Properties

Label 289.10.a.h.1.27
Level $289$
Weight $10$
Character 289.1
Self dual yes
Analytic conductor $148.845$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $1$

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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: \(36\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.27
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q+26.5808 q^{2} +204.952 q^{3} +194.540 q^{4} +2372.11 q^{5} +5447.81 q^{6} -6243.22 q^{7} -8438.34 q^{8} +22322.5 q^{9} +O(q^{10})\) \(q+26.5808 q^{2} +204.952 q^{3} +194.540 q^{4} +2372.11 q^{5} +5447.81 q^{6} -6243.22 q^{7} -8438.34 q^{8} +22322.5 q^{9} +63052.8 q^{10} +82629.5 q^{11} +39871.5 q^{12} +110834. q^{13} -165950. q^{14} +486171. q^{15} -323903. q^{16} +593351. q^{18} +562366. q^{19} +461472. q^{20} -1.27956e6 q^{21} +2.19636e6 q^{22} +1.19566e6 q^{23} -1.72946e6 q^{24} +3.67380e6 q^{25} +2.94607e6 q^{26} +540977. q^{27} -1.21456e6 q^{28} -1.98644e6 q^{29} +1.29228e7 q^{30} -9.43437e6 q^{31} -4.28917e6 q^{32} +1.69351e7 q^{33} -1.48096e7 q^{35} +4.34263e6 q^{36} -984052. q^{37} +1.49481e7 q^{38} +2.27158e7 q^{39} -2.00167e7 q^{40} -2.19605e6 q^{41} -3.40118e7 q^{42} +3.42984e6 q^{43} +1.60748e7 q^{44} +5.29516e7 q^{45} +3.17815e7 q^{46} -2.11033e7 q^{47} -6.63847e7 q^{48} -1.37586e6 q^{49} +9.76527e7 q^{50} +2.15617e7 q^{52} +2.19582e7 q^{53} +1.43796e7 q^{54} +1.96007e8 q^{55} +5.26824e7 q^{56} +1.15258e8 q^{57} -5.28011e7 q^{58} +4.21319e7 q^{59} +9.45798e7 q^{60} +6.01904e7 q^{61} -2.50773e8 q^{62} -1.39364e8 q^{63} +5.18285e7 q^{64} +2.62912e8 q^{65} +4.50150e8 q^{66} +2.11182e8 q^{67} +2.45053e8 q^{69} -3.93652e8 q^{70} +3.37272e8 q^{71} -1.88365e8 q^{72} -2.34922e8 q^{73} -2.61569e7 q^{74} +7.52955e8 q^{75} +1.09403e8 q^{76} -5.15874e8 q^{77} +6.03803e8 q^{78} +1.77751e8 q^{79} -7.68334e8 q^{80} -3.28500e8 q^{81} -5.83727e7 q^{82} +1.29416e8 q^{83} -2.48926e8 q^{84} +9.11679e7 q^{86} -4.07125e8 q^{87} -6.97256e8 q^{88} +2.82211e8 q^{89} +1.40750e9 q^{90} -6.91962e8 q^{91} +2.32603e8 q^{92} -1.93360e9 q^{93} -5.60944e8 q^{94} +1.33400e9 q^{95} -8.79076e8 q^{96} +4.77665e7 q^{97} -3.65716e7 q^{98} +1.84450e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 486q^{3} + 9216q^{4} + 3750q^{5} + 11061q^{6} + 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q + 486q^{3} + 9216q^{4} + 3750q^{5} + 11061q^{6} + 29040q^{7} + 24837q^{8} + 236196q^{9} + 60000q^{10} + 76902q^{11} + 373248q^{12} + 54216q^{13} + 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} + 6439479q^{20} - 138102q^{21} + 267324q^{22} + 4041462q^{23} + 7653888q^{24} + 16582356q^{25} + 15822744q^{26} + 13281612q^{27} + 18614784q^{28} + 4005936q^{29} + 22471686q^{30} + 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} + 22076682q^{37} - 27401376q^{38} + 62736162q^{39} - 12231630q^{40} + 59641782q^{41} + 150001536q^{42} - 47951586q^{43} - 49578936q^{44} + 129308238q^{45} + 140524827q^{46} - 118557912q^{47} + 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} + 209848575q^{54} - 365439924q^{55} + 203095059q^{56} - 4614108q^{57} - 179071413q^{58} + 343015128q^{59} + 427179186q^{60} + 175597116q^{61} + 720602571q^{62} + 587415936q^{63} + 853082511q^{64} + 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} + 1308709542q^{71} - 275337849q^{72} + 494841342q^{73} + 1545361890q^{74} + 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} + 2270624538q^{78} + 1980107868q^{79} + 2897000199q^{80} + 1598298840q^{81} + 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} - 2705904618q^{88} + 148394658q^{89} + 117916215q^{90} + 636340896q^{91} - 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} + 4878626298q^{95} - 8390096634q^{96} - 891786822q^{97} + 4285627647q^{98} - 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 26.5808 1.17472 0.587359 0.809327i \(-0.300168\pi\)
0.587359 + 0.809327i \(0.300168\pi\)
\(3\) 204.952 1.46086 0.730428 0.682989i \(-0.239321\pi\)
0.730428 + 0.682989i \(0.239321\pi\)
\(4\) 194.540 0.379961
\(5\) 2372.11 1.69735 0.848673 0.528917i \(-0.177402\pi\)
0.848673 + 0.528917i \(0.177402\pi\)
\(6\) 5447.81 1.71609
\(7\) −6243.22 −0.982805 −0.491402 0.870933i \(-0.663516\pi\)
−0.491402 + 0.870933i \(0.663516\pi\)
\(8\) −8438.34 −0.728370
\(9\) 22322.5 1.13410
\(10\) 63052.8 1.99390
\(11\) 82629.5 1.70164 0.850821 0.525456i \(-0.176105\pi\)
0.850821 + 0.525456i \(0.176105\pi\)
\(12\) 39871.5 0.555069
\(13\) 110834. 1.07629 0.538144 0.842853i \(-0.319125\pi\)
0.538144 + 0.842853i \(0.319125\pi\)
\(14\) −165950. −1.15452
\(15\) 486171. 2.47958
\(16\) −323903. −1.23559
\(17\) 0 0
\(18\) 593351. 1.33225
\(19\) 562366. 0.989983 0.494992 0.868898i \(-0.335171\pi\)
0.494992 + 0.868898i \(0.335171\pi\)
\(20\) 461472. 0.644926
\(21\) −1.27956e6 −1.43574
\(22\) 2.19636e6 1.99895
\(23\) 1.19566e6 0.890904 0.445452 0.895306i \(-0.353043\pi\)
0.445452 + 0.895306i \(0.353043\pi\)
\(24\) −1.72946e6 −1.06404
\(25\) 3.67380e6 1.88099
\(26\) 2.94607e6 1.26434
\(27\) 540977. 0.195903
\(28\) −1.21456e6 −0.373428
\(29\) −1.98644e6 −0.521535 −0.260767 0.965402i \(-0.583976\pi\)
−0.260767 + 0.965402i \(0.583976\pi\)
\(30\) 1.29228e7 2.91281
\(31\) −9.43437e6 −1.83478 −0.917392 0.397984i \(-0.869710\pi\)
−0.917392 + 0.397984i \(0.869710\pi\)
\(32\) −4.28917e6 −0.723100
\(33\) 1.69351e7 2.48585
\(34\) 0 0
\(35\) −1.48096e7 −1.66816
\(36\) 4.34263e6 0.430915
\(37\) −984052. −0.0863197 −0.0431599 0.999068i \(-0.513742\pi\)
−0.0431599 + 0.999068i \(0.513742\pi\)
\(38\) 1.49481e7 1.16295
