Properties

Label 8007.2.a.f.1.9
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 48
CM No

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(48\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00652 q^{2} -1.00000 q^{3} +2.02613 q^{4} -1.83243 q^{5} +2.00652 q^{6} -1.92586 q^{7} -0.0524220 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.00652 q^{2} -1.00000 q^{3} +2.02613 q^{4} -1.83243 q^{5} +2.00652 q^{6} -1.92586 q^{7} -0.0524220 q^{8} +1.00000 q^{9} +3.67682 q^{10} +3.86289 q^{11} -2.02613 q^{12} +6.14415 q^{13} +3.86428 q^{14} +1.83243 q^{15} -3.94707 q^{16} -1.00000 q^{17} -2.00652 q^{18} +0.890505 q^{19} -3.71274 q^{20} +1.92586 q^{21} -7.75098 q^{22} -5.99726 q^{23} +0.0524220 q^{24} -1.64219 q^{25} -12.3284 q^{26} -1.00000 q^{27} -3.90204 q^{28} +6.30206 q^{29} -3.67682 q^{30} -6.65982 q^{31} +8.02471 q^{32} -3.86289 q^{33} +2.00652 q^{34} +3.52902 q^{35} +2.02613 q^{36} +3.43677 q^{37} -1.78682 q^{38} -6.14415 q^{39} +0.0960598 q^{40} +10.4479 q^{41} -3.86428 q^{42} +9.99772 q^{43} +7.82671 q^{44} -1.83243 q^{45} +12.0336 q^{46} -1.34629 q^{47} +3.94707 q^{48} -3.29105 q^{49} +3.29508 q^{50} +1.00000 q^{51} +12.4488 q^{52} -11.2524 q^{53} +2.00652 q^{54} -7.07850 q^{55} +0.100958 q^{56} -0.890505 q^{57} -12.6452 q^{58} +2.14834 q^{59} +3.71274 q^{60} -14.3474 q^{61} +13.3631 q^{62} -1.92586 q^{63} -8.20762 q^{64} -11.2587 q^{65} +7.75098 q^{66} -4.33338 q^{67} -2.02613 q^{68} +5.99726 q^{69} -7.08105 q^{70} +8.04138 q^{71} -0.0524220 q^{72} -0.195770 q^{73} -6.89594 q^{74} +1.64219 q^{75} +1.80428 q^{76} -7.43940 q^{77} +12.3284 q^{78} -11.0344 q^{79} +7.23274 q^{80} +1.00000 q^{81} -20.9639 q^{82} -9.85496 q^{83} +3.90204 q^{84} +1.83243 q^{85} -20.0606 q^{86} -6.30206 q^{87} -0.202501 q^{88} -8.91778 q^{89} +3.67682 q^{90} -11.8328 q^{91} -12.1512 q^{92} +6.65982 q^{93} +2.70136 q^{94} -1.63179 q^{95} -8.02471 q^{96} -11.5640 q^{97} +6.60356 q^{98} +3.86289 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00652 −1.41882 −0.709412 0.704794i \(-0.751040\pi\)
−0.709412 + 0.704794i \(0.751040\pi\)
\(3\) −1.00000 −0.577350
\(4\) 2.02613 1.01306
\(5\) −1.83243 −0.819489 −0.409745 0.912200i \(-0.634382\pi\)
−0.409745 + 0.912200i \(0.634382\pi\)
\(6\) 2.00652 0.819159
\(7\) −1.92586 −0.727908 −0.363954 0.931417i \(-0.618573\pi\)
−0.363954 + 0.931417i \(0.618573\pi\)
\(8\) −0.0524220 −0.0185340
\(9\) 1.00000 0.333333
\(10\) 3.67682 1.16271
\(11\) 3.86289 1.16471 0.582353 0.812936i \(-0.302132\pi\)
0.582353 + 0.812936i \(0.302132\pi\)
\(12\) −2.02613 −0.584892
\(13\) 6.14415 1.70408 0.852040 0.523477i \(-0.175365\pi\)
0.852040 + 0.523477i \(0.175365\pi\)
\(14\) 3.86428 1.03277
\(15\) 1.83243 0.473132
\(16\) −3.94707 −0.986766
\(17\) −1.00000 −0.242536
\(18\) −2.00652 −0.472941
\(19\) 0.890505 0.204296 0.102148 0.994769i \(-0.467428\pi\)
0.102148 + 0.994769i \(0.467428\pi\)
\(20\) −3.71274 −0.830194
\(21\) 1.92586 0.420258
\(22\) −7.75098 −1.65251
\(23\) −5.99726 −1.25052 −0.625258 0.780418i \(-0.715006\pi\)
−0.625258 + 0.780418i \(0.715006\pi\)
\(24\) 0.0524220 0.0107006
\(25\) −1.64219 −0.328437
\(26\) −12.3284 −2.41779
\(27\) −1.00000 −0.192450
\(28\) −3.90204 −0.737416
\(29\) 6.30206 1.17026 0.585131 0.810939i \(-0.301043\pi\)
0.585131 + 0.810939i \(0.301043\pi\)
\(30\) −3.67682 −0.671292
\(31\) −6.65982 −1.19614 −0.598069 0.801444i \(-0.704065\pi\)
−0.598069 + 0.801444i \(0.704065\pi\)
\(32\) 8.02471 1.41858
\(33\) −3.86289 −0.672443
\(34\) 2.00652 0.344115
\(35\) 3.52902 0.596513
\(36\) 2.02613 0.337688
\(37\) 3.43677 0.565001 0.282500 0.959267i \(-0.408836\pi\)
0.282500 + 0.959267i \(0.408836\pi\)
\(38\) −1.78682 −0.289860
\(39\) −6.14415 −0.983851
\(40\) 0.0960598 0.0151884
\(41\) 10.4479 1.63168 0.815842 0.578274i \(-0.196274\pi\)
0.815842 + 0.578274i \(0.196274\pi\)
\(42\) −3.86428 −0.596272
\(43\) 9.99772 1.52464 0.762319 0.647202i \(-0.224061\pi\)
0.762319 + 0.647202i \(0.224061\pi\)
\(44\) 7.82671 1.17992
\(45\) −1.83243 −0.273163
\(46\) 12.0336 1.77426
\(47\) −1.34629 −0.196376 −0.0981882 0.995168i \(-0.531305\pi\)
−0.0981882 + 0.995168i \(0.531305\pi\)
\(48\) 3.94707 0.569710
\(49\) −3.29105 −0.470150
\(50\) 3.29508 0.465995
\(51\) 1.00000 0.140028
\(52\) 12.4488 1.72634
\(53\) −11.2524 −1.54563 −0.772817 0.634629i \(-0.781153\pi\)
−0.772817 + 0.634629i \(0.781153\pi\)
\(54\) 2.00652 0.273053
\(55\) −7.07850 −0.954464
\(56\) 0.100958 0.0134910
\(57\) −0.890505 −0.117950
\(58\) −12.6452 −1.66040
\(59\) 2.14834 0.279690 0.139845 0.990173i \(-0.455340\pi\)
0.139845 + 0.990173i \(0.455340\pi\)
\(60\) 3.71274 0.479313
\(61\) −14.3474 −1.83700 −0.918501 0.395420i \(-0.870599\pi\)
−0.918501 + 0.395420i \(0.870599\pi\)
\(62\) 13.3631 1.69711
\(63\) −1.92586 −0.242636
\(64\) −8.20762 −1.02595
\(65\) −11.2587 −1.39648
\(66\) 7.75098 0.954079
\(67\) −4.33338 −0.529406 −0.264703 0.964330i \(-0.585274\pi\)
−0.264703 + 0.964330i \(0.585274\pi\)
\(68\) −2.02613 −0.245704
\(69\) 5.99726 0.721985
\(70\) −7.08105 −0.846347
\(71\) 8.04138 0.954337 0.477168 0.878812i \(-0.341663\pi\)
0.477168 + 0.878812i \(0.341663\pi\)
