Properties

Label 1849.4.a.i.1.10
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 1.10
Character \(\chi\) \(=\) 1849.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.81936 q^{2} +8.34786 q^{3} +6.58755 q^{4} +2.56409 q^{5} -31.8835 q^{6} -3.42361 q^{7} +5.39467 q^{8} +42.6867 q^{9} +O(q^{10})\) \(q-3.81936 q^{2} +8.34786 q^{3} +6.58755 q^{4} +2.56409 q^{5} -31.8835 q^{6} -3.42361 q^{7} +5.39467 q^{8} +42.6867 q^{9} -9.79321 q^{10} -24.5225 q^{11} +54.9919 q^{12} -46.2969 q^{13} +13.0760 q^{14} +21.4047 q^{15} -73.3046 q^{16} +97.5824 q^{17} -163.036 q^{18} -131.921 q^{19} +16.8911 q^{20} -28.5798 q^{21} +93.6603 q^{22} +175.382 q^{23} +45.0339 q^{24} -118.425 q^{25} +176.825 q^{26} +130.950 q^{27} -22.5532 q^{28} -83.1501 q^{29} -81.7523 q^{30} +128.550 q^{31} +236.820 q^{32} -204.710 q^{33} -372.703 q^{34} -8.77845 q^{35} +281.201 q^{36} +301.363 q^{37} +503.853 q^{38} -386.480 q^{39} +13.8324 q^{40} -201.066 q^{41} +109.157 q^{42} -161.543 q^{44} +109.453 q^{45} -669.846 q^{46} -335.227 q^{47} -611.936 q^{48} -331.279 q^{49} +452.310 q^{50} +814.604 q^{51} -304.983 q^{52} +373.842 q^{53} -500.147 q^{54} -62.8779 q^{55} -18.4692 q^{56} -1101.25 q^{57} +317.581 q^{58} +578.431 q^{59} +141.004 q^{60} -892.641 q^{61} -490.980 q^{62} -146.143 q^{63} -318.064 q^{64} -118.710 q^{65} +781.862 q^{66} +2.66116 q^{67} +642.829 q^{68} +1464.06 q^{69} +33.5281 q^{70} +467.961 q^{71} +230.281 q^{72} -481.550 q^{73} -1151.01 q^{74} -988.598 q^{75} -869.034 q^{76} +83.9554 q^{77} +1476.11 q^{78} -296.213 q^{79} -187.960 q^{80} -59.3866 q^{81} +767.945 q^{82} +122.365 q^{83} -188.271 q^{84} +250.210 q^{85} -694.125 q^{87} -132.291 q^{88} +746.209 q^{89} -418.040 q^{90} +158.503 q^{91} +1155.33 q^{92} +1073.12 q^{93} +1280.36 q^{94} -338.257 q^{95} +1976.94 q^{96} -1723.34 q^{97} +1265.27 q^{98} -1046.78 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q - 10q^{2} - 2q^{3} + 186q^{4} + 8q^{5} - 51q^{6} - 6q^{7} - 138q^{8} + 360q^{9} + O(q^{10}) \) \( 50q - 10q^{2} - 2q^{3} + 186q^{4} + 8q^{5} - 51q^{6} - 6q^{7} - 138q^{8} + 360q^{9} - 137q^{10} - 252q^{11} - 48q^{12} - 192q^{13} - 272q^{14} - 314q^{15} + 542q^{16} - 236q^{17} - 386q^{18} + 12q^{19} + 108q^{20} - 408q^{21} + 1235q^{22} - 630q^{23} - 613q^{24} + 1098q^{25} + 1493q^{26} + 10q^{27} - 242q^{28} + 208q^{29} - 48q^{30} - 932q^{31} - 1124q^{32} + 254q^{33} + 765q^{34} - 1452q^{35} + 747q^{36} - 90q^{37} - 1213q^{38} - 1610q^{39} - 1693q^{40} - 1354q^{41} - 16q^{42} - 2704q^{44} + 4508q^{45} + 233q^{46} - 3484q^{47} - 376q^{48} + 1324q^{49} - 408q^{50} + 4054q^{51} - 2176q^{52} - 726q^{53} - 6497q^{54} - 3288q^{55} - 7097q^{56} - 870q^{57} + 275q^{58} - 4370q^{59} - 3891q^{60} + 1172q^{61} - 1546q^{62} - 3686q^{63} + 606q^{64} + 2610q^{65} - 4697q^{66} - 344q^{67} - 3221q^{68} + 136q^{69} - 1310q^{70} + 162q^{71} - 5814q^{72} + 746q^{73} - 4332q^{74} + 236q^{75} + 1338q^{76} + 2024q^{77} - 2782q^{78} - 2656q^{79} - 5713q^{80} - 86q^{81} - 4168q^{82} - 3514q^{83} - 4269q^{84} - 7558q^{85} - 10278q^{87} + 11692q^{88} + 2640q^{89} - 8286q^{90} - 5946q^{91} - 4271q^{92} - 2q^{93} + 9062q^{94} - 12140q^{95} - 700q^{96} - 3864q^{97} - 2826q^{98} - 8174q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.81936 −1.35035 −0.675175 0.737658i \(-0.735932\pi\)
−0.675175 + 0.737658i \(0.735932\pi\)
\(3\) 8.34786 1.60655 0.803273 0.595611i \(-0.203090\pi\)
0.803273 + 0.595611i \(0.203090\pi\)
\(4\) 6.58755 0.823443
\(5\) 2.56409 0.229339 0.114670 0.993404i \(-0.463419\pi\)
0.114670 + 0.993404i \(0.463419\pi\)
\(6\) −31.8835 −2.16940
\(7\) −3.42361 −0.184858 −0.0924288 0.995719i \(-0.529463\pi\)
−0.0924288 + 0.995719i \(0.529463\pi\)
\(8\) 5.39467 0.238413
\(9\) 42.6867 1.58099
\(10\) −9.79321 −0.309688
\(11\) −24.5225 −0.672164 −0.336082 0.941833i \(-0.609102\pi\)
−0.336082 + 0.941833i \(0.609102\pi\)
\(12\) 54.9919 1.32290
\(13\) −46.2969 −0.987727 −0.493864 0.869539i \(-0.664416\pi\)
−0.493864 + 0.869539i \(0.664416\pi\)
\(14\) 13.0760 0.249622
\(15\) 21.4047 0.368444
\(16\) −73.3046 −1.14538
\(17\) 97.5824 1.39219 0.696095 0.717950i \(-0.254919\pi\)
0.696095 + 0.717950i \(0.254919\pi\)
\(18\) −163.036 −2.13489
\(19\) −131.921 −1.59288 −0.796439 0.604719i \(-0.793285\pi\)
−0.796439 + 0.604719i \(0.793285\pi\)
\(20\) 16.8911 0.188848
\(21\) −28.5798 −0.296982
\(22\) 93.6603 0.907656
\(23\) 175.382 1.58998 0.794991 0.606621i \(-0.207475\pi\)
0.794991 + 0.606621i \(0.207475\pi\)
\(24\) 45.0339 0.383021
\(25\) −118.425 −0.947403
\(26\) 176.825 1.33378
\(27\) 130.950 0.933385
\(28\) −22.5532 −0.152220
\(29\) −83.1501 −0.532434 −0.266217 0.963913i \(-0.585774\pi\)
−0.266217 + 0.963913i \(0.585774\pi\)
\(30\) −81.7523 −0.497529
\(31\) 128.550 0.744783 0.372392 0.928076i \(-0.378538\pi\)
0.372392 + 0.928076i \(0.378538\pi\)
\(32\) 236.820 1.30826
\(33\) −204.710 −1.07986
\(34\) −372.703 −1.87994
\(35\) −8.77845 −0.0423951
\(36\) 281.201 1.30186
\(37\) 301.363 1.33902 0.669510 0.742803i \(-0.266504\pi\)
0.669510 + 0.742803i \(0.266504\pi\)
\(38\) 503.853 2.15094
\(39\) −386.480 −1.58683
\(40\) 13.8324 0.0546775
\(41\) −201.066 −0.765884 −0.382942 0.923772i \(-0.625089\pi\)
−0.382942 + 0.923772i \(0.625089\pi\)