\(39\) 2.27158e7 1.57230
\(40\) −2.00167e7 −1.23630
\(41\) −2.19605e6 −0.121371 −0.0606854 0.998157i \(-0.519329\pi\)
−0.0606854 + 0.998157i \(0.519329\pi\)
\(42\) −3.40118e7 −1.68658
\(43\) 3.42984e6 0.152991 0.0764954 0.997070i \(-0.475627\pi\)
0.0764954 + 0.997070i \(0.475627\pi\)
\(44\) 1.60748e7 0.646558
\(45\) 5.29516e7 1.92496
\(46\) 3.17815e7 1.04656
\(47\) −2.11033e7 −0.630827 −0.315414 0.948954i \(-0.602143\pi\)
−0.315414 + 0.948954i \(0.602143\pi\)
\(48\) −6.63847e7 −1.80502
\(49\) −1.37586e6 −0.0340952
\(50\) 9.76527e7 2.20963
\(51\) 0 0
\(52\) 2.15617e7 0.408948
\(53\) 2.19582e7 0.382258 0.191129 0.981565i \(-0.438785\pi\)
0.191129 + 0.981565i \(0.438785\pi\)
\(54\) 1.43796e7 0.230131
\(55\) 1.96007e8 2.88828
\(56\) 5.26824e7 0.715846
\(57\) 1.15258e8 1.44622
\(58\) −5.28011e7 −0.612656
\(59\) 4.21319e7 0.452665 0.226333 0.974050i \(-0.427326\pi\)
0.226333 + 0.974050i \(0.427326\pi\)
\(60\) 9.45798e7 0.942145
\(61\) 6.01904e7 0.556599 0.278300 0.960494i \(-0.410229\pi\)
0.278300 + 0.960494i \(0.410229\pi\)
\(62\) −2.50773e8 −2.15535
\(63\) −1.39364e8 −1.11460
\(64\) 5.18285e7 0.386153
\(65\) 2.62912e8 1.82684
\(66\) 4.50150e8 2.92018
\(67\) 2.11182e8 1.28032 0.640162 0.768240i \(-0.278867\pi\)
0.640162 + 0.768240i \(0.278867\pi\)
\(68\) 0 0
\(69\) 2.45053e8 1.30148
\(70\) −3.93652e8 −1.95962
\(71\) 3.37272e8 1.57513 0.787567 0.616229i \(-0.211340\pi\)
0.787567 + 0.616229i \(0.211340\pi\)
\(72\) −1.88365e8 −0.826046
\(73\) −2.34922e8 −0.968211 −0.484106 0.875010i \(-0.660855\pi\)
−0.484106 + 0.875010i \(0.660855\pi\)
\(74\) −2.61569e7 −0.101401
\(75\) 7.52955e8 2.74785
\(76\) 1.09403e8 0.376155
\(77\) −5.15874e8 −1.67238
\(78\) 6.03803e8 1.84701
\(79\) 1.77751e8 0.513440 0.256720 0.966486i \(-0.417358\pi\)
0.256720 + 0.966486i \(0.417358\pi\)
\(80\) −7.68334e8 −2.09723
\(81\) −3.28500e8 −0.847915
\(82\) −5.83727e7 −0.142576
\(83\) 1.29416e8 0.299321 0.149661 0.988737i \(-0.452182\pi\)
0.149661 + 0.988737i \(0.452182\pi\)
\(84\) −2.48926e8 −0.545524
\(85\) 0 0
\(86\) 9.11679e7 0.179721
\(87\) −4.07125e8 −0.761888
\(88\) −6.97256e8 −1.23943
\(89\) 2.82211e8 0.476782 0.238391 0.971169i \(-0.423380\pi\)
0.238391 + 0.971169i \(0.423380\pi\)
\(90\) 1.40750e9 2.26129
\(91\) −6.91962e8 −1.05778
\(92\) 2.32603e8 0.338509
\(93\) −1.93360e9 −2.68036
\(94\) −5.60944e8 −0.741044
\(95\) 1.33400e9 1.68034
\(96\) −8.79076e8 −1.05635
\(97\) 4.77665e7 0.0547836 0.0273918 0.999625i \(-0.491280\pi\)
0.0273918 + 0.999625i \(0.491280\pi\)
\(98\) −3.65716e7 −0.0400522
\(99\) 1.84450e9 1.92983
\(100\) 7.14702e8 0.714702
\(101\) 8.67959e8 0.829952 0.414976 0.909832i \(-0.363790\pi\)
0.414976 + 0.909832i \(0.363790\pi\)
\(102\) 0 0
\(103\) −1.70990e9 −1.49693 −0.748466 0.663173i \(-0.769209\pi\)
−0.748466 + 0.663173i \(0.769209\pi\)
\(104\) −9.35257e8 −0.783937
\(105\) −3.03527e9 −2.43694
\(106\) 5.83668e8 0.449045
\(107\) 4.88170e8 0.360034 0.180017 0.983663i \(-0.442385\pi\)
0.180017 + 0.983663i \(0.442385\pi\)
\(108\) 1.05242e8 0.0744357
\(109\) 1.68098e9 1.14062 0.570312 0.821428i \(-0.306822\pi\)
0.570312 + 0.821428i \(0.306822\pi\)
\(110\) 5.21002e9 3.39291
\(111\) −2.01684e8 −0.126101
\(112\) 2.02219e9 1.21434
\(113\) −6.53183e8 −0.376861 −0.188431 0.982086i \(-0.560340\pi\)
−0.188431 + 0.982086i \(0.560340\pi\)
\(114\) 3.06366e9 1.69890
\(115\) 2.83623e9 1.51217
\(116\) −3.86442e8 −0.198163
\(117\) 2.47410e9 1.22062
\(118\) 1.11990e9 0.531754
\(119\) 0 0
\(120\) −4.10248e9 −1.80605
\(121\) 4.46969e9 1.89559
\(122\) 1.59991e9 0.653847
\(123\) −4.50085e8 −0.177305
\(124\) −1.83536e9 −0.697147
\(125\) 4.08164e9 1.49534
\(126\) −3.70442e9 −1.30934
\(127\) −5.07472e9 −1.73099 −0.865496 0.500916i \(-0.832997\pi\)
−0.865496 + 0.500916i \(0.832997\pi\)
\(128\) 3.57370e9 1.17672
\(129\) 7.02954e8 0.223498
\(130\) 6.98840e9 2.14602
\(131\) 8.92114e7 0.0264667 0.0132333 0.999912i \(-0.495788\pi\)
0.0132333 + 0.999912i \(0.495788\pi\)
\(132\) 3.29456e9 0.944529
\(133\) −3.51097e9 −0.972960
\(134\) 5.61339e9 1.50402
\(135\) 1.28326e9 0.332516
\(136\) 0 0
\(137\) −4.14021e9 −1.00411 −0.502053 0.864837i \(-0.667422\pi\)
−0.502053 + 0.864837i \(0.667422\pi\)
\(138\) 6.51370e9 1.52888
\(139\) 3.35260e9 0.761754 0.380877 0.924626i \(-0.375622\pi\)
0.380877 + 0.924626i \(0.375622\pi\)
\(140\) −2.88107e9 −0.633837
\(141\) −4.32518e9 −0.921548
\(142\) 8.96496e9 1.85034
\(143\) 9.15818e9 1.83146
\(144\) −7.23033e9 −1.40129
\(145\) −4.71205e9 −0.885226
\(146\) −6.24441e9 −1.13737
\(147\) −2.81986e8 −0.0498081
\(148\) −1.91438e8 −0.0327982
\(149\) 5.04370e9 0.838323 0.419161 0.907912i \(-0.362324\pi\)
0.419161 + 0.907912i \(0.362324\pi\)
\(150\) 2.00142e10 3.22795
\(151\) −8.59842e9 −1.34593 −0.672965 0.739674i \(-0.734979\pi\)
−0.672965 + 0.739674i \(0.734979\pi\)
\(152\) −4.74544e9 −0.721074
\(153\) 0 0
\(154\) −1.37124e10 −1.96458
\(155\) −2.23794e10 −3.11427
\(156\) 4.41913e9 0.597415
\(157\) −1.24814e8 −0.0163951 −0.00819756 0.999966i \(-0.502609\pi\)
−0.00819756 + 0.999966i \(0.502609\pi\)
\(158\) 4.72476e9 0.603147
\(159\) 4.50040e9 0.558423
\(160\) −1.01744e10 −1.22735
\(161\) −7.46474e9 −0.875585
\(162\) −8.73179e9 −0.996061
\(163\) −1.44069e10 −1.59855 −0.799273 0.600969i \(-0.794782\pi\)
−0.799273 + 0.600969i \(0.794782\pi\)
\(164\) −4.27219e8 −0.0461162
\(165\) 4.01721e10 4.21936
\(166\) 3.43999e9 0.351618
\(167\) −5.26762e9 −0.524071 −0.262036 0.965058i \(-0.584394\pi\)
−0.262036 + 0.965058i \(0.584394\pi\)
\(168\) 1.07974e10 1.04575
\(169\) 1.67973e9 0.158398
\(170\) 0 0