\(72\) −0.0524220 −0.00617799
\(73\) −0.195770 −0.0229131 −0.0114565 0.999934i \(-0.503647\pi\)
−0.0114565 + 0.999934i \(0.503647\pi\)
\(74\) −6.89594 −0.801637
\(75\) 1.64219 0.189623
\(76\) 1.80428 0.206965
\(77\) −7.43940 −0.847799
\(78\) 12.3284 1.39591
\(79\) −11.0344 −1.24147 −0.620736 0.784020i \(-0.713166\pi\)
−0.620736 + 0.784020i \(0.713166\pi\)
\(80\) 7.23274 0.808645
\(81\) 1.00000 0.111111
\(82\) −20.9639 −2.31507
\(83\) −9.85496 −1.08172 −0.540861 0.841112i \(-0.681902\pi\)
−0.540861 + 0.841112i \(0.681902\pi\)
\(84\) 3.90204 0.425748
\(85\) 1.83243 0.198755
\(86\) −20.0606 −2.16319
\(87\) −6.30206 −0.675651
\(88\) −0.202501 −0.0215866
\(89\) −8.91778 −0.945283 −0.472641 0.881255i \(-0.656699\pi\)
−0.472641 + 0.881255i \(0.656699\pi\)
\(90\) 3.67682 0.387571
\(91\) −11.8328 −1.24041
\(92\) −12.1512 −1.26685
\(93\) 6.65982 0.690591
\(94\) 2.70136 0.278624
\(95\) −1.63179 −0.167418
\(96\) −8.02471 −0.819019
\(97\) −11.5640 −1.17415 −0.587074 0.809534i \(-0.699720\pi\)
−0.587074 + 0.809534i \(0.699720\pi\)
\(98\) 6.60356 0.667061
\(99\) 3.86289 0.388235
\(100\) −3.32728 −0.332728
\(101\) −0.668211 −0.0664895 −0.0332448 0.999447i \(-0.510584\pi\)
−0.0332448 + 0.999447i \(0.510584\pi\)
\(102\) −2.00652 −0.198675
\(103\) 5.30849 0.523061 0.261531 0.965195i \(-0.415773\pi\)
0.261531 + 0.965195i \(0.415773\pi\)
\(104\) −0.322088 −0.0315834
\(105\) −3.52902 −0.344397
\(106\) 22.5781 2.19298
\(107\) −5.00162 −0.483524 −0.241762 0.970336i \(-0.577725\pi\)
−0.241762 + 0.970336i \(0.577725\pi\)
\(108\) −2.02613 −0.194964
\(109\) −5.75725 −0.551445 −0.275722 0.961237i \(-0.588917\pi\)
−0.275722 + 0.961237i \(0.588917\pi\)
\(110\) 14.2032 1.35422
\(111\) −3.43677 −0.326203
\(112\) 7.60151 0.718275
\(113\) 8.38572 0.788862 0.394431 0.918925i \(-0.370942\pi\)
0.394431 + 0.918925i \(0.370942\pi\)
\(114\) 1.78682 0.167351
\(115\) 10.9896 1.02478
\(116\) 12.7688 1.18555
\(117\) 6.14415 0.568027
\(118\) −4.31069 −0.396831
\(119\) 1.92586 0.176544
\(120\) −0.0960598 −0.00876902
\(121\) 3.92194 0.356540
\(122\) 28.7884 2.60638
\(123\) −10.4479 −0.942054
\(124\) −13.4936 −1.21176
\(125\) 12.1714 1.08864
\(126\) 3.86428 0.344258
\(127\) 4.29246 0.380894 0.190447 0.981697i \(-0.439006\pi\)
0.190447 + 0.981697i \(0.439006\pi\)
\(128\) 0.419340 0.0370648
\(129\) −9.99772 −0.880250
\(130\) 22.5909 1.98135
\(131\) 8.79709 0.768605 0.384303 0.923207i \(-0.374442\pi\)
0.384303 + 0.923207i \(0.374442\pi\)
\(132\) −7.82671 −0.681227
\(133\) −1.71499 −0.148709
\(134\) 8.69501 0.751135
\(135\) 1.83243 0.157711
\(136\) 0.0524220 0.00449515
\(137\) −7.81121 −0.667356 −0.333678 0.942687i \(-0.608290\pi\)
−0.333678 + 0.942687i \(0.608290\pi\)
\(138\) −12.0336 −1.02437
\(139\) −7.10591 −0.602716 −0.301358 0.953511i \(-0.597440\pi\)
−0.301358 + 0.953511i \(0.597440\pi\)
\(140\) 7.15023 0.604305
\(141\) 1.34629 0.113378
\(142\) −16.1352 −1.35404
\(143\) 23.7342 1.98475
\(144\) −3.94707 −0.328922
\(145\) −11.5481 −0.959018
\(146\) 0.392816 0.0325096
\(147\) 3.29105 0.271441
\(148\) 6.96332 0.572381
\(149\) −6.36133 −0.521140 −0.260570 0.965455i \(-0.583911\pi\)
−0.260570 + 0.965455i \(0.583911\pi\)
\(150\) −3.29508 −0.269042
\(151\) 23.0557 1.87624 0.938122 0.346306i \(-0.112564\pi\)
0.938122 + 0.346306i \(0.112564\pi\)
\(152\) −0.0466821 −0.00378641
\(153\) −1.00000 −0.0808452
\(154\) 14.9273 1.20288
\(155\) 12.2037 0.980223
\(156\) −12.4488 −0.996703
\(157\) −1.00000 −0.0798087
\(158\) 22.1408 1.76143
\(159\) 11.2524 0.892372
\(160\) −14.7048 −1.16251
\(161\) 11.5499 0.910260
\(162\) −2.00652 −0.157647
\(163\) −12.4528 −0.975380 −0.487690 0.873017i \(-0.662160\pi\)
−0.487690 + 0.873017i \(0.662160\pi\)
\(164\) 21.1687 1.65300
\(165\) 7.07850 0.551060
\(166\) 19.7742 1.53477
\(167\) 16.1183 1.24727 0.623635 0.781716i \(-0.285655\pi\)
0.623635 + 0.781716i \(0.285655\pi\)
\(168\) −0.100958 −0.00778905
\(169\) 24.7506 1.90389
\(170\) −3.67682 −0.281999
\(171\) 0.890505 0.0680986
\(172\) 20.2566 1.54455
\(173\) 19.4724 1.48046 0.740230 0.672353i \(-0.234716\pi\)
0.740230 + 0.672353i \(0.234716\pi\)
\(174\) 12.6452 0.958631
\(175\) 3.16263 0.239072
\(176\) −15.2471 −1.14929
\(177\) −2.14834 −0.161479
\(178\) 17.8937 1.34119
\(179\) 15.4589 1.15545 0.577725 0.816231i \(-0.303940\pi\)
0.577725 + 0.816231i \(0.303940\pi\)
\(180\) −3.71274 −0.276731
\(181\) 5.64307 0.419446 0.209723 0.977761i \(-0.432744\pi\)
0.209723 + 0.977761i \(0.432744\pi\)
\(182\) 23.7427 1.75993
\(183\) 14.3474 1.06059
\(184\) 0.314388 0.0231770
\(185\) −6.29765 −0.463012
\(186\) −13.3631 −0.979827
\(187\) −3.86289 −0.282483
\(188\) −2.72775 −0.198942
\(189\) 1.92586 0.140086
\(190\) 3.27422 0.237537
\(191\) 24.8861 1.80069 0.900346 0.435175i \(-0.143313\pi\)
0.900346 + 0.435175i \(0.143313\pi\)
\(192\) 8.20762 0.592334
\(193\) −6.33620 −0.456089 −0.228045 0.973651i \(-0.573233\pi\)
−0.228045 + 0.973651i \(0.573233\pi\)
\(194\) 23.2034 1.66591
\(195\) 11.2587 0.806256
\(196\) −6.66808 −0.476292
\(197\) −25.6014 −1.82403 −0.912013 0.410162i \(-0.865472\pi\)
−0.912013 + 0.410162i \(0.865472\pi\)
