Properties

Label 2166.4.a.u.1.3
Level $2166$
Weight $4$
Character 2166.1
Self dual yes
Analytic conductor $127.798$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2166.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(127.798137072\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.14457.1
Defining polynomial: \(x^{3} - x^{2} - 32 x - 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3}\cdot 3 \)
Twist minimal: no (minimal twist has level 114)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-5.12716\) of defining polynomial
Character \(\chi\) \(=\) 2166.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +14.2543 q^{5} -6.00000 q^{6} +13.2543 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +14.2543 q^{5} -6.00000 q^{6} +13.2543 q^{7} +8.00000 q^{8} +9.00000 q^{9} +28.5086 q^{10} -65.9138 q^{11} -12.0000 q^{12} -68.5259 q^{13} +26.5086 q^{14} -42.7629 q^{15} +16.0000 q^{16} +99.6940 q^{17} +18.0000 q^{18} +57.0172 q^{20} -39.7629 q^{21} -131.828 q^{22} +3.53886 q^{23} -24.0000 q^{24} +78.1854 q^{25} -137.052 q^{26} -27.0000 q^{27} +53.0172 q^{28} -81.9008 q^{29} -85.5259 q^{30} -247.190 q^{31} +32.0000 q^{32} +197.741 q^{33} +199.388 q^{34} +188.931 q^{35} +36.0000 q^{36} +421.065 q^{37} +205.578 q^{39} +114.034 q^{40} -345.259 q^{41} -79.5259 q^{42} -366.168 q^{43} -263.655 q^{44} +128.289 q^{45} +7.07773 q^{46} -90.9399 q^{47} -48.0000 q^{48} -167.323 q^{49} +156.371 q^{50} -299.082 q^{51} -274.103 q^{52} -688.491 q^{53} -54.0000 q^{54} -939.556 q^{55} +106.034 q^{56} -163.802 q^{58} +182.289 q^{59} -171.052 q^{60} -0.517370 q^{61} -494.379 q^{62} +119.289 q^{63} +64.0000 q^{64} -976.789 q^{65} +395.483 q^{66} -159.862 q^{67} +398.776 q^{68} -10.6166 q^{69} +377.862 q^{70} -791.884 q^{71} +72.0000 q^{72} +322.129 q^{73} +842.130 q^{74} -234.556 q^{75} -873.642 q^{77} +411.155 q^{78} +318.371 q^{79} +228.069 q^{80} +81.0000 q^{81} -690.517 q^{82} +684.160 q^{83} -159.052 q^{84} +1421.07 q^{85} -732.336 q^{86} +245.703 q^{87} -527.311 q^{88} +720.406 q^{89} +256.578 q^{90} -908.263 q^{91} +14.1555 q^{92} +741.569 q^{93} -181.880 q^{94} -96.0000 q^{96} +415.392 q^{97} -334.646 q^{98} -593.224 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 6q^{2} - 9q^{3} + 12q^{4} + 10q^{5} - 18q^{6} + 7q^{7} + 24q^{8} + 27q^{9} + O(q^{10}) \) \( 3q + 6q^{2} - 9q^{3} + 12q^{4} + 10q^{5} - 18q^{6} + 7q^{7} + 24q^{8} + 27q^{9} + 20q^{10} - 44q^{11} - 36q^{12} - 9q^{13} + 14q^{14} - 30q^{15} + 48q^{16} - 84q^{17} + 54q^{18} + 40q^{20} - 21q^{21} - 88q^{22} - 2q^{23} - 72q^{24} - 83q^{25} - 18q^{26} - 81q^{27} + 28q^{28} + 92q^{29} - 60q^{30} - 109q^{31} + 96q^{32} + 132q^{33} - 168q^{34} + 282q^{35} + 108q^{36} + 245q^{37} + 27q^{39} + 80q^{40} - 688q^{41} - 42q^{42} - 103q^{43} - 176q^{44} + 90q^{45} - 4q^{46} + 322q^{47} - 144q^{48} - 754q^{49} - 166q^{50} + 252q^{51} - 36q^{52} - 1322q^{53} - 162q^{54} - 248q^{55} + 56q^{56} + 184q^{58} + 252q^{59} - 120q^{60} - 435q^{61} - 218q^{62} + 63q^{63} + 192q^{64} - 1582q^{65} + 264q^{66} - 719q^{67} - 336q^{68} + 6q^{69} + 564q^{70} - 62q^{71} + 216q^{72} - 581q^{73} + 490q^{74} + 249q^{75} - 204q^{77} + 54q^{78} - 489q^{79} + 160q^{80} + 243q^{81} - 1376q^{82} + 2496q^{83} - 84q^{84} + 1632q^{85} - 206q^{86} - 276q^{87} - 352q^{88} + 1584q^{89} + 180q^{90} - 1573q^{91} - 8q^{92} + 327q^{93} + 644q^{94} - 288q^{96} + 974q^{97} - 1508q^{98} - 396q^{99} + O(q^{100}) \)

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
\(5\) 14.2543 1.27494 0.637472 0.770473i \(-0.279980\pi\)
0.637472 + 0.770473i \(0.279980\pi\)
\(6\) −6.00000 −0.408248
\(7\) 13.2543 0.715666 0.357833 0.933786i \(-0.383516\pi\)
0.357833 + 0.933786i \(0.383516\pi\)
\(8\) 8.00000 0.353553
\(9\) 9.00000 0.333333
\(10\) 28.5086 0.901522
\(11\) −65.9138 −1.80671 −0.903353 0.428898i \(-0.858902\pi\)
−0.903353 + 0.428898i \(0.858902\pi\)
\(12\) −12.0000 −0.288675
\(13\) −68.5259 −1.46197 −0.730987 0.682392i \(-0.760940\pi\)
−0.730987 + 0.682392i \(0.760940\pi\)
\(14\) 26.5086 0.506052
\(15\) −42.7629 −0.736089
\(16\) 16.0000 0.250000
\(17\) 99.6940 1.42231 0.711157 0.703033i \(-0.248171\pi\)
0.711157 + 0.703033i \(0.248171\pi\)
\(18\) 18.0000 0.235702
\(19\) 0 0
\(20\) 57.0172 0.637472
\(21\) −39.7629 −0.413190
\(22\) −131.828 −1.27753
\(23\) 3.53886 0.0320828 0.0160414 0.999871i \(-0.494894\pi\)
0.0160414 + 0.999871i \(0.494894\pi\)
\(24\) −24.0000 −0.204124
\(25\) 78.1854 0.625483
\(26\) −137.052 −1.03377
\(27\) −27.0000 −0.192450
\(28\) 53.0172 0.357833
\(29\) −81.9008 −0.524435 −0.262217 0.965009i \(-0.584454\pi\)
−0.262217 + 0.965009i \(0.584454\pi\)
\(30\) −85.5259 −0.520494
\(31\) −247.190 −1.43215 −0.716074 0.698025i \(-0.754063\pi\)
−0.716074 + 0.698025i \(0.754063\pi\)
\(32\) 32.0000 0.176777
\(33\) 197.741 1.04310
\(34\) 199.388 1.00573
\(35\) 188.931 0.912434
\(36\) 36.0000 0.166667
\(37\) 421.065 1.87088 0.935441 0.353483i \(-0.115003\pi\)
0.935441 + 0.353483i \(0.115003\pi\)
\(38\) 0 0
\(39\) 205.578 0.844071
\(40\) 114.034 0.450761
\(41\) −345.259 −1.31513 −0.657565 0.753398i \(-0.728413\pi\)
−0.657565 + 0.753398i \(0.728413\pi\)
\(42\) −79.5259 −0.292169
\(43\) −366.168 −1.29861 −0.649304 0.760529i \(-0.724940\pi\)
