Properties

Label 177.10.a.a.1.1
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $1$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(91.1613430010\)
Analytic rank: \(1\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-43.9134 q^{2} +81.0000 q^{3} +1416.39 q^{4} -993.635 q^{5} -3556.99 q^{6} +3425.90 q^{7} -39714.8 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-43.9134 q^{2} +81.0000 q^{3} +1416.39 q^{4} -993.635 q^{5} -3556.99 q^{6} +3425.90 q^{7} -39714.8 q^{8} +6561.00 q^{9} +43633.9 q^{10} -75091.5 q^{11} +114727. q^{12} +66893.5 q^{13} -150443. q^{14} -80484.4 q^{15} +1.01882e6 q^{16} +199427. q^{17} -288116. q^{18} +79861.8 q^{19} -1.40737e6 q^{20} +277498. q^{21} +3.29753e6 q^{22} +2.06317e6 q^{23} -3.21690e6 q^{24} -965814. q^{25} -2.93752e6 q^{26} +531441. q^{27} +4.85241e6 q^{28} -5.68682e6 q^{29} +3.53435e6 q^{30} +1.44520e6 q^{31} -2.44059e7 q^{32} -6.08241e6 q^{33} -8.75750e6 q^{34} -3.40410e6 q^{35} +9.29292e6 q^{36} -6.74414e6 q^{37} -3.50700e6 q^{38} +5.41837e6 q^{39} +3.94620e7 q^{40} -3.10309e7 q^{41} -1.21859e7 q^{42} +3.99027e7 q^{43} -1.06359e8 q^{44} -6.51924e6 q^{45} -9.06009e7 q^{46} +1.76289e7 q^{47} +8.25245e7 q^{48} -2.86168e7 q^{49} +4.24122e7 q^{50} +1.61536e7 q^{51} +9.47471e7 q^{52} +9.14817e7 q^{53} -2.33374e7 q^{54} +7.46136e7 q^{55} -1.36059e8 q^{56} +6.46880e6 q^{57} +2.49728e8 q^{58} +1.21174e7 q^{59} -1.13997e8 q^{60} -3.45269e7 q^{61} -6.34637e7 q^{62} +2.24773e7 q^{63} +5.50112e8 q^{64} -6.64677e7 q^{65} +2.67100e8 q^{66} +4.20121e7 q^{67} +2.82465e8 q^{68} +1.67117e8 q^{69} +1.49485e8 q^{70} +2.88238e8 q^{71} -2.60569e8 q^{72} -4.61767e8 q^{73} +2.96158e8 q^{74} -7.82309e7 q^{75} +1.13115e8 q^{76} -2.57256e8 q^{77} -2.37939e8 q^{78} -3.32943e6 q^{79} -1.01234e9 q^{80} +4.30467e7 q^{81} +1.36267e9 q^{82} +4.97533e8 q^{83} +3.93045e8 q^{84} -1.98157e8 q^{85} -1.75226e9 q^{86} -4.60632e8 q^{87} +2.98224e9 q^{88} +5.53405e8 q^{89} +2.86282e8 q^{90} +2.29170e8 q^{91} +2.92225e9 q^{92} +1.17061e8 q^{93} -7.74147e8 q^{94} -7.93535e7 q^{95} -1.97688e9 q^{96} -4.40860e8 q^{97} +1.25666e9 q^{98} -4.92675e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} + O(q^{10}) \) \( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} - 54663q^{10} - 151769q^{11} + 421686q^{12} - 153611q^{13} - 286771q^{14} - 240084q^{15} + 805530q^{16} - 723621q^{17} - 433026q^{18} - 549388q^{19} - 527311q^{20} - 2492775q^{21} + 2973158q^{22} + 169962q^{23} - 1994301q^{24} + 8035779q^{25} - 2337392q^{26} + 11160261q^{27} - 22659054q^{28} - 16845442q^{29} - 4427703q^{30} - 19307976q^{31} - 44923568q^{32} - 12293289q^{33} - 35547496q^{34} - 34882596q^{35} + 34156566q^{36} - 41561129q^{37} - 52335371q^{38} - 12442491q^{39} - 125735038q^{40} - 68169291q^{41} - 23228451q^{42} - 25719587q^{43} - 126277032q^{44} - 19446804q^{45} - 292814271q^{46} - 174095332q^{47} + 65247930q^{48} + 7479350q^{49} - 227877439q^{50} - 58613301q^{51} - 232397708q^{52} - 228390500q^{53} - 35075106q^{54} - 29426208q^{55} + 326778474q^{56} - 44500428q^{57} + 480343762q^{58} + 254464581q^{59} - 42712191q^{60} - 183928964q^{61} - 21753862q^{62} - 201914775q^{63} + 310571245q^{64} + 5308466q^{65} + 240825798q^{66} - 82724114q^{67} - 138336205q^{68} + 13766922q^{69} + 1030274876q^{70} - 404721965q^{71} - 161538381q^{72} + 154162574q^{73} + 36352054q^{74} + 650898099q^{75} + 1068940636q^{76} - 448535481q^{77} - 189328752q^{78} + 272529635q^{79} - 345587859q^{80} + 903981141q^{81} - 38412637q^{82} + 432518643q^{83} - 1835383374q^{84} - 126211490q^{85} - 3699273072q^{86} - 1364480802q^{87} + 170111045q^{88} - 1255621070q^{89} - 358643943q^{90} + 1448885849q^{91} + 1568933320q^{92} - 1563946056q^{93} - 1908445164q^{94} - 2896546490q^{95} - 3638809008q^{96} + 1007235486q^{97} - 9506868248q^{98} - 995756409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −43.9134 −1.94072 −0.970359 0.241670i \(-0.922305\pi\)
−0.970359 + 0.241670i \(0.922305\pi\)
\(3\) 81.0000 0.577350
\(4\) 1416.39 2.76638
\(5\) −993.635 −0.710987 −0.355494 0.934679i \(-0.615687\pi\)
−0.355494 + 0.934679i \(0.615687\pi\)
\(6\) −3556.99 −1.12047
\(7\) 3425.90 0.539304 0.269652 0.962958i \(-0.413091\pi\)
0.269652 + 0.962958i \(0.413091\pi\)
\(8\) −39714.8 −3.42805
\(9\) 6561.00 0.333333
\(10\) 43633.9 1.37983
\(11\) −75091.5 −1.54641 −0.773204 0.634158i \(-0.781347\pi\)
−0.773204 + 0.634158i \(0.781347\pi\)
\(12\) 114727. 1.59717
\(13\) 66893.5 0.649589 0.324794 0.945785i \(-0.394705\pi\)
0.324794 + 0.945785i \(0.394705\pi\)
\(14\) −150443. −1.04664
\(15\) −80484.4 −0.410489
\(16\) 1.01882e6 3.88649
\(17\) 199427. 0.579112 0.289556 0.957161i \(-0.406492\pi\)
0.289556 + 0.957161i \(0.406492\pi\)
\(18\) −288116. −0.646906
\(19\) 79861.8 0.140588 0.0702939 0.997526i \(-0.477606\pi\)
0.0702939 + 0.997526i \(0.477606\pi\)
\(20\) −1.40737e6 −1.96686
\(21\) 277498. 0.311367
\(22\) 3.29753e6 3.00114
\(23\) 2.06317e6 1.53731 0.768653 0.639666i \(-0.220928\pi\)
0.768653 + 0.639666i \(0.220928\pi\)
\(24\) −3.21690e6 −1.97919
\(25\) −965814. −0.494497
\(26\) −2.93752e6 −1.26067
\(27\) 531441. 0.192450
\(28\) 4.85241e6 1.49192
\(29\) −5.68682e6 −1.49306 −0.746532 0.665349i \(-0.768283\pi\)
−0.746532 + 0.665349i \(0.768283\pi\)
\(30\) 3.53435e6 0.796643
\(31\) 1.44520e6 0.281061 0.140531 0.990076i \(-0.455119\pi\)
0.140531 + 0.990076i \(0.455119\pi\)
\(32\) −2.44059e7 −4.11453
\(33\) −6.08241e6 −0.892819
\(34\) −8.75750e6 −1.12389
\(35\) −3.40410e6 −0.383438
\(36\) 9.29292e6 0.922128
\(37\) −6.74414e6 −0.591588 −0.295794 0.955252i \(-0.595584\pi\)
−0.295794 + 0.955252i \(0.595584\pi\)
\(38\) −3.50700e6 −0.272841
\(39\) 5.41837e6 0.375040
