Properties

Label 8007.2.a.f.1.11
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 1.11
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.70660 q^{2} -1.00000 q^{3} +0.912495 q^{4} +1.58325 q^{5} +1.70660 q^{6} -2.98844 q^{7} +1.85594 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.70660 q^{2} -1.00000 q^{3} +0.912495 q^{4} +1.58325 q^{5} +1.70660 q^{6} -2.98844 q^{7} +1.85594 q^{8} +1.00000 q^{9} -2.70198 q^{10} -5.30703 q^{11} -0.912495 q^{12} -4.73542 q^{13} +5.10008 q^{14} -1.58325 q^{15} -4.99234 q^{16} -1.00000 q^{17} -1.70660 q^{18} +3.98397 q^{19} +1.44471 q^{20} +2.98844 q^{21} +9.05700 q^{22} +2.22152 q^{23} -1.85594 q^{24} -2.49331 q^{25} +8.08148 q^{26} -1.00000 q^{27} -2.72693 q^{28} -4.49329 q^{29} +2.70198 q^{30} +1.43303 q^{31} +4.80807 q^{32} +5.30703 q^{33} +1.70660 q^{34} -4.73145 q^{35} +0.912495 q^{36} +5.16394 q^{37} -6.79905 q^{38} +4.73542 q^{39} +2.93842 q^{40} +5.33662 q^{41} -5.10008 q^{42} +8.14627 q^{43} -4.84264 q^{44} +1.58325 q^{45} -3.79126 q^{46} -8.94635 q^{47} +4.99234 q^{48} +1.93075 q^{49} +4.25510 q^{50} +1.00000 q^{51} -4.32105 q^{52} +6.35475 q^{53} +1.70660 q^{54} -8.40237 q^{55} -5.54636 q^{56} -3.98397 q^{57} +7.66826 q^{58} +10.2910 q^{59} -1.44471 q^{60} +8.69973 q^{61} -2.44561 q^{62} -2.98844 q^{63} +1.77922 q^{64} -7.49736 q^{65} -9.05700 q^{66} +5.45083 q^{67} -0.912495 q^{68} -2.22152 q^{69} +8.07470 q^{70} -5.81011 q^{71} +1.85594 q^{72} +5.83679 q^{73} -8.81279 q^{74} +2.49331 q^{75} +3.63535 q^{76} +15.8597 q^{77} -8.08148 q^{78} +6.64504 q^{79} -7.90414 q^{80} +1.00000 q^{81} -9.10750 q^{82} +10.8193 q^{83} +2.72693 q^{84} -1.58325 q^{85} -13.9025 q^{86} +4.49329 q^{87} -9.84953 q^{88} +16.6858 q^{89} -2.70198 q^{90} +14.1515 q^{91} +2.02713 q^{92} -1.43303 q^{93} +15.2679 q^{94} +6.30763 q^{95} -4.80807 q^{96} -9.51320 q^{97} -3.29502 q^{98} -5.30703 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.70660 −1.20675 −0.603375 0.797457i \(-0.706178\pi\)
−0.603375 + 0.797457i \(0.706178\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.912495 0.456248
\(5\) 1.58325 0.708052 0.354026 0.935236i \(-0.384812\pi\)
0.354026 + 0.935236i \(0.384812\pi\)
\(6\) 1.70660 0.696718
\(7\) −2.98844 −1.12952 −0.564761 0.825254i \(-0.691032\pi\)
−0.564761 + 0.825254i \(0.691032\pi\)
\(8\) 1.85594 0.656174
\(9\) 1.00000 0.333333
\(10\) −2.70198 −0.854442
\(11\) −5.30703 −1.60013 −0.800065 0.599913i \(-0.795202\pi\)
−0.800065 + 0.599913i \(0.795202\pi\)
\(12\) −0.912495 −0.263415
\(13\) −4.73542 −1.31337 −0.656685 0.754165i \(-0.728042\pi\)
−0.656685 + 0.754165i \(0.728042\pi\)
\(14\) 5.10008 1.36305
\(15\) −1.58325 −0.408794
\(16\) −4.99234 −1.24809
\(17\) −1.00000 −0.242536
\(18\) −1.70660 −0.402250
\(19\) 3.98397 0.913985 0.456993 0.889471i \(-0.348927\pi\)
0.456993 + 0.889471i \(0.348927\pi\)
\(20\) 1.44471 0.323047
\(21\) 2.98844 0.652130
\(22\) 9.05700 1.93096
\(23\) 2.22152 0.463220 0.231610 0.972809i \(-0.425601\pi\)
0.231610 + 0.972809i \(0.425601\pi\)
\(24\) −1.85594 −0.378842
\(25\) −2.49331 −0.498663
\(26\) 8.08148 1.58491
\(27\) −1.00000 −0.192450
\(28\) −2.72693 −0.515342
\(29\) −4.49329 −0.834383 −0.417191 0.908819i \(-0.636986\pi\)
−0.417191 + 0.908819i \(0.636986\pi\)
\(30\) 2.70198 0.493312
\(31\) 1.43303 0.257379 0.128690 0.991685i \(-0.458923\pi\)
0.128690 + 0.991685i \(0.458923\pi\)
\(32\) 4.80807 0.849955
\(33\) 5.30703 0.923836
\(34\) 1.70660 0.292680
\(35\) −4.73145 −0.799760
\(36\) 0.912495 0.152083
\(37\) 5.16394 0.848946 0.424473 0.905441i \(-0.360459\pi\)
0.424473 + 0.905441i \(0.360459\pi\)
\(38\) −6.79905 −1.10295
\(39\) 4.73542 0.758274
\(40\) 2.93842 0.464605
\(41\) 5.33662 0.833441 0.416720 0.909035i \(-0.363179\pi\)
0.416720 + 0.909035i \(0.363179\pi\)
\(42\) −5.10008 −0.786959
\(43\) 8.14627 1.24229 0.621147 0.783694i \(-0.286667\pi\)
0.621147 + 0.783694i \(0.286667\pi\)
\(44\) −4.84264 −0.730056
\(45\) 1.58325 0.236017
\(46\) −3.79126 −0.558991
\(47\) −8.94635 −1.30496 −0.652480 0.757806i \(-0.726271\pi\)
−0.652480 + 0.757806i \(0.726271\pi\)
\(48\) 4.99234 0.720583
\(49\) 1.93075 0.275821
\(50\) 4.25510 0.601762
\(51\) 1.00000 0.140028
\(52\) −4.32105 −0.599222
\(53\) 6.35475 0.872892 0.436446 0.899730i \(-0.356237\pi\)
0.436446 + 0.899730i \(0.356237\pi\)
\(54\) 1.70660 0.232239
\(55\) −8.40237 −1.13297
\(56\) −5.54636 −0.741163
\(57\) −3.98397 −0.527690
\(58\) 7.66826 1.00689
\(59\) 10.2910 1.33977 0.669886 0.742464i \(-0.266343\pi\)
0.669886 + 0.742464i \(0.266343\pi\)
\(60\) −1.44471 −0.186511
\(61\) 8.69973 1.11389 0.556943 0.830551i \(-0.311974\pi\)
0.556943 + 0.830551i \(0.311974\pi\)
\(62\) −2.44561 −0.310593
\(63\) −2.98844 −0.376508
\(64\) 1.77922 0.222402
\(65\) −7.49736 −0.929933
\(66\) −9.05700 −1.11484
\(67\) 5.45083 0.665925 0.332963 0.942940i \(-0.391952\pi\)
0.332963 + 0.942940i \(0.391952\pi\)
\(68\) −0.912495 −0.110656
\(69\) −2.22152 −0.267440
\(70\) 8.07470 0.965112
\(71\) −5.81011 −0.689533 −0.344767 0.938688i \(-0.612042\pi\)
−0.344767 + 0.938688i \(0.612042\pi\)
\(72\) 1.85594 0.218725
