Properties

Label 289.10.a.g.1.1
Level $289$
Weight $10$
Character 289.1
Self dual yes
Analytic conductor $148.845$
Analytic rank $1$
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: \(1\)
Dimension: \(36\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-44.7383 q^{2} -202.519 q^{3} +1489.51 q^{4} -1685.49 q^{5} +9060.35 q^{6} +4589.24 q^{7} -43732.3 q^{8} +21330.9 q^{9} +O(q^{10})\) \(q-44.7383 q^{2} -202.519 q^{3} +1489.51 q^{4} -1685.49 q^{5} +9060.35 q^{6} +4589.24 q^{7} -43732.3 q^{8} +21330.9 q^{9} +75405.9 q^{10} -29147.4 q^{11} -301655. q^{12} +59631.0 q^{13} -205315. q^{14} +341343. q^{15} +1.19388e6 q^{16} -954309. q^{18} +393350. q^{19} -2.51056e6 q^{20} -929408. q^{21} +1.30401e6 q^{22} +581014. q^{23} +8.85662e6 q^{24} +887748. q^{25} -2.66779e6 q^{26} -333735. q^{27} +6.83573e6 q^{28} -5.69646e6 q^{29} -1.52711e7 q^{30} -557796. q^{31} -3.10211e7 q^{32} +5.90291e6 q^{33} -7.73511e6 q^{35} +3.17727e7 q^{36} +2.31924e6 q^{37} -1.75978e7 q^{38} -1.20764e7 q^{39} +7.37103e7 q^{40} -2.59418e7 q^{41} +4.15801e7 q^{42} +1.10106e7 q^{43} -4.34155e7 q^{44} -3.59530e7 q^{45} -2.59936e7 q^{46} -1.90477e7 q^{47} -2.41783e8 q^{48} -1.92925e7 q^{49} -3.97163e7 q^{50} +8.88212e7 q^{52} -8.95430e7 q^{53} +1.49307e7 q^{54} +4.91277e7 q^{55} -2.00698e8 q^{56} -7.96608e7 q^{57} +2.54850e8 q^{58} +1.61408e8 q^{59} +5.08436e8 q^{60} -8.62127e7 q^{61} +2.49548e7 q^{62} +9.78927e7 q^{63} +7.76564e8 q^{64} -1.00507e8 q^{65} -2.64086e8 q^{66} -7.28639e7 q^{67} -1.17666e8 q^{69} +3.46056e8 q^{70} +2.46821e8 q^{71} -9.32850e8 q^{72} +3.69817e7 q^{73} -1.03759e8 q^{74} -1.79786e8 q^{75} +5.85900e8 q^{76} -1.33765e8 q^{77} +5.40277e8 q^{78} -5.32700e8 q^{79} -2.01227e9 q^{80} -3.52269e8 q^{81} +1.16059e9 q^{82} +3.39461e8 q^{83} -1.38437e9 q^{84} -4.92595e8 q^{86} +1.15364e9 q^{87} +1.27468e9 q^{88} +4.69306e8 q^{89} +1.60848e9 q^{90} +2.73661e8 q^{91} +8.65429e8 q^{92} +1.12964e8 q^{93} +8.52161e8 q^{94} -6.62987e8 q^{95} +6.28235e9 q^{96} +6.49455e6 q^{97} +8.63113e8 q^{98} -6.21742e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} - 60000q^{10} - 76902q^{11} - 373248q^{12} + 54216q^{13} - 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} - 6439479q^{20} - 138102q^{21} - 267324q^{22} - 4041462q^{23} - 7653888q^{24} + 16582356q^{25} + 15822744q^{26} - 13281612q^{27} - 18614784q^{28} - 4005936q^{29} + 22471686q^{30} - 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} - 22076682q^{37} - 27401376q^{38} - 62736162q^{39} + 12231630q^{40} - 59641782q^{41} + 150001536q^{42} - 47951586q^{43} + 49578936q^{44} - 129308238q^{45} - 140524827q^{46} - 118557912q^{47} - 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} - 209848575q^{54} - 365439924q^{55} - 203095059q^{56} + 4614108q^{57} + 179071413q^{58} + 343015128q^{59} + 427179186q^{60} - 175597116q^{61} - 720602571q^{62} - 587415936q^{63} + 853082511q^{64} - 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} - 1308709542q^{71} - 275337849q^{72} - 494841342q^{73} - 1545361890q^{74} - 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} - 2270624538q^{78} - 1980107868q^{79} - 2897000199q^{80} + 1598298840q^{81} - 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} + 2705904618q^{88} + 148394658q^{89} - 117916215q^{90} - 636340896q^{91} + 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} - 4878626298q^{95} + 8390096634q^{96} + 891786822q^{97} + 4285627647q^{98} + 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −44.7383 −1.97717 −0.988586 0.150660i \(-0.951860\pi\)
−0.988586 + 0.150660i \(0.951860\pi\)
\(3\) −202.519 −1.44351 −0.721755 0.692148i \(-0.756664\pi\)
−0.721755 + 0.692148i \(0.756664\pi\)
\(4\) 1489.51 2.90921
\(5\) −1685.49 −1.20604 −0.603019 0.797727i \(-0.706036\pi\)
−0.603019 + 0.797727i \(0.706036\pi\)
\(6\) 9060.35 2.85407
\(7\) 4589.24 0.722436 0.361218 0.932481i \(-0.382361\pi\)
0.361218 + 0.932481i \(0.382361\pi\)
\(8\) −43732.3 −3.77483
\(9\) 21330.9 1.08372
\(10\) 75405.9 2.38454
\(11\) −29147.4 −0.600251 −0.300126 0.953900i \(-0.597029\pi\)
−0.300126 + 0.953900i \(0.597029\pi\)
\(12\) −301655. −4.19947
\(13\) 59631.0 0.579064 0.289532 0.957168i \(-0.406500\pi\)
0.289532 + 0.957168i \(0.406500\pi\)
\(14\) −205315. −1.42838
\(15\) 341343. 1.74093
\(16\) 1.19388e6 4.55428
\(17\) 0 0
\(18\) −954309. −2.14271
\(19\) 393350. 0.692449 0.346224 0.938152i \(-0.387464\pi\)
0.346224 + 0.938152i \(0.387464\pi\)
\(20\) −2.51056e6 −3.50861
\(21\) −929408. −1.04284
\(22\) 1.30401e6 1.18680
\(23\) 581014. 0.432924 0.216462 0.976291i \(-0.430548\pi\)
0.216462 + 0.976291i \(0.430548\pi\)
\(24\) 8.85662e6 5.44901
\(25\) 887748. 0.454527
\(26\) −2.66779e6 −1.14491
\(27\) −333735. −0.120855
\(28\) 6.83573e6 2.10172
\(29\) −5.69646e6 −1.49559 −0.747797 0.663927i \(-0.768888\pi\)
−0.747797 + 0.663927i \(0.768888\pi\)
\(30\) −1.52711e7 −3.44211
\(31\) −557796. −0.108480 −0.0542398 0.998528i \(-0.517274\pi\)
−0.0542398 + 0.998528i \(0.517274\pi\)
\(32\) −3.10211e7 −5.22976
\(33\) 5.90291e6 0.866469
\(34\) 0 0
\(35\) −7.73511e6 −0.871285
\(36\) 3.17727e7 3.15277
\(37\) 2.31924e6 0.203441 0.101720 0.994813i \(-0.467565\pi\)
0.101720 + 0.994813i \(0.467565\pi\)
\(38\) −1.75978e7 −1.36909
\(39\) −1.20764e7 −0.835885
\(40\) 7.37103e7 4.55259
\(41\) −2.59418e7 −1.43375 −0.716873 0.697204i \(-0.754427\pi\)
−0.716873 + 0.697204i \(0.754427\pi\)
\(42\) 4.15801e7 2.06188
\(43\) 1.10106e7 0.491137 0.245569 0.969379i \(-0.421025\pi\)
