Properties

Label 1849.4.a.i.1.49
Level $1849$
Weight $4$
Character 1849.1
Self dual yes
Analytic conductor $109.095$
Analytic rank $1$
Dimension $50$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1849 = 43^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1849.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(109.094531601\)
Analytic rank: \(1\)
Dimension: \(50\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.49
Character \(\chi\) \(=\) 1849.1

$q$-expansion

\(f(q)\) \(=\) \(q+5.20801 q^{2} +5.00842 q^{3} +19.1234 q^{4} -13.8519 q^{5} +26.0839 q^{6} -26.6225 q^{7} +57.9307 q^{8} -1.91570 q^{9} +O(q^{10})\) \(q+5.20801 q^{2} +5.00842 q^{3} +19.1234 q^{4} -13.8519 q^{5} +26.0839 q^{6} -26.6225 q^{7} +57.9307 q^{8} -1.91570 q^{9} -72.1409 q^{10} +47.0765 q^{11} +95.7780 q^{12} -60.3088 q^{13} -138.650 q^{14} -69.3762 q^{15} +148.717 q^{16} +69.2105 q^{17} -9.97699 q^{18} -9.96884 q^{19} -264.895 q^{20} -133.337 q^{21} +245.175 q^{22} -26.9731 q^{23} +290.142 q^{24} +66.8755 q^{25} -314.089 q^{26} -144.822 q^{27} -509.112 q^{28} -158.022 q^{29} -361.312 q^{30} -129.716 q^{31} +311.073 q^{32} +235.779 q^{33} +360.449 q^{34} +368.773 q^{35} -36.6347 q^{36} -59.9333 q^{37} -51.9178 q^{38} -302.052 q^{39} -802.451 q^{40} -415.611 q^{41} -694.419 q^{42} +900.263 q^{44} +26.5361 q^{45} -140.476 q^{46} -398.299 q^{47} +744.836 q^{48} +365.758 q^{49} +348.289 q^{50} +346.636 q^{51} -1153.31 q^{52} -280.790 q^{53} -754.235 q^{54} -652.100 q^{55} -1542.26 q^{56} -49.9282 q^{57} -822.981 q^{58} +143.280 q^{59} -1326.71 q^{60} +791.993 q^{61} -675.562 q^{62} +51.0008 q^{63} +430.337 q^{64} +835.392 q^{65} +1227.94 q^{66} -635.977 q^{67} +1323.54 q^{68} -135.093 q^{69} +1920.57 q^{70} +707.876 q^{71} -110.978 q^{72} -168.798 q^{73} -312.133 q^{74} +334.941 q^{75} -190.638 q^{76} -1253.30 q^{77} -1573.09 q^{78} -631.664 q^{79} -2060.01 q^{80} -673.606 q^{81} -2164.50 q^{82} +516.463 q^{83} -2549.85 q^{84} -958.698 q^{85} -791.441 q^{87} +2727.18 q^{88} +1272.00 q^{89} +138.200 q^{90} +1605.57 q^{91} -515.817 q^{92} -649.672 q^{93} -2074.34 q^{94} +138.088 q^{95} +1557.98 q^{96} -298.811 q^{97} +1904.87 q^{98} -90.1846 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q - 10q^{2} - 2q^{3} + 186q^{4} + 8q^{5} - 51q^{6} - 6q^{7} - 138q^{8} + 360q^{9} + O(q^{10}) \) \( 50q - 10q^{2} - 2q^{3} + 186q^{4} + 8q^{5} - 51q^{6} - 6q^{7} - 138q^{8} + 360q^{9} - 137q^{10} - 252q^{11} - 48q^{12} - 192q^{13} - 272q^{14} - 314q^{15} + 542q^{16} - 236q^{17} - 386q^{18} + 12q^{19} + 108q^{20} - 408q^{21} + 1235q^{22} - 630q^{23} - 613q^{24} + 1098q^{25} + 1493q^{26} + 10q^{27} - 242q^{28} + 208q^{29} - 48q^{30} - 932q^{31} - 1124q^{32} + 254q^{33} + 765q^{34} - 1452q^{35} + 747q^{36} - 90q^{37} - 1213q^{38} - 1610q^{39} - 1693q^{40} - 1354q^{41} - 16q^{42} - 2704q^{44} + 4508q^{45} + 233q^{46} - 3484q^{47} - 376q^{48} + 1324q^{49} - 408q^{50} + 4054q^{51} - 2176q^{52} - 726q^{53} - 6497q^{54} - 3288q^{55} - 7097q^{56} - 870q^{57} + 275q^{58} - 4370q^{59} - 3891q^{60} + 1172q^{61} - 1546q^{62} - 3686q^{63} + 606q^{64} + 2610q^{65} - 4697q^{66} - 344q^{67} - 3221q^{68} + 136q^{69} - 1310q^{70} + 162q^{71} - 5814q^{72} + 746q^{73} - 4332q^{74} + 236q^{75} + 1338q^{76} + 2024q^{77} - 2782q^{78} - 2656q^{79} - 5713q^{80} - 86q^{81} - 4168q^{82} - 3514q^{83} - 4269q^{84} - 7558q^{85} - 10278q^{87} + 11692q^{88} + 2640q^{89} - 8286q^{90} - 5946q^{91} - 4271q^{92} - 2q^{93} + 9062q^{94} - 12140q^{95} - 700q^{96} - 3864q^{97} - 2826q^{98} - 8174q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.20801 1.84131 0.920655 0.390377i \(-0.127655\pi\)
0.920655 + 0.390377i \(0.127655\pi\)
\(3\) 5.00842 0.963871 0.481936 0.876207i \(-0.339934\pi\)
0.481936 + 0.876207i \(0.339934\pi\)
\(4\) 19.1234 2.39042
\(5\) −13.8519 −1.23895 −0.619476 0.785015i \(-0.712655\pi\)
−0.619476 + 0.785015i \(0.712655\pi\)
\(6\) 26.0839 1.77479
\(7\) −26.6225 −1.43748 −0.718740 0.695279i \(-0.755281\pi\)
−0.718740 + 0.695279i \(0.755281\pi\)
\(8\) 57.9307 2.56020
\(9\) −1.91570 −0.0709519
\(10\) −72.1409 −2.28130
\(11\) 47.0765 1.29037 0.645187 0.764025i \(-0.276780\pi\)
0.645187 + 0.764025i \(0.276780\pi\)
\(12\) 95.7780 2.30406
\(13\) −60.3088 −1.28667 −0.643333 0.765587i \(-0.722449\pi\)
−0.643333 + 0.765587i \(0.722449\pi\)
\(14\) −138.650 −2.64685
\(15\) −69.3762 −1.19419
\(16\) 148.717 2.32370
\(17\) 69.2105 0.987413 0.493706 0.869629i \(-0.335642\pi\)
0.493706 + 0.869629i \(0.335642\pi\)
\(18\) −9.97699 −0.130644
\(19\) −9.96884 −0.120369 −0.0601845 0.998187i \(-0.519169\pi\)
−0.0601845 + 0.998187i \(0.519169\pi\)
\(20\) −264.895 −2.96162
\(21\) −133.337 −1.38555
\(22\) 245.175 2.37598
\(23\) −26.9731 −0.244534 −0.122267 0.992497i \(-0.539016\pi\)
−0.122267 + 0.992497i \(0.539016\pi\)
\(24\) 290.142 2.46770
\(25\) 66.8755 0.535004
\(26\) −314.089 −2.36915
\(27\) −144.822 −1.03226
\(28\) −509.112 −3.43619
\(29\) −158.022 −1.01186 −0.505930 0.862574i \(-0.668851\pi\)
−0.505930 + 0.862574i \(0.668851\pi\)
\(30\) −361.312 −2.19888
\(31\) −129.716 −0.751537 −0.375769 0.926713i \(-0.622621\pi\)
−0.375769 + 0.926713i \(0.622621\pi\)
\(32\) 311.073 1.71845
\(33\) 235.779 1.24375
\(34\) 360.449 1.81813
