Properties

Label 5077.2.a.c.1.13
Level 5077
Weight 2
Character 5077.1
Self dual Yes
Analytic conductor 40.540
Analytic rank 0
Dimension 216
CM No

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Newspace parameters

Level: \( N \) = \( 5077 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 5077.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(40.5400491062\)
Analytic rank: \(0\)
Dimension: \(216\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 5077.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.48492 q^{2} -1.01672 q^{3} +4.17484 q^{4} +0.988176 q^{5} +2.52648 q^{6} +3.63719 q^{7} -5.40431 q^{8} -1.96628 q^{9} +O(q^{10})\) \(q-2.48492 q^{2} -1.01672 q^{3} +4.17484 q^{4} +0.988176 q^{5} +2.52648 q^{6} +3.63719 q^{7} -5.40431 q^{8} -1.96628 q^{9} -2.45554 q^{10} +0.624460 q^{11} -4.24465 q^{12} -2.18793 q^{13} -9.03814 q^{14} -1.00470 q^{15} +5.07961 q^{16} +4.02301 q^{17} +4.88604 q^{18} +2.34236 q^{19} +4.12548 q^{20} -3.69801 q^{21} -1.55173 q^{22} -1.45796 q^{23} +5.49468 q^{24} -4.02351 q^{25} +5.43684 q^{26} +5.04932 q^{27} +15.1847 q^{28} +5.68065 q^{29} +2.49660 q^{30} -1.16585 q^{31} -1.81381 q^{32} -0.634902 q^{33} -9.99687 q^{34} +3.59418 q^{35} -8.20889 q^{36} -5.24356 q^{37} -5.82058 q^{38} +2.22452 q^{39} -5.34041 q^{40} -7.68601 q^{41} +9.18927 q^{42} -8.47532 q^{43} +2.60702 q^{44} -1.94303 q^{45} +3.62291 q^{46} -4.56245 q^{47} -5.16455 q^{48} +6.22916 q^{49} +9.99811 q^{50} -4.09028 q^{51} -9.13426 q^{52} +8.31041 q^{53} -12.5472 q^{54} +0.617076 q^{55} -19.6565 q^{56} -2.38153 q^{57} -14.1160 q^{58} -3.61586 q^{59} -4.19446 q^{60} +6.45215 q^{61} +2.89704 q^{62} -7.15172 q^{63} -5.65203 q^{64} -2.16206 q^{65} +1.57768 q^{66} +0.418439 q^{67} +16.7954 q^{68} +1.48234 q^{69} -8.93127 q^{70} +14.6848 q^{71} +10.6264 q^{72} +9.87776 q^{73} +13.0298 q^{74} +4.09079 q^{75} +9.77897 q^{76} +2.27128 q^{77} -5.52775 q^{78} +8.32119 q^{79} +5.01954 q^{80} +0.765073 q^{81} +19.0991 q^{82} +15.4844 q^{83} -15.4386 q^{84} +3.97544 q^{85} +21.0605 q^{86} -5.77564 q^{87} -3.37477 q^{88} -6.49830 q^{89} +4.82827 q^{90} -7.95792 q^{91} -6.08673 q^{92} +1.18534 q^{93} +11.3373 q^{94} +2.31466 q^{95} +1.84414 q^{96} +11.5609 q^{97} -15.4790 q^{98} -1.22786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + O(q^{10}) \) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + 24q^{10} + 89q^{11} + 114q^{12} + 34q^{13} + 53q^{14} + 61q^{15} + 229q^{16} + 76q^{17} + 57q^{18} + 54q^{19} + 118q^{20} + 25q^{21} + 26q^{22} + 109q^{23} + 65q^{24} + 232q^{25} + 58q^{26} + 236q^{27} + 57q^{28} + 54q^{29} + 6q^{30} + 77q^{31} + 155q^{32} + 80q^{33} + 28q^{34} + 137q^{35} + 257q^{36} + 42q^{37} + 104q^{38} + 46q^{39} + 47q^{40} + 109q^{41} + 27q^{42} + 68q^{43} + 145q^{44} + 109q^{45} - 7q^{46} + 264q^{47} + 198q^{48} + 222q^{49} + 86q^{50} + 57q^{51} + 68q^{52} + 95q^{53} + 79q^{54} + 50q^{55} + 108q^{56} + 55q^{57} + 38q^{58} + 292q^{59} + 91q^{60} + 16q^{61} + 91q^{62} + 113q^{63} + 231q^{64} + 68q^{65} - 15q^{66} + 152q^{67} + 199q^{68} + 83q^{69} + 24q^{70} + 131q^{71} + 162q^{72} + 71q^{73} + 10q^{74} + 232q^{75} + 60q^{76} + 131q^{77} + 102q^{78} + 10q^{79} + 236q^{80} + 268q^{81} + 54q^{82} + 299q^{83} - 9q^{85} + 35q^{86} + 103q^{87} + 45q^{88} + 134q^{89} + 8q^{90} + 79q^{91} + 206q^{92} + 95q^{93} + 18q^{94} + 119q^{95} + 77q^{96} + 129q^{97} + 150q^{98} + 221q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.48492 −1.75711 −0.878553 0.477645i \(-0.841490\pi\)
−0.878553 + 0.477645i \(0.841490\pi\)
\(3\) −1.01672 −0.587005 −0.293502 0.955958i \(-0.594821\pi\)
−0.293502 + 0.955958i \(0.594821\pi\)
\(4\) 4.17484 2.08742
\(5\) 0.988176 0.441926 0.220963 0.975282i \(-0.429080\pi\)
0.220963 + 0.975282i \(0.429080\pi\)
\(6\) 2.52648 1.03143
\(7\) 3.63719 1.37473 0.687364 0.726313i \(-0.258768\pi\)
0.687364 + 0.726313i \(0.258768\pi\)
\(8\) −5.40431 −1.91071
\(9\) −1.96628 −0.655426
\(10\) −2.45554 −0.776510
\(11\) 0.624460 0.188282 0.0941408 0.995559i \(-0.469990\pi\)
0.0941408 + 0.995559i \(0.469990\pi\)
\(12\) −4.24465 −1.22533
\(13\) −2.18793 −0.606823 −0.303411 0.952860i \(-0.598126\pi\)
−0.303411 + 0.952860i \(0.598126\pi\)
\(14\) −9.03814 −2.41554
\(15\) −1.00470 −0.259412
\(16\) 5.07961 1.26990
\(17\) 4.02301 0.975724 0.487862 0.872921i \(-0.337777\pi\)
0.487862 + 0.872921i \(0.337777\pi\)
\(18\) 4.88604 1.15165
\(19\) 2.34236 0.537374 0.268687 0.963228i \(-0.413410\pi\)
0.268687 + 0.963228i \(0.413410\pi\)
\(20\) 4.12548 0.922485
\(21\) −3.69801 −0.806972
\(22\) −1.55173 −0.330831
\(23\) −1.45796 −0.304005 −0.152002 0.988380i \(-0.548572\pi\)
−0.152002 + 0.988380i \(0.548572\pi\)
\(24\) 5.49468 1.12160
\(25\) −4.02351 −0.804702
\(26\) 5.43684 1.06625
\(27\) 5.04932 0.971743
\(28\) 15.1847 2.86964
\(29\) 5.68065 1.05487 0.527435 0.849595i \(-0.323154\pi\)
0.527435 + 0.849595i \(0.323154\pi\)
\(30\) 2.49660 0.455815
\(31\) −1.16585 −0.209392 −0.104696 0.994504i \(-0.533387\pi\)
−0.104696 + 0.994504i \(0.533387\pi\)
\(32\) −1.81381 −0.320640
\(33\) −0.634902 −0.110522
\(34\) −9.99687 −1.71445
\(35\) 3.59418 0.607528
\(36\) −8.20889 −1.36815
\(37\) −5.24356 −0.862035 −0.431018 0.902344i \(-0.641845\pi\)
−0.431018 + 0.902344i \(0.641845\pi\)
\(38\) −5.82058 −0.944223
