Properties

Label 546.4.a.a.1.1
Level $546$
Weight $4$
Character 546.1
Self dual yes
Analytic conductor $32.215$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 546.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2150428631\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 546.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +12.0000 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +12.0000 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -24.0000 q^{10} -22.0000 q^{11} -12.0000 q^{12} -13.0000 q^{13} -14.0000 q^{14} -36.0000 q^{15} +16.0000 q^{16} -2.00000 q^{17} -18.0000 q^{18} -88.0000 q^{19} +48.0000 q^{20} -21.0000 q^{21} +44.0000 q^{22} -80.0000 q^{23} +24.0000 q^{24} +19.0000 q^{25} +26.0000 q^{26} -27.0000 q^{27} +28.0000 q^{28} -22.0000 q^{29} +72.0000 q^{30} -92.0000 q^{31} -32.0000 q^{32} +66.0000 q^{33} +4.00000 q^{34} +84.0000 q^{35} +36.0000 q^{36} +118.000 q^{37} +176.000 q^{38} +39.0000 q^{39} -96.0000 q^{40} +324.000 q^{41} +42.0000 q^{42} +84.0000 q^{43} -88.0000 q^{44} +108.000 q^{45} +160.000 q^{46} -134.000 q^{47} -48.0000 q^{48} +49.0000 q^{49} -38.0000 q^{50} +6.00000 q^{51} -52.0000 q^{52} -194.000 q^{53} +54.0000 q^{54} -264.000 q^{55} -56.0000 q^{56} +264.000 q^{57} +44.0000 q^{58} +210.000 q^{59} -144.000 q^{60} -470.000 q^{61} +184.000 q^{62} +63.0000 q^{63} +64.0000 q^{64} -156.000 q^{65} -132.000 q^{66} -292.000 q^{67} -8.00000 q^{68} +240.000 q^{69} -168.000 q^{70} -66.0000 q^{71} -72.0000 q^{72} -506.000 q^{73} -236.000 q^{74} -57.0000 q^{75} -352.000 q^{76} -154.000 q^{77} -78.0000 q^{78} -776.000 q^{79} +192.000 q^{80} +81.0000 q^{81} -648.000 q^{82} -778.000 q^{83} -84.0000 q^{84} -24.0000 q^{85} -168.000 q^{86} +66.0000 q^{87} +176.000 q^{88} -920.000 q^{89} -216.000 q^{90} -91.0000 q^{91} -320.000 q^{92} +276.000 q^{93} +268.000 q^{94} -1056.00 q^{95} +96.0000 q^{96} -490.000 q^{97} -98.0000 q^{98} -198.000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −0.707107
\(3\) −3.00000 −0.577350
\(4\) 4.00000 0.500000
\(5\) 12.0000 1.07331 0.536656 0.843801i \(-0.319687\pi\)
0.536656 + 0.843801i \(0.319687\pi\)
\(6\) 6.00000 0.408248
\(7\) 7.00000 0.377964
\(8\) −8.00000 −0.353553
\(9\) 9.00000 0.333333
\(10\) −24.0000 −0.758947
\(11\) −22.0000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) −12.0000 −0.288675
\(13\) −13.0000 −0.277350
\(14\) −14.0000 −0.267261
\(15\) −36.0000 −0.619677
\(16\) 16.0000 0.250000
\(17\) −2.00000 −0.0285336 −0.0142668 0.999898i \(-0.504541\pi\)
−0.0142668 + 0.999898i \(0.504541\pi\)
\(18\) −18.0000 −0.235702
\(19\) −88.0000 −1.06256 −0.531279 0.847197i \(-0.678288\pi\)
−0.531279 + 0.847197i \(0.678288\pi\)
\(20\) 48.0000 0.536656
\(21\) −21.0000 −0.218218
\(22\) 44.0000 0.426401
\(23\) −80.0000 −0.725268 −0.362634 0.931932i \(-0.618122\pi\)
−0.362634 + 0.931932i \(0.618122\pi\)
\(24\) 24.0000 0.204124
\(25\) 19.0000 0.152000
\(26\) 26.0000 0.196116
\(27\) −27.0000 −0.192450
\(28\) 28.0000 0.188982
\(29\) −22.0000 −0.140872 −0.0704362 0.997516i \(-0.522439\pi\)
−0.0704362 + 0.997516i \(0.522439\pi\)
\(30\) 72.0000 0.438178
\(31\) −92.0000 −0.533022 −0.266511 0.963832i \(-0.585871\pi\)
−0.266511 + 0.963832i \(0.585871\pi\)
\(32\) −32.0000 −0.176777
\(33\) 66.0000 0.348155
\(34\) 4.00000 0.0201763
\(35\) 84.0000 0.405674
\(36\) 36.0000 0.166667
\(37\) 118.000 0.524299 0.262150 0.965027i \(-0.415569\pi\)
0.262150 + 0.965027i \(0.415569\pi\)
\(38\) 176.000 0.751341
\(39\) 39.0000 0.160128
\(40\) −96.0000 −0.379473
\(41\) 324.000 1.23415 0.617077 0.786903i \(-0.288317\pi\)
0.617077 + 0.786903i \(0.288317\pi\)
\(42\) 42.0000 0.154303
\(43\) 84.0000 0.297904 0.148952 0.988844i \(-0.452410\pi\)
0.148952 + 0.988844i \(0.452410\pi\)
\(44\) −88.0000 −0.301511
\(45\) 108.000 0.357771
\(46\) 160.000 0.512842
\(47\) −134.000 −0.415870 −0.207935 0.978143i \(-0.566674\pi\)
−0.207935 + 0.978143i \(0.566674\pi\)
\(48\) −48.0000 −0.144338
\(49\) 49.0000 0.142857
\(50\) −38.0000 −0.107480
\(51\) 6.00000 0.0164739
\(52\) −52.0000 −0.138675
\(53\) −194.000 −0.502791 −0.251396 0.967884i \(-0.580890\pi\)
−0.251396 + 0.967884i \(0.580890\pi\)
\(54\) 54.0000 0.136083
\(55\) −264.000 −0.647232
\(56\) −56.0000 −0.133631
\(57\) 264.000 0.613468
\(58\) 44.0000 0.0996118
\(59\) 210.000 0.463384 0.231692 0.972789i \(-0.425574\pi\)
0.231692 + 0.972789i \(0.425574\pi\)
\(60\) −144.000 −0.309839
\(61\) −470.000 −0.986514 −0.493257 0.869884i \(-0.664194\pi\)
−0.493257 + 0.869884i \(0.664194\pi\)
\(62\) 184.000 0.376904
\(63\) 63.0000 0.125988
\(64\) 64.0000 0.125000
\(65\) −156.000 −0.297683
\(66\) −132.000 −0.246183
\(67\) −292.000 −0.532440 −0.266220 0.963912i \(-0.585775\pi\)
−0.266220 + 0.963912i \(0.585775\pi\)
\(68\) −8.00000 −0.0142668
\(69\) 240.000 0.418733
\(70\) −168.000 −0.286855
\(71\) −66.0000 −0.110321 −0.0551603 0.998478i \(-0.517567\pi\)
−0.0551603 + 0.998478i \(0.517567\pi\)
\(72\) −72.0000 −0.117851
\(73\) −506.000 −0.811272 −0.405636 0.914035i \(-0.632950\pi\)
−0.405636 + 0.914035i \(0.632950\pi\)
\(74\) −236.000 −0.370736
\(75\) −57.0000 −0.0877572
\(76\) −352.000 −0.531279
