Properties

Label 289.10.a.i.1.9
Level $289$
Weight $10$
Character 289.1
Self dual yes
Analytic conductor $148.845$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $2$

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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 1.9
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-31.9341 q^{2} -159.334 q^{3} +507.789 q^{4} +1397.46 q^{5} +5088.20 q^{6} -9976.78 q^{7} +134.480 q^{8} +5704.34 q^{9} +O(q^{10})\) \(q-31.9341 q^{2} -159.334 q^{3} +507.789 q^{4} +1397.46 q^{5} +5088.20 q^{6} -9976.78 q^{7} +134.480 q^{8} +5704.34 q^{9} -44626.6 q^{10} +50614.6 q^{11} -80908.1 q^{12} -76005.9 q^{13} +318600. q^{14} -222662. q^{15} -264282. q^{16} -182163. q^{18} -650626. q^{19} +709613. q^{20} +1.58964e6 q^{21} -1.61633e6 q^{22} -592123. q^{23} -21427.2 q^{24} -239.413 q^{25} +2.42718e6 q^{26} +2.22728e6 q^{27} -5.06610e6 q^{28} -3.53259e6 q^{29} +7.11053e6 q^{30} +3.41000e6 q^{31} +8.37077e6 q^{32} -8.06462e6 q^{33} -1.39421e7 q^{35} +2.89660e6 q^{36} +6.22732e6 q^{37} +2.07772e7 q^{38} +1.21103e7 q^{39} +187930. q^{40} -16809.2 q^{41} -5.07638e7 q^{42} +3.25305e7 q^{43} +2.57015e7 q^{44} +7.97157e6 q^{45} +1.89089e7 q^{46} -5.02215e7 q^{47} +4.21092e7 q^{48} +5.91825e7 q^{49} +7645.44 q^{50} -3.85949e7 q^{52} +1.56012e7 q^{53} -7.11261e7 q^{54} +7.07317e7 q^{55} -1.34168e6 q^{56} +1.03667e8 q^{57} +1.12810e8 q^{58} +1.62168e8 q^{59} -1.13066e8 q^{60} -1.55917e8 q^{61} -1.08895e8 q^{62} -5.69110e7 q^{63} -1.32001e8 q^{64} -1.06215e8 q^{65} +2.57537e8 q^{66} -2.74298e8 q^{67} +9.43453e7 q^{69} +4.45229e8 q^{70} -2.72244e8 q^{71} +767119. q^{72} +8.57367e6 q^{73} -1.98864e8 q^{74} +38146.6 q^{75} -3.30381e8 q^{76} -5.04970e8 q^{77} -3.86733e8 q^{78} -2.87273e8 q^{79} -3.69323e8 q^{80} -4.67160e8 q^{81} +536788. q^{82} -3.71797e8 q^{83} +8.07202e8 q^{84} -1.03883e9 q^{86} +5.62862e8 q^{87} +6.80664e6 q^{88} -4.29631e8 q^{89} -2.54565e8 q^{90} +7.58294e8 q^{91} -3.00673e8 q^{92} -5.43330e8 q^{93} +1.60378e9 q^{94} -9.09222e8 q^{95} -1.33375e9 q^{96} -1.01912e9 q^{97} -1.88994e9 q^{98} +2.88723e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 64q^{2} + 13312q^{4} + 49152q^{8} + 341172q^{9} + O(q^{10}) \) \( 52q + 64q^{2} + 13312q^{4} + 49152q^{8} + 341172q^{9} + 156200q^{13} + 1207872q^{15} + 3407880q^{16} + 2193336q^{18} + 1185568q^{19} + 5198336q^{21} + 13827692q^{25} + 3618944q^{26} - 9167544q^{30} + 61884888q^{32} + 1635208q^{33} + 46992776q^{35} + 156027320q^{36} + 84813952q^{38} - 4635776q^{42} + 125448912q^{43} + 164193176q^{47} + 270850284q^{49} - 226223888q^{50} + 103553016q^{52} + 426167208q^{53} + 677761520q^{55} + 375214512q^{59} + 336918024q^{60} + 190014416q^{64} + 1377178928q^{66} + 311910088q^{67} + 533688136q^{69} + 1477690280q^{70} + 2757942680q^{72} + 4047975520q^{76} + 3440336432q^{77} + 3266558756q^{81} + 2072890608q^{83} + 2630025952q^{84} + 1538547296q^{86} - 1010436256q^{87} + 1873849184q^{89} - 1998451624q^{93} - 6880776704q^{94} - 4667454128q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −31.9341 −1.41130 −0.705651 0.708559i \(-0.749345\pi\)
−0.705651 + 0.708559i \(0.749345\pi\)
\(3\) −159.334 −1.13570 −0.567849 0.823133i \(-0.692224\pi\)
−0.567849 + 0.823133i \(0.692224\pi\)
\(4\) 507.789 0.991775
\(5\) 1397.46 0.999939 0.499969 0.866043i \(-0.333345\pi\)
0.499969 + 0.866043i \(0.333345\pi\)
\(6\) 5088.20 1.60281
\(7\) −9976.78 −1.57054 −0.785270 0.619153i \(-0.787476\pi\)
−0.785270 + 0.619153i \(0.787476\pi\)
\(8\) 134.480 0.0116079
\(9\) 5704.34 0.289811
\(10\) −44626.6 −1.41122
\(11\) 50614.6 1.04234 0.521169 0.853454i \(-0.325496\pi\)
0.521169 + 0.853454i \(0.325496\pi\)
\(12\) −80908.1 −1.12636
\(13\) −76005.9 −0.738078 −0.369039 0.929414i \(-0.620313\pi\)
−0.369039 + 0.929414i \(0.620313\pi\)
\(14\) 318600. 2.21651
\(15\) −222662. −1.13563
\(16\) −264282. −1.00816
\(17\) 0 0
\(18\) −182163. −0.409011
\(19\) −650626. −1.14536 −0.572678 0.819781i \(-0.694095\pi\)
−0.572678 + 0.819781i \(0.694095\pi\)
\(20\) 709613. 0.991714
\(21\) 1.58964e6 1.78366
\(22\) −1.61633e6 −1.47105
\(23\) −592123. −0.441201 −0.220600 0.975364i \(-0.570802\pi\)
−0.220600 + 0.975364i \(0.570802\pi\)
\(24\) −21427.2 −0.0131830
\(25\) −239.413 −0.000122579 0
\(26\) 2.42718e6 1.04165
\(27\) 2.22728e6 0.806561
\(28\) −5.06610e6 −1.55762
\(29\) −3.53259e6 −0.927475 −0.463737 0.885973i \(-0.653492\pi\)
−0.463737 + 0.885973i \(0.653492\pi\)
\(30\) 7.11053e6 1.60272
\(31\) 3.41000e6 0.663173 0.331587 0.943425i \(-0.392416\pi\)
0.331587 + 0.943425i \(0.392416\pi\)
\(32\) 8.37077e6 1.41121
\(33\) −8.06462e6 −1.18378
\(34\) 0 0
\(35\) −1.39421e7 −1.57044
\(36\) 2.89660e6 0.287427
\(37\) 6.22732e6 0.546253 0.273126 0.961978i \(-0.411942\pi\)
0.273126 + 0.961978i \(0.411942\pi\)
\(38\) 2.07772e7 1.61644
\(39\) 1.21103e7 0.838234
\(40\) 187930. 0.0116072
\(41\) −16809.2 −0.000929011 0 −0.000464505 1.00000i \(-0.500148\pi\)
−0.000464505 1.00000i \(0.500148\pi\)
\(42\) −5.07638e7 −2.51728
\(43\) 3.25305e7 1.45105 0.725525 0.688196i \(-0.241597\pi\)
0.725525 + 0.688196i \(0.241597\pi\)
\(44\) 2.57015e7 1.03376
\(45\) 7.97157e6 0.289793
\(46\) 1.89089e7 0.622668
\(47\) −5.02215e7 −1.50124 −0.750619 0.660736i \(-0.770244\pi\)
−0.750619 + 0.660736i \(0.770244\pi\)
\(48\) 4.21092e7 1.14496
\(49\) 5.91825e7 1.46660
\(50\) 7645.44 0.000172997 0
\(51\) 0 0
\(52\) −3.85949e7 −0.732007
\(53\) 1.56012e7 0.271592 0.135796 0.990737i \(-0.456641\pi\)
0.135796 + 0.990737i \(0.456641\pi\)
