Properties

Label 289.10.a.i.1.5
Level $289$
Weight $10$
Character 289.1
Self dual yes
Analytic conductor $148.845$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 289.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(148.845356651\)
Analytic rank: \(0\)
Dimension: \(52\)
Twist minimal: no (minimal twist has level 17)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-37.3725 q^{2} -245.740 q^{3} +884.705 q^{4} -1549.27 q^{5} +9183.93 q^{6} -9379.03 q^{7} -13928.9 q^{8} +40705.3 q^{9} +O(q^{10})\) \(q-37.3725 q^{2} -245.740 q^{3} +884.705 q^{4} -1549.27 q^{5} +9183.93 q^{6} -9379.03 q^{7} -13928.9 q^{8} +40705.3 q^{9} +57900.2 q^{10} -31847.9 q^{11} -217408. q^{12} -3836.87 q^{13} +350518. q^{14} +380719. q^{15} +67590.2 q^{16} -1.52126e6 q^{18} +704878. q^{19} -1.37065e6 q^{20} +2.30481e6 q^{21} +1.19024e6 q^{22} -141435. q^{23} +3.42290e6 q^{24} +447119. q^{25} +143393. q^{26} -5.16603e6 q^{27} -8.29768e6 q^{28} +5.40375e6 q^{29} -1.42284e7 q^{30} +8.78788e6 q^{31} +4.60560e6 q^{32} +7.82631e6 q^{33} +1.45307e7 q^{35} +3.60122e7 q^{36} -294998. q^{37} -2.63431e7 q^{38} +942873. q^{39} +2.15797e7 q^{40} +1.41403e7 q^{41} -8.61364e7 q^{42} +1.87804e7 q^{43} -2.81760e7 q^{44} -6.30636e7 q^{45} +5.28577e6 q^{46} +2.19574e7 q^{47} -1.66096e7 q^{48} +4.76127e7 q^{49} -1.67099e7 q^{50} -3.39450e6 q^{52} +8.33595e7 q^{53} +1.93067e8 q^{54} +4.93411e7 q^{55} +1.30640e8 q^{56} -1.73217e8 q^{57} -2.01952e8 q^{58} +1.05044e8 q^{59} +3.36824e8 q^{60} +9.79774e6 q^{61} -3.28425e8 q^{62} -3.81776e8 q^{63} -2.06729e8 q^{64} +5.94435e6 q^{65} -2.92489e8 q^{66} +1.49532e8 q^{67} +3.47562e7 q^{69} -5.43048e8 q^{70} -7.01885e6 q^{71} -5.66981e8 q^{72} -9.11878e7 q^{73} +1.10248e7 q^{74} -1.09875e8 q^{75} +6.23609e8 q^{76} +2.98703e8 q^{77} -3.52375e7 q^{78} -8.25648e7 q^{79} -1.04716e8 q^{80} +4.68298e8 q^{81} -5.28458e8 q^{82} -5.73696e7 q^{83} +2.03907e9 q^{84} -7.01872e8 q^{86} -1.32792e9 q^{87} +4.43607e8 q^{88} -6.66119e7 q^{89} +2.35684e9 q^{90} +3.59861e7 q^{91} -1.25128e8 q^{92} -2.15954e9 q^{93} -8.20603e8 q^{94} -1.09205e9 q^{95} -1.13178e9 q^{96} -5.74571e8 q^{97} -1.77941e9 q^{98} -1.29638e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 64q^{2} + 13312q^{4} + 49152q^{8} + 341172q^{9} + O(q^{10}) \) \( 52q + 64q^{2} + 13312q^{4} + 49152q^{8} + 341172q^{9} + 156200q^{13} + 1207872q^{15} + 3407880q^{16} + 2193336q^{18} + 1185568q^{19} + 5198336q^{21} + 13827692q^{25} + 3618944q^{26} - 9167544q^{30} + 61884888q^{32} + 1635208q^{33} + 46992776q^{35} + 156027320q^{36} + 84813952q^{38} - 4635776q^{42} + 125448912q^{43} + 164193176q^{47} + 270850284q^{49} - 226223888q^{50} + 103553016q^{52} + 426167208q^{53} + 677761520q^{55} + 375214512q^{59} + 336918024q^{60} + 190014416q^{64} + 1377178928q^{66} + 311910088q^{67} + 533688136q^{69} + 1477690280q^{70} + 2757942680q^{72} + 4047975520q^{76} + 3440336432q^{77} + 3266558756q^{81} + 2072890608q^{83} + 2630025952q^{84} + 1538547296q^{86} - 1010436256q^{87} + 1873849184q^{89} - 1998451624q^{93} - 6880776704q^{94} - 4667454128q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −37.3725 −1.65165 −0.825824 0.563928i \(-0.809289\pi\)
−0.825824 + 0.563928i \(0.809289\pi\)
\(3\) −245.740 −1.75158 −0.875792 0.482690i \(-0.839660\pi\)
−0.875792 + 0.482690i \(0.839660\pi\)
\(4\) 884.705 1.72794
\(5\) −1549.27 −1.10857 −0.554284 0.832327i \(-0.687008\pi\)
−0.554284 + 0.832327i \(0.687008\pi\)
\(6\) 9183.93 2.89300
\(7\) −9379.03 −1.47644 −0.738222 0.674558i \(-0.764334\pi\)
−0.738222 + 0.674558i \(0.764334\pi\)
\(8\) −13928.9 −1.20230
\(9\) 40705.3 2.06804
\(10\) 57900.2 1.83096
\(11\) −31847.9 −0.655864 −0.327932 0.944701i \(-0.606352\pi\)
−0.327932 + 0.944701i \(0.606352\pi\)
\(12\) −217408. −3.02663
\(13\) −3836.87 −0.0372590 −0.0186295 0.999826i \(-0.505930\pi\)
−0.0186295 + 0.999826i \(0.505930\pi\)
\(14\) 350518. 2.43856
\(15\) 380719. 1.94175
\(16\) 67590.2 0.257836
\(17\) 0 0
\(18\) −1.52126e6 −3.41568
\(19\) 704878. 1.24086 0.620430 0.784262i \(-0.286958\pi\)
0.620430 + 0.784262i \(0.286958\pi\)
\(20\) −1.37065e6 −1.91554
\(21\) 2.30481e6 2.58611
\(22\) 1.19024e6 1.08326
\(23\) −141435. −0.105385 −0.0526927 0.998611i \(-0.516780\pi\)
−0.0526927 + 0.998611i \(0.516780\pi\)
\(24\) 3.42290e6 2.10593
\(25\) 447119. 0.228925
\(26\) 143393. 0.0615388
\(27\) −5.16603e6 −1.87077
\(28\) −8.29768e6 −2.55121
\(29\) 5.40375e6 1.41874 0.709372 0.704834i \(-0.248978\pi\)
0.709372 + 0.704834i \(0.248978\pi\)
\(30\) −1.42284e7 −3.20709
\(31\) 8.78788e6 1.70906 0.854528 0.519405i \(-0.173846\pi\)
0.854528 + 0.519405i \(0.173846\pi\)
\(32\) 4.60560e6 0.776445
\(33\) 7.82631e6 1.14880
\(34\) 0 0
\(35\) 1.45307e7 1.63674
\(36\) 3.60122e7 3.57345
\(37\) −294998. −0.0258768 −0.0129384 0.999916i \(-0.504119\pi\)
−0.0129384 + 0.999916i \(0.504119\pi\)
\(38\) −2.63431e7 −2.04946
\(39\) 942873. 0.0652623
\(40\) 2.15797e7 1.33283
\(41\) 1.41403e7 0.781503 0.390752 0.920496i \(-0.372215\pi\)
0.390752 + 0.920496i \(0.372215\pi\)
\(42\) −8.61364e7 −4.27135
\(43\) 1.87804e7 0.837717 0.418858 0.908052i \(-0.362430\pi\)
0.418858 + 0.908052i \(0.362430\pi\)
\(44\) −2.81760e7 −1.13329
\(45\) −6.30636e7 −2.29257
\(46\) 5.28577e6 0.174060
\(47\) 2.19574e7 0.656357 0.328179 0.944616i \(-0.393565\pi\)
0.328179 + 0.944616i \(0.393565\pi\)
\(48\) −1.66096e7 −0.451622
\(49\) 4.76127e7 1.17989
\(50\) −1.67099e7 −0.378103
\(51\) 0 0
\(52\) −3.39450e6 −0.0643814
