Properties

Label 8007.2.a.e.1.28
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 46
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(46\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.28
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.569311 q^{2} +1.00000 q^{3} -1.67588 q^{4} +1.10171 q^{5} +0.569311 q^{6} +2.67084 q^{7} -2.09272 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.569311 q^{2} +1.00000 q^{3} -1.67588 q^{4} +1.10171 q^{5} +0.569311 q^{6} +2.67084 q^{7} -2.09272 q^{8} +1.00000 q^{9} +0.627218 q^{10} -5.58292 q^{11} -1.67588 q^{12} +5.66739 q^{13} +1.52054 q^{14} +1.10171 q^{15} +2.16036 q^{16} -1.00000 q^{17} +0.569311 q^{18} -8.17874 q^{19} -1.84634 q^{20} +2.67084 q^{21} -3.17842 q^{22} +1.82305 q^{23} -2.09272 q^{24} -3.78623 q^{25} +3.22651 q^{26} +1.00000 q^{27} -4.47602 q^{28} -0.370279 q^{29} +0.627218 q^{30} -0.983283 q^{31} +5.41536 q^{32} -5.58292 q^{33} -0.569311 q^{34} +2.94250 q^{35} -1.67588 q^{36} -7.61191 q^{37} -4.65625 q^{38} +5.66739 q^{39} -2.30558 q^{40} -0.900065 q^{41} +1.52054 q^{42} -0.382632 q^{43} +9.35632 q^{44} +1.10171 q^{45} +1.03788 q^{46} +11.8642 q^{47} +2.16036 q^{48} +0.133374 q^{49} -2.15554 q^{50} -1.00000 q^{51} -9.49789 q^{52} -6.33675 q^{53} +0.569311 q^{54} -6.15077 q^{55} -5.58932 q^{56} -8.17874 q^{57} -0.210804 q^{58} +2.76405 q^{59} -1.84634 q^{60} +4.73721 q^{61} -0.559794 q^{62} +2.67084 q^{63} -1.23769 q^{64} +6.24383 q^{65} -3.17842 q^{66} -15.6969 q^{67} +1.67588 q^{68} +1.82305 q^{69} +1.67520 q^{70} -10.4123 q^{71} -2.09272 q^{72} -3.19989 q^{73} -4.33354 q^{74} -3.78623 q^{75} +13.7066 q^{76} -14.9111 q^{77} +3.22651 q^{78} +9.43468 q^{79} +2.38009 q^{80} +1.00000 q^{81} -0.512417 q^{82} -6.69273 q^{83} -4.47602 q^{84} -1.10171 q^{85} -0.217837 q^{86} -0.370279 q^{87} +11.6835 q^{88} -5.70127 q^{89} +0.627218 q^{90} +15.1367 q^{91} -3.05523 q^{92} -0.983283 q^{93} +6.75442 q^{94} -9.01062 q^{95} +5.41536 q^{96} -6.95071 q^{97} +0.0759316 q^{98} -5.58292 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q - 5q^{2} + 46q^{3} + 43q^{4} - 19q^{5} - 5q^{6} + q^{7} - 18q^{8} + 46q^{9} + O(q^{10}) \) \( 46q - 5q^{2} + 46q^{3} + 43q^{4} - 19q^{5} - 5q^{6} + q^{7} - 18q^{8} + 46q^{9} - 10q^{10} - 25q^{11} + 43q^{12} - 8q^{13} - 28q^{14} - 19q^{15} + 33q^{16} - 46q^{17} - 5q^{18} - 2q^{19} - 56q^{20} + q^{21} - 19q^{22} - 64q^{23} - 18q^{24} + 11q^{25} - 13q^{26} + 46q^{27} - 38q^{28} - 51q^{29} - 10q^{30} - 19q^{31} - 61q^{32} - 25q^{33} + 5q^{34} - 39q^{35} + 43q^{36} - 46q^{37} - 48q^{38} - 8q^{39} - 10q^{40} - 53q^{41} - 28q^{42} - 33q^{43} - 62q^{44} - 19q^{45} + 2q^{46} - 45q^{47} + 33q^{48} + 21q^{49} - 60q^{50} - 46q^{51} - 63q^{52} - 47q^{53} - 5q^{54} + 5q^{55} - 82q^{56} - 2q^{57} - 21q^{58} - 65q^{59} - 56q^{60} - 37q^{61} - 46q^{62} + q^{63} + 74q^{64} - 85q^{65} - 19q^{66} - 52q^{67} - 43q^{68} - 64q^{69} - 20q^{70} - 48q^{71} - 18q^{72} - 39q^{73} - 16q^{74} + 11q^{75} + 42q^{76} - 78q^{77} - 13q^{78} - 26q^{79} - 78q^{80} + 46q^{81} + 3q^{82} - 47q^{83} - 38q^{84} + 19q^{85} - 6q^{86} - 51q^{87} - 58q^{88} - 58q^{89} - 10q^{90} - 43q^{91} - 68q^{92} - 19q^{93} - 78q^{95} - 61q^{96} - 44q^{97} - 4q^{98} - 25q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.569311 0.402564 0.201282 0.979533i \(-0.435489\pi\)
0.201282 + 0.979533i \(0.435489\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.67588 −0.837942
\(5\) 1.10171 0.492701 0.246351 0.969181i \(-0.420769\pi\)
0.246351 + 0.969181i \(0.420769\pi\)
\(6\) 0.569311 0.232420
\(7\) 2.67084 1.00948 0.504741 0.863271i \(-0.331588\pi\)
0.504741 + 0.863271i \(0.331588\pi\)
\(8\) −2.09272 −0.739889
\(9\) 1.00000 0.333333
\(10\) 0.627218 0.198344
\(11\) −5.58292 −1.68331 −0.841656 0.540013i \(-0.818419\pi\)
−0.841656 + 0.540013i \(0.818419\pi\)
\(12\) −1.67588 −0.483786
\(13\) 5.66739 1.57185 0.785925 0.618322i \(-0.212187\pi\)
0.785925 + 0.618322i \(0.212187\pi\)
\(14\) 1.52054 0.406381
\(15\) 1.10171 0.284461
\(16\) 2.16036 0.540090
\(17\) −1.00000 −0.242536
\(18\) 0.569311 0.134188
\(19\) −8.17874 −1.87633 −0.938165 0.346187i \(-0.887476\pi\)
−0.938165 + 0.346187i \(0.887476\pi\)
\(20\) −1.84634 −0.412855
\(21\) 2.67084 0.582825
\(22\) −3.17842 −0.677641
\(23\) 1.82305 0.380133 0.190066 0.981771i \(-0.439130\pi\)
0.190066 + 0.981771i \(0.439130\pi\)
\(24\) −2.09272 −0.427175
\(25\) −3.78623 −0.757246
\(26\) 3.22651 0.632770
\(27\) 1.00000 0.192450
\(28\) −4.47602 −0.845888
\(29\) −0.370279 −0.0687591 −0.0343796 0.999409i \(-0.510946\pi\)
−0.0343796 + 0.999409i \(0.510946\pi\)
\(30\) 0.627218 0.114514
\(31\) −0.983283 −0.176603 −0.0883015 0.996094i \(-0.528144\pi\)
−0.0883015 + 0.996094i \(0.528144\pi\)
\(32\) 5.41536 0.957310
\(33\) −5.58292 −0.971861
\(34\) −0.569311 −0.0976361
\(35\) 2.94250 0.497373
\(36\) −1.67588 −0.279314
\(37\) −7.61191 −1.25139 −0.625695 0.780068i \(-0.715184\pi\)
−0.625695 + 0.780068i \(0.715184\pi\)
\(38\) −4.65625 −0.755343
\(39\) 5.66739 0.907508
\(40\) −2.30558 −0.364544
\(41\) −0.900065 −0.140567 −0.0702833 0.997527i \(-0.522390\pi\)
−0.0702833 + 0.997527i \(0.522390\pi\)
\(42\) 1.52054 0.234624
\(43\) −0.382632 −0.0583508 −0.0291754 0.999574i \(-0.509288\pi\)
−0.0291754 + 0.999574i \(0.509288\pi\)
\(44\) 9.35632 1.41052