\(77\) −154.000 −0.227921
\(78\) −78.0000 −0.113228
\(79\) −776.000 −1.10515 −0.552575 0.833463i \(-0.686355\pi\)
−0.552575 + 0.833463i \(0.686355\pi\)
\(80\) 192.000 0.268328
\(81\) 81.0000 0.111111
\(82\) −648.000 −0.872678
\(83\) −778.000 −1.02887 −0.514437 0.857528i \(-0.671999\pi\)
−0.514437 + 0.857528i \(0.671999\pi\)
\(84\) −84.0000 −0.109109
\(85\) −24.0000 −0.0306255
\(86\) −168.000 −0.210650
\(87\) 66.0000 0.0813327
\(88\) 176.000 0.213201
\(89\) −920.000 −1.09573 −0.547864 0.836567i \(-0.684559\pi\)
−0.547864 + 0.836567i \(0.684559\pi\)
\(90\) −216.000 −0.252982
\(91\) −91.0000 −0.104828
\(92\) −320.000 −0.362634
\(93\) 276.000 0.307741
\(94\) 268.000 0.294065
\(95\) −1056.00 −1.14046
\(96\) 96.0000 0.102062
\(97\) −490.000 −0.512907 −0.256453 0.966557i \(-0.582554\pi\)
−0.256453 + 0.966557i \(0.582554\pi\)
\(98\) −98.0000 −0.101015
\(99\) −198.000 −0.201008
\(100\) 76.0000 0.0760000
\(101\) 966.000 0.951689 0.475845 0.879529i \(-0.342142\pi\)
0.475845 + 0.879529i \(0.342142\pi\)
\(102\) −12.0000 −0.0116488
\(103\) −1344.00 −1.28571 −0.642856 0.765987i \(-0.722250\pi\)
−0.642856 + 0.765987i \(0.722250\pi\)
\(104\) 104.000 0.0980581
\(105\) −252.000 −0.234216
\(106\) 388.000 0.355527
\(107\) −52.0000 −0.0469816 −0.0234908 0.999724i \(-0.507478\pi\)
−0.0234908 + 0.999724i \(0.507478\pi\)
\(108\) −108.000 −0.0962250
\(109\) −1542.00 −1.35502 −0.677508 0.735515i \(-0.736940\pi\)
−0.677508 + 0.735515i \(0.736940\pi\)
\(110\) 528.000 0.457662
\(111\) −354.000 −0.302704
\(112\) 112.000 0.0944911
\(113\) 1766.00 1.47019 0.735094 0.677965i \(-0.237138\pi\)
0.735094 + 0.677965i \(0.237138\pi\)
\(114\) −528.000 −0.433787
\(115\) −960.000 −0.778439
\(116\) −88.0000 −0.0704362
\(117\) −117.000 −0.0924500
\(118\) −420.000 −0.327662
\(119\) −14.0000 −0.0107847
\(120\) 288.000 0.219089
\(121\) −847.000 −0.636364
\(122\) 940.000 0.697571
\(123\) −972.000 −0.712539
\(124\) −368.000 −0.266511
\(125\) −1272.00 −0.910169
\(126\) −126.000 −0.0890871
\(127\) 696.000 0.486299 0.243150 0.969989i \(-0.421819\pi\)
0.243150 + 0.969989i \(0.421819\pi\)
\(128\) −128.000 −0.0883883
\(129\) −252.000 −0.171995
\(130\) 312.000 0.210494
\(131\) 1504.00 1.00309 0.501546 0.865131i \(-0.332765\pi\)
0.501546 + 0.865131i \(0.332765\pi\)
\(132\) 264.000 0.174078
\(133\) −616.000 −0.401609
\(134\) 584.000 0.376492
\(135\) −324.000 −0.206559
\(136\) 16.0000 0.0100882
\(137\) −648.000 −0.404105 −0.202052 0.979375i \(-0.564761\pi\)
−0.202052 + 0.979375i \(0.564761\pi\)
\(138\) −480.000 −0.296089
\(139\) −1388.00 −0.846969 −0.423484 0.905903i \(-0.639193\pi\)
−0.423484 + 0.905903i \(0.639193\pi\)
\(140\) 336.000 0.202837
\(141\) 402.000 0.240103
\(142\) 132.000 0.0780084
\(143\) 286.000 0.167248
\(144\) 144.000 0.0833333
\(145\) −264.000 −0.151200
\(146\) 1012.00 0.573656
\(147\) −147.000 −0.0824786
\(148\) 472.000 0.262150
\(149\) 2420.00 1.33056 0.665282 0.746592i \(-0.268311\pi\)
0.665282 + 0.746592i \(0.268311\pi\)
\(150\) 114.000 0.0620537
\(151\) −2268.00 −1.22230 −0.611150 0.791515i \(-0.709293\pi\)
−0.611150 + 0.791515i \(0.709293\pi\)
\(152\) 704.000 0.375671
\(153\) −18.0000 −0.00951120
\(154\) 308.000 0.161165
\(155\) −1104.00 −0.572099
\(156\) 156.000 0.0800641
\(157\) −602.000 −0.306018 −0.153009 0.988225i \(-0.548896\pi\)
−0.153009 + 0.988225i \(0.548896\pi\)
\(158\) 1552.00 0.781459
\(159\) 582.000 0.290287
\(160\) −384.000 −0.189737
\(161\) −560.000 −0.274125
\(162\) −162.000 −0.0785674
\(163\) 1216.00 0.584322 0.292161 0.956369i \(-0.405626\pi\)
0.292161 + 0.956369i \(0.405626\pi\)
\(164\) 1296.00 0.617077
\(165\) 792.000 0.373679
\(166\) 1556.00 0.727524
\(167\) −782.000 −0.362353 −0.181177 0.983451i \(-0.557991\pi\)
−0.181177 + 0.983451i \(0.557991\pi\)
\(168\) 168.000 0.0771517
\(169\) 169.000 0.0769231
\(170\) 48.0000 0.0216555
\(171\) −792.000 −0.354186
\(172\) 336.000 0.148952
\(173\) 3102.00 1.36324 0.681620 0.731706i \(-0.261276\pi\)
0.681620 + 0.731706i \(0.261276\pi\)
\(174\) −132.000 −0.0575109
\(175\) 133.000 0.0574506
\(176\) −352.000 −0.150756
\(177\) −630.000 −0.267535
\(178\) 1840.00 0.774797
\(179\) −2824.00 −1.17919 −0.589597 0.807698i \(-0.700713\pi\)
−0.589597 + 0.807698i \(0.700713\pi\)
\(180\) 432.000 0.178885
\(181\) −842.000 −0.345776 −0.172888 0.984942i \(-0.555310\pi\)
−0.172888 + 0.984942i \(0.555310\pi\)
\(182\) 182.000 0.0741249
\(183\) 1410.00 0.569564
\(184\) 640.000 0.256421
\(185\) 1416.00 0.562737
\(186\) −552.000 −0.217605
\(187\) 44.0000 0.0172064
\(188\) −536.000 −0.207935
\(189\) −189.000 −0.0727393
\(190\) 2112.00 0.806424
\(191\) 2548.00 0.965271 0.482636 0.875821i \(-0.339680\pi\)
0.482636 + 0.875821i \(0.339680\pi\)
\(192\) −192.000 −0.0721688
\(193\) −1118.00 −0.416971 −0.208485 0.978025i \(-0.566853\pi\)
−0.208485 + 0.978025i \(0.566853\pi\)
\(194\) 980.000 0.362680
\(195\) 468.000 0.171868
\(196\) 196.000 0.0714286
\(197\) 1992.00 0.720427 0.360214 0.932870i \(-0.382704\pi\)
0.360214 + 0.932870i \(0.382704\pi\)
\(198\) 396.000 0.142134
\(199\) −3536.00 −1.25960 −0.629800 0.776757i \(-0.716863\pi\)
−0.629800 + 0.776757i \(0.716863\pi\)
