Properties

Label 8027.2.a.f.1.15
Level 8027
Weight 2
Character 8027.1
Self dual Yes
Analytic conductor 64.096
Analytic rank 0
Dimension 176
CM No

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Newspace parameters

Level: \( N \) = \( 8027 = 23 \cdot 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0959177025\)
Analytic rank: \(0\)
Dimension: \(176\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 8027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.43642 q^{2} -3.01973 q^{3} +3.93613 q^{4} +2.61235 q^{5} +7.35732 q^{6} -1.67075 q^{7} -4.71721 q^{8} +6.11876 q^{9} +O(q^{10})\) \(q-2.43642 q^{2} -3.01973 q^{3} +3.93613 q^{4} +2.61235 q^{5} +7.35732 q^{6} -1.67075 q^{7} -4.71721 q^{8} +6.11876 q^{9} -6.36478 q^{10} -3.15935 q^{11} -11.8860 q^{12} +5.74300 q^{13} +4.07065 q^{14} -7.88859 q^{15} +3.62083 q^{16} -4.74863 q^{17} -14.9078 q^{18} +0.791197 q^{19} +10.2825 q^{20} +5.04522 q^{21} +7.69748 q^{22} +1.00000 q^{23} +14.2447 q^{24} +1.82438 q^{25} -13.9923 q^{26} -9.41780 q^{27} -6.57630 q^{28} -0.131990 q^{29} +19.2199 q^{30} -9.74098 q^{31} +0.612559 q^{32} +9.54037 q^{33} +11.5696 q^{34} -4.36460 q^{35} +24.0842 q^{36} -4.75435 q^{37} -1.92769 q^{38} -17.3423 q^{39} -12.3230 q^{40} -8.38920 q^{41} -12.2923 q^{42} +5.86775 q^{43} -12.4356 q^{44} +15.9843 q^{45} -2.43642 q^{46} -1.61269 q^{47} -10.9339 q^{48} -4.20858 q^{49} -4.44495 q^{50} +14.3396 q^{51} +22.6052 q^{52} +5.04031 q^{53} +22.9457 q^{54} -8.25332 q^{55} +7.88130 q^{56} -2.38920 q^{57} +0.321584 q^{58} -9.46781 q^{59} -31.0505 q^{60} +1.98037 q^{61} +23.7331 q^{62} -10.2229 q^{63} -8.73411 q^{64} +15.0027 q^{65} -23.2443 q^{66} -13.4173 q^{67} -18.6912 q^{68} -3.01973 q^{69} +10.6340 q^{70} -6.91127 q^{71} -28.8635 q^{72} +10.8566 q^{73} +11.5836 q^{74} -5.50914 q^{75} +3.11425 q^{76} +5.27849 q^{77} +42.2530 q^{78} +3.41290 q^{79} +9.45889 q^{80} +10.0829 q^{81} +20.4396 q^{82} -11.1177 q^{83} +19.8586 q^{84} -12.4051 q^{85} -14.2963 q^{86} +0.398575 q^{87} +14.9033 q^{88} +5.66608 q^{89} -38.9445 q^{90} -9.59514 q^{91} +3.93613 q^{92} +29.4151 q^{93} +3.92918 q^{94} +2.06689 q^{95} -1.84976 q^{96} +5.87627 q^{97} +10.2539 q^{98} -19.3313 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + O(q^{10}) \) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + 18q^{10} + 11q^{11} + 46q^{12} + 87q^{13} - 6q^{14} + 29q^{15} + 257q^{16} + 14q^{17} + 72q^{18} + 34q^{19} + 45q^{20} + 23q^{21} + 62q^{22} + 176q^{23} + 33q^{24} + 272q^{25} + 31q^{26} + 82q^{27} + 80q^{28} + 75q^{29} - 30q^{30} + 73q^{31} + 71q^{32} + 30q^{33} + 23q^{34} + 44q^{35} + 264q^{36} + 236q^{37} - 21q^{38} + 17q^{39} + 43q^{40} + 51q^{41} + 38q^{42} + 51q^{43} + 12q^{44} + 127q^{45} + 19q^{46} + 45q^{47} + 61q^{48} + 268q^{49} + 55q^{50} - 3q^{51} + 166q^{52} + 63q^{53} - 32q^{54} + 11q^{55} - 9q^{56} + 72q^{57} + 98q^{58} + 95q^{59} - 7q^{60} + 73q^{61} + 12q^{62} + 19q^{63} + 365q^{64} + 19q^{65} - 28q^{66} + 138q^{67} + 16q^{68} + 22q^{69} + 100q^{70} + 85q^{71} + 129q^{72} + 118q^{73} - 21q^{74} - 12q^{75} + 52q^{76} + 75q^{77} + 97q^{78} + 74q^{79} + 8q^{80} + 280q^{81} + 67q^{82} + 10q^{83} - 51q^{84} + 169q^{85} - 39q^{86} - 6q^{87} + 159q^{88} + 38q^{89} + 22q^{90} + 90q^{91} + 203q^{92} + 230q^{93} + 63q^{94} + 30q^{95} + 107q^{96} + 161q^{97} + 58q^{98} + 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.43642 −1.72281 −0.861403 0.507922i \(-0.830414\pi\)
−0.861403 + 0.507922i \(0.830414\pi\)
\(3\) −3.01973 −1.74344 −0.871720 0.490004i \(-0.836995\pi\)
−0.871720 + 0.490004i \(0.836995\pi\)
\(4\) 3.93613 1.96806
\(5\) 2.61235 1.16828 0.584140 0.811653i \(-0.301432\pi\)
0.584140 + 0.811653i \(0.301432\pi\)
\(6\) 7.35732 3.00361
\(7\) −1.67075 −0.631486 −0.315743 0.948845i \(-0.602254\pi\)
−0.315743 + 0.948845i \(0.602254\pi\)
\(8\) −4.71721 −1.66778
\(9\) 6.11876 2.03959
\(10\) −6.36478 −2.01272
\(11\) −3.15935 −0.952579 −0.476289 0.879289i \(-0.658019\pi\)
−0.476289 + 0.879289i \(0.658019\pi\)
\(12\) −11.8860 −3.43120
\(13\) 5.74300 1.59282 0.796410 0.604757i \(-0.206730\pi\)
0.796410 + 0.604757i \(0.206730\pi\)
\(14\) 4.07065 1.08793
\(15\) −7.88859 −2.03683
\(16\) 3.62083 0.905208
\(17\) −4.74863 −1.15171 −0.575856 0.817551i \(-0.695331\pi\)
−0.575856 + 0.817551i \(0.695331\pi\)
\(18\) −14.9078 −3.51381
\(19\) 0.791197 0.181513 0.0907565 0.995873i \(-0.471071\pi\)
0.0907565 + 0.995873i \(0.471071\pi\)
\(20\) 10.2825 2.29925
\(21\) 5.04522 1.10096
\(22\) 7.69748 1.64111
\(23\) 1.00000 0.208514
\(24\) 14.2447 2.90768
\(25\) 1.82438 0.364876
\(26\) −13.9923 −2.74412
\(27\) −9.41780 −1.81246
\(28\) −6.57630 −1.24280
\(29\) −0.131990 −0.0245100 −0.0122550 0.999925i \(-0.503901\pi\)
−0.0122550 + 0.999925i \(0.503901\pi\)
\(30\) 19.2199 3.50906
\(31\) −9.74098 −1.74953 −0.874766 0.484546i \(-0.838985\pi\)
−0.874766 + 0.484546i \(0.838985\pi\)
\(32\) 0.612559 0.108286
\(33\) 9.54037 1.66076
\(34\) 11.5696 1.98418
\(35\) −4.36460 −0.737752
\(36\) 24.0842 4.01403
\(37\) −4.75435 −0.781610 −0.390805 0.920473i \(-0.627803\pi\)
−0.390805 + 0.920473i \(0.627803\pi\)
\(38\) −1.92769 −0.312712
\(39\) −17.3423 −2.77699
\(40\) −12.3230 −1.94844
\(41\) −8.38920 −1.31017 −0.655087 0.755554i \(-0.727368\pi\)