\(73\) 5.83679 0.683144 0.341572 0.939856i \(-0.389041\pi\)
0.341572 + 0.939856i \(0.389041\pi\)
\(74\) −8.81279 −1.02447
\(75\) 2.49331 0.287903
\(76\) 3.63535 0.417004
\(77\) 15.8597 1.80738
\(78\) −8.08148 −0.915048
\(79\) 6.64504 0.747626 0.373813 0.927504i \(-0.378050\pi\)
0.373813 + 0.927504i \(0.378050\pi\)
\(80\) −7.90414 −0.883709
\(81\) 1.00000 0.111111
\(82\) −9.10750 −1.00576
\(83\) 10.8193 1.18757 0.593786 0.804623i \(-0.297633\pi\)
0.593786 + 0.804623i \(0.297633\pi\)
\(84\) 2.72693 0.297533
\(85\) −1.58325 −0.171728
\(86\) −13.9025 −1.49914
\(87\) 4.49329 0.481731
\(88\) −9.84953 −1.04996
\(89\) 16.6858 1.76869 0.884347 0.466830i \(-0.154604\pi\)
0.884347 + 0.466830i \(0.154604\pi\)
\(90\) −2.70198 −0.284814
\(91\) 14.1515 1.48348
\(92\) 2.02713 0.211343
\(93\) −1.43303 −0.148598
\(94\) 15.2679 1.57476
\(95\) 6.30763 0.647149
\(96\) −4.80807 −0.490722
\(97\) −9.51320 −0.965919 −0.482959 0.875643i \(-0.660438\pi\)
−0.482959 + 0.875643i \(0.660438\pi\)
\(98\) −3.29502 −0.332848
\(99\) −5.30703 −0.533377
\(100\) −2.27514 −0.227514
\(101\) −4.05167 −0.403156 −0.201578 0.979472i \(-0.564607\pi\)
−0.201578 + 0.979472i \(0.564607\pi\)
\(102\) −1.70660 −0.168979
\(103\) 12.9398 1.27500 0.637501 0.770450i \(-0.279968\pi\)
0.637501 + 0.770450i \(0.279968\pi\)
\(104\) −8.78865 −0.861798
\(105\) 4.73145 0.461742
\(106\) −10.8450 −1.05336
\(107\) 4.88513 0.472264 0.236132 0.971721i \(-0.424120\pi\)
0.236132 + 0.971721i \(0.424120\pi\)
\(108\) −0.912495 −0.0878049
\(109\) −15.2419 −1.45991 −0.729956 0.683494i \(-0.760459\pi\)
−0.729956 + 0.683494i \(0.760459\pi\)
\(110\) 14.3395 1.36722
\(111\) −5.16394 −0.490139
\(112\) 14.9193 1.40974
\(113\) −13.4676 −1.26692 −0.633461 0.773774i \(-0.718366\pi\)
−0.633461 + 0.773774i \(0.718366\pi\)
\(114\) 6.79905 0.636790
\(115\) 3.51723 0.327983
\(116\) −4.10011 −0.380685
\(117\) −4.73542 −0.437790
\(118\) −17.5626 −1.61677
\(119\) 2.98844 0.273949
\(120\) −2.93842 −0.268240
\(121\) 17.1646 1.56042
\(122\) −14.8470 −1.34418
\(123\) −5.33662 −0.481187
\(124\) 1.30763 0.117429
\(125\) −11.8638 −1.06113
\(126\) 5.10008 0.454351
\(127\) −16.8614 −1.49620 −0.748102 0.663584i \(-0.769035\pi\)
−0.748102 + 0.663584i \(0.769035\pi\)
\(128\) −12.6526 −1.11834
\(129\) −8.14627 −0.717239
\(130\) 12.7950 1.12220
\(131\) −2.62656 −0.229483 −0.114742 0.993395i \(-0.536604\pi\)
−0.114742 + 0.993395i \(0.536604\pi\)
\(132\) 4.84264 0.421498
\(133\) −11.9058 −1.03237
\(134\) −9.30241 −0.803606
\(135\) −1.58325 −0.136265
\(136\) −1.85594 −0.159145
\(137\) −18.4335 −1.57488 −0.787439 0.616393i \(-0.788593\pi\)
−0.787439 + 0.616393i \(0.788593\pi\)
\(138\) 3.79126 0.322733
\(139\) −18.8500 −1.59883 −0.799417 0.600776i \(-0.794858\pi\)
−0.799417 + 0.600776i \(0.794858\pi\)
\(140\) −4.31742 −0.364889
\(141\) 8.94635 0.753419
\(142\) 9.91555 0.832095
\(143\) 25.1310 2.10156
\(144\) −4.99234 −0.416029
\(145\) −7.11401 −0.590786
\(146\) −9.96108 −0.824385
\(147\) −1.93075 −0.159246
\(148\) 4.71207 0.387330
\(149\) −1.17154 −0.0959763 −0.0479881 0.998848i \(-0.515281\pi\)
−0.0479881 + 0.998848i \(0.515281\pi\)
\(150\) −4.25510 −0.347427
\(151\) 16.0241 1.30403 0.652013 0.758208i \(-0.273925\pi\)
0.652013 + 0.758208i \(0.273925\pi\)
\(152\) 7.39400 0.599733
\(153\) −1.00000 −0.0808452
\(154\) −27.0663 −2.18106
\(155\) 2.26884 0.182238
\(156\) 4.32105 0.345961
\(157\) −1.00000 −0.0798087
\(158\) −11.3405 −0.902198
\(159\) −6.35475 −0.503965
\(160\) 7.61239 0.601812
\(161\) −6.63888 −0.523217
\(162\) −1.70660 −0.134083
\(163\) −5.46553 −0.428094 −0.214047 0.976823i \(-0.568665\pi\)
−0.214047 + 0.976823i \(0.568665\pi\)
\(164\) 4.86964 0.380255
\(165\) 8.40237 0.654123
\(166\) −18.4643 −1.43310
\(167\) 9.60060 0.742917 0.371458 0.928450i \(-0.378858\pi\)
0.371458 + 0.928450i \(0.378858\pi\)
\(168\) 5.54636 0.427911
\(169\) 9.42420 0.724939
\(170\) 2.70198 0.207233
\(171\) 3.98397 0.304662
\(172\) 7.43343 0.566794
\(173\) −11.5673 −0.879444 −0.439722 0.898134i \(-0.644923\pi\)
−0.439722 + 0.898134i \(0.644923\pi\)
\(174\) −7.66826 −0.581330
\(175\) 7.45111 0.563251
\(176\) 26.4945 1.99710
\(177\) −10.2910 −0.773518
\(178\) −28.4761 −2.13437
\(179\) −9.03669 −0.675434 −0.337717 0.941248i \(-0.609655\pi\)
−0.337717 + 0.941248i \(0.609655\pi\)
\(180\) 1.44471 0.107682
\(181\) 3.17931 0.236316 0.118158 0.992995i \(-0.462301\pi\)
0.118158 + 0.992995i \(0.462301\pi\)
\(182\) −24.1510 −1.79019
\(183\) −8.69973 −0.643102
\(184\) 4.12301 0.303952
\(185\) 8.17581 0.601098
\(186\) 2.44561 0.179321
\(187\) 5.30703 0.388089
\(188\) −8.16350 −0.595385
\(189\) 2.98844 0.217377
\(190\) −10.7646 −0.780947
\(191\) 15.5947 1.12839 0.564197 0.825640i \(-0.309186\pi\)
0.564197 + 0.825640i \(0.309186\pi\)
\(192\) −1.77922 −0.128404
\(193\) 2.93545 0.211298 0.105649 0.994403i \(-0.466308\pi\)
0.105649 + 0.994403i \(0.466308\pi\)
\(194\) 16.2353 1.16562
\(195\) 7.49736 0.536897
\(196\) 1.76180 0.125843
\(197\) 20.0263 1.42682 0.713408 0.700749i \(-0.247151\pi\)
0.713408 + 0.700749i \(0.247151\pi\)
\(198\) 9.05700 0.643653