\(40\) 3.94620e7 2.43730
\(41\) −3.10309e7 −1.71501 −0.857507 0.514472i \(-0.827988\pi\)
−0.857507 + 0.514472i \(0.827988\pi\)
\(42\) −1.21859e7 −0.604276
\(43\) 3.99027e7 1.77989 0.889947 0.456065i \(-0.150741\pi\)
0.889947 + 0.456065i \(0.150741\pi\)
\(44\) −1.06359e8 −4.27795
\(45\) −6.51924e6 −0.236996
\(46\) −9.06009e7 −2.98347
\(47\) 1.76289e7 0.526970 0.263485 0.964663i \(-0.415128\pi\)
0.263485 + 0.964663i \(0.415128\pi\)
\(48\) 8.25245e7 2.24387
\(49\) −2.86168e7 −0.709151
\(50\) 4.24122e7 0.959678
\(51\) 1.61536e7 0.334351
\(52\) 9.47471e7 1.79701
\(53\) 9.14817e7 1.59255 0.796274 0.604936i \(-0.206801\pi\)
0.796274 + 0.604936i \(0.206801\pi\)
\(54\) −2.33374e7 −0.373491
\(55\) 7.46136e7 1.09948
\(56\) −1.36059e8 −1.84876
\(57\) 6.46880e6 0.0811684
\(58\) 2.49728e8 2.89762
\(59\) 1.21174e7 0.130189
\(60\) −1.13997e8 −1.13557
\(61\) −3.45269e7 −0.319281 −0.159640 0.987175i \(-0.551033\pi\)
−0.159640 + 0.987175i \(0.551033\pi\)
\(62\) −6.34637e7 −0.545460
\(63\) 2.24773e7 0.179768
\(64\) 5.50112e8 4.09865
\(65\) −6.64677e7 −0.461850
\(66\) 2.67100e8 1.73271
\(67\) 4.20121e7 0.254705 0.127353 0.991857i \(-0.459352\pi\)
0.127353 + 0.991857i \(0.459352\pi\)
\(68\) 2.82465e8 1.60205
\(69\) 1.67117e8 0.887564
\(70\) 1.49485e8 0.744145
\(71\) 2.88238e8 1.34613 0.673067 0.739582i \(-0.264977\pi\)
0.673067 + 0.739582i \(0.264977\pi\)
\(72\) −2.60569e8 −1.14268
\(73\) −4.61767e8 −1.90313 −0.951567 0.307440i \(-0.900528\pi\)
−0.951567 + 0.307440i \(0.900528\pi\)
\(74\) 2.96158e8 1.14810
\(75\) −7.82309e7 −0.285498
\(76\) 1.13115e8 0.388920
\(77\) −2.57256e8 −0.833984
\(78\) −2.37939e8 −0.727847
\(79\) −3.32943e6 −0.00961718 −0.00480859 0.999988i \(-0.501531\pi\)
−0.00480859 + 0.999988i \(0.501531\pi\)
\(80\) −1.01234e9 −2.76325
\(81\) 4.30467e7 0.111111
\(82\) 1.36267e9 3.32836
\(83\) 4.97533e8 1.15072 0.575361 0.817900i \(-0.304862\pi\)
0.575361 + 0.817900i \(0.304862\pi\)
\(84\) 3.93045e8 0.861361
\(85\) −1.98157e8 −0.411742
\(86\) −1.75226e9 −3.45427
\(87\) −4.60632e8 −0.862021
\(88\) 2.98224e9 5.30116
\(89\) 5.53405e8 0.934949 0.467474 0.884007i \(-0.345164\pi\)
0.467474 + 0.884007i \(0.345164\pi\)
\(90\) 2.86282e8 0.459942
\(91\) 2.29170e8 0.350326
\(92\) 2.92225e9 4.25278
\(93\) 1.17061e8 0.162271
\(94\) −7.74147e8 −1.02270
\(95\) −7.93535e7 −0.0999562
\(96\) −1.97688e9 −2.37553
\(97\) −4.40860e8 −0.505624 −0.252812 0.967515i \(-0.581355\pi\)
−0.252812 + 0.967515i \(0.581355\pi\)
\(98\) 1.25666e9 1.37626
\(99\) −4.92675e8 −0.515469
\(100\) −1.36797e9 −1.36797
\(101\) −1.27590e7 −0.0122003 −0.00610017 0.999981i \(-0.501942\pi\)
−0.00610017 + 0.999981i \(0.501942\pi\)
\(102\) −7.09358e8 −0.648880
\(103\) −3.19147e8 −0.279398 −0.139699 0.990194i \(-0.544613\pi\)
−0.139699 + 0.990194i \(0.544613\pi\)
\(104\) −2.65666e9 −2.22682
\(105\) −2.75732e8 −0.221378
\(106\) −4.01727e9 −3.09069
\(107\) −1.82659e9 −1.34715 −0.673573 0.739121i \(-0.735241\pi\)
−0.673573 + 0.739121i \(0.735241\pi\)
\(108\) 7.52727e8 0.532391
\(109\) −1.41497e9 −0.960125 −0.480062 0.877234i \(-0.659386\pi\)
−0.480062 + 0.877234i \(0.659386\pi\)
\(110\) −3.27654e9 −2.13377
\(111\) −5.46276e8 −0.341553
\(112\) 3.49038e9 2.09600
\(113\) −9.45147e8 −0.545314 −0.272657 0.962111i \(-0.587902\pi\)
−0.272657 + 0.962111i \(0.587902\pi\)
\(114\) −2.84067e8 −0.157525
\(115\) −2.05004e9 −1.09300
\(116\) −8.05474e9 −4.13039
\(117\) 4.38888e8 0.216530
\(118\) −5.32115e8 −0.252660
\(119\) 6.83216e8 0.312318
\(120\) 3.19642e9 1.40718
\(121\) 3.28079e9 1.39137
\(122\) 1.51619e9 0.619634
\(123\) −2.51351e9 −0.990164
\(124\) 2.04697e9 0.777523
\(125\) 2.90036e9 1.06257
\(126\) −9.87057e8 −0.348879
\(127\) 1.86091e9 0.634758 0.317379 0.948299i \(-0.397197\pi\)
0.317379 + 0.948299i \(0.397197\pi\)
\(128\) −1.16614e10 −3.83979
\(129\) 3.23212e9 1.02762
\(130\) 2.91882e9 0.896319
\(131\) −4.14751e9 −1.23046 −0.615228 0.788349i \(-0.710936\pi\)
−0.615228 + 0.788349i \(0.710936\pi\)
\(132\) −8.61506e9 −2.46988
\(133\) 2.73599e8 0.0758196
\(134\) −1.84490e9 −0.494311
\(135\) −5.28058e8 −0.136830
\(136\) −7.92018e9 −1.98523
\(137\) −4.07295e9 −0.987794 −0.493897 0.869521i \(-0.664428\pi\)
−0.493897 + 0.869521i \(0.664428\pi\)
\(138\) −7.33867e9 −1.72251
\(139\) 5.43583e9 1.23509 0.617546 0.786535i \(-0.288127\pi\)
0.617546 + 0.786535i \(0.288127\pi\)
\(140\) −4.82152e9 −1.06074
\(141\) 1.42794e9 0.304246
\(142\) −1.26575e10 −2.61246
\(143\) −5.02313e9 −1.00453
\(144\) 6.68448e9 1.29550
\(145\) 5.65062e9 1.06155
\(146\) 2.02777e10 3.69345
\(147\) −2.31796e9 −0.409429
\(148\) −9.55233e9 −1.63656
\(149\) 1.22909e8 0.0204289 0.0102145 0.999948i \(-0.496749\pi\)
0.0102145 + 0.999948i \(0.496749\pi\)
\(150\) 3.43539e9 0.554071
\(151\) 9.58481e9 1.50033 0.750166 0.661250i \(-0.229974\pi\)
0.750166 + 0.661250i \(0.229974\pi\)
\(152\) −3.17169e9 −0.481942
\(153\) 1.30844e9 0.193037
\(154\) 1.12970e10 1.61853
\(155\) −1.43600e9 −0.199831
\(156\) 7.67452e9 1.03751
\(157\) 6.23709e9 0.819283 0.409641 0.912247i \(-0.365654\pi\)
0.409641 + 0.912247i \(0.365654\pi\)
\(158\) 1.46207e8 0.0186642
\(159\) 7.41001e9 0.919458
\(160\) 2.42506e10 2.92538
\(161\) 7.06822e9 0.829075
\(162\) −1.89033e9 −0.215635
\(163\) −1.19932e10 −1.33073 −0.665366 0.746517i \(-0.731725\pi\)
−0.665366 + 0.746517i \(0.731725\pi\)
\(164\) −4.39519e10 −4.74439
\(165\) 6.04370e9 0.634783
\(166\) −2.18484e10 −2.23323
\(167\) −1.20055e9 −0.119442 −0.0597209 0.998215i \(-0.519021\pi\)
−0.0597209 + 0.998215i \(0.519021\pi\)
\(168\) −1.10208e10 −1.06738
\(169\) −6.12976e9 −0.578034
\(170\) 8.70176e9 0.799074
\(171\) 5.23973e8 0.0468626
\(172\) 5.65177e10 4.92387
