Properties

Label 528.6.a.a.1.1
Level $528$
Weight $6$
Character 528.1
Self dual yes
Analytic conductor $84.683$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 528.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(84.6826568613\)
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 \(\chi\) \(=\) 528.1

$q$-expansion

\(f(q)\) \(=\) \(q-9.00000 q^{3} -92.0000 q^{5} +26.0000 q^{7} +81.0000 q^{9} +O(q^{10})\) \(q-9.00000 q^{3} -92.0000 q^{5} +26.0000 q^{7} +81.0000 q^{9} -121.000 q^{11} -692.000 q^{13} +828.000 q^{15} -1442.00 q^{17} -2160.00 q^{19} -234.000 q^{21} +1582.00 q^{23} +5339.00 q^{25} -729.000 q^{27} -5526.00 q^{29} -4792.00 q^{31} +1089.00 q^{33} -2392.00 q^{35} -10194.0 q^{37} +6228.00 q^{39} -10622.0 q^{41} -8580.00 q^{43} -7452.00 q^{45} +2362.00 q^{47} -16131.0 q^{49} +12978.0 q^{51} -30804.0 q^{53} +11132.0 q^{55} +19440.0 q^{57} -6416.00 q^{59} +42096.0 q^{61} +2106.00 q^{63} +63664.0 q^{65} +28444.0 q^{67} -14238.0 q^{69} -45690.0 q^{71} -18374.0 q^{73} -48051.0 q^{75} -3146.00 q^{77} +105214. q^{79} +6561.00 q^{81} -62292.0 q^{83} +132664. q^{85} +49734.0 q^{87} -72246.0 q^{89} -17992.0 q^{91} +43128.0 q^{93} +198720. q^{95} +79262.0 q^{97} -9801.00 q^{99} +O(q^{100})\)

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
\(3\) −9.00000 −0.577350
\(4\) 0 0
\(5\) −92.0000 −1.64575 −0.822873 0.568225i \(-0.807630\pi\)
−0.822873 + 0.568225i \(0.807630\pi\)
\(6\) 0 0
\(7\) 26.0000 0.200553 0.100276 0.994960i \(-0.468027\pi\)
0.100276 + 0.994960i \(0.468027\pi\)
\(8\) 0 0
\(9\) 81.0000 0.333333
\(10\) 0 0
\(11\) −121.000 −0.301511
\(12\) 0 0
\(13\) −692.000 −1.13566 −0.567829 0.823146i \(-0.692217\pi\)
−0.567829 + 0.823146i \(0.692217\pi\)
\(14\) 0 0
\(15\) 828.000 0.950172
\(16\) 0 0
\(17\) −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 \(0.740784\pi\)
\(20\) 0 0
\(21\) −234.000 −0.115789
\(22\) 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
\(26\) 0 0
\(27\) −729.000 −0.192450
\(28\) 0 0
\(29\) −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 \(-0.647792\pi\)
−0.447798 + 0.894135i \(0.647792\pi\)
\(32\) 0 0
\(33\) 1089.00 0.174078
\(34\) 0 0
\(35\) −2392.00 −0.330059
\(36\) 0 0
\(37\) −10194.0 −1.22417 −0.612083 0.790794i \(-0.709668\pi\)
−0.612083 + 0.790794i \(0.709668\pi\)
\(38\) 0 0
\(39\) 6228.00 0.655673
\(40\) 0 0
\(41\) −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
\(45\) −7452.00 −0.548582
\(46\) 0 0
\(47\) 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
\(50\) 0 0
\(51\) 12978.0 0.698686
\(52\) 0 0
\(53\) −30804.0 −1.50632 −0.753160 0.657837i \(-0.771472\pi\)
−0.753160 + 0.657837i \(0.771472\pi\)
\(54\) 0 0
\(55\) 11132.0 0.496211
\(56\) 0 0
\(57\) 19440.0 0.792518
\(58\) 0 0
\(59\) −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 \(0.242188\pi\)
\(62\) 0 0
\(63\) 2106.00 0.0668509
\(64\) 0 0
\(65\) 63664.0 1.86901
\(66\) 0 0
\(67\) 28444.0 0.774112 0.387056 0.922056i \(-0.373492\pi\)
0.387056 + 0.922056i \(0.373492\pi\)
\(68\) 0 0
\(69\) −14238.0 −0.360020
\(70\) 0 0
\(71\) −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 \(0.564671\pi\)
\(74\) 0 0
\(75\) −48051.0 −0.986391
\(76\) 0 0
\(77\) −3146.00 −0.0604689
\(78\) 0 0
\(79\) 105214. 1.89673 0.948366 0.317179i \(-0.102736\pi\)
0.948366 + 0.317179i \(0.102736\pi\)
\(80\) 0 0
\(81\) 6561.00 0.111111
\(82\) 0 0
\(83\) −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
\(86\) 0 0
