Properties

Label 289.10.a.h.1.3
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 1.3
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-38.3451 q^{2} -247.035 q^{3} +958.344 q^{4} +875.650 q^{5} +9472.58 q^{6} +7072.73 q^{7} -17115.1 q^{8} +41343.4 q^{9} +O(q^{10})\) \(q-38.3451 q^{2} -247.035 q^{3} +958.344 q^{4} +875.650 q^{5} +9472.58 q^{6} +7072.73 q^{7} -17115.1 q^{8} +41343.4 q^{9} -33576.9 q^{10} -55297.3 q^{11} -236745. q^{12} -179715. q^{13} -271204. q^{14} -216316. q^{15} +165608. q^{16} -1.58531e6 q^{18} -56519.2 q^{19} +839175. q^{20} -1.74721e6 q^{21} +2.12038e6 q^{22} -2.36581e6 q^{23} +4.22803e6 q^{24} -1.18636e6 q^{25} +6.89118e6 q^{26} -5.35087e6 q^{27} +6.77811e6 q^{28} +1.38770e6 q^{29} +8.29467e6 q^{30} -430357. q^{31} +2.41270e6 q^{32} +1.36604e7 q^{33} +6.19324e6 q^{35} +3.96212e7 q^{36} -1.73171e7 q^{37} +2.16723e6 q^{38} +4.43959e7 q^{39} -1.49868e7 q^{40} -2.41560e7 q^{41} +6.69970e7 q^{42} -3.24198e6 q^{43} -5.29939e7 q^{44} +3.62023e7 q^{45} +9.07170e7 q^{46} -4.13306e7 q^{47} -4.09109e7 q^{48} +9.66988e6 q^{49} +4.54911e7 q^{50} -1.72229e8 q^{52} +1.71427e7 q^{53} +2.05180e8 q^{54} -4.84211e7 q^{55} -1.21050e8 q^{56} +1.39622e7 q^{57} -5.32115e7 q^{58} -3.33334e7 q^{59} -2.07306e8 q^{60} -5.58769e7 q^{61} +1.65021e7 q^{62} +2.92410e8 q^{63} -1.77306e8 q^{64} -1.57367e8 q^{65} -5.23808e8 q^{66} -1.25537e8 q^{67} +5.84437e8 q^{69} -2.37480e8 q^{70} +6.66690e7 q^{71} -7.07596e8 q^{72} +2.13031e6 q^{73} +6.64026e8 q^{74} +2.93073e8 q^{75} -5.41649e7 q^{76} -3.91103e8 q^{77} -1.70236e9 q^{78} +3.27561e8 q^{79} +1.45014e8 q^{80} +5.08092e8 q^{81} +9.26263e8 q^{82} +2.63136e8 q^{83} -1.67443e9 q^{84} +1.24314e8 q^{86} -3.42811e8 q^{87} +9.46420e8 q^{88} +1.86798e8 q^{89} -1.38818e9 q^{90} -1.27107e9 q^{91} -2.26726e9 q^{92} +1.06313e8 q^{93} +1.58482e9 q^{94} -4.94911e7 q^{95} -5.96022e8 q^{96} +9.45632e7 q^{97} -3.70792e8 q^{98} -2.28618e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 486q^{3} + 9216q^{4} + 3750q^{5} + 11061q^{6} + 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q + 486q^{3} + 9216q^{4} + 3750q^{5} + 11061q^{6} + 29040q^{7} + 24837q^{8} + 236196q^{9} + 60000q^{10} + 76902q^{11} + 373248q^{12} + 54216q^{13} + 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} + 6439479q^{20} - 138102q^{21} + 267324q^{22} + 4041462q^{23} + 7653888q^{24} + 16582356q^{25} + 15822744q^{26} + 13281612q^{27} + 18614784q^{28} + 4005936q^{29} + 22471686q^{30} + 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} + 22076682q^{37} - 27401376q^{38} + 62736162q^{39} - 12231630q^{40} + 59641782q^{41} + 150001536q^{42} - 47951586q^{43} - 49578936q^{44} + 129308238q^{45} + 140524827q^{46} - 118557912q^{47} + 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} + 209848575q^{54} - 365439924q^{55} + 203095059q^{56} - 4614108q^{57} - 179071413q^{58} + 343015128q^{59} + 427179186q^{60} + 175597116q^{61} + 720602571q^{62} + 587415936q^{63} + 853082511q^{64} + 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} + 1308709542q^{71} - 275337849q^{72} + 494841342q^{73} + 1545361890q^{74} + 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} + 2270624538q^{78} + 1980107868q^{79} + 2897000199q^{80} + 1598298840q^{81} + 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} - 2705904618q^{88} + 148394658q^{89} + 117916215q^{90} + 636340896q^{91} - 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} + 4878626298q^{95} - 8390096634q^{96} - 891786822q^{97} + 4285627647q^{98} - 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −38.3451 −1.69463 −0.847314 0.531092i \(-0.821782\pi\)
−0.847314 + 0.531092i \(0.821782\pi\)
\(3\) −247.035 −1.76081 −0.880406 0.474220i \(-0.842730\pi\)
−0.880406 + 0.474220i \(0.842730\pi\)
\(4\) 958.344 1.87177
\(5\) 875.650 0.626564 0.313282 0.949660i \(-0.398571\pi\)
0.313282 + 0.949660i \(0.398571\pi\)
\(6\) 9472.58 2.98392
\(7\) 7072.73 1.11339 0.556693 0.830718i \(-0.312070\pi\)
0.556693 + 0.830718i \(0.312070\pi\)
\(8\) −17115.1 −1.47732
\(9\) 41343.4 2.10046
\(10\) −33576.9 −1.06179
\(11\) −55297.3 −1.13877 −0.569386 0.822070i \(-0.692819\pi\)
−0.569386 + 0.822070i \(0.692819\pi\)
\(12\) −236745. −3.29583
\(13\) −179715. −1.74517 −0.872587 0.488458i \(-0.837559\pi\)
−0.872587 + 0.488458i \(0.837559\pi\)
\(14\) −271204. −1.88678
\(15\) −216316. −1.10326
\(16\) 165608. 0.631743
\(17\) 0 0
\(18\) −1.58531e6 −3.55950
\(19\) −56519.2 −0.0994958 −0.0497479 0.998762i \(-0.515842\pi\)
−0.0497479 + 0.998762i \(0.515842\pi\)
\(20\) 839175. 1.17278
\(21\) −1.74721e6 −1.96046
\(22\) 2.12038e6 1.92980
\(23\) −2.36581e6 −1.76280 −0.881402 0.472367i \(-0.843400\pi\)
−0.881402 + 0.472367i \(0.843400\pi\)
\(24\) 4.22803e6 2.60128
\(25\) −1.18636e6 −0.607417
\(26\) 6.89118e6 2.95742
\(27\) −5.35087e6 −1.93770
\(28\) 6.77811e6 2.08400
\(29\) 1.38770e6 0.364338 0.182169 0.983267i \(-0.441688\pi\)
0.182169 + 0.983267i \(0.441688\pi\)
\(30\) 8.29467e6 1.86962
\(31\) −430357. −0.0836953 −0.0418477 0.999124i \(-0.513324\pi\)
−0.0418477 + 0.999124i \(0.513324\pi\)
\(32\) 2.41270e6 0.406751
\(33\) 1.36604e7 2.00517
\(34\) 0 0
\(35\) 6.19324e6 0.697608
\(36\) 3.96212e7 3.93157
\(37\) −1.73171e7 −1.51903 −0.759517 0.650487i \(-0.774565\pi\)
−0.759517 + 0.650487i \(0.774565\pi\)
\(38\) 2.16723e6 0.168608
\(39\) 4.43959e7 3.07292
\(40\) −1.49868e7 −0.925636
\(41\) −2.41560e7 −1.33505 −0.667525 0.744588i \(-0.732646\pi\)
−0.667525 + 0.744588i \(0.732646\pi\)
\(42\) 6.69970e7 3.32226