\(39\) 2.22452 0.356208
\(40\) −5.34041 −0.844392
\(41\) −7.68601 −1.20035 −0.600176 0.799868i \(-0.704903\pi\)
−0.600176 + 0.799868i \(0.704903\pi\)
\(42\) 9.18927 1.41794
\(43\) −8.47532 −1.29247 −0.646237 0.763137i \(-0.723658\pi\)
−0.646237 + 0.763137i \(0.723658\pi\)
\(44\) 2.60702 0.393023
\(45\) −1.94303 −0.289649
\(46\) 3.62291 0.534169
\(47\) −4.56245 −0.665502 −0.332751 0.943015i \(-0.607977\pi\)
−0.332751 + 0.943015i \(0.607977\pi\)
\(48\) −5.16455 −0.745438
\(49\) 6.22916 0.889880
\(50\) 9.99811 1.41395
\(51\) −4.09028 −0.572754
\(52\) −9.13426 −1.26669
\(53\) 8.31041 1.14152 0.570761 0.821116i \(-0.306648\pi\)
0.570761 + 0.821116i \(0.306648\pi\)
\(54\) −12.5472 −1.70745
\(55\) 0.617076 0.0832065
\(56\) −19.6565 −2.62671
\(57\) −2.38153 −0.315441
\(58\) −14.1160 −1.85352
\(59\) −3.61586 −0.470745 −0.235373 0.971905i \(-0.575631\pi\)
−0.235373 + 0.971905i \(0.575631\pi\)
\(60\) −4.19446 −0.541503
\(61\) 6.45215 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(62\) 2.89704 0.367924
\(63\) −7.15172 −0.901032
\(64\) −5.65203 −0.706504
\(65\) −2.16206 −0.268171
\(66\) 1.57768 0.194199
\(67\) 0.418439 0.0511205 0.0255602 0.999673i \(-0.491863\pi\)
0.0255602 + 0.999673i \(0.491863\pi\)
\(68\) 16.7954 2.03674
\(69\) 1.48234 0.178452
\(70\) −8.93127 −1.06749
\(71\) 14.6848 1.74277 0.871383 0.490604i \(-0.163224\pi\)
0.871383 + 0.490604i \(0.163224\pi\)
\(72\) 10.6264 1.25233
\(73\) 9.87776 1.15610 0.578052 0.816000i \(-0.303813\pi\)
0.578052 + 0.816000i \(0.303813\pi\)
\(74\) 13.0298 1.51469
\(75\) 4.09079 0.472364
\(76\) 9.77897 1.12173
\(77\) 2.27128 0.258836
\(78\) −5.52775 −0.625895
\(79\) 8.32119 0.936207 0.468103 0.883674i \(-0.344938\pi\)
0.468103 + 0.883674i \(0.344938\pi\)
\(80\) 5.01954 0.561202
\(81\) 0.765073 0.0850081
\(82\) 19.0991 2.10915
\(83\) 15.4844 1.69964 0.849819 0.527074i \(-0.176711\pi\)
0.849819 + 0.527074i \(0.176711\pi\)
\(84\) −15.4386 −1.68449
\(85\) 3.97544 0.431197
\(86\) 21.0605 2.27101
\(87\) −5.77564 −0.619213
\(88\) −3.37477 −0.359752
\(89\) −6.49830 −0.688819 −0.344409 0.938820i \(-0.611921\pi\)
−0.344409 + 0.938820i \(0.611921\pi\)
\(90\) 4.82827 0.508945
\(91\) −7.95792 −0.834217
\(92\) −6.08673 −0.634586
\(93\) 1.18534 0.122914
\(94\) 11.3373 1.16936
\(95\) 2.31466 0.237479
\(96\) 1.84414 0.188217
\(97\) 11.5609 1.17384 0.586918 0.809646i \(-0.300341\pi\)
0.586918 + 0.809646i \(0.300341\pi\)
\(98\) −15.4790 −1.56361
\(99\) −1.22786 −0.123405
\(100\) −16.7975 −1.67975
\(101\) 7.23075 0.719487 0.359743 0.933051i \(-0.382864\pi\)
0.359743 + 0.933051i \(0.382864\pi\)
\(102\) 10.1640 1.00639
\(103\) −6.57102 −0.647462 −0.323731 0.946149i \(-0.604937\pi\)
−0.323731 + 0.946149i \(0.604937\pi\)
\(104\) 11.8243 1.15946
\(105\) −3.65429 −0.356622
\(106\) −20.6507 −2.00578
\(107\) −14.5074 −1.40249 −0.701244 0.712921i \(-0.747372\pi\)
−0.701244 + 0.712921i \(0.747372\pi\)
\(108\) 21.0801 2.02843
\(109\) 6.57188 0.629472 0.314736 0.949179i \(-0.398084\pi\)
0.314736 + 0.949179i \(0.398084\pi\)
\(110\) −1.53339 −0.146203
\(111\) 5.33124 0.506019
\(112\) 18.4755 1.74577
\(113\) 15.2742 1.43687 0.718437 0.695592i \(-0.244858\pi\)
0.718437 + 0.695592i \(0.244858\pi\)
\(114\) 5.91791 0.554263
\(115\) −1.44072 −0.134348
\(116\) 23.7158 2.20196
\(117\) 4.30208 0.397727
\(118\) 8.98514 0.827149
\(119\) 14.6325 1.34136
\(120\) 5.42971 0.495662
\(121\) −10.6101 −0.964550
\(122\) −16.0331 −1.45157
\(123\) 7.81453 0.704613
\(124\) −4.86722 −0.437089
\(125\) −8.91681 −0.797544
\(126\) 17.7715 1.58321
\(127\) −1.33877 −0.118797 −0.0593983 0.998234i \(-0.518918\pi\)
−0.0593983 + 0.998234i \(0.518918\pi\)
\(128\) 17.6725 1.56204
\(129\) 8.61705 0.758689
\(130\) 5.37255 0.471204
\(131\) 8.02998 0.701583 0.350791 0.936454i \(-0.385913\pi\)
0.350791 + 0.936454i \(0.385913\pi\)
\(132\) −2.65061 −0.230706
\(133\) 8.51961 0.738744
\(134\) −1.03979 −0.0898241
\(135\) 4.98962 0.429438
\(136\) −21.7416 −1.86433
\(137\) −0.943447 −0.0806041 −0.0403021 0.999188i \(-0.512832\pi\)
−0.0403021 + 0.999188i \(0.512832\pi\)
\(138\) −3.68349 −0.313560
\(139\) 2.23326 0.189423 0.0947114 0.995505i \(-0.469807\pi\)
0.0947114 + 0.995505i \(0.469807\pi\)
\(140\) 15.0051 1.26817
\(141\) 4.63874 0.390653
\(142\) −36.4906 −3.06222
\(143\) −1.36627 −0.114254
\(144\) −9.98791 −0.832326
\(145\) 5.61348 0.466174
\(146\) −24.5455 −2.03140
\(147\) −6.33332 −0.522364
\(148\) −21.8910 −1.79943
\(149\) −10.7238 −0.878525 −0.439263 0.898359i \(-0.644760\pi\)
−0.439263 + 0.898359i \(0.644760\pi\)
\(150\) −10.1653 −0.829993
\(151\) 5.74870 0.467823 0.233911 0.972258i \(-0.424847\pi\)
0.233911 + 0.972258i \(0.424847\pi\)
\(152\) −12.6588 −1.02677
\(153\) −7.91035 −0.639514
\(154\) −5.64395 −0.454803
\(155\) −1.15206 −0.0925357
\(156\) 9.28700 0.743555
\(157\) −13.1629 −1.05051 −0.525257 0.850944i \(-0.676031\pi\)
−0.525257 + 0.850944i \(0.676031\pi\)
\(158\) −20.6775 −1.64501
\(159\) −8.44938 −0.670079
\(160\) −1.79237 −0.141699
\(161\) −5.30287 −0.417924
\(162\) −1.90115 −0.149368
\(163\) −8.11829 −0.635873 −0.317937 0.948112i \(-0.602990\pi\)
−0.317937 + 0.948112i \(0.602990\pi\)
\(164\) −32.0879 −2.50564
\(165\) −0.627395 −0.0488426
\(166\) −38.4776 −2.98644
\(167\) 24.8440 1.92249 0.961245 0.275697i \(-0.0889086\pi\)
