Properties

Label 177.10.a.c.1.16
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $0$
Dimension $22$
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: \(0\)
Dimension: \(22\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+25.6716 q^{2} -81.0000 q^{3} +147.031 q^{4} -2019.49 q^{5} -2079.40 q^{6} +7281.90 q^{7} -9369.35 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+25.6716 q^{2} -81.0000 q^{3} +147.031 q^{4} -2019.49 q^{5} -2079.40 q^{6} +7281.90 q^{7} -9369.35 q^{8} +6561.00 q^{9} -51843.5 q^{10} -86162.6 q^{11} -11909.5 q^{12} +121383. q^{13} +186938. q^{14} +163579. q^{15} -315806. q^{16} -273452. q^{17} +168431. q^{18} -1.10855e6 q^{19} -296927. q^{20} -589834. q^{21} -2.21193e6 q^{22} -128745. q^{23} +758917. q^{24} +2.12521e6 q^{25} +3.11610e6 q^{26} -531441. q^{27} +1.07066e6 q^{28} +954314. q^{29} +4.19932e6 q^{30} +1.83072e6 q^{31} -3.31013e6 q^{32} +6.97917e6 q^{33} -7.01996e6 q^{34} -1.47057e7 q^{35} +964667. q^{36} +5.14004e6 q^{37} -2.84581e7 q^{38} -9.83203e6 q^{39} +1.89213e7 q^{40} -1.62054e7 q^{41} -1.51420e7 q^{42} +49859.5 q^{43} -1.26685e7 q^{44} -1.32499e7 q^{45} -3.30509e6 q^{46} +5.78551e7 q^{47} +2.55803e7 q^{48} +1.26725e7 q^{49} +5.45576e7 q^{50} +2.21496e7 q^{51} +1.78470e7 q^{52} +1.08839e7 q^{53} -1.36429e7 q^{54} +1.74004e8 q^{55} -6.82267e7 q^{56} +8.97922e7 q^{57} +2.44988e7 q^{58} +1.21174e7 q^{59} +2.40511e7 q^{60} +1.48636e8 q^{61} +4.69976e7 q^{62} +4.77766e7 q^{63} +7.67163e7 q^{64} -2.45132e8 q^{65} +1.79166e8 q^{66} -2.17717e7 q^{67} -4.02059e7 q^{68} +1.04283e7 q^{69} -3.77519e8 q^{70} +1.65152e8 q^{71} -6.14723e7 q^{72} +2.22431e8 q^{73} +1.31953e8 q^{74} -1.72142e8 q^{75} -1.62990e8 q^{76} -6.27428e8 q^{77} -2.52404e8 q^{78} +4.50547e8 q^{79} +6.37766e8 q^{80} +4.30467e7 q^{81} -4.16018e8 q^{82} +1.85548e8 q^{83} -8.67236e7 q^{84} +5.52234e8 q^{85} +1.27997e6 q^{86} -7.72994e7 q^{87} +8.07287e8 q^{88} -6.59420e8 q^{89} -3.40145e8 q^{90} +8.83900e8 q^{91} -1.89294e7 q^{92} -1.48289e8 q^{93} +1.48523e9 q^{94} +2.23870e9 q^{95} +2.68120e8 q^{96} +1.23039e9 q^{97} +3.25324e8 q^{98} -5.65313e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + 68441q^{10} - 68033q^{11} - 463158q^{12} + 283817q^{13} + 80285q^{14} - 65448q^{15} + 1067674q^{16} + 436893q^{17} + 236196q^{18} + 1207580q^{19} + 4209677q^{20} - 1721169q^{21} + 5460442q^{22} + 2421966q^{23} - 764235q^{24} + 7441842q^{25} - 2736526q^{26} - 11691702q^{27} + 4095246q^{28} - 2320594q^{29} - 5543721q^{30} - 3178024q^{31} - 20786874q^{32} + 5510673q^{33} - 13809336q^{34} - 2630800q^{35} + 37515798q^{36} + 3981807q^{37} - 24156377q^{38} - 22989177q^{39} - 29544450q^{40} - 885225q^{41} - 6503085q^{42} + 12360835q^{43} - 117711882q^{44} + 5301288q^{45} + 161066949q^{46} + 75901252q^{47} - 86481594q^{48} + 170907951q^{49} - 61318927q^{50} - 35388333q^{51} - 100762q^{52} - 34790192q^{53} - 19131876q^{54} + 151773316q^{55} - 417630344q^{56} - 97813980q^{57} - 432929294q^{58} + 266581942q^{59} - 340983837q^{60} - 290555332q^{61} + 158267098q^{62} + 139414689q^{63} - 131794443q^{64} - 650690086q^{65} - 442295802q^{66} + 86645184q^{67} + 62738541q^{68} - 196179246q^{69} + 429714610q^{70} - 36567631q^{71} + 61903035q^{72} + 907807228q^{73} - 171827242q^{74} - 602789202q^{75} + 1744504396q^{76} - 310688725q^{77} + 221658606q^{78} + 2508604687q^{79} + 3509441927q^{80} + 947027862q^{81} + 1759214793q^{82} + 2185672083q^{83} - 331714926q^{84} + 2868860198q^{85} + 2397001564q^{86} + 187968114q^{87} + 7683735877q^{88} + 1320145942q^{89} + 449041401q^{90} + 3894639897q^{91} + 3505964640q^{92} + 257419944q^{93} + 5406355552q^{94} + 3093659122q^{95} + 1683736794q^{96} + 3904552980q^{97} + 6137683116q^{98} - 446364513q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 25.6716 1.13453 0.567267 0.823534i \(-0.308001\pi\)
0.567267 + 0.823534i \(0.308001\pi\)
\(3\) −81.0000 −0.577350
\(4\) 147.031 0.287169
\(5\) −2019.49 −1.44503 −0.722514 0.691356i \(-0.757014\pi\)
−0.722514 + 0.691356i \(0.757014\pi\)
\(6\) −2079.40 −0.655024
\(7\) 7281.90 1.14631 0.573157 0.819445i \(-0.305718\pi\)
0.573157 + 0.819445i \(0.305718\pi\)
\(8\) −9369.35 −0.808732
\(9\) 6561.00 0.333333
\(10\) −51843.5 −1.63944
\(11\) −86162.6 −1.77440 −0.887200 0.461385i \(-0.847353\pi\)
−0.887200 + 0.461385i \(0.847353\pi\)
\(12\) −11909.5 −0.165797
\(13\) 121383. 1.17873 0.589364 0.807868i \(-0.299379\pi\)
0.589364 + 0.807868i \(0.299379\pi\)
\(14\) 186938. 1.30053
\(15\) 163579. 0.834288
\(16\) −315806. −1.20470
\(17\) −273452. −0.794075 −0.397038 0.917802i \(-0.629962\pi\)
−0.397038 + 0.917802i \(0.629962\pi\)
\(18\) 168431. 0.378178
\(19\) −1.10855e6 −1.95147 −0.975736 0.218951i \(-0.929736\pi\)
−0.975736 + 0.218951i \(0.929736\pi\)
\(20\) −296927. −0.414967
\(21\) −589834. −0.661825
\(22\) −2.21193e6 −2.01312
\(23\) −128745. −0.0959301 −0.0479650 0.998849i \(-0.515274\pi\)
−0.0479650 + 0.998849i \(0.515274\pi\)
\(24\) 758917. 0.466921
\(25\) 2.12521e6 1.08811
\(26\) 3.11610e6 1.33731
\(27\) −531441. −0.192450
\(28\) 1.07066e6 0.329186
\(29\) 954314. 0.250553 0.125277 0.992122i \(-0.460018\pi\)
0.125277 + 0.992122i \(0.460018\pi\)
\(30\) 4.19932e6 0.946529
\(31\) 1.83072e6 0.356037 0.178019 0.984027i \(-0.443031\pi\)
0.178019 + 0.984027i \(0.443031\pi\)
\(32\) −3.31013e6 −0.558046
\(33\) 6.97917e6 1.02445
\(34\) −7.01996e6 −0.900906
\(35\) −1.47057e7 −1.65646
\(36\) 964667. 0.0957230
\(37\) 5.14004e6 0.450877 0.225439 0.974257i \(-0.427618\pi\)
0.225439 + 0.974257i \(0.427618\pi\)
\(38\) −2.84581e7 −2.21401
\(39\) −9.83203e6 −0.680538
\(40\) 1.89213e7 1.16864
\(41\) −1.62054e7 −0.895636 −0.447818 0.894125i \(-0.647799\pi\)
