Properties

Label 177.12.a.d.1.6
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(135.996742959\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-47.6933 q^{2} +243.000 q^{3} +226.652 q^{4} +10067.2 q^{5} -11589.5 q^{6} +19897.8 q^{7} +86866.1 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-47.6933 q^{2} +243.000 q^{3} +226.652 q^{4} +10067.2 q^{5} -11589.5 q^{6} +19897.8 q^{7} +86866.1 q^{8} +59049.0 q^{9} -480139. q^{10} -256850. q^{11} +55076.4 q^{12} +1.87281e6 q^{13} -948992. q^{14} +2.44633e6 q^{15} -4.60712e6 q^{16} +3.91960e6 q^{17} -2.81624e6 q^{18} -1.36502e7 q^{19} +2.28175e6 q^{20} +4.83516e6 q^{21} +1.22500e7 q^{22} +4.09884e7 q^{23} +2.11085e7 q^{24} +5.25208e7 q^{25} -8.93203e7 q^{26} +1.43489e7 q^{27} +4.50987e6 q^{28} -2.21762e7 q^{29} -1.16674e8 q^{30} +2.03908e8 q^{31} +4.18268e7 q^{32} -6.24144e7 q^{33} -1.86939e8 q^{34} +2.00315e8 q^{35} +1.33836e7 q^{36} +7.60284e8 q^{37} +6.51025e8 q^{38} +4.55092e8 q^{39} +8.74500e8 q^{40} -1.05040e9 q^{41} -2.30605e8 q^{42} +6.64995e8 q^{43} -5.82155e7 q^{44} +5.94459e8 q^{45} -1.95487e9 q^{46} +1.48540e9 q^{47} -1.11953e9 q^{48} -1.58140e9 q^{49} -2.50489e9 q^{50} +9.52463e8 q^{51} +4.24475e8 q^{52} +9.91182e8 q^{53} -6.84347e8 q^{54} -2.58576e9 q^{55} +1.72844e9 q^{56} -3.31701e9 q^{57} +1.05765e9 q^{58} +7.14924e8 q^{59} +5.54466e8 q^{60} +8.36215e9 q^{61} -9.72503e9 q^{62} +1.17494e9 q^{63} +7.44051e9 q^{64} +1.88539e10 q^{65} +2.97675e9 q^{66} -1.21766e10 q^{67} +8.88385e8 q^{68} +9.96019e9 q^{69} -9.55371e9 q^{70} +4.45588e9 q^{71} +5.12936e9 q^{72} +6.92941e9 q^{73} -3.62604e10 q^{74} +1.27626e10 q^{75} -3.09385e9 q^{76} -5.11074e9 q^{77} -2.17048e10 q^{78} -1.11775e9 q^{79} -4.63809e10 q^{80} +3.48678e9 q^{81} +5.00969e10 q^{82} -6.93121e10 q^{83} +1.09590e9 q^{84} +3.94595e10 q^{85} -3.17158e10 q^{86} -5.38881e9 q^{87} -2.23115e10 q^{88} -4.21667e10 q^{89} -2.83517e10 q^{90} +3.72647e10 q^{91} +9.29011e9 q^{92} +4.95495e10 q^{93} -7.08437e10 q^{94} -1.37420e11 q^{95} +1.01639e10 q^{96} -7.55087e10 q^{97} +7.54224e10 q^{98} -1.51667e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 96q^{2} + 6804q^{3} + 29214q^{4} + 26562q^{5} + 23328q^{6} + 142333q^{7} + 332331q^{8} + 1653372q^{9} + O(q^{10}) \) \( 28q + 96q^{2} + 6804q^{3} + 29214q^{4} + 26562q^{5} + 23328q^{6} + 142333q^{7} + 332331q^{8} + 1653372q^{9} + 616281q^{10} + 1082362q^{11} + 7099002q^{12} + 503712q^{13} + 1321669q^{14} + 6454566q^{15} + 34870338q^{16} + 13513579q^{17} + 5668704q^{18} + 35971687q^{19} + 96105997q^{20} + 34586919q^{21} - 47598882q^{22} + 61380539q^{23} + 80756433q^{24} + 294744746q^{25} + 62820734q^{26} + 401769396q^{27} + 148068294q^{28} + 322339307q^{29} + 149756283q^{30} + 151247077q^{31} + 466383494q^{32} + 263013966q^{33} + 684479860q^{34} + 960297361q^{35} + 1725057486q^{36} + 863508437q^{37} + 992640509q^{38} + 122402016q^{39} + 3067680252q^{40} + 3081170377q^{41} + 321165567q^{42} + 2554238300q^{43} + 4350123570q^{44} + 1568459538q^{45} - 1987059155q^{46} + 6203398333q^{47} + 8473492134q^{48} + 10327857997q^{49} + 17577682253q^{50} + 3283799697q^{51} + 32137181618q^{52} + 14571770754q^{53} + 1377495072q^{54} + 18251419334q^{55} + 33498842836q^{56} + 8741119941q^{57} + 11860778276q^{58} + 20017880372q^{59} + 23353757271q^{60} + 2761613771q^{61} + 13785829526q^{62} + 8404621317q^{63} + 86547545293q^{64} + 32034985256q^{65} - 11566528326q^{66} + 39381333296q^{67} + 38995496621q^{68} + 14915470977q^{69} + 8551800364q^{70} + 26130020296q^{71} + 19623813219q^{72} + 41382402799q^{73} + 23815315058q^{74} + 71622973278q^{75} + 10611720128q^{76} - 8426124313q^{77} + 15265438362q^{78} + 59825111206q^{79} + 4009687655q^{80} + 97629963228q^{81} - 39592715115q^{82} + 35433122727q^{83} + 35980595442q^{84} - 8950496085q^{85} - 182032360688q^{86} + 78328451601q^{87} - 220003602335q^{88} + 102303043039q^{89} + 36390776769q^{90} - 111146323655q^{91} - 163000203526q^{92} + 36753039711q^{93} - 81314346008q^{94} + 208102168887q^{95} + 113331189042q^{96} - 171891031490q^{97} + 72304707792q^{98} + 63912393738q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −47.6933 −1.05388 −0.526942 0.849901i \(-0.676661\pi\)
−0.526942 + 0.849901i \(0.676661\pi\)
\(3\) 243.000 0.577350
\(4\) 226.652 0.110670
\(5\) 10067.2 1.44070 0.720352 0.693609i \(-0.243980\pi\)
0.720352 + 0.693609i \(0.243980\pi\)
\(6\) −11589.5 −0.608460
\(7\) 19897.8 0.447472 0.223736 0.974650i \(-0.428175\pi\)
0.223736 + 0.974650i \(0.428175\pi\)
\(8\) 86866.1 0.937250
\(9\) 59049.0 0.333333
\(10\) −480139. −1.51833
\(11\) −256850. −0.480860 −0.240430 0.970666i \(-0.577289\pi\)
−0.240430 + 0.970666i \(0.577289\pi\)
\(12\) 55076.4 0.0638953
\(13\) 1.87281e6 1.39896 0.699478 0.714654i \(-0.253416\pi\)
0.699478 + 0.714654i \(0.253416\pi\)
\(14\) −948992. −0.471583
\(15\) 2.44633e6 0.831790
\(16\) −4.60712e6 −1.09842
\(17\) 3.91960e6 0.669534 0.334767 0.942301i \(-0.391342\pi\)
0.334767 + 0.942301i \(0.391342\pi\)
\(18\) −2.81624e6 −0.351294
\(19\) −1.36502e7 −1.26472 −0.632361 0.774674i \(-0.717914\pi\)
−0.632361 + 0.774674i \(0.717914\pi\)
\(20\) 2.28175e6 0.159442
\(21\) 4.83516e6 0.258348
\(22\) 1.22500e7 0.506771
\(23\) 4.09884e7 1.32788 0.663939 0.747786i \(-0.268883\pi\)
0.663939 + 0.747786i \(0.268883\pi\)
\(24\) 2.11085e7 0.541122
\(25\) 5.25208e7 1.07563
\(26\) −8.93203e7 −1.47434
\(27\) 1.43489e7 0.192450
\(28\) 4.50987e6 0.0495217
\(29\) −2.21762e7 −0.200769 −0.100385 0.994949i \(-0.532007\pi\)
−0.100385 + 0.994949i \(0.532007\pi\)
\(30\) −1.16674e8 −0.876610
\(31\) 2.03908e8 1.27922 0.639608 0.768701i \(-0.279097\pi\)
0.639608 + 0.768701i \(0.279097\pi\)
\(32\) 4.18268e7 0.220359
\(33\) −6.24144e7 −0.277625