\(35\) 368.773 1.78097
\(36\) −36.6347 −0.169605
\(37\) −59.9333 −0.266296 −0.133148 0.991096i \(-0.542509\pi\)
−0.133148 + 0.991096i \(0.542509\pi\)
\(38\) −51.9178 −0.221636
\(39\) −302.052 −1.24018
\(40\) −802.451 −3.17197
\(41\) −415.611 −1.58311 −0.791554 0.611099i \(-0.790728\pi\)
−0.791554 + 0.611099i \(0.790728\pi\)
\(42\) −694.419 −2.55122
\(43\) 0 0
\(44\) 900.263 3.08454
\(45\) 26.5361 0.0879061
\(46\) −140.476 −0.450263
\(47\) −398.299 −1.23612 −0.618062 0.786129i \(-0.712082\pi\)
−0.618062 + 0.786129i \(0.712082\pi\)
\(48\) 744.836 2.23975
\(49\) 365.758 1.06635
\(50\) 348.289 0.985109
\(51\) 346.636 0.951739
\(52\) −1153.31 −3.07567
\(53\) −280.790 −0.727725 −0.363863 0.931453i \(-0.618542\pi\)
−0.363863 + 0.931453i \(0.618542\pi\)
\(54\) −754.235 −1.90071
\(55\) −652.100 −1.59871
\(56\) −1542.26 −3.68024
\(57\) −49.9282 −0.116020
\(58\) −822.981 −1.86315
\(59\) 143.280 0.316159 0.158080 0.987426i \(-0.449470\pi\)
0.158080 + 0.987426i \(0.449470\pi\)
\(60\) −1326.71 −2.85462
\(61\) 791.993 1.66237 0.831183 0.555999i \(-0.187664\pi\)
0.831183 + 0.555999i \(0.187664\pi\)
\(62\) −675.562 −1.38381
\(63\) 51.0008 0.101992
\(64\) 430.337 0.840502
\(65\) 835.392 1.59412
\(66\) 1227.94 2.29014
\(67\) −635.977 −1.15966 −0.579828 0.814739i \(-0.696880\pi\)
−0.579828 + 0.814739i \(0.696880\pi\)
\(68\) 1323.54 2.36033
\(69\) −135.093 −0.235699
\(70\) 1920.57 3.27932
\(71\) 707.876 1.18323 0.591615 0.806220i \(-0.298490\pi\)
0.591615 + 0.806220i \(0.298490\pi\)
\(72\) −110.978 −0.181651
\(73\) −168.798 −0.270634 −0.135317 0.990802i \(-0.543205\pi\)
−0.135317 + 0.990802i \(0.543205\pi\)
\(74\) −312.133 −0.490334
\(75\) 334.941 0.515675
\(76\) −190.638 −0.287733
\(77\) −1253.30 −1.85489
\(78\) −1573.09 −2.28356
\(79\) −631.664 −0.899591 −0.449796 0.893131i \(-0.648503\pi\)
−0.449796 + 0.893131i \(0.648503\pi\)
\(80\) −2060.01 −2.87895
\(81\) −673.606 −0.924014
\(82\) −2164.50 −2.91499
\(83\) 516.463 0.683002 0.341501 0.939881i \(-0.389065\pi\)
0.341501 + 0.939881i \(0.389065\pi\)
\(84\) −2549.85 −3.31204
\(85\) −958.698 −1.22336
\(86\) 0 0
\(87\) −791.441 −0.975303
\(88\) 2727.18 3.30361
\(89\) 1272.00 1.51496 0.757481 0.652857i \(-0.226430\pi\)
0.757481 + 0.652857i \(0.226430\pi\)
\(90\) 138.200 0.161862
\(91\) 1605.57 1.84956
\(92\) −515.817 −0.584540
\(93\) −649.672 −0.724385
\(94\) −2074.34 −2.27609
\(95\) 138.088 0.149131
\(96\) 1557.98 1.65637
\(97\) −298.811 −0.312780 −0.156390 0.987695i \(-0.549986\pi\)
−0.156390 + 0.987695i \(0.549986\pi\)
\(98\) 1904.87 1.96348
\(99\) −90.1846 −0.0915545
\(100\) 1278.89 1.27889
\(101\) −842.187 −0.829711 −0.414855 0.909887i \(-0.636168\pi\)
−0.414855 + 0.909887i \(0.636168\pi\)
\(102\) 1805.28 1.75245
\(103\) 330.701 0.316359 0.158179 0.987410i \(-0.449438\pi\)
0.158179 + 0.987410i \(0.449438\pi\)
\(104\) −3493.73 −3.29412
\(105\) 1846.97 1.71663
\(106\) −1462.36 −1.33997
\(107\) −691.923 −0.625147 −0.312573 0.949894i \(-0.601191\pi\)
−0.312573 + 0.949894i \(0.601191\pi\)
\(108\) −2769.49 −2.46754
\(109\) −1114.65 −0.979483 −0.489742 0.871868i \(-0.662909\pi\)
−0.489742 + 0.871868i \(0.662909\pi\)
\(110\) −3396.15 −2.94373
\(111\) −300.171 −0.256675
\(112\) −3959.21 −3.34027
\(113\) 1732.15 1.44201 0.721005 0.692929i \(-0.243680\pi\)
0.721005 + 0.692929i \(0.243680\pi\)
\(114\) −260.027 −0.213629
\(115\) 373.629 0.302966
\(116\) −3021.92 −2.41877
\(117\) 115.534 0.0912913
\(118\) 746.201 0.582148
\(119\) −1842.56 −1.41939
\(120\) −4019.02 −3.05737
\(121\) 885.201 0.665064
\(122\) 4124.71 3.06093
\(123\) −2081.55 −1.52591
\(124\) −2480.61 −1.79649
\(125\) 805.135 0.576108
\(126\) 265.613 0.187799
\(127\) 2426.06 1.69510 0.847550 0.530715i \(-0.178077\pi\)
0.847550 + 0.530715i \(0.178077\pi\)
\(128\) −247.383 −0.170826
\(129\) 0 0
\(130\) 4350.73 2.93527
\(131\) 260.318 0.173619 0.0868094 0.996225i \(-0.472333\pi\)
0.0868094 + 0.996225i \(0.472333\pi\)
\(132\) 4508.90 2.97310
\(133\) 265.396 0.173028
\(134\) −3312.18 −2.13529
\(135\) 2006.06 1.27892
\(136\) 4009.42 2.52797
\(137\) 209.330 0.130542 0.0652711 0.997868i \(-0.479209\pi\)
0.0652711 + 0.997868i \(0.479209\pi\)
\(138\) −703.565 −0.433996
\(139\) 253.533 0.154708 0.0773540 0.997004i \(-0.475353\pi\)
0.0773540 + 0.997004i \(0.475353\pi\)
\(140\) 7052.18 4.25727
\(141\) −1994.85 −1.19146
\(142\) 3686.62 2.17869
\(143\) −2839.13 −1.66028
\(144\) −284.897 −0.164871
\(145\) 2188.91 1.25365
\(146\) −879.100 −0.498321
\(147\) 1831.87 1.02782
\(148\) −1146.13 −0.636561
\(149\) 2506.92 1.37836 0.689178 0.724592i \(-0.257972\pi\)
0.689178 + 0.724592i \(0.257972\pi\)
\(150\) 1744.38 0.949518
\(151\) −1804.46 −0.972482 −0.486241 0.873825i \(-0.661632\pi\)
−0.486241 + 0.873825i \(0.661632\pi\)
\(152\) −577.502 −0.308168
\(153\) −132.587 −0.0700588
\(154\) −6527.18 −3.41542
\(155\) 1796.81 0.931120
\(156\) −5776.25 −2.96455
\(157\) −676.565 −0.343922 −0.171961 0.985104i \(-0.555010\pi\)
−0.171961 + 0.985104i \(0.555010\pi\)
\(158\) −3289.71 −1.65643
\(159\) −1406.31 −0.701433
\(160\) −4308.95 −2.12908
\(161\) 718.092 0.351513
\(162\) −3508.15 −1.70140
\(163\) 509.421 0.244791 0.122396 0.992481i \(-0.460942\pi\)
0.122396 + 0.992481i \(0.460942\pi\)
\(164\) −7947.88 −3.78430