\(198\) −7.75098 −0.550838
\(199\) 5.72472 0.405814 0.202907 0.979198i \(-0.434961\pi\)
0.202907 + 0.979198i \(0.434961\pi\)
\(200\) 0.0860866 0.00608725
\(201\) 4.33338 0.305653
\(202\) 1.34078 0.0943370
\(203\) −12.1369 −0.851843
\(204\) 2.02613 0.141857
\(205\) −19.1450 −1.33715
\(206\) −10.6516 −0.742132
\(207\) −5.99726 −0.416838
\(208\) −24.2514 −1.68153
\(209\) 3.43993 0.237945
\(210\) 7.08105 0.488639
\(211\) 0.0723951 0.00498388 0.00249194 0.999997i \(-0.499207\pi\)
0.00249194 + 0.999997i \(0.499207\pi\)
\(212\) −22.7988 −1.56582
\(213\) −8.04138 −0.550987
\(214\) 10.0358 0.686036
\(215\) −18.3202 −1.24942
\(216\) 0.0524220 0.00356686
\(217\) 12.8259 0.870679
\(218\) 11.5520 0.782403
\(219\) 0.195770 0.0132289
\(220\) −14.3419 −0.966932
\(221\) −6.14415 −0.413300
\(222\) 6.89594 0.462825
\(223\) −22.9352 −1.53585 −0.767926 0.640538i \(-0.778711\pi\)
−0.767926 + 0.640538i \(0.778711\pi\)
\(224\) −15.4545 −1.03260
\(225\) −1.64219 −0.109479
\(226\) −16.8261 −1.11926
\(227\) 24.2755 1.61122 0.805609 0.592447i \(-0.201838\pi\)
0.805609 + 0.592447i \(0.201838\pi\)
\(228\) −1.80428 −0.119491
\(229\) 5.32925 0.352167 0.176083 0.984375i \(-0.443657\pi\)
0.176083 + 0.984375i \(0.443657\pi\)
\(230\) −22.0508 −1.45399
\(231\) 7.43940 0.489477
\(232\) −0.330366 −0.0216896
\(233\) −5.24595 −0.343674 −0.171837 0.985125i \(-0.554970\pi\)
−0.171837 + 0.985125i \(0.554970\pi\)
\(234\) −12.3284 −0.805930
\(235\) 2.46699 0.160928
\(236\) 4.35281 0.283344
\(237\) 11.0344 0.716764
\(238\) −3.86428 −0.250484
\(239\) −2.19209 −0.141795 −0.0708974 0.997484i \(-0.522586\pi\)
−0.0708974 + 0.997484i \(0.522586\pi\)
\(240\) −7.23274 −0.466871
\(241\) 7.77245 0.500668 0.250334 0.968160i \(-0.419460\pi\)
0.250334 + 0.968160i \(0.419460\pi\)
\(242\) −7.86946 −0.505868
\(243\) −1.00000 −0.0641500
\(244\) −29.0697 −1.86100
\(245\) 6.03063 0.385283
\(246\) 20.9639 1.33661
\(247\) 5.47140 0.348137
\(248\) 0.349121 0.0221692
\(249\) 9.85496 0.624533
\(250\) −24.4221 −1.54459
\(251\) 25.2611 1.59447 0.797234 0.603670i \(-0.206296\pi\)
0.797234 + 0.603670i \(0.206296\pi\)
\(252\) −3.90204 −0.245805
\(253\) −23.1668 −1.45648
\(254\) −8.61291 −0.540422
\(255\) −1.83243 −0.114751
\(256\) 15.5738 0.973365
\(257\) −9.97646 −0.622314 −0.311157 0.950358i \(-0.600717\pi\)
−0.311157 + 0.950358i \(0.600717\pi\)
\(258\) 20.0606 1.24892
\(259\) −6.61874 −0.411268
\(260\) −22.8116 −1.41472
\(261\) 6.30206 0.390088
\(262\) −17.6515 −1.09052
\(263\) 14.1949 0.875293 0.437646 0.899147i \(-0.355812\pi\)
0.437646 + 0.899147i \(0.355812\pi\)
\(264\) 0.202501 0.0124630
\(265\) 20.6193 1.26663
\(266\) 3.44117 0.210991
\(267\) 8.91778 0.545759
\(268\) −8.77997 −0.536322
\(269\) −8.01771 −0.488849 −0.244424 0.969668i \(-0.578599\pi\)
−0.244424 + 0.969668i \(0.578599\pi\)
\(270\) −3.67682 −0.223764
\(271\) 6.63486 0.403039 0.201519 0.979485i \(-0.435412\pi\)
0.201519 + 0.979485i \(0.435412\pi\)
\(272\) 3.94707 0.239326
\(273\) 11.8328 0.716153
\(274\) 15.6733 0.946862
\(275\) −6.34359 −0.382533
\(276\) 12.1512 0.731416
\(277\) 11.7417 0.705490 0.352745 0.935719i \(-0.385248\pi\)
0.352745 + 0.935719i \(0.385248\pi\)
\(278\) 14.2582 0.855148
\(279\) −6.65982 −0.398713
\(280\) −0.184998 −0.0110558
\(281\) −25.2715 −1.50757 −0.753785 0.657121i \(-0.771774\pi\)
−0.753785 + 0.657121i \(0.771774\pi\)
\(282\) −2.70136 −0.160863
\(283\) −16.3299 −0.970709 −0.485355 0.874317i \(-0.661309\pi\)
−0.485355 + 0.874317i \(0.661309\pi\)
\(284\) 16.2929 0.966803
\(285\) 1.63179 0.0966590
\(286\) −47.6231 −2.81602
\(287\) −20.1212 −1.18772
\(288\) 8.02471 0.472861
\(289\) 1.00000 0.0588235
\(290\) 23.1715 1.36068
\(291\) 11.5640 0.677894
\(292\) −0.396654 −0.0232124
\(293\) 16.9866 0.992370 0.496185 0.868217i \(-0.334734\pi\)
0.496185 + 0.868217i \(0.334734\pi\)
\(294\) −6.60356 −0.385128
\(295\) −3.93669 −0.229203
\(296\) −0.180162 −0.0104717
\(297\) −3.86289 −0.224148
\(298\) 12.7641 0.739407
\(299\) −36.8481 −2.13098
\(300\) 3.32728 0.192100
\(301\) −19.2542 −1.10980
\(302\) −46.2617 −2.66206
\(303\) 0.668211 0.0383877
\(304\) −3.51488 −0.201592
\(305\) 26.2907 1.50540
\(306\) 2.00652 0.114705
\(307\) −20.3919 −1.16382 −0.581912 0.813251i \(-0.697695\pi\)
−0.581912 + 0.813251i \(0.697695\pi\)
\(308\) −15.0732 −0.858873
\(309\) −5.30849 −0.301990
\(310\) −24.4869 −1.39076
\(311\) 0.253731 0.0143878 0.00719389 0.999974i \(-0.497710\pi\)
0.00719389 + 0.999974i \(0.497710\pi\)
\(312\) 0.322088 0.0182347
\(313\) −18.9071 −1.06869 −0.534345 0.845266i \(-0.679442\pi\)
−0.534345 + 0.845266i \(0.679442\pi\)
\(314\) 2.00652 0.113235
\(315\) 3.52902 0.198838
\(316\) −22.3572 −1.25769
\(317\) −23.7699 −1.33505 −0.667525 0.744588i \(-0.732646\pi\)
−0.667525 + 0.744588i \(0.732646\pi\)
\(318\) −22.5781 −1.26612
\(319\) 24.3442 1.36301
\(320\) 15.0399 0.840758
\(321\) 5.00162 0.279163
\(322\) −23.1751 −1.29150
\(323\) −0.890505 −0.0495490
\(324\) 2.02613 0.112563
\(325\) −10.0898 −0.559683
\(326\) 24.9868 1.38389
\(327\) 5.75725 0.318377
\(328\) −0.547699 −0.0302416
\(329\) 2.59277 0.142944