\(45\) 1.10171 0.164234
\(46\) 1.03788 0.153028
\(47\) 11.8642 1.73057 0.865286 0.501279i \(-0.167137\pi\)
0.865286 + 0.501279i \(0.167137\pi\)
\(48\) 2.16036 0.311821
\(49\) 0.133374 0.0190535
\(50\) −2.15554 −0.304840
\(51\) −1.00000 −0.140028
\(52\) −9.49789 −1.31712
\(53\) −6.33675 −0.870419 −0.435210 0.900329i \(-0.643326\pi\)
−0.435210 + 0.900329i \(0.643326\pi\)
\(54\) 0.569311 0.0774735
\(55\) −6.15077 −0.829370
\(56\) −5.58932 −0.746905
\(57\) −8.17874 −1.08330
\(58\) −0.210804 −0.0276799
\(59\) 2.76405 0.359849 0.179925 0.983680i \(-0.442415\pi\)
0.179925 + 0.983680i \(0.442415\pi\)
\(60\) −1.84634 −0.238362
\(61\) 4.73721 0.606538 0.303269 0.952905i \(-0.401922\pi\)
0.303269 + 0.952905i \(0.401922\pi\)
\(62\) −0.559794 −0.0710940
\(63\) 2.67084 0.336494
\(64\) −1.23769 −0.154711
\(65\) 6.24383 0.774452
\(66\) −3.17842 −0.391236
\(67\) −15.6969 −1.91769 −0.958844 0.283935i \(-0.908360\pi\)
−0.958844 + 0.283935i \(0.908360\pi\)
\(68\) 1.67588 0.203231
\(69\) 1.82305 0.219470
\(70\) 1.67520 0.200224
\(71\) −10.4123 −1.23571 −0.617855 0.786292i \(-0.711998\pi\)
−0.617855 + 0.786292i \(0.711998\pi\)
\(72\) −2.09272 −0.246630
\(73\) −3.19989 −0.374519 −0.187259 0.982311i \(-0.559960\pi\)
−0.187259 + 0.982311i \(0.559960\pi\)
\(74\) −4.33354 −0.503764
\(75\) −3.78623 −0.437196
\(76\) 13.7066 1.57226
\(77\) −14.9111 −1.69927
\(78\) 3.22651 0.365330
\(79\) 9.43468 1.06148 0.530742 0.847533i \(-0.321913\pi\)
0.530742 + 0.847533i \(0.321913\pi\)
\(80\) 2.38009 0.266103
\(81\) 1.00000 0.111111
\(82\) −0.512417 −0.0565870
\(83\) −6.69273 −0.734622 −0.367311 0.930098i \(-0.619722\pi\)
−0.367311 + 0.930098i \(0.619722\pi\)
\(84\) −4.47602 −0.488373
\(85\) −1.10171 −0.119498
\(86\) −0.217837 −0.0234899
\(87\) −0.370279 −0.0396981
\(88\) 11.6835 1.24546
\(89\) −5.70127 −0.604333 −0.302166 0.953255i \(-0.597710\pi\)
−0.302166 + 0.953255i \(0.597710\pi\)
\(90\) 0.627218 0.0661145
\(91\) 15.1367 1.58675
\(92\) −3.05523 −0.318529
\(93\) −0.983283 −0.101962
\(94\) 6.75442 0.696666
\(95\) −9.01062 −0.924470
\(96\) 5.41536 0.552703
\(97\) −6.95071 −0.705738 −0.352869 0.935673i \(-0.614794\pi\)
−0.352869 + 0.935673i \(0.614794\pi\)
\(98\) 0.0759316 0.00767025
\(99\) −5.58292 −0.561104
\(100\) 6.34528 0.634528
\(101\) 4.56234 0.453970 0.226985 0.973898i \(-0.427113\pi\)
0.226985 + 0.973898i \(0.427113\pi\)
\(102\) −0.569311 −0.0563702
\(103\) −17.3272 −1.70730 −0.853651 0.520846i \(-0.825617\pi\)
−0.853651 + 0.520846i \(0.825617\pi\)
\(104\) −11.8603 −1.16300
\(105\) 2.94250 0.287158
\(106\) −3.60758 −0.350399
\(107\) −1.92613 −0.186206 −0.0931030 0.995656i \(-0.529679\pi\)
−0.0931030 + 0.995656i \(0.529679\pi\)
\(108\) −1.67588 −0.161262
\(109\) 5.30123 0.507766 0.253883 0.967235i \(-0.418292\pi\)
0.253883 + 0.967235i \(0.418292\pi\)
\(110\) −3.50170 −0.333874
\(111\) −7.61191 −0.722490
\(112\) 5.76997 0.545211
\(113\) −16.3132 −1.53462 −0.767309 0.641277i \(-0.778405\pi\)
−0.767309 + 0.641277i \(0.778405\pi\)
\(114\) −4.65625 −0.436097
\(115\) 2.00848 0.187292
\(116\) 0.620545 0.0576162
\(117\) 5.66739 0.523950
\(118\) 1.57361 0.144862
\(119\) −2.67084 −0.244835
\(120\) −2.30558 −0.210470
\(121\) 20.1690 1.83354
\(122\) 2.69695 0.244170
\(123\) −0.900065 −0.0811561
\(124\) 1.64787 0.147983
\(125\) −9.67990 −0.865797
\(126\) 1.52054 0.135460
\(127\) 6.14179 0.544996 0.272498 0.962156i \(-0.412150\pi\)
0.272498 + 0.962156i \(0.412150\pi\)
\(128\) −11.5354 −1.01959
\(129\) −0.382632 −0.0336889
\(130\) 3.55469 0.311767
\(131\) −6.41089 −0.560122 −0.280061 0.959982i \(-0.590355\pi\)
−0.280061 + 0.959982i \(0.590355\pi\)
\(132\) 9.35632 0.814363
\(133\) −21.8441 −1.89412
\(134\) −8.93645 −0.771992
\(135\) 1.10171 0.0948204
\(136\) 2.09272 0.179449
\(137\) −15.9195 −1.36010 −0.680049 0.733167i \(-0.738042\pi\)
−0.680049 + 0.733167i \(0.738042\pi\)
\(138\) 1.03788 0.0883506
\(139\) 3.75752 0.318709 0.159354 0.987221i \(-0.449059\pi\)
0.159354 + 0.987221i \(0.449059\pi\)
\(140\) −4.93128 −0.416770
\(141\) 11.8642 0.999146
\(142\) −5.92783 −0.497452
\(143\) −31.6406 −2.64592
\(144\) 2.16036 0.180030
\(145\) −0.407941 −0.0338777
\(146\) −1.82173 −0.150768
\(147\) 0.133374 0.0110005
\(148\) 12.7567 1.04859
\(149\) 19.6328 1.60838 0.804190 0.594372i \(-0.202599\pi\)
0.804190 + 0.594372i \(0.202599\pi\)
\(150\) −2.15554 −0.175999
\(151\) 5.24765 0.427048 0.213524 0.976938i \(-0.431506\pi\)
0.213524 + 0.976938i \(0.431506\pi\)
\(152\) 17.1158 1.38828
\(153\) −1.00000 −0.0808452
\(154\) −8.48904 −0.684066
\(155\) −1.08330 −0.0870124
\(156\) −9.49789 −0.760440
\(157\) 1.00000 0.0798087
\(158\) 5.37127 0.427315
\(159\) −6.33675 −0.502537
\(160\) 5.96617 0.471668
\(161\) 4.86908 0.383737
\(162\) 0.569311 0.0447293
\(163\) 24.9047 1.95068 0.975341 0.220702i \(-0.0708347\pi\)
0.975341 + 0.220702i \(0.0708347\pi\)
\(164\) 1.50841 0.117787
\(165\) −6.15077 −0.478837
\(166\) −3.81024 −0.295732
\(167\) 7.68036 0.594324 0.297162 0.954827i \(-0.403960\pi\)
0.297162 + 0.954827i \(0.403960\pi\)
\(168\) −5.58932 −0.431226
\(169\) 19.1193 1.47071
\(170\) −0.627218 −0.0481054
\(171\) −8.17874 −0.625444
\(172\) 0.641247 0.0488946
\(173\) 6.82989 0.519267 0.259634 0.965707i \(-0.416398\pi\)
0.259634 + 0.965707i \(0.416398\pi\)
\(174\) −0.210804 −0.0159810
