Properties

Label 1175.4.a.a.1.3
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 1.3
Root \(2.68740\)
Character \(\chi\) = 1175.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+4.90952 q^{2}\) \(+0.777884 q^{3}\) \(+16.1033 q^{4}\) \(+3.81903 q^{6}\) \(+30.3255 q^{7}\) \(+39.7835 q^{8}\) \(-26.3949 q^{9}\) \(+O(q^{10})\) \(q\)\(+4.90952 q^{2}\) \(+0.777884 q^{3}\) \(+16.1033 q^{4}\) \(+3.81903 q^{6}\) \(+30.3255 q^{7}\) \(+39.7835 q^{8}\) \(-26.3949 q^{9}\) \(+22.4298 q^{11}\) \(+12.5265 q^{12}\) \(+62.0257 q^{13}\) \(+148.883 q^{14}\) \(+66.4910 q^{16}\) \(+72.1639 q^{17}\) \(-129.586 q^{18}\) \(-25.0550 q^{19}\) \(+23.5897 q^{21}\) \(+110.119 q^{22}\) \(-103.176 q^{23}\) \(+30.9469 q^{24}\) \(+304.516 q^{26}\) \(-41.5350 q^{27}\) \(+488.341 q^{28}\) \(-234.381 q^{29}\) \(+198.714 q^{31}\) \(+8.17058 q^{32}\) \(+17.4477 q^{33}\) \(+354.290 q^{34}\) \(-425.046 q^{36}\) \(+203.083 q^{37}\) \(-123.008 q^{38}\) \(+48.2488 q^{39}\) \(+210.889 q^{41}\) \(+115.814 q^{42}\) \(-111.430 q^{43}\) \(+361.194 q^{44}\) \(-506.542 q^{46}\) \(-47.0000 q^{47}\) \(+51.7223 q^{48}\) \(+576.634 q^{49}\) \(+56.1351 q^{51}\) \(+998.822 q^{52}\) \(-499.576 q^{53}\) \(-203.917 q^{54}\) \(+1206.45 q^{56}\) \(-19.4898 q^{57}\) \(-1150.70 q^{58}\) \(-562.752 q^{59}\) \(+548.091 q^{61}\) \(+975.591 q^{62}\) \(-800.437 q^{63}\) \(-491.814 q^{64}\) \(+85.6600 q^{66}\) \(+760.831 q^{67}\) \(+1162.08 q^{68}\) \(-80.2586 q^{69}\) \(-668.059 q^{71}\) \(-1050.08 q^{72}\) \(+1145.92 q^{73}\) \(+997.040 q^{74}\) \(-403.469 q^{76}\) \(+680.193 q^{77}\) \(+236.878 q^{78}\) \(+975.010 q^{79}\) \(+680.353 q^{81}\) \(+1035.37 q^{82}\) \(-698.827 q^{83}\) \(+379.873 q^{84}\) \(-547.067 q^{86}\) \(-182.321 q^{87}\) \(+892.335 q^{88}\) \(+451.477 q^{89}\) \(+1880.96 q^{91}\) \(-1661.47 q^{92}\) \(+154.577 q^{93}\) \(-230.747 q^{94}\) \(+6.35576 q^{96}\) \(+390.906 q^{97}\) \(+2830.99 q^{98}\) \(-592.031 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(3q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 5q^{4} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 45q^{7} \) \(\mathstrut +\mathstrut 39q^{8} \) \(\mathstrut -\mathstrut 42q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 5q^{4} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 45q^{7} \) \(\mathstrut +\mathstrut 39q^{8} \) \(\mathstrut -\mathstrut 42q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut -\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 80q^{13} \) \(\mathstrut +\mathstrut 162q^{14} \) \(\mathstrut +\mathstrut 89q^{16} \) \(\mathstrut +\mathstrut 39q^{17} \) \(\mathstrut -\mathstrut 181q^{18} \) \(\mathstrut -\mathstrut 24q^{19} \) \(\mathstrut +\mathstrut 24q^{21} \) \(\mathstrut +\mathstrut 14q^{22} \) \(\mathstrut -\mathstrut 120q^{23} \) \(\mathstrut +\mathstrut 192q^{24} \) \(\mathstrut +\mathstrut 316q^{26} \) \(\mathstrut -\mathstrut 64q^{27} \) \(\mathstrut +\mathstrut 408q^{28} \) \(\mathstrut -\mathstrut 184q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut +\mathstrut 7q^{32} \) \(\mathstrut +\mathstrut 208q^{33} \) \(\mathstrut +\mathstrut 218q^{34} \) \(\mathstrut -\mathstrut 343q^{36} \) \(\mathstrut +\mathstrut 589q^{37} \) \(\mathstrut -\mathstrut 42q^{38} \) \(\mathstrut +\mathstrut 60q^{39} \) \(\mathstrut -\mathstrut 92q^{41} \) \(\mathstrut +\mathstrut 54q^{42} \) \(\mathstrut +\mathstrut 250q^{43} \) \(\mathstrut +\mathstrut 466q^{44} \) \(\mathstrut -\mathstrut 816q^{46} \) \(\mathstrut -\mathstrut 141q^{47} \) \(\mathstrut +\mathstrut 120q^{48} \) \(\mathstrut +\mathstrut 30q^{49} \) \(\mathstrut +\mathstrut 317q^{51} \) \(\mathstrut +\mathstrut 900q^{52} \) \(\mathstrut -\mathstrut 459q^{53} \) \(\mathstrut +\mathstrut 106q^{54} \) \(\mathstrut +\mathstrut 1032q^{56} \) \(\mathstrut -\mathstrut 216q^{57} \) \(\mathstrut -\mathstrut 684q^{58} \) \(\mathstrut +\mathstrut 579q^{59} \) \(\mathstrut +\mathstrut 267q^{61} \) \(\mathstrut +\mathstrut 244q^{62} \) \(\mathstrut -\mathstrut 1044q^{63} \) \(\mathstrut -\mathstrut 87q^{64} \) \(\mathstrut +\mathstrut 16q^{66} \) \(\mathstrut +\mathstrut 540q^{67} \) \(\mathstrut +\mathstrut 1334q^{68} \) \(\mathstrut +\mathstrut 642q^{69} \) \(\mathstrut +\mathstrut 749q^{71} \) \(\mathstrut -\mathstrut 357q^{72} \) \(\mathstrut +\mathstrut 1924q^{73} \) \(\mathstrut +\mathstrut 950q^{74} \) \(\mathstrut -\mathstrut 402q^{76} \) \(\mathstrut +\mathstrut 288q^{77} \) \(\mathstrut +\mathstrut 152q^{78} \) \(\mathstrut +\mathstrut 805q^{79} \) \(\mathstrut +\mathstrut 291q^{81} \) \(\mathstrut +\mathstrut 938q^{82} \) \(\mathstrut -\mathstrut 712q^{83} \) \(\mathstrut +\mathstrut 372q^{84} \) \(\mathstrut -\mathstrut 1294q^{86} \) \(\mathstrut -\mathstrut 1216q^{87} \) \(\mathstrut +\mathstrut 2190q^{88} \) \(\mathstrut +\mathstrut 835q^{89} \) \(\mathstrut +\mathstrut 2040q^{91} \) \(\mathstrut -\mathstrut 1596q^{92} \) \(\mathstrut +\mathstrut 1500q^{93} \) \(\mathstrut -\mathstrut 235q^{94} \) \(\mathstrut -\mathstrut 1432q^{96} \) \(\mathstrut +\mathstrut 2243q^{97} \) \(\mathstrut +\mathstrut 2989q^{98} \) \(\mathstrut +\mathstrut 554q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.90952 1.73578 0.867888 0.496760i \(-0.165477\pi\)
