Properties

Label 3.6.a.a.1.1
Level 3
Weight 6
Character 3.1
Self dual Yes
Analytic conductor 0.481
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 3.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.481151459439\)
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 \(\chi\) = 3.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-6.00000 q^{2}\) \(+9.00000 q^{3}\) \(+4.00000 q^{4}\) \(+6.00000 q^{5}\) \(-54.0000 q^{6}\) \(-40.0000 q^{7}\) \(+168.000 q^{8}\) \(+81.0000 q^{9}\) \(+O(q^{10})\) \(q\)\(-6.00000 q^{2}\) \(+9.00000 q^{3}\) \(+4.00000 q^{4}\) \(+6.00000 q^{5}\) \(-54.0000 q^{6}\) \(-40.0000 q^{7}\) \(+168.000 q^{8}\) \(+81.0000 q^{9}\) \(-36.0000 q^{10}\) \(-564.000 q^{11}\) \(+36.0000 q^{12}\) \(+638.000 q^{13}\) \(+240.000 q^{14}\) \(+54.0000 q^{15}\) \(-1136.00 q^{16}\) \(+882.000 q^{17}\) \(-486.000 q^{18}\) \(-556.000 q^{19}\) \(+24.0000 q^{20}\) \(-360.000 q^{21}\) \(+3384.00 q^{22}\) \(-840.000 q^{23}\) \(+1512.00 q^{24}\) \(-3089.00 q^{25}\) \(-3828.00 q^{26}\) \(+729.000 q^{27}\) \(-160.000 q^{28}\) \(+4638.00 q^{29}\) \(-324.000 q^{30}\) \(+4400.00 q^{31}\) \(+1440.00 q^{32}\) \(-5076.00 q^{33}\) \(-5292.00 q^{34}\) \(-240.000 q^{35}\) \(+324.000 q^{36}\) \(-2410.00 q^{37}\) \(+3336.00 q^{38}\) \(+5742.00 q^{39}\) \(+1008.00 q^{40}\) \(-6870.00 q^{41}\) \(+2160.00 q^{42}\) \(+9644.00 q^{43}\) \(-2256.00 q^{44}\) \(+486.000 q^{45}\) \(+5040.00 q^{46}\) \(-18672.0 q^{47}\) \(-10224.0 q^{48}\) \(-15207.0 q^{49}\) \(+18534.0 q^{50}\) \(+7938.00 q^{51}\) \(+2552.00 q^{52}\) \(+33750.0 q^{53}\) \(-4374.00 q^{54}\) \(-3384.00 q^{55}\) \(-6720.00 q^{56}\) \(-5004.00 q^{57}\) \(-27828.0 q^{58}\) \(-18084.0 q^{59}\) \(+216.000 q^{60}\) \(+39758.0 q^{61}\) \(-26400.0 q^{62}\) \(-3240.00 q^{63}\) \(+27712.0 q^{64}\) \(+3828.00 q^{65}\) \(+30456.0 q^{66}\) \(-23068.0 q^{67}\) \(+3528.00 q^{68}\) \(-7560.00 q^{69}\) \(+1440.00 q^{70}\) \(-4248.00 q^{71}\) \(+13608.0 q^{72}\) \(-41110.0 q^{73}\) \(+14460.0 q^{74}\) \(-27801.0 q^{75}\) \(-2224.00 q^{76}\) \(+22560.0 q^{77}\) \(-34452.0 q^{78}\) \(+21920.0 q^{79}\) \(-6816.00 q^{80}\) \(+6561.00 q^{81}\) \(+41220.0 q^{82}\) \(+82452.0 q^{83}\) \(-1440.00 q^{84}\) \(+5292.00 q^{85}\) \(-57864.0 q^{86}\) \(+41742.0 q^{87}\) \(-94752.0 q^{88}\) \(-94086.0 q^{89}\) \(-2916.00 q^{90}\) \(-25520.0 q^{91}\) \(-3360.00 q^{92}\) \(+39600.0 q^{93}\) \(+112032. q^{94}\) \(-3336.00 q^{95}\) \(+12960.0 q^{96}\) \(+49442.0 q^{97}\) \(+91242.0 q^{98}\) \(-45684.0 q^{99}\) \(+O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −6.00000 −1.06066 −0.530330 0.847791i \(-0.677932\pi\)
−0.530330 + 0.847791i \(0.677932\pi\)
\(3\) 9.00000 0.577350
\(4\) 4.00000 0.125000
\(5\) 6.00000 0.107331 0.0536656 0.998559i \(-0.482909\pi\)
0.0536656 + 0.998559i \(0.482909\pi\)
\(6\) −54.0000 −0.612372
\(7\) −40.0000 −0.308542 −0.154271 0.988029i \(-0.549303\pi\)
−0.154271 + 0.988029i \(0.549303\pi\)
\(8\) 168.000 0.928078
\(9\) 81.0000 0.333333
\(10\) −36.0000 −0.113842
\(11\) −564.000 −1.40539 −0.702696 0.711490i \(-0.748021\pi\)
−0.702696 + 0.711490i \(0.748021\pi\)
\(12\) 36.0000 0.0721688
\(13\) 638.000 1.04704 0.523519 0.852014i \(-0.324619\pi\)
0.523519 + 0.852014i \(0.324619\pi\)
\(14\) 240.000 0.327259
\(15\) 54.0000 0.0619677
\(16\) −1136.00 −1.10938
\(17\) 882.000 0.740195 0.370098 0.928993i \(-0.379324\pi\)
0.370098 + 0.928993i \(0.379324\pi\)
\(18\) −486.000 −0.353553
\(19\) −556.000 −0.353338 −0.176669 0.984270i \(-0.556532\pi\)
−0.176669 + 0.984270i \(0.556532\pi\)
\(20\) 24.0000 0.0134164
\(21\) −360.000 −0.178137
\(22\) 3384.00 1.49064
\(23\) −840.000 −0.331100 −0.165550 0.986201i \(-0.552940\pi\)
−0.165550 + 0.986201i \(0.552940\pi\)
\(24\) 1512.00 0.535826
\(25\) −3089.00 −0.988480
\(26\) −3828.00 −1.11055
\(27\) 729.000 0.192450
\(28\) −160.000 −0.0385678
\(29\) 4638.00 1.02408 0.512042 0.858960i \(-0.328889\pi\)
0.512042 + 0.858960i \(0.328889\pi\)
\(30\) −324.000 −0.0657267
\(31\) 4400.00 0.822334 0.411167 0.911560i \(-0.365121\pi\)
0.411167 + 0.911560i \(0.365121\pi\)
\(32\) 1440.00 0.248592
\(33\) −5076.00 −0.811403
\(34\) −5292.00 −0.785096
\(35\) −240.000 −0.0331162
\(36\) 324.000 0.0416667
\(37\) −2410.00 −0.289409 −0.144705 0.989475i \(-0.546223\pi\)
−0.144705 + 0.989475i \(0.546223\pi\)
\(38\) 3336.00 0.374772
\(39\) 5742.00 0.604507
\(40\) 1008.00 0.0996117
\(41\) −6870.00 −0.638259 −0.319130 0.947711i \(-0.603391\pi\)
−0.319130 + 0.947711i \(0.603391\pi\)
\(42\) 2160.00 0.188943
\(43\) 9644.00 0.795401 0.397700 0.917515i \(-0.369808\pi\)
0.397700 + 0.917515i \(0.369808\pi\)
\(44\) −2256.00 −0.175674
\(45\) 486.000 0.0357771
\(46\) 5040.00 0.351185
\(47\) −18672.0 −1.23295 −0.616476 0.787374i \(-0.711440\pi\)
−0.616476 + 0.787374i \(0.711440\pi\)
\(48\) −10224.0 −0.640498
\(49\) −15207.0 −0.904802
\(50\) 18534.0 1.04844
\(51\) 7938.00 0.427352
\(52\) 2552.00 0.130880
\(53\) 33750.0 1.65038 0.825190 0.564855i \(-0.191068\pi\)
0.825190 + 0.564855i \(0.191068\pi\)
\(54\) −4374.00 −0.204124
\(55\) −3384.00 −0.150842
\(56\) −6720.00 −0.286351
\(57\) −5004.00 −0.204000
\(58\) −27828.0 −1.08621
\(59\) −18084.0 −0.676339 −0.338170 0.941085i \(-0.609808\pi\)
−0.338170 + 0.941085i \(0.609808\pi\)
\(60\) 216.000 0.00774597
\(61\) 39758.0 1.36804 0.684022 0.729462i \(-0.260229\pi\)
