Properties

Label 9.6.a.a.1.1
Level 9
Weight 6
Character 9.1
Self dual Yes
Analytic conductor 1.443
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 9 = 3^{2} \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 9.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.44345437832\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0\)
Character \(\chi\) = 9.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+6.00000 q^{2}\) \(+4.00000 q^{4}\) \(-6.00000 q^{5}\) \(-40.0000 q^{7}\) \(-168.000 q^{8}\) \(+O(q^{10})\) \(q\)\(+6.00000 q^{2}\) \(+4.00000 q^{4}\) \(-6.00000 q^{5}\) \(-40.0000 q^{7}\) \(-168.000 q^{8}\) \(-36.0000 q^{10}\) \(+564.000 q^{11}\) \(+638.000 q^{13}\) \(-240.000 q^{14}\) \(-1136.00 q^{16}\) \(-882.000 q^{17}\) \(-556.000 q^{19}\) \(-24.0000 q^{20}\) \(+3384.00 q^{22}\) \(+840.000 q^{23}\) \(-3089.00 q^{25}\) \(+3828.00 q^{26}\) \(-160.000 q^{28}\) \(-4638.00 q^{29}\) \(+4400.00 q^{31}\) \(-1440.00 q^{32}\) \(-5292.00 q^{34}\) \(+240.000 q^{35}\) \(-2410.00 q^{37}\) \(-3336.00 q^{38}\) \(+1008.00 q^{40}\) \(+6870.00 q^{41}\) \(+9644.00 q^{43}\) \(+2256.00 q^{44}\) \(+5040.00 q^{46}\) \(+18672.0 q^{47}\) \(-15207.0 q^{49}\) \(-18534.0 q^{50}\) \(+2552.00 q^{52}\) \(-33750.0 q^{53}\) \(-3384.00 q^{55}\) \(+6720.00 q^{56}\) \(-27828.0 q^{58}\) \(+18084.0 q^{59}\) \(+39758.0 q^{61}\) \(+26400.0 q^{62}\) \(+27712.0 q^{64}\) \(-3828.00 q^{65}\) \(-23068.0 q^{67}\) \(-3528.00 q^{68}\) \(+1440.00 q^{70}\) \(+4248.00 q^{71}\) \(-41110.0 q^{73}\) \(-14460.0 q^{74}\) \(-2224.00 q^{76}\) \(-22560.0 q^{77}\) \(+21920.0 q^{79}\) \(+6816.00 q^{80}\) \(+41220.0 q^{82}\) \(-82452.0 q^{83}\) \(+5292.00 q^{85}\) \(+57864.0 q^{86}\) \(-94752.0 q^{88}\) \(+94086.0 q^{89}\) \(-25520.0 q^{91}\) \(+3360.00 q^{92}\) \(+112032. q^{94}\) \(+3336.00 q^{95}\) \(+49442.0 q^{97}\) \(-91242.0 q^{98}\) \(+O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.00000 1.06066 0.530330 0.847791i \(-0.322068\pi\)
0.530330 + 0.847791i \(0.322068\pi\)
\(3\) 0 0
\(4\) 4.00000 0.125000
\(5\) −6.00000 −0.107331 −0.0536656 0.998559i \(-0.517091\pi\)
−0.0536656 + 0.998559i \(0.517091\pi\)
\(6\) 0 0
\(7\) −40.0000 −0.308542 −0.154271 0.988029i \(-0.549303\pi\)
−0.154271 + 0.988029i \(0.549303\pi\)
\(8\) −168.000 −0.928078
\(9\) 0 0
\(10\) −36.0000 −0.113842
\(11\) 564.000 1.40539 0.702696 0.711490i \(-0.251979\pi\)
0.702696 + 0.711490i \(0.251979\pi\)
\(12\) 0 0
\(13\) 638.000 1.04704 0.523519 0.852014i \(-0.324619\pi\)
0.523519 + 0.852014i \(0.324619\pi\)
\(14\) −240.000 −0.327259
\(15\) 0 0
\(16\) −1136.00 −1.10938
\(17\) −882.000 −0.740195 −0.370098 0.928993i \(-0.620676\pi\)
−0.370098 + 0.928993i \(0.620676\pi\)
\(18\) 0 0
\(19\) −556.000 −0.353338 −0.176669 0.984270i \(-0.556532\pi\)
−0.176669 + 0.984270i \(0.556532\pi\)
\(20\) −24.0000 −0.0134164
\(21\) 0 0
\(22\) 3384.00 1.49064
\(23\) 840.000 0.331100 0.165550 0.986201i \(-0.447060\pi\)
0.165550 + 0.986201i \(0.447060\pi\)
\(24\) 0 0
\(25\) −3089.00 −0.988480
\(26\) 3828.00 1.11055
\(27\) 0 0
\(28\) −160.000 −0.0385678
\(29\) −4638.00 −1.02408 −0.512042 0.858960i \(-0.671111\pi\)
−0.512042 + 0.858960i \(0.671111\pi\)
\(30\) 0 0
\(31\) 4400.00 0.822334 0.411167 0.911560i \(-0.365121\pi\)
0.411167 + 0.911560i \(0.365121\pi\)
\(32\) −1440.00 −0.248592
\(33\) 0 0
\(34\) −5292.00 −0.785096
\(35\) 240.000 0.0331162
\(36\) 0 0
\(37\) −2410.00 −0.289409 −0.144705 0.989475i \(-0.546223\pi\)
−0.144705 + 0.989475i \(0.546223\pi\)
\(38\) −3336.00 −0.374772
\(39\) 0 0
\(40\) 1008.00 0.0996117
\(41\) 6870.00 0.638259 0.319130 0.947711i \(-0.396609\pi\)
0.319130 + 0.947711i \(0.396609\pi\)
\(42\) 0 0
\(43\) 9644.00 0.795401 0.397700 0.917515i \(-0.369808\pi\)
0.397700 + 0.917515i \(0.369808\pi\)
\(44\) 2256.00 0.175674
\(45\) 0 0
\(46\) 5040.00 0.351185
\(47\) 18672.0 1.23295 0.616476 0.787374i \(-0.288560\pi\)
0.616476 + 0.787374i \(0.288560\pi\)
\(48\) 0 0
\(49\) −15207.0 −0.904802
\(50\) −18534.0 −1.04844
\(51\) 0 0
\(52\) 2552.00 0.130880
\(53\) −33750.0 −1.65038 −0.825190 0.564855i \(-0.808932\pi\)
−0.825190 + 0.564855i \(0.808932\pi\)
\(54\) 0 0
\(55\) −3384.00 −0.150842
\(56\) 6720.00 0.286351
\(57\) 0 0
\(58\) −27828.0 −1.08621
\(59\) 18084.0 0.676339 0.338170 0.941085i \(-0.390192\pi\)
0.338170 + 0.941085i \(0.390192\pi\)
\(60\) 0 0
\(61\) 39758.0 1.36804 0.684022 0.729462i \(-0.260229\pi\)
0.684022 + 0.729462i \(0.260229\pi\)
\(62\) 26400.0 0.872217
\(63\) 0 0
\(64\) 27712.0 0.845703
\(65\) −3828.00 −0.112380
\(66\) 0 0
\(67\) −23068.0 −0.627802 −0.313901 0.949456i \(-0.601636\pi\)
−0.313901 + 0.949456i \(0.601636\pi\)