\(200\) −152.000 −0.0537401
\(201\) 876.000 0.307404
\(202\) −1932.00 −0.672946
\(203\) −154.000 −0.0532447
\(204\) 24.0000 0.00823694
\(205\) 3888.00 1.32463
\(206\) 2688.00 0.909135
\(207\) −720.000 −0.241756
\(208\) −208.000 −0.0693375
\(209\) 1936.00 0.640746
\(210\) 504.000 0.165616
\(211\) −2900.00 −0.946181 −0.473091 0.881014i \(-0.656862\pi\)
−0.473091 + 0.881014i \(0.656862\pi\)
\(212\) −776.000 −0.251396
\(213\) 198.000 0.0636936
\(214\) 104.000 0.0332210
\(215\) 1008.00 0.319744
\(216\) 216.000 0.0680414
\(217\) −644.000 −0.201463
\(218\) 3084.00 0.958141
\(219\) 1518.00 0.468388
\(220\) −1056.00 −0.323616
\(221\) 26.0000 0.00791380
\(222\) 708.000 0.214044
\(223\) 4212.00 1.26483 0.632413 0.774631i \(-0.282064\pi\)
0.632413 + 0.774631i \(0.282064\pi\)
\(224\) −224.000 −0.0668153
\(225\) 171.000 0.0506667
\(226\) −3532.00 −1.03958
\(227\) −2070.00 −0.605245 −0.302623 0.953110i \(-0.597862\pi\)
−0.302623 + 0.953110i \(0.597862\pi\)
\(228\) 1056.00 0.306734
\(229\) −2198.00 −0.634270 −0.317135 0.948380i \(-0.602721\pi\)
−0.317135 + 0.948380i \(0.602721\pi\)
\(230\) 1920.00 0.550439
\(231\) 462.000 0.131590
\(232\) 176.000 0.0498059
\(233\) −3378.00 −0.949786 −0.474893 0.880044i \(-0.657513\pi\)
−0.474893 + 0.880044i \(0.657513\pi\)
\(234\) 234.000 0.0653720
\(235\) −1608.00 −0.446359
\(236\) 840.000 0.231692
\(237\) 2328.00 0.638058
\(238\) 28.0000 0.00762593
\(239\) −2874.00 −0.777839 −0.388920 0.921272i \(-0.627152\pi\)
−0.388920 + 0.921272i \(0.627152\pi\)
\(240\) −576.000 −0.154919
\(241\) 1926.00 0.514791 0.257395 0.966306i \(-0.417136\pi\)
0.257395 + 0.966306i \(0.417136\pi\)
\(242\) 1694.00 0.449977
\(243\) −243.000 −0.0641500
\(244\) −1880.00 −0.493257
\(245\) 588.000 0.153330
\(246\) 1944.00 0.503841
\(247\) 1144.00 0.294700
\(248\) 736.000 0.188452
\(249\) 2334.00 0.594021
\(250\) 2544.00 0.643587
\(251\) −2024.00 −0.508979 −0.254490 0.967076i \(-0.581907\pi\)
−0.254490 + 0.967076i \(0.581907\pi\)
\(252\) 252.000 0.0629941
\(253\) 1760.00 0.437353
\(254\) −1392.00 −0.343866
\(255\) 72.0000 0.0176816
\(256\) 256.000 0.0625000
\(257\) 5642.00 1.36941 0.684705 0.728820i \(-0.259931\pi\)
0.684705 + 0.728820i \(0.259931\pi\)
\(258\) 504.000 0.121619
\(259\) 826.000 0.198167
\(260\) −624.000 −0.148842
\(261\) −198.000 −0.0469574
\(262\) −3008.00 −0.709293
\(263\) −4680.00 −1.09727 −0.548633 0.836063i \(-0.684852\pi\)
−0.548633 + 0.836063i \(0.684852\pi\)
\(264\) −528.000 −0.123091
\(265\) −2328.00 −0.539652
\(266\) 1232.00 0.283980
\(267\) 2760.00 0.632619
\(268\) −1168.00 −0.266220
\(269\) 3758.00 0.851782 0.425891 0.904775i \(-0.359961\pi\)
0.425891 + 0.904775i \(0.359961\pi\)
\(270\) 648.000 0.146059
\(271\) 128.000 0.0286917 0.0143458 0.999897i \(-0.495433\pi\)
0.0143458 + 0.999897i \(0.495433\pi\)
\(272\) −32.0000 −0.00713340
\(273\) 273.000 0.0605228
\(274\) 1296.00 0.285745
\(275\) −418.000 −0.0916594
\(276\) 960.000 0.209367
\(277\) −826.000 −0.179168 −0.0895840 0.995979i \(-0.528554\pi\)
−0.0895840 + 0.995979i \(0.528554\pi\)
\(278\) 2776.00 0.598897
\(279\) −828.000 −0.177674
\(280\) −672.000 −0.143427
\(281\) −1448.00 −0.307404 −0.153702 0.988117i \(-0.549120\pi\)
−0.153702 + 0.988117i \(0.549120\pi\)
\(282\) −804.000 −0.169778
\(283\) 6084.00 1.27794 0.638969 0.769233i \(-0.279361\pi\)
0.638969 + 0.769233i \(0.279361\pi\)
\(284\) −264.000 −0.0551603
\(285\) 3168.00 0.658443
\(286\) −572.000 −0.118262
\(287\) 2268.00 0.466466
\(288\) −288.000 −0.0589256
\(289\) −4909.00 −0.999186
\(290\) 528.000 0.106915
\(291\) 1470.00 0.296127
\(292\) −2024.00 −0.405636
\(293\) −648.000 −0.129203 −0.0646016 0.997911i \(-0.520578\pi\)
−0.0646016 + 0.997911i \(0.520578\pi\)
\(294\) 294.000 0.0583212
\(295\) 2520.00 0.497356
\(296\) −944.000 −0.185368
\(297\) 594.000 0.116052
\(298\) −4840.00 −0.940851
\(299\) 1040.00 0.201153
\(300\) −228.000 −0.0438786
\(301\) 588.000 0.112597
\(302\) 4536.00 0.864296
\(303\) −2898.00 −0.549458
\(304\) −1408.00 −0.265639
\(305\) −5640.00 −1.05884
\(306\) 36.0000 0.00672543
\(307\) 5636.00 1.04776 0.523882 0.851791i \(-0.324483\pi\)
0.523882 + 0.851791i \(0.324483\pi\)
\(308\) −616.000 −0.113961
\(309\) 4032.00 0.742306
\(310\) 2208.00 0.404535
\(311\) −4964.00 −0.905089 −0.452544 0.891742i \(-0.649484\pi\)
−0.452544 + 0.891742i \(0.649484\pi\)
\(312\) −312.000 −0.0566139
\(313\) 5934.00 1.07160 0.535798 0.844346i \(-0.320011\pi\)
0.535798 + 0.844346i \(0.320011\pi\)
\(314\) 1204.00 0.216387
\(315\) 756.000 0.135225
\(316\) −3104.00 −0.552575
\(317\) 2560.00 0.453577 0.226789 0.973944i \(-0.427177\pi\)
0.226789 + 0.973944i \(0.427177\pi\)
\(318\) −1164.00 −0.205264
\(319\) 484.000 0.0849492
\(320\) 768.000 0.134164
\(321\) 156.000 0.0271248
\(322\) 1120.00 0.193836
\(323\) 176.000 0.0303186
\(324\) 324.000 0.0555556
\(325\) −247.000 −0.0421572
\(326\) −2432.00 −0.413178
\(327\) 4626.00 0.782319
\(328\) −2592.00 −0.436339
\(329\) −938.000 −0.157184
\(330\) −1584.00 −0.264231
\(331\) 4020.00 0.667550 0.333775 0.942653i \(-0.391677\pi\)
0.333775 + 0.942653i \(0.391677\pi\)
\(332\) −3112.00 −0.514437