0.867888 + 0.496760i \(0.165477\pi\)
\(3\) 0.777884 0.149704 0.0748519 0.997195i \(-0.476152\pi\)
0.0748519 + 0.997195i \(0.476152\pi\)
\(4\) 16.1033 2.01292
\(5\) 0 0
\(6\) 3.81903 0.259852
\(7\) 30.3255 1.63742 0.818711 0.574206i \(-0.194689\pi\)
0.818711 + 0.574206i \(0.194689\pi\)
\(8\) 39.7835 1.75820
\(9\) −26.3949 −0.977589
\(10\) 0 0
\(11\) 22.4298 0.614803 0.307401 0.951580i \(-0.400541\pi\)
0.307401 + 0.951580i \(0.400541\pi\)
\(12\) 12.5265 0.301341
\(13\) 62.0257 1.32330 0.661648 0.749815i \(-0.269857\pi\)
0.661648 + 0.749815i \(0.269857\pi\)
\(14\) 148.883 2.84220
\(15\) 0 0
\(16\) 66.4910 1.03892
\(17\) 72.1639 1.02955 0.514774 0.857326i \(-0.327876\pi\)
0.514774 + 0.857326i \(0.327876\pi\)
\(18\) −129.586 −1.69688
\(19\) −25.0550 −0.302526 −0.151263 0.988494i \(-0.548334\pi\)
−0.151263 + 0.988494i \(0.548334\pi\)
\(20\) 0 0
\(21\) 23.5897 0.245128
\(22\) 110.119 1.06716
\(23\) −103.176 −0.935373 −0.467687 0.883894i \(-0.654912\pi\)
−0.467687 + 0.883894i \(0.654912\pi\)
\(24\) 30.9469 0.263209
\(25\) 0 0
\(26\) 304.516 2.29694
\(27\) −41.5350 −0.296052
\(28\) 488.341 3.29600
\(29\) −234.381 −1.50081 −0.750405 0.660978i \(-0.770142\pi\)
−0.750405 + 0.660978i \(0.770142\pi\)
\(30\) 0 0
\(31\) 198.714 1.15129 0.575647 0.817698i \(-0.304750\pi\)
0.575647 + 0.817698i \(0.304750\pi\)
\(32\) 8.17058 0.0451365
\(33\) 17.4477 0.0920383
\(34\) 354.290 1.78707
\(35\) 0 0
\(36\) −425.046 −1.96781
\(37\) 203.083 0.902343 0.451171 0.892437i \(-0.351006\pi\)
0.451171 + 0.892437i \(0.351006\pi\)
\(38\) −123.008 −0.525118
\(39\) 48.2488 0.198102
\(40\) 0 0
\(41\) 210.889 0.803303 0.401651 0.915793i \(-0.368436\pi\)
0.401651 + 0.915793i \(0.368436\pi\)
\(42\) 115.814 0.425487
\(43\) −111.430 −0.395184 −0.197592 0.980284i \(-0.563312\pi\)
−0.197592 + 0.980284i \(0.563312\pi\)
\(44\) 361.194 1.23755
\(45\) 0 0
\(46\) −506.542 −1.62360
\(47\) −47.0000 −0.145865
\(48\) 51.7223 0.155531
\(49\) 576.634 1.68115
\(50\) 0 0
\(51\) 56.1351 0.154127
\(52\) 998.822 2.66369
\(53\) −499.576 −1.29476 −0.647378 0.762169i \(-0.724134\pi\)
−0.647378 + 0.762169i \(0.724134\pi\)
\(54\) −203.917 −0.513881
\(55\) 0 0
\(56\) 1206.45 2.87891
\(57\) −19.4898 −0.0452894
\(58\) −1150.70 −2.60507
\(59\) −562.752 −1.24176 −0.620882 0.783904i \(-0.713225\pi\)
−0.620882 + 0.783904i \(0.713225\pi\)
\(60\) 0 0
\(61\) 548.091 1.15042 0.575212 0.818004i \(-0.304919\pi\)
0.575212 + 0.818004i \(0.304919\pi\)
\(62\) 975.591 1.99839
\(63\) −800.437 −1.60072
\(64\) −491.814 −0.960575
\(65\) 0 0
\(66\) 85.6600 0.159758
\(67\) 760.831 1.38732 0.693659 0.720304i \(-0.255998\pi\)
0.693659 + 0.720304i \(0.255998\pi\)
\(68\) 1162.08 2.07240
\(69\) −80.2586 −0.140029
\(70\) 0 0
\(71\) −668.059 −1.11668 −0.558338 0.829613i \(-0.688561\pi\)
−0.558338 + 0.829613i \(0.688561\pi\)
\(72\) −1050.08 −1.71880
\(73\) 1145.92 1.83726 0.918629 0.395121i \(-0.129297\pi\)
0.918629 + 0.395121i \(0.129297\pi\)
\(74\) 997.040 1.56626
\(75\) 0 0
\(76\) −403.469 −0.608961
\(77\) 680.193 1.00669
\(78\) 236.878 0.343861
\(79\) 975.010 1.38857 0.694286 0.719699i \(-0.255720\pi\)
0.694286 + 0.719699i \(0.255720\pi\)
\(80\) 0 0
\(81\) 680.353 0.933269
\(82\) 1035.37 1.39435
\(83\) −698.827 −0.924171 −0.462086 0.886835i \(-0.652899\pi\)
−0.462086 + 0.886835i \(0.652899\pi\)
\(84\) 379.873 0.493423
\(85\) 0 0
\(86\) −547.067 −0.685950
\(87\) −182.321 −0.224677
\(88\) 892.335 1.08095
\(89\) 451.477 0.537713 0.268857 0.963180i \(-0.413354\pi\)
0.268857 + 0.963180i \(0.413354\pi\)
\(90\) 0 0
\(91\) 1880.96 2.16679
\(92\) −1661.47 −1.88283
\(93\) 154.577 0.172353
\(94\) −230.747 −0.253189
\(95\) 0 0
\(96\) 6.35576 0.00675710
\(97\) 390.906 0.409180 0.204590 0.978848i \(-0.434414\pi\)
0.204590 + 0.978848i \(0.434414\pi\)
\(98\) 2830.99 2.91810
\(99\) −592.031 −0.601024
\(100\) 0 0
\(101\) −1112.66 −1.09618 −0.548089 0.836420i \(-0.684644\pi\)
−0.548089 + 0.836420i \(0.684644\pi\)
\(102\) 275.596 0.267530
\(103\) 882.574 0.844298 0.422149 0.906527i \(-0.361276\pi\)
0.422149 + 0.906527i \(0.361276\pi\)
\(104\) 2467.60 2.32662
\(105\) 0 0
\(106\) −2452.68 −2.24741
\(107\) −840.742 −0.759604 −0.379802 0.925068i \(-0.624008\pi\)
−0.379802 + 0.925068i \(0.624008\pi\)
\(108\) −668.853 −0.595930
\(109\) −1321.06 −1.16086 −0.580432 0.814309i \(-0.697116\pi\)
−0.580432 + 0.814309i \(0.697116\pi\)
\(110\) 0 0
\(111\) 157.975 0.135084
\(112\) 2016.37 1.70115
\(113\) −701.293 −0.583824 −0.291912 0.956445i \(-0.594291\pi\)
−0.291912 + 0.956445i \(0.594291\pi\)
\(114\) −95.6857 −0.0786122
\(115\) 0 0
\(116\) −3774.32 −3.02101
\(117\) −1637.16 −1.29364
\(118\) −2762.84 −2.15542
\(119\) 2188.40 1.68580
\(120\) 0 0
\(121\) −827.906 −0.622018
\(122\) 2690.86 1.99688
\(123\) 164.047 0.120257
\(124\) 3199.96 2.31746
\(125\) 0 0
\(126\) −3929.76 −2.77850
\(127\) −1142.65 −0.798374 −0.399187 0.916869i \(-0.630708\pi\)
−0.399187 + 0.916869i \(0.630708\pi\)
\(128\) −2479.94 −1.71248
\(129\) −86.6795 −0.0591605
\(130\) 0 0