\(68\) −3528.00 −0.0925244
\(69\) 0 0
\(70\) 1440.00 0.0351251
\(71\) 4248.00 0.100009 0.0500044 0.998749i \(-0.484076\pi\)
0.0500044 + 0.998749i \(0.484076\pi\)
\(72\) 0 0
\(73\) −41110.0 −0.902901 −0.451451 0.892296i \(-0.649093\pi\)
−0.451451 + 0.892296i \(0.649093\pi\)
\(74\) −14460.0 −0.306965
\(75\) 0 0
\(76\) −2224.00 −0.0441673
\(77\) −22560.0 −0.433623
\(78\) 0 0
\(79\) 21920.0 0.395160 0.197580 0.980287i \(-0.436692\pi\)
0.197580 + 0.980287i \(0.436692\pi\)
\(80\) 6816.00 0.119071
\(81\) 0 0
\(82\) 41220.0 0.676976
\(83\) −82452.0 −1.31373 −0.656865 0.754008i \(-0.728118\pi\)
−0.656865 + 0.754008i \(0.728118\pi\)
\(84\) 0 0
\(85\) 5292.00 0.0794461
\(86\) 57864.0 0.843650
\(87\) 0 0
\(88\) −94752.0 −1.30431
\(89\) 94086.0 1.25907 0.629535 0.776972i \(-0.283245\pi\)
0.629535 + 0.776972i \(0.283245\pi\)
\(90\) 0 0
\(91\) −25520.0 −0.323056
\(92\) 3360.00 0.0413875
\(93\) 0 0
\(94\) 112032. 1.30774
\(95\) 3336.00 0.0379243
\(96\) 0 0
\(97\) 49442.0 0.533540 0.266770 0.963760i \(-0.414044\pi\)
0.266770 + 0.963760i \(0.414044\pi\)
\(98\) −91242.0 −0.959687
\(99\) 0 0
\(100\) −12356.0 −0.123560
\(101\) 143034. 1.39520 0.697599 0.716488i \(-0.254252\pi\)
0.697599 + 0.716488i \(0.254252\pi\)
\(102\) 0 0
\(103\) 53144.0 0.493584 0.246792 0.969068i \(-0.420624\pi\)
0.246792 + 0.969068i \(0.420624\pi\)
\(104\) −107184. −0.971732
\(105\) 0 0
\(106\) −202500. −1.75049
\(107\) −90828.0 −0.766938 −0.383469 0.923554i \(-0.625271\pi\)
−0.383469 + 0.923554i \(0.625271\pi\)
\(108\) 0 0
\(109\) −61666.0 −0.497141 −0.248570 0.968614i \(-0.579961\pi\)
−0.248570 + 0.968614i \(0.579961\pi\)
\(110\) −20304.0 −0.159993
\(111\) 0 0
\(112\) 45440.0 0.342289
\(113\) −10482.0 −0.0772232 −0.0386116 0.999254i \(-0.512294\pi\)
−0.0386116 + 0.999254i \(0.512294\pi\)
\(114\) 0 0
\(115\) −5040.00 −0.0355374
\(116\) −18552.0 −0.128011
\(117\) 0 0
\(118\) 108504. 0.717366
\(119\) 35280.0 0.228382
\(120\) 0 0
\(121\) 157045. 0.975126
\(122\) 238548. 1.45103
\(123\) 0 0
\(124\) 17600.0 0.102792
\(125\) 37284.0 0.213426
\(126\) 0 0
\(127\) −171088. −0.941261 −0.470631 0.882330i \(-0.655974\pi\)
−0.470631 + 0.882330i \(0.655974\pi\)
\(128\) 212352. 1.14560
\(129\) 0 0
\(130\) −22968.0 −0.119197
\(131\) −258468. −1.31592 −0.657959 0.753054i \(-0.728580\pi\)
−0.657959 + 0.753054i \(0.728580\pi\)
\(132\) 0 0
\(133\) 22240.0 0.109020
\(134\) −138408. −0.665885
\(135\) 0 0
\(136\) 148176. 0.686959
\(137\) −300234. −1.36665 −0.683327 0.730113i \(-0.739468\pi\)
−0.683327 + 0.730113i \(0.739468\pi\)
\(138\) 0 0
\(139\) −350164. −1.53721 −0.768607 0.639721i \(-0.779050\pi\)
−0.768607 + 0.639721i \(0.779050\pi\)
\(140\) 960.000 0.00413953
\(141\) 0 0
\(142\) 25488.0 0.106075
\(143\) 359832. 1.47150
\(144\) 0 0
\(145\) 27828.0 0.109916
\(146\) −246660. −0.957672
\(147\) 0 0
\(148\) −9640.00 −0.0361762
\(149\) 105258. 0.388409 0.194205 0.980961i \(-0.437787\pi\)
0.194205 + 0.980961i \(0.437787\pi\)
\(150\) 0 0
\(151\) 396392. 1.41476 0.707380 0.706834i \(-0.249877\pi\)
0.707380 + 0.706834i \(0.249877\pi\)
\(152\) 93408.0 0.327925
\(153\) 0 0
\(154\) −135360. −0.459927
\(155\) −26400.0 −0.0882622
\(156\) 0 0
\(157\) −137746. −0.445995 −0.222997 0.974819i \(-0.571584\pi\)
−0.222997 + 0.974819i \(0.571584\pi\)
\(158\) 131520. 0.419130
\(159\) 0 0
\(160\) 8640.00 0.0266817
\(161\) −33600.0 −0.102159
\(162\) 0 0
\(163\) 352676. 1.03970 0.519849 0.854258i \(-0.325988\pi\)
0.519849 + 0.854258i \(0.325988\pi\)
\(164\) 27480.0 0.0797824
\(165\) 0 0
\(166\) −494712. −1.39342
\(167\) 217560. 0.603654 0.301827 0.953363i \(-0.402404\pi\)
0.301827 + 0.953363i \(0.402404\pi\)
\(168\) 0 0
\(169\) 35751.0 0.0962878
\(170\) 31752.0 0.0842653
\(171\) 0 0
\(172\) 38576.0 0.0994251
\(173\) 163698. 0.415842 0.207921 0.978146i \(-0.433330\pi\)
0.207921 + 0.978146i \(0.433330\pi\)
\(174\) 0 0
\(175\) 123560. 0.304988
\(176\) −640704. −1.55911
\(177\) 0 0
\(178\) 564516. 1.33545
\(179\) −358740. −0.836849 −0.418425 0.908252i \(-0.637418\pi\)
−0.418425 + 0.908252i \(0.637418\pi\)
\(180\) 0 0
\(181\) −507130. −1.15060 −0.575298 0.817944i \(-0.695114\pi\)
−0.575298 + 0.817944i \(0.695114\pi\)
\(182\) −153120. −0.342652
\(183\) 0 0
\(184\) −141120. −0.307287
\(185\) 14460.0 0.0310627
\(186\) 0 0
\(187\) −497448. −1.04026
\(188\) 74688.0 0.154119
\(189\) 0 0
\(190\) 20016.0 0.0402247
\(191\) 648384. 1.28602 0.643012 0.765856i \(-0.277685\pi\)
0.643012 + 0.765856i \(0.277685\pi\)
\(192\) 0 0
\(193\) −27838.0 −0.0537954 −0.0268977 0.999638i \(-0.508563\pi\)
−0.0268977 + 0.999638i \(0.508563\pi\)
\(194\) 296652. 0.565904
