Properties

Label 17.4.a.a.1.1
Level 17
Weight 4
Character 17.1
Self dual Yes
Analytic conductor 1.003
Analytic rank 1
Dimension 1
CM No
Inner twists 1

Related objects

Downloads

Learn more about

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: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0\)
Character \(\chi\) = 17.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.00000 q^{2} -8.00000 q^{3} +1.00000 q^{4} +6.00000 q^{5} +24.0000 q^{6} -28.0000 q^{7} +21.0000 q^{8} +37.0000 q^{9} +O(q^{10})\) \(q-3.00000 q^{2} -8.00000 q^{3} +1.00000 q^{4} +6.00000 q^{5} +24.0000 q^{6} -28.0000 q^{7} +21.0000 q^{8} +37.0000 q^{9} -18.0000 q^{10} -24.0000 q^{11} -8.00000 q^{12} -58.0000 q^{13} +84.0000 q^{14} -48.0000 q^{15} -71.0000 q^{16} +17.0000 q^{17} -111.000 q^{18} +116.000 q^{19} +6.00000 q^{20} +224.000 q^{21} +72.0000 q^{22} -60.0000 q^{23} -168.000 q^{24} -89.0000 q^{25} +174.000 q^{26} -80.0000 q^{27} -28.0000 q^{28} +30.0000 q^{29} +144.000 q^{30} -172.000 q^{31} +45.0000 q^{32} +192.000 q^{33} -51.0000 q^{34} -168.000 q^{35} +37.0000 q^{36} -58.0000 q^{37} -348.000 q^{38} +464.000 q^{39} +126.000 q^{40} -342.000 q^{41} -672.000 q^{42} -148.000 q^{43} -24.0000 q^{44} +222.000 q^{45} +180.000 q^{46} +288.000 q^{47} +568.000 q^{48} +441.000 q^{49} +267.000 q^{50} -136.000 q^{51} -58.0000 q^{52} +318.000 q^{53} +240.000 q^{54} -144.000 q^{55} -588.000 q^{56} -928.000 q^{57} -90.0000 q^{58} +252.000 q^{59} -48.0000 q^{60} +110.000 q^{61} +516.000 q^{62} -1036.00 q^{63} +433.000 q^{64} -348.000 q^{65} -576.000 q^{66} -484.000 q^{67} +17.0000 q^{68} +480.000 q^{69} +504.000 q^{70} -708.000 q^{71} +777.000 q^{72} +362.000 q^{73} +174.000 q^{74} +712.000 q^{75} +116.000 q^{76} +672.000 q^{77} -1392.00 q^{78} -484.000 q^{79} -426.000 q^{80} -359.000 q^{81} +1026.00 q^{82} +756.000 q^{83} +224.000 q^{84} +102.000 q^{85} +444.000 q^{86} -240.000 q^{87} -504.000 q^{88} -774.000 q^{89} -666.000 q^{90} +1624.00 q^{91} -60.0000 q^{92} +1376.00 q^{93} -864.000 q^{94} +696.000 q^{95} -360.000 q^{96} -382.000 q^{97} -1323.00 q^{98} -888.000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.00000 −1.06066 −0.530330 0.847791i \(-0.677932\pi\)
−0.530330 + 0.847791i \(0.677932\pi\)
\(3\) −8.00000 −1.53960 −0.769800 0.638285i \(-0.779644\pi\)
−0.769800 + 0.638285i \(0.779644\pi\)
\(4\) 1.00000 0.125000
\(5\) 6.00000 0.536656 0.268328 0.963328i \(-0.413529\pi\)
0.268328 + 0.963328i \(0.413529\pi\)
\(6\) 24.0000 1.63299
\(7\) −28.0000 −1.51186 −0.755929 0.654654i \(-0.772814\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 21.0000 0.928078
\(9\) 37.0000 1.37037
\(10\) −18.0000 −0.569210
\(11\) −24.0000 −0.657843 −0.328921 0.944357i \(-0.606685\pi\)
−0.328921 + 0.944357i \(0.606685\pi\)
\(12\) −8.00000 −0.192450
\(13\) −58.0000 −1.23741 −0.618704 0.785624i \(-0.712342\pi\)
−0.618704 + 0.785624i \(0.712342\pi\)
\(14\) 84.0000 1.60357
\(15\) −48.0000 −0.826236
\(16\) −71.0000 −1.10938
\(17\) 17.0000 0.242536
\(18\) −111.000 −1.45350
\(19\) 116.000 1.40064 0.700322 0.713827i \(-0.253040\pi\)
0.700322 + 0.713827i \(0.253040\pi\)
\(20\) 6.00000 0.0670820
\(21\) 224.000 2.32766
\(22\) 72.0000 0.697748
\(23\) −60.0000 −0.543951 −0.271975 0.962304i \(-0.587677\pi\)
−0.271975 + 0.962304i \(0.587677\pi\)
\(24\) −168.000 −1.42887
\(25\) −89.0000 −0.712000
\(26\) 174.000 1.31247
\(27\) −80.0000 −0.570222
\(28\) −28.0000 −0.188982
\(29\) 30.0000 0.192099 0.0960493 0.995377i \(-0.469379\pi\)
0.0960493 + 0.995377i \(0.469379\pi\)
\(30\) 144.000 0.876356
\(31\) −172.000 −0.996520 −0.498260 0.867028i \(-0.666027\pi\)
−0.498260 + 0.867028i \(0.666027\pi\)
\(32\) 45.0000 0.248592
\(33\) 192.000 1.01282
\(34\) −51.0000 −0.257248
\(35\) −168.000 −0.811348
\(36\) 37.0000 0.171296
\(37\) −58.0000 −0.257707 −0.128853 0.991664i \(-0.541130\pi\)
−0.128853 + 0.991664i \(0.541130\pi\)
\(38\) −348.000 −1.48561
\(39\) 464.000 1.90511
\(40\) 126.000 0.498059
\(41\) −342.000 −1.30272 −0.651359 0.758770i \(-0.725801\pi\)
−0.651359 + 0.758770i \(0.725801\pi\)
\(42\) −672.000 −2.46885
\(43\) −148.000 −0.524879 −0.262439 0.964948i \(-0.584527\pi\)
−0.262439 + 0.964948i \(0.584527\pi\)
\(44\) −24.0000 −0.0822304
\(45\) 222.000 0.735418
\(46\) 180.000 0.576947
\(47\) 288.000 0.893811 0.446906 0.894581i \(-0.352526\pi\)
0.446906 + 0.894581i \(0.352526\pi\)
\(48\) 568.000 1.70799
\(49\) 441.000 1.28571
\(50\) 267.000 0.755190
\(51\) −136.000 −0.373408
\(52\) −58.0000 −0.154676
\(53\) 318.000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 240.000 0.604812
\(55\) −144.000 −0.353036
\(56\) −588.000 −1.40312
\(57\) −928.000 −2.15643
\(58\) −90.0000 −0.203751
\(59\) 252.000 0.556061 0.278031 0.960572i \(-0.410318\pi\)
0.278031 + 0.960572i \(0.410318\pi\)
\(60\) −48.0000 −0.103280
\(61\) 110.000 0.230886 0.115443 0.993314i \(-0.463171\pi\)
0.115443 + 0.993314i \(0.463171\pi\)
\(62\) 516.000 1.05697
\(63\) −1036.00 −2.07181
\(64\) 433.000 0.845703
\(65\) −348.000 −0.664063
\(66\) −576.000 −1.07425
\(67\) −484.000 −0.882537 −0.441269 0.897375i \(-0.645471\pi\)