\(131\) 104.451 0.0696639 0.0348319 0.999393i \(-0.488910\pi\)
0.0348319 + 0.999393i \(0.488910\pi\)
\(132\) 280.967 0.185265
\(133\) −759.803 −0.495363
\(134\) 3735.31 2.40807
\(135\) 0 0
\(136\) 2870.93 1.81015
\(137\) 543.914 0.339195 0.169598 0.985513i \(-0.445753\pi\)
0.169598 + 0.985513i \(0.445753\pi\)
\(138\) −394.031 −0.243059
\(139\) −41.8374 −0.0255295 −0.0127647 0.999919i \(-0.504063\pi\)
−0.0127647 + 0.999919i \(0.504063\pi\)
\(140\) 0 0
\(141\) −36.5605 −0.0218365
\(142\) −3279.85 −1.93830
\(143\) 1391.22 0.813565
\(144\) −1755.02 −1.01564
\(145\) 0 0
\(146\) 5625.91 3.18907
\(147\) 448.554 0.251674
\(148\) 3270.32 1.81634
\(149\) 790.139 0.434435 0.217217 0.976123i \(-0.430302\pi\)
0.217217 + 0.976123i \(0.430302\pi\)
\(150\) 0 0
\(151\) −2073.79 −1.11763 −0.558816 0.829292i \(-0.688744\pi\)
−0.558816 + 0.829292i \(0.688744\pi\)
\(152\) −996.774 −0.531902
\(153\) −1904.76 −1.00648
\(154\) 3339.42 1.74739
\(155\) 0 0
\(156\) 776.967 0.398764
\(157\) −2501.12 −1.27141 −0.635704 0.771933i \(-0.719290\pi\)
−0.635704 + 0.771933i \(0.719290\pi\)
\(158\) 4786.83 2.41025
\(159\) −388.612 −0.193830
\(160\) 0 0
\(161\) −3128.85 −1.53160
\(162\) 3340.20 1.61995
\(163\) 97.0569 0.0466386 0.0233193 0.999728i \(-0.492577\pi\)
0.0233193 + 0.999728i \(0.492577\pi\)
\(164\) 3396.03 1.61698
\(165\) 0 0
\(166\) −3430.90 −1.60415
\(167\) 1826.71 0.846437 0.423218 0.906028i \(-0.360900\pi\)
0.423218 + 0.906028i \(0.360900\pi\)
\(168\) 938.480 0.430984
\(169\) 1650.19 0.751111
\(170\) 0 0
\(171\) 661.323 0.295746
\(172\) −1794.39 −0.795473
\(173\) 1843.63 0.810223 0.405111 0.914267i \(-0.367233\pi\)
0.405111 + 0.914267i \(0.367233\pi\)
\(174\) −895.109 −0.389989
\(175\) 0 0
\(176\) 1491.38 0.638732
\(177\) −437.756 −0.185897
\(178\) 2216.53 0.933350
\(179\) −370.515 −0.154713 −0.0773565 0.997003i \(-0.524648\pi\)
−0.0773565 + 0.997003i \(0.524648\pi\)
\(180\) 0 0
\(181\) −866.586 −0.355872 −0.177936 0.984042i \(-0.556942\pi\)
−0.177936 + 0.984042i \(0.556942\pi\)
\(182\) 9234.60 3.76107
\(183\) 426.351 0.172223
\(184\) −4104.69 −1.64457
\(185\) 0 0
\(186\) 758.896 0.299166
\(187\) 1618.62 0.632969
\(188\) −756.857 −0.293614
\(189\) −1259.57 −0.484763
\(190\) 0 0
\(191\) −3667.49 −1.38937 −0.694687 0.719312i \(-0.744457\pi\)
−0.694687 + 0.719312i \(0.744457\pi\)
\(192\) −382.574 −0.143802
\(193\) 4676.91 1.74431 0.872154 0.489231i \(-0.162723\pi\)
0.872154 + 0.489231i \(0.162723\pi\)
\(194\) 1919.16 0.710245
\(195\) 0 0
\(196\) 9285.73 3.38401
\(197\) −3700.99 −1.33850 −0.669251 0.743037i \(-0.733385\pi\)
−0.669251 + 0.743037i \(0.733385\pi\)
\(198\) −2906.59 −1.04324
\(199\) −1361.63 −0.485042 −0.242521 0.970146i \(-0.577974\pi\)
−0.242521 + 0.970146i \(0.577974\pi\)
\(200\) 0 0
\(201\) 591.838 0.207687
\(202\) −5462.63 −1.90272
\(203\) −7107.72 −2.45746
\(204\) 903.964 0.310246
\(205\) 0 0
\(206\) 4333.01 1.46551
\(207\) 2723.31 0.914411
\(208\) 4124.15 1.37480
\(209\) −561.977 −0.185994
\(210\) 0 0
\(211\) −2873.21 −0.937442 −0.468721 0.883346i \(-0.655285\pi\)
−0.468721 + 0.883346i \(0.655285\pi\)
\(212\) −8044.85 −2.60624
\(213\) −519.672 −0.167171
\(214\) −4127.64 −1.31850
\(215\) 0 0
\(216\) −1652.41 −0.520519
\(217\) 6026.10 1.88515
\(218\) −6485.74 −2.01500
\(219\) 891.393 0.275044
\(220\) 0 0
\(221\) 4476.02 1.36240
\(222\) 775.581 0.234476
\(223\) −3356.14 −1.00782 −0.503909 0.863757i \(-0.668105\pi\)
−0.503909 + 0.863757i \(0.668105\pi\)
\(224\) 247.777 0.0739074
\(225\) 0 0
\(226\) −3443.01 −1.01339
\(227\) 3991.01 1.16693 0.583464 0.812139i \(-0.301697\pi\)
0.583464 + 0.812139i \(0.301697\pi\)
\(228\) −313.852 −0.0911638
\(229\) −968.028 −0.279341 −0.139670 0.990198i \(-0.544604\pi\)
−0.139670 + 0.990198i \(0.544604\pi\)
\(230\) 0 0
\(231\) 529.111 0.150705
\(232\) −9324.51 −2.63872
\(233\) 1227.70 0.345189 0.172595 0.984993i \(-0.444785\pi\)
0.172595 + 0.984993i \(0.444785\pi\)
\(234\) −8037.68 −2.24547
\(235\) 0 0
\(236\) −9062.19 −2.49957
\(237\) 758.444 0.207875
\(238\) 10744.0 2.92618
\(239\) 647.534 0.175253 0.0876265 0.996153i \(-0.472072\pi\)
0.0876265 + 0.996153i \(0.472072\pi\)
\(240\) 0 0
\(241\) −4174.42 −1.11576 −0.557880 0.829922i \(-0.688385\pi\)
−0.557880 + 0.829922i \(0.688385\pi\)
\(242\) −4064.62 −1.07968
\(243\) 1650.68 0.435766
\(244\) 8826.10 2.31571
\(245\) 0 0
\(246\) 805.394 0.208740
\(247\) −1554.05 −0.400332
\(248\) 7905.55 2.02421
\(249\) −543.606 −0.138352
\(250\) 0 0
\(251\) −1368.39 −0.344112 −0.172056 0.985087i \(-0.555041\pi\)
−0.172056 + 0.985087i \(0.555041\pi\)
\(252\) −12889.7 −3.22213
\(253\) −2314.20 −0.575070
\(254\) −5609.84 −1.38580
\(255\) 0 0
\(256\) −8240.77 −2.01191
\(257\) −1709.94 −0.415031 −0.207515 0.978232i \(-0.566538\pi\)
−0.207515 + 0.978232i \(0.566538\pi\)
\(258\) −425.554 −0.102689
\(259\) 6158.59 1.47752
\(260\) 0 0
\(261\) 6186.47 1.46718
\(262\) 512.806 0.120921
\(263\) −5368.95 −1.25880 −0.629399 0.777082i \(-0.716699\pi\)
−0.629399 + 0.777082i \(0.716699\pi\)
\(264\) 694.133 0.161822
\(265\) 0 0
\(266\) −3730.27 −0.859840
\(267\) 351.197 0.0804977
\(268\) 12251.9 2.79256
