Properties

Label 4003.2.a.b.1.9
Level 4003
Weight 2
Character 4003.1
Self dual Yes
Analytic conductor 31.964
Analytic rank 1
Dimension 152
CM No

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Newspace parameters

Level: \( N \) = \( 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9641159291\)
Analytic rank: \(1\)
Dimension: \(152\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.60205 q^{2} +1.48054 q^{3} +4.77066 q^{4} +1.31197 q^{5} -3.85243 q^{6} +3.44490 q^{7} -7.20939 q^{8} -0.808005 q^{9} +O(q^{10})\) \(q-2.60205 q^{2} +1.48054 q^{3} +4.77066 q^{4} +1.31197 q^{5} -3.85243 q^{6} +3.44490 q^{7} -7.20939 q^{8} -0.808005 q^{9} -3.41380 q^{10} -4.34159 q^{11} +7.06314 q^{12} +1.60278 q^{13} -8.96381 q^{14} +1.94242 q^{15} +9.21787 q^{16} -2.68007 q^{17} +2.10247 q^{18} +1.39273 q^{19} +6.25894 q^{20} +5.10031 q^{21} +11.2970 q^{22} -1.41743 q^{23} -10.6738 q^{24} -3.27874 q^{25} -4.17050 q^{26} -5.63790 q^{27} +16.4345 q^{28} -9.46568 q^{29} -5.05426 q^{30} -8.88883 q^{31} -9.56656 q^{32} -6.42789 q^{33} +6.97367 q^{34} +4.51960 q^{35} -3.85472 q^{36} +6.69542 q^{37} -3.62395 q^{38} +2.37297 q^{39} -9.45848 q^{40} -3.03509 q^{41} -13.2713 q^{42} +11.4209 q^{43} -20.7122 q^{44} -1.06008 q^{45} +3.68821 q^{46} +1.90734 q^{47} +13.6474 q^{48} +4.86737 q^{49} +8.53145 q^{50} -3.96794 q^{51} +7.64630 q^{52} +9.71534 q^{53} +14.6701 q^{54} -5.69602 q^{55} -24.8357 q^{56} +2.06199 q^{57} +24.6302 q^{58} +1.71390 q^{59} +9.26661 q^{60} -11.5122 q^{61} +23.1292 q^{62} -2.78350 q^{63} +6.45693 q^{64} +2.10279 q^{65} +16.7257 q^{66} +0.441675 q^{67} -12.7857 q^{68} -2.09856 q^{69} -11.7602 q^{70} -7.97411 q^{71} +5.82522 q^{72} -5.45206 q^{73} -17.4218 q^{74} -4.85431 q^{75} +6.64423 q^{76} -14.9564 q^{77} -6.17459 q^{78} +2.73268 q^{79} +12.0935 q^{80} -5.92311 q^{81} +7.89745 q^{82} -15.9563 q^{83} +24.3319 q^{84} -3.51616 q^{85} -29.7176 q^{86} -14.0143 q^{87} +31.3002 q^{88} -10.0380 q^{89} +2.75837 q^{90} +5.52141 q^{91} -6.76206 q^{92} -13.1603 q^{93} -4.96299 q^{94} +1.82721 q^{95} -14.1637 q^{96} -0.127111 q^{97} -12.6651 q^{98} +3.50803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} + O(q^{10}) \) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} - 15q^{10} - 40q^{11} - 53q^{12} - 59q^{13} - 36q^{14} - 40q^{15} + 118q^{16} - 93q^{17} - 59q^{18} - 16q^{19} - 108q^{20} - 62q^{21} - 37q^{22} - 107q^{23} - 31q^{24} + 101q^{25} - 64q^{26} - 63q^{27} - 53q^{28} - 124q^{29} - 68q^{30} - 15q^{31} - 129q^{32} - 49q^{33} - 76q^{35} + 45q^{36} - 98q^{37} - 125q^{38} - 47q^{39} - 7q^{40} - 56q^{41} - 84q^{42} - 62q^{43} - 114q^{44} - 142q^{45} - 3q^{46} - 111q^{47} - 92q^{48} + 117q^{49} - 64q^{50} - 21q^{51} - 85q^{52} - 347q^{53} + 3q^{54} - 16q^{55} - 73q^{56} - 115q^{57} - 29q^{58} - 50q^{59} - 54q^{60} - 62q^{61} - 55q^{62} - 70q^{63} + 64q^{64} - 147q^{65} + 34q^{66} - 86q^{67} - 174q^{68} - 104q^{69} - 7q^{70} - 86q^{71} - 139q^{72} - 27q^{73} - 52q^{74} - 49q^{75} - 11q^{76} - 346q^{77} - 59q^{78} - 17q^{79} - 149q^{80} - 8q^{81} - 31q^{82} - 106q^{83} - 51q^{84} - 69q^{85} - 85q^{86} - 32q^{87} - 113q^{88} - 59q^{89} + 10q^{90} - 9q^{91} - 314q^{92} - 230q^{93} + 7q^{94} - 74q^{95} - 54q^{96} - 60q^{97} - 77q^{98} - 96q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.60205 −1.83993 −0.919963 0.392005i \(-0.871782\pi\)
−0.919963 + 0.392005i \(0.871782\pi\)
\(3\) 1.48054 0.854789 0.427395 0.904065i \(-0.359431\pi\)
0.427395 + 0.904065i \(0.359431\pi\)
\(4\) 4.77066 2.38533
\(5\) 1.31197 0.586729 0.293365 0.956001i \(-0.405225\pi\)
0.293365 + 0.956001i \(0.405225\pi\)
\(6\) −3.85243 −1.57275
\(7\) 3.44490 1.30205 0.651026 0.759056i \(-0.274339\pi\)
0.651026 + 0.759056i \(0.274339\pi\)
\(8\) −7.20939 −2.54890
\(9\) −0.808005 −0.269335
\(10\) −3.41380 −1.07954
\(11\) −4.34159 −1.30904 −0.654519 0.756045i \(-0.727129\pi\)
−0.654519 + 0.756045i \(0.727129\pi\)
\(12\) 7.06314 2.03895
\(13\) 1.60278 0.444530 0.222265 0.974986i \(-0.428655\pi\)
0.222265 + 0.974986i \(0.428655\pi\)
\(14\) −8.96381 −2.39568
\(15\) 1.94242 0.501530
\(16\) 9.21787 2.30447
\(17\) −2.68007 −0.650012 −0.325006 0.945712i \(-0.605366\pi\)
−0.325006 + 0.945712i \(0.605366\pi\)
\(18\) 2.10247 0.495557
\(19\) 1.39273 0.319514 0.159757 0.987156i \(-0.448929\pi\)
0.159757 + 0.987156i \(0.448929\pi\)
\(20\) 6.25894 1.39954
\(21\) 5.10031 1.11298
\(22\) 11.2970 2.40853
\(23\) −1.41743 −0.295554 −0.147777 0.989021i \(-0.547212\pi\)
−0.147777 + 0.989021i \(0.547212\pi\)
\(24\) −10.6738 −2.17878
\(25\) −3.27874 −0.655749
\(26\) −4.17050 −0.817902
\(27\) −5.63790 −1.08501
\(28\) 16.4345 3.10582
\(29\) −9.46568 −1.75773 −0.878866 0.477069i \(-0.841699\pi\)
−0.878866 + 0.477069i \(0.841699\pi\)
\(30\) −5.05426 −0.922778
\(31\) −8.88883 −1.59648 −0.798241 0.602338i \(-0.794236\pi\)
−0.798241 + 0.602338i \(0.794236\pi\)
\(32\) −9.56656 −1.69115
\(33\) −6.42789 −1.11895
\(34\) 6.97367 1.19597
\(35\) 4.51960 0.763952
\(36\) −3.85472 −0.642453
\(37\) 6.69542 1.10072 0.550360 0.834927i \(-0.314490\pi\)
0.550360 + 0.834927i \(0.314490\pi\)
\(38\) −3.62395 −0.587882
\(39\) 2.37297 0.379980
\(40\) −9.45848 −1.49552
\(41\) −3.03509 −0.474001 −0.237001 0.971509i \(-0.576164\pi\)