\(199\) −19.0037 −1.34714 −0.673568 0.739125i \(-0.735239\pi\)
−0.673568 + 0.739125i \(0.735239\pi\)
\(200\) −4.62744 −0.327209
\(201\) −5.45083 −0.384472
\(202\) 6.91459 0.486509
\(203\) 13.4279 0.942454
\(204\) 0.912495 0.0638874
\(205\) 8.44922 0.590119
\(206\) −22.0832 −1.53861
\(207\) 2.22152 0.154407
\(208\) 23.6408 1.63920
\(209\) −21.1430 −1.46250
\(210\) −8.07470 −0.557207
\(211\) 13.4375 0.925075 0.462538 0.886600i \(-0.346939\pi\)
0.462538 + 0.886600i \(0.346939\pi\)
\(212\) 5.79868 0.398255
\(213\) 5.81011 0.398102
\(214\) −8.33699 −0.569905
\(215\) 12.8976 0.879609
\(216\) −1.85594 −0.126281
\(217\) −4.28251 −0.290716
\(218\) 26.0119 1.76175
\(219\) −5.83679 −0.394414
\(220\) −7.66712 −0.516917
\(221\) 4.73542 0.318539
\(222\) 8.81279 0.591476
\(223\) 0.601749 0.0402961 0.0201481 0.999797i \(-0.493586\pi\)
0.0201481 + 0.999797i \(0.493586\pi\)
\(224\) −14.3686 −0.960043
\(225\) −2.49331 −0.166221
\(226\) 22.9838 1.52886
\(227\) −20.1295 −1.33604 −0.668021 0.744143i \(-0.732858\pi\)
−0.668021 + 0.744143i \(0.732858\pi\)
\(228\) −3.63535 −0.240757
\(229\) −26.9627 −1.78175 −0.890874 0.454251i \(-0.849907\pi\)
−0.890874 + 0.454251i \(0.849907\pi\)
\(230\) −6.00252 −0.395794
\(231\) −15.8597 −1.04349
\(232\) −8.33927 −0.547500
\(233\) −13.2736 −0.869583 −0.434792 0.900531i \(-0.643178\pi\)
−0.434792 + 0.900531i \(0.643178\pi\)
\(234\) 8.08148 0.528303
\(235\) −14.1643 −0.923979
\(236\) 9.39048 0.611268
\(237\) −6.64504 −0.431642
\(238\) −5.10008 −0.330589
\(239\) 3.63351 0.235032 0.117516 0.993071i \(-0.462507\pi\)
0.117516 + 0.993071i \(0.462507\pi\)
\(240\) 7.90414 0.510210
\(241\) −13.4151 −0.864142 −0.432071 0.901840i \(-0.642217\pi\)
−0.432071 + 0.901840i \(0.642217\pi\)
\(242\) −29.2931 −1.88303
\(243\) −1.00000 −0.0641500
\(244\) 7.93846 0.508208
\(245\) 3.05686 0.195296
\(246\) 9.10750 0.580673
\(247\) −18.8658 −1.20040
\(248\) 2.65961 0.168886
\(249\) −10.8193 −0.685645
\(250\) 20.2468 1.28052
\(251\) 26.3328 1.66211 0.831057 0.556188i \(-0.187737\pi\)
0.831057 + 0.556188i \(0.187737\pi\)
\(252\) −2.72693 −0.171781
\(253\) −11.7897 −0.741212
\(254\) 28.7757 1.80554
\(255\) 1.58325 0.0991471
\(256\) 18.0345 1.12715
\(257\) 25.7444 1.60589 0.802947 0.596051i \(-0.203264\pi\)
0.802947 + 0.596051i \(0.203264\pi\)
\(258\) 13.9025 0.865529
\(259\) −15.4321 −0.958904
\(260\) −6.84131 −0.424280
\(261\) −4.49329 −0.278128
\(262\) 4.48249 0.276929
\(263\) 6.10606 0.376516 0.188258 0.982120i \(-0.439716\pi\)
0.188258 + 0.982120i \(0.439716\pi\)
\(264\) 9.84953 0.606197
\(265\) 10.0612 0.618053
\(266\) 20.3185 1.24581
\(267\) −16.6858 −1.02116
\(268\) 4.97386 0.303827
\(269\) 4.32981 0.263993 0.131997 0.991250i \(-0.457861\pi\)
0.131997 + 0.991250i \(0.457861\pi\)
\(270\) 2.70198 0.164437
\(271\) 11.5810 0.703494 0.351747 0.936095i \(-0.385588\pi\)
0.351747 + 0.936095i \(0.385588\pi\)
\(272\) 4.99234 0.302705
\(273\) −14.1515 −0.856488
\(274\) 31.4586 1.90049
\(275\) 13.2321 0.797925
\(276\) −2.02713 −0.122019
\(277\) −14.3260 −0.860769 −0.430384 0.902646i \(-0.641622\pi\)
−0.430384 + 0.902646i \(0.641622\pi\)
\(278\) 32.1694 1.92940
\(279\) 1.43303 0.0857931
\(280\) −8.78128 −0.524782
\(281\) 7.93944 0.473628 0.236814 0.971555i \(-0.423897\pi\)
0.236814 + 0.971555i \(0.423897\pi\)
\(282\) −15.2679 −0.909189
\(283\) 30.8979 1.83669 0.918344 0.395784i \(-0.129527\pi\)
0.918344 + 0.395784i \(0.129527\pi\)
\(284\) −5.30170 −0.314598
\(285\) −6.30763 −0.373631
\(286\) −42.8887 −2.53606
\(287\) −15.9482 −0.941390
\(288\) 4.80807 0.283318
\(289\) 1.00000 0.0588235
\(290\) 12.1408 0.712932
\(291\) 9.51320 0.557674
\(292\) 5.32604 0.311683
\(293\) −19.2710 −1.12582 −0.562912 0.826517i \(-0.690319\pi\)
−0.562912 + 0.826517i \(0.690319\pi\)
\(294\) 3.29502 0.192170
\(295\) 16.2932 0.948629
\(296\) 9.58395 0.557056
\(297\) 5.30703 0.307945
\(298\) 1.99935 0.115819
\(299\) −10.5198 −0.608378
\(300\) 2.27514 0.131355
\(301\) −24.3446 −1.40320
\(302\) −27.3469 −1.57364
\(303\) 4.05167 0.232762
\(304\) −19.8893 −1.14073
\(305\) 13.7739 0.788689
\(306\) 1.70660 0.0975600
\(307\) −33.6426 −1.92009 −0.960043 0.279853i \(-0.909714\pi\)
−0.960043 + 0.279853i \(0.909714\pi\)
\(308\) 14.4719 0.824614
\(309\) −12.9398 −0.736122
\(310\) −3.87202 −0.219916
\(311\) 16.9130 0.959050 0.479525 0.877528i \(-0.340809\pi\)
0.479525 + 0.877528i \(0.340809\pi\)
\(312\) 8.78865 0.497559
\(313\) −32.6745 −1.84687 −0.923436 0.383753i \(-0.874631\pi\)
−0.923436 + 0.383753i \(0.874631\pi\)
\(314\) 1.70660 0.0963092
\(315\) −4.73145 −0.266587
\(316\) 6.06357 0.341102
\(317\) 13.7593 0.772799 0.386399 0.922332i \(-0.373719\pi\)
0.386399 + 0.922332i \(0.373719\pi\)
\(318\) 10.8450 0.608160
\(319\) 23.8460 1.33512
\(320\) 2.81695 0.157472
\(321\) −4.88513 −0.272662
\(322\) 11.3299 0.631393
\(323\) −3.98397 −0.221674
\(324\) 0.912495 0.0506942
\(325\) 11.8069 0.654928
\(326\) 9.32750 0.516602
\(327\) 15.2419 0.842880
\(328\) 9.90445 0.546882
\(329\) 26.7356 1.47398
\(330\) −14.3395 −0.789364
\(331\) 8.32969 0.457841 0.228921 0.973445i \(-0.426480\pi\)