\(54\) −7.11261e7 −1.13830
\(55\) 7.07317e7 1.04227
\(56\) −1.34168e6 −0.0182306
\(57\) 1.03667e8 1.30078
\(58\) 1.12810e8 1.30895
\(59\) 1.62168e8 1.74233 0.871165 0.490991i \(-0.163365\pi\)
0.871165 + 0.490991i \(0.163365\pi\)
\(60\) −1.13066e8 −1.12629
\(61\) −1.55917e8 −1.44181 −0.720906 0.693033i \(-0.756274\pi\)
−0.720906 + 0.693033i \(0.756274\pi\)
\(62\) −1.08895e8 −0.935938
\(63\) −5.69110e7 −0.455159
\(64\) −1.32001e8 −0.983483
\(65\) −1.06215e8 −0.738033
\(66\) 2.57537e8 1.67067
\(67\) −2.74298e8 −1.66298 −0.831488 0.555542i \(-0.812511\pi\)
−0.831488 + 0.555542i \(0.812511\pi\)
\(68\) 0 0
\(69\) 9.43453e7 0.501071
\(70\) 4.45229e8 2.21637
\(71\) −2.72244e8 −1.27144 −0.635721 0.771919i \(-0.719297\pi\)
−0.635721 + 0.771919i \(0.719297\pi\)
\(72\) 767119. 0.00336408
\(73\) 8.57367e6 0.0353357 0.0176679 0.999844i \(-0.494376\pi\)
0.0176679 + 0.999844i \(0.494376\pi\)
\(74\) −1.98864e8 −0.770928
\(75\) 38146.6 0.000139213 0
\(76\) −3.30381e8 −1.13593
\(77\) −5.04970e8 −1.63703
\(78\) −3.86733e8 −1.18300
\(79\) −2.87273e8 −0.829799 −0.414899 0.909867i \(-0.636183\pi\)
−0.414899 + 0.909867i \(0.636183\pi\)
\(80\) −3.69323e8 −1.00810
\(81\) −4.67160e8 −1.20582
\(82\) 536788. 0.00131112
\(83\) −3.71797e8 −0.859913 −0.429956 0.902850i \(-0.641471\pi\)
−0.429956 + 0.902850i \(0.641471\pi\)
\(84\) 8.07202e8 1.76899
\(85\) 0 0
\(86\) −1.03883e9 −2.04787
\(87\) 5.62862e8 1.05333
\(88\) 6.80664e6 0.0120993
\(89\) −4.29631e8 −0.725839 −0.362919 0.931821i \(-0.618220\pi\)
−0.362919 + 0.931821i \(0.618220\pi\)
\(90\) −2.54565e8 −0.408986
\(91\) 7.58294e8 1.15918
\(92\) −3.00673e8 −0.437572
\(93\) −5.43330e8 −0.753165
\(94\) 1.60378e9 2.11870
\(95\) −9.09222e8 −1.14529
\(96\) −1.33375e9 −1.60271
\(97\) −1.01912e9 −1.16884 −0.584418 0.811453i \(-0.698677\pi\)
−0.584418 + 0.811453i \(0.698677\pi\)
\(98\) −1.88994e9 −2.06981
\(99\) 2.88723e8 0.302081
\(100\) −121571. −0.000121571 0
\(101\) −5.60377e8 −0.535838 −0.267919 0.963441i \(-0.586336\pi\)
−0.267919 + 0.963441i \(0.586336\pi\)
\(102\) 0 0
\(103\) −1.44725e8 −0.126699 −0.0633497 0.997991i \(-0.520178\pi\)
−0.0633497 + 0.997991i \(0.520178\pi\)
\(104\) −1.02213e7 −0.00856751
\(105\) 2.22145e9 1.78355
\(106\) −4.98212e8 −0.383299
\(107\) −1.91158e9 −1.40983 −0.704914 0.709293i \(-0.749014\pi\)
−0.704914 + 0.709293i \(0.749014\pi\)
\(108\) 1.13099e9 0.799927
\(109\) 2.42408e9 1.64485 0.822426 0.568872i \(-0.192620\pi\)
0.822426 + 0.568872i \(0.192620\pi\)
\(110\) −2.25875e9 −1.47096
\(111\) −9.92225e8 −0.620379
\(112\) 2.63669e9 1.58335
\(113\) −1.14662e9 −0.661555 −0.330777 0.943709i \(-0.607311\pi\)
−0.330777 + 0.943709i \(0.607311\pi\)
\(114\) −3.31051e9 −1.83579
\(115\) −8.27466e8 −0.441174
\(116\) −1.79381e9 −0.919846
\(117\) −4.33564e8 −0.213903
\(118\) −5.17869e9 −2.45895
\(119\) 0 0
\(120\) −2.99436e7 −0.0131822
\(121\) 2.03886e8 0.0864676
\(122\) 4.97907e9 2.03483
\(123\) 2.67828e6 0.00105508
\(124\) 1.73156e9 0.657719
\(125\) −2.72974e9 −1.00006
\(126\) 1.81740e9 0.642368
\(127\) 2.47510e9 0.844260 0.422130 0.906535i \(-0.361283\pi\)
0.422130 + 0.906535i \(0.361283\pi\)
\(128\) −7.05038e7 −0.0232149
\(129\) −5.18321e9 −1.64796
\(130\) 3.39188e9 1.04159
\(131\) 2.01408e9 0.597526 0.298763 0.954327i \(-0.403426\pi\)
0.298763 + 0.954327i \(0.403426\pi\)
\(132\) −4.09513e9 −1.17404
\(133\) 6.49115e9 1.79883
\(134\) 8.75947e9 2.34696
\(135\) 3.11252e9 0.806511
\(136\) 0 0
\(137\) 2.91545e9 0.707070 0.353535 0.935421i \(-0.384979\pi\)
0.353535 + 0.935421i \(0.384979\pi\)
\(138\) −3.01284e9 −0.707163
\(139\) 7.52889e9 1.71066 0.855331 0.518081i \(-0.173353\pi\)
0.855331 + 0.518081i \(0.173353\pi\)
\(140\) −7.07965e9 −1.55753
\(141\) 8.00200e9 1.70495
\(142\) 8.69389e9 1.79439
\(143\) −3.84701e9 −0.769326
\(144\) −1.50756e9 −0.292175
\(145\) −4.93664e9 −0.927418
\(146\) −2.73793e8 −0.0498694
\(147\) −9.42979e9 −1.66561
\(148\) 3.16217e9 0.541760
\(149\) −8.08087e9 −1.34314 −0.671568 0.740943i \(-0.734379\pi\)
−0.671568 + 0.740943i \(0.734379\pi\)
\(150\) −1.21818e6 −0.000196472 0
\(151\) −3.19079e9 −0.499461 −0.249730 0.968315i \(-0.580342\pi\)
−0.249730 + 0.968315i \(0.580342\pi\)
\(152\) −8.74961e7 −0.0132951
\(153\) 0 0
\(154\) 1.61258e10 2.31035
\(155\) 4.76533e9 0.663133
\(156\) 6.14949e9 0.831339
\(157\) −2.16958e9 −0.284988 −0.142494 0.989796i \(-0.545512\pi\)
−0.142494 + 0.989796i \(0.545512\pi\)
\(158\) 9.17381e9 1.17110
\(159\) −2.48581e9 −0.308447
\(160\) 1.16978e10 1.41112
\(161\) 5.90748e9 0.692924
\(162\) 1.49183e10 1.70178
\(163\) −1.61234e10 −1.78900 −0.894502 0.447064i \(-0.852470\pi\)
−0.894502 + 0.447064i \(0.852470\pi\)
\(164\) −8.53554e6 −0.000921370 0
\(165\) −1.12700e10 −1.18371
\(166\) 1.18730e10 1.21360
\(167\) −1.11195e10 −1.10627 −0.553133 0.833093i \(-0.686568\pi\)
−0.553133 + 0.833093i \(0.686568\pi\)
\(168\) 2.13775e8 0.0207045
\(169\) −4.82760e9 −0.455241
\(170\) 0 0
\(171\) −3.71139e9 −0.331936
\(172\) 1.65186e10 1.43912
\(173\) −1.48857e10 −1.26346 −0.631729 0.775189i \(-0.717654\pi\)
−0.631729 + 0.775189i \(0.717654\pi\)
\(174\) −1.79745e10 −1.48657
\(175\) 2.38857e6 0.000192516 0
\(176\) −1.33765e10 −1.05084
\(177\) −2.58388e10 −1.97876
\(178\) 1.37199e10 1.02438
\(179\) 1.45764e10 1.06124 0.530618 0.847611i \(-0.321960\pi\)
0.530618 + 0.847611i \(0.321960\pi\)
\(180\) 4.04788e9 0.287409
\(181\) 2.90444e9 0.201145 0.100572 0.994930i \(-0.467933\pi\)
0.100572 + 0.994930i \(0.467933\pi\)
\(182\) −2.42155e10 −1.63596
\(183\) 2.48429e10 1.63746
