Properties

Label 1849.4.a.i.1.37
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 1.37
Character \(\chi\) \(=\) 1849.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.34626 q^{2} +7.09807 q^{3} -2.49508 q^{4} -10.0323 q^{5} +16.6539 q^{6} -1.59249 q^{7} -24.6242 q^{8} +23.3826 q^{9} +O(q^{10})\) \(q+2.34626 q^{2} +7.09807 q^{3} -2.49508 q^{4} -10.0323 q^{5} +16.6539 q^{6} -1.59249 q^{7} -24.6242 q^{8} +23.3826 q^{9} -23.5383 q^{10} +54.2230 q^{11} -17.7102 q^{12} +20.9047 q^{13} -3.73638 q^{14} -71.2098 q^{15} -37.8140 q^{16} -66.4021 q^{17} +54.8616 q^{18} -87.8191 q^{19} +25.0313 q^{20} -11.3036 q^{21} +127.221 q^{22} +106.974 q^{23} -174.784 q^{24} -24.3535 q^{25} +49.0478 q^{26} -25.6766 q^{27} +3.97338 q^{28} +270.053 q^{29} -167.076 q^{30} +131.936 q^{31} +108.272 q^{32} +384.879 q^{33} -155.797 q^{34} +15.9763 q^{35} -58.3414 q^{36} -62.8765 q^{37} -206.046 q^{38} +148.383 q^{39} +247.036 q^{40} -464.772 q^{41} -26.5211 q^{42} -135.291 q^{44} -234.581 q^{45} +250.989 q^{46} -205.162 q^{47} -268.406 q^{48} -340.464 q^{49} -57.1395 q^{50} -471.327 q^{51} -52.1588 q^{52} -296.839 q^{53} -60.2439 q^{54} -543.980 q^{55} +39.2136 q^{56} -623.346 q^{57} +633.613 q^{58} -493.751 q^{59} +177.674 q^{60} -617.044 q^{61} +309.555 q^{62} -37.2365 q^{63} +556.546 q^{64} -209.722 q^{65} +903.024 q^{66} -924.507 q^{67} +165.678 q^{68} +759.311 q^{69} +37.4844 q^{70} -254.048 q^{71} -575.776 q^{72} +170.044 q^{73} -147.525 q^{74} -172.863 q^{75} +219.115 q^{76} -86.3494 q^{77} +348.145 q^{78} -234.781 q^{79} +379.360 q^{80} -813.584 q^{81} -1090.47 q^{82} +1119.87 q^{83} +28.2033 q^{84} +666.165 q^{85} +1916.85 q^{87} -1335.20 q^{88} -1518.73 q^{89} -550.386 q^{90} -33.2905 q^{91} -266.909 q^{92} +936.490 q^{93} -481.362 q^{94} +881.026 q^{95} +768.521 q^{96} +273.132 q^{97} -798.816 q^{98} +1267.87 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q - 10q^{2} - 2q^{3} + 186q^{4} + 8q^{5} - 51q^{6} - 6q^{7} - 138q^{8} + 360q^{9} + O(q^{10}) \) \( 50q - 10q^{2} - 2q^{3} + 186q^{4} + 8q^{5} - 51q^{6} - 6q^{7} - 138q^{8} + 360q^{9} - 137q^{10} - 252q^{11} - 48q^{12} - 192q^{13} - 272q^{14} - 314q^{15} + 542q^{16} - 236q^{17} - 386q^{18} + 12q^{19} + 108q^{20} - 408q^{21} + 1235q^{22} - 630q^{23} - 613q^{24} + 1098q^{25} + 1493q^{26} + 10q^{27} - 242q^{28} + 208q^{29} - 48q^{30} - 932q^{31} - 1124q^{32} + 254q^{33} + 765q^{34} - 1452q^{35} + 747q^{36} - 90q^{37} - 1213q^{38} - 1610q^{39} - 1693q^{40} - 1354q^{41} - 16q^{42} - 2704q^{44} + 4508q^{45} + 233q^{46} - 3484q^{47} - 376q^{48} + 1324q^{49} - 408q^{50} + 4054q^{51} - 2176q^{52} - 726q^{53} - 6497q^{54} - 3288q^{55} - 7097q^{56} - 870q^{57} + 275q^{58} - 4370q^{59} - 3891q^{60} + 1172q^{61} - 1546q^{62} - 3686q^{63} + 606q^{64} + 2610q^{65} - 4697q^{66} - 344q^{67} - 3221q^{68} + 136q^{69} - 1310q^{70} + 162q^{71} - 5814q^{72} + 746q^{73} - 4332q^{74} + 236q^{75} + 1338q^{76} + 2024q^{77} - 2782q^{78} - 2656q^{79} - 5713q^{80} - 86q^{81} - 4168q^{82} - 3514q^{83} - 4269q^{84} - 7558q^{85} - 10278q^{87} + 11692q^{88} + 2640q^{89} - 8286q^{90} - 5946q^{91} - 4271q^{92} - 2q^{93} + 9062q^{94} - 12140q^{95} - 700q^{96} - 3864q^{97} - 2826q^{98} - 8174q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.34626 0.829527 0.414764 0.909929i \(-0.363864\pi\)
0.414764 + 0.909929i \(0.363864\pi\)
\(3\) 7.09807 1.36602 0.683012 0.730407i \(-0.260670\pi\)
0.683012 + 0.730407i \(0.260670\pi\)
\(4\) −2.49508 −0.311885
\(5\) −10.0323 −0.897314 −0.448657 0.893704i \(-0.648098\pi\)
−0.448657 + 0.893704i \(0.648098\pi\)
\(6\) 16.6539 1.13315
\(7\) −1.59249 −0.0859862 −0.0429931 0.999075i \(-0.513689\pi\)
−0.0429931 + 0.999075i \(0.513689\pi\)
\(8\) −24.6242 −1.08824
\(9\) 23.3826 0.866022
\(10\) −23.5383 −0.744346
\(11\) 54.2230 1.48626 0.743130 0.669147i \(-0.233341\pi\)
0.743130 + 0.669147i \(0.233341\pi\)
\(12\) −17.7102 −0.426042
\(13\) 20.9047 0.445994 0.222997 0.974819i \(-0.428416\pi\)
0.222997 + 0.974819i \(0.428416\pi\)
\(14\) −3.73638 −0.0713279
\(15\) −71.2098 −1.22575
\(16\) −37.8140 −0.590843
\(17\) −66.4021 −0.947346 −0.473673 0.880701i \(-0.657072\pi\)
−0.473673 + 0.880701i \(0.657072\pi\)
\(18\) 54.8616 0.718389
\(19\) −87.8191 −1.06037 −0.530187 0.847881i \(-0.677878\pi\)
−0.530187 + 0.847881i \(0.677878\pi\)
\(20\) 25.0313 0.279858
\(21\) −11.3036 −0.117459
\(22\) 127.221 1.23289
\(23\) 106.974 0.969812 0.484906 0.874566i \(-0.338854\pi\)
0.484906 + 0.874566i \(0.338854\pi\)
\(24\) −174.784 −1.48657
\(25\) −24.3535 −0.194828
\(26\) 49.0478 0.369964
\(27\) −25.6766 −0.183017
\(28\) 3.97338 0.0268178
\(29\) 270.053 1.72922 0.864612 0.502440i \(-0.167564\pi\)
0.864612 + 0.502440i \(0.167564\pi\)
\(30\) −167.076 −1.01680
\(31\) 131.936 0.764399 0.382200 0.924080i \(-0.375167\pi\)
0.382200 + 0.924080i \(0.375167\pi\)
\(32\) 108.272 0.598123
\(33\) 384.879 2.03027
\(34\) −155.797 −0.785849
\(35\) 15.9763 0.0771566
\(36\) −58.3414 −0.270099
\(37\) −62.8765 −0.279374 −0.139687 0.990196i \(-0.544610\pi\)
−0.139687 + 0.990196i \(0.544610\pi\)
\(38\) −206.046 −0.879608
\(39\) 148.383 0.609238
\(40\) 247.036 0.976497
\(41\) −464.772 −1.77037 −0.885185 0.465239i \(-0.845968\pi\)
−0.885185 + 0.465239i \(0.845968\pi\)
