Properties

Label 280.6.a.a.1.1
Level $280$
Weight $6$
Character 280.1
Self dual yes
Analytic conductor $44.907$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 280.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(44.9074695476\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 280.1

$q$-expansion

\(f(q)\) \(=\) \(q-12.0000 q^{3} +25.0000 q^{5} -49.0000 q^{7} -99.0000 q^{9} +O(q^{10})\) \(q-12.0000 q^{3} +25.0000 q^{5} -49.0000 q^{7} -99.0000 q^{9} +556.000 q^{11} -354.000 q^{13} -300.000 q^{15} +770.000 q^{17} -2684.00 q^{19} +588.000 q^{21} -1528.00 q^{23} +625.000 q^{25} +4104.00 q^{27} -2418.00 q^{29} +7840.00 q^{31} -6672.00 q^{33} -1225.00 q^{35} -314.000 q^{37} +4248.00 q^{39} -17878.0 q^{41} +16476.0 q^{43} -2475.00 q^{45} +5376.00 q^{47} +2401.00 q^{49} -9240.00 q^{51} +1654.00 q^{53} +13900.0 q^{55} +32208.0 q^{57} -29492.0 q^{59} +27630.0 q^{61} +4851.00 q^{63} -8850.00 q^{65} +57716.0 q^{67} +18336.0 q^{69} +70648.0 q^{71} +74202.0 q^{73} -7500.00 q^{75} -27244.0 q^{77} +74336.0 q^{79} -25191.0 q^{81} +44068.0 q^{83} +19250.0 q^{85} +29016.0 q^{87} +129306. q^{89} +17346.0 q^{91} -94080.0 q^{93} -67100.0 q^{95} -137646. q^{97} -55044.0 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −12.0000 −0.769800 −0.384900 0.922958i \(-0.625764\pi\)
−0.384900 + 0.922958i \(0.625764\pi\)
\(4\) 0 0
\(5\) 25.0000 0.447214
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 0 0
\(9\) −99.0000 −0.407407
\(10\) 0 0
\(11\) 556.000 1.38546 0.692729 0.721198i \(-0.256408\pi\)
0.692729 + 0.721198i \(0.256408\pi\)
\(12\) 0 0
\(13\) −354.000 −0.580958 −0.290479 0.956881i \(-0.593815\pi\)
−0.290479 + 0.956881i \(0.593815\pi\)
\(14\) 0 0
\(15\) −300.000 −0.344265
\(16\) 0 0
\(17\) 770.000 0.646202 0.323101 0.946364i \(-0.395275\pi\)
0.323101 + 0.946364i \(0.395275\pi\)
\(18\) 0 0
\(19\) −2684.00 −1.70568 −0.852842 0.522169i \(-0.825123\pi\)
−0.852842 + 0.522169i \(0.825123\pi\)
\(20\) 0 0
\(21\) 588.000 0.290957
\(22\) 0 0
\(23\) −1528.00 −0.602287 −0.301144 0.953579i \(-0.597368\pi\)
−0.301144 + 0.953579i \(0.597368\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 0 0
\(27\) 4104.00 1.08342
\(28\) 0 0
\(29\) −2418.00 −0.533902 −0.266951 0.963710i \(-0.586016\pi\)
−0.266951 + 0.963710i \(0.586016\pi\)
\(30\) 0 0
\(31\) 7840.00 1.46525 0.732625 0.680632i \(-0.238295\pi\)
0.732625 + 0.680632i \(0.238295\pi\)
\(32\) 0 0
\(33\) −6672.00 −1.06653
\(34\) 0 0
\(35\) −1225.00 −0.169031
\(36\) 0 0
\(37\) −314.000 −0.0377073 −0.0188536 0.999822i \(-0.506002\pi\)
−0.0188536 + 0.999822i \(0.506002\pi\)
\(38\) 0 0
\(39\) 4248.00 0.447222
\(40\) 0 0
\(41\) −17878.0 −1.66096 −0.830480 0.557048i \(-0.811934\pi\)
−0.830480 + 0.557048i \(0.811934\pi\)
\(42\) 0 0
\(43\) 16476.0 1.35888 0.679439 0.733732i \(-0.262223\pi\)
0.679439 + 0.733732i \(0.262223\pi\)
\(44\) 0 0
\(45\) −2475.00 −0.182198
\(46\) 0 0
\(47\) 5376.00 0.354989 0.177494 0.984122i \(-0.443201\pi\)
0.177494 + 0.984122i \(0.443201\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) −9240.00 −0.497447
\(52\) 0 0
\(53\) 1654.00 0.0808809 0.0404404 0.999182i \(-0.487124\pi\)
0.0404404 + 0.999182i \(0.487124\pi\)
\(54\) 0 0
\(55\) 13900.0 0.619595
\(56\) 0 0
\(57\) 32208.0 1.31304
\(58\) 0 0
\(59\) −29492.0 −1.10300 −0.551498 0.834176i \(-0.685944\pi\)
−0.551498 + 0.834176i \(0.685944\pi\)
\(60\) 0 0
\(61\) 27630.0 0.950728 0.475364 0.879789i \(-0.342316\pi\)
0.475364 + 0.879789i \(0.342316\pi\)
\(62\) 0 0
\(63\) 4851.00 0.153986
\(64\) 0 0
\(65\) −8850.00 −0.259812
\(66\) 0 0
\(67\) 57716.0 1.57076 0.785379 0.619015i \(-0.212468\pi\)
0.785379 + 0.619015i \(0.212468\pi\)
\(68\) 0 0
\(69\) 18336.0 0.463641
\(70\) 0 0
\(71\) 70648.0 1.66324 0.831618 0.555348i \(-0.187415\pi\)
0.831618 + 0.555348i \(0.187415\pi\)
\(72\) 0 0
\(73\) 74202.0 1.62970 0.814851 0.579670i \(-0.196818\pi\)
0.814851 + 0.579670i \(0.196818\pi\)
\(74\) 0 0
\(75\) −7500.00 −0.153960
\(76\) 0 0
\(77\) −27244.0 −0.523654
\(78\) 0 0
\(79\) 74336.0 1.34008 0.670041 0.742324i \(-0.266276\pi\)
0.670041 + 0.742324i \(0.266276\pi\)
\(80\) 0 0
\(81\) −25191.0 −0.426612
\(82\) 0 0
\(83\) 44068.0 0.702147 0.351074 0.936348i \(-0.385817\pi\)
