Properties

Label 17.4.a.b.1.3
Level 17
Weight 4
Character 17.1
Self dual Yes
Analytic conductor 1.003
Analytic rank 0
Dimension 3
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 17 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 17.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.0030324701\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.2636.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-0.287410\)
Character \(\chi\) = 17.1

$q$-expansion

\(f(q)\) \(=\) \(q+4.67129 q^{2} -7.62999 q^{3} +13.8209 q^{4} -11.9174 q^{5} -35.6419 q^{6} +26.1222 q^{7} +27.1912 q^{8} +31.2167 q^{9} +O(q^{10})\) \(q+4.67129 q^{2} -7.62999 q^{3} +13.8209 q^{4} -11.9174 q^{5} -35.6419 q^{6} +26.1222 q^{7} +27.1912 q^{8} +31.2167 q^{9} -55.6696 q^{10} -3.24412 q^{11} -105.453 q^{12} -20.0515 q^{13} +122.024 q^{14} +90.9296 q^{15} +16.4506 q^{16} -17.0000 q^{17} +145.822 q^{18} +57.3466 q^{19} -164.709 q^{20} -199.312 q^{21} -15.1542 q^{22} +77.0438 q^{23} -207.469 q^{24} +17.0243 q^{25} -93.6662 q^{26} -32.1732 q^{27} +361.033 q^{28} -286.162 q^{29} +424.758 q^{30} -8.54816 q^{31} -140.684 q^{32} +24.7526 q^{33} -79.4119 q^{34} -311.309 q^{35} +431.443 q^{36} +357.982 q^{37} +267.882 q^{38} +152.992 q^{39} -324.049 q^{40} +194.467 q^{41} -931.044 q^{42} -74.2619 q^{43} -44.8367 q^{44} -372.021 q^{45} +359.894 q^{46} +23.6130 q^{47} -125.518 q^{48} +339.369 q^{49} +79.5255 q^{50} +129.710 q^{51} -277.130 q^{52} +104.330 q^{53} -150.290 q^{54} +38.6614 q^{55} +710.295 q^{56} -437.553 q^{57} -1336.75 q^{58} +249.363 q^{59} +1256.73 q^{60} -370.384 q^{61} -39.9309 q^{62} +815.448 q^{63} -788.781 q^{64} +238.961 q^{65} +115.626 q^{66} +939.650 q^{67} -234.956 q^{68} -587.843 q^{69} -1454.21 q^{70} -520.197 q^{71} +848.820 q^{72} +348.741 q^{73} +1672.24 q^{74} -129.895 q^{75} +792.583 q^{76} -84.7434 q^{77} +714.672 q^{78} -953.827 q^{79} -196.049 q^{80} -597.369 q^{81} +908.412 q^{82} -1414.28 q^{83} -2754.68 q^{84} +202.596 q^{85} -346.899 q^{86} +2183.41 q^{87} -88.2115 q^{88} -486.132 q^{89} -1737.82 q^{90} -523.788 q^{91} +1064.82 q^{92} +65.2223 q^{93} +110.303 q^{94} -683.422 q^{95} +1073.42 q^{96} -685.281 q^{97} +1585.29 q^{98} -101.271 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + q^{2} + 4q^{3} + 25q^{4} - 8q^{5} - 74q^{6} + 22q^{7} - 39q^{8} + 59q^{9} + O(q^{10}) \) \( 3q + q^{2} + 4q^{3} + 25q^{4} - 8q^{5} - 74q^{6} + 22q^{7} - 39q^{8} + 59q^{9} - 56q^{10} - 28q^{11} + 22q^{12} + 30q^{13} + 92q^{14} + 108q^{15} + 137q^{16} - 51q^{17} - 103q^{18} + 80q^{19} - 168q^{20} - 192q^{21} + 286q^{22} + 142q^{23} - 666q^{24} - 223q^{25} + 26q^{26} - 20q^{27} + 476q^{28} - 456q^{29} + 400q^{30} + 230q^{31} - 71q^{32} - 332q^{33} - 17q^{34} - 332q^{35} + 1313q^{36} + 356q^{37} + 724q^{38} + 268q^{39} - 424q^{40} - 294q^{41} - 1128q^{42} + 556q^{43} - 1122q^{44} - 384q^{45} - 704q^{46} + 640q^{47} + 774q^{48} - 269q^{49} + 547q^{50} - 68q^{51} - 774q^{52} + 302q^{53} - 1100q^{54} + 76q^{55} + 684q^{56} - 720q^{57} - 1304q^{58} + 636q^{59} + 1328q^{60} - 84q^{61} + 508q^{62} + 1122q^{63} - 919q^{64} + 408q^{65} + 2468q^{66} + 1008q^{67} - 425q^{68} + 576q^{69} - 1504q^{70} - 402q^{71} - 927q^{72} + 838q^{73} + 836q^{74} - 1548q^{75} - 908q^{76} - 504q^{77} + 1308q^{78} - 594q^{79} - 40q^{80} - 505q^{81} + 358q^{82} - 2396q^{83} - 2040q^{84} + 136q^{85} - 1264q^{86} + 1428q^{87} + 1838q^{88} - 170q^{89} - 2008q^{90} - 1016q^{91} + 4896q^{92} + 632q^{93} - 2016q^{94} - 472q^{95} + 678q^{96} - 270q^{97} + 2857q^{98} - 2920q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.67129 1.65155 0.825775 0.564000i \(-0.190738\pi\)
0.825775 + 0.564000i \(0.190738\pi\)
\(3\) −7.62999 −1.46839 −0.734196 0.678938i \(-0.762441\pi\)
−0.734196 + 0.678938i \(0.762441\pi\)
\(4\) 13.8209 1.72762
\(5\) −11.9174 −1.06592 −0.532962 0.846139i \(-0.678921\pi\)
−0.532962 + 0.846139i \(0.678921\pi\)
\(6\) −35.6419 −2.42512
\(7\) 26.1222 1.41047 0.705233 0.708975i \(-0.250842\pi\)
0.705233 + 0.708975i \(0.250842\pi\)
\(8\) 27.1912 1.20169
\(9\) 31.2167 1.15617
\(10\) −55.6696 −1.76043
\(11\) −3.24412 −0.0889216 −0.0444608 0.999011i \(-0.514157\pi\)
−0.0444608 + 0.999011i \(0.514157\pi\)
\(12\) −105.453 −2.53682
\(13\) −20.0515 −0.427790 −0.213895 0.976857i \(-0.568615\pi\)
−0.213895 + 0.976857i \(0.568615\pi\)
\(14\) 122.024 2.32945
\(15\) 90.9296 1.56519
\(16\) 16.4506 0.257041
\(17\) −17.0000 −0.242536
\(18\) 145.822 1.90948
\(19\) 57.3466 0.692432 0.346216 0.938155i \(-0.387466\pi\)
0.346216 + 0.938155i \(0.387466\pi\)
\(20\) −164.709 −1.84151
\(21\) −199.312 −2.07112
\(22\) −15.1542 −0.146858
\(23\) 77.0438 0.698467 0.349233 0.937036i \(-0.386442\pi\)
0.349233 + 0.937036i \(0.386442\pi\)
\(24\) −207.469 −1.76456
\(25\) 17.0243 0.136195
\(26\) −93.6662 −0.706517
\(27\) −32.1732 −0.229323
\(28\) 361.033 2.43674
\(29\) −286.162 −1.83238 −0.916190 0.400744i \(-0.868752\pi\)
−0.916190 + 0.400744i \(0.868752\pi\)
\(30\) 424.758 2.58500
\(31\) −8.54816 −0.0495256 −0.0247628 0.999693i \(-0.507883\pi\)
−0.0247628 + 0.999693i \(0.507883\pi\)
\(32\) −140.684 −0.777178
\(33\) 24.7526 0.130572
\(34\) −79.4119 −0.400560
\(35\) −311.309 −1.50345
\(36\) 431.443 1.99742
\(37\) 357.982 1.59059 0.795296 0.606221i \(-0.207315\pi\)