\(42\) 109.157 0.401030
\(43\) 0 0
\(44\) −161.543 −0.553489
\(45\) 109.453 0.362583
\(46\) −669.846 −2.14703
\(47\) −335.227 −1.04038 −0.520191 0.854050i \(-0.674139\pi\)
−0.520191 + 0.854050i \(0.674139\pi\)
\(48\) −611.936 −1.84011
\(49\) −331.279 −0.965828
\(50\) 452.310 1.27933
\(51\) 814.604 2.23662
\(52\) −304.983 −0.813338
\(53\) 373.842 0.968891 0.484445 0.874822i \(-0.339021\pi\)
0.484445 + 0.874822i \(0.339021\pi\)
\(54\) −500.147 −1.26040
\(55\) −62.8779 −0.154154
\(56\) −18.4692 −0.0440724
\(57\) −1101.25 −2.55903
\(58\) 317.581 0.718972
\(59\) 578.431 1.27636 0.638180 0.769887i \(-0.279688\pi\)
0.638180 + 0.769887i \(0.279688\pi\)
\(60\) 141.004 0.303393
\(61\) −892.641 −1.87362 −0.936811 0.349835i \(-0.886238\pi\)
−0.936811 + 0.349835i \(0.886238\pi\)
\(62\) −490.980 −1.00572
\(63\) −146.143 −0.292258
\(64\) −318.064 −0.621218
\(65\) −118.710 −0.226525
\(66\) 781.862 1.45819
\(67\) 2.66116 0.00485242 0.00242621 0.999997i \(-0.499228\pi\)
0.00242621 + 0.999997i \(0.499228\pi\)
\(68\) 642.829 1.14639
\(69\) 1464.06 2.55438
\(70\) 33.5281 0.0572482
\(71\) 467.961 0.782208 0.391104 0.920346i \(-0.372093\pi\)
0.391104 + 0.920346i \(0.372093\pi\)
\(72\) 230.281 0.376928
\(73\) −481.550 −0.772070 −0.386035 0.922484i \(-0.626156\pi\)
−0.386035 + 0.922484i \(0.626156\pi\)
\(74\) −1151.01 −1.80814
\(75\) −988.598 −1.52205
\(76\) −869.034 −1.31164
\(77\) 83.9554 0.124255
\(78\) 1476.11 2.14277
\(79\) −296.213 −0.421856 −0.210928 0.977502i \(-0.567649\pi\)
−0.210928 + 0.977502i \(0.567649\pi\)
\(80\) −187.960 −0.262682
\(81\) −59.3866 −0.0814631
\(82\) 767.945 1.03421
\(83\) 122.365 0.161823 0.0809116 0.996721i \(-0.474217\pi\)
0.0809116 + 0.996721i \(0.474217\pi\)
\(84\) −188.271 −0.244548
\(85\) 250.210 0.319284
\(86\) 0 0
\(87\) −694.125 −0.855379
\(88\) −132.291 −0.160253
\(89\) 746.209 0.888742 0.444371 0.895843i \(-0.353427\pi\)
0.444371 + 0.895843i \(0.353427\pi\)
\(90\) −418.040 −0.489614
\(91\) 158.503 0.182589
\(92\) 1155.33 1.30926
\(93\) 1073.12 1.19653
\(94\) 1280.36 1.40488
\(95\) −338.257 −0.365310
\(96\) 1976.94 2.10177
\(97\) −1723.34 −1.80390 −0.901949 0.431842i \(-0.857864\pi\)
−0.901949 + 0.431842i \(0.857864\pi\)
\(98\) 1265.27 1.30420
\(99\) −1046.78 −1.06268
\(100\) −780.133 −0.780133
\(101\) −384.032 −0.378343 −0.189171 0.981944i \(-0.560580\pi\)
−0.189171 + 0.981944i \(0.560580\pi\)
\(102\) −3111.27 −3.02021
\(103\) 187.491 0.179360 0.0896798 0.995971i \(-0.471416\pi\)
0.0896798 + 0.995971i \(0.471416\pi\)
\(104\) −249.757 −0.235487
\(105\) −73.2813 −0.0681097
\(106\) −1427.84 −1.30834
\(107\) −1145.03 −1.03453 −0.517263 0.855827i \(-0.673049\pi\)
−0.517263 + 0.855827i \(0.673049\pi\)
\(108\) 862.641 0.768590
\(109\) −1108.95 −0.974482 −0.487241 0.873268i \(-0.661997\pi\)
−0.487241 + 0.873268i \(0.661997\pi\)
\(110\) 240.154 0.208161
\(111\) 2515.73 2.15120
\(112\) 250.966 0.211733
\(113\) −1450.93 −1.20789 −0.603947 0.797025i \(-0.706406\pi\)
−0.603947 + 0.797025i \(0.706406\pi\)
\(114\) 4206.09 3.45558
\(115\) 449.695 0.364646
\(116\) −547.755 −0.438429
\(117\) −1976.26 −1.56159
\(118\) −2209.24 −1.72353
\(119\) −334.084 −0.257357
\(120\) 115.471 0.0878419
\(121\) −729.648 −0.548196
\(122\) 3409.32 2.53004
\(123\) −1678.47 −1.23043
\(124\) 846.830 0.613287
\(125\) −624.165 −0.446616
\(126\) 558.172 0.394650
\(127\) −2025.38 −1.41515 −0.707574 0.706640i \(-0.750210\pi\)
−0.707574 + 0.706640i \(0.750210\pi\)
\(128\) −679.755 −0.469394
\(129\) 0 0
\(130\) 453.395 0.305888
\(131\) 2553.08 1.70278 0.851390 0.524534i \(-0.175760\pi\)
0.851390 + 0.524534i \(0.175760\pi\)
\(132\) −1348.54 −0.889205
\(133\) 451.645 0.294455
\(134\) −10.1639 −0.00655246
\(135\) 335.769 0.214062
\(136\) 526.425 0.331916
\(137\) −1338.26 −0.834564 −0.417282 0.908777i \(-0.637017\pi\)
−0.417282 + 0.908777i \(0.637017\pi\)
\(138\) −5591.78 −3.44930
\(139\) 687.366 0.419436 0.209718 0.977762i \(-0.432745\pi\)
0.209718 + 0.977762i \(0.432745\pi\)
\(140\) −57.8285 −0.0349100
\(141\) −2798.43 −1.67142
\(142\) −1787.31 −1.05625
\(143\) 1135.31 0.663915
\(144\) −3129.13 −1.81084
\(145\) −213.205 −0.122108
\(146\) 1839.21 1.04256
\(147\) −2765.47 −1.55165
\(148\) 1985.24 1.10261
\(149\) −467.843 −0.257230 −0.128615 0.991695i \(-0.541053\pi\)
−0.128615 + 0.991695i \(0.541053\pi\)
\(150\) 3775.82 2.05530
\(151\) −1726.18 −0.930293 −0.465147 0.885234i \(-0.653998\pi\)
−0.465147 + 0.885234i \(0.653998\pi\)
\(152\) −711.668 −0.379763
\(153\) 4165.47 2.20104
\(154\) −320.656 −0.167787
\(155\) 329.614 0.170808
\(156\) −2545.96 −1.30666
\(157\) 488.504 0.248324 0.124162 0.992262i \(-0.460376\pi\)
0.124162 + 0.992262i \(0.460376\pi\)
\(158\) 1131.35 0.569653
\(159\) 3120.78 1.55657
\(160\) 607.228 0.300035
\(161\) −600.438 −0.293920
\(162\) 226.819 0.110004
\(163\) 1013.08 0.486814 0.243407 0.969924i \(-0.421735\pi\)
0.243407 + 0.969924i \(0.421735\pi\)
\(164\) −1324.53 −0.630662
\(165\) −524.896 −0.247655
\(166\) −467.357 −0.218518
\(167\) −916.697 −0.424767 −0.212384 0.977186i \(-0.568123\pi\)
−0.212384 + 0.977186i \(0.568123\pi\)
\(168\) −154.179 −0.0708044
\(169\) −53.5953 −0.0243948
\(170\) −955.645 −0.431145
\(171\) −5631.26 −2.51832
\(172\) 0 0