\(175\) −10.1124 −0.764426
\(176\) −12.0611 −0.909140
\(177\) 2.76405 0.207759
\(178\) −3.24579 −0.243283
\(179\) −5.52492 −0.412952 −0.206476 0.978452i \(-0.566200\pi\)
−0.206476 + 0.978452i \(0.566200\pi\)
\(180\) −1.84634 −0.137618
\(181\) 4.66759 0.346940 0.173470 0.984839i \(-0.444502\pi\)
0.173470 + 0.984839i \(0.444502\pi\)
\(182\) 8.61748 0.638770
\(183\) 4.73721 0.350185
\(184\) −3.81515 −0.281256
\(185\) −8.38614 −0.616561
\(186\) −0.559794 −0.0410461
\(187\) 5.58292 0.408263
\(188\) −19.8830 −1.45012
\(189\) 2.67084 0.194275
\(190\) −5.12985 −0.372158
\(191\) 13.2139 0.956124 0.478062 0.878326i \(-0.341339\pi\)
0.478062 + 0.878326i \(0.341339\pi\)
\(192\) −1.23769 −0.0893226
\(193\) −13.7389 −0.988950 −0.494475 0.869192i \(-0.664640\pi\)
−0.494475 + 0.869192i \(0.664640\pi\)
\(194\) −3.95712 −0.284104
\(195\) 6.24383 0.447130
\(196\) −0.223520 −0.0159657
\(197\) −20.9742 −1.49435 −0.747173 0.664629i \(-0.768590\pi\)
−0.747173 + 0.664629i \(0.768590\pi\)
\(198\) −3.17842 −0.225880
\(199\) 20.8820 1.48029 0.740144 0.672449i \(-0.234757\pi\)
0.740144 + 0.672449i \(0.234757\pi\)
\(200\) 7.92353 0.560278
\(201\) −15.6969 −1.10718
\(202\) 2.59739 0.182752
\(203\) −0.988956 −0.0694111
\(204\) 1.67588 0.117335
\(205\) −0.991613 −0.0692573
\(206\) −9.86458 −0.687298
\(207\) 1.82305 0.126711
\(208\) 12.2436 0.848940
\(209\) 45.6612 3.15845
\(210\) 1.67520 0.115600
\(211\) −20.5762 −1.41653 −0.708263 0.705949i \(-0.750521\pi\)
−0.708263 + 0.705949i \(0.750521\pi\)
\(212\) 10.6197 0.729361
\(213\) −10.4123 −0.713437
\(214\) −1.09657 −0.0749598
\(215\) −0.421551 −0.0287495
\(216\) −2.09272 −0.142392
\(217\) −2.62619 −0.178277
\(218\) 3.01805 0.204408
\(219\) −3.19989 −0.216228
\(220\) 10.3080 0.694964
\(221\) −5.66739 −0.381230
\(222\) −4.33354 −0.290848
\(223\) 10.2001 0.683048 0.341524 0.939873i \(-0.389057\pi\)
0.341524 + 0.939873i \(0.389057\pi\)
\(224\) 14.4636 0.966387
\(225\) −3.78623 −0.252415
\(226\) −9.28730 −0.617782
\(227\) 11.9693 0.794432 0.397216 0.917725i \(-0.369976\pi\)
0.397216 + 0.917725i \(0.369976\pi\)
\(228\) 13.7066 0.907743
\(229\) 10.4011 0.687321 0.343661 0.939094i \(-0.388333\pi\)
0.343661 + 0.939094i \(0.388333\pi\)
\(230\) 1.14345 0.0753969
\(231\) −14.9111 −0.981076
\(232\) 0.774892 0.0508741
\(233\) 11.6668 0.764317 0.382158 0.924097i \(-0.375181\pi\)
0.382158 + 0.924097i \(0.375181\pi\)
\(234\) 3.22651 0.210923
\(235\) 13.0709 0.852654
\(236\) −4.63224 −0.301533
\(237\) 9.43468 0.612848
\(238\) −1.52054 −0.0985619
\(239\) −15.6723 −1.01376 −0.506878 0.862018i \(-0.669201\pi\)
−0.506878 + 0.862018i \(0.669201\pi\)
\(240\) 2.38009 0.153634
\(241\) −22.4327 −1.44502 −0.722509 0.691361i \(-0.757011\pi\)
−0.722509 + 0.691361i \(0.757011\pi\)
\(242\) 11.4824 0.738118
\(243\) 1.00000 0.0641500
\(244\) −7.93903 −0.508244
\(245\) 0.146940 0.00938768
\(246\) −0.512417 −0.0326705
\(247\) −46.3521 −2.94931
\(248\) 2.05774 0.130667
\(249\) −6.69273 −0.424134
\(250\) −5.51088 −0.348539
\(251\) −25.6094 −1.61645 −0.808227 0.588872i \(-0.799572\pi\)
−0.808227 + 0.588872i \(0.799572\pi\)
\(252\) −4.47602 −0.281963
\(253\) −10.1780 −0.639883
\(254\) 3.49659 0.219396
\(255\) −1.10171 −0.0689919
\(256\) −4.09183 −0.255739
\(257\) −11.3502 −0.708009 −0.354004 0.935244i \(-0.615180\pi\)
−0.354004 + 0.935244i \(0.615180\pi\)
\(258\) −0.217837 −0.0135619
\(259\) −20.3302 −1.26326
\(260\) −10.4639 −0.648946
\(261\) −0.370279 −0.0229197
\(262\) −3.64979 −0.225485
\(263\) −27.3107 −1.68405 −0.842024 0.539440i \(-0.818636\pi\)
−0.842024 + 0.539440i \(0.818636\pi\)
\(264\) 11.6835 0.719070
\(265\) −6.98128 −0.428856
\(266\) −12.4361 −0.762505
\(267\) −5.70127 −0.348912
\(268\) 26.3063 1.60691
\(269\) −23.4956 −1.43255 −0.716275 0.697818i \(-0.754154\pi\)
−0.716275 + 0.697818i \(0.754154\pi\)
\(270\) 0.627218 0.0381713
\(271\) 26.4862 1.60892 0.804460 0.594007i \(-0.202455\pi\)
0.804460 + 0.594007i \(0.202455\pi\)
\(272\) −2.16036 −0.130991
\(273\) 15.1367 0.916113
\(274\) −9.06317 −0.547526
\(275\) 21.1382 1.27468
\(276\) −3.05523 −0.183903
\(277\) −25.2646 −1.51800 −0.759002 0.651089i \(-0.774313\pi\)
−0.759002 + 0.651089i \(0.774313\pi\)
\(278\) 2.13920 0.128301
\(279\) −0.983283 −0.0588676
\(280\) −6.15783 −0.368001
\(281\) −17.7033 −1.05609 −0.528045 0.849217i \(-0.677075\pi\)
−0.528045 + 0.849217i \(0.677075\pi\)
\(282\) 6.75442 0.402220
\(283\) 4.60308 0.273625 0.136812 0.990597i \(-0.456314\pi\)
0.136812 + 0.990597i \(0.456314\pi\)
\(284\) 17.4498 1.03545
\(285\) −9.01062 −0.533743
\(286\) −18.0133 −1.06515
\(287\) −2.40393 −0.141899
\(288\) 5.41536 0.319103
\(289\) 1.00000 0.0588235
\(290\) −0.232246 −0.0136379
\(291\) −6.95071 −0.407458
\(292\) 5.36264 0.313825
\(293\) −22.8712 −1.33615 −0.668074 0.744095i \(-0.732881\pi\)
−0.668074 + 0.744095i \(0.732881\pi\)
\(294\) 0.0759316 0.00442842
\(295\) 3.04519 0.177298
\(296\) 15.9296 0.925890
\(297\) −5.58292 −0.323954
\(298\) 11.1772 0.647476
\(299\) 10.3319 0.597512
\(300\) 6.34528 0.366345
\(301\) −1.02195 −0.0589041
\(302\) 2.98755 0.171914
\(303\) 4.56234 0.262100
\(304\) −17.6690 −1.01339
\(305\) 5.21905 0.298842
\(306\) −0.569311 −0.0325454
\(307\) −4.19223 −0.239263 −0.119632 0.992818i \(-0.538171\pi\)
−0.119632 + 0.992818i \(0.538171\pi\)
