Properties

Label 1175.4.a.a.1.1
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 1.1
Root \(1.43163\)
Character \(\chi\) = 1175.1

$q$-expansion

\(f(q)\)  \(=\)  \(q\)\(-1.51882 q^{2}\) \(+5.95044 q^{3}\) \(-5.69320 q^{4}\) \(-9.03763 q^{6}\) \(+3.35636 q^{7}\) \(+20.7975 q^{8}\) \(+8.40778 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.51882 q^{2}\) \(+5.95044 q^{3}\) \(-5.69320 q^{4}\) \(-9.03763 q^{6}\) \(+3.35636 q^{7}\) \(+20.7975 q^{8}\) \(+8.40778 q^{9}\) \(+20.2172 q^{11}\) \(-33.8770 q^{12}\) \(+5.57597 q^{13}\) \(-5.09770 q^{14}\) \(+13.9580 q^{16}\) \(+26.5077 q^{17}\) \(-12.7699 q^{18}\) \(-25.3539 q^{19}\) \(+19.9718 q^{21}\) \(-30.7062 q^{22}\) \(+90.2723 q^{23}\) \(+123.754 q^{24}\) \(-8.46888 q^{26}\) \(-110.632 q^{27}\) \(-19.1084 q^{28}\) \(-123.275 q^{29}\) \(+129.587 q^{31}\) \(-187.579 q^{32}\) \(+120.301 q^{33}\) \(-40.2604 q^{34}\) \(-47.8671 q^{36}\) \(+213.578 q^{37}\) \(+38.5079 q^{38}\) \(+33.1795 q^{39}\) \(-124.700 q^{41}\) \(-30.3336 q^{42}\) \(+424.723 q^{43}\) \(-115.100 q^{44}\) \(-137.107 q^{46}\) \(-47.0000 q^{47}\) \(+83.0566 q^{48}\) \(-331.735 q^{49}\) \(+157.733 q^{51}\) \(-31.7451 q^{52}\) \(-361.680 q^{53}\) \(+168.030 q^{54}\) \(+69.8038 q^{56}\) \(-150.867 q^{57}\) \(+187.233 q^{58}\) \(+836.472 q^{59}\) \(-194.845 q^{61}\) \(-196.818 q^{62}\) \(+28.2195 q^{63}\) \(+173.234 q^{64}\) \(-182.715 q^{66}\) \(-902.163 q^{67}\) \(-150.914 q^{68}\) \(+537.160 q^{69}\) \(+690.711 q^{71}\) \(+174.860 q^{72}\) \(+698.209 q^{73}\) \(-324.386 q^{74}\) \(+144.345 q^{76}\) \(+67.8561 q^{77}\) \(-50.3936 q^{78}\) \(-449.718 q^{79}\) \(-885.319 q^{81}\) \(+189.396 q^{82}\) \(+543.425 q^{83}\) \(-113.704 q^{84}\) \(-645.076 q^{86}\) \(-733.543 q^{87}\) \(+420.465 q^{88}\) \(+725.592 q^{89}\) \(+18.7150 q^{91}\) \(-513.938 q^{92}\) \(+771.099 q^{93}\) \(+71.3844 q^{94}\) \(-1116.18 q^{96}\) \(+214.741 q^{97}\) \(+503.844 q^{98}\) \(+169.981 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)  \(=\)  \(3q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 5q^{4} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 45q^{7} \) \(\mathstrut +\mathstrut 39q^{8} \) \(\mathstrut -\mathstrut 42q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 5q^{4} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 45q^{7} \) \(\mathstrut +\mathstrut 39q^{8} \) \(\mathstrut -\mathstrut 42q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut -\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 80q^{13} \) \(\mathstrut +\mathstrut 162q^{14} \) \(\mathstrut +\mathstrut 89q^{16} \) \(\mathstrut +\mathstrut 39q^{17} \) \(\mathstrut -\mathstrut 181q^{18} \) \(\mathstrut -\mathstrut 24q^{19} \) \(\mathstrut +\mathstrut 24q^{21} \) \(\mathstrut +\mathstrut 14q^{22} \) \(\mathstrut -\mathstrut 120q^{23} \) \(\mathstrut +\mathstrut 192q^{24} \) \(\mathstrut +\mathstrut 316q^{26} \) \(\mathstrut -\mathstrut 64q^{27} \) \(\mathstrut +\mathstrut 408q^{28} \) \(\mathstrut -\mathstrut 184q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut +\mathstrut 7q^{32} \) \(\mathstrut +\mathstrut 208q^{33} \) \(\mathstrut +\mathstrut 218q^{34} \) \(\mathstrut -\mathstrut 343q^{36} \) \(\mathstrut +\mathstrut 589q^{37} \) \(\mathstrut -\mathstrut 42q^{38} \) \(\mathstrut +\mathstrut 60q^{39} \) \(\mathstrut -\mathstrut 92q^{41} \) \(\mathstrut +\mathstrut 54q^{42} \) \(\mathstrut +\mathstrut 250q^{43} \) \(\mathstrut +\mathstrut 466q^{44} \) \(\mathstrut -\mathstrut 816q^{46} \) \(\mathstrut -\mathstrut 141q^{47} \) \(\mathstrut +\mathstrut 120q^{48} \) \(\mathstrut +\mathstrut 30q^{49} \) \(\mathstrut +\mathstrut 317q^{51} \) \(\mathstrut +\mathstrut 900q^{52} \) \(\mathstrut -\mathstrut 459q^{53} \) \(\mathstrut +\mathstrut 106q^{54} \) \(\mathstrut +\mathstrut 1032q^{56} \) \(\mathstrut -\mathstrut 216q^{57} \) \(\mathstrut -\mathstrut 684q^{58} \) \(\mathstrut +\mathstrut 579q^{59} \) \(\mathstrut +\mathstrut 267q^{61} \) \(\mathstrut +\mathstrut 244q^{62} \) \(\mathstrut -\mathstrut 1044q^{63} \) \(\mathstrut -\mathstrut 87q^{64} \) \(\mathstrut +\mathstrut 16q^{66} \) \(\mathstrut +\mathstrut 540q^{67} \) \(\mathstrut +\mathstrut 1334q^{68} \) \(\mathstrut +\mathstrut 642q^{69} \) \(\mathstrut +\mathstrut 749q^{71} \) \(\mathstrut -\mathstrut 357q^{72} \) \(\mathstrut +\mathstrut 1924q^{73} \) \(\mathstrut +\mathstrut 950q^{74} \) \(\mathstrut -\mathstrut 402q^{76} \) \(\mathstrut +\mathstrut 288q^{77} \) \(\mathstrut +\mathstrut 152q^{78} \) \(\mathstrut +\mathstrut 805q^{79} \) \(\mathstrut +\mathstrut 291q^{81} \) \(\mathstrut +\mathstrut 938q^{82} \) \(\mathstrut -\mathstrut 712q^{83} \) \(\mathstrut +\mathstrut 372q^{84} \) \(\mathstrut -\mathstrut 1294q^{86} \) \(\mathstrut -\mathstrut 1216q^{87} \) \(\mathstrut +\mathstrut 2190q^{88} \) \(\mathstrut +\mathstrut 835q^{89} \) \(\mathstrut +\mathstrut 2040q^{91} \) \(\mathstrut -\mathstrut 1596q^{92} \) \(\mathstrut +\mathstrut 1500q^{93} \) \(\mathstrut -\mathstrut 235q^{94} \) \(\mathstrut -\mathstrut 1432q^{96} \) \(\mathstrut +\mathstrut 2243q^{97} \) \(\mathstrut +\mathstrut 2989q^{98} \) \(\mathstrut +\mathstrut 554q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.51882 −0.536983 −0.268491 0.963282i \(-0.586525\pi\)