0.351074 + 0.936348i \(0.385817\pi\)
\(84\) 0 0
\(85\) 19250.0 0.288990
\(86\) 0 0
\(87\) 29016.0 0.410998
\(88\) 0 0
\(89\) 129306. 1.73039 0.865194 0.501437i \(-0.167195\pi\)
0.865194 + 0.501437i \(0.167195\pi\)
\(90\) 0 0
\(91\) 17346.0 0.219582
\(92\) 0 0
\(93\) −94080.0 −1.12795
\(94\) 0 0
\(95\) −67100.0 −0.762805
\(96\) 0 0
\(97\) −137646. −1.48537 −0.742684 0.669642i \(-0.766448\pi\)
−0.742684 + 0.669642i \(0.766448\pi\)
\(98\) 0 0
\(99\) −55044.0 −0.564445
\(100\) 0 0
\(101\) 52086.0 0.508063 0.254032 0.967196i \(-0.418243\pi\)
0.254032 + 0.967196i \(0.418243\pi\)
\(102\) 0 0
\(103\) 128216. 1.19083 0.595414 0.803419i \(-0.296988\pi\)
0.595414 + 0.803419i \(0.296988\pi\)
\(104\) 0 0
\(105\) 14700.0 0.130120
\(106\) 0 0
\(107\) 113340. 0.957026 0.478513 0.878080i \(-0.341176\pi\)
0.478513 + 0.878080i \(0.341176\pi\)
\(108\) 0 0
\(109\) −138946. −1.12016 −0.560080 0.828439i \(-0.689229\pi\)
−0.560080 + 0.828439i \(0.689229\pi\)
\(110\) 0 0
\(111\) 3768.00 0.0290271
\(112\) 0 0
\(113\) −28046.0 −0.206621 −0.103311 0.994649i \(-0.532944\pi\)
−0.103311 + 0.994649i \(0.532944\pi\)
\(114\) 0 0
\(115\) −38200.0 −0.269351
\(116\) 0 0
\(117\) 35046.0 0.236687
\(118\) 0 0
\(119\) −37730.0 −0.244241
\(120\) 0 0
\(121\) 148085. 0.919491
\(122\) 0 0
\(123\) 214536. 1.27861
\(124\) 0 0
\(125\) 15625.0 0.0894427
\(126\) 0 0
\(127\) −26704.0 −0.146915 −0.0734576 0.997298i \(-0.523403\pi\)
−0.0734576 + 0.997298i \(0.523403\pi\)
\(128\) 0 0
\(129\) −197712. −1.04607
\(130\) 0 0
\(131\) 7028.00 0.0357811 0.0178905 0.999840i \(-0.494305\pi\)
0.0178905 + 0.999840i \(0.494305\pi\)
\(132\) 0 0
\(133\) 131516. 0.644688
\(134\) 0 0
\(135\) 102600. 0.484521
\(136\) 0 0
\(137\) 140202. 0.638194 0.319097 0.947722i \(-0.396620\pi\)
0.319097 + 0.947722i \(0.396620\pi\)
\(138\) 0 0
\(139\) −95876.0 −0.420894 −0.210447 0.977605i \(-0.567492\pi\)
−0.210447 + 0.977605i \(0.567492\pi\)
\(140\) 0 0
\(141\) −64512.0 −0.273270
\(142\) 0 0
\(143\) −196824. −0.804893
\(144\) 0 0
\(145\) −60450.0 −0.238768
\(146\) 0 0
\(147\) −28812.0 −0.109971
\(148\) 0 0
\(149\) −347002. −1.28046 −0.640230 0.768183i \(-0.721161\pi\)
−0.640230 + 0.768183i \(0.721161\pi\)
\(150\) 0 0
\(151\) −270328. −0.964825 −0.482413 0.875944i \(-0.660239\pi\)
−0.482413 + 0.875944i \(0.660239\pi\)
\(152\) 0 0
\(153\) −76230.0 −0.263268
\(154\) 0 0
\(155\) 196000. 0.655280
\(156\) 0 0
\(157\) −151186. −0.489511 −0.244755 0.969585i \(-0.578708\pi\)
−0.244755 + 0.969585i \(0.578708\pi\)
\(158\) 0 0
\(159\) −19848.0 −0.0622621
\(160\) 0 0
\(161\) 74872.0 0.227643
\(162\) 0 0
\(163\) 588148. 1.73387 0.866937 0.498417i \(-0.166085\pi\)
0.866937 + 0.498417i \(0.166085\pi\)
\(164\) 0 0
\(165\) −166800. −0.476965
\(166\) 0 0
\(167\) 61912.0 0.171784 0.0858922 0.996304i \(-0.472626\pi\)
0.0858922 + 0.996304i \(0.472626\pi\)
\(168\) 0 0
\(169\) −245977. −0.662488
\(170\) 0 0
\(171\) 265716. 0.694908
\(172\) 0 0
\(173\) 4862.00 0.0123509 0.00617547 0.999981i \(-0.498034\pi\)
0.00617547 + 0.999981i \(0.498034\pi\)
\(174\) 0 0
\(175\) −30625.0 −0.0755929
\(176\) 0 0
\(177\) 353904. 0.849087
\(178\) 0 0
\(179\) −17964.0 −0.0419054 −0.0209527 0.999780i \(-0.506670\pi\)
−0.0209527 + 0.999780i \(0.506670\pi\)
\(180\) 0 0
\(181\) 228422. 0.518253 0.259126 0.965843i \(-0.416565\pi\)
0.259126 + 0.965843i \(0.416565\pi\)
\(182\) 0 0
\(183\) −331560. −0.731871
\(184\) 0 0
\(185\) −7850.00 −0.0168632
\(186\) 0 0
\(187\) 428120. 0.895285
\(188\) 0 0
\(189\) −201096. −0.409495
\(190\) 0 0
\(191\) −357840. −0.709750 −0.354875 0.934914i \(-0.615477\pi\)
−0.354875 + 0.934914i \(0.615477\pi\)
\(192\) 0 0
\(193\) −494174. −0.954963 −0.477482 0.878642i \(-0.658450\pi\)
−0.477482 + 0.878642i \(0.658450\pi\)
\(194\) 0 0
\(195\) 106200. 0.200004
\(196\) 0 0
\(197\) 595302. 1.09288 0.546439 0.837499i \(-0.315983\pi\)
0.546439 + 0.837499i \(0.315983\pi\)
\(198\) 0 0
\(199\) −261208. −0.467578 −0.233789 0.972287i \(-0.575112\pi\)
−0.233789 + 0.972287i \(0.575112\pi\)
\(200\) 0 0
\(201\) −692592. −1.20917
\(202\) 0 0
\(203\) 118482. 0.201796
\(204\) 0 0
\(205\) −446950. −0.742804
\(206\) 0 0
\(207\) 151272. 0.245376
\(208\) 0 0
\(209\) −1.49230e6 −2.36315
\(210\) 0 0