−0.441269 + 0.897375i \(0.645471\pi\)
\(68\) 17.0000 0.0303170
\(69\) 480.000 0.837467
\(70\) 504.000 0.860565
\(71\) −708.000 −1.18344 −0.591719 0.806144i \(-0.701551\pi\)
−0.591719 + 0.806144i \(0.701551\pi\)
\(72\) 777.000 1.27181
\(73\) 362.000 0.580396 0.290198 0.956967i \(-0.406279\pi\)
0.290198 + 0.956967i \(0.406279\pi\)
\(74\) 174.000 0.273339
\(75\) 712.000 1.09620
\(76\) 116.000 0.175080
\(77\) 672.000 0.994565
\(78\) −1392.00 −2.02068
\(79\) −484.000 −0.689294 −0.344647 0.938732i \(-0.612001\pi\)
−0.344647 + 0.938732i \(0.612001\pi\)
\(80\) −426.000 −0.595353
\(81\) −359.000 −0.492455
\(82\) 1026.00 1.38174
\(83\) 756.000 0.999780 0.499890 0.866089i \(-0.333374\pi\)
0.499890 + 0.866089i \(0.333374\pi\)
\(84\) 224.000 0.290957
\(85\) 102.000 0.130158
\(86\) 444.000 0.556718
\(87\) −240.000 −0.295755
\(88\) −504.000 −0.610529
\(89\) −774.000 −0.921841 −0.460920 0.887441i \(-0.652481\pi\)
−0.460920 + 0.887441i \(0.652481\pi\)
\(90\) −666.000 −0.780028
\(91\) 1624.00 1.87079
\(92\) −60.0000 −0.0679938
\(93\) 1376.00 1.53424
\(94\) −864.000 −0.948030
\(95\) 696.000 0.751664
\(96\) −360.000 −0.382733
\(97\) −382.000 −0.399858 −0.199929 0.979810i \(-0.564071\pi\)
−0.199929 + 0.979810i \(0.564071\pi\)
\(98\) −1323.00 −1.36371
\(99\) −888.000 −0.901488
\(100\) −89.0000 −0.0890000
\(101\) −210.000 −0.206889 −0.103444 0.994635i \(-0.532986\pi\)
−0.103444 + 0.994635i \(0.532986\pi\)
\(102\) 408.000 0.396059
\(103\) −232.000 −0.221938 −0.110969 0.993824i \(-0.535395\pi\)
−0.110969 + 0.993824i \(0.535395\pi\)
\(104\) −1218.00 −1.14841
\(105\) 1344.00 1.24915
\(106\) −954.000 −0.874157
\(107\) 432.000 0.390309 0.195154 0.980773i \(-0.437479\pi\)
0.195154 + 0.980773i \(0.437479\pi\)
\(108\) −80.0000 −0.0712778
\(109\) −1186.00 −1.04219 −0.521093 0.853500i \(-0.674475\pi\)
−0.521093 + 0.853500i \(0.674475\pi\)
\(110\) 432.000 0.374451
\(111\) 464.000 0.396765
\(112\) 1988.00 1.67722
\(113\) −366.000 −0.304694 −0.152347 0.988327i \(-0.548683\pi\)
−0.152347 + 0.988327i \(0.548683\pi\)
\(114\) 2784.00 2.28724
\(115\) −360.000 −0.291915
\(116\) 30.0000 0.0240123
\(117\) −2146.00 −1.69571
\(118\) −756.000 −0.589792
\(119\) −476.000 −0.366679
\(120\) −1008.00 −0.766812
\(121\) −755.000 −0.567243
\(122\) −330.000 −0.244892
\(123\) 2736.00 2.00567
\(124\) −172.000 −0.124565
\(125\) −1284.00 −0.918756
\(126\) 3108.00 2.19748
\(127\) −472.000 −0.329789 −0.164895 0.986311i \(-0.552728\pi\)
−0.164895 + 0.986311i \(0.552728\pi\)
\(128\) −1659.00 −1.14560
\(129\) 1184.00 0.808104
\(130\) 1044.00 0.704345
\(131\) 2760.00 1.84078 0.920391 0.391000i \(-0.127871\pi\)
0.920391 + 0.391000i \(0.127871\pi\)
\(132\) 192.000 0.126602
\(133\) −3248.00 −2.11757
\(134\) 1452.00 0.936072
\(135\) −480.000 −0.306013
\(136\) 357.000 0.225092
\(137\) 1098.00 0.684733 0.342367 0.939566i \(-0.388771\pi\)
0.342367 + 0.939566i \(0.388771\pi\)
\(138\) −1440.00 −0.888268
\(139\) 2528.00 1.54261 0.771303 0.636468i \(-0.219605\pi\)
0.771303 + 0.636468i \(0.219605\pi\)
\(140\) −168.000 −0.101419
\(141\) −2304.00 −1.37611
\(142\) 2124.00 1.25523
\(143\) 1392.00 0.814020
\(144\) −2627.00 −1.52025
\(145\) 180.000 0.103091
\(146\) −1086.00 −0.615603
\(147\) −3528.00 −1.97949
\(148\) −58.0000 −0.0322133
\(149\) 1614.00 0.887410 0.443705 0.896173i \(-0.353664\pi\)
0.443705 + 0.896173i \(0.353664\pi\)
\(150\) −2136.00 −1.16269
\(151\) −3328.00 −1.79357 −0.896784 0.442468i \(-0.854103\pi\)
−0.896784 + 0.442468i \(0.854103\pi\)
\(152\) 2436.00 1.29991
\(153\) 629.000 0.332364
\(154\) −2016.00 −1.05490
\(155\) −1032.00 −0.534789
\(156\) 464.000 0.238139
\(157\) −2458.00 −1.24949 −0.624744 0.780829i \(-0.714797\pi\)
−0.624744 + 0.780829i \(0.714797\pi\)
\(158\) 1452.00 0.731107
\(159\) −2544.00 −1.26888
\(160\) 270.000 0.133409
\(161\) 1680.00 0.822376
\(162\) 1077.00 0.522328
\(163\) 272.000 0.130704 0.0653518 0.997862i \(-0.479183\pi\)
0.0653518 + 0.997862i \(0.479183\pi\)
\(164\) −342.000 −0.162840
\(165\) 1152.00 0.543534
\(166\) −2268.00 −1.06043
\(167\) 3516.00 1.62920 0.814600 0.580024i \(-0.196957\pi\)
0.814600 + 0.580024i \(0.196957\pi\)
\(168\) 4704.00 2.16025
\(169\) 1167.00 0.531179
\(170\) −306.000 −0.138054
\(171\) 4292.00 1.91940
\(172\) −148.000 −0.0656099
\(173\) −1842.00 −0.809507 −0.404753 0.914426i \(-0.632643\pi\)
−0.404753 + 0.914426i \(0.632643\pi\)
\(174\) 720.000 0.313696
\(175\) 2492.00 1.07644
\(176\) 1704.00 0.729795
\(177\) −2016.00 −0.856112
\(178\) 2322.00 0.977760
\(179\) −3516.00 −1.46815 −0.734073 0.679070i \(-0.762383\pi\)
−0.734073 + 0.679070i \(0.762383\pi\)
\(180\) 222.000 0.0919272
\(181\) 3398.00 1.39542 0.697711 0.716379i \(-0.254202\pi\)
0.697711 + 0.716379i \(0.254202\pi\)
\(182\) −4872.00 −1.98427
\(183\) −880.000 −0.355473
\(184\) −1260.00 −0.504828
\(185\) −348.000 −0.138300
\(186\) −4128.00 −1.62731
\(187\) −408.000 −0.159550
\(188\) 288.000 0.111726
\(189\) 2240.00 0.862095
\(190\) −2088.00 −0.797260
\(191\) −2640.00 −1.00012 −0.500062 0.865990i \(-0.666689\pi\)
−0.500062 + 0.865990i \(0.666689\pi\)
\(192\) −3464.00 −1.30205
