Properties

Label 99.6.a.a.1.1
Level $99$
Weight $6$
Character 99.1
Self dual yes
Analytic conductor $15.878$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 99.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(15.8779981615\)
Analytic rank: \(0\)
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 \(\chi\) \(=\) 99.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -31.0000 q^{4} +92.0000 q^{5} -26.0000 q^{7} +63.0000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} -31.0000 q^{4} +92.0000 q^{5} -26.0000 q^{7} +63.0000 q^{8} -92.0000 q^{10} -121.000 q^{11} -692.000 q^{13} +26.0000 q^{14} +929.000 q^{16} +1442.00 q^{17} +2160.00 q^{19} -2852.00 q^{20} +121.000 q^{22} +1582.00 q^{23} +5339.00 q^{25} +692.000 q^{26} +806.000 q^{28} +5526.00 q^{29} +4792.00 q^{31} -2945.00 q^{32} -1442.00 q^{34} -2392.00 q^{35} -10194.0 q^{37} -2160.00 q^{38} +5796.00 q^{40} +10622.0 q^{41} +8580.00 q^{43} +3751.00 q^{44} -1582.00 q^{46} +2362.00 q^{47} -16131.0 q^{49} -5339.00 q^{50} +21452.0 q^{52} +30804.0 q^{53} -11132.0 q^{55} -1638.00 q^{56} -5526.00 q^{58} -6416.00 q^{59} +42096.0 q^{61} -4792.00 q^{62} -26783.0 q^{64} -63664.0 q^{65} -28444.0 q^{67} -44702.0 q^{68} +2392.00 q^{70} -45690.0 q^{71} -18374.0 q^{73} +10194.0 q^{74} -66960.0 q^{76} +3146.00 q^{77} -105214. q^{79} +85468.0 q^{80} -10622.0 q^{82} -62292.0 q^{83} +132664. q^{85} -8580.00 q^{86} -7623.00 q^{88} +72246.0 q^{89} +17992.0 q^{91} -49042.0 q^{92} -2362.00 q^{94} +198720. q^{95} +79262.0 q^{97} +16131.0 q^{98} +O(q^{100})\)

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 \(-0.528172\pi\)
−0.0883883 + 0.996086i \(0.528172\pi\)
\(3\) 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 \(-0.531973\pi\)
−0.100276 + 0.994960i \(0.531973\pi\)
\(8\) 63.0000 0.348029
\(9\) 0 0
\(10\) −92.0000 −0.290930
\(11\) −121.000 −0.301511
\(12\) 0 0
\(13\) −692.000 −1.13566 −0.567829 0.823146i \(-0.692217\pi\)
−0.567829 + 0.823146i \(0.692217\pi\)
\(14\) 26.0000 0.0354530
\(15\) 0 0
\(16\) 929.000 0.907227
\(17\) 1442.00 1.21016 0.605080 0.796165i \(-0.293141\pi\)
0.605080 + 0.796165i \(0.293141\pi\)
\(18\) 0 0
\(19\) 2160.00 1.37268 0.686341 0.727280i \(-0.259216\pi\)
0.686341 + 0.727280i \(0.259216\pi\)
\(20\) −2852.00 −1.59432
\(21\) 0 0
\(22\) 121.000 0.0533002
\(23\) 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 \(-0.291138\pi\)
0.610079 + 0.792341i \(0.291138\pi\)
\(30\) 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 \(-0.335747\pi\)
0.493420 + 0.869791i \(0.335747\pi\)
\(42\) 0 0
\(43\) 8580.00 0.707646 0.353823 0.935312i \(-0.384881\pi\)
0.353823 + 0.935312i \(0.384881\pi\)
\(44\) 3751.00 0.292089
\(45\) 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
\(55\) −11132.0 −0.496211
\(56\) −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 \(-0.242188\pi\)
0.724246 + 0.689541i \(0.242188\pi\)
\(62\) −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 \(-0.564671\pi\)
−0.201775 + 0.979432i \(0.564671\pi\)
\(74\) 10194.0 0.216404
\(75\) 0 0
\(76\) −66960.0 −1.32979
\(77\) 3146.00 0.0604689
\(78\) 0 0
\(79\) −105214. −1.89673 −0.948366 0.317179i \(-0.897264\pi\)
−0.948366 + 0.317179i \(0.897264\pi\)
\(80\) 85468.0 1.49306
\(81\) 0 0
\(82\) −10622.0 −0.174450
\(83\) −62292.0 −0.992515 −0.496257 0.868175i \(-0.665293\pi\)
−0.496257 + 0.868175i \(0.665293\pi\)
\(84\) 0 0
\(85\) 132664. 1.99162
