Properties

Label 1849.4.a.j.1.23
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 1.23
Character \(\chi\) \(=\) 1849.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.618313 q^{2} -9.18025 q^{3} -7.61769 q^{4} +19.4242 q^{5} +5.67627 q^{6} +15.1594 q^{7} +9.65662 q^{8} +57.2770 q^{9} +O(q^{10})\) \(q-0.618313 q^{2} -9.18025 q^{3} -7.61769 q^{4} +19.4242 q^{5} +5.67627 q^{6} +15.1594 q^{7} +9.65662 q^{8} +57.2770 q^{9} -12.0103 q^{10} -7.19433 q^{11} +69.9323 q^{12} +36.4617 q^{13} -9.37325 q^{14} -178.319 q^{15} +54.9707 q^{16} +102.264 q^{17} -35.4151 q^{18} -51.6991 q^{19} -147.968 q^{20} -139.167 q^{21} +4.44835 q^{22} -102.545 q^{23} -88.6502 q^{24} +252.301 q^{25} -22.5447 q^{26} -277.950 q^{27} -115.480 q^{28} -96.3830 q^{29} +110.257 q^{30} -157.016 q^{31} -111.242 q^{32} +66.0458 q^{33} -63.2314 q^{34} +294.460 q^{35} -436.318 q^{36} -233.730 q^{37} +31.9662 q^{38} -334.728 q^{39} +187.572 q^{40} -39.6529 q^{41} +86.0488 q^{42} +54.8042 q^{44} +1112.56 q^{45} +63.4047 q^{46} -455.256 q^{47} -504.645 q^{48} -113.193 q^{49} -156.001 q^{50} -938.812 q^{51} -277.754 q^{52} -602.876 q^{53} +171.860 q^{54} -139.744 q^{55} +146.388 q^{56} +474.610 q^{57} +59.5949 q^{58} -124.432 q^{59} +1358.38 q^{60} +838.549 q^{61} +97.0852 q^{62} +868.284 q^{63} -370.983 q^{64} +708.241 q^{65} -40.8370 q^{66} -166.437 q^{67} -779.018 q^{68} +941.386 q^{69} -182.068 q^{70} +215.480 q^{71} +553.102 q^{72} -108.227 q^{73} +144.518 q^{74} -2316.18 q^{75} +393.827 q^{76} -109.062 q^{77} +206.966 q^{78} -494.914 q^{79} +1067.76 q^{80} +1005.17 q^{81} +24.5179 q^{82} +712.724 q^{83} +1060.13 q^{84} +1986.41 q^{85} +884.820 q^{87} -69.4729 q^{88} -431.700 q^{89} -687.911 q^{90} +552.738 q^{91} +781.154 q^{92} +1441.45 q^{93} +281.491 q^{94} -1004.21 q^{95} +1021.23 q^{96} +1299.31 q^{97} +69.9885 q^{98} -412.070 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} + O(q^{10}) \) \( 50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} - 137q^{10} - 252q^{11} + 48q^{12} - 192q^{13} - 272q^{14} - 314q^{15} + 542q^{16} - 236q^{17} + 386q^{18} - 12q^{19} - 108q^{20} - 408q^{21} - 1235q^{22} - 630q^{23} - 613q^{24} + 1098q^{25} - 1493q^{26} - 10q^{27} + 242q^{28} - 208q^{29} + 48q^{30} - 932q^{31} + 1124q^{32} - 254q^{33} - 765q^{34} - 1452q^{35} + 747q^{36} + 90q^{37} - 1213q^{38} + 1610q^{39} - 1693q^{40} - 1354q^{41} + 16q^{42} - 2704q^{44} - 4508q^{45} - 233q^{46} - 3484q^{47} + 376q^{48} + 1324q^{49} + 408q^{50} - 4054q^{51} - 2176q^{52} - 726q^{53} - 6497q^{54} + 3288q^{55} - 7097q^{56} - 870q^{57} + 275q^{58} - 4370q^{59} - 3891q^{60} - 1172q^{61} + 1546q^{62} + 3686q^{63} + 606q^{64} - 2610q^{65} - 4697q^{66} - 344q^{67} - 3221q^{68} - 136q^{69} + 1310q^{70} - 162q^{71} + 5814q^{72} - 746q^{73} - 4332q^{74} - 236q^{75} - 1338q^{76} - 2024q^{77} - 2782q^{78} - 2656q^{79} + 5713q^{80} - 86q^{81} + 4168q^{82} - 3514q^{83} - 4269q^{84} + 7558q^{85} - 10278q^{87} - 11692q^{88} - 2640q^{89} - 8286q^{90} + 5946q^{91} - 4271q^{92} + 2q^{93} - 9062q^{94} - 12140q^{95} - 700q^{96} - 3864q^{97} + 2826q^{98} - 8174q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.618313 −0.218607 −0.109303 0.994008i \(-0.534862\pi\)
−0.109303 + 0.994008i \(0.534862\pi\)
\(3\) −9.18025 −1.76674 −0.883370 0.468676i \(-0.844731\pi\)
−0.883370 + 0.468676i \(0.844731\pi\)
\(4\) −7.61769 −0.952211
\(5\) 19.4242 1.73736 0.868678 0.495377i \(-0.164970\pi\)
0.868678 + 0.495377i \(0.164970\pi\)
\(6\) 5.67627 0.386221
\(7\) 15.1594 0.818531 0.409265 0.912415i \(-0.365785\pi\)
0.409265 + 0.912415i \(0.365785\pi\)
\(8\) 9.65662 0.426766
\(9\) 57.2770 2.12137
\(10\) −12.0103 −0.379798
\(11\) −7.19433 −0.197198 −0.0985988 0.995127i \(-0.531436\pi\)
−0.0985988 + 0.995127i \(0.531436\pi\)
\(12\) 69.9323 1.68231
\(13\) 36.4617 0.777897 0.388948 0.921260i \(-0.372838\pi\)
0.388948 + 0.921260i \(0.372838\pi\)
\(14\) −9.37325 −0.178936
\(15\) −178.319 −3.06946
\(16\) 54.9707 0.858917
\(17\) 102.264 1.45899 0.729493 0.683989i \(-0.239756\pi\)
0.729493 + 0.683989i \(0.239756\pi\)
\(18\) −35.4151 −0.463745
\(19\) −51.6991 −0.624241 −0.312121 0.950043i \(-0.601039\pi\)
−0.312121 + 0.950043i \(0.601039\pi\)
\(20\) −147.968 −1.65433
\(21\) −139.167 −1.44613
\(22\) 4.44835 0.0431087
\(23\) −102.545 −0.929655 −0.464827 0.885401i \(-0.653884\pi\)
−0.464827 + 0.885401i \(0.653884\pi\)
\(24\) −88.6502 −0.753985
\(25\) 252.301 2.01841
\(26\) −22.5447 −0.170053
\(27\) −277.950 −1.98117
\(28\) −115.480 −0.779414
\(29\) −96.3830 −0.617168 −0.308584 0.951197i \(-0.599855\pi\)
−0.308584 + 0.951197i \(0.599855\pi\)
\(30\) 110.257 0.671003
\(31\) −157.016 −0.909709 −0.454854 0.890566i \(-0.650309\pi\)
−0.454854 + 0.890566i \(0.650309\pi\)
\(32\) −111.242 −0.614531
\(33\) 66.0458 0.348397
\(34\) −63.2314 −0.318944
\(35\) 294.460 1.42208
\(36\) −436.318 −2.01999
\(37\) −233.730 −1.03851 −0.519257 0.854618i \(-0.673791\pi\)
−0.519257 + 0.854618i \(0.673791\pi\)
\(38\) 31.9662 0.136463
\(39\) −334.728 −1.37434
\(40\) 187.572 0.741445
\(41\) −39.6529 −0.151043 −0.0755213 0.997144i \(-0.524062\pi\)
−0.0755213 + 0.997144i \(0.524062\pi\)
\(42\) 86.0488 0.316134
\(43\) 0 0
\(44\) 54.8042 0.187774
\(45\) 1112.56 3.68557
