Properties

Label 1175.4.a.a.1.2
Level 1175
Weight 4
Character 1175.1
Self dual Yes
Analytic conductor 69.327
Analytic rank 0
Dimension 3
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 1175 = 5^{2} \cdot 47 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 1175.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(69.3272442567\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.1101.1
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 1.2
Root \(-3.11903\)
Character \(\chi\) = 1175.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.60930 q^{2}\) \(-1.72833 q^{3}\) \(-5.41015 q^{4}\) \(-2.78140 q^{6}\) \(+11.3182 q^{7}\) \(-21.5810 q^{8}\) \(-24.0129 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.60930 q^{2}\) \(-1.72833 q^{3}\) \(-5.41015 q^{4}\) \(-2.78140 q^{6}\) \(+11.3182 q^{7}\) \(-21.5810 q^{8}\) \(-24.0129 q^{9}\) \(-40.6469 q^{11}\) \(+9.35051 q^{12}\) \(+12.3983 q^{13}\) \(+18.2143 q^{14}\) \(+8.55095 q^{16}\) \(-59.6717 q^{17}\) \(-38.6440 q^{18}\) \(+26.4089 q^{19}\) \(-19.5615 q^{21}\) \(-65.4131 q^{22}\) \(-107.097 q^{23}\) \(+37.2990 q^{24}\) \(+19.9526 q^{26}\) \(+88.1670 q^{27}\) \(-61.2330 q^{28}\) \(+173.657 q^{29}\) \(-332.301 q^{31}\) \(+186.409 q^{32}\) \(+70.2512 q^{33}\) \(-96.0296 q^{34}\) \(+129.913 q^{36}\) \(+172.339 q^{37}\) \(+42.4998 q^{38}\) \(-21.4283 q^{39}\) \(-178.190 q^{41}\) \(-31.4804 q^{42}\) \(-63.2928 q^{43}\) \(+219.906 q^{44}\) \(-172.351 q^{46}\) \(-47.0000 q^{47}\) \(-14.7788 q^{48}\) \(-214.899 q^{49}\) \(+103.132 q^{51}\) \(-67.0767 q^{52}\) \(+402.256 q^{53}\) \(+141.887 q^{54}\) \(-244.257 q^{56}\) \(-45.6432 q^{57}\) \(+279.466 q^{58}\) \(+305.280 q^{59}\) \(-86.2464 q^{61}\) \(-534.772 q^{62}\) \(-271.782 q^{63}\) \(+231.580 q^{64}\) \(+113.055 q^{66}\) \(+681.333 q^{67}\) \(+322.833 q^{68}\) \(+185.098 q^{69}\) \(+726.348 q^{71}\) \(+518.221 q^{72}\) \(+79.8711 q^{73}\) \(+277.345 q^{74}\) \(-142.876 q^{76}\) \(-460.049 q^{77}\) \(-34.4846 q^{78}\) \(+279.707 q^{79}\) \(+495.966 q^{81}\) \(-286.761 q^{82}\) \(-556.598 q^{83}\) \(+105.831 q^{84}\) \(-101.857 q^{86}\) \(-300.135 q^{87}\) \(+877.200 q^{88}\) \(-342.069 q^{89}\) \(+140.326 q^{91}\) \(+579.410 q^{92}\) \(+574.325 q^{93}\) \(-75.6371 q^{94}\) \(-322.175 q^{96}\) \(+1637.35 q^{97}\) \(-345.837 q^{98}\) \(+976.050 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(3q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 5q^{4} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 45q^{7} \) \(\mathstrut +\mathstrut 39q^{8} \) \(\mathstrut -\mathstrut 42q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 5q^{4} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 45q^{7} \) \(\mathstrut +\mathstrut 39q^{8} \) \(\mathstrut -\mathstrut 42q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut -\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 80q^{13} \) \(\mathstrut +\mathstrut 162q^{14} \) \(\mathstrut +\mathstrut 89q^{16} \) \(\mathstrut +\mathstrut 39q^{17} \) \(\mathstrut -\mathstrut 181q^{18} \) \(\mathstrut -\mathstrut 24q^{19} \) \(\mathstrut +\mathstrut 24q^{21} \) \(\mathstrut +\mathstrut 14q^{22} \) \(\mathstrut -\mathstrut 120q^{23} \) \(\mathstrut +\mathstrut 192q^{24} \) \(\mathstrut +\mathstrut 316q^{26} \) \(\mathstrut -\mathstrut 64q^{27} \) \(\mathstrut +\mathstrut 408q^{28} \) \(\mathstrut -\mathstrut 184q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut +\mathstrut 7q^{32} \) \(\mathstrut +\mathstrut 208q^{33} \) \(\mathstrut +\mathstrut 218q^{34} \) \(\mathstrut -\mathstrut 343q^{36} \) \(\mathstrut +\mathstrut 589q^{37} \) \(\mathstrut -\mathstrut 42q^{38} \) \(\mathstrut +\mathstrut 60q^{39} \) \(\mathstrut -\mathstrut 92q^{41} \) \(\mathstrut +\mathstrut 54q^{42} \) \(\mathstrut +\mathstrut 250q^{43} \) \(\mathstrut +\mathstrut 466q^{44} \) \(\mathstrut -\mathstrut 816q^{46} \) \(\mathstrut -\mathstrut 141q^{47} \) \(\mathstrut +\mathstrut 120q^{48} \) \(\mathstrut +\mathstrut 30q^{49} \) \(\mathstrut +\mathstrut 317q^{51} \) \(\mathstrut +\mathstrut 900q^{52} \) \(\mathstrut -\mathstrut 459q^{53} \) \(\mathstrut +\mathstrut 106q^{54} \) \(\mathstrut +\mathstrut 1032q^{56} \) \(\mathstrut -\mathstrut 216q^{57} \) \(\mathstrut -\mathstrut 684q^{58} \) \(\mathstrut +\mathstrut 579q^{59} \) \(\mathstrut +\mathstrut 267q^{61} \) \(\mathstrut +\mathstrut 244q^{62} \) \(\mathstrut -\mathstrut 1044q^{63} \) \(\mathstrut -\mathstrut 87q^{64} \) \(\mathstrut +\mathstrut 16q^{66} \) \(\mathstrut +\mathstrut 540q^{67} \) \(\mathstrut +\mathstrut 1334q^{68} \) \(\mathstrut +\mathstrut 642q^{69} \) \(\mathstrut +\mathstrut 749q^{71} \) \(\mathstrut -\mathstrut 357q^{72} \) \(\mathstrut +\mathstrut 1924q^{73} \) \(\mathstrut +\mathstrut 950q^{74} \) \(\mathstrut -\mathstrut 402q^{76} \) \(\mathstrut +\mathstrut 288q^{77} \) \(\mathstrut +\mathstrut 152q^{78} \) \(\mathstrut +\mathstrut 805q^{79} \) \(\mathstrut +\mathstrut 291q^{81} \) \(\mathstrut +\mathstrut 938q^{82} \) \(\mathstrut -\mathstrut 712q^{83} \) \(\mathstrut +\mathstrut 372q^{84} \) \(\mathstrut -\mathstrut 1294q^{86} \) \(\mathstrut -\mathstrut 1216q^{87} \) \(\mathstrut +\mathstrut 2190q^{88} \) \(\mathstrut +\mathstrut 835q^{89} \) \(\mathstrut +\mathstrut 2040q^{91} \) \(\mathstrut -\mathstrut 1596q^{92} \) \(\mathstrut +\mathstrut 1500q^{93} \) \(\mathstrut -\mathstrut 235q^{94} \) \(\mathstrut -\mathstrut 1432q^{96} \) \(\mathstrut +\mathstrut 2243q^{97} \) \(\mathstrut +\mathstrut 2989q^{98} \) \(\mathstrut +\mathstrut 554q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.60930 0.568974 0.284487 0.958680i \(-0.408177\pi\)
