Properties

Label 1849.4.a.j.1.48
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 1.48
Character \(\chi\) \(=\) 1849.1

$q$-expansion

\(f(q)\) \(=\) \(q+5.33984 q^{2} +6.59560 q^{3} +20.5139 q^{4} -12.0752 q^{5} +35.2195 q^{6} -18.2315 q^{7} +66.8223 q^{8} +16.5020 q^{9} +O(q^{10})\) \(q+5.33984 q^{2} +6.59560 q^{3} +20.5139 q^{4} -12.0752 q^{5} +35.2195 q^{6} -18.2315 q^{7} +66.8223 q^{8} +16.5020 q^{9} -64.4799 q^{10} -44.5541 q^{11} +135.302 q^{12} -45.4579 q^{13} -97.3531 q^{14} -79.6435 q^{15} +192.709 q^{16} -98.4784 q^{17} +88.1179 q^{18} -86.0301 q^{19} -247.710 q^{20} -120.247 q^{21} -237.912 q^{22} +142.930 q^{23} +440.733 q^{24} +20.8116 q^{25} -242.738 q^{26} -69.2408 q^{27} -373.998 q^{28} +162.790 q^{29} -425.284 q^{30} +68.1625 q^{31} +494.458 q^{32} -293.861 q^{33} -525.859 q^{34} +220.149 q^{35} +338.520 q^{36} -13.6258 q^{37} -459.387 q^{38} -299.822 q^{39} -806.895 q^{40} +17.3417 q^{41} -642.102 q^{42} -913.978 q^{44} -199.265 q^{45} +763.222 q^{46} +409.667 q^{47} +1271.03 q^{48} -10.6139 q^{49} +111.131 q^{50} -649.524 q^{51} -932.519 q^{52} -161.737 q^{53} -369.735 q^{54} +538.001 q^{55} -1218.27 q^{56} -567.420 q^{57} +869.274 q^{58} -400.387 q^{59} -1633.80 q^{60} -706.565 q^{61} +363.977 q^{62} -300.855 q^{63} +1098.65 q^{64} +548.916 q^{65} -1569.17 q^{66} +334.035 q^{67} -2020.18 q^{68} +942.708 q^{69} +1175.56 q^{70} +480.962 q^{71} +1102.70 q^{72} -1151.86 q^{73} -72.7597 q^{74} +137.265 q^{75} -1764.81 q^{76} +812.286 q^{77} -1601.00 q^{78} -250.741 q^{79} -2327.01 q^{80} -902.238 q^{81} +92.6018 q^{82} +351.657 q^{83} -2466.74 q^{84} +1189.15 q^{85} +1073.70 q^{87} -2977.20 q^{88} -117.413 q^{89} -1064.05 q^{90} +828.764 q^{91} +2932.05 q^{92} +449.573 q^{93} +2187.56 q^{94} +1038.83 q^{95} +3261.25 q^{96} -609.540 q^{97} -56.6763 q^{98} -735.230 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} + O(q^{10}) \) \( 50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} - 137q^{10} - 252q^{11} + 48q^{12} - 192q^{13} - 272q^{14} - 314q^{15} + 542q^{16} - 236q^{17} + 386q^{18} - 12q^{19} - 108q^{20} - 408q^{21} - 1235q^{22} - 630q^{23} - 613q^{24} + 1098q^{25} - 1493q^{26} - 10q^{27} + 242q^{28} - 208q^{29} + 48q^{30} - 932q^{31} + 1124q^{32} - 254q^{33} - 765q^{34} - 1452q^{35} + 747q^{36} + 90q^{37} - 1213q^{38} + 1610q^{39} - 1693q^{40} - 1354q^{41} + 16q^{42} - 2704q^{44} - 4508q^{45} - 233q^{46} - 3484q^{47} + 376q^{48} + 1324q^{49} + 408q^{50} - 4054q^{51} - 2176q^{52} - 726q^{53} - 6497q^{54} + 3288q^{55} - 7097q^{56} - 870q^{57} + 275q^{58} - 4370q^{59} - 3891q^{60} - 1172q^{61} + 1546q^{62} + 3686q^{63} + 606q^{64} - 2610q^{65} - 4697q^{66} - 344q^{67} - 3221q^{68} - 136q^{69} + 1310q^{70} - 162q^{71} + 5814q^{72} - 746q^{73} - 4332q^{74} - 236q^{75} - 1338q^{76} - 2024q^{77} - 2782q^{78} - 2656q^{79} + 5713q^{80} - 86q^{81} + 4168q^{82} - 3514q^{83} - 4269q^{84} + 7558q^{85} - 10278q^{87} - 11692q^{88} - 2640q^{89} - 8286q^{90} + 5946q^{91} - 4271q^{92} + 2q^{93} - 9062q^{94} - 12140q^{95} - 700q^{96} - 3864q^{97} + 2826q^{98} - 8174q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.33984 1.88792 0.943960 0.330061i \(-0.107069\pi\)
0.943960 + 0.330061i \(0.107069\pi\)
\(3\) 6.59560 1.26932 0.634662 0.772790i \(-0.281139\pi\)
0.634662 + 0.772790i \(0.281139\pi\)
\(4\) 20.5139 2.56424
\(5\) −12.0752 −1.08004 −0.540021 0.841651i \(-0.681584\pi\)
−0.540021 + 0.841651i \(0.681584\pi\)
\(6\) 35.2195 2.39638
\(7\) −18.2315 −0.984406 −0.492203 0.870480i \(-0.663808\pi\)
−0.492203 + 0.870480i \(0.663808\pi\)
\(8\) 66.8223 2.95315
\(9\) 16.5020 0.611184
\(10\) −64.4799 −2.03903
\(11\) −44.5541 −1.22123 −0.610616 0.791927i \(-0.709078\pi\)
−0.610616 + 0.791927i \(0.709078\pi\)
\(12\) 135.302 3.25485
\(13\) −45.4579 −0.969827 −0.484914 0.874562i \(-0.661149\pi\)
−0.484914 + 0.874562i \(0.661149\pi\)
\(14\) −97.3531 −1.85848
\(15\) −79.6435 −1.37092
\(16\) 192.709 3.01108
\(17\) −98.4784 −1.40497 −0.702486 0.711698i \(-0.747927\pi\)
−0.702486 + 0.711698i \(0.747927\pi\)
\(18\) 88.1179 1.15387
\(19\) −86.0301 −1.03877 −0.519386 0.854540i \(-0.673839\pi\)
−0.519386 + 0.854540i \(0.673839\pi\)
\(20\) −247.710 −2.76949
\(21\) −120.247 −1.24953
\(22\) −237.912 −2.30559
\(23\) 142.930 1.29578 0.647889 0.761734i \(-0.275652\pi\)
0.647889 + 0.761734i \(0.275652\pi\)
\(24\) 440.733 3.74851
\(25\) 20.8116 0.166493
\(26\) −242.738 −1.83096
\(27\) −69.2408 −0.493534
\(28\) −373.998 −2.52425
\(29\) 162.790 1.04239 0.521196 0.853437i \(-0.325486\pi\)
0.521196 + 0.853437i \(0.325486\pi\)
\(30\) −425.284 −2.58819
\(31\) 68.1625 0.394914 0.197457 0.980312i \(-0.436732\pi\)
0.197457 + 0.980312i \(0.436732\pi\)
\(32\) 494.458 2.73152
\(33\) −293.861 −1.55014
\(34\) −525.859 −2.65247
\(35\) 220.149 1.06320
\(36\) 338.520 1.56722
\(37\) −13.6258 −0.0605425 −0.0302712 0.999542i \(-0.509637\pi\)
−0.0302712 + 0.999542i \(0.509637\pi\)
\(38\) −459.387 −1.96112
\(39\) −299.822 −1.23103
\(40\) −806.895 −3.18953
\(41\) 17.3417 0.0660564 0.0330282 0.999454i \(-0.489485\pi\)
0.0330282 + 0.999454i \(0.489485\pi\)
\(42\) −642.102 −2.35901
\(43\) 0 0
\(44\) −913.978 −3.13153