0.245569 + 0.969379i \(0.421025\pi\)
\(44\) −4.34155e7 −1.74626
\(45\) −3.59530e7 −1.30701
\(46\) −2.59936e7 −0.855965
\(47\) −1.90477e7 −0.569380 −0.284690 0.958620i \(-0.591891\pi\)
−0.284690 + 0.958620i \(0.591891\pi\)
\(48\) −2.41783e8 −6.57415
\(49\) −1.92925e7 −0.478086
\(50\) −3.97163e7 −0.898678
\(51\) 0 0
\(52\) 8.88212e7 1.68462
\(53\) −8.95430e7 −1.55880 −0.779400 0.626527i \(-0.784476\pi\)
−0.779400 + 0.626527i \(0.784476\pi\)
\(54\) 1.49307e7 0.238951
\(55\) 4.91277e7 0.723926
\(56\) −2.00698e8 −2.72707
\(57\) −7.96608e7 −0.999557
\(58\) 2.54850e8 2.95705
\(59\) 1.61408e8 1.73417 0.867086 0.498158i \(-0.165990\pi\)
0.867086 + 0.498158i \(0.165990\pi\)
\(60\) 5.08436e8 5.06472
\(61\) −8.62127e7 −0.797237 −0.398618 0.917117i \(-0.630510\pi\)
−0.398618 + 0.917117i \(0.630510\pi\)
\(62\) 2.49548e7 0.214483
\(63\) 9.78927e7 0.782921
\(64\) 7.76564e8 5.78585
\(65\) −1.00507e8 −0.698373
\(66\) −2.64086e8 −1.71316
\(67\) −7.28639e7 −0.441749 −0.220875 0.975302i \(-0.570891\pi\)
−0.220875 + 0.975302i \(0.570891\pi\)
\(68\) 0 0
\(69\) −1.17666e8 −0.624930
\(70\) 3.46056e8 1.72268
\(71\) 2.46821e8 1.15271 0.576355 0.817200i \(-0.304475\pi\)
0.576355 + 0.817200i \(0.304475\pi\)
\(72\) −9.32850e8 −4.09087
\(73\) 3.69817e7 0.152417 0.0762085 0.997092i \(-0.475719\pi\)
0.0762085 + 0.997092i \(0.475719\pi\)
\(74\) −1.03759e8 −0.402237
\(75\) −1.79786e8 −0.656115
\(76\) 5.85900e8 2.01448
\(77\) −1.33765e8 −0.433643
\(78\) 5.40277e8 1.65269
\(79\) −5.32700e8 −1.53872 −0.769362 0.638812i \(-0.779426\pi\)
−0.769362 + 0.638812i \(0.779426\pi\)
\(80\) −2.01227e9 −5.49263
\(81\) −3.52269e8 −0.909267
\(82\) 1.16059e9 2.83476
\(83\) 3.39461e8 0.785125 0.392562 0.919725i \(-0.371589\pi\)
0.392562 + 0.919725i \(0.371589\pi\)
\(84\) −1.38437e9 −3.03385
\(85\) 0 0
\(86\) −4.92595e8 −0.971063
\(87\) 1.15364e9 2.15891
\(88\) 1.27468e9 2.26585
\(89\) 4.69306e8 0.792868 0.396434 0.918063i \(-0.370248\pi\)
0.396434 + 0.918063i \(0.370248\pi\)
\(90\) 1.60848e9 2.58418
\(91\) 2.73661e8 0.418337
\(92\) 8.65429e8 1.25946
\(93\) 1.12964e8 0.156591
\(94\) 8.52161e8 1.12576
\(95\) −6.62987e8 −0.835120
\(96\) 6.28235e9 7.54921
\(97\) 6.49455e6 0.00744863 0.00372432 0.999993i \(-0.498815\pi\)
0.00372432 + 0.999993i \(0.498815\pi\)
\(98\) 8.63113e8 0.945258
\(99\) −6.21742e8 −0.650506
\(100\) 1.32231e9 1.32231
\(101\) 2.04216e9 1.95273 0.976366 0.216123i \(-0.0693411\pi\)
0.976366 + 0.216123i \(0.0693411\pi\)
\(102\) 0 0
\(103\) 6.58293e8 0.576304 0.288152 0.957585i \(-0.406959\pi\)
0.288152 + 0.957585i \(0.406959\pi\)
\(104\) −2.60780e9 −2.18587
\(105\) 1.56651e9 1.25771
\(106\) 4.00600e9 3.08202
\(107\) 2.13709e9 1.57614 0.788071 0.615584i \(-0.211080\pi\)
0.788071 + 0.615584i \(0.211080\pi\)
\(108\) −4.97103e8 −0.351592
\(109\) −2.24135e8 −0.152087 −0.0760434 0.997105i \(-0.524229\pi\)
−0.0760434 + 0.997105i \(0.524229\pi\)
\(110\) −2.19789e9 −1.43133
\(111\) −4.69690e8 −0.293669
\(112\) 5.47898e9 3.29017
\(113\) 6.81116e8 0.392978 0.196489 0.980506i \(-0.437046\pi\)
0.196489 + 0.980506i \(0.437046\pi\)
\(114\) 3.56389e9 1.97630
\(115\) −9.79293e8 −0.522123
\(116\) −8.48495e9 −4.35099
\(117\) 1.27198e9 0.627545
\(118\) −7.22114e9 −3.42876
\(119\) 0 0
\(120\) −1.49277e10 −6.57171
\(121\) −1.50837e9 −0.639698
\(122\) 3.85701e9 1.57627
\(123\) 5.25370e9 2.06963
\(124\) −8.30845e8 −0.315589
\(125\) 1.79568e9 0.657861
\(126\) −4.37955e9 −1.54797
\(127\) 2.46598e9 0.841148 0.420574 0.907258i \(-0.361829\pi\)
0.420574 + 0.907258i \(0.361829\pi\)
\(128\) −1.88594e10 −6.20986
\(129\) −2.22986e9 −0.708962
\(130\) 4.49653e9 1.38080
\(131\) −2.56271e9 −0.760289 −0.380145 0.924927i \(-0.624126\pi\)
−0.380145 + 0.924927i \(0.624126\pi\)
\(132\) 8.79246e9 2.52074
\(133\) 1.80518e9 0.500250
\(134\) 3.25981e9 0.873414
\(135\) 5.62507e8 0.145756
\(136\) 0 0
\(137\) 7.21417e9 1.74962 0.874810 0.484466i \(-0.160986\pi\)
0.874810 + 0.484466i \(0.160986\pi\)
\(138\) 5.26419e9 1.23559
\(139\) −5.33039e8 −0.121114 −0.0605568 0.998165i \(-0.519288\pi\)
−0.0605568 + 0.998165i \(0.519288\pi\)
\(140\) −1.15216e10 −2.53475
\(141\) 3.85752e9 0.821905
\(142\) −1.10424e10 −2.27910
\(143\) −1.73809e9 −0.347584
\(144\) 2.54665e10 4.93558
\(145\) 9.60131e9 1.80374
\(146\) −1.65450e9 −0.301355
\(147\) 3.90710e9 0.690122
\(148\) 3.45454e9 0.591851
\(149\) −7.39170e9 −1.22859 −0.614294 0.789078i \(-0.710559\pi\)
−0.614294 + 0.789078i \(0.710559\pi\)
\(150\) 8.04331e9 1.29725
\(151\) −3.19788e9 −0.500572 −0.250286 0.968172i \(-0.580525\pi\)
−0.250286 + 0.968172i \(0.580525\pi\)
\(152\) −1.72021e10 −2.61388
\(153\) 0 0
\(154\) 5.98440e9 0.857387
\(155\) 9.40159e8 0.130830
\(156\) −1.79880e10 −2.43176
\(157\) 4.26085e9 0.559691 0.279845 0.960045i \(-0.409717\pi\)
0.279845 + 0.960045i \(0.409717\pi\)
\(158\) 2.38321e10 3.04232
\(159\) 1.81342e10 2.25014
\(160\) 5.22856e10 6.30729
\(161\) 2.66641e9 0.312760
\(162\) 1.57599e10 1.79778
\(163\) −2.55595e9 −0.283601 −0.141800 0.989895i \(-0.545289\pi\)
−0.141800 + 0.989895i \(0.545289\pi\)
\(164\) −3.86406e10 −4.17106
\(165\) −9.94929e9 −1.04499
\(166\) −1.51869e10 −1.55233
\(167\) −1.08794e10 −1.08238 −0.541191 0.840900i \(-0.682026\pi\)
−0.541191 + 0.840900i \(0.682026\pi\)
\(168\) 4.06451e10 3.93656
\(169\) −7.04865e9 −0.664685
\(170\) 0 0
\(171\) 8.39051e9 0.750423
\(172\) 1.64004e10 1.42882
\(173\) −1.34690e10 −1.14322 −0.571608 0.820527i \(-0.693680\pi\)
−0.571608 + 0.820527i \(0.693680\pi\)
\(174\) −5.16119e10 −4.26853