\(43\) −3.24198e6 −0.144611 −0.0723057 0.997383i \(-0.523036\pi\)
−0.0723057 + 0.997383i \(0.523036\pi\)
\(44\) −5.29939e7 −2.13152
\(45\) 3.62023e7 1.31607
\(46\) 9.07170e7 2.98730
\(47\) −4.13306e7 −1.23547 −0.617734 0.786387i \(-0.711949\pi\)
−0.617734 + 0.786387i \(0.711949\pi\)
\(48\) −4.09109e7 −1.11238
\(49\) 9.66988e6 0.239629
\(50\) 4.54911e7 1.02935
\(51\) 0 0
\(52\) −1.72229e8 −3.26656
\(53\) 1.71427e7 0.298428 0.149214 0.988805i \(-0.452326\pi\)
0.149214 + 0.988805i \(0.452326\pi\)
\(54\) 2.05180e8 3.28369
\(55\) −4.84211e7 −0.713515
\(56\) −1.21050e8 −1.64483
\(57\) 1.39622e7 0.175194
\(58\) −5.32115e7 −0.617418
\(59\) −3.33334e7 −0.358135 −0.179067 0.983837i \(-0.557308\pi\)
−0.179067 + 0.983837i \(0.557308\pi\)
\(60\) −2.07306e8 −2.06505
\(61\) −5.58769e7 −0.516711 −0.258356 0.966050i \(-0.583181\pi\)
−0.258356 + 0.966050i \(0.583181\pi\)
\(62\) 1.65021e7 0.141832
\(63\) 2.92410e8 2.33862
\(64\) −1.77306e8 −1.32103
\(65\) −1.57367e8 −1.09346
\(66\) −5.23808e8 −3.39801
\(67\) −1.25537e8 −0.761086 −0.380543 0.924763i \(-0.624263\pi\)
−0.380543 + 0.924763i \(0.624263\pi\)
\(68\) 0 0
\(69\) 5.84437e8 3.10397
\(70\) −2.37480e8 −1.18219
\(71\) 6.66690e7 0.311359 0.155680 0.987808i \(-0.450243\pi\)
0.155680 + 0.987808i \(0.450243\pi\)
\(72\) −7.07596e8 −3.10305
\(73\) 2.13031e6 0.00877990 0.00438995 0.999990i \(-0.498603\pi\)
0.00438995 + 0.999990i \(0.498603\pi\)
\(74\) 6.64026e8 2.57420
\(75\) 2.93073e8 1.06955
\(76\) −5.41649e7 −0.186233
\(77\) −3.91103e8 −1.26789
\(78\) −1.70236e9 −5.20747
\(79\) 3.27561e8 0.946174 0.473087 0.881016i \(-0.343140\pi\)
0.473087 + 0.881016i \(0.343140\pi\)
\(80\) 1.45014e8 0.395827
\(81\) 5.08092e8 1.31147
\(82\) 9.26263e8 2.26241
\(83\) 2.63136e8 0.608595 0.304298 0.952577i \(-0.401578\pi\)
0.304298 + 0.952577i \(0.401578\pi\)
\(84\) −1.67443e9 −3.66953
\(85\) 0 0
\(86\) 1.24314e8 0.245063
\(87\) −3.42811e8 −0.641532
\(88\) 9.46420e8 1.68233
\(89\) 1.86798e8 0.315586 0.157793 0.987472i \(-0.449562\pi\)
0.157793 + 0.987472i \(0.449562\pi\)
\(90\) −1.38818e9 −2.23026
\(91\) −1.27107e9 −1.94305
\(92\) −2.26726e9 −3.29956
\(93\) 1.06313e8 0.147372
\(94\) 1.58482e9 2.09366
\(95\) −4.94911e7 −0.0623405
\(96\) −5.96022e8 −0.716212
\(97\) 9.45632e7 0.108455 0.0542275 0.998529i \(-0.482730\pi\)
0.0542275 + 0.998529i \(0.482730\pi\)
\(98\) −3.70792e8 −0.406082
\(99\) −2.28618e9 −2.39195
\(100\) −1.13694e9 −1.13694
\(101\) −1.49062e9 −1.42535 −0.712673 0.701497i \(-0.752516\pi\)
−0.712673 + 0.701497i \(0.752516\pi\)
\(102\) 0 0
\(103\) −1.81795e9 −1.59153 −0.795763 0.605609i \(-0.792930\pi\)
−0.795763 + 0.605609i \(0.792930\pi\)
\(104\) 3.07584e9 2.57818
\(105\) −1.52995e9 −1.22836
\(106\) −6.57340e8 −0.505724
\(107\) −9.57357e8 −0.706069 −0.353034 0.935610i \(-0.614850\pi\)
−0.353034 + 0.935610i \(0.614850\pi\)
\(108\) −5.12798e9 −3.62693
\(109\) 6.70544e8 0.454997 0.227498 0.973778i \(-0.426945\pi\)
0.227498 + 0.973778i \(0.426945\pi\)
\(110\) 1.85671e9 1.20914
\(111\) 4.27793e9 2.67473
\(112\) 1.17130e9 0.703373
\(113\) 1.13895e9 0.657132 0.328566 0.944481i \(-0.393435\pi\)
0.328566 + 0.944481i \(0.393435\pi\)
\(114\) −5.35383e8 −0.296888
\(115\) −2.07162e9 −1.10451
\(116\) 1.32990e9 0.681956
\(117\) −7.43002e9 −3.66567
\(118\) 1.27817e9 0.606905
\(119\) 0 0
\(120\) 3.70228e9 1.62987
\(121\) 6.99848e8 0.296804
\(122\) 2.14260e9 0.875633
\(123\) 5.96738e9 2.35077
\(124\) −4.12430e8 −0.156658
\(125\) −2.74909e9 −1.00715
\(126\) −1.12125e10 −3.96310
\(127\) −1.48207e9 −0.505535 −0.252768 0.967527i \(-0.581341\pi\)
−0.252768 + 0.967527i \(0.581341\pi\)
\(128\) 5.56352e9 1.83191
\(129\) 8.00884e8 0.254634
\(130\) 6.03426e9 1.85302
\(131\) 3.68446e9 1.09308 0.546541 0.837432i \(-0.315944\pi\)
0.546541 + 0.837432i \(0.315944\pi\)
\(132\) 1.30914e10 3.75320
\(133\) −3.99745e8 −0.110777
\(134\) 4.81371e9 1.28976
\(135\) −4.68549e9 −1.21410
\(136\) 0 0
\(137\) 4.76832e9 1.15644 0.578220 0.815881i \(-0.303748\pi\)
0.578220 + 0.815881i \(0.303748\pi\)
\(138\) −2.24103e10 −5.26007
\(139\) −2.75609e9 −0.626220 −0.313110 0.949717i \(-0.601371\pi\)
−0.313110 + 0.949717i \(0.601371\pi\)
\(140\) 5.93525e9 1.30576
\(141\) 1.02101e10 2.17543
\(142\) −2.55643e9 −0.527638
\(143\) 9.93775e9 1.98736
\(144\) 6.84677e9 1.32695
\(145\) 1.21514e9 0.228281
\(146\) −8.16868e7 −0.0148787
\(147\) −2.38880e9 −0.421941
\(148\) −1.65957e10 −2.84328
\(149\) −8.50459e9 −1.41356 −0.706781 0.707432i \(-0.749854\pi\)
−0.706781 + 0.707432i \(0.749854\pi\)
\(150\) −1.12379e10 −1.81249
\(151\) −4.69221e8 −0.0734482 −0.0367241 0.999325i \(-0.511692\pi\)
−0.0367241 + 0.999325i \(0.511692\pi\)
\(152\) 9.67332e8 0.146987
\(153\) 0 0
\(154\) 1.49969e10 2.14861
\(155\) −3.76842e8 −0.0524405
\(156\) 4.25465e10 5.75180
\(157\) −9.71327e9 −1.27590 −0.637950 0.770077i \(-0.720218\pi\)
−0.637950 + 0.770077i \(0.720218\pi\)
\(158\) −1.25604e10 −1.60341
\(159\) −4.23486e9 −0.525475
\(160\) 2.11268e9 0.254856
\(161\) −1.67327e10 −1.96268
\(162\) −1.94828e10 −2.22246
\(163\) −1.18283e10 −1.31244 −0.656218 0.754572i \(-0.727845\pi\)
−0.656218 + 0.754572i \(0.727845\pi\)
\(164\) −2.31498e10 −2.49890
\(165\) 1.19617e10 1.25637
\(166\) −1.00900e10 −1.03134
\(167\) 1.36543e10 1.35845 0.679226 0.733929i \(-0.262316\pi\)
0.679226 + 0.733929i \(0.262316\pi\)
\(168\) 2.99037e10 2.89623
\(169\) 2.16929e10 2.04563
\(170\) 0 0
\(171\) −2.33669e9 −0.208987
\(172\) −3.10694e9 −0.270679
\(173\) 3.18021e9 0.269928 0.134964 0.990850i \(-0.456908\pi\)