\(333\) 1062.00 0.174766
\(334\) 1564.00 0.256222
\(335\) −3504.00 −0.571475
\(336\) −336.000 −0.0545545
\(337\) 4734.00 0.765215 0.382607 0.923911i \(-0.375026\pi\)
0.382607 + 0.923911i \(0.375026\pi\)
\(338\) −338.000 −0.0543928
\(339\) −5298.00 −0.848814
\(340\) −96.0000 −0.0153127
\(341\) 2024.00 0.321424
\(342\) 1584.00 0.250447
\(343\) 343.000 0.0539949
\(344\) −672.000 −0.105325
\(345\) 2880.00 0.449432
\(346\) −6204.00 −0.963957
\(347\) −7864.00 −1.21660 −0.608302 0.793706i \(-0.708149\pi\)
−0.608302 + 0.793706i \(0.708149\pi\)
\(348\) 264.000 0.0406663
\(349\) 5870.00 0.900326 0.450163 0.892946i \(-0.351366\pi\)
0.450163 + 0.892946i \(0.351366\pi\)
\(350\) −266.000 −0.0406237
\(351\) 351.000 0.0533761
\(352\) 704.000 0.106600
\(353\) 5532.00 0.834104 0.417052 0.908883i \(-0.363063\pi\)
0.417052 + 0.908883i \(0.363063\pi\)
\(354\) 1260.00 0.189176
\(355\) −792.000 −0.118408
\(356\) −3680.00 −0.547864
\(357\) 42.0000 0.00622654
\(358\) 5648.00 0.833816
\(359\) 5854.00 0.860619 0.430310 0.902681i \(-0.358404\pi\)
0.430310 + 0.902681i \(0.358404\pi\)
\(360\) −864.000 −0.126491
\(361\) 885.000 0.129028
\(362\) 1684.00 0.244500
\(363\) 2541.00 0.367405
\(364\) −364.000 −0.0524142
\(365\) −6072.00 −0.870748
\(366\) −2820.00 −0.402743
\(367\) −7576.00 −1.07756 −0.538779 0.842447i \(-0.681114\pi\)
−0.538779 + 0.842447i \(0.681114\pi\)
\(368\) −1280.00 −0.181317
\(369\) 2916.00 0.411385
\(370\) −2832.00 −0.397915
\(371\) −1358.00 −0.190037
\(372\) 1104.00 0.153870
\(373\) −1502.00 −0.208500 −0.104250 0.994551i \(-0.533244\pi\)
−0.104250 + 0.994551i \(0.533244\pi\)
\(374\) −88.0000 −0.0121668
\(375\) 3816.00 0.525486
\(376\) 1072.00 0.147032
\(377\) 286.000 0.0390710
\(378\) 378.000 0.0514344
\(379\) −8584.00 −1.16340 −0.581702 0.813402i \(-0.697613\pi\)
−0.581702 + 0.813402i \(0.697613\pi\)
\(380\) −4224.00 −0.570228
\(381\) −2088.00 −0.280765
\(382\) −5096.00 −0.682550
\(383\) 8598.00 1.14709 0.573547 0.819172i \(-0.305567\pi\)
0.573547 + 0.819172i \(0.305567\pi\)
\(384\) 384.000 0.0510310
\(385\) −1848.00 −0.244631
\(386\) 2236.00 0.294843
\(387\) 756.000 0.0993014
\(388\) −1960.00 −0.256453
\(389\) −11666.0 −1.52054 −0.760270 0.649608i \(-0.774933\pi\)
−0.760270 + 0.649608i \(0.774933\pi\)
\(390\) −936.000 −0.121529
\(391\) 160.000 0.0206945
\(392\) −392.000 −0.0505076
\(393\) −4512.00 −0.579136
\(394\) −3984.00 −0.509419
\(395\) −9312.00 −1.18617
\(396\) −792.000 −0.100504
\(397\) 5334.00 0.674322 0.337161 0.941447i \(-0.390533\pi\)
0.337161 + 0.941447i \(0.390533\pi\)
\(398\) 7072.00 0.890672
\(399\) 1848.00 0.231869
\(400\) 304.000 0.0380000
\(401\) 1852.00 0.230635 0.115317 0.993329i \(-0.463212\pi\)
0.115317 + 0.993329i \(0.463212\pi\)
\(402\) −1752.00 −0.217368
\(403\) 1196.00 0.147834
\(404\) 3864.00 0.475845
\(405\) 972.000 0.119257
\(406\) 308.000 0.0376497
\(407\) −2596.00 −0.316164
\(408\) −48.0000 −0.00582440
\(409\) −13530.0 −1.63573 −0.817867 0.575407i \(-0.804844\pi\)
−0.817867 + 0.575407i \(0.804844\pi\)
\(410\) −7776.00 −0.936657
\(411\) 1944.00 0.233310
\(412\) −5376.00 −0.642856
\(413\) 1470.00 0.175143
\(414\) 1440.00 0.170947
\(415\) −9336.00 −1.10430
\(416\) 416.000 0.0490290
\(417\) 4164.00 0.488997
\(418\) −3872.00 −0.453076
\(419\) 1320.00 0.153905 0.0769525 0.997035i \(-0.475481\pi\)
0.0769525 + 0.997035i \(0.475481\pi\)
\(420\) −1008.00 −0.117108
\(421\) 6322.00 0.731866 0.365933 0.930641i \(-0.380750\pi\)
0.365933 + 0.930641i \(0.380750\pi\)
\(422\) 5800.00 0.669051
\(423\) −1206.00 −0.138623
\(424\) 1552.00 0.177764
\(425\) −38.0000 −0.00433711
\(426\) −396.000 −0.0450382
\(427\) −3290.00 −0.372867
\(428\) −208.000 −0.0234908
\(429\) −858.000 −0.0965609
\(430\) −2016.00 −0.226093
\(431\) 3498.00 0.390934 0.195467 0.980710i \(-0.437378\pi\)
0.195467 + 0.980710i \(0.437378\pi\)
\(432\) −432.000 −0.0481125
\(433\) −394.000 −0.0437285 −0.0218642 0.999761i \(-0.506960\pi\)
−0.0218642 + 0.999761i \(0.506960\pi\)
\(434\) 1288.00 0.142456
\(435\) 792.000 0.0872954
\(436\) −6168.00 −0.677508
\(437\) 7040.00 0.770638
\(438\) −3036.00 −0.331200
\(439\) 10528.0 1.14459 0.572294 0.820049i \(-0.306054\pi\)
0.572294 + 0.820049i \(0.306054\pi\)
\(440\) 2112.00 0.228831
\(441\) 441.000 0.0476190
\(442\) −52.0000 −0.00559590
\(443\) −5028.00 −0.539249 −0.269625 0.962965i \(-0.586900\pi\)
−0.269625 + 0.962965i \(0.586900\pi\)
\(444\) −1416.00 −0.151352
\(445\) −11040.0 −1.17606
\(446\) −8424.00 −0.894368
\(447\) −7260.00 −0.768202
\(448\) 448.000 0.0472456
\(449\) −3012.00 −0.316581 −0.158291 0.987393i \(-0.550598\pi\)
−0.158291 + 0.987393i \(0.550598\pi\)
\(450\) −342.000 −0.0358267
\(451\) −7128.00 −0.744223
\(452\) 7064.00 0.735094
\(453\) 6804.00 0.705695
\(454\) 4140.00 0.427973
\(455\) −1092.00 −0.112514
\(456\) −2112.00 −0.216894
\(457\) −5506.00 −0.563588 −0.281794 0.959475i \(-0.590930\pi\)
−0.281794 + 0.959475i \(0.590930\pi\)
\(458\) 4396.00 0.448497
\(459\) 54.0000 0.00549129
\(460\) −3840.00 −0.389219
\(461\) 4764.00 0.481305 0.240652 0.970611i \(-0.422639\pi\)
0.240652 + 0.970611i \(0.422639\pi\)
\(462\) −924.000 −0.0930484