−0.237001 + 0.971509i \(0.576164\pi\)
\(42\) −13.2713 −2.04780
\(43\) 11.4209 1.74166 0.870832 0.491581i \(-0.163581\pi\)
0.870832 + 0.491581i \(0.163581\pi\)
\(44\) −20.7122 −3.12249
\(45\) −1.06008 −0.158027
\(46\) 3.68821 0.543797
\(47\) 1.90734 0.278214 0.139107 0.990277i \(-0.455577\pi\)
0.139107 + 0.990277i \(0.455577\pi\)
\(48\) 13.6474 1.96983
\(49\) 4.86737 0.695338
\(50\) 8.53145 1.20653
\(51\) −3.96794 −0.555623
\(52\) 7.64630 1.06035
\(53\) 9.71534 1.33451 0.667253 0.744832i \(-0.267470\pi\)
0.667253 + 0.744832i \(0.267470\pi\)
\(54\) 14.6701 1.99635
\(55\) −5.69602 −0.768051
\(56\) −24.8357 −3.31880
\(57\) 2.06199 0.273117
\(58\) 24.6302 3.23410
\(59\) 1.71390 0.223131 0.111566 0.993757i \(-0.464414\pi\)
0.111566 + 0.993757i \(0.464414\pi\)
\(60\) 9.26661 1.19631
\(61\) −11.5122 −1.47398 −0.736991 0.675902i \(-0.763754\pi\)
−0.736991 + 0.675902i \(0.763754\pi\)
\(62\) 23.1292 2.93741
\(63\) −2.78350 −0.350688
\(64\) 6.45693 0.807117
\(65\) 2.10279 0.260819
\(66\) 16.7257 2.05879
\(67\) 0.441675 0.0539592 0.0269796 0.999636i \(-0.491411\pi\)
0.0269796 + 0.999636i \(0.491411\pi\)
\(68\) −12.7857 −1.55049
\(69\) −2.09856 −0.252636
\(70\) −11.7602 −1.40561
\(71\) −7.97411 −0.946353 −0.473176 0.880968i \(-0.656893\pi\)
−0.473176 + 0.880968i \(0.656893\pi\)
\(72\) 5.82522 0.686509
\(73\) −5.45206 −0.638115 −0.319057 0.947735i \(-0.603366\pi\)
−0.319057 + 0.947735i \(0.603366\pi\)
\(74\) −17.4218 −2.02524
\(75\) −4.85431 −0.560527
\(76\) 6.64423 0.762146
\(77\) −14.9564 −1.70444
\(78\) −6.17459 −0.699134
\(79\) 2.73268 0.307450 0.153725 0.988114i \(-0.450873\pi\)
0.153725 + 0.988114i \(0.450873\pi\)
\(80\) 12.0935 1.35210
\(81\) −5.92311 −0.658124
\(82\) 7.89745 0.872128
\(83\) −15.9563 −1.75143 −0.875714 0.482829i \(-0.839609\pi\)
−0.875714 + 0.482829i \(0.839609\pi\)
\(84\) 24.3319 2.65482
\(85\) −3.51616 −0.381381
\(86\) −29.7176 −3.20453
\(87\) −14.0143 −1.50249
\(88\) 31.3002 3.33661
\(89\) −10.0380 −1.06403 −0.532015 0.846735i \(-0.678565\pi\)
−0.532015 + 0.846735i \(0.678565\pi\)
\(90\) 2.75837 0.290758
\(91\) 5.52141 0.578801
\(92\) −6.76206 −0.704993
\(93\) −13.1603 −1.36466
\(94\) −4.96299 −0.511893
\(95\) 1.82721 0.187468
\(96\) −14.1637 −1.44557
\(97\) −0.127111 −0.0129062 −0.00645309 0.999979i \(-0.502054\pi\)
−0.00645309 + 0.999979i \(0.502054\pi\)
\(98\) −12.6651 −1.27937
\(99\) 3.50803 0.352570
\(100\) −15.6418 −1.56418
\(101\) 17.1694 1.70842 0.854212 0.519926i \(-0.174040\pi\)
0.854212 + 0.519926i \(0.174040\pi\)
\(102\) 10.3248 1.02231
\(103\) −15.5235 −1.52958 −0.764789 0.644280i \(-0.777157\pi\)
−0.764789 + 0.644280i \(0.777157\pi\)
\(104\) −11.5550 −1.13306
\(105\) 6.69144 0.653018
\(106\) −25.2798 −2.45539
\(107\) −12.5337 −1.21168 −0.605841 0.795586i \(-0.707163\pi\)
−0.605841 + 0.795586i \(0.707163\pi\)
\(108\) −26.8965 −2.58812
\(109\) −12.3496 −1.18287 −0.591437 0.806351i \(-0.701439\pi\)
−0.591437 + 0.806351i \(0.701439\pi\)
\(110\) 14.8213 1.41316
\(111\) 9.91283 0.940884
\(112\) 31.7547 3.00053
\(113\) 11.0784 1.04217 0.521086 0.853504i \(-0.325527\pi\)
0.521086 + 0.853504i \(0.325527\pi\)
\(114\) −5.36539 −0.502515
\(115\) −1.85962 −0.173410
\(116\) −45.1575 −4.19277
\(117\) −1.29505 −0.119728
\(118\) −4.45966 −0.410545
\(119\) −9.23258 −0.846349
\(120\) −14.0036 −1.27835
\(121\) 7.84940 0.713582
\(122\) 29.9552 2.71202
\(123\) −4.49357 −0.405171
\(124\) −42.4056 −3.80814
\(125\) −10.8614 −0.971476
\(126\) 7.24280 0.645240
\(127\) −1.19854 −0.106354 −0.0531768 0.998585i \(-0.516935\pi\)
−0.0531768 + 0.998585i \(0.516935\pi\)
\(128\) 2.33187 0.206111
\(129\) 16.9090 1.48876
\(130\) −5.47156 −0.479887
\(131\) −9.66189 −0.844164 −0.422082 0.906558i \(-0.638700\pi\)
−0.422082 + 0.906558i \(0.638700\pi\)
\(132\) −30.6653 −2.66907
\(133\) 4.79782 0.416023
\(134\) −1.14926 −0.0992810
\(135\) −7.39673 −0.636609
\(136\) 19.3217 1.65682
\(137\) 3.72997 0.318673 0.159336 0.987224i \(-0.449065\pi\)
0.159336 + 0.987224i \(0.449065\pi\)
\(138\) 5.46054 0.464832
\(139\) −0.224646 −0.0190542 −0.00952711 0.999955i \(-0.503033\pi\)
−0.00952711 + 0.999955i \(0.503033\pi\)
\(140\) 21.5615 1.82228
\(141\) 2.82389 0.237814
\(142\) 20.7490 1.74122
\(143\) −6.95859 −0.581907
\(144\) −7.44809 −0.620674
\(145\) −12.4186 −1.03131
\(146\) 14.1865 1.17408
\(147\) 7.20632 0.594368
\(148\) 31.9416 2.62558
\(149\) −9.42229 −0.771904 −0.385952 0.922519i \(-0.626127\pi\)
−0.385952 + 0.922519i \(0.626127\pi\)
\(150\) 12.6311 1.03133
\(151\) 0.999601 0.0813464 0.0406732 0.999173i \(-0.487050\pi\)
0.0406732 + 0.999173i \(0.487050\pi\)
\(152\) −10.0407 −0.814410
\(153\) 2.16551 0.175071
\(154\) 38.9172 3.13604
\(155\) −11.6619 −0.936702
\(156\) 11.3206 0.906376
\(157\) −14.4240 −1.15116 −0.575579 0.817746i \(-0.695223\pi\)
−0.575579 + 0.817746i \(0.695223\pi\)
\(158\) −7.11056 −0.565686
\(159\) 14.3839 1.14072
\(160\) −12.5510 −0.992244
\(161\) −4.88290 −0.384826
\(162\) 15.4122 1.21090
\(163\) 21.5843 1.69061 0.845307 0.534281i \(-0.179418\pi\)
0.845307 + 0.534281i \(0.179418\pi\)
\(164\) −14.4794 −1.13065
\(165\) −8.43318 −0.656522
\(166\) 41.5190 3.22250
\(167\) 0.473361 0.0366298 0.0183149 0.999832i \(-0.494170\pi\)
0.0183149 + 0.999832i \(0.494170\pi\)
\(168\) −36.7702 −2.83688