0.284487 + 0.958680i \(0.408177\pi\)
\(3\) −1.72833 −0.332617 −0.166308 0.986074i \(-0.553185\pi\)
−0.166308 + 0.986074i \(0.553185\pi\)
\(4\) −5.41015 −0.676269
\(5\) 0 0
\(6\) −2.78140 −0.189250
\(7\) 11.3182 0.611124 0.305562 0.952172i \(-0.401156\pi\)
0.305562 + 0.952172i \(0.401156\pi\)
\(8\) −21.5810 −0.953753
\(9\) −24.0129 −0.889366
\(10\) 0 0
\(11\) −40.6469 −1.11414 −0.557069 0.830467i \(-0.688074\pi\)
−0.557069 + 0.830467i \(0.688074\pi\)
\(12\) 9.35051 0.224938
\(13\) 12.3983 0.264513 0.132257 0.991216i \(-0.457778\pi\)
0.132257 + 0.991216i \(0.457778\pi\)
\(14\) 18.2143 0.347714
\(15\) 0 0
\(16\) 8.55095 0.133609
\(17\) −59.6717 −0.851324 −0.425662 0.904882i \(-0.639959\pi\)
−0.425662 + 0.904882i \(0.639959\pi\)
\(18\) −38.6440 −0.506026
\(19\) 26.4089 0.318874 0.159437 0.987208i \(-0.449032\pi\)
0.159437 + 0.987208i \(0.449032\pi\)
\(20\) 0 0
\(21\) −19.5615 −0.203270
\(22\) −65.4131 −0.633915
\(23\) −107.097 −0.970923 −0.485461 0.874258i \(-0.661348\pi\)
−0.485461 + 0.874258i \(0.661348\pi\)
\(24\) 37.2990 0.317234
\(25\) 0 0
\(26\) 19.9526 0.150501
\(27\) 88.1670 0.628435
\(28\) −61.2330 −0.413284
\(29\) 173.657 1.11197 0.555987 0.831191i \(-0.312341\pi\)
0.555987 + 0.831191i \(0.312341\pi\)
\(30\) 0 0
\(31\) −332.301 −1.92526 −0.962629 0.270823i \(-0.912704\pi\)
−0.962629 + 0.270823i \(0.912704\pi\)
\(32\) 186.409 1.02977
\(33\) 70.2512 0.370581
\(34\) −96.0296 −0.484381
\(35\) 0 0
\(36\) 129.913 0.601451
\(37\) 172.339 0.765739 0.382869 0.923802i \(-0.374936\pi\)
0.382869 + 0.923802i \(0.374936\pi\)
\(38\) 42.4998 0.181431
\(39\) −21.4283 −0.0879815
\(40\) 0 0
\(41\) −178.190 −0.678746 −0.339373 0.940652i \(-0.610215\pi\)
−0.339373 + 0.940652i \(0.610215\pi\)
\(42\) −31.4804 −0.115655
\(43\) −63.2928 −0.224467 −0.112233 0.993682i \(-0.535800\pi\)
−0.112233 + 0.993682i \(0.535800\pi\)
\(44\) 219.906 0.753456
\(45\) 0 0
\(46\) −172.351 −0.552429
\(47\) −47.0000 −0.145865
\(48\) −14.7788 −0.0444404
\(49\) −214.899 −0.626527
\(50\) 0 0
\(51\) 103.132 0.283165
\(52\) −67.0767 −0.178882
\(53\) 402.256 1.04253 0.521266 0.853395i \(-0.325460\pi\)
0.521266 + 0.853395i \(0.325460\pi\)
\(54\) 141.887 0.357563
\(55\) 0 0
\(56\) −244.257 −0.582861
\(57\) −45.6432 −0.106063
\(58\) 279.466 0.632684
\(59\) 305.280 0.673628 0.336814 0.941571i \(-0.390651\pi\)
0.336814 + 0.941571i \(0.390651\pi\)
\(60\) 0 0
\(61\) −86.2464 −0.181028 −0.0905141 0.995895i \(-0.528851\pi\)
−0.0905141 + 0.995895i \(0.528851\pi\)
\(62\) −534.772 −1.09542
\(63\) −271.782 −0.543513
\(64\) 231.580 0.452305
\(65\) 0 0
\(66\) 113.055 0.210851
\(67\) 681.333 1.24236 0.621179 0.783668i \(-0.286654\pi\)
0.621179 + 0.783668i \(0.286654\pi\)
\(68\) 322.833 0.575724
\(69\) 185.098 0.322945
\(70\) 0 0
\(71\) 726.348 1.21411 0.607054 0.794661i \(-0.292351\pi\)
0.607054 + 0.794661i \(0.292351\pi\)
\(72\) 518.221 0.848236
\(73\) 79.8711 0.128058 0.0640288 0.997948i \(-0.479605\pi\)
0.0640288 + 0.997948i \(0.479605\pi\)
\(74\) 277.345 0.435685
\(75\) 0 0
\(76\) −142.876 −0.215645
\(77\) −460.049 −0.680876
\(78\) −34.4846 −0.0500591
\(79\) 279.707 0.398348 0.199174 0.979964i \(-0.436174\pi\)
0.199174 + 0.979964i \(0.436174\pi\)
\(80\) 0 0
\(81\) 495.966 0.680338
\(82\) −286.761 −0.386189
\(83\) −556.598 −0.736080 −0.368040 0.929810i \(-0.619971\pi\)
−0.368040 + 0.929810i \(0.619971\pi\)
\(84\) 105.831 0.137465
\(85\) 0 0
\(86\) −101.857 −0.127716
\(87\) −300.135 −0.369861
\(88\) 877.200 1.06261
\(89\) −342.069 −0.407408 −0.203704 0.979033i \(-0.565298\pi\)
−0.203704 + 0.979033i \(0.565298\pi\)
\(90\) 0 0
\(91\) 140.326 0.161650
\(92\) 579.410 0.656605
\(93\) 574.325 0.640373
\(94\) −75.6371 −0.0829933
\(95\) 0 0
\(96\) −322.175 −0.342520
\(97\) 1637.35 1.71390 0.856949 0.515402i \(-0.172357\pi\)
0.856949 + 0.515402i \(0.172357\pi\)
\(98\) −345.837 −0.356478
\(99\) 976.050 0.990876
\(100\) 0 0
\(101\) −1453.29 −1.43176 −0.715879 0.698224i \(-0.753974\pi\)
−0.715879 + 0.698224i \(0.753974\pi\)
\(102\) 165.971 0.161113
\(103\) −1363.10 −1.30398 −0.651992 0.758226i \(-0.726067\pi\)
−0.651992 + 0.758226i \(0.726067\pi\)
\(104\) −267.567 −0.252280
\(105\) 0 0
\(106\) 647.351 0.593173
\(107\) −274.746 −0.248231 −0.124116 0.992268i \(-0.539609\pi\)
−0.124116 + 0.992268i \(0.539609\pi\)
\(108\) −476.997 −0.424991
\(109\) 1448.56 1.27291 0.636454 0.771315i \(-0.280401\pi\)
0.636454 + 0.771315i \(0.280401\pi\)
\(110\) 0 0
\(111\) −297.858 −0.254698
\(112\) 96.7811 0.0816514
\(113\) 1591.30 1.32475 0.662376 0.749171i \(-0.269548\pi\)
0.662376 + 0.749171i \(0.269548\pi\)
\(114\) −73.4536 −0.0603470
\(115\) 0 0
\(116\) −939.509 −0.751993
\(117\) −297.719 −0.235249
\(118\) 491.287 0.383277
\(119\) −675.374 −0.520264
\(120\) 0 0