\(211\) 788564. 1.21936 0.609678 0.792649i \(-0.291299\pi\)
0.609678 + 0.792649i \(0.291299\pi\)
\(212\) 0 0
\(213\) −847776. −1.28036
\(214\) 0 0
\(215\) 411900. 0.607709
\(216\) 0 0
\(217\) −384160. −0.553813
\(218\) 0 0
\(219\) −890424. −1.25455
\(220\) 0 0
\(221\) −272580. −0.375416
\(222\) 0 0
\(223\) −1.35842e6 −1.82924 −0.914620 0.404315i \(-0.867510\pi\)
−0.914620 + 0.404315i \(0.867510\pi\)
\(224\) 0 0
\(225\) −61875.0 −0.0814815
\(226\) 0 0
\(227\) −461068. −0.593882 −0.296941 0.954896i \(-0.595967\pi\)
−0.296941 + 0.954896i \(0.595967\pi\)
\(228\) 0 0
\(229\) 1.25509e6 1.58157 0.790783 0.612096i \(-0.209673\pi\)
0.790783 + 0.612096i \(0.209673\pi\)
\(230\) 0 0
\(231\) 326928. 0.403109
\(232\) 0 0
\(233\) 503914. 0.608088 0.304044 0.952658i \(-0.401663\pi\)
0.304044 + 0.952658i \(0.401663\pi\)
\(234\) 0 0
\(235\) 134400. 0.158756
\(236\) 0 0
\(237\) −892032. −1.03160
\(238\) 0 0
\(239\) 1.50902e6 1.70884 0.854420 0.519583i \(-0.173913\pi\)
0.854420 + 0.519583i \(0.173913\pi\)
\(240\) 0 0
\(241\) −63022.0 −0.0698956 −0.0349478 0.999389i \(-0.511126\pi\)
−0.0349478 + 0.999389i \(0.511126\pi\)
\(242\) 0 0
\(243\) −694980. −0.755017
\(244\) 0 0
\(245\) 60025.0 0.0638877
\(246\) 0 0
\(247\) 950136. 0.990931
\(248\) 0 0
\(249\) −528816. −0.540513
\(250\) 0 0
\(251\) −964820. −0.966634 −0.483317 0.875445i \(-0.660568\pi\)
−0.483317 + 0.875445i \(0.660568\pi\)
\(252\) 0 0
\(253\) −849568. −0.834443
\(254\) 0 0
\(255\) −231000. −0.222465
\(256\) 0 0
\(257\) −495150. −0.467632 −0.233816 0.972281i \(-0.575121\pi\)
−0.233816 + 0.972281i \(0.575121\pi\)
\(258\) 0 0
\(259\) 15386.0 0.0142520
\(260\) 0 0
\(261\) 239382. 0.217516
\(262\) 0 0
\(263\) 2.18092e6 1.94424 0.972121 0.234479i \(-0.0753385\pi\)
0.972121 + 0.234479i \(0.0753385\pi\)
\(264\) 0 0
\(265\) 41350.0 0.0361710
\(266\) 0 0
\(267\) −1.55167e6 −1.33205
\(268\) 0 0
\(269\) −473346. −0.398839 −0.199420 0.979914i \(-0.563906\pi\)
−0.199420 + 0.979914i \(0.563906\pi\)
\(270\) 0 0
\(271\) −2.19234e6 −1.81336 −0.906680 0.421820i \(-0.861391\pi\)
−0.906680 + 0.421820i \(0.861391\pi\)
\(272\) 0 0
\(273\) −208152. −0.169034
\(274\) 0 0
\(275\) 347500. 0.277091
\(276\) 0 0
\(277\) 388502. 0.304224 0.152112 0.988363i \(-0.451393\pi\)
0.152112 + 0.988363i \(0.451393\pi\)
\(278\) 0 0
\(279\) −776160. −0.596954
\(280\) 0 0
\(281\) −75462.0 −0.0570115 −0.0285058 0.999594i \(-0.509075\pi\)
−0.0285058 + 0.999594i \(0.509075\pi\)
\(282\) 0 0
\(283\) 2.17272e6 1.61264 0.806319 0.591481i \(-0.201457\pi\)
0.806319 + 0.591481i \(0.201457\pi\)
\(284\) 0 0
\(285\) 805200. 0.587208
\(286\) 0 0
\(287\) 876022. 0.627784
\(288\) 0 0
\(289\) −826957. −0.582423
\(290\) 0 0
\(291\) 1.65175e6 1.14344
\(292\) 0 0
\(293\) 142902. 0.0972454 0.0486227 0.998817i \(-0.484517\pi\)
0.0486227 + 0.998817i \(0.484517\pi\)
\(294\) 0 0
\(295\) −737300. −0.493275
\(296\) 0 0
\(297\) 2.28182e6 1.50104
\(298\) 0 0
\(299\) 540912. 0.349904
\(300\) 0 0
\(301\) −807324. −0.513608
\(302\) 0 0
\(303\) −625032. −0.391107
\(304\) 0 0
\(305\) 690750. 0.425178
\(306\) 0 0
\(307\) 1.05277e6 0.637512 0.318756 0.947837i \(-0.396735\pi\)
0.318756 + 0.947837i \(0.396735\pi\)
\(308\) 0 0
\(309\) −1.53859e6 −0.916700
\(310\) 0 0
\(311\) −3.11214e6 −1.82456 −0.912279 0.409570i \(-0.865679\pi\)
−0.912279 + 0.409570i \(0.865679\pi\)
\(312\) 0 0
\(313\) −1.95676e6 −1.12895 −0.564477 0.825449i \(-0.690922\pi\)
−0.564477 + 0.825449i \(0.690922\pi\)
\(314\) 0 0
\(315\) 121275. 0.0688644
\(316\) 0 0
\(317\) 2.74800e6 1.53592 0.767959 0.640499i \(-0.221272\pi\)
0.767959 + 0.640499i \(0.221272\pi\)
\(318\) 0 0
\(319\) −1.34441e6 −0.739698
\(320\) 0 0
\(321\) −1.36008e6 −0.736719
\(322\) 0 0
\(323\) −2.06668e6 −1.10222
\(324\) 0 0
\(325\) −221250. −0.116192
\(326\) 0 0
\(327\) 1.66735e6 0.862299
\(328\) 0 0
\(329\) −263424. −0.134173
\(330\) 0 0
\(331\) 2.23019e6 1.11885 0.559425 0.828881i \(-0.311022\pi\)
0.559425 + 0.828881i \(0.311022\pi\)
\(332\) 0 0
\(333\) 31086.0 0.0153622
\(334\) 0 0
\(335\) 1.44290e6 0.702464
\(336\) 0 0
\(337\) 3.13439e6 1.50341 0.751706 0.659499i \(-0.229231\pi\)
0.751706 + 0.659499i \(0.229231\pi\)
\(338\) 0 0
\(339\) 336552. 0.159057
\(340\) 0 0
\(341\) 4.35904e6 2.03004