\(42\) −26.5211 −0.0974356
\(43\) 0 0
\(44\) −135.291 −0.463541
\(45\) −234.581 −0.777094
\(46\) 250.989 0.804486
\(47\) −205.162 −0.636721 −0.318361 0.947970i \(-0.603132\pi\)
−0.318361 + 0.947970i \(0.603132\pi\)
\(48\) −268.406 −0.807106
\(49\) −340.464 −0.992606
\(50\) −57.1395 −0.161615
\(51\) −471.327 −1.29410
\(52\) −52.1588 −0.139099
\(53\) −296.839 −0.769320 −0.384660 0.923058i \(-0.625681\pi\)
−0.384660 + 0.923058i \(0.625681\pi\)
\(54\) −60.2439 −0.151818
\(55\) −543.980 −1.33364
\(56\) 39.2136 0.0935740
\(57\) −623.346 −1.44850
\(58\) 633.613 1.43444
\(59\) −493.751 −1.08951 −0.544754 0.838596i \(-0.683377\pi\)
−0.544754 + 0.838596i \(0.683377\pi\)
\(60\) 177.674 0.382293
\(61\) −617.044 −1.29515 −0.647577 0.762000i \(-0.724218\pi\)
−0.647577 + 0.762000i \(0.724218\pi\)
\(62\) 309.555 0.634090
\(63\) −37.2365 −0.0744659
\(64\) 556.546 1.08700
\(65\) −209.722 −0.400197
\(66\) 903.024 1.68416
\(67\) −924.507 −1.68577 −0.842885 0.538094i \(-0.819144\pi\)
−0.842885 + 0.538094i \(0.819144\pi\)
\(68\) 165.678 0.295463
\(69\) 759.311 1.32479
\(70\) 37.4844 0.0640035
\(71\) −254.048 −0.424648 −0.212324 0.977199i \(-0.568103\pi\)
−0.212324 + 0.977199i \(0.568103\pi\)
\(72\) −575.776 −0.942443
\(73\) 170.044 0.272632 0.136316 0.990665i \(-0.456474\pi\)
0.136316 + 0.990665i \(0.456474\pi\)
\(74\) −147.525 −0.231748
\(75\) −172.863 −0.266139
\(76\) 219.115 0.330714
\(77\) −86.3494 −0.127798
\(78\) 348.145 0.505380
\(79\) −234.781 −0.334366 −0.167183 0.985926i \(-0.553467\pi\)
−0.167183 + 0.985926i \(0.553467\pi\)
\(80\) 379.360 0.530172
\(81\) −813.584 −1.11603
\(82\) −1090.47 −1.46857
\(83\) 1119.87 1.48099 0.740495 0.672061i \(-0.234591\pi\)
0.740495 + 0.672061i \(0.234591\pi\)
\(84\) 28.2033 0.0366337
\(85\) 666.165 0.850067
\(86\) 0 0
\(87\) 1916.85 2.36216
\(88\) −1335.20 −1.61741
\(89\) −1518.73 −1.80883 −0.904413 0.426658i \(-0.859691\pi\)
−0.904413 + 0.426658i \(0.859691\pi\)
\(90\) −550.386 −0.644620
\(91\) −33.2905 −0.0383493
\(92\) −266.909 −0.302470
\(93\) 936.490 1.04419
\(94\) −481.362 −0.528178
\(95\) 881.026 0.951488
\(96\) 768.521 0.817051
\(97\) 273.132 0.285900 0.142950 0.989730i \(-0.454341\pi\)
0.142950 + 0.989730i \(0.454341\pi\)
\(98\) −798.816 −0.823394
\(99\) 1267.87 1.28713
\(100\) 60.7637 0.0607637
\(101\) 1387.47 1.36692 0.683458 0.729990i \(-0.260475\pi\)
0.683458 + 0.729990i \(0.260475\pi\)
\(102\) −1105.85 −1.07349
\(103\) 467.337 0.447069 0.223534 0.974696i \(-0.428241\pi\)
0.223534 + 0.974696i \(0.428241\pi\)
\(104\) −514.760 −0.485350
\(105\) 113.401 0.105398
\(106\) −696.460 −0.638172
\(107\) −1143.64 −1.03327 −0.516634 0.856206i \(-0.672815\pi\)
−0.516634 + 0.856206i \(0.672815\pi\)
\(108\) 64.0651 0.0570803
\(109\) −1588.55 −1.39592 −0.697959 0.716138i \(-0.745908\pi\)
−0.697959 + 0.716138i \(0.745908\pi\)
\(110\) −1276.32 −1.10629
\(111\) −446.302 −0.381632
\(112\) 60.2183 0.0508044
\(113\) −1138.26 −0.947599 −0.473800 0.880633i \(-0.657118\pi\)
−0.473800 + 0.880633i \(0.657118\pi\)
\(114\) −1462.53 −1.20157
\(115\) −1073.20 −0.870226
\(116\) −673.802 −0.539318
\(117\) 488.806 0.386240
\(118\) −1158.47 −0.903776
\(119\) 105.745 0.0814587
\(120\) 1753.48 1.33392
\(121\) 1609.13 1.20897
\(122\) −1447.74 −1.07437
\(123\) −3298.98 −2.41837
\(124\) −329.190 −0.238404
\(125\) 1498.35 1.07214
\(126\) −87.3663 −0.0617715
\(127\) −1867.17 −1.30460 −0.652302 0.757959i \(-0.726197\pi\)
−0.652302 + 0.757959i \(0.726197\pi\)
\(128\) 439.624 0.303575
\(129\) 0 0
\(130\) −492.061 −0.331974
\(131\) 955.828 0.637489 0.318745 0.947841i \(-0.396739\pi\)
0.318745 + 0.947841i \(0.396739\pi\)
\(132\) −960.302 −0.633209
\(133\) 139.851 0.0911775
\(134\) −2169.13 −1.39839
\(135\) 257.595 0.164224
\(136\) 1635.10 1.03094
\(137\) 2405.03 1.49982 0.749910 0.661540i \(-0.230097\pi\)
0.749910 + 0.661540i \(0.230097\pi\)
\(138\) 1781.54 1.09895
\(139\) 280.828 0.171364 0.0856819 0.996323i \(-0.472693\pi\)
0.0856819 + 0.996323i \(0.472693\pi\)
\(140\) −39.8620 −0.0240640
\(141\) −1456.25 −0.869777
\(142\) −596.062 −0.352257
\(143\) 1133.52 0.662862
\(144\) −884.189 −0.511683
\(145\) −2709.24 −1.55166
\(146\) 398.967 0.226156
\(147\) −2416.64 −1.35592
\(148\) 156.882 0.0871325
\(149\) −890.919 −0.489845 −0.244923 0.969543i \(-0.578763\pi\)
−0.244923 + 0.969543i \(0.578763\pi\)
\(150\) −405.580 −0.220770
\(151\) 2669.04 1.43844 0.719218 0.694785i \(-0.244500\pi\)
0.719218 + 0.694785i \(0.244500\pi\)
\(152\) 2162.47 1.15394
\(153\) −1552.65 −0.820423
\(154\) −202.598 −0.106012
\(155\) −1323.62 −0.685906
\(156\) −370.227 −0.190012
\(157\) −1228.63 −0.624557 −0.312279 0.949991i \(-0.601092\pi\)
−0.312279 + 0.949991i \(0.601092\pi\)
\(158\) −550.856 −0.277365
\(159\) −2106.98 −1.05091
\(160\) −1086.21 −0.536704
\(161\) −170.355 −0.0833905
\(162\) −1908.88 −0.925776
\(163\) −1630.73 −0.783613 −0.391806 0.920048i \(-0.628150\pi\)
−0.391806 + 0.920048i \(0.628150\pi\)
\(164\) 1159.64 0.552151
\(165\) −3861.21 −1.82179
\(166\) 2627.51 1.22852
\(167\) −868.387 −0.402382 −0.201191 0.979552i \(-0.564481\pi\)
−0.201191 + 0.979552i \(0.564481\pi\)
\(168\) 278.341 0.127824
\(169\) −1759.99 −0.801089
\(170\) 1562.99 0.705154
\(171\) −2053.44 −0.918306