\(463\) 5016.00 0.503484 0.251742 0.967794i \(-0.418996\pi\)
0.251742 + 0.967794i \(0.418996\pi\)
\(464\) −352.000 −0.0352181
\(465\) 3312.00 0.330302
\(466\) 6756.00 0.671600
\(467\) −8928.00 −0.884665 −0.442333 0.896851i \(-0.645849\pi\)
−0.442333 + 0.896851i \(0.645849\pi\)
\(468\) −468.000 −0.0462250
\(469\) −2044.00 −0.201243
\(470\) 3216.00 0.315623
\(471\) 1806.00 0.176680
\(472\) −1680.00 −0.163831
\(473\) −1848.00 −0.179643
\(474\) −4656.00 −0.451175
\(475\) −1672.00 −0.161509
\(476\) −56.0000 −0.00539234
\(477\) −1746.00 −0.167597
\(478\) 5748.00 0.550015
\(479\) 3166.00 0.302000 0.151000 0.988534i \(-0.451751\pi\)
0.151000 + 0.988534i \(0.451751\pi\)
\(480\) 1152.00 0.109545
\(481\) −1534.00 −0.145415
\(482\) −3852.00 −0.364012
\(483\) 1680.00 0.158266
\(484\) −3388.00 −0.318182
\(485\) −5880.00 −0.550509
\(486\) 486.000 0.0453609
\(487\) −596.000 −0.0554565 −0.0277283 0.999615i \(-0.508827\pi\)
−0.0277283 + 0.999615i \(0.508827\pi\)
\(488\) 3760.00 0.348785
\(489\) −3648.00 −0.337358
\(490\) −1176.00 −0.108421
\(491\) −6940.00 −0.637877 −0.318939 0.947775i \(-0.603326\pi\)
−0.318939 + 0.947775i \(0.603326\pi\)
\(492\) −3888.00 −0.356269
\(493\) 44.0000 0.00401960
\(494\) −2288.00 −0.208385
\(495\) −2376.00 −0.215744
\(496\) −1472.00 −0.133256
\(497\) −462.000 −0.0416972
\(498\) −4668.00 −0.420036
\(499\) 1156.00 0.103707 0.0518534 0.998655i \(-0.483487\pi\)
0.0518534 + 0.998655i \(0.483487\pi\)
\(500\) −5088.00 −0.455085
\(501\) 2346.00 0.209205
\(502\) 4048.00 0.359903
\(503\) 2068.00 0.183315 0.0916576 0.995791i \(-0.470783\pi\)
0.0916576 + 0.995791i \(0.470783\pi\)
\(504\) −504.000 −0.0445435
\(505\) 11592.0 1.02146
\(506\) −3520.00 −0.309255
\(507\) −507.000 −0.0444116
\(508\) 2784.00 0.243150
\(509\) 1140.00 0.0992723 0.0496362 0.998767i \(-0.484194\pi\)
0.0496362 + 0.998767i \(0.484194\pi\)
\(510\) −144.000 −0.0125028
\(511\) −3542.00 −0.306632
\(512\) −512.000 −0.0441942
\(513\) 2376.00 0.204489
\(514\) −11284.0 −0.968319
\(515\) −16128.0 −1.37997
\(516\) −1008.00 −0.0859975
\(517\) 2948.00 0.250779
\(518\) −1652.00 −0.140125
\(519\) −9306.00 −0.787068
\(520\) 1248.00 0.105247
\(521\) −13606.0 −1.14413 −0.572063 0.820210i \(-0.693857\pi\)
−0.572063 + 0.820210i \(0.693857\pi\)
\(522\) 396.000 0.0332039
\(523\) −6868.00 −0.574219 −0.287110 0.957898i \(-0.592694\pi\)
−0.287110 + 0.957898i \(0.592694\pi\)
\(524\) 6016.00 0.501546
\(525\) −399.000 −0.0331691
\(526\) 9360.00 0.775885
\(527\) 184.000 0.0152090
\(528\) 1056.00 0.0870388
\(529\) −5767.00 −0.473987
\(530\) 4656.00 0.381592
\(531\) 1890.00 0.154461
\(532\) −2464.00 −0.200804
\(533\) −4212.00 −0.342293
\(534\) −5520.00 −0.447329
\(535\) −624.000 −0.0504259
\(536\) 2336.00 0.188246
\(537\) 8472.00 0.680808
\(538\) −7516.00 −0.602301
\(539\) −1078.00 −0.0861461
\(540\) −1296.00 −0.103280
\(541\) 1170.00 0.0929801 0.0464900 0.998919i \(-0.485196\pi\)
0.0464900 + 0.998919i \(0.485196\pi\)
\(542\) −256.000 −0.0202881
\(543\) 2526.00 0.199634
\(544\) 64.0000 0.00504408
\(545\) −18504.0 −1.45436
\(546\) −546.000 −0.0427960
\(547\) 5524.00 0.431790 0.215895 0.976417i \(-0.430733\pi\)
0.215895 + 0.976417i \(0.430733\pi\)
\(548\) −2592.00 −0.202052
\(549\) −4230.00 −0.328838
\(550\) 836.000 0.0648130
\(551\) 1936.00 0.149685
\(552\) −1920.00 −0.148045
\(553\) −5432.00 −0.417707
\(554\) 1652.00 0.126691
\(555\) −4248.00 −0.324897
\(556\) −5552.00 −0.423484
\(557\) 6204.00 0.471942 0.235971 0.971760i \(-0.424173\pi\)
0.235971 + 0.971760i \(0.424173\pi\)
\(558\) 1656.00 0.125635
\(559\) −1092.00 −0.0826238
\(560\) 1344.00 0.101419
\(561\) −132.000 −0.00993413
\(562\) 2896.00 0.217367
\(563\) 23140.0 1.73221 0.866105 0.499861i \(-0.166616\pi\)
0.866105 + 0.499861i \(0.166616\pi\)
\(564\) 1608.00 0.120051
\(565\) 21192.0 1.57797
\(566\) −12168.0 −0.903638
\(567\) 567.000 0.0419961
\(568\) 528.000 0.0390042
\(569\) 7086.00 0.522075 0.261037 0.965329i \(-0.415935\pi\)
0.261037 + 0.965329i \(0.415935\pi\)
\(570\) −6336.00 −0.465589
\(571\) 5956.00 0.436516 0.218258 0.975891i \(-0.429963\pi\)
0.218258 + 0.975891i \(0.429963\pi\)
\(572\) 1144.00 0.0836242
\(573\) −7644.00 −0.557300
\(574\) −4536.00 −0.329841
\(575\) −1520.00 −0.110241
\(576\) 576.000 0.0416667
\(577\) 8714.00 0.628715 0.314358 0.949305i \(-0.398211\pi\)
0.314358 + 0.949305i \(0.398211\pi\)
\(578\) 9818.00 0.706531
\(579\) 3354.00 0.240738
\(580\) −1056.00 −0.0756000
\(581\) −5446.00 −0.388878
\(582\) −2940.00 −0.209393
\(583\) 4268.00 0.303195
\(584\) 4048.00 0.286828
\(585\) −1404.00 −0.0992278
\(586\) 1296.00 0.0913605
\(587\) 17286.0 1.21545 0.607725 0.794147i \(-0.292082\pi\)
0.607725 + 0.794147i \(0.292082\pi\)
\(588\) −588.000 −0.0412393
\(589\) 8096.00 0.566366
\(590\) −5040.00 −0.351684
\(591\) −5976.00 −0.415939
\(592\) 1888.00 0.131075
\(593\) 4936.00 0.341817 0.170908 0.985287i \(-0.445330\pi\)
0.170908 + 0.985287i \(0.445330\pi\)
\(594\) −1188.00 −0.0820610
\(595\) −168.000 −0.0115753
\(596\) 9680.00 0.665282
\(597\) 10608.0 0.727230
\(598\) −2080.00 −0.142237
\(599\) −18936.0 −1.29166 −0.645830 0.763481i \(-0.723488\pi\)