\(53\) 8.33595e7 1.45115 0.725577 0.688141i \(-0.241573\pi\)
0.725577 + 0.688141i \(0.241573\pi\)
\(54\) 1.93067e8 3.08985
\(55\) 4.93411e7 0.727070
\(56\) 1.30640e8 1.77513
\(57\) −1.73217e8 −2.17347
\(58\) −2.01952e8 −2.34327
\(59\) 1.05044e8 1.12860 0.564298 0.825571i \(-0.309147\pi\)
0.564298 + 0.825571i \(0.309147\pi\)
\(60\) 3.36824e8 3.35523
\(61\) 9.79774e6 0.0906028 0.0453014 0.998973i \(-0.485575\pi\)
0.0453014 + 0.998973i \(0.485575\pi\)
\(62\) −3.28425e8 −2.82276
\(63\) −3.81776e8 −3.05335
\(64\) −2.06729e8 −1.54025
\(65\) 5.94435e6 0.0413042
\(66\) −2.92489e8 −1.89741
\(67\) 1.49532e8 0.906560 0.453280 0.891368i \(-0.350254\pi\)
0.453280 + 0.891368i \(0.350254\pi\)
\(68\) 0 0
\(69\) 3.47562e7 0.184591
\(70\) −5.43048e8 −2.70332
\(71\) −7.01885e6 −0.0327796 −0.0163898 0.999866i \(-0.505217\pi\)
−0.0163898 + 0.999866i \(0.505217\pi\)
\(72\) −5.66981e8 −2.48641
\(73\) −9.11878e7 −0.375824 −0.187912 0.982186i \(-0.560172\pi\)
−0.187912 + 0.982186i \(0.560172\pi\)
\(74\) 1.10248e7 0.0427394
\(75\) −1.09875e8 −0.400981
\(76\) 6.23609e8 2.14413
\(77\) 2.98703e8 0.968346
\(78\) −3.52375e7 −0.107790
\(79\) −8.25648e7 −0.238492 −0.119246 0.992865i \(-0.538048\pi\)
−0.119246 + 0.992865i \(0.538048\pi\)
\(80\) −1.04716e8 −0.285829
\(81\) 4.68298e8 1.20876
\(82\) −5.28458e8 −1.29077
\(83\) −5.73696e7 −0.132688 −0.0663438 0.997797i \(-0.521133\pi\)
−0.0663438 + 0.997797i \(0.521133\pi\)
\(84\) 2.03907e9 4.46865
\(85\) 0 0
\(86\) −7.01872e8 −1.38361
\(87\) −1.32792e9 −2.48505
\(88\) 4.43607e8 0.788545
\(89\) −6.66119e7 −0.112537 −0.0562687 0.998416i \(-0.517920\pi\)
−0.0562687 + 0.998416i \(0.517920\pi\)
\(90\) 2.35684e9 3.78651
\(91\) 3.59861e7 0.0550109
\(92\) −1.25128e8 −0.182100
\(93\) −2.15954e9 −2.99355
\(94\) −8.20603e8 −1.08407
\(95\) −1.09205e9 −1.37558
\(96\) −1.13178e9 −1.36001
\(97\) −5.74571e8 −0.658978 −0.329489 0.944159i \(-0.606876\pi\)
−0.329489 + 0.944159i \(0.606876\pi\)
\(98\) −1.77941e9 −1.94876
\(99\) −1.29638e9 −1.35636
\(100\) 3.95568e8 0.395568
\(101\) −4.50136e8 −0.430425 −0.215213 0.976567i \(-0.569044\pi\)
−0.215213 + 0.976567i \(0.569044\pi\)
\(102\) 0 0
\(103\) −7.34932e8 −0.643398 −0.321699 0.946842i \(-0.604254\pi\)
−0.321699 + 0.946842i \(0.604254\pi\)
\(104\) 5.34435e7 0.0447965
\(105\) −3.57077e9 −2.86689
\(106\) −3.11535e9 −2.39679
\(107\) −1.23544e9 −0.911161 −0.455580 0.890195i \(-0.650568\pi\)
−0.455580 + 0.890195i \(0.650568\pi\)
\(108\) −4.57041e9 −3.23257
\(109\) 3.55565e8 0.241268 0.120634 0.992697i \(-0.461507\pi\)
0.120634 + 0.992697i \(0.461507\pi\)
\(110\) −1.84400e9 −1.20086
\(111\) 7.24929e7 0.0453254
\(112\) −6.33931e8 −0.380681
\(113\) 7.14356e8 0.412156 0.206078 0.978536i \(-0.433930\pi\)
0.206078 + 0.978536i \(0.433930\pi\)
\(114\) 6.47355e9 3.58980
\(115\) 2.19121e8 0.116827
\(116\) 4.78073e9 2.45151
\(117\) −1.56181e8 −0.0770533
\(118\) −3.92577e9 −1.86404
\(119\) 0 0
\(120\) −5.30300e9 −2.33457
\(121\) −1.34366e9 −0.569842
\(122\) −3.66166e8 −0.149644
\(123\) −3.47484e9 −1.36887
\(124\) 7.77468e9 2.95315
\(125\) 2.33321e9 0.854790
\(126\) 1.42679e10 5.04306
\(127\) 1.03138e9 0.351806 0.175903 0.984407i \(-0.443715\pi\)
0.175903 + 0.984407i \(0.443715\pi\)
\(128\) 5.36792e9 1.76751
\(129\) −4.61511e9 −1.46733
\(130\) −2.22155e8 −0.0682200
\(131\) 5.41553e9 1.60665 0.803324 0.595543i \(-0.203063\pi\)
0.803324 + 0.595543i \(0.203063\pi\)
\(132\) 6.92398e9 1.98506
\(133\) −6.61107e9 −1.83206
\(134\) −5.58838e9 −1.49732
\(135\) 8.00358e9 2.07387
\(136\) 0 0
\(137\) 3.16964e9 0.768718 0.384359 0.923184i \(-0.374423\pi\)
0.384359 + 0.923184i \(0.374423\pi\)
\(138\) −1.29893e9 −0.304880
\(139\) 7.17848e9 1.63104 0.815522 0.578726i \(-0.196450\pi\)
0.815522 + 0.578726i \(0.196450\pi\)
\(140\) 1.28554e10 2.82819
\(141\) −5.39582e9 −1.14966
\(142\) 2.62312e8 0.0541403
\(143\) 1.22196e8 0.0244369
\(144\) 2.75128e9 0.533217
\(145\) −8.37188e9 −1.57278
\(146\) 3.40792e9 0.620728
\(147\) −1.17004e10 −2.06667
\(148\) −2.60986e8 −0.0447136
\(149\) 9.84251e9 1.63594 0.817971 0.575260i \(-0.195099\pi\)
0.817971 + 0.575260i \(0.195099\pi\)
\(150\) 4.10631e9 0.662279
\(151\) 9.89807e9 1.54937 0.774683 0.632350i \(-0.217909\pi\)
0.774683 + 0.632350i \(0.217909\pi\)
\(152\) −9.81819e9 −1.49189
\(153\) 0 0
\(154\) −1.11633e10 −1.59937
\(155\) −1.36148e10 −1.89461
\(156\) 8.34164e8 0.112769
\(157\) −1.10838e9 −0.145593 −0.0727964 0.997347i \(-0.523192\pi\)
−0.0727964 + 0.997347i \(0.523192\pi\)
\(158\) 3.08565e9 0.393904
\(159\) −2.04848e10 −2.54182
\(160\) −7.13532e9 −0.860743
\(161\) 1.32652e9 0.155596
\(162\) −1.75015e10 −1.99645
\(163\) 1.00573e10 1.11593 0.557967 0.829863i \(-0.311582\pi\)
0.557967 + 0.829863i \(0.311582\pi\)
\(164\) 1.25100e10 1.35039
\(165\) −1.21251e10 −1.27352
\(166\) 2.14405e9 0.219153
\(167\) −4.81504e6 −0.000479044 0 −0.000239522 1.00000i \(-0.500076\pi\)
−0.000239522 1.00000i \(0.500076\pi\)
\(168\) −3.21035e10 −3.10929
\(169\) −1.05898e10 −0.998612
\(170\) 0 0
\(171\) 2.86923e10 2.56615
\(172\) 1.66151e10 1.44752
\(173\) −7.29075e9 −0.618821 −0.309410 0.950929i \(-0.600132\pi\)
−0.309410 + 0.950929i \(0.600132\pi\)
\(174\) 4.96277e10 4.10443
\(175\) −4.19354e9 −0.337994
\(176\) −2.15261e9 −0.169106
\(177\) −2.58136e10 −1.97683
\(178\) 2.48946e9 0.185872
\(179\) −4.38658e9 −0.319365 −0.159682 0.987168i \(-0.551047\pi\)
−0.159682 + 0.987168i \(0.551047\pi\)
\(180\) −5.57927e10 −3.96142
\(181\) −9.95343e9 −0.689317 −0.344659 0.938728i \(-0.612005\pi\)