\(121\) 321.172 0.241301
\(122\) −138.796 −0.103000
\(123\) 307.970 0.225762
\(124\) 1797.80 1.30199
\(125\) 0 0
\(126\) −437.379 −0.309245
\(127\) −747.668 −0.522400 −0.261200 0.965285i \(-0.584118\pi\)
−0.261200 + 0.965285i \(0.584118\pi\)
\(128\) −1118.59 −0.772423
\(129\) 109.391 0.0746614
\(130\) 0 0
\(131\) −624.528 −0.416529 −0.208264 0.978073i \(-0.566781\pi\)
−0.208264 + 0.978073i \(0.566781\pi\)
\(132\) −380.070 −0.250612
\(133\) 298.900 0.194872
\(134\) 1096.47 0.706869
\(135\) 0 0
\(136\) 1287.77 0.811953
\(137\) 336.418 0.209796 0.104898 0.994483i \(-0.466548\pi\)
0.104898 + 0.994483i \(0.466548\pi\)
\(138\) 297.879 0.183747
\(139\) 1940.28 1.18397 0.591987 0.805948i \(-0.298344\pi\)
0.591987 + 0.805948i \(0.298344\pi\)
\(140\) 0 0
\(141\) 81.2314 0.0485171
\(142\) 1168.91 0.690795
\(143\) −503.953 −0.294704
\(144\) −205.333 −0.118827
\(145\) 0 0
\(146\) 128.537 0.0728614
\(147\) 371.416 0.208394
\(148\) −932.380 −0.517845
\(149\) 2810.71 1.54538 0.772692 0.634781i \(-0.218910\pi\)
0.772692 + 0.634781i \(0.218910\pi\)
\(150\) 0 0
\(151\) 1710.82 0.922014 0.461007 0.887396i \(-0.347488\pi\)
0.461007 + 0.887396i \(0.347488\pi\)
\(152\) −569.929 −0.304127
\(153\) 1432.89 0.757138
\(154\) −740.357 −0.387401
\(155\) 0 0
\(156\) 115.930 0.0594991
\(157\) 1378.36 0.700669 0.350334 0.936625i \(-0.386068\pi\)
0.350334 + 0.936625i \(0.386068\pi\)
\(158\) 450.133 0.226650
\(159\) −695.231 −0.346763
\(160\) 0 0
\(161\) −1212.14 −0.593354
\(162\) 798.159 0.387095
\(163\) 3255.46 1.56434 0.782170 0.623066i \(-0.214113\pi\)
0.782170 + 0.623066i \(0.214113\pi\)
\(164\) 964.034 0.459015
\(165\) 0 0
\(166\) −895.734 −0.418810
\(167\) 2337.08 1.08293 0.541463 0.840725i \(-0.317871\pi\)
0.541463 + 0.840725i \(0.317871\pi\)
\(168\) 422.156 0.193869
\(169\) −2043.28 −0.930033
\(170\) 0 0
\(171\) −634.153 −0.283596
\(172\) 342.424 0.151800
\(173\) 3269.43 1.43682 0.718412 0.695618i \(-0.244870\pi\)
0.718412 + 0.695618i \(0.244870\pi\)
\(174\) −483.008 −0.210441
\(175\) 0 0
\(176\) −347.570 −0.148858
\(177\) −527.624 −0.224060
\(178\) −550.492 −0.231804
\(179\) −2203.96 −0.920290 −0.460145 0.887844i \(-0.652203\pi\)
−0.460145 + 0.887844i \(0.652203\pi\)
\(180\) 0 0
\(181\) 1522.63 0.625282 0.312641 0.949871i \(-0.398786\pi\)
0.312641 + 0.949871i \(0.398786\pi\)
\(182\) 225.827 0.0919748
\(183\) 149.062 0.0602130
\(184\) 2311.25 0.926020
\(185\) 0 0
\(186\) 924.261 0.364356
\(187\) 2425.47 0.948491
\(188\) 254.277 0.0986440
\(189\) 997.889 0.384052
\(190\) 0 0
\(191\) −2019.27 −0.764968 −0.382484 0.923962i \(-0.624931\pi\)
−0.382484 + 0.923962i \(0.624931\pi\)
\(192\) −400.246 −0.150444
\(193\) 4447.95 1.65891 0.829456 0.558571i \(-0.188650\pi\)
0.829456 + 0.558571i \(0.188650\pi\)
\(194\) 2634.99 0.975163
\(195\) 0 0
\(196\) 1162.64 0.423701
\(197\) −1790.04 −0.647388 −0.323694 0.946162i \(-0.604925\pi\)
−0.323694 + 0.946162i \(0.604925\pi\)
\(198\) 1570.76 0.563782
\(199\) 3481.42 1.24016 0.620079 0.784540i \(-0.287101\pi\)
0.620079 + 0.784540i \(0.287101\pi\)
\(200\) 0 0
\(201\) −1177.57 −0.413229
\(202\) −2338.78 −0.814633
\(203\) 1965.48 0.679554
\(204\) −557.961 −0.191495
\(205\) 0 0
\(206\) −2193.64 −0.741933
\(207\) 2571.70 0.863506
\(208\) 106.017 0.0353412
\(209\) −1073.44 −0.355270
\(210\) 0 0
\(211\) 5216.72 1.70206 0.851028 0.525120i \(-0.175979\pi\)
0.851028 + 0.525120i \(0.175979\pi\)
\(212\) −2176.27 −0.705031
\(213\) −1255.37 −0.403833
\(214\) −442.150 −0.141237
\(215\) 0 0
\(216\) −1902.73 −0.599372
\(217\) −3761.04 −1.17657
\(218\) 2331.17 0.724251
\(219\) −138.043 −0.0425941
\(220\) 0 0
\(221\) −739.827 −0.225186
\(222\) −479.343 −0.144916
\(223\) −5075.44 −1.52411 −0.762055 0.647512i \(-0.775810\pi\)
−0.762055 + 0.647512i \(0.775810\pi\)
\(224\) 2109.81 0.629319
\(225\) 0 0
\(226\) 2560.88 0.753749
\(227\) −1752.66 −0.512460 −0.256230 0.966616i \(-0.582480\pi\)
−0.256230 + 0.966616i \(0.582480\pi\)
\(228\) 246.936 0.0717270
\(229\) −4676.77 −1.34956 −0.674781 0.738018i \(-0.735762\pi\)
−0.674781 + 0.738018i \(0.735762\pi\)
\(230\) 0 0
\(231\) 795.115 0.226471
\(232\) −3747.68 −1.06055
\(233\) −4261.89 −1.19831 −0.599154 0.800634i \(-0.704496\pi\)
−0.599154 + 0.800634i \(0.704496\pi\)
\(234\) −479.119 −0.133850
\(235\) 0 0
\(236\) −1651.61 −0.455554
\(237\) −483.426 −0.132497
\(238\) −1086.88 −0.296017
\(239\) −3227.38 −0.873479 −0.436740 0.899588i \(-0.643867\pi\)
−0.436740 + 0.899588i \(0.643867\pi\)
\(240\) 0 0
\(241\) −1310.37 −0.350242 −0.175121 0.984547i \(-0.556032\pi\)
−0.175121 + 0.984547i \(0.556032\pi\)
\(242\) 516.863 0.137294
\(243\) −3237.70 −0.854727
\(244\) 466.606 0.122424
\(245\) 0 0
\(246\) 495.617 0.128453
\(247\) 327.425 0.0843464
\(248\) 7171.38 1.83622
\(249\) 961.984 0.244832
\(250\) 0 0
\(251\) 4906.61 1.23387 0.616937 0.787013i \(-0.288373\pi\)
0.616937 + 0.787013i \(0.288373\pi\)
\(252\) 1470.38 0.367561
\(253\) 4353.15 1.08174
\(254\) −1203.22 −0.297232
\(255\) 0 0
\(256\) −3652.79 −0.891793
\(257\) −2103.21 −0.510485 −0.255243 0.966877i \(-0.582155\pi\)
−0.255243 + 0.966877i \(0.582155\pi\)
\(258\) 176.043 0.0424804
\(259\) 1950.56 0.467962
\(260\) 0 0
\(261\) −4170.00 −0.988951