\(184\) −7.96286e7 −0.00512140
\(185\) 8.70242e9 0.546219
\(186\) 1.73508e10 1.06294
\(187\) 0 0
\(188\) −2.55019e10 −1.48889
\(189\) −2.22210e10 −1.26674
\(190\) 2.90352e10 1.61634
\(191\) 1.67129e10 0.908658 0.454329 0.890834i \(-0.349879\pi\)
0.454329 + 0.890834i \(0.349879\pi\)
\(192\) 2.10322e10 1.11694
\(193\) −1.00548e10 −0.521635 −0.260818 0.965388i \(-0.583992\pi\)
−0.260818 + 0.965388i \(0.583992\pi\)
\(194\) 3.25448e10 1.64958
\(195\) 1.69237e10 0.838182
\(196\) 3.00522e10 1.45454
\(197\) 6.48737e9 0.306882 0.153441 0.988158i \(-0.450965\pi\)
0.153441 + 0.988158i \(0.450965\pi\)
\(198\) −9.22011e9 −0.426327
\(199\) 4.66693e8 0.0210956 0.0105478 0.999944i \(-0.496642\pi\)
0.0105478 + 0.999944i \(0.496642\pi\)
\(200\) −32196.2 −1.42288e−6 0
\(201\) 4.37050e10 1.88864
\(202\) 1.78951e10 0.756230
\(203\) 3.52439e10 1.45664
\(204\) 0 0
\(205\) −2.34902e7 −0.000928954 0
\(206\) 4.62165e9 0.178811
\(207\) −3.37767e9 −0.127865
\(208\) 2.00870e10 0.744099
\(209\) −3.29312e10 −1.19385
\(210\) −7.09402e10 −2.51713
\(211\) 1.06287e9 0.0369156 0.0184578 0.999830i \(-0.494124\pi\)
0.0184578 + 0.999830i \(0.494124\pi\)
\(212\) 7.92213e9 0.269359
\(213\) 4.33778e10 1.44397
\(214\) 6.10447e10 1.98969
\(215\) 4.54599e10 1.45096
\(216\) 2.99524e8 0.00936245
\(217\) −3.40208e10 −1.04154
\(218\) −7.74108e10 −2.32139
\(219\) −1.36608e9 −0.0401307
\(220\) 3.59167e10 1.03370
\(221\) 0 0
\(222\) 3.16858e10 0.875542
\(223\) −4.79547e10 −1.29855 −0.649276 0.760553i \(-0.724928\pi\)
−0.649276 + 0.760553i \(0.724928\pi\)
\(224\) −8.35134e10 −2.21636
\(225\) −1.36569e6 −3.55248e−5 0
\(226\) 3.66163e10 0.933654
\(227\) −2.10496e10 −0.526171 −0.263085 0.964773i \(-0.584740\pi\)
−0.263085 + 0.964773i \(0.584740\pi\)
\(228\) 5.26409e10 1.29008
\(229\) −1.60702e10 −0.386156 −0.193078 0.981183i \(-0.561847\pi\)
−0.193078 + 0.981183i \(0.561847\pi\)
\(230\) 2.64244e10 0.622630
\(231\) 8.04590e10 1.85918
\(232\) −4.75062e8 −0.0107660
\(233\) −6.08238e10 −1.35198 −0.675992 0.736909i \(-0.736285\pi\)
−0.675992 + 0.736909i \(0.736285\pi\)
\(234\) 1.38455e10 0.301882
\(235\) −7.01824e10 −1.50115
\(236\) 8.23470e10 1.72800
\(237\) 4.57724e10 0.942401
\(238\) 0 0
\(239\) 4.66769e10 0.925362 0.462681 0.886525i \(-0.346887\pi\)
0.462681 + 0.886525i \(0.346887\pi\)
\(240\) 5.88458e10 1.14489
\(241\) 9.83868e9 0.187871 0.0939356 0.995578i \(-0.470055\pi\)
0.0939356 + 0.995578i \(0.470055\pi\)
\(242\) −6.51093e9 −0.122032
\(243\) 3.05950e10 0.562887
\(244\) −7.91728e10 −1.42995
\(245\) 8.27050e10 1.46651
\(246\) −8.55287e7 −0.00148903
\(247\) 4.94514e10 0.845361
\(248\) 4.58577e8 0.00769803
\(249\) 5.92399e10 0.976601
\(250\) 8.71720e10 1.41139
\(251\) 5.71571e10 0.908947 0.454473 0.890760i \(-0.349827\pi\)
0.454473 + 0.890760i \(0.349827\pi\)
\(252\) −2.88988e10 −0.451416
\(253\) −2.99700e10 −0.459880
\(254\) −7.90402e10 −1.19151
\(255\) 0 0
\(256\) 6.98359e10 1.01625
\(257\) 8.59864e10 1.22951 0.614753 0.788720i \(-0.289256\pi\)
0.614753 + 0.788720i \(0.289256\pi\)
\(258\) 1.65521e11 2.32576
\(259\) −6.21286e10 −0.857912
\(260\) −5.39348e10 −0.731962
\(261\) −2.01511e10 −0.268792
\(262\) −6.43181e10 −0.843290
\(263\) 2.61461e10 0.336982 0.168491 0.985703i \(-0.446111\pi\)
0.168491 + 0.985703i \(0.446111\pi\)
\(264\) −1.08453e9 −0.0137412
\(265\) 2.18021e10 0.271576
\(266\) −2.07289e11 −2.53869
\(267\) 6.84548e10 0.824334
\(268\) −1.39285e11 −1.64930
\(269\) 2.14758e10 0.250072 0.125036 0.992152i \(-0.460095\pi\)
0.125036 + 0.992152i \(0.460095\pi\)
\(270\) −9.93957e10 −1.13823
\(271\) 1.61241e11 1.81599 0.907997 0.418976i \(-0.137611\pi\)
0.907997 + 0.418976i \(0.137611\pi\)
\(272\) 0 0
\(273\) −1.20822e11 −1.31648
\(274\) −9.31023e10 −0.997890
\(275\) −1.21178e7 −0.000127769 0
\(276\) 4.79075e10 0.496950
\(277\) 4.74856e10 0.484622 0.242311 0.970199i \(-0.422095\pi\)
0.242311 + 0.970199i \(0.422095\pi\)
\(278\) −2.40429e11 −2.41426
\(279\) 1.94518e10 0.192195
\(280\) −1.87493e9 −0.0182295
\(281\) 2.72583e9 0.0260808 0.0130404 0.999915i \(-0.495849\pi\)
0.0130404 + 0.999915i \(0.495849\pi\)
\(282\) −2.55537e11 −2.40620
\(283\) −4.24874e10 −0.393751 −0.196876 0.980428i \(-0.563079\pi\)
−0.196876 + 0.980428i \(0.563079\pi\)
\(284\) −1.38243e11 −1.26098
\(285\) 1.44870e11 1.30070
\(286\) 1.22851e11 1.08575
\(287\) 1.67702e8 0.00145905
\(288\) 4.77498e10 0.408983
\(289\) 0 0
\(290\) 1.57647e11 1.30887
\(291\) 1.62381e11 1.32744
\(292\) 4.35361e9 0.0350451
\(293\) 6.93631e9 0.0549825 0.0274912 0.999622i \(-0.491248\pi\)
0.0274912 + 0.999622i \(0.491248\pi\)
\(294\) 3.01132e11 2.35068
\(295\) 2.26622e11 1.74222
\(296\) 8.37450e8 0.00634083
\(297\) 1.12733e11 0.840709
\(298\) 2.58056e11 1.89557
\(299\) 4.50048e10 0.325641
\(300\) 1.93704e7 0.000138068 0
\(301\) −3.24549e11 −2.27893
\(302\) 1.01895e11 0.704891
\(303\) 8.92871e10 0.608551
\(304\) 1.71949e11 1.15470
\(305\) −2.17887e11 −1.44172
\(306\) 0 0
\(307\) 1.64410e10 0.105635 0.0528173 0.998604i \(-0.483180\pi\)
0.0528173 + 0.998604i \(0.483180\pi\)
\(308\) −2.56418e11 −1.62357
\(309\) 2.30595e10 0.143892
\(310\) −1.52177e11 −0.935881
\(311\) −1.22476e11 −0.742383 −0.371191 0.928556i \(-0.621051\pi\)
−0.371191 + 0.928556i \(0.621051\pi\)
\(312\) 1.62860e9 0.00973011
\(313\) −2.36493e11 −1.39274 −0.696368 0.717685i \(-0.745202\pi\)
−0.696368 + 0.717685i \(0.745202\pi\)
\(314\) 6.92836e10 0.402204
\(315\) −7.95306e10 −0.455132
\(316\) −1.45874e11 −0.822974
\(317\) 4.33607e10 0.241173 0.120587 0.992703i \(-0.461522\pi\)