\(165\) −3265.99 −1.54095
\(166\) 2689.74 1.25762
\(167\) −1635.97 −0.758057 −0.379028 0.925385i \(-0.623742\pi\)
−0.379028 + 0.925385i \(0.623742\pi\)
\(168\) −7724.29 −3.54727
\(169\) 1440.15 0.655507
\(170\) −4992.91 −2.25258
\(171\) 19.0973 0.00854040
\(172\) 0 0
\(173\) −336.002 −0.147663 −0.0738317 0.997271i \(-0.523523\pi\)
−0.0738317 + 0.997271i \(0.523523\pi\)
\(174\) −4121.83 −1.79584
\(175\) −1780.39 −0.769058
\(176\) 7001.07 2.99844
\(177\) 717.604 0.304737
\(178\) 6624.59 2.78952
\(179\) 885.817 0.369883 0.184941 0.982750i \(-0.440790\pi\)
0.184941 + 0.982750i \(0.440790\pi\)
\(180\) 507.461 0.210133
\(181\) −3866.02 −1.58762 −0.793808 0.608168i \(-0.791905\pi\)
−0.793808 + 0.608168i \(0.791905\pi\)
\(182\) 8361.83 3.40561
\(183\) 3966.64 1.60231
\(184\) −1562.57 −0.626056
\(185\) 830.190 0.329929
\(186\) −3383.50 −1.33382
\(187\) 3258.19 1.27413
\(188\) −7616.82 −2.95486
\(189\) 3855.53 1.48385
\(190\) 719.162 0.274597
\(191\) −3601.46 −1.36436 −0.682180 0.731184i \(-0.738968\pi\)
−0.682180 + 0.731184i \(0.738968\pi\)
\(192\) 2155.31 0.810136
\(193\) −907.399 −0.338425 −0.169213 0.985580i \(-0.554122\pi\)
−0.169213 + 0.985580i \(0.554122\pi\)
\(194\) −1556.21 −0.575926
\(195\) 4184.00 1.53652
\(196\) 6994.52 2.54902
\(197\) 3133.94 1.13342 0.566711 0.823917i \(-0.308216\pi\)
0.566711 + 0.823917i \(0.308216\pi\)
\(198\) −469.682 −0.168580
\(199\) −702.456 −0.250230 −0.125115 0.992142i \(-0.539930\pi\)
−0.125115 + 0.992142i \(0.539930\pi\)
\(200\) 3874.15 1.36972
\(201\) −3185.24 −1.11776
\(202\) −4386.12 −1.52775
\(203\) 4206.94 1.45453
\(204\) 6628.85 2.27506
\(205\) 5757.00 1.96140
\(206\) 1722.30 0.582515
\(207\) 51.6724 0.0173502
\(208\) −8968.93 −2.98982
\(209\) −469.299 −0.155321
\(210\) 9619.04 3.16084
\(211\) 2634.32 0.859497 0.429749 0.902949i \(-0.358602\pi\)
0.429749 + 0.902949i \(0.358602\pi\)
\(212\) −5369.65 −1.73957
\(213\) 3545.34 1.14048
\(214\) −3603.54 −1.15109
\(215\) 0 0
\(216\) −8389.65 −2.64279
\(217\) 3453.36 1.08032
\(218\) −5805.09 −1.80353
\(219\) −845.410 −0.260856
\(220\) −12470.4 −3.82160
\(221\) −4174.00 −1.27047
\(222\) −1563.29 −0.472619
\(223\) −5852.83 −1.75755 −0.878776 0.477234i \(-0.841639\pi\)
−0.878776 + 0.477234i \(0.841639\pi\)
\(224\) −8281.54 −2.47024
\(225\) −128.114 −0.0379596
\(226\) 9021.07 2.65519
\(227\) 2690.65 0.786718 0.393359 0.919385i \(-0.371313\pi\)
0.393359 + 0.919385i \(0.371313\pi\)
\(228\) −954.796 −0.277337
\(229\) 909.642 0.262493 0.131246 0.991350i \(-0.458102\pi\)
0.131246 + 0.991350i \(0.458102\pi\)
\(230\) 1945.87 0.557855
\(231\) −6277.03 −1.78787
\(232\) −9154.33 −2.59057
\(233\) 2711.93 0.762509 0.381255 0.924470i \(-0.375492\pi\)
0.381255 + 0.924470i \(0.375492\pi\)
\(234\) 601.700 0.168096
\(235\) 5517.20 1.53150
\(236\) 2739.99 0.755755
\(237\) −3163.64 −0.867090
\(238\) −9596.06 −2.61353
\(239\) 2199.65 0.595329 0.297665 0.954671i \(-0.403792\pi\)
0.297665 + 0.954671i \(0.403792\pi\)
\(240\) −10317.4 −2.77494
\(241\) −2700.40 −0.721776 −0.360888 0.932609i \(-0.617526\pi\)
−0.360888 + 0.932609i \(0.617526\pi\)
\(242\) 4610.14 1.22459
\(243\) 536.491 0.141629
\(244\) 15145.6 3.97376
\(245\) −5066.44 −1.32116
\(246\) −10840.8 −2.80968
\(247\) 601.209 0.154874
\(248\) −7514.53 −1.92409
\(249\) 2586.66 0.658326
\(250\) 4193.15 1.06079
\(251\) −5537.81 −1.39260 −0.696302 0.717749i \(-0.745173\pi\)
−0.696302 + 0.717749i \(0.745173\pi\)
\(252\) 975.307 0.243804
\(253\) −1269.80 −0.315540
\(254\) 12634.9 3.12121
\(255\) −4801.57 −1.17916
\(256\) −4731.07 −1.15505
\(257\) 468.256 0.113654 0.0568268 0.998384i \(-0.481902\pi\)
0.0568268 + 0.998384i \(0.481902\pi\)
\(258\) 0 0
\(259\) 1595.57 0.382796
\(260\) 15975.5 3.81062
\(261\) 302.723 0.0717934
\(262\) 1355.74 0.319686
\(263\) 6435.62 1.50889 0.754443 0.656365i \(-0.227907\pi\)
0.754443 + 0.656365i \(0.227907\pi\)
\(264\) 13658.9 3.18426
\(265\) 3889.47 0.901617
\(266\) 1382.18 0.318598
\(267\) 6370.71 1.46023
\(268\) −12162.0 −2.77207
\(269\) −882.896 −0.200116 −0.100058 0.994982i \(-0.531903\pi\)
−0.100058 + 0.994982i \(0.531903\pi\)
\(270\) 10447.6 2.35489
\(271\) 6424.80 1.44014 0.720071 0.693900i \(-0.244109\pi\)
0.720071 + 0.693900i \(0.244109\pi\)
\(272\) 10292.8 2.29445
\(273\) 8041.38 1.78273
\(274\) 1090.19 0.240369
\(275\) 3148.27 0.690356
\(276\) −2583.43 −0.563421
\(277\) −1236.99 −0.268315 −0.134158 0.990960i \(-0.542833\pi\)
−0.134158 + 0.990960i \(0.542833\pi\)
\(278\) 1320.41 0.284866
\(279\) 248.497 0.0533230
\(280\) 21363.3 4.55964
\(281\) 1461.25 0.310217 0.155109 0.987897i \(-0.450427\pi\)
0.155109 + 0.987897i \(0.450427\pi\)
\(282\) −10389.2 −2.19386
\(283\) 1698.07 0.356678 0.178339 0.983969i \(-0.442928\pi\)
0.178339 + 0.983969i \(0.442928\pi\)
\(284\) 13537.0 2.82842
\(285\) 691.601 0.143743
\(286\) −14786.2 −3.05709
\(287\) 11064.6 2.27569
\(288\) −595.923 −0.121927
\(289\) −122.902 −0.0250158
\(290\) 11399.9 2.30835
\(291\) −1496.57 −0.301480
\(292\) −3227.98 −0.646929
\(293\) 3559.87 0.709795 0.354897 0.934905i \(-0.384516\pi\)
0.354897 + 0.934905i \(0.384516\pi\)
\(294\) 9540.39 1.89254
\(295\) −1984.70 −0.391707
\(296\) −3471.98 −0.681772
\(297\) −6817.72 −1.33200
\(298\) 13056.1 2.53798