\(173\) −4040.24 −1.77557 −0.887786 0.460257i \(-0.847757\pi\)
−0.887786 + 0.460257i \(0.847757\pi\)
\(174\) 2651.12 1.15506
\(175\) 405.442 0.175135
\(176\) 1797.61 0.769886
\(177\) 4828.65 2.05053
\(178\) −2850.04 −1.20011
\(179\) −818.629 −0.341828 −0.170914 0.985286i \(-0.554672\pi\)
−0.170914 + 0.985286i \(0.554672\pi\)
\(180\) 721.025 0.298567
\(181\) −1761.43 −0.723350 −0.361675 0.932304i \(-0.617795\pi\)
−0.361675 + 0.932304i \(0.617795\pi\)
\(182\) −605.379 −0.246559
\(183\) −7451.64 −3.01006
\(184\) 946.126 0.379072
\(185\) 772.722 0.307090
\(186\) −4098.63 −1.61573
\(187\) −2392.96 −0.935779
\(188\) −2208.33 −0.856696
\(189\) −448.323 −0.172543
\(190\) 1291.93 0.493296
\(191\) 1206.69 0.457137 0.228568 0.973528i \(-0.426596\pi\)
0.228568 + 0.973528i \(0.426596\pi\)
\(192\) −2655.15 −0.998016
\(193\) −1227.19 −0.457694 −0.228847 0.973462i \(-0.573496\pi\)
−0.228847 + 0.973462i \(0.573496\pi\)
\(194\) 6582.05 2.43589
\(195\) −990.971 −0.363922
\(196\) −2182.32 −0.795305
\(197\) 2906.38 1.05112 0.525560 0.850756i \(-0.323856\pi\)
0.525560 + 0.850756i \(0.323856\pi\)
\(198\) 3998.05 1.43499
\(199\) 1960.29 0.698299 0.349149 0.937067i \(-0.386471\pi\)
0.349149 + 0.937067i \(0.386471\pi\)
\(200\) −638.866 −0.225873
\(201\) 22.2149 0.00779563
\(202\) 1466.76 0.510895
\(203\) 284.673 0.0984244
\(204\) 5366.24 1.84173
\(205\) −515.552 −0.175647
\(206\) −716.097 −0.242198
\(207\) 7486.46 2.51374
\(208\) 3393.78 1.13133
\(209\) 3235.02 1.07067
\(210\) 279.888 0.0919719
\(211\) 5227.84 1.70568 0.852841 0.522170i \(-0.174877\pi\)
0.852841 + 0.522170i \(0.174877\pi\)
\(212\) 2462.70 0.797827
\(213\) 3906.47 1.25665
\(214\) 4373.29 1.39697
\(215\) 0 0
\(216\) 706.434 0.222531
\(217\) −440.105 −0.137679
\(218\) 4235.50 1.31589
\(219\) −4019.91 −1.24037
\(220\) −414.211 −0.126937
\(221\) −4517.77 −1.37510
\(222\) −9608.50 −2.90487
\(223\) 1121.01 0.336631 0.168315 0.985733i \(-0.446167\pi\)
0.168315 + 0.985733i \(0.446167\pi\)
\(224\) −810.778 −0.241841
\(225\) −5055.19 −1.49783
\(226\) 5541.63 1.63108
\(227\) 499.397 0.146018 0.0730092 0.997331i \(-0.476740\pi\)
0.0730092 + 0.997331i \(0.476740\pi\)
\(228\) −7254.57 −2.10722
\(229\) 1384.89 0.399633 0.199817 0.979833i \(-0.435965\pi\)
0.199817 + 0.979833i \(0.435965\pi\)
\(230\) −1717.55 −0.492399
\(231\) 700.847 0.199621
\(232\) −448.567 −0.126939
\(233\) −259.379 −0.0729291 −0.0364646 0.999335i \(-0.511610\pi\)
−0.0364646 + 0.999335i \(0.511610\pi\)
\(234\) 7548.07 2.10869
\(235\) −859.554 −0.238601
\(236\) 3810.44 1.05101
\(237\) −2472.75 −0.677730
\(238\) 1275.99 0.347521
\(239\) 4228.11 1.14432 0.572162 0.820140i \(-0.306105\pi\)
0.572162 + 0.820140i \(0.306105\pi\)
\(240\) −1569.06 −0.422010
\(241\) 7388.11 1.97473 0.987365 0.158463i \(-0.0506539\pi\)
0.987365 + 0.158463i \(0.0506539\pi\)
\(242\) 2786.79 0.740256
\(243\) −4031.41 −1.06426
\(244\) −5880.32 −1.54282
\(245\) −849.430 −0.221502
\(246\) 6410.69 1.66151
\(247\) 6107.52 1.57333
\(248\) 693.485 0.177566
\(249\) 1021.49 0.259976
\(250\) 2383.92 0.603088
\(251\) −2006.43 −0.504561 −0.252280 0.967654i \(-0.581180\pi\)
−0.252280 + 0.967654i \(0.581180\pi\)
\(252\) −962.721 −0.240658
\(253\) −4300.79 −1.06873
\(254\) 7735.68 1.91094
\(255\) 2088.72 0.512944
\(256\) 5140.74 1.25506
\(257\) −356.050 −0.0864195 −0.0432098 0.999066i \(-0.513758\pi\)
−0.0432098 + 0.999066i \(0.513758\pi\)
\(258\) 0 0
\(259\) −1031.75 −0.247528
\(260\) −782.005 −0.186530
\(261\) −3549.40 −0.841772
\(262\) −9751.16 −2.29935
\(263\) −2558.23 −0.599800 −0.299900 0.953971i \(-0.596953\pi\)
−0.299900 + 0.953971i \(0.596953\pi\)
\(264\) −1104.34 −0.257453
\(265\) 958.567 0.222205
\(266\) −1725.00 −0.397618
\(267\) 6229.25 1.42780
\(268\) 17.5305 0.00399569
\(269\) 7645.48 1.73291 0.866455 0.499255i \(-0.166393\pi\)
0.866455 + 0.499255i \(0.166393\pi\)
\(270\) −1282.42 −0.289059
\(271\) −2563.79 −0.574683 −0.287342 0.957828i \(-0.592772\pi\)
−0.287342 + 0.957828i \(0.592772\pi\)
\(272\) −7153.24 −1.59459
\(273\) 1323.16 0.293337
\(274\) 5111.31 1.12695
\(275\) 2904.08 0.636810
\(276\) 9644.57 2.10339
\(277\) −5655.56 −1.22675 −0.613375 0.789792i \(-0.710189\pi\)
−0.613375 + 0.789792i \(0.710189\pi\)
\(278\) −2625.30 −0.566386
\(279\) 5487.38 1.17749
\(280\) −47.3568 −0.0101075
\(281\) −6410.59 −1.36094 −0.680469 0.732777i \(-0.738224\pi\)
−0.680469 + 0.732777i \(0.738224\pi\)
\(282\) 10688.2 2.25700
\(283\) −8030.69 −1.68684 −0.843419 0.537256i \(-0.819461\pi\)
−0.843419 + 0.537256i \(0.819461\pi\)
\(284\) 3082.72 0.644104
\(285\) −2823.72 −0.586887
\(286\) −4336.18 −0.896517
\(287\) 688.372 0.141579
\(288\) 10109.0 2.06834
\(289\) 4609.33 0.938191
\(290\) 814.306 0.164889
\(291\) −14386.2 −2.89805
\(292\) −3172.23 −0.635756
\(293\) −3612.22 −0.720232 −0.360116 0.932908i \(-0.617263\pi\)
−0.360116 + 0.932908i \(0.617263\pi\)
\(294\) 10562.3 2.09526
\(295\) 1483.15 0.292720
\(296\) 1625.75 0.319240
\(297\) −3211.23 −0.627388
\(298\) 1786.86 0.347350
\(299\) −8119.63 −1.57047
\(300\) −6512.44 −1.25332
\(301\) 0 0
\(302\) 6592.90 1.25622
\(303\) −3205.84 −0.607825
\(304\) 9670.39 1.82446
\(305\) −2288.81 −0.429696
\(306\) −15909.5 −2.97217
\(307\) −1282.10 −0.238349 −0.119174 0.992873i \(-0.538025\pi\)