−0.268491 + 0.963282i \(0.586525\pi\)
\(3\) 5.95044 1.14516 0.572582 0.819848i \(-0.305942\pi\)
0.572582 + 0.819848i \(0.305942\pi\)
\(4\) −5.69320 −0.711649
\(5\) 0 0
\(6\) −9.03763 −0.614933
\(7\) 3.35636 0.181226 0.0906132 0.995886i \(-0.471117\pi\)
0.0906132 + 0.995886i \(0.471117\pi\)
\(8\) 20.7975 0.919126
\(9\) 8.40778 0.311399
\(10\) 0 0
\(11\) 20.2172 0.554155 0.277077 0.960848i \(-0.410634\pi\)
0.277077 + 0.960848i \(0.410634\pi\)
\(12\) −33.8770 −0.814955
\(13\) 5.57597 0.118961 0.0594807 0.998229i \(-0.481056\pi\)
0.0594807 + 0.998229i \(0.481056\pi\)
\(14\) −5.09770 −0.0973155
\(15\) 0 0
\(16\) 13.9580 0.218094
\(17\) 26.5077 0.378180 0.189090 0.981960i \(-0.439446\pi\)
0.189090 + 0.981960i \(0.439446\pi\)
\(18\) −12.7699 −0.167216
\(19\) −25.3539 −0.306136 −0.153068 0.988216i \(-0.548915\pi\)
−0.153068 + 0.988216i \(0.548915\pi\)
\(20\) 0 0
\(21\) 19.9718 0.207534
\(22\) −30.7062 −0.297572
\(23\) 90.2723 0.818395 0.409197 0.912446i \(-0.365809\pi\)
0.409197 + 0.912446i \(0.365809\pi\)
\(24\) 123.754 1.05255
\(25\) 0 0
\(26\) −8.46888 −0.0638802
\(27\) −110.632 −0.788560
\(28\) −19.1084 −0.128970
\(29\) −123.275 −0.789368 −0.394684 0.918817i \(-0.629146\pi\)
−0.394684 + 0.918817i \(0.629146\pi\)
\(30\) 0 0
\(31\) 129.587 0.750789 0.375395 0.926865i \(-0.377507\pi\)
0.375395 + 0.926865i \(0.377507\pi\)
\(32\) −187.579 −1.03624
\(33\) 120.301 0.634598
\(34\) −40.2604 −0.203076
\(35\) 0 0
\(36\) −47.8671 −0.221607
\(37\) 213.578 0.948972 0.474486 0.880263i \(-0.342634\pi\)
0.474486 + 0.880263i \(0.342634\pi\)
\(38\) 38.5079 0.164390
\(39\) 33.1795 0.136230
\(40\) 0 0
\(41\) −124.700 −0.474995 −0.237498 0.971388i \(-0.576327\pi\)
−0.237498 + 0.971388i \(0.576327\pi\)
\(42\) −30.3336 −0.111442
\(43\) 424.723 1.50627 0.753135 0.657866i \(-0.228541\pi\)
0.753135 + 0.657866i \(0.228541\pi\)
\(44\) −115.100 −0.394364
\(45\) 0 0
\(46\) −137.107 −0.439464
\(47\) −47.0000 −0.145865
\(48\) 83.0566 0.249754
\(49\) −331.735 −0.967157
\(50\) 0 0
\(51\) 157.733 0.433078
\(52\) −31.7451 −0.0846588
\(53\) −361.680 −0.937370 −0.468685 0.883365i \(-0.655272\pi\)
−0.468685 + 0.883365i \(0.655272\pi\)
\(54\) 168.030 0.423443
\(55\) 0 0
\(56\) 69.8038 0.166570
\(57\) −150.867 −0.350576
\(58\) 187.233 0.423877
\(59\) 836.472 1.84575 0.922876 0.385097i \(-0.125832\pi\)
0.922876 + 0.385097i \(0.125832\pi\)
\(60\) 0 0
\(61\) −194.845 −0.408973 −0.204486 0.978869i \(-0.565552\pi\)
−0.204486 + 0.978869i \(0.565552\pi\)
\(62\) −196.818 −0.403161
\(63\) 28.2195 0.0564338
\(64\) 173.234 0.338348
\(65\) 0 0
\(66\) −182.715 −0.340768
\(67\) −902.163 −1.64503 −0.822513 0.568746i \(-0.807429\pi\)
−0.822513 + 0.568746i \(0.807429\pi\)
\(68\) −150.914 −0.269132
\(69\) 537.160 0.937196
\(70\) 0 0
\(71\) 690.711 1.15454 0.577270 0.816553i \(-0.304118\pi\)
0.577270 + 0.816553i \(0.304118\pi\)
\(72\) 174.860 0.286215
\(73\) 698.209 1.11944 0.559720 0.828682i \(-0.310909\pi\)
0.559720 + 0.828682i \(0.310909\pi\)
\(74\) −324.386 −0.509582
\(75\) 0 0
\(76\) 144.345 0.217862
\(77\) 67.8561 0.100427
\(78\) −50.3936 −0.0731533
\(79\) −449.718 −0.640471 −0.320235 0.947338i \(-0.603762\pi\)
−0.320235 + 0.947338i \(0.603762\pi\)
\(80\) 0 0
\(81\) −885.319 −1.21443
\(82\) 189.396 0.255064
\(83\) 543.425 0.718659 0.359329 0.933211i \(-0.383005\pi\)
0.359329 + 0.933211i \(0.383005\pi\)
\(84\) −113.704 −0.147691
\(85\) 0 0
\(86\) −645.076 −0.808841
\(87\) −733.543 −0.903955
\(88\) 420.465 0.509338
\(89\) 725.592 0.864187 0.432093 0.901829i \(-0.357775\pi\)
0.432093 + 0.901829i \(0.357775\pi\)
\(90\) 0 0
\(91\) 18.7150 0.0215589
\(92\) −513.938 −0.582410
\(93\) 771.099 0.859776
\(94\) 71.3844 0.0783270
\(95\) 0 0
\(96\) −1116.18 −1.18666
\(97\) 214.741 0.224780 0.112390 0.993664i \(-0.464149\pi\)
0.112390 + 0.993664i \(0.464149\pi\)
\(98\) 503.844 0.519347
\(99\) 169.981 0.172563
\(100\) 0 0
\(101\) 1390.95 1.37034 0.685171 0.728382i \(-0.259727\pi\)
0.685171 + 0.728382i \(0.259727\pi\)
\(102\) −239.567 −0.232556
\(103\) 1545.53 1.47850 0.739249 0.673432i \(-0.235181\pi\)
0.739249 + 0.673432i \(0.235181\pi\)
\(104\) 115.966 0.109340
\(105\) 0 0
\(106\) 549.326 0.503351
\(107\) 1327.49 1.19938 0.599688 0.800234i \(-0.295291\pi\)
0.599688 + 0.800234i \(0.295291\pi\)
\(108\) 629.849 0.561179
\(109\) −973.505 −0.855457 −0.427729 0.903907i \(-0.640686\pi\)
−0.427729 + 0.903907i \(0.640686\pi\)
\(110\) 0 0
\(111\) 1270.88 1.08673
\(112\) 46.8482 0.0395245
\(113\) 365.992 0.304687 0.152343 0.988328i \(-0.451318\pi\)
0.152343 + 0.988328i \(0.451318\pi\)
\(114\) 229.139 0.188253
\(115\) 0 0
\(116\) 701.831 0.561753
\(117\) 46.8816 0.0370445
\(118\) −1270.45 −0.991137
\(119\) 88.9695 0.0685363
\(120\) 0 0
\(121\) −922.266 −0.692912
\(122\) 295.934 0.219611
\(123\) −742.018 −0.543947
\(124\) −737.763 −0.534299
\(125\) 0 0
\(126\) −42.8603 −0.0303040
\(127\) 1034.31 0.722682 0.361341 0.932434i \(-0.382319\pi\)
0.361341 + 0.932434i \(0.382319\pi\)
\(128\) 1237.52 0.854552
\(129\) 2527.29 1.72493
\(130\) 0 0
