Properties

Label 17.4.a.b.1.2
Level 17
Weight 4
Character 17.1
Self dual Yes
Analytic conductor 1.003
Analytic rank 0
Dimension 3
CM No
Inner twists 1

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.2
Root \(3.87707\)
Character \(\chi\) = 17.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.36122 q^{2}\) \(+3.15463 q^{3}\) \(-6.14708 q^{4}\) \(+3.03171 q^{5}\) \(+4.29415 q^{6}\) \(-7.94049 q^{7}\) \(-19.2573 q^{8}\) \(-17.0483 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.36122 q^{2}\) \(+3.15463 q^{3}\) \(-6.14708 q^{4}\) \(+3.03171 q^{5}\) \(+4.29415 q^{6}\) \(-7.94049 q^{7}\) \(-19.2573 q^{8}\) \(-17.0483 q^{9}\) \(+4.12682 q^{10}\) \(+27.6161 q^{11}\) \(-19.3918 q^{12}\) \(+58.1117 q^{13}\) \(-10.8088 q^{14}\) \(+9.56391 q^{15}\) \(+22.9632 q^{16}\) \(-17.0000 q^{17}\) \(-23.2065 q^{18}\) \(+89.1688 q^{19}\) \(-18.6361 q^{20}\) \(-25.0493 q^{21}\) \(+37.5916 q^{22}\) \(-115.269 q^{23}\) \(-60.7497 q^{24}\) \(-115.809 q^{25}\) \(+79.1029 q^{26}\) \(-138.956 q^{27}\) \(+48.8108 q^{28}\) \(-128.558 q^{29}\) \(+13.0186 q^{30}\) \(+273.460 q^{31}\) \(+185.316 q^{32}\) \(+87.1187 q^{33}\) \(-23.1408 q^{34}\) \(-24.0732 q^{35}\) \(+104.797 q^{36}\) \(-132.351 q^{37}\) \(+121.379 q^{38}\) \(+183.321 q^{39}\) \(-58.3825 q^{40}\) \(-470.559 q^{41}\) \(-34.0977 q^{42}\) \(+352.642 q^{43}\) \(-169.758 q^{44}\) \(-51.6854 q^{45}\) \(-156.907 q^{46}\) \(+152.598 q^{47}\) \(+72.4403 q^{48}\) \(-279.949 q^{49}\) \(-157.641 q^{50}\) \(-53.6287 q^{51}\) \(-357.217 q^{52}\) \(+527.614 q^{53}\) \(-189.150 q^{54}\) \(+83.7239 q^{55}\) \(+152.912 q^{56}\) \(+281.295 q^{57}\) \(-174.995 q^{58}\) \(-292.020 q^{59}\) \(-58.7901 q^{60}\) \(-53.8962 q^{61}\) \(+372.239 q^{62}\) \(+135.372 q^{63}\) \(+68.5514 q^{64}\) \(+176.178 q^{65}\) \(+118.588 q^{66}\) \(+52.9572 q^{67}\) \(+104.500 q^{68}\) \(-363.632 q^{69}\) \(-32.7690 q^{70}\) \(+788.400 q^{71}\) \(+328.304 q^{72}\) \(+295.780 q^{73}\) \(-180.159 q^{74}\) \(-365.334 q^{75}\) \(-548.127 q^{76}\) \(-219.285 q^{77}\) \(+249.541 q^{78}\) \(-720.325 q^{79}\) \(+69.6175 q^{80}\) \(+21.9487 q^{81}\) \(-640.535 q^{82}\) \(-116.051 q^{83}\) \(+153.980 q^{84}\) \(-51.5390 q^{85}\) \(+480.024 q^{86}\) \(-405.552 q^{87}\) \(-531.812 q^{88}\) \(-813.329 q^{89}\) \(-70.3553 q^{90}\) \(-461.435 q^{91}\) \(+708.569 q^{92}\) \(+862.664 q^{93}\) \(+207.720 q^{94}\) \(+270.334 q^{95}\) \(+584.605 q^{96}\) \(+794.693 q^{97}\) \(-381.072 q^{98}\) \(-470.808 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(3q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 74q^{6} \) \(\mathstrut +\mathstrut 22q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 59q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 74q^{6} \) \(\mathstrut +\mathstrut 22q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 59q^{9} \) \(\mathstrut -\mathstrut 56q^{10} \) \(\mathstrut -\mathstrut 28q^{11} \) \(\mathstrut +\mathstrut 22q^{12} \) \(\mathstrut +\mathstrut 30q^{13} \) \(\mathstrut +\mathstrut 92q^{14} \) \(\mathstrut +\mathstrut 108q^{15} \) \(\mathstrut +\mathstrut 137q^{16} \) \(\mathstrut -\mathstrut 51q^{17} \) \(\mathstrut -\mathstrut 103q^{18} \) \(\mathstrut +\mathstrut 80q^{19} \) \(\mathstrut -\mathstrut 168q^{20} \) \(\mathstrut -\mathstrut 192q^{21} \) \(\mathstrut +\mathstrut 286q^{22} \) \(\mathstrut +\mathstrut 142q^{23} \) \(\mathstrut -\mathstrut 666q^{24} \) \(\mathstrut -\mathstrut 223q^{25} \) \(\mathstrut +\mathstrut 26q^{26} \) \(\mathstrut -\mathstrut 20q^{27} \) \(\mathstrut +\mathstrut 476q^{28} \) \(\mathstrut -\mathstrut 456q^{29} \) \(\mathstrut +\mathstrut 400q^{30} \) \(\mathstrut +\mathstrut 230q^{31} \) \(\mathstrut -\mathstrut 71q^{32} \) \(\mathstrut -\mathstrut 332q^{33} \) \(\mathstrut -\mathstrut 17q^{34} \) \(\mathstrut -\mathstrut 332q^{35} \) \(\mathstrut +\mathstrut 1313q^{36} \) \(\mathstrut +\mathstrut 356q^{37} \) \(\mathstrut +\mathstrut 724q^{38} \) \(\mathstrut +\mathstrut 268q^{39} \) \(\mathstrut -\mathstrut 424q^{40} \) \(\mathstrut -\mathstrut 294q^{41} \) \(\mathstrut -\mathstrut 1128q^{42} \) \(\mathstrut +\mathstrut 556q^{43} \) \(\mathstrut -\mathstrut 1122q^{44} \) \(\mathstrut -\mathstrut 384q^{45} \) \(\mathstrut -\mathstrut 704q^{46} \) \(\mathstrut +\mathstrut 640q^{47} \) \(\mathstrut +\mathstrut 774q^{48} \) \(\mathstrut -\mathstrut 269q^{49} \) \(\mathstrut +\mathstrut 547q^{50} \) \(\mathstrut -\mathstrut 68q^{51} \) \(\mathstrut -\mathstrut 774q^{52} \) \(\mathstrut +\mathstrut 302q^{53} \) \(\mathstrut -\mathstrut 1100q^{54} \) \(\mathstrut +\mathstrut 76q^{55} \) \(\mathstrut +\mathstrut 684q^{56} \) \(\mathstrut -\mathstrut 720q^{57} \) \(\mathstrut -\mathstrut 1304q^{58} \) \(\mathstrut +\mathstrut 636q^{59} \) \(\mathstrut +\mathstrut 1328q^{60} \) \(\mathstrut -\mathstrut 84q^{61} \) \(\mathstrut +\mathstrut 508q^{62} \) \(\mathstrut +\mathstrut 1122q^{63} \) \(\mathstrut -\mathstrut 919q^{64} \) \(\mathstrut +\mathstrut 408q^{65} \) \(\mathstrut +\mathstrut 2468q^{66} \) \(\mathstrut +\mathstrut 1008q^{67} \) \(\mathstrut -\mathstrut 425q^{68} \) \(\mathstrut +\mathstrut 576q^{69} \) \(\mathstrut -\mathstrut 1504q^{70} \) \(\mathstrut -\mathstrut 402q^{71} \) \(\mathstrut -\mathstrut 927q^{72} \) \(\mathstrut +\mathstrut 838q^{73} \) \(\mathstrut +\mathstrut 836q^{74} \) \(\mathstrut -\mathstrut 1548q^{75} \) \(\mathstrut -\mathstrut 908q^{76} \) \(\mathstrut -\mathstrut 504q^{77} \) \(\mathstrut +\mathstrut 1308q^{78} \) \(\mathstrut -\mathstrut 594q^{79} \) \(\mathstrut -\mathstrut 40q^{80} \) \(\mathstrut -\mathstrut 505q^{81} \) \(\mathstrut +\mathstrut 358q^{82} \) \(\mathstrut -\mathstrut 2396q^{83} \) \(\mathstrut -\mathstrut 2040q^{84} \) \(\mathstrut +\mathstrut 136q^{85} \) \(\mathstrut -\mathstrut 1264q^{86} \) \(\mathstrut +\mathstrut 1428q^{87} \) \(\mathstrut +\mathstrut 1838q^{88} \) \(\mathstrut -\mathstrut 170q^{89} \) \(\mathstrut -\mathstrut 2008q^{90} \) \(\mathstrut -\mathstrut 1016q^{91} \) \(\mathstrut +\mathstrut 4896q^{92} \) \(\mathstrut +\mathstrut 632q^{93} \) \(\mathstrut -\mathstrut 2016q^{94} \) \(\mathstrut -\mathstrut 472q^{95} \) \(\mathstrut +\mathstrut 678q^{96} \) \(\mathstrut -\mathstrut 270q^{97} \) \(\mathstrut +\mathstrut 2857q^{98} \) \(\mathstrut -\mathstrut 2920q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36122 0.481264 0.240632 0.970616i \(-0.422645\pi\)