\(34\) −1.86939e8 −0.705611
\(35\) 2.00315e8 0.644674
\(36\) 1.33836e7 0.0368900
\(37\) 7.60284e8 1.80246 0.901231 0.433339i \(-0.142665\pi\)
0.901231 + 0.433339i \(0.142665\pi\)
\(38\) 6.51025e8 1.33287
\(39\) 4.55092e8 0.807688
\(40\) 8.74500e8 1.35030
\(41\) −1.05040e9 −1.41593 −0.707966 0.706246i \(-0.750387\pi\)
−0.707966 + 0.706246i \(0.750387\pi\)
\(42\) −2.30605e8 −0.272269
\(43\) 6.64995e8 0.689830 0.344915 0.938634i \(-0.387908\pi\)
0.344915 + 0.938634i \(0.387908\pi\)
\(44\) −5.82155e7 −0.0532168
\(45\) 5.94459e8 0.480234
\(46\) −1.95487e9 −1.39943
\(47\) 1.48540e9 0.944725 0.472363 0.881404i \(-0.343401\pi\)
0.472363 + 0.881404i \(0.343401\pi\)
\(48\) −1.11953e9 −0.634174
\(49\) −1.58140e9 −0.799769
\(50\) −2.50489e9 −1.13358
\(51\) 9.52463e8 0.386556
\(52\) 4.24475e8 0.154822
\(53\) 9.91182e8 0.325564 0.162782 0.986662i \(-0.447953\pi\)
0.162782 + 0.986662i \(0.447953\pi\)
\(54\) −6.84347e8 −0.202820
\(55\) −2.58576e9 −0.692777
\(56\) 1.72844e9 0.419393
\(57\) −3.31701e9 −0.730188
\(58\) 1.05765e9 0.211587
\(59\) 7.14924e8 0.130189
\(60\) 5.54466e8 0.0920542
\(61\) 8.36215e9 1.26766 0.633832 0.773471i \(-0.281481\pi\)
0.633832 + 0.773471i \(0.281481\pi\)
\(62\) −9.72503e9 −1.34814
\(63\) 1.17494e9 0.149157
\(64\) 7.44051e9 0.866190
\(65\) 1.88539e10 2.01548
\(66\) 2.97675e9 0.292584
\(67\) −1.21766e10 −1.10183 −0.550913 0.834563i \(-0.685720\pi\)
−0.550913 + 0.834563i \(0.685720\pi\)
\(68\) 8.88385e8 0.0740973
\(69\) 9.96019e9 0.766651
\(70\) −9.55371e9 −0.679411
\(71\) 4.45588e9 0.293098 0.146549 0.989203i \(-0.453183\pi\)
0.146549 + 0.989203i \(0.453183\pi\)
\(72\) 5.12936e9 0.312417
\(73\) 6.92941e9 0.391219 0.195610 0.980682i \(-0.437331\pi\)
0.195610 + 0.980682i \(0.437331\pi\)
\(74\) −3.62604e10 −1.89958
\(75\) 1.27626e10 0.621013
\(76\) −3.09385e9 −0.139967
\(77\) −5.11074e9 −0.215172
\(78\) −2.17048e10 −0.851209
\(79\) −1.11775e9 −0.0408693 −0.0204346 0.999791i \(-0.506505\pi\)
−0.0204346 + 0.999791i \(0.506505\pi\)
\(80\) −4.63809e10 −1.58250
\(81\) 3.48678e9 0.111111
\(82\) 5.00969e10 1.49223
\(83\) −6.93121e10 −1.93143 −0.965716 0.259600i \(-0.916409\pi\)
−0.965716 + 0.259600i \(0.916409\pi\)
\(84\) 1.09590e9 0.0285913
\(85\) 3.94595e10 0.964600
\(86\) −3.17158e10 −0.727000
\(87\) −5.38881e9 −0.115914
\(88\) −2.23115e10 −0.450687
\(89\) −4.21667e10 −0.800432 −0.400216 0.916421i \(-0.631065\pi\)
−0.400216 + 0.916421i \(0.631065\pi\)
\(90\) −2.83517e10 −0.506111
\(91\) 3.72647e10 0.625994
\(92\) 9.29011e9 0.146956
\(93\) 4.95495e10 0.738556
\(94\) −7.08437e10 −0.995630
\(95\) −1.37420e11 −1.82209
\(96\) 1.01639e10 0.127224
\(97\) −7.55087e10 −0.892796 −0.446398 0.894835i \(-0.647293\pi\)
−0.446398 + 0.894835i \(0.647293\pi\)
\(98\) 7.54224e10 0.842863
\(99\) −1.51667e10 −0.160287
\(100\) 1.19039e10 0.119039
\(101\) −1.30355e11 −1.23413 −0.617065 0.786912i \(-0.711679\pi\)
−0.617065 + 0.786912i \(0.711679\pi\)
\(102\) −4.54261e10 −0.407385
\(103\) −1.76189e11 −1.49752 −0.748762 0.662839i \(-0.769351\pi\)
−0.748762 + 0.662839i \(0.769351\pi\)
\(104\) 1.62683e11 1.31117
\(105\) 4.86767e10 0.372203
\(106\) −4.72728e10 −0.343106
\(107\) 1.22677e11 0.845573 0.422787 0.906229i \(-0.361052\pi\)
0.422787 + 0.906229i \(0.361052\pi\)
\(108\) 3.25221e9 0.0212984
\(109\) 6.96262e10 0.433438 0.216719 0.976234i \(-0.430464\pi\)
0.216719 + 0.976234i \(0.430464\pi\)
\(110\) 1.23324e11 0.730106
\(111\) 1.84749e11 1.04065
\(112\) −9.16715e10 −0.491513
\(113\) 8.22738e10 0.420078 0.210039 0.977693i \(-0.432641\pi\)
0.210039 + 0.977693i \(0.432641\pi\)
\(114\) 1.58199e11 0.769533
\(115\) 4.12640e11 1.91308
\(116\) −5.02627e9 −0.0222191
\(117\) 1.10587e11 0.466319
\(118\) −3.40971e10 −0.137204
\(119\) 7.79914e10 0.299598
\(120\) 2.12504e11 0.779596
\(121\) −2.19340e11 −0.768773
\(122\) −3.98819e11 −1.33597
\(123\) −2.55247e11 −0.817489
\(124\) 4.62161e10 0.141571
\(125\) 3.71749e10 0.108954
\(126\) −5.60370e10 −0.157194
\(127\) 3.47214e10 0.0932560 0.0466280 0.998912i \(-0.485152\pi\)
0.0466280 + 0.998912i \(0.485152\pi\)
\(128\) −4.40524e11 −1.13322
\(129\) 1.61594e11 0.398273
\(130\) −8.99207e11 −2.12408
\(131\) 3.74267e11 0.847598 0.423799 0.905756i \(-0.360696\pi\)
0.423799 + 0.905756i \(0.360696\pi\)
\(132\) −1.41464e10 −0.0307247
\(133\) −2.71609e11 −0.565928
\(134\) 5.80740e11 1.16120
\(135\) 1.44454e11 0.277263
\(136\) 3.40481e11 0.627521
\(137\) −8.59009e11 −1.52067 −0.760334 0.649532i \(-0.774965\pi\)
−0.760334 + 0.649532i \(0.774965\pi\)
\(138\) −4.75035e11 −0.807961
\(139\) 6.85989e11 1.12134 0.560668 0.828040i \(-0.310544\pi\)
0.560668 + 0.828040i \(0.310544\pi\)
\(140\) 4.54019e10 0.0713460
\(141\) 3.60952e11 0.545437
\(142\) −2.12516e11 −0.308891
\(143\) −4.81029e11 −0.672703
\(144\) −2.72046e11 −0.366141
\(145\) −2.23252e11 −0.289249
\(146\) −3.30486e11 −0.412300
\(147\) −3.84281e11 −0.461747
\(148\) 1.72320e11 0.199478
\(149\) 1.04015e12 1.16030 0.580152 0.814508i \(-0.302993\pi\)
0.580152 + 0.814508i \(0.302993\pi\)
\(150\) −6.08688e11 −0.654475
\(151\) 5.73329e11 0.594335 0.297167 0.954825i \(-0.403958\pi\)
0.297167 + 0.954825i \(0.403958\pi\)
\(152\) −1.18574e12 −1.18536
\(153\) 2.31449e11 0.223178
\(154\) 2.43748e11 0.226766
\(155\) 2.05278e12 1.84297
\(156\) 1.03147e11 0.0893867
\(157\) −1.08917e10 −0.00911269 −0.00455635 0.999990i \(-0.501450\pi\)
−0.00455635 + 0.999990i \(0.501450\pi\)
\(158\) 5.33094e10 0.0430714
\(159\) 2.40857e11 0.187964
\(160\) 4.21080e11 0.317471
\(161\) 8.15580e11 0.594188
\(162\) −1.66296e11 −0.117098
\(163\) 2.44839e12 1.66667 0.833335 0.552769i \(-0.186429\pi\)
0.833335 + 0.552769i \(0.186429\pi\)
\(164\) −2.38075e11 −0.156701
\(165\) −6.28340e11 −0.399975
\(166\) 3.30572e12 2.03550
