Properties

Label 8041.2.a.g.1.1
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 1
Dimension 69
CM No

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.81130 q^{2} -0.519316 q^{3} +5.90341 q^{4} -3.87319 q^{5} +1.45995 q^{6} +3.50752 q^{7} -10.9737 q^{8} -2.73031 q^{9} +O(q^{10})\) \(q-2.81130 q^{2} -0.519316 q^{3} +5.90341 q^{4} -3.87319 q^{5} +1.45995 q^{6} +3.50752 q^{7} -10.9737 q^{8} -2.73031 q^{9} +10.8887 q^{10} -1.00000 q^{11} -3.06573 q^{12} +0.0114155 q^{13} -9.86070 q^{14} +2.01141 q^{15} +19.0435 q^{16} +1.00000 q^{17} +7.67573 q^{18} +1.70756 q^{19} -22.8650 q^{20} -1.82151 q^{21} +2.81130 q^{22} +2.63346 q^{23} +5.69880 q^{24} +10.0016 q^{25} -0.0320925 q^{26} +2.97584 q^{27} +20.7064 q^{28} +4.94129 q^{29} -5.65467 q^{30} -6.86928 q^{31} -31.5896 q^{32} +0.519316 q^{33} -2.81130 q^{34} -13.5853 q^{35} -16.1182 q^{36} -6.53968 q^{37} -4.80046 q^{38} -0.00592827 q^{39} +42.5031 q^{40} -1.91463 q^{41} +5.12082 q^{42} +1.00000 q^{43} -5.90341 q^{44} +10.5750 q^{45} -7.40345 q^{46} -7.40177 q^{47} -9.88957 q^{48} +5.30272 q^{49} -28.1174 q^{50} -0.519316 q^{51} +0.0673906 q^{52} +0.430107 q^{53} -8.36598 q^{54} +3.87319 q^{55} -38.4904 q^{56} -0.886761 q^{57} -13.8914 q^{58} -12.5197 q^{59} +11.8742 q^{60} +5.35709 q^{61} +19.3116 q^{62} -9.57663 q^{63} +50.7208 q^{64} -0.0442145 q^{65} -1.45995 q^{66} +2.50937 q^{67} +5.90341 q^{68} -1.36760 q^{69} +38.1923 q^{70} -1.55184 q^{71} +29.9615 q^{72} +4.21046 q^{73} +18.3850 q^{74} -5.19397 q^{75} +10.0804 q^{76} -3.50752 q^{77} +0.0166661 q^{78} -6.39281 q^{79} -73.7589 q^{80} +6.64553 q^{81} +5.38259 q^{82} +11.0497 q^{83} -10.7531 q^{84} -3.87319 q^{85} -2.81130 q^{86} -2.56609 q^{87} +10.9737 q^{88} +1.27161 q^{89} -29.7295 q^{90} +0.0400403 q^{91} +15.5464 q^{92} +3.56732 q^{93} +20.8086 q^{94} -6.61369 q^{95} +16.4050 q^{96} -10.2499 q^{97} -14.9075 q^{98} +2.73031 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} + O(q^{10}) \) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} - q^{10} - 69q^{11} - 3q^{12} - 28q^{13} - 15q^{14} - 45q^{15} + 53q^{16} + 69q^{17} - 17q^{18} - 32q^{19} - 21q^{20} - 38q^{21} + 11q^{22} - 41q^{23} - 11q^{24} + 67q^{25} - 6q^{26} - 3q^{27} - 21q^{28} - 22q^{29} - 22q^{30} - 27q^{31} - 87q^{32} + 3q^{33} - 11q^{34} - 44q^{35} + 59q^{36} + 24q^{37} - 22q^{38} - 59q^{39} + q^{40} - 43q^{41} - 15q^{42} + 69q^{43} - 65q^{44} - 12q^{45} - 21q^{46} - 99q^{47} + 2q^{48} + 64q^{49} - 78q^{50} - 3q^{51} - 57q^{52} - 50q^{53} + 20q^{54} + 6q^{55} - 59q^{56} - 15q^{57} + 22q^{58} - 82q^{59} - 86q^{60} - 24q^{61} + 15q^{62} - 63q^{63} + 63q^{64} - 23q^{65} + 10q^{66} - 54q^{67} + 65q^{68} + 36q^{69} + 9q^{70} - 128q^{71} - 69q^{72} + 2q^{73} - 58q^{74} - 31q^{75} - 76q^{76} + 11q^{77} - 19q^{78} - 43q^{79} - 19q^{80} + 49q^{81} - 2q^{82} - 62q^{83} - 82q^{84} - 6q^{85} - 11q^{86} - 62q^{87} + 33q^{88} - 49q^{89} - 37q^{90} - 2q^{91} - 96q^{92} - 29q^{93} - 75q^{94} - 133q^{95} - 86q^{96} + 5q^{97} - 72q^{98} - 56q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.81130 −1.98789 −0.993945 0.109879i \(-0.964954\pi\)
−0.993945 + 0.109879i \(0.964954\pi\)
\(3\) −0.519316 −0.299827 −0.149914 0.988699i \(-0.547900\pi\)
−0.149914 + 0.988699i \(0.547900\pi\)
\(4\) 5.90341 2.95171
\(5\) −3.87319 −1.73214 −0.866071 0.499922i \(-0.833362\pi\)
−0.866071 + 0.499922i \(0.833362\pi\)
\(6\) 1.45995 0.596023
\(7\) 3.50752 1.32572 0.662859 0.748744i \(-0.269343\pi\)
0.662859 + 0.748744i \(0.269343\pi\)
\(8\) −10.9737 −3.87978
\(9\) −2.73031 −0.910104
\(10\) 10.8887 3.44331
\(11\) −1.00000 −0.301511
\(12\) −3.06573 −0.885001
\(13\) 0.0114155 0.00316610 0.00158305 0.999999i \(-0.499496\pi\)
0.00158305 + 0.999999i \(0.499496\pi\)
\(14\) −9.86070 −2.63538
\(15\) 2.01141 0.519343
\(16\) 19.0435 4.76086
\(17\) 1.00000 0.242536
\(18\) 7.67573 1.80919
\(19\) 1.70756 0.391740 0.195870 0.980630i \(-0.437247\pi\)
0.195870 + 0.980630i \(0.437247\pi\)
\(20\) −22.8650 −5.11277
\(21\) −1.82151 −0.397486
\(22\) 2.81130 0.599371
\(23\) 2.63346 0.549115 0.274557 0.961571i \(-0.411469\pi\)
0.274557 + 0.961571i \(0.411469\pi\)
\(24\) 5.69880 1.16326
\(25\) 10.0016 2.00031
\(26\) −0.0320925 −0.00629386
\(27\) 2.97584 0.572701
\(28\) 20.7064 3.91313
\(29\) 4.94129 0.917574 0.458787 0.888546i \(-0.348284\pi\)
0.458787 + 0.888546i \(0.348284\pi\)
\(30\) −5.65467 −1.03240
\(31\) −6.86928 −1.23376 −0.616879 0.787058i \(-0.711603\pi\)
−0.616879 + 0.787058i \(0.711603\pi\)
\(32\) −31.5896 −5.58430
\(33\) 0.519316 0.0904012
\(34\) −2.81130 −0.482134
\(35\) −13.5853 −2.29633
\(36\) −16.1182 −2.68636
\(37\) −6.53968 −1.07512 −0.537558 0.843227i \(-0.680653\pi\)
−0.537558 + 0.843227i \(0.680653\pi\)
\(38\) −4.80046 −0.778737
\(39\) −0.00592827 −0.000949282 0
\(40\) 42.5031 6.72032
\(41\) −1.91463 −0.299014 −0.149507 0.988761i \(-0.547769\pi\)
−0.149507 + 0.988761i \(0.547769\pi\)
\(42\) 5.12082 0.790159
\(43\) 1.00000 0.152499
\(44\) −5.90341 −0.889973
\(45\) 10.5750 1.57643
\(46\) −7.40345 −1.09158
\(47\) −7.40177 −1.07966 −0.539830 0.841774i \(-0.681511\pi\)
−0.539830 + 0.841774i \(0.681511\pi\)
\(48\) −9.88957 −1.42744
\(49\) 5.30272 0.757531
\(50\) −28.1174 −3.97640
\(51\) −0.519316 −0.0727187