\(195\) 0 0
\(196\) −60828.0 −0.113100
\(197\) −611046. −1.12178 −0.560891 0.827890i \(-0.689541\pi\)
−0.560891 + 0.827890i \(0.689541\pi\)
\(198\) 0 0
\(199\) 879032. 1.57352 0.786760 0.617260i \(-0.211757\pi\)
0.786760 + 0.617260i \(0.211757\pi\)
\(200\) 518952. 0.917386
\(201\) 0 0
\(202\) 858204. 1.47983
\(203\) 185520. 0.315973
\(204\) 0 0
\(205\) −41220.0 −0.0685052
\(206\) 318864. 0.523525
\(207\) 0 0
\(208\) −724768. −1.16156
\(209\) −313584. −0.496579
\(210\) 0 0
\(211\) 48500.0 0.0749956 0.0374978 0.999297i \(-0.488061\pi\)
0.0374978 + 0.999297i \(0.488061\pi\)
\(212\) −135000. −0.206298
\(213\) 0 0
\(214\) −544968. −0.813461
\(215\) −57864.0 −0.0853714
\(216\) 0 0
\(217\) −176000. −0.253725
\(218\) −369996. −0.527298
\(219\) 0 0
\(220\) −13536.0 −0.0188553
\(221\) −562716. −0.775012
\(222\) 0 0
\(223\) −999472. −1.34589 −0.672943 0.739694i \(-0.734970\pi\)
−0.672943 + 0.739694i \(0.734970\pi\)
\(224\) 57600.0 0.0767012
\(225\) 0 0
\(226\) −62892.0 −0.0819076
\(227\) −606180. −0.780795 −0.390397 0.920646i \(-0.627662\pi\)
−0.390397 + 0.920646i \(0.627662\pi\)
\(228\) 0 0
\(229\) 1.35993e6 1.71367 0.856834 0.515593i \(-0.172428\pi\)
0.856834 + 0.515593i \(0.172428\pi\)
\(230\) −30240.0 −0.0376931
\(231\) 0 0
\(232\) 779184. 0.950430
\(233\) 392886. 0.474107 0.237054 0.971497i \(-0.423818\pi\)
0.237054 + 0.971497i \(0.423818\pi\)
\(234\) 0 0
\(235\) −112032. −0.132334
\(236\) 72336.0 0.0845424
\(237\) 0 0
\(238\) 211680. 0.242235
\(239\) 1.32514e6 1.50060 0.750301 0.661096i \(-0.229908\pi\)
0.750301 + 0.661096i \(0.229908\pi\)
\(240\) 0 0
\(241\) −990094. −1.09808 −0.549040 0.835796i \(-0.685006\pi\)
−0.549040 + 0.835796i \(0.685006\pi\)
\(242\) 942270. 1.03428
\(243\) 0 0
\(244\) 159032. 0.171005
\(245\) 91242.0 0.0971135
\(246\) 0 0
\(247\) −354728. −0.369959
\(248\) −739200. −0.763190
\(249\) 0 0
\(250\) 223704. 0.226373
\(251\) −147132. −0.147409 −0.0737043 0.997280i \(-0.523482\pi\)
−0.0737043 + 0.997280i \(0.523482\pi\)
\(252\) 0 0
\(253\) 473760. 0.465326
\(254\) −1.02653e6 −0.998358
\(255\) 0 0
\(256\) 387328. 0.369385
\(257\) 483582. 0.456707 0.228353 0.973578i \(-0.426666\pi\)
0.228353 + 0.973578i \(0.426666\pi\)
\(258\) 0 0
\(259\) 96400.0 0.0892951
\(260\) −15312.0 −0.0140475
\(261\) 0 0
\(262\) −1.55081e6 −1.39574
\(263\) −813576. −0.725285 −0.362643 0.931928i \(-0.618125\pi\)
−0.362643 + 0.931928i \(0.618125\pi\)
\(264\) 0 0
\(265\) 202500. 0.177137
\(266\) 133440. 0.115633
\(267\) 0 0
\(268\) −92272.0 −0.0784753
\(269\) 461106. 0.388526 0.194263 0.980949i \(-0.437768\pi\)
0.194263 + 0.980949i \(0.437768\pi\)
\(270\) 0 0
\(271\) 1.67514e6 1.38556 0.692782 0.721147i \(-0.256385\pi\)
0.692782 + 0.721147i \(0.256385\pi\)
\(272\) 1.00195e6 0.821154
\(273\) 0 0
\(274\) −1.80140e6 −1.44956
\(275\) −1.74220e6 −1.38920
\(276\) 0 0
\(277\) 401126. 0.314110 0.157055 0.987590i \(-0.449800\pi\)
0.157055 + 0.987590i \(0.449800\pi\)
\(278\) −2.10098e6 −1.63046
\(279\) 0 0
\(280\) −40320.0 −0.0307344
\(281\) 2.30977e6 1.74503 0.872514 0.488590i \(-0.162489\pi\)
0.872514 + 0.488590i \(0.162489\pi\)
\(282\) 0 0
\(283\) −1.12877e6 −0.837800 −0.418900 0.908032i \(-0.637584\pi\)
−0.418900 + 0.908032i \(0.637584\pi\)
\(284\) 16992.0 0.0125011
\(285\) 0 0
\(286\) 2.15899e6 1.56076
\(287\) −274800. −0.196930
\(288\) 0 0
\(289\) −641933. −0.452111
\(290\) 166968. 0.116584
\(291\) 0 0
\(292\) −164440. −0.112863
\(293\) 938874. 0.638908 0.319454 0.947602i \(-0.396501\pi\)
0.319454 + 0.947602i \(0.396501\pi\)
\(294\) 0 0
\(295\) −108504. −0.0725923
\(296\) 404880. 0.268594
\(297\) 0 0
\(298\) 631548. 0.411970
\(299\) 535920. 0.346675
\(300\) 0 0
\(301\) −385760. −0.245415
\(302\) 2.37835e6 1.50058
\(303\) 0 0
\(304\) 631616. 0.391985
\(305\) −238548. −0.146834
\(306\) 0 0
\(307\) 692948. 0.419619 0.209809 0.977742i \(-0.432716\pi\)
0.209809 + 0.977742i \(0.432716\pi\)
\(308\) −90240.0 −0.0542029
\(309\) 0 0
\(310\) −158400. −0.0936162
\(311\) −2.94310e6 −1.72545 −0.862727 0.505670i \(-0.831245\pi\)
−0.862727 + 0.505670i \(0.831245\pi\)
\(312\) 0 0
\(313\) 885146. 0.510686 0.255343 0.966851i \(-0.417812\pi\)
0.255343 + 0.966851i \(0.417812\pi\)
\(314\) −826476. −0.473049
\(315\) 0 0
\(316\) 87680.0 0.0493950
\(317\) −2.50880e6 −1.40222 −0.701112 0.713051i \(-0.747313\pi\)
−0.701112 + 0.713051i \(0.747313\pi\)
\(318\) 0 0
\(319\) −2.61583e6 −1.43924
\(320\) −166272. −0.0907704
\(321\) 0 0
\(322\) −201600. −0.108355
\(323\) 490392. 0.261539
\(324\) 0 0
\(325\) −1.97078e6 −1.03498
\(326\) 2.11606e6 1.10277
\(327\) 0 0
\(328\) −1.15416e6 −0.592354