\(173\) −7.45260e8 −0.0632558 −0.0316279 0.999500i \(-0.510069\pi\)
−0.0316279 + 0.999500i \(0.510069\pi\)
\(174\) 2.02279e10 1.67294
\(175\) −3.30878e9 −0.266684
\(176\) −7.65048e10 −6.01010
\(177\) 9.81506e8 0.0751646
\(178\) −2.43019e10 −1.81447
\(179\) −7.16883e9 −0.521927 −0.260963 0.965349i \(-0.584040\pi\)
−0.260963 + 0.965349i \(0.584040\pi\)
\(180\) −9.23377e9 −0.655621
\(181\) 1.17303e9 0.0812376 0.0406188 0.999175i \(-0.487067\pi\)
0.0406188 + 0.999175i \(0.487067\pi\)
\(182\) −1.00637e10 −0.679883
\(183\) −2.79668e9 −0.184337
\(184\) −8.19384e10 −5.26996
\(185\) 6.70122e9 0.420611
\(186\) −5.14056e9 −0.314921
\(187\) −1.49752e10 −0.895544
\(188\) 2.49694e10 1.45780
\(189\) 1.82066e9 0.103789
\(190\) 3.48468e9 0.193987
\(191\) 4.15563e9 0.225936 0.112968 0.993599i \(-0.463964\pi\)
0.112968 + 0.993599i \(0.463964\pi\)
\(192\) 4.45590e10 2.36636
\(193\) −2.61187e10 −1.35501 −0.677506 0.735517i \(-0.736939\pi\)
−0.677506 + 0.735517i \(0.736939\pi\)
\(194\) 1.93597e10 0.981273
\(195\) −5.38388e9 −0.266649
\(196\) −4.05325e10 −1.96178
\(197\) −2.92561e10 −1.38394 −0.691972 0.721925i \(-0.743258\pi\)
−0.691972 + 0.721925i \(0.743258\pi\)
\(198\) 2.16351e10 1.00038
\(199\) −1.80017e10 −0.813721 −0.406861 0.913490i \(-0.633377\pi\)
−0.406861 + 0.913490i \(0.633377\pi\)
\(200\) 3.83571e10 1.69516
\(201\) 3.40298e9 0.147054
\(202\) 5.60293e8 0.0236774
\(203\) −1.94825e10 −0.805216
\(204\) 2.28797e10 0.924942
\(205\) 3.08334e10 1.21935
\(206\) 1.40148e10 0.542232
\(207\) 1.35365e10 0.512435
\(208\) 6.81524e10 2.52462
\(209\) −5.99694e9 −0.217406
\(210\) 1.21083e10 0.429633
\(211\) −1.97777e10 −0.686919 −0.343459 0.939168i \(-0.611599\pi\)
−0.343459 + 0.939168i \(0.611599\pi\)
\(212\) 1.29574e11 4.40560
\(213\) 2.33472e10 0.777190
\(214\) 8.02119e10 2.61443
\(215\) −3.96487e10 −1.26548
\(216\) −2.11061e10 −0.659729
\(217\) 4.95112e9 0.151577
\(218\) 6.21361e10 1.86333
\(219\) −3.74031e10 −1.09878
\(220\) 1.05682e11 3.04157
\(221\) 1.33403e10 0.376185
\(222\) 2.39888e10 0.662858
\(223\) −5.70225e10 −1.54410 −0.772048 0.635565i \(-0.780767\pi\)
−0.772048 + 0.635565i \(0.780767\pi\)
\(224\) −8.36123e10 −2.21898
\(225\) −6.33671e9 −0.164832
\(226\) 4.15046e10 1.05830
\(227\) 1.51234e10 0.378035 0.189018 0.981974i \(-0.439470\pi\)
0.189018 + 0.981974i \(0.439470\pi\)
\(228\) 9.16234e9 0.224543
\(229\) −1.70590e10 −0.409915 −0.204958 0.978771i \(-0.565706\pi\)
−0.204958 + 0.978771i \(0.565706\pi\)
\(230\) 9.00243e10 2.12121
\(231\) −2.08377e10 −0.481501
\(232\) 2.25851e11 5.11830
\(233\) −1.69879e10 −0.377605 −0.188802 0.982015i \(-0.560461\pi\)
−0.188802 + 0.982015i \(0.560461\pi\)
\(234\) −1.92731e10 −0.420223
\(235\) −1.75167e10 −0.374669
\(236\) 1.71629e10 0.360152
\(237\) −2.69684e8 −0.00555248
\(238\) −3.00023e10 −0.606120
\(239\) 6.50543e10 1.28969 0.644845 0.764314i \(-0.276922\pi\)
0.644845 + 0.764314i \(0.276922\pi\)
\(240\) −8.19992e10 −1.59536
\(241\) −1.97716e10 −0.377542 −0.188771 0.982021i \(-0.560450\pi\)
−0.188771 + 0.982021i \(0.560450\pi\)
\(242\) −1.44071e11 −2.70026
\(243\) 3.48678e9 0.0641500
\(244\) −4.89034e10 −0.883253
\(245\) 2.84347e10 0.504198
\(246\) 1.10377e11 1.92163
\(247\) 5.34223e9 0.0913243
\(248\) −5.73958e10 −0.963491
\(249\) 4.03002e10 0.664370
\(250\) −1.27365e11 −2.06214
\(251\) −5.38268e10 −0.855987 −0.427993 0.903782i \(-0.640779\pi\)
−0.427993 + 0.903782i \(0.640779\pi\)
\(252\) 3.18366e10 0.497307
\(253\) −1.54927e11 −2.37730
\(254\) −8.17189e10 −1.23189
\(255\) −1.60507e10 −0.237719
\(256\) 2.30437e11 3.35330
\(257\) −1.17069e11 −1.67396 −0.836978 0.547236i \(-0.815680\pi\)
−0.836978 + 0.547236i \(0.815680\pi\)
\(258\) −1.41933e11 −1.99432
\(259\) −2.31048e10 −0.319046
\(260\) −9.41441e10 −1.27765
\(261\) −3.73112e10 −0.497688
\(262\) 1.82131e11 2.38797
\(263\) 2.07653e10 0.267631 0.133816 0.991006i \(-0.457277\pi\)
0.133816 + 0.991006i \(0.457277\pi\)
\(264\) 2.41562e11 3.06063
\(265\) −9.08994e10 −1.13228
\(266\) −1.20146e10 −0.147144
\(267\) 4.48258e10 0.539793
\(268\) 5.95055e10 0.704613
\(269\) −1.57983e11 −1.83961 −0.919805 0.392375i \(-0.871654\pi\)
−0.919805 + 0.392375i \(0.871654\pi\)
\(270\) 2.31889e10 0.265548
\(271\) −7.82662e10 −0.881480 −0.440740 0.897635i \(-0.645284\pi\)
−0.440740 + 0.897635i \(0.645284\pi\)
\(272\) 2.03180e11 2.25072
\(273\) 1.85628e10 0.202261
\(274\) 1.78857e11 1.91703
\(275\) 7.25245e10 0.764693
\(276\) 2.36702e11 2.45534
\(277\) 1.45137e11 1.48122 0.740611 0.671934i \(-0.234536\pi\)
0.740611 + 0.671934i \(0.234536\pi\)
\(278\) −2.38706e11 −2.39696
\(279\) 9.48196e9 0.0936870
\(280\) 1.35193e11 1.31445
\(281\) −9.06795e10 −0.867622 −0.433811 0.901004i \(-0.642831\pi\)
−0.433811 + 0.901004i \(0.642831\pi\)
\(282\) −6.27059e10 −0.590456
\(283\) 6.43589e10 0.596444 0.298222 0.954497i \(-0.403607\pi\)
0.298222 + 0.954497i \(0.403607\pi\)
\(284\) 4.08256e11 3.72392
\(285\) −6.42763e9 −0.0577097
\(286\) 2.20583e11 1.94951
\(287\) −1.06309e11 −0.924914
\(288\) −1.60127e11 −1.37151
\(289\) −7.88169e10 −0.664629
\(290\) −2.48138e11 −2.06017
\(291\) −3.57097e10 −0.291922
\(292\) −6.54041e11 −5.26480
\(293\) −2.18801e11 −1.73438 −0.867190 0.497977i \(-0.834076\pi\)
−0.867190 + 0.497977i \(0.834076\pi\)
\(294\) 1.01790e11 0.794585
\(295\) −1.20402e10 −0.0925627
\(296\) 2.67842e11 2.02799
\(297\) −3.99067e10 −0.297606
\(298\) −5.39736e9 −0.0396468
\(299\) 1.38013e11 0.998616
\(300\) −1.10805e11 −0.789797
\(301\) 1.36703e11 0.959904
\(302\) −4.20902e11 −2.91172
\(303\) −1.03348e9 −0.00704386
\(304\) 8.13648e10 0.546393
\(305\) 3.43071e10 0.227005
\(306\) −5.74580e10 −0.374631
