Properties

Label 8015.2.a.l.1.21
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.21
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.05535 q^{2} +0.176354 q^{3} -0.886237 q^{4} -1.00000 q^{5} -0.186115 q^{6} -1.00000 q^{7} +3.04599 q^{8} -2.96890 q^{9} +O(q^{10})\) \(q-1.05535 q^{2} +0.176354 q^{3} -0.886237 q^{4} -1.00000 q^{5} -0.186115 q^{6} -1.00000 q^{7} +3.04599 q^{8} -2.96890 q^{9} +1.05535 q^{10} +3.44108 q^{11} -0.156292 q^{12} +6.99973 q^{13} +1.05535 q^{14} -0.176354 q^{15} -1.44211 q^{16} -1.17778 q^{17} +3.13323 q^{18} +1.90054 q^{19} +0.886237 q^{20} -0.176354 q^{21} -3.63154 q^{22} +7.72001 q^{23} +0.537173 q^{24} +1.00000 q^{25} -7.38716 q^{26} -1.05264 q^{27} +0.886237 q^{28} +9.32486 q^{29} +0.186115 q^{30} -5.28696 q^{31} -4.57005 q^{32} +0.606848 q^{33} +1.24297 q^{34} +1.00000 q^{35} +2.63115 q^{36} -8.69853 q^{37} -2.00574 q^{38} +1.23443 q^{39} -3.04599 q^{40} +7.81091 q^{41} +0.186115 q^{42} +2.29810 q^{43} -3.04961 q^{44} +2.96890 q^{45} -8.14731 q^{46} +8.63688 q^{47} -0.254322 q^{48} +1.00000 q^{49} -1.05535 q^{50} -0.207706 q^{51} -6.20342 q^{52} +5.56374 q^{53} +1.11090 q^{54} -3.44108 q^{55} -3.04599 q^{56} +0.335169 q^{57} -9.84099 q^{58} +1.85923 q^{59} +0.156292 q^{60} +0.0439074 q^{61} +5.57960 q^{62} +2.96890 q^{63} +7.70722 q^{64} -6.99973 q^{65} -0.640437 q^{66} -2.23381 q^{67} +1.04379 q^{68} +1.36145 q^{69} -1.05535 q^{70} +15.3936 q^{71} -9.04324 q^{72} +8.20243 q^{73} +9.17999 q^{74} +0.176354 q^{75} -1.68433 q^{76} -3.44108 q^{77} -1.30276 q^{78} -4.53514 q^{79} +1.44211 q^{80} +8.72106 q^{81} -8.24324 q^{82} -7.32652 q^{83} +0.156292 q^{84} +1.17778 q^{85} -2.42530 q^{86} +1.64448 q^{87} +10.4815 q^{88} -14.6526 q^{89} -3.13323 q^{90} -6.99973 q^{91} -6.84176 q^{92} -0.932378 q^{93} -9.11492 q^{94} -1.90054 q^{95} -0.805947 q^{96} -8.10190 q^{97} -1.05535 q^{98} -10.2162 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.05535 −0.746245 −0.373122 0.927782i \(-0.621713\pi\)
−0.373122 + 0.927782i \(0.621713\pi\)
\(3\) 0.176354 0.101818 0.0509090 0.998703i \(-0.483788\pi\)
0.0509090 + 0.998703i \(0.483788\pi\)
\(4\) −0.886237 −0.443119
\(5\) −1.00000 −0.447214
\(6\) −0.186115 −0.0759812
\(7\) −1.00000 −0.377964
\(8\) 3.04599 1.07692
\(9\) −2.96890 −0.989633
\(10\) 1.05535 0.333731
\(11\) 3.44108 1.03752 0.518762 0.854919i \(-0.326393\pi\)
0.518762 + 0.854919i \(0.326393\pi\)
\(12\) −0.156292 −0.0451175
\(13\) 6.99973 1.94137 0.970687 0.240346i \(-0.0772609\pi\)
0.970687 + 0.240346i \(0.0772609\pi\)
\(14\) 1.05535 0.282054
\(15\) −0.176354 −0.0455344
\(16\) −1.44211 −0.360527
\(17\) −1.17778 −0.285654 −0.142827 0.989748i \(-0.545619\pi\)
−0.142827 + 0.989748i \(0.545619\pi\)
\(18\) 3.13323 0.738509
\(19\) 1.90054 0.436015 0.218007 0.975947i \(-0.430044\pi\)
0.218007 + 0.975947i \(0.430044\pi\)
\(20\) 0.886237 0.198169
\(21\) −0.176354 −0.0384836
\(22\) −3.63154 −0.774246
\(23\) 7.72001 1.60973 0.804866 0.593456i \(-0.202237\pi\)
0.804866 + 0.593456i \(0.202237\pi\)
\(24\) 0.537173 0.109650
\(25\) 1.00000 0.200000
\(26\) −7.38716 −1.44874
\(27\) −1.05264 −0.202581
\(28\) 0.886237 0.167483
\(29\) 9.32486 1.73158 0.865791 0.500405i \(-0.166816\pi\)
0.865791 + 0.500405i \(0.166816\pi\)
\(30\) 0.186115 0.0339798
\(31\) −5.28696 −0.949567 −0.474783 0.880103i \(-0.657474\pi\)
−0.474783 + 0.880103i \(0.657474\pi\)
\(32\) −4.57005 −0.807878
\(33\) 0.606848 0.105639
\(34\) 1.24297 0.213167
\(35\) 1.00000 0.169031
\(36\) 2.63115 0.438525
\(37\) −8.69853 −1.43003 −0.715015 0.699109i \(-0.753580\pi\)
−0.715015 + 0.699109i \(0.753580\pi\)
\(38\) −2.00574 −0.325374
\(39\) 1.23443 0.197667
\(40\) −3.04599 −0.481613
\(41\) 7.81091 1.21986 0.609930 0.792456i \(-0.291198\pi\)
0.609930 + 0.792456i \(0.291198\pi\)
\(42\) 0.186115 0.0287182
\(43\) 2.29810 0.350458 0.175229 0.984528i \(-0.443933\pi\)
0.175229 + 0.984528i \(0.443933\pi\)
\(44\) −3.04961 −0.459746
\(45\) 2.96890 0.442577
\(46\) −8.14731 −1.20125
\(47\) 8.63688 1.25982 0.629909 0.776669i \(-0.283092\pi\)
0.629909 + 0.776669i \(0.283092\pi\)
\(48\) −0.254322 −0.0367082
\(49\) 1.00000 0.142857
\(50\) −1.05535 −0.149249
\(51\) −0.207706 −0.0290847
\(52\) −6.20342 −0.860259
\(53\) 5.56374 0.764238 0.382119 0.924113i \(-0.375194\pi\)
0.382119 + 0.924113i \(0.375194\pi\)
\(54\) 1.11090 0.151175
\(55\) −3.44108 −0.463995
\(56\) −3.04599 −0.407037
\(57\) 0.335169 0.0443942
\(58\) −9.84099 −1.29218
\(59\) 1.85923 0.242051 0.121026 0.992649i \(-0.461382\pi\)
0.121026 + 0.992649i \(0.461382\pi\)
\(60\) 0.156292 0.0201772
\(61\) 0.0439074 0.00562177 0.00281088 0.999996i \(-0.499105\pi\)
0.00281088 + 0.999996i \(0.499105\pi\)
\(62\) 5.57960 0.708609
\(63\) 2.96890 0.374046
\(64\) 7.70722 0.963402
\(65\) −6.99973 −0.868209
\(66\) −0.640437 −0.0788323
\(67\) −2.23381 −0.272903 −0.136452 0.990647i \(-0.543570\pi\)
−0.136452 + 0.990647i \(0.543570\pi\)
\(68\) 1.04379 0.126578
\(69\) 1.36145 0.163900
\(70\) −1.05535 −0.126138
\(71\) 15.3936 1.82688 0.913440 0.406972i \(-0.133415\pi\)
0.913440 + 0.406972i \(0.133415\pi\)
\(72\) −9.04324 −1.06576
\(73\) 8.20243 0.960022 0.480011 0.877262i \(-0.340633\pi\)