−0.344659 + 0.938728i \(0.612005\pi\)
\(182\) −1.34489e9 −0.0908586
\(183\) −2.40770e9 −0.158698
\(184\) 1.97003e9 0.126705
\(185\) 4.57032e8 0.0286863
\(186\) 8.07073e10 4.94430
\(187\) 0 0
\(188\) 1.94258e10 1.13415
\(189\) 4.84523e10 2.76208
\(190\) 4.08126e10 2.27197
\(191\) −3.59313e9 −0.195354 −0.0976771 0.995218i \(-0.531141\pi\)
−0.0976771 + 0.995218i \(0.531141\pi\)
\(192\) 5.08016e10 2.69788
\(193\) 1.85484e10 0.962272 0.481136 0.876646i \(-0.340224\pi\)
0.481136 + 0.876646i \(0.340224\pi\)
\(194\) 2.14732e10 1.08840
\(195\) −1.46077e9 −0.0723477
\(196\) 4.21232e10 2.03877
\(197\) 2.31892e10 1.09695 0.548477 0.836166i \(-0.315208\pi\)
0.548477 + 0.836166i \(0.315208\pi\)
\(198\) 4.84489e10 2.24022
\(199\) 2.35070e10 1.06257 0.531287 0.847192i \(-0.321709\pi\)
0.531287 + 0.847192i \(0.321709\pi\)
\(200\) −6.22788e9 −0.275236
\(201\) −3.67460e10 −1.58792
\(202\) 1.68227e10 0.710911
\(203\) −5.06820e10 −2.09470
\(204\) 0 0
\(205\) −2.19071e10 −0.866350
\(206\) 2.74663e10 1.06267
\(207\) −5.75714e9 −0.217942
\(208\) −2.59335e8 −0.00960673
\(209\) −2.24489e10 −0.813835
\(210\) 1.33449e11 4.73508
\(211\) 2.50626e10 0.870474 0.435237 0.900316i \(-0.356665\pi\)
0.435237 + 0.900316i \(0.356665\pi\)
\(212\) 7.37485e10 2.50751
\(213\) 1.72481e9 0.0574162
\(214\) 4.61715e10 1.50492
\(215\) −2.90960e10 −0.928667
\(216\) 7.19572e10 2.24922
\(217\) −8.24218e10 −2.52333
\(218\) −1.32884e10 −0.398489
\(219\) 2.24085e10 0.658286
\(220\) 4.36523e10 1.25633
\(221\) 0 0
\(222\) −2.70924e9 −0.0748616
\(223\) 3.01971e10 0.817699 0.408850 0.912602i \(-0.365930\pi\)
0.408850 + 0.912602i \(0.365930\pi\)
\(224\) −4.31960e10 −1.14638
\(225\) 1.82001e10 0.473426
\(226\) −2.66973e10 −0.680737
\(227\) −5.94304e10 −1.48557 −0.742783 0.669532i \(-0.766495\pi\)
−0.742783 + 0.669532i \(0.766495\pi\)
\(228\) −1.53246e11 −3.75562
\(229\) 3.17019e10 0.761772 0.380886 0.924622i \(-0.375619\pi\)
0.380886 + 0.924622i \(0.375619\pi\)
\(230\) −8.18909e9 −0.192957
\(231\) −7.34033e10 −1.69614
\(232\) −7.52685e10 −1.70576
\(233\) 7.42261e10 1.64989 0.824945 0.565212i \(-0.191206\pi\)
0.824945 + 0.565212i \(0.191206\pi\)
\(234\) 5.83687e9 0.127265
\(235\) −3.40180e10 −0.727617
\(236\) 9.29333e10 1.95015
\(237\) 2.02895e10 0.417738
\(238\) 0 0
\(239\) −5.76902e10 −1.14370 −0.571850 0.820358i \(-0.693774\pi\)
−0.571850 + 0.820358i \(0.693774\pi\)
\(240\) 2.57329e10 0.500654
\(241\) −3.06790e10 −0.585820 −0.292910 0.956140i \(-0.594624\pi\)
−0.292910 + 0.956140i \(0.594624\pi\)
\(242\) 5.02159e10 0.941179
\(243\) −1.33969e10 −0.246477
\(244\) 8.66811e9 0.156556
\(245\) −7.37650e10 −1.30799
\(246\) 1.29863e11 2.26089
\(247\) −2.70452e9 −0.0462332
\(248\) −1.22406e11 −2.05480
\(249\) 1.40980e10 0.232413
\(250\) −8.71981e10 −1.41181
\(251\) 6.41373e10 1.01995 0.509975 0.860189i \(-0.329655\pi\)
0.509975 + 0.860189i \(0.329655\pi\)
\(252\) −3.37760e11 −5.27600
\(253\) 4.50440e9 0.0691185
\(254\) −3.85454e10 −0.581060
\(255\) 0 0
\(256\) −9.47673e10 −1.37905
\(257\) 9.19659e9 0.131501 0.0657503 0.997836i \(-0.479056\pi\)
0.0657503 + 0.997836i \(0.479056\pi\)
\(258\) 1.72478e11 2.42351
\(259\) 2.76680e9 0.0382057
\(260\) 5.25900e9 0.0713712
\(261\) 2.19961e11 2.93403
\(262\) −2.02392e11 −2.65361
\(263\) 6.78885e10 0.874975 0.437487 0.899225i \(-0.355868\pi\)
0.437487 + 0.899225i \(0.355868\pi\)
\(264\) −1.09012e11 −1.38120
\(265\) −1.29146e11 −1.60870
\(266\) 2.47072e11 3.02592
\(267\) 1.63692e10 0.197119
\(268\) 1.32291e11 1.56648
\(269\) 1.36377e11 1.58802 0.794009 0.607906i \(-0.207990\pi\)
0.794009 + 0.607906i \(0.207990\pi\)
\(270\) −2.99114e11 −3.42531
\(271\) 2.89117e10 0.325621 0.162810 0.986657i \(-0.447944\pi\)
0.162810 + 0.986657i \(0.447944\pi\)
\(272\) 0 0
\(273\) −8.84324e9 −0.0963561
\(274\) −1.18457e11 −1.26965
\(275\) −1.42398e10 −0.150143
\(276\) 3.07490e10 0.318963
\(277\) −1.70630e11 −1.74139 −0.870694 0.491825i \(-0.836330\pi\)
−0.870694 + 0.491825i \(0.836330\pi\)
\(278\) −2.68278e11 −2.69391
\(279\) 3.57713e11 3.53440
\(280\) −2.02397e11 −1.96785
\(281\) 7.62266e10 0.729336 0.364668 0.931138i \(-0.381182\pi\)
0.364668 + 0.931138i \(0.381182\pi\)
\(282\) 2.01655e11 1.89884
\(283\) −7.83779e10 −0.726364 −0.363182 0.931718i \(-0.618310\pi\)
−0.363182 + 0.931718i \(0.618310\pi\)
\(284\) −6.20961e9 −0.0566412
\(285\) 2.68360e11 2.40944
\(286\) −4.56678e9 −0.0403611
\(287\) −1.32622e11 −1.15385
\(288\) 1.87472e11 1.60572
\(289\) 0 0
\(290\) 3.12878e11 2.59767
\(291\) 1.41195e11 1.15426
\(292\) −8.06744e10 −0.649401
\(293\) 4.34293e10 0.344253 0.172127 0.985075i \(-0.444936\pi\)
0.172127 + 0.985075i \(0.444936\pi\)
\(294\) 4.37272e11 3.41341
\(295\) −1.62742e11 −1.25113
\(296\) 4.10901e9 0.0311117
\(297\) 1.64527e11 1.22697
\(298\) −3.67840e11 −2.70200
\(299\) 5.42666e8 0.00392656
\(300\) −9.72070e10 −0.692870
\(301\) −1.76142e11 −1.23684
\(302\) −3.69916e11 −2.55901
\(303\) 1.10617e11 0.753925
\(304\) 4.76429e10 0.319939
\(305\) −1.51794e10 −0.100439
\(306\) 0 0
\(307\) −2.26738e11 −1.45681 −0.728404 0.685148i \(-0.759738\pi\)
−0.728404 + 0.685148i \(0.759738\pi\)
\(308\) 2.64264e11 1.67324
\(309\) 1.80603e11 1.12697
\(310\) 5.08820e11 3.12922
\(311\) 2.50433e11 1.51799 0.758997 0.651094i \(-0.225690\pi\)
0.758997 + 0.651094i \(0.225690\pi\)
\(312\) −1.31332e10 −0.0784649
\(313\) 1.81824e11 1.07078 0.535390 0.844605i \(-0.320165\pi\)
0.535390 + 0.844605i \(0.320165\pi\)
\(314\) 4.14229e10 0.240468
\(315\) 5.91475e11 3.38485