\(269\) −4213.70 −0.955070 −0.477535 0.878613i \(-0.658470\pi\)
−0.477535 + 0.878613i \(0.658470\pi\)
\(270\) 0 0
\(271\) 4769.83 1.06918 0.534588 0.845113i \(-0.320467\pi\)
0.534588 + 0.845113i \(0.320467\pi\)
\(272\) 4798.25 1.06962
\(273\) 1463.17 0.324377
\(274\) 2670.36 0.588767
\(275\) 0 0
\(276\) −1292.43 −0.281867
\(277\) −5651.38 −1.22584 −0.612922 0.790144i \(-0.710006\pi\)
−0.612922 + 0.790144i \(0.710006\pi\)
\(278\) −205.401 −0.0443135
\(279\) −5245.04 −1.12549
\(280\) 0 0
\(281\) 3264.83 0.693109 0.346554 0.938030i \(-0.387352\pi\)
0.346554 + 0.938030i \(0.387352\pi\)
\(282\) −179.495 −0.0379033
\(283\) −2019.38 −0.424169 −0.212084 0.977251i \(-0.568025\pi\)
−0.212084 + 0.977251i \(0.568025\pi\)
\(284\) −10758.0 −2.24778
\(285\) 0 0
\(286\) 6830.23 1.41217
\(287\) 6395.32 1.31534
\(288\) −215.662 −0.0441249
\(289\) 294.634 0.0599703
\(290\) 0 0
\(291\) 304.079 0.0612558
\(292\) 18453.2 3.69825
\(293\) −3432.28 −0.684354 −0.342177 0.939636i \(-0.611164\pi\)
−0.342177 + 0.939636i \(0.611164\pi\)
\(294\) 2202.18 0.436850
\(295\) 0 0
\(296\) 8079.36 1.58650
\(297\) −931.621 −0.182014
\(298\) 3879.20 0.754081
\(299\) −6399.54 −1.23778
\(300\) 0 0
\(301\) −3379.16 −0.647082
\(302\) −10181.3 −1.93996
\(303\) −865.521 −0.164102
\(304\) −1665.93 −0.314301
\(305\) 0 0
\(306\) −9351.45 −1.74702
\(307\) 6327.92 1.17640 0.588198 0.808717i \(-0.299838\pi\)
0.588198 + 0.808717i \(0.299838\pi\)
\(308\) 10953.4 2.02639
\(309\) 686.540 0.126395
\(310\) 0 0
\(311\) 9118.69 1.66262 0.831308 0.555812i \(-0.187592\pi\)
0.831308 + 0.555812i \(0.187592\pi\)
\(312\) 1919.51 0.348303
\(313\) −4611.70 −0.832808 −0.416404 0.909180i \(-0.636710\pi\)
−0.416404 + 0.909180i \(0.636710\pi\)
\(314\) −12279.3 −2.20688
\(315\) 0 0
\(316\) 15700.9 2.79508
\(317\) 4243.78 0.751907 0.375954 0.926638i \(-0.377315\pi\)
0.375954 + 0.926638i \(0.377315\pi\)
\(318\) −1907.90 −0.336445
\(319\) −5257.12 −0.922702
\(320\) 0 0
\(321\) −654.000 −0.113716
\(322\) −15361.1 −2.65851
\(323\) −1808.06 −0.311466
\(324\) 10956.0 1.87859
\(325\) 0 0
\(326\) 476.502 0.0809541
\(327\) −1027.63 −0.173786
\(328\) 8389.92 1.41237
\(329\) −1425.30 −0.238842
\(330\) 0 0
\(331\) −3803.59 −0.631613 −0.315807 0.948824i \(-0.602275\pi\)
−0.315807 + 0.948824i \(0.602275\pi\)
\(332\) −11253.5 −1.86028
\(333\) −5360.36 −0.882120
\(334\) 8968.25 1.46922
\(335\) 0 0
\(336\) 1568.50 0.254669
\(337\) 6419.12 1.03760 0.518801 0.854895i \(-0.326379\pi\)
0.518801 + 0.854895i \(0.326379\pi\)
\(338\) 8101.64 1.30376
\(339\) −545.524 −0.0874006
\(340\) 0 0
\(341\) 4457.11 0.707819
\(342\) 3246.78 0.513350
\(343\) 7085.05 1.11533
\(344\) −4433.07 −0.694812
\(345\) 0 0
\(346\) 9051.33 1.40637
\(347\) 3495.57 0.540783 0.270392 0.962750i \(-0.412847\pi\)
0.270392 + 0.962750i \(0.412847\pi\)
\(348\) −2935.98 −0.452256
\(349\) −435.838 −0.0668477 −0.0334239 0.999441i \(-0.510641\pi\)
−0.0334239 + 0.999441i \(0.510641\pi\)
\(350\) 0 0
\(351\) −2576.24 −0.391765
\(352\) 183.264 0.0277500
\(353\) −1941.73 −0.292771 −0.146385 0.989228i \(-0.546764\pi\)
−0.146385 + 0.989228i \(0.546764\pi\)
\(354\) −2149.17 −0.322675
\(355\) 0 0
\(356\) 7270.29 1.08237
\(357\) 1702.32 0.252371
\(358\) −1819.05 −0.268547
\(359\) 7188.88 1.05687 0.528433 0.848975i \(-0.322780\pi\)
0.528433 + 0.848975i \(0.322780\pi\)
\(360\) 0 0
\(361\) −6231.25 −0.908478
\(362\) −4254.52 −0.617714
\(363\) −644.014 −0.0931184
\(364\) 30289.7 4.36158
\(365\) 0 0
\(366\) 2093.18 0.298940
\(367\) −1674.78 −0.238209 −0.119105 0.992882i \(-0.538002\pi\)
−0.119105 + 0.992882i \(0.538002\pi\)
\(368\) −6860.25 −0.971780
\(369\) −5566.41 −0.785300
\(370\) 0 0
\(371\) −15149.9 −2.12006
\(372\) 2489.20 0.346933
\(373\) −6028.31 −0.836820 −0.418410 0.908258i \(-0.637412\pi\)
−0.418410 + 0.908258i \(0.637412\pi\)
\(374\) 7946.64 1.09869
\(375\) 0 0
\(376\) −1869.83 −0.256460
\(377\) −14537.7 −1.98602
\(378\) −6183.87 −0.841439
\(379\) −2065.63 −0.279959 −0.139979 0.990154i \(-0.544704\pi\)
−0.139979 + 0.990154i \(0.544704\pi\)
\(380\) 0 0
\(381\) −888.846 −0.119520
\(382\) −18005.6 −2.41164
\(383\) −7634.28 −1.01852 −0.509260 0.860613i \(-0.670081\pi\)
−0.509260 + 0.860613i \(0.670081\pi\)
\(384\) −1929.10 −0.256365
\(385\) 0 0
\(386\) 22961.4 3.02773
\(387\) 2941.18 0.386327
\(388\) 6294.89 0.823646
\(389\) −2814.13 −0.366792 −0.183396 0.983039i \(-0.558709\pi\)
−0.183396 + 0.983039i \(0.558709\pi\)
\(390\) 0 0
\(391\) −7445.55 −0.963012
\(392\) 22940.5 2.95579
\(393\) 81.2511 0.0104289
\(394\) −18170.1 −2.32334
\(395\) 0 0
\(396\) −9533.69 −1.20981
\(397\) −8990.52 −1.13658 −0.568288 0.822829i \(-0.692394\pi\)
−0.568288 + 0.822829i \(0.692394\pi\)
\(398\) −6684.94 −0.841924
\(399\) −591.039 −0.0741577
\(400\) 0 0
\(401\) −4829.93 −0.601484 −0.300742 0.953706i \(-0.597234\pi\)
−0.300742 + 0.953706i \(0.597234\pi\)
\(402\) 2905.64 0.360497
\(403\) 12325.4 1.52350
\(404\) −17917.6 −2.20652
\(405\) 0 0
\(406\) −34895.5 −4.26560
\(407\) 4555.11 0.554763
\(408\) 2233.25 0.270987
\(409\) −6551.78 −0.792089 −0.396045 0.918231i \(-0.629617\pi\)
−0.396045 + 0.918231i \(0.629617\pi\)