\(52\) 0.0673906 0.00934540
\(53\) 0.430107 0.0590798 0.0295399 0.999564i \(-0.490596\pi\)
0.0295399 + 0.999564i \(0.490596\pi\)
\(54\) −8.36598 −1.13847
\(55\) 3.87319 0.522260
\(56\) −38.4904 −5.14349
\(57\) −0.886761 −0.117454
\(58\) −13.8914 −1.82404
\(59\) −12.5197 −1.62992 −0.814961 0.579516i \(-0.803241\pi\)
−0.814961 + 0.579516i \(0.803241\pi\)
\(60\) 11.8742 1.53295
\(61\) 5.35709 0.685905 0.342952 0.939353i \(-0.388573\pi\)
0.342952 + 0.939353i \(0.388573\pi\)
\(62\) 19.3116 2.45258
\(63\) −9.57663 −1.20654
\(64\) 50.7208 6.34010
\(65\) −0.0442145 −0.00548413
\(66\) −1.45995 −0.179708
\(67\) 2.50937 0.306569 0.153284 0.988182i \(-0.451015\pi\)
0.153284 + 0.988182i \(0.451015\pi\)
\(68\) 5.90341 0.715894
\(69\) −1.36760 −0.164639
\(70\) 38.1923 4.56486
\(71\) −1.55184 −0.184170 −0.0920848 0.995751i \(-0.529353\pi\)
−0.0920848 + 0.995751i \(0.529353\pi\)
\(72\) 29.9615 3.53100
\(73\) 4.21046 0.492797 0.246399 0.969169i \(-0.420753\pi\)
0.246399 + 0.969169i \(0.420753\pi\)
\(74\) 18.3850 2.13721
\(75\) −5.19397 −0.599748
\(76\) 10.0804 1.15630
\(77\) −3.50752 −0.399719
\(78\) 0.0166661 0.00188707
\(79\) −6.39281 −0.719248 −0.359624 0.933097i \(-0.617095\pi\)
−0.359624 + 0.933097i \(0.617095\pi\)
\(80\) −73.7589 −8.24649
\(81\) 6.64553 0.738393
\(82\) 5.38259 0.594408
\(83\) 11.0497 1.21287 0.606434 0.795134i \(-0.292600\pi\)
0.606434 + 0.795134i \(0.292600\pi\)
\(84\) −10.7531 −1.17326
\(85\) −3.87319 −0.420106
\(86\) −2.81130 −0.303150
\(87\) −2.56609 −0.275114
\(88\) 10.9737 1.16980
\(89\) 1.27161 0.134790 0.0673952 0.997726i \(-0.478531\pi\)
0.0673952 + 0.997726i \(0.478531\pi\)
\(90\) −29.7295 −3.13377
\(91\) 0.0400403 0.00419736
\(92\) 15.5464 1.62083
\(93\) 3.56732 0.369914
\(94\) 20.8086 2.14624
\(95\) −6.61369 −0.678550
\(96\) 16.4050 1.67432
\(97\) −10.2499 −1.04072 −0.520361 0.853946i \(-0.674203\pi\)
−0.520361 + 0.853946i \(0.674203\pi\)
\(98\) −14.9075 −1.50589
\(99\) 2.73031 0.274407
\(100\) 59.0434 5.90434
\(101\) 17.4115 1.73251 0.866255 0.499603i \(-0.166521\pi\)
0.866255 + 0.499603i \(0.166521\pi\)
\(102\) 1.45995 0.144557
\(103\) 10.8954 1.07356 0.536779 0.843723i \(-0.319641\pi\)
0.536779 + 0.843723i \(0.319641\pi\)
\(104\) −0.125270 −0.0122838
\(105\) 7.05505 0.688503
\(106\) −1.20916 −0.117444
\(107\) −15.4999 −1.49843 −0.749214 0.662328i \(-0.769569\pi\)
−0.749214 + 0.662328i \(0.769569\pi\)
\(108\) 17.5676 1.69044
\(109\) 3.04624 0.291777 0.145889 0.989301i \(-0.453396\pi\)
0.145889 + 0.989301i \(0.453396\pi\)
\(110\) −10.8887 −1.03820
\(111\) 3.39616 0.322349
\(112\) 66.7954 6.31157
\(113\) 7.57424 0.712524 0.356262 0.934386i \(-0.384051\pi\)
0.356262 + 0.934386i \(0.384051\pi\)
\(114\) 2.49295 0.233486
\(115\) −10.1999 −0.951145
\(116\) 29.1705 2.70841
\(117\) −0.0311680 −0.00288148
\(118\) 35.1965 3.24010
\(119\) 3.50752 0.321534
\(120\) −22.0725 −2.01493
\(121\) 1.00000 0.0909091
\(122\) −15.0604 −1.36350
\(123\) 0.994295 0.0896526
\(124\) −40.5522 −3.64169
\(125\) −19.3720 −1.73269
\(126\) 26.9228 2.39847
\(127\) −16.3259 −1.44869 −0.724345 0.689437i \(-0.757858\pi\)
−0.724345 + 0.689437i \(0.757858\pi\)
\(128\) −79.4124 −7.01913
\(129\) −0.519316 −0.0457232
\(130\) 0.124300 0.0109019
\(131\) 11.9335 1.04263 0.521316 0.853364i \(-0.325441\pi\)
0.521316 + 0.853364i \(0.325441\pi\)
\(132\) 3.06573 0.266838
\(133\) 5.98929 0.519338
\(134\) −7.05461 −0.609425
\(135\) −11.5260 −0.991999
\(136\) −10.9737 −0.940984
\(137\) 8.09105 0.691265 0.345633 0.938370i \(-0.387664\pi\)
0.345633 + 0.938370i \(0.387664\pi\)
\(138\) 3.84473 0.327285
\(139\) −6.10137 −0.517512 −0.258756 0.965943i \(-0.583312\pi\)
−0.258756 + 0.965943i \(0.583312\pi\)
\(140\) −80.1996 −6.77810
\(141\) 3.84386 0.323711
\(142\) 4.36269 0.366109
\(143\) −0.0114155 −0.000954615 0
\(144\) −51.9946 −4.33288
\(145\) −19.1385 −1.58937
\(146\) −11.8369 −0.979627
\(147\) −2.75378 −0.227128
\(148\) −38.6064 −3.17343
\(149\) 20.3360 1.66599 0.832995 0.553281i \(-0.186624\pi\)
0.832995 + 0.553281i \(0.186624\pi\)
\(150\) 14.6018 1.19223
\(151\) −10.5607 −0.859421 −0.429711 0.902967i \(-0.641384\pi\)
−0.429711 + 0.902967i \(0.641384\pi\)
\(152\) −18.7382 −1.51987
\(153\) −2.73031 −0.220733
\(154\) 9.86070 0.794598
\(155\) 26.6060 2.13704
\(156\) −0.0349970 −0.00280200
\(157\) −5.50421 −0.439283 −0.219642 0.975581i \(-0.570489\pi\)
−0.219642 + 0.975581i \(0.570489\pi\)
\(158\) 17.9721 1.42979
\(159\) −0.223361 −0.0177137
\(160\) 122.352 9.67279
\(161\) 9.23693 0.727972
\(162\) −18.6826 −1.46784
\(163\) 3.58687 0.280945 0.140473 0.990085i \(-0.455138\pi\)
0.140473 + 0.990085i \(0.455138\pi\)
\(164\) −11.3028 −0.882603
\(165\) −2.01141 −0.156588
\(166\) −31.0642 −2.41105
\(167\) 4.62741 0.358080 0.179040 0.983842i \(-0.442701\pi\)
0.179040 + 0.983842i \(0.442701\pi\)
\(168\) 19.9887 1.54216
\(169\) −12.9999 −0.999990
\(170\) 10.8887 0.835125
\(171\) −4.66216 −0.356524
\(172\) 5.90341 0.450131
\(173\) 10.0133 0.761299 0.380649 0.924719i \(-0.375701\pi\)
0.380649 + 0.924719i \(0.375701\pi\)
\(174\) 7.21405 0.546895
\(175\) 35.0807 2.65185
\(176\) −19.0435 −1.43545
\(177\) 6.50166 0.488694
\(178\) −3.57488 −0.267948
\(179\) 23.3686 1.74665 0.873324 0.487139i \(-0.161960\pi\)