\(308\) 24.9892 1.42389
\(309\) −17.3272 −0.985711
\(310\) −0.616733 −0.0350281
\(311\) −2.94310 −0.166888 −0.0834439 0.996512i \(-0.526592\pi\)
−0.0834439 + 0.996512i \(0.526592\pi\)
\(312\) −11.8603 −0.671456
\(313\) −1.06581 −0.0602431 −0.0301216 0.999546i \(-0.509589\pi\)
−0.0301216 + 0.999546i \(0.509589\pi\)
\(314\) 0.569311 0.0321281
\(315\) 2.94250 0.165791
\(316\) −15.8114 −0.889463
\(317\) −10.0695 −0.565560 −0.282780 0.959185i \(-0.591257\pi\)
−0.282780 + 0.959185i \(0.591257\pi\)
\(318\) −3.60758 −0.202303
\(319\) 2.06724 0.115743
\(320\) −1.36358 −0.0762264
\(321\) −1.92613 −0.107506
\(322\) 2.77202 0.154479
\(323\) 8.17874 0.455077
\(324\) −1.67588 −0.0931047
\(325\) −21.4580 −1.19028
\(326\) 14.1785 0.785274
\(327\) 5.30123 0.293159
\(328\) 1.88359 0.104004
\(329\) 31.6874 1.74698
\(330\) −3.50170 −0.192762
\(331\) 18.9636 1.04234 0.521168 0.853454i \(-0.325497\pi\)
0.521168 + 0.853454i \(0.325497\pi\)
\(332\) 11.2162 0.615571
\(333\) −7.61191 −0.417130
\(334\) 4.37251 0.239253
\(335\) −17.2935 −0.944846
\(336\) 5.76997 0.314778
\(337\) −22.5790 −1.22996 −0.614978 0.788544i \(-0.710835\pi\)
−0.614978 + 0.788544i \(0.710835\pi\)
\(338\) 10.8848 0.592056
\(339\) −16.3132 −0.886013
\(340\) 1.84634 0.100132
\(341\) 5.48959 0.297278
\(342\) −4.65625 −0.251781
\(343\) −18.3396 −0.990248
\(344\) 0.800743 0.0431731
\(345\) 2.00848 0.108133
\(346\) 3.88834 0.209038
\(347\) 23.8497 1.28032 0.640161 0.768241i \(-0.278868\pi\)
0.640161 + 0.768241i \(0.278868\pi\)
\(348\) 0.620545 0.0332647
\(349\) 33.6034 1.79875 0.899375 0.437177i \(-0.144022\pi\)
0.899375 + 0.437177i \(0.144022\pi\)
\(350\) −5.75711 −0.307730
\(351\) 5.66739 0.302503
\(352\) −30.2335 −1.61145
\(353\) 9.02875 0.480552 0.240276 0.970705i \(-0.422762\pi\)
0.240276 + 0.970705i \(0.422762\pi\)
\(354\) 1.57361 0.0836363
\(355\) −11.4713 −0.608835
\(356\) 9.55466 0.506396
\(357\) −2.67084 −0.141356
\(358\) −3.14540 −0.166240
\(359\) −35.8080 −1.88987 −0.944937 0.327252i \(-0.893878\pi\)
−0.944937 + 0.327252i \(0.893878\pi\)
\(360\) −2.30558 −0.121515
\(361\) 47.8917 2.52062
\(362\) 2.65731 0.139665
\(363\) 20.1690 1.05860
\(364\) −25.3673 −1.32961
\(365\) −3.52536 −0.184526
\(366\) 2.69695 0.140972
\(367\) 6.08980 0.317885 0.158943 0.987288i \(-0.449192\pi\)
0.158943 + 0.987288i \(0.449192\pi\)
\(368\) 3.93845 0.205306
\(369\) −0.900065 −0.0468555
\(370\) −4.77432 −0.248205
\(371\) −16.9244 −0.878672
\(372\) 1.64787 0.0854381
\(373\) −20.3227 −1.05227 −0.526135 0.850401i \(-0.676359\pi\)
−0.526135 + 0.850401i \(0.676359\pi\)
\(374\) 3.17842 0.164352
\(375\) −9.67990 −0.499868
\(376\) −24.8285 −1.28043
\(377\) −2.09852 −0.108079
\(378\) 1.52054 0.0782080
\(379\) 16.5189 0.848519 0.424260 0.905541i \(-0.360534\pi\)
0.424260 + 0.905541i \(0.360534\pi\)
\(380\) 15.1008 0.774653
\(381\) 6.14179 0.314654
\(382\) 7.52282 0.384901
\(383\) 0.851323 0.0435006 0.0217503 0.999763i \(-0.493076\pi\)
0.0217503 + 0.999763i \(0.493076\pi\)
\(384\) −11.5354 −0.588661
\(385\) −16.4277 −0.837234
\(386\) −7.82173 −0.398115
\(387\) −0.382632 −0.0194503
\(388\) 11.6486 0.591367
\(389\) −12.6242 −0.640070 −0.320035 0.947406i \(-0.603695\pi\)
−0.320035 + 0.947406i \(0.603695\pi\)
\(390\) 3.55469 0.179998
\(391\) −1.82305 −0.0921958
\(392\) −0.279116 −0.0140975
\(393\) −6.41089 −0.323386
\(394\) −11.9408 −0.601570
\(395\) 10.3943 0.522994
\(396\) 9.35632 0.470173
\(397\) −10.2699 −0.515433 −0.257717 0.966221i \(-0.582970\pi\)
−0.257717 + 0.966221i \(0.582970\pi\)
\(398\) 11.8884 0.595910
\(399\) −21.8441 −1.09357
\(400\) −8.17961 −0.408981
\(401\) −9.76594 −0.487688 −0.243844 0.969815i \(-0.578408\pi\)
−0.243844 + 0.969815i \(0.578408\pi\)
\(402\) −8.93645 −0.445710
\(403\) −5.57265 −0.277593
\(404\) −7.64596 −0.380401
\(405\) 1.10171 0.0547446
\(406\) −0.563024 −0.0279424
\(407\) 42.4966 2.10648
\(408\) 2.09272 0.103605
\(409\) −8.55321 −0.422929 −0.211464 0.977386i \(-0.567823\pi\)
−0.211464 + 0.977386i \(0.567823\pi\)
\(410\) −0.564537 −0.0278805
\(411\) −15.9195 −0.785253
\(412\) 29.0384 1.43062
\(413\) 7.38234 0.363261
\(414\) 1.03788 0.0510093
\(415\) −7.37346 −0.361949
\(416\) 30.6910 1.50475
\(417\) 3.75752 0.184007
\(418\) 25.9954 1.27148
\(419\) −13.6583 −0.667253 −0.333626 0.942705i \(-0.608272\pi\)
−0.333626 + 0.942705i \(0.608272\pi\)
\(420\) −4.93128 −0.240622
\(421\) 39.5480 1.92745 0.963725 0.266897i \(-0.0859985\pi\)
0.963725 + 0.266897i \(0.0859985\pi\)
\(422\) −11.7143 −0.570242
\(423\) 11.8642 0.576857
\(424\) 13.2611 0.644014
\(425\) 3.78623 0.183659
\(426\) −5.92783 −0.287204
\(427\) 12.6523 0.612289
\(428\) 3.22797 0.156030
\(429\) −31.6406 −1.52762
\(430\) −0.239994 −0.0115735
\(431\) −23.4392 −1.12903 −0.564514 0.825424i \(-0.690936\pi\)
−0.564514 + 0.825424i \(0.690936\pi\)
\(432\) 2.16036 0.103940
\(433\) 2.14183 0.102930 0.0514648 0.998675i \(-0.483611\pi\)
0.0514648 + 0.998675i \(0.483611\pi\)
\(434\) −1.49512 −0.0717681
\(435\) −0.407941 −0.0195593
\(436\) −8.88425 −0.425478
\(437\) −14.9103 −0.713255
\(438\) −1.82173 −0.0870458
\(439\) −11.5639 −0.551916 −0.275958 0.961170i \(-0.588995\pi\)
−0.275958 + 0.961170i \(0.588995\pi\)
\(440\) 12.8719 0.613642
\(441\) 0.133374 0.00635117
\(442\) −3.22651 −0.153469