−0.447818 + 0.894125i \(0.647799\pi\)
\(42\) −1.51420e7 −0.750863
\(43\) 49859.5 0.00222403 0.00111201 0.999999i \(-0.499646\pi\)
0.00111201 + 0.999999i \(0.499646\pi\)
\(44\) −1.26685e7 −0.509553
\(45\) −1.32499e7 −0.481676
\(46\) −3.30509e6 −0.108836
\(47\) 5.78551e7 1.72942 0.864712 0.502268i \(-0.167501\pi\)
0.864712 + 0.502268i \(0.167501\pi\)
\(48\) 2.55803e7 0.695536
\(49\) 1.26725e7 0.314037
\(50\) 5.45576e7 1.23450
\(51\) 2.21496e7 0.458460
\(52\) 1.78470e7 0.338494
\(53\) 1.08839e7 0.189471 0.0947357 0.995502i \(-0.469799\pi\)
0.0947357 + 0.995502i \(0.469799\pi\)
\(54\) −1.36429e7 −0.218341
\(55\) 1.74004e8 2.56406
\(56\) −6.82267e7 −0.927061
\(57\) 8.97922e7 1.12668
\(58\) 2.44988e7 0.284261
\(59\) 1.21174e7 0.130189
\(60\) 2.40511e7 0.239582
\(61\) 1.48636e8 1.37448 0.687242 0.726429i \(-0.258821\pi\)
0.687242 + 0.726429i \(0.258821\pi\)
\(62\) 4.69976e7 0.403937
\(63\) 4.77766e7 0.382105
\(64\) 7.67163e7 0.571581
\(65\) −2.45132e8 −1.70329
\(66\) 1.79166e8 1.16227
\(67\) −2.17717e7 −0.131994 −0.0659972 0.997820i \(-0.521023\pi\)
−0.0659972 + 0.997820i \(0.521023\pi\)
\(68\) −4.02059e7 −0.228034
\(69\) 1.04283e7 0.0553853
\(70\) −3.77519e8 −1.87931
\(71\) 1.65152e8 0.771296 0.385648 0.922646i \(-0.373978\pi\)
0.385648 + 0.922646i \(0.373978\pi\)
\(72\) −6.14723e7 −0.269577
\(73\) 2.22431e8 0.916730 0.458365 0.888764i \(-0.348435\pi\)
0.458365 + 0.888764i \(0.348435\pi\)
\(74\) 1.31953e8 0.511536
\(75\) −1.72142e8 −0.628220
\(76\) −1.62990e8 −0.560402
\(77\) −6.27428e8 −2.03402
\(78\) −2.52404e8 −0.772094
\(79\) 4.50547e8 1.30142 0.650711 0.759326i \(-0.274471\pi\)
0.650711 + 0.759326i \(0.274471\pi\)
\(80\) 6.37766e8 1.74083
\(81\) 4.30467e7 0.111111
\(82\) −4.16018e8 −1.01613
\(83\) 1.85548e8 0.429146 0.214573 0.976708i \(-0.431164\pi\)
0.214573 + 0.976708i \(0.431164\pi\)
\(84\) −8.67236e7 −0.190056
\(85\) 5.52234e8 1.14746
\(86\) 1.27997e6 0.00252324
\(87\) −7.72994e7 −0.144657
\(88\) 8.07287e8 1.43501
\(89\) −6.59420e8 −1.11406 −0.557028 0.830494i \(-0.688058\pi\)
−0.557028 + 0.830494i \(0.688058\pi\)
\(90\) −3.40145e8 −0.546478
\(91\) 8.83900e8 1.35119
\(92\) −1.89294e7 −0.0275481
\(93\) −1.48289e8 −0.205558
\(94\) 1.48523e9 1.96209
\(95\) 2.23870e9 2.81993
\(96\) 2.68120e8 0.322188
\(97\) 1.23039e9 1.41114 0.705570 0.708641i \(-0.250691\pi\)
0.705570 + 0.708641i \(0.250691\pi\)
\(98\) 3.25324e8 0.356285
\(99\) −5.65313e8 −0.591467
\(100\) 3.12471e8 0.312471
\(101\) −1.38809e9 −1.32731 −0.663653 0.748041i \(-0.730995\pi\)
−0.663653 + 0.748041i \(0.730995\pi\)
\(102\) 5.68617e8 0.520138
\(103\) −1.37636e9 −1.20494 −0.602468 0.798143i \(-0.705816\pi\)
−0.602468 + 0.798143i \(0.705816\pi\)
\(104\) −1.13728e9 −0.953274
\(105\) 1.19116e9 0.956356
\(106\) 2.79407e8 0.214962
\(107\) −4.99064e7 −0.0368069 −0.0184034 0.999831i \(-0.505858\pi\)
−0.0184034 + 0.999831i \(0.505858\pi\)
\(108\) −7.81380e7 −0.0552657
\(109\) −2.39001e9 −1.62174 −0.810869 0.585227i \(-0.801005\pi\)
−0.810869 + 0.585227i \(0.801005\pi\)
\(110\) 4.46697e9 2.90901
\(111\) −4.16343e8 −0.260314
\(112\) −2.29967e9 −1.38097
\(113\) −1.64219e9 −0.947481 −0.473740 0.880665i \(-0.657096\pi\)
−0.473740 + 0.880665i \(0.657096\pi\)
\(114\) 2.30511e9 1.27826
\(115\) 2.59999e8 0.138622
\(116\) 1.40313e8 0.0719511
\(117\) 7.96395e8 0.392909
\(118\) 3.11072e8 0.147704
\(119\) −1.99125e9 −0.910260
\(120\) −1.53262e9 −0.674715
\(121\) 5.06604e9 2.14850
\(122\) 3.81572e9 1.55940
\(123\) 1.31263e9 0.517096
\(124\) 2.69172e8 0.102243
\(125\) −3.47528e8 −0.127319
\(126\) 1.22650e9 0.433511
\(127\) 3.82527e9 1.30481 0.652403 0.757872i \(-0.273761\pi\)
0.652403 + 0.757872i \(0.273761\pi\)
\(128\) 3.66421e9 1.20652
\(129\) −4.03862e6 −0.00128404
\(130\) −6.29293e9 −1.93245
\(131\) −2.14603e9 −0.636671 −0.318336 0.947978i \(-0.603124\pi\)
−0.318336 + 0.947978i \(0.603124\pi\)
\(132\) 1.02615e9 0.294190
\(133\) −8.07232e9 −2.23700
\(134\) −5.58914e8 −0.149752
\(135\) 1.07324e9 0.278096
\(136\) 2.56207e9 0.642194
\(137\) 4.20140e9 1.01895 0.509473 0.860487i \(-0.329840\pi\)
0.509473 + 0.860487i \(0.329840\pi\)
\(138\) 2.67712e8 0.0628365
\(139\) −1.95076e9 −0.443238 −0.221619 0.975133i \(-0.571134\pi\)
−0.221619 + 0.975133i \(0.571134\pi\)
\(140\) −2.16219e9 −0.475683
\(141\) −4.68627e9 −0.998484
\(142\) 4.23971e9 0.875062
\(143\) −1.04587e10 −2.09153
\(144\) −2.07200e9 −0.401568
\(145\) −1.92723e9 −0.362057
\(146\) 5.71015e9 1.04006
\(147\) −1.02647e9 −0.181309
\(148\) 7.55742e8 0.129478
\(149\) 4.83950e9 0.804381 0.402191 0.915556i \(-0.368249\pi\)
0.402191 + 0.915556i \(0.368249\pi\)
\(150\) −4.41916e9 −0.712737
\(151\) −1.26115e10 −1.97411 −0.987053 0.160397i \(-0.948723\pi\)
−0.987053 + 0.160397i \(0.948723\pi\)
\(152\) 1.03863e10 1.57822
\(153\) −1.79412e9 −0.264692
\(154\) −1.61071e10 −2.30767
\(155\) −3.69713e9 −0.514484
\(156\) −1.44561e9 −0.195430
\(157\) 3.00690e8 0.0394976 0.0197488 0.999805i \(-0.493713\pi\)
0.0197488 + 0.999805i \(0.493713\pi\)
\(158\) 1.15663e10 1.47651
\(159\) −8.81597e8 −0.109391
\(160\) 6.68477e9 0.806392
\(161\) −9.37508e8 −0.109966
\(162\) 1.10508e9 0.126059
\(163\) 1.23969e10 1.37553 0.687764 0.725935i \(-0.258593\pi\)
0.687764 + 0.725935i \(0.258593\pi\)
\(164\) −2.38268e9 −0.257199
\(165\) −1.40944e10 −1.48036
\(166\) 4.76331e9 0.486881
\(167\) −6.24839e8 −0.0621647 −0.0310824 0.999517i \(-0.509895\pi\)
−0.0310824 + 0.999517i \(0.509895\pi\)
\(168\) 5.52636e9 0.535239
\(169\) 4.12937e9 0.389398
\(170\) 1.41767e10 1.30184
\(171\) −7.27317e9 −0.650491
\(172\) 7.33087e6 0.000638672 0
\(173\) −1.47010e10 −1.24778 −0.623892 0.781510i \(-0.714450\pi\)
−0.623892 + 0.781510i \(0.714450\pi\)