\(46\) 63.4047 0.203229
\(47\) −455.256 −1.41289 −0.706446 0.707767i \(-0.749703\pi\)
−0.706446 + 0.707767i \(0.749703\pi\)
\(48\) −504.645 −1.51748
\(49\) −113.193 −0.330008
\(50\) −156.001 −0.441237
\(51\) −938.812 −2.57765
\(52\) −277.754 −0.740722
\(53\) −602.876 −1.56248 −0.781240 0.624231i \(-0.785413\pi\)
−0.781240 + 0.624231i \(0.785413\pi\)
\(54\) 171.860 0.433096
\(55\) −139.744 −0.342602
\(56\) 146.388 0.349321
\(57\) 474.610 1.10287
\(58\) 59.5949 0.134917
\(59\) −124.432 −0.274571 −0.137285 0.990532i \(-0.543838\pi\)
−0.137285 + 0.990532i \(0.543838\pi\)
\(60\) 1358.38 2.92277
\(61\) 838.549 1.76008 0.880042 0.474896i \(-0.157514\pi\)
0.880042 + 0.474896i \(0.157514\pi\)
\(62\) 97.0852 0.198868
\(63\) 868.284 1.73641
\(64\) −370.983 −0.724577
\(65\) 708.241 1.35148
\(66\) −40.8370 −0.0761618
\(67\) −166.437 −0.303486 −0.151743 0.988420i \(-0.548489\pi\)
−0.151743 + 0.988420i \(0.548489\pi\)
\(68\) −779.018 −1.38926
\(69\) 941.386 1.64246
\(70\) −182.068 −0.310876
\(71\) 215.480 0.360180 0.180090 0.983650i \(-0.442361\pi\)
0.180090 + 0.983650i \(0.442361\pi\)
\(72\) 553.102 0.905329
\(73\) −108.227 −0.173521 −0.0867606 0.996229i \(-0.527652\pi\)
−0.0867606 + 0.996229i \(0.527652\pi\)
\(74\) 144.518 0.227026
\(75\) −2316.18 −3.56600
\(76\) 393.827 0.594409
\(77\) −109.062 −0.161412
\(78\) 206.966 0.300440
\(79\) −494.914 −0.704837 −0.352419 0.935843i \(-0.614641\pi\)
−0.352419 + 0.935843i \(0.614641\pi\)
\(80\) 1067.76 1.49225
\(81\) 1005.17 1.37884
\(82\) 24.5179 0.0330189
\(83\) 712.724 0.942549 0.471275 0.881987i \(-0.343794\pi\)
0.471275 + 0.881987i \(0.343794\pi\)
\(84\) 1060.13 1.37702
\(85\) 1986.41 2.53478
\(86\) 0 0
\(87\) 884.820 1.09038
\(88\) −69.4729 −0.0841573
\(89\) −431.700 −0.514158 −0.257079 0.966390i \(-0.582760\pi\)
−0.257079 + 0.966390i \(0.582760\pi\)
\(90\) −687.911 −0.805691
\(91\) 552.738 0.636732
\(92\) 781.154 0.885227
\(93\) 1441.45 1.60722
\(94\) 281.491 0.308868
\(95\) −1004.21 −1.08453
\(96\) 1021.23 1.08572
\(97\) 1299.31 1.36005 0.680025 0.733189i \(-0.261969\pi\)
0.680025 + 0.733189i \(0.261969\pi\)
\(98\) 69.9885 0.0721419
\(99\) −412.070 −0.418329
\(100\) −1921.95 −1.92195
\(101\) −1475.52 −1.45366 −0.726831 0.686817i \(-0.759007\pi\)
−0.726831 + 0.686817i \(0.759007\pi\)
\(102\) 580.480 0.563491
\(103\) −291.930 −0.279269 −0.139635 0.990203i \(-0.544593\pi\)
−0.139635 + 0.990203i \(0.544593\pi\)
\(104\) 352.097 0.331980
\(105\) −2703.21 −2.51244
\(106\) 372.766 0.341568
\(107\) −1552.74 −1.40289 −0.701444 0.712725i \(-0.747461\pi\)
−0.701444 + 0.712725i \(0.747461\pi\)
\(108\) 2117.34 1.88649
\(109\) 1809.11 1.58973 0.794867 0.606784i \(-0.207541\pi\)
0.794867 + 0.606784i \(0.207541\pi\)
\(110\) 86.4058 0.0748952
\(111\) 2145.70 1.83478
\(112\) 833.323 0.703050
\(113\) −677.063 −0.563652 −0.281826 0.959466i \(-0.590940\pi\)
−0.281826 + 0.959466i \(0.590940\pi\)
\(114\) −293.458 −0.241095
\(115\) −1991.85 −1.61514
\(116\) 734.216 0.587675
\(117\) 2088.42 1.65021
\(118\) 76.9380 0.0600230
\(119\) 1550.27 1.19422
\(120\) −1721.96 −1.30994
\(121\) −1279.24 −0.961113
\(122\) −518.485 −0.384766
\(123\) 364.024 0.266853
\(124\) 1196.10 0.866235
\(125\) 2472.72 1.76934
\(126\) −536.871 −0.379590
\(127\) −10.4671 −0.00731340 −0.00365670 0.999993i \(-0.501164\pi\)
−0.00365670 + 0.999993i \(0.501164\pi\)
\(128\) 1119.32 0.772928
\(129\) 0 0
\(130\) −437.914 −0.295443
\(131\) −26.6364 −0.0177652 −0.00888258 0.999961i \(-0.502827\pi\)
−0.00888258 + 0.999961i \(0.502827\pi\)
\(132\) −503.116 −0.331747
\(133\) −783.727 −0.510960
\(134\) 102.910 0.0663439
\(135\) −5398.97 −3.44199
\(136\) 987.528 0.622646
\(137\) 748.264 0.466632 0.233316 0.972401i \(-0.425042\pi\)
0.233316 + 0.972401i \(0.425042\pi\)
\(138\) −582.071 −0.359052
\(139\) −1029.41 −0.628152 −0.314076 0.949398i \(-0.601695\pi\)
−0.314076 + 0.949398i \(0.601695\pi\)
\(140\) −2243.10 −1.35412
\(141\) 4179.37 2.49621
\(142\) −133.234 −0.0787378
\(143\) −262.318 −0.153399
\(144\) 3148.56 1.82208
\(145\) −1872.17 −1.07224
\(146\) 66.9183 0.0379329
\(147\) 1039.14 0.583038
\(148\) 1780.48 0.988885
\(149\) −1048.80 −0.576649 −0.288324 0.957533i \(-0.593098\pi\)
−0.288324 + 0.957533i \(0.593098\pi\)
\(150\) 1432.13 0.779551
\(151\) −2902.66 −1.56434 −0.782168 0.623068i \(-0.785886\pi\)
−0.782168 + 0.623068i \(0.785886\pi\)
\(152\) −499.238 −0.266405
\(153\) 5857.39 3.09505
\(154\) 67.4343 0.0352858
\(155\) −3049.92 −1.58049
\(156\) 2549.85 1.30866
\(157\) −524.942 −0.266847 −0.133423 0.991059i \(-0.542597\pi\)
−0.133423 + 0.991059i \(0.542597\pi\)
\(158\) 306.011 0.154082
\(159\) 5534.56 2.76050
\(160\) −2160.79 −1.06766
\(161\) −1554.52 −0.760951
\(162\) −621.512 −0.301423
\(163\) −40.9398 −0.0196727 −0.00983635 0.999952i \(-0.503131\pi\)
−0.00983635 + 0.999952i \(0.503131\pi\)
\(164\) 302.064 0.143824
\(165\) 1282.89 0.605289
\(166\) −440.686 −0.206047
\(167\) −1168.95 −0.541652 −0.270826 0.962628i \(-0.587297\pi\)
−0.270826 + 0.962628i \(0.587297\pi\)
\(168\) −1343.88 −0.617160
\(169\) −867.544 −0.394877
\(170\) −1228.22 −0.554119
\(171\) −2961.17 −1.32425
\(172\) 0 0
\(173\) −2210.67 −0.971528 −0.485764 0.874090i \(-0.661459\pi\)