0.961245 + 0.275697i \(0.0889086\pi\)
\(168\) 19.9852 1.54189
\(169\) −8.21296 −0.631766
\(170\) −9.87867 −0.757659
\(171\) −4.60573 −0.352209
\(172\) −35.3831 −2.69794
\(173\) 17.7256 1.34765 0.673824 0.738892i \(-0.264650\pi\)
0.673824 + 0.738892i \(0.264650\pi\)
\(174\) 14.3520 1.08802
\(175\) −14.6343 −1.10625
\(176\) 3.17201 0.239099
\(177\) 3.67633 0.276330
\(178\) 16.1478 1.21033
\(179\) −17.0896 −1.27733 −0.638667 0.769483i \(-0.720514\pi\)
−0.638667 + 0.769483i \(0.720514\pi\)
\(180\) −8.11183 −0.604620
\(181\) 15.6493 1.16321 0.581603 0.813473i \(-0.302426\pi\)
0.581603 + 0.813473i \(0.302426\pi\)
\(182\) 19.7748 1.46581
\(183\) −6.56005 −0.484933
\(184\) 7.87925 0.580866
\(185\) −5.18156 −0.380956
\(186\) −2.94548 −0.215973
\(187\) 2.51221 0.183711
\(188\) −19.0475 −1.38918
\(189\) 18.3653 1.33588
\(190\) −5.75176 −0.417276
\(191\) 22.7148 1.64358 0.821791 0.569789i \(-0.192975\pi\)
0.821791 + 0.569789i \(0.192975\pi\)
\(192\) 5.74654 0.414721
\(193\) −19.3702 −1.39430 −0.697149 0.716926i \(-0.745549\pi\)
−0.697149 + 0.716926i \(0.745549\pi\)
\(194\) −28.7281 −2.06255
\(195\) 2.19822 0.157417
\(196\) 26.0057 1.85755
\(197\) 22.6028 1.61039 0.805193 0.593013i \(-0.202062\pi\)
0.805193 + 0.593013i \(0.202062\pi\)
\(198\) 3.05114 0.216835
\(199\) −21.2481 −1.50624 −0.753119 0.657885i \(-0.771451\pi\)
−0.753119 + 0.657885i \(0.771451\pi\)
\(200\) 21.7443 1.53755
\(201\) −0.425436 −0.0300080
\(202\) −17.9679 −1.26421
\(203\) 20.6616 1.45016
\(204\) −17.0763 −1.19558
\(205\) −7.59513 −0.530467
\(206\) 16.3285 1.13766
\(207\) 2.86675 0.199253
\(208\) −11.1138 −0.770605
\(209\) 1.46271 0.101178
\(210\) 9.08062 0.626622
\(211\) 10.5163 0.723970 0.361985 0.932184i \(-0.382099\pi\)
0.361985 + 0.932184i \(0.382099\pi\)
\(212\) 34.6946 2.38284
\(213\) −14.9304 −1.02301
\(214\) 36.0499 2.46432
\(215\) −8.37511 −0.571178
\(216\) −27.2881 −1.85672
\(217\) −4.24040 −0.287857
\(218\) −16.3306 −1.10605
\(219\) −10.0429 −0.678639
\(220\) 2.57619 0.173687
\(221\) −8.80207 −0.592092
\(222\) −13.2477 −0.889128
\(223\) −11.1717 −0.748112 −0.374056 0.927406i \(-0.622033\pi\)
−0.374056 + 0.927406i \(0.622033\pi\)
\(224\) −6.59718 −0.440793
\(225\) 7.91133 0.527422
\(226\) −37.9552 −2.52474
\(227\) −5.17318 −0.343356 −0.171678 0.985153i \(-0.554919\pi\)
−0.171678 + 0.985153i \(0.554919\pi\)
\(228\) −9.94250 −0.658458
\(229\) −1.19125 −0.0787200 −0.0393600 0.999225i \(-0.512532\pi\)
−0.0393600 + 0.999225i \(0.512532\pi\)
\(230\) 3.58007 0.236063
\(231\) −2.30926 −0.151938
\(232\) −30.7000 −2.01555
\(233\) −2.04746 −0.134134 −0.0670668 0.997748i \(-0.521364\pi\)
−0.0670668 + 0.997748i \(0.521364\pi\)
\(234\) −10.6903 −0.698849
\(235\) −4.50850 −0.294102
\(236\) −15.0957 −0.982643
\(237\) −8.46033 −0.549558
\(238\) −36.3605 −2.35690
\(239\) 18.1662 1.17507 0.587536 0.809198i \(-0.300098\pi\)
0.587536 + 0.809198i \(0.300098\pi\)
\(240\) −5.10348 −0.329428
\(241\) 4.54739 0.292923 0.146461 0.989216i \(-0.453212\pi\)
0.146461 + 0.989216i \(0.453212\pi\)
\(242\) 26.3652 1.69482
\(243\) −15.9258 −1.02164
\(244\) 26.9367 1.72445
\(245\) 6.15551 0.393261
\(246\) −19.4185 −1.23808
\(247\) −5.12492 −0.326091
\(248\) 6.30059 0.400088
\(249\) −15.7434 −0.997696
\(250\) 22.1576 1.40137
\(251\) −19.6105 −1.23781 −0.618903 0.785468i \(-0.712422\pi\)
−0.618903 + 0.785468i \(0.712422\pi\)
\(252\) −29.8573 −1.88083
\(253\) −0.910435 −0.0572386
\(254\) 3.32674 0.208738
\(255\) −4.04192 −0.253115
\(256\) −32.6107 −2.03817
\(257\) −0.823088 −0.0513428 −0.0256714 0.999670i \(-0.508172\pi\)
−0.0256714 + 0.999670i \(0.508172\pi\)
\(258\) −21.4127 −1.33310
\(259\) −19.0718 −1.18506
\(260\) −9.02626 −0.559785
\(261\) −11.1697 −0.691388
\(262\) −19.9539 −1.23276
\(263\) 25.3624 1.56391 0.781957 0.623332i \(-0.214221\pi\)
0.781957 + 0.623332i \(0.214221\pi\)
\(264\) 3.43120 0.211176
\(265\) 8.21215 0.504468
\(266\) −21.1706 −1.29805
\(267\) 6.60697 0.404340
\(268\) 1.74692 0.106710
\(269\) −3.12700 −0.190657 −0.0953283 0.995446i \(-0.530390\pi\)
−0.0953283 + 0.995446i \(0.530390\pi\)
\(270\) −12.3988 −0.754568
\(271\) −5.44132 −0.330537 −0.165268 0.986249i \(-0.552849\pi\)
−0.165268 + 0.986249i \(0.552849\pi\)
\(272\) 20.4353 1.23907
\(273\) 8.09100 0.489689
\(274\) 2.34439 0.141630
\(275\) −2.51252 −0.151511
\(276\) 6.18852 0.372505
\(277\) 20.8112 1.25042 0.625212 0.780455i \(-0.285013\pi\)
0.625212 + 0.780455i \(0.285013\pi\)
\(278\) −5.54948 −0.332836
\(279\) 2.29237 0.137241
\(280\) −19.4241 −1.16081
\(281\) 23.4113 1.39660 0.698302 0.715803i \(-0.253939\pi\)
0.698302 + 0.715803i \(0.253939\pi\)
\(282\) −11.5269 −0.686418
\(283\) −16.1980 −0.962873 −0.481436 0.876481i \(-0.659885\pi\)
−0.481436 + 0.876481i \(0.659885\pi\)
\(284\) 61.3067 3.63788
\(285\) −2.35337 −0.139402
\(286\) 3.39509 0.200756
\(287\) −27.9555 −1.65016
\(288\) 3.56646 0.210155
\(289\) −0.815375 −0.0479633
\(290\) −13.9491 −0.819117
\(291\) −11.7543 −0.689048
\(292\) 41.2381 2.41328
\(293\) 14.3088 0.835929 0.417965 0.908463i \(-0.362744\pi\)
0.417965 + 0.908463i \(0.362744\pi\)
\(294\) 15.7378 0.917848
\(295\) −3.57311 −0.208035
\(296\) 28.3378 1.64710
\(297\) 3.15310 0.182961
\(298\) 26.6477 1.54366
\(299\) 3.18991 0.184477