\(262\) −1005.05 −0.236994
\(263\) 6993.90 1.63978 0.819890 0.572521i \(-0.194035\pi\)
0.819890 + 0.572521i \(0.194035\pi\)
\(264\) −1516.09 −0.353442
\(265\) 0 0
\(266\) 481.020 0.110877
\(267\) 591.208 0.135511
\(268\) −3686.11 −0.840168
\(269\) 6466.63 1.46571 0.732857 0.680382i \(-0.238186\pi\)
0.732857 + 0.680382i \(0.238186\pi\)
\(270\) 0 0
\(271\) −8154.65 −1.82790 −0.913948 0.405831i \(-0.866982\pi\)
−0.913948 + 0.405831i \(0.866982\pi\)
\(272\) −510.249 −0.113744
\(273\) −242.530 −0.0537676
\(274\) 541.397 0.119369
\(275\) 0 0
\(276\) −1001.41 −0.218398
\(277\) −3722.71 −0.807495 −0.403748 0.914870i \(-0.632293\pi\)
−0.403748 + 0.914870i \(0.632293\pi\)
\(278\) 3122.49 0.673650
\(279\) 7979.50 1.71226
\(280\) 0 0
\(281\) −6046.33 −1.28361 −0.641804 0.766869i \(-0.721814\pi\)
−0.641804 + 0.766869i \(0.721814\pi\)
\(282\) 130.726 0.0276050
\(283\) −268.000 −0.0562931 −0.0281466 0.999604i \(-0.508961\pi\)
−0.0281466 + 0.999604i \(0.508961\pi\)
\(284\) −3929.65 −0.821063
\(285\) 0 0
\(286\) −811.011 −0.167679
\(287\) −2016.78 −0.414798
\(288\) −4476.21 −0.915845
\(289\) −1352.29 −0.275248
\(290\) 0 0
\(291\) −2829.88 −0.570071
\(292\) −432.115 −0.0866014
\(293\) −2731.03 −0.544535 −0.272267 0.962222i \(-0.587774\pi\)
−0.272267 + 0.962222i \(0.587774\pi\)
\(294\) 597.719 0.118570
\(295\) 0 0
\(296\) −3719.24 −0.730326
\(297\) −3583.72 −0.700163
\(298\) 4523.28 0.879283
\(299\) −1327.82 −0.256822
\(300\) 0 0
\(301\) −716.360 −0.137177
\(302\) 2753.22 0.524602
\(303\) 2511.76 0.476227
\(304\) 225.821 0.0426043
\(305\) 0 0
\(306\) 2305.95 0.430792
\(307\) 7009.57 1.30312 0.651559 0.758598i \(-0.274115\pi\)
0.651559 + 0.758598i \(0.274115\pi\)
\(308\) 2488.93 0.460455
\(309\) 2355.89 0.433727
\(310\) 0 0
\(311\) −867.418 −0.158157 −0.0790784 0.996868i \(-0.525198\pi\)
−0.0790784 + 0.996868i \(0.525198\pi\)
\(312\) 462.444 0.0839126
\(313\) −5724.10 −1.03369 −0.516845 0.856079i \(-0.672894\pi\)
−0.516845 + 0.856079i \(0.672894\pi\)
\(314\) 2218.19 0.398662
\(315\) 0 0
\(316\) −1513.26 −0.269391
\(317\) −5821.24 −1.03140 −0.515700 0.856769i \(-0.672468\pi\)
−0.515700 + 0.856769i \(0.672468\pi\)
\(318\) −1118.84 −0.197299
\(319\) −7058.61 −1.23889
\(320\) 0 0
\(321\) 474.852 0.0825659
\(322\) −1950.70 −0.337603
\(323\) −1575.86 −0.271465
\(324\) −2683.25 −0.460092
\(325\) 0 0
\(326\) 5239.01 0.890068
\(327\) −2503.59 −0.423390
\(328\) 3845.51 0.647356
\(329\) −531.954 −0.0891416
\(330\) 0 0
\(331\) −2300.44 −0.382005 −0.191002 0.981590i \(-0.561174\pi\)
−0.191002 + 0.981590i \(0.561174\pi\)
\(332\) 3011.28 0.497788
\(333\) −4138.35 −0.681022
\(334\) 3761.06 0.616156
\(335\) 0 0
\(336\) −167.269 −0.0271586
\(337\) 6399.32 1.03440 0.517201 0.855864i \(-0.326974\pi\)
0.517201 + 0.855864i \(0.326974\pi\)
\(338\) −3288.26 −0.529164
\(339\) −2750.29 −0.440635
\(340\) 0 0
\(341\) 13507.0 2.14500
\(342\) −1020.54 −0.161359
\(343\) −6314.40 −0.994010
\(344\) 1365.92 0.214086
\(345\) 0 0
\(346\) 5261.50 0.817515
\(347\) 9188.96 1.42158 0.710791 0.703403i \(-0.248337\pi\)
0.710791 + 0.703403i \(0.248337\pi\)
\(348\) 1623.78 0.250125
\(349\) 6327.24 0.970457 0.485229 0.874387i \(-0.338736\pi\)
0.485229 + 0.874387i \(0.338736\pi\)
\(350\) 0 0
\(351\) 1093.12 0.166229
\(352\) −7576.94 −1.14731
\(353\) −8212.76 −1.23830 −0.619152 0.785271i \(-0.712523\pi\)
−0.619152 + 0.785271i \(0.712523\pi\)
\(354\) −849.105 −0.127484
\(355\) 0 0
\(356\) 1850.65 0.275517
\(357\) 1167.27 0.173049
\(358\) −3546.84 −0.523621
\(359\) −5614.24 −0.825371 −0.412685 0.910874i \(-0.635409\pi\)
−0.412685 + 0.910874i \(0.635409\pi\)
\(360\) 0 0
\(361\) −6161.57 −0.898319
\(362\) 2450.37 0.355769
\(363\) −555.091 −0.0802609
\(364\) −759.186 −0.109319
\(365\) 0 0
\(366\) 239.886 0.0342596
\(367\) 3282.91 0.466938 0.233469 0.972364i \(-0.424992\pi\)
0.233469 + 0.972364i \(0.424992\pi\)
\(368\) −915.778 −0.129724
\(369\) 4278.85 0.603654
\(370\) 0 0
\(371\) 4552.81 0.637116
\(372\) −3107.18 −0.433065
\(373\) 9749.67 1.35340 0.676701 0.736258i \(-0.263409\pi\)
0.676701 + 0.736258i \(0.263409\pi\)
\(374\) 3903.31 0.539667
\(375\) 0 0
\(376\) 1014.31 0.139119
\(377\) 2153.05 0.294131
\(378\) 1605.90 0.218515
\(379\) −7875.26 −1.06735 −0.533674 0.845690i \(-0.679189\pi\)
−0.533674 + 0.845690i \(0.679189\pi\)
\(380\) 0 0
\(381\) 1292.21 0.173759
\(382\) −3249.61 −0.435247
\(383\) 1599.65 0.213416 0.106708 0.994290i \(-0.465969\pi\)
0.106708 + 0.994290i \(0.465969\pi\)
\(384\) 1933.29 0.256921
\(385\) 0 0
\(386\) 7158.08 0.943878
\(387\) 1519.84 0.199633
\(388\) −8858.33 −1.15906
\(389\) −5101.31 −0.664901 −0.332451 0.943121i \(-0.607876\pi\)
−0.332451 + 0.943121i \(0.607876\pi\)
\(390\) 0 0
\(391\) 6390.64 0.826569
\(392\) 4637.73 0.597552
\(393\) 1079.39 0.138544
\(394\) −2880.72 −0.368347
\(395\) 0 0
\(396\) −5280.58 −0.670098
\(397\) 8835.01 1.11692 0.558459 0.829532i \(-0.311393\pi\)
0.558459 + 0.829532i \(0.311393\pi\)
\(398\) 5602.65 0.705617
\(399\) −516.597 −0.0648176
\(400\) 0 0
\(401\) −15444.1 −1.92330 −0.961649 0.274284i \(-0.911559\pi\)
−0.961649 + 0.274284i \(0.911559\pi\)
\(402\) −1895.06 −0.235117
\(403\) −4119.97 −0.509256
\(404\) 7862.51 0.968253
\(405\) 0 0
