Properties

Label 1089.6.a.h.1.1
Level $1089$
Weight $6$
Character 1089.1
Self dual yes
Analytic conductor $174.658$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1089.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(174.657979776\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 33)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1089.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -31.0000 q^{4} +92.0000 q^{5} +26.0000 q^{7} -63.0000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} -31.0000 q^{4} +92.0000 q^{5} +26.0000 q^{7} -63.0000 q^{8} +92.0000 q^{10} +692.000 q^{13} +26.0000 q^{14} +929.000 q^{16} -1442.00 q^{17} -2160.00 q^{19} -2852.00 q^{20} +1582.00 q^{23} +5339.00 q^{25} +692.000 q^{26} -806.000 q^{28} -5526.00 q^{29} +4792.00 q^{31} +2945.00 q^{32} -1442.00 q^{34} +2392.00 q^{35} -10194.0 q^{37} -2160.00 q^{38} -5796.00 q^{40} -10622.0 q^{41} -8580.00 q^{43} +1582.00 q^{46} +2362.00 q^{47} -16131.0 q^{49} +5339.00 q^{50} -21452.0 q^{52} +30804.0 q^{53} -1638.00 q^{56} -5526.00 q^{58} -6416.00 q^{59} -42096.0 q^{61} +4792.00 q^{62} -26783.0 q^{64} +63664.0 q^{65} -28444.0 q^{67} +44702.0 q^{68} +2392.00 q^{70} -45690.0 q^{71} +18374.0 q^{73} -10194.0 q^{74} +66960.0 q^{76} +105214. q^{79} +85468.0 q^{80} -10622.0 q^{82} +62292.0 q^{83} -132664. q^{85} -8580.00 q^{86} +72246.0 q^{89} +17992.0 q^{91} -49042.0 q^{92} +2362.00 q^{94} -198720. q^{95} +79262.0 q^{97} -16131.0 q^{98} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.176777 0.0883883 0.996086i \(-0.471828\pi\)
0.0883883 + 0.996086i \(0.471828\pi\)
\(3\) 0 0
\(4\) −31.0000 −0.968750
\(5\) 92.0000 1.64575 0.822873 0.568225i \(-0.192370\pi\)
0.822873 + 0.568225i \(0.192370\pi\)
\(6\) 0 0
\(7\) 26.0000 0.200553 0.100276 0.994960i \(-0.468027\pi\)
0.100276 + 0.994960i \(0.468027\pi\)
\(8\) −63.0000 −0.348029
\(9\) 0 0
\(10\) 92.0000 0.290930
\(11\) 0 0
\(12\) 0 0
\(13\) 692.000 1.13566 0.567829 0.823146i \(-0.307783\pi\)
0.567829 + 0.823146i \(0.307783\pi\)
\(14\) 26.0000 0.0354530
\(15\) 0 0
\(16\) 929.000 0.907227
\(17\) −1442.00 −1.21016 −0.605080 0.796165i \(-0.706859\pi\)
−0.605080 + 0.796165i \(0.706859\pi\)
\(18\) 0 0
\(19\) −2160.00 −1.37268 −0.686341 0.727280i \(-0.740784\pi\)
−0.686341 + 0.727280i \(0.740784\pi\)
\(20\) −2852.00 −1.59432
\(21\) 0 0
\(22\) 0 0
\(23\) 1582.00 0.623572 0.311786 0.950152i \(-0.399073\pi\)
0.311786 + 0.950152i \(0.399073\pi\)
\(24\) 0 0
\(25\) 5339.00 1.70848
\(26\) 692.000 0.200758
\(27\) 0 0
\(28\) −806.000 −0.194285
\(29\) −5526.00 −1.22016 −0.610079 0.792341i \(-0.708862\pi\)
−0.610079 + 0.792341i \(0.708862\pi\)
\(30\) 0 0
\(31\) 4792.00 0.895597 0.447798 0.894135i \(-0.352208\pi\)
0.447798 + 0.894135i \(0.352208\pi\)
\(32\) 2945.00 0.508406
\(33\) 0 0
\(34\) −1442.00 −0.213928
\(35\) 2392.00 0.330059
\(36\) 0 0
\(37\) −10194.0 −1.22417 −0.612083 0.790794i \(-0.709668\pi\)
−0.612083 + 0.790794i \(0.709668\pi\)
\(38\) −2160.00 −0.242658
\(39\) 0 0
\(40\) −5796.00 −0.572768
\(41\) −10622.0 −0.986840 −0.493420 0.869791i \(-0.664253\pi\)
−0.493420 + 0.869791i \(0.664253\pi\)
\(42\) 0 0
\(43\) −8580.00 −0.707646 −0.353823 0.935312i \(-0.615119\pi\)
−0.353823 + 0.935312i \(0.615119\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 1582.00 0.110233
\(47\) 2362.00 0.155968 0.0779840 0.996955i \(-0.475152\pi\)
0.0779840 + 0.996955i \(0.475152\pi\)
\(48\) 0 0
\(49\) −16131.0 −0.959779
\(50\) 5339.00 0.302019
\(51\) 0 0
\(52\) −21452.0 −1.10017
\(53\) 30804.0 1.50632 0.753160 0.657837i \(-0.228528\pi\)
0.753160 + 0.657837i \(0.228528\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1638.00 −0.0697981
\(57\) 0 0
\(58\) −5526.00 −0.215695
\(59\) −6416.00 −0.239957 −0.119979 0.992776i \(-0.538283\pi\)
−0.119979 + 0.992776i \(0.538283\pi\)
\(60\) 0 0
\(61\) −42096.0 −1.44849 −0.724246 0.689541i \(-0.757812\pi\)
−0.724246 + 0.689541i \(0.757812\pi\)
\(62\) 4792.00 0.158321
\(63\) 0 0
\(64\) −26783.0 −0.817352
\(65\) 63664.0 1.86901
\(66\) 0 0
\(67\) −28444.0 −0.774112 −0.387056 0.922056i \(-0.626508\pi\)
−0.387056 + 0.922056i \(0.626508\pi\)
\(68\) 44702.0 1.17234
\(69\) 0 0
\(70\) 2392.00 0.0583467
\(71\) −45690.0 −1.07566 −0.537830 0.843053i \(-0.680756\pi\)
−0.537830 + 0.843053i \(0.680756\pi\)
\(72\) 0 0
\(73\) 18374.0 0.403549 0.201775 0.979432i \(-0.435329\pi\)
0.201775 + 0.979432i \(0.435329\pi\)
\(74\) −10194.0 −0.216404
\(75\) 0 0
\(76\) 66960.0 1.32979
\(77\) 0 0
\(78\) 0 0
\(79\) 105214. 1.89673 0.948366 0.317179i \(-0.102736\pi\)