\(175\) 4.07409e9 0.328367
\(176\) −3.47984e10 −2.73371
\(177\) −3.26883e10 −2.50330
\(178\) −2.09959e10 −1.56764
\(179\) 6.61516e9 0.481617 0.240809 0.970573i \(-0.422587\pi\)
0.240809 + 0.970573i \(0.422587\pi\)
\(180\) −5.35525e10 −3.80237
\(181\) −4.23515e9 −0.293302 −0.146651 0.989188i \(-0.546849\pi\)
−0.146651 + 0.989188i \(0.546849\pi\)
\(182\) −1.22431e10 −0.827124
\(183\) 1.74597e10 1.15082
\(184\) −2.54091e10 −1.63421
\(185\) −3.90905e9 −0.245357
\(186\) −5.05383e9 −0.309608
\(187\) 0 0
\(188\) −2.83718e10 −1.65644
\(189\) −1.53159e9 −0.0873101
\(190\) 2.96609e10 1.65117
\(191\) 2.04632e10 1.11256 0.556279 0.830996i \(-0.312229\pi\)
0.556279 + 0.830996i \(0.312229\pi\)
\(192\) −1.57269e11 −8.35194
\(193\) 2.03719e10 1.05688 0.528438 0.848972i \(-0.322778\pi\)
0.528438 + 0.848972i \(0.322778\pi\)
\(194\) −2.90555e8 −0.0147272
\(195\) 2.03546e10 1.00811
\(196\) −2.87364e10 −1.39085
\(197\) 3.14257e9 0.148658 0.0743289 0.997234i \(-0.476319\pi\)
0.0743289 + 0.997234i \(0.476319\pi\)
\(198\) 2.78156e10 1.28616
\(199\) 2.17856e10 0.984761 0.492381 0.870380i \(-0.336127\pi\)
0.492381 + 0.870380i \(0.336127\pi\)
\(200\) −3.88233e10 −1.71576
\(201\) 1.47563e10 0.637670
\(202\) −9.13626e10 −3.86089
\(203\) −2.61424e10 −1.08047
\(204\) 0 0
\(205\) 4.37245e10 1.72915
\(206\) −2.94509e10 −1.13945
\(207\) 1.23936e10 0.469170
\(208\) 7.11920e10 2.63722
\(209\) −1.14651e10 −0.415643
\(210\) −7.00828e10 −2.48671
\(211\) 1.80701e10 0.627608 0.313804 0.949488i \(-0.398396\pi\)
0.313804 + 0.949488i \(0.398396\pi\)
\(212\) −1.33376e11 −4.53487
\(213\) −4.99860e10 −1.66395
\(214\) −9.56097e10 −3.11630
\(215\) −1.85583e10 −0.592330
\(216\) 1.45950e10 0.456207
\(217\) −2.55986e9 −0.0783695
\(218\) 1.00274e10 0.300702
\(219\) −7.48949e9 −0.220016
\(220\) 7.31764e10 2.10605
\(221\) 0 0
\(222\) 2.10131e10 0.580633
\(223\) −2.54770e10 −0.689883 −0.344942 0.938624i \(-0.612101\pi\)
−0.344942 + 0.938624i \(0.612101\pi\)
\(224\) −1.42363e11 −3.77817
\(225\) 1.89365e10 0.492582
\(226\) −3.04720e10 −0.776985
\(227\) 5.83836e10 1.45940 0.729700 0.683767i \(-0.239660\pi\)
0.729700 + 0.683767i \(0.239660\pi\)
\(228\) −1.18656e11 −2.90792
\(229\) 9.30702e9 0.223641 0.111820 0.993728i \(-0.464332\pi\)
0.111820 + 0.993728i \(0.464332\pi\)
\(230\) 4.38119e10 1.03233
\(231\) 2.70899e10 0.625969
\(232\) 2.49119e11 5.64561
\(233\) 1.79447e10 0.398873 0.199436 0.979911i \(-0.436089\pi\)
0.199436 + 0.979911i \(0.436089\pi\)
\(234\) −5.69064e10 −1.24076
\(235\) 3.21047e10 0.686693
\(236\) 2.40420e11 5.04507
\(237\) 1.07882e11 2.22117
\(238\) 0 0
\(239\) −7.54713e10 −1.49621 −0.748103 0.663582i \(-0.769035\pi\)
−0.748103 + 0.663582i \(0.769035\pi\)
\(240\) 4.07522e11 7.92867
\(241\) −8.81448e10 −1.68314 −0.841570 0.540148i \(-0.818368\pi\)
−0.841570 + 0.540148i \(0.818368\pi\)
\(242\) 6.74821e10 1.26479
\(243\) 7.79100e10 1.43339
\(244\) −1.28415e11 −2.31933
\(245\) 3.25173e10 0.576590
\(246\) −2.35041e11 −4.09201
\(247\) 2.34558e10 0.400972
\(248\) 2.43937e10 0.409492
\(249\) −6.87473e10 −1.13334
\(250\) −8.03357e10 −1.30070
\(251\) 5.70117e10 0.906635 0.453317 0.891349i \(-0.350240\pi\)
0.453317 + 0.891349i \(0.350240\pi\)
\(252\) 1.45813e11 2.27768
\(253\) −1.69351e10 −0.259863
\(254\) −1.10324e11 −1.66309
\(255\) 0 0
\(256\) 4.46134e11 6.49211
\(257\) 8.70477e10 1.24468 0.622341 0.782747i \(-0.286182\pi\)
0.622341 + 0.782747i \(0.286182\pi\)
\(258\) 9.97599e10 1.40174
\(259\) 1.06435e10 0.146973
\(260\) −1.49707e11 −2.03171
\(261\) −1.21511e11 −1.62081
\(262\) 1.14651e11 1.50322
\(263\) 1.02557e11 1.32180 0.660900 0.750474i \(-0.270175\pi\)
0.660900 + 0.750474i \(0.270175\pi\)
\(264\) −2.58148e11 −3.27077
\(265\) 1.50924e11 1.87997
\(266\) −8.07605e10 −0.989080
\(267\) −9.50433e10 −1.14451
\(268\) −1.08532e11 −1.28514
\(269\) 6.29115e10 0.732563 0.366281 0.930504i \(-0.380631\pi\)
0.366281 + 0.930504i \(0.380631\pi\)
\(270\) −2.51656e10 −0.288184
\(271\) 7.40442e10 0.833929 0.416965 0.908923i \(-0.363094\pi\)
0.416965 + 0.908923i \(0.363094\pi\)
\(272\) 0 0
\(273\) −5.54215e10 −0.603874
\(274\) −3.22750e11 −3.45930
\(275\) −2.58756e10 −0.272831
\(276\) −1.75266e11 −1.81805
\(277\) −4.14432e10 −0.422955 −0.211477 0.977383i \(-0.567827\pi\)
−0.211477 + 0.977383i \(0.567827\pi\)
\(278\) 2.38473e10 0.239462
\(279\) −1.18983e10 −0.117562
\(280\) 3.38274e11 3.28895
\(281\) −5.09100e10 −0.487107 −0.243554 0.969887i \(-0.578313\pi\)
−0.243554 + 0.969887i \(0.578313\pi\)
\(282\) −1.72579e11 −1.62505
\(283\) 6.84392e9 0.0634258 0.0317129 0.999497i \(-0.489904\pi\)
0.0317129 + 0.999497i \(0.489904\pi\)
\(284\) 3.67644e11 3.35347
\(285\) 1.34267e11 1.20550
\(286\) 7.77591e10 0.687233
\(287\) −1.19053e11 −1.03579
\(288\) −6.61708e11 −5.66761
\(289\) 0 0
\(290\) −4.29546e11 −3.56631
\(291\) −1.31527e9 −0.0107522
\(292\) 5.50847e10 0.443413
\(293\) 2.94258e10 0.233251 0.116626 0.993176i \(-0.462792\pi\)
0.116626 + 0.993176i \(0.462792\pi\)
\(294\) −1.74797e11 −1.36449
\(295\) −2.72052e11 −2.09148
\(296\) −1.01426e11 −0.767954
\(297\) 9.72752e9 0.0725434
\(298\) 3.30692e11 2.42913
\(299\) 3.46464e10 0.250691
\(300\) −2.67794e11 −1.90877
\(301\) 5.05303e10 0.354815
\(302\) 1.43068e11 0.989716
\(303\) −4.13575e11 −2.81879
\(304\) 4.69611e11 3.15360
\(305\) 1.45311e11 0.961497
\(306\) 0 0
\(307\) 2.13656e10 0.137275 0.0686377 0.997642i \(-0.478135\pi\)
0.0686377 + 0.997642i \(0.478135\pi\)
\(308\) −1.99244e11 −1.26156
\(309\) −1.33317e11 −0.831901
\(310\) −4.20611e10 −0.258674