0.240632 + 0.970616i \(0.422645\pi\)
\(3\) 3.15463 0.607109 0.303555 0.952814i \(-0.401827\pi\)
0.303555 + 0.952814i \(0.401827\pi\)
\(4\) −6.14708 −0.768385
\(5\) 3.03171 0.271164 0.135582 0.990766i \(-0.456710\pi\)
0.135582 + 0.990766i \(0.456710\pi\)
\(6\) 4.29415 0.292180
\(7\) −7.94049 −0.428746 −0.214373 0.976752i \(-0.568771\pi\)
−0.214373 + 0.976752i \(0.568771\pi\)
\(8\) −19.2573 −0.851061
\(9\) −17.0483 −0.631419
\(10\) 4.12682 0.130502
\(11\) 27.6161 0.756961 0.378481 0.925609i \(-0.376447\pi\)
0.378481 + 0.925609i \(0.376447\pi\)
\(12\) −19.3918 −0.466493
\(13\) 58.1117 1.23979 0.619896 0.784684i \(-0.287175\pi\)
0.619896 + 0.784684i \(0.287175\pi\)
\(14\) −10.8088 −0.206340
\(15\) 9.56391 0.164626
\(16\) 22.9632 0.358799
\(17\) −17.0000 −0.242536
\(18\) −23.2065 −0.303879
\(19\) 89.1688 1.07667 0.538335 0.842731i \(-0.319054\pi\)
0.538335 + 0.842731i \(0.319054\pi\)
\(20\) −18.6361 −0.208358
\(21\) −25.0493 −0.260296
\(22\) 37.5916 0.364298
\(23\) −115.269 −1.04501 −0.522507 0.852635i \(-0.675003\pi\)
−0.522507 + 0.852635i \(0.675003\pi\)
\(24\) −60.7497 −0.516687
\(25\) −115.809 −0.926470
\(26\) 79.1029 0.596668
\(27\) −138.956 −0.990449
\(28\) 48.8108 0.329442
\(29\) −128.558 −0.823191 −0.411596 0.911367i \(-0.635028\pi\)
−0.411596 + 0.911367i \(0.635028\pi\)
\(30\) 13.0186 0.0792287
\(31\) 273.460 1.58435 0.792174 0.610295i \(-0.208949\pi\)
0.792174 + 0.610295i \(0.208949\pi\)
\(32\) 185.316 1.02374
\(33\) 87.1187 0.459558
\(34\) −23.1408 −0.116724
\(35\) −24.0732 −0.116260
\(36\) 104.797 0.485172
\(37\) −132.351 −0.588063 −0.294031 0.955796i \(-0.594997\pi\)
−0.294031 + 0.955796i \(0.594997\pi\)
\(38\) 121.379 0.518163
\(39\) 183.321 0.752689
\(40\) −58.3825 −0.230777
\(41\) −470.559 −1.79241 −0.896207 0.443636i \(-0.853688\pi\)
−0.896207 + 0.443636i \(0.853688\pi\)
\(42\) −34.0977 −0.125271
\(43\) 352.642 1.25064 0.625318 0.780370i \(-0.284969\pi\)
0.625318 + 0.780370i \(0.284969\pi\)
\(44\) −169.758 −0.581637
\(45\) −51.6854 −0.171218
\(46\) −156.907 −0.502928
\(47\) 152.598 0.473589 0.236795 0.971560i \(-0.423903\pi\)
0.236795 + 0.971560i \(0.423903\pi\)
\(48\) 72.4403 0.217830
\(49\) −279.949 −0.816177
\(50\) −157.641 −0.445877
\(51\) −53.6287 −0.147246
\(52\) −357.217 −0.952637
\(53\) 527.614 1.36742 0.683711 0.729753i \(-0.260365\pi\)
0.683711 + 0.729753i \(0.260365\pi\)
\(54\) −189.150 −0.476668
\(55\) 83.7239 0.205261
\(56\) 152.912 0.364889
\(57\) 281.295 0.653656
\(58\) −174.995 −0.396173
\(59\) −292.020 −0.644368 −0.322184 0.946677i \(-0.604417\pi\)
−0.322184 + 0.946677i \(0.604417\pi\)
\(60\) −58.7901 −0.126496
\(61\) −53.8962 −0.113126 −0.0565632 0.998399i \(-0.518014\pi\)
−0.0565632 + 0.998399i \(0.518014\pi\)
\(62\) 372.239 0.762490
\(63\) 135.372 0.270718
\(64\) 68.5514 0.133889
\(65\) 176.178 0.336187
\(66\) 118.588 0.221169
\(67\) 52.9572 0.0965635 0.0482817 0.998834i \(-0.484625\pi\)
0.0482817 + 0.998834i \(0.484625\pi\)
\(68\) 104.500 0.186361
\(69\) −363.632 −0.634437
\(70\) −32.7690 −0.0559520
\(71\) 788.400 1.31783 0.658915 0.752218i \(-0.271016\pi\)
0.658915 + 0.752218i \(0.271016\pi\)
\(72\) 328.304 0.537375
\(73\) 295.780 0.474224 0.237112 0.971482i \(-0.423799\pi\)
0.237112 + 0.971482i \(0.423799\pi\)
\(74\) −180.159 −0.283014
\(75\) −365.334 −0.562468
\(76\) −548.127 −0.827296
\(77\) −219.285 −0.324544
\(78\) 249.541 0.362242
\(79\) −720.325 −1.02586 −0.512930 0.858430i \(-0.671440\pi\)
−0.512930 + 0.858430i \(0.671440\pi\)
\(80\) 69.6175 0.0972934
\(81\) 21.9487 0.0301079
\(82\) −640.535 −0.862625
\(83\) −116.051 −0.153473 −0.0767363 0.997051i \(-0.524450\pi\)
−0.0767363 + 0.997051i \(0.524450\pi\)
\(84\) 153.980 0.200007
\(85\) −51.5390 −0.0657669
\(86\) 480.024 0.601887
\(87\) −405.552 −0.499767
\(88\) −531.812 −0.644220
\(89\) −813.329 −0.968682 −0.484341 0.874879i \(-0.660941\pi\)
−0.484341 + 0.874879i \(0.660941\pi\)
\(90\) −70.3553 −0.0824011
\(91\) −461.435 −0.531556
\(92\) 708.569 0.802972
\(93\) 862.664 0.961872
\(94\) 207.720 0.227922
\(95\) 270.334 0.291954
\(96\) 584.605 0.621521
\(97\) 794.693 0.831844 0.415922 0.909400i \(-0.363459\pi\)
0.415922 + 0.909400i \(0.363459\pi\)
\(98\) −381.072 −0.392797
\(99\) −470.808 −0.477959
\(100\) 711.885 0.711885
\(101\) 265.513 0.261579 0.130790 0.991410i \(-0.458249\pi\)
0.130790 + 0.991410i \(0.458249\pi\)
\(102\) −73.0006 −0.0708641
\(103\) 523.107 0.500420 0.250210 0.968192i \(-0.419500\pi\)
0.250210 + 0.968192i \(0.419500\pi\)
\(104\) −1119.07 −1.05514
\(105\) −75.9421 −0.0705828
\(106\) 718.199 0.658091
\(107\) −986.039 −0.890878 −0.445439 0.895312i \(-0.646952\pi\)
−0.445439 + 0.895312i \(0.646952\pi\)
\(108\) 854.174 0.761046
\(109\) 1814.39 1.59438 0.797188 0.603732i \(-0.206320\pi\)
0.797188 + 0.603732i \(0.206320\pi\)
\(110\) 113.967 0.0987846
\(111\) −417.518 −0.357018
\(112\) −182.339 −0.153834
\(113\) −707.339 −0.588857 −0.294429 0.955673i \(-0.595129\pi\)
