Properties

Label 1849.4.a.i.1.3
Level $1849$
Weight $4$
Character 1849.1
Self dual yes
Analytic conductor $109.095$
Analytic rank $1$
Dimension $50$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

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 1.3
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 \(-0.892931\pi\)
−0.943960 + 0.330061i \(0.892931\pi\)
\(3\) −6.59560 −1.26932 −0.634662 0.772790i \(-0.718861\pi\)
−0.634662 + 0.772790i \(0.718861\pi\)
\(4\) 20.5139 2.56424
\(5\) 12.0752 1.08004 0.540021 0.841651i \(-0.318416\pi\)
0.540021 + 0.841651i \(0.318416\pi\)
\(6\) 35.2195 2.39638
\(7\) 18.2315 0.984406 0.492203 0.870480i \(-0.336192\pi\)
0.492203 + 0.870480i \(0.336192\pi\)
\(8\) −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 \(-0.326161\pi\)
0.519386 + 0.854540i \(0.326161\pi\)
\(20\) 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 \(-0.674514\pi\)
−0.521196 + 0.853437i \(0.674514\pi\)
\(30\) 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 \(-0.490363\pi\)
0.0302712 + 0.999542i \(0.490363\pi\)
\(38\) −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 \(-0.234102\pi\)
0.741528 + 0.670922i \(0.234102\pi\)
\(62\) −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 \(-0.631674\pi\)
−0.401970 + 0.915653i \(0.631674\pi\)
\(72\) −1102.70 −1.80492
\(73\) 1151.86 1.84678 0.923390 0.383863i \(-0.125407\pi\)
0.923390 + 0.383863i \(0.125407\pi\)
\(74\) −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 \(-0.477726\pi\)
0.0699202 + 0.997553i \(0.477726\pi\)
\(90\) −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 \(-0.671600\pi\)
−0.513363 + 0.858172i \(0.671600\pi\)
\(114\) 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 \(-0.529426\pi\)
−0.0923130 + 0.995730i \(0.529426\pi\)
\(132\) 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 \(-0.445250\pi\)
0.171155 + 0.985244i \(0.445250\pi\)
\(138\) 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 \(-0.351491\pi\)
0.449812 + 0.893123i \(0.351491\pi\)
\(150\) 732.973 0.398980
\(151\) −2732.46 −1.47261 −0.736305 0.676650i \(-0.763431\pi\)
−0.736305 + 0.676650i \(0.763431\pi\)
\(152\) −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 \(-0.312958\pi\)
0.554374 + 0.832268i \(0.312958\pi\)
\(158\) 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 \(-0.840671\pi\)
−0.877320 + 0.479905i \(0.840671\pi\)
\(164\) 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 \(-0.810222\pi\)
−0.827472 + 0.561507i \(0.810222\pi\)
\(180\) 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 \(-0.547873\pi\)
−0.149831 + 0.988712i \(0.547873\pi\)
\(192\) −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 \(-0.425644\pi\)
0.231477 + 0.972840i \(0.425644\pi\)
\(200\) −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 \(-0.111126\pi\)
0.939676 + 0.342065i \(0.111126\pi\)
\(212\) −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 \(-0.326110\pi\)
0.519522 + 0.854457i \(0.326110\pi\)
\(224\) −9014.69 −2.68892
\(225\) 343.432 0.101758
\(226\) 6585.68 1.93837
\(227\) 6727.15 1.96695 0.983473 0.181057i \(-0.0579517\pi\)
0.983473 + 0.181057i \(0.0579517\pi\)
\(228\) −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 \(-0.245470\pi\)
0.717097 + 0.696973i \(0.245470\pi\)
\(234\) 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 \(-0.564597\pi\)
−0.201548 + 0.979479i \(0.564597\pi\)
\(242\) −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 \(-0.669654\pi\)
−0.508105 + 0.861295i \(0.669654\pi\)
\(258\) 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 \(-0.548918\pi\)