\(193\) 2882.00 1.07488 0.537438 0.843304i \(-0.319392\pi\)
0.537438 + 0.843304i \(0.319392\pi\)
\(194\) 1146.00 0.424113
\(195\) 2784.00 1.02239
\(196\) 441.000 0.160714
\(197\) −42.0000 −0.0151897 −0.00759486 0.999971i \(-0.502418\pi\)
−0.00759486 + 0.999971i \(0.502418\pi\)
\(198\) 2664.00 0.956173
\(199\) −3220.00 −1.14703 −0.573517 0.819194i \(-0.694421\pi\)
−0.573517 + 0.819194i \(0.694421\pi\)
\(200\) −1869.00 −0.660791
\(201\) 3872.00 1.35876
\(202\) 630.000 0.219439
\(203\) −840.000 −0.290426
\(204\) −136.000 −0.0466760
\(205\) −2052.00 −0.699112
\(206\) 696.000 0.235401
\(207\) −2220.00 −0.745414
\(208\) 4118.00 1.37275
\(209\) −2784.00 −0.921403
\(210\) −4032.00 −1.32493
\(211\) −2080.00 −0.678640 −0.339320 0.940671i \(-0.610197\pi\)
−0.339320 + 0.940671i \(0.610197\pi\)
\(212\) 318.000 0.103020
\(213\) 5664.00 1.82202
\(214\) −1296.00 −0.413985
\(215\) −888.000 −0.281680
\(216\) −1680.00 −0.529211
\(217\) 4816.00 1.50660
\(218\) 3558.00 1.10540
\(219\) −2896.00 −0.893578
\(220\) −144.000 −0.0441294
\(221\) −986.000 −0.300116
\(222\) −1392.00 −0.420833
\(223\) 4664.00 1.40056 0.700279 0.713869i \(-0.253059\pi\)
0.700279 + 0.713869i \(0.253059\pi\)
\(224\) −1260.00 −0.375836
\(225\) −3293.00 −0.975704
\(226\) 1098.00 0.323176
\(227\) −1440.00 −0.421040 −0.210520 0.977590i \(-0.567516\pi\)
−0.210520 + 0.977590i \(0.567516\pi\)
\(228\) −928.000 −0.269554
\(229\) −1186.00 −0.342241 −0.171120 0.985250i \(-0.554739\pi\)
−0.171120 + 0.985250i \(0.554739\pi\)
\(230\) 1080.00 0.309622
\(231\) −5376.00 −1.53123
\(232\) 630.000 0.178282
\(233\) −5334.00 −1.49975 −0.749875 0.661579i \(-0.769887\pi\)
−0.749875 + 0.661579i \(0.769887\pi\)
\(234\) 6438.00 1.79857
\(235\) 1728.00 0.479669
\(236\) 252.000 0.0695076
\(237\) 3872.00 1.06124
\(238\) 1428.00 0.388922
\(239\) 5328.00 1.44201 0.721003 0.692931i \(-0.243681\pi\)
0.721003 + 0.692931i \(0.243681\pi\)
\(240\) 3408.00 0.916606
\(241\) 5618.00 1.50161 0.750803 0.660526i \(-0.229667\pi\)
0.750803 + 0.660526i \(0.229667\pi\)
\(242\) 2265.00 0.601652
\(243\) 5032.00 1.32841
\(244\) 110.000 0.0288608
\(245\) 2646.00 0.689987
\(246\) −8208.00 −2.12733
\(247\) −6728.00 −1.73317
\(248\) −3612.00 −0.924848
\(249\) −6048.00 −1.53926
\(250\) 3852.00 0.974487
\(251\) −2028.00 −0.509985 −0.254992 0.966943i \(-0.582073\pi\)
−0.254992 + 0.966943i \(0.582073\pi\)
\(252\) −1036.00 −0.258976
\(253\) 1440.00 0.357834
\(254\) 1416.00 0.349794
\(255\) −816.000 −0.200392
\(256\) 1513.00 0.369385
\(257\) −1902.00 −0.461648 −0.230824 0.972996i \(-0.574142\pi\)
−0.230824 + 0.972996i \(0.574142\pi\)
\(258\) −3552.00 −0.857123
\(259\) 1624.00 0.389616
\(260\) −348.000 −0.0830079
\(261\) 1110.00 0.263246
\(262\) −8280.00 −1.95244
\(263\) −5472.00 −1.28296 −0.641479 0.767141i \(-0.721679\pi\)
−0.641479 + 0.767141i \(0.721679\pi\)
\(264\) 4032.00 0.939971
\(265\) 1908.00 0.442292
\(266\) 9744.00 2.24603
\(267\) 6192.00 1.41927
\(268\) −484.000 −0.110317
\(269\) −3570.00 −0.809170 −0.404585 0.914500i \(-0.632584\pi\)
−0.404585 + 0.914500i \(0.632584\pi\)
\(270\) 1440.00 0.324576
\(271\) 272.000 0.0609698 0.0304849 0.999535i \(-0.490295\pi\)
0.0304849 + 0.999535i \(0.490295\pi\)
\(272\) −1207.00 −0.269063
\(273\) −12992.0 −2.88026
\(274\) −3294.00 −0.726269
\(275\) 2136.00 0.468384
\(276\) 480.000 0.104683
\(277\) 3830.00 0.830767 0.415383 0.909646i \(-0.363647\pi\)
0.415383 + 0.909646i \(0.363647\pi\)
\(278\) −7584.00 −1.63618
\(279\) −6364.00 −1.36560
\(280\) −3528.00 −0.752994
\(281\) 8874.00 1.88391 0.941955 0.335740i \(-0.108986\pi\)
0.941955 + 0.335740i \(0.108986\pi\)
\(282\) 6912.00 1.45959
\(283\) −2632.00 −0.552849 −0.276424 0.961036i \(-0.589150\pi\)
−0.276424 + 0.961036i \(0.589150\pi\)
\(284\) −708.000 −0.147930
\(285\) −5568.00 −1.15726
\(286\) −4176.00 −0.863399
\(287\) 9576.00 1.96952
\(288\) 1665.00 0.340663
\(289\) 289.000 0.0588235
\(290\) −540.000 −0.109344
\(291\) 3056.00 0.615622
\(292\) 362.000 0.0725495
\(293\) −6402.00 −1.27648 −0.638240 0.769837i \(-0.720337\pi\)
−0.638240 + 0.769837i \(0.720337\pi\)
\(294\) 10584.0 2.09956
\(295\) 1512.00 0.298414
\(296\) −1218.00 −0.239172
\(297\) 1920.00 0.375117
\(298\) −4842.00 −0.941240
\(299\) 3480.00 0.673089
\(300\) 712.000 0.137024
\(301\) 4144.00 0.793542
\(302\) 9984.00 1.90237
\(303\) 1680.00 0.318526
\(304\) −8236.00 −1.55384
\(305\) 660.000 0.123907
\(306\) −1887.00 −0.352525
\(307\) −8980.00 −1.66943 −0.834716 0.550681i \(-0.814368\pi\)
−0.834716 + 0.550681i \(0.814368\pi\)
\(308\) 672.000 0.124321
\(309\) 1856.00 0.341696
\(310\) 3096.00 0.567229
\(311\) −3972.00 −0.724217 −0.362108 0.932136i \(-0.617943\pi\)
−0.362108 + 0.932136i \(0.617943\pi\)
\(312\) 9744.00 1.76809
\(313\) 4730.00 0.854171 0.427085 0.904211i \(-0.359540\pi\)
0.427085 + 0.904211i \(0.359540\pi\)
\(314\) 7374.00 1.32528
\(315\) −6216.00 −1.11185
\(316\) −484.000 −0.0861618
\(317\) −2898.00 −0.513463 −0.256732 0.966483i \(-0.582646\pi\)
−0.256732 + 0.966483i \(0.582646\pi\)
\(318\) 7632.00 1.34585
\(319\) −720.000 −0.126371
\(320\) 2598.00 0.453852
\(321\) −3456.00 −0.600919
\(322\) −5040.00 −0.872262