−0.294429 + 0.955673i \(0.595129\pi\)
\(114\) 382.904 0.314581
\(115\) −349.463 −0.283370
\(116\) 790.253 0.632527
\(117\) −990.706 −0.782827
\(118\) −397.503 −0.310112
\(119\) 134.988 0.103986
\(120\) −184.175 −0.140107
\(121\) −568.350 −0.427010
\(122\) −73.3647 −0.0544437
\(123\) −1484.44 −1.08819
\(124\) −1680.98 −1.21739
\(125\) −730.061 −0.522389
\(126\) 184.271 0.130287
\(127\) 2648.18 1.85030 0.925151 0.379600i \(-0.123938\pi\)
0.925151 + 0.379600i \(0.123938\pi\)
\(128\) −1389.22 −0.959302
\(129\) 1112.46 0.759273
\(130\) 239.817 0.161795
\(131\) −1979.08 −1.31995 −0.659974 0.751289i \(-0.729433\pi\)
−0.659974 + 0.751289i \(0.729433\pi\)
\(132\) −535.525 −0.353117
\(133\) −708.044 −0.461618
\(134\) 72.0865 0.0464726
\(135\) −421.274 −0.268574
\(136\) 327.374 0.206413
\(137\) 3141.92 1.95936 0.979679 0.200570i \(-0.0642794\pi\)
0.979679 + 0.200570i \(0.0642794\pi\)
\(138\) −494.984 −0.305332
\(139\) 1468.07 0.895830 0.447915 0.894076i \(-0.352167\pi\)
0.447915 + 0.894076i \(0.352167\pi\)
\(140\) 147.980 0.0893327
\(141\) 481.390 0.287520
\(142\) 1073.19 0.634224
\(143\) 1604.82 0.938474
\(144\) −391.483 −0.226553
\(145\) −389.749 −0.223220
\(146\) 402.621 0.228227
\(147\) −883.135 −0.495508
\(148\) 813.570 0.451858
\(149\) −286.027 −0.157263 −0.0786316 0.996904i \(-0.525055\pi\)
−0.0786316 + 0.996904i \(0.525055\pi\)
\(150\) −497.300 −0.270696
\(151\) −669.626 −0.360883 −0.180442 0.983586i \(-0.557753\pi\)
−0.180442 + 0.983586i \(0.557753\pi\)
\(152\) −1717.15 −0.916311
\(153\) 289.821 0.153141
\(154\) −298.496 −0.156191
\(155\) 829.049 0.429618
\(156\) −1126.89 −0.578354
\(157\) 720.809 0.366413 0.183206 0.983074i \(-0.441352\pi\)
0.183206 + 0.983074i \(0.441352\pi\)
\(158\) −980.522 −0.493710
\(159\) 1664.43 0.830174
\(160\) 561.825 0.277601
\(161\) 915.294 0.448045
\(162\) 29.8770 0.0144899
\(163\) −676.599 −0.325125 −0.162562 0.986698i \(-0.551976\pi\)
−0.162562 + 0.986698i \(0.551976\pi\)
\(164\) 2892.56 1.37726
\(165\) 264.118 0.124616
\(166\) −157.971 −0.0738609
\(167\) −2835.67 −1.31396 −0.656979 0.753909i \(-0.728166\pi\)
−0.656979 + 0.753909i \(0.728166\pi\)
\(168\) 482.382 0.221527
\(169\) 1179.97 0.537083
\(170\) −70.1560 −0.0316513
\(171\) −1520.18 −0.679829
\(172\) −2167.72 −0.960970
\(173\) −177.314 −0.0779243 −0.0389621 0.999241i \(-0.512405\pi\)
−0.0389621 + 0.999241i \(0.512405\pi\)
\(174\) −552.046 −0.240520
\(175\) 919.578 0.397220
\(176\) 634.153 0.271597
\(177\) −921.214 −0.391202
\(178\) −1107.12 −0.466192
\(179\) −1023.76 −0.427483 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(180\) 317.714 0.131561
\(181\) −3450.21 −1.41686 −0.708432 0.705779i \(-0.750597\pi\)
−0.708432 + 0.705779i \(0.750597\pi\)
\(182\) −628.116 −0.255819
\(183\) −170.023 −0.0686800
\(184\) 2219.78 0.889370
\(185\) −401.248 −0.159461
\(186\) 1174.28 0.462915
\(187\) −469.474 −0.183590
\(188\) −938.031 −0.363899
\(189\) 1103.38 0.424651
\(190\) 367.984 0.140507
\(191\) −490.894 −0.185968 −0.0929839 0.995668i \(-0.529640\pi\)
−0.0929839 + 0.995668i \(0.529640\pi\)
\(192\) 216.254 0.0812855
\(193\) −3548.80 −1.32357 −0.661783 0.749696i \(-0.730200\pi\)
−0.661783 + 0.749696i \(0.730200\pi\)
\(194\) 1081.75 0.400337
\(195\) 555.775 0.204102
\(196\) 1720.87 0.627138
\(197\) 1363.15 0.492996 0.246498 0.969143i \(-0.420720\pi\)
0.246498 + 0.969143i \(0.420720\pi\)
\(198\) −640.874 −0.230025
\(199\) 3737.46 1.33137 0.665683 0.746235i \(-0.268140\pi\)
0.665683 + 0.746235i \(0.268140\pi\)
\(200\) 2230.16 0.788482
\(201\) 167.060 0.0586246
\(202\) 361.422 0.125889
\(203\) 1020.81 0.352940
\(204\) 329.660 0.113141
\(205\) −1426.60 −0.486038
\(206\) 712.064 0.240834
\(207\) 1965.15 0.659841
\(208\) 1334.43 0.444836
\(209\) 2462.50 0.814997
\(210\) −103.374 −0.0339690
\(211\) −5266.12 −1.71817 −0.859087 0.511829i \(-0.828968\pi\)
−0.859087 + 0.511829i \(0.828968\pi\)
\(212\) −3243.28 −1.05071
\(213\) 2487.11 0.800066
\(214\) −1342.22 −0.428748
\(215\) 1069.11 0.339128
\(216\) 2675.92 0.842932
\(217\) −2171.40 −0.679283
\(218\) 2469.78 0.767316
\(219\) 933.075 0.287906
\(220\) −514.657 −0.157719
\(221\) −987.899 −0.300694
\(222\) −568.334 −0.171820
\(223\) 704.546 0.211569 0.105785 0.994389i \(-0.466265\pi\)
0.105785 + 0.994389i \(0.466265\pi\)
\(224\) −1471.50 −0.438923
\(225\) 1974.34 0.584990
\(226\) −962.845 −0.283396
\(227\) −2151.26 −0.629006 −0.314503 0.949256i \(-0.601838\pi\)
−0.314503 + 0.949256i \(0.601838\pi\)
\(228\) −1729.14 −0.502259
\(229\) −3916.94 −1.13030 −0.565149 0.824989i \(-0.691181\pi\)
−0.565149 + 0.824989i \(0.691181\pi\)
\(230\) −475.696 −0.136376
\(231\) −691.764 −0.197034
\(232\) 2475.67 0.700586
\(233\) −5192.74 −1.46003 −0.730017 0.683429i \(-0.760488\pi\)
−0.730017 + 0.683429i \(0.760488\pi\)
\(234\) −1348.57 −0.376747
\(235\) 462.632 0.128420
\(236\) 1795.07 0.495123
\(237\) −2272.36 −0.622809
\(238\) 183.749 0.0500448
\(239\) 334.305 0.0904786 0.0452393 0.998976i \(-0.485595\pi\)
0.0452393 + 0.998976i \(0.485595\pi\)
\(240\) 219.618 0.0590677
\(241\) −1918.45 −0.512773 −0.256386 0.966574i \(-0.582532\pi\)
−0.256386 + 0.966574i \(0.582532\pi\)
\(242\) −773.651 −0.205505
\(243\) 3821.06 1.00873
\(244\) 331.304 0.0869245
\(245\) −848.722 −0.221318
\(246\) −2020.65 −0.523708
\(247\) 5181.75 1.33485
\(248\) −5266.09 −1.34838
\(249\) −366.097 −0.0931746
\(250\) −993.775 −0.251407
\(251\) 7695.71 1.93525 0.967627 0.252385i \(-0.0812148\pi\)
0.967627 + 0.252385i \(0.0812148\pi\)
\(252\) −832.141 −0.208016
\(253\) −3183.29 −0.791035
\(254\) 3604.76 0.890484
\(255\) −162.587 −0.0399277
\(256\) −2439.44 −0.595567