0.120587 + 0.992703i \(0.461522\pi\)
\(318\) 7.93821e10 0.435312
\(319\) −1.78800e11 −0.966742
\(320\) −1.84466e11 −0.983423
\(321\) 3.04580e11 1.60114
\(322\) −1.88650e11 −0.977926
\(323\) 0 0
\(324\) −2.37218e11 −1.19590
\(325\) 1.81968e7 9.04731e−5 0
\(326\) 5.14885e11 2.52483
\(327\) −3.86238e11 −1.86806
\(328\) −2.26050e6 −1.07838e−5 0
\(329\) 5.01049e11 2.35775
\(330\) 3.59897e11 1.67057
\(331\) −1.69990e11 −0.778392 −0.389196 0.921155i \(-0.627247\pi\)
−0.389196 + 0.921155i \(0.627247\pi\)
\(332\) −1.88794e11 −0.852840
\(333\) 3.55228e10 0.158310
\(334\) 3.55090e11 1.56128
\(335\) −3.83320e11 −1.66287
\(336\) −4.20114e11 −1.79821
\(337\) −1.02637e10 −0.0433478 −0.0216739 0.999765i \(-0.506900\pi\)
−0.0216739 + 0.999765i \(0.506900\pi\)
\(338\) 1.54165e11 0.642483
\(339\) 1.82695e11 0.751327
\(340\) 0 0
\(341\) 1.72596e11 0.691251
\(342\) 1.18520e11 0.468462
\(343\) −1.87852e11 −0.732811
\(344\) 4.37469e9 0.0168436
\(345\) 1.31844e11 0.501040
\(346\) 4.75361e11 1.78312
\(347\) −1.50419e11 −0.556957 −0.278478 0.960443i \(-0.589830\pi\)
−0.278478 + 0.960443i \(0.589830\pi\)
\(348\) 2.85815e11 1.04467
\(349\) 4.38444e11 1.58197 0.790987 0.611833i \(-0.209567\pi\)
0.790987 + 0.611833i \(0.209567\pi\)
\(350\) −7.62769e7 −0.000271698 0
\(351\) −1.69286e11 −0.595305
\(352\) 4.23683e11 1.47095
\(353\) 3.32465e10 0.113962 0.0569810 0.998375i \(-0.481853\pi\)
0.0569810 + 0.998375i \(0.481853\pi\)
\(354\) 8.25141e11 2.79263
\(355\) −3.80450e11 −1.27136
\(356\) −2.18162e11 −0.719869
\(357\) 0 0
\(358\) −4.65485e11 −1.49773
\(359\) 2.04791e11 0.650707 0.325354 0.945592i \(-0.394517\pi\)
0.325354 + 0.945592i \(0.394517\pi\)
\(360\) 1.07202e9 0.00336388
\(361\) 1.00627e11 0.311839
\(362\) −9.27507e10 −0.283876
\(363\) −3.24860e10 −0.0982012
\(364\) 3.85053e11 1.14965
\(365\) 1.19813e10 0.0353336
\(366\) −7.93335e11 −2.31096
\(367\) −3.19895e11 −0.920472 −0.460236 0.887797i \(-0.652235\pi\)
−0.460236 + 0.887797i \(0.652235\pi\)
\(368\) 1.56488e11 0.444800
\(369\) −9.58857e7 −0.000269237 0
\(370\) −2.77904e11 −0.770881
\(371\) −1.55650e11 −0.426547
\(372\) −2.75897e11 −0.746970
\(373\) −1.73495e11 −0.464084 −0.232042 0.972706i \(-0.574541\pi\)
−0.232042 + 0.972706i \(0.574541\pi\)
\(374\) 0 0
\(375\) 4.34941e11 1.13577
\(376\) −6.75378e9 −0.0174262
\(377\) 2.68498e11 0.684549
\(378\) 7.09610e11 1.78775
\(379\) −1.34082e11 −0.333807 −0.166903 0.985973i \(-0.553377\pi\)
−0.166903 + 0.985973i \(0.553377\pi\)
\(380\) −4.61693e11 −1.13587
\(381\) −3.94368e11 −0.958824
\(382\) −5.33711e11 −1.28239
\(383\) −5.78666e11 −1.37415 −0.687074 0.726588i \(-0.741105\pi\)
−0.687074 + 0.726588i \(0.741105\pi\)
\(384\) 1.12337e10 0.0263652
\(385\) −7.05674e11 −1.63693
\(386\) 3.21092e11 0.736185
\(387\) 1.85565e11 0.420530
\(388\) −5.17499e11 −1.15922
\(389\) 3.40387e11 0.753702 0.376851 0.926274i \(-0.377007\pi\)
0.376851 + 0.926274i \(0.377007\pi\)
\(390\) −5.40442e11 −1.18293
\(391\) 0 0
\(392\) 7.95886e9 0.0170241
\(393\) −3.20912e11 −0.678610
\(394\) −2.07169e11 −0.433103
\(395\) −4.01452e11 −0.829748
\(396\) 1.46610e11 0.299596
\(397\) −3.37985e11 −0.682874 −0.341437 0.939905i \(-0.610914\pi\)
−0.341437 + 0.939905i \(0.610914\pi\)
\(398\) −1.49034e10 −0.0297723
\(399\) −1.03426e12 −2.04292
\(400\) 6.32726e7 0.000123579 0
\(401\) −6.78361e11 −1.31012 −0.655060 0.755577i \(-0.727357\pi\)
−0.655060 + 0.755577i \(0.727357\pi\)
\(402\) −1.39568e12 −2.66544
\(403\) −2.59180e11 −0.489474
\(404\) −2.84553e11 −0.531431
\(405\) −6.52835e11 −1.20575
\(406\) −1.12548e12 −2.05576
\(407\) 3.15193e11 0.569380
\(408\) 0 0
\(409\) 3.79922e11 0.671336 0.335668 0.941980i \(-0.391038\pi\)
0.335668 + 0.941980i \(0.391038\pi\)
\(410\) 7.50139e8 0.00131103
\(411\) −4.64530e11 −0.803018
\(412\) −7.34895e10 −0.125657
\(413\) −1.61791e12 −2.73640
\(414\) 1.07863e11 0.180456
\(415\) −5.19570e11 −0.859860
\(416\) −6.36228e11 −1.04158
\(417\) −1.19961e12 −1.94280
\(418\) 1.05163e12 1.68488
\(419\) 6.30348e11 0.999118 0.499559 0.866280i \(-0.333495\pi\)
0.499559 + 0.866280i \(0.333495\pi\)
\(420\) 1.12803e12 1.76888
\(421\) 3.36779e11 0.522488 0.261244 0.965273i \(-0.415867\pi\)
0.261244 + 0.965273i \(0.415867\pi\)
\(422\) −3.39419e10 −0.0520990
\(423\) −2.86481e11 −0.435075
\(424\) 2.09805e9 0.00315261
\(425\) 0 0
\(426\) −1.38523e12 −2.03788
\(427\) 1.55555e12 2.26443
\(428\) −9.70680e11 −1.39823
\(429\) 6.12959e11 0.873723
\(430\) −1.45172e12 −2.04775
\(431\) 2.07449e11 0.289576 0.144788 0.989463i \(-0.453750\pi\)
0.144788 + 0.989463i \(0.453750\pi\)
\(432\) −5.88630e11 −0.813140
\(433\) 6.52648e11 0.892243 0.446122 0.894972i \(-0.352805\pi\)
0.446122 + 0.894972i \(0.352805\pi\)
\(434\) 1.08643e12 1.46993
\(435\) 7.86575e11 1.05327
\(436\) 1.23092e12 1.63132
\(437\) 3.85250e11 0.505332
\(438\) 4.36245e10 0.0566366
\(439\) 5.99383e11 0.770218 0.385109 0.922871i \(-0.374164\pi\)
0.385109 + 0.922871i \(0.374164\pi\)
\(440\) 9.51199e9 0.0120986
\(441\) 3.37597e11 0.425036
\(442\) 0 0
\(443\) 1.38710e11 0.171117 0.0855583 0.996333i \(-0.472733\pi\)
0.0855583 + 0.996333i \(0.472733\pi\)
\(444\) −5.03841e11 −0.615276
\(445\) −6.00390e11 −0.725794
\(446\) 1.53139e12 1.83265
\(447\) 1.28756e12 1.52540
\(448\) 1.31694e12 1.54460
\(449\) −1.78071e11 −0.206769 −0.103385 0.994641i \(-0.532967\pi\)
−0.103385 + 0.994641i \(0.532967\pi\)
\(450\) 4.36122e7 5.01362e−5 0
\(451\) −8.50792e8 −0.000968343 0
\(452\) −5.82240e11 −0.656114
\(453\) 5.08401e11 0.567237