−0.645830 + 0.763481i \(0.723488\pi\)
\(600\) 456.000 0.0310269
\(601\) 62.0000 0.00420804 0.00210402 0.999998i \(-0.499330\pi\)
0.00210402 + 0.999998i \(0.499330\pi\)
\(602\) −1176.00 −0.0796182
\(603\) −2628.00 −0.177480
\(604\) −9072.00 −0.611150
\(605\) −10164.0 −0.683017
\(606\) 5796.00 0.388525
\(607\) 22792.0 1.52405 0.762025 0.647547i \(-0.224205\pi\)
0.762025 + 0.647547i \(0.224205\pi\)
\(608\) 2816.00 0.187835
\(609\) 462.000 0.0307409
\(610\) 11280.0 0.748711
\(611\) 1742.00 0.115342
\(612\) −72.0000 −0.00475560
\(613\) 30022.0 1.97810 0.989052 0.147571i \(-0.0471454\pi\)
0.989052 + 0.147571i \(0.0471454\pi\)
\(614\) −11272.0 −0.740881
\(615\) −11664.0 −0.764777
\(616\) 1232.00 0.0805823
\(617\) 26640.0 1.73823 0.869113 0.494613i \(-0.164690\pi\)
0.869113 + 0.494613i \(0.164690\pi\)
\(618\) −8064.00 −0.524889
\(619\) −180.000 −0.0116879 −0.00584395 0.999983i \(-0.501860\pi\)
−0.00584395 + 0.999983i \(0.501860\pi\)
\(620\) −4416.00 −0.286050
\(621\) 2160.00 0.139578
\(622\) 9928.00 0.639994
\(623\) −6440.00 −0.414146
\(624\) 624.000 0.0400320
\(625\) −17639.0 −1.12890
\(626\) −11868.0 −0.757733
\(627\) −5808.00 −0.369935
\(628\) −2408.00 −0.153009
\(629\) −236.000 −0.0149602
\(630\) −1512.00 −0.0956183
\(631\) 6652.00 0.419670 0.209835 0.977737i \(-0.432707\pi\)
0.209835 + 0.977737i \(0.432707\pi\)
\(632\) 6208.00 0.390729
\(633\) 8700.00 0.546278
\(634\) −5120.00 −0.320727
\(635\) 8352.00 0.521951
\(636\) 2328.00 0.145143
\(637\) −637.000 −0.0396214
\(638\) −968.000 −0.0600682
\(639\) −594.000 −0.0367735
\(640\) −1536.00 −0.0948683
\(641\) 15258.0 0.940179 0.470090 0.882619i \(-0.344222\pi\)
0.470090 + 0.882619i \(0.344222\pi\)
\(642\) −312.000 −0.0191802
\(643\) −17124.0 −1.05024 −0.525120 0.851028i \(-0.675980\pi\)
−0.525120 + 0.851028i \(0.675980\pi\)
\(644\) −2240.00 −0.137063
\(645\) −3024.00 −0.184604
\(646\) −352.000 −0.0214385
\(647\) 7032.00 0.427290 0.213645 0.976911i \(-0.431466\pi\)
0.213645 + 0.976911i \(0.431466\pi\)
\(648\) −648.000 −0.0392837
\(649\) −4620.00 −0.279431
\(650\) 494.000 0.0298097
\(651\) 1932.00 0.116315
\(652\) 4864.00 0.292161
\(653\) −19254.0 −1.15385 −0.576927 0.816795i \(-0.695748\pi\)
−0.576927 + 0.816795i \(0.695748\pi\)
\(654\) −9252.00 −0.553183
\(655\) 18048.0 1.07663
\(656\) 5184.00 0.308538
\(657\) −4554.00 −0.270424
\(658\) 1876.00 0.111146
\(659\) −1136.00 −0.0671506 −0.0335753 0.999436i \(-0.510689\pi\)
−0.0335753 + 0.999436i \(0.510689\pi\)
\(660\) 3168.00 0.186840
\(661\) 20638.0 1.21441 0.607205 0.794545i \(-0.292291\pi\)
0.607205 + 0.794545i \(0.292291\pi\)
\(662\) −8040.00 −0.472029
\(663\) −78.0000 −0.00456903
\(664\) 6224.00 0.363762
\(665\) −7392.00 −0.431052
\(666\) −2124.00 −0.123579
\(667\) 1760.00 0.102170
\(668\) −3128.00 −0.181177
\(669\) −12636.0 −0.730248
\(670\) 7008.00 0.404094
\(671\) 10340.0 0.594890
\(672\) 672.000 0.0385758
\(673\) 14466.0 0.828564 0.414282 0.910149i \(-0.364033\pi\)
0.414282 + 0.910149i \(0.364033\pi\)
\(674\) −9468.00 −0.541089
\(675\) −513.000 −0.0292524
\(676\) 676.000 0.0384615
\(677\) 3162.00 0.179506 0.0897530 0.995964i \(-0.471392\pi\)
0.0897530 + 0.995964i \(0.471392\pi\)
\(678\) 10596.0 0.600202
\(679\) −3430.00 −0.193861
\(680\) 192.000 0.0108277
\(681\) 6210.00 0.349439
\(682\) −4048.00 −0.227281
\(683\) −26334.0 −1.47532 −0.737659 0.675173i \(-0.764069\pi\)
−0.737659 + 0.675173i \(0.764069\pi\)
\(684\) −3168.00 −0.177093
\(685\) −7776.00 −0.433731
\(686\) −686.000 −0.0381802
\(687\) 6594.00 0.366196
\(688\) 1344.00 0.0744760
\(689\) 2522.00 0.139449
\(690\) −5760.00 −0.317796
\(691\) 11124.0 0.612412 0.306206 0.951965i \(-0.400940\pi\)
0.306206 + 0.951965i \(0.400940\pi\)
\(692\) 12408.0 0.681620
\(693\) −1386.00 −0.0759737
\(694\) 15728.0 0.860269
\(695\) −16656.0 −0.909062
\(696\) −528.000 −0.0287554
\(697\) −648.000 −0.0352148
\(698\) −11740.0 −0.636627
\(699\) 10134.0 0.548359
\(700\) 532.000 0.0287253
\(701\) 6270.00 0.337824 0.168912 0.985631i \(-0.445975\pi\)
0.168912 + 0.985631i \(0.445975\pi\)
\(702\) −702.000 −0.0377426
\(703\) −10384.0 −0.557098
\(704\) −1408.00 −0.0753778
\(705\) 4824.00 0.257705
\(706\) −11064.0 −0.589800
\(707\) 6762.00 0.359705
\(708\) −2520.00 −0.133768
\(709\) 17186.0 0.910344 0.455172 0.890404i \(-0.349578\pi\)
0.455172 + 0.890404i \(0.349578\pi\)
\(710\) 1584.00 0.0837274
\(711\) −6984.00 −0.368383
\(712\) 7360.00 0.387398
\(713\) 7360.00 0.386584
\(714\) −84.0000 −0.00440283
\(715\) 3432.00 0.179510
\(716\) −11296.0 −0.589597
\(717\) 8622.00 0.449086
\(718\) −11708.0 −0.608550
\(719\) 29244.0 1.51685 0.758426 0.651759i \(-0.225969\pi\)
0.758426 + 0.651759i \(0.225969\pi\)
\(720\) 1728.00 0.0894427
\(721\) −9408.00 −0.485953
\(722\) −1770.00 −0.0912363
\(723\) −5778.00 −0.297215
\(724\) −3368.00 −0.172888
\(725\) −418.000 −0.0214126
\(726\) −5082.00 −0.259794
\(727\) 22760.0 1.16110 0.580551 0.814224i \(-0.302837\pi\)
0.580551 + 0.814224i \(0.302837\pi\)
\(728\) 728.000 0.0370625
\(729\) 729.000 0.0370370
\(730\) 12144.0 0.615712
\(731\) −168.000 −0.00850028
\(732\) 5640.00 0.284782