\(410\) 0 0
\(411\) 423.102 0.0507788
\(412\) 14212.4 1.69950
\(413\) −17065.7 −2.03329
\(414\) 13370.1 1.58721
\(415\) 0 0
\(416\) 506.786 0.0597289
\(417\) −32.5446 −0.00382186
\(418\) −2759.03 −0.322844
\(419\) 10660.5 1.24296 0.621481 0.783429i \(-0.286531\pi\)
0.621481 + 0.783429i \(0.286531\pi\)
\(420\) 0 0
\(421\) −8654.47 −1.00188 −0.500942 0.865481i \(-0.667013\pi\)
−0.500942 + 0.865481i \(0.667013\pi\)
\(422\) −14106.1 −1.62719
\(423\) 1240.56 0.142596
\(424\) −19874.9 −2.27644
\(425\) 0 0
\(426\) −2551.34 −0.290171
\(427\) 16621.1 1.88373
\(428\) −13538.8 −1.52902
\(429\) 1082.21 0.121794
\(430\) 0 0
\(431\) 4990.22 0.557703 0.278852 0.960334i \(-0.410046\pi\)
0.278852 + 0.960334i \(0.410046\pi\)
\(432\) −2761.71 −0.307575
\(433\) 7921.49 0.879174 0.439587 0.898200i \(-0.355125\pi\)
0.439587 + 0.898200i \(0.355125\pi\)
\(434\) 29585.2 3.27220
\(435\) 0 0
\(436\) −21273.4 −2.33673
\(437\) 2585.06 0.282975
\(438\) 4376.31 0.477416
\(439\) 11034.1 1.19961 0.599807 0.800145i \(-0.295244\pi\)
0.599807 + 0.800145i \(0.295244\pi\)
\(440\) 0 0
\(441\) −15220.2 −1.64347
\(442\) 21975.1 2.36482
\(443\) −9160.66 −0.982474 −0.491237 0.871026i \(-0.663455\pi\)
−0.491237 + 0.871026i \(0.663455\pi\)
\(444\) 2543.93 0.271913
\(445\) 0 0
\(446\) −16477.0 −1.74935
\(447\) 614.636 0.0650365
\(448\) −14914.5 −1.57287
\(449\) −10071.1 −1.05854 −0.529271 0.848453i \(-0.677535\pi\)
−0.529271 + 0.848453i \(0.677535\pi\)
\(450\) 0 0
\(451\) 4730.20 0.493872
\(452\) −11293.2 −1.17519
\(453\) −1613.16 −0.167314
\(454\) 19593.9 2.02553
\(455\) 0 0
\(456\) −775.374 −0.0796277
\(457\) 2988.54 0.305904 0.152952 0.988234i \(-0.451122\pi\)
0.152952 + 0.988234i \(0.451122\pi\)
\(458\) −4752.55 −0.484873
\(459\) −2997.33 −0.304800
\(460\) 0 0
\(461\) 956.638 0.0966487 0.0483244 0.998832i \(-0.484612\pi\)
0.0483244 + 0.998832i \(0.484612\pi\)
\(462\) 2597.68 0.261591
\(463\) 4352.75 0.436910 0.218455 0.975847i \(-0.429898\pi\)
0.218455 + 0.975847i \(0.429898\pi\)
\(464\) −15584.2 −1.55923
\(465\) 0 0
\(466\) 6027.40 0.599171
\(467\) −8131.35 −0.805725 −0.402863 0.915260i \(-0.631985\pi\)
−0.402863 + 0.915260i \(0.631985\pi\)
\(468\) −26363.8 −2.60399
\(469\) 23072.5 2.27162
\(470\) 0 0
\(471\) −1945.58 −0.190335
\(472\) −22388.2 −2.18327
\(473\) −2499.35 −0.242960
\(474\) 3723.60 0.360824
\(475\) 0 0
\(476\) 35240.6 3.39339
\(477\) 13186.3 1.26574
\(478\) 3179.08 0.304200
\(479\) −12912.4 −1.23170 −0.615849 0.787864i \(-0.711187\pi\)
−0.615849 + 0.787864i \(0.711187\pi\)
\(480\) 0 0
\(481\) 12596.4 1.19407
\(482\) −20494.4 −1.93671
\(483\) −2433.88 −0.229286
\(484\) −13332.1 −1.25207
\(485\) 0 0
\(486\) 8104.04 0.756393
\(487\) 11010.0 1.02446 0.512228 0.858850i \(-0.328820\pi\)
0.512228 + 0.858850i \(0.328820\pi\)
\(488\) 21805.0 2.02268
\(489\) 75.4990 0.00698197
\(490\) 0 0
\(491\) −14636.7 −1.34531 −0.672655 0.739956i \(-0.734846\pi\)
−0.672655 + 0.739956i \(0.734846\pi\)
\(492\) 2641.71 0.242068
\(493\) −16913.9 −1.54516
\(494\) −7629.64 −0.694887
\(495\) 0 0
\(496\) 13212.7 1.19611
\(497\) −20259.2 −1.82847
\(498\) −2668.84 −0.240148
\(499\) −7549.78 −0.677304 −0.338652 0.940912i \(-0.609971\pi\)
−0.338652 + 0.940912i \(0.609971\pi\)
\(500\) 0 0
\(501\) 1420.97 0.126715
\(502\) −6718.14 −0.597301
\(503\) 16150.9 1.43167 0.715837 0.698267i \(-0.246045\pi\)
0.715837 + 0.698267i \(0.246045\pi\)
\(504\) −31844.2 −2.81439
\(505\) 0 0
\(506\) −11361.6 −0.998193
\(507\) 1283.66 0.112444
\(508\) −18400.4 −1.60706
\(509\) 19183.7 1.67053 0.835266 0.549846i \(-0.185314\pi\)
0.835266 + 0.549846i \(0.185314\pi\)
\(510\) 0 0
\(511\) 34750.6 3.00836
\(512\) −20618.7 −1.77974
\(513\) 1040.66 0.0895637
\(514\) −8394.96 −0.720400
\(515\) 0 0
\(516\) −1395.83 −0.119085
\(517\) −1054.20 −0.0896782
\(518\) 30235.7 2.56464
\(519\) 1434.13 0.121293
\(520\) 0 0
\(521\) 6867.69 0.577503 0.288751 0.957404i \(-0.406760\pi\)
0.288751 + 0.957404i \(0.406760\pi\)
\(522\) 30372.6 2.54669
\(523\) −11205.2 −0.936841 −0.468420 0.883506i \(-0.655177\pi\)
−0.468420 + 0.883506i \(0.655177\pi\)
\(524\) 1682.02 0.140228
\(525\) 0 0
\(526\) −26359.0 −2.18499
\(527\) 14340.0 1.18531
\(528\) 1160.12 0.0956206
\(529\) −1521.81 −0.125076
\(530\) 0 0
\(531\) 14853.8 1.21393
\(532\) −12235.4 −0.997126
\(533\) 13080.6 1.06301
\(534\) 1724.21 0.139726
\(535\) 0 0
\(536\) 30268.5 2.43918
\(537\) −288.218 −0.0231611
\(538\) −20687.2 −1.65779
\(539\) 12933.8 1.03357
\(540\) 0 0
\(541\) 14471.4 1.15004 0.575021 0.818139i \(-0.304994\pi\)
0.575021 + 0.818139i \(0.304994\pi\)
\(542\) 23417.6 1.85585
\(543\) −674.103 −0.0532754
\(544\) 589.621 0.0464702
\(545\) 0 0
\(546\) 7183.44 0.563046
\(547\) 13482.7 1.05389 0.526946 0.849899i \(-0.323337\pi\)
0.526946 + 0.849899i \(0.323337\pi\)
\(548\) 8758.84 0.682772
\(549\) −14466.8 −1.12464
\(550\) 0 0
\(551\) 5872.41 0.454035
\(552\) −3192.97 −0.246199
\(553\) 29567.6 2.27368
\(554\) −27745.6 −2.12779
\(555\) 0 0
\(556\) −673.722 −0.0513888
\(557\) −10194.0 −0.775466 −0.387733 0.921772i \(-0.626742\pi\)
−0.387733 + 0.921772i \(0.626742\pi\)
\(558\) −25750.6 −1.95360