0.480011 + 0.877262i \(0.340633\pi\)
\(74\) 9.17999 1.06715
\(75\) 0.176354 0.0203636
\(76\) −1.68433 −0.193206
\(77\) −3.44108 −0.392147
\(78\) −1.30276 −0.147508
\(79\) −4.53514 −0.510243 −0.255121 0.966909i \(-0.582115\pi\)
−0.255121 + 0.966909i \(0.582115\pi\)
\(80\) 1.44211 0.161233
\(81\) 8.72106 0.969007
\(82\) −8.24324 −0.910314
\(83\) −7.32652 −0.804190 −0.402095 0.915598i \(-0.631718\pi\)
−0.402095 + 0.915598i \(0.631718\pi\)
\(84\) 0.156292 0.0170528
\(85\) 1.17778 0.127748
\(86\) −2.42530 −0.261527
\(87\) 1.64448 0.176306
\(88\) 10.4815 1.11733
\(89\) −14.6526 −1.55317 −0.776587 0.630010i \(-0.783051\pi\)
−0.776587 + 0.630010i \(0.783051\pi\)
\(90\) −3.13323 −0.330271
\(91\) −6.99973 −0.733771
\(92\) −6.84176 −0.713303
\(93\) −0.932378 −0.0966831
\(94\) −9.11492 −0.940133
\(95\) −1.90054 −0.194992
\(96\) −0.805947 −0.0822566
\(97\) −8.10190 −0.822624 −0.411312 0.911495i \(-0.634929\pi\)
−0.411312 + 0.911495i \(0.634929\pi\)
\(98\) −1.05535 −0.106606
\(99\) −10.2162 −1.02677
\(100\) −0.886237 −0.0886237
\(101\) 6.83585 0.680193 0.340096 0.940391i \(-0.389540\pi\)
0.340096 + 0.940391i \(0.389540\pi\)
\(102\) 0.219203 0.0217043
\(103\) 12.1047 1.19271 0.596354 0.802722i \(-0.296616\pi\)
0.596354 + 0.802722i \(0.296616\pi\)
\(104\) 21.3211 2.09070
\(105\) 0.176354 0.0172104
\(106\) −5.87169 −0.570309
\(107\) −3.99447 −0.386160 −0.193080 0.981183i \(-0.561848\pi\)
−0.193080 + 0.981183i \(0.561848\pi\)
\(108\) 0.932888 0.0897672
\(109\) −8.18543 −0.784022 −0.392011 0.919960i \(-0.628221\pi\)
−0.392011 + 0.919960i \(0.628221\pi\)
\(110\) 3.63154 0.346254
\(111\) −1.53402 −0.145603
\(112\) 1.44211 0.136267
\(113\) −16.8701 −1.58701 −0.793504 0.608566i \(-0.791745\pi\)
−0.793504 + 0.608566i \(0.791745\pi\)
\(114\) −0.353720 −0.0331289
\(115\) −7.72001 −0.719894
\(116\) −8.26404 −0.767296
\(117\) −20.7815 −1.92125
\(118\) −1.96214 −0.180629
\(119\) 1.17778 0.107967
\(120\) −0.537173 −0.0490369
\(121\) 0.841001 0.0764546
\(122\) −0.0463377 −0.00419522
\(123\) 1.37749 0.124204
\(124\) 4.68550 0.420771
\(125\) −1.00000 −0.0894427
\(126\) −3.13323 −0.279130
\(127\) −14.1236 −1.25327 −0.626634 0.779313i \(-0.715568\pi\)
−0.626634 + 0.779313i \(0.715568\pi\)
\(128\) 1.00629 0.0889441
\(129\) 0.405280 0.0356829
\(130\) 7.38716 0.647897
\(131\) −12.0149 −1.04975 −0.524874 0.851180i \(-0.675887\pi\)
−0.524874 + 0.851180i \(0.675887\pi\)
\(132\) −0.537811 −0.0468104
\(133\) −1.90054 −0.164798
\(134\) 2.35745 0.203653
\(135\) 1.05264 0.0905968
\(136\) −3.58750 −0.307626
\(137\) 8.09677 0.691754 0.345877 0.938280i \(-0.387581\pi\)
0.345877 + 0.938280i \(0.387581\pi\)
\(138\) −1.43681 −0.122309
\(139\) 4.28815 0.363716 0.181858 0.983325i \(-0.441789\pi\)
0.181858 + 0.983325i \(0.441789\pi\)
\(140\) −0.886237 −0.0749007
\(141\) 1.52315 0.128272
\(142\) −16.2456 −1.36330
\(143\) 24.0866 2.01422
\(144\) 4.28148 0.356790
\(145\) −9.32486 −0.774387
\(146\) −8.65643 −0.716412
\(147\) 0.176354 0.0145454
\(148\) 7.70896 0.633673
\(149\) 6.63875 0.543867 0.271934 0.962316i \(-0.412337\pi\)
0.271934 + 0.962316i \(0.412337\pi\)
\(150\) −0.186115 −0.0151962
\(151\) −0.535768 −0.0436002 −0.0218001 0.999762i \(-0.506940\pi\)
−0.0218001 + 0.999762i \(0.506940\pi\)
\(152\) 5.78903 0.469553
\(153\) 3.49671 0.282692
\(154\) 3.63154 0.292638
\(155\) 5.28696 0.424659
\(156\) −1.09400 −0.0875899
\(157\) 8.74303 0.697769 0.348885 0.937166i \(-0.386560\pi\)
0.348885 + 0.937166i \(0.386560\pi\)
\(158\) 4.78615 0.380766
\(159\) 0.981188 0.0778132
\(160\) 4.57005 0.361294
\(161\) −7.72001 −0.608422
\(162\) −9.20377 −0.723116
\(163\) −17.0760 −1.33749 −0.668747 0.743490i \(-0.733169\pi\)
−0.668747 + 0.743490i \(0.733169\pi\)
\(164\) −6.92232 −0.540542
\(165\) −0.606848 −0.0472430
\(166\) 7.73204 0.600122
\(167\) 6.63610 0.513517 0.256758 0.966476i \(-0.417346\pi\)
0.256758 + 0.966476i \(0.417346\pi\)
\(168\) −0.537173 −0.0414438
\(169\) 35.9962 2.76894
\(170\) −1.24297 −0.0953314
\(171\) −5.64252 −0.431494
\(172\) −2.03667 −0.155294
\(173\) −10.7189 −0.814939 −0.407470 0.913219i \(-0.633589\pi\)
−0.407470 + 0.913219i \(0.633589\pi\)
\(174\) −1.73550 −0.131568
\(175\) −1.00000 −0.0755929
\(176\) −4.96241 −0.374056
\(177\) 0.327883 0.0246452
\(178\) 15.4636 1.15905
\(179\) −18.7926 −1.40462 −0.702312 0.711870i \(-0.747849\pi\)
−0.702312 + 0.711870i \(0.747849\pi\)
\(180\) −2.63115 −0.196114
\(181\) 0.679653 0.0505182 0.0252591 0.999681i \(-0.491959\pi\)
0.0252591 + 0.999681i \(0.491959\pi\)
\(182\) 7.38716 0.547573
\(183\) 0.00774325 0.000572398 0
\(184\) 23.5151 1.73355
\(185\) 8.69853 0.639529
\(186\) 0.983985 0.0721492
\(187\) −4.05283 −0.296372
\(188\) −7.65432 −0.558249
\(189\) 1.05264 0.0765683
\(190\) 2.00574 0.145512
\(191\) 9.78238 0.707828 0.353914 0.935278i \(-0.384850\pi\)
0.353914 + 0.935278i \(0.384850\pi\)
\(192\) 1.35920 0.0980918
\(193\) −11.3460 −0.816706 −0.408353 0.912824i \(-0.633897\pi\)
−0.408353 + 0.912824i \(0.633897\pi\)
\(194\) 8.55034 0.613879
\(195\) −1.23443 −0.0883994
\(196\) −0.886237 −0.0633027
\(197\) −13.0279 −0.928201 −0.464100 0.885783i \(-0.653622\pi\)