\(257\) 5335.10 1.29492 0.647460 0.762099i \(-0.275831\pi\)
0.647460 + 0.762099i \(0.275831\pi\)
\(258\) 1514.30 0.365411
\(259\) 1050.93 0.252130
\(260\) −1082.98 −0.258321
\(261\) 2191.69 0.519778
\(262\) −2693.97 −0.635244
\(263\) 3934.15 0.922396 0.461198 0.887297i \(-0.347420\pi\)
0.461198 + 0.887297i \(0.347420\pi\)
\(264\) −1677.67 −0.391112
\(265\) 1599.57 0.370795
\(266\) −963.804 −0.222160
\(267\) −2565.75 −0.588095
\(268\) −325.532 −0.0741979
\(269\) 3424.04 0.776088 0.388044 0.921641i \(-0.373151\pi\)
0.388044 + 0.921641i \(0.373151\pi\)
\(270\) −573.447 −0.129255
\(271\) 549.034 0.123068 0.0615340 0.998105i \(-0.480401\pi\)
0.0615340 + 0.998105i \(0.480401\pi\)
\(272\) −390.374 −0.0870216
\(273\) −1455.66 −0.322712
\(274\) 4276.85 0.942970
\(275\) −3198.19 −0.701302
\(276\) 2235.27 0.487492
\(277\) 5203.65 1.12873 0.564363 0.825527i \(-0.309122\pi\)
0.564363 + 0.825527i \(0.309122\pi\)
\(278\) 1998.37 0.431131
\(279\) −4662.02 −1.00039
\(280\) 463.585 0.0989447
\(281\) −1986.73 −0.421774 −0.210887 0.977510i \(-0.567635\pi\)
−0.210887 + 0.977510i \(0.567635\pi\)
\(282\) 655.279 0.138373
\(283\) 753.696 0.158313 0.0791565 0.996862i \(-0.474777\pi\)
0.0791565 + 0.996862i \(0.474777\pi\)
\(284\) −4846.36 −1.01260
\(285\) 852.803 0.177248
\(286\) 2184.51 0.451654
\(287\) 3736.47 0.768490
\(288\) −3159.33 −0.646407
\(289\) 289.000 0.0588235
\(290\) −530.534 −0.107428
\(291\) 2506.96 0.505020
\(292\) −1818.18 −0.364387
\(293\) −7202.22 −1.43603 −0.718017 0.696025i \(-0.754950\pi\)
−0.718017 + 0.696025i \(0.754950\pi\)
\(294\) −1202.14 −0.238471
\(295\) −885.318 −0.174729
\(296\) 2548.72 0.500477
\(297\) −3837.43 −0.749731
\(298\) −389.345 −0.0756852
\(299\) −6698.50 −1.29560
\(300\) 2245.74 0.432192
\(301\) −2800.15 −0.536205
\(302\) −911.509 −0.173680
\(303\) 837.595 0.158807
\(304\) 2047.60 0.386308
\(305\) −163.398 −0.0306758
\(306\) 394.511 0.0737016
\(307\) 2425.71 0.450953 0.225477 0.974249i \(-0.427606\pi\)
0.225477 + 0.974249i \(0.427606\pi\)
\(308\) 1347.96 0.249375
\(309\) 1650.21 0.303809
\(310\) 1128.52 0.206760
\(311\) −9544.94 −1.74033 −0.870167 0.492757i \(-0.835989\pi\)
−0.870167 + 0.492757i \(0.835989\pi\)
\(312\) −3530.27 −0.640584
\(313\) 588.379 0.106253 0.0531264 0.998588i \(-0.483081\pi\)
0.0531264 + 0.998588i \(0.483081\pi\)
\(314\) 981.180 0.176341
\(315\) 410.407 0.0734090
\(316\) 4427.89 0.788255
\(317\) 7653.31 1.35600 0.678001 0.735061i \(-0.262846\pi\)
0.678001 + 0.735061i \(0.262846\pi\)
\(318\) 2265.65 0.399533
\(319\) −3550.26 −0.623124
\(320\) 207.828 0.0363060
\(321\) −3110.59 −0.540860
\(322\) 1245.92 0.215628
\(323\) −1515.87 −0.261131
\(324\) −134.920 −0.0231345
\(325\) −6729.85 −1.14863
\(326\) −921.001 −0.156471
\(327\) 5723.73 0.967960
\(328\) 9061.70 1.52545
\(329\) −1211.70 −0.203050
\(330\) 359.523 0.0599730
\(331\) 752.266 0.124919 0.0624597 0.998047i \(-0.480106\pi\)
0.0624597 + 0.998047i \(0.480106\pi\)
\(332\) 713.373 0.117926
\(333\) 2256.36 0.371314
\(334\) −3859.98 −0.632361
\(335\) 160.551 0.0261845
\(336\) −575.211 −0.0933939
\(337\) −1968.57 −0.318204 −0.159102 0.987262i \(-0.550860\pi\)
−0.159102 + 0.987262i \(0.550860\pi\)
\(338\) 1606.20 0.258479
\(339\) −2231.39 −0.357501
\(340\) 316.814 0.0505343
\(341\) 7551.89 1.19929
\(342\) −2069.30 −0.327178
\(343\) 4946.52 0.778678
\(344\) −6790.93 −1.06437
\(345\) −1102.43 −0.172037
\(346\) −241.363 −0.0375022
\(347\) 3983.10 0.616207 0.308104 0.951353i \(-0.400306\pi\)
0.308104 + 0.951353i \(0.400306\pi\)
\(348\) 2492.96 0.384013
\(349\) 1495.61 0.229393 0.114697 0.993401i \(-0.463410\pi\)
0.114697 + 0.993401i \(0.463410\pi\)
\(350\) 1251.75 0.191168
\(351\) −8074.98 −1.22795
\(352\) 5117.72 0.774930
\(353\) 6482.49 0.977417 0.488708 0.872447i \(-0.337468\pi\)
0.488708 + 0.872447i \(0.337468\pi\)
\(354\) −1253.98 −0.188272
\(355\) 2390.20 0.357348
\(356\) 4999.59 0.744320
\(357\) 425.838 0.0631309
\(358\) −1393.56 −0.205732
\(359\) −4943.42 −0.726751 −0.363376 0.931643i \(-0.618376\pi\)
−0.363376 + 0.931643i \(0.618376\pi\)
\(360\) 995.322 0.145717
\(361\) 1092.08 0.159218
\(362\) −4696.50 −0.681886
\(363\) −1792.94 −0.259242
\(364\) 2836.48 0.408439
\(365\) 896.717 0.128593
\(366\) −231.439 −0.0330533
\(367\) −14.8871 −0.00211743 −0.00105872 0.999999i \(-0.500337\pi\)
−0.00105872 + 0.999999i \(0.500337\pi\)
\(368\) −2646.95 −0.374950
\(369\) 8022.23 1.13176
\(370\) −546.188 −0.0767431
\(371\) −4189.51 −0.586276
\(372\) −5302.86 −0.739088
\(373\) 1923.18 0.266966 0.133483 0.991051i \(-0.457384\pi\)
0.133483 + 0.991051i \(0.457384\pi\)
\(374\) −639.058 −0.0883554
\(375\) −2303.07 −0.317147
\(376\) −2938.63 −0.403053
\(377\) −7470.70 −1.02059
\(378\) 1501.94 0.204369
\(379\) −9592.87 −1.30014 −0.650069 0.759875i \(-0.725260\pi\)
−0.650069 + 0.759875i \(0.725260\pi\)
\(380\) −1661.76 −0.224333
\(381\) 8354.04 1.12333
\(382\) −668.215 −0.0894996
\(383\) −9083.77 −1.21190 −0.605951 0.795502i \(-0.707207\pi\)
−0.605951 + 0.795502i \(0.707207\pi\)
\(384\) −4382.47 −0.582401
\(385\) −664.809 −0.0880046
\(386\) −4830.70 −0.636985
\(387\) −6011.95 −0.789675
\(388\) −4885.04 −0.639176
\(389\) −1143.78 −0.149079 −0.0745396 0.997218i \(-0.523749\pi\)
−0.0745396 + 0.997218i \(0.523749\pi\)
\(390\) 756.533 0.0982271
\(391\) 1959.58 0.253453
\(392\) 5391.06 0.694616
\(393\) −6243.27 −0.801352
\(394\) 1855.55 0.237262
\(395\) −2183.81 −0.278176
\(396\) 2894.09 0.367256
\(397\) 10604.5 1.34061 0.670307 0.742084i \(-0.266162\pi\)
0.670307 + 0.742084i \(0.266162\pi\)
\(398\) 5087.51 0.640739
\(399\) −2233.62 −0.280252
\(400\) −2659.33 −0.332417
\(401\) 13785.4 1.71674 0.858368 0.513035i \(-0.171479\pi\)