−0.119174 + 0.992873i \(0.538025\pi\)
\(308\) 553.060 0.102317
\(309\) 1565.15 0.288149
\(310\) −1258.92 −0.230651
\(311\) −9145.70 −1.66754 −0.833770 0.552111i \(-0.813822\pi\)
−0.833770 + 0.552111i \(0.813822\pi\)
\(312\) −2084.93 −0.378321
\(313\) −3256.64 −0.588103 −0.294051 0.955790i \(-0.595004\pi\)
−0.294051 + 0.955790i \(0.595004\pi\)
\(314\) −1865.78 −0.335324
\(315\) −374.723 −0.0670262
\(316\) −1951.32 −0.347374
\(317\) 6460.36 1.14464 0.572319 0.820031i \(-0.306044\pi\)
0.572319 + 0.820031i \(0.306044\pi\)
\(318\) −11919.4 −2.10191
\(319\) 2039.05 0.357883
\(320\) −815.545 −0.142470
\(321\) −9558.54 −1.66201
\(322\) 2293.29 0.396895
\(323\) −12873.1 −2.21759
\(324\) −391.212 −0.0670802
\(325\) 5482.73 0.935776
\(326\) −3869.33 −0.657369
\(327\) −9257.39 −1.56555
\(328\) −1084.69 −0.182597
\(329\) 1147.69 0.192322
\(330\) 2004.77 0.334421
\(331\) −6472.81 −1.07486 −0.537429 0.843309i \(-0.680604\pi\)
−0.537429 + 0.843309i \(0.680604\pi\)
\(332\) 806.086 0.133252
\(333\) 12864.2 2.11697
\(334\) 3501.20 0.573584
\(335\) 6.82345 0.00111285
\(336\) 2095.03 0.340159
\(337\) 1072.36 0.173339 0.0866695 0.996237i \(-0.472378\pi\)
0.0866695 + 0.996237i \(0.472378\pi\)
\(338\) 204.700 0.0329415
\(339\) −12112.2 −1.94054
\(340\) 1648.27 0.262912
\(341\) −3152.37 −0.500616
\(342\) 21507.8 3.40061
\(343\) 2308.47 0.363398
\(344\) 0 0
\(345\) 3753.99 0.585820
\(346\) 15431.2 2.39764
\(347\) 1353.35 0.209371 0.104686 0.994505i \(-0.466616\pi\)
0.104686 + 0.994505i \(0.466616\pi\)
\(348\) −4572.58 −0.704357
\(349\) 8713.86 1.33651 0.668256 0.743932i \(-0.267041\pi\)
0.668256 + 0.743932i \(0.267041\pi\)
\(350\) −1548.53 −0.236493
\(351\) −6062.60 −0.921930
\(352\) −5807.40 −0.879363
\(353\) 6064.05 0.914325 0.457163 0.889383i \(-0.348866\pi\)
0.457163 + 0.889383i \(0.348866\pi\)
\(354\) −18442.4 −2.76893
\(355\) 1199.90 0.179391
\(356\) 4915.69 0.731829
\(357\) −2788.89 −0.413455
\(358\) 3126.64 0.461587
\(359\) 2672.80 0.392939 0.196469 0.980510i \(-0.437052\pi\)
0.196469 + 0.980510i \(0.437052\pi\)
\(360\) 590.461 0.0864445
\(361\) 10544.1 1.53726
\(362\) 6727.56 0.976775
\(363\) −6091.00 −0.880701
\(364\) 1044.14 0.150352
\(365\) −1234.74 −0.177066
\(366\) 28460.5 4.06463
\(367\) 3206.83 0.456117 0.228059 0.973647i \(-0.426762\pi\)
0.228059 + 0.973647i \(0.426762\pi\)
\(368\) −12856.3 −1.82114
\(369\) −8582.85 −1.21085
\(370\) −2951.31 −0.414679
\(371\) −1279.89 −0.179107
\(372\) 7069.22 0.985273
\(373\) −2341.81 −0.325079 −0.162539 0.986702i \(-0.551968\pi\)
−0.162539 + 0.986702i \(0.551968\pi\)
\(374\) 9139.60 1.26363
\(375\) −5210.44 −0.717510
\(376\) −1808.44 −0.248041
\(377\) 3849.59 0.525900
\(378\) 1712.31 0.232994
\(379\) −12165.1 −1.64876 −0.824382 0.566034i \(-0.808477\pi\)
−0.824382 + 0.566034i \(0.808477\pi\)
\(380\) −2228.28 −0.300812
\(381\) −16907.6 −2.27350
\(382\) −4608.80 −0.617295
\(383\) 10219.7 1.36345 0.681727 0.731606i \(-0.261229\pi\)
0.681727 + 0.731606i \(0.261229\pi\)
\(384\) −5674.50 −0.754103
\(385\) 215.269 0.0284965
\(386\) 4687.08 0.618047
\(387\) 0 0
\(388\) −11352.6 −1.48541
\(389\) −9610.28 −1.25260 −0.626299 0.779583i \(-0.715431\pi\)
−0.626299 + 0.779583i \(0.715431\pi\)
\(390\) 3784.88 0.491422
\(391\) 17114.2 2.21356
\(392\) −1787.14 −0.230266
\(393\) 21312.8 2.73559
\(394\) −11100.5 −1.41938
\(395\) −759.518 −0.0967481
\(396\) −6895.74 −0.875060
\(397\) 8283.95 1.04725 0.523627 0.851948i \(-0.324579\pi\)
0.523627 + 0.851948i \(0.324579\pi\)
\(398\) −7487.07 −0.942947
\(399\) 3770.26 0.473056
\(400\) 8681.13 1.08514
\(401\) −12685.4 −1.57975 −0.789874 0.613269i \(-0.789854\pi\)
−0.789874 + 0.613269i \(0.789854\pi\)
\(402\) −84.8470 −0.0105268
\(403\) −5951.47 −0.735643
\(404\) −2529.83 −0.311544
\(405\) −152.273 −0.0186827
\(406\) −1087.27 −0.132907
\(407\) −7390.16 −0.900040
\(408\) 4394.52 0.533238
\(409\) 981.857 0.118703 0.0593517 0.998237i \(-0.481097\pi\)
0.0593517 + 0.998237i \(0.481097\pi\)
\(410\) 1969.08 0.237185
\(411\) −11171.6 −1.34077
\(412\) 1235.11 0.147693
\(413\) −1980.32 −0.235945
\(414\) −28593.5 −3.39443
\(415\) 313.756 0.0371124
\(416\) −10964.0 −1.29220
\(417\) 5738.03 0.673844
\(418\) −12355.7 −1.44578
\(419\) −10930.0 −1.27439 −0.637193 0.770704i \(-0.719905\pi\)
−0.637193 + 0.770704i \(0.719905\pi\)
\(420\) −482.744 −0.0560845
\(421\) −12352.3 −1.42996 −0.714980 0.699145i \(-0.753564\pi\)
−0.714980 + 0.699145i \(0.753564\pi\)
\(422\) −19967.0 −2.30327
\(423\) −14309.8 −1.64483
\(424\) 2016.76 0.230996
\(425\) −11556.2 −1.31896
\(426\) −14920.2 −1.69692
\(427\) 3056.05 0.346353
\(428\) −7542.94 −0.851873
\(429\) 9477.44 1.06661
\(430\) 0 0
\(431\) −6534.96 −0.730343 −0.365172 0.930940i \(-0.618990\pi\)
−0.365172 + 0.930940i \(0.618990\pi\)
\(432\) −9599.26 −1.06908
\(433\) −12272.7 −1.36210 −0.681048 0.732239i \(-0.738476\pi\)
−0.681048 + 0.732239i \(0.738476\pi\)
\(434\) 1680.92 0.185914
\(435\) −1779.80 −0.196172
\(436\) −7305.29 −0.802431
\(437\) −23136.5 −2.53265
\(438\) 15353.5 1.67493
\(439\) −2806.41 −0.305108 −0.152554 0.988295i \(-0.548750\pi\)
−0.152554 + 0.988295i \(0.548750\pi\)
\(440\) −339.205 −0.0367522
\(441\) −14141.2 −1.52696
\(442\) 17255.0 1.85687