−0.655087 + 0.755554i \(0.727368\pi\)
\(42\) −12.2923 −1.89674
\(43\) 5.86775 0.894824 0.447412 0.894328i \(-0.352346\pi\)
0.447412 + 0.894328i \(0.352346\pi\)
\(44\) −12.4356 −1.87473
\(45\) 15.9843 2.38281
\(46\) −2.43642 −0.359230
\(47\) −1.61269 −0.235235 −0.117617 0.993059i \(-0.537526\pi\)
−0.117617 + 0.993059i \(0.537526\pi\)
\(48\) −10.9339 −1.57818
\(49\) −4.20858 −0.601226
\(50\) −4.44495 −0.628611
\(51\) 14.3396 2.00794
\(52\) 22.6052 3.13477
\(53\) 5.04031 0.692340 0.346170 0.938172i \(-0.387482\pi\)
0.346170 + 0.938172i \(0.387482\pi\)
\(54\) 22.9457 3.12251
\(55\) −8.25332 −1.11288
\(56\) 7.88130 1.05318
\(57\) −2.38920 −0.316457
\(58\) 0.321584 0.0422260
\(59\) −9.46781 −1.23260 −0.616302 0.787510i \(-0.711370\pi\)
−0.616302 + 0.787510i \(0.711370\pi\)
\(60\) −31.0505 −4.00860
\(61\) 1.98037 0.253560 0.126780 0.991931i \(-0.459536\pi\)
0.126780 + 0.991931i \(0.459536\pi\)
\(62\) 23.7331 3.01410
\(63\) −10.2229 −1.28797
\(64\) −8.73411 −1.09176
\(65\) 15.0027 1.86086
\(66\) −23.2443 −2.86118
\(67\) −13.4173 −1.63919 −0.819593 0.572947i \(-0.805800\pi\)
−0.819593 + 0.572947i \(0.805800\pi\)
\(68\) −18.6912 −2.26664
\(69\) −3.01973 −0.363533
\(70\) 10.6340 1.27100
\(71\) −6.91127 −0.820217 −0.410109 0.912037i \(-0.634509\pi\)
−0.410109 + 0.912037i \(0.634509\pi\)
\(72\) −28.8635 −3.40159
\(73\) 10.8566 1.27067 0.635334 0.772238i \(-0.280862\pi\)
0.635334 + 0.772238i \(0.280862\pi\)
\(74\) 11.5836 1.34656
\(75\) −5.50914 −0.636140
\(76\) 3.11425 0.357229
\(77\) 5.27849 0.601540
\(78\) 42.2530 4.78421
\(79\) 3.41290 0.383981 0.191990 0.981397i \(-0.438506\pi\)
0.191990 + 0.981397i \(0.438506\pi\)
\(80\) 9.45889 1.05754
\(81\) 10.0829 1.12033
\(82\) 20.4396 2.25718
\(83\) −11.1177 −1.22033 −0.610164 0.792275i \(-0.708896\pi\)
−0.610164 + 0.792275i \(0.708896\pi\)
\(84\) 19.8586 2.16676
\(85\) −12.4051 −1.34552
\(86\) −14.2963 −1.54161
\(87\) 0.398575 0.0427317
\(88\) 14.9033 1.58870
\(89\) 5.66608 0.600603 0.300302 0.953844i \(-0.402913\pi\)
0.300302 + 0.953844i \(0.402913\pi\)
\(90\) −38.9445 −4.10511
\(91\) −9.59514 −1.00584
\(92\) 3.93613 0.410369
\(93\) 29.4151 3.05020
\(94\) 3.92918 0.405264
\(95\) 2.06689 0.212058
\(96\) −1.84976 −0.188791
\(97\) 5.87627 0.596645 0.298323 0.954465i \(-0.403573\pi\)
0.298323 + 0.954465i \(0.403573\pi\)
\(98\) 10.2539 1.03580
\(99\) −19.3313 −1.94287
\(100\) 7.18099 0.718099
\(101\) −15.3945 −1.53181 −0.765904 0.642955i \(-0.777708\pi\)
−0.765904 + 0.642955i \(0.777708\pi\)
\(102\) −34.9372 −3.45930
\(103\) 3.10900 0.306339 0.153169 0.988200i \(-0.451052\pi\)
0.153169 + 0.988200i \(0.451052\pi\)
\(104\) −27.0909 −2.65648
\(105\) 13.1799 1.28623
\(106\) −12.2803 −1.19277
\(107\) −2.29765 −0.222122 −0.111061 0.993814i \(-0.535425\pi\)
−0.111061 + 0.993814i \(0.535425\pi\)
\(108\) −37.0697 −3.56703
\(109\) 20.7668 1.98910 0.994548 0.104277i \(-0.0332527\pi\)
0.994548 + 0.104277i \(0.0332527\pi\)
\(110\) 20.1085 1.91727
\(111\) 14.3568 1.36269
\(112\) −6.04952 −0.571626
\(113\) −8.23562 −0.774742 −0.387371 0.921924i \(-0.626617\pi\)
−0.387371 + 0.921924i \(0.626617\pi\)
\(114\) 5.82109 0.545195
\(115\) 2.61235 0.243603
\(116\) −0.519531 −0.0482372
\(117\) 35.1400 3.24870
\(118\) 23.0675 2.12354
\(119\) 7.93380 0.727290
\(120\) 37.2121 3.39699
\(121\) −1.01853 −0.0925937
\(122\) −4.82499 −0.436835
\(123\) 25.3331 2.28421
\(124\) −38.3417 −3.44319
\(125\) −8.29583 −0.742002
\(126\) 24.9073 2.21892
\(127\) 10.7850 0.957017 0.478508 0.878083i \(-0.341178\pi\)
0.478508 + 0.878083i \(0.341178\pi\)
\(128\) 20.0548 1.77261
\(129\) −17.7190 −1.56007
\(130\) −36.5529 −3.20590
\(131\) 16.6325 1.45319 0.726593 0.687069i \(-0.241103\pi\)
0.726593 + 0.687069i \(0.241103\pi\)
\(132\) 37.5521 3.26849
\(133\) −1.32190 −0.114623
\(134\) 32.6902 2.82400
\(135\) −24.6026 −2.11746
\(136\) 22.4003 1.92081
\(137\) 13.3033 1.13658 0.568289 0.822829i \(-0.307606\pi\)
0.568289 + 0.822829i \(0.307606\pi\)
\(138\) 7.35732 0.626296
\(139\) −0.408853 −0.0346785 −0.0173392 0.999850i \(-0.505520\pi\)
−0.0173392 + 0.999850i \(0.505520\pi\)
\(140\) −17.1796 −1.45194
\(141\) 4.86988 0.410118
\(142\) 16.8387 1.41308
\(143\) −18.1441 −1.51729
\(144\) 22.1550 1.84625
\(145\) −0.344805 −0.0286345
\(146\) −26.4512 −2.18911
\(147\) 12.7088 1.04820
\(148\) −18.7137 −1.53826
\(149\) 11.9972 0.982847 0.491423 0.870921i \(-0.336477\pi\)
0.491423 + 0.870921i \(0.336477\pi\)
\(150\) 13.4225 1.09595
\(151\) 14.6009 1.18820 0.594102 0.804389i \(-0.297507\pi\)
0.594102 + 0.804389i \(0.297507\pi\)
\(152\) −3.73224 −0.302725
\(153\) −29.0557 −2.34902
\(154\) −12.8606 −1.03634
\(155\) −25.4469 −2.04394
\(156\) −68.2614 −5.46529
\(157\) 0.968319 0.0772803 0.0386401 0.999253i \(-0.487697\pi\)
0.0386401 + 0.999253i \(0.487697\pi\)
\(158\) −8.31524 −0.661525
\(159\) −15.2204 −1.20705
\(160\) 1.60022 0.126508
\(161\) −1.67075 −0.131674
\(162\) −24.5662 −1.93010
\(163\) −15.6204 −1.22348 −0.611741 0.791058i \(-0.709530\pi\)
−0.611741 + 0.791058i \(0.709530\pi\)
\(164\) −33.0210 −2.57850
\(165\) 24.9228 1.94024
\(166\) 27.0874 2.10239
\(167\) 20.8315 1.61199 0.805995 0.591922i \(-0.201631\pi\)
0.805995 + 0.591922i \(0.201631\pi\)