\(323\) 1972.00 0.339706
\(324\) −359.000 −0.0615569
\(325\) 5162.00 0.881035
\(326\) −816.000 −0.138632
\(327\) 9488.00 1.60455
\(328\) −7182.00 −1.20902
\(329\) −8064.00 −1.35132
\(330\) −3456.00 −0.576505
\(331\) −4564.00 −0.757886 −0.378943 0.925420i \(-0.623712\pi\)
−0.378943 + 0.925420i \(0.623712\pi\)
\(332\) 756.000 0.124973
\(333\) −2146.00 −0.353153
\(334\) −10548.0 −1.72803
\(335\) −2904.00 −0.473619
\(336\) −15904.0 −2.58225
\(337\) 722.000 0.116706 0.0583529 0.998296i \(-0.481415\pi\)
0.0583529 + 0.998296i \(0.481415\pi\)
\(338\) −3501.00 −0.563400
\(339\) 2928.00 0.469107
\(340\) 102.000 0.0162698
\(341\) 4128.00 0.655553
\(342\) −12876.0 −2.03583
\(343\) −2744.00 −0.431959
\(344\) −3108.00 −0.487128
\(345\) 2880.00 0.449432
\(346\) 5526.00 0.858612
\(347\) 5544.00 0.857687 0.428844 0.903379i \(-0.358921\pi\)
0.428844 + 0.903379i \(0.358921\pi\)
\(348\) −240.000 −0.0369694
\(349\) 11126.0 1.70648 0.853239 0.521519i \(-0.174635\pi\)
0.853239 + 0.521519i \(0.174635\pi\)
\(350\) −7476.00 −1.14174
\(351\) 4640.00 0.705598
\(352\) −1080.00 −0.163535
\(353\) 7842.00 1.18240 0.591200 0.806525i \(-0.298654\pi\)
0.591200 + 0.806525i \(0.298654\pi\)
\(354\) 6048.00 0.908044
\(355\) −4248.00 −0.635100
\(356\) −774.000 −0.115230
\(357\) 3808.00 0.564540
\(358\) 10548.0 1.55720
\(359\) 5040.00 0.740950 0.370475 0.928842i \(-0.379195\pi\)
0.370475 + 0.928842i \(0.379195\pi\)
\(360\) 4662.00 0.682525
\(361\) 6597.00 0.961802
\(362\) −10194.0 −1.48007
\(363\) 6040.00 0.873327
\(364\) 1624.00 0.233848
\(365\) 2172.00 0.311473
\(366\) 2640.00 0.377036
\(367\) −8404.00 −1.19533 −0.597664 0.801747i \(-0.703904\pi\)
−0.597664 + 0.801747i \(0.703904\pi\)
\(368\) 4260.00 0.603445
\(369\) −12654.0 −1.78521
\(370\) 1044.00 0.146689
\(371\) −8904.00 −1.24602
\(372\) 1376.00 0.191780
\(373\) −8098.00 −1.12412 −0.562062 0.827095i \(-0.689992\pi\)
−0.562062 + 0.827095i \(0.689992\pi\)
\(374\) 1224.00 0.169229
\(375\) 10272.0 1.41452
\(376\) 6048.00 0.829526
\(377\) −1740.00 −0.237704
\(378\) −6720.00 −0.914390
\(379\) 320.000 0.0433702 0.0216851 0.999765i \(-0.493097\pi\)
0.0216851 + 0.999765i \(0.493097\pi\)
\(380\) 696.000 0.0939580
\(381\) 3776.00 0.507744
\(382\) 7920.00 1.06079
\(383\) −10872.0 −1.45048 −0.725239 0.688497i \(-0.758271\pi\)
−0.725239 + 0.688497i \(0.758271\pi\)
\(384\) 13272.0 1.76376
\(385\) 4032.00 0.533740
\(386\) −8646.00 −1.14008
\(387\) −5476.00 −0.719278
\(388\) −382.000 −0.0499822
\(389\) 1374.00 0.179086 0.0895431 0.995983i \(-0.471459\pi\)
0.0895431 + 0.995983i \(0.471459\pi\)
\(390\) −8352.00 −1.08441
\(391\) −1020.00 −0.131927
\(392\) 9261.00 1.19324
\(393\) −22080.0 −2.83407
\(394\) 126.000 0.0161111
\(395\) −2904.00 −0.369914
\(396\) −888.000 −0.112686
\(397\) −7522.00 −0.950928 −0.475464 0.879735i \(-0.657720\pi\)
−0.475464 + 0.879735i \(0.657720\pi\)
\(398\) 9660.00 1.21661
\(399\) 25984.0 3.26022
\(400\) 6319.00 0.789875
\(401\) 2706.00 0.336986 0.168493 0.985703i \(-0.446110\pi\)
0.168493 + 0.985703i \(0.446110\pi\)
\(402\) −11616.0 −1.44118
\(403\) 9976.00 1.23310
\(404\) −210.000 −0.0258611
\(405\) −2154.00 −0.264279
\(406\) 2520.00 0.308043
\(407\) 1392.00 0.169530
\(408\) −2856.00 −0.346552
\(409\) 266.000 0.0321586 0.0160793 0.999871i \(-0.494882\pi\)
0.0160793 + 0.999871i \(0.494882\pi\)
\(410\) 6156.00 0.741520
\(411\) −8784.00 −1.05422
\(412\) −232.000 −0.0277423
\(413\) −7056.00 −0.840685
\(414\) 6660.00 0.790631
\(415\) 4536.00 0.536539
\(416\) −2610.00 −0.307610
\(417\) −20224.0 −2.37500
\(418\) 8352.00 0.977296
\(419\) 2688.00 0.313407 0.156703 0.987646i \(-0.449913\pi\)
0.156703 + 0.987646i \(0.449913\pi\)
\(420\) 1344.00 0.156144
\(421\) −13810.0 −1.59871 −0.799357 0.600857i \(-0.794826\pi\)
−0.799357 + 0.600857i \(0.794826\pi\)
\(422\) 6240.00 0.719807
\(423\) 10656.0 1.22485
\(424\) 6678.00 0.764888
\(425\) −1513.00 −0.172685
\(426\) −16992.0 −1.93255
\(427\) −3080.00 −0.349067
\(428\) 432.000 0.0487886
\(429\) −11136.0 −1.25327
\(430\) 2664.00 0.298766
\(431\) 3036.00 0.339302 0.169651 0.985504i \(-0.445736\pi\)
0.169651 + 0.985504i \(0.445736\pi\)
\(432\) 5680.00 0.632591
\(433\) −11422.0 −1.26768 −0.633841 0.773463i \(-0.718523\pi\)
−0.633841 + 0.773463i \(0.718523\pi\)
\(434\) −14448.0 −1.59799
\(435\) −1440.00 −0.158719
\(436\) −1186.00 −0.130273
\(437\) −6960.00 −0.761881
\(438\) 8688.00 0.947782
\(439\) −52.0000 −0.00565336 −0.00282668 0.999996i \(-0.500900\pi\)
−0.00282668 + 0.999996i \(0.500900\pi\)
\(440\) −3024.00 −0.327644
\(441\) 16317.0 1.76190
\(442\) 2958.00 0.318321
\(443\) 3108.00 0.333331 0.166665 0.986014i \(-0.446700\pi\)
0.166665 + 0.986014i \(0.446700\pi\)
\(444\) 464.000 0.0495956
\(445\) −4644.00 −0.494712
\(446\) −13992.0 −1.48552
\(447\) −12912.0 −1.36626
\(448\) −12124.0 −1.27858
\(449\) 6114.00 0.642622 0.321311 0.946974i \(-0.395876\pi\)
0.321311 + 0.946974i \(0.395876\pi\)
\(450\) 9879.00 1.03489
\(451\) 8208.00 0.856984
\(452\) −366.000 −0.0380867
\(453\) 26624.0 2.76138
\(454\) 4320.00 0.446581
\(455\) 9744.00 1.00397
\(456\) −19488.0 −2.00134