\(172\) 0 0
\(173\) 568.588 0.249878 0.124939 0.992164i \(-0.460126\pi\)
0.124939 + 0.992164i \(0.460126\pi\)
\(174\) 4497.43 1.95948
\(175\) 38.7826 0.0167525
\(176\) −2050.39 −0.878146
\(177\) −3504.68 −1.48829
\(178\) −3563.34 −1.50047
\(179\) 2061.54 0.860819 0.430410 0.902634i \(-0.358369\pi\)
0.430410 + 0.902634i \(0.358369\pi\)
\(180\) 585.297 0.242364
\(181\) −466.885 −0.191731 −0.0958654 0.995394i \(-0.530562\pi\)
−0.0958654 + 0.995394i \(0.530562\pi\)
\(182\) −78.1080 −0.0318118
\(183\) −4379.82 −1.76921
\(184\) −2634.15 −1.05539
\(185\) 630.795 0.250686
\(186\) 2197.25 0.866182
\(187\) −3600.52 −1.40800
\(188\) 511.894 0.198584
\(189\) 40.8897 0.0157370
\(190\) 2067.11 0.789285
\(191\) −2820.00 −1.06831 −0.534157 0.845385i \(-0.679371\pi\)
−0.534157 + 0.845385i \(0.679371\pi\)
\(192\) 3950.40 1.48487
\(193\) −126.041 −0.0470085 −0.0235043 0.999724i \(-0.507482\pi\)
−0.0235043 + 0.999724i \(0.507482\pi\)
\(194\) 640.837 0.237162
\(195\) −1488.62 −0.546678
\(196\) 849.484 0.309579
\(197\) 3366.96 1.21769 0.608847 0.793288i \(-0.291632\pi\)
0.608847 + 0.793288i \(0.291632\pi\)
\(198\) 2974.76 1.06771
\(199\) −621.425 −0.221365 −0.110683 0.993856i \(-0.535304\pi\)
−0.110683 + 0.993856i \(0.535304\pi\)
\(200\) 599.683 0.212020
\(201\) −6562.22 −2.30280
\(202\) 3255.36 1.13389
\(203\) −430.055 −0.148689
\(204\) 1176.00 0.403609
\(205\) 4662.72 1.58858
\(206\) 1096.49 0.370855
\(207\) 2501.34 0.839879
\(208\) −790.490 −0.263512
\(209\) −4761.82 −1.57599
\(210\) 266.067 0.0874304
\(211\) 5419.38 1.76818 0.884090 0.467317i \(-0.154779\pi\)
0.884090 + 0.467317i \(0.154779\pi\)
\(212\) 740.636 0.239939
\(213\) −1803.25 −0.580079
\(214\) −2683.27 −0.857124
\(215\) 0 0
\(216\) 632.265 0.199167
\(217\) −210.106 −0.0657278
\(218\) −3727.14 −1.15795
\(219\) 1206.98 0.372422
\(220\) 1357.27 0.415942
\(221\) −1388.12 −0.422511
\(222\) −1047.14 −0.316574
\(223\) −4538.64 −1.36291 −0.681457 0.731859i \(-0.738653\pi\)
−0.681457 + 0.731859i \(0.738653\pi\)
\(224\) −172.422 −0.0514304
\(225\) −569.447 −0.168725
\(226\) −2670.66 −0.786059
\(227\) −19.2993 −0.00564291 −0.00282146 0.999996i \(-0.500898\pi\)
−0.00282146 + 0.999996i \(0.500898\pi\)
\(228\) 1555.30 0.451763
\(229\) −3286.03 −0.948241 −0.474120 0.880460i \(-0.657234\pi\)
−0.474120 + 0.880460i \(0.657234\pi\)
\(230\) −2517.99 −0.721876
\(231\) −612.914 −0.174575
\(232\) −6649.81 −1.88182
\(233\) 6911.23 1.94322 0.971610 0.236590i \(-0.0760298\pi\)
0.971610 + 0.236590i \(0.0760298\pi\)
\(234\) 1146.86 0.320397
\(235\) 2058.24 0.571339
\(236\) 1231.95 0.339801
\(237\) −1666.49 −0.456752
\(238\) 248.104 0.0675722
\(239\) 5845.44 1.58205 0.791026 0.611783i \(-0.209547\pi\)
0.791026 + 0.611783i \(0.209547\pi\)
\(240\) 2692.73 0.724228
\(241\) 3122.07 0.834483 0.417241 0.908796i \(-0.362997\pi\)
0.417241 + 0.908796i \(0.362997\pi\)
\(242\) 3775.44 1.00287
\(243\) −5081.61 −1.34150
\(244\) 1539.57 0.403939
\(245\) 3415.63 0.890680
\(246\) −7740.26 −2.00610
\(247\) −1835.83 −0.472920
\(248\) −3248.81 −0.831853
\(249\) 7948.95 2.02307
\(250\) 3515.53 0.889366
\(251\) −3719.55 −0.935361 −0.467681 0.883898i \(-0.654910\pi\)
−0.467681 + 0.883898i \(0.654910\pi\)
\(252\) 92.9079 0.0232248
\(253\) 5800.47 1.44139
\(254\) −4380.87 −1.08220
\(255\) 4728.48 1.16121
\(256\) −3420.89 −0.835179
\(257\) −101.022 −0.0245197 −0.0122598 0.999925i \(-0.503903\pi\)
−0.0122598 + 0.999925i \(0.503903\pi\)
\(258\) 0 0
\(259\) 100.130 0.0240223
\(260\) 523.272 0.124815
\(261\) 6314.53 1.49755
\(262\) 2242.62 0.528815
\(263\) 511.815 0.119999 0.0599997 0.998198i \(-0.480890\pi\)
0.0599997 + 0.998198i \(0.480890\pi\)
\(264\) −9477.31 −2.20942
\(265\) 2977.97 0.690321
\(266\) 328.126 0.0756342
\(267\) −10780.1 −2.47090
\(268\) 2306.72 0.525766
\(269\) −1540.91 −0.349259 −0.174630 0.984634i \(-0.555873\pi\)
−0.174630 + 0.984634i \(0.555873\pi\)
\(270\) 604.384 0.136228
\(271\) 6941.15 1.55589 0.777943 0.628335i \(-0.216263\pi\)
0.777943 + 0.628335i \(0.216263\pi\)
\(272\) 2510.93 0.559733
\(273\) −236.298 −0.0523861
\(274\) 5642.81 1.24414
\(275\) −1320.52 −0.289564
\(276\) −1894.54 −0.413181
\(277\) −6181.58 −1.34085 −0.670425 0.741977i \(-0.733888\pi\)
−0.670425 + 0.741977i \(0.733888\pi\)
\(278\) 658.896 0.142151
\(279\) 3085.00 0.661987
\(280\) −393.402 −0.0839652
\(281\) −4813.12 −1.02180 −0.510901 0.859639i \(-0.670688\pi\)
−0.510901 + 0.859639i \(0.670688\pi\)
\(282\) −3416.74 −0.721504
\(283\) 2174.68 0.456789 0.228394 0.973569i \(-0.426652\pi\)
0.228394 + 0.973569i \(0.426652\pi\)
\(284\) 633.870 0.132441
\(285\) 6253.58 1.29976
\(286\) 2659.52 0.549862
\(287\) 740.143 0.152227
\(288\) 2531.68 0.517988
\(289\) −503.755 −0.102535
\(290\) −6356.58 −1.28714
\(291\) 1938.71 0.390546
\(292\) −424.272 −0.0850297
\(293\) −1256.47 −0.250524 −0.125262 0.992124i \(-0.539977\pi\)
−0.125262 + 0.992124i \(0.539977\pi\)
\(294\) −5670.05 −1.12478
\(295\) 4953.45 0.977630
\(296\) 1548.28 0.304027
\(297\) −1392.26 −0.272011
\(298\) −2090.33 −0.406340
\(299\) 2236.27 0.432530
\(300\) 431.305 0.0830047
\(301\) 0 0
\(302\) 6262.26 1.19322
\(303\) 9848.36 1.86724
\(304\) 3320.79 0.626514
\(305\) 6190.36 1.16216
\(306\) −3642.93 −0.680563