\(171\) 1.25534e10 1.12274
\(172\) 6.67241e8 0.0581306
\(173\) −9.75496e9 −0.827977 −0.413988 0.910282i \(-0.635865\pi\)
−0.413988 + 0.910282i \(0.635865\pi\)
\(174\) −1.08217e10 −0.895003
\(175\) −2.29363e10 −1.84864
\(176\) −2.67639e10 −2.10253
\(177\) 8.63504e9 0.661279
\(178\) 7.50141e9 0.560084
\(179\) −2.35794e9 −0.171670 −0.0858349 0.996309i \(-0.527356\pi\)
−0.0858349 + 0.996309i \(0.527356\pi\)
\(180\) 1.03012e10 0.731412
\(181\) −1.48765e10 −1.03026 −0.515131 0.857111i \(-0.672257\pi\)
−0.515131 + 0.857111i \(0.672257\pi\)
\(182\) −1.83929e10 −1.24259
\(183\) 1.23362e10 0.813112
\(184\) −1.00894e10 −0.648908
\(185\) −2.33428e9 −0.146515
\(186\) −5.13966e10 −3.14866
\(187\) 0 0
\(188\) −4.10544e9 −0.239690
\(189\) −3.37743e9 −0.192535
\(190\) 3.54587e10 1.97393
\(191\) 1.91683e10 1.04216 0.521079 0.853509i \(-0.325530\pi\)
0.521079 + 0.853509i \(0.325530\pi\)
\(192\) 1.06224e10 0.564113
\(193\) −2.10127e10 −1.09012 −0.545060 0.838397i \(-0.683493\pi\)
−0.545060 + 0.838397i \(0.683493\pi\)
\(194\) 1.26967e9 0.0643553
\(195\) 5.38844e10 2.66874
\(196\) −2.67661e8 −0.0129548
\(197\) 4.16011e10 1.96792 0.983958 0.178402i \(-0.0570929\pi\)
0.983958 + 0.178402i \(0.0570929\pi\)
\(198\) 4.90283e10 2.26701
\(199\) 2.14454e10 0.969382 0.484691 0.874686i \(-0.338932\pi\)
0.484691 + 0.874686i \(0.338932\pi\)
\(200\) −3.10008e10 −1.37005
\(201\) 4.32822e10 1.87037
\(202\) 2.30711e10 0.974959
\(203\) 1.24017e10 0.512567
\(204\) 0 0
\(205\) −5.20927e9 −0.206008
\(206\) −4.54504e10 −1.75847
\(207\) 2.66901e10 1.01038
\(208\) −3.58995e10 −1.32985
\(209\) 4.64680e10 1.68460
\(210\) −8.06800e10 −2.86272
\(211\) −4.84300e10 −1.68207 −0.841034 0.540982i \(-0.818053\pi\)
−0.841034 + 0.540982i \(0.818053\pi\)
\(212\) 4.27176e9 0.145243
\(213\) 6.91247e10 2.30104
\(214\) 1.29760e10 0.422939
\(215\) 8.13597e9 0.259679
\(216\) −4.56495e9 −0.142690
\(217\) 5.89008e10 1.80323
\(218\) 4.46817e10 1.33991
\(219\) −4.81478e10 −1.41442
\(220\) 3.81312e10 1.09743
\(221\) 0 0
\(222\) −5.36092e9 −0.148133
\(223\) 4.89472e9 0.132543 0.0662713 0.997802i \(-0.478890\pi\)
0.0662713 + 0.997802i \(0.478890\pi\)
\(224\) 2.67782e10 0.710666
\(225\) 8.20085e10 2.13323
\(226\) −1.73621e10 −0.442706
\(227\) −7.30390e10 −1.82574 −0.912869 0.408253i \(-0.866138\pi\)
−0.912869 + 0.408253i \(0.866138\pi\)
\(228\) 2.24224e10 0.549509
\(229\) −6.16423e10 −1.48122 −0.740609 0.671936i \(-0.765463\pi\)
−0.740609 + 0.671936i \(0.765463\pi\)
\(230\) 7.53894e10 1.77638
\(231\) −1.05730e11 −2.44311
\(232\) 1.67622e10 0.379871
\(233\) −3.99787e10 −0.888642 −0.444321 0.895868i \(-0.646555\pi\)
−0.444321 + 0.895868i \(0.646555\pi\)
\(234\) 6.57636e10 1.43388
\(235\) −5.00595e10 −1.07073
\(236\) 8.19636e9 0.171995
\(237\) 3.64305e10 0.750062
\(238\) 0 0
\(239\) 6.22662e10 1.23442 0.617209 0.786800i \(-0.288263\pi\)
0.617209 + 0.786800i \(0.288263\pi\)
\(240\) −1.57472e11 −3.06375
\(241\) 5.24041e10 1.00067 0.500333 0.865833i \(-0.333211\pi\)
0.500333 + 0.865833i \(0.333211\pi\)
\(242\) 1.18808e11 2.22678
\(243\) −7.79749e10 −1.43459
\(244\) 1.17094e10 0.211486
\(245\) −3.26370e9 −0.0578713
\(246\) −1.19636e10 −0.208284
\(247\) 6.23294e10 1.06551
\(248\) 7.96104e10 1.33640
\(249\) 2.65242e10 0.437266
\(250\) 1.08493e11 1.75660
\(251\) −1.25587e10 −0.199717 −0.0998584 0.995002i \(-0.531839\pi\)
−0.0998584 + 0.995002i \(0.531839\pi\)
\(252\) −2.71120e10 −0.423505
\(253\) 9.87965e10 1.51600
\(254\) −1.34890e11 −2.03343
\(255\) 0 0
\(256\) 6.84557e10 0.996161
\(257\) 3.80725e10 0.544393 0.272196 0.962242i \(-0.412250\pi\)
0.272196 + 0.962242i \(0.412250\pi\)
\(258\) 1.86851e10 0.262547
\(259\) 6.14365e9 0.0848354
\(260\) 5.11469e10 0.694127
\(261\) −4.43422e10 −0.591474
\(262\) 2.37131e9 0.0310909
\(263\) −1.29507e11 −1.66914 −0.834570 0.550902i \(-0.814284\pi\)
−0.834570 + 0.550902i \(0.814284\pi\)
\(264\) −1.42904e11 −1.81062
\(265\) 5.20874e10 0.648824
\(266\) −9.33245e10 −1.14295
\(267\) 5.78399e10 0.696509
\(268\) 4.10834e10 0.486474
\(269\) −6.99912e10 −0.815001 −0.407500 0.913205i \(-0.633599\pi\)
−0.407500 + 0.913205i \(0.633599\pi\)
\(270\) 3.41101e10 0.390612
\(271\) 3.71493e10 0.418397 0.209199 0.977873i \(-0.432914\pi\)
0.209199 + 0.977873i \(0.432914\pi\)
\(272\) 0 0
\(273\) −1.41819e11 −1.54527
\(274\) −1.10050e11 −1.17954
\(275\) 3.03565e11 3.20077
\(276\) 4.76726e10 0.494513
\(277\) −1.10314e11 −1.12583 −0.562915 0.826515i \(-0.690320\pi\)
−0.562915 + 0.826515i \(0.690320\pi\)
\(278\) 8.91148e10 0.894846
\(279\) −2.10599e11 −2.08083
\(280\) 1.24969e11 1.21504
\(281\) −5.01827e10 −0.480148 −0.240074 0.970755i \(-0.577172\pi\)
−0.240074 + 0.970755i \(0.577172\pi\)
\(282\) −1.14967e11 −1.08256
\(283\) −1.75840e9 −0.0162959 −0.00814795 0.999967i \(-0.502594\pi\)
−0.00814795 + 0.999967i \(0.502594\pi\)
\(284\) 6.56129e10 0.598490
\(285\) 2.73406e11 2.45474
\(286\) 2.43432e11 2.15145
\(287\) 1.37104e10 0.119284
\(288\) −9.57451e10 −0.820069
\(289\) 0 0
\(290\) −1.25250e11 −1.03989
\(291\) 9.78986e9 0.0800310
\(292\) −4.57017e10 −0.367883
\(293\) −1.52956e11 −1.21245 −0.606223 0.795294i \(-0.707316\pi\)
−0.606223 + 0.795294i \(0.707316\pi\)
\(294\) −7.49543e9 −0.0585105
\(295\) 9.99418e10 0.768330
\(296\) 8.30376e9 0.0628727
\(297\) 4.47007e10 0.333357
\(298\) 1.34066e11 0.984793
\(299\) 1.32520e11 0.958870
\(300\) 1.46480e11 1.04408
\(301\) −2.14132e10 −0.150360
\(302\) −2.28553e11 −1.58109
\(303\) 1.77890e11 1.21244
\(304\) −1.82152e11 −1.22321
\(305\) 1.42778e11 0.944742
\(306\) 0 0