\(457\) 4106.00 0.420286 0.210143 0.977671i \(-0.432607\pi\)
0.210143 + 0.977671i \(0.432607\pi\)
\(458\) 3558.00 0.363001
\(459\) −1360.00 −0.138299
\(460\) −360.000 −0.0364893
\(461\) 3366.00 0.340066 0.170033 0.985438i \(-0.445613\pi\)
0.170033 + 0.985438i \(0.445613\pi\)
\(462\) 16128.0 1.62412
\(463\) 896.000 0.0899366 0.0449683 0.998988i \(-0.485681\pi\)
0.0449683 + 0.998988i \(0.485681\pi\)
\(464\) −2130.00 −0.213109
\(465\) 8256.00 0.823361
\(466\) 16002.0 1.59073
\(467\) −10236.0 −1.01427 −0.507137 0.861866i \(-0.669296\pi\)
−0.507137 + 0.861866i \(0.669296\pi\)
\(468\) −2146.00 −0.211963
\(469\) 13552.0 1.33427
\(470\) −5184.00 −0.508766
\(471\) 19664.0 1.92371
\(472\) 5292.00 0.516068
\(473\) 3552.00 0.345288
\(474\) −11616.0 −1.12561
\(475\) −10324.0 −0.997258
\(476\) −476.000 −0.0458349
\(477\) 11766.0 1.12941
\(478\) −15984.0 −1.52948
\(479\) 5172.00 0.493350 0.246675 0.969098i \(-0.420662\pi\)
0.246675 + 0.969098i \(0.420662\pi\)
\(480\) −2160.00 −0.205396
\(481\) 3364.00 0.318888
\(482\) −16854.0 −1.59269
\(483\) −13440.0 −1.26613
\(484\) −755.000 −0.0709053
\(485\) −2292.00 −0.214586
\(486\) −15096.0 −1.40899
\(487\) −15052.0 −1.40056 −0.700278 0.713870i \(-0.746941\pi\)
−0.700278 + 0.713870i \(0.746941\pi\)
\(488\) 2310.00 0.214280
\(489\) −2176.00 −0.201231
\(490\) −7938.00 −0.731841
\(491\) 8700.00 0.799645 0.399822 0.916593i \(-0.369072\pi\)
0.399822 + 0.916593i \(0.369072\pi\)
\(492\) 2736.00 0.250708
\(493\) 510.000 0.0465908
\(494\) 20184.0 1.83830
\(495\) −5328.00 −0.483789
\(496\) 12212.0 1.10551
\(497\) 19824.0 1.78919
\(498\) 18144.0 1.63263
\(499\) −1168.00 −0.104783 −0.0523916 0.998627i \(-0.516684\pi\)
−0.0523916 + 0.998627i \(0.516684\pi\)
\(500\) −1284.00 −0.114844
\(501\) −28128.0 −2.50832
\(502\) 6084.00 0.540921
\(503\) −1740.00 −0.154240 −0.0771200 0.997022i \(-0.524572\pi\)
−0.0771200 + 0.997022i \(0.524572\pi\)
\(504\) −21756.0 −1.92280
\(505\) −1260.00 −0.111028
\(506\) −4320.00 −0.379540
\(507\) −9336.00 −0.817803
\(508\) −472.000 −0.0412236
\(509\) −12570.0 −1.09461 −0.547304 0.836934i \(-0.684346\pi\)
−0.547304 + 0.836934i \(0.684346\pi\)
\(510\) 2448.00 0.212548
\(511\) −10136.0 −0.877476
\(512\) 8733.00 0.753804
\(513\) −9280.00 −0.798678
\(514\) 5706.00 0.489651
\(515\) −1392.00 −0.119105
\(516\) 1184.00 0.101013
\(517\) −6912.00 −0.587987
\(518\) −4872.00 −0.413250
\(519\) 14736.0 1.24632
\(520\) −7308.00 −0.616302
\(521\) 11658.0 0.980319 0.490160 0.871633i \(-0.336939\pi\)
0.490160 + 0.871633i \(0.336939\pi\)
\(522\) −3330.00 −0.279215
\(523\) 13700.0 1.14543 0.572714 0.819755i \(-0.305890\pi\)
0.572714 + 0.819755i \(0.305890\pi\)
\(524\) 2760.00 0.230098
\(525\) −19936.0 −1.65729
\(526\) 16416.0 1.36078
\(527\) −2924.00 −0.241692
\(528\) −13632.0 −1.12359
\(529\) −8567.00 −0.704118
\(530\) −5724.00 −0.469122
\(531\) 9324.00 0.762010
\(532\) −3248.00 −0.264697
\(533\) 19836.0 1.61199
\(534\) −18576.0 −1.50536
\(535\) 2592.00 0.209462
\(536\) −10164.0 −0.819063
\(537\) 28128.0 2.26036
\(538\) 10710.0 0.858254
\(539\) −10584.0 −0.845798
\(540\) −480.000 −0.0382517
\(541\) 17822.0 1.41632 0.708159 0.706053i \(-0.249526\pi\)
0.708159 + 0.706053i \(0.249526\pi\)
\(542\) −816.000 −0.0646683
\(543\) −27184.0 −2.14839
\(544\) 765.000 0.0602925
\(545\) −7116.00 −0.559295
\(546\) 38976.0 3.05498
\(547\) 3800.00 0.297032 0.148516 0.988910i \(-0.452550\pi\)
0.148516 + 0.988910i \(0.452550\pi\)
\(548\) 1098.00 0.0855917
\(549\) 4070.00 0.316400
\(550\) −6408.00 −0.496796
\(551\) 3480.00 0.269062
\(552\) 10080.0 0.777234
\(553\) 13552.0 1.04212
\(554\) −11490.0 −0.881161
\(555\) 2784.00 0.212927
\(556\) 2528.00 0.192826
\(557\) −10074.0 −0.766336 −0.383168 0.923679i \(-0.625167\pi\)
−0.383168 + 0.923679i \(0.625167\pi\)
\(558\) 19092.0 1.44844
\(559\) 8584.00 0.649489
\(560\) 11928.0 0.900089
\(561\) 3264.00 0.245644
\(562\) −26622.0 −1.99819
\(563\) −15948.0 −1.19383 −0.596917 0.802303i \(-0.703608\pi\)
−0.596917 + 0.802303i \(0.703608\pi\)
\(564\) −2304.00 −0.172014
\(565\) −2196.00 −0.163516
\(566\) 7896.00 0.586385
\(567\) 10052.0 0.744523
\(568\) −14868.0 −1.09832
\(569\) 21834.0 1.60866 0.804331 0.594181i \(-0.202524\pi\)
0.804331 + 0.594181i \(0.202524\pi\)
\(570\) 16704.0 1.22746
\(571\) −21208.0 −1.55434 −0.777169 0.629292i \(-0.783345\pi\)
−0.777169 + 0.629292i \(0.783345\pi\)
\(572\) 1392.00 0.101753
\(573\) 21120.0 1.53979
\(574\) −28728.0 −2.08900
\(575\) 5340.00 0.387293
\(576\) 16021.0 1.15893
\(577\) 12530.0 0.904039 0.452020 0.892008i \(-0.350704\pi\)
0.452020 + 0.892008i \(0.350704\pi\)
\(578\) −867.000 −0.0623918
\(579\) −23056.0 −1.65488
\(580\) 180.000 0.0128864
\(581\) −21168.0 −1.51153
\(582\) −9168.00 −0.652965
\(583\) −7632.00 −0.542170
\(584\) 7602.00 0.538652
\(585\) −12876.0 −0.910012
\(586\) 19206.0 1.35391
\(587\) 2220.00 0.156097 0.0780487 0.996950i \(-0.475131\pi\)
0.0780487 + 0.996950i \(0.475131\pi\)
\(588\) −3528.00 −0.247436
\(589\) −19952.0 −1.39577
\(590\) −4536.00 −0.316516
\(591\) 336.000 0.0233861
\(592\) 4118.00 0.285893
\(593\) −25038.0 −1.73387 −0.866937 0.498418i \(-0.833915\pi\)