\(300\) 17.0784 0.986021
\(301\) −30.8264 −1.77680
\(302\) −14.2851 −0.822014
\(303\) −7.35166 −0.422342
\(304\) 11.8983 0.682412
\(305\) 6.37586 0.365081
\(306\) 19.6566 1.12369
\(307\) −17.7442 −1.01272 −0.506359 0.862323i \(-0.669009\pi\)
−0.506359 + 0.862323i \(0.669009\pi\)
\(308\) 9.48222 0.540300
\(309\) 6.68090 0.380063
\(310\) 2.86278 0.162595
\(311\) −32.1906 −1.82536 −0.912680 0.408675i \(-0.865991\pi\)
−0.912680 + 0.408675i \(0.865991\pi\)
\(312\) −12.0220 −0.680610
\(313\) 24.5305 1.38655 0.693273 0.720675i \(-0.256168\pi\)
0.693273 + 0.720675i \(0.256168\pi\)
\(314\) 32.7088 1.84586
\(315\) −7.06716 −0.398189
\(316\) 34.7396 1.95426
\(317\) −18.4095 −1.03398 −0.516992 0.855991i \(-0.672948\pi\)
−0.516992 + 0.855991i \(0.672948\pi\)
\(318\) 20.9960 1.17740
\(319\) 3.54733 0.198613
\(320\) −5.58520 −0.312222
\(321\) 14.7500 0.823267
\(322\) 13.1772 0.734337
\(323\) 9.42334 0.524329
\(324\) 3.19406 0.177448
\(325\) 8.80316 0.488311
\(326\) 20.1733 1.11730
\(327\) −6.68177 −0.369503
\(328\) 41.5376 2.29353
\(329\) −16.5945 −0.914885
\(330\) 1.55903 0.0858216
\(331\) 21.5825 1.18628 0.593140 0.805099i \(-0.297888\pi\)
0.593140 + 0.805099i \(0.297888\pi\)
\(332\) 64.6451 3.54786
\(333\) 10.3103 0.565000
\(334\) −61.7355 −3.37802
\(335\) 0.413492 0.0225915
\(336\) −18.7844 −1.02478
\(337\) 20.9053 1.13879 0.569393 0.822065i \(-0.307178\pi\)
0.569393 + 0.822065i \(0.307178\pi\)
\(338\) 20.4086 1.11008
\(339\) −15.5296 −0.843452
\(340\) 16.5968 0.900090
\(341\) −0.728023 −0.0394247
\(342\) 11.4449 0.618868
\(343\) −2.80370 −0.151385
\(344\) 45.8032 2.46955
\(345\) 1.46481 0.0788627
\(346\) −44.0466 −2.36796
\(347\) 5.25339 0.282017 0.141008 0.990008i \(-0.454966\pi\)
0.141008 + 0.990008i \(0.454966\pi\)
\(348\) −24.1124 −1.29256
\(349\) −25.6279 −1.37183 −0.685915 0.727682i \(-0.740598\pi\)
−0.685915 + 0.727682i \(0.740598\pi\)
\(350\) 36.3650 1.94379
\(351\) −11.0476 −0.589676
\(352\) −1.13265 −0.0603706
\(353\) 24.5561 1.30699 0.653495 0.756930i \(-0.273302\pi\)
0.653495 + 0.756930i \(0.273302\pi\)
\(354\) −9.13539 −0.485541
\(355\) 14.5112 0.770173
\(356\) −27.1294 −1.43785
\(357\) −14.8771 −0.787382
\(358\) 42.4662 2.24441
\(359\) −8.71875 −0.460158 −0.230079 0.973172i \(-0.573898\pi\)
−0.230079 + 0.973172i \(0.573898\pi\)
\(360\) 10.5007 0.553436
\(361\) −13.5134 −0.711229
\(362\) −38.8874 −2.04388
\(363\) 10.7875 0.566195
\(364\) −33.2231 −1.74136
\(365\) 9.76097 0.510912
\(366\) 16.3012 0.852078
\(367\) 33.9166 1.77043 0.885217 0.465179i \(-0.154010\pi\)
0.885217 + 0.465179i \(0.154010\pi\)
\(368\) −7.40584 −0.386056
\(369\) 15.1128 0.786742
\(370\) 12.8758 0.669379
\(371\) 30.2265 1.56928
\(372\) 4.94861 0.256573
\(373\) 9.18720 0.475695 0.237848 0.971302i \(-0.423558\pi\)
0.237848 + 0.971302i \(0.423558\pi\)
\(374\) −6.24264 −0.322799
\(375\) 9.06592 0.468162
\(376\) 24.6569 1.27158
\(377\) −12.4289 −0.640119
\(378\) −45.6365 −2.34729
\(379\) −17.3311 −0.890237 −0.445119 0.895472i \(-0.646839\pi\)
−0.445119 + 0.895472i \(0.646839\pi\)
\(380\) 9.66335 0.495719
\(381\) 1.36116 0.0697342
\(382\) −56.4444 −2.88795
\(383\) 24.1713 1.23510 0.617548 0.786533i \(-0.288126\pi\)
0.617548 + 0.786533i \(0.288126\pi\)
\(384\) −17.9680 −0.916926
\(385\) 2.24442 0.114386
\(386\) 48.1335 2.44993
\(387\) 16.6648 0.847121
\(388\) 48.2651 2.45029
\(389\) −17.5722 −0.890946 −0.445473 0.895295i \(-0.646965\pi\)
−0.445473 + 0.895295i \(0.646965\pi\)
\(390\) −5.46239 −0.276599
\(391\) −5.86538 −0.296625
\(392\) −33.6643 −1.70030
\(393\) −8.16426 −0.411832
\(394\) −56.1663 −2.82962
\(395\) 8.22280 0.413734
\(396\) −5.12612 −0.257597
\(397\) 8.08127 0.405587 0.202794 0.979221i \(-0.434998\pi\)
0.202794 + 0.979221i \(0.434998\pi\)
\(398\) 52.7999 2.64662
\(399\) −8.66207 −0.433646
\(400\) −20.4378 −1.02189
\(401\) −6.14445 −0.306839 −0.153420 0.988161i \(-0.549029\pi\)
−0.153420 + 0.988161i \(0.549029\pi\)
\(402\) 1.05718 0.0527272
\(403\) 2.55079 0.127064
\(404\) 30.1872 1.50187
\(405\) 0.756027 0.0375673
\(406\) −51.3425 −2.54808
\(407\) −3.27439 −0.162305
\(408\) 22.1052 1.09437
\(409\) 19.5110 0.964758 0.482379 0.875963i \(-0.339773\pi\)
0.482379 + 0.875963i \(0.339773\pi\)
\(410\) 18.8733 0.932086
\(411\) 0.959223 0.0473150
\(412\) −27.4330 −1.35152
\(413\) −13.1516 −0.647147
\(414\) −7.12364 −0.350108
\(415\) 15.3014 0.751114
\(416\) 3.96850 0.194571
\(417\) −2.27061 −0.111192
\(418\) −3.63472 −0.177780
\(419\) 7.34814 0.358980 0.179490 0.983760i \(-0.442555\pi\)
0.179490 + 0.983760i \(0.442555\pi\)
\(420\) −15.2561 −0.744420
\(421\) 18.7072 0.911734 0.455867 0.890048i \(-0.349329\pi\)
0.455867 + 0.890048i \(0.349329\pi\)
\(422\) −26.1321 −1.27209
\(423\) 8.97104 0.436187
\(424\) −44.9120 −2.18112
\(425\) −16.1866 −0.785166
\(426\) 37.1008 1.79754
\(427\) 23.4677 1.13568
\(428\) −60.5663 −2.92758
\(429\) 1.38912 0.0670674
\(430\) 20.8115 1.00362
\(431\) −5.79410 −0.279092 −0.139546 0.990216i \(-0.544564\pi\)
−0.139546 + 0.990216i \(0.544564\pi\)
\(432\) 25.6486 1.23402
\(433\) 8.35735 0.401629 0.200814 0.979629i \(-0.435641\pi\)
0.200814 + 0.979629i \(0.435641\pi\)
\(434\) 10.5371 0.505796
\(435\) −5.70735 −0.273646
\(436\) 27.4365 1.31397
\(437\) −3.41506 −0.163364
\(438\) 24.9559 1.19244