\(330\) −14.2032 −0.781858
\(331\) 5.64108 0.310062 0.155031 0.987910i \(-0.450452\pi\)
0.155031 + 0.987910i \(0.450452\pi\)
\(332\) −19.9674 −1.09585
\(333\) 3.43677 0.188334
\(334\) −32.3417 −1.76966
\(335\) 7.94063 0.433843
\(336\) −7.60151 −0.414696
\(337\) 6.97492 0.379948 0.189974 0.981789i \(-0.439160\pi\)
0.189974 + 0.981789i \(0.439160\pi\)
\(338\) −49.6625 −2.70128
\(339\) −8.38572 −0.455450
\(340\) 3.71274 0.201352
\(341\) −25.7262 −1.39315
\(342\) −1.78682 −0.0966200
\(343\) 19.8192 1.07013
\(344\) −0.524100 −0.0282576
\(345\) −10.9896 −0.591659
\(346\) −39.0718 −2.10051
\(347\) −26.4785 −1.42144 −0.710720 0.703475i \(-0.751631\pi\)
−0.710720 + 0.703475i \(0.751631\pi\)
\(348\) −12.7688 −0.684477
\(349\) −36.0079 −1.92746 −0.963729 0.266884i \(-0.914006\pi\)
−0.963729 + 0.266884i \(0.914006\pi\)
\(350\) −6.34587 −0.339201
\(351\) −6.14415 −0.327950
\(352\) 30.9986 1.65223
\(353\) 24.4545 1.30158 0.650790 0.759258i \(-0.274438\pi\)
0.650790 + 0.759258i \(0.274438\pi\)
\(354\) 4.31069 0.229110
\(355\) −14.7353 −0.782069
\(356\) −18.0685 −0.957631
\(357\) −1.92586 −0.101927
\(358\) −31.0186 −1.63938
\(359\) 24.7684 1.30722 0.653612 0.756830i \(-0.273253\pi\)
0.653612 + 0.756830i \(0.273253\pi\)
\(360\) 0.0960598 0.00506280
\(361\) −18.2070 −0.958263
\(362\) −11.3229 −0.595120
\(363\) −3.92194 −0.205849
\(364\) −23.9747 −1.25662
\(365\) 0.358735 0.0187770
\(366\) −28.7884 −1.50480
\(367\) 22.0639 1.15172 0.575862 0.817547i \(-0.304667\pi\)
0.575862 + 0.817547i \(0.304667\pi\)
\(368\) 23.6716 1.23397
\(369\) 10.4479 0.543895
\(370\) 12.6364 0.656933
\(371\) 21.6706 1.12508
\(372\) 13.4936 0.699612
\(373\) 0.584279 0.0302528 0.0151264 0.999886i \(-0.495185\pi\)
0.0151264 + 0.999886i \(0.495185\pi\)
\(374\) 7.75098 0.400793
\(375\) −12.1714 −0.628527
\(376\) 0.0705751 0.00363963
\(377\) 38.7208 1.99422
\(378\) −3.86428 −0.198757
\(379\) −18.6260 −0.956752 −0.478376 0.878155i \(-0.658774\pi\)
−0.478376 + 0.878155i \(0.658774\pi\)
\(380\) −3.30622 −0.169605
\(381\) −4.29246 −0.219909
\(382\) −49.9344 −2.55487
\(383\) 22.8502 1.16759 0.583796 0.811901i \(-0.301567\pi\)
0.583796 + 0.811901i \(0.301567\pi\)
\(384\) −0.419340 −0.0213994
\(385\) 13.6322 0.694762
\(386\) 12.7137 0.647111
\(387\) 9.99772 0.508213
\(388\) −23.4301 −1.18949
\(389\) 2.92273 0.148188 0.0740942 0.997251i \(-0.476393\pi\)
0.0740942 + 0.997251i \(0.476393\pi\)
\(390\) −22.5909 −1.14394
\(391\) 5.99726 0.303294
\(392\) 0.172523 0.00871375
\(393\) −8.79709 −0.443754
\(394\) 51.3698 2.58797
\(395\) 20.2199 1.01737
\(396\) 7.82671 0.393307
\(397\) −7.77571 −0.390252 −0.195126 0.980778i \(-0.562512\pi\)
−0.195126 + 0.980778i \(0.562512\pi\)
\(398\) −11.4868 −0.575779
\(399\) 1.71499 0.0858570
\(400\) 6.48182 0.324091
\(401\) 35.4766 1.77162 0.885809 0.464050i \(-0.153604\pi\)
0.885809 + 0.464050i \(0.153604\pi\)
\(402\) −8.69501 −0.433668
\(403\) −40.9189 −2.03832
\(404\) −1.35388 −0.0673581
\(405\) −1.83243 −0.0910544
\(406\) 24.3529 1.20862
\(407\) 13.2759 0.658060
\(408\) −0.0524220 −0.00259528
\(409\) −8.22238 −0.406571 −0.203285 0.979120i \(-0.565162\pi\)
−0.203285 + 0.979120i \(0.565162\pi\)
\(410\) 38.4149 1.89718
\(411\) 7.81121 0.385298
\(412\) 10.7557 0.529894
\(413\) −4.13741 −0.203589
\(414\) 12.0336 0.591420
\(415\) 18.0586 0.886460
\(416\) 49.3050 2.41738
\(417\) 7.10591 0.347978
\(418\) −6.90228 −0.337602
\(419\) −6.38908 −0.312127 −0.156064 0.987747i \(-0.549880\pi\)
−0.156064 + 0.987747i \(0.549880\pi\)
\(420\) −7.15023 −0.348896
\(421\) −3.46000 −0.168630 −0.0843151 0.996439i \(-0.526870\pi\)
−0.0843151 + 0.996439i \(0.526870\pi\)
\(422\) −0.145262 −0.00707126
\(423\) −1.34629 −0.0654588
\(424\) 0.589873 0.0286467
\(425\) 1.64219 0.0796577
\(426\) 16.1352 0.781753
\(427\) 27.6312 1.33717
\(428\) −10.1339 −0.489841
\(429\) −23.7342 −1.14590
\(430\) 36.7598 1.77271
\(431\) −32.6003 −1.57030 −0.785152 0.619304i \(-0.787415\pi\)
−0.785152 + 0.619304i \(0.787415\pi\)
\(432\) 3.94707 0.189903
\(433\) 27.3070 1.31229 0.656145 0.754635i \(-0.272186\pi\)
0.656145 + 0.754635i \(0.272186\pi\)
\(434\) −25.7354 −1.23534
\(435\) 11.5481 0.553689
\(436\) −11.6649 −0.558648
\(437\) −5.34059 −0.255475
\(438\) −0.392816 −0.0187695
\(439\) −11.6003 −0.553650 −0.276825 0.960920i \(-0.589282\pi\)
−0.276825 + 0.960920i \(0.589282\pi\)
\(440\) 0.371069 0.0176900
\(441\) −3.29105 −0.156717
\(442\) 12.3284 0.586400
\(443\) −24.5529 −1.16654 −0.583272 0.812277i \(-0.698228\pi\)
−0.583272 + 0.812277i \(0.698228\pi\)
\(444\) −6.96332 −0.330465
\(445\) 16.3412 0.774649
\(446\) 46.0199 2.17910
\(447\) 6.36133 0.300881
\(448\) 15.8068 0.746799
\(449\) −21.5051 −1.01489 −0.507444 0.861685i \(-0.669409\pi\)
−0.507444 + 0.861685i \(0.669409\pi\)
\(450\) 3.29508 0.155332
\(451\) 40.3590 1.90043
\(452\) 16.9905 0.799167
\(453\) −23.0557 −1.08325
\(454\) −48.7092 −2.28604
\(455\) 21.6828 1.01651
\(456\) 0.0466821 0.00218609
\(457\) −32.7765 −1.53322 −0.766609 0.642114i \(-0.778057\pi\)
−0.766609 + 0.642114i \(0.778057\pi\)
\(458\) −10.6933 −0.499663
\(459\) 1.00000 0.0466760