\(168\) −23.7994 −1.83616
\(169\) 19.9820 1.53708
\(170\) 30.2240 2.31807
\(171\) 4.84114 0.370212
\(172\) 23.0962 1.76107
\(173\) 1.88450 0.143276 0.0716378 0.997431i \(-0.477177\pi\)
0.0716378 + 0.997431i \(0.477177\pi\)
\(174\) −0.971095 −0.0736185
\(175\) −3.04809 −0.230414
\(176\) −11.4395 −0.862282
\(177\) 28.5902 2.14897
\(178\) −13.8049 −1.03472
\(179\) 19.5433 1.46074 0.730369 0.683053i \(-0.239348\pi\)
0.730369 + 0.683053i \(0.239348\pi\)
\(180\) 62.9164 4.68951
\(181\) 11.3746 0.845466 0.422733 0.906254i \(-0.361071\pi\)
0.422733 + 0.906254i \(0.361071\pi\)
\(182\) 23.3778 1.73287
\(183\) −5.98017 −0.442067
\(184\) −4.71721 −0.347757
\(185\) −12.4200 −0.913139
\(186\) −71.6674 −5.25491
\(187\) 15.0026 1.09710
\(188\) −6.34774 −0.462957
\(189\) 15.7348 1.14454
\(190\) −5.03579 −0.365335
\(191\) −13.2328 −0.957495 −0.478748 0.877953i \(-0.658909\pi\)
−0.478748 + 0.877953i \(0.658909\pi\)
\(192\) 26.3747 1.90343
\(193\) 16.7239 1.20381 0.601905 0.798568i \(-0.294409\pi\)
0.601905 + 0.798568i \(0.294409\pi\)
\(194\) −14.3170 −1.02790
\(195\) −45.3042 −3.24430
\(196\) −16.5655 −1.18325
\(197\) −4.94853 −0.352568 −0.176284 0.984339i \(-0.556408\pi\)
−0.176284 + 0.984339i \(0.556408\pi\)
\(198\) 47.0990 3.34718
\(199\) 16.6286 1.17877 0.589385 0.807852i \(-0.299370\pi\)
0.589385 + 0.807852i \(0.299370\pi\)
\(200\) −8.60599 −0.608535
\(201\) 40.5166 2.85782
\(202\) 37.5074 2.63901
\(203\) 0.220524 0.0154777
\(204\) 56.4424 3.95176
\(205\) −21.9155 −1.53065
\(206\) −7.57482 −0.527763
\(207\) 6.11876 0.425283
\(208\) 20.7944 1.44183
\(209\) −2.49967 −0.172905
\(210\) −32.1117 −2.21592
\(211\) −15.3954 −1.05986 −0.529930 0.848041i \(-0.677782\pi\)
−0.529930 + 0.848041i \(0.677782\pi\)
\(212\) 19.8393 1.36257
\(213\) 20.8702 1.43000
\(214\) 5.59802 0.382673
\(215\) 15.3286 1.04540
\(216\) 44.4257 3.02279
\(217\) 16.2748 1.10480
\(218\) −50.5965 −3.42683
\(219\) −32.7840 −2.21533
\(220\) −32.4861 −2.19021
\(221\) −27.2714 −1.83447
\(222\) −34.9792 −2.34765
\(223\) −9.25134 −0.619516 −0.309758 0.950815i \(-0.600248\pi\)
−0.309758 + 0.950815i \(0.600248\pi\)
\(224\) −1.02344 −0.0683812
\(225\) 11.1629 0.744197
\(226\) 20.0654 1.33473
\(227\) 9.21489 0.611613 0.305807 0.952094i \(-0.401074\pi\)
0.305807 + 0.952094i \(0.401074\pi\)
\(228\) −9.40419 −0.622808
\(229\) −21.5800 −1.42604 −0.713022 0.701142i \(-0.752674\pi\)
−0.713022 + 0.701142i \(0.752674\pi\)
\(230\) −6.36478 −0.419681
\(231\) −15.9396 −1.04875
\(232\) 0.622626 0.0408774
\(233\) 24.0900 1.57819 0.789093 0.614274i \(-0.210551\pi\)
0.789093 + 0.614274i \(0.210551\pi\)
\(234\) −85.6157 −5.59687
\(235\) −4.21291 −0.274820
\(236\) −37.2665 −2.42584
\(237\) −10.3060 −0.669448
\(238\) −19.3300 −1.25298
\(239\) −6.93888 −0.448839 −0.224419 0.974493i \(-0.572049\pi\)
−0.224419 + 0.974493i \(0.572049\pi\)
\(240\) −28.5633 −1.84375
\(241\) −22.7903 −1.46805 −0.734027 0.679121i \(-0.762361\pi\)
−0.734027 + 0.679121i \(0.762361\pi\)
\(242\) 2.48157 0.159521
\(243\) −2.19430 −0.140765
\(244\) 7.79497 0.499022
\(245\) −10.9943 −0.702399
\(246\) −61.7220 −3.93525
\(247\) 4.54384 0.289118
\(248\) 45.9502 2.91784
\(249\) 33.5725 2.12757
\(250\) 20.2121 1.27833
\(251\) −19.4117 −1.22526 −0.612628 0.790372i \(-0.709887\pi\)
−0.612628 + 0.790372i \(0.709887\pi\)
\(252\) −40.2388 −2.53481
\(253\) −3.15935 −0.198626
\(254\) −26.2768 −1.64875
\(255\) 37.4600 2.34584
\(256\) −31.3937 −1.96210
\(257\) −2.91235 −0.181668 −0.0908338 0.995866i \(-0.528953\pi\)
−0.0908338 + 0.995866i \(0.528953\pi\)
\(258\) 43.1709 2.68770
\(259\) 7.94335 0.493576
\(260\) 59.0526 3.66229
\(261\) −0.807618 −0.0499903
\(262\) −40.5236 −2.50356
\(263\) −9.63250 −0.593965 −0.296983 0.954883i \(-0.595980\pi\)
−0.296983 + 0.954883i \(0.595980\pi\)
\(264\) −45.0039 −2.76980
\(265\) 13.1671 0.808847
\(266\) 3.22069 0.197473
\(267\) −17.1100 −1.04712
\(268\) −52.8122 −3.22602
\(269\) −14.9550 −0.911820 −0.455910 0.890026i \(-0.650686\pi\)
−0.455910 + 0.890026i \(0.650686\pi\)
\(270\) 59.9422 3.64797
\(271\) −20.1036 −1.22121 −0.610604 0.791936i \(-0.709073\pi\)
−0.610604 + 0.791936i \(0.709073\pi\)
\(272\) −17.1940 −1.04254
\(273\) 28.9747 1.75363
\(274\) −32.4124 −1.95810
\(275\) −5.76385 −0.347573
\(276\) −11.8860 −0.715455
\(277\) 26.8898 1.61565 0.807825 0.589422i \(-0.200644\pi\)
0.807825 + 0.589422i \(0.200644\pi\)
\(278\) 0.996136 0.0597443
\(279\) −59.6027 −3.56832
\(280\) 20.5887 1.23041
\(281\) −28.4525 −1.69733 −0.848666 0.528929i \(-0.822594\pi\)
−0.848666 + 0.528929i \(0.822594\pi\)
\(282\) −11.8651 −0.706553
\(283\) −0.0438726 −0.00260796 −0.00130398 0.999999i \(-0.500415\pi\)
−0.00130398 + 0.999999i \(0.500415\pi\)
\(284\) −27.2036 −1.61424
\(285\) −6.24143 −0.369710
\(286\) 44.2066 2.61399
\(287\) 14.0163 0.827356
\(288\) 3.74810 0.220859
\(289\) 5.54952 0.326442
\(290\) 0.840090 0.0493318
\(291\) −17.7447 −1.04022
\(292\) 42.7329 2.50075
\(293\) −4.43306 −0.258982 −0.129491 0.991581i \(-0.541334\pi\)
−0.129491 + 0.991581i \(0.541334\pi\)
\(294\) −30.9638 −1.80585
\(295\) −24.7332 −1.44002
\(296\) 22.4272 1.30356
\(297\) 29.7541 1.72651
\(298\) −29.2301 −1.69326
\(299\) 5.74300 0.332126
\(300\) −21.6846 −1.25196
\(301\) −9.80358 −0.565069