\(406\) 3163.04 0.386648
\(407\) −7005.05 −0.853138
\(408\) −2225.69 −0.270069
\(409\) −13309.7 −1.60910 −0.804552 0.593882i \(-0.797595\pi\)
−0.804552 + 0.593882i \(0.797595\pi\)
\(410\) 0 0
\(411\) −581.440 −0.0697818
\(412\) 7374.59 0.881844
\(413\) 3455.21 0.411671
\(414\) 4138.64 0.491312
\(415\) 0 0
\(416\) 2311.15 0.272388
\(417\) −3353.44 −0.393809
\(418\) −1727.49 −0.202139
\(419\) −2074.44 −0.241869 −0.120934 0.992661i \(-0.538589\pi\)
−0.120934 + 0.992661i \(0.538589\pi\)
\(420\) 0 0
\(421\) 14903.2 1.72526 0.862631 0.505833i \(-0.168815\pi\)
0.862631 + 0.505833i \(0.168815\pi\)
\(422\) 8395.27 0.968426
\(423\) 1128.61 0.129727
\(424\) −8681.08 −0.994317
\(425\) 0 0
\(426\) −2020.26 −0.229770
\(427\) −976.152 −0.110631
\(428\) 1486.42 0.167871
\(429\) 870.995 0.0980234
\(430\) 0 0
\(431\) 7434.74 0.830902 0.415451 0.909616i \(-0.363624\pi\)
0.415451 + 0.909616i \(0.363624\pi\)
\(432\) 753.911 0.0839642
\(433\) −4385.47 −0.486725 −0.243363 0.969935i \(-0.578251\pi\)
−0.243363 + 0.969935i \(0.578251\pi\)
\(434\) −6052.65 −0.669438
\(435\) 0 0
\(436\) −7836.93 −0.860828
\(437\) −2828.30 −0.309602
\(438\) −222.153 −0.0242349
\(439\) −10300.7 −1.11988 −0.559939 0.828534i \(-0.689175\pi\)
−0.559939 + 0.828534i \(0.689175\pi\)
\(440\) 0 0
\(441\) 5160.34 0.557212
\(442\) −1190.60 −0.128125
\(443\) −5700.48 −0.611372 −0.305686 0.952132i \(-0.598886\pi\)
−0.305686 + 0.952132i \(0.598886\pi\)
\(444\) 1611.46 0.172244
\(445\) 0 0
\(446\) −8167.91 −0.867179
\(447\) −4857.83 −0.514021
\(448\) 2621.07 0.276415
\(449\) −8946.30 −0.940317 −0.470158 0.882582i \(-0.655803\pi\)
−0.470158 + 0.882582i \(0.655803\pi\)
\(450\) 0 0
\(451\) 7242.87 0.756216
\(452\) −8609.18 −0.895889
\(453\) −2956.85 −0.306677
\(454\) −2820.56 −0.291576
\(455\) 0 0
\(456\) 985.024 0.101158
\(457\) 16498.3 1.68875 0.844374 0.535755i \(-0.179973\pi\)
0.844374 + 0.535755i \(0.179973\pi\)
\(458\) −7526.33 −0.767865
\(459\) −5261.07 −0.535001
\(460\) 0 0
\(461\) 9016.08 0.910891 0.455445 0.890264i \(-0.349480\pi\)
0.455445 + 0.890264i \(0.349480\pi\)
\(462\) 1279.58 0.128856
\(463\) −3241.41 −0.325359 −0.162679 0.986679i \(-0.552014\pi\)
−0.162679 + 0.986679i \(0.552014\pi\)
\(464\) 1484.93 0.148569
\(465\) 0 0
\(466\) −6858.67 −0.681806
\(467\) −12186.1 −1.20751 −0.603755 0.797170i \(-0.706329\pi\)
−0.603755 + 0.797170i \(0.706329\pi\)
\(468\) 1610.70 0.159092
\(469\) 7711.44 0.759235
\(470\) 0 0
\(471\) −2382.25 −0.233054
\(472\) −6588.24 −0.642475
\(473\) 2572.66 0.250087
\(474\) −777.977 −0.0753875
\(475\) 0 0
\(476\) 3653.88 0.351839
\(477\) −9659.33 −0.927192
\(478\) −5193.82 −0.496987
\(479\) −9110.87 −0.869074 −0.434537 0.900654i \(-0.643088\pi\)
−0.434537 + 0.900654i \(0.643088\pi\)
\(480\) 0 0
\(481\) 2136.71 0.202548
\(482\) −2108.78 −0.199279
\(483\) 2094.97 0.197360
\(484\) −1737.59 −0.163185
\(485\) 0 0
\(486\) −5210.43 −0.486317
\(487\) −535.218 −0.0498009 −0.0249004 0.999690i \(-0.507927\pi\)
−0.0249004 + 0.999690i \(0.507927\pi\)
\(488\) 1861.28 0.172656
\(489\) −5626.50 −0.520325
\(490\) 0 0
\(491\) 10810.8 0.993658 0.496829 0.867848i \(-0.334498\pi\)
0.496829 + 0.867848i \(0.334498\pi\)
\(492\) −1666.17 −0.152676
\(493\) −10362.4 −0.946649
\(494\) 526.925 0.0479909
\(495\) 0 0
\(496\) −2841.49 −0.257231
\(497\) 8220.93 0.741970
\(498\) 1548.12 0.139303
\(499\) 16736.4 1.50146 0.750728 0.660612i \(-0.229703\pi\)
0.750728 + 0.660612i \(0.229703\pi\)
\(500\) 0 0
\(501\) −4039.24 −0.360199
\(502\) 7896.21 0.702042
\(503\) −6612.65 −0.586170 −0.293085 0.956086i \(-0.594682\pi\)
−0.293085 + 0.956086i \(0.594682\pi\)
\(504\) 5865.32 0.518377
\(505\) 0 0
\(506\) 7005.53 0.615482
\(507\) 3531.46 0.309345
\(508\) 4045.00 0.353283
\(509\) 14953.5 1.30216 0.651081 0.759008i \(-0.274316\pi\)
0.651081 + 0.759008i \(0.274316\pi\)
\(510\) 0 0
\(511\) 903.995 0.0782591
\(512\) 3070.27 0.265016
\(513\) 2328.39 0.200392
\(514\) −3384.70 −0.290453
\(515\) 0 0
\(516\) −591.820 −0.0504912
\(517\) 1910.41 0.162514
\(518\) 3139.04 0.266258
\(519\) −5650.65 −0.477911
\(520\) 0 0
\(521\) 822.169 0.0691361 0.0345680 0.999402i \(-0.488994\pi\)
0.0345680 + 0.999402i \(0.488994\pi\)
\(522\) −6710.78 −0.562687
\(523\) −97.2265 −0.00812890 −0.00406445 0.999992i \(-0.501294\pi\)
−0.00406445 + 0.999992i \(0.501294\pi\)
\(524\) 3378.79 0.281685
\(525\) 0 0
\(526\) 11255.3 0.932992
\(527\) 19828.9 1.63902
\(528\) 600.714 0.0495127
\(529\) −697.284 −0.0573095
\(530\) 0 0
\(531\) −7330.65 −0.599102
\(532\) −1617.10 −0.131786
\(533\) −2209.25 −0.179537
\(534\) 951.431 0.0771020
\(535\) 0 0
\(536\) −14703.8 −1.18490
\(537\) 3809.17 0.306104
\(538\) 10406.7 0.833953
\(539\) 8734.98 0.698037
\(540\) 0 0
\(541\) −3856.31 −0.306462 −0.153231 0.988190i \(-0.548968\pi\)
−0.153231 + 0.988190i \(0.548968\pi\)
\(542\) −13123.3 −1.04003
\(543\) −2631.60 −0.207979
\(544\) −11123.3 −0.876670
\(545\) 0 0
\(546\) −390.303 −0.0305923
\(547\) 4147.40 0.324186 0.162093 0.986775i \(-0.448175\pi\)
0.162093 + 0.986775i \(0.448175\pi\)
\(548\) −1820.07 −0.141879
\(549\) 2071.03 0.161000
\(550\) 0 0
\(551\) 4586.07 0.354580
\(552\) −3994.60 −0.308010
\(553\) 3165.78 0.243440
\(554\) −5990.96 −0.459443