0.948366 + 0.317179i \(0.102736\pi\)
\(80\) 85468.0 1.49306
\(81\) 0 0
\(82\) −10622.0 −0.174450
\(83\) 62292.0 0.992515 0.496257 0.868175i \(-0.334707\pi\)
0.496257 + 0.868175i \(0.334707\pi\)
\(84\) 0 0
\(85\) −132664. −1.99162
\(86\) −8580.00 −0.125095
\(87\) 0 0
\(88\) 0 0
\(89\) 72246.0 0.966805 0.483402 0.875398i \(-0.339401\pi\)
0.483402 + 0.875398i \(0.339401\pi\)
\(90\) 0 0
\(91\) 17992.0 0.227759
\(92\) −49042.0 −0.604086
\(93\) 0 0
\(94\) 2362.00 0.0275715
\(95\) −198720. −2.25908
\(96\) 0 0
\(97\) 79262.0 0.855334 0.427667 0.903936i \(-0.359336\pi\)
0.427667 + 0.903936i \(0.359336\pi\)
\(98\) −16131.0 −0.169667
\(99\) 0 0
\(100\) −165509. −1.65509
\(101\) −24958.0 −0.243448 −0.121724 0.992564i \(-0.538842\pi\)
−0.121724 + 0.992564i \(0.538842\pi\)
\(102\) 0 0
\(103\) −56812.0 −0.527651 −0.263826 0.964570i \(-0.584984\pi\)
−0.263826 + 0.964570i \(0.584984\pi\)
\(104\) −43596.0 −0.395242
\(105\) 0 0
\(106\) 30804.0 0.266282
\(107\) −12492.0 −0.105481 −0.0527403 0.998608i \(-0.516796\pi\)
−0.0527403 + 0.998608i \(0.516796\pi\)
\(108\) 0 0
\(109\) −198748. −1.60227 −0.801137 0.598482i \(-0.795771\pi\)
−0.801137 + 0.598482i \(0.795771\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 24154.0 0.181947
\(113\) −166554. −1.22704 −0.613520 0.789679i \(-0.710247\pi\)
−0.613520 + 0.789679i \(0.710247\pi\)
\(114\) 0 0
\(115\) 145544. 1.02624
\(116\) 171306. 1.18203
\(117\) 0 0
\(118\) −6416.00 −0.0424189
\(119\) −37492.0 −0.242701
\(120\) 0 0
\(121\) 0 0
\(122\) −42096.0 −0.256060
\(123\) 0 0
\(124\) −148552. −0.867609
\(125\) 203688. 1.16598
\(126\) 0 0
\(127\) −304226. −1.67374 −0.836868 0.547405i \(-0.815616\pi\)
−0.836868 + 0.547405i \(0.815616\pi\)
\(128\) −121023. −0.652894
\(129\) 0 0
\(130\) 63664.0 0.330397
\(131\) 274428. 1.39717 0.698586 0.715526i \(-0.253813\pi\)
0.698586 + 0.715526i \(0.253813\pi\)
\(132\) 0 0
\(133\) −56160.0 −0.275295
\(134\) −28444.0 −0.136845
\(135\) 0 0
\(136\) 90846.0 0.421171
\(137\) 245458. 1.11732 0.558658 0.829398i \(-0.311317\pi\)
0.558658 + 0.829398i \(0.311317\pi\)
\(138\) 0 0
\(139\) 59888.0 0.262907 0.131454 0.991322i \(-0.458036\pi\)
0.131454 + 0.991322i \(0.458036\pi\)
\(140\) −74152.0 −0.319744
\(141\) 0 0
\(142\) −45690.0 −0.190152
\(143\) 0 0
\(144\) 0 0
\(145\) −508392. −2.00807
\(146\) 18374.0 0.0713381
\(147\) 0 0
\(148\) 316014. 1.18591
\(149\) 72038.0 0.265825 0.132913 0.991128i \(-0.457567\pi\)
0.132913 + 0.991128i \(0.457567\pi\)
\(150\) 0 0
\(151\) 323110. 1.15321 0.576605 0.817023i \(-0.304377\pi\)
0.576605 + 0.817023i \(0.304377\pi\)
\(152\) 136080. 0.477733
\(153\) 0 0
\(154\) 0 0
\(155\) 440864. 1.47393
\(156\) 0 0
\(157\) −318766. −1.03210 −0.516051 0.856558i \(-0.672599\pi\)
−0.516051 + 0.856558i \(0.672599\pi\)
\(158\) 105214. 0.335298
\(159\) 0 0
\(160\) 270940. 0.836707
\(161\) 41132.0 0.125059
\(162\) 0 0
\(163\) −431996. −1.27353 −0.636767 0.771056i \(-0.719729\pi\)
−0.636767 + 0.771056i \(0.719729\pi\)
\(164\) 329282. 0.956001
\(165\) 0 0
\(166\) 62292.0 0.175454
\(167\) −251580. −0.698047 −0.349024 0.937114i \(-0.613487\pi\)
−0.349024 + 0.937114i \(0.613487\pi\)
\(168\) 0 0
\(169\) 107571. 0.289720
\(170\) −132664. −0.352071
\(171\) 0 0
\(172\) 265980. 0.685532
\(173\) 476634. 1.21079 0.605396 0.795924i \(-0.293015\pi\)
0.605396 + 0.795924i \(0.293015\pi\)
\(174\) 0 0
\(175\) 138814. 0.342640
\(176\) 0 0
\(177\) 0 0
\(178\) 72246.0 0.170909
\(179\) −90192.0 −0.210395 −0.105198 0.994451i \(-0.533547\pi\)
−0.105198 + 0.994451i \(0.533547\pi\)
\(180\) 0 0
\(181\) 248002. 0.562676 0.281338 0.959609i \(-0.409222\pi\)
0.281338 + 0.959609i \(0.409222\pi\)
\(182\) 17992.0 0.0402625
\(183\) 0 0
\(184\) −99666.0 −0.217021
\(185\) −937848. −2.01467
\(186\) 0 0
\(187\) 0 0
\(188\) −73222.0 −0.151094
\(189\) 0 0
\(190\) −198720. −0.399354
\(191\) 156802. 0.311006 0.155503 0.987835i \(-0.450300\pi\)
0.155503 + 0.987835i \(0.450300\pi\)
\(192\) 0 0
\(193\) 431234. 0.833335 0.416668 0.909059i \(-0.363198\pi\)
0.416668 + 0.909059i \(0.363198\pi\)
\(194\) 79262.0 0.151203
\(195\) 0 0
\(196\) 500061. 0.929786
\(197\) −864974. −1.58795 −0.793976 0.607949i \(-0.791993\pi\)
−0.793976 + 0.607949i \(0.791993\pi\)
\(198\) 0 0
\(199\) −480060. −0.859336 −0.429668 0.902987i \(-0.641369\pi\)
−0.429668 + 0.902987i \(0.641369\pi\)
\(200\) −336357. −0.594601
\(201\) 0 0
\(202\) −24958.0 −0.0430359
\(203\) −143676. −0.244706
\(204\) 0 0
\(205\) −977224. −1.62409
\(206\) −56812.0 −0.0932765
\(207\) 0 0