\(302\) −35.5739 −2.04705
\(303\) 46.4871 2.67062
\(304\) 2.86479 0.164307
\(305\) 5.17341 0.296229
\(306\) 70.7919 4.04690
\(307\) −23.7391 −1.35486 −0.677430 0.735587i \(-0.736906\pi\)
−0.677430 + 0.735587i \(0.736906\pi\)
\(308\) 20.7768 1.18387
\(309\) −9.38834 −0.534084
\(310\) 61.9991 3.52131
\(311\) −9.43499 −0.535009 −0.267505 0.963557i \(-0.586199\pi\)
−0.267505 + 0.963557i \(0.586199\pi\)
\(312\) 81.8072 4.63142
\(313\) −0.414487 −0.0234282 −0.0117141 0.999931i \(-0.503729\pi\)
−0.0117141 + 0.999931i \(0.503729\pi\)
\(314\) −2.35923 −0.133139
\(315\) −26.7059 −1.50471
\(316\) 13.4336 0.755699
\(317\) −24.1531 −1.35657 −0.678287 0.734797i \(-0.737277\pi\)
−0.678287 + 0.734797i \(0.737277\pi\)
\(318\) 37.0832 2.07952
\(319\) 0.417003 0.0233477
\(320\) −22.8166 −1.27549
\(321\) 6.93827 0.387256
\(322\) 4.07065 0.226849
\(323\) −3.75710 −0.209051
\(324\) 39.6877 2.20487
\(325\) 10.4774 0.581182
\(326\) 38.0577 2.10782
\(327\) −62.7100 −3.46787
\(328\) 39.5736 2.18509
\(329\) 2.69440 0.148547
\(330\) −60.7223 −3.34265
\(331\) 7.63321 0.419559 0.209780 0.977749i \(-0.432725\pi\)
0.209780 + 0.977749i \(0.432725\pi\)
\(332\) −43.7607 −2.40168
\(333\) −29.0907 −1.59416
\(334\) −50.7542 −2.77715
\(335\) −35.0507 −1.91503
\(336\) 18.2679 0.996597
\(337\) −29.6998 −1.61785 −0.808927 0.587909i \(-0.799951\pi\)
−0.808927 + 0.587909i \(0.799951\pi\)
\(338\) −48.6845 −2.64809
\(339\) 24.8693 1.35072
\(340\) −48.8280 −2.64807
\(341\) 30.7751 1.66657
\(342\) −11.7950 −0.637803
\(343\) 18.7268 1.01115
\(344\) −27.6794 −1.49237
\(345\) −7.88859 −0.424708
\(346\) −4.59142 −0.246836
\(347\) 14.3919 0.772600 0.386300 0.922373i \(-0.373753\pi\)
0.386300 + 0.922373i \(0.373753\pi\)
\(348\) 1.56884 0.0840988
\(349\) −1.00000 −0.0535288
\(350\) 7.42642 0.396959
\(351\) −54.0864 −2.88692
\(352\) −1.93529 −0.103151
\(353\) 11.5712 0.615871 0.307936 0.951407i \(-0.400362\pi\)
0.307936 + 0.951407i \(0.400362\pi\)
\(354\) −69.6576 −3.70226
\(355\) −18.0547 −0.958242
\(356\) 22.3024 1.18203
\(357\) −23.9579 −1.26799
\(358\) −47.6157 −2.51657
\(359\) 9.25082 0.488239 0.244120 0.969745i \(-0.421501\pi\)
0.244120 + 0.969745i \(0.421501\pi\)
\(360\) −75.4015 −3.97401
\(361\) −18.3740 −0.967053
\(362\) −27.7132 −1.45657
\(363\) 3.07569 0.161432
\(364\) −37.7677 −1.97956
\(365\) 28.3612 1.48449
\(366\) 14.5702 0.761595
\(367\) 9.40578 0.490978 0.245489 0.969399i \(-0.421052\pi\)
0.245489 + 0.969399i \(0.421052\pi\)
\(368\) 3.62083 0.188749
\(369\) −51.3315 −2.67221
\(370\) 30.2604 1.57316
\(371\) −8.42113 −0.437203
\(372\) 115.782 6.00299
\(373\) −19.0790 −0.987874 −0.493937 0.869498i \(-0.664443\pi\)
−0.493937 + 0.869498i \(0.664443\pi\)
\(374\) −36.5525 −1.89009
\(375\) 25.0512 1.29364
\(376\) 7.60738 0.392321
\(377\) −0.758021 −0.0390400
\(378\) −38.3366 −1.97182
\(379\) 24.1949 1.24281 0.621405 0.783490i \(-0.286562\pi\)
0.621405 + 0.783490i \(0.286562\pi\)
\(380\) 8.13552 0.417343
\(381\) −32.5679 −1.66850
\(382\) 32.2407 1.64958
\(383\) 21.6310 1.10529 0.552647 0.833416i \(-0.313618\pi\)
0.552647 + 0.833416i \(0.313618\pi\)
\(384\) −60.5601 −3.09045
\(385\) 13.7893 0.702767
\(386\) −40.7463 −2.07393
\(387\) 35.9034 1.82507
\(388\) 23.1297 1.17424
\(389\) 3.23130 0.163833 0.0819167 0.996639i \(-0.473896\pi\)
0.0819167 + 0.996639i \(0.473896\pi\)
\(390\) 110.380 5.58930
\(391\) −4.74863 −0.240149
\(392\) 19.8527 1.00272
\(393\) −50.2255 −2.53354
\(394\) 12.0567 0.607407
\(395\) 8.91569 0.448597
\(396\) −76.0903 −3.82368
\(397\) 20.5294 1.03034 0.515170 0.857088i \(-0.327729\pi\)
0.515170 + 0.857088i \(0.327729\pi\)
\(398\) −40.5142 −2.03079
\(399\) 3.99177 0.199838
\(400\) 6.60578 0.330289
\(401\) 24.9096 1.24392 0.621962 0.783047i \(-0.286336\pi\)
0.621962 + 0.783047i \(0.286336\pi\)
\(402\) −98.7154 −4.92348
\(403\) −55.9424 −2.78669
\(404\) −60.5946 −3.01469
\(405\) 26.3402 1.30885
\(406\) −0.537287 −0.0266651
\(407\) 15.0206 0.744545
\(408\) −67.6428 −3.34882
\(409\) 16.9284 0.837057 0.418529 0.908204i \(-0.362546\pi\)
0.418529 + 0.908204i \(0.362546\pi\)
\(410\) 53.3954 2.63701
\(411\) −40.1723 −1.98156
\(412\) 12.2374 0.602894
\(413\) 15.8184 0.778372
\(414\) −14.9078 −0.732681
\(415\) −29.0434 −1.42568
\(416\) 3.51792 0.172480
\(417\) 1.23463 0.0604599
\(418\) 6.09023 0.297883
\(419\) −31.2105 −1.52473 −0.762367 0.647145i \(-0.775963\pi\)
−0.762367 + 0.647145i \(0.775963\pi\)
\(420\) 51.8777 2.53137
\(421\) −25.1222 −1.22438 −0.612191 0.790710i \(-0.709712\pi\)
−0.612191 + 0.790710i \(0.709712\pi\)
\(422\) 37.5095 1.82593
\(423\) −9.86764 −0.479781
\(424\) −23.7762 −1.15467
\(425\) −8.66332 −0.420233
\(426\) −50.8484 −2.46361
\(427\) −3.30870 −0.160119
\(428\) −9.04382 −0.437150
\(429\) 54.7903 2.64530
\(430\) −37.3469 −1.80103
\(431\) 24.5573 1.18289 0.591443 0.806347i \(-0.298558\pi\)
0.591443 + 0.806347i \(0.298558\pi\)
\(432\) −34.1003 −1.64065
\(433\) 24.5274 1.17871 0.589356 0.807873i \(-0.299381\pi\)
0.589356 + 0.807873i \(0.299381\pi\)
\(434\) −39.6521 −1.90336
\(435\) 1.04122 0.0499226
\(436\) 81.7406 3.91467
\(437\) 0.791197 0.0378481
\(438\) 79.8754 3.81659
\(439\) 8.54063 0.407622 0.203811 0.979010i \(-0.434667\pi\)
0.203811 + 0.979010i \(0.434667\pi\)