\(555\) 0 0
\(556\) −10497.2 −0.800684
\(557\) −85.2280 −0.00648335 −0.00324168 0.999995i \(-0.501032\pi\)
−0.00324168 + 0.999995i \(0.501032\pi\)
\(558\) 12841.4 0.974231
\(559\) −784.724 −0.0593744
\(560\) 0 0
\(561\) −4192.00 −0.315484
\(562\) −9730.37 −0.730340
\(563\) −12824.3 −0.960003 −0.480001 0.877268i \(-0.659364\pi\)
−0.480001 + 0.877268i \(0.659364\pi\)
\(564\) −439.474 −0.0328106
\(565\) 0 0
\(566\) −431.293 −0.0320293
\(567\) 5613.44 0.415771
\(568\) −15675.3 −1.15796
\(569\) −12096.8 −0.891253 −0.445626 0.895219i \(-0.647019\pi\)
−0.445626 + 0.895219i \(0.647019\pi\)
\(570\) 0 0
\(571\) 5688.49 0.416910 0.208455 0.978032i \(-0.433156\pi\)
0.208455 + 0.978032i \(0.433156\pi\)
\(572\) 2726.46 0.199299
\(573\) 3489.95 0.254441
\(574\) −3245.61 −0.236009
\(575\) 0 0
\(576\) −5560.91 −0.402265
\(577\) 9878.78 0.712754 0.356377 0.934342i \(-0.384012\pi\)
0.356377 + 0.934342i \(0.384012\pi\)
\(578\) −2176.25 −0.156609
\(579\) −7687.51 −0.551782
\(580\) 0 0
\(581\) −6299.68 −0.449836
\(582\) −4554.13 −0.324355
\(583\) −16350.5 −1.16152
\(584\) −1723.70 −0.122135
\(585\) 0 0
\(586\) −4395.05 −0.309826
\(587\) 17342.9 1.21945 0.609726 0.792613i \(-0.291280\pi\)
0.609726 + 0.792613i \(0.291280\pi\)
\(588\) −2009.41 −0.140930
\(589\) −8775.69 −0.613915
\(590\) 0 0
\(591\) 3093.78 0.215332
\(592\) 1473.66 0.102309
\(593\) −698.313 −0.0483580 −0.0241790 0.999708i \(-0.507697\pi\)
−0.0241790 + 0.999708i \(0.507697\pi\)
\(594\) −5767.28 −0.398374
\(595\) 0 0
\(596\) −15206.4 −1.04510
\(597\) −6017.03 −0.412497
\(598\) −2136.86 −0.146125
\(599\) 9549.46 0.651386 0.325693 0.945476i \(-0.394402\pi\)
0.325693 + 0.945476i \(0.394402\pi\)
\(600\) 0 0
\(601\) 27369.5 1.85761 0.928805 0.370568i \(-0.120837\pi\)
0.928805 + 0.370568i \(0.120837\pi\)
\(602\) −1152.84 −0.0780501
\(603\) −16360.8 −1.10491
\(604\) −9255.77 −0.623530
\(605\) 0 0
\(606\) 4042.17 0.270960
\(607\) −18179.8 −1.21564 −0.607821 0.794074i \(-0.707956\pi\)
−0.607821 + 0.794074i \(0.707956\pi\)
\(608\) 4922.84 0.328368
\(609\) −3396.99 −0.226031
\(610\) 0 0
\(611\) −582.720 −0.0385832
\(612\) −7752.14 −0.512029
\(613\) 3148.69 0.207462 0.103731 0.994605i \(-0.466922\pi\)
0.103731 + 0.994605i \(0.466922\pi\)
\(614\) 11280.5 0.741440
\(615\) 0 0
\(616\) 9928.30 0.649387
\(617\) 24002.0 1.56610 0.783050 0.621959i \(-0.213663\pi\)
0.783050 + 0.621959i \(0.213663\pi\)
\(618\) 3791.33 0.246779
\(619\) 17997.2 1.16861 0.584304 0.811535i \(-0.301367\pi\)
0.584304 + 0.811535i \(0.301367\pi\)
\(620\) 0 0
\(621\) −9442.40 −0.610162
\(622\) −1395.94 −0.0899871
\(623\) −3871.60 −0.248977
\(624\) −183.232 −0.0117551
\(625\) 0 0
\(626\) −9211.80 −0.588143
\(627\) 1855.25 0.118169
\(628\) −7457.13 −0.473840
\(629\) −10283.7 −0.651892
\(630\) 0 0
\(631\) 5508.64 0.347536 0.173768 0.984787i \(-0.444406\pi\)
0.173768 + 0.984787i \(0.444406\pi\)
\(632\) −6036.35 −0.379926
\(633\) −9016.20 −0.566133
\(634\) −9368.13 −0.586839
\(635\) 0 0
\(636\) 3761.30 0.234505
\(637\) −2664.38 −0.165725
\(638\) −11359.4 −0.704896
\(639\) −17441.7 −1.07979
\(640\) 0 0
\(641\) 11605.9 0.715142 0.357571 0.933886i \(-0.383605\pi\)
0.357571 + 0.933886i \(0.383605\pi\)
\(642\) 764.179 0.0469778
\(643\) −7998.88 −0.490583 −0.245292 0.969449i \(-0.578884\pi\)
−0.245292 + 0.969449i \(0.578884\pi\)
\(644\) 6557.86 0.401267
\(645\) 0 0
\(646\) −2536.03 −0.154457
\(647\) 5421.64 0.329438 0.164719 0.986341i \(-0.447328\pi\)
0.164719 + 0.986341i \(0.447328\pi\)
\(648\) −10703.4 −0.648875
\(649\) −12408.7 −0.750514
\(650\) 0 0
\(651\) 6500.31 0.391348
\(652\) −17612.5 −1.05791
\(653\) 21419.1 1.28361 0.641804 0.766869i \(-0.278186\pi\)
0.641804 + 0.766869i \(0.278186\pi\)
\(654\) −4029.02 −0.240898
\(655\) 0 0
\(656\) −1523.69 −0.0906862
\(657\) −1917.94 −0.113890
\(658\) −856.074 −0.0507192
\(659\) −11435.7 −0.675982 −0.337991 0.941149i \(-0.609747\pi\)
−0.337991 + 0.941149i \(0.609747\pi\)
\(660\) 0 0
\(661\) 27123.2 1.59602 0.798011 0.602643i \(-0.205886\pi\)
0.798011 + 0.602643i \(0.205886\pi\)
\(662\) −3702.10 −0.217351
\(663\) 1278.66 0.0749007
\(664\) 12011.9 0.702038
\(665\) 0 0
\(666\) −6659.86 −0.387484
\(667\) −18598.1 −1.07964
\(668\) −12644.0 −0.732349
\(669\) 8772.02 0.506945
\(670\) 0 0
\(671\) 3505.65 0.201690
\(672\) −3646.44 −0.209322
\(673\) 11097.2 0.635612 0.317806 0.948156i \(-0.397054\pi\)
0.317806 + 0.948156i \(0.397054\pi\)
\(674\) 10298.4 0.588547
\(675\) 0 0
\(676\) 11054.5 0.628952
\(677\) 1647.83 0.0935468 0.0467734 0.998906i \(-0.485106\pi\)
0.0467734 + 0.998906i \(0.485106\pi\)
\(678\) −4426.04 −0.250710
\(679\) 18531.9 1.04740
\(680\) 0 0
\(681\) 3029.18 0.170453
\(682\) 21736.8 1.22045
\(683\) −9256.41 −0.518575 −0.259287 0.965800i \(-0.583488\pi\)
−0.259287 + 0.965800i \(0.583488\pi\)
\(684\) 3430.86 0.191787
\(685\) 0 0
\(686\) −10161.8 −0.565566
\(687\) 8082.99 0.448887
\(688\) −541.214 −0.0299907
\(689\) 4987.29 0.275763
\(690\) 0 0
\(691\) −2404.88 −0.132397 −0.0661983 0.997806i \(-0.521087\pi\)
−0.0661983 + 0.997806i \(0.521087\pi\)
\(692\) −17688.1 −0.971679
\(693\) 11047.1 0.605548
\(694\) 14787.8 0.808843
\(695\) 0 0
\(696\) 6477.21 0.352756
\(697\) 10632.9 0.577833