\(307\) −2.89373e10 −0.185924 −0.0929618 0.995670i \(-0.529633\pi\)
−0.0929618 + 0.995670i \(0.529633\pi\)
\(308\) −3.64375e11 −2.30712
\(309\) −2.58509e10 −0.161310
\(310\) 6.30598e10 0.387815
\(311\) −7.72235e10 −0.468088 −0.234044 0.972226i \(-0.575196\pi\)
−0.234044 + 0.972226i \(0.575196\pi\)
\(312\) −2.15189e11 −1.28566
\(313\) 1.62389e11 0.956330 0.478165 0.878270i \(-0.341302\pi\)
0.478165 + 0.878270i \(0.341302\pi\)
\(314\) −2.73892e11 −1.59000
\(315\) −2.23343e10 −0.127813
\(316\) −4.71576e9 −0.0266048
\(317\) −3.15230e10 −0.175332 −0.0876660 0.996150i \(-0.527941\pi\)
−0.0876660 + 0.996150i \(0.527941\pi\)
\(318\) −3.25399e11 −1.78441
\(319\) 4.27032e11 2.30888
\(320\) −5.46610e11 −2.91409
\(321\) −1.47954e11 −0.777775
\(322\) −3.10390e11 −1.60900
\(323\) 1.59266e10 0.0814162
\(324\) 6.09709e10 0.307376
\(325\) −6.46066e10 −0.321220
\(326\) 5.26662e11 2.58257
\(327\) −1.14612e11 −0.554328
\(328\) 1.23239e12 5.87915
\(329\) 6.03950e10 0.284197
\(330\) −2.65399e11 −1.23193
\(331\) 1.25675e11 0.575468 0.287734 0.957710i \(-0.407098\pi\)
0.287734 + 0.957710i \(0.407098\pi\)
\(332\) 7.04700e11 3.18334
\(333\) −4.42483e10 −0.197196
\(334\) 5.27203e10 0.231803
\(335\) −4.17447e10 −0.181092
\(336\) 2.82721e11 1.21013
\(337\) 7.04245e9 0.0297433 0.0148717 0.999889i \(-0.495266\pi\)
0.0148717 + 0.999889i \(0.495266\pi\)
\(338\) 2.69179e11 1.12180
\(339\) −7.65569e10 −0.314837
\(340\) −2.80668e11 −1.13904
\(341\) −1.08522e11 −0.434635
\(342\) −2.30094e10 −0.0909471
\(343\) −2.36286e11 −0.921752
\(344\) −1.58473e12 −6.10156
\(345\) −1.66053e11 −0.631047
\(346\) 3.27269e10 0.122762
\(347\) 6.16137e10 0.228136 0.114068 0.993473i \(-0.463612\pi\)
0.114068 + 0.993473i \(0.463612\pi\)
\(348\) −6.52434e11 −2.38468
\(349\) −3.69141e11 −1.33192 −0.665960 0.745988i \(-0.731978\pi\)
−0.665960 + 0.745988i \(0.731978\pi\)
\(350\) 1.45300e11 0.517558
\(351\) 3.55499e10 0.125013
\(352\) 1.83268e12 6.36274
\(353\) −8.47433e10 −0.290482 −0.145241 0.989396i \(-0.546396\pi\)
−0.145241 + 0.989396i \(0.546396\pi\)
\(354\) −4.31013e10 −0.145873
\(355\) −2.86403e11 −0.957084
\(356\) 7.83836e11 2.58643
\(357\) 5.53405e10 0.180317
\(358\) 3.14808e11 1.01291
\(359\) −4.96385e11 −1.57722 −0.788612 0.614891i \(-0.789200\pi\)
−0.788612 + 0.614891i \(0.789200\pi\)
\(360\) 2.58910e11 0.812434
\(361\) −3.16310e11 −0.980235
\(362\) −5.15119e10 −0.157659
\(363\) 2.65744e11 0.803311
\(364\) 3.24594e11 0.969136
\(365\) 4.58827e11 1.35311
\(366\) 1.22812e11 0.357746
\(367\) 3.02132e10 0.0869359 0.0434680 0.999055i \(-0.486159\pi\)
0.0434680 + 0.999055i \(0.486159\pi\)
\(368\) 2.10200e12 5.97472
\(369\) −2.03594e11 −0.571671
\(370\) −2.94273e11 −0.816288
\(371\) 3.13407e11 0.858868
\(372\) 1.65804e11 0.448903
\(373\) −9.04302e10 −0.241893 −0.120947 0.992659i \(-0.538593\pi\)
−0.120947 + 0.992659i \(0.538593\pi\)
\(374\) 6.57614e11 1.73800
\(375\) 2.34929e11 0.613474
\(376\) −7.00130e11 −1.80648
\(377\) −3.80411e11 −0.969878
\(378\) −7.99516e10 −0.201425
\(379\) −2.02163e11 −0.503299 −0.251650 0.967818i \(-0.580973\pi\)
−0.251650 + 0.967818i \(0.580973\pi\)
\(380\) −1.12395e11 −0.276517
\(381\) 1.50734e11 0.366478
\(382\) −1.82488e11 −0.438479
\(383\) −6.62686e10 −0.157367 −0.0786835 0.996900i \(-0.525072\pi\)
−0.0786835 + 0.996900i \(0.525072\pi\)
\(384\) −9.44577e11 −2.21690
\(385\) 2.55619e11 0.592952
\(386\) 1.14696e12 2.62969
\(387\) 2.61801e11 0.593298
\(388\) −6.24429e11 −1.39875
\(389\) 7.03704e11 1.55818 0.779088 0.626914i \(-0.215682\pi\)
0.779088 + 0.626914i \(0.215682\pi\)
\(390\) 2.36425e11 0.517490
\(391\) 4.11451e11 0.890273
\(392\) 1.13651e12 2.43101
\(393\) −3.35948e11 −0.710405
\(394\) 1.28473e12 2.68584
\(395\) 3.30824e9 0.00683770
\(396\) −6.97820e11 −1.42598
\(397\) −5.59407e11 −1.13024 −0.565120 0.825009i \(-0.691170\pi\)
−0.565120 + 0.825009i \(0.691170\pi\)
\(398\) 7.90518e11 1.57920
\(399\) 2.21615e10 0.0437745
\(400\) −9.83991e11 −1.92186
\(401\) 4.71707e11 0.911010 0.455505 0.890233i \(-0.349459\pi\)
0.455505 + 0.890233i \(0.349459\pi\)
\(402\) −1.49437e11 −0.285391
\(403\) 9.66745e10 0.182574
\(404\) −1.80717e10 −0.0337508
\(405\) −4.27727e10 −0.0789986
\(406\) 8.55542e11 1.56270
\(407\) 5.06428e11 0.914835
\(408\) −6.41535e11 −1.14617
\(409\) −8.77400e11 −1.55040 −0.775198 0.631718i \(-0.782350\pi\)
−0.775198 + 0.631718i \(0.782350\pi\)
\(410\) −1.35400e12 −2.36642
\(411\) −3.29909e11 −0.570303
\(412\) −4.52035e11 −0.772921
\(413\) 4.15129e10 0.0702114
\(414\) −5.94433e11 −0.994492
\(415\) −4.94366e11 −0.818149
\(416\) −1.63260e12 −2.67275
\(417\) 4.40302e11 0.713081
\(418\) 2.63346e11 0.421924
\(419\) −2.19302e11 −0.347599 −0.173800 0.984781i \(-0.555604\pi\)
−0.173800 + 0.984781i \(0.555604\pi\)
\(420\) −3.90543e11 −0.612417
\(421\) 5.11479e11 0.793521 0.396761 0.917922i \(-0.370134\pi\)
0.396761 + 0.917922i \(0.370134\pi\)
\(422\) 8.68508e11 1.33311
\(423\) 1.15664e11 0.175657
\(424\) −3.63317e12 −5.45933
\(425\) −1.92609e11 −0.286369
\(426\) −1.02526e12 −1.50831
\(427\) −1.18286e11 −0.172189
\(428\) −2.58716e12 −3.72672
\(429\) −4.06874e11 −0.579965
\(430\) 1.74111e12 2.45594
\(431\) 8.61585e11 1.20268 0.601340 0.798993i \(-0.294634\pi\)
0.601340 + 0.798993i \(0.294634\pi\)
\(432\) 5.41443e11 0.747956
\(433\) −9.73320e11 −1.33064 −0.665319 0.746559i \(-0.731705\pi\)
−0.665319 + 0.746559i \(0.731705\pi\)
\(434\) −2.17420e11 −0.294169
\(435\) 4.57701e11 0.612886
\(436\) −2.00415e12 −2.65607
\(437\) 1.64769e11 0.216126
\(438\) 1.64250e12 2.13241
\(439\) 4.35557e11 0.559699 0.279849 0.960044i \(-0.409715\pi\)
0.279849 + 0.960044i \(0.409715\pi\)
\(440\) −2.96326e12 −3.76906
\(441\) −1.87755e11 −0.236384
