Properties

Label 1849.4.a.i.1.28
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 1.28
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 \(-0.465138\pi\)
0.109303 + 0.994008i \(0.465138\pi\)
\(3\) 9.18025 1.76674 0.883370 0.468676i \(-0.155269\pi\)
0.883370 + 0.468676i \(0.155269\pi\)
\(4\) −7.61769 −0.952211
\(5\) −19.4242 −1.73736 −0.868678 0.495377i \(-0.835030\pi\)
−0.868678 + 0.495377i \(0.835030\pi\)
\(6\) 5.67627 0.386221
\(7\) −15.1594 −0.818531 −0.409265 0.912415i \(-0.634215\pi\)
−0.409265 + 0.912415i \(0.634215\pi\)
\(8\) −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 \(-0.398961\pi\)
0.312121 + 0.950043i \(0.398961\pi\)
\(20\) 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 \(-0.400145\pi\)
0.308584 + 0.951197i \(0.400145\pi\)
\(30\) −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 \(-0.326209\pi\)
0.519257 + 0.854618i \(0.326209\pi\)
\(38\) 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 \(-0.842486\pi\)
−0.880042 + 0.474896i \(0.842486\pi\)
\(62\) −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 \(-0.557639\pi\)
−0.180090 + 0.983650i \(0.557639\pi\)
\(72\) −553.102 −0.905329
\(73\) 108.227 0.173521 0.0867606 0.996229i \(-0.472348\pi\)
0.0867606 + 0.996229i \(0.472348\pi\)
\(74\) 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 \(-0.417240\pi\)
0.257079 + 0.966390i \(0.417240\pi\)
\(90\) −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 \(-0.409060\pi\)
0.281826 + 0.959466i \(0.409060\pi\)
\(114\) 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 \(-0.497173\pi\)
0.00888258 + 0.999961i \(0.497173\pi\)
\(132\) 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 \(-0.574958\pi\)
−0.233316 + 0.972401i \(0.574958\pi\)
\(138\) −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 \(-0.406902\pi\)
0.288324 + 0.957533i \(0.406902\pi\)
\(150\) 1432.13 0.779551
\(151\) 2902.66 1.56434 0.782168 0.623068i \(-0.214114\pi\)
0.782168 + 0.623068i \(0.214114\pi\)
\(152\) −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 \(-0.457403\pi\)
0.133423 + 0.991059i \(0.457403\pi\)
\(158\) −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 \(-0.496869\pi\)
0.00983635 + 0.999952i \(0.496869\pi\)
\(164\) 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 \(-0.333107\pi\)
0.500615 + 0.865670i \(0.333107\pi\)
\(180\) 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 \(-0.535383\pi\)
−0.110931 + 0.993828i \(0.535383\pi\)
\(192\) −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 \(-0.812987\pi\)
−0.832319 + 0.554297i \(0.812987\pi\)
\(200\) −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 \(-0.560191\pi\)
−0.187969 + 0.982175i \(0.560191\pi\)
\(212\) 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 \(-0.630543\pi\)
−0.398713 + 0.917076i \(0.630543\pi\)
\(224\) −1686.36 −0.503013
\(225\) 14451.0 4.28179
\(226\) 418.636 0.123218
\(227\) −3747.98 −1.09587 −0.547934 0.836521i \(-0.684586\pi\)
−0.547934 + 0.836521i \(0.684586\pi\)
\(228\) −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 \(-0.371211\pi\)
0.393652 + 0.919259i \(0.371211\pi\)
\(234\) 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 \(-0.502060\pi\)
−0.00647027 + 0.999979i \(0.502060\pi\)
\(242\) −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 \(-0.524857\pi\)
−0.0780100 + 0.996953i \(0.524857\pi\)
\(258\) 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 \(-0.719504\pi\)
−0.636223 + 0.771505i \(0.719504\pi\)
\(264\) 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 \(-0.0887215\pi\)
