Properties

Label 8015.2.a.l.1.36
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 1.36
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.335014 q^{2} -2.24041 q^{3} -1.88777 q^{4} -1.00000 q^{5} -0.750569 q^{6} -1.00000 q^{7} -1.30246 q^{8} +2.01944 q^{9} +O(q^{10})\) \(q+0.335014 q^{2} -2.24041 q^{3} -1.88777 q^{4} -1.00000 q^{5} -0.750569 q^{6} -1.00000 q^{7} -1.30246 q^{8} +2.01944 q^{9} -0.335014 q^{10} +3.08966 q^{11} +4.22937 q^{12} -2.34431 q^{13} -0.335014 q^{14} +2.24041 q^{15} +3.33919 q^{16} +0.387513 q^{17} +0.676540 q^{18} +2.68213 q^{19} +1.88777 q^{20} +2.24041 q^{21} +1.03508 q^{22} +7.98383 q^{23} +2.91804 q^{24} +1.00000 q^{25} -0.785378 q^{26} +2.19687 q^{27} +1.88777 q^{28} -9.13609 q^{29} +0.750569 q^{30} -5.31346 q^{31} +3.72359 q^{32} -6.92211 q^{33} +0.129822 q^{34} +1.00000 q^{35} -3.81222 q^{36} -0.994796 q^{37} +0.898552 q^{38} +5.25222 q^{39} +1.30246 q^{40} +4.24736 q^{41} +0.750569 q^{42} +4.40582 q^{43} -5.83256 q^{44} -2.01944 q^{45} +2.67470 q^{46} +4.86496 q^{47} -7.48115 q^{48} +1.00000 q^{49} +0.335014 q^{50} -0.868188 q^{51} +4.42551 q^{52} -13.1706 q^{53} +0.735982 q^{54} -3.08966 q^{55} +1.30246 q^{56} -6.00907 q^{57} -3.06072 q^{58} +10.2348 q^{59} -4.22937 q^{60} -4.84523 q^{61} -1.78009 q^{62} -2.01944 q^{63} -5.43092 q^{64} +2.34431 q^{65} -2.31901 q^{66} -15.4928 q^{67} -0.731533 q^{68} -17.8871 q^{69} +0.335014 q^{70} -6.13446 q^{71} -2.63023 q^{72} -6.33820 q^{73} -0.333271 q^{74} -2.24041 q^{75} -5.06323 q^{76} -3.08966 q^{77} +1.75957 q^{78} -7.92124 q^{79} -3.33919 q^{80} -10.9802 q^{81} +1.42293 q^{82} -9.73242 q^{83} -4.22937 q^{84} -0.387513 q^{85} +1.47601 q^{86} +20.4686 q^{87} -4.02416 q^{88} +11.9796 q^{89} -0.676540 q^{90} +2.34431 q^{91} -15.0716 q^{92} +11.9043 q^{93} +1.62983 q^{94} -2.68213 q^{95} -8.34237 q^{96} +8.91853 q^{97} +0.335014 q^{98} +6.23938 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.335014 0.236891 0.118445 0.992961i \(-0.462209\pi\)
0.118445 + 0.992961i \(0.462209\pi\)
\(3\) −2.24041 −1.29350 −0.646751 0.762702i \(-0.723873\pi\)
−0.646751 + 0.762702i \(0.723873\pi\)
\(4\) −1.88777 −0.943883
\(5\) −1.00000 −0.447214
\(6\) −0.750569 −0.306419
\(7\) −1.00000 −0.377964
\(8\) −1.30246 −0.460488
\(9\) 2.01944 0.673145
\(10\) −0.335014 −0.105941
\(11\) 3.08966 0.931569 0.465784 0.884898i \(-0.345772\pi\)
0.465784 + 0.884898i \(0.345772\pi\)
\(12\) 4.22937 1.22091
\(13\) −2.34431 −0.650195 −0.325098 0.945680i \(-0.605397\pi\)
−0.325098 + 0.945680i \(0.605397\pi\)
\(14\) −0.335014 −0.0895364
\(15\) 2.24041 0.578471
\(16\) 3.33919 0.834797
\(17\) 0.387513 0.0939857 0.0469928 0.998895i \(-0.485036\pi\)
0.0469928 + 0.998895i \(0.485036\pi\)
\(18\) 0.676540 0.159462
\(19\) 2.68213 0.615323 0.307661 0.951496i \(-0.400454\pi\)
0.307661 + 0.951496i \(0.400454\pi\)
\(20\) 1.88777 0.422117
\(21\) 2.24041 0.488897
\(22\) 1.03508 0.220680
\(23\) 7.98383 1.66474 0.832372 0.554217i \(-0.186982\pi\)
0.832372 + 0.554217i \(0.186982\pi\)
\(24\) 2.91804 0.595642
\(25\) 1.00000 0.200000
\(26\) −0.785378 −0.154025
\(27\) 2.19687 0.422787
\(28\) 1.88777 0.356754
\(29\) −9.13609 −1.69653 −0.848265 0.529572i \(-0.822353\pi\)
−0.848265 + 0.529572i \(0.822353\pi\)
\(30\) 0.750569 0.137035
\(31\) −5.31346 −0.954326 −0.477163 0.878815i \(-0.658335\pi\)
−0.477163 + 0.878815i \(0.658335\pi\)
\(32\) 3.72359 0.658244
\(33\) −6.92211 −1.20499
\(34\) 0.129822 0.0222644
\(35\) 1.00000 0.169031
\(36\) −3.81222 −0.635370
\(37\) −0.994796 −0.163543 −0.0817717 0.996651i \(-0.526058\pi\)
−0.0817717 + 0.996651i \(0.526058\pi\)
\(38\) 0.898552 0.145764
\(39\) 5.25222 0.841028
\(40\) 1.30246 0.205937
\(41\) 4.24736 0.663326 0.331663 0.943398i \(-0.392390\pi\)
0.331663 + 0.943398i \(0.392390\pi\)
\(42\) 0.750569 0.115815
\(43\) 4.40582 0.671881 0.335941 0.941883i \(-0.390946\pi\)
0.335941 + 0.941883i \(0.390946\pi\)
\(44\) −5.83256 −0.879292
\(45\) −2.01944 −0.301040
\(46\) 2.67470 0.394363
\(47\) 4.86496 0.709627 0.354814 0.934937i \(-0.384544\pi\)
0.354814 + 0.934937i \(0.384544\pi\)
\(48\) −7.48115 −1.07981
\(49\) 1.00000 0.142857
\(50\) 0.335014 0.0473782
\(51\) −0.868188 −0.121571
\(52\) 4.42551 0.613708
\(53\) −13.1706 −1.80913 −0.904564 0.426338i \(-0.859803\pi\)
−0.904564 + 0.426338i \(0.859803\pi\)
\(54\) 0.735982 0.100154
\(55\) −3.08966 −0.416610
\(56\) 1.30246 0.174048
\(57\) −6.00907 −0.795921
\(58\) −3.06072 −0.401893
\(59\) 10.2348 1.33245 0.666226 0.745750i \(-0.267909\pi\)
0.666226 + 0.745750i \(0.267909\pi\)
\(60\) −4.22937 −0.546009
\(61\) −4.84523 −0.620368 −0.310184 0.950676i \(-0.600391\pi\)
−0.310184 + 0.950676i \(0.600391\pi\)
\(62\) −1.78009 −0.226071
\(63\) −2.01944 −0.254425
\(64\) −5.43092 −0.678865
\(65\) 2.34431 0.290776
\(66\) −2.31901 −0.285450
\(67\) −15.4928 −1.89275 −0.946376 0.323067i \(-0.895286\pi\)
−0.946376 + 0.323067i \(0.895286\pi\)
\(68\) −0.731533 −0.0887115
\(69\) −17.8871 −2.15335
\(70\) 0.335014 0.0400419
\(71\) −6.13446 −0.728027 −0.364013 0.931394i \(-0.618594\pi\)
−0.364013 + 0.931394i \(0.618594\pi\)
\(72\) −2.63023 −0.309975