\(87\) 49734.0 0.704458
\(88\) 0 0
\(89\) −72246.0 −0.966805 −0.483402 0.875398i \(-0.660599\pi\)
−0.483402 + 0.875398i \(0.660599\pi\)
\(90\) 0 0
\(91\) −17992.0 −0.227759
\(92\) 0 0
\(93\) 43128.0 0.517073
\(94\) 0 0
\(95\) 198720. 2.25908
\(96\) 0 0
\(97\) 79262.0 0.855334 0.427667 0.903936i \(-0.359336\pi\)
0.427667 + 0.903936i \(0.359336\pi\)
\(98\) 0 0
\(99\) −9801.00 −0.100504
\(100\) 0 0
\(101\) −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 \(-0.415016\pi\)
0.263826 + 0.964570i \(0.415016\pi\)
\(104\) 0 0
\(105\) 21528.0 0.190559
\(106\) 0 0
\(107\) 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 \(0.204229\pi\)
\(110\) 0 0
\(111\) 91746.0 0.706773
\(112\) 0 0
\(113\) 166554. 1.22704 0.613520 0.789679i \(-0.289753\pi\)
0.613520 + 0.789679i \(0.289753\pi\)
\(114\) 0 0
\(115\) −145544. −1.02624
\(116\) 0 0
\(117\) −56052.0 −0.378553
\(118\) 0 0
\(119\) −37492.0 −0.242701
\(120\) 0 0
\(121\) 14641.0 0.0909091
\(122\) 0 0
\(123\) 95598.0 0.569752
\(124\) 0 0
\(125\) −203688. −1.16598
\(126\) 0 0
\(127\) −304226. −1.67374 −0.836868 0.547405i \(-0.815616\pi\)
−0.836868 + 0.547405i \(0.815616\pi\)
\(128\) 0 0
\(129\) 77220.0 0.408560
\(130\) 0 0
\(131\) −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
\(134\) 0 0
\(135\) 67068.0 0.316724
\(136\) 0 0
\(137\) −245458. −1.11732 −0.558658 0.829398i \(-0.688683\pi\)
−0.558658 + 0.829398i \(0.688683\pi\)
\(138\) 0 0
\(139\) 59888.0 0.262907 0.131454 0.991322i \(-0.458036\pi\)
0.131454 + 0.991322i \(0.458036\pi\)
\(140\) 0 0
\(141\) −21258.0 −0.0900481
\(142\) 0 0
\(143\) 83732.0 0.342414
\(144\) 0 0
\(145\) 508392. 2.00807
\(146\) 0 0
\(147\) 145179. 0.554128
\(148\) 0 0
\(149\) 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 \(0.304377\pi\)
\(152\) 0 0
\(153\) −116802. −0.403387
\(154\) 0 0
\(155\) 440864. 1.47393
\(156\) 0 0
\(157\) −318766. −1.03210 −0.516051 0.856558i \(-0.672599\pi\)
−0.516051 + 0.856558i \(0.672599\pi\)
\(158\) 0 0
\(159\) 277236. 0.869675
\(160\) 0 0
\(161\) 41132.0 0.125059
\(162\) 0 0
\(163\) 431996. 1.27353 0.636767 0.771056i \(-0.280271\pi\)
0.636767 + 0.771056i \(0.280271\pi\)
\(164\) 0 0
\(165\) −100188. −0.286488
\(166\) 0 0
\(167\) 251580. 0.698047 0.349024 0.937114i \(-0.386513\pi\)
0.349024 + 0.937114i \(0.386513\pi\)
\(168\) 0 0
\(169\) 107571. 0.289720
\(170\) 0 0
\(171\) −174960. −0.457560
\(172\) 0 0
\(173\) 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
\(177\) 57744.0 0.138540
\(178\) 0 0
\(179\) −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 \(0.409222\pi\)
\(182\) 0 0
\(183\) −378864. −0.836288
\(184\) 0 0
\(185\) 937848. 2.01467
\(186\) 0 0
\(187\) 174482. 0.364877
\(188\) 0 0
\(189\) −18954.0 −0.0385964
\(190\) 0 0
\(191\) 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 \(0.636802\pi\)
\(194\) 0 0
\(195\) −572976. −1.07907
\(196\) 0 0
\(197\) −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 \(-0.358631\pi\)
0.429668 + 0.902987i \(0.358631\pi\)
\(200\) 0 0
\(201\) −255996. −0.446934
\(202\) 0 0
\(203\) −143676. −0.244706
\(204\) 0 0
\(205\) 977224. 1.62409
\(206\) 0 0
\(207\) 128142. 0.207857
\(208\) 0 0
\(209\) 261360. 0.413879
\(210\) 0 0
\(211\) −525900. −0.813199 −0.406600 0.913606i \(-0.633286\pi\)
−0.406600 + 0.913606i \(0.633286\pi\)
\(212\) 0 0
\(213\) 411210. 0.621033
\(214\) 0 0
\(215\) 789360. 1.16461
\(216\) 0 0
\(217\) −124592. −0.179614
\(218\) 0 0
\(219\) 165366. 0.232989