\(45\) −199.265 −0.660105
\(46\) 763.222 2.44633
\(47\) 409.667 1.27141 0.635704 0.771933i \(-0.280710\pi\)
0.635704 + 0.771933i \(0.280710\pi\)
\(48\) 1271.03 3.82204
\(49\) −10.6139 −0.0309442
\(50\) 111.131 0.314325
\(51\) −649.524 −1.78336
\(52\) −932.519 −2.48687
\(53\) −161.737 −0.419175 −0.209588 0.977790i \(-0.567212\pi\)
−0.209588 + 0.977790i \(0.567212\pi\)
\(54\) −369.735 −0.931751
\(55\) 538.001 1.31898
\(56\) −1218.27 −2.90710
\(57\) −567.420 −1.31854
\(58\) 869.274 1.96795
\(59\) −400.387 −0.883491 −0.441746 0.897140i \(-0.645641\pi\)
−0.441746 + 0.897140i \(0.645641\pi\)
\(60\) −1633.80 −3.51538
\(61\) −706.565 −1.48306 −0.741528 0.670922i \(-0.765898\pi\)
−0.741528 + 0.670922i \(0.765898\pi\)
\(62\) 363.977 0.745566
\(63\) −300.855 −0.601653
\(64\) 1098.65 2.14581
\(65\) 548.916 1.04746
\(66\) −1569.17 −2.92654
\(67\) 334.035 0.609088 0.304544 0.952498i \(-0.401496\pi\)
0.304544 + 0.952498i \(0.401496\pi\)
\(68\) −2020.18 −3.60268
\(69\) 942.708 1.64476
\(70\) 1175.56 2.00724
\(71\) 480.962 0.803940 0.401970 0.915653i \(-0.368326\pi\)
0.401970 + 0.915653i \(0.368326\pi\)
\(72\) 1102.70 1.80492
\(73\) −1151.86 −1.84678 −0.923390 0.383863i \(-0.874593\pi\)
−0.923390 + 0.383863i \(0.874593\pi\)
\(74\) −72.7597 −0.114299
\(75\) 137.265 0.211333
\(76\) −1764.81 −2.66366
\(77\) 812.286 1.20219
\(78\) −1601.00 −2.32408
\(79\) −250.741 −0.357096 −0.178548 0.983931i \(-0.557140\pi\)
−0.178548 + 0.983931i \(0.557140\pi\)
\(80\) −2327.01 −3.25209
\(81\) −902.238 −1.23764
\(82\) 92.6018 0.124709
\(83\) 351.657 0.465052 0.232526 0.972590i \(-0.425301\pi\)
0.232526 + 0.972590i \(0.425301\pi\)
\(84\) −2466.74 −3.20409
\(85\) 1189.15 1.51743
\(86\) 0 0
\(87\) 1073.70 1.32313
\(88\) −2977.20 −3.60649
\(89\) −117.413 −0.139840 −0.0699202 0.997553i \(-0.522274\pi\)
−0.0699202 + 0.997553i \(0.522274\pi\)
\(90\) −1064.05 −1.24622
\(91\) 828.764 0.954704
\(92\) 2932.05 3.32269
\(93\) 449.573 0.501274
\(94\) 2187.56 2.40031
\(95\) 1038.83 1.12192
\(96\) 3261.25 3.46718
\(97\) −609.540 −0.638035 −0.319018 0.947749i \(-0.603353\pi\)
−0.319018 + 0.947749i \(0.603353\pi\)
\(98\) −56.6763 −0.0584201
\(99\) −735.230 −0.746398
\(100\) 426.927 0.426927
\(101\) 641.822 0.632314 0.316157 0.948707i \(-0.397607\pi\)
0.316157 + 0.948707i \(0.397607\pi\)
\(102\) −3468.36 −3.36685
\(103\) 277.249 0.265225 0.132613 0.991168i \(-0.457663\pi\)
0.132613 + 0.991168i \(0.457663\pi\)
\(104\) −3037.60 −2.86405
\(105\) 1452.02 1.34955
\(106\) −863.650 −0.791369
\(107\) 797.093 0.720167 0.360084 0.932920i \(-0.382748\pi\)
0.360084 + 0.932920i \(0.382748\pi\)
\(108\) −1420.40 −1.26554
\(109\) 673.160 0.591532 0.295766 0.955260i \(-0.404425\pi\)
0.295766 + 0.955260i \(0.404425\pi\)
\(110\) 2872.84 2.49013
\(111\) −89.8705 −0.0768480
\(112\) −3513.37 −2.96413
\(113\) 1233.31 1.02673 0.513363 0.858172i \(-0.328400\pi\)
0.513363 + 0.858172i \(0.328400\pi\)
\(114\) −3029.93 −2.48929
\(115\) −1725.91 −1.39950
\(116\) 3339.46 2.67294
\(117\) −750.145 −0.592743
\(118\) −2138.00 −1.66796
\(119\) 1795.40 1.38306
\(120\) −5321.96 −4.04855
\(121\) 654.064 0.491408
\(122\) −3772.94 −2.79989
\(123\) 114.379 0.0838470
\(124\) 1398.28 1.01265
\(125\) 1258.10 0.900224
\(126\) −1606.52 −1.13587
\(127\) 70.5831 0.0493168 0.0246584 0.999696i \(-0.492150\pi\)
0.0246584 + 0.999696i \(0.492150\pi\)
\(128\) 1910.97 1.31959
\(129\) 0 0
\(130\) 2931.12 1.97751
\(131\) 276.822 0.184626 0.0923130 0.995730i \(-0.470574\pi\)
0.0923130 + 0.995730i \(0.470574\pi\)
\(132\) −6028.23 −3.97493
\(133\) 1568.45 1.02257
\(134\) 1783.69 1.14991
\(135\) 836.100 0.533037
\(136\) −6580.55 −4.14910
\(137\) −548.908 −0.342309 −0.171155 0.985244i \(-0.554750\pi\)
−0.171155 + 0.985244i \(0.554750\pi\)
\(138\) 5033.91 3.10518
\(139\) −1429.65 −0.872385 −0.436192 0.899853i \(-0.643673\pi\)
−0.436192 + 0.899853i \(0.643673\pi\)
\(140\) 4516.12 2.72630
\(141\) 2702.00 1.61383
\(142\) 2568.26 1.51777
\(143\) 2025.33 1.18438
\(144\) 3180.08 1.84032
\(145\) −1965.73 −1.12583
\(146\) −6150.75 −3.48657
\(147\) −70.0047 −0.0392782
\(148\) −279.519 −0.155245
\(149\) −1636.22 −0.899624 −0.449812 0.893123i \(-0.648509\pi\)
−0.449812 + 0.893123i \(0.648509\pi\)
\(150\) 732.973 0.398980
\(151\) 2732.46 1.47261 0.736305 0.676650i \(-0.236569\pi\)
0.736305 + 0.676650i \(0.236569\pi\)
\(152\) −5748.72 −3.06765
\(153\) −1625.09 −0.858696
\(154\) 4337.48 2.26964
\(155\) −823.079 −0.426525
\(156\) −6150.53 −3.15664
\(157\) −2181.13 −1.10875 −0.554374 0.832268i \(-0.687042\pi\)
−0.554374 + 0.832268i \(0.687042\pi\)
\(158\) −1338.92 −0.674169
\(159\) −1066.75 −0.532069
\(160\) −5970.70 −2.95016
\(161\) −2605.82 −1.27557
\(162\) −4817.81 −2.33656
\(163\) 3651.49 1.75464 0.877320 0.479905i \(-0.159329\pi\)
0.877320 + 0.479905i \(0.159329\pi\)
\(164\) 355.745 0.169384
\(165\) 3548.44 1.67422
\(166\) 1877.79 0.877981
\(167\) 2247.21 1.04128 0.520641 0.853776i \(-0.325693\pi\)
0.520641 + 0.853776i \(0.325693\pi\)
\(168\) −8035.21 −3.69006
\(169\) −130.578 −0.0594347
\(170\) 6349.88 2.86478
\(171\) −1419.67 −0.634880
\(172\) 0 0
\(173\) −1431.95 −0.629302 −0.314651 0.949207i \(-0.601887\pi\)