\(86\) −8580.00 −0.125095
\(87\) 0 0
\(88\) −7623.00 −0.104935
\(89\) 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 \(-0.461158\pi\)
0.121724 + 0.992564i \(0.461158\pi\)
\(102\) 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 \(-0.483204\pi\)
0.0527403 + 0.998608i \(0.483204\pi\)
\(108\) 0 0
\(109\) 198748. 1.60227 0.801137 0.598482i \(-0.204229\pi\)
0.801137 + 0.598482i \(0.204229\pi\)
\(110\) 11132.0 0.0877186
\(111\) 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
\(121\) 14641.0 0.0909091
\(122\) −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 \(-0.184384\pi\)
0.836868 + 0.547405i \(0.184384\pi\)
\(128\) 121023. 0.652894
\(129\) 0 0
\(130\) 63664.0 0.330397
\(131\) −274428. −1.39717 −0.698586 0.715526i \(-0.746187\pi\)
−0.698586 + 0.715526i \(0.746187\pi\)
\(132\) 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 \(-0.541964\pi\)
−0.131454 + 0.991322i \(0.541964\pi\)
\(140\) 74152.0 0.319744
\(141\) 0 0
\(142\) 45690.0 0.190152
\(143\) 83732.0 0.342414
\(144\) 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 \(-0.542433\pi\)
−0.132913 + 0.991128i \(0.542433\pi\)
\(150\) 0 0
\(151\) −323110. −1.15321 −0.576605 0.817023i \(-0.695623\pi\)
−0.576605 + 0.817023i \(0.695623\pi\)
\(152\) 136080. 0.477733
\(153\) 0 0
\(154\) −3146.00 −0.0106895
\(155\) 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 \(-0.386513\pi\)
0.349024 + 0.937114i \(0.386513\pi\)
\(168\) 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 \(-0.706985\pi\)
−0.605396 + 0.795924i \(0.706985\pi\)
\(174\) 0 0
\(175\) −138814. −0.342640
\(176\) −112409. −0.273539
\(177\) 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
\(187\) −174482. −0.364877
\(188\) −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 \(-0.636802\pi\)
−0.416668 + 0.909059i \(0.636802\pi\)
\(194\) −79262.0 −0.151203
\(195\) 0 0
\(196\) 500061. 0.929786
\(197\) 864974. 1.58795 0.793976 0.607949i \(-0.208007\pi\)
0.793976 + 0.607949i \(0.208007\pi\)
\(198\) 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
\(209\) −261360. −0.413879
\(210\) 0 0
\(211\) 525900. 0.813199 0.406600 0.913606i \(-0.366714\pi\)
0.406600 + 0.913606i \(0.366714\pi\)
\(212\) −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
\(220\) 345092. 0.480705
\(221\) −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 \(-0.327875\pi\)
0.514777 + 0.857324i \(0.327875\pi\)
\(228\) 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 \(-0.356562\pi\)
0.435527 + 0.900176i \(0.356562\pi\)
\(234\) 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 \(-0.382269\pi\)
0.361487 + 0.932377i \(0.382269\pi\)
\(240\) 0 0
\(241\) 220990. 0.245092 0.122546 0.992463i \(-0.460894\pi\)
0.122546 + 0.992463i \(0.460894\pi\)
\(242\) −14641.0 −0.0160706
\(243\) 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
\(253\) −191422. −0.188014
\(254\) −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 \(-0.741824\pi\)
−0.688713 + 0.725034i \(0.741824\pi\)
\(264\) 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 \(-0.272067\pi\)
0.656427 + 0.754389i \(0.272067\pi\)
\(272\) 1.33962e6 1.09789
\(273\) 0 0
\(274\) −245458. −0.197515
\(275\) −646019. −0.515126
\(276\) 0 0
\(277\) 692704. 0.542436 0.271218 0.962518i \(-0.412574\pi\)
0.271218 + 0.962518i \(0.412574\pi\)
\(278\) 59888.0 0.0464759
\(279\) 0 0
\(280\) −150696. −0.114870
\(281\) 567018. 0.428382 0.214191 0.976792i \(-0.431289\pi\)