\(311\) −1.54702e11 −0.937721 −0.468861 0.883272i \(-0.655335\pi\)
−0.468861 + 0.883272i \(0.655335\pi\)
\(312\) 5.28129e11 3.15532
\(313\) 2.42927e11 1.43063 0.715314 0.698803i \(-0.246284\pi\)
0.715314 + 0.698803i \(0.246284\pi\)
\(314\) −1.90623e11 −1.10660
\(315\) −1.64997e11 −0.944232
\(316\) −7.93464e11 −4.47647
\(317\) −1.16285e11 −0.646781 −0.323390 0.946266i \(-0.604823\pi\)
−0.323390 + 0.946266i \(0.604823\pi\)
\(318\) −8.11291e11 −4.44892
\(319\) 1.66037e11 0.897732
\(320\) −1.30889e12 −6.97795
\(321\) −4.32801e11 −2.27518
\(322\) −1.19291e11 −0.618380
\(323\) 0 0
\(324\) −5.24709e11 −2.64525
\(325\) 5.29373e10 0.263200
\(326\) 1.14349e11 0.560727
\(327\) 4.53917e10 0.219539
\(328\) 1.13449e12 5.41214
\(329\) −8.74144e10 −0.411340
\(330\) 4.45114e11 2.06613
\(331\) 4.77798e10 0.218786 0.109393 0.993999i \(-0.465109\pi\)
0.109393 + 0.993999i \(0.465109\pi\)
\(332\) 5.05632e11 2.28409
\(333\) 4.94715e10 0.220473
\(334\) 4.86725e11 2.14005
\(335\) 1.22811e11 0.532766
\(336\) −1.10960e12 −4.74940
\(337\) 2.52033e11 1.06444 0.532222 0.846605i \(-0.321357\pi\)
0.532222 + 0.846605i \(0.321357\pi\)
\(338\) 3.15344e11 1.31420
\(339\) −1.37939e11 −0.567268
\(340\) 0 0
\(341\) 1.62583e10 0.0651150
\(342\) −3.75377e11 −1.48371
\(343\) −2.73730e11 −1.06782
\(344\) −4.81519e11 −1.85396
\(345\) 1.98325e11 0.753689
\(346\) 6.02581e11 2.26033
\(347\) −1.56803e11 −0.580591 −0.290296 0.956937i \(-0.593754\pi\)
−0.290296 + 0.956937i \(0.593754\pi\)
\(348\) 1.71836e12 6.28070
\(349\) −3.68186e11 −1.32847 −0.664237 0.747522i \(-0.731243\pi\)
−0.664237 + 0.747522i \(0.731243\pi\)
\(350\) −1.82268e11 −0.649238
\(351\) −1.99009e10 −0.0699829
\(352\) 9.04184e11 3.13917
\(353\) 3.45826e11 1.18542 0.592708 0.805417i \(-0.298059\pi\)
0.592708 + 0.805417i \(0.298059\pi\)
\(354\) 1.46242e12 4.94945
\(355\) −4.16014e11 −1.39021
\(356\) 6.99038e11 2.30662
\(357\) 0 0
\(358\) −2.95951e11 −0.952240
\(359\) 8.59874e10 0.273218 0.136609 0.990625i \(-0.456380\pi\)
0.136609 + 0.990625i \(0.456380\pi\)
\(360\) 1.57231e12 4.93374
\(361\) −1.67964e11 −0.520515
\(362\) 1.89474e11 0.579909
\(363\) 3.05474e11 0.923411
\(364\) 4.07621e11 1.21703
\(365\) −6.23322e10 −0.183821
\(366\) −7.81118e11 −2.27537
\(367\) 8.64170e10 0.248658 0.124329 0.992241i \(-0.460322\pi\)
0.124329 + 0.992241i \(0.460322\pi\)
\(368\) 6.93659e11 1.97166
\(369\) −5.53361e11 −1.55378
\(370\) 1.74884e11 0.485113
\(371\) −4.10934e11 −1.12613
\(372\) 1.68262e11 0.455557
\(373\) −4.74953e11 −1.27046 −0.635230 0.772323i \(-0.719095\pi\)
−0.635230 + 0.772323i \(0.719095\pi\)
\(374\) 0 0
\(375\) −3.63659e11 −0.949629
\(376\) 8.32999e11 2.14931
\(377\) −3.39685e11 −0.866045
\(378\) 6.85207e10 0.172627
\(379\) 2.21680e11 0.551887 0.275943 0.961174i \(-0.411010\pi\)
0.275943 + 0.961174i \(0.411010\pi\)
\(380\) −9.87528e11 −2.42954
\(381\) −4.99407e11 −1.21421
\(382\) −9.15487e11 −2.19972
\(383\) −3.14470e10 −0.0746766 −0.0373383 0.999303i \(-0.511888\pi\)
−0.0373383 + 0.999303i \(0.511888\pi\)
\(384\) 3.81938e12 8.96400
\(385\) 2.25459e11 0.522990
\(386\) −9.11404e11 −2.08962
\(387\) 2.34866e11 0.532257
\(388\) 9.67373e9 0.0216696
\(389\) −9.75546e10 −0.216010 −0.108005 0.994150i \(-0.534446\pi\)
−0.108005 + 0.994150i \(0.534446\pi\)
\(390\) −9.10632e11 −1.99321
\(391\) 0 0
\(392\) 8.43705e11 1.80469
\(393\) 5.18998e11 1.09749
\(394\) −1.40593e11 −0.293922
\(395\) 8.97860e11 1.85576
\(396\) −9.26093e11 −1.89246
\(397\) 5.98808e10 0.120985 0.0604923 0.998169i \(-0.480733\pi\)
0.0604923 + 0.998169i \(0.480733\pi\)
\(398\) −9.74651e11 −1.94704
\(399\) −3.65582e11 −0.722116
\(400\) 1.05986e12 2.07004
\(401\) −3.95262e11 −0.763370 −0.381685 0.924292i \(-0.624656\pi\)
−0.381685 + 0.924292i \(0.624656\pi\)
\(402\) −6.60173e11 −1.26078
\(403\) −3.32619e10 −0.0628166
\(404\) 3.04182e12 5.68090
\(405\) 5.93745e11 1.09661
\(406\) 1.16957e12 2.13628
\(407\) −6.75998e10 −0.122116
\(408\) 0 0
\(409\) −4.42152e11 −0.781299 −0.390649 0.920540i \(-0.627749\pi\)
−0.390649 + 0.920540i \(0.627749\pi\)
\(410\) −1.95616e12 −3.41883
\(411\) −1.46101e12 −2.52560
\(412\) 9.80536e11 1.67659
\(413\) 7.40742e11 1.25283
\(414\) −5.54467e11 −0.927629
\(415\) −5.72158e11 −0.946890
\(416\) −1.84982e12 −3.02837
\(417\) 1.07951e11 0.174829
\(418\) 5.12931e11 0.821798
\(419\) 5.57958e10 0.0884380 0.0442190 0.999022i \(-0.485920\pi\)
0.0442190 + 0.999022i \(0.485920\pi\)
\(420\) 2.33333e12 3.65894
\(421\) −6.67629e11 −1.03578 −0.517888 0.855449i \(-0.673281\pi\)
−0.517888 + 0.855449i \(0.673281\pi\)
\(422\) −8.08424e11 −1.24089
\(423\) −4.06305e11 −0.617050
\(424\) 3.91592e12 5.88420
\(425\) 0 0
\(426\) 2.23629e12 3.28991
\(427\) −3.95651e11 −0.575953
\(428\) 3.18322e12 4.58532
\(429\) 3.51996e11 0.501741
\(430\) 8.30264e11 1.17114
\(431\) −1.16472e12 −1.62583 −0.812916 0.582381i \(-0.802121\pi\)
−0.812916 + 0.582381i \(0.802121\pi\)
\(432\) −3.98438e11 −0.550408
\(433\) 8.51716e11 1.16439 0.582196 0.813048i \(-0.302193\pi\)
0.582196 + 0.813048i \(0.302193\pi\)
\(434\) 1.14524e11 0.154950
\(435\) −1.94445e12 −2.60372
\(436\) −3.33853e11 −0.442452
\(437\) 2.28542e11 0.299778
\(438\) 3.35067e11 0.435009
\(439\) −3.21133e10 −0.0412662 −0.0206331 0.999787i \(-0.506568\pi\)
−0.0206331 + 0.999787i \(0.506568\pi\)
\(440\) −2.14847e12 −2.73270
\(441\) −4.11527e11 −0.518113
\(442\) 0 0
\(443\) 1.46852e12 1.81160 0.905799 0.423707i \(-0.139271\pi\)
0.905799 + 0.423707i \(0.139271\pi\)
\(444\) −6.99609e11 −0.854343