\(208\) 642868. 1.03030
\(209\) 0 0
\(210\) 0 0
\(211\) −525900. −0.813199 −0.406600 0.913606i \(-0.633286\pi\)
−0.406600 + 0.913606i \(0.633286\pi\)
\(212\) −954924. −1.45925
\(213\) 0 0
\(214\) −12492.0 −0.0186465
\(215\) −789360. −1.16461
\(216\) 0 0
\(217\) 124592. 0.179614
\(218\) −198748. −0.283245
\(219\) 0 0
\(220\) 0 0
\(221\) −997864. −1.37433
\(222\) 0 0
\(223\) −245264. −0.330272 −0.165136 0.986271i \(-0.552806\pi\)
−0.165136 + 0.986271i \(0.552806\pi\)
\(224\) 76570.0 0.101962
\(225\) 0 0
\(226\) −166554. −0.216912
\(227\) −799308. −1.02955 −0.514777 0.857324i \(-0.672125\pi\)
−0.514777 + 0.857324i \(0.672125\pi\)
\(228\) 0 0
\(229\) −1.53989e6 −1.94045 −0.970224 0.242208i \(-0.922128\pi\)
−0.970224 + 0.242208i \(0.922128\pi\)
\(230\) 145544. 0.181416
\(231\) 0 0
\(232\) 348138. 0.424650
\(233\) −721830. −0.871054 −0.435527 0.900176i \(-0.643438\pi\)
−0.435527 + 0.900176i \(0.643438\pi\)
\(234\) 0 0
\(235\) 217304. 0.256684
\(236\) 198896. 0.232459
\(237\) 0 0
\(238\) −37492.0 −0.0429038
\(239\) −638436. −0.722974 −0.361487 0.932377i \(-0.617731\pi\)
−0.361487 + 0.932377i \(0.617731\pi\)
\(240\) 0 0
\(241\) −220990. −0.245092 −0.122546 0.992463i \(-0.539106\pi\)
−0.122546 + 0.992463i \(0.539106\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 1.30498e6 1.40323
\(245\) −1.48405e6 −1.57955
\(246\) 0 0
\(247\) −1.49472e6 −1.55890
\(248\) −301896. −0.311694
\(249\) 0 0
\(250\) 203688. 0.206118
\(251\) −627304. −0.628483 −0.314242 0.949343i \(-0.601750\pi\)
−0.314242 + 0.949343i \(0.601750\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −304226. −0.295878
\(255\) 0 0
\(256\) 736033. 0.701936
\(257\) 468014. 0.442004 0.221002 0.975273i \(-0.429067\pi\)
0.221002 + 0.975273i \(0.429067\pi\)
\(258\) 0 0
\(259\) −265044. −0.245510
\(260\) −1.97358e6 −1.81060
\(261\) 0 0
\(262\) 274428. 0.246988
\(263\) 1.54510e6 1.37743 0.688713 0.725034i \(-0.258176\pi\)
0.688713 + 0.725034i \(0.258176\pi\)
\(264\) 0 0
\(265\) 2.83397e6 2.47902
\(266\) −56160.0 −0.0486657
\(267\) 0 0
\(268\) 881764. 0.749921
\(269\) 1.07457e6 0.905430 0.452715 0.891655i \(-0.350456\pi\)
0.452715 + 0.891655i \(0.350456\pi\)
\(270\) 0 0
\(271\) −1.58723e6 −1.31285 −0.656427 0.754389i \(-0.727933\pi\)
−0.656427 + 0.754389i \(0.727933\pi\)
\(272\) −1.33962e6 −1.09789
\(273\) 0 0
\(274\) 245458. 0.197515
\(275\) 0 0
\(276\) 0 0
\(277\) −692704. −0.542436 −0.271218 0.962518i \(-0.587426\pi\)
−0.271218 + 0.962518i \(0.587426\pi\)
\(278\) 59888.0 0.0464759
\(279\) 0 0
\(280\) −150696. −0.114870
\(281\) −567018. −0.428382 −0.214191 0.976792i \(-0.568711\pi\)
−0.214191 + 0.976792i \(0.568711\pi\)
\(282\) 0 0
\(283\) −714916. −0.530626 −0.265313 0.964162i \(-0.585475\pi\)
−0.265313 + 0.964162i \(0.585475\pi\)
\(284\) 1.41639e6 1.04205
\(285\) 0 0
\(286\) 0 0
\(287\) −276172. −0.197913
\(288\) 0 0
\(289\) 659507. 0.464488
\(290\) −508392. −0.354980
\(291\) 0 0
\(292\) −569594. −0.390938
\(293\) 2.14409e6 1.45907 0.729533 0.683946i \(-0.239738\pi\)
0.729533 + 0.683946i \(0.239738\pi\)
\(294\) 0 0
\(295\) −590272. −0.394909
\(296\) 642222. 0.426045
\(297\) 0 0
\(298\) 72038.0 0.0469917
\(299\) 1.09474e6 0.708165
\(300\) 0 0
\(301\) −223080. −0.141920
\(302\) 323110. 0.203860
\(303\) 0 0
\(304\) −2.00664e6 −1.24533
\(305\) −3.87283e6 −2.38385
\(306\) 0 0
\(307\) 588808. 0.356556 0.178278 0.983980i \(-0.442947\pi\)
0.178278 + 0.983980i \(0.442947\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 440864. 0.260556
\(311\) −2.51827e6 −1.47639 −0.738194 0.674588i \(-0.764321\pi\)
−0.738194 + 0.674588i \(0.764321\pi\)
\(312\) 0 0
\(313\) −2.23562e6 −1.28985 −0.644923 0.764248i \(-0.723110\pi\)
−0.644923 + 0.764248i \(0.723110\pi\)
\(314\) −318766. −0.182452
\(315\) 0 0
\(316\) −3.26163e6 −1.83746
\(317\) −1.06079e6 −0.592901 −0.296450 0.955048i \(-0.595803\pi\)
−0.296450 + 0.955048i \(0.595803\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −2.46404e6 −1.34515
\(321\) 0 0
\(322\) 41132.0 0.0221075
\(323\) 3.11472e6 1.66116
\(324\) 0 0
\(325\) 3.69459e6 1.94025
\(326\) −431996. −0.225131
\(327\) 0 0
\(328\) 669186. 0.343449
\(329\) 61412.0 0.0312798
\(330\) 0 0
\(331\) −2.34566e6 −1.17678 −0.588390 0.808577i \(-0.700238\pi\)
−0.588390 + 0.808577i \(0.700238\pi\)
\(332\) −1.93105e6 −0.961499
\(333\) 0 0
\(334\) −251580. −0.123399
\(335\) −2.61685e6 −1.27399
\(336\) 0 0
\(337\) −839978. −0.402896 −0.201448 0.979499i \(-0.564565\pi\)
−0.201448 + 0.979499i \(0.564565\pi\)
\(338\) 107571. 0.0512157