\(174\) −1.98440e9 −0.164118
\(175\) 1.54756e10 1.24731
\(176\) 2.72106e10 2.13763
\(177\) −9.81506e8 −0.0751646
\(178\) −1.69284e10 −1.26394
\(179\) 1.27897e10 0.931158 0.465579 0.885006i \(-0.345846\pi\)
0.465579 + 0.885006i \(0.345846\pi\)
\(180\) −1.94814e9 −0.138322
\(181\) 1.84616e10 1.27854 0.639271 0.768982i \(-0.279236\pi\)
0.639271 + 0.768982i \(0.279236\pi\)
\(182\) 2.26911e10 1.53297
\(183\) −1.20395e10 −0.793559
\(184\) 1.20626e9 0.0775817
\(185\) −1.03802e10 −0.651531
\(186\) −3.80681e9 −0.233213
\(187\) 2.35614e10 1.40901
\(188\) 8.50647e9 0.496637
\(189\) −3.86990e9 −0.220608
\(190\) 5.74709e10 3.19931
\(191\) 2.61673e10 1.42268 0.711341 0.702847i \(-0.248088\pi\)
0.711341 + 0.702847i \(0.248088\pi\)
\(192\) −6.21402e9 −0.330002
\(193\) −1.67493e10 −0.868940 −0.434470 0.900686i \(-0.643064\pi\)
−0.434470 + 0.900686i \(0.643064\pi\)
\(194\) 3.15861e10 1.60099
\(195\) 1.98557e10 0.983398
\(196\) 1.86325e9 0.0901816
\(197\) −2.98703e10 −1.41300 −0.706499 0.707714i \(-0.749726\pi\)
−0.706499 + 0.707714i \(0.749726\pi\)
\(198\) −1.45125e10 −0.671039
\(199\) 1.85693e10 0.839377 0.419689 0.907668i \(-0.362139\pi\)
0.419689 + 0.907668i \(0.362139\pi\)
\(200\) −1.99118e10 −0.879988
\(201\) 1.76351e9 0.0762070
\(202\) −3.56344e10 −1.50587
\(203\) 6.94922e9 0.287213
\(204\) 3.25667e9 0.131655
\(205\) 3.27266e10 1.29422
\(206\) −3.53333e10 −1.36704
\(207\) −8.44695e8 −0.0319767
\(208\) −3.83335e10 −1.42002
\(209\) 9.55151e10 3.46269
\(210\) 3.05791e10 1.08502
\(211\) −4.39736e10 −1.52729 −0.763643 0.645638i \(-0.776591\pi\)
−0.763643 + 0.645638i \(0.776591\pi\)
\(212\) 1.60027e9 0.0544103
\(213\) −1.33773e10 −0.445308
\(214\) −1.28118e9 −0.0417587
\(215\) −1.00691e8 −0.00321378
\(216\) 4.97926e9 0.155640
\(217\) 1.33312e10 0.408131
\(218\) −6.13554e10 −1.83992
\(219\) −1.80169e10 −0.529274
\(220\) 2.55840e10 0.736318
\(221\) −3.31925e10 −0.935998
\(222\) −1.06882e10 −0.295335
\(223\) 6.43333e10 1.74206 0.871032 0.491226i \(-0.163451\pi\)
0.871032 + 0.491226i \(0.163451\pi\)
\(224\) −2.41040e10 −0.639696
\(225\) 1.39435e10 0.362703
\(226\) −4.21576e10 −1.07495
\(227\) 6.30758e10 1.57669 0.788346 0.615233i \(-0.210938\pi\)
0.788346 + 0.615233i \(0.210938\pi\)
\(228\) 1.32022e10 0.323548
\(229\) −1.87955e10 −0.451641 −0.225820 0.974169i \(-0.572506\pi\)
−0.225820 + 0.974169i \(0.572506\pi\)
\(230\) 6.67459e9 0.157271
\(231\) 5.08216e10 1.17434
\(232\) −8.94130e9 −0.202630
\(233\) −5.24266e10 −1.16533 −0.582667 0.812711i \(-0.697991\pi\)
−0.582667 + 0.812711i \(0.697991\pi\)
\(234\) 2.04447e10 0.445769
\(235\) −1.16838e11 −2.49907
\(236\) 1.78162e9 0.0373862
\(237\) −3.64943e10 −0.751376
\(238\) −5.11187e10 −1.03272
\(239\) 5.25503e9 0.104180 0.0520900 0.998642i \(-0.483412\pi\)
0.0520900 + 0.998642i \(0.483412\pi\)
\(240\) −5.16591e10 −1.00507
\(241\) −1.43455e10 −0.273929 −0.136965 0.990576i \(-0.543735\pi\)
−0.136965 + 0.990576i \(0.543735\pi\)
\(242\) 1.30053e11 2.43754
\(243\) −3.48678e9 −0.0641500
\(244\) 2.18540e10 0.394709
\(245\) −2.55920e10 −0.453792
\(246\) 3.36974e10 0.586663
\(247\) −1.34559e11 −2.30025
\(248\) −1.71527e10 −0.287938
\(249\) −1.50294e10 −0.247767
\(250\) −8.92160e9 −0.144448
\(251\) −3.33985e10 −0.531124 −0.265562 0.964094i \(-0.585557\pi\)
−0.265562 + 0.964094i \(0.585557\pi\)
\(252\) 7.02461e9 0.109729
\(253\) 1.10930e10 0.170218
\(254\) 9.82009e10 1.48035
\(255\) −4.47310e10 −0.662487
\(256\) 5.47875e10 0.797263
\(257\) 1.10485e10 0.157981 0.0789904 0.996875i \(-0.474830\pi\)
0.0789904 + 0.996875i \(0.474830\pi\)
\(258\) −1.03678e8 −0.00145679
\(259\) 3.74292e10 0.516847
\(260\) −3.60419e10 −0.489133
\(261\) 6.26125e9 0.0835178
\(262\) −5.50920e10 −0.722326
\(263\) −2.21057e10 −0.284907 −0.142454 0.989801i \(-0.545499\pi\)
−0.142454 + 0.989801i \(0.545499\pi\)
\(264\) −6.53902e10 −0.828505
\(265\) −2.19800e10 −0.273792
\(266\) −2.07229e11 −2.53795
\(267\) 5.34130e10 0.643201
\(268\) −3.20110e9 −0.0379047
\(269\) 4.75498e10 0.553685 0.276843 0.960915i \(-0.410712\pi\)
0.276843 + 0.960915i \(0.410712\pi\)
\(270\) 2.75518e10 0.315510
\(271\) 2.43589e10 0.274344 0.137172 0.990547i \(-0.456199\pi\)
0.137172 + 0.990547i \(0.456199\pi\)
\(272\) 8.63578e10 0.956625
\(273\) −7.15959e10 −0.780111
\(274\) 1.07857e11 1.15603
\(275\) −1.83114e11 −1.93074
\(276\) 1.53328e9 0.0159049
\(277\) 7.34877e10 0.749991 0.374995 0.927027i \(-0.377644\pi\)
0.374995 + 0.927027i \(0.377644\pi\)
\(278\) −5.00791e10 −0.502869
\(279\) 1.20114e10 0.118679
\(280\) 1.37783e11 1.33963
\(281\) 1.90585e11 1.82352 0.911761 0.410721i \(-0.134723\pi\)
0.911761 + 0.410721i \(0.134723\pi\)
\(282\) −1.20304e11 −1.13281
\(283\) −1.44956e11 −1.34337 −0.671685 0.740837i \(-0.734429\pi\)
−0.671685 + 0.740837i \(0.734429\pi\)
\(284\) 2.42824e10 0.221492
\(285\) −1.81334e11 −1.62809
\(286\) −2.68491e11 −2.37292
\(287\) −1.18006e11 −1.02668
\(288\) −2.17177e10 −0.186015
\(289\) −4.38116e10 −0.369445
\(290\) −4.94750e10 −0.410766
\(291\) −9.96616e10 −0.814722
\(292\) 3.27041e10 0.263256
\(293\) −1.42136e11 −1.12667 −0.563337 0.826227i \(-0.690483\pi\)
−0.563337 + 0.826227i \(0.690483\pi\)
\(294\) −2.63512e10 −0.205702
\(295\) −2.44709e10 −0.188127
\(296\) −4.81588e10 −0.364639
\(297\) 4.57903e10 0.341483
\(298\) 1.24238e11 0.912598
\(299\) −1.56275e10 −0.113075
\(300\) −2.53102e10 −0.180405
\(301\) 3.63072e8 0.00254943
\(302\) −3.23757e11 −2.23969
\(303\) 1.12435e11 0.766320
\(304\) 3.50085e11 2.35094
\(305\) −3.00169e11 −1.98617
\(306\) −4.60579e10 −0.300302
\(307\) 3.98803e10 0.256233 0.128117 0.991759i \(-0.459107\pi\)
0.128117 + 0.991759i \(0.459107\pi\)
\(308\) −9.22510e10 −0.584108