\(299\) 1626.72 0.314634
\(300\) 6405.21 1.23268
\(301\) 0 0
\(302\) −9397.64 −1.79064
\(303\) −4218.03 −0.799734
\(304\) −1482.53 −0.279701
\(305\) −10970.6 −2.05959
\(306\) −690.513 −0.129000
\(307\) −5590.48 −1.03930 −0.519651 0.854379i \(-0.673938\pi\)
−0.519651 + 0.854379i \(0.673938\pi\)
\(308\) −23967.2 −4.43396
\(309\) 1656.29 0.304929
\(310\) 9357.83 1.71448
\(311\) 2708.95 0.493924 0.246962 0.969025i \(-0.420568\pi\)
0.246962 + 0.969025i \(0.420568\pi\)
\(312\) −17498.1 −3.17511
\(313\) −6730.92 −1.21551 −0.607754 0.794125i \(-0.707929\pi\)
−0.607754 + 0.794125i \(0.707929\pi\)
\(314\) −3523.56 −0.633267
\(315\) −706.458 −0.126363
\(316\) −12079.5 −2.15040
\(317\) 5984.74 1.06037 0.530184 0.847883i \(-0.322123\pi\)
0.530184 + 0.847883i \(0.322123\pi\)
\(318\) −7324.10 −1.29156
\(319\) −7439.13 −1.30568
\(320\) −5960.99 −1.04134
\(321\) −3465.44 −0.602561
\(322\) 3739.83 0.647244
\(323\) −689.949 −0.118854
\(324\) −12881.6 −2.20878
\(325\) −4033.18 −0.688372
\(326\) 2653.07 0.450737
\(327\) −5582.62 −0.944096
\(328\) −24076.6 −4.05308
\(329\) 10603.7 1.77690
\(330\) −17009.3 −2.83737
\(331\) 2114.28 0.351092 0.175546 0.984471i \(-0.443831\pi\)
0.175546 + 0.984471i \(0.443831\pi\)
\(332\) 9876.51 1.63266
\(333\) 114.814 0.0188942
\(334\) −8520.17 −1.39582
\(335\) 8809.51 1.43676
\(336\) −19829.4 −3.21959
\(337\) 10476.9 1.69351 0.846756 0.531982i \(-0.178552\pi\)
0.846756 + 0.531982i \(0.178552\pi\)
\(338\) 7500.32 1.20699
\(339\) 8675.35 1.38991
\(340\) −18333.6 −2.92434
\(341\) −6106.58 −0.969764
\(342\) 99.4591 0.0157255
\(343\) −605.864 −0.0953749
\(344\) 0 0
\(345\) 1871.29 0.292021
\(346\) −1749.90 −0.271894
\(347\) 11253.4 1.74096 0.870482 0.492199i \(-0.163807\pi\)
0.870482 + 0.492199i \(0.163807\pi\)
\(348\) −15135.0 −2.33139
\(349\) −1170.22 −0.179486 −0.0897428 0.995965i \(-0.528604\pi\)
−0.0897428 + 0.995965i \(0.528604\pi\)
\(350\) −9272.31 −1.41607
\(351\) 8734.04 1.32817
\(352\) 14644.2 2.21744
\(353\) −804.464 −0.121295 −0.0606477 0.998159i \(-0.519317\pi\)
−0.0606477 + 0.998159i \(0.519317\pi\)
\(354\) 3737.29 0.561115
\(355\) −9805.43 −1.46597
\(356\) 24324.9 3.62140
\(357\) −9228.31 −1.36811
\(358\) 4613.34 0.681069
\(359\) 9746.71 1.43290 0.716451 0.697638i \(-0.245765\pi\)
0.716451 + 0.697638i \(0.245765\pi\)
\(360\) 1537.26 0.225057
\(361\) −6759.62 −0.985511
\(362\) −20134.3 −2.92329
\(363\) 4433.46 0.641037
\(364\) 30703.9 4.42122
\(365\) 2338.17 0.335303
\(366\) 20658.3 2.95034
\(367\) −3663.53 −0.521075 −0.260538 0.965464i \(-0.583900\pi\)
−0.260538 + 0.965464i \(0.583900\pi\)
\(368\) −4011.36 −0.568224
\(369\) 796.186 0.112325
\(370\) 4323.64 0.607501
\(371\) 7475.32 1.04609
\(372\) −12423.9 −1.73159
\(373\) −13468.9 −1.86969 −0.934846 0.355053i \(-0.884463\pi\)
−0.934846 + 0.355053i \(0.884463\pi\)
\(374\) 16968.7 2.34607
\(375\) 4032.46 0.555294
\(376\) −23073.7 −3.16472
\(377\) 9530.12 1.30193
\(378\) 20079.6 2.73223
\(379\) 2326.69 0.315341 0.157670 0.987492i \(-0.449602\pi\)
0.157670 + 0.987492i \(0.449602\pi\)
\(380\) 2640.70 0.356487
\(381\) 12150.7 1.63386
\(382\) −18756.5 −2.51221
\(383\) 1329.44 0.177366 0.0886831 0.996060i \(-0.471734\pi\)
0.0886831 + 0.996060i \(0.471734\pi\)
\(384\) −1239.00 −0.164655
\(385\) 17360.5 2.29812
\(386\) −4725.75 −0.623145
\(387\) 0 0
\(388\) −5714.28 −0.747677
\(389\) 10163.9 1.32475 0.662375 0.749172i \(-0.269549\pi\)
0.662375 + 0.749172i \(0.269549\pi\)
\(390\) 21790.3 2.82922
\(391\) −1866.82 −0.241456
\(392\) 21188.6 2.73007
\(393\) 1303.78 0.167346
\(394\) 16321.6 2.08698
\(395\) 8749.75 1.11455
\(396\) −1724.63 −0.218854
\(397\) −13306.5 −1.68221 −0.841103 0.540875i \(-0.818093\pi\)
−0.841103 + 0.540875i \(0.818093\pi\)
\(398\) −3658.40 −0.460751
\(399\) 1329.21 0.166777
\(400\) 9945.51 1.24319
\(401\) 15275.3 1.90228 0.951140 0.308759i \(-0.0999137\pi\)
0.951140 + 0.308759i \(0.0999137\pi\)
\(402\) −16588.8 −2.05814
\(403\) 7823.01 0.966977
\(404\) −16105.5 −1.98336
\(405\) 9330.74 1.14481
\(406\) 21909.8 2.67824
\(407\) −2821.45 −0.343622
\(408\) 20080.8 2.43664
\(409\) −16043.3 −1.93958 −0.969792 0.243931i \(-0.921563\pi\)
−0.969792 + 0.243931i \(0.921563\pi\)
\(410\) 29982.5 3.61154
\(411\) 1048.41 0.125826
\(412\) 6324.13 0.756232
\(413\) −3814.46 −0.454473
\(414\) 269.111 0.0319470
\(415\) −7154.00 −0.846207
\(416\) −18760.4 −2.21107
\(417\) 1269.80 0.149119
\(418\) −2444.11 −0.285994
\(419\) −8887.02 −1.03618 −0.518090 0.855326i \(-0.673357\pi\)
−0.518090 + 0.855326i \(0.673357\pi\)
\(420\) 35320.3 4.10346
\(421\) −600.862 −0.0695587 −0.0347794 0.999395i \(-0.511073\pi\)
−0.0347794 + 0.999395i \(0.511073\pi\)
\(422\) 13719.6 1.58260
\(423\) 763.021 0.0877053
\(424\) −16266.3 −1.86312
\(425\) 4628.49 0.528270
\(426\) 18464.2 2.09998
\(427\) −21084.8 −2.38962
\(428\) −13231.9 −1.49436
\(429\) −14219.6 −1.60030
\(430\) 0 0
\(431\) −16834.7 −1.88143 −0.940717 0.339193i \(-0.889846\pi\)
−0.940717 + 0.339193i \(0.889846\pi\)
\(432\) −21537.5 −2.39866
\(433\) 1169.19 0.129764 0.0648820 0.997893i \(-0.479333\pi\)
0.0648820 + 0.997893i \(0.479333\pi\)
\(434\) 17985.1 1.98920
\(435\) 10963.0 1.20836
\(436\) −21315.8 −2.34138
\(437\) 268.891 0.0294343
\(438\) −4402.91 −0.480317