0.134964 + 0.990850i \(0.456908\pi\)
\(174\) 1.31451e10 1.08716
\(175\) −8.39081e9 −0.676290
\(176\) −9.15765e9 −0.719411
\(177\) 8.23453e9 0.630608
\(178\) −7.16279e9 −0.534801
\(179\) −6.21740e9 −0.452658 −0.226329 0.974051i \(-0.572672\pi\)
−0.226329 + 0.974051i \(0.572672\pi\)
\(180\) 3.46943e10 2.46338
\(181\) 5.79688e9 0.401458 0.200729 0.979647i \(-0.435669\pi\)
0.200729 + 0.979647i \(0.435669\pi\)
\(182\) 4.87394e10 3.29275
\(183\) 1.38035e10 0.909831
\(184\) 4.04910e10 2.60423
\(185\) −1.51637e10 −0.951773
\(186\) −4.07659e9 −0.249740
\(187\) 0 0
\(188\) −3.96089e10 −2.31251
\(189\) −3.78453e10 −2.15741
\(190\) 1.89774e9 0.105644
\(191\) 1.62977e10 0.886084 0.443042 0.896501i \(-0.353899\pi\)
0.443042 + 0.896501i \(0.353899\pi\)
\(192\) 4.38009e10 2.32609
\(193\) −2.77841e10 −1.44141 −0.720707 0.693240i \(-0.756183\pi\)
−0.720707 + 0.693240i \(0.756183\pi\)
\(194\) −3.62603e9 −0.183791
\(195\) 3.88753e10 1.92539
\(196\) 9.26707e9 0.448529
\(197\) −3.12035e10 −1.47606 −0.738032 0.674766i \(-0.764245\pi\)
−0.738032 + 0.674766i \(0.764245\pi\)
\(198\) 8.76637e10 4.05346
\(199\) −1.90992e10 −0.863330 −0.431665 0.902034i \(-0.642074\pi\)
−0.431665 + 0.902034i \(0.642074\pi\)
\(200\) 2.03047e10 0.897349
\(201\) 3.10120e10 1.34013
\(202\) 5.71579e10 2.41543
\(203\) 9.81483e9 0.405649
\(204\) 0 0
\(205\) −2.11522e10 −0.836495
\(206\) 6.97093e10 2.69704
\(207\) −9.78104e10 −3.70270
\(208\) −2.97621e10 −1.10250
\(209\) 3.12536e9 0.113303
\(210\) 5.86659e10 2.08161
\(211\) 4.18494e10 1.45351 0.726755 0.686896i \(-0.241027\pi\)
0.726755 + 0.686896i \(0.241027\pi\)
\(212\) 1.64286e10 0.558587
\(213\) −1.64696e10 −0.548245
\(214\) 3.67099e10 1.19652
\(215\) −2.83884e9 −0.0906084
\(216\) 9.15807e10 2.86261
\(217\) −3.04380e9 −0.0931852
\(218\) −2.57121e10 −0.771050
\(219\) −5.26261e8 −0.0154598
\(220\) −4.64041e10 −1.33553
\(221\) 0 0
\(222\) −1.64038e11 −4.53268
\(223\) −1.10890e10 −0.300276 −0.150138 0.988665i \(-0.547972\pi\)
−0.150138 + 0.988665i \(0.547972\pi\)
\(224\) 1.70644e10 0.452871
\(225\) −4.90482e10 −1.27586
\(226\) −4.36732e10 −1.11359
\(227\) 4.43462e10 1.10851 0.554256 0.832346i \(-0.313003\pi\)
0.554256 + 0.832346i \(0.313003\pi\)
\(228\) 1.33806e10 0.327921
\(229\) −9.70253e8 −0.0233145 −0.0116572 0.999932i \(-0.503711\pi\)
−0.0116572 + 0.999932i \(0.503711\pi\)
\(230\) 7.94364e10 1.87173
\(231\) 9.66162e10 2.23252
\(232\) −2.37506e10 −0.538244
\(233\) −2.73732e10 −0.608448 −0.304224 0.952601i \(-0.598397\pi\)
−0.304224 + 0.952601i \(0.598397\pi\)
\(234\) 2.84904e11 6.21195
\(235\) −3.61912e10 −0.774100
\(236\) −3.19449e10 −0.670344
\(237\) −8.09192e10 −1.66603
\(238\) 0 0
\(239\) −5.26614e10 −1.04400 −0.522002 0.852944i \(-0.674815\pi\)
−0.522002 + 0.852944i \(0.674815\pi\)
\(240\) −3.58236e10 −0.696978
\(241\) 4.93288e10 0.941941 0.470971 0.882149i \(-0.343904\pi\)
0.470971 + 0.882149i \(0.343904\pi\)
\(242\) −2.68357e10 −0.502972
\(243\) −2.01954e10 −0.371556
\(244\) −5.35493e10 −0.967162
\(245\) 8.46743e9 0.150143
\(246\) −2.28820e11 −3.98369
\(247\) 1.01573e10 0.173638
\(248\) 7.36560e9 0.123645
\(249\) −6.50038e10 −1.07162
\(250\) 1.05414e11 1.70675
\(251\) −2.44127e10 −0.388225 −0.194113 0.980979i \(-0.562183\pi\)
−0.194113 + 0.980979i \(0.562183\pi\)
\(252\) 2.80230e11 4.37736
\(253\) 1.30823e11 2.00743
\(254\) 5.68300e10 0.856695
\(255\) 0 0
\(256\) −1.22553e11 −1.78338
\(257\) 1.14345e10 0.163500 0.0817502 0.996653i \(-0.473949\pi\)
0.0817502 + 0.996653i \(0.473949\pi\)
\(258\) −3.07099e10 −0.431510
\(259\) −1.22479e11 −1.69127
\(260\) −1.50812e11 −2.04671
\(261\) 5.73722e10 0.765279
\(262\) −1.41281e11 −1.85237
\(263\) −1.47919e10 −0.190644 −0.0953218 0.995447i \(-0.530388\pi\)
−0.0953218 + 0.995447i \(0.530388\pi\)
\(264\) −2.33799e11 −2.96227
\(265\) 1.50110e10 0.186984
\(266\) 1.53283e10 0.187726
\(267\) −4.61458e10 −0.555688
\(268\) −1.20307e11 −1.42458
\(269\) 1.08472e11 1.26309 0.631544 0.775340i \(-0.282421\pi\)
0.631544 + 0.775340i \(0.282421\pi\)
\(270\) 1.79666e11 2.05744
\(271\) −1.24948e11 −1.40724 −0.703621 0.710575i \(-0.748435\pi\)
−0.703621 + 0.710575i \(0.748435\pi\)
\(272\) 0 0
\(273\) 3.14000e11 3.42135
\(274\) −1.82842e11 −1.95974
\(275\) 6.56026e10 0.691710
\(276\) 5.60092e11 5.80990
\(277\) −4.37655e10 −0.446656 −0.223328 0.974743i \(-0.571692\pi\)
−0.223328 + 0.974743i \(0.571692\pi\)
\(278\) 1.05682e11 1.06121
\(279\) −1.77924e10 −0.175799
\(280\) −1.05998e11 −1.03059
\(281\) −9.36224e10 −0.895780 −0.447890 0.894089i \(-0.647824\pi\)
−0.447890 + 0.894089i \(0.647824\pi\)
\(282\) −3.91507e11 −3.68654
\(283\) 3.44641e10 0.319395 0.159697 0.987166i \(-0.448948\pi\)
0.159697 + 0.987166i \(0.448948\pi\)
\(284\) 6.38919e10 0.582791
\(285\) 1.22260e10 0.109770
\(286\) −3.81064e11 −3.36783
\(287\) −1.70849e11 −1.48643
\(288\) 9.97492e10 0.854364
\(289\) 0 0
\(290\) −4.65947e10 −0.386852
\(291\) −2.33604e10 −0.190969
\(292\) 2.04157e9 0.0164339
\(293\) −2.08082e11 −1.64942 −0.824709 0.565557i \(-0.808661\pi\)
−0.824709 + 0.565557i \(0.808661\pi\)
\(294\) 9.15987e10 0.715033
\(295\) −2.91884e10 −0.224394
\(296\) 2.96384e11 2.24410
\(297\) 2.95889e11 2.20661
\(298\) 3.26109e11 2.39546
\(299\) 4.25171e11 3.07640
\(300\) 2.80865e11 2.00194
\(301\) −2.29297e10 −0.161008
\(302\) 1.79923e10 0.124467
\(303\) 3.68235e11 2.50977
\(304\) −9.36001e9 −0.0628557
\(305\) −4.89286e10 −0.323753
\(306\) 0 0
\(307\) −1.09580e11 −0.704060 −0.352030 0.935989i \(-0.614508\pi\)
−0.352030 + 0.935989i \(0.614508\pi\)