−0.464100 + 0.885783i \(0.653622\pi\)
\(198\) 10.7817 0.766220
\(199\) 6.11713 0.433632 0.216816 0.976212i \(-0.430433\pi\)
0.216816 + 0.976212i \(0.430433\pi\)
\(200\) 3.04599 0.215384
\(201\) −0.393942 −0.0277865
\(202\) −7.21422 −0.507590
\(203\) −9.32486 −0.654477
\(204\) 0.184077 0.0128880
\(205\) −7.81091 −0.545538
\(206\) −12.7747 −0.890052
\(207\) −22.9199 −1.59304
\(208\) −10.0944 −0.699919
\(209\) 6.53991 0.452375
\(210\) −0.186115 −0.0128432
\(211\) 5.38574 0.370770 0.185385 0.982666i \(-0.440647\pi\)
0.185385 + 0.982666i \(0.440647\pi\)
\(212\) −4.93079 −0.338648
\(213\) 2.71472 0.186010
\(214\) 4.21556 0.288170
\(215\) −2.29810 −0.156729
\(216\) −3.20633 −0.218163
\(217\) 5.28696 0.358903
\(218\) 8.63849 0.585073
\(219\) 1.44653 0.0977476
\(220\) 3.04961 0.205605
\(221\) −8.24413 −0.554560
\(222\) 1.61893 0.108655
\(223\) 2.53650 0.169857 0.0849284 0.996387i \(-0.472934\pi\)
0.0849284 + 0.996387i \(0.472934\pi\)
\(224\) 4.57005 0.305349
\(225\) −2.96890 −0.197927
\(226\) 17.8039 1.18430
\(227\) −14.8731 −0.987164 −0.493582 0.869699i \(-0.664313\pi\)
−0.493582 + 0.869699i \(0.664313\pi\)
\(228\) −0.297039 −0.0196719
\(229\) 1.00000 0.0660819
\(230\) 8.14731 0.537218
\(231\) −0.606848 −0.0399277
\(232\) 28.4034 1.86478
\(233\) −6.46901 −0.423799 −0.211899 0.977292i \(-0.567965\pi\)
−0.211899 + 0.977292i \(0.567965\pi\)
\(234\) 21.9317 1.43372
\(235\) −8.63688 −0.563408
\(236\) −1.64772 −0.107257
\(237\) −0.799790 −0.0519519
\(238\) −1.24297 −0.0805697
\(239\) 10.3407 0.668882 0.334441 0.942417i \(-0.391452\pi\)
0.334441 + 0.942417i \(0.391452\pi\)
\(240\) 0.254322 0.0164164
\(241\) −11.1851 −0.720497 −0.360249 0.932856i \(-0.617308\pi\)
−0.360249 + 0.932856i \(0.617308\pi\)
\(242\) −0.887550 −0.0570539
\(243\) 4.69591 0.301243
\(244\) −0.0389124 −0.00249111
\(245\) −1.00000 −0.0638877
\(246\) −1.45373 −0.0926864
\(247\) 13.3033 0.846468
\(248\) −16.1040 −1.02261
\(249\) −1.29206 −0.0818810
\(250\) 1.05535 0.0667462
\(251\) 14.7123 0.928633 0.464316 0.885669i \(-0.346300\pi\)
0.464316 + 0.885669i \(0.346300\pi\)
\(252\) −2.63115 −0.165747
\(253\) 26.5651 1.67014
\(254\) 14.9054 0.935245
\(255\) 0.207706 0.0130071
\(256\) −16.4764 −1.02978
\(257\) 31.0456 1.93657 0.968286 0.249845i \(-0.0803796\pi\)
0.968286 + 0.249845i \(0.0803796\pi\)
\(258\) −0.427712 −0.0266282
\(259\) 8.69853 0.540501
\(260\) 6.20342 0.384720
\(261\) −27.6846 −1.71363
\(262\) 12.6799 0.783369
\(263\) 13.4504 0.829384 0.414692 0.909962i \(-0.363889\pi\)
0.414692 + 0.909962i \(0.363889\pi\)
\(264\) 1.84845 0.113764
\(265\) −5.56374 −0.341778
\(266\) 2.00574 0.122980
\(267\) −2.58405 −0.158141
\(268\) 1.97969 0.120929
\(269\) −2.69957 −0.164596 −0.0822980 0.996608i \(-0.526226\pi\)
−0.0822980 + 0.996608i \(0.526226\pi\)
\(270\) −1.11090 −0.0676074
\(271\) 3.68602 0.223910 0.111955 0.993713i \(-0.464289\pi\)
0.111955 + 0.993713i \(0.464289\pi\)
\(272\) 1.69849 0.102986
\(273\) −1.23443 −0.0747111
\(274\) −8.54493 −0.516218
\(275\) 3.44108 0.207505
\(276\) −1.20657 −0.0726271
\(277\) 25.9698 1.56037 0.780187 0.625547i \(-0.215124\pi\)
0.780187 + 0.625547i \(0.215124\pi\)
\(278\) −4.52550 −0.271421
\(279\) 15.6965 0.939723
\(280\) 3.04599 0.182033
\(281\) 3.83290 0.228652 0.114326 0.993443i \(-0.463529\pi\)
0.114326 + 0.993443i \(0.463529\pi\)
\(282\) −1.60745 −0.0957225
\(283\) −24.3622 −1.44818 −0.724092 0.689704i \(-0.757741\pi\)
−0.724092 + 0.689704i \(0.757741\pi\)
\(284\) −13.6424 −0.809525
\(285\) −0.335169 −0.0198537
\(286\) −25.4198 −1.50310
\(287\) −7.81091 −0.461064
\(288\) 13.5680 0.799503
\(289\) −15.6128 −0.918402
\(290\) 9.84099 0.577883
\(291\) −1.42880 −0.0837580
\(292\) −7.26930 −0.425404
\(293\) −11.2255 −0.655804 −0.327902 0.944712i \(-0.606342\pi\)
−0.327902 + 0.944712i \(0.606342\pi\)
\(294\) −0.186115 −0.0108545
\(295\) −1.85923 −0.108249
\(296\) −26.4956 −1.54003
\(297\) −3.62221 −0.210182
\(298\) −7.00620 −0.405858
\(299\) 54.0379 3.12509
\(300\) −0.156292 −0.00902350
\(301\) −2.29810 −0.132461
\(302\) 0.565423 0.0325364
\(303\) 1.20553 0.0692559
\(304\) −2.74079 −0.157195
\(305\) −0.0439074 −0.00251413
\(306\) −3.69025 −0.210958
\(307\) 34.5744 1.97326 0.986631 0.162967i \(-0.0521065\pi\)
0.986631 + 0.162967i \(0.0521065\pi\)
\(308\) 3.04961 0.173768
\(309\) 2.13471 0.121439
\(310\) −5.57960 −0.316900
\(311\) −18.8728 −1.07018 −0.535090 0.844795i \(-0.679722\pi\)
−0.535090 + 0.844795i \(0.679722\pi\)
\(312\) 3.76006 0.212872
\(313\) 22.2370 1.25691 0.628455 0.777846i \(-0.283688\pi\)
0.628455 + 0.777846i \(0.283688\pi\)
\(314\) −9.22695 −0.520707
\(315\) −2.96890 −0.167279
\(316\) 4.01921 0.226098
\(317\) 14.7211 0.826822 0.413411 0.910545i \(-0.364337\pi\)
0.413411 + 0.910545i \(0.364337\pi\)
\(318\) −1.03550 −0.0580677
\(319\) 32.0875 1.79656
\(320\) −7.70722 −0.430847
\(321\) −0.704441 −0.0393181
\(322\) 8.14731 0.454032
\(323\) −2.23842 −0.124549
\(324\) −7.72893 −0.429385
\(325\) 6.99973 0.388275
\(326\) 18.0211 0.998098
\(327\) −1.44353 −0.0798276
\(328\) 23.7920 1.31369
\(329\) −8.63688 −0.476166
\(330\) 0.640437 0.0352549