\(309\) 1.11485e11 0.695670
\(310\) −9.49112e10 −0.583700
\(311\) −2.22773e11 −1.35033 −0.675166 0.737666i \(-0.735928\pi\)
−0.675166 + 0.737666i \(0.735928\pi\)
\(312\) 9.21197e10 0.550373
\(313\) 2.84025e11 1.67266 0.836328 0.548229i \(-0.184698\pi\)
0.836328 + 0.548229i \(0.184698\pi\)
\(314\) 7.71920e9 0.0448114
\(315\) −9.64843e10 −0.552152
\(316\) 6.62441e10 0.373728
\(317\) −9.62320e10 −0.535245 −0.267623 0.963524i \(-0.586238\pi\)
−0.267623 + 0.963524i \(0.586238\pi\)
\(318\) −2.26320e10 −0.124108
\(319\) −8.22261e10 −0.444582
\(320\) −1.54928e11 −0.825951
\(321\) 4.04242e9 0.0212505
\(322\) −2.40673e10 −0.124760
\(323\) 3.03134e11 1.54962
\(324\) 6.32918e9 0.0319077
\(325\) 2.57965e11 1.28258
\(326\) 3.18248e11 1.56058
\(327\) 1.93591e11 0.936311
\(328\) 1.51834e11 0.724329
\(329\) 4.21296e11 1.98246
\(330\) −3.61825e11 −1.67952
\(331\) 9.82059e10 0.449688 0.224844 0.974395i \(-0.427813\pi\)
0.224844 + 0.974395i \(0.427813\pi\)
\(332\) 2.72812e10 0.123237
\(333\) 3.37238e10 0.150292
\(334\) −1.60406e10 −0.0705280
\(335\) 4.39677e10 0.190736
\(336\) 1.86273e11 0.797302
\(337\) −2.71246e11 −1.14559 −0.572794 0.819700i \(-0.694140\pi\)
−0.572794 + 0.819700i \(0.694140\pi\)
\(338\) 1.06007e11 0.441785
\(339\) 1.33017e11 0.547028
\(340\) 8.11953e10 0.329515
\(341\) −1.57740e11 −0.631752
\(342\) −1.86714e11 −0.738004
\(343\) −2.01571e11 −0.786330
\(344\) −4.67151e8 −0.00179864
\(345\) −2.10599e10 −0.0800333
\(346\) −3.77398e11 −1.41566
\(347\) −2.87548e11 −1.06470 −0.532350 0.846524i \(-0.678691\pi\)
−0.532350 + 0.846524i \(0.678691\pi\)
\(348\) −1.13654e10 −0.0415410
\(349\) 8.42622e10 0.304031 0.152016 0.988378i \(-0.451424\pi\)
0.152016 + 0.988378i \(0.451424\pi\)
\(350\) 3.97283e11 1.41512
\(351\) −6.45080e10 −0.226846
\(352\) 2.85209e11 0.990196
\(353\) −5.23831e11 −1.79558 −0.897791 0.440423i \(-0.854829\pi\)
−0.897791 + 0.440423i \(0.854829\pi\)
\(354\) −2.51968e10 −0.0852768
\(355\) −3.33522e11 −1.11454
\(356\) −9.69549e10 −0.319922
\(357\) 1.61292e11 0.525539
\(358\) 3.28333e11 1.05643
\(359\) 1.43427e11 0.455727 0.227864 0.973693i \(-0.426826\pi\)
0.227864 + 0.973693i \(0.426826\pi\)
\(360\) 1.24143e11 0.389547
\(361\) 9.06185e11 2.80824
\(362\) 4.73938e11 1.45055
\(363\) −4.10349e11 −1.24043
\(364\) 1.29960e11 0.388020
\(365\) −4.49196e11 −1.32470
\(366\) −3.09073e11 −0.900320
\(367\) 5.93569e8 0.00170794 0.000853972 1.00000i \(-0.499728\pi\)
0.000853972 1.00000i \(0.499728\pi\)
\(368\) 4.06584e10 0.115567
\(369\) −1.06323e11 −0.298545
\(370\) −2.66477e11 −0.739184
\(371\) 7.92556e10 0.217194
\(372\) −2.18030e10 −0.0590299
\(373\) −2.43189e11 −0.650510 −0.325255 0.945626i \(-0.605450\pi\)
−0.325255 + 0.945626i \(0.605450\pi\)
\(374\) 6.04858e11 1.59857
\(375\) 2.81498e10 0.0735079
\(376\) −5.42065e11 −1.39864
\(377\) 1.15838e11 0.295334
\(378\) −9.93465e10 −0.250288
\(379\) −2.11144e11 −0.525656 −0.262828 0.964843i \(-0.584655\pi\)
−0.262828 + 0.964843i \(0.584655\pi\)
\(380\) 3.29157e11 0.809797
\(381\) −3.09847e11 −0.753330
\(382\) 6.71755e11 1.61408
\(383\) −4.91641e11 −1.16749 −0.583745 0.811937i \(-0.698413\pi\)
−0.583745 + 0.811937i \(0.698413\pi\)
\(384\) −2.96801e11 −0.696587
\(385\) 1.26708e12 2.93922
\(386\) −4.29982e11 −0.985843
\(387\) 3.27128e8 0.000741342 0
\(388\) 1.80905e11 0.405235
\(389\) 7.15758e11 1.58487 0.792433 0.609958i \(-0.208814\pi\)
0.792433 + 0.609958i \(0.208814\pi\)
\(390\) 5.09727e11 1.11570
\(391\) 3.52056e10 0.0761757
\(392\) −1.18733e11 −0.253971
\(393\) 1.73829e11 0.367582
\(394\) −7.66818e11 −1.60310
\(395\) −9.09875e11 −1.88059
\(396\) −8.31182e10 −0.169851
\(397\) 4.88616e11 0.987213 0.493606 0.869685i \(-0.335678\pi\)
0.493606 + 0.869685i \(0.335678\pi\)
\(398\) 4.76704e11 0.952303
\(399\) 6.53858e11 1.29153
\(400\) −6.71154e11 −1.31085
\(401\) 8.18775e11 1.58130 0.790652 0.612266i \(-0.209742\pi\)
0.790652 + 0.612266i \(0.209742\pi\)
\(402\) 4.52720e10 0.0864594
\(403\) 2.22219e11 0.419671
\(404\) −2.04091e11 −0.381161
\(405\) −8.69324e10 −0.160559
\(406\) 1.78398e11 0.325853
\(407\) −4.42879e11 −0.800037
\(408\) −2.07528e11 −0.370771
\(409\) 7.64637e11 1.35114 0.675570 0.737296i \(-0.263898\pi\)
0.675570 + 0.737296i \(0.263898\pi\)
\(410\) 8.40143e11 1.46834
\(411\) −3.40313e11 −0.588289
\(412\) −2.02367e11 −0.346020
\(413\) 8.82375e10 0.149237
\(414\) −2.16847e10 −0.0362787
\(415\) −3.74712e11 −0.620128
\(416\) −4.01794e11 −0.657784
\(417\) 1.58012e11 0.255904
\(418\) 2.45202e12 3.92854
\(419\) 1.73762e11 0.275418 0.137709 0.990473i \(-0.456026\pi\)
0.137709 + 0.990473i \(0.456026\pi\)
\(420\) 1.75137e11 0.274636
\(421\) −1.98906e11 −0.308588 −0.154294 0.988025i \(-0.549310\pi\)
−0.154294 + 0.988025i \(0.549310\pi\)
\(422\) −1.12887e12 −1.73276
\(423\) 3.79588e11 0.576475
\(424\) −1.01975e11 −0.153232
\(425\) −5.81144e11 −0.864040
\(426\) −3.43416e11 −0.505217
\(427\) 1.08235e12 1.57559
\(428\) −7.33776e9 −0.0105698
\(429\) 8.47153e11 1.20755
\(430\) −2.58489e9 −0.00364615
\(431\) 1.05068e11 0.146663 0.0733316 0.997308i \(-0.476637\pi\)
0.0733316 + 0.997308i \(0.476637\pi\)
\(432\) 1.67832e11 0.231845
\(433\) 1.19082e12 1.62799 0.813995 0.580872i \(-0.197288\pi\)
0.813995 + 0.580872i \(0.197288\pi\)
\(434\) 3.42232e11 0.463038
\(435\) 1.56105e11 0.209034
\(436\) −3.51405e11 −0.465713
\(437\) 1.42720e11 0.187205
\(438\) −4.62522e11 −0.600480
\(439\) 1.37501e11 0.176692 0.0883459 0.996090i \(-0.471842\pi\)
0.0883459 + 0.996090i \(0.471842\pi\)
\(440\) −1.63031e12 −2.07364
\(441\) 8.31443e10 0.104679
\(442\) −8.52105e11 −1.06192
\(443\) 5.09348e11 0.628345 0.314172 0.949366i \(-0.398273\pi\)
0.314172 + 0.949366i \(0.398273\pi\)