0.214191 + 0.976792i \(0.431289\pi\)
\(282\) 0 0
\(283\) 714916. 0.530626 0.265313 0.964162i \(-0.414525\pi\)
0.265313 + 0.964162i \(0.414525\pi\)
\(284\) 1.41639e6 1.04205
\(285\) 0 0
\(286\) −83732.0 −0.0605308
\(287\) −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 \(-0.760262\pi\)
−0.729533 + 0.683946i \(0.760262\pi\)
\(294\) 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 \(-0.557053\pi\)
−0.178278 + 0.983980i \(0.557053\pi\)
\(308\) −97526.0 −0.0585792
\(309\) 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
\(319\) −668646. −0.367891
\(320\) −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 \(-0.435435\pi\)
0.201448 + 0.979499i \(0.435435\pi\)
\(338\) −107571. −0.0512157
\(339\) 0 0
\(340\) −4.11258e6 −1.92938
\(341\) −579832. −0.270033
\(342\) 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 \(-0.350874\pi\)
0.451543 + 0.892249i \(0.350874\pi\)
\(348\) 0 0
\(349\) −378924. −0.166528 −0.0832642 0.996528i \(-0.526535\pi\)
−0.0832642 + 0.996528i \(0.526535\pi\)
\(350\) 138814. 0.0605708
\(351\) 0 0
\(352\) 356345. 0.153290
\(353\) 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 \(-0.251259\pi\)
0.704305 + 0.709898i \(0.251259\pi\)
\(360\) 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 \(-0.586066\pi\)
−0.267100 + 0.963669i \(0.586066\pi\)
\(374\) 174482. 0.0645018
\(375\) 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
\(385\) 289432. 0.0995164
\(386\) 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
\(407\) 1.23347e6 0.369100
\(408\) 0 0
\(409\) 1.38212e6 0.408542 0.204271 0.978914i \(-0.434518\pi\)
0.204271 + 0.978914i \(0.434518\pi\)
\(410\) −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
\(418\) 261360. 0.0731642
\(419\) −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 \(-0.267659\pi\)
0.666810 + 0.745228i \(0.267659\pi\)
\(432\) 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 \(-0.235558\pi\)
0.738450 + 0.674309i \(0.235558\pi\)
\(440\) −701316. −0.172696
\(441\) 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
\(451\) −1.28526e6 −0.297543
\(452\) 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 \(-0.532135\pi\)
−0.100782 + 0.994908i \(0.532135\pi\)
\(458\) 1.53989e6 0.343026
\(459\) 0 0
\(460\) −4.51186e6 −0.994172
\(461\) −1.13619e6 −0.249000 −0.124500 0.992220i \(-0.539733\pi\)
−0.124500 + 0.992220i \(0.539733\pi\)
\(462\) 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
\(473\) −1.03818e6 −0.213363
\(474\) 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 \(-0.763413\pi\)
−0.736266 + 0.676692i \(0.763413\pi\)
\(480\) 0 0
\(481\) 7.05425e6 1.39023
\(482\) −220990. −0.0433266
\(483\) 0 0
\(484\) −453871. −0.0880682
\(485\) 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 \(-0.550779\pi\)
−0.158851 + 0.987303i \(0.550779\pi\)
\(492\) 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 \(-0.677655\pi\)
−0.529591 + 0.848253i \(0.677655\pi\)
\(504\) 0 0
\(505\) 2.29614e6 0.400654
\(506\) 191422. 0.0332365
\(507\) 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
\(517\) −285802. −0.0470261
\(518\) −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 \(-0.502918\pi\)
−0.00916618 + 0.999958i \(0.502918\pi\)
\(524\) 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
\(539\) 1.95185e6 0.289384
\(540\) 0 0
\(541\) −2.12404e6 −0.312011 −0.156006 0.987756i \(-0.549862\pi\)