\(331\) 29.4760 1.62015 0.810074 0.586327i \(-0.199427\pi\)
0.810074 + 0.586327i \(0.199427\pi\)
\(332\) 6.49303 0.356351
\(333\) 25.8251 1.41521
\(334\) −7.00340 −0.383209
\(335\) 2.23381 0.122046
\(336\) 0.254322 0.0138744
\(337\) 20.5174 1.11765 0.558827 0.829284i \(-0.311252\pi\)
0.558827 + 0.829284i \(0.311252\pi\)
\(338\) −37.9885 −2.06630
\(339\) −2.97511 −0.161586
\(340\) −1.04379 −0.0566076
\(341\) −18.1928 −0.985198
\(342\) 5.95483 0.322001
\(343\) −1.00000 −0.0539949
\(344\) 7.00000 0.377415
\(345\) −1.36145 −0.0732983
\(346\) 11.3121 0.608144
\(347\) 15.9899 0.858384 0.429192 0.903213i \(-0.358798\pi\)
0.429192 + 0.903213i \(0.358798\pi\)
\(348\) −1.45740 −0.0781246
\(349\) 15.5304 0.831326 0.415663 0.909519i \(-0.363550\pi\)
0.415663 + 0.909519i \(0.363550\pi\)
\(350\) 1.05535 0.0564108
\(351\) −7.36819 −0.393285
\(352\) −15.7259 −0.838192
\(353\) −16.1927 −0.861852 −0.430926 0.902387i \(-0.641813\pi\)
−0.430926 + 0.902387i \(0.641813\pi\)
\(354\) −0.346031 −0.0183913
\(355\) −15.3936 −0.817006
\(356\) 12.9857 0.688240
\(357\) 0.207706 0.0109930
\(358\) 19.8327 1.04819
\(359\) 29.1666 1.53935 0.769677 0.638434i \(-0.220417\pi\)
0.769677 + 0.638434i \(0.220417\pi\)
\(360\) 9.04324 0.476620
\(361\) −15.3879 −0.809891
\(362\) −0.717271 −0.0376989
\(363\) 0.148314 0.00778446
\(364\) 6.20342 0.325147
\(365\) −8.20243 −0.429335
\(366\) −0.00817184 −0.000427149 0
\(367\) −5.07904 −0.265124 −0.132562 0.991175i \(-0.542320\pi\)
−0.132562 + 0.991175i \(0.542320\pi\)
\(368\) −11.1331 −0.580353
\(369\) −23.1898 −1.20721
\(370\) −9.17999 −0.477245
\(371\) −5.56374 −0.288855
\(372\) 0.826308 0.0428421
\(373\) 21.3097 1.10338 0.551688 0.834050i \(-0.313984\pi\)
0.551688 + 0.834050i \(0.313984\pi\)
\(374\) 4.27715 0.221166
\(375\) −0.176354 −0.00910689
\(376\) 26.3078 1.35672
\(377\) 65.2714 3.36165
\(378\) −1.11090 −0.0571387
\(379\) −36.5100 −1.87539 −0.937697 0.347455i \(-0.887046\pi\)
−0.937697 + 0.347455i \(0.887046\pi\)
\(380\) 1.68433 0.0864044
\(381\) −2.49076 −0.127605
\(382\) −10.3238 −0.528213
\(383\) 4.21828 0.215544 0.107772 0.994176i \(-0.465628\pi\)
0.107772 + 0.994176i \(0.465628\pi\)
\(384\) 0.177463 0.00905612
\(385\) 3.44108 0.175373
\(386\) 11.9740 0.609462
\(387\) −6.82284 −0.346824
\(388\) 7.18021 0.364520
\(389\) −2.43112 −0.123263 −0.0616313 0.998099i \(-0.519630\pi\)
−0.0616313 + 0.998099i \(0.519630\pi\)
\(390\) 1.30276 0.0659676
\(391\) −9.09247 −0.459826
\(392\) 3.04599 0.153846
\(393\) −2.11888 −0.106883
\(394\) 13.7490 0.692665
\(395\) 4.53514 0.228187
\(396\) 9.05398 0.454980
\(397\) 3.62747 0.182057 0.0910287 0.995848i \(-0.470984\pi\)
0.0910287 + 0.995848i \(0.470984\pi\)
\(398\) −6.45571 −0.323596
\(399\) −0.335169 −0.0167794
\(400\) −1.44211 −0.0721055
\(401\) 17.3416 0.866000 0.433000 0.901394i \(-0.357455\pi\)
0.433000 + 0.901394i \(0.357455\pi\)
\(402\) 0.415746 0.0207355
\(403\) −37.0073 −1.84346
\(404\) −6.05819 −0.301406
\(405\) −8.72106 −0.433353
\(406\) 9.84099 0.488400
\(407\) −29.9323 −1.48369
\(408\) −0.632671 −0.0313219
\(409\) 2.41659 0.119493 0.0597465 0.998214i \(-0.480971\pi\)
0.0597465 + 0.998214i \(0.480971\pi\)
\(410\) 8.24324 0.407105
\(411\) 1.42790 0.0704331
\(412\) −10.7276 −0.528511
\(413\) −1.85923 −0.0914868
\(414\) 24.1885 1.18880
\(415\) 7.32652 0.359644
\(416\) −31.9891 −1.56839
\(417\) 0.756233 0.0370329
\(418\) −6.90190 −0.337583
\(419\) 7.35049 0.359095 0.179548 0.983749i \(-0.442537\pi\)
0.179548 + 0.983749i \(0.442537\pi\)
\(420\) −0.156292 −0.00762625
\(421\) 8.66867 0.422485 0.211243 0.977434i \(-0.432249\pi\)
0.211243 + 0.977434i \(0.432249\pi\)
\(422\) −5.68384 −0.276685
\(423\) −25.6420 −1.24676
\(424\) 16.9471 0.823023
\(425\) −1.17778 −0.0571307
\(426\) −2.86498 −0.138809
\(427\) −0.0439074 −0.00212483
\(428\) 3.54005 0.171115
\(429\) 4.24777 0.205084
\(430\) 2.42530 0.116959
\(431\) 18.9096 0.910842 0.455421 0.890276i \(-0.349489\pi\)
0.455421 + 0.890276i \(0.349489\pi\)
\(432\) 1.51802 0.0730359
\(433\) 30.7692 1.47867 0.739337 0.673335i \(-0.235139\pi\)
0.739337 + 0.673335i \(0.235139\pi\)
\(434\) −5.57960 −0.267829
\(435\) −1.64448 −0.0788466
\(436\) 7.25423 0.347415
\(437\) 14.6722 0.701867
\(438\) −1.52660 −0.0729437
\(439\) −25.3465 −1.20972 −0.604861 0.796331i \(-0.706771\pi\)
−0.604861 + 0.796331i \(0.706771\pi\)
\(440\) −10.4815 −0.499685
\(441\) −2.96890 −0.141376
\(442\) 8.70044 0.413838
\(443\) −16.2193 −0.770604 −0.385302 0.922790i \(-0.625903\pi\)
−0.385302 + 0.922790i \(0.625903\pi\)
\(444\) 1.35951 0.0645194
\(445\) 14.6526 0.694601
\(446\) −2.67690 −0.126755
\(447\) 1.17077 0.0553755
\(448\) −7.70722 −0.364132
\(449\) −33.2507 −1.56920 −0.784599 0.620003i \(-0.787131\pi\)
−0.784599 + 0.620003i \(0.787131\pi\)
\(450\) 3.13323 0.147702
\(451\) 26.8779 1.26563
\(452\) 14.9509 0.703232
\(453\) −0.0944849 −0.00443929
\(454\) 15.6963 0.736666
\(455\) 6.99973 0.328152
\(456\) 1.02092 0.0478090
\(457\) −14.7416 −0.689583 −0.344792 0.938679i \(-0.612050\pi\)
−0.344792 + 0.938679i \(0.612050\pi\)
\(458\) −1.05535 −0.0493132
\(459\) 1.23978 0.0578679
\(460\) 6.84176 0.318999