0.795296 + 0.606221i \(0.207315\pi\)
\(38\) 267.882 1.14359
\(39\) 152.992 0.628164
\(40\) −324.049 −1.28091
\(41\) 194.467 0.740748 0.370374 0.928883i \(-0.379230\pi\)
0.370374 + 0.928883i \(0.379230\pi\)
\(42\) −931.044 −3.42055
\(43\) −74.2619 −0.263368 −0.131684 0.991292i \(-0.542038\pi\)
−0.131684 + 0.991292i \(0.542038\pi\)
\(44\) −44.8367 −0.153622
\(45\) −372.021 −1.23239
\(46\) 359.894 1.15355
\(47\) 23.6130 0.0732831 0.0366416 0.999328i \(-0.488334\pi\)
0.0366416 + 0.999328i \(0.488334\pi\)
\(48\) −125.518 −0.377437
\(49\) 339.369 0.989415
\(50\) 79.5255 0.224932
\(51\) 129.710 0.356137
\(52\) −277.130 −0.739058
\(53\) 104.330 0.270393 0.135197 0.990819i \(-0.456833\pi\)
0.135197 + 0.990819i \(0.456833\pi\)
\(54\) −150.290 −0.378739
\(55\) 38.6614 0.0947837
\(56\) 710.295 1.69495
\(57\) −437.553 −1.01676
\(58\) −1336.75 −3.02627
\(59\) 249.363 0.550243 0.275122 0.961409i \(-0.411282\pi\)
0.275122 + 0.961409i \(0.411282\pi\)
\(60\) 1256.73 2.70405
\(61\) −370.384 −0.777424 −0.388712 0.921359i \(-0.627080\pi\)
−0.388712 + 0.921359i \(0.627080\pi\)
\(62\) −39.9309 −0.0817940
\(63\) 815.448 1.63074
\(64\) −788.781 −1.54059
\(65\) 238.961 0.455992
\(66\) 115.626 0.215646
\(67\) 939.650 1.71338 0.856691 0.515830i \(-0.172517\pi\)
0.856691 + 0.515830i \(0.172517\pi\)
\(68\) −234.956 −0.419008
\(69\) −587.843 −1.02562
\(70\) −1454.21 −2.48302
\(71\) −520.197 −0.869522 −0.434761 0.900546i \(-0.643167\pi\)
−0.434761 + 0.900546i \(0.643167\pi\)
\(72\) 848.820 1.38937
\(73\) 348.741 0.559137 0.279568 0.960126i \(-0.409809\pi\)
0.279568 + 0.960126i \(0.409809\pi\)
\(74\) 1672.24 2.62694
\(75\) −129.895 −0.199987
\(76\) 792.583 1.19626
\(77\) −84.7434 −0.125421
\(78\) 714.672 1.03744
\(79\) −953.827 −1.35840 −0.679202 0.733951i \(-0.737674\pi\)
−0.679202 + 0.733951i \(0.737674\pi\)
\(80\) −196.049 −0.273986
\(81\) −597.369 −0.819437
\(82\) 908.412 1.22338
\(83\) −1414.28 −1.87033 −0.935166 0.354211i \(-0.884750\pi\)
−0.935166 + 0.354211i \(0.884750\pi\)
\(84\) −2754.68 −3.57809
\(85\) 202.596 0.258525
\(86\) −346.899 −0.434966
\(87\) 2183.41 2.69065
\(88\) −88.2115 −0.106857
\(89\) −486.132 −0.578987 −0.289493 0.957180i \(-0.593487\pi\)
−0.289493 + 0.957180i \(0.593487\pi\)
\(90\) −1737.82 −2.03536
\(91\) −523.788 −0.603384
\(92\) 1064.82 1.20668
\(93\) 65.2223 0.0727230
\(94\) 110.303 0.121031
\(95\) −683.422 −0.738080
\(96\) 1073.42 1.14120
\(97\) −685.281 −0.717317 −0.358659 0.933469i \(-0.616766\pi\)
−0.358659 + 0.933469i \(0.616766\pi\)
\(98\) 1585.29 1.63407
\(99\) −101.271 −0.102809
\(100\) 235.292 0.235292
\(101\) 864.755 0.851944 0.425972 0.904736i \(-0.359932\pi\)
0.425972 + 0.904736i \(0.359932\pi\)
\(102\) 605.912 0.588178
\(103\) 1880.91 1.79933 0.899665 0.436580i \(-0.143810\pi\)
0.899665 + 0.436580i \(0.143810\pi\)
\(104\) −545.224 −0.514073
\(105\) 2375.28 2.20765
\(106\) 487.355 0.446567
\(107\) −32.8149 −0.0296480 −0.0148240 0.999890i \(-0.504719\pi\)
−0.0148240 + 0.999890i \(0.504719\pi\)
\(108\) −444.663 −0.396183
\(109\) 528.727 0.464613 0.232307 0.972643i \(-0.425373\pi\)
0.232307 + 0.972643i \(0.425373\pi\)
\(110\) 180.599 0.156540
\(111\) −2731.40 −2.33561
\(112\) 429.727 0.362548
\(113\) 414.691 0.345229 0.172614 0.984989i \(-0.444779\pi\)
0.172614 + 0.984989i \(0.444779\pi\)
\(114\) −2043.94 −1.67923
\(115\) −918.161 −0.744513
\(116\) −3955.03 −3.16565
\(117\) −625.940 −0.494600
\(118\) 1164.85 0.908754
\(119\) −444.077 −0.342088
\(120\) 2472.49 1.88088
\(121\) −1320.48 −0.992093
\(122\) −1730.17 −1.28395
\(123\) −1483.78 −1.08771
\(124\) −118.143 −0.0855613
\(125\) 1286.79 0.920751
\(126\) 3809.19 2.69325
\(127\) 596.093 0.416494 0.208247 0.978076i \(-0.433224\pi\)
0.208247 + 0.978076i \(0.433224\pi\)
\(128\) −2559.15 −1.76718
\(129\) 566.617 0.386728
\(130\) 1116.26 0.753094
\(131\) 121.819 0.0812472 0.0406236 0.999175i \(-0.487066\pi\)
0.0406236 + 0.999175i \(0.487066\pi\)
\(132\) 342.103 0.225578
\(133\) 1498.02 0.976652
\(134\) 4389.38 2.82973
\(135\) 383.420 0.244441
\(136\) −462.251 −0.291454
\(137\) −897.365 −0.559614 −0.279807 0.960056i \(-0.590270\pi\)
−0.279807 + 0.960056i \(0.590270\pi\)
\(138\) −2745.98 −1.69387
\(139\) −2113.61 −1.28974 −0.644871 0.764292i \(-0.723089\pi\)
−0.644871 + 0.764292i \(0.723089\pi\)
\(140\) −4302.57 −2.59738
\(141\) −180.167 −0.107608
\(142\) −2429.99 −1.43606
\(143\) 65.0493 0.0380398
\(144\) 513.534 0.297184
\(145\) 3410.31 1.95318
\(146\) 1629.07 0.923442
\(147\) −2589.38 −1.45285
\(148\) 4947.65 2.74793
\(149\) 2580.76 1.41895 0.709476 0.704729i \(-0.248932\pi\)
0.709476 + 0.704729i \(0.248932\pi\)
\(150\) −606.778 −0.330288
\(151\) 1342.77 0.723662 0.361831 0.932244i \(-0.382152\pi\)
0.361831 + 0.932244i \(0.382152\pi\)
\(152\) 1559.32 0.832091
\(153\) −530.683 −0.280413
\(154\) −395.861 −0.207139
\(155\) 101.872 0.0527906
\(156\) 2114.50 1.08523
\(157\) −2495.82 −1.26871 −0.634357 0.773041i \(-0.718735\pi\)
−0.634357 + 0.773041i \(0.718735\pi\)
\(158\) −4455.60 −2.24347
\(159\) −796.036 −0.397043
\(160\) 1676.59 0.828413
\(161\) 2012.55 0.985164
\(162\) −2790.48 −1.35334
\(163\) 1961.58 0.942595 0.471297 0.881974i \(-0.343786\pi\)
0.471297 + 0.881974i \(0.343786\pi\)
\(164\) 2687.72 1.27973
\(165\) −294.986 −0.139180