−0.649304 + 0.760529i \(0.724940\pi\)
\(44\) −263.655 −0.903353
\(45\) 128.289 0.424981
\(46\) 7.07773 0.0226860
\(47\) −90.9399 −0.282233 −0.141116 0.989993i \(-0.545069\pi\)
−0.141116 + 0.989993i \(0.545069\pi\)
\(48\) −48.0000 −0.144338
\(49\) −167.323 −0.487823
\(50\) 156.371 0.442283
\(51\) −299.082 −0.821174
\(52\) −274.103 −0.730987
\(53\) −688.491 −1.78437 −0.892185 0.451671i \(-0.850828\pi\)
−0.892185 + 0.451671i \(0.850828\pi\)
\(54\) −54.0000 −0.136083
\(55\) −939.556 −2.30345
\(56\) 106.034 0.253026
\(57\) 0 0
\(58\) −163.802 −0.370831
\(59\) 182.289 0.402237 0.201118 0.979567i \(-0.435542\pi\)
0.201118 + 0.979567i \(0.435542\pi\)
\(60\) −171.052 −0.368045
\(61\) −0.517370 −0.00108594 −0.000542971 1.00000i \(-0.500173\pi\)
−0.000542971 1.00000i \(0.500173\pi\)
\(62\) −494.379 −1.01268
\(63\) 119.289 0.238555
\(64\) 64.0000 0.125000
\(65\) −976.789 −1.86393
\(66\) 395.483 0.737585
\(67\) −159.862 −0.291496 −0.145748 0.989322i \(-0.546559\pi\)
−0.145748 + 0.989322i \(0.546559\pi\)
\(68\) 398.776 0.711157
\(69\) −10.6166 −0.0185230
\(70\) 377.862 0.645188
\(71\) −791.884 −1.32365 −0.661826 0.749657i \(-0.730218\pi\)
−0.661826 + 0.749657i \(0.730218\pi\)
\(72\) 72.0000 0.117851
\(73\) 322.129 0.516471 0.258235 0.966082i \(-0.416859\pi\)
0.258235 + 0.966082i \(0.416859\pi\)
\(74\) 842.130 1.32291
\(75\) −234.556 −0.361123
\(76\) 0 0
\(77\) −873.642 −1.29300
\(78\) 411.155 0.596848
\(79\) 318.371 0.453412 0.226706 0.973963i \(-0.427204\pi\)
0.226706 + 0.973963i \(0.427204\pi\)
\(80\) 228.069 0.318736
\(81\) 81.0000 0.111111
\(82\) −690.517 −0.929937
\(83\) 684.160 0.904774 0.452387 0.891822i \(-0.350573\pi\)
0.452387 + 0.891822i \(0.350573\pi\)
\(84\) −159.052 −0.206595
\(85\) 1421.07 1.81337
\(86\) −732.336 −0.918254
\(87\) 245.703 0.302782
\(88\) −527.311 −0.638767
\(89\) 720.406 0.858009 0.429005 0.903302i \(-0.358864\pi\)
0.429005 + 0.903302i \(0.358864\pi\)
\(90\) 256.578 0.300507
\(91\) −908.263 −1.04628
\(92\) 14.1555 0.0160414
\(93\) 741.569 0.826851
\(94\) −181.880 −0.199569
\(95\) 0 0
\(96\) −96.0000 −0.102062
\(97\) 415.392 0.434811 0.217406 0.976081i \(-0.430241\pi\)
0.217406 + 0.976081i \(0.430241\pi\)
\(98\) −334.646 −0.344943
\(99\) −593.224 −0.602235
\(100\) 312.742 0.312742
\(101\) 337.341 0.332343 0.166172 0.986097i \(-0.446859\pi\)
0.166172 + 0.986097i \(0.446859\pi\)
\(102\) −598.164 −0.580658
\(103\) −1467.05 −1.40342 −0.701711 0.712462i \(-0.747580\pi\)
−0.701711 + 0.712462i \(0.747580\pi\)
\(104\) −548.207 −0.516886
\(105\) −566.793 −0.526794
\(106\) −1376.98 −1.26174
\(107\) 382.014 0.345146 0.172573 0.984997i \(-0.444792\pi\)
0.172573 + 0.984997i \(0.444792\pi\)
\(108\) −108.000 −0.0962250
\(109\) −132.857 −0.116747 −0.0583736 0.998295i \(-0.518591\pi\)
−0.0583736 + 0.998295i \(0.518591\pi\)
\(110\) −1879.11 −1.62879
\(111\) −1263.19 −1.08015
\(112\) 212.069 0.178916
\(113\) −1137.94 −0.947331 −0.473665 0.880705i \(-0.657069\pi\)
−0.473665 + 0.880705i \(0.657069\pi\)
\(114\) 0 0
\(115\) 50.4441 0.0409038
\(116\) −327.603 −0.262217
\(117\) −616.733 −0.487325
\(118\) 364.578 0.284424
\(119\) 1321.38 1.01790
\(120\) −342.103 −0.260247
\(121\) 3013.63 2.26419
\(122\) −1.03474 −0.000767877 0
\(123\) 1035.78 0.759291
\(124\) −988.759 −0.716074
\(125\) −667.310 −0.477488
\(126\) 238.578 0.168684
\(127\) −1509.97 −1.05503 −0.527514 0.849546i \(-0.676876\pi\)
−0.527514 + 0.849546i \(0.676876\pi\)
\(128\) 128.000 0.0883883
\(129\) 1098.50 0.749751
\(130\) −1953.58 −1.31800
\(131\) −370.944 −0.247401 −0.123701 0.992320i \(-0.539476\pi\)
−0.123701 + 0.992320i \(0.539476\pi\)
\(132\) 790.966 0.521551
\(133\) 0 0
\(134\) −319.724 −0.206119
\(135\) −384.866 −0.245363
\(136\) 797.552 0.502864
\(137\) −1690.37 −1.05415 −0.527075 0.849819i \(-0.676711\pi\)
−0.527075 + 0.849819i \(0.676711\pi\)
\(138\) −21.2332 −0.0130977
\(139\) −2711.52 −1.65459 −0.827296 0.561766i \(-0.810122\pi\)
−0.827296 + 0.561766i \(0.810122\pi\)
\(140\) 755.724 0.456217
\(141\) 272.820 0.162947
\(142\) −1583.77 −0.935964
\(143\) 4516.80 2.64136
\(144\) 144.000 0.0833333
\(145\) −1167.44 −0.668625
\(146\) 644.258 0.365200
\(147\) 501.970 0.281645
\(148\) 1684.26 0.935441
\(149\) 2598.90 1.42893 0.714464 0.699672i \(-0.246671\pi\)
0.714464 + 0.699672i \(0.246671\pi\)
\(150\) −469.112 −0.255352
\(151\) 594.863 0.320591 0.160296 0.987069i \(-0.448755\pi\)
0.160296 + 0.987069i \(0.448755\pi\)
\(152\) 0 0
\(153\) 897.246 0.474105
\(154\) −1747.28 −0.914287
\(155\) −3523.52 −1.82591
\(156\) 822.310 0.422035
\(157\) −58.2549 −0.0296130 −0.0148065 0.999890i \(-0.504713\pi\)
−0.0148065 + 0.999890i \(0.504713\pi\)
\(158\) 636.742 0.320610
\(159\) 2065.47 1.03021
\(160\) 456.138 0.225380
\(161\) 46.9052 0.0229605
\(162\) 162.000 0.0785674
\(163\) 1152.53 0.553825 0.276912 0.960895i \(-0.410689\pi\)
0.276912 + 0.960895i \(0.410689\pi\)
\(164\) −1381.03 −0.657565
\(165\) 2818.67 1.32990
\(166\) 1368.32 0.639772
\(167\) 1259.11 0.583430 0.291715 0.956505i \(-0.405774\pi\)
0.291715 + 0.956505i \(0.405774\pi\)
\(168\) −318.103 −0.146085
\(169\) 2498.79 1.13737
\(170\) 2842.14 1.28225
\(171\) 0 0
\(172\) −1464.67 −0.649304
\(173\) −1274.10 −0.559931 −0.279965 0.960010i \(-0.590323\pi\)