\(307\) −4.31909e10 −0.277504 −0.138752 0.990327i \(-0.544309\pi\)
−0.138752 + 0.990327i \(0.544309\pi\)
\(308\) −1.00358e11 −0.635440
\(309\) −3.50447e11 −2.18680
\(310\) −5.94863e11 −3.65838
\(311\) 1.43948e10 0.0872538 0.0436269 0.999048i \(-0.486109\pi\)
0.0436269 + 0.999048i \(0.486109\pi\)
\(312\) −1.91683e11 −1.14522
\(313\) 8.86698e10 0.522187 0.261094 0.965313i \(-0.415917\pi\)
0.261094 + 0.965313i \(0.415917\pi\)
\(314\) −3.31766e9 −0.0192596
\(315\) −3.30588e11 −1.89186
\(316\) 3.45797e10 0.195087
\(317\) 2.84750e11 1.58379 0.791894 0.610658i \(-0.209095\pi\)
0.791894 + 0.610658i \(0.209095\pi\)
\(318\) 1.19624e11 0.655990
\(319\) −1.64138e11 −0.887466
\(320\) 1.22943e11 0.655435
\(321\) 1.00052e11 0.525959
\(322\) −1.98419e11 −1.02856
\(323\) 0 0
\(324\) −6.39064e10 −0.322175
\(325\) 4.07183e11 2.02449
\(326\) −3.82946e11 −1.87784
\(327\) 3.44520e11 1.66629
\(328\) 1.85310e10 0.0884029
\(329\) 1.31753e11 0.619980
\(330\) 1.06781e12 4.95655
\(331\) 2.34561e11 1.07406 0.537032 0.843562i \(-0.319546\pi\)
0.537032 + 0.843562i \(0.319546\pi\)
\(332\) 2.51767e10 0.113731
\(333\) −2.19665e10 −0.0978954
\(334\) −1.40018e11 −0.615635
\(335\) 5.00948e11 2.17315
\(336\) 4.14454e11 1.77398
\(337\) −2.30248e11 −0.972435 −0.486217 0.873838i \(-0.661624\pi\)
−0.486217 + 0.873838i \(0.661624\pi\)
\(338\) 4.46486e10 0.186073
\(339\) −1.33871e11 −0.550541
\(340\) 0 0
\(341\) −7.79557e11 −3.12215
\(342\) 3.33680e11 1.31890
\(343\) 2.60526e11 1.01631
\(344\) −2.89421e10 −0.111434
\(345\) 5.81293e11 2.20907
\(346\) −2.59295e11 −0.972639
\(347\) −3.95650e11 −1.46497 −0.732486 0.680783i \(-0.761640\pi\)
−0.732486 + 0.680783i \(0.761640\pi\)
\(348\) −7.92022e10 −0.289488
\(349\) 1.96752e10 0.0709912 0.0354956 0.999370i \(-0.488699\pi\)
0.0354956 + 0.999370i \(0.488699\pi\)
\(350\) −6.09667e11 −2.17163
\(351\) 5.99587e10 0.210849
\(352\) −3.54412e11 −1.23046
\(353\) −3.77116e11 −1.29267 −0.646336 0.763053i \(-0.723700\pi\)
−0.646336 + 0.763053i \(0.723700\pi\)
\(354\) 2.29527e11 0.776816
\(355\) 8.00047e11 2.67355
\(356\) 5.49015e10 0.181159
\(357\) 0 0
\(358\) −6.26760e10 −0.201664
\(359\) −1.70850e11 −0.542864 −0.271432 0.962458i \(-0.587497\pi\)
−0.271432 + 0.962458i \(0.587497\pi\)
\(360\) −4.46824e11 −1.40209
\(361\) −6.43229e9 −0.0199335
\(362\) −3.95430e11 −1.21027
\(363\) 9.16074e11 2.76918
\(364\) −1.34614e11 −0.401916
\(365\) −5.57261e11 −1.64339
\(366\) 3.27905e11 0.955177
\(367\) 5.44356e11 1.56634 0.783169 0.621809i \(-0.213602\pi\)
0.783169 + 0.621809i \(0.213602\pi\)
\(368\) −3.87276e11 −1.10079
\(369\) −4.90213e10 −0.137647
\(370\) −6.20472e10 −0.172113
\(371\) −1.37090e11 −0.375684
\(372\) −3.76162e11 −1.01843
\(373\) 1.31625e11 0.352086 0.176043 0.984383i \(-0.443670\pi\)
0.176043 + 0.984383i \(0.443670\pi\)
\(374\) 0 0
\(375\) 8.36543e11 2.18448
\(376\) 1.78077e11 0.459476
\(377\) −2.20165e11 −0.561322
\(378\) −8.97750e10 −0.226174
\(379\) −4.36513e11 −1.08673 −0.543363 0.839498i \(-0.682849\pi\)
−0.543363 + 0.839498i \(0.682849\pi\)
\(380\) 2.59516e11 0.638466
\(381\) −1.04008e12 −2.52873
\(382\) 5.09509e11 1.22424
\(383\) −4.54186e11 −1.07855 −0.539274 0.842131i \(-0.681301\pi\)
−0.539274 + 0.842131i \(0.681301\pi\)
\(384\) 7.32439e11 1.71902
\(385\) −1.22371e12 −2.83861
\(386\) −5.58535e11 −1.28058
\(387\) 7.65626e10 0.173507
\(388\) 9.29251e9 0.0208157
\(389\) −3.33633e11 −0.738746 −0.369373 0.929281i \(-0.620428\pi\)
−0.369373 + 0.929281i \(0.620428\pi\)
\(390\) 1.43229e12 3.13502
\(391\) 0 0
\(392\) 1.16100e10 0.0248339
\(393\) 1.82841e10 0.0386640
\(394\) 1.10579e12 2.31174
\(395\) 4.21645e11 0.871486
\(396\) 3.58829e11 0.733263
\(397\) −6.05717e9 −0.0122381 −0.00611903 0.999981i \(-0.501948\pi\)
−0.00611903 + 0.999981i \(0.501948\pi\)
\(398\) 5.70036e11 1.13875
\(399\) −7.19582e11 −1.42135
\(400\) −1.18995e12 −2.32413
\(401\) −5.77300e11 −1.11494 −0.557470 0.830197i \(-0.688228\pi\)
−0.557470 + 0.830197i \(0.688228\pi\)
\(402\) 1.15048e12 2.19716
\(403\) −1.04565e12 −1.97476
\(404\) 1.68853e11 0.315350
\(405\) −7.79239e11 −1.43921
\(406\) 3.29649e11 0.602121
\(407\) −8.13117e10 −0.146885
\(408\) 0 0
\(409\) 4.95915e11 0.876299 0.438150 0.898902i \(-0.355634\pi\)
0.438150 + 0.898902i \(0.355634\pi\)
\(410\) −1.38467e11 −0.242002
\(411\) −8.48545e11 −1.46685
\(412\) −3.32644e11 −0.568777
\(413\) −2.63039e11 −0.444882
\(414\) 7.09444e11 1.18691
\(415\) 3.06990e11 0.508052
\(416\) −4.75387e11 −0.778264
\(417\) 6.87124e11 1.11281
\(418\) 1.23516e12 1.97893
\(419\) 2.71184e10 0.0429835 0.0214917 0.999769i \(-0.493158\pi\)
0.0214917 + 0.999769i \(0.493158\pi\)
\(420\) −5.90482e11 −0.925944
\(421\) 4.56222e10 0.0707794 0.0353897 0.999374i \(-0.488733\pi\)
0.0353897 + 0.999374i \(0.488733\pi\)
\(422\) −1.28731e12 −1.97596
\(423\) −4.71079e11 −0.715422
\(424\) −1.85291e11 −0.278425
\(425\) 0 0
\(426\) 1.83739e12 2.70308
\(427\) −3.75781e11 −0.547028
\(428\) 9.49687e10 0.136799
\(429\) 1.87699e12 2.67550
\(430\) 2.16261e11 0.305049
\(431\) 4.84347e11 0.676097 0.338049 0.941129i \(-0.390233\pi\)
0.338049 + 0.941129i \(0.390233\pi\)
\(432\) −1.75224e11 −0.242056
\(433\) −3.69939e11 −0.505748 −0.252874 0.967499i \(-0.581376\pi\)
−0.252874 + 0.967499i \(0.581376\pi\)
\(434\) 1.56563e12 2.11829
\(435\) −9.65747e11 −1.29319
\(436\) 3.27017e11 0.433393
\(437\) 6.72396e11 0.881980
\(438\) −1.27981e12 −1.66154
\(439\) 4.40589e11 0.566165 0.283083 0.959096i \(-0.408643\pi\)
0.283083 + 0.959096i \(0.408643\pi\)
\(440\) −1.65397e12 −2.10373
\(441\) −3.07127e10 −0.0386674
\(442\) 0 0