\(461\) 20.2338 0.942382 0.471191 0.882031i \(-0.343824\pi\)
0.471191 + 0.882031i \(0.343824\pi\)
\(462\) 0.640437 0.0297958
\(463\) 9.79492 0.455209 0.227604 0.973754i \(-0.426911\pi\)
0.227604 + 0.973754i \(0.426911\pi\)
\(464\) −13.4475 −0.624283
\(465\) 0.932378 0.0432380
\(466\) 6.82706 0.316258
\(467\) −0.857035 −0.0396589 −0.0198294 0.999803i \(-0.506312\pi\)
−0.0198294 + 0.999803i \(0.506312\pi\)
\(468\) 18.4173 0.851341
\(469\) 2.23381 0.103148
\(470\) 9.11492 0.420440
\(471\) 1.54187 0.0710456
\(472\) 5.66320 0.260670
\(473\) 7.90795 0.363608
\(474\) 0.844058 0.0387689
\(475\) 1.90054 0.0872029
\(476\) −1.04379 −0.0478421
\(477\) −16.5182 −0.756315
\(478\) −10.9130 −0.499150
\(479\) −27.9193 −1.27567 −0.637834 0.770174i \(-0.720169\pi\)
−0.637834 + 0.770174i \(0.720169\pi\)
\(480\) 0.805947 0.0367863
\(481\) −60.8873 −2.77622
\(482\) 11.8042 0.537668
\(483\) −1.36145 −0.0619483
\(484\) −0.745326 −0.0338785
\(485\) 8.10190 0.367888
\(486\) −4.95583 −0.224801
\(487\) 30.3011 1.37307 0.686537 0.727095i \(-0.259130\pi\)
0.686537 + 0.727095i \(0.259130\pi\)
\(488\) 0.133742 0.00605419
\(489\) −3.01142 −0.136181
\(490\) 1.05535 0.0476758
\(491\) −8.69063 −0.392203 −0.196101 0.980584i \(-0.562828\pi\)
−0.196101 + 0.980584i \(0.562828\pi\)
\(492\) −1.22078 −0.0550370
\(493\) −10.9826 −0.494633
\(494\) −14.0396 −0.631672
\(495\) 10.2162 0.459184
\(496\) 7.62438 0.342345
\(497\) −15.3936 −0.690496
\(498\) 1.36358 0.0611033
\(499\) 11.1086 0.497290 0.248645 0.968595i \(-0.420015\pi\)
0.248645 + 0.968595i \(0.420015\pi\)
\(500\) 0.886237 0.0396337
\(501\) 1.17030 0.0522853
\(502\) −15.5266 −0.692987
\(503\) 1.81849 0.0810823 0.0405412 0.999178i \(-0.487092\pi\)
0.0405412 + 0.999178i \(0.487092\pi\)
\(504\) 9.04324 0.402818
\(505\) −6.83585 −0.304192
\(506\) −28.0355 −1.24633
\(507\) 6.34807 0.281928
\(508\) 12.5169 0.555347
\(509\) 23.4429 1.03909 0.519544 0.854443i \(-0.326102\pi\)
0.519544 + 0.854443i \(0.326102\pi\)
\(510\) −0.219203 −0.00970646
\(511\) −8.20243 −0.362854
\(512\) 15.3758 0.679521
\(513\) −2.00059 −0.0883281
\(514\) −32.7640 −1.44516
\(515\) −12.1047 −0.533395
\(516\) −0.359174 −0.0158118
\(517\) 29.7201 1.30709
\(518\) −9.17999 −0.403346
\(519\) −1.89031 −0.0829756
\(520\) −21.3211 −0.934992
\(521\) −25.8648 −1.13316 −0.566579 0.824007i \(-0.691733\pi\)
−0.566579 + 0.824007i \(0.691733\pi\)
\(522\) 29.2169 1.27879
\(523\) −1.38587 −0.0605997 −0.0302999 0.999541i \(-0.509646\pi\)
−0.0302999 + 0.999541i \(0.509646\pi\)
\(524\) 10.6481 0.465163
\(525\) −0.176354 −0.00769672
\(526\) −14.1948 −0.618924
\(527\) 6.22688 0.271247
\(528\) −0.875141 −0.0380856
\(529\) 36.5985 1.59124
\(530\) 5.87169 0.255050
\(531\) −5.51987 −0.239542
\(532\) 1.68433 0.0730251
\(533\) 54.6742 2.36820
\(534\) 2.72707 0.118012
\(535\) 3.99447 0.172696
\(536\) −6.80416 −0.293895
\(537\) −3.31415 −0.143016
\(538\) 2.84900 0.122829
\(539\) 3.44108 0.148218
\(540\) −0.932888 −0.0401451
\(541\) 0.469849 0.0202004 0.0101002 0.999949i \(-0.496785\pi\)
0.0101002 + 0.999949i \(0.496785\pi\)
\(542\) −3.89004 −0.167092
\(543\) 0.119860 0.00514367
\(544\) 5.38251 0.230773
\(545\) 8.18543 0.350625
\(546\) 1.30276 0.0557528
\(547\) 22.5965 0.966156 0.483078 0.875577i \(-0.339519\pi\)
0.483078 + 0.875577i \(0.339519\pi\)
\(548\) −7.17566 −0.306529
\(549\) −0.130357 −0.00556349
\(550\) −3.63154 −0.154849
\(551\) 17.7223 0.754995
\(552\) 4.14698 0.176507
\(553\) 4.53514 0.192854
\(554\) −27.4072 −1.16442
\(555\) 1.53402 0.0651156
\(556\) −3.80032 −0.161169
\(557\) −11.2564 −0.476949 −0.238474 0.971149i \(-0.576647\pi\)
−0.238474 + 0.971149i \(0.576647\pi\)
\(558\) −16.5653 −0.701263
\(559\) 16.0861 0.680369
\(560\) −1.44211 −0.0609402
\(561\) −0.714733 −0.0301760
\(562\) −4.04505 −0.170630
\(563\) −16.8583 −0.710493 −0.355246 0.934773i \(-0.615603\pi\)
−0.355246 + 0.934773i \(0.615603\pi\)
\(564\) −1.34987 −0.0568398
\(565\) 16.8701 0.709731
\(566\) 25.7107 1.08070
\(567\) −8.72106 −0.366250
\(568\) 46.8887 1.96740
\(569\) −21.2557 −0.891084 −0.445542 0.895261i \(-0.646989\pi\)
−0.445542 + 0.895261i \(0.646989\pi\)
\(570\) 0.353720 0.0148157
\(571\) 32.7283 1.36964 0.684819 0.728713i \(-0.259881\pi\)
0.684819 + 0.728713i \(0.259881\pi\)
\(572\) −21.3464 −0.892539
\(573\) 1.72516 0.0720697
\(574\) 8.24324 0.344066
\(575\) 7.72001 0.321947
\(576\) −22.8820 −0.953415
\(577\) −4.36463 −0.181702 −0.0908510 0.995864i \(-0.528959\pi\)
−0.0908510 + 0.995864i \(0.528959\pi\)
\(578\) 16.4770 0.685353
\(579\) −2.00092 −0.0831554
\(580\) 8.26404 0.343145
\(581\) 7.32652 0.303955
\(582\) 1.50789 0.0625039
\(583\) 19.1452 0.792915
\(584\) 24.9845 1.03387
\(585\) 20.7815 0.859208
\(586\) 11.8469 0.489390
\(587\) 25.0269 1.03297 0.516485 0.856296i \(-0.327240\pi\)
0.516485 + 0.856296i \(0.327240\pi\)
\(588\) −0.156292 −0.00644535
\(589\) −10.0481 −0.414025
\(590\) 1.96214 0.0807800
\(591\) −2.29753 −0.0945076
\(592\) 12.5442 0.515565
\(593\) 21.3000 0.874685 0.437342 0.899295i \(-0.355920\pi\)
0.437342 + 0.899295i \(0.355920\pi\)
\(594\) 3.82270 0.156847
\(595\) −1.17778 −0.0482843