\(316\) −7.30455e10 −0.412099
\(317\) −3.08703e11 −1.71701 −0.858507 0.512802i \(-0.828607\pi\)
−0.858507 + 0.512802i \(0.828607\pi\)
\(318\) 7.65568e11 4.19819
\(319\) −1.72098e11 −0.930504
\(320\) 3.20279e11 1.70747
\(321\) 3.03598e11 1.59597
\(322\) −4.95754e10 −0.256989
\(323\) 0 0
\(324\) 4.14306e11 2.08866
\(325\) −1.71553e9 −0.00852951
\(326\) −3.75868e11 −1.84313
\(327\) −8.73766e10 −0.422601
\(328\) −1.96959e11 −0.939601
\(329\) −2.05939e11 −0.969075
\(330\) 4.53145e11 2.10341
\(331\) −2.42882e11 −1.11216 −0.556082 0.831127i \(-0.687696\pi\)
−0.556082 + 0.831127i \(0.687696\pi\)
\(332\) −5.07552e10 −0.229276
\(333\) −1.20080e10 −0.0535144
\(334\) 1.79950e8 0.000791213 0
\(335\) −2.31665e11 −1.00498
\(336\) 1.55782e11 0.666794
\(337\) 1.17468e11 0.496117 0.248059 0.968745i \(-0.420207\pi\)
0.248059 + 0.968745i \(0.420207\pi\)
\(338\) 3.95767e11 1.64935
\(339\) −1.75546e11 −0.721926
\(340\) 0 0
\(341\) −2.79876e11 −1.12091
\(342\) −1.07230e12 −4.23838
\(343\) −6.80830e10 −0.265592
\(344\) −2.61591e11 −1.00719
\(345\) −5.38468e10 −0.204632
\(346\) 2.72474e11 1.02207
\(347\) 2.60408e11 0.964208 0.482104 0.876114i \(-0.339873\pi\)
0.482104 + 0.876114i \(0.339873\pi\)
\(348\) −1.17482e12 −4.29402
\(349\) −4.81285e11 −1.73655 −0.868276 0.496081i \(-0.834772\pi\)
−0.868276 + 0.496081i \(0.834772\pi\)
\(350\) 1.56723e11 0.558248
\(351\) 1.98213e10 0.0697030
\(352\) −1.46679e11 −0.509243
\(353\) 1.13877e11 0.390347 0.195173 0.980769i \(-0.437473\pi\)
0.195173 + 0.980769i \(0.437473\pi\)
\(354\) 9.64721e11 3.26503
\(355\) 1.08741e10 0.0363384
\(356\) −5.89319e10 −0.194458
\(357\) 0 0
\(358\) 1.63937e11 0.527478
\(359\) 4.78307e11 1.51978 0.759891 0.650050i \(-0.225252\pi\)
0.759891 + 0.650050i \(0.225252\pi\)
\(360\) 8.78408e11 2.75635
\(361\) 1.74165e11 0.539732
\(362\) 3.71985e11 1.13851
\(363\) 3.30191e11 0.998126
\(364\) 3.18371e10 0.0950555
\(365\) 1.41275e11 0.416626
\(366\) 8.99818e10 0.262114
\(367\) 3.77978e11 1.08760 0.543800 0.839215i \(-0.316985\pi\)
0.543800 + 0.839215i \(0.316985\pi\)
\(368\) −9.55960e9 −0.0271722
\(369\) 5.75584e11 1.61618
\(370\) −1.70804e10 −0.0473796
\(371\) −7.81831e11 −2.14255
\(372\) −1.91055e12 −5.17268
\(373\) 6.03744e10 0.161496 0.0807482 0.996735i \(-0.474269\pi\)
0.0807482 + 0.996735i \(0.474269\pi\)
\(374\) 0 0
\(375\) −5.73365e11 −1.49724
\(376\) −3.05843e11 −0.789139
\(377\) −2.07335e10 −0.0528611
\(378\) −1.81079e12 −4.56199
\(379\) 5.35886e11 1.33412 0.667062 0.745003i \(-0.267552\pi\)
0.667062 + 0.745003i \(0.267552\pi\)
\(380\) −9.66140e11 −2.37692
\(381\) −2.53453e11 −0.616218
\(382\) 1.34284e11 0.322656
\(383\) 6.19459e11 1.47102 0.735509 0.677514i \(-0.236943\pi\)
0.735509 + 0.677514i \(0.236943\pi\)
\(384\) −1.31911e12 −3.09593
\(385\) −4.62772e11 −1.07348
\(386\) −6.93199e11 −1.58933
\(387\) 7.64462e11 1.73243
\(388\) −5.08326e11 −1.13867
\(389\) 1.39515e10 0.0308921 0.0154460 0.999881i \(-0.495083\pi\)
0.0154460 + 0.999881i \(0.495083\pi\)
\(390\) 5.45925e10 0.119493
\(391\) 0 0
\(392\) −6.63194e11 −1.41858
\(393\) −1.33082e12 −2.81418
\(394\) −8.66640e11 −1.81178
\(395\) 1.27915e11 0.264384
\(396\) −1.14691e12 −2.34370
\(397\) −8.11705e11 −1.63999 −0.819995 0.572371i \(-0.806024\pi\)
−0.819995 + 0.572371i \(0.806024\pi\)
\(398\) −8.78518e11 −1.75500
\(399\) 1.62461e12 3.20900
\(400\) 3.02208e10 0.0590251
\(401\) 6.78845e10 0.131106 0.0655528 0.997849i \(-0.479119\pi\)
0.0655528 + 0.997849i \(0.479119\pi\)
\(402\) 1.37329e12 2.62268
\(403\) −3.37179e10 −0.0636778
\(404\) −3.98238e11 −0.743749
\(405\) −7.25521e11 −1.33999
\(406\) 1.89411e12 3.45970
\(407\) 9.39507e9 0.0169717
\(408\) 0 0
\(409\) −3.62017e11 −0.639697 −0.319848 0.947469i \(-0.603632\pi\)
−0.319848 + 0.947469i \(0.603632\pi\)
\(410\) 8.18725e11 1.43090
\(411\) −7.78908e11 −1.34647
\(412\) −6.50198e11 −1.11175
\(413\) −9.85215e11 −1.66631
\(414\) 2.15159e11 0.359963
\(415\) 8.88811e10 0.147093
\(416\) −1.76711e10 −0.0289296
\(417\) −1.76404e12 −2.85691
\(418\) 8.38971e11 1.34417
\(419\) −5.23509e11 −0.829777 −0.414889 0.909872i \(-0.636179\pi\)
−0.414889 + 0.909872i \(0.636179\pi\)
\(420\) −3.15908e12 −4.95381
\(421\) −3.45685e11 −0.536303 −0.268152 0.963377i \(-0.586413\pi\)
−0.268152 + 0.963377i \(0.586413\pi\)
\(422\) −9.36654e11 −1.43772
\(423\) 8.93782e11 1.35738
\(424\) −1.16111e12 −1.74472
\(425\) 0 0
\(426\) −6.44607e10 −0.0948313
\(427\) −9.18933e10 −0.133770
\(428\) −1.09300e12 −1.57443
\(429\) −3.00285e10 −0.0428032
\(430\) 1.08739e12 1.53383
\(431\) −3.61546e11 −0.504680 −0.252340 0.967639i \(-0.581200\pi\)
−0.252340 + 0.967639i \(0.581200\pi\)
\(432\) −3.49173e11 −0.482351
\(433\) −1.39065e12 −1.90118 −0.950588 0.310454i \(-0.899519\pi\)
−0.950588 + 0.310454i \(0.899519\pi\)
\(434\) 3.08031e12 4.16765
\(435\) 2.05731e12 2.75485
\(436\) 3.14570e11 0.416896
\(437\) −9.96941e10 −0.130769
\(438\) −8.37463e11 −1.08726
\(439\) 5.58212e11 0.717313 0.358656 0.933470i \(-0.383235\pi\)
0.358656 + 0.933470i \(0.383235\pi\)
\(440\) −6.87268e11 −0.874157
\(441\) 1.93809e12 2.44006
\(442\) 0 0
\(443\) 1.13238e12 1.39693 0.698463 0.715646i \(-0.253868\pi\)
0.698463 + 0.715646i \(0.253868\pi\)
\(444\) 6.41348e10 0.0783196
\(445\) 1.03200e11 0.124755
\(446\) −1.12854e12 −1.35055
\(447\) −2.41870e12 −2.86549
\(448\) 1.93892e12 2.27409
\(449\) 8.27212e11 0.960524 0.480262 0.877125i \(-0.340542\pi\)
0.480262 + 0.877125i \(0.340542\pi\)
\(450\) −6.80183e11 −0.781933
\(451\) −4.50338e11 −0.512560