\(443\) −5.93995e11 −0.732767 −0.366383 0.930464i \(-0.619404\pi\)
−0.366383 + 0.930464i \(0.619404\pi\)
\(444\) −3.92356e10 −0.0479134
\(445\) 6.69438e11 0.809264
\(446\) 1.30106e11 0.155700
\(447\) 1.03372e12 1.22467
\(448\) −3.23577e11 −0.379512
\(449\) 1.04989e12 1.21909 0.609546 0.792751i \(-0.291352\pi\)
0.609546 + 0.792751i \(0.291352\pi\)
\(450\) 2.17985e12 2.50594
\(451\) −1.81458e11 −0.206530
\(452\) −1.27070e11 −0.143193
\(453\) −1.76227e12 −1.96621
\(454\) −1.94144e12 −2.14473
\(455\) −1.64141e12 −1.79542
\(456\) −9.72589e11 −1.05339
\(457\) −1.90102e11 −0.203875 −0.101937 0.994791i \(-0.532504\pi\)
−0.101937 + 0.994791i \(0.532504\pi\)
\(458\) −1.63850e12 −1.74001
\(459\) 0 0
\(460\) 5.51761e11 0.574568
\(461\) −1.73350e11 −0.178760 −0.0893798 0.995998i \(-0.528489\pi\)
−0.0893798 + 0.995998i \(0.528489\pi\)
\(462\) −2.81038e12 −2.86996
\(463\) −8.10491e11 −0.819660 −0.409830 0.912162i \(-0.634412\pi\)
−0.409830 + 0.912162i \(0.634412\pi\)
\(464\) 6.43412e11 0.644404
\(465\) −4.58671e12 −4.54950
\(466\) −1.06267e12 −1.04390
\(467\) 1.10255e12 1.07269 0.536343 0.844000i \(-0.319805\pi\)
0.536343 + 0.844000i \(0.319805\pi\)
\(468\) 4.81312e11 0.463789
\(469\) −1.31845e12 −1.25831
\(470\) −1.33062e12 −1.25781
\(471\) −2.55809e10 −0.0239509
\(472\) −3.55524e11 −0.329708
\(473\) 2.83406e11 0.260336
\(474\) 9.68352e11 0.881111
\(475\) 2.06602e12 1.86215
\(476\) 0 0
\(477\) 4.90163e11 0.433519
\(478\) 1.65509e12 1.45009
\(479\) −1.26632e12 −1.09909 −0.549546 0.835463i \(-0.685199\pi\)
−0.549546 + 0.835463i \(0.685199\pi\)
\(480\) −2.08527e12 −1.79298
\(481\) −1.09067e11 −0.0929050
\(482\) 1.39294e12 1.17550
\(483\) −1.52992e12 −1.27910
\(484\) 8.69535e11 0.720249
\(485\) 1.13308e11 0.0929868
\(486\) −2.07264e12 −1.68523
\(487\) 1.15988e12 0.934400 0.467200 0.884152i \(-0.345263\pi\)
0.467200 + 0.884152i \(0.345263\pi\)
\(488\) −5.07907e11 −0.405410
\(489\) −2.95272e12 −2.33524
\(490\) −8.67519e10 −0.0679824
\(491\) −5.92953e11 −0.460420 −0.230210 0.973141i \(-0.573941\pi\)
−0.230210 + 0.973141i \(0.573941\pi\)
\(492\) −8.75597e10 −0.0673692
\(493\) 0 0
\(494\) 1.65677e12 1.25167
\(495\) 4.37536e12 3.27560
\(496\) 3.05582e12 2.26704
\(497\) −2.10566e12 −1.54805
\(498\) 7.05035e11 0.513664
\(499\) −2.80366e11 −0.202429 −0.101214 0.994865i \(-0.532273\pi\)
−0.101214 + 0.994865i \(0.532273\pi\)
\(500\) 7.94044e11 0.568172
\(501\) −1.07961e12 −0.765593
\(502\) −3.33822e11 −0.234611
\(503\) 2.37709e12 1.65573 0.827866 0.560926i \(-0.189555\pi\)
0.827866 + 0.560926i \(0.189555\pi\)
\(504\) 1.17600e12 0.811842
\(505\) 2.05890e12 1.40872
\(506\) 2.62609e12 1.78087
\(507\) 3.44265e11 0.231396
\(508\) −9.87236e11 −0.657710
\(509\) −7.61106e11 −0.502591 −0.251296 0.967910i \(-0.580857\pi\)
−0.251296 + 0.967910i \(0.580857\pi\)
\(510\) 0 0
\(511\) 1.46667e12 0.951563
\(512\) −1.01257e10 −0.00651191
\(513\) 3.04227e11 0.193941
\(514\) 1.01200e12 0.639508
\(515\) −4.05607e12 −2.54081
\(516\) 1.36753e11 0.0849205
\(517\) −1.74376e12 −1.07344
\(518\) 1.63303e11 0.0996577
\(519\) −1.99930e12 −1.20956
\(520\) −2.21854e12 −1.33061
\(521\) 1.80892e12 1.07560 0.537800 0.843073i \(-0.319256\pi\)
0.537800 + 0.843073i \(0.319256\pi\)
\(522\) −1.17865e12 −0.694815
\(523\) 2.49717e11 0.145946 0.0729728 0.997334i \(-0.476751\pi\)
0.0729728 + 0.997334i \(0.476751\pi\)
\(524\) 1.73552e10 0.0100563
\(525\) −4.70086e12 −2.70060
\(526\) −3.44241e12 −1.96077
\(527\) 0 0
\(528\) −5.48533e12 −3.07150
\(529\) −3.71559e11 −0.206290
\(530\) 1.38453e12 0.762185
\(531\) 9.40491e11 0.513369
\(532\) −6.83025e11 −0.369687
\(533\) −2.43397e11 −0.130630
\(534\) 1.53743e12 0.818202
\(535\) 1.15799e12 0.611103
\(536\) −1.78202e12 −0.932550
\(537\) −4.83266e11 −0.250785
\(538\) −1.86042e12 −0.957396
\(539\) −1.13687e11 −0.0580177
\(540\) 2.49645e11 0.126343
\(541\) −1.08050e12 −0.542297 −0.271148 0.962538i \(-0.587403\pi\)
−0.271148 + 0.962538i \(0.587403\pi\)
\(542\) 9.87459e11 0.491499
\(543\) −3.04898e12 −1.50507
\(544\) 0 0
\(545\) 3.98747e12 1.93603
\(546\) −3.76968e12 −1.81525
\(547\) −2.42243e12 −1.15693 −0.578466 0.815707i \(-0.696348\pi\)
−0.578466 + 0.815707i \(0.696348\pi\)
\(548\) −8.05437e11 −0.381521
\(549\) 1.34360e12 0.631240
\(550\) 8.06900e12 3.76000
\(551\) −1.11710e12 −0.516311
\(552\) −2.06784e12 −0.947962
\(553\) −1.10974e12 −0.504611
\(554\) −2.93225e12 −1.32253
\(555\) −4.78417e11 −0.214037
\(556\) 6.52215e11 0.289437
\(557\) −1.69897e12 −0.747890 −0.373945 0.927451i \(-0.621995\pi\)
−0.373945 + 0.927451i \(0.621995\pi\)
\(558\) −5.59789e12 −2.44439
\(559\) 3.80143e11 0.164662
\(560\) 4.79688e12 2.06116
\(561\) 0 0
\(562\) −1.33390e12 −0.564038
\(563\) −2.39306e12 −1.00384 −0.501921 0.864913i \(-0.667373\pi\)
−0.501921 + 0.864913i \(0.667373\pi\)
\(564\) −8.41421e11 −0.350153
\(565\) −1.54942e12 −0.639665
\(566\) −4.67397e10 −0.0191431
\(567\) 2.05089e12 0.833335
\(568\) −2.84602e12 −1.14728
\(569\) −2.71831e12 −1.08716 −0.543581 0.839357i \(-0.682932\pi\)
−0.543581 + 0.839357i \(0.682932\pi\)
\(570\) 7.26735e12 2.88363
\(571\) −1.20499e12 −0.474374 −0.237187 0.971464i \(-0.576225\pi\)
−0.237187 + 0.971464i \(0.576225\pi\)
\(572\) 1.78163e12 0.695883
\(573\) 3.92859e12 1.52244
\(574\) 3.64434e11 0.140125
\(575\) 4.39260e12 1.67578
\(576\) 1.15694e12 0.437936
\(577\) 2.39602e12 0.899910 0.449955 0.893051i \(-0.351440\pi\)
0.449955 + 0.893051i \(0.351440\pi\)
\(578\) 0 0
\(579\) −4.30661e12 −1.59251
\(580\) −9.16684e11 −0.336352
\(581\) −8.07974e11 −0.294175
\(582\) 2.60223e11 0.0940138