−0.314651 + 0.949207i \(0.601887\pi\)
\(174\) 5733.38 2.49797
\(175\) −379.425 −0.163896
\(176\) −8585.97 −3.67723
\(177\) −2640.79 −1.12144
\(178\) −626.969 −0.264007
\(179\) 3963.35 1.65494 0.827472 0.561507i \(-0.189778\pi\)
0.827472 + 0.561507i \(0.189778\pi\)
\(180\) −4087.71 −1.69267
\(181\) −1046.09 −0.429588 −0.214794 0.976659i \(-0.568908\pi\)
−0.214794 + 0.976659i \(0.568908\pi\)
\(182\) 4425.47 1.80240
\(183\) −4660.22 −1.88248
\(184\) 9550.89 3.82664
\(185\) 164.535 0.0653885
\(186\) 2400.65 0.946366
\(187\) 4387.61 1.71580
\(188\) 8403.88 3.26019
\(189\) 1262.36 0.485838
\(190\) 5547.21 2.11809
\(191\) 791.007 0.299661 0.149831 0.988712i \(-0.452127\pi\)
0.149831 + 0.988712i \(0.452127\pi\)
\(192\) 7246.28 2.72372
\(193\) −315.336 −0.117608 −0.0588042 0.998270i \(-0.518729\pi\)
−0.0588042 + 0.998270i \(0.518729\pi\)
\(194\) −3254.85 −1.20456
\(195\) 3620.43 1.32956
\(196\) −217.732 −0.0793482
\(197\) −5234.95 −1.89327 −0.946637 0.322301i \(-0.895544\pi\)
−0.946637 + 0.322301i \(0.895544\pi\)
\(198\) −3926.01 −1.40914
\(199\) −1299.62 −0.462955 −0.231477 0.972840i \(-0.574356\pi\)
−0.231477 + 0.972840i \(0.574356\pi\)
\(200\) 1390.68 0.491679
\(201\) 2203.16 0.773130
\(202\) 3427.23 1.19376
\(203\) −2967.90 −1.02614
\(204\) −13324.3 −4.57297
\(205\) −209.405 −0.0713438
\(206\) 1480.47 0.500724
\(207\) 2358.62 0.791959
\(208\) −8760.15 −2.92023
\(209\) 3832.99 1.26858
\(210\) 7753.54 2.54784
\(211\) −5760.12 −1.87935 −0.939676 0.342065i \(-0.888874\pi\)
−0.939676 + 0.342065i \(0.888874\pi\)
\(212\) −3317.86 −1.07486
\(213\) 3172.24 1.02046
\(214\) 4256.35 1.35962
\(215\) 0 0
\(216\) −4626.83 −1.45748
\(217\) −1242.70 −0.388756
\(218\) 3594.57 1.11677
\(219\) −7597.21 −2.34416
\(220\) 11036.5 3.38219
\(221\) 4476.62 1.36258
\(222\) −479.894 −0.145083
\(223\) −3460.12 −1.03904 −0.519522 0.854457i \(-0.673890\pi\)
−0.519522 + 0.854457i \(0.673890\pi\)
\(224\) −9014.69 −2.68892
\(225\) 343.432 0.101758
\(226\) 6585.68 1.93837
\(227\) −6727.15 −1.96695 −0.983473 0.181057i \(-0.942048\pi\)
−0.983473 + 0.181057i \(0.942048\pi\)
\(228\) −11640.0 −3.38104
\(229\) 3081.40 0.889190 0.444595 0.895732i \(-0.353348\pi\)
0.444595 + 0.895732i \(0.353348\pi\)
\(230\) −9216.10 −2.64214
\(231\) 5357.51 1.52597
\(232\) 10878.0 3.07835
\(233\) −5100.84 −1.43419 −0.717097 0.696973i \(-0.754530\pi\)
−0.717097 + 0.696973i \(0.754530\pi\)
\(234\) −4005.66 −1.11905
\(235\) −4946.84 −1.37317
\(236\) −8213.51 −2.26548
\(237\) −1653.79 −0.453271
\(238\) 9587.18 2.61111
\(239\) −6634.06 −1.79549 −0.897744 0.440517i \(-0.854795\pi\)
−0.897744 + 0.440517i \(0.854795\pi\)
\(240\) −15348.0 −4.12796
\(241\) 1508.12 0.403097 0.201548 0.979479i \(-0.435403\pi\)
0.201548 + 0.979479i \(0.435403\pi\)
\(242\) 3492.60 0.927739
\(243\) −4081.30 −1.07743
\(244\) −14494.4 −3.80291
\(245\) 128.165 0.0334210
\(246\) 610.764 0.158296
\(247\) 3910.75 1.00743
\(248\) 4554.77 1.16624
\(249\) 2319.39 0.590302
\(250\) 6718.06 1.69955
\(251\) 1448.36 0.364223 0.182111 0.983278i \(-0.441707\pi\)
0.182111 + 0.983278i \(0.441707\pi\)
\(252\) −6171.71 −1.54278
\(253\) −6368.10 −1.58245
\(254\) 376.903 0.0931062
\(255\) 7843.16 1.92611
\(256\) 1415.06 0.345474
\(257\) 4186.81 1.01621 0.508105 0.861295i \(-0.330346\pi\)
0.508105 + 0.861295i \(0.330346\pi\)
\(258\) 0 0
\(259\) 248.419 0.0595984
\(260\) 11260.4 2.68592
\(261\) 2686.36 0.637094
\(262\) 1478.18 0.348559
\(263\) 1305.78 0.306152 0.153076 0.988214i \(-0.451082\pi\)
0.153076 + 0.988214i \(0.451082\pi\)
\(264\) −19636.4 −4.57780
\(265\) 1953.01 0.452727
\(266\) 8375.29 1.93053
\(267\) −774.412 −0.177503
\(268\) 6852.36 1.56185
\(269\) −1244.74 −0.282131 −0.141066 0.990000i \(-0.545053\pi\)
−0.141066 + 0.990000i \(0.545053\pi\)
\(270\) 4464.64 1.00633
\(271\) 1989.22 0.445891 0.222945 0.974831i \(-0.428433\pi\)
0.222945 + 0.974831i \(0.428433\pi\)
\(272\) −18977.7 −4.23048
\(273\) 5466.20 1.21183
\(274\) −2931.08 −0.646253
\(275\) −927.240 −0.203326
\(276\) 19338.6 4.21756
\(277\) 1174.72 0.254809 0.127404 0.991851i \(-0.459335\pi\)
0.127404 + 0.991851i \(0.459335\pi\)
\(278\) −7634.11 −1.64699
\(279\) 1124.82 0.241365
\(280\) 14710.9 3.13980
\(281\) −1511.73 −0.320934 −0.160467 0.987041i \(-0.551300\pi\)
−0.160467 + 0.987041i \(0.551300\pi\)
\(282\) 14428.3 3.04678
\(283\) 5919.78 1.24344 0.621722 0.783238i \(-0.286434\pi\)
0.621722 + 0.783238i \(0.286434\pi\)
\(284\) 9866.41 2.06149
\(285\) 6851.74 1.42408
\(286\) 10815.0 2.23602
\(287\) −316.164 −0.0650264
\(288\) 8159.52 1.66946
\(289\) 4784.99 0.973945
\(290\) −10496.7 −2.12547
\(291\) −4020.28 −0.809873
\(292\) −23629.1 −4.73558
\(293\) −5612.12 −1.11899 −0.559494 0.828834i \(-0.689005\pi\)
−0.559494 + 0.828834i \(0.689005\pi\)
\(294\) −373.814 −0.0741540
\(295\) 4834.77 0.954208
\(296\) −910.508 −0.178791
\(297\) 3084.96 0.602719
\(298\) −8737.13 −1.69842
\(299\) −6497.29 −1.25668
\(300\) 2815.84 0.541908
\(301\) 0 0
\(302\) 14590.9 2.78017
\(303\) 4233.20 0.802611
\(304\) −16578.8 −3.12782
\(305\) 8531.94 1.60176
\(306\) −8677.71 −1.62115
\(307\) −5016.73 −0.932638 −0.466319 0.884617i \(-0.654420\pi\)
−0.466319 + 0.884617i \(0.654420\pi\)