0.873324 + 0.487139i \(0.161960\pi\)
\(180\) 62.4286 4.65315
\(181\) −6.54397 −0.486410 −0.243205 0.969975i \(-0.578199\pi\)
−0.243205 + 0.969975i \(0.578199\pi\)
\(182\) −0.112565 −0.00834389
\(183\) −2.78202 −0.205653
\(184\) −28.8987 −2.13044
\(185\) 25.3294 1.86225
\(186\) −10.0288 −0.735349
\(187\) −1.00000 −0.0731272
\(188\) −43.6957 −3.18684
\(189\) 10.4378 0.759240
\(190\) 18.5931 1.34888
\(191\) −15.2554 −1.10385 −0.551923 0.833895i \(-0.686106\pi\)
−0.551923 + 0.833895i \(0.686106\pi\)
\(192\) −26.3401 −1.90093
\(193\) 18.0746 1.30104 0.650518 0.759491i \(-0.274552\pi\)
0.650518 + 0.759491i \(0.274552\pi\)
\(194\) 28.8156 2.06884
\(195\) 0.0229613 0.00164429
\(196\) 31.3041 2.23601
\(197\) 7.93803 0.565561 0.282781 0.959185i \(-0.408743\pi\)
0.282781 + 0.959185i \(0.408743\pi\)
\(198\) −7.67573 −0.545490
\(199\) 19.7886 1.40277 0.701387 0.712781i \(-0.252565\pi\)
0.701387 + 0.712781i \(0.252565\pi\)
\(200\) −109.754 −7.76077
\(201\) −1.30316 −0.0919176
\(202\) −48.9490 −3.44404
\(203\) 17.3317 1.21645
\(204\) −3.06573 −0.214644
\(205\) 7.41570 0.517935
\(206\) −30.6303 −2.13412
\(207\) −7.19017 −0.499751
\(208\) 0.217391 0.0150734
\(209\) −1.70756 −0.118114
\(210\) −19.8339 −1.36867
\(211\) −26.9419 −1.85476 −0.927379 0.374124i \(-0.877944\pi\)
−0.927379 + 0.374124i \(0.877944\pi\)
\(212\) 2.53910 0.174386
\(213\) 0.805895 0.0552190
\(214\) 43.5748 2.97871
\(215\) −3.87319 −0.264149
\(216\) −32.6559 −2.22195
\(217\) −24.0942 −1.63562
\(218\) −8.56391 −0.580021
\(219\) −2.18656 −0.147754
\(220\) 22.8650 1.54156
\(221\) 0.0114155 0.000767892 0
\(222\) −9.54762 −0.640794
\(223\) −6.99258 −0.468258 −0.234129 0.972206i \(-0.575224\pi\)
−0.234129 + 0.972206i \(0.575224\pi\)
\(224\) −110.801 −7.40321
\(225\) −27.3074 −1.82049
\(226\) −21.2935 −1.41642
\(227\) 19.1614 1.27178 0.635892 0.771778i \(-0.280632\pi\)
0.635892 + 0.771778i \(0.280632\pi\)
\(228\) −5.23492 −0.346691
\(229\) −21.9250 −1.44885 −0.724424 0.689355i \(-0.757894\pi\)
−0.724424 + 0.689355i \(0.757894\pi\)
\(230\) 28.6750 1.89077
\(231\) 1.82151 0.119847
\(232\) −54.2241 −3.55998
\(233\) 19.3320 1.26648 0.633239 0.773956i \(-0.281725\pi\)
0.633239 + 0.773956i \(0.281725\pi\)
\(234\) 0.0876225 0.00572806
\(235\) 28.6684 1.87012
\(236\) −73.9087 −4.81105
\(237\) 3.31989 0.215650
\(238\) −9.86070 −0.639174
\(239\) −8.14894 −0.527111 −0.263556 0.964644i \(-0.584895\pi\)
−0.263556 + 0.964644i \(0.584895\pi\)
\(240\) 38.3041 2.47252
\(241\) 13.7348 0.884739 0.442370 0.896833i \(-0.354138\pi\)
0.442370 + 0.896833i \(0.354138\pi\)
\(242\) −2.81130 −0.180717
\(243\) −12.3787 −0.794091
\(244\) 31.6251 2.02459
\(245\) −20.5384 −1.31215
\(246\) −2.79526 −0.178219
\(247\) 0.0194927 0.00124029
\(248\) 75.3812 4.78671
\(249\) −5.73831 −0.363650
\(250\) 54.4606 3.44439
\(251\) 11.7603 0.742303 0.371152 0.928572i \(-0.378963\pi\)
0.371152 + 0.928572i \(0.378963\pi\)
\(252\) −56.5348 −3.56136
\(253\) −2.63346 −0.165564
\(254\) 45.8971 2.87984
\(255\) 2.01141 0.125959
\(256\) 121.811 7.61316
\(257\) −13.9806 −0.872084 −0.436042 0.899926i \(-0.643620\pi\)
−0.436042 + 0.899926i \(0.643620\pi\)
\(258\) 1.45995 0.0908927
\(259\) −22.9381 −1.42530
\(260\) −0.261016 −0.0161876
\(261\) −13.4913 −0.835088
\(262\) −33.5486 −2.07264
\(263\) 8.07374 0.497848 0.248924 0.968523i \(-0.419923\pi\)
0.248924 + 0.968523i \(0.419923\pi\)
\(264\) −5.69880 −0.350737
\(265\) −1.66589 −0.102335
\(266\) −16.8377 −1.03239
\(267\) −0.660367 −0.0404138
\(268\) 14.8139 0.904901
\(269\) −17.3290 −1.05657 −0.528283 0.849068i \(-0.677164\pi\)
−0.528283 + 0.849068i \(0.677164\pi\)
\(270\) 32.4030 1.97198
\(271\) −28.0503 −1.70393 −0.851966 0.523597i \(-0.824590\pi\)
−0.851966 + 0.523597i \(0.824590\pi\)
\(272\) 19.0435 1.15468
\(273\) −0.0207935 −0.00125848
\(274\) −22.7464 −1.37416
\(275\) −10.0016 −0.603117
\(276\) −8.07350 −0.485967
\(277\) 17.2215 1.03474 0.517369 0.855762i \(-0.326911\pi\)
0.517369 + 0.855762i \(0.326911\pi\)
\(278\) 17.1528 1.02876
\(279\) 18.7553 1.12285
\(280\) 149.080 8.90926
\(281\) 7.01067 0.418221 0.209111 0.977892i \(-0.432943\pi\)
0.209111 + 0.977892i \(0.432943\pi\)
\(282\) −10.8062 −0.643502
\(283\) −6.49607 −0.386151 −0.193076 0.981184i \(-0.561846\pi\)
−0.193076 + 0.981184i \(0.561846\pi\)
\(284\) −9.16116 −0.543615
\(285\) 3.43459 0.203448
\(286\) 0.0320925 0.00189767
\(287\) −6.71559 −0.396409
\(288\) 86.2493 5.08229
\(289\) 1.00000 0.0588235
\(290\) 53.8042 3.15949
\(291\) 5.32294 0.312037
\(292\) 24.8561 1.45459
\(293\) −13.7967 −0.806013 −0.403006 0.915197i \(-0.632035\pi\)
−0.403006 + 0.915197i \(0.632035\pi\)
\(294\) 7.74171 0.451506
\(295\) 48.4910 2.82325
\(296\) 71.7642 4.17121
\(297\) −2.97584 −0.172676
\(298\) −57.1706 −3.31180
\(299\) 0.0300624 0.00173855
\(300\) −30.6622 −1.77028
\(301\) 3.50752 0.202170
\(302\) 29.6894 1.70843
\(303\) −9.04207 −0.519453
\(304\) 32.5178 1.86502
\(305\) −20.7490 −1.18808
\(306\) 7.67573 0.438792
\(307\) −3.35831 −0.191669 −0.0958344 0.995397i \(-0.530552\pi\)
−0.0958344 + 0.995397i \(0.530552\pi\)
\(308\) −20.7064 −1.17985
\(309\) −5.65817 −0.321882
\(310\) −74.7975 −4.24821
\(311\) 21.9669 1.24563 0.622813 0.782370i \(-0.285990\pi\)