0.961407 + 0.275132i \(0.0887215\pi\)
\(278\) −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 \(-0.196053\pi\)
0.816243 + 0.577709i \(0.196053\pi\)
\(314\) 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 \(-0.609533\pi\)
−0.337357 + 0.941377i \(0.609533\pi\)
\(332\) −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 \(-0.473562\pi\)
0.0829633 + 0.996553i \(0.473562\pi\)
\(348\) −6740.29 −1.03827
\(349\) −293.309 −0.0449870 −0.0224935 0.999747i \(-0.507161\pi\)
−0.0224935 + 0.999747i \(0.507161\pi\)
\(350\) −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 \(-0.658667\pi\)
−0.478079 + 0.878317i \(0.658667\pi\)
\(374\) −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 \(-0.574008\pi\)
−0.230413 + 0.973093i \(0.574008\pi\)
\(384\) −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 \(-0.943984\pi\)
−0.984555 + 0.175073i \(0.943984\pi\)
\(390\) −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 \(-0.537898\pi\)
−0.118778 + 0.992921i \(0.537898\pi\)
\(410\) 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 \(-0.771515\pi\)
−0.753249 + 0.657735i \(0.771515\pi\)
\(420\) −20592.2 −2.39238
\(421\) −1779.75 −0.206033 −0.103016 0.994680i \(-0.532849\pi\)
−0.103016 + 0.994680i \(0.532849\pi\)
\(422\) −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 \(-0.499368\pi\)
0.00198481 + 0.999998i \(0.499368\pi\)
\(434\) 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 \(-0.712848\pi\)
−0.619952 + 0.784640i \(0.712848\pi\)
\(450\) 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 \(-0.636088\pi\)
−0.414628 + 0.909991i \(0.636088\pi\)
\(458\) 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 \(-0.182405\pi\)
0.840255 + 0.542191i \(0.182405\pi\)
\(464\) 5298.24 0.530096
\(465\) 27999.1 2.79231
\(466\) 1731.35 0.172110
\(467\) −16116.5 −1.59697 −0.798485 0.602015i \(-0.794365\pi\)
−0.798485 + 0.602015i \(0.794365\pi\)
\(468\) −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 \(-0.366584\pi\)
0.406975 + 0.913439i \(0.366584\pi\)
\(492\) 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 \(-0.689287\pi\)
−0.560229 + 0.828338i \(0.689287\pi\)
\(500\) 18836.4 1.68478
\(501\) −10731.2 −0.956958
\(502\) −2928.17 −0.260339
\(503\) −1022.04 −0.0905977 −0.0452989 0.998973i \(-0.514424\pi\)
−0.0452989 + 0.998973i \(0.514424\pi\)
\(504\) 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 \(-0.420955\pi\)
0.245782 + 0.969325i \(0.420955\pi\)
\(522\) 3413.41 0.286209
\(523\) −16090.3 −1.34528 −0.672639 0.739971i \(-0.734839\pi\)
−0.672639 + 0.739971i \(0.734839\pi\)
\(524\) −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 \(-0.228665\pi\)
0.752879 + 0.658159i \(0.228665\pi\)
\(572\) 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 \(-0.873214\pi\)
−0.921718 + 0.387861i \(0.873214\pi\)
\(578\) 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 \(-0.778854\pi\)
−0.768214 + 0.640193i \(0.778854\pi\)
\(588\) 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 \(-0.324355\pi\)
0.524224 + 0.851580i \(0.324355\pi\)
\(594\) −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 \(-0.376908\pi\)
0.377140 + 0.926156i \(0.376908\pi\)
\(602\) 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 \(-0.697480\pi\)
−0.581361 + 0.813646i \(0.697480\pi\)
\(608\) 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 \(-0.610416\pi\)
−0.339967 + 0.940437i \(0.610416\pi\)
\(632\) 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 \(-0.303791\pi\)
0.578109 + 0.815959i \(0.303791\pi\)