−0.153076 + 0.988214i \(0.548918\pi\)
\(264\) −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 \(-0.540665\pi\)
−0.127404 + 0.991851i \(0.540665\pi\)
\(278\) 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 \(-0.282703\pi\)
0.630859 + 0.775898i \(0.282703\pi\)
\(314\) −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 \(-0.462812\pi\)
0.116565 + 0.993183i \(0.462812\pi\)
\(332\) 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 \(-0.714563\pi\)
−0.624171 + 0.781287i \(0.714563\pi\)
\(348\) 22025.8 3.39283
\(349\) −1789.13 −0.274412 −0.137206 0.990543i \(-0.543812\pi\)
−0.137206 + 0.990543i \(0.543812\pi\)
\(350\) −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 \(-0.561533\pi\)
−0.192110 + 0.981373i \(0.561533\pi\)
\(374\) −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 \(-0.644943\pi\)
−0.439780 + 0.898106i \(0.644943\pi\)
\(384\) 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 \(-0.200740\pi\)
0.807648 + 0.589665i \(0.200740\pi\)
\(390\) −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 \(-0.626667\pi\)
−0.387517 + 0.921862i \(0.626667\pi\)
\(410\) −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 \(-0.768804\pi\)
−0.747620 + 0.664127i \(0.768804\pi\)
\(420\) −29786.6 −3.46056
\(421\) −1184.03 −0.137069 −0.0685347 0.997649i \(-0.521832\pi\)
−0.0685347 + 0.997649i \(0.521832\pi\)
\(422\) −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 \(-0.380203\pi\)
0.367532 + 0.930011i \(0.380203\pi\)
\(434\) −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 \(-0.415856\pi\)
0.261279 + 0.965263i \(0.415856\pi\)
\(450\) −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 \(-0.730359\pi\)
−0.662158 + 0.749365i \(0.730359\pi\)
\(458\) −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 \(-0.405133\pi\)
0.293641 + 0.955916i \(0.405133\pi\)
\(464\) −31371.1 −3.13873
\(465\) −5428.70 −0.541398
\(466\) −27237.7 −2.70764
\(467\) 16089.6 1.59430 0.797149 0.603782i \(-0.206340\pi\)
0.797149 + 0.603782i \(0.206340\pi\)
\(468\) −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 \(-0.653058\pi\)
−0.462530 + 0.886604i \(0.653058\pi\)
\(492\) −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 \(-0.497433\pi\)
0.00806501 + 0.999967i \(0.497433\pi\)
\(500\) −25808.6 −2.30839
\(501\) −14821.7 −1.32172
\(502\) −7734.03 −0.687623
\(503\) −4805.81 −0.426005 −0.213002 0.977052i \(-0.568324\pi\)
−0.213002 + 0.977052i \(0.568324\pi\)
\(504\) −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 \(-0.357848\pi\)
0.431886 + 0.901928i \(0.357848\pi\)
\(522\) 14344.7 1.20278
\(523\) −3569.87 −0.298470 −0.149235 0.988802i \(-0.547681\pi\)
−0.149235 + 0.988802i \(0.547681\pi\)
\(524\) −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 \(-0.554010\pi\)
−0.168864 + 0.985639i \(0.554010\pi\)
\(572\) 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 \(-0.419784\pi\)
0.249347 + 0.968414i \(0.419784\pi\)
\(578\) −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 \(-0.532449\pi\)
−0.101766 + 0.994808i \(0.532449\pi\)
\(588\) 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 \(-0.503141\pi\)
−0.00986738 + 0.999951i \(0.503141\pi\)
\(594\) 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 \(-0.591659\pi\)
−0.283992 + 0.958827i \(0.591659\pi\)
\(602\) 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 \(-0.297479\pi\)
0.594175 + 0.804336i \(0.297479\pi\)
\(608\) −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 \(-0.802632\pi\)
−0.813850 + 0.581075i \(0.802632\pi\)
\(632\) 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 \(-0.678178\pi\)