−0.279965 + 0.960010i \(0.590323\pi\)
\(174\) 491.405 0.214100
\(175\) 1036.29 0.447637
\(176\) −1054.62 −0.451677
\(177\) −546.866 −0.232232
\(178\) 1440.81 0.606704
\(179\) 2034.50 0.849528 0.424764 0.905304i \(-0.360357\pi\)
0.424764 + 0.905304i \(0.360357\pi\)
\(180\) 513.155 0.212491
\(181\) 1033.31 0.424340 0.212170 0.977233i \(-0.431947\pi\)
0.212170 + 0.977233i \(0.431947\pi\)
\(182\) −1816.53 −0.739835
\(183\) 1.55211 0.000626969 0
\(184\) 28.3109 0.0113430
\(185\) 6001.99 2.38527
\(186\) 1483.14 0.584672
\(187\) −6571.21 −2.56970
\(188\) −363.760 −0.141116
\(189\) −357.866 −0.137730
\(190\) 0 0
\(191\) −1135.46 −0.430154 −0.215077 0.976597i \(-0.569000\pi\)
−0.215077 + 0.976597i \(0.569000\pi\)
\(192\) −192.000 −0.0721688
\(193\) 1091.07 0.406928 0.203464 0.979082i \(-0.434780\pi\)
0.203464 + 0.979082i \(0.434780\pi\)
\(194\) 830.784 0.307458
\(195\) 2930.37 1.07614
\(196\) −669.293 −0.243911
\(197\) 4138.08 1.49658 0.748289 0.663373i \(-0.230876\pi\)
0.748289 + 0.663373i \(0.230876\pi\)
\(198\) −1186.45 −0.425845
\(199\) −2734.23 −0.973993 −0.486997 0.873404i \(-0.661908\pi\)
−0.486997 + 0.873404i \(0.661908\pi\)
\(200\) 625.483 0.221142
\(201\) 479.586 0.168296
\(202\) 674.682 0.235002
\(203\) −1085.54 −0.375320
\(204\) −1196.33 −0.410587
\(205\) −4921.42 −1.67672
\(206\) −2934.10 −0.992369
\(207\) 31.8498 0.0106943
\(208\) −1096.41 −0.365493
\(209\) 0 0
\(210\) −1133.59 −0.372500
\(211\) 3058.01 0.997734 0.498867 0.866679i \(-0.333750\pi\)
0.498867 + 0.866679i \(0.333750\pi\)
\(212\) −2753.97 −0.892185
\(213\) 2375.65 0.764211
\(214\) 764.027 0.244055
\(215\) −5219.48 −1.65565
\(216\) −216.000 −0.0680414
\(217\) −3276.33 −1.02494
\(218\) −265.715 −0.0825527
\(219\) −966.388 −0.298185
\(220\) −3758.23 −1.15172
\(221\) −6831.62 −2.07939
\(222\) −2526.39 −0.763784
\(223\) 1618.27 0.485951 0.242976 0.970032i \(-0.421876\pi\)
0.242976 + 0.970032i \(0.421876\pi\)
\(224\) 424.138 0.126513
\(225\) 703.668 0.208494
\(226\) −2275.88 −0.669864
\(227\) −6065.43 −1.77347 −0.886733 0.462282i \(-0.847031\pi\)
−0.886733 + 0.462282i \(0.847031\pi\)
\(228\) 0 0
\(229\) −1916.36 −0.552999 −0.276500 0.961014i \(-0.589174\pi\)
−0.276500 + 0.961014i \(0.589174\pi\)
\(230\) 100.888 0.0289233
\(231\) 2620.93 0.746512
\(232\) −655.207 −0.185416
\(233\) −4008.54 −1.12707 −0.563537 0.826091i \(-0.690560\pi\)
−0.563537 + 0.826091i \(0.690560\pi\)
\(234\) −1233.47 −0.344590
\(235\) −1296.29 −0.359831
\(236\) 729.155 0.201118
\(237\) −955.112 −0.261777
\(238\) 2642.75 0.719765
\(239\) 530.292 0.143522 0.0717610 0.997422i \(-0.477138\pi\)
0.0717610 + 0.997422i \(0.477138\pi\)
\(240\) −684.207 −0.184022
\(241\) 1271.23 0.339779 0.169890 0.985463i \(-0.445659\pi\)
0.169890 + 0.985463i \(0.445659\pi\)
\(242\) 6027.27 1.60102
\(243\) −243.000 −0.0641500
\(244\) −2.06948 −0.000542971 0
\(245\) −2385.08 −0.621947
\(246\) 2071.55 0.536900
\(247\) 0 0
\(248\) −1977.52 −0.506341
\(249\) −2052.48 −0.522372
\(250\) −1334.62 −0.337635
\(251\) 551.989 0.138810 0.0694048 0.997589i \(-0.477890\pi\)
0.0694048 + 0.997589i \(0.477890\pi\)
\(252\) 477.155 0.119278
\(253\) −233.260 −0.0579642
\(254\) −3019.95 −0.746018
\(255\) −4263.21 −1.04695
\(256\) 256.000 0.0625000
\(257\) −5235.84 −1.27083 −0.635414 0.772172i \(-0.719170\pi\)
−0.635414 + 0.772172i \(0.719170\pi\)
\(258\) 2197.01 0.530154
\(259\) 5580.92 1.33893
\(260\) −3907.16 −0.931967
\(261\) −737.108 −0.174812
\(262\) −741.888 −0.174939
\(263\) −1814.26 −0.425368 −0.212684 0.977121i \(-0.568221\pi\)
−0.212684 + 0.977121i \(0.568221\pi\)
\(264\) 1581.93 0.368792
\(265\) −9813.97 −2.27497
\(266\) 0 0
\(267\) −2161.22 −0.495372
\(268\) −639.448 −0.145748
\(269\) 1013.40 0.229695 0.114848 0.993383i \(-0.463362\pi\)
0.114848 + 0.993383i \(0.463362\pi\)
\(270\) −769.733 −0.173498
\(271\) −1918.52 −0.430043 −0.215021 0.976609i \(-0.568982\pi\)
−0.215021 + 0.976609i \(0.568982\pi\)
\(272\) 1595.10 0.355579
\(273\) 2724.79 0.604072
\(274\) −3380.75 −0.745396
\(275\) −5153.50 −1.13006
\(276\) −42.4664 −0.00926150
\(277\) 6283.45 1.36295 0.681473 0.731844i \(-0.261340\pi\)
0.681473 + 0.731844i \(0.261340\pi\)
\(278\) −5423.04 −1.16997
\(279\) −2224.71 −0.477382
\(280\) 1511.45 0.322594
\(281\) −8057.36 −1.71054 −0.855270 0.518182i \(-0.826609\pi\)
−0.855270 + 0.518182i \(0.826609\pi\)
\(282\) 545.639 0.115221
\(283\) −193.417 −0.0406269 −0.0203135 0.999794i \(-0.506466\pi\)
−0.0203135 + 0.999794i \(0.506466\pi\)
\(284\) −3167.54 −0.661826
\(285\) 0 0
\(286\) 9033.61 1.86772
\(287\) −4576.16 −0.941193
\(288\) 288.000 0.0589256
\(289\) 5025.90 1.02298
\(290\) −2334.88 −0.472789
\(291\) −1246.18 −0.251038
\(292\) 1288.52 0.258235
\(293\) −4735.47 −0.944194 −0.472097 0.881547i \(-0.656503\pi\)
−0.472097 + 0.881547i \(0.656503\pi\)
\(294\) 1003.94 0.199153
\(295\) 2598.40 0.512830
\(296\) 3368.52 0.661457
\(297\) 1779.67 0.347701
\(298\) 5197.80 1.01040
\(299\) −242.504 −0.0469042
\(300\) −938.225 −0.180561
\(301\) −4853.31 −0.929369
\(302\) 1189.73 0.226692
\(303\) −1012.02 −0.191879
\(304\) 0 0
\(305\) −7.37475 −0.00138451
\(306\) 1794.49 0.335243
\(307\) −28.7122 −0.00533775 −0.00266888 0.999996i \(-0.500850\pi\)
−0.00266888 + 0.999996i \(0.500850\pi\)