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) 0 0
\(345\) 458400. 0.207347
\(346\) 0 0
\(347\) 2.43003e6 1.08340 0.541698 0.840573i \(-0.317781\pi\)
0.541698 + 0.840573i \(0.317781\pi\)
\(348\) 0 0
\(349\) 3.46062e6 1.52086 0.760432 0.649417i \(-0.224987\pi\)
0.760432 + 0.649417i \(0.224987\pi\)
\(350\) 0 0
\(351\) −1.45282e6 −0.629423
\(352\) 0 0
\(353\) −1.25627e6 −0.536595 −0.268297 0.963336i \(-0.586461\pi\)
−0.268297 + 0.963336i \(0.586461\pi\)
\(354\) 0 0
\(355\) 1.76620e6 0.743822
\(356\) 0 0
\(357\) 452760. 0.188017
\(358\) 0 0
\(359\) 878712. 0.359841 0.179920 0.983681i \(-0.442416\pi\)
0.179920 + 0.983681i \(0.442416\pi\)
\(360\) 0 0
\(361\) 4.72776e6 1.90936
\(362\) 0 0
\(363\) −1.77702e6 −0.707825
\(364\) 0 0
\(365\) 1.85505e6 0.728825
\(366\) 0 0
\(367\) 234880. 0.0910292 0.0455146 0.998964i \(-0.485507\pi\)
0.0455146 + 0.998964i \(0.485507\pi\)
\(368\) 0 0
\(369\) 1.76992e6 0.676688
\(370\) 0 0
\(371\) −81046.0 −0.0305701
\(372\) 0 0
\(373\) 97430.0 0.0362594 0.0181297 0.999836i \(-0.494229\pi\)
0.0181297 + 0.999836i \(0.494229\pi\)
\(374\) 0 0
\(375\) −187500. −0.0688530
\(376\) 0 0
\(377\) 855972. 0.310175
\(378\) 0 0
\(379\) −1.99722e6 −0.714213 −0.357107 0.934064i \(-0.616237\pi\)
−0.357107 + 0.934064i \(0.616237\pi\)
\(380\) 0 0
\(381\) 320448. 0.113095
\(382\) 0 0
\(383\) 119664. 0.0416837 0.0208419 0.999783i \(-0.493365\pi\)
0.0208419 + 0.999783i \(0.493365\pi\)
\(384\) 0 0
\(385\) −681100. −0.234185
\(386\) 0 0
\(387\) −1.63112e6 −0.553617
\(388\) 0 0
\(389\) 327670. 0.109790 0.0548950 0.998492i \(-0.482518\pi\)
0.0548950 + 0.998492i \(0.482518\pi\)
\(390\) 0 0
\(391\) −1.17656e6 −0.389199
\(392\) 0 0
\(393\) −84336.0 −0.0275443
\(394\) 0 0
\(395\) 1.85840e6 0.599303
\(396\) 0 0
\(397\) 4.46653e6 1.42231 0.711154 0.703036i \(-0.248173\pi\)
0.711154 + 0.703036i \(0.248173\pi\)
\(398\) 0 0
\(399\) −1.57819e6 −0.496281
\(400\) 0 0
\(401\) −1.83249e6 −0.569091 −0.284545 0.958663i \(-0.591843\pi\)
−0.284545 + 0.958663i \(0.591843\pi\)
\(402\) 0 0
\(403\) −2.77536e6 −0.851249
\(404\) 0 0
\(405\) −629775. −0.190787
\(406\) 0 0
\(407\) −174584. −0.0522418
\(408\) 0 0
\(409\) −5.59393e6 −1.65352 −0.826758 0.562558i \(-0.809817\pi\)
−0.826758 + 0.562558i \(0.809817\pi\)
\(410\) 0 0
\(411\) −1.68242e6 −0.491282
\(412\) 0 0
\(413\) 1.44511e6 0.416894
\(414\) 0 0
\(415\) 1.10170e6 0.314010
\(416\) 0 0
\(417\) 1.15051e6 0.324004
\(418\) 0 0
\(419\) 562772. 0.156602 0.0783010 0.996930i \(-0.475050\pi\)
0.0783010 + 0.996930i \(0.475050\pi\)
\(420\) 0 0
\(421\) 679158. 0.186752 0.0933761 0.995631i \(-0.470234\pi\)
0.0933761 + 0.995631i \(0.470234\pi\)
\(422\) 0 0
\(423\) −532224. −0.144625
\(424\) 0 0
\(425\) 481250. 0.129240
\(426\) 0 0
\(427\) −1.35387e6 −0.359341
\(428\) 0 0
\(429\) 2.36189e6 0.619607
\(430\) 0 0
\(431\) 5.89466e6 1.52850 0.764250 0.644920i \(-0.223109\pi\)
0.764250 + 0.644920i \(0.223109\pi\)
\(432\) 0 0
\(433\) −1.64499e6 −0.421642 −0.210821 0.977525i \(-0.567614\pi\)
−0.210821 + 0.977525i \(0.567614\pi\)
\(434\) 0 0
\(435\) 725400. 0.183804
\(436\) 0 0
\(437\) 4.10115e6 1.02731
\(438\) 0 0
\(439\) −4.20138e6 −1.04047 −0.520237 0.854022i \(-0.674156\pi\)
−0.520237 + 0.854022i \(0.674156\pi\)
\(440\) 0 0
\(441\) −237699. −0.0582011
\(442\) 0 0
\(443\) −565684. −0.136951 −0.0684754 0.997653i \(-0.521813\pi\)
−0.0684754 + 0.997653i \(0.521813\pi\)
\(444\) 0 0
\(445\) 3.23265e6 0.773853
\(446\) 0 0
\(447\) 4.16402e6 0.985699
\(448\) 0 0
\(449\) 648386. 0.151781 0.0758906 0.997116i \(-0.475820\pi\)
0.0758906 + 0.997116i \(0.475820\pi\)
\(450\) 0 0
\(451\) −9.94017e6 −2.30119
\(452\) 0 0
\(453\) 3.24394e6 0.742723
\(454\) 0 0
\(455\) 433650. 0.0981999
\(456\) 0 0
\(457\) −1.74713e6 −0.391322 −0.195661 0.980672i \(-0.562685\pi\)
−0.195661 + 0.980672i \(0.562685\pi\)
\(458\) 0 0
\(459\) 3.16008e6 0.700110
\(460\) 0 0
\(461\) −317378. −0.0695544 −0.0347772 0.999395i \(-0.511072\pi\)
−0.0347772 + 0.999395i \(0.511072\pi\)
\(462\) 0 0
\(463\) −5.84678e6 −1.26755 −0.633774 0.773518i \(-0.718495\pi\)
−0.633774 + 0.773518i \(0.718495\pi\)
\(464\) 0 0
\(465\) −2.35200e6 −0.504435
\(466\) 0 0
\(467\) −3.67257e6 −0.779252 −0.389626 0.920973i \(-0.627396\pi\)