\(452\) 6.31995e11 0.712181
\(453\) −2.43235e12 −2.71384
\(454\) 2.22106e12 2.45363
\(455\) −5.57523e10 −0.0609833
\(456\) 2.41273e12 2.61316
\(457\) 1.17863e12 1.26402 0.632011 0.774960i \(-0.282230\pi\)
0.632011 + 0.774960i \(0.282230\pi\)
\(458\) −1.18478e12 −1.25818
\(459\) 0 0
\(460\) 1.93857e11 0.201870
\(461\) −2.50375e11 −0.258188 −0.129094 0.991632i \(-0.541207\pi\)
−0.129094 + 0.991632i \(0.541207\pi\)
\(462\) 2.74327e12 2.80142
\(463\) 8.92342e10 0.0902437 0.0451218 0.998981i \(-0.485632\pi\)
0.0451218 + 0.998981i \(0.485632\pi\)
\(464\) 3.65241e11 0.365804
\(465\) 3.34571e12 3.31856
\(466\) −2.77402e12 −2.72504
\(467\) 7.95224e11 0.773684 0.386842 0.922146i \(-0.373566\pi\)
0.386842 + 0.922146i \(0.373566\pi\)
\(468\) −1.38174e11 −0.133143
\(469\) −1.40246e12 −1.33849
\(470\) 1.27134e12 1.20177
\(471\) 2.72373e11 0.255018
\(472\) −1.46316e12 −1.35691
\(473\) −5.98117e11 −0.549428
\(474\) −7.58270e11 −0.689956
\(475\) 3.15164e11 0.284063
\(476\) 0 0
\(477\) 3.39317e12 3.00105
\(478\) 2.15603e12 1.88899
\(479\) 6.73511e11 0.584568 0.292284 0.956332i \(-0.405585\pi\)
0.292284 + 0.956332i \(0.405585\pi\)
\(480\) 1.75344e12 1.50766
\(481\) 1.13187e9 0.000964146 0
\(482\) 1.14655e12 0.967568
\(483\) −3.25980e11 −0.272539
\(484\) −1.18874e12 −0.984653
\(485\) 8.90167e11 0.730523
\(486\) 5.00676e11 0.407093
\(487\) 1.30057e12 1.04774 0.523869 0.851799i \(-0.324488\pi\)
0.523869 + 0.851799i \(0.324488\pi\)
\(488\) −1.36472e11 −0.108932
\(489\) −2.47149e12 −1.95465
\(490\) 2.75678e12 2.16033
\(491\) 1.27535e11 0.0990288 0.0495144 0.998773i \(-0.484233\pi\)
0.0495144 + 0.998773i \(0.484233\pi\)
\(492\) −3.07421e12 −2.36532
\(493\) 0 0
\(494\) 1.01075e11 0.0763610
\(495\) 2.00844e12 1.50361
\(496\) 5.93975e11 0.440657
\(497\) 6.58300e10 0.0483972
\(498\) −5.26879e11 −0.383865
\(499\) −4.44774e11 −0.321134 −0.160567 0.987025i \(-0.551332\pi\)
−0.160567 + 0.987025i \(0.551332\pi\)
\(500\) 2.06421e12 1.47703
\(501\) 1.18325e9 0.000839086 0
\(502\) −2.39697e12 −1.68460
\(503\) 1.27414e12 0.887482 0.443741 0.896155i \(-0.353651\pi\)
0.443741 + 0.896155i \(0.353651\pi\)
\(504\) 5.31774e12 3.67104
\(505\) 6.97383e11 0.477156
\(506\) −1.68341e11 −0.114159
\(507\) 2.60234e12 1.74915
\(508\) 9.12471e11 0.607900
\(509\) −1.02878e12 −0.679348 −0.339674 0.940543i \(-0.610317\pi\)
−0.339674 + 0.940543i \(0.610317\pi\)
\(510\) 0 0
\(511\) 8.55254e11 0.554882
\(512\) 7.93321e11 0.510192
\(513\) −3.64142e12 −2.32136
\(514\) −3.43700e11 −0.217193
\(515\) 1.13861e12 0.713251
\(516\) −4.08301e12 −2.53546
\(517\) −6.99297e11 −0.430481
\(518\) −1.03402e11 −0.0631023
\(519\) 1.79163e12 1.08392
\(520\) −8.27984e10 −0.0496600
\(521\) −1.60781e11 −0.0956014 −0.0478007 0.998857i \(-0.515221\pi\)
−0.0478007 + 0.998857i \(0.515221\pi\)
\(522\) −8.22051e12 −4.84598
\(523\) 5.92253e11 0.346138 0.173069 0.984910i \(-0.444632\pi\)
0.173069 + 0.984910i \(0.444632\pi\)
\(524\) 4.79115e12 2.77619
\(525\) 1.03052e12 0.592025
\(526\) −2.53717e12 −1.44515
\(527\) 0 0
\(528\) 5.28982e11 0.296202
\(529\) −1.78115e12 −0.988894
\(530\) 4.82653e12 2.65701
\(531\) 4.27586e12 2.33399
\(532\) −5.84885e12 −3.16569
\(533\) −5.42544e10 −0.0291180
\(534\) −6.11760e11 −0.325571
\(535\) 1.91403e12 1.01008
\(536\) −2.08282e12 −1.08996
\(537\) 1.07796e12 0.559394
\(538\) −5.09675e12 −2.62285
\(539\) −1.51636e12 −0.773845
\(540\) 7.08081e12 3.58353
\(541\) −3.17243e12 −1.59222 −0.796112 0.605149i \(-0.793113\pi\)
−0.796112 + 0.605149i \(0.793113\pi\)
\(542\) −1.08050e12 −0.537810
\(543\) 2.44596e12 1.20740
\(544\) 0 0
\(545\) −5.50867e11 −0.267462
\(546\) 3.30494e11 0.159146
\(547\) −3.50051e12 −1.67182 −0.835908 0.548870i \(-0.815058\pi\)
−0.835908 + 0.548870i \(0.815058\pi\)
\(548\) 2.80419e12 1.32830
\(549\) 3.98820e11 0.187371
\(550\) 5.32177e11 0.247984
\(551\) 3.80898e12 1.76046
\(552\) −4.84117e11 −0.221934
\(553\) 7.74378e11 0.352119
\(554\) 6.37686e12 2.87616
\(555\) −1.12311e11 −0.0502464
\(556\) 6.35084e12 2.81835
\(557\) 1.35176e12 0.595045 0.297522 0.954715i \(-0.403840\pi\)
0.297522 + 0.954715i \(0.403840\pi\)
\(558\) −1.33686e13 −5.83759
\(559\) −7.20580e10 −0.0312125
\(560\) 9.82132e11 0.422011
\(561\) 0 0
\(562\) −2.84878e12 −1.20461
\(563\) 1.35952e12 0.570292 0.285146 0.958484i \(-0.407958\pi\)
0.285146 + 0.958484i \(0.407958\pi\)
\(564\) −4.77371e12 −1.98655
\(565\) −1.10673e12 −0.456903
\(566\) 2.92918e12 1.19970
\(567\) −4.39219e12 −1.78467
\(568\) 9.77651e10 0.0394109
\(569\) 1.47215e12 0.588774 0.294387 0.955686i \(-0.404885\pi\)
0.294387 + 0.955686i \(0.404885\pi\)
\(570\) −1.00293e13 −3.97954
\(571\) −2.07965e12 −0.818706 −0.409353 0.912376i \(-0.634246\pi\)
−0.409353 + 0.912376i \(0.634246\pi\)
\(572\) 1.08108e11 0.0422254
\(573\) 8.82977e11 0.342179
\(574\) 4.95642e12 1.90575
\(575\) −6.32380e10 −0.0241253
\(576\) −8.41496e12 −3.18530
\(577\) 4.38287e12 1.64614 0.823072 0.567938i \(-0.192259\pi\)
0.823072 + 0.567938i \(0.192259\pi\)
\(578\) 0 0
\(579\) −4.55808e12 −1.68550
\(580\) −7.40664e12 −2.71766
\(581\) 5.38072e11 0.195906
\(582\) −5.27682e12 −1.90642
\(583\) −2.65482e12 −0.951760
\(584\) 1.27015e12 0.451853
\(585\) 2.41967e11 0.0854189
\(586\) −1.62306e12 −0.568585
\(587\) 1.49551e12 0.519897 0.259948 0.965623i \(-0.416294\pi\)
0.259948 + 0.965623i \(0.416294\pi\)
\(588\) −1.03514e13 −3.57108
\(589\) 6.19438e12 2.12070
\(590\) 6.08209e12 2.06642
\(591\) −5.69853e12 −1.92141
\(592\) −1.99390e10 −0.00667199