0.228921 + 0.973445i \(0.426480\pi\)
\(332\) 9.87256 0.541827
\(333\) 5.16394 0.282982
\(334\) −16.3844 −0.896515
\(335\) 8.63004 0.471509
\(336\) −14.9193 −0.813914
\(337\) 26.0897 1.42120 0.710598 0.703598i \(-0.248424\pi\)
0.710598 + 0.703598i \(0.248424\pi\)
\(338\) −16.0834 −0.874820
\(339\) 13.4676 0.731458
\(340\) −1.44471 −0.0783504
\(341\) −7.60512 −0.411840
\(342\) −6.79905 −0.367651
\(343\) 15.1491 0.817976
\(344\) 15.1190 0.815161
\(345\) −3.51723 −0.189361
\(346\) 19.7408 1.06127
\(347\) −7.35317 −0.394739 −0.197369 0.980329i \(-0.563240\pi\)
−0.197369 + 0.980329i \(0.563240\pi\)
\(348\) 4.10011 0.219789
\(349\) −5.90447 −0.316059 −0.158030 0.987434i \(-0.550514\pi\)
−0.158030 + 0.987434i \(0.550514\pi\)
\(350\) −12.7161 −0.679703
\(351\) 4.73542 0.252758
\(352\) −25.5166 −1.36004
\(353\) 30.0930 1.60169 0.800845 0.598872i \(-0.204384\pi\)
0.800845 + 0.598872i \(0.204384\pi\)
\(354\) 17.5626 0.933444
\(355\) −9.19887 −0.488225
\(356\) 15.2257 0.806962
\(357\) −2.98844 −0.158165
\(358\) 15.4221 0.815081
\(359\) 26.8603 1.41763 0.708815 0.705394i \(-0.249230\pi\)
0.708815 + 0.705394i \(0.249230\pi\)
\(360\) 2.93842 0.154868
\(361\) −3.12799 −0.164631
\(362\) −5.42581 −0.285174
\(363\) −17.1646 −0.900907
\(364\) 12.9132 0.676834
\(365\) 9.24110 0.483702
\(366\) 14.8470 0.776064
\(367\) 21.2227 1.10782 0.553909 0.832577i \(-0.313136\pi\)
0.553909 + 0.832577i \(0.313136\pi\)
\(368\) −11.0906 −0.578138
\(369\) 5.33662 0.277814
\(370\) −13.9529 −0.725375
\(371\) −18.9908 −0.985951
\(372\) −1.30763 −0.0677975
\(373\) −6.43659 −0.333274 −0.166637 0.986018i \(-0.553291\pi\)
−0.166637 + 0.986018i \(0.553291\pi\)
\(374\) −9.05700 −0.468326
\(375\) 11.8638 0.612644
\(376\) −16.6039 −0.856280
\(377\) 21.2776 1.09585
\(378\) −5.10008 −0.262320
\(379\) −16.8129 −0.863619 −0.431809 0.901965i \(-0.642125\pi\)
−0.431809 + 0.901965i \(0.642125\pi\)
\(380\) 5.75568 0.295260
\(381\) 16.8614 0.863834
\(382\) −26.6140 −1.36169
\(383\) −22.9187 −1.17109 −0.585546 0.810639i \(-0.699120\pi\)
−0.585546 + 0.810639i \(0.699120\pi\)
\(384\) 12.6526 0.645673
\(385\) 25.1099 1.27972
\(386\) −5.00965 −0.254984
\(387\) 8.14627 0.414098
\(388\) −8.68075 −0.440698
\(389\) 11.3421 0.575067 0.287533 0.957771i \(-0.407165\pi\)
0.287533 + 0.957771i \(0.407165\pi\)
\(390\) −12.7950 −0.647901
\(391\) −2.22152 −0.112347
\(392\) 3.58335 0.180987
\(393\) 2.62656 0.132492
\(394\) −34.1770 −1.72181
\(395\) 10.5208 0.529358
\(396\) −4.84264 −0.243352
\(397\) −18.4634 −0.926650 −0.463325 0.886188i \(-0.653344\pi\)
−0.463325 + 0.886188i \(0.653344\pi\)
\(398\) 32.4318 1.62566
\(399\) 11.9058 0.596037
\(400\) 12.4475 0.622374
\(401\) 30.3499 1.51560 0.757801 0.652486i \(-0.226274\pi\)
0.757801 + 0.652486i \(0.226274\pi\)
\(402\) 9.30241 0.463962
\(403\) −6.78599 −0.338034
\(404\) −3.69713 −0.183939
\(405\) 1.58325 0.0786724
\(406\) −22.9161 −1.13731
\(407\) −27.4052 −1.35842
\(408\) 1.85594 0.0918827
\(409\) −36.6991 −1.81466 −0.907328 0.420424i \(-0.861881\pi\)
−0.907328 + 0.420424i \(0.861881\pi\)
\(410\) −14.4195 −0.712127
\(411\) 18.4335 0.909256
\(412\) 11.8075 0.581716
\(413\) −30.7540 −1.51330
\(414\) −3.79126 −0.186330
\(415\) 17.1297 0.840863
\(416\) −22.7682 −1.11630
\(417\) 18.8500 0.923088
\(418\) 36.0828 1.76487
\(419\) 0.318181 0.0155442 0.00777209 0.999970i \(-0.497526\pi\)
0.00777209 + 0.999970i \(0.497526\pi\)
\(420\) 4.31742 0.210669
\(421\) −14.7746 −0.720072 −0.360036 0.932938i \(-0.617236\pi\)
−0.360036 + 0.932938i \(0.617236\pi\)
\(422\) −22.9325 −1.11634
\(423\) −8.94635 −0.434987
\(424\) 11.7940 0.572769
\(425\) 2.49331 0.120943
\(426\) −9.91555 −0.480410
\(427\) −25.9986 −1.25816
\(428\) 4.45766 0.215469
\(429\) −25.1310 −1.21334
\(430\) −22.0111 −1.06147
\(431\) −25.8797 −1.24658 −0.623291 0.781990i \(-0.714205\pi\)
−0.623291 + 0.781990i \(0.714205\pi\)
\(432\) 4.99234 0.240194
\(433\) −32.6606 −1.56957 −0.784784 0.619769i \(-0.787226\pi\)
−0.784784 + 0.619769i \(0.787226\pi\)
\(434\) 7.30855 0.350822
\(435\) 7.11401 0.341091
\(436\) −13.9082 −0.666081
\(437\) 8.85048 0.423376
\(438\) 9.96108 0.475959
\(439\) 37.6504 1.79696 0.898478 0.439019i \(-0.144674\pi\)
0.898478 + 0.439019i \(0.144674\pi\)
\(440\) −15.5943 −0.743428
\(441\) 1.93075 0.0919405
\(442\) −8.08148 −0.384397
\(443\) −5.10926 −0.242748 −0.121374 0.992607i \(-0.538730\pi\)
−0.121374 + 0.992607i \(0.538730\pi\)
\(444\) −4.71207 −0.223625
\(445\) 26.4179 1.25233
\(446\) −1.02695 −0.0486274
\(447\) 1.17154 0.0554119
\(448\) −5.31707 −0.251208
\(449\) −13.2384 −0.624759 −0.312379 0.949957i \(-0.601126\pi\)
−0.312379 + 0.949957i \(0.601126\pi\)
\(450\) 4.25510 0.200587
\(451\) −28.3216 −1.33361
\(452\) −12.2891 −0.578030
\(453\) −16.0241 −0.752880
\(454\) 34.3531 1.61227
\(455\) 22.4054 1.05038
\(456\) −7.39400 −0.346256
\(457\) −31.1957 −1.45927 −0.729636 0.683836i \(-0.760310\pi\)
−0.729636 + 0.683836i \(0.760310\pi\)
\(458\) 46.0147 2.15013
\(459\) 1.00000 0.0466760
\(460\) 3.20946 0.149642
\(461\) 23.7441 1.10587 0.552936 0.833224i \(-0.313508\pi\)