\(167\) 2.37729e12 1.41625 0.708127 0.706085i \(-0.249540\pi\)
0.708127 + 0.706085i \(0.249540\pi\)
\(168\) 4.20012e11 0.242137
\(169\) 1.71524e12 0.957080
\(170\) −1.88195e12 −1.01658
\(171\) −8.06032e11 −0.421574
\(172\) 1.50722e11 0.0763434
\(173\) 7.48267e11 0.367116 0.183558 0.983009i \(-0.441239\pi\)
0.183558 + 0.983009i \(0.441239\pi\)
\(174\) 2.57010e11 0.122160
\(175\) 1.04505e12 0.481312
\(176\) 1.18334e12 0.528188
\(177\) 1.73727e11 0.0751646
\(178\) 2.01107e12 0.843562
\(179\) −1.89651e11 −0.0771372 −0.0385686 0.999256i \(-0.512280\pi\)
−0.0385686 + 0.999256i \(0.512280\pi\)
\(180\) 1.34735e11 0.0531475
\(181\) −1.13759e12 −0.435266 −0.217633 0.976031i \(-0.569834\pi\)
−0.217633 + 0.976031i \(0.569834\pi\)
\(182\) −1.77728e12 −0.659724
\(183\) 2.03200e12 0.731886
\(184\) 3.56051e12 1.24455
\(185\) 7.65394e12 2.59681
\(186\) −2.36318e12 −0.778352
\(187\) −1.00675e12 −0.321953
\(188\) 3.36669e11 0.104553
\(189\) 2.85512e11 0.0861160
\(190\) 6.55401e12 1.92027
\(191\) 2.41641e12 0.687839 0.343920 0.938999i \(-0.388245\pi\)
0.343920 + 0.938999i \(0.388245\pi\)
\(192\) 1.80805e12 0.500095
\(193\) −1.61769e12 −0.434841 −0.217421 0.976078i \(-0.569764\pi\)
−0.217421 + 0.976078i \(0.569764\pi\)
\(194\) 3.60126e12 0.940903
\(195\) 4.58151e12 1.16364
\(196\) −3.58428e11 −0.0885103
\(197\) 3.30183e12 0.792850 0.396425 0.918067i \(-0.370251\pi\)
0.396425 + 0.918067i \(0.370251\pi\)
\(198\) 7.23351e11 0.168924
\(199\) −6.57007e12 −1.49238 −0.746188 0.665736i \(-0.768118\pi\)
−0.746188 + 0.665736i \(0.768118\pi\)
\(200\) 4.56228e12 1.00813
\(201\) −2.95890e12 −0.636139
\(202\) 6.21707e12 1.30063
\(203\) −4.41257e11 −0.0898386
\(204\) 2.15878e11 0.0427801
\(205\) −1.05746e13 −2.03994
\(206\) 8.40303e12 1.57822
\(207\) 2.42033e12 0.442626
\(208\) −8.62823e12 −1.53664
\(209\) 3.50606e12 0.608155
\(210\) −2.32155e12 −0.392258
\(211\) 9.22870e12 1.51910 0.759551 0.650447i \(-0.225419\pi\)
0.759551 + 0.650447i \(0.225419\pi\)
\(212\) 2.24653e11 0.0360301
\(213\) 1.08278e12 0.169220
\(214\) −5.85086e12 −0.891136
\(215\) 6.69465e12 0.993840
\(216\) 1.24643e12 0.180374
\(217\) 4.05731e12 0.572413
\(218\) −3.32070e12 −0.456793
\(219\) 1.68385e12 0.225871
\(220\) −5.86068e11 −0.0766696
\(221\) 7.34065e12 0.936649
\(222\) −8.81129e12 −1.09673
\(223\) −4.71766e12 −0.572862 −0.286431 0.958101i \(-0.592469\pi\)
−0.286431 + 0.958101i \(0.592469\pi\)
\(224\) 8.32261e11 0.0986042
\(225\) 3.10130e12 0.358542
\(226\) −3.92391e12 −0.442713
\(227\) 1.08803e13 1.19812 0.599059 0.800705i \(-0.295542\pi\)
0.599059 + 0.800705i \(0.295542\pi\)
\(228\) −7.51806e11 −0.0808098
\(229\) −6.39892e12 −0.671446 −0.335723 0.941961i \(-0.608981\pi\)
−0.335723 + 0.941961i \(0.608981\pi\)
\(230\) −1.96802e13 −2.01616
\(231\) −1.24191e12 −0.124229
\(232\) −1.92636e12 −0.188171
\(233\) 6.18274e12 0.589826 0.294913 0.955524i \(-0.404709\pi\)
0.294913 + 0.955524i \(0.404709\pi\)
\(234\) −5.27427e12 −0.491446
\(235\) 1.49539e13 1.36107
\(236\) 1.62039e11 0.0144080
\(237\) −2.71614e11 −0.0235959
\(238\) −3.71967e12 −0.315741
\(239\) 7.82182e12 0.648813 0.324406 0.945918i \(-0.394835\pi\)
0.324406 + 0.945918i \(0.394835\pi\)
\(240\) −1.12705e13 −0.913657
\(241\) −2.29486e13 −1.81829 −0.909145 0.416480i \(-0.863264\pi\)
−0.909145 + 0.416480i \(0.863264\pi\)
\(242\) 1.04610e13 0.810197
\(243\) 8.47289e11 0.0641500
\(244\) 1.89530e12 0.140292
\(245\) −1.59203e13 −1.15223
\(246\) 1.21736e13 0.861538
\(247\) −2.55642e13 −1.76929
\(248\) 1.77127e13 1.19895
\(249\) −1.68428e13 −1.11511
\(250\) −1.77299e12 −0.114825
\(251\) 1.14535e13 0.725660 0.362830 0.931855i \(-0.381810\pi\)
0.362830 + 0.931855i \(0.381810\pi\)
\(252\) 2.66304e11 0.0165072
\(253\) −1.05279e13 −0.638524
\(254\) −1.65598e12 −0.0982810
\(255\) 9.58866e12 0.556912
\(256\) 5.77188e12 0.328093
\(257\) 1.26561e13 0.704155 0.352077 0.935971i \(-0.385475\pi\)
0.352077 + 0.935971i \(0.385475\pi\)
\(258\) −7.70694e12 −0.419734
\(259\) 1.51280e13 0.806551
\(260\) 4.27328e12 0.223053
\(261\) −1.30948e12 −0.0669231
\(262\) −1.78501e13 −0.893269
\(263\) −3.37616e13 −1.65450 −0.827248 0.561837i \(-0.810095\pi\)
−0.827248 + 0.561837i \(0.810095\pi\)
\(264\) −5.42170e12 −0.260204
\(265\) 9.97845e12 0.469041
\(266\) 1.29540e13 0.596422
\(267\) −1.02465e13 −0.462130
\(268\) −2.75984e12 −0.121939
\(269\) 2.88764e13 1.24999 0.624993 0.780630i \(-0.285102\pi\)
0.624993 + 0.780630i \(0.285102\pi\)
\(270\) −6.88947e12 −0.292203
\(271\) 6.85896e12 0.285054 0.142527 0.989791i \(-0.454477\pi\)
0.142527 + 0.989791i \(0.454477\pi\)
\(272\) −1.80581e13 −0.735431
\(273\) 9.05532e12 0.361418
\(274\) 4.09690e13 1.60261
\(275\) −1.34899e13 −0.517226
\(276\) 2.25750e12 0.0848452
\(277\) −8.47203e11 −0.0312139 −0.0156070 0.999878i \(-0.504968\pi\)
−0.0156070 + 0.999878i \(0.504968\pi\)
\(278\) −3.27171e13 −1.18176
\(279\) 1.20405e13 0.426406
\(280\) 1.74006e13 0.604221
\(281\) −3.05709e13 −1.04093 −0.520467 0.853882i \(-0.674242\pi\)
−0.520467 + 0.853882i \(0.674242\pi\)
\(282\) −1.72150e13 −0.574827
\(283\) 7.56230e12 0.247644 0.123822 0.992304i \(-0.460485\pi\)
0.123822 + 0.992304i \(0.460485\pi\)
\(284\) 1.00993e12 0.0324371
\(285\) −3.33930e13 −1.05198
\(286\) 2.29419e13 0.708950
\(287\) −2.09006e13 −0.633590
\(288\) 2.46983e12 0.0734528
\(289\) −1.89086e13 −0.551724
\(290\) 1.06476e13 0.304835
\(291\) −1.83486e13 −0.515456
\(292\) 1.57056e12 0.0432962
\(293\) 6.01099e13 1.62620 0.813101 0.582123i \(-0.197778\pi\)
0.813101 + 0.582123i \(0.197778\pi\)
\(294\) 1.83276e13 0.486627
\(295\) 7.19730e12 0.187564
\(296\) 6.60429e13 1.68936
\(297\) −3.68551e12 −0.0925416
\(298\) −4.96082e13 −1.22283
\(299\) 7.67634e13 1.85764
\(300\) 2.89266e12 0.0687274
\(301\) 1.32319e13 0.308679