\(559\) −6911.52 −0.522945
\(560\) 0 0
\(561\) 1259.10 0.0947579
\(562\) 16028.7 1.20308
\(563\) −3725.21 −0.278862 −0.139431 0.990232i \(-0.544527\pi\)
−0.139431 + 0.990232i \(0.544527\pi\)
\(564\) −588.747 −0.0439552
\(565\) 0 0
\(566\) −9914.18 −0.736262
\(567\) 20632.0 1.52815
\(568\) −26577.7 −1.96334
\(569\) −6274.57 −0.462291 −0.231145 0.972919i \(-0.574247\pi\)
−0.231145 + 0.972919i \(0.574247\pi\)
\(570\) 0 0
\(571\) 20390.6 1.49443 0.747214 0.664584i \(-0.231391\pi\)
0.747214 + 0.664584i \(0.231391\pi\)
\(572\) 22403.3 1.63764
\(573\) −2852.88 −0.207995
\(574\) 31397.9 2.28314
\(575\) 0 0
\(576\) 12981.4 0.939048
\(577\) −675.385 −0.0487290 −0.0243645 0.999703i \(-0.507756\pi\)
−0.0243645 + 0.999703i \(0.507756\pi\)
\(578\) 1446.51 0.104095
\(579\) 3638.09 0.261130
\(580\) 0 0
\(581\) −21192.3 −1.51326
\(582\) 1492.88 0.106326
\(583\) −11205.4 −0.796019
\(584\) 45588.7 3.23027
\(585\) 0 0
\(586\) −16850.8 −1.18788
\(587\) 5949.63 0.418343 0.209172 0.977879i \(-0.432923\pi\)
0.209172 + 0.977879i \(0.432923\pi\)
\(588\) 7223.22 0.506600
\(589\) −4978.78 −0.348297
\(590\) 0 0
\(591\) −2878.94 −0.200379
\(592\) 13503.2 0.937464
\(593\) 22071.9 1.52847 0.764235 0.644937i \(-0.223117\pi\)
0.764235 + 0.644937i \(0.223117\pi\)
\(594\) −4573.81 −0.315935
\(595\) 0 0
\(596\) 12723.9 0.874481
\(597\) −1059.19 −0.0726126
\(598\) −31418.6 −2.14850
\(599\) −9547.79 −0.651272 −0.325636 0.945495i \(-0.605578\pi\)
−0.325636 + 0.945495i \(0.605578\pi\)
\(600\) 0 0
\(601\) −12303.7 −0.835076 −0.417538 0.908660i \(-0.637107\pi\)
−0.417538 + 0.908660i \(0.637107\pi\)
\(602\) −16590.1 −1.12319
\(603\) −20082.0 −1.35623
\(604\) −33394.9 −2.24970
\(605\) 0 0
\(606\) −4249.29 −0.284844
\(607\) −18252.2 −1.22049 −0.610243 0.792214i \(-0.708928\pi\)
−0.610243 + 0.792214i \(0.708928\pi\)
\(608\) −204.714 −0.0136550
\(609\) −5528.98 −0.367891
\(610\) 0 0
\(611\) −2915.21 −0.193022
\(612\) −30673.0 −2.02595
\(613\) 13990.5 0.921809 0.460905 0.887450i \(-0.347525\pi\)
0.460905 + 0.887450i \(0.347525\pi\)
\(614\) 31067.0 2.04196
\(615\) 0 0
\(616\) 27060.5 1.76996
\(617\) 5747.16 0.374995 0.187498 0.982265i \(-0.439962\pi\)
0.187498 + 0.982265i \(0.439962\pi\)
\(618\) 3370.58 0.219393
\(619\) −3913.70 −0.254127 −0.127064 0.991895i \(-0.540555\pi\)
−0.127064 + 0.991895i \(0.540555\pi\)
\(620\) 0 0
\(621\) 4285.40 0.276920
\(622\) 44768.4 2.88593
\(623\) 13691.3 0.880463
\(624\) 3208.11 0.205813
\(625\) 0 0
\(626\) −22641.2 −1.44557
\(627\) −437.153 −0.0278440
\(628\) −40276.4 −2.55924
\(629\) 14655.3 0.929006
\(630\) 0 0
\(631\) 26311.5 1.65998 0.829988 0.557781i \(-0.188347\pi\)
0.829988 + 0.557781i \(0.188347\pi\)
\(632\) 38789.3 2.44139
\(633\) −2235.03 −0.140339
\(634\) 20834.9 1.30514
\(635\) 0 0
\(636\) −6257.96 −0.390164
\(637\) 35766.1 2.22466
\(638\) −25809.9 −1.60160
\(639\) 17633.4 1.09165
\(640\) 0 0
\(641\) 15538.7 0.957476 0.478738 0.877958i \(-0.341094\pi\)
0.478738 + 0.877958i \(0.341094\pi\)
\(642\) −3210.82 −0.197385
\(643\) −6125.10 −0.375661 −0.187831 0.982201i \(-0.560146\pi\)
−0.187831 + 0.982201i \(0.560146\pi\)
\(644\) −50384.9 −3.08299
\(645\) 0 0
\(646\) −8876.72 −0.540635
\(647\) −4635.86 −0.281692 −0.140846 0.990032i \(-0.544982\pi\)
−0.140846 + 0.990032i \(0.544982\pi\)
\(648\) 27066.8 1.64087
\(649\) −12622.4 −0.763440
\(650\) 0 0
\(651\) 4687.61 0.282215
\(652\) 1562.94 0.0938796
\(653\) 11926.6 0.714740 0.357370 0.933963i \(-0.383674\pi\)
0.357370 + 0.933963i \(0.383674\pi\)
\(654\) −5045.15 −0.301653
\(655\) 0 0
\(656\) 14022.3 0.834569
\(657\) −30246.4 −1.79608
\(658\) −6997.52 −0.414577
\(659\) 881.384 0.0520999 0.0260500 0.999661i \(-0.491707\pi\)
0.0260500 + 0.999661i \(0.491707\pi\)
\(660\) 0 0
\(661\) −19161.6 −1.12753 −0.563766 0.825935i \(-0.690648\pi\)
−0.563766 + 0.825935i \(0.690648\pi\)
\(662\) −18673.8 −1.09634
\(663\) 3481.82 0.203956
\(664\) −27801.8 −1.62488
\(665\) 0 0
\(666\) −26316.8 −1.53116
\(667\) 24182.4 1.40382
\(668\) 29416.1 1.70381
\(669\) −2610.68 −0.150874
\(670\) 0 0
\(671\) 12293.6 0.707284
\(672\) 192.741 0.0110642
\(673\) −20156.0 −1.15447 −0.577235 0.816578i \(-0.695868\pi\)
−0.577235 + 0.816578i \(0.695868\pi\)
\(674\) 31514.8 1.80104
\(675\) 0 0
\(676\) 26573.6 1.51192
\(677\) −5567.34 −0.316056 −0.158028 0.987435i \(-0.550514\pi\)
−0.158028 + 0.987435i \(0.550514\pi\)
\(678\) −2678.26 −0.151708
\(679\) 11854.4 0.670000
\(680\) 0 0
\(681\) 3104.54 0.174694
\(682\) 21882.3 1.22861
\(683\) 27835.8 1.55946 0.779728 0.626118i \(-0.215357\pi\)
0.779728 + 0.626118i \(0.215357\pi\)
\(684\) 10649.5 0.595314
\(685\) 0 0
\(686\) 34784.2 1.93596
\(687\) −753.013 −0.0418184
\(688\) −7409.09 −0.410565
\(689\) −30986.6 −1.71334
\(690\) 0 0
\(691\) 17125.7 0.942824 0.471412 0.881913i \(-0.343745\pi\)
0.471412 + 0.881913i \(0.343745\pi\)
\(692\) 29688.6 1.63091
\(693\) −17953.6 −0.984129
\(694\) 17161.5 0.938679
\(695\) 0 0
\(696\) −7253.38 −0.395027
\(697\) 15218.6 0.827039
\(698\) −2139.75 −0.116033
\(699\) 955.005 0.0516761
\(700\) 0 0
\(701\) 5107.63 0.275196 0.137598 0.990488i \(-0.456062\pi\)
0.137598 + 0.990488i \(0.456062\pi\)