\(73\) −6.33820 −0.741830 −0.370915 0.928667i \(-0.620956\pi\)
−0.370915 + 0.928667i \(0.620956\pi\)
\(74\) −0.333271 −0.0387420
\(75\) −2.24041 −0.258700
\(76\) −5.06323 −0.580793
\(77\) −3.08966 −0.352100
\(78\) 1.75957 0.199232
\(79\) −7.92124 −0.891209 −0.445604 0.895230i \(-0.647011\pi\)
−0.445604 + 0.895230i \(0.647011\pi\)
\(80\) −3.33919 −0.373333
\(81\) −10.9802 −1.22002
\(82\) 1.42293 0.157136
\(83\) −9.73242 −1.06827 −0.534136 0.845399i \(-0.679363\pi\)
−0.534136 + 0.845399i \(0.679363\pi\)
\(84\) −4.22937 −0.461462
\(85\) −0.387513 −0.0420317
\(86\) 1.47601 0.159163
\(87\) 20.4686 2.19446
\(88\) −4.02416 −0.428976
\(89\) 11.9796 1.26984 0.634919 0.772579i \(-0.281033\pi\)
0.634919 + 0.772579i \(0.281033\pi\)
\(90\) −0.676540 −0.0713136
\(91\) 2.34431 0.245751
\(92\) −15.0716 −1.57132
\(93\) 11.9043 1.23442
\(94\) 1.62983 0.168104
\(95\) −2.68213 −0.275181
\(96\) −8.34237 −0.851439
\(97\) 8.91853 0.905539 0.452770 0.891628i \(-0.350436\pi\)
0.452770 + 0.891628i \(0.350436\pi\)
\(98\) 0.335014 0.0338416
\(99\) 6.23938 0.627081
\(100\) −1.88777 −0.188777
\(101\) −1.24600 −0.123982 −0.0619908 0.998077i \(-0.519745\pi\)
−0.0619908 + 0.998077i \(0.519745\pi\)
\(102\) −0.290855 −0.0287990
\(103\) 8.02045 0.790278 0.395139 0.918621i \(-0.370696\pi\)
0.395139 + 0.918621i \(0.370696\pi\)
\(104\) 3.05337 0.299407
\(105\) −2.24041 −0.218642
\(106\) −4.41236 −0.428566
\(107\) 13.4191 1.29727 0.648636 0.761099i \(-0.275340\pi\)
0.648636 + 0.761099i \(0.275340\pi\)
\(108\) −4.14717 −0.399061
\(109\) −5.11814 −0.490229 −0.245114 0.969494i \(-0.578825\pi\)
−0.245114 + 0.969494i \(0.578825\pi\)
\(110\) −1.03508 −0.0986912
\(111\) 2.22875 0.211544
\(112\) −3.33919 −0.315524
\(113\) 9.16426 0.862101 0.431050 0.902328i \(-0.358143\pi\)
0.431050 + 0.902328i \(0.358143\pi\)
\(114\) −2.01312 −0.188546
\(115\) −7.98383 −0.744496
\(116\) 17.2468 1.60133
\(117\) −4.73419 −0.437676
\(118\) 3.42879 0.315646
\(119\) −0.387513 −0.0355232
\(120\) −2.91804 −0.266379
\(121\) −1.45398 −0.132180
\(122\) −1.62322 −0.146960
\(123\) −9.51583 −0.858014
\(124\) 10.0306 0.900772
\(125\) −1.00000 −0.0894427
\(126\) −0.676540 −0.0602710
\(127\) 16.3534 1.45113 0.725563 0.688156i \(-0.241580\pi\)
0.725563 + 0.688156i \(0.241580\pi\)
\(128\) −9.26662 −0.819061
\(129\) −9.87084 −0.869079
\(130\) 0.785378 0.0688822
\(131\) −8.49544 −0.742250 −0.371125 0.928583i \(-0.621028\pi\)
−0.371125 + 0.928583i \(0.621028\pi\)
\(132\) 13.0673 1.13736
\(133\) −2.68213 −0.232570
\(134\) −5.19033 −0.448376
\(135\) −2.19687 −0.189076
\(136\) −0.504719 −0.0432793
\(137\) −6.22459 −0.531803 −0.265901 0.964000i \(-0.585670\pi\)
−0.265901 + 0.964000i \(0.585670\pi\)
\(138\) −5.99242 −0.510109
\(139\) −16.1363 −1.36866 −0.684330 0.729172i \(-0.739905\pi\)
−0.684330 + 0.729172i \(0.739905\pi\)
\(140\) −1.88777 −0.159545
\(141\) −10.8995 −0.917903
\(142\) −2.05513 −0.172463
\(143\) −7.24314 −0.605702
\(144\) 6.74328 0.561940
\(145\) 9.13609 0.758711
\(146\) −2.12339 −0.175733
\(147\) −2.24041 −0.184786
\(148\) 1.87794 0.154366
\(149\) −4.91856 −0.402944 −0.201472 0.979494i \(-0.564573\pi\)
−0.201472 + 0.979494i \(0.564573\pi\)
\(150\) −0.750569 −0.0612837
\(151\) 11.6046 0.944371 0.472186 0.881499i \(-0.343465\pi\)
0.472186 + 0.881499i \(0.343465\pi\)
\(152\) −3.49336 −0.283349
\(153\) 0.782557 0.0632660
\(154\) −1.03508 −0.0834093
\(155\) 5.31346 0.426788
\(156\) −9.91496 −0.793832
\(157\) 13.3293 1.06380 0.531899 0.846808i \(-0.321479\pi\)
0.531899 + 0.846808i \(0.321479\pi\)
\(158\) −2.65373 −0.211119
\(159\) 29.5076 2.34011
\(160\) −3.72359 −0.294376
\(161\) −7.98383 −0.629214
\(162\) −3.67852 −0.289012
\(163\) −14.1670 −1.10965 −0.554824 0.831968i \(-0.687215\pi\)
−0.554824 + 0.831968i \(0.687215\pi\)
\(164\) −8.01802 −0.626102
\(165\) 6.92211 0.538886
\(166\) −3.26050 −0.253064
\(167\) 5.01242 0.387873 0.193936 0.981014i \(-0.437874\pi\)
0.193936 + 0.981014i \(0.437874\pi\)
\(168\) −2.91804 −0.225131
\(169\) −7.50420 −0.577246
\(170\) −0.129822 −0.00995692
\(171\) 5.41639 0.414202
\(172\) −8.31715 −0.634177
\(173\) 1.96609 0.149479 0.0747394 0.997203i \(-0.476188\pi\)
0.0747394 + 0.997203i \(0.476188\pi\)
\(174\) 6.85727 0.519848
\(175\) −1.00000 −0.0755929
\(176\) 10.3170 0.777671
\(177\) −22.9300 −1.72353
\(178\) 4.01335 0.300813
\(179\) −6.13097 −0.458250 −0.229125 0.973397i \(-0.573586\pi\)
−0.229125 + 0.973397i \(0.573586\pi\)
\(180\) 3.81222 0.284146
\(181\) −22.1672 −1.64768 −0.823839 0.566824i \(-0.808172\pi\)
−0.823839 + 0.566824i \(0.808172\pi\)
\(182\) 0.785378 0.0582161
\(183\) 10.8553 0.802447
\(184\) −10.3986 −0.766595
\(185\) 0.994796 0.0731388
\(186\) 3.98812 0.292423
\(187\) 1.19728 0.0875541
\(188\) −9.18390 −0.669805
\(189\) −2.19687 −0.159799
\(190\) −0.898552 −0.0651878
\(191\) 3.66299 0.265045 0.132522 0.991180i \(-0.457692\pi\)
0.132522 + 0.991180i \(0.457692\pi\)
\(192\) 12.1675 0.878113
\(193\) −5.69038 −0.409602 −0.204801 0.978804i \(-0.565655\pi\)
−0.204801 + 0.978804i \(0.565655\pi\)
\(194\) 2.98784 0.214514
\(195\) −5.25222 −0.376119
\(196\) −1.88777 −0.134840