−0.389626 + 0.920973i \(0.627396\pi\)
\(468\) 0 0
\(469\) −2.82808e6 −0.593691
\(470\) 0 0
\(471\) 1.81423e6 0.376826
\(472\) 0 0
\(473\) 9.16066e6 1.88267
\(474\) 0 0
\(475\) −1.67750e6 −0.341137
\(476\) 0 0
\(477\) −163746. −0.0329515
\(478\) 0 0
\(479\) −1.66333e6 −0.331237 −0.165619 0.986190i \(-0.552962\pi\)
−0.165619 + 0.986190i \(0.552962\pi\)
\(480\) 0 0
\(481\) 111156. 0.0219064
\(482\) 0 0
\(483\) −898464. −0.175240
\(484\) 0 0
\(485\) −3.44115e6 −0.664277
\(486\) 0 0
\(487\) 4.34505e6 0.830180 0.415090 0.909780i \(-0.363750\pi\)
0.415090 + 0.909780i \(0.363750\pi\)
\(488\) 0 0
\(489\) −7.05778e6 −1.33474
\(490\) 0 0
\(491\) −6.65016e6 −1.24488 −0.622442 0.782666i \(-0.713859\pi\)
−0.622442 + 0.782666i \(0.713859\pi\)
\(492\) 0 0
\(493\) −1.86186e6 −0.345008
\(494\) 0 0
\(495\) −1.37610e6 −0.252428
\(496\) 0 0
\(497\) −3.46175e6 −0.628644
\(498\) 0 0
\(499\) 742996. 0.133578 0.0667890 0.997767i \(-0.478725\pi\)
0.0667890 + 0.997767i \(0.478725\pi\)
\(500\) 0 0
\(501\) −742944. −0.132240
\(502\) 0 0
\(503\) −5.57126e6 −0.981823 −0.490911 0.871209i \(-0.663336\pi\)
−0.490911 + 0.871209i \(0.663336\pi\)
\(504\) 0 0
\(505\) 1.30215e6 0.227213
\(506\) 0 0
\(507\) 2.95172e6 0.509983
\(508\) 0 0
\(509\) −5.91247e6 −1.01152 −0.505760 0.862674i \(-0.668788\pi\)
−0.505760 + 0.862674i \(0.668788\pi\)
\(510\) 0 0
\(511\) −3.63590e6 −0.615970
\(512\) 0 0
\(513\) −1.10151e7 −1.84798
\(514\) 0 0
\(515\) 3.20540e6 0.532555
\(516\) 0 0
\(517\) 2.98906e6 0.491822
\(518\) 0 0
\(519\) −58344.0 −0.00950775
\(520\) 0 0
\(521\) 6.34065e6 1.02339 0.511693 0.859168i \(-0.329019\pi\)
0.511693 + 0.859168i \(0.329019\pi\)
\(522\) 0 0
\(523\) 118300. 0.0189117 0.00945585 0.999955i \(-0.496990\pi\)
0.00945585 + 0.999955i \(0.496990\pi\)
\(524\) 0 0
\(525\) 367500. 0.0581914
\(526\) 0 0
\(527\) 6.03680e6 0.946848
\(528\) 0 0
\(529\) −4.10156e6 −0.637250
\(530\) 0 0
\(531\) 2.91971e6 0.449369
\(532\) 0 0
\(533\) 6.32881e6 0.964949
\(534\) 0 0
\(535\) 2.83350e6 0.427995
\(536\) 0 0
\(537\) 215568. 0.0322588
\(538\) 0 0
\(539\) 1.33496e6 0.197922
\(540\) 0 0
\(541\) 5.36248e6 0.787721 0.393860 0.919170i \(-0.371139\pi\)
0.393860 + 0.919170i \(0.371139\pi\)
\(542\) 0 0
\(543\) −2.74106e6 −0.398951
\(544\) 0 0
\(545\) −3.47365e6 −0.500950
\(546\) 0 0
\(547\) −579116. −0.0827556 −0.0413778 0.999144i \(-0.513175\pi\)
−0.0413778 + 0.999144i \(0.513175\pi\)
\(548\) 0 0
\(549\) −2.73537e6 −0.387334
\(550\) 0 0
\(551\) 6.48991e6 0.910667
\(552\) 0 0
\(553\) −3.64246e6 −0.506503
\(554\) 0 0
\(555\) 94200.0 0.0129813
\(556\) 0 0
\(557\) 6.61880e6 0.903943 0.451972 0.892032i \(-0.350721\pi\)
0.451972 + 0.892032i \(0.350721\pi\)
\(558\) 0 0
\(559\) −5.83250e6 −0.789452
\(560\) 0 0
\(561\) −5.13744e6 −0.689191
\(562\) 0 0
\(563\) −2.65907e6 −0.353556 −0.176778 0.984251i \(-0.556567\pi\)
−0.176778 + 0.984251i \(0.556567\pi\)
\(564\) 0 0
\(565\) −701150. −0.0924038
\(566\) 0 0
\(567\) 1.23436e6 0.161244
\(568\) 0 0
\(569\) −1.12650e7 −1.45865 −0.729324 0.684169i \(-0.760165\pi\)
−0.729324 + 0.684169i \(0.760165\pi\)
\(570\) 0 0
\(571\) −4.05242e6 −0.520145 −0.260072 0.965589i \(-0.583746\pi\)
−0.260072 + 0.965589i \(0.583746\pi\)
\(572\) 0 0
\(573\) 4.29408e6 0.546366
\(574\) 0 0
\(575\) −955000. −0.120457
\(576\) 0 0
\(577\) −5.07566e6 −0.634678 −0.317339 0.948312i \(-0.602789\pi\)
−0.317339 + 0.948312i \(0.602789\pi\)
\(578\) 0 0
\(579\) 5.93009e6 0.735131
\(580\) 0 0
\(581\) −2.15933e6 −0.265387
\(582\) 0 0
\(583\) 919624. 0.112057
\(584\) 0 0
\(585\) 876150. 0.105849
\(586\) 0 0
\(587\) −9.07079e6 −1.08655 −0.543275 0.839555i \(-0.682816\pi\)
−0.543275 + 0.839555i \(0.682816\pi\)
\(588\) 0 0
\(589\) −2.10426e7 −2.49925
\(590\) 0 0
\(591\) −7.14362e6 −0.841298
\(592\) 0 0
\(593\) 1.47793e7 1.72590 0.862951 0.505288i \(-0.168614\pi\)
0.862951 + 0.505288i \(0.168614\pi\)
\(594\) 0 0
\(595\) −943250. −0.109228
\(596\) 0 0
\(597\) 3.13450e6 0.359941
\(598\) 0 0
\(599\) 9.06212e6 1.03196 0.515980 0.856601i \(-0.327428\pi\)
0.515980 + 0.856601i \(0.327428\pi\)
\(600\) 0 0
\(601\) −2.65482e6 −0.299812 −0.149906 0.988700i \(-0.547897\pi\)
−0.149906 + 0.988700i \(0.547897\pi\)
\(602\) 0 0