\(442\) −5.85820e11 −0.730069
\(443\) −6.79092e11 −0.837745 −0.418873 0.908045i \(-0.637575\pi\)
−0.418873 + 0.908045i \(0.637575\pi\)
\(444\) −7.73738e11 −0.944867
\(445\) −5.49882e11 −0.664737
\(446\) 2.50405e12 2.99665
\(447\) 9.95563e9 0.0117946
\(448\) 1.88463e12 2.21042
\(449\) −7.23578e11 −0.840188 −0.420094 0.907481i \(-0.638003\pi\)
−0.420094 + 0.907481i \(0.638003\pi\)
\(450\) 2.78266e11 0.319893
\(451\) 2.33016e12 2.65211
\(452\) −1.33870e12 −1.50855
\(453\) 7.76370e11 0.866217
\(454\) −6.64119e11 −0.733660
\(455\) −2.27712e11 −0.249077
\(456\) −2.56907e11 −0.278249
\(457\) 6.67676e10 0.0716049 0.0358025 0.999359i \(-0.488601\pi\)
0.0358025 + 0.999359i \(0.488601\pi\)
\(458\) 7.49119e11 0.795530
\(459\) 1.05983e11 0.111450
\(460\) −2.90365e12 −3.02367
\(461\) 1.20243e12 1.23995 0.619975 0.784622i \(-0.287143\pi\)
0.619975 + 0.784622i \(0.287143\pi\)
\(462\) 9.15057e11 0.934457
\(463\) −2.35427e11 −0.238090 −0.119045 0.992889i \(-0.537983\pi\)
−0.119045 + 0.992889i \(0.537983\pi\)
\(464\) −5.79385e12 −5.80278
\(465\) −1.16316e11 −0.115372
\(466\) 7.45996e11 0.732824
\(467\) 1.35968e12 1.32285 0.661424 0.750012i \(-0.269952\pi\)
0.661424 + 0.750012i \(0.269952\pi\)
\(468\) 6.21636e11 0.599004
\(469\) 1.43929e11 0.137364
\(470\) 7.69220e11 0.727127
\(471\) 5.05204e11 0.473013
\(472\) −4.81238e11 −0.446294
\(473\) −2.99635e12 −2.75244
\(474\) 1.18427e10 0.0107758
\(475\) −7.71316e10 −0.0695202
\(476\) 9.67699e11 0.863990
\(477\) 6.00211e11 0.530849
\(478\) −2.85675e12 −2.50292
\(479\) −1.19605e12 −1.03811 −0.519053 0.854742i \(-0.673715\pi\)
−0.519053 + 0.854742i \(0.673715\pi\)
\(480\) 1.96430e12 1.68897
\(481\) −4.51139e11 −0.384289
\(482\) 8.68238e11 0.732702
\(483\) 5.72526e11 0.478667
\(484\) 4.64687e12 3.84908
\(485\) 4.38054e11 0.359492
\(486\) −1.53117e11 −0.124497
\(487\) 4.71067e11 0.379492 0.189746 0.981833i \(-0.439234\pi\)
0.189746 + 0.981833i \(0.439234\pi\)
\(488\) 1.37123e12 1.09451
\(489\) −9.71449e11 −0.768299
\(490\) −1.24866e12 −0.978505
\(491\) −1.37541e12 −1.06798 −0.533991 0.845490i \(-0.679308\pi\)
−0.533991 + 0.845490i \(0.679308\pi\)
\(492\) −3.56010e12 −2.73917
\(493\) −1.13410e12 −0.864652
\(494\) −2.34596e11 −0.177235
\(495\) 4.89540e11 0.366492
\(496\) 1.47240e12 1.09234
\(497\) 9.87474e11 0.725975
\(498\) −1.76972e12 −1.28935
\(499\) −1.67648e12 −1.21044 −0.605222 0.796057i \(-0.706916\pi\)
−0.605222 + 0.796057i \(0.706916\pi\)
\(500\) 4.10804e12 2.93947
\(501\) −9.72447e10 −0.0689598
\(502\) 2.36372e12 1.66123
\(503\) 8.76570e11 0.610563 0.305282 0.952262i \(-0.401249\pi\)
0.305282 + 0.952262i \(0.401249\pi\)
\(504\) −8.92682e11 −0.616254
\(505\) 1.26778e10 0.00867428
\(506\) 6.80336e12 4.61367
\(507\) −4.96511e11 −0.333728
\(508\) 2.63577e12 1.75598
\(509\) −1.40681e12 −0.928976 −0.464488 0.885579i \(-0.653762\pi\)
−0.464488 + 0.885579i \(0.653762\pi\)
\(510\) 7.04843e11 0.461346
\(511\) −1.58197e12 −1.02637
\(512\) −4.14860e12 −2.66801
\(513\) 4.24418e10 0.0270561
\(514\) 5.14091e12 3.24868
\(515\) 3.17115e11 0.198648
\(516\) 4.57793e12 2.84280
\(517\) −1.32378e12 −0.814910
\(518\) 1.01461e12 0.619177
\(519\) −6.03661e10 −0.0365208
\(520\) 2.63975e12 1.58324
\(521\) 2.24585e12 1.33540 0.667700 0.744430i \(-0.267279\pi\)
0.667700 + 0.744430i \(0.267279\pi\)
\(522\) 1.63846e12 0.965872
\(523\) −2.36065e12 −1.37967 −0.689833 0.723969i \(-0.742316\pi\)
−0.689833 + 0.723969i \(0.742316\pi\)
\(524\) −5.87448e12 −3.40391
\(525\) −2.68011e11 −0.153970
\(526\) −9.11875e11 −0.519397
\(527\) 2.88212e11 0.162766
\(528\) −6.19689e12 −3.46993
\(529\) 2.45552e12 1.36331
\(530\) 3.99170e12 2.19744
\(531\) 7.95020e10 0.0433963
\(532\) 3.87522e11 0.209746
\(533\) −2.07577e12 −1.11405
\(534\) −1.96845e12 −1.04759
\(535\) 1.81497e12 0.957804
\(536\) −1.66850e12 −0.873143
\(537\) −5.80675e11 −0.301335
\(538\) 6.93759e12 3.57016
\(539\) 2.14888e12 1.09664
\(540\) −7.47936e11 −0.378523
\(541\) −1.15338e12 −0.578874 −0.289437 0.957197i \(-0.593468\pi\)
−0.289437 + 0.957197i \(0.593468\pi\)
\(542\) 3.43694e12 1.71070
\(543\) 9.50157e10 0.0469025
\(544\) −4.86719e12 −2.38278
\(545\) 1.40596e12 0.682637
\(546\) −8.15156e11 −0.392531
\(547\) −2.92047e12 −1.39479 −0.697397 0.716685i \(-0.745659\pi\)
−0.697397 + 0.716685i \(0.745659\pi\)
\(548\) −5.76887e12 −2.73262
\(549\) −2.26531e11 −0.106427
\(550\) −3.18480e12 −1.48405
\(551\) −4.54159e11 −0.209907
\(552\) −6.63701e12 −3.04261
\(553\) −1.14063e10 −0.00518659
\(554\) −6.37348e12 −2.87463
\(555\) 5.42799e11 0.242840
\(556\) 7.69925e12 3.41674
\(557\) 4.06498e11 0.178941 0.0894706 0.995989i \(-0.471482\pi\)
0.0894706 + 0.995989i \(0.471482\pi\)
\(558\) −4.16385e11 −0.181820
\(559\) 2.66923e12 1.15620
\(560\) −3.46816e12 −1.49023
\(561\) −1.21299e12 −0.517042
\(562\) 3.98205e12 1.68381
\(563\) −3.37014e12 −1.41371 −0.706854 0.707359i \(-0.749886\pi\)
−0.706854 + 0.707359i \(0.749886\pi\)
\(564\) 2.02252e12 0.841662
\(565\) 9.39131e11 0.387711
\(566\) −2.82622e12 −1.15753
\(567\) 1.47474e11 0.0599227
\(568\) −1.14473e13 −4.61461
\(569\) 3.49409e12 1.39742 0.698712 0.715403i \(-0.253757\pi\)
0.698712 + 0.715403i \(0.253757\pi\)
\(570\) 2.82259e11 0.111998
\(571\) 4.63108e12 1.82314 0.911569 0.411147i \(-0.134872\pi\)
0.911569 + 0.411147i \(0.134872\pi\)
\(572\) −7.11470e12 −2.77891
\(573\) 3.36606e11 0.130444
\(574\) 4.66839e12 1.79500
\(575\) −1.99264e12 −0.760193
\(576\) 3.60928e12 1.36622
\(577\) −4.42077e12 −1.66038 −0.830188 0.557483i \(-0.811767\pi\)
−0.830188 + 0.557483i \(0.811767\pi\)
\(578\) 3.46112e12 1.28986
\(579\) −2.11561e12 −0.782316
\(580\) 8.00348e12 2.93665
\(581\) 1.70450e12 0.620589