\(583\) 1.81440e12 0.650465
\(584\) 1.98235e12 0.705216
\(585\) 5.86885e12 2.07182
\(586\) −4.06570e12 −1.42428
\(587\) −1.88643e12 −0.655796 −0.327898 0.944713i \(-0.606340\pi\)
−0.327898 + 0.944713i \(0.606340\pi\)
\(588\) −5.48577e10 −0.0189252
\(589\) −5.30557e12 −1.81641
\(590\) 2.65653e12 0.902571
\(591\) 8.52624e12 2.87484
\(592\) 3.18737e11 0.106656
\(593\) 1.28573e12 0.426976 0.213488 0.976946i \(-0.431518\pi\)
0.213488 + 0.976946i \(0.431518\pi\)
\(594\) 1.18818e12 0.391601
\(595\) 0 0
\(596\) 9.81203e11 0.318530
\(597\) 4.39528e12 1.41613
\(598\) 3.52248e12 1.12640
\(599\) 4.18407e12 1.32794 0.663969 0.747760i \(-0.268871\pi\)
0.663969 + 0.747760i \(0.268871\pi\)
\(600\) −6.35369e12 −2.00145
\(601\) 2.40265e12 0.751199 0.375599 0.926782i \(-0.377437\pi\)
0.375599 + 0.926782i \(0.377437\pi\)
\(602\) −5.69181e11 −0.176631
\(603\) 4.71411e12 1.45202
\(604\) −1.67274e12 −0.511401
\(605\) 1.06026e13 3.21747
\(606\) 4.72847e12 1.42428
\(607\) 1.65529e12 0.494908 0.247454 0.968900i \(-0.420406\pi\)
0.247454 + 0.968900i \(0.420406\pi\)
\(608\) −2.41208e12 −0.715857
\(609\) 2.54177e12 0.748787
\(610\) 3.79517e12 1.10981
\(611\) −2.33897e12 −0.678952
\(612\) 0 0
\(613\) −1.56192e11 −0.0446772 −0.0223386 0.999750i \(-0.507111\pi\)
−0.0223386 + 0.999750i \(0.507111\pi\)
\(614\) −1.14805e12 −0.325989
\(615\) −1.06765e12 −0.300949
\(616\) 4.35312e12 1.21811
\(617\) −1.41213e12 −0.392277 −0.196138 0.980576i \(-0.562840\pi\)
−0.196138 + 0.980576i \(0.562840\pi\)
\(618\) −9.31518e12 −2.56888
\(619\) −2.21421e12 −0.606193 −0.303096 0.952960i \(-0.598020\pi\)
−0.303096 + 0.952960i \(0.598020\pi\)
\(620\) −4.35369e12 −1.18330
\(621\) 6.46822e11 0.174531
\(622\) 3.82626e11 0.102499
\(623\) −1.76191e12 −0.468583
\(624\) −7.35769e12 −1.94272
\(625\) 2.50673e12 0.657124
\(626\) 2.35692e12 0.613423
\(627\) 9.52374e12 2.46095
\(628\) −2.42813e10 −0.00622951
\(629\) 0 0
\(630\) −8.78731e12 −2.22241
\(631\) 5.77311e12 1.44970 0.724849 0.688908i \(-0.241909\pi\)
0.724849 + 0.688908i \(0.241909\pi\)
\(632\) −1.49992e12 −0.373974
\(633\) −9.92586e12 −2.45726
\(634\) 7.56889e12 1.86050
\(635\) −1.20378e13 −2.93809
\(636\) 8.75508e11 0.212179
\(637\) −1.52493e11 −0.0366962
\(638\) −4.36293e12 −1.04252
\(639\) 7.52876e12 1.78636
\(640\) 8.47722e12 1.99730
\(641\) −4.73882e12 −1.10869 −0.554344 0.832288i \(-0.687031\pi\)
−0.554344 + 0.832288i \(0.687031\pi\)
\(642\) 2.65946e12 0.617853
\(643\) 6.93341e12 1.59955 0.799774 0.600301i \(-0.204952\pi\)
0.799774 + 0.600301i \(0.204952\pi\)
\(644\) −1.45219e12 −0.332688
\(645\) 1.66749e12 0.379353
\(646\) 0 0
\(647\) 5.27307e12 1.18302 0.591512 0.806296i \(-0.298531\pi\)
0.591512 + 0.806296i \(0.298531\pi\)
\(648\) 2.77199e12 0.617596
\(649\) 3.48134e12 0.770274
\(650\) 1.08233e13 2.37820
\(651\) 1.20719e13 2.63427
\(652\) −2.80271e12 −0.607385
\(653\) 5.48140e12 1.17973 0.589864 0.807503i \(-0.299181\pi\)
0.589864 + 0.807503i \(0.299181\pi\)
\(654\) 9.15763e12 1.95742
\(655\) 2.11620e11 0.0449231
\(656\) 7.11305e11 0.149965
\(657\) −5.24404e12 −1.09805
\(658\) 3.50209e12 0.728301
\(659\) −1.18012e12 −0.243749 −0.121874 0.992546i \(-0.538891\pi\)
−0.121874 + 0.992546i \(0.538891\pi\)
\(660\) 7.81508e12 1.60319
\(661\) 7.91914e12 1.61351 0.806755 0.590886i \(-0.201222\pi\)
0.806755 + 0.590886i \(0.201222\pi\)
\(662\) 6.23483e12 1.26172
\(663\) 0 0
\(664\) −1.09206e12 −0.218017
\(665\) −8.32843e12 −1.65145
\(666\) −5.83888e11 −0.114999
\(667\) −2.37509e12 −0.464638
\(668\) −1.02476e12 −0.199127
\(669\) 1.00318e12 0.193626
\(670\) 1.33156e13 2.55284
\(671\) 4.97350e12 0.947133
\(672\) 5.48826e12 1.03818
\(673\) −4.57851e12 −0.860312 −0.430156 0.902755i \(-0.641541\pi\)
−0.430156 + 0.902755i \(0.641541\pi\)
\(674\) −6.12017e12 −1.14234
\(675\) 1.98744e12 0.368491
\(676\) 3.26775e11 0.0601850
\(677\) 2.03823e12 0.372909 0.186455 0.982464i \(-0.440300\pi\)
0.186455 + 0.982464i \(0.440300\pi\)
\(678\) −3.55841e12 −0.646730
\(679\) −2.98217e11 −0.0538416
\(680\) 0 0
\(681\) −1.49695e13 −2.66714
\(682\) −2.07213e13 −3.66764
\(683\) −6.08765e12 −1.07042 −0.535212 0.844718i \(-0.679768\pi\)
−0.535212 + 0.844718i \(0.679768\pi\)
\(684\) 2.44215e12 0.426598
\(685\) −9.82104e12 −1.70432
\(686\) 6.92500e12 1.19388
\(687\) −1.26337e13 −2.16385
\(688\) −1.11093e12 −0.189034
\(689\) 2.43372e12 0.411420
\(690\) 1.54512e13 2.59503
\(691\) 9.24898e12 1.54327 0.771636 0.636064i \(-0.219439\pi\)
0.771636 + 0.636064i \(0.219439\pi\)
\(692\) −1.89773e12 −0.314599
\(693\) −1.15156e13 −1.89665
\(694\) −1.05167e13 −1.72093
\(695\) 7.95275e12 1.29296
\(696\) 3.43546e12 0.554936
\(697\) 0 0
\(698\) 5.22983e11 0.0833946
\(699\) −8.19373e12 −1.29818
\(700\) −4.46204e12 −0.702413
\(701\) 5.92651e11 0.0926974 0.0463487 0.998925i \(-0.485241\pi\)
0.0463487 + 0.998925i \(0.485241\pi\)
\(702\) 1.59375e12 0.247687
\(703\) −5.53397e11 −0.0854551
\(704\) 4.28257e12 0.657093
\(705\) −1.02598e13 −1.56419
\(706\) −1.00241e13 −1.51853
\(707\) −5.41886e12 −0.815681
\(708\) 1.67986e12 0.251261
\(709\) 1.07708e13 1.60082 0.800408 0.599456i \(-0.204616\pi\)
0.800408 + 0.599456i \(0.204616\pi\)
\(710\) 2.12659e13 3.14067
\(711\) 3.96785e12 0.582293
\(712\) −2.38140e12 −0.347274
\(713\) −1.12803e13 −1.63462
\(714\) 0 0
\(715\) 2.17243e13 3.10862
\(716\) −4.58714e11 −0.0652279
\(717\) 1.27616e13 1.80331
\(718\) −4.54134e12 −0.637712
\(719\) 7.91653e12 1.10473 0.552363 0.833604i \(-0.313726\pi\)
0.552363 + 0.833604i \(0.313726\pi\)
\(720\) −1.71512e13 −2.37847
\(721\) 1.06752e13 1.47119