\(603\) −5.71388e6 −0.639938
\(604\) 0 0
\(605\) 3.70212e6 0.411209
\(606\) 0 0
\(607\) 1.52930e7 1.68470 0.842349 0.538932i \(-0.181172\pi\)
0.842349 + 0.538932i \(0.181172\pi\)
\(608\) 0 0
\(609\) −1.42178e6 −0.155343
\(610\) 0 0
\(611\) −1.90310e6 −0.206234
\(612\) 0 0
\(613\) 1.49070e7 1.60228 0.801139 0.598479i \(-0.204228\pi\)
0.801139 + 0.598479i \(0.204228\pi\)
\(614\) 0 0
\(615\) 5.36340e6 0.571811
\(616\) 0 0
\(617\) 5.12030e6 0.541480 0.270740 0.962653i \(-0.412732\pi\)
0.270740 + 0.962653i \(0.412732\pi\)
\(618\) 0 0
\(619\) −4.83140e6 −0.506811 −0.253405 0.967360i \(-0.581551\pi\)
−0.253405 + 0.967360i \(0.581551\pi\)
\(620\) 0 0
\(621\) −6.27091e6 −0.652532
\(622\) 0 0
\(623\) −6.33599e6 −0.654025
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 0 0
\(627\) 1.79076e7 1.81915
\(628\) 0 0
\(629\) −241780. −0.0243665
\(630\) 0 0
\(631\) 5.78212e6 0.578114 0.289057 0.957312i \(-0.406658\pi\)
0.289057 + 0.957312i \(0.406658\pi\)
\(632\) 0 0
\(633\) −9.46277e6 −0.938661
\(634\) 0 0
\(635\) −667600. −0.0657025
\(636\) 0 0
\(637\) −849954. −0.0829940
\(638\) 0 0
\(639\) −6.99415e6 −0.677615
\(640\) 0 0
\(641\) −1.65691e7 −1.59277 −0.796386 0.604789i \(-0.793257\pi\)
−0.796386 + 0.604789i \(0.793257\pi\)
\(642\) 0 0
\(643\) −9.28491e6 −0.885626 −0.442813 0.896614i \(-0.646019\pi\)
−0.442813 + 0.896614i \(0.646019\pi\)
\(644\) 0 0
\(645\) −4.94280e6 −0.467815
\(646\) 0 0
\(647\) −1.31505e7 −1.23504 −0.617519 0.786556i \(-0.711862\pi\)
−0.617519 + 0.786556i \(0.711862\pi\)
\(648\) 0 0
\(649\) −1.63976e7 −1.52815
\(650\) 0 0
\(651\) 4.60992e6 0.426325
\(652\) 0 0
\(653\) −6.28207e6 −0.576527 −0.288263 0.957551i \(-0.593078\pi\)
−0.288263 + 0.957551i \(0.593078\pi\)
\(654\) 0 0
\(655\) 175700. 0.0160018
\(656\) 0 0
\(657\) −7.34600e6 −0.663953
\(658\) 0 0
\(659\) −2.16007e7 −1.93756 −0.968779 0.247927i \(-0.920251\pi\)
−0.968779 + 0.247927i \(0.920251\pi\)
\(660\) 0 0
\(661\) −5.79235e6 −0.515645 −0.257823 0.966192i \(-0.583005\pi\)
−0.257823 + 0.966192i \(0.583005\pi\)
\(662\) 0 0
\(663\) 3.27096e6 0.288996
\(664\) 0 0
\(665\) 3.28790e6 0.288313
\(666\) 0 0
\(667\) 3.69470e6 0.321562
\(668\) 0 0
\(669\) 1.63010e7 1.40815
\(670\) 0 0
\(671\) 1.53623e7 1.31719
\(672\) 0 0
\(673\) 1.45071e7 1.23465 0.617324 0.786709i \(-0.288217\pi\)
0.617324 + 0.786709i \(0.288217\pi\)
\(674\) 0 0
\(675\) 2.56500e6 0.216685
\(676\) 0 0
\(677\) 1.66775e7 1.39849 0.699243 0.714884i \(-0.253520\pi\)
0.699243 + 0.714884i \(0.253520\pi\)
\(678\) 0 0
\(679\) 6.74465e6 0.561417
\(680\) 0 0
\(681\) 5.53282e6 0.457171
\(682\) 0 0
\(683\) 3.35555e6 0.275240 0.137620 0.990485i \(-0.456055\pi\)
0.137620 + 0.990485i \(0.456055\pi\)
\(684\) 0 0
\(685\) 3.50505e6 0.285409
\(686\) 0 0
\(687\) −1.50611e7 −1.21749
\(688\) 0 0
\(689\) −585516. −0.0469884
\(690\) 0 0
\(691\) 80036.0 0.00637662 0.00318831 0.999995i \(-0.498985\pi\)
0.00318831 + 0.999995i \(0.498985\pi\)
\(692\) 0 0
\(693\) 2.69716e6 0.213340
\(694\) 0 0
\(695\) −2.39690e6 −0.188230
\(696\) 0 0
\(697\) −1.37661e7 −1.07332
\(698\) 0 0
\(699\) −6.04697e6 −0.468107
\(700\) 0 0
\(701\) 1.26403e7 0.971544 0.485772 0.874086i \(-0.338539\pi\)
0.485772 + 0.874086i \(0.338539\pi\)
\(702\) 0 0
\(703\) 842776. 0.0643167
\(704\) 0 0
\(705\) −1.61280e6 −0.122210
\(706\) 0 0
\(707\) −2.55221e6 −0.192030
\(708\) 0 0
\(709\) 1.03203e7 0.771043 0.385521 0.922699i \(-0.374022\pi\)
0.385521 + 0.922699i \(0.374022\pi\)
\(710\) 0 0
\(711\) −7.35926e6 −0.545959
\(712\) 0 0
\(713\) −1.19795e7 −0.882502
\(714\) 0 0
\(715\) −4.92060e6 −0.359959
\(716\) 0 0
\(717\) −1.81083e7 −1.31547
\(718\) 0 0
\(719\) 1.32330e7 0.954630 0.477315 0.878732i \(-0.341610\pi\)
0.477315 + 0.878732i \(0.341610\pi\)
\(720\) 0 0
\(721\) −6.28258e6 −0.450091
\(722\) 0 0
\(723\) 756264. 0.0538056
\(724\) 0 0
\(725\) −1.51125e6 −0.106780
\(726\) 0 0
\(727\) 1.89447e6 0.132939 0.0664695 0.997788i \(-0.478827\pi\)
0.0664695 + 0.997788i \(0.478827\pi\)
\(728\) 0 0
\(729\) 1.44612e7 1.00782
\(730\) 0 0
\(731\) 1.26865e7 0.878110
\(732\) 0 0
\(733\) −3.25023e6 −0.223436 −0.111718 0.993740i \(-0.535635\pi\)
−0.111718 + 0.993740i \(0.535635\pi\)
\(734\) 0 0
\(735\) −720300. −0.0491807