\(582\) 1.56813e12 0.566539
\(583\) −6.86950e12 −2.46273
\(584\) 1.83390e13 6.52404
\(585\) −4.36095e11 −0.153950
\(586\) 9.60828e12 3.36594
\(587\) 3.53913e12 1.23034 0.615170 0.788394i \(-0.289087\pi\)
0.615170 + 0.788394i \(0.289087\pi\)
\(588\) −3.28313e12 −1.13264
\(589\) 1.15416e11 0.0395138
\(590\) 5.28728e11 0.179638
\(591\) −2.36974e12 −0.799020
\(592\) −6.87107e12 −2.29920
\(593\) 4.75888e12 1.58037 0.790185 0.612868i \(-0.209984\pi\)
0.790185 + 0.612868i \(0.209984\pi\)
\(594\) 1.75244e12 0.577569
\(595\) −6.78867e11 −0.222054
\(596\) 1.74087e11 0.0565142
\(597\) −1.45814e12 −0.469802
\(598\) −6.06061e12 −1.93803
\(599\) −3.24559e12 −1.03009 −0.515043 0.857164i \(-0.672224\pi\)
−0.515043 + 0.857164i \(0.672224\pi\)
\(600\) 3.10692e12 0.978701
\(601\) −3.78568e12 −1.18361 −0.591805 0.806081i \(-0.701585\pi\)
−0.591805 + 0.806081i \(0.701585\pi\)
\(602\) −6.00308e12 −1.86290
\(603\) 2.75642e11 0.0849018
\(604\) 1.35758e13 4.15049
\(605\) −3.25991e12 −0.989250
\(606\) 4.53837e10 0.0136701
\(607\) 4.14733e12 1.23999 0.619997 0.784604i \(-0.287134\pi\)
0.619997 + 0.784604i \(0.287134\pi\)
\(608\) −1.94910e12 −0.578453
\(609\) −1.57808e12 −0.464891
\(610\) −1.50654e12 −0.440552
\(611\) 1.17926e12 0.342314
\(612\) 1.85326e12 0.534016
\(613\) 6.39011e12 1.82783 0.913916 0.405904i \(-0.133043\pi\)
0.913916 + 0.405904i \(0.133043\pi\)
\(614\) 1.27073e12 0.360825
\(615\) 2.49751e12 0.703994
\(616\) 1.02169e13 2.85894
\(617\) 5.61739e12 1.56045 0.780227 0.625496i \(-0.215103\pi\)
0.780227 + 0.625496i \(0.215103\pi\)
\(618\) 1.13520e12 0.313058
\(619\) −1.48141e12 −0.405573 −0.202786 0.979223i \(-0.565000\pi\)
−0.202786 + 0.979223i \(0.565000\pi\)
\(620\) −2.03394e12 −0.552809
\(621\) 1.09645e12 0.295855
\(622\) 3.39115e12 0.908427
\(623\) 1.89591e12 0.504222
\(624\) 5.52035e12 1.45759
\(625\) −9.95545e11 −0.260976
\(626\) −7.13107e12 −1.85597
\(627\) −4.85752e11 −0.125519
\(628\) 8.83414e12 2.26645
\(629\) −1.34496e12 −0.342596
\(630\) 9.80774e11 0.248048
\(631\) 2.81353e12 0.706511 0.353256 0.935527i \(-0.385075\pi\)
0.353256 + 0.935527i \(0.385075\pi\)
\(632\) 1.32228e11 0.0329682
\(633\) −1.60200e12 −0.396593
\(634\) 1.38428e12 0.340270
\(635\) −1.84906e12 −0.451305
\(636\) 1.04955e13 2.54357
\(637\) −1.91428e12 −0.460657
\(638\) −1.87524e13 −4.48089
\(639\) 1.89113e12 0.448711
\(640\) 1.15872e13 2.73004
\(641\) 2.06430e12 0.482961 0.241481 0.970406i \(-0.422367\pi\)
0.241481 + 0.970406i \(0.422367\pi\)
\(642\) 6.49717e12 1.50944
\(643\) 3.21655e12 0.742063 0.371031 0.928620i \(-0.379004\pi\)
0.371031 + 0.928620i \(0.379004\pi\)
\(644\) 1.00113e13 2.29354
\(645\) −3.21155e12 −0.730626
\(646\) −6.99390e11 −0.158006
\(647\) 1.60571e12 0.360245 0.180122 0.983644i \(-0.442351\pi\)
0.180122 + 0.983644i \(0.442351\pi\)
\(648\) −1.70959e12 −0.380894
\(649\) −9.09911e11 −0.201325
\(650\) 2.83710e12 0.623396
\(651\) 4.01040e11 0.0875132
\(652\) −1.69870e13 −3.68131
\(653\) 5.16633e12 1.11192 0.555959 0.831210i \(-0.312351\pi\)
0.555959 + 0.831210i \(0.312351\pi\)
\(654\) 5.03303e12 1.07579
\(655\) 4.12111e12 0.874839
\(656\) −3.16150e13 −6.66539
\(657\) −3.02965e12 −0.634378
\(658\) −2.65215e12 −0.551546
\(659\) 7.28418e12 1.50451 0.752257 0.658870i \(-0.228965\pi\)
0.752257 + 0.658870i \(0.228965\pi\)
\(660\) 8.56022e12 1.75605
\(661\) 2.45718e12 0.500645 0.250323 0.968162i \(-0.419463\pi\)
0.250323 + 0.968162i \(0.419463\pi\)
\(662\) −5.51880e12 −1.11682
\(663\) 1.08057e12 0.217191
\(664\) −1.97594e13 −3.94473
\(665\) −2.71857e11 −0.0539068
\(666\) 1.94310e12 0.382701
\(667\) −1.17329e13 −2.29530
\(668\) −1.70045e12 −0.330422
\(669\) −4.61882e12 −0.891484
\(670\) 1.83315e12 0.351449
\(671\) 2.59268e12 0.493738
\(672\) −6.77260e12 −1.28113
\(673\) −4.76030e12 −0.894471 −0.447236 0.894416i \(-0.647591\pi\)
−0.447236 + 0.894416i \(0.647591\pi\)
\(674\) −3.09258e11 −0.0577233
\(675\) −5.13273e11 −0.0951660
\(676\) −8.68213e12 −1.59906
\(677\) 1.06786e12 0.195373 0.0976865 0.995217i \(-0.468856\pi\)
0.0976865 + 0.995217i \(0.468856\pi\)
\(678\) 3.36188e12 0.611010
\(679\) −1.51034e12 −0.272685
\(680\) 7.86977e12 1.41147
\(681\) 1.22499e12 0.218259
\(682\) 4.76559e12 0.843503
\(683\) −7.12649e12 −1.25309 −0.626545 0.779385i \(-0.715532\pi\)
−0.626545 + 0.779385i \(0.715532\pi\)
\(684\) 7.42149e11 0.129640
\(685\) 4.04702e12 0.702309
\(686\) 1.03761e13 1.78886
\(687\) −1.38178e12 −0.236665
\(688\) 4.06537e13 6.91754
\(689\) 6.11952e12 1.03450
\(690\) 7.29196e12 1.22468
\(691\) 1.91579e12 0.319666 0.159833 0.987144i \(-0.448904\pi\)
0.159833 + 0.987144i \(0.448904\pi\)
\(692\) −1.05558e12 −0.174990
\(693\) −1.68786e12 −0.277995
\(694\) −2.70567e12 −0.442748
\(695\) −5.40123e12 −0.878135
\(696\) 1.82939e13 2.95505
\(697\) −6.18840e12 −0.993186
\(698\) 1.62102e13 2.58488
\(699\) −1.37602e12 −0.218010
\(700\) −4.68652e12 −0.737750
\(701\) −9.03925e12 −1.41384 −0.706922 0.707292i \(-0.749917\pi\)
−0.706922 + 0.707292i \(0.749917\pi\)
\(702\) −1.56112e12 −0.242616
\(703\) −5.38599e11 −0.0831700
\(704\) −4.13087e13 −6.33818
\(705\) −1.41886e12 −0.216315
\(706\) 3.72137e12 0.563743
\(707\) −4.37112e10 −0.00657969
\(708\) 1.39019e12 0.207934
\(709\) 1.12846e13 1.67717 0.838586 0.544769i \(-0.183383\pi\)
0.838586 + 0.544769i \(0.183383\pi\)
\(710\) 1.25769e13 1.85743
\(711\) −2.18444e10 −0.00320573
\(712\) −2.19783e13 −3.20505
\(713\) 2.98170e12 0.432077
\(714\) −2.43019e12 −0.349944
\(715\) 4.99116e12 0.714207
\(716\) −1.01538e13 −1.44385
\(717\) 5.26939e12 0.744603
\(718\) 2.17980e13 3.06095
\(719\) 2.15065e12 0.300116 0.150058 0.988677i \(-0.452054\pi\)
0.150058 + 0.988677i \(0.452054\pi\)