\(445\) −7.91010e11 −0.956229
\(446\) 1.13980e12 1.36402
\(447\) 1.49696e12 1.77348
\(448\) 3.56384e12 4.17991
\(449\) 2.98654e11 0.346784 0.173392 0.984853i \(-0.444527\pi\)
0.173392 + 0.984853i \(0.444527\pi\)
\(450\) −8.47186e11 −0.973918
\(451\) 7.56136e11 0.860608
\(452\) 1.01453e12 1.14325
\(453\) 6.47632e11 0.722580
\(454\) −2.61198e12 −2.88548
\(455\) −4.61252e11 −0.504530
\(456\) 3.48375e12 3.77316
\(457\) −3.16156e11 −0.339061 −0.169531 0.985525i \(-0.554225\pi\)
−0.169531 + 0.985525i \(0.554225\pi\)
\(458\) −4.16380e11 −0.442176
\(459\) 0 0
\(460\) −1.45867e12 −1.51896
\(461\) 7.38260e11 0.761298 0.380649 0.924720i \(-0.375701\pi\)
0.380649 + 0.924720i \(0.375701\pi\)
\(462\) −1.21195e12 −1.23765
\(463\) 1.74516e12 1.76490 0.882452 0.470402i \(-0.155891\pi\)
0.882452 + 0.470402i \(0.155891\pi\)
\(464\) −6.80086e12 −6.81135
\(465\) −1.90400e11 −0.188855
\(466\) −8.02815e11 −0.788640
\(467\) 4.90423e11 0.477139 0.238569 0.971125i \(-0.423322\pi\)
0.238569 + 0.971125i \(0.423322\pi\)
\(468\) 1.89464e12 1.82566
\(469\) −3.34390e11 −0.319136
\(470\) −1.43631e12 −1.35771
\(471\) −8.62904e11 −0.807920
\(472\) −7.05876e12 −6.54620
\(473\) −3.20931e11 −0.294806
\(474\) −4.82645e12 −4.39163
\(475\) 3.49196e11 0.314737
\(476\) 0 0
\(477\) −1.91004e12 −1.68931
\(478\) 3.37646e12 2.95826
\(479\) −3.66099e11 −0.317752 −0.158876 0.987299i \(-0.550787\pi\)
−0.158876 + 0.987299i \(0.550787\pi\)
\(480\) −1.05888e13 −9.10463
\(481\) 1.38298e11 0.117805
\(482\) 3.94345e12 3.32786
\(483\) −5.39999e11 −0.451472
\(484\) −2.24675e12 −1.86101
\(485\) −1.09465e10 −0.00898333
\(486\) −3.48556e12 −2.83406
\(487\) −1.83184e12 −1.47573 −0.737866 0.674948i \(-0.764166\pi\)
−0.737866 + 0.674948i \(0.764166\pi\)
\(488\) 3.77028e12 3.00943
\(489\) 5.17628e11 0.409381
\(490\) −1.45477e12 −1.14002
\(491\) 6.41422e11 0.498055 0.249027 0.968496i \(-0.419889\pi\)
0.249027 + 0.968496i \(0.419889\pi\)
\(492\) 7.82545e12 6.02097
\(493\) 0 0
\(494\) −1.04937e12 −0.792791
\(495\) 1.04794e12 0.784535
\(496\) −6.65939e11 −0.494046
\(497\) 1.13272e12 0.832759
\(498\) 3.07564e12 2.24080
\(499\) 8.16394e10 0.0589451 0.0294725 0.999566i \(-0.490617\pi\)
0.0294725 + 0.999566i \(0.490617\pi\)
\(500\) 2.67469e12 1.91385
\(501\) 2.20328e12 1.56243
\(502\) −2.55061e12 −1.79257
\(503\) −2.05382e12 −1.43056 −0.715281 0.698837i \(-0.753701\pi\)
−0.715281 + 0.698837i \(0.753701\pi\)
\(504\) −4.28107e12 −2.95539
\(505\) −3.44203e12 −2.35507
\(506\) 7.57646e11 0.513794
\(507\) 1.42748e12 0.959479
\(508\) 3.67311e12 2.44707
\(509\) −1.53618e11 −0.101441 −0.0507203 0.998713i \(-0.516152\pi\)
−0.0507203 + 0.998713i \(0.516152\pi\)
\(510\) 0 0
\(511\) 1.69718e11 0.110112
\(512\) −1.03033e13 −6.62615
\(513\) −1.31275e11 −0.0836860
\(514\) −3.89436e12 −2.46095
\(515\) −1.10954e12 −0.695044
\(516\) −3.32140e12 −2.06252
\(517\) 5.55191e11 0.341771
\(518\) −4.76174e11 −0.290591
\(519\) 2.72773e12 1.65024
\(520\) 4.39542e12 2.63624
\(521\) −9.45774e11 −0.562364 −0.281182 0.959654i \(-0.590727\pi\)
−0.281182 + 0.959654i \(0.590727\pi\)
\(522\) 5.43618e12 3.20462
\(523\) 1.60345e12 0.937123 0.468561 0.883431i \(-0.344772\pi\)
0.468561 + 0.883431i \(0.344772\pi\)
\(524\) −3.81719e12 −2.21184
\(525\) −8.25080e11 −0.474001
\(526\) −4.58824e12 −2.61342
\(527\) 0 0
\(528\) 7.04734e12 3.94614
\(529\) −1.46358e12 −0.812577
\(530\) −6.75207e12 −3.71703
\(531\) 3.44299e12 1.87936
\(532\) 2.68883e12 1.45533
\(533\) −1.54693e12 −0.830231
\(534\) 4.25207e12 2.26290
\(535\) −3.60204e12 −1.90089
\(536\) 3.18651e12 1.66753
\(537\) −1.33970e12 −0.695219
\(538\) −2.81455e12 −1.44840
\(539\) 5.62327e11 0.286972
\(540\) 8.37862e11 0.424034
\(541\) 1.70973e12 0.858102 0.429051 0.903280i \(-0.358848\pi\)
0.429051 + 0.903280i \(0.358848\pi\)
\(542\) −3.31261e12 −1.64882
\(543\) 8.57699e11 0.423385
\(544\) 0 0
\(545\) 3.77778e11 0.183422
\(546\) 2.47946e12 1.19396
\(547\) 2.56587e12 1.22544 0.612720 0.790300i \(-0.290075\pi\)
0.612720 + 0.790300i \(0.290075\pi\)
\(548\) 1.07456e13 5.09001
\(549\) −1.83900e12 −0.863984
\(550\) 1.15763e12 0.539433
\(551\) −2.24070e12 −1.03562
\(552\) 5.14582e12 2.35900
\(553\) −2.44469e12 −1.11163
\(554\) 1.85410e12 0.836254
\(555\) 7.91657e11 0.354176
\(556\) −7.93970e11 −0.352344
\(557\) 2.29359e12 1.00964 0.504820 0.863225i \(-0.331559\pi\)
0.504820 + 0.863225i \(0.331559\pi\)
\(558\) 5.32310e11 0.232440
\(559\) 6.56573e11 0.284400
\(560\) −9.23477e12 −3.96808
\(561\) 0 0
\(562\) 2.27763e12 0.963094
\(563\) −2.87194e12 −1.20472 −0.602362 0.798223i \(-0.705774\pi\)
−0.602362 + 0.798223i \(0.705774\pi\)
\(564\) 5.74583e12 2.39109
\(565\) −1.14801e12 −0.473946
\(566\) −3.06185e11 −0.125404
\(567\) −1.61665e12 −0.656888
\(568\) −1.07941e13 −4.35128
\(569\) 3.45359e12 1.38123 0.690615 0.723222i \(-0.257340\pi\)
0.690615 + 0.723222i \(0.257340\pi\)
\(570\) −6.00689e12 −2.38349
\(571\) −1.13524e12 −0.446916 −0.223458 0.974714i \(-0.571735\pi\)
−0.223458 + 0.974714i \(0.571735\pi\)
\(572\) −2.58891e12 −1.01119
\(573\) −4.14418e12 −1.60599
\(574\) 5.32622e12 2.04793
\(575\) 5.15794e11 0.196776
\(576\) 1.65648e13 6.27026
\(577\) 1.00514e11 0.0377516 0.0188758 0.999822i \(-0.493991\pi\)
0.0188758 + 0.999822i \(0.493991\pi\)
\(578\) 0 0
\(579\) −4.12570e12 −1.52561
\(580\) 1.43013e13 5.24746
\(581\) 1.55787e12 0.567202
\(582\) 5.88429e10 0.0212589
\(583\) 2.60995e12 0.935672
\(584\) −1.61729e12 −0.575348
\(585\) −2.14391e12 −0.756843
\(586\) −1.31646e12 −0.461178