\(593\) 3.53473e12 1.17384 0.586921 0.809644i \(-0.300340\pi\)
0.586921 + 0.809644i \(0.300340\pi\)
\(594\) −6.14879e12 −2.02652
\(595\) 0 0
\(596\) 8.70772e12 2.82681
\(597\) −5.77663e12 −1.86119
\(598\) −2.02808e10 −0.00648529
\(599\) −1.01514e12 −0.322186 −0.161093 0.986939i \(-0.551502\pi\)
−0.161093 + 0.986939i \(0.551502\pi\)
\(600\) 1.53044e12 0.482099
\(601\) 4.12211e12 1.28880 0.644399 0.764689i \(-0.277108\pi\)
0.644399 + 0.764689i \(0.277108\pi\)
\(602\) 6.58288e12 2.04283
\(603\) 6.08673e12 1.87481
\(604\) 8.75687e12 2.67721
\(605\) 2.08169e12 0.631709
\(606\) −4.13402e12 −1.24522
\(607\) −1.34313e12 −0.401577 −0.200789 0.979635i \(-0.564350\pi\)
−0.200789 + 0.979635i \(0.564350\pi\)
\(608\) 3.24638e12 0.963460
\(609\) 1.24546e13 3.66904
\(610\) 5.67291e11 0.165891
\(611\) −8.42476e10 −0.0244552
\(612\) 0 0
\(613\) −2.53955e11 −0.0726413 −0.0363207 0.999340i \(-0.511564\pi\)
−0.0363207 + 0.999340i \(0.511564\pi\)
\(614\) 8.47379e12 2.40613
\(615\) 5.38347e12 1.51748
\(616\) −4.16061e12 −1.16424
\(617\) −8.49667e11 −0.236029 −0.118015 0.993012i \(-0.537653\pi\)
−0.118015 + 0.993012i \(0.537653\pi\)
\(618\) −6.74957e12 −1.86135
\(619\) 2.81906e12 0.771784 0.385892 0.922544i \(-0.373894\pi\)
0.385892 + 0.922544i \(0.373894\pi\)
\(620\) −1.20451e13 −3.27377
\(621\) 7.30655e11 0.197152
\(622\) −9.35932e12 −2.50719
\(623\) 6.24756e11 0.166155
\(624\) 6.37290e10 0.0168270
\(625\) −4.48806e12 −1.17652
\(626\) −6.79520e12 −1.76855
\(627\) 5.51659e12 1.42550
\(628\) −9.80589e11 −0.251576
\(629\) 0 0
\(630\) −2.21049e13 −5.59058
\(631\) −5.32991e12 −1.33841 −0.669203 0.743080i \(-0.733364\pi\)
−0.669203 + 0.743080i \(0.733364\pi\)
\(632\) 1.15004e12 0.286738
\(633\) −6.15890e12 −1.52471
\(634\) 1.15370e13 2.83590
\(635\) −1.59789e12 −0.390002
\(636\) −1.81230e13 −4.39211
\(637\) −1.82683e11 −0.0439614
\(638\) 6.43174e12 1.53686
\(639\) −2.85704e11 −0.0677896
\(640\) −8.31636e12 −1.95940
\(641\) 7.83977e12 1.83418 0.917090 0.398679i \(-0.130531\pi\)
0.917090 + 0.398679i \(0.130531\pi\)
\(642\) −1.13462e13 −2.63599
\(643\) 7.96124e12 1.83667 0.918336 0.395802i \(-0.129533\pi\)
0.918336 + 0.395802i \(0.129533\pi\)
\(644\) 1.17358e12 0.268860
\(645\) 7.15005e12 1.62664
\(646\) 0 0
\(647\) −6.01408e12 −1.34927 −0.674636 0.738150i \(-0.735700\pi\)
−0.674636 + 0.738150i \(0.735700\pi\)
\(648\) −6.52290e12 −1.45329
\(649\) −3.34544e12 −0.740206
\(650\) 6.41138e10 0.0140877
\(651\) 2.02544e13 4.41981
\(652\) 8.89777e12 1.92827
\(653\) 3.99158e12 0.859083 0.429542 0.903047i \(-0.358675\pi\)
0.429542 + 0.903047i \(0.358675\pi\)
\(654\) 3.26548e12 0.697987
\(655\) −8.39014e12 −1.78108
\(656\) 9.55745e11 0.201500
\(657\) −3.71183e12 −0.777219
\(658\) 7.69646e12 1.60057
\(659\) 5.58329e12 1.15320 0.576601 0.817026i \(-0.304379\pi\)
0.576601 + 0.817026i \(0.304379\pi\)
\(660\) −1.07271e13 −2.20057
\(661\) −7.26295e12 −1.47981 −0.739906 0.672711i \(-0.765130\pi\)
−0.739906 + 0.672711i \(0.765130\pi\)
\(662\) 9.07710e12 1.83690
\(663\) 0 0
\(664\) 7.99098e11 0.159530
\(665\) 1.02423e13 2.03096
\(666\) 4.48768e11 0.0883870
\(667\) −7.64277e11 −0.149515
\(668\) −4.25989e9 −0.000827760 0
\(669\) −7.42065e12 −1.43227
\(670\) 8.65791e12 1.65988
\(671\) −3.12038e11 −0.0594231
\(672\) 1.06150e13 2.00798
\(673\) −2.22311e12 −0.417727 −0.208863 0.977945i \(-0.566976\pi\)
−0.208863 + 0.977945i \(0.566976\pi\)
\(674\) −4.39007e12 −0.819410
\(675\) −2.30983e12 −0.428265
\(676\) −9.36883e12 −1.72554
\(677\) −9.57742e11 −0.175226 −0.0876132 0.996155i \(-0.527924\pi\)
−0.0876132 + 0.996155i \(0.527924\pi\)
\(678\) 6.56060e12 1.19237
\(679\) 5.38892e12 0.972944
\(680\) 0 0
\(681\) 1.46044e13 2.60209
\(682\) 1.04597e13 1.85135
\(683\) 5.01362e12 0.881574 0.440787 0.897612i \(-0.354699\pi\)
0.440787 + 0.897612i \(0.354699\pi\)
\(684\) 2.53842e13 4.43415
\(685\) −4.91063e12 −0.852177
\(686\) 2.54443e12 0.438665
\(687\) −7.79043e12 −1.33431
\(688\) 1.26937e12 0.215994
\(689\) −3.19839e11 −0.0540686
\(690\) 2.01239e12 0.337980
\(691\) 2.77965e12 0.463809 0.231905 0.972739i \(-0.425504\pi\)
0.231905 + 0.972739i \(0.425504\pi\)
\(692\) −6.45017e12 −1.06929
\(693\) 1.21588e13 2.00258
\(694\) −9.73209e12 −1.59253
\(695\) −1.11214e13 −1.80812
\(696\) 1.84965e13 2.98777
\(697\) 0 0
\(698\) 1.79868e13 2.86817
\(699\) −1.82404e13 −2.88992
\(700\) −3.71005e12 −0.584034
\(701\) −2.98928e12 −0.467558 −0.233779 0.972290i \(-0.575109\pi\)
−0.233779 + 0.972290i \(0.575109\pi\)
\(702\) −7.40774e11 −0.115125
\(703\) −2.07937e11 −0.0321095
\(704\) 6.58388e12 1.01019
\(705\) 8.35959e12 1.27448
\(706\) −4.25588e12 −0.644715
\(707\) 4.22184e12 0.635498
\(708\) −2.28375e13 −3.41585
\(709\) −1.62623e12 −0.241699 −0.120850 0.992671i \(-0.538562\pi\)
−0.120850 + 0.992671i \(0.538562\pi\)
\(710\) −4.06393e11 −0.0600183
\(711\) −3.36082e12 −0.493211
\(712\) 9.27833e11 0.135304
\(713\) −1.24291e12 −0.180110
\(714\) 0 0
\(715\) −1.89315e11 −0.0270899
\(716\) −3.88083e12 −0.551843
\(717\) 1.41768e13 2.00328
\(718\) −1.78755e13 −2.51014
\(719\) −3.20372e12 −0.447069 −0.223535 0.974696i \(-0.571760\pi\)
−0.223535 + 0.974696i \(0.571760\pi\)
\(720\) −4.26248e12 −0.591107
\(721\) 6.89296e12 0.949941
\(722\) −6.50898e12 −0.891448
\(723\) 7.53906e12 1.02611
\(724\) −8.80585e12 −1.19110
\(725\) 2.41612e12 0.324786
\(726\) −1.23401e13 −1.64855
\(727\) −1.01002e13 −1.34099 −0.670495 0.741914i \(-0.733918\pi\)
−0.670495 + 0.741914i \(0.733918\pi\)
\(728\) −5.01248e11 −0.0661396