0.858368 + 0.513035i \(0.171479\pi\)
\(402\) 227.406 0.0282139
\(403\) 15891.2 1.96426
\(404\) −1632.13 −0.200993
\(405\) 66.5420 0.00816419
\(406\) 1389.55 0.169857
\(407\) −3655.01 −0.445141
\(408\) 1032.74 0.125315
\(409\) −9505.94 −1.14924 −0.574619 0.818421i \(-0.694850\pi\)
−0.574619 + 0.818421i \(0.694850\pi\)
\(410\) −1941.91 −0.233913
\(411\) 9911.59 1.18954
\(412\) −3215.58 −0.384515
\(413\) 2318.78 0.276270
\(414\) 2675.00 0.317558
\(415\) −351.832 −0.0416162
\(416\) 10769.1 1.26922
\(417\) 4631.23 0.543866
\(418\) 3352.00 0.392229
\(419\) 9680.86 1.12874 0.564369 0.825523i \(-0.309120\pi\)
0.564369 + 0.825523i \(0.309120\pi\)
\(420\) 466.822 0.0542347
\(421\) −12360.3 −1.43089 −0.715444 0.698671i \(-0.753775\pi\)
−0.715444 + 0.698671i \(0.753775\pi\)
\(422\) −7168.36 −0.826897
\(423\) −2601.54 −0.299033
\(424\) −10160.4 −1.16376
\(425\) 1968.75 0.224702
\(426\) 3385.51 0.385043
\(427\) 427.962 0.0485025
\(428\) 6061.25 0.684537
\(429\) 5062.61 0.569756
\(430\) 1455.29 0.163210
\(431\) 2970.58 0.331990 0.165995 0.986127i \(-0.446916\pi\)
0.165995 + 0.986127i \(0.446916\pi\)
\(432\) −3190.87 −0.355372
\(433\) 6131.50 0.680510 0.340255 0.940333i \(-0.389487\pi\)
0.340255 + 0.940333i \(0.389487\pi\)
\(434\) −2955.76 −0.326915
\(435\) −1229.51 −0.135519
\(436\) −11153.2 −1.22509
\(437\) −10278.4 −1.12513
\(438\) 1270.12 0.138559
\(439\) −2544.91 −0.276679 −0.138339 0.990385i \(-0.544176\pi\)
−0.138339 + 0.990385i \(0.544176\pi\)
\(440\) −1612.30 −0.174689
\(441\) 4772.65 0.515349
\(442\) −1344.75 −0.144713
\(443\) 8529.82 0.914817 0.457408 0.889257i \(-0.348778\pi\)
0.457408 + 0.889257i \(0.348778\pi\)
\(444\) 2566.51 0.274327
\(445\) −2465.77 −0.262672
\(446\) 959.043 0.101821
\(447\) −902.308 −0.0954759
\(448\) −544.331 −0.0574046
\(449\) 8855.74 0.930798 0.465399 0.885101i \(-0.345911\pi\)
0.465399 + 0.885101i \(0.345911\pi\)
\(450\) 2687.52 0.281535
\(451\) −12995.0 −1.35679
\(452\) 4348.07 0.452469
\(453\) −2112.42 −0.219095
\(454\) −2928.35 −0.302718
\(455\) −1398.94 −0.144139
\(456\) −5416.98 −0.556301
\(457\) −7154.78 −0.732356 −0.366178 0.930545i \(-0.619334\pi\)
−0.366178 + 0.930545i \(0.619334\pi\)
\(458\) −5331.82 −0.543973
\(459\) 2362.25 0.240219
\(460\) 2148.17 0.217737
\(461\) −7263.06 −0.733784 −0.366892 0.930264i \(-0.619578\pi\)
−0.366892 + 0.930264i \(0.619578\pi\)
\(462\) −941.645 −0.0948253
\(463\) 352.898 0.0354224 0.0177112 0.999843i \(-0.494362\pi\)
0.0177112 + 0.999843i \(0.494362\pi\)
\(464\) −2952.09 −0.295360
\(465\) 2615.34 0.260825
\(466\) −7068.47 −0.702662
\(467\) 1483.02 0.146951 0.0734753 0.997297i \(-0.476591\pi\)
0.0734753 + 0.997297i \(0.476591\pi\)
\(468\) 6089.94 0.601512
\(469\) −420.506 −0.0414012
\(470\) 629.745 0.0618042
\(471\) 2273.89 0.222452
\(472\) 5623.51 0.548396
\(473\) 9738.60 0.946683
\(474\) −3093.19 −0.299736
\(475\) −10326.5 −0.997502
\(476\) −829.783 −0.0799014
\(477\) −8994.92 −0.863415
\(478\) 455.063 0.0435441
\(479\) −9990.10 −0.952942 −0.476471 0.879190i \(-0.658084\pi\)
−0.476471 + 0.879190i \(0.658084\pi\)
\(480\) 1772.35 0.168534
\(481\) −7691.13 −0.729075
\(482\) −2611.44 −0.246779
\(483\) 2887.42 0.272012
\(484\) 3493.69 0.328108
\(485\) 2409.27 0.225566
\(486\) 5201.30 0.485465
\(487\) −1129.88 −0.105133 −0.0525663 0.998617i \(-0.516740\pi\)
−0.0525663 + 0.998617i \(0.516740\pi\)
\(488\) 1037.90 0.0962774
\(489\) −2134.42 −0.197386
\(490\) −1155.30 −0.106512
\(491\) 18774.9 1.72566 0.862832 0.505491i \(-0.168689\pi\)
0.862832 + 0.505491i \(0.168689\pi\)
\(492\) 9124.97 0.836149
\(493\) 2185.48 0.199653
\(494\) 7053.51 0.642414
\(495\) −1427.35 −0.129605
\(496\) 6279.49 0.568463
\(497\) −6260.28 −0.565014
\(498\) −498.339 −0.0448416
\(499\) 17329.1 1.55462 0.777310 0.629118i \(-0.216584\pi\)
0.777310 + 0.629118i \(0.216584\pi\)
\(500\) 4487.74 0.401396
\(501\) −8945.50 −0.797716
\(502\) 10475.6 0.931369
\(503\) −20837.0 −1.84707 −0.923533 0.383518i \(-0.874712\pi\)
−0.923533 + 0.383518i \(0.874712\pi\)
\(504\) −2606.90 −0.230398
\(505\) 804.957 0.0709309
\(506\) −4333.16 −0.380697
\(507\) 3722.37 0.326068
\(508\) −16278.6 −1.42174
\(509\) 11835.0 1.03060 0.515301 0.857009i \(-0.327680\pi\)
0.515301 + 0.857009i \(0.327680\pi\)
\(510\) −221.316 −0.0192158
\(511\) −2348.63 −0.203322
\(512\) 7793.12 0.672676
\(513\) −12390.6 −1.06639
\(514\) 7262.26 0.623199
\(515\) 1585.91 0.135696
\(516\) −6838.35 −0.583414
\(517\) 4214.16 0.358489
\(518\) 1430.55 0.121341
\(519\) −559.359 −0.0473086
\(520\) −3392.71 −0.286115
\(521\) 7686.37 0.646346 0.323173 0.946340i \(-0.395250\pi\)
0.323173 + 0.946340i \(0.395250\pi\)
\(522\) 2983.37 0.250151
\(523\) 11476.4 0.959518 0.479759 0.877400i \(-0.340724\pi\)
0.479759 + 0.877400i \(0.340724\pi\)
\(524\) 12165.6 1.01423
\(525\) 2900.93 0.241156
\(526\) 5355.25 0.443916
\(527\) −4648.81 −0.384261
\(528\) 2000.52 0.164889
\(529\) 1120.01 0.0920535
\(530\) 2177.37 0.178451
\(531\) 4978.44 0.406866
\(532\) 4352.40 0.354700
\(533\) −27345.0 −2.22222
\(534\) −3492.56 −0.283029
\(535\) −2989.38 −0.241574
\(536\) −1019.81 −0.0821814
\(537\) −3229.59 −0.259529
\(538\) 4660.88 0.373504
\(539\) −7731.09 −0.617814
\(540\) 2589.60 0.206368
\(541\) −546.481 −0.0434289 −0.0217145 0.999764i \(-0.506912\pi\)
−0.0217145 + 0.999764i \(0.506912\pi\)
\(542\) 747.357 0.0592283
\(543\) −10884.1 −0.860191
\(544\) −3150.38 −0.248293
\(545\) 5500.69 0.432337
\(546\) −1981.47 −0.155310
\(547\) 8397.33 0.656388 0.328194 0.944610i \(-0.393560\pi\)
0.328194 + 0.944610i \(0.393560\pi\)
\(548\) −19313.6 −1.50554
\(549\) 918.839 0.0714301
\(550\) −4353.44 −0.337512
\(551\) −11463.3 −0.886305