\(440\) 38.9326 1.85604
\(441\) −25.7513 −1.22625
\(442\) 66.4445 3.16044
\(443\) 26.9284 1.27941 0.639703 0.768622i \(-0.279057\pi\)
0.639703 + 0.768622i \(0.279057\pi\)
\(444\) 56.5103 2.68186
\(445\) 14.8018 0.701672
\(446\) 22.5401 1.06731
\(447\) −36.2282 −1.71354
\(448\) 14.5926 0.689434
\(449\) 35.6900 1.68432 0.842158 0.539231i \(-0.181285\pi\)
0.842158 + 0.539231i \(0.181285\pi\)
\(450\) −27.1976 −1.28211
\(451\) 26.5044 1.24804
\(452\) −32.4164 −1.52474
\(453\) −44.0908 −2.07156
\(454\) −22.4513 −1.05369
\(455\) −25.0659 −1.17511
\(456\) 11.2704 0.527783
\(457\) 38.2768 1.79051 0.895257 0.445549i \(-0.146992\pi\)
0.895257 + 0.445549i \(0.146992\pi\)
\(458\) 52.5778 2.45680
\(459\) 44.7217 2.08743
\(460\) 10.2825 0.479426
\(461\) 2.61753 0.121911 0.0609553 0.998140i \(-0.480585\pi\)
0.0609553 + 0.998140i \(0.480585\pi\)
\(462\) 38.8355 1.80679
\(463\) 19.9385 0.926621 0.463310 0.886196i \(-0.346661\pi\)
0.463310 + 0.886196i \(0.346661\pi\)
\(464\) −0.477915 −0.0221867
\(465\) 76.8426 3.56349
\(466\) −58.6932 −2.71891
\(467\) −10.2731 −0.475382 −0.237691 0.971341i \(-0.576391\pi\)
−0.237691 + 0.971341i \(0.576391\pi\)
\(468\) 138.316 6.39364
\(469\) 22.4170 1.03512
\(470\) 10.2644 0.473461
\(471\) −2.92406 −0.134734
\(472\) 44.6616 2.05572
\(473\) −18.5383 −0.852390
\(474\) 25.1098 1.15333
\(475\) 1.44345 0.0662298
\(476\) 31.2284 1.43135
\(477\) 30.8405 1.41209
\(478\) 16.9060 0.773262
\(479\) −9.58116 −0.437775 −0.218887 0.975750i \(-0.570243\pi\)
−0.218887 + 0.975750i \(0.570243\pi\)
\(480\) −4.83223 −0.220560
\(481\) −27.3042 −1.24496
\(482\) 55.5267 2.52917
\(483\) 5.04522 0.229566
\(484\) −4.00907 −0.182230
\(485\) 15.3509 0.697048
\(486\) 5.34624 0.242510
\(487\) 36.1071 1.63617 0.818084 0.575099i \(-0.195036\pi\)
0.818084 + 0.575099i \(0.195036\pi\)
\(488\) −9.34180 −0.422883
\(489\) 47.1693 2.13307
\(490\) 26.7867 1.21010
\(491\) −11.2738 −0.508779 −0.254389 0.967102i \(-0.581875\pi\)
−0.254389 + 0.967102i \(0.581875\pi\)
\(492\) 99.7143 4.49547
\(493\) 0.626774 0.0282285
\(494\) −11.0707 −0.498094
\(495\) −50.5001 −2.26981
\(496\) −35.2705 −1.58369
\(497\) 11.5470 0.517955
\(498\) −81.7965 −3.66539
\(499\) 21.8883 0.979856 0.489928 0.871763i \(-0.337023\pi\)
0.489928 + 0.871763i \(0.337023\pi\)
\(500\) −32.6534 −1.46031
\(501\) −62.9055 −2.81041
\(502\) 47.2950 2.11088
\(503\) 15.1308 0.674650 0.337325 0.941388i \(-0.390478\pi\)
0.337325 + 0.941388i \(0.390478\pi\)
\(504\) 48.2238 2.14806
\(505\) −40.2158 −1.78958
\(506\) 7.69748 0.342195
\(507\) −60.3403 −2.67980
\(508\) 42.4512 1.88347
\(509\) −8.78028 −0.389179 −0.194590 0.980885i \(-0.562337\pi\)
−0.194590 + 0.980885i \(0.562337\pi\)
\(510\) −91.2682 −4.04143
\(511\) −18.1387 −0.802409
\(512\) 36.3784 1.60771
\(513\) −7.45134 −0.328985
\(514\) 7.09571 0.312978
\(515\) 8.12180 0.357889
\(516\) −69.7443 −3.07032
\(517\) 5.09504 0.224080
\(518\) −19.3533 −0.850335
\(519\) −5.69066 −0.249792
\(520\) −70.7710 −3.10351
\(521\) −30.4706 −1.33494 −0.667470 0.744636i \(-0.732623\pi\)
−0.667470 + 0.744636i \(0.732623\pi\)
\(522\) 1.96769 0.0861236
\(523\) 17.8875 0.782164 0.391082 0.920356i \(-0.372101\pi\)
0.391082 + 0.920356i \(0.372101\pi\)
\(524\) 65.4675 2.85996
\(525\) 9.20441 0.401714
\(526\) 23.4688 1.02329
\(527\) 46.2563 2.01496
\(528\) 34.5441 1.50334
\(529\) 1.00000 0.0434783
\(530\) −32.0805 −1.39349
\(531\) −57.9312 −2.51400
\(532\) −5.20315 −0.225585
\(533\) −48.1792 −2.08687
\(534\) 41.6871 1.80398
\(535\) −6.00226 −0.259500
\(536\) 63.2922 2.73381
\(537\) −59.0156 −2.54671
\(538\) 36.4365 1.57089
\(539\) 13.2964 0.572715
\(540\) −96.8390 −4.16729
\(541\) −19.1321 −0.822552 −0.411276 0.911511i \(-0.634917\pi\)
−0.411276 + 0.911511i \(0.634917\pi\)
\(542\) 48.9808 2.10391
\(543\) −34.3481 −1.47402
\(544\) −2.90882 −0.124715
\(545\) 54.2501 2.32382
\(546\) −70.5945 −3.02116
\(547\) −17.5666 −0.751094 −0.375547 0.926803i \(-0.622545\pi\)
−0.375547 + 0.926803i \(0.622545\pi\)
\(548\) 52.3634 2.23686
\(549\) 12.1174 0.517157
\(550\) 14.0431 0.598802
\(551\) −0.104430 −0.00444889
\(552\) 14.2447 0.606294
\(553\) −5.70211 −0.242479
\(554\) −65.5147 −2.78345
\(555\) 37.5051 1.59200
\(556\) −1.60930 −0.0682494
\(557\) −18.6109 −0.788570 −0.394285 0.918988i \(-0.629008\pi\)
−0.394285 + 0.918988i \(0.629008\pi\)
\(558\) 145.217 6.14752
\(559\) 33.6985 1.42529
\(560\) −15.8035 −0.667819
\(561\) −45.3037 −1.91272
\(562\) 69.3221 2.92417
\(563\) −30.2806 −1.27617 −0.638087 0.769965i \(-0.720274\pi\)
−0.638087 + 0.769965i \(0.720274\pi\)
\(564\) 19.1684 0.807137
\(565\) −21.5143 −0.905115
\(566\) 0.106892 0.00449301
\(567\) −16.8461 −0.707470
\(568\) 32.6019 1.36795
\(569\) −29.4342 −1.23395 −0.616973 0.786985i \(-0.711641\pi\)
−0.616973 + 0.786985i \(0.711641\pi\)
\(570\) 15.2067 0.636940
\(571\) 40.2500 1.68441 0.842204 0.539159i \(-0.181258\pi\)
0.842204 + 0.539159i \(0.181258\pi\)
\(572\) −71.4175 −2.98612
\(573\) 39.9596 1.66934
\(574\) −34.1495 −1.42537
\(575\) 1.82438 0.0760820
\(576\) −53.4419 −2.22675
\(577\) 24.1173 1.00402 0.502009 0.864863i \(-0.332595\pi\)
0.502009 + 0.864863i \(0.332595\pi\)
\(578\) −13.5209 −0.562397
\(579\) −50.5015 −2.09877