\(729\) −5.92536e12 −0.777035
\(730\) −5.27979e12 −0.688120
\(731\) 0 0
\(732\) −2.13010e12 −0.274221
\(733\) 1.50783e13 1.92923 0.964613 0.263669i \(-0.0849326\pi\)
0.964613 + 0.263669i \(0.0849326\pi\)
\(734\) −1.41260e13 −1.79633
\(735\) 1.81270e13 2.29104
\(736\) −6.51391e11 −0.0818260
\(737\) −4.76227e12 −0.594580
\(738\) −2.15110e13 −2.66936
\(739\) −4.47241e12 −0.551622 −0.275811 0.961212i \(-0.588946\pi\)
−0.275811 + 0.961212i \(0.588946\pi\)
\(740\) 4.04339e11 0.0495681
\(741\) 6.64610e11 0.0809813
\(742\) 2.92190e13 3.53873
\(743\) −1.32246e13 −1.59197 −0.795984 0.605318i \(-0.793046\pi\)
−0.795984 + 0.605318i \(0.793046\pi\)
\(744\) 3.00800e13 3.59915
\(745\) −1.52487e13 −1.81355
\(746\) −2.25634e12 −0.266735
\(747\) −2.33525e12 −0.274404
\(748\) 0 0
\(749\) 1.15872e13 1.34528
\(750\) 2.14281e13 2.47291
\(751\) 4.66313e10 0.00534931 0.00267466 0.999996i \(-0.499149\pi\)
0.00267466 + 0.999996i \(0.499149\pi\)
\(752\) 1.48411e12 0.169233
\(753\) −1.57611e13 −1.78653
\(754\) 7.74862e11 0.0873078
\(755\) −1.53348e13 −1.71758
\(756\) 4.28660e13 4.77271
\(757\) −8.50250e12 −0.941056 −0.470528 0.882385i \(-0.655936\pi\)
−0.470528 + 0.882385i \(0.655936\pi\)
\(758\) −2.00274e13 −2.20350
\(759\) −1.10691e12 −0.121067
\(760\) 1.52111e13 1.65386
\(761\) −1.78762e12 −0.193217 −0.0966083 0.995322i \(-0.530799\pi\)
−0.0966083 + 0.995322i \(0.530799\pi\)
\(762\) 9.47217e12 1.01778
\(763\) −3.33485e12 −0.356218
\(764\) −3.17886e12 −0.337560
\(765\) 0 0
\(766\) −2.31508e13 −2.42960
\(767\) −4.03041e11 −0.0420504
\(768\) 2.32882e13 2.41551
\(769\) 9.44034e12 0.973462 0.486731 0.873552i \(-0.338189\pi\)
0.486731 + 0.873552i \(0.338189\pi\)
\(770\) 1.72949e13 1.77301
\(771\) −2.25997e12 −0.230334
\(772\) 1.64098e13 1.66275
\(773\) 1.07678e12 0.108472 0.0542362 0.998528i \(-0.482728\pi\)
0.0542362 + 0.998528i \(0.482728\pi\)
\(774\) −2.85699e13 −2.86137
\(775\) 3.92922e12 0.391245
\(776\) 8.00316e12 0.792290
\(777\) −6.79913e11 −0.0669205
\(778\) −5.21402e11 −0.0510228
\(779\) 9.96717e12 0.969736
\(780\) −1.29235e12 −0.125013
\(781\) 2.23536e11 0.0214990
\(782\) 0 0
\(783\) −2.79159e13 −2.65414
\(784\) 3.21815e12 0.304218
\(785\) 1.71718e12 0.161400
\(786\) 4.97359e13 4.64803
\(787\) 6.72445e11 0.0624842 0.0312421 0.999512i \(-0.490054\pi\)
0.0312421 + 0.999512i \(0.490054\pi\)
\(788\) 2.05156e13 1.89547
\(789\) −1.66829e13 −1.53259
\(790\) −4.78052e12 −0.436670
\(791\) −6.69997e12 −0.608525
\(792\) 1.80572e13 1.63075
\(793\) −3.75926e10 −0.00337577
\(794\) 3.03355e13 2.70868
\(795\) 3.17365e13 2.81778
\(796\) 2.07968e13 1.83606
\(797\) 7.96983e12 0.699659 0.349829 0.936813i \(-0.386240\pi\)
0.349829 + 0.936813i \(0.386240\pi\)
\(798\) −6.07157e13 −5.30014
\(799\) 0 0
\(800\) 2.05925e12 0.177748
\(801\) −2.71146e12 −0.232732
\(802\) −2.53702e12 −0.216540
\(803\) 2.90414e12 0.246489
\(804\) −3.25093e13 −2.74382
\(805\) −2.05514e12 −0.172488
\(806\) 1.26012e12 0.105173
\(807\) −3.35133e13 −2.78155
\(808\) 6.26991e12 0.517500
\(809\) −1.71821e12 −0.141029 −0.0705146 0.997511i \(-0.522464\pi\)
−0.0705146 + 0.997511i \(0.522464\pi\)
\(810\) 2.71146e13 2.21320
\(811\) 1.78570e13 1.44949 0.724743 0.689019i \(-0.241959\pi\)
0.724743 + 0.689019i \(0.241959\pi\)
\(812\) −4.48386e13 −3.61951
\(813\) −7.10477e12 −0.570351
\(814\) −3.51117e11 −0.0280312
\(815\) −1.55815e13 −1.23709
\(816\) 0 0
\(817\) 1.32379e13 1.03949
\(818\) 1.35295e13 1.05655
\(819\) 1.46482e12 0.113765
\(820\) −1.93814e13 −1.49700
\(821\) −1.45867e13 −1.12051 −0.560253 0.828322i \(-0.689296\pi\)
−0.560253 + 0.828322i \(0.689296\pi\)
\(822\) 2.91097e13 2.22390
\(823\) 9.62246e12 0.731117 0.365559 0.930788i \(-0.380878\pi\)
0.365559 + 0.930788i \(0.380878\pi\)
\(824\) 1.02368e13 0.773558
\(825\) 3.49929e12 0.262989
\(826\) 3.68200e13 2.75216
\(827\) −2.45399e13 −1.82430 −0.912152 0.409852i \(-0.865580\pi\)
−0.912152 + 0.409852i \(0.865580\pi\)
\(828\) −5.09337e12 −0.376590
\(829\) 8.58781e12 0.631520 0.315760 0.948839i \(-0.397741\pi\)
0.315760 + 0.948839i \(0.397741\pi\)
\(830\) −3.32171e12 −0.242946
\(831\) 4.19306e13 3.05019
\(832\) 7.93191e11 0.0573882
\(833\) 0 0
\(834\) 6.59267e13 4.71861
\(835\) 7.45981e9 0.000531054 0
\(836\) −1.98606e13 −1.40626
\(837\) −4.53984e13 −3.19725
\(838\) 1.95649e13 1.37050
\(839\) 1.66622e13 1.16092 0.580461 0.814288i \(-0.302872\pi\)
0.580461 + 0.814288i \(0.302872\pi\)
\(840\) 4.97370e13 3.44686
\(841\) 1.46934e13 1.01284
\(842\) 1.29191e13 0.885784
\(843\) −1.87319e13 −1.27749
\(844\) 2.21730e13 1.50413
\(845\) 1.64064e13 1.10703
\(846\) −3.34029e13 −2.24191
\(847\) 1.26022e13 0.841340
\(848\) 5.63428e12 0.374160
\(849\) 1.92606e13 1.27229
\(850\) 0 0
\(851\) 4.17229e10 0.00272704
\(852\) 1.52595e12 0.0992117
\(853\) −1.23286e13 −0.797342 −0.398671 0.917094i \(-0.630528\pi\)
−0.398671 + 0.917094i \(0.630528\pi\)
\(854\) 3.43429e12 0.220941
\(855\) −4.44521e13 −2.84476
\(856\) 1.72084e13 1.09549
\(857\) −3.69217e12 −0.233813 −0.116906 0.993143i \(-0.537298\pi\)
−0.116906 + 0.993143i \(0.537298\pi\)
\(858\) 1.12224e12 0.0706958
\(859\) −3.06191e13 −1.91877 −0.959385 0.282101i \(-0.908969\pi\)
−0.959385 + 0.282101i \(0.908969\pi\)
\(860\) −2.57414e13 −1.60468
\(861\) 3.25906e13 2.02106
\(862\) 1.35119e13 0.833554
\(863\) 1.76323e13 1.08208 0.541042 0.840996i \(-0.318030\pi\)
0.541042 + 0.840996i \(0.318030\pi\)
\(864\) −2.37926e13 −1.45255
\(865\) 1.12954e13 0.686006
\(866\) 5.19721e13 3.14007