0.552936 + 0.833224i \(0.313508\pi\)
\(462\) 27.0663 1.25924
\(463\) 13.8377 0.643093 0.321546 0.946894i \(-0.395797\pi\)
0.321546 + 0.946894i \(0.395797\pi\)
\(464\) 22.4320 1.04138
\(465\) −2.26884 −0.105215
\(466\) 22.6528 1.04937
\(467\) −26.0006 −1.20316 −0.601581 0.798812i \(-0.705462\pi\)
−0.601581 + 0.798812i \(0.705462\pi\)
\(468\) −4.32105 −0.199741
\(469\) −16.2895 −0.752178
\(470\) 24.1729 1.11501
\(471\) 1.00000 0.0460776
\(472\) 19.0995 0.879124
\(473\) −43.2325 −1.98783
\(474\) 11.3405 0.520884
\(475\) −9.93328 −0.455770
\(476\) 2.72693 0.124989
\(477\) 6.35475 0.290964
\(478\) −6.20096 −0.283625
\(479\) 14.4517 0.660314 0.330157 0.943926i \(-0.392898\pi\)
0.330157 + 0.943926i \(0.392898\pi\)
\(480\) −7.61239 −0.347456
\(481\) −24.4534 −1.11498
\(482\) 22.8942 1.04280
\(483\) 6.63888 0.302079
\(484\) 15.6626 0.711936
\(485\) −15.0618 −0.683921
\(486\) 1.70660 0.0774131
\(487\) 29.8133 1.35097 0.675485 0.737374i \(-0.263934\pi\)
0.675485 + 0.737374i \(0.263934\pi\)
\(488\) 16.1462 0.730903
\(489\) 5.46553 0.247160
\(490\) −5.21685 −0.235673
\(491\) −2.91710 −0.131647 −0.0658235 0.997831i \(-0.520967\pi\)
−0.0658235 + 0.997831i \(0.520967\pi\)
\(492\) −4.86964 −0.219541
\(493\) 4.49329 0.202368
\(494\) 32.1964 1.44858
\(495\) −8.40237 −0.377658
\(496\) −7.15416 −0.321231
\(497\) 17.3631 0.778843
\(498\) 18.4643 0.827403
\(499\) −29.7092 −1.32996 −0.664982 0.746859i \(-0.731561\pi\)
−0.664982 + 0.746859i \(0.731561\pi\)
\(500\) −10.8257 −0.484138
\(501\) −9.60060 −0.428923
\(502\) −44.9397 −2.00576
\(503\) −31.5673 −1.40752 −0.703759 0.710439i \(-0.748496\pi\)
−0.703759 + 0.710439i \(0.748496\pi\)
\(504\) −5.54636 −0.247054
\(505\) −6.41481 −0.285455
\(506\) 20.1203 0.894458
\(507\) −9.42420 −0.418543
\(508\) −15.3859 −0.682639
\(509\) −35.2096 −1.56064 −0.780319 0.625382i \(-0.784943\pi\)
−0.780319 + 0.625382i \(0.784943\pi\)
\(510\) −2.70198 −0.119646
\(511\) −17.4429 −0.771627
\(512\) −5.47257 −0.241855
\(513\) −3.98397 −0.175897
\(514\) −43.9355 −1.93791
\(515\) 20.4870 0.902767
\(516\) −7.43343 −0.327239
\(517\) 47.4786 2.08811
\(518\) 26.3365 1.15716
\(519\) 11.5673 0.507747
\(520\) −13.9146 −0.610198
\(521\) −0.0532116 −0.00233124 −0.00116562 0.999999i \(-0.500371\pi\)
−0.00116562 + 0.999999i \(0.500371\pi\)
\(522\) 7.66826 0.335631
\(523\) −41.5141 −1.81528 −0.907642 0.419744i \(-0.862120\pi\)
−0.907642 + 0.419744i \(0.862120\pi\)
\(524\) −2.39672 −0.104701
\(525\) −7.45111 −0.325193
\(526\) −10.4206 −0.454361
\(527\) −1.43303 −0.0624237
\(528\) −26.4945 −1.15303
\(529\) −18.0648 −0.785428
\(530\) −17.1704 −0.745836
\(531\) 10.2910 0.446591
\(532\) −10.8640 −0.471015
\(533\) −25.2712 −1.09462
\(534\) 28.4761 1.23228
\(535\) 7.73440 0.334387
\(536\) 10.1164 0.436963
\(537\) 9.03669 0.389962
\(538\) −7.38927 −0.318574
\(539\) −10.2465 −0.441350
\(540\) −1.44471 −0.0621704
\(541\) 3.04132 0.130756 0.0653782 0.997861i \(-0.479175\pi\)
0.0653782 + 0.997861i \(0.479175\pi\)
\(542\) −19.7641 −0.848943
\(543\) −3.17931 −0.136437
\(544\) −4.80807 −0.206144
\(545\) −24.1318 −1.03369
\(546\) 24.1510 1.03357
\(547\) −30.9921 −1.32513 −0.662563 0.749006i \(-0.730531\pi\)
−0.662563 + 0.749006i \(0.730531\pi\)
\(548\) −16.8205 −0.718534
\(549\) 8.69973 0.371295
\(550\) −22.5819 −0.962897
\(551\) −17.9011 −0.762614
\(552\) −4.12301 −0.175487
\(553\) −19.8583 −0.844460
\(554\) 24.4489 1.03873
\(555\) −8.17581 −0.347044
\(556\) −17.2005 −0.729464
\(557\) 1.10942 0.0470078 0.0235039 0.999724i \(-0.492518\pi\)
0.0235039 + 0.999724i \(0.492518\pi\)
\(558\) −2.44561 −0.103531
\(559\) −38.5760 −1.63159
\(560\) 23.6210 0.998170
\(561\) −5.30703 −0.224063
\(562\) −13.5495 −0.571550
\(563\) 7.19951 0.303423 0.151712 0.988425i \(-0.451522\pi\)
0.151712 + 0.988425i \(0.451522\pi\)
\(564\) 8.16350 0.343746
\(565\) −21.3226 −0.897047
\(566\) −52.7304 −2.21642
\(567\) −2.98844 −0.125503
\(568\) −10.7832 −0.452454
\(569\) 35.5366 1.48977 0.744885 0.667193i \(-0.232504\pi\)
0.744885 + 0.667193i \(0.232504\pi\)
\(570\) 10.7646 0.450880
\(571\) −3.09160 −0.129380 −0.0646898 0.997905i \(-0.520606\pi\)
−0.0646898 + 0.997905i \(0.520606\pi\)
\(572\) 22.9319 0.958832
\(573\) −15.5947 −0.651479
\(574\) 27.2172 1.13602
\(575\) −5.53895 −0.230990
\(576\) 1.77922 0.0741340
\(577\) −2.96579 −0.123468 −0.0617338 0.998093i \(-0.519663\pi\)
−0.0617338 + 0.998093i \(0.519663\pi\)
\(578\) −1.70660 −0.0709853
\(579\) −2.93545 −0.121993
\(580\) −6.49150 −0.269545
\(581\) −32.3328 −1.34139
\(582\) −16.2353 −0.672973
\(583\) −33.7249 −1.39674
\(584\) 10.8327 0.448261
\(585\) −7.49736 −0.309978
\(586\) 32.8880 1.35859
\(587\) −26.4881 −1.09328 −0.546641 0.837367i \(-0.684094\pi\)
−0.546641 + 0.837367i \(0.684094\pi\)
\(588\) −1.76180 −0.0726554
\(589\) 5.70914 0.235241
\(590\) −27.8061 −1.14476
\(591\) −20.0263 −0.823772
\(592\) −25.7801 −1.05956
\(593\) 3.33098 0.136787 0.0683935 0.997658i \(-0.478213\pi\)
0.0683935 + 0.997658i \(0.478213\pi\)
\(594\) −9.05700 −0.371613
\(595\) 4.73145 0.193970