\(580\) −1.35720 −0.0563546
\(581\) 18.5750 0.770619
\(582\) 43.2336 1.79209
\(583\) −15.9241 −0.659509
\(584\) −51.2128 −2.11920
\(585\) 91.7981 3.79538
\(586\) 10.8008 0.446176
\(587\) −36.9619 −1.52558 −0.762791 0.646645i \(-0.776172\pi\)
−0.762791 + 0.646645i \(0.776172\pi\)
\(588\) 50.0233 2.06293
\(589\) −7.70703 −0.317563
\(590\) 60.2605 2.48088
\(591\) 14.9432 0.614682
\(592\) −17.2147 −0.707520
\(593\) −26.0090 −1.06806 −0.534031 0.845465i \(-0.679323\pi\)
−0.534031 + 0.845465i \(0.679323\pi\)
\(594\) −72.4934 −2.97444
\(595\) 20.7259 0.849678
\(596\) 47.2224 1.93430
\(597\) −50.2139 −2.05512
\(598\) −13.9923 −0.572189
\(599\) 31.8299 1.30053 0.650267 0.759705i \(-0.274657\pi\)
0.650267 + 0.759705i \(0.274657\pi\)
\(600\) 25.9877 1.06095
\(601\) 8.37677 0.341695 0.170848 0.985297i \(-0.445349\pi\)
0.170848 + 0.985297i \(0.445349\pi\)
\(602\) 23.8856 0.973504
\(603\) −82.0973 −3.34326
\(604\) 57.4710 2.33846
\(605\) −2.66076 −0.108175
\(606\) −113.262 −4.60096
\(607\) −1.94966 −0.0791343 −0.0395672 0.999217i \(-0.512598\pi\)
−0.0395672 + 0.999217i \(0.512598\pi\)
\(608\) 0.484655 0.0196554
\(609\) −0.665921 −0.0269845
\(610\) −12.6046 −0.510345
\(611\) −9.26166 −0.374687
\(612\) −114.367 −4.62301
\(613\) 28.3980 1.14698 0.573492 0.819211i \(-0.305588\pi\)
0.573492 + 0.819211i \(0.305588\pi\)
\(614\) 57.8383 2.33416
\(615\) 66.1790 2.66859
\(616\) −24.8997 −1.00324
\(617\) −5.77207 −0.232375 −0.116187 0.993227i \(-0.537067\pi\)
−0.116187 + 0.993227i \(0.537067\pi\)
\(618\) 22.8739 0.920123
\(619\) 17.8778 0.718569 0.359285 0.933228i \(-0.383021\pi\)
0.359285 + 0.933228i \(0.383021\pi\)
\(620\) −100.162 −4.02260
\(621\) −9.41780 −0.377923
\(622\) 22.9876 0.921717
\(623\) −9.46663 −0.379273
\(624\) −62.7935 −2.51375
\(625\) −30.7935 −1.23174
\(626\) 1.00986 0.0403622
\(627\) 7.54831 0.301451
\(628\) 3.81143 0.152092
\(629\) 22.5767 0.900190
\(630\) 65.0668 2.59232
\(631\) −10.3415 −0.411690 −0.205845 0.978585i \(-0.565994\pi\)
−0.205845 + 0.978585i \(0.565994\pi\)
\(632\) −16.0993 −0.640398
\(633\) 46.4898 1.84780
\(634\) 58.8471 2.33712
\(635\) 28.1743 1.11806
\(636\) −59.9093 −2.37556
\(637\) −24.1699 −0.957645
\(638\) −1.01599 −0.0402236
\(639\) −42.2884 −1.67290
\(640\) 52.3903 2.07091
\(641\) −6.50092 −0.256771 −0.128385 0.991724i \(-0.540979\pi\)
−0.128385 + 0.991724i \(0.540979\pi\)
\(642\) −16.9045 −0.667168
\(643\) −13.3659 −0.527099 −0.263549 0.964646i \(-0.584893\pi\)
−0.263549 + 0.964646i \(0.584893\pi\)
\(644\) −6.57630 −0.259143
\(645\) −46.2883 −1.82260
\(646\) 9.15387 0.360154
\(647\) −46.5640 −1.83062 −0.915310 0.402749i \(-0.868055\pi\)
−0.915310 + 0.402749i \(0.868055\pi\)
\(648\) −47.5633 −1.86846
\(649\) 29.9121 1.17415
\(650\) −25.5273 −1.00127
\(651\) −49.1454 −1.92616
\(652\) −61.4837 −2.40789
\(653\) −15.9703 −0.624966 −0.312483 0.949923i \(-0.601161\pi\)
−0.312483 + 0.949923i \(0.601161\pi\)
\(654\) 152.788 5.97447
\(655\) 43.4498 1.69773
\(656\) −30.3759 −1.18598
\(657\) 66.4289 2.59164
\(658\) −6.56469 −0.255918
\(659\) 8.67092 0.337771 0.168886 0.985636i \(-0.445983\pi\)
0.168886 + 0.985636i \(0.445983\pi\)
\(660\) 98.0992 3.81851
\(661\) 39.7126 1.54464 0.772321 0.635232i \(-0.219096\pi\)
0.772321 + 0.635232i \(0.219096\pi\)
\(662\) −18.5977 −0.722819
\(663\) 82.3522 3.19829
\(664\) 52.4445 2.03524
\(665\) −3.45326 −0.133912
\(666\) 70.8771 2.74643
\(667\) −0.131990 −0.00511069
\(668\) 81.9954 3.17250
\(669\) 27.9365 1.08009
\(670\) 85.3982 3.29922
\(671\) −6.25666 −0.241536
\(672\) 3.09050 0.119219
\(673\) −26.5903 −1.02498 −0.512491 0.858693i \(-0.671277\pi\)
−0.512491 + 0.858693i \(0.671277\pi\)
\(674\) 72.3612 2.78725
\(675\) −17.1817 −0.661323
\(676\) 78.6517 3.02507
\(677\) 22.3917 0.860584 0.430292 0.902690i \(-0.358411\pi\)
0.430292 + 0.902690i \(0.358411\pi\)
\(678\) −60.5921 −2.32702
\(679\) −9.81781 −0.376773
\(680\) 58.5174 2.24404
\(681\) −27.8265 −1.06631
\(682\) −74.9810 −2.87117
\(683\) 32.1430 1.22992 0.614959 0.788559i \(-0.289172\pi\)
0.614959 + 0.788559i \(0.289172\pi\)
\(684\) 19.0554 0.728600
\(685\) 34.7529 1.32784
\(686\) −45.6262 −1.74202
\(687\) 65.1656 2.48622
\(688\) 21.2462 0.810002
\(689\) 28.9465 1.10277
\(690\) 19.2199 0.731689
\(691\) −6.05487 −0.230338 −0.115169 0.993346i \(-0.536741\pi\)
−0.115169 + 0.993346i \(0.536741\pi\)
\(692\) 7.41761 0.281975
\(693\) 32.2978 1.22689
\(694\) −35.0648 −1.33104
\(695\) −1.06807 −0.0405141
\(696\) −1.88016 −0.0712674
\(697\) 39.8373 1.50894
\(698\) 2.43642 0.0922197
\(699\) −72.7452 −2.75147
\(700\) −11.9977 −0.453470
\(701\) −28.9957 −1.09515 −0.547576 0.836756i \(-0.684449\pi\)
−0.547576 + 0.836756i \(0.684449\pi\)
\(702\) 131.777 4.97360
\(703\) −3.76163 −0.141872
\(704\) 27.5941 1.03999
\(705\) 12.7218 0.479132
\(706\) −28.1922 −1.06103
\(707\) 25.7204 0.967315
\(708\) 112.535 4.22931
\(709\) 26.2953 0.987539 0.493770 0.869593i \(-0.335619\pi\)
0.493770 + 0.869593i \(0.335619\pi\)
\(710\) 43.9887 1.65087
\(711\) 20.8827 0.783162
\(712\) −26.7281 −1.00168
\(713\) −9.74098 −0.364802
\(714\) 58.3715 2.18450
\(715\) −47.3988 −1.77262
\(716\) 76.9250 2.87482
\(717\) 20.9535 0.782524
\(718\) −22.5388 −0.841142
\(719\) 3.09876 0.115564 0.0577822 0.998329i \(-0.481597\pi\)