\(220\) 0 0
\(221\) 997864. 1.37433
\(222\) 0 0
\(223\) 245264. 0.330272 0.165136 0.986271i \(-0.447194\pi\)
0.165136 + 0.986271i \(0.447194\pi\)
\(224\) 0 0
\(225\) 432459. 0.569493
\(226\) 0 0
\(227\) 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 \(0.922128\pi\)
\(230\) 0 0
\(231\) 28314.0 0.0349117
\(232\) 0 0
\(233\) −721830. −0.871054 −0.435527 0.900176i \(-0.643438\pi\)
−0.435527 + 0.900176i \(0.643438\pi\)
\(234\) 0 0
\(235\) −217304. −0.256684
\(236\) 0 0
\(237\) −946926. −1.09508
\(238\) 0 0
\(239\) 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 \(0.460894\pi\)
\(242\) 0 0
\(243\) −59049.0 −0.0641500
\(244\) 0 0
\(245\) 1.48405e6 1.57955
\(246\) 0 0
\(247\) 1.49472e6 1.55890
\(248\) 0 0
\(249\) 560628. 0.573029
\(250\) 0 0
\(251\) −627304. −0.628483 −0.314242 0.949343i \(-0.601750\pi\)
−0.314242 + 0.949343i \(0.601750\pi\)
\(252\) 0 0
\(253\) −191422. −0.188014
\(254\) 0 0
\(255\) −1.19398e6 −1.14986
\(256\) 0 0
\(257\) −468014. −0.442004 −0.221002 0.975273i \(-0.570933\pi\)
−0.221002 + 0.975273i \(0.570933\pi\)
\(258\) 0 0
\(259\) −265044. −0.245510
\(260\) 0 0
\(261\) −447606. −0.406719
\(262\) 0 0
\(263\) −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
\(266\) 0 0
\(267\) 650214. 0.558185
\(268\) 0 0
\(269\) −1.07457e6 −0.905430 −0.452715 0.891655i \(-0.649544\pi\)
−0.452715 + 0.891655i \(0.649544\pi\)
\(270\) 0 0
\(271\) −1.58723e6 −1.31285 −0.656427 0.754389i \(-0.727933\pi\)
−0.656427 + 0.754389i \(0.727933\pi\)
\(272\) 0 0
\(273\) 161928. 0.131497
\(274\) 0 0
\(275\) −646019. −0.515126
\(276\) 0 0
\(277\) 692704. 0.542436 0.271218 0.962518i \(-0.412574\pi\)
0.271218 + 0.962518i \(0.412574\pi\)
\(278\) 0 0
\(279\) −388152. −0.298532
\(280\) 0 0
\(281\) −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 \(0.585475\pi\)
\(284\) 0 0
\(285\) −1.78848e6 −1.30428
\(286\) 0 0
\(287\) −276172. −0.197913
\(288\) 0 0
\(289\) 659507. 0.464488
\(290\) 0 0
\(291\) −713358. −0.493827
\(292\) 0 0
\(293\) 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
\(296\) 0 0
\(297\) 88209.0 0.0580259
\(298\) 0 0
\(299\) −1.09474e6 −0.708165
\(300\) 0 0
\(301\) −223080. −0.141920
\(302\) 0 0
\(303\) 224622. 0.140555
\(304\) 0 0
\(305\) −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
\(309\) −511308. −0.304640
\(310\) 0 0
\(311\) −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 \(0.723110\pi\)
\(314\) 0 0
\(315\) −193752. −0.110020
\(316\) 0 0
\(317\) 1.06079e6 0.592901 0.296450 0.955048i \(-0.404197\pi\)
0.296450 + 0.955048i \(0.404197\pi\)
\(318\) 0 0
\(319\) 668646. 0.367891
\(320\) 0 0
\(321\) −112428. −0.0608992
\(322\) 0 0
\(323\) 3.11472e6 1.66116
\(324\) 0 0
\(325\) −3.69459e6 −1.94025
\(326\) 0 0
\(327\) −1.78873e6 −0.925073
\(328\) 0 0
\(329\) 61412.0 0.0312798
\(330\) 0 0
\(331\) 2.34566e6 1.17678 0.588390 0.808577i \(-0.299762\pi\)
0.588390 + 0.808577i \(0.299762\pi\)
\(332\) 0 0
\(333\) −825714. −0.408055
\(334\) 0 0
\(335\) −2.61685e6 −1.27399
\(336\) 0 0
\(337\) 839978. 0.402896 0.201448 0.979499i \(-0.435435\pi\)
0.201448 + 0.979499i \(0.435435\pi\)
\(338\) 0 0
\(339\) −1.49899e6 −0.708432
\(340\) 0 0
\(341\) 579832. 0.270033
\(342\) 0 0
\(343\) −856388. −0.393039
\(344\) 0 0
\(345\) 1.30990e6 0.592501
\(346\) 0 0
\(347\) 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 \(0.526535\pi\)
\(350\) 0 0
\(351\) 504468. 0.218558
\(352\) 0 0