\(329\) −746880. −0.380418
\(330\) 0 0
\(331\) −216148. −0.108438 −0.0542190 0.998529i \(-0.517267\pi\)
−0.0542190 + 0.998529i \(0.517267\pi\)
\(332\) −329808. −0.164216
\(333\) 0 0
\(334\) 1.30536e6 0.640271
\(335\) 138408. 0.0673828
\(336\) 0 0
\(337\) 3.25263e6 1.56012 0.780062 0.625702i \(-0.215187\pi\)
0.780062 + 0.625702i \(0.215187\pi\)
\(338\) 214506. 0.102129
\(339\) 0 0
\(340\) 21168.0 0.00993076
\(341\) 2.48160e6 1.15570
\(342\) 0 0
\(343\) 1.28056e6 0.587712
\(344\) −1.62019e6 −0.738194
\(345\) 0 0
\(346\) 982188. 0.441067
\(347\) 2.93207e6 1.30723 0.653613 0.756829i \(-0.273253\pi\)
0.653613 + 0.756829i \(0.273253\pi\)
\(348\) 0 0
\(349\) 905198. 0.397814 0.198907 0.980018i \(-0.436261\pi\)
0.198907 + 0.980018i \(0.436261\pi\)
\(350\) 741360. 0.323489
\(351\) 0 0
\(352\) −812160. −0.349369
\(353\) −1.91786e6 −0.819181 −0.409590 0.912270i \(-0.634328\pi\)
−0.409590 + 0.912270i \(0.634328\pi\)
\(354\) 0 0
\(355\) −25488.0 −0.0107341
\(356\) 376344. 0.157384
\(357\) 0 0
\(358\) −2.15244e6 −0.887613
\(359\) 2.43698e6 0.997968 0.498984 0.866611i \(-0.333707\pi\)
0.498984 + 0.866611i \(0.333707\pi\)
\(360\) 0 0
\(361\) −2.16696e6 −0.875152
\(362\) −3.04278e6 −1.22039
\(363\) 0 0
\(364\) −102080. −0.0403819
\(365\) 246660. 0.0969095
\(366\) 0 0
\(367\) −984064. −0.381380 −0.190690 0.981650i \(-0.561073\pi\)
−0.190690 + 0.981650i \(0.561073\pi\)
\(368\) −954240. −0.367314
\(369\) 0 0
\(370\) 86760.0 0.0329470
\(371\) 1.35000e6 0.509212
\(372\) 0 0
\(373\) 1.70365e6 0.634029 0.317015 0.948421i \(-0.397320\pi\)
0.317015 + 0.948421i \(0.397320\pi\)
\(374\) −2.98469e6 −1.10337
\(375\) 0 0
\(376\) −3.13690e6 −1.14428
\(377\) −2.95904e6 −1.07225
\(378\) 0 0
\(379\) 2.75654e6 0.985749 0.492874 0.870100i \(-0.335946\pi\)
0.492874 + 0.870100i \(0.335946\pi\)
\(380\) 13344.0 0.00474053
\(381\) 0 0
\(382\) 3.89030e6 1.36403
\(383\) −456576. −0.159044 −0.0795218 0.996833i \(-0.525339\pi\)
−0.0795218 + 0.996833i \(0.525339\pi\)
\(384\) 0 0
\(385\) 135360. 0.0465413
\(386\) −167028. −0.0570586
\(387\) 0 0
\(388\) 197768. 0.0666925
\(389\) 2.00639e6 0.672268 0.336134 0.941814i \(-0.390881\pi\)
0.336134 + 0.941814i \(0.390881\pi\)
\(390\) 0 0
\(391\) −740880. −0.245079
\(392\) 2.55478e6 0.839726
\(393\) 0 0
\(394\) −3.66628e6 −1.18983
\(395\) −131520. −0.0424130
\(396\) 0 0
\(397\) −5.77040e6 −1.83751 −0.918755 0.394828i \(-0.870804\pi\)
−0.918755 + 0.394828i \(0.870804\pi\)
\(398\) 5.27419e6 1.66897
\(399\) 0 0
\(400\) 3.50910e6 1.09659
\(401\) −3.00626e6 −0.933610 −0.466805 0.884360i \(-0.654595\pi\)
−0.466805 + 0.884360i \(0.654595\pi\)
\(402\) 0 0
\(403\) 2.80720e6 0.861015
\(404\) 572136. 0.174400
\(405\) 0 0
\(406\) 1.11312e6 0.335140
\(407\) −1.35924e6 −0.406734
\(408\) 0 0
\(409\) 1.53363e6 0.453327 0.226663 0.973973i \(-0.427218\pi\)
0.226663 + 0.973973i \(0.427218\pi\)
\(410\) −247320. −0.0726607
\(411\) 0 0
\(412\) 212576. 0.0616980
\(413\) −723360. −0.208679
\(414\) 0 0
\(415\) 494712. 0.141004
\(416\) −918720. −0.260285
\(417\) 0 0
\(418\) −1.88150e6 −0.526701
\(419\) 3.87376e6 1.07795 0.538973 0.842323i \(-0.318812\pi\)
0.538973 + 0.842323i \(0.318812\pi\)
\(420\) 0 0
\(421\) −1.33307e6 −0.366561 −0.183281 0.983061i \(-0.558672\pi\)
−0.183281 + 0.983061i \(0.558672\pi\)
\(422\) 291000. 0.0795448
\(423\) 0 0
\(424\) 5.67000e6 1.53168
\(425\) 2.72450e6 0.731668
\(426\) 0 0
\(427\) −1.59032e6 −0.422099
\(428\) −363312. −0.0958673
\(429\) 0 0
\(430\) −347184. −0.0905500
\(431\) −6.45192e6 −1.67300 −0.836500 0.547967i \(-0.815402\pi\)
−0.836500 + 0.547967i \(0.815402\pi\)
\(432\) 0 0
\(433\) −4.16577e6 −1.06777 −0.533883 0.845558i \(-0.679268\pi\)
−0.533883 + 0.845558i \(0.679268\pi\)
\(434\) −1.05600e6 −0.269116
\(435\) 0 0
\(436\) −246664. −0.0621426
\(437\) −467040. −0.116990
\(438\) 0 0
\(439\) 792680. 0.196307 0.0981537 0.995171i \(-0.468706\pi\)
0.0981537 + 0.995171i \(0.468706\pi\)
\(440\) 568512. 0.139994
\(441\) 0 0
\(442\) −3.37630e6 −0.822025
\(443\) 1.39981e6 0.338891 0.169446 0.985540i \(-0.445802\pi\)
0.169446 + 0.985540i \(0.445802\pi\)
\(444\) 0 0
\(445\) −564516. −0.135138
\(446\) −5.99683e6 −1.42753
\(447\) 0 0
\(448\) −1.10848e6 −0.260935
\(449\) −2.99248e6 −0.700512 −0.350256 0.936654i \(-0.613905\pi\)
−0.350256 + 0.936654i \(0.613905\pi\)
\(450\) 0 0
\(451\) 3.87468e6 0.897004
\(452\) −41928.0 −0.00965291
\(453\) 0 0
\(454\) −3.63708e6 −0.828158
\(455\) 153120. 0.0346740
\(456\) 0 0
\(457\) 6.29969e6 1.41101 0.705503 0.708707i \(-0.250721\pi\)
0.705503 + 0.708707i \(0.250721\pi\)
\(458\) 8.15956e6 1.81762
\(459\) 0 0