\(307\) −5966.37 −1.10918 −0.554590 0.832124i \(-0.687125\pi\)
−0.554590 + 0.832124i \(0.687125\pi\)
\(308\) 215.448 0.0398582
\(309\) 3317.19 0.610706
\(310\) −3105.55 −0.568978
\(311\) −9796.87 −1.78627 −0.893135 0.449789i \(-0.851499\pi\)
−0.893135 + 0.449789i \(0.851499\pi\)
\(312\) −3653.81 −0.663000
\(313\) −2338.77 −0.422349 −0.211175 0.977448i \(-0.567729\pi\)
−0.211175 + 0.977448i \(0.567729\pi\)
\(314\) −2882.69 −0.518087
\(315\) 373.567 0.0668193
\(316\) 585.796 0.104284
\(317\) −3796.22 −0.672608 −0.336304 0.941753i \(-0.609177\pi\)
−0.336304 + 0.941753i \(0.609177\pi\)
\(318\) −4943.52 −0.871758
\(319\) 14643.1 2.57008
\(320\) −5583.42 −0.975383
\(321\) −8117.62 −1.41147
\(322\) −399.697 −0.0691747
\(323\) 5831.38 1.00454
\(324\) 2029.96 0.348072
\(325\) −509.102 −0.0868919
\(326\) −3826.12 −0.650028
\(327\) −11275.6 −1.90686
\(328\) 11444.6 1.92659
\(329\) 326.717 0.0547493
\(330\) −9059.39 −1.51122
\(331\) 7319.01 1.21537 0.607687 0.794176i \(-0.292097\pi\)
0.607687 + 0.794176i \(0.292097\pi\)
\(332\) −2794.17 −0.461898
\(333\) −1470.22 −0.241944
\(334\) −2037.46 −0.333787
\(335\) 9274.91 1.51266
\(336\) 427.433 0.0694000
\(337\) 3275.07 0.529389 0.264695 0.964332i \(-0.414729\pi\)
0.264695 + 0.964332i \(0.414729\pi\)
\(338\) −4129.40 −0.664526
\(339\) −8079.47 −1.29444
\(340\) −1662.13 −0.265123
\(341\) 7153.96 1.13610
\(342\) −4817.90 −0.761760
\(343\) 1088.41 0.171337
\(344\) 0 0
\(345\) −7617.62 −1.18875
\(346\) 1334.05 0.207281
\(347\) 5180.13 0.801394 0.400697 0.916211i \(-0.368768\pi\)
0.400697 + 0.916211i \(0.368768\pi\)
\(348\) −4782.69 −0.736722
\(349\) −8216.57 −1.26024 −0.630119 0.776499i \(-0.716994\pi\)
−0.630119 + 0.776499i \(0.716994\pi\)
\(350\) 90.9939 0.0138966
\(351\) −536.762 −0.0816246
\(352\) 5870.83 0.888966
\(353\) −4792.83 −0.722653 −0.361327 0.932439i \(-0.617676\pi\)
−0.361327 + 0.932439i \(0.617676\pi\)
\(354\) −8222.88 −1.23458
\(355\) 2548.68 0.381042
\(356\) 3789.36 0.564145
\(357\) 750.582 0.111275
\(358\) 4836.90 0.714073
\(359\) −5364.53 −0.788660 −0.394330 0.918969i \(-0.629023\pi\)
−0.394330 + 0.918969i \(0.629023\pi\)
\(360\) 5776.35 0.845667
\(361\) 853.200 0.124391
\(362\) −1095.43 −0.159046
\(363\) 11421.7 1.65148
\(364\) 83.0623 0.0119606
\(365\) −1705.93 −0.244636
\(366\) −10276.2 −1.46761
\(367\) −6048.71 −0.860327 −0.430164 0.902751i \(-0.641544\pi\)
−0.430164 + 0.902751i \(0.641544\pi\)
\(368\) −4045.12 −0.573007
\(369\) −10867.6 −1.53318
\(370\) 1480.01 0.207951
\(371\) 472.712 0.0661509
\(372\) −2336.61 −0.325666
\(373\) −1134.30 −0.157458 −0.0787288 0.996896i \(-0.525086\pi\)
−0.0787288 + 0.996896i \(0.525086\pi\)
\(374\) −8447.76 −1.16798
\(375\) 10635.4 1.46456
\(376\) 5051.93 0.692908
\(377\) 5645.37 0.771223
\(378\) 95.9377 0.0130542
\(379\) 2181.24 0.295628 0.147814 0.989015i \(-0.452776\pi\)
0.147814 + 0.989015i \(0.452776\pi\)
\(380\) −2198.23 −0.296754
\(381\) −13253.3 −1.78212
\(382\) −6616.44 −0.886195
\(383\) −2240.94 −0.298973 −0.149486 0.988764i \(-0.547762\pi\)
−0.149486 + 0.988764i \(0.547762\pi\)
\(384\) 3120.48 0.414691
\(385\) 866.281 0.114675
\(386\) −295.725 −0.0389949
\(387\) 0 0
\(388\) −681.484 −0.0891678
\(389\) 3329.27 0.433935 0.216967 0.976179i \(-0.430383\pi\)
0.216967 + 0.976179i \(0.430383\pi\)
\(390\) −3492.68 −0.453484
\(391\) −7103.32 −0.918748
\(392\) 8383.64 1.08020
\(393\) 6784.53 0.870826
\(394\) 7899.75 1.01011
\(395\) 2355.38 0.300031
\(396\) −3163.44 −0.401437
\(397\) 10745.2 1.35841 0.679204 0.733949i \(-0.262325\pi\)
0.679204 + 0.733949i \(0.262325\pi\)
\(398\) −1458.02 −0.183628
\(399\) 992.671 0.124551
\(400\) 920.901 0.115113
\(401\) 12059.5 1.50181 0.750904 0.660412i \(-0.229618\pi\)
0.750904 + 0.660412i \(0.229618\pi\)
\(402\) −15396.7 −1.91024
\(403\) 2758.08 0.340917
\(404\) −3461.85 −0.426320
\(405\) 8162.10 1.00143
\(406\) −1009.02 −0.123342
\(407\) −3409.35 −0.415222
\(408\) 11606.0 1.40829
\(409\) 10179.7 1.23069 0.615346 0.788257i \(-0.289016\pi\)
0.615346 + 0.788257i \(0.289016\pi\)
\(410\) 10939.9 1.31777
\(411\) 17071.1 2.04879
\(412\) −1166.04 −0.139434
\(413\) 786.292 0.0936826
\(414\) 5868.78 0.696702
\(415\) −11234.9 −1.32891
\(416\) 2263.39 0.266759
\(417\) 1993.34 0.234087
\(418\) −11172.4 −1.30733
\(419\) 5651.04 0.658881 0.329441 0.944176i \(-0.393140\pi\)
0.329441 + 0.944176i \(0.393140\pi\)
\(420\) −282.943 −0.0328720
\(421\) 1615.31 0.186996 0.0934979 0.995619i \(-0.470195\pi\)
0.0934979 + 0.995619i \(0.470195\pi\)
\(422\) 12715.3 1.46675
\(423\) −4797.21 −0.551415
\(424\) 7309.40 0.837207
\(425\) 1617.12 0.184569
\(426\) −4230.89 −0.481191
\(427\) 982.635 0.111365
\(428\) 2853.47 0.322260
\(429\) 8045.77 0.905486
\(430\) 0 0
\(431\) 11004.8 1.22990 0.614948 0.788568i \(-0.289177\pi\)
0.614948 + 0.788568i \(0.289177\pi\)
\(432\) 970.935 0.108135
\(433\) 2902.19 0.322103 0.161051 0.986946i \(-0.448512\pi\)
0.161051 + 0.986946i \(0.448512\pi\)
\(434\) −492.963 −0.0545230
\(435\) −19230.4 −2.11960
\(436\) 3963.54 0.435365
\(437\) −9394.39 −1.02836
\(438\) 2831.89 0.308934
\(439\) 16349.7 1.77752 0.888759 0.458374i \(-0.151568\pi\)
0.888759 + 0.458374i \(0.151568\pi\)
\(440\) 13395.0 1.45133
\(441\) −7960.93 −0.859619
\(442\) −3256.88 −0.350484