\(308\) −3494.57 −0.646499
\(309\) 4401.14 0.810266
\(310\) −7047.04 −1.29111
\(311\) −1165.69 −0.212540 −0.106270 0.994337i \(-0.533891\pi\)
−0.106270 + 0.994337i \(0.533891\pi\)
\(312\) 1644.62 0.298424
\(313\) 2512.75 0.453767 0.226884 0.973922i \(-0.427146\pi\)
0.226884 + 0.973922i \(0.427146\pi\)
\(314\) −116.510 −0.0209396
\(315\) 1700.38 0.304145
\(316\) 1273.48 0.226706
\(317\) −1727.57 −0.306087 −0.153044 0.988219i \(-0.548908\pi\)
−0.153044 + 0.988219i \(0.548908\pi\)
\(318\) 4130.95 0.728466
\(319\) 5398.40 0.947499
\(320\) 912.276 0.159368
\(321\) −1146.04 −0.199270
\(322\) 93.8104 0.0162356
\(323\) 0 0
\(324\) 324.000 0.0555556
\(325\) −5357.72 −0.914440
\(326\) 2305.07 0.391613
\(327\) 398.572 0.0674040
\(328\) −2762.07 −0.464969
\(329\) −1205.35 −0.201984
\(330\) 5637.34 0.940379
\(331\) −6816.13 −1.13187 −0.565934 0.824450i \(-0.691484\pi\)
−0.565934 + 0.824450i \(0.691484\pi\)
\(332\) 2736.64 0.452387
\(333\) 3789.58 0.623627
\(334\) 2518.22 0.412547
\(335\) −2278.72 −0.371642
\(336\) −636.207 −0.103297
\(337\) −10408.4 −1.68244 −0.841218 0.540696i \(-0.818161\pi\)
−0.841218 + 0.540696i \(0.818161\pi\)
\(338\) 4997.59 0.804240
\(339\) 3413.82 0.546942
\(340\) 5684.28 0.906686
\(341\) 16293.2 2.58747
\(342\) 0 0
\(343\) −6763.98 −1.06478
\(344\) −2929.35 −0.459127
\(345\) −151.332 −0.0236158
\(346\) −2548.20 −0.395931
\(347\) −5584.03 −0.863881 −0.431940 0.901902i \(-0.642171\pi\)
−0.431940 + 0.901902i \(0.642171\pi\)
\(348\) 982.810 0.151391
\(349\) 5505.82 0.844470 0.422235 0.906486i \(-0.361246\pi\)
0.422235 + 0.906486i \(0.361246\pi\)
\(350\) 2072.59 0.316527
\(351\) 1850.20 0.281357
\(352\) −2109.24 −0.319384
\(353\) −5782.46 −0.871868 −0.435934 0.899979i \(-0.643582\pi\)
−0.435934 + 0.899979i \(0.643582\pi\)
\(354\) −1093.73 −0.164213
\(355\) −11287.8 −1.68758
\(356\) 2881.62 0.429005
\(357\) −3964.13 −0.587686
\(358\) 4068.99 0.600707
\(359\) −1903.64 −0.279861 −0.139931 0.990161i \(-0.544688\pi\)
−0.139931 + 0.990161i \(0.544688\pi\)
\(360\) 1026.31 0.150254
\(361\) 0 0
\(362\) 2066.63 0.300054
\(363\) −9040.90 −1.30723
\(364\) −3633.05 −0.523142
\(365\) 4591.73 0.658472
\(366\) 3.10422 0.000443334 0
\(367\) −12748.0 −1.81319 −0.906597 0.421998i \(-0.861329\pi\)
−0.906597 + 0.421998i \(0.861329\pi\)
\(368\) 56.6218 0.00802070
\(369\) −3107.33 −0.438377
\(370\) 12004.0 1.68664
\(371\) −9125.48 −1.27701
\(372\) 2966.28 0.413425
\(373\) −736.660 −0.102260 −0.0511298 0.998692i \(-0.516282\pi\)
−0.0511298 + 0.998692i \(0.516282\pi\)
\(374\) −13142.4 −1.81706
\(375\) 2001.93 0.275678
\(376\) −727.519 −0.0997844
\(377\) 5612.33 0.766710
\(378\) −715.733 −0.0973897
\(379\) 1543.57 0.209202 0.104601 0.994514i \(-0.466643\pi\)
0.104601 + 0.994514i \(0.466643\pi\)
\(380\) 0 0
\(381\) 4529.92 0.609121
\(382\) −2270.93 −0.304165
\(383\) 6564.36 0.875779 0.437889 0.899029i \(-0.355726\pi\)
0.437889 + 0.899029i \(0.355726\pi\)
\(384\) −384.000 −0.0510310
\(385\) −12453.2 −1.64850
\(386\) 2182.15 0.287742
\(387\) −3295.51 −0.432869
\(388\) 1661.57 0.217406
\(389\) −3498.27 −0.455962 −0.227981 0.973666i \(-0.573212\pi\)
−0.227981 + 0.973666i \(0.573212\pi\)
\(390\) 5860.73 0.760948
\(391\) 352.803 0.0456318
\(392\) −1338.59 −0.172471
\(393\) 1112.83 0.142837
\(394\) 8276.16 1.05824
\(395\) 4538.16 0.578075
\(396\) −2372.90 −0.301118
\(397\) 8610.60 1.08855 0.544274 0.838908i \(-0.316805\pi\)
0.544274 + 0.838908i \(0.316805\pi\)
\(398\) −5468.47 −0.688717
\(399\) 0 0
\(400\) 1250.97 0.156371
\(401\) 1765.74 0.219893 0.109946 0.993938i \(-0.464932\pi\)
0.109946 + 0.993938i \(0.464932\pi\)
\(402\) 959.173 0.119003
\(403\) 16938.9 2.09376
\(404\) 1349.36 0.166172
\(405\) 1154.60 0.141660
\(406\) −2171.08 −0.265391
\(407\) −27754.0 −3.38013
\(408\) −2392.66 −0.290329
\(409\) 13395.7 1.61950 0.809751 0.586774i \(-0.199602\pi\)
0.809751 + 0.586774i \(0.199602\pi\)
\(410\) −9842.85 −1.18562
\(411\) 5071.12 0.608613
\(412\) −5868.19 −0.701711
\(413\) 2416.11 0.287867
\(414\) 63.6995 0.00756198
\(415\) 9752.22 1.15354
\(416\) −2192.83 −0.258443
\(417\) 8134.57 0.955279
\(418\) 0 0
\(419\) 9117.71 1.06308 0.531539 0.847034i \(-0.321614\pi\)
0.531539 + 0.847034i \(0.321614\pi\)
\(420\) −2267.17 −0.263397
\(421\) 8204.45 0.949788 0.474894 0.880043i \(-0.342486\pi\)
0.474894 + 0.880043i \(0.342486\pi\)
\(422\) 6116.01 0.705504
\(423\) −818.459 −0.0940776
\(424\) −5507.93 −0.630870
\(425\) 7794.61 0.889634
\(426\) 4751.30 0.540379
\(427\) −6.85738 −0.000777171 0
\(428\) 1528.05 0.172573
\(429\) −13550.4 −1.52499
\(430\) −10439.0 −1.17072
\(431\) −1271.34 −0.142085 −0.0710423 0.997473i \(-0.522633\pi\)
−0.0710423 + 0.997473i \(0.522633\pi\)
\(432\) −432.000 −0.0481125
\(433\) −3967.59 −0.440347 −0.220173 0.975461i \(-0.570662\pi\)
−0.220173 + 0.975461i \(0.570662\pi\)
\(434\) −6552.66 −0.724741
\(435\) 3502.32 0.386031
\(436\) −531.430 −0.0583736
\(437\) 0 0
\(438\) −1932.78 −0.210848
\(439\) 209.038 0.0227263 0.0113632 0.999935i \(-0.496383\pi\)
0.0113632 + 0.999935i \(0.496383\pi\)
\(440\) −7516.45 −0.814393
\(441\) −1505.91 −0.162608
\(442\) −13663.2 −1.47035
\(443\) 5734.04 0.614972 0.307486 0.951553i \(-0.400512\pi\)
0.307486 + 0.951553i \(0.400512\pi\)