\(308\) 16663.1 3.08270
\(309\) 1828.63 0.336657
\(310\) −4395.11 −0.805244
\(311\) 1101.33 0.200806 0.100403 0.994947i \(-0.467987\pi\)
0.100403 + 0.994947i \(0.467987\pi\)
\(312\) −20034.8 −3.63541
\(313\) −6986.81 −1.26172 −0.630859 0.775898i \(-0.717297\pi\)
−0.630859 + 0.775898i \(0.717297\pi\)
\(314\) −11646.9 −2.09323
\(315\) 3632.90 0.649811
\(316\) −5143.68 −0.915680
\(317\) 8578.02 1.51984 0.759920 0.650016i \(-0.225238\pi\)
0.759920 + 0.650016i \(0.225238\pi\)
\(318\) −5696.29 −1.00450
\(319\) −7252.96 −1.27300
\(320\) −13266.5 −2.31756
\(321\) 5257.31 0.914125
\(322\) −13914.7 −2.40818
\(323\) 8472.10 1.45944
\(324\) −18508.4 −3.17360
\(325\) −946.051 −0.161469
\(326\) 19498.4 3.31262
\(327\) 4439.90 0.750846
\(328\) 1158.81 0.195075
\(329\) −7468.84 −1.25158
\(330\) 18948.1 3.16079
\(331\) −1403.92 −0.233130 −0.116565 0.993183i \(-0.537188\pi\)
−0.116565 + 0.993183i \(0.537188\pi\)
\(332\) 7213.86 1.19251
\(333\) −224.853 −0.0370026
\(334\) 11999.7 1.96586
\(335\) −4033.56 −0.657841
\(336\) −23172.8 −3.76244
\(337\) −9324.11 −1.50717 −0.753585 0.657350i \(-0.771677\pi\)
−0.753585 + 0.657350i \(0.771677\pi\)
\(338\) −697.267 −0.112208
\(339\) 8134.42 1.30325
\(340\) 24394.1 3.89105
\(341\) −3036.92 −0.482282
\(342\) −7580.79 −1.19860
\(343\) 6446.90 1.01487
\(344\) 0 0
\(345\) −11383.4 −1.77641
\(346\) −7646.39 −1.18807
\(347\) 8069.15 1.24834 0.624171 0.781287i \(-0.285437\pi\)
0.624171 + 0.781287i \(0.285437\pi\)
\(348\) 22025.8 3.39283
\(349\) 1789.13 0.274412 0.137206 0.990543i \(-0.456188\pi\)
0.137206 + 0.990543i \(0.456188\pi\)
\(350\) −2026.07 −0.309423
\(351\) 3147.54 0.478642
\(352\) −22030.1 −3.33582
\(353\) 10988.6 1.65683 0.828416 0.560113i \(-0.189242\pi\)
0.828416 + 0.560113i \(0.189242\pi\)
\(354\) −14101.4 −2.11718
\(355\) −5807.74 −0.868289
\(356\) −2408.61 −0.358584
\(357\) 11841.8 1.75556
\(358\) 21163.7 3.12440
\(359\) −7248.69 −1.06566 −0.532829 0.846223i \(-0.678871\pi\)
−0.532829 + 0.846223i \(0.678871\pi\)
\(360\) −13315.4 −1.94939
\(361\) 542.172 0.0790453
\(362\) −5585.96 −0.811027
\(363\) 4313.95 0.623756
\(364\) 17001.2 2.44809
\(365\) 13909.0 1.99460
\(366\) −24884.8 −3.55397
\(367\) −6760.61 −0.961583 −0.480791 0.876835i \(-0.659651\pi\)
−0.480791 + 0.876835i \(0.659651\pi\)
\(368\) 27543.9 3.90169
\(369\) 286.172 0.0403726
\(370\) 878.592 0.123448
\(371\) 2948.70 0.412639
\(372\) 9222.49 1.28539
\(373\) 2767.85 0.384220 0.192110 0.981373i \(-0.438467\pi\)
0.192110 + 0.981373i \(0.438467\pi\)
\(374\) 23429.1 3.23928
\(375\) 8297.93 1.14268
\(376\) 27374.9 3.75466
\(377\) −7400.10 −1.01094
\(378\) 6740.81 0.917222
\(379\) 9178.35 1.24396 0.621979 0.783034i \(-0.286329\pi\)
0.621979 + 0.783034i \(0.286329\pi\)
\(380\) 21310.5 2.87686
\(381\) 465.538 0.0625990
\(382\) 4223.85 0.565736
\(383\) 6592.70 0.879559 0.439780 0.898106i \(-0.355057\pi\)
0.439780 + 0.898106i \(0.355057\pi\)
\(384\) 12604.0 1.67499
\(385\) −9808.55 −1.29842
\(386\) −1683.85 −0.222035
\(387\) 0 0
\(388\) −12504.0 −1.63607
\(389\) −12393.0 −1.61530 −0.807648 0.589665i \(-0.799260\pi\)
−0.807648 + 0.589665i \(0.799260\pi\)
\(390\) 19332.5 2.51010
\(391\) −14075.5 −1.82053
\(392\) −709.242 −0.0913829
\(393\) 1825.81 0.234350
\(394\) −27953.8 −3.57435
\(395\) 3027.76 0.385679
\(396\) −15082.4 −1.91394
\(397\) −5802.01 −0.733488 −0.366744 0.930322i \(-0.619527\pi\)
−0.366744 + 0.930322i \(0.619527\pi\)
\(398\) −6939.79 −0.874021
\(399\) 10344.9 1.29798
\(400\) 4010.58 0.501322
\(401\) −11595.0 −1.44396 −0.721980 0.691914i \(-0.756768\pi\)
−0.721980 + 0.691914i \(0.756768\pi\)
\(402\) 11764.5 1.45961
\(403\) −3098.53 −0.382999
\(404\) 13166.3 1.62140
\(405\) 10894.7 1.33670
\(406\) −15848.1 −1.93726
\(407\) 607.086 0.0739364
\(408\) −43402.7 −5.26655
\(409\) 6410.71 0.775035 0.387517 0.921862i \(-0.373333\pi\)
0.387517 + 0.921862i \(0.373333\pi\)
\(410\) −1118.19 −0.134691
\(411\) −3620.38 −0.434502
\(412\) 5687.47 0.680100
\(413\) 7299.64 0.869714
\(414\) 12594.7 1.49515
\(415\) −4246.34 −0.502277
\(416\) −22477.0 −2.64910
\(417\) −9429.42 −1.10734
\(418\) 20467.6 2.39498
\(419\) 12824.3 1.49524 0.747620 0.664127i \(-0.231196\pi\)
0.747620 + 0.664127i \(0.231196\pi\)
\(420\) 29786.6 3.46056
\(421\) 1184.03 0.137069 0.0685347 0.997649i \(-0.478168\pi\)
0.0685347 + 0.997649i \(0.478168\pi\)
\(422\) −30758.2 −3.54807
\(423\) 6760.32 0.777064
\(424\) −10807.6 −1.23789
\(425\) −2049.49 −0.233917
\(426\) 16939.2 1.92655
\(427\) 12881.7 1.45993
\(428\) 16351.5 1.84668
\(429\) 13358.3 1.50337
\(430\) 0 0
\(431\) −5668.01 −0.633453 −0.316726 0.948517i \(-0.602584\pi\)
−0.316726 + 0.948517i \(0.602584\pi\)
\(432\) −13343.3 −1.48607
\(433\) −6623.04 −0.735064 −0.367532 0.930011i \(-0.619797\pi\)
−0.367532 + 0.930011i \(0.619797\pi\)
\(434\) −6635.83 −0.733940
\(435\) −12965.2 −1.42904
\(436\) 13809.1 1.51683
\(437\) −12296.3 −1.34602
\(438\) −40567.9 −4.42559
\(439\) −5719.79 −0.621847 −0.310923 0.950435i \(-0.600638\pi\)
−0.310923 + 0.950435i \(0.600638\pi\)
\(440\) 35950.5 3.89516
\(441\) −175.149 −0.0189126
\(442\) 23904.4 2.57244
\(443\) 9082.79 0.974123 0.487061 0.873368i \(-0.338069\pi\)