\(439\) 12.8535 0.613463 0.306732 0.951796i \(-0.400765\pi\)
0.306732 + 0.951796i \(0.400765\pi\)
\(440\) −3.33487 −0.158984
\(441\) −12.2482 −0.583250
\(442\) 21.8725 1.04037
\(443\) 31.9042 1.51581 0.757907 0.652362i \(-0.226222\pi\)
0.757907 + 0.652362i \(0.226222\pi\)
\(444\) 22.2571 1.05627
\(445\) −6.42147 −0.304407
\(446\) 27.7608 1.31451
\(447\) 10.9031 0.515698
\(448\) −20.5575 −0.971251
\(449\) −30.3400 −1.43183 −0.715916 0.698187i \(-0.753991\pi\)
−0.715916 + 0.698187i \(0.753991\pi\)
\(450\) −19.6590 −0.926736
\(451\) −4.79960 −0.226004
\(452\) 63.7673 2.99936
\(453\) −5.84483 −0.274614
\(454\) 12.8549 0.603313
\(455\) −7.86383 −0.368662
\(456\) 12.8705 0.602717
\(457\) −28.2348 −1.32077 −0.660385 0.750927i \(-0.729607\pi\)
−0.660385 + 0.750927i \(0.729607\pi\)
\(458\) 2.96016 0.138319
\(459\) 20.3135 0.948152
\(460\) −6.01477 −0.280440
\(461\) 1.33906 0.0623660 0.0311830 0.999514i \(-0.490073\pi\)
0.0311830 + 0.999514i \(0.490073\pi\)
\(462\) 5.73833 0.266971
\(463\) 14.6917 0.682781 0.341391 0.939922i \(-0.389102\pi\)
0.341391 + 0.939922i \(0.389102\pi\)
\(464\) 28.8554 1.33958
\(465\) 1.17133 0.0543189
\(466\) 5.08778 0.235687
\(467\) −6.83882 −0.316463 −0.158231 0.987402i \(-0.550579\pi\)
−0.158231 + 0.987402i \(0.550579\pi\)
\(468\) 17.9605 0.830224
\(469\) 1.52194 0.0702768
\(470\) 11.2033 0.516769
\(471\) 13.3830 0.616657
\(472\) 19.5412 0.899459
\(473\) −5.29250 −0.243349
\(474\) 21.0233 0.965631
\(475\) −9.42450 −0.432426
\(476\) 61.0882 2.79997
\(477\) −16.3406 −0.748183
\(478\) −45.1415 −2.06472
\(479\) −31.4716 −1.43797 −0.718987 0.695023i \(-0.755394\pi\)
−0.718987 + 0.695023i \(0.755394\pi\)
\(480\) 1.82234 0.0831779
\(481\) 11.4725 0.523103
\(482\) −11.2999 −0.514696
\(483\) 5.39154 0.245324
\(484\) −44.2953 −2.01342
\(485\) 11.4243 0.518749
\(486\) 39.5745 1.79513
\(487\) 15.4593 0.700526 0.350263 0.936651i \(-0.386092\pi\)
0.350263 + 0.936651i \(0.386092\pi\)
\(488\) −34.8694 −1.57846
\(489\) 8.25404 0.373261
\(490\) −15.2960 −0.691001
\(491\) 4.05713 0.183096 0.0915478 0.995801i \(-0.470819\pi\)
0.0915478 + 0.995801i \(0.470819\pi\)
\(492\) 32.6244 1.47082
\(493\) 22.8533 1.02926
\(494\) 12.7350 0.572976
\(495\) −1.21334 −0.0545357
\(496\) −5.92204 −0.265907
\(497\) 53.4114 2.39583
\(498\) 39.1211 1.75306
\(499\) 25.9311 1.16084 0.580419 0.814318i \(-0.302889\pi\)
0.580419 + 0.814318i \(0.302889\pi\)
\(500\) −37.2263 −1.66481
\(501\) −25.2595 −1.12851
\(502\) 48.7306 2.17495
\(503\) −4.36970 −0.194835 −0.0974176 0.995244i \(-0.531058\pi\)
−0.0974176 + 0.995244i \(0.531058\pi\)
\(504\) 38.6501 1.72161
\(505\) 7.14526 0.317960
\(506\) 2.26236 0.100574
\(507\) 8.35029 0.370850
\(508\) −5.58915 −0.247979
\(509\) −8.57581 −0.380116 −0.190058 0.981773i \(-0.560868\pi\)
−0.190058 + 0.981773i \(0.560868\pi\)
\(510\) 10.0439 0.444750
\(511\) 35.9273 1.58933
\(512\) 45.6901 2.01923
\(513\) 11.8273 0.522189
\(514\) 2.04531 0.0902148
\(515\) −6.49333 −0.286130
\(516\) 35.9748 1.58370
\(517\) −2.84907 −0.125302
\(518\) 47.3920 2.08228
\(519\) −18.0220 −0.791076
\(520\) 11.6844 0.512397
\(521\) 35.6554 1.56209 0.781046 0.624474i \(-0.214686\pi\)
0.781046 + 0.624474i \(0.214686\pi\)
\(522\) 27.7559 1.21484
\(523\) −31.8977 −1.39479 −0.697396 0.716686i \(-0.745658\pi\)
−0.697396 + 0.716686i \(0.745658\pi\)
\(524\) 33.5239 1.46450
\(525\) 14.8790 0.649372
\(526\) −63.0237 −2.74796
\(527\) −4.69021 −0.204309
\(528\) −3.22505 −0.140352
\(529\) −20.8744 −0.907581
\(530\) −20.4066 −0.886404
\(531\) 7.10979 0.308539
\(532\) 35.5680 1.54207
\(533\) 16.8165 0.728402
\(534\) −16.4178 −0.710468
\(535\) −14.3359 −0.619795
\(536\) −2.26137 −0.0976765
\(537\) 17.3753 0.749801
\(538\) 7.77035 0.335004
\(539\) 3.88986 0.167548
\(540\) 20.8309 0.896417
\(541\) 25.7069 1.10523 0.552614 0.833438i \(-0.313631\pi\)
0.552614 + 0.833438i \(0.313631\pi\)
\(542\) 13.5213 0.580788
\(543\) −15.9110 −0.682807
\(544\) −7.29699 −0.312856
\(545\) 6.49417 0.278180
\(546\) −20.1055 −0.860436
\(547\) 34.9436 1.49408 0.747039 0.664780i \(-0.231475\pi\)
0.747039 + 0.664780i \(0.231475\pi\)
\(548\) −3.93874 −0.168255
\(549\) −12.6867 −0.541456
\(550\) 6.24341 0.266220
\(551\) 13.3061 0.566860
\(552\) −8.01100 −0.340971
\(553\) 30.2657 1.28703
\(554\) −51.7142 −2.19713
\(555\) 5.26820 0.223623
\(556\) 9.32351 0.395405
\(557\) 32.4500 1.37495 0.687475 0.726208i \(-0.258719\pi\)
0.687475 + 0.726208i \(0.258719\pi\)
\(558\) −5.69637 −0.241147
\(559\) 18.5434 0.784303
\(560\) 18.2570 0.771501
\(561\) −2.55422 −0.107839
\(562\) −58.1754 −2.45398
\(563\) 29.0044 1.22239 0.611194 0.791481i \(-0.290689\pi\)
0.611194 + 0.791481i \(0.290689\pi\)
\(564\) 19.3660 0.815456
\(565\) 15.0936 0.634992
\(566\) 40.2508 1.69187
\(567\) 2.78272 0.116863
\(568\) −79.3612 −3.32992
\(569\) −43.8271 −1.83733 −0.918663 0.395042i \(-0.870730\pi\)
−0.918663 + 0.395042i \(0.870730\pi\)
\(570\) 5.84794 0.244943
\(571\) 8.87583 0.371442 0.185721 0.982603i \(-0.440538\pi\)
0.185721 + 0.982603i \(0.440538\pi\)
\(572\) −5.70398 −0.238495
\(573\) −23.0946 −0.964791
\(574\) 69.4672 2.89951
\(575\) 5.86610 0.244633
\(576\) 11.1135 0.463061
\(577\) −5.52846 −0.230153 −0.115076 0.993357i \(-0.536711\pi\)
−0.115076 + 0.993357i \(0.536711\pi\)