\(444\) −5052.78 −0.540077
\(445\) 10268.9 1.09391
\(446\) 3236.53 0.343619
\(447\) −7796.70 −0.824992
\(448\) 848.276 0.0894582
\(449\) 9741.13 1.02386 0.511929 0.859028i \(-0.328931\pi\)
0.511929 + 0.859028i \(0.328931\pi\)
\(450\) 1407.34 0.147428
\(451\) 22757.3 2.37605
\(452\) −4551.76 −0.473665
\(453\) −1784.59 −0.185093
\(454\) −12130.9 −1.25403
\(455\) −12946.7 −1.33395
\(456\) 0 0
\(457\) −17233.8 −1.76403 −0.882016 0.471220i \(-0.843814\pi\)
−0.882016 + 0.471220i \(0.843814\pi\)
\(458\) −3832.73 −0.391029
\(459\) −2691.74 −0.273725
\(460\) 201.776 0.0204519
\(461\) 1665.23 0.168238 0.0841190 0.996456i \(-0.473192\pi\)
0.0841190 + 0.996456i \(0.473192\pi\)
\(462\) 5241.85 0.527864
\(463\) −10694.0 −1.07342 −0.536710 0.843767i \(-0.680333\pi\)
−0.536710 + 0.843767i \(0.680333\pi\)
\(464\) −1310.41 −0.131109
\(465\) 10570.6 1.05419
\(466\) −8017.08 −0.796961
\(467\) 13212.7 1.30923 0.654614 0.755963i \(-0.272831\pi\)
0.654614 + 0.755963i \(0.272831\pi\)
\(468\) −2466.93 −0.243662
\(469\) −2118.86 −0.208614
\(470\) −2592.57 −0.254439
\(471\) 174.765 0.0170971
\(472\) 1458.31 0.142212
\(473\) 24135.5 2.34620
\(474\) −1910.22 −0.185105
\(475\) 0 0
\(476\) 5285.50 0.508951
\(477\) −6196.42 −0.594790
\(478\) 1060.58 0.101485
\(479\) 5409.53 0.516008 0.258004 0.966144i \(-0.416935\pi\)
0.258004 + 0.966144i \(0.416935\pi\)
\(480\) −1368.41 −0.130123
\(481\) −28853.8 −2.73518
\(482\) 2542.45 0.240260
\(483\) −140.716 −0.0132563
\(484\) 12054.5 1.13209
\(485\) 5921.13 0.554360
\(486\) −486.000 −0.0453609
\(487\) 14297.0 1.33031 0.665154 0.746706i \(-0.268366\pi\)
0.665154 + 0.746706i \(0.268366\pi\)
\(488\) −4.13896 −0.000383938 0
\(489\) −3457.60 −0.319751
\(490\) −4770.15 −0.439783
\(491\) 2802.42 0.257580 0.128790 0.991672i \(-0.458891\pi\)
0.128790 + 0.991672i \(0.458891\pi\)
\(492\) 4143.10 0.379645
\(493\) −8165.02 −0.745911
\(494\) 0 0
\(495\) −8456.01 −0.767817
\(496\) −3955.03 −0.358037
\(497\) −10495.9 −0.947293
\(498\) −4104.96 −0.369373
\(499\) 14178.3 1.27196 0.635978 0.771708i \(-0.280597\pi\)
0.635978 + 0.771708i \(0.280597\pi\)
\(500\) −2669.24 −0.238744
\(501\) −3777.33 −0.336843
\(502\) 1103.98 0.0981533
\(503\) −5537.85 −0.490896 −0.245448 0.969410i \(-0.578935\pi\)
−0.245448 + 0.969410i \(0.578935\pi\)
\(504\) 954.310 0.0843420
\(505\) 4808.56 0.423719
\(506\) −466.520 −0.0409869
\(507\) −7496.38 −0.656659
\(508\) −6039.90 −0.527514
\(509\) 9115.09 0.793751 0.396876 0.917872i \(-0.370094\pi\)
0.396876 + 0.917872i \(0.370094\pi\)
\(510\) −8526.42 −0.740306
\(511\) 4269.60 0.369620
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) −10471.7 −0.898610
\(515\) −20911.8 −1.78929
\(516\) 4394.02 0.374876
\(517\) 5994.20 0.509912
\(518\) 11161.8 0.946763
\(519\) 3822.30 0.323276
\(520\) −7814.31 −0.659001
\(521\) −2705.46 −0.227502 −0.113751 0.993509i \(-0.536287\pi\)
−0.113751 + 0.993509i \(0.536287\pi\)
\(522\) −1474.22 −0.123610
\(523\) −23128.3 −1.93371 −0.966856 0.255323i \(-0.917818\pi\)
−0.966856 + 0.255323i \(0.917818\pi\)
\(524\) −1483.78 −0.123701
\(525\) −3108.88 −0.258443
\(526\) −3628.52 −0.300781
\(527\) −24643.3 −2.03696
\(528\) 3163.86 0.260776
\(529\) −12154.5 −0.998971
\(530\) −19627.9 −1.60865
\(531\) 1640.60 0.134079
\(532\) 0 0
\(533\) 23659.1 1.92269
\(534\) −4322.43 −0.350281
\(535\) 5445.34 0.440042
\(536\) −1278.90 −0.103060
\(537\) −6103.49 −0.490475
\(538\) 2026.80 0.162419
\(539\) 11028.9 0.881353
\(540\) −1539.47 −0.122682
\(541\) −9641.17 −0.766185 −0.383093 0.923710i \(-0.625141\pi\)
−0.383093 + 0.923710i \(0.625141\pi\)
\(542\) −3837.03 −0.304086
\(543\) −3099.94 −0.244993
\(544\) 3190.21 0.251432
\(545\) −1893.79 −0.148846
\(546\) 5449.58 0.427144
\(547\) −17377.0 −1.35829 −0.679147 0.734002i \(-0.737650\pi\)
−0.679147 + 0.734002i \(0.737650\pi\)
\(548\) −6761.50 −0.527075
\(549\) −4.65633 −0.000361980 0
\(550\) −10307.0 −0.799076
\(551\) 0 0
\(552\) −84.9327 −0.00654887
\(553\) 4219.79 0.324491
\(554\) 12566.9 0.963748
\(555\) −18006.0 −1.37714
\(556\) −10846.1 −0.827296
\(557\) 18744.3 1.42589 0.712945 0.701220i \(-0.247361\pi\)
0.712945 + 0.701220i \(0.247361\pi\)
\(558\) −4449.41 −0.337560
\(559\) 25092.0 1.89853
\(560\) 3022.90 0.228108
\(561\) 19713.6 1.48362
\(562\) −16114.7 −1.20953
\(563\) −7618.70 −0.570320 −0.285160 0.958480i \(-0.592047\pi\)
−0.285160 + 0.958480i \(0.592047\pi\)
\(564\) 1091.28 0.0814736
\(565\) −16220.6 −1.20779
\(566\) −386.833 −0.0287276
\(567\) 1073.60 0.0795184
\(568\) −6335.07 −0.467982
\(569\) −13081.6 −0.963816 −0.481908 0.876222i \(-0.660056\pi\)
−0.481908 + 0.876222i \(0.660056\pi\)
\(570\) 0 0
\(571\) 8643.49 0.633483 0.316741 0.948512i \(-0.397411\pi\)
0.316741 + 0.948512i \(0.397411\pi\)
\(572\) 18067.2 1.32068
\(573\) 3406.39 0.248349
\(574\) −9152.33 −0.665524
\(575\) 276.687 0.0200672
\(576\) 576.000 0.0416667
\(577\) 9841.26 0.710047 0.355024 0.934857i \(-0.384473\pi\)
0.355024 + 0.934857i \(0.384473\pi\)
\(578\) 10051.8 0.723355
\(579\) −3273.22 −0.234940
\(580\) −4669.76 −0.334312
\(581\) 9068.06 0.647516
\(582\) −2492.35 −0.177511
\(583\) 45381.1 3.22383
\(584\) 2577.03 0.182600
\(585\) −8791.10 −0.621312
\(586\) −9470.93 −0.667646
\(587\) 19898.5 1.39915 0.699573 0.714562i \(-0.253374\pi\)