\(596\) −5.88351 −0.240998
\(597\) 1.07878 0.0441516
\(598\) −57.0289 −2.33209
\(599\) 10.6826 0.436478 0.218239 0.975895i \(-0.429969\pi\)
0.218239 + 0.975895i \(0.429969\pi\)
\(600\) 0.537173 0.0219300
\(601\) −32.1515 −1.31149 −0.655744 0.754984i \(-0.727645\pi\)
−0.655744 + 0.754984i \(0.727645\pi\)
\(602\) 2.42530 0.0988480
\(603\) 6.63196 0.270074
\(604\) 0.474818 0.0193201
\(605\) −0.841001 −0.0341915
\(606\) −1.27226 −0.0516819
\(607\) −7.63372 −0.309843 −0.154922 0.987927i \(-0.549512\pi\)
−0.154922 + 0.987927i \(0.549512\pi\)
\(608\) −8.68558 −0.352247
\(609\) −1.64448 −0.0666376
\(610\) 0.0463377 0.00187616
\(611\) 60.4558 2.44578
\(612\) −3.09891 −0.125266
\(613\) 41.3140 1.66866 0.834329 0.551267i \(-0.185856\pi\)
0.834329 + 0.551267i \(0.185856\pi\)
\(614\) −36.4880 −1.47254
\(615\) −1.37749 −0.0555456
\(616\) −10.4815 −0.422311
\(617\) −37.6139 −1.51428 −0.757140 0.653252i \(-0.773404\pi\)
−0.757140 + 0.653252i \(0.773404\pi\)
\(618\) −2.25286 −0.0906234
\(619\) 8.96197 0.360212 0.180106 0.983647i \(-0.442356\pi\)
0.180106 + 0.983647i \(0.442356\pi\)
\(620\) −4.68550 −0.188174
\(621\) −8.12639 −0.326101
\(622\) 19.9174 0.798617
\(623\) 14.6526 0.587045
\(624\) −1.78018 −0.0712644
\(625\) 1.00000 0.0400000
\(626\) −23.4678 −0.937962
\(627\) 1.15334 0.0460600
\(628\) −7.74839 −0.309195
\(629\) 10.2450 0.408493
\(630\) 3.13323 0.124831
\(631\) −23.8093 −0.947835 −0.473917 0.880569i \(-0.657160\pi\)
−0.473917 + 0.880569i \(0.657160\pi\)
\(632\) −13.8140 −0.549490
\(633\) 0.949797 0.0377510
\(634\) −15.5360 −0.617011
\(635\) 14.1236 0.560479
\(636\) −0.869565 −0.0344805
\(637\) 6.99973 0.277339
\(638\) −33.8636 −1.34067
\(639\) −45.7020 −1.80794
\(640\) −1.00629 −0.0397770
\(641\) −39.3068 −1.55252 −0.776262 0.630411i \(-0.782887\pi\)
−0.776262 + 0.630411i \(0.782887\pi\)
\(642\) 0.743432 0.0293409
\(643\) −30.3638 −1.19743 −0.598715 0.800962i \(-0.704322\pi\)
−0.598715 + 0.800962i \(0.704322\pi\)
\(644\) 6.84176 0.269603
\(645\) −0.405280 −0.0159579
\(646\) 2.36232 0.0929441
\(647\) 19.4049 0.762884 0.381442 0.924393i \(-0.375428\pi\)
0.381442 + 0.924393i \(0.375428\pi\)
\(648\) 26.5643 1.04354
\(649\) 6.39775 0.251134
\(650\) −7.38716 −0.289748
\(651\) 0.932378 0.0365428
\(652\) 15.1334 0.592668
\(653\) −37.5277 −1.46857 −0.734285 0.678841i \(-0.762483\pi\)
−0.734285 + 0.678841i \(0.762483\pi\)
\(654\) 1.52343 0.0595710
\(655\) 12.0149 0.469461
\(656\) −11.2642 −0.439793
\(657\) −24.3522 −0.950070
\(658\) 9.11492 0.355337
\(659\) −7.91358 −0.308269 −0.154135 0.988050i \(-0.549259\pi\)
−0.154135 + 0.988050i \(0.549259\pi\)
\(660\) 0.537811 0.0209343
\(661\) −9.73139 −0.378507 −0.189254 0.981928i \(-0.560607\pi\)
−0.189254 + 0.981928i \(0.560607\pi\)
\(662\) −31.1075 −1.20903
\(663\) −1.45389 −0.0564643
\(664\) −22.3165 −0.866048
\(665\) 1.90054 0.0736999
\(666\) −27.2545 −1.05609
\(667\) 71.9880 2.78739
\(668\) −5.88116 −0.227549
\(669\) 0.447323 0.0172945
\(670\) −2.35745 −0.0910763
\(671\) 0.151089 0.00583272
\(672\) 0.805947 0.0310901
\(673\) 13.7602 0.530417 0.265208 0.964191i \(-0.414559\pi\)
0.265208 + 0.964191i \(0.414559\pi\)
\(674\) −21.6530 −0.834044
\(675\) −1.05264 −0.0405161
\(676\) −31.9011 −1.22697
\(677\) −36.7348 −1.41183 −0.705917 0.708295i \(-0.749465\pi\)
−0.705917 + 0.708295i \(0.749465\pi\)
\(678\) 3.13979 0.120583
\(679\) 8.10190 0.310922
\(680\) 3.58750 0.137575
\(681\) −2.62294 −0.100511
\(682\) 19.1998 0.735199
\(683\) 39.9800 1.52979 0.764895 0.644155i \(-0.222791\pi\)
0.764895 + 0.644155i \(0.222791\pi\)
\(684\) 5.00061 0.191203
\(685\) −8.09677 −0.309362
\(686\) 1.05535 0.0402934
\(687\) 0.176354 0.00672833
\(688\) −3.31412 −0.126350
\(689\) 38.9446 1.48367
\(690\) 1.43681 0.0546985
\(691\) −21.4525 −0.816092 −0.408046 0.912961i \(-0.633790\pi\)
−0.408046 + 0.912961i \(0.633790\pi\)
\(692\) 9.49945 0.361115
\(693\) 10.2162 0.388082
\(694\) −16.8750 −0.640565
\(695\) −4.28815 −0.162659
\(696\) 5.00906 0.189868
\(697\) −9.19953 −0.348457
\(698\) −16.3900 −0.620373
\(699\) −1.14084 −0.0431504
\(700\) 0.886237 0.0334966
\(701\) 13.2233 0.499439 0.249720 0.968318i \(-0.419662\pi\)
0.249720 + 0.968318i \(0.419662\pi\)
\(702\) 7.77602 0.293487
\(703\) −16.5319 −0.623514
\(704\) 26.5211 0.999552
\(705\) −1.52315 −0.0573651
\(706\) 17.0890 0.643152
\(707\) −6.83585 −0.257089
\(708\) −0.290582 −0.0109207
\(709\) −22.7931 −0.856014 −0.428007 0.903775i \(-0.640784\pi\)
−0.428007 + 0.903775i \(0.640784\pi\)
\(710\) 16.2456 0.609687
\(711\) 13.4644 0.504953
\(712\) −44.6317 −1.67264
\(713\) −40.8154 −1.52855
\(714\) −0.219203 −0.00820346
\(715\) −24.0866 −0.900787
\(716\) 16.6547 0.622415
\(717\) 1.82362 0.0681043
\(718\) −30.7810 −1.14873
\(719\) −23.9806 −0.894325 −0.447163 0.894453i \(-0.647565\pi\)
−0.447163 + 0.894453i \(0.647565\pi\)
\(720\) −4.28148 −0.159561
\(721\) −12.1047 −0.450801
\(722\) 16.2397 0.604377
\(723\) −1.97254 −0.0733597
\(724\) −0.602334 −0.0223856
\(725\) 9.32486 0.346317
\(726\) −0.156523 −0.00580911
\(727\) −14.9127 −0.553080 −0.276540 0.961002i \(-0.589188\pi\)
−0.276540 + 0.961002i \(0.589188\pi\)