\(587\) −1.73536e12 −0.603279 −0.301640 0.953422i \(-0.597534\pi\)
−0.301640 + 0.953422i \(0.597534\pi\)
\(588\) 5.81967e12 2.00771
\(589\) −2.19409e11 −0.0751165
\(590\) 1.21711e13 4.13521
\(591\) −6.36431e11 −0.214589
\(592\) 2.76888e12 0.926525
\(593\) −5.34487e12 −1.77497 −0.887485 0.460836i \(-0.847550\pi\)
−0.887485 + 0.460836i \(0.847550\pi\)
\(594\) −4.35193e11 −0.143431
\(595\) 0 0
\(596\) −1.10100e13 −3.57421
\(597\) −4.41200e12 −1.42151
\(598\) −1.55002e12 −0.495659
\(599\) −3.97236e12 −1.26075 −0.630374 0.776292i \(-0.717098\pi\)
−0.630374 + 0.776292i \(0.717098\pi\)
\(600\) 7.86245e12 2.47672
\(601\) −2.57946e12 −0.806480 −0.403240 0.915094i \(-0.632116\pi\)
−0.403240 + 0.915094i \(0.632116\pi\)
\(602\) −2.26064e12 −0.701531
\(603\) −1.55425e12 −0.478734
\(604\) −4.76329e12 −1.45627
\(605\) 2.54235e12 0.771500
\(606\) 1.85026e13 5.57323
\(607\) −4.42720e12 −1.32367 −0.661836 0.749649i \(-0.730222\pi\)
−0.661836 + 0.749649i \(0.730222\pi\)
\(608\) −1.22021e13 −3.62134
\(609\) 5.29433e12 1.55967
\(610\) −6.50095e12 −1.90105
\(611\) −1.13583e12 −0.329707
\(612\) 0 0
\(613\) −2.14087e12 −0.612376 −0.306188 0.951971i \(-0.599054\pi\)
−0.306188 + 0.951971i \(0.599054\pi\)
\(614\) −9.55861e11 −0.271417
\(615\) −8.85505e12 −2.49605
\(616\) 5.84983e12 1.63693
\(617\) −6.79042e11 −0.188631 −0.0943155 0.995542i \(-0.530066\pi\)
−0.0943155 + 0.995542i \(0.530066\pi\)
\(618\) 5.96436e12 1.64481
\(619\) 6.49200e12 1.77734 0.888671 0.458546i \(-0.151630\pi\)
0.888671 + 0.458546i \(0.151630\pi\)
\(620\) 1.40038e12 0.380613
\(621\) −1.93905e11 −0.0523210
\(622\) 6.92110e12 1.85404
\(623\) 2.15376e12 0.572797
\(624\) −1.44177e13 −3.80685
\(625\) −4.76048e12 −1.24793
\(626\) −1.08682e13 −2.82860
\(627\) 2.32191e12 0.599986
\(628\) 6.34660e12 1.62826
\(629\) 0 0
\(630\) 7.38168e12 1.86691
\(631\) −3.66553e12 −0.920459 −0.460230 0.887800i \(-0.652233\pi\)
−0.460230 + 0.887800i \(0.652233\pi\)
\(632\) 2.32962e13 5.80842
\(633\) −3.65953e12 −0.905960
\(634\) 5.20239e12 1.27880
\(635\) −4.15638e12 −1.01446
\(636\) 2.70111e13 6.54614
\(637\) −1.15043e12 −0.276843
\(638\) −7.42821e12 −1.77497
\(639\) 5.26492e12 1.24922
\(640\) 3.17872e13 7.48933
\(641\) −1.67471e12 −0.391813 −0.195907 0.980623i \(-0.562765\pi\)
−0.195907 + 0.980623i \(0.562765\pi\)
\(642\) 1.93628e13 4.49842
\(643\) 1.46537e12 0.338064 0.169032 0.985611i \(-0.445936\pi\)
0.169032 + 0.985611i \(0.445936\pi\)
\(644\) 3.97166e12 0.909883
\(645\) 3.75840e12 0.855035
\(646\) 0 0
\(647\) −2.25306e12 −0.505479 −0.252739 0.967534i \(-0.581332\pi\)
−0.252739 + 0.967534i \(0.581332\pi\)
\(648\) 1.54055e13 3.43233
\(649\) −4.70464e12 −1.04094
\(650\) −2.36832e12 −0.520392
\(651\) 5.18420e11 0.113127
\(652\) −3.80712e12 −0.825053
\(653\) −4.56703e12 −0.982935 −0.491467 0.870896i \(-0.663539\pi\)
−0.491467 + 0.870896i \(0.663539\pi\)
\(654\) −2.03075e12 −0.434066
\(655\) 4.31942e12 0.916938
\(656\) −3.09712e13 −6.52967
\(657\) 7.88853e11 0.165178
\(658\) 3.91077e12 0.813290
\(659\) 2.93270e12 0.605735 0.302868 0.953033i \(-0.402056\pi\)
0.302868 + 0.953033i \(0.402056\pi\)
\(660\) −1.48196e13 −3.04011
\(661\) 1.85770e12 0.378502 0.189251 0.981929i \(-0.439394\pi\)
0.189251 + 0.981929i \(0.439394\pi\)
\(662\) −2.13759e12 −0.432576
\(663\) 0 0
\(664\) −1.48454e13 −2.96371
\(665\) −3.04260e12 −0.603321
\(666\) −2.21327e12 −0.435913
\(667\) −3.30972e12 −0.647478
\(668\) −1.62050e13 −3.14887
\(669\) 5.15957e12 0.995854
\(670\) −5.49437e12 −1.05337
\(671\) 2.51288e12 0.478542
\(672\) 2.88312e13 5.45382
\(673\) −1.36336e12 −0.256178 −0.128089 0.991763i \(-0.540884\pi\)
−0.128089 + 0.991763i \(0.540884\pi\)
\(674\) −1.12755e13 −2.10459
\(675\) −2.96273e11 −0.0549319
\(676\) −1.04991e13 −1.93370
\(677\) −2.24931e12 −0.411529 −0.205764 0.978602i \(-0.565968\pi\)
−0.205764 + 0.978602i \(0.565968\pi\)
\(678\) 6.17115e12 1.12159
\(679\) 2.98051e10 0.00538116
\(680\) 0 0
\(681\) −1.18238e13 −2.10666
\(682\) −7.27369e11 −0.128743
\(683\) −6.85651e12 −1.20562 −0.602810 0.797885i \(-0.705952\pi\)
−0.602810 + 0.797885i \(0.705952\pi\)
\(684\) 1.24978e13 2.18314
\(685\) −1.21594e13 −2.11011
\(686\) 1.22462e13 2.11127
\(687\) −1.88485e12 −0.322828
\(688\) 1.31453e13 2.23678
\(689\) −5.33954e12 −0.902645
\(690\) −8.87274e12 −1.49017
\(691\) 4.67266e12 0.779674 0.389837 0.920884i \(-0.372531\pi\)
0.389837 + 0.920884i \(0.372531\pi\)
\(692\) −2.00623e13 −3.32585
\(693\) −2.85332e12 −0.469949
\(694\) 7.01508e12 1.14793
\(695\) 8.98432e11 0.146068
\(696\) −5.04513e13 −8.14950
\(697\) 0 0
\(698\) 1.64720e13 2.62662
\(699\) −3.63414e12 −0.575777
\(700\) 6.06841e12 0.955287
\(701\) −1.94630e12 −0.304423 −0.152212 0.988348i \(-0.548640\pi\)
−0.152212 + 0.988348i \(0.548640\pi\)
\(702\) 8.90334e11 0.138368
\(703\) 9.12272e11 0.140872
\(704\) −2.26348e13 −3.47297
\(705\) −6.50180e12 −0.991249
\(706\) −1.54716e13 −2.34377
\(707\) 9.37194e12 1.41072
\(708\) −4.86896e13 −7.28261
\(709\) 1.10631e13 1.64425 0.822127 0.569304i \(-0.192787\pi\)
0.822127 + 0.569304i \(0.192787\pi\)
\(710\) 1.86118e13 2.74869
\(711\) −1.13630e13 −1.66755
\(712\) −2.05238e13 −2.99294
\(713\) −3.24087e11 −0.0469634
\(714\) 0 0
\(715\) 2.92953e12 0.419200
\(716\) 9.85338e12 1.40112
\(717\) 1.52844e13 2.15979
\(718\) −3.84693e12 −0.540199
\(719\) 1.25182e13 1.74688 0.873438 0.486935i \(-0.161885\pi\)
0.873438 + 0.486935i \(0.161885\pi\)
\(720\) −4.29235e13 −5.95249
\(721\) 3.02106e12 0.416343
\(722\) 7.51440e12 1.02915