\(443\) −6987.71 −0.749427 −0.374713 0.927141i \(-0.622259\pi\)
−0.374713 + 0.927141i \(0.622259\pi\)
\(444\) 1113.56 0.119025
\(445\) 15236.4 1.62309
\(446\) −10648.8 −1.13057
\(447\) −6323.81 −0.669140
\(448\) −886.291 −0.0934673
\(449\) 1212.50 0.127442 0.0637209 0.997968i \(-0.479703\pi\)
0.0637209 + 0.997968i \(0.479703\pi\)
\(450\) −1336.07 −0.139962
\(451\) −25201.3 −2.63123
\(452\) 2840.05 0.295542
\(453\) 18945.1 1.96494
\(454\) −45.2812 −0.00468095
\(455\) 333.979 0.0344114
\(456\) 15349.4 1.57632
\(457\) −14320.1 −1.46579 −0.732895 0.680342i \(-0.761831\pi\)
−0.732895 + 0.680342i \(0.761831\pi\)
\(458\) −7709.88 −0.786591
\(459\) 1704.98 0.173381
\(460\) 2677.71 0.271410
\(461\) 1937.58 0.195753 0.0978765 0.995199i \(-0.468795\pi\)
0.0978765 + 0.995199i \(0.468795\pi\)
\(462\) −1438.05 −0.144815
\(463\) −7764.53 −0.779370 −0.389685 0.920948i \(-0.627416\pi\)
−0.389685 + 0.920948i \(0.627416\pi\)
\(464\) −10211.8 −1.02170
\(465\) −9395.12 −0.936964
\(466\) 16215.5 1.61195
\(467\) 4416.04 0.437580 0.218790 0.975772i \(-0.429789\pi\)
0.218790 + 0.975772i \(0.429789\pi\)
\(468\) −1219.61 −0.120462
\(469\) 1472.27 0.144953
\(470\) 4829.16 0.473941
\(471\) −8720.91 −0.853160
\(472\) 12158.2 1.18565
\(473\) 0 0
\(474\) −3910.01 −0.378888
\(475\) 2138.70 0.206590
\(476\) −263.841 −0.0254057
\(477\) −6940.86 −0.666248
\(478\) 13714.9 1.31235
\(479\) 7251.07 0.691670 0.345835 0.938295i \(-0.387596\pi\)
0.345835 + 0.938295i \(0.387596\pi\)
\(480\) −7710.02 −0.733151
\(481\) −1314.41 −0.124599
\(482\) 7325.19 0.692226
\(483\) −1209.19 −0.113913
\(484\) −4014.91 −0.377058
\(485\) −2740.13 −0.256542
\(486\) −11922.8 −1.11281
\(487\) 5573.78 0.518628 0.259314 0.965793i \(-0.416503\pi\)
0.259314 + 0.965793i \(0.416503\pi\)
\(488\) 15194.2 1.40944
\(489\) −11575.1 −1.07043
\(490\) 8013.94 0.738843
\(491\) 4398.58 0.404287 0.202144 0.979356i \(-0.435209\pi\)
0.202144 + 0.979356i \(0.435209\pi\)
\(492\) 8231.22 0.754252
\(493\) −17932.1 −1.63817
\(494\) −4307.34 −0.392300
\(495\) −12719.7 −1.15496
\(496\) −4989.02 −0.451640
\(497\) 404.568 0.0365138
\(498\) 18650.3 1.67819
\(499\) 6822.62 0.612069 0.306035 0.952020i \(-0.400998\pi\)
0.306035 + 0.952020i \(0.400998\pi\)
\(500\) −3738.51 −0.334383
\(501\) −6163.87 −0.549664
\(502\) −8727.01 −0.775907
\(503\) 4502.57 0.399124 0.199562 0.979885i \(-0.436048\pi\)
0.199562 + 0.979885i \(0.436048\pi\)
\(504\) 916.917 0.0810371
\(505\) −13919.5 −1.22655
\(506\) 13609.4 1.19567
\(507\) −12492.6 −1.09431
\(508\) 4658.74 0.406886
\(509\) 11276.1 0.981938 0.490969 0.871177i \(-0.336643\pi\)
0.490969 + 0.871177i \(0.336643\pi\)
\(510\) 11094.2 0.963257
\(511\) −270.793 −0.0234426
\(512\) −11543.3 −0.996379
\(513\) 2254.90 0.194067
\(514\) −237.023 −0.0203397
\(515\) −4688.45 −0.401161
\(516\) 0 0
\(517\) −11124.5 −0.946333
\(518\) 234.931 0.0199272
\(519\) 4035.87 0.341339
\(520\) 5164.22 0.435511
\(521\) −11275.7 −0.948171 −0.474086 0.880479i \(-0.657221\pi\)
−0.474086 + 0.880479i \(0.657221\pi\)
\(522\) 14815.5 1.24226
\(523\) 7792.77 0.651537 0.325769 0.945449i \(-0.394377\pi\)
0.325769 + 0.945449i \(0.394377\pi\)
\(524\) −2384.86 −0.198823
\(525\) 275.281 0.0228843
\(526\) 1200.85 0.0995428
\(527\) −8760.82 −0.724151
\(528\) −14553.8 −1.19957
\(529\) −723.497 −0.0594639
\(530\) 6987.08 0.572640
\(531\) −11545.2 −0.943537
\(532\) −348.939 −0.0284369
\(533\) −9715.92 −0.789574
\(534\) −25292.8 −2.04968
\(535\) 11473.3 0.927166
\(536\) 22765.2 1.83453
\(537\) 14632.9 1.17590
\(538\) −3615.36 −0.289720
\(539\) −18461.0 −1.47527
\(540\) −642.719 −0.0512189
\(541\) −13189.7 −1.04819 −0.524094 0.851660i \(-0.675596\pi\)
−0.524094 + 0.851660i \(0.675596\pi\)
\(542\) 16285.7 1.29065
\(543\) −3313.98 −0.261909
\(544\) −7189.49 −0.566630
\(545\) 15936.7 1.25258
\(546\) −554.416 −0.0434557
\(547\) 1883.02 0.147189 0.0735943 0.997288i \(-0.476553\pi\)
0.0735943 + 0.997288i \(0.476553\pi\)
\(548\) −6000.73 −0.467771
\(549\) −14428.1 −1.12163
\(550\) −3098.27 −0.240202
\(551\) −23715.8 −1.83362
\(552\) −18697.4 −1.44169
\(553\) 373.885 0.0287508
\(554\) −14503.6 −1.11227
\(555\) 4477.42 0.342443
\(556\) −700.689 −0.0534457
\(557\) −11319.0 −0.861045 −0.430522 0.902580i \(-0.641671\pi\)
−0.430522 + 0.902580i \(0.641671\pi\)
\(558\) 7238.21 0.549136
\(559\) 0 0
\(560\) −604.126 −0.0455875
\(561\) −25556.8 −1.92336
\(562\) −11292.8 −0.847613
\(563\) −16486.4 −1.23414 −0.617068 0.786910i \(-0.711680\pi\)
−0.617068 + 0.786910i \(0.711680\pi\)
\(564\) 3633.46 0.271270
\(565\) 11419.4 0.850294
\(566\) 5102.36 0.378919
\(567\) 1295.62 0.0959630
\(568\) 6255.72 0.462120
\(569\) 8711.61 0.641844 0.320922 0.947106i \(-0.396007\pi\)
0.320922 + 0.947106i \(0.396007\pi\)
\(570\) 14672.5 1.07818
\(571\) 2922.89 0.214219 0.107109 0.994247i \(-0.465840\pi\)
0.107109 + 0.994247i \(0.465840\pi\)
\(572\) −2828.21 −0.206737
\(573\) −20016.5 −1.45934
\(574\) 1736.57 0.126277
\(575\) −2605.19 −0.188946
\(576\) 13013.5 0.941368
\(577\) −10164.6 −0.733378 −0.366689 0.930344i \(-0.619509\pi\)
−0.366689 + 0.930344i \(0.619509\pi\)
\(578\) −1181.94 −0.0850556
\(579\) −894.649 −0.0642148
\(580\) 6759.77 0.483938
\(581\) −1783.39 −0.127345
\(582\) 4548.70 0.323969