0.487061 + 0.873368i \(0.338069\pi\)
\(444\) −1843.59 −0.197057
\(445\) 1417.80 0.151034
\(446\) −18476.5 −1.96163
\(447\) −10791.8 −1.14191
\(448\) −20030.0 −2.11235
\(449\) −4971.70 −0.522559 −0.261279 0.965263i \(-0.584144\pi\)
−0.261279 + 0.965263i \(0.584144\pi\)
\(450\) 1833.87 0.192110
\(451\) −772.642 −0.0806702
\(452\) 25300.0 2.63277
\(453\) 18022.2 1.86922
\(454\) −35921.9 −3.71343
\(455\) −10007.5 −1.03112
\(456\) −37916.3 −3.89384
\(457\) 12938.0 1.32432 0.662158 0.749365i \(-0.269641\pi\)
0.662158 + 0.749365i \(0.269641\pi\)
\(458\) 16454.2 1.67872
\(459\) 6818.73 0.693401
\(460\) −35405.2 −3.58864
\(461\) −10910.1 −1.10224 −0.551121 0.834425i \(-0.685800\pi\)
−0.551121 + 0.834425i \(0.685800\pi\)
\(462\) 28608.3 2.88090
\(463\) −5850.83 −0.587281 −0.293641 0.955916i \(-0.594867\pi\)
−0.293641 + 0.955916i \(0.594867\pi\)
\(464\) 31371.1 3.13873
\(465\) −5428.70 −0.541398
\(466\) −27237.7 −2.70764
\(467\) −16089.6 −1.59430 −0.797149 0.603782i \(-0.793660\pi\)
−0.797149 + 0.603782i \(0.793660\pi\)
\(468\) −15388.4 −1.51993
\(469\) −6089.95 −0.599590
\(470\) −26415.3 −2.59244
\(471\) −14385.9 −1.40736
\(472\) −26754.8 −2.60909
\(473\) 0 0
\(474\) −8830.98 −0.855739
\(475\) −1790.42 −0.172948
\(476\) 36830.8 3.54650
\(477\) −2668.98 −0.256193
\(478\) −35424.8 −3.38974
\(479\) −5637.28 −0.537732 −0.268866 0.963178i \(-0.586649\pi\)
−0.268866 + 0.963178i \(0.586649\pi\)
\(480\) −39380.4 −3.74471
\(481\) 619.401 0.0587157
\(482\) 8053.10 0.761014
\(483\) −17186.9 −1.61912
\(484\) 13417.4 1.26009
\(485\) 7360.34 0.689105
\(486\) −21793.5 −2.03410
\(487\) −15208.3 −1.41510 −0.707548 0.706665i \(-0.750199\pi\)
−0.707548 + 0.706665i \(0.750199\pi\)
\(488\) −47214.3 −4.37969
\(489\) 24083.7 2.22721
\(490\) 684.380 0.0630962
\(491\) 10064.5 0.925059 0.462530 0.886604i \(-0.346942\pi\)
0.462530 + 0.886604i \(0.346942\pi\)
\(492\) 2346.35 0.215004
\(493\) −16031.3 −1.46453
\(494\) 20882.8 1.90194
\(495\) 8878.08 0.806141
\(496\) 13135.5 1.18912
\(497\) −8768.64 −0.791403
\(498\) 12385.2 1.11444
\(499\) −179.798 −0.0161300 −0.00806501 0.999967i \(-0.502567\pi\)
−0.00806501 + 0.999967i \(0.502567\pi\)
\(500\) 25808.6 2.30839
\(501\) 14821.7 1.32172
\(502\) 7734.03 0.687623
\(503\) 4805.81 0.426005 0.213002 0.977052i \(-0.431676\pi\)
0.213002 + 0.977052i \(0.431676\pi\)
\(504\) −20103.8 −1.77678
\(505\) −7750.16 −0.682926
\(506\) −34004.6 −2.98753
\(507\) −861.241 −0.0754420
\(508\) 1447.94 0.126460
\(509\) 18265.8 1.59060 0.795302 0.606213i \(-0.207312\pi\)
0.795302 + 0.606213i \(0.207312\pi\)
\(510\) 41881.3 3.63634
\(511\) 21000.1 1.81798
\(512\) −7731.58 −0.667364
\(513\) 5956.79 0.512668
\(514\) 22356.9 1.91852
\(515\) −3347.85 −0.286455
\(516\) 0 0
\(517\) −18252.3 −1.55268
\(518\) 1326.52 0.112517
\(519\) −9444.58 −0.798788
\(520\) 36679.8 3.09330
\(521\) −10272.0 −0.863772 −0.431886 0.901928i \(-0.642152\pi\)
−0.431886 + 0.901928i \(0.642152\pi\)
\(522\) 14344.7 1.20278
\(523\) 3569.87 0.298470 0.149235 0.988802i \(-0.452319\pi\)
0.149235 + 0.988802i \(0.452319\pi\)
\(524\) 5678.69 0.473425
\(525\) −2502.54 −0.208038
\(526\) 6972.68 0.577991
\(527\) −6712.53 −0.554843
\(528\) −56629.7 −4.66759
\(529\) 8261.91 0.679043
\(530\) 10428.8 0.854712
\(531\) −6607.18 −0.539976
\(532\) 32175.1 2.62212
\(533\) −788.316 −0.0640633
\(534\) −4135.24 −0.335111
\(535\) −9625.09 −0.777811
\(536\) 22321.0 1.79873
\(537\) 26140.7 2.10066
\(538\) −6646.73 −0.532641
\(539\) 472.890 0.0377900
\(540\) 17151.7 1.36683
\(541\) 23215.7 1.84496 0.922478 0.386050i \(-0.126161\pi\)
0.922478 + 0.386050i \(0.126161\pi\)
\(542\) 10622.1 0.841806
\(543\) −6899.60 −0.545286
\(544\) −48693.4 −3.83771
\(545\) −8128.57 −0.638880
\(546\) 29188.6 2.28784
\(547\) −5631.22 −0.440171 −0.220086 0.975481i \(-0.570634\pi\)
−0.220086 + 0.975481i \(0.570634\pi\)
\(548\) −11260.3 −0.877763
\(549\) −11659.7 −0.906419
\(550\) −4951.32 −0.383863
\(551\) −14004.9 −1.08281
\(552\) 62993.9 4.85724
\(553\) 4571.38 0.351528
\(554\) 6272.81 0.481058
\(555\) 1085.21 0.0829992
\(556\) −29327.7 −2.23700
\(557\) −23630.2 −1.79756 −0.898782 0.438397i \(-0.855547\pi\)
−0.898782 + 0.438397i \(0.855547\pi\)
\(558\) 6006.34 0.455678
\(559\) 0 0
\(560\) 42424.8 3.20138
\(561\) 28938.9 2.17790
\(562\) −8072.42 −0.605898
\(563\) −10592.6 −0.792942 −0.396471 0.918047i \(-0.629765\pi\)
−0.396471 + 0.918047i \(0.629765\pi\)
\(564\) 55428.6 4.13824
\(565\) −14892.5 −1.10891
\(566\) 31610.7 2.34752
\(567\) 16449.1 1.21834
\(568\) 32139.0 2.37416
\(569\) 5540.16 0.408182 0.204091 0.978952i \(-0.434576\pi\)
0.204091 + 0.978952i \(0.434576\pi\)
\(570\) 36587.2 2.68854
\(571\) 4608.09 0.337728 0.168864 0.985639i \(-0.445990\pi\)
0.168864 + 0.985639i \(0.445990\pi\)
\(572\) 41547.5 3.03704
\(573\) 5217.17 0.380367
\(574\) −1688.27 −0.122765
\(575\) 2974.59 0.215738
\(576\) 18129.9 1.31148
\(577\) −6911.91 −0.498694 −0.249347 0.968414i \(-0.580216\pi\)
−0.249347 + 0.968414i \(0.580216\pi\)
\(578\) 25551.1 1.83873
\(579\) −2079.83 −0.149283
\(580\) −40324.8 −2.88689
\(581\) −6411.22 −0.457801
\(582\) −21467.7 −1.52898
\(583\) 7206.04 0.511910
\(584\) −76969.9 −5.45383