−0.485764 + 0.874090i \(0.661459\pi\)
\(174\) −547.096 −0.238363
\(175\) 3824.73 1.65213
\(176\) −395.478 −0.169376
\(177\) 1142.32 0.485095
\(178\) 266.925 0.112398
\(179\) −2397.80 −1.00123 −0.500615 0.865670i \(-0.666893\pi\)
−0.500615 + 0.865670i \(0.666893\pi\)
\(180\) −8475.15 −3.50945
\(181\) 68.3076 0.0280512 0.0140256 0.999902i \(-0.495535\pi\)
0.0140256 + 0.999902i \(0.495535\pi\)
\(182\) −341.765 −0.139194
\(183\) −7698.08 −3.10961
\(184\) −990.235 −0.396745
\(185\) −4540.03 −1.80427
\(186\) −891.267 −0.351349
\(187\) −735.724 −0.287708
\(188\) 3468.00 1.34537
\(189\) −4213.56 −1.62165
\(190\) 620.919 0.237085
\(191\) 585.643 0.221862 0.110931 0.993828i \(-0.464617\pi\)
0.110931 + 0.993828i \(0.464617\pi\)
\(192\) 3405.72 1.28014
\(193\) −4104.42 −1.53079 −0.765395 0.643561i \(-0.777456\pi\)
−0.765395 + 0.643561i \(0.777456\pi\)
\(194\) −803.380 −0.297316
\(195\) −6501.83 −2.38772
\(196\) 862.267 0.314237
\(197\) 787.155 0.284683 0.142341 0.989818i \(-0.454537\pi\)
0.142341 + 0.989818i \(0.454537\pi\)
\(198\) 254.788 0.0914495
\(199\) 4673.04 1.66464 0.832319 0.554297i \(-0.187013\pi\)
0.832319 + 0.554297i \(0.187013\pi\)
\(200\) 2436.37 0.861388
\(201\) 1527.93 0.536180
\(202\) 912.333 0.317780
\(203\) −1461.11 −0.505171
\(204\) 7151.58 2.45446
\(205\) −770.227 −0.262415
\(206\) 180.504 0.0610501
\(207\) −5873.45 −1.97214
\(208\) 2004.33 0.668149
\(209\) 371.940 0.123099
\(210\) 1671.43 0.549237
\(211\) 1152.23 0.375939 0.187969 0.982175i \(-0.439809\pi\)
0.187969 + 0.982175i \(0.439809\pi\)
\(212\) 4592.53 1.48781
\(213\) −1978.16 −0.636345
\(214\) 960.079 0.306680
\(215\) 0 0
\(216\) −2684.06 −0.845496
\(217\) −2380.27 −0.744624
\(218\) −1118.59 −0.347526
\(219\) 993.554 0.306567
\(220\) 1064.53 0.326230
\(221\) 3728.73 1.13494
\(222\) −1326.72 −0.401096
\(223\) 2655.51 0.797426 0.398713 0.917076i \(-0.369457\pi\)
0.398713 + 0.917076i \(0.369457\pi\)
\(224\) −1686.36 −0.503013
\(225\) 14451.0 4.28179
\(226\) 418.636 0.123218
\(227\) 3747.98 1.09587 0.547934 0.836521i \(-0.315414\pi\)
0.547934 + 0.836521i \(0.315414\pi\)
\(228\) −3615.43 −1.05017
\(229\) 1183.25 0.341446 0.170723 0.985319i \(-0.445390\pi\)
0.170723 + 0.985319i \(0.445390\pi\)
\(230\) 1231.59 0.353080
\(231\) 1001.21 0.285173
\(232\) −930.734 −0.263387
\(233\) −2800.12 −0.787304 −0.393652 0.919259i \(-0.628789\pi\)
−0.393652 + 0.919259i \(0.628789\pi\)
\(234\) −1291.29 −0.360746
\(235\) −8843.00 −2.45470
\(236\) 947.885 0.261449
\(237\) 4543.43 1.24526
\(238\) −958.549 −0.261065
\(239\) −2888.20 −0.781682 −0.390841 0.920458i \(-0.627816\pi\)
−0.390841 + 0.920458i \(0.627816\pi\)
\(240\) −9802.34 −2.63641
\(241\) 48.4148 0.0129405 0.00647027 0.999979i \(-0.497940\pi\)
0.00647027 + 0.999979i \(0.497940\pi\)
\(242\) 790.971 0.210106
\(243\) −1723.09 −0.454882
\(244\) −6387.80 −1.67597
\(245\) −2198.68 −0.573341
\(246\) −225.080 −0.0583358
\(247\) −1885.04 −0.485595
\(248\) −1516.25 −0.388233
\(249\) −6542.98 −1.66524
\(250\) −1528.92 −0.386788
\(251\) −4735.73 −1.19090 −0.595452 0.803391i \(-0.703027\pi\)
−0.595452 + 0.803391i \(0.703027\pi\)
\(252\) −6614.32 −1.65342
\(253\) 737.741 0.183326
\(254\) 6.47192 0.00159876
\(255\) −18235.7 −4.47829
\(256\) 2275.78 0.555609
\(257\) 642.806 0.156020 0.0780100 0.996953i \(-0.475143\pi\)
0.0780100 + 0.996953i \(0.475143\pi\)
\(258\) 0 0
\(259\) −3543.21 −0.850055
\(260\) −5395.16 −1.28690
\(261\) −5520.53 −1.30924
\(262\) 16.4696 0.00388358
\(263\) 5427.16 1.27245 0.636223 0.771505i \(-0.280496\pi\)
0.636223 + 0.771505i \(0.280496\pi\)
\(264\) 637.779 0.148684
\(265\) −11710.4 −2.71458
\(266\) 484.588 0.111699
\(267\) 3963.11 0.908383
\(268\) 1267.87 0.288982
\(269\) 4408.39 0.999199 0.499599 0.866257i \(-0.333481\pi\)
0.499599 + 0.866257i \(0.333481\pi\)
\(270\) 3338.25 0.752443
\(271\) 5005.29 1.12196 0.560978 0.827831i \(-0.310425\pi\)
0.560978 + 0.827831i \(0.310425\pi\)
\(272\) 5621.54 1.25315
\(273\) −5074.27 −1.12494
\(274\) −462.661 −0.102009
\(275\) −1815.14 −0.398025
\(276\) −7171.19 −1.56397
\(277\) −8864.55 −1.92281 −0.961407 0.275132i \(-0.911279\pi\)
−0.961407 + 0.275132i \(0.911279\pi\)
\(278\) 636.495 0.137318
\(279\) −8993.42 −1.92983
\(280\) 2843.48 0.606895
\(281\) 3796.45 0.805968 0.402984 0.915207i \(-0.367973\pi\)
0.402984 + 0.915207i \(0.367973\pi\)
\(282\) −2584.16 −0.545689
\(283\) −4707.79 −0.988867 −0.494433 0.869216i \(-0.664624\pi\)
−0.494433 + 0.869216i \(0.664624\pi\)
\(284\) −1641.46 −0.342968
\(285\) 9218.94 1.91608
\(286\) 162.194 0.0335341
\(287\) −601.114 −0.123633
\(288\) −6371.61 −1.30365
\(289\) 5545.00 1.12864
\(290\) 1157.58 0.234399
\(291\) −11928.0 −2.40286
\(292\) 824.442 0.165229
\(293\) −6455.57 −1.28716 −0.643581 0.765378i \(-0.722552\pi\)
−0.643581 + 0.765378i \(0.722552\pi\)
\(294\) −642.512 −0.127456
\(295\) −2417.00 −0.477027
\(296\) −2257.04 −0.443203
\(297\) 1999.67 0.390682
\(298\) 648.484 0.126059
\(299\) −3738.96 −0.723175
\(300\) 17644.0 3.39558
\(301\) 0 0
\(302\) 1794.75 0.341974
\(303\) 13545.6 2.56824
\(304\) −2841.93 −0.536171
\(305\) 16288.2 3.05789
\(306\) −3621.70 −0.676598
\(307\) 373.270 0.0693930 0.0346965 0.999398i \(-0.488954\pi\)
0.0346965 + 0.999398i \(0.488954\pi\)