\(454\) 6.72199e11 0.742586
\(455\) 1.05968e12 1.15911
\(456\) 1.39411e10 0.0150993
\(457\) −1.62766e11 −0.174558 −0.0872790 0.996184i \(-0.527817\pi\)
−0.0872790 + 0.996184i \(0.527817\pi\)
\(458\) 5.13189e11 0.544983
\(459\) 0 0
\(460\) −4.20178e11 −0.437545
\(461\) −1.43453e12 −1.47930 −0.739648 0.672994i \(-0.765008\pi\)
−0.739648 + 0.672994i \(0.765008\pi\)
\(462\) −2.56939e12 −2.62386
\(463\) 8.05823e11 0.814939 0.407470 0.913219i \(-0.366411\pi\)
0.407470 + 0.913219i \(0.366411\pi\)
\(464\) 9.33601e11 0.935040
\(465\) −7.59280e11 −0.753119
\(466\) 1.94235e12 1.90806
\(467\) 9.22766e11 0.897771 0.448886 0.893589i \(-0.351821\pi\)
0.448886 + 0.893589i \(0.351821\pi\)
\(468\) −2.20159e11 −0.212144
\(469\) 2.73661e12 2.61177
\(470\) 2.24121e12 2.11857
\(471\) 3.45688e11 0.323661
\(472\) 2.18083e10 0.0202247
\(473\) 1.64652e12 1.51248
\(474\) −1.46170e12 −1.33001
\(475\) 1.55768e8 0.000140397 0
\(476\) 0 0
\(477\) 8.89948e10 0.0787104
\(478\) −1.49059e12 −1.30597
\(479\) 4.10737e11 0.356496 0.178248 0.983986i \(-0.442957\pi\)
0.178248 + 0.983986i \(0.442957\pi\)
\(480\) −1.86386e12 −1.60261
\(481\) −4.73313e11 −0.403177
\(482\) −3.14190e11 −0.265143
\(483\) −9.41262e11 −0.786953
\(484\) 1.03531e11 0.0857565
\(485\) −1.42418e12 −1.16876
\(486\) −9.77023e11 −0.794405
\(487\) 7.30098e11 0.588167 0.294083 0.955780i \(-0.404986\pi\)
0.294083 + 0.955780i \(0.404986\pi\)
\(488\) −2.09677e10 −0.0167364
\(489\) 2.56900e12 2.03177
\(490\) −2.64111e12 −2.06969
\(491\) 2.19308e12 1.70289 0.851446 0.524442i \(-0.175726\pi\)
0.851446 + 0.524442i \(0.175726\pi\)
\(492\) 1.36000e9 0.00104640
\(493\) 0 0
\(494\) −1.57919e12 −1.19306
\(495\) 4.03478e11 0.302062
\(496\) −9.01204e11 −0.668583
\(497\) 2.71612e12 1.99685
\(498\) −1.89178e12 −1.37828
\(499\) 2.10713e12 1.52138 0.760691 0.649115i \(-0.224860\pi\)
0.760691 + 0.649115i \(0.224860\pi\)
\(500\) −1.38613e12 −0.991836
\(501\) 1.77171e12 1.25638
\(502\) −1.82526e12 −1.28280
\(503\) −2.92024e11 −0.203406 −0.101703 0.994815i \(-0.532429\pi\)
−0.101703 + 0.994815i \(0.532429\pi\)
\(504\) −7.65338e9 −0.00528343
\(505\) −7.83102e11 −0.535806
\(506\) 9.57067e11 0.649030
\(507\) 7.69202e11 0.517016
\(508\) 1.25683e12 0.837316
\(509\) −3.27240e11 −0.216091 −0.108045 0.994146i \(-0.534459\pi\)
−0.108045 + 0.994146i \(0.534459\pi\)
\(510\) 0 0
\(511\) −8.55376e10 −0.0554962
\(512\) −2.19405e12 −1.41102
\(513\) −1.44912e12 −0.923799
\(514\) −2.74590e12 −1.73521
\(515\) −2.02246e11 −0.126692
\(516\) −2.63198e12 −1.63440
\(517\) −2.54194e12 −1.56480
\(518\) 1.98402e12 1.21077
\(519\) 2.37179e12 1.43491
\(520\) −1.42838e10 −0.00856698
\(521\) 4.58716e11 0.272756 0.136378 0.990657i \(-0.456454\pi\)
0.136378 + 0.990657i \(0.456454\pi\)
\(522\) 6.43508e11 0.379347
\(523\) 2.19925e11 0.128534 0.0642669 0.997933i \(-0.479529\pi\)
0.0642669 + 0.997933i \(0.479529\pi\)
\(524\) 1.02273e12 0.592612
\(525\) −3.80580e8 −0.000218640 0
\(526\) −8.34954e11 −0.475583
\(527\) 0 0
\(528\) 2.13134e12 1.19344
\(529\) −1.45054e12 −0.805342
\(530\) −6.96230e11 −0.383276
\(531\) 9.25060e11 0.504946
\(532\) 3.29613e12 1.78403
\(533\) 1.27760e9 0.000685682 0
\(534\) −2.18604e12 −1.16338
\(535\) −2.67135e12 −1.40974
\(536\) −3.68876e10 −0.0193036
\(537\) −2.32252e12 −1.20524
\(538\) −6.85812e11 −0.352927
\(539\) 2.99550e12 1.52869
\(540\) 1.58050e12 0.799878
\(541\) 1.58562e12 0.795815 0.397907 0.917426i \(-0.369737\pi\)
0.397907 + 0.917426i \(0.369737\pi\)
\(542\) −5.14910e12 −2.56292
\(543\) −4.62776e11 −0.228440
\(544\) 0 0
\(545\) 3.38754e12 1.64475
\(546\) 3.85835e12 1.85795
\(547\) 3.66475e12 1.75025 0.875127 0.483893i \(-0.160778\pi\)
0.875127 + 0.483893i \(0.160778\pi\)
\(548\) 1.48043e12 0.701255
\(549\) −8.89403e11 −0.417853
\(550\) 3.86971e8 0.000180321 0
\(551\) 2.29839e12 1.06229
\(552\) 1.26875e10 0.00581637
\(553\) 2.86606e12 1.30323
\(554\) −1.51641e12 −0.683948
\(555\) −1.38659e12 −0.620340
\(556\) 3.82309e12 1.69659
\(557\) −1.44850e12 −0.637632 −0.318816 0.947817i \(-0.603285\pi\)
−0.318816 + 0.947817i \(0.603285\pi\)
\(558\) −6.21177e11 −0.271245
\(559\) −2.47251e12 −1.07099
\(560\) 3.68466e12 1.58326
\(561\) 0 0
\(562\) −8.70470e10 −0.0368079
\(563\) 3.44734e12 1.44609 0.723046 0.690800i \(-0.242742\pi\)
0.723046 + 0.690800i \(0.242742\pi\)
\(564\) 4.06332e12 1.69093
\(565\) −1.60235e12 −0.661514
\(566\) 1.35680e12 0.555702
\(567\) 4.66075e12 1.89379
\(568\) −3.66114e10 −0.0147587
\(569\) −2.93321e12 −1.17311 −0.586554 0.809910i \(-0.699516\pi\)
−0.586554 + 0.809910i \(0.699516\pi\)
\(570\) −4.62630e12 −1.83568
\(571\) 4.85517e12 1.91136 0.955678 0.294414i \(-0.0951243\pi\)
0.955678 + 0.294414i \(0.0951243\pi\)
\(572\) −1.95347e12 −0.762999
\(573\) −2.66293e12 −1.03196
\(574\) −5.35542e9 −0.00205916
\(575\) 1.41762e8 5.40821e−5 0
\(576\) −7.52978e11 −0.285024
\(577\) −3.14368e12 −1.18072 −0.590360 0.807140i \(-0.701014\pi\)
−0.590360 + 0.807140i \(0.701014\pi\)
\(578\) 0 0
\(579\) 1.60208e12 0.592420
\(580\) −2.50677e12 −0.919790
\(581\) 3.70934e12 1.35053
\(582\) −5.18549e12 −1.87343
\(583\) 7.89650e11 0.283091
\(584\) 1.15299e9 0.000410172 0
\(585\) −6.05887e11 −0.213890
\(586\) −2.21505e11 −0.0775969
\(587\) 5.29849e11 0.184196 0.0920981 0.995750i \(-0.470643\pi\)
0.0920981 + 0.995750i \(0.470643\pi\)
\(588\) −4.78834e12 −1.65191
\(589\) −2.21864e12 −0.759569
\(590\) −7.23699e12 −2.45880
\(591\) −1.03366e12 −0.348525
\(592\) −1.64577e12 −0.550709
\(593\) 1.85102e12 0.614702 0.307351 0.951596i \(-0.400557\pi\)