−0.866937 + 0.498418i \(0.833915\pi\)
\(594\) −5760.00 −0.397871
\(595\) −2856.00 −0.196781
\(596\) 1614.00 0.110926
\(597\) 25760.0 1.76597
\(598\) −10440.0 −0.713919
\(599\) 5784.00 0.394537 0.197269 0.980349i \(-0.436793\pi\)
0.197269 + 0.980349i \(0.436793\pi\)
\(600\) 14952.0 1.01735
\(601\) −4198.00 −0.284925 −0.142463 0.989800i \(-0.545502\pi\)
−0.142463 + 0.989800i \(0.545502\pi\)
\(602\) −12432.0 −0.841679
\(603\) −17908.0 −1.20940
\(604\) −3328.00 −0.224196
\(605\) −4530.00 −0.304414
\(606\) −5040.00 −0.337848
\(607\) −12124.0 −0.810705 −0.405353 0.914160i \(-0.632851\pi\)
−0.405353 + 0.914160i \(0.632851\pi\)
\(608\) 5220.00 0.348189
\(609\) 6720.00 0.447140
\(610\) −1980.00 −0.131423
\(611\) −16704.0 −1.10601
\(612\) 629.000 0.0415455
\(613\) 7454.00 0.491133 0.245566 0.969380i \(-0.421026\pi\)
0.245566 + 0.969380i \(0.421026\pi\)
\(614\) 26940.0 1.77070
\(615\) 16416.0 1.07635
\(616\) 14112.0 0.923034
\(617\) 28842.0 1.88190 0.940952 0.338539i \(-0.109933\pi\)
0.940952 + 0.338539i \(0.109933\pi\)
\(618\) −5568.00 −0.362424
\(619\) −17224.0 −1.11840 −0.559201 0.829032i \(-0.688892\pi\)
−0.559201 + 0.829032i \(0.688892\pi\)
\(620\) −1032.00 −0.0668486
\(621\) 4800.00 0.310173
\(622\) 11916.0 0.768148
\(623\) 21672.0 1.39369
\(624\) −32944.0 −2.11349
\(625\) 3421.00 0.218944
\(626\) −14190.0 −0.905985
\(627\) 22272.0 1.41859
\(628\) −2458.00 −0.156186
\(629\) −986.000 −0.0625030
\(630\) 18648.0 1.17929
\(631\) −12448.0 −0.785336 −0.392668 0.919680i \(-0.628448\pi\)
−0.392668 + 0.919680i \(0.628448\pi\)
\(632\) −10164.0 −0.639719
\(633\) 16640.0 1.04484
\(634\) 8694.00 0.544610
\(635\) −2832.00 −0.176983
\(636\) −2544.00 −0.158610
\(637\) −25578.0 −1.59095
\(638\) 2160.00 0.134036
\(639\) −26196.0 −1.62175
\(640\) −9954.00 −0.614791
\(641\) −25182.0 −1.55168 −0.775842 0.630927i \(-0.782675\pi\)
−0.775842 + 0.630927i \(0.782675\pi\)
\(642\) 10368.0 0.637371
\(643\) 17048.0 1.04558 0.522790 0.852462i \(-0.324891\pi\)
0.522790 + 0.852462i \(0.324891\pi\)
\(644\) 1680.00 0.102797
\(645\) 7104.00 0.433674
\(646\) −5916.00 −0.360313
\(647\) 7128.00 0.433123 0.216562 0.976269i \(-0.430516\pi\)
0.216562 + 0.976269i \(0.430516\pi\)
\(648\) −7539.00 −0.457037
\(649\) −6048.00 −0.365801
\(650\) −15486.0 −0.934478
\(651\) −38528.0 −2.31956
\(652\) 272.000 0.0163379
\(653\) 18462.0 1.10639 0.553196 0.833051i \(-0.313408\pi\)
0.553196 + 0.833051i \(0.313408\pi\)
\(654\) −28464.0 −1.70188
\(655\) 16560.0 0.987867
\(656\) 24282.0 1.44520
\(657\) 13394.0 0.795357
\(658\) 24192.0 1.43329
\(659\) 28092.0 1.66056 0.830280 0.557347i \(-0.188181\pi\)
0.830280 + 0.557347i \(0.188181\pi\)
\(660\) 1152.00 0.0679417
\(661\) 10910.0 0.641982 0.320991 0.947082i \(-0.395984\pi\)
0.320991 + 0.947082i \(0.395984\pi\)
\(662\) 13692.0 0.803859
\(663\) 7888.00 0.462058
\(664\) 15876.0 0.927874
\(665\) −19488.0 −1.13641
\(666\) 6438.00 0.374576
\(667\) −1800.00 −0.104492
\(668\) 3516.00 0.203650
\(669\) −37312.0 −2.15630
\(670\) 8712.00 0.502349
\(671\) −2640.00 −0.151887
\(672\) 10080.0 0.578638
\(673\) −28414.0 −1.62746 −0.813729 0.581244i \(-0.802566\pi\)
−0.813729 + 0.581244i \(0.802566\pi\)
\(674\) −2166.00 −0.123785
\(675\) 7120.00 0.405998
\(676\) 1167.00 0.0663974
\(677\) −6042.00 −0.343003 −0.171501 0.985184i \(-0.554862\pi\)
−0.171501 + 0.985184i \(0.554862\pi\)
\(678\) −8784.00 −0.497563
\(679\) 10696.0 0.604528
\(680\) 2142.00 0.120797
\(681\) 11520.0 0.648234
\(682\) −12384.0 −0.695319
\(683\) 34752.0 1.94692 0.973461 0.228851i \(-0.0734969\pi\)
0.973461 + 0.228851i \(0.0734969\pi\)
\(684\) 4292.00 0.239925
\(685\) 6588.00 0.367466
\(686\) 8232.00 0.458162
\(687\) 9488.00 0.526914
\(688\) 10508.0 0.582287
\(689\) −18444.0 −1.01983
\(690\) −8640.00 −0.476694
\(691\) 18320.0 1.00858 0.504288 0.863536i \(-0.331755\pi\)
0.504288 + 0.863536i \(0.331755\pi\)
\(692\) −1842.00 −0.101188
\(693\) 24864.0 1.36292
\(694\) −16632.0 −0.909715
\(695\) 15168.0 0.827849
\(696\) −5040.00 −0.274484
\(697\) −5814.00 −0.315955
\(698\) −33378.0 −1.80999
\(699\) 42672.0 2.30902
\(700\) 2492.00 0.134555
\(701\) −22890.0 −1.23330 −0.616650 0.787237i \(-0.711511\pi\)
−0.616650 + 0.787237i \(0.711511\pi\)
\(702\) −13920.0 −0.748400
\(703\) −6728.00 −0.360955
\(704\) −10392.0 −0.556340
\(705\) −13824.0 −0.738499
\(706\) −23526.0 −1.25413
\(707\) 5880.00 0.312787
\(708\) −2016.00 −0.107014
\(709\) 22886.0 1.21227 0.606137 0.795361i \(-0.292718\pi\)
0.606137 + 0.795361i \(0.292718\pi\)
\(710\) 12744.0 0.673625
\(711\) −17908.0 −0.944589
\(712\) −16254.0 −0.855540
\(713\) 10320.0 0.542058
\(714\) −11424.0 −0.598785
\(715\) 8352.00 0.436849
\(716\) −3516.00 −0.183518
\(717\) −42624.0 −2.22011
\(718\) −15120.0 −0.785896
\(719\) −13452.0 −0.697740 −0.348870 0.937171i \(-0.613435\pi\)
−0.348870 + 0.937171i \(0.613435\pi\)
\(720\) −15762.0 −0.815854
\(721\) 6496.00 0.335539
\(722\) −19791.0 −1.02015
\(723\) −44944.0 −2.31187
\(724\) 3398.00 0.174428
\(725\) −2670.00 −0.136774
\(726\) −18120.0 −0.926303
\(727\) −27304.0 −1.39292 −0.696458 0.717598i \(-0.745242\pi\)