\(131\) −98.9237 −0.0659771 −0.0329885 0.999456i \(-0.510502\pi\)
−0.0329885 + 0.999456i \(0.510502\pi\)
\(132\) −684.898 −0.451611
\(133\) −85.0968 −0.0554799
\(134\) 1370.22 0.883351
\(135\) 0 0
\(136\) 551.293 0.347596
\(137\) 1607.67 1.00257 0.501286 0.865282i \(-0.332860\pi\)
0.501286 + 0.865282i \(0.332860\pi\)
\(138\) −815.848 −0.503258
\(139\) 3175.56 1.93775 0.968875 0.247549i \(-0.0796251\pi\)
0.968875 + 0.247549i \(0.0796251\pi\)
\(140\) 0 0
\(141\) −279.671 −0.167039
\(142\) −1049.06 −0.619968
\(143\) 112.730 0.0659230
\(144\) 117.356 0.0679145
\(145\) 0 0
\(146\) −1060.45 −0.601120
\(147\) −1973.97 −1.10755
\(148\) −1215.94 −0.675336
\(149\) −1155.85 −0.635509 −0.317754 0.948173i \(-0.602929\pi\)
−0.317754 + 0.948173i \(0.602929\pi\)
\(150\) 0 0
\(151\) −1941.03 −1.04608 −0.523042 0.852307i \(-0.675203\pi\)
−0.523042 + 0.852307i \(0.675203\pi\)
\(152\) −527.297 −0.281378
\(153\) 222.871 0.117765
\(154\) −103.061 −0.0539278
\(155\) 0 0
\(156\) −188.898 −0.0969481
\(157\) 1023.76 0.520414 0.260207 0.965553i \(-0.416209\pi\)
0.260207 + 0.965553i \(0.416209\pi\)
\(158\) 683.038 0.343922
\(159\) −2152.16 −1.07344
\(160\) 0 0
\(161\) 302.986 0.148315
\(162\) 1344.64 0.652128
\(163\) −728.517 −0.350073 −0.175036 0.984562i \(-0.556004\pi\)
−0.175036 + 0.984562i \(0.556004\pi\)
\(164\) 709.939 0.338030
\(165\) 0 0
\(166\) −825.363 −0.385907
\(167\) 1594.21 0.738706 0.369353 0.929289i \(-0.379579\pi\)
0.369353 + 0.929289i \(0.379579\pi\)
\(168\) 415.363 0.190750
\(169\) −2165.91 −0.985848
\(170\) 0 0
\(171\) −213.170 −0.0953306
\(172\) −2418.03 −1.07194
\(173\) 1111.94 0.488665 0.244332 0.969692i \(-0.421431\pi\)
0.244332 + 0.969692i \(0.421431\pi\)
\(174\) 1114.12 0.485408
\(175\) 0 0
\(176\) 282.192 0.120858
\(177\) 4977.38 2.11369
\(178\) −1102.04 −0.464053
\(179\) 924.477 0.386026 0.193013 0.981196i \(-0.438174\pi\)
0.193013 + 0.981196i \(0.438174\pi\)
\(180\) 0 0
\(181\) 1695.96 0.696462 0.348231 0.937409i \(-0.386783\pi\)
0.348231 + 0.937409i \(0.386783\pi\)
\(182\) −28.4246 −0.0115768
\(183\) −1159.41 −0.468340
\(184\) 1877.43 0.752208
\(185\) 0 0
\(186\) −1171.16 −0.461685
\(187\) 535.911 0.209570
\(188\) 267.580 0.103805
\(189\) −371.321 −0.142908
\(190\) 0 0
\(191\) −1985.24 −0.752079 −0.376039 0.926604i \(-0.622714\pi\)
−0.376039 + 0.926604i \(0.622714\pi\)
\(192\) 1030.82 0.387464
\(193\) −172.859 −0.0644696 −0.0322348 0.999480i \(-0.510262\pi\)
−0.0322348 + 0.999480i \(0.510262\pi\)
\(194\) −326.152 −0.120703
\(195\) 0 0
\(196\) 1888.63 0.688277
\(197\) −18.9634 −0.00685829 −0.00342915 0.999994i \(-0.501092\pi\)
−0.00342915 + 0.999994i \(0.501092\pi\)
\(198\) −258.171 −0.0926636
\(199\) 2200.21 0.783762 0.391881 0.920016i \(-0.371824\pi\)
0.391881 + 0.920016i \(0.371824\pi\)
\(200\) 0 0
\(201\) −5368.27 −1.88382
\(202\) −2112.60 −0.735850
\(203\) −413.757 −0.143054
\(204\) −898.003 −0.308200
\(205\) 0 0
\(206\) −2347.37 −0.793928
\(207\) 758.990 0.254848
\(208\) 77.8297 0.0259448
\(209\) −512.584 −0.169647
\(210\) 0 0
\(211\) 236.491 0.0771599 0.0385800 0.999256i \(-0.487717\pi\)
0.0385800 + 0.999256i \(0.487717\pi\)
\(212\) 2059.12 0.667079
\(213\) 4110.04 1.32214
\(214\) −2016.21 −0.644044
\(215\) 0 0
\(216\) −2300.86 −0.724787
\(217\) 434.940 0.136063
\(218\) 1478.58 0.459366
\(219\) 4154.65 1.28194
\(220\) 0 0
\(221\) 147.806 0.0449888
\(222\) −1930.24 −0.583555
\(223\) −1396.42 −0.419334 −0.209667 0.977773i \(-0.567238\pi\)
−0.209667 + 0.977773i \(0.567238\pi\)
\(224\) −629.584 −0.187794
\(225\) 0 0
\(226\) −555.874 −0.163612
\(227\) −3034.35 −0.887211 −0.443605 0.896222i \(-0.646301\pi\)
−0.443605 + 0.896222i \(0.646301\pi\)
\(228\) 858.915 0.249487
\(229\) 4938.80 1.42517 0.712587 0.701584i \(-0.247523\pi\)
0.712587 + 0.701584i \(0.247523\pi\)
\(230\) 0 0
\(231\) 403.774 0.115006
\(232\) −2563.81 −0.725529
\(233\) −4759.80 −1.33831 −0.669153 0.743125i \(-0.733343\pi\)
−0.669153 + 0.743125i \(0.733343\pi\)
\(234\) −71.2045 −0.0198922
\(235\) 0 0
\(236\) −4762.20 −1.31353
\(237\) −2676.02 −0.733443
\(238\) −135.128 −0.0368028
\(239\) 3666.84 0.992419 0.496210 0.868203i \(-0.334725\pi\)
0.496210 + 0.868203i \(0.334725\pi\)
\(240\) 0 0
\(241\) 6119.79 1.63573 0.817864 0.575412i \(-0.195158\pi\)
0.817864 + 0.575412i \(0.195158\pi\)
\(242\) 1400.75 0.372082
\(243\) −2280.98 −0.602160
\(244\) 1109.29 0.291045
\(245\) 0 0
\(246\) 1126.99 0.292090
\(247\) −141.373 −0.0364183
\(248\) 2695.07 0.690070
\(249\) 3233.62 0.822982
\(250\) 0 0
\(251\) −4257.22 −1.07057 −0.535285 0.844671i \(-0.679796\pi\)
−0.535285 + 0.844671i \(0.679796\pi\)
\(252\) −160.659 −0.0401611
\(253\) 1825.05 0.453517
\(254\) −1570.93 −0.388068
\(255\) 0 0
\(256\) −3265.45 −0.797228
\(257\) 6251.15 1.51726 0.758630 0.651522i \(-0.225869\pi\)
0.758630 + 0.651522i \(0.225869\pi\)
\(258\) −3838.49 −0.926255
\(259\) 716.844 0.171979
\(260\) 0 0
\(261\) −1036.47 −0.245809
\(262\) 150.247 0.0354286
\(263\) 5008.06 1.17418 0.587091 0.809521i \(-0.300273\pi\)
0.587091 + 0.809521i \(0.300273\pi\)
\(264\) 2501.96 0.583276
\(265\) 0 0
\(266\) 129.247 0.0297918
\(267\) 4317.60 0.989635
\(268\) 5136.19 1.17068