\(443\) 32.3237 1.53575 0.767873 0.640602i \(-0.221315\pi\)
0.767873 + 0.640602i \(0.221315\pi\)
\(444\) 12.7567 0.605405
\(445\) −6.28116 −0.297755
\(446\) 5.80702 0.274970
\(447\) 19.6328 0.928599
\(448\) −3.30567 −0.156178
\(449\) 6.62478 0.312642 0.156321 0.987706i \(-0.450036\pi\)
0.156321 + 0.987706i \(0.450036\pi\)
\(450\) −2.15554 −0.101613
\(451\) 5.02499 0.236617
\(452\) 27.3391 1.28592
\(453\) 5.24765 0.246556
\(454\) 6.81427 0.319810
\(455\) 16.6763 0.781795
\(456\) 17.1158 0.801522
\(457\) −7.37796 −0.345127 −0.172563 0.984998i \(-0.555205\pi\)
−0.172563 + 0.984998i \(0.555205\pi\)
\(458\) 5.92144 0.276691
\(459\) −1.00000 −0.0466760
\(460\) −3.36598 −0.156940
\(461\) −21.1982 −0.987301 −0.493650 0.869660i \(-0.664338\pi\)
−0.493650 + 0.869660i \(0.664338\pi\)
\(462\) −8.48904 −0.394946
\(463\) 7.83100 0.363937 0.181969 0.983304i \(-0.441753\pi\)
0.181969 + 0.983304i \(0.441753\pi\)
\(464\) −0.799936 −0.0371361
\(465\) −1.08330 −0.0502367
\(466\) 6.64203 0.307686
\(467\) −9.18216 −0.424900 −0.212450 0.977172i \(-0.568144\pi\)
−0.212450 + 0.977172i \(0.568144\pi\)
\(468\) −9.49789 −0.439040
\(469\) −41.9240 −1.93587
\(470\) 7.44144 0.343248
\(471\) 1.00000 0.0460776
\(472\) −5.78440 −0.266249
\(473\) 2.13620 0.0982227
\(474\) 5.37127 0.246711
\(475\) 30.9666 1.42084
\(476\) 4.47602 0.205158
\(477\) −6.33675 −0.290140
\(478\) −8.92241 −0.408102
\(479\) −15.2005 −0.694529 −0.347265 0.937767i \(-0.612889\pi\)
−0.347265 + 0.937767i \(0.612889\pi\)
\(480\) 5.96617 0.272317
\(481\) −43.1396 −1.96700
\(482\) −12.7712 −0.581712
\(483\) 4.86908 0.221551
\(484\) −33.8008 −1.53640
\(485\) −7.65769 −0.347718
\(486\) 0.569311 0.0258245
\(487\) 0.00509170 0.000230727 0 0.000115363 1.00000i \(-0.499963\pi\)
0.000115363 1.00000i \(0.499963\pi\)
\(488\) −9.91368 −0.448771
\(489\) 24.9047 1.12623
\(490\) 0.0836548 0.00377914
\(491\) −1.11204 −0.0501855 −0.0250928 0.999685i \(-0.507988\pi\)
−0.0250928 + 0.999685i \(0.507988\pi\)
\(492\) 1.50841 0.0680042
\(493\) 0.370279 0.0166765
\(494\) −26.3888 −1.18729
\(495\) −6.15077 −0.276457
\(496\) −2.12424 −0.0953814
\(497\) −27.8095 −1.24743
\(498\) −3.81024 −0.170741
\(499\) 23.8754 1.06881 0.534405 0.845228i \(-0.320536\pi\)
0.534405 + 0.845228i \(0.320536\pi\)
\(500\) 16.2224 0.725488
\(501\) 7.68036 0.343133
\(502\) −14.5797 −0.650726
\(503\) −13.3991 −0.597435 −0.298717 0.954342i \(-0.596559\pi\)
−0.298717 + 0.954342i \(0.596559\pi\)
\(504\) −5.58932 −0.248968
\(505\) 5.02639 0.223671
\(506\) −5.79442 −0.257594
\(507\) 19.1193 0.849117
\(508\) −10.2929 −0.456675
\(509\) 5.38725 0.238786 0.119393 0.992847i \(-0.461905\pi\)
0.119393 + 0.992847i \(0.461905\pi\)
\(510\) −0.627218 −0.0277737
\(511\) −8.54638 −0.378070
\(512\) 20.7412 0.916640
\(513\) −8.17874 −0.361100
\(514\) −6.46182 −0.285019
\(515\) −19.0896 −0.841189
\(516\) 0.641247 0.0282293
\(517\) −66.2368 −2.91309
\(518\) −11.5742 −0.508541
\(519\) 6.82989 0.299799
\(520\) −13.0666 −0.573009
\(521\) −19.5475 −0.856391 −0.428195 0.903686i \(-0.640850\pi\)
−0.428195 + 0.903686i \(0.640850\pi\)
\(522\) −0.210804 −0.00922665
\(523\) 11.0809 0.484532 0.242266 0.970210i \(-0.422109\pi\)
0.242266 + 0.970210i \(0.422109\pi\)
\(524\) 10.7439 0.469350
\(525\) −10.1124 −0.441341
\(526\) −15.5483 −0.677937
\(527\) 0.983283 0.0428325
\(528\) −12.0611 −0.524892
\(529\) −19.6765 −0.855499
\(530\) −3.97452 −0.172642
\(531\) 2.76405 0.119950
\(532\) 36.6082 1.58716
\(533\) −5.10102 −0.220950
\(534\) −3.24579 −0.140459
\(535\) −2.12204 −0.0917439
\(536\) 32.8494 1.41888
\(537\) −5.52492 −0.238418
\(538\) −13.3763 −0.576693
\(539\) −0.744619 −0.0320730
\(540\) −1.84634 −0.0794540
\(541\) −11.4194 −0.490957 −0.245479 0.969402i \(-0.578945\pi\)
−0.245479 + 0.969402i \(0.578945\pi\)
\(542\) 15.0789 0.647693
\(543\) 4.66759 0.200306
\(544\) −5.41536 −0.232182
\(545\) 5.84043 0.250177
\(546\) 8.61748 0.368794
\(547\) 44.6050 1.90717 0.953586 0.301120i \(-0.0973604\pi\)
0.953586 + 0.301120i \(0.0973604\pi\)
\(548\) 26.6793 1.13968
\(549\) 4.73721 0.202179
\(550\) 12.0342 0.513141
\(551\) 3.02842 0.129015
\(552\) −3.81515 −0.162383
\(553\) 25.1985 1.07155
\(554\) −14.3834 −0.611093
\(555\) −8.38614 −0.355972
\(556\) −6.29717 −0.267060
\(557\) 33.1695 1.40544 0.702719 0.711468i \(-0.251969\pi\)
0.702719 + 0.711468i \(0.251969\pi\)
\(558\) −0.559794 −0.0236980
\(559\) −2.16852 −0.0917188
\(560\) 6.35685 0.268626
\(561\) 5.58292 0.235711
\(562\) −10.0787 −0.425143
\(563\) 13.1059 0.552348 0.276174 0.961108i \(-0.410933\pi\)
0.276174 + 0.961108i \(0.410933\pi\)
\(564\) −19.8830 −0.837227
\(565\) −17.9725 −0.756108
\(566\) 2.62059 0.110152
\(567\) 2.67084 0.112165
\(568\) 21.7900 0.914288
\(569\) 7.89068 0.330794 0.165397 0.986227i \(-0.447109\pi\)
0.165397 + 0.986227i \(0.447109\pi\)
\(570\) −5.12985 −0.214866
\(571\) −29.8410 −1.24881 −0.624403 0.781102i \(-0.714658\pi\)
−0.624403 + 0.781102i \(0.714658\pi\)
\(572\) 53.0259 2.21712
\(573\) 13.2139 0.552018
\(574\) −1.36858 −0.0571236
\(575\) −6.90250 −0.287854
\(576\) −1.23769 −0.0515704
\(577\) 18.3241 0.762843 0.381421 0.924401i \(-0.375435\pi\)
0.381421 + 0.924401i \(0.375435\pi\)
\(578\) 0.569311 0.0236802
\(579\) −13.7389 −0.570970
\(580\) 0.683663 0.0283876
\(581\) −17.8752 −0.741588
\(582\) −3.95712 −0.164028