\(339\) 0 0
\(340\) 4.11258e6 1.92938
\(341\) 0 0
\(342\) 0 0
\(343\) −856388. −0.393039
\(344\) 540540. 0.246281
\(345\) 0 0
\(346\) 476634. 0.214040
\(347\) −2.02560e6 −0.903086 −0.451543 0.892249i \(-0.649126\pi\)
−0.451543 + 0.892249i \(0.649126\pi\)
\(348\) 0 0
\(349\) 378924. 0.166528 0.0832642 0.996528i \(-0.473465\pi\)
0.0832642 + 0.996528i \(0.473465\pi\)
\(350\) 138814. 0.0605708
\(351\) 0 0
\(352\) 0 0
\(353\) 1.98730e6 0.848842 0.424421 0.905465i \(-0.360478\pi\)
0.424421 + 0.905465i \(0.360478\pi\)
\(354\) 0 0
\(355\) −4.20348e6 −1.77026
\(356\) −2.23963e6 −0.936592
\(357\) 0 0
\(358\) −90192.0 −0.0371929
\(359\) −3.43975e6 −1.40861 −0.704305 0.709898i \(-0.748741\pi\)
−0.704305 + 0.709898i \(0.748741\pi\)
\(360\) 0 0
\(361\) 2.18950e6 0.884254
\(362\) 248002. 0.0994681
\(363\) 0 0
\(364\) −557752. −0.220642
\(365\) 1.69041e6 0.664140
\(366\) 0 0
\(367\) −1.79679e6 −0.696358 −0.348179 0.937428i \(-0.613200\pi\)
−0.348179 + 0.937428i \(0.613200\pi\)
\(368\) 1.46968e6 0.565721
\(369\) 0 0
\(370\) −937848. −0.356146
\(371\) 800904. 0.302096
\(372\) 0 0
\(373\) 1.43541e6 0.534201 0.267100 0.963669i \(-0.413934\pi\)
0.267100 + 0.963669i \(0.413934\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −148806. −0.0542814
\(377\) −3.82399e6 −1.38568
\(378\) 0 0
\(379\) 2.66235e6 0.952065 0.476033 0.879428i \(-0.342074\pi\)
0.476033 + 0.879428i \(0.342074\pi\)
\(380\) 6.16032e6 2.18849
\(381\) 0 0
\(382\) 156802. 0.0549785
\(383\) −2.04091e6 −0.710932 −0.355466 0.934689i \(-0.615678\pi\)
−0.355466 + 0.934689i \(0.615678\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 431234. 0.147314
\(387\) 0 0
\(388\) −2.45712e6 −0.828605
\(389\) 4.29947e6 1.44059 0.720296 0.693667i \(-0.244006\pi\)
0.720296 + 0.693667i \(0.244006\pi\)
\(390\) 0 0
\(391\) −2.28124e6 −0.754623
\(392\) 1.01625e6 0.334031
\(393\) 0 0
\(394\) −864974. −0.280713
\(395\) 9.67969e6 3.12154
\(396\) 0 0
\(397\) 728818. 0.232083 0.116041 0.993244i \(-0.462979\pi\)
0.116041 + 0.993244i \(0.462979\pi\)
\(398\) −480060. −0.151911
\(399\) 0 0
\(400\) 4.95993e6 1.54998
\(401\) 5.92515e6 1.84009 0.920044 0.391814i \(-0.128152\pi\)
0.920044 + 0.391814i \(0.128152\pi\)
\(402\) 0 0
\(403\) 3.31606e6 1.01709
\(404\) 773698. 0.235840
\(405\) 0 0
\(406\) −143676. −0.0432583
\(407\) 0 0
\(408\) 0 0
\(409\) −1.38212e6 −0.408542 −0.204271 0.978914i \(-0.565482\pi\)
−0.204271 + 0.978914i \(0.565482\pi\)
\(410\) −977224. −0.287101
\(411\) 0 0
\(412\) 1.76117e6 0.511162
\(413\) −166816. −0.0481241
\(414\) 0 0
\(415\) 5.73086e6 1.63343
\(416\) 2.03794e6 0.577375
\(417\) 0 0
\(418\) 0 0
\(419\) −5.47794e6 −1.52434 −0.762170 0.647377i \(-0.775866\pi\)
−0.762170 + 0.647377i \(0.775866\pi\)
\(420\) 0 0
\(421\) 1.02873e6 0.282877 0.141439 0.989947i \(-0.454827\pi\)
0.141439 + 0.989947i \(0.454827\pi\)
\(422\) −525900. −0.143755
\(423\) 0 0
\(424\) −1.94065e6 −0.524243
\(425\) −7.69884e6 −2.06753
\(426\) 0 0
\(427\) −1.09450e6 −0.290499
\(428\) 387252. 0.102184
\(429\) 0 0
\(430\) −789360. −0.205875
\(431\) −5.14310e6 −1.33362 −0.666810 0.745228i \(-0.732341\pi\)
−0.666810 + 0.745228i \(0.732341\pi\)
\(432\) 0 0
\(433\) 412954. 0.105848 0.0529239 0.998599i \(-0.483146\pi\)
0.0529239 + 0.998599i \(0.483146\pi\)
\(434\) 124592. 0.0317516
\(435\) 0 0
\(436\) 6.16119e6 1.55220
\(437\) −3.41712e6 −0.855966
\(438\) 0 0
\(439\) −5.96365e6 −1.47690 −0.738450 0.674309i \(-0.764442\pi\)
−0.738450 + 0.674309i \(0.764442\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −997864. −0.242949
\(443\) −2.18433e6 −0.528821 −0.264410 0.964410i \(-0.585177\pi\)
−0.264410 + 0.964410i \(0.585177\pi\)
\(444\) 0 0
\(445\) 6.64663e6 1.59112
\(446\) −245264. −0.0583844
\(447\) 0 0
\(448\) −696358. −0.163922
\(449\) 7858.00 0.00183948 0.000919742 1.00000i \(-0.499707\pi\)
0.000919742 1.00000i \(0.499707\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 5.16317e6 1.18870
\(453\) 0 0
\(454\) −799308. −0.182001
\(455\) 1.65526e6 0.374834
\(456\) 0 0
\(457\) 899922. 0.201565 0.100782 0.994908i \(-0.467865\pi\)
0.100782 + 0.994908i \(0.467865\pi\)
\(458\) −1.53989e6 −0.343026
\(459\) 0 0
\(460\) −4.51186e6 −0.994172
\(461\) 1.13619e6 0.249000 0.124500 0.992220i \(-0.460267\pi\)
0.124500 + 0.992220i \(0.460267\pi\)
\(462\) 0 0
\(463\) −7.38964e6 −1.60203 −0.801016 0.598643i \(-0.795707\pi\)
−0.801016 + 0.598643i \(0.795707\pi\)
\(464\) −5.13365e6 −1.10696
\(465\) 0 0
\(466\) −721830. −0.153982
\(467\) −4.20851e6 −0.892968 −0.446484 0.894792i \(-0.647324\pi\)