\(269\) 4565.07 1.03471 0.517356 0.855770i \(-0.326916\pi\)
0.517356 + 0.855770i \(0.326916\pi\)
\(270\) 0 0
\(271\) 3111.82 0.697526 0.348763 0.937211i \(-0.386602\pi\)
0.348763 + 0.937211i \(0.386602\pi\)
\(272\) 369.996 0.0824790
\(273\) 111.362 0.0246885
\(274\) −2441.75 −0.538364
\(275\) 0 0
\(276\) −3058.16 −0.666955
\(277\) 4349.10 0.943364 0.471682 0.881769i \(-0.343647\pi\)
0.471682 + 0.881769i \(0.343647\pi\)
\(278\) −4823.09 −1.04054
\(279\) 1089.54 0.233795
\(280\) 0 0
\(281\) −1640.50 −0.348271 −0.174135 0.984722i \(-0.555713\pi\)
−0.174135 + 0.984722i \(0.555713\pi\)
\(282\) 424.769 0.0896972
\(283\) 6268.38 1.31667 0.658333 0.752727i \(-0.271262\pi\)
0.658333 + 0.752727i \(0.271262\pi\)
\(284\) −3932.36 −0.821628
\(285\) 0 0
\(286\) −171.217 −0.0353995
\(287\) −418.537 −0.0860817
\(288\) −1577.13 −0.322684
\(289\) −4210.34 −0.856980
\(290\) 0 0
\(291\) 1277.80 0.257410
\(292\) −3975.04 −0.796649
\(293\) −4720.69 −0.941248 −0.470624 0.882334i \(-0.655971\pi\)
−0.470624 + 0.882334i \(0.655971\pi\)
\(294\) 2998.10 0.594737
\(295\) 0 0
\(296\) 4441.88 0.872226
\(297\) −2236.66 −0.436984
\(298\) 1755.52 0.341257
\(299\) 503.356 0.0973573
\(300\) 0 0
\(301\) 1425.52 0.272976
\(302\) 2948.07 0.561729
\(303\) 8276.76 1.56927
\(304\) −353.891 −0.0667666
\(305\) 0 0
\(306\) −338.500 −0.0632378
\(307\) 9475.50 1.76155 0.880774 0.473536i \(-0.157023\pi\)
0.880774 + 0.473536i \(0.157023\pi\)
\(308\) −386.318 −0.0714692
\(309\) 9196.57 1.69312
\(310\) 0 0
\(311\) 7724.72 1.40845 0.704227 0.709975i \(-0.251294\pi\)
0.704227 + 0.709975i \(0.251294\pi\)
\(312\) 690.050 0.125213
\(313\) 7719.80 1.39409 0.697043 0.717029i \(-0.254499\pi\)
0.697043 + 0.717029i \(0.254499\pi\)
\(314\) −1554.91 −0.279454
\(315\) 0 0
\(316\) 2560.33 0.455791
\(317\) −10756.5 −1.90583 −0.952914 0.303241i \(-0.901931\pi\)
−0.952914 + 0.303241i \(0.901931\pi\)
\(318\) 3268.73 0.576420
\(319\) −2492.28 −0.437432
\(320\) 0 0
\(321\) 7899.15 1.37348
\(322\) −460.181 −0.0796425
\(323\) −672.074 −0.115775
\(324\) 5040.30 0.864248
\(325\) 0 0
\(326\) 1106.48 0.187983
\(327\) −5792.79 −0.979638
\(328\) −2593.43 −0.436581
\(329\) −157.749 −0.0264346
\(330\) 0 0
\(331\) 3699.02 0.614250 0.307125 0.951669i \(-0.400633\pi\)
0.307125 + 0.951669i \(0.400633\pi\)
\(332\) −3093.83 −0.511433
\(333\) 1795.72 0.295509
\(334\) −2421.32 −0.396672
\(335\) 0 0
\(336\) 278.768 0.0452620
\(337\) −9917.45 −1.60308 −0.801540 0.597942i \(-0.795985\pi\)
−0.801540 + 0.597942i \(0.795985\pi\)
\(338\) 3289.62 0.529384
\(339\) 2177.81 0.348916
\(340\) 0 0
\(341\) 2619.88 0.416053
\(342\) 323.766 0.0511909
\(343\) −2264.65 −0.356501
\(344\) 8833.15 1.38445
\(345\) 0 0
\(346\) −1688.83 −0.262405
\(347\) 7738.48 1.19719 0.598593 0.801054i \(-0.295727\pi\)
0.598593 + 0.801054i \(0.295727\pi\)
\(348\) 4176.21 0.643299
\(349\) −8939.40 −1.37110 −0.685552 0.728024i \(-0.740439\pi\)
−0.685552 + 0.728024i \(0.740439\pi\)
\(350\) 0 0
\(351\) −616.881 −0.0938082
\(352\) −3792.32 −0.574237
\(353\) −7812.51 −1.17795 −0.588977 0.808150i \(-0.700469\pi\)
−0.588977 + 0.808150i \(0.700469\pi\)
\(354\) −7559.73 −1.13501
\(355\) 0 0
\(356\) −4130.94 −0.614998
\(357\) 529.408 0.0784852
\(358\) −1404.11 −0.207289
\(359\) 4671.36 0.686754 0.343377 0.939198i \(-0.388429\pi\)
0.343377 + 0.939198i \(0.388429\pi\)
\(360\) 0 0
\(361\) −6216.18 −0.906281
\(362\) −2575.85 −0.373988
\(363\) −5487.89 −0.793498
\(364\) −106.548 −0.0153424
\(365\) 0 0
\(366\) 1760.94 0.251491
\(367\) 2391.88 0.340204 0.170102 0.985426i \(-0.445590\pi\)
0.170102 + 0.985426i \(0.445590\pi\)
\(368\) 1260.03 0.178487
\(369\) −1048.45 −0.147913
\(370\) 0 0
\(371\) −1213.93 −0.169876
\(372\) −4390.02 −0.611859
\(373\) −13119.4 −1.82117 −0.910583 0.413326i \(-0.864367\pi\)
−0.910583 + 0.413326i \(0.864367\pi\)
\(374\) −813.950 −0.112536
\(375\) 0 0
\(376\) −977.480 −0.134068
\(377\) −687.380 −0.0939042
\(378\) 563.968 0.0767391
\(379\) −8968.11 −1.21546 −0.607732 0.794142i \(-0.707920\pi\)
−0.607732 + 0.794142i \(0.707920\pi\)
\(380\) 0 0
\(381\) 6154.63 0.827589
\(382\) 3015.22 0.403853
\(383\) 10643.6 1.42001 0.710005 0.704197i \(-0.248693\pi\)
0.710005 + 0.704197i \(0.248693\pi\)
\(384\) 7363.82 0.978602
\(385\) 0 0
\(386\) 262.541 0.0346191
\(387\) 3570.98 0.469051
\(388\) −1222.56 −0.159964
\(389\) −4554.56 −0.593639 −0.296819 0.954934i \(-0.595926\pi\)
−0.296819 + 0.954934i \(0.595926\pi\)
\(390\) 0 0
\(391\) 2392.91 0.309501
\(392\) −6899.24 −0.888939
\(393\) −588.640 −0.0755546
\(394\) 28.8019 0.00368278
\(395\) 0 0
\(396\) −967.738 −0.122805
\(397\) 2676.50 0.338362 0.169181 0.985585i \(-0.445888\pi\)
0.169181 + 0.985585i \(0.445888\pi\)
\(398\) −3341.71 −0.420867
\(399\) −506.364 −0.0635336
\(400\) 0 0
\(401\) −2570.96 −0.320169 −0.160084 0.987103i \(-0.551177\pi\)
−0.160084 + 0.987103i \(0.551177\pi\)
\(402\) 8153.42 1.01158
\(403\) 722.572 0.0893149
\(404\) −7918.94 −0.975203
\(405\) 0 0
\(406\) 628.420 0.0768177
\(407\) 4317.94 0.525878
\(408\) 3280.44 0.398054
\(409\) −2904.50 −0.351145 −0.175572 0.984467i \(-0.556178\pi\)
−0.175572 + 0.984467i \(0.556178\pi\)
\(410\) 0 0