\(583\) 35.3775 1.46519
\(584\) 6.69648 0.277102
\(585\) 6.24383 0.258151
\(586\) −13.0208 −0.537885
\(587\) 19.4001 0.800728 0.400364 0.916356i \(-0.368884\pi\)
0.400364 + 0.916356i \(0.368884\pi\)
\(588\) −0.223520 −0.00921782
\(589\) 8.04202 0.331365
\(590\) 1.73366 0.0713738
\(591\) −20.9742 −0.862762
\(592\) −16.4444 −0.675863
\(593\) −14.7220 −0.604559 −0.302280 0.953219i \(-0.597748\pi\)
−0.302280 + 0.953219i \(0.597748\pi\)
\(594\) −3.17842 −0.130412
\(595\) −2.94250 −0.120631
\(596\) −32.9023 −1.34773
\(597\) 20.8820 0.854645
\(598\) 5.88210 0.240537
\(599\) 30.0065 1.22603 0.613016 0.790070i \(-0.289956\pi\)
0.613016 + 0.790070i \(0.289956\pi\)
\(600\) 7.92353 0.323477
\(601\) 7.46250 0.304402 0.152201 0.988350i \(-0.451364\pi\)
0.152201 + 0.988350i \(0.451364\pi\)
\(602\) −0.581806 −0.0237127
\(603\) −15.6969 −0.639229
\(604\) −8.79445 −0.357841
\(605\) 22.2204 0.903388
\(606\) 2.59739 0.105512
\(607\) −9.36442 −0.380090 −0.190045 0.981775i \(-0.560863\pi\)
−0.190045 + 0.981775i \(0.560863\pi\)
\(608\) −44.2908 −1.79623
\(609\) −0.988956 −0.0400745
\(610\) 2.97126 0.120303
\(611\) 67.2390 2.72020
\(612\) 1.67588 0.0677436
\(613\) −21.0112 −0.848634 −0.424317 0.905514i \(-0.639486\pi\)
−0.424317 + 0.905514i \(0.639486\pi\)
\(614\) −2.38668 −0.0963187
\(615\) −0.991613 −0.0399857
\(616\) 31.2047 1.25727
\(617\) −16.4104 −0.660658 −0.330329 0.943866i \(-0.607160\pi\)
−0.330329 + 0.943866i \(0.607160\pi\)
\(618\) −9.86458 −0.396812
\(619\) −6.70602 −0.269538 −0.134769 0.990877i \(-0.543029\pi\)
−0.134769 + 0.990877i \(0.543029\pi\)
\(620\) 1.81548 0.0729114
\(621\) 1.82305 0.0731566
\(622\) −1.67554 −0.0671830
\(623\) −15.2272 −0.610063
\(624\) 12.2436 0.490136
\(625\) 8.26667 0.330667
\(626\) −0.606778 −0.0242517
\(627\) 45.6612 1.82353
\(628\) −1.67588 −0.0668751
\(629\) 7.61191 0.303507
\(630\) 1.67520 0.0667414
\(631\) −2.95048 −0.117457 −0.0587283 0.998274i \(-0.518705\pi\)
−0.0587283 + 0.998274i \(0.518705\pi\)
\(632\) −19.7442 −0.785381
\(633\) −20.5762 −0.817831
\(634\) −5.73268 −0.227674
\(635\) 6.76649 0.268520
\(636\) 10.6197 0.421097
\(637\) 0.755885 0.0299492
\(638\) 1.17690 0.0465940
\(639\) −10.4123 −0.411903
\(640\) −12.7086 −0.502353
\(641\) 12.8600 0.507940 0.253970 0.967212i \(-0.418263\pi\)
0.253970 + 0.967212i \(0.418263\pi\)
\(642\) −1.09657 −0.0432781
\(643\) 34.9143 1.37688 0.688442 0.725291i \(-0.258295\pi\)
0.688442 + 0.725291i \(0.258295\pi\)
\(644\) −8.16002 −0.321550
\(645\) −0.421551 −0.0165985
\(646\) 4.65625 0.183198
\(647\) −14.9014 −0.585834 −0.292917 0.956138i \(-0.594626\pi\)
−0.292917 + 0.956138i \(0.594626\pi\)
\(648\) −2.09272 −0.0822099
\(649\) −15.4315 −0.605739
\(650\) −12.2163 −0.479163
\(651\) −2.62619 −0.102929
\(652\) −41.7373 −1.63456
\(653\) −19.8946 −0.778538 −0.389269 0.921124i \(-0.627272\pi\)
−0.389269 + 0.921124i \(0.627272\pi\)
\(654\) 3.01805 0.118015
\(655\) −7.06296 −0.275972
\(656\) −1.94446 −0.0759185
\(657\) −3.19989 −0.124840
\(658\) 18.0400 0.703271
\(659\) −33.0855 −1.28883 −0.644414 0.764677i \(-0.722899\pi\)
−0.644414 + 0.764677i \(0.722899\pi\)
\(660\) 10.3080 0.401238
\(661\) 9.48152 0.368788 0.184394 0.982852i \(-0.440968\pi\)
0.184394 + 0.982852i \(0.440968\pi\)
\(662\) 10.7962 0.419607
\(663\) −5.66739 −0.220103
\(664\) 14.0060 0.543539
\(665\) −24.0659 −0.933236
\(666\) −4.33354 −0.167921
\(667\) −0.675039 −0.0261376
\(668\) −12.8714 −0.498009
\(669\) 10.2001 0.394358
\(670\) −9.84540 −0.380361
\(671\) −26.4475 −1.02099
\(672\) 14.4636 0.557944
\(673\) −33.0905 −1.27555 −0.637773 0.770225i \(-0.720144\pi\)
−0.637773 + 0.770225i \(0.720144\pi\)
\(674\) −12.8545 −0.495136
\(675\) −3.78623 −0.145732
\(676\) −32.0417 −1.23237
\(677\) 34.1850 1.31384 0.656918 0.753962i \(-0.271860\pi\)
0.656918 + 0.753962i \(0.271860\pi\)
\(678\) −9.28730 −0.356677
\(679\) −18.5642 −0.712429
\(680\) 2.30558 0.0884149
\(681\) 11.9693 0.458665
\(682\) 3.12529 0.119673
\(683\) 4.10493 0.157071 0.0785355 0.996911i \(-0.474976\pi\)
0.0785355 + 0.996911i \(0.474976\pi\)
\(684\) 13.7066 0.524086
\(685\) −17.5388 −0.670122
\(686\) −10.4410 −0.398638
\(687\) 10.4011 0.396825
\(688\) −0.826622 −0.0315147
\(689\) −35.9128 −1.36817
\(690\) 1.14345 0.0435304
\(691\) 34.7293 1.32116 0.660582 0.750754i \(-0.270310\pi\)
0.660582 + 0.750754i \(0.270310\pi\)
\(692\) −11.4461 −0.435116
\(693\) −14.9111 −0.566425
\(694\) 13.5779 0.515411
\(695\) 4.13971 0.157028
\(696\) 0.774892 0.0293722
\(697\) 0.900065 0.0340924
\(698\) 19.1308 0.724112
\(699\) 11.6668 0.441278
\(700\) 16.9472 0.640545
\(701\) 37.0322 1.39869 0.699344 0.714785i \(-0.253475\pi\)
0.699344 + 0.714785i \(0.253475\pi\)
\(702\) 3.22651 0.121777
\(703\) 62.2558 2.34802
\(704\) 6.90992 0.260427
\(705\) 13.0709 0.492280
\(706\) 5.14017 0.193453
\(707\) 12.1853 0.458274
\(708\) −4.63224 −0.174090
\(709\) 23.7078 0.890363 0.445182 0.895440i \(-0.353139\pi\)
0.445182 + 0.895440i \(0.353139\pi\)
\(710\) −6.53076 −0.245095
\(711\) 9.43468 0.353828
\(712\) 11.9312 0.447139
\(713\) −1.79258 −0.0671326
\(714\) −1.52054 −0.0569047
\(715\) −34.8588 −1.30365
\(716\) 9.25914 0.346030
\(717\) −15.6723 −0.585292
\(718\) −20.3859 −0.760795
\(719\) −13.0832 −0.487922 −0.243961 0.969785i \(-0.578447\pi\)