\(308\) 830.799 0.153699
\(309\) 2679.99 0.493396
\(310\) 1885.81 0.345505
\(311\) 2560.85 0.466921 0.233461 0.972366i \(-0.424995\pi\)
0.233461 + 0.972366i \(0.424995\pi\)
\(312\) −3232.34 −0.586522
\(313\) −9039.94 −1.63249 −0.816243 0.577709i \(-0.803947\pi\)
−0.816243 + 0.577709i \(0.803947\pi\)
\(314\) 324.578 0.0583344
\(315\) 16865.8 3.01676
\(316\) 3770.10 0.671154
\(317\) 2482.03 0.439762 0.219881 0.975527i \(-0.429433\pi\)
0.219881 + 0.975527i \(0.429433\pi\)
\(318\) −3422.09 −0.603463
\(319\) 693.412 0.121704
\(320\) −7206.07 −1.25885
\(321\) 14254.5 2.47854
\(322\) 961.177 0.166349
\(323\) −5286.97 −0.910758
\(324\) −7657.10 −1.31295
\(325\) 9199.32 1.57011
\(326\) 25.3136 0.00430058
\(327\) −16608.0 −2.80864
\(328\) −382.913 −0.0644599
\(329\) −6901.41 −1.15650
\(330\) −793.227 −0.132320
\(331\) 4063.14 0.674715 0.337357 0.941377i \(-0.390467\pi\)
0.337357 + 0.941377i \(0.390467\pi\)
\(332\) −5429.31 −0.897506
\(333\) −13387.4 −2.20307
\(334\) 722.775 0.118409
\(335\) −3232.91 −0.527263
\(336\) −7650.11 −1.24211
\(337\) −985.260 −0.159260 −0.0796299 0.996824i \(-0.525374\pi\)
−0.0796299 + 0.996824i \(0.525374\pi\)
\(338\) 536.413 0.0863226
\(339\) 6215.60 0.995827
\(340\) −15131.8 −2.41364
\(341\) 1129.63 0.179392
\(342\) 1830.93 0.289489
\(343\) −6915.61 −1.08865
\(344\) 0 0
\(345\) 18285.7 2.85353
\(346\) 1366.89 0.212383
\(347\) −1072.53 −0.165927 −0.0829633 0.996553i \(-0.526438\pi\)
−0.0829633 + 0.996553i \(0.526438\pi\)
\(348\) −6740.29 −1.03827
\(349\) 293.309 0.0449870 0.0224935 0.999747i \(-0.492839\pi\)
0.0224935 + 0.999747i \(0.492839\pi\)
\(350\) −2364.88 −0.361166
\(351\) −10134.5 −1.54114
\(352\) 800.312 0.121184
\(353\) −1149.23 −0.173279 −0.0866396 0.996240i \(-0.527613\pi\)
−0.0866396 + 0.996240i \(0.527613\pi\)
\(354\) −706.310 −0.106045
\(355\) 4185.54 0.625762
\(356\) 3288.55 0.489587
\(357\) −14231.8 −2.10988
\(358\) 1482.59 0.218875
\(359\) 8685.57 1.27690 0.638450 0.769663i \(-0.279576\pi\)
0.638450 + 0.769663i \(0.279576\pi\)
\(360\) 10743.6 1.57288
\(361\) −4186.21 −0.610323
\(362\) −42.2354 −0.00613217
\(363\) 11743.8 1.69804
\(364\) −4210.58 −0.606304
\(365\) −2102.23 −0.301468
\(366\) 4759.82 0.679781
\(367\) −12096.1 −1.72047 −0.860234 0.509899i \(-0.829683\pi\)
−0.860234 + 0.509899i \(0.829683\pi\)
\(368\) −5636.96 −0.798496
\(369\) −2271.20 −0.320417
\(370\) 2807.16 0.394425
\(371\) −9139.24 −1.27894
\(372\) −10980.5 −1.53041
\(373\) 6887.99 0.956157 0.478079 0.878317i \(-0.341333\pi\)
0.478079 + 0.878317i \(0.341333\pi\)
\(374\) 454.908 0.0628949
\(375\) −22700.2 −3.12595
\(376\) −4396.23 −0.602975
\(377\) −3514.29 −0.480093
\(378\) 2605.30 0.354503
\(379\) −2089.36 −0.283175 −0.141588 0.989926i \(-0.545221\pi\)
−0.141588 + 0.989926i \(0.545221\pi\)
\(380\) 7649.80 1.03270
\(381\) 96.0903 0.0129209
\(382\) −362.110 −0.0485005
\(383\) 3454.11 0.460827 0.230413 0.973093i \(-0.425992\pi\)
0.230413 + 0.973093i \(0.425992\pi\)
\(384\) −10275.6 −1.36556
\(385\) −2118.44 −0.280431
\(386\) 2537.81 0.334641
\(387\) 0 0
\(388\) −9897.74 −1.29506
\(389\) 15107.6 1.96911 0.984555 0.175073i \(-0.0560162\pi\)
0.984555 + 0.175073i \(0.0560162\pi\)
\(390\) 4020.16 0.521971
\(391\) −10486.7 −1.35635
\(392\) −1093.06 −0.140836
\(393\) 244.529 0.0313864
\(394\) −486.708 −0.0622335
\(395\) −9613.32 −1.22455
\(396\) 3139.02 0.398338
\(397\) 1850.76 0.233972 0.116986 0.993134i \(-0.462677\pi\)
0.116986 + 0.993134i \(0.462677\pi\)
\(398\) −2889.40 −0.363901
\(399\) 7194.81 0.902734
\(400\) 13869.2 1.73364
\(401\) −4757.23 −0.592430 −0.296215 0.955121i \(-0.595725\pi\)
−0.296215 + 0.955121i \(0.595725\pi\)
\(402\) −944.741 −0.117212
\(403\) −5725.09 −0.707660
\(404\) 11240.1 1.38419
\(405\) 19524.7 2.39553
\(406\) 903.422 0.110434
\(407\) 1681.53 0.204792
\(408\) −9065.75 −1.10005
\(409\) 1964.94 0.237555 0.118778 0.992921i \(-0.462102\pi\)
0.118778 + 0.992921i \(0.462102\pi\)
\(410\) 476.241 0.0573656
\(411\) −6869.25 −0.824417
\(412\) 2223.83 0.265923
\(413\) −1886.32 −0.224745
\(414\) 3631.63 0.431123
\(415\) 13844.1 1.63754
\(416\) −4056.07 −0.478042
\(417\) 9450.21 1.10978
\(418\) −229.976 −0.0269102
\(419\) 12920.8 1.50650 0.753249 0.657735i \(-0.228485\pi\)
0.753249 + 0.657735i \(0.228485\pi\)
\(420\) 20592.2 2.39238
\(421\) 1779.75 0.206033 0.103016 0.994680i \(-0.467151\pi\)
0.103016 + 0.994680i \(0.467151\pi\)
\(422\) −712.441 −0.0821827
\(423\) −26075.7 −2.99727
\(424\) −5821.75 −0.666814
\(425\) 25801.4 2.94483
\(426\) 1223.12 0.139109
\(427\) 12711.9 1.44068
\(428\) 11828.3 1.33585
\(429\) 2408.14 0.271017
\(430\) 0 0
\(431\) −10329.4 −1.15441 −0.577205 0.816599i \(-0.695857\pi\)
−0.577205 + 0.816599i \(0.695857\pi\)
\(432\) −15279.1 −1.70166
\(433\) −35.7668 −0.00396961 −0.00198481 0.999998i \(-0.500632\pi\)
−0.00198481 + 0.999998i \(0.500632\pi\)
\(434\) 1471.75 0.162780
\(435\) 17187.0 1.89437
\(436\) −13781.2 −1.51376
\(437\) 5301.47 0.580329
\(438\) −614.327 −0.0670175
\(439\) 5776.48 0.628010 0.314005 0.949421i \(-0.398329\pi\)
0.314005 + 0.949421i \(0.398329\pi\)
\(440\) −1349.46 −0.146211
\(441\) −6483.33 −0.700068
\(442\) −2305.52 −0.248105
\(443\) −12268.5 −1.31578 −0.657892 0.753112i \(-0.728552\pi\)