\(353\) −1.98730e6 −0.848842 −0.424421 0.905465i \(-0.639522\pi\)
−0.424421 + 0.905465i \(0.639522\pi\)
\(354\) 0 0
\(355\) 4.20348e6 1.77026
\(356\) 0 0
\(357\) 337428. 0.140123
\(358\) 0 0
\(359\) 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
\(362\) 0 0
\(363\) −131769. −0.0524864
\(364\) 0 0
\(365\) 1.69041e6 0.664140
\(366\) 0 0
\(367\) 1.79679e6 0.696358 0.348179 0.937428i \(-0.386800\pi\)
0.348179 + 0.937428i \(0.386800\pi\)
\(368\) 0 0
\(369\) −860382. −0.328947
\(370\) 0 0
\(371\) −800904. −0.302096
\(372\) 0 0
\(373\) −1.43541e6 −0.534201 −0.267100 0.963669i \(-0.586066\pi\)
−0.267100 + 0.963669i \(0.586066\pi\)
\(374\) 0 0
\(375\) 1.83319e6 0.673178
\(376\) 0 0
\(377\) 3.82399e6 1.38568
\(378\) 0 0
\(379\) −2.66235e6 −0.952065 −0.476033 0.879428i \(-0.657926\pi\)
−0.476033 + 0.879428i \(0.657926\pi\)
\(380\) 0 0
\(381\) 2.73803e6 0.966332
\(382\) 0 0
\(383\) −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
\(386\) 0 0
\(387\) −694980. −0.235882
\(388\) 0 0
\(389\) −4.29947e6 −1.44059 −0.720296 0.693667i \(-0.755994\pi\)
−0.720296 + 0.693667i \(0.755994\pi\)
\(390\) 0 0
\(391\) −2.28124e6 −0.754623
\(392\) 0 0
\(393\) 2.46985e6 0.806658
\(394\) 0 0
\(395\) −9.67969e6 −3.12154
\(396\) 0 0
\(397\) 728818. 0.232083 0.116041 0.993244i \(-0.462979\pi\)
0.116041 + 0.993244i \(0.462979\pi\)
\(398\) 0 0
\(399\) 505440. 0.158942
\(400\) 0 0
\(401\) −5.92515e6 −1.84009 −0.920044 0.391814i \(-0.871848\pi\)
−0.920044 + 0.391814i \(0.871848\pi\)
\(402\) 0 0
\(403\) 3.31606e6 1.01709
\(404\) 0 0
\(405\) −603612. −0.182861
\(406\) 0 0
\(407\) 1.23347e6 0.369100
\(408\) 0 0
\(409\) 1.38212e6 0.408542 0.204271 0.978914i \(-0.434518\pi\)
0.204271 + 0.978914i \(0.434518\pi\)
\(410\) 0 0
\(411\) 2.20912e6 0.645082
\(412\) 0 0
\(413\) −166816. −0.0481241
\(414\) 0 0
\(415\) 5.73086e6 1.63343
\(416\) 0 0
\(417\) −538992. −0.151790
\(418\) 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 \(0.454827\pi\)
\(422\) 0 0
\(423\) 191322. 0.0519893
\(424\) 0 0
\(425\) −7.69884e6 −2.06753
\(426\) 0 0
\(427\) 1.09450e6 0.290499
\(428\) 0 0
\(429\) −753588. −0.197693
\(430\) 0 0
\(431\) 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 \(0.483146\pi\)
\(434\) 0 0
\(435\) −4.57553e6 −1.15936
\(436\) 0 0
\(437\) −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
\(441\) −1.30661e6 −0.319926
\(442\) 0 0
\(443\) −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
\(446\) 0 0
\(447\) −648342. −0.153474
\(448\) 0 0
\(449\) −7858.00 −0.00183948 −0.000919742 1.00000i \(-0.500293\pi\)
−0.000919742 1.00000i \(0.500293\pi\)
\(450\) 0 0
\(451\) 1.28526e6 0.297543
\(452\) 0 0
\(453\) −2.90799e6 −0.665806
\(454\) 0 0
\(455\) 1.65526e6 0.374834
\(456\) 0 0
\(457\) −899922. −0.201565 −0.100782 0.994908i \(-0.532135\pi\)
−0.100782 + 0.994908i \(0.532135\pi\)
\(458\) 0 0
\(459\) 1.05122e6 0.232895
\(460\) 0 0
\(461\) 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 \(-0.204293\pi\)
0.801016 + 0.598643i \(0.204293\pi\)
\(464\) 0 0
\(465\) −3.96778e6 −0.850971
\(466\) 0 0
\(467\) −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
\(470\) 0 0
\(471\) 2.86889e6 0.595885
\(472\) 0 0
\(473\) 1.03818e6 0.213363
\(474\) 0 0
\(475\) −1.15322e7 −2.34520
\(476\) 0 0
\(477\) −2.49512e6 −0.502107
\(478\) 0 0
\(479\) −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
\(482\) 0 0
\(483\) −370188. −0.0722029
\(484\) 0 0
\(485\) −7.29210e6 −1.40766
\(486\) 0 0