\(460\) −20160.0 −0.00444218
\(461\) −3.40318e6 −0.745818 −0.372909 0.927868i \(-0.621640\pi\)
−0.372909 + 0.927868i \(0.621640\pi\)
\(462\) 0 0
\(463\) −2.23034e6 −0.483524 −0.241762 0.970336i \(-0.577725\pi\)
−0.241762 + 0.970336i \(0.577725\pi\)
\(464\) 5.26877e6 1.13609
\(465\) 0 0
\(466\) 2.35732e6 0.502867
\(467\) 6.51409e6 1.38217 0.691085 0.722773i \(-0.257133\pi\)
0.691085 + 0.722773i \(0.257133\pi\)
\(468\) 0 0
\(469\) 922720. 0.193704
\(470\) −672192. −0.140362
\(471\) 0 0
\(472\) −3.03811e6 −0.627695
\(473\) 5.43922e6 1.11785
\(474\) 0 0
\(475\) 1.71748e6 0.349268
\(476\) 141120. 0.0285477
\(477\) 0 0
\(478\) 7.95082e6 1.59163
\(479\) −2.39232e6 −0.476410 −0.238205 0.971215i \(-0.576559\pi\)
−0.238205 + 0.971215i \(0.576559\pi\)
\(480\) 0 0
\(481\) −1.53758e6 −0.303023
\(482\) −5.94056e6 −1.16469
\(483\) 0 0
\(484\) 628180. 0.121891
\(485\) −296652. −0.0572655
\(486\) 0 0
\(487\) −6.13089e6 −1.17139 −0.585694 0.810532i \(-0.699178\pi\)
−0.585694 + 0.810532i \(0.699178\pi\)
\(488\) −6.67934e6 −1.26965
\(489\) 0 0
\(490\) 547452. 0.103004
\(491\) 1.23589e6 0.231354 0.115677 0.993287i \(-0.463096\pi\)
0.115677 + 0.993287i \(0.463096\pi\)
\(492\) 0 0
\(493\) 4.09072e6 0.758022
\(494\) −2.12837e6 −0.392400
\(495\) 0 0
\(496\) −4.99840e6 −0.912277
\(497\) −169920. −0.0308570
\(498\) 0 0
\(499\) −9.85496e6 −1.77175 −0.885877 0.463921i \(-0.846442\pi\)
−0.885877 + 0.463921i \(0.846442\pi\)
\(500\) 149136. 0.0266783
\(501\) 0 0
\(502\) −882792. −0.156350
\(503\) −1.16777e6 −0.205796 −0.102898 0.994692i \(-0.532812\pi\)
−0.102898 + 0.994692i \(0.532812\pi\)
\(504\) 0 0
\(505\) −858204. −0.149748
\(506\) 2.84256e6 0.493552
\(507\) 0 0
\(508\) −684352. −0.117658
\(509\) −1.04941e6 −0.179535 −0.0897675 0.995963i \(-0.528612\pi\)
−0.0897675 + 0.995963i \(0.528612\pi\)
\(510\) 0 0
\(511\) 1.64440e6 0.278583
\(512\) −4.47130e6 −0.753804
\(513\) 0 0
\(514\) 2.90149e6 0.484411
\(515\) −318864. −0.0529770
\(516\) 0 0
\(517\) 1.05310e7 1.73278
\(518\) 578400. 0.0947118
\(519\) 0 0
\(520\) 643104. 0.104297
\(521\) 9.61407e6 1.55172 0.775859 0.630906i \(-0.217317\pi\)
0.775859 + 0.630906i \(0.217317\pi\)
\(522\) 0 0
\(523\) 6.96148e6 1.11288 0.556439 0.830888i \(-0.312167\pi\)
0.556439 + 0.830888i \(0.312167\pi\)
\(524\) −1.03387e6 −0.164490
\(525\) 0 0
\(526\) −4.88146e6 −0.769281
\(527\) −3.88080e6 −0.608688
\(528\) 0 0
\(529\) −5.73074e6 −0.890373
\(530\) 1.21500e6 0.187883
\(531\) 0 0
\(532\) 88960.0 0.0136275
\(533\) 4.38306e6 0.668281
\(534\) 0 0
\(535\) 544968. 0.0823164
\(536\) 3.87542e6 0.582649
\(537\) 0 0
\(538\) 2.76664e6 0.412094
\(539\) −8.57675e6 −1.27160
\(540\) 0 0
\(541\) −712690. −0.104691 −0.0523453 0.998629i \(-0.516670\pi\)
−0.0523453 + 0.998629i \(0.516670\pi\)
\(542\) 1.00508e7 1.46961
\(543\) 0 0
\(544\) 1.27008e6 0.184007
\(545\) 369996. 0.0533588
\(546\) 0 0
\(547\) −3.62614e6 −0.518175 −0.259087 0.965854i \(-0.583422\pi\)
−0.259087 + 0.965854i \(0.583422\pi\)
\(548\) −1.20094e6 −0.170832
\(549\) 0 0
\(550\) −1.04532e7 −1.47347
\(551\) 2.57873e6 0.361848
\(552\) 0 0
\(553\) −876800. −0.121924
\(554\) 2.40676e6 0.333164
\(555\) 0 0
\(556\) −1.40066e6 −0.192152
\(557\) −4.84846e6 −0.662165 −0.331082 0.943602i \(-0.607414\pi\)
−0.331082 + 0.943602i \(0.607414\pi\)
\(558\) 0 0
\(559\) 6.15287e6 0.832815
\(560\) −272640. −0.0367383
\(561\) 0 0
\(562\) 1.38586e7 1.85088
\(563\) −8.50405e6 −1.13072 −0.565360 0.824844i \(-0.691263\pi\)
−0.565360 + 0.824844i \(0.691263\pi\)
\(564\) 0 0
\(565\) 62892.0 0.00828847
\(566\) −6.77263e6 −0.888621
\(567\) 0 0
\(568\) −713664. −0.0928160
\(569\) −362874. −0.0469867 −0.0234934 0.999724i \(-0.507479\pi\)
−0.0234934 + 0.999724i \(0.507479\pi\)
\(570\) 0 0
\(571\) 4.11024e6 0.527566 0.263783 0.964582i \(-0.415030\pi\)
0.263783 + 0.964582i \(0.415030\pi\)
\(572\) 1.43933e6 0.183937
\(573\) 0 0
\(574\) −1.64880e6 −0.208876
\(575\) −2.59476e6 −0.327286
\(576\) 0 0
\(577\) −7.87680e6 −0.984941 −0.492470 0.870329i \(-0.663906\pi\)
−0.492470 + 0.870329i \(0.663906\pi\)
\(578\) −3.85160e6 −0.479536
\(579\) 0 0
\(580\) 111312. 0.0137395
\(581\) 3.29808e6 0.405341
\(582\) 0 0
\(583\) −1.90350e7 −2.31943
\(584\) 6.90648e6 0.837963
\(585\) 0 0
\(586\) 5.63324e6 0.677664
\(587\) −603948. −0.0723443 −0.0361721 0.999346i \(-0.511516\pi\)
−0.0361721 + 0.999346i \(0.511516\pi\)
\(588\) 0 0
\(589\) −2.44640e6 −0.290562
\(590\) −651024. −0.0769958
\(591\) 0 0
\(592\) 2.73776e6 0.321064
\(593\) 5.39077e6 0.629526 0.314763 0.949170i \(-0.398075\pi\)
0.314763 + 0.949170i \(0.398075\pi\)
\(594\) 0 0
\(595\) −211680. −0.0245125