0.307351 + 0.951596i \(0.400557\pi\)
\(594\) −3.60002e12 −1.18649
\(595\) 0 0
\(596\) −4.10338e12 −1.33209
\(597\) −7.43601e10 −0.0239583
\(598\) −1.43719e12 −0.459578
\(599\) 9.54735e11 0.303014 0.151507 0.988456i \(-0.451587\pi\)
0.151507 + 0.988456i \(0.451587\pi\)
\(600\) 5.12995e6 1.61597e−6 0
\(601\) −5.29994e12 −1.65705 −0.828526 0.559951i \(-0.810820\pi\)
−0.828526 + 0.559951i \(0.810820\pi\)
\(602\) 1.03642e13 3.21626
\(603\) −1.56469e12 −0.481948
\(604\) −1.62025e12 −0.495353
\(605\) 2.84922e11 0.0864623
\(606\) −2.85131e12 −0.858849
\(607\) 2.76852e12 0.827748 0.413874 0.910334i \(-0.364175\pi\)
0.413874 + 0.910334i \(0.364175\pi\)
\(608\) −5.44624e12 −1.61633
\(609\) −5.61555e12 −1.65430
\(610\) 6.95803e12 2.03471
\(611\) 3.81713e12 1.10803
\(612\) 0 0
\(613\) 6.26290e11 0.179144 0.0895722 0.995980i \(-0.471450\pi\)
0.0895722 + 0.995980i \(0.471450\pi\)
\(614\) −5.25030e11 −0.149082
\(615\) 3.74279e9 0.00105501
\(616\) −6.79083e10 −0.0190025
\(617\) −3.77388e12 −1.04835 −0.524173 0.851612i \(-0.675625\pi\)
−0.524173 + 0.851612i \(0.675625\pi\)
\(618\) −7.36387e11 −0.203076
\(619\) −1.48879e12 −0.407592 −0.203796 0.979013i \(-0.565328\pi\)
−0.203796 + 0.979013i \(0.565328\pi\)
\(620\) 2.41978e12 0.657679
\(621\) −1.31882e12 −0.355855
\(622\) 3.91115e12 1.04773
\(623\) 4.28633e12 1.13996
\(624\) −3.20055e12 −0.845072
\(625\) −3.81423e12 −0.999877
\(626\) 7.55220e12 1.96557
\(627\) 5.24705e12 1.35585
\(628\) −1.10169e12 −0.282644
\(629\) 0 0
\(630\) 2.53974e12 0.642328
\(631\) −8.19149e10 −0.0205698 −0.0102849 0.999947i \(-0.503274\pi\)
−0.0102849 + 0.999947i \(0.503274\pi\)
\(632\) −3.86324e10 −0.00963219
\(633\) −1.69352e11 −0.0419249
\(634\) −1.38469e12 −0.340368
\(635\) 3.45885e12 0.844208
\(636\) −1.26227e12 −0.305910
\(637\) −4.49822e12 −1.08246
\(638\) 5.70984e12 1.36437
\(639\) −1.55298e12 −0.368477
\(640\) −9.85260e10 −0.0232135
\(641\) 8.71629e11 0.203925 0.101962 0.994788i \(-0.467488\pi\)
0.101962 + 0.994788i \(0.467488\pi\)
\(642\) −9.72650e12 −2.25969
\(643\) 7.01475e11 0.161831 0.0809157 0.996721i \(-0.474216\pi\)
0.0809157 + 0.996721i \(0.474216\pi\)
\(644\) 2.99975e12 0.687225
\(645\) −7.24332e12 −1.64785
\(646\) 0 0
\(647\) −6.30742e12 −1.41509 −0.707543 0.706671i \(-0.750196\pi\)
−0.707543 + 0.706671i \(0.750196\pi\)
\(648\) −6.28236e10 −0.0139970
\(649\) 8.20805e12 1.81610
\(650\) −5.81098e8 −0.000127685 0
\(651\) 5.42068e12 1.18288
\(652\) −8.18726e12 −1.77429
\(653\) −2.08016e12 −0.447701 −0.223850 0.974624i \(-0.571863\pi\)
−0.223850 + 0.974624i \(0.571863\pi\)
\(654\) 1.23342e13 2.63639
\(655\) 2.81460e12 0.597490
\(656\) 4.44239e9 0.000936589 0
\(657\) 4.89072e10 0.0102407
\(658\) −1.60006e13 −3.32751
\(659\) −1.77225e12 −0.366051 −0.183025 0.983108i \(-0.558589\pi\)
−0.183025 + 0.983108i \(0.558589\pi\)
\(660\) −5.72276e12 −1.17397
\(661\) −1.32844e12 −0.270666 −0.135333 0.990800i \(-0.543210\pi\)
−0.135333 + 0.990800i \(0.543210\pi\)
\(662\) 5.42849e12 1.09855
\(663\) 0 0
\(664\) −4.99992e10 −0.00998175
\(665\) 9.07111e12 1.79872
\(666\) −1.13439e12 −0.223423
\(667\) 2.09173e12 0.409203
\(668\) −5.64634e12 −1.09717
\(669\) 7.64081e12 1.47476
\(670\) 1.22410e13 2.34682
\(671\) −7.89166e12 −1.50286
\(672\) 1.33065e13 2.51711
\(673\) −7.10413e12 −1.33488 −0.667441 0.744662i \(-0.732611\pi\)
−0.667441 + 0.744662i \(0.732611\pi\)
\(674\) 3.27761e11 0.0611769
\(675\) −5.33238e8 −9.88677e−5 0
\(676\) −2.45140e12 −0.451497
\(677\) 1.12958e11 0.0206665 0.0103333 0.999947i \(-0.496711\pi\)
0.0103333 + 0.999947i \(0.496711\pi\)
\(678\) −5.83422e12 −1.06035
\(679\) 1.01676e13 1.83570
\(680\) 0 0
\(681\) 3.35391e12 0.597571
\(682\) −5.51170e12 −0.975564
\(683\) −3.35112e12 −0.589246 −0.294623 0.955614i \(-0.595194\pi\)
−0.294623 + 0.955614i \(0.595194\pi\)
\(684\) −1.88460e12 −0.329206
\(685\) 4.07421e12 0.707027
\(686\) 5.99889e12 1.03422
\(687\) 2.56054e12 0.438557
\(688\) −8.59723e12 −1.46289
\(689\) −1.18579e12 −0.200456
\(690\) −4.21031e12 −0.707120
\(691\) −7.54720e12 −1.25932 −0.629658 0.776873i \(-0.716805\pi\)
−0.629658 + 0.776873i \(0.716805\pi\)
\(692\) −7.55877e12 −1.25307
\(693\) −2.88052e12 −0.474430
\(694\) 4.80351e12 0.786034
\(695\) 1.05213e13 1.71056
\(696\) 7.56936e10 0.0122269
\(697\) 0 0
\(698\) −1.40013e13 −2.23264
\(699\) 9.69130e12 1.53545
\(700\) 1.21289e9 0.000190932 0
\(701\) 1.61959e12 0.253323 0.126662 0.991946i \(-0.459574\pi\)
0.126662 + 0.991946i \(0.459574\pi\)
\(702\) 5.40601e12 0.840155
\(703\) −4.05166e12 −0.625654
\(704\) −6.68117e12 −1.02512
\(705\) 1.11824e13 1.70485
\(706\) −1.06170e12 −0.160835
\(707\) 5.59075e12 0.841556
\(708\) −1.31207e13 −1.96249
\(709\) 1.71850e12 0.255413 0.127706 0.991812i \(-0.459239\pi\)
0.127706 + 0.991812i \(0.459239\pi\)
\(710\) 1.21493e13 1.79428
\(711\) −1.63870e12 −0.240485
\(712\) −5.77767e10 −0.00842544
\(713\) −2.01914e12 −0.292593
\(714\) 0 0
\(715\) −5.37602e12 −0.769279
\(716\) 7.40174e12 1.05251
\(717\) −7.43723e12 −1.05093
\(718\) −6.53982e12 −0.918345
\(719\) 1.34411e13 1.87566 0.937832 0.347089i \(-0.112830\pi\)
0.937832 + 0.347089i \(0.112830\pi\)
\(720\) −2.10675e12 −0.292157
\(721\) 1.44388e12 0.198987
\(722\) −3.21342e12 −0.440099
\(723\) −1.56764e12 −0.213365
\(724\) 1.47484e12 0.199490
\(725\) 8.45747e8 0.000113689 0
\(726\) 1.03741e12 0.138592
\(727\) 1.27527e13 1.69316 0.846579 0.532263i \(-0.178658\pi\)
0.846579 + 0.532263i \(0.178658\pi\)
\(728\) 1.01975e11 0.0134556