−0.156006 + 0.987756i \(0.549862\pi\)
\(542\) −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 \(-0.159876\pi\)
0.876494 + 0.481413i \(0.159876\pi\)
\(548\) −7.60920e6 −1.08240
\(549\) 0 0
\(550\) 646019. 0.0910623
\(551\) 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 \(-0.773745\pi\)
−0.757839 + 0.652442i \(0.773745\pi\)
\(558\) 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 \(-0.599369\pi\)
−0.307132 + 0.951667i \(0.599369\pi\)
\(564\) 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 \(-0.728824\pi\)
−0.658537 + 0.752548i \(0.728824\pi\)
\(570\) 0 0
\(571\) −9.36866e6 −1.20251 −0.601253 0.799059i \(-0.705331\pi\)
−0.601253 + 0.799059i \(0.705331\pi\)
\(572\) −2.59569e6 −0.331713
\(573\) 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
\(583\) −3.72728e6 −0.454173
\(584\) −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 \(-0.437943\pi\)
0.193726 + 0.981056i \(0.437943\pi\)
\(594\) 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 \(-0.368075\pi\)
0.402691 + 0.915336i \(0.368075\pi\)
\(602\) 223080. 0.0250882
\(603\) 0 0
\(604\) 1.00164e7 1.11717
\(605\) 1.34697e6 0.149613
\(606\) 0 0
\(607\) −9.64617e6 −1.06263 −0.531317 0.847173i \(-0.678303\pi\)
−0.531317 + 0.847173i \(0.678303\pi\)
\(608\) −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 \(-0.436599\pi\)
0.197864 + 0.980229i \(0.436599\pi\)
\(614\) 588808. 0.0630308
\(615\) 0 0
\(616\) 198198. 0.0210449
\(617\) −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
\(638\) 668646. 0.0650346
\(639\) 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
\(649\) 776336. 0.0723499
\(650\) 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 \(-0.661287\pi\)
−0.485294 + 0.874351i \(0.661287\pi\)
\(660\) 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
\(671\) −5.09362e6 −0.436737
\(672\) 0 0
\(673\) −2.03858e7 −1.73496 −0.867482 0.497468i \(-0.834263\pi\)
−0.867482 + 0.497468i \(0.834263\pi\)
\(674\) −839978. −0.0712227
\(675\) 0 0
\(676\) −3.33470e6 −0.280666
\(677\) −6.09278e6 −0.510909 −0.255455 0.966821i \(-0.582225\pi\)
−0.255455 + 0.966821i \(0.582225\pi\)
\(678\) 0 0
\(679\) −2.06081e6 −0.171539
\(680\) 8.35783e6 0.693141
\(681\) 0 0
\(682\) 579832. 0.0477355
\(683\) −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 \(-0.578522\pi\)
−0.244191 + 0.969727i \(0.578522\pi\)
\(702\) 0 0
\(703\) −2.20190e7 −1.68039
\(704\) 3.24074e6 0.246441
\(705\) 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
\(715\) 7.70334e6 0.563526
\(716\) 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 \(-0.722995\pi\)
−0.644646 + 0.764481i \(0.722995\pi\)
\(734\) 1.79679e6 0.123100
\(735\) 0 0
\(736\) −4.65899e6 −0.317028
\(737\) 3.44172e6 0.233403
\(738\) 0 0
\(739\) 2.79727e6 0.188418 0.0942091 0.995552i \(-0.469968\pi\)
0.0942091 + 0.995552i \(0.469968\pi\)
\(740\) 2.90733e7 1.95171
\(741\) 0 0
\(742\) 800904. 0.0534036
\(743\) 2.25651e7 1.49956 0.749781 0.661686i \(-0.230159\pi\)
0.749781 + 0.661686i \(0.230159\pi\)
\(744\) 0 0
\(745\) −6.62750e6 −0.437481
\(746\) 1.43541e6 0.0944342
\(747\) 0 0
\(748\) 5.40894e6 0.353475
\(749\) −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 \(-0.403250\pi\)
0.299291 + 0.954162i \(0.403250\pi\)
\(762\) 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 \(-0.507230\pi\)
−0.0227118 + 0.999742i \(0.507230\pi\)
\(770\) −289432. −0.0175922