\(723\) 1.78510e13 2.42963
\(724\) −6.30832e12 −0.853277
\(725\) −5.05702e12 −0.679788
\(726\) −1.36664e13 −1.82574
\(727\) −5.12484e11 −0.0680417 −0.0340208 0.999421i \(-0.510831\pi\)
−0.0340208 + 0.999421i \(0.510831\pi\)
\(728\) −1.19678e13 −1.57915
\(729\) −8.84455e12 −1.15985
\(730\) 2.78863e12 0.363445
\(731\) 0 0
\(732\) 2.60065e13 3.34797
\(733\) −8.38135e12 −1.07237 −0.536187 0.844099i \(-0.680136\pi\)
−0.536187 + 0.844099i \(0.680136\pi\)
\(734\) −3.86615e12 −0.491639
\(735\) −6.58537e12 −0.832314
\(736\) −1.80237e13 −2.26409
\(737\) 2.12380e12 0.265161
\(738\) 2.47564e13 3.07209
\(739\) 6.99883e12 0.863228 0.431614 0.902058i \(-0.357944\pi\)
0.431614 + 0.902058i \(0.357944\pi\)
\(740\) −5.82259e12 −0.713794
\(741\) −4.75025e12 −0.578808
\(742\) 1.83845e13 2.22656
\(743\) 9.88346e12 1.18976 0.594880 0.803814i \(-0.297199\pi\)
0.594880 + 0.803814i \(0.297199\pi\)
\(744\) −4.94019e12 −0.591106
\(745\) 1.24586e13 1.48172
\(746\) 2.12486e13 2.51192
\(747\) 7.24102e12 0.850858
\(748\) 0 0
\(749\) 9.80761e12 1.13866
\(750\) 1.62695e13 1.87758
\(751\) 1.11071e13 1.27415 0.637077 0.770800i \(-0.280143\pi\)
0.637077 + 0.770800i \(0.280143\pi\)
\(752\) −2.27406e13 −2.59311
\(753\) −1.15460e13 −1.30874
\(754\) 1.51969e13 1.71232
\(755\) 5.38999e12 0.603708
\(756\) −2.28132e12 −0.254003
\(757\) 6.98226e12 0.772796 0.386398 0.922332i \(-0.373719\pi\)
0.386398 + 0.922332i \(0.373719\pi\)
\(758\) −9.91758e12 −1.09118
\(759\) 3.42967e12 0.375115
\(760\) 2.89939e13 3.15243
\(761\) −1.11765e12 −0.120802 −0.0604009 0.998174i \(-0.519238\pi\)
−0.0604009 + 0.998174i \(0.519238\pi\)
\(762\) 2.23426e13 2.40069
\(763\) −1.02861e12 −0.109873
\(764\) 3.04802e13 3.23666
\(765\) 0 0
\(766\) 1.40688e12 0.147649
\(767\) 9.62494e12 1.00420
\(768\) −9.03506e13 −9.37143
\(769\) 1.47341e13 1.51934 0.759671 0.650307i \(-0.225360\pi\)
0.759671 + 0.650307i \(0.225360\pi\)
\(770\) −1.00866e13 −1.03404
\(771\) −1.76288e13 −1.79671
\(772\) 3.03442e13 3.07467
\(773\) 8.37182e12 0.843358 0.421679 0.906745i \(-0.361441\pi\)
0.421679 + 0.906745i \(0.361441\pi\)
\(774\) −1.05075e13 −1.05236
\(775\) −4.95182e11 −0.0493069
\(776\) −2.84022e11 −0.0281173
\(777\) −2.15552e12 −0.212157
\(778\) 4.36442e12 0.427089
\(779\) −1.02042e13 −0.992795
\(780\) 3.03185e13 2.93280
\(781\) −7.19420e12 −0.691915
\(782\) 0 0
\(783\) 1.90111e12 0.180750
\(784\) −2.30329e13 −2.17734
\(785\) −7.18162e12 −0.675008
\(786\) −2.32191e13 −2.16992
\(787\) 1.86469e13 1.73269 0.866345 0.499445i \(-0.166463\pi\)
0.866345 + 0.499445i \(0.166463\pi\)
\(788\) 4.68091e12 0.432476
\(789\) −2.07698e13 −1.90803
\(790\) −4.01687e13 −3.66916
\(791\) 3.12580e12 0.283901
\(792\) 2.71902e13 2.45555
\(793\) −5.14095e12 −0.461651
\(794\) −2.67896e12 −0.239207
\(795\) −3.05649e13 −2.71376
\(796\) 3.24500e13 2.86487
\(797\) 7.45382e12 0.654360 0.327180 0.944962i \(-0.393902\pi\)
0.327180 + 0.944962i \(0.393902\pi\)
\(798\) 1.63555e13 1.42775
\(799\) 0 0
\(800\) −2.75389e13 −2.37707
\(801\) 1.00107e13 0.859249
\(802\) 1.76833e13 1.50931
\(803\) −1.07792e12 −0.0914885
\(804\) 2.19798e13 1.85511
\(805\) −4.49421e12 −0.377200
\(806\) 1.48808e12 0.124199
\(807\) −1.27408e13 −1.05746
\(808\) −8.93082e13 −7.37123
\(809\) 1.42628e13 1.17068 0.585338 0.810790i \(-0.300962\pi\)
0.585338 + 0.810790i \(0.300962\pi\)
\(810\) −2.65631e13 −2.16819
\(811\) −1.18731e12 −0.0963766 −0.0481883 0.998838i \(-0.515345\pi\)
−0.0481883 + 0.998838i \(0.515345\pi\)
\(812\) −3.89395e13 −3.14331
\(813\) −1.49954e13 −1.20379
\(814\) 3.02430e12 0.241443
\(815\) 4.30802e12 0.342033
\(816\) 0 0
\(817\) 4.33102e12 0.340088
\(818\) 1.97811e13 1.54476
\(819\) 5.83744e12 0.453361
\(820\) 6.51283e13 5.03046
\(821\) −1.56983e13 −1.20589 −0.602947 0.797781i \(-0.706007\pi\)
−0.602947 + 0.797781i \(0.706007\pi\)
\(822\) 6.53629e13 4.99354
\(823\) −1.41366e13 −1.07410 −0.537052 0.843549i \(-0.680462\pi\)
−0.537052 + 0.843549i \(0.680462\pi\)
\(824\) −2.87886e13 −2.17545
\(825\) 5.24030e12 0.393834
\(826\) −3.31395e13 −2.47706
\(827\) 7.28652e12 0.541683 0.270842 0.962624i \(-0.412698\pi\)
0.270842 + 0.962624i \(0.412698\pi\)
\(828\) 1.84604e13 1.36491
\(829\) −2.46257e13 −1.81089 −0.905447 0.424460i \(-0.860464\pi\)
−0.905447 + 0.424460i \(0.860464\pi\)
\(830\) 2.55974e13 1.87216
\(831\) 8.39303e12 0.610540
\(832\) 4.63072e13 3.35038
\(833\) 0 0
\(834\) −4.82952e12 −0.345666
\(835\) 1.83371e13 1.30539
\(836\) −1.70775e13 −1.20919
\(837\) 1.86156e11 0.0131103
\(838\) −2.49621e12 −0.174857
\(839\) 5.37332e12 0.374381 0.187191 0.982324i \(-0.440062\pi\)
0.187191 + 0.982324i \(0.440062\pi\)
\(840\) −6.85069e13 −4.74764
\(841\) 1.79425e13 1.23680
\(842\) 2.98686e13 2.04790
\(843\) 1.03102e13 0.703144
\(844\) 2.69156e13 1.82584
\(845\) 1.18804e13 0.801635
\(846\) 1.81774e13 1.22001
\(847\) −6.92229e12 −0.462141
\(848\) −1.06903e14 −7.09921
\(849\) −1.38602e12 −0.0915558
\(850\) 0 0
\(851\) 1.34751e12 0.0880743
\(852\) −7.44548e13 −4.84077
\(853\) 1.32534e13 0.857150 0.428575 0.903506i \(-0.359016\pi\)
0.428575 + 0.903506i \(0.359016\pi\)
\(854\) 1.77007e13 1.13876
\(855\) −1.41421e13 −0.905038
\(856\) −9.34598e13 −5.94967
\(857\) −2.61157e13 −1.65382 −0.826909 0.562335i \(-0.809903\pi\)
−0.826909 + 0.562335i \(0.809903\pi\)
\(858\) −1.57477e13 −0.992029
\(859\) 1.81576e13 1.13786 0.568929 0.822387i \(-0.307358\pi\)
0.568929 + 0.822387i \(0.307358\pi\)
\(860\) −2.76428e13 −1.72321
\(861\) 2.41105e13 1.49517
\(862\) 5.21078e13 3.21455