\(720\) −6.64194e12 −0.921082
\(721\) −1.09336e12 −0.150680
\(722\) 1.38902e13 1.90236
\(723\) −1.60150e12 −0.217974
\(724\) 1.66147e12 0.224734
\(725\) 5.49241e12 0.738316
\(726\) −1.16697e13 −1.55900
\(727\) −3.66096e12 −0.486061 −0.243030 0.970019i \(-0.578141\pi\)
−0.243030 + 0.970019i \(0.578141\pi\)
\(728\) −9.10145e12 −1.20093
\(729\) 2.82430e11 0.0370370
\(730\) −2.01487e13 −2.62599
\(731\) 7.95766e12 1.03076
\(732\) −3.96118e12 −0.509947
\(733\) −8.51645e12 −1.08966 −0.544829 0.838547i \(-0.683406\pi\)
−0.544829 + 0.838547i \(0.683406\pi\)
\(734\) −1.32676e12 −0.168718
\(735\) 2.30321e12 0.291099
\(736\) −5.03536e13 −6.32529
\(737\) −3.15475e12 −0.393878
\(738\) 8.94051e12 1.10945
\(739\) −1.04799e13 −1.29258 −0.646291 0.763091i \(-0.723681\pi\)
−0.646291 + 0.763091i \(0.723681\pi\)
\(740\) 9.49153e12 1.16357
\(741\) 4.32721e11 0.0527261
\(742\) −1.37628e13 −1.66682
\(743\) −9.83152e12 −1.18351 −0.591754 0.806119i \(-0.701564\pi\)
−0.591754 + 0.806119i \(0.701564\pi\)
\(744\) −4.64906e12 −0.556272
\(745\) −1.22127e11 −0.0145247
\(746\) 3.97110e12 0.469446
\(747\) 3.26431e12 0.383574
\(748\) −2.12108e13 −2.47742
\(749\) −6.25773e12 −0.726521
\(750\) −1.03165e13 −1.19058
\(751\) 8.73479e12 1.00201 0.501006 0.865444i \(-0.332964\pi\)
0.501006 + 0.865444i \(0.332964\pi\)
\(752\) 1.79607e13 2.04807
\(753\) −4.35997e12 −0.494204
\(754\) 1.67051e13 1.88226
\(755\) −9.52381e12 −1.06672
\(756\) 2.57877e12 0.287120
\(757\) 8.83748e12 0.978130 0.489065 0.872247i \(-0.337338\pi\)
0.489065 + 0.872247i \(0.337338\pi\)
\(758\) 8.87769e12 0.976761
\(759\) −1.25491e13 −1.37253
\(760\) 3.15150e12 0.342655
\(761\) −1.34581e13 −1.45463 −0.727314 0.686305i \(-0.759232\pi\)
−0.727314 + 0.686305i \(0.759232\pi\)
\(762\) −6.61923e12 −0.711230
\(763\) −4.84754e12 −0.517799
\(764\) 5.88598e12 0.625027
\(765\) −1.30011e12 −0.137247
\(766\) 2.91008e12 0.305405
\(767\) 8.10572e11 0.0845693
\(768\) 1.86654e13 1.93603
\(769\) 2.86965e12 0.295911 0.147955 0.988994i \(-0.452731\pi\)
0.147955 + 0.988994i \(0.452731\pi\)
\(770\) −1.12251e13 −1.15075
\(771\) −9.48262e12 −0.966459
\(772\) −3.69942e13 −3.74848
\(773\) 1.77419e13 1.78728 0.893640 0.448786i \(-0.148143\pi\)
0.893640 + 0.448786i \(0.148143\pi\)
\(774\) −1.14966e13 −1.15142
\(775\) −1.39580e12 −0.138984
\(776\) 1.75087e13 1.73330
\(777\) −1.87149e12 −0.184201
\(778\) −3.09020e13 −3.02398
\(779\) −2.47819e12 −0.241110
\(780\) −7.62567e12 −0.737653
\(781\) −2.16442e13 −2.08167
\(782\) −1.80682e13 −1.72777
\(783\) −3.02221e12 −0.287340
\(784\) −2.91554e13 −2.75611
\(785\) −6.19739e12 −0.582500
\(786\) 1.47526e13 1.37869
\(787\) −1.14046e13 −1.05973 −0.529864 0.848082i \(-0.677757\pi\)
−0.529864 + 0.848082i \(0.677757\pi\)
\(788\) −4.14380e13 −3.82852
\(789\) 1.68199e12 0.154517
\(790\) −1.45276e11 −0.0132700
\(791\) −3.23798e12 −0.294090
\(792\) 1.95665e13 1.76705
\(793\) −2.30962e12 −0.207401
\(794\) 2.45655e13 2.19348
\(795\) −7.36285e12 −0.653723
\(796\) −2.54975e13 −2.25106
\(797\) 1.37607e13 1.20803 0.604015 0.796973i \(-0.293567\pi\)
0.604015 + 0.796973i \(0.293567\pi\)
\(798\) −9.73186e11 −0.0849538
\(799\) 3.51568e12 0.305175
\(800\) 2.35716e13 2.03462
\(801\) 3.63089e12 0.311650
\(802\) −2.07143e13 −1.76801
\(803\) 3.46747e13 2.94302
\(804\) 4.81994e12 0.406808
\(805\) −7.02323e12 −0.589462
\(806\) −4.24531e12 −0.354325
\(807\) −1.27966e13 −1.06210
\(808\) 5.06722e11 0.0418233
\(809\) −2.09569e13 −1.72012 −0.860061 0.510192i \(-0.829574\pi\)
−0.860061 + 0.510192i \(0.829574\pi\)
\(810\) 1.87830e12 0.153314
\(811\) 1.71895e13 1.39531 0.697654 0.716435i \(-0.254228\pi\)
0.697654 + 0.716435i \(0.254228\pi\)
\(812\) −2.75948e13 −2.22753
\(813\) −6.33957e12 −0.508923
\(814\) −2.22390e13 −1.77544
\(815\) 1.19169e13 0.946134
\(816\) 1.64576e13 1.29945
\(817\) 3.18670e12 0.250231
\(818\) 3.85296e13 3.00888
\(819\) 1.50359e12 0.116775
\(820\) 4.36721e13 3.37320
\(821\) 5.60147e11 0.0430286 0.0215143 0.999769i \(-0.493151\pi\)
0.0215143 + 0.999769i \(0.493151\pi\)
\(822\) 1.44874e13 1.10680
\(823\) −6.40278e12 −0.486485 −0.243243 0.969965i \(-0.578211\pi\)
−0.243243 + 0.969965i \(0.578211\pi\)
\(824\) 1.26748e13 0.957789
\(825\) 5.87448e12 0.441496
\(826\) −1.82297e12 −0.136260
\(827\) 1.23366e13 0.917110 0.458555 0.888666i \(-0.348367\pi\)
0.458555 + 0.888666i \(0.348367\pi\)
\(828\) 1.91729e13 1.41759
\(829\) −1.37312e13 −1.00975 −0.504873 0.863194i \(-0.668460\pi\)
−0.504873 + 0.863194i \(0.668460\pi\)
\(830\) 2.17093e13 1.58780
\(831\) 1.17561e13 0.855184
\(832\) 3.67989e13 2.66244
\(833\) −5.70695e12 −0.410678
\(834\) −1.93352e13 −1.38389
\(835\) 1.19291e12 0.0849217
\(836\) −8.49400e12 −0.601428
\(837\) 7.68039e11 0.0540902
\(838\) 9.63028e12 0.674592
\(839\) −9.04675e12 −0.630324 −0.315162 0.949038i \(-0.602059\pi\)
−0.315162 + 0.949038i \(0.602059\pi\)
\(840\) 1.09506e13 0.758896
\(841\) 1.78328e13 1.22924
\(842\) −2.24608e13 −1.54000
\(843\) −7.34504e12 −0.500922
\(844\) −2.80129e13 −1.90028
\(845\) 6.09075e12 0.410975
\(846\) −5.07918e12 −0.340900
\(847\) 1.12397e13 0.750374
\(848\) 9.32034e13 6.18943
\(849\) 5.21307e12 0.344357
\(850\) 8.45812e12 0.555762
\(851\) −1.39143e13 −0.909451
\(852\) 3.30688e13 2.15001
\(853\) −1.99730e13 −1.29174 −0.645868 0.763449i \(-0.723504\pi\)
−0.645868 + 0.763449i \(0.723504\pi\)
\(854\) 5.19433e12 0.334171
\(855\) −5.20638e11 −0.0333187
\(856\) 7.25427e13 4.61808
\(857\) −8.24335e12 −0.522023 −0.261012 0.965336i \(-0.584056\pi\)
−0.261012 + 0.965336i \(0.584056\pi\)
\(858\) 1.78672e13 1.12555
\(859\) 2.68595e12 0.168317 0.0841586 0.996452i \(-0.473180\pi\)
0.0841586 + 0.996452i \(0.473180\pi\)