\(583\) −16095.5 −1.14341
\(584\) −4187.18 −0.296690
\(585\) −4903.84 −0.346579
\(586\) −2947.99 −0.207816
\(587\) 15863.8 1.11545 0.557725 0.830026i \(-0.311675\pi\)
0.557725 + 0.830026i \(0.311675\pi\)
\(588\) 6029.70 0.422892
\(589\) −11586.5 −0.810549
\(590\) 11622.1 0.810971
\(591\) 23898.9 1.66340
\(592\) 2377.61 0.165066
\(593\) −6490.70 −0.449479 −0.224740 0.974419i \(-0.572153\pi\)
−0.224740 + 0.974419i \(0.572153\pi\)
\(594\) −3266.61 −0.225641
\(595\) −1060.86 −0.0730940
\(596\) 2222.91 0.152775
\(597\) −4410.92 −0.302390
\(598\) 5246.85 0.358796
\(599\) 10183.6 0.694642 0.347321 0.937746i \(-0.387091\pi\)
0.347321 + 0.937746i \(0.387091\pi\)
\(600\) 4256.59 0.289624
\(601\) −5118.21 −0.347381 −0.173691 0.984800i \(-0.555569\pi\)
−0.173691 + 0.984800i \(0.555569\pi\)
\(602\) 0 0
\(603\) −21617.4 −1.45991
\(604\) −6659.47 −0.448626
\(605\) −16143.3 −1.08482
\(606\) 23106.8 1.54893
\(607\) 12487.3 0.834996 0.417498 0.908678i \(-0.362907\pi\)
0.417498 + 0.908678i \(0.362907\pi\)
\(608\) −9508.34 −0.634234
\(609\) −3052.56 −0.203113
\(610\) 14524.2 0.964044
\(611\) −4288.84 −0.283974
\(612\) 3873.99 0.255877
\(613\) −5061.06 −0.333466 −0.166733 0.986002i \(-0.553322\pi\)
−0.166733 + 0.986002i \(0.553322\pi\)
\(614\) −13998.6 −0.920095
\(615\) 33096.3 2.17004
\(616\) 2126.28 0.139075
\(617\) 5779.32 0.377093 0.188547 0.982064i \(-0.439622\pi\)
0.188547 + 0.982064i \(0.439622\pi\)
\(618\) 7782.98 0.506598
\(619\) −4571.39 −0.296833 −0.148416 0.988925i \(-0.547418\pi\)
−0.148416 + 0.988925i \(0.547418\pi\)
\(620\) 3302.53 0.213924
\(621\) −2746.74 −0.177492
\(622\) −22986.0 −1.48176
\(623\) 2418.56 0.155534
\(624\) −5610.95 −0.359964
\(625\) −11987.7 −0.767215
\(626\) −5487.36 −0.350350
\(627\) −33799.7 −2.15284
\(628\) 3065.53 0.194790
\(629\) 4175.14 0.264664
\(630\) 876.483 0.0554285
\(631\) −731.783 −0.0461677 −0.0230838 0.999734i \(-0.507348\pi\)
−0.0230838 + 0.999734i \(0.507348\pi\)
\(632\) 5781.28 0.363872
\(633\) 38467.2 2.41538
\(634\) −8906.91 −0.557947
\(635\) 18732.0 1.17064
\(636\) 5257.08 0.327762
\(637\) −7117.30 −0.442696
\(638\) 34356.4 2.13195
\(639\) −5940.31 −0.367754
\(640\) −4410.43 −0.272402
\(641\) −10111.3 −0.623047 −0.311523 0.950238i \(-0.600839\pi\)
−0.311523 + 0.950238i \(0.600839\pi\)
\(642\) −19046.0 −1.17085
\(643\) 31984.3 1.96164 0.980822 0.194905i \(-0.0624399\pi\)
0.980822 + 0.194905i \(0.0624399\pi\)
\(644\) 425.049 0.0260082
\(645\) 0 0
\(646\) 13681.9 0.833294
\(647\) −17819.5 −1.08277 −0.541387 0.840773i \(-0.682101\pi\)
−0.541387 + 0.840773i \(0.682101\pi\)
\(648\) 20033.8 1.21451
\(649\) −26772.7 −1.61929
\(650\) −1194.48 −0.0720792
\(651\) −1491.35 −0.0897858
\(652\) 4068.80 0.244397
\(653\) −10472.7 −0.627612 −0.313806 0.949487i \(-0.601604\pi\)
−0.313806 + 0.949487i \(0.601604\pi\)
\(654\) −26455.5 −1.58179
\(655\) −9589.13 −0.572028
\(656\) 17574.9 1.04601
\(657\) 3976.07 0.236105
\(658\) 766.563 0.0454160
\(659\) −24995.2 −1.47750 −0.738751 0.673979i \(-0.764584\pi\)
−0.738751 + 0.673979i \(0.764584\pi\)
\(660\) 9634.01 0.568187
\(661\) −29750.6 −1.75063 −0.875313 0.483556i \(-0.839345\pi\)
−0.875313 + 0.483556i \(0.839345\pi\)
\(662\) 17172.3 1.00819
\(663\) −9852.95 −0.577160
\(664\) −27576.0 −1.61168
\(665\) −1403.02 −0.0818148
\(666\) −3449.51 −0.200699
\(667\) 28888.7 1.67702
\(668\) 2166.69 0.125497
\(669\) −32215.6 −1.86177
\(670\) 21761.3 1.25480
\(671\) −33458.0 −1.92494
\(672\) −1223.86 −0.0702551
\(673\) 17343.2 0.993360 0.496680 0.867934i \(-0.334552\pi\)
0.496680 + 0.867934i \(0.334552\pi\)
\(674\) 7684.15 0.439143
\(675\) 625.314 0.0356568
\(676\) 4391.32 0.249847
\(677\) 551.002 0.0312802 0.0156401 0.999878i \(-0.495021\pi\)
0.0156401 + 0.999878i \(0.495021\pi\)
\(678\) −18956.5 −1.07378
\(679\) −434.958 −0.0245835
\(680\) −16403.7 −0.925080
\(681\) −136.988 −0.00770836
\(682\) 16785.0 0.942422
\(683\) 28298.7 1.58539 0.792695 0.609618i \(-0.208677\pi\)
0.792695 + 0.609618i \(0.208677\pi\)
\(684\) 5123.49 0.286406
\(685\) −24127.9 −1.34581
\(686\) 2553.68 0.142128
\(687\) −23324.5 −1.29532
\(688\) 0 0
\(689\) −6205.32 −0.343112
\(690\) −17872.9 −0.986100
\(691\) 2711.59 0.149282 0.0746408 0.997210i \(-0.476219\pi\)
0.0746408 + 0.997210i \(0.476219\pi\)
\(692\) −1418.67 −0.0779331
\(693\) −2019.07 −0.110676
\(694\) 12153.9 0.664778
\(695\) −2817.35 −0.153767
\(696\) −47200.8 −2.57061
\(697\) 30861.9 1.67715
\(698\) −19278.2 −1.04540
\(699\) 49056.4 2.65448
\(700\) −96.7655 −0.00522484
\(701\) −314.529 −0.0169466 −0.00847332 0.999964i \(-0.502697\pi\)
−0.00847332 + 0.999964i \(0.502697\pi\)
\(702\) −1259.38 −0.0677098
\(703\) 5521.76 0.296241
\(704\) 30177.6 1.61557
\(705\) 14609.5 0.780463
\(706\) −11245.2 −0.599460
\(707\) −2209.53 −0.117536
\(708\) 8744.45 0.464176
\(709\) −20992.9 −1.11200 −0.555999 0.831183i \(-0.687664\pi\)
−0.555999 + 0.831183i \(0.687664\pi\)
\(710\) 5979.86 0.316085
\(711\) −5489.78 −0.289568
\(712\) 37397.5 1.96844
\(713\) 14113.7 0.741324
\(714\) 1761.06 0.0923053
\(715\) −11371.7 −0.594796
\(716\) −5143.70 −0.268476
\(717\) 41491.4 2.16112
\(718\) −12586.6 −0.654215
\(719\) −22863.7 −1.18591 −0.592957 0.805234i \(-0.702040\pi\)
−0.592957 + 0.805234i \(0.702040\pi\)