\(308\) −3.74811e11 −2.37320
\(309\) 4.49097e11 2.80238
\(310\) 1.44500e10 0.0888672
\(311\) 1.65183e11 1.00125 0.500627 0.865663i \(-0.333103\pi\)
0.500627 + 0.865663i \(0.333103\pi\)
\(312\) −7.59840e11 −4.53969
\(313\) 2.08573e11 1.22831 0.614156 0.789185i \(-0.289497\pi\)
0.614156 + 0.789185i \(0.289497\pi\)
\(314\) 3.72456e11 2.16218
\(315\) 2.56049e11 1.46530
\(316\) 3.13917e11 1.77102
\(317\) −5.75119e10 −0.319883 −0.159941 0.987127i \(-0.551131\pi\)
−0.159941 + 0.987127i \(0.551131\pi\)
\(318\) 1.62386e11 0.890485
\(319\) −7.67362e10 −0.414899
\(320\) −1.55258e11 −0.827713
\(321\) 2.36501e11 1.24325
\(322\) 6.41617e11 3.32602
\(323\) 0 0
\(324\) 4.86927e11 2.45477
\(325\) 2.13207e11 1.06005
\(326\) 4.53557e11 2.22409
\(327\) −1.65648e11 −0.801164
\(328\) 4.13432e11 1.97230
\(329\) −2.92320e11 −1.37555
\(330\) −4.58673e11 −2.12907
\(331\) 3.17672e11 1.45463 0.727316 0.686303i \(-0.240767\pi\)
0.727316 + 0.686303i \(0.240767\pi\)
\(332\) 2.52175e11 1.13915
\(333\) −7.15947e11 −3.19067
\(334\) −5.23574e11 −2.30207
\(335\) −1.09926e11 −0.476869
\(336\) −2.89352e11 −1.23851
\(337\) −4.55316e11 −1.92300 −0.961498 0.274813i \(-0.911384\pi\)
−0.961498 + 0.274813i \(0.911384\pi\)
\(338\) −8.31817e11 −3.46659
\(339\) −2.81361e11 −1.15709
\(340\) 0 0
\(341\) 2.37976e10 0.0953100
\(342\) 8.96007e10 0.354155
\(343\) −2.17018e11 −0.846587
\(344\) 5.54869e10 0.213637
\(345\) 5.11763e11 1.94484
\(346\) −1.21945e11 −0.457428
\(347\) −2.81867e10 −0.104367 −0.0521833 0.998638i \(-0.516618\pi\)
−0.0521833 + 0.998638i \(0.516618\pi\)
\(348\) −3.28531e11 −1.20080
\(349\) −2.63818e11 −0.951898 −0.475949 0.879473i \(-0.657895\pi\)
−0.475949 + 0.879473i \(0.657895\pi\)
\(350\) 3.21746e11 1.14606
\(351\) 9.61631e11 3.38163
\(352\) −1.33416e11 −0.463197
\(353\) −1.51848e10 −0.0520502 −0.0260251 0.999661i \(-0.508285\pi\)
−0.0260251 + 0.999661i \(0.508285\pi\)
\(354\) −3.15754e11 −1.06865
\(355\) 5.83788e10 0.195087
\(356\) 1.79017e11 0.590703
\(357\) 0 0
\(358\) 2.38407e11 0.767087
\(359\) −1.10621e11 −0.351490 −0.175745 0.984436i \(-0.556233\pi\)
−0.175745 + 0.984436i \(0.556233\pi\)
\(360\) −6.19607e11 −1.94426
\(361\) −3.19493e11 −0.990101
\(362\) −2.22282e11 −0.680323
\(363\) −1.72887e11 −0.522616
\(364\) −1.21813e12 −3.63694
\(365\) 1.86541e9 0.00550117
\(366\) −5.29298e11 −1.54183
\(367\) −1.63544e11 −0.470586 −0.235293 0.971925i \(-0.575605\pi\)
−0.235293 + 0.971925i \(0.575605\pi\)
\(368\) −3.91795e11 −1.11364
\(369\) −9.98690e11 −2.80422
\(370\) 5.81454e11 1.61290
\(371\) 1.21246e11 0.332265
\(372\) 1.01885e11 0.275845
\(373\) −6.59311e11 −1.76360 −0.881801 0.471621i \(-0.843669\pi\)
−0.881801 + 0.471621i \(0.843669\pi\)
\(374\) 0 0
\(375\) 6.79122e11 1.77340
\(376\) 7.07378e11 1.82518
\(377\) −2.49390e11 −0.635834
\(378\) 1.45118e12 3.65602
\(379\) −6.18091e11 −1.53878 −0.769389 0.638781i \(-0.779439\pi\)
−0.769389 + 0.638781i \(0.779439\pi\)
\(380\) −4.74295e10 −0.116687
\(381\) 3.66123e11 0.890153
\(382\) −6.24935e11 −1.50158
\(383\) 6.31833e11 1.50040 0.750202 0.661209i \(-0.229956\pi\)
0.750202 + 0.661209i \(0.229956\pi\)
\(384\) −1.37438e12 −3.22565
\(385\) −3.42470e11 −0.794417
\(386\) 1.06538e12 2.44266
\(387\) −1.34035e11 −0.303751
\(388\) 9.06241e10 0.203002
\(389\) −1.82637e11 −0.404403 −0.202202 0.979344i \(-0.564810\pi\)
−0.202202 + 0.979344i \(0.564810\pi\)
\(390\) −1.49067e12 −3.26281
\(391\) 0 0
\(392\) −1.65501e11 −0.354008
\(393\) −9.10191e11 −1.92471
\(394\) 1.19650e12 2.50138
\(395\) 2.86829e11 0.592839
\(396\) −2.19095e12 −4.47717
\(397\) 2.05793e11 0.415790 0.207895 0.978151i \(-0.433339\pi\)
0.207895 + 0.978151i \(0.433339\pi\)
\(398\) 7.32361e11 1.46302
\(399\) 9.87511e10 0.195058
\(400\) −1.96470e11 −0.383731
\(401\) 8.48355e11 1.63843 0.819215 0.573487i \(-0.194410\pi\)
0.819215 + 0.573487i \(0.194410\pi\)
\(402\) −1.18916e12 −2.27102
\(403\) 7.73415e10 0.146063
\(404\) −1.42853e12 −2.66791
\(405\) 4.44911e11 0.821723
\(406\) −3.76350e11 −0.687425
\(407\) 9.57590e11 1.72983
\(408\) 0 0
\(409\) −7.80687e11 −1.37950 −0.689750 0.724047i \(-0.742280\pi\)
−0.689750 + 0.724047i \(0.742280\pi\)
\(410\) 8.11083e11 1.41755
\(411\) −1.17794e12 −2.03627
\(412\) −1.74222e12 −2.97896
\(413\) −2.35758e11 −0.398742
\(414\) 3.75055e12 6.27470
\(415\) 2.30415e11 0.381324
\(416\) −4.33598e11 −0.709851
\(417\) 6.80851e11 1.10266
\(418\) −1.19842e11 −0.192007
\(419\) 3.43347e11 0.544215 0.272108 0.962267i \(-0.412279\pi\)
0.272108 + 0.962267i \(0.412279\pi\)
\(420\) −1.46622e12 −2.29920
\(421\) 4.68264e11 0.726477 0.363238 0.931696i \(-0.381671\pi\)
0.363238 + 0.931696i \(0.381671\pi\)
\(422\) −1.60472e12 −2.46316
\(423\) −1.70875e12 −2.59505
\(424\) −2.93400e11 −0.440873
\(425\) 0 0
\(426\) 6.31528e11 0.929072
\(427\) −3.95202e11 −0.575299
\(428\) −9.17478e11 −1.32160
\(429\) −2.45497e12 −3.49936
\(430\) 1.08856e11 0.153548
\(431\) 1.08014e12 1.50775 0.753877 0.657015i \(-0.228181\pi\)
0.753877 + 0.657015i \(0.228181\pi\)
\(432\) −8.86145e11 −1.22413
\(433\) −1.19984e12 −1.64031 −0.820157 0.572139i \(-0.806114\pi\)
−0.820157 + 0.572139i \(0.806114\pi\)
\(434\) 1.16715e11 0.157914
\(435\) −3.00183e11 −0.401961
\(436\) 6.42612e11 0.851647
\(437\) 1.33714e11 0.175392
\(438\) 2.01795e10 0.0261986
\(439\) 1.20760e12 1.55178 0.775892 0.630865i \(-0.217300\pi\)
0.775892 + 0.630865i \(0.217300\pi\)
\(440\) 8.28733e11 1.05409
\(441\) 3.99785e11 0.503331
\(442\) 0 0
\(443\) −7.07890e11 −0.873271 −0.436636 0.899638i \(-0.643830\pi\)