\(460\) 22.2663 1.03817
\(461\) 20.3967 0.949967 0.474983 0.879995i \(-0.342454\pi\)
0.474983 + 0.879995i \(0.342454\pi\)
\(462\) −14.9273 −0.694482
\(463\) −25.3223 −1.17683 −0.588414 0.808560i \(-0.700247\pi\)
−0.588414 + 0.808560i \(0.700247\pi\)
\(464\) −24.8746 −1.15478
\(465\) −12.2037 −0.565932
\(466\) 10.5261 0.487613
\(467\) −25.1858 −1.16546 −0.582730 0.812666i \(-0.698015\pi\)
−0.582730 + 0.812666i \(0.698015\pi\)
\(468\) 12.4488 0.575447
\(469\) 8.34549 0.385359
\(470\) −4.95006 −0.228329
\(471\) 1.00000 0.0460776
\(472\) −0.112620 −0.00518377
\(473\) 38.6201 1.77576
\(474\) −22.1408 −1.01696
\(475\) −1.46238 −0.0670984
\(476\) 3.90204 0.178850
\(477\) −11.2524 −0.515211
\(478\) 4.39848 0.201182
\(479\) −2.19637 −0.100355 −0.0501775 0.998740i \(-0.515979\pi\)
−0.0501775 + 0.998740i \(0.515979\pi\)
\(480\) 14.7048 0.671177
\(481\) 21.1160 0.962807
\(482\) −15.5956 −0.710359
\(483\) −11.5499 −0.525539
\(484\) 7.94635 0.361198
\(485\) 21.1903 0.962201
\(486\) 2.00652 0.0910176
\(487\) −14.5496 −0.659306 −0.329653 0.944102i \(-0.606932\pi\)
−0.329653 + 0.944102i \(0.606932\pi\)
\(488\) 0.752121 0.0340469
\(489\) 12.4528 0.563136
\(490\) −12.1006 −0.546649
\(491\) 38.3968 1.73282 0.866412 0.499330i \(-0.166420\pi\)
0.866412 + 0.499330i \(0.166420\pi\)
\(492\) −21.1687 −0.954360
\(493\) −6.30206 −0.283830
\(494\) −10.9785 −0.493945
\(495\) −7.07850 −0.318155
\(496\) 26.2867 1.18031
\(497\) −15.4866 −0.694669
\(498\) −19.7742 −0.886102
\(499\) 1.97846 0.0885679 0.0442840 0.999019i \(-0.485899\pi\)
0.0442840 + 0.999019i \(0.485899\pi\)
\(500\) 24.6607 1.10286
\(501\) −16.1183 −0.720111
\(502\) −50.6870 −2.26227
\(503\) −9.12840 −0.407015 −0.203508 0.979073i \(-0.565234\pi\)
−0.203508 + 0.979073i \(0.565234\pi\)
\(504\) 0.100958 0.00449701
\(505\) 1.22445 0.0544875
\(506\) 46.4846 2.06649
\(507\) −24.7506 −1.09921
\(508\) 8.69706 0.385870
\(509\) −36.3313 −1.61036 −0.805179 0.593032i \(-0.797931\pi\)
−0.805179 + 0.593032i \(0.797931\pi\)
\(510\) 3.67682 0.162812
\(511\) 0.377025 0.0166786
\(512\) −32.0879 −1.41810
\(513\) −0.890505 −0.0393168
\(514\) 20.0180 0.882955
\(515\) −9.72746 −0.428643
\(516\) −20.2566 −0.891749
\(517\) −5.20057 −0.228721
\(518\) 13.2806 0.583518
\(519\) −19.4724 −0.854744
\(520\) 0.590206 0.0258822
\(521\) −16.0917 −0.704991 −0.352495 0.935814i \(-0.614667\pi\)
−0.352495 + 0.935814i \(0.614667\pi\)
\(522\) −12.6452 −0.553466
\(523\) 4.30024 0.188036 0.0940182 0.995570i \(-0.470029\pi\)
0.0940182 + 0.995570i \(0.470029\pi\)
\(524\) 17.8240 0.778645
\(525\) −3.16263 −0.138028
\(526\) −28.4823 −1.24189
\(527\) 6.65982 0.290106
\(528\) 15.2471 0.663545
\(529\) 12.9671 0.563788
\(530\) −41.3730 −1.79713
\(531\) 2.14834 0.0932300
\(532\) −3.47479 −0.150651
\(533\) 64.1933 2.78052
\(534\) −17.8937 −0.774336
\(535\) 9.16513 0.396243
\(536\) 0.227164 0.00981200
\(537\) −15.4589 −0.667100
\(538\) 16.0877 0.693590
\(539\) −12.7130 −0.547587
\(540\) 3.71274 0.159771
\(541\) 25.1234 1.08014 0.540069 0.841620i \(-0.318398\pi\)
0.540069 + 0.841620i \(0.318398\pi\)
\(542\) −13.3130 −0.571841
\(543\) −5.64307 −0.242167
\(544\) −8.02471 −0.344057
\(545\) 10.5498 0.451903
\(546\) −23.7427 −1.01610
\(547\) −37.1417 −1.58807 −0.794033 0.607875i \(-0.792022\pi\)
−0.794033 + 0.607875i \(0.792022\pi\)
\(548\) −15.8265 −0.676074
\(549\) −14.3474 −0.612334
\(550\) 12.7285 0.542747
\(551\) 5.61202 0.239080
\(552\) −0.314388 −0.0133813
\(553\) 21.2508 0.903677
\(554\) −23.5600 −1.00097
\(555\) 6.29765 0.267320
\(556\) −14.3975 −0.610589
\(557\) −27.2639 −1.15521 −0.577603 0.816317i \(-0.696012\pi\)
−0.577603 + 0.816317i \(0.696012\pi\)
\(558\) 13.3631 0.565704
\(559\) 61.4275 2.59811
\(560\) −13.9293 −0.588619
\(561\) 3.86289 0.163091
\(562\) 50.7078 2.13898
\(563\) −21.7338 −0.915971 −0.457986 0.888960i \(-0.651429\pi\)
−0.457986 + 0.888960i \(0.651429\pi\)
\(564\) 2.72775 0.114859
\(565\) −15.3663 −0.646464
\(566\) 32.7662 1.37727
\(567\) −1.92586 −0.0808786
\(568\) −0.421545 −0.0176876
\(569\) −8.37425 −0.351067 −0.175533 0.984473i \(-0.556165\pi\)
−0.175533 + 0.984473i \(0.556165\pi\)
\(570\) −3.27422 −0.137142
\(571\) −18.8762 −0.789944 −0.394972 0.918693i \(-0.629246\pi\)
−0.394972 + 0.918693i \(0.629246\pi\)
\(572\) 48.0885 2.01068
\(573\) −24.8861 −1.03963
\(574\) 40.3736 1.68516
\(575\) 9.84861 0.410716
\(576\) −8.20762 −0.341984
\(577\) −15.8753 −0.660898 −0.330449 0.943824i \(-0.607200\pi\)
−0.330449 + 0.943824i \(0.607200\pi\)
\(578\) −2.00652 −0.0834603
\(579\) 6.33620 0.263323
\(580\) −23.3979 −0.971545
\(581\) 18.9793 0.787394
\(582\) −23.2034 −0.961813
\(583\) −43.4668 −1.80021
\(584\) 0.0102626 0.000424671 0
\(585\) −11.2587 −0.465492
\(586\) −34.0840 −1.40800
\(587\) 5.14095 0.212190 0.106095 0.994356i \(-0.466165\pi\)
0.106095 + 0.994356i \(0.466165\pi\)
\(588\) 6.66808 0.274987
\(589\) −5.93060 −0.244366
\(590\) 7.89905 0.325199
\(591\) 25.6014 1.05310
\(592\) −13.5651 −0.557524
\(593\) −10.1063 −0.415017 −0.207509 0.978233i \(-0.566536\pi\)
−0.207509 + 0.978233i \(0.566536\pi\)
\(594\) 7.75098 0.318026