\(596\) 421032. 0.0485511
\(597\) 0 0
\(598\) 3.21552e6 0.367704
\(599\) −4.27999e6 −0.487389 −0.243695 0.969852i \(-0.578359\pi\)
−0.243695 + 0.969852i \(0.578359\pi\)
\(600\) 0 0
\(601\) 1.02483e6 0.115735 0.0578674 0.998324i \(-0.481570\pi\)
0.0578674 + 0.998324i \(0.481570\pi\)
\(602\) −2.31456e6 −0.260302
\(603\) 0 0
\(604\) 1.58557e6 0.176845
\(605\) −942270. −0.104661
\(606\) 0 0
\(607\) 1.24342e7 1.36976 0.684882 0.728654i \(-0.259854\pi\)
0.684882 + 0.728654i \(0.259854\pi\)
\(608\) 800640. 0.0878372
\(609\) 0 0
\(610\) −1.43129e6 −0.155741
\(611\) 1.19127e7 1.29095
\(612\) 0 0
\(613\) 4.21506e6 0.453057 0.226528 0.974005i \(-0.427262\pi\)
0.226528 + 0.974005i \(0.427262\pi\)
\(614\) 4.15769e6 0.445073
\(615\) 0 0
\(616\) 3.79008e6 0.402436
\(617\) 4.40665e6 0.466010 0.233005 0.972476i \(-0.425144\pi\)
0.233005 + 0.972476i \(0.425144\pi\)
\(618\) 0 0
\(619\) 4.80168e6 0.503693 0.251847 0.967767i \(-0.418962\pi\)
0.251847 + 0.967767i \(0.418962\pi\)
\(620\) −105600. −0.0110328
\(621\) 0 0
\(622\) −1.76586e7 −1.83012
\(623\) −3.76344e6 −0.388477
\(624\) 0 0
\(625\) 9.42942e6 0.965573
\(626\) 5.31088e6 0.541664
\(627\) 0 0
\(628\) −550984. −0.0557494
\(629\) 2.12562e6 0.214220
\(630\) 0 0
\(631\) 8.30727e6 0.830587 0.415293 0.909688i \(-0.363679\pi\)
0.415293 + 0.909688i \(0.363679\pi\)
\(632\) −3.68256e6 −0.366739
\(633\) 0 0
\(634\) −1.50528e7 −1.48728
\(635\) 1.02653e6 0.101027
\(636\) 0 0
\(637\) −9.70207e6 −0.947361
\(638\) −1.56950e7 −1.52654
\(639\) 0 0
\(640\) −1.27411e6 −0.122958
\(641\) −1.76956e7 −1.70107 −0.850534 0.525921i \(-0.823721\pi\)
−0.850534 + 0.525921i \(0.823721\pi\)
\(642\) 0 0
\(643\) −1.28394e7 −1.22466 −0.612330 0.790602i \(-0.709768\pi\)
−0.612330 + 0.790602i \(0.709768\pi\)
\(644\) −134400. −0.0127698
\(645\) 0 0
\(646\) 2.94235e6 0.277404
\(647\) 2.08468e7 1.95785 0.978924 0.204226i \(-0.0654678\pi\)
0.978924 + 0.204226i \(0.0654678\pi\)
\(648\) 0 0
\(649\) 1.01994e7 0.950521
\(650\) −1.18247e7 −1.09776
\(651\) 0 0
\(652\) 1.41070e6 0.129962
\(653\) −1.29632e7 −1.18968 −0.594841 0.803843i \(-0.702785\pi\)
−0.594841 + 0.803843i \(0.702785\pi\)
\(654\) 0 0
\(655\) 1.55081e6 0.141239
\(656\) −7.80432e6 −0.708069
\(657\) 0 0
\(658\) −4.48128e6 −0.403494
\(659\) 5.66862e6 0.508468 0.254234 0.967143i \(-0.418177\pi\)
0.254234 + 0.967143i \(0.418177\pi\)
\(660\) 0 0
\(661\) −3.11430e6 −0.277240 −0.138620 0.990346i \(-0.544267\pi\)
−0.138620 + 0.990346i \(0.544267\pi\)
\(662\) −1.29689e6 −0.115016
\(663\) 0 0
\(664\) 1.38519e7 1.21924
\(665\) −133440. −0.0117012
\(666\) 0 0
\(667\) −3.89592e6 −0.339075
\(668\) 870240. 0.0754567
\(669\) 0 0
\(670\) 830448. 0.0714703
\(671\) 2.24235e7 1.92264
\(672\) 0 0
\(673\) 105890. 0.00901192 0.00450596 0.999990i \(-0.498566\pi\)
0.00450596 + 0.999990i \(0.498566\pi\)
\(674\) 1.95158e7 1.65476
\(675\) 0 0
\(676\) 143004. 0.0120360
\(677\) 1.60910e7 1.34931 0.674656 0.738132i \(-0.264292\pi\)
0.674656 + 0.738132i \(0.264292\pi\)
\(678\) 0 0
\(679\) −1.97768e6 −0.164620
\(680\) −889056. −0.0737321
\(681\) 0 0
\(682\) 1.48896e7 1.22581
\(683\) −1.60780e7 −1.31880 −0.659402 0.751791i \(-0.729190\pi\)
−0.659402 + 0.751791i \(0.729190\pi\)
\(684\) 0 0
\(685\) 1.80140e6 0.146685
\(686\) 7.68336e6 0.623363
\(687\) 0 0
\(688\) −1.09556e7 −0.882398
\(689\) −2.15325e7 −1.72801
\(690\) 0 0
\(691\) −165964. −0.0132227 −0.00661133 0.999978i \(-0.502104\pi\)
−0.00661133 + 0.999978i \(0.502104\pi\)
\(692\) 654792. 0.0519802
\(693\) 0 0
\(694\) 1.75924e7 1.38652
\(695\) 2.10098e6 0.164991
\(696\) 0 0
\(697\) −6.05934e6 −0.472436
\(698\) 5.43119e6 0.421945
\(699\) 0 0
\(700\) 494240. 0.0381235
\(701\) −1.77248e7 −1.36234 −0.681171 0.732124i \(-0.738529\pi\)
−0.681171 + 0.732124i \(0.738529\pi\)
\(702\) 0 0
\(703\) 1.33996e6 0.102259
\(704\) 1.56296e7 1.18854
\(705\) 0 0
\(706\) −1.15071e7 −0.868872
\(707\) −5.72136e6 −0.430478
\(708\) 0 0
\(709\) −1.06023e7 −0.792112 −0.396056 0.918226i \(-0.629621\pi\)
−0.396056 + 0.918226i \(0.629621\pi\)
\(710\) −152928. −0.0113852
\(711\) 0 0
\(712\) −1.58064e7 −1.16852
\(713\) 3.69600e6 0.272275
\(714\) 0 0
\(715\) −2.15899e6 −0.157938
\(716\) −1.43496e6 −0.104606
\(717\) 0 0
\(718\) 1.46219e7 1.05850
\(719\) −9.03211e6 −0.651579 −0.325790 0.945442i \(-0.605630\pi\)
−0.325790 + 0.945442i \(0.605630\pi\)
\(720\) 0 0
\(721\) −2.12576e6 −0.152292
\(722\) −1.30018e7 −0.928239
\(723\) 0 0
\(724\) −2.02852e6 −0.143825
\(725\) 1.43268e7 1.01229
\(726\) 0 0
\(727\) 1.87575e7 1.31625 0.658127 0.752907i \(-0.271349\pi\)
0.658127 + 0.752907i \(0.271349\pi\)
\(728\) 4.28736e6 0.299821