\(443\) −9336.79 −1.00136 −0.500682 0.865631i \(-0.666917\pi\)
−0.500682 + 0.865631i \(0.666917\pi\)
\(444\) 16572.5 1.77139
\(445\) 1913.35 0.203824
\(446\) −4281.56 −0.454569
\(447\) −3905.49 −0.413251
\(448\) 1088.93 0.114837
\(449\) −7212.30 −0.758062 −0.379031 0.925384i \(-0.623743\pi\)
−0.379031 + 0.925384i \(0.623743\pi\)
\(450\) 19307.6 2.02260
\(451\) 4930.64 0.514800
\(452\) −9558.07 −0.994632
\(453\) −14409.9 −1.49456
\(454\) −1907.38 −0.197176
\(455\) 406.415 0.0418748
\(456\) −5940.90 −0.610106
\(457\) 1378.40 0.141091 0.0705455 0.997509i \(-0.477526\pi\)
0.0705455 + 0.997509i \(0.477526\pi\)
\(458\) −5289.40 −0.539645
\(459\) 12778.4 1.29945
\(460\) 2962.39 0.300265
\(461\) −11245.2 −1.13610 −0.568048 0.822996i \(-0.692301\pi\)
−0.568048 + 0.822996i \(0.692301\pi\)
\(462\) −2676.79 −0.269558
\(463\) −2077.54 −0.208535 −0.104267 0.994549i \(-0.533250\pi\)
−0.104267 + 0.994549i \(0.533250\pi\)
\(464\) 6095.28 0.609842
\(465\) 2751.57 0.274411
\(466\) 990.663 0.0984798
\(467\) 2016.77 0.199839 0.0999197 0.994996i \(-0.468141\pi\)
0.0999197 + 0.994996i \(0.468141\pi\)
\(468\) −13018.7 −1.28588
\(469\) −9.11076 −0.000897006 0
\(470\) 3282.95 0.322194
\(471\) 4077.96 0.398944
\(472\) 3120.44 0.304301
\(473\) 0 0
\(474\) 9444.32 0.915173
\(475\) 15622.8 1.50910
\(476\) −2200.80 −0.211919
\(477\) 15958.1 1.53181
\(478\) −16148.7 −1.54524
\(479\) 10427.0 0.994620 0.497310 0.867573i \(-0.334321\pi\)
0.497310 + 0.867573i \(0.334321\pi\)
\(480\) 5069.05 0.482019
\(481\) −13952.2 −1.32259
\(482\) −28217.9 −2.66658
\(483\) −5012.37 −0.472196
\(484\) −4806.59 −0.451408
\(485\) −4418.79 −0.413705
\(486\) 15397.4 1.43712
\(487\) −4165.93 −0.387631 −0.193815 0.981038i \(-0.562086\pi\)
−0.193815 + 0.981038i \(0.562086\pi\)
\(488\) −4815.50 −0.446696
\(489\) 8457.06 0.782089
\(490\) 3244.28 0.299106
\(491\) 11303.6 1.03895 0.519475 0.854486i \(-0.326127\pi\)
0.519475 + 0.854486i \(0.326127\pi\)
\(492\) −11057.0 −1.01319
\(493\) −8113.99 −0.741249
\(494\) −23326.8 −2.12454
\(495\) −2684.05 −0.243715
\(496\) −9423.31 −0.853063
\(497\) −1602.12 −0.144597
\(498\) −3901.43 −0.351059
\(499\) −13070.3 −1.17256 −0.586281 0.810108i \(-0.699408\pi\)
−0.586281 + 0.810108i \(0.699408\pi\)
\(500\) −4111.72 −0.367763
\(501\) −7652.45 −0.682408
\(502\) 7663.29 0.681333
\(503\) −9968.27 −0.883625 −0.441812 0.897107i \(-0.645664\pi\)
−0.441812 + 0.897107i \(0.645664\pi\)
\(504\) −788.391 −0.0696780
\(505\) −984.694 −0.0867689
\(506\) 16426.3 1.44316
\(507\) −447.406 −0.0391913
\(508\) −13342.3 −1.16529
\(509\) 11910.6 1.03719 0.518594 0.855021i \(-0.326456\pi\)
0.518594 + 0.855021i \(0.326456\pi\)
\(510\) −7977.59 −0.692654
\(511\) 1648.64 0.142723
\(512\) −14196.3 −1.22538
\(513\) −17275.0 −1.48677
\(514\) 1359.89 0.116697
\(515\) 480.744 0.0411342
\(516\) 0 0
\(517\) 8220.61 0.699307
\(518\) 3940.62 0.334249
\(519\) −33727.4 −2.85254
\(520\) −640.399 −0.0540065
\(521\) 7264.31 0.610854 0.305427 0.952215i \(-0.401201\pi\)
0.305427 + 0.952215i \(0.401201\pi\)
\(522\) 13556.5 1.13669
\(523\) 11647.5 0.973823 0.486912 0.873451i \(-0.338123\pi\)
0.486912 + 0.873451i \(0.338123\pi\)
\(524\) 16818.6 1.40214
\(525\) 3384.57 0.281362
\(526\) 9770.83 0.809940
\(527\) 12544.2 1.03688
\(528\) 15006.2 1.23686
\(529\) 18591.7 1.52804
\(530\) −3661.12 −0.300054
\(531\) 24691.3 2.01791
\(532\) 2975.23 0.242467
\(533\) 9308.74 0.756485
\(534\) −23791.8 −1.92803
\(535\) −2935.96 −0.237257
\(536\) 14.3561 0.00115688
\(537\) −6833.80 −0.549162
\(538\) −29200.9 −2.34003
\(539\) 8123.78 0.649195
\(540\) 2211.89 0.176268
\(541\) 3578.45 0.284380 0.142190 0.989839i \(-0.454586\pi\)
0.142190 + 0.989839i \(0.454586\pi\)
\(542\) 9792.05 0.776023
\(543\) −14704.2 −1.16209
\(544\) 23109.4 1.82134
\(545\) −2843.46 −0.223487
\(546\) −5053.62 −0.396108
\(547\) −15440.8 −1.20695 −0.603475 0.797382i \(-0.706218\pi\)
−0.603475 + 0.797382i \(0.706218\pi\)
\(548\) −8815.86 −0.687217
\(549\) −38103.9 −2.96218
\(550\) −11091.8 −0.859917
\(551\) 10969.2 0.848102
\(552\) 7898.12 0.608997
\(553\) 1014.12 0.0779832
\(554\) 21600.7 1.65654
\(555\) 6450.57 0.493354
\(556\) 4528.06 0.345382
\(557\) −2684.18 −0.204187 −0.102094 0.994775i \(-0.532554\pi\)
−0.102094 + 0.994775i \(0.532554\pi\)
\(558\) −20958.3 −1.59003
\(559\) 0 0
\(560\) 643.501 0.0485587
\(561\) −19976.1 −1.50337
\(562\) 24484.4 1.83774
\(563\) −10345.1 −0.774412 −0.387206 0.921993i \(-0.626560\pi\)
−0.387206 + 0.921993i \(0.626560\pi\)
\(564\) −18434.8 −1.37632
\(565\) −3720.32 −0.277018
\(566\) 30672.1 2.27782
\(567\) 203.316 0.0150591
\(568\) 2524.50 0.186489
\(569\) 60.6533 0.00446875 0.00223438 0.999998i \(-0.499289\pi\)
0.00223438 + 0.999998i \(0.499289\pi\)
\(570\) 10784.8 0.792502
\(571\) 2225.56 0.163111 0.0815557 0.996669i \(-0.474011\pi\)
0.0815557 + 0.996669i \(0.474011\pi\)
\(572\) 7478.94 0.546696
\(573\) 10073.3 0.734411
\(574\) −2629.14 −0.191182
\(575\) −20769.6 −1.50635
\(576\) −13577.1 −0.982139
\(577\) 16249.2 1.17238 0.586190 0.810173i \(-0.300627\pi\)
0.586190 + 0.810173i \(0.300627\pi\)
\(578\) −17604.7 −1.26689
\(579\) −10244.4 −0.735306
\(580\) −1404.50 −0.100549
\(581\) −418.930 −0.0299142
\(582\) 54946.0 3.91337