\(585\) 9058.19 0.640188
\(586\) −29967.8 −2.11256
\(587\) 2894.60 0.203531 0.101766 0.994808i \(-0.467551\pi\)
0.101766 + 0.994808i \(0.467551\pi\)
\(588\) −1436.07 −0.100719
\(589\) −5864.02 −0.410226
\(590\) 25816.9 1.80147
\(591\) −34527.7 −2.40318
\(592\) −2625.82 −0.182298
\(593\) 284.980 0.0197348 0.00986738 0.999951i \(-0.496859\pi\)
0.00986738 + 0.999951i \(0.496859\pi\)
\(594\) 16473.2 1.13788
\(595\) −21680.0 −1.49377
\(596\) −33565.2 −2.30685
\(597\) −8571.81 −0.587639
\(598\) −34694.5 −2.37251
\(599\) −17636.8 −1.20304 −0.601521 0.798857i \(-0.705438\pi\)
−0.601521 + 0.798857i \(0.705438\pi\)
\(600\) 9172.35 0.624099
\(601\) 8368.50 0.567984 0.283992 0.958827i \(-0.408341\pi\)
0.283992 + 0.958827i \(0.408341\pi\)
\(602\) 0 0
\(603\) 5512.23 0.372265
\(604\) 56053.3 3.77612
\(605\) −7897.99 −0.530742
\(606\) 22604.6 1.51527
\(607\) −17771.6 −1.18835 −0.594175 0.804336i \(-0.702521\pi\)
−0.594175 + 0.804336i \(0.702521\pi\)
\(608\) −42538.2 −2.83742
\(609\) −19575.1 −1.30250
\(610\) 45559.2 3.02400
\(611\) −18622.6 −1.23305
\(612\) −33336.9 −2.20190
\(613\) −15578.5 −1.02645 −0.513223 0.858255i \(-0.671549\pi\)
−0.513223 + 0.858255i \(0.671549\pi\)
\(614\) −26788.5 −1.76074
\(615\) −1381.15 −0.0905584
\(616\) 54278.8 3.55025
\(617\) 17840.6 1.16407 0.582037 0.813162i \(-0.302256\pi\)
0.582037 + 0.813162i \(0.302256\pi\)
\(618\) 9764.58 0.635581
\(619\) −9101.50 −0.590986 −0.295493 0.955345i \(-0.595484\pi\)
−0.295493 + 0.955345i \(0.595484\pi\)
\(620\) −16884.6 −1.09371
\(621\) −9896.58 −0.639510
\(622\) 5880.94 0.379106
\(623\) 2140.62 0.137660
\(624\) −57778.5 −3.70672
\(625\) −17793.3 −1.13877
\(626\) −37308.4 −2.38202
\(627\) 25280.9 1.61024
\(628\) −44743.6 −2.84309
\(629\) 1341.85 0.0850604
\(630\) 19399.1 1.22679
\(631\) 25799.9 1.62770 0.813850 0.581075i \(-0.197368\pi\)
0.813850 + 0.581075i \(0.197368\pi\)
\(632\) −16755.1 −1.05456
\(633\) −37991.5 −2.38551
\(634\) 45805.3 2.86934
\(635\) −852.308 −0.0532643
\(636\) −21883.3 −1.36435
\(637\) 482.484 0.0300105
\(638\) −38729.7 −2.40333
\(639\) 7936.82 0.491355
\(640\) −23075.5 −1.42521
\(641\) 17234.5 1.06197 0.530984 0.847382i \(-0.321822\pi\)
0.530984 + 0.847382i \(0.321822\pi\)
\(642\) 28073.2 1.72579
\(643\) 1598.30 0.0980263 0.0490131 0.998798i \(-0.484392\pi\)
0.0490131 + 0.998798i \(0.484392\pi\)
\(644\) −53455.5 −3.27087
\(645\) 0 0
\(646\) 45239.7 2.75531
\(647\) −15691.0 −0.953443 −0.476722 0.879054i \(-0.658175\pi\)
−0.476722 + 0.879054i \(0.658175\pi\)
\(648\) −60289.6 −3.65494
\(649\) 17838.9 1.07895
\(650\) −5051.76 −0.304841
\(651\) −8196.37 −0.493458
\(652\) 74906.2 4.49932
\(653\) 27692.4 1.65955 0.829776 0.558097i \(-0.188468\pi\)
0.829776 + 0.558097i \(0.188468\pi\)
\(654\) 23708.3 1.41754
\(655\) −3342.69 −0.199404
\(656\) 3341.90 0.198901
\(657\) −19007.9 −1.12872
\(658\) −39882.4 −2.36288
\(659\) −7256.63 −0.428950 −0.214475 0.976729i \(-0.568804\pi\)
−0.214475 + 0.976729i \(0.568804\pi\)
\(660\) 72792.4 4.29309
\(661\) 9023.69 0.530985 0.265492 0.964113i \(-0.414465\pi\)
0.265492 + 0.964113i \(0.414465\pi\)
\(662\) −7496.69 −0.440131
\(663\) 29526.0 1.72956
\(664\) 23498.5 1.37337
\(665\) −18939.5 −1.10442
\(666\) −1200.68 −0.0698579
\(667\) 23267.6 1.35071
\(668\) 46099.0 2.67010
\(669\) −22821.6 −1.31888
\(670\) −21538.5 −1.24195
\(671\) 31480.3 1.81115
\(672\) −59457.3 −3.41312
\(673\) −7238.86 −0.414617 −0.207309 0.978276i \(-0.566470\pi\)
−0.207309 + 0.978276i \(0.566470\pi\)
\(674\) −49789.3 −2.84542
\(675\) −1441.01 −0.0821697
\(676\) −2678.67 −0.152405
\(677\) −16437.0 −0.933122 −0.466561 0.884489i \(-0.654507\pi\)
−0.466561 + 0.884489i \(0.654507\pi\)
\(678\) 43436.5 2.46043
\(679\) 11112.8 0.628086
\(680\) 79461.7 4.48120
\(681\) −44369.6 −2.49669
\(682\) −16216.7 −0.910510
\(683\) −16644.8 −0.932498 −0.466249 0.884654i \(-0.654395\pi\)
−0.466249 + 0.884654i \(0.654395\pi\)
\(684\) −29122.9 −1.62798
\(685\) 6628.20 0.369709
\(686\) 34425.4 1.91599
\(687\) 20323.7 1.12867
\(688\) 0 0
\(689\) 7352.23 0.406528
\(690\) −60785.7 −3.35373
\(691\) 20899.8 1.15060 0.575301 0.817942i \(-0.304885\pi\)
0.575301 + 0.817942i \(0.304885\pi\)
\(692\) −29374.9 −1.61368
\(693\) 13404.3 0.734758
\(694\) 43088.0 2.35677
\(695\) 17263.4 0.942213
\(696\) 71747.0 3.90742
\(697\) −1707.78 −0.0928074
\(698\) 9553.65 0.518067
\(699\) −33643.1 −1.82046
\(700\) −7783.50 −0.420269
\(701\) −31205.4 −1.68133 −0.840664 0.541557i \(-0.817835\pi\)
−0.840664 + 0.541557i \(0.817835\pi\)
\(702\) 16807.4 0.903638
\(703\) 1172.23 0.0628898
\(704\) −48949.5 −2.62053
\(705\) −32627.4 −1.74300
\(706\) 58677.2 3.12797
\(707\) −11701.4 −0.622454
\(708\) −54173.0 −2.87563
\(709\) 17422.0 0.922845 0.461422 0.887181i \(-0.347339\pi\)
0.461422 + 0.887181i \(0.347339\pi\)
\(710\) −31012.4 −1.63926
\(711\) −4137.73 −0.218252
\(712\) −7845.83 −0.412970
\(713\) 9742.45 0.511722
\(714\) 63233.2 3.31435
\(715\) −24456.4 −1.27919
\(716\) 81303.8 4.24367
\(717\) −43755.6 −2.27906
\(718\) −38706.9 −2.01188
\(719\) −9699.27 −0.503090 −0.251545 0.967846i \(-0.580939\pi\)
−0.251545 + 0.967846i \(0.580939\pi\)
\(720\) −38400.2 −1.98763
\(721\) −5054.66 −0.261089