\(720\) 8870.43 0.459141
\(721\) −744.228 −0.0384417
\(722\) 2001.83 0.103186
\(723\) 22160.7 1.13992
\(724\) 1164.91 0.0597979
\(725\) −6576.71 −0.336901
\(726\) 26798.4 1.36995
\(727\) −8267.30 −0.421757 −0.210878 0.977512i \(-0.567632\pi\)
−0.210878 + 0.977512i \(0.567632\pi\)
\(728\) 819.749 0.0417334
\(729\) −14102.8 −0.716499
\(730\) −4002.54 −0.202933
\(731\) 0 0
\(732\) 10928.0 0.551790
\(733\) 20903.6 1.05333 0.526665 0.850073i \(-0.323442\pi\)
0.526665 + 0.850073i \(0.323442\pi\)
\(734\) −14191.8 −0.713665
\(735\) 24244.4 1.21669
\(736\) 11582.3 0.580067
\(737\) −50129.6 −2.50549
\(738\) −25498.1 −1.27181
\(739\) 13780.4 0.685953 0.342977 0.939344i \(-0.388565\pi\)
0.342977 + 0.939344i \(0.388565\pi\)
\(740\) −1573.88 −0.0781852
\(741\) −13030.9 −0.646020
\(742\) 1109.10 0.0548740
\(743\) 21172.0 1.04539 0.522696 0.852519i \(-0.324926\pi\)
0.522696 + 0.852519i \(0.324926\pi\)
\(744\) −23060.3 −1.13633
\(745\) 8937.95 0.439545
\(746\) −2661.35 −0.130615
\(747\) 26185.6 1.28257
\(748\) 8983.58 0.439134
\(749\) 1821.23 0.0888468
\(750\) 24953.4 1.21489
\(751\) 29508.3 1.43379 0.716893 0.697183i \(-0.245564\pi\)
0.716893 + 0.697183i \(0.245564\pi\)
\(752\) 7757.98 0.376203
\(753\) −26401.6 −1.27773
\(754\) 13245.5 0.639751
\(755\) −26776.6 −1.29073
\(756\) −102.023 −0.00490812
\(757\) −15358.9 −0.737425 −0.368712 0.929544i \(-0.620201\pi\)
−0.368712 + 0.929544i \(0.620201\pi\)
\(758\) 5117.76 0.245231
\(759\) 41172.1 1.96898
\(760\) −21694.5 −1.03545
\(761\) −39393.9 −1.87651 −0.938256 0.345941i \(-0.887560\pi\)
−0.938256 + 0.345941i \(0.887560\pi\)
\(762\) −31095.7 −1.47832
\(763\) 2529.74 0.120030
\(764\) 7036.11 0.333191
\(765\) 15576.7 0.736177
\(766\) −5257.82 −0.248006
\(767\) −10321.7 −0.485914
\(768\) −24281.7 −1.14087
\(769\) −5471.24 −0.256564 −0.128282 0.991738i \(-0.540946\pi\)
−0.128282 + 0.991738i \(0.540946\pi\)
\(770\) 2032.52 0.0951258
\(771\) −717.059 −0.0334945
\(772\) 314.483 0.0146612
\(773\) 18610.1 0.865925 0.432963 0.901412i \(-0.357468\pi\)
0.432963 + 0.901412i \(0.357468\pi\)
\(774\) 0 0
\(775\) −3213.09 −0.148926
\(776\) −6725.63 −0.311129
\(777\) 710.730 0.0328151
\(778\) 7811.32 0.359961
\(779\) 40815.9 1.87725
\(780\) 3714.22 0.170500
\(781\) −13775.3 −0.631136
\(782\) −16666.2 −0.762127
\(783\) −6934.03 −0.316478
\(784\) 12874.3 0.586475
\(785\) 12326.0 0.560424
\(786\) 15918.3 0.722373
\(787\) −8975.52 −0.406534 −0.203267 0.979123i \(-0.565156\pi\)
−0.203267 + 0.979123i \(0.565156\pi\)
\(788\) −8400.82 −0.379780
\(789\) 3632.90 0.163922
\(790\) 5526.34 0.248884
\(791\) 1812.67 0.0814805
\(792\) −31220.3 −1.40071
\(793\) −12899.1 −0.577631
\(794\) 25211.1 1.12684
\(795\) 21137.8 0.942995
\(796\) 1550.50 0.0690404
\(797\) 13935.6 0.619353 0.309677 0.950842i \(-0.399779\pi\)
0.309677 + 0.950842i \(0.399779\pi\)
\(798\) 2329.06 0.103318
\(799\) 13623.2 0.603196
\(800\) −2636.79 −0.116531
\(801\) −35511.9 −1.56648
\(802\) 28294.8 1.24579
\(803\) 9220.29 0.405202
\(804\) 16373.2 0.718208
\(805\) 1709.05 0.0748275
\(806\) 6471.16 0.282800
\(807\) −10937.5 −0.477096
\(808\) −34165.3 −1.48754
\(809\) 8171.16 0.355108 0.177554 0.984111i \(-0.443181\pi\)
0.177554 + 0.984111i \(0.443181\pi\)
\(810\) 19150.4 0.830711
\(811\) 9788.80 0.423836 0.211918 0.977287i \(-0.432029\pi\)
0.211918 + 0.977287i \(0.432029\pi\)
\(812\) 1073.02 0.0463739
\(813\) 49268.8 2.12538
\(814\) −7999.22 −0.344438
\(815\) 16360.0 0.703147
\(816\) 17822.7 0.764609
\(817\) 0 0
\(818\) 23884.2 1.02089
\(819\) −778.417 −0.0332114
\(820\) −11633.8 −0.495453
\(821\) 19485.2 0.828306 0.414153 0.910207i \(-0.364078\pi\)
0.414153 + 0.910207i \(0.364078\pi\)
\(822\) 40053.1 1.69953
\(823\) 26957.2 1.14176 0.570880 0.821033i \(-0.306602\pi\)
0.570880 + 0.821033i \(0.306602\pi\)
\(824\) −11507.8 −0.486520
\(825\) −9373.12 −0.395552
\(826\) 1844.84 0.0777123
\(827\) 7495.65 0.315174 0.157587 0.987505i \(-0.449628\pi\)
0.157587 + 0.987505i \(0.449628\pi\)
\(828\) −6241.03 −0.261945
\(829\) 35871.9 1.50288 0.751438 0.659804i \(-0.229361\pi\)
0.751438 + 0.659804i \(0.229361\pi\)
\(830\) −26360.0 −1.10237
\(831\) −43877.3 −1.83163
\(832\) 11634.4 0.484797
\(833\) 22607.5 0.940342
\(834\) 4676.89 0.194182
\(835\) 8711.90 0.361063
\(836\) 11881.1 0.491527
\(837\) −3387.67 −0.139898
\(838\) 13258.8 0.546560
\(839\) 14302.9 0.588546 0.294273 0.955721i \(-0.404922\pi\)
0.294273 + 0.955721i \(0.404922\pi\)
\(840\) −2792.39 −0.114699
\(841\) 48539.4 1.99022
\(842\) 3789.93 0.155118
\(843\) −34163.8 −1.39581
\(844\) −13521.8 −0.551468
\(845\) 17656.7 0.718829
\(846\) −11255.5 −0.457414
\(847\) −2562.53 −0.103954
\(848\) 11224.7 0.454547
\(849\) 15436.0 0.623985
\(850\) 3794.18 0.153105
\(851\) −6726.17 −0.270940
\(852\) 4499.25 0.180918
\(853\) −19082.5 −0.765969 −0.382984 0.923755i \(-0.625104\pi\)
−0.382984 + 0.923755i \(0.625104\pi\)
\(854\) 2305.51 0.0923807
\(855\) 20600.7 0.824009
\(856\) 28161.1 1.12445
\(857\) −26022.2 −1.03723 −0.518613 0.855009i \(-0.673552\pi\)
−0.518613 + 0.855009i \(0.673552\pi\)
\(858\) 18877.5 0.751125
\(859\) −31705.0 −1.25932 −0.629662 0.776869i \(-0.716807\pi\)
−0.629662 + 0.776869i \(0.716807\pi\)
\(860\) 0 0
\(861\) 5253.59 0.207946