\(166\) −6606.51 −3.08894
\(167\) 2179.24 1.00979 0.504894 0.863182i \(-0.331532\pi\)
0.504894 + 0.863182i \(0.331532\pi\)
\(168\) −5419.54 −2.48885
\(169\) −1794.94 −0.816995
\(170\) 946.383 0.426966
\(171\) 1790.17 0.800571
\(172\) −1026.37 −0.454999
\(173\) 3111.45 1.36739 0.683697 0.729766i \(-0.260371\pi\)
0.683697 + 0.729766i \(0.260371\pi\)
\(174\) 10199.4 4.44374
\(175\) 444.713 0.192098
\(176\) −53.3677 −0.0228565
\(177\) −1902.64 −0.807972
\(178\) −2270.86 −0.956226
\(179\) 810.106 0.338269 0.169135 0.985593i \(-0.445903\pi\)
0.169135 + 0.985593i \(0.445903\pi\)
\(180\) −5141.68 −2.12910
\(181\) −3356.23 −1.37827 −0.689134 0.724634i \(-0.742009\pi\)
−0.689134 + 0.724634i \(0.742009\pi\)
\(182\) −2446.77 −0.996519
\(183\) 2826.03 1.14156
\(184\) 2094.92 0.839343
\(185\) −4266.22 −1.69545
\(186\) 304.672 0.120106
\(187\) 55.1500 0.0215667
\(188\) 326.353 0.126605
\(189\) −840.434 −0.323453
\(190\) −3192.46 −1.21898
\(191\) 1338.41 0.507038 0.253519 0.967330i \(-0.418412\pi\)
0.253519 + 0.967330i \(0.418412\pi\)
\(192\) 6018.39 2.26219
\(193\) −227.465 −0.0848358 −0.0424179 0.999100i \(-0.513506\pi\)
−0.0424179 + 0.999100i \(0.513506\pi\)
\(194\) −3201.15 −1.18468
\(195\) −1823.27 −0.669575
\(196\) 4690.40 1.70933
\(197\) 815.549 0.294952 0.147476 0.989066i \(-0.452885\pi\)
0.147476 + 0.989066i \(0.452885\pi\)
\(198\) −473.064 −0.169794
\(199\) 1866.90 0.665030 0.332515 0.943098i \(-0.392103\pi\)
0.332515 + 0.943098i \(0.392103\pi\)
\(200\) 462.912 0.163664
\(201\) −7169.52 −2.51591
\(202\) 4039.52 1.40703
\(203\) −7475.19 −2.58451
\(204\) 1792.71 0.615268
\(205\) −2317.54 −0.789581
\(206\) 8786.25 2.97168
\(207\) 2405.05 0.807549
\(208\) −329.859 −0.109960
\(209\) −186.039 −0.0615721
\(210\) 11095.6 3.64605
\(211\) −1102.88 −0.359836 −0.179918 0.983682i \(-0.557583\pi\)
−0.179918 + 0.983682i \(0.557583\pi\)
\(212\) 1441.94 0.467135
\(213\) 3969.10 1.27680
\(214\) −153.288 −0.0489651
\(215\) 885.008 0.280731
\(216\) −874.828 −0.275576
\(217\) −223.297 −0.0698542
\(218\) 2469.84 0.767332
\(219\) −2660.89 −0.821032
\(220\) 534.337 0.163750
\(221\) 340.875 0.103754
\(222\) −12759.2 −3.85738
\(223\) −568.848 −0.170820 −0.0854100 0.996346i \(-0.527220\pi\)
−0.0854100 + 0.996346i \(0.527220\pi\)
\(224\) −3674.98 −1.09618
\(225\) 531.442 0.157464
\(226\) 1937.14 0.570163
\(227\) 2106.99 0.616061 0.308030 0.951377i \(-0.400330\pi\)
0.308030 + 0.951377i \(0.400330\pi\)
\(228\) −6047.39 −1.75657
\(229\) 4336.30 1.25131 0.625656 0.780099i \(-0.284831\pi\)
0.625656 + 0.780099i \(0.284831\pi\)
\(230\) −4289.00 −1.22960
\(231\) 646.591 0.184167
\(232\) −7781.11 −2.20196
\(233\) −4517.39 −1.27014 −0.635072 0.772453i \(-0.719030\pi\)
−0.635072 + 0.772453i \(0.719030\pi\)
\(234\) −2923.95 −0.816856
\(235\) −281.405 −0.0781143
\(236\) 3446.43 0.950609
\(237\) 7277.69 1.99467
\(238\) −2074.41 −0.564976
\(239\) 5300.88 1.43467 0.717333 0.696731i \(-0.245363\pi\)
0.717333 + 0.696731i \(0.245363\pi\)
\(240\) 1495.85 0.402319
\(241\) −1368.82 −0.365864 −0.182932 0.983126i \(-0.558559\pi\)
−0.182932 + 0.983126i \(0.558559\pi\)
\(242\) −6168.32 −1.63849
\(243\) 5426.60 1.43258
\(244\) −5119.05 −1.34309
\(245\) −4044.40 −1.05464
\(246\) −6931.17 −1.79640
\(247\) −1149.88 −0.296216
\(248\) −232.435 −0.0595146
\(249\) 10790.9 2.74638
\(250\) 6010.96 1.52067
\(251\) −5547.63 −1.39507 −0.697536 0.716549i \(-0.745720\pi\)
−0.697536 + 0.716549i \(0.745720\pi\)
\(252\) 11270.3 2.81730
\(253\) −249.939 −0.0621088
\(254\) 2784.52 0.687860
\(255\) −1545.80 −0.379615
\(256\) −5644.28 −1.37800
\(257\) −193.949 −0.0470748 −0.0235374 0.999723i \(-0.507493\pi\)
−0.0235374 + 0.999723i \(0.507493\pi\)
\(258\) 2646.83 0.638700
\(259\) 9351.29 2.24348
\(260\) 3302.67 0.787780
\(261\) −8933.04 −2.11855
\(262\) 569.052 0.134184
\(263\) −1345.63 −0.315494 −0.157747 0.987480i \(-0.550423\pi\)
−0.157747 + 0.987480i \(0.550423\pi\)
\(264\) 673.052 0.156907
\(265\) −1243.34 −0.288218
\(266\) 6997.67 1.61299
\(267\) 3709.18 0.850180
\(268\) 12986.8 2.96007
\(269\) −3083.04 −0.698797 −0.349398 0.936974i \(-0.613614\pi\)
−0.349398 + 0.936974i \(0.613614\pi\)
\(270\) 1791.07 0.403707
\(271\) −422.163 −0.0946294 −0.0473147 0.998880i \(-0.515066\pi\)
−0.0473147 + 0.998880i \(0.515066\pi\)
\(272\) −279.661 −0.0623416
\(273\) 3996.50 0.886004
\(274\) −4191.85 −0.924230
\(275\) −55.2288 −0.0121106
\(276\) −8124.54 −1.77188
\(277\) −8260.00 −1.79168 −0.895840 0.444377i \(-0.853425\pi\)
−0.895840 + 0.444377i \(0.853425\pi\)
\(278\) −9873.28 −2.13007
\(279\) −266.845 −0.0572602
\(280\) −8464.86 −1.80669
\(281\) 3321.91 0.705226 0.352613 0.935769i \(-0.385293\pi\)
0.352613 + 0.935769i \(0.385293\pi\)
\(282\) −841.611 −0.177721
\(283\) −7954.43 −1.67082 −0.835409 0.549629i \(-0.814769\pi\)
−0.835409 + 0.549629i \(0.814769\pi\)
\(284\) −7189.61 −1.50220
\(285\) 5214.50 1.08379
\(286\) 303.864 0.0628246
\(287\) 5079.91 1.04480
\(288\) −4391.69 −0.898552
\(289\) 289.000 0.0588235
\(290\) 15930.5 3.22577
\(291\) 5228.69 1.05330
\(292\) 4819.92 0.965974
\(293\) −1171.99 −0.233681 −0.116841 0.993151i \(-0.537277\pi\)
−0.116841 + 0.993151i \(0.537277\pi\)
\(294\) −12095.8 −2.39945
\(295\) −2971.76 −0.586517
\(296\) 9733.98 1.91141
\(297\) 104.374 0.0203918