−0.446484 + 0.894792i \(0.647324\pi\)
\(468\) 0 0
\(469\) −739544. −0.155250
\(470\) 217304. 0.0453757
\(471\) 0 0
\(472\) 404208. 0.0835122
\(473\) 0 0
\(474\) 0 0
\(475\) −1.15322e7 −2.34520
\(476\) 1.16225e6 0.235116
\(477\) 0 0
\(478\) −638436. −0.127805
\(479\) 7.39441e6 1.47253 0.736266 0.676692i \(-0.236587\pi\)
0.736266 + 0.676692i \(0.236587\pi\)
\(480\) 0 0
\(481\) −7.05425e6 −1.39023
\(482\) −220990. −0.0433266
\(483\) 0 0
\(484\) 0 0
\(485\) 7.29210e6 1.40766
\(486\) 0 0
\(487\) −3.81644e6 −0.729181 −0.364591 0.931168i \(-0.618791\pi\)
−0.364591 + 0.931168i \(0.618791\pi\)
\(488\) 2.65205e6 0.504118
\(489\) 0 0
\(490\) −1.48405e6 −0.279228
\(491\) 1.69716e6 0.317702 0.158851 0.987303i \(-0.449221\pi\)
0.158851 + 0.987303i \(0.449221\pi\)
\(492\) 0 0
\(493\) 7.96849e6 1.47659
\(494\) −1.49472e6 −0.275577
\(495\) 0 0
\(496\) 4.45177e6 0.812509
\(497\) −1.18794e6 −0.215727
\(498\) 0 0
\(499\) 6.95160e6 1.24978 0.624889 0.780713i \(-0.285144\pi\)
0.624889 + 0.780713i \(0.285144\pi\)
\(500\) −6.31433e6 −1.12954
\(501\) 0 0
\(502\) −627304. −0.111101
\(503\) 6.01023e6 1.05918 0.529591 0.848253i \(-0.322345\pi\)
0.529591 + 0.848253i \(0.322345\pi\)
\(504\) 0 0
\(505\) −2.29614e6 −0.400654
\(506\) 0 0
\(507\) 0 0
\(508\) 9.43101e6 1.62143
\(509\) −624660. −0.106868 −0.0534342 0.998571i \(-0.517017\pi\)
−0.0534342 + 0.998571i \(0.517017\pi\)
\(510\) 0 0
\(511\) 477724. 0.0809328
\(512\) 4.60877e6 0.776980
\(513\) 0 0
\(514\) 468014. 0.0781360
\(515\) −5.22670e6 −0.868380
\(516\) 0 0
\(517\) 0 0
\(518\) −265044. −0.0434004
\(519\) 0 0
\(520\) −4.01083e6 −0.650468
\(521\) 647490. 0.104505 0.0522527 0.998634i \(-0.483360\pi\)
0.0522527 + 0.998634i \(0.483360\pi\)
\(522\) 0 0
\(523\) 114676. 0.0183324 0.00916618 0.999958i \(-0.497082\pi\)
0.00916618 + 0.999958i \(0.497082\pi\)
\(524\) −8.50727e6 −1.35351
\(525\) 0 0
\(526\) 1.54510e6 0.243497
\(527\) −6.91006e6 −1.08382
\(528\) 0 0
\(529\) −3.93362e6 −0.611157
\(530\) 2.83397e6 0.438233
\(531\) 0 0
\(532\) 1.74096e6 0.266692
\(533\) −7.35042e6 −1.12071
\(534\) 0 0
\(535\) −1.14926e6 −0.173594
\(536\) 1.79197e6 0.269413
\(537\) 0 0
\(538\) 1.07457e6 0.160059
\(539\) 0 0
\(540\) 0 0
\(541\) 2.12404e6 0.312011 0.156006 0.987756i \(-0.450138\pi\)
0.156006 + 0.987756i \(0.450138\pi\)
\(542\) −1.58723e6 −0.232082
\(543\) 0 0
\(544\) −4.24669e6 −0.615252
\(545\) −1.82848e7 −2.63693
\(546\) 0 0
\(547\) −1.22672e7 −1.75299 −0.876494 0.481413i \(-0.840124\pi\)
−0.876494 + 0.481413i \(0.840124\pi\)
\(548\) −7.60920e6 −1.08240
\(549\) 0 0
\(550\) 0 0
\(551\) 1.19362e7 1.67489
\(552\) 0 0
\(553\) 2.73556e6 0.380394
\(554\) −692704. −0.0958900
\(555\) 0 0
\(556\) −1.85653e6 −0.254692
\(557\) 1.10980e7 1.51568 0.757839 0.652442i \(-0.226255\pi\)
0.757839 + 0.652442i \(0.226255\pi\)
\(558\) 0 0
\(559\) −5.93736e6 −0.803644
\(560\) 2.22217e6 0.299438
\(561\) 0 0
\(562\) −567018. −0.0757279
\(563\) 4.61984e6 0.614265 0.307132 0.951667i \(-0.400631\pi\)
0.307132 + 0.951667i \(0.400631\pi\)
\(564\) 0 0
\(565\) −1.53230e7 −2.01940
\(566\) −714916. −0.0938024
\(567\) 0 0
\(568\) 2.87847e6 0.374361
\(569\) 1.01716e7 1.31707 0.658537 0.752548i \(-0.271176\pi\)
0.658537 + 0.752548i \(0.271176\pi\)
\(570\) 0 0
\(571\) 9.36866e6 1.20251 0.601253 0.799059i \(-0.294669\pi\)
0.601253 + 0.799059i \(0.294669\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −276172. −0.0349865
\(575\) 8.44630e6 1.06536
\(576\) 0 0
\(577\) −6.14973e6 −0.768983 −0.384491 0.923129i \(-0.625623\pi\)
−0.384491 + 0.923129i \(0.625623\pi\)
\(578\) 659507. 0.0821107
\(579\) 0 0
\(580\) 1.57602e7 1.94532
\(581\) 1.61959e6 0.199051
\(582\) 0 0
\(583\) 0 0
\(584\) −1.15756e6 −0.140447
\(585\) 0 0
\(586\) 2.14409e6 0.257929
\(587\) −1.04649e6 −0.125354 −0.0626771 0.998034i \(-0.519964\pi\)
−0.0626771 + 0.998034i \(0.519964\pi\)
\(588\) 0 0
\(589\) −1.03507e7 −1.22937
\(590\) −590272. −0.0698107
\(591\) 0 0
\(592\) −9.47023e6 −1.11060
\(593\) −3.31784e6 −0.387453 −0.193726 0.981056i \(-0.562057\pi\)
−0.193726 + 0.981056i \(0.562057\pi\)
\(594\) 0 0
\(595\) −3.44926e6 −0.399424
\(596\) −2.23318e6 −0.257518
\(597\) 0 0
\(598\) 1.09474e6 0.125187
\(599\) 1.73991e7 1.98134 0.990670 0.136280i \(-0.0435146\pi\)
0.990670 + 0.136280i \(0.0435146\pi\)
\(600\) 0 0
\(601\) −7.13163e6 −0.805383 −0.402691 0.915336i \(-0.631925\pi\)
−0.402691 + 0.915336i \(0.631925\pi\)
\(602\) −223080. −0.0250882
\(603\) 0 0
\(604\) −1.00164e7 −1.11717
\(605\) 0 0
\(606\) 0 0