\(411\) 9566.34 1.14811
\(412\) −8798.99 −1.05217
\(413\) 2807.50 0.334499
\(414\) −1152.77 −0.136849
\(415\) 0 0
\(416\) −1045.94 −0.123272
\(417\) 18896.0 2.21904
\(418\) 778.521 0.0910974
\(419\) −10586.1 −1.23428 −0.617141 0.786852i \(-0.711709\pi\)
−0.617141 + 0.786852i \(0.711709\pi\)
\(420\) 0 0
\(421\) 8155.31 0.944098 0.472049 0.881572i \(-0.343514\pi\)
0.472049 + 0.881572i \(0.343514\pi\)
\(422\) −359.187 −0.0414336
\(423\) −395.166 −0.0454223
\(424\) −7522.03 −0.861561
\(425\) 0 0
\(426\) −6242.40 −0.709965
\(427\) −653.969 −0.0741166
\(428\) −7557.65 −0.853535
\(429\) 670.796 0.0754926
\(430\) 0 0
\(431\) 170.047 0.0190043 0.00950217 0.999955i \(-0.496975\pi\)
0.00950217 + 0.999955i \(0.496975\pi\)
\(432\) −1544.21 −0.171981
\(433\) 8139.98 0.903424 0.451712 0.892164i \(-0.350814\pi\)
0.451712 + 0.892164i \(0.350814\pi\)
\(434\) −660.594 −0.0730634
\(435\) 0 0
\(436\) 5542.35 0.608786
\(437\) −2288.76 −0.250540
\(438\) −6310.15 −0.688381
\(439\) −9489.42 −1.03168 −0.515838 0.856686i \(-0.672519\pi\)
−0.515838 + 0.856686i \(0.672519\pi\)
\(440\) 0 0
\(441\) −2789.15 −0.301172
\(442\) −224.491 −0.0241582
\(443\) 8297.13 0.889862 0.444931 0.895565i \(-0.353228\pi\)
0.444931 + 0.895565i \(0.353228\pi\)
\(444\) −7235.39 −0.773370
\(445\) 0 0
\(446\) 2120.91 0.225175
\(447\) −6877.81 −0.727761
\(448\) 581.437 0.0613176
\(449\) 3521.42 0.370125 0.185063 0.982727i \(-0.440751\pi\)
0.185063 + 0.982727i \(0.440751\pi\)
\(450\) 0 0
\(451\) −2521.07 −0.263221
\(452\) −2083.66 −0.216830
\(453\) −11550.0 −1.19794
\(454\) 4608.62 0.476417
\(455\) 0 0
\(456\) −3137.65 −0.322223
\(457\) 2750.17 0.281504 0.140752 0.990045i \(-0.455048\pi\)
0.140752 + 0.990045i \(0.455048\pi\)
\(458\) −7501.13 −0.765294
\(459\) −2932.60 −0.298218
\(460\) 0 0
\(461\) −4820.72 −0.487035 −0.243518 0.969896i \(-0.578301\pi\)
−0.243518 + 0.969896i \(0.578301\pi\)
\(462\) −613.258 −0.0617562
\(463\) −12993.3 −1.30422 −0.652108 0.758126i \(-0.726115\pi\)
−0.652108 + 0.758126i \(0.726115\pi\)
\(464\) −1720.68 −0.172157
\(465\) 0 0
\(466\) 7229.27 0.718647
\(467\) −2516.52 −0.249359 −0.124679 0.992197i \(-0.539790\pi\)
−0.124679 + 0.992197i \(0.539790\pi\)
\(468\) −266.906 −0.0263627
\(469\) −3027.99 −0.298122
\(470\) 0 0
\(471\) 6091.83 0.595959
\(472\) 17396.5 1.69648
\(473\) 8586.69 0.834707
\(474\) 4064.38 0.393847
\(475\) 0 0
\(476\) −506.521 −0.0487738
\(477\) −3040.93 −0.291896
\(478\) −5569.26 −0.532912
\(479\) 9282.30 0.885426 0.442713 0.896663i \(-0.354016\pi\)
0.442713 + 0.896663i \(0.354016\pi\)
\(480\) 0 0
\(481\) 1190.90 0.112891
\(482\) −9294.84 −0.878357
\(483\) 1802.90 0.169845
\(484\) 5250.64 0.493111
\(485\) 0 0
\(486\) 3464.39 0.323350
\(487\) −10070.8 −0.937063 −0.468532 0.883447i \(-0.655217\pi\)
−0.468532 + 0.883447i \(0.655217\pi\)
\(488\) −4052.28 −0.375897
\(489\) −4335.00 −0.400890
\(490\) 0 0
\(491\) −8493.09 −0.780627 −0.390313 0.920682i \(-0.627633\pi\)
−0.390313 + 0.920682i \(0.627633\pi\)
\(492\) 4224.45 0.387100
\(493\) −3267.75 −0.298523
\(494\) 214.719 0.0195560
\(495\) 0 0
\(496\) 1808.78 0.163743
\(497\) 2318.28 0.209233
\(498\) −4911.28 −0.441927
\(499\) −11520.7 −1.03354 −0.516769 0.856125i \(-0.672866\pi\)
−0.516769 + 0.856125i \(0.672866\pi\)
\(500\) 0 0
\(501\) 9486.27 0.845939
\(502\) 6465.93 0.574878
\(503\) −15802.2 −1.40077 −0.700385 0.713766i \(-0.746988\pi\)
−0.700385 + 0.713766i \(0.746988\pi\)
\(504\) 586.895 0.0518698
\(505\) 0 0
\(506\) −2771.92 −0.243531
\(507\) −12888.1 −1.12896
\(508\) −5888.56 −0.514296
\(509\) −18133.1 −1.57905 −0.789525 0.613718i \(-0.789673\pi\)
−0.789525 + 0.613718i \(0.789673\pi\)
\(510\) 0 0
\(511\) 2343.44 0.202872
\(512\) −4940.58 −0.426454
\(513\) 2804.95 0.241407
\(514\) −9494.35 −0.814742
\(515\) 0 0
\(516\) −14388.3 −1.22754
\(517\) −950.206 −0.0808318
\(518\) −1088.75 −0.0923497
\(519\) 6616.52 0.559601
\(520\) 0 0
\(521\) 1617.14 0.135985 0.0679926 0.997686i \(-0.478341\pi\)
0.0679926 + 0.997686i \(0.478341\pi\)
\(522\) 1574.21 0.131995
\(523\) −7545.61 −0.630873 −0.315436 0.948947i \(-0.602151\pi\)
−0.315436 + 0.948947i \(0.602151\pi\)
\(524\) 563.192 0.0469526
\(525\) 0 0
\(526\) −7606.32 −0.630516
\(527\) 3435.05 0.283934
\(528\) 1679.17 0.138402
\(529\) −4017.91 −0.330230
\(530\) 0 0
\(531\) 7032.87 0.574766
\(532\) 484.473 0.0394823
\(533\) −695.322 −0.0565061
\(534\) −6557.64 −0.531417
\(535\) 0 0
\(536\) −18762.7 −1.51199
\(537\) 5501.05 0.442063
\(538\) −6933.51 −0.555622
\(539\) −6706.74 −0.535955
\(540\) 0 0
\(541\) 12142.0 0.964923 0.482461 0.875917i \(-0.339743\pi\)
0.482461 + 0.875917i \(0.339743\pi\)
\(542\) −4726.28 −0.374560
\(543\) 10091.7 0.797562
\(544\) −4972.30 −0.391885
\(545\) 0 0
\(546\) −169.139 −0.0132573
\(547\) −17852.1 −1.39543 −0.697715 0.716375i \(-0.745800\pi\)
−0.697715 + 0.716375i \(0.745800\pi\)
\(548\) −9152.77 −0.713480
\(549\) −1638.21 −0.127354
\(550\) 0 0
\(551\) 3125.51 0.241654
\(552\) 11171.6 0.861401
\(553\) −1509.41 −0.116070
\(554\) −6605.48 −0.506570
\(555\) 0 0
\(556\) −18079.1 −1.37900
\(557\) −10350.7 −0.787388 −0.393694 0.919242i \(-0.628803\pi\)
−0.393694 + 0.919242i \(0.628803\pi\)