\(169\) −10.4311 −0.802393
\(170\) 9.14922 0.701713
\(171\) −1.12533 −0.0860563
\(172\) 54.4850 4.15444
\(173\) 18.9142 1.43802 0.719008 0.695001i \(-0.244596\pi\)
0.719008 + 0.695001i \(0.244596\pi\)
\(174\) 36.4659 2.76447
\(175\) −11.2950 −0.853819
\(176\) −40.0202 −3.01664
\(177\) 2.53750 0.190730
\(178\) 26.1194 1.95774
\(179\) 5.48237 0.409772 0.204886 0.978786i \(-0.434318\pi\)
0.204886 + 0.978786i \(0.434318\pi\)
\(180\) −5.05726 −0.376946
\(181\) 12.4653 0.926535 0.463268 0.886218i \(-0.346677\pi\)
0.463268 + 0.886218i \(0.346677\pi\)
\(182\) −14.3670 −1.06495
\(183\) −17.0442 −1.25994
\(184\) 10.2188 0.753339
\(185\) 8.78417 0.645825
\(186\) 34.2437 2.51087
\(187\) 11.6358 0.850891
\(188\) 9.09926 0.663632
\(189\) −19.4220 −1.41274
\(190\) −4.75450 −0.344927
\(191\) −3.06566 −0.221823 −0.110912 0.993830i \(-0.535377\pi\)
−0.110912 + 0.993830i \(0.535377\pi\)
\(192\) 9.55974 0.689915
\(193\) 1.51384 0.108969 0.0544844 0.998515i \(-0.482648\pi\)
0.0544844 + 0.998515i \(0.482648\pi\)
\(194\) 0.330749 0.0237464
\(195\) 3.11326 0.222945
\(196\) 23.2205 1.65861
\(197\) 2.60094 0.185309 0.0926546 0.995698i \(-0.470465\pi\)
0.0926546 + 0.995698i \(0.470465\pi\)
\(198\) −9.12806 −0.648703
\(199\) 10.1842 0.721937 0.360968 0.932578i \(-0.382446\pi\)
0.360968 + 0.932578i \(0.382446\pi\)
\(200\) 23.6377 1.67144
\(201\) 0.653917 0.0461238
\(202\) −44.6757 −3.14337
\(203\) −32.6083 −2.28866
\(204\) −18.9297 −1.32534
\(205\) −3.98193 −0.278110
\(206\) 40.3930 2.81431
\(207\) 1.14529 0.0796030
\(208\) 14.7742 1.02440
\(209\) −6.04666 −0.418256
\(210\) −17.4115 −1.20150
\(211\) −23.7382 −1.63421 −0.817103 0.576491i \(-0.804421\pi\)
−0.817103 + 0.576491i \(0.804421\pi\)
\(212\) 46.3486 3.18323
\(213\) −11.8060 −0.808932
\(214\) 32.6134 2.22941
\(215\) 14.9838 1.02189
\(216\) 40.6458 2.76560
\(217\) −30.6212 −2.07870
\(218\) 32.1342 2.17640
\(219\) −8.07198 −0.545454
\(220\) −27.1738 −1.83205
\(221\) −4.29555 −0.288950
\(222\) −25.7937 −1.73116
\(223\) −2.63196 −0.176249 −0.0881245 0.996109i \(-0.528087\pi\)
−0.0881245 + 0.996109i \(0.528087\pi\)
\(224\) −32.9559 −2.20196
\(225\) 2.64924 0.176616
\(226\) −28.8266 −1.91752
\(227\) 13.6806 0.908011 0.454006 0.890999i \(-0.349995\pi\)
0.454006 + 0.890999i \(0.349995\pi\)
\(228\) 9.83704 0.651474
\(229\) −13.8201 −0.913259 −0.456629 0.889657i \(-0.650943\pi\)
−0.456629 + 0.889657i \(0.650943\pi\)
\(230\) 4.83881 0.319062
\(231\) −22.1435 −1.45693
\(232\) 68.2417 4.48029
\(233\) 12.1247 0.794315 0.397157 0.917750i \(-0.369997\pi\)
0.397157 + 0.917750i \(0.369997\pi\)
\(234\) 3.36979 0.220290
\(235\) 2.50236 0.163236
\(236\) 8.17644 0.532241
\(237\) 4.04584 0.262805
\(238\) 24.0236 1.55722
\(239\) 1.62258 0.104956 0.0524780 0.998622i \(-0.483288\pi\)
0.0524780 + 0.998622i \(0.483288\pi\)
\(240\) 17.9049 1.15576
\(241\) 0.150756 0.00971105 0.00485552 0.999988i \(-0.498454\pi\)
0.00485552 + 0.999988i \(0.498454\pi\)
\(242\) −20.4245 −1.31294
\(243\) 8.14430 0.522457
\(244\) −54.9207 −3.51593
\(245\) 6.38582 0.407975
\(246\) 11.6925 0.745485
\(247\) 2.23223 0.142033
\(248\) 64.0831 4.06928
\(249\) −23.6239 −1.49710
\(250\) 28.2620 1.78744
\(251\) 4.44342 0.280466 0.140233 0.990119i \(-0.455215\pi\)
0.140233 + 0.990119i \(0.455215\pi\)
\(252\) −13.2791 −0.836507
\(253\) 6.15389 0.386891
\(254\) 3.11867 0.195683
\(255\) −5.20581 −0.326000
\(256\) −18.9815 −1.18634
\(257\) −21.8189 −1.36103 −0.680513 0.732736i \(-0.738243\pi\)
−0.680513 + 0.732736i \(0.738243\pi\)
\(258\) −43.9981 −2.73920
\(259\) 23.0651 1.43319
\(260\) 10.0317 0.622139
\(261\) 7.64832 0.473419
\(262\) 25.1407 1.55320
\(263\) −11.9036 −0.734010 −0.367005 0.930219i \(-0.619617\pi\)
−0.367005 + 0.930219i \(0.619617\pi\)
\(264\) 46.3412 2.85210
\(265\) 12.7462 0.782993
\(266\) −12.4842 −0.765453
\(267\) −14.8617 −0.909521
\(268\) 2.10708 0.128711
\(269\) 22.6301 1.37978 0.689889 0.723915i \(-0.257659\pi\)
0.689889 + 0.723915i \(0.257659\pi\)
\(270\) 19.2467 1.17131
\(271\) 19.0156 1.15511 0.577557 0.816350i \(-0.304006\pi\)
0.577557 + 0.816350i \(0.304006\pi\)
\(272\) −24.7045 −1.49793
\(273\) 8.17466 0.494753
\(274\) −9.70557 −0.586335
\(275\) 14.2350 0.858401
\(276\) −10.0115 −0.602621
\(277\) 1.69360 0.101758 0.0508791 0.998705i \(-0.483798\pi\)
0.0508791 + 0.998705i \(0.483798\pi\)
\(278\) 0.584540 0.0350584
\(279\) 7.18222 0.429989
\(280\) −32.5835 −1.94724
\(281\) −11.7182 −0.699047 −0.349524 0.936928i \(-0.613657\pi\)
−0.349524 + 0.936928i \(0.613657\pi\)
\(282\) −7.34789 −0.437561
\(283\) −2.12721 −0.126450 −0.0632248 0.997999i \(-0.520139\pi\)
−0.0632248 + 0.997999i \(0.520139\pi\)
\(284\) −38.0418 −2.25736
\(285\) 2.70526 0.160246
\(286\) 18.1066 1.07067
\(287\) −10.4556 −0.617174
\(288\) 7.72983 0.455485
\(289\) −9.81724 −0.577485
\(290\) 32.3139 1.89754
\(291\) −0.188193 −0.0110321
\(292\) −26.0099 −1.52211
\(293\) 26.7323 1.56172 0.780859 0.624708i \(-0.214782\pi\)
0.780859 + 0.624708i \(0.214782\pi\)
\(294\) −18.7512 −1.09359
\(295\) 2.24858 0.130918
\(296\) −48.2699 −2.80563
\(297\) 24.4774 1.42033
\(298\) 24.5173 1.42025
\(299\) −2.27182 −0.131383
\(300\) −23.1582 −1.33704
\(301\) 39.3438 2.26774
\(302\) −2.60101 −0.149671
\(303\) 25.4200 1.46034