\(702\) −12648.1 −0.680016
\(703\) −5088.24 −0.272983
\(704\) −11031.3 −0.590564
\(705\) 0 0
\(706\) −9532.97 −0.508184
\(707\) −33742.0 −1.79490
\(708\) −7049.33 −0.374195
\(709\) 11258.0 0.596335 0.298167 0.954514i \(-0.403625\pi\)
0.298167 + 0.954514i \(0.403625\pi\)
\(710\) 0 0
\(711\) −25735.3 −1.35745
\(712\) 17961.3 0.945407
\(713\) −20502.5 −1.07689
\(714\) 8357.59 0.438060
\(715\) 0 0
\(716\) −5966.54 −0.311425
\(717\) 503.706 0.0262360
\(718\) 35293.9 1.83448
\(719\) −13735.6 −0.712448 −0.356224 0.934401i \(-0.615936\pi\)
−0.356224 + 0.934401i \(0.615936\pi\)
\(720\) 0 0
\(721\) 26764.5 1.38247
\(722\) −30592.4 −1.57691
\(723\) −3247.21 −0.167033
\(724\) −13954.9 −0.716341
\(725\) 0 0
\(726\) −3161.80 −0.161633
\(727\) −14515.4 −0.740502 −0.370251 0.928932i \(-0.620728\pi\)
−0.370251 + 0.928932i \(0.620728\pi\)
\(728\) 74831.1 3.80965
\(729\) −17085.5 −0.868033
\(730\) 0 0
\(731\) −8041.22 −0.406861
\(732\) 6865.68 0.346671
\(733\) −14218.5 −0.716471 −0.358236 0.933631i \(-0.616622\pi\)
−0.358236 + 0.933631i \(0.616622\pi\)
\(734\) −8222.36 −0.413478
\(735\) 0 0
\(736\) −843.004 −0.0422195
\(737\) 17065.3 0.852926
\(738\) −27328.4 −1.36310
\(739\) 8651.36 0.430643 0.215322 0.976543i \(-0.430920\pi\)
0.215322 + 0.976543i \(0.430920\pi\)
\(740\) 0 0
\(741\) −1208.87 −0.0599312
\(742\) −74378.6 −3.67995
\(743\) 37263.7 1.83993 0.919967 0.391996i \(-0.128215\pi\)
0.919967 + 0.391996i \(0.128215\pi\)
\(744\) 6149.60 0.303031
\(745\) 0 0
\(746\) −29596.1 −1.45253
\(747\) 18445.5 0.903460
\(748\) 26065.2 1.27412
\(749\) −25495.9 −1.24379
\(750\) 0 0
\(751\) −33980.7 −1.65110 −0.825548 0.564331i \(-0.809134\pi\)
−0.825548 + 0.564331i \(0.809134\pi\)
\(752\) −3125.08 −0.151542
\(753\) −1064.45 −0.0515148
\(754\) −71372.9 −3.44728
\(755\) 0 0
\(756\) −20283.3 −0.975788
\(757\) 33247.9 1.59632 0.798161 0.602445i \(-0.205807\pi\)
0.798161 + 0.602445i \(0.205807\pi\)
\(758\) −10141.2 −0.485945
\(759\) −1800.18 −0.0860901
\(760\) 0 0
\(761\) −13023.6 −0.620376 −0.310188 0.950675i \(-0.600392\pi\)
−0.310188 + 0.950675i \(0.600392\pi\)
\(762\) −4363.81 −0.207459
\(763\) −40061.6 −1.90082
\(764\) −59058.9 −2.79670
\(765\) 0 0
\(766\) −37480.6 −1.76792
\(767\) −34905.1 −1.64322
\(768\) −6410.36 −0.301190
\(769\) 26526.2 1.24390 0.621949 0.783057i \(-0.286341\pi\)
0.621949 + 0.783057i \(0.286341\pi\)
\(770\) 0 0
\(771\) −1330.13 −0.0621316
\(772\) 75313.9 3.51115
\(773\) −1143.17 −0.0531914 −0.0265957 0.999646i \(-0.508467\pi\)
−0.0265957 + 0.999646i \(0.508467\pi\)
\(774\) 14439.8 0.670577
\(775\) 0 0
\(776\) 15551.6 0.719420
\(777\) 4790.67 0.221190
\(778\) −13816.0 −0.636668
\(779\) −5283.83 −0.243020
\(780\) 0 0
\(781\) −14984.4 −0.686536
\(782\) −36554.1 −1.67157
\(783\) 9735.03 0.444319
\(784\) 38341.0 1.74658
\(785\) 0 0
\(786\) 398.904 0.0181023
\(787\) −41354.8 −1.87311 −0.936556 0.350519i \(-0.886005\pi\)
−0.936556 + 0.350519i \(0.886005\pi\)
\(788\) −59598.4 −2.69429
\(789\) −4176.42 −0.188447
\(790\) 0 0
\(791\) −21267.0 −0.955965
\(792\) −23553.1 −1.05672
\(793\) 33995.8 1.52235
\(794\) −44139.1 −1.97284
\(795\) 0 0
\(796\) −21926.8 −0.976349
\(797\) −8795.77 −0.390918 −0.195459 0.980712i \(-0.562620\pi\)
−0.195459 + 0.980712i \(0.562620\pi\)
\(798\) −2901.71 −0.128721
\(799\) −3391.71 −0.150175
\(800\) 0 0
\(801\) −11916.7 −0.525662
\(802\) −23712.6 −1.04404
\(803\) 25702.7 1.12955
\(804\) 9530.57 0.418056
\(805\) 0 0
\(806\) 60511.7 2.64446
\(807\) −3277.77 −0.142978
\(808\) −44265.6 −1.92730
\(809\) 2152.09 0.0935272 0.0467636 0.998906i \(-0.485109\pi\)
0.0467636 + 0.998906i \(0.485109\pi\)
\(810\) 0 0
\(811\) 24307.1 1.05245 0.526225 0.850346i \(-0.323607\pi\)
0.526225 + 0.850346i \(0.323607\pi\)
\(812\) −114458. −4.94666
\(813\) 3710.38 0.160060
\(814\) 22363.4 0.962944
\(815\) 0 0
\(816\) 3732.48 0.160126
\(817\) 2791.87 0.119554
\(818\) −32166.0 −1.37489
\(819\) −49647.7 −2.11823
\(820\) 0 0
\(821\) 45118.9 1.91798 0.958988 0.283446i \(-0.0914775\pi\)
0.958988 + 0.283446i \(0.0914775\pi\)
\(822\) 2077.23 0.0881406
\(823\) −38608.9 −1.63526 −0.817631 0.575742i \(-0.804713\pi\)
−0.817631 + 0.575742i \(0.804713\pi\)
\(824\) 35111.9 1.48444
\(825\) 0 0
\(826\) −83784.4 −3.52934
\(827\) 17908.8 0.753023 0.376512 0.926412i \(-0.377124\pi\)
0.376512 + 0.926412i \(0.377124\pi\)
\(828\) 43854.4 1.84063
\(829\) 42616.2 1.78543 0.892716 0.450620i \(-0.148797\pi\)
0.892716 + 0.450620i \(0.148797\pi\)
\(830\) 0 0
\(831\) −4396.12 −0.183513
\(832\) −30505.2 −1.27112
\(833\) 41612.2 1.73082
\(834\) −159.778 −0.00663389
\(835\) 0 0
\(836\) −9049.71 −0.374391
\(837\) −8253.60 −0.340844
\(838\) 52338.1 2.15750
\(839\) 9077.30 0.373520 0.186760 0.982406i \(-0.440201\pi\)
0.186760 + 0.982406i \(0.440201\pi\)
\(840\) 0 0
\(841\) 30545.6 1.25243
\(842\) −42489.2 −1.73905
\(843\) 2539.66 0.103761
\(844\) −46268.4 −1.88699
\(845\) 0 0
\(846\) 6090.55 0.247515
\(847\) −25106.6 −1.01851
\(848\) −33217.3 −1.34515
\(849\) −1570.84 −0.0634997
\(850\) 0 0
\(851\) −20953.2 −0.844027
\(852\) −8368.47 −0.336501
\(853\) 18315.0 0.735163 0.367581 0.929991i \(-0.380186\pi\)