\(771\) 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
\(781\) 5.52849e6 0.324324
\(782\) −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 \(-0.639544\pi\)
−0.424483 + 0.905436i \(0.639544\pi\)
\(788\) −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
\(803\) 2.22325e6 0.121675
\(804\) 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 \(-0.739889\pi\)
−0.684293 + 0.729207i \(0.739889\pi\)
\(810\) 0 0
\(811\) −1.91915e7 −1.02460 −0.512302 0.858805i \(-0.671207\pi\)
−0.512302 + 0.858805i \(0.671207\pi\)
\(812\) 4.45396e6 0.237059
\(813\) 0 0
\(814\) −1.23347e6 −0.0652483
\(815\) −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 \(-0.526988\pi\)
−0.0846840 + 0.996408i \(0.526988\pi\)
\(822\) 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 \(-0.714595\pi\)
−0.624248 + 0.781226i \(0.714595\pi\)
\(828\) 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
\(836\) 8.10216e6 0.400945
\(837\) 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
\(847\) −380666. −0.0182321
\(848\) 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 \(-0.628702\pi\)
−0.393403 + 0.919366i \(0.628702\pi\)
\(854\) 1.09450e6 0.0513534
\(855\) 0 0
\(856\) 786996. 0.0367103
\(857\) 9.15871e6 0.425973 0.212987 0.977055i \(-0.431681\pi\)
0.212987 + 0.977055i \(0.431681\pi\)
\(858\) 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
\(869\) 1.27309e7 0.571886
\(870\) 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 \(-0.589931\pi\)
−0.278784 + 0.960354i \(0.589931\pi\)
\(878\) −5.96365e6 −0.261081
\(879\) 0 0
\(880\) −1.03416e7 −0.450176
\(881\) 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 \(-0.427971\pi\)
0.224359 + 0.974507i \(0.427971\pi\)
\(888\) 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
\(902\) 1.28526e6 0.0525987
\(903\) 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
\(913\) 7.53733e6 0.299255
\(914\) 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 \(-0.275916\pi\)
0.647256 + 0.762273i \(0.275916\pi\)
\(920\) 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
\(935\) −1.60523e7 −0.600495
\(936\) 0 0
\(937\) −3.10737e7 −1.15623 −0.578115 0.815955i \(-0.696212\pi\)
−0.578115 + 0.815955i \(0.696212\pi\)
\(938\) −739544. −0.0274446
\(939\) 0 0
\(940\) −6.73642e6 −0.248662
\(941\) 2.50349e7 0.921664 0.460832 0.887488i \(-0.347551\pi\)
0.460832 + 0.887488i \(0.347551\pi\)
\(942\) 0 0
\(943\) 1.68040e7 0.615366
\(944\) −5.96046e6 −0.217696
\(945\) 0 0
\(946\) 1.03818e6 0.0377177
\(947\) 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 \(-0.541380\pi\)
−0.129634 + 0.991562i \(0.541380\pi\)
\(954\) 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 \(-0.644133\pi\)
−0.437491 + 0.899223i \(0.644133\pi\)
\(968\) 922383. 0.0316390
\(969\) 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
\(979\) −8.74177e6 −0.291503
\(980\) 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 \(-0.507863\pi\)
−0.0247000 + 0.999695i \(0.507863\pi\)
\(998\) −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 99.6.a.a.1.1 1
3.2 odd 2 33.6.a.b.1.1 1
11.10 odd 2 1089.6.a.h.1.1 1
12.11 even 2 528.6.a.a.1.1 1
15.14 odd 2 825.6.a.a.1.1 1
33.32 even 2 363.6.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.6.a.b.1.1 1 3.2 odd 2
99.6.a.a.1.1 1 1.1 even 1 trivial
363.6.a.b.1.1 1 33.32 even 2
528.6.a.a.1.1 1 12.11 even 2
825.6.a.a.1.1 1 15.14 odd 2
1089.6.a.h.1.1 1 11.10 odd 2