\(302\) −2.73440e13 −0.626359
\(303\) −3.16763e13 −0.712526
\(304\) 6.28882e13 1.38920
\(305\) 8.41836e13 1.82633
\(306\) −1.10385e13 −0.235204
\(307\) −4.07056e13 −0.851910 −0.425955 0.904744i \(-0.640062\pi\)
−0.425955 + 0.904744i \(0.640062\pi\)
\(308\) −1.15836e12 −0.0238130
\(309\) −4.28139e13 −0.864596
\(310\) −9.79040e13 −1.94228
\(311\) −1.69524e13 −0.330408 −0.165204 0.986259i \(-0.552828\pi\)
−0.165204 + 0.986259i \(0.552828\pi\)
\(312\) 3.95321e13 0.757006
\(313\) −4.57468e13 −0.860730 −0.430365 0.902655i \(-0.641615\pi\)
−0.430365 + 0.902655i \(0.641615\pi\)
\(314\) 5.19460e11 0.00960372
\(315\) 1.18284e13 0.214891
\(316\) −2.53341e11 −0.00452300
\(317\) −9.76435e13 −1.71324 −0.856619 0.515950i \(-0.827439\pi\)
−0.856619 + 0.515950i \(0.827439\pi\)
\(318\) −1.14873e13 −0.198093
\(319\) 5.69594e12 0.0965420
\(320\) 7.49053e13 1.24792
\(321\) 2.98104e13 0.488192
\(322\) −3.88977e13 −0.626205
\(323\) −5.35035e13 −0.846775
\(324\) 7.90286e11 0.0122967
\(325\) 9.83612e13 1.50475
\(326\) −1.16772e14 −1.75648
\(327\) 1.69192e13 0.250246
\(328\) −9.12440e13 −1.32708
\(329\) 2.95562e13 0.422738
\(330\) 2.99676e13 0.421527
\(331\) 7.91062e13 1.09435 0.547176 0.837018i \(-0.315703\pi\)
0.547176 + 0.837018i \(0.315703\pi\)
\(332\) −1.57097e13 −0.213751
\(333\) 4.48940e13 0.600821
\(334\) −1.13381e14 −1.49257
\(335\) −1.22584e14 −1.58740
\(336\) −2.22762e13 −0.283775
\(337\) −6.52137e13 −0.817287 −0.408643 0.912694i \(-0.633998\pi\)
−0.408643 + 0.912694i \(0.633998\pi\)
\(338\) −8.18055e13 −1.00865
\(339\) 1.99925e13 0.242532
\(340\) 8.94357e12 0.106752
\(341\) −5.23736e13 −0.615125
\(342\) 3.84424e13 0.444290
\(343\) −7.08109e13 −0.805346
\(344\) 5.77655e13 0.646543
\(345\) 1.00271e14 1.10452
\(346\) −3.56873e13 −0.386897
\(347\) 1.40426e14 1.49843 0.749215 0.662327i \(-0.230431\pi\)
0.749215 + 0.662327i \(0.230431\pi\)
\(348\) −1.22138e12 −0.0128282
\(349\) −9.96355e13 −1.03009 −0.515044 0.857164i \(-0.672224\pi\)
−0.515044 + 0.857164i \(0.672224\pi\)
\(350\) −4.98418e13 −0.507247
\(351\) 2.68727e13 0.269229
\(352\) −1.07432e13 −0.105962
\(353\) −1.16903e13 −0.113518 −0.0567591 0.998388i \(-0.518077\pi\)
−0.0567591 + 0.998388i \(0.518077\pi\)
\(354\) −8.28560e12 −0.0792147
\(355\) 4.48583e13 0.422267
\(356\) −9.55716e12 −0.0885837
\(357\) 1.89519e13 0.172973
\(358\) 9.04509e12 0.0812936
\(359\) 1.09916e14 0.972840 0.486420 0.873725i \(-0.338302\pi\)
0.486420 + 0.873725i \(0.338302\pi\)
\(360\) 5.16384e13 0.450100
\(361\) 6.98385e13 0.599522
\(362\) 5.42555e13 0.458719
\(363\) −5.32996e13 −0.443851
\(364\) 8.44612e12 0.0692787
\(365\) 6.97599e13 0.563631
\(366\) −9.69129e13 −0.771322
\(367\) 1.86818e14 1.46472 0.732361 0.680917i \(-0.238418\pi\)
0.732361 + 0.680917i \(0.238418\pi\)
\(368\) −1.88839e14 −1.45857
\(369\) −6.20249e13 −0.471978
\(370\) −3.65042e14 −2.73674
\(371\) 1.97223e13 0.145681
\(372\) 1.12305e13 0.0817359
\(373\) −1.50943e14 −1.08247 −0.541233 0.840873i \(-0.682042\pi\)
−0.541233 + 0.840873i \(0.682042\pi\)
\(374\) 4.80151e13 0.339300
\(375\) 9.03350e12 0.0629048
\(376\) 1.29031e14 0.885444
\(377\) −4.15316e13 −0.280868
\(378\) −1.36170e13 −0.0907562
\(379\) 6.75399e13 0.443654 0.221827 0.975086i \(-0.428798\pi\)
0.221827 + 0.975086i \(0.428798\pi\)
\(380\) −3.11465e13 −0.201650
\(381\) 8.43730e12 0.0538414
\(382\) −1.15247e14 −0.724902
\(383\) 1.30035e14 0.806245 0.403123 0.915146i \(-0.367925\pi\)
0.403123 + 0.915146i \(0.367925\pi\)
\(384\) −1.07047e14 −0.654266
\(385\) −5.14509e13 −0.309998
\(386\) 7.71531e13 0.458272
\(387\) 3.92673e13 0.229943
\(388\) −1.71142e13 −0.0988056
\(389\) 2.60472e13 0.148265 0.0741325 0.997248i \(-0.476381\pi\)
0.0741325 + 0.997248i \(0.476381\pi\)
\(390\) −2.18507e14 −1.22634
\(391\) 1.60658e14 0.889060
\(392\) −1.37370e14 −0.749583
\(393\) 9.09470e13 0.489361
\(394\) −1.57475e14 −0.835571
\(395\) −1.12527e13 −0.0588805
\(396\) −3.43756e12 −0.0177389
\(397\) 3.22209e14 1.63980 0.819899 0.572508i \(-0.194029\pi\)
0.819899 + 0.572508i \(0.194029\pi\)
\(398\) 3.13348e14 1.57279
\(399\) −6.60011e13 −0.326738
\(400\) −2.41969e14 −1.18149
\(401\) 3.46864e14 1.67057 0.835286 0.549815i \(-0.185302\pi\)
0.835286 + 0.549815i \(0.185302\pi\)
\(402\) 1.41120e14 0.670417
\(403\) 3.81879e14 1.78957
\(404\) −2.95453e13 −0.136581
\(405\) 3.51022e13 0.160078
\(406\) 2.10450e13 0.0946794
\(407\) −1.95278e14 −0.866733
\(408\) 8.27368e13 0.362299
\(409\) −1.91290e14 −0.826447 −0.413224 0.910630i \(-0.635597\pi\)
−0.413224 + 0.910630i \(0.635597\pi\)
\(410\) 5.04337e14 2.14986
\(411\) −2.08739e14 −0.877959
\(412\) −3.99336e13 −0.165731
\(413\) 1.42254e13 0.0582559
\(414\) −1.15433e14 −0.466476
\(415\) −6.97780e14 −2.78262
\(416\) 7.83335e13 0.308272
\(417\) 1.66695e14 0.647404
\(418\) −1.67215e14 −0.640924
\(419\) 2.19873e14 0.831755 0.415877 0.909421i \(-0.363475\pi\)
0.415877 + 0.909421i \(0.363475\pi\)
\(420\) 1.10327e13 0.0411916
\(421\) −1.43384e14 −0.528384 −0.264192 0.964470i \(-0.585105\pi\)
−0.264192 + 0.964470i \(0.585105\pi\)
\(422\) −4.40147e14 −1.60096
\(423\) 8.77115e13 0.314908
\(424\) 8.61002e13 0.305135
\(425\) 2.05861e14 0.720168
\(426\) −5.16413e13 −0.178338
\(427\) 1.66388e14 0.567244
\(428\) 2.78049e13 0.0935795
\(429\) −1.16890e14 −0.388385
\(430\) −3.19290e14 −1.04739
\(431\) 5.57672e13 0.180615 0.0903076 0.995914i \(-0.471215\pi\)
0.0903076 + 0.995914i \(0.471215\pi\)
\(432\) −6.61071e13 −0.211391
\(433\) −3.40207e14 −1.07414 −0.537069 0.843538i \(-0.680468\pi\)
−0.537069 + 0.843538i \(0.680468\pi\)
\(434\) −1.93507e14 −0.603257
\(435\) −5.42503e13 −0.166998
\(436\) 1.57809e13 0.0479685
\(437\) −5.59502e14 −1.67940
\(438\) −8.03082e13 −0.238041