\(439\) 404.634 0.0439912 0.0219956 0.999758i \(-0.492998\pi\)
0.0219956 + 0.999758i \(0.492998\pi\)
\(440\) −37776.6 −4.09302
\(441\) −700.682 −0.0756595
\(442\) −21738.3 −2.33933
\(443\) 8522.87 0.914071 0.457036 0.889448i \(-0.348911\pi\)
0.457036 + 0.889448i \(0.348911\pi\)
\(444\) −5740.29 −0.613563
\(445\) −17619.6 −1.87697
\(446\) −30481.6 −3.23620
\(447\) 12555.7 1.32856
\(448\) −11456.6 −1.20820
\(449\) −2477.35 −0.260386 −0.130193 0.991489i \(-0.541560\pi\)
−0.130193 + 0.991489i \(0.541560\pi\)
\(450\) −667.217 −0.0698954
\(451\) −19565.5 −2.04280
\(452\) 33124.6 3.44702
\(453\) −9037.49 −0.937347
\(454\) 14013.0 1.44859
\(455\) −22240.2 −2.29151
\(456\) −2892.37 −0.297035
\(457\) −4605.88 −0.471453 −0.235727 0.971819i \(-0.575747\pi\)
−0.235727 + 0.971819i \(0.575747\pi\)
\(458\) 4737.42 0.483330
\(459\) −10023.2 −1.01927
\(460\) 7145.06 0.724218
\(461\) −11285.7 −1.14019 −0.570093 0.821580i \(-0.693093\pi\)
−0.570093 + 0.821580i \(0.693093\pi\)
\(462\) −32690.9 −3.29203
\(463\) −508.870 −0.0510782 −0.0255391 0.999674i \(-0.508130\pi\)
−0.0255391 + 0.999674i \(0.508130\pi\)
\(464\) −23500.5 −2.35126
\(465\) 8999.20 0.897480
\(466\) 14123.8 1.40402
\(467\) 568.788 0.0563606 0.0281803 0.999603i \(-0.491029\pi\)
0.0281803 + 0.999603i \(0.491029\pi\)
\(468\) 2209.39 0.218225
\(469\) 16931.3 1.66698
\(470\) 28733.6 2.81997
\(471\) −3388.52 −0.331497
\(472\) 8300.29 0.809431
\(473\) 0 0
\(474\) −16476.3 −1.59658
\(475\) −666.672 −0.0643979
\(476\) −35235.9 −3.39293
\(477\) 537.909 0.0516335
\(478\) 11455.8 1.09619
\(479\) −3278.52 −0.312734 −0.156367 0.987699i \(-0.549978\pi\)
−0.156367 + 0.987699i \(0.549978\pi\)
\(480\) −21581.1 −2.05216
\(481\) 3614.50 0.342634
\(482\) −14063.7 −1.32901
\(483\) 3596.51 0.338813
\(484\) 16928.0 1.58979
\(485\) 4139.11 0.387520
\(486\) 2794.05 0.260783
\(487\) 3439.30 0.320020 0.160010 0.987115i \(-0.448847\pi\)
0.160010 + 0.987115i \(0.448847\pi\)
\(488\) 45880.7 4.25599
\(489\) 2551.40 0.235947
\(490\) −26386.1 −2.43266
\(491\) −3116.14 −0.286414 −0.143207 0.989693i \(-0.545741\pi\)
−0.143207 + 0.989693i \(0.545741\pi\)
\(492\) −39806.3 −3.64758
\(493\) −10936.8 −0.999124
\(494\) 3131.10 0.285172
\(495\) 1249.23 0.113432
\(496\) −19290.9 −1.74635
\(497\) −18845.4 −1.70087
\(498\) 13471.4 1.21218
\(499\) −16962.6 −1.52175 −0.760874 0.648899i \(-0.775230\pi\)
−0.760874 + 0.648899i \(0.775230\pi\)
\(500\) 15396.9 1.37714
\(501\) −8193.65 −0.730669
\(502\) −28841.0 −2.56422
\(503\) −17725.1 −1.57122 −0.785610 0.618722i \(-0.787651\pi\)
−0.785610 + 0.618722i \(0.787651\pi\)
\(504\) 2954.51 0.261120
\(505\) 11665.9 1.02797
\(506\) −6613.14 −0.581008
\(507\) 7212.88 0.631825
\(508\) 46394.4 4.05201
\(509\) 3044.24 0.265095 0.132548 0.991177i \(-0.457684\pi\)
0.132548 + 0.991177i \(0.457684\pi\)
\(510\) −25006.6 −2.17120
\(511\) 4493.82 0.389031
\(512\) −22660.4 −1.95597
\(513\) 1443.71 0.124252
\(514\) 2438.68 0.209272
\(515\) −4580.85 −0.391954
\(516\) 0 0
\(517\) −18750.5 −1.59506
\(518\) 8309.76 0.704846
\(519\) −1682.84 −0.142329
\(520\) 48394.9 4.08126
\(521\) −12593.9 −1.05902 −0.529509 0.848304i \(-0.677624\pi\)
−0.529509 + 0.848304i \(0.677624\pi\)
\(522\) 1576.59 0.132194
\(523\) −15100.1 −1.26249 −0.631243 0.775585i \(-0.717455\pi\)
−0.631243 + 0.775585i \(0.717455\pi\)
\(524\) 4978.16 0.415023
\(525\) −8916.97 −0.741273
\(526\) 33516.8 2.77833
\(527\) −8977.71 −0.742078
\(528\) 35064.3 2.89011
\(529\) −11439.5 −0.940203
\(530\) 20256.4 1.66016
\(531\) −274.481 −0.0224321
\(532\) 5075.26 0.413610
\(533\) 25065.0 2.03693
\(534\) 33178.7 2.68873
\(535\) 9584.45 0.774527
\(536\) −36842.6 −2.96895
\(537\) 4436.54 0.356520
\(538\) −4598.13 −0.368475
\(539\) 17218.6 1.37599
\(540\) 38362.7 3.05716
\(541\) −11318.5 −0.899485 −0.449743 0.893158i \(-0.648484\pi\)
−0.449743 + 0.893158i \(0.648484\pi\)
\(542\) 33460.4 2.65175
\(543\) −19362.6 −1.53026
\(544\) 21529.5 1.69682
\(545\) 15440.0 1.21353
\(546\) 41879.6 3.28257
\(547\) −4299.81 −0.336100 −0.168050 0.985778i \(-0.553747\pi\)
−0.168050 + 0.985778i \(0.553747\pi\)
\(548\) 4003.10 0.312051
\(549\) −1517.22 −0.117948
\(550\) 16396.2 1.27116
\(551\) 1575.30 0.121797
\(552\) −7826.02 −0.603438
\(553\) 16816.5 1.29314
\(554\) −6442.24 −0.494052
\(555\) 4157.94 0.318009
\(556\) 4848.42 0.369818
\(557\) −8356.80 −0.635707 −0.317854 0.948140i \(-0.602962\pi\)
−0.317854 + 0.948140i \(0.602962\pi\)
\(558\) 1294.17 0.0981842
\(559\) 0 0
\(560\) 54842.7 4.13844
\(561\) 16318.4 1.22810
\(562\) 7610.22 0.571206
\(563\) −17758.8 −1.32938 −0.664692 0.747118i \(-0.731437\pi\)
−0.664692 + 0.747118i \(0.731437\pi\)
\(564\) −38148.2 −2.84810
\(565\) −23993.6 −1.78658
\(566\) 8843.57 0.656754
\(567\) 17933.1 1.32825
\(568\) 41007.7 3.02931
\(569\) −6954.03 −0.512352 −0.256176 0.966630i \(-0.582463\pi\)
−0.256176 + 0.966630i \(0.582463\pi\)
\(570\) 3601.87 0.264676
\(571\) −20289.4 −1.48701 −0.743505 0.668730i \(-0.766838\pi\)
−0.743505 + 0.668730i \(0.766838\pi\)
\(572\) −54293.8 −3.96877
\(573\) −18037.6 −1.31507
\(574\) 57624.5 4.19025
\(575\) −1803.84 −0.130827
\(576\) −824.397 −0.0596352
\(577\) 5613.49 0.405013 0.202507 0.979281i \(-0.435091\pi\)
0.202507 + 0.979281i \(0.435091\pi\)