0.0577822 + 0.998329i \(0.481597\pi\)
\(720\) 57.8767 2.15694
\(721\) −5.19438 −0.193449
\(722\) 44.7667 1.66605
\(723\) 68.8206 2.55946
\(724\) 44.7718 1.66393
\(725\) −0.240801 −0.00894312
\(726\) −7.49366 −0.278116
\(727\) 25.7756 0.955965 0.477983 0.878369i \(-0.341368\pi\)
0.477983 + 0.878369i \(0.341368\pi\)
\(728\) 45.2623 1.67753
\(729\) −23.6226 −0.874911
\(730\) −69.0998 −2.55750
\(731\) −27.8638 −1.03058
\(732\) −23.5387 −0.870015
\(733\) −34.9384 −1.29048 −0.645240 0.763980i \(-0.723243\pi\)
−0.645240 + 0.763980i \(0.723243\pi\)
\(734\) −22.9164 −0.845860
\(735\) 33.1998 1.22459
\(736\) 0.612559 0.0225792
\(737\) 42.3899 1.56145
\(738\) 125.065 4.60370
\(739\) −5.29026 −0.194605 −0.0973027 0.995255i \(-0.531021\pi\)
−0.0973027 + 0.995255i \(0.531021\pi\)
\(740\) −48.8868 −1.79711
\(741\) −13.7212 −0.504060
\(742\) 20.5174 0.753217
\(743\) 27.7567 1.01830 0.509148 0.860679i \(-0.329961\pi\)
0.509148 + 0.860679i \(0.329961\pi\)
\(744\) −138.757 −5.08708
\(745\) 31.3408 1.14824
\(746\) 46.4844 1.70192
\(747\) −68.0266 −2.48896
\(748\) 59.0520 2.15916
\(749\) 3.83880 0.140267
\(750\) −61.0351 −2.22869
\(751\) −42.0831 −1.53563 −0.767817 0.640669i \(-0.778657\pi\)
−0.767817 + 0.640669i \(0.778657\pi\)
\(752\) −5.83927 −0.212936
\(753\) 58.6180 2.13616
\(754\) 1.84685 0.0672585
\(755\) 38.1427 1.38815
\(756\) 61.9343 2.25253
\(757\) 49.6104 1.80312 0.901560 0.432655i \(-0.142423\pi\)
0.901560 + 0.432655i \(0.142423\pi\)
\(758\) −58.9489 −2.14112
\(759\) 9.54037 0.346293
\(760\) −9.74993 −0.353667
\(761\) 31.9028 1.15648 0.578238 0.815868i \(-0.303740\pi\)
0.578238 + 0.815868i \(0.303740\pi\)
\(762\) 79.3489 2.87451
\(763\) −34.6962 −1.25609
\(764\) −52.0861 −1.88441
\(765\) −75.9038 −2.74431
\(766\) −52.7022 −1.90421
\(767\) −54.3736 −1.96332
\(768\) 94.8004 3.42081
\(769\) 35.7865 1.29049 0.645247 0.763974i \(-0.276754\pi\)
0.645247 + 0.763974i \(0.276754\pi\)
\(770\) −33.5964 −1.21073
\(771\) 8.79452 0.316727
\(772\) 65.8272 2.36917
\(773\) 32.8032 1.17985 0.589925 0.807458i \(-0.299157\pi\)
0.589925 + 0.807458i \(0.299157\pi\)
\(774\) −87.4756 −3.14424
\(775\) −17.7713 −0.638362
\(776\) −27.7196 −0.995076
\(777\) −23.9868 −0.860520
\(778\) −7.87279 −0.282253
\(779\) −6.63751 −0.237814
\(780\) −178.323 −6.38498
\(781\) 21.8351 0.781321
\(782\) 11.5696 0.413730
\(783\) 1.24306 0.0444233
\(784\) −15.2386 −0.544234
\(785\) 2.52959 0.0902849
\(786\) 122.370 4.36480
\(787\) 15.6011 0.556119 0.278060 0.960564i \(-0.410309\pi\)
0.278060 + 0.960564i \(0.410309\pi\)
\(788\) −19.4781 −0.693877
\(789\) 29.0875 1.03554
\(790\) −21.7223 −0.772846
\(791\) 13.7597 0.489239
\(792\) 91.1897 3.24028
\(793\) 11.3732 0.403875
\(794\) −50.0181 −1.77508
\(795\) −39.7610 −1.41018
\(796\) 65.4523 2.31989
\(797\) −0.905480 −0.0320738 −0.0160369 0.999871i \(-0.505105\pi\)
−0.0160369 + 0.999871i \(0.505105\pi\)
\(798\) −9.72561 −0.344283
\(799\) 7.65806 0.270923
\(800\) 1.11754 0.0395110
\(801\) 34.6694 1.22498
\(802\) −60.6901 −2.14304
\(803\) −34.2997 −1.21041
\(804\) 159.479 5.62437
\(805\) −4.36460 −0.153832
\(806\) 136.299 4.80093
\(807\) 45.1599 1.58970
\(808\) 72.6190 2.55473
\(809\) −51.1243 −1.79744 −0.898718 0.438528i \(-0.855500\pi\)
−0.898718 + 0.438528i \(0.855500\pi\)
\(810\) −64.1756 −2.25490
\(811\) −29.7633 −1.04513 −0.522566 0.852599i \(-0.675025\pi\)
−0.522566 + 0.852599i \(0.675025\pi\)
\(812\) 0.868009 0.0304611
\(813\) 60.7075 2.12910
\(814\) −36.5965 −1.28271
\(815\) −40.8059 −1.42937
\(816\) 51.9212 1.81761
\(817\) 4.64255 0.162422
\(818\) −41.2447 −1.44209
\(819\) −58.7103 −2.05151
\(820\) −86.2624 −3.01241
\(821\) −28.7463 −1.00325 −0.501627 0.865084i \(-0.667265\pi\)
−0.501627 + 0.865084i \(0.667265\pi\)
\(822\) 97.8765 3.41384
\(823\) 46.2762 1.61309 0.806544 0.591174i \(-0.201335\pi\)
0.806544 + 0.591174i \(0.201335\pi\)
\(824\) −14.6658 −0.510907
\(825\) 17.4053 0.605974
\(826\) −38.5402 −1.34098
\(827\) −35.7122 −1.24183 −0.620917 0.783876i \(-0.713240\pi\)
−0.620917 + 0.783876i \(0.713240\pi\)
\(828\) 24.0842 0.836984
\(829\) −0.802378 −0.0278678 −0.0139339 0.999903i \(-0.504435\pi\)
−0.0139339 + 0.999903i \(0.504435\pi\)
\(830\) 70.7617 2.45618
\(831\) −81.1999 −2.81679
\(832\) −50.1600 −1.73898
\(833\) 19.9850 0.692439
\(834\) −3.00806 −0.104161
\(835\) 54.4192 1.88325
\(836\) −9.83900 −0.340289
\(837\) 91.7386 3.17095
\(838\) 76.0418 2.62682
\(839\) 18.3045 0.631941 0.315970 0.948769i \(-0.397670\pi\)
0.315970 + 0.948769i \(0.397670\pi\)
\(840\) −62.1723 −2.14515
\(841\) −28.9826 −0.999399
\(842\) 61.2082 2.10937
\(843\) 85.9187 2.95920
\(844\) −60.5981 −2.08587
\(845\) 52.2000 1.79574
\(846\) 24.0417 0.826570
\(847\) 1.70172 0.0584716
\(848\) 18.2501 0.626712
\(849\) 0.132483 0.00454682
\(850\) 21.1075 0.723980
\(851\) −4.75435 −0.162977
\(852\) 82.1476 2.81433
\(853\) 17.7658 0.608291 0.304145 0.952626i \(-0.401629\pi\)
0.304145 + 0.952626i \(0.401629\pi\)
\(854\) 8.06138 0.275855
\(855\) 12.6468 0.432510
\(856\) 10.8385 0.370451
\(857\) −16.2061 −0.553590 −0.276795 0.960929i \(-0.589272\pi\)
−0.276795 + 0.960929i \(0.589272\pi\)
\(858\) −133.492 −4.55734
\(859\) 38.4894 1.31324 0.656621 0.754221i \(-0.271985\pi\)