\(552\) 7002.58 0.539945
\(553\) 5719.73 0.439833
\(554\) 7083.32 0.543215
\(555\) −1265.79 −0.0968105
\(556\) −9024.36 −0.688342
\(557\) −4881.65 −0.371350 −0.185675 0.982611i \(-0.559447\pi\)
−0.185675 + 0.982611i \(0.559447\pi\)
\(558\) −6346.04 −0.481451
\(559\) 20492.6 1.55053
\(560\) −552.797 −0.0417142
\(561\) −1481.02 −0.111459
\(562\) −2704.38 −0.202985
\(563\) 7198.57 0.538870 0.269435 0.963019i \(-0.413163\pi\)
0.269435 + 0.963019i \(0.413163\pi\)
\(564\) −2959.14 −0.220926
\(565\) −2144.44 −0.159677
\(566\) 1025.95 0.0761904
\(567\) −174.283 −0.0129087
\(568\) −15182.5 −1.12155
\(569\) −23946.9 −1.76433 −0.882167 0.470937i \(-0.843916\pi\)
−0.882167 + 0.470937i \(0.843916\pi\)
\(570\) 1160.85 0.0853032
\(571\) 1593.15 0.116763 0.0583813 0.998294i \(-0.481406\pi\)
0.0583813 + 0.998294i \(0.481406\pi\)
\(572\) −9864.95 −0.721109
\(573\) −1548.59 −0.112903
\(574\) 5086.16 0.369847
\(575\) 13349.2 0.968174
\(576\) −1168.69 −0.0845403
\(577\) 12937.4 0.933435 0.466717 0.884406i \(-0.345436\pi\)
0.466717 + 0.884406i \(0.345436\pi\)
\(578\) 393.393 0.0283097
\(579\) −11195.2 −0.803549
\(580\) 2395.82 0.171519
\(581\) 921.499 0.0658007
\(582\) 3412.53 0.243048
\(583\) 14570.6 1.03508
\(584\) −5695.92 −0.403594
\(585\) −3003.53 −0.212275
\(586\) −9803.82 −0.691112
\(587\) −12899.2 −0.906998 −0.453499 0.891257i \(-0.649824\pi\)
−0.453499 + 0.891257i \(0.649824\pi\)
\(588\) 5428.70 0.380741
\(589\) 24384.1 1.70582
\(590\) −1205.11 −0.0840911
\(591\) 4300.23 0.299302
\(592\) −3039.19 −0.210997
\(593\) 4357.13 0.301730 0.150865 0.988554i \(-0.451794\pi\)
0.150865 + 0.988554i \(0.451794\pi\)
\(594\) −5223.59 −0.360819
\(595\) 409.245 0.0281973
\(596\) 1758.23 0.120839
\(597\) 11790.3 0.808284
\(598\) −9118.14 −0.623526
\(599\) 13726.8 0.936328 0.468164 0.883642i \(-0.344916\pi\)
0.468164 + 0.883642i \(0.344916\pi\)
\(600\) 7035.35 0.478695
\(601\) 2531.41 0.171811 0.0859056 0.996303i \(-0.472622\pi\)
0.0859056 + 0.996303i \(0.472622\pi\)
\(602\) −3811.62 −0.258057
\(603\) −902.830 −0.0609720
\(604\) 4116.24 0.277297
\(605\) −1723.07 −0.115790
\(606\) 1140.15 0.0764283
\(607\) 185.004 0.0123708 0.00618540 0.999981i \(-0.498031\pi\)
0.00618540 + 0.999981i \(0.498031\pi\)
\(608\) 16524.4 1.10223
\(609\) 3220.28 0.214273
\(610\) −222.420 −0.0147632
\(611\) 8867.73 0.587152
\(612\) −1781.55 −0.117672
\(613\) −17706.9 −1.16668 −0.583339 0.812228i \(-0.698254\pi\)
−0.583339 + 0.812228i \(0.698254\pi\)
\(614\) 3301.93 0.217028
\(615\) −4500.39 −0.295078
\(616\) 4222.84 0.276207
\(617\) −6183.89 −0.403491 −0.201746 0.979438i \(-0.564661\pi\)
−0.201746 + 0.979438i \(0.564661\pi\)
\(618\) 2246.30 0.146213
\(619\) −1247.51 −0.0810046 −0.0405023 0.999179i \(-0.512896\pi\)
−0.0405023 + 0.999179i \(0.512896\pi\)
\(620\) −5096.23 −0.330112
\(621\) 16017.4 1.03503
\(622\) −12992.8 −0.837561
\(623\) 6458.23 0.415318
\(624\) 4209.63 0.270064
\(625\) 12262.8 0.784817
\(626\) 800.914 0.0511357
\(627\) 7768.27 0.494792
\(628\) −4430.87 −0.281546
\(629\) 2249.96 0.142626
\(630\) 558.655 0.0353292
\(631\) 24053.3 1.51750 0.758752 0.651379i \(-0.225809\pi\)
0.758752 + 0.651379i \(0.225809\pi\)
\(632\) 13871.5 0.873069
\(633\) −16612.7 −1.04312
\(634\) 10417.8 0.652596
\(635\) 8028.51 0.501735
\(636\) −10231.4 −0.637893
\(637\) −16268.3 −1.01189
\(638\) −4832.69 −0.299887
\(639\) −13440.9 −0.832102
\(640\) −4211.70 −0.260128
\(641\) −21286.8 −1.31167 −0.655834 0.754905i \(-0.727683\pi\)
−0.655834 + 0.754905i \(0.727683\pi\)
\(642\) −4234.20 −0.260297
\(643\) −1789.41 −0.109747 −0.0548736 0.998493i \(-0.517476\pi\)
−0.0548736 + 0.998493i \(0.517476\pi\)
\(644\) −5626.38 −0.344271
\(645\) 3372.64 0.205888
\(646\) −2063.43 −0.125673
\(647\) −4378.61 −0.266060 −0.133030 0.991112i \(-0.542471\pi\)
−0.133030 + 0.991112i \(0.542471\pi\)
\(648\) −422.672 −0.0256237
\(649\) −8064.45 −0.487762
\(650\) −9160.81 −0.552795
\(651\) −6849.97 −0.412399
\(652\) 4159.11 0.249821
\(653\) −7665.15 −0.459358 −0.229679 0.973266i \(-0.573768\pi\)
−0.229679 + 0.973266i \(0.573768\pi\)
\(654\) 7791.26 0.465845
\(655\) −5999.99 −0.357922
\(656\) −10805.5 −0.643117
\(657\) −5042.54 −0.299434
\(658\) −1649.39 −0.0977205
\(659\) −4710.22 −0.278428 −0.139214 0.990262i \(-0.544458\pi\)
−0.139214 + 0.990262i \(0.544458\pi\)
\(660\) −1623.55 −0.0957527
\(661\) −31266.6 −1.83983 −0.919916 0.392116i \(-0.871743\pi\)
−0.919916 + 0.392116i \(0.871743\pi\)
\(662\) 1024.00 0.0601192
\(663\) −3116.46 −0.182554
\(664\) 2234.82 0.130614
\(665\) −2146.58 −0.125174
\(666\) 3071.40 0.178700
\(667\) 14818.7 0.860246
\(668\) 17431.1 1.00962
\(669\) 2222.58 0.128446
\(670\) 218.545 0.0126017
\(671\) −1488.40 −0.0856322
\(672\) −4642.05 −0.266474
\(673\) 11723.0 0.671454 0.335727 0.941959i \(-0.391018\pi\)
0.335727 + 0.941959i \(0.391018\pi\)
\(674\) −2679.65 −0.153140
\(675\) 16092.3 0.917621
\(676\) −7253.37 −0.412686
\(677\) −289.531 −0.0164366 −0.00821829 0.999966i \(-0.502616\pi\)
−0.00821829 + 0.999966i \(0.502616\pi\)
\(678\) −3037.42 −0.172052
\(679\) −6310.25 −0.356650
\(680\) 992.502 0.0559716
\(681\) −6786.45 −0.381875
\(682\) 10279.8 0.577175
\(683\) 1720.10 0.0963660 0.0481830 0.998839i \(-0.484657\pi\)
0.0481830 + 0.998839i \(0.484657\pi\)
\(684\) 9344.64 0.522370
\(685\) 9525.37 0.531308
\(686\) 6733.30 0.374750
\(687\) −12356.5 −0.686215
\(688\) 8097.77 0.448728
\(689\) 30660.5 1.69532
\(690\) −1500.65 −0.0827951
\(691\) −16777.7 −0.923665 −0.461832 0.886967i \(-0.652808\pi\)
−0.461832 + 0.886967i \(0.652808\pi\)
\(692\) 1089.96 0.0598758
\(693\) 3738.44 0.204923
\(694\) 5421.88 0.296559
\(695\) 4450.77 0.242917
\(696\) 7809.84 0.425332