−0.436636 + 0.899638i \(0.643830\pi\)
\(444\) 4.09973e12 5.00648
\(445\) 1.63570e11 0.197735
\(446\) 4.25208e11 0.508856
\(447\) 2.10093e12 2.48902
\(448\) −1.25404e12 −1.47082
\(449\) −4.16466e11 −0.483583 −0.241791 0.970328i \(-0.577735\pi\)
−0.241791 + 0.970328i \(0.577735\pi\)
\(450\) 1.88076e12 2.16210
\(451\) 1.33576e12 1.52032
\(452\) 1.09151e12 1.23000
\(453\) 1.15914e11 0.129329
\(454\) −1.70046e12 −1.87852
\(455\) −1.11302e12 −1.21745
\(456\) −2.38965e11 −0.258817
\(457\) 4.97073e11 0.533086 0.266543 0.963823i \(-0.414119\pi\)
0.266543 + 0.963823i \(0.414119\pi\)
\(458\) 3.72044e10 0.0395093
\(459\) 0 0
\(460\) −1.98532e12 −2.06738
\(461\) −9.75376e11 −1.00581 −0.502907 0.864340i \(-0.667736\pi\)
−0.502907 + 0.864340i \(0.667736\pi\)
\(462\) −3.70475e12 −3.78330
\(463\) 1.43284e12 1.44905 0.724523 0.689251i \(-0.242060\pi\)
0.724523 + 0.689251i \(0.242060\pi\)
\(464\) 2.29814e11 0.230168
\(465\) 9.30933e10 0.0923379
\(466\) 1.04963e12 1.03109
\(467\) 1.42742e12 1.38876 0.694378 0.719610i \(-0.255680\pi\)
0.694378 + 0.719610i \(0.255680\pi\)
\(468\) −7.12051e12 −6.86128
\(469\) −8.87886e11 −0.847383
\(470\) 1.38775e12 1.31181
\(471\) 2.39952e12 2.24662
\(472\) 5.70505e11 0.529079
\(473\) 1.79273e11 0.164680
\(474\) 3.10285e12 2.82331
\(475\) 6.70522e10 0.0604355
\(476\) 0 0
\(477\) 7.08739e11 0.626835
\(478\) 2.01931e12 1.76920
\(479\) 3.08239e10 0.0267533 0.0133766 0.999911i \(-0.495742\pi\)
0.0133766 + 0.999911i \(0.495742\pi\)
\(480\) −5.21907e11 −0.448753
\(481\) 3.11214e12 2.65098
\(482\) −1.89152e12 −1.59624
\(483\) 4.13357e12 3.45591
\(484\) 6.70695e11 0.555547
\(485\) 8.28043e10 0.0679540
\(486\) 7.74393e11 0.629649
\(487\) −4.56397e11 −0.367674 −0.183837 0.982957i \(-0.558852\pi\)
−0.183837 + 0.982957i \(0.558852\pi\)
\(488\) 9.56338e11 0.763348
\(489\) 2.92200e12 2.31095
\(490\) −3.24684e11 −0.254436
\(491\) −1.49685e12 −1.16228 −0.581139 0.813804i \(-0.697393\pi\)
−0.581139 + 0.813804i \(0.697393\pi\)
\(492\) 5.71880e12 4.40010
\(493\) 0 0
\(494\) −3.89484e11 −0.294251
\(495\) −2.00189e12 −1.49871
\(496\) −7.12703e10 −0.0528739
\(497\) 4.71532e11 0.346663
\(498\) 2.49257e12 1.81600
\(499\) 9.86104e11 0.711984 0.355992 0.934489i \(-0.384143\pi\)
0.355992 + 0.934489i \(0.384143\pi\)
\(500\) −2.63458e12 −1.88515
\(501\) −3.37309e12 −2.39198
\(502\) 9.36106e11 0.657897
\(503\) −5.92003e11 −0.412352 −0.206176 0.978515i \(-0.566102\pi\)
−0.206176 + 0.978515i \(0.566102\pi\)
\(504\) −5.00463e12 −3.45490
\(505\) −1.30526e12 −0.893071
\(506\) −5.01641e12 −3.40185
\(507\) −5.35891e12 −3.60198
\(508\) −1.42033e12 −0.946244
\(509\) 9.84420e11 0.650055 0.325028 0.945705i \(-0.394626\pi\)
0.325028 + 0.945705i \(0.394626\pi\)
\(510\) 0 0
\(511\) 1.50671e10 0.00977542
\(512\) 1.85077e12 1.19025
\(513\) 3.02427e11 0.192794
\(514\) −4.38457e11 −0.277072
\(515\) −1.59189e12 −0.997193
\(516\) 7.67522e11 0.476615
\(517\) 2.28547e12 1.40692
\(518\) 4.69647e12 2.86608
\(519\) −7.85623e11 −0.475293
\(520\) 2.69336e12 1.61540
\(521\) 7.78676e11 0.463006 0.231503 0.972834i \(-0.425636\pi\)
0.231503 + 0.972834i \(0.425636\pi\)
\(522\) −2.19994e12 −1.29686
\(523\) −1.54298e12 −0.901786 −0.450893 0.892578i \(-0.648894\pi\)
−0.450893 + 0.892578i \(0.648894\pi\)
\(524\) 3.53098e12 2.04600
\(525\) 2.07283e12 1.19082
\(526\) 5.67195e11 0.323070
\(527\) 0 0
\(528\) 2.26226e12 1.26675
\(529\) 3.79589e12 2.10748
\(530\) −5.75600e11 −0.316869
\(531\) −1.37812e12 −0.752248
\(532\) −3.83093e11 −0.207349
\(533\) 4.34119e12 2.32989
\(534\) 1.76946e12 0.941685
\(535\) −8.38310e11 −0.442398
\(536\) 2.14857e12 1.12437
\(537\) 1.53592e12 0.797046
\(538\) −4.15938e12 −2.14047
\(539\) −5.34719e11 −0.272883
\(540\) −4.49032e12 −2.27251
\(541\) 2.37260e12 1.19079 0.595397 0.803432i \(-0.296995\pi\)
0.595397 + 0.803432i \(0.296995\pi\)
\(542\) 4.79115e12 2.38475
\(543\) −1.43203e12 −0.706893
\(544\) 0 0
\(545\) 5.87162e11 0.285085
\(546\) −1.20404e13 −5.79792
\(547\) 1.52298e12 0.727364 0.363682 0.931523i \(-0.381520\pi\)
0.363682 + 0.931523i \(0.381520\pi\)
\(548\) 4.56969e12 2.16458
\(549\) −2.31014e12 −1.08533
\(550\) −2.51554e12 −1.17219
\(551\) −7.84318e10 −0.0362502
\(552\) −1.00027e13 −4.58555
\(553\) 2.31675e12 1.05346
\(554\) 1.67819e12 0.756916
\(555\) 3.74597e12 1.67589
\(556\) −2.64128e12 −1.17214
\(557\) 9.15324e11 0.402927 0.201464 0.979496i \(-0.435430\pi\)
0.201464 + 0.979496i \(0.435430\pi\)
\(558\) 6.82251e11 0.297914
\(559\) 5.82632e11 0.252372
\(560\) 1.02565e12 0.440709
\(561\) 0 0
\(562\) 3.58996e12 1.51801
\(563\) −3.29684e12 −1.38296 −0.691482 0.722394i \(-0.743042\pi\)
−0.691482 + 0.722394i \(0.743042\pi\)
\(564\) 9.78480e12 4.07189
\(565\) 9.97324e11 0.411736
\(566\) −1.32153e12 −0.541255
\(567\) 3.59360e12 1.46018
\(568\) −1.14105e12 −0.459977
\(569\) 2.75031e12 1.09996 0.549979 0.835178i \(-0.314636\pi\)
0.549979 + 0.835178i \(0.314636\pi\)
\(570\) −4.68808e11 −0.186019
\(571\) −1.83309e12 −0.721640 −0.360820 0.932635i \(-0.617503\pi\)
−0.360820 + 0.932635i \(0.617503\pi\)
\(572\) 9.52379e12 3.71987
\(573\) −4.02610e12 −1.56023
\(574\) 6.55121e12 2.51894
\(575\) 2.80670e12 1.07076
\(576\) −7.33044e12 −2.77478
\(577\) −1.48112e12 −0.556288 −0.278144 0.960539i \(-0.589719\pi\)
−0.278144 + 0.960539i \(0.589719\pi\)
\(578\) 0 0
\(579\) 6.86365e12 2.53806
\(580\) 1.16452e12 0.427290
\(581\) 1.86109e12 0.677601
\(582\) 8.95758e11 0.323621
\(583\) −9.47948e11 −0.339841
\(584\) −3.64605e10 −0.0129707
\(585\) −6.50610e12 −2.29678