\(197\) −11.3511 −0.808732 −0.404366 0.914597i \(-0.632508\pi\)
−0.404366 + 0.914597i \(0.632508\pi\)
\(198\) 2.09028 0.148550
\(199\) 6.02661 0.427215 0.213608 0.976920i \(-0.431479\pi\)
0.213608 + 0.976920i \(0.431479\pi\)
\(200\) −1.30246 −0.0920976
\(201\) 34.7103 2.44828
\(202\) −0.417428 −0.0293701
\(203\) 9.13609 0.641228
\(204\) 1.63893 0.114748
\(205\) −4.24736 −0.296649
\(206\) 2.68697 0.187210
\(207\) 16.1228 1.12061
\(208\) −7.82810 −0.542781
\(209\) 8.28688 0.573216
\(210\) −0.750569 −0.0517942
\(211\) −12.1781 −0.838376 −0.419188 0.907900i \(-0.637685\pi\)
−0.419188 + 0.907900i \(0.637685\pi\)
\(212\) 24.8631 1.70760
\(213\) 13.7437 0.941704
\(214\) 4.49558 0.307312
\(215\) −4.40582 −0.300474
\(216\) −2.86132 −0.194688
\(217\) 5.31346 0.360701
\(218\) −1.71465 −0.116131
\(219\) 14.2002 0.959558
\(220\) 5.83256 0.393231
\(221\) −0.908451 −0.0611090
\(222\) 0.746663 0.0501128
\(223\) 12.2152 0.817992 0.408996 0.912536i \(-0.365879\pi\)
0.408996 + 0.912536i \(0.365879\pi\)
\(224\) −3.72359 −0.248793
\(225\) 2.01944 0.134629
\(226\) 3.07016 0.204224
\(227\) 26.7572 1.77594 0.887969 0.459904i \(-0.152116\pi\)
0.887969 + 0.459904i \(0.152116\pi\)
\(228\) 11.3437 0.751256
\(229\) 1.00000 0.0660819
\(230\) −2.67470 −0.176364
\(231\) 6.92211 0.455442
\(232\) 11.8994 0.781232
\(233\) −27.2797 −1.78715 −0.893577 0.448911i \(-0.851812\pi\)
−0.893577 + 0.448911i \(0.851812\pi\)
\(234\) −1.58602 −0.103681
\(235\) −4.86496 −0.317355
\(236\) −19.3208 −1.25768
\(237\) 17.7468 1.15278
\(238\) −0.129822 −0.00841514
\(239\) −9.68197 −0.626274 −0.313137 0.949708i \(-0.601380\pi\)
−0.313137 + 0.949708i \(0.601380\pi\)
\(240\) 7.48115 0.482906
\(241\) 14.2686 0.919122 0.459561 0.888146i \(-0.348007\pi\)
0.459561 + 0.888146i \(0.348007\pi\)
\(242\) −0.487103 −0.0313121
\(243\) 18.0095 1.15531
\(244\) 9.14666 0.585555
\(245\) −1.00000 −0.0638877
\(246\) −3.18794 −0.203256
\(247\) −6.28775 −0.400080
\(248\) 6.92056 0.439456
\(249\) 21.8046 1.38181
\(250\) −0.335014 −0.0211882
\(251\) 22.6824 1.43170 0.715849 0.698255i \(-0.246040\pi\)
0.715849 + 0.698255i \(0.246040\pi\)
\(252\) 3.81222 0.240147
\(253\) 24.6674 1.55082
\(254\) 5.47861 0.343758
\(255\) 0.868188 0.0543680
\(256\) 7.75739 0.484837
\(257\) 17.2507 1.07607 0.538036 0.842922i \(-0.319167\pi\)
0.538036 + 0.842922i \(0.319167\pi\)
\(258\) −3.30687 −0.205877
\(259\) 0.994796 0.0618136
\(260\) −4.42551 −0.274459
\(261\) −18.4497 −1.14201
\(262\) −2.84609 −0.175832
\(263\) 17.8368 1.09987 0.549933 0.835209i \(-0.314653\pi\)
0.549933 + 0.835209i \(0.314653\pi\)
\(264\) 9.01576 0.554881
\(265\) 13.1706 0.809067
\(266\) −0.898552 −0.0550938
\(267\) −26.8393 −1.64254
\(268\) 29.2469 1.78654
\(269\) 21.8253 1.33071 0.665356 0.746526i \(-0.268280\pi\)
0.665356 + 0.746526i \(0.268280\pi\)
\(270\) −0.735982 −0.0447904
\(271\) 11.1052 0.674593 0.337297 0.941398i \(-0.390488\pi\)
0.337297 + 0.941398i \(0.390488\pi\)
\(272\) 1.29398 0.0784590
\(273\) −5.25222 −0.317879
\(274\) −2.08533 −0.125979
\(275\) 3.08966 0.186314
\(276\) 33.7666 2.03251
\(277\) 21.2309 1.27564 0.637820 0.770185i \(-0.279836\pi\)
0.637820 + 0.770185i \(0.279836\pi\)
\(278\) −5.40588 −0.324223
\(279\) −10.7302 −0.642400
\(280\) −1.30246 −0.0778367
\(281\) −10.6590 −0.635863 −0.317932 0.948114i \(-0.602988\pi\)
−0.317932 + 0.948114i \(0.602988\pi\)
\(282\) −3.65149 −0.217443
\(283\) −16.4149 −0.975767 −0.487884 0.872909i \(-0.662231\pi\)
−0.487884 + 0.872909i \(0.662231\pi\)
\(284\) 11.5804 0.687172
\(285\) 6.00907 0.355947
\(286\) −2.42656 −0.143485
\(287\) −4.24736 −0.250714
\(288\) 7.51955 0.443094
\(289\) −16.8498 −0.991167
\(290\) 3.06072 0.179732
\(291\) −19.9812 −1.17132
\(292\) 11.9650 0.700200
\(293\) −11.0893 −0.647846 −0.323923 0.946084i \(-0.605002\pi\)
−0.323923 + 0.946084i \(0.605002\pi\)
\(294\) −0.750569 −0.0437741
\(295\) −10.2348 −0.595890
\(296\) 1.29568 0.0753098
\(297\) 6.78758 0.393855
\(298\) −1.64779 −0.0954539
\(299\) −18.7166 −1.08241
\(300\) 4.22937 0.244183
\(301\) −4.40582 −0.253947
\(302\) 3.88772 0.223713
\(303\) 2.79155 0.160370
\(304\) 8.95614 0.513670
\(305\) 4.84523 0.277437
\(306\) 0.262168 0.0149871
\(307\) −2.20307 −0.125736 −0.0628680 0.998022i \(-0.520025\pi\)
−0.0628680 + 0.998022i \(0.520025\pi\)
\(308\) 5.83256 0.332341
\(309\) −17.9691 −1.02223
\(310\) 1.78009 0.101102
\(311\) −6.04539 −0.342802 −0.171401 0.985201i \(-0.554829\pi\)
−0.171401 + 0.985201i \(0.554829\pi\)
\(312\) −6.84079 −0.387284
\(313\) −2.93484 −0.165887 −0.0829436 0.996554i \(-0.526432\pi\)
−0.0829436 + 0.996554i \(0.526432\pi\)
\(314\) 4.46552 0.252004
\(315\) 2.01944 0.113782
\(316\) 14.9534 0.841197
\(317\) 10.9997 0.617807 0.308903 0.951093i \(-0.400038\pi\)
0.308903 + 0.951093i \(0.400038\pi\)
\(318\) 9.88549 0.554351
\(319\) −28.2275 −1.58043
\(320\) 5.43092 0.303598
\(321\) −30.0642 −1.67802
\(322\) −2.67470 −0.149055
\(323\) 1.03936 0.0578315
\(324\) 20.7280 1.15156
\(325\) −2.34431 −0.130039
\(326\) −4.74616 −0.262866
\(327\) 11.4667 0.634111
\(328\) −5.53201 −0.305454
\(329\) −4.86496 −0.268214