\(736\) 0 0
\(737\) 3.20901e7 2.17622
\(738\) 0 0
\(739\) 2.56366e7 1.72683 0.863415 0.504495i \(-0.168321\pi\)
0.863415 + 0.504495i \(0.168321\pi\)
\(740\) 0 0
\(741\) −1.14016e7 −0.762819
\(742\) 0 0
\(743\) −1.10332e7 −0.733209 −0.366605 0.930377i \(-0.619480\pi\)
−0.366605 + 0.930377i \(0.619480\pi\)
\(744\) 0 0
\(745\) −8.67505e6 −0.572640
\(746\) 0 0
\(747\) −4.36273e6 −0.286060
\(748\) 0 0
\(749\) −5.55366e6 −0.361722
\(750\) 0 0
\(751\) 1.75977e7 1.13856 0.569279 0.822144i \(-0.307222\pi\)
0.569279 + 0.822144i \(0.307222\pi\)
\(752\) 0 0
\(753\) 1.15778e7 0.744115
\(754\) 0 0
\(755\) −6.75820e6 −0.431483
\(756\) 0 0
\(757\) −9.25444e6 −0.586963 −0.293481 0.955965i \(-0.594814\pi\)
−0.293481 + 0.955965i \(0.594814\pi\)
\(758\) 0 0
\(759\) 1.01948e7 0.642355
\(760\) 0 0
\(761\) 1.36640e7 0.855293 0.427647 0.903946i \(-0.359343\pi\)
0.427647 + 0.903946i \(0.359343\pi\)
\(762\) 0 0
\(763\) 6.80835e6 0.423380
\(764\) 0 0
\(765\) −1.90575e6 −0.117737
\(766\) 0 0
\(767\) 1.04402e7 0.640795
\(768\) 0 0
\(769\) −2.98498e7 −1.82023 −0.910114 0.414357i \(-0.864006\pi\)
−0.910114 + 0.414357i \(0.864006\pi\)
\(770\) 0 0
\(771\) 5.94180e6 0.359983
\(772\) 0 0
\(773\) 2.32878e7 1.40178 0.700891 0.713269i \(-0.252786\pi\)
0.700891 + 0.713269i \(0.252786\pi\)
\(774\) 0 0
\(775\) 4.90000e6 0.293050
\(776\) 0 0
\(777\) −184632. −0.0109712
\(778\) 0 0
\(779\) 4.79846e7 2.83307
\(780\) 0 0
\(781\) 3.92803e7 2.30434
\(782\) 0 0
\(783\) −9.92347e6 −0.578441
\(784\) 0 0
\(785\) −3.77965e6 −0.218916
\(786\) 0 0
\(787\) −1.01691e7 −0.585259 −0.292629 0.956226i \(-0.594530\pi\)
−0.292629 + 0.956226i \(0.594530\pi\)
\(788\) 0 0
\(789\) −2.61710e7 −1.49668
\(790\) 0 0
\(791\) 1.37425e6 0.0780955
\(792\) 0 0
\(793\) −9.78102e6 −0.552333
\(794\) 0 0
\(795\) −496200. −0.0278445
\(796\) 0 0
\(797\) 2.43192e6 0.135614 0.0678068 0.997698i \(-0.478400\pi\)
0.0678068 + 0.997698i \(0.478400\pi\)
\(798\) 0 0
\(799\) 4.13952e6 0.229395
\(800\) 0 0
\(801\) −1.28013e7 −0.704973
\(802\) 0 0
\(803\) 4.12563e7 2.25788
\(804\) 0 0
\(805\) 1.87180e6 0.101805
\(806\) 0 0
\(807\) 5.68015e6 0.307027
\(808\) 0 0
\(809\) 1.41960e7 0.762595 0.381298 0.924452i \(-0.375477\pi\)
0.381298 + 0.924452i \(0.375477\pi\)
\(810\) 0 0
\(811\) 1.75548e6 0.0937227 0.0468613 0.998901i \(-0.485078\pi\)
0.0468613 + 0.998901i \(0.485078\pi\)
\(812\) 0 0
\(813\) 2.63080e7 1.39592
\(814\) 0 0
\(815\) 1.47037e7 0.775412
\(816\) 0 0
\(817\) −4.42216e7 −2.31782
\(818\) 0 0
\(819\) −1.71725e6 −0.0894592
\(820\) 0 0
\(821\) 1.69715e7 0.878742 0.439371 0.898306i \(-0.355201\pi\)
0.439371 + 0.898306i \(0.355201\pi\)
\(822\) 0 0
\(823\) −8.85241e6 −0.455577 −0.227789 0.973711i \(-0.573149\pi\)
−0.227789 + 0.973711i \(0.573149\pi\)
\(824\) 0 0
\(825\) −4.17000e6 −0.213305
\(826\) 0 0
\(827\) 2.48418e7 1.26304 0.631522 0.775358i \(-0.282430\pi\)
0.631522 + 0.775358i \(0.282430\pi\)
\(828\) 0 0
\(829\) 3.55691e6 0.179757 0.0898787 0.995953i \(-0.471352\pi\)
0.0898787 + 0.995953i \(0.471352\pi\)
\(830\) 0 0
\(831\) −4.66202e6 −0.234192
\(832\) 0 0
\(833\) 1.84877e6 0.0923146
\(834\) 0 0
\(835\) 1.54780e6 0.0768243
\(836\) 0 0
\(837\) 3.21754e7 1.58749
\(838\) 0 0
\(839\) 2.51401e7 1.23300 0.616499 0.787356i \(-0.288551\pi\)
0.616499 + 0.787356i \(0.288551\pi\)
\(840\) 0 0
\(841\) −1.46644e7 −0.714949
\(842\) 0 0
\(843\) 905544. 0.0438875
\(844\) 0 0
\(845\) −6.14942e6 −0.296273
\(846\) 0 0
\(847\) −7.25616e6 −0.347535
\(848\) 0 0
\(849\) −2.60726e7 −1.24141
\(850\) 0 0
\(851\) 479792. 0.0227106
\(852\) 0 0
\(853\) −1.01242e7 −0.476419 −0.238209 0.971214i \(-0.576560\pi\)
−0.238209 + 0.971214i \(0.576560\pi\)
\(854\) 0 0
\(855\) 6.64290e6 0.310772
\(856\) 0 0
\(857\) −1.05522e7 −0.490784 −0.245392 0.969424i \(-0.578917\pi\)
−0.245392 + 0.969424i \(0.578917\pi\)
\(858\) 0 0
\(859\) 3.37758e7 1.56179 0.780894 0.624663i \(-0.214764\pi\)
0.780894 + 0.624663i \(0.214764\pi\)
\(860\) 0 0
\(861\) −1.05123e7 −0.483268
\(862\) 0 0
\(863\) −3.12652e7 −1.42901 −0.714503 0.699633i \(-0.753347\pi\)
−0.714503 + 0.699633i \(0.753347\pi\)
\(864\) 0 0
\(865\) 121550. 0.00552350
\(866\) 0 0
\(867\) 9.92348e6 0.448349
\(868\) 0 0
\(869\) 4.13308e7 1.85663
\(870\) 0 0