\(487\) 3.81644e6 0.729181 0.364591 0.931168i \(-0.381209\pi\)
0.364591 + 0.931168i \(0.381209\pi\)
\(488\) 0 0
\(489\) −3.88796e6 −0.735275
\(490\) 0 0
\(491\) −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
\(494\) 0 0
\(495\) 901692. 0.165404
\(496\) 0 0
\(497\) −1.18794e6 −0.215727
\(498\) 0 0
\(499\) −6.95160e6 −1.24978 −0.624889 0.780713i \(-0.714856\pi\)
−0.624889 + 0.780713i \(0.714856\pi\)
\(500\) 0 0
\(501\) −2.26422e6 −0.403018
\(502\) 0 0
\(503\) −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
\(506\) 0 0
\(507\) −968139. −0.167270
\(508\) 0 0
\(509\) 624660. 0.106868 0.0534342 0.998571i \(-0.482983\pi\)
0.0534342 + 0.998571i \(0.482983\pi\)
\(510\) 0 0
\(511\) −477724. −0.0809328
\(512\) 0 0
\(513\) 1.57464e6 0.264173
\(514\) 0 0
\(515\) −5.22670e6 −0.868380
\(516\) 0 0
\(517\) −285802. −0.0470261
\(518\) 0 0
\(519\) −4.28971e6 −0.699051
\(520\) 0 0
\(521\) −647490. −0.104505 −0.0522527 0.998634i \(-0.516640\pi\)
−0.0522527 + 0.998634i \(0.516640\pi\)
\(522\) 0 0
\(523\) 114676. 0.0183324 0.00916618 0.999958i \(-0.497082\pi\)
0.00916618 + 0.999958i \(0.497082\pi\)
\(524\) 0 0
\(525\) −1.24933e6 −0.197823
\(526\) 0 0
\(527\) 6.91006e6 1.08382
\(528\) 0 0
\(529\) −3.93362e6 −0.611157
\(530\) 0 0
\(531\) −519696. −0.0799858
\(532\) 0 0
\(533\) 7.35042e6 1.12071
\(534\) 0 0
\(535\) −1.14926e6 −0.173594
\(536\) 0 0
\(537\) 811728. 0.121472
\(538\) 0 0
\(539\) 1.95185e6 0.289384
\(540\) 0 0
\(541\) −2.12404e6 −0.312011 −0.156006 0.987756i \(-0.549862\pi\)
−0.156006 + 0.987756i \(0.549862\pi\)
\(542\) 0 0
\(543\) −2.23202e6 −0.324861
\(544\) 0 0
\(545\) −1.82848e7 −2.63693
\(546\) 0 0
\(547\) −1.22672e7 −1.75299 −0.876494 0.481413i \(-0.840124\pi\)
−0.876494 + 0.481413i \(0.840124\pi\)
\(548\) 0 0
\(549\) 3.40978e6 0.482831
\(550\) 0 0
\(551\) 1.19362e7 1.67489
\(552\) 0 0
\(553\) 2.73556e6 0.380394
\(554\) 0 0
\(555\) −8.44063e6 −1.16317
\(556\) 0 0
\(557\) 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
\(560\) 0 0
\(561\) −1.57034e6 −0.210662
\(562\) 0 0
\(563\) −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
\(566\) 0 0
\(567\) 170586. 0.0222836
\(568\) 0 0
\(569\) 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
\(573\) −1.41122e6 −0.179559
\(574\) 0 0
\(575\) 8.44630e6 1.06536
\(576\) 0 0
\(577\) −6.14973e6 −0.768983 −0.384491 0.923129i \(-0.625623\pi\)
−0.384491 + 0.923129i \(0.625623\pi\)
\(578\) 0 0
\(579\) 3.88111e6 0.481126
\(580\) 0 0
\(581\) −1.61959e6 −0.199051
\(582\) 0 0
\(583\) 3.72728e6 0.454173
\(584\) 0 0
\(585\) 5.15678e6 0.623002
\(586\) 0 0
\(587\) −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
\(590\) 0 0
\(591\) 7.78477e6 0.916805
\(592\) 0 0
\(593\) −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
\(596\) 0 0
\(597\) −4.32054e6 −0.496138
\(598\) 0 0
\(599\) 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 \(0.368075\pi\)
\(602\) 0 0
\(603\) 2.30396e6 0.258037
\(604\) 0 0
\(605\) −1.34697e6 −0.149613
\(606\) 0 0
\(607\) 9.64617e6 1.06263 0.531317 0.847173i \(-0.321697\pi\)
0.531317 + 0.847173i \(0.321697\pi\)
\(608\) 0 0
\(609\) 1.29308e6 0.141281
\(610\) 0 0
\(611\) −1.63450e6 −0.177126
\(612\) 0 0
\(613\) 3.68170e6 0.395729 0.197864 0.980229i \(-0.436599\pi\)
0.197864 + 0.980229i \(0.436599\pi\)
\(614\) 0 0
\(615\) −8.79502e6 −0.937667
\(616\) 0 0
\(617\) 1.83190e7 1.93727 0.968635 0.248489i \(-0.0799340\pi\)
0.968635 + 0.248489i \(0.0799340\pi\)