\(607\) 9.64617e6 1.06263 0.531317 0.847173i \(-0.321697\pi\)
0.531317 + 0.847173i \(0.321697\pi\)
\(608\) −6.36120e6 −0.697879
\(609\) 0 0
\(610\) −3.87283e6 −0.421409
\(611\) 1.63450e6 0.177126
\(612\) 0 0
\(613\) −3.68170e6 −0.395729 −0.197864 0.980229i \(-0.563401\pi\)
−0.197864 + 0.980229i \(0.563401\pi\)
\(614\) 588808. 0.0630308
\(615\) 0 0
\(616\) 0 0
\(617\) −1.83190e7 −1.93727 −0.968635 0.248489i \(-0.920066\pi\)
−0.968635 + 0.248489i \(0.920066\pi\)
\(618\) 0 0
\(619\) 1.09660e6 0.115033 0.0575166 0.998345i \(-0.481682\pi\)
0.0575166 + 0.998345i \(0.481682\pi\)
\(620\) −1.36668e7 −1.42786
\(621\) 0 0
\(622\) −2.51827e6 −0.260991
\(623\) 1.87840e6 0.193895
\(624\) 0 0
\(625\) 2.05492e6 0.210424
\(626\) −2.23562e6 −0.228015
\(627\) 0 0
\(628\) 9.88175e6 0.999849
\(629\) 1.46997e7 1.48144
\(630\) 0 0
\(631\) −9.58030e6 −0.957869 −0.478934 0.877851i \(-0.658977\pi\)
−0.478934 + 0.877851i \(0.658977\pi\)
\(632\) −6.62848e6 −0.660118
\(633\) 0 0
\(634\) −1.06079e6 −0.104811
\(635\) −2.79888e7 −2.75454
\(636\) 0 0
\(637\) −1.11627e7 −1.08998
\(638\) 0 0
\(639\) 0 0
\(640\) −1.11341e7 −1.07450
\(641\) 1.18062e7 1.13492 0.567462 0.823400i \(-0.307925\pi\)
0.567462 + 0.823400i \(0.307925\pi\)
\(642\) 0 0
\(643\) −5.88298e6 −0.561138 −0.280569 0.959834i \(-0.590523\pi\)
−0.280569 + 0.959834i \(0.590523\pi\)
\(644\) −1.27509e6 −0.121151
\(645\) 0 0
\(646\) 3.11472e6 0.293655
\(647\) 3.62822e6 0.340748 0.170374 0.985379i \(-0.445502\pi\)
0.170374 + 0.985379i \(0.445502\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 3.69459e6 0.342991
\(651\) 0 0
\(652\) 1.33919e7 1.23374
\(653\) 5.70795e6 0.523838 0.261919 0.965090i \(-0.415645\pi\)
0.261919 + 0.965090i \(0.415645\pi\)
\(654\) 0 0
\(655\) 2.52474e7 2.29939
\(656\) −9.86784e6 −0.895287
\(657\) 0 0
\(658\) 61412.0 0.00552953
\(659\) 1.08205e7 0.970588 0.485294 0.874351i \(-0.338713\pi\)
0.485294 + 0.874351i \(0.338713\pi\)
\(660\) 0 0
\(661\) 1.14311e7 1.01762 0.508809 0.860879i \(-0.330086\pi\)
0.508809 + 0.860879i \(0.330086\pi\)
\(662\) −2.34566e6 −0.208027
\(663\) 0 0
\(664\) −3.92440e6 −0.345424
\(665\) −5.16672e6 −0.453065
\(666\) 0 0
\(667\) −8.74213e6 −0.760857
\(668\) 7.79898e6 0.676233
\(669\) 0 0
\(670\) −2.61685e6 −0.225212
\(671\) 0 0
\(672\) 0 0
\(673\) 2.03858e7 1.73496 0.867482 0.497468i \(-0.165737\pi\)
0.867482 + 0.497468i \(0.165737\pi\)
\(674\) −839978. −0.0712227
\(675\) 0 0
\(676\) −3.33470e6 −0.280666
\(677\) 6.09278e6 0.510909 0.255455 0.966821i \(-0.417775\pi\)
0.255455 + 0.966821i \(0.417775\pi\)
\(678\) 0 0
\(679\) 2.06081e6 0.171539
\(680\) 8.35783e6 0.693141
\(681\) 0 0
\(682\) 0 0
\(683\) −1.44978e7 −1.18918 −0.594592 0.804027i \(-0.702686\pi\)
−0.594592 + 0.804027i \(0.702686\pi\)
\(684\) 0 0
\(685\) 2.25821e7 1.83882
\(686\) −856388. −0.0694801
\(687\) 0 0
\(688\) −7.97082e6 −0.641995
\(689\) 2.13164e7 1.71067
\(690\) 0 0
\(691\) 9.87069e6 0.786416 0.393208 0.919449i \(-0.371365\pi\)
0.393208 + 0.919449i \(0.371365\pi\)
\(692\) −1.47757e7 −1.17296
\(693\) 0 0
\(694\) −2.02560e6 −0.159645
\(695\) 5.50970e6 0.432679
\(696\) 0 0
\(697\) 1.53169e7 1.19423
\(698\) 378924. 0.0294384
\(699\) 0 0
\(700\) −4.30323e6 −0.331933
\(701\) 6.35411e6 0.488382 0.244191 0.969727i \(-0.421478\pi\)
0.244191 + 0.969727i \(0.421478\pi\)
\(702\) 0 0
\(703\) 2.20190e7 1.68039
\(704\) 0 0
\(705\) 0 0
\(706\) 1.98730e6 0.150056
\(707\) −648908. −0.0488241
\(708\) 0 0
\(709\) −411382. −0.0307348 −0.0153674 0.999882i \(-0.504892\pi\)
−0.0153674 + 0.999882i \(0.504892\pi\)
\(710\) −4.20348e6 −0.312941
\(711\) 0 0
\(712\) −4.55150e6 −0.336476
\(713\) 7.58094e6 0.558470
\(714\) 0 0
\(715\) 0 0
\(716\) 2.79595e6 0.203820
\(717\) 0 0
\(718\) −3.43975e6 −0.249009
\(719\) −6.29795e6 −0.454336 −0.227168 0.973856i \(-0.572947\pi\)
−0.227168 + 0.973856i \(0.572947\pi\)
\(720\) 0 0
\(721\) −1.47711e6 −0.105822
\(722\) 2.18950e6 0.156316
\(723\) 0 0
\(724\) −7.68806e6 −0.545093
\(725\) −2.95033e7 −2.08461
\(726\) 0 0
\(727\) 1.14699e7 0.804866 0.402433 0.915449i \(-0.368165\pi\)
0.402433 + 0.915449i \(0.368165\pi\)
\(728\) −1.13350e6 −0.0792668
\(729\) 0 0
\(730\) 1.69041e6 0.117404
\(731\) 1.23724e7 0.856365
\(732\) 0 0
\(733\) 1.87547e7 1.28929 0.644646 0.764481i \(-0.277005\pi\)
0.644646 + 0.764481i \(0.277005\pi\)
\(734\) −1.79679e6 −0.123100
\(735\) 0 0
\(736\) 4.65899e6 0.317028
\(737\) 0 0
\(738\) 0 0
\(739\) −2.79727e6 −0.188418 −0.0942091 0.995552i \(-0.530032\pi\)
−0.0942091 + 0.995552i \(0.530032\pi\)