\(698\) 10182.4 0.552165
\(699\) 7365.94 0.398577
\(700\) 0 0
\(701\) 1158.57 0.0624232 0.0312116 0.999513i \(-0.490063\pi\)
0.0312116 + 0.999513i \(0.490063\pi\)
\(702\) 1759.16 0.0945801
\(703\) 4551.28 0.244174
\(704\) −9413.02 −0.503930
\(705\) 0 0
\(706\) −13216.8 −0.704562
\(707\) −16448.6 −0.874982
\(708\) 2854.52 0.151525
\(709\) −26868.0 −1.42320 −0.711600 0.702585i \(-0.752029\pi\)
−0.711600 + 0.702585i \(0.752029\pi\)
\(710\) 0 0
\(711\) −6716.58 −0.354278
\(712\) 7382.19 0.388566
\(713\) 35588.4 1.86928
\(714\) 1878.49 0.0984601
\(715\) 0 0
\(716\) 11923.8 0.622363
\(717\) 5577.96 0.290534
\(718\) −9035.00 −0.469614
\(719\) 12313.1 0.638666 0.319333 0.947643i \(-0.396541\pi\)
0.319333 + 0.947643i \(0.396541\pi\)
\(720\) 0 0
\(721\) −15427.8 −0.796896
\(722\) −9915.82 −0.511120
\(723\) 2264.75 0.116496
\(724\) −8237.65 −0.422859
\(725\) 0 0
\(726\) −893.308 −0.0456663
\(727\) −4104.02 −0.209367 −0.104683 0.994506i \(-0.533383\pi\)
−0.104683 + 0.994506i \(0.533383\pi\)
\(728\) −3028.37 −0.154174
\(729\) −7795.29 −0.396042
\(730\) 0 0
\(731\) 3776.79 0.191094
\(732\) −806.448 −0.0407202
\(733\) −36113.9 −1.81978 −0.909888 0.414854i \(-0.863833\pi\)
−0.909888 + 0.414854i \(0.863833\pi\)
\(734\) 5283.18 0.265675
\(735\) 0 0
\(736\) −19963.8 −0.999829
\(737\) −27694.1 −1.38416
\(738\) 6885.96 0.343463
\(739\) −4185.77 −0.208357 −0.104179 0.994559i \(-0.533221\pi\)
−0.104179 + 0.994559i \(0.533221\pi\)
\(740\) 0 0
\(741\) −565.898 −0.0280550
\(742\) 7326.84 0.362502
\(743\) 24708.4 1.22001 0.610003 0.792399i \(-0.291168\pi\)
0.610003 + 0.792399i \(0.291168\pi\)
\(744\) −12394.5 −0.610758
\(745\) 0 0
\(746\) 15690.2 0.770050
\(747\) 13365.5 0.654644
\(748\) −13122.2 −0.641435
\(749\) −3109.63 −0.151700
\(750\) 0 0
\(751\) 24154.5 1.17365 0.586824 0.809714i \(-0.300378\pi\)
0.586824 + 0.809714i \(0.300378\pi\)
\(752\) −401.894 −0.0194888
\(753\) −8480.22 −0.410407
\(754\) 3464.90 0.167353
\(755\) 0 0
\(756\) −5398.73 −0.259722
\(757\) 29215.5 1.40272 0.701358 0.712809i \(-0.252577\pi\)
0.701358 + 0.712809i \(0.252577\pi\)
\(758\) −12673.7 −0.607293
\(759\) −7523.67 −0.359805
\(760\) 0 0
\(761\) 29582.7 1.40916 0.704581 0.709624i \(-0.251135\pi\)
0.704581 + 0.709624i \(0.251135\pi\)
\(762\) 2079.56 0.0988643
\(763\) 16395.1 0.777905
\(764\) 10924.5 0.517324
\(765\) 0 0
\(766\) 2574.32 0.121428
\(767\) 3784.95 0.178183
\(768\) 6313.21 0.296625
\(769\) −30737.1 −1.44136 −0.720682 0.693265i \(-0.756171\pi\)
−0.720682 + 0.693265i \(0.756171\pi\)
\(770\) 0 0
\(771\) 3635.04 0.169796
\(772\) −24064.1 −1.12187
\(773\) 13581.6 0.631947 0.315973 0.948768i \(-0.397669\pi\)
0.315973 + 0.948768i \(0.397669\pi\)
\(774\) 2445.89 0.113586
\(775\) 0 0
\(776\) −35335.7 −1.63463
\(777\) −3371.21 −0.155652
\(778\) −8209.54 −0.378311
\(779\) −4705.79 −0.216435
\(780\) 0 0
\(781\) −29523.8 −1.35268
\(782\) 10284.5 0.470296
\(783\) 15310.8 0.698803
\(784\) −1837.59 −0.0837094
\(785\) 0 0
\(786\) 1737.06 0.0788281
\(787\) 37723.8 1.70865 0.854325 0.519739i \(-0.173971\pi\)
0.854325 + 0.519739i \(0.173971\pi\)
\(788\) 9684.41 0.437808
\(789\) −12087.7 −0.545418
\(790\) 0 0
\(791\) 18010.6 0.809588
\(792\) −21064.1 −0.945051
\(793\) −1069.31 −0.0478843
\(794\) 14218.2 0.635497
\(795\) 0 0
\(796\) −18835.0 −0.838680
\(797\) 6349.61 0.282202 0.141101 0.989995i \(-0.454936\pi\)
0.141101 + 0.989995i \(0.454936\pi\)
\(798\) −831.361 −0.0368795
\(799\) 2804.57 0.124178
\(800\) 0 0
\(801\) 8214.07 0.362334
\(802\) −24854.2 −1.09431
\(803\) −3246.51 −0.142674
\(804\) 6370.81 0.279454
\(805\) 0 0
\(806\) −6630.27 −0.289753
\(807\) −11176.4 −0.487521
\(808\) 31363.4 1.36554
\(809\) 32315.3 1.40438 0.702191 0.711988i \(-0.252205\pi\)
0.702191 + 0.711988i \(0.252205\pi\)
\(810\) 0 0
\(811\) −27000.2 −1.16906 −0.584528 0.811373i \(-0.698720\pi\)
−0.584528 + 0.811373i \(0.698720\pi\)
\(812\) −10633.5 −0.459561
\(813\) 14093.9 0.607989
\(814\) −11273.2 −0.485413
\(815\) 0 0
\(816\) 881.877 0.0378332
\(817\) −1671.49 −0.0715766
\(818\) −21419.4 −0.915538
\(819\) −3369.64 −0.143766
\(820\) 0 0
\(821\) −8734.23 −0.371287 −0.185644 0.982617i \(-0.559437\pi\)
−0.185644 + 0.982617i \(0.559437\pi\)
\(822\) −935.712 −0.0397040
\(823\) −37165.8 −1.57414 −0.787070 0.616864i \(-0.788403\pi\)
−0.787070 + 0.616864i \(0.788403\pi\)
\(824\) 29417.1 1.24368
\(825\) 0 0
\(826\) 5560.48 0.234230
\(827\) −44504.9 −1.87133 −0.935664 0.352892i \(-0.885198\pi\)
−0.935664 + 0.352892i \(0.885198\pi\)
\(828\) −13913.3 −0.583962
\(829\) 8435.36 0.353404 0.176702 0.984264i \(-0.443457\pi\)
0.176702 + 0.984264i \(0.443457\pi\)
\(830\) 0 0
\(831\) 6434.07 0.268586
\(832\) 2871.20 0.119641
\(833\) 12823.4 0.533378
\(834\) −5396.69 −0.224067
\(835\) 0 0
\(836\) 5807.47 0.240258
\(837\) −29298.0 −1.20990
\(838\) −3338.40 −0.137617
\(839\) −15830.0 −0.651384 −0.325692 0.945476i \(-0.605597\pi\)
−0.325692 + 0.945476i \(0.605597\pi\)
\(840\) 0 0
\(841\) 5767.62 0.236484
\(842\) 23983.7 0.981629
\(843\) 10450.0 0.426950
\(844\) −28223.3 −1.15105
\(845\) 0 0
\(846\) 1816.27 0.0738115
\(847\) 3635.08 0.147465
\(848\) 3439.67 0.139291
\(849\) 463.192 0.0187240
\(850\) 0 0
\(851\) −18456.9 −0.743473