0.656621 + 0.754221i \(0.271985\pi\)
\(860\) 60.3354 2.05742
\(861\) −42.3254 −1.44245
\(862\) −59.8319 −2.03788
\(863\) 26.5984 0.905421 0.452711 0.891657i \(-0.350457\pi\)
0.452711 + 0.891657i \(0.350457\pi\)
\(864\) −5.76896 −0.196264
\(865\) 4.92296 0.167386
\(866\) −59.7590 −2.03069
\(867\) −16.7580 −0.569133
\(868\) 64.0596 2.17432
\(869\) −10.7825 −0.365772
\(870\) −2.53684 −0.0860070
\(871\) −77.0556 −2.61093
\(872\) −97.9612 −3.31739
\(873\) 35.9555 1.21691
\(874\) −1.92769 −0.0652049
\(875\) 13.8603 0.468564
\(876\) −129.042 −4.35992
\(877\) 22.7766 0.769111 0.384555 0.923102i \(-0.374355\pi\)
0.384555 + 0.923102i \(0.374355\pi\)
\(878\) −20.8085 −0.702254
\(879\) 13.3866 0.451520
\(880\) −29.8839 −1.00739
\(881\) −38.2881 −1.28996 −0.644979 0.764201i \(-0.723134\pi\)
−0.644979 + 0.764201i \(0.723134\pi\)
\(882\) 62.7408 2.11259
\(883\) −29.3563 −0.987920 −0.493960 0.869485i \(-0.664451\pi\)
−0.493960 + 0.869485i \(0.664451\pi\)
\(884\) −107.344 −3.61036
\(885\) 74.6877 2.51060
\(886\) −65.6088 −2.20417
\(887\) −2.03266 −0.0682499 −0.0341250 0.999418i \(-0.510864\pi\)
−0.0341250 + 0.999418i \(0.510864\pi\)
\(888\) −67.7242 −2.27268
\(889\) −18.0191 −0.604343
\(890\) −36.0633 −1.20885
\(891\) −31.8555 −1.06720
\(892\) −36.4144 −1.21925
\(893\) −1.27595 −0.0426982
\(894\) 88.2670 2.95209
\(895\) 51.0541 1.70655
\(896\) −33.5067 −1.11938
\(897\) −17.3423 −0.579042
\(898\) −86.9557 −2.90175
\(899\) 1.28572 0.0428810
\(900\) 43.9388 1.46463
\(901\) −23.9346 −0.797377
\(902\) −64.5758 −2.15014
\(903\) 29.6041 0.985164
\(904\) 38.8491 1.29210
\(905\) 29.7144 0.987740
\(906\) 107.423 3.56891
\(907\) 19.1723 0.636606 0.318303 0.947989i \(-0.396887\pi\)
0.318303 + 0.947989i \(0.396887\pi\)
\(908\) 36.2709 1.20369
\(909\) −94.1951 −3.12425
\(910\) 61.0709 2.02448
\(911\) −28.8864 −0.957051 −0.478525 0.878074i \(-0.658829\pi\)
−0.478525 + 0.878074i \(0.658829\pi\)
\(912\) −8.65090 −0.286460
\(913\) 35.1247 1.16246
\(914\) −93.2583 −3.08471
\(915\) −15.6223 −0.516457
\(916\) −84.9414 −2.80654
\(917\) −27.7888 −0.917666
\(918\) −108.961 −3.59624
\(919\) −50.8723 −1.67812 −0.839061 0.544038i \(-0.816895\pi\)
−0.839061 + 0.544038i \(0.816895\pi\)
\(920\) −12.3230 −0.406278
\(921\) 71.6855 2.36212
\(922\) −6.37740 −0.210028
\(923\) −39.6914 −1.30646
\(924\) −62.7403 −2.06400
\(925\) −8.67374 −0.285191
\(926\) −48.5785 −1.59639
\(927\) 19.0232 0.624805
\(928\) −0.0808519 −0.00265409
\(929\) 46.2201 1.51643 0.758216 0.652003i \(-0.226071\pi\)
0.758216 + 0.652003i \(0.226071\pi\)
\(930\) −187.221 −6.13920
\(931\) −3.32982 −0.109130
\(932\) 94.8211 3.10597
\(933\) 28.4911 0.932757
\(934\) 25.0295 0.818991
\(935\) 39.1920 1.28172
\(936\) −165.763 −5.41813
\(937\) −28.3378 −0.925754 −0.462877 0.886422i \(-0.653183\pi\)
−0.462877 + 0.886422i \(0.653183\pi\)
\(938\) −54.6172 −1.78332
\(939\) 1.25164 0.0408457
\(940\) −16.5825 −0.540862
\(941\) 30.9464 1.00882 0.504412 0.863463i \(-0.331709\pi\)
0.504412 + 0.863463i \(0.331709\pi\)
\(942\) 7.12423 0.232120
\(943\) −8.38920 −0.273190
\(944\) −34.2813 −1.11576
\(945\) 41.1049 1.33714
\(946\) 45.1669 1.46850
\(947\) 33.3038 1.08223 0.541114 0.840949i \(-0.318003\pi\)
0.541114 + 0.840949i \(0.318003\pi\)
\(948\) −40.5658 −1.31752
\(949\) 62.3494 2.02395
\(950\) −3.51683 −0.114101
\(951\) 72.9359 2.36511
\(952\) −37.4254 −1.21296
\(953\) −1.16448 −0.0377212 −0.0188606 0.999822i \(-0.506004\pi\)
−0.0188606 + 0.999822i \(0.506004\pi\)
\(954\) −75.1402 −2.43275
\(955\) −34.5688 −1.11862
\(956\) −27.3123 −0.883343
\(957\) −1.25924 −0.0407054
\(958\) 23.3437 0.754201
\(959\) −22.2265 −0.717732
\(960\) 68.8999 2.22373
\(961\) 63.8866 2.06086
\(962\) 66.5244 2.14483
\(963\) −14.0587 −0.453037
\(964\) −89.7055 −2.88922
\(965\) 43.6886 1.40639
\(966\) −12.2923 −0.395497
\(967\) 25.4670 0.818964 0.409482 0.912318i \(-0.365709\pi\)
0.409482 + 0.912318i \(0.365709\pi\)
\(968\) 4.80462 0.154426
\(969\) 11.3454 0.364468
\(970\) −37.4012 −1.20088
\(971\) 39.3817 1.26382 0.631909 0.775043i \(-0.282272\pi\)
0.631909 + 0.775043i \(0.282272\pi\)
\(972\) −8.63706 −0.277034
\(973\) 0.683093 0.0218990
\(974\) −87.9719 −2.81880
\(975\) −31.6389 −1.01326
\(976\) 7.17057 0.229524
\(977\) −30.8832 −0.988041 −0.494021 0.869450i \(-0.664473\pi\)
−0.494021 + 0.869450i \(0.664473\pi\)
\(978\) −114.924 −3.67486
\(979\) −17.9011 −0.572122
\(980\) −43.2749 −1.38237
\(981\) 127.067 4.05693
\(982\) 27.4676 0.876528
\(983\) −6.00724 −0.191601 −0.0958005 0.995401i \(-0.530541\pi\)
−0.0958005 + 0.995401i \(0.530541\pi\)
\(984\) −119.502 −3.80957
\(985\) −12.9273 −0.411898
\(986\) −1.52708 −0.0486322
\(987\) −8.13637 −0.258984
\(988\) 17.8851 0.569002
\(989\) 5.86775 0.186584
\(990\) 123.039 3.91044
\(991\) −19.7731 −0.628113 −0.314056 0.949404i \(-0.601688\pi\)
−0.314056 + 0.949404i \(0.601688\pi\)
\(992\) −5.96692 −0.189450
\(993\) −23.0502 −0.731477
\(994\) −28.1334 −0.892337
\(995\) 43.4398 1.37713
\(996\) 132.145 4.18719
\(997\) −17.7526 −0.562229 −0.281115 0.959674i \(-0.590704\pi\)
−0.281115 + 0.959674i \(0.590704\pi\)
\(998\) −53.3291 −1.68810
\(999\) 44.7755 1.41663
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 \(a_p\))