0.699573 + 0.714562i \(0.253374\pi\)
\(588\) 2007.88 0.140822
\(589\) 0 0
\(590\) 5196.80 0.362625
\(591\) −12414.2 −0.864050
\(592\) 6737.04 0.467720
\(593\) 22195.0 1.53699 0.768497 0.639853i \(-0.221005\pi\)
0.768497 + 0.639853i \(0.221005\pi\)
\(594\) 3559.35 0.245862
\(595\) 18835.3 1.29777
\(596\) 10395.6 0.714464
\(597\) 8202.70 0.562335
\(598\) −485.007 −0.0331663
\(599\) 19696.2 1.34352 0.671758 0.740771i \(-0.265540\pi\)
0.671758 + 0.740771i \(0.265540\pi\)
\(600\) −1876.45 −0.127676
\(601\) −14626.5 −0.992724 −0.496362 0.868116i \(-0.665331\pi\)
−0.496362 + 0.868116i \(0.665331\pi\)
\(602\) −9706.61 −0.657163
\(603\) −1438.76 −0.0971655
\(604\) 2379.45 0.160296
\(605\) 42957.3 2.88671
\(606\) −2024.05 −0.135679
\(607\) −16312.0 −1.09075 −0.545375 0.838192i \(-0.683613\pi\)
−0.545375 + 0.838192i \(0.683613\pi\)
\(608\) 0 0
\(609\) 3256.62 0.216691
\(610\) −14.7495 −0.000979000 0
\(611\) 6231.73 0.412617
\(612\) 3588.98 0.237052
\(613\) 17748.7 1.16944 0.584718 0.811237i \(-0.301205\pi\)
0.584718 + 0.811237i \(0.301205\pi\)
\(614\) −57.4243 −0.00377436
\(615\) 14764.3 0.968053
\(616\) −6989.14 −0.457144
\(617\) 3729.80 0.243365 0.121682 0.992569i \(-0.461171\pi\)
0.121682 + 0.992569i \(0.461171\pi\)
\(618\) 8802.29 0.572945
\(619\) −1003.67 −0.0651714 −0.0325857 0.999469i \(-0.510374\pi\)
−0.0325857 + 0.999469i \(0.510374\pi\)
\(620\) −14094.1 −0.912954
\(621\) −95.5493 −0.00617433
\(622\) −2331.37 −0.150289
\(623\) 9548.48 0.614048
\(624\) 3289.24 0.211018
\(625\) −19285.2 −1.23425
\(626\) 5025.51 0.320862
\(627\) 0 0
\(628\) −233.019 −0.0148065
\(629\) 41977.6 2.66098
\(630\) 3400.76 0.215063
\(631\) 16846.8 1.06285 0.531426 0.847105i \(-0.321656\pi\)
0.531426 + 0.847105i \(0.321656\pi\)
\(632\) 2546.97 0.160305
\(633\) −9174.02 −0.576042
\(634\) −3455.13 −0.216437
\(635\) −21523.7 −1.34510
\(636\) 8261.90 0.515103
\(637\) 11466.0 0.713184
\(638\) 10796.8 0.669983
\(639\) −7126.96 −0.441218
\(640\) 1824.55 0.112690
\(641\) −161.995 −0.00998196 −0.00499098 0.999988i \(-0.501589\pi\)
−0.00499098 + 0.999988i \(0.501589\pi\)
\(642\) −2292.08 −0.140905
\(643\) 6290.91 0.385831 0.192915 0.981215i \(-0.438206\pi\)
0.192915 + 0.981215i \(0.438206\pi\)
\(644\) 187.621 0.0114803
\(645\) 15658.4 0.955891
\(646\) 0 0
\(647\) 28249.8 1.71656 0.858280 0.513181i \(-0.171533\pi\)
0.858280 + 0.513181i \(0.171533\pi\)
\(648\) 648.000 0.0392837
\(649\) −12015.4 −0.726724
\(650\) −10715.4 −0.646607
\(651\) 9828.99 0.591749
\(652\) 4610.14 0.276912
\(653\) 11423.5 0.684587 0.342293 0.939593i \(-0.388796\pi\)
0.342293 + 0.939593i \(0.388796\pi\)
\(654\) 797.145 0.0476618
\(655\) −5287.55 −0.315423
\(656\) −5524.14 −0.328782
\(657\) 2899.16 0.172157
\(658\) −2410.69 −0.142824
\(659\) 200.138 0.0118304 0.00591522 0.999983i \(-0.498117\pi\)
0.00591522 + 0.999983i \(0.498117\pi\)
\(660\) 11274.7 0.664949
\(661\) −2607.01 −0.153405 −0.0767026 0.997054i \(-0.524439\pi\)
−0.0767026 + 0.997054i \(0.524439\pi\)
\(662\) −13632.3 −0.800352
\(663\) 20494.9 1.20053
\(664\) 5473.28 0.319886
\(665\) 0 0
\(666\) 7579.17 0.440971
\(667\) −289.836 −0.0168253
\(668\) 5036.44 0.291715
\(669\) −4854.80 −0.280564
\(670\) −4557.45 −0.262790
\(671\) 34.1018 0.00196198
\(672\) −1272.41 −0.0730423
\(673\) 14561.2 0.834015 0.417007 0.908903i \(-0.363079\pi\)
0.417007 + 0.908903i \(0.363079\pi\)
\(674\) −20816.8 −1.18966
\(675\) −2111.01 −0.120374
\(676\) 9995.18 0.568683
\(677\) 12684.6 0.720100 0.360050 0.932933i \(-0.382760\pi\)
0.360050 + 0.932933i \(0.382760\pi\)
\(678\) 6827.64 0.386746
\(679\) 5505.74 0.311179
\(680\) 11368.6 0.641124
\(681\) 18196.3 1.02391
\(682\) 32586.4 1.82962
\(683\) 12054.5 0.675332 0.337666 0.941266i \(-0.390363\pi\)
0.337666 + 0.941266i \(0.390363\pi\)
\(684\) 0 0
\(685\) −24095.1 −1.34398
\(686\) −13528.0 −0.752916
\(687\) 5749.09 0.319274
\(688\) −5858.69 −0.324652
\(689\) 47179.5 2.60870
\(690\) −302.664 −0.0166989
\(691\) 3338.42 0.183791 0.0918953 0.995769i \(-0.470707\pi\)
0.0918953 + 0.995769i \(0.470707\pi\)
\(692\) −5096.40 −0.279965
\(693\) −7862.78 −0.430999
\(694\) −11168.1 −0.610856
\(695\) −38650.9 −2.10951
\(696\) 1965.62 0.107050
\(697\) −34420.2 −1.87053
\(698\) 11011.6 0.597130
\(699\) 12025.6 0.650716
\(700\) 4145.17 0.223818
\(701\) −23782.8 −1.28140 −0.640702 0.767790i \(-0.721356\pi\)
−0.640702 + 0.767790i \(0.721356\pi\)
\(702\) 3700.40 0.198949
\(703\) 0 0
\(704\) −4218.49 −0.225838
\(705\) 3888.86 0.207749
\(706\) −11564.9 −0.616504
\(707\) 4471.22 0.237847
\(708\) −2187.47 −0.116116
\(709\) 32185.1 1.70485 0.852424 0.522851i \(-0.175132\pi\)
0.852424 + 0.522851i \(0.175132\pi\)
\(710\) −22575.5 −1.19330
\(711\) 2865.34 0.151137
\(712\) 5763.24 0.303352
\(713\) −874.770 −0.0459473
\(714\) −7928.25 −0.415557
\(715\) 64383.9 3.36758
\(716\) 8137.99 0.424764
\(717\) −1590.88 −0.0828624
\(718\) −3807.28 −0.197892
\(719\) −38319.4 −1.98758 −0.993791 0.111266i \(-0.964509\pi\)
−0.993791 + 0.111266i \(0.964509\pi\)
\(720\) 2052.62 0.106245
\(721\) −19444.7 −1.00438
\(722\) 0 0
\(723\) −3813.68 −0.196172
\(724\) 4133.26 0.212170
\(725\) −6403.45 −0.328025
\(726\) −18081.8 −0.924351
\(727\) −36543.1 −1.86425 −0.932125 0.362138i \(-0.882047\pi\)