\(595\) −3.52902 −0.144676
\(596\) −12.8889 −0.527948
\(597\) −5.72472 −0.234297
\(598\) 73.9364 3.02348
\(599\) 37.2839 1.52338 0.761688 0.647943i \(-0.224371\pi\)
0.761688 + 0.647943i \(0.224371\pi\)
\(600\) −0.0860866 −0.00351447
\(601\) −44.1884 −1.80248 −0.901241 0.433318i \(-0.857343\pi\)
−0.901241 + 0.433318i \(0.857343\pi\)
\(602\) 38.6340 1.57461
\(603\) −4.33338 −0.176469
\(604\) 46.7137 1.90075
\(605\) −7.18670 −0.292181
\(606\) −1.34078 −0.0544655
\(607\) −29.4875 −1.19686 −0.598430 0.801175i \(-0.704209\pi\)
−0.598430 + 0.801175i \(0.704209\pi\)
\(608\) 7.14605 0.289811
\(609\) 12.1369 0.491812
\(610\) −52.7529 −2.13590
\(611\) −8.27180 −0.334641
\(612\) −2.02613 −0.0819013
\(613\) −15.9150 −0.642802 −0.321401 0.946943i \(-0.604154\pi\)
−0.321401 + 0.946943i \(0.604154\pi\)
\(614\) 40.9167 1.65126
\(615\) 19.1450 0.772003
\(616\) 0.389988 0.0157131
\(617\) −42.5319 −1.71227 −0.856134 0.516753i \(-0.827140\pi\)
−0.856134 + 0.516753i \(0.827140\pi\)
\(618\) 10.6516 0.428470
\(619\) −2.25945 −0.0908151 −0.0454075 0.998969i \(-0.514459\pi\)
−0.0454075 + 0.998969i \(0.514459\pi\)
\(620\) 24.7262 0.993027
\(621\) 5.99726 0.240662
\(622\) −0.509117 −0.0204137
\(623\) 17.1744 0.688079
\(624\) 24.2514 0.970831
\(625\) −14.0923 −0.563692
\(626\) 37.9374 1.51628
\(627\) −3.43993 −0.137377
\(628\) −2.02613 −0.0808512
\(629\) −3.43677 −0.137033
\(630\) −7.08105 −0.282116
\(631\) 12.9756 0.516551 0.258276 0.966071i \(-0.416846\pi\)
0.258276 + 0.966071i \(0.416846\pi\)
\(632\) 0.578447 0.0230094
\(633\) −0.0723951 −0.00287745
\(634\) 47.6948 1.89420
\(635\) −7.86565 −0.312139
\(636\) 22.7988 0.904029
\(637\) −20.2207 −0.801174
\(638\) −48.8471 −1.93387
\(639\) 8.04138 0.318112
\(640\) −0.768413 −0.0303742
\(641\) −26.5958 −1.05047 −0.525235 0.850957i \(-0.676022\pi\)
−0.525235 + 0.850957i \(0.676022\pi\)
\(642\) −10.0358 −0.396083
\(643\) −18.4224 −0.726509 −0.363254 0.931690i \(-0.618334\pi\)
−0.363254 + 0.931690i \(0.618334\pi\)
\(644\) 23.4016 0.922150
\(645\) 18.3202 0.721356
\(646\) 1.78682 0.0703014
\(647\) 29.4426 1.15751 0.578755 0.815502i \(-0.303539\pi\)
0.578755 + 0.815502i \(0.303539\pi\)
\(648\) −0.0524220 −0.00205933
\(649\) 8.29881 0.325757
\(650\) 20.2455 0.794092
\(651\) −12.8259 −0.502687
\(652\) −25.2310 −0.988121
\(653\) 19.1072 0.747722 0.373861 0.927485i \(-0.378034\pi\)
0.373861 + 0.927485i \(0.378034\pi\)
\(654\) −11.5520 −0.451721
\(655\) −16.1201 −0.629864
\(656\) −41.2385 −1.61009
\(657\) −0.195770 −0.00763770
\(658\) −5.20244 −0.202812
\(659\) 5.01331 0.195291 0.0976455 0.995221i \(-0.468869\pi\)
0.0976455 + 0.995221i \(0.468869\pi\)
\(660\) 14.3419 0.558259
\(661\) 17.5057 0.680893 0.340447 0.940264i \(-0.389422\pi\)
0.340447 + 0.940264i \(0.389422\pi\)
\(662\) −11.3189 −0.439923
\(663\) 6.14415 0.238619
\(664\) 0.516616 0.0200486
\(665\) 3.14261 0.121865
\(666\) −6.89594 −0.267212
\(667\) −37.7951 −1.46343
\(668\) 32.6576 1.26356
\(669\) 22.9352 0.886725
\(670\) −15.9330 −0.615547
\(671\) −55.4226 −2.13957
\(672\) 15.4545 0.596170
\(673\) −34.2041 −1.31847 −0.659235 0.751937i \(-0.729120\pi\)
−0.659235 + 0.751937i \(0.729120\pi\)
\(674\) −13.9953 −0.539080
\(675\) 1.64219 0.0632078
\(676\) 50.1477 1.92876
\(677\) −36.9819 −1.42133 −0.710664 0.703531i \(-0.751605\pi\)
−0.710664 + 0.703531i \(0.751605\pi\)
\(678\) 16.8261 0.646204
\(679\) 22.2707 0.854671
\(680\) −0.0960598 −0.00368373
\(681\) −24.2755 −0.930237
\(682\) 51.6201 1.97664
\(683\) −15.5900 −0.596535 −0.298267 0.954482i \(-0.596409\pi\)
−0.298267 + 0.954482i \(0.596409\pi\)
\(684\) 1.80428 0.0689882
\(685\) 14.3135 0.546891
\(686\) −39.7675 −1.51833
\(687\) −5.32925 −0.203324
\(688\) −39.4617 −1.50446
\(689\) −69.1363 −2.63388
\(690\) 22.0508 0.839461
\(691\) −12.4194 −0.472457 −0.236229 0.971698i \(-0.575911\pi\)
−0.236229 + 0.971698i \(0.575911\pi\)
\(692\) 39.4536 1.49980
\(693\) −7.43940 −0.282600
\(694\) 53.1297 2.01678
\(695\) 13.0211 0.493919
\(696\) 0.330366 0.0125225
\(697\) −10.4479 −0.395742
\(698\) 72.2505 2.73472
\(699\) 5.24595 0.198420
\(700\) 6.40788 0.242195
\(701\) 45.8308 1.73101 0.865504 0.500903i \(-0.166999\pi\)
0.865504 + 0.500903i \(0.166999\pi\)
\(702\) 12.3284 0.465304
\(703\) 3.06046 0.115427
\(704\) −31.7052 −1.19493
\(705\) −2.46699 −0.0929120
\(706\) −49.0684 −1.84671
\(707\) 1.28688 0.0483982
\(708\) −4.35281 −0.163588
\(709\) 12.1609 0.456712 0.228356 0.973578i \(-0.426665\pi\)
0.228356 + 0.973578i \(0.426665\pi\)
\(710\) 29.5667 1.10962
\(711\) −11.0344 −0.413824
\(712\) 0.467488 0.0175198
\(713\) 39.9407 1.49579
\(714\) 3.86428 0.144617
\(715\) −43.4913 −1.62648
\(716\) 31.3216 1.17054
\(717\) 2.19209 0.0818653
\(718\) −49.6982 −1.85472
\(719\) 47.2832 1.76337 0.881683 0.471843i \(-0.156411\pi\)
0.881683 + 0.471843i \(0.156411\pi\)
\(720\) 7.23274 0.269548
\(721\) −10.2234 −0.380740
\(722\) 36.5327 1.35961
\(723\) −7.77245 −0.289061
\(724\) 11.4336 0.424925
\(725\) −10.3491 −0.384358
\(726\) 7.86946 0.292063
\(727\) 10.2019 0.378366 0.189183 0.981942i \(-0.439416\pi\)
0.189183 + 0.981942i \(0.439416\pi\)