\(729\) 0 0
\(730\) 1.47996e6 0.102788
\(731\) −8.50601e6 −0.588752
\(732\) 0 0
\(733\) −1.17773e7 −0.809626 −0.404813 0.914399i \(-0.632663\pi\)
−0.404813 + 0.914399i \(0.632663\pi\)
\(734\) −5.90438e6 −0.404515
\(735\) 0 0
\(736\) −1.20960e6 −0.0823090
\(737\) −1.30104e7 −0.882308
\(738\) 0 0
\(739\) 5.88948e6 0.396703 0.198352 0.980131i \(-0.436441\pi\)
0.198352 + 0.980131i \(0.436441\pi\)
\(740\) 57840.0 0.00388284
\(741\) 0 0
\(742\) 8.10000e6 0.540101
\(743\) 1.00476e7 0.667712 0.333856 0.942624i \(-0.391650\pi\)
0.333856 + 0.942624i \(0.391650\pi\)
\(744\) 0 0
\(745\) −631548. −0.0416884
\(746\) 1.02219e7 0.672490
\(747\) 0 0
\(748\) −1.98979e6 −0.130033
\(749\) 3.63312e6 0.236633
\(750\) 0 0
\(751\) 4.81530e6 0.311547 0.155773 0.987793i \(-0.450213\pi\)
0.155773 + 0.987793i \(0.450213\pi\)
\(752\) −2.12114e7 −1.36781
\(753\) 0 0
\(754\) −1.77543e7 −1.13730
\(755\) −2.37835e6 −0.151848
\(756\) 0 0
\(757\) 3.12973e6 0.198503 0.0992516 0.995062i \(-0.468355\pi\)
0.0992516 + 0.995062i \(0.468355\pi\)
\(758\) 1.65392e7 1.04554
\(759\) 0 0
\(760\) −560448. −0.0351967
\(761\) 1.17773e7 0.737197 0.368599 0.929589i \(-0.379838\pi\)
0.368599 + 0.929589i \(0.379838\pi\)
\(762\) 0 0
\(763\) 2.46664e6 0.153389
\(764\) 2.59354e6 0.160753
\(765\) 0 0
\(766\) −2.73946e6 −0.168691
\(767\) 1.15376e7 0.708152
\(768\) 0 0
\(769\) −1.49376e6 −0.0910887 −0.0455443 0.998962i \(-0.514502\pi\)
−0.0455443 + 0.998962i \(0.514502\pi\)
\(770\) 812160. 0.0493645
\(771\) 0 0
\(772\) −111352. −0.00672442
\(773\) 2.25125e7 1.35511 0.677555 0.735472i \(-0.263040\pi\)
0.677555 + 0.735472i \(0.263040\pi\)
\(774\) 0 0
\(775\) −1.35916e7 −0.812861
\(776\) −8.30626e6 −0.495166
\(777\) 0 0
\(778\) 1.20384e7 0.713048
\(779\) −3.81972e6 −0.225521
\(780\) 0 0
\(781\) 2.39587e6 0.140552
\(782\) −4.44528e6 −0.259945
\(783\) 0 0
\(784\) 1.72752e7 1.00376
\(785\) 826476. 0.0478692
\(786\) 0 0
\(787\) 1.19547e7 0.688022 0.344011 0.938966i \(-0.388214\pi\)
0.344011 + 0.938966i \(0.388214\pi\)
\(788\) −2.44418e6 −0.140223
\(789\) 0 0
\(790\) −789120. −0.0449858
\(791\) 419280. 0.0238266
\(792\) 0 0
\(793\) 2.53656e7 1.43239
\(794\) −3.46224e7 −1.94897
\(795\) 0 0
\(796\) 3.51613e6 0.196690
\(797\) −540798. −0.0301571 −0.0150785 0.999886i \(-0.504800\pi\)
−0.0150785 + 0.999886i \(0.504800\pi\)
\(798\) 0 0
\(799\) −1.64687e7 −0.912625
\(800\) 4.44816e6 0.245728
\(801\) 0 0
\(802\) −1.80375e7 −0.990243
\(803\) −2.31860e7 −1.26893
\(804\) 0 0
\(805\) 201600. 0.0109648
\(806\) 1.68432e7 0.913244
\(807\) 0 0
\(808\) −2.40297e7 −1.29485
\(809\) 6.14223e6 0.329955 0.164978 0.986297i \(-0.447245\pi\)
0.164978 + 0.986297i \(0.447245\pi\)
\(810\) 0 0
\(811\) −3.16734e7 −1.69100 −0.845499 0.533977i \(-0.820697\pi\)
−0.845499 + 0.533977i \(0.820697\pi\)
\(812\) 742080. 0.0394967
\(813\) 0 0
\(814\) −8.15544e6 −0.431406
\(815\) −2.11606e6 −0.111592
\(816\) 0 0
\(817\) −5.36206e6 −0.281046
\(818\) 9.20176e6 0.480825
\(819\) 0 0
\(820\) −164880. −0.00856315
\(821\) −2.66175e7 −1.37819 −0.689095 0.724671i \(-0.741992\pi\)
−0.689095 + 0.724671i \(0.741992\pi\)
\(822\) 0 0
\(823\) 3.62817e7 1.86719 0.933593 0.358335i \(-0.116655\pi\)
0.933593 + 0.358335i \(0.116655\pi\)
\(824\) −8.92819e6 −0.458084
\(825\) 0 0
\(826\) −4.34016e6 −0.221338
\(827\) −1.09033e6 −0.0554364 −0.0277182 0.999616i \(-0.508824\pi\)
−0.0277182 + 0.999616i \(0.508824\pi\)
\(828\) 0 0
\(829\) −1.03016e7 −0.520620 −0.260310 0.965525i \(-0.583825\pi\)
−0.260310 + 0.965525i \(0.583825\pi\)
\(830\) 2.96827e6 0.149558
\(831\) 0 0
\(832\) 1.76803e7 0.885483
\(833\) 1.34126e7 0.669730
\(834\) 0 0
\(835\) −1.30536e6 −0.0647909
\(836\) −1.25434e6 −0.0620724
\(837\) 0 0
\(838\) 2.32425e7 1.14333
\(839\) 1.96134e7 0.961940 0.480970 0.876737i \(-0.340285\pi\)
0.480970 + 0.876737i \(0.340285\pi\)
\(840\) 0 0
\(841\) 999895. 0.0487489
\(842\) −7.99840e6 −0.388797
\(843\) 0 0
\(844\) 194000. 0.00937445
\(845\) −214506. −0.0103347
\(846\) 0 0
\(847\) −6.28180e6 −0.300868
\(848\) 3.83400e7 1.83089
\(849\) 0 0
\(850\) 1.63470e7 0.776051
\(851\) −2.02440e6 −0.0958236
\(852\) 0 0
\(853\) 3.27565e7 1.54143 0.770717 0.637178i \(-0.219898\pi\)
0.770717 + 0.637178i \(0.219898\pi\)
\(854\) −9.54192e6 −0.447704
\(855\) 0 0
\(856\) 1.52591e7 0.711778
\(857\) 2.57953e7 1.19974 0.599872 0.800096i \(-0.295218\pi\)
0.599872 + 0.800096i \(0.295218\pi\)
\(858\) 0 0
\(859\) −1.98548e7 −0.918085 −0.459043 0.888414i \(-0.651807\pi\)
−0.459043 + 0.888414i \(0.651807\pi\)
\(860\) −231456. −0.0106714
\(861\) 0 0
\(862\) −3.87115e7 −1.77448