−0.932125 + 0.362138i \(0.882047\pi\)
\(728\) −7266.11 −0.369917
\(729\) 729.000 0.0370370
\(730\) 9183.46 0.465610
\(731\) −36504.8 −1.84703
\(732\) 6.20844 0.000313484 0
\(733\) −15689.3 −0.790584 −0.395292 0.918555i \(-0.629357\pi\)
−0.395292 + 0.918555i \(0.629357\pi\)
\(734\) −25496.1 −1.28212
\(735\) 7155.23 0.359081
\(736\) 113.244 0.00567149
\(737\) 10537.1 0.526648
\(738\) −6214.65 −0.309979
\(739\) −36445.7 −1.81418 −0.907088 0.420940i \(-0.861700\pi\)
−0.907088 + 0.420940i \(0.861700\pi\)
\(740\) 24008.0 1.19264
\(741\) 0 0
\(742\) −18251.0 −0.902984
\(743\) 1678.29 0.0828673 0.0414337 0.999141i \(-0.486807\pi\)
0.0414337 + 0.999141i \(0.486807\pi\)
\(744\) 5932.55 0.292336
\(745\) 37045.6 1.82180
\(746\) −1473.32 −0.0723084
\(747\) 6157.44 0.301591
\(748\) −26284.9 −1.28485
\(749\) 5063.33 0.247009
\(750\) 4003.86 0.194934
\(751\) 8641.67 0.419892 0.209946 0.977713i \(-0.432671\pi\)
0.209946 + 0.977713i \(0.432671\pi\)
\(752\) −1455.04 −0.0705582
\(753\) −1655.97 −0.0801418
\(754\) 11224.7 0.542145
\(755\) 8479.36 0.408736
\(756\) −1431.47 −0.0688649
\(757\) 3586.79 0.172212 0.0861058 0.996286i \(-0.472558\pi\)
0.0861058 + 0.996286i \(0.472558\pi\)
\(758\) 3087.13 0.147928
\(759\) 699.780 0.0334656
\(760\) 0 0
\(761\) −11615.4 −0.553297 −0.276649 0.960971i \(-0.589224\pi\)
−0.276649 + 0.960971i \(0.589224\pi\)
\(762\) 9059.85 0.430714
\(763\) −1760.93 −0.0835519
\(764\) −4541.86 −0.215077
\(765\) 12789.6 0.604457
\(766\) 13128.7 0.619269
\(767\) −12491.5 −0.588060
\(768\) −768.000 −0.0360844
\(769\) 6021.83 0.282383 0.141192 0.989982i \(-0.454907\pi\)
0.141192 + 0.989982i \(0.454907\pi\)
\(770\) −24906.3 −1.16567
\(771\) 15707.5 0.733712
\(772\) 4364.29 0.203464
\(773\) −1508.99 −0.0702128 −0.0351064 0.999384i \(-0.511177\pi\)
−0.0351064 + 0.999384i \(0.511177\pi\)
\(774\) −6591.03 −0.306085
\(775\) −19326.6 −0.895784
\(776\) 3323.14 0.153729
\(777\) −16742.8 −0.773029
\(778\) −6996.54 −0.322414
\(779\) 0 0
\(780\) 11721.5 0.538072
\(781\) 52196.1 2.39145
\(782\) 705.607 0.0322666
\(783\) 2211.32 0.100927
\(784\) −2677.17 −0.121956
\(785\) −830.383 −0.0377550
\(786\) 2225.67 0.101001
\(787\) 3255.84 0.147469 0.0737346 0.997278i \(-0.476508\pi\)
0.0737346 + 0.997278i \(0.476508\pi\)
\(788\) 16552.3 0.748289
\(789\) 5442.77 0.245587
\(790\) 9076.31 0.408760
\(791\) −15082.6 −0.677972
\(792\) −4745.80 −0.212922
\(793\) 35.4532 0.00158762
\(794\) 17221.2 0.769720
\(795\) 29441.9 1.31346
\(796\) −10936.9 −0.486997
\(797\) 31732.8 1.41033 0.705164 0.709044i \(-0.250873\pi\)
0.705164 + 0.709044i \(0.250873\pi\)
\(798\) 0 0
\(799\) −9066.16 −0.401424
\(800\) 2501.93 0.110571
\(801\) 6483.65 0.286003
\(802\) 3531.49 0.155488
\(803\) −21232.8 −0.933111
\(804\) 1918.35 0.0841478
\(805\) 668.601 0.0292734
\(806\) 33877.8 1.48051
\(807\) −3040.20 −0.132615
\(808\) 2698.73 0.117501
\(809\) 3853.96 0.167488 0.0837441 0.996487i \(-0.473312\pi\)
0.0837441 + 0.996487i \(0.473312\pi\)
\(810\) 2309.20 0.100169
\(811\) 31871.8 1.37999 0.689995 0.723814i \(-0.257613\pi\)
0.689995 + 0.723814i \(0.257613\pi\)
\(812\) −4342.16 −0.187660
\(813\) 5755.55 0.248285
\(814\) −55508.0 −2.39012
\(815\) 16428.6 0.706096
\(816\) −4785.31 −0.205293
\(817\) 0 0
\(818\) 26791.4 1.14516
\(819\) −8174.37 −0.348761
\(820\) −19685.7 −0.838359
\(821\) −39170.0 −1.66509 −0.832547 0.553954i \(-0.813118\pi\)
−0.832547 + 0.553954i \(0.813118\pi\)
\(822\) 10142.2 0.430355
\(823\) −18838.8 −0.797910 −0.398955 0.916971i \(-0.630627\pi\)
−0.398955 + 0.916971i \(0.630627\pi\)
\(824\) −11736.4 −0.496185
\(825\) 15460.5 0.652443
\(826\) 4832.22 0.203553
\(827\) 887.307 0.0373092 0.0186546 0.999826i \(-0.494062\pi\)
0.0186546 + 0.999826i \(0.494062\pi\)
\(828\) 127.399 0.00534713
\(829\) 32877.0 1.37740 0.688700 0.725046i \(-0.258182\pi\)
0.688700 + 0.725046i \(0.258182\pi\)
\(830\) 19504.4 0.815674
\(831\) −18850.3 −0.786897
\(832\) −4385.66 −0.182747
\(833\) −16681.1 −0.693838
\(834\) 16269.1 0.675484
\(835\) 17947.7 0.743840
\(836\) 0 0
\(837\) 6674.12 0.275617
\(838\) 18235.4 0.751709
\(839\) −41512.7 −1.70820 −0.854099 0.520110i \(-0.825891\pi\)
−0.854099 + 0.520110i \(0.825891\pi\)
\(840\) −4534.35 −0.186250
\(841\) −17681.3 −0.724968
\(842\) 16408.9 0.671601
\(843\) 24172.1 0.987581
\(844\) 12232.0 0.498867
\(845\) 35618.6 1.45008
\(846\) −1636.92 −0.0665229
\(847\) 39943.6 1.62040
\(848\) −11015.9 −0.446092
\(849\) 580.250 0.0234560
\(850\) 15589.2 0.629066
\(851\) 1490.09 0.0600231
\(852\) 9502.61 0.382106
\(853\) 1487.75 0.0597182 0.0298591 0.999554i \(-0.490494\pi\)
0.0298591 + 0.999554i \(0.490494\pi\)
\(854\) −13.7148 −0.000549543 0
\(855\) 0 0
\(856\) 3056.11 0.122028
\(857\) 20276.1 0.808188 0.404094 0.914718i \(-0.367587\pi\)
0.404094 + 0.914718i \(0.367587\pi\)
\(858\) −27100.8 −1.07833
\(859\) 7436.86 0.295393 0.147696 0.989033i \(-0.452814\pi\)
0.147696 + 0.989033i \(0.452814\pi\)
\(860\) −20877.9 −0.827826
\(861\) 13728.5 0.543398
\(862\) −2542.69 −0.100469
\(863\) 35570.4 1.40305 0.701524 0.712646i \(-0.252503\pi\)
0.701524 + 0.712646i \(0.252503\pi\)
\(864\) −864.000 −0.0340207
\(865\) −18161.4 −0.713880
\(866\) −7935.18 −0.311372
\(867\) −15077.7 −0.590617