0.684022 + 0.729462i \(0.260229\pi\)
\(62\) −26400.0 −0.872217
\(63\) −3240.00 −0.102847
\(64\) 27712.0 0.845703
\(65\) 3828.00 0.112380
\(66\) 30456.0 0.860623
\(67\) −23068.0 −0.627802 −0.313901 0.949456i \(-0.601636\pi\)
−0.313901 + 0.949456i \(0.601636\pi\)
\(68\) 3528.00 0.0925244
\(69\) −7560.00 −0.191161
\(70\) 1440.00 0.0351251
\(71\) −4248.00 −0.100009 −0.0500044 0.998749i \(-0.515924\pi\)
−0.0500044 + 0.998749i \(0.515924\pi\)
\(72\) 13608.0 0.309359
\(73\) −41110.0 −0.902901 −0.451451 0.892296i \(-0.649093\pi\)
−0.451451 + 0.892296i \(0.649093\pi\)
\(74\) 14460.0 0.306965
\(75\) −27801.0 −0.570699
\(76\) −2224.00 −0.0441673
\(77\) 22560.0 0.433623
\(78\) −34452.0 −0.641177
\(79\) 21920.0 0.395160 0.197580 0.980287i \(-0.436692\pi\)
0.197580 + 0.980287i \(0.436692\pi\)
\(80\) −6816.00 −0.119071
\(81\) 6561.00 0.111111
\(82\) 41220.0 0.676976
\(83\) 82452.0 1.31373 0.656865 0.754008i \(-0.271882\pi\)
0.656865 + 0.754008i \(0.271882\pi\)
\(84\) −1440.00 −0.0222671
\(85\) 5292.00 0.0794461
\(86\) −57864.0 −0.843650
\(87\) 41742.0 0.591255
\(88\) −94752.0 −1.30431
\(89\) −94086.0 −1.25907 −0.629535 0.776972i \(-0.716755\pi\)
−0.629535 + 0.776972i \(0.716755\pi\)
\(90\) −2916.00 −0.0379473
\(91\) −25520.0 −0.323056
\(92\) −3360.00 −0.0413875
\(93\) 39600.0 0.474775
\(94\) 112032. 1.30774
\(95\) −3336.00 −0.0379243
\(96\) 12960.0 0.143525
\(97\) 49442.0 0.533540 0.266770 0.963760i \(-0.414044\pi\)
0.266770 + 0.963760i \(0.414044\pi\)
\(98\) 91242.0 0.959687
\(99\) −45684.0 −0.468464
\(100\) −12356.0 −0.123560
\(101\) −143034. −1.39520 −0.697599 0.716488i \(-0.745748\pi\)
−0.697599 + 0.716488i \(0.745748\pi\)
\(102\) −47628.0 −0.453275
\(103\) 53144.0 0.493584 0.246792 0.969068i \(-0.420624\pi\)
0.246792 + 0.969068i \(0.420624\pi\)
\(104\) 107184. 0.971732
\(105\) −2160.00 −0.0191197
\(106\) −202500. −1.75049
\(107\) 90828.0 0.766938 0.383469 0.923554i \(-0.374729\pi\)
0.383469 + 0.923554i \(0.374729\pi\)
\(108\) 2916.00 0.0240563
\(109\) −61666.0 −0.497141 −0.248570 0.968614i \(-0.579961\pi\)
−0.248570 + 0.968614i \(0.579961\pi\)
\(110\) 20304.0 0.159993
\(111\) −21690.0 −0.167091
\(112\) 45440.0 0.342289
\(113\) 10482.0 0.0772232 0.0386116 0.999254i \(-0.487706\pi\)
0.0386116 + 0.999254i \(0.487706\pi\)
\(114\) 30024.0 0.216375
\(115\) −5040.00 −0.0355374
\(116\) 18552.0 0.128011
\(117\) 51678.0 0.349013
\(118\) 108504. 0.717366
\(119\) −35280.0 −0.228382
\(120\) 9072.00 0.0575109
\(121\) 157045. 0.975126
\(122\) −238548. −1.45103
\(123\) −61830.0 −0.368499
\(124\) 17600.0 0.102792
\(125\) −37284.0 −0.213426
\(126\) 19440.0 0.109086
\(127\) −171088. −0.941261 −0.470631 0.882330i \(-0.655974\pi\)
−0.470631 + 0.882330i \(0.655974\pi\)
\(128\) −212352. −1.14560
\(129\) 86796.0 0.459225
\(130\) −22968.0 −0.119197
\(131\) 258468. 1.31592 0.657959 0.753054i \(-0.271420\pi\)
0.657959 + 0.753054i \(0.271420\pi\)
\(132\) −20304.0 −0.101425
\(133\) 22240.0 0.109020
\(134\) 138408. 0.665885
\(135\) 4374.00 0.0206559
\(136\) 148176. 0.686959
\(137\) 300234. 1.36665 0.683327 0.730113i \(-0.260532\pi\)
0.683327 + 0.730113i \(0.260532\pi\)
\(138\) 45360.0 0.202757
\(139\) −350164. −1.53721 −0.768607 0.639721i \(-0.779050\pi\)
−0.768607 + 0.639721i \(0.779050\pi\)
\(140\) −960.000 −0.00413953
\(141\) −168048. −0.711845
\(142\) 25488.0 0.106075
\(143\) −359832. −1.47150
\(144\) −92016.0 −0.369792
\(145\) 27828.0 0.109916
\(146\) 246660. 0.957672
\(147\) −136863. −0.522387
\(148\) −9640.00 −0.0361762
\(149\) −105258. −0.388409 −0.194205 0.980961i \(-0.562213\pi\)
−0.194205 + 0.980961i \(0.562213\pi\)
\(150\) 166806. 0.605318
\(151\) 396392. 1.41476 0.707380 0.706834i \(-0.249877\pi\)
0.707380 + 0.706834i \(0.249877\pi\)
\(152\) −93408.0 −0.327925
\(153\) 71442.0 0.246732
\(154\) −135360. −0.459927
\(155\) 26400.0 0.0882622
\(156\) 22968.0 0.0755634
\(157\) −137746. −0.445995 −0.222997 0.974819i \(-0.571584\pi\)
−0.222997 + 0.974819i \(0.571584\pi\)
\(158\) −131520. −0.419130
\(159\) 303750. 0.952848
\(160\) 8640.00 0.0266817
\(161\) 33600.0 0.102159
\(162\) −39366.0 −0.117851
\(163\) 352676. 1.03970 0.519849 0.854258i \(-0.325988\pi\)
0.519849 + 0.854258i \(0.325988\pi\)
\(164\) −27480.0 −0.0797824
\(165\) −30456.0 −0.0870889
\(166\) −494712. −1.39342
\(167\) −217560. −0.603654 −0.301827 0.953363i \(-0.597596\pi\)
−0.301827 + 0.953363i \(0.597596\pi\)
\(168\) −60480.0 −0.165325
\(169\) 35751.0 0.0962878
\(170\) −31752.0 −0.0842653
\(171\) −45036.0 −0.117779
\(172\) 38576.0 0.0994251
\(173\) −163698. −0.415842 −0.207921 0.978146i \(-0.566670\pi\)
−0.207921 + 0.978146i \(0.566670\pi\)
\(174\) −250452. −0.627121
\(175\) 123560. 0.304988
\(176\) 640704. 1.55911
\(177\) −162756. −0.390485
\(178\) 564516. 1.33545
\(179\) 358740. 0.836849 0.418425 0.908252i \(-0.362582\pi\)
0.418425 + 0.908252i \(0.362582\pi\)
\(180\) 1944.00 0.00447214
\(181\) −507130. −1.15060 −0.575298 0.817944i \(-0.695114\pi\)
−0.575298 + 0.817944i \(0.695114\pi\)
\(182\) 153120. 0.342652
\(183\) 357822. 0.789840
\(184\) −141120. −0.307287
\(185\) −14460.0 −0.0310627
\(186\) −237600. −0.503575
\(187\) −497448. −1.04026
\(188\) −74688.0 −0.154119
\(189\) −29160.0 −0.0593790
\(190\) 20016.0 0.0402247
\(191\) −648384. −1.28602 −0.643012 0.765856i \(-0.722315\pi\)
−0.643012 + 0.765856i \(0.722315\pi\)