\(330\) 2.31901 0.127657
\(331\) 27.7886 1.52740 0.763700 0.645571i \(-0.223381\pi\)
0.763700 + 0.645571i \(0.223381\pi\)
\(332\) 18.3725 1.00832
\(333\) −2.00893 −0.110088
\(334\) 1.67923 0.0918835
\(335\) 15.4928 0.846465
\(336\) 7.48115 0.408130
\(337\) 3.48215 0.189685 0.0948424 0.995492i \(-0.469765\pi\)
0.0948424 + 0.995492i \(0.469765\pi\)
\(338\) −2.51401 −0.136744
\(339\) −20.5317 −1.11513
\(340\) 0.731533 0.0396730
\(341\) −16.4168 −0.889020
\(342\) 1.81457 0.0981206
\(343\) −1.00000 −0.0539949
\(344\) −5.73839 −0.309393
\(345\) 17.8871 0.963007
\(346\) 0.658667 0.0354102
\(347\) 28.6632 1.53872 0.769360 0.638815i \(-0.220575\pi\)
0.769360 + 0.638815i \(0.220575\pi\)
\(348\) −38.6399 −2.07132
\(349\) 6.12059 0.327628 0.163814 0.986491i \(-0.447620\pi\)
0.163814 + 0.986491i \(0.447620\pi\)
\(350\) −0.335014 −0.0179073
\(351\) −5.15014 −0.274894
\(352\) 11.5046 0.613200
\(353\) −1.64350 −0.0874748 −0.0437374 0.999043i \(-0.513926\pi\)
−0.0437374 + 0.999043i \(0.513926\pi\)
\(354\) −7.68189 −0.408288
\(355\) 6.13446 0.325584
\(356\) −22.6147 −1.19858
\(357\) 0.868188 0.0459494
\(358\) −2.05396 −0.108555
\(359\) −9.75230 −0.514707 −0.257353 0.966317i \(-0.582850\pi\)
−0.257353 + 0.966317i \(0.582850\pi\)
\(360\) 2.63023 0.138625
\(361\) −11.8062 −0.621378
\(362\) −7.42634 −0.390320
\(363\) 3.25750 0.170974
\(364\) −4.42551 −0.231960
\(365\) 6.33820 0.331756
\(366\) 3.63668 0.190092
\(367\) 16.8750 0.880868 0.440434 0.897785i \(-0.354825\pi\)
0.440434 + 0.897785i \(0.354825\pi\)
\(368\) 26.6595 1.38972
\(369\) 8.57727 0.446515
\(370\) 0.333271 0.0173259
\(371\) 13.1706 0.683786
\(372\) −22.4726 −1.16515
\(373\) −15.4879 −0.801932 −0.400966 0.916093i \(-0.631325\pi\)
−0.400966 + 0.916093i \(0.631325\pi\)
\(374\) 0.401108 0.0207408
\(375\) 2.24041 0.115694
\(376\) −6.33640 −0.326775
\(377\) 21.4179 1.10308
\(378\) −0.735982 −0.0378548
\(379\) −13.4710 −0.691958 −0.345979 0.938242i \(-0.612453\pi\)
−0.345979 + 0.938242i \(0.612453\pi\)
\(380\) 5.06323 0.259738
\(381\) −36.6382 −1.87703
\(382\) 1.22715 0.0627867
\(383\) −4.84972 −0.247809 −0.123905 0.992294i \(-0.539542\pi\)
−0.123905 + 0.992294i \(0.539542\pi\)
\(384\) 20.7610 1.05946
\(385\) 3.08966 0.157464
\(386\) −1.90636 −0.0970311
\(387\) 8.89727 0.452274
\(388\) −16.8361 −0.854723
\(389\) 1.80404 0.0914684 0.0457342 0.998954i \(-0.485437\pi\)
0.0457342 + 0.998954i \(0.485437\pi\)
\(390\) −1.75957 −0.0890992
\(391\) 3.09384 0.156462
\(392\) −1.30246 −0.0657840
\(393\) 19.0333 0.960101
\(394\) −3.80278 −0.191581
\(395\) 7.92124 0.398561
\(396\) −11.7785 −0.591891
\(397\) 9.67307 0.485477 0.242739 0.970092i \(-0.421954\pi\)
0.242739 + 0.970092i \(0.421954\pi\)
\(398\) 2.01900 0.101203
\(399\) 6.00907 0.300830
\(400\) 3.33919 0.166959
\(401\) 4.92980 0.246183 0.123091 0.992395i \(-0.460719\pi\)
0.123091 + 0.992395i \(0.460719\pi\)
\(402\) 11.6285 0.579975
\(403\) 12.4564 0.620498
\(404\) 2.35216 0.117024
\(405\) 10.9802 0.545610
\(406\) 3.06072 0.151901
\(407\) −3.07359 −0.152352
\(408\) 1.13078 0.0559818
\(409\) −5.43787 −0.268885 −0.134443 0.990921i \(-0.542924\pi\)
−0.134443 + 0.990921i \(0.542924\pi\)
\(410\) −1.42293 −0.0702734
\(411\) 13.9456 0.687887
\(412\) −15.1407 −0.745930
\(413\) −10.2348 −0.503619
\(414\) 5.40138 0.265463
\(415\) 9.73242 0.477745
\(416\) −8.72926 −0.427987
\(417\) 36.1519 1.77036
\(418\) 2.77622 0.135790
\(419\) 3.19118 0.155899 0.0779497 0.996957i \(-0.475163\pi\)
0.0779497 + 0.996957i \(0.475163\pi\)
\(420\) 4.22937 0.206372
\(421\) −4.22398 −0.205864 −0.102932 0.994688i \(-0.532822\pi\)
−0.102932 + 0.994688i \(0.532822\pi\)
\(422\) −4.07984 −0.198604
\(423\) 9.82447 0.477682
\(424\) 17.1542 0.833082
\(425\) 0.387513 0.0187971
\(426\) 4.60434 0.223081
\(427\) 4.84523 0.234477
\(428\) −25.3321 −1.22447
\(429\) 16.2276 0.783476
\(430\) −1.47601 −0.0711797
\(431\) 30.8051 1.48383 0.741916 0.670493i \(-0.233917\pi\)
0.741916 + 0.670493i \(0.233917\pi\)
\(432\) 7.33575 0.352942
\(433\) 13.3957 0.643754 0.321877 0.946781i \(-0.395686\pi\)
0.321877 + 0.946781i \(0.395686\pi\)
\(434\) 1.78009 0.0854469
\(435\) −20.4686 −0.981394
\(436\) 9.66184 0.462718
\(437\) 21.4137 1.02436
\(438\) 4.75726 0.227311
\(439\) −19.5760 −0.934310 −0.467155 0.884175i \(-0.654721\pi\)
−0.467155 + 0.884175i \(0.654721\pi\)
\(440\) 4.02416 0.191844
\(441\) 2.01944 0.0961636
\(442\) −0.304344 −0.0144762
\(443\) 41.3997 1.96696 0.983480 0.181016i \(-0.0579385\pi\)
0.983480 + 0.181016i \(0.0579385\pi\)
\(444\) −4.20736 −0.199672
\(445\) −11.9796 −0.567889
\(446\) 4.09228 0.193775
\(447\) 11.0196 0.521209
\(448\) 5.43092 0.256587
\(449\) −12.3489 −0.582781 −0.291390 0.956604i \(-0.594118\pi\)
−0.291390 + 0.956604i \(0.594118\pi\)
\(450\) 0.676540 0.0318924
\(451\) 13.1229 0.617934
\(452\) −17.3000 −0.813722
\(453\) −25.9991 −1.22155
\(454\) 8.96405 0.420703
\(455\) −2.34431 −0.109903
\(456\) 7.82656 0.366512
\(457\) 14.2761 0.667807 0.333904 0.942607i \(-0.391634\pi\)
0.333904 + 0.942607i \(0.391634\pi\)
\(458\) 0.335014 0.0156542
\(459\) 0.851314 0.0397359