\(578\) 2.02614 0.0842765
\(579\) 19.6941 0.818460
\(580\) 23.4354 0.973101
\(581\) 56.3199 2.33654
\(582\) 29.2084 1.21073
\(583\) 5.18952 0.214928
\(584\) −53.3825 −2.20898
\(585\) 4.25121 0.175766
\(586\) −35.5563 −1.46882
\(587\) −21.4131 −0.883814 −0.441907 0.897061i \(-0.645698\pi\)
−0.441907 + 0.897061i \(0.645698\pi\)
\(588\) −26.4406 −1.09039
\(589\) −2.73083 −0.112522
\(590\) 8.87890 0.365539
\(591\) −22.9808 −0.945304
\(592\) −26.6352 −1.09470
\(593\) 31.5205 1.29439 0.647196 0.762324i \(-0.275941\pi\)
0.647196 + 0.762324i \(0.275941\pi\)
\(594\) −7.83520 −0.321482
\(595\) 14.4594 0.592780
\(596\) −44.7700 −1.83385
\(597\) 21.6034 0.884169
\(598\) −7.92668 −0.324146
\(599\) −8.82326 −0.360509 −0.180254 0.983620i \(-0.557692\pi\)
−0.180254 + 0.983620i \(0.557692\pi\)
\(600\) −22.1079 −0.902550
\(601\) 21.1253 0.861718 0.430859 0.902419i \(-0.358211\pi\)
0.430859 + 0.902419i \(0.358211\pi\)
\(602\) 76.6011 3.12203
\(603\) −0.822767 −0.0335057
\(604\) 23.9999 0.976543
\(605\) −10.4846 −0.426259
\(606\) 18.2683 0.742100
\(607\) −23.3445 −0.947523 −0.473762 0.880653i \(-0.657104\pi\)
−0.473762 + 0.880653i \(0.657104\pi\)
\(608\) −4.24860 −0.172303
\(609\) −21.0071 −0.851251
\(610\) −15.8435 −0.641486
\(611\) 9.98233 0.403842
\(612\) −33.0245 −1.33493
\(613\) −10.4762 −0.423128 −0.211564 0.977364i \(-0.567856\pi\)
−0.211564 + 0.977364i \(0.567856\pi\)
\(614\) 44.0931 1.77945
\(615\) 7.72213 0.311387
\(616\) −12.2747 −0.494561
\(617\) −34.9105 −1.40545 −0.702723 0.711464i \(-0.748033\pi\)
−0.702723 + 0.711464i \(0.748033\pi\)
\(618\) −16.6015 −0.667811
\(619\) −47.1354 −1.89453 −0.947265 0.320451i \(-0.896165\pi\)
−0.947265 + 0.320451i \(0.896165\pi\)
\(620\) −4.80967 −0.193161
\(621\) −7.36169 −0.295415
\(622\) 79.9911 3.20735
\(623\) −23.6356 −0.946939
\(624\) 11.2997 0.452349
\(625\) 11.3062 0.452246
\(626\) −60.9564 −2.43631
\(627\) −1.48717 −0.0593918
\(628\) −54.9530 −2.19286
\(629\) −21.0949 −0.841108
\(630\) 17.5613 0.699661
\(631\) 36.8985 1.46891 0.734453 0.678659i \(-0.237439\pi\)
0.734453 + 0.678659i \(0.237439\pi\)
\(632\) −44.9702 −1.78882
\(633\) −10.6921 −0.424974
\(634\) 45.7463 1.81682
\(635\) −1.32294 −0.0524993
\(636\) −35.2748 −1.39874
\(637\) −13.6290 −0.540000
\(638\) −8.81485 −0.348983
\(639\) −28.8744 −1.14225
\(640\) 17.4635 0.690306
\(641\) 20.3616 0.804236 0.402118 0.915588i \(-0.368274\pi\)
0.402118 + 0.915588i \(0.368274\pi\)
\(642\) −36.6527 −1.44657
\(643\) 3.16593 0.124852 0.0624261 0.998050i \(-0.480116\pi\)
0.0624261 + 0.998050i \(0.480116\pi\)
\(644\) −22.1386 −0.872384
\(645\) 8.51516 0.335284
\(646\) −23.4163 −0.921301
\(647\) −25.5296 −1.00367 −0.501837 0.864962i \(-0.667342\pi\)
−0.501837 + 0.864962i \(0.667342\pi\)
\(648\) −4.13469 −0.162426
\(649\) −2.25796 −0.0886327
\(650\) −21.8752 −0.858015
\(651\) 4.31131 0.168974
\(652\) −33.8925 −1.32733
\(653\) 0.951977 0.0372537 0.0186269 0.999827i \(-0.494071\pi\)
0.0186269 + 0.999827i \(0.494071\pi\)
\(654\) 16.6037 0.649255
\(655\) 7.93504 0.310048
\(656\) −39.0419 −1.52433
\(657\) −19.4224 −0.757741
\(658\) 41.2361 1.60755
\(659\) 43.3788 1.68980 0.844899 0.534927i \(-0.179661\pi\)
0.844899 + 0.534927i \(0.179661\pi\)
\(660\) −2.61927 −0.101955
\(661\) 0.913915 0.0355472 0.0177736 0.999842i \(-0.494342\pi\)
0.0177736 + 0.999842i \(0.494342\pi\)
\(662\) −53.6308 −2.08442
\(663\) 8.94926 0.347561
\(664\) −83.6827 −3.24752
\(665\) 8.41887 0.326470
\(666\) −25.6202 −0.992764
\(667\) −8.28214 −0.320686
\(668\) 103.720 4.01304
\(669\) 11.3585 0.439145
\(670\) −1.02749 −0.0396956
\(671\) 4.02911 0.155542
\(672\) 6.70750 0.258747
\(673\) −8.73710 −0.336790 −0.168395 0.985720i \(-0.553858\pi\)
−0.168395 + 0.985720i \(0.553858\pi\)
\(674\) −51.9482 −2.00097
\(675\) −20.3160 −0.781963
\(676\) −34.2878 −1.31876
\(677\) 24.2923 0.933628 0.466814 0.884355i \(-0.345402\pi\)
0.466814 + 0.884355i \(0.345402\pi\)
\(678\) 38.5898 1.48203
\(679\) 42.0494 1.61371
\(680\) −21.4845 −0.823894
\(681\) 5.25969 0.201552
\(682\) 1.80908 0.0692733
\(683\) 33.5716 1.28458 0.642290 0.766462i \(-0.277984\pi\)
0.642290 + 0.766462i \(0.277984\pi\)
\(684\) −19.2282 −0.735207
\(685\) −0.932292 −0.0356210
\(686\) 6.96697 0.266000
\(687\) 1.21117 0.0462090
\(688\) −43.0513 −1.64132
\(689\) −18.1826 −0.692702
\(690\) −3.63994 −0.138570
\(691\) −34.5440 −1.31411 −0.657057 0.753841i \(-0.728199\pi\)
−0.657057 + 0.753841i \(0.728199\pi\)
\(692\) 74.0013 2.81311
\(693\) −4.46596 −0.169648
\(694\) −13.0543 −0.495533
\(695\) 2.20686 0.0837108
\(696\) 31.2133 1.18314
\(697\) −30.9209 −1.17121
\(698\) 63.6833 2.41045
\(699\) 2.08170 0.0787370
\(700\) −61.0957 −2.30920
\(701\) −39.0620 −1.47535 −0.737676 0.675155i \(-0.764077\pi\)
−0.737676 + 0.675155i \(0.764077\pi\)
\(702\) 27.4524 1.03612
\(703\) −12.2823 −0.463235
\(704\) −3.52946 −0.133022
\(705\) 4.58390 0.172639
\(706\) −61.0201 −2.29652
\(707\) 26.2996 0.989099
\(708\) 15.3481 0.576816
\(709\) −21.4201 −0.804447 −0.402224 0.915541i \(-0.631763\pi\)
−0.402224 + 0.915541i \(0.631763\pi\)
\(710\) −36.0591 −1.35328
\(711\) −16.3618 −0.613614
\(712\) 35.1188 1.31613
\(713\) 1.69975 0.0636562
\(714\) 36.9686 1.38351
\(715\) −1.35012 −0.0504916
\(716\) −71.3462 −2.66633
\(717\) −18.4699 −0.689772