\(852\) 6791.73 0.273099
\(853\) 25517.9 1.02429 0.512144 0.858900i \(-0.328852\pi\)
0.512144 + 0.858900i \(0.328852\pi\)
\(854\) −1570.92 −0.0629460
\(855\) 0 0
\(856\) 5929.29 0.236751
\(857\) −1353.59 −0.0539530 −0.0269765 0.999636i \(-0.508588\pi\)
−0.0269765 + 0.999636i \(0.508588\pi\)
\(858\) 1401.69 0.0557728
\(859\) 44829.9 1.78065 0.890325 0.455326i \(-0.150477\pi\)
0.890325 + 0.455326i \(0.150477\pi\)
\(860\) 0 0
\(861\) 3485.66 0.137969
\(862\) 11964.7 0.472761
\(863\) 22467.5 0.886216 0.443108 0.896468i \(-0.353876\pi\)
0.443108 + 0.896468i \(0.353876\pi\)
\(864\) 16435.1 0.647145
\(865\) 0 0
\(866\) −7057.53 −0.276934
\(867\) 2337.21 0.0915521
\(868\) 20347.8 0.795679
\(869\) −11369.2 −0.443815
\(870\) 0 0
\(871\) 8447.37 0.328620
\(872\) −31261.3 −1.21404
\(873\) −39317.6 −1.52428
\(874\) −4551.59 −0.176155
\(875\) 0 0
\(876\) 746.836 0.0288051
\(877\) −408.941 −0.0157457 −0.00787283 0.999969i \(-0.502506\pi\)
−0.00787283 + 0.999969i \(0.502506\pi\)
\(878\) −16576.9 −0.637181
\(879\) 4720.12 0.181121
\(880\) 0 0
\(881\) −20458.5 −0.782366 −0.391183 0.920313i \(-0.627934\pi\)
−0.391183 + 0.920313i \(0.627934\pi\)
\(882\) 8304.54 0.317039
\(883\) −3746.69 −0.142793 −0.0713965 0.997448i \(-0.522746\pi\)
−0.0713965 + 0.997448i \(0.522746\pi\)
\(884\) 4002.58 0.152286
\(885\) 0 0
\(886\) −9173.78 −0.347855
\(887\) −5289.38 −0.200225 −0.100113 0.994976i \(-0.531920\pi\)
−0.100113 + 0.994976i \(0.531920\pi\)
\(888\) 6428.06 0.242919
\(889\) −8462.24 −0.319251
\(890\) 0 0
\(891\) −20159.5 −0.757990
\(892\) 27458.9 1.03071
\(893\) −1241.22 −0.0465126
\(894\) −7817.70 −0.292464
\(895\) 0 0
\(896\) −12660.4 −0.472046
\(897\) 2294.90 0.0854232
\(898\) −14397.3 −0.535015
\(899\) −57706.3 −2.14084
\(900\) 0 0
\(901\) −24003.3 −0.887531
\(902\) 11656.0 0.430267
\(903\) 1238.10 0.0456274
\(904\) −34341.8 −1.26349
\(905\) 0 0
\(906\) −4758.46 −0.174491
\(907\) 10720.8 0.392480 0.196240 0.980556i \(-0.437127\pi\)
0.196240 + 0.980556i \(0.437127\pi\)
\(908\) 9482.18 0.346561
\(909\) 34897.6 1.27336
\(910\) 0 0
\(911\) 3405.66 0.123858 0.0619290 0.998081i \(-0.480275\pi\)
0.0619290 + 0.998081i \(0.480275\pi\)
\(912\) −390.292 −0.0141709
\(913\) 22624.0 0.820094
\(914\) 26550.7 0.960853
\(915\) 0 0
\(916\) 25302.0 0.912666
\(917\) −7068.52 −0.254551
\(918\) −8466.64 −0.304402
\(919\) 3184.34 0.114300 0.0571500 0.998366i \(-0.481799\pi\)
0.0571500 + 0.998366i \(0.481799\pi\)
\(920\) 0 0
\(921\) −12114.8 −0.433439
\(922\) 14509.6 0.518273
\(923\) 9005.48 0.321147
\(924\) −4301.69 −0.153155
\(925\) 0 0
\(926\) −5216.40 −0.185121
\(927\) 32732.0 1.15972
\(928\) 32371.1 1.14508
\(929\) 24847.1 0.877510 0.438755 0.898607i \(-0.355420\pi\)
0.438755 + 0.898607i \(0.355420\pi\)
\(930\) 0 0
\(931\) −5675.24 −0.199783
\(932\) 23057.5 0.810379
\(933\) 1499.18 0.0526056
\(934\) −19611.2 −0.687041
\(935\) 0 0
\(936\) 6425.06 0.224369
\(937\) −16072.8 −0.560381 −0.280191 0.959944i \(-0.590398\pi\)
−0.280191 + 0.959944i \(0.590398\pi\)
\(938\) 12410.0 0.431985
\(939\) 9893.12 0.343823
\(940\) 0 0
\(941\) 49359.1 1.70995 0.854974 0.518672i \(-0.173573\pi\)
0.854974 + 0.518672i \(0.173573\pi\)
\(942\) −3833.76 −0.132602
\(943\) 19083.6 0.659010
\(944\) 2610.43 0.0900025
\(945\) 0 0
\(946\) 4140.18 0.142293
\(947\) −19624.5 −0.673400 −0.336700 0.941612i \(-0.609311\pi\)
−0.336700 + 0.941612i \(0.609311\pi\)
\(948\) 2615.41 0.0896038
\(949\) 990.266 0.0338729
\(950\) 0 0
\(951\) 10061.0 0.343061
\(952\) 14575.2 0.496204
\(953\) −39172.6 −1.33151 −0.665753 0.746172i \(-0.731890\pi\)
−0.665753 + 0.746172i \(0.731890\pi\)
\(954\) −15544.8 −0.527548
\(955\) 0 0
\(956\) 17460.6 0.590707
\(957\) 12199.6 0.412076
\(958\) −14662.1 −0.494480
\(959\) 3807.64 0.128212
\(960\) 0 0
\(961\) 80632.9 2.70662
\(962\) 3438.61 0.115244
\(963\) 6597.46 0.220768
\(964\) 7089.30 0.236858
\(965\) 0 0
\(966\) 3371.44 0.112292
\(967\) 50809.7 1.68969 0.844845 0.535010i \(-0.179692\pi\)
0.844845 + 0.535010i \(0.179692\pi\)
\(968\) −6931.21 −0.230142
\(969\) 2723.60 0.0902939
\(970\) 0 0
\(971\) −49995.3 −1.65235 −0.826173 0.563417i \(-0.809486\pi\)
−0.826173 + 0.563417i \(0.809486\pi\)
\(972\) 17516.4 0.578025
\(973\) 21960.4 0.723555
\(974\) −861.326 −0.0283354
\(975\) 0 0
\(976\) −737.488 −0.0241869
\(977\) 6507.03 0.213079 0.106540 0.994308i \(-0.466023\pi\)
0.106540 + 0.994308i \(0.466023\pi\)
\(978\) −9054.73 −0.296052
\(979\) 13904.1 0.453908
\(980\) 0 0
\(981\) −34784.1 −1.13208
\(982\) 17397.9 0.565365
\(983\) 37044.4 1.20197 0.600983 0.799262i \(-0.294776\pi\)
0.600983 + 0.799262i \(0.294776\pi\)
\(984\) −6646.30 −0.215321
\(985\) 0 0
\(986\) −16676.2 −0.538618
\(987\) 919.391 0.0296500
\(988\) −1771.42 −0.0570408
\(989\) 6778.46 0.217940
\(990\) 0 0
\(991\) −17372.8 −0.556877 −0.278439 0.960454i \(-0.589817\pi\)
−0.278439 + 0.960454i \(0.589817\pi\)
\(992\) −61943.8 −1.98258
\(993\) 3975.91 0.127061
\(994\) 13230.0 0.422162
\(995\) 0 0
\(996\) −5204.48 −0.165573
\(997\) 45015.4 1.42994 0.714971 0.699154i \(-0.246440\pi\)
0.714971 + 0.699154i \(0.246440\pi\)
\(998\) 26934.0 0.854289
\(999\) 15194.6 0.481217
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 \(a_p\))