\(460\) 15.0716 0.702717
\(461\) −16.3596 −0.761944 −0.380972 0.924587i \(-0.624411\pi\)
−0.380972 + 0.924587i \(0.624411\pi\)
\(462\) 2.31901 0.107890
\(463\) −31.5238 −1.46504 −0.732518 0.680747i \(-0.761655\pi\)
−0.732518 + 0.680747i \(0.761655\pi\)
\(464\) −30.5071 −1.41626
\(465\) −11.9043 −0.552050
\(466\) −9.13909 −0.423360
\(467\) −12.2226 −0.565593 −0.282797 0.959180i \(-0.591262\pi\)
−0.282797 + 0.959180i \(0.591262\pi\)
\(468\) 8.93704 0.413115
\(469\) 15.4928 0.715393
\(470\) −1.62983 −0.0751785
\(471\) −29.8632 −1.37602
\(472\) −13.3303 −0.613578
\(473\) 13.6125 0.625904
\(474\) 5.94544 0.273083
\(475\) 2.68213 0.123065
\(476\) 0.731533 0.0335298
\(477\) −26.5973 −1.21781
\(478\) −3.24360 −0.148359
\(479\) −4.92589 −0.225070 −0.112535 0.993648i \(-0.535897\pi\)
−0.112535 + 0.993648i \(0.535897\pi\)
\(480\) 8.34237 0.380775
\(481\) 2.33211 0.106335
\(482\) 4.78019 0.217732
\(483\) 17.8871 0.813889
\(484\) 2.74476 0.124762
\(485\) −8.91853 −0.404970
\(486\) 6.03345 0.273683
\(487\) 40.3102 1.82663 0.913315 0.407253i \(-0.133513\pi\)
0.913315 + 0.407253i \(0.133513\pi\)
\(488\) 6.31071 0.285672
\(489\) 31.7400 1.43533
\(490\) −0.335014 −0.0151344
\(491\) 20.1638 0.909981 0.454990 0.890496i \(-0.349643\pi\)
0.454990 + 0.890496i \(0.349643\pi\)
\(492\) 17.9637 0.809864
\(493\) −3.54035 −0.159450
\(494\) −2.10649 −0.0947753
\(495\) −6.23938 −0.280439
\(496\) −17.7427 −0.796669
\(497\) 6.13446 0.275168
\(498\) 7.30485 0.327338
\(499\) −8.30873 −0.371950 −0.185975 0.982555i \(-0.559544\pi\)
−0.185975 + 0.982555i \(0.559544\pi\)
\(500\) 1.88777 0.0844234
\(501\) −11.2299 −0.501714
\(502\) 7.59892 0.339156
\(503\) 4.33965 0.193496 0.0967478 0.995309i \(-0.469156\pi\)
0.0967478 + 0.995309i \(0.469156\pi\)
\(504\) 2.63023 0.117160
\(505\) 1.24600 0.0554463
\(506\) 8.26392 0.367376
\(507\) 16.8125 0.746668
\(508\) −30.8713 −1.36969
\(509\) −6.28405 −0.278536 −0.139268 0.990255i \(-0.544475\pi\)
−0.139268 + 0.990255i \(0.544475\pi\)
\(510\) 0.290855 0.0128793
\(511\) 6.33820 0.280385
\(512\) 21.1321 0.933915
\(513\) 5.89228 0.260151
\(514\) 5.77925 0.254912
\(515\) −8.02045 −0.353423
\(516\) 18.6338 0.820309
\(517\) 15.0311 0.661066
\(518\) 0.333271 0.0146431
\(519\) −4.40484 −0.193351
\(520\) −3.05337 −0.133899
\(521\) 25.1102 1.10010 0.550049 0.835133i \(-0.314609\pi\)
0.550049 + 0.835133i \(0.314609\pi\)
\(522\) −6.18093 −0.270532
\(523\) −13.7141 −0.599675 −0.299837 0.953990i \(-0.596932\pi\)
−0.299837 + 0.953990i \(0.596932\pi\)
\(524\) 16.0374 0.700597
\(525\) 2.24041 0.0977795
\(526\) 5.97559 0.260548
\(527\) −2.05903 −0.0896930
\(528\) −23.1142 −1.00592
\(529\) 40.7416 1.77137
\(530\) 4.41236 0.191661
\(531\) 20.6684 0.896933
\(532\) 5.06323 0.219519
\(533\) −9.95714 −0.431292
\(534\) −8.99154 −0.389102
\(535\) −13.4191 −0.580157
\(536\) 20.1788 0.871590
\(537\) 13.7359 0.592747
\(538\) 7.31179 0.315234
\(539\) 3.08966 0.133081
\(540\) 4.14717 0.178466
\(541\) 6.28269 0.270114 0.135057 0.990838i \(-0.456878\pi\)
0.135057 + 0.990838i \(0.456878\pi\)
\(542\) 3.72040 0.159805
\(543\) 49.6637 2.13127
\(544\) 1.44294 0.0618655
\(545\) 5.11814 0.219237
\(546\) −1.75957 −0.0753026
\(547\) −24.6002 −1.05183 −0.525915 0.850537i \(-0.676277\pi\)
−0.525915 + 0.850537i \(0.676277\pi\)
\(548\) 11.7506 0.501959
\(549\) −9.78463 −0.417598
\(550\) 1.03508 0.0441360
\(551\) −24.5042 −1.04391
\(552\) 23.2971 0.991592
\(553\) 7.92124 0.336845
\(554\) 7.11265 0.302188
\(555\) −2.22875 −0.0946052
\(556\) 30.4615 1.29186
\(557\) 24.3518 1.03182 0.515910 0.856643i \(-0.327454\pi\)
0.515910 + 0.856643i \(0.327454\pi\)
\(558\) −3.59477 −0.152179
\(559\) −10.3286 −0.436854
\(560\) 3.33919 0.141106
\(561\) −2.68241 −0.113251
\(562\) −3.57092 −0.150630
\(563\) −40.9017 −1.72380 −0.861900 0.507078i \(-0.830726\pi\)
−0.861900 + 0.507078i \(0.830726\pi\)
\(564\) 20.5757 0.866393
\(565\) −9.16426 −0.385543
\(566\) −5.49924 −0.231150
\(567\) 10.9802 0.461125
\(568\) 7.98988 0.335248
\(569\) 30.8329 1.29258 0.646291 0.763091i \(-0.276319\pi\)
0.646291 + 0.763091i \(0.276319\pi\)
\(570\) 2.01312 0.0843205
\(571\) −12.1919 −0.510214 −0.255107 0.966913i \(-0.582111\pi\)
−0.255107 + 0.966913i \(0.582111\pi\)
\(572\) 13.6733 0.571711
\(573\) −8.20660 −0.342836
\(574\) −1.42293 −0.0593918
\(575\) 7.98383 0.332949
\(576\) −10.9674 −0.456975
\(577\) −35.5602 −1.48039 −0.740196 0.672391i \(-0.765267\pi\)
−0.740196 + 0.672391i \(0.765267\pi\)
\(578\) −5.64494 −0.234798
\(579\) 12.7488 0.529821
\(580\) −17.2468 −0.716134
\(581\) 9.73242 0.403769
\(582\) −6.69397 −0.277474
\(583\) −40.6929 −1.68533
\(584\) 8.25523 0.341604
\(585\) 4.73419 0.195735
\(586\) −3.71509 −0.153469
\(587\) 3.31738 0.136923 0.0684616 0.997654i \(-0.478191\pi\)
0.0684616 + 0.997654i \(0.478191\pi\)
\(588\) 4.22937 0.174416
\(589\) −14.2514 −0.587219
\(590\) −3.42879 −0.141161
\(591\) 25.4311 1.04610
\(592\) −3.32181 −0.136526
\(593\) 16.6255 0.682727 0.341364 0.939931i \(-0.389111\pi\)
0.341364 + 0.939931i \(0.389111\pi\)
\(594\) 2.27394 0.0933007
\(595\) 0.387513 0.0158865
\(596\) 9.28509 0.380332