\(718\) 21.6654 0.808546
\(719\) 6.27683 0.234086 0.117043 0.993127i \(-0.462658\pi\)
0.117043 + 0.993127i \(0.462658\pi\)
\(720\) −9.86981 −0.367826
\(721\) −23.9001 −0.890085
\(722\) 33.5796 1.24970
\(723\) −4.62343 −0.171947
\(724\) 65.3335 2.42810
\(725\) −22.8561 −0.848855
\(726\) −26.8060 −0.994865
\(727\) 28.5799 1.05997 0.529985 0.848007i \(-0.322197\pi\)
0.529985 + 0.848007i \(0.322197\pi\)
\(728\) 43.0071 1.59395
\(729\) 13.8969 0.514701
\(730\) −24.2552 −0.897727
\(731\) −34.0963 −1.26110
\(732\) −27.3871 −1.01226
\(733\) 31.9135 1.17875 0.589376 0.807859i \(-0.299374\pi\)
0.589376 + 0.807859i \(0.299374\pi\)
\(734\) −84.2802 −3.11084
\(735\) −6.25844 −0.230846
\(736\) 2.64446 0.0974760
\(737\) 0.261298 0.00962505
\(738\) −37.5542 −1.38239
\(739\) 10.0008 0.367886 0.183943 0.982937i \(-0.441114\pi\)
0.183943 + 0.982937i \(0.441114\pi\)
\(740\) −21.6322 −0.795214
\(741\) 5.21062 0.191417
\(742\) −75.1106 −2.75740
\(743\) 29.6922 1.08930 0.544651 0.838663i \(-0.316662\pi\)
0.544651 + 0.838663i \(0.316662\pi\)
\(744\) −6.40595 −0.234853
\(745\) −10.5970 −0.388243
\(746\) −22.8295 −0.835847
\(747\) −30.4467 −1.11399
\(748\) 10.4881 0.383482
\(749\) −52.7664 −1.92804
\(750\) −22.5281 −0.822610
\(751\) 41.7543 1.52364 0.761819 0.647790i \(-0.224307\pi\)
0.761819 + 0.647790i \(0.224307\pi\)
\(752\) −23.1755 −0.845122
\(753\) 19.9385 0.726598
\(754\) 30.8848 1.12476
\(755\) 5.68073 0.206743
\(756\) 76.6724 2.78855
\(757\) −14.0926 −0.512203 −0.256101 0.966650i \(-0.582438\pi\)
−0.256101 + 0.966650i \(0.582438\pi\)
\(758\) 43.0664 1.56424
\(759\) 0.925659 0.0335993
\(760\) −12.5091 −0.453755
\(761\) 36.2927 1.31561 0.657805 0.753188i \(-0.271485\pi\)
0.657805 + 0.753188i \(0.271485\pi\)
\(762\) −3.38237 −0.122530
\(763\) 23.9032 0.865353
\(764\) 94.8305 3.43085
\(765\) −7.81682 −0.282618
\(766\) −60.0638 −2.17019
\(767\) 7.91126 0.285659
\(768\) 33.1560 1.19641
\(769\) −19.6555 −0.708796 −0.354398 0.935095i \(-0.615314\pi\)
−0.354398 + 0.935095i \(0.615314\pi\)
\(770\) −5.57722 −0.200989
\(771\) 0.836852 0.0301385
\(772\) −80.8675 −2.91049
\(773\) 21.2641 0.764815 0.382408 0.923994i \(-0.375095\pi\)
0.382408 + 0.923994i \(0.375095\pi\)
\(774\) −41.4108 −1.48848
\(775\) 4.69079 0.168498
\(776\) −62.4789 −2.24286
\(777\) 19.3907 0.695639
\(778\) 43.6656 1.56549
\(779\) −18.0034 −0.645038
\(780\) 9.17720 0.328596
\(781\) 9.17007 0.328131
\(782\) 14.5750 0.521201
\(783\) 28.6834 1.02506
\(784\) 31.6417 1.13006
\(785\) −13.0073 −0.464249
\(786\) 20.2876 0.723633
\(787\) 48.1034 1.71470 0.857351 0.514732i \(-0.172109\pi\)
0.857351 + 0.514732i \(0.172109\pi\)
\(788\) 94.3632 3.36155
\(789\) −25.7865 −0.918025
\(790\) −20.4330 −0.726974
\(791\) 55.5551 1.97531
\(792\) 6.63573 0.235791
\(793\) −14.1169 −0.501305
\(794\) −20.0813 −0.712660
\(795\) −8.34947 −0.296125
\(796\) −88.7074 −3.14415
\(797\) 49.7859 1.76351 0.881753 0.471711i \(-0.156364\pi\)
0.881753 + 0.471711i \(0.156364\pi\)
\(798\) 21.5246 0.761962
\(799\) −18.3548 −0.649346
\(800\) 7.29789 0.258019
\(801\) 12.7775 0.451470
\(802\) 15.2685 0.539149
\(803\) 6.16826 0.217673
\(804\) −1.77613 −0.0626392
\(805\) −5.24017 −0.184692
\(806\) −6.33852 −0.223265
\(807\) 3.17929 0.111916
\(808\) −39.0772 −1.37473
\(809\) −0.196582 −0.00691146 −0.00345573 0.999994i \(-0.501100\pi\)
−0.00345573 + 0.999994i \(0.501100\pi\)
\(810\) −1.87867 −0.0660097
\(811\) 50.4884 1.77289 0.886444 0.462835i \(-0.153168\pi\)
0.886444 + 0.462835i \(0.153168\pi\)
\(812\) 86.2589 3.02709
\(813\) 5.53231 0.194027
\(814\) 8.13660 0.285188
\(815\) −8.02230 −0.281009
\(816\) −20.7770 −0.727342
\(817\) −19.8522 −0.694542
\(818\) −48.4834 −1.69518
\(819\) 15.6475 0.546767
\(820\) −31.7084 −1.10731
\(821\) −5.26563 −0.183772 −0.0918858 0.995770i \(-0.529289\pi\)
−0.0918858 + 0.995770i \(0.529289\pi\)
\(822\) −2.38360 −0.0831375
\(823\) 18.4950 0.644695 0.322347 0.946621i \(-0.395528\pi\)
0.322347 + 0.946621i \(0.395528\pi\)
\(824\) 35.5118 1.23711
\(825\) 2.55453 0.0889374
\(826\) 32.6807 1.13711
\(827\) 41.9103 1.45736 0.728682 0.684852i \(-0.240133\pi\)
0.728682 + 0.684852i \(0.240133\pi\)
\(828\) 11.9682 0.415924
\(829\) 0.892350 0.0309926 0.0154963 0.999880i \(-0.495067\pi\)
0.0154963 + 0.999880i \(0.495067\pi\)
\(830\) −38.0227 −1.31979
\(831\) −21.1592 −0.734005
\(832\) 12.3663 0.428723
\(833\) 25.0600 0.868277
\(834\) 5.64228 0.195376
\(835\) 24.5503 0.849597
\(836\) 6.10657 0.211200
\(837\) −5.88673 −0.203475
\(838\) −18.2595 −0.630766
\(839\) 24.5608 0.847933 0.423967 0.905678i \(-0.360637\pi\)
0.423967 + 0.905678i \(0.360637\pi\)
\(840\) 19.7489 0.681401
\(841\) 3.26975 0.112750
\(842\) −46.4860 −1.60201
\(843\) −23.8028 −0.819813
\(844\) 43.9038 1.51123
\(845\) −8.11585 −0.279194
\(846\) −22.2923 −0.766426
\(847\) −38.5908 −1.32599
\(848\) 42.2136 1.44962
\(849\) 16.4689 0.565211
\(850\) 40.2225 1.37962
\(851\) 7.64488 0.262063
\(852\) −62.3319 −2.13545
\(853\) 37.9859 1.30061 0.650306 0.759672i \(-0.274641\pi\)
0.650306 + 0.759672i \(0.274641\pi\)
\(854\) −58.3155 −1.99551
\(855\) −4.55127 −0.155650
\(856\) 78.4027 2.67975
\(857\) −14.9397 −0.510331 −0.255165 0.966897i \(-0.582130\pi\)
−0.255165 + 0.966897i \(0.582130\pi\)
\(858\) −3.45186 −0.117845