\(583\) −9167.54 −0.651253
\(584\) −2597.80 −0.184072
\(585\) −5067.32 −0.358133
\(586\) 13796.4 0.972564
\(587\) −10104.6 −0.710496 −0.355248 0.934772i \(-0.615604\pi\)
−0.355248 + 0.934772i \(0.615604\pi\)
\(588\) −18217.7 −1.27769
\(589\) −16958.4 −1.18635
\(590\) −5664.69 −0.395274
\(591\) 24262.0 1.68867
\(592\) −22091.3 −1.53369
\(593\) 10930.9 0.756962 0.378481 0.925609i \(-0.376447\pi\)
0.378481 + 0.925609i \(0.376447\pi\)
\(594\) 12264.8 0.847193
\(595\) −856.623 −0.0590220
\(596\) −3081.94 −0.211814
\(597\) 16364.2 1.12185
\(598\) 31011.8 2.12068
\(599\) −21584.2 −1.47230 −0.736149 0.676819i \(-0.763358\pi\)
−0.736149 + 0.676819i \(0.763358\pi\)
\(600\) −5333.16 −0.362876
\(601\) 18226.1 1.23704 0.618519 0.785770i \(-0.287733\pi\)
0.618519 + 0.785770i \(0.287733\pi\)
\(602\) 0 0
\(603\) 113.596 0.00767162
\(604\) −11371.3 −0.766044
\(605\) −1870.89 −0.125723
\(606\) 12244.3 0.820776
\(607\) 24757.1 1.65546 0.827728 0.561130i \(-0.189633\pi\)
0.827728 + 0.561130i \(0.189633\pi\)
\(608\) −31241.4 −2.08389
\(609\) 2376.41 0.158123
\(610\) 8741.82 0.580239
\(611\) 15520.0 1.02761
\(612\) 27440.2 1.81243
\(613\) −19983.4 −1.31668 −0.658339 0.752722i \(-0.728741\pi\)
−0.658339 + 0.752722i \(0.728741\pi\)
\(614\) 4896.79 0.321854
\(615\) −4303.76 −0.282186
\(616\) 452.911 0.0296239
\(617\) 26758.7 1.74597 0.872985 0.487746i \(-0.162181\pi\)
0.872985 + 0.487746i \(0.162181\pi\)
\(618\) −5977.87 −0.389102
\(619\) 3557.65 0.231008 0.115504 0.993307i \(-0.463152\pi\)
0.115504 + 0.993307i \(0.463152\pi\)
\(620\) 2171.35 0.140651
\(621\) 22966.3 1.48407
\(622\) 34930.8 2.25176
\(623\) −2554.73 −0.164291
\(624\) 28330.8 1.81753
\(625\) 13202.8 0.844977
\(626\) 12438.3 0.794144
\(627\) 27005.5 1.72009
\(628\) 3218.05 0.204481
\(629\) 29407.7 1.86417
\(630\) 1431.20 0.0905088
\(631\) −22683.1 −1.43106 −0.715532 0.698580i \(-0.753816\pi\)
−0.715532 + 0.698580i \(0.753816\pi\)
\(632\) −1597.97 −0.100576
\(633\) 43641.2 2.74026
\(634\) −24674.5 −1.54566
\(635\) −5193.27 −0.324549
\(636\) 20558.3 1.28174
\(637\) 15337.2 0.953974
\(638\) −7787.86 −0.483267
\(639\) 19975.7 1.23666
\(640\) −1742.96 −0.107651
\(641\) −3214.41 −0.198068 −0.0990341 0.995084i \(-0.531575\pi\)
−0.0990341 + 0.995084i \(0.531575\pi\)
\(642\) 36507.6 2.24430
\(643\) 5096.07 0.312550 0.156275 0.987714i \(-0.450051\pi\)
0.156275 + 0.987714i \(0.450051\pi\)
\(644\) −3955.42 −0.242027
\(645\) 0 0
\(646\) 49167.2 2.99452
\(647\) −2031.59 −0.123447 −0.0617234 0.998093i \(-0.519660\pi\)
−0.0617234 + 0.998093i \(0.519660\pi\)
\(648\) −320.371 −0.0194218
\(649\) −14184.5 −0.857923
\(650\) −20940.6 −1.26362
\(651\) −3673.94 −0.221187
\(652\) 6673.72 0.400864
\(653\) −6868.13 −0.411594 −0.205797 0.978595i \(-0.565979\pi\)
−0.205797 + 0.978595i \(0.565979\pi\)
\(654\) 35357.3 2.11404
\(655\) 6546.35 0.390514
\(656\) 14739.1 0.877232
\(657\) −20555.8 −1.22063
\(658\) −4383.44 −0.259702
\(659\) −11046.0 −0.652947 −0.326474 0.945206i \(-0.605860\pi\)
−0.326474 + 0.945206i \(0.605860\pi\)
\(660\) −3457.78 −0.203930
\(661\) 19990.5 1.17631 0.588156 0.808748i \(-0.299854\pi\)
0.588156 + 0.808748i \(0.299854\pi\)
\(662\) 24722.0 1.45143
\(663\) −37713.7 −2.20917
\(664\) 660.120 0.0385807
\(665\) 1158.06 0.0675302
\(666\) −49133.0 −2.85865
\(667\) −14583.0 −0.846561
\(668\) −6038.78 −0.349772
\(669\) 9358.06 0.540812
\(670\) −26.0612 −0.00150274
\(671\) 21889.8 1.25938
\(672\) −6768.26 −0.388529
\(673\) −17975.7 −1.02958 −0.514792 0.857315i \(-0.672131\pi\)
−0.514792 + 0.857315i \(0.672131\pi\)
\(674\) −4095.74 −0.234068
\(675\) −15507.8 −0.884292
\(676\) −353.062 −0.0200877
\(677\) −742.490 −0.0421510 −0.0210755 0.999778i \(-0.506709\pi\)
−0.0210755 + 0.999778i \(0.506709\pi\)
\(678\) 46260.7 2.62040
\(679\) 5900.03 0.333464
\(680\) 1349.80 0.0761214
\(681\) 4168.90 0.234585
\(682\) 12040.0 0.676007
\(683\) 29791.7 1.66903 0.834514 0.550987i \(-0.185748\pi\)
0.834514 + 0.550987i \(0.185748\pi\)
\(684\) −37096.2 −2.07370
\(685\) −3431.42 −0.191399
\(686\) −8816.88 −0.490714
\(687\) 11560.9 0.642029
\(688\) 0 0
\(689\) −17307.7 −0.957000
\(690\) −14337.8 −0.791062
\(691\) −3361.09 −0.185039 −0.0925196 0.995711i \(-0.529492\pi\)
−0.0925196 + 0.995711i \(0.529492\pi\)
\(692\) −26615.3 −1.46208
\(693\) 3583.78 0.196445
\(694\) −5168.95 −0.282724
\(695\) 1762.47 0.0961933
\(696\) −3744.58 −0.203934
\(697\) −19620.5 −1.06626
\(698\) −33281.4 −1.80476
\(699\) −2165.26 −0.117164
\(700\) 2670.87 0.144213
\(701\) 23288.1 1.25475 0.627373 0.778719i \(-0.284130\pi\)
0.627373 + 0.778719i \(0.284130\pi\)
\(702\) 23155.3 1.24493
\(703\) −39755.9 −2.13289
\(704\) 7799.71 0.417561
\(705\) −7175.44 −0.383323
\(706\) −23160.8 −1.23466
\(707\) 1314.78 0.0699395
\(708\) 31809.0 1.68850
\(709\) 17503.7 0.927171 0.463585 0.886052i \(-0.346563\pi\)
0.463585 + 0.886052i \(0.346563\pi\)
\(710\) −4582.84 −0.242241
\(711\) −12644.4 −0.666949
\(712\) 4025.55 0.211888
\(713\) 22545.3 1.18419
\(714\) 10651.8 0.558309
\(715\) 2911.05 0.152262
\(716\) −5392.76 −0.281476
\(717\) 35295.6 1.83841
\(718\) −10208.4 −0.530605
\(719\) −10970.4 −0.569024 −0.284512 0.958673i \(-0.591832\pi\)
−0.284512 + 0.958673i \(0.591832\pi\)
\(720\) −8023.38 −0.415297