\(192\) 249408. 0.488267
\(193\) −27838.0 −0.0537954 −0.0268977 0.999638i \(-0.508563\pi\)
−0.0268977 + 0.999638i \(0.508563\pi\)
\(194\) −296652. −0.565904
\(195\) 34452.0 0.0648826
\(196\) −60828.0 −0.113100
\(197\) 611046. 1.12178 0.560891 0.827890i \(-0.310459\pi\)
0.560891 + 0.827890i \(0.310459\pi\)
\(198\) 274104. 0.496881
\(199\) 879032. 1.57352 0.786760 0.617260i \(-0.211757\pi\)
0.786760 + 0.617260i \(0.211757\pi\)
\(200\) −518952. −0.917386
\(201\) −207612. −0.362462
\(202\) 858204. 1.47983
\(203\) −185520. −0.315973
\(204\) 31752.0 0.0534190
\(205\) −41220.0 −0.0685052
\(206\) −318864. −0.523525
\(207\) −68040.0 −0.110367
\(208\) −724768. −1.16156
\(209\) 313584. 0.496579
\(210\) 12960.0 0.0202795
\(211\) 48500.0 0.0749956 0.0374978 0.999297i \(-0.488061\pi\)
0.0374978 + 0.999297i \(0.488061\pi\)
\(212\) 135000. 0.206298
\(213\) −38232.0 −0.0577402
\(214\) −544968. −0.813461
\(215\) 57864.0 0.0853714
\(216\) 122472. 0.178609
\(217\) −176000. −0.253725
\(218\) 369996. 0.527298
\(219\) −369990. −0.521290
\(220\) −13536.0 −0.0188553
\(221\) 562716. 0.775012
\(222\) 130140. 0.177226
\(223\) −999472. −1.34589 −0.672943 0.739694i \(-0.734970\pi\)
−0.672943 + 0.739694i \(0.734970\pi\)
\(224\) −57600.0 −0.0767012
\(225\) −250209. −0.329493
\(226\) −62892.0 −0.0819076
\(227\) 606180. 0.780795 0.390397 0.920646i \(-0.372338\pi\)
0.390397 + 0.920646i \(0.372338\pi\)
\(228\) −20016.0 −0.0255000
\(229\) 1.35993e6 1.71367 0.856834 0.515593i \(-0.172428\pi\)
0.856834 + 0.515593i \(0.172428\pi\)
\(230\) 30240.0 0.0376931
\(231\) 203040. 0.250352
\(232\) 779184. 0.950430
\(233\) −392886. −0.474107 −0.237054 0.971497i \(-0.576182\pi\)
−0.237054 + 0.971497i \(0.576182\pi\)
\(234\) −310068. −0.370184
\(235\) −112032. −0.132334
\(236\) −72336.0 −0.0845424
\(237\) 197280. 0.228146
\(238\) 211680. 0.242235
\(239\) −1.32514e6 −1.50060 −0.750301 0.661096i \(-0.770092\pi\)
−0.750301 + 0.661096i \(0.770092\pi\)
\(240\) −61344.0 −0.0687455
\(241\) −990094. −1.09808 −0.549040 0.835796i \(-0.685006\pi\)
−0.549040 + 0.835796i \(0.685006\pi\)
\(242\) −942270. −1.03428
\(243\) 59049.0 0.0641500
\(244\) 159032. 0.171005
\(245\) −91242.0 −0.0971135
\(246\) 370980. 0.390852
\(247\) −354728. −0.369959
\(248\) 739200. 0.763190
\(249\) 742068. 0.758482
\(250\) 223704. 0.226373
\(251\) 147132. 0.147409 0.0737043 0.997280i \(-0.476518\pi\)
0.0737043 + 0.997280i \(0.476518\pi\)
\(252\) −12960.0 −0.0128559
\(253\) 473760. 0.465326
\(254\) 1.02653e6 0.998358
\(255\) 47628.0 0.0458682
\(256\) 387328. 0.369385
\(257\) −483582. −0.456707 −0.228353 0.973578i \(-0.573334\pi\)
−0.228353 + 0.973578i \(0.573334\pi\)
\(258\) −520776. −0.487082
\(259\) 96400.0 0.0892951
\(260\) 15312.0 0.0140475
\(261\) 375678. 0.341361
\(262\) −1.55081e6 −1.39574
\(263\) 813576. 0.725285 0.362643 0.931928i \(-0.381875\pi\)
0.362643 + 0.931928i \(0.381875\pi\)
\(264\) −852768. −0.753045
\(265\) 202500. 0.177137
\(266\) −133440. −0.115633
\(267\) −846774. −0.726925
\(268\) −92272.0 −0.0784753
\(269\) −461106. −0.388526 −0.194263 0.980949i \(-0.562232\pi\)
−0.194263 + 0.980949i \(0.562232\pi\)
\(270\) −26244.0 −0.0219089
\(271\) 1.67514e6 1.38556 0.692782 0.721147i \(-0.256385\pi\)
0.692782 + 0.721147i \(0.256385\pi\)
\(272\) −1.00195e6 −0.821154
\(273\) −229680. −0.186516
\(274\) −1.80140e6 −1.44956
\(275\) 1.74220e6 1.38920
\(276\) −30240.0 −0.0238951
\(277\) 401126. 0.314110 0.157055 0.987590i \(-0.449800\pi\)
0.157055 + 0.987590i \(0.449800\pi\)
\(278\) 2.10098e6 1.63046
\(279\) 356400. 0.274111
\(280\) −40320.0 −0.0307344
\(281\) −2.30977e6 −1.74503 −0.872514 0.488590i \(-0.837511\pi\)
−0.872514 + 0.488590i \(0.837511\pi\)
\(282\) 1.00829e6 0.755026
\(283\) −1.12877e6 −0.837800 −0.418900 0.908032i \(-0.637584\pi\)
−0.418900 + 0.908032i \(0.637584\pi\)
\(284\) −16992.0 −0.0125011
\(285\) −30024.0 −0.0218956
\(286\) 2.15899e6 1.56076
\(287\) 274800. 0.196930
\(288\) 116640. 0.0828641
\(289\) −641933. −0.452111
\(290\) −166968. −0.116584
\(291\) 444978. 0.308039
\(292\) −164440. −0.112863
\(293\) −938874. −0.638908 −0.319454 0.947602i \(-0.603499\pi\)
−0.319454 + 0.947602i \(0.603499\pi\)
\(294\) 821178. 0.554076
\(295\) −108504. −0.0725923
\(296\) −404880. −0.268594
\(297\) −411156. −0.270468
\(298\) 631548. 0.411970
\(299\) −535920. −0.346675
\(300\) −111204. −0.0713374
\(301\) −385760. −0.245415
\(302\) −2.37835e6 −1.50058
\(303\) −1.28731e6 −0.805518
\(304\) 631616. 0.391985
\(305\) 238548. 0.146834
\(306\) −428652. −0.261699
\(307\) 692948. 0.419619 0.209809 0.977742i \(-0.432716\pi\)
0.209809 + 0.977742i \(0.432716\pi\)
\(308\) 90240.0 0.0542029
\(309\) 478296. 0.284971
\(310\) −158400. −0.0936162
\(311\) 2.94310e6 1.72545 0.862727 0.505670i \(-0.168755\pi\)
0.862727 + 0.505670i \(0.168755\pi\)
\(312\) 964656. 0.561030
\(313\) 885146. 0.510686 0.255343 0.966851i \(-0.417812\pi\)
0.255343 + 0.966851i \(0.417812\pi\)
\(314\) 826476. 0.473049
\(315\) −19440.0 −0.0110387
\(316\) 87680.0 0.0493950
\(317\) 2.50880e6 1.40222 0.701112 0.713051i \(-0.252687\pi\)
0.701112 + 0.713051i \(0.252687\pi\)
\(318\) −1.82250e6 −1.01065
\(319\) −2.61583e6 −1.43924
\(320\) 166272. 0.0907704
\(321\) 817452. 0.442792
\(322\) −201600. −0.108355
\(323\) −490392. −0.261539
\(324\) 26244.0 0.0138889
\(325\) −1.97078e6 −1.03498