\(597\) −13.5021 −0.552604
\(598\) −6.27033 −0.256413
\(599\) −1.47184 −0.0601378 −0.0300689 0.999548i \(-0.509573\pi\)
−0.0300689 + 0.999548i \(0.509573\pi\)
\(600\) 2.91804 0.119128
\(601\) 24.4064 0.995558 0.497779 0.867304i \(-0.334149\pi\)
0.497779 + 0.867304i \(0.334149\pi\)
\(602\) −1.47601 −0.0601578
\(603\) −31.2868 −1.27410
\(604\) −21.9068 −0.891376
\(605\) 1.45398 0.0591125
\(606\) 0.935209 0.0379903
\(607\) −30.4277 −1.23502 −0.617511 0.786563i \(-0.711859\pi\)
−0.617511 + 0.786563i \(0.711859\pi\)
\(608\) 9.98716 0.405033
\(609\) −20.4686 −0.829429
\(610\) 1.62322 0.0657224
\(611\) −11.4050 −0.461396
\(612\) −1.47728 −0.0597157
\(613\) −6.16136 −0.248855 −0.124427 0.992229i \(-0.539709\pi\)
−0.124427 + 0.992229i \(0.539709\pi\)
\(614\) −0.738061 −0.0297857
\(615\) 9.51583 0.383715
\(616\) 4.02416 0.162138
\(617\) 42.1317 1.69616 0.848078 0.529871i \(-0.177760\pi\)
0.848078 + 0.529871i \(0.177760\pi\)
\(618\) −6.01990 −0.242156
\(619\) 12.5510 0.504468 0.252234 0.967666i \(-0.418835\pi\)
0.252234 + 0.967666i \(0.418835\pi\)
\(620\) −10.0306 −0.402837
\(621\) 17.5394 0.703833
\(622\) −2.02529 −0.0812068
\(623\) −11.9796 −0.479954
\(624\) 17.5382 0.702088
\(625\) 1.00000 0.0400000
\(626\) −0.983215 −0.0392972
\(627\) −18.5660 −0.741455
\(628\) −25.1627 −1.00410
\(629\) −0.385496 −0.0153707
\(630\) 0.676540 0.0269540
\(631\) 20.4775 0.815198 0.407599 0.913161i \(-0.366366\pi\)
0.407599 + 0.913161i \(0.366366\pi\)
\(632\) 10.3171 0.410391
\(633\) 27.2840 1.08444
\(634\) 3.68507 0.146353
\(635\) −16.3534 −0.648963
\(636\) −55.7035 −2.20879
\(637\) −2.34431 −0.0928850
\(638\) −9.45660 −0.374391
\(639\) −12.3882 −0.490068
\(640\) 9.26662 0.366295
\(641\) −9.31252 −0.367822 −0.183911 0.982943i \(-0.558876\pi\)
−0.183911 + 0.982943i \(0.558876\pi\)
\(642\) −10.0719 −0.397508
\(643\) 29.5314 1.16461 0.582303 0.812972i \(-0.302152\pi\)
0.582303 + 0.812972i \(0.302152\pi\)
\(644\) 15.0716 0.593904
\(645\) 9.87084 0.388664
\(646\) 0.348201 0.0136998
\(647\) −26.9368 −1.05899 −0.529496 0.848312i \(-0.677619\pi\)
−0.529496 + 0.848312i \(0.677619\pi\)
\(648\) 14.3012 0.561805
\(649\) 31.6220 1.24127
\(650\) −0.785378 −0.0308051
\(651\) −11.9043 −0.466568
\(652\) 26.7441 1.04738
\(653\) 5.23289 0.204779 0.102389 0.994744i \(-0.467351\pi\)
0.102389 + 0.994744i \(0.467351\pi\)
\(654\) 3.84152 0.150215
\(655\) 8.49544 0.331944
\(656\) 14.1827 0.553743
\(657\) −12.7996 −0.499359
\(658\) −1.62983 −0.0635374
\(659\) 8.18222 0.318734 0.159367 0.987219i \(-0.449055\pi\)
0.159367 + 0.987219i \(0.449055\pi\)
\(660\) −13.0673 −0.508645
\(661\) 36.5815 1.42286 0.711429 0.702758i \(-0.248049\pi\)
0.711429 + 0.702758i \(0.248049\pi\)
\(662\) 9.30958 0.361827
\(663\) 2.03530 0.0790446
\(664\) 12.6761 0.491926
\(665\) 2.68213 0.104009
\(666\) −0.673019 −0.0260790
\(667\) −72.9410 −2.82429
\(668\) −9.46227 −0.366106
\(669\) −27.3671 −1.05807
\(670\) 5.19033 0.200520
\(671\) −14.9701 −0.577916
\(672\) 8.34237 0.321814
\(673\) 30.5860 1.17900 0.589502 0.807767i \(-0.299324\pi\)
0.589502 + 0.807767i \(0.299324\pi\)
\(674\) 1.16657 0.0449346
\(675\) 2.19687 0.0845574
\(676\) 14.1662 0.544853
\(677\) 24.9903 0.960455 0.480228 0.877144i \(-0.340554\pi\)
0.480228 + 0.877144i \(0.340554\pi\)
\(678\) −6.87841 −0.264164
\(679\) −8.91853 −0.342262
\(680\) 0.504719 0.0193551
\(681\) −59.9471 −2.29718
\(682\) −5.49987 −0.210601
\(683\) 39.1779 1.49910 0.749550 0.661948i \(-0.230270\pi\)
0.749550 + 0.661948i \(0.230270\pi\)
\(684\) −10.2249 −0.390958
\(685\) 6.22459 0.237829
\(686\) −0.335014 −0.0127909
\(687\) −2.24041 −0.0854770
\(688\) 14.7119 0.560885
\(689\) 30.8761 1.17629
\(690\) 5.99242 0.228128
\(691\) −18.6598 −0.709852 −0.354926 0.934894i \(-0.615494\pi\)
−0.354926 + 0.934894i \(0.615494\pi\)
\(692\) −3.71151 −0.141090
\(693\) −6.23938 −0.237014
\(694\) 9.60258 0.364509
\(695\) 16.1363 0.612084
\(696\) −26.6595 −1.01052
\(697\) 1.64591 0.0623432
\(698\) 2.05048 0.0776120
\(699\) 61.1177 2.31168
\(700\) 1.88777 0.0713508
\(701\) −0.375612 −0.0141867 −0.00709334 0.999975i \(-0.502258\pi\)
−0.00709334 + 0.999975i \(0.502258\pi\)
\(702\) −1.72537 −0.0651199
\(703\) −2.66817 −0.100632
\(704\) −16.7797 −0.632410
\(705\) 10.8995 0.410499
\(706\) −0.550597 −0.0207220
\(707\) 1.24600 0.0468607
\(708\) 43.2865 1.62681
\(709\) −7.74436 −0.290845 −0.145423 0.989370i \(-0.546454\pi\)
−0.145423 + 0.989370i \(0.546454\pi\)
\(710\) 2.05513 0.0771278
\(711\) −15.9964 −0.599913
\(712\) −15.6030 −0.584745
\(713\) −42.4218 −1.58871
\(714\) 0.290855 0.0108850
\(715\) 7.24314 0.270878
\(716\) 11.5738 0.432534
\(717\) 21.6916 0.810087
\(718\) −3.26716 −0.121929
\(719\) −37.2087 −1.38765 −0.693824 0.720144i \(-0.744076\pi\)
−0.693824 + 0.720144i \(0.744076\pi\)
\(720\) −6.74328 −0.251307
\(721\) −8.02045 −0.298697
\(722\) −3.95524 −0.147199
\(723\) −31.9675 −1.18889
\(724\) 41.8466 1.55521
\(725\) −9.13609 −0.339306
\(726\) 1.09131 0.0405023
\(727\) −9.80771 −0.363748 −0.181874 0.983322i \(-0.558216\pi\)
−0.181874 + 0.983322i \(0.558216\pi\)
\(728\) −3.05337 −0.113165