\(728\) 0.620298 0.0229898
\(729\) 1.00000 0.0370370
\(730\) −0.719809 −0.0266413
\(731\) −9.99772 −0.369779
\(732\) 29.0697 1.07445
\(733\) −7.70062 −0.284429 −0.142214 0.989836i \(-0.545422\pi\)
−0.142214 + 0.989836i \(0.545422\pi\)
\(734\) −44.2716 −1.63409
\(735\) −6.03063 −0.222443
\(736\) −48.1263 −1.77396
\(737\) −16.7394 −0.616603
\(738\) −20.9639 −0.771691
\(739\) −16.0844 −0.591675 −0.295838 0.955238i \(-0.595599\pi\)
−0.295838 + 0.955238i \(0.595599\pi\)
\(740\) −12.7598 −0.469060
\(741\) −5.47140 −0.200997
\(742\) −43.4824 −1.59629
\(743\) 1.92699 0.0706943 0.0353471 0.999375i \(-0.488746\pi\)
0.0353471 + 0.999375i \(0.488746\pi\)
\(744\) −0.349121 −0.0127994
\(745\) 11.6567 0.427069
\(746\) −1.17237 −0.0429235
\(747\) −9.85496 −0.360574
\(748\) −7.82671 −0.286173
\(749\) 9.63243 0.351961
\(750\) 24.4221 0.891769
\(751\) 28.0063 1.02196 0.510982 0.859591i \(-0.329282\pi\)
0.510982 + 0.859591i \(0.329282\pi\)
\(752\) 5.31389 0.193778
\(753\) −25.2611 −0.920567
\(754\) −77.6940 −2.82945
\(755\) −42.2480 −1.53756
\(756\) 3.90204 0.141916
\(757\) 7.75500 0.281860 0.140930 0.990020i \(-0.454991\pi\)
0.140930 + 0.990020i \(0.454991\pi\)
\(758\) 37.3734 1.35746
\(759\) 23.1668 0.840901
\(760\) 0.0855418 0.00310293
\(761\) 15.5413 0.563373 0.281686 0.959507i \(-0.409106\pi\)
0.281686 + 0.959507i \(0.409106\pi\)
\(762\) 8.61291 0.312013
\(763\) 11.0877 0.401401
\(764\) 50.4223 1.82421
\(765\) 1.83243 0.0662518
\(766\) −45.8494 −1.65661
\(767\) 13.1997 0.476614
\(768\) −15.5738 −0.561972
\(769\) −13.4400 −0.484657 −0.242329 0.970194i \(-0.577911\pi\)
−0.242329 + 0.970194i \(0.577911\pi\)
\(770\) −27.3533 −0.985745
\(771\) 9.97646 0.359293
\(772\) −12.8379 −0.462047
\(773\) −35.4138 −1.27374 −0.636872 0.770969i \(-0.719772\pi\)
−0.636872 + 0.770969i \(0.719772\pi\)
\(774\) −20.0606 −0.721065
\(775\) 10.9367 0.392856
\(776\) 0.606208 0.0217616
\(777\) 6.61874 0.237446
\(778\) −5.86453 −0.210253
\(779\) 9.30389 0.333347
\(780\) 22.8116 0.816788
\(781\) 31.0630 1.11152
\(782\) −12.0336 −0.430322
\(783\) −6.30206 −0.225217
\(784\) 12.9900 0.463928
\(785\) 1.83243 0.0654024
\(786\) 17.6515 0.629610
\(787\) 39.4330 1.40564 0.702818 0.711370i \(-0.251925\pi\)
0.702818 + 0.711370i \(0.251925\pi\)
\(788\) −51.8717 −1.84785
\(789\) −14.1949 −0.505351
\(790\) −40.5716 −1.44347
\(791\) −16.1498 −0.574219
\(792\) −0.202501 −0.00719554
\(793\) −88.1528 −3.13040
\(794\) 15.6021 0.553698
\(795\) −20.6193 −0.731290
\(796\) 11.5990 0.411116
\(797\) 36.5285 1.29390 0.646952 0.762530i \(-0.276043\pi\)
0.646952 + 0.762530i \(0.276043\pi\)
\(798\) −3.44117 −0.121816
\(799\) 1.34629 0.0476283
\(800\) −13.1781 −0.465915
\(801\) −8.91778 −0.315094
\(802\) −71.1846 −2.51362
\(803\) −0.756237 −0.0266870
\(804\) 8.77997 0.309646
\(805\) −21.1644 −0.745948
\(806\) 82.1046 2.89201
\(807\) 8.01771 0.282237
\(808\) 0.0350290 0.00123231
\(809\) −48.4476 −1.70333 −0.851663 0.524090i \(-0.824406\pi\)
−0.851663 + 0.524090i \(0.824406\pi\)
\(810\) 3.67682 0.129190
\(811\) 9.64546 0.338698 0.169349 0.985556i \(-0.445834\pi\)
0.169349 + 0.985556i \(0.445834\pi\)
\(812\) −24.5909 −0.862971
\(813\) −6.63486 −0.232695
\(814\) −26.6383 −0.933671
\(815\) 22.8190 0.799314
\(816\) −3.94707 −0.138175
\(817\) 8.90302 0.311477
\(818\) 16.4984 0.576852
\(819\) −11.8328 −0.413471
\(820\) −38.7903 −1.35462
\(821\) 44.8788 1.56628 0.783141 0.621845i \(-0.213616\pi\)
0.783141 + 0.621845i \(0.213616\pi\)
\(822\) −15.6733 −0.546671
\(823\) −21.3854 −0.745450 −0.372725 0.927942i \(-0.621576\pi\)
−0.372725 + 0.927942i \(0.621576\pi\)
\(824\) −0.278282 −0.00969440
\(825\) 6.34359 0.220855
\(826\) 8.30180 0.288856
\(827\) 11.8470 0.411960 0.205980 0.978556i \(-0.433962\pi\)
0.205980 + 0.978556i \(0.433962\pi\)
\(828\) −12.1512 −0.422283
\(829\) 2.36211 0.0820394 0.0410197 0.999158i \(-0.486939\pi\)
0.0410197 + 0.999158i \(0.486939\pi\)
\(830\) −36.2349 −1.25773
\(831\) −11.7417 −0.407315
\(832\) −50.4289 −1.74831
\(833\) 3.29105 0.114028
\(834\) −14.2582 −0.493720
\(835\) −29.5357 −1.02212
\(836\) 6.96972 0.241053
\(837\) 6.65982 0.230197
\(838\) 12.8198 0.442854
\(839\) −12.0025 −0.414373 −0.207187 0.978301i \(-0.566431\pi\)
−0.207187 + 0.978301i \(0.566431\pi\)
\(840\) 0.184998 0.00638304
\(841\) 10.7159 0.369515
\(842\) 6.94257 0.239257
\(843\) 25.2715 0.870396
\(844\) 0.146682 0.00504899
\(845\) −45.3538 −1.56022
\(846\) 2.70136 0.0928745
\(847\) −7.55313 −0.259529
\(848\) 44.4139 1.52518
\(849\) 16.3299 0.560439
\(850\) −3.29508 −0.113020
\(851\) −20.6112 −0.706542
\(852\) −16.2929 −0.558184
\(853\) 40.3937 1.38305 0.691527 0.722351i \(-0.256938\pi\)
0.691527 + 0.722351i \(0.256938\pi\)
\(854\) −55.4426 −1.89721
\(855\) −1.63179 −0.0558061
\(856\) 0.262195 0.00896163
\(857\) −4.99326 −0.170566 −0.0852832 0.996357i \(-0.527179\pi\)
−0.0852832 + 0.996357i \(0.527179\pi\)
\(858\) 47.6231 1.62583
\(859\) 45.4208 1.54974 0.774868 0.632123i \(-0.217816\pi\)
0.774868 + 0.632123i \(0.217816\pi\)
\(860\) −37.1190 −1.26575
\(861\) 20.1212 0.685728
\(862\) 65.4133 2.22798
\(863\) 37.4242 1.27393 0.636967 0.770891i \(-0.280189\pi\)