−0.243961 + 0.969785i \(0.578447\pi\)
\(720\) 2.38009 0.0887009
\(721\) −46.2782 −1.72349
\(722\) 27.2653 1.01471
\(723\) −22.4327 −0.834282
\(724\) −7.82235 −0.290715
\(725\) 1.40196 0.0520676
\(726\) 11.4824 0.426152
\(727\) 24.4396 0.906413 0.453207 0.891405i \(-0.350280\pi\)
0.453207 + 0.891405i \(0.350280\pi\)
\(728\) −31.6769 −1.17402
\(729\) 1.00000 0.0370370
\(730\) −2.00703 −0.0742834
\(731\) 0.382632 0.0141522
\(732\) −7.93903 −0.293435
\(733\) −43.8336 −1.61903 −0.809516 0.587097i \(-0.800271\pi\)
−0.809516 + 0.587097i \(0.800271\pi\)
\(734\) 3.46699 0.127969
\(735\) 0.146940 0.00541998
\(736\) 9.87249 0.363905
\(737\) 87.6347 3.22807
\(738\) −0.512417 −0.0188623
\(739\) −12.9690 −0.477072 −0.238536 0.971134i \(-0.576668\pi\)
−0.238536 + 0.971134i \(0.576668\pi\)
\(740\) 14.0542 0.516642
\(741\) −46.3521 −1.70279
\(742\) −9.63526 −0.353722
\(743\) 10.7100 0.392912 0.196456 0.980513i \(-0.437057\pi\)
0.196456 + 0.980513i \(0.437057\pi\)
\(744\) 2.05774 0.0754404
\(745\) 21.6297 0.792451
\(746\) −11.5700 −0.423606
\(747\) −6.69273 −0.244874
\(748\) −9.35632 −0.342101
\(749\) −5.14438 −0.187972
\(750\) −5.51088 −0.201229
\(751\) 17.0558 0.622376 0.311188 0.950348i \(-0.399273\pi\)
0.311188 + 0.950348i \(0.399273\pi\)
\(752\) 25.6309 0.934664
\(753\) −25.6094 −0.933260
\(754\) −1.19471 −0.0435087
\(755\) 5.78140 0.210407
\(756\) −4.47602 −0.162791
\(757\) −19.3246 −0.702363 −0.351182 0.936307i \(-0.614220\pi\)
−0.351182 + 0.936307i \(0.614220\pi\)
\(758\) 9.40440 0.341583
\(759\) −10.1780 −0.369436
\(760\) 18.8567 0.684005
\(761\) −52.9253 −1.91854 −0.959270 0.282492i \(-0.908839\pi\)
−0.959270 + 0.282492i \(0.908839\pi\)
\(762\) 3.49659 0.126668
\(763\) 14.1587 0.512580
\(764\) −22.1450 −0.801176
\(765\) −1.10171 −0.0398325
\(766\) 0.484668 0.0175118
\(767\) 15.6650 0.565629
\(768\) −4.09183 −0.147651
\(769\) −18.1482 −0.654442 −0.327221 0.944948i \(-0.606112\pi\)
−0.327221 + 0.944948i \(0.606112\pi\)
\(770\) −9.35248 −0.337040
\(771\) −11.3502 −0.408769
\(772\) 23.0249 0.828683
\(773\) 27.4209 0.986261 0.493131 0.869955i \(-0.335852\pi\)
0.493131 + 0.869955i \(0.335852\pi\)
\(774\) −0.217837 −0.00782998
\(775\) 3.72294 0.133732
\(776\) 14.5459 0.522168
\(777\) −20.3302 −0.729341
\(778\) −7.18707 −0.257669
\(779\) 7.36139 0.263749
\(780\) −10.4639 −0.374669
\(781\) 58.1309 2.08009
\(782\) −1.03788 −0.0371147
\(783\) −0.370279 −0.0132327
\(784\) 0.288137 0.0102906
\(785\) 1.10171 0.0393218
\(786\) −3.64979 −0.130184
\(787\) 52.8139 1.88261 0.941306 0.337553i \(-0.109599\pi\)
0.941306 + 0.337553i \(0.109599\pi\)
\(788\) 35.1503 1.25218
\(789\) −27.3107 −0.972285
\(790\) 5.91760 0.210539
\(791\) −43.5700 −1.54917
\(792\) 11.6835 0.415155
\(793\) 26.8476 0.953387
\(794\) −5.84679 −0.207495
\(795\) −6.98128 −0.247600
\(796\) −34.9959 −1.24040
\(797\) −40.3233 −1.42832 −0.714162 0.699980i \(-0.753192\pi\)
−0.714162 + 0.699980i \(0.753192\pi\)
\(798\) −12.4361 −0.440232
\(799\) −11.8642 −0.419725
\(800\) −20.5038 −0.724919
\(801\) −5.70127 −0.201444
\(802\) −5.55986 −0.196325
\(803\) 17.8647 0.630432
\(804\) 26.3063 0.927751
\(805\) 5.36433 0.189068
\(806\) −3.17257 −0.111749
\(807\) −23.4956 −0.827083
\(808\) −9.54771 −0.335887
\(809\) 10.1569 0.357098 0.178549 0.983931i \(-0.442860\pi\)
0.178549 + 0.983931i \(0.442860\pi\)
\(810\) 0.627218 0.0220382
\(811\) −2.32921 −0.0817896 −0.0408948 0.999163i \(-0.513021\pi\)
−0.0408948 + 0.999163i \(0.513021\pi\)
\(812\) 1.65738 0.0581625
\(813\) 26.4862 0.928910
\(814\) 24.1938 0.847993
\(815\) 27.4378 0.961103
\(816\) −2.16036 −0.0756277
\(817\) 3.12945 0.109485
\(818\) −4.86944 −0.170256
\(819\) 15.1367 0.528918
\(820\) 1.66183 0.0580336
\(821\) −46.3377 −1.61720 −0.808599 0.588360i \(-0.799774\pi\)
−0.808599 + 0.588360i \(0.799774\pi\)
\(822\) −9.06317 −0.316114
\(823\) −36.8757 −1.28541 −0.642703 0.766116i \(-0.722187\pi\)
−0.642703 + 0.766116i \(0.722187\pi\)
\(824\) 36.2611 1.26321
\(825\) 21.1382 0.735938
\(826\) 4.20285 0.146236
\(827\) −10.0503 −0.349484 −0.174742 0.984614i \(-0.555909\pi\)
−0.174742 + 0.984614i \(0.555909\pi\)
\(828\) −3.05523 −0.106176
\(829\) 29.4371 1.02239 0.511196 0.859464i \(-0.329203\pi\)
0.511196 + 0.859464i \(0.329203\pi\)
\(830\) −4.19780 −0.145708
\(831\) −25.2646 −0.876420
\(832\) −7.01447 −0.243183
\(833\) −0.133374 −0.00462115
\(834\) 2.13920 0.0740744
\(835\) 8.46155 0.292824
\(836\) −76.5229 −2.64660
\(837\) −0.983283 −0.0339872
\(838\) −7.77584 −0.268612
\(839\) 40.3755 1.39392 0.696959 0.717111i \(-0.254536\pi\)
0.696959 + 0.717111i \(0.254536\pi\)
\(840\) −6.15783 −0.212465
\(841\) −28.8629 −0.995272
\(842\) 22.5151 0.775922
\(843\) −17.7033 −0.609733
\(844\) 34.4834 1.18697
\(845\) 21.0640 0.724622
\(846\) 6.75442 0.232222
\(847\) 53.8680 1.85093
\(848\) −13.6896 −0.470104
\(849\) 4.60308 0.157977
\(850\) 2.15554 0.0739345
\(851\) −13.8769 −0.475694
\(852\) 17.4498 0.597819
\(853\) 22.3613 0.765638 0.382819 0.923823i \(-0.374953\pi\)
0.382819 + 0.923823i \(0.374953\pi\)
\(854\) 7.20312 0.246486
\(855\) −9.01062 −0.308157
\(856\) 4.03086 0.137772
\(857\) −18.2212 −0.622426 −0.311213 0.950340i \(-0.600735\pi\)
−0.311213 + 0.950340i \(0.600735\pi\)
\(858\) −18.0133 −0.614965
\(859\) 55.0141 1.87706 0.938529 0.345201i \(-0.112189\pi\)