\(863\) 673056. 0.0307627 0.0153813 0.999882i \(-0.495104\pi\)
0.0153813 + 0.999882i \(0.495104\pi\)
\(864\) 0 0
\(865\) −982188. −0.0446328
\(866\) −2.49946e7 −1.13254
\(867\) 0 0
\(868\) −704000. −0.0317156
\(869\) 1.23629e7 0.555354
\(870\) 0 0
\(871\) −1.47174e7 −0.657333
\(872\) 1.03599e7 0.461385
\(873\) 0 0
\(874\) −2.80224e6 −0.124087
\(875\) −1.49136e6 −0.0658510
\(876\) 0 0
\(877\) 5.32115e6 0.233618 0.116809 0.993154i \(-0.462733\pi\)
0.116809 + 0.993154i \(0.462733\pi\)
\(878\) 4.75608e6 0.208215
\(879\) 0 0
\(880\) 3.84422e6 0.167341
\(881\) −2.78891e7 −1.21058 −0.605291 0.796004i \(-0.706943\pi\)
−0.605291 + 0.796004i \(0.706943\pi\)
\(882\) 0 0
\(883\) −2.83786e7 −1.22487 −0.612435 0.790521i \(-0.709810\pi\)
−0.612435 + 0.790521i \(0.709810\pi\)
\(884\) −2.25086e6 −0.0968765
\(885\) 0 0
\(886\) 8.39887e6 0.359448
\(887\) −4.22678e7 −1.80385 −0.901925 0.431893i \(-0.857846\pi\)
−0.901925 + 0.431893i \(0.857846\pi\)
\(888\) 0 0
\(889\) 6.84352e6 0.290419
\(890\) −3.38710e6 −0.143335
\(891\) 0 0
\(892\) −3.99789e6 −0.168236
\(893\) −1.03816e7 −0.435649
\(894\) 0 0
\(895\) 2.15244e6 0.0898201
\(896\) −8.49408e6 −0.353465
\(897\) 0 0
\(898\) −1.79549e7 −0.743005
\(899\) −2.04072e7 −0.842140
\(900\) 0 0
\(901\) 2.97675e7 1.22160
\(902\) 2.32481e7 0.951417
\(903\) 0 0
\(904\) 1.76098e6 0.0716692
\(905\) 3.04278e6 0.123495
\(906\) 0 0
\(907\) 3.19526e7 1.28970 0.644849 0.764310i \(-0.276920\pi\)
0.644849 + 0.764310i \(0.276920\pi\)
\(908\) −2.42472e6 −0.0975994
\(909\) 0 0
\(910\) 918720. 0.0367773
\(911\) 1.16429e7 0.464800 0.232400 0.972620i \(-0.425342\pi\)
0.232400 + 0.972620i \(0.425342\pi\)
\(912\) 0 0
\(913\) −4.65029e7 −1.84630
\(914\) 3.77981e7 1.49660
\(915\) 0 0
\(916\) 5.43970e6 0.214208
\(917\) 1.03387e7 0.406016
\(918\) 0 0
\(919\) 1.39844e6 0.0546204 0.0273102 0.999627i \(-0.491306\pi\)
0.0273102 + 0.999627i \(0.491306\pi\)
\(920\) 846720. 0.0329815
\(921\) 0 0
\(922\) −2.04191e7 −0.791059
\(923\) 2.71022e6 0.104713
\(924\) 0 0
\(925\) 7.44449e6 0.286075
\(926\) −1.33820e7 −0.512854
\(927\) 0 0
\(928\) 6.67872e6 0.254579
\(929\) 1.66792e7 0.634067 0.317033 0.948414i \(-0.397313\pi\)
0.317033 + 0.948414i \(0.397313\pi\)
\(930\) 0 0
\(931\) 8.45509e6 0.319701
\(932\) 1.57154e6 0.0592634
\(933\) 0 0
\(934\) 3.90846e7 1.46601
\(935\) 2.98469e6 0.111653
\(936\) 0 0
\(937\) −2.47956e7 −0.922625 −0.461312 0.887238i \(-0.652621\pi\)
−0.461312 + 0.887238i \(0.652621\pi\)
\(938\) 5.53632e6 0.205454
\(939\) 0 0
\(940\) −448128. −0.0165418
\(941\) −2.79574e7 −1.02925 −0.514627 0.857414i \(-0.672070\pi\)
−0.514627 + 0.857414i \(0.672070\pi\)
\(942\) 0 0
\(943\) 5.77080e6 0.211328
\(944\) −2.05434e7 −0.750314
\(945\) 0 0
\(946\) 3.26353e7 1.18566
\(947\) −7.64936e6 −0.277173 −0.138586 0.990350i \(-0.544256\pi\)
−0.138586 + 0.990350i \(0.544256\pi\)
\(948\) 0 0
\(949\) −2.62282e7 −0.945372
\(950\) 1.03049e7 0.370455
\(951\) 0 0
\(952\) −5.92704e6 −0.211956
\(953\) 4.62179e7 1.64846 0.824228 0.566257i \(-0.191609\pi\)
0.824228 + 0.566257i \(0.191609\pi\)
\(954\) 0 0
\(955\) −3.89030e6 −0.138031
\(956\) 5.30054e6 0.187575
\(957\) 0 0
\(958\) −1.43539e7 −0.505309
\(959\) 1.20094e7 0.421671
\(960\) 0 0
\(961\) −9.26915e6 −0.323766
\(962\) −9.22548e6 −0.321404
\(963\) 0 0
\(964\) −3.96038e6 −0.137260
\(965\) 167028. 0.00577392
\(966\) 0 0
\(967\) 2.08557e7 0.717229 0.358615 0.933486i \(-0.383249\pi\)
0.358615 + 0.933486i \(0.383249\pi\)
\(968\) −2.63836e7 −0.904993
\(969\) 0 0
\(970\) −1.77991e6 −0.0607392
\(971\) 4.58152e7 1.55941 0.779707 0.626144i \(-0.215368\pi\)
0.779707 + 0.626144i \(0.215368\pi\)
\(972\) 0 0
\(973\) 1.40066e7 0.474296
\(974\) −3.67853e7 −1.24245
\(975\) 0 0
\(976\) −4.51651e7 −1.51767
\(977\) 1.09544e6 0.0367157 0.0183578 0.999831i \(-0.494156\pi\)
0.0183578 + 0.999831i \(0.494156\pi\)
\(978\) 0 0
\(979\) 5.30645e7 1.76949
\(980\) 364968. 0.0121392
\(981\) 0 0
\(982\) 7.41535e6 0.245388
\(983\) −5.25817e7 −1.73561 −0.867803 0.496909i \(-0.834468\pi\)
−0.867803 + 0.496909i \(0.834468\pi\)
\(984\) 0 0
\(985\) 3.66628e6 0.120402
\(986\) 2.45443e7 0.804004
\(987\) 0 0
\(988\) −1.41891e6 −0.0462448
\(989\) 8.10096e6 0.263358
\(990\) 0 0
\(991\) −4.90389e7 −1.58620 −0.793098 0.609094i \(-0.791533\pi\)
−0.793098 + 0.609094i \(0.791533\pi\)
\(992\) −6.33600e6 −0.204426
\(993\) 0 0
\(994\) −1.01952e6 −0.0327288
\(995\) −5.27419e6 −0.168888
\(996\) 0 0
\(997\) 3.05461e6 0.0973237 0.0486618 0.998815i \(-0.484504\pi\)
0.0486618 + 0.998815i \(0.484504\pi\)
\(998\) −5.91297e7 −1.87923
\(999\) 0 0
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 \(a_p\))