\(697\) 7999.50 0.434724
\(698\) 2035.86 0.110399
\(699\) −16381.2 −0.886400
\(700\) −5652.71 −0.305218
\(701\) 23981.1 1.29209 0.646043 0.763301i \(-0.276423\pi\)
0.646043 + 0.763301i \(0.276423\pi\)
\(702\) −10991.8 −0.590969
\(703\) −11801.6 −0.633150
\(704\) 1893.12 0.101349
\(705\) 1459.43 0.0779652
\(706\) 8824.10 0.470396
\(707\) −2108.30 −0.112151
\(708\) 5662.78 0.300593
\(709\) −7709.28 −0.408361 −0.204181 0.978933i \(-0.565453\pi\)
−0.204181 + 0.978933i \(0.565453\pi\)
\(710\) 3253.59 0.171979
\(711\) 12280.3 0.647747
\(712\) 15662.5 0.824407
\(713\) −31521.5 −1.65567
\(714\) 579.660 0.0303827
\(715\) 4865.34 0.254480
\(716\) 6293.13 0.328471
\(717\) 1054.61 0.0549304
\(718\) −6729.09 −0.349760
\(719\) −11976.5 −0.621209 −0.310605 0.950539i \(-0.600532\pi\)
−0.310605 + 0.950539i \(0.600532\pi\)
\(720\) −1186.86 −0.0614329
\(721\) −4153.72 −0.214553
\(722\) 1486.56 0.0766260
\(723\) −6052.00 −0.311309
\(724\) 21208.7 1.08870
\(725\) 14888.1 0.762662
\(726\) −2440.58 −0.124764
\(727\) −18597.3 −0.948745 −0.474372 0.880324i \(-0.657325\pi\)
−0.474372 + 0.880324i \(0.657325\pi\)
\(728\) 8886.00 0.452386
\(729\) 11461.4 0.582300
\(730\) 1220.63 0.0618870
\(731\) −5994.91 −0.303324
\(732\) 1045.14 0.0527727
\(733\) −23569.5 −1.18767 −0.593833 0.804588i \(-0.702386\pi\)
−0.593833 + 0.804588i \(0.702386\pi\)
\(734\) −20.2646 −0.00101905
\(735\) −2677.41 −0.134364
\(736\) −21361.3 −1.06982
\(737\) 1462.47 0.0730948
\(738\) 10920.0 0.544678
\(739\) 10149.1 0.505199 0.252599 0.967571i \(-0.418715\pi\)
0.252599 + 0.967571i \(0.418715\pi\)
\(740\) 2466.50 0.122528
\(741\) 16346.5 0.810397
\(742\) −5702.85 −0.282154
\(743\) 27758.0 1.37058 0.685291 0.728269i \(-0.259675\pi\)
0.685291 + 0.728269i \(0.259675\pi\)
\(744\) −16612.6 −0.818611
\(745\) −867.148 −0.0426441
\(746\) 2617.87 0.128481
\(747\) 1978.47 0.0969054
\(748\) 2885.89 0.141068
\(749\) 7829.63 0.381960
\(750\) −3134.99 −0.152632
\(751\) −815.225 −0.0396112 −0.0198056 0.999804i \(-0.506305\pi\)
−0.0198056 + 0.999804i \(0.506305\pi\)
\(752\) 3504.13 0.169924
\(753\) 24277.1 1.17491
\(754\) −10169.3 −0.491172
\(755\) −2030.11 −0.0978585
\(756\) −6782.56 −0.326295
\(757\) −13239.4 −0.635659 −0.317829 0.948148i \(-0.602954\pi\)
−0.317829 + 0.948148i \(0.602954\pi\)
\(758\) −13058.0 −0.625710
\(759\) −10042.1 −0.480244
\(760\) −5205.90 −0.248471
\(761\) −11028.2 −0.525324 −0.262662 0.964888i \(-0.584600\pi\)
−0.262662 + 0.964888i \(0.584600\pi\)
\(762\) 11371.7 0.540621
\(763\) −14407.1 −0.683582
\(764\) 3017.56 0.142895
\(765\) 878.652 0.0415265
\(766\) −12365.0 −0.583246
\(767\) −16969.8 −0.798882
\(768\) −7695.55 −0.361574
\(769\) −18921.2 −0.887277 −0.443639 0.896206i \(-0.646313\pi\)
−0.443639 + 0.896206i \(0.646313\pi\)
\(770\) −904.952 −0.0423535
\(771\) 16830.3 0.786158
\(772\) 21814.7 1.01701
\(773\) 38728.6 1.80203 0.901016 0.433786i \(-0.142823\pi\)
0.901016 + 0.433786i \(0.142823\pi\)
\(774\) −8183.59 −0.380043
\(775\) −31669.0 −1.46785
\(776\) −15303.6 −0.707949
\(777\) 3315.29 0.153070
\(778\) −1556.93 −0.0717465
\(779\) −41959.2 −1.92984
\(780\) −3416.39 −0.156829
\(781\) 21772.5 0.997545
\(782\) 2667.42 0.121978
\(783\) 17863.9 0.815329
\(784\) −6428.50 −0.292844
\(785\) 2185.28 0.0993579
\(786\) −8498.47 −0.385662
\(787\) −20587.3 −0.932477 −0.466239 0.884659i \(-0.654391\pi\)
−0.466239 + 0.884659i \(0.654391\pi\)
\(788\) −8379.37 −0.378811
\(789\) 12410.8 0.559995
\(790\) −2972.66 −0.133876
\(791\) 5616.62 0.252470
\(792\) 9066.49 0.406772
\(793\) −3132.00 −0.140253
\(794\) 14435.0 0.645190
\(795\) 5046.05 0.225113
\(796\) −22974.5 −1.02300
\(797\) −15871.4 −0.705385 −0.352693 0.935739i \(-0.614734\pi\)
−0.352693 + 0.935739i \(0.614734\pi\)
\(798\) −3040.45 −0.134876
\(799\) −2594.17 −0.114862
\(800\) −21461.3 −0.948463
\(801\) 13865.9 0.611644
\(802\) 18765.0 0.826204
\(803\) 8168.28 0.358969
\(804\) −1026.93 −0.0450462
\(805\) 2774.90 0.121494
\(806\) 21631.4 0.945329
\(807\) 10801.6 0.471170
\(808\) −5113.06 −0.222620
\(809\) 39667.1 1.72388 0.861942 0.507007i \(-0.169248\pi\)
0.861942 + 0.507007i \(0.169248\pi\)
\(810\) 90.5783 0.00392913
\(811\) 8003.87 0.346552 0.173276 0.984873i \(-0.444565\pi\)
0.173276 + 0.984873i \(0.444565\pi\)
\(812\) −6275.00 −0.271194
\(813\) 1732.00 0.0747157
\(814\) −4975.28 −0.214230
\(815\) −2051.25 −0.0881621
\(816\) −1231.48 −0.0528316
\(817\) 31444.7 1.34652
\(818\) −12939.7 −0.553088
\(819\) 7866.69 0.335634
\(820\) 8769.40 0.373464
\(821\) −13279.1 −0.564489 −0.282244 0.959343i \(-0.591079\pi\)
−0.282244 + 0.959343i \(0.591079\pi\)
\(822\) 13491.9 0.572486
\(823\) 28934.0 1.22549 0.612745 0.790281i \(-0.290065\pi\)
0.612745 + 0.790281i \(0.290065\pi\)
\(824\) −10073.6 −0.425887
\(825\) −10089.1 −0.425767
\(826\) 3156.37 0.132959
\(827\) −13679.6 −0.575193 −0.287597 0.957752i \(-0.592856\pi\)
−0.287597 + 0.957752i \(0.592856\pi\)
\(828\) −12079.9 −0.507012
\(829\) 16514.5 0.691886 0.345943 0.938256i \(-0.387559\pi\)
0.345943 + 0.938256i \(0.387559\pi\)
\(830\) −478.921 −0.0200284
\(831\) 16415.6 0.685260
\(832\) 3983.64 0.165995
\(833\) 4759.13 0.197952
\(834\) 6304.13 0.261744
\(835\) −8596.93 −0.356298
\(836\) −15137.1 −0.626231
\(837\) −37998.9 −1.56922
\(838\) 13177.8 0.543221
\(839\) −87.9839 −0.00362043 −0.00181022 0.999998i \(-0.500576\pi\)
−0.00181022 + 0.999998i \(0.500576\pi\)
\(840\) 1462.44 0.0600702
\(841\) −7861.94 −0.322356
\(842\) −16825.1 −0.688635
\(843\) −6267.41 −0.256063
\(844\) 32371.3 1.32022
\(845\) 3577.33 0.145638
\(846\) −3541.27 −0.143914
\(847\) 4512.98 0.183079
\(848\) 12115.7 0.490630
\(849\) 2377.63 0.0961133
\(850\) 2679.90 0.108141