\(642\) −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 \(-0.283366\pi\)
0.629241 + 0.777210i \(0.283366\pi\)
\(648\) −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 \(-0.436062\pi\)
0.199520 + 0.979894i \(0.436062\pi\)
\(654\) 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 \(-0.284168\pi\)
0.627279 + 0.778794i \(0.284168\pi\)
\(674\) −609.199 −0.0348152
\(675\) 70127.1 3.99880
\(676\) 6608.68 0.376006
\(677\) −12230.4 −0.694317 −0.347159 0.937806i \(-0.612853\pi\)
−0.347159 + 0.937806i \(0.612853\pi\)
\(678\) 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 \(-0.749279\pi\)
−0.705504 + 0.708706i \(0.749279\pi\)
\(692\) 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 \(-0.409289\pi\)
0.281135 + 0.959668i \(0.409289\pi\)
\(728\) 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 \(-0.236111\pi\)
0.737277 + 0.675590i \(0.236111\pi\)
\(734\) −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 \(-0.613507\pi\)
−0.349083 + 0.937092i \(0.613507\pi\)
\(740\) 34584.5 1.71804
\(741\) 17305.1 0.857920
\(742\) 5650.91 0.279584
\(743\) 2161.22 0.106712 0.0533562 0.998576i \(-0.483008\pi\)
0.0533562 + 0.998576i \(0.483008\pi\)
\(744\) 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 \(-0.249485\pi\)
0.708250 + 0.705962i \(0.249485\pi\)
\(752\) −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 \(-0.276263\pi\)
0.646427 + 0.762976i \(0.276263\pi\)
\(758\) −1291.88 −0.0619040
\(759\) 6772.65 0.323889
\(760\) 9697.32 0.462840
\(761\) −1001.36 −0.0476996 −0.0238498 0.999716i \(-0.507592\pi\)
−0.0238498 + 0.999716i \(0.507592\pi\)
\(762\) −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 \(-0.405165\pi\)
0.293545 + 0.955945i \(0.405165\pi\)
\(774\) 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 \(-0.157450\pi\)
0.880138 + 0.474719i \(0.157450\pi\)
\(812\) 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 \(-0.550176\pi\)
−0.156980 + 0.987602i \(0.550176\pi\)
\(830\) −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 \(-0.278889\pi\)
0.640110 + 0.768283i \(0.278889\pi\)
\(840\) −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 \(-0.604262\pi\)
−0.321723 + 0.946834i \(0.604262\pi\)
\(860\) 0 0
\(861\) 5518.38 0.218427
\(862\) −6386.81 −0.252362
\(863\) 33115.5 1.30622 0.653108 0.757264i \(-0.273465\pi\)
0.653108 + 0.757264i \(0.273465\pi\)
\(864\) 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 \(-0.792599\pi\)
−0.795133 + 0.606435i \(0.792599\pi\)
\(888\) −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 \(-0.531166\pi\)
−0.0977552 + 0.995210i \(0.531166\pi\)
\(912\) 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 \(-0.618926\pi\)
−0.364987 + 0.931013i \(0.618926\pi\)
\(930\) 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 \(-0.318255\pi\)
0.540449 + 0.841377i \(0.318255\pi\)
\(938\) 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 \(-0.377527\pi\)
0.375338 + 0.926888i \(0.377527\pi\)
\(954\) −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 \(-0.545109\pi\)
−0.141240 + 0.989975i \(0.545109\pi\)
\(984\) 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 \(-0.501196\pi\)
−0.00375866 + 0.999993i \(0.501196\pi\)
\(992\) −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 \(-0.696488\pi\)
−0.578822 + 0.815454i \(0.696488\pi\)
\(998\) −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.i.1.28 50
43.42 odd 2 1849.4.a.j.1.23 yes 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.i.1.28 50 1.1 even 1 trivial
1849.4.a.j.1.23 yes 50 43.42 odd 2