\(439\) 3.95069e14 1.15643 0.578213 0.815886i \(-0.303750\pi\)
0.578213 + 0.815886i \(0.303750\pi\)
\(440\) −2.24615e14 −0.649306
\(441\) −9.33804e13 −0.266590
\(442\) −3.50100e14 −0.987119
\(443\) −6.07338e14 −1.69126 −0.845629 0.533771i \(-0.820774\pi\)
−0.845629 + 0.533771i \(0.820774\pi\)
\(444\) 4.18737e13 0.115169
\(445\) −4.24501e14 −1.15318
\(446\) 2.25001e14 0.603730
\(447\) 2.52757e14 0.669902
\(448\) 1.48050e14 0.387596
\(449\) 6.28780e14 1.62609 0.813043 0.582203i \(-0.197809\pi\)
0.813043 + 0.582203i \(0.197809\pi\)
\(450\) −1.47911e14 −0.377861
\(451\) 2.69794e14 0.680866
\(452\) 1.86475e13 0.0464900
\(453\) 1.39319e14 0.343139
\(454\) −5.18918e14 −1.26268
\(455\) 3.75152e14 0.901871
\(456\) −2.88135e14 −0.684368
\(457\) 8.41019e13 0.197363 0.0986817 0.995119i \(-0.468537\pi\)
0.0986817 + 0.995119i \(0.468537\pi\)
\(458\) 3.05185e14 0.707626
\(459\) 5.62420e13 0.128852
\(460\) 9.35256e13 0.211720
\(461\) −5.29887e14 −1.18530 −0.592650 0.805460i \(-0.701918\pi\)
−0.592650 + 0.805460i \(0.701918\pi\)
\(462\) 5.92308e13 0.130923
\(463\) −5.25570e14 −1.14798 −0.573991 0.818862i \(-0.694606\pi\)
−0.573991 + 0.818862i \(0.694606\pi\)
\(464\) 1.02168e14 0.220529
\(465\) 4.98826e14 1.06404
\(466\) −2.94876e14 −0.621607
\(467\) −7.96126e13 −0.165859 −0.0829295 0.996555i \(-0.526428\pi\)
−0.0829295 + 0.996555i \(0.526428\pi\)
\(468\) 2.50648e13 0.0516075
\(469\) −2.42287e14 −0.493036
\(470\) −7.13199e14 −1.43441
\(471\) −2.64668e12 −0.00526122
\(472\) 6.21027e13 0.122020
\(473\) −1.70804e14 −0.331712
\(474\) 1.29542e13 0.0248673
\(475\) −7.16921e14 −1.36037
\(476\) 1.76769e13 0.0331565
\(477\) 5.85283e13 0.108521
\(478\) −3.73048e14 −0.683773
\(479\) 3.82897e14 0.693803 0.346902 0.937902i \(-0.387234\pi\)
0.346902 + 0.937902i \(0.387234\pi\)
\(480\) 1.02322e14 0.183292
\(481\) 1.42386e15 2.52157
\(482\) 1.09450e15 1.91627
\(483\) 1.98186e14 0.343055
\(484\) −4.97138e13 −0.0850801
\(485\) −7.60162e14 −1.28625
\(486\) −4.04100e13 −0.0676066
\(487\) 1.08358e15 1.79246 0.896231 0.443587i \(-0.146294\pi\)
0.896231 + 0.443587i \(0.146294\pi\)
\(488\) 7.26388e14 1.18812
\(489\) 5.94960e14 0.962252
\(490\) 7.59294e14 1.21432
\(491\) −6.31358e14 −0.998453 −0.499226 0.866472i \(-0.666382\pi\)
−0.499226 + 0.866472i \(0.666382\pi\)
\(492\) −5.78521e13 −0.0904714
\(493\) −8.69217e13 −0.134422
\(494\) 1.21924e15 1.86463
\(495\) −1.52687e14 −0.230926
\(496\) −9.39426e14 −1.40512
\(497\) 8.86622e13 0.131153
\(498\) 8.03291e14 1.17520
\(499\) 2.71326e14 0.392589 0.196295 0.980545i \(-0.437109\pi\)
0.196295 + 0.980545i \(0.437109\pi\)
\(500\) 8.42576e12 0.0120580
\(501\) 5.77681e14 0.817675
\(502\) −5.46256e14 −0.764761
\(503\) 2.14150e14 0.296547 0.148274 0.988946i \(-0.452628\pi\)
0.148274 + 0.988946i \(0.452628\pi\)
\(504\) 1.02063e14 0.139798
\(505\) −1.31232e15 −1.77802
\(506\) 5.02109e14 0.672930
\(507\) 4.16803e14 0.552570
\(508\) 7.86968e12 0.0103206
\(509\) −7.12359e13 −0.0924168 −0.0462084 0.998932i \(-0.514714\pi\)
−0.0462084 + 0.998932i \(0.514714\pi\)
\(510\) −4.57315e14 −0.586920
\(511\) 1.37880e14 0.175060
\(512\) 6.26913e14 0.787450
\(513\) −1.95866e14 −0.243396
\(514\) −6.03612e14 −0.742097
\(515\) −1.77373e15 −2.15749
\(516\) 3.66255e13 0.0440769
\(517\) −3.81525e14 −0.454281
\(518\) −7.21503e14 −0.850011
\(519\) 1.81829e14 0.211954
\(520\) 1.63777e15 1.88901
\(521\) 5.83431e14 0.665859 0.332929 0.942952i \(-0.391963\pi\)
0.332929 + 0.942952i \(0.391963\pi\)
\(522\) 6.24534e13 0.0705291
\(523\) −8.94909e14 −1.00005 −0.500023 0.866012i \(-0.666675\pi\)
−0.500023 + 0.866012i \(0.666675\pi\)
\(524\) 8.48284e13 0.0938036
\(525\) 2.53947e14 0.277886
\(526\) 1.61020e15 1.74365
\(527\) 7.99236e14 0.856479
\(528\) 2.87551e14 0.304949
\(529\) 7.27243e14 0.763262
\(530\) −4.75905e14 −0.494314
\(531\) 4.22156e13 0.0433963
\(532\) −6.15608e13 −0.0626311
\(533\) −1.96719e15 −1.98083
\(534\) 4.88690e14 0.487031
\(535\) 1.23501e15 1.21822
\(536\) −1.05773e15 −1.03269
\(537\) −4.60852e13 −0.0445352
\(538\) −1.37721e15 −1.31734
\(539\) 4.06183e14 0.384577
\(540\) 3.27407e13 0.0306847
\(541\) 1.14946e15 1.06637 0.533186 0.845998i \(-0.320994\pi\)
0.533186 + 0.845998i \(0.320994\pi\)
\(542\) −3.27127e14 −0.300414
\(543\) −2.76435e14 −0.251301
\(544\) 1.63944e14 0.147538
\(545\) 7.00942e14 0.624456
\(546\) −4.31878e14 −0.380892
\(547\) 1.43162e15 1.24996 0.624982 0.780639i \(-0.285106\pi\)
0.624982 + 0.780639i \(0.285106\pi\)
\(548\) −1.94696e14 −0.168292
\(549\) 4.93777e14 0.422554
\(550\) 6.43380e14 0.545096
\(551\) 3.02710e14 0.253917
\(552\) 8.65203e14 0.718544
\(553\) −2.22408e13 −0.0182879
\(554\) 4.04059e13 0.0328958
\(555\) 1.85991e15 1.49927
\(556\) 1.55481e14 0.124098
\(557\) 1.90773e15 1.50770 0.753848 0.657049i \(-0.228196\pi\)
0.753848 + 0.657049i \(0.228196\pi\)
\(558\) −5.74253e14 −0.449382
\(559\) 1.24541e15 0.965042
\(560\) −9.22877e14 −0.708124
\(561\) −2.44640e14 −0.185879
\(562\) 1.45803e15 1.09702
\(563\) −1.75838e15 −1.31014 −0.655070 0.755568i \(-0.727361\pi\)
−0.655070 + 0.755568i \(0.727361\pi\)
\(564\) 8.18106e13 0.0603635
\(565\) 8.28269e14 0.605208
\(566\) −3.60671e14 −0.260988
\(567\) 6.93793e13 0.0497191
\(568\) 3.87065e14 0.274706
\(569\) 1.20198e15 0.844853 0.422426 0.906397i \(-0.361178\pi\)
0.422426 + 0.906397i \(0.361178\pi\)
\(570\) 1.59262e15 1.10867
\(571\) −2.41179e15 −1.66280 −0.831402 0.555672i \(-0.812461\pi\)
−0.831402 + 0.555672i \(0.812461\pi\)
\(572\) −1.09026e14 −0.0744480
\(573\) 5.87187e14 0.397124
\(574\) 9.96819e14 0.667730
\(575\) 2.15275e15 1.42830
\(576\) 4.39355e14 0.288730
\(577\) 1.37637e15 0.895915 0.447957 0.894055i \(-0.352152\pi\)
0.447957 + 0.894055i \(0.352152\pi\)
\(578\) 9.01815e14 0.581453
\(579\) −3.93099e14 −0.251056