\(326\) −2.11606e6 −1.10277
\(327\) −554994. −0.287024
\(328\) −1.15416e6 −0.592354
\(329\) 746880. 0.380418
\(330\) 182736. 0.0923718
\(331\) −216148. −0.108438 −0.0542190 0.998529i \(-0.517267\pi\)
−0.0542190 + 0.998529i \(0.517267\pi\)
\(332\) 329808. 0.164216
\(333\) −195210. −0.0964698
\(334\) 1.30536e6 0.640271
\(335\) −138408. −0.0673828
\(336\) 408960. 0.197621
\(337\) 3.25263e6 1.56012 0.780062 0.625702i \(-0.215187\pi\)
0.780062 + 0.625702i \(0.215187\pi\)
\(338\) −214506. −0.102129
\(339\) 94338.0 0.0445849
\(340\) 21168.0 0.00993076
\(341\) −2.48160e6 −1.15570
\(342\) 270216. 0.124924
\(343\) 1.28056e6 0.587712
\(344\) 1.62019e6 0.738194
\(345\) −45360.0 −0.0205175
\(346\) 982188. 0.441067
\(347\) −2.93207e6 −1.30723 −0.653613 0.756829i \(-0.726747\pi\)
−0.653613 + 0.756829i \(0.726747\pi\)
\(348\) 166968. 0.0739069
\(349\) 905198. 0.397814 0.198907 0.980018i \(-0.436261\pi\)
0.198907 + 0.980018i \(0.436261\pi\)
\(350\) −741360. −0.323489
\(351\) 465102. 0.201502
\(352\) −812160. −0.349369
\(353\) 1.91786e6 0.819181 0.409590 0.912270i \(-0.365672\pi\)
0.409590 + 0.912270i \(0.365672\pi\)
\(354\) 976536. 0.414171
\(355\) −25488.0 −0.0107341
\(356\) −376344. −0.157384
\(357\) −317520. −0.131856
\(358\) −2.15244e6 −0.887613
\(359\) −2.43698e6 −0.997968 −0.498984 0.866611i \(-0.666293\pi\)
−0.498984 + 0.866611i \(0.666293\pi\)
\(360\) 81648.0 0.0332039
\(361\) −2.16696e6 −0.875152
\(362\) 3.04278e6 1.22039
\(363\) 1.41341e6 0.562989
\(364\) −102080. −0.0403819
\(365\) −246660. −0.0969095
\(366\) −2.14693e6 −0.837752
\(367\) −984064. −0.381380 −0.190690 0.981650i \(-0.561073\pi\)
−0.190690 + 0.981650i \(0.561073\pi\)
\(368\) 954240. 0.367314
\(369\) −556470. −0.212753
\(370\) 86760.0 0.0329470
\(371\) −1.35000e6 −0.509212
\(372\) 158400. 0.0593469
\(373\) 1.70365e6 0.634029 0.317015 0.948421i \(-0.397320\pi\)
0.317015 + 0.948421i \(0.397320\pi\)
\(374\) 2.98469e6 1.10337
\(375\) −335556. −0.123222
\(376\) −3.13690e6 −1.14428
\(377\) 2.95904e6 1.07225
\(378\) 174960. 0.0629810
\(379\) 2.75654e6 0.985749 0.492874 0.870100i \(-0.335946\pi\)
0.492874 + 0.870100i \(0.335946\pi\)
\(380\) −13344.0 −0.00474053
\(381\) −1.53979e6 −0.543438
\(382\) 3.89030e6 1.36403
\(383\) 456576. 0.159044 0.0795218 0.996833i \(-0.474661\pi\)
0.0795218 + 0.996833i \(0.474661\pi\)
\(384\) −1.91117e6 −0.661410
\(385\) 135360. 0.0465413
\(386\) 167028. 0.0570586
\(387\) 781164. 0.265134
\(388\) 197768. 0.0666925
\(389\) −2.00639e6 −0.672268 −0.336134 0.941814i \(-0.609119\pi\)
−0.336134 + 0.941814i \(0.609119\pi\)
\(390\) −206712. −0.0688183
\(391\) −740880. −0.245079
\(392\) −2.55478e6 −0.839726
\(393\) 2.32621e6 0.759745
\(394\) −3.66628e6 −1.18983
\(395\) 131520. 0.0424130
\(396\) −182736. −0.0585580
\(397\) −5.77040e6 −1.83751 −0.918755 0.394828i \(-0.870804\pi\)
−0.918755 + 0.394828i \(0.870804\pi\)
\(398\) −5.27419e6 −1.66897
\(399\) 200160. 0.0629427
\(400\) 3.50910e6 1.09659
\(401\) 3.00626e6 0.933610 0.466805 0.884360i \(-0.345405\pi\)
0.466805 + 0.884360i \(0.345405\pi\)
\(402\) 1.24567e6 0.384449
\(403\) 2.80720e6 0.861015
\(404\) −572136. −0.174400
\(405\) 39366.0 0.0119257
\(406\) 1.11312e6 0.335140
\(407\) 1.35924e6 0.406734
\(408\) 1.33358e6 0.396616
\(409\) 1.53363e6 0.453327 0.226663 0.973973i \(-0.427218\pi\)
0.226663 + 0.973973i \(0.427218\pi\)
\(410\) 247320. 0.0726607
\(411\) 2.70211e6 0.789038
\(412\) 212576. 0.0616980
\(413\) 723360. 0.208679
\(414\) 408240. 0.117062
\(415\) 494712. 0.141004
\(416\) 918720. 0.260285
\(417\) −3.15148e6 −0.887511
\(418\) −1.88150e6 −0.526701
\(419\) −3.87376e6 −1.07795 −0.538973 0.842323i \(-0.681188\pi\)
−0.538973 + 0.842323i \(0.681188\pi\)
\(420\) −8640.00 −0.00238996
\(421\) −1.33307e6 −0.366561 −0.183281 0.983061i \(-0.558672\pi\)
−0.183281 + 0.983061i \(0.558672\pi\)
\(422\) −291000. −0.0795448
\(423\) −1.51243e6 −0.410984
\(424\) 5.67000e6 1.53168
\(425\) −2.72450e6 −0.731668
\(426\) 229392. 0.0612427
\(427\) −1.59032e6 −0.422099
\(428\) 363312. 0.0958673
\(429\) −3.23849e6 −0.849570
\(430\) −347184. −0.0905500
\(431\) 6.45192e6 1.67300 0.836500 0.547967i \(-0.184598\pi\)
0.836500 + 0.547967i \(0.184598\pi\)
\(432\) −828144. −0.213499
\(433\) −4.16577e6 −1.06777 −0.533883 0.845558i \(-0.679268\pi\)
−0.533883 + 0.845558i \(0.679268\pi\)
\(434\) 1.05600e6 0.269116
\(435\) 250452. 0.0634602
\(436\) −246664. −0.0621426
\(437\) 467040. 0.116990
\(438\) 2.21994e6 0.552912
\(439\) 792680. 0.196307 0.0981537 0.995171i \(-0.468706\pi\)
0.0981537 + 0.995171i \(0.468706\pi\)
\(440\) −568512. −0.139994
\(441\) −1.23177e6 −0.301601
\(442\) −3.37630e6 −0.822025
\(443\) −1.39981e6 −0.338891 −0.169446 0.985540i \(-0.554198\pi\)
−0.169446 + 0.985540i \(0.554198\pi\)
\(444\) −86760.0 −0.0208863
\(445\) −564516. −0.135138
\(446\) 5.99683e6 1.42753
\(447\) −947322. −0.224248
\(448\) −1.10848e6 −0.260935
\(449\) 2.99248e6 0.700512 0.350256 0.936654i \(-0.386095\pi\)
0.350256 + 0.936654i \(0.386095\pi\)
\(450\) 1.50125e6 0.349480
\(451\) 3.87468e6 0.897004
\(452\) 41928.0 0.00965291
\(453\) 3.56753e6 0.816812
\(454\) −3.63708e6 −0.828158
\(455\) −153120. −0.0346740
\(456\) −840672. −0.189328
\(457\) 6.29969e6 1.41101 0.705503 0.708707i \(-0.250721\pi\)
0.705503 + 0.708707i \(0.250721\pi\)
\(458\) −8.15956e6 −1.81762
\(459\) 642978. 0.142451