\(863\) −9.67154e12 −0.593536 −0.296768 0.954950i \(-0.595909\pi\)
−0.296768 + 0.954950i \(0.595909\pi\)
\(864\) 1.03528e13 0.632043
\(865\) 2.27019e13 1.37876
\(866\) −3.81043e13 −2.30220
\(867\) 0 0
\(868\) −3.81295e12 −0.227993
\(869\) 1.55268e13 0.923622
\(870\) 8.69912e13 5.14800
\(871\) −4.34495e12 −0.255801
\(872\) 9.80196e12 0.574102
\(873\) 1.38535e11 0.00807225
\(874\) −1.02246e13 −0.592712
\(875\) 8.24081e12 0.475262
\(876\) −1.11557e13 −0.640071
\(877\) 2.58930e13 1.47803 0.739016 0.673688i \(-0.235291\pi\)
0.739016 + 0.673688i \(0.235291\pi\)
\(878\) 1.43669e12 0.0815903
\(879\) −5.95929e12 −0.336701
\(880\) 5.86524e13 3.29696
\(881\) −3.09147e12 −0.172891 −0.0864457 0.996257i \(-0.527551\pi\)
−0.0864457 + 0.996257i \(0.527551\pi\)
\(882\) 1.84110e13 1.02440
\(883\) −1.12784e13 −0.624345 −0.312173 0.950025i \(-0.601057\pi\)
−0.312173 + 0.950025i \(0.601057\pi\)
\(884\) 0 0
\(885\) 5.50957e13 3.01907
\(886\) −6.56989e13 −3.58184
\(887\) −2.10294e13 −1.14070 −0.570348 0.821403i \(-0.693191\pi\)
−0.570348 + 0.821403i \(0.693191\pi\)
\(888\) 2.05406e13 1.10855
\(889\) 1.13170e13 0.607676
\(890\) 3.53884e13 1.89063
\(891\) 1.02677e13 0.545789
\(892\) −3.79483e13 −2.00701
\(893\) −7.49240e12 −0.394266
\(894\) −6.69714e13 −3.50647
\(895\) −1.11498e13 −0.580848
\(896\) −8.65501e13 −4.48623
\(897\) −7.01656e12 −0.361875
\(898\) −1.33612e13 −0.685652
\(899\) 3.17746e12 0.162241
\(900\) 2.82062e13 1.43302
\(901\) 0 0
\(902\) −3.38282e13 −1.70157
\(903\) −1.02333e13 −0.512180
\(904\) −2.97868e13 −1.48342
\(905\) 7.13831e12 0.353734
\(906\) −2.89739e13 −1.42867
\(907\) −1.65206e13 −0.810576 −0.405288 0.914189i \(-0.632829\pi\)
−0.405288 + 0.914189i \(0.632829\pi\)
\(908\) 8.69632e13 4.24570
\(909\) 4.35611e13 2.11622
\(910\) 2.06356e13 0.997543
\(911\) 1.94745e13 0.936773 0.468387 0.883524i \(-0.344835\pi\)
0.468387 + 0.883524i \(0.344835\pi\)
\(912\) −9.51051e13 −4.55226
\(913\) −9.89442e12 −0.471272
\(914\) 1.41443e13 0.670382
\(915\) −2.94282e13 −1.38793
\(916\) 1.38629e13 0.650617
\(917\) −1.17609e13 −0.549260
\(918\) 0 0
\(919\) 7.57232e12 0.350194 0.175097 0.984551i \(-0.443976\pi\)
0.175097 + 0.984551i \(0.443976\pi\)
\(920\) 4.28267e13 1.97092
\(921\) −4.32694e12 −0.198159
\(922\) −3.30285e13 −1.50522
\(923\) 1.47182e13 0.667493
\(924\) 4.03507e13 1.82107
\(925\) 2.05890e12 0.0924693
\(926\) −7.80756e13 −3.48952
\(927\) 1.40420e13 0.624554
\(928\) 1.76710e14 7.82159
\(929\) −2.50574e12 −0.110374 −0.0551868 0.998476i \(-0.517575\pi\)
−0.0551868 + 0.998476i \(0.517575\pi\)
\(930\) 8.51817e12 0.373399
\(931\) −7.58870e12 −0.331050
\(932\) 2.67289e13 1.16040
\(933\) 3.13301e13 1.35361
\(934\) −2.19407e13 −0.943385
\(935\) 0 0
\(936\) −5.56267e13 −2.36888
\(937\) −3.81545e13 −1.61703 −0.808515 0.588476i \(-0.799728\pi\)
−0.808515 + 0.588476i \(0.799728\pi\)
\(938\) 1.49600e13 0.630986
\(939\) −4.91974e13 −2.06513
\(940\) 4.78203e13 1.99773
\(941\) 3.98075e13 1.65505 0.827526 0.561427i \(-0.189747\pi\)
0.827526 + 0.561427i \(0.189747\pi\)
\(942\) 3.86048e13 1.59740
\(943\) −1.50725e13 −0.620702
\(944\) 1.92702e14 7.89790
\(945\) 2.58148e12 0.105299
\(946\) 1.43579e13 0.582882
\(947\) 3.10230e13 1.25345 0.626727 0.779239i \(-0.284394\pi\)
0.626727 + 0.779239i \(0.284394\pi\)
\(948\) 1.60692e14 6.46183
\(949\) 2.20525e12 0.0882593
\(950\) −1.56224e13 −0.622289
\(951\) 2.35499e13 0.933635
\(952\) 0 0
\(953\) 2.23124e13 0.876252 0.438126 0.898914i \(-0.355642\pi\)
0.438126 + 0.898914i \(0.355642\pi\)
\(954\) 8.54517e13 3.34005
\(955\) −3.44904e13 −1.34179
\(956\) −1.12416e14 −4.35277
\(957\) −3.36256e13 −1.29589
\(958\) 1.63786e13 0.628251
\(959\) 3.31075e13 1.26399
\(960\) 2.65075e14 10.0728
\(961\) −2.61285e13 −0.988232
\(962\) −6.18723e12 −0.232921
\(963\) 4.55861e13 1.70810
\(964\) −1.31293e14 −4.89660
\(965\) −3.43366e13 −1.27463
\(966\) 2.41586e13 0.892638
\(967\) 3.20654e13 1.17928 0.589640 0.807666i \(-0.299270\pi\)
0.589640 + 0.807666i \(0.299270\pi\)
\(968\) 6.59647e13 2.41475
\(969\) 0 0
\(970\) 4.89728e11 0.0177616
\(971\) 1.32073e13 0.476791 0.238395 0.971168i \(-0.423379\pi\)
0.238395 + 0.971168i \(0.423379\pi\)
\(972\) 1.16048e14 4.17003
\(973\) −2.44625e12 −0.0874968
\(974\) 8.19534e13 2.91777
\(975\) −1.07208e13 −0.379933
\(976\) −1.02927e14 −3.63084
\(977\) 5.28646e13 1.85626 0.928131 0.372254i \(-0.121415\pi\)
0.928131 + 0.372254i \(0.121415\pi\)
\(978\) −2.31578e13 −0.809416
\(979\) −1.36791e13 −0.475920
\(980\) 4.84350e13 1.67742
\(981\) −4.78102e12 −0.164820
\(982\) −2.86961e13 −0.984739
\(983\) −1.32999e13 −0.454316 −0.227158 0.973858i \(-0.572943\pi\)
−0.227158 + 0.973858i \(0.572943\pi\)
\(984\) −2.29756e14 −7.81249
\(985\) −5.29677e12 −0.179287
\(986\) 0 0
\(987\) 1.77031e13 0.593774
\(988\) 3.49378e13 1.16651
\(989\) 6.39732e12 0.212625
\(990\) −4.68830e13 −1.55116
\(991\) −4.09247e13 −1.34789 −0.673945 0.738782i \(-0.735402\pi\)
−0.673945 + 0.738782i \(0.735402\pi\)
\(992\) 1.73034e13 0.567322
\(993\) −9.67632e12 −0.315819
\(994\) −5.06760e13 −1.64651
\(995\) −3.67194e13 −1.18766
\(996\) −1.02400e14 −3.29711
\(997\) −7.60358e12 −0.243719 −0.121860 0.992547i \(-0.538886\pi\)
−0.121860 + 0.992547i \(0.538886\pi\)
\(998\) −3.65241e12 −0.116544
\(999\) −7.74011e11 −0.0245868
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.g.1.1 36
17.16 even 2 289.10.a.h.1.1 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.1 36 1.1 even 1 trivial
289.10.a.h.1.1 yes 36 17.16 even 2