\(867\) 0 0
\(868\) −7.29190e13 −4.36016
\(869\) 2.62952e12 0.156418
\(870\) −7.68868e13 −4.55004
\(871\) −5.73733e11 −0.0337776
\(872\) −4.95264e12 −0.290076
\(873\) −2.33881e13 −1.36280
\(874\) 3.72582e12 0.215983
\(875\) −2.18833e13 −1.26205
\(876\) 1.98249e13 1.13748
\(877\) −8.61760e12 −0.491913 −0.245956 0.969281i \(-0.579102\pi\)
−0.245956 + 0.969281i \(0.579102\pi\)
\(878\) −2.08618e13 −1.18475
\(879\) −1.06723e13 −0.602989
\(880\) 3.33497e12 0.187465
\(881\) 1.33579e13 0.747043 0.373521 0.927622i \(-0.378150\pi\)
0.373521 + 0.927622i \(0.378150\pi\)
\(882\) −7.24312e13 −4.03011
\(883\) −6.98562e12 −0.386707 −0.193354 0.981129i \(-0.561936\pi\)
−0.193354 + 0.981129i \(0.561936\pi\)
\(884\) 0 0
\(885\) 3.99924e13 2.19145
\(886\) −4.23197e13 −2.30723
\(887\) 3.15821e13 1.71311 0.856555 0.516056i \(-0.172600\pi\)
0.856555 + 0.516056i \(0.172600\pi\)
\(888\) −1.00975e12 −0.0544948
\(889\) −9.67339e12 −0.519422
\(890\) −3.85684e12 −0.206052
\(891\) −1.49143e13 −0.792782
\(892\) 2.67155e13 1.41294
\(893\) 1.54773e13 0.814447
\(894\) 9.03930e13 4.73278
\(895\) 6.79600e12 0.354038
\(896\) −5.03459e13 −2.60962
\(897\) −1.33355e11 −0.00687769
\(898\) −3.09150e13 −1.58645
\(899\) 4.74875e13 2.42471
\(900\) 1.61017e13 0.818052
\(901\) 0 0
\(902\) 1.68303e13 0.846568
\(903\) 4.32852e13 2.16643
\(904\) −9.95022e12 −0.495535
\(905\) 1.54206e13 0.764156
\(906\) 9.09032e13 4.48231
\(907\) −3.17616e12 −0.155837 −0.0779183 0.996960i \(-0.524827\pi\)
−0.0779183 + 0.996960i \(0.524827\pi\)
\(908\) −5.25784e13 −2.56697
\(909\) −1.83229e13 −0.890138
\(910\) 2.08360e12 0.100723
\(911\) −7.76844e12 −0.373681 −0.186840 0.982390i \(-0.559825\pi\)
−0.186840 + 0.982390i \(0.559825\pi\)
\(912\) −1.17078e13 −0.560399
\(913\) 1.82710e12 0.0870251
\(914\) −4.40484e13 −2.08772
\(915\) 3.73018e12 0.175928
\(916\) 2.80468e13 1.31630
\(917\) −5.07925e13 −2.37212
\(918\) 0 0
\(919\) −2.31177e13 −1.06912 −0.534559 0.845131i \(-0.679522\pi\)
−0.534559 + 0.845131i \(0.679522\pi\)
\(920\) −3.05212e12 −0.140461
\(921\) 5.57188e13 2.55172
\(922\) 9.35713e12 0.426436
\(923\) 2.69304e10 0.00122134
\(924\) −6.49403e13 −2.93083
\(925\) −1.31899e11 −0.00592385
\(926\) −3.33491e12 −0.149051
\(927\) −2.99156e13 −1.33058
\(928\) 2.48875e13 1.10158
\(929\) −3.14470e13 −1.38519 −0.692593 0.721329i \(-0.743532\pi\)
−0.692593 + 0.721329i \(0.743532\pi\)
\(930\) −1.25038e14 −5.48109
\(931\) 3.35611e13 1.46407
\(932\) 6.56682e13 2.85091
\(933\) −6.15415e13 −2.65889
\(934\) −2.97195e13 −1.27785
\(935\) 0 0
\(936\) 2.17543e12 0.0926412
\(937\) −3.04920e13 −1.29228 −0.646142 0.763217i \(-0.723619\pi\)
−0.646142 + 0.763217i \(0.723619\pi\)
\(938\) 5.24136e13 2.21071
\(939\) −4.46814e13 −1.87556
\(940\) −3.00959e13 −1.25728
\(941\) −2.55953e13 −1.06416 −0.532081 0.846694i \(-0.678590\pi\)
−0.532081 + 0.846694i \(0.678590\pi\)
\(942\) −1.01793e13 −0.421200
\(943\) −1.99993e12 −0.0823590
\(944\) 7.09998e12 0.290993
\(945\) −7.50658e13 −3.06196
\(946\) 2.23531e13 0.907462
\(947\) −1.98034e13 −0.800137 −0.400069 0.916485i \(-0.631014\pi\)
−0.400069 + 0.916485i \(0.631014\pi\)
\(948\) 1.79502e13 0.721826
\(949\) 3.49876e11 0.0140028
\(950\) −1.17785e13 −0.469173
\(951\) 7.58607e13 3.00749
\(952\) 0 0
\(953\) −3.81669e13 −1.49889 −0.749444 0.662068i \(-0.769679\pi\)
−0.749444 + 0.662068i \(0.769679\pi\)
\(954\) −1.26811e14 −4.95668
\(955\) 5.56673e12 0.216564
\(956\) −5.10389e13 −1.97624
\(957\) 4.22914e13 1.62985
\(958\) −2.51708e13 −0.965500
\(959\) −2.97281e13 −1.13497
\(960\) −7.87055e13 −2.99078
\(961\) 5.07872e13 1.92087
\(962\) −4.23007e10 −0.00159243
\(963\) −5.02890e13 −1.88432
\(964\) −2.71418e13 −1.01226
\(965\) −2.87365e13 −1.06674
\(966\) 1.21827e13 0.450138
\(967\) −4.29739e13 −1.58047 −0.790234 0.612805i \(-0.790041\pi\)
−0.790234 + 0.612805i \(0.790041\pi\)
\(968\) 1.87157e13 0.685122
\(969\) 0 0
\(970\) −3.32678e13 −1.20657
\(971\) 1.07872e13 0.389425 0.194712 0.980860i \(-0.437623\pi\)
0.194712 + 0.980860i \(0.437623\pi\)
\(972\) −1.18523e13 −0.425897
\(973\) −6.73272e13 −2.40815
\(974\) −4.86055e13 −1.73049
\(975\) 4.21576e11 0.0149401
\(976\) 6.62232e11 0.0233607
\(977\) 1.08674e13 0.381594 0.190797 0.981629i \(-0.438893\pi\)
0.190797 + 0.981629i \(0.438893\pi\)
\(978\) 9.23658e13 3.22839
\(979\) 2.12145e12 0.0738093
\(980\) −6.52603e13 −2.26012
\(981\) 1.44734e13 0.498952
\(982\) −4.76629e12 −0.163561
\(983\) −1.21504e13 −0.415050 −0.207525 0.978230i \(-0.566541\pi\)
−0.207525 + 0.978230i \(0.566541\pi\)
\(984\) 4.84008e13 1.64579
\(985\) −3.59264e13 −1.21605
\(986\) 0 0
\(987\) 5.06075e13 1.69742
\(988\) −2.39270e12 −0.0798882
\(989\) −2.65620e12 −0.0882831
\(990\) −7.50606e13 −2.48344
\(991\) 1.69943e13 0.559723 0.279861 0.960040i \(-0.409712\pi\)
0.279861 + 0.960040i \(0.409712\pi\)
\(992\) 4.04734e13 1.32699
\(993\) 5.96858e13 1.94805
\(994\) −2.46023e12 −0.0799352
\(995\) −3.64188e13 −1.17794
\(996\) 1.24726e13 0.401597
\(997\) 4.80699e13 1.54079 0.770397 0.637564i \(-0.220058\pi\)
0.770397 + 0.637564i \(0.220058\pi\)
\(998\) 1.66223e13 0.530401
\(999\) 1.52397e12 0.0484095
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 289.10.a.i.1.5 52
17.10 odd 16 17.10.d.a.15.12 yes 52
17.12 odd 16 17.10.d.a.8.12 52
17.16 even 2 inner 289.10.a.i.1.6 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.10.d.a.8.12 52 17.12 odd 16
17.10.d.a.15.12 yes 52 17.10 odd 16
289.10.a.i.1.5 52 1.1 even 1 trivial
289.10.a.i.1.6 52 17.16 even 2 inner