\(304\) 12.8380 0.736309
\(305\) −15.1036 −0.864829
\(306\) −5.63476 −0.322118
\(307\) −11.0660 −0.631571 −0.315786 0.948831i \(-0.602268\pi\)
−0.315786 + 0.948831i \(0.602268\pi\)
\(308\) −71.3517 −4.06564
\(309\) −22.9832 −1.30747
\(310\) 30.3447 1.72346
\(311\) 0.166353 0.00943300 0.00471650 0.999989i \(-0.498499\pi\)
0.00471650 + 0.999989i \(0.498499\pi\)
\(312\) −17.1077 −0.968531
\(313\) −34.0108 −1.92241 −0.961203 0.275842i \(-0.911043\pi\)
−0.961203 + 0.275842i \(0.911043\pi\)
\(314\) 37.5319 2.11805
\(315\) −3.65186 −0.205759
\(316\) 13.0367 0.733370
\(317\) −19.8900 −1.11713 −0.558567 0.829459i \(-0.688649\pi\)
−0.558567 + 0.829459i \(0.688649\pi\)
\(318\) −37.4277 −2.09884
\(319\) 41.0961 2.30094
\(320\) 8.47128 0.473559
\(321\) −18.5567 −1.03573
\(322\) 12.7055 0.708052
\(323\) −3.73261 −0.207688
\(324\) −28.2571 −1.56984
\(325\) −5.25509 −0.291500
\(326\) −56.1634 −3.11061
\(327\) −18.2840 −1.01111
\(328\) 21.8811 1.20818
\(329\) 6.57060 0.362249
\(330\) 21.9435 1.20795
\(331\) 12.5197 0.688144 0.344072 0.938943i \(-0.388194\pi\)
0.344072 + 0.938943i \(0.388194\pi\)
\(332\) −76.1220 −4.17773
\(333\) −5.40994 −0.296463
\(334\) −1.23171 −0.0673961
\(335\) 0.579463 0.0316595
\(336\) 47.0140 2.56483
\(337\) 35.0463 1.90910 0.954548 0.298058i \(-0.0963389\pi\)
0.954548 + 0.298058i \(0.0963389\pi\)
\(338\) 27.1423 1.47634
\(339\) 16.4021 0.890837
\(340\) −16.7744 −0.909719
\(341\) 38.5917 2.08986
\(342\) 2.92817 0.158337
\(343\) −7.34672 −0.396686
\(344\) −82.3374 −4.43933
\(345\) −2.75323 −0.148229
\(346\) −49.2156 −2.64585
\(347\) 9.95569 0.534449 0.267225 0.963634i \(-0.413893\pi\)
0.267225 + 0.963634i \(0.413893\pi\)
\(348\) −66.8574 −3.58394
\(349\) −5.64792 −0.302326 −0.151163 0.988509i \(-0.548302\pi\)
−0.151163 + 0.988509i \(0.548302\pi\)
\(350\) 29.3900 1.57096
\(351\) −9.03629 −0.482321
\(352\) 41.5341 2.21377
\(353\) 17.1652 0.913613 0.456806 0.889566i \(-0.348993\pi\)
0.456806 + 0.889566i \(0.348993\pi\)
\(354\) −6.60270 −0.350929
\(355\) −10.4618 −0.555253
\(356\) −47.8880 −2.53806
\(357\) −13.6692 −0.723450
\(358\) −14.2654 −0.753950
\(359\) −4.59637 −0.242587 −0.121294 0.992617i \(-0.538704\pi\)
−0.121294 + 0.992617i \(0.538704\pi\)
\(360\) 7.64250 0.402795
\(361\) −17.0603 −0.897911
\(362\) −32.4352 −1.70476
\(363\) 11.6213 0.609962
\(364\) 26.3408 1.38063
\(365\) −7.15291 −0.374401
\(366\) 44.3499 2.31821
\(367\) 19.6206 1.02419 0.512093 0.858930i \(-0.328870\pi\)
0.512093 + 0.858930i \(0.328870\pi\)
\(368\) −13.0657 −0.681094
\(369\) 2.45237 0.127665
\(370\) −22.8568 −1.18827
\(371\) 33.4684 1.73759
\(372\) −62.7831 −3.25515
\(373\) 18.1650 0.940547 0.470274 0.882521i \(-0.344155\pi\)
0.470274 + 0.882521i \(0.344155\pi\)
\(374\) −30.2768 −1.56558
\(375\) −16.0808 −0.830408
\(376\) −13.7507 −0.709140
\(377\) −15.1714 −0.781365
\(378\) 50.5371 2.59935
\(379\) −29.2836 −1.50420 −0.752098 0.659051i \(-0.770958\pi\)
−0.752098 + 0.659051i \(0.770958\pi\)
\(380\) 8.71701 0.447173
\(381\) −1.77449 −0.0909100
\(382\) 7.97700 0.408139
\(383\) 6.87287 0.351187 0.175594 0.984463i \(-0.443816\pi\)
0.175594 + 0.984463i \(0.443816\pi\)
\(384\) 3.45243 0.176181
\(385\) −19.6222 −1.00004
\(386\) −3.93910 −0.200495
\(387\) −9.22811 −0.469091
\(388\) −0.606404 −0.0307855
\(389\) −2.96440 −0.150301 −0.0751506 0.997172i \(-0.523944\pi\)
−0.0751506 + 0.997172i \(0.523944\pi\)
\(390\) −8.10085 −0.410203
\(391\) 3.79880 0.192114
\(392\) −35.0907 −1.77235
\(393\) −14.3048 −0.721582
\(394\) −6.76777 −0.340955
\(395\) 3.58518 0.180390
\(396\) 16.7356 0.840996
\(397\) 11.0763 0.555905 0.277952 0.960595i \(-0.410344\pi\)
0.277952 + 0.960595i \(0.410344\pi\)
\(398\) −26.4997 −1.32831
\(399\) 7.10335 0.355612
\(400\) −30.2230 −1.51115
\(401\) −13.5713 −0.677717 −0.338859 0.940837i \(-0.610041\pi\)
−0.338859 + 0.940837i \(0.610041\pi\)
\(402\) −1.70153 −0.0848644
\(403\) −14.2468 −0.709684
\(404\) 81.9095 4.07515
\(405\) −7.77092 −0.386140
\(406\) 84.8485 4.21096
\(407\) −29.0688 −1.44089
\(408\) 28.6065 1.41623
\(409\) 14.4605 0.715025 0.357512 0.933908i \(-0.383625\pi\)
0.357512 + 0.933908i \(0.383625\pi\)
\(410\) 10.3612 0.511703
\(411\) 5.52237 0.272398
\(412\) −74.0575 −3.64855
\(413\) 5.90423 0.290528
\(414\) −2.98010 −0.146464
\(415\) −20.9341 −1.02761
\(416\) −15.3331 −0.751765
\(417\) −0.332597 −0.0162873
\(418\) 15.7337 0.769560
\(419\) 30.1880 1.47478 0.737389 0.675468i \(-0.236058\pi\)
0.737389 + 0.675468i \(0.236058\pi\)
\(420\) 31.9226 1.55766
\(421\) 34.0938 1.66163 0.830815 0.556549i \(-0.187875\pi\)
0.830815 + 0.556549i \(0.187875\pi\)
\(422\) 61.7680 3.00682
\(423\) −1.54114 −0.0749327
\(424\) −70.0417 −3.40153
\(425\) 8.78726 0.426245
\(426\) 30.7197 1.48838
\(427\) −39.6583 −1.91920
\(428\) −59.7942 −2.89026
\(429\) −10.3025 −0.497408
\(430\) −38.9885 −1.88019
\(431\) −6.56659 −0.316302 −0.158151 0.987415i \(-0.550553\pi\)
−0.158151 + 0.987415i \(0.550553\pi\)
\(432\) −51.9694 −2.50038
\(433\) −9.39563 −0.451525 −0.225763 0.974182i \(-0.572487\pi\)
−0.225763 + 0.974182i \(0.572487\pi\)
\(434\) 79.6778 3.82466
\(435\) −18.3863 −0.881555
\(436\) −58.9156 −2.82155
\(437\) −1.97409 −0.0944336
\(438\) 21.0037 1.00360
\(439\) 22.7287 1.08478 0.542390 0.840127i \(-0.317520\pi\)