\(733\) 26546.0 1.33765 0.668826 0.743419i \(-0.266797\pi\)
0.668826 + 0.743419i \(0.266797\pi\)
\(734\) 15152.0 0.761949
\(735\) −1764.00 −0.0885253
\(736\) 2560.00 0.128210
\(737\) 6424.00 0.321073
\(738\) −5832.00 −0.290893
\(739\) 932.000 0.0463927 0.0231963 0.999731i \(-0.492616\pi\)
0.0231963 + 0.999731i \(0.492616\pi\)
\(740\) 5664.00 0.281369
\(741\) −3432.00 −0.170145
\(742\) 2716.00 0.134377
\(743\) −8418.00 −0.415648 −0.207824 0.978166i \(-0.566638\pi\)
−0.207824 + 0.978166i \(0.566638\pi\)
\(744\) −2208.00 −0.108803
\(745\) 29040.0 1.42811
\(746\) 3004.00 0.147432
\(747\) −7002.00 −0.342958
\(748\) 176.000 0.00860320
\(749\) −364.000 −0.0177574
\(750\) −7632.00 −0.371575
\(751\) −15704.0 −0.763045 −0.381523 0.924359i \(-0.624600\pi\)
−0.381523 + 0.924359i \(0.624600\pi\)
\(752\) −2144.00 −0.103968
\(753\) 6072.00 0.293859
\(754\) −572.000 −0.0276273
\(755\) −27216.0 −1.31191
\(756\) −756.000 −0.0363696
\(757\) −16734.0 −0.803445 −0.401722 0.915762i \(-0.631588\pi\)
−0.401722 + 0.915762i \(0.631588\pi\)
\(758\) 17168.0 0.822652
\(759\) −5280.00 −0.252506
\(760\) 8448.00 0.403212
\(761\) −11196.0 −0.533318 −0.266659 0.963791i \(-0.585920\pi\)
−0.266659 + 0.963791i \(0.585920\pi\)
\(762\) 4176.00 0.198531
\(763\) −10794.0 −0.512148
\(764\) 10192.0 0.482636
\(765\) −216.000 −0.0102085
\(766\) −17196.0 −0.811118
\(767\) −2730.00 −0.128520
\(768\) −768.000 −0.0360844
\(769\) 18938.0 0.888065 0.444032 0.896011i \(-0.353548\pi\)
0.444032 + 0.896011i \(0.353548\pi\)
\(770\) 3696.00 0.172980
\(771\) −16926.0 −0.790629
\(772\) −4472.00 −0.208485
\(773\) −13672.0 −0.636155 −0.318077 0.948065i \(-0.603037\pi\)
−0.318077 + 0.948065i \(0.603037\pi\)
\(774\) −1512.00 −0.0702167
\(775\) −1748.00 −0.0810194
\(776\) 3920.00 0.181340
\(777\) −2478.00 −0.114412
\(778\) 23332.0 1.07518
\(779\) −28512.0 −1.31136
\(780\) 1872.00 0.0859338
\(781\) 1452.00 0.0665258
\(782\) −320.000 −0.0146332
\(783\) 594.000 0.0271109
\(784\) 784.000 0.0357143
\(785\) −7224.00 −0.328453
\(786\) 9024.00 0.409511
\(787\) 16484.0 0.746622 0.373311 0.927706i \(-0.378223\pi\)
0.373311 + 0.927706i \(0.378223\pi\)
\(788\) 7968.00 0.360214
\(789\) 14040.0 0.633507
\(790\) 18624.0 0.838750
\(791\) 12362.0 0.555679
\(792\) 1584.00 0.0710669
\(793\) 6110.00 0.273610
\(794\) −10668.0 −0.476818
\(795\) 6984.00 0.311568
\(796\) −14144.0 −0.629800
\(797\) 17778.0 0.790124 0.395062 0.918654i \(-0.370723\pi\)
0.395062 + 0.918654i \(0.370723\pi\)
\(798\) −3696.00 −0.163956
\(799\) 268.000 0.0118663
\(800\) −608.000 −0.0268701
\(801\) −8280.00 −0.365243
\(802\) −3704.00 −0.163083
\(803\) 11132.0 0.489215
\(804\) 3504.00 0.153702
\(805\) −6720.00 −0.294222
\(806\) −2392.00 −0.104534
\(807\) −11274.0 −0.491776
\(808\) −7728.00 −0.336473
\(809\) −33138.0 −1.44014 −0.720068 0.693903i \(-0.755889\pi\)
−0.720068 + 0.693903i \(0.755889\pi\)
\(810\) −1944.00 −0.0843274
\(811\) 10888.0 0.471430 0.235715 0.971822i \(-0.424257\pi\)
0.235715 + 0.971822i \(0.424257\pi\)
\(812\) −616.000 −0.0266224
\(813\) −384.000 −0.0165652
\(814\) 5192.00 0.223562
\(815\) 14592.0 0.627160
\(816\) 96.0000 0.00411847
\(817\) −7392.00 −0.316540
\(818\) 27060.0 1.15664
\(819\) −819.000 −0.0349428
\(820\) 15552.0 0.662316
\(821\) −13716.0 −0.583059 −0.291530 0.956562i \(-0.594164\pi\)
−0.291530 + 0.956562i \(0.594164\pi\)
\(822\) −3888.00 −0.164975
\(823\) −32016.0 −1.35602 −0.678012 0.735051i \(-0.737158\pi\)
−0.678012 + 0.735051i \(0.737158\pi\)
\(824\) 10752.0 0.454568
\(825\) 1254.00 0.0529196
\(826\) −2940.00 −0.123845
\(827\) 40050.0 1.68401 0.842004 0.539471i \(-0.181376\pi\)
0.842004 + 0.539471i \(0.181376\pi\)
\(828\) −2880.00 −0.120878
\(829\) 46602.0 1.95242 0.976209 0.216832i \(-0.0695724\pi\)
0.976209 + 0.216832i \(0.0695724\pi\)
\(830\) 18672.0 0.780861
\(831\) 2478.00 0.103443
\(832\) −832.000 −0.0346688
\(833\) −98.0000 −0.00407623
\(834\) −8328.00 −0.345773
\(835\) −9384.00 −0.388918
\(836\) 7744.00 0.320373
\(837\) 2484.00 0.102580
\(838\) −2640.00 −0.108827
\(839\) −18578.0 −0.764462 −0.382231 0.924067i \(-0.624844\pi\)
−0.382231 + 0.924067i \(0.624844\pi\)
\(840\) 2016.00 0.0828079
\(841\) −23905.0 −0.980155
\(842\) −12644.0 −0.517507
\(843\) 4344.00 0.177480
\(844\) −11600.0 −0.473091
\(845\) 2028.00 0.0825625
\(846\) 2412.00 0.0980216
\(847\) −5929.00 −0.240523
\(848\) −3104.00 −0.125698
\(849\) −18252.0 −0.737817
\(850\) 76.0000 0.00306680
\(851\) −9440.00 −0.380257
\(852\) 792.000 0.0318468
\(853\) 21254.0 0.853134 0.426567 0.904456i \(-0.359723\pi\)
0.426567 + 0.904456i \(0.359723\pi\)
\(854\) 6580.00 0.263657
\(855\) −9504.00 −0.380152
\(856\) 416.000 0.0166105
\(857\) 17818.0 0.710212 0.355106 0.934826i \(-0.384445\pi\)
0.355106 + 0.934826i \(0.384445\pi\)
\(858\) 1716.00 0.0682789
\(859\) −29476.0 −1.17079 −0.585395 0.810748i \(-0.699060\pi\)
−0.585395 + 0.810748i \(0.699060\pi\)
\(860\) 4032.00 0.159872
\(861\) −6804.00 −0.269314
\(862\) −6996.00 −0.276432
\(863\) 21378.0 0.843239 0.421620 0.906773i \(-0.361462\pi\)
0.421620 + 0.906773i \(0.361462\pi\)
\(864\) 864.000 0.0340207
\(865\) 37224.0 1.46318
\(866\) 788.000 0.0309207