\(558\) −1654.81 −0.125544
\(559\) 2368.24 0.179188
\(560\) 0 0
\(561\) 3188.91 0.239992
\(562\) 2491.62 0.187015
\(563\) 12353.6 0.924761 0.462380 0.886682i \(-0.346995\pi\)
0.462380 + 0.886682i \(0.346995\pi\)
\(564\) 1592.22 0.118873
\(565\) 0 0
\(566\) −9520.52 −0.707027
\(567\) −2971.45 −0.220087
\(568\) 14365.0 1.06117
\(569\) −24894.7 −1.83416 −0.917081 0.398700i \(-0.869461\pi\)
−0.917081 + 0.398700i \(0.869461\pi\)
\(570\) 0 0
\(571\) 10062.0 0.737442 0.368721 0.929540i \(-0.379796\pi\)
0.368721 + 0.929540i \(0.379796\pi\)
\(572\) −641.796 −0.0469141
\(573\) −11813.1 −0.861253
\(574\) 635.681 0.0462244
\(575\) 0 0
\(576\) 1456.52 0.105361
\(577\) −4187.40 −0.302121 −0.151060 0.988525i \(-0.548269\pi\)
−0.151060 + 0.988525i \(0.548269\pi\)
\(578\) 6394.74 0.460183
\(579\) −1028.59 −0.0738283
\(580\) 0 0
\(581\) 1823.93 0.130240
\(582\) −1940.75 −0.138224
\(583\) −7312.14 −0.519448
\(584\) 14521.0 1.02891
\(585\) 0 0
\(586\) 7169.86 0.505434
\(587\) 4333.47 0.304704 0.152352 0.988326i \(-0.451315\pi\)
0.152352 + 0.988326i \(0.451315\pi\)
\(588\) 11238.2 0.788189
\(589\) −3285.53 −0.229844
\(590\) 0 0
\(591\) −112.840 −0.00785386
\(592\) 2981.13 0.206966
\(593\) 6152.44 0.426055 0.213027 0.977046i \(-0.431668\pi\)
0.213027 + 0.977046i \(0.431668\pi\)
\(594\) 3397.08 0.234653
\(595\) 0 0
\(596\) 6580.47 0.452259
\(597\) 13092.2 0.897536
\(598\) −764.506 −0.0522792
\(599\) −7257.67 −0.495059 −0.247529 0.968880i \(-0.579619\pi\)
−0.247529 + 0.968880i \(0.579619\pi\)
\(600\) 0 0
\(601\) −15872.7 −1.07731 −0.538654 0.842527i \(-0.681067\pi\)
−0.538654 + 0.842527i \(0.681067\pi\)
\(602\) −2165.11 −0.146583
\(603\) −7585.19 −0.512260
\(604\) 11050.7 0.744445
\(605\) 0 0
\(606\) −12570.9 −0.842669
\(607\) 15068.0 1.00757 0.503783 0.863830i \(-0.331941\pi\)
0.503783 + 0.863830i \(0.331941\pi\)
\(608\) 4755.87 0.317230
\(609\) −2462.04 −0.163821
\(610\) 0 0
\(611\) −262.071 −0.0173523
\(612\) −1268.85 −0.0838075
\(613\) −12024.1 −0.792252 −0.396126 0.918196i \(-0.629646\pi\)
−0.396126 + 0.918196i \(0.629646\pi\)
\(614\) −14391.6 −0.945921
\(615\) 0 0
\(616\) 1411.23 0.0923056
\(617\) −4814.15 −0.314117 −0.157059 0.987589i \(-0.550201\pi\)
−0.157059 + 0.987589i \(0.550201\pi\)
\(618\) −13967.9 −0.909178
\(619\) −9575.51 −0.621764 −0.310882 0.950448i \(-0.600624\pi\)
−0.310882 + 0.950448i \(0.600624\pi\)
\(620\) 0 0
\(621\) −9987.00 −0.645354
\(622\) −11732.4 −0.756315
\(623\) 2435.35 0.156613
\(624\) 463.121 0.0297110
\(625\) 0 0
\(626\) −11725.0 −0.748600
\(627\) −3050.10 −0.194273
\(628\) −5828.47 −0.370353
\(629\) 5661.46 0.358883
\(630\) 0 0
\(631\) 21583.8 1.36171 0.680855 0.732418i \(-0.261608\pi\)
0.680855 + 0.732418i \(0.261608\pi\)
\(632\) −9352.98 −0.588673
\(633\) 1407.23 0.0883607
\(634\) 16337.2 1.02340
\(635\) 0 0
\(636\) 12252.7 0.763914
\(637\) −1849.75 −0.115054
\(638\) 3785.31 0.234893
\(639\) 5807.35 0.359523
\(640\) 0 0
\(641\) −11164.6 −0.687951 −0.343975 0.938979i \(-0.611774\pi\)
−0.343975 + 0.938979i \(0.611774\pi\)
\(642\) −11997.4 −0.737536
\(643\) −8679.03 −0.532298 −0.266149 0.963932i \(-0.585751\pi\)
−0.266149 + 0.963932i \(0.585751\pi\)
\(644\) −1724.96 −0.105548
\(645\) 0 0
\(646\) 1020.76 0.0621690
\(647\) −9386.78 −0.570374 −0.285187 0.958472i \(-0.592056\pi\)
−0.285187 + 0.958472i \(0.592056\pi\)
\(648\) −18412.4 −1.11621
\(649\) 16911.1 1.02283
\(650\) 0 0
\(651\) 2588.08 0.155814
\(652\) 4147.59 0.249129
\(653\) −25776.8 −1.54475 −0.772376 0.635166i \(-0.780932\pi\)
−0.772376 + 0.635166i \(0.780932\pi\)
\(654\) 8798.18 0.526049
\(655\) 0 0
\(656\) −1740.56 −0.103594
\(657\) 5870.38 0.348593
\(658\) 239.592 0.0141949
\(659\) −176.671 −0.0104433 −0.00522164 0.999986i \(-0.501662\pi\)
−0.00522164 + 0.999986i \(0.501662\pi\)
\(660\) 0 0
\(661\) 443.366 0.0260892 0.0130446 0.999915i \(-0.495848\pi\)
0.0130446 + 0.999915i \(0.495848\pi\)
\(662\) −5618.14 −0.329842
\(663\) 879.514 0.0515196
\(664\) 11301.9 0.660538
\(665\) 0 0
\(666\) −2727.36 −0.158683
\(667\) −11128.4 −0.646014
\(668\) −9076.16 −0.525700
\(669\) −8309.34 −0.480206
\(670\) 0 0
\(671\) −3939.21 −0.226634
\(672\) −3746.30 −0.215055
\(673\) 33702.8 1.93038 0.965192 0.261544i \(-0.0842316\pi\)
0.965192 + 0.261544i \(0.0842316\pi\)
\(674\) 15062.8 0.860826
\(675\) 0 0
\(676\) 12330.9 0.701578
\(677\) −7298.49 −0.414334 −0.207167 0.978306i \(-0.566424\pi\)
−0.207167 + 0.978306i \(0.566424\pi\)
\(678\) −3307.70 −0.187362
\(679\) 720.748 0.0407360
\(680\) 0 0
\(681\) −18055.7 −1.01600
\(682\) −3979.11 −0.223414
\(683\) −27754.4 −1.55490 −0.777448 0.628948i \(-0.783486\pi\)
−0.777448 + 0.628948i \(0.783486\pi\)
\(684\) 1213.62 0.0678419
\(685\) 0 0
\(686\) 3439.59 0.191435
\(687\) 29388.0 1.63206
\(688\) 5928.30 0.328509
\(689\) −2016.72 −0.111511
\(690\) 0 0
\(691\) 19119.2 1.05257 0.526287 0.850307i \(-0.323584\pi\)
0.526287 + 0.850307i \(0.323584\pi\)
\(692\) −6330.48 −0.347758
\(693\) 570.519 0.0312731
\(694\) −11753.3 −0.642868
\(695\) 0 0
\(696\) −15255.8 −0.830849
\(697\) −3305.50 −0.179634
\(698\) 13577.3 0.736259
\(699\) −28322.9 −1.53258
\(700\) 0 0