\(298\) 12055.5 2.34347
\(299\) −1544.84 −0.298798
\(300\) −1795.27 −0.345500
\(301\) −1939.88 −0.371472
\(302\) 6272.46 1.19516
\(303\) −6598.07 −1.25099
\(304\) 943.387 0.177983
\(305\) 4414.01 0.828675
\(306\) −2478.98 −0.463116
\(307\) 865.763 0.160950 0.0804751 0.996757i \(-0.474356\pi\)
0.0804751 + 0.996757i \(0.474356\pi\)
\(308\) −1171.23 −0.216679
\(309\) −14351.3 −2.64212
\(310\) 475.872 0.0871862
\(311\) 6994.83 1.27537 0.637685 0.770297i \(-0.279892\pi\)
0.637685 + 0.770297i \(0.279892\pi\)
\(312\) 4160.05 0.754861
\(313\) 3442.33 0.621635 0.310818 0.950470i \(-0.399397\pi\)
0.310818 + 0.950470i \(0.399397\pi\)
\(314\) −11658.7 −2.09534
\(315\) −9718.02 −1.73825
\(316\) −13182.8 −2.34680
\(317\) 2066.15 0.366078 0.183039 0.983106i \(-0.441407\pi\)
0.183039 + 0.983106i \(0.441407\pi\)
\(318\) −3718.52 −0.655736
\(319\) 928.344 0.162938
\(320\) 9400.22 1.64215
\(321\) 250.377 0.0435349
\(322\) 9401.21 1.62705
\(323\) −974.892 −0.167939
\(324\) −8256.20 −1.41567
\(325\) −341.362 −0.0582627
\(326\) 9163.11 1.55674
\(327\) −4034.18 −0.682234
\(328\) 5287.80 0.890152
\(329\) 616.823 0.103363
\(330\) −1377.96 −0.229862
\(331\) 9027.44 1.49907 0.749536 0.661964i \(-0.230277\pi\)
0.749536 + 0.661964i \(0.230277\pi\)
\(332\) −19546.7 −3.23121
\(333\) 11175.0 1.83900
\(334\) 10179.8 1.66771
\(335\) −11198.2 −1.82633
\(336\) −3278.81 −0.532362
\(337\) 204.309 0.0330250 0.0165125 0.999864i \(-0.494744\pi\)
0.0165125 + 0.999864i \(0.494744\pi\)
\(338\) −8384.67 −1.34931
\(339\) −3164.09 −0.506931
\(340\) 2800.06 0.446631
\(341\) 27.7312 0.00440390
\(342\) 8362.39 1.32218
\(343\) −94.8397 −0.0149296
\(344\) −2019.27 −0.316488
\(345\) 7005.56 1.09324
\(346\) 14534.5 2.25832
\(347\) 143.063 0.0221326 0.0110663 0.999939i \(-0.496477\pi\)
0.0110663 + 0.999939i \(0.496477\pi\)
\(348\) 30176.8 4.64841
\(349\) −3998.42 −0.613268 −0.306634 0.951828i \(-0.599203\pi\)
−0.306634 + 0.951828i \(0.599203\pi\)
\(350\) 2077.38 0.317259
\(351\) 645.119 0.0981024
\(352\) 456.396 0.0691079
\(353\) −5809.57 −0.875956 −0.437978 0.898986i \(-0.644305\pi\)
−0.437978 + 0.898986i \(0.644305\pi\)
\(354\) −8887.77 −1.33441
\(355\) 6199.39 0.926844
\(356\) −6718.79 −1.00027
\(357\) 3388.30 0.502320
\(358\) 3784.24 0.558668
\(359\) −4895.37 −0.719687 −0.359844 0.933013i \(-0.617170\pi\)
−0.359844 + 0.933013i \(0.617170\pi\)
\(360\) −10115.7 −1.48096
\(361\) −3570.37 −0.520538
\(362\) −15677.9 −2.27628
\(363\) 10075.2 1.45678
\(364\) −7239.24 −1.04242
\(365\) −4156.08 −0.595998
\(366\) 13201.2 1.88535
\(367\) 528.151 0.0751206 0.0375603 0.999294i \(-0.488041\pi\)
0.0375603 + 0.999294i \(0.488041\pi\)
\(368\) 1267.42 0.179535
\(369\) 6070.62 0.856433
\(370\) −19928.7 −2.80012
\(371\) 2725.33 0.381380
\(372\) 901.433 0.125637
\(373\) −10113.5 −1.40390 −0.701950 0.712226i \(-0.747687\pi\)
−0.701950 + 0.712226i \(0.747687\pi\)
\(374\) 257.621 0.0356184
\(375\) −9818.18 −1.35202
\(376\) 642.066 0.0880639
\(377\) 5737.98 0.783875
\(378\) −3925.91 −0.534198
\(379\) 729.385 0.0988548 0.0494274 0.998778i \(-0.484260\pi\)
0.0494274 + 0.998778i \(0.484260\pi\)
\(380\) −9445.52 −1.27512
\(381\) −4548.18 −0.611576
\(382\) 6252.12 0.837399
\(383\) −1608.08 −0.214540 −0.107270 0.994230i \(-0.534211\pi\)
−0.107270 + 0.994230i \(0.534211\pi\)
\(384\) 19526.3 2.59491
\(385\) 1009.92 0.133689
\(386\) −1062.56 −0.140111
\(387\) −2318.21 −0.304499
\(388\) −9471.22 −1.23925
\(389\) 9824.09 1.28047 0.640233 0.768181i \(-0.278838\pi\)
0.640233 + 0.768181i \(0.278838\pi\)
\(390\) −8517.02 −1.10584
\(391\) −1309.74 −0.169403
\(392\) 9227.87 1.18897
\(393\) −929.478 −0.119303
\(394\) 3809.66 0.487127
\(395\) 11367.1 1.44796
\(396\) −1399.65 −0.177614
\(397\) 2876.88 0.363694 0.181847 0.983327i \(-0.441792\pi\)
0.181847 + 0.983327i \(0.441792\pi\)
\(398\) 8720.82 1.09833
\(399\) −11429.9 −1.43411
\(400\) 280.061 0.0350076
\(401\) −6515.91 −0.811444 −0.405722 0.913996i \(-0.632980\pi\)
−0.405722 + 0.913996i \(0.632980\pi\)
\(402\) −33490.9 −4.15516
\(403\) 171.403 0.0211866
\(404\) 11951.7 1.47183
\(405\) 7119.09 0.873457
\(406\) −34918.8 −4.26845
\(407\) −1161.34 −0.141438
\(408\) 3526.97 0.427968
\(409\) −8870.10 −1.07237 −0.536183 0.844101i \(-0.680134\pi\)
−0.536183 + 0.844101i \(0.680134\pi\)
\(410\) −10825.9 −1.30403
\(411\) 6846.89 0.821732
\(412\) 25995.9 3.10855
\(413\) 6513.92 0.776099
\(414\) 11234.7 1.33371
\(415\) 16854.5 1.99363
\(416\) 2820.93 0.332469
\(417\) 16126.8 1.89385
\(418\) −869.041 −0.101689
\(419\) −1009.53 −0.117706 −0.0588531 0.998267i \(-0.518744\pi\)
−0.0588531 + 0.998267i \(0.518744\pi\)
\(420\) 32828.6 3.81398
\(421\) −3253.60 −0.376652 −0.188326 0.982107i \(-0.560306\pi\)
−0.188326 + 0.982107i \(0.560306\pi\)
\(422\) −5151.87 −0.594287
\(423\) 737.119 0.0847280
\(424\) 2836.86 0.324930
\(425\) −289.413 −0.0330320
\(426\) 18540.8 2.10870
\(427\) −9675.25 −1.09653
\(428\) −453.532 −0.0512203
\(429\) −496.325 −0.0558573
\(430\) 4134.13 0.463640
\(431\) −2352.51 −0.262915 −0.131457 0.991322i \(-0.541966\pi\)
−0.131457 + 0.991322i \(0.541966\pi\)
\(432\) −529.269 −0.0589455
\(433\) −5860.51 −0.650434 −0.325217 0.945639i \(-0.605437\pi\)
−0.325217 + 0.945639i \(0.605437\pi\)
\(434\) −1043.08 −0.115368
\(435\) −26020.6 −2.86803