\(618\) 0 0
\(619\) −1.09660e6 −0.115033 −0.0575166 0.998345i \(-0.518318\pi\)
−0.0575166 + 0.998345i \(0.518318\pi\)
\(620\) 0 0
\(621\) −1.15328e6 −0.120007
\(622\) 0 0
\(623\) −1.87840e6 −0.193895
\(624\) 0 0
\(625\) 2.05492e6 0.210424
\(626\) 0 0
\(627\) −2.35224e6 −0.238953
\(628\) 0 0
\(629\) 1.46997e7 1.48144
\(630\) 0 0
\(631\) 9.58030e6 0.957869 0.478934 0.877851i \(-0.341023\pi\)
0.478934 + 0.877851i \(0.341023\pi\)
\(632\) 0 0
\(633\) 4.73310e6 0.469501
\(634\) 0 0
\(635\) 2.79888e7 2.75454
\(636\) 0 0
\(637\) 1.11627e7 1.08998
\(638\) 0 0
\(639\) −3.70089e6 −0.358554
\(640\) 0 0
\(641\) −1.18062e7 −1.13492 −0.567462 0.823400i \(-0.692075\pi\)
−0.567462 + 0.823400i \(0.692075\pi\)
\(642\) 0 0
\(643\) 5.88298e6 0.561138 0.280569 0.959834i \(-0.409477\pi\)
0.280569 + 0.959834i \(0.409477\pi\)
\(644\) 0 0
\(645\) −7.10424e6 −0.672385
\(646\) 0 0
\(647\) 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
\(650\) 0 0
\(651\) 1.12133e6 0.103700
\(652\) 0 0
\(653\) −5.70795e6 −0.523838 −0.261919 0.965090i \(-0.584355\pi\)
−0.261919 + 0.965090i \(0.584355\pi\)
\(654\) 0 0
\(655\) 2.52474e7 2.29939
\(656\) 0 0
\(657\) −1.48829e6 −0.134516
\(658\) 0 0
\(659\) −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 \(0.330086\pi\)
\(662\) 0 0
\(663\) −8.98078e6 −0.793469
\(664\) 0 0
\(665\) 5.16672e6 0.453065
\(666\) 0 0
\(667\) −8.74213e6 −0.760857
\(668\) 0 0
\(669\) −2.20738e6 −0.190683
\(670\) 0 0
\(671\) −5.09362e6 −0.436737
\(672\) 0 0
\(673\) −2.03858e7 −1.73496 −0.867482 0.497468i \(-0.834263\pi\)
−0.867482 + 0.497468i \(0.834263\pi\)
\(674\) 0 0
\(675\) −3.89213e6 −0.328797
\(676\) 0 0
\(677\) 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
\(680\) 0 0
\(681\) −7.19377e6 −0.594414
\(682\) 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
\(686\) 0 0
\(687\) 1.38590e7 1.12032
\(688\) 0 0
\(689\) 2.13164e7 1.71067
\(690\) 0 0
\(691\) −9.87069e6 −0.786416 −0.393208 0.919449i \(-0.628635\pi\)
−0.393208 + 0.919449i \(0.628635\pi\)
\(692\) 0 0
\(693\) −254826. −0.0201563
\(694\) 0 0
\(695\) −5.50970e6 −0.432679
\(696\) 0 0
\(697\) 1.53169e7 1.19423
\(698\) 0 0
\(699\) 6.49647e6 0.502903
\(700\) 0 0
\(701\) 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
\(705\) 1.95574e6 0.148196
\(706\) 0 0
\(707\) −648908. −0.0488241
\(708\) 0 0
\(709\) −411382. −0.0307348 −0.0153674 0.999882i \(-0.504892\pi\)
−0.0153674 + 0.999882i \(0.504892\pi\)
\(710\) 0 0
\(711\) 8.52233e6 0.632244
\(712\) 0 0
\(713\) −7.58094e6 −0.558470
\(714\) 0 0
\(715\) −7.70334e6 −0.563526
\(716\) 0 0
\(717\) −5.74592e6 −0.417409
\(718\) 0 0
\(719\) −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
\(722\) 0 0
\(723\) −1.98891e6 −0.141504
\(724\) 0 0
\(725\) −2.95033e7 −2.08461
\(726\) 0 0
\(727\) −1.14699e7 −0.804866 −0.402433 0.915449i \(-0.631835\pi\)
−0.402433 + 0.915449i \(0.631835\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) 0 0
\(731\) 1.23724e7 0.856365
\(732\) 0 0
\(733\) −1.87547e7 −1.28929 −0.644646 0.764481i \(-0.722995\pi\)
−0.644646 + 0.764481i \(0.722995\pi\)
\(734\) 0 0
\(735\) −1.33565e7 −0.911955
\(736\) 0 0
\(737\) −3.44172e6 −0.233403
\(738\) 0 0
\(739\) −2.79727e6 −0.188418 −0.0942091 0.995552i \(-0.530032\pi\)
−0.0942091 + 0.995552i \(0.530032\pi\)
\(740\) 0 0
\(741\) −1.34525e7 −0.900030
\(742\) 0 0
\(743\) 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
\(746\) 0 0