−0.696458 + 0.717598i \(0.745242\pi\)
\(728\) 34104.0 1.73623
\(729\) −30563.0 −1.55276
\(730\) −6516.00 −0.330367
\(731\) −2516.00 −0.127302
\(732\) −880.000 −0.0444341
\(733\) 24470.0 1.23304 0.616521 0.787338i \(-0.288541\pi\)
0.616521 + 0.787338i \(0.288541\pi\)
\(734\) 25212.0 1.26784
\(735\) −21168.0 −1.06230
\(736\) −2700.00 −0.135222
\(737\) 11616.0 0.580571
\(738\) 37962.0 1.89350
\(739\) 35252.0 1.75476 0.877379 0.479798i \(-0.159290\pi\)
0.877379 + 0.479798i \(0.159290\pi\)
\(740\) −348.000 −0.0172875
\(741\) 53824.0 2.66839
\(742\) 26712.0 1.32160
\(743\) 1548.00 0.0764342 0.0382171 0.999269i \(-0.487832\pi\)
0.0382171 + 0.999269i \(0.487832\pi\)
\(744\) 28896.0 1.42390
\(745\) 9684.00 0.476234
\(746\) 24294.0 1.19231
\(747\) 27972.0 1.37007
\(748\) −408.000 −0.0199438
\(749\) −12096.0 −0.590091
\(750\) −30816.0 −1.50032
\(751\) 2948.00 0.143241 0.0716205 0.997432i \(-0.477183\pi\)
0.0716205 + 0.997432i \(0.477183\pi\)
\(752\) −20448.0 −0.991572
\(753\) 16224.0 0.785173
\(754\) 5220.00 0.252124
\(755\) −19968.0 −0.962530
\(756\) 2240.00 0.107762
\(757\) −754.000 −0.0362016 −0.0181008 0.999836i \(-0.505762\pi\)
−0.0181008 + 0.999836i \(0.505762\pi\)
\(758\) −960.000 −0.0460010
\(759\) −11520.0 −0.550922
\(760\) 14616.0 0.697603
\(761\) −41574.0 −1.98036 −0.990182 0.139787i \(-0.955358\pi\)
−0.990182 + 0.139787i \(0.955358\pi\)
\(762\) −11328.0 −0.538543
\(763\) 33208.0 1.57564
\(764\) −2640.00 −0.125016
\(765\) 3774.00 0.178365
\(766\) 32616.0 1.53846
\(767\) −14616.0 −0.688075
\(768\) −12104.0 −0.568705
\(769\) −15118.0 −0.708932 −0.354466 0.935069i \(-0.615337\pi\)
−0.354466 + 0.935069i \(0.615337\pi\)
\(770\) −12096.0 −0.566116
\(771\) 15216.0 0.710753
\(772\) 2882.00 0.134359
\(773\) 23550.0 1.09578 0.547888 0.836552i \(-0.315432\pi\)
0.547888 + 0.836552i \(0.315432\pi\)
\(774\) 16428.0 0.762910
\(775\) 15308.0 0.709522
\(776\) −8022.00 −0.371099
\(777\) −12992.0 −0.599853
\(778\) −4122.00 −0.189950
\(779\) −39672.0 −1.82464
\(780\) 2784.00 0.127799
\(781\) 16992.0 0.778517
\(782\) 3060.00 0.139930
\(783\) −2400.00 −0.109539
\(784\) −31311.0 −1.42634
\(785\) −14748.0 −0.670546
\(786\) 66240.0 3.00598
\(787\) 5240.00 0.237339 0.118670 0.992934i \(-0.462137\pi\)
0.118670 + 0.992934i \(0.462137\pi\)
\(788\) −42.0000 −0.00189872
\(789\) 43776.0 1.97524
\(790\) 8712.00 0.392353
\(791\) 10248.0 0.460654
\(792\) −18648.0 −0.836651
\(793\) −6380.00 −0.285700
\(794\) 22566.0 1.00861
\(795\) −15264.0 −0.680954
\(796\) −3220.00 −0.143379
\(797\) 5526.00 0.245597 0.122799 0.992432i \(-0.460813\pi\)
0.122799 + 0.992432i \(0.460813\pi\)
\(798\) −77952.0 −3.45798
\(799\) 4896.00 0.216781
\(800\) −4005.00 −0.176998
\(801\) −28638.0 −1.26326
\(802\) −8118.00 −0.357427
\(803\) −8688.00 −0.381809
\(804\) 3872.00 0.169844
\(805\) 10080.0 0.441333
\(806\) −29928.0 −1.30790
\(807\) 28560.0 1.24580
\(808\) −4410.00 −0.192009
\(809\) −438.000 −0.0190349 −0.00951747 0.999955i \(-0.503030\pi\)
−0.00951747 + 0.999955i \(0.503030\pi\)
\(810\) 6462.00 0.280311
\(811\) −30448.0 −1.31834 −0.659170 0.751994i \(-0.729092\pi\)
−0.659170 + 0.751994i \(0.729092\pi\)
\(812\) −840.000 −0.0363032
\(813\) −2176.00 −0.0938692
\(814\) −4176.00 −0.179814
\(815\) 1632.00 0.0701429
\(816\) 9656.00 0.414250
\(817\) −17168.0 −0.735168
\(818\) −798.000 −0.0341093
\(819\) 60088.0 2.56367
\(820\) −2052.00 −0.0873890
\(821\) −21930.0 −0.932232 −0.466116 0.884724i \(-0.654347\pi\)
−0.466116 + 0.884724i \(0.654347\pi\)
\(822\) 26352.0 1.11816
\(823\) −27436.0 −1.16204 −0.581020 0.813889i \(-0.697346\pi\)
−0.581020 + 0.813889i \(0.697346\pi\)
\(824\) −4872.00 −0.205976
\(825\) −17088.0 −0.721125
\(826\) 21168.0 0.891681
\(827\) −17832.0 −0.749794 −0.374897 0.927067i \(-0.622322\pi\)
−0.374897 + 0.927067i \(0.622322\pi\)
\(828\) −2220.00 −0.0931767
\(829\) −4090.00 −0.171353 −0.0856765 0.996323i \(-0.527305\pi\)
−0.0856765 + 0.996323i \(0.527305\pi\)
\(830\) −13608.0 −0.569085
\(831\) −30640.0 −1.27905
\(832\) −25114.0 −1.04648
\(833\) 7497.00 0.311832
\(834\) 60672.0 2.51906
\(835\) 21096.0 0.874320
\(836\) −2784.00 −0.115175
\(837\) 13760.0 0.568238
\(838\) −8064.00 −0.332418
\(839\) −2508.00 −0.103201 −0.0516006 0.998668i \(-0.516432\pi\)
−0.0516006 + 0.998668i \(0.516432\pi\)
\(840\) 28224.0 1.15931
\(841\) −23489.0 −0.963098
\(842\) 41430.0 1.69569
\(843\) −70992.0 −2.90047
\(844\) −2080.00 −0.0848300
\(845\) 7002.00 0.285061
\(846\) −31968.0 −1.29915
\(847\) 21140.0 0.857590
\(848\) −22578.0 −0.914306
\(849\) 21056.0 0.851166
\(850\) 4539.00 0.183160
\(851\) 3480.00 0.140180
\(852\) 5664.00 0.227753
\(853\) −42442.0 −1.70362 −0.851809 0.523852i \(-0.824494\pi\)
−0.851809 + 0.523852i \(0.824494\pi\)
\(854\) 9240.00 0.370242
\(855\) 25752.0 1.03006
\(856\) 9072.00 0.362237
\(857\) 32730.0 1.30459 0.652296 0.757964i \(-0.273806\pi\)
0.652296 + 0.757964i \(0.273806\pi\)
\(858\) 33408.0 1.32929
\(859\) −6148.00 −0.244199 −0.122100 0.992518i \(-0.538963\pi\)
−0.122100 + 0.992518i \(0.538963\pi\)
\(860\) −888.000 −0.0352099
\(861\) −76608.0 −3.03228
\(862\) −9108.00 −0.359884