\(436\) 7307.50 0.802674
\(437\) 4418.20 0.483641
\(438\) −12429.8 −1.35597
\(439\) 2894.17 0.314650 0.157325 0.987547i \(-0.449713\pi\)
0.157325 + 0.987547i \(0.449713\pi\)
\(440\) 1051.25 0.113901
\(441\) 10594.0 1.14394
\(442\) 1592.32 0.171356
\(443\) −8256.85 −0.885541 −0.442771 0.896635i \(-0.646004\pi\)
−0.442771 + 0.896635i \(0.646004\pi\)
\(444\) −37750.5 −4.03504
\(445\) 5793.42 0.617156
\(446\) −2657.25 −0.282118
\(447\) −19691.1 −2.08358
\(448\) −20604.7 −2.17295
\(449\) 15487.1 1.62779 0.813897 0.581009i \(-0.197342\pi\)
0.813897 + 0.581009i \(0.197342\pi\)
\(450\) 2482.52 0.260060
\(451\) −630.874 −0.0658685
\(452\) 5731.42 0.596423
\(453\) −10245.3 −1.06262
\(454\) 9842.35 1.01745
\(455\) 6242.19 0.643162
\(456\) −11897.6 −1.22184
\(457\) −16055.6 −1.64343 −0.821716 0.569897i \(-0.806983\pi\)
−0.821716 + 0.569897i \(0.806983\pi\)
\(458\) 20256.1 2.06661
\(459\) 546.944 0.0556191
\(460\) −12689.8 −1.28623
\(461\) 14064.0 1.42088 0.710440 0.703758i \(-0.248496\pi\)
0.710440 + 0.703758i \(0.248496\pi\)
\(462\) 3020.41 0.304161
\(463\) −8071.30 −0.810162 −0.405081 0.914281i \(-0.632757\pi\)
−0.405081 + 0.914281i \(0.632757\pi\)
\(464\) −4707.55 −0.470997
\(465\) −777.280 −0.0775172
\(466\) −21102.0 −2.09771
\(467\) 8582.41 0.850421 0.425211 0.905094i \(-0.360200\pi\)
0.425211 + 0.905094i \(0.360200\pi\)
\(468\) −8651.07 −0.854479
\(469\) 24545.7 2.41667
\(470\) −1314.53 −0.129010
\(471\) 19043.1 1.86297
\(472\) 6780.49 0.661224
\(473\) 240.914 0.0234191
\(474\) 33996.2 3.29429
\(475\) 976.286 0.0943054
\(476\) −6137.56 −0.590997
\(477\) 3256.84 0.312621
\(478\) 24761.9 2.36942
\(479\) −6320.96 −0.602948 −0.301474 0.953474i \(-0.597479\pi\)
−0.301474 + 0.953474i \(0.597479\pi\)
\(480\) −12792.4 −1.21643
\(481\) −7178.07 −0.680441
\(482\) −6394.13 −0.604242
\(483\) −15355.8 −1.44661
\(484\) −18250.2 −1.71396
\(485\) 8166.77 0.764606
\(486\) 25349.2 2.36597
\(487\) 7336.47 0.682643 0.341321 0.939947i \(-0.389126\pi\)
0.341321 + 0.939947i \(0.389126\pi\)
\(488\) −10071.2 −0.934225
\(489\) −14966.8 −1.38410
\(490\) −18892.6 −1.74179
\(491\) 6672.53 0.613294 0.306647 0.951823i \(-0.400793\pi\)
0.306647 + 0.951823i \(0.400793\pi\)
\(492\) −20507.2 −1.87914
\(493\) 4864.76 0.444417
\(494\) −5371.43 −0.489215
\(495\) 1206.88 0.109586
\(496\) −140.623 −0.0127301
\(497\) −13588.7 −1.22643
\(498\) 50407.6 4.53578
\(499\) 17920.9 1.60772 0.803858 0.594821i \(-0.202777\pi\)
0.803858 + 0.594821i \(0.202777\pi\)
\(500\) 17784.6 1.59070
\(501\) −16627.6 −1.48276
\(502\) −25914.6 −2.30403
\(503\) −11325.3 −1.00392 −0.501959 0.864891i \(-0.667387\pi\)
−0.501959 + 0.864891i \(0.667387\pi\)
\(504\) 22173.0 1.95965
\(505\) −10305.6 −0.908108
\(506\) −1167.54 −0.102576
\(507\) 13695.4 1.19967
\(508\) 8238.56 0.719541
\(509\) −8313.78 −0.723972 −0.361986 0.932184i \(-0.617901\pi\)
−0.361986 + 0.932184i \(0.617901\pi\)
\(510\) −7220.89 −0.626953
\(511\) 9109.87 0.788644
\(512\) −5892.85 −0.508651
\(513\) −1845.02 −0.158791
\(514\) −905.993 −0.0777464
\(515\) −22415.5 −1.91795
\(516\) 7831.17 0.668117
\(517\) −76.6033 −0.00651646
\(518\) 43682.6 3.70521
\(519\) −23740.3 −2.00787
\(520\) 6497.65 0.547963
\(521\) 5121.64 0.430677 0.215339 0.976539i \(-0.430914\pi\)
0.215339 + 0.976539i \(0.430914\pi\)
\(522\) −41728.8 −3.49889
\(523\) 13378.5 1.11855 0.559275 0.828982i \(-0.311080\pi\)
0.559275 + 0.828982i \(0.311080\pi\)
\(524\) 1683.65 0.140364
\(525\) −3393.15 −0.282075
\(526\) −6285.81 −0.521054
\(527\) 145.319 0.0120117
\(528\) 407.195 0.0335623
\(529\) −6231.26 −0.512144
\(530\) −5808.01 −0.476007
\(531\) 7784.29 0.636176
\(532\) 20704.0 1.68728
\(533\) −3899.35 −0.316885
\(534\) 17326.6 1.40411
\(535\) 391.068 0.0316025
\(536\) 25550.2 2.05896
\(537\) −6181.10 −0.496712
\(538\) −14401.8 −1.15410
\(539\) −1100.95 −0.0879804
\(540\) 5299.23 0.422301
\(541\) 9906.81 0.787296 0.393648 0.919261i \(-0.371213\pi\)
0.393648 + 0.919261i \(0.371213\pi\)
\(542\) −1972.04 −0.156285
\(543\) 25608.0 2.02384
\(544\) 2391.63 0.188493
\(545\) −6301.05 −0.495243
\(546\) 18668.8 1.46328
\(547\) 16399.6 1.28189 0.640947 0.767585i \(-0.278542\pi\)
0.640947 + 0.767585i \(0.278542\pi\)
\(548\) −12402.4 −0.966798
\(549\) −11562.2 −0.898836
\(550\) −257.990 −0.0200013
\(551\) −16410.4 −1.26880
\(552\) −15984.2 −1.23248
\(553\) −24916.1 −1.91598
\(554\) −38584.8 −2.95905
\(555\) 32551.2 2.48959
\(556\) −29212.0 −2.22818
\(557\) 22044.3 1.67692 0.838461 0.544962i \(-0.183456\pi\)
0.838461 + 0.544962i \(0.183456\pi\)
\(558\) −1246.51 −0.0945681
\(559\) 1489.06 0.112666
\(560\) −5121.22 −0.386448
\(561\) −420.793 −0.0316683
\(562\) 15517.6 1.16472
\(563\) 12048.8 0.901947 0.450973 0.892537i \(-0.351077\pi\)
0.450973 + 0.892537i \(0.351077\pi\)
\(564\) −2490.07 −0.185906
\(565\) −4942.04 −0.367988
\(566\) −37157.4 −2.75944
\(567\) −15604.6 −1.15579
\(568\) −14144.8 −1.04490
\(569\) −23785.4 −1.75243 −0.876217 0.481916i \(-0.839941\pi\)
−0.876217 + 0.481916i \(0.839941\pi\)
\(570\) 24358.4 1.78993
\(571\) −10878.3 −0.797271 −0.398635 0.917110i \(-0.630516\pi\)
−0.398635 + 0.917110i \(0.630516\pi\)
\(572\) 899.041 0.0657182
\(573\) −10212.1 −0.744531
\(574\) 23729.7 1.72554
\(575\) 1311.62 0.0951274
\(576\) −24623.1 −1.78119