\(701\) −29188.2 −1.57264 −0.786322 0.617817i \(-0.788017\pi\)
−0.786322 + 0.617817i \(0.788017\pi\)
\(702\) 936.929 0.0503734
\(703\) −5415.03 −0.290515
\(704\) 3502.30 0.187497
\(705\) 0 0
\(706\) 11865.8 0.632541
\(707\) 4668.53 0.248342
\(708\) −28337.2 −1.50420
\(709\) −11377.0 −0.602639 −0.301320 0.953523i \(-0.597427\pi\)
−0.301320 + 0.953523i \(0.597427\pi\)
\(710\) 0 0
\(711\) −3781.13 −0.199442
\(712\) 15090.5 0.794297
\(713\) 11698.1 0.614442
\(714\) −804.073 −0.0421452
\(715\) 0 0
\(716\) −5263.23 −0.274715
\(717\) 21819.3 1.13648
\(718\) −7094.93 −0.368775
\(719\) −8170.53 −0.423796 −0.211898 0.977292i \(-0.567964\pi\)
−0.211898 + 0.977292i \(0.567964\pi\)
\(720\) 0 0
\(721\) 5187.35 0.267943
\(722\) 9441.24 0.486657
\(723\) 36415.5 1.87318
\(724\) −9655.42 −0.495637
\(725\) 0 0
\(726\) 8335.11 0.426095
\(727\) −19612.6 −1.00054 −0.500270 0.865870i \(-0.666766\pi\)
−0.500270 + 0.865870i \(0.666766\pi\)
\(728\) 389.224 0.0198154
\(729\) 10330.8 0.524858
\(730\) 0 0
\(731\) 11258.4 0.569642
\(732\) 6600.77 0.333294
\(733\) 16619.4 0.837451 0.418725 0.908113i \(-0.362477\pi\)
0.418725 + 0.908113i \(0.362477\pi\)
\(734\) −3632.82 −0.182684
\(735\) 0 0
\(736\) −16933.2 −0.848053
\(737\) −18239.2 −0.911599
\(738\) 1592.40 0.0794268
\(739\) −19520.6 −0.971686 −0.485843 0.874046i \(-0.661487\pi\)
−0.485843 + 0.874046i \(0.661487\pi\)
\(740\) 0 0
\(741\) −841.231 −0.0417050
\(742\) 1843.74 0.0912206
\(743\) −162.092 −0.00800345 −0.00400172 0.999992i \(-0.501274\pi\)
−0.00400172 + 0.999992i \(0.501274\pi\)
\(744\) 16036.9 0.790243
\(745\) 0 0
\(746\) 19925.9 0.977935
\(747\) 4569.00 0.223790
\(748\) −3051.04 −0.149141
\(749\) 4455.53 0.217359
\(750\) 0 0
\(751\) 30012.2 1.45827 0.729135 0.684370i \(-0.239923\pi\)
0.729135 + 0.684370i \(0.239923\pi\)
\(752\) −656.028 −0.0318123
\(753\) −25332.3 −1.22598
\(754\) 1044.00 0.0504250
\(755\) 0 0
\(756\) 2114.00 0.101700
\(757\) 25232.6 1.21148 0.605742 0.795661i \(-0.292876\pi\)
0.605742 + 0.795661i \(0.292876\pi\)
\(758\) 13620.9 0.652683
\(759\) 10859.9 0.519351
\(760\) 0 0
\(761\) −26393.1 −1.25723 −0.628613 0.777719i \(-0.716377\pi\)
−0.628613 + 0.777719i \(0.716377\pi\)
\(762\) −9347.76 −0.444401
\(763\) −3267.43 −0.155031
\(764\) 11302.4 0.535217
\(765\) 0 0
\(766\) −16165.7 −0.762521
\(767\) 4664.15 0.219573
\(768\) −19430.9 −0.912956
\(769\) −12734.0 −0.597140 −0.298570 0.954388i \(-0.596510\pi\)
−0.298570 + 0.954388i \(0.596510\pi\)
\(770\) 0 0
\(771\) 37197.1 1.73751
\(772\) 984.118 0.0458798
\(773\) −29097.4 −1.35389 −0.676947 0.736032i \(-0.736697\pi\)
−0.676947 + 0.736032i \(0.736697\pi\)
\(774\) −5423.66 −0.251873
\(775\) 0 0
\(776\) 4466.06 0.206601
\(777\) 4265.54 0.196944
\(778\) 6917.55 0.318774
\(779\) 3161.62 0.145413
\(780\) 0 0
\(781\) 13964.2 0.639794
\(782\) −3634.40 −0.166197
\(783\) 13638.2 0.622464
\(784\) −4630.37 −0.210932
\(785\) 0 0
\(786\) 894.036 0.0405715
\(787\) 4595.00 0.208124 0.104062 0.994571i \(-0.466816\pi\)
0.104062 + 0.994571i \(0.466816\pi\)
\(788\) 107.962 0.00488070
\(789\) 29800.2 1.34463
\(790\) 0 0
\(791\) 1228.40 0.0552173
\(792\) 3535.18 0.158608
\(793\) −1086.45 −0.0486519
\(794\) −4065.12 −0.181695
\(795\) 0 0
\(796\) −12526.2 −0.557764
\(797\) 29030.2 1.29021 0.645107 0.764092i \(-0.276813\pi\)
0.645107 + 0.764092i \(0.276813\pi\)
\(798\) 769.074 0.0341164
\(799\) −1245.86 −0.0551633
\(800\) 0 0
\(801\) 6100.62 0.269107
\(802\) 3904.82 0.171925
\(803\) 14115.8 0.620343
\(804\) 30562.6 1.34062
\(805\) 0 0
\(806\) −1097.46 −0.0479606
\(807\) 27164.2 1.18491
\(808\) 28928.2 1.25952
\(809\) −25943.4 −1.12747 −0.563734 0.825957i \(-0.690636\pi\)
−0.563734 + 0.825957i \(0.690636\pi\)
\(810\) 0 0
\(811\) 18828.1 0.815222 0.407611 0.913156i \(-0.366362\pi\)
0.407611 + 0.913156i \(0.366362\pi\)
\(812\) 2355.60 0.101805
\(813\) 18516.7 0.798782
\(814\) −6558.15 −0.282387
\(815\) 0 0
\(816\) 2201.64 0.0944520
\(817\) −10768.4 −0.461124
\(818\) 4411.40 0.188559
\(819\) 157.351 0.00671344
\(820\) 0 0
\(821\) 23631.4 1.00456 0.502278 0.864706i \(-0.332495\pi\)
0.502278 + 0.864706i \(0.332495\pi\)
\(822\) −14529.5 −0.616515
\(823\) 37638.6 1.59417 0.797084 0.603868i \(-0.206375\pi\)
0.797084 + 0.603868i \(0.206375\pi\)
\(824\) 32143.0 1.35893
\(825\) 0 0
\(826\) −4264.08 −0.179620
\(827\) −3452.86 −0.145185 −0.0725924 0.997362i \(-0.523127\pi\)
−0.0725924 + 0.997362i \(0.523127\pi\)
\(828\) −4321.08 −0.181362
\(829\) −2949.59 −0.123575 −0.0617875 0.998089i \(-0.519680\pi\)
−0.0617875 + 0.998089i \(0.519680\pi\)
\(830\) 0 0
\(831\) 25879.1 1.08031
\(832\) 965.950 0.0402503
\(833\) −8793.53 −0.365760
\(834\) −28699.5 −1.19159
\(835\) 0 0
\(836\) 2918.24 0.120729
\(837\) −14336.4 −0.592043
\(838\) 16078.3 0.662789
\(839\) −21099.3 −0.868212 −0.434106 0.900862i \(-0.642936\pi\)
−0.434106 + 0.900862i \(0.642936\pi\)
\(840\) 0 0
\(841\) −9192.18 −0.376899
\(842\) −12386.4 −0.506965
\(843\) −9761.70 −0.398827
\(844\) −1346.39 −0.0549108
\(845\) 0 0
\(846\) 600.184 0.0243910
\(847\) −3095.46 −0.125574
\(848\) −5048.35 −0.204435
\(849\) 37299.7 1.50780
\(850\) 0 0
\(851\) 19280.2 0.776634
\(852\) −23399.3 −0.940898