0.622813 + 0.782370i \(0.285990\pi\)
\(312\) 0.0650548 0.00368300
\(313\) 23.8686 1.34913 0.674567 0.738214i \(-0.264330\pi\)
0.674567 + 0.738214i \(0.264330\pi\)
\(314\) 15.4740 0.873247
\(315\) 37.0921 2.08990
\(316\) −37.7394 −2.12301
\(317\) −22.9099 −1.28675 −0.643375 0.765551i \(-0.722466\pi\)
−0.643375 + 0.765551i \(0.722466\pi\)
\(318\) 0.627936 0.0352129
\(319\) −4.94129 −0.276659
\(320\) −196.451 −10.9820
\(321\) 8.04932 0.449269
\(322\) −25.9678 −1.44713
\(323\) 1.70756 0.0950110
\(324\) 39.2313 2.17952
\(325\) 0.114173 0.00633319
\(326\) −10.0838 −0.558488
\(327\) −1.58196 −0.0874827
\(328\) 21.0105 1.16011
\(329\) −25.9619 −1.43133
\(330\) 5.65467 0.311279
\(331\) −9.74697 −0.535742 −0.267871 0.963455i \(-0.586320\pi\)
−0.267871 + 0.963455i \(0.586320\pi\)
\(332\) 65.2312 3.58003
\(333\) 17.8554 0.978467
\(334\) −13.0090 −0.711824
\(335\) −9.71927 −0.531021
\(336\) −34.6879 −1.89238
\(337\) 29.8767 1.62749 0.813743 0.581225i \(-0.197426\pi\)
0.813743 + 0.581225i \(0.197426\pi\)
\(338\) 36.5465 1.98787
\(339\) −3.93342 −0.213634
\(340\) −22.8650 −1.24003
\(341\) 6.86928 0.371992
\(342\) 13.1067 0.708731
\(343\) −5.95326 −0.321446
\(344\) −10.9737 −0.591661
\(345\) 5.29696 0.285179
\(346\) −28.1505 −1.51338
\(347\) −8.49655 −0.456119 −0.228059 0.973647i \(-0.573238\pi\)
−0.228059 + 0.973647i \(0.573238\pi\)
\(348\) −15.1487 −0.812054
\(349\) 1.48664 0.0795779 0.0397890 0.999208i \(-0.487331\pi\)
0.0397890 + 0.999208i \(0.487331\pi\)
\(350\) −98.6225 −5.27159
\(351\) 0.0339708 0.00181323
\(352\) 31.5896 1.68373
\(353\) −25.1072 −1.33632 −0.668161 0.744016i \(-0.732918\pi\)
−0.668161 + 0.744016i \(0.732918\pi\)
\(354\) −18.2781 −0.971471
\(355\) 6.01057 0.319008
\(356\) 7.50684 0.397861
\(357\) −1.82151 −0.0964046
\(358\) −65.6961 −3.47215
\(359\) −21.7552 −1.14819 −0.574097 0.818787i \(-0.694647\pi\)
−0.574097 + 0.818787i \(0.694647\pi\)
\(360\) −116.047 −6.11619
\(361\) −16.0842 −0.846539
\(362\) 18.3971 0.966929
\(363\) −0.519316 −0.0272570
\(364\) 0.236374 0.0123894
\(365\) −16.3079 −0.853595
\(366\) 7.82109 0.408815
\(367\) 35.0902 1.83169 0.915847 0.401527i \(-0.131520\pi\)
0.915847 + 0.401527i \(0.131520\pi\)
\(368\) 50.1502 2.61426
\(369\) 5.22753 0.272134
\(370\) −71.2085 −3.70195
\(371\) 1.50861 0.0783232
\(372\) 21.0594 1.09188
\(373\) −27.1535 −1.40595 −0.702977 0.711212i \(-0.748147\pi\)
−0.702977 + 0.711212i \(0.748147\pi\)
\(374\) 2.81130 0.145369
\(375\) 10.0602 0.519506
\(376\) 81.2246 4.18884
\(377\) 0.0564075 0.00290513
\(378\) −29.3439 −1.50929
\(379\) 13.6401 0.700647 0.350324 0.936629i \(-0.386072\pi\)
0.350324 + 0.936629i \(0.386072\pi\)
\(380\) −39.0433 −2.00288
\(381\) 8.47830 0.434357
\(382\) 42.8876 2.19432
\(383\) 24.8297 1.26874 0.634369 0.773030i \(-0.281260\pi\)
0.634369 + 0.773030i \(0.281260\pi\)
\(384\) 41.2401 2.10453
\(385\) 13.5853 0.692370
\(386\) −50.8130 −2.58631
\(387\) −2.73031 −0.138790
\(388\) −60.5095 −3.07191
\(389\) 32.2088 1.63305 0.816525 0.577310i \(-0.195898\pi\)
0.816525 + 0.577310i \(0.195898\pi\)
\(390\) −0.0645511 −0.00326867
\(391\) 2.63346 0.133180
\(392\) −58.1902 −2.93905
\(393\) −6.19724 −0.312609
\(394\) −22.3162 −1.12427
\(395\) 24.7606 1.24584
\(396\) 16.1182 0.809968
\(397\) 8.01945 0.402485 0.201242 0.979541i \(-0.435502\pi\)
0.201242 + 0.979541i \(0.435502\pi\)
\(398\) −55.6316 −2.78856
\(399\) −3.11033 −0.155711
\(400\) 190.464 9.52322
\(401\) −36.4306 −1.81926 −0.909628 0.415424i \(-0.863633\pi\)
−0.909628 + 0.415424i \(0.863633\pi\)
\(402\) 3.66357 0.182722
\(403\) −0.0784165 −0.00390620
\(404\) 102.787 5.11386
\(405\) −25.7394 −1.27900
\(406\) −48.7246 −2.41816
\(407\) 6.53968 0.324160
\(408\) 5.69880 0.282133
\(409\) −12.2378 −0.605118 −0.302559 0.953131i \(-0.597841\pi\)
−0.302559 + 0.953131i \(0.597841\pi\)
\(410\) −20.8478 −1.02960
\(411\) −4.20181 −0.207260
\(412\) 64.3202 3.16883
\(413\) −43.9130 −2.16082
\(414\) 20.2137 0.993451
\(415\) −42.7977 −2.10086
\(416\) −0.360612 −0.0176804
\(417\) 3.16854 0.155164
\(418\) 4.80046 0.234798
\(419\) −31.6029 −1.54390 −0.771952 0.635680i \(-0.780720\pi\)
−0.771952 + 0.635680i \(0.780720\pi\)
\(420\) 41.6489 2.03226
\(421\) 0.303317 0.0147828 0.00739139 0.999973i \(-0.497647\pi\)
0.00739139 + 0.999973i \(0.497647\pi\)
\(422\) 75.7418 3.68705
\(423\) 20.2091 0.982602
\(424\) −4.71985 −0.229216
\(425\) 10.0016 0.485147
\(426\) −2.26561 −0.109769
\(427\) 18.7901 0.909317
\(428\) −91.5021 −4.42292
\(429\) 0.00592827 0.000286219 0
\(430\) 10.8887 0.525099
\(431\) 19.4718 0.937922 0.468961 0.883219i \(-0.344628\pi\)
0.468961 + 0.883219i \(0.344628\pi\)
\(432\) 56.6703 2.72655
\(433\) 37.7078 1.81212 0.906061 0.423146i \(-0.139074\pi\)
0.906061 + 0.423146i \(0.139074\pi\)
\(434\) 67.7359 3.25143
\(435\) 9.93894 0.476536
\(436\) 17.9832 0.861241
\(437\) 4.49679 0.215110
\(438\) 6.14708 0.293719
\(439\) 15.1155 0.721424 0.360712 0.932677i \(-0.382534\pi\)
0.360712 + 0.932677i \(0.382534\pi\)
\(440\) −42.5031 −2.02625
\(441\) −14.4781 −0.689432
\(442\) −0.0320925 −0.00152648
\(443\) 14.3934 0.683851 0.341926 0.939727i \(-0.388921\pi\)
0.341926 + 0.939727i \(0.388921\pi\)
\(444\) 20.0489 0.951479
\(445\) −4.92518 −0.233476
\(446\) 19.6582 0.930845