\(596\) −1.06902 −0.0437890
\(597\) 19.0037 0.777770
\(598\) 17.9532 0.734161
\(599\) −22.0337 −0.900272 −0.450136 0.892960i \(-0.648625\pi\)
−0.450136 + 0.892960i \(0.648625\pi\)
\(600\) 4.62744 0.188914
\(601\) −16.6199 −0.677942 −0.338971 0.940797i \(-0.610079\pi\)
−0.338971 + 0.940797i \(0.610079\pi\)
\(602\) 41.5466 1.69331
\(603\) 5.45083 0.221975
\(604\) 14.6220 0.594959
\(605\) 27.1759 1.10486
\(606\) −6.91459 −0.280886
\(607\) −9.93566 −0.403276 −0.201638 0.979460i \(-0.564626\pi\)
−0.201638 + 0.979460i \(0.564626\pi\)
\(608\) 19.1552 0.776846
\(609\) −13.4279 −0.544126
\(610\) −23.5065 −0.951751
\(611\) 42.3647 1.71389
\(612\) −0.912495 −0.0368854
\(613\) 4.07679 0.164660 0.0823299 0.996605i \(-0.473764\pi\)
0.0823299 + 0.996605i \(0.473764\pi\)
\(614\) 57.4146 2.31706
\(615\) −8.44922 −0.340705
\(616\) 29.4347 1.18596
\(617\) −0.623090 −0.0250847 −0.0125423 0.999921i \(-0.503992\pi\)
−0.0125423 + 0.999921i \(0.503992\pi\)
\(618\) 22.0832 0.888316
\(619\) 20.8957 0.839868 0.419934 0.907555i \(-0.362053\pi\)
0.419934 + 0.907555i \(0.362053\pi\)
\(620\) 2.07031 0.0831456
\(621\) −2.22152 −0.0891466
\(622\) −28.8638 −1.15733
\(623\) −49.8645 −1.99778
\(624\) −23.6408 −0.946391
\(625\) −6.31682 −0.252673
\(626\) 55.7624 2.22871
\(627\) 21.1430 0.844372
\(628\) −0.912495 −0.0364125
\(629\) −5.16394 −0.205900
\(630\) 8.07470 0.321704
\(631\) 47.6768 1.89798 0.948991 0.315304i \(-0.102106\pi\)
0.948991 + 0.315304i \(0.102106\pi\)
\(632\) 12.3328 0.490572
\(633\) −13.4375 −0.534093
\(634\) −23.4817 −0.932576
\(635\) −26.6958 −1.05939
\(636\) −5.79868 −0.229933
\(637\) −9.14291 −0.362255
\(638\) −40.6957 −1.61116
\(639\) −5.81011 −0.229844
\(640\) −20.0322 −0.791842
\(641\) 33.2075 1.31162 0.655809 0.754927i \(-0.272328\pi\)
0.655809 + 0.754927i \(0.272328\pi\)
\(642\) 8.33699 0.329035
\(643\) 33.4870 1.32060 0.660299 0.751003i \(-0.270429\pi\)
0.660299 + 0.751003i \(0.270429\pi\)
\(644\) −6.05795 −0.238716
\(645\) −12.8976 −0.507842
\(646\) 6.79905 0.267505
\(647\) 1.94123 0.0763178 0.0381589 0.999272i \(-0.487851\pi\)
0.0381589 + 0.999272i \(0.487851\pi\)
\(648\) 1.85594 0.0729082
\(649\) −54.6146 −2.14381
\(650\) −20.1497 −0.790335
\(651\) 4.28251 0.167845
\(652\) −4.98727 −0.195317
\(653\) −7.27826 −0.284820 −0.142410 0.989808i \(-0.545485\pi\)
−0.142410 + 0.989808i \(0.545485\pi\)
\(654\) −26.0119 −1.01715
\(655\) −4.15850 −0.162486
\(656\) −26.6423 −1.04021
\(657\) 5.83679 0.227715
\(658\) −45.6271 −1.77873
\(659\) −30.2782 −1.17947 −0.589735 0.807597i \(-0.700768\pi\)
−0.589735 + 0.807597i \(0.700768\pi\)
\(660\) 7.66712 0.298442
\(661\) −15.9877 −0.621848 −0.310924 0.950435i \(-0.600639\pi\)
−0.310924 + 0.950435i \(0.600639\pi\)
\(662\) −14.2155 −0.552501
\(663\) −4.73542 −0.183908
\(664\) 20.0800 0.779254
\(665\) −18.8499 −0.730969
\(666\) −8.81279 −0.341489
\(667\) −9.98195 −0.386502
\(668\) 8.76050 0.338954
\(669\) −0.601749 −0.0232650
\(670\) −14.7281 −0.568994
\(671\) −46.1697 −1.78236
\(672\) 14.3686 0.554281
\(673\) −21.9336 −0.845479 −0.422740 0.906251i \(-0.638932\pi\)
−0.422740 + 0.906251i \(0.638932\pi\)
\(674\) −44.5248 −1.71503
\(675\) 2.49331 0.0959677
\(676\) 8.59954 0.330751
\(677\) 0.642987 0.0247120 0.0123560 0.999924i \(-0.496067\pi\)
0.0123560 + 0.999924i \(0.496067\pi\)
\(678\) −22.9838 −0.882688
\(679\) 28.4296 1.09103
\(680\) −2.93842 −0.112683
\(681\) 20.1295 0.771364
\(682\) 12.9789 0.496989
\(683\) −9.32600 −0.356850 −0.178425 0.983954i \(-0.557100\pi\)
−0.178425 + 0.983954i \(0.557100\pi\)
\(684\) 3.63535 0.139001
\(685\) −29.1848 −1.11510
\(686\) −25.8536 −0.987093
\(687\) 26.9627 1.02869
\(688\) −40.6690 −1.55049
\(689\) −30.0924 −1.14643
\(690\) 6.00252 0.228512
\(691\) −9.35528 −0.355892 −0.177946 0.984040i \(-0.556945\pi\)
−0.177946 + 0.984040i \(0.556945\pi\)
\(692\) −10.5551 −0.401244
\(693\) 15.8597 0.602461
\(694\) 12.5489 0.476351
\(695\) −29.8443 −1.13206
\(696\) 8.33927 0.316099
\(697\) −5.33662 −0.202139
\(698\) 10.0766 0.381404
\(699\) 13.2736 0.502054
\(700\) 6.79910 0.256982
\(701\) 25.6211 0.967694 0.483847 0.875153i \(-0.339239\pi\)
0.483847 + 0.875153i \(0.339239\pi\)
\(702\) −8.08148 −0.305016
\(703\) 20.5730 0.775924
\(704\) −9.44236 −0.355872
\(705\) 14.1643 0.533460
\(706\) −51.3569 −1.93284
\(707\) 12.1082 0.455374
\(708\) −9.39048 −0.352916
\(709\) 3.50092 0.131480 0.0657400 0.997837i \(-0.479059\pi\)
0.0657400 + 0.997837i \(0.479059\pi\)
\(710\) 15.6988 0.589166
\(711\) 6.64504 0.249209
\(712\) 30.9679 1.16057
\(713\) 3.18350 0.119223
\(714\) 5.10008 0.190866
\(715\) 39.7887 1.48801
\(716\) −8.24594 −0.308165
\(717\) −3.63351 −0.135696
\(718\) −45.8398 −1.71073
\(719\) 3.66890 0.136827 0.0684134 0.997657i \(-0.478206\pi\)
0.0684134 + 0.997657i \(0.478206\pi\)
\(720\) −7.90414 −0.294570
\(721\) −38.6699 −1.44014
\(722\) 5.33824 0.198669
\(723\) 13.4151 0.498913
\(724\) 2.90110 0.107819
\(725\) 11.2032 0.416076
\(726\) 29.2931 1.08717
\(727\) −32.4531 −1.20362 −0.601809 0.798640i \(-0.705553\pi\)
−0.601809 + 0.798640i \(0.705553\pi\)
\(728\) 26.2643 0.973421