\(444\) −6.12151e10 −0.0747541
\(445\) 1.33169e12 1.60984
\(446\) 1.65154e12 1.97643
\(447\) −3.91999e11 −0.464410
\(448\) 5.58640e11 0.655211
\(449\) 4.35623e11 0.505828 0.252914 0.967489i \(-0.418611\pi\)
0.252914 + 0.967489i \(0.418611\pi\)
\(450\) 3.57952e11 0.411499
\(451\) 1.39630e12 1.58922
\(452\) −2.41452e11 −0.272087
\(453\) 1.02153e12 1.13975
\(454\) 1.61926e12 1.78881
\(455\) −1.78503e12 −1.95251
\(456\) −8.41294e11 −0.911184
\(457\) 1.02198e12 1.09602 0.548009 0.836472i \(-0.315386\pi\)
0.548009 + 0.836472i \(0.315386\pi\)
\(458\) −4.82509e11 −0.512402
\(459\) 1.45324e11 0.152820
\(460\) 3.82278e10 0.0398079
\(461\) −3.26178e11 −0.336357 −0.168179 0.985757i \(-0.553789\pi\)
−0.168179 + 0.985757i \(0.553789\pi\)
\(462\) 1.30467e12 1.33233
\(463\) −1.63884e11 −0.165738 −0.0828688 0.996560i \(-0.526408\pi\)
−0.0828688 + 0.996560i \(0.526408\pi\)
\(464\) −3.01378e11 −0.301842
\(465\) 2.99467e11 0.297037
\(466\) −1.34587e12 −1.32211
\(467\) −1.39487e12 −1.35708 −0.678542 0.734561i \(-0.737388\pi\)
−0.678542 + 0.734561i \(0.737388\pi\)
\(468\) 1.17094e11 0.112831
\(469\) −1.58539e11 −0.151307
\(470\) −2.99941e12 −2.83528
\(471\) −2.43559e10 −0.0228040
\(472\) −1.13532e11 −0.105288
\(473\) −4.29602e9 −0.00394631
\(474\) −9.36867e11 −0.852462
\(475\) −2.35589e12 −2.12341
\(476\) −2.92775e11 −0.261398
\(477\) 7.14094e10 0.0631571
\(478\) 1.34905e11 0.118196
\(479\) 1.53130e11 0.132908 0.0664541 0.997789i \(-0.478831\pi\)
0.0664541 + 0.997789i \(0.478831\pi\)
\(480\) −5.41466e11 −0.465571
\(481\) 6.23914e11 0.531461
\(482\) −3.68271e11 −0.310782
\(483\) 7.59381e10 0.0634889
\(484\) 7.44863e11 0.616981
\(485\) −2.48476e12 −2.03914
\(486\) −8.95113e10 −0.0727804
\(487\) −1.17338e12 −0.945272 −0.472636 0.881258i \(-0.656697\pi\)
−0.472636 + 0.881258i \(0.656697\pi\)
\(488\) −1.39262e12 −1.11159
\(489\) −1.00415e12 −0.794161
\(490\) −6.56987e11 −0.514843
\(491\) 6.67484e11 0.518292 0.259146 0.965838i \(-0.416559\pi\)
0.259146 + 0.965838i \(0.416559\pi\)
\(492\) 1.92997e11 0.148494
\(493\) −2.60959e11 −0.198958
\(494\) −3.45434e12 −2.60972
\(495\) 1.14164e12 0.854686
\(496\) −5.78153e11 −0.428919
\(497\) 1.20262e12 0.884147
\(498\) −3.85828e11 −0.281101
\(499\) −3.75717e11 −0.271274 −0.135637 0.990759i \(-0.543308\pi\)
−0.135637 + 0.990759i \(0.543308\pi\)
\(500\) −5.10972e10 −0.0365622
\(501\) 5.06120e10 0.0358908
\(502\) −8.57394e11 −0.602579
\(503\) 2.35917e12 1.64325 0.821626 0.570027i \(-0.193067\pi\)
0.821626 + 0.570027i \(0.193067\pi\)
\(504\) −4.47635e11 −0.309020
\(505\) 2.80323e12 1.91799
\(506\) 2.84775e11 0.193119
\(507\) −3.34479e11 −0.224819
\(508\) 5.62432e11 0.374700
\(509\) 1.79979e12 1.18848 0.594240 0.804287i \(-0.297453\pi\)
0.594240 + 0.804287i \(0.297453\pi\)
\(510\) −1.14832e12 −0.751615
\(511\) 1.61972e12 1.05086
\(512\) −4.69596e11 −0.302002
\(513\) 5.89126e11 0.375561
\(514\) 2.83632e11 0.179235
\(515\) 2.77954e12 1.74117
\(516\) −5.93801e8 −0.000368737 0
\(517\) −4.98495e12 −3.06869
\(518\) 9.60868e11 0.586381
\(519\) 1.19078e12 0.720409
\(520\) 2.29673e12 1.37751
\(521\) −7.29526e11 −0.433781 −0.216891 0.976196i \(-0.569592\pi\)
−0.216891 + 0.976196i \(0.569592\pi\)
\(522\) 1.60736e11 0.0947538
\(523\) 3.36585e12 1.96715 0.983574 0.180505i \(-0.0577731\pi\)
0.983574 + 0.180505i \(0.0577731\pi\)
\(524\) −3.15532e11 −0.182832
\(525\) −1.25352e12 −0.720137
\(526\) −5.67489e11 −0.323237
\(527\) −5.00616e11 −0.282720
\(528\) −2.20406e12 −1.23416
\(529\) −1.78458e12 −0.990797
\(530\) −5.64260e11 −0.310626
\(531\) 7.95020e10 0.0433963
\(532\) −1.18688e12 −0.642397
\(533\) −1.96706e12 −1.05571
\(534\) 1.37120e12 0.729734
\(535\) 1.00785e11 0.0531870
\(536\) 2.03986e11 0.106748
\(537\) −1.03597e12 −0.537604
\(538\) 1.22068e12 0.628175
\(539\) −1.09190e12 −0.557227
\(540\) 1.57799e11 0.0798605
\(541\) 1.15874e12 0.581564 0.290782 0.956789i \(-0.406085\pi\)
0.290782 + 0.956789i \(0.406085\pi\)
\(542\) 6.25331e11 0.311253
\(543\) −1.49539e12 −0.738166
\(544\) 9.05162e11 0.443130
\(545\) 4.82660e12 2.34346
\(546\) −1.83798e12 −0.885063
\(547\) −1.75266e12 −0.837054 −0.418527 0.908204i \(-0.637454\pi\)
−0.418527 + 0.908204i \(0.637454\pi\)
\(548\) 6.17734e11 0.292610
\(549\) 9.75200e11 0.458161
\(550\) −4.70082e12 −2.19049
\(551\) −1.05790e12 −0.488948
\(552\) −9.77067e10 −0.0447918
\(553\) 3.28084e12 1.49184
\(554\) 1.88655e12 0.850890
\(555\) 8.40800e11 0.376161
\(556\) −2.86821e11 −0.127284
\(557\) −6.84039e11 −0.301115 −0.150558 0.988601i \(-0.548107\pi\)
−0.150558 + 0.988601i \(0.548107\pi\)
\(558\) 3.08351e11 0.134646
\(559\) 6.05211e9 0.00262152
\(560\) 4.64415e12 1.99554
\(561\) −1.90847e12 −0.813491
\(562\) 4.89263e12 2.06885
\(563\) −1.16614e12 −0.489173 −0.244587 0.969627i \(-0.578652\pi\)
−0.244587 + 0.969627i \(0.578652\pi\)
\(564\) −6.89024e11 −0.286734
\(565\) 3.31638e12 1.36914
\(566\) −3.72124e12 −1.52410
\(567\) 3.13462e11 0.127368
\(568\) −1.54736e12 −0.623771
\(569\) 3.47046e12 1.38798 0.693988 0.719987i \(-0.255852\pi\)
0.693988 + 0.719987i \(0.255852\pi\)
\(570\) −4.65514e12 −1.84712
\(571\) 3.51126e12 1.38230 0.691148 0.722714i \(-0.257105\pi\)
0.691148 + 0.722714i \(0.257105\pi\)
\(572\) −1.53775e12 −0.600624
\(573\) −2.11955e12 −0.821386
\(574\) −3.02940e12 −1.16480
\(575\) −2.73610e11 −0.104382
\(576\) 5.03335e11 0.190527
\(577\) −2.62974e12 −0.987690 −0.493845 0.869550i \(-0.664409\pi\)
−0.493845 + 0.869550i \(0.664409\pi\)
\(578\) −1.12471e12 −0.419148
\(579\) 1.35670e12 0.501683
\(580\) −2.83361e11 −0.103971
\(581\) 1.35114e12 0.491936
\(582\) −2.55847e12 −0.924330
\(583\) −9.37786e11 −0.336198
\(584\) −2.08403e12 −0.741389