\(447\) −10.5608 −0.499509
\(448\) 177.904 8.40520
\(449\) −10.6901 −0.504499 −0.252249 0.967662i \(-0.581170\pi\)
−0.252249 + 0.967662i \(0.581170\pi\)
\(450\) 76.7693 3.61894
\(451\) 1.91463 0.0901562
\(452\) 44.7139 2.10316
\(453\) 5.48436 0.257678
\(454\) −53.8684 −2.52817
\(455\) −0.155083 −0.00727042
\(456\) 9.73102 0.455697
\(457\) 38.1362 1.78393 0.891967 0.452100i \(-0.149325\pi\)
0.891967 + 0.452100i \(0.149325\pi\)
\(458\) 61.6379 2.88015
\(459\) 2.97584 0.138900
\(460\) −60.2142 −2.80750
\(461\) −13.3416 −0.621379 −0.310690 0.950511i \(-0.600560\pi\)
−0.310690 + 0.950511i \(0.600560\pi\)
\(462\) −5.12082 −0.238242
\(463\) 2.64649 0.122993 0.0614964 0.998107i \(-0.480413\pi\)
0.0614964 + 0.998107i \(0.480413\pi\)
\(464\) 94.0992 4.36845
\(465\) −13.8169 −0.640744
\(466\) −54.3479 −2.51762
\(467\) 4.76154 0.220338 0.110169 0.993913i \(-0.464861\pi\)
0.110169 + 0.993913i \(0.464861\pi\)
\(468\) −0.183997 −0.00850528
\(469\) 8.80169 0.406424
\(470\) −80.5956 −3.71760
\(471\) 2.85842 0.131709
\(472\) 137.387 6.32373
\(473\) −1.00000 −0.0459800
\(474\) −9.33320 −0.428688
\(475\) 17.0782 0.783604
\(476\) 20.7064 0.949074
\(477\) −1.17433 −0.0537687
\(478\) 22.9091 1.04784
\(479\) −22.9002 −1.04634 −0.523169 0.852229i \(-0.675251\pi\)
−0.523169 + 0.852229i \(0.675251\pi\)
\(480\) −63.5394 −2.90016
\(481\) −0.0746539 −0.00340393
\(482\) −38.6128 −1.75876
\(483\) −4.79688 −0.218266
\(484\) 5.90341 0.268337
\(485\) 39.6998 1.80268
\(486\) 34.8001 1.57857
\(487\) −9.92863 −0.449909 −0.224954 0.974369i \(-0.572223\pi\)
−0.224954 + 0.974369i \(0.572223\pi\)
\(488\) −58.7869 −2.66116
\(489\) −1.86272 −0.0842349
\(490\) 57.7396 2.60841
\(491\) −4.36191 −0.196850 −0.0984250 0.995144i \(-0.531380\pi\)
−0.0984250 + 0.995144i \(0.531380\pi\)
\(492\) 5.86974 0.264628
\(493\) 4.94129 0.222544
\(494\) −0.0547998 −0.00246556
\(495\) −10.5750 −0.475311
\(496\) −130.815 −5.87376
\(497\) −5.44312 −0.244157
\(498\) 16.1321 0.722897
\(499\) −13.3366 −0.597027 −0.298513 0.954405i \(-0.596491\pi\)
−0.298513 + 0.954405i \(0.596491\pi\)
\(500\) −114.361 −5.11438
\(501\) −2.40309 −0.107362
\(502\) −33.0617 −1.47562
\(503\) −28.4232 −1.26733 −0.633664 0.773608i \(-0.718450\pi\)
−0.633664 + 0.773608i \(0.718450\pi\)
\(504\) 105.091 4.68111
\(505\) −67.4380 −3.00095
\(506\) 7.40345 0.329124
\(507\) 6.75104 0.299824
\(508\) −96.3786 −4.27611
\(509\) 44.4414 1.96983 0.984915 0.173041i \(-0.0553594\pi\)
0.984915 + 0.173041i \(0.0553594\pi\)
\(510\) −5.65467 −0.250393
\(511\) 14.7683 0.653311
\(512\) −183.621 −8.11499
\(513\) 5.08142 0.224350
\(514\) 39.3036 1.73361
\(515\) −42.2000 −1.85956
\(516\) −3.06573 −0.134961
\(517\) 7.40177 0.325530
\(518\) 64.4858 2.83334
\(519\) −5.20007 −0.228258
\(520\) 0.485195 0.0212772
\(521\) −35.9245 −1.57388 −0.786941 0.617028i \(-0.788336\pi\)
−0.786941 + 0.617028i \(0.788336\pi\)
\(522\) 37.9280 1.66006
\(523\) −24.5289 −1.07258 −0.536288 0.844035i \(-0.680174\pi\)
−0.536288 + 0.844035i \(0.680174\pi\)
\(524\) 70.4482 3.07754
\(525\) −18.2180 −0.795098
\(526\) −22.6977 −0.989668
\(527\) −6.86928 −0.299230
\(528\) 9.88957 0.430388
\(529\) −16.0649 −0.698473
\(530\) 4.68330 0.203430
\(531\) 34.1826 1.48340
\(532\) 35.3573 1.53293
\(533\) −0.0218565 −0.000946709 0
\(534\) 1.85649 0.0803382
\(535\) 60.0339 2.59549
\(536\) −27.5370 −1.18942
\(537\) −12.1357 −0.523692
\(538\) 48.7169 2.10034
\(539\) −5.30272 −0.228404
\(540\) −68.0426 −2.92809
\(541\) −15.4188 −0.662904 −0.331452 0.943472i \(-0.607539\pi\)
−0.331452 + 0.943472i \(0.607539\pi\)
\(542\) 78.8577 3.38723
\(543\) 3.39839 0.145839
\(544\) −31.5896 −1.35439
\(545\) −11.7987 −0.505400
\(546\) 0.0584569 0.00250172
\(547\) 34.5557 1.47750 0.738748 0.673982i \(-0.235417\pi\)
0.738748 + 0.673982i \(0.235417\pi\)
\(548\) 47.7648 2.04041
\(549\) −14.6265 −0.624244
\(550\) 28.1174 1.19893
\(551\) 8.43753 0.359451
\(552\) 15.0076 0.638765
\(553\) −22.4229 −0.953520
\(554\) −48.4148 −2.05695
\(555\) −13.1539 −0.558354
\(556\) −36.0189 −1.52754
\(557\) −33.5109 −1.41990 −0.709952 0.704250i \(-0.751283\pi\)
−0.709952 + 0.704250i \(0.751283\pi\)
\(558\) −52.7267 −2.23210
\(559\) 0.0114155 0.000482826 0
\(560\) −258.711 −10.9325
\(561\) 0.519316 0.0219255
\(562\) −19.7091 −0.831378
\(563\) 9.69280 0.408503 0.204251 0.978918i \(-0.434524\pi\)
0.204251 + 0.978918i \(0.434524\pi\)
\(564\) 22.6919 0.955500
\(565\) −29.3364 −1.23419
\(566\) 18.2624 0.767626
\(567\) 23.3094 0.978901
\(568\) 17.0294 0.714537
\(569\) −26.2214 −1.09926 −0.549629 0.835409i \(-0.685231\pi\)
−0.549629 + 0.835409i \(0.685231\pi\)
\(570\) −9.65567 −0.404431
\(571\) −28.9091 −1.20981 −0.604904 0.796298i \(-0.706789\pi\)
−0.604904 + 0.796298i \(0.706789\pi\)
\(572\) −0.0673906 −0.00281774
\(573\) 7.92239 0.330963
\(574\) 18.8796 0.788018
\(575\) 26.3388 1.09840
\(576\) −138.484 −5.77015
\(577\) 28.9096 1.20352 0.601762 0.798676i \(-0.294466\pi\)
0.601762 + 0.798676i \(0.294466\pi\)
\(578\) −2.81130 −0.116935
\(579\) −9.38640 −0.390085
\(580\) −112.983 −4.69135
\(581\) 38.7572 1.60792
\(582\) −14.9644 −0.620294
\(583\) −0.430107 −0.0178132
\(584\) −46.2042 −1.91194
\(585\) 0.120719 0.00499113
\(586\) 38.7867 1.60226