0.636967 + 0.770891i \(0.280189\pi\)
\(864\) −8.02471 −0.273006
\(865\) −35.6819 −1.21322
\(866\) −54.7920 −1.86191
\(867\) −1.00000 −0.0339618
\(868\) 25.9869 0.882052
\(869\) −42.6249 −1.44595
\(870\) −23.1715 −0.785588
\(871\) −26.6249 −0.902151
\(872\) 0.301807 0.0102205
\(873\) −11.5640 −0.391382
\(874\) 10.7160 0.362474
\(875\) −23.4404 −0.792430
\(876\) 0.396654 0.0134017
\(877\) −23.0996 −0.780018 −0.390009 0.920811i \(-0.627528\pi\)
−0.390009 + 0.920811i \(0.627528\pi\)
\(878\) 23.2762 0.785532
\(879\) −16.9866 −0.572945
\(880\) 27.9393 0.941833
\(881\) −28.8715 −0.972705 −0.486353 0.873763i \(-0.661673\pi\)
−0.486353 + 0.873763i \(0.661673\pi\)
\(882\) 6.60356 0.222354
\(883\) −21.2169 −0.714004 −0.357002 0.934104i \(-0.616201\pi\)
−0.357002 + 0.934104i \(0.616201\pi\)
\(884\) −12.4488 −0.418699
\(885\) 3.93669 0.132330
\(886\) 49.2659 1.65512
\(887\) 2.45408 0.0823999 0.0412000 0.999151i \(-0.486882\pi\)
0.0412000 + 0.999151i \(0.486882\pi\)
\(888\) 0.180162 0.00604584
\(889\) −8.26669 −0.277256
\(890\) −32.7890 −1.09909
\(891\) 3.86289 0.129412
\(892\) −46.4695 −1.55591
\(893\) −1.19888 −0.0401189
\(894\) −12.7641 −0.426897
\(895\) −28.3274 −0.946880
\(896\) −0.807592 −0.0269797
\(897\) 36.8481 1.23032
\(898\) 43.1504 1.43995
\(899\) −41.9706 −1.39980
\(900\) −3.32728 −0.110909
\(901\) 11.2524 0.374871
\(902\) −80.9813 −2.69638
\(903\) 19.2542 0.640741
\(904\) −0.439596 −0.0146208
\(905\) −10.3406 −0.343732
\(906\) 46.2617 1.53694
\(907\) −1.66296 −0.0552176 −0.0276088 0.999619i \(-0.508789\pi\)
−0.0276088 + 0.999619i \(0.508789\pi\)
\(908\) 49.1851 1.63227
\(909\) −0.668211 −0.0221632
\(910\) −43.5070 −1.44224
\(911\) −35.6558 −1.18133 −0.590665 0.806917i \(-0.701135\pi\)
−0.590665 + 0.806917i \(0.701135\pi\)
\(912\) 3.51488 0.116389
\(913\) −38.0686 −1.25989
\(914\) 65.7666 2.17537
\(915\) −26.2907 −0.869145
\(916\) 10.7977 0.356767
\(917\) −16.9420 −0.559474
\(918\) −2.00652 −0.0662251
\(919\) 23.0236 0.759480 0.379740 0.925093i \(-0.376014\pi\)
0.379740 + 0.925093i \(0.376014\pi\)
\(920\) −0.576096 −0.0189933
\(921\) 20.3919 0.671935
\(922\) −40.9263 −1.34784
\(923\) 49.4075 1.62627
\(924\) 15.0732 0.495871
\(925\) −5.64381 −0.185567
\(926\) 50.8098 1.66971
\(927\) 5.30849 0.174354
\(928\) 50.5722 1.66011
\(929\) 44.0824 1.44630 0.723149 0.690693i \(-0.242694\pi\)
0.723149 + 0.690693i \(0.242694\pi\)
\(930\) 24.4869 0.802958
\(931\) −2.93070 −0.0960498
\(932\) −10.6290 −0.348163
\(933\) −0.253731 −0.00830679
\(934\) 50.5358 1.65358
\(935\) 7.07850 0.231492
\(936\) −0.322088 −0.0105278
\(937\) 27.4483 0.896698 0.448349 0.893859i \(-0.352012\pi\)
0.448349 + 0.893859i \(0.352012\pi\)
\(938\) −16.7454 −0.546757
\(939\) 18.9071 0.617009
\(940\) 4.99842 0.163031
\(941\) −48.8533 −1.59257 −0.796285 0.604921i \(-0.793205\pi\)
−0.796285 + 0.604921i \(0.793205\pi\)
\(942\) −2.00652 −0.0653760
\(943\) −62.6586 −2.04045
\(944\) −8.47964 −0.275989
\(945\) −3.52902 −0.114799
\(946\) −77.4921 −2.51948
\(947\) −20.3405 −0.660977 −0.330488 0.943810i \(-0.607213\pi\)
−0.330488 + 0.943810i \(0.607213\pi\)
\(948\) 22.3572 0.726127
\(949\) −1.20284 −0.0390457
\(950\) 2.93429 0.0952008
\(951\) 23.7699 0.770791
\(952\) −0.100958 −0.00327205
\(953\) 19.8704 0.643667 0.321833 0.946796i \(-0.395701\pi\)
0.321833 + 0.946796i \(0.395701\pi\)
\(954\) 22.5781 0.730995
\(955\) −45.6021 −1.47565
\(956\) −4.44146 −0.143647
\(957\) −24.3442 −0.786935
\(958\) 4.40707 0.142386
\(959\) 15.0433 0.485774
\(960\) −15.0399 −0.485412
\(961\) 13.3532 0.430747
\(962\) −42.3697 −1.36605
\(963\) −5.00162 −0.161175
\(964\) 15.7480 0.507208
\(965\) 11.6107 0.373760
\(966\) 23.1751 0.745647
\(967\) −39.1328 −1.25843 −0.629213 0.777233i \(-0.716623\pi\)
−0.629213 + 0.777233i \(0.716623\pi\)
\(968\) −0.205596 −0.00660811
\(969\) 0.890505 0.0286072
\(970\) −42.5187 −1.36519
\(971\) −39.1577 −1.25663 −0.628315 0.777959i \(-0.716255\pi\)
−0.628315 + 0.777959i \(0.716255\pi\)
\(972\) −2.02613 −0.0649880
\(973\) 13.6850 0.438721
\(974\) 29.1941 0.935440
\(975\) 10.0898 0.323133
\(976\) 56.6303 1.81269
\(977\) 6.32794 0.202449 0.101224 0.994864i \(-0.467724\pi\)
0.101224 + 0.994864i \(0.467724\pi\)
\(978\) −24.9868 −0.798991
\(979\) −34.4484 −1.10098
\(980\) 12.2188 0.390316
\(981\) −5.75725 −0.183815
\(982\) −77.0440 −2.45857
\(983\) −14.0117 −0.446903 −0.223451 0.974715i \(-0.571732\pi\)
−0.223451 + 0.974715i \(0.571732\pi\)
\(984\) 0.547699 0.0174600
\(985\) 46.9129 1.49477
\(986\) 12.6452 0.402706
\(987\) −2.59277 −0.0825287
\(988\) 11.0857 0.352684
\(989\) −59.9589 −1.90658
\(990\) 14.2032 0.451406
\(991\) −61.5751 −1.95600 −0.977999 0.208611i \(-0.933106\pi\)
−0.977999 + 0.208611i \(0.933106\pi\)
\(992\) −53.4431 −1.69682
\(993\) −5.64108 −0.179014
\(994\) 31.0742 0.985614
\(995\) −10.4902 −0.332561
\(996\) 19.9674 0.632691
\(997\) 17.1467 0.543042 0.271521 0.962433i \(-0.412473\pi\)
0.271521 + 0.962433i \(0.412473\pi\)
\(998\) −3.96982 −0.125662
\(999\) −3.43677 −0.108734
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 \(a_p\))