\(585\) −1.60831e12 −0.567765
\(586\) −3.64885e12 −1.27825
\(587\) 2.57580e12 0.895448 0.447724 0.894172i \(-0.352235\pi\)
0.447724 + 0.894172i \(0.352235\pi\)
\(588\) −1.50923e11 −0.0520664
\(589\) −2.02944e12 −0.694796
\(590\) −6.28206e11 −0.213436
\(591\) 2.41949e12 0.815795
\(592\) −1.62325e12 −0.543173
\(593\) 8.45161e11 0.280668 0.140334 0.990104i \(-0.455182\pi\)
0.140334 + 0.990104i \(0.455182\pi\)
\(594\) 1.17551e12 0.387425
\(595\) 4.02132e12 1.31535
\(596\) 7.11554e11 0.230993
\(597\) −1.50412e12 −0.484615
\(598\) −4.01182e11 −0.128288
\(599\) 2.50472e12 0.794947 0.397473 0.917614i \(-0.369887\pi\)
0.397473 + 0.917614i \(0.369887\pi\)
\(600\) 1.61286e12 0.508061
\(601\) −5.79764e12 −1.81266 −0.906330 0.422571i \(-0.861128\pi\)
−0.906330 + 0.422571i \(0.861128\pi\)
\(602\) 9.32064e9 0.00289242
\(603\) −1.42844e11 −0.0439981
\(604\) −1.85427e12 −0.566902
\(605\) −1.02308e13 −3.10464
\(606\) 2.88639e12 0.869417
\(607\) 3.04472e12 0.910330 0.455165 0.890407i \(-0.349580\pi\)
0.455165 + 0.890407i \(0.349580\pi\)
\(608\) 3.66943e12 1.08901
\(609\) −5.62887e11 −0.165822
\(610\) −7.70581e12 −2.25338
\(611\) 7.02264e12 2.03852
\(612\) −2.63791e11 −0.0760113
\(613\) −3.19278e12 −0.913266 −0.456633 0.889655i \(-0.650945\pi\)
−0.456633 + 0.889655i \(0.650945\pi\)
\(614\) 1.02379e12 0.290705
\(615\) −2.65085e12 −0.747218
\(616\) 5.87859e12 1.64498
\(617\) 1.16343e12 0.323191 0.161595 0.986857i \(-0.448336\pi\)
0.161595 + 0.986857i \(0.448336\pi\)
\(618\) 2.86200e12 0.789262
\(619\) 6.45412e12 1.76697 0.883485 0.468460i \(-0.155191\pi\)
0.883485 + 0.468460i \(0.155191\pi\)
\(620\) −5.43591e11 −0.147744
\(621\) 6.84203e10 0.0184618
\(622\) −5.71893e12 −1.53200
\(623\) −4.80183e12 −1.27706
\(624\) 3.10501e12 0.819847
\(625\) −3.44898e12 −0.904128
\(626\) 7.29137e12 1.89769
\(627\) −7.73672e12 −1.99919
\(628\) 4.42107e10 0.0113425
\(629\) −1.40556e12 −0.358031
\(630\) −2.47690e12 −0.626436
\(631\) −6.31981e12 −1.58698 −0.793490 0.608583i \(-0.791738\pi\)
−0.793490 + 0.608583i \(0.791738\pi\)
\(632\) −4.22133e12 −1.05250
\(633\) 3.56186e12 0.881779
\(634\) −2.47043e12 −0.607254
\(635\) −7.72510e12 −1.88548
\(636\) −1.29622e11 −0.0314138
\(637\) 1.53823e12 0.370164
\(638\) −2.11088e12 −0.504394
\(639\) 1.08356e12 0.257099
\(640\) −7.39984e12 −1.74346
\(641\) 4.92603e11 0.115249 0.0576243 0.998338i \(-0.481647\pi\)
0.0576243 + 0.998338i \(0.481647\pi\)
\(642\) 1.03775e11 0.0241094
\(643\) 2.11852e11 0.0488747 0.0244373 0.999701i \(-0.492221\pi\)
0.0244373 + 0.999701i \(0.492221\pi\)
\(644\) −1.37842e11 −0.0315788
\(645\) 8.15595e9 0.00185548
\(646\) 7.78194e12 1.75809
\(647\) 6.22138e12 1.39578 0.697891 0.716204i \(-0.254122\pi\)
0.697891 + 0.716204i \(0.254122\pi\)
\(648\) −4.03320e11 −0.0898591
\(649\) −1.04406e12 −0.231007
\(650\) 6.62237e12 1.45514
\(651\) −1.07982e12 −0.235634
\(652\) 1.82272e12 0.395009
\(653\) 3.04506e11 0.0655369 0.0327685 0.999463i \(-0.489568\pi\)
0.0327685 + 0.999463i \(0.489568\pi\)
\(654\) 4.96979e12 1.06228
\(655\) 4.33389e12 0.920009
\(656\) 5.11775e12 1.07898
\(657\) 1.45937e12 0.305577
\(658\) 1.08153e13 2.24917
\(659\) 1.79160e12 0.370047 0.185024 0.982734i \(-0.440764\pi\)
0.185024 + 0.982734i \(0.440764\pi\)
\(660\) −2.07230e12 −0.425114
\(661\) −3.20964e12 −0.653957 −0.326979 0.945032i \(-0.606031\pi\)
−0.326979 + 0.945032i \(0.606031\pi\)
\(662\) 2.52110e12 0.510187
\(663\) 2.68859e12 0.540399
\(664\) −1.73846e12 −0.347064
\(665\) 1.63020e13 3.23253
\(666\) 8.65743e11 0.170512
\(667\) −1.22863e11 −0.0240356
\(668\) −9.18704e10 −0.0178518
\(669\) −5.21100e12 −1.00578
\(670\) 1.12872e12 0.216396
\(671\) −1.28069e13 −2.43888
\(672\) 1.95243e12 0.369329
\(673\) −3.90980e12 −0.734661 −0.367331 0.930090i \(-0.619728\pi\)
−0.367331 + 0.930090i \(0.619728\pi\)
\(674\) −6.96331e12 −1.29971
\(675\) −1.12942e12 −0.209407
\(676\) 6.07143e11 0.111823
\(677\) 6.06447e12 1.10954 0.554771 0.832003i \(-0.312806\pi\)
0.554771 + 0.832003i \(0.312806\pi\)
\(678\) 3.41477e12 0.620622
\(679\) 8.95958e12 1.61761
\(680\) −5.17407e12 −0.927988
\(681\) −5.10914e12 −0.910303
\(682\) −4.04943e12 −0.716745
\(683\) 5.03456e12 0.885254 0.442627 0.896706i \(-0.354047\pi\)
0.442627 + 0.896706i \(0.354047\pi\)
\(684\) −1.06938e12 −0.186801
\(685\) −8.48468e12 −1.47241
\(686\) −5.17465e12 −0.892118
\(687\) 1.52243e12 0.260755
\(688\) −1.57459e10 −0.00267929
\(689\) 1.32112e12 0.223335
\(690\) −5.40641e11 −0.0908005
\(691\) 1.01339e13 1.69093 0.845465 0.534031i \(-0.179323\pi\)
0.845465 + 0.534031i \(0.179323\pi\)
\(692\) −2.16150e12 −0.358325
\(693\) −4.11655e12 −0.678007
\(694\) −7.38181e12 −1.20794
\(695\) 3.93954e12 0.640492
\(696\) 7.24245e11 0.116989
\(697\) 4.43140e12 0.711202
\(698\) 2.16314e12 0.344934
\(699\) 4.24656e12 0.672805
\(700\) 2.27538e12 0.358190
\(701\) 2.79267e12 0.436806 0.218403 0.975859i \(-0.429915\pi\)
0.218403 + 0.975859i \(0.429915\pi\)
\(702\) −1.65602e12 −0.257365
\(703\) −5.69796e12 −0.879874
\(704\) −6.61007e12 −1.01421
\(705\) 9.46386e12 1.44284
\(706\) −1.34476e13 −2.03715
\(707\) −1.01079e13 −1.52151
\(708\) −1.44311e11 −0.0215849
\(709\) −1.84958e12 −0.274894 −0.137447 0.990509i \(-0.543890\pi\)
−0.137447 + 0.990509i \(0.543890\pi\)
\(710\) −8.56205e12 −1.26449
\(711\) 2.95604e12 0.433807
\(712\) 6.17834e12 0.900973
\(713\) −2.35696e11 −0.0341547
\(714\) 4.14061e12 0.596242
\(715\) 2.11212e13 3.02233
\(716\) 1.88048e12 0.267400
\(717\) −4.25658e11 −0.0601484
\(718\) 3.68199e12 0.517038
\(719\) 5.47240e12 0.763656 0.381828 0.924233i \(-0.375295\pi\)
0.381828 + 0.924233i \(0.375295\pi\)
\(720\) 4.18438e12 0.580277
\(721\) −1.00225e13 −1.38124