\(580\) −5.06006e13 −0.0320112
\(581\) −1.37916e15 −0.864262
\(582\) 8.75106e14 0.543230
\(583\) −2.54585e14 −0.156551
\(584\) 6.01931e14 0.366671
\(585\) 1.11331e15 0.671827
\(586\) −2.86684e15 −1.71383
\(587\) −3.61030e14 −0.213813 −0.106906 0.994269i \(-0.534095\pi\)
−0.106906 + 0.994269i \(0.534095\pi\)
\(588\) −8.70981e13 −0.0511015
\(589\) −2.78339e15 −1.61785
\(590\) −3.43263e14 −0.197670
\(591\) 8.02346e14 0.457752
\(592\) −3.50271e15 −1.97986
\(593\) 5.56473e14 0.311633 0.155817 0.987786i \(-0.450199\pi\)
0.155817 + 0.987786i \(0.450199\pi\)
\(594\) 1.75774e14 0.0975281
\(595\) 7.85157e14 0.431631
\(596\) 2.35752e14 0.128411
\(597\) −1.59653e15 −0.861623
\(598\) −3.66110e15 −1.95774
\(599\) −2.56924e15 −1.36131 −0.680656 0.732603i \(-0.738305\pi\)
−0.680656 + 0.732603i \(0.738305\pi\)
\(600\) 1.10863e15 0.582044
\(601\) −2.73554e15 −1.42309 −0.711547 0.702638i \(-0.752005\pi\)
−0.711547 + 0.702638i \(0.752005\pi\)
\(602\) −6.31075e14 −0.325312
\(603\) −7.19013e14 −0.367275
\(604\) 1.29946e14 0.0657750
\(605\) −2.20814e15 −1.10757
\(606\) 1.51075e15 0.750919
\(607\) 2.21689e15 1.09196 0.545980 0.837798i \(-0.316158\pi\)
0.545980 + 0.837798i \(0.316158\pi\)
\(608\) −5.70945e14 −0.278692
\(609\) −1.07225e14 −0.0518684
\(610\) −4.01500e15 −1.92474
\(611\) 2.78187e15 1.32163
\(612\) 5.24583e13 0.0246991
\(613\) 3.99454e15 1.86395 0.931974 0.362524i \(-0.118085\pi\)
0.931974 + 0.362524i \(0.118085\pi\)
\(614\) 1.94139e15 0.897813
\(615\) −2.56962e15 −1.17776
\(616\) −4.43950e14 −0.201670
\(617\) 4.38705e14 0.197517 0.0987585 0.995111i \(-0.468513\pi\)
0.0987585 + 0.995111i \(0.468513\pi\)
\(618\) 2.04194e15 0.911183
\(619\) −3.34765e14 −0.148061 −0.0740306 0.997256i \(-0.523586\pi\)
−0.0740306 + 0.997256i \(0.523586\pi\)
\(620\) 4.65267e14 0.203961
\(621\) 5.88139e14 0.255550
\(622\) 8.08518e14 0.348211
\(623\) −8.39024e14 −0.358171
\(624\) −2.09666e15 −0.887182
\(625\) −2.19024e15 −0.918655
\(626\) 2.18182e15 0.907109
\(627\) 8.51971e14 0.351118
\(628\) −2.46862e12 −0.00100850
\(629\) 2.98001e15 1.20681
\(630\) −5.64137e14 −0.226470
\(631\) 1.03484e15 0.411823 0.205911 0.978571i \(-0.433984\pi\)
0.205911 + 0.978571i \(0.433984\pi\)
\(632\) −9.70949e13 −0.0383047
\(633\) 2.24257e15 0.877054
\(634\) 4.65694e15 1.80555
\(635\) 3.49548e14 0.134354
\(636\) 5.45908e13 0.0208020
\(637\) −2.96166e15 −1.11884
\(638\) −2.71658e14 −0.101744
\(639\) 2.63115e14 0.0976993
\(640\) −4.43485e15 −1.63264
\(641\) −2.48580e15 −0.907291 −0.453646 0.891182i \(-0.649877\pi\)
−0.453646 + 0.891182i \(0.649877\pi\)
\(642\) −1.42176e15 −0.514497
\(643\) 4.42130e15 1.58632 0.793158 0.609016i \(-0.208436\pi\)
0.793158 + 0.609016i \(0.208436\pi\)
\(644\) 1.84853e14 0.0657588
\(645\) 1.62680e15 0.573794
\(646\) 2.55176e15 0.892402
\(647\) 1.68139e15 0.583037 0.291518 0.956565i \(-0.405840\pi\)
0.291518 + 0.956565i \(0.405840\pi\)
\(648\) 3.02883e14 0.104139
\(649\) −1.83628e14 −0.0626027
\(650\) −4.69117e15 −1.58583
\(651\) 9.85927e14 0.330483
\(652\) 5.54933e14 0.184450
\(653\) 2.19708e15 0.724142 0.362071 0.932151i \(-0.382070\pi\)
0.362071 + 0.932151i \(0.382070\pi\)
\(654\) −8.06931e14 −0.263730
\(655\) 3.76783e15 1.22114
\(656\) 4.83930e15 1.55529
\(657\) 4.09175e14 0.130406
\(658\) −1.40963e15 −0.445516
\(659\) 5.21720e15 1.63519 0.817594 0.575795i \(-0.195307\pi\)
0.817594 + 0.575795i \(0.195307\pi\)
\(660\) −1.42414e14 −0.0442652
\(661\) 5.47364e13 0.0168721 0.00843603 0.999964i \(-0.497315\pi\)
0.00843603 + 0.999964i \(0.497315\pi\)
\(662\) −3.77284e15 −1.15332
\(663\) 1.78378e15 0.540775
\(664\) −6.02087e15 −1.81024
\(665\) −2.73435e15 −0.815334
\(666\) −2.14114e15 −0.633195
\(667\) −9.08966e14 −0.266597
\(668\) 5.38817e14 0.156737
\(669\) −1.14639e15 −0.330742
\(670\) 5.84644e15 1.67294
\(671\) −2.14782e15 −0.609569
\(672\) 2.02239e14 0.0569292
\(673\) −7.52893e14 −0.210208 −0.105104 0.994461i \(-0.533518\pi\)
−0.105104 + 0.994461i \(0.533518\pi\)
\(674\) 3.11026e15 0.861325
\(675\) 7.53616e14 0.207004
\(676\) 3.88762e14 0.105920
\(677\) −5.26803e15 −1.42368 −0.711838 0.702344i \(-0.752137\pi\)
−0.711838 + 0.702344i \(0.752137\pi\)
\(678\) −9.53510e14 −0.255601
\(679\) −1.50246e15 −0.399501
\(680\) 3.42769e15 0.904072
\(681\) 2.64392e15 0.691733
\(682\) 2.49787e15 0.648270
\(683\) −2.69775e15 −0.694525 −0.347262 0.937768i \(-0.612889\pi\)
−0.347262 + 0.937768i \(0.612889\pi\)
\(684\) −1.82689e14 −0.0466556
\(685\) −8.64783e15 −2.19083
\(686\) 3.37721e15 0.848741
\(687\) −1.55494e15 −0.387660
\(688\) −3.06371e15 −0.757724
\(689\) 1.85629e15 0.455450
\(690\) −4.78228e15 −1.16403
\(691\) −8.85718e14 −0.213878 −0.106939 0.994266i \(-0.534105\pi\)
−0.106939 + 0.994266i \(0.534105\pi\)
\(692\) 1.69596e14 0.0406287
\(693\) −3.01784e14 −0.0717238
\(694\) −6.69740e15 −1.57917
\(695\) 6.90601e15 1.61551
\(696\) −4.68105e14 −0.108641
\(697\) −4.11714e15 −0.948015
\(698\) 4.75195e15 1.08559
\(699\) 1.50241e15 0.340536
\(700\) 2.36862e14 0.0532668
\(701\) −1.95996e15 −0.437319 −0.218659 0.975801i \(-0.570168\pi\)
−0.218659 + 0.975801i \(0.570168\pi\)
\(702\) −1.28165e15 −0.283736
\(703\) −1.03780e16 −2.27961
\(704\) −1.91109e15 −0.416516
\(705\) 3.63379e15 0.785813
\(706\) 5.57550e14 0.119635
\(707\) −2.59378e15 −0.552239
\(708\) 3.93755e13 0.00831846
\(709\) −5.58013e15 −1.16974 −0.584871 0.811126i \(-0.698855\pi\)
−0.584871 + 0.811126i \(0.698855\pi\)
\(710\) −2.13944e15 −0.445020
\(711\) −6.60022e13 −0.0136231
\(712\) −3.66286e15 −0.750205
\(713\) 8.35786e15 1.69864
\(714\) −9.03880e14 −0.182293
\(715\) −4.84263e15 −0.969165
\(716\) −4.29848e13 −0.00853676
\(717\) 1.90070e15 0.374592
\(718\) −5.24226e15 −1.02526
\(719\) −8.80656e15 −1.70922 −0.854609 0.519272i \(-0.826203\pi\)