−0.657892 + 0.753112i \(0.728552\pi\)
\(444\) −16345.3 −1.74710
\(445\) −8385.43 −0.893276
\(446\) −1641.93 −0.174323
\(447\) 9628.20 1.01879
\(448\) −5623.88 −0.593088
\(449\) 11796.6 1.23990 0.619952 0.784640i \(-0.287152\pi\)
0.619952 + 0.784640i \(0.287152\pi\)
\(450\) −8935.26 −0.936027
\(451\) 285.276 0.0297852
\(452\) 5157.65 0.536716
\(453\) 26647.1 2.76377
\(454\) −2317.42 −0.239564
\(455\) 10736.5 1.10623
\(456\) 4583.13 0.470668
\(457\) 8101.46 0.829256 0.414628 0.909991i \(-0.363912\pi\)
0.414628 + 0.909991i \(0.363912\pi\)
\(458\) −731.616 −0.0746423
\(459\) −28424.4 −2.89050
\(460\) 15173.3 1.53796
\(461\) 11117.9 1.12324 0.561618 0.827396i \(-0.310179\pi\)
0.561618 + 0.827396i \(0.310179\pi\)
\(462\) −619.064 −0.0623408
\(463\) −16742.2 −1.68051 −0.840255 0.542191i \(-0.817595\pi\)
−0.840255 + 0.542191i \(0.817595\pi\)
\(464\) −5298.24 −0.530096
\(465\) 27999.1 2.79231
\(466\) 1731.35 0.172110
\(467\) 16116.5 1.59697 0.798485 0.602015i \(-0.205635\pi\)
0.798485 + 0.602015i \(0.205635\pi\)
\(468\) −15908.9 −1.57135
\(469\) −2523.09 −0.248412
\(470\) 5467.74 0.536613
\(471\) 4819.10 0.471448
\(472\) −1201.59 −0.117178
\(473\) 0 0
\(474\) −2809.26 −0.272223
\(475\) −13043.7 −1.25997
\(476\) −11809.4 −1.13715
\(477\) −34530.9 −3.31460
\(478\) 1785.81 0.170881
\(479\) 2987.24 0.284949 0.142474 0.989798i \(-0.454494\pi\)
0.142474 + 0.989798i \(0.454494\pi\)
\(480\) 19836.6 1.88628
\(481\) −8522.21 −0.807857
\(482\) −29.9355 −0.00282889
\(483\) 14270.8 1.34440
\(484\) 9744.86 0.915183
\(485\) 25238.1 2.36289
\(486\) 1065.41 0.0994402
\(487\) −19072.7 −1.77468 −0.887338 0.461119i \(-0.847448\pi\)
−0.887338 + 0.461119i \(0.847448\pi\)
\(488\) 8097.54 0.751144
\(489\) 375.837 0.0347566
\(490\) 1359.47 0.125336
\(491\) −8855.63 −0.813949 −0.406975 0.913439i \(-0.633416\pi\)
−0.406975 + 0.913439i \(0.633416\pi\)
\(492\) −2773.02 −0.254100
\(493\) −9856.55 −0.900439
\(494\) 1165.54 0.106154
\(495\) −8004.14 −0.726786
\(496\) −8631.30 −0.781365
\(497\) 3266.55 0.294819
\(498\) 4045.61 0.364032
\(499\) 12489.5 1.12046 0.560229 0.828338i \(-0.310713\pi\)
0.560229 + 0.828338i \(0.310713\pi\)
\(500\) −18836.4 −1.68478
\(501\) 10731.2 0.956958
\(502\) 2928.17 0.260339
\(503\) 1022.04 0.0905977 0.0452989 0.998973i \(-0.485576\pi\)
0.0452989 + 0.998973i \(0.485576\pi\)
\(504\) 8384.69 0.741039
\(505\) −28660.9 −2.52553
\(506\) −456.155 −0.0400762
\(507\) 7964.27 0.697644
\(508\) 79.7349 0.00696390
\(509\) 3665.05 0.319156 0.159578 0.987185i \(-0.448987\pi\)
0.159578 + 0.987185i \(0.448987\pi\)
\(510\) 11275.4 0.978984
\(511\) −1640.66 −0.142032
\(512\) −10361.7 −0.894388
\(513\) 14369.8 1.23673
\(514\) −397.455 −0.0341070
\(515\) −5670.52 −0.485190
\(516\) 0 0
\(517\) 3275.27 0.278619
\(518\) 2190.81 0.185828
\(519\) 20294.5 1.71644
\(520\) 6839.21 0.576768
\(521\) −5845.70 −0.491564 −0.245782 0.969325i \(-0.579045\pi\)
−0.245782 + 0.969325i \(0.579045\pi\)
\(522\) 3413.41 0.286209
\(523\) 16090.3 1.34528 0.672639 0.739971i \(-0.265161\pi\)
0.672639 + 0.739971i \(0.265161\pi\)
\(524\) 202.908 0.0169162
\(525\) −35112.0 −2.91888
\(526\) −3355.69 −0.278165
\(527\) −16057.2 −1.32725
\(528\) 3630.58 0.299244
\(529\) −1651.58 −0.135743
\(530\) 7240.70 0.593426
\(531\) −7127.09 −0.582466
\(532\) 5970.19 0.486542
\(533\) −1445.81 −0.117496
\(534\) −2450.44 −0.198579
\(535\) −30160.8 −2.43732
\(536\) −1607.22 −0.129517
\(537\) 22012.4 1.76891
\(538\) −2725.77 −0.218431
\(539\) 814.346 0.0650767
\(540\) 41127.7 3.27751
\(541\) 2502.60 0.198882 0.0994410 0.995043i \(-0.468295\pi\)
0.0994410 + 0.995043i \(0.468295\pi\)
\(542\) −3094.84 −0.245267
\(543\) −627.080 −0.0495591
\(544\) −11376.1 −0.896592
\(545\) 35140.5 2.76193
\(546\) 3137.49 0.245919
\(547\) 25182.5 1.96842 0.984210 0.177004i \(-0.0566405\pi\)
0.984210 + 0.177004i \(0.0566405\pi\)
\(548\) −5700.04 −0.444332
\(549\) 48029.5 3.73379
\(550\) 1122.32 0.0870109
\(551\) 4982.91 0.385262
\(552\) 9090.61 0.700945
\(553\) −7502.59 −0.576931
\(554\) 5481.07 0.420340
\(555\) 41678.6 3.18767
\(556\) 7841.70 0.598133
\(557\) 3635.57 0.276560 0.138280 0.990393i \(-0.455843\pi\)
0.138280 + 0.990393i \(0.455843\pi\)
\(558\) 5560.75 0.421873
\(559\) 0 0
\(560\) 16186.7 1.22145
\(561\) 6754.13 0.508306
\(562\) −2347.39 −0.176190
\(563\) 12158.4 0.910153 0.455077 0.890452i \(-0.349612\pi\)
0.455077 + 0.890452i \(0.349612\pi\)
\(564\) −31837.1 −2.37692
\(565\) −13151.4 −0.979264
\(566\) 2910.89 0.216173
\(567\) 15237.8 1.12862
\(568\) 2080.81 0.153713
\(569\) −16684.3 −1.22925 −0.614625 0.788819i \(-0.710693\pi\)
−0.614625 + 0.788819i \(0.710693\pi\)
\(570\) −5700.19 −0.418868
\(571\) −20545.1 −1.50576 −0.752879 0.658159i \(-0.771335\pi\)
−0.752879 + 0.658159i \(0.771335\pi\)
\(572\) 1998.26 0.146069
\(573\) −5376.35 −0.391972
\(574\) 371.677 0.0270270
\(575\) −25872.1 −1.87642
\(576\) −21248.8 −1.53709
\(577\) 25550.0 1.84344 0.921718 0.387861i \(-0.126786\pi\)
0.921718 + 0.387861i \(0.126786\pi\)
\(578\) −3428.54 −0.246728
\(579\) 37679.6 2.70451
\(580\) 14261.6 1.02100
\(581\) 10804.5 0.771505
\(582\) 7375.23 0.525280
\(583\) 4337.30 0.308117
\(584\) −1045.11 −0.0740530
\(585\) 40565.9 2.86700