\(586\) 7.97893e12 2.79515
\(587\) −1.81141e12 −0.629716 −0.314858 0.949139i \(-0.601957\pi\)
−0.314858 + 0.949139i \(0.601957\pi\)
\(588\) −2.28929e12 −0.789775
\(589\) 2.43234e10 0.00832734
\(590\) 1.11923e12 0.380265
\(591\) 7.70836e12 2.59907
\(592\) −2.86784e12 −0.959638
\(593\) −1.94583e12 −0.646188 −0.323094 0.946367i \(-0.604723\pi\)
−0.323094 + 0.946367i \(0.604723\pi\)
\(594\) −1.13459e13 −3.73938
\(595\) 0 0
\(596\) −8.15033e12 −2.64586
\(597\) 4.71818e12 1.52016
\(598\) −1.63032e13 −5.21336
\(599\) 1.39777e12 0.443625 0.221812 0.975089i \(-0.428803\pi\)
0.221812 + 0.975089i \(0.428803\pi\)
\(600\) −5.01597e12 −1.58006
\(601\) −2.87702e12 −0.899513 −0.449756 0.893151i \(-0.648489\pi\)
−0.449756 + 0.893151i \(0.648489\pi\)
\(602\) 8.79240e11 0.272849
\(603\) −5.19011e12 −1.59863
\(604\) −4.49675e11 −0.137478
\(605\) 6.12822e11 0.185967
\(606\) −1.41200e13 −4.25312
\(607\) −1.04761e11 −0.0313221 −0.0156610 0.999877i \(-0.504985\pi\)
−0.0156610 + 0.999877i \(0.504985\pi\)
\(608\) −1.36364e11 −0.0404700
\(609\) −2.42461e12 −0.714272
\(610\) 1.87617e12 0.548641
\(611\) 7.42772e12 2.15611
\(612\) 0 0
\(613\) 3.07681e12 0.880094 0.440047 0.897975i \(-0.354962\pi\)
0.440047 + 0.897975i \(0.354962\pi\)
\(614\) 4.20186e12 1.19312
\(615\) 5.22534e12 1.47291
\(616\) 6.69377e12 1.87309
\(617\) −1.02089e12 −0.283593 −0.141797 0.989896i \(-0.545288\pi\)
−0.141797 + 0.989896i \(0.545288\pi\)
\(618\) −1.72206e13 −4.74899
\(619\) −4.26264e12 −1.16700 −0.583500 0.812113i \(-0.698317\pi\)
−0.583500 + 0.812113i \(0.698317\pi\)
\(620\) −3.61145e11 −0.0981564
\(621\) 1.26591e13 3.41579
\(622\) −6.33396e12 −1.69675
\(623\) 1.32117e12 0.351369
\(624\) 7.35229e12 1.94130
\(625\) −9.01317e10 −0.0236275
\(626\) −7.99774e12 −2.08153
\(627\) −7.72074e11 −0.199506
\(628\) −9.30865e12 −2.38819
\(629\) 0 0
\(630\) −9.81823e12 −2.48314
\(631\) 2.55988e12 0.642818 0.321409 0.946940i \(-0.395844\pi\)
0.321409 + 0.946940i \(0.395844\pi\)
\(632\) −5.60625e12 −1.39780
\(633\) −1.03383e13 −2.55936
\(634\) 2.20530e12 0.542083
\(635\) −1.29777e12 −0.316750
\(636\) −4.05845e12 −0.983566
\(637\) −1.73782e12 −0.418194
\(638\) 2.94245e12 0.703099
\(639\) 2.75632e12 0.653998
\(640\) 4.87170e12 1.14781
\(641\) 7.00235e12 1.63826 0.819130 0.573608i \(-0.194457\pi\)
0.819130 + 0.573608i \(0.194457\pi\)
\(642\) −9.06864e12 −2.10686
\(643\) 3.17520e12 0.732523 0.366261 0.930512i \(-0.380638\pi\)
0.366261 + 0.930512i \(0.380638\pi\)
\(644\) −1.60357e13 −3.67368
\(645\) 7.01294e11 0.159544
\(646\) 0 0
\(647\) 1.28689e12 0.288717 0.144359 0.989525i \(-0.453888\pi\)
0.144359 + 0.989525i \(0.453888\pi\)
\(648\) −8.69605e12 −1.93747
\(649\) 1.84325e12 0.407834
\(650\) −8.17543e12 −1.79639
\(651\) 7.51925e11 0.164082
\(652\) −1.13356e13 −2.45657
\(653\) −6.54997e12 −1.40971 −0.704856 0.709351i \(-0.748988\pi\)
−0.704856 + 0.709351i \(0.748988\pi\)
\(654\) 6.35178e12 1.35767
\(655\) 3.22630e12 0.684887
\(656\) −4.00041e12 −0.843408
\(657\) 8.80741e10 0.0184418
\(658\) 1.12090e13 2.33105
\(659\) 4.44729e12 0.918567 0.459284 0.888290i \(-0.348106\pi\)
0.459284 + 0.888290i \(0.348106\pi\)
\(660\) 1.14634e13 2.35162
\(661\) 4.35836e12 0.888007 0.444004 0.896025i \(-0.353558\pi\)
0.444004 + 0.896025i \(0.353558\pi\)
\(662\) −1.21812e13 −2.46506
\(663\) 0 0
\(664\) −4.50360e12 −0.899090
\(665\) −3.50037e11 −0.0694091
\(666\) 2.74531e13 5.40700
\(667\) −3.28303e12 −0.642257
\(668\) 1.30855e13 2.54271
\(669\) 2.73937e12 0.528730
\(670\) 4.21513e12 0.808117
\(671\) 3.08984e12 0.588417
\(672\) −4.21550e12 −0.797421
\(673\) 8.69544e12 1.63389 0.816946 0.576713i \(-0.195665\pi\)
0.816946 + 0.576713i \(0.195665\pi\)
\(674\) 1.74591e13 3.25876
\(675\) 6.34807e12 1.17700
\(676\) 2.07893e13 3.82895
\(677\) −7.41727e12 −1.35705 −0.678524 0.734578i \(-0.737380\pi\)
−0.678524 + 0.734578i \(0.737380\pi\)
\(678\) 1.07888e13 1.96083
\(679\) 6.68820e11 0.120752
\(680\) 0 0
\(681\) −1.09551e13 −1.95188
\(682\) −9.12520e11 −0.161515
\(683\) −2.91239e12 −0.512103 −0.256051 0.966663i \(-0.582422\pi\)
−0.256051 + 0.966663i \(0.582422\pi\)
\(684\) −2.23936e12 −0.391175
\(685\) 4.17538e12 0.724584
\(686\) 8.32156e12 1.43465
\(687\) 2.39687e11 0.0410524
\(688\) −5.36897e11 −0.0913572
\(689\) −3.08080e12 −0.520808
\(690\) −1.96236e13 −3.29577
\(691\) 3.84355e12 0.641330 0.320665 0.947193i \(-0.396094\pi\)
0.320665 + 0.947193i \(0.396094\pi\)
\(692\) 3.04773e12 0.505242
\(693\) −1.61695e13 −2.66316
\(694\) 1.08082e12 0.176863
\(695\) −2.41337e12 −0.392367
\(696\) 5.86725e12 0.947748
\(697\) 0 0
\(698\) 1.01161e13 1.61311
\(699\) 6.76214e12 1.07136
\(700\) −8.04129e12 −1.26586
\(701\) 8.00517e12 1.25210 0.626051 0.779782i \(-0.284670\pi\)
0.626051 + 0.779782i \(0.284670\pi\)
\(702\) −3.68738e13 −5.73061
\(703\) 9.78749e11 0.151138
\(704\) 9.80456e12 1.50436
\(705\) 8.94049e12 1.36305
\(706\) 5.82261e11 0.0882057
\(707\) −1.05427e13 −1.58696
\(708\) 7.89152e12 1.18035
\(709\) −1.29517e13 −1.92495 −0.962476 0.271367i \(-0.912524\pi\)
−0.962476 + 0.271367i \(0.912524\pi\)
\(710\) −2.23854e12 −0.330599
\(711\) 1.35425e13 1.98740
\(712\) −3.19707e12 −0.466222
\(713\) 1.01814e12 0.147538
\(714\) 0 0
\(715\) 8.70200e12 1.24521
\(716\) −5.95841e12 −0.847270
\(717\) 1.30092e13 1.83830
\(718\) 4.24178e12 0.595646
\(719\) 9.90952e12 1.38284 0.691421 0.722452i \(-0.256985\pi\)
0.691421 + 0.722452i \(0.256985\pi\)
\(720\) 5.99538e12 0.831420
\(721\) −1.28578e13 −1.77198
\(722\) 1.22510e13 1.67785
\(723\) −1.21859e13 −1.65858