\(747\) −5.04565e6 −0.330838
\(748\) 0 0
\(749\) 324792. 0.0211544
\(750\) 0 0
\(751\) 7.49233e6 0.484749 0.242375 0.970183i \(-0.422074\pi\)
0.242375 + 0.970183i \(0.422074\pi\)
\(752\) 0 0
\(753\) 5.64574e6 0.362855
\(754\) 0 0
\(755\) −2.97261e7 −1.89789
\(756\) 0 0
\(757\) 2.88492e7 1.82976 0.914880 0.403727i \(-0.132285\pi\)
0.914880 + 0.403727i \(0.132285\pi\)
\(758\) 0 0
\(759\) 1.72280e6 0.108550
\(760\) 0 0
\(761\) −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
\(764\) 0 0
\(765\) 1.07458e7 0.663872
\(766\) 0 0
\(767\) 4.43987e6 0.272510
\(768\) 0 0
\(769\) −744898. −0.0454235 −0.0227118 0.999742i \(-0.507230\pi\)
−0.0227118 + 0.999742i \(0.507230\pi\)
\(770\) 0 0
\(771\) 4.21213e6 0.255191
\(772\) 0 0
\(773\) 6.07336e6 0.365578 0.182789 0.983152i \(-0.441487\pi\)
0.182789 + 0.983152i \(0.441487\pi\)
\(774\) 0 0
\(775\) −2.55845e7 −1.53011
\(776\) 0 0
\(777\) 2.38540e6 0.141745
\(778\) 0 0
\(779\) 2.29435e7 1.35462
\(780\) 0 0
\(781\) 5.52849e6 0.324324
\(782\) 0 0
\(783\) 4.02845e6 0.234819
\(784\) 0 0
\(785\) 2.93265e7 1.69858
\(786\) 0 0
\(787\) 1.47512e7 0.848966 0.424483 0.905436i \(-0.360456\pi\)
0.424483 + 0.905436i \(0.360456\pi\)
\(788\) 0 0
\(789\) 1.39059e7 0.795257
\(790\) 0 0
\(791\) 4.33040e6 0.246086
\(792\) 0 0
\(793\) −2.91304e7 −1.64499
\(794\) 0 0
\(795\) −2.55057e7 −1.43126
\(796\) 0 0
\(797\) −2.78359e7 −1.55224 −0.776121 0.630584i \(-0.782815\pi\)
−0.776121 + 0.630584i \(0.782815\pi\)
\(798\) 0 0
\(799\) −3.40600e6 −0.188746
\(800\) 0 0
\(801\) −5.85193e6 −0.322268
\(802\) 0 0
\(803\) 2.22325e6 0.121675
\(804\) 0 0
\(805\) −3.78414e6 −0.205815
\(806\) 0 0
\(807\) 9.67115e6 0.522750
\(808\) 0 0
\(809\) 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 \(0.328793\pi\)
\(812\) 0 0
\(813\) 1.42851e7 0.757977
\(814\) 0 0
\(815\) −3.97436e7 −2.09591
\(816\) 0 0
\(817\) 1.85328e7 0.971373
\(818\) 0 0
\(819\) −1.45735e6 −0.0759197
\(820\) 0 0
\(821\) 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 \(-0.193223\pi\)
0.821347 + 0.570430i \(0.193223\pi\)
\(824\) 0 0
\(825\) 5.81417e6 0.297408
\(826\) 0 0
\(827\) −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 \(0.615931\pi\)
\(830\) 0 0
\(831\) −6.23434e6 −0.313175
\(832\) 0 0
\(833\) 2.32609e7 1.16149
\(834\) 0 0
\(835\) −2.31454e7 −1.14881
\(836\) 0 0
\(837\) 3.49337e6 0.172358
\(838\) 0 0
\(839\) 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
\(842\) 0 0
\(843\) 5.10316e6 0.247326
\(844\) 0 0
\(845\) −9.89653e6 −0.476806
\(846\) 0 0
\(847\) 380666. 0.0182321
\(848\) 0 0
\(849\) 6.43424e6 0.306357
\(850\) 0 0
\(851\) −1.61269e7 −0.763356
\(852\) 0 0
\(853\) −1.67201e7 −0.786806 −0.393403 0.919366i \(-0.628702\pi\)
−0.393403 + 0.919366i \(0.628702\pi\)
\(854\) 0 0
\(855\) 1.60963e7 0.753028
\(856\) 0 0
\(857\) −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 \(-0.613570\pi\)
−0.349268 + 0.937023i \(0.613570\pi\)
\(860\) 0 0
\(861\) 2.48555e6 0.114265
\(862\) 0 0
\(863\) −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
\(866\) 0 0
\(867\) −5.93556e6 −0.268172
\(868\) 0 0
\(869\) −1.27309e7 −0.571886
\(870\) 0 0
\(871\) −1.96832e7 −0.879127
\(872\) 0 0
\(873\) 6.42022e6 0.285111
\(874\) 0 0
\(875\) −5.29589e6 −0.233840
\(876\) 0 0
\(877\) −1.26998e7 −0.557568 −0.278784 0.960354i \(-0.589931\pi\)
−0.278784 + 0.960354i \(0.589931\pi\)
\(878\) 0 0
\(879\) −1.92968e7 −0.842392
\(880\) 0 0
\(881\) −8.38173e6 −0.363826 −0.181913 0.983315i \(-0.558229\pi\)