\(721\) −641.896 −0.0331560
\(722\) −40271.6 −2.07584
\(723\) 61674.9 3.17249
\(724\) −11603.5 −0.595638
\(725\) 9847.09 0.504430
\(726\) 23263.8 1.18925
\(727\) 747.962 0.0381573 0.0190787 0.999818i \(-0.493927\pi\)
0.0190787 + 0.999818i \(0.493927\pi\)
\(728\) 855.069 0.0435315
\(729\) −32050.2 −1.62832
\(730\) 4715.91 0.239101
\(731\) 0 0
\(732\) −49088.0 −2.47861
\(733\) 21811.3 1.09907 0.549534 0.835471i \(-0.314805\pi\)
0.549534 + 0.835471i \(0.314805\pi\)
\(734\) −12248.0 −0.615918
\(735\) −7090.92 −0.355854
\(736\) 41533.8 2.08010
\(737\) −65.2581 −0.00326162
\(738\) 32781.0 1.63508
\(739\) 13215.5 0.657834 0.328917 0.944359i \(-0.393316\pi\)
0.328917 + 0.944359i \(0.393316\pi\)
\(740\) 5090.34 0.252871
\(741\) 50984.7 2.52762
\(742\) 4888.37 0.241857
\(743\) 25963.2 1.28196 0.640980 0.767558i \(-0.278528\pi\)
0.640980 + 0.767558i \(0.278528\pi\)
\(744\) 5789.12 0.285268
\(745\) −1199.59 −0.0589929
\(746\) 8944.24 0.438970
\(747\) 5223.36 0.255841
\(748\) −15763.8 −0.770561
\(749\) 3920.13 0.191240
\(750\) 19900.6 0.968889
\(751\) −3717.93 −0.180651 −0.0903256 0.995912i \(-0.528791\pi\)
−0.0903256 + 0.995912i \(0.528791\pi\)
\(752\) 24573.7 1.19164
\(753\) −16749.4 −0.810600
\(754\) −14703.0 −0.710148
\(755\) −4426.08 −0.213353
\(756\) −2953.35 −0.142080
\(757\) 120.818 0.00580079 0.00290039 0.999996i \(-0.499077\pi\)
0.00290039 + 0.999996i \(0.499077\pi\)
\(758\) 46463.1 2.22641
\(759\) −35902.4 −1.71696
\(760\) −1824.78 −0.0870945
\(761\) 23248.7 1.10744 0.553722 0.832702i \(-0.313207\pi\)
0.553722 + 0.832702i \(0.313207\pi\)
\(762\) 64576.3 3.07002
\(763\) 3796.62 0.180140
\(764\) 7949.14 0.376426
\(765\) 10680.7 0.504784
\(766\) −39032.8 −1.84114
\(767\) −26779.6 −1.26070
\(768\) 42914.2 2.01632
\(769\) 12713.4 0.596174 0.298087 0.954539i \(-0.403651\pi\)
0.298087 + 0.954539i \(0.403651\pi\)
\(770\) −822.192 −0.0384802
\(771\) −2972.26 −0.138837
\(772\) −8084.16 −0.376885
\(773\) −6472.11 −0.301146 −0.150573 0.988599i \(-0.548112\pi\)
−0.150573 + 0.988599i \(0.548112\pi\)
\(774\) 0 0
\(775\) −15223.6 −0.705610
\(776\) −9296.82 −0.430073
\(777\) −8612.88 −0.397665
\(778\) 36705.2 1.69144
\(779\) 26524.8 1.21996
\(780\) −6528.07 −0.299670
\(781\) −11475.6 −0.525772
\(782\) −65365.2 −2.98907
\(783\) −10888.5 −0.496966
\(784\) 24284.3 1.10624
\(785\) 1252.57 0.0569505
\(786\) −81401.3 −3.69401
\(787\) −25596.9 −1.15938 −0.579689 0.814838i \(-0.696826\pi\)
−0.579689 + 0.814838i \(0.696826\pi\)
\(788\) 19145.9 0.865538
\(789\) −21355.8 −0.963606
\(790\) 2900.88 0.130644
\(791\) 4967.42 0.223288
\(792\) −5647.05 −0.253358
\(793\) 41326.5 1.85063
\(794\) −31639.4 −1.41416
\(795\) 8001.98 0.356982
\(796\) 12913.5 0.575010
\(797\) −26835.0 −1.19265 −0.596327 0.802742i \(-0.703374\pi\)
−0.596327 + 0.802742i \(0.703374\pi\)
\(798\) −14400.0 −0.638791
\(799\) −32712.3 −1.44841
\(800\) −28045.5 −1.23945
\(801\) 31853.2 1.40509
\(802\) 48450.2 2.13321
\(803\) 11808.8 0.518958
\(804\) 146.342 0.00641926
\(805\) −1539.58 −0.0674075
\(806\) 22730.9 0.993375
\(807\) 63823.3 2.78400
\(808\) −2071.73 −0.0902018
\(809\) −22386.4 −0.972887 −0.486443 0.873712i \(-0.661706\pi\)
−0.486443 + 0.873712i \(0.661706\pi\)
\(810\) 581.585 0.0252282
\(811\) −12050.9 −0.521781 −0.260891 0.965368i \(-0.584016\pi\)
−0.260891 + 0.965368i \(0.584016\pi\)
\(812\) 1875.30 0.0810470
\(813\) −21402.2 −0.923255
\(814\) 28225.7 1.21537
\(815\) 2597.64 0.111646
\(816\) −59714.2 −2.56178
\(817\) 0 0
\(818\) −3750.07 −0.160291
\(819\) 6765.95 0.288671
\(820\) −3396.23 −0.144636
\(821\) 2118.86 0.0900717 0.0450358 0.998985i \(-0.485660\pi\)
0.0450358 + 0.998985i \(0.485660\pi\)
\(822\) 42668.4 1.81050
\(823\) −15733.7 −0.666396 −0.333198 0.942857i \(-0.608128\pi\)
−0.333198 + 0.942857i \(0.608128\pi\)
\(824\) 1011.45 0.0427617
\(825\) 24242.9 1.02306
\(826\) 7563.57 0.318608
\(827\) −19983.4 −0.840256 −0.420128 0.907465i \(-0.638015\pi\)
−0.420128 + 0.907465i \(0.638015\pi\)
\(828\) 49317.4 2.06993
\(829\) −34475.6 −1.44437 −0.722187 0.691698i \(-0.756863\pi\)
−0.722187 + 0.691698i \(0.756863\pi\)
\(830\) −1198.35 −0.0501147
\(831\) −47211.8 −1.97083
\(832\) 14725.4 0.613594
\(833\) −32327.0 −1.34461
\(834\) −21915.6 −0.909924
\(835\) −2350.50 −0.0974159
\(836\) 21310.8 0.881640
\(837\) 16833.7 0.695170
\(838\) 41745.8 1.72087
\(839\) 9582.61 0.394313 0.197156 0.980372i \(-0.436829\pi\)
0.197156 + 0.980372i \(0.436829\pi\)
\(840\) −395.328 −0.0162382
\(841\) −17475.1 −0.716514
\(842\) 47177.9 1.93095
\(843\) −53514.7 −2.18641
\(844\) 34438.6 1.40453
\(845\) −137.423 −0.00559468
\(846\) 54654.2 2.22110
\(847\) 2498.03 0.101338
\(848\) −27404.4 −1.10975
\(849\) −67039.1 −2.70998
\(850\) 44137.5 1.78106
\(851\) 52853.5 2.12902
\(852\) 25734.1 1.03478
\(853\) −31343.1 −1.25811 −0.629055 0.777361i \(-0.716558\pi\)
−0.629055 + 0.777361i \(0.716558\pi\)
\(854\) −11672.2 −0.467698
\(855\) −14439.1 −0.577550
\(856\) −6177.06 −0.246644
\(857\) −3018.06 −0.120298 −0.0601488 0.998189i \(-0.519158\pi\)
−0.0601488 + 0.998189i \(0.519158\pi\)
\(858\) −36197.8 −1.44030
\(859\) 20259.2 0.804697 0.402349 0.915487i \(-0.368194\pi\)
0.402349 + 0.915487i \(0.368194\pi\)
\(860\) 0 0
\(861\) 5746.43 0.227454