\(863\) −22512.0 −0.887969 −0.443985 0.896034i \(-0.646436\pi\)
−0.443985 + 0.896034i \(0.646436\pi\)
\(864\) −3600.00 −0.141753
\(865\) −11052.0 −0.434427
\(866\) 34266.0 1.34458
\(867\) −2312.00 −0.0905647
\(868\) 4816.00 0.188325
\(869\) 11616.0 0.453447
\(870\) 4320.00 0.168347
\(871\) 28072.0 1.09206
\(872\) −24906.0 −0.967229
\(873\) −14134.0 −0.547954
\(874\) 20880.0 0.808097
\(875\) 35952.0 1.38903
\(876\) −2896.00 −0.111697
\(877\) 9182.00 0.353539 0.176770 0.984252i \(-0.443435\pi\)
0.176770 + 0.984252i \(0.443435\pi\)
\(878\) 156.000 0.00599629
\(879\) 51216.0 1.96527
\(880\) 10224.0 0.391649
\(881\) 28530.0 1.09103 0.545517 0.838100i \(-0.316334\pi\)
0.545517 + 0.838100i \(0.316334\pi\)
\(882\) −48951.0 −1.86878
\(883\) −12436.0 −0.473958 −0.236979 0.971515i \(-0.576157\pi\)
−0.236979 + 0.971515i \(0.576157\pi\)
\(884\) −986.000 −0.0375144
\(885\) −12096.0 −0.459438
\(886\) −9324.00 −0.353551
\(887\) 7404.00 0.280273 0.140136 0.990132i \(-0.455246\pi\)
0.140136 + 0.990132i \(0.455246\pi\)
\(888\) 9744.00 0.368229
\(889\) 13216.0 0.498594
\(890\) 13932.0 0.524721
\(891\) 8616.00 0.323958
\(892\) 4664.00 0.175070
\(893\) 33408.0 1.25191
\(894\) 38736.0 1.44913
\(895\) −21096.0 −0.787890
\(896\) 46452.0 1.73198
\(897\) −27840.0 −1.03629
\(898\) −18342.0 −0.681604
\(899\) −5160.00 −0.191430
\(900\) −3293.00 −0.121963
\(901\) 5406.00 0.199889
\(902\) −24624.0 −0.908968
\(903\) −33152.0 −1.22174
\(904\) −7686.00 −0.282779
\(905\) 20388.0 0.748862
\(906\) −79872.0 −2.92888
\(907\) 15368.0 0.562609 0.281304 0.959619i \(-0.409233\pi\)
0.281304 + 0.959619i \(0.409233\pi\)
\(908\) −1440.00 −0.0526300
\(909\) −7770.00 −0.283514
\(910\) −29232.0 −1.06487
\(911\) 27276.0 0.991980 0.495990 0.868328i \(-0.334805\pi\)
0.495990 + 0.868328i \(0.334805\pi\)
\(912\) 65888.0 2.39229
\(913\) −18144.0 −0.657699
\(914\) −12318.0 −0.445780
\(915\) −5280.00 −0.190767
\(916\) −1186.00 −0.0427801
\(917\) −77280.0 −2.78300
\(918\) 4080.00 0.146689
\(919\) −46456.0 −1.66751 −0.833755 0.552134i \(-0.813814\pi\)
−0.833755 + 0.552134i \(0.813814\pi\)
\(920\) −7560.00 −0.270919
\(921\) 71840.0 2.57026
\(922\) −10098.0 −0.360694
\(923\) 41064.0 1.46440
\(924\) −5376.00 −0.191404
\(925\) 5162.00 0.183487
\(926\) −2688.00 −0.0953922
\(927\) −8584.00 −0.304138
\(928\) 1350.00 0.0477542
\(929\) 13026.0 0.460031 0.230016 0.973187i \(-0.426122\pi\)
0.230016 + 0.973187i \(0.426122\pi\)
\(930\) −24768.0 −0.873306
\(931\) 51156.0 1.80083
\(932\) −5334.00 −0.187469
\(933\) 31776.0 1.11500
\(934\) 30708.0 1.07580
\(935\) −2448.00 −0.0856237
\(936\) −45066.0 −1.57375
\(937\) 26330.0 0.917997 0.458999 0.888437i \(-0.348208\pi\)
0.458999 + 0.888437i \(0.348208\pi\)
\(938\) −40656.0 −1.41521
\(939\) −37840.0 −1.31508
\(940\) 1728.00 0.0599587
\(941\) 28254.0 0.978803 0.489402 0.872058i \(-0.337215\pi\)
0.489402 + 0.872058i \(0.337215\pi\)
\(942\) −58992.0 −2.04041
\(943\) 20520.0 0.708614
\(944\) −17892.0 −0.616880
\(945\) 13440.0 0.462649
\(946\) −10656.0 −0.366233
\(947\) 49272.0 1.69073 0.845367 0.534186i \(-0.179382\pi\)
0.845367 + 0.534186i \(0.179382\pi\)
\(948\) 3872.00 0.132655
\(949\) −20996.0 −0.718187
\(950\) 30972.0 1.05775
\(951\) 23184.0 0.790529
\(952\) −9996.00 −0.340307
\(953\) 32922.0 1.11904 0.559522 0.828816i \(-0.310985\pi\)
0.559522 + 0.828816i \(0.310985\pi\)
\(954\) −35298.0 −1.19792
\(955\) −15840.0 −0.536723
\(956\) 5328.00 0.180251
\(957\) 5760.00 0.194560
\(958\) −15516.0 −0.523277
\(959\) −30744.0 −1.03522
\(960\) −20784.0 −0.698751
\(961\) −207.000 −0.00694841
\(962\) −10092.0 −0.338232
\(963\) 15984.0 0.534867
\(964\) 5618.00 0.187701
\(965\) 17292.0 0.576839
\(966\) 40320.0 1.34293
\(967\) −1168.00 −0.0388421 −0.0194211 0.999811i \(-0.506182\pi\)
−0.0194211 + 0.999811i \(0.506182\pi\)
\(968\) −15855.0 −0.526445
\(969\) −15776.0 −0.523011
\(970\) 6876.00 0.227603
\(971\) −19812.0 −0.654786 −0.327393 0.944888i \(-0.606170\pi\)
−0.327393 + 0.944888i \(0.606170\pi\)
\(972\) 5032.00 0.166051
\(973\) −70784.0 −2.33220
\(974\) 45156.0 1.48551
\(975\) −41296.0 −1.35644
\(976\) −7810.00 −0.256139
\(977\) −28494.0 −0.933064 −0.466532 0.884504i \(-0.654497\pi\)
−0.466532 + 0.884504i \(0.654497\pi\)
\(978\) 6528.00 0.213438
\(979\) 18576.0 0.606426
\(980\) 2646.00 0.0862483
\(981\) −43882.0 −1.42818
\(982\) −26100.0 −0.848151
\(983\) −42708.0 −1.38573 −0.692866 0.721067i \(-0.743652\pi\)
−0.692866 + 0.721067i \(0.743652\pi\)
\(984\) 57456.0 1.86141
\(985\) −252.000 −0.00815166
\(986\) −1530.00 −0.0494170
\(987\) 64512.0 2.08049
\(988\) −6728.00 −0.216646
\(989\) 8880.00 0.285508
\(990\) 15984.0 0.513136
\(991\) −29500.0 −0.945609 −0.472804 0.881167i \(-0.656758\pi\)
−0.472804 + 0.881167i \(0.656758\pi\)
\(992\) −7740.00 −0.247727
\(993\) 36512.0 1.16684
\(994\) −59472.0 −1.89772
\(995\) −19320.0 −0.615563
\(996\) −6048.00 −0.192408
\(997\) −9322.00 −0.296119 −0.148060 0.988978i \(-0.547303\pi\)
−0.148060 + 0.988978i \(0.547303\pi\)
\(998\) 3504.00 0.111139
\(999\) 4640.00 0.146950
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 \(a_p\))