−0.854609 + 0.519272i \(0.826203\pi\)
\(720\) −2.73874e15 −0.527500
\(721\) −3.50577e15 −0.670100
\(722\) −3.33083e15 −0.631826
\(723\) −5.57652e15 −1.04979
\(724\) −2.57837e14 −0.0481708
\(725\) −1.16471e15 −0.215953
\(726\) 2.54204e15 0.467768
\(727\) −1.26060e15 −0.230217 −0.115109 0.993353i \(-0.536722\pi\)
−0.115109 + 0.993353i \(0.536722\pi\)
\(728\) 3.23704e15 0.586713
\(729\) 2.05891e14 0.0370370
\(730\) −3.32708e15 −0.594001
\(731\) 2.60651e15 0.461865
\(732\) 4.60557e14 0.0809977
\(733\) 1.28404e15 0.224134 0.112067 0.993701i \(-0.464253\pi\)
0.112067 + 0.993701i \(0.464253\pi\)
\(734\) −8.90997e15 −1.54365
\(735\) −3.86864e15 −0.665240
\(736\) 1.71442e15 0.292609
\(737\) 3.12754e15 0.529824
\(738\) 2.95817e15 0.497409
\(739\) −1.92179e15 −0.320746 −0.160373 0.987056i \(-0.551270\pi\)
−0.160373 + 0.987056i \(0.551270\pi\)
\(740\) 1.73478e15 0.287389
\(741\) −6.21211e15 −1.02150
\(742\) −9.40624e14 −0.153530
\(743\) 4.74326e15 0.768491 0.384245 0.923231i \(-0.374462\pi\)
0.384245 + 0.923231i \(0.374462\pi\)
\(744\) 4.30418e15 0.692212
\(745\) 1.04714e16 1.67165
\(746\) 7.19897e15 1.14079
\(747\) −4.09281e15 −0.643811
\(748\) −2.28181e14 −0.0356305
\(749\) 2.44100e15 0.378370
\(750\) −4.30837e14 −0.0662943
\(751\) −4.09969e15 −0.626226 −0.313113 0.949716i \(-0.601372\pi\)
−0.313113 + 0.949716i \(0.601372\pi\)
\(752\) −6.84342e15 −1.03771
\(753\) 2.78321e15 0.418960
\(754\) 1.98078e15 0.296002
\(755\) 5.77183e15 0.856260
\(756\) 6.47118e13 0.00953045
\(757\) −1.11823e16 −1.63495 −0.817476 0.575963i \(-0.804627\pi\)
−0.817476 + 0.575963i \(0.804627\pi\)
\(758\) −3.22120e15 −0.467560
\(759\) −2.55827e15 −0.368652
\(760\) −1.19371e16 −1.70775
\(761\) −1.23688e16 −1.75676 −0.878379 0.477964i \(-0.841375\pi\)
−0.878379 + 0.477964i \(0.841375\pi\)
\(762\) −4.02403e14 −0.0567425
\(763\) 1.38541e15 0.193951
\(764\) 5.47684e14 0.0761231
\(765\) 2.33004e15 0.321533
\(766\) −6.20180e15 −0.849688
\(767\) 1.33891e15 0.182129
\(768\) 1.40257e15 0.189425
\(769\) −2.71460e14 −0.0364008 −0.0182004 0.999834i \(-0.505794\pi\)
−0.0182004 + 0.999834i \(0.505794\pi\)
\(770\) 2.45387e15 0.326702
\(771\) 3.07543e15 0.406544
\(772\) −3.66653e14 −0.0481238
\(773\) −7.15121e15 −0.931949 −0.465974 0.884798i \(-0.654296\pi\)
−0.465974 + 0.884798i \(0.654296\pi\)
\(774\) −1.87279e15 −0.242333
\(775\) 1.07094e16 1.37596
\(776\) −6.55914e15 −0.836773
\(777\) 3.67610e15 0.465662
\(778\) −1.24228e15 −0.156254
\(779\) 1.43382e16 1.79076
\(780\) 1.03841e15 0.128780
\(781\) −1.14449e15 −0.140939
\(782\) −7.66233e15 −0.936966
\(783\) −3.18204e14 −0.0386381
\(784\) 7.28571e15 0.878484
\(785\) −1.09649e14 −0.0131287
\(786\) −4.33756e15 −0.515729
\(787\) 5.43037e15 0.641163 0.320581 0.947221i \(-0.396122\pi\)
0.320581 + 0.947221i \(0.396122\pi\)
\(788\) 7.48367e14 0.0877446
\(789\) −8.20406e15 −0.955224
\(790\) 5.36677e14 0.0620532
\(791\) 1.63707e15 0.187973
\(792\) −1.31747e15 −0.150229
\(793\) 1.56607e16 1.77341
\(794\) −1.53672e16 −1.72816
\(795\) 2.42476e15 0.270801
\(796\) −1.48912e15 −0.165161
\(797\) 2.89325e15 0.318688 0.159344 0.987223i \(-0.449062\pi\)
0.159344 + 0.987223i \(0.449062\pi\)
\(798\) 3.14781e15 0.344344
\(799\) 5.82218e15 0.632526
\(800\) 2.19678e15 0.237023
\(801\) −2.48990e15 −0.266811
\(802\) −1.65431e16 −1.76059
\(803\) −1.77982e15 −0.188122
\(804\) −6.70641e14 −0.0704015
\(805\) 8.21062e15 0.856049
\(806\) −1.82131e16 −1.88600
\(807\) 7.01696e15 0.721680
\(808\) −1.13235e16 −1.15669
\(809\) 7.66943e14 0.0778120 0.0389060 0.999243i \(-0.487613\pi\)
0.0389060 + 0.999243i \(0.487613\pi\)
\(810\) −1.67414e15 −0.168704
\(811\) 2.35899e15 0.236108 0.118054 0.993007i \(-0.462334\pi\)
0.118054 + 0.993007i \(0.462334\pi\)
\(812\) −1.00012e14 −0.00994243
\(813\) 1.66673e15 0.164576
\(814\) 9.31348e15 0.913435
\(815\) 2.46485e16 2.40118
\(816\) −4.38811e15 −0.424601
\(817\) −9.07733e15 −0.872443
\(818\) 9.12327e15 0.870979
\(819\) 2.20044e15 0.208665
\(820\) −2.39675e15 −0.225760
\(821\) −1.62872e16 −1.52391 −0.761955 0.647630i \(-0.775760\pi\)
−0.761955 + 0.647630i \(0.775760\pi\)
\(822\) 9.95546e15 0.925266
\(823\) −3.12466e15 −0.288472 −0.144236 0.989543i \(-0.546073\pi\)
−0.144236 + 0.989543i \(0.546073\pi\)
\(824\) −1.53048e16 −1.40355
\(825\) −3.27806e15 −0.298621
\(826\) −6.78457e14 −0.0613949
\(827\) −8.65810e14 −0.0778291 −0.0389146 0.999243i \(-0.512390\pi\)
−0.0389146 + 0.999243i \(0.512390\pi\)
\(828\) 5.48572e14 0.0489854
\(829\) 1.32091e16 1.17171 0.585857 0.810414i \(-0.300758\pi\)
0.585857 + 0.810414i \(0.300758\pi\)
\(830\) 3.32794e16 2.93256
\(831\) −2.05870e14 −0.0180214
\(832\) 1.39346e16 1.21176
\(833\) −6.19847e15 −0.535473
\(834\) −7.95026e15 −0.682288
\(835\) 2.39327e16 2.04040
\(836\) 7.94654e14 0.0673044
\(837\) 2.92585e15 0.246185
\(838\) −1.04865e16 −0.876572
\(839\) 1.47090e16 1.22149 0.610747 0.791826i \(-0.290869\pi\)
0.610747 + 0.791826i \(0.290869\pi\)
\(840\) 4.22835e15 0.348847
\(841\) −1.17087e16 −0.959692
\(842\) 6.83846e15 0.556855
\(843\) −7.42872e15 −0.600983
\(844\) 2.09170e15 0.168119
\(845\) 1.72677e16 1.37887
\(846\) −4.18325e15 −0.331877
\(847\) −4.36438e15 −0.344004
\(848\) −4.56649e15 −0.357607
\(849\) 1.83764e15 0.142978
\(850\) −9.81817e15 −0.758973
\(851\) 3.11628e16 2.39345
\(852\) 2.45414e14 0.0187276
\(853\) 9.35697e15 0.709440 0.354720 0.934973i \(-0.384576\pi\)
0.354720 + 0.934973i \(0.384576\pi\)
\(854\) −7.93561e15 −0.597809
\(855\) −8.11450e15 −0.607363
\(856\) 1.06564e16 0.792514
\(857\) 1.71450e16 1.26690 0.633451 0.773783i \(-0.281638\pi\)
0.633451 + 0.773783i \(0.281638\pi\)
\(858\) 5.57488e15 0.409313
\(859\) 2.02187e16 1.47499 0.737496 0.675351i \(-0.236008\pi\)