\(586\) 3991.56 0.281382
\(587\) 21850.9 1.53643 0.768214 0.640193i \(-0.221146\pi\)
0.768214 + 0.640193i \(0.221146\pi\)
\(588\) −7915.82 −0.555175
\(589\) 8117.60 0.567878
\(590\) 1494.46 0.104281
\(591\) −7226.28 −0.502960
\(592\) −12848.3 −0.891998
\(593\) −15140.1 −1.04845 −0.524224 0.851580i \(-0.675645\pi\)
−0.524224 + 0.851580i \(0.675645\pi\)
\(594\) −1236.42 −0.0854056
\(595\) 30112.7 2.07479
\(596\) 7989.40 0.549091
\(597\) −42899.7 −2.94098
\(598\) 2311.84 0.158091
\(599\) −7836.05 −0.534511 −0.267256 0.963626i \(-0.586117\pi\)
−0.267256 + 0.963626i \(0.586117\pi\)
\(600\) −22366.5 −1.52185
\(601\) −11113.3 −0.754279 −0.377140 0.926156i \(-0.623092\pi\)
−0.377140 + 0.926156i \(0.623092\pi\)
\(602\) 0 0
\(603\) −9533.02 −0.643805
\(604\) 22111.5 1.48958
\(605\) −24848.3 −1.66980
\(606\) −8375.45 −0.561434
\(607\) 17388.4 1.16272 0.581361 0.813646i \(-0.302520\pi\)
0.581361 + 0.813646i \(0.302520\pi\)
\(608\) 5751.11 0.383616
\(609\) 13413.3 0.892506
\(610\) −10071.2 −0.668476
\(611\) −16599.4 −1.09908
\(612\) −44619.8 −2.94714
\(613\) 16616.6 1.09484 0.547421 0.836857i \(-0.315610\pi\)
0.547421 + 0.836857i \(0.315610\pi\)
\(614\) −230.798 −0.0151698
\(615\) 7070.88 0.463619
\(616\) −1053.17 −0.0688853
\(617\) 4402.51 0.287258 0.143629 0.989632i \(-0.454123\pi\)
0.143629 + 0.989632i \(0.454123\pi\)
\(618\) −1657.07 −0.107860
\(619\) −16295.5 −1.05811 −0.529055 0.848587i \(-0.677454\pi\)
−0.529055 + 0.848587i \(0.677454\pi\)
\(620\) 23233.4 1.50496
\(621\) 28502.3 1.84180
\(622\) −1583.41 −0.102072
\(623\) −6544.30 −0.420854
\(624\) −18400.2 −1.18045
\(625\) 16493.1 1.05556
\(626\) 5589.51 0.356872
\(627\) −3414.51 −0.217484
\(628\) 3998.84 0.254094
\(629\) −23902.3 −1.51518
\(630\) −10428.3 −0.659483
\(631\) 10777.3 0.679935 0.339967 0.940437i \(-0.389584\pi\)
0.339967 + 0.940437i \(0.389584\pi\)
\(632\) −4779.19 −0.300801
\(633\) −10577.8 −0.664186
\(634\) −1534.67 −0.0961350
\(635\) −203.315 −0.0127060
\(636\) −42160.5 −2.62858
\(637\) −4127.20 −0.256712
\(638\) −428.745 −0.0266053
\(639\) 12342.1 0.764076
\(640\) 21741.9 1.34285
\(641\) −18764.1 −1.15622 −0.578109 0.815959i \(-0.696209\pi\)
−0.578109 + 0.815959i \(0.696209\pi\)
\(642\) −8813.76 −0.541825
\(643\) −7517.75 −0.461075 −0.230537 0.973063i \(-0.574048\pi\)
−0.230537 + 0.973063i \(0.574048\pi\)
\(644\) 11841.8 0.724586
\(645\) 0 0
\(646\) 3269.00 0.199098
\(647\) −20711.1 −1.25848 −0.629241 0.777210i \(-0.716634\pi\)
−0.629241 + 0.777210i \(0.716634\pi\)
\(648\) 9706.58 0.588442
\(649\) 895.206 0.0541447
\(650\) −5688.06 −0.343237
\(651\) 21851.5 1.31556
\(652\) 311.867 0.0187326
\(653\) −6658.64 −0.399039 −0.199520 0.979894i \(-0.563938\pi\)
−0.199520 + 0.979894i \(0.563938\pi\)
\(654\) 10269.0 0.613988
\(655\) −517.392 −0.0308644
\(656\) −2179.75 −0.129733
\(657\) −6198.93 −0.368103
\(658\) 4267.23 0.252818
\(659\) −11926.7 −0.705004 −0.352502 0.935811i \(-0.614669\pi\)
−0.352502 + 0.935811i \(0.614669\pi\)
\(660\) −9772.65 −0.576363
\(661\) −31886.9 −1.87634 −0.938168 0.346180i \(-0.887479\pi\)
−0.938168 + 0.346180i \(0.887479\pi\)
\(662\) −2512.29 −0.147497
\(663\) −34230.7 −2.00514
\(664\) 6882.50 0.402248
\(665\) −15223.3 −0.887720
\(666\) 8277.58 0.481606
\(667\) 9883.57 0.573753
\(668\) 8904.67 0.515767
\(669\) −24378.2 −1.40884
\(670\) 1998.95 0.115263
\(671\) −6032.80 −0.347084
\(672\) 15481.2 0.888692
\(673\) −21903.5 −1.25456 −0.627279 0.778794i \(-0.715832\pi\)
−0.627279 + 0.778794i \(0.715832\pi\)
\(674\) 609.199 0.0348152
\(675\) −70127.1 −3.99880
\(676\) 6608.68 0.376006
\(677\) 12230.4 0.694317 0.347159 0.937806i \(-0.387147\pi\)
0.347159 + 0.937806i \(0.387147\pi\)
\(678\) −3843.19 −0.217694
\(679\) 19696.8 1.11324
\(680\) 19182.0 1.08176
\(681\) −34407.4 −1.93611
\(682\) −698.464 −0.0392164
\(683\) −17621.4 −0.987207 −0.493604 0.869687i \(-0.664321\pi\)
−0.493604 + 0.869687i \(0.664321\pi\)
\(684\) 22557.2 1.26096
\(685\) 14534.5 0.810705
\(686\) 4276.01 0.237986
\(687\) −10862.5 −0.603246
\(688\) 0 0
\(689\) −21981.9 −1.21545
\(690\) −11306.3 −0.623801
\(691\) 25629.9 1.41101 0.705504 0.708706i \(-0.250721\pi\)
0.705504 + 0.708706i \(0.250721\pi\)
\(692\) 16840.2 0.925100
\(693\) −6246.73 −0.342415
\(694\) 663.160 0.0362726
\(695\) −19995.4 −1.09132
\(696\) 8544.37 0.465336
\(697\) −4055.08 −0.220369
\(698\) −181.357 −0.00983445
\(699\) 25705.8 1.39096
\(700\) −29135.6 −1.57317
\(701\) 6140.99 0.330873 0.165437 0.986220i \(-0.447097\pi\)
0.165437 + 0.986220i \(0.447097\pi\)
\(702\) 6266.32 0.336904
\(703\) 12083.6 0.648283
\(704\) 2668.98 0.142885
\(705\) 81181.0 4.33681
\(706\) 710.587 0.0378800
\(707\) −22368.0 −1.18987
\(708\) −8701.82 −0.461913
\(709\) −36700.3 −1.94402 −0.972009 0.234943i \(-0.924510\pi\)
−0.972009 + 0.234943i \(0.924510\pi\)
\(710\) −2587.97 −0.136796
\(711\) −28347.2 −1.49522
\(712\) −4168.76 −0.219425
\(713\) 16101.2 0.845715
\(714\) 8799.72 0.461234
\(715\) −5095.32 −0.266509
\(716\) 18265.7 0.953382
\(717\) 26514.4 1.38103
\(718\) −5370.40 −0.279139
\(719\) 19467.1 1.00973 0.504867 0.863197i \(-0.331542\pi\)
0.504867 + 0.863197i \(0.331542\pi\)
\(720\) 61158.3 3.16560
\(721\) −4425.49 −0.228590
\(722\) 2588.38 0.133421