\(460\) −20160.0 −0.00444218
\(461\) 3.40318e6 0.745818 0.372909 0.927868i \(-0.378360\pi\)
0.372909 + 0.927868i \(0.378360\pi\)
\(462\) −1.21824e6 −0.265539
\(463\) −2.23034e6 −0.483524 −0.241762 0.970336i \(-0.577725\pi\)
−0.241762 + 0.970336i \(0.577725\pi\)
\(464\) −5.26877e6 −1.13609
\(465\) 237600. 0.0509582
\(466\) 2.35732e6 0.502867
\(467\) −6.51409e6 −1.38217 −0.691085 0.722773i \(-0.742867\pi\)
−0.691085 + 0.722773i \(0.742867\pi\)
\(468\) 206712. 0.0436266
\(469\) 922720. 0.193704
\(470\) 672192. 0.140362
\(471\) −1.23971e6 −0.257495
\(472\) −3.03811e6 −0.627695
\(473\) −5.43922e6 −1.11785
\(474\) −1.18368e6 −0.241985
\(475\) 1.71748e6 0.349268
\(476\) −141120. −0.0285477
\(477\) 2.73375e6 0.550127
\(478\) 7.95082e6 1.59163
\(479\) 2.39232e6 0.476410 0.238205 0.971215i \(-0.423441\pi\)
0.238205 + 0.971215i \(0.423441\pi\)
\(480\) 77760.0 0.0154047
\(481\) −1.53758e6 −0.303023
\(482\) 5.94056e6 1.16469
\(483\) 302400. 0.0589812
\(484\) 628180. 0.121891
\(485\) 296652. 0.0572655
\(486\) −354294. −0.0680414
\(487\) −6.13089e6 −1.17139 −0.585694 0.810532i \(-0.699178\pi\)
−0.585694 + 0.810532i \(0.699178\pi\)
\(488\) 6.67934e6 1.26965
\(489\) 3.17408e6 0.600269
\(490\) 547452. 0.103004
\(491\) −1.23589e6 −0.231354 −0.115677 0.993287i \(-0.536904\pi\)
−0.115677 + 0.993287i \(0.536904\pi\)
\(492\) −247320. −0.0460624
\(493\) 4.09072e6 0.758022
\(494\) 2.12837e6 0.392400
\(495\) −274104. −0.0502808
\(496\) −4.99840e6 −0.912277
\(497\) 169920. 0.0308570
\(498\) −4.45241e6 −0.804492
\(499\) −9.85496e6 −1.77175 −0.885877 0.463921i \(-0.846442\pi\)
−0.885877 + 0.463921i \(0.846442\pi\)
\(500\) −149136. −0.0266783
\(501\) −1.95804e6 −0.348520
\(502\) −882792. −0.156350
\(503\) 1.16777e6 0.205796 0.102898 0.994692i \(-0.467188\pi\)
0.102898 + 0.994692i \(0.467188\pi\)
\(504\) −544320. −0.0954504
\(505\) −858204. −0.149748
\(506\) −2.84256e6 −0.493552
\(507\) 321759. 0.0555918
\(508\) −684352. −0.117658
\(509\) 1.04941e6 0.179535 0.0897675 0.995963i \(-0.471388\pi\)
0.0897675 + 0.995963i \(0.471388\pi\)
\(510\) −285768. −0.0486506
\(511\) 1.64440e6 0.278583
\(512\) 4.47130e6 0.753804
\(513\) −405324. −0.0680000
\(514\) 2.90149e6 0.484411
\(515\) 318864. 0.0529770
\(516\) 347184. 0.0574031
\(517\) 1.05310e7 1.73278
\(518\) −578400. −0.0947118
\(519\) −1.47328e6 −0.240086
\(520\) 643104. 0.104297
\(521\) −9.61407e6 −1.55172 −0.775859 0.630906i \(-0.782683\pi\)
−0.775859 + 0.630906i \(0.782683\pi\)
\(522\) −2.25407e6 −0.362069
\(523\) 6.96148e6 1.11288 0.556439 0.830888i \(-0.312167\pi\)
0.556439 + 0.830888i \(0.312167\pi\)
\(524\) 1.03387e6 0.164490
\(525\) 1.11204e6 0.176085
\(526\) −4.88146e6 −0.769281
\(527\) 3.88080e6 0.608688
\(528\) 5.76634e6 0.900151
\(529\) −5.73074e6 −0.890373
\(530\) −1.21500e6 −0.187883
\(531\) −1.46480e6 −0.225446
\(532\) 88960.0 0.0136275
\(533\) −4.38306e6 −0.668281
\(534\) 5.08064e6 0.771020
\(535\) 544968. 0.0823164
\(536\) −3.87542e6 −0.582649
\(537\) 3.22866e6 0.483155
\(538\) 2.76664e6 0.412094
\(539\) 8.57675e6 1.27160
\(540\) 17496.0 0.00258199
\(541\) −712690. −0.104691 −0.0523453 0.998629i \(-0.516670\pi\)
−0.0523453 + 0.998629i \(0.516670\pi\)
\(542\) −1.00508e7 −1.46961
\(543\) −4.56417e6 −0.664297
\(544\) 1.27008e6 0.184007
\(545\) −369996. −0.0533588
\(546\) 1.37808e6 0.197830
\(547\) −3.62614e6 −0.518175 −0.259087 0.965854i \(-0.583422\pi\)
−0.259087 + 0.965854i \(0.583422\pi\)
\(548\) 1.20094e6 0.170832
\(549\) 3.22040e6 0.456015
\(550\) −1.04532e7 −1.47347
\(551\) −2.57873e6 −0.361848
\(552\) −1.27008e6 −0.177412
\(553\) −876800. −0.121924
\(554\) −2.40676e6 −0.333164
\(555\) −130140. −0.0179340
\(556\) −1.40066e6 −0.192152
\(557\) 4.84846e6 0.662165 0.331082 0.943602i \(-0.392586\pi\)
0.331082 + 0.943602i \(0.392586\pi\)
\(558\) −2.13840e6 −0.290739
\(559\) 6.15287e6 0.832815
\(560\) 272640. 0.0367383
\(561\) −4.47703e6 −0.600597
\(562\) 1.38586e7 1.85088
\(563\) 8.50405e6 1.13072 0.565360 0.824844i \(-0.308737\pi\)
0.565360 + 0.824844i \(0.308737\pi\)
\(564\) −672192. −0.0889807
\(565\) 62892.0 0.00828847
\(566\) 6.77263e6 0.888621
\(567\) −262440. −0.0342825
\(568\) −713664. −0.0928160
\(569\) 362874. 0.0469867 0.0234934 0.999724i \(-0.492521\pi\)
0.0234934 + 0.999724i \(0.492521\pi\)
\(570\) 180144. 0.0232238
\(571\) 4.11024e6 0.527566 0.263783 0.964582i \(-0.415030\pi\)
0.263783 + 0.964582i \(0.415030\pi\)
\(572\) −1.43933e6 −0.183937
\(573\) −5.83546e6 −0.742486
\(574\) −1.64880e6 −0.208876
\(575\) 2.59476e6 0.327286
\(576\) 2.24467e6 0.281901
\(577\) −7.87680e6 −0.984941 −0.492470 0.870329i \(-0.663906\pi\)
−0.492470 + 0.870329i \(0.663906\pi\)
\(578\) 3.85160e6 0.479536
\(579\) −250542. −0.0310588
\(580\) 111312. 0.0137395
\(581\) −3.29808e6 −0.405341
\(582\) −2.66987e6 −0.326725
\(583\) −1.90350e7 −2.31943
\(584\) −6.90648e6 −0.837963
\(585\) 310068. 0.0374600
\(586\) 5.63324e6 0.677664
\(587\) 603948. 0.0723443 0.0361721 0.999346i \(-0.488484\pi\)
0.0361721 + 0.999346i \(0.488484\pi\)
\(588\) −547452. −0.0652984
\(589\) −2.44640e6 −0.290562
\(590\) 651024. 0.0769958
\(591\) 5.49941e6 0.647661
\(592\) 2.73776e6 0.321064
\(593\) −5.39077e6 −0.629526 −0.314763 0.949170i \(-0.601925\pi\)
−0.314763 + 0.949170i \(0.601925\pi\)
\(594\) 2.46694e6 0.286874
\(595\) −211680. −0.0245125
\(596\) −421032. −0.0485511