\(578\) −640.078 −0.0460618
\(579\) −4544.64 −0.326198
\(580\) 41859.3 2.99675
\(581\) −13749.5 −0.981801
\(582\) −7794.17 −0.555118
\(583\) −13218.6 −0.939037
\(584\) −9778.57 −0.692877
\(585\) −1600.36 −0.113106
\(586\) 18539.8 1.30695
\(587\) 8010.42 0.563246 0.281623 0.959525i \(-0.409127\pi\)
0.281623 + 0.959525i \(0.409127\pi\)
\(588\) 35031.5 2.45693
\(589\) 1293.12 0.0904617
\(590\) −10336.3 −0.721253
\(591\) 15696.1 1.09247
\(592\) −8913.08 −0.618793
\(593\) 6472.49 0.448218 0.224109 0.974564i \(-0.428053\pi\)
0.224109 + 0.974564i \(0.428053\pi\)
\(594\) −35506.8 −2.45263
\(595\) 25522.9 1.75855
\(596\) 47940.8 3.29485
\(597\) −3518.20 −0.241190
\(598\) 8471.96 0.579338
\(599\) −25455.3 −1.73635 −0.868176 0.496257i \(-0.834708\pi\)
−0.868176 + 0.496257i \(0.834708\pi\)
\(600\) 19403.4 1.32023
\(601\) 13600.1 0.923064 0.461532 0.887124i \(-0.347300\pi\)
0.461532 + 0.887124i \(0.347300\pi\)
\(602\) 0 0
\(603\) 1218.34 0.0822799
\(604\) −34507.4 −2.32464
\(605\) −12261.7 −0.823983
\(606\) −21967.5 −1.47256
\(607\) 8144.66 0.544616 0.272308 0.962210i \(-0.412213\pi\)
0.272308 + 0.962210i \(0.412213\pi\)
\(608\) −3101.04 −0.206848
\(609\) 21070.1 1.40198
\(610\) −57135.1 −3.79235
\(611\) 24020.9 1.59048
\(612\) −2535.51 −0.167470
\(613\) 21750.5 1.43311 0.716554 0.697531i \(-0.245718\pi\)
0.716554 + 0.697531i \(0.245718\pi\)
\(614\) −29115.3 −1.91368
\(615\) 28833.5 1.89053
\(616\) −72604.3 −4.74888
\(617\) 11659.4 0.760758 0.380379 0.924831i \(-0.375793\pi\)
0.380379 + 0.924831i \(0.375793\pi\)
\(618\) 8625.99 0.561469
\(619\) 17054.3 1.10738 0.553692 0.832722i \(-0.313219\pi\)
0.553692 + 0.832722i \(0.313219\pi\)
\(620\) 34361.2 2.22577
\(621\) 3906.30 0.252423
\(622\) 14108.2 0.909467
\(623\) −33863.8 −2.17773
\(624\) −44920.2 −2.88180
\(625\) −19512.1 −1.24877
\(626\) −35054.7 −2.23813
\(627\) −2350.45 −0.149709
\(628\) −12938.2 −0.822119
\(629\) −4148.01 −0.262944
\(630\) −3679.24 −0.232674
\(631\) 15049.7 0.949475 0.474737 0.880128i \(-0.342543\pi\)
0.474737 + 0.880128i \(0.342543\pi\)
\(632\) −36592.7 −2.30313
\(633\) 13193.8 0.828445
\(634\) 31168.6 1.95247
\(635\) −33605.5 −2.10015
\(636\) −26893.5 −1.67672
\(637\) −22058.4 −1.37203
\(638\) −38743.1 −2.40416
\(639\) −1356.08 −0.0839525
\(640\) 3426.73 0.211646
\(641\) −22558.3 −1.39002 −0.695008 0.719002i \(-0.744599\pi\)
−0.695008 + 0.719002i \(0.744599\pi\)
\(642\) −18048.1 −1.10950
\(643\) 16170.3 0.991748 0.495874 0.868395i \(-0.334848\pi\)
0.495874 + 0.868395i \(0.334848\pi\)
\(644\) 13732.3 0.840265
\(645\) 0 0
\(646\) −3593.26 −0.218847
\(647\) 16223.2 0.985778 0.492889 0.870092i \(-0.335941\pi\)
0.492889 + 0.870092i \(0.335941\pi\)
\(648\) −39022.5 −2.36566
\(649\) 6745.10 0.407964
\(650\) −21004.9 −1.26751
\(651\) 17295.9 1.04129
\(652\) 9741.86 0.585155
\(653\) −6142.50 −0.368108 −0.184054 0.982916i \(-0.558922\pi\)
−0.184054 + 0.982916i \(0.558922\pi\)
\(654\) −29074.3 −1.73837
\(655\) −3605.90 −0.215106
\(656\) −61808.3 −3.67867
\(657\) 323.366 0.0192020
\(658\) 55224.2 3.27183
\(659\) −14009.5 −0.828123 −0.414061 0.910249i \(-0.635890\pi\)
−0.414061 + 0.910249i \(0.635890\pi\)
\(660\) −62456.9 −3.68353
\(661\) −26667.6 −1.56921 −0.784605 0.619996i \(-0.787134\pi\)
−0.784605 + 0.619996i \(0.787134\pi\)
\(662\) 11011.2 0.646470
\(663\) −20905.2 −1.22457
\(664\) 29919.0 1.74862
\(665\) −3676.24 −0.214373
\(666\) 597.954 0.0347901
\(667\) 4262.35 0.247434
\(668\) −31285.4 −1.81208
\(669\) −29313.4 −1.69405
\(670\) 45880.0 2.64552
\(671\) 37284.3 2.14507
\(672\) −41477.4 −2.38099
\(673\) −26390.1 −1.51153 −0.755767 0.654841i \(-0.772736\pi\)
−0.755767 + 0.654841i \(0.772736\pi\)
\(674\) 54563.8 3.11828
\(675\) −9685.05 −0.552264
\(676\) 27540.5 1.56694
\(677\) −10340.1 −0.587006 −0.293503 0.955958i \(-0.594821\pi\)
−0.293503 + 0.955958i \(0.594821\pi\)
\(678\) 45181.3 2.55926
\(679\) 7955.10 0.449615
\(680\) −55538.1 −3.13204
\(681\) 13475.9 0.758295
\(682\) −31803.1 −1.78564
\(683\) 3929.56 0.220147 0.110074 0.993923i \(-0.464891\pi\)
0.110074 + 0.993923i \(0.464891\pi\)
\(684\) 365.205 0.0204152
\(685\) −2899.62 −0.161736
\(686\) −3155.35 −0.175615
\(687\) 4555.87 0.253009
\(688\) 0 0
\(689\) 16934.1 0.936339
\(690\) 9745.72 0.537700
\(691\) 2660.45 0.146466 0.0732332 0.997315i \(-0.476668\pi\)
0.0732332 + 0.997315i \(0.476668\pi\)
\(692\) −6425.50 −0.352978
\(693\) 2400.94 0.131608
\(694\) 58607.9 3.20566
\(695\) −3511.92 −0.191676
\(696\) −45848.8 −2.49697
\(697\) −28764.6 −1.56318
\(698\) −6094.52 −0.330489
\(699\) 13582.5 0.734961
\(700\) −34047.2 −1.83837
\(701\) 27310.9 1.47150 0.735749 0.677255i \(-0.236830\pi\)
0.735749 + 0.677255i \(0.236830\pi\)
\(702\) 45487.0 2.44558
\(703\) 597.465 0.0320538
\(704\) 20258.8 1.08456
\(705\) 27632.5 1.47617
\(706\) −4189.66 −0.223342
\(707\) 22421.1 1.19269
\(708\) 13723.0 0.728450
\(709\) 2281.77 0.120866 0.0604328 0.998172i \(-0.480752\pi\)
0.0604328 + 0.998172i \(0.480752\pi\)
\(710\) −51066.8 −2.69930
\(711\) 1210.08 0.0638277
\(712\) 73687.8 3.87861
\(713\) 3498.84 0.183777
\(714\) −48061.1 −2.51911
\(715\) 39327.4 2.05701
\(716\) 16939.8 0.884177
\(717\) 11016.8 0.573821
\(718\) 50761.0 2.63842
\(719\) −7427.41 −0.385251 −0.192626 0.981272i \(-0.561700\pi\)