\(723\) −444.460 −0.0228626
\(724\) −520.346 −0.0267106
\(725\) −24317.5 −1.24570
\(726\) −7261.31 −0.371202
\(727\) −11021.6 −0.562269 −0.281135 0.959668i \(-0.590711\pi\)
−0.281135 + 0.959668i \(0.590711\pi\)
\(728\) 5337.57 0.271736
\(729\) −11321.3 −0.575181
\(730\) 1299.84 0.0659029
\(731\) 0 0
\(732\) 58641.6 2.96101
\(733\) −29262.9 −1.47455 −0.737277 0.675590i \(-0.763889\pi\)
−0.737277 + 0.675590i \(0.763889\pi\)
\(734\) 7479.18 0.376106
\(735\) 20184.4 1.01294
\(736\) 11407.3 0.571302
\(737\) 1197.40 0.0598466
\(738\) 1404.31 0.0700453
\(739\) 14025.7 0.698167 0.349083 0.937092i \(-0.386493\pi\)
0.349083 + 0.937092i \(0.386493\pi\)
\(740\) 34584.5 1.71804
\(741\) 17305.1 0.857920
\(742\) 5650.91 0.279584
\(743\) −2161.22 −0.106712 −0.0533562 0.998576i \(-0.516992\pi\)
−0.0533562 + 0.998576i \(0.516992\pi\)
\(744\) 13919.5 0.685907
\(745\) −20372.0 −1.00184
\(746\) −4258.93 −0.209022
\(747\) 40822.7 1.99950
\(748\) 5604.52 0.273959
\(749\) −23538.6 −1.14831
\(750\) 14035.8 0.683354
\(751\) −29152.5 −1.41650 −0.708250 0.705962i \(-0.750515\pi\)
−0.708250 + 0.705962i \(0.750515\pi\)
\(752\) −25025.8 −1.21356
\(753\) 43475.2 2.10402
\(754\) 2172.93 0.104952
\(755\) −56381.9 −2.71781
\(756\) 32097.6 1.54415
\(757\) −26927.3 −1.29285 −0.646427 0.762976i \(-0.723737\pi\)
−0.646427 + 0.762976i \(0.723737\pi\)
\(758\) 1291.88 0.0619040
\(759\) −6772.65 −0.323889
\(760\) −9697.32 −0.462840
\(761\) 1001.36 0.0476996 0.0238498 0.999716i \(-0.492408\pi\)
0.0238498 + 0.999716i \(0.492408\pi\)
\(762\) −59.4139 −0.00282459
\(763\) 27425.0 1.30125
\(764\) −4461.24 −0.211259
\(765\) 113775. 5.37720
\(766\) −2135.72 −0.100740
\(767\) −4537.01 −0.213588
\(768\) −20892.2 −0.981617
\(769\) 34146.0 1.60122 0.800609 0.599187i \(-0.204510\pi\)
0.800609 + 0.599187i \(0.204510\pi\)
\(770\) 1309.86 0.0613040
\(771\) −5901.12 −0.275647
\(772\) 31266.2 1.45764
\(773\) −12617.5 −0.587090 −0.293545 0.955945i \(-0.594835\pi\)
−0.293545 + 0.955945i \(0.594835\pi\)
\(774\) 0 0
\(775\) −39615.4 −1.83616
\(776\) 12546.9 0.580424
\(777\) 32527.6 1.50183
\(778\) −9341.20 −0.430461
\(779\) 2050.02 0.0942870
\(780\) 49528.9 2.27361
\(781\) −1550.24 −0.0710267
\(782\) 6484.04 0.296508
\(783\) 26789.7 1.22271
\(784\) −6222.28 −0.283449
\(785\) −10196.6 −0.463608
\(786\) −151.195 −0.00686128
\(787\) −3944.55 −0.178663 −0.0893317 0.996002i \(-0.528473\pi\)
−0.0893317 + 0.996002i \(0.528473\pi\)
\(788\) −5996.30 −0.271078
\(789\) −49822.7 −2.24808
\(790\) 5944.04 0.267695
\(791\) −10263.9 −0.461366
\(792\) −3979.20 −0.178529
\(793\) 30574.9 1.36916
\(794\) −1144.35 −0.0511479
\(795\) 107505. 4.79596
\(796\) −35597.7 −1.58509
\(797\) −15295.0 −0.679768 −0.339884 0.940467i \(-0.610388\pi\)
−0.339884 + 0.940467i \(0.610388\pi\)
\(798\) −4448.64 −0.197344
\(799\) −46556.5 −2.06139
\(800\) −28066.5 −1.24037
\(801\) −24726.4 −1.09072
\(802\) 2941.45 0.129509
\(803\) 778.624 0.0342180
\(804\) −11639.3 −0.510557
\(805\) −30195.3 −1.32204
\(806\) 3539.89 0.154699
\(807\) −40470.1 −1.76532
\(808\) −14248.5 −0.620374
\(809\) −10980.7 −0.477208 −0.238604 0.971117i \(-0.576690\pi\)
−0.238604 + 0.971117i \(0.576690\pi\)
\(810\) −12072.4 −0.523680
\(811\) −40654.8 −1.76028 −0.880138 0.474719i \(-0.842550\pi\)
−0.880138 + 0.474719i \(0.842550\pi\)
\(812\) 11130.3 0.481030
\(813\) −45949.8 −1.98220
\(814\) −1039.71 −0.0447690
\(815\) −795.224 −0.0341785
\(816\) −51607.2 −2.21399
\(817\) 0 0
\(818\) −1214.95 −0.0519312
\(819\) 31659.1 1.35074
\(820\) 5867.35 0.249874
\(821\) 21851.2 0.928880 0.464440 0.885604i \(-0.346256\pi\)
0.464440 + 0.885604i \(0.346256\pi\)
\(822\) 4247.35 0.180223
\(823\) −8135.35 −0.344569 −0.172285 0.985047i \(-0.555115\pi\)
−0.172285 + 0.985047i \(0.555115\pi\)
\(824\) −2819.06 −0.119183
\(825\) 16663.4 0.703206
\(826\) 1166.33 0.0491307
\(827\) −39430.9 −1.65798 −0.828988 0.559266i \(-0.811083\pi\)
−0.828988 + 0.559266i \(0.811083\pi\)
\(828\) 44742.1 1.87789
\(829\) 7493.89 0.313961 0.156980 0.987602i \(-0.449824\pi\)
0.156980 + 0.987602i \(0.449824\pi\)
\(830\) −8559.99 −0.357978
\(831\) 81378.8 3.39711
\(832\) −13526.7 −0.563646
\(833\) −11575.6 −0.481476
\(834\) −5843.18 −0.242605
\(835\) −22705.9 −0.941042
\(836\) −2833.33 −0.117216
\(837\) 43642.7 1.80229
\(838\) −7989.10 −0.329330
\(839\) −31112.0 −1.28022 −0.640110 0.768283i \(-0.721111\pi\)
−0.640110 + 0.768283i \(0.721111\pi\)
\(840\) −26103.9 −1.07223
\(841\) −15099.3 −0.619103
\(842\) −1100.44 −0.0450401
\(843\) −34852.3 −1.42394
\(844\) −8777.36 −0.357973
\(845\) −16851.4 −0.686041
\(846\) 16122.9 0.655222
\(847\) −19392.5 −0.786700
\(848\) −33140.5 −1.34204
\(849\) 43218.7 1.74707
\(850\) −15953.3 −0.643758
\(851\) 23967.8 0.965459
\(852\) 15069.0 0.605935
\(853\) 34197.2 1.37267 0.686336 0.727284i \(-0.259218\pi\)
0.686336 + 0.727284i \(0.259218\pi\)
\(854\) −7859.92 −0.314943
\(855\) −57518.4 −2.30069
\(856\) −14994.2 −0.598705
\(857\) 48162.3 1.91971 0.959856 0.280493i \(-0.0904981\pi\)
0.959856 + 0.280493i \(0.0904981\pi\)
\(858\) −1488.99 −0.0592461
\(859\) 16199.5 0.643447 0.321723 0.946834i \(-0.395738\pi\)
0.321723 + 0.946834i \(0.395738\pi\)
\(860\) 0 0
\(861\) 5518.38 0.218427
\(862\) 6386.81 0.252362