\(722\) −1.70976e11 −0.0234162
\(723\) 1.07404e13 1.46183
\(724\) −2.89408e12 −0.391460
\(725\) −7.29777e12 −0.981000
\(726\) 2.43500e13 3.25300
\(727\) −8.90450e12 −1.18224 −0.591119 0.806585i \(-0.701313\pi\)
−0.591119 + 0.806585i \(0.701313\pi\)
\(728\) 5.83901e12 0.770457
\(729\) −9.51529e12 −1.24781
\(730\) −1.48125e13 −1.93052
\(731\) 0 0
\(732\) 2.39988e12 0.308951
\(733\) −1.21085e13 −1.54926 −0.774628 0.632417i \(-0.782063\pi\)
−0.774628 + 0.632417i \(0.782063\pi\)
\(734\) 1.44694e13 1.84001
\(735\) −6.68904e11 −0.0845417
\(736\) −5.12837e12 −0.644213
\(737\) 1.74499e13 2.17865
\(738\) −1.30303e12 −0.161696
\(739\) −6.25896e12 −0.771973 −0.385987 0.922504i \(-0.626139\pi\)
−0.385987 + 0.922504i \(0.626139\pi\)
\(740\) −4.54112e11 −0.0556699
\(741\) 1.27746e13 1.55655
\(742\) −3.64397e12 −0.441323
\(743\) −8.59497e12 −1.03465 −0.517326 0.855788i \(-0.673073\pi\)
−0.517326 + 0.855788i \(0.673073\pi\)
\(744\) 1.63164e13 1.95229
\(745\) 1.19642e13 1.42292
\(746\) 3.49870e12 0.413601
\(747\) 2.88890e12 0.339461
\(748\) 0 0
\(749\) −3.04775e12 −0.353843
\(750\) 2.22360e13 2.56614
\(751\) 1.13458e13 1.30153 0.650767 0.759277i \(-0.274447\pi\)
0.650767 + 0.759277i \(0.274447\pi\)
\(752\) 6.83542e12 0.779444
\(753\) −2.57395e12 −0.291758
\(754\) −5.85217e12 −0.659395
\(755\) −2.03964e13 −2.28451
\(756\) −6.57047e11 −0.0731557
\(757\) −1.34405e13 −1.48759 −0.743797 0.668406i \(-0.766977\pi\)
−0.743797 + 0.668406i \(0.766977\pi\)
\(758\) −1.16029e13 −1.27660
\(759\) 2.02486e13 2.21466
\(760\) −1.12567e13 −1.22391
\(761\) 2.20957e12 0.238823 0.119412 0.992845i \(-0.461899\pi\)
0.119412 + 0.992845i \(0.461899\pi\)
\(762\) −2.76461e13 −2.97054
\(763\) −1.04947e13 −1.12101
\(764\) 3.72901e12 0.395980
\(765\) 0 0
\(766\) −1.20726e13 −1.26699
\(767\) 4.66966e12 0.487199
\(768\) 1.40302e13 1.45525
\(769\) 6.08633e12 0.627605 0.313803 0.949488i \(-0.398397\pi\)
0.313803 + 0.949488i \(0.398397\pi\)
\(770\) −3.25273e13 −3.33457
\(771\) 7.80306e12 0.795280
\(772\) −4.08782e12 −0.414204
\(773\) −6.60486e11 −0.0665359 −0.0332680 0.999446i \(-0.510591\pi\)
−0.0332680 + 0.999446i \(0.510591\pi\)
\(774\) 2.03510e12 0.203822
\(775\) −3.46600e13 −3.45121
\(776\) −4.03070e11 −0.0399027
\(777\) 1.25916e12 0.123932
\(778\) −8.86823e12 −0.867818
\(779\) −1.23498e12 −0.120155
\(780\) 1.04827e13 1.01402
\(781\) 2.78686e13 2.68031
\(782\) 0 0
\(783\) −1.07462e12 −0.102170
\(784\) 4.45646e11 0.0421277
\(785\) −2.96073e11 −0.0278282
\(786\) 4.86006e11 0.0454193
\(787\) 4.67412e12 0.434324 0.217162 0.976136i \(-0.430320\pi\)
0.217162 + 0.976136i \(0.430320\pi\)
\(788\) 8.09308e12 0.747732
\(789\) −2.65428e13 −2.43837
\(790\) 1.12077e13 1.02375
\(791\) 4.07796e12 0.370381
\(792\) −1.55645e13 −1.40563
\(793\) 6.67115e12 0.599062
\(794\) −1.61005e11 −0.0143763
\(795\) 1.06755e13 0.947838
\(796\) 4.17199e12 0.368328
\(797\) −4.83102e12 −0.424108 −0.212054 0.977258i \(-0.568015\pi\)
−0.212054 + 0.977258i \(0.568015\pi\)
\(798\) −1.91271e13 −1.66969
\(799\) 0 0
\(800\) −1.57576e13 −1.36014
\(801\) 6.29967e12 0.540719
\(802\) −1.53451e13 −1.30974
\(803\) −1.94115e13 −1.64755
\(804\) 8.42014e12 0.710668
\(805\) −1.77072e13 −1.48617
\(806\) −2.77943e13 −2.31978
\(807\) −1.43449e13 −1.19060
\(808\) −7.32413e12 −0.604512
\(809\) 1.13819e13 0.934213 0.467106 0.884201i \(-0.345297\pi\)
0.467106 + 0.884201i \(0.345297\pi\)
\(810\) −2.07128e13 −1.69066
\(811\) 1.59699e13 1.29631 0.648154 0.761510i \(-0.275541\pi\)
0.648154 + 0.761510i \(0.275541\pi\)
\(812\) 2.41264e12 0.194756
\(813\) 7.61384e12 0.611218
\(814\) −2.16133e12 −0.172549
\(815\) −3.41747e13 −2.71329
\(816\) 0 0
\(817\) 1.92882e12 0.151458
\(818\) 1.31818e13 1.02940
\(819\) −1.54463e13 −1.19963
\(820\) −1.01341e12 −0.0782752
\(821\) −6.88013e12 −0.528509 −0.264254 0.964453i \(-0.585126\pi\)
−0.264254 + 0.964453i \(0.585126\pi\)
\(822\) −2.25550e13 −1.72314
\(823\) 2.46473e13 1.87271 0.936353 0.351061i \(-0.114179\pi\)
0.936353 + 0.351061i \(0.114179\pi\)
\(824\) 1.44287e13 1.09032
\(825\) 6.22163e13 4.67586
\(826\) −6.99179e12 −0.522610
\(827\) 2.43084e13 1.80709 0.903547 0.428489i \(-0.140954\pi\)
0.903547 + 0.428489i \(0.140954\pi\)
\(828\) 5.19229e12 0.383904
\(829\) −1.07060e11 −0.00787282 −0.00393641 0.999992i \(-0.501253\pi\)
−0.00393641 + 0.999992i \(0.501253\pi\)
\(830\) 8.16006e12 0.596818
\(831\) −2.26092e13 −1.64468
\(832\) 5.74437e12 0.415612
\(833\) 0 0
\(834\) 1.82643e13 1.30724
\(835\) −1.24954e13 −0.889530
\(836\) 9.03990e12 0.640082
\(837\) −5.10377e12 −0.359440
\(838\) 7.20830e11 0.0504934
\(839\) 2.29541e12 0.159930 0.0799652 0.996798i \(-0.474519\pi\)
0.0799652 + 0.996798i \(0.474519\pi\)
\(840\) 2.56126e13 1.77500
\(841\) −1.05612e13 −0.728001
\(842\) 1.21268e12 0.0831458
\(843\) −1.02851e13 −0.701427
\(844\) −9.42159e12 −0.639121
\(845\) 3.98451e12 0.268856
\(846\) −1.25217e13 −0.840419
\(847\) −2.79052e13 −1.86299
\(848\) −7.11233e12 −0.472314
\(849\) −3.60388e11 −0.0238060
\(850\) 0 0
\(851\) −1.17659e12 −0.0769026
\(852\) 1.34475e13 0.874308
\(853\) −8.93269e12 −0.577713 −0.288856 0.957372i \(-0.593275\pi\)
−0.288856 + 0.957372i \(0.593275\pi\)
\(854\) −9.98858e12 −0.642604
\(855\) 2.97782e13 1.90568
\(856\) −4.11934e12 −0.262238
\(857\) 1.66952e13 1.05725 0.528626 0.848855i \(-0.322707\pi\)
0.528626 + 0.848855i \(0.322707\pi\)
\(858\) 4.98920e13 3.14295
\(859\) −8.71639e12 −0.546220 −0.273110 0.961983i \(-0.588052\pi\)
−0.273110 + 0.961983i \(0.588052\pi\)
\(860\) 1.58277e12 0.0986678
\(861\) 2.80998e12 0.174256