\(577\) 6315.86 0.455689 0.227845 0.973698i \(-0.426832\pi\)
0.227845 + 0.973698i \(0.426832\pi\)
\(578\) 1350.00 0.0971500
\(579\) 1735.56 0.124572
\(580\) 47133.7 3.37434
\(581\) −36944.1 −2.63804
\(582\) 24424.7 1.73958
\(583\) −338.459 −0.0240438
\(584\) 9482.69 0.671912
\(585\) 7459.58 0.527206
\(586\) −5474.72 −0.385936
\(587\) 18192.1 1.27916 0.639581 0.768724i \(-0.279108\pi\)
0.639581 + 0.768724i \(0.279108\pi\)
\(588\) −35787.7 −2.50996
\(589\) −490.207 −0.0342931
\(590\) −13882.0 −0.968663
\(591\) −6222.63 −0.433104
\(592\) 5889.03 0.408848
\(593\) −9828.72 −0.680636 −0.340318 0.940310i \(-0.610535\pi\)
−0.340318 + 0.940310i \(0.610535\pi\)
\(594\) 487.559 0.0336781
\(595\) 5292.25 0.364640
\(596\) 35668.5 2.45140
\(597\) −14244.4 −0.976524
\(598\) −7216.40 −0.493479
\(599\) 4662.57 0.318043 0.159021 0.987275i \(-0.449166\pi\)
0.159021 + 0.987275i \(0.449166\pi\)
\(600\) −3532.01 −0.240323
\(601\) 21658.6 1.47000 0.735001 0.678066i \(-0.237182\pi\)
0.735001 + 0.678066i \(0.237182\pi\)
\(602\) −9061.76 −0.613504
\(603\) 29332.8 1.98097
\(604\) 18558.3 1.25021
\(605\) 15736.6 1.05750
\(606\) −30821.5 −2.06607
\(607\) 25764.7 1.72283 0.861415 0.507902i \(-0.169579\pi\)
0.861415 + 0.507902i \(0.169579\pi\)
\(608\) −8067.76 −0.538143
\(609\) 57035.6 3.79507
\(610\) 20619.1 1.36860
\(611\) −473.475 −0.0313498
\(612\) −7334.54 −0.484446
\(613\) 16018.1 1.05541 0.527705 0.849428i \(-0.323053\pi\)
0.527705 + 0.849428i \(0.323053\pi\)
\(614\) 4044.23 0.265817
\(615\) 17682.8 1.15941
\(616\) −2304.28 −0.150718
\(617\) 22250.3 1.45180 0.725902 0.687798i \(-0.241422\pi\)
0.725902 + 0.687798i \(0.241422\pi\)
\(618\) −67038.9 −4.36360
\(619\) −3765.95 −0.244534 −0.122267 0.992497i \(-0.539016\pi\)
−0.122267 + 0.992497i \(0.539016\pi\)
\(620\) 1407.96 0.0912018
\(621\) −2478.74 −0.160175
\(622\) 32674.9 2.10634
\(623\) −12698.8 −0.816642
\(624\) 2516.82 0.161464
\(625\) −17463.2 −1.11765
\(626\) 16080.1 1.02666
\(627\) 1419.47 0.0904120
\(628\) −34494.5 −2.19185
\(629\) −6085.70 −0.385775
\(630\) −45395.7 −2.87080
\(631\) −20806.5 −1.31267 −0.656334 0.754470i \(-0.727894\pi\)
−0.656334 + 0.754470i \(0.727894\pi\)
\(632\) −25935.7 −1.63239
\(633\) 8414.96 0.528380
\(634\) 9651.60 0.604596
\(635\) −7103.88 −0.443951
\(636\) −11002.0 −0.685937
\(637\) −6804.85 −0.423262
\(638\) 4336.56 0.269100
\(639\) −16238.8 −1.00532
\(640\) 30498.4 1.88368
\(641\) 2439.58 0.150324 0.0751620 0.997171i \(-0.476053\pi\)
0.0751620 + 0.997171i \(0.476053\pi\)
\(642\) 1169.58 0.0719000
\(643\) −19320.1 −1.18493 −0.592466 0.805595i \(-0.701846\pi\)
−0.592466 + 0.805595i \(0.701846\pi\)
\(644\) 27815.4 1.70199
\(645\) −6752.60 −0.412222
\(646\) −4554.00 −0.277360
\(647\) −14067.1 −0.854766 −0.427383 0.904071i \(-0.640564\pi\)
−0.427383 + 0.904071i \(0.640564\pi\)
\(648\) −16243.2 −0.984712
\(649\) −808.963 −0.0489285
\(650\) −1594.60 −0.0962238
\(651\) 1703.75 0.102573
\(652\) 27110.9 1.62844
\(653\) 15893.7 0.952478 0.476239 0.879316i \(-0.342000\pi\)
0.476239 + 0.879316i \(0.342000\pi\)
\(654\) −18844.8 −1.12674
\(655\) −1451.77 −0.0866033
\(656\) 3199.11 0.190403
\(657\) 10886.5 0.646459
\(658\) 2881.36 0.170710
\(659\) −9653.54 −0.570635 −0.285318 0.958433i \(-0.592099\pi\)
−0.285318 + 0.958433i \(0.592099\pi\)
\(660\) −4076.98 −0.240449
\(661\) 5389.06 0.317111 0.158555 0.987350i \(-0.449316\pi\)
0.158555 + 0.987350i \(0.449316\pi\)
\(662\) 42169.7 2.47579
\(663\) −2600.87 −0.152352
\(664\) −38456.0 −2.24757
\(665\) −17852.5 −1.04104
\(666\) 52201.7 3.03720
\(667\) −22047.0 −1.27986
\(668\) 30119.1 1.74453
\(669\) 4340.30 0.250831
\(670\) −52309.9 −3.01628
\(671\) 1201.57 0.0691297
\(672\) 28040.1 1.60963
\(673\) −3032.18 −0.173673 −0.0868366 0.996223i \(-0.527676\pi\)
−0.0868366 + 0.996223i \(0.527676\pi\)
\(674\) 954.386 0.0545424
\(675\) −547.726 −0.0312326
\(676\) −24807.7 −1.41145
\(677\) −22029.2 −1.25059 −0.625295 0.780388i \(-0.715021\pi\)
−0.625295 + 0.780388i \(0.715021\pi\)
\(678\) −14780.4 −0.837222
\(679\) −17901.1 −1.01175
\(680\) 5508.83 0.310667
\(681\) −16076.3 −0.904618
\(682\) 129.540 0.00727326
\(683\) −9040.72 −0.506491 −0.253246 0.967402i \(-0.581498\pi\)
−0.253246 + 0.967402i \(0.581498\pi\)
\(684\) 24741.8 1.38308
\(685\) 10694.3 0.596506
\(686\) −443.023 −0.0246570
\(687\) −33085.9 −1.83742
\(688\) −1221.65 −0.0676964
\(689\) −2091.97 −0.115672
\(690\) 32725.0 1.80553
\(691\) −22863.5 −1.25871 −0.629355 0.777118i \(-0.716681\pi\)
−0.629355 + 0.777118i \(0.716681\pi\)
\(692\) 43003.1 2.36233
\(693\) −2645.41 −0.145008
\(694\) 668.288 0.0365531
\(695\) 25188.7 1.37477
\(696\) 59369.7 3.23334
\(697\) −3305.94 −0.179658
\(698\) −18677.8 −1.01284
\(699\) 34467.6 1.86507
\(700\) 6146.34 0.331871
\(701\) 1753.00 0.0944507 0.0472253 0.998884i \(-0.484962\pi\)
0.0472253 + 0.998884i \(0.484962\pi\)
\(702\) 3013.54 0.162021
\(703\) 20529.1 1.10138
\(704\) 2558.90 0.136992
\(705\) 2147.12 0.114702
\(706\) −27138.2 −1.44668
\(707\) 22589.3 1.20164
\(708\) −26296.2 −1.39587
\(709\) 11547.0 0.611645 0.305823 0.952089i \(-0.401069\pi\)
0.305823 + 0.952089i \(0.401069\pi\)
\(710\) 28959.2 1.53073
\(711\) −29775.3 −1.57055
\(712\) −13218.5 −0.695765
\(713\) −658.582 −0.0345920
\(714\) 15827.7 0.829606
\(715\) −775.218 −0.0405476