\(729\) −7.40813 −0.274375
\(730\) 2.12339 0.0785901
\(731\) 1.70731 0.0631472
\(732\) −20.4923 −0.757416
\(733\) 16.8853 0.623673 0.311836 0.950136i \(-0.399056\pi\)
0.311836 + 0.950136i \(0.399056\pi\)
\(734\) 5.65337 0.208670
\(735\) 2.24041 0.0826388
\(736\) 29.7285 1.09581
\(737\) −47.8677 −1.76323
\(738\) 2.87351 0.105775
\(739\) −3.52987 −0.129849 −0.0649243 0.997890i \(-0.520681\pi\)
−0.0649243 + 0.997890i \(0.520681\pi\)
\(740\) −1.87794 −0.0690345
\(741\) 14.0871 0.517504
\(742\) 4.41236 0.161983
\(743\) −34.9510 −1.28223 −0.641114 0.767445i \(-0.721528\pi\)
−0.641114 + 0.767445i \(0.721528\pi\)
\(744\) −15.5049 −0.568437
\(745\) 4.91856 0.180202
\(746\) −5.18866 −0.189970
\(747\) −19.6540 −0.719102
\(748\) −2.26019 −0.0826408
\(749\) −13.4191 −0.490322
\(750\) 0.750569 0.0274069
\(751\) −41.7657 −1.52405 −0.762025 0.647547i \(-0.775795\pi\)
−0.762025 + 0.647547i \(0.775795\pi\)
\(752\) 16.2450 0.592395
\(753\) −50.8178 −1.85190
\(754\) 7.17529 0.261309
\(755\) −11.6046 −0.422336
\(756\) 4.14717 0.150831
\(757\) −9.56815 −0.347760 −0.173880 0.984767i \(-0.555631\pi\)
−0.173880 + 0.984767i \(0.555631\pi\)
\(758\) −4.51297 −0.163919
\(759\) −55.2650 −2.00599
\(760\) 3.49336 0.126717
\(761\) 24.5402 0.889581 0.444790 0.895635i \(-0.353278\pi\)
0.444790 + 0.895635i \(0.353278\pi\)
\(762\) −12.2743 −0.444652
\(763\) 5.11814 0.185289
\(764\) −6.91487 −0.250171
\(765\) −0.782557 −0.0282934
\(766\) −1.62473 −0.0587037
\(767\) −23.9935 −0.866354
\(768\) −17.3797 −0.627137
\(769\) 1.72991 0.0623821 0.0311910 0.999513i \(-0.490070\pi\)
0.0311910 + 0.999513i \(0.490070\pi\)
\(770\) 1.03508 0.0373018
\(771\) −38.6487 −1.39190
\(772\) 10.7421 0.386617
\(773\) 37.3269 1.34256 0.671278 0.741206i \(-0.265746\pi\)
0.671278 + 0.741206i \(0.265746\pi\)
\(774\) 2.98071 0.107140
\(775\) −5.31346 −0.190865
\(776\) −11.6160 −0.416990
\(777\) −2.22875 −0.0799560
\(778\) 0.604379 0.0216680
\(779\) 11.3920 0.408160
\(780\) 9.91496 0.355013
\(781\) −18.9534 −0.678207
\(782\) 1.03648 0.0370645
\(783\) −20.0708 −0.717271
\(784\) 3.33919 0.119257
\(785\) −13.3293 −0.475745
\(786\) 6.37641 0.227439
\(787\) 0.999973 0.0356452 0.0178226 0.999841i \(-0.494327\pi\)
0.0178226 + 0.999841i \(0.494327\pi\)
\(788\) 21.4282 0.763348
\(789\) −39.9618 −1.42268
\(790\) 2.65373 0.0944154
\(791\) −9.16426 −0.325843
\(792\) −8.12652 −0.288763
\(793\) 11.3587 0.403361
\(794\) 3.24062 0.115005
\(795\) −29.5076 −1.04653
\(796\) −11.3768 −0.403241
\(797\) −5.95192 −0.210828 −0.105414 0.994428i \(-0.533617\pi\)
−0.105414 + 0.994428i \(0.533617\pi\)
\(798\) 2.01312 0.0712639
\(799\) 1.88523 0.0666948
\(800\) 3.72359 0.131649
\(801\) 24.1921 0.854785
\(802\) 1.65155 0.0583184
\(803\) −19.5829 −0.691066
\(804\) −65.5249 −2.31089
\(805\) 7.98383 0.281393
\(806\) 4.17308 0.146990
\(807\) −48.8976 −1.72128
\(808\) 1.62286 0.0570921
\(809\) 5.05286 0.177649 0.0888245 0.996047i \(-0.471689\pi\)
0.0888245 + 0.996047i \(0.471689\pi\)
\(810\) 3.67852 0.129250
\(811\) 28.0490 0.984935 0.492467 0.870331i \(-0.336095\pi\)
0.492467 + 0.870331i \(0.336095\pi\)
\(812\) −17.2468 −0.605244
\(813\) −24.8802 −0.872587
\(814\) −1.02970 −0.0360908
\(815\) 14.1670 0.496250
\(816\) −2.89904 −0.101487
\(817\) 11.8170 0.413424
\(818\) −1.82176 −0.0636965
\(819\) 4.73419 0.165426
\(820\) 8.01802 0.280001
\(821\) −7.31960 −0.255456 −0.127728 0.991809i \(-0.540768\pi\)
−0.127728 + 0.991809i \(0.540768\pi\)
\(822\) 4.67199 0.162954
\(823\) −17.9358 −0.625202 −0.312601 0.949884i \(-0.601200\pi\)
−0.312601 + 0.949884i \(0.601200\pi\)
\(824\) −10.4463 −0.363914
\(825\) −6.92211 −0.240997
\(826\) −3.42879 −0.119303
\(827\) −4.40875 −0.153307 −0.0766537 0.997058i \(-0.524424\pi\)
−0.0766537 + 0.997058i \(0.524424\pi\)
\(828\) −30.4361 −1.05773
\(829\) 1.28356 0.0445800 0.0222900 0.999752i \(-0.492904\pi\)
0.0222900 + 0.999752i \(0.492904\pi\)
\(830\) 3.26050 0.113174
\(831\) −47.5659 −1.65004
\(832\) 12.7318 0.441395
\(833\) 0.387513 0.0134265
\(834\) 12.1114 0.419383
\(835\) −5.01242 −0.173462
\(836\) −15.6437 −0.541048
\(837\) −11.6730 −0.403477
\(838\) 1.06909 0.0369311
\(839\) −35.5928 −1.22880 −0.614401 0.788994i \(-0.710602\pi\)
−0.614401 + 0.788994i \(0.710602\pi\)
\(840\) 2.91804 0.100682
\(841\) 54.4682 1.87821
\(842\) −1.41509 −0.0487674
\(843\) 23.8805 0.822490
\(844\) 22.9894 0.791328
\(845\) 7.50420 0.258152
\(846\) 3.29134 0.113159
\(847\) 1.45398 0.0499592
\(848\) −43.9793 −1.51025
\(849\) 36.7762 1.26216
\(850\) 0.129822 0.00445287
\(851\) −7.94228 −0.272258
\(852\) −25.9449 −0.888858
\(853\) −11.0497 −0.378334 −0.189167 0.981945i \(-0.560579\pi\)
−0.189167 + 0.981945i \(0.560579\pi\)
\(854\) 1.62322 0.0555455
\(855\) −5.41639 −0.185237
\(856\) −17.4778 −0.597378
\(857\) −18.5622 −0.634072 −0.317036 0.948413i \(-0.602688\pi\)
−0.317036 + 0.948413i \(0.602688\pi\)
\(858\) 5.43648 0.185598
\(859\) 48.5446 1.65632 0.828160 0.560491i \(-0.189388\pi\)
0.828160 + 0.560491i \(0.189388\pi\)
\(860\) 8.31715 0.283613
\(861\) 9.51583 0.324299
\(862\) 10.3202 0.351506