\(729\) 1.00000 0.0370370
\(730\) −15.7709 −0.583707
\(731\) −8.14627 −0.301301
\(732\) −7.93846 −0.293414
\(733\) 45.3168 1.67381 0.836906 0.547346i \(-0.184362\pi\)
0.836906 + 0.547346i \(0.184362\pi\)
\(734\) −36.2188 −1.33686
\(735\) −3.05686 −0.112754
\(736\) 10.6812 0.393716
\(737\) −28.9277 −1.06557
\(738\) −9.10750 −0.335252
\(739\) 2.51206 0.0924078 0.0462039 0.998932i \(-0.485288\pi\)
0.0462039 + 0.998932i \(0.485288\pi\)
\(740\) 7.46039 0.274249
\(741\) 18.8658 0.693051
\(742\) 32.4097 1.18980
\(743\) 2.55061 0.0935728 0.0467864 0.998905i \(-0.485102\pi\)
0.0467864 + 0.998905i \(0.485102\pi\)
\(744\) −2.65961 −0.0975061
\(745\) −1.85484 −0.0679562
\(746\) 10.9847 0.402179
\(747\) 10.8193 0.395857
\(748\) 4.84264 0.177064
\(749\) −14.5989 −0.533433
\(750\) −20.2468 −0.739309
\(751\) −48.1233 −1.75605 −0.878023 0.478619i \(-0.841138\pi\)
−0.878023 + 0.478619i \(0.841138\pi\)
\(752\) 44.6633 1.62870
\(753\) −26.3328 −0.959621
\(754\) −36.3124 −1.32242
\(755\) 25.3703 0.923318
\(756\) 2.72693 0.0991776
\(757\) 22.1231 0.804080 0.402040 0.915622i \(-0.368301\pi\)
0.402040 + 0.915622i \(0.368301\pi\)
\(758\) 28.6929 1.04217
\(759\) 11.7897 0.427939
\(760\) 11.7066 0.424642
\(761\) 14.7885 0.536084 0.268042 0.963407i \(-0.413623\pi\)
0.268042 + 0.963407i \(0.413623\pi\)
\(762\) −28.7757 −1.04243
\(763\) 45.5495 1.64900
\(764\) 14.2301 0.514827
\(765\) −1.58325 −0.0572426
\(766\) 39.1132 1.41322
\(767\) −48.7322 −1.75962
\(768\) −18.0345 −0.650763
\(769\) −23.5975 −0.850947 −0.425474 0.904971i \(-0.639892\pi\)
−0.425474 + 0.904971i \(0.639892\pi\)
\(770\) −42.8527 −1.54430
\(771\) −25.7444 −0.927163
\(772\) 2.67858 0.0964044
\(773\) 23.3675 0.840470 0.420235 0.907415i \(-0.361948\pi\)
0.420235 + 0.907415i \(0.361948\pi\)
\(774\) −13.9025 −0.499713
\(775\) −3.57299 −0.128345
\(776\) −17.6559 −0.633811
\(777\) 15.4321 0.553623
\(778\) −19.3564 −0.693962
\(779\) 21.2609 0.761752
\(780\) 6.84131 0.244958
\(781\) 30.8344 1.10334
\(782\) 3.79126 0.135575
\(783\) 4.49329 0.160577
\(784\) −9.63897 −0.344249
\(785\) −1.58325 −0.0565087
\(786\) −4.48249 −0.159885
\(787\) −0.0168349 −0.000600098 0 −0.000300049 1.00000i \(-0.500096\pi\)
−0.000300049 1.00000i \(0.500096\pi\)
\(788\) 18.2739 0.650981
\(789\) −6.10606 −0.217382
\(790\) −17.9548 −0.638803
\(791\) 40.2470 1.43102
\(792\) −9.84953 −0.349988
\(793\) −41.1969 −1.46294
\(794\) 31.5096 1.11824
\(795\) −10.0612 −0.356833
\(796\) −17.3408 −0.614628
\(797\) −10.6564 −0.377469 −0.188735 0.982028i \(-0.560439\pi\)
−0.188735 + 0.982028i \(0.560439\pi\)
\(798\) −20.3185 −0.719268
\(799\) 8.94635 0.316499
\(800\) −11.9880 −0.423841
\(801\) 16.6858 0.589565
\(802\) −51.7952 −1.82895
\(803\) −30.9760 −1.09312
\(804\) −4.97386 −0.175414
\(805\) −10.5110 −0.370465
\(806\) 11.5810 0.407923
\(807\) −4.32981 −0.152417
\(808\) −7.51965 −0.264540
\(809\) 30.3673 1.06766 0.533829 0.845593i \(-0.320753\pi\)
0.533829 + 0.845593i \(0.320753\pi\)
\(810\) −2.70198 −0.0949380
\(811\) −29.3949 −1.03219 −0.516097 0.856530i \(-0.672616\pi\)
−0.516097 + 0.856530i \(0.672616\pi\)
\(812\) 12.2529 0.429993
\(813\) −11.5810 −0.406163
\(814\) 46.7698 1.63928
\(815\) −8.65332 −0.303113
\(816\) −4.99234 −0.174767
\(817\) 32.4545 1.13544
\(818\) 62.6309 2.18984
\(819\) 14.1515 0.494493
\(820\) 7.70987 0.269240
\(821\) 9.09630 0.317463 0.158732 0.987322i \(-0.449260\pi\)
0.158732 + 0.987322i \(0.449260\pi\)
\(822\) −31.4586 −1.09725
\(823\) 26.9248 0.938539 0.469269 0.883055i \(-0.344517\pi\)
0.469269 + 0.883055i \(0.344517\pi\)
\(824\) 24.0156 0.836622
\(825\) −13.2321 −0.460682
\(826\) 52.4848 1.82618
\(827\) 26.8242 0.932768 0.466384 0.884582i \(-0.345556\pi\)
0.466384 + 0.884582i \(0.345556\pi\)
\(828\) 2.02713 0.0704476
\(829\) 2.34382 0.0814043 0.0407022 0.999171i \(-0.487041\pi\)
0.0407022 + 0.999171i \(0.487041\pi\)
\(830\) −29.2336 −1.01471
\(831\) 14.3260 0.496965
\(832\) −8.42534 −0.292096
\(833\) −1.93075 −0.0668965
\(834\) −32.1694 −1.11394
\(835\) 15.2002 0.526023
\(836\) −19.2929 −0.667260
\(837\) −1.43303 −0.0495327
\(838\) −0.543009 −0.0187579
\(839\) −41.7270 −1.44058 −0.720289 0.693674i \(-0.755991\pi\)
−0.720289 + 0.693674i \(0.755991\pi\)
\(840\) 8.78128 0.302983
\(841\) −8.81035 −0.303805
\(842\) 25.2145 0.868948
\(843\) −7.93944 −0.273449
\(844\) 12.2617 0.422063
\(845\) 14.9209 0.513294
\(846\) 15.2679 0.524920
\(847\) −51.2953 −1.76253
\(848\) −31.7251 −1.08944
\(849\) −30.8979 −1.06041
\(850\) −4.25510 −0.145949
\(851\) 11.4718 0.393248
\(852\) 5.30170 0.181633
\(853\) 11.3703 0.389312 0.194656 0.980872i \(-0.437641\pi\)
0.194656 + 0.980872i \(0.437641\pi\)
\(854\) 44.3693 1.51829
\(855\) 6.30763 0.215716
\(856\) 9.06651 0.309887
\(857\) −22.3512 −0.763501 −0.381751 0.924265i \(-0.624679\pi\)
−0.381751 + 0.924265i \(0.624679\pi\)
\(858\) 42.8887 1.46420
\(859\) 32.6149 1.11280 0.556402 0.830913i \(-0.312181\pi\)
0.556402 + 0.830913i \(0.312181\pi\)
\(860\) 11.7690 0.401319
\(861\) 15.9482 0.543512
\(862\) 44.1664 1.50431
\(863\) −42.3016 −1.43996 −0.719982 0.693993i \(-0.755850\pi\)