\(716\) 11196.4 0.584399
\(717\) −40445.6 −2.10665
\(718\) −22867.7 −1.18860
\(719\) −10289.8 −0.533720 −0.266860 0.963735i \(-0.585986\pi\)
−0.266860 + 0.963735i \(0.585986\pi\)
\(720\) −6119.99 −0.316776
\(721\) 49133.4 2.53790
\(722\) −16678.2 −0.859695
\(723\) 10444.0 0.537231
\(724\) −46386.2 −2.38112
\(725\) −4871.72 −0.249560
\(726\) 47064.2 2.40595
\(727\) 2950.10 0.150499 0.0752497 0.997165i \(-0.476025\pi\)
0.0752497 + 0.997165i \(0.476025\pi\)
\(728\) −14242.5 −0.725083
\(729\) −25275.9 −1.28415
\(730\) −19414.2 −0.984320
\(731\) 1262.45 0.0638762
\(732\) 39058.3 1.97218
\(733\) 24348.2 1.22691 0.613453 0.789731i \(-0.289780\pi\)
0.613453 + 0.789731i \(0.289780\pi\)
\(734\) 2467.15 0.124065
\(735\) 30858.7 1.54863
\(736\) −10838.8 −0.542833
\(737\) −3048.33 −0.152357
\(738\) 28357.6 1.41444
\(739\) −29233.5 −1.45517 −0.727585 0.686017i \(-0.759358\pi\)
−0.727585 + 0.686017i \(0.759358\pi\)
\(740\) −58963.1 −2.92909
\(741\) 8773.59 0.434961
\(742\) 12730.8 0.629868
\(743\) 15340.6 0.757457 0.378729 0.925508i \(-0.376361\pi\)
0.378729 + 0.925508i \(0.376361\pi\)
\(744\) 1773.47 0.0873908
\(745\) −30755.9 −1.51250
\(746\) −47242.9 −2.31861
\(747\) −44149.2 −2.16243
\(748\) 762.224 0.0372589
\(749\) −857.197 −0.0418175
\(750\) −45863.5 −2.23293
\(751\) 39862.6 1.93689 0.968446 0.249223i \(-0.0801752\pi\)
0.968446 + 0.249223i \(0.0801752\pi\)
\(752\) 388.448 0.0188368
\(753\) 42328.3 2.04851
\(754\) 26803.7 1.29461
\(755\) −16002.3 −0.771369
\(756\) −11615.6 −0.558802
\(757\) 26375.1 1.26634 0.633169 0.774013i \(-0.281754\pi\)
0.633169 + 0.774013i \(0.281754\pi\)
\(758\) 3407.17 0.163264
\(759\) 1907.03 0.0912000
\(760\) −18583.1 −0.886946
\(761\) 7848.63 0.373867 0.186933 0.982373i \(-0.440145\pi\)
0.186933 + 0.982373i \(0.440145\pi\)
\(762\) −21245.9 −1.01005
\(763\) 13811.5 0.655322
\(764\) 18498.1 0.875967
\(765\) 6324.37 0.298899
\(766\) −7511.78 −0.354323
\(767\) −5000.10 −0.235389
\(768\) 43065.8 2.02344
\(769\) 31818.9 1.49209 0.746046 0.665895i \(-0.231950\pi\)
0.746046 + 0.665895i \(0.231950\pi\)
\(770\) 4717.63 0.220794
\(771\) 1479.83 0.0691242
\(772\) −3143.78 −0.146564
\(773\) −29559.8 −1.37541 −0.687706 0.725990i \(-0.741382\pi\)
−0.687706 + 0.725990i \(0.741382\pi\)
\(774\) −10829.0 −0.502896
\(775\) −145.527 −0.00674512
\(776\) −18633.6 −0.861996
\(777\) −71350.2 −3.29430
\(778\) 45891.2 2.11475
\(779\) 11152.0 0.512917
\(780\) −25199.3 −1.15677
\(781\) 1687.58 0.0773193
\(782\) −6118.19 −0.279778
\(783\) 9206.75 0.420208
\(784\) 5582.84 0.254320
\(785\) 29743.6 1.35235
\(786\) −4341.86 −0.197034
\(787\) −28038.7 −1.26998 −0.634989 0.772521i \(-0.718995\pi\)
−0.634989 + 0.772521i \(0.718995\pi\)
\(788\) 11271.6 0.509563
\(789\) 10267.1 0.463269
\(790\) 53099.2 2.39137
\(791\) 10832.6 0.486934
\(792\) −2753.67 −0.123545
\(793\) 7426.75 0.332574
\(794\) 13438.7 0.600659
\(795\) 9486.68 0.423217
\(796\) 25802.3 1.14892
\(797\) 5320.45 0.236462 0.118231 0.992986i \(-0.462278\pi\)
0.118231 + 0.992986i \(0.462278\pi\)
\(798\) −53392.2 −2.36850
\(799\) −401.421 −0.0177738
\(800\) −2395.05 −0.105847
\(801\) −15175.4 −0.669409
\(802\) −30437.7 −1.34014
\(803\) −1131.35 −0.0497194
\(804\) −99089.4 −4.34653
\(805\) −23984.4 −1.05011
\(806\) 800.673 0.0349907
\(807\) 23523.6 1.02611
\(808\) 23513.8 1.02378
\(809\) 30934.0 1.34435 0.672177 0.740390i \(-0.265359\pi\)
0.672177 + 0.740390i \(0.265359\pi\)
\(810\) 33255.3 1.44256
\(811\) −40364.5 −1.74771 −0.873854 0.486189i \(-0.838387\pi\)
−0.873854 + 0.486189i \(0.838387\pi\)
\(812\) −103314. −4.46504
\(813\) 3221.10 0.138953
\(814\) −5424.94 −0.233592
\(815\) −23376.9 −1.00473
\(816\) 2133.81 0.0915419
\(817\) −4258.66 −0.182364
\(818\) −41434.8 −1.77107
\(819\) −16350.9 −0.697616
\(820\) −32030.6 −1.36409
\(821\) 19799.7 0.841672 0.420836 0.907137i \(-0.361737\pi\)
0.420836 + 0.907137i \(0.361737\pi\)
\(822\) 31983.8 1.35713
\(823\) 18756.4 0.794419 0.397210 0.917728i \(-0.369979\pi\)
0.397210 + 0.917728i \(0.369979\pi\)
\(824\) 51144.1 2.16225
\(825\) 421.395 0.0177832
\(826\) 30428.4 1.28177
\(827\) 20958.0 0.881234 0.440617 0.897695i \(-0.354760\pi\)
0.440617 + 0.897695i \(0.354760\pi\)
\(828\) 33240.0 1.39513
\(829\) −31320.3 −1.31218 −0.656091 0.754682i \(-0.727791\pi\)
−0.656091 + 0.754682i \(0.727791\pi\)
\(830\) 78732.4 3.29258
\(831\) 63023.7 2.63089
\(832\) 15816.2 0.659049
\(833\) −5769.28 −0.239968
\(834\) 75333.0 3.12778
\(835\) −25970.8 −1.07636
\(836\) −2571.23 −0.106373
\(837\) 275.021 0.0113574
\(838\) −4715.82 −0.194398
\(839\) −30290.6 −1.24642 −0.623212 0.782053i \(-0.714173\pi\)
−0.623212 + 0.782053i \(0.714173\pi\)
\(840\) 64586.8 2.65292
\(841\) 57499.9 2.35762
\(842\) −15198.5 −0.622060
\(843\) −25346.1 −1.03555
\(844\) −15242.8 −0.621659
\(845\) 21391.0 0.870855
\(846\) 3443.29 0.139933
\(847\) −34493.7 −1.39931
\(848\) 1716.29 0.0695021
\(849\) 60692.2 2.45342
\(850\) −1351.93 −0.0545540
\(851\) 27580.3 1.11098
\(852\) 54856.6 2.20582
\(853\) −21111.8 −0.847425 −0.423712 0.905797i \(-0.639273\pi\)
−0.423712 + 0.905797i \(0.639273\pi\)
\(854\) −45195.9 −1.81097
\(855\) −21334.2 −0.853348
\(856\) −892.277 −0.0356278
\(857\) −39983.0 −1.59369 −0.796845 0.604184i \(-0.793499\pi\)
−0.796845 + 0.604184i \(0.793499\pi\)