\(597\) 7.91129e6 0.908472
\(598\) 3.21552e6 0.367704
\(599\) 4.27999e6 0.487389 0.243695 0.969852i \(-0.421641\pi\)
0.243695 + 0.969852i \(0.421641\pi\)
\(600\) −4.67057e6 −0.529653
\(601\) 1.02483e6 0.115735 0.0578674 0.998324i \(-0.481570\pi\)
0.0578674 + 0.998324i \(0.481570\pi\)
\(602\) 2.31456e6 0.260302
\(603\) −1.86851e6 −0.209267
\(604\) 1.58557e6 0.176845
\(605\) 942270. 0.104661
\(606\) 7.72384e6 0.854381
\(607\) 1.24342e7 1.36976 0.684882 0.728654i \(-0.259854\pi\)
0.684882 + 0.728654i \(0.259854\pi\)
\(608\) −800640. −0.0878372
\(609\) −1.66968e6 −0.182427
\(610\) −1.43129e6 −0.155741
\(611\) −1.19127e7 −1.29095
\(612\) 285768. 0.0308415
\(613\) 4.21506e6 0.453057 0.226528 0.974005i \(-0.427262\pi\)
0.226528 + 0.974005i \(0.427262\pi\)
\(614\) −4.15769e6 −0.445073
\(615\) −370980. −0.0395515
\(616\) 3.79008e6 0.402436
\(617\) −4.40665e6 −0.466010 −0.233005 0.972476i \(-0.574856\pi\)
−0.233005 + 0.972476i \(0.574856\pi\)
\(618\) −2.86978e6 −0.302257
\(619\) 4.80168e6 0.503693 0.251847 0.967767i \(-0.418962\pi\)
0.251847 + 0.967767i \(0.418962\pi\)
\(620\) 105600. 0.0110328
\(621\) −612360. −0.0637203
\(622\) −1.76586e7 −1.83012
\(623\) 3.76344e6 0.388477
\(624\) −6.52291e6 −0.670625
\(625\) 9.42942e6 0.965573
\(626\) −5.31088e6 −0.541664
\(627\) 2.82226e6 0.286700
\(628\) −550984. −0.0557494
\(629\) −2.12562e6 −0.214220
\(630\) 116640. 0.0117084
\(631\) 8.30727e6 0.830587 0.415293 0.909688i \(-0.363679\pi\)
0.415293 + 0.909688i \(0.363679\pi\)
\(632\) 3.68256e6 0.366739
\(633\) 436500. 0.0432987
\(634\) −1.50528e7 −1.48728
\(635\) −1.02653e6 −0.101027
\(636\) 1.21500e6 0.119106
\(637\) −9.70207e6 −0.947361
\(638\) 1.56950e7 1.52654
\(639\) −344088. −0.0333363
\(640\) −1.27411e6 −0.122958
\(641\) 1.76956e7 1.70107 0.850534 0.525921i \(-0.176279\pi\)
0.850534 + 0.525921i \(0.176279\pi\)
\(642\) −4.90471e6 −0.469652
\(643\) −1.28394e7 −1.22466 −0.612330 0.790602i \(-0.709768\pi\)
−0.612330 + 0.790602i \(0.709768\pi\)
\(644\) 134400. 0.0127698
\(645\) 520776. 0.0492892
\(646\) 2.94235e6 0.277404
\(647\) −2.08468e7 −1.95785 −0.978924 0.204226i \(-0.934532\pi\)
−0.978924 + 0.204226i \(0.934532\pi\)
\(648\) 1.10225e6 0.103120
\(649\) 1.01994e7 0.950521
\(650\) 1.18247e7 1.09776
\(651\) −1.58400e6 −0.146488
\(652\) 1.41070e6 0.129962
\(653\) 1.29632e7 1.18968 0.594841 0.803843i \(-0.297215\pi\)
0.594841 + 0.803843i \(0.297215\pi\)
\(654\) 3.32996e6 0.304435
\(655\) 1.55081e6 0.141239
\(656\) 7.80432e6 0.708069
\(657\) −3.32991e6 −0.300967
\(658\) −4.48128e6 −0.403494
\(659\) −5.66862e6 −0.508468 −0.254234 0.967143i \(-0.581823\pi\)
−0.254234 + 0.967143i \(0.581823\pi\)
\(660\) −121824. −0.0108861
\(661\) −3.11430e6 −0.277240 −0.138620 0.990346i \(-0.544267\pi\)
−0.138620 + 0.990346i \(0.544267\pi\)
\(662\) 1.29689e6 0.115016
\(663\) 5.06444e6 0.447454
\(664\) 1.38519e7 1.21924
\(665\) 133440. 0.0117012
\(666\) 1.17126e6 0.102322
\(667\) −3.89592e6 −0.339075
\(668\) −870240. −0.0754567
\(669\) −8.99525e6 −0.777048
\(670\) 830448. 0.0714703
\(671\) −2.24235e7 −1.92264
\(672\) −518400. −0.0442835
\(673\) 105890. 0.00901192 0.00450596 0.999990i \(-0.498566\pi\)
0.00450596 + 0.999990i \(0.498566\pi\)
\(674\) −1.95158e7 −1.65476
\(675\) −2.25188e6 −0.190233
\(676\) 143004. 0.0120360
\(677\) −1.60910e7 −1.34931 −0.674656 0.738132i \(-0.735708\pi\)
−0.674656 + 0.738132i \(0.735708\pi\)
\(678\) −566028. −0.0472894
\(679\) −1.97768e6 −0.164620
\(680\) 889056. 0.0737321
\(681\) 5.45562e6 0.450792
\(682\) 1.48896e7 1.22581
\(683\) 1.60780e7 1.31880 0.659402 0.751791i \(-0.270810\pi\)
0.659402 + 0.751791i \(0.270810\pi\)
\(684\) −180144. −0.0147224
\(685\) 1.80140e6 0.146685
\(686\) −7.68336e6 −0.623363
\(687\) 1.22393e7 0.989386
\(688\) −1.09556e7 −0.882398
\(689\) 2.15325e7 1.72801
\(690\) 272160. 0.0217621
\(691\) −165964. −0.0132227 −0.00661133 0.999978i \(-0.502104\pi\)
−0.00661133 + 0.999978i \(0.502104\pi\)
\(692\) −654792. −0.0519802
\(693\) 1.82736e6 0.144541
\(694\) 1.75924e7 1.38652
\(695\) −2.10098e6 −0.164991
\(696\) 7.01266e6 0.548731
\(697\) −6.05934e6 −0.472436
\(698\) −5.43119e6 −0.421945
\(699\) −3.53597e6 −0.273726
\(700\) 494240. 0.0381235
\(701\) 1.77248e7 1.36234 0.681171 0.732124i \(-0.261471\pi\)
0.681171 + 0.732124i \(0.261471\pi\)
\(702\) −2.79061e6 −0.213726
\(703\) 1.33996e6 0.102259
\(704\) −1.56296e7 −1.18854
\(705\) −1.00829e6 −0.0764032
\(706\) −1.15071e7 −0.868872
\(707\) 5.72136e6 0.430478
\(708\) −651024. −0.0488106
\(709\) −1.06023e7 −0.792112 −0.396056 0.918226i \(-0.629621\pi\)
−0.396056 + 0.918226i \(0.629621\pi\)
\(710\) 152928. 0.0113852
\(711\) 1.77552e6 0.131720
\(712\) −1.58064e7 −1.16852
\(713\) −3.69600e6 −0.272275
\(714\) 1.90512e6 0.139855
\(715\) −2.15899e6 −0.157938
\(716\) 1.43496e6 0.104606
\(717\) −1.19262e7 −0.866373
\(718\) 1.46219e7 1.05850
\(719\) 9.03211e6 0.651579 0.325790 0.945442i \(-0.394370\pi\)
0.325790 + 0.945442i \(0.394370\pi\)
\(720\) −552096. −0.0396902
\(721\) −2.12576e6 −0.152292
\(722\) 1.30018e7 0.928239
\(723\) −8.91085e6 −0.633977
\(724\) −2.02852e6 −0.143825
\(725\) −1.43268e7 −1.01229
\(726\) −8.48043e6 −0.597140
\(727\) 1.87575e7 1.31625 0.658127 0.752907i \(-0.271349\pi\)
0.658127 + 0.752907i \(0.271349\pi\)
\(728\) −4.28736e6 −0.299821
\(729\) 531441. 0.0370370