\(862\) 25820.2 1.02023
\(863\) −31860.1 −1.25670 −0.628349 0.777932i \(-0.716269\pi\)
−0.628349 + 0.777932i \(0.716269\pi\)
\(864\) −2780.06 −0.109467
\(865\) −5704.23 −0.224219
\(866\) 6809.29 0.267193
\(867\) −3575.69 −0.140065
\(868\) 524.231 0.0204995
\(869\) −12730.5 −0.496954
\(870\) −45119.4 −1.75827
\(871\) −19326.5 −0.751843
\(872\) 39116.6 1.51910
\(873\) 6386.52 0.247596
\(874\) −22041.7 −0.853055
\(875\) −2386.11 −0.0921889
\(876\) −3011.52 −0.116153
\(877\) 14629.7 0.563295 0.281648 0.959518i \(-0.409119\pi\)
0.281648 + 0.959518i \(0.409119\pi\)
\(878\) 38360.7 1.47450
\(879\) −8918.48 −0.342222
\(880\) 20570.1 0.787973
\(881\) −36569.5 −1.39848 −0.699239 0.714888i \(-0.746478\pi\)
−0.699239 + 0.714888i \(0.746478\pi\)
\(882\) −18678.4 −0.713077
\(883\) −10161.1 −0.387258 −0.193629 0.981075i \(-0.562026\pi\)
−0.193629 + 0.981075i \(0.562026\pi\)
\(884\) 3463.46 0.131775
\(885\) 35159.9 1.33547
\(886\) −16395.0 −0.621670
\(887\) 4969.66 0.188123 0.0940614 0.995566i \(-0.470015\pi\)
0.0940614 + 0.995566i \(0.470015\pi\)
\(888\) 10989.8 0.415308
\(889\) 2973.45 0.112178
\(890\) 35748.4 1.34639
\(891\) −44115.0 −1.65871
\(892\) 11324.2 0.425072
\(893\) 18017.1 0.675162
\(894\) −14837.3 −0.555070
\(895\) −20681.9 −0.772425
\(896\) −700.095 −0.0261033
\(897\) 15873.2 0.590847
\(898\) 2844.84 0.105717
\(899\) 35629.6 1.32182
\(900\) 1420.81 0.0526227
\(901\) 19710.7 0.728812
\(902\) −59128.8 −2.18268
\(903\) 0 0
\(904\) 28028.7 1.03122
\(905\) 4683.91 0.172043
\(906\) 44450.0 1.62997
\(907\) 28846.8 1.05606 0.528028 0.849227i \(-0.322932\pi\)
0.528028 + 0.849227i \(0.322932\pi\)
\(908\) 48.1533 0.00175994
\(909\) 32442.7 1.18378
\(910\) 783.601 0.0285452
\(911\) 33816.9 1.22986 0.614930 0.788582i \(-0.289184\pi\)
0.614930 + 0.788582i \(0.289184\pi\)
\(912\) 23571.2 0.855834
\(913\) 60723.0 2.20114
\(914\) −33598.6 −1.21591
\(915\) 43939.6 1.58754
\(916\) 8198.90 0.295742
\(917\) −1522.14 −0.0548153
\(918\) 4000.33 0.143824
\(919\) −1296.33 −0.0465310 −0.0232655 0.999729i \(-0.507406\pi\)
−0.0232655 + 0.999729i \(0.507406\pi\)
\(920\) 26426.5 0.947018
\(921\) −42349.7 −1.51517
\(922\) 4546.07 0.162383
\(923\) −5310.80 −0.189390
\(924\) 1529.27 0.0544472
\(925\) 1531.26 0.0544298
\(926\) −18217.6 −0.646509
\(927\) 10927.5 0.387171
\(928\) 29239.1 1.03429
\(929\) −17438.6 −0.615867 −0.307934 0.951408i \(-0.599637\pi\)
−0.307934 + 0.951408i \(0.599637\pi\)
\(930\) −22043.4 −0.777237
\(931\) 29899.3 1.05253
\(932\) −17244.1 −0.606060
\(933\) −69538.9 −2.44009
\(934\) 10361.2 0.362985
\(935\) 36121.4 1.26342
\(936\) −12036.4 −0.420324
\(937\) 19320.4 0.673608 0.336804 0.941575i \(-0.390654\pi\)
0.336804 + 0.941575i \(0.390654\pi\)
\(938\) 3454.31 0.120242
\(939\) −16600.8 −0.576939
\(940\) −5135.46 −0.178192
\(941\) −41843.1 −1.44957 −0.724785 0.688975i \(-0.758061\pi\)
−0.724785 + 0.688975i \(0.758061\pi\)
\(942\) −20461.5 −0.707719
\(943\) −49718.7 −1.71693
\(944\) 18670.7 0.643728
\(945\) −410.216 −0.0141210
\(946\) 0 0
\(947\) 3650.02 0.125248 0.0626239 0.998037i \(-0.480053\pi\)
0.0626239 + 0.998037i \(0.480053\pi\)
\(948\) 4158.02 0.142454
\(949\) 3554.71 0.121592
\(950\) 5017.94 0.171372
\(951\) −26945.8 −0.918799
\(952\) −2603.87 −0.0886470
\(953\) 34358.9 1.16789 0.583943 0.811795i \(-0.301509\pi\)
0.583943 + 0.811795i \(0.301509\pi\)
\(954\) −16285.0 −0.552671
\(955\) 28291.0 0.958613
\(956\) −14584.8 −0.493417
\(957\) 103937. 3.51078
\(958\) 17012.9 0.573759
\(959\) −3829.97 −0.128964
\(960\) −39631.5 −1.33240
\(961\) −12383.9 −0.415694
\(962\) −3083.96 −0.103358
\(963\) −26741.2 −0.894833
\(964\) −7789.81 −0.260262
\(965\) 1264.48 0.0421814
\(966\) −2837.08 −0.0944943
\(967\) 52067.1 1.73150 0.865752 0.500474i \(-0.166841\pi\)
0.865752 + 0.500474i \(0.166841\pi\)
\(968\) −39623.6 −1.31565
\(969\) 41391.5 1.37223
\(970\) −6429.05 −0.212809
\(971\) −30305.0 −1.00158 −0.500790 0.865569i \(-0.666957\pi\)
−0.500790 + 0.865569i \(0.666957\pi\)
\(972\) 12679.0 0.418394
\(973\) −447.216 −0.0147349
\(974\) 13077.5 0.430216
\(975\) −3613.64 −0.118696
\(976\) 23332.9 0.765233
\(977\) 41395.2 1.35553 0.677763 0.735281i \(-0.262950\pi\)
0.677763 + 0.735281i \(0.262950\pi\)
\(978\) −27158.1 −0.887954
\(979\) −82350.3 −2.68838
\(980\) −8522.26 −0.277789
\(981\) −37144.3 −1.20890
\(982\) 10320.2 0.335367
\(983\) −12824.2 −0.416102 −0.208051 0.978118i \(-0.566712\pi\)
−0.208051 + 0.978118i \(0.566712\pi\)
\(984\) 81234.7 2.63177
\(985\) −33778.2 −1.09265
\(986\) −42073.2 −1.35891
\(987\) 2319.06 0.0747888
\(988\) 4580.54 0.147496
\(989\) 0 0
\(990\) −29843.6 −0.958073
\(991\) −1778.93 −0.0570226 −0.0285113 0.999593i \(-0.509077\pi\)
−0.0285113 + 0.999593i \(0.509077\pi\)
\(992\) 14284.9 0.457205
\(993\) 51950.8 1.66023
\(994\) 949.222 0.0302892
\(995\) 6234.31 0.198634
\(996\) −19833.2 −0.630964
\(997\) 39240.5 1.24650 0.623249 0.782024i \(-0.285812\pi\)
0.623249 + 0.782024i \(0.285812\pi\)
\(998\) 16007.6 0.507728
\(999\) 1614.46 0.0511303
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.1.37 50
43.42 odd 2 1849.4.a.j.1.14 yes 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.i.1.37 50 1.1 even 1 trivial
1849.4.a.j.1.14 yes 50 43.42 odd 2