0.542390 + 0.840127i \(0.317520\pi\)
\(440\) 41.0648 1.95769
\(441\) −3.93286 −0.187279
\(442\) 11.1772 0.531646
\(443\) 17.7833 0.844910 0.422455 0.906384i \(-0.361168\pi\)
0.422455 + 0.906384i \(0.361168\pi\)
\(444\) 47.2907 2.24432
\(445\) −13.1696 −0.624297
\(446\) 6.84848 0.324285
\(447\) −13.9501 −0.659816
\(448\) 22.2435 1.05091
\(449\) 1.65386 0.0780505 0.0390253 0.999238i \(-0.487575\pi\)
0.0390253 + 0.999238i \(0.487575\pi\)
\(450\) −6.89346 −0.324961
\(451\) 13.1771 0.620486
\(452\) 52.8514 2.48592
\(453\) 1.47995 0.0695340
\(454\) −35.5975 −1.67067
\(455\) 7.24390 0.339599
\(456\) −14.8657 −0.696149
\(457\) −39.0553 −1.82693 −0.913464 0.406919i \(-0.866603\pi\)
−0.913464 + 0.406919i \(0.866603\pi\)
\(458\) 35.9606 1.68033
\(459\) 15.1099 0.705272
\(460\) −8.87159 −0.413640
\(461\) 22.6274 1.05386 0.526932 0.849908i \(-0.323342\pi\)
0.526932 + 0.849908i \(0.323342\pi\)
\(462\) 57.6184 2.68065
\(463\) 36.5371 1.69802 0.849012 0.528374i \(-0.177198\pi\)
0.849012 + 0.528374i \(0.177198\pi\)
\(464\) −87.2534 −4.05064
\(465\) −17.2658 −0.800683
\(466\) −31.5490 −1.46148
\(467\) −37.2025 −1.72152 −0.860762 0.509007i \(-0.830013\pi\)
−0.860762 + 0.509007i \(0.830013\pi\)
\(468\) −6.17825 −0.285590
\(469\) 1.52153 0.0702577
\(470\) −6.51127 −0.300343
\(471\) −21.3552 −0.983997
\(472\) −12.3562 −0.568740
\(473\) −49.5847 −2.27991
\(474\) −10.5275 −0.483542
\(475\) −4.56640 −0.209521
\(476\) −44.0455 −2.01882
\(477\) −7.85005 −0.359429
\(478\) −4.22203 −0.193111
\(479\) −12.4048 −0.566788 −0.283394 0.959004i \(-0.591460\pi\)
−0.283394 + 0.959004i \(0.591460\pi\)
\(480\) −18.5823 −0.848160
\(481\) 10.7313 0.489303
\(482\) −0.392274 −0.0178676
\(483\) −7.22932 −0.328946
\(484\) 37.4468 1.70213
\(485\) −0.166765 −0.00757243
\(486\) −21.1919 −0.961283
\(487\) −28.1608 −1.27609 −0.638045 0.769999i \(-0.720256\pi\)
−0.638045 + 0.769999i \(0.720256\pi\)
\(488\) 82.9958 3.75704
\(489\) 31.9564 1.44512
\(490\) −16.6162 −0.750644
\(491\) −31.2776 −1.41154 −0.705769 0.708443i \(-0.749398\pi\)
−0.705769 + 0.708443i \(0.749398\pi\)
\(492\) −21.4373 −0.966467
\(493\) 25.3686 1.14255
\(494\) −5.80838 −0.261331
\(495\) 4.60241 0.206863
\(496\) −81.9361 −3.67904
\(497\) −27.4700 −1.23220
\(498\) 61.4705 2.75456
\(499\) −30.5993 −1.36981 −0.684907 0.728631i \(-0.740157\pi\)
−0.684907 + 0.728631i \(0.740157\pi\)
\(500\) −51.8162 −2.31729
\(501\) 0.700829 0.0313107
\(502\) −11.5620 −0.516037
\(503\) 3.50860 0.156441 0.0782203 0.996936i \(-0.475076\pi\)
0.0782203 + 0.996936i \(0.475076\pi\)
\(504\) 20.0673 0.893870
\(505\) 22.5257 1.00238
\(506\) −16.0127 −0.711852
\(507\) −15.4437 −0.685877
\(508\) −5.71785 −0.253688
\(509\) −0.315424 −0.0139809 −0.00699047 0.999976i \(-0.502225\pi\)
−0.00699047 + 0.999976i \(0.502225\pi\)
\(510\) 13.5458 0.599817
\(511\) −18.7818 −0.830859
\(512\) 44.7271 1.97668
\(513\) −7.85206 −0.346677
\(514\) 56.7738 2.50419
\(515\) −20.3663 −0.897448
\(516\) 80.6672 3.55117
\(517\) −8.28088 −0.364193
\(518\) −60.0165 −2.63697
\(519\) 28.0031 1.22920
\(520\) −15.1598 −0.664802
\(521\) −37.9517 −1.66269 −0.831346 0.555755i \(-0.812429\pi\)
−0.831346 + 0.555755i \(0.812429\pi\)
\(522\) −19.9013 −0.871056
\(523\) −16.5865 −0.725279 −0.362639 0.931930i \(-0.618124\pi\)
−0.362639 + 0.931930i \(0.618124\pi\)
\(524\) −46.0936 −2.01361
\(525\) −16.7226 −0.729835
\(526\) 30.9738 1.35052
\(527\) 23.8227 1.03773
\(528\) −59.2515 −2.57859
\(529\) −20.9909 −0.912648
\(530\) −33.1662 −1.44065
\(531\) −1.38484 −0.0600970
\(532\) 22.8887 0.992353
\(533\) −4.86457 −0.210708
\(534\) 38.6709 1.67345
\(535\) −16.4438 −0.710929
\(536\) −3.18421 −0.137537
\(537\) 8.11686 0.350268
\(538\) −58.8845 −2.53869
\(539\) −21.1321 −0.910224
\(540\) −35.2873 −1.51852
\(541\) 18.7201 0.804838 0.402419 0.915456i \(-0.368169\pi\)
0.402419 + 0.915456i \(0.368169\pi\)
\(542\) −49.4795 −2.12532
\(543\) 18.4553 0.791992
\(544\) 25.6390 1.09926
\(545\) −16.2022 −0.694027
\(546\) −21.2709 −0.910309
\(547\) 7.78139 0.332708 0.166354 0.986066i \(-0.446801\pi\)
0.166354 + 0.986066i \(0.446801\pi\)
\(548\) 17.7944 0.760140
\(549\) 9.30190 0.396995
\(550\) −37.0401 −1.57939
\(551\) −13.1831 −0.561620
\(552\) 15.1293 0.643946
\(553\) 9.41381 0.400316
\(554\) −4.40682 −0.187228
\(555\) 13.0053 0.552044
\(556\) −1.07171 −0.0454506
\(557\) 4.05324 0.171741 0.0858707 0.996306i \(-0.472633\pi\)
0.0858707 + 0.996306i \(0.472633\pi\)
\(558\) −18.6885 −0.791147
\(559\) 18.3051 0.774222
\(560\) 41.6611 1.76050
\(561\) 17.2272 0.727332
\(562\) 30.4912 1.28620
\(563\) 26.2850 1.10778 0.553891 0.832589i \(-0.313142\pi\)
0.553891 + 0.832589i \(0.313142\pi\)
\(564\) 13.4718 0.567265
\(565\) 14.5345 0.611473
\(566\) 5.53511 0.232658
\(567\) −20.4046 −0.856911
\(568\) 57.4885 2.41216
\(569\) 43.4456 1.82134 0.910668 0.413139i \(-0.135568\pi\)
0.910668 + 0.413139i \(0.135568\pi\)
\(570\) −7.03922 −0.294840
\(571\) −12.0931 −0.506079 −0.253040 0.967456i \(-0.581430\pi\)
−0.253040 + 0.967456i \(0.581430\pi\)
\(572\) −33.1971 −1.38804
\(573\) −4.53883 −0.189612
\(574\) 27.2060 1.13556
\(575\) 4.64738 0.193809
\(576\) −5.21723 −0.217385
\(577\) 27.3145 1.13712 0.568559 0.822642i \(-0.307501\pi\)