\(863\) −33115.5 −1.30622 −0.653108 0.757264i \(-0.726535\pi\)
−0.653108 + 0.757264i \(0.726535\pi\)
\(864\) 30919.7 1.21749
\(865\) −42940.6 −1.68789
\(866\) 22.1151 0.000867784 0
\(867\) −50904.5 −1.99401
\(868\) 18132.2 0.709040
\(869\) 3560.57 0.138992
\(870\) −10626.9 −0.414122
\(871\) −6068.58 −0.236080
\(872\) 17469.8 0.678444
\(873\) 74420.5 2.88517
\(874\) −3277.96 −0.126864
\(875\) 37485.0 1.44825
\(876\) −7568.58 −0.291916
\(877\) −1323.92 −0.0509756 −0.0254878 0.999675i \(-0.508114\pi\)
−0.0254878 + 0.999675i \(0.508114\pi\)
\(878\) −3571.67 −0.137287
\(879\) 59263.8 2.27408
\(880\) −7681.85 −0.294267
\(881\) −27090.2 −1.03597 −0.517987 0.855388i \(-0.673318\pi\)
−0.517987 + 0.855388i \(0.673318\pi\)
\(882\) 4008.73 0.153040
\(883\) 42910.9 1.63541 0.817705 0.575637i \(-0.195246\pi\)
0.817705 + 0.575637i \(0.195246\pi\)
\(884\) −28404.3 −1.08070
\(885\) 22188.6 0.842783
\(886\) 7585.75 0.287639
\(887\) 42010.3 1.59027 0.795133 0.606435i \(-0.207401\pi\)
0.795133 + 0.606435i \(0.207401\pi\)
\(888\) 20720.2 0.783024
\(889\) −158.674 −0.00598624
\(890\) 5184.82 0.195276
\(891\) −7231.56 −0.271904
\(892\) −20228.8 −0.759318
\(893\) 23536.3 0.881985
\(894\) −5953.24 −0.222714
\(895\) −46575.4 −1.73949
\(896\) 16968.2 0.632666
\(897\) 34324.5 1.27766
\(898\) −7294.00 −0.271051
\(899\) 15133.7 0.561443
\(900\) −110083. −4.07716
\(901\) −61652.8 −2.27964
\(902\) −176.390 −0.00651125
\(903\) 0 0
\(904\) −6538.13 −0.240548
\(905\) 1326.82 0.0487349
\(906\) −16476.2 −0.604179
\(907\) 11550.7 0.422861 0.211431 0.977393i \(-0.432188\pi\)
0.211431 + 0.977393i \(0.432188\pi\)
\(908\) −28550.9 −1.04350
\(909\) −84513.4 −3.08375
\(910\) −6638.52 −0.241829
\(911\) 5375.85 0.195510 0.0977552 0.995210i \(-0.468834\pi\)
0.0977552 + 0.995210i \(0.468834\pi\)
\(912\) 26089.7 0.947275
\(913\) −5127.57 −0.185868
\(914\) −5009.23 −0.181281
\(915\) −149529. −5.40250
\(916\) −9013.60 −0.325129
\(917\) −403.792 −0.0145413
\(918\) 17575.2 0.631881
\(919\) 1541.87 0.0553447 0.0276723 0.999617i \(-0.491190\pi\)
0.0276723 + 0.999617i \(0.491190\pi\)
\(920\) −19234.6 −0.689288
\(921\) −3426.72 −0.122599
\(922\) −6874.34 −0.245547
\(923\) 7856.78 0.280183
\(924\) −7626.94 −0.271545
\(925\) −58970.3 −2.09614
\(926\) 10351.9 0.367371
\(927\) −16720.9 −0.592433
\(928\) 10721.8 0.379269
\(929\) 20669.5 0.729973 0.364987 0.931013i \(-0.381074\pi\)
0.364987 + 0.931013i \(0.381074\pi\)
\(930\) −17312.2 −0.610418
\(931\) 5851.96 0.206004
\(932\) 21330.4 0.749680
\(933\) −23509.3 −0.824929
\(934\) −9965.07 −0.349108
\(935\) −14290.9 −0.499852
\(936\) 20167.0 0.704252
\(937\) −31002.3 −1.08090 −0.540449 0.841377i \(-0.681745\pi\)
−0.540449 + 0.841377i \(0.681745\pi\)
\(938\) 1560.06 0.0543045
\(939\) 82988.9 2.88418
\(940\) 67363.2 2.33739
\(941\) −31759.6 −1.10025 −0.550124 0.835083i \(-0.685420\pi\)
−0.550124 + 0.835083i \(0.685420\pi\)
\(942\) −2979.71 −0.103062
\(943\) 4066.20 0.140417
\(944\) −6840.12 −0.235834
\(945\) −81845.1 −2.81738
\(946\) 0 0
\(947\) 31056.3 1.06567 0.532837 0.846218i \(-0.321126\pi\)
0.532837 + 0.846218i \(0.321126\pi\)
\(948\) −34610.4 −1.18575
\(949\) −3946.15 −0.134982
\(950\) 8065.10 0.275438
\(951\) −22785.7 −0.776946
\(952\) 14970.3 0.509654
\(953\) −22084.7 −0.750676 −0.375338 0.926888i \(-0.622473\pi\)
−0.375338 + 0.926888i \(0.622473\pi\)
\(954\) 21350.9 0.724593
\(955\) 11375.7 0.385453
\(956\) 22001.4 0.744327
\(957\) −6365.69 −0.215019
\(958\) −1847.05 −0.0622917
\(959\) 11343.2 0.381952
\(960\) 66153.5 2.22406
\(961\) −5136.86 −0.172430
\(962\) 5269.39 0.176603
\(963\) −88936.2 −2.97604
\(964\) −368.809 −0.0123221
\(965\) −79725.2 −2.65953
\(966\) −8823.85 −0.293895
\(967\) 45620.1 1.51711 0.758554 0.651610i \(-0.225906\pi\)
0.758554 + 0.651610i \(0.225906\pi\)
\(968\) −12353.1 −0.410171
\(969\) 48535.7 1.60907
\(970\) −15605.0 −0.516544
\(971\) −39645.2 −1.31027 −0.655137 0.755510i \(-0.727389\pi\)
−0.655137 + 0.755510i \(0.727389\pi\)
\(972\) 13126.0 0.433144
\(973\) −15605.2 −0.514162
\(974\) 11792.9 0.387956
\(975\) −84452.0 −2.77398
\(976\) 46095.6 1.51177
\(977\) −58085.8 −1.90208 −0.951038 0.309074i \(-0.899981\pi\)
−0.951038 + 0.309074i \(0.899981\pi\)
\(978\) −232.385 −0.00759801
\(979\) 3105.79 0.101391
\(980\) 16748.9 0.545942
\(981\) 103620. 3.37241
\(982\) 5475.55 0.177935
\(983\) 8705.96 0.282479 0.141240 0.989975i \(-0.454891\pi\)
0.141240 + 0.989975i \(0.454891\pi\)
\(984\) 3515.24 0.113884
\(985\) 15289.9 0.494595
\(986\) 6094.43 0.196842
\(987\) 63356.7 2.04323
\(988\) 14359.6 0.462389
\(989\) 0 0
\(990\) 4949.06 0.158880
\(991\) 234.516 0.00751732 0.00375866 0.999993i \(-0.498804\pi\)
0.00375866 + 0.999993i \(0.498804\pi\)
\(992\) 17466.8 0.559044
\(993\) −37300.7 −1.19205
\(994\) −2019.75 −0.0644493
\(995\) 90770.2 2.89207
\(996\) 49842.4 1.58566
\(997\) 36443.3 1.15764 0.578822 0.815454i \(-0.303512\pi\)
0.578822 + 0.815454i \(0.303512\pi\)
\(998\) −7722.44 −0.244939
\(999\) 64965.4 2.05747
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.1.23 yes 50
43.42 odd 2 1849.4.a.i.1.28 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.i.1.28 50 43.42 odd 2
1849.4.a.j.1.23 yes 50 1.1 even 1 trivial