\(853\) 5832.07 0.234099 0.117049 0.993126i \(-0.462656\pi\)
0.117049 + 0.993126i \(0.462656\pi\)
\(854\) 993.260 0.0397994
\(855\) 0 0
\(856\) 27608.4 1.10238
\(857\) 3182.86 0.126866 0.0634331 0.997986i \(-0.479795\pi\)
0.0634331 + 0.997986i \(0.479795\pi\)
\(858\) −1018.82 −0.0405382
\(859\) 34773.9 1.38122 0.690610 0.723227i \(-0.257342\pi\)
0.690610 + 0.723227i \(0.257342\pi\)
\(860\) 0 0
\(861\) −2490.48 −0.0985776
\(862\) −258.270 −0.0102050
\(863\) 13655.6 0.538636 0.269318 0.963051i \(-0.413202\pi\)
0.269318 + 0.963051i \(0.413202\pi\)
\(864\) 20752.3 0.817137
\(865\) 0 0
\(866\) −12363.1 −0.485123
\(867\) −25053.4 −0.981382
\(868\) −2476.20 −0.0968290
\(869\) −9092.01 −0.354920
\(870\) 0 0
\(871\) −5030.44 −0.195695
\(872\) −20246.4 −0.786273
\(873\) 1805.49 0.0699962
\(874\) 3476.20 0.134536
\(875\) 0 0
\(876\) −23653.2 −0.912293
\(877\) 43458.4 1.67330 0.836651 0.547736i \(-0.184510\pi\)
0.836651 + 0.547736i \(0.184510\pi\)
\(878\) 14412.7 0.553992
\(879\) −28090.2 −1.07788
\(880\) 0 0
\(881\) 26874.5 1.02772 0.513862 0.857873i \(-0.328214\pi\)
0.513862 + 0.857873i \(0.328214\pi\)
\(882\) 4236.21 0.161724
\(883\) 9065.53 0.345503 0.172752 0.984965i \(-0.444734\pi\)
0.172752 + 0.984965i \(0.444734\pi\)
\(884\) −841.491 −0.0320163
\(885\) 0 0
\(886\) −12601.8 −0.477840
\(887\) −42928.3 −1.62502 −0.812510 0.582947i \(-0.801899\pi\)
−0.812510 + 0.582947i \(0.801899\pi\)
\(888\) 26431.1 0.998841
\(889\) 3471.53 0.130969
\(890\) 0 0
\(891\) −17898.6 −0.672982
\(892\) 7950.11 0.298419
\(893\) 1191.63 0.0446545
\(894\) 10446.1 0.390795
\(895\) 0 0
\(896\) 4153.58 0.154867
\(897\) 2995.19 0.111490
\(898\) −5348.39 −0.198751
\(899\) −15974.9 −0.592649
\(900\) 0 0
\(901\) −9587.32 −0.354495
\(902\) 3829.05 0.141345
\(903\) 8482.49 0.312602
\(904\) 7611.70 0.280046
\(905\) 0 0
\(906\) 17542.3 0.643272
\(907\) 13748.8 0.503330 0.251665 0.967814i \(-0.419022\pi\)
0.251665 + 0.967814i \(0.419022\pi\)
\(908\) 17275.1 0.631383
\(909\) 11694.8 0.426724
\(910\) 0 0
\(911\) −15009.6 −0.545874 −0.272937 0.962032i \(-0.587995\pi\)
−0.272937 + 0.962032i \(0.587995\pi\)
\(912\) −2105.81 −0.0764586
\(913\) 10986.5 0.398248
\(914\) −4177.00 −0.151163
\(915\) 0 0
\(916\) −28117.5 −1.01422
\(917\) −332.023 −0.0119568
\(918\) 4454.08 0.160138
\(919\) 40518.6 1.45439 0.727195 0.686431i \(-0.240823\pi\)
0.727195 + 0.686431i \(0.240823\pi\)
\(920\) 0 0
\(921\) 56383.4 2.01726
\(922\) 7321.79 0.261530
\(923\) 3851.39 0.137346
\(924\) −2298.76 −0.0818439
\(925\) 0 0
\(926\) 19734.5 0.700341
\(927\) 12994.5 0.460403
\(928\) 23123.9 0.817974
\(929\) 14399.3 0.508531 0.254265 0.967135i \(-0.418166\pi\)
0.254265 + 0.967135i \(0.418166\pi\)
\(930\) 0 0
\(931\) 8410.77 0.296082
\(932\) 27098.5 0.952404
\(933\) 45965.5 1.61291
\(934\) 3822.13 0.133901
\(935\) 0 0
\(936\) 975.017 0.0340486
\(937\) 48380.8 1.68680 0.843400 0.537286i \(-0.180550\pi\)
0.843400 + 0.537286i \(0.180550\pi\)
\(938\) 4598.95 0.160087
\(939\) 45936.3 1.59646
\(940\) 0 0
\(941\) −31933.6 −1.10628 −0.553139 0.833089i \(-0.686570\pi\)
−0.553139 + 0.833089i \(0.686570\pi\)
\(942\) −9252.38 −0.320020
\(943\) −11256.9 −0.388734
\(944\) 11675.5 0.402548
\(945\) 0 0
\(946\) −13041.6 −0.448223
\(947\) 50096.9 1.71904 0.859519 0.511103i \(-0.170763\pi\)
0.859519 + 0.511103i \(0.170763\pi\)
\(948\) 15235.1 0.521955
\(949\) 3893.19 0.133170
\(950\) 0 0
\(951\) −64006.2 −2.18248
\(952\) 1850.34 0.0629935
\(953\) −12685.9 −0.431205 −0.215602 0.976481i \(-0.569171\pi\)
−0.215602 + 0.976481i \(0.569171\pi\)
\(954\) 4618.61 0.156743
\(955\) 0 0
\(956\) −20876.0 −0.706255
\(957\) −14830.2 −0.500931
\(958\) −14098.1 −0.475458
\(959\) 5395.91 0.181693
\(960\) 0 0
\(961\) −12998.3 −0.436316
\(962\) −1808.77 −0.0606205
\(963\) 11161.2 0.373485
\(964\) −34841.2 −1.16406
\(965\) 0 0
\(966\) −2738.28 −0.0912036
\(967\) −35048.9 −1.16556 −0.582780 0.812630i \(-0.698035\pi\)
−0.582780 + 0.812630i \(0.698035\pi\)
\(968\) −19180.8 −0.636874
\(969\) −3999.14 −0.132581
\(970\) 0 0
\(971\) 29484.5 0.974462 0.487231 0.873273i \(-0.338007\pi\)
0.487231 + 0.873273i \(0.338007\pi\)
\(972\) 12986.1 0.428527
\(973\) 10658.3 0.351172
\(974\) 15295.6 0.503187
\(975\) 0 0
\(976\) −2719.65 −0.0891946
\(977\) 25899.3 0.848100 0.424050 0.905639i \(-0.360608\pi\)
0.424050 + 0.905639i \(0.360608\pi\)
\(978\) 6584.07 0.215271
\(979\) 14669.4 0.478893
\(980\) 0 0
\(981\) −8185.02 −0.266389
\(982\) 12899.4 0.419183
\(983\) −20316.8 −0.659210 −0.329605 0.944119i \(-0.606916\pi\)
−0.329605 + 0.944119i \(0.606916\pi\)
\(984\) −15432.1 −0.499956
\(985\) 0 0
\(986\) 4963.11 0.160302
\(987\) −938.676 −0.0302719
\(988\) 804.863 0.0259171
\(989\) 38340.7 1.23272
\(990\) 0 0
\(991\) 52179.6 1.67259 0.836297 0.548276i \(-0.184716\pi\)
0.836297 + 0.548276i \(0.184716\pi\)
\(992\) −24307.8 −0.777997
\(993\) 22010.8 0.703417
\(994\) −3521.04 −0.112355
\(995\) 0 0
\(996\) −18409.6 −0.585675
\(997\) −13574.2 −0.431193 −0.215596 0.976483i \(-0.569170\pi\)
−0.215596 + 0.976483i \(0.569170\pi\)
\(998\) 17497.8 0.554993
\(999\) −23628.5 −0.748322
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 \(a_p\))