0.568559 + 0.822642i \(0.307501\pi\)
\(578\) 25.5449 1.06253
\(579\) 2.24130 0.0931454
\(580\) −59.2451 −2.46002
\(581\) −54.9678 −2.28045
\(582\) 0.489687 0.0202982
\(583\) −42.1800 −1.74692
\(584\) 39.3060 1.62649
\(585\) −1.69906 −0.0702476
\(586\) −69.5587 −2.87345
\(587\) −23.6528 −0.976255 −0.488128 0.872772i \(-0.662320\pi\)
−0.488128 + 0.872772i \(0.662320\pi\)
\(588\) 34.3789 1.41776
\(589\) −12.3797 −0.510098
\(590\) −5.85092 −0.240879
\(591\) 3.85079 0.158400
\(592\) 61.7175 2.53657
\(593\) 5.32673 0.218743 0.109371 0.994001i \(-0.465116\pi\)
0.109371 + 0.994001i \(0.465116\pi\)
\(594\) −63.6915 −2.61329
\(595\) −12.1128 −0.496578
\(596\) −44.9505 −1.84125
\(597\) 15.0781 0.617104
\(598\) 5.91138 0.241734
\(599\) −10.6513 −0.435200 −0.217600 0.976038i \(-0.569823\pi\)
−0.217600 + 0.976038i \(0.569823\pi\)
\(600\) 34.9966 1.42873
\(601\) −41.2415 −1.68228 −0.841139 0.540820i \(-0.818114\pi\)
−0.841139 + 0.540820i \(0.818114\pi\)
\(602\) −102.374 −4.17247
\(603\) −0.356876 −0.0145331
\(604\) 4.76876 0.194038
\(605\) 10.2982 0.418679
\(606\) −66.1441 −2.68692
\(607\) 18.8857 0.766547 0.383273 0.923635i \(-0.374797\pi\)
0.383273 + 0.923635i \(0.374797\pi\)
\(608\) −13.3236 −0.540344
\(609\) −48.2779 −1.95632
\(610\) 39.3003 1.59122
\(611\) 3.05703 0.123674
\(612\) 10.3309 0.417602
\(613\) −10.7188 −0.432928 −0.216464 0.976291i \(-0.569452\pi\)
−0.216464 + 0.976291i \(0.569452\pi\)
\(614\) 28.7943 1.16204
\(615\) −5.89541 −0.237726
\(616\) 107.826 4.34444
\(617\) −38.2334 −1.53922 −0.769609 0.638515i \(-0.779549\pi\)
−0.769609 + 0.638515i \(0.779549\pi\)
\(618\) 59.8034 2.40564
\(619\) −12.0424 −0.484024 −0.242012 0.970273i \(-0.577807\pi\)
−0.242012 + 0.970273i \(0.577807\pi\)
\(620\) −55.6347 −2.23434
\(621\) 7.99131 0.320680
\(622\) −0.432858 −0.0173560
\(623\) −34.5801 −1.38542
\(624\) 21.8737 0.875650
\(625\) 2.14389 0.0857555
\(626\) 88.4978 3.53709
\(627\) −8.95231 −0.357521
\(628\) −68.8118 −2.74589
\(629\) −17.9442 −0.715481
\(630\) 9.50232 0.378581
\(631\) −39.6422 −1.57813 −0.789065 0.614310i \(-0.789435\pi\)
−0.789065 + 0.614310i \(0.789435\pi\)
\(632\) −19.7009 −0.783661
\(633\) −35.1454 −1.39690
\(634\) 51.7548 2.05545
\(635\) −1.57245 −0.0624008
\(636\) 68.6209 2.72099
\(637\) 7.80130 0.309099
\(638\) −106.934 −4.23356
\(639\) 6.44312 0.254886
\(640\) 3.05934 0.120931
\(641\) −35.5559 −1.40438 −0.702188 0.711992i \(-0.747793\pi\)
−0.702188 + 0.711992i \(0.747793\pi\)
\(642\) 48.2854 1.90567
\(643\) 10.1768 0.401335 0.200667 0.979659i \(-0.435689\pi\)
0.200667 + 0.979659i \(0.435689\pi\)
\(644\) −23.2946 −0.917938
\(645\) 22.1841 0.873497
\(646\) 9.71242 0.382130
\(647\) −32.6724 −1.28449 −0.642243 0.766501i \(-0.721996\pi\)
−0.642243 + 0.766501i \(0.721996\pi\)
\(648\) 42.7020 1.67749
\(649\) −7.44106 −0.292087
\(650\) 13.6740 0.536339
\(651\) −45.3359 −1.77685
\(652\) 102.971 4.03267
\(653\) −45.5013 −1.78061 −0.890303 0.455369i \(-0.849507\pi\)
−0.890303 + 0.455369i \(0.849507\pi\)
\(654\) 47.5759 1.86037
\(655\) −12.6761 −0.495295
\(656\) −27.9771 −1.09232
\(657\) 4.40529 0.171867
\(658\) −17.0970 −0.666511
\(659\) 22.6247 0.881335 0.440667 0.897670i \(-0.354742\pi\)
0.440667 + 0.897670i \(0.354742\pi\)
\(660\) −40.2318 −1.56602
\(661\) 5.20283 0.202367 0.101183 0.994868i \(-0.467737\pi\)
0.101183 + 0.994868i \(0.467737\pi\)
\(662\) −32.5768 −1.26613
\(663\) −6.35972 −0.246991
\(664\) 115.035 4.46422
\(665\) 6.29457 0.244093
\(666\) 14.0769 0.545469
\(667\) 13.4169 0.519505
\(668\) 2.25824 0.0873741
\(669\) −3.89672 −0.150656
\(670\) −1.50779 −0.0582511
\(671\) 49.9811 1.92950
\(672\) −48.7925 −1.88221
\(673\) −11.2688 −0.434380 −0.217190 0.976129i \(-0.569689\pi\)
−0.217190 + 0.976129i \(0.569689\pi\)
\(674\) −91.1923 −3.51260
\(675\) 18.4852 0.711497
\(676\) −49.7633 −1.91397
\(677\) 30.4679 1.17098 0.585489 0.810681i \(-0.300903\pi\)
0.585489 + 0.810681i \(0.300903\pi\)
\(678\) −42.6790 −1.63908
\(679\) −0.437886 −0.0168045
\(680\) 25.3494 0.972103
\(681\) 20.2546 0.776158
\(682\) −100.417 −3.84518
\(683\) 10.0579 0.384855 0.192428 0.981311i \(-0.438364\pi\)
0.192428 + 0.981311i \(0.438364\pi\)
\(684\) −5.36857 −0.205273
\(685\) 4.89360 0.186975
\(686\) 19.1165 0.729872
\(687\) −20.4612 −0.780644
\(688\) 105.276 4.01361
\(689\) 15.5715 0.593227
\(690\) 7.16405 0.272731
\(691\) 4.87401 0.185416 0.0927080 0.995693i \(-0.470448\pi\)
0.0927080 + 0.995693i \(0.470448\pi\)
\(692\) 90.2330 3.43014
\(693\) 12.0848 0.459064
\(694\) −25.9052 −0.983348
\(695\) −0.294728 −0.0111797
\(696\) 101.035 3.82970
\(697\) 8.13424 0.308106
\(698\) 14.6962 0.556258
\(699\) 17.9511 0.678972
\(700\) −53.8844 −2.03664
\(701\) 31.7819 1.20039 0.600193 0.799855i \(-0.295090\pi\)
0.600193 + 0.799855i \(0.295090\pi\)
\(702\) 23.5129 0.887436
\(703\) 9.32490 0.351695
\(704\) −28.0334 −1.05655
\(705\) 3.70485 0.139533
\(706\) −44.6647 −1.68098
\(707\) 59.1471 2.22445
\(708\) 12.1055 0.454954
\(709\) 43.1464 1.62040 0.810199 0.586155i \(-0.199359\pi\)
0.810199 + 0.586155i \(0.199359\pi\)
\(710\) 27.2220 1.02162
\(711\) −2.20802 −0.0828071
\(712\) 72.3681 2.71211
\(713\) 12.5993 0.471846
\(714\) 35.5679 1.33109
\(715\) −9.12944 −0.341422
\(716\) 26.1545 0.977440