\(867\) 14727.0 0.576880
\(868\) −2576.00 −0.100732
\(869\) 17072.0 0.666430
\(870\) −1584.00 −0.0617272
\(871\) 3796.00 0.147672
\(872\) 12336.0 0.479071
\(873\) −4410.00 −0.170969
\(874\) −14080.0 −0.544923
\(875\) −8904.00 −0.344012
\(876\) 6072.00 0.234194
\(877\) −9218.00 −0.354926 −0.177463 0.984128i \(-0.556789\pi\)
−0.177463 + 0.984128i \(0.556789\pi\)
\(878\) −21056.0 −0.809346
\(879\) 1944.00 0.0745956
\(880\) −4224.00 −0.161808
\(881\) 36762.0 1.40584 0.702919 0.711270i \(-0.251880\pi\)
0.702919 + 0.711270i \(0.251880\pi\)
\(882\) −882.000 −0.0336718
\(883\) −40308.0 −1.53621 −0.768104 0.640325i \(-0.778800\pi\)
−0.768104 + 0.640325i \(0.778800\pi\)
\(884\) 104.000 0.00395690
\(885\) −7560.00 −0.287149
\(886\) 10056.0 0.381307
\(887\) −7512.00 −0.284361 −0.142181 0.989841i \(-0.545411\pi\)
−0.142181 + 0.989841i \(0.545411\pi\)
\(888\) 2832.00 0.107022
\(889\) 4872.00 0.183804
\(890\) 22080.0 0.831599
\(891\) −1782.00 −0.0670025
\(892\) 16848.0 0.632413
\(893\) 11792.0 0.441886
\(894\) 14520.0 0.543201
\(895\) −33888.0 −1.26564
\(896\) −896.000 −0.0334077
\(897\) −3120.00 −0.116136
\(898\) 6024.00 0.223857
\(899\) 2024.00 0.0750881
\(900\) 684.000 0.0253333
\(901\) 388.000 0.0143465
\(902\) 14256.0 0.526245
\(903\) −1764.00 −0.0650080
\(904\) −14128.0 −0.519790
\(905\) −10104.0 −0.371125
\(906\) −13608.0 −0.499002
\(907\) −26164.0 −0.957841 −0.478920 0.877858i \(-0.658972\pi\)
−0.478920 + 0.877858i \(0.658972\pi\)
\(908\) −8280.00 −0.302623
\(909\) 8694.00 0.317230
\(910\) 2184.00 0.0795592
\(911\) −28300.0 −1.02922 −0.514611 0.857424i \(-0.672064\pi\)
−0.514611 + 0.857424i \(0.672064\pi\)
\(912\) 4224.00 0.153367
\(913\) 17116.0 0.620435
\(914\) 11012.0 0.398517
\(915\) 16920.0 0.611320
\(916\) −8792.00 −0.317135
\(917\) 10528.0 0.379133
\(918\) −108.000 −0.00388293
\(919\) −15896.0 −0.570577 −0.285289 0.958442i \(-0.592089\pi\)
−0.285289 + 0.958442i \(0.592089\pi\)
\(920\) 7680.00 0.275220
\(921\) −16908.0 −0.604927
\(922\) −9528.00 −0.340334
\(923\) 858.000 0.0305974
\(924\) 1848.00 0.0657952
\(925\) 2242.00 0.0796935
\(926\) −10032.0 −0.356017
\(927\) −12096.0 −0.428570
\(928\) 704.000 0.0249029
\(929\) −4108.00 −0.145080 −0.0725399 0.997366i \(-0.523110\pi\)
−0.0725399 + 0.997366i \(0.523110\pi\)
\(930\) −6624.00 −0.233559
\(931\) −4312.00 −0.151794
\(932\) −13512.0 −0.474893
\(933\) 14892.0 0.522553
\(934\) 17856.0 0.625553
\(935\) 528.000 0.0184679
\(936\) 936.000 0.0326860
\(937\) −43034.0 −1.50038 −0.750192 0.661220i \(-0.770039\pi\)
−0.750192 + 0.661220i \(0.770039\pi\)
\(938\) 4088.00 0.142301
\(939\) −17802.0 −0.618686
\(940\) −6432.00 −0.223179
\(941\) −17568.0 −0.608608 −0.304304 0.952575i \(-0.598424\pi\)
−0.304304 + 0.952575i \(0.598424\pi\)
\(942\) −3612.00 −0.124931
\(943\) −25920.0 −0.895092
\(944\) 3360.00 0.115846
\(945\) −2268.00 −0.0780720
\(946\) 3696.00 0.127027
\(947\) −8426.00 −0.289132 −0.144566 0.989495i \(-0.546179\pi\)
−0.144566 + 0.989495i \(0.546179\pi\)
\(948\) 9312.00 0.319029
\(949\) 6578.00 0.225006
\(950\) 3344.00 0.114204
\(951\) −7680.00 −0.261873
\(952\) 112.000 0.00381296
\(953\) −25938.0 −0.881652 −0.440826 0.897593i \(-0.645314\pi\)
−0.440826 + 0.897593i \(0.645314\pi\)
\(954\) 3492.00 0.118509
\(955\) 30576.0 1.03604
\(956\) −11496.0 −0.388920
\(957\) −1452.00 −0.0490454
\(958\) −6332.00 −0.213547
\(959\) −4536.00 −0.152737
\(960\) −2304.00 −0.0774597
\(961\) −21327.0 −0.715887
\(962\) 3068.00 0.102824
\(963\) −468.000 −0.0156605
\(964\) 7704.00 0.257395
\(965\) −13416.0 −0.447540
\(966\) −3360.00 −0.111911
\(967\) 13028.0 0.433249 0.216625 0.976255i \(-0.430495\pi\)
0.216625 + 0.976255i \(0.430495\pi\)
\(968\) 6776.00 0.224989
\(969\) −528.000 −0.0175044
\(970\) 11760.0 0.389269
\(971\) 16524.0 0.546118 0.273059 0.961997i \(-0.411965\pi\)
0.273059 + 0.961997i \(0.411965\pi\)
\(972\) −972.000 −0.0320750
\(973\) −9716.00 −0.320124
\(974\) 1192.00 0.0392137
\(975\) 741.000 0.0243395
\(976\) −7520.00 −0.246628
\(977\) −18532.0 −0.606849 −0.303424 0.952856i \(-0.598130\pi\)
−0.303424 + 0.952856i \(0.598130\pi\)
\(978\) 7296.00 0.238548
\(979\) 20240.0 0.660749
\(980\) 2352.00 0.0766652
\(981\) −13878.0 −0.451672
\(982\) 13880.0 0.451047
\(983\) 16646.0 0.540107 0.270053 0.962845i \(-0.412959\pi\)
0.270053 + 0.962845i \(0.412959\pi\)
\(984\) 7776.00 0.251921
\(985\) 23904.0 0.773243
\(986\) −88.0000 −0.00284228
\(987\) 2814.00 0.0907504
\(988\) 4576.00 0.147350
\(989\) −6720.00 −0.216060
\(990\) 4752.00 0.152554
\(991\) −3016.00 −0.0966765 −0.0483382 0.998831i \(-0.515393\pi\)
−0.0483382 + 0.998831i \(0.515393\pi\)
\(992\) 2944.00 0.0942259
\(993\) −12060.0 −0.385410
\(994\) 924.000 0.0294844
\(995\) −42432.0 −1.35194
\(996\) 9336.00 0.297011
\(997\) 33438.0 1.06218 0.531089 0.847316i \(-0.321783\pi\)
0.531089 + 0.847316i \(0.321783\pi\)
\(998\) −2312.00 −0.0733317
\(999\) −3186.00 −0.100901
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 546.4.a.a.1.1 1
3.2 odd 2 1638.4.a.i.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.4.a.a.1.1 1 1.1 even 1 trivial
1638.4.a.i.1.1 1 3.2 odd 2