−0.181913 + 0.983315i \(0.558229\pi\)
\(882\) 0 0
\(883\) 1.69529e7 0.731715 0.365858 0.930671i \(-0.380776\pi\)
0.365858 + 0.930671i \(0.380776\pi\)
\(884\) 0 0
\(885\) −5.31245e6 −0.228001
\(886\) 0 0
\(887\) 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
\(890\) 0 0
\(891\) −793881. −0.0335013
\(892\) 0 0
\(893\) −5.10192e6 −0.214094
\(894\) 0 0
\(895\) 8.29766e6 0.346257
\(896\) 0 0
\(897\) 9.85270e6 0.408859
\(898\) 0 0
\(899\) 2.64806e7 1.09277
\(900\) 0 0
\(901\) 4.44194e7 1.82289
\(902\) 0 0
\(903\) 2.00772e6 0.0819377
\(904\) 0 0
\(905\) −2.28162e7 −0.926023
\(906\) 0 0
\(907\) 1.53747e7 0.620569 0.310284 0.950644i \(-0.399576\pi\)
0.310284 + 0.950644i \(0.399576\pi\)
\(908\) 0 0
\(909\) −2.02160e6 −0.0811494
\(910\) 0 0
\(911\) −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
\(914\) 0 0
\(915\) 3.48555e7 1.37632
\(916\) 0 0
\(917\) −7.13513e6 −0.280207
\(918\) 0 0
\(919\) −3.31432e7 −1.29451 −0.647256 0.762273i \(-0.724084\pi\)
−0.647256 + 0.762273i \(0.724084\pi\)
\(920\) 0 0
\(921\) −5.29927e6 −0.205858
\(922\) 0 0
\(923\) 3.16175e7 1.22158
\(924\) 0 0
\(925\) −5.44258e7 −2.09146
\(926\) 0 0
\(927\) 4.60177e6 0.175884
\(928\) 0 0
\(929\) 3.10442e7 1.18016 0.590080 0.807345i \(-0.299096\pi\)
0.590080 + 0.807345i \(0.299096\pi\)
\(930\) 0 0
\(931\) 3.48430e7 1.31747
\(932\) 0 0
\(933\) 2.26644e7 0.852393
\(934\) 0 0
\(935\) −1.60523e7 −0.600495
\(936\) 0 0
\(937\) −3.10737e7 −1.15623 −0.578115 0.815955i \(-0.696212\pi\)
−0.578115 + 0.815955i \(0.696212\pi\)
\(938\) 0 0
\(939\) 2.01206e7 0.744692
\(940\) 0 0
\(941\) −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
\(944\) 0 0
\(945\) 1.74377e6 0.0635198
\(946\) 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
\(950\) 0 0
\(951\) −9.54713e6 −0.342311
\(952\) 0 0
\(953\) 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
\(956\) 0 0
\(957\) −6.01781e6 −0.212402
\(958\) 0 0
\(959\) −6.38191e6 −0.224080
\(960\) 0 0
\(961\) −5.66589e6 −0.197906
\(962\) 0 0
\(963\) 1.01185e6 0.0351602
\(964\) 0 0
\(965\) 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
\(969\) −2.80325e7 −0.959074
\(970\) 0 0
\(971\) −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
\(974\) 0 0
\(975\) 3.32513e7 1.12020
\(976\) 0 0
\(977\) 2.22197e6 0.0744736 0.0372368 0.999306i \(-0.488144\pi\)
0.0372368 + 0.999306i \(0.488144\pi\)
\(978\) 0 0
\(979\) 8.74177e6 0.291503
\(980\) 0 0
\(981\) 1.60986e7 0.534091
\(982\) 0 0
\(983\) −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
\(986\) 0 0
\(987\) −552708. −0.0180594
\(988\) 0 0
\(989\) −1.35736e7 −0.441269
\(990\) 0 0
\(991\) −3.24132e7 −1.04843 −0.524214 0.851587i \(-0.675641\pi\)
−0.524214 + 0.851587i \(0.675641\pi\)
\(992\) 0 0
\(993\) −2.11109e7 −0.679414
\(994\) 0 0
\(995\) −4.41655e7 −1.41425
\(996\) 0 0
\(997\) −1.55048e6 −0.0494000 −0.0247000 0.999695i \(-0.507863\pi\)
−0.0247000 + 0.999695i \(0.507863\pi\)
\(998\) 0 0
\(999\) 7.43143e6 0.235591
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 528.6.a.a.1.1 1
4.3 odd 2 33.6.a.b.1.1 1
12.11 even 2 99.6.a.a.1.1 1
20.19 odd 2 825.6.a.a.1.1 1
44.43 even 2 363.6.a.b.1.1 1
132.131 odd 2 1089.6.a.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.6.a.b.1.1 1 4.3 odd 2
99.6.a.a.1.1 1 12.11 even 2
363.6.a.b.1.1 1 44.43 even 2
528.6.a.a.1.1 1 1.1 even 1 trivial
825.6.a.a.1.1 1 20.19 odd 2
1089.6.a.h.1.1 1 132.131 odd 2