\(587\) 45.7431 1.88802 0.944010 0.329917i \(-0.107021\pi\)
0.944010 + 0.329917i \(0.107021\pi\)
\(588\) −16.2567 −0.670416
\(589\) −11.7297 −0.483313
\(590\) −136.323 −5.61232
\(591\) −4.12234 −0.169570
\(592\) −124.538 −5.11848
\(593\) −23.9941 −0.985321 −0.492661 0.870222i \(-0.663976\pi\)
−0.492661 + 0.870222i \(0.663976\pi\)
\(594\) 8.36598 0.343260
\(595\) −13.5853 −0.556942
\(596\) 120.052 4.91751
\(597\) −10.2765 −0.420590
\(598\) −0.0845144 −0.00345605
\(599\) −42.6384 −1.74216 −0.871078 0.491145i \(-0.836579\pi\)
−0.871078 + 0.491145i \(0.836579\pi\)
\(600\) 56.9969 2.32689
\(601\) −6.56555 −0.267814 −0.133907 0.990994i \(-0.542752\pi\)
−0.133907 + 0.990994i \(0.542752\pi\)
\(602\) −9.86070 −0.401892
\(603\) −6.85137 −0.279009
\(604\) −62.3444 −2.53676
\(605\) −3.87319 −0.157467
\(606\) 25.4200 1.03262
\(607\) −2.51778 −0.102194 −0.0510968 0.998694i \(-0.516272\pi\)
−0.0510968 + 0.998694i \(0.516272\pi\)
\(608\) −53.9410 −2.18759
\(609\) −9.00061 −0.364723
\(610\) 58.3317 2.36178
\(611\) −0.0844952 −0.00341831
\(612\) −16.1182 −0.651538
\(613\) 24.8885 1.00524 0.502619 0.864508i \(-0.332370\pi\)
0.502619 + 0.864508i \(0.332370\pi\)
\(614\) 9.44122 0.381017
\(615\) −3.85109 −0.155291
\(616\) 38.4904 1.55082
\(617\) 9.97405 0.401540 0.200770 0.979638i \(-0.435656\pi\)
0.200770 + 0.979638i \(0.435656\pi\)
\(618\) 15.9068 0.639866
\(619\) 27.3384 1.09882 0.549412 0.835551i \(-0.314852\pi\)
0.549412 + 0.835551i \(0.314852\pi\)
\(620\) 157.066 6.30793
\(621\) 7.83676 0.314478
\(622\) −61.7555 −2.47617
\(623\) 4.46020 0.178694
\(624\) −0.112895 −0.00451940
\(625\) 25.0236 1.00094
\(626\) −67.1018 −2.68193
\(627\) 0.886761 0.0354138
\(628\) −32.4936 −1.29664
\(629\) −6.53968 −0.260754
\(630\) −104.277 −4.15449
\(631\) 0.604598 0.0240687 0.0120343 0.999928i \(-0.496169\pi\)
0.0120343 + 0.999928i \(0.496169\pi\)
\(632\) 70.1526 2.79052
\(633\) 13.9914 0.556106
\(634\) 64.4067 2.55792
\(635\) 63.2333 2.50934
\(636\) −1.31859 −0.0522857
\(637\) 0.0605333 0.00239842
\(638\) 13.8914 0.549968
\(639\) 4.23701 0.167613
\(640\) 307.579 12.1581
\(641\) −39.7157 −1.56867 −0.784337 0.620334i \(-0.786997\pi\)
−0.784337 + 0.620334i \(0.786997\pi\)
\(642\) −22.6291 −0.893098
\(643\) −11.6165 −0.458109 −0.229054 0.973414i \(-0.573563\pi\)
−0.229054 + 0.973414i \(0.573563\pi\)
\(644\) 54.5294 2.14876
\(645\) 2.01141 0.0791990
\(646\) −4.80046 −0.188871
\(647\) 21.4472 0.843175 0.421587 0.906788i \(-0.361473\pi\)
0.421587 + 0.906788i \(0.361473\pi\)
\(648\) −72.9259 −2.86480
\(649\) 12.5197 0.491440
\(650\) −0.320975 −0.0125897
\(651\) 12.5125 0.490402
\(652\) 21.1748 0.829267
\(653\) 17.6162 0.689375 0.344687 0.938718i \(-0.387985\pi\)
0.344687 + 0.938718i \(0.387985\pi\)
\(654\) 4.44737 0.173906
\(655\) −46.2205 −1.80599
\(656\) −36.4611 −1.42357
\(657\) −11.4959 −0.448497
\(658\) 72.9867 2.84532
\(659\) 2.66401 0.103775 0.0518876 0.998653i \(-0.483476\pi\)
0.0518876 + 0.998653i \(0.483476\pi\)
\(660\) −11.8742 −0.462201
\(661\) 14.2659 0.554878 0.277439 0.960743i \(-0.410514\pi\)
0.277439 + 0.960743i \(0.410514\pi\)
\(662\) 27.4017 1.06500
\(663\) −0.00592827 −0.000230235 0
\(664\) −121.256 −4.70566
\(665\) −23.1977 −0.899566
\(666\) −50.1968 −1.94509
\(667\) 13.0127 0.503854
\(668\) 27.3175 1.05695
\(669\) 3.63136 0.140396
\(670\) 27.3238 1.05561
\(671\) −5.35709 −0.206808
\(672\) 57.5407 2.21968
\(673\) −34.9716 −1.34806 −0.674029 0.738705i \(-0.735438\pi\)
−0.674029 + 0.738705i \(0.735438\pi\)
\(674\) −83.9923 −3.23526
\(675\) 29.7631 1.14558
\(676\) −76.7436 −2.95168
\(677\) −0.574667 −0.0220862 −0.0110431 0.999939i \(-0.503515\pi\)
−0.0110431 + 0.999939i \(0.503515\pi\)
\(678\) 11.0580 0.424681
\(679\) −35.9518 −1.37970
\(680\) 42.5031 1.62992
\(681\) −9.95080 −0.381315
\(682\) −19.3116 −0.739480
\(683\) 11.9641 0.457793 0.228897 0.973451i \(-0.426488\pi\)
0.228897 + 0.973451i \(0.426488\pi\)
\(684\) −27.5227 −1.05236
\(685\) −31.3381 −1.19737
\(686\) 16.7364 0.638999
\(687\) 11.3860 0.434404
\(688\) 19.0435 0.726025
\(689\) 0.00490990 0.000187052 0
\(690\) −14.8914 −0.566904
\(691\) −40.1588 −1.52771 −0.763857 0.645386i \(-0.776697\pi\)
−0.763857 + 0.645386i \(0.776697\pi\)
\(692\) 59.1128 2.24713
\(693\) 9.57663 0.363786
\(694\) 23.8864 0.906714
\(695\) 23.6317 0.896403
\(696\) 28.1594 1.06738
\(697\) −1.91463 −0.0725216
\(698\) −4.17939 −0.158192
\(699\) −10.0394 −0.379725
\(700\) 207.096 7.82750
\(701\) −43.6561 −1.64887 −0.824434 0.565958i \(-0.808506\pi\)
−0.824434 + 0.565958i \(0.808506\pi\)
\(702\) −0.0955022 −0.00360450
\(703\) −11.1669 −0.421166
\(704\) −50.7208 −1.91161
\(705\) −14.8880 −0.560714
\(706\) 70.5840 2.65646
\(707\) 61.0712 2.29682
\(708\) 38.3820 1.44248
\(709\) 31.1498 1.16985 0.584927 0.811086i \(-0.301123\pi\)
0.584927 + 0.811086i \(0.301123\pi\)
\(710\) −16.8975 −0.634152
\(711\) 17.4544 0.654590
\(712\) −13.9542 −0.522957
\(713\) −18.0900 −0.677475
\(714\) 5.12082 0.191642
\(715\) 0.0442145 0.00165353
\(716\) 137.954 5.15559
\(717\) 4.23187 0.158042
\(718\) 61.1603 2.28248
\(719\) 18.1012 0.675060 0.337530 0.941315i \(-0.390409\pi\)
0.337530 + 0.941315i \(0.390409\pi\)
\(720\) 201.385 7.50516
\(721\) 38.2160 1.42324
\(722\) 45.2177 1.68283