\(863\) 18.5868 0.632701 0.316350 0.948642i \(-0.397542\pi\)
0.316350 + 0.948642i \(0.397542\pi\)
\(864\) 8.18023 0.278297
\(865\) −1.96609 −0.0668489
\(866\) 4.48774 0.152500
\(867\) 37.7505 1.28208
\(868\) −10.0306 −0.340460
\(869\) −24.4740 −0.830222
\(870\) −6.85727 −0.232483
\(871\) 36.3201 1.23066
\(872\) 6.66615 0.225744
\(873\) 18.0104 0.609559
\(874\) 7.17389 0.242660
\(875\) 1.00000 0.0338062
\(876\) −26.8066 −0.905710
\(877\) −3.11892 −0.105318 −0.0526592 0.998613i \(-0.516770\pi\)
−0.0526592 + 0.998613i \(0.516770\pi\)
\(878\) −6.55823 −0.221330
\(879\) 24.8446 0.837989
\(880\) −10.3170 −0.347785
\(881\) −3.25242 −0.109577 −0.0547885 0.998498i \(-0.517448\pi\)
−0.0547885 + 0.998498i \(0.517448\pi\)
\(882\) 0.676540 0.0227803
\(883\) 2.80699 0.0944627 0.0472314 0.998884i \(-0.484960\pi\)
0.0472314 + 0.998884i \(0.484960\pi\)
\(884\) 1.71494 0.0576798
\(885\) 22.9300 0.770785
\(886\) 13.8695 0.465955
\(887\) −20.4029 −0.685063 −0.342532 0.939506i \(-0.611284\pi\)
−0.342532 + 0.939506i \(0.611284\pi\)
\(888\) −2.90285 −0.0974133
\(889\) −16.3534 −0.548474
\(890\) −4.01335 −0.134528
\(891\) −33.9251 −1.13653
\(892\) −23.0595 −0.772089
\(893\) 13.0485 0.436650
\(894\) 3.69172 0.123470
\(895\) 6.13097 0.204936
\(896\) 9.26662 0.309576
\(897\) 41.9329 1.40010
\(898\) −4.13706 −0.138055
\(899\) 48.5443 1.61904
\(900\) −3.81222 −0.127074
\(901\) −5.10380 −0.170032
\(902\) 4.39637 0.146383
\(903\) 9.87084 0.328481
\(904\) −11.9360 −0.396987
\(905\) 22.1672 0.736864
\(906\) −8.71008 −0.289373
\(907\) −45.1193 −1.49816 −0.749081 0.662479i \(-0.769505\pi\)
−0.749081 + 0.662479i \(0.769505\pi\)
\(908\) −50.5113 −1.67628
\(909\) −2.51622 −0.0834576
\(910\) −0.785378 −0.0260350
\(911\) −29.4454 −0.975571 −0.487785 0.872964i \(-0.662195\pi\)
−0.487785 + 0.872964i \(0.662195\pi\)
\(912\) −20.0654 −0.664433
\(913\) −30.0699 −0.995168
\(914\) 4.78269 0.158197
\(915\) −10.8553 −0.358865
\(916\) −1.88777 −0.0623735
\(917\) 8.49544 0.280544
\(918\) 0.285202 0.00941308
\(919\) 34.4829 1.13749 0.568743 0.822515i \(-0.307430\pi\)
0.568743 + 0.822515i \(0.307430\pi\)
\(920\) 10.3986 0.342832
\(921\) 4.93579 0.162640
\(922\) −5.48071 −0.180498
\(923\) 14.3811 0.473360
\(924\) −13.0673 −0.429883
\(925\) −0.994796 −0.0327087
\(926\) −10.5609 −0.347054
\(927\) 16.1968 0.531972
\(928\) −34.0191 −1.11673
\(929\) −25.4432 −0.834764 −0.417382 0.908731i \(-0.637052\pi\)
−0.417382 + 0.908731i \(0.637052\pi\)
\(930\) −3.98812 −0.130776
\(931\) 2.68213 0.0879033
\(932\) 51.4977 1.68686
\(933\) 13.5441 0.443415
\(934\) −4.09474 −0.133984
\(935\) −1.19728 −0.0391554
\(936\) 6.16608 0.201545
\(937\) 47.2850 1.54473 0.772367 0.635177i \(-0.219073\pi\)
0.772367 + 0.635177i \(0.219073\pi\)
\(938\) 5.19033 0.169470
\(939\) 6.57525 0.214575
\(940\) 9.18390 0.299546
\(941\) −32.3707 −1.05525 −0.527627 0.849476i \(-0.676918\pi\)
−0.527627 + 0.849476i \(0.676918\pi\)
\(942\) −10.0046 −0.325967
\(943\) 33.9102 1.10427
\(944\) 34.1758 1.11233
\(945\) 2.19687 0.0714641
\(946\) 4.56038 0.148271
\(947\) 55.2679 1.79597 0.897983 0.440030i \(-0.145032\pi\)
0.897983 + 0.440030i \(0.145032\pi\)
\(948\) −33.5018 −1.08809
\(949\) 14.8587 0.482334
\(950\) 0.898552 0.0291529
\(951\) −24.6439 −0.799134
\(952\) 0.504719 0.0163580
\(953\) −40.2474 −1.30374 −0.651870 0.758331i \(-0.726015\pi\)
−0.651870 + 0.758331i \(0.726015\pi\)
\(954\) −8.91047 −0.288487
\(955\) −3.66299 −0.118532
\(956\) 18.2773 0.591130
\(957\) 63.2411 2.04429
\(958\) −1.65024 −0.0533170
\(959\) 6.22459 0.201002
\(960\) −12.1675 −0.392704
\(961\) −2.76713 −0.0892621
\(962\) 0.781291 0.0251898
\(963\) 27.0990 0.873252
\(964\) −26.9358 −0.867544
\(965\) 5.69038 0.183180
\(966\) 5.99242 0.192803
\(967\) 0.139045 0.00447140 0.00223570 0.999998i \(-0.499288\pi\)
0.00223570 + 0.999998i \(0.499288\pi\)
\(968\) 1.89374 0.0608671
\(969\) −2.32859 −0.0748052
\(970\) −2.98784 −0.0959336
\(971\) 30.2278 0.970057 0.485028 0.874498i \(-0.338809\pi\)
0.485028 + 0.874498i \(0.338809\pi\)
\(972\) −33.9977 −1.09048
\(973\) 16.1363 0.517305
\(974\) 13.5045 0.432712
\(975\) 5.25222 0.168206
\(976\) −16.1791 −0.517882
\(977\) 40.6852 1.30164 0.650818 0.759234i \(-0.274426\pi\)
0.650818 + 0.759234i \(0.274426\pi\)
\(978\) 10.6333 0.340017
\(979\) 37.0130 1.18294
\(980\) 1.88777 0.0603025
\(981\) −10.3357 −0.329995
\(982\) 6.75517 0.215566
\(983\) 32.1677 1.02599 0.512996 0.858391i \(-0.328536\pi\)
0.512996 + 0.858391i \(0.328536\pi\)
\(984\) 12.3940 0.395105
\(985\) 11.3511 0.361676
\(986\) −1.18607 −0.0377721
\(987\) 10.8995 0.346935
\(988\) 11.8698 0.377629
\(989\) 35.1753 1.11851
\(990\) −2.09028 −0.0664335
\(991\) 14.8819 0.472739 0.236369 0.971663i \(-0.424042\pi\)
0.236369 + 0.971663i \(0.424042\pi\)
\(992\) −19.7852 −0.628179
\(993\) −62.2579 −1.97569
\(994\) 2.05513 0.0651849
\(995\) −6.02661 −0.191057
\(996\) −41.1620 −1.30427
\(997\) 54.4571 1.72467 0.862337 0.506335i \(-0.169000\pi\)
0.862337 + 0.506335i \(0.169000\pi\)
\(998\) −2.78354 −0.0881115
\(999\) −2.18543 −0.0691441
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 \(a_p\))