\(740\) 2.90733e7 1.95171
\(741\) 0 0
\(742\) 800904. 0.0534036
\(743\) −2.25651e7 −1.49956 −0.749781 0.661686i \(-0.769841\pi\)
−0.749781 + 0.661686i \(0.769841\pi\)
\(744\) 0 0
\(745\) 6.62750e6 0.437481
\(746\) 1.43541e6 0.0944342
\(747\) 0 0
\(748\) 0 0
\(749\) −324792. −0.0211544
\(750\) 0 0
\(751\) −7.49233e6 −0.484749 −0.242375 0.970183i \(-0.577926\pi\)
−0.242375 + 0.970183i \(0.577926\pi\)
\(752\) 2.19430e6 0.141498
\(753\) 0 0
\(754\) −3.82399e6 −0.244956
\(755\) 2.97261e7 1.89789
\(756\) 0 0
\(757\) 2.88492e7 1.82976 0.914880 0.403727i \(-0.132285\pi\)
0.914880 + 0.403727i \(0.132285\pi\)
\(758\) 2.66235e6 0.168303
\(759\) 0 0
\(760\) 1.25194e7 0.786227
\(761\) −9.56279e6 −0.598581 −0.299291 0.954162i \(-0.596750\pi\)
−0.299291 + 0.954162i \(0.596750\pi\)
\(762\) 0 0
\(763\) −5.16745e6 −0.321340
\(764\) −4.86086e6 −0.301287
\(765\) 0 0
\(766\) −2.04091e6 −0.125676
\(767\) −4.43987e6 −0.272510
\(768\) 0 0
\(769\) 744898. 0.0454235 0.0227118 0.999742i \(-0.492770\pi\)
0.0227118 + 0.999742i \(0.492770\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.33683e7 −0.807293
\(773\) −6.07336e6 −0.365578 −0.182789 0.983152i \(-0.558513\pi\)
−0.182789 + 0.983152i \(0.558513\pi\)
\(774\) 0 0
\(775\) 2.55845e7 1.53011
\(776\) −4.99351e6 −0.297681
\(777\) 0 0
\(778\) 4.29947e6 0.254663
\(779\) 2.29435e7 1.35462
\(780\) 0 0
\(781\) 0 0
\(782\) −2.28124e6 −0.133400
\(783\) 0 0
\(784\) −1.49857e7 −0.870737
\(785\) −2.93265e7 −1.69858
\(786\) 0 0
\(787\) 1.47512e7 0.848966 0.424483 0.905436i \(-0.360456\pi\)
0.424483 + 0.905436i \(0.360456\pi\)
\(788\) 2.68142e7 1.53833
\(789\) 0 0
\(790\) 9.67969e6 0.551815
\(791\) −4.33040e6 −0.246086
\(792\) 0 0
\(793\) −2.91304e7 −1.64499
\(794\) 728818. 0.0410268
\(795\) 0 0
\(796\) 1.48819e7 0.832481
\(797\) 2.78359e7 1.55224 0.776121 0.630584i \(-0.217185\pi\)
0.776121 + 0.630584i \(0.217185\pi\)
\(798\) 0 0
\(799\) −3.40600e6 −0.188746
\(800\) 1.57234e7 0.868601
\(801\) 0 0
\(802\) 5.92515e6 0.325285
\(803\) 0 0
\(804\) 0 0
\(805\) 3.78414e6 0.205815
\(806\) 3.31606e6 0.179798
\(807\) 0 0
\(808\) 1.57235e6 0.0847270
\(809\) 2.54767e7 1.36859 0.684293 0.729207i \(-0.260111\pi\)
0.684293 + 0.729207i \(0.260111\pi\)
\(810\) 0 0
\(811\) 1.91915e7 1.02460 0.512302 0.858805i \(-0.328793\pi\)
0.512302 + 0.858805i \(0.328793\pi\)
\(812\) 4.45396e6 0.237059
\(813\) 0 0
\(814\) 0 0
\(815\) −3.97436e7 −2.09591
\(816\) 0 0
\(817\) 1.85328e7 0.971373
\(818\) −1.38212e6 −0.0722207
\(819\) 0 0
\(820\) 3.02939e7 1.57333
\(821\) 3.27107e6 0.169368 0.0846840 0.996408i \(-0.473012\pi\)
0.0846840 + 0.996408i \(0.473012\pi\)
\(822\) 0 0
\(823\) −3.19195e7 −1.64269 −0.821347 0.570430i \(-0.806777\pi\)
−0.821347 + 0.570430i \(0.806777\pi\)
\(824\) 3.57916e6 0.183638
\(825\) 0 0
\(826\) −166816. −0.00850722
\(827\) 2.45556e7 1.24850 0.624248 0.781226i \(-0.285405\pi\)
0.624248 + 0.781226i \(0.285405\pi\)
\(828\) 0 0
\(829\) −1.40969e7 −0.712421 −0.356211 0.934406i \(-0.615931\pi\)
−0.356211 + 0.934406i \(0.615931\pi\)
\(830\) 5.73086e6 0.288752
\(831\) 0 0
\(832\) −1.85338e7 −0.928233
\(833\) 2.32609e7 1.16149
\(834\) 0 0
\(835\) −2.31454e7 −1.14881
\(836\) 0 0
\(837\) 0 0
\(838\) −5.47794e6 −0.269468
\(839\) 3.01443e6 0.147843 0.0739213 0.997264i \(-0.476449\pi\)
0.0739213 + 0.997264i \(0.476449\pi\)
\(840\) 0 0
\(841\) 1.00255e7 0.488784
\(842\) 1.02873e6 0.0500061
\(843\) 0 0
\(844\) 1.63029e7 0.787787
\(845\) 9.89653e6 0.476806
\(846\) 0 0
\(847\) 0 0
\(848\) 2.86169e7 1.36657
\(849\) 0 0
\(850\) −7.69884e6 −0.365492
\(851\) −1.61269e7 −0.763356
\(852\) 0 0
\(853\) 1.67201e7 0.786806 0.393403 0.919366i \(-0.371298\pi\)
0.393403 + 0.919366i \(0.371298\pi\)
\(854\) −1.09450e6 −0.0513534
\(855\) 0 0
\(856\) 786996. 0.0367103
\(857\) −9.15871e6 −0.425973 −0.212987 0.977055i \(-0.568319\pi\)
−0.212987 + 0.977055i \(0.568319\pi\)
\(858\) 0 0
\(859\) 1.51068e7 0.698536 0.349268 0.937023i \(-0.386430\pi\)
0.349268 + 0.937023i \(0.386430\pi\)
\(860\) 2.44702e7 1.12821
\(861\) 0 0
\(862\) −5.14310e6 −0.235753
\(863\) −5.11568e6 −0.233817 −0.116909 0.993143i \(-0.537298\pi\)
−0.116909 + 0.993143i \(0.537298\pi\)
\(864\) 0 0
\(865\) 4.38503e7 1.99266
\(866\) 412954. 0.0187114
\(867\) 0 0
\(868\) −3.86235e6 −0.174001
\(869\) 0 0
\(870\) 0 0
\(871\) −1.96832e7 −0.879127
\(872\) 1.25211e7 0.557638
\(873\) 0 0
\(874\) −3.41712e6 −0.151315
\(875\) 5.29589e6 0.233840
\(876\) 0 0
\(877\) 1.26998e7 0.557568 0.278784 0.960354i \(-0.410069\pi\)
0.278784 + 0.960354i \(0.410069\pi\)