−0.530984 + 0.847382i \(0.678178\pi\)
\(642\) 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 \(-0.341825\pi\)
0.476722 + 0.879054i \(0.341825\pi\)
\(648\) 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 \(-0.811532\pi\)
−0.829776 + 0.558097i \(0.811532\pi\)
\(654\) 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 \(-0.433530\pi\)
0.207309 + 0.978276i \(0.433530\pi\)
\(674\) 49789.3 2.84542
\(675\) 1441.01 0.0821697
\(676\) −2678.67 −0.152405
\(677\) 16437.0 0.933122 0.466561 0.884489i \(-0.345493\pi\)
0.466561 + 0.884489i \(0.345493\pi\)
\(678\) −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 \(-0.695115\pi\)
−0.575301 + 0.817942i \(0.695115\pi\)
\(692\) −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 \(-0.386362\pi\)
0.349470 + 0.936948i \(0.386362\pi\)
\(728\) 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 \(-0.726035\pi\)
−0.651918 + 0.758289i \(0.726035\pi\)
\(734\) 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 \(-0.573157\pi\)
−0.227812 + 0.973705i \(0.573157\pi\)
\(740\) 3375.26 0.167672
\(741\) 25793.7 1.27875
\(742\) 15745.6 0.779028
\(743\) −19565.2 −0.966052 −0.483026 0.875606i \(-0.660462\pi\)
−0.483026 + 0.875606i \(0.660462\pi\)
\(744\) 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 \(-0.700562\pi\)
−0.589212 + 0.807978i \(0.700562\pi\)
\(752\) 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 \(-0.133863\pi\)
0.912867 + 0.408257i \(0.133863\pi\)
\(758\) −49011.0 −2.34849
\(759\) 42001.5 2.00864
\(760\) −69417.3 −3.31320
\(761\) −7521.42 −0.358280 −0.179140 0.983824i \(-0.557332\pi\)
−0.179140 + 0.983824i \(0.557332\pi\)
\(762\) 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 \(-0.466332\pi\)
0.105575 + 0.994411i \(0.466332\pi\)
\(774\) 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 \(-0.767948\pi\)
−0.745833 + 0.666133i \(0.767948\pi\)
\(812\) −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 \(-0.633408\pi\)
−0.406950 + 0.913450i \(0.633408\pi\)
\(830\) −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 \(-0.745219\pi\)
−0.696407 + 0.717648i \(0.745219\pi\)
\(840\) 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 \(-0.194168\pi\)
0.819650 + 0.572865i \(0.194168\pi\)
\(860\) 0 0
\(861\) −2085.29 −0.0825395
\(862\) 30266.2 1.19591
\(863\) 13944.1 0.550014 0.275007 0.961442i \(-0.411320\pi\)
0.275007 + 0.961442i \(0.411320\pi\)
\(864\) −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 \(-0.725290\pi\)
−0.650140 + 0.759814i \(0.725290\pi\)
\(888\) 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 \(-0.402304\pi\)
0.302125 + 0.953268i \(0.402304\pi\)
\(912\) −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 \(-0.295401\pi\)
0.599413 + 0.800440i \(0.295401\pi\)
\(930\) 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 \(-0.499848\pi\)
0.000476771 1.00000i \(0.499848\pi\)
\(938\) −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 \(-0.315667\pi\)
0.547271 + 0.836956i \(0.315667\pi\)
\(954\) 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 \(-0.812795\pi\)
−0.831984 + 0.554800i \(0.812795\pi\)
\(984\) 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 \(-0.601124\pi\)
−0.312373 + 0.949960i \(0.601124\pi\)
\(992\) −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 \(-0.467060\pi\)
0.103300 + 0.994650i \(0.467060\pi\)
\(998\) −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.i.1.3 50
43.42 odd 2 1849.4.a.j.1.48 yes 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.i.1.3 50 1.1 even 1 trivial
1849.4.a.j.1.48 yes 50 43.42 odd 2