−0.719982 + 0.693993i \(0.755850\pi\)
\(864\) −4.80807 −0.163574
\(865\) −18.3139 −0.622692
\(866\) 55.7387 1.89408
\(867\) −1.00000 −0.0339618
\(868\) −3.90777 −0.132638
\(869\) −35.2654 −1.19630
\(870\) −12.1408 −0.411611
\(871\) −25.8120 −0.874606
\(872\) −28.2881 −0.957955
\(873\) −9.51320 −0.321973
\(874\) −15.1043 −0.510909
\(875\) 35.4542 1.19857
\(876\) −5.32604 −0.179950
\(877\) −49.8839 −1.68446 −0.842229 0.539120i \(-0.818757\pi\)
−0.842229 + 0.539120i \(0.818757\pi\)
\(878\) −64.2543 −2.16848
\(879\) 19.2710 0.649995
\(880\) 41.9475 1.41405
\(881\) −11.4855 −0.386955 −0.193478 0.981105i \(-0.561977\pi\)
−0.193478 + 0.981105i \(0.561977\pi\)
\(882\) −3.29502 −0.110949
\(883\) −28.6380 −0.963747 −0.481873 0.876241i \(-0.660043\pi\)
−0.481873 + 0.876241i \(0.660043\pi\)
\(884\) 4.32105 0.145333
\(885\) −16.2932 −0.547691
\(886\) 8.71948 0.292937
\(887\) 54.8525 1.84177 0.920884 0.389838i \(-0.127469\pi\)
0.920884 + 0.389838i \(0.127469\pi\)
\(888\) −9.58395 −0.321616
\(889\) 50.3891 1.69000
\(890\) −45.0848 −1.51125
\(891\) −5.30703 −0.177792
\(892\) 0.549093 0.0183850
\(893\) −35.6420 −1.19271
\(894\) −1.99935 −0.0668684
\(895\) −14.3074 −0.478242
\(896\) 37.8114 1.26319
\(897\) 10.5198 0.351247
\(898\) 22.5927 0.753928
\(899\) −6.43901 −0.214753
\(900\) −2.27514 −0.0758379
\(901\) −6.35475 −0.211707
\(902\) 48.3338 1.60934
\(903\) 24.3446 0.810138
\(904\) −24.9950 −0.831321
\(905\) 5.03364 0.167324
\(906\) 27.3469 0.908539
\(907\) −22.1890 −0.736773 −0.368387 0.929673i \(-0.620090\pi\)
−0.368387 + 0.929673i \(0.620090\pi\)
\(908\) −18.3681 −0.609566
\(909\) −4.05167 −0.134385
\(910\) −38.2371 −1.26755
\(911\) 27.8992 0.924342 0.462171 0.886791i \(-0.347071\pi\)
0.462171 + 0.886791i \(0.347071\pi\)
\(912\) 19.8893 0.658602
\(913\) −57.4184 −1.90027
\(914\) 53.2386 1.76098
\(915\) −13.7739 −0.455350
\(916\) −24.6034 −0.812918
\(917\) 7.84929 0.259207
\(918\) −1.70660 −0.0563263
\(919\) 24.1146 0.795466 0.397733 0.917501i \(-0.369797\pi\)
0.397733 + 0.917501i \(0.369797\pi\)
\(920\) 6.52777 0.215214
\(921\) 33.6426 1.10856
\(922\) −40.5217 −1.33451
\(923\) 27.5133 0.905612
\(924\) −14.4719 −0.476091
\(925\) −12.8753 −0.423338
\(926\) −23.6155 −0.776053
\(927\) 12.9398 0.425000
\(928\) −21.6041 −0.709188
\(929\) 15.5873 0.511402 0.255701 0.966756i \(-0.417694\pi\)
0.255701 + 0.966756i \(0.417694\pi\)
\(930\) 3.87202 0.126968
\(931\) 7.69205 0.252097
\(932\) −12.1121 −0.396745
\(933\) −16.9130 −0.553708
\(934\) 44.3726 1.45192
\(935\) 8.40237 0.274787
\(936\) −8.78865 −0.287266
\(937\) −33.5502 −1.09604 −0.548018 0.836466i \(-0.684618\pi\)
−0.548018 + 0.836466i \(0.684618\pi\)
\(938\) 27.7997 0.907691
\(939\) 32.6745 1.06629
\(940\) −12.9249 −0.421563
\(941\) 42.1254 1.37325 0.686624 0.727013i \(-0.259092\pi\)
0.686624 + 0.727013i \(0.259092\pi\)
\(942\) −1.70660 −0.0556041
\(943\) 11.8554 0.386066
\(944\) −51.3762 −1.67215
\(945\) 4.73145 0.153914
\(946\) 73.7807 2.39882
\(947\) 6.69346 0.217508 0.108754 0.994069i \(-0.465314\pi\)
0.108754 + 0.994069i \(0.465314\pi\)
\(948\) −6.06357 −0.196936
\(949\) −27.6396 −0.897221
\(950\) 16.9522 0.550001
\(951\) −13.7593 −0.446176
\(952\) 5.54636 0.179758
\(953\) −32.1266 −1.04068 −0.520342 0.853958i \(-0.674196\pi\)
−0.520342 + 0.853958i \(0.674196\pi\)
\(954\) −10.8450 −0.351121
\(955\) 24.6904 0.798961
\(956\) 3.31556 0.107233
\(957\) −23.8460 −0.770833
\(958\) −24.6633 −0.796834
\(959\) 55.0873 1.77886
\(960\) −2.81695 −0.0909166
\(961\) −28.9464 −0.933756
\(962\) 41.7323 1.34550
\(963\) 4.88513 0.157421
\(964\) −12.2412 −0.394263
\(965\) 4.64756 0.149610
\(966\) −11.3299 −0.364535
\(967\) −23.9371 −0.769766 −0.384883 0.922965i \(-0.625758\pi\)
−0.384883 + 0.922965i \(0.625758\pi\)
\(968\) 31.8564 1.02390
\(969\) 3.98397 0.127984
\(970\) 25.7045 0.825322
\(971\) 13.1915 0.423335 0.211668 0.977342i \(-0.432111\pi\)
0.211668 + 0.977342i \(0.432111\pi\)
\(972\) −0.912495 −0.0292683
\(973\) 56.3320 1.80592
\(974\) −50.8795 −1.63028
\(975\) −11.8069 −0.378123
\(976\) −43.4320 −1.39023
\(977\) −33.9761 −1.08699 −0.543496 0.839412i \(-0.682900\pi\)
−0.543496 + 0.839412i \(0.682900\pi\)
\(978\) −9.32750 −0.298261
\(979\) −88.5522 −2.83014
\(980\) 2.78937 0.0891033
\(981\) −15.2419 −0.486637
\(982\) 4.97834 0.158865
\(983\) 11.6144 0.370442 0.185221 0.982697i \(-0.440700\pi\)
0.185221 + 0.982697i \(0.440700\pi\)
\(984\) −9.90445 −0.315742
\(985\) 31.7067 1.01026
\(986\) −7.66826 −0.244207
\(987\) −26.7356 −0.851004
\(988\) −17.2149 −0.547680
\(989\) 18.0971 0.575455
\(990\) 14.3395 0.455739
\(991\) 43.7480 1.38970 0.694851 0.719154i \(-0.255470\pi\)
0.694851 + 0.719154i \(0.255470\pi\)
\(992\) 6.89010 0.218761
\(993\) −8.32969 −0.264335
\(994\) −29.6320 −0.939870
\(995\) −30.0876 −0.953842
\(996\) −9.87256 −0.312824
\(997\) −50.2662 −1.59195 −0.795973 0.605332i \(-0.793041\pi\)
−0.795973 + 0.605332i \(0.793041\pi\)
\(998\) 50.7017 1.60494
\(999\) −5.16394 −0.163380
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 \(a_p\))