\(729\) 4.32028e12 0.566550
\(730\) −3.82614e11 −0.0498663
\(731\) 0 0
\(732\) 1.26149e13 1.62400
\(733\) 1.14507e13 1.46509 0.732547 0.680717i \(-0.238332\pi\)
0.732547 + 0.680717i \(0.238332\pi\)
\(734\) 1.02156e13 1.29906
\(735\) −1.31777e13 −1.66551
\(736\) −4.95653e12 −0.622626
\(737\) −1.38835e13 −1.73338
\(738\) 3.06203e9 0.000379975 0
\(739\) 1.27616e13 1.57400 0.787000 0.616953i \(-0.211633\pi\)
0.787000 + 0.616953i \(0.211633\pi\)
\(740\) 4.41899e12 0.541727
\(741\) −7.87930e12 −0.960076
\(742\) 4.97055e12 0.601987
\(743\) 4.54322e12 0.546907 0.273454 0.961885i \(-0.411834\pi\)
0.273454 + 0.961885i \(0.411834\pi\)
\(744\) −7.30669e10 −0.00874264
\(745\) −1.12927e13 −1.34305
\(746\) 5.54041e12 0.654963
\(747\) −2.12086e12 −0.249212
\(748\) 0 0
\(749\) 1.90714e13 2.21419
\(750\) −1.38895e13 −1.60291
\(751\) 8.88851e12 1.01965 0.509823 0.860279i \(-0.329711\pi\)
0.509823 + 0.860279i \(0.329711\pi\)
\(752\) 1.32727e13 1.51348
\(753\) −9.10707e12 −1.03229
\(754\) −8.57424e12 −0.966105
\(755\) −4.45899e12 −0.499430
\(756\) −1.12836e13 −1.25632
\(757\) 6.29935e12 0.697211 0.348605 0.937270i \(-0.386655\pi\)
0.348605 + 0.937270i \(0.386655\pi\)
\(758\) 4.28180e12 0.471102
\(759\) 4.77525e12 0.522285
\(760\) −1.22272e11 −0.0132943
\(761\) 2.40574e12 0.260026 0.130013 0.991512i \(-0.458498\pi\)
0.130013 + 0.991512i \(0.458498\pi\)
\(762\) 1.25938e13 1.35319
\(763\) −2.41845e13 −2.58331
\(764\) 8.48660e12 0.901185
\(765\) 0 0
\(766\) 1.84792e13 1.93934
\(767\) −1.23257e13 −1.28598
\(768\) −1.11272e13 −1.15415
\(769\) −1.51735e12 −0.156465 −0.0782326 0.996935i \(-0.524928\pi\)
−0.0782326 + 0.996935i \(0.524928\pi\)
\(770\) 2.25351e13 2.31021
\(771\) −1.37006e13 −1.39635
\(772\) −5.10573e12 −0.517345
\(773\) 1.39024e13 1.40050 0.700251 0.713897i \(-0.253072\pi\)
0.700251 + 0.713897i \(0.253072\pi\)
\(774\) −5.92586e12 −0.593495
\(775\) −8.16398e8 −8.12914e−5 0
\(776\) −1.37051e11 −0.0135677
\(777\) 9.89921e12 0.974330
\(778\) −1.08700e13 −1.06370
\(779\) 1.09365e10 0.00106405
\(780\) 8.59365e12 0.831289
\(781\) −1.37795e13 −1.32527
\(782\) 0 0
\(783\) −7.86805e12 −0.748065
\(784\) −1.56409e13 −1.47856
\(785\) −3.03189e12 −0.284971
\(786\) 1.02481e13 0.957723
\(787\) −1.50319e13 −1.39678 −0.698391 0.715716i \(-0.746100\pi\)
−0.698391 + 0.715716i \(0.746100\pi\)
\(788\) 3.29422e12 0.304358
\(789\) −4.16597e12 −0.382710
\(790\) 1.28200e13 1.17103
\(791\) 1.14396e13 1.03900
\(792\) 3.88274e10 0.00350651
\(793\) 1.18506e13 1.06417
\(794\) 1.07933e13 0.963741
\(795\) −3.47381e12 −0.308428
\(796\) 2.36982e11 0.0209221
\(797\) 1.82924e13 1.60586 0.802930 0.596073i \(-0.203273\pi\)
0.802930 + 0.596073i \(0.203273\pi\)
\(798\) 3.30283e13 2.88319
\(799\) 0 0
\(800\) −2.00407e9 −0.000172985 0
\(801\) −2.45076e12 −0.210356
\(802\) 2.16629e13 1.84897
\(803\) 4.33953e11 0.0368317
\(804\) 2.21929e13 1.87311
\(805\) 8.25545e12 0.692882
\(806\) 8.27670e12 0.690796
\(807\) −3.42183e12 −0.284006
\(808\) −7.53594e10 −0.00621994
\(809\) −6.91099e11 −0.0567246 −0.0283623 0.999598i \(-0.509029\pi\)
−0.0283623 + 0.999598i \(0.509029\pi\)
\(810\) 2.08477e13 1.70167
\(811\) 1.42607e13 1.15757 0.578785 0.815480i \(-0.303527\pi\)
0.578785 + 0.815480i \(0.303527\pi\)
\(812\) 1.78964e13 1.44466
\(813\) −2.56912e13 −2.06242
\(814\) −1.00654e13 −0.803567
\(815\) −2.25317e13 −1.78889
\(816\) 0 0
\(817\) −2.11652e13 −1.66197
\(818\) −1.21325e13 −0.947458
\(819\) 4.32557e12 0.335943
\(820\) −1.19281e10 −0.000921313 0
\(821\) −4.35431e12 −0.334484 −0.167242 0.985916i \(-0.553486\pi\)
−0.167242 + 0.985916i \(0.553486\pi\)
\(822\) 1.48344e13 1.13330
\(823\) 1.25808e13 0.955892 0.477946 0.878389i \(-0.341381\pi\)
0.477946 + 0.878389i \(0.341381\pi\)
\(824\) −1.94625e10 −0.00147071
\(825\) 1.93077e9 0.000145107 0
\(826\) 5.16666e13 3.86189
\(827\) 1.63352e13 1.21437 0.607183 0.794562i \(-0.292300\pi\)
0.607183 + 0.794562i \(0.292300\pi\)
\(828\) −1.71514e12 −0.126813
\(829\) 2.48744e13 1.82918 0.914591 0.404380i \(-0.132513\pi\)
0.914591 + 0.404380i \(0.132513\pi\)
\(830\) 1.65920e13 1.21352
\(831\) −7.56607e12 −0.550384
\(832\) 1.00328e13 0.725887
\(833\) 0 0
\(834\) 3.83085e13 2.74187
\(835\) −1.55390e13 −1.10620
\(836\) −1.67221e13 −1.18403
\(837\) 7.59502e12 0.534890
\(838\) −2.01296e13 −1.41006
\(839\) −1.61316e13 −1.12396 −0.561978 0.827152i \(-0.689960\pi\)
−0.561978 + 0.827152i \(0.689960\pi\)
\(840\) 2.98741e11 0.0207032
\(841\) −2.02796e12 −0.139791
\(842\) −1.07548e13 −0.737388
\(843\) −4.34318e11 −0.0296199
\(844\) 5.39714e11 0.0366119
\(845\) −6.74637e12 −0.455213
\(846\) 9.14851e12 0.614022
\(847\) −2.03413e12 −0.135801
\(848\) −4.12313e12 −0.273808
\(849\) 6.76970e12 0.447182
\(850\) 0 0
\(851\) −3.68734e12 −0.241007
\(852\) 2.20268e13 1.43210
\(853\) −1.29304e10 −0.000836263 0 −0.000418132 1.00000i \(-0.500133\pi\)
−0.000418132 1.00000i \(0.500133\pi\)
\(854\) −4.96751e13 −3.19579
\(855\) −5.18651e12 −0.331916
\(856\) −2.57069e11 −0.0163651
\(857\) −1.42717e12 −0.0903779 −0.0451889 0.998978i \(-0.514389\pi\)
−0.0451889 + 0.998978i \(0.514389\pi\)
\(858\) −1.95743e13 −1.23309
\(859\) −9.05087e12 −0.567180 −0.283590 0.958946i \(-0.591526\pi\)
−0.283590 + 0.958946i \(0.591526\pi\)
\(860\) 2.30840e13 1.43903
\(861\) −2.67207e10 −0.00165704
\(862\) −6.62469e12 −0.408680
\(863\) 1.02844e13 0.631148 0.315574 0.948901i \(-0.397803\pi\)
0.315574 + 0.948901i \(0.397803\pi\)
\(864\) 1.86440e13 1.13822
\(865\) −2.08021e13 −1.26338
\(866\) −2.08417e13 −1.25923
\(867\) 0 0