\(860\) −5.61580e13 −3.50081
\(861\) −8.61103e12 −0.533999
\(862\) −3.78351e13 −2.33406
\(863\) −1.84104e13 −1.12984 −0.564918 0.825147i \(-0.691092\pi\)
−0.564918 + 0.825147i \(0.691092\pi\)
\(864\) −1.29703e13 −0.791842
\(865\) 7.40517e11 0.0449741
\(866\) 4.27418e13 2.58239
\(867\) −6.38417e12 −0.383724
\(868\) 7.01270e12 0.419321
\(869\) 2.50012e11 0.0148721
\(870\) −2.00992e13 −1.18944
\(871\) 2.81034e12 0.165454
\(872\) 5.61952e13 3.29136
\(873\) −2.89248e12 −0.168541
\(874\) −7.23555e12 −0.419440
\(875\) 9.93635e12 0.573047
\(876\) −5.29773e13 −3.03963
\(877\) 2.63357e13 1.50331 0.751653 0.659559i \(-0.229257\pi\)
0.751653 + 0.659559i \(0.229257\pi\)
\(878\) −1.91268e13 −1.08622
\(879\) −1.77229e13 −1.00134
\(880\) 7.60178e13 4.27310
\(881\) −2.53338e13 −1.41680 −0.708401 0.705810i \(-0.750583\pi\)
−0.708401 + 0.705810i \(0.750583\pi\)
\(882\) 8.24496e12 0.458754
\(883\) 3.23574e13 1.79122 0.895612 0.444837i \(-0.146738\pi\)
0.895612 + 0.444837i \(0.146738\pi\)
\(884\) 1.88951e13 1.04067
\(885\) −9.75259e11 −0.0534411
\(886\) 2.98213e13 1.62583
\(887\) 9.07362e12 0.492180 0.246090 0.969247i \(-0.420854\pi\)
0.246090 + 0.969247i \(0.420854\pi\)
\(888\) 2.16952e13 1.17086
\(889\) 6.37529e12 0.342328
\(890\) 2.41472e13 1.29007
\(891\) −3.23244e12 −0.171823
\(892\) −8.07659e13 −4.27156
\(893\) 1.40788e12 0.0740856
\(894\) −4.37186e11 −0.0228901
\(895\) 7.12320e12 0.371083
\(896\) −3.99510e13 −2.07081
\(897\) 1.11790e13 0.576551
\(898\) 3.17748e13 1.63057
\(899\) −8.21860e12 −0.419642
\(900\) −8.97524e12 −0.455989
\(901\) 1.82439e13 0.922265
\(902\) −1.02325e14 −5.14700
\(903\) 1.10729e13 0.554201
\(904\) 3.75363e13 1.86936
\(905\) −1.16557e12 −0.0577589
\(906\) −3.40930e13 −1.68108
\(907\) −8.04078e12 −0.394517 −0.197258 0.980352i \(-0.563204\pi\)
−0.197258 + 0.980352i \(0.563204\pi\)
\(908\) 2.14206e13 1.04579
\(909\) −8.37120e10 −0.00406678
\(910\) 9.99960e12 0.483389
\(911\) 1.44263e13 0.693942 0.346971 0.937876i \(-0.387210\pi\)
0.346971 + 0.937876i \(0.387210\pi\)
\(912\) 6.59055e12 0.315460
\(913\) −3.73605e13 −1.77948
\(914\) −2.93199e12 −0.138965
\(915\) 2.77888e12 0.131061
\(916\) −2.41622e13 −1.13398
\(917\) −1.42090e13 −0.663590
\(918\) −4.65410e12 −0.216293
\(919\) −1.26368e13 −0.584408 −0.292204 0.956356i \(-0.594389\pi\)
−0.292204 + 0.956356i \(0.594389\pi\)
\(920\) 8.14169e13 3.74687
\(921\) −2.34392e12 −0.107343
\(922\) −5.28026e13 −2.40639
\(923\) 1.92812e13 0.874433
\(924\) −2.95143e13 −1.33202
\(925\) 6.51359e12 0.292538
\(926\) 1.03384e13 0.462066
\(927\) −2.09392e12 −0.0931325
\(928\) 1.38792e14 6.14326
\(929\) 3.76990e13 1.66058 0.830290 0.557332i \(-0.188175\pi\)
0.830290 + 0.557332i \(0.188175\pi\)
\(930\) 5.10784e12 0.223905
\(931\) −2.28539e12 −0.0996980
\(932\) −2.40614e13 −1.04460
\(933\) −6.25511e12 −0.270251
\(934\) −5.97081e13 −2.56727
\(935\) 1.48799e13 0.636720
\(936\) −1.74303e13 −0.742274
\(937\) −3.01281e13 −1.27686 −0.638430 0.769680i \(-0.720416\pi\)
−0.638430 + 0.769680i \(0.720416\pi\)
\(938\) −6.32043e12 −0.266584
\(939\) 1.31535e13 0.552138
\(940\) −2.48105e13 −1.03648
\(941\) −3.31424e12 −0.137794 −0.0688972 0.997624i \(-0.521948\pi\)
−0.0688972 + 0.997624i \(0.521948\pi\)
\(942\) −2.21853e13 −0.917984
\(943\) −6.40222e13 −2.63650
\(944\) 1.23454e13 0.505978
\(945\) −1.80908e12 −0.0737928
\(946\) 1.31580e14 5.34171
\(947\) 1.29122e13 0.521705 0.260853 0.965379i \(-0.415996\pi\)
0.260853 + 0.965379i \(0.415996\pi\)
\(948\) −3.81977e11 −0.0153603
\(949\) −3.08892e13 −1.23626
\(950\) 3.38711e12 0.134919
\(951\) −2.55336e12 −0.101228
\(952\) −2.71338e13 −1.07064
\(953\) −3.68198e13 −1.44598 −0.722992 0.690857i \(-0.757234\pi\)
−0.722992 + 0.690857i \(0.757234\pi\)
\(954\) −2.63573e13 −1.03023
\(955\) −4.12918e12 −0.160638
\(956\) 9.21421e13 3.56778
\(957\) 3.45896e13 1.33304
\(958\) 5.25229e13 2.01467
\(959\) −1.39535e13 −0.532721
\(960\) −4.42754e13 −1.68245
\(961\) −2.43510e13 −0.921005
\(962\) 1.98111e13 0.745796
\(963\) −1.19843e13 −0.449049
\(964\) −2.80042e13 −1.04442
\(965\) 2.59524e13 0.963396
\(966\) −2.51416e13 −0.928957
\(967\) 2.42967e13 0.893569 0.446784 0.894642i \(-0.352569\pi\)
0.446784 + 0.894642i \(0.352569\pi\)
\(968\) −1.30296e14 −4.76970
\(969\) 1.29005e12 0.0470056
\(970\) −1.92364e13 −0.697673
\(971\) 3.70876e13 1.33888 0.669442 0.742865i \(-0.266533\pi\)
0.669442 + 0.742865i \(0.266533\pi\)
\(972\) 4.93864e12 0.177464
\(973\) 1.86226e13 0.666090
\(974\) −2.06862e13 −0.736487
\(975\) −5.23314e12 −0.185456
\(976\) −3.51767e13 −1.24088
\(977\) −3.37506e13 −1.18510 −0.592551 0.805533i \(-0.701879\pi\)
−0.592551 + 0.805533i \(0.701879\pi\)
\(978\) 4.26596e13 1.49105
\(979\) −4.15560e13 −1.44581
\(980\) 4.02745e13 1.39480
\(981\) −9.28361e12 −0.320042
\(982\) 6.03987e13 2.07265
\(983\) 1.32805e13 0.453652 0.226826 0.973935i \(-0.427165\pi\)
0.226826 + 0.973935i \(0.427165\pi\)
\(984\) 9.98234e13 3.39433
\(985\) 2.90699e13 0.983966
\(986\) 4.98023e13 1.67805
\(987\) 4.89200e12 0.164081
\(988\) 7.56667e12 0.252638
\(989\) 8.23261e13 2.73624
\(990\) −2.14974e13 −0.711257
\(991\) −2.92040e12 −0.0961857 −0.0480928 0.998843i \(-0.515314\pi\)
−0.0480928 + 0.998843i \(0.515314\pi\)
\(992\) −3.52715e13 −1.15643
\(993\) 1.01796e13 0.332247
\(994\) −4.33633e13 −1.40891
\(995\) 1.78872e13 0.578546
\(996\) 5.70807e13 1.83790
\(997\) −6.86175e12 −0.219941 −0.109971 0.993935i \(-0.535076\pi\)
−0.109971 + 0.993935i \(0.535076\pi\)
\(998\) 7.36197e13 2.34913
\(999\) −3.58411e12 −0.113851
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 177.10.a.a.1.1 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.a.1.1 21 1.1 even 1 trivial