\(724\) 5.55540e12 0.751436
\(725\) −1.64632e12 −0.221305
\(726\) 6.62936e12 0.885640
\(727\) 3.54774e12 0.471028 0.235514 0.971871i \(-0.424323\pi\)
0.235514 + 0.971871i \(0.424323\pi\)
\(728\) 2.17546e13 2.87051
\(729\) −5.01181e12 −0.657235
\(730\) −7.15291e10 −0.00932245
\(731\) 0 0
\(732\) 1.32286e13 1.70299
\(733\) −1.45595e13 −1.86285 −0.931425 0.363935i \(-0.881433\pi\)
−0.931425 + 0.363935i \(0.881433\pi\)
\(734\) 6.27112e12 0.797468
\(735\) −2.09175e12 −0.264373
\(736\) −5.70798e12 −0.717022
\(737\) 6.94184e12 0.866704
\(738\) 3.82948e13 4.75211
\(739\) −1.38078e13 −1.70304 −0.851522 0.524319i \(-0.824320\pi\)
−0.851522 + 0.524319i \(0.824320\pi\)
\(740\) −1.45321e13 −1.78150
\(741\) −2.50922e12 −0.305743
\(742\) −4.64918e12 −0.563066
\(743\) −3.03587e12 −0.365455 −0.182728 0.983164i \(-0.558493\pi\)
−0.182728 + 0.983164i \(0.558493\pi\)
\(744\) −1.81956e12 −0.217715
\(745\) −7.44705e12 −0.885688
\(746\) 2.52813e13 2.98865
\(747\) 1.08789e13 1.27833
\(748\) 0 0
\(749\) −6.77113e12 −0.786127
\(750\) −2.60410e13 −3.00526
\(751\) −6.03816e12 −0.692668 −0.346334 0.938111i \(-0.612574\pi\)
−0.346334 + 0.938111i \(0.612574\pi\)
\(752\) −6.84466e12 −0.780498
\(753\) 6.03079e12 0.683592
\(754\) 9.56290e12 1.07750
\(755\) −4.10874e11 −0.0460200
\(756\) −3.62688e13 −4.03817
\(757\) −1.82580e12 −0.202079 −0.101040 0.994882i \(-0.532217\pi\)
−0.101040 + 0.994882i \(0.532217\pi\)
\(758\) 2.37007e13 2.60766
\(759\) −3.23178e13 −3.53471
\(760\) 8.47045e11 0.0920969
\(761\) 5.83576e12 0.630763 0.315382 0.948965i \(-0.397867\pi\)
0.315382 + 0.948965i \(0.397867\pi\)
\(762\) −1.40390e13 −1.50848
\(763\) 4.74258e12 0.506587
\(764\) 1.56188e13 1.65854
\(765\) 0 0
\(766\) −2.42277e13 −2.54263
\(767\) 5.99052e12 0.625007
\(768\) 3.02748e13 3.14019
\(769\) 6.20247e12 0.639582 0.319791 0.947488i \(-0.396387\pi\)
0.319791 + 0.947488i \(0.396387\pi\)
\(770\) 1.31320e13 1.34624
\(771\) −2.82473e12 −0.287894
\(772\) −2.66267e13 −2.69799
\(773\) 1.11694e13 1.12518 0.562592 0.826735i \(-0.309804\pi\)
0.562592 + 0.826735i \(0.309804\pi\)
\(774\) 5.13956e12 0.514745
\(775\) 5.10559e11 0.0508380
\(776\) −1.61846e12 −0.160223
\(777\) 3.02567e13 2.97801
\(778\) 7.00321e12 0.685313
\(779\) 1.36528e12 0.132832
\(780\) 3.72559e13 3.60387
\(781\) −3.68662e12 −0.354567
\(782\) 0 0
\(783\) −7.42541e12 −0.705980
\(784\) 1.60140e12 0.151384
\(785\) −8.50543e12 −0.799434
\(786\) 3.49013e13 3.26168
\(787\) −5.54415e12 −0.515168 −0.257584 0.966256i \(-0.582926\pi\)
−0.257584 + 0.966256i \(0.582926\pi\)
\(788\) −2.99037e13 −2.76285
\(789\) 3.65411e12 0.335687
\(790\) −1.09985e13 −1.00464
\(791\) 8.05550e12 0.731642
\(792\) 3.91282e13 3.53367
\(793\) 1.00419e13 0.901751
\(794\) −7.89117e12 −0.704610
\(795\) −3.70826e12 −0.329244
\(796\) −1.83036e13 −1.61595
\(797\) 3.28819e12 0.288665 0.144333 0.989529i \(-0.453896\pi\)
0.144333 + 0.989529i \(0.453896\pi\)
\(798\) −3.78662e12 −0.330551
\(799\) 0 0
\(800\) −2.86234e12 −0.247067
\(801\) 7.72287e12 0.662876
\(802\) −3.25302e13 −2.77653
\(803\) −1.17800e11 −0.00999831
\(804\) 2.97201e13 2.50841
\(805\) −1.46520e13 −1.22975
\(806\) −2.96567e12 −0.247522
\(807\) −2.67965e13 −2.22406
\(808\) 2.55121e13 2.10569
\(809\) 3.73326e12 0.306422 0.153211 0.988194i \(-0.451039\pi\)
0.153211 + 0.988194i \(0.451039\pi\)
\(810\) −1.70601e13 −1.39252
\(811\) −2.19138e12 −0.177879 −0.0889395 0.996037i \(-0.528348\pi\)
−0.0889395 + 0.996037i \(0.528348\pi\)
\(812\) 9.40599e12 0.759281
\(813\) 3.08666e13 2.47789
\(814\) −3.67188e13 −2.93143
\(815\) −1.03575e13 −0.822325
\(816\) 0 0
\(817\) 1.83234e11 0.0143882
\(818\) 2.99355e13 2.33774
\(819\) −5.25505e13 −4.08131
\(820\) −2.02711e13 −1.56572
\(821\) 1.53840e13 1.18175 0.590873 0.806765i \(-0.298784\pi\)
0.590873 + 0.806765i \(0.298784\pi\)
\(822\) 4.51683e13 3.45073
\(823\) 1.43392e13 1.08949 0.544747 0.838601i \(-0.316626\pi\)
0.544747 + 0.838601i \(0.316626\pi\)
\(824\) 3.11143e13 2.35119
\(825\) −1.62062e13 −1.21797
\(826\) 9.04017e12 0.675720
\(827\) −7.37627e12 −0.548355 −0.274178 0.961679i \(-0.588406\pi\)
−0.274178 + 0.961679i \(0.588406\pi\)
\(828\) −9.37361e13 −6.93059
\(829\) −1.99770e13 −1.46905 −0.734524 0.678583i \(-0.762594\pi\)
−0.734524 + 0.678583i \(0.762594\pi\)
\(830\) −8.83528e12 −0.646203
\(831\) 1.08116e13 0.786477
\(832\) 3.18646e13 2.30544
\(833\) 0 0
\(834\) −2.61073e13 −1.86859
\(835\) 1.19564e13 0.851158
\(836\) 2.99517e12 0.212077
\(837\) 2.30278e12 0.162177
\(838\) −1.31657e13 −0.922243
\(839\) −1.62969e13 −1.13547 −0.567734 0.823212i \(-0.692180\pi\)
−0.567734 + 0.823212i \(0.692180\pi\)
\(840\) 2.61852e13 1.81468
\(841\) −1.25814e13 −0.867258
\(842\) −1.79556e13 −1.23111
\(843\) 2.31280e13 1.57730
\(844\) 4.01061e13 2.72063
\(845\) 1.89954e13 1.28172
\(846\) 6.55220e13 4.39765
\(847\) 4.94983e12 0.330457
\(848\) 2.83897e12 0.188529
\(849\) −8.51384e12 −0.562394
\(850\) 0 0
\(851\) 4.09689e13 2.67776
\(852\) −1.57835e13 −1.02619
\(853\) −2.73583e13 −1.76937 −0.884686 0.466188i \(-0.845627\pi\)
−0.884686 + 0.466188i \(0.845627\pi\)
\(854\) 1.51540e13 0.974918
\(855\) −2.04613e12 −0.130944
\(856\) 1.63853e13 1.04309
\(857\) −8.05643e12 −0.510187 −0.255093 0.966916i \(-0.582106\pi\)
−0.255093 + 0.966916i \(0.582106\pi\)
\(858\) 9.41361e13 5.93012
\(859\) 2.97873e13 1.86665 0.933324 0.359036i \(-0.116895\pi\)
0.933324 + 0.359036i \(0.116895\pi\)
\(860\) −2.72059e12 −0.169598
\(861\) 4.22056e13 2.61732
\(862\) −4.14179e13 −2.55508