0.367581 + 0.929991i \(0.380186\pi\)
\(854\) 81601.7 3.26973
\(855\) 0 0
\(856\) −33447.7 −1.33554
\(857\) 13738.7 0.547615 0.273807 0.961785i \(-0.411717\pi\)
0.273807 + 0.961785i \(0.411717\pi\)
\(858\) 5313.12 0.211407
\(859\) 9424.20 0.374330 0.187165 0.982328i \(-0.440070\pi\)
0.187165 + 0.982328i \(0.440070\pi\)
\(860\) 0 0
\(861\) 4974.82 0.196912
\(862\) 24499.5 0.968048
\(863\) 40557.8 1.59977 0.799887 0.600151i \(-0.204893\pi\)
0.799887 + 0.600151i \(0.204893\pi\)
\(864\) −339.365 −0.0133628
\(865\) 0 0
\(866\) 38890.7 1.52605
\(867\) 229.191 0.00897778
\(868\) 97040.4 3.79466
\(869\) 21869.2 0.853698
\(870\) 0 0
\(871\) 47191.1 1.83583
\(872\) −52556.2 −2.04103
\(873\) −10317.9 −0.400010
\(874\) 12691.4 0.491182
\(875\) 0 0
\(876\) 14354.4 0.553642
\(877\) 12966.5 0.499258 0.249629 0.968342i \(-0.419691\pi\)
0.249629 + 0.968342i \(0.419691\pi\)
\(878\) 54172.2 2.08226
\(879\) −2669.91 −0.102450
\(880\) 0 0
\(881\) −15640.0 −0.598098 −0.299049 0.954238i \(-0.596669\pi\)
−0.299049 + 0.954238i \(0.596669\pi\)
\(882\) −74723.8 −2.85270
\(883\) 10326.2 0.393548 0.196774 0.980449i \(-0.436953\pi\)
0.196774 + 0.980449i \(0.436953\pi\)
\(884\) 72078.9 2.74239
\(885\) 0 0
\(886\) −44974.4 −1.70535
\(887\) 2173.72 0.0822846 0.0411423 0.999153i \(-0.486900\pi\)
0.0411423 + 0.999153i \(0.486900\pi\)
\(888\) 6284.81 0.237505
\(889\) −34651.3 −1.30727
\(890\) 0 0
\(891\) 15260.2 0.573776
\(892\) −54045.0 −2.02866
\(893\) 1177.58 0.0441280
\(894\) 3017.57 0.112889
\(895\) 0 0
\(896\) −75205.2 −2.80405
\(897\) −4978.10 −0.185300
\(898\) −49444.3 −1.83739
\(899\) −46574.9 −1.72787
\(900\) 0 0
\(901\) −36051.4 −1.33301
\(902\) 23223.0 0.857252
\(903\) −2628.60 −0.0968706
\(904\) −27899.9 −1.02648
\(905\) 0 0
\(906\) −7919.85 −0.290419
\(907\) −29981.6 −1.09760 −0.548800 0.835954i \(-0.684915\pi\)
−0.548800 + 0.835954i \(0.684915\pi\)
\(908\) 64268.7 2.34893
\(909\) 29368.6 1.07161
\(910\) 0 0
\(911\) −725.040 −0.0263684 −0.0131842 0.999913i \(-0.504197\pi\)
−0.0131842 + 0.999913i \(0.504197\pi\)
\(912\) −1295.90 −0.0470521
\(913\) −15674.5 −0.568183
\(914\) 14672.3 0.530980
\(915\) 0 0
\(916\) −15588.5 −0.562291
\(917\) 3167.54 0.114069
\(918\) −14715.4 −0.529065
\(919\) −1750.94 −0.0628488 −0.0314244 0.999506i \(-0.510004\pi\)
−0.0314244 + 0.999506i \(0.510004\pi\)
\(920\) 0 0
\(921\) 4922.39 0.176111
\(922\) 4696.63 0.167761
\(923\) −41436.9 −1.47769
\(924\) 8520.46 0.303358
\(925\) 0 0
\(926\) 21369.9 0.758378
\(927\) −23295.5 −0.825376
\(928\) −1915.03 −0.0677413
\(929\) 5500.62 0.194262 0.0971311 0.995272i \(-0.469033\pi\)
0.0971311 + 0.995272i \(0.469033\pi\)
\(930\) 0 0
\(931\) −14447.5 −0.508592
\(932\) 19770.0 0.694838
\(933\) 7093.28 0.248900
\(934\) −39921.0 −1.39856
\(935\) 0 0
\(936\) −65132.1 −2.27448
\(937\) 55288.1 1.92762 0.963811 0.266586i \(-0.0858956\pi\)
0.963811 + 0.266586i \(0.0858956\pi\)
\(938\) 113275. 3.94303
\(939\) −3587.37 −0.124675
\(940\) 0 0
\(941\) 47729.6 1.65350 0.826748 0.562573i \(-0.190188\pi\)
0.826748 + 0.562573i \(0.190188\pi\)
\(942\) −9551.86 −0.330378
\(943\) −21758.6 −0.751388
\(944\) −37417.9 −1.29010
\(945\) 0 0
\(946\) −12270.6 −0.421724
\(947\) 27191.6 0.933061 0.466530 0.884505i \(-0.345504\pi\)
0.466530 + 0.884505i \(0.345504\pi\)
\(948\) 12213.5 0.418434
\(949\) 71076.5 2.43124
\(950\) 0 0
\(951\) 3301.17 0.112563
\(952\) 87062.4 2.96398
\(953\) −2941.45 −0.0999822 −0.0499911 0.998750i \(-0.515919\pi\)
−0.0499911 + 0.998750i \(0.515919\pi\)
\(954\) 64738.2 2.19704
\(955\) 0 0
\(956\) 10427.5 0.352770
\(957\) −4089.42 −0.138132
\(958\) −63393.8 −2.13795
\(959\) 16494.5 0.555405
\(960\) 0 0
\(961\) 9696.35 0.325479
\(962\) 61842.2 2.07263
\(963\) 22191.3 0.742580
\(964\) −67222.1 −2.24593
\(965\) 0 0
\(966\) −11949.2 −0.397990
\(967\) −45733.8 −1.52089 −0.760445 0.649402i \(-0.775019\pi\)
−0.760445 + 0.649402i \(0.775019\pi\)
\(968\) −32937.0 −1.09363
\(969\) −1406.46 −0.0466276
\(970\) 0 0
\(971\) 57658.9 1.90562 0.952812 0.303561i \(-0.0981757\pi\)
0.952812 + 0.303561i \(0.0981757\pi\)
\(972\) 26581.5 0.877162
\(973\) −1268.74 −0.0418025
\(974\) 54053.7 1.77823
\(975\) 0 0
\(976\) 36443.1 1.19520
\(977\) −46156.4 −1.51144 −0.755718 0.654897i \(-0.772712\pi\)
−0.755718 + 0.654897i \(0.772712\pi\)
\(978\) 370.663 0.0121191
\(979\) 10126.5 0.330587
\(980\) 0 0
\(981\) 34869.1 1.13485
\(982\) −71859.3 −2.33516
\(983\) −10931.6 −0.354694 −0.177347 0.984148i \(-0.556752\pi\)
−0.177347 + 0.984148i \(0.556752\pi\)
\(984\) 6526.38 0.211437
\(985\) 0 0
\(986\) −83038.9 −2.68205
\(987\) −1108.71 −0.0357556
\(988\) −25025.4 −0.805835
\(989\) 11496.8 0.369644
\(990\) 0 0
\(991\) −15279.8 −0.489788 −0.244894 0.969550i \(-0.578753\pi\)
−0.244894 + 0.969550i \(0.578753\pi\)
\(992\) 1623.61 0.0519654
\(993\) −2958.75 −0.0945549
\(994\) −99462.9 −3.17382
\(995\) 0 0
\(996\) −8753.88 −0.278491
\(997\) 7648.81 0.242969 0.121485 0.992593i \(-0.461234\pi\)
0.121485 + 0.992593i \(0.461234\pi\)
\(998\) −37065.8 −1.17565
\(999\) −8435.07 −0.267141
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 \(a_p\))