\(871\) −2.04315e7 −0.912545
\(872\) 0 0
\(873\) 1.36270e7 0.605150
\(874\) 0 0
\(875\) −765625. −0.0338062
\(876\) 0 0
\(877\) −2.89921e7 −1.27286 −0.636430 0.771334i \(-0.719590\pi\)
−0.636430 + 0.771334i \(0.719590\pi\)
\(878\) 0 0
\(879\) −1.71482e6 −0.0748596
\(880\) 0 0
\(881\) −6.43211e6 −0.279199 −0.139599 0.990208i \(-0.544581\pi\)
−0.139599 + 0.990208i \(0.544581\pi\)
\(882\) 0 0
\(883\) −2.41164e7 −1.04090 −0.520452 0.853891i \(-0.674236\pi\)
−0.520452 + 0.853891i \(0.674236\pi\)
\(884\) 0 0
\(885\) 8.84760e6 0.379723
\(886\) 0 0
\(887\) 4.16359e6 0.177688 0.0888442 0.996046i \(-0.471683\pi\)
0.0888442 + 0.996046i \(0.471683\pi\)
\(888\) 0 0
\(889\) 1.30850e6 0.0555288
\(890\) 0 0
\(891\) −1.40062e7 −0.591052
\(892\) 0 0
\(893\) −1.44292e7 −0.605499
\(894\) 0 0
\(895\) −449100. −0.0187407
\(896\) 0 0
\(897\) −6.49094e6 −0.269356
\(898\) 0 0
\(899\) −1.89571e7 −0.782300
\(900\) 0 0
\(901\) 1.27358e6 0.0522654
\(902\) 0 0
\(903\) 9.68789e6 0.395375
\(904\) 0 0
\(905\) 5.71055e6 0.231770
\(906\) 0 0
\(907\) −4.18248e7 −1.68817 −0.844083 0.536212i \(-0.819855\pi\)
−0.844083 + 0.536212i \(0.819855\pi\)
\(908\) 0 0
\(909\) −5.15651e6 −0.206989
\(910\) 0 0
\(911\) −2.96323e6 −0.118296 −0.0591480 0.998249i \(-0.518838\pi\)
−0.0591480 + 0.998249i \(0.518838\pi\)
\(912\) 0 0
\(913\) 2.45018e7 0.972795
\(914\) 0 0
\(915\) −8.28900e6 −0.327303
\(916\) 0 0
\(917\) −344372. −0.0135240
\(918\) 0 0
\(919\) 2.22355e7 0.868476 0.434238 0.900798i \(-0.357018\pi\)
0.434238 + 0.900798i \(0.357018\pi\)
\(920\) 0 0
\(921\) −1.26333e7 −0.490757
\(922\) 0 0
\(923\) −2.50094e7 −0.966271
\(924\) 0 0
\(925\) −196250. −0.00754146
\(926\) 0 0
\(927\) −1.26934e7 −0.485152
\(928\) 0 0
\(929\) −9.65046e6 −0.366867 −0.183434 0.983032i \(-0.558721\pi\)
−0.183434 + 0.983032i \(0.558721\pi\)
\(930\) 0 0
\(931\) −6.44428e6 −0.243669
\(932\) 0 0
\(933\) 3.73456e7 1.40455
\(934\) 0 0
\(935\) 1.07030e7 0.400384
\(936\) 0 0
\(937\) −4.45116e7 −1.65624 −0.828122 0.560548i \(-0.810590\pi\)
−0.828122 + 0.560548i \(0.810590\pi\)
\(938\) 0 0
\(939\) 2.34811e7 0.869069
\(940\) 0 0
\(941\) 1.08983e7 0.401223 0.200612 0.979671i \(-0.435707\pi\)
0.200612 + 0.979671i \(0.435707\pi\)
\(942\) 0 0
\(943\) 2.73176e7 1.00038
\(944\) 0 0
\(945\) −5.02740e6 −0.183132
\(946\) 0 0
\(947\) −1.37370e7 −0.497757 −0.248879 0.968535i \(-0.580062\pi\)
−0.248879 + 0.968535i \(0.580062\pi\)
\(948\) 0 0
\(949\) −2.62675e7 −0.946789
\(950\) 0 0
\(951\) −3.29760e7 −1.18235
\(952\) 0 0
\(953\) −2.78867e7 −0.994639 −0.497319 0.867568i \(-0.665682\pi\)
−0.497319 + 0.867568i \(0.665682\pi\)
\(954\) 0 0
\(955\) −8.94600e6 −0.317410
\(956\) 0 0
\(957\) 1.61329e7 0.569420
\(958\) 0 0
\(959\) −6.86990e6 −0.241215
\(960\) 0 0
\(961\) 3.28364e7 1.14696
\(962\) 0 0
\(963\) −1.12207e7 −0.389900
\(964\) 0 0
\(965\) −1.23543e7 −0.427073
\(966\) 0 0
\(967\) 7.36444e6 0.253264 0.126632 0.991950i \(-0.459583\pi\)
0.126632 + 0.991950i \(0.459583\pi\)
\(968\) 0 0
\(969\) 2.48002e7 0.848487
\(970\) 0 0
\(971\) −8.71508e6 −0.296635 −0.148318 0.988940i \(-0.547386\pi\)
−0.148318 + 0.988940i \(0.547386\pi\)
\(972\) 0 0
\(973\) 4.69792e6 0.159083
\(974\) 0 0
\(975\) 2.65500e6 0.0894444
\(976\) 0 0
\(977\) −1.60032e7 −0.536377 −0.268188 0.963366i \(-0.586425\pi\)
−0.268188 + 0.963366i \(0.586425\pi\)
\(978\) 0 0
\(979\) 7.18941e7 2.39738
\(980\) 0 0
\(981\) 1.37557e7 0.456361
\(982\) 0 0
\(983\) −3.81746e7 −1.26006 −0.630030 0.776571i \(-0.716957\pi\)
−0.630030 + 0.776571i \(0.716957\pi\)
\(984\) 0 0
\(985\) 1.48826e7 0.488750
\(986\) 0 0
\(987\) 3.16109e6 0.103287
\(988\) 0 0
\(989\) −2.51753e7 −0.818435
\(990\) 0 0
\(991\) −3.76979e7 −1.21936 −0.609681 0.792647i \(-0.708702\pi\)
−0.609681 + 0.792647i \(0.708702\pi\)
\(992\) 0 0
\(993\) −2.67623e7 −0.861290
\(994\) 0 0
\(995\) −6.53020e6 −0.209107
\(996\) 0 0
\(997\) 4.40251e7 1.40269 0.701347 0.712820i \(-0.252582\pi\)
0.701347 + 0.712820i \(0.252582\pi\)
\(998\) 0 0
\(999\) −1.28866e6 −0.0408529
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 280.6.a.a.1.1 1
4.3 odd 2 560.6.a.g.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.6.a.a.1.1 1 1.1 even 1 trivial
560.6.a.g.1.1 1 4.3 odd 2