\(868\) −1.72754e13 −1.03297
\(869\) −1.45402e13 −0.864931
\(870\) −2.51186e13 −1.48648
\(871\) 2.08483e13 1.22741
\(872\) 3.25989e11 0.0190932
\(873\) −5.81342e12 −0.338741
\(874\) −1.23026e13 −0.713176
\(875\) 2.72340e13 1.57064
\(876\) −6.93679e11 −0.0398006
\(877\) 6.79965e12 0.388140 0.194070 0.980988i \(-0.437831\pi\)
0.194070 + 0.980988i \(0.437831\pi\)
\(878\) −1.91408e13 −1.08701
\(879\) −1.10519e12 −0.0624435
\(880\) −1.86931e13 −1.05078
\(881\) −3.08404e13 −1.72476 −0.862380 0.506262i \(-0.831027\pi\)
−0.862380 + 0.506262i \(0.831027\pi\)
\(882\) −1.07809e13 −0.599854
\(883\) 3.17104e13 1.75541 0.877706 0.479200i \(-0.159073\pi\)
0.877706 + 0.479200i \(0.159073\pi\)
\(884\) 0 0
\(885\) −3.61087e13 −1.97864
\(886\) −4.42960e12 −0.241497
\(887\) 6.89150e12 0.373816 0.186908 0.982377i \(-0.440153\pi\)
0.186908 + 0.982377i \(0.440153\pi\)
\(888\) −1.33434e11 −0.00720127
\(889\) −2.46935e13 −1.32594
\(890\) 1.91729e13 1.02432
\(891\) −2.36451e13 −1.25687
\(892\) −2.43508e13 −1.28787
\(893\) 3.26754e13 1.71945
\(894\) −4.11171e13 −2.15280
\(895\) 2.03699e13 1.06117
\(896\) 7.03401e11 0.0364600
\(897\) −7.17080e12 −0.369830
\(898\) 5.68656e12 0.291814
\(899\) −1.20461e13 −0.615077
\(900\) −6.93484e8 −3.52326e−5 0
\(901\) 0 0
\(902\) 2.71693e10 0.00136662
\(903\) 5.17118e13 2.58818
\(904\) −1.54197e11 −0.00767924
\(905\) 4.05883e12 0.201132
\(906\) −1.62353e13 −0.800543
\(907\) −2.11844e13 −1.03940 −0.519700 0.854349i \(-0.673956\pi\)
−0.519700 + 0.854349i \(0.673956\pi\)
\(908\) −1.06887e13 −0.521843
\(909\) −3.19658e12 −0.155292
\(910\) −3.38401e13 −1.63586
\(911\) −3.86760e13 −1.86041 −0.930206 0.367039i \(-0.880372\pi\)
−0.930206 + 0.367039i \(0.880372\pi\)
\(912\) −2.73973e13 −1.31139
\(913\) −1.88183e13 −0.896319
\(914\) 5.19778e12 0.246354
\(915\) 3.47168e13 1.63736
\(916\) −8.16029e12 −0.382980
\(917\) −2.00941e13 −0.938439
\(918\) 0 0
\(919\) 3.05320e11 0.0141200 0.00706000 0.999975i \(-0.497753\pi\)
0.00706000 + 0.999975i \(0.497753\pi\)
\(920\) −1.11278e11 −0.00512109
\(921\) −2.61962e12 −0.119969
\(922\) 4.58105e13 2.08774
\(923\) 2.06922e13 0.938423
\(924\) 4.08562e13 1.84388
\(925\) −1.49090e9 −6.69593e−5 0
\(926\) −2.57333e13 −1.15013
\(927\) −8.25558e11 −0.0367188
\(928\) −2.95705e13 −1.30886
\(929\) −1.17442e13 −0.517313 −0.258656 0.965969i \(-0.583280\pi\)
−0.258656 + 0.965969i \(0.583280\pi\)
\(930\) 2.42469e13 1.06288
\(931\) −3.85057e13 −1.67978
\(932\) −3.08856e13 −1.34086
\(933\) 1.95145e13 0.843123
\(934\) −2.94677e13 −1.26703
\(935\) 0 0
\(936\) −5.83056e10 −0.00248296
\(937\) −2.08580e13 −0.883983 −0.441991 0.897019i \(-0.645728\pi\)
−0.441991 + 0.897019i \(0.645728\pi\)
\(938\) −8.73913e13 −3.68600
\(939\) 3.76814e13 1.58173
\(940\) −3.56378e13 −1.48880
\(941\) 3.69821e13 1.53758 0.768791 0.639500i \(-0.220859\pi\)
0.768791 + 0.639500i \(0.220859\pi\)
\(942\) −1.10392e13 −0.456783
\(943\) 9.95313e9 0.000409880 0
\(944\) −4.28581e13 −1.75654
\(945\) −3.10529e13 −1.26666
\(946\) −5.25801e13 −2.13457
\(947\) 3.26913e13 1.32086 0.660432 0.750886i \(-0.270373\pi\)
0.660432 + 0.750886i \(0.270373\pi\)
\(948\) 2.32427e13 0.934650
\(949\) −6.51650e11 −0.0260805
\(950\) −4.97432e9 −0.000198143 0
\(951\) −6.90883e12 −0.273900
\(952\) 0 0
\(953\) −3.10457e13 −1.21922 −0.609612 0.792700i \(-0.708675\pi\)
−0.609612 + 0.792700i \(0.708675\pi\)
\(954\) −2.84197e12 −0.111084
\(955\) 2.33555e13 0.908603
\(956\) 2.37020e13 0.917751
\(957\) 2.84890e13 1.09793
\(958\) −1.31165e13 −0.503124
\(959\) −2.90868e13 −1.11048
\(960\) 2.93916e13 1.11687
\(961\) −1.48115e13 −0.560201
\(962\) 1.51149e13 0.569005
\(963\) −1.09043e13 −0.408583
\(964\) 4.99597e12 0.186326
\(965\) −1.40512e13 −0.521603
\(966\) 3.00584e13 1.11063
\(967\) 1.13694e13 0.418138 0.209069 0.977901i \(-0.432957\pi\)
0.209069 + 0.977901i \(0.432957\pi\)
\(968\) 2.74186e10 0.00100370
\(969\) 0 0
\(970\) 4.54799e13 1.64948
\(971\) 2.34437e13 0.846330 0.423165 0.906053i \(-0.360919\pi\)
0.423165 + 0.906053i \(0.360919\pi\)
\(972\) 1.55358e13 0.558258
\(973\) −7.51141e13 −2.68667
\(974\) −2.33150e13 −0.830082
\(975\) −2.89937e9 −0.000102750 0
\(976\) 4.12061e13 1.45357
\(977\) −8.22524e11 −0.0288817 −0.0144409 0.999896i \(-0.504597\pi\)
−0.0144409 + 0.999896i \(0.504597\pi\)
\(978\) −8.20388e13 −2.86744
\(979\) −2.17456e13 −0.756569
\(980\) 4.19967e13 1.45445
\(981\) 1.38278e13 0.476696
\(982\) −7.00340e13 −2.40330
\(983\) −2.37832e12 −0.0812417 −0.0406209 0.999175i \(-0.512934\pi\)
−0.0406209 + 0.999175i \(0.512934\pi\)
\(984\) 3.60175e8 1.22472e−5 0
\(985\) 9.06583e12 0.306863
\(986\) 0 0
\(987\) −7.98342e13 −2.67770
\(988\) 2.51109e13 0.838408
\(989\) −1.92620e13 −0.640205
\(990\) −1.28847e13 −0.426301
\(991\) 4.31408e11 0.0142088 0.00710439 0.999975i \(-0.497739\pi\)
0.00710439 + 0.999975i \(0.497739\pi\)
\(992\) 2.85444e13 0.935875
\(993\) 2.70852e13 0.884018
\(994\) −8.67370e13 −2.81816
\(995\) 6.52184e11 0.0210943
\(996\) 3.00814e13 0.968569
\(997\) 3.60987e13 1.15708 0.578539 0.815655i \(-0.303623\pi\)
0.578539 + 0.815655i \(0.303623\pi\)
\(998\) −6.72892e13 −2.14713
\(999\) 1.38700e13 0.440586
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.1.9 52
17.11 odd 16 17.10.d.a.2.3 52
17.14 odd 16 17.10.d.a.9.3 yes 52
17.16 even 2 inner 289.10.a.i.1.10 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.10.d.a.2.3 52 17.11 odd 16
17.10.d.a.9.3 yes 52 17.14 odd 16
289.10.a.i.1.9 52 1.1 even 1 trivial
289.10.a.i.1.10 52 17.16 even 2 inner