−0.192626 + 0.981272i \(0.561700\pi\)
\(720\) 3946.37 0.204267
\(721\) −8804.10 −0.454760
\(722\) −35204.2 −1.81463
\(723\) −13524.7 −0.695699
\(724\) −73931.3 −3.79508
\(725\) −10567.8 −0.541350
\(726\) 23089.5 1.18035
\(727\) −31960.7 −1.63048 −0.815240 0.579124i \(-0.803395\pi\)
−0.815240 + 0.579124i \(0.803395\pi\)
\(728\) 93011.9 4.73523
\(729\) 20874.3 1.06053
\(730\) 12177.2 0.617396
\(731\) 0 0
\(732\) 75855.5 3.83019
\(733\) −3379.50 −0.170293 −0.0851463 0.996368i \(-0.527136\pi\)
−0.0851463 + 0.996368i \(0.527136\pi\)
\(734\) −19079.7 −0.959462
\(735\) −25374.9 −1.27342
\(736\) −8390.61 −0.420220
\(737\) −29939.6 −1.49639
\(738\) 4146.54 0.206824
\(739\) 32194.7 1.60257 0.801285 0.598283i \(-0.204150\pi\)
0.801285 + 0.598283i \(0.204150\pi\)
\(740\) 15876.0 0.788669
\(741\) 3011.11 0.149279
\(742\) 38931.6 1.92618
\(743\) 8237.10 0.406716 0.203358 0.979104i \(-0.434815\pi\)
0.203358 + 0.979104i \(0.434815\pi\)
\(744\) −37636.0 −1.85457
\(745\) −34725.6 −1.70772
\(746\) −70146.4 −3.44268
\(747\) −989.388 −0.0484603
\(748\) 62307.7 3.04571
\(749\) 18420.7 0.898636
\(750\) 21001.1 1.02247
\(751\) 33321.1 1.61904 0.809522 0.587089i \(-0.199726\pi\)
0.809522 + 0.587089i \(0.199726\pi\)
\(752\) −59233.7 −2.87238
\(753\) −27735.7 −1.34229
\(754\) 49633.0 2.39725
\(755\) 24995.2 1.20486
\(756\) 73730.7 3.54704
\(757\) −40005.7 −1.92078 −0.960391 0.278656i \(-0.910111\pi\)
−0.960391 + 0.278656i \(0.910111\pi\)
\(758\) 12117.4 0.580640
\(759\) −6359.70 −0.304140
\(760\) 7999.51 0.381806
\(761\) 1344.71 0.0640549 0.0320274 0.999487i \(-0.489804\pi\)
0.0320274 + 0.999487i \(0.489804\pi\)
\(762\) 63281.1 3.00844
\(763\) 29674.6 1.40799
\(764\) −68872.1 −3.26140
\(765\) 1836.58 0.0867996
\(766\) 6923.74 0.326586
\(767\) −8641.02 −0.406791
\(768\) −23695.2 −1.11332
\(769\) −41407.9 −1.94175 −0.970875 0.239586i \(-0.922988\pi\)
−0.970875 + 0.239586i \(0.922988\pi\)
\(770\) 90413.9 4.23155
\(771\) 2345.22 0.109547
\(772\) −17352.5 −0.808979
\(773\) −10328.8 −0.480598 −0.240299 0.970699i \(-0.577245\pi\)
−0.240299 + 0.970699i \(0.577245\pi\)
\(774\) 0 0
\(775\) −8674.82 −0.402076
\(776\) −17310.4 −0.800780
\(777\) 7991.30 0.368966
\(778\) 52933.5 2.43928
\(779\) 4143.16 0.190557
\(780\) 80012.2 3.67294
\(781\) 33324.3 1.52681
\(782\) −9722.44 −0.444596
\(783\) 22885.1 1.04450
\(784\) 54394.3 2.47787
\(785\) 9371.72 0.426103
\(786\) 6790.11 0.308136
\(787\) −35833.2 −1.62302 −0.811509 0.584341i \(-0.801353\pi\)
−0.811509 + 0.584341i \(0.801353\pi\)
\(788\) 59931.5 2.70936
\(789\) 32232.3 1.45437
\(790\) 45568.8 2.05223
\(791\) −46114.2 −2.07286
\(792\) −5224.46 −0.234398
\(793\) −47764.2 −2.13891
\(794\) −69300.6 −3.09746
\(795\) 19480.1 0.869043
\(796\) −13433.3 −0.598156
\(797\) 9312.94 0.413904 0.206952 0.978351i \(-0.433646\pi\)
0.206952 + 0.978351i \(0.433646\pi\)
\(798\) 6922.56 0.307088
\(799\) −27566.5 −1.22056
\(800\) 20803.2 0.919379
\(801\) −2436.77 −0.107489
\(802\) 79554.2 3.50269
\(803\) −7946.41 −0.349219
\(804\) −60912.6 −2.67192
\(805\) −9946.95 −0.435508
\(806\) 40742.3 1.78050
\(807\) −4421.92 −0.192886
\(808\) −48788.5 −2.12422
\(809\) 29114.8 1.26529 0.632646 0.774441i \(-0.281969\pi\)
0.632646 + 0.774441i \(0.281969\pi\)
\(810\) 48594.6 2.10795
\(811\) 41592.3 1.80087 0.900434 0.434993i \(-0.143249\pi\)
0.900434 + 0.434993i \(0.143249\pi\)
\(812\) 80451.0 3.47694
\(813\) 32178.1 1.38811
\(814\) −14694.1 −0.632714
\(815\) −7056.46 −0.303285
\(816\) 51550.5 2.21156
\(817\) 0 0
\(818\) −83553.7 −3.57138
\(819\) −3075.79 −0.131229
\(820\) 110093. 4.68857
\(821\) −39650.4 −1.68551 −0.842757 0.538294i \(-0.819069\pi\)
−0.842757 + 0.538294i \(0.819069\pi\)
\(822\) 5460.15 0.231684
\(823\) −18879.4 −0.799629 −0.399815 0.916596i \(-0.630925\pi\)
−0.399815 + 0.916596i \(0.630925\pi\)
\(824\) 19157.8 0.809942
\(825\) 15767.9 0.665414
\(826\) −19865.8 −0.836825
\(827\) 19740.1 0.830024 0.415012 0.909816i \(-0.363777\pi\)
0.415012 + 0.909816i \(0.363777\pi\)
\(828\) 988.152 0.0414742
\(829\) 26241.2 1.09939 0.549695 0.835365i \(-0.314744\pi\)
0.549695 + 0.835365i \(0.314744\pi\)
\(830\) −37258.1 −1.55813
\(831\) −6195.35 −0.258621
\(832\) −25953.1 −1.08144
\(833\) 25314.3 1.05293
\(834\) 6613.15 0.274574
\(835\) 22661.4 0.939197
\(836\) −8974.58 −0.371283
\(837\) 18785.7 0.775782
\(838\) −46283.7 −1.90793
\(839\) 9598.19 0.394954 0.197477 0.980308i \(-0.436725\pi\)
0.197477 + 0.980308i \(0.436725\pi\)
\(840\) 106996. 4.39491
\(841\) 581.966 0.0238618
\(842\) −3129.30 −0.128079
\(843\) 7318.57 0.299009
\(844\) 50377.1 2.05456
\(845\) −19948.8 −0.812143
\(846\) 3973.82 0.161493
\(847\) −23566.3 −0.956017
\(848\) −41758.1 −1.69101
\(849\) 8504.65 0.343791
\(850\) 24105.2 0.972709
\(851\) 1616.59 0.0651186
\(852\) 67798.9 2.72623
\(853\) −13278.1 −0.532981 −0.266490 0.963838i \(-0.585864\pi\)
−0.266490 + 0.963838i \(0.585864\pi\)
\(854\) −109810. −4.40003
\(855\) −264.534 −0.0105812
\(856\) −40083.6 −1.60050
\(857\) −18835.6 −0.750773 −0.375386 0.926868i \(-0.622490\pi\)
−0.375386 + 0.926868i \(0.622490\pi\)
\(858\) −74055.6 −2.94664
\(859\) 8470.49 0.336449 0.168224 0.985749i \(-0.446197\pi\)
0.168224 + 0.985749i \(0.446197\pi\)
\(860\) 0 0