\(862\) 24959.4 0.986219
\(863\) 40225.7 1.58667 0.793336 0.608785i \(-0.208343\pi\)
0.793336 + 0.608785i \(0.208343\pi\)
\(864\) 31011.6 1.22111
\(865\) −10359.6 −0.407209
\(866\) 46873.9 1.83931
\(867\) 38478.0 1.50725
\(868\) −2899.22 −0.113371
\(869\) 7263.88 0.283556
\(870\) 6797.71 0.264901
\(871\) −123.203 −0.00479286
\(872\) −5982.44 −0.232329
\(873\) −73563.5 −2.85194
\(874\) 88366.6 3.41996
\(875\) 2136.90 0.0825604
\(876\) −26481.3 −1.02137
\(877\) 9078.63 0.349559 0.174780 0.984608i \(-0.444079\pi\)
0.174780 + 0.984608i \(0.444079\pi\)
\(878\) 10718.7 0.412003
\(879\) −30154.3 −1.15708
\(880\) 4609.24 0.176565
\(881\) −1661.65 −0.0635440 −0.0317720 0.999495i \(-0.510115\pi\)
−0.0317720 + 0.999495i \(0.510115\pi\)
\(882\) 54010.4 2.06193
\(883\) 10862.1 0.413974 0.206987 0.978344i \(-0.433634\pi\)
0.206987 + 0.978344i \(0.433634\pi\)
\(884\) −29761.0 −1.13232
\(885\) 12381.1 0.470268
\(886\) 35660.6 1.35219
\(887\) 12633.9 0.478248 0.239124 0.970989i \(-0.423140\pi\)
0.239124 + 0.970989i \(0.423140\pi\)
\(888\) 13571.5 0.512873
\(889\) 6934.12 0.261601
\(890\) −7307.78 −0.275233
\(891\) 1456.31 0.0547565
\(892\) 7384.73 0.277196
\(893\) 44223.4 1.65720
\(894\) 14916.5 0.558034
\(895\) −2099.04 −0.0783946
\(896\) 2327.22 0.0867710
\(897\) −67781.5 −2.52303
\(898\) 27546.4 1.02365
\(899\) −10689.0 −0.396548
\(900\) −33301.3 −1.23338
\(901\) 36480.4 1.34888
\(902\) −18831.9 −0.695160
\(903\) 0 0
\(904\) −7827.29 −0.287977
\(905\) −4516.48 −0.165893
\(906\) 55036.6 2.01818
\(907\) 43157.9 1.57997 0.789987 0.613124i \(-0.210087\pi\)
0.789987 + 0.613124i \(0.210087\pi\)
\(908\) 3289.80 0.120238
\(909\) −16393.1 −0.598156
\(910\) −1552.25 −0.0565456
\(911\) −8726.36 −0.317363 −0.158681 0.987330i \(-0.550724\pi\)
−0.158681 + 0.987330i \(0.550724\pi\)
\(912\) 80727.0 2.93107
\(913\) −3000.70 −0.108772
\(914\) −5264.59 −0.190522
\(915\) −19106.7 −0.690325
\(916\) 9123.02 0.329076
\(917\) −8740.76 −0.314772
\(918\) −48805.6 −1.75471
\(919\) −25907.4 −0.929932 −0.464966 0.885328i \(-0.653934\pi\)
−0.464966 + 0.885328i \(0.653934\pi\)
\(920\) 2425.95 0.0869363
\(921\) −10702.8 −0.382918
\(922\) 42949.4 1.53413
\(923\) −21665.2 −0.772609
\(924\) 4616.86 0.164376
\(925\) −35689.0 −1.26859
\(926\) 7934.89 0.281595
\(927\) 8003.37 0.283566
\(928\) −19691.6 −0.696560
\(929\) 32728.1 1.15584 0.577919 0.816094i \(-0.303865\pi\)
0.577919 + 0.816094i \(0.303865\pi\)
\(930\) −10509.3 −0.370551
\(931\) 43702.5 1.53845
\(932\) −1708.67 −0.0600530
\(933\) −76347.0 −2.67898
\(934\) −7702.78 −0.269853
\(935\) −6135.78 −0.214611
\(936\) −10661.3 −0.372302
\(937\) 5170.31 0.180263 0.0901316 0.995930i \(-0.471271\pi\)
0.0901316 + 0.995930i \(0.471271\pi\)
\(938\) 34.7973 0.00121127
\(939\) −27186.0 −0.944814
\(940\) −5662.36 −0.196474
\(941\) −23338.4 −0.808511 −0.404255 0.914646i \(-0.632469\pi\)
−0.404255 + 0.914646i \(0.632469\pi\)
\(942\) −15575.2 −0.538714
\(943\) −35263.3 −1.21774
\(944\) −42401.6 −1.46192
\(945\) −1149.54 −0.0395710
\(946\) 0 0
\(947\) 6979.11 0.239483 0.119742 0.992805i \(-0.461793\pi\)
0.119742 + 0.992805i \(0.461793\pi\)
\(948\) −16289.3 −0.558073
\(949\) 22294.3 0.762595
\(950\) −59669.0 −2.03781
\(951\) 53930.2 1.83891
\(952\) −1802.27 −0.0613572
\(953\) 15961.8 0.542552 0.271276 0.962502i \(-0.412554\pi\)
0.271276 + 0.962502i \(0.412554\pi\)
\(954\) −60949.8 −2.06847
\(955\) 3094.07 0.104840
\(956\) 27852.9 0.942287
\(957\) 17021.7 0.574955
\(958\) −39824.6 −1.34308
\(959\) 4581.68 0.154276
\(960\) −6808.05 −0.228884
\(961\) −13265.9 −0.445298
\(962\) 53288.4 1.78595
\(963\) −48877.5 −1.63557
\(964\) 48669.5 1.62608
\(965\) −3146.62 −0.104967
\(966\) 19144.1 0.637630
\(967\) −15404.6 −0.512283 −0.256142 0.966639i \(-0.582451\pi\)
−0.256142 + 0.966639i \(0.582451\pi\)
\(968\) −3936.21 −0.130697
\(969\) −107463. −3.56265
\(970\) 16877.0 0.558646
\(971\) −814.407 −0.0269161 −0.0134581 0.999909i \(-0.504284\pi\)
−0.0134581 + 0.999909i \(0.504284\pi\)
\(972\) −26557.1 −0.876357
\(973\) −2353.27 −0.0775360
\(974\) 15911.2 0.523437
\(975\) 45769.1 1.50337
\(976\) 65434.7 2.14602
\(977\) 3952.69 0.129435 0.0647174 0.997904i \(-0.479385\pi\)
0.0647174 + 0.997904i \(0.479385\pi\)
\(978\) −32300.6 −1.05609
\(979\) −18298.9 −0.597380
\(980\) −5595.66 −0.182395
\(981\) −47337.6 −1.54064
\(982\) −43172.6 −1.40295
\(983\) 2736.55 0.0887918 0.0443959 0.999014i \(-0.485864\pi\)
0.0443959 + 0.999014i \(0.485864\pi\)
\(984\) −9054.80 −0.293350
\(985\) 7452.22 0.241063
\(986\) 30990.3 1.00094
\(987\) 9580.73 0.308975
\(988\) 40233.6 1.29555
\(989\) 0 0
\(990\) 10251.4 0.329101
\(991\) 24139.6 0.773783 0.386892 0.922125i \(-0.373549\pi\)
0.386892 + 0.922125i \(0.373549\pi\)
\(992\) 30443.2 0.974367
\(993\) −54034.1 −1.72681
\(994\) 6119.07 0.195257
\(995\) 5026.37 0.160147
\(996\) 6729.09 0.214076
\(997\) −27188.4 −0.863656 −0.431828 0.901956i \(-0.642131\pi\)
−0.431828 + 0.901956i \(0.642131\pi\)
\(998\) 49920.3 1.58337
\(999\) 39463.5 1.24982
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.1.10 50
43.42 odd 2 1849.4.a.j.1.41 yes 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.i.1.10 50 1.1 even 1 trivial
1849.4.a.j.1.41 yes 50 43.42 odd 2