\(722\) 2895.11 0.149231
\(723\) 9946.94 0.511661
\(724\) −21459.4 −1.10157
\(725\) 3387.92 0.173551
\(726\) 23035.8 1.17760
\(727\) −13700.6 −0.698939 −0.349470 0.936948i \(-0.613638\pi\)
−0.349470 + 0.936948i \(0.613638\pi\)
\(728\) 55379.9 2.81939
\(729\) −2558.21 −0.129970
\(730\) 74271.8 3.76565
\(731\) 0 0
\(732\) −95599.3 −4.82712
\(733\) 25874.9 1.30384 0.651918 0.758289i \(-0.273965\pi\)
0.651918 + 0.758289i \(0.273965\pi\)
\(734\) −36100.6 −1.81539
\(735\) 845.325 0.0424221
\(736\) 70672.7 3.53944
\(737\) −14882.6 −0.743837
\(738\) 1528.11 0.0762203
\(739\) 9153.21 0.455624 0.227812 0.973705i \(-0.426843\pi\)
0.227812 + 0.973705i \(0.426843\pi\)
\(740\) 3375.26 0.167672
\(741\) 25793.7 1.27875
\(742\) 15745.6 0.779028
\(743\) 19565.2 0.966052 0.483026 0.875606i \(-0.339538\pi\)
0.483026 + 0.875606i \(0.339538\pi\)
\(744\) 30041.5 1.48034
\(745\) 19757.7 0.971632
\(746\) 14779.9 0.725376
\(747\) 5803.03 0.284233
\(748\) 90007.0 4.39971
\(749\) −14532.2 −0.708937
\(750\) 44309.6 2.15728
\(751\) 24252.8 1.17842 0.589212 0.807978i \(-0.299438\pi\)
0.589212 + 0.807978i \(0.299438\pi\)
\(752\) 78946.6 3.82831
\(753\) 9552.83 0.462317
\(754\) −39515.4 −1.90857
\(755\) −32995.1 −1.59048
\(756\) 25896.0 1.24580
\(757\) −38026.1 −1.82573 −0.912867 0.408257i \(-0.866137\pi\)
−0.912867 + 0.408257i \(0.866137\pi\)
\(758\) 49011.0 2.34849
\(759\) −42001.5 −2.00864
\(760\) 69417.3 3.31320
\(761\) 7521.42 0.358280 0.179140 0.983824i \(-0.442668\pi\)
0.179140 + 0.983824i \(0.442668\pi\)
\(762\) 2485.90 0.118182
\(763\) −12272.7 −0.582308
\(764\) 16226.6 0.768403
\(765\) 19623.3 0.927428
\(766\) 35204.0 1.66054
\(767\) 18200.8 0.856834
\(768\) 9333.17 0.438518
\(769\) 21632.7 1.01443 0.507213 0.861821i \(-0.330676\pi\)
0.507213 + 0.861821i \(0.330676\pi\)
\(770\) −52376.1 −2.45130
\(771\) 27614.5 1.28990
\(772\) −6468.78 −0.301576
\(773\) −4537.97 −0.211151 −0.105575 0.994411i \(-0.533668\pi\)
−0.105575 + 0.994411i \(0.533668\pi\)
\(774\) 0 0
\(775\) 1418.57 0.0657503
\(776\) −40730.8 −1.88422
\(777\) 1638.47 0.0756497
\(778\) −66176.7 −3.04955
\(779\) −1491.90 −0.0686175
\(780\) 74269.1 3.40931
\(781\) −21428.8 −0.981797
\(782\) −75160.9 −3.43702
\(783\) −11271.7 −0.514456
\(784\) −2045.39 −0.0931754
\(785\) 26337.7 1.19749
\(786\) 9749.51 0.442434
\(787\) 33633.9 1.52340 0.761702 0.647928i \(-0.224364\pi\)
0.761702 + 0.647928i \(0.224364\pi\)
\(788\) −107389. −4.85481
\(789\) 8612.43 0.388607
\(790\) 16167.8 0.728131
\(791\) −22485.0 −1.01072
\(792\) −49129.7 −2.20423
\(793\) 32119.0 1.43831
\(794\) −30981.8 −1.38477
\(795\) 12881.3 0.574657
\(796\) −26660.4 −1.18713
\(797\) −15416.5 −0.685172 −0.342586 0.939487i \(-0.611303\pi\)
−0.342586 + 0.939487i \(0.611303\pi\)
\(798\) 55240.1 2.45047
\(799\) −40343.4 −1.78629
\(800\) 10290.4 0.454778
\(801\) −1937.55 −0.0854682
\(802\) −61915.6 −2.72608
\(803\) 51320.0 2.25535
\(804\) 45195.5 1.98249
\(805\) 31465.9 1.37767
\(806\) −16545.6 −0.723071
\(807\) −8209.83 −0.358116
\(808\) 42888.0 1.86732
\(809\) 16077.3 0.698698 0.349349 0.936993i \(-0.386403\pi\)
0.349349 + 0.936993i \(0.386403\pi\)
\(810\) 58176.2 2.52359
\(811\) 34451.1 1.49167 0.745833 0.666133i \(-0.232052\pi\)
0.745833 + 0.666133i \(0.232052\pi\)
\(812\) −60883.3 −2.63126
\(813\) 13120.1 0.565980
\(814\) 3241.74 0.139586
\(815\) −44092.6 −1.89509
\(816\) −125169. −5.36985
\(817\) 0 0
\(818\) 34232.2 1.46320
\(819\) 13676.2 0.583500
\(820\) −4295.71 −0.182942
\(821\) −21764.4 −0.925194 −0.462597 0.886569i \(-0.653082\pi\)
−0.462597 + 0.886569i \(0.653082\pi\)
\(822\) −19332.3 −0.820304
\(823\) 30308.2 1.28369 0.641845 0.766834i \(-0.278169\pi\)
0.641845 + 0.766834i \(0.278169\pi\)
\(824\) 18526.4 0.783251
\(825\) −6115.71 −0.258087
\(826\) 38978.9 1.64195
\(827\) 17936.3 0.754179 0.377089 0.926177i \(-0.376925\pi\)
0.377089 + 0.926177i \(0.376925\pi\)
\(828\) 48384.5 2.03077
\(829\) 19426.9 0.813900 0.406950 0.913450i \(-0.366592\pi\)
0.406950 + 0.913450i \(0.366592\pi\)
\(830\) −22674.8 −0.948257
\(831\) 7747.98 0.323435
\(832\) −49942.5 −2.08106
\(833\) 1045.23 0.0434757
\(834\) −50351.6 −2.09057
\(835\) −27135.6 −1.12463
\(836\) 78629.6 3.25294
\(837\) −4719.63 −0.194904
\(838\) 68479.5 2.82289
\(839\) 33848.2 1.39281 0.696407 0.717648i \(-0.254781\pi\)
0.696407 + 0.717648i \(0.254781\pi\)
\(840\) 97027.1 3.98542
\(841\) 2111.65 0.0865821
\(842\) 6322.55 0.258776
\(843\) −9970.80 −0.407370
\(844\) −118163. −4.81911
\(845\) 1576.76 0.0641921
\(846\) 36099.0 1.46703
\(847\) −11924.5 −0.483745
\(848\) −31168.2 −1.26217
\(849\) 39044.5 1.57833
\(850\) −10944.0 −0.441617
\(851\) −1947.54 −0.0784496
\(852\) 65074.9 2.61670
\(853\) 41193.8 1.65352 0.826759 0.562557i \(-0.190182\pi\)
0.826759 + 0.562557i \(0.190182\pi\)
\(854\) 68786.3 2.75623
\(855\) 17142.8 0.685698
\(856\) 53263.6 2.12676
\(857\) −44688.6 −1.78125 −0.890625 0.454738i \(-0.849733\pi\)
−0.890625 + 0.454738i \(0.849733\pi\)
\(858\) 71331.2 2.83824
\(859\) −41271.3 −1.63930 −0.819650 0.572865i \(-0.805832\pi\)
−0.819650 + 0.572865i \(0.805832\pi\)
\(860\) 0 0
\(861\) −2085.29 −0.0825395
\(862\) −30266.2 −1.19591