0.737496 + 0.675351i \(0.236008\pi\)
\(860\) 1.51736e15 0.109988
\(861\) −5.07885e15 −0.365803
\(862\) −2.65972e15 −0.190347
\(863\) −2.31489e16 −1.64615 −0.823077 0.567930i \(-0.807744\pi\)
−0.823077 + 0.567930i \(0.807744\pi\)
\(864\) 6.00169e14 0.0424080
\(865\) 7.53297e15 0.528905
\(866\) 1.62256e16 1.13202
\(867\) −4.59480e15 −0.318538
\(868\) 9.19598e14 0.0633489
\(869\) 2.87094e14 0.0196524
\(870\) 2.58738e15 0.175996
\(871\) −2.28043e16 −1.54141
\(872\) 6.04816e15 0.406240
\(873\) −4.45871e15 −0.297599
\(874\) 2.66845e16 1.76989
\(875\) 7.39698e14 0.0487540
\(876\) 3.81647e14 0.0249971
\(877\) −1.34296e16 −0.874110 −0.437055 0.899435i \(-0.643979\pi\)
−0.437055 + 0.899435i \(0.643979\pi\)
\(878\) −1.88421e16 −1.21874
\(879\) 1.46067e16 0.938888
\(880\) 1.19129e16 0.760962
\(881\) 1.10383e16 0.700705 0.350352 0.936618i \(-0.386062\pi\)
0.350352 + 0.936618i \(0.386062\pi\)
\(882\) 4.45362e15 0.280954
\(883\) −2.83712e16 −1.77866 −0.889331 0.457264i \(-0.848830\pi\)
−0.889331 + 0.457264i \(0.848830\pi\)
\(884\) 1.66377e15 0.103659
\(885\) 1.74894e15 0.108290
\(886\) 2.89660e16 1.78239
\(887\) 6.60674e15 0.404024 0.202012 0.979383i \(-0.435252\pi\)
0.202012 + 0.979383i \(0.435252\pi\)
\(888\) 1.60484e16 0.975351
\(889\) 6.90880e14 0.0417295
\(890\) 2.02459e16 1.21532
\(891\) −8.95579e14 −0.0534289
\(892\) −1.06927e15 −0.0633986
\(893\) −2.02761e16 −1.19481
\(894\) −1.20548e16 −0.705999
\(895\) −1.90926e15 −0.111132
\(896\) −8.76546e15 −0.507085
\(897\) 1.86535e16 1.07251
\(898\) −2.99886e16 −1.71371
\(899\) −4.52189e15 −0.256827
\(900\) 7.02916e14 0.0396798
\(901\) 3.88504e15 0.217976
\(902\) −1.28674e16 −0.717553
\(903\) 3.21536e15 0.178216
\(904\) 7.14681e15 0.393718
\(905\) −1.14524e16 −0.627089
\(906\) −6.64459e15 −0.361629
\(907\) −2.35979e16 −1.27654 −0.638269 0.769813i \(-0.720349\pi\)
−0.638269 + 0.769813i \(0.720349\pi\)
\(908\) 2.46605e15 0.132596
\(909\) −7.69735e15 −0.411377
\(910\) −1.78922e16 −0.950467
\(911\) −1.51944e15 −0.0802294 −0.0401147 0.999195i \(-0.512772\pi\)
−0.0401147 + 0.999195i \(0.512772\pi\)
\(912\) 1.52818e16 0.802054
\(913\) 1.78028e16 0.928750
\(914\) −4.01110e15 −0.207998
\(915\) 2.04566e16 1.05443
\(916\) −1.45033e15 −0.0743089
\(917\) 7.44710e15 0.379276
\(918\) −2.68237e15 −0.135795
\(919\) 3.25419e16 1.63760 0.818799 0.574080i \(-0.194640\pi\)
0.818799 + 0.574080i \(0.194640\pi\)
\(920\) 3.58444e16 1.79303
\(921\) −9.89147e15 −0.491850
\(922\) 2.52721e16 1.24917
\(923\) 8.34500e15 0.410031
\(924\) −2.81481e14 −0.0137484
\(925\) 3.99307e16 1.93877
\(926\) 2.50662e16 1.20984
\(927\) −1.04038e16 −0.499175
\(928\) −9.27558e14 −0.0442412
\(929\) 1.52117e16 0.721261 0.360630 0.932709i \(-0.382562\pi\)
0.360630 + 0.932709i \(0.382562\pi\)
\(930\) −2.37907e16 −1.12137
\(931\) 2.15865e16 1.01149
\(932\) 1.40133e15 0.0652759
\(933\) −4.11944e15 −0.190761
\(934\) 3.79699e15 0.174796
\(935\) −1.01352e16 −0.463838
\(936\) 9.60629e15 0.437057
\(937\) −2.78623e16 −1.26023 −0.630114 0.776503i \(-0.716992\pi\)
−0.630114 + 0.776503i \(0.716992\pi\)
\(938\) 1.15554e16 0.519602
\(939\) −1.11165e16 −0.496943
\(940\) 3.38932e15 0.150629
\(941\) 3.85825e15 0.170470 0.0852349 0.996361i \(-0.472836\pi\)
0.0852349 + 0.996361i \(0.472836\pi\)
\(942\) 1.26229e14 0.00554471
\(943\) −4.30542e16 −1.88019
\(944\) −3.29374e15 −0.143002
\(945\) 2.87431e15 0.124068
\(946\) 8.14619e15 0.349585
\(947\) 9.91197e15 0.422897 0.211449 0.977389i \(-0.432182\pi\)
0.211449 + 0.977389i \(0.432182\pi\)
\(948\) −6.15619e13 −0.00261135
\(949\) 1.29774e16 0.547299
\(950\) 3.41923e16 1.43367
\(951\) −2.37274e16 −0.989138
\(952\) 6.77481e15 0.280798
\(953\) −7.57779e15 −0.312271 −0.156135 0.987736i \(-0.549904\pi\)
−0.156135 + 0.987736i \(0.549904\pi\)
\(954\) −2.79141e15 −0.114369
\(955\) 2.43265e16 0.990972
\(956\) 1.77283e15 0.0718040
\(957\) 1.38411e15 0.0557386
\(958\) −1.82616e16 −0.731188
\(959\) −1.70924e16 −0.680457
\(960\) 1.82020e16 0.720488
\(961\) 1.61698e16 0.636395
\(962\) −6.79087e16 −2.65744
\(963\) 7.24394e15 0.281858
\(964\) −5.20135e15 −0.201230
\(965\) −1.62857e16 −0.626477
\(966\) −9.45214e15 −0.361540
\(967\) −3.22702e16 −1.22731 −0.613657 0.789573i \(-0.710302\pi\)
−0.613657 + 0.789573i \(0.710302\pi\)
\(968\) −1.90532e16 −0.720533
\(969\) −1.30013e16 −0.488886
\(970\) 3.62547e16 1.35556
\(971\) −4.14383e16 −1.54062 −0.770312 0.637667i \(-0.779900\pi\)
−0.770312 + 0.637667i \(0.779900\pi\)
\(972\) 1.92040e14 0.00709948
\(973\) 1.36497e16 0.501767
\(974\) −5.16793e16 −1.88905
\(975\) 2.39018e16 0.868770
\(976\) −3.85254e16 −1.39243
\(977\) 2.39601e16 0.861128 0.430564 0.902560i \(-0.358315\pi\)
0.430564 + 0.902560i \(0.358315\pi\)
\(978\) −2.83756e16 −1.01410
\(979\) 1.08305e16 0.384896
\(980\) −3.60838e15 −0.127517
\(981\) 4.11136e15 0.144479
\(982\) 3.01116e16 1.05225
\(983\) −5.49845e16 −1.91072 −0.955358 0.295452i \(-0.904530\pi\)
−0.955358 + 0.295452i \(0.904530\pi\)
\(984\) −2.21723e16 −0.766192
\(985\) 3.32403e16 1.14226
\(986\) 4.14558e15 0.141665
\(987\) 7.18216e15 0.244068
\(988\) −5.79418e15 −0.195807
\(989\) 2.72571e16 0.916010
\(990\) 7.28213e15 0.243369
\(991\) −2.23721e16 −0.743534 −0.371767 0.928326i \(-0.621248\pi\)
−0.371767 + 0.928326i \(0.621248\pi\)
\(992\) 8.52880e15 0.281886
\(993\) 1.92228e16 0.631824
\(994\) −4.22860e15 −0.138220
\(995\) −6.61423e16 −2.15007
\(996\) −3.81746e15 −0.123409
\(997\) 1.06303e15 0.0341760 0.0170880 0.999854i \(-0.494560\pi\)
0.0170880 + 0.999854i \(0.494560\pi\)
\(998\) −1.29404e16 −0.413743
\(999\) 1.09092e16 0.346884
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 177.12.a.d.1.6 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.d.1.6 28 1.1 even 1 trivial