\(863\) 1.30714e13 0.802183 0.401091 0.916038i \(-0.368631\pi\)
0.401091 + 0.916038i \(0.368631\pi\)
\(864\) −1.29101e13 −0.788163
\(865\) 2.78475e12 0.169127
\(866\) 4.60078e13 2.77972
\(867\) 0 0
\(868\) −2.91701e12 −0.174421
\(869\) −1.81133e13 −1.07748
\(870\) 1.15105e13 0.681174
\(871\) 2.25608e13 1.32823
\(872\) −1.14764e13 −0.672176
\(873\) 3.90956e12 0.227805
\(874\) −5.12725e12 −0.297224
\(875\) −1.94436e13 −1.12135
\(876\) −5.04339e11 −0.0289371
\(877\) 2.52703e13 1.44249 0.721245 0.692680i \(-0.243570\pi\)
0.721245 + 0.692680i \(0.243570\pi\)
\(878\) −4.63054e13 −2.62970
\(879\) 5.14036e13 2.90432
\(880\) −8.01890e12 −0.450758
\(881\) 5.05069e12 0.282461 0.141231 0.989977i \(-0.454894\pi\)
0.141231 + 0.989977i \(0.454894\pi\)
\(882\) −1.53298e13 −0.852958
\(883\) −3.49182e13 −1.93299 −0.966493 0.256695i \(-0.917367\pi\)
−0.966493 + 0.256695i \(0.917367\pi\)
\(884\) 0 0
\(885\) 7.21057e12 0.395116
\(886\) 2.71441e13 1.47987
\(887\) 1.88815e13 1.02419 0.512095 0.858929i \(-0.328870\pi\)
0.512095 + 0.858929i \(0.328870\pi\)
\(888\) −7.32173e13 −3.95144
\(889\) −1.04823e13 −0.562856
\(890\) −6.27210e12 −0.335087
\(891\) −2.80961e13 −1.49347
\(892\) −1.06271e13 −0.562046
\(893\) 2.33597e12 0.122924
\(894\) −8.05604e13 −4.21796
\(895\) −5.44427e12 −0.283619
\(896\) 3.93492e13 2.03963
\(897\) −1.05032e14 −5.41696
\(898\) 1.59694e13 0.819494
\(899\) −5.97207e11 −0.0304934
\(900\) −4.70050e13 −2.38810
\(901\) 0 0
\(902\) −5.12199e13 −2.57638
\(903\) 5.66443e12 0.283506
\(904\) −1.94933e13 −0.970794
\(905\) 5.07604e12 0.251539
\(906\) −4.44474e12 −0.219164
\(907\) −1.79530e13 −0.880856 −0.440428 0.897788i \(-0.645173\pi\)
−0.440428 + 0.897788i \(0.645173\pi\)
\(908\) 4.24989e13 2.07487
\(909\) −6.16272e13 −2.99388
\(910\) 4.26787e13 2.06312
\(911\) −2.70781e12 −0.130252 −0.0651262 0.997877i \(-0.520745\pi\)
−0.0651262 + 0.997877i \(0.520745\pi\)
\(912\) 2.31225e12 0.110677
\(913\) −1.45507e13 −0.693052
\(914\) −1.90603e13 −0.903383
\(915\) 1.20871e13 0.570068
\(916\) −9.29836e11 −0.0436392
\(917\) 2.60592e13 1.21702
\(918\) 0 0
\(919\) −2.13588e13 −0.987773 −0.493886 0.869527i \(-0.664424\pi\)
−0.493886 + 0.869527i \(0.664424\pi\)
\(920\) 3.54560e13 1.63172
\(921\) 2.70702e13 1.23972
\(922\) 3.74009e13 1.70448
\(923\) −1.19814e13 −0.543376
\(924\) 9.25916e13 4.17876
\(925\) 2.05443e13 0.922687
\(926\) −5.49422e13 −2.45559
\(927\) −7.51600e13 −3.34294
\(928\) 3.34811e12 0.148195
\(929\) −3.90195e13 −1.71874 −0.859371 0.511353i \(-0.829144\pi\)
−0.859371 + 0.511353i \(0.829144\pi\)
\(930\) −3.56967e12 −0.156478
\(931\) −5.46534e11 −0.0238420
\(932\) −2.62329e13 −1.13887
\(933\) −4.08061e13 −1.76302
\(934\) −5.47345e13 −2.35343
\(935\) 0 0
\(936\) 1.27165e14 5.41537
\(937\) −9.65920e12 −0.409367 −0.204684 0.978828i \(-0.565617\pi\)
−0.204684 + 0.978828i \(0.565617\pi\)
\(938\) 3.40461e13 1.43600
\(939\) −5.15248e13 −2.16283
\(940\) −3.46836e13 −1.44893
\(941\) 5.33826e12 0.221946 0.110973 0.993823i \(-0.464603\pi\)
0.110973 + 0.993823i \(0.464603\pi\)
\(942\) −9.20097e13 −3.80719
\(943\) 5.71484e13 2.35343
\(944\) −5.52027e12 −0.226249
\(945\) −3.31392e13 −1.35176
\(946\) −6.87424e12 −0.279071
\(947\) −2.92169e13 −1.18048 −0.590241 0.807227i \(-0.700967\pi\)
−0.590241 + 0.807227i \(0.700967\pi\)
\(948\) −7.75484e13 −3.11843
\(949\) −3.82848e11 −0.0153225
\(950\) −2.57112e12 −0.102416
\(951\) 1.42075e13 0.563254
\(952\) 0 0
\(953\) 1.10222e13 0.432864 0.216432 0.976298i \(-0.430558\pi\)
0.216432 + 0.976298i \(0.430558\pi\)
\(954\) −2.71766e13 −1.06225
\(955\) 1.42711e13 0.555189
\(956\) −5.04678e13 −1.95413
\(957\) 1.89565e13 0.730559
\(958\) −1.18194e12 −0.0453369
\(959\) 3.37250e13 1.28756
\(960\) 3.83543e13 1.45745
\(961\) −2.62544e13 −0.992995
\(962\) −1.19335e14 −4.49243
\(963\) −3.95804e13 −1.48307
\(964\) 4.72740e13 1.76309
\(965\) −2.43292e13 −0.903138
\(966\) −1.58502e14 −5.85649
\(967\) −8.21374e12 −0.302080 −0.151040 0.988528i \(-0.548262\pi\)
−0.151040 + 0.988528i \(0.548262\pi\)
\(968\) −1.19780e13 −0.438474
\(969\) 0 0
\(970\) −3.17514e12 −0.115157
\(971\) 3.39952e13 1.22724 0.613622 0.789600i \(-0.289712\pi\)
0.613622 + 0.789600i \(0.289712\pi\)
\(972\) −1.93541e13 −0.695465
\(973\) −1.94931e13 −0.697225
\(974\) 1.75006e13 0.623070
\(975\) −5.26696e13 −1.86655
\(976\) −9.25363e12 −0.326428
\(977\) −2.44752e13 −0.859409 −0.429704 0.902970i \(-0.641382\pi\)
−0.429704 + 0.902970i \(0.641382\pi\)
\(978\) −1.12044e14 −3.91621
\(979\) −1.03294e13 −0.359381
\(980\) 8.11472e12 0.281032
\(981\) 2.77226e13 0.955702
\(982\) 5.73967e13 1.96963
\(983\) 2.23624e13 0.763884 0.381942 0.924186i \(-0.375255\pi\)
0.381942 + 0.924186i \(0.375255\pi\)
\(984\) −1.02132e14 −3.47284
\(985\) −2.73234e13 −0.924849
\(986\) 0 0
\(987\) 7.22133e13 2.42209
\(988\) 9.73423e12 0.325009
\(989\) 7.66991e12 0.254922
\(990\) 7.67627e13 2.53976
\(991\) −3.63013e13 −1.19561 −0.597807 0.801640i \(-0.703961\pi\)
−0.597807 + 0.801640i \(0.703961\pi\)
\(992\) −1.03832e12 −0.0340432
\(993\) −7.84762e13 −2.56133
\(994\) −1.80809e13 −0.587465
\(995\) −1.67242e13 −0.540932
\(996\) −6.22960e13 −2.00583
\(997\) −4.17526e13 −1.33831 −0.669153 0.743125i \(-0.733343\pi\)
−0.669153 + 0.743125i \(0.733343\pi\)
\(998\) −3.78122e13 −1.20655
\(999\) 9.26616e13 2.94344
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.1.3 yes 36
17.16 even 2 289.10.a.g.1.3 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.3 36 17.16 even 2
289.10.a.h.1.3 yes 36 1.1 even 1 trivial