\(722\) 2.32632e13 3.18605
\(723\) 1.16198e12 0.158153
\(724\) 2.71441e12 0.367157
\(725\) 2.02812e12 0.272629
\(726\) −1.05343e13 −1.40732
\(727\) −5.66930e12 −0.752705 −0.376353 0.926477i \(-0.622822\pi\)
−0.376353 + 0.926477i \(0.622822\pi\)
\(728\) −8.28157e12 −1.09275
\(729\) 2.82430e11 0.0370370
\(730\) −1.15316e13 −1.50292
\(731\) −1.36342e10 −0.00176604
\(732\) −1.77018e12 −0.227885
\(733\) 1.91881e12 0.245507 0.122753 0.992437i \(-0.460828\pi\)
0.122753 + 0.992437i \(0.460828\pi\)
\(734\) 1.52378e10 0.00193772
\(735\) 2.07295e12 0.261997
\(736\) 4.26162e11 0.0535334
\(737\) 1.87590e12 0.234211
\(738\) −2.72949e12 −0.338710
\(739\) −7.05873e12 −0.870616 −0.435308 0.900282i \(-0.643360\pi\)
−0.435308 + 0.900282i \(0.643360\pi\)
\(740\) −1.52621e12 −0.187099
\(741\) 1.08993e13 1.32805
\(742\) 2.03462e12 0.246414
\(743\) −4.34677e12 −0.523259 −0.261630 0.965168i \(-0.584260\pi\)
−0.261630 + 0.965168i \(0.584260\pi\)
\(744\) 1.38937e12 0.166241
\(745\) −9.77331e12 −1.16235
\(746\) −6.24305e12 −0.738026
\(747\) 1.21738e12 0.143049
\(748\) 3.46424e12 0.404623
\(749\) −3.63413e11 −0.0421923
\(750\) 7.22650e11 0.0833973
\(751\) 9.76256e12 1.11991 0.559956 0.828522i \(-0.310818\pi\)
0.559956 + 0.828522i \(0.310818\pi\)
\(752\) −1.82710e13 −2.08344
\(753\) 2.70528e12 0.306645
\(754\) 2.97374e12 0.335067
\(755\) 2.54688e13 2.85264
\(756\) −5.68994e11 −0.0633519
\(757\) −6.23303e12 −0.689871 −0.344936 0.938626i \(-0.612099\pi\)
−0.344936 + 0.938626i \(0.612099\pi\)
\(758\) −5.42039e12 −0.596375
\(759\) −8.98532e11 −0.0982756
\(760\) −2.09751e13 −2.28057
\(761\) −2.40522e12 −0.259970 −0.129985 0.991516i \(-0.541493\pi\)
−0.129985 + 0.991516i \(0.541493\pi\)
\(762\) −7.95427e12 −0.854679
\(763\) −1.74038e13 −1.85902
\(764\) 3.84738e12 0.408550
\(765\) 3.62321e12 0.382487
\(766\) −1.26212e13 −1.32456
\(767\) 1.47084e12 0.153457
\(768\) −4.43778e12 −0.460300
\(769\) 1.04575e13 1.07835 0.539176 0.842193i \(-0.318736\pi\)
0.539176 + 0.842193i \(0.318736\pi\)
\(770\) 3.25280e13 3.33465
\(771\) −8.94928e11 −0.0912102
\(772\) −2.46266e12 −0.249533
\(773\) −1.05202e13 −1.05978 −0.529891 0.848066i \(-0.677767\pi\)
−0.529891 + 0.848066i \(0.677767\pi\)
\(774\) 8.39790e9 0.000841079 0
\(775\) 3.89068e12 0.387407
\(776\) −1.15279e13 −1.14123
\(777\) −3.03177e12 −0.298402
\(778\) 1.83746e13 1.79809
\(779\) 1.79644e13 1.74781
\(780\) 2.91939e12 0.282401
\(781\) −1.42299e13 −1.36859
\(782\) 9.03784e11 0.0864240
\(783\) −5.07161e11 −0.0482190
\(784\) −4.00205e12 −0.378321
\(785\) −6.07241e11 −0.0570752
\(786\) 4.46246e12 0.417035
\(787\) 1.24667e13 1.15842 0.579209 0.815179i \(-0.303362\pi\)
0.579209 + 0.815179i \(0.303362\pi\)
\(788\) −4.39184e12 −0.405769
\(789\) 1.79056e12 0.164491
\(790\) −2.33579e13 −2.13360
\(791\) −1.19583e13 −1.08611
\(792\) 5.29661e12 0.478338
\(793\) 1.80419e13 1.62014
\(794\) 1.25436e13 1.12003
\(795\) 1.78038e12 0.158074
\(796\) 2.73026e12 0.241043
\(797\) 1.88289e12 0.165296 0.0826480 0.996579i \(-0.473662\pi\)
0.0826480 + 0.996579i \(0.473662\pi\)
\(798\) 1.67856e13 1.46529
\(799\) −1.58206e13 −1.37329
\(800\) −7.03472e12 −0.607214
\(801\) −4.32646e12 −0.371352
\(802\) 2.10193e13 1.79404
\(803\) −1.91652e13 −1.62665
\(804\) 2.59289e11 0.0218843
\(805\) 1.89329e12 0.158904
\(806\) 5.70472e12 0.476131
\(807\) −3.85153e12 −0.319670
\(808\) 1.30055e13 1.07343
\(809\) −9.15128e12 −0.751127 −0.375564 0.926797i \(-0.622551\pi\)
−0.375564 + 0.926797i \(0.622551\pi\)
\(810\) −2.23169e12 −0.182159
\(811\) −4.40188e12 −0.357310 −0.178655 0.983912i \(-0.557175\pi\)
−0.178655 + 0.983912i \(0.557175\pi\)
\(812\) 1.02175e12 0.0824786
\(813\) −1.97307e12 −0.158392
\(814\) −1.13694e13 −0.907670
\(815\) −2.50354e13 −1.98768
\(816\) −6.99498e12 −0.552308
\(817\) −5.52715e10 −0.00434013
\(818\) 1.96294e13 1.53291
\(819\) 5.79927e12 0.450397
\(820\) 4.81180e12 0.371660
\(821\) −2.66826e12 −0.204967 −0.102484 0.994735i \(-0.532679\pi\)
−0.102484 + 0.994735i \(0.532679\pi\)
\(822\) −8.73638e12 −0.667434
\(823\) 2.10292e13 1.59781 0.798904 0.601459i \(-0.205414\pi\)
0.798904 + 0.601459i \(0.205414\pi\)
\(824\) 1.28956e13 0.974470
\(825\) 1.48322e13 1.11471
\(826\) 2.26520e12 0.169315
\(827\) 1.99714e13 1.48468 0.742340 0.670023i \(-0.233716\pi\)
0.742340 + 0.670023i \(0.233716\pi\)
\(828\) −1.24196e11 −0.00918271
\(829\) 1.06510e13 0.783237 0.391619 0.920128i \(-0.371915\pi\)
0.391619 + 0.920128i \(0.371915\pi\)
\(830\) −9.61945e12 −0.703557
\(831\) −5.95251e12 −0.433007
\(832\) 9.31206e12 0.673738
\(833\) −3.46533e12 −0.249369
\(834\) 4.05641e12 0.290332
\(835\) 1.26186e12 0.0898298
\(836\) 1.40436e13 0.994377
\(837\) −9.72922e11 −0.0685194
\(838\) 4.46076e12 0.312472
\(839\) −1.34668e13 −0.938289 −0.469145 0.883121i \(-0.655438\pi\)
−0.469145 + 0.883121i \(0.655438\pi\)
\(840\) −1.11604e13 −0.773435
\(841\) −1.35964e13 −0.937223
\(842\) −5.10624e12 −0.350104
\(843\) −1.54374e13 −1.05281
\(844\) −6.46545e12 −0.438589
\(845\) −8.33922e12 −0.562691
\(846\) 9.74462e12 0.654031
\(847\) 3.68904e13 2.46285
\(848\) −3.43720e12 −0.228257
\(849\) 1.17414e13 0.775595
\(850\) −1.49189e13 −0.980283
\(851\) −6.61753e11 −0.0432527
\(852\) −1.96687e12 −0.127879
\(853\) 1.33396e13 0.862723 0.431362 0.902179i \(-0.358033\pi\)
0.431362 + 0.902179i \(0.358033\pi\)
\(854\) 2.77857e13 1.78756
\(855\) 1.46881e13 0.939978
\(856\) 4.67590e11 0.0297669
\(857\) 6.50528e12 0.411957 0.205979 0.978556i \(-0.433962\pi\)
0.205979 + 0.978556i \(0.433962\pi\)
\(858\) 2.17478e13 1.37000
\(859\) −8.99466e12 −0.563658 −0.281829 0.959465i \(-0.590941\pi\)
−0.281829 + 0.959465i \(0.590941\pi\)
\(860\) −1.48046e10 −0.000922899 0