\(723\) −7.13272 −0.265269
\(724\) −38.6318 −1.43574
\(725\) 49.4206 1.83544
\(726\) 1.45995 0.0541839
\(727\) −5.20586 −0.193075 −0.0965374 0.995329i \(-0.530777\pi\)
−0.0965374 + 0.995329i \(0.530777\pi\)
\(728\) −0.439388 −0.0162848
\(729\) −13.5082 −0.500303
\(730\) 45.8464 1.69685
\(731\) 1.00000 0.0369863
\(732\) −16.4234 −0.607027
\(733\) −15.5626 −0.574819 −0.287410 0.957808i \(-0.592794\pi\)
−0.287410 + 0.957808i \(0.592794\pi\)
\(734\) −98.6492 −3.64121
\(735\) 10.6659 0.393418
\(736\) −83.1899 −3.06642
\(737\) −2.50937 −0.0924340
\(738\) −14.6961 −0.540973
\(739\) −14.5384 −0.534802 −0.267401 0.963585i \(-0.586165\pi\)
−0.267401 + 0.963585i \(0.586165\pi\)
\(740\) 149.530 5.49683
\(741\) −0.0101229 −0.000371872 0
\(742\) −4.24116 −0.155698
\(743\) −1.08904 −0.0399531 −0.0199765 0.999800i \(-0.506359\pi\)
−0.0199765 + 0.999800i \(0.506359\pi\)
\(744\) −39.1466 −1.43519
\(745\) −78.7651 −2.88573
\(746\) 76.3367 2.79488
\(747\) −30.1692 −1.10384
\(748\) −5.90341 −0.215850
\(749\) −54.3661 −1.98650
\(750\) −28.2822 −1.03272
\(751\) −4.64806 −0.169610 −0.0848051 0.996398i \(-0.527027\pi\)
−0.0848051 + 0.996398i \(0.527027\pi\)
\(752\) −140.955 −5.14011
\(753\) −6.10731 −0.222563
\(754\) −0.158578 −0.00577508
\(755\) 40.9037 1.48864
\(756\) 61.6188 2.24105
\(757\) −10.5012 −0.381673 −0.190837 0.981622i \(-0.561120\pi\)
−0.190837 + 0.981622i \(0.561120\pi\)
\(758\) −38.3466 −1.39281
\(759\) 1.36760 0.0496407
\(760\) 72.5764 2.63262
\(761\) 42.4589 1.53913 0.769566 0.638567i \(-0.220473\pi\)
0.769566 + 0.638567i \(0.220473\pi\)
\(762\) −23.8351 −0.863453
\(763\) 10.6848 0.386815
\(764\) −90.0592 −3.25823
\(765\) 10.5750 0.382340
\(766\) −69.8037 −2.52211
\(767\) −0.142919 −0.00516049
\(768\) −63.2581 −2.28263
\(769\) 28.8096 1.03890 0.519450 0.854501i \(-0.326137\pi\)
0.519450 + 0.854501i \(0.326137\pi\)
\(770\) −38.1923 −1.37636
\(771\) 7.26033 0.261474
\(772\) 106.702 3.84027
\(773\) −2.31475 −0.0832557 −0.0416278 0.999133i \(-0.513254\pi\)
−0.0416278 + 0.999133i \(0.513254\pi\)
\(774\) 7.67573 0.275898
\(775\) −68.7036 −2.46791
\(776\) 112.479 4.03777
\(777\) 11.9121 0.427344
\(778\) −90.5486 −3.24632
\(779\) −3.26933 −0.117136
\(780\) 0.135550 0.00485347
\(781\) 1.55184 0.0555292
\(782\) −7.40345 −0.264747
\(783\) 14.7045 0.525495
\(784\) 100.982 3.60650
\(785\) 21.3188 0.760901
\(786\) 17.4223 0.621433
\(787\) 11.3616 0.404998 0.202499 0.979282i \(-0.435094\pi\)
0.202499 + 0.979282i \(0.435094\pi\)
\(788\) 46.8615 1.66937
\(789\) −4.19282 −0.149268
\(790\) −69.6094 −2.47659
\(791\) 26.5668 0.944607
\(792\) −29.9615 −1.06464
\(793\) 0.0611540 0.00217164
\(794\) −22.5451 −0.800095
\(795\) 0.865120 0.0306827
\(796\) 116.820 4.14058
\(797\) −42.5118 −1.50584 −0.752922 0.658110i \(-0.771356\pi\)
−0.752922 + 0.658110i \(0.771356\pi\)
\(798\) 8.74409 0.309537
\(799\) −7.40177 −0.261856
\(800\) −315.945 −11.1703
\(801\) −3.47189 −0.122673
\(802\) 102.417 3.61648
\(803\) −4.21046 −0.148584
\(804\) −7.69308 −0.271314
\(805\) −35.7763 −1.26095
\(806\) 0.220452 0.00776510
\(807\) 8.99920 0.316787
\(808\) −191.068 −6.72175
\(809\) −22.7019 −0.798156 −0.399078 0.916917i \(-0.630670\pi\)
−0.399078 + 0.916917i \(0.630670\pi\)
\(810\) 72.3612 2.54251
\(811\) −38.7505 −1.36071 −0.680356 0.732881i \(-0.738175\pi\)
−0.680356 + 0.732881i \(0.738175\pi\)
\(812\) 102.316 3.59059
\(813\) 14.5669 0.510885
\(814\) −18.3850 −0.644394
\(815\) −13.8926 −0.486637
\(816\) −9.88957 −0.346204
\(817\) 1.70756 0.0597399
\(818\) 34.4040 1.20291
\(819\) −0.109322 −0.00382003
\(820\) 43.7780 1.52879
\(821\) 15.9746 0.557517 0.278759 0.960361i \(-0.410077\pi\)
0.278759 + 0.960361i \(0.410077\pi\)
\(822\) 11.8125 0.412010
\(823\) −5.92180 −0.206421 −0.103211 0.994660i \(-0.532912\pi\)
−0.103211 + 0.994660i \(0.532912\pi\)
\(824\) −119.563 −4.16517
\(825\) 5.19397 0.180831
\(826\) 123.453 4.29547
\(827\) −16.4543 −0.572170 −0.286085 0.958204i \(-0.592354\pi\)
−0.286085 + 0.958204i \(0.592354\pi\)
\(828\) −42.4466 −1.47512
\(829\) −15.7088 −0.545588 −0.272794 0.962072i \(-0.587948\pi\)
−0.272794 + 0.962072i \(0.587948\pi\)
\(830\) 120.317 4.17627
\(831\) −8.94338 −0.310243
\(832\) 0.579005 0.0200734
\(833\) 5.30272 0.183728
\(834\) −8.90771 −0.308449
\(835\) −17.9228 −0.620245
\(836\) −10.0804 −0.348638
\(837\) −20.4419 −0.706575
\(838\) 88.8454 3.06911
\(839\) 12.5643 0.433769 0.216884 0.976197i \(-0.430411\pi\)
0.216884 + 0.976197i \(0.430411\pi\)
\(840\) −77.4198 −2.67124
\(841\) −4.58367 −0.158057
\(842\) −0.852716 −0.0293865
\(843\) −3.64075 −0.125394
\(844\) −159.049 −5.47470
\(845\) 50.3509 1.73212
\(846\) −56.8140 −1.95331
\(847\) 3.50752 0.120520
\(848\) 8.19073 0.281271
\(849\) 3.37351 0.115779
\(850\) −28.1174 −0.964420
\(851\) −17.2220 −0.590362
\(852\) 4.75753 0.162990
\(853\) −51.2404 −1.75444 −0.877218 0.480092i \(-0.840603\pi\)
−0.877218 + 0.480092i \(0.840603\pi\)
\(854\) −52.8246 −1.80762
\(855\) 18.0574 0.617551
\(856\) 170.090 5.81357
\(857\) −12.5459 −0.428560 −0.214280 0.976772i \(-0.568741\pi\)
−0.214280 + 0.976772i \(0.568741\pi\)
\(858\) −0.0166661 −0.000568973 0
\(859\) 5.16346 0.176175 0.0880875 0.996113i \(-0.471924\pi\)
0.0880875 + 0.996113i \(0.471924\pi\)