\(862\) 1.28744e13 0.794223
\(863\) −3.01729e12 −0.185169 −0.0925844 0.995705i \(-0.529513\pi\)
−0.0925844 + 0.995705i \(0.529513\pi\)
\(864\) −2.32034e12 −0.141658
\(865\) −2.31399e13 −1.40536
\(866\) −9.83328e12 −0.594112
\(867\) 0 0
\(868\) 1.14586e13 0.685160
\(869\) 1.46875e13 0.873691
\(870\) −2.56703e13 −1.51913
\(871\) 2.34062e13 1.37800
\(872\) −1.41846e13 −0.830796
\(873\) 1.06627e12 0.0621302
\(874\) 1.78728e13 1.03608
\(875\) −2.54826e13 −1.46963
\(876\) −9.36668e12 −0.537424
\(877\) 2.25993e13 1.29002 0.645012 0.764173i \(-0.276853\pi\)
0.645012 + 0.764173i \(0.276853\pi\)
\(878\) 1.17112e13 0.665084
\(879\) −3.13487e13 −1.77121
\(880\) −6.34871e13 −3.56873
\(881\) −2.64062e13 −1.47678 −0.738388 0.674376i \(-0.764413\pi\)
−0.738388 + 0.674376i \(0.764413\pi\)
\(882\) −8.16369e11 −0.0454232
\(883\) −8.21138e12 −0.454562 −0.227281 0.973829i \(-0.572984\pi\)
−0.227281 + 0.973829i \(0.572984\pi\)
\(884\) 0 0
\(885\) 2.04833e13 1.12242
\(886\) −1.57889e13 −0.860794
\(887\) 2.49193e12 0.135170 0.0675848 0.997714i \(-0.478471\pi\)
0.0675848 + 0.997714i \(0.478471\pi\)
\(888\) 1.70188e12 0.0918480
\(889\) 3.16825e13 1.70123
\(890\) 1.77942e13 0.950656
\(891\) −2.71438e13 −1.44285
\(892\) 9.52219e11 0.0503611
\(893\) −1.18678e13 −0.624508
\(894\) 2.74771e13 1.43864
\(895\) −5.59330e12 −0.291383
\(896\) −2.23114e13 −1.15649
\(897\) 2.71602e13 1.40077
\(898\) 2.79070e13 1.43209
\(899\) 1.87408e13 0.956904
\(900\) 1.59540e13 0.810545
\(901\) 0 0
\(902\) −4.82331e12 −0.242614
\(903\) −4.38869e12 −0.219654
\(904\) 5.51178e12 0.274495
\(905\) −3.52888e13 −1.74871
\(906\) −4.68425e13 −2.30974
\(907\) 2.95913e13 1.45188 0.725940 0.687758i \(-0.241405\pi\)
0.725940 + 0.687758i \(0.241405\pi\)
\(908\) −1.42090e13 −0.693710
\(909\) 1.93750e13 0.941250
\(910\) −4.36301e13 −2.10911
\(911\) −2.96554e12 −0.142650 −0.0713250 0.997453i \(-0.522723\pi\)
−0.0713250 + 0.997453i \(0.522723\pi\)
\(912\) −3.73325e13 −1.78694
\(913\) 1.06936e13 0.509338
\(914\) −5.05307e12 −0.239496
\(915\) 2.92628e13 1.38013
\(916\) −1.19919e13 −0.562806
\(917\) −5.56966e11 −0.0260116
\(918\) 0 0
\(919\) 1.87888e13 0.868918 0.434459 0.900692i \(-0.356940\pi\)
0.434459 + 0.900692i \(0.356940\pi\)
\(920\) −2.39331e13 −1.10142
\(921\) −8.85209e12 −0.405394
\(922\) −4.60778e12 −0.209992
\(923\) 3.73813e13 1.69530
\(924\) −2.05687e13 −0.928287
\(925\) −3.61521e12 −0.162366
\(926\) −2.15435e13 −0.962869
\(927\) −3.81692e13 −1.69767
\(928\) 8.52016e12 0.377122
\(929\) −4.36911e13 −1.92452 −0.962259 0.272135i \(-0.912270\pi\)
−0.962259 + 0.272135i \(0.912270\pi\)
\(930\) −1.21919e14 −5.34437
\(931\) −7.73738e11 −0.0337536
\(932\) −7.77746e12 −0.337650
\(933\) 2.95025e12 0.127465
\(934\) 2.93067e13 1.26010
\(935\) 0 0
\(936\) −2.08773e13 −0.889064
\(937\) 6.48044e12 0.274648 0.137324 0.990526i \(-0.456150\pi\)
0.137324 + 0.990526i \(0.456150\pi\)
\(938\) −3.50456e13 −1.47816
\(939\) 1.81731e13 0.762841
\(940\) −9.73858e12 −0.406837
\(941\) 7.36913e12 0.306382 0.153191 0.988197i \(-0.451045\pi\)
0.153191 + 0.988197i \(0.451045\pi\)
\(942\) −6.79962e11 −0.0281356
\(943\) −2.62572e12 −0.108130
\(944\) −1.36466e13 −0.559309
\(945\) −8.01166e12 −0.326798
\(946\) 7.53316e12 0.305821
\(947\) 1.63100e11 0.00658988 0.00329494 0.999995i \(-0.498951\pi\)
0.00329494 + 0.999995i \(0.498951\pi\)
\(948\) 7.08719e12 0.284995
\(949\) −2.60374e13 −1.04208
\(950\) 5.49165e13 2.18749
\(951\) 5.83602e13 2.31369
\(952\) 0 0
\(953\) 3.44725e13 1.35380 0.676901 0.736074i \(-0.263322\pi\)
0.676901 + 0.736074i \(0.263322\pi\)
\(954\) 1.30289e13 0.509262
\(955\) 4.54694e13 1.76890
\(956\) 1.21133e13 0.469031
\(957\) −3.36405e13 −1.29646
\(958\) −3.36599e13 −1.29112
\(959\) 2.58482e13 0.986839
\(960\) 2.51975e13 0.957496
\(961\) 6.25677e13 2.36644
\(962\) −2.89908e12 −0.109137
\(963\) 1.08972e13 0.408316
\(964\) 1.01947e13 0.380214
\(965\) −4.98446e13 −1.85031
\(966\) −4.06664e13 −1.50259
\(967\) 4.11357e13 1.51286 0.756431 0.654073i \(-0.226941\pi\)
0.756431 + 0.654073i \(0.226941\pi\)
\(968\) −3.77168e13 −1.38069
\(969\) 0 0
\(970\) 3.01181e12 0.109233
\(971\) −2.31458e12 −0.0835577 −0.0417789 0.999127i \(-0.513302\pi\)
−0.0417789 + 0.999127i \(0.513302\pi\)
\(972\) −1.51693e13 −0.545087
\(973\) −2.09310e13 −0.748656
\(974\) 3.08306e13 1.09766
\(975\) 8.34532e13 2.95748
\(976\) −1.94958e13 −0.687729
\(977\) −4.08077e13 −1.43290 −0.716450 0.697638i \(-0.754234\pi\)
−0.716450 + 0.697638i \(0.754234\pi\)
\(978\) −7.84857e13 −2.74325
\(979\) 2.33190e13 0.811312
\(980\) −6.34922e11 −0.0219889
\(981\) 3.75236e13 1.29358
\(982\) −1.57612e13 −0.540863
\(983\) 3.41341e13 1.16600 0.582998 0.812473i \(-0.301879\pi\)
0.582998 + 0.812473i \(0.301879\pi\)
\(984\) 3.79797e12 0.129144
\(985\) 9.86825e13 3.34023
\(986\) 0 0
\(987\) 2.70030e13 0.905701
\(988\) 1.21256e13 0.404852
\(989\) 4.10090e12 0.136300
\(990\) 1.16301e14 3.84790
\(991\) 2.85414e13 0.940035 0.470017 0.882657i \(-0.344248\pi\)
0.470017 + 0.882657i \(0.344248\pi\)
\(992\) 4.04656e13 1.32673
\(993\) 4.80739e13 1.56905
\(994\) −5.59702e13 −1.81852
\(995\) 5.08709e13 1.64538
\(996\) 5.16003e12 0.166144
\(997\) −4.47702e13 −1.43503 −0.717515 0.696544i \(-0.754720\pi\)
−0.717515 + 0.696544i \(0.754720\pi\)
\(998\) −7.45235e12 −0.237797
\(999\) −5.32349e11 −0.0169103
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.h.1.27 yes 36
17.16 even 2 289.10.a.g.1.27 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.27 36 17.16 even 2
289.10.a.h.1.27 yes 36 1.1 even 1 trivial