0.938529 + 0.345201i \(0.112189\pi\)
\(860\) 0.706470 0.0240904
\(861\) −2.40393 −0.0819256
\(862\) −13.3442 −0.454506
\(863\) −27.1421 −0.923930 −0.461965 0.886898i \(-0.652855\pi\)
−0.461965 + 0.886898i \(0.652855\pi\)
\(864\) 5.41536 0.184234
\(865\) 7.52458 0.255843
\(866\) 1.21937 0.0414358
\(867\) 1.00000 0.0339618
\(868\) 4.40119 0.149386
\(869\) −52.6730 −1.78681
\(870\) −0.232246 −0.00787387
\(871\) −88.9607 −3.01432
\(872\) −11.0940 −0.375690
\(873\) −6.95071 −0.235246
\(874\) −8.48859 −0.287131
\(875\) −25.8534 −0.874006
\(876\) 5.36264 0.181187
\(877\) 17.8740 0.603561 0.301781 0.953377i \(-0.402419\pi\)
0.301781 + 0.953377i \(0.402419\pi\)
\(878\) −6.58347 −0.222181
\(879\) −22.8712 −0.771425
\(880\) −13.2879 −0.447934
\(881\) −13.0232 −0.438764 −0.219382 0.975639i \(-0.570404\pi\)
−0.219382 + 0.975639i \(0.570404\pi\)
\(882\) 0.0759316 0.00255675
\(883\) −44.5019 −1.49761 −0.748804 0.662792i \(-0.769371\pi\)
−0.748804 + 0.662792i \(0.769371\pi\)
\(884\) 9.49789 0.319449
\(885\) 3.04519 0.102363
\(886\) 18.4023 0.618236
\(887\) −42.4944 −1.42682 −0.713410 0.700747i \(-0.752850\pi\)
−0.713410 + 0.700747i \(0.752850\pi\)
\(888\) 15.9296 0.534563
\(889\) 16.4037 0.550164
\(890\) −3.57593 −0.119866
\(891\) −5.58292 −0.187035
\(892\) −17.0942 −0.572355
\(893\) −97.0342 −3.24712
\(894\) 11.1772 0.373820
\(895\) −6.08688 −0.203462
\(896\) −30.8091 −1.02926
\(897\) 10.3319 0.344974
\(898\) 3.77156 0.125859
\(899\) 0.364089 0.0121431
\(900\) 6.34528 0.211509
\(901\) 6.33675 0.211108
\(902\) 2.86078 0.0952536
\(903\) −1.02195 −0.0340083
\(904\) 34.1390 1.13545
\(905\) 5.14235 0.170937
\(906\) 2.98755 0.0992546
\(907\) 2.83718 0.0942069 0.0471035 0.998890i \(-0.485001\pi\)
0.0471035 + 0.998890i \(0.485001\pi\)
\(908\) −20.0592 −0.665688
\(909\) 4.56234 0.151323
\(910\) 9.49399 0.314723
\(911\) 36.1695 1.19835 0.599175 0.800618i \(-0.295496\pi\)
0.599175 + 0.800618i \(0.295496\pi\)
\(912\) −17.6690 −0.585079
\(913\) 37.3649 1.23660
\(914\) −4.20036 −0.138935
\(915\) 5.21905 0.172537
\(916\) −17.4310 −0.575936
\(917\) −17.1224 −0.565433
\(918\) −0.569311 −0.0187901
\(919\) 43.0251 1.41927 0.709634 0.704571i \(-0.248860\pi\)
0.709634 + 0.704571i \(0.248860\pi\)
\(920\) −4.20319 −0.138575
\(921\) −4.19223 −0.138139
\(922\) −12.0684 −0.397452
\(923\) −59.0104 −1.94235
\(924\) 24.9892 0.822085
\(925\) 28.8204 0.947609
\(926\) 4.45828 0.146508
\(927\) −17.3272 −0.569101
\(928\) −2.00520 −0.0658238
\(929\) −7.58073 −0.248716 −0.124358 0.992237i \(-0.539687\pi\)
−0.124358 + 0.992237i \(0.539687\pi\)
\(930\) −0.616733 −0.0202235
\(931\) −1.09083 −0.0357507
\(932\) −19.5522 −0.640453
\(933\) −2.94310 −0.0963527
\(934\) −5.22751 −0.171049
\(935\) 6.15077 0.201152
\(936\) −11.8603 −0.387665
\(937\) 30.5451 0.997865 0.498933 0.866641i \(-0.333726\pi\)
0.498933 + 0.866641i \(0.333726\pi\)
\(938\) −23.8678 −0.779312
\(939\) −1.06581 −0.0347814
\(940\) −21.9054 −0.714475
\(941\) −9.27347 −0.302307 −0.151153 0.988510i \(-0.548299\pi\)
−0.151153 + 0.988510i \(0.548299\pi\)
\(942\) 0.569311 0.0185492
\(943\) −1.64087 −0.0534340
\(944\) 5.97135 0.194351
\(945\) 2.94250 0.0957194
\(946\) 1.21616 0.0395409
\(947\) 52.3298 1.70049 0.850245 0.526387i \(-0.176454\pi\)
0.850245 + 0.526387i \(0.176454\pi\)
\(948\) −15.8114 −0.513531
\(949\) −18.1350 −0.588687
\(950\) 17.6296 0.571980
\(951\) −10.0695 −0.326526
\(952\) 5.58932 0.181151
\(953\) −32.0217 −1.03728 −0.518642 0.854991i \(-0.673562\pi\)
−0.518642 + 0.854991i \(0.673562\pi\)
\(954\) −3.60758 −0.116800
\(955\) 14.5579 0.471083
\(956\) 26.2650 0.849469
\(957\) 2.06724 0.0668243
\(958\) −8.65383 −0.279592
\(959\) −42.5185 −1.37299
\(960\) −1.36358 −0.0440093
\(961\) −30.0332 −0.968811
\(962\) −24.5599 −0.791842
\(963\) −1.92613 −0.0620687
\(964\) 37.5946 1.21084
\(965\) −15.1364 −0.487257
\(966\) 2.77202 0.0891884
\(967\) −35.7784 −1.15055 −0.575277 0.817958i \(-0.695106\pi\)
−0.575277 + 0.817958i \(0.695106\pi\)
\(968\) −42.2080 −1.35662
\(969\) 8.17874 0.262739
\(970\) −4.35961 −0.139979
\(971\) −20.9514 −0.672364 −0.336182 0.941797i \(-0.609136\pi\)
−0.336182 + 0.941797i \(0.609136\pi\)
\(972\) −1.67588 −0.0537540
\(973\) 10.0357 0.321731
\(974\) 0.00289876 9.28823e−5 0
\(975\) −21.4580 −0.687207
\(976\) 10.2341 0.327585
\(977\) 20.2146 0.646723 0.323362 0.946275i \(-0.395187\pi\)
0.323362 + 0.946275i \(0.395187\pi\)
\(978\) 14.1785 0.453378
\(979\) 31.8297 1.01728
\(980\) −0.246255 −0.00786633
\(981\) 5.30123 0.169255
\(982\) −0.633095 −0.0202029
\(983\) −2.31944 −0.0739786 −0.0369893 0.999316i \(-0.511777\pi\)
−0.0369893 + 0.999316i \(0.511777\pi\)
\(984\) 1.88359 0.0600465
\(985\) −23.1075 −0.736266
\(986\) 0.210804 0.00671337
\(987\) 31.6874 1.00862
\(988\) 77.6807 2.47135
\(989\) −0.697558 −0.0221811
\(990\) −3.50170 −0.111291
\(991\) 13.4184 0.426250 0.213125 0.977025i \(-0.431636\pi\)
0.213125 + 0.977025i \(0.431636\pi\)
\(992\) −5.32484 −0.169064
\(993\) 18.9636 0.601792
\(994\) −15.8323 −0.502169
\(995\) 23.0060 0.729339
\(996\) 11.2162 0.355400
\(997\) 13.6777 0.433178 0.216589 0.976263i \(-0.430507\pi\)
0.216589 + 0.976263i \(0.430507\pi\)
\(998\) 13.5925 0.430265
\(999\) −7.61191 −0.240830
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 \(a_p\))