\(858\) −2318.48 −0.0922512
\(859\) −39503.3 −1.56907 −0.784537 0.620082i \(-0.787099\pi\)
−0.784537 + 0.620082i \(0.787099\pi\)
\(860\) 12231.6 0.484995
\(861\) −38759.6 −1.53418
\(862\) −10989.2 −0.434217
\(863\) 26019.9 1.02634 0.513168 0.858288i \(-0.328472\pi\)
0.513168 + 0.858288i \(0.328472\pi\)
\(864\) 4526.26 0.178225
\(865\) −37080.4 −1.45754
\(866\) −27376.1 −1.07422
\(867\) −2205.07 −0.0863760
\(868\) −3086.17 −0.120681
\(869\) 3094.33 0.120791
\(870\) −121550. −4.73669
\(871\) −18841.4 −0.732968
\(872\) 14376.7 0.558323
\(873\) −21392.2 −0.829343
\(874\) 20638.7 0.798757
\(875\) 33613.8 1.29869
\(876\) −36775.9 −1.41843
\(877\) 15038.3 0.579027 0.289514 0.957174i \(-0.406506\pi\)
0.289514 + 0.957174i \(0.406506\pi\)
\(878\) 13519.5 0.519660
\(879\) 8942.30 0.343136
\(880\) 636.004 0.0243633
\(881\) −18334.3 −0.701133 −0.350567 0.936538i \(-0.614011\pi\)
−0.350567 + 0.936538i \(0.614011\pi\)
\(882\) 49487.5 1.88927
\(883\) 26659.5 1.01604 0.508020 0.861345i \(-0.330378\pi\)
0.508020 + 0.861345i \(0.330378\pi\)
\(884\) 4711.21 0.179248
\(885\) 22674.5 0.861237
\(886\) −38570.1 −1.46251
\(887\) 11473.7 0.434327 0.217163 0.976135i \(-0.430320\pi\)
0.217163 + 0.976135i \(0.430320\pi\)
\(888\) −74270.1 −2.80669
\(889\) 15571.3 0.587450
\(890\) 27062.7 1.01926
\(891\) 1937.94 0.0728656
\(892\) −7862.01 −0.295111
\(893\) 1354.12 0.0507436
\(894\) −91983.0 −3.44113
\(895\) −9654.36 −0.360569
\(896\) −66850.7 −2.49255
\(897\) 11787.1 0.438752
\(898\) 72344.6 2.68838
\(899\) 2446.16 0.0907498
\(900\) 7345.03 0.272038
\(901\) −1773.61 −0.0655799
\(902\) −2946.99 −0.108785
\(903\) 14801.3 0.545466
\(904\) 11276.0 0.414860
\(905\) 39997.5 1.46913
\(906\) −47858.8 −1.75497
\(907\) −20361.6 −0.745421 −0.372710 0.927948i \(-0.621571\pi\)
−0.372710 + 0.927948i \(0.621571\pi\)
\(908\) 29120.5 1.06432
\(909\) 26994.8 0.984995
\(910\) 29159.1 1.06221
\(911\) −19261.9 −0.700523 −0.350262 0.936652i \(-0.613907\pi\)
−0.350262 + 0.936652i \(0.613907\pi\)
\(912\) −7198.03 −0.261349
\(913\) 4588.09 0.166313
\(914\) −75000.3 −2.71421
\(915\) −33678.9 −1.21682
\(916\) 59931.7 2.16179
\(917\) 3182.18 0.114596
\(918\) 2554.93 0.0918577
\(919\) −21191.8 −0.760666 −0.380333 0.924850i \(-0.624191\pi\)
−0.380333 + 0.924850i \(0.624191\pi\)
\(920\) −24965.9 −0.894677
\(921\) −6605.76 −0.236338
\(922\) 65697.0 2.34665
\(923\) 10430.7 0.371973
\(924\) 8936.49 0.318170
\(925\) 6094.40 0.216630
\(926\) −37703.4 −1.33802
\(927\) 58715.6 2.08034
\(928\) 40258.5 1.42409
\(929\) 40815.0 1.44144 0.720719 0.693227i \(-0.243812\pi\)
0.720719 + 0.693227i \(0.243812\pi\)
\(930\) −3630.90 −0.128024
\(931\) 19461.7 0.685102
\(932\) −62434.5 −2.19432
\(933\) −53370.4 −1.87274
\(934\) 40090.9 1.40451
\(935\) −657.244 −0.0229884
\(936\) −17020.1 −0.594358
\(937\) −38439.1 −1.34018 −0.670092 0.742278i \(-0.733745\pi\)
−0.670092 + 0.742278i \(0.733745\pi\)
\(938\) 114660. 3.99124
\(939\) −26264.9 −0.912804
\(940\) −3889.28 −0.134951
\(941\) −2244.08 −0.0777415 −0.0388708 0.999244i \(-0.512376\pi\)
−0.0388708 + 0.999244i \(0.512376\pi\)
\(942\) 88955.6 3.07678
\(943\) 14982.5 0.517388
\(944\) 4102.18 0.141435
\(945\) 10015.8 0.344776
\(946\) 1125.38 0.0386778
\(947\) −42289.0 −1.45112 −0.725559 0.688160i \(-0.758419\pi\)
−0.725559 + 0.688160i \(0.758419\pi\)
\(948\) 100584. 3.44602
\(949\) −6992.76 −0.239193
\(950\) 4560.51 0.155750
\(951\) −15764.7 −0.537546
\(952\) −12075.0 −0.411085
\(953\) 37426.2 1.27214 0.636072 0.771629i \(-0.280558\pi\)
0.636072 + 0.771629i \(0.280558\pi\)
\(954\) 15213.6 0.516309
\(955\) −15950.4 −0.540464
\(956\) 73263.0 2.47855
\(957\) −7083.25 −0.239257
\(958\) −29527.0 −0.995799
\(959\) −23441.2 −0.789317
\(960\) −71723.5 −2.41132
\(961\) −29717.9 −0.997547
\(962\) −33530.8 −1.12378
\(963\) −1024.37 −0.0342782
\(964\) −18918.3 −0.632072
\(965\) 2710.80 0.0904286
\(966\) −71731.1 −2.38914
\(967\) 1088.56 0.0362003 0.0181001 0.999836i \(-0.494238\pi\)
0.0181001 + 0.999836i \(0.494238\pi\)
\(968\) −35905.4 −1.19219
\(969\) 7438.41 0.246601
\(970\) 38149.3 1.26278
\(971\) 39506.5 1.30569 0.652845 0.757491i \(-0.273575\pi\)
0.652845 + 0.757491i \(0.273575\pi\)
\(972\) 75000.6 2.47494
\(973\) −55212.1 −1.81914
\(974\) 34270.8 1.12742
\(975\) 2604.59 0.0855525
\(976\) −6093.05 −0.199830
\(977\) −43326.8 −1.41878 −0.709389 0.704817i \(-0.751029\pi\)
−0.709389 + 0.704817i \(0.751029\pi\)
\(978\) −69914.4 −2.28591
\(979\) 1577.07 0.0514845
\(980\) −55897.3 −1.82202
\(981\) 16505.1 0.537174
\(982\) 31169.3 1.01288
\(983\) 10664.1 0.346014 0.173007 0.984921i \(-0.444652\pi\)
0.173007 + 0.984921i \(0.444652\pi\)
\(984\) −40345.9 −1.30709
\(985\) −9719.22 −0.314396
\(986\) 22724.7 0.733977
\(987\) −4706.35 −0.151778
\(988\) −15892.4 −0.511747
\(989\) −5721.42 −0.183954
\(990\) 5637.69 0.180987
\(991\) 15461.4 0.495609 0.247804 0.968810i \(-0.420291\pi\)
0.247804 + 0.968810i \(0.420291\pi\)
\(992\) 1202.59 0.0384902
\(993\) −68879.2 −2.20122
\(994\) −63476.7 −2.02551
\(995\) −22248.6 −0.708871
\(996\) 149141. 4.74469
\(997\) 46061.1 1.46316 0.731579 0.681756i \(-0.238784\pi\)
0.731579 + 0.681756i \(0.238784\pi\)
\(998\) 83713.7 2.65522
\(999\) −11517.4 −0.364760
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 \(a_p\))