\(717\) 2.40229 0.0897153
\(718\) 11.9600 0.446343
\(719\) −40.5854 −1.51358 −0.756790 0.653658i \(-0.773234\pi\)
−0.756790 + 0.653658i \(0.773234\pi\)
\(720\) −9.77164 −0.364167
\(721\) −53.4771 −1.99159
\(722\) 44.3918 1.65209
\(723\) 0.223200 0.00830090
\(724\) 59.4675 2.21009
\(725\) 31.0355 1.15263
\(726\) −30.2393 −1.12229
\(727\) 41.3587 1.53391 0.766954 0.641702i \(-0.221771\pi\)
0.766954 + 0.641702i \(0.221771\pi\)
\(728\) −39.8060 −1.47531
\(729\) 29.8273 1.10471
\(730\) 18.6122 0.688870
\(731\) −30.6087 −1.13210
\(732\) −81.3122 −3.00538
\(733\) 42.4747 1.56884 0.784419 0.620231i \(-0.212961\pi\)
0.784419 + 0.620231i \(0.212961\pi\)
\(734\) −51.0537 −1.88443
\(735\) 9.45445 0.348733
\(736\) 13.5599 0.499825
\(737\) −1.91757 −0.0706347
\(738\) −6.38118 −0.234895
\(739\) 29.2367 1.07549 0.537744 0.843108i \(-0.319277\pi\)
0.537744 + 0.843108i \(0.319277\pi\)
\(740\) 41.9063 1.54050
\(741\) 3.30490 0.121409
\(742\) −87.0865 −3.19705
\(743\) 21.3907 0.784750 0.392375 0.919805i \(-0.371653\pi\)
0.392375 + 0.919805i \(0.371653\pi\)
\(744\) 94.8775 3.47838
\(745\) −12.3617 −0.452899
\(746\) −47.2662 −1.73054
\(747\) 12.8928 0.471721
\(748\) 55.5102 2.02965
\(749\) −43.1775 −1.57767
\(750\) 41.8430 1.52789
\(751\) 45.7959 1.67112 0.835558 0.549402i \(-0.185144\pi\)
0.835558 + 0.549402i \(0.185144\pi\)
\(752\) 17.5816 0.641135
\(753\) 6.57865 0.239739
\(754\) 39.4766 1.43765
\(755\) 1.31144 0.0477283
\(756\) −92.6558 −3.36986
\(757\) −42.7929 −1.55533 −0.777667 0.628677i \(-0.783597\pi\)
−0.777667 + 0.628677i \(0.783597\pi\)
\(758\) 76.1973 2.76761
\(759\) 9.11107 0.330711
\(760\) −13.1731 −0.477838
\(761\) 6.55615 0.237660 0.118830 0.992915i \(-0.462086\pi\)
0.118830 + 0.992915i \(0.462086\pi\)
\(762\) 4.61731 0.167268
\(763\) −42.5431 −1.54016
\(764\) −14.6252 −0.529122
\(765\) 2.84107 0.102719
\(766\) −17.8835 −0.646158
\(767\) 2.74700 0.0991885
\(768\) −28.1029 −1.01407
\(769\) 25.8243 0.931246 0.465623 0.884983i \(-0.345830\pi\)
0.465623 + 0.884983i \(0.345830\pi\)
\(770\) 51.0580 1.84000
\(771\) −32.3037 −1.16339
\(772\) 7.22203 0.259927
\(773\) −41.8808 −1.50635 −0.753174 0.657822i \(-0.771478\pi\)
−0.753174 + 0.657822i \(0.771478\pi\)
\(774\) 24.0120 0.863093
\(775\) 29.1442 1.04689
\(776\) 0.916393 0.0328966
\(777\) 34.1488 1.22508
\(778\) 7.71353 0.276543
\(779\) −4.22706 −0.151450
\(780\) 14.8523 0.531797
\(781\) 34.6203 1.23881
\(782\) −9.88466 −0.353475
\(783\) 53.3665 1.90716
\(784\) 44.8667 1.60238
\(785\) −18.9238 −0.675418
\(786\) 37.2218 1.32766
\(787\) 1.46512 0.0522259 0.0261129 0.999659i \(-0.491687\pi\)
0.0261129 + 0.999659i \(0.491687\pi\)
\(788\) 12.4082 0.442023
\(789\) −17.6238 −0.627424
\(790\) −9.32882 −0.331904
\(791\) 38.1642 1.35696
\(792\) −25.2907 −0.898667
\(793\) −18.4514 −0.655230
\(794\) −28.8211 −1.02282
\(795\) 18.8712 0.669294
\(796\) 48.5852 1.72206
\(797\) −2.22341 −0.0787572 −0.0393786 0.999224i \(-0.512538\pi\)
−0.0393786 + 0.999224i \(0.512538\pi\)
\(798\) −18.4833 −0.654301
\(799\) −5.11179 −0.180842
\(800\) 31.3663 1.10897
\(801\) 8.11078 0.286580
\(802\) 35.3131 1.24695
\(803\) 23.6706 0.835317
\(804\) 3.11962 0.110020
\(805\) −6.40620 −0.225789
\(806\) 37.0709 1.30577
\(807\) 33.5047 1.17942
\(808\) −123.781 −4.35461
\(809\) −1.45886 −0.0512908 −0.0256454 0.999671i \(-0.508164\pi\)
−0.0256454 + 0.999671i \(0.508164\pi\)
\(810\) 20.2203 0.710470
\(811\) −8.64314 −0.303502 −0.151751 0.988419i \(-0.548491\pi\)
−0.151751 + 0.988419i \(0.548491\pi\)
\(812\) −155.563 −5.45920
\(813\) 28.1533 0.987379
\(814\) 75.6384 2.65112
\(815\) 28.3179 0.991932
\(816\) −36.5760 −1.28042
\(817\) 15.9061 0.556486
\(818\) −37.6269 −1.31559
\(819\) −4.46133 −0.155891
\(820\) −18.9965 −0.663385
\(821\) 23.7587 0.829185 0.414592 0.910007i \(-0.363924\pi\)
0.414592 + 0.910007i \(0.363924\pi\)
\(822\) −14.3695 −0.501193
\(823\) −42.8423 −1.49339 −0.746694 0.665167i \(-0.768360\pi\)
−0.746694 + 0.665167i \(0.768360\pi\)
\(824\) 111.915 3.89875
\(825\) 21.0754 0.733752
\(826\) −15.3631 −0.534550
\(827\) −14.3999 −0.500733 −0.250367 0.968151i \(-0.580551\pi\)
−0.250367 + 0.968151i \(0.580551\pi\)
\(828\) 5.46378 0.189879
\(829\) −46.3832 −1.61095 −0.805477 0.592627i \(-0.798091\pi\)
−0.805477 + 0.592627i \(0.798091\pi\)
\(830\) 54.4715 1.89073
\(831\) 2.50743 0.0869819
\(832\) 10.3490 0.358787
\(833\) −13.0449 −0.451978
\(834\) 0.865434 0.0299675
\(835\) 0.621034 0.0214918
\(836\) −28.8465 −0.997678
\(837\) 50.1144 1.73221
\(838\) −78.5506 −2.71348
\(839\) 18.0317 0.622524 0.311262 0.950324i \(-0.399248\pi\)
0.311262 + 0.950324i \(0.399248\pi\)
\(840\) −48.2412 −1.66448
\(841\) 60.5990 2.08962
\(842\) −88.7137 −3.05728
\(843\) −17.3492 −0.597538
\(844\) −113.247 −3.89812
\(845\) −13.6853 −0.470787
\(846\) 4.01012 0.137871
\(847\) 27.0404 0.929121
\(848\) 89.5548 3.07532
\(849\) −3.14942 −0.108088
\(850\) −22.8649 −0.784259
\(851\) −9.49027 −0.325322
\(852\) −56.3223 −1.92957
\(853\) 24.3943 0.835245 0.417623 0.908621i \(-0.362863\pi\)
0.417623 + 0.908621i \(0.362863\pi\)
\(854\) 103.193 3.53119
\(855\) −1.47640 −0.0504917
\(856\) 90.3606 3.08846
\(857\) −18.6142 −0.635848 −0.317924 0.948116i \(-0.602986\pi\)
−0.317924 + 0.948116i \(0.602986\pi\)