\(728\) −21.3211 −0.790212
\(729\) −25.3350 −0.938335
\(730\) 8.65643 0.320389
\(731\) −2.70666 −0.100109
\(732\) −0.00686236 −0.000253640 0
\(733\) 41.8848 1.54705 0.773526 0.633764i \(-0.218491\pi\)
0.773526 + 0.633764i \(0.218491\pi\)
\(734\) 5.36016 0.197847
\(735\) −0.176354 −0.00650492
\(736\) −35.2808 −1.30047
\(737\) −7.68671 −0.283144
\(738\) 24.4734 0.900877
\(739\) 23.6216 0.868933 0.434467 0.900688i \(-0.356937\pi\)
0.434467 + 0.900688i \(0.356937\pi\)
\(740\) −7.70896 −0.283387
\(741\) 2.34609 0.0861857
\(742\) 5.87169 0.215556
\(743\) 36.0578 1.32283 0.661416 0.750020i \(-0.269956\pi\)
0.661416 + 0.750020i \(0.269956\pi\)
\(744\) −2.84001 −0.104120
\(745\) −6.63875 −0.243225
\(746\) −22.4892 −0.823389
\(747\) 21.7517 0.795853
\(748\) 3.59177 0.131328
\(749\) 3.99447 0.145955
\(750\) 0.186115 0.00679597
\(751\) −9.26373 −0.338038 −0.169019 0.985613i \(-0.554060\pi\)
−0.169019 + 0.985613i \(0.554060\pi\)
\(752\) −12.4553 −0.454199
\(753\) 2.59458 0.0945516
\(754\) −68.8842 −2.50861
\(755\) 0.535768 0.0194986
\(756\) −0.932888 −0.0339288
\(757\) −33.0741 −1.20210 −0.601050 0.799212i \(-0.705251\pi\)
−0.601050 + 0.799212i \(0.705251\pi\)
\(758\) 38.5308 1.39950
\(759\) 4.68487 0.170050
\(760\) −5.78903 −0.209990
\(761\) 10.4377 0.378368 0.189184 0.981942i \(-0.439416\pi\)
0.189184 + 0.981942i \(0.439416\pi\)
\(762\) 2.62862 0.0952249
\(763\) 8.18543 0.296333
\(764\) −8.66951 −0.313652
\(765\) −3.49671 −0.126424
\(766\) −4.45176 −0.160849
\(767\) 13.0141 0.469912
\(768\) −2.90568 −0.104850
\(769\) 6.24782 0.225302 0.112651 0.993635i \(-0.464066\pi\)
0.112651 + 0.993635i \(0.464066\pi\)
\(770\) −3.63154 −0.130872
\(771\) 5.47502 0.197178
\(772\) 10.0553 0.361897
\(773\) 37.3719 1.34417 0.672087 0.740473i \(-0.265398\pi\)
0.672087 + 0.740473i \(0.265398\pi\)
\(774\) 7.20048 0.258816
\(775\) −5.28696 −0.189913
\(776\) −24.6783 −0.885900
\(777\) 1.53402 0.0550327
\(778\) 2.56568 0.0919841
\(779\) 14.8450 0.531876
\(780\) 1.09400 0.0391714
\(781\) 52.9704 1.89543
\(782\) 9.59573 0.343143
\(783\) −9.81572 −0.350785
\(784\) −1.44211 −0.0515039
\(785\) −8.74303 −0.312052
\(786\) 2.23616 0.0797611
\(787\) 10.6026 0.377940 0.188970 0.981983i \(-0.439485\pi\)
0.188970 + 0.981983i \(0.439485\pi\)
\(788\) 11.5458 0.411303
\(789\) 2.37202 0.0844463
\(790\) −4.78615 −0.170284
\(791\) 16.8701 0.599832
\(792\) −31.1185 −1.10575
\(793\) 0.307340 0.0109140
\(794\) −3.82825 −0.135859
\(795\) −0.981188 −0.0347991
\(796\) −5.42123 −0.192150
\(797\) 4.88587 0.173066 0.0865332 0.996249i \(-0.472421\pi\)
0.0865332 + 0.996249i \(0.472421\pi\)
\(798\) 0.353720 0.0125216
\(799\) −10.1723 −0.359871
\(800\) −4.57005 −0.161576
\(801\) 43.5021 1.53707
\(802\) −18.3015 −0.646248
\(803\) 28.2252 0.996045
\(804\) 0.349126 0.0123127
\(805\) 7.72001 0.272095
\(806\) 39.0556 1.37568
\(807\) −0.476081 −0.0167588
\(808\) 20.8219 0.732513
\(809\) 8.15712 0.286789 0.143395 0.989666i \(-0.454198\pi\)
0.143395 + 0.989666i \(0.454198\pi\)
\(810\) 9.20377 0.323387
\(811\) 20.0066 0.702527 0.351264 0.936277i \(-0.385752\pi\)
0.351264 + 0.936277i \(0.385752\pi\)
\(812\) 8.26404 0.290011
\(813\) 0.650045 0.0227981
\(814\) 31.5891 1.10720
\(815\) 17.0760 0.598145
\(816\) 0.299535 0.0104858
\(817\) 4.36765 0.152805
\(818\) −2.55035 −0.0891710
\(819\) 20.7815 0.726164
\(820\) 6.92232 0.241738
\(821\) −21.3976 −0.746783 −0.373391 0.927674i \(-0.621805\pi\)
−0.373391 + 0.927674i \(0.621805\pi\)
\(822\) −1.50693 −0.0525603
\(823\) −49.0475 −1.70969 −0.854844 0.518885i \(-0.826347\pi\)
−0.854844 + 0.518885i \(0.826347\pi\)
\(824\) 36.8707 1.28445
\(825\) 0.606848 0.0211277
\(826\) 1.96214 0.0682715
\(827\) 6.48400 0.225471 0.112735 0.993625i \(-0.464039\pi\)
0.112735 + 0.993625i \(0.464039\pi\)
\(828\) 20.3125 0.705908
\(829\) −5.09284 −0.176882 −0.0884408 0.996081i \(-0.528188\pi\)
−0.0884408 + 0.996081i \(0.528188\pi\)
\(830\) −7.73204 −0.268383
\(831\) 4.57988 0.158874
\(832\) 53.9484 1.87032
\(833\) −1.17778 −0.0408076
\(834\) −0.798090 −0.0276356
\(835\) −6.63610 −0.229652
\(836\) −5.79591 −0.200456
\(837\) 5.56527 0.192364
\(838\) −7.75734 −0.267973
\(839\) −0.820289 −0.0283195 −0.0141598 0.999900i \(-0.504507\pi\)
−0.0141598 + 0.999900i \(0.504507\pi\)
\(840\) 0.537173 0.0185342
\(841\) 57.9530 1.99838
\(842\) −9.14848 −0.315277
\(843\) 0.675948 0.0232809
\(844\) −4.77304 −0.164295
\(845\) −35.9962 −1.23831
\(846\) 27.0613 0.930386
\(847\) −0.841001 −0.0288971
\(848\) −8.02352 −0.275529
\(849\) −4.29638 −0.147451
\(850\) 1.24297 0.0426335
\(851\) −67.1527 −2.30197
\(852\) −2.40589 −0.0824243
\(853\) −40.9686 −1.40274 −0.701370 0.712798i \(-0.747428\pi\)
−0.701370 + 0.712798i \(0.747428\pi\)
\(854\) 0.0463377 0.00158564
\(855\) 5.64252 0.192970
\(856\) −12.1671 −0.415863
\(857\) 54.4420 1.85970 0.929852 0.367935i \(-0.119935\pi\)
0.929852 + 0.367935i \(0.119935\pi\)
\(858\) −4.48288 −0.153043
\(859\) −39.6992 −1.35452 −0.677260 0.735744i \(-0.736833\pi\)
−0.677260 + 0.735744i \(0.736833\pi\)
\(860\) 2.03667 0.0694497
\(861\) −1.37749 −0.0469446
\(862\) −19.9562 −0.679711