\(878\) −5.96365e6 −0.261081
\(879\) 0 0
\(880\) 0 0
\(881\) 8.38173e6 0.363826 0.181913 0.983315i \(-0.441771\pi\)
0.181913 + 0.983315i \(0.441771\pi\)
\(882\) 0 0
\(883\) −1.69529e7 −0.731715 −0.365858 0.930671i \(-0.619224\pi\)
−0.365858 + 0.930671i \(0.619224\pi\)
\(884\) 3.09338e7 1.33138
\(885\) 0 0
\(886\) −2.18433e6 −0.0934832
\(887\) −1.05143e7 −0.448717 −0.224359 0.974507i \(-0.572029\pi\)
−0.224359 + 0.974507i \(0.572029\pi\)
\(888\) 0 0
\(889\) −7.90988e6 −0.335672
\(890\) 6.64663e6 0.281272
\(891\) 0 0
\(892\) 7.60318e6 0.319951
\(893\) −5.10192e6 −0.214094
\(894\) 0 0
\(895\) −8.29766e6 −0.346257
\(896\) −3.14660e6 −0.130940
\(897\) 0 0
\(898\) 7858.00 0.000325178 0
\(899\) −2.64806e7 −1.09277
\(900\) 0 0
\(901\) −4.44194e7 −1.82289
\(902\) 0 0
\(903\) 0 0
\(904\) 1.04929e7 0.427046
\(905\) 2.28162e7 0.926023
\(906\) 0 0
\(907\) −1.53747e7 −0.620569 −0.310284 0.950644i \(-0.600424\pi\)
−0.310284 + 0.950644i \(0.600424\pi\)
\(908\) 2.47785e7 0.997381
\(909\) 0 0
\(910\) 1.65526e6 0.0662619
\(911\) −1.25424e7 −0.500708 −0.250354 0.968154i \(-0.580547\pi\)
−0.250354 + 0.968154i \(0.580547\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 899922. 0.0356319
\(915\) 0 0
\(916\) 4.77367e7 1.87981
\(917\) 7.13513e6 0.280207
\(918\) 0 0
\(919\) −3.31432e7 −1.29451 −0.647256 0.762273i \(-0.724084\pi\)
−0.647256 + 0.762273i \(0.724084\pi\)
\(920\) −9.16927e6 −0.357162
\(921\) 0 0
\(922\) 1.13619e6 0.0440173
\(923\) −3.16175e7 −1.22158
\(924\) 0 0
\(925\) −5.44258e7 −2.09146
\(926\) −7.38964e6 −0.283202
\(927\) 0 0
\(928\) −1.62741e7 −0.620335
\(929\) −3.10442e7 −1.18016 −0.590080 0.807345i \(-0.700904\pi\)
−0.590080 + 0.807345i \(0.700904\pi\)
\(930\) 0 0
\(931\) 3.48430e7 1.31747
\(932\) 2.23767e7 0.843834
\(933\) 0 0
\(934\) −4.20851e6 −0.157856
\(935\) 0 0
\(936\) 0 0
\(937\) 3.10737e7 1.15623 0.578115 0.815955i \(-0.303788\pi\)
0.578115 + 0.815955i \(0.303788\pi\)
\(938\) −739544. −0.0274446
\(939\) 0 0
\(940\) −6.73642e6 −0.248662
\(941\) −2.50349e7 −0.921664 −0.460832 0.887488i \(-0.652449\pi\)
−0.460832 + 0.887488i \(0.652449\pi\)
\(942\) 0 0
\(943\) −1.68040e7 −0.615366
\(944\) −5.96046e6 −0.217696
\(945\) 0 0
\(946\) 0 0
\(947\) 5.37383e6 0.194719 0.0973596 0.995249i \(-0.468960\pi\)
0.0973596 + 0.995249i \(0.468960\pi\)
\(948\) 0 0
\(949\) 1.27148e7 0.458294
\(950\) −1.15322e7 −0.414576
\(951\) 0 0
\(952\) 2.36200e6 0.0844669
\(953\) 7.26908e6 0.259267 0.129634 0.991562i \(-0.458620\pi\)
0.129634 + 0.991562i \(0.458620\pi\)
\(954\) 0 0
\(955\) 1.44258e7 0.511836
\(956\) 1.97915e7 0.700381
\(957\) 0 0
\(958\) 7.39441e6 0.260309
\(959\) 6.38191e6 0.224080
\(960\) 0 0
\(961\) −5.66589e6 −0.197906
\(962\) −7.05425e6 −0.245761
\(963\) 0 0
\(964\) 6.85069e6 0.237433
\(965\) 3.96735e7 1.37146
\(966\) 0 0
\(967\) 2.54428e7 0.874983 0.437491 0.899223i \(-0.355867\pi\)
0.437491 + 0.899223i \(0.355867\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 7.29210e6 0.248842
\(971\) −9.88213e6 −0.336358 −0.168179 0.985756i \(-0.553789\pi\)
−0.168179 + 0.985756i \(0.553789\pi\)
\(972\) 0 0
\(973\) 1.55709e6 0.0527268
\(974\) −3.81644e6 −0.128902
\(975\) 0 0
\(976\) −3.91072e7 −1.31411
\(977\) −2.22197e6 −0.0744736 −0.0372368 0.999306i \(-0.511856\pi\)
−0.0372368 + 0.999306i \(0.511856\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 4.60056e7 1.53019
\(981\) 0 0
\(982\) 1.69716e6 0.0561623
\(983\) −2.53706e7 −0.837428 −0.418714 0.908118i \(-0.637519\pi\)
−0.418714 + 0.908118i \(0.637519\pi\)
\(984\) 0 0
\(985\) −7.95776e7 −2.61337
\(986\) 7.96849e6 0.261026
\(987\) 0 0
\(988\) 4.63363e7 1.51018
\(989\) −1.35736e7 −0.441269
\(990\) 0 0
\(991\) 3.24132e7 1.04843 0.524214 0.851587i \(-0.324359\pi\)
0.524214 + 0.851587i \(0.324359\pi\)
\(992\) 1.41124e7 0.455327
\(993\) 0 0
\(994\) −1.18794e6 −0.0381354
\(995\) −4.41655e7 −1.41425
\(996\) 0 0
\(997\) 1.55048e6 0.0494000 0.0247000 0.999695i \(-0.492137\pi\)
0.0247000 + 0.999695i \(0.492137\pi\)
\(998\) 6.95160e6 0.220932
\(999\) 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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1089.6.a.h.1.1 1
3.2 odd 2 363.6.a.b.1.1 1
11.10 odd 2 99.6.a.a.1.1 1
33.32 even 2 33.6.a.b.1.1 1
132.131 odd 2 528.6.a.a.1.1 1
165.164 even 2 825.6.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.6.a.b.1.1 1 33.32 even 2
99.6.a.a.1.1 1 11.10 odd 2
363.6.a.b.1.1 1 3.2 odd 2
528.6.a.a.1.1 1 132.131 odd 2
825.6.a.a.1.1 1 165.164 even 2
1089.6.a.h.1.1 1 1.1 even 1 trivial