\(861\) 9.55848e12 0.592754
\(862\) 2.69725e12 0.166394
\(863\) −2.37965e13 −1.46037 −0.730187 0.683248i \(-0.760567\pi\)
−0.730187 + 0.683248i \(0.760567\pi\)
\(864\) 1.75914e12 0.107396
\(865\) 2.96885e13 1.80309
\(866\) 3.05703e13 1.84701
\(867\) 3.54874e12 0.213299
\(868\) 1.96009e12 0.117202
\(869\) −3.88203e13 −2.30924
\(870\) 4.00747e12 0.237156
\(871\) −2.64271e12 −0.155585
\(872\) 2.23929e13 1.31155
\(873\) 8.07259e12 0.470380
\(874\) 3.66384e12 0.212390
\(875\) −2.53067e12 −0.145948
\(876\) −2.64903e12 −0.151991
\(877\) −3.02374e13 −1.72602 −0.863012 0.505183i \(-0.831425\pi\)
−0.863012 + 0.505183i \(0.831425\pi\)
\(878\) 3.52988e12 0.200463
\(879\) 1.15130e13 0.650486
\(880\) −5.49516e13 −3.08893
\(881\) 2.94014e13 1.64428 0.822140 0.569285i \(-0.192780\pi\)
0.822140 + 0.569285i \(0.192780\pi\)
\(882\) 2.13445e12 0.118762
\(883\) −2.29732e13 −1.27174 −0.635869 0.771797i \(-0.719358\pi\)
−0.635869 + 0.771797i \(0.719358\pi\)
\(884\) −4.88031e12 −0.268790
\(885\) 1.98214e12 0.108615
\(886\) 1.30758e13 0.712879
\(887\) 1.88614e13 1.02310 0.511548 0.859255i \(-0.329072\pi\)
0.511548 + 0.859255i \(0.329072\pi\)
\(888\) 3.90086e12 0.210524
\(889\) 2.78553e13 1.49572
\(890\) 3.41867e13 1.82642
\(891\) −3.70902e12 −0.197156
\(892\) 9.45896e12 0.500267
\(893\) −6.41350e13 −3.37492
\(894\) −1.00632e13 −0.526889
\(895\) −2.58288e13 −1.34555
\(896\) 2.66824e13 1.38306
\(897\) 1.26582e12 0.0652841
\(898\) 1.11831e13 0.573879
\(899\) 1.74709e12 0.0892063
\(900\) 2.05012e12 0.104157
\(901\) −2.97623e12 −0.150455
\(902\) 3.58451e13 1.80302
\(903\) −2.94089e10 −0.00147192
\(904\) 1.53862e13 0.766257
\(905\) −3.72829e13 −1.84753
\(906\) 2.62243e13 1.29309
\(907\) −6.04222e12 −0.296458 −0.148229 0.988953i \(-0.547357\pi\)
−0.148229 + 0.988953i \(0.547357\pi\)
\(908\) 9.27407e12 0.452777
\(909\) −9.10725e12 −0.442435
\(910\) −4.58245e13 −2.21519
\(911\) 1.53279e13 0.737307 0.368654 0.929567i \(-0.379819\pi\)
0.368654 + 0.929567i \(0.379819\pi\)
\(912\) −2.83569e13 −1.35732
\(913\) −1.59873e13 −0.761476
\(914\) 2.62358e13 1.24347
\(915\) 2.43137e13 1.14672
\(916\) −2.76351e12 −0.129697
\(917\) −1.56272e13 −0.729826
\(918\) 3.73069e12 0.173379
\(919\) 5.80728e12 0.268567 0.134283 0.990943i \(-0.457127\pi\)
0.134283 + 0.990943i \(0.457127\pi\)
\(920\) −2.43602e12 −0.112108
\(921\) −3.23030e12 −0.147936
\(922\) −8.37352e12 −0.381609
\(923\) 2.00466e13 0.909147
\(924\) 7.47233e12 0.337235
\(925\) 1.09237e13 0.490604
\(926\) −4.20715e12 −0.188035
\(927\) −9.03029e12 −0.401645
\(928\) −3.15890e12 −0.139820
\(929\) −9.08031e12 −0.399972 −0.199986 0.979799i \(-0.564090\pi\)
−0.199986 + 0.979799i \(0.564090\pi\)
\(930\) 7.68780e12 0.336999
\(931\) −1.40481e13 −0.612834
\(932\) −7.70831e12 −0.334648
\(933\) 1.80446e13 0.779614
\(934\) −3.58085e13 −1.53966
\(935\) −4.75819e13 −2.03606
\(936\) −7.46170e12 −0.317758
\(937\) −3.06374e13 −1.29845 −0.649224 0.760597i \(-0.724906\pi\)
−0.649224 + 0.760597i \(0.724906\pi\)
\(938\) −4.06995e12 −0.171663
\(939\) −2.30060e13 −0.965709
\(940\) −1.71787e13 −0.717655
\(941\) 3.17750e13 1.32109 0.660545 0.750786i \(-0.270325\pi\)
0.660545 + 0.750786i \(0.270325\pi\)
\(942\) −6.25255e11 −0.0258719
\(943\) 2.08636e12 0.0859184
\(944\) −3.82673e12 −0.156839
\(945\) 7.81523e12 0.318785
\(946\) −1.10286e11 −0.00447723
\(947\) −1.90180e13 −0.768403 −0.384202 0.923249i \(-0.625523\pi\)
−0.384202 + 0.923249i \(0.625523\pi\)
\(948\) −5.36578e12 −0.215772
\(949\) 2.69993e13 1.08057
\(950\) −6.04795e13 −2.40909
\(951\) 7.79479e12 0.309024
\(952\) 1.86568e13 0.736156
\(953\) 2.19755e13 0.863020 0.431510 0.902108i \(-0.357981\pi\)
0.431510 + 0.902108i \(0.357981\pi\)
\(954\) 1.83319e12 0.0716540
\(955\) −5.28445e13 −2.05582
\(956\) 7.72650e11 0.0299173
\(957\) 6.66032e12 0.256679
\(958\) 3.93110e12 0.150789
\(959\) 3.05942e13 1.16803
\(960\) 1.25491e13 0.476863
\(961\) −2.30881e13 −0.873238
\(962\) 1.60169e13 0.602961
\(963\) −3.27436e11 −0.0122690
\(964\) −2.10922e12 −0.0786640
\(965\) 3.38251e13 1.25564
\(966\) 1.94945e12 0.0720304
\(967\) 2.78666e13 1.02486 0.512431 0.858728i \(-0.328745\pi\)
0.512431 + 0.858728i \(0.328745\pi\)
\(968\) −4.74655e13 −1.73756
\(969\) −2.45539e13 −0.894671
\(970\) −6.37877e13 −2.31347
\(971\) −3.36055e13 −1.21318 −0.606589 0.795016i \(-0.707462\pi\)
−0.606589 + 0.795016i \(0.707462\pi\)
\(972\) −5.12664e11 −0.0184219
\(973\) −1.42053e13 −0.508091
\(974\) −3.01224e13 −1.07244
\(975\) −2.08952e13 −0.740500
\(976\) −4.69401e13 −1.65584
\(977\) −2.76720e12 −0.0971661 −0.0485831 0.998819i \(-0.515471\pi\)
−0.0485831 + 0.998819i \(0.515471\pi\)
\(978\) −2.57781e13 −0.901003
\(979\) 5.68173e13 1.97678
\(980\) −3.76281e12 −0.130315
\(981\) −1.56809e13 −0.540580
\(982\) 1.71354e13 0.588020
\(983\) 7.12928e12 0.243531 0.121766 0.992559i \(-0.461144\pi\)
0.121766 + 0.992559i \(0.461144\pi\)
\(984\) −1.22985e13 −0.418192
\(985\) 6.03227e13 2.04182
\(986\) −6.69924e12 −0.225725
\(987\) −3.41249e13 −1.14458
\(988\) −1.97842e13 −0.660561
\(989\) −6.41916e9 −0.000213351 0
\(990\) 2.93078e13 0.969671
\(991\) 5.12279e13 1.68723 0.843616 0.536946i \(-0.180422\pi\)
0.843616 + 0.536946i \(0.180422\pi\)
\(992\) −6.05993e12 −0.198685
\(993\) −7.95468e12 −0.259628
\(994\) 3.08732e13 1.00310
\(995\) −3.75005e13 −1.21292
\(996\) −2.20978e12 −0.0711511
\(997\) −4.84414e12 −0.155270 −0.0776352 0.996982i \(-0.524737\pi\)
−0.0776352 + 0.996982i \(0.524737\pi\)
\(998\) −9.64525e12 −0.307770
\(999\) −2.73163e12 −0.0867714
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.c.1.16 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.c.1.16 22 1.1 even 1 trivial