\(730\) 1.47996e6 0.102788
\(731\) 8.50601e6 0.588752
\(732\) 1.43129e6 0.0987300
\(733\) −1.17773e7 −0.809626 −0.404813 0.914399i \(-0.632663\pi\)
−0.404813 + 0.914399i \(0.632663\pi\)
\(734\) 5.90438e6 0.404515
\(735\) −821178. −0.0560685
\(736\) −1.20960e6 −0.0823090
\(737\) 1.30104e7 0.882308
\(738\) 3.33882e6 0.225659
\(739\) 5.88948e6 0.396703 0.198352 0.980131i \(-0.436441\pi\)
0.198352 + 0.980131i \(0.436441\pi\)
\(740\) −57840.0 −0.00388284
\(741\) −3.19255e6 −0.213596
\(742\) 8.10000e6 0.540101
\(743\) −1.00476e7 −0.667712 −0.333856 0.942624i \(-0.608350\pi\)
−0.333856 + 0.942624i \(0.608350\pi\)
\(744\) 6.65280e6 0.440628
\(745\) −631548. −0.0416884
\(746\) −1.02219e7 −0.672490
\(747\) 6.67861e6 0.437910
\(748\) −1.98979e6 −0.130033
\(749\) −3.63312e6 −0.236633
\(750\) 2.01334e6 0.130696
\(751\) 4.81530e6 0.311547 0.155773 0.987793i \(-0.450213\pi\)
0.155773 + 0.987793i \(0.450213\pi\)
\(752\) 2.12114e7 1.36781
\(753\) 1.32419e6 0.0851064
\(754\) −1.77543e7 −1.13730
\(755\) 2.37835e6 0.151848
\(756\) −116640. −0.00742238
\(757\) 3.12973e6 0.198503 0.0992516 0.995062i \(-0.468355\pi\)
0.0992516 + 0.995062i \(0.468355\pi\)
\(758\) −1.65392e7 −1.04554
\(759\) 4.26384e6 0.268656
\(760\) −560448. −0.0351967
\(761\) −1.17773e7 −0.737197 −0.368599 0.929589i \(-0.620162\pi\)
−0.368599 + 0.929589i \(0.620162\pi\)
\(762\) 9.23875e6 0.576403
\(763\) 2.46664e6 0.153389
\(764\) −2.59354e6 −0.160753
\(765\) 428652. 0.0264820
\(766\) −2.73946e6 −0.168691
\(767\) −1.15376e7 −0.708152
\(768\) 3.48595e6 0.213264
\(769\) −1.49376e6 −0.0910887 −0.0455443 0.998962i \(-0.514502\pi\)
−0.0455443 + 0.998962i \(0.514502\pi\)
\(770\) −812160. −0.0493645
\(771\) −4.35224e6 −0.263680
\(772\) −111352. −0.00672442
\(773\) −2.25125e7 −1.35511 −0.677555 0.735472i \(-0.736960\pi\)
−0.677555 + 0.735472i \(0.736960\pi\)
\(774\) −4.68698e6 −0.281217
\(775\) −1.35916e7 −0.812861
\(776\) 8.30626e6 0.495166
\(777\) 867600. 0.0515545
\(778\) 1.20384e7 0.713048
\(779\) 3.81972e6 0.225521
\(780\) 137808. 0.00811032
\(781\) 2.39587e6 0.140552
\(782\) 4.44528e6 0.259945
\(783\) 3.38110e6 0.197085
\(784\) 1.72752e7 1.00376
\(785\) −826476. −0.0478692
\(786\) −1.39573e7 −0.805831
\(787\) 1.19547e7 0.688022 0.344011 0.938966i \(-0.388214\pi\)
0.344011 + 0.938966i \(0.388214\pi\)
\(788\) 2.44418e6 0.140223
\(789\) 7.32218e6 0.418744
\(790\) −789120. −0.0449858
\(791\) −419280. −0.0238266
\(792\) −7.67491e6 −0.434771
\(793\) 2.53656e7 1.43239
\(794\) 3.46224e7 1.94897
\(795\) 1.82250e6 0.102270
\(796\) 3.51613e6 0.196690
\(797\) 540798. 0.0301571 0.0150785 0.999886i \(-0.495200\pi\)
0.0150785 + 0.999886i \(0.495200\pi\)
\(798\) −1.20096e6 −0.0667608
\(799\) −1.64687e7 −0.912625
\(800\) −4.44816e6 −0.245728
\(801\) −7.62097e6 −0.419690
\(802\) −1.80375e7 −0.990243
\(803\) 2.31860e7 1.26893
\(804\) −830448. −0.0453077
\(805\) 201600. 0.0109648
\(806\) −1.68432e7 −0.913244
\(807\) −4.14995e6 −0.224316
\(808\) −2.40297e7 −1.29485
\(809\) −6.14223e6 −0.329955 −0.164978 0.986297i \(-0.552755\pi\)
−0.164978 + 0.986297i \(0.552755\pi\)
\(810\) −236196. −0.0126491
\(811\) −3.16734e7 −1.69100 −0.845499 0.533977i \(-0.820697\pi\)
−0.845499 + 0.533977i \(0.820697\pi\)
\(812\) −742080. −0.0394967
\(813\) 1.50762e7 0.799956
\(814\) −8.15544e6 −0.431406
\(815\) 2.11606e6 0.111592
\(816\) −9.01757e6 −0.474094
\(817\) −5.36206e6 −0.281046
\(818\) −9.20176e6 −0.480825
\(819\) −2.06712e6 −0.107685
\(820\) −164880. −0.00856315
\(821\) 2.66175e7 1.37819 0.689095 0.724671i \(-0.258008\pi\)
0.689095 + 0.724671i \(0.258008\pi\)
\(822\) −1.62126e7 −0.836901
\(823\) 3.62817e7 1.86719 0.933593 0.358335i \(-0.116655\pi\)
0.933593 + 0.358335i \(0.116655\pi\)
\(824\) 8.92819e6 0.458084
\(825\) 1.56798e7 0.802056
\(826\) −4.34016e6 −0.221338
\(827\) 1.09033e6 0.0554364 0.0277182 0.999616i \(-0.491176\pi\)
0.0277182 + 0.999616i \(0.491176\pi\)
\(828\) −272160. −0.0137958
\(829\) −1.03016e7 −0.520620 −0.260310 0.965525i \(-0.583825\pi\)
−0.260310 + 0.965525i \(0.583825\pi\)
\(830\) −2.96827e6 −0.149558
\(831\) 3.61013e6 0.181351
\(832\) 1.76803e7 0.885483
\(833\) −1.34126e7 −0.669730
\(834\) 1.89089e7 0.941348
\(835\) −1.30536e6 −0.0647909
\(836\) 1.25434e6 0.0620724
\(837\) 3.20760e6 0.158258
\(838\) 2.32425e7 1.14333
\(839\) −1.96134e7 −0.961940 −0.480970 0.876737i \(-0.659715\pi\)
−0.480970 + 0.876737i \(0.659715\pi\)
\(840\) −362880. −0.0177445
\(841\) 999895. 0.0487489
\(842\) 7.99840e6 0.388797
\(843\) −2.07879e7 −1.00749
\(844\) 194000. 0.00937445
\(845\) 214506. 0.0103347
\(846\) 9.07459e6 0.435914
\(847\) −6.28180e6 −0.300868
\(848\) −3.83400e7 −1.83089
\(849\) −1.01589e7 −0.483704
\(850\) 1.63470e7 0.776051
\(851\) 2.02440e6 0.0958236
\(852\) −152928. −0.00721752
\(853\) 3.27565e7 1.54143 0.770717 0.637178i \(-0.219898\pi\)
0.770717 + 0.637178i \(0.219898\pi\)
\(854\) 9.54192e6 0.447704
\(855\) −270216. −0.0126414
\(856\) 1.52591e7 0.711778
\(857\) −2.57953e7 −1.19974 −0.599872 0.800096i \(-0.704782\pi\)
−0.599872 + 0.800096i \(0.704782\pi\)
\(858\) 1.94309e7 0.901105
\(859\) −1.98548e7 −0.918085 −0.459043 0.888414i \(-0.651807\pi\)
−0.459043 + 0.888414i \(0.651807\pi\)
\(860\) 231456. 0.0106714
\(861\) 2.47320e6 0.113698
\(862\) −3.87115e7 −1.77448
\(863\) −673056. −0.0307627 −0.0153813 0.999882i \(-0.504896\pi\)