\(868\) −13105.3 −0.512469
\(869\) −20985.0 −0.819182
\(870\) 7004.64 0.272965
\(871\) 10954.7 0.426160
\(872\) −1062.86 −0.0412764
\(873\) 3738.53 0.144937
\(874\) 0 0
\(875\) −8844.74 −0.341722
\(876\) −3865.55 −0.149092
\(877\) 3868.42 0.148948 0.0744740 0.997223i \(-0.476272\pi\)
0.0744740 + 0.997223i \(0.476272\pi\)
\(878\) 418.076 0.0160699
\(879\) 14206.4 0.545131
\(880\) −15032.9 −0.575862
\(881\) −20877.4 −0.798384 −0.399192 0.916867i \(-0.630709\pi\)
−0.399192 + 0.916867i \(0.630709\pi\)
\(882\) −3011.82 −0.114981
\(883\) −24206.8 −0.922565 −0.461283 0.887253i \(-0.652611\pi\)
−0.461283 + 0.887253i \(0.652611\pi\)
\(884\) −27326.5 −1.03969
\(885\) −7795.20 −0.296082
\(886\) 11468.1 0.434851
\(887\) −27117.5 −1.02651 −0.513256 0.858235i \(-0.671561\pi\)
−0.513256 + 0.858235i \(0.671561\pi\)
\(888\) −10105.6 −0.381892
\(889\) −20013.7 −0.755047
\(890\) 20537.8 0.773514
\(891\) −5339.02 −0.200745
\(892\) 6473.07 0.242976
\(893\) 0 0
\(894\) −15593.4 −0.583357
\(895\) 29000.4 1.08310
\(896\) 1696.55 0.0632565
\(897\) 727.511 0.0270801
\(898\) 19482.3 0.723977
\(899\) 20245.0 0.751068
\(900\) 2814.67 0.104247
\(901\) −68638.5 −2.53793
\(902\) 45514.6 1.68012
\(903\) 14559.9 0.536571
\(904\) −9103.52 −0.334932
\(905\) 14729.2 0.541010
\(906\) −3569.18 −0.130881
\(907\) −35594.9 −1.30310 −0.651548 0.758608i \(-0.725880\pi\)
−0.651548 + 0.758608i \(0.725880\pi\)
\(908\) −24261.7 −0.886733
\(909\) 3036.07 0.110781
\(910\) −25893.3 −0.943248
\(911\) 27909.5 1.01502 0.507510 0.861646i \(-0.330566\pi\)
0.507510 + 0.861646i \(0.330566\pi\)
\(912\) 0 0
\(913\) −45095.6 −1.63466
\(914\) −34467.6 −1.24736
\(915\) 22.1243 0.000799350 0
\(916\) −7665.45 −0.276500
\(917\) −4916.61 −0.177056
\(918\) −5383.48 −0.193553
\(919\) −48960.0 −1.75739 −0.878696 0.477383i \(-0.841586\pi\)
−0.878696 + 0.477383i \(0.841586\pi\)
\(920\) 403.552 0.0144617
\(921\) 86.1365 0.00308175
\(922\) 3330.47 0.118962
\(923\) 54264.5 1.93515
\(924\) 10483.7 0.373256
\(925\) 32921.1 1.17020
\(926\) −21388.1 −0.759023
\(927\) −13203.4 −0.467807
\(928\) −2620.83 −0.0927078
\(929\) −11971.7 −0.422799 −0.211399 0.977400i \(-0.567802\pi\)
−0.211399 + 0.977400i \(0.567802\pi\)
\(930\) 21141.1 0.745424
\(931\) 0 0
\(932\) −16034.2 −0.563537
\(933\) 3497.06 0.122710
\(934\) 26425.4 0.925765
\(935\) −93668.1 −3.27623
\(936\) −4933.86 −0.172295
\(937\) −50434.2 −1.75839 −0.879197 0.476459i \(-0.841920\pi\)
−0.879197 + 0.476459i \(0.841920\pi\)
\(938\) −4237.72 −0.147512
\(939\) −7538.26 −0.261983
\(940\) −5185.14 −0.179916
\(941\) 12594.3 0.436303 0.218151 0.975915i \(-0.429997\pi\)
0.218151 + 0.975915i \(0.429997\pi\)
\(942\) 349.529 0.0120895
\(943\) −1221.82 −0.0421930
\(944\) 2916.62 0.100559
\(945\) −5101.14 −0.175598
\(946\) 48271.1 1.65902
\(947\) 27632.6 0.948192 0.474096 0.880473i \(-0.342775\pi\)
0.474096 + 0.880473i \(0.342775\pi\)
\(948\) −3820.45 −0.130889
\(949\) −22074.2 −0.755067
\(950\) 0 0
\(951\) 5182.70 0.176720
\(952\) 10571.0 0.359883
\(953\) 32021.7 1.08844 0.544221 0.838942i \(-0.316825\pi\)
0.544221 + 0.838942i \(0.316825\pi\)
\(954\) −12392.8 −0.420580
\(955\) −16185.3 −0.548422
\(956\) 2121.17 0.0717610
\(957\) −16195.2 −0.547039
\(958\) 10819.1 0.364873
\(959\) −22404.8 −0.754418
\(960\) −2736.83 −0.0920112
\(961\) 31311.7 1.05105
\(962\) −57707.7 −1.93406
\(963\) 3438.12 0.115049
\(964\) 5084.90 0.169890
\(965\) 15552.5 0.518811
\(966\) −281.431 −0.00937360
\(967\) −12876.4 −0.428209 −0.214104 0.976811i \(-0.568683\pi\)
−0.214104 + 0.976811i \(0.568683\pi\)
\(968\) 24109.1 0.800511
\(969\) 0 0
\(970\) 11842.3 0.391992
\(971\) 2414.51 0.0797996 0.0398998 0.999204i \(-0.487296\pi\)
0.0398998 + 0.999204i \(0.487296\pi\)
\(972\) −972.000 −0.0320750
\(973\) −35939.4 −1.18413
\(974\) 28594.0 0.940670
\(975\) 16073.2 0.527952
\(976\) −8.27792 −0.000271485 0
\(977\) −14131.4 −0.462746 −0.231373 0.972865i \(-0.574322\pi\)
−0.231373 + 0.972865i \(0.574322\pi\)
\(978\) −6915.21 −0.226098
\(979\) −47484.7 −1.55017
\(980\) −9540.31 −0.310973
\(981\) −1195.72 −0.0389157
\(982\) 5604.85 0.182136
\(983\) −20268.2 −0.657634 −0.328817 0.944394i \(-0.606650\pi\)
−0.328817 + 0.944394i \(0.606650\pi\)
\(984\) 8286.21 0.268450
\(985\) 58985.5 1.90805
\(986\) −16330.0 −0.527439
\(987\) 3616.04 0.116616
\(988\) 0 0
\(989\) −1295.82 −0.0416629
\(990\) −16912.0 −0.542928
\(991\) 15550.2 0.498453 0.249226 0.968445i \(-0.419824\pi\)
0.249226 + 0.968445i \(0.419824\pi\)
\(992\) −7910.07 −0.253170
\(993\) 20448.4 0.653485
\(994\) −20991.8 −0.669837
\(995\) −38974.6 −1.24179
\(996\) −8209.92 −0.261186
\(997\) 12715.8 0.403925 0.201962 0.979393i \(-0.435268\pi\)
0.201962 + 0.979393i \(0.435268\pi\)
\(998\) 28356.5 0.899408
\(999\) −11368.7 −0.360051
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 2166.4.a.u.1.3 3
19.7 even 3 114.4.e.d.49.1 yes 6
19.11 even 3 114.4.e.d.7.1 6
19.18 odd 2 2166.4.a.t.1.3 3
57.11 odd 6 342.4.g.h.235.3 6
57.26 odd 6 342.4.g.h.163.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
114.4.e.d.7.1 6 19.11 even 3
114.4.e.d.49.1 yes 6 19.7 even 3
342.4.g.h.163.3 6 57.26 odd 6
342.4.g.h.235.3 6 57.11 odd 6
2166.4.a.t.1.3 3 19.18 odd 2
2166.4.a.u.1.3 3 1.1 even 1 trivial