\(863\) 14.8822 0.506595 0.253298 0.967388i \(-0.418485\pi\)
0.253298 + 0.967388i \(0.418485\pi\)
\(864\) 4.81062 0.163660
\(865\) 10.7189 0.364452
\(866\) −32.4723 −1.10345
\(867\) −2.75339 −0.0935099
\(868\) −4.68550 −0.159036
\(869\) −15.6057 −0.529389
\(870\) 1.73550 0.0588389
\(871\) −15.6361 −0.529808
\(872\) −24.9327 −0.844329
\(873\) 24.0537 0.814095
\(874\) −15.4843 −0.523765
\(875\) 1.00000 0.0338062
\(876\) −1.28197 −0.0433138
\(877\) −37.4492 −1.26457 −0.632284 0.774736i \(-0.717883\pi\)
−0.632284 + 0.774736i \(0.717883\pi\)
\(878\) 26.7494 0.902748
\(879\) −1.97967 −0.0667727
\(880\) 4.96241 0.167283
\(881\) 11.0613 0.372664 0.186332 0.982487i \(-0.440340\pi\)
0.186332 + 0.982487i \(0.440340\pi\)
\(882\) 3.13323 0.105501
\(883\) 4.25775 0.143285 0.0716423 0.997430i \(-0.477176\pi\)
0.0716423 + 0.997430i \(0.477176\pi\)
\(884\) 7.30626 0.245736
\(885\) −0.327883 −0.0110217
\(886\) 17.1171 0.575060
\(887\) 8.24772 0.276931 0.138466 0.990367i \(-0.455783\pi\)
0.138466 + 0.990367i \(0.455783\pi\)
\(888\) −4.67261 −0.156803
\(889\) 14.1236 0.473691
\(890\) −15.4636 −0.518342
\(891\) 30.0098 1.00537
\(892\) −2.24794 −0.0752667
\(893\) 16.4148 0.549299
\(894\) −1.23557 −0.0413237
\(895\) 18.7926 0.628167
\(896\) −1.00629 −0.0336177
\(897\) 9.52981 0.318191
\(898\) 35.0911 1.17101
\(899\) −49.3002 −1.64425
\(900\) 2.63115 0.0877050
\(901\) −6.55286 −0.218307
\(902\) −28.3656 −0.944472
\(903\) −0.405280 −0.0134869
\(904\) −51.3862 −1.70908
\(905\) −0.679653 −0.0225924
\(906\) 0.0997147 0.00331280
\(907\) 37.9050 1.25862 0.629308 0.777156i \(-0.283338\pi\)
0.629308 + 0.777156i \(0.283338\pi\)
\(908\) 13.1811 0.437431
\(909\) −20.2950 −0.673141
\(910\) −7.38716 −0.244882
\(911\) 0.389540 0.0129060 0.00645302 0.999979i \(-0.497946\pi\)
0.00645302 + 0.999979i \(0.497946\pi\)
\(912\) −0.483350 −0.0160053
\(913\) −25.2111 −0.834365
\(914\) 15.5576 0.514598
\(915\) −0.00774325 −0.000255984 0
\(916\) −0.886237 −0.0292821
\(917\) 12.0149 0.396767
\(918\) −1.30840 −0.0431836
\(919\) −22.0521 −0.727431 −0.363715 0.931510i \(-0.618492\pi\)
−0.363715 + 0.931510i \(0.618492\pi\)
\(920\) −23.5151 −0.775269
\(921\) 6.09733 0.200914
\(922\) −21.3537 −0.703248
\(923\) 107.751 3.54666
\(924\) 0.537811 0.0176927
\(925\) −8.69853 −0.286006
\(926\) −10.3371 −0.339697
\(927\) −35.9375 −1.18034
\(928\) −42.6151 −1.39891
\(929\) 23.2441 0.762614 0.381307 0.924449i \(-0.375474\pi\)
0.381307 + 0.924449i \(0.375474\pi\)
\(930\) −0.983985 −0.0322661
\(931\) 1.90054 0.0622878
\(932\) 5.73307 0.187793
\(933\) −3.32830 −0.108964
\(934\) 0.904472 0.0295952
\(935\) 4.05283 0.132542
\(936\) −63.3002 −2.06903
\(937\) 28.3995 0.927771 0.463885 0.885895i \(-0.346455\pi\)
0.463885 + 0.885895i \(0.346455\pi\)
\(938\) −2.35745 −0.0769735
\(939\) 3.92159 0.127976
\(940\) 7.65432 0.249656
\(941\) −8.65126 −0.282023 −0.141012 0.990008i \(-0.545035\pi\)
−0.141012 + 0.990008i \(0.545035\pi\)
\(942\) −1.62721 −0.0530174
\(943\) 60.3003 1.96365
\(944\) −2.68121 −0.0872661
\(945\) −1.05264 −0.0342424
\(946\) −8.34565 −0.271341
\(947\) −57.0061 −1.85245 −0.926224 0.376974i \(-0.876965\pi\)
−0.926224 + 0.376974i \(0.876965\pi\)
\(948\) 0.708803 0.0230209
\(949\) 57.4148 1.86376
\(950\) −2.00574 −0.0650747
\(951\) 2.59613 0.0841854
\(952\) 3.58750 0.116272
\(953\) −18.9213 −0.612921 −0.306461 0.951883i \(-0.599145\pi\)
−0.306461 + 0.951883i \(0.599145\pi\)
\(954\) 17.4324 0.564396
\(955\) −9.78238 −0.316550
\(956\) −9.16428 −0.296394
\(957\) 5.65877 0.182922
\(958\) 29.4647 0.951960
\(959\) −8.09677 −0.261458
\(960\) −1.35920 −0.0438680
\(961\) −3.04801 −0.0983228
\(962\) 64.2574 2.07174
\(963\) 11.8592 0.382157
\(964\) 9.91268 0.319266
\(965\) 11.3460 0.365242
\(966\) 1.43681 0.0462286
\(967\) 6.72890 0.216387 0.108193 0.994130i \(-0.465493\pi\)
0.108193 + 0.994130i \(0.465493\pi\)
\(968\) 2.56168 0.0823355
\(969\) −0.394755 −0.0126814
\(970\) −8.55034 −0.274535
\(971\) 20.8492 0.669083 0.334541 0.942381i \(-0.391419\pi\)
0.334541 + 0.942381i \(0.391419\pi\)
\(972\) −4.16169 −0.133486
\(973\) −4.28815 −0.137472
\(974\) −31.9783 −1.02465
\(975\) 1.23443 0.0395334
\(976\) −0.0633193 −0.00202680
\(977\) −47.1315 −1.50787 −0.753935 0.656949i \(-0.771847\pi\)
−0.753935 + 0.656949i \(0.771847\pi\)
\(978\) 3.17810 0.101624
\(979\) −50.4208 −1.61145
\(980\) 0.886237 0.0283098
\(981\) 24.3017 0.775894
\(982\) 9.17165 0.292679
\(983\) 42.2594 1.34787 0.673933 0.738793i \(-0.264604\pi\)
0.673933 + 0.738793i \(0.264604\pi\)
\(984\) 4.19581 0.133757
\(985\) 13.0279 0.415104
\(986\) 11.5905 0.369117
\(987\) −1.52315 −0.0484823
\(988\) −11.7899 −0.375086
\(989\) 17.7414 0.564143
\(990\) −10.7817 −0.342664
\(991\) −39.1637 −1.24408 −0.622038 0.782987i \(-0.713695\pi\)
−0.622038 + 0.782987i \(0.713695\pi\)
\(992\) 24.1617 0.767134
\(993\) 5.19822 0.164960
\(994\) 16.2456 0.515279
\(995\) −6.11713 −0.193926
\(996\) 1.14507 0.0362830
\(997\) 11.3276 0.358749 0.179375 0.983781i \(-0.442593\pi\)
0.179375 + 0.983781i \(0.442593\pi\)
\(998\) −11.7235 −0.371100
\(999\) 9.15642 0.289696
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 \(a_p\))