\(860\) −22.8650 −0.779691
\(861\) 3.48751 0.118854
\(862\) −54.7410 −1.86449
\(863\) −32.1977 −1.09602 −0.548012 0.836471i \(-0.684615\pi\)
−0.548012 + 0.836471i \(0.684615\pi\)
\(864\) −94.0055 −3.19813
\(865\) −38.7835 −1.31868
\(866\) −106.008 −3.60230
\(867\) −0.519316 −0.0176369
\(868\) −142.238 −4.82786
\(869\) 6.39281 0.216861
\(870\) −27.9413 −0.947300
\(871\) 0.0286459 0.000970628 0
\(872\) −33.4285 −1.13203
\(873\) 27.9855 0.947165
\(874\) −12.6418 −0.427616
\(875\) −67.9478 −2.29705
\(876\) −12.9082 −0.436126
\(877\) 31.4856 1.06319 0.531596 0.846998i \(-0.321592\pi\)
0.531596 + 0.846998i \(0.321592\pi\)
\(878\) −42.4942 −1.43411
\(879\) 7.16485 0.241664
\(880\) 73.7589 2.48641
\(881\) −39.5941 −1.33396 −0.666980 0.745076i \(-0.732413\pi\)
−0.666980 + 0.745076i \(0.732413\pi\)
\(882\) 40.7022 1.37051
\(883\) 4.83234 0.162621 0.0813106 0.996689i \(-0.474089\pi\)
0.0813106 + 0.996689i \(0.474089\pi\)
\(884\) 0.0673906 0.00226659
\(885\) −25.1821 −0.846488
\(886\) −40.4642 −1.35942
\(887\) −39.7939 −1.33615 −0.668074 0.744095i \(-0.732881\pi\)
−0.668074 + 0.744095i \(0.732881\pi\)
\(888\) −37.2683 −1.25064
\(889\) −57.2635 −1.92056
\(890\) 13.8462 0.464124
\(891\) −6.64553 −0.222634
\(892\) −41.2801 −1.38216
\(893\) −12.6390 −0.422946
\(894\) 29.6896 0.992968
\(895\) −90.5108 −3.02544
\(896\) −278.541 −9.30540
\(897\) −0.0156119 −0.000521265 0
\(898\) 30.0532 1.00289
\(899\) −33.9431 −1.13207
\(900\) −161.207 −5.37356
\(901\) 0.430107 0.0143289
\(902\) −5.38259 −0.179221
\(903\) −1.82151 −0.0606161
\(904\) −83.1172 −2.76444
\(905\) 25.3460 0.842530
\(906\) −15.4182 −0.512235
\(907\) 35.7701 1.18773 0.593863 0.804566i \(-0.297602\pi\)
0.593863 + 0.804566i \(0.297602\pi\)
\(908\) 113.117 3.75394
\(909\) −47.5388 −1.57676
\(910\) 0.435986 0.0144528
\(911\) 10.2524 0.339676 0.169838 0.985472i \(-0.445676\pi\)
0.169838 + 0.985472i \(0.445676\pi\)
\(912\) −16.8870 −0.559184
\(913\) −11.0497 −0.365693
\(914\) −107.212 −3.54627
\(915\) 10.7753 0.356220
\(916\) −129.433 −4.27657
\(917\) 41.8569 1.38224
\(918\) −8.36598 −0.276119
\(919\) −48.2450 −1.59146 −0.795728 0.605654i \(-0.792912\pi\)
−0.795728 + 0.605654i \(0.792912\pi\)
\(920\) 111.930 3.69023
\(921\) 1.74402 0.0574675
\(922\) 37.5072 1.23523
\(923\) −0.0177151 −0.000583099 0
\(924\) 10.7531 0.353752
\(925\) −65.4070 −2.15057
\(926\) −7.44008 −0.244496
\(927\) −29.7479 −0.977050
\(928\) −156.093 −5.12401
\(929\) −46.0633 −1.51129 −0.755643 0.654983i \(-0.772676\pi\)
−0.755643 + 0.654983i \(0.772676\pi\)
\(930\) 38.8435 1.27373
\(931\) 9.05469 0.296755
\(932\) 114.125 3.73827
\(933\) −11.4077 −0.373473
\(934\) −13.3861 −0.438007
\(935\) 3.87319 0.126667
\(936\) 0.342027 0.0111795
\(937\) −51.5586 −1.68435 −0.842173 0.539207i \(-0.818724\pi\)
−0.842173 + 0.539207i \(0.818724\pi\)
\(938\) −24.7442 −0.807927
\(939\) −12.3953 −0.404507
\(940\) 169.242 5.52006
\(941\) −39.5505 −1.28931 −0.644654 0.764474i \(-0.722999\pi\)
−0.644654 + 0.764474i \(0.722999\pi\)
\(942\) −8.03588 −0.261823
\(943\) −5.04210 −0.164193
\(944\) −238.418 −7.75983
\(945\) −40.4276 −1.31511
\(946\) 2.81130 0.0914033
\(947\) −10.2925 −0.334463 −0.167231 0.985918i \(-0.553483\pi\)
−0.167231 + 0.985918i \(0.553483\pi\)
\(948\) 19.5987 0.636535
\(949\) 0.0480647 0.00156025
\(950\) −48.0121 −1.55772
\(951\) 11.8975 0.385802
\(952\) −38.4904 −1.24748
\(953\) −34.3129 −1.11150 −0.555752 0.831348i \(-0.687570\pi\)
−0.555752 + 0.831348i \(0.687570\pi\)
\(954\) 3.30139 0.106886
\(955\) 59.0872 1.91202
\(956\) −48.1066 −1.55588
\(957\) 2.56609 0.0829499
\(958\) 64.3795 2.08001
\(959\) 28.3795 0.916423
\(960\) 102.020 3.29269
\(961\) 16.1870 0.522161
\(962\) 0.209875 0.00676663
\(963\) 42.3195 1.36373
\(964\) 81.0825 2.61149
\(965\) −70.0061 −2.25358
\(966\) 13.4855 0.433888
\(967\) 0.729577 0.0234616 0.0117308 0.999931i \(-0.496266\pi\)
0.0117308 + 0.999931i \(0.496266\pi\)
\(968\) −10.9737 −0.352707
\(969\) −0.886761 −0.0284869
\(970\) −111.608 −3.58352
\(971\) 39.5844 1.27032 0.635162 0.772379i \(-0.280933\pi\)
0.635162 + 0.772379i \(0.280933\pi\)
\(972\) −73.0763 −2.34392
\(973\) −21.4007 −0.686075
\(974\) 27.9124 0.894369
\(975\) −0.0592920 −0.00189886
\(976\) 102.017 3.26550
\(977\) −19.5297 −0.624811 −0.312405 0.949949i \(-0.601135\pi\)
−0.312405 + 0.949949i \(0.601135\pi\)
\(978\) 5.23666 0.167450
\(979\) −1.27161 −0.0406408
\(980\) −121.247 −3.87308
\(981\) −8.31720 −0.265548
\(982\) 12.2626 0.391316
\(983\) −45.1335 −1.43954 −0.719768 0.694215i \(-0.755752\pi\)
−0.719768 + 0.694215i \(0.755752\pi\)
\(984\) −10.9111 −0.347832
\(985\) −30.7455 −0.979632
\(986\) −13.8914 −0.442394
\(987\) 13.4824 0.429150
\(988\) 0.115073 0.00366097
\(989\) 2.63346 0.0837392
\(990\) 29.7295 0.944866
\(991\) −14.3895 −0.457099 −0.228549 0.973532i \(-0.573398\pi\)
−0.228549 + 0.973532i \(0.573398\pi\)
\(992\) 216.997 6.88968
\(993\) 5.06175 0.160630
\(994\) 15.3022 0.485358
\(995\) −76.6448 −2.42980
\(996\) −33.8756 −1.07339
\(997\) −21.3458 −0.676029 −0.338015 0.941141i \(-0.609755\pi\)
−0.338015 + 0.941141i \(0.609755\pi\)
\(998\) 37.4931 1.18682
\(999\) −19.4610 −0.615720
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 \(a_p\))