0.770617\pi\)
−0.751392 + 0.659856i \(0.770617\pi\)
\(938\) −7.80710e24 −0.425369
\(939\) 4.07662e24 0.220111
\(940\) −1.60781e22 −0.000860295 0
\(941\) 2.01276e24 0.106728 0.0533642 0.998575i \(-0.483006\pi\)
0.0533642 + 0.998575i \(0.483006\pi\)
\(942\) −5.34335e24 −0.280790
\(943\) −4.18305e23 −0.0217843
\(944\) 4.49948e24 0.232220
\(945\) 3.49940e24 0.178988
\(946\) −3.77407e24 −0.191309
\(947\) 2.29048e25 1.15067 0.575337 0.817916i \(-0.304871\pi\)
0.575337 + 0.817916i \(0.304871\pi\)
\(948\) 9.92488e21 0.000494145 0
\(949\) −4.26086e24 −0.210249
\(950\) −9.45021e24 −0.462159
\(951\) −9.57459e23 −0.0464072
\(952\) 2.33587e25 1.12211
\(953\) 6.92070e23 0.0329504 0.0164752 0.999864i \(-0.494756\pi\)
0.0164752 + 0.999864i \(0.494756\pi\)
\(954\) 6.71436e24 0.316842
\(955\) −7.78317e24 −0.364022
\(956\) −9.83935e22 −0.00456115
\(957\) 2.58630e23 0.0118830
\(958\) −2.62014e25 −1.19321
\(959\) −2.76830e25 −1.24955
\(960\) 2.21591e24 0.0991393
\(961\) −2.14006e25 −0.949023
\(962\) 3.20336e25 1.40805
\(963\) 3.10976e25 1.35489
\(964\) −2.12279e22 −0.000916754 0
\(965\) 6.45546e24 0.276341
\(966\) 9.09827e23 0.0386058
\(967\) −4.42650e24 −0.186181 −0.0930906 0.995658i \(-0.529675\pi\)
−0.0930906 + 0.995658i \(0.529675\pi\)
\(968\) 2.15568e25 0.898761
\(969\) −3.57523e24 −0.147758
\(970\) −6.28932e24 −0.257658
\(971\) −2.88845e25 −1.17301 −0.586505 0.809945i \(-0.699497\pi\)
−0.586505 + 0.809945i \(0.699497\pi\)
\(972\) 7.31939e22 0.00294654
\(973\) 1.11887e25 0.446498
\(974\) −3.28209e25 −1.29837
\(975\) 5.59473e24 0.219402
\(976\) −1.02986e25 −0.400364
\(977\) −1.35303e25 −0.521439 −0.260719 0.965415i \(-0.583960\pi\)
−0.260719 + 0.965415i \(0.583960\pi\)
\(978\) −2.09346e24 −0.0799805
\(979\) 1.13982e25 0.431701
\(980\) −9.85417e21 −0.000369997 0
\(981\) 3.87017e24 0.144060
\(982\) −3.03062e25 −1.11837
\(983\) −1.80376e25 −0.659894 −0.329947 0.944000i \(-0.607031\pi\)
−0.329947 + 0.944000i \(0.607031\pi\)
\(984\) −5.69446e23 −0.0206535
\(985\) 1.45273e25 0.522368
\(986\) 6.28171e24 0.223936
\(987\) −1.73341e24 −0.0612642
\(988\) −1.33748e23 −0.00468656
\(989\) 3.60783e24 0.125337
\(990\) −4.43935e24 −0.152905
\(991\) 3.71782e25 1.26959 0.634794 0.772681i \(-0.281085\pi\)
0.634794 + 0.772681i \(0.281085\pi\)
\(992\) −6.95032e22 −0.00235318
\(993\) −1.75081e24 −0.0587719
\(994\) −4.75645e25 −1.58306
\(995\) 2.43144e25 0.802356
\(996\) 3.98691e22 0.00130446
\(997\) −1.96631e25 −0.637886 −0.318943 0.947774i \(-0.603328\pi\)
−0.318943 + 0.947774i \(0.603328\pi\)
\(998\) 1.09131e25 0.351025
\(999\) 1.17923e25 0.376091
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.1.16 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.18.a.b.1.16 21 1.1 even 1 trivial