\(859\) 44.0371 1.50253 0.751263 0.660002i \(-0.229445\pi\)
0.751263 + 0.660002i \(0.229445\pi\)
\(860\) −34.9647 −1.19229
\(861\) 28.4230 0.968652
\(862\) 14.3979 0.490394
\(863\) −34.6695 −1.18016 −0.590081 0.807344i \(-0.700904\pi\)
−0.590081 + 0.807344i \(0.700904\pi\)
\(864\) −9.15852 −0.311579
\(865\) 17.5160 0.595561
\(866\) −20.7674 −0.705704
\(867\) 0.829010 0.0281547
\(868\) −17.7030 −0.600879
\(869\) 5.19624 0.176271
\(870\) 14.1823 0.480826
\(871\) −0.915516 −0.0310211
\(872\) −35.5164 −1.20274
\(873\) −22.7320 −0.769362
\(874\) 8.48615 0.287048
\(875\) −32.4322 −1.09641
\(876\) −41.9277 −1.41660
\(877\) −36.5805 −1.23523 −0.617617 0.786479i \(-0.711902\pi\)
−0.617617 + 0.786479i \(0.711902\pi\)
\(878\) −31.9399 −1.07792
\(879\) −14.5481 −0.490694
\(880\) 3.13450 0.105664
\(881\) 6.48790 0.218583 0.109292 0.994010i \(-0.465142\pi\)
0.109292 + 0.994010i \(0.465142\pi\)
\(882\) 30.4359 1.02483
\(883\) −39.8087 −1.33967 −0.669834 0.742510i \(-0.733635\pi\)
−0.669834 + 0.742510i \(0.733635\pi\)
\(884\) −36.7472 −1.23594
\(885\) 3.63286 0.122117
\(886\) −79.2795 −2.66345
\(887\) 49.5576 1.66398 0.831990 0.554791i \(-0.187202\pi\)
0.831990 + 0.554791i \(0.187202\pi\)
\(888\) −28.8116 −0.966856
\(889\) −4.86936 −0.163313
\(890\) 15.9569 0.534875
\(891\) 0.477757 0.0160055
\(892\) −46.6400 −1.56162
\(893\) −10.6869 −0.357623
\(894\) −27.0933 −0.906136
\(895\) −16.8875 −0.564487
\(896\) 64.2782 2.14738
\(897\) −3.24325 −0.108289
\(898\) 75.3925 2.51588
\(899\) −6.62276 −0.220881
\(900\) 33.0285 1.10095
\(901\) 33.4329 1.11381
\(902\) 11.9266 0.397114
\(903\) 31.3418 1.04299
\(904\) −82.5464 −2.74545
\(905\) 15.4643 0.514051
\(906\) 14.5240 0.482526
\(907\) 13.3321 0.442684 0.221342 0.975196i \(-0.428956\pi\)
0.221342 + 0.975196i \(0.428956\pi\)
\(908\) −21.5972 −0.716728
\(909\) −14.2177 −0.471570
\(910\) 19.5410 0.647778
\(911\) −16.6277 −0.550901 −0.275451 0.961315i \(-0.588827\pi\)
−0.275451 + 0.961315i \(0.588827\pi\)
\(912\) −12.0972 −0.400579
\(913\) 9.66941 0.320011
\(914\) 70.1614 2.32073
\(915\) −6.48248 −0.214304
\(916\) −4.97328 −0.164322
\(917\) 29.2066 0.964486
\(918\) −50.4774 −1.66600
\(919\) 34.4272 1.13565 0.567823 0.823150i \(-0.307786\pi\)
0.567823 + 0.823150i \(0.307786\pi\)
\(920\) 7.78608 0.256700
\(921\) 18.0410 0.594470
\(922\) −3.32745 −0.109584
\(923\) −32.1293 −1.05755
\(924\) −9.64079 −0.317159
\(925\) 21.0975 0.693681
\(926\) −36.5077 −1.19972
\(927\) 12.9204 0.424363
\(928\) −10.3036 −0.338233
\(929\) −19.6997 −0.646327 −0.323163 0.946343i \(-0.604746\pi\)
−0.323163 + 0.946343i \(0.604746\pi\)
\(930\) −2.91065 −0.0954441
\(931\) 14.5909 0.478198
\(932\) −8.54782 −0.279993
\(933\) 32.7289 1.07149
\(934\) 16.9939 0.556058
\(935\) 2.48250 0.0811866
\(936\) −23.2498 −0.759942
\(937\) −3.26052 −0.106517 −0.0532583 0.998581i \(-0.516961\pi\)
−0.0532583 + 0.998581i \(0.516961\pi\)
\(938\) −3.78191 −0.123484
\(939\) −24.9407 −0.813909
\(940\) −18.8223 −0.613915
\(941\) −35.2142 −1.14795 −0.573975 0.818873i \(-0.694599\pi\)
−0.573975 + 0.818873i \(0.694599\pi\)
\(942\) −33.2557 −1.08353
\(943\) 11.2059 0.364913
\(944\) −18.3672 −0.597800
\(945\) 18.1482 0.590361
\(946\) 13.1514 0.427590
\(947\) −9.72004 −0.315859 −0.157929 0.987450i \(-0.550482\pi\)
−0.157929 + 0.987450i \(0.550482\pi\)
\(948\) −35.3205 −1.14716
\(949\) −21.6119 −0.701551
\(950\) 23.4192 0.759818
\(951\) 18.7174 0.606953
\(952\) −79.0783 −2.56294
\(953\) 23.6615 0.766470 0.383235 0.923651i \(-0.374810\pi\)
0.383235 + 0.923651i \(0.374810\pi\)
\(954\) 40.6050 1.31464
\(955\) 22.4462 0.726342
\(956\) 75.8408 2.45287
\(957\) −3.60665 −0.116587
\(958\) 78.2045 2.52667
\(959\) −3.43150 −0.110809
\(960\) 5.67860 0.183276
\(961\) −29.6408 −0.956155
\(962\) −28.5084 −0.919147
\(963\) 28.5257 0.919226
\(964\) 18.9846 0.611453
\(965\) −19.1412 −0.616176
\(966\) −13.3976 −0.431059
\(967\) −21.7257 −0.698652 −0.349326 0.937001i \(-0.613589\pi\)
−0.349326 + 0.937001i \(0.613589\pi\)
\(968\) 57.3400 1.84298
\(969\) −9.58091 −0.307783
\(970\) −28.3884 −0.911496
\(971\) 19.2563 0.617963 0.308981 0.951068i \(-0.400012\pi\)
0.308981 + 0.951068i \(0.400012\pi\)
\(972\) −66.4878 −2.13260
\(973\) 8.12280 0.260405
\(974\) −38.4150 −1.23090
\(975\) −8.95037 −0.286641
\(976\) 32.7744 1.04908
\(977\) −16.3671 −0.523631 −0.261816 0.965118i \(-0.584321\pi\)
−0.261816 + 0.965118i \(0.584321\pi\)
\(978\) −20.5106 −0.655858
\(979\) −4.05793 −0.129692
\(980\) 25.6982 0.820900
\(981\) −12.9221 −0.412572
\(982\) −10.0817 −0.321718
\(983\) 37.9693 1.21103 0.605516 0.795833i \(-0.292967\pi\)
0.605516 + 0.795833i \(0.292967\pi\)
\(984\) −42.2321 −1.34631
\(985\) 22.3356 0.711671
\(986\) −56.7887 −1.80852
\(987\) 16.8720 0.537042
\(988\) −21.3957 −0.680689
\(989\) 12.3567 0.392919
\(990\) 3.01506 0.0958249
\(991\) 15.5782 0.494858 0.247429 0.968906i \(-0.420414\pi\)
0.247429 + 0.968906i \(0.420414\pi\)
\(992\) 2.11462 0.0671394
\(993\) −21.9434 −0.696352
\(994\) −132.723 −4.20973
\(995\) −20.9969 −0.665645
\(996\) −65.7261 −2.08261
\(997\) 37.2630 1.18013 0.590065 0.807355i \(-0.299102\pi\)
0.590065 + 0.807355i \(0.299102\pi\)
\(998\) −64.4369 −2.03971
\(999\) −26.4764 −0.837676
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 \(a_p\))