\(858\) 26.8075 0.915194
\(859\) 11.9363 0.407262 0.203631 0.979048i \(-0.434726\pi\)
0.203631 + 0.979048i \(0.434726\pi\)
\(860\) 71.4825 2.43753
\(861\) −15.4799 −0.527554
\(862\) 17.0866 0.581972
\(863\) −34.0880 −1.16037 −0.580184 0.814485i \(-0.697019\pi\)
−0.580184 + 0.814485i \(0.697019\pi\)
\(864\) 53.9353 1.83492
\(865\) 24.8147 0.843726
\(866\) 24.4479 0.830773
\(867\) −14.5348 −0.493628
\(868\) −146.083 −4.95839
\(869\) −11.8642 −0.402464
\(870\) 47.8420 1.62200
\(871\) 0.707907 0.0239865
\(872\) 89.0329 3.01503
\(873\) 0.102706 0.00347609
\(874\) 5.13668 0.173751
\(875\) −37.4166 −1.26491
\(876\) −38.5087 −1.30109
\(877\) 12.6060 0.425676 0.212838 0.977088i \(-0.431729\pi\)
0.212838 + 0.977088i \(0.431729\pi\)
\(878\) −59.1411 −1.99591
\(879\) 39.5782 1.33494
\(880\) −52.5052 −1.76995
\(881\) 20.9995 0.707491 0.353745 0.935342i \(-0.384908\pi\)
0.353745 + 0.935342i \(0.384908\pi\)
\(882\) 10.2335 0.344579
\(883\) −40.6386 −1.36760 −0.683799 0.729670i \(-0.739674\pi\)
−0.683799 + 0.729670i \(0.739674\pi\)
\(884\) −20.4926 −0.689240
\(885\) 3.32911 0.111907
\(886\) −46.2730 −1.55457
\(887\) 29.8058 1.00078 0.500390 0.865800i \(-0.333190\pi\)
0.500390 + 0.865800i \(0.333190\pi\)
\(888\) −71.4655 −2.39822
\(889\) −4.12887 −0.138478
\(890\) 34.2678 1.14866
\(891\) 25.7157 0.861509
\(892\) −12.5562 −0.420412
\(893\) 2.65640 0.0888932
\(894\) 36.2988 1.21401
\(895\) 7.19268 0.240425
\(896\) 8.03308 0.268367
\(897\) −3.36351 −0.112304
\(898\) −4.30343 −0.143607
\(899\) 84.1388 2.80619
\(900\) 12.6386 0.421288
\(901\) −26.0378 −0.867444
\(902\) −34.2875 −1.14165
\(903\) 58.2499 1.93844
\(904\) −79.8688 −2.65640
\(905\) 16.3540 0.543625
\(906\) −3.85090 −0.127938
\(907\) 7.29489 0.242223 0.121111 0.992639i \(-0.461354\pi\)
0.121111 + 0.992639i \(0.461354\pi\)
\(908\) 65.2653 2.16591
\(909\) −13.8730 −0.460138
\(910\) −18.8490 −0.624838
\(911\) −41.9506 −1.38989 −0.694943 0.719065i \(-0.744570\pi\)
−0.694943 + 0.719065i \(0.744570\pi\)
\(912\) 19.0071 0.629389
\(913\) 69.2756 2.29269
\(914\) 101.624 3.36141
\(915\) −22.3614 −0.739246
\(916\) −65.9310 −2.17842
\(917\) −33.2843 −1.09914
\(918\) −39.3168 −1.29765
\(919\) 16.6118 0.547971 0.273986 0.961734i \(-0.411658\pi\)
0.273986 + 0.961734i \(0.411658\pi\)
\(920\) 13.4067 0.442006
\(921\) −16.3837 −0.539861
\(922\) −58.8776 −1.93903
\(923\) −12.7807 −0.420682
\(924\) −105.639 −3.47527
\(925\) −21.9526 −0.721796
\(926\) −95.0714 −3.12424
\(927\) 12.5431 0.411969
\(928\) 90.5540 2.97258
\(929\) −8.29258 −0.272071 −0.136035 0.990704i \(-0.543436\pi\)
−0.136035 + 0.990704i \(0.543436\pi\)
\(930\) 44.9265 1.47320
\(931\) 6.77892 0.222170
\(932\) 57.8428 1.89470
\(933\) 0.246292 0.00806323
\(934\) 96.8026 3.16748
\(935\) 15.2657 0.499242
\(936\) 9.33653 0.305174
\(937\) −39.6407 −1.29500 −0.647502 0.762063i \(-0.724186\pi\)
−0.647502 + 0.762063i \(0.724186\pi\)
\(938\) −3.95909 −0.129269
\(939\) −50.3543 −1.64325
\(940\) 11.9379 0.389372
\(941\) 33.5679 1.09428 0.547141 0.837040i \(-0.315716\pi\)
0.547141 + 0.837040i \(0.315716\pi\)
\(942\) 55.5674 1.81048
\(943\) 4.30202 0.140093
\(944\) 15.7985 0.514198
\(945\) −25.4810 −0.828898
\(946\) 129.022 4.19486
\(947\) −6.22150 −0.202172 −0.101086 0.994878i \(-0.532232\pi\)
−0.101086 + 0.994878i \(0.532232\pi\)
\(948\) 19.3013 0.626877
\(949\) −8.73842 −0.283661
\(950\) 11.8820 0.385503
\(951\) −29.4479 −0.954915
\(952\) 66.5612 2.15726
\(953\) 29.0411 0.940732 0.470366 0.882471i \(-0.344122\pi\)
0.470366 + 0.882471i \(0.344122\pi\)
\(954\) 20.4262 0.661323
\(955\) −4.02204 −0.130150
\(956\) 7.74078 0.250355
\(957\) 60.8443 1.96682
\(958\) 32.2778 1.04285
\(959\) 12.8494 0.414928
\(960\) 12.5421 0.404793
\(961\) 48.0114 1.54875
\(962\) −27.9233 −0.900282
\(963\) 10.1273 0.326348
\(964\) 0.719205 0.0231640
\(965\) 1.98611 0.0639352
\(966\) 18.8110 0.605236
\(967\) 34.5250 1.11025 0.555125 0.831767i \(-0.312670\pi\)
0.555125 + 0.831767i \(0.312670\pi\)
\(968\) −56.5894 −1.81885
\(969\) −5.52627 −0.177529
\(970\) 0.433932 0.0139327
\(971\) −14.1435 −0.453885 −0.226943 0.973908i \(-0.572873\pi\)
−0.226943 + 0.973908i \(0.572873\pi\)
\(972\) 38.8537 1.24623
\(973\) −0.773884 −0.0248096
\(974\) 73.2759 2.34791
\(975\) −7.78037 −0.249171
\(976\) −106.118 −3.39674
\(977\) 25.1451 0.804463 0.402232 0.915538i \(-0.368235\pi\)
0.402232 + 0.915538i \(0.368235\pi\)
\(978\) −83.1521 −2.65891
\(979\) 43.5810 1.39286
\(980\) 30.4646 0.973155
\(981\) 9.97852 0.318590
\(982\) 81.3858 2.59712
\(983\) −10.0409 −0.320254 −0.160127 0.987096i \(-0.551190\pi\)
−0.160127 + 0.987096i \(0.551190\pi\)
\(984\) 32.3959 1.03274
\(985\) 3.41234 0.108726
\(986\) −66.0105 −2.10220
\(987\) 9.72802 0.309646
\(988\) 10.6492 0.338797
\(989\) −16.1882 −0.514756
\(990\) −11.9757 −0.380613
\(991\) −29.1337 −0.925461 −0.462731 0.886499i \(-0.653130\pi\)
−0.462731 + 0.886499i \(0.653130\pi\)
\(992\) 85.0356 2.69988
\(993\) 18.5359 0.588218
\(994\) 71.4784 2.26716
\(995\) 13.3613 0.423581
\(996\) −112.701 −3.57108
\(997\) 4.72192 0.149545 0.0747724 0.997201i \(-0.476177\pi\)
0.0747724 + 0.997201i \(0.476177\pi\)
\(998\) 79.6209 2.52036
\(999\) −37.7481 −1.19430
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 \(a_p\))