−0.0153813 + 0.999882i \(0.504896\pi\)
\(864\) 1.04976e6 0.0478416
\(865\) −982188. −0.0446328
\(866\) 2.49946e7 1.13254
\(867\) −5.77740e6 −0.261026
\(868\) −704000. −0.0317156
\(869\) −1.23629e7 −0.555354
\(870\) −1.50271e6 −0.0673097
\(871\) −1.47174e7 −0.657333
\(872\) −1.03599e7 −0.461385
\(873\) 4.00480e6 0.177847
\(874\) −2.80224e6 −0.124087
\(875\) 1.49136e6 0.0658510
\(876\) −1.47996e6 −0.0651613
\(877\) 5.32115e6 0.233618 0.116809 0.993154i \(-0.462733\pi\)
0.116809 + 0.993154i \(0.462733\pi\)
\(878\) −4.75608e6 −0.208215
\(879\) −8.44987e6 −0.368874
\(880\) 3.84422e6 0.167341
\(881\) 2.78891e7 1.21058 0.605291 0.796004i \(-0.293057\pi\)
0.605291 + 0.796004i \(0.293057\pi\)
\(882\) 7.39060e6 0.319896
\(883\) −2.83786e7 −1.22487 −0.612435 0.790521i \(-0.709810\pi\)
−0.612435 + 0.790521i \(0.709810\pi\)
\(884\) 2.25086e6 0.0968765
\(885\) −976536. −0.0419112
\(886\) 8.39887e6 0.359448
\(887\) 4.22678e7 1.80385 0.901925 0.431893i \(-0.142154\pi\)
0.901925 + 0.431893i \(0.142154\pi\)
\(888\) −3.64392e6 −0.155073
\(889\) 6.84352e6 0.290419
\(890\) 3.38710e6 0.143335
\(891\) −3.70040e6 −0.156155
\(892\) −3.99789e6 −0.168236
\(893\) 1.03816e7 0.435649
\(894\) 5.68393e6 0.237851
\(895\) 2.15244e6 0.0898201
\(896\) 8.49408e6 0.353465
\(897\) −4.82328e6 −0.200153
\(898\) −1.79549e7 −0.743005
\(899\) 2.04072e7 0.842140
\(900\) −1.00084e6 −0.0411867
\(901\) 2.97675e7 1.22160
\(902\) −2.32481e7 −0.951417
\(903\) −3.47184e6 −0.141690
\(904\) 1.76098e6 0.0716692
\(905\) −3.04278e6 −0.123495
\(906\) −2.14052e7 −0.866360
\(907\) 3.19526e7 1.28970 0.644849 0.764310i \(-0.276920\pi\)
0.644849 + 0.764310i \(0.276920\pi\)
\(908\) 2.42472e6 0.0975994
\(909\) −1.15858e7 −0.465066
\(910\) 918720. 0.0367773
\(911\) −1.16429e7 −0.464800 −0.232400 0.972620i \(-0.574658\pi\)
−0.232400 + 0.972620i \(0.574658\pi\)
\(912\) 5.68454e6 0.226312
\(913\) −4.65029e7 −1.84630
\(914\) −3.77981e7 −1.49660
\(915\) 2.14693e6 0.0847746
\(916\) 5.43970e6 0.214208
\(917\) −1.03387e7 −0.406016
\(918\) −3.85787e6 −0.151092
\(919\) 1.39844e6 0.0546204 0.0273102 0.999627i \(-0.491306\pi\)
0.0273102 + 0.999627i \(0.491306\pi\)
\(920\) −846720. −0.0329815
\(921\) 6.23653e6 0.242267
\(922\) −2.04191e7 −0.791059
\(923\) −2.71022e6 −0.104713
\(924\) 812160. 0.0312940
\(925\) 7.44449e6 0.286075
\(926\) 1.33820e7 0.512854
\(927\) 4.30466e6 0.164528
\(928\) 6.67872e6 0.254579
\(929\) −1.66792e7 −0.634067 −0.317033 0.948414i \(-0.602687\pi\)
−0.317033 + 0.948414i \(0.602687\pi\)
\(930\) −1.42560e6 −0.0540493
\(931\) 8.45509e6 0.319701
\(932\) −1.57154e6 −0.0592634
\(933\) 2.64879e7 0.996191
\(934\) 3.90846e7 1.46601
\(935\) −2.98469e6 −0.111653
\(936\) 8.68190e6 0.323911
\(937\) −2.47956e7 −0.922625 −0.461312 0.887238i \(-0.652621\pi\)
−0.461312 + 0.887238i \(0.652621\pi\)
\(938\) −5.53632e6 −0.205454
\(939\) 7.96631e6 0.294845
\(940\) −448128. −0.0165418
\(941\) 2.79574e7 1.02925 0.514627 0.857414i \(-0.327930\pi\)
0.514627 + 0.857414i \(0.327930\pi\)
\(942\) 7.43828e6 0.273115
\(943\) 5.77080e6 0.211328
\(944\) 2.05434e7 0.750314
\(945\) −174960. −0.00637322
\(946\) 3.26353e7 1.18566
\(947\) 7.64936e6 0.277173 0.138586 0.990350i \(-0.455744\pi\)
0.138586 + 0.990350i \(0.455744\pi\)
\(948\) 789120. 0.0285182
\(949\) −2.62282e7 −0.945372
\(950\) −1.03049e7 −0.370455
\(951\) 2.25792e7 0.809575
\(952\) −5.92704e6 −0.211956
\(953\) −4.62179e7 −1.64846 −0.824228 0.566257i \(-0.808391\pi\)
−0.824228 + 0.566257i \(0.808391\pi\)
\(954\) −1.64025e7 −0.583498
\(955\) −3.89030e6 −0.138031
\(956\) −5.30054e6 −0.187575
\(957\) −2.35425e7 −0.830945
\(958\) −1.43539e7 −0.505309
\(959\) −1.20094e7 −0.421671
\(960\) 1.49645e6 0.0524063
\(961\) −9.26915e6 −0.323766
\(962\) 9.22548e6 0.321404
\(963\) 7.35707e6 0.255646
\(964\) −3.96038e6 −0.137260
\(965\) −167028. −0.00577392
\(966\) −1.81440e6 −0.0625591
\(967\) 2.08557e7 0.717229 0.358615 0.933486i \(-0.383249\pi\)
0.358615 + 0.933486i \(0.383249\pi\)
\(968\) 2.63836e7 0.904993
\(969\) −4.41353e6 −0.151000
\(970\) −1.77991e6 −0.0607392
\(971\) −4.58152e7 −1.55941 −0.779707 0.626144i \(-0.784632\pi\)
−0.779707 + 0.626144i \(0.784632\pi\)
\(972\) 236196. 0.00801875
\(973\) 1.40066e7 0.474296
\(974\) 3.67853e7 1.24245
\(975\) −1.77370e7 −0.597544
\(976\) −4.51651e7 −1.51767
\(977\) −1.09544e6 −0.0367157 −0.0183578 0.999831i \(-0.505844\pi\)
−0.0183578 + 0.999831i \(0.505844\pi\)
\(978\) −1.90445e7 −0.636682
\(979\) 5.30645e7 1.76949
\(980\) −364968. −0.0121392
\(981\) −4.99495e6 −0.165714
\(982\) 7.41535e6 0.245388
\(983\) 5.25817e7 1.73561 0.867803 0.496909i \(-0.165532\pi\)
0.867803 + 0.496909i \(0.165532\pi\)
\(984\) −1.03874e7 −0.341996
\(985\) 3.66628e6 0.120402
\(986\) −2.45443e7 −0.804004
\(987\) 6.72192e6 0.219634
\(988\) −1.41891e6 −0.0462448
\(989\) −8.10096e6 −0.263358
\(990\) 1.64462e6 0.0533309
\(991\) −4.90389e7 −1.58620 −0.793098 0.609094i \(-0.791533\pi\)
−0.793098 + 0.609094i \(0.791533\pi\)
\(992\) 6.33600e6 0.204426
\(993\) −1.94533e6 −0.0626067
\(994\) −1.01952e6 −0.0327288
\(995\) 5.27419e6 0.168888
\(996\) 2.96827e6 0.0948103
\(997\) 3.05461e6 0.0973237 0.0486618 0.998815i \(-0.484504\pi\)
0.0486618 + 0.998815i \(0.484504\pi\)
\(998\) 5.91297e7 1.87923
\(999\) −1.75689e6 −0.0556969
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 \(a_p\))