\(851\) 15256.0 0.614534
\(852\) −15288.5 −0.614758
\(853\) 8162.96 0.327660 0.163830 0.986489i \(-0.447615\pi\)
0.163830 + 0.986489i \(0.447615\pi\)
\(854\) 582.551 0.0233425
\(855\) −4608.73 −0.184345
\(856\) 18988.4 0.758191
\(857\) 18724.9 0.746361 0.373181 0.927759i \(-0.378267\pi\)
0.373181 + 0.927759i \(0.378267\pi\)
\(858\) 6891.34 0.274203
\(859\) −46422.5 −1.84391 −0.921953 0.387301i \(-0.873407\pi\)
−0.921953 + 0.387301i \(0.873407\pi\)
\(860\) −6571.88 −0.260580
\(861\) 11787.2 0.466557
\(862\) 4043.61 0.159775
\(863\) 29112.3 1.14831 0.574157 0.818746i \(-0.305330\pi\)
0.574157 + 0.818746i \(0.305330\pi\)
\(864\) −25750.8 −1.01396
\(865\) −537.563 −0.0211303
\(866\) 8346.33 0.327505
\(867\) 911.688 0.0357123
\(868\) 13347.8 0.521950
\(869\) −19892.6 −0.776536
\(870\) −1673.64 −0.0652204
\(871\) 3077.43 0.119719
\(872\) −34940.2 −1.35691
\(873\) −13548.2 −0.525241
\(874\) −13991.2 −0.541487
\(875\) 5797.04 0.223972
\(876\) −5735.69 −0.221222
\(877\) 39163.0 1.50791 0.753957 0.656924i \(-0.228143\pi\)
0.753957 + 0.656924i \(0.228143\pi\)
\(878\) −3464.19 −0.133156
\(879\) −22720.3 −0.871830
\(880\) 1922.57 0.0736473
\(881\) −35073.2 −1.34125 −0.670627 0.741795i \(-0.733975\pi\)
−0.670627 + 0.741795i \(0.733975\pi\)
\(882\) 6496.63 0.248019
\(883\) −48775.7 −1.85893 −0.929463 0.368915i \(-0.879729\pi\)
−0.929463 + 0.368915i \(0.879729\pi\)
\(884\) 6072.69 0.231048
\(885\) −2792.85 −0.106080
\(886\) 11611.0 0.440269
\(887\) 13296.0 0.503309 0.251654 0.967817i \(-0.419025\pi\)
0.251654 + 0.967817i \(0.419025\pi\)
\(888\) 8040.27 0.303844
\(889\) −21027.9 −0.793309
\(890\) −3356.46 −0.126415
\(891\) 606.137 0.0227905
\(892\) −4330.90 −0.162566
\(893\) 13607.0 0.509899
\(894\) −1228.24 −0.0459492
\(895\) −3103.74 −0.115918
\(896\) 11031.1 0.411297
\(897\) −21131.3 −0.786570
\(898\) 12054.6 0.447960
\(899\) −35155.3 −1.30422
\(900\) −12136.4 −0.449498
\(901\) −8969.43 −0.331648
\(902\) −17689.1 −0.652974
\(903\) −8833.44 −0.325535
\(904\) 13621.4 0.501153
\(905\) −10460.0 −0.384202
\(906\) −2875.47 −0.105443
\(907\) −11675.0 −0.427410 −0.213705 0.976898i \(-0.568553\pi\)
−0.213705 + 0.976898i \(0.568553\pi\)
\(908\) 13224.0 0.483319
\(909\) −4526.54 −0.165166
\(910\) −1904.26 −0.0693689
\(911\) 18552.9 0.674738 0.337369 0.941372i \(-0.390463\pi\)
0.337369 + 0.941372i \(0.390463\pi\)
\(912\) 6459.41 0.234531
\(913\) −3204.87 −0.116173
\(914\) −9739.24 −0.352457
\(915\) −515.459 −0.0186235
\(916\) 24077.7 0.868504
\(917\) 15714.9 0.565922
\(918\) 3215.55 0.115609
\(919\) 33956.8 1.21886 0.609429 0.792841i \(-0.291399\pi\)
0.609429 + 0.792841i \(0.291399\pi\)
\(920\) 6729.71 0.241165
\(921\) 7652.23 0.273778
\(922\) −9886.63 −0.353144
\(923\) 45815.3 1.63383
\(924\) 4252.33 0.151398
\(925\) 15327.4 0.544823
\(926\) 480.372 0.0170475
\(927\) −8918.08 −0.315974
\(928\) −23823.8 −0.842732
\(929\) −23695.3 −0.836832 −0.418416 0.908256i \(-0.637415\pi\)
−0.418416 + 0.908256i \(0.637415\pi\)
\(930\) 3560.06 0.125526
\(931\) −24962.7 −0.878753
\(932\) 31920.2 1.12187
\(933\) −30110.8 −1.05657
\(934\) 2018.72 0.0707221
\(935\) −1423.31 −0.0497830
\(936\) 19078.3 0.666234
\(937\) 7990.62 0.278593 0.139297 0.990251i \(-0.455516\pi\)
0.139297 + 0.990251i \(0.455516\pi\)
\(938\) −572.402 −0.0199249
\(939\) 1856.12 0.0645071
\(940\) −2843.83 −0.0986762
\(941\) 24385.9 0.844799 0.422400 0.906410i \(-0.361188\pi\)
0.422400 + 0.906410i \(0.361188\pi\)
\(942\) 3095.26 0.107058
\(943\) 54241.0 1.87310
\(944\) −6705.69 −0.231199
\(945\) 3345.12 0.115150
\(946\) 13256.4 0.455605
\(947\) −1174.62 −0.0403064 −0.0201532 0.999797i \(-0.506415\pi\)
−0.0201532 + 0.999797i \(0.506415\pi\)
\(948\) 13968.4 0.478557
\(949\) 17188.3 0.587939
\(950\) −14056.7 −0.480063
\(951\) 24143.4 0.823241
\(952\) −2599.51 −0.0884985
\(953\) −33546.9 −1.14029 −0.570143 0.821546i \(-0.693112\pi\)
−0.570143 + 0.821546i \(0.693112\pi\)
\(954\) −12244.1 −0.415531
\(955\) −1488.25 −0.0504277
\(956\) −2055.00 −0.0695224
\(957\) −11199.8 −0.378304
\(958\) −13598.7 −0.458617
\(959\) −24948.4 −0.840067
\(960\) 655.620 0.0220417
\(961\) 44989.1 1.51016
\(962\) −10469.3 −0.350878
\(963\) 16810.3 0.562517
\(964\) 11792.9 0.394007
\(965\) −10758.9 −0.358903
\(966\) 3930.41 0.130910
\(967\) 24766.8 0.823625 0.411813 0.911269i \(-0.364896\pi\)
0.411813 + 0.911269i \(0.364896\pi\)
\(968\) 10944.9 0.363411
\(969\) −4782.01 −0.158535
\(970\) 3279.56 0.108557
\(971\) 42324.3 1.39882 0.699409 0.714721i \(-0.253447\pi\)
0.699409 + 0.714721i \(0.253447\pi\)
\(972\) −23488.3 −0.775091
\(973\) −11657.2 −0.384083
\(974\) −1538.01 −0.0505966
\(975\) −21230.2 −0.697344
\(976\) −1237.63 −0.0405896
\(977\) −11320.4 −0.370698 −0.185349 0.982673i \(-0.559342\pi\)
−0.185349 + 0.982673i \(0.559342\pi\)
\(978\) −2905.42 −0.0949949
\(979\) −22461.0 −0.733254
\(980\) 5217.16 0.170057
\(981\) −30932.2 −1.00672
\(982\) 25556.8 0.830500
\(983\) −11311.9 −0.367032 −0.183516 0.983017i \(-0.558748\pi\)
−0.183516 + 0.983017i \(0.558748\pi\)
\(984\) 28586.3 0.926116
\(985\) 4132.66 0.133683
\(986\) 2974.92 0.0960860
\(987\) −3822.47 −0.123273
\(988\) −31852.6 −1.02568
\(989\) −40648.8 −1.30693
\(990\) −1942.94 −0.0623744
\(991\) −29405.5 −0.942580 −0.471290 0.881978i \(-0.656212\pi\)
−0.471290 + 0.881978i \(0.656212\pi\)
\(992\) 50676.5 1.62196
\(993\) 2373.12 0.0758397
\(994\) −8521.63 −0.271921
\(995\) 11330.9 0.361018
\(996\) 2250.43 0.0715939
\(997\) −54905.9 −1.74412 −0.872060 0.489398i \(-0.837216\pi\)
−0.872060 + 0.489398i \(0.837216\pi\)
\(998\) 23588.7 0.748183
\(999\) 18390.9 0.582446
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 \(a_p\))