\(863\) −13944.1 −0.550014 −0.275007 0.961442i \(-0.588680\pi\)
−0.275007 + 0.961442i \(0.588680\pi\)
\(864\) −34236.7 −1.34810
\(865\) 17291.2 0.679673
\(866\) −35366.0 −1.38774
\(867\) 31559.9 1.23625
\(868\) −25492.7 −0.996864
\(869\) 11171.5 0.436097
\(870\) −69232.0 −2.69791
\(871\) −15184.5 −0.590710
\(872\) 44982.1 1.74689
\(873\) −10058.6 −0.389957
\(874\) −65660.0 −2.54117
\(875\) −22937.0 −0.886186
\(876\) −155848. −6.01099
\(877\) −1539.42 −0.0592731 −0.0296366 0.999561i \(-0.509435\pi\)
−0.0296366 + 0.999561i \(0.509435\pi\)
\(878\) −30542.8 −1.17400
\(879\) −37015.3 −1.42036
\(880\) 103678. 3.97156
\(881\) −30429.5 −1.16367 −0.581837 0.813306i \(-0.697666\pi\)
−0.581837 + 0.813306i \(0.697666\pi\)
\(882\) −935.270 −0.0357054
\(883\) 41762.4 1.59164 0.795819 0.605535i \(-0.207041\pi\)
0.795819 + 0.605535i \(0.207041\pi\)
\(884\) 91833.0 3.49398
\(885\) 31888.2 1.21120
\(886\) 48500.6 1.83906
\(887\) 34349.7 1.30028 0.650140 0.759814i \(-0.274710\pi\)
0.650140 + 0.759814i \(0.274710\pi\)
\(888\) −6005.35 −0.226944
\(889\) −1286.83 −0.0485478
\(890\) 7570.80 0.285139
\(891\) 40198.4 1.51144
\(892\) −70980.6 −2.66436
\(893\) −35243.7 −1.32070
\(894\) −57626.6 −2.15584
\(895\) −47858.5 −1.78741
\(896\) −34839.8 −1.29901
\(897\) −42853.5 −1.59514
\(898\) −26548.1 −0.986548
\(899\) 11096.2 0.411656
\(900\) 7045.13 0.260931
\(901\) 15927.6 0.588929
\(902\) −4125.78 −0.152299
\(903\) 0 0
\(904\) 82412.5 3.03208
\(905\) 12631.8 0.463973
\(906\) 96235.6 3.52893
\(907\) 1799.82 0.0658897 0.0329449 0.999457i \(-0.489511\pi\)
0.0329449 + 0.999457i \(0.489511\pi\)
\(908\) −138000. −5.04372
\(909\) 10591.3 0.386460
\(910\) −53438.6 −1.94667
\(911\) −16614.8 −0.604250 −0.302125 0.953268i \(-0.597696\pi\)
−0.302125 + 0.953268i \(0.597696\pi\)
\(912\) −109347. −3.97022
\(913\) −15667.7 −0.567937
\(914\) 69086.6 2.50020
\(915\) 56273.3 2.03316
\(916\) 63211.5 2.28010
\(917\) −5046.86 −0.181747
\(918\) 36410.9 1.30908
\(919\) −27368.9 −0.982389 −0.491194 0.871050i \(-0.663440\pi\)
−0.491194 + 0.871050i \(0.663440\pi\)
\(920\) −115329. −4.13293
\(921\) −33088.3 −1.18382
\(922\) −58258.2 −2.08094
\(923\) −21863.5 −0.779683
\(924\) 109904. 3.91294
\(925\) −283.575 −0.0100799
\(926\) −31242.5 −1.10874
\(927\) 4575.16 0.162101
\(928\) 80492.9 2.84731
\(929\) −33945.3 −1.19883 −0.599413 0.800440i \(-0.704599\pi\)
−0.599413 + 0.800440i \(0.704599\pi\)
\(930\) −28988.4 −1.02212
\(931\) 913.110 0.0321439
\(932\) −104638. −3.67762
\(933\) 7263.95 0.254889
\(934\) −85915.8 −3.00991
\(935\) −52981.5 −1.85313
\(936\) −50126.4 −1.75046
\(937\) −27.3495 −0.000953542 0 −0.000476771 1.00000i \(-0.500152\pi\)
−0.000476771 1.00000i \(0.500152\pi\)
\(938\) −32519.3 −1.13198
\(939\) −46082.2 −1.60153
\(940\) −101479. −3.52115
\(941\) −30082.0 −1.04213 −0.521066 0.853517i \(-0.674465\pi\)
−0.521066 + 0.853517i \(0.674465\pi\)
\(942\) −76818.3 −2.65698
\(943\) 2478.64 0.0855945
\(944\) −77158.3 −2.66026
\(945\) −15243.3 −0.524725
\(946\) 0 0
\(947\) −9281.65 −0.318493 −0.159247 0.987239i \(-0.550907\pi\)
−0.159247 + 0.987239i \(0.550907\pi\)
\(948\) −33925.7 −1.16229
\(949\) 52361.1 1.79106
\(950\) −9560.57 −0.326511
\(951\) 56577.2 1.92917
\(952\) 119973. 4.08440
\(953\) −32201.2 −1.09454 −0.547271 0.836956i \(-0.684333\pi\)
−0.547271 + 0.836956i \(0.684333\pi\)
\(954\) −14251.9 −0.483672
\(955\) −9551.61 −0.323647
\(956\) −136091. −4.60406
\(957\) −47837.7 −1.61585
\(958\) −30102.2 −1.01520
\(959\) 10007.4 0.336972
\(960\) −87500.6 −2.94174
\(961\) −25144.9 −0.844043
\(962\) 3307.51 0.110851
\(963\) 13153.6 0.440155
\(964\) 30937.4 1.03364
\(965\) 3807.76 0.127022
\(966\) −91775.5 −3.05676
\(967\) −45786.9 −1.52266 −0.761328 0.648367i \(-0.775452\pi\)
−0.761328 + 0.648367i \(0.775452\pi\)
\(968\) 43706.1 1.45120
\(969\) 55878.6 1.85251
\(970\) 39303.1 1.30097
\(971\) 13807.1 0.456326 0.228163 0.973623i \(-0.426728\pi\)
0.228163 + 0.973623i \(0.426728\pi\)
\(972\) −83723.4 −2.76279
\(973\) 26064.6 0.858781
\(974\) −81209.7 −2.67159
\(975\) −6239.78 −0.204957
\(976\) −136161. −4.46560
\(977\) −19774.4 −0.647532 −0.323766 0.946137i \(-0.604949\pi\)
−0.323766 + 0.946137i \(0.604949\pi\)
\(978\) 128603. 4.20479
\(979\) 5231.24 0.170778
\(980\) 2629.16 0.0856995
\(981\) 11108.5 0.361535
\(982\) 53742.8 1.74644
\(983\) 51283.2 1.66397 0.831984 0.554800i \(-0.187205\pi\)
0.831984 + 0.554800i \(0.187205\pi\)
\(984\) 7643.05 0.247613
\(985\) 63213.4 2.04482
\(986\) −85604.7 −2.76492
\(987\) −49261.5 −1.58866
\(988\) 80224.7 2.58329
\(989\) 0 0
\(990\) 47407.5 1.52193
\(991\) 19490.1 0.624746 0.312373 0.949960i \(-0.398876\pi\)
0.312373 + 0.949960i \(0.398876\pi\)
\(992\) 33703.5 1.07872
\(993\) −9259.67 −0.295918
\(994\) −46823.2 −1.49411
\(995\) 15693.3 0.500011
\(996\) 47579.7 1.51368
\(997\) −6503.90 −0.206600 −0.103300 0.994650i \(-0.532940\pi\)
−0.103300 + 0.994650i \(0.532940\pi\)
\(998\) −960.095 −0.0304522
\(999\) 943.463 0.0298797
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.j.1.48 yes 50
43.42 odd 2 1849.4.a.i.1.3 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.i.1.3 50 43.42 odd 2
1849.4.a.j.1.48 yes 50 1.1 even 1 trivial