\(861\) 55416.2 2.19347
\(862\) −87675.2 −3.46430
\(863\) 14654.0 0.578017 0.289008 0.957327i \(-0.406674\pi\)
0.289008 + 0.957327i \(0.406674\pi\)
\(864\) −45050.2 −1.77389
\(865\) 4654.27 0.182948
\(866\) 6089.17 0.238936
\(867\) −615.548 −0.0241120
\(868\) 66040.0 2.58242
\(869\) −29736.5 −1.16081
\(870\) 57095.3 2.22496
\(871\) 38355.0 1.49209
\(872\) −64572.2 −2.50767
\(873\) 572.433 0.0221924
\(874\) 1400.39 0.0541977
\(875\) −21434.7 −0.828143
\(876\) −16167.1 −0.623557
\(877\) 31034.9 1.19495 0.597477 0.801886i \(-0.296170\pi\)
0.597477 + 0.801886i \(0.296170\pi\)
\(878\) 2107.34 0.0810015
\(879\) 17829.3 0.684151
\(880\) −96978.2 −3.71493
\(881\) −2331.10 −0.0891449 −0.0445725 0.999006i \(-0.514193\pi\)
−0.0445725 + 0.999006i \(0.514193\pi\)
\(882\) −3649.16 −0.139313
\(883\) 38070.6 1.45094 0.725469 0.688255i \(-0.241623\pi\)
0.725469 + 0.688255i \(0.241623\pi\)
\(884\) −79821.1 −3.03696
\(885\) −9940.20 −0.377555
\(886\) 44387.2 1.68309
\(887\) −19683.4 −0.745102 −0.372551 0.928012i \(-0.621517\pi\)
−0.372551 + 0.928012i \(0.621517\pi\)
\(888\) −17389.1 −0.657141
\(889\) −64587.7 −2.43667
\(890\) −91763.2 −3.45608
\(891\) −31711.0 −1.19232
\(892\) −111926. −4.20129
\(893\) 3970.58 0.148791
\(894\) 65390.3 2.44629
\(895\) −12270.3 −0.458268
\(896\) 6585.95 0.245559
\(897\) 8147.28 0.303266
\(898\) −12902.1 −0.479451
\(899\) 20498.0 0.760451
\(900\) −2449.97 −0.0907394
\(901\) −19433.6 −0.718565
\(902\) −101897. −3.76143
\(903\) 0 0
\(904\) 100345. 3.69184
\(905\) 53551.7 1.96698
\(906\) −47067.4 −1.72595
\(907\) −3322.49 −0.121633 −0.0608167 0.998149i \(-0.519371\pi\)
−0.0608167 + 0.998149i \(0.519371\pi\)
\(908\) 51454.4 1.88059
\(909\) 1613.38 0.0588695
\(910\) −115827. −4.21938
\(911\) −36251.9 −1.31842 −0.659209 0.751959i \(-0.729109\pi\)
−0.659209 + 0.751959i \(0.729109\pi\)
\(912\) −7425.16 −0.269596
\(913\) 24313.3 0.881327
\(914\) −23987.5 −0.868092
\(915\) −54945.5 −1.98518
\(916\) 17395.4 0.627468
\(917\) −6930.31 −0.249574
\(918\) −52201.0 −1.87679
\(919\) 20127.9 0.722477 0.361239 0.932473i \(-0.382354\pi\)
0.361239 + 0.932473i \(0.382354\pi\)
\(920\) 21644.6 0.775654
\(921\) −27999.5 −1.00175
\(922\) −58775.9 −2.09944
\(923\) −42691.1 −1.52242
\(924\) −120038. −4.27377
\(925\) −4008.07 −0.142470
\(926\) −2650.20 −0.0940508
\(927\) −633.525 −0.0224463
\(928\) −49156.4 −1.73883
\(929\) 39220.1 1.38511 0.692557 0.721364i \(-0.256484\pi\)
0.692557 + 0.721364i \(0.256484\pi\)
\(930\) 46867.9 1.65254
\(931\) −3646.18 −0.128355
\(932\) 51861.4 1.82272
\(933\) 13567.5 0.476079
\(934\) 2962.26 0.103777
\(935\) −45132.2 −1.57859
\(936\) 6692.94 0.233724
\(937\) −12798.4 −0.446218 −0.223109 0.974794i \(-0.571621\pi\)
−0.223109 + 0.974794i \(0.571621\pi\)
\(938\) 88178.5 3.06943
\(939\) −33711.3 −1.17159
\(940\) 105507. 3.66093
\(941\) −45827.7 −1.58761 −0.793805 0.608172i \(-0.791903\pi\)
−0.793805 + 0.608172i \(0.791903\pi\)
\(942\) −17647.5 −0.610388
\(943\) 11210.3 0.387124
\(944\) 21308.1 0.734659
\(945\) −53406.4 −1.83842
\(946\) 0 0
\(947\) 8956.69 0.307342 0.153671 0.988122i \(-0.450890\pi\)
0.153671 + 0.988122i \(0.450890\pi\)
\(948\) −60499.5 −2.07271
\(949\) 10180.0 0.348215
\(950\) −3472.03 −0.118576
\(951\) 29974.1 1.02206
\(952\) −106741. −3.63391
\(953\) 32038.7 1.08902 0.544510 0.838754i \(-0.316715\pi\)
0.544510 + 0.838754i \(0.316715\pi\)
\(954\) 2801.44 0.0950732
\(955\) 49887.2 1.69038
\(956\) 42064.8 1.42309
\(957\) −37258.3 −1.25851
\(958\) −17074.6 −0.575840
\(959\) −5572.89 −0.187652
\(960\) −29855.2 −1.00372
\(961\) −12964.8 −0.435191
\(962\) 18824.4 0.630896
\(963\) 1325.52 0.0443553
\(964\) −51640.8 −1.72535
\(965\) 12569.2 0.419293
\(966\) 18730.7 0.623860
\(967\) −33896.0 −1.12722 −0.563610 0.826041i \(-0.690588\pi\)
−0.563610 + 0.826041i \(0.690588\pi\)
\(968\) 51280.3 1.70270
\(969\) −3455.56 −0.114560
\(970\) 21556.5 0.713545
\(971\) −37446.8 −1.23762 −0.618808 0.785542i \(-0.712384\pi\)
−0.618808 + 0.785542i \(0.712384\pi\)
\(972\) 10259.5 0.338554
\(973\) −6749.69 −0.222390
\(974\) 17911.9 0.589256
\(975\) −20199.9 −0.663502
\(976\) 117783. 3.86284
\(977\) 23276.6 0.762214 0.381107 0.924531i \(-0.375543\pi\)
0.381107 + 0.924531i \(0.375543\pi\)
\(978\) 13287.7 0.434452
\(979\) 59881.3 1.95487
\(980\) −96887.5 −3.15812
\(981\) 2135.33 0.0694962
\(982\) −16228.9 −0.527377
\(983\) −20647.7 −0.669947 −0.334974 0.942228i \(-0.608727\pi\)
−0.334974 + 0.942228i \(0.608727\pi\)
\(984\) −120586. −3.90664
\(985\) −43411.1 −1.40426
\(986\) −56958.9 −1.83970
\(987\) 53107.8 1.71271
\(988\) 11497.1 0.370216
\(989\) 0 0
\(990\) 6506.00 0.208863
\(991\) 20706.8 0.663745 0.331873 0.943324i \(-0.392320\pi\)
0.331873 + 0.943324i \(0.392320\pi\)
\(992\) −40351.1 −1.29148
\(993\) 10589.2 0.338408
\(994\) −98147.2 −3.13183
\(995\) 9730.36 0.310023
\(996\) 49465.7 1.57368
\(997\) −55958.1 −1.77754 −0.888771 0.458351i \(-0.848440\pi\)
−0.888771 + 0.458351i \(0.848440\pi\)
\(998\) −88341.7 −2.80201
\(999\) 8679.66 0.274887
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 1849.4.a.i.1.49 50
43.42 odd 2 1849.4.a.j.1.2 yes 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.i.1.49 50 1.1 even 1 trivial
1849.4.a.j.1.2 yes 50 43.42 odd 2